LMFDB - Embedded newform 90.13.g.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,13,Mod(37,90)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("90.37");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	90.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$82.2594435549$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 43009x^{4} + 461169144x^{2} + 392422062096 $ x^6 + 43009x^4 + 461169144x^2 + 392422062096
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2}\cdot 5^{5} $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.1
Root			$159.940i$ of defining polynomial
Character	$\chi$	$=$	90.37
Dual form			90.13.g.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-32.0000 - 32.0000i) q^{2} +2048.00i q^{4} +(-11268.2 - 10824.4i) q^{5} +(-121018. - 121018. i) q^{7} +(65536.0 - 65536.0i) q^{8} +O(q^{10})$	\(q+(-32.0000 - 32.0000i) q^{2} +2048.00i q^{4} +(-11268.2 - 10824.4i) q^{5} +(-121018. - 121018. i) q^{7} +(65536.0 - 65536.0i) q^{8} +(14201.0 + 706964. i) q^{10} +855152. q^{11} +(563543. - 563543. i) q^{13} +7.74518e6i q^{14} -4.19430e6 q^{16} +(1.33894e7 + 1.33894e7i) q^{17} +9.07626e7i q^{19} +(2.21684e7 - 2.30773e7i) q^{20} +(-2.73649e7 - 2.73649e7i) q^{22} +(-6.22062e7 + 6.22062e7i) q^{23} +(9.80431e6 + 2.43944e8i) q^{25} -3.60667e7 q^{26} +(2.47846e8 - 2.47846e8i) q^{28} -9.61877e8i q^{29} -1.55856e9 q^{31} +(1.34218e8 + 1.34218e8i) q^{32} -8.56919e8i q^{34} +(5.37058e7 + 2.67361e9i) q^{35} +(7.41446e8 + 7.41446e8i) q^{37} +(2.90440e9 - 2.90440e9i) q^{38} +(-1.44786e9 + 2.90837e7i) q^{40} -9.28740e8 q^{41} +(-2.23346e9 + 2.23346e9i) q^{43} +1.75135e9i q^{44} +3.98120e9 q^{46} +(7.22768e9 + 7.22768e9i) q^{47} +1.54496e10i q^{49} +(7.49246e9 - 8.11994e9i) q^{50} +(1.15414e9 + 1.15414e9i) q^{52} +(9.05683e8 - 9.05683e8i) q^{53} +(-9.63603e9 - 9.25652e9i) q^{55} -1.58621e10 q^{56} +(-3.07801e10 + 3.07801e10i) q^{58} -1.35545e10i q^{59} +6.94051e10 q^{61} +(4.98740e10 + 4.98740e10i) q^{62} -8.58993e9i q^{64} +(-1.24501e10 + 2.50090e8i) q^{65} +(1.13753e11 + 1.13753e11i) q^{67} +(-2.74214e10 + 2.74214e10i) q^{68} +(8.38371e10 - 8.72743e10i) q^{70} -1.09453e11 q^{71} +(-8.58305e9 + 8.58305e9i) q^{73} -4.74526e10i q^{74} -1.85882e11 q^{76} +(-1.03489e11 - 1.03489e11i) q^{77} -1.74264e11i q^{79} +(4.72623e10 + 4.54009e10i) q^{80} +(2.97197e10 + 2.97197e10i) q^{82} +(2.87263e11 - 2.87263e11i) q^{83} +(-5.94196e9 - 2.95806e11i) q^{85} +1.42941e11 q^{86} +(5.60432e10 - 5.60432e10i) q^{88} -2.51008e11i q^{89} -1.36398e11 q^{91} +(-1.27398e11 - 1.27398e11i) q^{92} -4.62572e11i q^{94} +(9.82453e11 - 1.02273e12i) q^{95} +(2.97289e11 + 2.97289e11i) q^{97} +(4.94388e11 - 4.94388e11i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 192 q^{2} - 14460 q^{5} - 322104 q^{7} + 393216 q^{8}+O(q^{10}) $ 6 * q - 192 * q^2 - 14460 * q^5 - 322104 * q^7 + 393216 * q^8	\( 6 q - 192 q^{2} - 14460 q^{5} - 322104 q^{7} + 393216 q^{8} - 18240 q^{10} - 1652712 q^{11} - 4646814 q^{13} - 25165824 q^{16} - 51200226 q^{17} + 30781440 q^{20} + 52886784 q^{22} - 105826896 q^{23} - 161517150 q^{25} + 297396096 q^{26} + 659668992 q^{28} - 2667117168 q^{31} + 805306368 q^{32} + 7758629520 q^{35} + 1747956246 q^{37} + 2125152000 q^{38} - 1932656640 q^{40} - 22722098232 q^{41} - 15890524824 q^{43} + 6772921344 q^{46} + 18495531264 q^{47} - 8149569600 q^{50} - 9516675072 q^{52} + 88020413514 q^{53} + 37466287320 q^{55} - 42218815488 q^{56} - 107861859840 q^{58} + 291794891352 q^{61} + 85347749376 q^{62} - 26961608790 q^{65} - 3887251464 q^{67} + 104858062848 q^{68} - 110954853120 q^{70} - 929135015472 q^{71} + 12678070086 q^{73} - 136009728000 q^{76} + 436526954808 q^{77} + 60649635840 q^{80} + 727107143424 q^{82} - 68676615456 q^{83} + 142549278930 q^{85} + 1016993588736 q^{86} - 108312133632 q^{88} - 1619146872048 q^{91} - 216733483008 q^{92} + 1510780128600 q^{95} + 675735777846 q^{97} + 1327663144512 q^{98}+O(q^{100}) \) 6 * q - 192 * q^2 - 14460 * q^5 - 322104 * q^7 + 393216 * q^8 - 18240 * q^10 - 1652712 * q^11 - 4646814 * q^13 - 25165824 * q^16 - 51200226 * q^17 + 30781440 * q^20 + 52886784 * q^22 - 105826896 * q^23 - 161517150 * q^25 + 297396096 * q^26 + 659668992 * q^28 - 2667117168 * q^31 + 805306368 * q^32 + 7758629520 * q^35 + 1747956246 * q^37 + 2125152000 * q^38 - 1932656640 * q^40 - 22722098232 * q^41 - 15890524824 * q^43 + 6772921344 * q^46 + 18495531264 * q^47 - 8149569600 * q^50 - 9516675072 * q^52 + 88020413514 * q^53 + 37466287320 * q^55 - 42218815488 * q^56 - 107861859840 * q^58 + 291794891352 * q^61 + 85347749376 * q^62 - 26961608790 * q^65 - 3887251464 * q^67 + 104858062848 * q^68 - 110954853120 * q^70 - 929135015472 * q^71 + 12678070086 * q^73 - 136009728000 * q^76 + 436526954808 * q^77 + 60649635840 * q^80 + 727107143424 * q^82 - 68676615456 * q^83 + 142549278930 * q^85 + 1016993588736 * q^86 - 108312133632 * q^88 - 1619146872048 * q^91 - 216733483008 * q^92 + 1510780128600 * q^95 + 675735777846 * q^97 + 1327663144512 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−32.0000	−	32.0000i	−0.500000	−	0.500000i
$2$	−32.0000	−	32.0000i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			2048.00i			0.500000i
$5$	−11268.2	−	10824.4i	−0.721165	−	0.692763i
$5$	−11268.2	−	10824.4i	−0.721165	−	0.692763i
$6$		0			0
$7$	−121018.	−	121018.i	−1.02864	−	1.02864i	−0.999578	−	0.0290619i	$-0.990748\pi$
$7$	−121018.	−	121018.i	−1.02864	−	1.02864i	−0.0290619	−	0.999578i	$-0.509252\pi$
$8$	65536.0	−	65536.0i	0.250000	−	0.250000i
$9$		0			0
$10$	14201.0	+	706964.i	0.0142010	+	0.706964i
$11$	855152.			0.482711			0.241355	−	0.970437i	$-0.422408\pi$
$11$	855152.			0.482711			0.241355	+	0.970437i	$0.422408\pi$
$12$		0			0
$13$	563543.	−	563543.i	0.116753	−	0.116753i	−0.646317	−	0.763069i	$-0.723691\pi$
$13$	563543.	−	563543.i	0.116753	−	0.116753i	0.763069	+	0.646317i	$0.223691\pi$
$14$			7.74518e6i			1.02864i
$15$		0			0
$16$	−4.19430e6			−0.250000
$17$	1.33894e7	+	1.33894e7i	0.554710	+	0.554710i	0.927797	−	0.373086i	$-0.121700\pi$
$17$	1.33894e7	+	1.33894e7i	0.554710	+	0.554710i	−0.373086	+	0.927797i	$0.621700\pi$
$18$		0			0
$19$			9.07626e7i			1.92924i	0.263650	+	0.964618i	$0.415074\pi$
$19$			9.07626e7i			1.92924i	−0.263650	+	0.964618i	$0.584926\pi$
$20$	2.21684e7	−	2.30773e7i	0.346382	−	0.360583i
$21$		0			0
$22$	−2.73649e7	−	2.73649e7i	−0.241355	−	0.241355i
$23$	−6.22062e7	+	6.22062e7i	−0.420210	+	0.420210i	−0.885276	−	0.465066i	$-0.846031\pi$
$23$	−6.22062e7	+	6.22062e7i	−0.420210	+	0.420210i	0.465066	+	0.885276i	$0.346031\pi$
$24$		0			0
$25$	9.80431e6	+	2.43944e8i	0.0401585	+	0.999193i
$26$	−3.60667e7			−0.116753
$27$		0			0
$28$	2.47846e8	−	2.47846e8i	0.514320	−	0.514320i
$29$		−	9.61877e8i		−	1.61708i	−0.588441	−	0.808540i	$-0.700258\pi$
$29$		−	9.61877e8i		−	1.61708i	0.588441	−	0.808540i	$-0.299742\pi$
$30$		0			0
$31$	−1.55856e9			−1.75612			−0.878060	−	0.478551i	$-0.841162\pi$
$31$	−1.55856e9			−1.75612			−0.878060	+	0.478551i	$0.841162\pi$
$32$	1.34218e8	+	1.34218e8i	0.125000	+	0.125000i
$33$		0			0
$34$		−	8.56919e8i		−	0.554710i
$35$	5.37058e7	+	2.67361e9i	0.0292155	+	1.45442i
$36$		0			0
$37$	7.41446e8	+	7.41446e8i	0.288981	+	0.288981i	0.836677	−	0.547696i	$-0.184495\pi$
$37$	7.41446e8	+	7.41446e8i	0.288981	+	0.288981i	−0.547696	+	0.836677i	$0.684495\pi$
$38$	2.90440e9	−	2.90440e9i	0.964618	−	0.964618i
$39$		0			0
$40$	−1.44786e9	+	2.90837e7i	−0.353482	+	0.00710051i
$41$	−9.28740e8			−0.195520			−0.0977600	−	0.995210i	$-0.531168\pi$
$41$	−9.28740e8			−0.195520			−0.0977600	+	0.995210i	$0.531168\pi$
$42$		0			0
$43$	−2.23346e9	+	2.23346e9i	−0.353319	+	0.353319i	−0.861343	−	0.508024i	$-0.830376\pi$
$43$	−2.23346e9	+	2.23346e9i	−0.353319	+	0.353319i	0.508024	+	0.861343i	$0.330376\pi$
$44$			1.75135e9i			0.241355i
$45$		0			0
$46$	3.98120e9			0.420210
$47$	7.22768e9	+	7.22768e9i	0.670520	+	0.670520i	0.957836	−	0.287316i	$-0.0927628\pi$
$47$	7.22768e9	+	7.22768e9i	0.670520	+	0.670520i	−0.287316	+	0.957836i	$0.592763\pi$
$48$		0			0
$49$			1.54496e10i			1.11620i
$50$	7.49246e9	−	8.11994e9i	0.479517	−	0.519676i
$51$		0			0
$52$	1.15414e9	+	1.15414e9i	0.0583763	+	0.0583763i
$53$	9.05683e8	−	9.05683e8i	0.0408621	−	0.0408621i	−0.686380	−	0.727243i	$-0.740802\pi$
$53$	9.05683e8	−	9.05683e8i	0.0408621	−	0.0408621i	0.727243	+	0.686380i	$0.240802\pi$
$54$		0			0
$55$	−9.63603e9	−	9.25652e9i	−0.348114	−	0.334404i
$56$	−1.58621e10			−0.514320
$57$		0			0
$58$	−3.07801e10	+	3.07801e10i	−0.808540	+	0.808540i
$59$		−	1.35545e10i		−	0.321346i	−0.987008	−	0.160673i	$-0.948634\pi$
$59$		−	1.35545e10i		−	0.321346i	0.987008	−	0.160673i	$-0.0513665\pi$
$60$		0			0
$61$	6.94051e10			1.34714			0.673570	−	0.739124i	$-0.264760\pi$
$61$	6.94051e10			1.34714			0.673570	+	0.739124i	$0.264760\pi$
$62$	4.98740e10	+	4.98740e10i	0.878060	+	0.878060i
$63$		0			0
$64$		−	8.58993e9i		−	0.125000i
$65$	−1.24501e10	+	2.50090e8i	−0.165080	+	0.00331602i
$66$		0			0
$67$	1.13753e11	+	1.13753e11i	1.25752	+	1.25752i	0.952275	+	0.305243i	$0.0987376\pi$
$67$	1.13753e11	+	1.13753e11i	1.25752	+	1.25752i	0.305243	+	0.952275i	$0.401262\pi$
$68$	−2.74214e10	+	2.74214e10i	−0.277355	+	0.277355i
$69$		0			0
$70$	8.38371e10	−	8.72743e10i	0.712604	−	0.741819i
$71$	−1.09453e11			−0.854434			−0.427217	−	0.904149i	$-0.640506\pi$
$71$	−1.09453e11			−0.854434			−0.427217	+	0.904149i	$0.640506\pi$
$72$		0			0
$73$	−8.58305e9	+	8.58305e9i	−0.0567158	+	0.0567158i	−0.734896	−	0.678180i	$-0.762769\pi$
$73$	−8.58305e9	+	8.58305e9i	−0.0567158	+	0.0567158i	0.678180	+	0.734896i	$0.262769\pi$
$74$		−	4.74526e10i		−	0.288981i
$75$		0			0
$76$	−1.85882e11			−0.964618
$77$	−1.03489e11	−	1.03489e11i	−0.496535	−	0.496535i
$78$		0			0
$79$		−	1.74264e11i		−	0.716880i	−0.933553	−	0.358440i	$-0.883309\pi$
$79$		−	1.74264e11i		−	0.716880i	0.933553	−	0.358440i	$-0.116691\pi$
$80$	4.72623e10	+	4.54009e10i	0.180291	+	0.173191i
$81$		0			0
$82$	2.97197e10	+	2.97197e10i	0.0977600	+	0.0977600i
$83$	2.87263e11	−	2.87263e11i	0.878639	−	0.878639i	−0.114754	−	0.993394i	$-0.536608\pi$
$83$	2.87263e11	−	2.87263e11i	0.878639	−	0.878639i	0.993394	+	0.114754i	$0.0366081\pi$
$84$		0			0
$85$	−5.94196e9	−	2.95806e11i	−0.0157549	−	0.784321i
$86$	1.42941e11			0.353319
$87$		0			0
$88$	5.60432e10	−	5.60432e10i	0.120678	−	0.120678i
$89$		−	2.51008e11i		−	0.505066i	−0.967588	−	0.252533i	$-0.918736\pi$
$89$		−	2.51008e11i		−	0.505066i	0.967588	−	0.252533i	$-0.0812636\pi$
$90$		0			0
$91$	−1.36398e11			−0.240193
$92$	−1.27398e11	−	1.27398e11i	−0.210105	−	0.210105i
$93$		0			0
$94$		−	4.62572e11i		−	0.670520i
$95$	9.82453e11	−	1.02273e12i	1.33650	−	1.39130i
$96$		0			0
$97$	2.97289e11	+	2.97289e11i	0.356901	+	0.356901i	0.862669	−	0.505768i	$-0.168791\pi$
$97$	2.97289e11	+	2.97289e11i	0.356901	+	0.356901i	−0.505768	+	0.862669i	$0.668791\pi$
$98$	4.94388e11	−	4.94388e11i	0.558099	−	0.558099i
$99$		0			0
$100$	−4.99597e11	+	2.00792e10i	−0.499597	+	0.0200792i
$101$	−5.97476e10			−0.0562850			−0.0281425	−	0.999604i	$-0.508959\pi$
$101$	−5.97476e10			−0.0562850			−0.0281425	+	0.999604i	$0.508959\pi$
$102$		0			0
$103$	4.83171e11	−	4.83171e11i	0.404648	−	0.404648i	−0.475219	−	0.879867i	$-0.657631\pi$
$103$	4.83171e11	−	4.83171e11i	0.404648	−	0.404648i	0.879867	+	0.475219i	$0.157631\pi$
$104$		−	7.38647e10i		−	0.0583763i
$105$		0			0
$106$	−5.79637e10			−0.0408621
$107$	4.37350e11	+	4.37350e11i	0.291425	+	0.291425i	0.837643	−	0.546218i	$-0.183933\pi$
$107$	4.37350e11	+	4.37350e11i	0.291425	+	0.291425i	−0.546218	+	0.837643i	$0.683933\pi$
$108$		0			0
$109$		−	1.92444e12i		−	1.14748i	−0.819037	−	0.573741i	$-0.805492\pi$
$109$		−	1.92444e12i		−	1.14748i	0.819037	−	0.573741i	$-0.194508\pi$
$110$	1.21440e10	+	6.04562e11i	0.00685499	+	0.341259i
$111$		0			0
$112$	5.07588e11	+	5.07588e11i	0.257160	+	0.257160i
$113$	9.05644e11	−	9.05644e11i	0.434997	−	0.434997i	−0.455327	−	0.890324i	$-0.650478\pi$
$113$	9.05644e11	−	9.05644e11i	0.434997	−	0.434997i	0.890324	+	0.455327i	$0.150478\pi$
$114$		0			0
$115$	1.37430e12	−	2.76060e10i	0.594147	−	0.0119348i
$116$	1.96992e12			0.808540
$117$		0			0
$118$	−4.33746e11	+	4.33746e11i	−0.160673	+	0.160673i
$119$		−	3.24072e12i		−	1.14119i
$120$		0			0
$121$	−2.40714e12			−0.766990
$122$	−2.22096e12	−	2.22096e12i	−0.673570	−	0.673570i
$123$		0			0
$124$		−	3.19194e12i		−	0.878060i
$125$	2.53007e12	−	2.85493e12i	0.663243	−	0.748404i
$126$		0			0
$127$	−1.67708e12	−	1.67708e12i	−0.399697	−	0.399697i	0.478429	−	0.878126i	$-0.341206\pi$
$127$	−1.67708e12	−	1.67708e12i	−0.399697	−	0.399697i	−0.878126	+	0.478429i	$0.841206\pi$
$128$	−2.74878e11	+	2.74878e11i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	4.06408e11	+	3.90402e11i	0.0841980	+	0.0808820i
$131$	7.97530e11			0.157805			0.0789023	−	0.996882i	$-0.474858\pi$
$131$	7.97530e11			0.157805			0.0789023	+	0.996882i	$0.474858\pi$
$132$		0			0
$133$	1.09840e13	−	1.09840e13i	1.98449	−	1.98449i
$134$		−	7.28019e12i		−	1.25752i
$135$		0			0
$136$	1.75497e12			0.277355
$137$	−2.43459e12	−	2.43459e12i	−0.368216	−	0.368216i	0.498610	−	0.866826i	$-0.333844\pi$
$137$	−2.43459e12	−	2.43459e12i	−0.368216	−	0.368216i	−0.866826	+	0.498610i	$0.833844\pi$
$138$		0			0
$139$			5.33949e12i			0.740305i	0.928971	+	0.370153i	$0.120695\pi$
$139$			5.33949e12i			0.740305i	−0.928971	+	0.370153i	$0.879305\pi$
$140$	−5.47556e12	+	1.09989e11i	−0.727211	+	0.0146077i
$141$		0			0
$142$	3.50250e12	+	3.50250e12i	0.427217	+	0.427217i
$143$	4.81915e11	−	4.81915e11i	0.0563578	−	0.0563578i
$144$		0			0
$145$	−1.04118e13	+	1.08386e13i	−1.12025	+	1.16618i
$146$	5.49315e11			0.0567158
$147$		0			0
$148$	−1.51848e12	+	1.51848e12i	−0.144491	+	0.144491i
$149$			5.11787e12i			0.467705i	0.972272	+	0.233852i	$0.0751333\pi$
$149$			5.11787e12i			0.467705i	−0.972272	+	0.233852i	$0.924867\pi$
$150$		0			0
$151$	1.53338e13			1.29356			0.646781	−	0.762676i	$-0.276115\pi$
$151$	1.53338e13			1.29356			0.646781	+	0.762676i	$0.276115\pi$
$152$	5.94822e12	+	5.94822e12i	0.482309	+	0.482309i
$153$		0			0
$154$			6.62330e12i			0.496535i
$155$	1.75622e13	+	1.68705e13i	1.26645	+	1.21657i
$156$		0			0
$157$	−1.80237e12	−	1.80237e12i	−0.120350	−	0.120350i	0.644367	−	0.764717i	$-0.277121\pi$
$157$	−1.80237e12	−	1.80237e12i	−0.120350	−	0.120350i	−0.764717	+	0.644367i	$0.777121\pi$
$158$	−5.57646e12	+	5.57646e12i	−0.358440	+	0.358440i
$159$		0			0
$160$	−5.95634e10	−	2.96522e12i	−0.00355026	−	0.176741i
$161$	1.50562e13			0.864490
$162$		0			0
$163$	−3.11771e12	+	3.11771e12i	−0.166230	+	0.166230i	−0.785320	−	0.619090i	$-0.787502\pi$
$163$	−3.11771e12	+	3.11771e12i	−0.166230	+	0.166230i	0.619090	+	0.785320i	$0.287502\pi$
$164$		−	1.90206e12i		−	0.0977600i
$165$		0			0
$166$	−1.83848e13			−0.878639
$167$	−9.05825e12	−	9.05825e12i	−0.417586	−	0.417586i	0.466785	−	0.884371i	$-0.345412\pi$
$167$	−9.05825e12	−	9.05825e12i	−0.417586	−	0.417586i	−0.884371	+	0.466785i	$0.845412\pi$
$168$		0			0
$169$			2.26629e13i			0.972738i
$170$	−9.27565e12	+	9.65594e12i	−0.384283	+	0.400038i
$171$		0			0
$172$	−4.57412e12	−	4.57412e12i	−0.176659	−	0.176659i
$173$	1.08460e13	−	1.08460e13i	0.404568	−	0.404568i	−0.475272	−	0.879839i	$-0.657650\pi$
$173$	1.08460e13	−	1.08460e13i	0.404568	−	0.404568i	0.879839	+	0.475272i	$0.157650\pi$
$174$		0			0
$175$	2.83352e13	−	3.07082e13i	0.986501	−	1.06912i
$176$	−3.58677e12			−0.120678
$177$		0			0
$178$	−8.03226e12	+	8.03226e12i	−0.252533	+	0.252533i
$179$		−	3.24354e13i		−	0.986055i	−0.870014	−	0.493028i	$-0.835890\pi$
$179$		−	3.24354e13i		−	0.986055i	0.870014	−	0.493028i	$-0.164110\pi$
$180$		0			0
$181$	−3.61575e13			−1.02832			−0.514158	−	0.857695i	$-0.671896\pi$
$181$	−3.61575e13			−1.02832			−0.514158	+	0.857695i	$0.671896\pi$
$182$	4.36474e12	+	4.36474e12i	0.120096	+	0.120096i
$183$		0			0
$184$			8.15349e12i			0.210105i
$185$	−3.29041e11	−	1.63805e13i	−0.00820765	−	0.408598i
$186$		0			0
$187$	1.14499e13	+	1.14499e13i	0.267765	+	0.267765i
$188$	−1.48023e13	+	1.48023e13i	−0.335260	+	0.335260i
$189$		0			0
$190$	−6.41659e13	+	1.28892e12i	−1.36390	+	0.0273971i
$191$	−7.85798e13			−1.61849			−0.809246	−	0.587470i	$-0.800124\pi$
$191$	−7.85798e13			−1.61849			−0.809246	+	0.587470i	$0.800124\pi$
$192$		0			0
$193$	4.88933e13	−	4.88933e13i	0.946031	−	0.946031i	−0.0525853	−	0.998616i	$-0.516746\pi$
$193$	4.88933e13	−	4.88933e13i	0.946031	−	0.946031i	0.998616	+	0.0525853i	$0.0167461\pi$
$194$		−	1.90265e13i		−	0.356901i
$195$		0			0
$196$	−3.16408e13			−0.558099
$197$	5.71062e13	+	5.71062e13i	0.976981	+	0.976981i	0.999741	−	0.0227601i	$-0.00724539\pi$
$197$	5.71062e13	+	5.71062e13i	0.976981	+	0.976981i	−0.0227601	+	0.999741i	$0.507245\pi$
$198$		0			0
$199$		−	1.89668e13i		−	0.305404i	−0.988272	−	0.152702i	$-0.951202\pi$
$199$		−	1.89668e13i		−	0.305404i	0.988272	−	0.152702i	$-0.0487975\pi$
$200$	1.66296e13	+	1.53446e13i	0.259838	+	0.239759i
$201$		0			0
$202$	1.91192e12	+	1.91192e12i	0.0281425	+	0.0281425i
$203$	−1.16405e14	+	1.16405e14i	−1.66339	+	1.66339i
$204$		0			0
$205$	1.04652e13	+	1.00531e13i	0.141002	+	0.135449i
$206$	−3.09229e13			−0.404648
$207$		0			0
$208$	−2.36367e12	+	2.36367e12i	−0.0291882	+	0.0291882i
$209$			7.76158e13i			0.931264i
$210$		0			0
$211$	−4.49925e13			−0.509854			−0.254927	−	0.966960i	$-0.582051\pi$
$211$	−4.49925e13			−0.509854			−0.254927	+	0.966960i	$0.582051\pi$
$212$	1.85484e12	+	1.85484e12i	0.0204311	+	0.0204311i
$213$		0			0
$214$		−	2.79904e13i		−	0.291425i
$215$	4.93429e13	−	9.91168e11i	0.499567	−	0.0100350i
$216$		0			0
$217$	1.88615e14	+	1.88615e14i	1.80641	+	1.80641i
$218$	−6.15821e13	+	6.15821e13i	−0.573741	+	0.573741i
$219$		0			0
$220$	1.89574e13	−	1.97346e13i	0.167202	−	0.174057i
$221$	1.50910e13			0.129528
$222$		0			0
$223$	−2.61788e13	+	2.61788e13i	−0.212873	+	0.212873i	−0.805487	−	0.592614i	$-0.798096\pi$
$223$	−2.61788e13	+	2.61788e13i	−0.212873	+	0.212873i	0.592614	+	0.805487i	$0.298096\pi$
$224$		−	3.24856e13i		−	0.257160i
$225$		0			0
$226$	−5.79612e13			−0.434997
$227$	−1.30078e14	−	1.30078e14i	−0.950711	−	0.950711i	0.0481299	−	0.998841i	$-0.484674\pi$
$227$	−1.30078e14	−	1.30078e14i	−0.950711	−	0.950711i	−0.998841	+	0.0481299i	$0.984674\pi$
$228$		0			0
$229$			1.72785e13i			0.119810i	0.998204	+	0.0599051i	$0.0190798\pi$
$229$			1.72785e13i			0.119810i	−0.998204	+	0.0599051i	$0.980920\pi$
$230$	−4.48609e13	−	4.30942e13i	−0.303041	−	0.291106i
$231$		0			0
$232$	−6.30376e13	−	6.30376e13i	−0.404270	−	0.404270i
$233$	−9.01182e13	+	9.01182e13i	−0.563218	+	0.563218i	−0.930220	−	0.367002i	$-0.880384\pi$
$233$	−9.01182e13	+	9.01182e13i	−0.563218	+	0.563218i	0.367002	+	0.930220i	$0.380384\pi$
$234$		0			0
$235$	−3.20752e12	−	1.59679e14i	−0.0190442	−	0.948068i
$236$	2.77597e13			0.160673
$237$		0			0
$238$	−1.03703e14	+	1.03703e14i	−0.570597	+	0.570597i
$239$			5.48888e13i			0.294508i	0.989099	+	0.147254i	$0.0470434\pi$
$239$			5.48888e13i			0.294508i	−0.989099	+	0.147254i	$0.952957\pi$
$240$		0			0
$241$	9.29129e13			0.474213			0.237107	−	0.971484i	$-0.423801\pi$
$241$	9.29129e13			0.474213			0.237107	+	0.971484i	$0.423801\pi$
$242$	7.70286e13	+	7.70286e13i	0.383495	+	0.383495i
$243$		0			0
$244$			1.42142e14i			0.673570i
$245$	1.67233e14	−	1.74090e14i	0.773261	−	0.804964i
$246$		0			0
$247$	5.11486e13	+	5.11486e13i	0.225244	+	0.225244i
$248$	−1.02142e14	+	1.02142e14i	−0.439030	+	0.439030i
$249$		0			0
$250$	−1.72320e14	+	1.03955e13i	−0.705824	+	0.0425802i
$251$	4.19707e14			1.67843			0.839216	−	0.543798i	$-0.183014\pi$
$251$	4.19707e14			1.67843			0.839216	+	0.543798i	$0.183014\pi$
$252$		0			0
$253$	−5.31957e13	+	5.31957e13i	−0.202840	+	0.202840i
$254$			1.07333e14i			0.399697i
$255$		0			0
$256$	1.75922e13			0.0625000
$257$	2.85003e14	+	2.85003e14i	0.989123	+	0.989123i	0.999941	−	0.0108183i	$-0.00344363\pi$
$257$	2.85003e14	+	2.85003e14i	0.989123	+	0.989123i	−0.0108183	+	0.999941i	$0.503444\pi$
$258$		0			0
$259$		−	1.79457e14i		−	0.594515i
$260$	−5.12185e11	−	2.54979e13i	−0.00165801	−	0.0825400i
$261$		0			0
$262$	−2.55210e13	−	2.55210e13i	−0.0789023	−	0.0789023i
$263$	6.06586e13	−	6.06586e13i	0.183298	−	0.183298i	−0.609493	−	0.792791i	$-0.708627\pi$
$263$	6.06586e13	−	6.06586e13i	0.183298	−	0.183298i	0.792791	+	0.609493i	$0.208627\pi$
$264$		0			0
$265$	−2.00089e13	+	4.01926e11i	−0.0577761	+	0.00116057i
$266$	−7.02973e14			−1.98449
$267$		0			0
$268$	−2.32966e14	+	2.32966e14i	−0.628759	+	0.628759i
$269$		−	5.47959e14i		−	1.44622i	−0.690733	−	0.723110i	$-0.742712\pi$
$269$		−	5.47959e14i		−	1.44622i	0.690733	−	0.723110i	$-0.257288\pi$
$270$		0			0
$271$	2.37596e14			0.599822			0.299911	−	0.953967i	$-0.403043\pi$
$271$	2.37596e14			0.599822			0.299911	+	0.953967i	$0.403043\pi$
$272$	−5.61590e13	−	5.61590e13i	−0.138678	−	0.138678i
$273$		0			0
$274$			1.55814e14i			0.368216i
$275$	8.38418e12	+	2.08609e14i	0.0193849	+	0.482321i
$276$		0			0
$277$	1.41768e13	+	1.41768e13i	0.0313834	+	0.0313834i	0.722624	−	0.691241i	$-0.242936\pi$
$277$	1.41768e13	+	1.41768e13i	0.0313834	+	0.0313834i	−0.691241	+	0.722624i	$0.742936\pi$
$278$	1.70864e14	−	1.70864e14i	0.370153	−	0.370153i
$279$		0			0
$280$	1.78738e14	+	1.71698e14i	0.370910	+	0.356302i
$281$	−2.37323e14			−0.482061			−0.241030	−	0.970518i	$-0.577485\pi$
$281$	−2.37323e14			−0.482061			−0.241030	+	0.970518i	$0.577485\pi$
$282$		0			0
$283$	4.23007e14	−	4.23007e14i	0.823435	−	0.823435i	−0.163164	−	0.986599i	$-0.552170\pi$
$283$	4.23007e14	−	4.23007e14i	0.823435	−	0.823435i	0.986599	+	0.163164i	$0.0521700\pi$
$284$		−	2.24160e14i		−	0.427217i
$285$		0			0
$286$	−3.08425e13			−0.0563578
$287$	1.12395e14	+	1.12395e14i	0.201120	+	0.201120i
$288$		0			0
$289$		−	2.24072e14i		−	0.384593i
$290$	6.80013e14	−	1.36596e13i	1.14322	−	0.0229642i
$291$		0			0
$292$	−1.75781e13	−	1.75781e13i	−0.0283579	−	0.0283579i
$293$	7.05611e14	−	7.05611e14i	1.11522	−	1.11522i	0.122784	−	0.992433i	$-0.460818\pi$
$293$	7.05611e14	−	7.05611e14i	1.11522	−	1.11522i	0.992433	−	0.122784i	$-0.0391822\pi$
$294$		0			0
$295$	−1.46720e14	+	1.52735e14i	−0.222617	+	0.231744i
$296$	9.71828e13			0.144491
$297$		0			0
$298$	1.63772e14	−	1.63772e14i	0.233852	−	0.233852i
$299$			7.01117e13i			0.0981213i
$300$		0			0
$301$	5.40579e14			0.726875
$302$	−4.90681e14	−	4.90681e14i	−0.646781	−	0.646781i
$303$		0			0
$304$		−	3.80686e14i		−	0.482309i
$305$	−7.82071e14	−	7.51270e14i	−0.971510	−	0.933248i
$306$		0			0
$307$	−3.72483e13	−	3.72483e13i	−0.0444914	−	0.0444914i	0.684511	−	0.729002i	$-0.260016\pi$
$307$	−3.72483e13	−	3.72483e13i	−0.0444914	−	0.0444914i	−0.729002	+	0.684511i	$0.760016\pi$
$308$	2.11946e14	−	2.11946e14i	0.248268	−	0.248268i
$309$		0			0
$310$	−2.21332e13	−	1.10185e15i	−0.0249387	−	1.24151i
$311$	7.13323e14			0.788358			0.394179	−	0.919034i	$-0.371029\pi$
$311$	7.13323e14			0.788358			0.394179	+	0.919034i	$0.371029\pi$
$312$		0			0
$313$	−3.18840e14	+	3.18840e14i	−0.339084	+	0.339084i	−0.856023	−	0.516939i	$-0.827072\pi$
$313$	−3.18840e14	+	3.18840e14i	−0.339084	+	0.339084i	0.516939	+	0.856023i	$0.327072\pi$
$314$			1.15352e14i			0.120350i
$315$		0			0
$316$	3.56894e14			0.358440
$317$	5.96896e14	+	5.96896e14i	0.588224	+	0.588224i	0.937150	−	0.348926i	$-0.113454\pi$
$317$	5.96896e14	+	5.96896e14i	0.588224	+	0.588224i	−0.348926	+	0.937150i	$0.613454\pi$
$318$		0			0
$319$		−	8.22551e14i		−	0.780582i
$320$	−9.29811e13	+	9.67932e13i	−0.0865954	+	0.0901456i
$321$		0			0
$322$	−4.81798e14	−	4.81798e14i	−0.432245	−	0.432245i
$323$	−1.21525e15	+	1.21525e15i	−1.07017	+	1.07017i
$324$		0			0
$325$	1.42998e14	+	1.31948e14i	0.121347	+	0.111970i
$326$	1.99534e14			0.166230
$327$		0			0
$328$	−6.08659e13	+	6.08659e13i	−0.0488800	+	0.0488800i
$329$		−	1.74937e15i		−	1.37945i
$330$		0			0
$331$	1.16106e15			0.882850			0.441425	−	0.897298i	$-0.354473\pi$
$331$	1.16106e15			0.882850			0.441425	+	0.897298i	$0.354473\pi$
$332$	5.88314e14	+	5.88314e14i	0.439320	+	0.439320i
$333$		0			0
$334$			5.79728e14i			0.417586i
$335$	−5.04815e13	−	2.51310e15i	−0.0357161	−	1.77804i
$336$		0			0
$337$	−4.47217e14	−	4.47217e14i	−0.305308	−	0.305308i	0.537778	−	0.843086i	$-0.319264\pi$
$337$	−4.47217e14	−	4.47217e14i	−0.305308	−	0.305308i	−0.843086	+	0.537778i	$0.819264\pi$
$338$	7.25214e14	−	7.25214e14i	0.486369	−	0.486369i
$339$		0			0
$340$	6.05811e14	−	1.21691e13i	0.392160	−	0.00787746i
$341$	−1.33281e15			−0.847698
$342$		0			0
$343$	1.94638e14	−	1.94638e14i	0.119526	−	0.119526i
$344$			2.92744e14i			0.176659i
$345$		0			0
$346$	−6.94141e14			−0.404568
$347$	1.67027e15	+	1.67027e15i	0.956776	+	0.956776i	0.999104	−	0.0423279i	$-0.0134774\pi$
$347$	1.67027e15	+	1.67027e15i	0.956776	+	0.956776i	−0.0423279	+	0.999104i	$0.513477\pi$
$348$		0			0
$349$		−	2.71867e15i		−	1.50454i	−0.658853	−	0.752272i	$-0.728958\pi$
$349$		−	2.71867e15i		−	1.50454i	0.658853	−	0.752272i	$-0.271042\pi$
$350$	−1.88939e15	+	7.59362e13i	−1.02781	+	0.0413086i
$351$		0			0
$352$	1.14777e14	+	1.14777e14i	0.0603389	+	0.0603389i
$353$	4.34561e14	−	4.34561e14i	0.224596	−	0.224596i	−0.585835	−	0.810431i	$-0.699233\pi$
$353$	4.34561e14	−	4.34561e14i	0.224596	−	0.224596i	0.810431	+	0.585835i	$0.199233\pi$
$354$		0			0
$355$	1.23334e15	+	1.18477e15i	0.616188	+	0.591920i
$356$	5.14065e14			0.252533
$357$		0			0
$358$	−1.03793e15	+	1.03793e15i	−0.493028	+	0.493028i
$359$			4.03664e14i			0.188562i	0.995546	+	0.0942808i	$0.0300552\pi$
$359$			4.03664e14i			0.188562i	−0.995546	+	0.0942808i	$0.969945\pi$
$360$		0			0
$361$	−6.02454e15			−2.72195
$362$	1.15704e15	+	1.15704e15i	0.514158	+	0.514158i
$363$		0			0
$364$		−	2.79343e14i		−	0.120096i
$365$	1.89622e14	−	3.80900e12i	0.0801921	−	0.00161085i
$366$		0			0
$367$	3.14067e15	+	3.14067e15i	1.28536	+	1.28536i	0.937573	+	0.347789i	$0.113067\pi$
$367$	3.14067e15	+	3.14067e15i	1.28536	+	1.28536i	0.347789	+	0.937573i	$0.386933\pi$
$368$	2.60912e14	−	2.60912e14i	0.105053	−	0.105053i
$369$		0			0
$370$	−5.13647e14	+	5.34705e14i	−0.200195	+	0.208403i
$371$	−2.19209e14			−0.0840648
$372$		0			0
$373$	−2.88499e15	+	2.88499e15i	−1.07125	+	1.07125i	−0.0739924	+	0.997259i	$0.523574\pi$
$373$	−2.88499e15	+	2.88499e15i	−1.07125	+	1.07125i	−0.997259	+	0.0739924i	$0.976426\pi$
$374$		−	7.32796e14i		−	0.267765i
$375$		0			0
$376$	9.47347e14			0.335260
$377$	−5.42059e14	−	5.42059e14i	−0.188798	−	0.188798i
$378$		0			0
$379$		−	9.94190e14i		−	0.335455i	−0.985833	−	0.167727i	$-0.946357\pi$
$379$		−	9.94190e14i		−	0.335455i	0.985833	−	0.167727i	$-0.0536428\pi$
$380$	2.09456e15	+	2.01206e15i	0.695649	+	0.668252i
$381$		0			0
$382$	2.51455e15	+	2.51455e15i	0.809246	+	0.809246i
$383$	−3.15021e15	+	3.15021e15i	−0.998037	+	0.998037i	−0.999998	−	0.00196149i	$-0.999376\pi$
$383$	−3.15021e15	+	3.15021e15i	−0.998037	+	0.998037i	0.00196149	+	0.999998i	$0.499376\pi$
$384$		0			0
$385$	4.59266e13	+	2.28635e15i	0.0141026	+	0.702066i
$386$	−3.12917e15			−0.946031
$387$		0			0
$388$	−6.08847e14	+	6.08847e14i	−0.178451	+	0.178451i
$389$			2.91921e15i			0.842497i	0.906945	+	0.421248i	$0.138408\pi$
$389$			2.91921e15i			0.842497i	−0.906945	+	0.421248i	$0.861592\pi$
$390$		0			0
$391$	−1.66580e15			−0.466190
$392$	1.01251e15	+	1.01251e15i	0.279050	+	0.279050i
$393$		0			0
$394$		−	3.65480e15i		−	0.976981i
$395$	−1.88631e15	+	1.96365e15i	−0.496628	+	0.516989i
$396$		0			0
$397$	2.06257e15	+	2.06257e15i	0.526825	+	0.526825i	0.919624	−	0.392799i	$-0.128493\pi$
$397$	2.06257e15	+	2.06257e15i	0.526825	+	0.526825i	−0.392799	+	0.919624i	$0.628493\pi$
$398$	−6.06937e14	+	6.06937e14i	−0.152702	+	0.152702i
$399$		0			0
$400$	−4.11223e13	−	1.02317e15i	−0.0100396	−	0.249798i
$401$	−1.15805e14			−0.0278523			−0.0139262	−	0.999903i	$-0.504433\pi$
$401$	−1.15805e14			−0.0278523			−0.0139262	+	0.999903i	$0.504433\pi$
$402$		0			0
$403$	−8.78317e14	+	8.78317e14i	−0.205032	+	0.205032i
$404$		−	1.22363e14i		−	0.0281425i
$405$		0			0
$406$	7.44991e15			1.66339
$407$	6.34049e14	+	6.34049e14i	0.139494	+	0.139494i
$408$		0			0
$409$			1.65778e15i			0.354149i	0.984197	+	0.177074i	$0.0566633\pi$
$409$			1.65778e15i			0.354149i	−0.984197	+	0.177074i	$0.943337\pi$
$410$	−1.31891e13	−	6.56586e14i	−0.00277658	−	0.138226i
$411$		0			0
$412$	9.89534e14	+	9.89534e14i	0.202324	+	0.202324i
$413$	−1.64035e15	+	1.64035e15i	−0.330549	+	0.330549i
$414$		0			0
$415$	−6.34639e15	+	1.27482e14i	−1.24233	+	0.0249552i
$416$	1.51275e14			0.0291882
$417$		0			0
$418$	2.48371e15	−	2.48371e15i	0.465632	−	0.465632i
$419$			5.93151e15i			1.09618i	0.836420	+	0.548089i	$0.184645\pi$
$419$			5.93151e15i			1.09618i	−0.836420	+	0.548089i	$0.815355\pi$
$420$		0			0
$421$	4.46283e15			0.801526			0.400763	−	0.916182i	$-0.368745\pi$
$421$	4.46283e15			0.801526			0.400763	+	0.916182i	$0.368745\pi$
$422$	1.43976e15	+	1.43976e15i	0.254927	+	0.254927i
$423$		0			0
$424$		−	1.18710e14i		−	0.0204311i
$425$	−3.13498e15	+	3.39752e15i	−0.531987	+	0.576539i
$426$		0			0
$427$	−8.39930e15	−	8.39930e15i	−1.38572	−	1.38572i
$428$	−8.95693e14	+	8.95693e14i	−0.145712	+	0.145712i
$429$		0			0
$430$	−1.61069e15	−	1.54726e15i	−0.254801	−	0.244766i
$431$	−6.40433e15			−0.999103			−0.499552	−	0.866284i	$-0.666502\pi$
$431$	−6.40433e15			−0.999103			−0.499552	+	0.866284i	$0.666502\pi$
$432$		0			0
$433$	−2.32112e15	+	2.32112e15i	−0.352185	+	0.352185i	−0.860922	−	0.508737i	$-0.830113\pi$
$433$	−2.32112e15	+	2.32112e15i	−0.352185	+	0.352185i	0.508737	+	0.860922i	$0.330113\pi$
$434$		−	1.20713e16i		−	1.80641i
$435$		0			0
$436$	3.94125e15			0.573741
$437$	−5.64600e15	−	5.64600e15i	−0.810685	−	0.810685i
$438$		0			0
$439$			2.58953e15i			0.361771i	0.983504	+	0.180885i	$0.0578963\pi$
$439$			2.58953e15i			0.361771i	−0.983504	+	0.180885i	$0.942104\pi$
$440$	−1.23814e15	+	2.48710e13i	−0.170630	+	0.00342749i
$441$		0			0
$442$	−4.82911e14	−	4.82911e14i	−0.0647639	−	0.0647639i
$443$	3.47542e15	−	3.47542e15i	0.459817	−	0.459817i	−0.438778	−	0.898595i	$-0.644589\pi$
$443$	3.47542e15	−	3.47542e15i	0.459817	−	0.459817i	0.898595	+	0.438778i	$0.144589\pi$
$444$		0			0
$445$	−2.71702e15	+	2.82841e15i	−0.349891	+	0.364236i
$446$	1.67544e15			0.212873
$447$		0			0
$448$	−1.03954e15	+	1.03954e15i	−0.128580	+	0.128580i
$449$			9.29319e15i			1.13419i	0.823652	+	0.567096i	$0.191933\pi$
$449$			9.29319e15i			1.13419i	−0.823652	+	0.567096i	$0.808067\pi$
$450$		0			0
$451$	−7.94214e14			−0.0943796
$452$	1.85476e15	+	1.85476e15i	0.217499	+	0.217499i
$453$		0			0
$454$			8.32499e15i			0.950711i
$455$	1.53696e15	+	1.47643e15i	0.173219	+	0.166397i
$456$		0			0
$457$	4.17939e15	+	4.17939e15i	0.458792	+	0.458792i	0.898259	−	0.439467i	$-0.144833\pi$
$457$	4.17939e15	+	4.17939e15i	0.458792	+	0.458792i	−0.439467	+	0.898259i	$0.644833\pi$
$458$	5.52913e14	−	5.52913e14i	0.0599051	−	0.0599051i
$459$		0			0
$460$	5.65371e13	+	2.81456e15i	0.00596742	+	0.297074i
$461$	1.61867e16			1.68637			0.843183	−	0.537627i	$-0.180679\pi$
$461$	1.61867e16			1.68637			0.843183	+	0.537627i	$0.180679\pi$
$462$		0			0
$463$	−1.00417e15	+	1.00417e15i	−0.101934	+	0.101934i	−0.756235	−	0.654300i	$-0.772963\pi$
$463$	−1.00417e15	+	1.00417e15i	−0.101934	+	0.101934i	0.654300	+	0.756235i	$0.272963\pi$
$464$			4.03440e15i			0.404270i
$465$		0			0
$466$	5.76756e15			0.563218
$467$	−8.83224e15	−	8.83224e15i	−0.851471	−	0.851471i	0.138843	−	0.990314i	$-0.455662\pi$
$467$	−8.83224e15	−	8.83224e15i	−0.851471	−	0.851471i	−0.990314	+	0.138843i	$0.955662\pi$
$468$		0			0
$469$		−	2.75324e16i		−	2.58706i
$470$	−5.00707e15	+	5.21235e15i	−0.464512	+	0.483556i
$471$		0			0
$472$	−8.88311e14	−	8.88311e14i	−0.0803365	−	0.0803365i
$473$	−1.90994e15	+	1.90994e15i	−0.170551	+	0.170551i
$474$		0			0
$475$	−2.21410e16	+	8.89865e14i	−1.92768	+	0.0774752i
$476$	6.63699e15			0.570597
$477$		0			0
$478$	1.75644e15	−	1.75644e15i	0.147254	−	0.147254i
$479$		−	1.93454e16i		−	1.60164i	−0.598903	−	0.800821i	$-0.704397\pi$
$479$		−	1.93454e16i		−	1.60164i	0.598903	−	0.800821i	$-0.295603\pi$
$480$		0			0
$481$	8.35674e14			0.0674786
$482$	−2.97321e15	−	2.97321e15i	−0.237107	−	0.237107i
$483$		0			0
$484$		−	4.92983e15i		−	0.383495i
$485$	−1.31931e14	−	6.56789e15i	−0.0101367	−	0.504633i
$486$		0			0
$487$	1.18030e16	+	1.18030e16i	0.884744	+	0.884744i	0.994012	−	0.109268i	$-0.0348508\pi$
$487$	1.18030e16	+	1.18030e16i	0.884744	+	0.884744i	−0.109268	+	0.994012i	$0.534851\pi$
$488$	4.54853e15	−	4.54853e15i	0.336785	−	0.336785i
$489$		0			0
$490$	−1.09223e16	+	2.19401e14i	−0.789112	+	0.0158512i
$491$	1.58301e16			1.12978			0.564890	−	0.825166i	$-0.308919\pi$
$491$	1.58301e16			1.12978			0.564890	+	0.825166i	$0.308919\pi$
$492$		0			0
$493$	1.28789e16	−	1.28789e16i	0.897011	−	0.897011i
$494$		−	3.27351e15i		−	0.225244i
$495$		0			0
$496$	6.53708e15			0.439030
$497$	1.32459e16	+	1.32459e16i	0.878904	+	0.878904i
$498$		0			0
$499$			3.75944e15i			0.243512i	0.992560	+	0.121756i	$0.0388525\pi$
$499$			3.75944e15i			0.243512i	−0.992560	+	0.121756i	$0.961147\pi$
$500$	5.84690e15	+	5.18159e15i	0.374202	+	0.331622i
$501$		0			0
$502$	−1.34306e16	−	1.34306e16i	−0.839216	−	0.839216i
$503$	3.05571e15	−	3.05571e15i	0.188671	−	0.188671i	−0.606451	−	0.795121i	$-0.707407\pi$
$503$	3.05571e15	−	3.05571e15i	0.188671	−	0.188671i	0.795121	+	0.606451i	$0.207407\pi$
$504$		0			0
$505$	6.73249e14	+	6.46734e14i	0.0405908	+	0.0389922i
$506$	3.40453e15			0.202840
$507$		0			0
$508$	3.43465e15	−	3.43465e15i	0.199848	−	0.199848i
$509$		−	3.31917e16i		−	1.90863i	−0.298796	−	0.954317i	$-0.596585\pi$
$509$		−	3.31917e16i		−	1.90863i	0.298796	−	0.954317i	$-0.403415\pi$
$510$		0			0
$511$	2.07741e15			0.116680
$512$	−5.62950e14	−	5.62950e14i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	1.82402e16i		−	0.989123i
$515$	−1.06745e16	+	2.14423e14i	−0.572143	+	0.0114928i
$516$		0			0
$517$	6.18077e15	+	6.18077e15i	0.323667	+	0.323667i
$518$	−5.74263e15	+	5.74263e15i	−0.297257	+	0.297257i
$519$		0			0
$520$	−7.99543e14	+	8.32323e14i	−0.0404410	+	0.0420990i
$521$	−5.90021e15			−0.295013			−0.147506	−	0.989061i	$-0.547125\pi$
$521$	−5.90021e15			−0.295013			−0.147506	+	0.989061i	$0.547125\pi$
$522$		0			0
$523$	1.06234e16	−	1.06234e16i	0.519104	−	0.519104i	−0.398196	−	0.917300i	$-0.630364\pi$
$523$	1.06234e16	−	1.06234e16i	0.519104	−	0.519104i	0.917300	+	0.398196i	$0.130364\pi$
$524$			1.63334e15i			0.0789023i
$525$		0			0
$526$	−3.88215e15			−0.183298
$527$	−2.08682e16	−	2.08682e16i	−0.974138	−	0.974138i
$528$		0			0
$529$			1.41754e16i			0.646847i
$530$	6.53147e14	+	6.27424e14i	0.0294683	+	0.0283078i
$531$		0			0
$532$	2.24951e16	+	2.24951e16i	0.992245	+	0.992245i
$533$	−5.23385e14	+	5.23385e14i	−0.0228275	+	0.0228275i
$534$		0			0
$535$	−1.94088e14	−	9.66222e15i	−0.00827707	−	0.412054i
$536$	1.49098e16			0.628759
$537$		0			0
$538$	−1.75347e16	+	1.75347e16i	−0.723110	+	0.723110i
$539$			1.32118e16i			0.538801i
$540$		0			0
$541$	3.33454e16			1.33000			0.665001	−	0.746843i	$-0.268431\pi$
$541$	3.33454e16			1.33000			0.665001	+	0.746843i	$0.268431\pi$
$542$	−7.60306e15	−	7.60306e15i	−0.299911	−	0.299911i
$543$		0			0
$544$			3.59418e15i			0.138678i
$545$	−2.08310e16	+	2.16850e16i	−0.794933	+	0.827523i
$546$		0			0
$547$	2.55655e16	+	2.55655e16i	0.954399	+	0.954399i	0.999005	−	0.0446060i	$-0.0142032\pi$
$547$	2.55655e16	+	2.55655e16i	0.954399	+	0.954399i	−0.0446060	+	0.999005i	$0.514203\pi$
$548$	4.98604e15	−	4.98604e15i	0.184108	−	0.184108i
$549$		0			0
$550$	6.40719e15	−	6.94378e15i	0.231468	−	0.250853i
$551$	8.73025e16			3.11973
$552$		0			0
$553$	−2.10892e16	+	2.10892e16i	−0.737411	+	0.737411i
$554$		−	9.07317e14i		−	0.0313834i
$555$		0			0
$556$	−1.09353e16			−0.370153
$557$	1.86183e16	+	1.86183e16i	0.623462	+	0.623462i	0.946415	−	0.322953i	$-0.104676\pi$
$557$	1.86183e16	+	1.86183e16i	0.623462	+	0.623462i	−0.322953	+	0.946415i	$0.604676\pi$
$558$		0			0
$559$			2.51730e15i			0.0825018i
$560$	−2.25258e14	−	1.12140e16i	−0.00730387	−	0.363606i
$561$		0			0
$562$	7.59434e15	+	7.59434e15i	0.241030	+	0.241030i
$563$	−2.80927e16	+	2.80927e16i	−0.882152	+	0.882152i	−0.993753	−	0.111601i	$-0.964402\pi$
$563$	−2.80927e16	+	2.80927e16i	−0.882152	+	0.882152i	0.111601	+	0.993753i	$0.464402\pi$
$564$		0			0
$565$	−2.00081e16	+	4.01908e14i	−0.615055	+	0.0123548i
$566$	−2.70725e16			−0.823435
$567$		0			0
$568$	−7.17313e15	+	7.17313e15i	−0.213608	+	0.213608i
$569$		−	2.18381e16i		−	0.643490i	−0.946826	−	0.321745i	$-0.895731\pi$
$569$		−	2.18381e16i		−	0.643490i	0.946826	−	0.321745i	$-0.104269\pi$
$570$		0			0
$571$	4.28319e16			1.23581			0.617903	−	0.786254i	$-0.287982\pi$
$571$	4.28319e16			1.23581			0.617903	+	0.786254i	$0.287982\pi$
$572$	9.86961e14	+	9.86961e14i	0.0281789	+	0.0281789i
$573$		0			0
$574$		−	7.19326e15i		−	0.201120i
$575$	−1.57847e16	−	1.45649e16i	−0.436746	−	0.402996i
$576$		0			0
$577$	−2.40074e16	−	2.40074e16i	−0.650565	−	0.650565i	0.302564	−	0.953129i	$-0.402157\pi$
$577$	−2.40074e16	−	2.40074e16i	−0.650565	−	0.650565i	−0.953129	+	0.302564i	$0.902157\pi$
$578$	−7.17032e15	+	7.17032e15i	−0.192296	+	0.192296i
$579$		0			0
$580$	−2.21975e16	−	2.13233e16i	−0.583091	−	0.560127i
$581$	−6.95281e16			−1.80761
$582$		0			0
$583$	7.74496e14	−	7.74496e14i	0.0197246	−	0.0197246i
$584$			1.12500e15i			0.0283579i
$585$		0			0
$586$	−4.51591e16			−1.11522
$587$	1.53437e16	+	1.53437e16i	0.375060	+	0.375060i	0.869316	−	0.494256i	$-0.164559\pi$
$587$	1.53437e16	+	1.53437e16i	0.375060	+	0.375060i	−0.494256	+	0.869316i	$0.664559\pi$
$588$		0			0
$589$		−	1.41459e17i		−	3.38797i
$590$	9.58258e15	−	1.92489e14i	0.227180	−	0.00456344i
$591$		0			0
$592$	−3.10985e15	−	3.10985e15i	−0.0722453	−	0.0722453i
$593$	5.21562e16	−	5.21562e16i	1.19944	−	1.19944i	0.225103	−	0.974335i	$-0.427728\pi$
$593$	5.21562e16	−	5.21562e16i	1.19944	−	1.19944i	0.974335	−	0.225103i	$-0.0722717\pi$
$594$		0			0
$595$	−3.50789e16	+	3.65171e16i	−0.790577	+	0.822989i
$596$	−1.04814e16			−0.233852
$597$		0			0
$598$	2.24357e15	−	2.24357e15i	0.0490607	−	0.0490607i
$599$		−	4.12581e16i		−	0.893199i	−0.894734	−	0.446600i	$-0.852635\pi$
$599$		−	4.12581e16i		−	0.893199i	0.894734	−	0.446600i	$-0.147365\pi$
$600$		0			0
$601$	3.84045e16			0.814959			0.407479	−	0.913214i	$-0.366408\pi$
$601$	3.84045e16			0.814959			0.407479	+	0.913214i	$0.366408\pi$
$602$	−1.72985e16	−	1.72985e16i	−0.363438	−	0.363438i
$603$		0			0
$604$			3.14036e16i			0.646781i
$605$	2.71242e16	+	2.60559e16i	0.553127	+	0.531343i
$606$		0			0
$607$	3.27763e16	+	3.27763e16i	0.655281	+	0.655281i	0.954260	−	0.298979i	$-0.0966460\pi$
$607$	3.27763e16	+	3.27763e16i	0.655281	+	0.655281i	−0.298979	+	0.954260i	$0.596646\pi$
$608$	−1.21820e16	+	1.21820e16i	−0.241155	+	0.241155i
$609$		0			0
$610$	9.85624e14	+	4.90669e16i	0.0191308	+	0.952379i
$611$	8.14622e15			0.156570
$612$		0			0
$613$	−1.03368e16	+	1.03368e16i	−0.194816	+	0.194816i	−0.797773	−	0.602958i	$-0.793989\pi$
$613$	−1.03368e16	+	1.03368e16i	−0.194816	+	0.194816i	0.602958	+	0.797773i	$0.293989\pi$
$614$			2.38389e15i			0.0444914i
$615$		0			0
$616$	−1.35645e16			−0.248268
$617$	4.21087e16	+	4.21087e16i	0.763240	+	0.763240i	0.976907	−	0.213667i	$-0.0685407\pi$
$617$	4.21087e16	+	4.21087e16i	0.763240	+	0.763240i	−0.213667	+	0.976907i	$0.568541\pi$
$618$		0			0
$619$			5.48244e15i			0.0974608i	0.998812	+	0.0487304i	$0.0155175\pi$
$619$			5.48244e15i			0.0974608i	−0.998812	+	0.0487304i	$0.984482\pi$
$620$	−3.45509e16	+	3.59674e16i	−0.608287	+	0.633226i
$621$		0			0
$622$	−2.28263e16	−	2.28263e16i	−0.394179	−	0.394179i
$623$	−3.03766e16	+	3.03766e16i	−0.519531	+	0.519531i
$624$		0			0
$625$	−5.94124e16	+	4.78340e15i	−0.996775	+	0.0802521i
$626$	2.04058e16			0.339084
$627$		0			0
$628$	3.69125e15	−	3.69125e15i	0.0601750	−	0.0601750i
$629$			1.98550e16i			0.320601i
$630$		0			0
$631$	2.86138e16			0.453314			0.226657	−	0.973975i	$-0.427220\pi$
$631$	2.86138e16			0.453314			0.226657	+	0.973975i	$0.427220\pi$
$632$	−1.14206e16	−	1.14206e16i	−0.179220	−	0.179220i
$633$		0			0
$634$		−	3.82013e16i		−	0.588224i
$635$	7.44257e14	+	3.70510e16i	0.0113522	+	0.565143i
$636$		0			0
$637$	8.70653e15	+	8.70653e15i	0.130319	+	0.130319i
$638$	−2.63216e16	+	2.63216e16i	−0.390291	+	0.390291i
$639$		0			0
$640$	6.07278e15	−	1.21986e14i	0.0883705	−	0.00177513i
$641$	−3.53007e16			−0.508903			−0.254451	−	0.967086i	$-0.581895\pi$
$641$	−3.53007e16			−0.508903			−0.254451	+	0.967086i	$0.581895\pi$
$642$		0			0
$643$	−8.33444e16	+	8.33444e16i	−1.17926	+	1.17926i	−0.199330	+	0.979932i	$0.563877\pi$
$643$	−8.33444e16	+	8.33444e16i	−1.17926	+	1.17926i	−0.979932	+	0.199330i	$0.936123\pi$
$644$			3.08351e16i			0.432245i
$645$		0			0
$646$	7.77762e16			1.07017
$647$	7.64041e16	+	7.64041e16i	1.04158	+	1.04158i	0.999097	+	0.0424790i	$0.0135256\pi$
$647$	7.64041e16	+	7.64041e16i	1.04158	+	1.04158i	0.0424790	+	0.999097i	$0.486474\pi$
$648$		0			0
$649$		−	1.15912e16i		−	0.155117i
$650$	−3.53610e14	−	8.79826e15i	−0.00468861	−	0.116659i
$651$		0			0
$652$	−6.38507e15	−	6.38507e15i	−0.0831152	−	0.0831152i
$653$	3.17563e16	−	3.17563e16i	0.409591	−	0.409591i	−0.472005	−	0.881596i	$-0.656470\pi$
$653$	3.17563e16	−	3.17563e16i	0.409591	−	0.409591i	0.881596	+	0.472005i	$0.156470\pi$
$654$		0			0
$655$	−8.98674e15	−	8.63281e15i	−0.113803	−	0.109321i
$656$	3.89542e15			0.0488800
$657$		0			0
$658$	−5.59797e16	+	5.59797e16i	−0.689724	+	0.689724i
$659$			4.91804e16i			0.600453i	0.953868	+	0.300227i	$0.0970623\pi$
$659$			4.91804e16i			0.600453i	−0.953868	+	0.300227i	$0.902938\pi$
$660$		0			0
$661$	7.37994e15			0.0884798			0.0442399	−	0.999021i	$-0.485913\pi$
$661$	7.37994e15			0.0884798			0.0442399	+	0.999021i	$0.485913\pi$
$662$	−3.71539e16	−	3.71539e16i	−0.441425	−	0.441425i
$663$		0			0
$664$		−	3.76521e16i		−	0.439320i
$665$	−2.42664e17	+	4.87448e15i	−2.80593	+	0.0563636i
$666$		0			0
$667$	5.98347e16	+	5.98347e16i	0.679514	+	0.679514i
$668$	1.85513e16	−	1.85513e16i	0.208793	−	0.208793i
$669$		0			0
$670$	−7.88039e16	+	8.20347e16i	−0.871162	+	0.906878i
$671$	5.93519e16			0.650279
$672$		0			0
$673$	1.01038e17	−	1.01038e17i	1.08741	−	1.08741i	0.0916177	−	0.995794i	$-0.470796\pi$
$673$	1.01038e17	−	1.01038e17i	1.08741	−	1.08741i	0.995794	−	0.0916177i	$-0.0292038\pi$
$674$			2.86219e16i			0.305308i
$675$		0			0
$676$	−4.64137e16			−0.486369
$677$	−5.28834e16	−	5.28834e16i	−0.549272	−	0.549272i	0.376958	−	0.926230i	$-0.376970\pi$
$677$	−5.28834e16	−	5.28834e16i	−0.549272	−	0.549272i	−0.926230	+	0.376958i	$0.876970\pi$
$678$		0			0
$679$		−	7.19548e16i		−	0.734245i
$680$	−1.97754e16	−	1.89965e16i	−0.200019	−	0.192141i
$681$		0			0
$682$	4.26498e16	+	4.26498e16i	0.423849	+	0.423849i
$683$	−2.14631e16	+	2.14631e16i	−0.211430	+	0.211430i	−0.804875	−	0.593444i	$-0.797768\pi$
$683$	−2.14631e16	+	2.14631e16i	−0.211430	+	0.211430i	0.593444	+	0.804875i	$0.297768\pi$
$684$		0			0
$685$	1.08043e15	+	5.37865e16i	0.0104581	+	0.520631i
$686$	−1.24569e16			−0.119526
$687$		0			0
$688$	9.36779e15	−	9.36779e15i	0.0883297	−	0.0883297i
$689$		−	1.02078e15i		−	0.00954153i
$690$		0			0
$691$	1.37238e17			1.26068			0.630341	−	0.776318i	$-0.282915\pi$
$691$	1.37238e17			1.26068			0.630341	+	0.776318i	$0.282915\pi$
$692$	2.22125e16	+	2.22125e16i	0.202284	+	0.202284i
$693$		0			0
$694$		−	1.06897e17i		−	0.956776i
$695$	5.77969e16	−	6.01665e16i	0.512856	−	0.533882i
$696$		0			0
$697$	−1.24352e16	−	1.24352e16i	−0.108457	−	0.108457i
$698$	−8.69976e16	+	8.69976e16i	−0.752272	+	0.752272i
$699$		0			0
$700$	6.28904e16	+	5.80304e16i	0.534559	+	0.493251i
$701$	−1.99406e17			−1.68046			−0.840232	−	0.542227i	$-0.817581\pi$
$701$	−1.99406e17			−1.68046			−0.840232	+	0.542227i	$0.817581\pi$
$702$		0			0
$703$	−6.72956e16	+	6.72956e16i	−0.557513	+	0.557513i
$704$		−	7.34570e15i		−	0.0603389i
$705$		0			0
$706$	−2.78119e16			−0.224596
$707$	7.23056e15	+	7.23056e15i	0.0578970	+	0.0578970i
$708$		0			0
$709$		−	2.16689e16i		−	0.170592i	−0.996356	−	0.0852962i	$-0.972816\pi$
$709$		−	2.16689e16i		−	0.170592i	0.996356	−	0.0852962i	$-0.0271837\pi$
$710$	−1.55435e15	−	7.73795e16i	−0.0121338	−	0.604054i
$711$		0			0
$712$	−1.64501e16	−	1.64501e16i	−0.126266	−	0.126266i
$713$	9.69522e16	−	9.69522e16i	0.737939	−	0.737939i
$714$		0			0
$715$	−1.06468e16	+	2.13865e14i	−0.0796859	+	0.00160068i
$716$	6.64277e16			0.493028
$717$		0			0
$718$	1.29173e16	−	1.29173e16i	0.0942808	−	0.0942808i
$719$			7.26842e16i			0.526098i	0.964783	+	0.263049i	$0.0847281\pi$
$719$			7.26842e16i			0.526098i	−0.964783	+	0.263049i	$0.915272\pi$
$720$		0			0
$721$	−1.16945e17			−0.832474
$722$	1.92785e17	+	1.92785e17i	1.36098	+	1.36098i
$723$		0			0
$724$		−	7.40505e16i		−	0.514158i
$725$	2.34644e17	−	9.43054e15i	1.61578	−	0.0649395i
$726$		0			0
$727$	3.35546e16	+	3.35546e16i	0.227272	+	0.227272i	0.811552	−	0.584280i	$-0.198623\pi$
$727$	3.35546e16	+	3.35546e16i	0.227272	+	0.227272i	−0.584280	+	0.811552i	$0.698623\pi$
$728$	−8.93899e15	+	8.93899e15i	−0.0600482	+	0.0600482i
$729$		0			0
$730$	−6.18980e15	−	5.94602e15i	−0.0409015	−	0.0392906i
$731$	−5.98091e16			−0.391979
$732$		0			0
$733$	−4.31922e16	+	4.31922e16i	−0.278472	+	0.278472i	−0.832499	−	0.554027i	$-0.813090\pi$
$733$	−4.31922e16	+	4.31922e16i	−0.278472	+	0.278472i	0.554027	+	0.832499i	$0.313090\pi$
$734$		−	2.01003e17i		−	1.28536i
$735$		0			0
$736$	−1.66983e16			−0.105053
$737$	9.72761e16	+	9.72761e16i	0.607017	+	0.607017i
$738$		0			0
$739$			1.04593e17i			0.642148i	0.947054	+	0.321074i	$0.104044\pi$
$739$			1.04593e17i			0.642148i	−0.947054	+	0.321074i	$0.895956\pi$
$740$	3.35473e16	−	6.73875e14i	0.204299	−	0.00410383i
$741$		0			0
$742$	7.01468e15	+	7.01468e15i	0.0420324	+	0.0420324i
$743$	−7.60382e16	+	7.60382e16i	−0.451959	+	0.451959i	−0.896004	−	0.444045i	$-0.853543\pi$
$743$	−7.60382e16	+	7.60382e16i	−0.451959	+	0.451959i	0.444045	+	0.896004i	$0.353543\pi$
$744$		0			0
$745$	5.53980e16	−	5.76693e16i	0.324009	−	0.337293i
$746$	1.84639e17			1.07125
$747$		0			0
$748$	−2.34495e16	+	2.34495e16i	−0.133882	+	0.133882i
$749$		−	1.05855e17i		−	0.599542i
$750$		0			0
$751$	−6.59827e16			−0.367782			−0.183891	−	0.982947i	$-0.558869\pi$
$751$	−6.59827e16			−0.367782			−0.183891	+	0.982947i	$0.558869\pi$
$752$	−3.03151e16	−	3.03151e16i	−0.167630	−	0.167630i
$753$		0			0
$754$			3.46918e16i			0.188798i
$755$	−1.72784e17	−	1.65979e17i	−0.932872	−	0.896132i
$756$		0			0
$757$	2.16222e17	+	2.16222e17i	1.14901	+	1.14901i	0.986748	+	0.162262i	$0.0518790\pi$
$757$	2.16222e17	+	2.16222e17i	1.14901	+	1.14901i	0.162262	+	0.986748i	$0.448121\pi$
$758$	−3.18141e16	+	3.18141e16i	−0.167727	+	0.167727i
$759$		0			0
$760$	−2.63971e15	−	1.31412e17i	−0.0136986	−	0.681951i
$761$	2.00671e17			1.03318			0.516592	−	0.856232i	$-0.327201\pi$
$761$	2.00671e17			1.03318			0.516592	+	0.856232i	$0.327201\pi$
$762$		0			0
$763$	−2.32893e17	+	2.32893e17i	−1.18034	+	1.18034i
$764$		−	1.60931e17i		−	0.809246i
$765$		0			0
$766$	2.01613e17			0.998037
$767$	−7.63857e15	−	7.63857e15i	−0.0375180	−	0.0375180i
$768$		0			0
$769$		−	1.35328e17i		−	0.654379i	−0.944959	−	0.327189i	$-0.893898\pi$
$769$		−	1.35328e17i		−	0.654379i	0.944959	−	0.327189i	$-0.106102\pi$
$770$	7.16934e16	−	7.46327e16i	0.343981	−	0.358084i
$771$		0			0
$772$	1.00133e17	+	1.00133e17i	0.473016	+	0.473016i
$773$	2.13648e17	−	2.13648e17i	1.00143	−	1.00143i	0.00143473	−	0.999999i	$-0.499543\pi$
$773$	2.13648e17	−	2.13648e17i	1.00143	−	1.00143i	0.999999	−	0.00143473i	$-0.000456688\pi$
$774$		0			0
$775$	−1.52806e16	−	3.80201e17i	−0.0705231	−	1.75470i
$776$	3.89662e16			0.178451
$777$		0			0
$778$	9.34148e16	−	9.34148e16i	0.421248	−	0.421248i
$779$		−	8.42949e16i		−	0.377204i
$780$		0			0
$781$	−9.35991e16			−0.412444
$782$	5.33057e16	+	5.33057e16i	0.233095	+	0.233095i
$783$		0			0
$784$		−	6.48004e16i		−	0.279050i
$785$	7.99860e14	+	3.98191e16i	0.00341819	+	0.170166i
$786$		0			0
$787$	−2.72581e17	−	2.72581e17i	−1.14722	−	1.14722i	−0.987097	−	0.160125i	$-0.948810\pi$
$787$	−2.72581e17	−	2.72581e17i	−1.14722	−	1.14722i	−0.160125	−	0.987097i	$-0.551190\pi$
$788$	−1.16954e17	+	1.16954e17i	−0.488490	+	0.488490i
$789$		0			0
$790$	1.23199e17	−	2.47473e15i	0.506808	−	0.0101804i
$791$	−2.19199e17			−0.894911
$792$		0			0
$793$	3.91128e16	−	3.91128e16i	0.157282	−	0.157282i
$794$		−	1.32005e17i		−	0.526825i
$795$		0			0
$796$	3.88440e16			0.152702
$797$	9.95129e15	+	9.95129e15i	0.0388266	+	0.0388266i	0.726254	−	0.687427i	$-0.241260\pi$
$797$	9.95129e15	+	9.95129e15i	0.0388266	+	0.0388266i	−0.687427	+	0.726254i	$0.741260\pi$
$798$		0			0
$799$			1.93548e17i			0.743889i
$800$	−3.14257e16	+	3.40575e16i	−0.119879	+	0.129919i
$801$		0			0
$802$	3.70576e15	+	3.70576e15i	0.0139262	+	0.0139262i
$803$	−7.33981e15	+	7.33981e15i	−0.0273774	+	0.0273774i
$804$		0			0
$805$	−1.69656e17	−	1.62975e17i	−0.623440	−	0.598887i
$806$	5.62123e16			0.205032
$807$		0			0
$808$	−3.91562e15	+	3.91562e15i	−0.0140712	+	0.0140712i
$809$		−	4.20362e17i		−	1.49945i	−0.661749	−	0.749726i	$-0.730185\pi$
$809$		−	4.20362e17i		−	1.49945i	0.661749	−	0.749726i	$-0.269815\pi$
$810$		0			0
$811$	2.82759e17			0.993782			0.496891	−	0.867813i	$-0.334475\pi$
$811$	2.82759e17			0.993782			0.496891	+	0.867813i	$0.334475\pi$
$812$	−2.38397e17	−	2.38397e17i	−0.831696	−	0.831696i
$813$		0			0
$814$		−	4.05791e16i		−	0.139494i
$815$	6.88785e16	−	1.38358e15i	0.235038	−	0.00472128i
$816$		0			0
$817$	−2.02714e17	−	2.02714e17i	−0.681636	−	0.681636i
$818$	5.30488e16	−	5.30488e16i	0.177074	−	0.177074i
$819$		0			0
$820$	−2.05887e16	+	2.14328e16i	−0.0677245	+	0.0705011i
$821$	−2.52092e17			−0.823190			−0.411595	−	0.911367i	$-0.635028\pi$
$821$	−2.52092e17			−0.823190			−0.411595	+	0.911367i	$0.635028\pi$
$822$		0			0
$823$	2.88876e17	−	2.88876e17i	0.929636	−	0.929636i	−0.0680459	−	0.997682i	$-0.521676\pi$
$823$	2.88876e17	−	2.88876e17i	0.929636	−	0.929636i	0.997682	+	0.0680459i	$0.0216764\pi$
$824$		−	6.33302e16i		−	0.202324i
$825$		0			0
$826$	1.04982e17			0.330549
$827$	3.11943e17	+	3.11943e17i	0.975086	+	0.975086i	0.999697	−	0.0246114i	$-0.00783484\pi$
$827$	3.11943e17	+	3.11943e17i	0.975086	+	0.975086i	−0.0246114	+	0.999697i	$0.507835\pi$
$828$		0			0
$829$		−	3.36774e17i		−	1.03756i	−0.854909	−	0.518778i	$-0.826387\pi$
$829$		−	3.36774e17i		−	1.03756i	0.854909	−	0.518778i	$-0.173613\pi$
$830$	2.07164e17	+	1.99005e17i	0.633644	+	0.608689i
$831$		0			0
$832$	−4.84080e15	−	4.84080e15i	−0.0145941	−	0.0145941i
$833$	−2.06861e17	+	2.06861e17i	−0.619167	+	0.619167i
$834$		0			0
$835$	4.01989e15	+	2.00121e17i	0.0118603	+	0.590436i
$836$	−1.58957e17			−0.465632
$837$		0			0
$838$	1.89808e17	−	1.89808e17i	0.548089	−	0.548089i
$839$			1.34274e17i			0.384965i	0.981300	+	0.192482i	$0.0616538\pi$
$839$			1.34274e17i			0.384965i	−0.981300	+	0.192482i	$0.938346\pi$
$840$		0			0
$841$	−5.71392e17			−1.61495
$842$	−1.42811e17	−	1.42811e17i	−0.400763	−	0.400763i
$843$		0			0
$844$		−	9.21446e16i		−	0.254927i
$845$	2.45313e17	−	2.55370e17i	0.673877	−	0.701505i
$846$		0			0
$847$	2.91309e17	+	2.91309e17i	0.788956	+	0.788956i
$848$	−3.79871e15	+	3.79871e15i	−0.0102155	+	0.0102155i
$849$		0			0
$850$	2.09040e17	−	8.40150e15i	0.554263	−	0.0222763i
$851$	−9.22451e16			−0.242866
$852$		0			0
$853$	−1.62154e16	+	1.62154e16i	−0.0420953	+	0.0420953i	−0.727841	−	0.685746i	$-0.759476\pi$
$853$	−1.62154e16	+	1.62154e16i	−0.0420953	+	0.0420953i	0.685746	+	0.727841i	$0.259476\pi$
$854$			5.37555e17i			1.38572i
$855$		0			0
$856$	5.73244e16			0.145712
$857$	−2.45382e17	−	2.45382e17i	−0.619382	−	0.619382i	0.325991	−	0.945373i	$-0.394302\pi$
$857$	−2.45382e17	−	2.45382e17i	−0.619382	−	0.619382i	−0.945373	+	0.325991i	$0.894302\pi$
$858$		0			0
$859$			4.32544e17i			1.07664i	0.842740	+	0.538322i	$0.180941\pi$
$859$			4.32544e17i			1.07664i	−0.842740	+	0.538322i	$0.819059\pi$
$860$	2.02991e15	+	1.01054e17i	0.00501749	+	0.249784i
$861$		0			0
$862$	2.04939e17	+	2.04939e17i	0.499552	+	0.499552i
$863$	8.55095e16	−	8.55095e16i	0.206990	−	0.206990i	−0.595997	−	0.802987i	$-0.703243\pi$
$863$	8.55095e16	−	8.55095e16i	0.206990	−	0.206990i	0.802987	+	0.595997i	$0.203243\pi$
$864$		0			0
$865$	−2.39616e17	+	4.81324e15i	−0.572030	+	0.0114906i
$866$	1.48552e17			0.352185
$867$		0			0
$868$	−3.86283e17	+	3.86283e17i	−0.903207	+	0.903207i
$869$		−	1.49023e17i		−	0.346046i
$870$		0			0
$871$	1.28209e17			0.293637
$872$	−1.26120e17	−	1.26120e17i	−0.286870	−	0.286870i
$873$		0			0
$874$			3.61344e17i			0.810685i
$875$	−6.51685e17	+	3.93142e16i	−1.45208	+	0.0875993i
$876$		0			0
$877$	−2.87016e17	−	2.87016e17i	−0.630825	−	0.630825i	0.317450	−	0.948275i	$-0.397173\pi$
$877$	−2.87016e17	−	2.87016e17i	−0.630825	−	0.630825i	−0.948275	+	0.317450i	$0.897173\pi$
$878$	8.28648e16	−	8.28648e16i	0.180885	−	0.180885i
$879$		0			0
$880$	4.04164e16	+	3.88247e16i	0.0870286	+	0.0836011i
$881$	6.23644e17			1.33377			0.666886	−	0.745160i	$-0.267627\pi$
$881$	6.23644e17			1.33377			0.666886	+	0.745160i	$0.267627\pi$
$882$		0			0
$883$	1.06372e17	−	1.06372e17i	0.224420	−	0.224420i	−0.585937	−	0.810357i	$-0.699273\pi$
$883$	1.06372e17	−	1.06372e17i	0.224420	−	0.224420i	0.810357	+	0.585937i	$0.199273\pi$
$884$			3.09063e16i			0.0647639i
$885$		0			0
$886$	−2.22427e17			−0.459817
$887$	−6.98501e16	−	6.98501e16i	−0.143425	−	0.143425i	0.631748	−	0.775173i	$-0.282338\pi$
$887$	−6.98501e16	−	6.98501e16i	−0.143425	−	0.143425i	−0.775173	+	0.631748i	$0.782338\pi$
$888$		0			0
$889$			4.05914e17i			0.822288i
$890$	1.77454e17	−	3.56457e15i	0.357063	−	0.00717245i
$891$		0			0
$892$	−5.36142e16	−	5.36142e16i	−0.106436	−	0.106436i
$893$	−6.56004e17	+	6.56004e17i	−1.29359	+	1.29359i
$894$		0			0
$895$	−3.51095e17	+	3.65489e17i	−0.683103	+	0.711109i
$896$	6.65306e16			0.128580
$897$		0			0
$898$	2.97382e17	−	2.97382e17i	0.567096	−	0.567096i
$899$			1.49915e18i			2.83979i
$900$		0			0
$901$	2.42530e16			0.0453333
$902$	2.54148e16	+	2.54148e16i	0.0471898	+	0.0471898i
$903$		0			0
$904$		−	1.18705e17i		−	0.217499i
$905$	4.07430e17	+	3.91384e17i	0.741586	+	0.712380i
$906$		0			0
$907$	6.48283e17	+	6.48283e17i	1.16445	+	1.16445i	0.983490	+	0.180960i	$0.0579204\pi$
$907$	6.48283e17	+	6.48283e17i	1.16445	+	1.16445i	0.180960	+	0.983490i	$0.442080\pi$
$908$	2.66400e17	−	2.66400e17i	0.475356	−	0.475356i
$909$		0			0
$910$	−1.93699e15	−	9.64286e16i	−0.00341099	−	0.169808i
$911$	2.62366e17			0.458983			0.229491	−	0.973311i	$-0.426294\pi$
$911$	2.62366e17			0.458983			0.229491	+	0.973311i	$0.426294\pi$
$912$		0			0
$913$	2.45653e17	−	2.45653e17i	0.424129	−	0.424129i
$914$		−	2.67481e17i		−	0.458792i
$915$		0			0
$916$	−3.53864e16			−0.0599051
$917$	−9.65159e16	−	9.65159e16i	−0.162324	−	0.162324i
$918$		0			0
$919$			1.04985e18i			1.74275i	0.490621	+	0.871373i	$0.336770\pi$
$919$			1.04985e18i			1.74275i	−0.490621	+	0.871373i	$0.663230\pi$
$920$	8.82568e16	−	9.18752e16i	0.145553	−	0.151520i
$921$		0			0
$922$	−5.17973e17	−	5.17973e17i	−0.843183	−	0.843183i
$923$	−6.16816e16	+	6.16816e16i	−0.0997574	+	0.0997574i
$924$		0			0
$925$	−1.73602e17	+	1.88140e17i	−0.277143	+	0.300353i
$926$	6.42667e16			0.101934
$927$		0			0
$928$	1.29101e17	−	1.29101e17i	0.202135	−	0.202135i
$929$			3.83066e17i			0.595909i	0.954580	+	0.297954i	$0.0963044\pi$
$929$			3.83066e17i			0.595909i	−0.954580	+	0.297954i	$0.903696\pi$
$930$		0			0
$931$	−1.40225e18			−2.15341
$932$	−1.84562e17	−	1.84562e17i	−0.281609	−	0.281609i
$933$		0			0
$934$			5.65264e17i			0.851471i
$935$	−5.08128e15	−	2.52959e17i	−0.00760507	−	0.378600i
$936$		0			0
$937$	−7.09184e17	−	7.09184e17i	−1.04790	−	1.04790i	−0.998793	−	0.0491098i	$-0.984362\pi$
$937$	−7.09184e17	−	7.09184e17i	−1.04790	−	1.04790i	−0.0491098	−	0.998793i	$-0.515638\pi$
$938$	−8.81037e17	+	8.81037e17i	−1.29353	+	1.29353i
$939$		0			0
$940$	3.27022e17	−	6.56899e15i	0.474034	−	0.00952208i
$941$	−1.20839e18			−1.74049			−0.870244	−	0.492621i	$-0.836039\pi$
$941$	−1.20839e18			−1.74049			−0.870244	+	0.492621i	$0.836039\pi$
$942$		0			0
$943$	5.77734e16	−	5.77734e16i	0.0821595	−	0.0821595i
$944$			5.68519e16i			0.0803365i
$945$		0			0
$946$	1.22236e17			0.170551
$947$	3.32493e17	+	3.32493e17i	0.460980	+	0.460980i	0.898977	−	0.437996i	$-0.144312\pi$
$947$	3.32493e17	+	3.32493e17i	0.460980	+	0.460980i	−0.437996	+	0.898977i	$0.644312\pi$
$948$		0			0
$949$			9.67383e15i			0.0132435i
$950$	7.36987e17	+	6.80035e17i	1.00258	+	0.925103i
$951$		0			0
$952$	−2.12384e17	−	2.12384e17i	−0.285298	−	0.285298i
$953$	9.36824e17	−	9.36824e17i	1.25055	−	1.25055i	0.295074	−	0.955474i	$-0.404656\pi$
$953$	9.36824e17	−	9.36824e17i	1.25055	−	1.25055i	0.955474	−	0.295074i	$-0.0953443\pi$
$954$		0			0
$955$	8.85453e17	+	8.50581e17i	1.16720	+	1.12123i
$956$	−1.12412e17			−0.147254
$957$		0			0
$958$	−6.19054e17	+	6.19054e17i	−0.800821	+	0.800821i
$959$			5.89260e17i			0.757523i
$960$		0			0
$961$	1.64145e18			2.08396
$962$	−2.67416e16	−	2.67416e16i	−0.0337393	−	0.0337393i
$963$		0			0
$964$			1.90286e17i			0.237107i
$965$	−1.08018e18	+	2.16980e16i	−1.33762	+	0.0268692i
$966$		0			0
$967$	−2.43094e17	−	2.43094e17i	−0.297314	−	0.297314i	0.542647	−	0.839961i	$-0.317422\pi$
$967$	−2.43094e17	−	2.43094e17i	−0.297314	−	0.297314i	−0.839961	+	0.542647i	$0.817422\pi$
$968$	−1.57755e17	+	1.57755e17i	−0.191748	+	0.191748i
$969$		0			0
$970$	−2.05951e17	+	2.14394e17i	−0.247248	+	0.257385i
$971$	−4.97139e16			−0.0593147			−0.0296573	−	0.999560i	$-0.509442\pi$
$971$	−4.97139e16			−0.0593147			−0.0296573	+	0.999560i	$0.509442\pi$
$972$		0			0
$973$	6.46176e17	−	6.46176e17i	0.761507	−	0.761507i
$974$		−	7.55390e17i		−	0.884744i
$975$		0			0
$976$	−2.91106e17			−0.336785
$977$	−9.75153e17	−	9.75153e17i	−1.12126	−	1.12126i	−0.991553	−	0.129705i	$-0.958597\pi$
$977$	−9.75153e17	−	9.75153e17i	−1.12126	−	1.12126i	−0.129705	−	0.991553i	$-0.541403\pi$
$978$		0			0
$979$		−	2.14650e17i		−	0.243801i
$980$	3.56535e17	+	3.42494e17i	0.402482	+	0.386631i
$981$		0			0
$982$	−5.06562e17	−	5.06562e17i	−0.564890	−	0.564890i
$983$	7.61743e17	−	7.61743e17i	0.844282	−	0.844282i	−0.145131	−	0.989412i	$-0.546360\pi$
$983$	7.61743e17	−	7.61743e17i	0.844282	−	0.844282i	0.989412	+	0.145131i	$0.0463603\pi$
$984$		0			0
$985$	−2.53427e16	−	1.26163e18i	−0.0277483	−	1.38138i
$986$	−8.24251e17			−0.897011
$987$		0			0
$988$	−1.04752e17	+	1.04752e17i	−0.112622	+	0.112622i
$989$		−	2.77870e17i		−	0.296936i
$990$		0			0
$991$	−1.12196e18			−1.18450			−0.592252	−	0.805753i	$-0.701761\pi$
$991$	−1.12196e18			−1.18450			−0.592252	+	0.805753i	$0.701761\pi$
$992$	−2.09187e17	−	2.09187e17i	−0.219515	−	0.219515i
$993$		0			0
$994$		−	8.47735e17i		−	0.878904i
$995$	−2.05304e17	+	2.13722e17i	−0.211573	+	0.220247i
$996$		0			0
$997$	1.03110e18	+	1.03110e18i	1.04985	+	1.04985i	0.998690	+	0.0511616i	$0.0162923\pi$
$997$	1.03110e18	+	1.03110e18i	1.04985	+	1.04985i	0.0511616	+	0.998690i	$0.483708\pi$
$998$	1.20302e17	−	1.20302e17i	0.121756	−	0.121756i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.13.g.a.37.1		6
3.2	odd	2		10.13.c.b.7.1	yes	6
5.3	odd	4	inner	90.13.g.a.73.1		6
12.11	even	2		80.13.p.a.17.3		6
15.2	even	4		50.13.c.c.43.3		6
15.8	even	4		10.13.c.b.3.1	✓	6
15.14	odd	2		50.13.c.c.7.3		6
60.23	odd	4		80.13.p.a.33.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.13.c.b.3.1	✓	6	15.8	even	4
10.13.c.b.7.1	yes	6	3.2	odd	2
50.13.c.c.7.3		6	15.14	odd	2
50.13.c.c.43.3		6	15.2	even	4
80.13.p.a.17.3		6	12.11	even	2
80.13.p.a.33.3		6	60.23	odd	4
90.13.g.a.37.1		6	1.1	even	1	trivial
90.13.g.a.73.1		6	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	90.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-32.0000 - 32.0000i) q^{2} +2048.00i q^{4} +(-11268.2 - 10824.4i) q^{5} +(-121018. - 121018. i) q^{7} +(65536.0 - 65536.0i) q^{8} +O(q^{10})\)	\(q+(-32.0000 - 32.0000i) q^{2} +2048.00i q^{4} +(-11268.2 - 10824.4i) q^{5} +(-121018. - 121018. i) q^{7} +(65536.0 - 65536.0i) q^{8} +(14201.0 + 706964. i) q^{10} +855152. q^{11} +(563543. - 563543. i) q^{13} +7.74518e6i q^{14} -4.19430e6 q^{16} +(1.33894e7 + 1.33894e7i) q^{17} +9.07626e7i q^{19} +(2.21684e7 - 2.30773e7i) q^{20} +(-2.73649e7 - 2.73649e7i) q^{22} +(-6.22062e7 + 6.22062e7i) q^{23} +(9.80431e6 + 2.43944e8i) q^{25} -3.60667e7 q^{26} +(2.47846e8 - 2.47846e8i) q^{28} -9.61877e8i q^{29} -1.55856e9 q^{31} +(1.34218e8 + 1.34218e8i) q^{32} -8.56919e8i q^{34} +(5.37058e7 + 2.67361e9i) q^{35} +(7.41446e8 + 7.41446e8i) q^{37} +(2.90440e9 - 2.90440e9i) q^{38} +(-1.44786e9 + 2.90837e7i) q^{40} -9.28740e8 q^{41} +(-2.23346e9 + 2.23346e9i) q^{43} +1.75135e9i q^{44} +3.98120e9 q^{46} +(7.22768e9 + 7.22768e9i) q^{47} +1.54496e10i q^{49} +(7.49246e9 - 8.11994e9i) q^{50} +(1.15414e9 + 1.15414e9i) q^{52} +(9.05683e8 - 9.05683e8i) q^{53} +(-9.63603e9 - 9.25652e9i) q^{55} -1.58621e10 q^{56} +(-3.07801e10 + 3.07801e10i) q^{58} -1.35545e10i q^{59} +6.94051e10 q^{61} +(4.98740e10 + 4.98740e10i) q^{62} -8.58993e9i q^{64} +(-1.24501e10 + 2.50090e8i) q^{65} +(1.13753e11 + 1.13753e11i) q^{67} +(-2.74214e10 + 2.74214e10i) q^{68} +(8.38371e10 - 8.72743e10i) q^{70} -1.09453e11 q^{71} +(-8.58305e9 + 8.58305e9i) q^{73} -4.74526e10i q^{74} -1.85882e11 q^{76} +(-1.03489e11 - 1.03489e11i) q^{77} -1.74264e11i q^{79} +(4.72623e10 + 4.54009e10i) q^{80} +(2.97197e10 + 2.97197e10i) q^{82} +(2.87263e11 - 2.87263e11i) q^{83} +(-5.94196e9 - 2.95806e11i) q^{85} +1.42941e11 q^{86} +(5.60432e10 - 5.60432e10i) q^{88} -2.51008e11i q^{89} -1.36398e11 q^{91} +(-1.27398e11 - 1.27398e11i) q^{92} -4.62572e11i q^{94} +(9.82453e11 - 1.02273e12i) q^{95} +(2.97289e11 + 2.97289e11i) q^{97} +(4.94388e11 - 4.94388e11i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 192 q^{2} - 14460 q^{5} - 322104 q^{7} + 393216 q^{8}+O(q^{10}) \) 6 * q - 192 * q^2 - 14460 * q^5 - 322104 * q^7 + 393216 * q^8	\( 6 q - 192 q^{2} - 14460 q^{5} - 322104 q^{7} + 393216 q^{8} - 18240 q^{10} - 1652712 q^{11} - 4646814 q^{13} - 25165824 q^{16} - 51200226 q^{17} + 30781440 q^{20} + 52886784 q^{22} - 105826896 q^{23} - 161517150 q^{25} + 297396096 q^{26} + 659668992 q^{28} - 2667117168 q^{31} + 805306368 q^{32} + 7758629520 q^{35} + 1747956246 q^{37} + 2125152000 q^{38} - 1932656640 q^{40} - 22722098232 q^{41} - 15890524824 q^{43} + 6772921344 q^{46} + 18495531264 q^{47} - 8149569600 q^{50} - 9516675072 q^{52} + 88020413514 q^{53} + 37466287320 q^{55} - 42218815488 q^{56} - 107861859840 q^{58} + 291794891352 q^{61} + 85347749376 q^{62} - 26961608790 q^{65} - 3887251464 q^{67} + 104858062848 q^{68} - 110954853120 q^{70} - 929135015472 q^{71} + 12678070086 q^{73} - 136009728000 q^{76} + 436526954808 q^{77} + 60649635840 q^{80} + 727107143424 q^{82} - 68676615456 q^{83} + 142549278930 q^{85} + 1016993588736 q^{86} - 108312133632 q^{88} - 1619146872048 q^{91} - 216733483008 q^{92} + 1510780128600 q^{95} + 675735777846 q^{97} + 1327663144512 q^{98}+O(q^{100}) \) 6 * q - 192 * q^2 - 14460 * q^5 - 322104 * q^7 + 393216 * q^8 - 18240 * q^10 - 1652712 * q^11 - 4646814 * q^13 - 25165824 * q^16 - 51200226 * q^17 + 30781440 * q^20 + 52886784 * q^22 - 105826896 * q^23 - 161517150 * q^25 + 297396096 * q^26 + 659668992 * q^28 - 2667117168 * q^31 + 805306368 * q^32 + 7758629520 * q^35 + 1747956246 * q^37 + 2125152000 * q^38 - 1932656640 * q^40 - 22722098232 * q^41 - 15890524824 * q^43 + 6772921344 * q^46 + 18495531264 * q^47 - 8149569600 * q^50 - 9516675072 * q^52 + 88020413514 * q^53 + 37466287320 * q^55 - 42218815488 * q^56 - 107861859840 * q^58 + 291794891352 * q^61 + 85347749376 * q^62 - 26961608790 * q^65 - 3887251464 * q^67 + 104858062848 * q^68 - 110954853120 * q^70 - 929135015472 * q^71 + 12678070086 * q^73 - 136009728000 * q^76 + 436526954808 * q^77 + 60649635840 * q^80 + 727107143424 * q^82 - 68676615456 * q^83 + 142549278930 * q^85 + 1016993588736 * q^86 - 108312133632 * q^88 - 1619146872048 * q^91 - 216733483008 * q^92 + 1510780128600 * q^95 + 675735777846 * q^97 + 1327663144512 * q^98

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