LMFDB - Embedded newform 126.9.s.a.53.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,9,Mod(53,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("126.53");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	126.s (of order $6$, 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:	$51.3297048677$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 10 x^{19} + 5826111 x^{18} - 52434714 x^{17} + 14609902138197 x^{16} - 116878028586684 x^{15} + \cdots + 46\!\cdots\!67 $ x^20 - 10x^19 + 5826111x^18 - 52434714x^17 + 14609902138197x^16 - 116878028586684x^15 + 20570415019216091666x^14 - 143990859773172188876x^13 + 17778850839861393261577389x^12 - 106671233163309243180965870x^11 + 9680290789684647638481756224861x^10 - 48400476132217676087684309052126x^9 + 3275735646651808421941058995933509711x^8 - 13102652184923818063474053937427650164x^7 + 653502209053902071586784989674537854288110x^6 - 1960460768082339807775059434296031383524340x^5 + 68850375563113059318225998877994832003827914811x^4 - 137697483706898978818817917958243091010522758690x^3 + 3066443413106133675142280126674379287603657139937675x^2 - 3066374564691021503239083252322344289284140820347058*x + 46867859601845955405133191126273914741044351570054374867
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{16}\cdot 7^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.7
Root			$0.500000 + 843.859i$ of defining polynomial
Character	$\chi$	$=$	126.53
Dual form			126.9.s.a.107.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.79796 - 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(-731.553 + 422.362i) q^{5} +(-647.353 + 2312.08i) q^{7} -1448.15i q^{8} +O(q^{10})$	\(q+(9.79796 - 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(-731.553 + 422.362i) q^{5} +(-647.353 + 2312.08i) q^{7} -1448.15i q^{8} +(-4778.48 + 8276.58i) q^{10} +(1469.13 + 848.203i) q^{11} -12036.4 q^{13} +(6736.39 + 26315.7i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(48324.5 + 27900.2i) q^{17} +(-51037.4 - 88399.3i) q^{19} +108125. i q^{20} +19192.6 q^{22} +(133672. - 77175.6i) q^{23} +(161467. - 279670. i) q^{25} +(-117932. + 68087.9i) q^{26} +(214867. + 219733. i) q^{28} -1.12748e6i q^{29} +(265260. - 459443. i) q^{31} +(-160530. - 92681.9i) q^{32} +631308. q^{34} +(-502965. - 1.96483e6i) q^{35} +(-165677. - 286961. i) q^{37} +(-1.00012e6 - 577422. i) q^{38} +(611646. + 1.05940e6i) q^{40} -1.44438e6i q^{41} -941986. q^{43} +(188049. - 108570. i) q^{44} +(873142. - 1.51233e6i) q^{46} +(-311247. + 179698. i) q^{47} +(-4.92667e6 - 2.99347e6i) q^{49} -3.65359e6i q^{50} +(-770327. + 1.33425e6i) q^{52} +(3.84323e6 + 2.21889e6i) q^{53} -1.43300e6 q^{55} +(3.34826e6 + 937467. i) q^{56} +(-6.37798e6 - 1.10470e7i) q^{58} +(8.10977e6 + 4.68218e6i) q^{59} +(-4.37667e6 - 7.58062e6i) q^{61} -6.00214e6i q^{62} -2.09715e6 q^{64} +(8.80524e6 - 5.08371e6i) q^{65} +(8.83223e6 - 1.52979e7i) q^{67} +(6.18553e6 - 3.57122e6i) q^{68} +(-1.60428e7 - 1.64061e7i) q^{70} -4.61781e7i q^{71} +(-1.80301e7 + 3.12291e7i) q^{73} +(-3.24659e6 - 1.87442e6i) q^{74} -1.30656e7 q^{76} +(-2.91216e6 + 2.84767e6i) q^{77} +(-2.53495e7 - 4.39066e7i) q^{79} +(1.19858e7 + 6.91998e6i) q^{80} +(-8.17063e6 - 1.41520e7i) q^{82} +3.31554e7i q^{83} -4.71359e7 q^{85} +(-9.22954e6 + 5.32868e6i) q^{86} +(1.22833e6 - 2.12753e6i) q^{88} +(7.90789e7 - 4.56562e7i) q^{89} +(7.79177e6 - 2.78291e7i) q^{91} -1.97570e7i q^{92} +(-2.03305e6 + 3.52135e6i) q^{94} +(7.46731e7 + 4.31125e7i) q^{95} -1.64910e8 q^{97} +(-6.52049e7 - 1.46042e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 1280 q^{4} - 3710 q^{7}+O(q^{10}) $ 20 * q + 1280 * q^4 - 3710 * q^7	$ 20 q + 1280 q^{4} - 3710 q^{7} - 3040 q^{10} + 133668 q^{13} - 163840 q^{16} + 180526 q^{19} - 371648 q^{22} + 1919806 q^{25} + 136192 q^{28} - 2496630 q^{31} - 7741568 q^{34} + 2579434 q^{37} + 389120 q^{40} + 9786628 q^{43} + 6602944 q^{46} - 16557394 q^{49} + 8554752 q^{52} - 48224 q^{55} + 11294336 q^{58} - 45256440 q^{61} - 41943040 q^{64} - 5459674 q^{67} + 36416128 q^{70} - 154260166 q^{73} + 46214656 q^{76} - 147636618 q^{79} - 123306336 q^{82} - 6742976 q^{85} - 23785472 q^{88} - 32944086 q^{91} - 95141856 q^{94} + 268865432 q^{97}+O(q^{100}) $ 20 * q + 1280 * q^4 - 3710 * q^7 - 3040 * q^10 + 133668 * q^13 - 163840 * q^16 + 180526 * q^19 - 371648 * q^22 + 1919806 * q^25 + 136192 * q^28 - 2496630 * q^31 - 7741568 * q^34 + 2579434 * q^37 + 389120 * q^40 + 9786628 * q^43 + 6602944 * q^46 - 16557394 * q^49 + 8554752 * q^52 - 48224 * q^55 + 11294336 * q^58 - 45256440 * q^61 - 41943040 * q^64 - 5459674 * q^67 + 36416128 * q^70 - 154260166 * q^73 + 46214656 * q^76 - 147636618 * q^79 - 123306336 * q^82 - 6742976 * q^85 - 23785472 * q^88 - 32944086 * q^91 - 95141856 * q^94 + 268865432 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	9.79796	−	5.65685i	0.612372	−	0.353553i
$2$	9.79796	−	5.65685i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	64.0000	−	110.851i	0.250000	−	0.433013i
$5$	−731.553	+	422.362i	−1.17048	+	0.675780i	−0.953794	−	0.300461i	$-0.902860\pi$
$5$	−731.553	+	422.362i	−1.17048	+	0.675780i	−0.216691	+	0.976240i	$0.569526\pi$
$6$		0			0
$7$	−647.353	+	2312.08i	−0.269618	+	0.962967i
$7$	−647.353	+	2312.08i	−0.269618	+	0.962967i
$8$		−	1448.15i		−	0.353553i
$9$		0			0
$10$	−4778.48	+	8276.58i	−0.477848	+	0.827658i
$11$	1469.13	+	848.203i	0.100344	+	0.0579334i	0.549332	−	0.835604i	$-0.314882\pi$
$11$	1469.13	+	848.203i	0.100344	+	0.0579334i	−0.448988	+	0.893538i	$0.648216\pi$
$12$		0			0
$13$	−12036.4			−0.421426			−0.210713	−	0.977548i	$-0.567579\pi$
$13$	−12036.4			−0.421426			−0.210713	+	0.977548i	$0.567579\pi$
$14$	6736.39	+	26315.7i	0.175354	+	0.685019i
$15$		0			0
$16$	−8192.00	−	14189.0i	−0.125000	−	0.216506i
$17$	48324.5	+	27900.2i	0.578591	+	0.334050i	0.760573	−	0.649252i	$-0.224918\pi$
$17$	48324.5	+	27900.2i	0.578591	+	0.334050i	−0.181982	+	0.983302i	$0.558251\pi$
$18$		0			0
$19$	−51037.4	−	88399.3i	−0.391628	−	0.678320i	0.601036	−	0.799222i	$-0.294755\pi$
$19$	−51037.4	−	88399.3i	−0.391628	−	0.678320i	−0.992664	+	0.120902i	$0.961421\pi$
$20$			108125.i			0.675780i
$21$		0			0
$22$	19192.6			0.0819302
$23$	133672.	−	77175.6i	0.477672	−	0.275784i	−0.241774	−	0.970333i	$-0.577729\pi$
$23$	133672.	−	77175.6i	0.477672	−	0.275784i	0.719446	+	0.694549i	$0.244396\pi$
$24$		0			0
$25$	161467.	−	279670.i	0.413357	−	0.715955i
$26$	−117932.	+	68087.9i	−0.258070	+	0.148997i
$27$		0			0
$28$	214867.	+	219733.i	0.349573	+	0.357490i
$29$		−	1.12748e6i		−	1.59410i	−0.603912	−	0.797051i	$-0.706392\pi$
$29$		−	1.12748e6i		−	1.59410i	0.603912	−	0.797051i	$-0.293608\pi$
$30$		0			0
$31$	265260.	−	459443.i	0.287226	−	0.497491i	−0.685920	−	0.727677i	$-0.740600\pi$
$31$	265260.	−	459443.i	0.287226	−	0.497491i	0.973147	+	0.230186i	$0.0739334\pi$
$32$	−160530.	−	92681.9i	−0.153093	−	0.0883883i
$33$		0			0
$34$	631308.			0.472417
$35$	−502965.	−	1.96483e6i	−0.335170	−	1.30934i
$36$		0			0
$37$	−165677.	−	286961.i	−0.0884005	−	0.153114i	0.818435	−	0.574600i	$-0.194842\pi$
$37$	−165677.	−	286961.i	−0.0884005	−	0.153114i	−0.906835	+	0.421485i	$0.861509\pi$
$38$	−1.00012e6	−	577422.i	−0.479645	−	0.276923i
$39$		0			0
$40$	611646.	+	1.05940e6i	0.238924	+	0.413829i
$41$		−	1.44438e6i		−	0.511146i	−0.966790	−	0.255573i	$-0.917736\pi$
$41$		−	1.44438e6i		−	0.511146i	0.966790	−	0.255573i	$-0.0822642\pi$
$42$		0			0
$43$	−941986.			−0.275531			−0.137766	−	0.990465i	$-0.543992\pi$
$43$	−941986.			−0.275531			−0.137766	+	0.990465i	$0.543992\pi$
$44$	188049.	−	108570.i	0.0501718	−	0.0289667i
$45$		0			0
$46$	873142.	−	1.51233e6i	0.195009	−	0.337765i
$47$	−311247.	+	179698.i	−0.0637842	+	0.0368258i	−0.531553	−	0.847025i	$-0.678391\pi$
$47$	−311247.	+	179698.i	−0.0637842	+	0.0368258i	0.467769	+	0.883851i	$0.345058\pi$
$48$		0			0
$49$	−4.92667e6	−	2.99347e6i	−0.854612	−	0.519267i
$50$		−	3.65359e6i		−	0.584575i
$51$		0			0
$52$	−770327.	+	1.33425e6i	−0.105357	+	0.182483i
$53$	3.84323e6	+	2.21889e6i	0.487072	+	0.281211i	0.723359	−	0.690472i	$-0.242597\pi$
$53$	3.84323e6	+	2.21889e6i	0.487072	+	0.281211i	−0.236287	+	0.971683i	$0.575931\pi$
$54$		0			0
$55$	−1.43300e6			−0.156601
$56$	3.34826e6	+	937467.i	0.340460	+	0.0953243i
$57$		0			0
$58$	−6.37798e6	−	1.10470e7i	−0.563600	−	0.976184i
$59$	8.10977e6	+	4.68218e6i	0.669269	+	0.386402i	0.795799	−	0.605560i	$-0.207051\pi$
$59$	8.10977e6	+	4.68218e6i	0.669269	+	0.386402i	−0.126531	+	0.991963i	$0.540384\pi$
$60$		0			0
$61$	−4.37667e6	−	7.58062e6i	−0.316100	−	0.547501i	0.663571	−	0.748114i	$-0.269040\pi$
$61$	−4.37667e6	−	7.58062e6i	−0.316100	−	0.547501i	−0.979671	+	0.200612i	$0.935707\pi$
$62$		−	6.00214e6i		−	0.406200i
$63$		0			0
$64$	−2.09715e6			−0.125000
$65$	8.80524e6	−	5.08371e6i	0.493273	−	0.284791i
$66$		0			0
$67$	8.83223e6	−	1.52979e7i	0.438300	−	0.759157i	−0.559259	−	0.828993i	$-0.688914\pi$
$67$	8.83223e6	−	1.52979e7i	0.438300	−	0.759157i	0.997559	+	0.0698357i	$0.0222475\pi$
$68$	6.18553e6	−	3.57122e6i	0.289295	−	0.167025i
$69$		0			0
$70$	−1.60428e7	−	1.64061e7i	−0.668171	−	0.683304i
$71$		−	4.61781e7i		−	1.81720i	−0.417666	−	0.908601i	$-0.637152\pi$
$71$		−	4.61781e7i		−	1.81720i	0.417666	−	0.908601i	$-0.362848\pi$
$72$		0			0
$73$	−1.80301e7	+	3.12291e7i	−0.634902	+	1.09968i	0.351634	+	0.936138i	$0.385626\pi$
$73$	−1.80301e7	+	3.12291e7i	−0.634902	+	1.09968i	−0.986536	+	0.163545i	$0.947707\pi$
$74$	−3.24659e6	−	1.87442e6i	−0.108268	−	0.0625086i
$75$		0			0
$76$	−1.30656e7			−0.391628
$77$	−2.91216e6	+	2.84767e6i	−0.0828424	+	0.0810077i
$78$		0			0
$79$	−2.53495e7	−	4.39066e7i	−0.650821	−	1.12725i	−0.982924	−	0.184011i	$-0.941092\pi$
$79$	−2.53495e7	−	4.39066e7i	−0.650821	−	1.12725i	0.332104	−	0.943243i	$-0.392242\pi$
$80$	1.19858e7	+	6.91998e6i	0.292621	+	0.168945i
$81$		0			0
$82$	−8.17063e6	−	1.41520e7i	−0.180718	−	0.313012i
$83$			3.31554e7i			0.698622i	0.937007	+	0.349311i	$0.113584\pi$
$83$			3.31554e7i			0.698622i	−0.937007	+	0.349311i	$0.886416\pi$
$84$		0			0
$85$	−4.71359e7			−0.902976
$86$	−9.22954e6	+	5.32868e6i	−0.168728	+	0.0974149i
$87$		0			0
$88$	1.22833e6	−	2.12753e6i	0.0204825	−	0.0354768i
$89$	7.90789e7	−	4.56562e7i	1.26038	−	0.727679i	0.287229	−	0.957862i	$-0.407266\pi$
$89$	7.90789e7	−	4.56562e7i	1.26038	−	0.727679i	0.973147	+	0.230183i	$0.0739325\pi$
$90$		0			0
$91$	7.79177e6	−	2.78291e7i	0.113624	−	0.405820i
$92$		−	1.97570e7i		−	0.275784i
$93$		0			0
$94$	−2.03305e6	+	3.52135e6i	−0.0260398	+	0.0451022i
$95$	7.46731e7	+	4.31125e7i	0.916790	+	0.529309i
$96$		0			0
$97$	−1.64910e8			−1.86278			−0.931388	−	0.364027i	$-0.881402\pi$
$97$	−1.64910e8			−1.86278			−0.931388	+	0.364027i	$0.881402\pi$
$98$	−6.52049e7	−	1.46042e6i	−0.706929	−	0.0158334i
$99$		0			0
$100$	−2.06678e7	−	3.57977e7i	−0.206678	−	0.357977i
$101$	1.26639e8	+	7.31150e7i	1.21697	+	0.702621i	0.964270	−	0.264923i	$-0.0853464\pi$
$101$	1.26639e8	+	7.31150e7i	1.21697	+	0.702621i	0.252705	+	0.967543i	$0.418680\pi$
$102$		0			0
$103$	−4.33878e7	−	7.51499e7i	−0.385495	−	0.667697i	0.606343	−	0.795203i	$-0.292636\pi$
$103$	−4.33878e7	−	7.51499e7i	−0.385495	−	0.667697i	−0.991838	+	0.127506i	$0.959303\pi$
$104$			1.74305e7i			0.148997i
$105$		0			0
$106$	5.02078e7			0.397693
$107$	−1.57711e7	+	9.10547e6i	−0.120317	+	0.0694652i	−0.558951	−	0.829201i	$-0.688796\pi$
$107$	−1.57711e7	+	9.10547e6i	−0.120317	+	0.0694652i	0.438634	+	0.898666i	$0.355463\pi$
$108$		0			0
$109$	−5.61897e7	+	9.73235e7i	−0.398062	+	0.689464i	−0.993487	−	0.113947i	$-0.963651\pi$
$109$	−5.61897e7	+	9.73235e7i	−0.398062	+	0.689464i	0.595425	+	0.803411i	$0.296984\pi$
$110$	−1.40404e7	+	8.10625e6i	−0.0958980	+	0.0553668i
$111$		0			0
$112$	3.81092e7	−	9.75534e6i	0.242191	−	0.0619969i
$113$		−	2.98022e8i		−	1.82783i	−0.405910	−	0.913913i	$-0.633046\pi$
$113$		−	2.98022e8i		−	1.82783i	0.405910	−	0.913913i	$-0.366954\pi$
$114$		0			0
$115$	−6.51922e7	+	1.12916e8i	−0.372738	+	0.645602i
$116$	−1.24982e8	−	7.21586e7i	−0.690266	−	0.398526i
$117$		0			0
$118$	1.05946e8			0.546456
$119$	−9.57905e7	+	9.36691e7i	−0.477677	+	0.467098i
$120$		0			0
$121$	−1.05741e8	−	1.83148e8i	−0.493287	−	0.854399i
$122$	−8.57649e7	−	4.95164e7i	−0.387142	−	0.223516i
$123$		0			0
$124$	−3.39532e7	−	5.88087e7i	−0.143613	−	0.248745i
$125$		−	5.71795e7i		−	0.234207i
$126$		0			0
$127$	4.95803e8			1.90587			0.952937	−	0.303169i	$-0.0980447\pi$
$127$	4.95803e8			1.90587			0.952937	+	0.303169i	$0.0980447\pi$
$128$	−2.05478e7	+	1.18633e7i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	5.75156e7	−	9.96199e7i	0.201378	−	0.348797i
$131$	3.36540e8	−	1.94301e8i	1.14275	−	0.659767i	0.195640	−	0.980676i	$-0.437322\pi$
$131$	3.36540e8	−	1.94301e8i	1.14275	−	0.659767i	0.947110	+	0.320909i	$0.103988\pi$
$132$		0			0
$133$	2.37426e8	−	6.07772e7i	0.758790	−	0.194238i
$134$		−	1.99851e8i		−	0.619849i
$135$		0			0
$136$	4.04037e7	−	6.99813e7i	0.118104	−	0.204563i
$137$	9.13138e7	+	5.27201e7i	0.259212	+	0.149656i	0.623975	−	0.781444i	$-0.285517\pi$
$137$	9.13138e7	+	5.27201e7i	0.259212	+	0.149656i	−0.364763	+	0.931100i	$0.618850\pi$
$138$		0			0
$139$	2.10106e8			0.562833			0.281416	−	0.959586i	$-0.409196\pi$
$139$	2.10106e8			0.562833			0.281416	+	0.959586i	$0.409196\pi$
$140$	−2.49994e8	−	6.99949e7i	−0.650754	−	0.182202i
$141$		0			0
$142$	−2.61223e8	−	4.52452e8i	−0.642478	−	1.11280i
$143$	−1.76830e7	−	1.02093e7i	−0.0422874	−	0.0244147i
$144$		0			0
$145$	4.76204e8	+	8.24810e8i	1.07726	+	1.86587i
$146$			4.07975e8i			0.897887i
$147$		0			0
$148$	−4.24133e7			−0.0884005
$149$	−3.17975e8	+	1.83583e8i	−0.645131	+	0.372466i	−0.786588	−	0.617478i	$-0.788154\pi$
$149$	−3.17975e8	+	1.83583e8i	−0.645131	+	0.372466i	0.141457	+	0.989944i	$0.454821\pi$
$150$		0			0
$151$	2.85064e6	−	4.93745e6i	0.00548320	−	0.00949719i	−0.863271	−	0.504741i	$-0.831588\pi$
$151$	2.85064e6	−	4.93745e6i	0.00548320	−	0.00949719i	0.868754	+	0.495244i	$0.164921\pi$
$152$	−1.28016e8	+	7.39100e7i	−0.239822	+	0.138461i
$153$		0			0
$154$	−1.24244e7	+	4.43750e7i	−0.0220898	+	0.0788961i
$155$			4.48143e8i			0.776407i
$156$		0			0
$157$	−5.64508e8	+	9.77756e8i	−0.929119	+	1.60928i	−0.144320	+	0.989531i	$0.546100\pi$
$157$	−5.64508e8	+	9.77756e8i	−0.929119	+	1.60928i	−0.784799	+	0.619750i	$0.787234\pi$
$158$	−4.96747e8	−	2.86797e8i	−0.797089	−	0.460200i
$159$		0			0
$160$	1.56581e8			0.238924
$161$	9.19036e7	+	3.59021e8i	0.136782	+	0.534338i
$162$		0			0
$163$	6.05612e8	+	1.04895e9i	0.857915	+	1.48595i	0.873914	+	0.486080i	$0.161574\pi$
$163$	6.05612e8	+	1.04895e9i	0.857915	+	1.48595i	−0.0159995	+	0.999872i	$0.505093\pi$
$164$	−1.60111e8	−	9.24402e7i	−0.221333	−	0.127787i
$165$		0			0
$166$	1.87555e8	+	3.24855e8i	0.247000	+	0.427817i
$167$			1.31517e9i			1.69089i	0.534060	+	0.845447i	$0.320666\pi$
$167$			1.31517e9i			1.69089i	−0.534060	+	0.845447i	$0.679334\pi$
$168$		0			0
$169$	−6.70857e8			−0.822400
$170$	−4.61836e8	+	2.66641e8i	−0.552957	+	0.319250i
$171$		0			0
$172$	−6.02871e7	+	1.04420e8i	−0.0688828	+	0.119308i
$173$	−4.68916e7	+	2.70729e7i	−0.0523493	+	0.0302239i	−0.525946	−	0.850518i	$-0.676289\pi$
$173$	−4.68916e7	+	2.70729e7i	−0.0523493	+	0.0302239i	0.473597	+	0.880742i	$0.342955\pi$
$174$		0			0
$175$	5.42094e8	+	5.54371e8i	0.577993	+	0.591083i
$176$		−	2.77939e7i		−	0.0289667i
$177$		0			0
$178$	5.16541e8	−	8.94675e8i	0.514547	−	0.891221i
$179$	6.55277e8	+	3.78325e8i	0.638283	+	0.368513i	0.783953	−	0.620821i	$-0.213200\pi$
$179$	6.55277e8	+	3.78325e8i	0.638283	+	0.368513i	−0.145670	+	0.989333i	$0.546534\pi$
$180$		0			0
$181$	−1.97525e8			−0.184038			−0.0920191	−	0.995757i	$-0.529332\pi$
$181$	−1.97525e8			−0.184038			−0.0920191	+	0.995757i	$0.529332\pi$
$182$	−8.10816e7	−	3.16745e8i	−0.0738987	−	0.288685i
$183$		0			0
$184$	−1.11762e8	−	1.93578e8i	−0.0975043	−	0.168882i
$185$	2.42403e8	+	1.39951e8i	0.206943	+	0.119479i
$186$		0			0
$187$	4.73300e7	+	8.19779e7i	0.0387052	+	0.0670395i
$188$			4.60028e7i			0.0368258i
$189$		0			0
$190$	9.75525e8			0.748556
$191$	2.42410e8	−	1.39955e8i	0.182145	−	0.105161i	−0.406155	−	0.913804i	$-0.633131\pi$
$191$	2.42410e8	−	1.39955e8i	0.182145	−	0.105161i	0.588300	+	0.808643i	$0.299797\pi$
$192$		0			0
$193$	8.52486e8	−	1.47655e9i	0.614409	−	1.06419i	−0.376079	−	0.926588i	$-0.622728\pi$
$193$	8.52486e8	−	1.47655e9i	0.614409	−	1.06419i	0.990488	−	0.137600i	$-0.0439389\pi$
$194$	−1.61578e9	+	9.32874e8i	−1.14071	+	0.658591i
$195$		0			0
$196$	−6.47137e8	+	3.54546e8i	−0.438502	+	0.240241i
$197$		−	4.25026e8i		−	0.282196i	−0.989996	−	0.141098i	$-0.954937\pi$
$197$		−	4.25026e8i		−	0.282196i	0.989996	−	0.141098i	$-0.0450632\pi$
$198$		0			0
$199$	−1.22474e8	+	2.12131e8i	−0.0780965	+	0.135267i	−0.902429	−	0.430839i	$-0.858218\pi$
$199$	−1.22474e8	+	2.12131e8i	−0.0780965	+	0.135267i	0.824332	+	0.566106i	$0.191551\pi$
$200$	−4.05005e8	−	2.33830e8i	−0.253128	−	0.146144i
$201$		0			0
$202$	1.65440e9			0.993656
$203$	2.60682e9	+	7.29876e8i	1.53507	+	0.429799i
$204$		0			0
$205$	6.10051e8	+	1.05664e9i	0.345422	+	0.598289i
$206$	−8.50224e8	−	4.90877e8i	−0.472133	−	0.272586i
$207$		0			0
$208$	9.86019e7	+	1.70783e8i	0.0526783	+	0.0912415i
$209$		−	1.73160e8i		−	0.0907534i
$210$		0			0
$211$	−1.92483e9			−0.971094			−0.485547	−	0.874210i	$-0.661380\pi$
$211$	−1.92483e9			−0.971094			−0.485547	+	0.874210i	$0.661380\pi$
$212$	4.91934e8	−	2.84018e8i	0.243536	−	0.140606i
$213$		0			0
$214$	−1.03017e8	+	1.78430e8i	−0.0491193	+	0.0850772i
$215$	6.89113e8	−	3.97859e8i	0.322505	−	0.186198i
$216$		0			0
$217$	8.90555e8	+	9.10725e8i	0.401626	+	0.410722i
$218$			1.27143e9i			0.562945i
$219$		0			0
$220$	−9.17117e7	+	1.58849e8i	−0.0391502	+	0.0678102i
$221$	−5.81651e8	−	3.35816e8i	−0.243833	−	0.140777i
$222$		0			0
$223$	−4.03330e9			−1.63095			−0.815476	−	0.578791i	$-0.803525\pi$
$223$	−4.03330e9			−1.63095			−0.815476	+	0.578791i	$0.803525\pi$
$224$	3.18208e8	−	3.11161e8i	0.126392	−	0.123593i
$225$		0			0
$226$	−1.68587e9	−	2.92001e9i	−0.646234	−	1.11931i
$227$	−2.32808e9	−	1.34411e9i	−0.876786	−	0.506213i	−0.00718864	−	0.999974i	$-0.502288\pi$
$227$	−2.32808e9	−	1.34411e9i	−0.876786	−	0.506213i	−0.869597	+	0.493762i	$0.835622\pi$
$228$		0			0
$229$	1.33522e8	+	2.31267e8i	0.0485525	+	0.0840954i	0.889280	−	0.457363i	$-0.151206\pi$
$229$	1.33522e8	+	2.31267e8i	0.0485525	+	0.0840954i	−0.840728	+	0.541458i	$0.817873\pi$
$230$			1.47513e9i			0.527132i
$231$		0			0
$232$	−1.63276e9			−0.563600
$233$	−1.92245e8	+	1.10993e8i	−0.0652275	+	0.0376591i	−0.532259	−	0.846582i	$-0.678657\pi$
$233$	−1.92245e8	+	1.10993e8i	−0.0652275	+	0.0376591i	0.467032	+	0.884241i	$0.345323\pi$
$234$		0			0
$235$	1.51796e8	−	2.62918e8i	0.0497723	−	0.0862081i
$236$	1.03805e9	−	5.99319e8i	0.334634	−	0.193201i
$237$		0			0
$238$	−4.08679e8	+	1.45964e9i	−0.127372	+	0.454923i
$239$			4.93517e8i			0.151255i	0.997136	+	0.0756276i	$0.0240960\pi$
$239$			4.93517e8i			0.151255i	−0.997136	+	0.0756276i	$0.975904\pi$
$240$		0			0
$241$	2.35587e9	−	4.08049e9i	0.698367	−	1.20961i	−0.270665	−	0.962674i	$-0.587244\pi$
$241$	2.35587e9	−	4.08049e9i	0.698367	−	1.20961i	0.969032	−	0.246934i	$-0.0794231\pi$
$242$	−2.07208e9	−	1.19632e9i	−0.604151	−	0.348807i
$243$		0			0
$244$	−1.12043e9			−0.316100
$245$	4.86845e9	+	1.09041e8i	1.35122	+	0.0302639i
$246$		0			0
$247$	6.14304e8	+	1.06401e9i	0.165042	+	0.285862i
$248$	−6.65345e8	−	3.84137e8i	−0.175890	−	0.101550i
$249$		0			0
$250$	−3.23456e8	−	5.60243e8i	−0.0828048	−	0.143422i
$251$		−	4.28808e9i		−	1.08036i	−0.841550	−	0.540180i	$-0.818356\pi$
$251$		−	4.28808e9i		−	1.08036i	0.841550	−	0.540180i	$-0.181644\pi$
$252$		0			0
$253$	2.61842e8			0.0639084
$254$	4.85786e9	−	2.80468e9i	1.16710	−	0.673828i
$255$		0			0
$256$	−1.34218e8	+	2.32472e8i	−0.0312500	+	0.0541266i
$257$	1.87367e9	−	1.08176e9i	0.429497	−	0.247970i	−0.269635	−	0.962963i	$-0.586903\pi$
$257$	1.87367e9	−	1.08176e9i	0.429497	−	0.247970i	0.699133	+	0.714992i	$0.253570\pi$
$258$		0			0
$259$	7.70728e8	−	1.97294e8i	0.171278	−	0.0438445i
$260$		−	1.30143e9i		−	0.284791i
$261$		0			0
$262$	2.19827e9	−	3.80751e9i	0.466526	−	0.808046i
$263$	−8.17862e9	−	4.72193e9i	−1.70945	−	0.986953i	−0.935231	−	0.354038i	$-0.884808\pi$
$263$	−8.17862e9	−	4.72193e9i	−1.70945	−	0.986953i	−0.774221	−	0.632915i	$-0.781858\pi$
$264$		0			0
$265$	−3.74870e9			−0.760147
$266$	1.98248e9	−	1.93858e9i	0.395989	−	0.387219i
$267$		0			0
$268$	−1.13053e9	−	1.95813e9i	−0.219150	−	0.379579i
$269$	1.55230e8	+	8.96221e7i	0.0296460	+	0.0171161i	0.514750	−	0.857340i	$-0.327885\pi$
$269$	1.55230e8	+	8.96221e7i	0.0296460	+	0.0171161i	−0.485104	+	0.874457i	$0.661218\pi$
$270$		0			0
$271$	−2.60539e9	−	4.51267e9i	−0.483054	−	0.836674i	0.516757	−	0.856132i	$-0.327139\pi$
$271$	−2.60539e9	−	4.51267e9i	−0.483054	−	0.836674i	−0.999811	+	0.0194580i	$0.993806\pi$
$272$		−	9.14232e8i		−	0.167025i
$273$		0			0
$274$	1.19292e9			0.211645
$275$	4.74433e8	−	2.73914e8i	0.0829554	−	0.0478943i
$276$		0			0
$277$	1.50145e9	−	2.60059e9i	0.255030	−	0.441725i	−0.709874	−	0.704329i	$-0.751248\pi$
$277$	1.50145e9	−	2.60059e9i	0.255030	−	0.441725i	0.964904	+	0.262604i	$0.0845813\pi$
$278$	2.05861e9	−	1.18854e9i	0.344663	−	0.198991i
$279$		0			0
$280$	−2.84538e9	+	7.28371e8i	−0.462922	+	0.118501i
$281$		−	3.30227e9i		−	0.529647i	−0.964297	−	0.264824i	$-0.914686\pi$
$281$		−	3.30227e9i		−	0.529647i	0.964297	−	0.264824i	$-0.0853137\pi$
$282$		0			0
$283$	3.37306e9	−	5.84231e9i	0.525870	−	0.910833i	−0.473676	−	0.880699i	$-0.657073\pi$
$283$	3.37306e9	−	5.84231e9i	0.525870	−	0.910833i	0.999546	−	0.0301341i	$-0.00959343\pi$
$284$	−5.11891e9	−	2.95540e9i	−0.786871	−	0.454300i
$285$		0			0
$286$	−2.31009e8			−0.0345275
$287$	3.33952e9	+	9.35022e8i	0.492217	+	0.137814i
$288$		0			0
$289$	−1.93104e9	−	3.34466e9i	−0.276822	−	0.479469i
$290$	9.33166e9	+	5.38764e9i	1.31937	+	0.761739i
$291$		0			0
$292$	2.30785e9	+	3.99732e9i	0.317451	+	0.549841i
$293$			2.75048e9i			0.373197i	0.982436	+	0.186599i	$0.0597464\pi$
$293$			2.75048e9i			0.373197i	−0.982436	+	0.186599i	$0.940254\pi$
$294$		0			0
$295$	−7.91030e9			−1.04449
$296$	−4.15563e8	+	2.39926e8i	−0.0541340	+	0.0312543i
$297$		0			0
$298$	−2.07700e9	+	3.59747e9i	−0.263374	+	0.456176i
$299$	−1.60893e9	+	9.28914e8i	−0.201303	+	0.116223i
$300$		0			0
$301$	6.09797e8	−	2.17795e9i	0.0742881	−	0.265327i
$302$		−	6.45026e7i		−	0.00775442i
$303$		0			0
$304$	−8.36196e8	+	1.44833e9i	−0.0979071	+	0.169580i
$305$	6.40353e9	+	3.69708e9i	0.739981	+	0.427228i
$306$		0			0
$307$	−1.32344e10			−1.48988			−0.744940	−	0.667131i	$-0.767522\pi$
$307$	−1.32344e10			−1.48988			−0.744940	+	0.667131i	$0.767522\pi$
$308$	1.29289e8	+	5.05068e8i	0.0143668	+	0.0561237i
$309$		0			0
$310$	2.53508e9	+	4.39088e9i	0.274501	+	0.475450i
$311$	−1.96469e9	−	1.13432e9i	−0.210016	−	0.121253i	0.391303	−	0.920262i	$-0.372025\pi$
$311$	−1.96469e9	−	1.13432e9i	−0.210016	−	0.121253i	−0.601319	+	0.799009i	$0.705358\pi$
$312$		0			0
$313$	3.96740e9	+	6.87175e9i	0.413361	+	0.715962i	0.995255	−	0.0973029i	$-0.0310216\pi$
$313$	3.96740e9	+	6.87175e9i	0.413361	+	0.715962i	−0.581894	+	0.813264i	$0.697688\pi$
$314$			1.27734e10i			1.31397i
$315$		0			0
$316$	−6.48948e9			−0.650821
$317$	−1.16622e10	+	6.73316e9i	−1.15490	+	0.666779i	−0.950075	−	0.312021i	$-0.898994\pi$
$317$	−1.16622e10	+	6.73316e9i	−1.15490	+	0.666779i	−0.204820	+	0.978800i	$0.565661\pi$
$318$		0			0
$319$	9.56330e8	−	1.65641e9i	0.0923517	−	0.159958i
$320$	1.53418e9	−	8.85758e8i	0.146311	−	0.0844725i
$321$		0			0
$322$	2.93140e9	+	2.99779e9i	0.272679	+	0.278854i
$323$		−	5.69580e9i		−	0.523293i
$324$		0			0
$325$	−1.94348e9	+	3.36621e9i	−0.174199	+	0.301722i
$326$	1.18675e10	+	6.85172e9i	1.05073	+	0.606637i
$327$		0			0
$328$	−2.09168e9			−0.180718
$329$	−2.13991e8	−	8.35956e8i	−0.0182647	−	0.0713510i
$330$		0			0
$331$	−6.23324e9	−	1.07963e10i	−0.519281	−	0.899420i	−0.999749	−	0.0224084i	$-0.992867\pi$
$331$	−6.23324e9	−	1.07963e10i	−0.519281	−	0.899420i	0.480468	−	0.877012i	$-0.340467\pi$
$332$	3.67532e9	+	2.12195e9i	0.302512	+	0.174655i
$333$		0			0
$334$	7.43973e9	+	1.28860e10i	0.597821	+	1.03546i
$335$			1.49216e10i			1.18478i
$336$		0			0
$337$	1.05232e10			0.815886			0.407943	−	0.913007i	$-0.366246\pi$
$337$	1.05232e10			0.815886			0.407943	+	0.913007i	$0.366246\pi$
$338$	−6.57303e9	+	3.79494e9i	−0.503615	+	0.290762i
$339$		0			0
$340$	−3.01670e9	+	5.22507e9i	−0.225744	+	0.391000i
$341$	7.79402e8	−	4.49988e8i	0.0576427	−	0.0332800i
$342$		0			0
$343$	1.01104e10	−	9.45305e9i	0.730456	−	0.682960i
$344$			1.36414e9i			0.0974149i
$345$		0			0
$346$	−3.06295e8	+	5.30518e8i	−0.0213715	+	0.0370166i
$347$	−1.60563e10	−	9.27012e9i	−1.10746	−	0.639393i	−0.169290	−	0.985566i	$-0.554147\pi$
$347$	−1.60563e10	−	9.27012e9i	−1.10746	−	0.639393i	−0.938170	+	0.346174i	$0.887481\pi$
$348$		0			0
$349$	−1.19145e9			−0.0803109			−0.0401554	−	0.999193i	$-0.512785\pi$
$349$	−1.19145e9			−0.0803109			−0.0401554	+	0.999193i	$0.512785\pi$
$350$	8.44741e9	+	2.36516e9i	0.562926	+	0.157612i
$351$		0			0
$352$	−1.57226e8	−	2.72324e8i	−0.0102413	−	0.0177384i
$353$	−1.20722e9	−	6.96988e8i	−0.0777476	−	0.0448876i	0.460622	−	0.887596i	$-0.347626\pi$
$353$	−1.20722e9	−	6.96988e8i	−0.0777476	−	0.0448876i	−0.538370	+	0.842709i	$0.680960\pi$
$354$		0			0
$355$	1.95039e10	+	3.37818e10i	1.22803	+	2.12701i
$356$		−	1.16880e10i		−	0.727679i
$357$		0			0
$358$	8.56051e9			0.521156
$359$	−2.02633e10	+	1.16990e10i	−1.21992	+	0.704322i	−0.964901	−	0.262613i	$-0.915416\pi$
$359$	−2.02633e10	+	1.16990e10i	−1.21992	+	0.704322i	−0.255021	+	0.966936i	$0.582082\pi$
$360$		0			0
$361$	3.28215e9	−	5.68486e9i	0.193255	−	0.334727i
$362$	−1.93534e9	+	1.11737e9i	−0.112700	+	0.0650674i
$363$		0			0
$364$	−2.58622e9	−	2.64479e9i	−0.147319	−	0.150656i
$365$		−	3.04610e10i		−	1.71622i
$366$		0			0
$367$	5.42308e9	−	9.39305e9i	0.298939	−	0.517777i	−0.676955	−	0.736025i	$-0.736701\pi$
$367$	5.42308e9	−	9.39305e9i	0.298939	−	0.517777i	0.975893	+	0.218248i	$0.0700341\pi$
$368$	−2.19008e9	−	1.26445e9i	−0.119418	−	0.0689460i
$369$		0			0
$370$	3.16674e9			0.168968
$371$	−7.61819e9	+	7.44947e9i	−0.402120	+	0.393215i
$372$		0			0
$373$	8.00431e9	+	1.38639e10i	0.413512	+	0.716224i	0.995271	−	0.0971372i	$-0.0309686\pi$
$373$	8.00431e9	+	1.38639e10i	0.413512	+	0.716224i	−0.581759	+	0.813361i	$0.697635\pi$
$374$	9.27474e8	+	5.35478e8i	0.0474041	+	0.0273687i
$375$		0			0
$376$	2.60231e8	+	4.50733e8i	0.0130199	+	0.0225511i
$377$			1.35707e10i			0.671797i
$378$		0			0
$379$	1.85021e10			0.896736			0.448368	−	0.893849i	$-0.352005\pi$
$379$	1.85021e10			0.896736			0.448368	+	0.893849i	$0.352005\pi$
$380$	9.55816e9	−	5.51840e9i	0.458395	−	0.264654i
$381$		0			0
$382$	1.58341e9	−	2.74255e9i	0.0743602	−	0.128796i
$383$	−3.46335e10	+	1.99957e10i	−1.60954	+	0.929268i	−0.620067	+	0.784549i	$0.712895\pi$
$383$	−3.46335e10	+	1.99957e10i	−1.60954	+	0.929268i	−0.989473	+	0.144719i	$0.953772\pi$
$384$		0			0
$385$	9.27654e8	−	3.31321e9i	0.0422224	−	0.150802i
$386$		−	1.92895e10i		−	0.868906i
$387$		0			0
$388$	−1.05543e10	+	1.82805e10i	−0.465694	+	0.806606i
$389$	−2.81326e10	−	1.62424e10i	−1.22860	−	0.709334i	−0.261865	−	0.965105i	$-0.584337\pi$
$389$	−2.81326e10	−	1.62424e10i	−1.22860	−	0.709334i	−0.966737	+	0.255771i	$0.917671\pi$
$390$		0			0
$391$	8.61285e9			0.368502
$392$	−4.33501e9	+	7.13458e9i	−0.183588	+	0.302151i
$393$		0			0
$394$	−2.40431e9	−	4.16438e9i	−0.0997712	−	0.172809i
$395$	3.70890e10	+	2.14134e10i	1.52355	+	0.879623i
$396$		0			0
$397$	1.85018e10	+	3.20461e10i	0.744822	+	1.29007i	0.950278	+	0.311403i	$0.100799\pi$
$397$	1.85018e10	+	3.20461e10i	0.744822	+	1.29007i	−0.205456	+	0.978666i	$0.565868\pi$
$398$			2.77127e9i			0.110445i
$399$		0			0
$400$	−5.29096e9			−0.206678
$401$	1.24837e10	−	7.20745e9i	0.482797	−	0.278743i	−0.238784	−	0.971073i	$-0.576749\pi$
$401$	1.24837e10	−	7.20745e9i	0.482797	−	0.278743i	0.721581	+	0.692330i	$0.243416\pi$
$402$		0			0
$403$	−3.19276e9	+	5.53002e9i	−0.121045	+	0.209656i
$404$	1.62098e10	−	9.35872e9i	0.608487	−	0.351310i
$405$		0			0
$406$	2.96704e10	−	7.59513e9i	1.09199	−	0.279532i
$407$		−	5.62110e8i		−	0.0204854i
$408$		0			0
$409$	1.32226e10	−	2.29021e10i	0.472522	−	0.818432i	−0.526984	−	0.849875i	$-0.676677\pi$
$409$	1.32226e10	−	2.29021e10i	0.472522	−	0.818432i	0.999506	+	0.0314434i	$0.0100104\pi$
$410$	1.19545e10	+	6.90194e9i	0.423054	+	0.244251i
$411$		0			0
$412$	−1.11073e10			−0.385495
$413$	−1.60755e10	+	1.57195e10i	−0.552540	+	0.540303i
$414$		0			0
$415$	−1.40036e10	−	2.42549e10i	−0.472114	−	0.817726i
$416$	1.93219e9	+	1.11555e9i	0.0645175	+	0.0372492i
$417$		0			0
$418$	−9.79542e8	−	1.69662e9i	−0.0320862	−	0.0555749i
$419$			1.61701e10i			0.524636i	0.964982	+	0.262318i	$0.0844869\pi$
$419$			1.61701e10i			0.524636i	−0.964982	+	0.262318i	$0.915513\pi$
$420$		0			0
$421$	−4.17039e10			−1.32754			−0.663770	−	0.747936i	$-0.731045\pi$
$421$	−4.17039e10			−1.32754			−0.663770	+	0.747936i	$0.731045\pi$
$422$	−1.88594e10	+	1.08885e10i	−0.594671	+	0.343334i
$423$		0			0
$424$	3.21330e9	−	5.56559e9i	0.0994231	−	0.172206i
$425$	1.56057e10	−	9.00993e9i	0.478329	−	0.276163i
$426$		0			0
$427$	2.03603e10	−	5.21190e9i	0.612452	−	0.156778i
$428$			2.33100e9i			0.0694652i
$429$		0			0
$430$	4.50127e9	−	7.79642e9i	0.131662	−	0.228045i
$431$	5.85744e9	+	3.38180e9i	0.169746	+	0.0980028i	0.582466	−	0.812855i	$-0.302088\pi$
$431$	5.85744e9	+	3.38180e9i	0.169746	+	0.0980028i	−0.412720	+	0.910858i	$0.635421\pi$
$432$		0			0
$433$	3.43703e10			0.977759			0.488880	−	0.872351i	$-0.337406\pi$
$433$	3.43703e10			0.977759			0.488880	+	0.872351i	$0.337406\pi$
$434$	1.38775e10	+	3.88550e9i	0.391157	+	0.109519i
$435$		0			0
$436$	7.19228e9	+	1.24574e10i	0.199031	+	0.344732i
$437$	−1.36445e10	−	7.87768e9i	−0.374139	−	0.216009i
$438$		0			0
$439$	−5.18172e9	−	8.97500e9i	−0.139513	−	0.241644i	0.787799	−	0.615932i	$-0.211220\pi$
$439$	−5.18172e9	−	8.97500e9i	−0.139513	−	0.241644i	−0.927313	+	0.374288i	$0.877887\pi$
$440$			2.07520e9i			0.0553668i
$441$		0			0
$442$	−7.59865e9			−0.199089
$443$	4.14114e10	−	2.39089e10i	1.07524	−	0.620790i	0.145631	−	0.989339i	$-0.453479\pi$
$443$	4.14114e10	−	2.39089e10i	1.07524	−	0.620790i	0.929608	+	0.368549i	$0.120145\pi$
$444$		0			0
$445$	−3.85669e10	+	6.67999e10i	−0.983501	+	1.70347i
$446$	−3.95181e10	+	2.28158e10i	−0.998750	+	0.576628i
$447$		0			0
$448$	1.35760e9	−	4.84879e9i	0.0337022	−	0.120371i
$449$		−	5.12527e10i		−	1.26105i	−0.776170	−	0.630523i	$-0.782840\pi$
$449$		−	5.12527e10i		−	1.26105i	0.776170	−	0.630523i	$-0.217160\pi$
$450$		0			0
$451$	1.22513e9	−	2.12198e9i	0.0296125	−	0.0512903i
$452$	−3.30361e10	−	1.90734e10i	−0.791472	−	0.456956i
$453$		0			0
$454$	−3.04138e10			−0.715893
$455$	6.05386e9	+	2.36494e10i	0.141250	+	0.551791i
$456$		0			0
$457$	−3.59657e10	−	6.22944e10i	−0.824563	−	1.42819i	−0.902253	−	0.431208i	$-0.858088\pi$
$457$	−3.59657e10	−	6.22944e10i	−0.824563	−	1.42819i	0.0776896	−	0.996978i	$-0.475246\pi$
$458$	2.61649e9	+	1.51063e9i	0.0594644	+	0.0343318i
$459$		0			0
$460$	8.34460e9	+	1.44533e10i	0.186369	+	0.322801i
$461$		−	5.18441e10i		−	1.14788i	−0.818898	−	0.573939i	$-0.805415\pi$
$461$		−	5.18441e10i		−	1.14788i	0.818898	−	0.573939i	$-0.194585\pi$
$462$		0			0
$463$	−4.70292e10			−1.02340			−0.511698	−	0.859166i	$-0.670983\pi$
$463$	−4.70292e10			−1.02340			−0.511698	+	0.859166i	$0.670983\pi$
$464$	−1.59977e10	+	9.23630e9i	−0.345133	+	0.199263i
$465$		0			0
$466$	−1.25574e9	+	2.17500e9i	−0.0266290	+	0.0461228i
$467$	−2.16138e10	+	1.24787e10i	−0.454426	+	0.262363i	−0.709698	−	0.704506i	$-0.751168\pi$
$467$	−2.16138e10	+	1.24787e10i	−0.454426	+	0.262363i	0.255272	+	0.966869i	$0.417835\pi$
$468$		0			0
$469$	2.96524e10	+	3.03240e10i	0.612870	+	0.626751i
$470$		−	3.43474e9i		−	0.0703886i
$471$		0			0
$472$	6.78052e9	−	1.17442e10i	0.136614	−	0.236622i
$473$	−1.38390e9	−	7.98995e8i	−0.0276478	−	0.0159625i
$474$		0			0
$475$	−3.29635e10			−0.647528
$476$	4.25274e9	+	1.66133e10i	0.0828402	+	0.323615i
$477$		0			0
$478$	2.79175e9	+	4.83546e9i	0.0534768	+	0.0926245i
$479$	−3.85080e9	−	2.22326e9i	−0.0731491	−	0.0422327i	0.462979	−	0.886369i	$-0.346780\pi$
$479$	−3.85080e9	−	2.22326e9i	−0.0731491	−	0.0422327i	−0.536128	+	0.844136i	$0.680114\pi$
$480$		0			0
$481$	1.99415e9	+	3.45396e9i	0.0372543	+	0.0645264i
$482$		−	5.33073e10i		−	0.987641i
$483$		0			0
$484$	−2.70696e10			−0.493287
$485$	1.20641e11	−	6.96519e10i	2.18035	−	1.25883i
$486$		0			0
$487$	−1.55453e10	+	2.69253e10i	−0.276365	+	0.478679i	−0.970479	−	0.241187i	$-0.922463\pi$
$487$	−1.55453e10	+	2.69253e10i	−0.276365	+	0.478679i	0.694113	+	0.719866i	$0.255797\pi$
$488$	−1.09779e10	+	6.33810e9i	−0.193571	+	0.111758i
$489$		0			0
$490$	4.83177e10	−	2.64717e10i	0.838150	−	0.459196i
$491$			4.14663e10i			0.713460i	0.934207	+	0.356730i	$0.116108\pi$
$491$			4.14663e10i			0.713460i	−0.934207	+	0.356730i	$0.883892\pi$
$492$		0			0
$493$	3.14568e10	−	5.44848e10i	0.532509	−	0.922333i
$494$	1.20379e10	+	6.95006e9i	0.202135	+	0.116703i
$495$		0			0
$496$	−8.69203e9			−0.143613
$497$	1.06768e11	+	2.98935e10i	1.74991	+	0.489950i
$498$		0			0
$499$	−3.63571e10	−	6.29723e10i	−0.586390	−	1.01566i	−0.994701	−	0.102814i	$-0.967215\pi$
$499$	−3.63571e10	−	6.29723e10i	−0.586390	−	1.01566i	0.408310	−	0.912843i	$-0.366118\pi$
$500$	−6.33842e9	−	3.65949e9i	−0.101415	−	0.0585518i
$501$		0			0
$502$	−2.42571e10	−	4.20145e10i	−0.381965	−	0.661583i
$503$			2.18782e10i			0.341774i	0.985291	+	0.170887i	$0.0546633\pi$
$503$			2.18782e10i			0.341774i	−0.985291	+	0.170887i	$0.945337\pi$
$504$		0			0
$505$	−1.23524e11			−1.89927
$506$	2.56552e9	−	1.48120e9i	0.0391357	−	0.0225950i
$507$		0			0
$508$	3.17314e10	−	5.49604e10i	0.476468	−	0.825267i
$509$	−6.41248e10	+	3.70224e10i	−0.955333	+	0.551562i	−0.894733	−	0.446601i	$-0.852634\pi$
$509$	−6.41248e10	+	3.70224e10i	−0.955333	+	0.551562i	−0.0605992	+	0.998162i	$0.519301\pi$
$510$		0			0
$511$	−6.05324e10	−	6.19033e10i	−0.887778	−	0.907884i
$512$			3.03700e9i			0.0441942i
$513$		0			0
$514$	1.22388e10	−	2.11982e10i	0.175342	−	0.303701i
$515$	6.34810e10	+	3.66508e10i	0.902432	+	0.521020i
$516$		0			0
$517$	−6.09682e8			−0.00853378
$518$	6.43550e9	−	6.29298e9i	0.0893847	−	0.0874052i
$519$		0			0
$520$	−7.36199e9	−	1.27513e10i	−0.100689	−	0.174398i
$521$	1.07925e11	+	6.23105e10i	1.46477	+	0.845688i	0.999226	−	0.0393343i	$-0.0125237\pi$
$521$	1.07925e11	+	6.23105e10i	1.46477	+	0.845688i	0.465549	+	0.885022i	$0.345857\pi$
$522$		0			0
$523$	2.77379e10	+	4.80434e10i	0.370738	+	0.642137i	0.989679	−	0.143301i	$-0.0457715\pi$
$523$	2.77379e10	+	4.80434e10i	0.370738	+	0.642137i	−0.618942	+	0.785437i	$0.712438\pi$
$524$		−	4.97411e10i		−	0.659767i
$525$		0			0
$526$	−1.06845e11			−1.39576
$527$	2.56371e10	−	1.48016e10i	0.332373	−	0.191896i
$528$		0			0
$529$	−2.72433e10	+	4.71868e10i	−0.347887	+	0.602557i
$530$	−3.67296e10	+	2.12059e10i	−0.465493	+	0.268753i
$531$		0			0
$532$	8.45803e9	−	3.02087e10i	0.105590	−	0.377125i
$533$			1.73851e10i			0.215411i
$534$		0			0
$535$	7.69162e9	−	1.33223e10i	0.0938864	−	0.162616i
$536$	−2.21537e10	−	1.27904e10i	−0.268403	−	0.154962i
$537$		0			0
$538$	2.02792e9			0.0242059
$539$	−4.69885e9	−	8.57661e9i	−0.0556720	−	0.101616i
$540$		0			0
$541$	5.92291e10	+	1.02588e11i	0.691427	+	1.19759i	0.971371	+	0.237570i	$0.0763508\pi$
$541$	5.92291e10	+	1.02588e11i	0.691427	+	1.19759i	−0.279944	+	0.960016i	$0.590316\pi$
$542$	−5.10550e10	−	2.94766e10i	−0.591618	−	0.341571i
$543$		0			0
$544$	−5.17168e9	−	8.95761e9i	−0.0590522	−	0.102281i
$545$		−	9.49297e10i		−	1.07601i
$546$		0			0
$547$	−1.06011e11			−1.18414			−0.592068	−	0.805888i	$-0.701688\pi$
$547$	−1.06011e11			−1.18414			−0.592068	+	0.805888i	$0.701688\pi$
$548$	1.16882e10	−	6.74817e9i	0.129606	−	0.0748279i
$549$		0			0
$550$	3.09899e9	−	5.36760e9i	0.0338664	−	0.0586583i
$551$	−9.96683e10	+	5.75435e10i	−1.08131	+	0.624295i
$552$		0			0
$553$	1.17926e11	−	3.01871e10i	1.26098	−	0.322791i
$554$		−	3.39739e10i		−	0.360667i
$555$		0			0
$556$	1.34468e10	−	2.32905e10i	0.140708	−	0.243714i
$557$	2.65235e10	+	1.53134e10i	0.275556	+	0.159092i	0.631410	−	0.775449i	$-0.282477\pi$
$557$	2.65235e10	+	1.53134e10i	0.275556	+	0.159092i	−0.355854	+	0.934542i	$0.615810\pi$
$558$		0			0
$559$	1.13381e10			0.116116
$560$	−2.37586e10	+	2.32324e10i	−0.241584	+	0.236234i
$561$		0			0
$562$	−1.86804e10	−	3.23555e10i	−0.187259	−	0.324341i
$563$	−1.43821e11	−	8.30351e10i	−1.43149	−	0.826472i	−0.434257	−	0.900789i	$-0.642989\pi$
$563$	−1.43821e11	−	8.30351e10i	−1.43149	−	0.826472i	−0.997235	+	0.0743166i	$0.976322\pi$
$564$		0			0
$565$	1.25873e11	+	2.18019e11i	1.23521	+	2.13944i
$566$		−	7.63236e10i		−	0.743692i
$567$		0			0
$568$	−6.68731e10			−0.642478
$569$	1.37935e11	−	7.96366e10i	1.31590	−	0.759737i	0.332837	−	0.942985i	$-0.391994\pi$
$569$	1.37935e11	−	7.96366e10i	1.31590	−	0.759737i	0.983067	+	0.183247i	$0.0586609\pi$
$570$		0			0
$571$	−3.14494e10	+	5.44720e10i	−0.295848	+	0.512423i	−0.975182	−	0.221406i	$-0.928935\pi$
$571$	−3.14494e10	+	5.44720e10i	−0.295848	+	0.512423i	0.679334	+	0.733829i	$0.262269\pi$
$572$	−2.26342e9	+	1.30679e9i	−0.0211437	+	0.0122073i
$573$		0			0
$574$	3.80098e10	−	9.72989e9i	0.350145	−	0.0896315i
$575$		−	4.98454e10i		−	0.455988i
$576$		0			0
$577$	8.94833e10	−	1.54990e11i	0.807307	−	1.39830i	−0.107416	−	0.994214i	$-0.534258\pi$
$577$	8.94833e10	−	1.54990e11i	0.807307	−	1.39830i	0.914723	−	0.404083i	$-0.132409\pi$
$578$	−3.78405e10	−	2.18472e10i	−0.339036	−	0.195743i
$579$		0			0
$580$	1.21908e11			1.07726
$581$	−7.66581e10	−	2.14632e10i	−0.672750	−	0.188361i
$582$		0			0
$583$	3.76414e9	+	6.51968e9i	0.0325830	+	0.0564355i
$584$	4.52245e10	+	2.61104e10i	0.388797	+	0.224472i
$585$		0			0
$586$	1.55591e10	+	2.69491e10i	0.131945	+	0.228536i
$587$		−	2.10749e10i		−	0.177506i	−0.996054	−	0.0887530i	$-0.971712\pi$
$587$		−	2.10749e10i		−	0.177506i	0.996054	−	0.0887530i	$-0.0282882\pi$
$588$		0			0
$589$	−5.41526e10			−0.449944
$590$	−7.75048e10	+	4.47474e10i	−0.639618	+	0.369284i
$591$		0			0
$592$	−2.71445e9	+	4.70156e9i	−0.0221001	+	0.0382785i
$593$	9.57522e9	−	5.52825e9i	0.0774337	−	0.0447064i	−0.460783	−	0.887513i	$-0.652431\pi$
$593$	9.57522e9	−	5.52825e9i	0.0774337	−	0.0447064i	0.538217	+	0.842806i	$0.319098\pi$
$594$		0			0
$595$	3.05135e10	−	1.08982e11i	0.243458	−	0.869536i
$596$			4.69972e10i			0.372466i
$597$		0			0
$598$	−1.05095e10	+	1.82029e10i	−0.0821818	+	0.142343i
$599$	−1.41467e11	−	8.16762e10i	−1.09888	−	0.634436i	−0.162950	−	0.986634i	$-0.552101\pi$
$599$	−1.41467e11	−	8.16762e10i	−1.09888	−	0.634436i	−0.935926	+	0.352198i	$0.885434\pi$
$600$		0			0
$601$	1.85269e11			1.42005			0.710025	−	0.704176i	$-0.248683\pi$
$601$	1.85269e11			1.42005			0.710025	+	0.704176i	$0.248683\pi$
$602$	−6.34559e9	−	2.47890e10i	−0.0483154	−	0.188744i
$603$		0			0
$604$	−3.64882e8	−	6.31994e8i	−0.00274160	−	0.00474859i
$605$	1.54710e11	+	8.93217e10i	1.15477	+	0.666707i
$606$		0			0
$607$	3.15978e10	+	5.47290e10i	0.232757	+	0.403146i	0.958618	−	0.284694i	$-0.0918921\pi$
$607$	3.15978e10	+	5.47290e10i	0.232757	+	0.403146i	−0.725862	+	0.687841i	$0.758559\pi$
$608$			1.89210e10i			0.138461i
$609$		0			0
$610$	8.36554e10			0.604192
$611$	3.74627e9	−	2.16291e9i	0.0268803	−	0.0155194i
$612$		0			0
$613$	−3.86765e10	+	6.69897e10i	−0.273908	+	0.474423i	−0.969859	−	0.243666i	$-0.921650\pi$
$613$	−3.86765e10	+	6.69897e10i	−0.273908	+	0.474423i	0.695951	+	0.718090i	$0.254983\pi$
$614$	−1.29670e11	+	7.48652e10i	−0.912362	+	0.526752i
$615$		0			0
$616$	4.12386e9	+	4.21726e9i	0.0286406	+	0.0292892i
$617$		−	1.59903e11i		−	1.10336i	−0.834057	−	0.551678i	$-0.813988\pi$
$617$		−	1.59903e11i		−	1.10336i	0.834057	−	0.551678i	$-0.186012\pi$
$618$		0			0
$619$	5.61094e10	−	9.71843e10i	0.382184	−	0.661962i	−0.609190	−	0.793024i	$-0.708505\pi$
$619$	5.61094e10	−	9.71843e10i	0.382184	−	0.661962i	0.991374	+	0.131062i	$0.0418387\pi$
$620$	4.96772e10	+	2.86811e10i	0.336194	+	0.194102i
$621$		0			0
$622$	−2.56666e10			−0.171478
$623$	5.43691e10	+	2.12393e11i	0.360911	+	1.40990i
$624$		0			0
$625$	8.72237e10	+	1.51076e11i	0.571629	+	0.990091i
$626$	7.77449e10	+	4.48861e10i	0.506261	+	0.292290i
$627$		0			0
$628$	7.22570e10	+	1.25153e11i	0.464560	+	0.804641i
$629$		−	1.84896e10i		−	0.118121i
$630$		0			0
$631$	−5.05138e10			−0.318634			−0.159317	−	0.987227i	$-0.550929\pi$
$631$	−5.05138e10			−0.318634			−0.159317	+	0.987227i	$0.550929\pi$
$632$	−6.35836e10	+	3.67100e10i	−0.398545	+	0.230100i
$633$		0			0
$634$	−7.61770e10	+	1.31942e11i	−0.471484	+	0.816634i
$635$	−3.62706e11	+	2.09408e11i	−2.23080	+	1.28795i
$636$		0			0
$637$	5.92992e10	+	3.60305e10i	0.360156	+	0.218833i
$638$		−	2.16393e10i		−	0.130605i
$639$		0			0
$640$	1.00212e10	−	1.73572e10i	0.0597311	−	0.103457i
$641$	1.95315e11	+	1.12765e11i	1.15692	+	0.667949i	0.950564	−	0.310528i	$-0.100506\pi$
$641$	1.95315e11	+	1.12765e11i	1.15692	+	0.667949i	0.206357	+	0.978477i	$0.433839\pi$
$642$		0			0
$643$	−2.67710e11			−1.56611			−0.783053	−	0.621956i	$-0.786338\pi$
$643$	−2.67710e11			−1.56611			−0.783053	+	0.621956i	$0.786338\pi$
$644$	4.56798e10	+	1.27897e10i	0.265571	+	0.0743563i
$645$		0			0
$646$	−3.22203e10	−	5.58072e10i	−0.185012	−	0.320450i
$647$	1.65264e11	+	9.54153e10i	0.943109	+	0.544504i	0.890933	−	0.454134i	$-0.150051\pi$
$647$	1.65264e11	+	9.54153e10i	0.943109	+	0.544504i	0.0521752	+	0.998638i	$0.483385\pi$
$648$		0			0
$649$	7.94287e9	+	1.37575e10i	0.0447712	+	0.0775460i
$650$			4.39759e10i			0.246355i
$651$		0			0
$652$	1.55037e11			0.857915
$653$	−1.42377e11	+	8.22012e10i	−0.783044	+	0.452091i	−0.837508	−	0.546425i	$-0.815988\pi$
$653$	−1.42377e11	+	8.22012e10i	−0.783044	+	0.452091i	0.0544639	+	0.998516i	$0.482655\pi$
$654$		0			0
$655$	−1.64131e11	+	2.84283e11i	−0.891714	+	1.54449i
$656$	−2.04942e10	+	1.18323e10i	−0.110666	+	0.0638933i
$657$		0			0
$658$	−6.82556e9	−	6.98015e9i	−0.0364112	−	0.0372358i
$659$			1.00539e11i			0.533082i	0.963824	+	0.266541i	$0.0858808\pi$
$659$			1.00539e11i			0.533082i	−0.963824	+	0.266541i	$0.914119\pi$
$660$		0			0
$661$	−9.22615e8	+	1.59802e9i	−0.00483298	+	0.00837096i	−0.868432	−	0.495809i	$-0.834872\pi$
$661$	−9.22615e8	+	1.59802e9i	−0.00483298	+	0.00837096i	0.863599	+	0.504180i	$0.168205\pi$
$662$	−1.22146e11	−	7.05211e10i	−0.635986	−	0.367187i
$663$		0			0
$664$	4.80142e10			0.247000
$665$	−1.48020e11	+	1.44742e11i	−0.756890	+	0.740128i
$666$		0			0
$667$	−8.70138e10	−	1.50712e11i	−0.439628	−	0.761457i
$668$	1.45788e11	+	8.41709e10i	0.732178	+	0.422723i
$669$		0			0
$670$	8.44094e10	+	1.46201e11i	0.418882	+	0.725524i
$671$		−	1.48492e10i		−	0.0732510i
$672$		0			0
$673$	1.84807e11			0.900860			0.450430	−	0.892812i	$-0.351271\pi$
$673$	1.84807e11			0.900860			0.450430	+	0.892812i	$0.351271\pi$
$674$	1.03106e11	−	5.95284e10i	0.499626	−	0.288459i
$675$		0			0
$676$	−4.29348e10	+	7.43653e10i	−0.205600	+	0.356110i
$677$	1.02617e11	−	5.92457e10i	0.488498	−	0.282035i	−0.235453	−	0.971886i	$-0.575657\pi$
$677$	1.02617e11	−	5.92457e10i	0.488498	−	0.282035i	0.723951	+	0.689851i	$0.242324\pi$
$678$		0			0
$679$	1.06755e11	−	3.81287e11i	0.502238	−	1.79379i
$680$			6.82601e10i			0.319250i
$681$		0			0
$682$	5.09103e9	−	8.81793e9i	0.0235325	−	0.0407595i
$683$	5.72075e10	+	3.30288e10i	0.262888	+	0.151778i	0.625651	−	0.780103i	$-0.284833\pi$
$683$	5.72075e10	+	3.30288e10i	0.262888	+	0.151778i	−0.362764	+	0.931881i	$0.618167\pi$
$684$		0			0
$685$	−8.90679e10			−0.404538
$686$	4.55872e10	−	1.49814e11i	0.205848	−	0.676481i
$687$		0			0
$688$	7.71675e9	+	1.33658e10i	0.0344414	+	0.0596542i
$689$	−4.62585e10	−	2.67074e10i	−0.205265	−	0.118510i
$690$		0			0
$691$	1.61973e11	+	2.80545e11i	0.710443	+	1.23052i	0.964691	+	0.263385i	$0.0848389\pi$
$691$	1.61973e11	+	2.80545e11i	0.710443	+	1.23052i	−0.254247	+	0.967139i	$0.581828\pi$
$692$			6.93066e9i			0.0302239i
$693$		0			0
$694$	−2.09759e11			−0.904238
$695$	−1.53704e11	+	8.87409e10i	−0.658787	+	0.380351i
$696$		0			0
$697$	4.02984e10	−	6.97988e10i	0.170748	−	0.295745i
$698$	−1.16738e10	+	6.73986e9i	−0.0491802	+	0.0283942i
$699$		0			0
$700$	9.61468e10	−	2.46120e10i	0.400445	−	0.102507i
$701$		−	4.16821e11i		−	1.72614i	−0.505081	−	0.863072i	$-0.668537\pi$
$701$		−	4.16821e11i		−	1.72614i	0.505081	−	0.863072i	$-0.331463\pi$
$702$		0			0
$703$	−1.69114e10	+	2.92914e10i	−0.0692403	+	0.119928i
$704$	−3.08099e9	−	1.77881e9i	−0.0125429	−	0.00724167i
$705$		0			0
$706$	−1.57710e10			−0.0634807
$707$	−2.51028e11	+	2.45469e11i	−1.00472	+	0.982468i
$708$		0			0
$709$	9.61540e10	+	1.66544e11i	0.380524	+	0.659088i	0.991137	−	0.132842i	$-0.0424102\pi$
$709$	9.61540e10	+	1.66544e11i	0.380524	+	0.659088i	−0.610613	+	0.791929i	$0.709077\pi$
$710$	3.82197e11	+	2.20662e11i	1.50402	+	0.868347i
$711$		0			0
$712$	−6.61172e10	−	1.14518e11i	−0.257273	−	0.445610i
$713$		−	8.18863e10i		−	0.316850i
$714$		0			0
$715$	1.72481e10			0.0659957
$716$	8.38755e10	−	4.84255e10i	0.319141	−	0.184256i
$717$		0			0
$718$	−1.32359e11	+	2.29253e11i	−0.498031	+	0.862615i
$719$	−4.27537e10	+	2.46838e10i	−0.159977	+	0.0923628i	−0.577851	−	0.816142i	$-0.696109\pi$
$719$	−4.27537e10	+	2.46838e10i	−0.159977	+	0.0923628i	0.417874	+	0.908505i	$0.362775\pi$
$720$		0			0
$721$	2.01840e11	−	5.16678e10i	0.746907	−	0.191196i
$722$		−	7.42666e10i		−	0.273303i
$723$		0			0
$724$	−1.26416e10	+	2.18959e10i	−0.0460096	+	0.0796909i
$725$	−3.15322e11	−	1.82051e11i	−1.14130	−	0.658933i
$726$		0			0
$727$	−3.82914e10			−0.137077			−0.0685383	−	0.997648i	$-0.521834\pi$
$727$	−3.82914e10			−0.137077			−0.0685383	+	0.997648i	$0.521834\pi$
$728$	−4.03008e10	−	1.12837e10i	−0.143479	−	0.0401722i
$729$		0			0
$730$	−1.72313e11	−	2.98455e11i	−0.606774	−	1.05096i
$731$	−4.55210e10	−	2.62816e10i	−0.159420	−	0.0920410i
$732$		0			0
$733$	−2.41122e10	−	4.17635e10i	−0.0835258	−	0.144671i	0.821236	−	0.570588i	$-0.193285\pi$
$733$	−2.41122e10	−	4.17635e10i	−0.0835258	−	0.144671i	−0.904762	+	0.425917i	$0.859951\pi$
$734$		−	1.22710e11i		−	0.422763i
$735$		0			0
$736$	−2.86111e10			−0.0975043
$737$	2.59514e10	−	1.49830e10i	0.0879611	−	0.0507844i
$738$		0			0
$739$	1.34093e11	−	2.32256e11i	0.449602	−	0.778733i	−0.548758	−	0.835981i	$-0.684899\pi$
$739$	1.34093e11	−	2.32256e11i	0.449602	−	0.778733i	0.998360	+	0.0572483i	$0.0182327\pi$
$740$	3.10275e10	−	1.79138e10i	0.103471	−	0.0597393i
$741$		0			0
$742$	−3.25021e10	+	1.16085e11i	−0.107225	+	0.382965i
$743$		−	9.81008e10i		−	0.321897i	−0.986963	−	0.160949i	$-0.948545\pi$
$743$		−	9.81008e10i		−	0.321897i	0.986963	−	0.160949i	$-0.0514553\pi$
$744$		0			0
$745$	1.55077e11	−	2.68601e11i	0.503411	−	0.871933i
$746$	1.56852e11	+	9.05584e10i	0.506447	+	0.292397i
$747$		0			0
$748$	1.21165e10			0.0387052
$749$	−1.08431e10	−	4.23587e10i	−0.0344530	−	0.134591i
$750$		0			0
$751$	−2.27717e10	−	3.94417e10i	−0.0715872	−	0.123993i	0.828010	−	0.560714i	$-0.189473\pi$
$751$	−2.27717e10	−	3.94417e10i	−0.0715872	−	0.123993i	−0.899597	+	0.436721i	$0.856140\pi$
$752$	5.09946e9	+	2.94418e9i	0.0159460	+	0.00920646i
$753$		0			0
$754$	7.67677e10	+	1.32965e11i	0.237516	+	0.411390i
$755$			4.81601e9i			0.0148218i
$756$		0			0
$757$	−2.98900e11			−0.910210			−0.455105	−	0.890438i	$-0.650398\pi$
$757$	−2.98900e11			−0.910210			−0.455105	+	0.890438i	$0.650398\pi$
$758$	1.81283e11	−	1.04664e11i	0.549136	−	0.317044i
$759$		0			0
$760$	6.24336e10	−	1.08138e11i	0.187139	−	0.324134i
$761$	6.79144e10	−	3.92104e10i	0.202499	−	0.116913i	−0.395321	−	0.918543i	$-0.629367\pi$
$761$	6.79144e10	−	3.92104e10i	0.202499	−	0.116913i	0.597821	+	0.801630i	$0.296033\pi$
$762$		0			0
$763$	−1.88646e11	−	1.92918e11i	−0.556607	−	0.569213i
$764$		−	3.58285e10i		−	0.105161i
$765$		0			0
$766$	−2.26225e11	+	3.91834e11i	−0.657092	+	1.13812i
$767$	−9.76121e10	−	5.63564e10i	−0.282047	−	0.162840i
$768$		0			0
$769$	−5.07864e11			−1.45225			−0.726126	−	0.687561i	$-0.758681\pi$
$769$	−5.07864e11			−1.45225			−0.726126	+	0.687561i	$0.758681\pi$
$770$	−9.65322e9	−	3.77103e10i	−0.0274606	−	0.107275i
$771$		0			0
$772$	−1.09118e11	−	1.88998e11i	−0.307205	−	0.532094i
$773$	4.00143e10	+	2.31022e10i	0.112072	+	0.0647048i	0.554988	−	0.831858i	$-0.312723\pi$
$773$	4.00143e10	+	2.31022e10i	0.112072	+	0.0647048i	−0.442916	+	0.896563i	$0.646056\pi$
$774$		0			0
$775$	−8.56616e10	−	1.48370e11i	−0.237454	−	0.411282i
$776$			2.38816e11i			0.658591i
$777$		0			0
$778$	−3.67523e11			−1.00315
$779$	−1.27682e11	+	7.37173e10i	−0.346721	+	0.200179i
$780$		0			0
$781$	3.91684e10	−	6.78417e10i	0.105277	−	0.182345i
$782$	8.43883e10	−	4.87216e10i	0.225660	−	0.130285i
$783$		0			0
$784$	−2.11492e9	+	9.44268e10i	−0.00559796	+	0.249937i
$785$		−	9.53708e11i		−	2.51152i
$786$		0			0
$787$	1.22719e11	−	2.12556e11i	0.319899	−	0.554082i	−0.660568	−	0.750767i	$-0.729684\pi$
$787$	1.22719e11	−	2.12556e11i	0.319899	−	0.554082i	0.980467	+	0.196685i	$0.0630176\pi$
$788$	−4.71146e10	−	2.72016e10i	−0.122194	−	0.0705489i
$789$		0			0
$790$	4.84529e11			1.24397
$791$	6.89052e11	+	1.92925e11i	1.76014	+	0.492815i
$792$		0			0
$793$	5.26792e10	+	9.12430e10i	0.133213	+	0.230732i
$794$	3.62560e11	+	2.09324e11i	0.912217	+	0.526669i
$795$		0			0
$796$	1.56767e10	+	2.71528e10i	0.0390483	+	0.0676336i
$797$		−	1.50650e11i		−	0.373367i	−0.982420	−	0.186684i	$-0.940226\pi$
$797$		−	1.50650e11i		−	0.373367i	0.982420	−	0.186684i	$-0.0597739\pi$
$798$		0			0
$799$	−2.00544e10			−0.0492066
$800$	−5.18407e10	+	2.99302e10i	−0.126564	+	0.0730718i
$801$		0			0
$802$	8.15430e10	−	1.41237e11i	0.197101	−	0.341389i
$803$	−5.29772e10	+	3.05864e10i	−0.127417	+	0.0735641i
$804$		0			0
$805$	−2.18869e11	−	2.23826e11i	−0.521196	−	0.533001i
$806$			7.22439e10i			0.171183i
$807$		0			0
$808$	1.05882e11	−	1.83393e11i	0.248414	−	0.430266i
$809$	2.71344e11	+	1.56661e11i	0.633470	+	0.365734i	0.782095	−	0.623160i	$-0.214151\pi$
$809$	2.71344e11	+	1.56661e11i	0.633470	+	0.365734i	−0.148625	+	0.988894i	$0.547485\pi$
$810$		0			0
$811$	−3.31391e11			−0.766051			−0.383026	−	0.923738i	$-0.625118\pi$
$811$	−3.31391e11			−0.766051			−0.383026	+	0.923738i	$0.625118\pi$
$812$	2.47744e11	−	2.42258e11i	0.569875	−	0.557254i
$813$		0			0
$814$	−3.17977e9	−	5.50753e9i	−0.00724267	−	0.0125447i
$815$	−8.86075e11	−	5.11576e11i	−2.00835	−	1.15952i
$816$		0			0
$817$	4.80765e10	+	8.32709e10i	0.107906	+	0.186898i
$818$		−	2.99192e11i		−	0.668247i
$819$		0			0
$820$	1.56173e11			0.345422
$821$	4.51275e11	−	2.60544e11i	0.993272	−	0.573466i	0.0870215	−	0.996206i	$-0.472265\pi$
$821$	4.51275e11	−	2.60544e11i	0.993272	−	0.573466i	0.906251	+	0.422740i	$0.138932\pi$
$822$		0			0
$823$	1.86290e11	−	3.22663e11i	0.406059	−	0.703315i	−0.588385	−	0.808581i	$-0.700236\pi$
$823$	1.86290e11	−	3.22663e11i	0.406059	−	0.703315i	0.994444	+	0.105266i	$0.0335694\pi$
$824$	−1.08829e11	+	6.28323e10i	−0.236067	+	0.136293i
$825$		0			0
$826$	−6.85841e10	+	2.44955e11i	−0.147334	+	0.526219i
$827$			5.96875e11i			1.27603i	0.770023	+	0.638016i	$0.220245\pi$
$827$			5.96875e11i			1.27603i	−0.770023	+	0.638016i	$0.779755\pi$
$828$		0			0
$829$	1.67255e11	−	2.89695e11i	0.354129	−	0.613370i	−0.632839	−	0.774283i	$-0.718111\pi$
$829$	1.67255e11	−	2.89695e11i	0.354129	−	0.613370i	0.986969	+	0.160913i	$0.0514440\pi$
$830$	−2.74413e11	−	1.58433e11i	−0.578220	−	0.333835i
$831$		0			0
$832$	2.52421e10			0.0526783
$833$	−1.54561e11	−	2.82113e11i	−0.321010	−	0.585926i
$834$		0			0
$835$	−5.55478e11	−	9.62117e11i	−1.14267	−	1.97916i
$836$	−1.91950e10	−	1.10823e10i	−0.0392974	−	0.0226884i
$837$		0			0
$838$	9.14722e10	+	1.58434e11i	0.185487	+	0.321272i
$839$			3.83697e11i			0.774355i	0.922005	+	0.387177i	$0.126550\pi$
$839$			3.83697e11i			0.774355i	−0.922005	+	0.387177i	$0.873450\pi$
$840$		0			0
$841$	−7.70961e11			−1.54116
$842$	−4.08613e11	+	2.35913e11i	−0.812949	+	0.469357i
$843$		0			0
$844$	−1.23189e11	+	2.13369e11i	−0.242774	+	0.420496i
$845$	4.90767e11	−	2.83345e11i	0.962607	−	0.555761i
$846$		0			0
$847$	4.91905e11	−	1.25920e11i	0.955757	−	0.244658i
$848$		−	7.27086e10i		−	0.140606i
$849$		0			0
$850$	1.01936e11	−	1.76558e11i	0.195277	−	0.338229i
$851$	−4.42927e10	−	2.55724e10i	−0.0844528	−	0.0487589i
$852$		0			0
$853$	3.60879e11			0.681657			0.340828	−	0.940126i	$-0.389292\pi$
$853$	3.60879e11			0.681657			0.340828	+	0.940126i	$0.389292\pi$
$854$	1.70006e11	−	1.66241e11i	0.319619	−	0.312541i
$855$		0			0
$856$	1.31861e10	+	2.28390e10i	0.0245597	+	0.0425386i
$857$	−4.97218e11	−	2.87069e11i	−0.921773	−	0.532186i	−0.0375727	−	0.999294i	$-0.511963\pi$
$857$	−4.97218e11	−	2.87069e11i	−0.921773	−	0.532186i	−0.884200	+	0.467108i	$0.845296\pi$
$858$		0			0
$859$	−6.22188e10	−	1.07766e11i	−0.114274	−	0.197929i	0.803215	−	0.595689i	$-0.203121\pi$
$859$	−6.22188e10	−	1.07766e11i	−0.114274	−	0.197929i	−0.917489	+	0.397760i	$0.869788\pi$
$860$		−	1.01852e11i		−	0.186198i
$861$		0			0
$862$	7.65213e10			0.138597
$863$	7.66891e11	−	4.42765e11i	1.38258	−	0.798234i	0.390117	−	0.920765i	$-0.372435\pi$
$863$	7.66891e11	−	4.42765e11i	1.38258	−	0.798234i	0.992465	+	0.122532i	$0.0391013\pi$
$864$		0			0
$865$	2.28691e10	−	3.96105e10i	0.0408494	−	0.0707532i
$866$	3.36759e11	−	1.94428e11i	0.598753	−	0.345690i
$867$		0			0
$868$	1.57950e11	−	4.04328e10i	0.278254	−	0.0712286i
$869$		−	8.60061e10i		−	0.150817i
$870$		0			0
$871$	−1.06308e11	+	1.84131e11i	−0.184711	+	0.319929i
$872$	1.40939e11	+	8.13714e10i	0.243762	+	0.140736i
$873$		0			0
$874$	−1.78252e11			−0.305484
$875$	1.32204e11	+	3.70153e10i	0.225534	+	0.0631465i
$876$		0			0
$877$	4.30719e11	+	7.46027e11i	0.728107	+	1.26112i	0.957682	+	0.287828i	$0.0929331\pi$
$877$	4.30719e11	+	7.46027e11i	0.728107	+	1.26112i	−0.229575	+	0.973291i	$0.573734\pi$
$878$	−1.01541e11	−	5.86244e10i	−0.170868	−	0.0986508i
$879$		0			0
$880$	1.17391e10	+	2.03327e10i	0.0195751	+	0.0339051i
$881$			8.46266e11i			1.40476i	0.711800	+	0.702382i	$0.247880\pi$
$881$			8.46266e11i			1.40476i	−0.711800	+	0.702382i	$0.752120\pi$
$882$		0			0
$883$	5.59201e11			0.919867			0.459933	−	0.887953i	$-0.347873\pi$
$883$	5.59201e11			0.919867			0.459933	+	0.887953i	$0.347873\pi$
$884$	−7.44513e10	+	4.29845e10i	−0.121917	+	0.0703886i
$885$		0			0
$886$	2.70498e11	−	4.68517e11i	0.438965	−	0.760309i
$887$	−6.30318e11	+	3.63914e11i	−1.01828	+	0.587901i	−0.913604	−	0.406605i	$-0.866712\pi$
$887$	−6.30318e11	+	3.63914e11i	−1.01828	+	0.587901i	−0.104671	+	0.994507i	$0.533379\pi$
$888$		0			0
$889$	−3.20959e11	+	1.14634e12i	−0.513858	+	1.83529i
$890$			8.72670e11i			1.39088i
$891$		0			0
$892$	−2.58131e11	+	4.47096e11i	−0.407738	+	0.706223i
$893$	3.17704e10	+	1.83427e10i	0.0499594	+	0.0288441i
$894$		0			0
$895$	−6.39160e11			−0.996134
$896$	−1.41272e10	−	5.51880e10i	−0.0219192	−	0.0856274i
$897$		0			0
$898$	−2.89929e11	−	5.02172e11i	−0.445847	−	0.772230i
$899$	−5.18012e11	−	2.99074e11i	−0.793051	−	0.457868i
$900$		0			0
$901$	1.23815e11	+	2.14453e11i	0.187877	+	0.325412i
$902$		−	2.77214e10i		−	0.0418783i
$903$		0			0
$904$	−4.31582e11			−0.646234
$905$	1.44500e11	−	8.34272e10i	0.215414	−	0.124369i
$906$		0			0
$907$	−3.85355e11	+	6.67454e11i	−0.569418	+	0.986262i	0.427205	+	0.904155i	$0.359498\pi$
$907$	−3.85355e11	+	6.67454e11i	−0.569418	+	0.986262i	−0.996624	+	0.0821069i	$0.973835\pi$
$908$	−2.97994e11	+	1.72047e11i	−0.438393	+	0.253106i
$909$		0			0
$910$	1.93097e11	+	1.97470e11i	0.281585	+	0.287962i
$911$			8.24759e11i			1.19744i	0.800959	+	0.598720i	$0.204324\pi$
$911$			8.24759e11i			1.19744i	−0.800959	+	0.598720i	$0.795676\pi$
$912$		0			0
$913$	−2.81225e10	+	4.87096e10i	−0.0404735	+	0.0701022i
$914$	−7.04781e11	−	4.06906e11i	−1.00988	−	0.583054i
$915$		0			0
$916$	3.41817e10			0.0485525
$917$	2.31381e11	+	9.03890e11i	0.327228	+	1.27832i
$918$		0			0
$919$	4.64107e11	+	8.03857e11i	0.650663	+	1.12698i	0.982962	+	0.183807i	$0.0588422\pi$
$919$	4.64107e11	+	8.03857e11i	0.650663	+	1.12698i	−0.332299	+	0.943174i	$0.607824\pi$
$920$	1.63520e11	+	9.44083e10i	0.228255	+	0.131783i
$921$		0			0
$922$	−2.93274e11	−	5.07966e11i	−0.405836	−	0.702928i
$923$			5.55817e11i			0.765817i
$924$		0			0
$925$	−1.07006e11			−0.146164
$926$	−4.60790e11	+	2.66037e11i	−0.626699	+	0.361825i
$927$		0			0
$928$	−1.04497e11	+	1.80994e11i	−0.140900	+	0.244046i
$929$	4.48981e11	−	2.59219e11i	0.602789	−	0.348020i	−0.167349	−	0.985898i	$-0.553521\pi$
$929$	4.48981e11	−	2.59219e11i	0.602789	−	0.348020i	0.770138	+	0.637877i	$0.220187\pi$
$930$		0			0
$931$	−1.31763e10	+	5.88293e11i	−0.0175385	+	0.783060i
$932$			2.84141e10i			0.0376591i
$933$		0			0
$934$	−1.41181e11	+	2.44532e11i	−0.185519	+	0.321328i
$935$	−6.92488e10	−	3.99808e10i	−0.0906078	−	0.0523124i
$936$		0			0
$937$	7.17388e11			0.930670			0.465335	−	0.885135i	$-0.345934\pi$
$937$	7.17388e11			0.930670			0.465335	+	0.885135i	$0.345934\pi$
$938$	4.62071e11	+	1.29374e11i	0.596895	+	0.167123i
$939$		0			0
$940$	−1.94298e10	−	3.36535e10i	−0.0248861	−	0.0431041i
$941$	3.51244e11	+	2.02791e11i	0.447972	+	0.258637i	0.706973	−	0.707240i	$-0.250060\pi$
$941$	3.51244e11	+	2.02791e11i	0.447972	+	0.258637i	−0.259002	+	0.965877i	$0.583393\pi$
$942$		0			0
$943$	−1.11471e11	−	1.93073e11i	−0.140966	−	0.244160i
$944$		−	1.53426e11i		−	0.193201i
$945$		0			0
$946$	−1.80792e10			−0.0225743
$947$	−1.55937e11	+	9.00300e10i	−0.193887	+	0.111941i	−0.593801	−	0.804612i	$-0.702373\pi$
$947$	−1.55937e11	+	9.00300e10i	−0.193887	+	0.111941i	0.399914	+	0.916553i	$0.369040\pi$
$948$		0			0
$949$	2.17017e11	−	3.75884e11i	0.267565	−	0.463435i
$950$	−3.22975e11	+	1.86470e11i	−0.396529	+	0.228936i
$951$		0			0
$952$	1.35647e11	+	1.38719e11i	0.165144	+	0.168884i
$953$			4.39326e11i			0.532618i	0.963888	+	0.266309i	$0.0858041\pi$
$953$			4.39326e11i			0.532618i	−0.963888	+	0.266309i	$0.914196\pi$
$954$		0			0
$955$	−1.18224e11	+	2.04769e11i	−0.142132	+	0.246179i
$956$	5.47070e10	+	3.15851e10i	0.0654954	+	0.0378138i
$957$		0			0
$958$	−5.03067e10			−0.0597260
$959$	−1.81006e11	+	1.76997e11i	−0.214002	+	0.209262i
$960$		0			0
$961$	2.85720e11	+	4.94882e11i	0.335002	+	0.580240i
$962$	3.90771e10	+	2.25612e10i	0.0456270	+	0.0263428i
$963$		0			0
$964$	−3.01552e11	−	5.22303e11i	−0.349184	−	0.604804i
$965$			1.44023e12i			1.66082i
$966$		0			0
$967$	1.52491e12			1.74397			0.871983	−	0.489536i	$-0.162834\pi$
$967$	1.52491e12			1.74397			0.871983	+	0.489536i	$0.162834\pi$
$968$	−2.65227e11	+	1.53129e11i	−0.302076	+	0.174403i
$969$		0			0
$970$	7.88021e11	−	1.36489e12i	0.890125	−	1.54174i
$971$	1.04882e12	−	6.05539e11i	1.17985	−	0.681185i	0.223868	−	0.974619i	$-0.428131\pi$
$971$	1.04882e12	−	6.05539e11i	1.17985	−	0.681185i	0.955979	+	0.293434i	$0.0947981\pi$
$972$		0			0
$973$	−1.36013e11	+	4.85783e11i	−0.151750	+	0.541990i
$974$			3.51750e11i			0.390840i
$975$		0			0
$976$	−7.17074e10	+	1.24201e11i	−0.0790250	+	0.136875i
$977$	−4.04125e10	−	2.33322e10i	−0.0443545	−	0.0256081i	0.477659	−	0.878545i	$-0.341486\pi$
$977$	−4.04125e10	−	2.33322e10i	−0.0443545	−	0.0256081i	−0.522013	+	0.852937i	$0.674819\pi$
$978$		0			0
$979$	1.54903e11			0.168628
$980$	3.23668e11	−	5.32695e11i	0.350910	−	0.577530i
$981$		0			0
$982$	2.34569e11	+	4.06286e11i	0.252246	+	0.436903i
$983$	−5.34099e11	−	3.08362e11i	−0.572015	−	0.330253i	0.185939	−	0.982561i	$-0.440467\pi$
$983$	−5.34099e11	−	3.08362e11i	−0.572015	−	0.330253i	−0.757954	+	0.652308i	$0.773801\pi$
$984$		0			0
$985$	1.79515e11	+	3.10929e11i	0.190702	+	0.330306i
$986$		−	7.11786e11i		−	0.753082i
$987$		0			0
$988$	1.57262e11			0.165042
$989$	−1.25917e11	+	7.26984e10i	−0.131613	+	0.0759870i
$990$		0			0
$991$	1.69128e11	−	2.92939e11i	0.175356	−	0.303726i	−0.764928	−	0.644116i	$-0.777226\pi$
$991$	1.69128e11	−	2.92939e11i	0.175356	−	0.303726i	0.940285	+	0.340389i	$0.110559\pi$
$992$	−8.51641e10	+	4.91695e10i	−0.0879448	+	0.0507749i
$993$		0			0
$994$	1.21521e12	−	3.11074e11i	1.24482	−	0.318653i
$995$		−	2.06914e11i		−	0.211104i
$996$		0			0
$997$	9.77026e11	−	1.69226e12i	0.988839	−	1.71272i	0.365389	−	0.930855i	$-0.380936\pi$
$997$	9.77026e11	−	1.69226e12i	0.988839	−	1.71272i	0.623449	−	0.781864i	$-0.285731\pi$
$998$	−7.12450e11	−	4.11333e11i	−0.718178	−	0.414640i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.9.s.a.53.7	yes	20
3.2	odd	2	inner	126.9.s.a.53.4	✓	20
7.2	even	3	inner	126.9.s.a.107.4	yes	20
21.2	odd	6	inner	126.9.s.a.107.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.9.s.a.53.4	✓	20	3.2	odd	2	inner
126.9.s.a.53.7	yes	20	1.1	even	1	trivial
126.9.s.a.107.4	yes	20	7.2	even	3	inner
126.9.s.a.107.7	yes	20	21.2	odd	6	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	126.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(9.79796 - 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(-731.553 + 422.362i) q^{5} +(-647.353 + 2312.08i) q^{7} -1448.15i q^{8} +O(q^{10})\)	\(q+(9.79796 - 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(-731.553 + 422.362i) q^{5} +(-647.353 + 2312.08i) q^{7} -1448.15i q^{8} +(-4778.48 + 8276.58i) q^{10} +(1469.13 + 848.203i) q^{11} -12036.4 q^{13} +(6736.39 + 26315.7i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(48324.5 + 27900.2i) q^{17} +(-51037.4 - 88399.3i) q^{19} +108125. i q^{20} +19192.6 q^{22} +(133672. - 77175.6i) q^{23} +(161467. - 279670. i) q^{25} +(-117932. + 68087.9i) q^{26} +(214867. + 219733. i) q^{28} -1.12748e6i q^{29} +(265260. - 459443. i) q^{31} +(-160530. - 92681.9i) q^{32} +631308. q^{34} +(-502965. - 1.96483e6i) q^{35} +(-165677. - 286961. i) q^{37} +(-1.00012e6 - 577422. i) q^{38} +(611646. + 1.05940e6i) q^{40} -1.44438e6i q^{41} -941986. q^{43} +(188049. - 108570. i) q^{44} +(873142. - 1.51233e6i) q^{46} +(-311247. + 179698. i) q^{47} +(-4.92667e6 - 2.99347e6i) q^{49} -3.65359e6i q^{50} +(-770327. + 1.33425e6i) q^{52} +(3.84323e6 + 2.21889e6i) q^{53} -1.43300e6 q^{55} +(3.34826e6 + 937467. i) q^{56} +(-6.37798e6 - 1.10470e7i) q^{58} +(8.10977e6 + 4.68218e6i) q^{59} +(-4.37667e6 - 7.58062e6i) q^{61} -6.00214e6i q^{62} -2.09715e6 q^{64} +(8.80524e6 - 5.08371e6i) q^{65} +(8.83223e6 - 1.52979e7i) q^{67} +(6.18553e6 - 3.57122e6i) q^{68} +(-1.60428e7 - 1.64061e7i) q^{70} -4.61781e7i q^{71} +(-1.80301e7 + 3.12291e7i) q^{73} +(-3.24659e6 - 1.87442e6i) q^{74} -1.30656e7 q^{76} +(-2.91216e6 + 2.84767e6i) q^{77} +(-2.53495e7 - 4.39066e7i) q^{79} +(1.19858e7 + 6.91998e6i) q^{80} +(-8.17063e6 - 1.41520e7i) q^{82} +3.31554e7i q^{83} -4.71359e7 q^{85} +(-9.22954e6 + 5.32868e6i) q^{86} +(1.22833e6 - 2.12753e6i) q^{88} +(7.90789e7 - 4.56562e7i) q^{89} +(7.79177e6 - 2.78291e7i) q^{91} -1.97570e7i q^{92} +(-2.03305e6 + 3.52135e6i) q^{94} +(7.46731e7 + 4.31125e7i) q^{95} -1.64910e8 q^{97} +(-6.52049e7 - 1.46042e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 1280 q^{4} - 3710 q^{7}+O(q^{10}) \) 20 * q + 1280 * q^4 - 3710 * q^7	\( 20 q + 1280 q^{4} - 3710 q^{7} - 3040 q^{10} + 133668 q^{13} - 163840 q^{16} + 180526 q^{19} - 371648 q^{22} + 1919806 q^{25} + 136192 q^{28} - 2496630 q^{31} - 7741568 q^{34} + 2579434 q^{37} + 389120 q^{40} + 9786628 q^{43} + 6602944 q^{46} - 16557394 q^{49} + 8554752 q^{52} - 48224 q^{55} + 11294336 q^{58} - 45256440 q^{61} - 41943040 q^{64} - 5459674 q^{67} + 36416128 q^{70} - 154260166 q^{73} + 46214656 q^{76} - 147636618 q^{79} - 123306336 q^{82} - 6742976 q^{85} - 23785472 q^{88} - 32944086 q^{91} - 95141856 q^{94} + 268865432 q^{97}+O(q^{100}) \) 20 * q + 1280 * q^4 - 3710 * q^7 - 3040 * q^10 + 133668 * q^13 - 163840 * q^16 + 180526 * q^19 - 371648 * q^22 + 1919806 * q^25 + 136192 * q^28 - 2496630 * q^31 - 7741568 * q^34 + 2579434 * q^37 + 389120 * q^40 + 9786628 * q^43 + 6602944 * q^46 - 16557394 * q^49 + 8554752 * q^52 - 48224 * q^55 + 11294336 * q^58 - 45256440 * q^61 - 41943040 * q^64 - 5459674 * q^67 + 36416128 * q^70 - 154260166 * q^73 + 46214656 * q^76 - 147636618 * q^79 - 123306336 * q^82 - 6742976 * q^85 - 23785472 * q^88 - 32944086 * q^91 - 95141856 * q^94 + 268865432 * q^97

Introduction

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