LMFDB - Embedded newform 126.7.n.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,7,Mod(19,126)]

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([0, 5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("126.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	126.n (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:	$28.9868145361$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 33x^{6} + 2x^{5} + 701x^{4} - 28x^{3} + 6468x^{2} + 5488x + 38416 $ x^8 - 2x^7 + 33x^6 + 2x^5 + 701x^4 - 28x^3 + 6468x^2 + 5488*x + 38416
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.1
Root			$-1.97725 - 3.42469i$ of defining polynomial
Character	$\chi$	$=$	126.19
Dual form			126.7.n.b.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.82843 + 4.89898i) q^{2} +(-16.0000 - 27.7128i) q^{4} +(-182.133 - 105.155i) q^{5} +(186.289 + 288.003i) q^{7} +181.019 q^{8} +O(q^{10})$	\(q+(-2.82843 + 4.89898i) q^{2} +(-16.0000 - 27.7128i) q^{4} +(-182.133 - 105.155i) q^{5} +(186.289 + 288.003i) q^{7} +181.019 q^{8} +(1030.30 - 594.844i) q^{10} +(-485.969 - 841.723i) q^{11} -3559.78i q^{13} +(-1937.82 + 98.0306i) q^{14} +(-512.000 + 886.810i) q^{16} +(2916.87 - 1684.05i) q^{17} +(-1621.56 - 936.209i) q^{19} +6729.89i q^{20} +5498.11 q^{22} +(-9942.27 + 17220.5i) q^{23} +(14302.4 + 24772.6i) q^{25} +(17439.3 + 10068.6i) q^{26} +(5000.74 - 9770.63i) q^{28} +18697.0 q^{29} +(-17628.0 + 10177.5i) q^{31} +(-2896.31 - 5016.55i) q^{32} +19052.9i q^{34} +(-3644.56 - 72043.9i) q^{35} +(-44846.5 + 77676.4i) q^{37} +(9172.94 - 5296.00i) q^{38} +(-32969.6 - 19035.0i) q^{40} +10931.8i q^{41} +3887.60 q^{43} +(-15551.0 + 26935.2i) q^{44} +(-56242.0 - 97413.9i) q^{46} +(67906.5 + 39205.8i) q^{47} +(-48242.0 + 107303. i) q^{49} -161814. q^{50} +(-98651.6 + 56956.6i) q^{52} +(53856.2 + 93281.7i) q^{53} +204407. i q^{55} +(33721.9 + 52134.0i) q^{56} +(-52883.1 + 91596.2i) q^{58} +(-212952. + 122948. i) q^{59} +(274561. + 158518. i) q^{61} -115145. i q^{62} +32768.0 q^{64} +(-374327. + 648354. i) q^{65} +(-242122. - 419367. i) q^{67} +(-93339.7 - 53889.7i) q^{68} +(363250. + 185916. i) q^{70} +69288.4 q^{71} +(-141741. + 81834.1i) q^{73} +(-253690. - 439404. i) q^{74} +59917.4i q^{76} +(151888. - 296764. i) q^{77} +(91467.9 - 158427. i) q^{79} +(186504. - 107678. i) q^{80} +(-53554.6 - 30919.8i) q^{82} -364891. i q^{83} -708343. q^{85} +(-10995.8 + 19045.3i) q^{86} +(-87969.8 - 152368. i) q^{88} +(981810. + 566848. i) q^{89} +(1.02523e6 - 663148. i) q^{91} +636305. q^{92} +(-384137. + 221782. i) q^{94} +(196893. + 341029. i) q^{95} +1.38167e6i q^{97} +(-389228. - 539836. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 128 q^{4} - 210 q^{5} - 608 q^{7}+O(q^{10}) $ 8 * q - 128 * q^4 - 210 * q^5 - 608 * q^7	$ 8 q - 128 q^{4} - 210 q^{5} - 608 q^{7} + 1440 q^{10} - 2058 q^{11} - 1824 q^{14} - 4096 q^{16} + 11244 q^{17} + 21834 q^{19} - 17664 q^{22} - 15504 q^{23} - 6550 q^{25} + 19200 q^{26} + 22976 q^{28} - 35316 q^{29} - 51060 q^{31} - 71460 q^{35} + 20282 q^{37} + 234336 q^{38} - 46080 q^{40} + 387812 q^{43} - 65856 q^{44} - 98016 q^{46} + 55212 q^{47} - 277780 q^{49} - 499200 q^{50} - 361536 q^{52} + 336174 q^{53} + 3072 q^{56} - 128064 q^{58} + 560454 q^{59} + 850728 q^{61} + 262144 q^{64} - 826380 q^{65} - 947882 q^{67} - 359808 q^{68} + 1265280 q^{70} - 147192 q^{71} - 533034 q^{73} - 452544 q^{74} + 1848102 q^{77} - 6260 q^{79} + 215040 q^{80} - 174528 q^{82} + 560040 q^{85} - 505056 q^{86} + 282624 q^{88} - 413460 q^{89} + 256074 q^{91} + 992256 q^{92} - 1620000 q^{94} + 170880 q^{95} - 2259072 q^{98}+O(q^{100}) $ 8 * q - 128 * q^4 - 210 * q^5 - 608 * q^7 + 1440 * q^10 - 2058 * q^11 - 1824 * q^14 - 4096 * q^16 + 11244 * q^17 + 21834 * q^19 - 17664 * q^22 - 15504 * q^23 - 6550 * q^25 + 19200 * q^26 + 22976 * q^28 - 35316 * q^29 - 51060 * q^31 - 71460 * q^35 + 20282 * q^37 + 234336 * q^38 - 46080 * q^40 + 387812 * q^43 - 65856 * q^44 - 98016 * q^46 + 55212 * q^47 - 277780 * q^49 - 499200 * q^50 - 361536 * q^52 + 336174 * q^53 + 3072 * q^56 - 128064 * q^58 + 560454 * q^59 + 850728 * q^61 + 262144 * q^64 - 826380 * q^65 - 947882 * q^67 - 359808 * q^68 + 1265280 * q^70 - 147192 * q^71 - 533034 * q^73 - 452544 * q^74 + 1848102 * q^77 - 6260 * q^79 + 215040 * q^80 - 174528 * q^82 + 560040 * q^85 - 505056 * q^86 + 282624 * q^88 - 413460 * q^89 + 256074 * q^91 + 992256 * q^92 - 1620000 * q^94 + 170880 * q^95 - 2259072 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−2.82843	+	4.89898i	−0.353553	+	0.612372i
$2$	−2.82843	+	4.89898i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−16.0000	−	27.7128i	−0.250000	−	0.433013i
$5$	−182.133	−	105.155i	−1.45706	−	0.841236i	−0.458198	−	0.888850i	$-0.651505\pi$
$5$	−182.133	−	105.155i	−1.45706	−	0.841236i	−0.998866	+	0.0476139i	$0.984838\pi$
$6$		0			0
$7$	186.289	+	288.003i	0.543116	+	0.839658i
$7$	186.289	+	288.003i	0.543116	+	0.839658i
$8$	181.019			0.353553
$9$		0			0
$10$	1030.30	−	594.844i	1.03030	−	0.594844i
$11$	−485.969	−	841.723i	−0.365116	−	0.632399i	0.623679	−	0.781681i	$-0.285637\pi$
$11$	−485.969	−	841.723i	−0.365116	−	0.632399i	−0.988795	+	0.149281i	$0.952304\pi$
$12$		0			0
$13$		−	3559.78i		−	1.62029i	−0.586227	−	0.810147i	$-0.699387\pi$
$13$		−	3559.78i		−	1.62029i	0.586227	−	0.810147i	$-0.300613\pi$
$14$	−1937.82	+	98.0306i	−0.706204	+	0.0357254i
$15$		0			0
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$	2916.87	−	1684.05i	0.593704	−	0.342775i	−0.172857	−	0.984947i	$-0.555300\pi$
$17$	2916.87	−	1684.05i	0.593704	−	0.342775i	0.766561	+	0.642172i	$0.221966\pi$
$18$		0			0
$19$	−1621.56	−	936.209i	−0.236414	−	0.136494i	0.377114	−	0.926167i	$-0.376917\pi$
$19$	−1621.56	−	936.209i	−0.236414	−	0.136494i	−0.613527	+	0.789673i	$0.710250\pi$
$20$			6729.89i			0.841236i
$21$		0			0
$22$	5498.11			0.516352
$23$	−9942.27	+	17220.5i	−0.817150	+	1.41535i	0.0906234	+	0.995885i	$0.471114\pi$
$23$	−9942.27	+	17220.5i	−0.817150	+	1.41535i	−0.907774	+	0.419460i	$0.862219\pi$
$24$		0			0
$25$	14302.4	+	24772.6i	0.915357	+	1.58544i
$26$	17439.3	+	10068.6i	0.992223	+	0.572860i
$27$		0			0
$28$	5000.74	−	9770.63i	0.227803	−	0.445091i
$29$	18697.0			0.766616			0.383308	−	0.923621i	$-0.374785\pi$
$29$	18697.0			0.766616			0.383308	+	0.923621i	$0.374785\pi$
$30$		0			0
$31$	−17628.0	+	10177.5i	−0.591721	+	0.341630i	−0.765778	−	0.643105i	$-0.777646\pi$
$31$	−17628.0	+	10177.5i	−0.591721	+	0.341630i	0.174057	+	0.984736i	$0.444312\pi$
$32$	−2896.31	−	5016.55i	−0.0883883	−	0.153093i
$33$		0			0
$34$			19052.9i			0.484757i
$35$	−3644.56	−	72043.9i	−0.0850042	−	1.68032i
$36$		0			0
$37$	−44846.5	+	77676.4i	−0.885367	+	1.53350i	−0.0400751	+	0.999197i	$0.512760\pi$
$37$	−44846.5	+	77676.4i	−0.885367	+	1.53350i	−0.845292	+	0.534304i	$0.820574\pi$
$38$	9172.94	−	5296.00i	0.167170	−	0.0965155i
$39$		0			0
$40$	−32969.6	−	19035.0i	−0.515150	−	0.297422i
$41$			10931.8i			0.158613i	0.996850	+	0.0793067i	$0.0252706\pi$
$41$			10931.8i			0.158613i	−0.996850	+	0.0793067i	$0.974729\pi$
$42$		0			0
$43$	3887.60			0.0488963			0.0244482	−	0.999701i	$-0.492217\pi$
$43$	3887.60			0.0488963			0.0244482	+	0.999701i	$0.492217\pi$
$44$	−15551.0	+	26935.2i	−0.182558	+	0.316200i
$45$		0			0
$46$	−56242.0	−	97413.9i	−0.577812	−	1.00080i
$47$	67906.5	+	39205.8i	0.654060	+	0.377622i	0.790010	−	0.613094i	$-0.210075\pi$
$47$	67906.5	+	39205.8i	0.654060	+	0.377622i	−0.135950	+	0.990716i	$0.543409\pi$
$48$		0			0
$49$	−48242.0	+	107303.i	−0.410050	+	0.912063i
$50$	−161814.			−1.29451
$51$		0			0
$52$	−98651.6	+	56956.6i	−0.701608	+	0.405073i
$53$	53856.2	+	93281.7i	0.361750	+	0.626569i	0.988249	−	0.152853i	$-0.0488462\pi$
$53$	53856.2	+	93281.7i	0.361750	+	0.626569i	−0.626499	+	0.779422i	$0.715513\pi$
$54$		0			0
$55$			204407.i			1.22859i
$56$	33721.9	+	52134.0i	0.192021	+	0.296864i
$57$		0			0
$58$	−52883.1	+	91596.2i	−0.271040	+	0.469455i
$59$	−212952.	+	122948.i	−1.03688	+	0.598640i	−0.918947	−	0.394382i	$-0.870959\pi$
$59$	−212952.	+	122948.i	−1.03688	+	0.598640i	−0.117929	+	0.993022i	$0.537625\pi$
$60$		0			0
$61$	274561.	+	158518.i	1.20962	+	0.698376i	0.962677	−	0.270653i	$-0.0872397\pi$
$61$	274561.	+	158518.i	1.20962	+	0.698376i	0.246946	+	0.969029i	$0.420573\pi$
$62$		−	115145.i		−	0.483138i
$63$		0			0
$64$	32768.0			0.125000
$65$	−374327.	+	648354.i	−1.36305	+	2.36087i
$66$		0			0
$67$	−242122.	−	419367.i	−0.805025	−	1.39434i	−0.916274	−	0.400551i	$-0.868819\pi$
$67$	−242122.	−	419367.i	−0.805025	−	1.39434i	0.111250	−	0.993793i	$-0.464515\pi$
$68$	−93339.7	−	53889.7i	−0.296852	−	0.171387i
$69$		0			0
$70$	363250.	+	185916.i	1.05904	+	0.542030i
$71$	69288.4			0.193591			0.0967956	−	0.995304i	$-0.469141\pi$
$71$	69288.4			0.193591			0.0967956	+	0.995304i	$0.469141\pi$
$72$		0			0
$73$	−141741.	+	81834.1i	−0.364356	+	0.210361i	−0.670990	−	0.741466i	$-0.734131\pi$
$73$	−141741.	+	81834.1i	−0.364356	+	0.210361i	0.306634	+	0.951828i	$0.400797\pi$
$74$	−253690.	−	439404.i	−0.626049	−	1.08435i
$75$		0			0
$76$			59917.4i			0.136494i
$77$	151888.	−	296764.i	0.332699	−	0.650039i
$78$		0			0
$79$	91467.9	−	158427.i	0.185519	−	0.321328i	−0.758233	−	0.651984i	$-0.773937\pi$
$79$	91467.9	−	158427.i	0.185519	−	0.321328i	0.943751	+	0.330657i	$0.107270\pi$
$80$	186504.	−	107678.i	0.364266	−	0.210309i
$81$		0			0
$82$	−53554.6	−	30919.8i	−0.0971304	−	0.0560783i
$83$		−	364891.i		−	0.638160i	−0.947728	−	0.319080i	$-0.896626\pi$
$83$		−	364891.i		−	0.638160i	0.947728	−	0.319080i	$-0.103374\pi$
$84$		0			0
$85$	−708343.			−1.15342
$86$	−10995.8	+	19045.3i	−0.0172875	+	0.0299428i
$87$		0			0
$88$	−87969.8	−	152368.i	−0.129088	−	0.223587i
$89$	981810.	+	566848.i	1.39270	+	0.804075i	0.993613	−	0.112838i	$-0.0359941\pi$
$89$	981810.	+	566848.i	1.39270	+	0.804075i	0.399086	+	0.916913i	$0.369327\pi$
$90$		0			0
$91$	1.02523e6	−	663148.i	1.36049	−	0.880007i
$92$	636305.			0.817150
$93$		0			0
$94$	−384137.	+	221782.i	−0.462491	+	0.267019i
$95$	196893.	+	341029.i	0.229647	+	0.397760i
$96$		0			0
$97$			1.38167e6i			1.51387i	0.653488	+	0.756937i	$0.273305\pi$
$97$			1.38167e6i			1.51387i	−0.653488	+	0.756937i	$0.726695\pi$
$98$	−389228.	−	539836.i	−0.413548	−	0.573566i
$99$		0			0
$100$	457678.	−	792722.i	0.457678	−	0.792722i
$101$	1.45252e6	−	838613.i	1.40980	−	0.813950i	0.414433	−	0.910080i	$-0.363980\pi$
$101$	1.45252e6	−	838613.i	1.40980	−	0.813950i	0.995369	+	0.0961301i	$0.0306465\pi$
$102$		0			0
$103$	−1.06488e6	−	614811.i	−0.974520	−	0.562639i	−0.0739088	−	0.997265i	$-0.523547\pi$
$103$	−1.06488e6	−	614811.i	−0.974520	−	0.562639i	−0.900611	+	0.434626i	$0.856881\pi$
$104$		−	644390.i		−	0.572860i
$105$		0			0
$106$	−609314.			−0.511591
$107$	−884286.	+	1.53163e6i	−0.721841	+	1.25026i	0.238420	+	0.971162i	$0.423370\pi$
$107$	−884286.	+	1.53163e6i	−0.721841	+	1.25026i	−0.960261	+	0.279103i	$0.909963\pi$
$108$		0			0
$109$	637301.	+	1.10384e6i	0.492113	+	0.852365i	0.999959	−	0.00908330i	$-0.00289134\pi$
$109$	637301.	+	1.10384e6i	0.492113	+	0.852365i	−0.507846	+	0.861448i	$0.669558\pi$
$110$	−1.00139e6	−	578152.i	−0.752358	−	0.434374i
$111$		0			0
$112$	−350783.	+	17745.4i	−0.249681	+	0.0126309i
$113$	1.13727e6			0.788188			0.394094	−	0.919070i	$-0.371058\pi$
$113$	1.13727e6			0.788188			0.394094	+	0.919070i	$0.371058\pi$
$114$		0			0
$115$	3.62163e6	−	2.09095e6i	2.38128	−	1.37483i
$116$	−299152.	−	518146.i	−0.191654	−	0.331955i
$117$		0			0
$118$		−	1.39100e6i		−	0.846605i
$119$	1.02839e6	+	526345.i	0.610264	+	0.312341i
$120$		0			0
$121$	413448.	−	716113.i	0.233381	−	0.404227i
$122$	−1.55315e6	+	896714.i	−0.855333	+	0.493826i
$123$		0			0
$124$	564094.	+	325680.i	0.295860	+	0.170815i
$125$		−	2.72979e6i		−	1.39765i
$126$		0			0
$127$	696850.			0.340195			0.170097	−	0.985427i	$-0.445592\pi$
$127$	696850.			0.340195			0.170097	+	0.985427i	$0.445592\pi$
$128$	−92681.9	+	160530.i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−2.11752e6	−	3.66765e6i	−0.963822	−	1.66939i
$131$	−2.17981e6	−	1.25851e6i	−0.969626	−	0.559814i	−0.0705041	−	0.997511i	$-0.522461\pi$
$131$	−2.17981e6	−	1.25851e6i	−0.969626	−	0.559814i	−0.899122	+	0.437697i	$0.855794\pi$
$132$		0			0
$133$	−32448.1	−	641419.i	−0.0137922	−	0.272638i
$134$	2.73929e6			1.13848
$135$		0			0
$136$	528009.	−	304846.i	0.209906	−	0.121189i
$137$	301363.	+	521976.i	0.117200	+	0.202997i	0.918657	−	0.395056i	$-0.129275\pi$
$137$	301363.	+	521976.i	0.117200	+	0.202997i	−0.801457	+	0.598052i	$0.795941\pi$
$138$		0			0
$139$			3.66866e6i			1.36604i	0.730400	+	0.683020i	$0.239334\pi$
$139$			3.66866e6i			1.36604i	−0.730400	+	0.683020i	$0.760666\pi$
$140$	−1.93823e6	+	1.25370e6i	−0.706350	+	0.456889i
$141$		0			0
$142$	−195977.	+	339443.i	−0.0684448	+	0.118550i
$143$	−2.99635e6	+	1.72995e6i	−1.02467	+	0.591595i
$144$		0			0
$145$	−3.40534e6	−	1.96607e6i	−1.11701	−	0.644905i
$146$		−	925847.i		−	0.297496i
$147$		0			0
$148$	2.87018e6			0.885367
$149$	94655.9	−	163949.i	0.0286147	−	0.0495621i	−0.851363	−	0.524576i	$-0.824224\pi$
$149$	94655.9	−	163949.i	0.0286147	−	0.0495621i	0.879978	+	0.475014i	$0.157557\pi$
$150$		0			0
$151$	−7645.03	−	13241.6i	−0.00222049	−	0.00384600i	0.864913	−	0.501922i	$-0.167373\pi$
$151$	−7645.03	−	13241.6i	−0.00222049	−	0.00384600i	−0.867134	+	0.498076i	$0.834040\pi$
$152$	−293534.	−	169472.i	−0.0835849	−	0.0482577i
$153$		0			0
$154$	1.02424e6	+	1.58347e6i	0.280439	+	0.433559i
$155$	4.28084e6			1.14957
$156$		0			0
$157$	2.54625e6	−	1.47008e6i	0.657964	−	0.379876i	−0.133537	−	0.991044i	$-0.542633\pi$
$157$	2.54625e6	−	1.47008e6i	0.657964	−	0.379876i	0.791501	+	0.611168i	$0.209300\pi$
$158$	517421.	+	896199.i	0.131181	+	0.227213i
$159$		0			0
$160$			1.21824e6i			0.297422i
$161$	−6.81168e6	+	344590.i	−1.63221	+	0.0825704i
$162$		0			0
$163$	−458195.	+	793618.i	−0.105801	+	0.183252i	−0.914065	−	0.405568i	$-0.867074\pi$
$163$	−458195.	+	793618.i	−0.105801	+	0.183252i	0.808264	+	0.588820i	$0.200407\pi$
$164$	302951.	−	174909.i	0.0686816	−	0.0396533i
$165$		0			0
$166$	1.78760e6	+	1.03207e6i	0.390791	+	0.225623i
$167$			3.49297e6i			0.749972i	0.927031	+	0.374986i	$0.122352\pi$
$167$			3.49297e6i			0.749972i	−0.927031	+	0.374986i	$0.877648\pi$
$168$		0			0
$169$	−7.84526e6			−1.62535
$170$	2.00350e6	−	3.47016e6i	0.407795	−	0.706322i
$171$		0			0
$172$	−62201.6	−	107736.i	−0.0122241	−	0.0211727i
$173$	−595541.	−	343836.i	−0.115020	−	0.0664069i	0.441386	−	0.897317i	$-0.354487\pi$
$173$	−595541.	−	343836.i	−0.115020	−	0.0664069i	−0.556406	+	0.830910i	$0.687820\pi$
$174$		0			0
$175$	−4.47018e6	+	8.73399e6i	−0.834086	+	1.62967i
$176$	995265.			0.182558
$177$		0			0
$178$	−5.55396e6	+	3.20658e6i	−0.984787	+	0.568567i
$179$	−39555.6	−	68512.3i	−0.00689681	−	0.0119456i	0.862556	−	0.505961i	$-0.168862\pi$
$179$	−39555.6	−	68512.3i	−0.00689681	−	0.0119456i	−0.869453	+	0.494015i	$0.835529\pi$
$180$		0			0
$181$		−	4.28637e6i		−	0.722860i	−0.932399	−	0.361430i	$-0.882289\pi$
$181$		−	4.28637e6i		−	0.722860i	0.932399	−	0.361430i	$-0.117711\pi$
$182$	348968.	+	6.89823e6i	0.0578857	+	1.14426i
$183$		0			0
$184$	−1.79974e6	+	3.11725e6i	−0.288906	+	0.500400i
$185$	1.63361e7	−	9.43163e6i	2.58007	−	1.48961i
$186$		0			0
$187$	−2.83501e6	−	1.63680e6i	−0.433541	−	0.250305i
$188$		−	2.50917e6i		−	0.377622i
$189$		0			0
$190$	−2.22759e6			−0.324769
$191$	−4.72334e6	+	8.18106e6i	−0.677874	+	1.17411i	0.297746	+	0.954645i	$0.403765\pi$
$191$	−4.72334e6	+	8.18106e6i	−0.677874	+	1.17411i	−0.975620	+	0.219467i	$0.929568\pi$
$192$		0			0
$193$	4.68418e6	+	8.11323e6i	0.651570	+	1.12855i	0.982742	+	0.184982i	$0.0592228\pi$
$193$	4.68418e6	+	8.11323e6i	0.651570	+	1.12855i	−0.331171	+	0.943571i	$0.607444\pi$
$194$	−6.76878e6	−	3.90796e6i	−0.927055	−	0.535235i
$195$		0			0
$196$	3.74555e6	−	379932.i	0.497447	−	0.0504589i
$197$	−3.86436e6			−0.505450			−0.252725	−	0.967538i	$-0.581327\pi$
$197$	−3.86436e6			−0.505450			−0.252725	+	0.967538i	$0.581327\pi$
$198$		0			0
$199$	8.61379e6	−	4.97318e6i	1.09304	−	0.631066i	0.158654	−	0.987334i	$-0.449284\pi$
$199$	8.61379e6	−	4.97318e6i	1.09304	−	0.631066i	0.934384	+	0.356268i	$0.115951\pi$
$200$	2.58902e6	+	4.48431e6i	0.323627	+	0.560539i
$201$		0			0
$202$			9.48782e6i			1.15110i
$203$	3.48304e6	+	5.38478e6i	0.416361	+	0.643695i
$204$		0			0
$205$	1.14953e6	−	1.99104e6i	0.133431	−	0.231110i
$206$	6.02390e6	−	3.47790e6i	0.689090	−	0.397846i
$207$		0			0
$208$	3.15685e6	+	1.82261e6i	0.350804	+	0.202537i
$209$			1.81988e6i			0.199344i
$210$		0			0
$211$	4.42876e6			0.471449			0.235724	−	0.971820i	$-0.424254\pi$
$211$	4.42876e6			0.471449			0.235724	+	0.971820i	$0.424254\pi$
$212$	1.72340e6	−	2.98501e6i	0.180875	−	0.313284i
$213$		0			0
$214$	−5.00228e6	−	8.66420e6i	−0.510418	−	0.884071i
$215$	−708061.	−	408799.i	−0.0712451	−	0.0411334i
$216$		0			0
$217$	−6.21504e6	−	3.18094e6i	−0.608225	−	0.311298i
$218$	−7.21023e6			−0.695953
$219$		0			0
$220$	5.66471e6	−	3.27052e6i	0.531997	−	0.307149i
$221$	−5.99487e6	−	1.03834e7i	−0.555396	−	0.961974i
$222$		0			0
$223$			1.12907e7i			1.01814i	0.860726	+	0.509068i	$0.170010\pi$
$223$			1.12907e7i			1.01814i	−0.860726	+	0.509068i	$0.829990\pi$
$224$	905231.	−	1.76867e6i	0.0805407	−	0.157363i
$225$		0			0
$226$	−3.21670e6	+	5.57148e6i	−0.278667	+	0.482665i
$227$	−7.74694e6	+	4.47270e6i	−0.662297	+	0.382377i	−0.793151	−	0.609024i	$-0.791561\pi$
$227$	−7.74694e6	+	4.47270e6i	−0.662297	+	0.382377i	0.130855	+	0.991402i	$0.458228\pi$
$228$		0			0
$229$	5.93107e6	+	3.42431e6i	0.493886	+	0.285145i	0.726185	−	0.687499i	$-0.241291\pi$
$229$	5.93107e6	+	3.42431e6i	0.493886	+	0.285145i	−0.232299	+	0.972644i	$0.574625\pi$
$230$			2.36564e7i			1.94431i
$231$		0			0
$232$	3.38452e6			0.271040
$233$	−1.00855e7	+	1.74686e7i	−0.797313	+	1.38099i	0.124048	+	0.992276i	$0.460412\pi$
$233$	−1.00855e7	+	1.74686e7i	−0.797313	+	1.38099i	−0.921360	+	0.388710i	$0.872921\pi$
$234$		0			0
$235$	−8.24534e6	−	1.42814e7i	−0.635339	−	1.10044i
$236$	6.81448e6	+	3.93434e6i	0.518438	+	0.299320i
$237$		0			0
$238$	−5.48728e6	+	3.54934e6i	−0.407030	+	0.263279i
$239$	−2.24773e7			−1.64645			−0.823227	−	0.567712i	$-0.807829\pi$
$239$	−2.24773e7			−1.64645			−0.823227	+	0.567712i	$0.807829\pi$
$240$		0			0
$241$	−4.19282e6	+	2.42073e6i	−0.299540	+	0.172940i	−0.642236	−	0.766507i	$-0.721993\pi$
$241$	−4.19282e6	+	2.42073e6i	−0.299540	+	0.172940i	0.342696	+	0.939446i	$0.388660\pi$
$242$	2.33882e6	+	4.05095e6i	0.165025	+	0.285832i
$243$		0			0
$244$		−	1.01452e7i		−	0.698376i
$245$	2.00699e7	−	1.44706e7i	1.36473	−	0.983985i
$246$		0			0
$247$	−3.33270e6	+	5.77241e6i	−0.221160	+	0.383060i
$248$	−3.19100e6	+	1.84232e6i	−0.209205	+	0.120784i
$249$		0			0
$250$	1.33732e7	+	7.72101e6i	0.855884	+	0.494145i
$251$		−	2.19206e7i		−	1.38622i	−0.720834	−	0.693108i	$-0.756241\pi$
$251$		−	2.19206e7i		−	1.38622i	0.720834	−	0.693108i	$-0.243759\pi$
$252$		0			0
$253$	1.93265e7			1.19342
$254$	−1.97099e6	+	3.41385e6i	−0.120277	+	0.208326i
$255$		0			0
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	−748568.	−	432186.i	−0.0440993	−	0.0254608i	0.477788	−	0.878475i	$-0.341439\pi$
$257$	−748568.	−	432186.i	−0.0440993	−	0.0254608i	−0.521888	+	0.853014i	$0.674772\pi$
$258$		0			0
$259$	−3.07254e7	+	1.55434e6i	−1.76847	+	0.0894635i
$260$	2.39570e7			1.36305
$261$		0			0
$262$	1.23309e7	−	7.11922e6i	0.685629	−	0.395848i
$263$	−1.17280e7	−	2.03134e7i	−0.644696	−	1.11665i	−0.984372	−	0.176104i	$-0.943651\pi$
$263$	−1.17280e7	−	2.03134e7i	−0.644696	−	1.11665i	0.339675	−	0.940543i	$-0.389683\pi$
$264$		0			0
$265$		−	2.26529e7i		−	1.21727i
$266$	3.23408e6	+	1.65524e6i	0.171833	+	0.0879462i
$267$		0			0
$268$	−7.74789e6	+	1.34197e7i	−0.402512	+	0.697172i
$269$	1.21794e7	−	7.03179e6i	0.625705	−	0.361251i	−0.153382	−	0.988167i	$-0.549016\pi$
$269$	1.21794e7	−	7.03179e6i	0.625705	−	0.361251i	0.779087	+	0.626916i	$0.215683\pi$
$270$		0			0
$271$	−1.08536e6	−	626633.i	−0.0545338	−	0.0314851i	0.472485	−	0.881339i	$-0.343357\pi$
$271$	−1.08536e6	−	626633.i	−0.0545338	−	0.0314851i	−0.527019	+	0.849853i	$0.676690\pi$
$272$			3.44894e6i			0.171387i
$273$		0			0
$274$	−3.40953e6			−0.165746
$275$	1.39011e7	−	2.40774e7i	0.668423	−	1.15774i
$276$		0			0
$277$	−1.62307e7	−	2.81125e7i	−0.763658	−	1.32270i	−0.940953	−	0.338537i	$-0.890068\pi$
$277$	−1.62307e7	−	2.81125e7i	−0.763658	−	1.32270i	0.177295	−	0.984158i	$-0.443265\pi$
$278$	−1.79727e7	−	1.03765e7i	−0.836525	−	0.482968i
$279$		0			0
$280$	−659735.	−	1.30413e7i	−0.0300535	−	0.594084i
$281$	−1.81052e7			−0.815989			−0.407995	−	0.912984i	$-0.633772\pi$
$281$	−1.81052e7			−0.815989			−0.407995	+	0.912984i	$0.633772\pi$
$282$		0			0
$283$	−1.18049e7	+	6.81558e6i	−0.520840	+	0.300707i	−0.737278	−	0.675589i	$-0.763889\pi$
$283$	−1.18049e7	+	6.81558e6i	−0.520840	+	0.300707i	0.216439	+	0.976296i	$0.430556\pi$
$284$	−1.10862e6	−	1.92018e6i	−0.0483978	−	0.0838275i
$285$		0			0
$286$		−	1.95721e7i		−	0.836641i
$287$	−3.14838e6	+	2.03647e6i	−0.133181	+	0.0861454i
$288$		0			0
$289$	−6.39671e6	+	1.10794e7i	−0.265011	+	0.459012i
$290$	1.92635e7	−	1.11218e7i	0.789844	−	0.456017i
$291$		0			0
$292$	4.53570e6	+	2.61869e6i	0.182178	+	0.105181i
$293$			5.71340e6i			0.227139i	0.993530	+	0.113570i	$0.0362285\pi$
$293$			5.71340e6i			0.227139i	−0.993530	+	0.113570i	$0.963772\pi$
$294$		0			0
$295$	5.17142e7			2.01439
$296$	−8.11809e6	+	1.40609e7i	−0.313025	+	0.542175i
$297$		0			0
$298$	535454.	+	927434.i	0.0202336	+	0.0350457i
$299$	6.13013e7	+	3.53923e7i	2.29328	+	1.32402i
$300$		0			0
$301$	724217.	+	1.11964e6i	0.0265564	+	0.0410562i
$302$	86493.6			0.00314024
$303$		0			0
$304$	1.66048e6	−	958678.i	0.0591034	−	0.0341234i
$305$	−3.33378e7	−	5.77427e7i	−1.17500	−	2.03516i
$306$		0			0
$307$			7.04957e6i			0.243639i	0.992552	+	0.121820i	$0.0388730\pi$
$307$			7.04957e6i			0.243639i	−0.992552	+	0.121820i	$0.961127\pi$
$308$	−1.06544e7	+	538984.i	−0.364650	+	0.0184469i
$309$		0			0
$310$	−1.21081e7	+	2.09718e7i	−0.406433	+	0.703963i
$311$	4.50891e6	−	2.60322e6i	0.149896	−	0.0865426i	−0.423176	−	0.906047i	$-0.639085\pi$
$311$	4.50891e6	−	2.60322e6i	0.149896	−	0.0865426i	0.573072	+	0.819505i	$0.305751\pi$
$312$		0			0
$313$	2.26504e7	+	1.30772e7i	0.738656	+	0.426463i	0.821580	−	0.570093i	$-0.193093\pi$
$313$	2.26504e7	+	1.30772e7i	0.738656	+	0.426463i	−0.0829244	+	0.996556i	$0.526426\pi$
$314$			1.66320e7i			0.537225i
$315$		0			0
$316$	−5.85395e6			−0.185519
$317$	−3.29139e6	+	5.70085e6i	−0.103324	+	0.178963i	−0.913052	−	0.407843i	$-0.866281\pi$
$317$	−3.29139e6	+	5.70085e6i	−0.103324	+	0.178963i	0.809728	+	0.586805i	$0.199615\pi$
$318$		0			0
$319$	−9.08617e6	−	1.57377e7i	−0.279904	−	0.484808i
$320$	−5.96813e6	−	3.44570e6i	−0.182133	−	0.105155i
$321$		0			0
$322$	1.75782e7	−	3.43449e7i	0.526511	−	1.02872i
$323$	−6.30650e6			−0.187146
$324$		0			0
$325$	8.81850e7	−	5.09136e7i	2.56889	−	1.48315i
$326$	−2.59194e6	−	4.48938e6i	−0.0748123	−	0.129579i
$327$		0			0
$328$			1.97887e6i			0.0560783i
$329$	1.35884e6	+	2.68609e7i	0.0381575	+	0.754279i
$330$		0			0
$331$	7.38720e6	−	1.27950e7i	0.203702	−	0.352823i	−0.746016	−	0.665928i	$-0.768036\pi$
$331$	7.38720e6	−	1.27950e7i	0.203702	−	0.352823i	0.949718	+	0.313105i	$0.101369\pi$
$332$	−1.01122e7	+	5.83826e6i	−0.276331	+	0.159540i
$333$		0			0
$334$	−1.71120e7	−	9.87960e6i	−0.459262	−	0.265155i
$335$			1.01841e8i			2.70886i
$336$		0			0
$337$	−6.86189e6			−0.179289			−0.0896445	−	0.995974i	$-0.528573\pi$
$337$	−6.86189e6			−0.179289			−0.0896445	+	0.995974i	$0.528573\pi$
$338$	2.21897e7	−	3.84338e7i	0.574648	−	0.995320i
$339$		0			0
$340$	1.13335e7	+	1.96302e7i	0.288355	+	0.499445i
$341$	1.71333e7	+	9.89191e6i	0.432093	+	0.249469i
$342$		0			0
$343$	−3.98906e7	+	6.09559e6i	−0.988525	+	0.151054i
$344$	703731.			0.0172875
$345$		0			0
$346$	3.36889e6	−	1.94503e6i	0.0813315	−	0.0469567i
$347$	8.62186e6	+	1.49335e7i	0.206354	+	0.357415i	0.950563	−	0.310531i	$-0.100507\pi$
$347$	8.62186e6	+	1.49335e7i	0.206354	+	0.357415i	−0.744209	+	0.667946i	$0.767174\pi$
$348$		0			0
$349$			6.43913e7i			1.51478i	0.652960	+	0.757392i	$0.273527\pi$
$349$			6.43913e7i			1.51478i	−0.652960	+	0.757392i	$0.726473\pi$
$350$	−3.01441e7	−	4.66028e7i	−0.703069	−	1.08695i
$351$		0			0
$352$	−2.81503e6	+	4.87578e6i	−0.0645440	+	0.111793i
$353$	−5.92558e6	+	3.42114e6i	−0.134712	+	0.0777761i	−0.565842	−	0.824514i	$-0.691449\pi$
$353$	−5.92558e6	+	3.42114e6i	−0.134712	+	0.0777761i	0.431129	+	0.902290i	$0.358115\pi$
$354$		0			0
$355$	−1.26197e7	−	7.28599e6i	−0.282075	−	0.162856i
$356$		−	3.62783e7i		−	0.804075i
$357$		0			0
$358$	447520.			0.00975357
$359$	1.61260e7	−	2.79311e7i	0.348533	−	0.603677i	−0.637456	−	0.770487i	$-0.720013\pi$
$359$	1.61260e7	−	2.79311e7i	0.348533	−	0.603677i	0.985989	+	0.166810i	$0.0533467\pi$
$360$		0			0
$361$	−2.17700e7	−	3.77067e7i	−0.462739	−	0.801488i
$362$	2.09988e7	+	1.21237e7i	0.442659	+	0.255570i
$363$		0			0
$364$	−3.47813e7	−	1.78016e7i	−0.721177	−	0.369108i
$365$	3.44209e7			0.707854
$366$		0			0
$367$	1.25873e6	−	726727.i	0.0254644	−	0.0147019i	−0.487214	−	0.873283i	$-0.661987\pi$
$367$	1.25873e6	−	726727.i	0.0254644	−	0.0147019i	0.512678	+	0.858581i	$0.328653\pi$
$368$	−1.01809e7	−	1.76338e7i	−0.204288	−	0.353836i
$369$		0			0
$370$			1.06707e8i			2.10662i
$371$	−1.68326e7	+	3.28881e7i	−0.329631	+	0.644046i
$372$		0			0
$373$	1.58502e7	−	2.74533e7i	0.305427	−	0.529015i	−0.671929	−	0.740615i	$-0.734534\pi$
$373$	1.58502e7	−	2.74533e7i	0.305427	−	0.529015i	0.977356	+	0.211600i	$0.0678675\pi$
$374$	1.60373e7	−	9.25912e6i	0.306560	−	0.176992i
$375$		0			0
$376$	1.22924e7	+	7.09702e6i	0.231245	+	0.133510i
$377$		−	6.65573e7i		−	1.24214i
$378$		0			0
$379$	−6.98752e7			−1.28353			−0.641764	−	0.766902i	$-0.721797\pi$
$379$	−6.98752e7			−1.28353			−0.641764	+	0.766902i	$0.721797\pi$
$380$	6.30058e6	−	1.09129e7i	0.114823	−	0.198880i
$381$		0			0
$382$	−2.67192e7	−	4.62791e7i	−0.479329	−	0.830223i
$383$	−6.53554e7	−	3.77329e7i	−1.16328	−	0.671621i	−0.211193	−	0.977444i	$-0.567735\pi$
$383$	−6.53554e7	−	3.77329e7i	−1.16328	−	0.671621i	−0.952088	+	0.305823i	$0.901068\pi$
$384$		0			0
$385$	−5.88699e7	+	3.80788e7i	−1.03160	+	0.667270i
$386$	−5.29954e7			−0.921460
$387$		0			0
$388$	3.82900e7	−	2.21068e7i	0.655527	−	0.378469i
$389$	4.30868e7	+	7.46285e7i	0.731973	+	1.26781i	0.956039	+	0.293240i	$0.0947337\pi$
$389$	4.30868e7	+	7.46285e7i	0.731973	+	1.26781i	−0.224066	+	0.974574i	$0.571933\pi$
$390$		0			0
$391$			6.69732e7i			1.12039i
$392$	−8.73273e6	+	1.94240e7i	−0.144975	+	0.322463i
$393$		0			0
$394$	1.09301e7	−	1.89314e7i	0.178704	−	0.309524i
$395$	−3.33186e7	+	1.92365e7i	−0.540625	+	0.312130i
$396$		0			0
$397$	6.71952e7	+	3.87951e7i	1.07391	+	0.620020i	0.929246	−	0.369461i	$-0.120458\pi$
$397$	6.71952e7	+	3.87951e7i	1.07391	+	0.620020i	0.144660	+	0.989481i	$0.453791\pi$
$398$			5.62651e7i			0.892462i
$399$		0			0
$400$	−2.92914e7			−0.457678
$401$	−1.84833e6	+	3.20140e6i	−0.0286647	+	0.0496486i	−0.880002	−	0.474970i	$-0.842459\pi$
$401$	−1.84833e6	+	3.20140e6i	−0.0286647	+	0.0496486i	0.851337	+	0.524619i	$0.175792\pi$
$402$		0			0
$403$	3.62297e7	+	6.27517e7i	0.553541	+	0.958761i
$404$	−4.64807e7	−	2.68356e7i	−0.704901	−	0.406975i
$405$		0			0
$406$	−3.62315e7	+	1.83288e6i	−0.541387	+	0.0273877i
$407$	8.71761e7			1.29305
$408$		0			0
$409$	−5.00824e7	+	2.89151e7i	−0.732007	+	0.422624i	−0.819156	−	0.573571i	$-0.805558\pi$
$409$	−5.00824e7	+	2.89151e7i	−0.732007	+	0.422624i	0.0871493	+	0.996195i	$0.472224\pi$
$410$	6.50271e6	+	1.12630e7i	0.0943501	+	0.163419i
$411$		0			0
$412$			3.93479e7i			0.562639i
$413$	−7.50800e7	−	3.84270e7i	−1.06580	−	0.545489i
$414$		0			0
$415$	−3.83700e7	+	6.64587e7i	−0.536843	+	0.929839i
$416$	−1.78579e7	+	1.03102e7i	−0.248056	+	0.143215i
$417$		0			0
$418$	−8.91553e6	−	5.14738e6i	−0.122073	−	0.0704787i
$419$			8.02169e7i			1.09050i	0.838275	+	0.545248i	$0.183565\pi$
$419$			8.02169e7i			1.09050i	−0.838275	+	0.545248i	$0.816435\pi$
$420$		0			0
$421$	−1.93511e6			−0.0259334			−0.0129667	−	0.999916i	$-0.504128\pi$
$421$	−1.93511e6			−0.0259334			−0.0129667	+	0.999916i	$0.504128\pi$
$422$	−1.25264e7	+	2.16964e7i	−0.166682	+	0.288702i
$423$		0			0
$424$	9.74902e6	+	1.68858e7i	0.127898	+	0.221526i
$425$	8.34367e7	+	4.81722e7i	1.08690	+	0.627523i
$426$		0			0
$427$	5.49409e6	+	1.08605e8i	0.0705687	+	1.39497i
$428$	5.65943e7			0.721841
$429$		0			0
$430$	4.00540e6	−	2.31252e6i	0.0503779	−	0.0290857i
$431$	5.67563e6	+	9.83048e6i	0.0708896	+	0.122784i	0.899291	−	0.437350i	$-0.144083\pi$
$431$	5.67563e6	+	9.83048e6i	0.0708896	+	0.122784i	−0.828402	+	0.560134i	$0.810750\pi$
$432$		0			0
$433$			9.23707e7i			1.13781i	0.822402	+	0.568906i	$0.192633\pi$
$433$			9.23707e7i			1.13781i	−0.822402	+	0.568906i	$0.807367\pi$
$434$	3.31621e7	−	2.14503e7i	0.405671	−	0.262400i
$435$		0			0
$436$	2.03936e7	−	3.53228e7i	0.246057	−	0.426182i
$437$	3.22440e7	−	1.86161e7i	0.386371	−	0.223071i
$438$		0			0
$439$	−5.24472e7	−	3.02804e7i	−0.619910	−	0.357905i	0.156924	−	0.987611i	$-0.449842\pi$
$439$	−5.24472e7	−	3.02804e7i	−0.619910	−	0.357905i	−0.776834	+	0.629705i	$0.783176\pi$
$440$			3.70017e7i			0.434374i
$441$		0			0
$442$	6.78242e7			0.785449
$443$	−6.26388e7	+	1.08494e8i	−0.720498	+	1.24794i	0.240303	+	0.970698i	$0.422753\pi$
$443$	−6.26388e7	+	1.08494e8i	−0.720498	+	1.24794i	−0.960801	+	0.277241i	$0.910580\pi$
$444$		0			0
$445$	−1.19213e8	−	2.06484e8i	−1.35283	−	2.34318i
$446$	−5.53129e7	−	3.19349e7i	−0.623479	−	0.359966i
$447$		0			0
$448$	6.10431e6	+	9.43727e6i	0.0678895	+	0.104957i
$449$	−4.26832e6			−0.0471539			−0.0235770	−	0.999722i	$-0.507505\pi$
$449$	−4.26832e6			−0.0471539			−0.0235770	+	0.999722i	$0.507505\pi$
$450$		0			0
$451$	9.20154e6	−	5.31251e6i	0.100307	−	0.0579122i
$452$	−1.81964e7	−	3.15171e7i	−0.197047	−	0.341295i
$453$		0			0
$454$		−	5.06028e7i		−	0.540763i
$455$	−2.56461e8	+	1.29738e7i	−2.72262	+	0.137732i
$456$		0			0
$457$	4.34066e7	−	7.51825e7i	0.454786	−	0.787713i	−0.543890	−	0.839157i	$-0.683049\pi$
$457$	4.34066e7	−	7.51825e7i	0.454786	−	0.787713i	0.998676	+	0.0514437i	$0.0163823\pi$
$458$	−3.35512e7	+	1.93708e7i	−0.349230	+	0.201628i
$459$		0			0
$460$	−1.15892e8	−	6.69104e7i	−1.19064	−	0.687416i
$461$		−	1.65906e8i		−	1.69339i	−0.532075	−	0.846697i	$-0.678588\pi$
$461$		−	1.65906e8i		−	1.69339i	0.532075	−	0.846697i	$-0.321412\pi$
$462$		0			0
$463$	1.41475e8			1.42540			0.712699	−	0.701470i	$-0.247473\pi$
$463$	1.41475e8			1.42540			0.712699	+	0.701470i	$0.247473\pi$
$464$	−9.57286e6	+	1.65807e7i	−0.0958270	+	0.165977i
$465$		0			0
$466$	−5.70521e7	−	9.88171e7i	−0.563785	−	0.976505i
$467$	4.53153e7	+	2.61628e7i	0.444932	+	0.256882i	0.705688	−	0.708523i	$-0.250638\pi$
$467$	4.53153e7	+	2.61628e7i	0.444932	+	0.256882i	−0.260755	+	0.965405i	$0.583972\pi$
$468$		0			0
$469$	7.56742e7	−	1.47855e8i	0.733550	−	1.43324i
$470$	9.32854e7			0.898504
$471$		0			0
$472$	−3.85485e7	+	2.22560e7i	−0.366591	+	0.211651i
$473$	−1.88926e6	−	3.27229e6i	−0.0178528	−	0.0309220i
$474$		0			0
$475$		−	5.35603e7i		−	0.499761i
$476$	−1.86777e6	−	3.69211e7i	−0.0173182	−	0.342337i
$477$		0			0
$478$	6.35753e7	−	1.10116e8i	0.582110	−	1.00824i
$479$	1.29684e8	−	7.48728e7i	1.17999	−	0.681268i	0.223978	−	0.974594i	$-0.428096\pi$
$479$	1.29684e8	−	7.48728e7i	1.17999	−	0.681268i	0.956012	+	0.293327i	$0.0947623\pi$
$480$		0			0
$481$	2.76511e8	+	1.59644e8i	2.48472	+	1.43455i
$482$		−	2.73874e7i		−	0.244574i
$483$		0			0
$484$	−2.64607e7			−0.233381
$485$	1.45289e8	−	2.51648e8i	1.27353	−	2.20581i
$486$		0			0
$487$	9.37604e7	+	1.62398e8i	0.811769	+	1.40603i	0.911625	+	0.411023i	$0.134829\pi$
$487$	9.37604e7	+	1.62398e8i	0.811769	+	1.40603i	−0.0998558	+	0.995002i	$0.531838\pi$
$488$	4.97009e7	+	2.86948e7i	0.427666	+	0.246913i
$489$		0			0
$490$	1.41250e7	+	1.39251e8i	0.120061	+	1.18361i
$491$	−1.41921e8			−1.19895			−0.599476	−	0.800393i	$-0.704624\pi$
$491$	−1.41921e8			−1.19895			−0.599476	+	0.800393i	$0.704624\pi$
$492$		0			0
$493$	5.45366e7	−	3.14867e7i	0.455143	−	0.262777i
$494$	−1.88526e7	−	3.26537e7i	−0.156383	−	0.270864i
$495$		0			0
$496$		−	2.08435e7i		−	0.170815i
$497$	1.29077e7	+	1.99553e7i	0.105143	+	0.162550i
$498$		0			0
$499$	5.33587e7	−	9.24200e7i	0.429441	−	0.743814i	−0.567382	−	0.823454i	$-0.692044\pi$
$499$	5.33587e7	−	9.24200e7i	0.429441	−	0.743814i	0.996824	+	0.0796405i	$0.0253772\pi$
$500$	−7.56502e7	+	4.36766e7i	−0.605201	+	0.349413i
$501$		0			0
$502$	1.07388e8	+	6.20007e7i	0.848880	+	0.490101i
$503$			2.73080e6i			0.0214578i	0.999942	+	0.0107289i	$0.00341518\pi$
$503$			2.73080e6i			0.0214578i	−0.999942	+	0.0107289i	$0.996585\pi$
$504$		0			0
$505$	−3.52736e8			−2.73890
$506$	−5.46637e7	+	9.46803e7i	−0.421937	+	0.730816i
$507$		0			0
$508$	−1.11496e7	−	1.93117e7i	−0.0850487	−	0.147309i
$509$	1.39488e8	+	8.05333e7i	1.05775	+	0.610692i	0.924809	−	0.380432i	$-0.124225\pi$
$509$	1.39488e8	+	8.05333e7i	1.05775	+	0.610692i	0.132941	+	0.991124i	$0.457558\pi$
$510$		0			0
$511$	−4.99731e7	−	2.55769e7i	−0.374519	−	0.191684i
$512$	5.93164e6			0.0441942
$513$		0			0
$514$	4.23454e6	−	2.44481e6i	0.0311829	−	0.0180035i
$515$	1.29300e8	+	2.23955e8i	0.946625	+	1.63960i
$516$		0			0
$517$		−	7.62113e7i		−	0.551503i
$518$	7.92899e7	−	1.54920e8i	0.570465	−	1.11459i
$519$		0			0
$520$	−6.77605e7	+	1.17365e8i	−0.481911	+	0.834694i
$521$	3.57813e7	−	2.06583e7i	0.253013	−	0.146077i	−0.368130	−	0.929774i	$-0.620002\pi$
$521$	3.57813e7	−	2.06583e7i	0.253013	−	0.146077i	0.621143	+	0.783697i	$0.286669\pi$
$522$		0			0
$523$	−5.39683e7	−	3.11586e7i	−0.377254	−	0.217807i	0.299369	−	0.954137i	$-0.403224\pi$
$523$	−5.39683e7	−	3.11586e7i	−0.377254	−	0.217807i	−0.676623	+	0.736330i	$0.736557\pi$
$524$			8.05448e7i			0.559814i
$525$		0			0
$526$	1.32687e8			0.911738
$527$	−3.42789e7	+	5.93728e7i	−0.234205	+	0.405654i
$528$		0			0
$529$	−1.23679e8	−	2.14219e8i	−0.835469	−	1.44707i
$530$	1.10976e8	+	6.40721e7i	0.745421	+	0.430369i
$531$		0			0
$532$	−1.72564e7	+	1.11619e7i	−0.114608	+	0.0741318i
$533$	3.89148e7			0.257000
$534$		0			0
$535$	3.22115e8	−	1.85973e8i	2.10354	−	1.21448i
$536$	−4.38287e7	−	7.59135e7i	−0.284619	−	0.492975i
$537$		0			0
$538$			7.95556e7i			0.510886i
$539$	1.13764e8	−	1.15397e7i	0.726504	−	0.0736934i
$540$		0			0
$541$	−1.54969e8	+	2.68415e8i	−0.978709	+	1.69517i	−0.311602	+	0.950213i	$0.600865\pi$
$541$	−1.54969e8	+	2.68415e8i	−0.978709	+	1.69517i	−0.667108	+	0.744961i	$0.732468\pi$
$542$	6.13972e6	−	3.54477e6i	0.0385612	−	0.0222633i
$543$		0			0
$544$	−1.68963e7	−	9.75508e6i	−0.104953	−	0.0605946i
$545$		−	2.68060e8i		−	1.65593i
$546$		0			0
$547$	−1.89819e8			−1.15979			−0.579893	−	0.814693i	$-0.696905\pi$
$547$	−1.89819e8			−1.15979			−0.579893	+	0.814693i	$0.696905\pi$
$548$	9.64362e6	−	1.67032e7i	0.0586001	−	0.101498i
$549$		0			0
$550$	7.86365e7	+	1.36202e8i	0.472646	+	0.818647i
$551$	−3.03183e7	−	1.75043e7i	−0.181239	−	0.104638i
$552$		0			0
$553$	6.26668e7	−	3.17019e6i	0.370563	−	0.0187461i
$554$	1.83630e8			1.07998
$555$		0			0
$556$	1.01669e8	−	5.86986e7i	0.591512	−	0.341510i
$557$	−1.40106e8	−	2.42671e8i	−0.810758	−	1.40427i	−0.912334	−	0.409447i	$-0.865722\pi$
$557$	−1.40106e8	−	2.42671e8i	−0.810758	−	1.40427i	0.101575	−	0.994828i	$-0.467612\pi$
$558$		0			0
$559$		−	1.38390e7i		−	0.0792264i
$560$	6.57552e7	+	3.36544e7i	0.374426	+	0.191637i
$561$		0			0
$562$	5.12093e7	−	8.86970e7i	0.288496	−	0.499689i
$563$	6.08041e7	−	3.51053e7i	0.340728	−	0.196719i	−0.319866	−	0.947463i	$-0.603638\pi$
$563$	6.08041e7	−	3.51053e7i	0.340728	−	0.196719i	0.660594	+	0.750743i	$0.270305\pi$
$564$		0			0
$565$	−2.07135e8	−	1.19590e8i	−1.14844	−	0.663052i
$566$		−	7.71095e7i		−	0.425264i
$567$		0			0
$568$	1.25425e7			0.0684448
$569$	−1.10988e8	+	1.92237e8i	−0.602476	+	1.04352i	0.389968	+	0.920828i	$0.372486\pi$
$569$	−1.10988e8	+	1.92237e8i	−0.602476	+	1.04352i	−0.992445	+	0.122691i	$0.960847\pi$
$570$		0			0
$571$	−9.94189e7	−	1.72199e8i	−0.534024	−	0.924956i	−0.999210	−	0.0397433i	$-0.987346\pi$
$571$	−9.94189e7	−	1.72199e8i	−0.534024	−	0.924956i	0.465186	−	0.885213i	$-0.345987\pi$
$572$	9.58833e7	+	5.53583e7i	0.512336	+	0.295797i
$573$		0			0
$574$	−1.07165e6	−	2.11839e7i	−0.00566653	−	0.112013i
$575$	−5.68795e8			−2.99194
$576$		0			0
$577$	1.93148e8	−	1.11514e8i	1.00546	−	0.580501i	0.0955992	−	0.995420i	$-0.469523\pi$
$577$	1.93148e8	−	1.11514e8i	1.00546	−	0.580501i	0.909859	+	0.414919i	$0.136190\pi$
$578$	−3.61853e7	−	6.26747e7i	−0.187391	−	0.324570i
$579$		0			0
$580$			1.25829e8i			0.644905i
$581$	1.05090e8	−	6.79752e7i	0.535836	−	0.346595i
$582$		0			0
$583$	5.23449e7	−	9.06641e7i	0.264161	−	0.457541i
$584$	−2.56578e7	+	1.48135e7i	−0.128819	+	0.0743739i
$585$		0			0
$586$	−2.79898e7	−	1.61599e7i	−0.139094	−	0.0803058i
$587$			7.09053e7i			0.350561i	0.984518	+	0.175281i	$0.0560833\pi$
$587$			7.09053e7i			0.350561i	−0.984518	+	0.175281i	$0.943917\pi$
$588$		0			0
$589$	3.81131e7			0.186521
$590$	−1.46270e8	+	2.53347e8i	−0.712195	+	1.23356i
$591$		0			0
$592$	−4.59228e7	−	7.95407e7i	−0.221342	−	0.383375i
$593$	−2.20611e8	−	1.27370e8i	−1.05795	−	0.610805i	−0.133083	−	0.991105i	$-0.542488\pi$
$593$	−2.20611e8	−	1.27370e8i	−1.05795	−	0.610805i	−0.924863	+	0.380300i	$0.875821\pi$
$594$		0			0
$595$	−1.31956e8	−	2.04005e8i	−0.626440	−	0.968477i
$596$	−6.05797e6			−0.0286147
$597$		0			0
$598$	−3.46773e8	+	2.00209e8i	−1.62159	+	0.936226i
$599$	−9.52522e7	−	1.64982e8i	−0.443195	−	0.767636i	0.554730	−	0.832031i	$-0.312822\pi$
$599$	−9.52522e7	−	1.64982e8i	−0.443195	−	0.767636i	−0.997924	+	0.0643949i	$0.979488\pi$
$600$		0			0
$601$		−	8.79125e7i		−	0.404974i	−0.979285	−	0.202487i	$-0.935098\pi$
$601$		−	8.79125e7i		−	0.404974i	0.979285	−	0.202487i	$-0.0649024\pi$
$602$	−7.53348e6	+	381104.i	−0.0345308	+	0.00174684i
$603$		0			0
$604$	−244641.	+	423731.i	−0.00111024	+	0.00192300i
$605$	−1.50605e8	+	8.69519e7i	−0.680101	+	0.392657i
$606$		0			0
$607$	2.49954e8	+	1.44311e8i	1.11762	+	0.645259i	0.940792	−	0.338983i	$-0.110083\pi$
$607$	2.49954e8	+	1.44311e8i	1.11762	+	0.645259i	0.176828	+	0.984242i	$0.443416\pi$
$608$			1.08462e7i			0.0482577i
$609$		0			0
$610$	3.77174e8			1.66170
$611$	1.39564e8	−	2.41733e8i	0.611858	−	1.05977i
$612$		0			0
$613$	1.82049e8	+	3.15319e8i	0.790329	+	1.36889i	0.925763	+	0.378103i	$0.123424\pi$
$613$	1.82049e8	+	3.15319e8i	0.790329	+	1.36889i	−0.135435	+	0.990786i	$0.543243\pi$
$614$	−3.45357e7	−	1.99392e7i	−0.149198	−	0.0861396i
$615$		0			0
$616$	2.74946e7	−	5.37200e7i	0.117627	−	0.229823i
$617$	2.33610e8			0.994571			0.497286	−	0.867587i	$-0.334330\pi$
$617$	2.33610e8			0.994571			0.497286	+	0.867587i	$0.334330\pi$
$618$		0			0
$619$	−3.44277e8	+	1.98769e8i	−1.45157	+	0.838062i	−0.998570	−	0.0534515i	$-0.982978\pi$
$619$	−3.44277e8	+	1.98769e8i	−1.45157	+	0.838062i	−0.452995	+	0.891513i	$0.649644\pi$
$620$	−6.84935e7	−	1.18634e8i	−0.287392	−	0.497777i
$621$		0			0
$622$			2.94521e7i			0.122390i
$623$	1.96464e7	+	3.88361e8i	0.0812493	+	1.60610i
$624$		0			0
$625$	−6.35740e7	+	1.10113e8i	−0.260399	+	0.451025i
$626$	−1.28130e8	+	7.39758e7i	−0.522309	+	0.301555i
$627$		0			0
$628$	−8.14800e7	−	4.70425e7i	−0.328982	−	0.189938i
$629$			3.02096e8i			1.21393i
$630$		0			0
$631$	−1.47291e8			−0.586258			−0.293129	−	0.956073i	$-0.594696\pi$
$631$	−1.47291e8			−0.586258			−0.293129	+	0.956073i	$0.594696\pi$
$632$	1.65575e7	−	2.86784e7i	0.0655907	−	0.113606i
$633$		0			0
$634$	−1.86189e7	−	3.22489e7i	−0.0730612	−	0.126546i
$635$	−1.26919e8	−	7.32769e7i	−0.495686	−	0.286184i
$636$		0			0
$637$	3.81977e8	+	1.71731e8i	1.47781	+	0.664401i
$638$	1.02798e8			0.395844
$639$		0			0
$640$	3.37609e7	−	1.94918e7i	0.128787	−	0.0743555i
$641$	−398057.	−	689455.i	−0.00151137	−	0.00261777i	0.865269	−	0.501308i	$-0.167148\pi$
$641$	−398057.	−	689455.i	−0.00151137	−	0.00261777i	−0.866780	+	0.498691i	$0.833814\pi$
$642$		0			0
$643$		−	3.43701e8i		−	1.29285i	−0.762978	−	0.646425i	$-0.776263\pi$
$643$		−	3.43701e8i		−	1.29285i	0.762978	−	0.646425i	$-0.223737\pi$
$644$	1.18537e8	+	1.83258e8i	0.443807	+	0.686126i
$645$		0			0
$646$	1.78375e7	−	3.08954e7i	0.0661662	−	0.114603i
$647$	3.65961e7	−	2.11288e7i	0.135121	−	0.0780120i	−0.430916	−	0.902392i	$-0.641809\pi$
$647$	3.65961e7	−	2.11288e7i	0.135121	−	0.0780120i	0.566037	+	0.824380i	$0.308476\pi$
$648$		0			0
$649$	2.06977e8	+	1.19498e8i	0.757159	+	0.437146i
$650$			5.76022e8i			2.09749i
$651$		0			0
$652$	2.93245e7			0.105801
$653$	−1.10631e8	+	1.91618e8i	−0.397316	+	0.688171i	−0.993394	−	0.114756i	$-0.963392\pi$
$653$	−1.10631e8	+	1.91618e8i	−0.397316	+	0.688171i	0.596078	+	0.802926i	$0.296725\pi$
$654$		0			0
$655$	2.64677e8	+	4.58433e8i	0.941872	+	1.63137i
$656$	−9.69442e6	−	5.59708e6i	−0.0343408	−	0.0198267i
$657$		0			0
$658$	−1.35434e8	−	6.93171e7i	−0.475391	−	0.243311i
$659$	1.16774e8			0.408027			0.204014	−	0.978968i	$-0.434601\pi$
$659$	1.16774e8			0.408027			0.204014	+	0.978968i	$0.434601\pi$
$660$		0			0
$661$	−4.61650e8	+	2.66534e8i	−1.59848	+	0.922886i	−0.606705	+	0.794927i	$0.707509\pi$
$661$	−4.61650e8	+	2.66534e8i	−1.59848	+	0.922886i	−0.991780	+	0.127959i	$0.959158\pi$
$662$	4.17883e7	+	7.23795e7i	0.144039	+	0.249483i
$663$		0			0
$664$		−	6.60524e7i		−	0.225623i
$665$	−6.15383e7	+	1.20236e8i	−0.209257	+	0.408854i
$666$		0			0
$667$	−1.85891e8	+	3.21972e8i	−0.626441	+	1.08503i
$668$	9.67999e7	−	5.58874e7i	0.324747	−	0.187493i
$669$		0			0
$670$	−4.98916e8	−	2.88049e8i	−1.65883	−	0.957728i
$671$		−	3.08140e8i		−	1.01995i
$672$		0			0
$673$	7.89690e7			0.259067			0.129533	−	0.991575i	$-0.458652\pi$
$673$	7.89690e7			0.259067			0.129533	+	0.991575i	$0.458652\pi$
$674$	1.94083e7	−	3.36162e7i	0.0633882	−	0.109792i
$675$		0			0
$676$	1.25524e8	+	2.17414e8i	0.406338	+	0.703797i
$677$	7.85243e7	+	4.53360e7i	0.253068	+	0.146109i	0.621168	−	0.783677i	$-0.286658\pi$
$677$	7.85243e7	+	4.53360e7i	0.253068	+	0.146109i	−0.368100	+	0.929786i	$0.619992\pi$
$678$		0			0
$679$	−3.97925e8	+	2.57390e8i	−1.27114	+	0.822209i
$680$	−1.28224e8			−0.407795
$681$		0			0
$682$	−9.69205e7	+	5.59571e7i	−0.305536	+	0.176401i
$683$	1.21588e8	+	2.10596e8i	0.381617	+	0.660981i	0.991294	−	0.131670i	$-0.0420339\pi$
$683$	1.21588e8	+	2.10596e8i	0.381617	+	0.660981i	−0.609676	+	0.792651i	$0.708701\pi$
$684$		0			0
$685$		−	1.26759e8i		−	0.394372i
$686$	8.29654e7	−	2.12664e8i	0.256995	−	0.658752i
$687$		0			0
$688$	−1.99045e6	+	3.44756e6i	−0.00611204	+	0.0105864i
$689$	3.32063e8	−	1.91717e8i	1.01523	−	0.586141i
$690$		0			0
$691$	−1.35131e8	−	7.80178e7i	−0.409563	−	0.236461i	0.281039	−	0.959696i	$-0.409321\pi$
$691$	−1.35131e8	−	7.80178e7i	−0.409563	−	0.236461i	−0.690602	+	0.723235i	$0.742654\pi$
$692$			2.20055e7i			0.0664069i
$693$		0			0
$694$	−9.75452e7			−0.291828
$695$	3.85776e8	−	6.68184e8i	1.14916	−	1.99041i
$696$		0			0
$697$	1.84097e7	+	3.18866e7i	0.0543687	+	0.0941693i
$698$	−3.15452e8	−	1.82126e8i	−0.927612	−	0.535557i
$699$		0			0
$700$	3.13566e8	−	1.58627e7i	0.914188	−	0.0462469i
$701$	−1.55020e8			−0.450023			−0.225012	−	0.974356i	$-0.572242\pi$
$701$	−1.55020e8			−0.450023			−0.225012	+	0.974356i	$0.572242\pi$
$702$		0			0
$703$	1.45443e8	−	8.39714e7i	0.418626	−	0.241694i
$704$	−1.59242e7	−	2.75816e7i	−0.0456395	−	0.0790499i
$705$		0			0
$706$		−	3.87057e7i		−	0.109992i
$707$	5.12111e8	+	2.62105e8i	1.44913	+	0.741682i
$708$		0			0
$709$	−3.22565e8	+	5.58698e8i	−0.905061	+	1.56761i	−0.0842258	+	0.996447i	$0.526842\pi$
$709$	−3.22565e8	+	5.58698e8i	−0.905061	+	1.56761i	−0.820835	+	0.571165i	$0.806492\pi$
$710$	7.13879e7	−	4.12158e7i	0.199457	−	0.115157i
$711$		0			0
$712$	1.77727e8	+	1.02610e8i	0.492394	+	0.284284i
$713$		−	4.04750e8i		−	1.11665i
$714$		0			0
$715$	7.27647e8			1.99068
$716$	−1.26578e6	+	2.19239e6i	−0.00344841	+	0.00597282i
$717$		0			0
$718$	9.12225e7	+	1.58002e8i	0.246450	+	0.426864i
$719$	−4.75380e8	−	2.74461e8i	−1.27895	−	0.738404i	−0.302297	−	0.953214i	$-0.597753\pi$
$719$	−4.75380e8	−	2.74461e8i	−1.27895	−	0.738404i	−0.976656	+	0.214810i	$0.931087\pi$
$720$		0			0
$721$	−2.13088e7	−	4.21222e8i	−0.0568529	−	1.12384i
$722$	2.46299e8			0.654412
$723$		0			0
$724$	−1.18787e8	+	6.85819e7i	−0.313007	+	0.180715i
$725$	2.67413e8	+	4.63173e8i	0.701727	+	1.21543i
$726$		0			0
$727$		−	3.37493e8i		−	0.878338i	−0.898404	−	0.439169i	$-0.855273\pi$
$727$		−	3.37493e8i		−	0.878338i	0.898404	−	0.439169i	$-0.144727\pi$
$728$	1.85586e8	−	1.20043e8i	0.481006	−	0.311130i
$729$		0			0
$730$	−9.73570e7	+	1.68627e8i	−0.250264	+	0.433470i
$731$	1.13396e7	−	6.54693e6i	0.0290299	−	0.0167604i
$732$		0			0
$733$	−4.10304e8	−	2.36889e8i	−1.04182	−	0.601497i	−0.121474	−	0.992595i	$-0.538762\pi$
$733$	−4.10304e8	−	2.36889e8i	−1.04182	−	0.601497i	−0.920349	+	0.391098i	$0.872095\pi$
$734$			8.22198e6i			0.0207916i
$735$		0			0
$736$	1.15184e8			0.288906
$737$	−2.35327e8	+	4.07599e8i	−0.587855	+	1.01819i
$738$		0			0
$739$	2.55575e7	+	4.42670e7i	0.0633265	+	0.109685i	0.895950	−	0.444154i	$-0.146496\pi$
$739$	2.55575e7	+	4.42670e7i	0.0633265	+	0.109685i	−0.832624	+	0.553839i	$0.813162\pi$
$740$	−5.22754e8	−	3.01812e8i	−1.29004	−	0.744803i
$741$		0			0
$742$	−1.13508e8	−	1.75484e8i	−0.277853	−	0.429562i
$743$	−3.07500e8			−0.749684			−0.374842	−	0.927089i	$-0.622303\pi$
$743$	−3.07500e8			−0.749684			−0.374842	+	0.927089i	$0.622303\pi$
$744$		0			0
$745$	−3.44799e7	+	1.99070e7i	−0.0833868	+	0.0481434i
$746$	8.96620e7	+	1.55299e8i	0.215969	+	0.374070i
$747$		0			0
$748$			1.04755e8i			0.250305i
$749$	−6.05845e8	+	3.06485e7i	−1.44184	+	0.0729397i
$750$		0			0
$751$	2.90979e8	−	5.03991e8i	0.686977	−	1.18988i	−0.285835	−	0.958279i	$-0.592271\pi$
$751$	2.90979e8	−	5.03991e8i	0.686977	−	1.18988i	0.972811	−	0.231599i	$-0.0743958\pi$
$752$	−6.95363e7	+	4.01468e7i	−0.163515	+	0.0944055i
$753$		0			0
$754$	3.26063e8	+	1.88252e8i	0.760654	+	0.439164i
$755$			3.21564e6i			0.00747182i
$756$		0			0
$757$	4.40250e7			0.101487			0.0507436	−	0.998712i	$-0.483841\pi$
$757$	4.40250e7			0.101487			0.0507436	+	0.998712i	$0.483841\pi$
$758$	1.97637e8	−	3.42317e8i	0.453796	−	0.785998i
$759$		0			0
$760$	3.56415e7	+	6.17329e7i	0.0811923	+	0.140629i
$761$	2.09687e8	+	1.21063e8i	0.475792	+	0.274698i	0.718661	−	0.695361i	$-0.244755\pi$
$761$	2.09687e8	+	1.21063e8i	0.475792	+	0.274698i	−0.242869	+	0.970059i	$0.578089\pi$
$762$		0			0
$763$	−1.99186e8	+	3.89177e8i	−0.448420	+	0.876139i
$764$	3.02294e8			0.677874
$765$		0			0
$766$	3.69706e8	−	2.13450e8i	0.822564	−	0.474908i
$767$	4.37669e8	+	7.58065e8i	0.969973	+	1.68004i
$768$		0			0
$769$		−	2.23515e8i		−	0.491505i	−0.969333	−	0.245753i	$-0.920965\pi$
$769$		−	2.23515e8i		−	0.491505i	0.969333	−	0.245753i	$-0.0790351\pi$
$770$	−2.00382e7	−	3.96105e8i	−0.0438921	−	0.867638i
$771$		0			0
$772$	1.49894e8	−	2.59623e8i	0.325785	−	0.564276i
$773$	−1.95041e8	+	1.12607e8i	−0.422266	+	0.243796i	−0.696047	−	0.717997i	$-0.745059\pi$
$773$	−1.95041e8	+	1.12607e8i	−0.422266	+	0.243796i	0.273780	+	0.961792i	$0.411726\pi$
$774$		0			0
$775$	−5.04246e8	−	2.91126e8i	−1.08327	−	0.625427i
$776$			2.50109e8i			0.535235i
$777$		0			0
$778$	−4.87471e8			−1.03517
$779$	1.02344e7	−	1.77266e7i	0.0216497	−	0.0374984i
$780$		0			0
$781$	−3.36721e7	−	5.83217e7i	−0.0706832	−	0.122427i
$782$	−3.28100e8	−	1.89429e8i	−0.686099	−	0.396119i
$783$		0			0
$784$	−7.04578e7	−	9.77208e7i	−0.146211	−	0.202786i
$785$	−6.18341e8			−1.27826
$786$		0			0
$787$	−4.82030e8	+	2.78300e8i	−0.988895	+	0.570939i	−0.904944	−	0.425531i	$-0.860087\pi$
$787$	−4.82030e8	+	2.78300e8i	−0.988895	+	0.570939i	−0.0839513	+	0.996470i	$0.526754\pi$
$788$	6.18297e7	+	1.07092e8i	0.126363	+	0.218866i
$789$		0			0
$790$		−	2.17636e8i		−	0.441418i
$791$	2.11861e8	+	3.27538e8i	0.428078	+	0.661808i
$792$		0			0
$793$	5.64290e8	−	9.77379e8i	1.13157	−	1.95994i
$794$	−3.80113e8	+	2.19458e8i	−0.759367	+	0.438420i
$795$		0			0
$796$	−2.75641e8	−	1.59142e8i	−0.546519	−	0.315533i
$797$			1.25601e6i			0.00248095i	0.999999	+	0.00124048i	$0.000394856\pi$
$797$			1.25601e6i			0.00248095i	−0.999999	+	0.00124048i	$0.999605\pi$
$798$		0			0
$799$	2.64099e8			0.517757
$800$	8.28486e7	−	1.43498e8i	0.161814	−	0.280270i
$801$		0			0
$802$	−1.04557e7	−	1.81099e7i	−0.0202690	−	0.0351069i
$803$	1.37763e8	+	7.95377e7i	0.266065	+	0.153612i
$804$		0			0
$805$	1.27687e9	+	6.53518e8i	2.44770	+	1.25277i
$806$	−4.09892e8			−0.782825
$807$		0			0
$808$	2.62934e8	−	1.51805e8i	0.498440	−	0.287775i
$809$	8.24366e7	+	1.42784e8i	0.155695	+	0.269672i	0.933312	−	0.359067i	$-0.116905\pi$
$809$	8.24366e7	+	1.42784e8i	0.155695	+	0.269672i	−0.777617	+	0.628738i	$0.783572\pi$
$810$		0			0
$811$		−	1.67902e8i		−	0.314771i	−0.987537	−	0.157385i	$-0.949694\pi$
$811$		−	1.67902e8i		−	0.314771i	0.987537	−	0.157385i	$-0.0503064\pi$
$812$	9.34989e7	−	1.82681e8i	0.174638	−	0.341214i
$813$		0			0
$814$	−2.46571e8	+	4.27074e8i	−0.457161	+	0.791826i
$815$	1.66905e8	−	9.63626e7i	0.308316	−	0.178006i
$816$		0			0
$817$	−6.30399e6	−	3.63961e6i	−0.0115598	−	0.00667403i
$818$		−	3.27137e8i		−	0.597681i
$819$		0			0
$820$	−7.35697e7			−0.133431
$821$	−7.86482e7	+	1.36223e8i	−0.142121	+	0.246161i	−0.928295	−	0.371844i	$-0.878726\pi$
$821$	−7.86482e7	+	1.36223e8i	−0.142121	+	0.246161i	0.786174	+	0.618005i	$0.212059\pi$
$822$		0			0
$823$	2.44122e8	+	4.22832e8i	0.437933	+	0.758522i	0.997530	−	0.0702428i	$-0.0223774\pi$
$823$	2.44122e8	+	4.22832e8i	0.437933	+	0.758522i	−0.559597	+	0.828765i	$0.689044\pi$
$824$	−1.92765e8	−	1.11293e8i	−0.344545	−	0.198923i
$825$		0			0
$826$	4.00611e8	−	2.59128e8i	0.710858	−	0.459805i
$827$	3.44930e8			0.609839			0.304919	−	0.952378i	$-0.401370\pi$
$827$	3.44930e8			0.609839			0.304919	+	0.952378i	$0.401370\pi$
$828$		0			0
$829$	1.72654e8	−	9.96817e7i	0.303049	−	0.174965i	−0.340763	−	0.940149i	$-0.610685\pi$
$829$	1.72654e8	−	9.96817e7i	0.303049	−	0.174965i	0.643812	+	0.765184i	$0.277352\pi$
$830$	−2.17053e8	−	3.75947e8i	−0.379605	−	0.657496i
$831$		0			0
$832$		−	1.16647e8i		−	0.202537i
$833$	3.99891e7	+	3.94231e8i	0.0691842	+	0.682050i
$834$		0			0
$835$	3.67301e8	−	6.36184e8i	0.630903	−	1.09276i
$836$	5.04339e7	−	2.91180e7i	0.0863184	−	0.0498360i
$837$		0			0
$838$	−3.92981e8	−	2.26888e8i	−0.667790	−	0.385549i
$839$		−	6.44765e8i		−	1.09173i	−0.837873	−	0.545865i	$-0.816201\pi$
$839$		−	6.44765e8i		−	1.09173i	0.837873	−	0.545865i	$-0.183799\pi$
$840$		0			0
$841$	−2.45245e8			−0.412300
$842$	5.47333e6	−	9.48008e6i	0.00916886	−	0.0158809i
$843$		0			0
$844$	−7.08601e7	−	1.22733e8i	−0.117862	−	0.204143i
$845$	1.42888e9	+	8.24964e8i	2.36824	+	1.36730i
$846$		0			0
$847$	2.83263e8	−	1.43297e7i	0.466165	−	0.0235824i
$848$	−1.10298e8			−0.180875
$849$		0			0
$850$	−4.71989e8	+	2.72503e8i	−0.768555	+	0.443726i
$851$	−8.91752e8	−	1.54456e9i	−1.44696	−	2.50620i
$852$		0			0
$853$		−	6.39556e8i		−	1.03046i	−0.857052	−	0.515231i	$-0.827706\pi$
$853$		−	6.39556e8i		−	1.03046i	0.857052	−	0.515231i	$-0.172294\pi$
$854$	−5.47591e8	−	2.80265e8i	−0.879190	−	0.449981i
$855$		0			0
$856$	−1.60073e8	+	2.77254e8i	−0.255209	+	0.442035i
$857$	−7.38721e7	+	4.26501e7i	−0.117365	+	0.0677606i	−0.557533	−	0.830155i	$-0.688252\pi$
$857$	−7.38721e7	+	4.26501e7i	−0.117365	+	0.0677606i	0.440168	+	0.897915i	$0.354919\pi$
$858$		0			0
$859$	5.01049e8	+	2.89281e8i	0.790499	+	0.456395i	0.840138	−	0.542373i	$-0.182474\pi$
$859$	5.01049e8	+	2.89281e8i	0.790499	+	0.456395i	−0.0496394	+	0.998767i	$0.515807\pi$
$860$			2.61631e7i			0.0411334i
$861$		0			0
$862$	−6.42125e7			−0.100253
$863$	2.74923e8	−	4.76180e8i	0.427738	−	0.740864i	−0.568934	−	0.822383i	$-0.692644\pi$
$863$	2.74923e8	−	4.76180e8i	0.427738	−	0.740864i	0.996672	+	0.0815193i	$0.0259772\pi$
$864$		0			0
$865$	7.23118e7	+	1.25248e8i	0.111728	+	0.193518i
$866$	−4.52522e8	−	2.61264e8i	−0.696765	−	0.402277i
$867$		0			0
$868$	1.12878e7	+	2.23131e8i	0.0172603	+	0.341194i
$869$	−1.77802e8			−0.270943
$870$		0			0
$871$	−1.49286e9	+	8.61901e8i	−2.25925	+	1.30438i
$872$	1.15364e8	+	1.99816e8i	0.173988	+	0.301356i
$873$		0			0
$874$			2.10617e8i			0.315471i
$875$	7.86187e8	−	5.08529e8i	1.17355	−	0.759087i
$876$		0			0
$877$	5.43435e8	−	9.41257e8i	0.805655	−	1.39543i	−0.110194	−	0.993910i	$-0.535147\pi$
$877$	5.43435e8	−	9.41257e8i	0.805655	−	1.39543i	0.915848	−	0.401525i	$-0.131520\pi$
$878$	2.96686e8	−	1.71292e8i	0.438343	−	0.253077i
$879$		0			0
$880$	−1.81271e8	−	1.04657e8i	−0.265999	−	0.153574i
$881$		−	1.50334e8i		−	0.219852i	−0.993940	−	0.109926i	$-0.964939\pi$
$881$		−	1.50334e8i		−	0.219852i	0.993940	−	0.109926i	$-0.0350614\pi$
$882$		0			0
$883$	−6.63235e8			−0.963352			−0.481676	−	0.876349i	$-0.659972\pi$
$883$	−6.63235e8			−0.963352			−0.481676	+	0.876349i	$0.659972\pi$
$884$	−1.91836e8	+	3.32269e8i	−0.277698	+	0.480987i
$885$		0			0
$886$	−3.54339e8	−	6.13733e8i	−0.509469	−	0.882426i
$887$	3.83371e8	+	2.21339e8i	0.549349	+	0.317167i	0.748859	−	0.662729i	$-0.230602\pi$
$887$	3.83371e8	+	2.21339e8i	0.549349	+	0.317167i	−0.199510	+	0.979896i	$0.563935\pi$
$888$		0			0
$889$	1.29815e8	+	2.00694e8i	0.184765	+	0.285647i
$890$	1.34874e9			1.91320
$891$		0			0
$892$	3.12897e8	−	1.80651e8i	0.440866	−	0.254534i
$893$	−7.34097e7	−	1.27149e8i	−0.103086	−	0.178550i
$894$		0			0
$895$			1.66378e7i			0.0232074i
$896$	−6.34986e7	+	3.21227e6i	−0.0882755	+	0.00446568i
$897$		0			0
$898$	1.20726e7	−	2.09104e7i	0.0166714	−	0.0288758i
$899$	−3.29590e8	+	1.90289e8i	−0.453623	+	0.261899i
$900$		0			0
$901$	3.14183e8	+	1.81393e8i	0.429544	+	0.247998i
$902$			6.01042e7i			0.0819003i
$903$		0			0
$904$	2.05869e8			0.278667
$905$	−4.50731e8	+	7.80690e8i	−0.608096	+	1.05325i
$906$		0			0
$907$	2.05909e8	+	3.56644e8i	0.275964	+	0.477984i	0.970378	−	0.241592i	$-0.0776695\pi$
$907$	2.05909e8	+	3.56644e8i	0.275964	+	0.477984i	−0.694414	+	0.719576i	$0.744336\pi$
$908$	2.47902e8	+	1.43126e8i	0.331148	+	0.191189i
$909$		0			0
$910$	6.61822e8	−	1.29309e9i	0.878247	−	1.71595i
$911$	8.39816e8			1.11078			0.555391	−	0.831589i	$-0.312568\pi$
$911$	8.39816e8			1.11078			0.555391	+	0.831589i	$0.312568\pi$
$912$		0			0
$913$	−3.07138e8	+	1.77326e8i	−0.403572	+	0.233002i
$914$	2.45545e8	+	4.25296e8i	0.321583	+	0.556997i
$915$		0			0
$916$		−	2.19156e8i		−	0.285145i
$917$	−4.36189e7	−	8.62237e8i	−0.0565674	−	1.11820i
$918$		0			0
$919$	−2.39254e8	+	4.14400e8i	−0.308257	+	0.533917i	−0.977981	−	0.208693i	$-0.933079\pi$
$919$	−2.39254e8	+	4.14400e8i	−0.308257	+	0.533917i	0.669724	+	0.742610i	$0.266412\pi$
$920$	6.55585e8	−	3.78502e8i	0.841910	−	0.486077i
$921$		0			0
$922$	8.12768e8	+	4.69252e8i	1.03699	+	0.598705i
$923$		−	2.46652e8i		−	0.313675i
$924$		0			0
$925$	−2.56566e9			−3.24171
$926$	−4.00151e8	+	6.93082e8i	−0.503954	+	0.872874i
$927$		0			0
$928$	−5.41523e7	−	9.37945e7i	−0.0677599	−	0.117364i
$929$	−7.68390e8	−	4.43630e8i	−0.958373	−	0.553317i	−0.0627011	−	0.998032i	$-0.519971\pi$
$929$	−7.68390e8	−	4.43630e8i	−0.958373	−	0.553317i	−0.895672	+	0.444715i	$0.853305\pi$
$930$		0			0
$931$	1.78686e8	−	1.28834e8i	0.221432	−	0.159655i
$932$	6.45471e8			0.797313
$933$		0			0
$934$	−2.56342e8	+	1.47999e8i	−0.314615	+	0.181643i
$935$	3.44233e8	+	5.96229e8i	0.421132	+	0.729421i
$936$		0			0
$937$			1.19816e9i			1.45646i	0.685334	+	0.728229i	$0.259656\pi$
$937$			1.19816e9i			1.45646i	−0.685334	+	0.728229i	$0.740344\pi$
$938$	5.10300e8	+	7.88924e8i	0.618325	+	0.955931i
$939$		0			0
$940$	−2.63851e8	+	4.57003e8i	−0.317669	+	0.550219i
$941$	−9.75385e8	+	5.63139e8i	−1.17060	+	0.675844i	−0.953820	−	0.300378i	$-0.902887\pi$
$941$	−9.75385e8	+	5.63139e8i	−1.17060	+	0.675844i	−0.216776	+	0.976221i	$0.569554\pi$
$942$		0			0
$943$	−1.88251e8	−	1.08687e8i	−0.224493	−	0.129611i
$944$		−	2.51798e8i		−	0.299320i
$945$		0			0
$946$	2.13745e7			0.0252477
$947$	−3.53545e8	+	6.12359e8i	−0.416289	+	0.721034i	−0.995563	−	0.0940990i	$-0.970003\pi$
$947$	−3.53545e8	+	6.12359e8i	−0.416289	+	0.721034i	0.579274	+	0.815133i	$0.303336\pi$
$948$		0			0
$949$	2.91312e8	+	5.04567e8i	0.340847	+	0.590364i
$950$	2.62391e8	+	1.51491e8i	0.306040	+	0.176692i
$951$		0			0
$952$	1.86159e8	+	9.52786e7i	0.215761	+	0.110429i
$953$	−2.87519e8			−0.332191			−0.166095	−	0.986110i	$-0.553116\pi$
$953$	−2.87519e8			−0.332191			−0.166095	+	0.986110i	$0.553116\pi$
$954$		0			0
$955$	1.72055e9	−	9.93361e8i	1.97541	−	1.14050i
$956$	3.59636e8	+	6.22908e8i	0.411614	+	0.712936i
$957$		0			0
$958$			8.47090e8i			0.963458i
$959$	−9.41899e7	+	1.84032e8i	−0.106794	+	0.208659i
$960$		0			0
$961$	−2.36589e8	+	4.09784e8i	−0.266578	+	0.461726i
$962$	−1.56418e9	+	9.03082e8i	−1.75696	+	1.01438i
$963$		0			0
$964$	1.34170e8	+	7.74633e7i	0.149770	+	0.0864699i
$965$		−	1.97025e9i		−	2.19250i
$966$		0			0
$967$	1.48175e9			1.63869			0.819343	−	0.573304i	$-0.194339\pi$
$967$	1.48175e9			1.63869			0.819343	+	0.573304i	$0.194339\pi$
$968$	7.48421e7	−	1.29630e8i	0.0825126	−	0.142916i
$969$		0			0
$970$	8.21879e8	+	1.42354e9i	0.900519	+	1.55974i
$971$	1.50641e9	+	8.69728e8i	1.64546	+	0.950005i	0.978846	+	0.204598i	$0.0655888\pi$
$971$	1.50641e9	+	8.69728e8i	1.64546	+	0.950005i	0.666610	+	0.745406i	$0.267745\pi$
$972$		0			0
$973$	−1.05658e9	+	6.83430e8i	−1.14701	+	0.741918i
$974$	−1.06078e9			−1.14801
$975$		0			0
$976$	−2.81151e8	+	1.62323e8i	−0.302406	+	0.174594i
$977$	5.55082e8	+	9.61429e8i	0.595214	+	1.03094i	0.993517	+	0.113687i	$0.0362660\pi$
$977$	5.55082e8	+	9.61429e8i	0.595214	+	1.03094i	−0.398303	+	0.917254i	$0.630401\pi$
$978$		0			0
$979$		−	1.10188e9i		−	1.17432i
$980$	−7.22139e8	−	3.24663e8i	−0.767260	−	0.344949i
$981$		0			0
$982$	4.01413e8	−	6.95268e8i	0.423894	−	0.734205i
$983$	−9.45759e8	+	5.46034e8i	−0.995681	+	0.574857i	−0.906968	−	0.421201i	$-0.861609\pi$
$983$	−9.45759e8	+	5.46034e8i	−0.995681	+	0.574857i	−0.0887133	+	0.996057i	$0.528275\pi$
$984$		0			0
$985$	7.03827e8	+	4.06355e8i	0.736473	+	0.425203i
$986$			3.56232e8i			0.371623i
$987$		0			0
$988$	2.13293e8			0.221160
$989$	−3.86516e7	+	6.69465e7i	−0.0399557	+	0.0692052i
$990$		0			0
$991$	1.15604e8	+	2.00232e8i	0.118782	+	0.205737i	0.919285	−	0.393591i	$-0.128768\pi$
$991$	1.15604e8	+	2.00232e8i	0.118782	+	0.205737i	−0.800503	+	0.599329i	$0.795434\pi$
$992$	1.02112e8	+	5.89544e7i	0.104602	+	0.0603922i
$993$		0			0
$994$	−1.34269e8	+	6.79239e6i	−0.136715	+	0.00691613i
$995$	−2.09181e9			−2.12350
$996$		0			0
$997$	5.60304e8	−	3.23492e8i	0.565377	−	0.326421i	−0.189924	−	0.981799i	$-0.560824\pi$
$997$	5.60304e8	−	3.23492e8i	0.565377	−	0.326421i	0.755301	+	0.655378i	$0.227491\pi$
$998$	3.01842e8	+	5.22806e8i	0.303661	+	0.525956i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.7.n.b.19.1		8
3.2	odd	2		42.7.g.b.19.4	✓	8
7.3	odd	6	inner	126.7.n.b.73.1		8
12.11	even	2		336.7.bh.c.145.4		8
21.2	odd	6		294.7.c.a.97.3		8
21.5	even	6		294.7.c.a.97.2		8
21.11	odd	6		294.7.g.b.31.3		8
21.17	even	6		42.7.g.b.31.4	yes	8
21.20	even	2		294.7.g.b.19.3		8
84.59	odd	6		336.7.bh.c.241.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.7.g.b.19.4	✓	8	3.2	odd	2
42.7.g.b.31.4	yes	8	21.17	even	6
126.7.n.b.19.1		8	1.1	even	1	trivial
126.7.n.b.73.1		8	7.3	odd	6	inner
294.7.c.a.97.2		8	21.5	even	6
294.7.c.a.97.3		8	21.2	odd	6
294.7.g.b.19.3		8	21.20	even	2
294.7.g.b.31.3		8	21.11	odd	6
336.7.bh.c.145.4		8	12.11	even	2
336.7.bh.c.241.4		8	84.59	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	126.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.82843 + 4.89898i) q^{2} +(-16.0000 - 27.7128i) q^{4} +(-182.133 - 105.155i) q^{5} +(186.289 + 288.003i) q^{7} +181.019 q^{8} +O(q^{10})\)	\(q+(-2.82843 + 4.89898i) q^{2} +(-16.0000 - 27.7128i) q^{4} +(-182.133 - 105.155i) q^{5} +(186.289 + 288.003i) q^{7} +181.019 q^{8} +(1030.30 - 594.844i) q^{10} +(-485.969 - 841.723i) q^{11} -3559.78i q^{13} +(-1937.82 + 98.0306i) q^{14} +(-512.000 + 886.810i) q^{16} +(2916.87 - 1684.05i) q^{17} +(-1621.56 - 936.209i) q^{19} +6729.89i q^{20} +5498.11 q^{22} +(-9942.27 + 17220.5i) q^{23} +(14302.4 + 24772.6i) q^{25} +(17439.3 + 10068.6i) q^{26} +(5000.74 - 9770.63i) q^{28} +18697.0 q^{29} +(-17628.0 + 10177.5i) q^{31} +(-2896.31 - 5016.55i) q^{32} +19052.9i q^{34} +(-3644.56 - 72043.9i) q^{35} +(-44846.5 + 77676.4i) q^{37} +(9172.94 - 5296.00i) q^{38} +(-32969.6 - 19035.0i) q^{40} +10931.8i q^{41} +3887.60 q^{43} +(-15551.0 + 26935.2i) q^{44} +(-56242.0 - 97413.9i) q^{46} +(67906.5 + 39205.8i) q^{47} +(-48242.0 + 107303. i) q^{49} -161814. q^{50} +(-98651.6 + 56956.6i) q^{52} +(53856.2 + 93281.7i) q^{53} +204407. i q^{55} +(33721.9 + 52134.0i) q^{56} +(-52883.1 + 91596.2i) q^{58} +(-212952. + 122948. i) q^{59} +(274561. + 158518. i) q^{61} -115145. i q^{62} +32768.0 q^{64} +(-374327. + 648354. i) q^{65} +(-242122. - 419367. i) q^{67} +(-93339.7 - 53889.7i) q^{68} +(363250. + 185916. i) q^{70} +69288.4 q^{71} +(-141741. + 81834.1i) q^{73} +(-253690. - 439404. i) q^{74} +59917.4i q^{76} +(151888. - 296764. i) q^{77} +(91467.9 - 158427. i) q^{79} +(186504. - 107678. i) q^{80} +(-53554.6 - 30919.8i) q^{82} -364891. i q^{83} -708343. q^{85} +(-10995.8 + 19045.3i) q^{86} +(-87969.8 - 152368. i) q^{88} +(981810. + 566848. i) q^{89} +(1.02523e6 - 663148. i) q^{91} +636305. q^{92} +(-384137. + 221782. i) q^{94} +(196893. + 341029. i) q^{95} +1.38167e6i q^{97} +(-389228. - 539836. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 128 q^{4} - 210 q^{5} - 608 q^{7}+O(q^{10}) \) 8 * q - 128 * q^4 - 210 * q^5 - 608 * q^7	\( 8 q - 128 q^{4} - 210 q^{5} - 608 q^{7} + 1440 q^{10} - 2058 q^{11} - 1824 q^{14} - 4096 q^{16} + 11244 q^{17} + 21834 q^{19} - 17664 q^{22} - 15504 q^{23} - 6550 q^{25} + 19200 q^{26} + 22976 q^{28} - 35316 q^{29} - 51060 q^{31} - 71460 q^{35} + 20282 q^{37} + 234336 q^{38} - 46080 q^{40} + 387812 q^{43} - 65856 q^{44} - 98016 q^{46} + 55212 q^{47} - 277780 q^{49} - 499200 q^{50} - 361536 q^{52} + 336174 q^{53} + 3072 q^{56} - 128064 q^{58} + 560454 q^{59} + 850728 q^{61} + 262144 q^{64} - 826380 q^{65} - 947882 q^{67} - 359808 q^{68} + 1265280 q^{70} - 147192 q^{71} - 533034 q^{73} - 452544 q^{74} + 1848102 q^{77} - 6260 q^{79} + 215040 q^{80} - 174528 q^{82} + 560040 q^{85} - 505056 q^{86} + 282624 q^{88} - 413460 q^{89} + 256074 q^{91} + 992256 q^{92} - 1620000 q^{94} + 170880 q^{95} - 2259072 q^{98}+O(q^{100}) \) 8 * q - 128 * q^4 - 210 * q^5 - 608 * q^7 + 1440 * q^10 - 2058 * q^11 - 1824 * q^14 - 4096 * q^16 + 11244 * q^17 + 21834 * q^19 - 17664 * q^22 - 15504 * q^23 - 6550 * q^25 + 19200 * q^26 + 22976 * q^28 - 35316 * q^29 - 51060 * q^31 - 71460 * q^35 + 20282 * q^37 + 234336 * q^38 - 46080 * q^40 + 387812 * q^43 - 65856 * q^44 - 98016 * q^46 + 55212 * q^47 - 277780 * q^49 - 499200 * q^50 - 361536 * q^52 + 336174 * q^53 + 3072 * q^56 - 128064 * q^58 + 560454 * q^59 + 850728 * q^61 + 262144 * q^64 - 826380 * q^65 - 947882 * q^67 - 359808 * q^68 + 1265280 * q^70 - 147192 * q^71 - 533034 * q^73 - 452544 * q^74 + 1848102 * q^77 - 6260 * q^79 + 215040 * q^80 - 174528 * q^82 + 560040 * q^85 - 505056 * q^86 + 282624 * q^88 - 413460 * q^89 + 256074 * q^91 + 992256 * q^92 - 1620000 * q^94 + 170880 * q^95 - 2259072 * q^98

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