LMFDB - Embedded newform 126.9.s.b.53.10

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} + 3140415 x^{18} - 28263450 x^{17} + 4166681580501 x^{16} - 33332812007100 x^{15} + \cdots + 75\!\cdots\!79 $ x^20 - 10x^19 + 3140415x^18 - 28263450x^17 + 4166681580501x^16 - 33332812007100x^15 + 3031999370323294994x^14 - 21223412270295167948x^13 + 1313283359586691659338157x^12 - 7879424254677270736897262x^11 + 343395008585647382793738362717x^10 - 1716902815378389725958443657694x^9 + 52358316972954959192126259265947855x^8 - 209422966561600366110762067553592180x^7 + 4229075043327500600602686549793780016622x^6 - 12686492156810441352359584184417459023348x^5 + 144254968239046675448003125054039788454888507x^4 - 288488792568822027386658361381507315488125730x^3 + 639027248533334160181502914078717624884446094987x^2 - 638883006251430205323520488726745011115535930034*x + 758989993652521448576631480355366113559097835556179
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{18}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.10
Root			$0.500000 - 778.834i$ of defining polynomial
Character	$\chi$	$=$	126.53
Dual form			126.9.s.b.107.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.79796 - 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(675.240 - 389.850i) q^{5} +(-2257.29 + 818.185i) q^{7} -1448.15i q^{8} +O(q^{10})$	\(q+(9.79796 - 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(675.240 - 389.850i) q^{5} +(-2257.29 + 818.185i) q^{7} -1448.15i q^{8} +(4410.65 - 7639.47i) q^{10} +(22350.7 + 12904.2i) q^{11} +2645.78 q^{13} +(-17488.5 + 20785.7i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(64112.8 + 37015.5i) q^{17} +(-19975.2 - 34598.0i) q^{19} -99801.6i q^{20} +291989. q^{22} +(391111. - 225808. i) q^{23} +(108654. - 188193. i) q^{25} +(25923.2 - 14966.8i) q^{26} +(-53769.9 + 302588. i) q^{28} -16119.2i q^{29} +(-130548. + 226117. i) q^{31} +(-160530. - 92681.9i) q^{32} +837566. q^{34} +(-1.20525e6 + 1.43248e6i) q^{35} +(-704165. - 1.21965e6i) q^{37} +(-391432. - 225993. i) q^{38} +(-564563. - 977852. i) q^{40} +1.52892e6i q^{41} -1.63384e6 q^{43} +(2.86090e6 - 1.65174e6i) q^{44} +(2.55473e6 - 4.42492e6i) q^{46} +(8.03301e6 - 4.63786e6i) q^{47} +(4.42595e6 - 3.69377e6i) q^{49} -2.45855e6i q^{50} +(169330. - 293288. i) q^{52} +(2.72214e6 + 1.57163e6i) q^{53} +2.01228e7 q^{55} +(1.18486e6 + 3.26891e6i) q^{56} +(-91184.2 - 157936. i) q^{58} +(-1.44666e7 - 8.35227e6i) q^{59} +(4.37015e6 + 7.56932e6i) q^{61} +2.95397e6i q^{62} -2.09715e6 q^{64} +(1.78653e6 - 1.03146e6i) q^{65} +(1.40514e7 - 2.43378e7i) q^{67} +(8.20644e6 - 4.73799e6i) q^{68} +(-3.70563e6 + 2.08533e7i) q^{70} -4.04624e7i q^{71} +(5.58975e6 - 9.68173e6i) q^{73} +(-1.37988e7 - 7.96672e6i) q^{74} -5.11364e6 q^{76} +(-6.10102e7 - 1.08415e7i) q^{77} +(3.35502e7 + 5.81107e7i) q^{79} +(-1.10631e7 - 6.38730e6i) q^{80} +(8.64888e6 + 1.49803e7i) q^{82} -4.64460e7i q^{83} +5.77220e7 q^{85} +(-1.60083e7 + 9.24239e6i) q^{86} +(1.86873e7 - 3.23673e7i) q^{88} +(-3.34937e7 + 1.93376e7i) q^{89} +(-5.97229e6 + 2.16474e6i) q^{91} -5.78069e7i q^{92} +(5.24714e7 - 9.08831e7i) q^{94} +(-2.69761e7 - 1.55746e7i) q^{95} +9.56235e7 q^{97} +(2.24701e7 - 6.12283e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 1280 q^{4} + 3778 q^{7}+O(q^{10}) $ 20 * q + 1280 * q^4 + 3778 * q^7	$ 20 q + 1280 q^{4} + 3778 q^{7} + 14816 q^{10} + 17700 q^{13} - 163840 q^{16} - 267794 q^{19} + 453568 q^{22} - 765890 q^{25} - 232448 q^{28} - 2604342 q^{31} + 4087936 q^{34} + 1127530 q^{37} - 1896448 q^{40} - 4460924 q^{43} - 180416 q^{46} - 25278034 q^{49} + 1132800 q^{52} - 18833120 q^{55} + 5146496 q^{58} - 25730232 q^{61} - 41943040 q^{64} + 58134374 q^{67} - 76724864 q^{70} + 5811002 q^{73} - 68555264 q^{76} + 74799798 q^{79} - 9883296 q^{82} + 119739328 q^{85} + 29028352 q^{88} - 479039766 q^{91} + 169364448 q^{94} - 658133608 q^{97}+O(q^{100}) $ 20 * q + 1280 * q^4 + 3778 * q^7 + 14816 * q^10 + 17700 * q^13 - 163840 * q^16 - 267794 * q^19 + 453568 * q^22 - 765890 * q^25 - 232448 * q^28 - 2604342 * q^31 + 4087936 * q^34 + 1127530 * q^37 - 1896448 * q^40 - 4460924 * q^43 - 180416 * q^46 - 25278034 * q^49 + 1132800 * q^52 - 18833120 * q^55 + 5146496 * q^58 - 25730232 * q^61 - 41943040 * q^64 + 58134374 * q^67 - 76724864 * q^70 + 5811002 * q^73 - 68555264 * q^76 + 74799798 * q^79 - 9883296 * q^82 + 119739328 * q^85 + 29028352 * q^88 - 479039766 * q^91 + 169364448 * q^94 - 658133608 * 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
$5$	675.240	−	389.850i	1.08038	−	0.623760i	0.149384	−	0.988779i	$-0.452271\pi$
$5$	675.240	−	389.850i	1.08038	−	0.623760i	0.931000	+	0.365019i	$0.118938\pi$
$6$		0			0
$7$	−2257.29	+	818.185i	−0.940147	+	0.340769i
$7$	−2257.29	+	818.185i	−0.940147	+	0.340769i
$8$		−	1448.15i		−	0.353553i
$9$		0			0
$10$	4410.65	−	7639.47i	0.441065	−	0.763947i
$11$	22350.7	+	12904.2i	1.52659	+	0.881375i	0.999502	+	0.0315619i	$0.0100481\pi$
$11$	22350.7	+	12904.2i	1.52659	+	0.881375i	0.527084	+	0.849813i	$0.323285\pi$
$12$		0			0
$13$	2645.78			0.0926360			0.0463180	−	0.998927i	$-0.485251\pi$
$13$	2645.78			0.0926360			0.0463180	+	0.998927i	$0.485251\pi$
$14$	−17488.5	+	20785.7i	−0.455240	+	0.541069i
$15$		0			0
$16$	−8192.00	−	14189.0i	−0.125000	−	0.216506i
$17$	64112.8	+	37015.5i	0.767625	+	0.443188i	0.832027	−	0.554736i	$-0.187181\pi$
$17$	64112.8	+	37015.5i	0.767625	+	0.443188i	−0.0644020	+	0.997924i	$0.520514\pi$
$18$		0			0
$19$	−19975.2	−	34598.0i	−0.153277	−	0.265483i	0.779154	−	0.626833i	$-0.215649\pi$
$19$	−19975.2	−	34598.0i	−0.153277	−	0.265483i	−0.932430	+	0.361350i	$0.882316\pi$
$20$		−	99801.6i		−	0.623760i
$21$		0			0
$22$	291989.			1.24645
$23$	391111.	−	225808.i	1.39762	−	0.806916i	0.403477	−	0.914990i	$-0.367801\pi$
$23$	391111.	−	225808.i	1.39762	−	0.806916i	0.994143	+	0.108073i	$0.0344681\pi$
$24$		0			0
$25$	108654.	−	188193.i	0.278153	−	0.481775i
$26$	25923.2	−	14966.8i	0.0567277	−	0.0327518i
$27$		0			0
$28$	−53769.9	+	302588.i	−0.0874797	+	0.492288i
$29$		−	16119.2i		−	0.0227904i	−0.999935	−	0.0113952i	$-0.996373\pi$
$29$		−	16119.2i		−	0.0227904i	0.999935	−	0.0113952i	$-0.00362729\pi$
$30$		0			0
$31$	−130548.	+	226117.i	−0.141359	+	0.244842i	−0.928009	−	0.372558i	$-0.878481\pi$
$31$	−130548.	+	226117.i	−0.141359	+	0.244842i	0.786649	+	0.617400i	$0.211814\pi$
$32$	−160530.	−	92681.9i	−0.153093	−	0.0883883i
$33$		0			0
$34$	837566.			0.626763
$35$	−1.20525e6	+	1.43248e6i	−0.803162	+	0.954587i
$36$		0			0
$37$	−704165.	−	1.21965e6i	−0.375723	−	0.650771i	0.614712	−	0.788751i	$-0.289272\pi$
$37$	−704165.	−	1.21965e6i	−0.375723	−	0.650771i	−0.990435	+	0.137981i	$0.955939\pi$
$38$	−391432.	−	225993.i	−0.187725	−	0.108383i
$39$		0			0
$40$	−564563.	−	977852.i	−0.220532	−	0.381973i
$41$			1.52892e6i			0.541065i	0.962711	+	0.270533i	$0.0871998\pi$
$41$			1.52892e6i			0.541065i	−0.962711	+	0.270533i	$0.912800\pi$
$42$		0			0
$43$	−1.63384e6			−0.477898			−0.238949	−	0.971032i	$-0.576803\pi$
$43$	−1.63384e6			−0.477898			−0.238949	+	0.971032i	$0.576803\pi$
$44$	2.86090e6	−	1.65174e6i	0.763293	−	0.440687i
$45$		0			0
$46$	2.55473e6	−	4.42492e6i	0.570576	−	0.988267i
$47$	8.03301e6	−	4.63786e6i	1.64622	−	0.950443i	0.667658	−	0.744468i	$-0.267297\pi$
$47$	8.03301e6	−	4.63786e6i	1.64622	−	0.950443i	0.978557	−	0.205975i	$-0.0660365\pi$
$48$		0			0
$49$	4.42595e6	−	3.69377e6i	0.767754	−	0.640745i
$50$		−	2.45855e6i		−	0.393368i
$51$		0			0
$52$	169330.	−	293288.i	0.0231590	−	0.0401126i
$53$	2.72214e6	+	1.57163e6i	0.344991	+	0.199181i	0.662477	−	0.749082i	$-0.269505\pi$
$53$	2.72214e6	+	1.57163e6i	0.344991	+	0.199181i	−0.317486	+	0.948263i	$0.602839\pi$
$54$		0			0
$55$	2.01228e7			2.19907
$56$	1.18486e6	+	3.26891e6i	0.120480	+	0.332392i
$57$		0			0
$58$	−91184.2	−	157936.i	−0.00805764	−	0.0139562i
$59$	−1.44666e7	−	8.35227e6i	−1.19387	−	0.689282i	−0.234689	−	0.972071i	$-0.575407\pi$
$59$	−1.44666e7	−	8.35227e6i	−1.19387	−	0.689282i	−0.959182	+	0.282789i	$0.908740\pi$
$60$		0			0
$61$	4.37015e6	+	7.56932e6i	0.315629	+	0.546686i	0.979571	−	0.201099i	$-0.0644511\pi$
$61$	4.37015e6	+	7.56932e6i	0.315629	+	0.546686i	−0.663942	+	0.747784i	$0.731118\pi$
$62$			2.95397e6i			0.199913i
$63$		0			0
$64$	−2.09715e6			−0.125000
$65$	1.78653e6	−	1.03146e6i	0.100082	−	0.0577826i
$66$		0			0
$67$	1.40514e7	−	2.43378e7i	0.697302	−	1.20776i	−0.272096	−	0.962270i	$-0.587717\pi$
$67$	1.40514e7	−	2.43378e7i	0.697302	−	1.20776i	0.969398	−	0.245493i	$-0.0789497\pi$
$68$	8.20644e6	−	4.73799e6i	0.383812	−	0.221594i
$69$		0			0
$70$	−3.70563e6	+	2.08533e7i	−0.154337	+	0.868524i
$71$		−	4.04624e7i		−	1.59228i	−0.605115	−	0.796138i	$-0.706873\pi$
$71$		−	4.04624e7i		−	1.59228i	0.605115	−	0.796138i	$-0.293127\pi$
$72$		0			0
$73$	5.58975e6	−	9.68173e6i	0.196834	−	0.340927i	−0.750666	−	0.660682i	$-0.770267\pi$
$73$	5.58975e6	−	9.68173e6i	0.196834	−	0.340927i	0.947500	+	0.319755i	$0.103601\pi$
$74$	−1.37988e7	−	7.96672e6i	−0.460164	−	0.265676i
$75$		0			0
$76$	−5.11364e6			−0.153277
$77$	−6.10102e7	−	1.08415e7i	−1.73556	−	0.308410i
$78$		0			0
$79$	3.35502e7	+	5.81107e7i	0.861364	+	1.49193i	0.870612	+	0.491969i	$0.163723\pi$
$79$	3.35502e7	+	5.81107e7i	0.861364	+	1.49193i	−0.00924818	+	0.999957i	$0.502944\pi$
$80$	−1.10631e7	−	6.38730e6i	−0.270096	−	0.155940i
$81$		0			0
$82$	8.64888e6	+	1.49803e7i	0.191295	+	0.331333i
$83$		−	4.64460e7i		−	0.978670i	−0.872096	−	0.489335i	$-0.837240\pi$
$83$		−	4.64460e7i		−	0.978670i	0.872096	−	0.489335i	$-0.162760\pi$
$84$		0			0
$85$	5.77220e7			1.10577
$86$	−1.60083e7	+	9.24239e6i	−0.292652	+	0.168963i
$87$		0			0
$88$	1.86873e7	−	3.23673e7i	0.311613	−	0.539730i
$89$	−3.34937e7	+	1.93376e7i	−0.533831	+	0.308207i	−0.742575	−	0.669763i	$-0.766396\pi$
$89$	−3.34937e7	+	1.93376e7i	−0.533831	+	0.308207i	0.208744	+	0.977970i	$0.433062\pi$
$90$		0			0
$91$	−5.97229e6	+	2.16474e6i	−0.0870915	+	0.0315674i
$92$		−	5.78069e7i		−	0.806916i
$93$		0			0
$94$	5.24714e7	−	9.08831e7i	0.672065	−	1.16405i
$95$	−2.69761e7	−	1.55746e7i	−0.331195	−	0.191216i
$96$		0			0
$97$	9.56235e7			1.08013			0.540067	−	0.841622i	$-0.318399\pi$
$97$	9.56235e7			1.08013			0.540067	+	0.841622i	$0.318399\pi$
$98$	2.24701e7	−	6.12283e7i	0.243614	−	0.663817i
$99$		0			0
$100$	−1.39077e7	−	2.40888e7i	−0.139077	−	0.240888i
$101$	1.35263e8	+	7.80940e7i	1.29985	+	0.750468i	0.980378	−	0.197129i	$-0.0631616\pi$
$101$	1.35263e8	+	7.80940e7i	1.29985	+	0.750468i	0.319470	+	0.947596i	$0.396495\pi$
$102$		0			0
$103$	−5.25743e7	−	9.10614e7i	−0.467116	−	0.809069i	0.532178	−	0.846633i	$-0.321374\pi$
$103$	−5.25743e7	−	9.10614e7i	−0.467116	−	0.809069i	−0.999294	+	0.0375634i	$0.988040\pi$
$104$		−	3.83149e6i		−	0.0327518i
$105$		0			0
$106$	3.55619e7			0.281684
$107$	−1.38955e8	+	8.02260e7i	−1.06008	+	0.612040i	−0.925456	−	0.378856i	$-0.876318\pi$
$107$	−1.38955e8	+	8.02260e7i	−1.06008	+	0.612040i	−0.134629	+	0.990896i	$0.542984\pi$
$108$		0			0
$109$	−8.80822e7	+	1.52563e8i	−0.623996	+	1.08079i	0.364738	+	0.931110i	$0.381159\pi$
$109$	−8.80822e7	+	1.52563e8i	−0.623996	+	1.08079i	−0.988734	+	0.149683i	$0.952175\pi$
$110$	1.97163e8	−	1.13832e8i	1.34665	−	0.777487i
$111$		0			0
$112$	3.01009e7	+	2.53261e7i	0.191297	+	0.160952i
$113$		−	1.00369e8i		−	0.615579i	−0.951454	−	0.307789i	$-0.900411\pi$
$113$		−	1.00369e8i		−	0.615579i	0.951454	−	0.307789i	$-0.0995892\pi$
$114$		0			0
$115$	1.76063e8	−	3.04950e8i	1.00664	−	1.74356i
$116$	−1.78684e6	−	1.03163e6i	−0.00986855	−	0.00569761i
$117$		0			0
$118$	−1.88990e8			−0.974791
$119$	−1.75007e8	−	3.10988e7i	−0.872705	−	0.155080i
$120$		0			0
$121$	2.25858e8	+	3.91197e8i	1.05364	+	1.82496i
$122$	8.56371e7	+	4.94426e7i	0.386565	+	0.223183i
$123$		0			0
$124$	1.67102e7	+	2.89429e7i	0.0706797	+	0.122421i
$125$			1.35136e8i			0.553517i
$126$		0			0
$127$	−1.64854e8			−0.633701			−0.316850	−	0.948476i	$-0.602625\pi$
$127$	−1.64854e8			−0.633701			−0.316850	+	0.948476i	$0.602625\pi$
$128$	−2.05478e7	+	1.18633e7i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	1.16696e7	−	2.02123e7i	0.0408585	−	0.0707690i
$131$	−1.72726e8	+	9.97232e7i	−0.586505	+	0.338619i	−0.763714	−	0.645554i	$-0.776626\pi$
$131$	−1.72726e8	+	9.97232e7i	−0.586505	+	0.338619i	0.177209	+	0.984173i	$0.443293\pi$
$132$		0			0
$133$	7.33974e7	+	6.17545e7i	0.234571	+	0.197361i
$134$		−	3.17947e8i		−	0.986134i
$135$		0			0
$136$	5.36042e7	−	9.28452e7i	0.156691	−	0.271396i
$137$	4.44341e8	+	2.56540e8i	1.26135	+	0.728238i	0.973335	−	0.229389i	$-0.0736729\pi$
$137$	4.44341e8	+	2.56540e8i	1.26135	+	0.728238i	0.288010	+	0.957627i	$0.407006\pi$
$138$		0			0
$139$	−1.58313e8			−0.424089			−0.212045	−	0.977260i	$-0.568012\pi$
$139$	−1.58313e8			−0.424089			−0.212045	+	0.977260i	$0.568012\pi$
$140$	8.16562e7	+	2.25282e8i	0.212558	+	0.586426i
$141$		0			0
$142$	−2.28890e8	−	3.96449e8i	−0.562955	−	0.975066i
$143$	5.91351e7	+	3.41417e7i	0.141417	+	0.0816470i
$144$		0			0
$145$	−6.28409e6	−	1.08844e7i	−0.0142158	−	0.0246224i
$146$		−	1.26482e8i		−	0.278366i
$147$		0			0
$148$	−1.80266e8			−0.375723
$149$	3.10376e8	−	1.79196e8i	0.629714	−	0.363565i	−0.150928	−	0.988545i	$-0.548226\pi$
$149$	3.10376e8	−	1.79196e8i	0.629714	−	0.363565i	0.780641	+	0.624980i	$0.214893\pi$
$150$		0			0
$151$	1.69312e8	−	2.93257e8i	0.325671	−	0.564079i	−0.655977	−	0.754781i	$-0.727743\pi$
$151$	1.69312e8	−	2.93257e8i	0.325671	−	0.564079i	0.981648	+	0.190702i	$0.0610763\pi$
$152$	−5.01033e7	+	2.89271e7i	−0.0938624	+	0.0541915i
$153$		0			0
$154$	−6.59105e8	+	2.38901e8i	−1.17185	+	0.424752i
$155$			2.03577e8i			0.352698i
$156$		0			0
$157$	−2.32041e8	+	4.01907e8i	−0.381915	+	0.661495i	−0.991336	−	0.131351i	$-0.958068\pi$
$157$	−2.32041e8	+	4.01907e8i	−0.381915	+	0.661495i	0.609421	+	0.792847i	$0.291402\pi$
$158$	6.57447e8	+	3.79577e8i	1.05495	+	0.609077i
$159$		0			0
$160$	−1.44528e8			−0.220532
$161$	−6.98100e8	+	8.29717e8i	−1.03900	+	1.23489i
$162$		0			0
$163$	1.56909e7	+	2.71775e7i	0.0222279	+	0.0384998i	0.876925	−	0.480627i	$-0.159591\pi$
$163$	1.56909e7	+	2.71775e7i	0.0222279	+	0.0384998i	−0.854698	+	0.519126i	$0.826257\pi$
$164$	1.69483e8	+	9.78509e7i	0.234288	+	0.135266i
$165$		0			0
$166$	−2.62738e8	−	4.55076e8i	−0.346012	−	0.599310i
$167$			1.40833e9i			1.81067i	0.424700	+	0.905334i	$0.360380\pi$
$167$			1.40833e9i			1.81067i	−0.424700	+	0.905334i	$0.639620\pi$
$168$		0			0
$169$	−8.08731e8			−0.991419
$170$	5.65558e8	−	3.26525e8i	0.677145	−	0.390950i
$171$		0			0
$172$	−1.04566e8	+	1.81113e8i	−0.119475	+	0.206936i
$173$	−7.55605e8	+	4.36249e8i	−0.843549	+	0.487023i	−0.858469	−	0.512865i	$-0.828584\pi$
$173$	−7.55605e8	+	4.36249e8i	−0.843549	+	0.487023i	0.0149198	+	0.999889i	$0.495251\pi$
$174$		0			0
$175$	−9.12858e7	+	5.13707e8i	−0.0973310	+	0.547725i
$176$		−	4.22845e8i		−	0.440687i
$177$		0			0
$178$	−2.18780e8	+	3.78938e8i	−0.217935	+	0.377475i
$179$	−8.41666e8	−	4.85936e8i	−0.819838	−	0.473333i	0.0305229	−	0.999534i	$-0.490283\pi$
$179$	−8.41666e8	−	4.85936e8i	−0.819838	−	0.473333i	−0.850360	+	0.526201i	$0.823616\pi$
$180$		0			0
$181$	−1.54973e9			−1.44392			−0.721958	−	0.691937i	$-0.756758\pi$
$181$	−1.54973e9			−1.44392			−0.721958	+	0.691937i	$0.756758\pi$
$182$	−4.62707e7	+	5.49944e7i	−0.0421716	+	0.0501225i
$183$		0			0
$184$	−3.27005e8	−	5.66390e8i	−0.285288	−	0.494133i
$185$	−9.50961e8	−	5.49037e8i	−0.811850	−	0.468722i
$186$		0			0
$187$	9.55312e8	+	1.65465e9i	0.781230	+	1.35313i
$188$		−	1.18729e9i		−	0.950443i
$189$		0			0
$190$	−3.52414e8			−0.270420
$191$	−2.28740e8	+	1.32063e8i	−0.171873	+	0.0992312i	−0.583469	−	0.812135i	$-0.698305\pi$
$191$	−2.28740e8	+	1.32063e8i	−0.171873	+	0.0992312i	0.411595	+	0.911367i	$0.364972\pi$
$192$		0			0
$193$	−7.73659e7	+	1.34002e8i	−0.0557597	+	0.0965787i	−0.892558	−	0.450933i	$-0.851091\pi$
$193$	−7.73659e7	+	1.34002e8i	−0.0557597	+	0.0965787i	0.836798	+	0.547511i	$0.184425\pi$
$194$	9.36915e8	−	5.40928e8i	0.661444	−	0.381885i
$195$		0			0
$196$	−1.26198e8	−	7.27023e8i	−0.0855124	−	0.492633i
$197$			2.10067e9i			1.39474i	0.716712	+	0.697369i	$0.245646\pi$
$197$			2.10067e9i			1.39474i	−0.716712	+	0.697369i	$0.754354\pi$
$198$		0			0
$199$	−1.13927e9	+	1.97327e9i	−0.726464	+	1.25827i	0.231904	+	0.972739i	$0.425504\pi$
$199$	−1.13927e9	+	1.97327e9i	−0.726464	+	1.25827i	−0.958368	+	0.285534i	$0.907829\pi$
$200$	−2.72533e8	−	1.57347e8i	−0.170333	−	0.0983420i
$201$		0			0
$202$	1.76706e9			1.06132
$203$	1.31885e7	+	3.63859e7i	0.00776627	+	0.0214264i
$204$		0			0
$205$	5.96050e8	+	1.03239e9i	0.337495	+	0.584558i
$206$	−1.03024e9	−	5.94811e8i	−0.572098	−	0.330301i
$207$		0			0
$208$	−2.16742e7	−	3.75408e7i	−0.0115795	−	0.0200563i
$209$		−	1.03106e9i		−	0.540377i
$210$		0			0
$211$	3.13704e9			1.58267			0.791335	−	0.611383i	$-0.209387\pi$
$211$	3.13704e9			1.58267			0.791335	+	0.611383i	$0.209387\pi$
$212$	3.48434e8	−	2.01169e8i	0.172495	−	0.0995903i
$213$		0			0
$214$	−9.07653e8	+	1.57210e9i	−0.432778	+	0.749593i
$215$	−1.10323e9	+	6.36952e8i	−0.516314	+	0.298094i
$216$		0			0
$217$	1.09681e8	−	6.17224e8i	0.0494643	−	0.278358i
$218$			1.99307e9i			0.882464i
$219$		0			0
$220$	1.28786e9	−	2.23064e9i	0.549766	−	0.952223i
$221$	1.69628e8	+	9.79348e7i	0.0711097	+	0.0410552i
$222$		0			0
$223$	−4.46779e9			−1.80665			−0.903323	−	0.428961i	$-0.858880\pi$
$223$	−4.46779e9			−1.80665			−0.903323	+	0.428961i	$0.858880\pi$
$224$	4.38194e8	+	7.78672e7i	0.174050	+	0.0309287i
$225$		0			0
$226$	−5.67770e8	−	9.83407e8i	−0.217640	−	0.376964i
$227$	2.67606e9	+	1.54503e9i	1.00784	+	0.581879i	0.910559	−	0.413378i	$-0.135651\pi$
$227$	2.67606e9	+	1.54503e9i	1.00784	+	0.581879i	0.0972837	+	0.995257i	$0.468985\pi$
$228$		0			0
$229$	−1.00286e9	−	1.73700e9i	−0.364668	−	0.631623i	0.624055	−	0.781380i	$-0.285484\pi$
$229$	−1.00286e9	−	1.73700e9i	−0.364668	−	0.631623i	−0.988723	+	0.149757i	$0.952151\pi$
$230$		−	3.98384e9i		−	1.42361i
$231$		0			0
$232$	−2.33432e7			−0.00805764
$233$	2.53529e9	−	1.46375e9i	0.860210	−	0.496642i	−0.00387268	−	0.999993i	$-0.501233\pi$
$233$	2.53529e9	−	1.46375e9i	0.860210	−	0.496642i	0.864083	+	0.503350i	$0.167899\pi$
$234$		0			0
$235$	3.61614e9	−	6.26333e9i	1.18570	−	2.05369i
$236$	−1.85172e9	+	1.06909e9i	−0.596935	+	0.344641i
$237$		0			0
$238$	−1.89063e9	+	6.85284e8i	−0.589249	+	0.213581i
$239$			1.79081e9i			0.548855i	0.961608	+	0.274427i	$0.0884883\pi$
$239$			1.79081e9i			0.548855i	−0.961608	+	0.274427i	$0.911512\pi$
$240$		0			0
$241$	1.40746e9	−	2.43779e9i	0.417222	−	0.722650i	−0.578437	−	0.815727i	$-0.696337\pi$
$241$	1.40746e9	−	2.43779e9i	0.417222	−	0.722650i	0.995659	+	0.0930775i	$0.0296704\pi$
$242$	4.42589e9	+	2.55529e9i	1.29044	+	0.745038i
$243$		0			0
$244$	1.11876e9			0.315629
$245$	1.54856e9	−	4.21964e9i	0.429798	−	1.17114i
$246$		0			0
$247$	−5.28498e7	−	9.15386e7i	−0.0141989	−	0.0245933i
$248$	3.27452e8	+	1.89054e8i	0.0865647	+	0.0499781i
$249$		0			0
$250$	7.64445e8	+	1.32406e9i	0.195698	+	0.338959i
$251$		−	7.21522e9i		−	1.81784i	−0.416976	−	0.908918i	$-0.636910\pi$
$251$		−	7.21522e9i		−	1.81784i	0.416976	−	0.908918i	$-0.363090\pi$
$252$		0			0
$253$	1.16555e10			2.84478
$254$	−1.61523e9	+	9.32554e8i	−0.388061	+	0.224047i
$255$		0			0
$256$	−1.34218e8	+	2.32472e8i	−0.0312500	+	0.0541266i
$257$	−5.64972e9	+	3.26187e9i	−1.29507	+	0.747711i	−0.979549	−	0.201206i	$-0.935514\pi$
$257$	−5.64972e9	+	3.26187e9i	−1.29507	+	0.747711i	−0.315525	+	0.948917i	$0.602181\pi$
$258$		0			0
$259$	2.58741e9	+	2.17697e9i	0.574997	+	0.483786i
$260$		−	2.64053e8i		−	0.0577826i
$261$		0			0
$262$	−1.12824e9	+	1.95417e9i	−0.239440	+	0.414722i
$263$	−1.34840e9	−	7.78501e8i	−0.281836	−	0.162718i	0.352418	−	0.935843i	$-0.385359\pi$
$263$	−1.34840e9	−	7.78501e8i	−0.281836	−	0.162718i	−0.634254	+	0.773124i	$0.718693\pi$
$264$		0			0
$265$	2.45080e9			0.496964
$266$	1.06848e9	+	1.89869e8i	0.213423	+	0.0379252i
$267$		0			0
$268$	−1.79858e9	−	3.11523e9i	−0.348651	−	0.603881i
$269$	−2.73106e9	−	1.57678e9i	−0.521581	−	0.301135i	0.216000	−	0.976393i	$-0.430699\pi$
$269$	−2.73106e9	−	1.57678e9i	−0.521581	−	0.301135i	−0.737581	+	0.675258i	$0.764032\pi$
$270$		0			0
$271$	5.86553e8	+	1.01594e9i	0.108750	+	0.188361i	0.915264	−	0.402854i	$-0.131982\pi$
$271$	5.86553e8	+	1.01594e9i	0.108750	+	0.188361i	−0.806514	+	0.591215i	$0.798648\pi$
$272$		−	1.21292e9i		−	0.221594i
$273$		0			0
$274$	5.80484e9			1.02988
$275$	4.85698e9	−	2.80418e9i	0.849249	−	0.490314i
$276$		0			0
$277$	1.24447e9	−	2.15548e9i	0.211380	−	0.366121i	−0.740767	−	0.671762i	$-0.765538\pi$
$277$	1.24447e9	−	2.15548e9i	0.211380	−	0.366121i	0.952147	+	0.305641i	$0.0988709\pi$
$278$	−1.55114e9	+	8.95553e8i	−0.259701	+	0.149938i
$279$		0			0
$280$	2.07445e9	+	1.74538e9i	0.337498	+	0.283961i
$281$		−	3.91158e9i		−	0.627375i	−0.949526	−	0.313688i	$-0.898436\pi$
$281$		−	3.91158e9i		−	0.627375i	0.949526	−	0.313688i	$-0.101564\pi$
$282$		0			0
$283$	−3.37066e9	+	5.83815e9i	−0.525495	+	0.910184i	0.474064	+	0.880490i	$0.342787\pi$
$283$	−3.37066e9	+	5.83815e9i	−0.525495	+	0.910184i	−0.999559	+	0.0296938i	$0.990547\pi$
$284$	−4.48531e9	−	2.58960e9i	−0.689476	−	0.398069i
$285$		0			0
$286$	7.72538e8			0.115466
$287$	−1.25094e9	−	3.45122e9i	−0.184378	−	0.508681i
$288$		0			0
$289$	−7.47580e8	−	1.29485e9i	−0.107168	−	0.185621i
$290$	−1.23143e8	−	7.10964e7i	−0.0174107	−	0.0100521i
$291$		0			0
$292$	−7.15488e8	−	1.23926e9i	−0.0984172	−	0.170464i
$293$		−	2.94512e7i		−	0.00399607i	−0.999998	−	0.00199803i	$-0.999364\pi$
$293$		−	2.94512e7i		−	0.00399607i	0.999998	−	0.00199803i	$-0.000635994\pi$
$294$		0			0
$295$	−1.30245e10			−1.71979
$296$	−1.76624e9	+	1.01974e9i	−0.230082	+	0.132838i
$297$		0			0
$298$	2.02737e9	−	3.51150e9i	0.257079	−	0.445275i
$299$	1.03479e9	−	5.97438e8i	0.129470	−	0.0747495i
$300$		0			0
$301$	3.68806e9	−	1.33678e9i	0.449295	−	0.162853i
$302$		−	3.83109e9i		−	0.460569i
$303$		0			0
$304$	−3.27273e8	+	5.66854e8i	−0.0383192	+	0.0663708i
$305$	5.90180e9	+	3.40741e9i	0.682001	+	0.393754i
$306$		0			0
$307$	3.89847e9			0.438875			0.219438	−	0.975627i	$-0.429578\pi$
$307$	3.89847e9			0.438875			0.219438	+	0.975627i	$0.429578\pi$
$308$	−5.10645e9	+	6.06920e9i	−0.567435	+	0.674417i
$309$		0			0
$310$	1.15161e9	+	1.99464e9i	0.124697	+	0.215982i
$311$	3.80983e9	+	2.19960e9i	0.407252	+	0.235127i	0.689608	−	0.724182i	$-0.257783\pi$
$311$	3.80983e9	+	2.19960e9i	0.407252	+	0.235127i	−0.282356	+	0.959310i	$0.591116\pi$
$312$		0			0
$313$	−2.94059e9	−	5.09325e9i	−0.306377	−	0.530661i	0.671190	−	0.741286i	$-0.265784\pi$
$313$	−2.94059e9	−	5.09325e9i	−0.306377	−	0.530661i	−0.977567	+	0.210625i	$0.932450\pi$
$314$			5.25049e9i			0.540109i
$315$		0			0
$316$	8.58885e9			0.861364
$317$	9.34717e9	−	5.39659e9i	0.925643	−	0.534420i	0.0402117	−	0.999191i	$-0.487197\pi$
$317$	9.34717e9	−	5.39659e9i	0.925643	−	0.534420i	0.885431	+	0.464771i	$0.153863\pi$
$318$		0			0
$319$	2.08006e8	−	3.60277e8i	0.0200869	−	0.0347916i
$320$	−1.41608e9	+	8.17575e8i	−0.135048	+	0.0779700i
$321$		0			0
$322$	−2.14637e9	+	1.20786e10i	−0.199655	+	1.12355i
$323$		−	2.95757e9i		−	0.271722i
$324$		0			0
$325$	2.87473e8	−	4.97918e8i	0.0257670	−	0.0446297i
$326$	3.07478e8	+	1.77522e8i	0.0272235	+	0.0157175i
$327$		0			0
$328$	2.21411e9			0.191295
$329$	−1.43382e10	+	1.70415e10i	−1.22380	+	1.45453i
$330$		0			0
$331$	−3.47821e9	−	6.02443e9i	−0.289763	−	0.501885i	0.683990	−	0.729492i	$-0.260243\pi$
$331$	−3.47821e9	−	6.02443e9i	−0.289763	−	0.501885i	−0.973753	+	0.227607i	$0.926910\pi$
$332$	−5.14860e9	−	2.97254e9i	−0.423776	−	0.244667i
$333$		0			0
$334$	7.96672e9	+	1.37988e10i	0.640168	+	1.10880i
$335$		−	2.19118e10i		−	1.73980i
$336$		0			0
$337$	−1.06229e10			−0.823612			−0.411806	−	0.911272i	$-0.635102\pi$
$337$	−1.06229e10			−0.823612			−0.411806	+	0.911272i	$0.635102\pi$
$338$	−7.92391e9	+	4.57487e9i	−0.607117	+	0.350519i
$339$		0			0
$340$	3.69421e9	−	6.39856e9i	0.276443	−	0.478814i
$341$	−5.83571e9	+	3.36925e9i	−0.431595	+	0.249181i
$342$		0			0
$343$	−6.96847e9	+	1.19592e10i	−0.503456	+	0.864021i
$344$			2.36605e9i			0.168963i
$345$		0			0
$346$	−4.93559e9	+	8.54870e9i	−0.344378	+	0.596479i
$347$	3.30767e9	+	1.90969e9i	0.228142	+	0.131718i	0.609714	−	0.792621i	$-0.291284\pi$
$347$	3.30767e9	+	1.90969e9i	0.228142	+	0.131718i	−0.381573	+	0.924339i	$0.624617\pi$
$348$		0			0
$349$	−2.32842e10			−1.56950			−0.784748	−	0.619815i	$-0.787208\pi$
$349$	−2.32842e10			−1.56950			−0.784748	+	0.619815i	$0.787208\pi$
$350$	2.01155e9	+	5.54967e9i	0.134047	+	0.369824i
$351$		0			0
$352$	−2.39197e9	−	4.14302e9i	−0.155807	−	0.269865i
$353$	2.16865e10	+	1.25207e10i	1.39666	+	0.806362i	0.994041	−	0.109005i	$-0.0347666\pi$
$353$	2.16865e10	+	1.25207e10i	1.39666	+	0.806362i	0.402619	+	0.915368i	$0.368100\pi$
$354$		0			0
$355$	−1.57743e10	−	2.73218e10i	−0.993198	−	1.72027i
$356$			4.95043e9i			0.308207i
$357$		0			0
$358$	−1.09955e10			−0.669395
$359$	1.61578e9	−	9.32869e8i	0.0972755	−	0.0561620i	−0.450573	−	0.892740i	$-0.648780\pi$
$359$	1.61578e9	−	9.32869e8i	0.0972755	−	0.0561620i	0.547849	+	0.836578i	$0.315447\pi$
$360$		0			0
$361$	7.69377e9	−	1.33260e10i	0.453013	−	0.784641i
$362$	−1.51842e10	+	8.76660e9i	−0.884215	+	0.510502i
$363$		0			0
$364$	−1.42263e8	+	8.00579e8i	−0.00810377	+	0.0456036i
$365$		−	8.71666e9i		−	0.491110i
$366$		0			0
$367$	−1.42157e10	+	2.46223e10i	−0.783616	+	1.35726i	0.146206	+	0.989254i	$0.453294\pi$
$367$	−1.42157e10	+	2.46223e10i	−0.783616	+	1.35726i	−0.929822	+	0.368009i	$0.880040\pi$
$368$	−6.40797e9	−	3.69964e9i	−0.349405	−	0.201729i
$369$		0			0
$370$	−1.24233e10			−0.662872
$371$	−7.43056e9	−	1.32041e9i	−0.392217	−	0.0696970i
$372$		0			0
$373$	1.45252e10	+	2.51585e10i	0.750392	+	1.29972i	0.947633	+	0.319362i	$0.103469\pi$
$373$	1.45252e10	+	2.51585e10i	0.750392	+	1.29972i	−0.197241	+	0.980355i	$0.563198\pi$
$374$	1.87202e10	+	1.08081e10i	0.956807	+	0.552413i
$375$		0			0
$376$	−6.71634e9	−	1.16330e10i	−0.336032	−	0.582025i
$377$		−	4.26479e7i		−	0.00211122i
$378$		0			0
$379$	1.73844e9			0.0842562			0.0421281	−	0.999112i	$-0.486586\pi$
$379$	1.73844e9			0.0842562			0.0421281	+	0.999112i	$0.486586\pi$
$380$	−3.45294e9	+	1.99355e9i	−0.165598	+	0.0956079i
$381$		0			0
$382$	−1.49412e9	+	2.58790e9i	−0.0701671	+	0.121533i
$383$	−1.46545e10	+	8.46078e9i	−0.681046	+	0.393202i	−0.800249	−	0.599668i	$-0.795299\pi$
$383$	−1.46545e10	+	8.46078e9i	−0.681046	+	0.393202i	0.119203	+	0.992870i	$0.461966\pi$
$384$		0			0
$385$	−4.54231e10	+	1.64642e10i	−2.06745	+	0.749372i
$386$			1.75059e9i			0.0788561i
$387$		0			0
$388$	6.11990e9	−	1.06000e10i	0.270033	−	0.467712i
$389$	2.16794e10	+	1.25166e10i	0.946778	+	0.546623i	0.892079	−	0.451880i	$-0.149247\pi$
$389$	2.16794e10	+	1.25166e10i	0.946778	+	0.546623i	0.0546996	+	0.998503i	$0.482580\pi$
$390$		0			0
$391$	3.34337e10			1.43046
$392$	−5.34915e9	−	6.40946e9i	−0.226538	−	0.271442i
$393$		0			0
$394$	1.18832e10	+	2.05823e10i	0.493114	+	0.854099i
$395$	4.53089e10	+	2.61591e10i	1.86121	+	1.07457i
$396$		0			0
$397$	−2.48881e9	−	4.31075e9i	−0.100191	−	0.173536i	0.811572	−	0.584252i	$-0.198612\pi$
$397$	−2.48881e9	−	4.31075e9i	−0.100191	−	0.173536i	−0.911763	+	0.410716i	$0.865279\pi$
$398$			2.57787e10i			1.02738i
$399$		0			0
$400$	−3.56036e9			−0.139077
$401$	−1.60657e10	+	9.27552e9i	−0.621329	+	0.358724i	−0.777386	−	0.629024i	$-0.783455\pi$
$401$	−1.60657e10	+	9.27552e9i	−0.621329	+	0.358724i	0.156057	+	0.987748i	$0.450122\pi$
$402$		0			0
$403$	−3.45402e8	+	5.98254e8i	−0.0130950	+	0.0226812i
$404$	1.73136e10	−	9.99603e9i	0.649924	−	0.375234i
$405$		0			0
$406$	3.35050e8	+	2.81902e8i	0.0123312	+	0.0103751i
$407$		−	3.63468e10i		−	1.32461i
$408$		0			0
$409$	2.58593e10	−	4.47897e10i	0.924111	−	1.60061i	0.131126	−	0.991366i	$-0.458141\pi$
$409$	2.58593e10	−	4.47897e10i	0.924111	−	1.60061i	0.792985	−	0.609241i	$-0.208526\pi$
$410$	1.16801e10	+	6.74353e9i	0.413345	+	0.238645i
$411$		0			0
$412$	−1.34590e10			−0.467116
$413$	3.94890e10	+	7.01721e9i	1.35730	+	0.241193i
$414$		0			0
$415$	−1.81070e10	−	3.13622e10i	−0.610455	−	1.05734i
$416$	−4.24726e8	−	2.45216e8i	−0.0141819	−	0.00818794i
$417$		0			0
$418$	−5.83253e9	−	1.01022e10i	−0.191052	−	0.330912i
$419$		−	1.89186e9i		−	0.0613808i	−0.999529	−	0.0306904i	$-0.990229\pi$
$419$		−	1.89186e9i		−	0.0613808i	0.999529	−	0.0306904i	$-0.00977059\pi$
$420$		0			0
$421$	5.72596e10			1.82272			0.911361	−	0.411609i	$-0.135033\pi$
$421$	5.72596e10			1.82272			0.911361	+	0.411609i	$0.135033\pi$
$422$	3.07366e10	−	1.77458e10i	0.969183	−	0.559558i
$423$		0			0
$424$	2.27596e9	−	3.94209e9i	0.0704210	−	0.121973i
$425$	1.39322e10	−	8.04374e9i	0.427034	−	0.246548i
$426$		0			0
$427$	−1.60578e10	−	1.35106e10i	−0.483031	−	0.406408i
$428$			2.05378e10i			0.612040i
$429$		0			0
$430$	−7.20629e9	+	1.24817e10i	−0.210784	+	0.365089i
$431$	−2.34325e10	−	1.35288e10i	−0.679062	−	0.392057i	0.120439	−	0.992721i	$-0.461570\pi$
$431$	−2.34325e10	−	1.35288e10i	−0.679062	−	0.392057i	−0.799502	+	0.600664i	$0.794903\pi$
$432$		0			0
$433$	−3.99631e10			−1.13686			−0.568431	−	0.822731i	$-0.692449\pi$
$433$	−3.99631e10			−1.13686			−0.568431	+	0.822731i	$0.692449\pi$
$434$	−2.41690e9	−	6.66799e9i	−0.0681239	−	0.187947i
$435$		0			0
$436$	1.12745e10	+	1.95280e10i	0.311998	+	0.540397i
$437$	−1.56250e10	−	9.02112e9i	−0.428445	−	0.247363i
$438$		0			0
$439$	−1.50184e10	−	2.60126e10i	−0.404358	−	0.700368i	0.589889	−	0.807485i	$-0.299172\pi$
$439$	−1.50184e10	−	2.60126e10i	−0.404358	−	0.700368i	−0.994246	+	0.107116i	$0.965838\pi$
$440$		−	2.91410e10i		−	0.777487i
$441$		0			0
$442$	2.21601e9			0.0580608
$443$	−3.55301e10	+	2.05133e10i	−0.922531	+	0.532624i	−0.884442	−	0.466651i	$-0.845460\pi$
$443$	−3.55301e10	+	2.05133e10i	−0.922531	+	0.532624i	−0.0380893	+	0.999274i	$0.512127\pi$
$444$		0			0
$445$	−1.50775e10	+	2.61151e10i	−0.384495	+	0.665965i
$446$	−4.37752e10	+	2.52736e10i	−1.10634	+	0.638746i
$447$		0			0
$448$	4.73389e9	−	1.71586e9i	0.117518	−	0.0425961i
$449$			6.29285e9i			0.154832i	0.996999	+	0.0774162i	$0.0246670\pi$
$449$			6.29285e9i			0.154832i	−0.996999	+	0.0774162i	$0.975333\pi$
$450$		0			0
$451$	−1.97295e10	+	3.41725e10i	−0.476881	+	0.825982i
$452$	−1.11260e10	−	6.42359e9i	−0.266554	−	0.153895i
$453$		0			0
$454$	3.49599e10			0.822901
$455$	−3.18881e9	+	3.79002e9i	−0.0744017	+	0.0884291i
$456$		0			0
$457$	2.44547e10	+	4.23568e10i	0.560658	+	0.971088i	0.997439	+	0.0715201i	$0.0227850\pi$
$457$	2.44547e10	+	4.23568e10i	0.560658	+	0.971088i	−0.436781	+	0.899568i	$0.643882\pi$
$458$	−1.96519e10	−	1.13460e10i	−0.446625	−	0.257859i
$459$		0			0
$460$	−2.25360e10	−	3.90335e10i	−0.503322	−	0.871780i
$461$			3.67947e10i			0.814670i	0.913279	+	0.407335i	$0.133542\pi$
$461$			3.67947e10i			0.814670i	−0.913279	+	0.407335i	$0.866458\pi$
$462$		0			0
$463$	6.59669e10			1.43550			0.717748	−	0.696303i	$-0.245173\pi$
$463$	6.59669e10			1.43550			0.717748	+	0.696303i	$0.245173\pi$
$464$	−2.28715e8	+	1.32049e8i	−0.00493428	+	0.00284881i
$465$		0			0
$466$	1.65605e10	−	2.86836e10i	0.351179	−	0.608260i
$467$	−3.96405e10	+	2.28865e10i	−0.833435	+	0.481184i	−0.855027	−	0.518583i	$-0.826460\pi$
$467$	−3.96405e10	+	2.28865e10i	−0.833435	+	0.481184i	0.0215925	+	0.999767i	$0.493126\pi$
$468$		0			0
$469$	−1.18054e10	+	6.64342e10i	−0.243999	+	1.37309i
$470$		−	8.18239e10i		−	1.67683i
$471$		0			0
$472$	−1.20954e10	+	2.09498e10i	−0.243698	+	0.422097i
$473$	−3.65175e10	−	2.10834e10i	−0.729553	−	0.421208i
$474$		0			0
$475$	−8.68149e9			−0.170538
$476$	−1.46478e10	+	1.74094e10i	−0.285328	+	0.339122i
$477$		0			0
$478$	1.01303e10	+	1.75463e10i	0.194049	+	0.336103i
$479$	−7.57248e10	−	4.37197e10i	−1.43845	−	0.830491i	−0.440711	−	0.897649i	$-0.645274\pi$
$479$	−7.57248e10	−	4.37197e10i	−1.43845	−	0.830491i	−0.997742	+	0.0671575i	$0.978607\pi$
$480$		0			0
$481$	−1.86306e9	−	3.22692e9i	−0.0348054	−	0.0602848i
$482$		−	3.18471e10i		−	0.590041i
$483$		0			0
$484$	5.78196e10			1.05364
$485$	6.45688e10	−	3.72788e10i	1.16696	−	0.673744i
$486$		0			0
$487$	1.25118e10	−	2.16712e10i	0.222436	−	0.385271i	−0.733111	−	0.680109i	$-0.761932\pi$
$487$	1.25118e10	−	2.16712e10i	0.222436	−	0.385271i	0.955547	+	0.294838i	$0.0952657\pi$
$488$	1.09615e10	−	6.32865e9i	0.193283	−	0.111592i
$489$		0			0
$490$	−8.69713e9	−	5.01038e10i	−0.150866	−	0.869133i
$491$		−	4.17596e10i		−	0.718507i	−0.933240	−	0.359253i	$-0.883031\pi$
$491$		−	4.17596e10i		−	0.718507i	0.933240	−	0.359253i	$-0.116969\pi$
$492$		0			0
$493$	5.96663e8	−	1.03345e9i	0.0101005	−	0.0174945i
$494$	−1.03564e9	−	5.97928e8i	−0.0173901	−	0.0100402i
$495$		0			0
$496$	4.27781e9			0.0706797
$497$	3.31058e10	+	9.13356e10i	0.542598	+	1.49697i
$498$		0			0
$499$	−6.67262e9	−	1.15573e10i	−0.107620	−	0.186404i	0.807185	−	0.590298i	$-0.200990\pi$
$499$	−6.67262e9	−	1.15573e10i	−0.107620	−	0.186404i	−0.914806	+	0.403894i	$0.867656\pi$
$500$	1.49800e10	+	8.64870e9i	0.239680	+	0.138379i
$501$		0			0
$502$	−4.08154e10	−	7.06944e10i	−0.642702	−	1.11319i
$503$		−	8.73433e10i		−	1.36445i	−0.731143	−	0.682225i	$-0.761013\pi$
$503$		−	8.73433e10i		−	1.36445i	0.731143	−	0.682225i	$-0.238987\pi$
$504$		0			0
$505$	1.21780e11			1.87245
$506$	1.14200e11	−	6.59335e10i	1.74207	−	1.00578i
$507$		0			0
$508$	−1.05506e10	+	1.82743e10i	−0.158425	+	0.274400i
$509$	−7.12548e10	+	4.11390e10i	−1.06156	+	0.612889i	−0.925862	−	0.377861i	$-0.876660\pi$
$509$	−7.12548e10	+	4.11390e10i	−1.06156	+	0.612889i	−0.135694	+	0.990751i	$0.543326\pi$
$510$		0			0
$511$	−4.69626e9	+	2.64280e10i	−0.0688761	+	0.387597i
$512$			3.03700e9i			0.0441942i
$513$		0			0
$514$	−3.69038e10	+	6.39193e10i	−0.528712	+	0.915756i
$515$	−7.10006e10	−	4.09922e10i	−1.00933	−	0.582737i
$516$		0			0
$517$	2.39392e11			3.35079
$518$	3.76661e10	+	6.69328e9i	0.523156	+	0.0929651i
$519$		0			0
$520$	−1.49371e9	−	2.58718e9i	−0.0204292	−	0.0353845i
$521$	−6.46157e10	−	3.73059e10i	−0.876975	−	0.506322i	−0.00731548	−	0.999973i	$-0.502329\pi$
$521$	−6.46157e10	−	3.73059e10i	−0.876975	−	0.506322i	−0.869660	+	0.493651i	$0.835662\pi$
$522$		0			0
$523$	−2.98505e9	−	5.17026e9i	−0.0398975	−	0.0691044i	0.845387	−	0.534154i	$-0.179370\pi$
$523$	−2.98505e9	−	5.17026e9i	−0.0398975	−	0.0691044i	−0.885285	+	0.465050i	$0.846036\pi$
$524$			2.55291e10i			0.338619i
$525$		0			0
$526$	−1.76155e10			−0.230118
$527$	−1.67396e10	+	9.66464e9i	−0.217022	+	0.125298i
$528$		0			0
$529$	6.28233e10	−	1.08813e11i	0.802228	−	1.38950i
$530$	2.40128e10	−	1.38638e10i	0.304327	−	0.175703i
$531$		0			0
$532$	1.15430e10	−	4.18391e9i	0.144103	−	0.0522319i
$533$			4.04518e9i			0.0501221i
$534$		0			0
$535$	−6.25522e10	+	1.08344e11i	−0.763532	+	1.32248i
$536$	−3.52449e10	−	2.03486e10i	−0.427009	−	0.246534i
$537$		0			0
$538$	−3.56784e10			−0.425869
$539$	1.46588e11	−	2.54451e10i	1.73678	−	0.301474i
$540$		0			0
$541$	2.29828e10	+	3.98074e10i	0.268296	+	0.464702i	0.968422	−	0.249317i	$-0.0802062\pi$
$541$	2.29828e10	+	3.98074e10i	0.268296	+	0.464702i	−0.700126	+	0.714019i	$0.746873\pi$
$542$	1.14940e10	+	6.63609e9i	0.133191	+	0.0768980i
$543$		0			0
$544$	−6.86134e9	−	1.18842e10i	−0.0783454	−	0.135698i
$545$			1.37355e11i			1.55690i
$546$		0			0
$547$	7.80036e10			0.871295			0.435648	−	0.900117i	$-0.356519\pi$
$547$	7.80036e10			0.871295			0.435648	+	0.900117i	$0.356519\pi$
$548$	5.68756e10	−	3.28372e10i	0.630673	−	0.364119i
$549$		0			0
$550$	3.17256e10	−	5.49504e10i	0.346705	−	0.600510i
$551$	−5.57694e8	+	3.21985e8i	−0.00605048	+	0.00349324i
$552$		0			0
$553$	−1.23278e11	−	1.03723e11i	−1.31821	−	1.10910i
$554$		−	2.81591e10i		−	0.298937i
$555$		0			0
$556$	−1.01320e10	+	1.75492e10i	−0.106022	+	0.183636i
$557$	−6.47127e10	−	3.73619e10i	−0.672308	−	0.388157i	0.124642	−	0.992202i	$-0.460222\pi$
$557$	−6.47127e10	−	3.73619e10i	−0.672308	−	0.388157i	−0.796951	+	0.604044i	$0.793555\pi$
$558$		0			0
$559$	−4.32278e9			−0.0442706
$560$	3.01987e10	+	5.36632e9i	0.307069	+	0.0545663i
$561$		0			0
$562$	−2.21273e10	−	3.83255e10i	−0.221811	−	0.384187i
$563$	8.31674e10	+	4.80167e10i	0.827789	+	0.477924i	0.853095	−	0.521755i	$-0.174723\pi$
$563$	8.31674e10	+	4.80167e10i	0.827789	+	0.477924i	−0.0253059	+	0.999680i	$0.508056\pi$
$564$		0			0
$565$	−3.91287e10	−	6.77728e10i	−0.383974	−	0.665062i
$566$			7.62692e10i			0.743162i
$567$		0			0
$568$	−5.85959e10			−0.562955
$569$	−5.54903e10	+	3.20374e10i	−0.529381	+	0.305638i	−0.740764	−	0.671765i	$-0.765536\pi$
$569$	−5.54903e10	+	3.20374e10i	−0.529381	+	0.305638i	0.211383	+	0.977403i	$0.432203\pi$
$570$		0			0
$571$	−6.16135e10	+	1.06718e11i	−0.579604	+	1.00390i	0.415920	+	0.909401i	$0.363460\pi$
$571$	−6.16135e10	+	1.06718e11i	−0.579604	+	1.00390i	−0.995525	+	0.0945029i	$0.969874\pi$
$572$	7.56929e9	−	4.37013e9i	0.0707084	−	0.0408235i
$573$		0			0
$574$	−3.17797e10	−	2.67386e10i	−0.292754	−	0.246315i
$575$		−	9.81395e10i		−	0.897785i
$576$		0			0
$577$	2.48192e10	−	4.29881e10i	0.223916	−	0.387834i	−0.732078	−	0.681221i	$-0.761449\pi$
$577$	2.48192e10	−	4.29881e10i	0.223916	−	0.387834i	0.955994	+	0.293387i	$0.0947826\pi$
$578$	−1.46495e10	−	8.45790e9i	−0.131254	−	0.0757794i
$579$		0			0
$580$	−1.60873e9			−0.0142158
$581$	3.80014e10	+	1.04842e11i	0.333500	+	0.920093i
$582$		0			0
$583$	4.05613e10	+	7.02542e10i	0.351106	+	0.608133i
$584$	−1.40206e10	−	8.09482e9i	−0.120536	−	0.0695915i
$585$		0			0
$586$	−1.66601e8	−	2.88562e8i	−0.00141282	−	0.00244708i
$587$		−	7.25661e10i		−	0.611198i	−0.952160	−	0.305599i	$-0.901143\pi$
$587$		−	7.25661e10i		−	0.611198i	0.952160	−	0.305599i	$-0.0988566\pi$
$588$		0			0
$589$	1.04309e10			0.0866685
$590$	−1.27614e11	+	7.36779e10i	−1.05315	+	0.608036i
$591$		0			0
$592$	−1.15370e10	+	1.99827e10i	−0.0939307	+	0.162693i
$593$	−1.49261e11	+	8.61757e10i	−1.20705	+	0.696893i	−0.962115	−	0.272645i	$-0.912102\pi$
$593$	−1.49261e11	+	8.61757e10i	−1.20705	+	0.696893i	−0.244940	+	0.969538i	$0.578768\pi$
$594$		0			0
$595$	−1.30296e11	+	4.72273e10i	−1.03959	+	0.376812i
$596$		−	4.58741e10i		−	0.363565i
$597$		0			0
$598$	6.75924e9	−	1.17074e10i	0.0528559	−	0.0915491i
$599$	−8.64440e10	−	4.99085e10i	−0.671472	−	0.387674i	0.125162	−	0.992136i	$-0.460055\pi$
$599$	−8.64440e10	−	4.99085e10i	−0.671472	−	0.387674i	−0.796634	+	0.604462i	$0.793388\pi$
$600$		0			0
$601$	−1.58869e10			−0.121770			−0.0608850	−	0.998145i	$-0.519392\pi$
$601$	−1.58869e10			−0.121770			−0.0608850	+	0.998145i	$0.519392\pi$
$602$	2.85734e10	−	3.39605e10i	0.217559	−	0.258576i
$603$		0			0
$604$	−2.16719e10	−	3.75369e10i	−0.162836	−	0.282040i
$605$	3.05016e11	+	1.76101e11i	2.27668	+	1.31444i
$606$		0			0
$607$	−1.17901e11	−	2.04211e11i	−0.868486	−	1.50426i	−0.863543	−	0.504275i	$-0.831760\pi$
$607$	−1.17901e11	−	2.04211e11i	−0.868486	−	1.50426i	−0.00494305	−	0.999988i	$-0.501573\pi$
$608$			7.40535e9i			0.0541915i
$609$		0			0
$610$	7.71008e10			0.556852
$611$	2.12535e10	−	1.22707e10i	0.152499	−	0.0880452i
$612$		0			0
$613$	1.74582e10	−	3.02385e10i	0.123640	−	0.214150i	−0.797561	−	0.603239i	$-0.793877\pi$
$613$	1.74582e10	−	3.02385e10i	0.123640	−	0.214150i	0.921200	+	0.389089i	$0.127210\pi$
$614$	3.81971e10	−	2.20531e10i	0.268755	−	0.155166i
$615$		0			0
$616$	−1.57002e10	+	8.83522e10i	−0.109039	+	0.613613i
$617$			2.41723e11i			1.66793i	0.551819	+	0.833964i	$0.313934\pi$
$617$			2.41723e11i			1.66793i	−0.551819	+	0.833964i	$0.686066\pi$
$618$		0			0
$619$	−1.23409e11	+	2.13750e11i	−0.840589	+	1.45594i	0.0488090	+	0.998808i	$0.484457\pi$
$619$	−1.23409e11	+	2.13750e11i	−0.840589	+	1.45594i	−0.889398	+	0.457134i	$0.848876\pi$
$620$	2.25668e10	+	1.30289e10i	0.152723	+	0.0881744i
$621$		0			0
$622$	4.97714e10			0.332520
$623$	5.97834e10	−	7.10548e10i	0.396852	−	0.471673i
$624$		0			0
$625$	9.51256e10	+	1.64762e11i	0.623415	+	1.07979i
$626$	−5.76235e10	−	3.32689e10i	−0.375234	−	0.216641i
$627$		0			0
$628$	2.97013e10	+	5.14441e10i	0.190957	+	0.330748i
$629$		−	1.04260e11i		−	0.666064i
$630$		0			0
$631$	3.28164e10			0.207002			0.103501	−	0.994629i	$-0.466996\pi$
$631$	3.28164e10			0.207002			0.103501	+	0.994629i	$0.466996\pi$
$632$	8.41532e10	−	4.85859e10i	0.527476	−	0.304538i
$633$		0			0
$634$	6.10555e10	−	1.05751e11i	0.377892	−	0.654528i
$635$	−1.11316e11	+	6.42683e10i	−0.684640	+	0.395277i
$636$		0			0
$637$	1.17101e10	−	9.77289e9i	0.0711216	−	0.0593561i
$638$		−	4.70664e9i		−	0.0284072i
$639$		0			0
$640$	−9.24980e9	+	1.60211e10i	−0.0551331	+	0.0954934i
$641$	7.20582e10	+	4.16028e10i	0.426826	+	0.246428i	0.697994	−	0.716104i	$-0.254076\pi$
$641$	7.20582e10	+	4.16028e10i	0.426826	+	0.246428i	−0.271167	+	0.962532i	$0.587410\pi$
$642$		0			0
$643$	−2.05289e11			−1.20094			−0.600472	−	0.799646i	$-0.705020\pi$
$643$	−2.05289e11			−1.20094			−0.600472	+	0.799646i	$0.705020\pi$
$644$	4.72968e10	+	1.30487e11i	0.274972	+	0.758620i
$645$		0			0
$646$	−1.67305e10	−	2.89781e10i	−0.0960681	−	0.166395i
$647$	2.52702e11	+	1.45897e11i	1.44208	+	0.832588i	0.997989	−	0.0633912i	$-0.0201916\pi$
$647$	2.52702e11	+	1.45897e11i	1.44208	+	0.832588i	0.444096	+	0.895979i	$0.353525\pi$
$648$		0			0
$649$	−2.15559e11	−	3.73359e11i	−1.21503	−	2.10450i
$650$		−	6.50477e9i		−	0.0364400i
$651$		0			0
$652$	4.01687e9			0.0222279
$653$	−2.34842e11	+	1.35586e11i	−1.29158	+	0.745697i	−0.978935	−	0.204172i	$-0.934550\pi$
$653$	−2.34842e11	+	1.35586e11i	−1.29158	+	0.745697i	−0.312650	+	0.949868i	$0.601217\pi$
$654$		0			0
$655$	−7.77542e10	+	1.34674e11i	−0.422434	+	0.731677i
$656$	2.16938e10	−	1.25249e10i	0.117144	−	0.0676331i
$657$		0			0
$658$	−4.40841e10	+	2.48081e11i	−0.235168	+	1.32340i
$659$		−	3.60700e11i		−	1.91251i	−0.292529	−	0.956257i	$-0.594497\pi$
$659$		−	3.60700e11i		−	1.91251i	0.292529	−	0.956257i	$-0.405503\pi$
$660$		0			0
$661$	−8.46973e10	+	1.46700e11i	−0.443674	+	0.768465i	−0.997959	−	0.0638616i	$-0.979658\pi$
$661$	−8.46973e10	+	1.46700e11i	−0.443674	+	0.768465i	0.554285	+	0.832327i	$0.312992\pi$
$662$	−6.81587e10	−	3.93514e10i	−0.354886	−	0.204894i
$663$		0			0
$664$	−6.72610e10			−0.346012
$665$	7.36359e10	+	1.30851e10i	0.376533	+	0.0669100i
$666$		0			0
$667$	−3.63986e9	−	6.30442e9i	−0.0183900	−	0.0318524i
$668$	1.56115e11	+	9.01332e10i	0.784042	+	0.452667i
$669$		0			0
$670$	−1.23952e11	−	2.14691e11i	−0.615111	−	1.06540i
$671$			2.25573e11i			1.11275i
$672$		0			0
$673$	−1.16293e11			−0.566885			−0.283442	−	0.958989i	$-0.591476\pi$
$673$	−1.16293e11			−0.566885			−0.283442	+	0.958989i	$0.591476\pi$
$674$	−1.04083e11	+	6.00921e10i	−0.504357	+	0.291191i
$675$		0			0
$676$	−5.17588e10	+	8.96488e10i	−0.247855	+	0.429297i
$677$	1.79007e10	−	1.03350e10i	0.0852150	−	0.0491989i	−0.456787	−	0.889576i	$-0.651000\pi$
$677$	1.79007e10	−	1.03350e10i	0.0852150	−	0.0491989i	0.542002	+	0.840377i	$0.317667\pi$
$678$		0			0
$679$	−2.15850e11	+	7.82377e10i	−1.01548	+	0.368076i
$680$		−	8.35904e10i		−	0.390950i
$681$		0			0
$682$	−3.81187e10	+	6.60235e10i	−0.176198	+	0.305184i
$683$	−1.75494e11	−	1.01321e11i	−0.806452	−	0.465605i	0.0392701	−	0.999229i	$-0.487497\pi$
$683$	−1.75494e11	−	1.01321e11i	−0.806452	−	0.465605i	−0.845722	+	0.533623i	$0.820830\pi$
$684$		0			0
$685$	4.00049e11			1.81698
$686$	−6.25575e8	+	1.56595e11i	−0.00282477	+	0.707101i
$687$		0			0
$688$	1.33844e10	+	2.31825e10i	0.0597373	+	0.103468i
$689$	7.20219e9	+	4.15818e9i	0.0319586	+	0.0184513i
$690$		0			0
$691$	−8.23091e10	−	1.42564e11i	−0.361024	−	0.625311i	0.627106	−	0.778934i	$-0.284239\pi$
$691$	−8.23091e10	−	1.42564e11i	−0.361024	−	0.625311i	−0.988130	+	0.153623i	$0.950906\pi$
$692$			1.11680e11i			0.487023i
$693$		0			0
$694$	4.32113e10			0.186277
$695$	−1.06899e11	+	6.17183e10i	−0.458179	+	0.264530i
$696$		0			0
$697$	−5.65938e10	+	9.80234e10i	−0.239794	+	0.415335i
$698$	−2.28138e11	+	1.31716e11i	−0.961116	+	0.554901i
$699$		0			0
$700$	5.11027e10	+	4.29964e10i	0.212839	+	0.179077i
$701$		−	2.11004e11i		−	0.873814i	−0.899507	−	0.436907i	$-0.856074\pi$
$701$		−	2.11004e11i		−	0.873814i	0.899507	−	0.436907i	$-0.143926\pi$
$702$		0			0
$703$	−2.81316e10	+	4.87254e10i	−0.115179	+	0.199496i
$704$	−4.68729e10	−	2.70621e10i	−0.190823	−	0.110172i
$705$		0			0
$706$	2.83311e11			1.14037
$707$	−3.69223e11	−	6.56110e10i	−1.47778	−	0.262603i
$708$		0			0
$709$	1.64436e11	+	2.84812e11i	0.650748	+	1.12713i	0.982942	+	0.183917i	$0.0588778\pi$
$709$	1.64436e11	+	2.84812e11i	0.650748	+	1.12713i	−0.332194	+	0.943211i	$0.607789\pi$
$710$	−3.09111e11	−	1.78466e11i	−1.21641	−	0.702297i
$711$		0			0
$712$	2.80039e10	+	4.85041e10i	0.108968	+	0.188738i
$713$			1.17916e11i			0.456261i
$714$		0			0
$715$	5.32405e10			0.203713
$716$	−1.07733e11	+	6.21998e10i	−0.409919	+	0.236667i
$717$		0			0
$718$	1.05542e10	−	1.82804e10i	0.0397125	−	0.0687841i
$719$	2.84195e11	−	1.64080e11i	1.06341	−	0.613960i	0.137036	−	0.990566i	$-0.456242\pi$
$719$	2.84195e11	−	1.64080e11i	1.06341	−	0.613960i	0.926374	+	0.376606i	$0.122909\pi$
$720$		0			0
$721$	1.93181e11	+	1.62537e11i	0.714863	+	0.601466i
$722$		−	1.74090e11i		−	0.640656i
$723$		0			0
$724$	−9.91828e10	+	1.71790e11i	−0.360979	+	0.625234i
$725$	−3.03354e9	−	1.75141e9i	−0.0109799	−	0.00633923i
$726$		0			0
$727$	−2.26272e11			−0.810015			−0.405007	−	0.914313i	$-0.632731\pi$
$727$	−2.26272e11			−0.810015			−0.405007	+	0.914313i	$0.632731\pi$
$728$	3.13487e9	+	8.64881e9i	0.0111608	+	0.0307915i
$729$		0			0
$730$	−4.93089e10	−	8.54055e10i	−0.173634	−	0.300742i
$731$	−1.04750e11	−	6.04774e10i	−0.366847	−	0.211799i
$732$		0			0
$733$	−7.42855e10	−	1.28666e11i	−0.257329	−	0.445706i	0.708197	−	0.706015i	$-0.249509\pi$
$733$	−7.42855e10	−	1.28666e11i	−0.257329	−	0.445706i	−0.965525	+	0.260309i	$0.916176\pi$
$734$			3.21664e11i			1.10820i
$735$		0			0
$736$	−8.37134e10			−0.285288
$737$	6.28119e11	−	3.62645e11i	2.12898	−	1.22917i
$738$		0			0
$739$	2.25140e11	−	3.89955e11i	0.754876	−	1.30748i	−0.190559	−	0.981676i	$-0.561030\pi$
$739$	2.25140e11	−	3.89955e11i	0.754876	−	1.30748i	0.945436	−	0.325809i	$-0.105637\pi$
$740$	−1.21723e11	+	7.02768e10i	−0.405925	+	0.234361i
$741$		0			0
$742$	−8.02737e10	+	2.90963e10i	−0.264824	+	0.0959890i
$743$		−	3.77594e11i		−	1.23900i	−0.784998	−	0.619498i	$-0.787336\pi$
$743$		−	3.77594e11i		−	1.23900i	0.784998	−	0.619498i	$-0.212664\pi$
$744$		0			0
$745$	1.39719e11	−	2.42000e11i	0.453555	−	0.785580i
$746$	2.84636e11	+	1.64334e11i	0.919039	+	0.530607i
$747$		0			0
$748$	2.44560e11			0.781230
$749$	2.48024e11	−	2.94785e11i	0.788071	−	0.936651i
$750$		0			0
$751$	−1.02313e11	−	1.77211e11i	−0.321641	−	0.557099i	0.659186	−	0.751980i	$-0.270901\pi$
$751$	−1.02313e11	−	1.77211e11i	−0.321641	−	0.557099i	−0.980827	+	0.194882i	$0.937568\pi$
$752$	−1.31613e11	−	7.59867e10i	−0.411554	−	0.237611i
$753$		0			0
$754$	−2.41253e8	−	4.17863e8i	−0.000746427	−	0.00129285i
$755$		−	2.64025e11i		−	0.812563i
$756$		0			0
$757$	−8.70658e10			−0.265133			−0.132567	−	0.991174i	$-0.542322\pi$
$757$	−8.70658e10			−0.265133			−0.132567	+	0.991174i	$0.542322\pi$
$758$	1.70331e10	−	9.83408e9i	0.0515962	−	0.0297891i
$759$		0			0
$760$	−2.25545e10	+	3.90655e10i	−0.0676050	+	0.117095i
$761$	−2.84741e11	+	1.64395e11i	−0.849006	+	0.490174i	−0.860315	−	0.509762i	$-0.829733\pi$
$761$	−2.84741e11	+	1.64395e11i	−0.849006	+	0.490174i	0.0113090	+	0.999936i	$0.496400\pi$
$762$		0			0
$763$	7.40027e10	−	4.16447e11i	0.218348	−	1.22874i
$764$			3.38082e10i			0.0992312i
$765$		0			0
$766$	−9.57229e10	+	1.65797e11i	−0.278036	+	0.481572i
$767$	−3.82753e10	−	2.20983e10i	−0.110595	−	0.0638523i
$768$		0			0
$769$	−9.18048e10			−0.262519			−0.131259	−	0.991348i	$-0.541902\pi$
$769$	−9.18048e10			−0.262519			−0.131259	+	0.991348i	$0.541902\pi$
$770$	−3.51918e11	+	4.18268e11i	−1.00110	+	1.18985i
$771$		0			0
$772$	9.90284e9	+	1.71522e10i	0.0278799	+	0.0482893i
$773$	5.47968e11	+	3.16370e11i	1.53475	+	0.886088i	0.999133	+	0.0416263i	$0.0132539\pi$
$773$	5.47968e11	+	3.16370e11i	1.53475	+	0.886088i	0.535616	+	0.844462i	$0.320079\pi$
$774$		0			0
$775$	2.83691e10	+	4.91367e10i	0.0786392	+	0.136207i
$776$		−	1.38478e11i		−	0.381885i
$777$		0			0
$778$	2.83218e11			0.773041
$779$	5.28976e10	−	3.05405e10i	0.143644	−	0.0829327i
$780$		0			0
$781$	5.22136e11	−	9.04365e11i	1.40339	−	2.43075i
$782$	3.27582e11	−	1.89129e11i	0.875976	−	0.505745i
$783$		0			0
$784$	−8.86681e10	−	3.25402e10i	−0.234695	−	0.0861304i
$785$			3.61845e11i			0.952892i
$786$		0			0
$787$	1.28463e11	−	2.22504e11i	0.334872	−	0.580015i	−0.648589	−	0.761139i	$-0.724640\pi$
$787$	1.28463e11	−	2.22504e11i	0.334872	−	0.580015i	0.983460	+	0.181125i	$0.0579737\pi$
$788$	2.32862e11	+	1.34443e11i	0.603939	+	0.348685i
$789$		0			0
$790$	5.91913e11			1.51967
$791$	8.21200e10	+	2.26561e11i	0.209770	+	0.578735i
$792$		0			0
$793$	1.15624e10	+	2.00267e10i	0.0292386	+	0.0506428i
$794$	−4.87705e10	−	2.81577e10i	−0.122709	−	0.0708459i
$795$		0			0
$796$	1.45827e11	+	2.52579e11i	0.363232	+	0.629136i
$797$		−	3.19145e11i		−	0.790961i	−0.918474	−	0.395480i	$-0.870578\pi$
$797$		−	3.19145e11i		−	0.790961i	0.918474	−	0.395480i	$-0.129422\pi$
$798$		0			0
$799$	6.86691e11			1.68490
$800$	−3.48843e10	+	2.01404e10i	−0.0851666	+	0.0491710i
$801$		0			0
$802$	−1.04941e11	+	1.81762e11i	−0.253656	+	0.439346i
$803$	2.49870e11	−	1.44263e11i	0.600969	−	0.346970i
$804$		0			0
$805$	−1.47920e11	+	8.32413e11i	−0.352244	+	1.98223i
$806$			7.81556e9i			0.0185191i
$807$		0			0
$808$	1.13092e11	−	1.95881e11i	0.265330	−	0.459566i
$809$	−4.48871e10	−	2.59156e10i	−0.104792	−	0.0605016i	0.446688	−	0.894690i	$-0.352603\pi$
$809$	−4.48871e10	−	2.59156e10i	−0.104792	−	0.0605016i	−0.551480	+	0.834188i	$0.685937\pi$
$810$		0			0
$811$	−4.00088e11			−0.924851			−0.462426	−	0.886658i	$-0.653021\pi$
$811$	−4.00088e11			−0.924851			−0.462426	+	0.886658i	$0.653021\pi$
$812$	4.87749e9	+	8.66731e8i	0.0112195	+	0.00199370i
$813$		0			0
$814$	−2.05608e11	−	3.56124e11i	−0.468320	−	0.811155i
$815$	2.11903e10	+	1.22342e10i	0.0480293	+	0.0277297i
$816$		0			0
$817$	3.26362e10	+	5.65276e10i	0.0732507	+	0.126874i
$818$		−	5.85130e11i		−	1.30689i
$819$		0			0
$820$	1.52589e11			0.337495
$821$	−1.01508e11	+	5.86055e10i	−0.223422	+	0.128993i	−0.607534	−	0.794294i	$-0.707841\pi$
$821$	−1.01508e11	+	5.86055e10i	−0.223422	+	0.128993i	0.384112	+	0.923287i	$0.374508\pi$
$822$		0			0
$823$	5.46164e10	−	9.45984e10i	0.119048	−	0.206198i	−0.800342	−	0.599543i	$-0.795349\pi$
$823$	5.46164e10	−	9.45984e10i	0.119048	−	0.206198i	0.919391	+	0.393345i	$0.128682\pi$
$824$	−1.31871e11	+	7.61358e10i	−0.286049	+	0.165151i
$825$		0			0
$826$	4.26607e11	−	1.54629e11i	0.916448	−	0.332178i
$827$		−	7.08230e11i		−	1.51409i	−0.653362	−	0.757046i	$-0.726642\pi$
$827$		−	7.08230e11i		−	1.51409i	0.653362	−	0.757046i	$-0.273358\pi$
$828$		0			0
$829$	3.10465e10	−	5.37741e10i	0.0657347	−	0.113856i	−0.831285	−	0.555847i	$-0.812394\pi$
$829$	3.10465e10	−	5.37741e10i	0.0657347	−	0.113856i	0.897020	+	0.441991i	$0.145728\pi$
$830$	−3.54823e11	−	2.04857e11i	−0.747652	−	0.431657i
$831$		0			0
$832$	−5.54860e9			−0.0115795
$833$	4.20487e11	−	7.29890e10i	0.873317	−	0.151592i
$834$		0			0
$835$	5.49038e11	+	9.50962e11i	1.12942	+	1.95622i
$836$	−1.14294e11	−	6.59875e10i	−0.233990	−	0.135094i
$837$		0			0
$838$	−1.07020e10	−	1.85363e10i	−0.0217014	−	0.0375879i
$839$		−	7.16019e11i		−	1.44503i	−0.691356	−	0.722515i	$-0.742986\pi$
$839$		−	7.16019e11i		−	1.44503i	0.691356	−	0.722515i	$-0.257014\pi$
$840$		0			0
$841$	4.99987e11			0.999481
$842$	5.61028e11	−	3.23909e11i	1.11618	−	0.644429i
$843$		0			0
$844$	2.00770e11	−	3.47745e11i	0.395667	−	0.685316i
$845$	−5.46087e11	+	3.15284e11i	−1.07111	+	0.618407i
$846$		0			0
$847$	−8.29899e11	−	6.98253e11i	−1.61247	−	1.35669i
$848$		−	5.14992e10i		−	0.0995903i
$849$		0			0
$850$	9.10045e10	−	1.57624e11i	0.174336	−	0.301959i
$851$	−5.50814e11	−	3.18013e11i	−1.05024	−	0.606354i
$852$		0			0
$853$	−4.62404e11			−0.873424			−0.436712	−	0.899601i	$-0.643857\pi$
$853$	−4.62404e11			−0.873424			−0.436712	+	0.899601i	$0.643857\pi$
$854$	−2.33761e11	−	4.15395e10i	−0.439482	−	0.0780961i
$855$		0			0
$856$	1.16180e11	+	2.01229e11i	0.216389	+	0.374796i
$857$	3.27193e10	+	1.88905e10i	0.0606570	+	0.0350203i	0.530022	−	0.847984i	$-0.322184\pi$
$857$	3.27193e10	+	1.88905e10i	0.0606570	+	0.0350203i	−0.469365	+	0.883004i	$0.655517\pi$
$858$		0			0
$859$	2.93184e11	+	5.07809e11i	0.538477	+	0.932670i	0.998986	+	0.0450151i	$0.0143336\pi$
$859$	2.93184e11	+	5.07809e11i	0.538477	+	0.932670i	−0.460509	+	0.887655i	$0.652333\pi$
$860$			1.63060e11i			0.298094i
$861$		0			0
$862$	−3.06121e11			−0.554452
$863$	1.31160e11	−	7.57251e10i	0.236460	−	0.136520i	−0.377089	−	0.926177i	$-0.623075\pi$
$863$	1.31160e11	−	7.57251e10i	0.236460	−	0.136520i	0.613549	+	0.789657i	$0.289742\pi$
$864$		0			0
$865$	−3.40143e11	+	5.89145e11i	−0.607571	+	1.05234i
$866$	−3.91557e11	+	2.26066e11i	−0.696183	+	0.401941i
$867$		0			0
$868$	−6.14005e10	−	5.16606e10i	−0.108167	−	0.0910082i
$869$			1.73176e12i			3.03674i
$870$		0			0
$871$	3.71769e10	−	6.43923e10i	0.0645953	−	0.111882i
$872$	2.20935e11	+	1.27557e11i	0.382118	+	0.220616i
$873$		0			0
$874$	−2.04125e11			−0.349824
$875$	−1.10566e11	−	3.05042e11i	−0.188621	−	0.520387i
$876$		0			0
$877$	−2.79915e11	−	4.84827e11i	−0.473182	−	0.819575i	0.526347	−	0.850270i	$-0.323561\pi$
$877$	−2.79915e11	−	4.84827e11i	−0.473182	−	0.819575i	−0.999529	+	0.0306947i	$0.990228\pi$
$878$	−2.94300e11	−	1.69914e11i	−0.495235	−	0.285924i
$879$		0			0
$880$	−1.64846e11	−	2.85522e11i	−0.274883	−	0.476112i
$881$		−	2.92022e11i		−	0.484743i	−0.970184	−	0.242371i	$-0.922075\pi$
$881$		−	2.92022e11i		−	0.484743i	0.970184	−	0.242371i	$-0.0779253\pi$
$882$		0			0
$883$	2.88065e11			0.473857			0.236929	−	0.971527i	$-0.423859\pi$
$883$	2.88065e11			0.473857			0.236929	+	0.971527i	$0.423859\pi$
$884$	2.17124e10	−	1.25357e10i	0.0355548	−	0.0205276i
$885$		0			0
$886$	−2.32081e11	+	4.01977e11i	−0.376622	+	0.652328i
$887$	−5.79275e11	+	3.34444e11i	−0.935815	+	0.540293i	−0.888646	−	0.458594i	$-0.848353\pi$
$887$	−5.79275e11	+	3.34444e11i	−0.935815	+	0.540293i	−0.0471692	+	0.998887i	$0.515020\pi$
$888$		0			0
$889$	3.72123e11	−	1.34881e11i	0.595772	−	0.215945i
$890$			3.41166e11i			0.543758i
$891$		0			0
$892$	−2.85938e11	+	4.95260e11i	−0.451661	+	0.782301i
$893$	−3.20921e11	−	1.85284e11i	−0.504653	−	0.291361i
$894$		0			0
$895$	−7.57769e11			−1.18099
$896$	3.66761e10	−	4.35908e10i	0.0569050	−	0.0676337i
$897$		0			0
$898$	3.55977e10	+	6.16571e10i	0.0547415	+	0.0948151i
$899$	3.64483e9	+	2.10434e9i	0.00558005	+	0.00322165i
$900$		0			0
$901$	1.16349e11	+	2.01523e11i	0.176549	+	0.305792i
$902$			4.46428e11i			0.674412i
$903$		0			0
$904$	−1.45349e11			−0.217640
$905$	−1.04644e12	+	6.04163e11i	−1.55998	+	0.900657i
$906$		0			0
$907$	−4.59412e11	+	7.95724e11i	−0.678848	+	1.17580i	0.296480	+	0.955039i	$0.404187\pi$
$907$	−4.59412e11	+	7.95724e11i	−0.678848	+	1.17580i	−0.975328	+	0.220761i	$0.929146\pi$
$908$	3.42536e11	−	1.97763e11i	0.503922	−	0.290939i
$909$		0			0
$910$	−9.80427e9	+	5.51730e10i	−0.0142972	+	0.0804565i
$911$			5.97229e11i			0.867097i	0.901130	+	0.433548i	$0.142739\pi$
$911$			5.97229e11i			0.867097i	−0.901130	+	0.433548i	$0.857261\pi$
$912$		0			0
$913$	5.99349e11	−	1.03810e12i	0.862575	−	1.49402i
$914$	4.79213e11	+	2.76674e11i	0.686663	+	0.396445i
$915$		0			0
$916$	−2.56732e11			−0.364668
$917$	3.08300e11	−	3.66426e11i	0.436010	−	0.518214i
$918$		0			0
$919$	−3.20081e11	−	5.54397e11i	−0.448743	−	0.777246i	0.549561	−	0.835453i	$-0.314795\pi$
$919$	−3.20081e11	−	5.54397e11i	−0.448743	−	0.777246i	−0.998305	+	0.0582073i	$0.981462\pi$
$920$	−4.41614e11	−	2.54966e11i	−0.616441	−	0.355903i
$921$		0			0
$922$	2.08142e11	+	3.60513e11i	0.288029	+	0.498882i
$923$		−	1.07055e11i		−	0.147502i
$924$		0			0
$925$	−3.06040e11			−0.418034
$926$	6.46341e11	−	3.73165e11i	0.879058	−	0.507524i
$927$		0			0
$928$	−1.49396e9	+	2.58762e9i	−0.00201441	+	0.00348906i
$929$	5.18326e11	−	2.99255e11i	0.695889	−	0.401772i	−0.109926	−	0.993940i	$-0.535061\pi$
$929$	5.18326e11	−	2.99255e11i	0.695889	−	0.401772i	0.805814	+	0.592168i	$0.201728\pi$
$930$		0			0
$931$	−2.16206e11	−	7.93453e10i	−0.287786	−	0.105614i
$932$		−	3.74720e11i		−	0.496642i
$933$		0			0
$934$	−2.58931e11	+	4.48481e11i	−0.340248	+	0.589327i
$935$	1.29013e12	+	7.44857e11i	1.68806	+	0.974600i
$936$		0			0
$937$	7.39512e10			0.0959372			0.0479686	−	0.998849i	$-0.484725\pi$
$937$	7.39512e10			0.0959372			0.0479686	+	0.998849i	$0.484725\pi$
$938$	2.60140e11	+	7.17700e11i	0.336043	+	0.927111i
$939$		0			0
$940$	−4.62866e11	−	8.01707e11i	−0.592848	−	1.02684i
$941$	−1.52415e11	−	8.79969e10i	−0.194388	−	0.112230i	0.399647	−	0.916669i	$-0.369133\pi$
$941$	−1.52415e11	−	8.79969e10i	−0.194388	−	0.112230i	−0.594035	+	0.804439i	$0.702466\pi$
$942$		0			0
$943$	3.45243e11	+	5.97978e11i	0.436594	+	0.756204i
$944$			2.73687e11i			0.344641i
$945$		0			0
$946$	−4.77063e11			−0.595678
$947$	6.03824e11	−	3.48618e11i	0.750776	−	0.433461i	−0.0751982	−	0.997169i	$-0.523959\pi$
$947$	6.03824e11	−	3.48618e11i	0.750776	−	0.433461i	0.825974	+	0.563708i	$0.190626\pi$
$948$		0			0
$949$	1.47892e10	−	2.56157e10i	0.0182340	−	0.0315821i
$950$	−8.50609e10	+	4.91099e10i	−0.104432	+	0.0602941i
$951$		0			0
$952$	−4.50358e10	+	2.53437e11i	−0.0548290	+	0.308548i
$953$		−	1.12350e11i		−	0.136208i	−0.997678	−	0.0681040i	$-0.978305\pi$
$953$		−	1.12350e11i		−	0.136208i	0.997678	−	0.0681040i	$-0.0216950\pi$
$954$		0			0
$955$	−1.02970e11	+	1.78349e11i	−0.123793	+	0.214416i
$956$	1.98513e11	+	1.14612e11i	0.237661	+	0.137214i
$957$		0			0
$958$	−9.89264e11			−1.17449
$959$	−1.21291e12	−	2.15534e11i	−1.43401	−	0.254824i
$960$		0			0
$961$	3.92360e11	+	6.79587e11i	0.460035	+	0.796804i
$962$	−3.65084e10	−	2.10782e10i	−0.0426278	−	0.0246112i
$963$		0			0
$964$	−1.80155e11	−	3.12037e11i	−0.208611	−	0.361325i
$965$			1.20644e11i			0.139123i
$966$		0			0
$967$	8.88077e10			0.101565			0.0507826	−	0.998710i	$-0.483828\pi$
$967$	8.88077e10			0.101565			0.0507826	+	0.998710i	$0.483828\pi$
$968$	5.66514e11	−	3.27077e11i	0.645222	−	0.372519i
$969$		0			0
$970$	4.21762e11	−	7.30513e11i	0.476409	−	0.825165i
$971$	−7.75014e11	+	4.47455e11i	−0.871832	+	0.503352i	−0.867957	−	0.496640i	$-0.834567\pi$
$971$	−7.75014e11	+	4.47455e11i	−0.871832	+	0.503352i	−0.00387540	+	0.999992i	$0.501234\pi$
$972$		0			0
$973$	3.57359e11	−	1.29529e11i	0.398706	−	0.144516i
$974$		−	2.83111e11i		−	0.314572i
$975$		0			0
$976$	7.16005e10	−	1.24016e11i	0.0789073	−	0.136671i
$977$	1.10216e12	+	6.36332e11i	1.20967	+	0.698402i	0.962687	−	0.270618i	$-0.0872280\pi$
$977$	1.10216e12	+	6.36332e11i	1.20967	+	0.698402i	0.246981	+	0.969020i	$0.420561\pi$
$978$		0			0
$979$	−9.98147e11			−1.08658
$980$	−3.68644e11	−	4.41717e11i	−0.399671	−	0.478894i
$981$		0			0
$982$	−2.36228e11	−	4.09159e11i	−0.254030	−	0.439994i
$983$	−2.88779e11	−	1.66726e11i	−0.309279	−	0.178563i	0.337325	−	0.941388i	$-0.390478\pi$
$983$	−2.88779e11	−	1.66726e11i	−0.309279	−	0.178563i	−0.646604	+	0.762826i	$0.723811\pi$
$984$		0			0
$985$	8.18946e11	+	1.41846e12i	0.869982	+	1.50685i
$986$		−	1.35009e10i		−	0.0142842i
$987$		0			0
$988$	−1.35296e10			−0.0141989
$989$	−6.39013e11	+	3.68935e11i	−0.667921	+	0.385624i
$990$		0			0
$991$	−6.75362e11	+	1.16976e12i	−0.700232	+	1.21284i	0.268153	+	0.963376i	$0.413587\pi$
$991$	−6.75362e11	+	1.16976e12i	−0.700232	+	1.21284i	−0.968385	+	0.249461i	$0.919746\pi$
$992$	4.19138e10	−	2.41990e10i	0.0432823	−	0.0249891i
$993$		0			0
$994$	8.41041e11	+	7.07628e11i	0.861532	+	0.724869i
$995$			1.77658e12i			1.81256i
$996$		0			0
$997$	−6.12674e11	+	1.06118e12i	−0.620082	+	1.07401i	0.369388	+	0.929275i	$0.379567\pi$
$997$	−6.12674e11	+	1.06118e12i	−0.620082	+	1.07401i	−0.989470	+	0.144738i	$0.953766\pi$
$998$	−1.30756e11	−	7.54921e10i	−0.131808	−	0.0760991i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.9.s.b.53.10	yes	20
3.2	odd	2	inner	126.9.s.b.53.1	✓	20
7.2	even	3	inner	126.9.s.b.107.1	yes	20
21.2	odd	6	inner	126.9.s.b.107.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.9.s.b.53.1	✓	20	3.2	odd	2	inner
126.9.s.b.53.10	yes	20	1.1	even	1	trivial
126.9.s.b.107.1	yes	20	7.2	even	3	inner
126.9.s.b.107.10	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)

\(f(q)\)	\(=\)	\(q+(9.79796 - 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(675.240 - 389.850i) q^{5} +(-2257.29 + 818.185i) q^{7} -1448.15i q^{8} +O(q^{10})\)	\(q+(9.79796 - 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(675.240 - 389.850i) q^{5} +(-2257.29 + 818.185i) q^{7} -1448.15i q^{8} +(4410.65 - 7639.47i) q^{10} +(22350.7 + 12904.2i) q^{11} +2645.78 q^{13} +(-17488.5 + 20785.7i) q^{14} +(-8192.00 - 14189.0i) q^{16} +(64112.8 + 37015.5i) q^{17} +(-19975.2 - 34598.0i) q^{19} -99801.6i q^{20} +291989. q^{22} +(391111. - 225808. i) q^{23} +(108654. - 188193. i) q^{25} +(25923.2 - 14966.8i) q^{26} +(-53769.9 + 302588. i) q^{28} -16119.2i q^{29} +(-130548. + 226117. i) q^{31} +(-160530. - 92681.9i) q^{32} +837566. q^{34} +(-1.20525e6 + 1.43248e6i) q^{35} +(-704165. - 1.21965e6i) q^{37} +(-391432. - 225993. i) q^{38} +(-564563. - 977852. i) q^{40} +1.52892e6i q^{41} -1.63384e6 q^{43} +(2.86090e6 - 1.65174e6i) q^{44} +(2.55473e6 - 4.42492e6i) q^{46} +(8.03301e6 - 4.63786e6i) q^{47} +(4.42595e6 - 3.69377e6i) q^{49} -2.45855e6i q^{50} +(169330. - 293288. i) q^{52} +(2.72214e6 + 1.57163e6i) q^{53} +2.01228e7 q^{55} +(1.18486e6 + 3.26891e6i) q^{56} +(-91184.2 - 157936. i) q^{58} +(-1.44666e7 - 8.35227e6i) q^{59} +(4.37015e6 + 7.56932e6i) q^{61} +2.95397e6i q^{62} -2.09715e6 q^{64} +(1.78653e6 - 1.03146e6i) q^{65} +(1.40514e7 - 2.43378e7i) q^{67} +(8.20644e6 - 4.73799e6i) q^{68} +(-3.70563e6 + 2.08533e7i) q^{70} -4.04624e7i q^{71} +(5.58975e6 - 9.68173e6i) q^{73} +(-1.37988e7 - 7.96672e6i) q^{74} -5.11364e6 q^{76} +(-6.10102e7 - 1.08415e7i) q^{77} +(3.35502e7 + 5.81107e7i) q^{79} +(-1.10631e7 - 6.38730e6i) q^{80} +(8.64888e6 + 1.49803e7i) q^{82} -4.64460e7i q^{83} +5.77220e7 q^{85} +(-1.60083e7 + 9.24239e6i) q^{86} +(1.86873e7 - 3.23673e7i) q^{88} +(-3.34937e7 + 1.93376e7i) q^{89} +(-5.97229e6 + 2.16474e6i) q^{91} -5.78069e7i q^{92} +(5.24714e7 - 9.08831e7i) q^{94} +(-2.69761e7 - 1.55746e7i) q^{95} +9.56235e7 q^{97} +(2.24701e7 - 6.12283e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 1280 q^{4} + 3778 q^{7}+O(q^{10}) \) 20 * q + 1280 * q^4 + 3778 * q^7	\( 20 q + 1280 q^{4} + 3778 q^{7} + 14816 q^{10} + 17700 q^{13} - 163840 q^{16} - 267794 q^{19} + 453568 q^{22} - 765890 q^{25} - 232448 q^{28} - 2604342 q^{31} + 4087936 q^{34} + 1127530 q^{37} - 1896448 q^{40} - 4460924 q^{43} - 180416 q^{46} - 25278034 q^{49} + 1132800 q^{52} - 18833120 q^{55} + 5146496 q^{58} - 25730232 q^{61} - 41943040 q^{64} + 58134374 q^{67} - 76724864 q^{70} + 5811002 q^{73} - 68555264 q^{76} + 74799798 q^{79} - 9883296 q^{82} + 119739328 q^{85} + 29028352 q^{88} - 479039766 q^{91} + 169364448 q^{94} - 658133608 q^{97}+O(q^{100}) \) 20 * q + 1280 * q^4 + 3778 * q^7 + 14816 * q^10 + 17700 * q^13 - 163840 * q^16 - 267794 * q^19 + 453568 * q^22 - 765890 * q^25 - 232448 * q^28 - 2604342 * q^31 + 4087936 * q^34 + 1127530 * q^37 - 1896448 * q^40 - 4460924 * q^43 - 180416 * q^46 - 25278034 * q^49 + 1132800 * q^52 - 18833120 * q^55 + 5146496 * q^58 - 25730232 * q^61 - 41943040 * q^64 + 58134374 * q^67 - 76724864 * q^70 + 5811002 * q^73 - 68555264 * q^76 + 74799798 * q^79 - 9883296 * q^82 + 119739328 * q^85 + 29028352 * q^88 - 479039766 * q^91 + 169364448 * q^94 - 658133608 * q^97

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