LMFDB - Embedded newform 126.10.g.d.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,10,Mod(37,126)]

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, 2]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, 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:	$64.8945153566$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 373x^{4} - 756x^{3} + 139129x^{2} - 140994x + 142884 $ x^6 + 373x^4 - 756x^3 + 139129x^2 - 140994x + 142884
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 5^{2}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.3
Root			$0.508109 + 0.880071i$ of defining polynomial
Character	$\chi$	$=$	126.109
Dual form			126.10.g.d.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.00000 - 13.8564i) q^{2} +(-128.000 + 221.703i) q^{4} +(1126.21 + 1950.65i) q^{5} +(5935.39 + 2263.80i) q^{7} +4096.00 q^{8} +(18019.3 - 31210.4i) q^{10} +(29000.0 - 50229.5i) q^{11} -123815. q^{13} +(-16115.0 - 100354. i) q^{14} +(-32768.0 - 56755.8i) q^{16} +(193518. - 335182. i) q^{17} +(-322875. - 559237. i) q^{19} -576619. q^{20} -928000. q^{22} +(-729071. - 1.26279e6i) q^{23} +(-1.56013e6 + 2.70222e6i) q^{25} +(990522. + 1.71564e6i) q^{26} +(-1.26162e6 + 1.02612e6i) q^{28} +7.13633e6 q^{29} +(3.83843e6 - 6.64835e6i) q^{31} +(-524288. + 908093. i) q^{32} -6.19256e6 q^{34} +(2.26860e6 + 1.41274e7i) q^{35} +(-2.14853e6 - 3.72137e6i) q^{37} +(-5.16601e6 + 8.94778e6i) q^{38} +(4.61295e6 + 7.98986e6i) q^{40} +2.96407e7 q^{41} -1.12086e7 q^{43} +(7.42400e6 + 1.28587e7i) q^{44} +(-1.16651e7 + 2.02046e7i) q^{46} +(-2.14828e7 - 3.72093e7i) q^{47} +(3.01040e7 + 2.68731e7i) q^{49} +4.99241e7 q^{50} +(1.58484e7 - 2.74502e7i) q^{52} +(3.49518e6 - 6.05383e6i) q^{53} +1.30640e8 q^{55} +(2.43113e7 + 9.27253e6i) q^{56} +(-5.70907e7 - 9.88839e7i) q^{58} +(-5.81810e7 + 1.00772e8i) q^{59} +(8.40279e6 + 1.45541e7i) q^{61} -1.22830e8 q^{62} +1.67772e7 q^{64} +(-1.39442e8 - 2.41520e8i) q^{65} +(-6.23234e7 + 1.07947e8i) q^{67} +(4.95405e7 + 8.58067e7i) q^{68} +(1.77606e8 - 1.44454e8i) q^{70} -1.67870e7 q^{71} +(1.26280e8 - 2.18724e8i) q^{73} +(-3.43765e7 + 5.95419e7i) q^{74} +1.65312e8 q^{76} +(2.85836e8 - 2.32481e8i) q^{77} +(-5.19052e6 - 8.99025e6i) q^{79} +(7.38072e7 - 1.27838e8i) q^{80} +(-2.37126e8 - 4.10714e8i) q^{82} -2.71782e8 q^{83} +8.71765e8 q^{85} +(8.96684e7 + 1.55310e8i) q^{86} +(1.18784e8 - 2.05740e8i) q^{88} +(3.52986e8 + 6.11390e8i) q^{89} +(-7.34892e8 - 2.80293e8i) q^{91} +3.73285e8 q^{92} +(-3.43725e8 + 5.95349e8i) q^{94} +(7.27250e8 - 1.25963e9i) q^{95} -1.76754e8 q^{97} +(1.31532e8 - 6.32118e8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 48 q^{2} - 768 q^{4} - 361 q^{5} + 12509 q^{7} + 24576 q^{8} - 5776 q^{10} - 37799 q^{11} - 441172 q^{13} - 38752 q^{14} - 196608 q^{16} + 781816 q^{17} - 620154 q^{19} + 184832 q^{20} + 1209568 q^{22}+ \cdots + 2185772400 q^{98}+O(q^{100}) $ 6 * q - 48 * q^2 - 768 * q^4 - 361 * q^5 + 12509 * q^7 + 24576 * q^8 - 5776 * q^10 - 37799 * q^11 - 441172 * q^13 - 38752 * q^14 - 196608 * q^16 + 781816 * q^17 - 620154 * q^19 + 184832 * q^20 + 1209568 * q^22 - 1204784 * q^23 - 4020946 * q^25 + 3529376 * q^26 - 2582272 * q^28 + 10561070 * q^29 + 12838457 * q^31 - 3145728 * q^32 - 25018112 * q^34 + 20450416 * q^35 + 8014770 * q^37 - 9922464 * q^38 - 1478656 * q^40 - 13006056 * q^41 - 45086976 * q^43 - 9676544 * q^44 - 19276544 * q^46 + 21473082 * q^47 - 92935311 * q^49 + 128670272 * q^50 + 56470016 * q^52 - 13685715 * q^53 + 610214782 * q^55 + 51236864 * q^56 - 84488560 * q^58 + 92528141 * q^59 - 7516114 * q^61 - 410830624 * q^62 + 100663296 * q^64 - 79637616 * q^65 - 137325404 * q^67 + 200144896 * q^68 + 33639760 * q^70 - 16380692 * q^71 + 394016164 * q^73 + 128236320 * q^74 + 317518848 * q^76 - 140332213 * q^77 + 35090117 * q^79 - 23658496 * q^80 + 104048448 * q^82 - 1913896010 * q^83 - 823798640 * q^85 + 360695808 * q^86 - 154824704 * q^88 + 855499686 * q^89 - 1675912546 * q^91 + 616849408 * q^92 + 343569312 * q^94 + 2705508088 * q^95 + 4021139590 * q^97 + 2185772400 * q^98

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 $

$2$	−8.00000	−	13.8564i	−0.353553	−	0.612372i
$2$	−8.00000	−	13.8564i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	1126.21	+	1950.65i	0.805849	+	1.39577i	0.915716	+	0.401825i	$0.131624\pi$
$5$	1126.21	+	1950.65i	0.805849	+	1.39577i	−0.109867	+	0.993946i	$0.535043\pi$
$6$		0			0
$7$	5935.39	+	2263.80i	0.934346	+	0.356367i
$7$	5935.39	+	2263.80i	0.934346	+	0.356367i
$8$	4096.00			0.353553
$9$		0			0
$10$	18019.3	−	31210.4i	0.569821	−	0.986960i
$11$	29000.0	−	50229.5i	0.597215	−	1.03441i	−0.396015	−	0.918244i	$-0.629607\pi$
$11$	29000.0	−	50229.5i	0.597215	−	1.03441i	0.993230	−	0.116163i	$-0.0370594\pi$
$12$		0			0
$13$	−123815.			−1.20235			−0.601173	−	0.799119i	$-0.705300\pi$
$13$	−123815.			−1.20235			−0.601173	+	0.799119i	$0.705300\pi$
$14$	−16115.0	−	100354.i	−0.112112	−	0.698162i
$15$		0			0
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	193518.	−	335182.i	0.561954	−	0.973332i	−0.435372	−	0.900250i	$-0.643383\pi$
$17$	193518.	−	335182.i	0.561954	−	0.973332i	0.997326	−	0.0730816i	$-0.0232834\pi$
$18$		0			0
$19$	−322875.	−	559237.i	−0.568386	−	0.984474i	−0.996726	−	0.0808562i	$-0.974235\pi$
$19$	−322875.	−	559237.i	−0.568386	−	0.984474i	0.428339	−	0.903618i	$-0.359099\pi$
$20$	−576619.			−0.805849
$21$		0			0
$22$	−928000.			−0.844590
$23$	−729071.	−	1.26279e6i	−0.543244	−	0.940926i	−0.998715	−	0.0506754i	$-0.983863\pi$
$23$	−729071.	−	1.26279e6i	−0.543244	−	0.940926i	0.455471	−	0.890250i	$-0.349471\pi$
$24$		0			0
$25$	−1.56013e6	+	2.70222e6i	−0.798786	+	1.38354i
$26$	990522.	+	1.71564e6i	0.425093	+	0.736283i
$27$		0			0
$28$	−1.26162e6	+	1.02612e6i	−0.387898	+	0.315492i
$29$	7.13633e6			1.87363			0.936816	−	0.349823i	$-0.113758\pi$
$29$	7.13633e6			1.87363			0.936816	+	0.349823i	$0.113758\pi$
$30$		0			0
$31$	3.83843e6	−	6.64835e6i	0.746493	−	1.29296i	−0.203001	−	0.979178i	$-0.565070\pi$
$31$	3.83843e6	−	6.64835e6i	0.746493	−	1.29296i	0.949494	−	0.313785i	$-0.101597\pi$
$32$	−524288.	+	908093.i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−6.19256e6			−0.794722
$35$	2.26860e6	+	1.41274e7i	0.255536	+	1.59131i
$36$		0			0
$37$	−2.14853e6	−	3.72137e6i	−0.188467	−	0.326434i	0.756273	−	0.654257i	$-0.227018\pi$
$37$	−2.14853e6	−	3.72137e6i	−0.188467	−	0.326434i	−0.944739	+	0.327823i	$0.893685\pi$
$38$	−5.16601e6	+	8.94778e6i	−0.401910	+	0.696128i
$39$		0			0
$40$	4.61295e6	+	7.98986e6i	0.284911	+	0.493480i
$41$	2.96407e7			1.63818			0.819089	−	0.573666i	$-0.194479\pi$
$41$	2.96407e7			1.63818			0.819089	+	0.573666i	$0.194479\pi$
$42$		0			0
$43$	−1.12086e7			−0.499967			−0.249984	−	0.968250i	$-0.580425\pi$
$43$	−1.12086e7			−0.499967			−0.249984	+	0.968250i	$0.580425\pi$
$44$	7.42400e6	+	1.28587e7i	0.298608	+	0.517203i
$45$		0			0
$46$	−1.16651e7	+	2.02046e7i	−0.384131	+	0.665335i
$47$	−2.14828e7	−	3.72093e7i	−0.642171	−	1.11227i	−0.984947	−	0.172856i	$-0.944701\pi$
$47$	−2.14828e7	−	3.72093e7i	−0.642171	−	1.11227i	0.342776	−	0.939417i	$-0.388633\pi$
$48$		0			0
$49$	3.01040e7	+	2.68731e7i	0.746006	+	0.665939i
$50$	4.99241e7			1.12965
$51$		0			0
$52$	1.58484e7	−	2.74502e7i	0.300586	−	0.520631i
$53$	3.49518e6	−	6.05383e6i	0.0608455	−	0.105387i	−0.833998	−	0.551767i	$-0.813954\pi$
$53$	3.49518e6	−	6.05383e6i	0.0608455	−	0.105387i	0.894844	+	0.446380i	$0.147287\pi$
$54$		0			0
$55$	1.30640e8			1.92506
$56$	2.43113e7	+	9.27253e6i	0.330341	+	0.125995i
$57$		0			0
$58$	−5.70907e7	−	9.88839e7i	−0.662429	−	1.14736i
$59$	−5.81810e7	+	1.00772e8i	−0.625096	+	1.08270i	0.363426	+	0.931623i	$0.381607\pi$
$59$	−5.81810e7	+	1.00772e8i	−0.625096	+	1.08270i	−0.988522	+	0.151075i	$0.951726\pi$
$60$		0			0
$61$	8.40279e6	+	1.45541e7i	0.0777032	+	0.134586i	0.902259	−	0.431195i	$-0.141908\pi$
$61$	8.40279e6	+	1.45541e7i	0.0777032	+	0.134586i	−0.824555	+	0.565781i	$0.808575\pi$
$62$	−1.22830e8			−1.05570
$63$		0			0
$64$	1.67772e7			0.125000
$65$	−1.39442e8	−	2.41520e8i	−0.968909	−	1.67820i
$66$		0			0
$67$	−6.23234e7	+	1.07947e8i	−0.377846	+	0.654448i	−0.990749	−	0.135710i	$-0.956668\pi$
$67$	−6.23234e7	+	1.07947e8i	−0.377846	+	0.654448i	0.612903	+	0.790158i	$0.290002\pi$
$68$	4.95405e7	+	8.58067e7i	0.280977	+	0.486666i
$69$		0			0
$70$	1.77606e8	−	1.44454e8i	0.884130	−	0.719097i
$71$	−1.67870e7			−0.0783991			−0.0391995	−	0.999231i	$-0.512481\pi$
$71$	−1.67870e7			−0.0783991			−0.0391995	+	0.999231i	$0.512481\pi$
$72$		0			0
$73$	1.26280e8	−	2.18724e8i	0.520454	−	0.901453i	−0.479263	−	0.877671i	$-0.659096\pi$
$73$	1.26280e8	−	2.18724e8i	0.520454	−	0.901453i	0.999717	−	0.0237817i	$-0.00757067\pi$
$74$	−3.43765e7	+	5.95419e7i	−0.133266	+	0.230823i
$75$		0			0
$76$	1.65312e8			0.568386
$77$	2.85836e8	−	2.32481e8i	0.926634	−	0.753667i
$78$		0			0
$79$	−5.19052e6	−	8.99025e6i	−0.0149930	−	0.0259687i	0.858432	−	0.512928i	$-0.171439\pi$
$79$	−5.19052e6	−	8.99025e6i	−0.0149930	−	0.0259687i	−0.873425	+	0.486959i	$0.838106\pi$
$80$	7.38072e7	−	1.27838e8i	0.201462	−	0.348943i
$81$		0			0
$82$	−2.37126e8	−	4.10714e8i	−0.579184	−	1.00318i
$83$	−2.71782e8			−0.628593			−0.314296	−	0.949325i	$-0.601769\pi$
$83$	−2.71782e8			−0.628593			−0.314296	+	0.949325i	$0.601769\pi$
$84$		0			0
$85$	8.71765e8			1.81140
$86$	8.96684e7	+	1.55310e8i	0.176765	+	0.306166i
$87$		0			0
$88$	1.18784e8	−	2.05740e8i	0.211147	−	0.365718i
$89$	3.52986e8	+	6.11390e8i	0.596352	+	1.03291i	0.993355	+	0.115095i	$0.0367171\pi$
$89$	3.52986e8	+	6.11390e8i	0.596352	+	1.03291i	−0.397002	+	0.917818i	$0.629950\pi$
$90$		0			0
$91$	−7.34892e8	−	2.80293e8i	−1.12341	−	0.428476i
$92$	3.73285e8			0.543244
$93$		0			0
$94$	−3.43725e8	+	5.95349e8i	−0.454083	+	0.786496i
$95$	7.27250e8	−	1.25963e9i	0.916067	−	1.58668i
$96$		0			0
$97$	−1.76754e8			−0.202720			−0.101360	−	0.994850i	$-0.532319\pi$
$97$	−1.76754e8			−0.202720			−0.101360	+	0.994850i	$0.532319\pi$
$98$	1.31532e8	−	6.32118e8i	0.144050	−	0.692279i
$99$		0			0
$100$	−3.99393e8	−	6.91769e8i	−0.399393	−	0.691769i
$101$	2.77453e8	−	4.80563e8i	0.265304	−	0.459520i	−0.702339	−	0.711842i	$-0.747861\pi$
$101$	2.77453e8	−	4.80563e8i	0.265304	−	0.459520i	0.967643	+	0.252322i	$0.0811944\pi$
$102$		0			0
$103$	−2.29436e8	−	3.97395e8i	−0.200861	−	0.347901i	0.747945	−	0.663760i	$-0.231041\pi$
$103$	−2.29436e8	−	3.97395e8i	−0.200861	−	0.347901i	−0.948806	+	0.315860i	$0.897707\pi$
$104$	−5.07147e8			−0.425093
$105$		0			0
$106$	−1.11846e8			−0.0860485
$107$	−2.31927e8	−	4.01709e8i	−0.171050	−	0.296268i	0.767737	−	0.640765i	$-0.221383\pi$
$107$	−2.31927e8	−	4.01709e8i	−0.171050	−	0.296268i	−0.938787	+	0.344497i	$0.888049\pi$
$108$		0			0
$109$	1.21755e9	−	2.10886e9i	0.826167	−	1.43096i	−0.0748571	−	0.997194i	$-0.523850\pi$
$109$	1.21755e9	−	2.10886e9i	0.826167	−	1.43096i	0.901024	−	0.433769i	$-0.142817\pi$
$110$	−1.04512e9	−	1.81020e9i	−0.680612	−	1.17885i
$111$		0			0
$112$	−6.60069e7	−	4.11048e8i	−0.0396377	−	0.246838i
$113$	1.85359e9			1.06945			0.534726	−	0.845025i	$-0.320415\pi$
$113$	1.85359e9			1.06945			0.534726	+	0.845025i	$0.320415\pi$
$114$		0			0
$115$	1.64217e9	−	2.84433e9i	0.875545	−	1.51649i
$116$	−9.13451e8	+	1.58214e9i	−0.468408	+	0.811306i
$117$		0			0
$118$	1.86179e9			0.884019
$119$	1.90739e9	−	1.55135e9i	0.871922	−	0.709168i
$120$		0			0
$121$	−5.03025e8	−	8.71265e8i	−0.213332	−	0.369501i
$122$	1.34445e8	−	2.32865e8i	0.0549445	−	0.0951666i
$123$		0			0
$124$	9.82637e8	+	1.70198e9i	0.373246	+	0.646482i
$125$	−2.62887e9			−0.963104
$126$		0			0
$127$	1.67106e9			0.570001			0.285000	−	0.958527i	$-0.408006\pi$
$127$	1.67106e9			0.570001			0.285000	+	0.958527i	$0.408006\pi$
$128$	−1.34218e8	−	2.32472e8i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−2.23107e9	+	3.86433e9i	−0.685122	+	1.18667i
$131$	7.98748e8	+	1.38347e9i	0.236968	+	0.410440i	0.959843	−	0.280539i	$-0.0905131\pi$
$131$	7.98748e8	+	1.38347e9i	0.236968	+	0.410440i	−0.722875	+	0.690979i	$0.757180\pi$
$132$		0			0
$133$	−6.50390e8	−	4.05021e9i	−0.180236	−	1.12239i
$134$	1.99435e9			0.534355
$135$		0			0
$136$	7.92648e8	−	1.37291e9i	0.198681	−	0.344125i
$137$	−8.88612e8	+	1.53912e9i	−0.215511	+	0.373276i	−0.953431	−	0.301613i	$-0.902475\pi$
$137$	−8.88612e8	+	1.53912e9i	−0.215511	+	0.373276i	0.737919	+	0.674889i	$0.235808\pi$
$138$		0			0
$139$	−1.73884e9			−0.395088			−0.197544	−	0.980294i	$-0.563297\pi$
$139$	−1.73884e9			−0.395088			−0.197544	+	0.980294i	$0.563297\pi$
$140$	−3.42245e9	−	1.30535e9i	−0.752942	−	0.287178i
$141$		0			0
$142$	1.34296e8	+	2.32608e8i	0.0277183	+	0.0480094i
$143$	−3.59064e9	+	6.21918e9i	−0.718059	+	1.24371i
$144$		0			0
$145$	8.03700e9	+	1.39205e10i	1.50986	+	2.61516i
$146$	−4.04097e9			−0.736033
$147$		0			0
$148$	1.10005e9			0.188467
$149$	3.77688e9	+	6.54175e9i	0.627763	+	1.08732i	0.988000	+	0.154456i	$0.0493624\pi$
$149$	3.77688e9	+	6.54175e9i	0.627763	+	1.08732i	−0.360237	+	0.932861i	$0.617304\pi$
$150$		0			0
$151$	4.55323e9	−	7.88643e9i	0.712728	−	1.23448i	−0.251102	−	0.967961i	$-0.580793\pi$
$151$	4.55323e9	−	7.88643e9i	0.712728	−	1.23448i	0.963829	−	0.266520i	$-0.0858738\pi$
$152$	−1.32250e9	−	2.29063e9i	−0.200955	−	0.348064i
$153$		0			0
$154$	−5.50804e9	−	2.10081e9i	−0.789139	−	0.300983i
$155$	1.72915e10			2.40624
$156$		0			0
$157$	−6.21362e9	+	1.07623e10i	−0.816200	+	1.41370i	0.0922632	+	0.995735i	$0.470590\pi$
$157$	−6.21362e9	+	1.07623e10i	−0.816200	+	1.41370i	−0.908463	+	0.417965i	$0.862743\pi$
$158$	−8.30484e7	+	1.43844e8i	−0.0106017	+	0.0183626i
$159$		0			0
$160$	−2.36183e9			−0.284911
$161$	−1.46862e9	−	9.14561e9i	−0.172263	−	1.07274i
$162$		0			0
$163$	−2.02713e9	−	3.51109e9i	−0.224925	−	0.389581i	0.731372	−	0.681979i	$-0.238880\pi$
$163$	−2.02713e9	−	3.51109e9i	−0.224925	−	0.389581i	−0.956297	+	0.292397i	$0.905547\pi$
$164$	−3.79401e9	+	6.57142e9i	−0.409545	+	0.709352i
$165$		0			0
$166$	2.17426e9	+	3.76592e9i	0.222241	+	0.384933i
$167$	−2.87424e9			−0.285955			−0.142978	−	0.989726i	$-0.545668\pi$
$167$	−2.87424e9			−0.285955			−0.142978	+	0.989726i	$0.545668\pi$
$168$		0			0
$169$	4.72573e9			0.445634
$170$	−6.97412e9	−	1.20795e10i	−0.640426	−	1.10925i
$171$		0			0
$172$	1.43469e9	−	2.48496e9i	0.124992	−	0.216492i
$173$	3.10666e9	+	5.38089e9i	0.263685	+	0.456716i	0.967218	−	0.253946i	$-0.0817287\pi$
$173$	3.10666e9	+	5.38089e9i	0.263685	+	0.456716i	−0.703533	+	0.710662i	$0.748395\pi$
$174$		0			0
$175$	−1.53773e10	+	1.25069e10i	−1.23939	+	1.00804i
$176$	−3.80109e9			−0.298608
$177$		0			0
$178$	5.64778e9	−	9.78224e9i	0.421685	−	0.730379i
$179$	−7.50964e9	+	1.30071e10i	−0.546740	+	0.946981i	0.451756	+	0.892142i	$0.350798\pi$
$179$	−7.50964e9	+	1.30071e10i	−0.546740	+	0.946981i	−0.998495	+	0.0548389i	$0.982535\pi$
$180$		0			0
$181$	2.99148e9			0.207173			0.103586	−	0.994620i	$-0.466968\pi$
$181$	2.99148e9			0.207173			0.103586	+	0.994620i	$0.466968\pi$
$182$	1.99528e9	+	1.24253e10i	0.134798	+	0.839432i
$183$		0			0
$184$	−2.98628e9	−	5.17238e9i	−0.192066	−	0.332668i
$185$	4.83939e9	−	8.38207e9i	0.303751	−	0.526112i
$186$		0			0
$187$	−1.12240e10	−	1.94406e10i	−0.671214	−	1.16258i
$188$	1.09992e10			0.642171
$189$		0			0
$190$	−2.32720e10			−1.29551
$191$	−1.16557e10	−	2.01883e10i	−0.633706	−	1.09761i	−0.986788	−	0.162019i	$-0.948199\pi$
$191$	−1.16557e10	−	2.01883e10i	−0.633706	−	1.09761i	0.353081	−	0.935593i	$-0.385134\pi$
$192$		0			0
$193$	−4.88839e9	+	8.46694e9i	−0.253605	+	0.439257i	−0.964516	−	0.264025i	$-0.914950\pi$
$193$	−4.88839e9	+	8.46694e9i	−0.253605	+	0.439257i	0.710911	+	0.703282i	$0.248283\pi$
$194$	1.41403e9	+	2.44918e9i	0.0716724	+	0.124140i
$195$		0			0
$196$	−9.81114e9	+	3.23439e9i	−0.474862	+	0.156545i
$197$	2.16185e10			1.02265			0.511325	−	0.859387i	$-0.329155\pi$
$197$	2.16185e10			1.02265			0.511325	+	0.859387i	$0.329155\pi$
$198$		0			0
$199$	−1.81008e10	+	3.13515e10i	−0.818200	+	1.41716i	0.0888074	+	0.996049i	$0.471694\pi$
$199$	−1.81008e10	+	3.13515e10i	−0.818200	+	1.41716i	−0.907007	+	0.421115i	$0.861639\pi$
$200$	−6.39028e9	+	1.10683e10i	−0.282413	+	0.489154i
$201$		0			0
$202$	−8.87850e9			−0.375196
$203$	4.23569e10	+	1.61552e10i	1.75062	+	0.667700i
$204$		0			0
$205$	3.33816e10	+	5.78186e10i	1.32012	+	2.28652i
$206$	−3.67098e9	+	6.35833e9i	−0.142030	+	0.246003i
$207$		0			0
$208$	4.05718e9	+	7.02724e9i	0.150293	+	0.260315i
$209$	−3.74535e10			−1.35780
$210$		0			0
$211$	−2.26761e10			−0.787584			−0.393792	−	0.919200i	$-0.628837\pi$
$211$	−2.26761e10			−0.787584			−0.393792	+	0.919200i	$0.628837\pi$
$212$	8.94766e8	+	1.54978e9i	0.0304227	+	0.0526937i
$213$		0			0
$214$	−3.71083e9	+	6.42734e9i	−0.120951	+	0.209493i
$215$	−1.26232e10	−	2.18640e10i	−0.402898	−	0.697840i
$216$		0			0
$217$	3.78331e10	−	3.07711e10i	1.15825	−	0.942050i
$218$	−3.89616e10			−1.16838
$219$		0			0
$220$	−1.67219e10	+	2.89632e10i	−0.481265	+	0.833576i
$221$	−2.39604e10	+	4.15007e10i	−0.675662	+	1.17028i
$222$		0			0
$223$	−3.15180e10			−0.853466			−0.426733	−	0.904378i	$-0.640336\pi$
$223$	−3.15180e10			−0.853466			−0.426733	+	0.904378i	$0.640336\pi$
$224$	−5.16759e9	+	4.20300e9i	−0.137143	+	0.111543i
$225$		0			0
$226$	−1.48287e10	−	2.56841e10i	−0.378109	−	0.654903i
$227$	3.53578e10	−	6.12415e10i	0.883830	−	1.53084i	0.0367808	−	0.999323i	$-0.488290\pi$
$227$	3.53578e10	−	6.12415e10i	0.883830	−	1.53084i	0.847049	−	0.531515i	$-0.178377\pi$
$228$		0			0
$229$	2.25668e10	+	3.90868e10i	0.542263	+	0.939226i	0.998774	+	0.0495087i	$0.0157655\pi$
$229$	2.25668e10	+	3.90868e10i	0.542263	+	0.939226i	−0.456511	+	0.889718i	$0.650901\pi$
$230$	−5.25495e10			−1.23821
$231$		0			0
$232$	2.92304e10			0.662429
$233$	−3.97897e9	−	6.89177e9i	−0.0884441	−	0.153190i	0.818410	−	0.574635i	$-0.194856\pi$
$233$	−3.97897e9	−	6.89177e9i	−0.0884441	−	0.153190i	−0.906854	+	0.421446i	$0.861523\pi$
$234$		0			0
$235$	4.83882e10	−	8.38109e10i	1.03499	−	1.79265i
$236$	−1.48943e10	−	2.57977e10i	−0.312548	−	0.541349i
$237$		0			0
$238$	−3.67553e10	−	1.40187e10i	−0.742546	−	0.283212i
$239$	1.62139e10			0.321438			0.160719	−	0.987000i	$-0.448619\pi$
$239$	1.62139e10			0.321438			0.160719	+	0.987000i	$0.448619\pi$
$240$		0			0
$241$	4.69601e10	−	8.13372e10i	0.896710	−	1.55315i	0.0650356	−	0.997883i	$-0.479284\pi$
$241$	4.69601e10	−	8.13372e10i	0.896710	−	1.55315i	0.831674	−	0.555264i	$-0.187383\pi$
$242$	−8.04840e9	+	1.39402e10i	−0.150848	+	0.261277i
$243$		0			0
$244$	−4.30223e9			−0.0777032
$245$	−1.85165e10	+	8.89871e10i	−0.328331	+	1.57790i
$246$		0			0
$247$	3.99769e10	+	6.92420e10i	0.683397	+	1.18368i
$248$	1.57222e10	−	2.72316e10i	0.263925	−	0.457132i
$249$		0			0
$250$	2.10309e10	+	3.64266e10i	0.340509	+	0.589779i
$251$	1.05570e10			0.167884			0.0839420	−	0.996471i	$-0.473249\pi$
$251$	1.05570e10			0.167884			0.0839420	+	0.996471i	$0.473249\pi$
$252$		0			0
$253$	−8.45722e10			−1.29773
$254$	−1.33685e10	−	2.31549e10i	−0.201526	−	0.349053i
$255$		0			0
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	−2.68280e10	−	4.64675e10i	−0.383610	−	0.664432i	0.607965	−	0.793964i	$-0.291986\pi$
$257$	−2.68280e10	−	4.64675e10i	−0.383610	−	0.664432i	−0.991575	+	0.129532i	$0.958653\pi$
$258$		0			0
$259$	−4.32794e9	−	2.69516e10i	−0.0597630	−	0.372165i
$260$	7.13942e10			0.968909
$261$		0			0
$262$	1.27800e10	−	2.21356e10i	0.167561	−	0.290225i
$263$	4.57417e10	−	7.92270e10i	0.589538	−	1.02111i	−0.404755	−	0.914425i	$-0.632643\pi$
$263$	4.57417e10	−	7.92270e10i	0.589538	−	1.02111i	0.994293	−	0.106684i	$-0.0340235\pi$
$264$		0			0
$265$	1.57452e10			0.196129
$266$	−5.09182e10	+	4.14138e10i	−0.623600	+	0.507198i
$267$		0			0
$268$	−1.59548e10	−	2.76345e10i	−0.188923	−	0.327224i
$269$	3.21537e9	−	5.56918e9i	0.0374408	−	0.0648494i	−0.846698	−	0.532074i	$-0.821413\pi$
$269$	3.21537e9	−	5.56918e9i	0.0374408	−	0.0648494i	0.884139	+	0.467225i	$0.154746\pi$
$270$		0			0
$271$	2.86845e10	+	4.96831e10i	0.323062	+	0.559560i	0.981118	−	0.193409i	$-0.0619544\pi$
$271$	2.86845e10	+	4.96831e10i	0.323062	+	0.559560i	−0.658056	+	0.752969i	$0.728621\pi$
$272$	−2.53647e10			−0.280977
$273$		0			0
$274$	2.84356e10			0.304779
$275$	9.04874e10	+	1.56729e11i	0.954094	+	1.65254i
$276$		0			0
$277$	3.21069e10	−	5.56109e10i	0.327673	−	0.567545i	−0.654377	−	0.756168i	$-0.727069\pi$
$277$	3.21069e10	−	5.56109e10i	0.327673	−	0.567545i	0.982050	+	0.188623i	$0.0604024\pi$
$278$	1.39107e10	+	2.40941e10i	0.139685	+	0.241941i
$279$		0			0
$280$	9.29219e9	+	5.78657e10i	0.0903456	+	0.562614i
$281$	4.95099e10			0.473711			0.236855	−	0.971545i	$-0.423883\pi$
$281$	4.95099e10			0.473711			0.236855	+	0.971545i	$0.423883\pi$
$282$		0			0
$283$	−2.63003e10	+	4.55534e10i	−0.243737	+	0.422164i	−0.961776	−	0.273839i	$-0.911707\pi$
$283$	−2.63003e10	+	4.55534e10i	−0.243737	+	0.422164i	0.718039	+	0.696003i	$0.245040\pi$
$284$	2.14874e9	−	3.72172e9i	0.0195998	−	0.0339478i
$285$		0			0
$286$	1.14901e11			1.01549
$287$	1.75929e11	+	6.71006e10i	1.53063	+	0.583792i
$288$		0			0
$289$	−1.56042e10	−	2.70273e10i	−0.131583	−	0.227909i
$290$	1.28592e11	−	2.22728e11i	1.06764	−	1.84920i
$291$		0			0
$292$	3.23277e10	+	5.59933e10i	0.260227	+	0.450727i
$293$	9.36052e9			0.0741986			0.0370993	−	0.999312i	$-0.488188\pi$
$293$	9.36052e9			0.0741986			0.0370993	+	0.999312i	$0.488188\pi$
$294$		0			0
$295$	−2.62096e11			−2.01493
$296$	−8.80039e9	−	1.52427e10i	−0.0666330	−	0.115412i
$297$		0			0
$298$	6.04301e10	−	1.04668e11i	0.443895	−	0.768849i
$299$	9.02702e10	+	1.56353e11i	0.653167	+	1.13132i
$300$		0			0
$301$	−6.65271e10	−	2.53739e10i	−0.467142	−	0.178172i
$302$	−1.45703e11			−1.00795
$303$		0			0
$304$	−2.11600e10	+	3.66501e10i	−0.142097	+	0.246119i
$305$	−1.89266e10	+	3.27818e10i	−0.125234	+	0.216912i
$306$		0			0
$307$	1.06487e11			0.684187			0.342093	−	0.939666i	$-0.388864\pi$
$307$	1.06487e11			0.684187			0.342093	+	0.939666i	$0.388864\pi$
$308$	1.49547e10	+	9.31280e10i	0.0946888	+	0.589661i
$309$		0			0
$310$	−1.38332e11	−	2.39598e11i	−0.850735	−	1.47352i
$311$	−1.38512e10	+	2.39910e10i	−0.0839588	+	0.145421i	−0.904947	−	0.425524i	$-0.860090\pi$
$311$	−1.38512e10	+	2.39910e10i	−0.0839588	+	0.145421i	0.820988	+	0.570945i	$0.193423\pi$
$312$		0			0
$313$	−7.31791e9	−	1.26750e10i	−0.0430960	−	0.0746445i	0.843673	−	0.536858i	$-0.180389\pi$
$313$	−7.31791e9	−	1.26750e10i	−0.0430960	−	0.0746445i	−0.886769	+	0.462213i	$0.847055\pi$
$314$	1.98836e11			1.15428
$315$		0			0
$316$	2.65755e9			0.0149930
$317$	−1.30946e11	−	2.26805e11i	−0.728325	−	1.26150i	−0.957591	−	0.288132i	$-0.906966\pi$
$317$	−1.30946e11	−	2.26805e11i	−0.728325	−	1.26150i	0.229266	−	0.973364i	$-0.426367\pi$
$318$		0			0
$319$	2.06954e11	−	3.58454e11i	1.11896	−	1.93810i
$320$	1.88946e10	+	3.27265e10i	0.100731	+	0.174471i
$321$		0			0
$322$	−1.14976e11	+	9.35147e10i	−0.596015	+	0.484762i
$323$	−2.49928e11			−1.27763
$324$		0			0
$325$	1.93168e11	−	3.34576e11i	0.960416	−	1.66349i
$326$	−3.24341e10	+	5.61775e10i	−0.159046	+	0.275476i
$327$		0			0
$328$	1.21408e11			0.579184
$329$	−4.32743e10	−	2.69484e11i	−0.203633	−	1.26810i
$330$		0			0
$331$	5.46508e10	+	9.46580e10i	0.250248	+	0.433443i	0.963594	−	0.267370i	$-0.0861545\pi$
$331$	5.46508e10	+	9.46580e10i	0.250248	+	0.433443i	−0.713346	+	0.700812i	$0.752821\pi$
$332$	3.47881e10	−	6.02548e10i	0.157148	−	0.272189i
$333$		0			0
$334$	2.29939e10	+	3.98266e10i	0.101100	+	0.175111i
$335$	−2.80757e11			−1.21795
$336$		0			0
$337$	2.28449e11			0.964839			0.482419	−	0.875940i	$-0.339758\pi$
$337$	2.28449e11			0.964839			0.482419	+	0.875940i	$0.339758\pi$
$338$	−3.78058e10	−	6.54816e10i	−0.157556	−	0.272894i
$339$		0			0
$340$	−1.11586e11	+	1.93272e11i	−0.452850	+	0.784359i
$341$	−2.22629e11	−	3.85604e11i	−0.891633	−	1.54435i
$342$		0			0
$343$	1.17844e11	+	2.27651e11i	0.459709	+	0.888070i
$344$	−4.59102e10			−0.176765
$345$		0			0
$346$	4.97065e10	−	8.60942e10i	0.186454	−	0.322947i
$347$	2.45799e11	−	4.25736e11i	0.910117	−	1.57637i	0.0962200	−	0.995360i	$-0.469325\pi$
$347$	2.45799e11	−	4.25736e11i	0.910117	−	1.57637i	0.813897	−	0.581009i	$-0.197342\pi$
$348$		0			0
$349$	−2.48686e11			−0.897299			−0.448650	−	0.893708i	$-0.648095\pi$
$349$	−2.48686e11			−0.897299			−0.448650	+	0.893708i	$0.648095\pi$
$350$	2.96319e11	+	1.13018e11i	1.05549	+	0.402571i
$351$		0			0
$352$	3.04087e10	+	5.26694e10i	0.105574	+	0.182859i
$353$	−2.18204e11	+	3.77941e11i	−0.747958	+	1.29550i	0.200842	+	0.979624i	$0.435632\pi$
$353$	−2.18204e11	+	3.77941e11i	−0.747958	+	1.29550i	−0.948800	+	0.315877i	$0.897701\pi$
$354$		0			0
$355$	−1.89057e10	−	3.27456e10i	−0.0631778	−	0.109427i
$356$	−1.80729e11			−0.596352
$357$		0			0
$358$	2.40308e11			0.773206
$359$	−1.02506e11	−	1.77546e11i	−0.325706	−	0.564139i	0.655949	−	0.754805i	$-0.272269\pi$
$359$	−1.02506e11	−	1.77546e11i	−0.325706	−	0.564139i	−0.981655	+	0.190666i	$0.938935\pi$
$360$		0			0
$361$	−4.71532e10	+	8.16717e10i	−0.146126	+	0.253098i
$362$	−2.39318e10	−	4.14511e10i	−0.0732465	−	0.126867i
$363$		0			0
$364$	1.56208e11	−	1.27050e11i	0.466387	−	0.379331i
$365$	5.68871e11			1.67763
$366$		0			0
$367$	−2.34956e11	+	4.06955e11i	−0.676066	+	1.17098i	0.300090	+	0.953911i	$0.402983\pi$
$367$	−2.34956e11	+	4.06955e11i	−0.676066	+	1.17098i	−0.976156	+	0.217069i	$0.930350\pi$
$368$	−4.77804e10	+	8.27581e10i	−0.135811	+	0.235231i
$369$		0			0
$370$	−1.54861e11			−0.429569
$371$	3.44499e10	−	2.80194e10i	0.0944073	−	0.0767851i
$372$		0			0
$373$	−2.07053e11	−	3.58626e11i	−0.553849	−	0.959295i	−0.997992	−	0.0633393i	$-0.979825\pi$
$373$	−2.07053e11	−	3.58626e11i	−0.553849	−	0.959295i	0.444143	−	0.895956i	$-0.353508\pi$
$374$	−1.79584e11	+	3.11049e11i	−0.474620	+	0.822066i
$375$		0			0
$376$	−8.79936e10	−	1.52409e11i	−0.227042	−	0.393248i
$377$	−8.83587e11			−2.25275
$378$		0			0
$379$	−5.62652e10			−0.140076			−0.0700379	−	0.997544i	$-0.522312\pi$
$379$	−5.62652e10			−0.140076			−0.0700379	+	0.997544i	$0.522312\pi$
$380$	1.86176e11	+	3.22466e11i	0.458034	+	0.793338i
$381$		0			0
$382$	−1.86491e11	+	3.23012e11i	−0.448098	+	0.776129i
$383$	3.76926e11	+	6.52855e11i	0.895080	+	1.55032i	0.833706	+	0.552209i	$0.186215\pi$
$383$	3.76926e11	+	6.52855e11i	0.895080	+	1.55032i	0.0613741	+	0.998115i	$0.480452\pi$
$384$		0			0
$385$	7.75400e11	+	2.95743e11i	1.79867	+	0.686027i
$386$	1.56429e11			0.358652
$387$		0			0
$388$	2.26245e10	−	3.91868e10i	0.0506800	−	0.0877804i
$389$	3.97828e10	−	6.89059e10i	0.0880891	−	0.152575i	−0.818614	−	0.574344i	$-0.805257\pi$
$389$	3.97828e10	−	6.89059e10i	0.0880891	−	0.152575i	0.906703	+	0.421769i	$0.138591\pi$
$390$		0			0
$391$	−5.64353e11			−1.22111
$392$	1.23306e11	+	1.10072e11i	0.263753	+	0.235445i
$393$		0			0
$394$	−1.72948e11	−	2.99555e11i	−0.361562	−	0.626243i
$395$	1.16912e10	−	2.02498e10i	0.0241642	−	0.0418537i
$396$		0			0
$397$	2.78539e11	+	4.82444e11i	0.562768	+	0.974742i	0.997254	+	0.0740637i	$0.0235968\pi$
$397$	2.78539e11	+	4.82444e11i	0.562768	+	0.974742i	−0.434486	+	0.900679i	$0.643070\pi$
$398$	5.79226e11			1.15711
$399$		0			0
$400$	2.04489e11			0.399393
$401$	−9.40464e10	−	1.62893e11i	−0.181632	−	0.314596i	0.760804	−	0.648981i	$-0.224805\pi$
$401$	−9.40464e10	−	1.62893e11i	−0.181632	−	0.314596i	−0.942436	+	0.334385i	$0.891471\pi$
$402$		0			0
$403$	−4.75256e11	+	8.23167e11i	−0.897542	+	1.55459i
$404$	7.10280e10	+	1.23024e11i	0.132652	+	0.229760i
$405$		0			0
$406$	−1.15002e11	−	7.16156e11i	−0.210057	−	1.30810i
$407$	−2.49230e11			−0.450220
$408$		0			0
$409$	−2.63478e11	+	4.56357e11i	−0.465575	+	0.806399i	−0.999227	−	0.0393049i	$-0.987486\pi$
$409$	−2.63478e11	+	4.56357e11i	−0.465575	+	0.806399i	0.533653	+	0.845704i	$0.320819\pi$
$410$	5.34106e11	−	9.25098e11i	0.933469	−	1.61682i
$411$		0			0
$412$	1.17471e11			0.200861
$413$	−5.73455e11	+	4.66413e11i	−0.969894	+	0.788852i
$414$		0			0
$415$	−3.06083e11	−	5.30152e11i	−0.506551	−	0.877372i
$416$	6.49149e10	−	1.12436e11i	0.106273	−	0.184071i
$417$		0			0
$418$	2.99628e11	+	5.18971e11i	0.480053	+	0.831477i
$419$	−5.68924e11			−0.901760			−0.450880	−	0.892585i	$-0.648890\pi$
$419$	−5.68924e11			−0.901760			−0.450880	+	0.892585i	$0.648890\pi$
$420$		0			0
$421$	−1.20331e12			−1.86684			−0.933421	−	0.358783i	$-0.883192\pi$
$421$	−1.20331e12			−1.86684			−0.933421	+	0.358783i	$0.883192\pi$
$422$	1.81409e11	+	3.14209e11i	0.278453	+	0.482295i
$423$		0			0
$424$	1.43163e10	−	2.47965e10i	0.0215121	−	0.0372601i
$425$	6.03825e11	+	1.04585e12i	0.897761	+	1.55497i
$426$		0			0
$427$	1.69263e10	+	1.05406e11i	0.0246398	+	0.153441i
$428$	1.18747e11			0.171050
$429$		0			0
$430$	−2.01971e11	+	3.49823e11i	−0.284892	+	0.493447i
$431$	−1.88761e11	+	3.26944e11i	−0.263490	+	0.456379i	−0.967167	−	0.254142i	$-0.918207\pi$
$431$	−1.88761e11	+	3.26944e11i	−0.263490	+	0.456379i	0.703677	+	0.710520i	$0.251540\pi$
$432$		0			0
$433$	−7.52013e11			−1.02809			−0.514043	−	0.857764i	$-0.671853\pi$
$433$	−7.52013e11			−1.02809			−0.514043	+	0.857764i	$0.671853\pi$
$434$	−7.29041e11	−	2.78062e11i	−0.986390	−	0.376216i
$435$		0			0
$436$	3.11693e11	+	5.39868e11i	0.413084	+	0.715482i
$437$	−4.70798e11	+	8.15447e11i	−0.617545	+	1.06962i
$438$		0			0
$439$	−3.58606e11	−	6.21123e11i	−0.460815	−	0.798155i	0.538187	−	0.842826i	$-0.319110\pi$
$439$	−3.58606e11	−	6.21123e11i	−0.460815	−	0.798155i	−0.999002	+	0.0446706i	$0.985776\pi$
$440$	5.35102e11			0.680612
$441$		0			0
$442$	7.66734e11			0.955531
$443$	−4.78364e11	−	8.28551e11i	−0.590122	−	1.02212i	−0.994215	−	0.107404i	$-0.965746\pi$
$443$	−4.78364e11	−	8.28551e11i	−0.590122	−	1.02212i	0.404093	−	0.914718i	$-0.367587\pi$
$444$		0			0
$445$	−7.95072e11	+	1.37711e12i	−0.961140	+	1.66474i
$446$	2.52144e11	+	4.36726e11i	0.301746	+	0.522639i
$447$		0			0
$448$	9.95793e10	+	3.79803e10i	0.116793	+	0.0445458i
$449$	9.36350e11			1.08725			0.543626	−	0.839328i	$-0.317051\pi$
$449$	9.36350e11			1.08725			0.543626	+	0.839328i	$0.317051\pi$
$450$		0			0
$451$	8.59580e11	−	1.48884e12i	0.978345	−	1.69454i
$452$	−2.37260e11	+	4.10946e11i	−0.267363	+	0.463087i
$453$		0			0
$454$	−1.13145e12			−1.24992
$455$	−2.80887e11	−	1.74919e12i	−0.307242	−	1.91331i
$456$		0			0
$457$	2.60052e11	+	4.50423e11i	0.278893	+	0.483057i	0.971110	−	0.238633i	$-0.0766992\pi$
$457$	2.60052e11	+	4.50423e11i	0.278893	+	0.483057i	−0.692217	+	0.721689i	$0.743366\pi$
$458$	3.61068e11	−	6.25389e11i	0.383438	−	0.664133i
$459$		0			0
$460$	4.20396e11	+	7.28147e11i	0.437772	+	0.758244i
$461$	6.01482e11			0.620253			0.310126	−	0.950695i	$-0.399629\pi$
$461$	6.01482e11			0.620253			0.310126	+	0.950695i	$0.399629\pi$
$462$		0			0
$463$	1.12146e11			0.113414			0.0567072	−	0.998391i	$-0.481940\pi$
$463$	1.12146e11			0.113414			0.0567072	+	0.998391i	$0.481940\pi$
$464$	−2.33843e11	−	4.05029e11i	−0.234204	−	0.405653i
$465$		0			0
$466$	−6.36635e10	+	1.10268e11i	−0.0625394	+	0.108321i
$467$	8.07872e11	+	1.39928e12i	0.785990	+	1.36137i	0.928406	+	0.371567i	$0.121179\pi$
$467$	8.07872e11	+	1.39928e12i	0.785990	+	1.36137i	−0.142416	+	0.989807i	$0.545487\pi$
$468$		0			0
$469$	−6.14285e11	+	4.99621e11i	−0.586262	+	0.476830i
$470$	−1.54842e12			−1.46369
$471$		0			0
$472$	−2.38309e11	+	4.12764e11i	−0.221005	+	0.382792i
$473$	−3.25048e11	+	5.62999e11i	−0.298588	+	0.517169i
$474$		0			0
$475$	2.01491e12			1.81608
$476$	9.97929e10	+	6.21446e11i	0.0890981	+	0.554845i
$477$		0			0
$478$	−1.29711e11	−	2.24666e11i	−0.113645	−	0.196840i
$479$	6.50890e10	−	1.12738e11i	0.0564934	−	0.0978495i	−0.836396	−	0.548126i	$-0.815341\pi$
$479$	6.50890e10	−	1.12738e11i	0.0564934	−	0.0978495i	0.892889	+	0.450277i	$0.148675\pi$
$480$		0			0
$481$	2.66021e11	+	4.60762e11i	0.226602	+	0.392486i
$482$	−1.50272e12			−1.26814
$483$		0			0
$484$	2.57549e11			0.213332
$485$	−1.99062e11	−	3.44785e11i	−0.163362	−	0.282951i
$486$		0			0
$487$	5.56957e11	−	9.64678e11i	0.448685	−	0.777145i	−0.549616	−	0.835418i	$-0.685226\pi$
$487$	5.56957e11	−	9.64678e11i	0.448685	−	0.777145i	0.998301	+	0.0582724i	$0.0185592\pi$
$488$	3.44178e10	+	5.96134e10i	0.0274722	+	0.0475833i
$489$		0			0
$490$	1.38117e12	−	4.55324e11i	1.08235	−	0.356811i
$491$	−6.75227e11			−0.524304			−0.262152	−	0.965027i	$-0.584432\pi$
$491$	−6.75227e11			−0.524304			−0.262152	+	0.965027i	$0.584432\pi$
$492$		0			0
$493$	1.38101e12	−	2.39197e12i	1.05289	−	1.82367i
$494$	6.39631e11	−	1.10787e12i	0.483235	−	0.836987i
$495$		0			0
$496$	−5.03110e11			−0.373246
$497$	−9.96374e10	−	3.80024e10i	−0.0732519	−	0.0279388i
$498$		0			0
$499$	8.34220e11	+	1.44491e12i	0.602321	+	1.04325i	0.992469	+	0.122499i	$0.0390908\pi$
$499$	8.34220e11	+	1.44491e12i	0.602321	+	1.04325i	−0.390147	+	0.920752i	$0.627576\pi$
$500$	3.36495e11	−	5.82826e11i	0.240776	−	0.417036i
$501$		0			0
$502$	−8.44561e10	−	1.46282e11i	−0.0593560	−	0.102808i
$503$	−3.46503e11			−0.241352			−0.120676	−	0.992692i	$-0.538506\pi$
$503$	−3.46503e11			−0.241352			−0.120676	+	0.992692i	$0.538506\pi$
$504$		0			0
$505$	1.24988e12			0.855180
$506$	6.76578e11	+	1.17187e12i	0.458818	+	0.794696i
$507$		0			0
$508$	−2.13896e11	+	3.70478e11i	−0.142500	+	0.246818i
$509$	1.20259e12	+	2.08295e12i	0.794124	+	1.37546i	0.923394	+	0.383853i	$0.125403\pi$
$509$	1.20259e12	+	2.08295e12i	0.794124	+	1.37546i	−0.129271	+	0.991609i	$0.541264\pi$
$510$		0			0
$511$	1.24467e12	−	1.01234e12i	0.807532	−	0.656797i
$512$	6.87195e10			0.0441942
$513$		0			0
$514$	−4.29249e11	+	7.43481e11i	−0.271253	+	0.469824i
$515$	5.16786e11	−	8.95100e11i	0.323727	−	0.560711i
$516$		0			0
$517$	−2.49200e12			−1.53406
$518$	−3.38829e11	+	2.75583e11i	−0.206774	+	0.168177i
$519$		0			0
$520$	−5.71154e11	−	9.89267e11i	−0.342561	−	0.593333i
$521$	7.32058e11	−	1.26796e12i	0.435287	−	0.753940i	−0.562032	−	0.827116i	$-0.689980\pi$
$521$	7.32058e11	−	1.26796e12i	0.435287	−	0.753940i	0.997319	+	0.0731760i	$0.0233135\pi$
$522$		0			0
$523$	−9.52063e11	−	1.64902e12i	−0.556427	−	0.963759i	−0.997791	−	0.0664313i	$-0.978839\pi$
$523$	−9.52063e11	−	1.64902e12i	−0.556427	−	0.963759i	0.441364	−	0.897328i	$-0.354495\pi$
$524$	−4.08959e11			−0.236968
$525$		0			0
$526$	−1.46374e12			−0.833732
$527$	−1.48561e12	−	2.57315e12i	−0.838988	−	1.45317i
$528$		0			0
$529$	−1.62514e11	+	2.81482e11i	−0.0902276	+	0.156279i
$530$	−1.25962e11	−	2.18172e11i	−0.0693421	−	0.120104i
$531$		0			0
$532$	9.81192e11	+	3.74234e11i	0.531070	+	0.202554i
$533$	−3.66997e12			−1.96966
$534$		0			0
$535$	5.22396e11	−	9.04816e11i	0.275682	−	0.477494i
$536$	−2.55277e11	+	4.42152e11i	−0.133589	+	0.231382i
$537$		0			0
$538$	−1.02892e11			−0.0529493
$539$	2.22284e12	−	7.32790e11i	1.13438	−	0.373964i
$540$		0			0
$541$	−1.14872e12	−	1.98965e12i	−0.576537	−	0.998592i	−0.995873	−	0.0907604i	$-0.971070\pi$
$541$	−1.14872e12	−	1.98965e12i	−0.576537	−	0.998592i	0.419336	−	0.907831i	$-0.362263\pi$
$542$	4.58953e11	−	7.94929e11i	0.228439	−	0.395669i
$543$		0			0
$544$	2.02918e11	+	3.51464e11i	0.0993403	+	0.172062i
$545$	5.48486e12			2.66306
$546$		0			0
$547$	−2.86900e12			−1.37021			−0.685105	−	0.728444i	$-0.740244\pi$
$547$	−2.86900e12			−1.37021			−0.685105	+	0.728444i	$0.740244\pi$
$548$	−2.27485e11	−	3.94015e11i	−0.107756	−	0.186638i
$549$		0			0
$550$	1.44780e12	−	2.50766e12i	0.674646	−	1.16852i
$551$	−2.30415e12	−	3.99090e12i	−1.06495	−	1.84454i
$552$		0			0
$553$	−1.04556e10	−	6.51109e10i	−0.00475431	−	0.0296068i
$554$	−1.02742e12			−0.463399
$555$		0			0
$556$	2.22572e11	−	3.85506e11i	0.0987720	−	0.171078i
$557$	9.59606e10	−	1.66209e11i	0.0422420	−	0.0731653i	−0.844131	−	0.536136i	$-0.819883\pi$
$557$	9.59606e10	−	1.66209e11i	0.0422420	−	0.0731653i	0.886373	+	0.462971i	$0.153217\pi$
$558$		0			0
$559$	1.38779e12			0.601133
$560$	7.27473e11	−	5.91682e11i	0.312587	−	0.254239i
$561$		0			0
$562$	−3.96079e11	−	6.86029e11i	−0.167482	−	0.290087i
$563$	−6.12000e11	+	1.06002e12i	−0.256723	+	0.444656i	−0.965362	−	0.260914i	$-0.915976\pi$
$563$	−6.12000e11	+	1.06002e12i	−0.256723	+	0.444656i	0.708639	+	0.705571i	$0.249309\pi$
$564$		0			0
$565$	2.08753e12	+	3.61571e12i	0.861817	+	1.49271i
$566$	8.41608e11			0.344696
$567$		0			0
$568$	−6.87596e10			−0.0277183
$569$	1.11297e12	+	1.92771e12i	0.445119	+	0.770969i	0.998061	−	0.0622510i	$-0.0198279\pi$
$569$	1.11297e12	+	1.92771e12i	0.445119	+	0.770969i	−0.552941	+	0.833220i	$0.686495\pi$
$570$		0			0
$571$	−5.69461e11	+	9.86336e11i	−0.224183	+	0.388296i	−0.956074	−	0.293126i	$-0.905305\pi$
$571$	−5.69461e11	+	9.86336e11i	−0.224183	+	0.388296i	0.731891	+	0.681421i	$0.238638\pi$
$572$	−9.19204e11	−	1.59211e12i	−0.359029	−	0.621857i
$573$		0			0
$574$	−4.77659e11	−	2.97455e12i	−0.183660	−	1.14371i
$575$	4.54978e12			1.73574
$576$		0			0
$577$	1.79762e12	−	3.11357e12i	0.675160	−	1.16941i	−0.301263	−	0.953541i	$-0.597408\pi$
$577$	1.79762e12	−	3.11357e12i	0.675160	−	1.16941i	0.976422	−	0.215870i	$-0.0692586\pi$
$578$	−2.49667e11	+	4.32436e11i	−0.0930436	+	0.161156i
$579$		0			0
$580$	−4.11494e12			−1.50986
$581$	−1.61313e12	−	6.15260e11i	−0.587323	−	0.224009i
$582$		0			0
$583$	−2.02720e11	−	3.51122e11i	−0.0726757	−	0.125878i
$584$	5.17244e11	−	8.95893e11i	0.184008	−	0.318712i
$585$		0			0
$586$	−7.48841e10	−	1.29703e11i	−0.0262332	−	0.0454372i
$587$	3.32627e11			0.115634			0.0578170	−	0.998327i	$-0.481586\pi$
$587$	3.32627e11			0.115634			0.0578170	+	0.998327i	$0.481586\pi$
$588$		0			0
$589$	−4.95733e12			−1.69719
$590$	2.09676e12	+	3.63170e12i	0.712386	+	1.23389i
$591$		0			0
$592$	−1.40806e11	+	2.43884e11i	−0.0471166	+	0.0816084i
$593$	3.89298e11	+	6.74284e11i	0.129281	+	0.223922i	0.923398	−	0.383843i	$-0.125400\pi$
$593$	3.89298e11	+	6.74284e11i	0.129281	+	0.223922i	−0.794117	+	0.607765i	$0.792066\pi$
$594$		0			0
$595$	5.17426e12	+	1.97350e12i	1.69247	+	0.645522i
$596$	−1.93376e12			−0.627763
$597$		0			0
$598$	1.44432e12	−	2.50164e12i	0.461859	−	0.799962i
$599$	9.21805e11	−	1.59661e12i	0.292562	−	0.506733i	−0.681853	−	0.731490i	$-0.738825\pi$
$599$	9.21805e11	−	1.59661e12i	0.292562	−	0.506733i	0.974415	+	0.224757i	$0.0721588\pi$
$600$		0			0
$601$	4.75336e12			1.48616			0.743080	−	0.669202i	$-0.233364\pi$
$601$	4.75336e12			1.48616			0.743080	+	0.669202i	$0.233364\pi$
$602$	1.80625e11	+	1.12482e12i	0.0560524	+	0.349058i
$603$		0			0
$604$	1.16563e12	+	2.01893e12i	0.356364	+	0.617240i
$605$	1.13302e12	−	1.96245e12i	0.343826	−	0.595525i
$606$		0			0
$607$	2.28872e12	+	3.96418e12i	0.684295	+	1.18523i	0.973658	+	0.228014i	$0.0732233\pi$
$607$	2.28872e12	+	3.96418e12i	0.684295	+	1.18523i	−0.289363	+	0.957220i	$0.593443\pi$
$608$	6.77119e11			0.200955
$609$		0			0
$610$	6.05650e11			0.177108
$611$	2.65990e12	+	4.60708e12i	0.772111	+	1.33734i
$612$		0			0
$613$	−1.96745e12	+	3.40773e12i	−0.562772	+	0.974750i	0.434481	+	0.900681i	$0.356932\pi$
$613$	−1.96745e12	+	3.40773e12i	−0.562772	+	0.974750i	−0.997253	+	0.0740689i	$0.976402\pi$
$614$	−8.51898e11	−	1.47553e12i	−0.241897	−	0.418977i
$615$		0			0
$616$	1.17078e12	−	9.52242e11i	0.327614	−	0.266461i
$617$	−1.62043e12			−0.450140			−0.225070	−	0.974343i	$-0.572261\pi$
$617$	−1.62043e12			−0.450140			−0.225070	+	0.974343i	$0.572261\pi$
$618$		0			0
$619$	1.53624e12	−	2.66085e12i	0.420583	−	0.728471i	−0.575413	−	0.817863i	$-0.695159\pi$
$619$	1.53624e12	−	2.66085e12i	0.420583	−	0.728471i	0.995997	+	0.0893913i	$0.0284922\pi$
$620$	−2.21331e12	+	3.83356e12i	−0.601561	+	1.04193i
$621$		0			0
$622$	4.43239e11			0.118736
$623$	7.11045e11	+	4.42793e12i	0.189104	+	1.17762i
$624$		0			0
$625$	8.64747e10	+	1.49778e11i	0.0226688	+	0.0392635i
$626$	−1.17087e11	+	2.02800e11i	−0.0304735	+	0.0527817i
$627$		0			0
$628$	−1.59069e12	−	2.75515e12i	−0.408100	−	0.706850i
$629$	−1.66312e12			−0.423638
$630$		0			0
$631$	−2.89789e11			−0.0727696			−0.0363848	−	0.999338i	$-0.511584\pi$
$631$	−2.89789e11			−0.0727696			−0.0363848	+	0.999338i	$0.511584\pi$
$632$	−2.12604e10	−	3.68241e10i	−0.00530084	−	0.00918132i
$633$		0			0
$634$	−2.09513e12	+	3.62888e12i	−0.515003	+	0.892012i
$635$	1.88196e12	+	3.25966e12i	0.459335	+	0.795591i
$636$		0			0
$637$	−3.72734e12	−	3.32730e12i	−0.896957	−	0.800689i
$638$	−6.62252e12			−1.58245
$639$		0			0
$640$	3.02314e11	−	5.23624e11i	0.0712277	−	0.123370i
$641$	−3.93795e12	+	6.82073e12i	−0.921317	+	1.59577i	−0.123938	+	0.992290i	$0.539552\pi$
$641$	−3.93795e12	+	6.82073e12i	−0.921317	+	1.59577i	−0.797379	+	0.603479i	$0.793781\pi$
$642$		0			0
$643$	8.30296e12			1.91551			0.957754	−	0.287590i	$-0.0928541\pi$
$643$	8.30296e12			1.91551			0.957754	+	0.287590i	$0.0928541\pi$
$644$	2.21559e12	+	8.45042e11i	0.507578	+	0.193594i
$645$		0			0
$646$	1.99943e12	+	3.46311e12i	0.451709	+	0.782384i
$647$	2.94053e12	−	5.09315e12i	0.659715	−	1.14266i	−0.320975	−	0.947088i	$-0.604010\pi$
$647$	2.94053e12	−	5.09315e12i	0.659715	−	1.14266i	0.980689	−	0.195572i	$-0.0626562\pi$
$648$		0			0
$649$	3.37449e12	+	5.84480e12i	0.746634	+	1.29321i
$650$	−6.18137e12			−1.35823
$651$		0			0
$652$	1.03789e12			0.224925
$653$	−1.29217e12	−	2.23810e12i	−0.278106	−	0.481694i	0.692808	−	0.721122i	$-0.256373\pi$
$653$	−1.29217e12	−	2.23810e12i	−0.278106	−	0.481694i	−0.970914	+	0.239428i	$0.923040\pi$
$654$		0			0
$655$	−1.79911e12	+	3.11616e12i	−0.381920	+	0.661505i
$656$	−9.71267e11	−	1.68228e12i	−0.204772	−	0.354676i
$657$		0			0
$658$	−3.38789e12	+	2.75550e12i	−0.704552	+	0.573039i
$659$	−6.13192e12			−1.26652			−0.633260	−	0.773939i	$-0.718284\pi$
$659$	−6.13192e12			−1.26652			−0.633260	+	0.773939i	$0.718284\pi$
$660$		0			0
$661$	−5.64211e10	+	9.77243e10i	−0.0114957	+	0.0199111i	−0.871716	−	0.490011i	$-0.836993\pi$
$661$	−5.64211e10	+	9.77243e10i	−0.0114957	+	0.0199111i	0.860220	+	0.509923i	$0.170326\pi$
$662$	8.74413e11	−	1.51453e12i	0.176952	−	0.306490i
$663$		0			0
$664$	−1.11322e12			−0.222241
$665$	7.16807e12	−	5.83007e12i	1.42136	−	1.15605i
$666$		0			0
$667$	−5.20290e12	−	9.01168e12i	−1.01784	−	1.76295i
$668$	3.67902e11	−	6.37225e11i	0.0714888	−	0.123822i
$669$		0			0
$670$	2.24605e12	+	3.89028e12i	0.430609	+	0.745837i
$671$	9.74723e11			0.185622
$672$		0			0
$673$	−5.40433e12			−1.01549			−0.507743	−	0.861509i	$-0.669520\pi$
$673$	−5.40433e12			−1.01549			−0.507743	+	0.861509i	$0.669520\pi$
$674$	−1.82759e12	−	3.16548e12i	−0.341122	−	0.590841i
$675$		0			0
$676$	−6.04893e11	+	1.04771e12i	−0.111409	+	0.192965i
$677$	−9.23227e11	−	1.59908e12i	−0.168912	−	0.292564i	0.769126	−	0.639097i	$-0.220692\pi$
$677$	−9.23227e11	−	1.59908e12i	−0.168912	−	0.292564i	−0.938037	+	0.346534i	$0.887359\pi$
$678$		0			0
$679$	−1.04910e12	−	4.00136e11i	−0.189411	−	0.0722427i
$680$	3.57075e12			0.640426
$681$		0			0
$682$	−3.56206e12	+	6.16967e12i	−0.630480	+	1.09202i
$683$	−1.48317e12	+	2.56892e12i	−0.260793	+	0.451707i	−0.966453	−	0.256844i	$-0.917317\pi$
$683$	−1.48317e12	+	2.56892e12i	−0.260793	+	0.451707i	0.705660	+	0.708551i	$0.250651\pi$
$684$		0			0
$685$	−4.00305e12			−0.694678
$686$	2.21168e12	−	3.45410e12i	0.381298	−	0.595493i
$687$		0			0
$688$	3.67282e11	+	6.36151e11i	0.0624959	+	0.108246i
$689$	−4.32757e11	+	7.49557e11i	−0.0731573	+	0.126712i
$690$		0			0
$691$	1.47397e12	+	2.55299e12i	0.245944	+	0.425988i	0.962397	−	0.271648i	$-0.0875687\pi$
$691$	1.47397e12	+	2.55299e12i	0.245944	+	0.425988i	−0.716452	+	0.697636i	$0.754235\pi$
$692$	−1.59061e12			−0.263685
$693$		0			0
$694$	−7.86556e12			−1.28710
$695$	−1.95830e12	−	3.39187e12i	−0.318381	−	0.551452i
$696$		0			0
$697$	5.73600e12	−	9.93504e12i	0.920580	−	1.59449i
$698$	1.98949e12	+	3.44590e12i	0.317243	+	0.549481i
$699$		0			0
$700$	−8.04525e11	−	5.01006e12i	−0.126648	−	0.788682i
$701$	6.64689e12			1.03965			0.519826	−	0.854272i	$-0.325997\pi$
$701$	6.64689e12			1.03965			0.519826	+	0.854272i	$0.325997\pi$
$702$		0			0
$703$	−1.38742e12	+	2.40308e12i	−0.214244	+	0.371081i
$704$	4.86539e11	−	8.42710e11i	0.0746519	−	0.129301i
$705$		0			0
$706$	6.98254e12			1.05777
$707$	2.73469e12	−	2.22423e12i	0.411643	−	0.334805i
$708$		0			0
$709$	1.71074e12	+	2.96308e12i	0.254258	+	0.440388i	0.964694	−	0.263374i	$-0.0848353\pi$
$709$	1.71074e12	+	2.96308e12i	0.254258	+	0.440388i	−0.710436	+	0.703762i	$0.751502\pi$
$710$	−3.02491e11	+	5.23929e11i	−0.0446735	+	0.0773767i
$711$		0			0
$712$	1.44583e12	+	2.50425e12i	0.210842	+	0.365190i
$713$	−1.11939e13			−1.62211
$714$		0			0
$715$	−1.61752e13			−2.31459
$716$	−1.92247e12	−	3.32981e12i	−0.273370	−	0.473490i
$717$		0			0
$718$	−1.64010e12	+	2.84074e12i	−0.230309	+	0.398907i
$719$	−1.09736e12	−	1.90068e12i	−0.153133	−	0.265234i	0.779245	−	0.626720i	$-0.215603\pi$
$719$	−1.09736e12	−	1.90068e12i	−0.153133	−	0.265234i	−0.932378	+	0.361486i	$0.882270\pi$
$720$		0			0
$721$	−4.62170e11	−	2.87809e12i	−0.0636932	−	0.396640i
$722$	1.50890e12			0.206654
$723$		0			0
$724$	−3.82909e11	+	6.63218e11i	−0.0517931	+	0.0897083i
$725$	−1.11336e13	+	1.92840e13i	−1.49663	+	2.59224i
$726$		0			0
$727$	−6.12356e12			−0.813016			−0.406508	−	0.913647i	$-0.633254\pi$
$727$	−6.12356e12			−0.813016			−0.406508	+	0.913647i	$0.633254\pi$
$728$	−3.01012e12	−	1.14808e12i	−0.397184	−	0.151489i
$729$		0			0
$730$	−4.55097e12	−	7.88251e12i	−0.593132	−	1.02733i
$731$	−2.16905e12	+	3.75691e12i	−0.280958	+	0.486634i
$732$		0			0
$733$	1.81651e11	+	3.14629e11i	0.0232419	+	0.0402561i	0.877412	−	0.479737i	$-0.159268\pi$
$733$	1.81651e11	+	3.14629e11i	0.0232419	+	0.0402561i	−0.854171	+	0.519993i	$0.825935\pi$
$734$	7.51859e12			0.956101
$735$		0			0
$736$	1.52897e12			0.192066
$737$	3.61476e12	+	6.26094e12i	0.451310	+	0.781692i
$738$		0			0
$739$	−4.25145e12	+	7.36373e12i	−0.524369	+	0.908234i	0.475228	+	0.879863i	$0.342365\pi$
$739$	−4.25145e12	+	7.36373e12i	−0.524369	+	0.908234i	−0.999597	+	0.0283716i	$0.990968\pi$
$740$	1.23888e12	+	2.14581e12i	0.151876	+	0.263056i
$741$		0			0
$742$	−6.63848e11	−	2.53197e11i	−0.0803991	−	0.0306648i
$743$	1.21515e13			1.46278			0.731391	−	0.681959i	$-0.238872\pi$
$743$	1.21515e13			1.46278			0.731391	+	0.681959i	$0.238872\pi$
$744$		0			0
$745$	−8.50712e12	+	1.47348e13i	−1.01176	+	1.75243i
$746$	−3.31285e12	+	5.73802e12i	−0.391631	+	0.678324i
$747$		0			0
$748$	5.74670e12			0.671214
$749$	−4.67186e11	−	2.90933e12i	−0.0542403	−	0.337773i
$750$		0			0
$751$	2.56775e12	+	4.44746e12i	0.294559	+	0.510191i	0.974882	−	0.222721i	$-0.0714939\pi$
$751$	2.56775e12	+	4.44746e12i	0.294559	+	0.510191i	−0.680323	+	0.732912i	$0.738161\pi$
$752$	−1.40790e12	+	2.43855e12i	−0.160543	+	0.278068i
$753$		0			0
$754$	7.06870e12	+	1.22433e13i	0.796468	+	1.37952i
$755$	2.05116e13			2.29740
$756$		0			0
$757$	−1.43960e12			−0.159335			−0.0796675	−	0.996821i	$-0.525386\pi$
$757$	−1.43960e12			−0.159335			−0.0796675	+	0.996821i	$0.525386\pi$
$758$	4.50122e11	+	7.79633e11i	0.0495243	+	0.0857786i
$759$		0			0
$760$	2.97882e12	−	5.15946e12i	0.323879	−	0.560974i
$761$	1.00476e12	+	1.74030e12i	0.108601	+	0.188102i	0.915204	−	0.402992i	$-0.132030\pi$
$761$	1.00476e12	+	1.74030e12i	0.108601	+	0.188102i	−0.806603	+	0.591094i	$0.798696\pi$
$762$		0			0
$763$	1.20007e13	−	9.76061e12i	1.28187	−	1.04260i
$764$	5.96772e12			0.633706
$765$		0			0
$766$	6.03082e12	−	1.04457e13i	0.632917	−	1.09624i
$767$	7.20369e12	−	1.24772e13i	0.751582	−	1.30178i
$768$		0			0
$769$	−8.97077e12			−0.925042			−0.462521	−	0.886608i	$-0.653055\pi$
$769$	−8.97077e12			−0.925042			−0.462521	+	0.886608i	$0.653055\pi$
$770$	−2.10526e12	−	1.31102e13i	−0.215823	−	1.34401i
$771$		0			0
$772$	−1.25143e12	−	2.16754e12i	−0.126803	−	0.219628i
$773$	−8.38920e12	+	1.45305e13i	−0.845109	+	1.46377i	0.0404173	+	0.999183i	$0.487131\pi$
$773$	−8.38920e12	+	1.45305e13i	−0.845109	+	1.46377i	−0.885526	+	0.464589i	$0.846202\pi$
$774$		0			0
$775$	1.19769e13	+	2.07446e13i	1.19258	+	2.06560i
$776$	−7.23985e11			−0.0716724
$777$		0			0
$778$	−1.27305e12			−0.124577
$779$	−9.57025e12	−	1.65762e13i	−0.931118	−	1.61274i
$780$		0			0
$781$	−4.86823e11	+	8.43203e11i	−0.0468211	+	0.0810965i
$782$	4.51482e12	+	7.81990e12i	0.431728	+	0.747775i
$783$		0			0
$784$	5.38754e11	−	2.58916e12i	0.0509294	−	0.244757i
$785$	−2.79913e13			−2.63094
$786$		0			0
$787$	9.89536e12	−	1.71393e13i	0.919486	−	1.59260i	0.119290	−	0.992859i	$-0.461938\pi$
$787$	9.89536e12	−	1.71393e13i	0.919486	−	1.59260i	0.800197	−	0.599738i	$-0.204728\pi$
$788$	−2.76717e12	+	4.79287e12i	−0.255663	+	0.442821i
$789$		0			0
$790$	−3.74119e11			−0.0341734
$791$	1.10018e13	+	4.19617e12i	0.999239	+	0.381117i
$792$		0			0
$793$	−1.04039e12	−	1.80201e12i	−0.0934261	−	0.161819i
$794$	4.45663e12	−	7.71911e12i	0.397937	−	0.689247i
$795$		0			0
$796$	−4.63381e12	−	8.02599e12i	−0.409100	−	0.708582i
$797$	−1.91358e13			−1.67990			−0.839951	−	0.542663i	$-0.817416\pi$
$797$	−1.91358e13			−1.67990			−0.839951	+	0.542663i	$0.817416\pi$
$798$		0			0
$799$	−1.66292e13			−1.44348
$800$	−1.63591e12	−	2.83348e12i	−0.141207	−	0.244577i
$801$		0			0
$802$	−1.50474e12	+	2.60629e12i	−0.128433	+	0.222453i
$803$	−7.32425e12	−	1.26860e13i	−0.621646	−	1.07672i
$804$		0			0
$805$	1.61859e13	−	1.31646e13i	1.35849	−	1.10491i
$806$	1.52082e13			1.26932
$807$		0			0
$808$	1.13645e12	−	1.96839e12i	0.0937991	−	0.162465i
$809$	4.06948e12	−	7.04855e12i	0.334019	−	0.578537i	−0.649277	−	0.760552i	$-0.724928\pi$
$809$	4.06948e12	−	7.04855e12i	0.334019	−	0.578537i	0.983296	+	0.182015i	$0.0582618\pi$
$810$		0			0
$811$	−3.43326e12			−0.278684			−0.139342	−	0.990244i	$-0.544499\pi$
$811$	−3.43326e12			−0.278684			−0.139342	+	0.990244i	$0.544499\pi$
$812$	−9.00334e12	+	7.32276e12i	−0.726777	+	0.591116i
$813$		0			0
$814$	1.99384e12	+	3.45343e12i	0.159177	+	0.275702i
$815$	4.56594e12	−	7.90844e12i	0.362511	−	0.627887i
$816$		0			0
$817$	3.61897e12	+	6.26823e12i	0.284175	+	0.492205i
$818$	8.43129e12			0.658422
$819$		0			0
$820$	−1.70914e13			−1.32012
$821$	−8.81289e12	−	1.52644e13i	−0.676977	−	1.17256i	−0.975887	−	0.218277i	$-0.929956\pi$
$821$	−8.81289e12	−	1.52644e13i	−0.676977	−	1.17256i	0.298910	−	0.954281i	$-0.403377\pi$
$822$		0			0
$823$	9.16295e12	−	1.58707e13i	0.696203	−	1.20586i	−0.273570	−	0.961852i	$-0.588204\pi$
$823$	9.16295e12	−	1.58707e13i	0.696203	−	1.20586i	0.969773	−	0.244008i	$-0.0784622\pi$
$824$	−9.39771e11	−	1.62773e12i	−0.0710150	−	0.123002i
$825$		0			0
$826$	1.10504e13	+	4.21472e12i	0.825980	+	0.315035i
$827$	−1.66782e13			−1.23987			−0.619933	−	0.784655i	$-0.712840\pi$
$827$	−1.66782e13			−1.23987			−0.619933	+	0.784655i	$0.712840\pi$
$828$		0			0
$829$	−1.11795e13	+	1.93635e13i	−0.822106	+	1.42393i	0.0820047	+	0.996632i	$0.473868\pi$
$829$	−1.11795e13	+	1.93635e13i	−0.822106	+	1.42393i	−0.904111	+	0.427298i	$0.859466\pi$
$830$	−4.89733e12	+	8.48243e12i	−0.358186	+	0.620396i
$831$		0			0
$832$	−2.07728e12			−0.150293
$833$	1.48330e13	−	4.88993e12i	1.06740	−	0.351884i
$834$		0			0
$835$	−3.23699e12	−	5.60663e12i	−0.230437	−	0.399128i
$836$	4.79405e12	−	8.30354e12i	0.339449	−	0.587943i
$837$		0			0
$838$	4.55139e12	+	7.88324e12i	0.318820	+	0.552213i
$839$	4.56271e12			0.317902			0.158951	−	0.987286i	$-0.449189\pi$
$839$	4.56271e12			0.317902			0.158951	+	0.987286i	$0.449189\pi$
$840$		0			0
$841$	3.64201e13			2.51049
$842$	9.62647e12	+	1.66735e13i	0.660028	+	1.14320i
$843$		0			0
$844$	2.90254e12	−	5.02734e12i	0.196896	−	0.341034i
$845$	5.32216e12	+	9.21825e12i	0.359114	+	0.622004i
$846$		0			0
$847$	−1.01328e12	−	6.31004e12i	−0.0676478	−	0.421266i
$848$	−4.58120e11			−0.0304227
$849$		0			0
$850$	9.66119e12	−	1.67337e13i	0.634813	−	1.09953i
$851$	−3.13287e12	+	5.42629e12i	−0.204767	+	0.354666i
$852$		0			0
$853$	3.32776e12			0.215219			0.107610	−	0.994193i	$-0.465680\pi$
$853$	3.32776e12			0.215219			0.107610	+	0.994193i	$0.465680\pi$
$854$	1.32514e12	−	1.07779e12i	0.0852514	−	0.0693382i
$855$		0			0
$856$	−9.49972e11	−	1.64540e12i	−0.0604754	−	0.104747i
$857$	−1.18941e13	+	2.06012e13i	−0.753214	+	1.30461i	0.193043	+	0.981190i	$0.438164\pi$
$857$	−1.18941e13	+	2.06012e13i	−0.753214	+	1.30461i	−0.946257	+	0.323415i	$0.895169\pi$
$858$		0			0
$859$	−9.23089e12	−	1.59884e13i	−0.578461	−	1.00192i	−0.995656	−	0.0931074i	$-0.970320\pi$
$859$	−9.23089e12	−	1.59884e13i	−0.578461	−	1.00192i	0.417195	−	0.908817i	$-0.363013\pi$
$860$	6.46306e12			0.402898
$861$		0			0
$862$	6.04036e12			0.372632
$863$	3.52216e12	+	6.10056e12i	0.216153	+	0.374388i	0.953629	−	0.300986i	$-0.0973157\pi$
$863$	3.52216e12	+	6.10056e12i	0.216153	+	0.374388i	−0.737476	+	0.675374i	$0.763982\pi$
$864$		0			0
$865$	−6.99749e12	+	1.21200e13i	−0.424981	+	0.736089i
$866$	6.01610e12	+	1.04202e13i	0.363484	+	0.629572i
$867$		0			0
$868$	1.97939e12	+	1.23264e13i	0.118357	+	0.737050i
$869$	−6.02101e11			−0.0358162
$870$		0			0
$871$	7.71659e12	−	1.33655e13i	0.454301	−	0.786873i
$872$	4.98709e12	−	8.63789e12i	0.292094	−	0.505922i
$873$		0			0
$874$	1.50655e13			0.873340
$875$	−1.56033e13	−	5.95123e12i	−0.899873	−	0.343218i
$876$		0			0
$877$	−5.96444e11	−	1.03307e12i	−0.0340464	−	0.0589701i	0.848500	−	0.529195i	$-0.177506\pi$
$877$	−5.96444e11	−	1.03307e12i	−0.0340464	−	0.0589701i	−0.882547	+	0.470225i	$0.844173\pi$
$878$	−5.73769e12	+	9.93797e12i	−0.325845	+	0.564381i
$879$		0			0
$880$	−4.28082e12	−	7.41459e12i	−0.240633	−	0.416788i
$881$	2.12338e13			1.18751			0.593754	−	0.804647i	$-0.297645\pi$
$881$	2.12338e13			1.18751			0.593754	+	0.804647i	$0.297645\pi$
$882$		0			0
$883$	1.08414e13			0.600155			0.300078	−	0.953915i	$-0.402987\pi$
$883$	1.08414e13			0.600155			0.300078	+	0.953915i	$0.402987\pi$
$884$	−6.13387e12	−	1.06242e13i	−0.337831	−	0.585141i
$885$		0			0
$886$	−7.65383e12	+	1.32568e13i	−0.417279	+	0.722749i
$887$	3.87438e12	+	6.71063e12i	0.210158	+	0.364005i	0.951764	−	0.306831i	$-0.0992688\pi$
$887$	3.87438e12	+	6.71063e12i	0.210158	+	0.364005i	−0.741606	+	0.670836i	$0.765935\pi$
$888$		0			0
$889$	9.91839e12	+	3.78295e12i	0.532578	+	0.203129i
$890$	2.54423e13			1.35926
$891$		0			0
$892$	4.03430e12	−	6.98761e12i	0.213367	−	0.369562i
$893$	−1.38725e13	+	2.40279e13i	−0.730003	+	1.26440i
$894$		0			0
$895$	−3.38297e13			−1.76236
$896$	−2.70364e11	−	1.68365e12i	−0.0140140	−	0.0872703i
$897$		0			0
$898$	−7.49080e12	−	1.29745e13i	−0.384401	−	0.665803i
$899$	2.73923e13	−	4.74448e13i	1.39865	−	2.42254i
$900$		0			0
$901$	−1.35276e12	−	2.34305e12i	−0.0683847	−	0.118446i
$902$	−2.75066e13			−1.38359
$903$		0			0
$904$	7.59232e12			0.378109
$905$	3.36903e12	+	5.83533e12i	0.166950	+	0.289166i
$906$		0			0
$907$	−2.85796e12	+	4.95013e12i	−0.140224	+	0.242875i	−0.927581	−	0.373622i	$-0.878116\pi$
$907$	−2.85796e12	+	4.95013e12i	−0.140224	+	0.242875i	0.787357	+	0.616498i	$0.211449\pi$
$908$	9.05159e12	+	1.56778e13i	0.441915	+	0.765419i
$909$		0			0
$910$	−2.19903e13	+	1.78856e13i	−1.06303	+	0.864603i
$911$	−5.49279e12			−0.264217			−0.132108	−	0.991235i	$-0.542175\pi$
$911$	−5.49279e12			−0.264217			−0.132108	+	0.991235i	$0.542175\pi$
$912$		0			0
$913$	−7.88168e12	+	1.36515e13i	−0.375405	+	0.650221i
$914$	4.16083e12	−	7.20677e12i	0.197207	−	0.341573i
$915$		0			0
$916$	−1.15542e13			−0.542263
$917$	1.60897e12	+	1.00197e13i	0.0751428	+	0.467940i
$918$		0			0
$919$	−1.57120e12	−	2.72140e12i	−0.0726627	−	0.125856i	0.827405	−	0.561606i	$-0.189816\pi$
$919$	−1.57120e12	−	2.72140e12i	−0.0726627	−	0.125856i	−0.900067	+	0.435751i	$0.856483\pi$
$920$	6.72634e12	−	1.16504e13i	0.309552	−	0.536160i
$921$		0			0
$922$	−4.81186e12	−	8.33438e12i	−0.219292	−	0.379826i
$923$	2.07849e12			0.0942628
$924$		0			0
$925$	1.34079e13			0.602177
$926$	−8.97165e11	−	1.55394e12i	−0.0400980	−	0.0694518i
$927$		0			0
$928$	−3.74149e12	+	6.48046e12i	−0.165607	+	0.286840i
$929$	−1.37546e12	−	2.38237e12i	−0.0605867	−	0.104939i	0.834141	−	0.551551i	$-0.185964\pi$
$929$	−1.37546e12	−	2.38237e12i	−0.0605867	−	0.104939i	−0.894728	+	0.446612i	$0.852630\pi$
$930$		0			0
$931$	5.30855e12	−	2.55119e13i	0.231581	−	1.11293i
$932$	2.03723e12			0.0884441
$933$		0			0
$934$	1.29260e13	−	2.23884e13i	0.555779	−	0.962637i
$935$	2.52812e13	−	4.37883e13i	1.08179	−	1.87372i
$936$		0			0
$937$	6.32915e12			0.268236			0.134118	−	0.990965i	$-0.457180\pi$
$937$	6.32915e12			0.268236			0.134118	+	0.990965i	$0.457180\pi$
$938$	1.18372e13	+	4.51481e12i	0.499272	+	0.190426i
$939$		0			0
$940$	1.23874e13	+	2.14556e13i	0.517493	+	0.896324i
$941$	1.11972e13	−	1.93940e13i	0.465537	−	0.806334i	−0.533688	−	0.845681i	$-0.679194\pi$
$941$	1.11972e13	−	1.93940e13i	0.465537	−	0.806334i	0.999226	+	0.0393470i	$0.0125278\pi$
$942$		0			0
$943$	−2.16102e13	−	3.74299e13i	−0.889930	−	1.54140i
$944$	7.62590e12			0.312548
$945$		0			0
$946$	1.04015e13			0.422267
$947$	1.16873e13	+	2.02429e13i	0.472213	+	0.817896i	0.999494	−	0.0317942i	$-0.0101221\pi$
$947$	1.16873e13	+	2.02429e13i	0.472213	+	0.817896i	−0.527282	+	0.849690i	$0.676789\pi$
$948$		0			0
$949$	−1.56354e13	+	2.70813e13i	−0.625766	+	1.08386i
$950$	−1.61193e13	−	2.79194e13i	−0.642080	−	1.11211i
$951$		0			0
$952$	7.81266e12	−	6.35434e12i	0.308271	−	0.250729i
$953$	−2.63265e13			−1.03389			−0.516947	−	0.856018i	$-0.672931\pi$
$953$	−2.63265e13			−1.03389			−0.516947	+	0.856018i	$0.672931\pi$
$954$		0			0
$955$	2.62535e13	−	4.54724e13i	1.02134	−	1.76902i
$956$	−2.07538e12	+	3.59466e12i	−0.0803595	+	0.139187i
$957$		0			0
$958$	−2.08285e12			−0.0798938
$959$	−8.75852e12	+	7.12364e12i	−0.334385	+	0.271968i
$960$		0			0
$961$	−1.62472e13	−	2.81410e13i	−0.614503	−	1.06435i
$962$	4.25634e12	−	7.37220e12i	0.160232	−	0.277529i
$963$		0			0
$964$	1.20218e13	+	2.08223e13i	0.448355	+	0.776573i
$965$	−2.20214e13			−0.817470
$966$		0			0
$967$	−4.79277e13			−1.76266			−0.881328	−	0.472505i	$-0.843350\pi$
$967$	−4.79277e13			−1.76266			−0.881328	+	0.472505i	$0.843350\pi$
$968$	−2.06039e12	−	3.56870e12i	−0.0754241	−	0.130638i
$969$		0			0
$970$	−3.18499e12	+	5.51657e12i	−0.115514	+	0.200077i
$971$	2.36803e13	+	4.10156e13i	0.854873	+	1.48068i	0.876763	+	0.480923i	$0.159698\pi$
$971$	2.36803e13	+	4.10156e13i	0.854873	+	1.48068i	−0.0218899	+	0.999760i	$0.506968\pi$
$972$		0			0
$973$	−1.03207e13	−	3.93639e12i	−0.369149	−	0.140796i
$974$	−1.78226e13			−0.634536
$975$		0			0
$976$	5.50685e11	−	9.53814e11i	0.0194258	−	0.0336465i
$977$	2.74088e13	−	4.74734e13i	0.962420	−	1.66696i	0.246026	−	0.969263i	$-0.420875\pi$
$977$	2.74088e13	−	4.74734e13i	0.962420	−	1.66696i	0.716393	−	0.697697i	$-0.245792\pi$
$978$		0			0
$979$	4.09464e13			1.42460
$980$	−1.73585e13	−	1.54955e13i	−0.601168	−	0.536647i
$981$		0			0
$982$	5.40182e12	+	9.35622e12i	0.185369	+	0.321069i
$983$	4.28550e12	−	7.42271e12i	0.146390	−	0.253555i	−0.783501	−	0.621391i	$-0.786568\pi$
$983$	4.28550e12	−	7.42271e12i	0.146390	−	0.253555i	0.929891	+	0.367836i	$0.119901\pi$
$984$		0			0
$985$	2.43469e13	+	4.21701e13i	0.824102	+	1.42739i
$986$	−4.41922e13			−1.48902
$987$		0			0
$988$	−2.04682e13			−0.683397
$989$	8.17183e12	+	1.41540e13i	0.271604	+	0.470432i
$990$		0			0
$991$	−1.65382e13	+	2.86451e13i	−0.544701	+	0.943449i	0.453925	+	0.891040i	$0.350023\pi$
$991$	−1.65382e13	+	2.86451e13i	−0.544701	+	0.943449i	−0.998626	+	0.0524093i	$0.983310\pi$
$992$	4.02488e12	+	6.97130e12i	0.131963	+	0.228566i
$993$		0			0
$994$	2.70522e11	+	1.68464e12i	0.00878950	+	0.0547353i
$995$	−8.15412e13			−2.63738
$996$		0			0
$997$	−1.18985e12	+	2.06089e12i	−0.0381386	+	0.0660581i	−0.884465	−	0.466607i	$-0.845476\pi$
$997$	−1.18985e12	+	2.06089e12i	−0.0381386	+	0.0660581i	0.846326	+	0.532665i	$0.178810\pi$
$998$	1.33475e13	−	2.31186e13i	0.425906	−	0.737690i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.10.g.d.109.3		6
3.2	odd	2		42.10.e.d.25.1	✓	6
7.2	even	3	inner	126.10.g.d.37.3		6
21.2	odd	6		42.10.e.d.37.1	yes	6
21.11	odd	6		294.10.a.r.1.3		3
21.17	even	6		294.10.a.u.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.10.e.d.25.1	✓	6	3.2	odd	2
42.10.e.d.37.1	yes	6	21.2	odd	6
126.10.g.d.37.3		6	7.2	even	3	inner
126.10.g.d.109.3		6	1.1	even	1	trivial
294.10.a.r.1.3		3	21.11	odd	6
294.10.a.u.1.1		3	21.17	even	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.00000 - 13.8564i) q^{2} +(-128.000 + 221.703i) q^{4} +(1126.21 + 1950.65i) q^{5} +(5935.39 + 2263.80i) q^{7} +4096.00 q^{8} +(18019.3 - 31210.4i) q^{10} +(29000.0 - 50229.5i) q^{11} -123815. q^{13} +(-16115.0 - 100354. i) q^{14} +(-32768.0 - 56755.8i) q^{16} +(193518. - 335182. i) q^{17} +(-322875. - 559237. i) q^{19} -576619. q^{20} -928000. q^{22} +(-729071. - 1.26279e6i) q^{23} +(-1.56013e6 + 2.70222e6i) q^{25} +(990522. + 1.71564e6i) q^{26} +(-1.26162e6 + 1.02612e6i) q^{28} +7.13633e6 q^{29} +(3.83843e6 - 6.64835e6i) q^{31} +(-524288. + 908093. i) q^{32} -6.19256e6 q^{34} +(2.26860e6 + 1.41274e7i) q^{35} +(-2.14853e6 - 3.72137e6i) q^{37} +(-5.16601e6 + 8.94778e6i) q^{38} +(4.61295e6 + 7.98986e6i) q^{40} +2.96407e7 q^{41} -1.12086e7 q^{43} +(7.42400e6 + 1.28587e7i) q^{44} +(-1.16651e7 + 2.02046e7i) q^{46} +(-2.14828e7 - 3.72093e7i) q^{47} +(3.01040e7 + 2.68731e7i) q^{49} +4.99241e7 q^{50} +(1.58484e7 - 2.74502e7i) q^{52} +(3.49518e6 - 6.05383e6i) q^{53} +1.30640e8 q^{55} +(2.43113e7 + 9.27253e6i) q^{56} +(-5.70907e7 - 9.88839e7i) q^{58} +(-5.81810e7 + 1.00772e8i) q^{59} +(8.40279e6 + 1.45541e7i) q^{61} -1.22830e8 q^{62} +1.67772e7 q^{64} +(-1.39442e8 - 2.41520e8i) q^{65} +(-6.23234e7 + 1.07947e8i) q^{67} +(4.95405e7 + 8.58067e7i) q^{68} +(1.77606e8 - 1.44454e8i) q^{70} -1.67870e7 q^{71} +(1.26280e8 - 2.18724e8i) q^{73} +(-3.43765e7 + 5.95419e7i) q^{74} +1.65312e8 q^{76} +(2.85836e8 - 2.32481e8i) q^{77} +(-5.19052e6 - 8.99025e6i) q^{79} +(7.38072e7 - 1.27838e8i) q^{80} +(-2.37126e8 - 4.10714e8i) q^{82} -2.71782e8 q^{83} +8.71765e8 q^{85} +(8.96684e7 + 1.55310e8i) q^{86} +(1.18784e8 - 2.05740e8i) q^{88} +(3.52986e8 + 6.11390e8i) q^{89} +(-7.34892e8 - 2.80293e8i) q^{91} +3.73285e8 q^{92} +(-3.43725e8 + 5.95349e8i) q^{94} +(7.27250e8 - 1.25963e9i) q^{95} -1.76754e8 q^{97} +(1.31532e8 - 6.32118e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 48 q^{2} - 768 q^{4} - 361 q^{5} + 12509 q^{7} + 24576 q^{8} - 5776 q^{10} - 37799 q^{11} - 441172 q^{13} - 38752 q^{14} - 196608 q^{16} + 781816 q^{17} - 620154 q^{19} + 184832 q^{20} + 1209568 q^{22}+ \cdots + 2185772400 q^{98}+O(q^{100}) \) 6 * q - 48 * q^2 - 768 * q^4 - 361 * q^5 + 12509 * q^7 + 24576 * q^8 - 5776 * q^10 - 37799 * q^11 - 441172 * q^13 - 38752 * q^14 - 196608 * q^16 + 781816 * q^17 - 620154 * q^19 + 184832 * q^20 + 1209568 * q^22 - 1204784 * q^23 - 4020946 * q^25 + 3529376 * q^26 - 2582272 * q^28 + 10561070 * q^29 + 12838457 * q^31 - 3145728 * q^32 - 25018112 * q^34 + 20450416 * q^35 + 8014770 * q^37 - 9922464 * q^38 - 1478656 * q^40 - 13006056 * q^41 - 45086976 * q^43 - 9676544 * q^44 - 19276544 * q^46 + 21473082 * q^47 - 92935311 * q^49 + 128670272 * q^50 + 56470016 * q^52 - 13685715 * q^53 + 610214782 * q^55 + 51236864 * q^56 - 84488560 * q^58 + 92528141 * q^59 - 7516114 * q^61 - 410830624 * q^62 + 100663296 * q^64 - 79637616 * q^65 - 137325404 * q^67 + 200144896 * q^68 + 33639760 * q^70 - 16380692 * q^71 + 394016164 * q^73 + 128236320 * q^74 + 317518848 * q^76 - 140332213 * q^77 + 35090117 * q^79 - 23658496 * q^80 + 104048448 * q^82 - 1913896010 * q^83 - 823798640 * q^85 + 360695808 * q^86 - 154824704 * q^88 + 855499686 * q^89 - 1675912546 * q^91 + 616849408 * q^92 + 343569312 * q^94 + 2705508088 * q^95 + 4021139590 * q^97 + 2185772400 * q^98

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