LMFDB - Embedded newform 126.11.n.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,11,Mod(19,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("126.19");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	126.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$80.0550138369$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 7168 x^{10} - 191104 x^{9} + 39872585 x^{8} - 837614684 x^{7} + 83400850488 x^{6} + \cdots + 16\!\cdots\!56 $ x^12 + 7168x^10 - 191104x^9 + 39872585x^8 - 837614684x^7 + 83400850488x^6 - 1089499860800x^5 + 117569881085905x^4 - 972128975671236x^3 + 70590565447335180x^2 + 627290085157877232x + 16876036055394640656
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{6}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Root			$26.6851 + 46.2199i$ of defining polynomial
Character	$\chi$	$=$	126.19
Dual form			126.11.n.b.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.3137 + 19.5959i) q^{2} +(-256.000 - 443.405i) q^{4} +(-32.1973 - 18.5891i) q^{5} +(-11036.6 + 12675.5i) q^{7} +11585.2 q^{8} +O(q^{10})$	\(q+(-11.3137 + 19.5959i) q^{2} +(-256.000 - 443.405i) q^{4} +(-32.1973 - 18.5891i) q^{5} +(-11036.6 + 12675.5i) q^{7} +11585.2 q^{8} +(728.542 - 420.624i) q^{10} +(-67040.0 - 116117. i) q^{11} +182276. i q^{13} +(-123524. - 359679. i) q^{14} +(-131072. + 227023. i) q^{16} +(1.39715e6 - 806648. i) q^{17} +(-1.40947e6 - 813758. i) q^{19} +19035.3i q^{20} +3.03388e6 q^{22} +(-2.93644e6 + 5.08607e6i) q^{23} +(-4.88212e6 - 8.45608e6i) q^{25} +(-3.57187e6 - 2.06222e6i) q^{26} +(8.44576e6 + 1.64875e6i) q^{28} -4.34134e6 q^{29} +(-2.35447e7 + 1.35935e7i) q^{31} +(-2.96582e6 - 5.13695e6i) q^{32} +3.65047e7i q^{34} +(590975. - 202957. i) q^{35} +(-1.98766e7 + 3.44273e7i) q^{37} +(3.18927e7 - 1.84132e7i) q^{38} +(-373013. - 215359. i) q^{40} -1.69868e8i q^{41} +1.87794e8 q^{43} +(-3.43245e7 + 5.94517e7i) q^{44} +(-6.64441e7 - 1.15085e8i) q^{46} +(-1.73904e7 - 1.00404e7i) q^{47} +(-3.88623e7 - 2.79789e8i) q^{49} +2.20940e8 q^{50} +(8.08223e7 - 4.66628e7i) q^{52} +(-8.95226e7 - 1.55058e8i) q^{53} +4.98486e6i q^{55} +(-1.27862e8 + 1.46849e8i) q^{56} +(4.91166e7 - 8.50725e7i) q^{58} +(4.15536e8 - 2.39910e8i) q^{59} +(5.46484e8 + 3.15513e8i) q^{61} -6.15173e8i q^{62} +1.34218e8 q^{64} +(3.38836e6 - 5.86881e6i) q^{65} +(5.11294e8 + 8.85587e8i) q^{67} +(-7.15343e8 - 4.13004e8i) q^{68} +(-2.70900e6 + 1.38769e7i) q^{70} +1.95589e9 q^{71} +(-2.04271e9 + 1.17936e9i) q^{73} +(-4.49757e8 - 7.79001e8i) q^{74} +8.33288e8i q^{76} +(2.21173e9 + 4.31766e8i) q^{77} +(2.86793e9 - 4.96740e9i) q^{79} +(8.44033e6 - 4.87302e6i) q^{80} +(3.32871e9 + 1.92183e9i) q^{82} +5.54809e9i q^{83} -5.99795e7 q^{85} +(-2.12465e9 + 3.68000e9i) q^{86} +(-7.76674e8 - 1.34524e9i) q^{88} +(-6.80781e9 - 3.93049e9i) q^{89} +(-2.31045e9 - 2.01171e9i) q^{91} +3.00692e9 q^{92} +(3.93500e8 - 2.27187e8i) q^{94} +(3.02541e7 + 5.24016e7i) q^{95} +1.40393e10i q^{97} +(5.92240e9 + 2.40391e9i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3072 q^{4} + 6666 q^{5} + 30576 q^{7}+O(q^{10}) $ 12 * q - 3072 * q^4 + 6666 * q^5 + 30576 * q^7	$ 12 q - 3072 q^{4} + 6666 q^{5} + 30576 q^{7} + 130944 q^{10} + 111210 q^{11} + 38976 q^{14} - 1572864 q^{16} - 1439502 q^{17} - 452814 q^{19} - 1922688 q^{22} - 853074 q^{23} + 16905804 q^{25} + 8671872 q^{26} + 4064256 q^{28} - 60157248 q^{29} + 87231186 q^{31} - 153795138 q^{35} - 7666506 q^{37} + 21703872 q^{38} - 67043328 q^{40} + 1066803336 q^{43} + 56939520 q^{44} - 168245184 q^{46} + 985909398 q^{47} + 456183924 q^{49} - 1764094464 q^{50} - 538871808 q^{52} + 600022554 q^{53} + 243597312 q^{56} - 294598272 q^{58} + 2101762050 q^{59} - 2201391150 q^{61} + 1610612736 q^{64} - 1536128076 q^{65} - 1590058326 q^{67} + 737025024 q^{68} - 3745457856 q^{70} + 7739561160 q^{71} + 2008593834 q^{73} - 1042308096 q^{74} - 464655282 q^{77} + 2310562242 q^{79} - 1747451904 q^{80} + 9636272256 q^{82} - 39581743596 q^{85} + 4924086912 q^{86} + 492208128 q^{88} - 2541648690 q^{89} - 4866473640 q^{91} + 873547776 q^{92} + 28852652352 q^{94} - 29024266590 q^{95} + 11553118080 q^{98}+O(q^{100}) $ 12 * q - 3072 * q^4 + 6666 * q^5 + 30576 * q^7 + 130944 * q^10 + 111210 * q^11 + 38976 * q^14 - 1572864 * q^16 - 1439502 * q^17 - 452814 * q^19 - 1922688 * q^22 - 853074 * q^23 + 16905804 * q^25 + 8671872 * q^26 + 4064256 * q^28 - 60157248 * q^29 + 87231186 * q^31 - 153795138 * q^35 - 7666506 * q^37 + 21703872 * q^38 - 67043328 * q^40 + 1066803336 * q^43 + 56939520 * q^44 - 168245184 * q^46 + 985909398 * q^47 + 456183924 * q^49 - 1764094464 * q^50 - 538871808 * q^52 + 600022554 * q^53 + 243597312 * q^56 - 294598272 * q^58 + 2101762050 * q^59 - 2201391150 * q^61 + 1610612736 * q^64 - 1536128076 * q^65 - 1590058326 * q^67 + 737025024 * q^68 - 3745457856 * q^70 + 7739561160 * q^71 + 2008593834 * q^73 - 1042308096 * q^74 - 464655282 * q^77 + 2310562242 * q^79 - 1747451904 * q^80 + 9636272256 * q^82 - 39581743596 * q^85 + 4924086912 * q^86 + 492208128 * q^88 - 2541648690 * q^89 - 4866473640 * q^91 + 873547776 * q^92 + 28852652352 * q^94 - 29024266590 * q^95 + 11553118080 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−11.3137	+	19.5959i	−0.353553	+	0.612372i
$2$	−11.3137	+	19.5959i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−256.000	−	443.405i	−0.250000	−	0.433013i
$5$	−32.1973	−	18.5891i	−0.0103031	−	0.00594852i	0.494840	−	0.868984i	$-0.335227\pi$
$5$	−32.1973	−	18.5891i	−0.0103031	−	0.00594852i	−0.505143	+	0.863036i	$0.668560\pi$
$6$		0			0
$7$	−11036.6	+	12675.5i	−0.656667	+	0.754181i
$7$	−11036.6	+	12675.5i	−0.656667	+	0.754181i
$8$	11585.2			0.353553
$9$		0			0
$10$	728.542	−	420.624i	0.00728542	−	0.00420624i
$11$	−67040.0	−	116117.i	−0.416266	−	0.720993i	0.579295	−	0.815118i	$-0.303328\pi$
$11$	−67040.0	−	116117.i	−0.416266	−	0.720993i	−0.995560	+	0.0941250i	$0.969995\pi$
$12$		0			0
$13$			182276.i			0.490923i	0.969406	+	0.245462i	$0.0789396\pi$
$13$			182276.i			0.490923i	−0.969406	+	0.245462i	$0.921060\pi$
$14$	−123524.	−	359679.i	−0.229673	−	0.668768i
$15$		0			0
$16$	−131072.	+	227023.i	−0.125000	+	0.216506i
$17$	1.39715e6	−	806648.i	0.984011	−	0.568119i	0.0805323	−	0.996752i	$-0.474338\pi$
$17$	1.39715e6	−	806648.i	0.984011	−	0.568119i	0.903479	+	0.428633i	$0.141005\pi$
$18$		0			0
$19$	−1.40947e6	−	813758.i	−0.569230	−	0.328645i	0.187612	−	0.982243i	$-0.439925\pi$
$19$	−1.40947e6	−	813758.i	−0.569230	−	0.328645i	−0.756842	+	0.653598i	$0.773259\pi$
$20$			19035.3i			0.00594852i
$21$		0			0
$22$	3.03388e6			0.588688
$23$	−2.93644e6	+	5.08607e6i	−0.456228	+	0.790211i	−0.998758	−	0.0498260i	$-0.984133\pi$
$23$	−2.93644e6	+	5.08607e6i	−0.456228	+	0.790211i	0.542530	+	0.840037i	$0.317467\pi$
$24$		0			0
$25$	−4.88212e6	−	8.45608e6i	−0.499929	−	0.865903i
$26$	−3.57187e6	−	2.06222e6i	−0.300628	−	0.173568i
$27$		0			0
$28$	8.44576e6	+	1.64875e6i	0.490737	+	0.0957998i
$29$	−4.34134e6			−0.211657			−0.105829	−	0.994384i	$-0.533750\pi$
$29$	−4.34134e6			−0.211657			−0.105829	+	0.994384i	$0.533750\pi$
$30$		0			0
$31$	−2.35447e7	+	1.35935e7i	−0.822403	+	0.474815i	−0.851244	−	0.524769i	$-0.824152\pi$
$31$	−2.35447e7	+	1.35935e7i	−0.822403	+	0.474815i	0.0288413	+	0.999584i	$0.490818\pi$
$32$	−2.96582e6	−	5.13695e6i	−0.0883883	−	0.153093i
$33$		0			0
$34$			3.65047e7i			0.803442i
$35$	590975.	−	202957.i	0.0112520	−	0.00386423i
$36$		0			0
$37$	−1.98766e7	+	3.44273e7i	−0.286638	+	0.496472i	−0.973005	−	0.230784i	$-0.925871\pi$
$37$	−1.98766e7	+	3.44273e7i	−0.286638	+	0.496472i	0.686367	+	0.727255i	$0.259204\pi$
$38$	3.18927e7	−	1.84132e7i	0.402507	−	0.232387i
$39$		0			0
$40$	−373013.	−	215359.i	−0.00364271	−	0.00210312i
$41$		−	1.69868e8i		−	1.46619i	−0.680124	−	0.733097i	$-0.738074\pi$
$41$		−	1.69868e8i		−	1.46619i	0.680124	−	0.733097i	$-0.261926\pi$
$42$		0			0
$43$	1.87794e8			1.27744			0.638719	−	0.769440i	$-0.279465\pi$
$43$	1.87794e8			1.27744			0.638719	+	0.769440i	$0.279465\pi$
$44$	−3.43245e7	+	5.94517e7i	−0.208133	+	0.360497i
$45$		0			0
$46$	−6.64441e7	−	1.15085e8i	−0.322602	−	0.558763i
$47$	−1.73904e7	−	1.00404e7i	−0.0758264	−	0.0437784i	0.461607	−	0.887084i	$-0.347273\pi$
$47$	−1.73904e7	−	1.00404e7i	−0.0758264	−	0.0437784i	−0.537434	+	0.843306i	$0.680606\pi$
$48$		0			0
$49$	−3.88623e7	−	2.79789e8i	−0.137578	−	0.990491i
$50$	2.20940e8			0.707007
$51$		0			0
$52$	8.08223e7	−	4.66628e7i	0.212576	−	0.122731i
$53$	−8.95226e7	−	1.55058e8i	−0.214069	−	0.370778i	0.738915	−	0.673798i	$-0.235338\pi$
$53$	−8.95226e7	−	1.55058e8i	−0.214069	−	0.370778i	−0.952984	+	0.303020i	$0.902005\pi$
$54$		0			0
$55$			4.98486e6i			0.00990465i
$56$	−1.27862e8	+	1.46849e8i	−0.232167	+	0.266643i
$57$		0			0
$58$	4.91166e7	−	8.50725e7i	0.0748322	−	0.129613i
$59$	4.15536e8	−	2.39910e8i	0.581231	−	0.335574i	−0.180392	−	0.983595i	$-0.557737\pi$
$59$	4.15536e8	−	2.39910e8i	0.581231	−	0.335574i	0.761622	+	0.648021i	$0.224403\pi$
$60$		0			0
$61$	5.46484e8	+	3.15513e8i	0.647035	+	0.373566i	0.787320	−	0.616545i	$-0.211468\pi$
$61$	5.46484e8	+	3.15513e8i	0.647035	+	0.373566i	−0.140284	+	0.990111i	$0.544802\pi$
$62$		−	6.15173e8i		−	0.671489i
$63$		0			0
$64$	1.34218e8			0.125000
$65$	3.38836e6	−	5.86881e6i	0.00292027	−	0.00505805i
$66$		0			0
$67$	5.11294e8	+	8.85587e8i	0.378701	+	0.655930i	0.990874	−	0.134795i	$-0.0430375\pi$
$67$	5.11294e8	+	8.85587e8i	0.378701	+	0.655930i	−0.612172	+	0.790724i	$0.709704\pi$
$68$	−7.15343e8	−	4.13004e8i	−0.492006	−	0.284060i
$69$		0			0
$70$	−2.70900e6	+	1.38769e7i	−0.00161183	+	0.00825662i
$71$	1.95589e9			1.08406			0.542028	−	0.840360i	$-0.317657\pi$
$71$	1.95589e9			1.08406			0.542028	+	0.840360i	$0.317657\pi$
$72$		0			0
$73$	−2.04271e9	+	1.17936e9i	−0.985355	+	0.568895i	−0.903883	−	0.427780i	$-0.859296\pi$
$73$	−2.04271e9	+	1.17936e9i	−0.985355	+	0.568895i	−0.0814726	+	0.996676i	$0.525962\pi$
$74$	−4.49757e8	−	7.79001e8i	−0.202684	−	0.351059i
$75$		0			0
$76$			8.33288e8i			0.328645i
$77$	2.21173e9	+	4.31766e8i	0.817107	+	0.159513i
$78$		0			0
$79$	2.86793e9	−	4.96740e9i	0.932036	−	1.61433i	0.152201	−	0.988350i	$-0.451364\pi$
$79$	2.86793e9	−	4.96740e9i	0.932036	−	1.61433i	0.779836	−	0.625984i	$-0.215303\pi$
$80$	8.44033e6	−	4.87302e6i	0.00257578	−	0.00148713i
$81$		0			0
$82$	3.32871e9	+	1.92183e9i	0.897857	+	0.518378i
$83$			5.54809e9i			1.40849i	0.709958	+	0.704244i	$0.248714\pi$
$83$			5.54809e9i			1.40849i	−0.709958	+	0.704244i	$0.751286\pi$
$84$		0			0
$85$	−5.99795e7			−0.0135179
$86$	−2.12465e9	+	3.68000e9i	−0.451642	+	0.782267i
$87$		0			0
$88$	−7.76674e8	−	1.34524e9i	−0.147172	−	0.254910i
$89$	−6.80781e9	−	3.93049e9i	−1.21915	−	0.703877i	−0.254414	−	0.967095i	$-0.581883\pi$
$89$	−6.80781e9	−	3.93049e9i	−1.21915	−	0.703877i	−0.964736	+	0.263219i	$0.915216\pi$
$90$		0			0
$91$	−2.31045e9	−	2.01171e9i	−0.370245	−	0.322373i
$92$	3.00692e9			0.456228
$93$		0			0
$94$	3.93500e8	−	2.27187e8i	0.0536174	−	0.0309560i
$95$	3.02541e7	+	5.24016e7i	0.00390990	+	0.00677215i
$96$		0			0
$97$			1.40393e10i			1.63488i	0.576014	+	0.817440i	$0.304607\pi$
$97$			1.40393e10i			1.63488i	−0.576014	+	0.817440i	$0.695393\pi$
$98$	5.92240e9	+	2.40391e9i	0.655190	+	0.265943i
$99$		0			0
$100$	−2.49965e9	+	4.32951e9i	−0.249965	+	0.432951i
$101$	1.40477e10	−	8.11046e9i	1.33659	−	0.771683i	0.350293	−	0.936640i	$-0.386082\pi$
$101$	1.40477e10	−	8.11046e9i	1.33659	−	0.771683i	0.986301	+	0.164958i	$0.0527487\pi$
$102$		0			0
$103$	1.63450e10	+	9.43676e9i	1.40993	+	0.814023i	0.995381	−	0.0960036i	$-0.0306060\pi$
$103$	1.63450e10	+	9.43676e9i	1.40993	+	0.814023i	0.414549	+	0.910027i	$0.363939\pi$
$104$			2.11172e9i			0.173568i
$105$		0			0
$106$	4.05133e9			0.302739
$107$	−9.05563e9	+	1.56848e10i	−0.645654	+	1.11831i	0.338496	+	0.940968i	$0.390082\pi$
$107$	−9.05563e9	+	1.56848e10i	−0.645654	+	1.11831i	−0.984150	+	0.177338i	$0.943252\pi$
$108$		0			0
$109$	1.47944e10	+	2.56246e10i	0.961532	+	1.66542i	0.718657	+	0.695365i	$0.244757\pi$
$109$	1.47944e10	+	2.56246e10i	0.961532	+	1.66542i	0.242875	+	0.970058i	$0.421910\pi$
$110$	−9.76828e7	−	5.63972e7i	−0.00606534	−	0.00350182i
$111$		0			0
$112$	−1.43105e9	−	4.16697e9i	−0.0812016	−	0.236445i
$113$	1.26465e10			0.686403			0.343201	−	0.939262i	$-0.388489\pi$
$113$	1.26465e10			0.686403			0.343201	+	0.939262i	$0.388489\pi$
$114$		0			0
$115$	1.89091e8	−	1.09172e8i	0.00940116	−	0.00542776i
$116$	1.11138e9	+	1.92497e9i	0.0529144	+	0.0916504i
$117$		0			0
$118$			1.08571e10i			0.474573i
$119$	−5.19516e9	+	2.66123e10i	−0.217703	+	1.11519i
$120$		0			0
$121$	3.97999e9	−	6.89355e9i	0.153446	−	0.265776i
$122$	−1.23655e10	+	7.13923e9i	−0.457523	+	0.264151i
$123$		0			0
$124$	1.20549e10	+	6.95989e9i	0.411202	+	0.237407i
$125$			7.26086e8i			0.0237924i
$126$		0			0
$127$	2.05694e10			0.622592			0.311296	−	0.950313i	$-0.399237\pi$
$127$	2.05694e10			0.622592			0.311296	+	0.950313i	$0.399237\pi$
$128$	−1.51850e9	+	2.63012e9i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	7.66698e7	+	1.32796e8i	0.00206494	+	0.00357658i
$131$	5.25665e10	+	3.03493e10i	1.36255	+	0.786669i	0.989963	−	0.141328i	$-0.0451373\pi$
$131$	5.25665e10	+	3.03493e10i	1.36255	+	0.786669i	0.372587	+	0.927997i	$0.378471\pi$
$132$		0			0
$133$	2.58706e10	−	8.88465e9i	0.621652	−	0.213492i
$134$	−2.31385e10			−0.535564
$135$		0			0
$136$	1.61864e10	−	9.34521e9i	0.347900	−	0.200860i
$137$	−1.72731e7	−	2.99180e7i	−0.000357906	−	0.000619911i	0.865846	−	0.500310i	$-0.166781\pi$
$137$	−1.72731e7	−	2.99180e7i	−0.000357906	−	0.000619911i	−0.866204	+	0.499690i	$0.833447\pi$
$138$		0			0
$139$			2.00016e10i			0.385470i	0.981251	+	0.192735i	$0.0617358\pi$
$139$			2.00016e10i			0.385470i	−0.981251	+	0.192735i	$0.938264\pi$
$140$	−2.41282e8	−	2.10084e8i	−0.00448626	−	0.00390619i
$141$		0			0
$142$	−2.21283e10	+	3.83274e10i	−0.383272	+	0.663846i
$143$	2.11653e10	−	1.22198e10i	0.353952	−	0.204355i
$144$		0			0
$145$	1.39779e8	+	8.07016e7i	0.00218073	+	0.00125905i
$146$		−	5.33718e10i		−	0.804539i
$147$		0			0
$148$	2.03537e10			0.286638
$149$	2.93256e10	−	5.07935e10i	0.399315	−	0.691635i	−0.594326	−	0.804224i	$-0.702581\pi$
$149$	2.93256e10	−	5.07935e10i	0.399315	−	0.691635i	0.993642	+	0.112590i	$0.0359145\pi$
$150$		0			0
$151$	2.14956e10	+	3.72315e10i	0.273820	+	0.474270i	0.969837	−	0.243756i	$-0.0783795\pi$
$151$	2.14956e10	+	3.72315e10i	0.273820	+	0.474270i	−0.696017	+	0.718025i	$0.745046\pi$
$152$	−1.63290e10	−	9.42758e9i	−0.201253	−	0.116194i
$153$		0			0
$154$	−3.34838e10	+	3.84560e10i	−0.386572	+	0.443978i
$155$	1.01077e9			0.0112978
$156$		0			0
$157$	−2.22325e9	+	1.28359e9i	−0.0233072	+	0.0134564i	−0.511608	−	0.859219i	$-0.670950\pi$
$157$	−2.22325e9	+	1.28359e9i	−0.0233072	+	0.0134564i	0.488301	+	0.872675i	$0.337617\pi$
$158$	6.48938e10	+	1.12399e11i	0.659049	+	1.14151i
$159$		0			0
$160$			2.20528e8i			0.00210312i
$161$	−3.20602e10	−	9.33538e10i	−0.296372	−	0.862984i
$162$		0			0
$163$	−2.63114e10	+	4.55727e10i	−0.228668	+	0.396065i	−0.957414	−	0.288720i	$-0.906770\pi$
$163$	−2.63114e10	+	4.55727e10i	−0.228668	+	0.396065i	0.728745	+	0.684785i	$0.240104\pi$
$164$	−7.53202e10	+	4.34861e10i	−0.634881	+	0.366549i
$165$		0			0
$166$	−1.08720e11	−	6.27695e10i	−0.862519	−	0.497975i
$167$			1.38652e11i			1.06744i	0.845661	+	0.533720i	$0.179206\pi$
$167$			1.38652e11i			1.06744i	−0.845661	+	0.533720i	$0.820794\pi$
$168$		0			0
$169$	1.04634e11			0.758994
$170$	6.78590e8	−	1.17535e9i	0.00477929	−	0.00827797i
$171$		0			0
$172$	−4.80753e10	−	8.32688e10i	−0.319359	−	0.553147i
$173$	9.07834e10	+	5.24138e10i	0.585836	+	0.338232i	0.763449	−	0.645868i	$-0.223504\pi$
$173$	9.07834e10	+	5.24138e10i	0.585836	+	0.338232i	−0.177613	+	0.984100i	$0.556838\pi$
$174$		0			0
$175$	1.61067e11	+	3.14430e10i	0.981334	+	0.191572i
$176$	3.51483e10			0.208133
$177$		0			0
$178$	1.54043e11	−	8.89368e10i	0.862069	−	0.497716i
$179$	−1.48620e11	−	2.57418e11i	−0.808749	−	1.40079i	−0.913731	−	0.406319i	$-0.866812\pi$
$179$	−1.48620e11	−	2.57418e11i	−0.808749	−	1.40079i	0.104983	−	0.994474i	$-0.466521\pi$
$180$		0			0
$181$		−	2.97932e11i		−	1.53364i	−0.641860	−	0.766822i	$-0.721837\pi$
$181$		−	2.97932e11i		−	1.53364i	0.641860	−	0.766822i	$-0.278163\pi$
$182$	6.55611e10	−	2.25154e10i	0.328314	−	0.112752i
$183$		0			0
$184$	−3.40194e10	+	5.89233e10i	−0.161301	+	0.279382i
$185$	1.27995e9	−	7.38978e8i	0.00590654	−	0.00341014i
$186$		0			0
$187$	−1.87331e11	−	1.08155e11i	−0.819220	−	0.472977i
$188$			1.02813e10i			0.0437784i
$189$		0			0
$190$	−1.36914e9			−0.00552944
$191$	1.97207e11	−	3.41573e11i	0.775811	−	1.34374i	−0.158526	−	0.987355i	$-0.550674\pi$
$191$	1.97207e11	−	3.41573e11i	0.775811	−	1.34374i	0.934338	−	0.356389i	$-0.115992\pi$
$192$		0			0
$193$	−1.92270e10	−	3.33021e10i	−0.0718001	−	0.124361i	0.827890	−	0.560890i	$-0.189541\pi$
$193$	−1.92270e10	−	3.33021e10i	−0.0718001	−	0.124361i	−0.899690	+	0.436529i	$0.856208\pi$
$194$	−2.75112e11	−	1.58836e11i	−1.00115	−	0.578017i
$195$		0			0
$196$	−1.14111e11	+	8.88578e10i	−0.394501	+	0.307196i
$197$	1.91495e11			0.645396			0.322698	−	0.946502i	$-0.395410\pi$
$197$	1.91495e11			0.645396			0.322698	+	0.946502i	$0.395410\pi$
$198$		0			0
$199$	−1.39430e11	+	8.04998e10i	−0.446776	+	0.257946i	−0.706468	−	0.707745i	$-0.749712\pi$
$199$	−1.39430e11	+	8.04998e10i	−0.446776	+	0.257946i	0.259691	+	0.965692i	$0.416379\pi$
$200$	−5.65605e10	−	9.79657e10i	−0.176752	−	0.306143i
$201$		0			0
$202$			3.67038e11i			1.09132i
$203$	4.79136e10	−	5.50287e10i	0.138988	−	0.159628i
$204$		0			0
$205$	−3.15769e9	+	5.46928e9i	−0.00872168	+	0.0151064i
$206$	−3.69844e11	+	2.13530e11i	−0.996971	+	0.575601i
$207$		0			0
$208$	−4.13810e10	−	2.38913e10i	−0.106288	−	0.0613654i
$209$			2.18217e11i			0.547215i
$210$		0			0
$211$	−1.08000e11			−0.258232			−0.129116	−	0.991629i	$-0.541214\pi$
$211$	−1.08000e11			−0.258232			−0.129116	+	0.991629i	$0.541214\pi$
$212$	−4.58356e10	+	7.93895e10i	−0.107034	+	0.185389i
$213$		0			0
$214$	−2.04906e11	−	3.54907e11i	−0.456546	−	0.790761i
$215$	−6.04646e9	−	3.49093e9i	−0.0131616	−	0.00759886i
$216$		0			0
$217$	8.75482e10	−	4.48468e11i	0.181949	−	0.932036i
$218$	−6.69516e11			−1.35981
$219$		0			0
$220$	2.21031e9	−	1.27612e9i	0.00428884	−	0.00247616i
$221$	1.47033e11	+	2.54668e11i	0.278903	+	0.483074i
$222$		0			0
$223$		−	1.70102e10i		−	0.0308449i	−0.999881	−	0.0154225i	$-0.995091\pi$
$223$		−	1.70102e10i		−	0.0308449i	0.999881	−	0.0154225i	$-0.00490932\pi$
$224$	9.78461e10	+	1.91012e10i	0.173502	+	0.0338703i
$225$		0			0
$226$	−1.43079e11	+	2.47820e11i	−0.242680	+	0.420334i
$227$	5.04346e11	−	2.91184e11i	0.836757	−	0.483102i	−0.0194033	−	0.999812i	$-0.506177\pi$
$227$	5.04346e11	−	2.91184e11i	0.836757	−	0.483102i	0.856161	+	0.516710i	$0.172843\pi$
$228$		0			0
$229$	−4.06444e11	−	2.34660e11i	−0.645391	−	0.372617i	0.141297	−	0.989967i	$-0.454873\pi$
$229$	−4.06444e11	−	2.34660e11i	−0.645391	−	0.372617i	−0.786688	+	0.617351i	$0.788206\pi$
$230$			4.94055e9i			0.00767602i
$231$		0			0
$232$	−5.02954e10			−0.0748322
$233$	−4.70675e11	+	8.15233e11i	−0.685396	+	1.18714i	0.287917	+	0.957655i	$0.407037\pi$
$233$	−4.70675e11	+	8.15233e11i	−0.685396	+	1.18714i	−0.973312	+	0.229485i	$0.926296\pi$
$234$		0			0
$235$	3.73283e8	+	6.46545e8i	0.000520833	+	0.000902109i
$236$	−2.12754e11	−	1.22834e11i	−0.290615	−	0.167787i
$237$		0			0
$238$	−4.62716e11	−	4.02888e11i	−0.605940	−	0.527593i
$239$	2.93858e11			0.376832			0.188416	−	0.982089i	$-0.439665\pi$
$239$	2.93858e11			0.376832			0.188416	+	0.982089i	$0.439665\pi$
$240$		0			0
$241$	−9.20012e11	+	5.31169e11i	−1.13164	+	0.653352i	−0.944347	−	0.328952i	$-0.893305\pi$
$241$	−9.20012e11	+	5.31169e11i	−1.13164	+	0.653352i	−0.187293	+	0.982304i	$0.559971\pi$
$242$	9.00569e10	+	1.55983e11i	0.108503	+	0.187932i
$243$		0			0
$244$		−	3.23085e11i		−	0.373566i
$245$	−3.94977e9	+	9.73087e9i	−0.00447447	+	0.0110235i
$246$		0			0
$247$	1.48329e11	−	2.56913e11i	0.161340	−	0.279448i
$248$	−2.72771e11	+	1.57484e11i	−0.290763	+	0.167872i
$249$		0			0
$250$	−1.42283e10	−	8.21472e9i	−0.0145698	−	0.00841188i
$251$		−	9.83808e11i		−	0.987511i	−0.869601	−	0.493755i	$-0.835624\pi$
$251$		−	9.83808e11i		−	0.987511i	0.869601	−	0.493755i	$-0.164376\pi$
$252$		0			0
$253$	7.87436e11			0.759649
$254$	−2.32716e11	+	4.03077e11i	−0.220120	+	0.381258i
$255$		0			0
$256$	−3.43597e10	−	5.95128e10i	−0.0312500	−	0.0541266i
$257$	−1.19646e12	−	6.90779e11i	−1.06717	−	0.616132i	−0.139764	−	0.990185i	$-0.544634\pi$
$257$	−1.19646e12	−	6.90779e11i	−1.06717	−	0.616132i	−0.927407	+	0.374053i	$0.877968\pi$
$258$		0			0
$259$	−2.17014e11	−	6.31907e11i	−0.186204	−	0.542193i
$260$	−3.46968e9			−0.00292027
$261$		0			0
$262$	−1.18944e12	+	6.86726e11i	−0.963468	+	0.556259i
$263$	−3.97782e11	−	6.88978e11i	−0.316130	−	0.547554i	0.663547	−	0.748135i	$-0.269050\pi$
$263$	−3.97782e11	−	6.88978e11i	−0.316130	−	0.547554i	−0.979677	+	0.200581i	$0.935717\pi$
$264$		0			0
$265$			6.65658e9i			0.00509356i
$266$	−1.18589e11	+	6.07476e11i	−0.0890506	+	0.456164i
$267$		0			0
$268$	2.61783e11	−	4.53421e11i	0.189351	−	0.327965i
$269$	2.05810e12	−	1.18825e12i	1.46119	−	0.843616i	0.462120	−	0.886817i	$-0.347089\pi$
$269$	2.05810e12	−	1.18825e12i	1.46119	−	0.843616i	0.999066	+	0.0432009i	$0.0137556\pi$
$270$		0			0
$271$	−5.69693e10	−	3.28912e10i	−0.0389757	−	0.0225026i	0.480386	−	0.877057i	$-0.340497\pi$
$271$	−5.69693e10	−	3.28912e10i	−0.0389757	−	0.0225026i	−0.519361	+	0.854555i	$0.673830\pi$
$272$			4.22916e11i			0.284060i
$273$		0			0
$274$	7.81693e8			0.000506155
$275$	−6.54595e11	+	1.13379e12i	−0.416207	+	0.720891i
$276$		0			0
$277$	−1.94329e11	−	3.36587e11i	−0.119162	−	0.206395i	0.800274	−	0.599635i	$-0.204687\pi$
$277$	−1.94329e11	−	3.36587e11i	−0.119162	−	0.206395i	−0.919436	+	0.393240i	$0.871354\pi$
$278$	−3.91950e11	−	2.26292e11i	−0.236051	−	0.136284i
$279$		0			0
$280$	6.84659e9	−	2.35130e9i	0.00397818	−	0.00136621i
$281$	1.52718e12			0.871682			0.435841	−	0.900024i	$-0.356451\pi$
$281$	1.52718e12			0.871682			0.435841	+	0.900024i	$0.356451\pi$
$282$		0			0
$283$	2.82144e12	−	1.62896e12i	1.55431	−	0.897384i	0.556532	−	0.830826i	$-0.312132\pi$
$283$	2.82144e12	−	1.62896e12i	1.55431	−	0.897384i	0.997783	−	0.0665581i	$-0.0212018\pi$
$284$	−5.00707e11	−	8.67250e11i	−0.271014	−	0.469410i
$285$		0			0
$286$			5.53005e11i			0.289001i
$287$	2.15316e12	+	1.87476e12i	1.10578	+	0.962801i
$288$		0			0
$289$	2.93364e11	−	5.08122e11i	0.145518	−	0.252045i
$290$	−3.16284e9	+	1.82607e9i	−0.00154201	+	0.000890281i
$291$		0			0
$292$	1.04587e12	+	6.03832e11i	0.492678	+	0.284448i
$293$			2.64317e11i			0.122402i	0.998125	+	0.0612008i	$0.0194930\pi$
$293$			2.64317e11i			0.122402i	−0.998125	+	0.0612008i	$0.980507\pi$
$294$		0			0
$295$	−1.78388e10			−0.00798466
$296$	−2.30275e11	+	3.98849e11i	−0.101342	+	0.175529i
$297$		0			0
$298$	6.63563e11	+	1.14933e12i	0.282359	+	0.489059i
$299$	−9.27070e11	−	5.35244e11i	−0.387933	−	0.223973i
$300$		0			0
$301$	−2.07261e12	+	2.38039e12i	−0.838850	+	0.963419i
$302$	−9.72780e11			−0.387240
$303$		0			0
$304$	3.69484e11	−	2.13322e11i	0.142308	−	0.0821613i
$305$	−1.17302e10	−	2.03173e10i	−0.00444433	−	0.00769780i
$306$		0			0
$307$			4.69415e10i			0.0172133i	0.999963	+	0.00860667i	$0.00273962\pi$
$307$			4.69415e10i			0.0172133i	−0.999963	+	0.00860667i	$0.997260\pi$
$308$	−3.74756e11	−	1.09123e12i	−0.135206	−	0.393696i
$309$		0			0
$310$	−1.14355e10	+	1.98069e10i	−0.00399437	+	0.00691844i
$311$	1.80607e12	−	1.04274e12i	0.620773	−	0.358404i	−0.156397	−	0.987694i	$-0.549988\pi$
$311$	1.80607e12	−	1.04274e12i	0.620773	−	0.358404i	0.777170	+	0.629291i	$0.216655\pi$
$312$		0			0
$313$	3.10397e12	+	1.79208e12i	1.03323	+	0.596533i	0.917907	−	0.396795i	$-0.129878\pi$
$313$	3.10397e12	+	1.79208e12i	1.03323	+	0.596533i	0.115319	+	0.993329i	$0.463211\pi$
$314$		−	5.80888e10i		−	0.0190302i
$315$		0			0
$316$	−2.93676e12			−0.932036
$317$	2.30652e12	−	3.99502e12i	0.720546	−	1.24802i	−0.240236	−	0.970715i	$-0.577225\pi$
$317$	2.30652e12	−	3.99502e12i	0.720546	−	1.24802i	0.960781	−	0.277307i	$-0.0894420\pi$
$318$		0			0
$319$	2.91043e11	+	5.04102e11i	0.0881057	+	0.152604i
$320$	−4.32145e9	−	2.49499e9i	−0.00128789	−	0.000743565i
$321$		0			0
$322$	2.19207e12	+	4.27929e11i	0.633251	+	0.123621i
$323$	−2.62566e12			−0.746838
$324$		0			0
$325$	1.54134e12	−	8.89896e11i	0.425092	−	0.245427i
$326$	−5.95359e11	−	1.03119e12i	−0.161693	−	0.280060i
$327$		0			0
$328$		−	1.96796e12i		−	0.518378i
$329$	3.19198e11	−	1.09621e11i	0.0828095	−	0.0284390i
$330$		0			0
$331$	−2.58373e12	+	4.47515e12i	−0.650290	+	1.12633i	0.332763	+	0.943010i	$0.392019\pi$
$331$	−2.58373e12	+	4.47515e12i	−0.650290	+	1.12633i	−0.983053	+	0.183324i	$0.941314\pi$
$332$	2.46005e12	−	1.42031e12i	0.609893	−	0.352122i
$333$		0			0
$334$	−2.71701e12	−	1.56867e12i	−0.653671	−	0.377397i
$335$		−	3.80180e10i		−	0.00901084i
$336$		0			0
$337$	6.46509e12			1.48739			0.743695	−	0.668519i	$-0.233072\pi$
$337$	6.46509e12			1.48739			0.743695	+	0.668519i	$0.233072\pi$
$338$	−1.18380e12	+	2.05040e12i	−0.268345	+	0.464787i
$339$		0			0
$340$	1.53547e10	+	2.65952e10i	0.00337947	+	0.00585341i
$341$	3.15687e12	+	1.82262e12i	0.684676	+	0.395298i
$342$		0			0
$343$	3.97538e12	+	2.59532e12i	0.837352	+	0.546664i
$344$	2.17564e12			0.451642
$345$		0			0
$346$	−2.05419e12	+	1.18599e12i	−0.414248	+	0.239166i
$347$	2.25170e12	+	3.90006e12i	0.447572	+	0.775217i	0.998227	−	0.0595152i	$-0.0189555\pi$
$347$	2.25170e12	+	3.90006e12i	0.447572	+	0.775217i	−0.550655	+	0.834733i	$0.685622\pi$
$348$		0			0
$349$		−	3.43325e11i		−	0.0663099i	−0.999450	−	0.0331549i	$-0.989445\pi$
$349$		−	3.43325e11i		−	0.0663099i	0.999450	−	0.0331549i	$-0.0105555\pi$
$350$	−2.43842e12	+	2.80052e12i	−0.464268	+	0.533211i
$351$		0			0
$352$	−3.97657e11	+	6.88762e11i	−0.0735861	+	0.127455i
$353$	−7.55018e12	+	4.35910e12i	−1.37748	+	0.795286i	−0.991855	−	0.127371i	$-0.959346\pi$
$353$	−7.55018e12	+	4.35910e12i	−1.37748	+	0.795286i	−0.385621	+	0.922657i	$0.626013\pi$
$354$		0			0
$355$	−6.29742e10	−	3.63582e10i	−0.0111692	−	0.00644853i
$356$			4.02482e12i			0.703877i
$357$		0			0
$358$	6.72580e12			1.14374
$359$	−9.86269e11	+	1.70827e12i	−0.165395	+	0.286473i	−0.936796	−	0.349877i	$-0.886223\pi$
$359$	−9.86269e11	+	1.70827e12i	−0.165395	+	0.286473i	0.771400	+	0.636350i	$0.219557\pi$
$360$		0			0
$361$	−1.74113e12	−	3.01572e12i	−0.283985	−	0.491876i
$362$	5.83825e12	+	3.37072e12i	0.939161	+	0.542225i
$363$		0			0
$364$	−3.00528e11	+	1.53946e12i	−0.0470304	+	0.240914i
$365$	8.76931e10			0.0135363
$366$		0			0
$367$	3.13627e12	−	1.81072e12i	0.471067	−	0.271971i	−0.245619	−	0.969366i	$-0.578991\pi$
$367$	3.13627e12	−	1.81072e12i	0.471067	−	0.271971i	0.716686	+	0.697396i	$0.245658\pi$
$368$	−7.69771e11	−	1.33328e12i	−0.114057	−	0.197553i
$369$		0			0
$370$			3.34423e10i			0.00482267i
$371$	2.95346e12	+	5.76564e11i	0.420205	+	0.0820310i
$372$		0			0
$373$	−4.62636e12	+	8.01309e12i	−0.640760	+	1.10983i	0.344503	+	0.938785i	$0.388047\pi$
$373$	−4.62636e12	+	8.01309e12i	−0.640760	+	1.10983i	−0.985263	+	0.171044i	$0.945286\pi$
$374$	4.23881e12	−	2.44728e12i	0.579276	−	0.334445i
$375$		0			0
$376$	−2.01472e11	−	1.16320e11i	−0.0268087	−	0.0154780i
$377$		−	7.91323e11i		−	0.103908i
$378$		0			0
$379$	−2.53428e12			−0.324084			−0.162042	−	0.986784i	$-0.551808\pi$
$379$	−2.53428e12			−0.324084			−0.162042	+	0.986784i	$0.551808\pi$
$380$	1.54901e10	−	2.68296e10i	0.00195495	−	0.00338608i
$381$		0			0
$382$	4.46229e12	+	7.72891e12i	0.548581	+	0.950171i
$383$	−3.27007e12	−	1.88798e12i	−0.396792	−	0.229088i	0.288307	−	0.957538i	$-0.406908\pi$
$383$	−3.27007e12	−	1.88798e12i	−0.396792	−	0.229088i	−0.685099	+	0.728450i	$0.740241\pi$
$384$		0			0
$385$	−6.31856e10	−	5.50159e10i	−0.00746990	−	0.00650405i
$386$	8.70114e11			0.101541
$387$		0			0
$388$	6.22508e12	−	3.59405e12i	0.707923	−	0.408720i
$389$	2.13262e12	+	3.69380e12i	0.239422	+	0.414691i	0.960549	−	0.278112i	$-0.0897086\pi$
$389$	2.13262e12	+	3.69380e12i	0.239422	+	0.414691i	−0.721126	+	0.692804i	$0.756375\pi$
$390$		0			0
$391$			9.47470e12i			1.03677i
$392$	−4.50229e11	−	3.24142e12i	−0.0486411	−	0.350191i
$393$		0			0
$394$	−2.16652e12	+	3.75252e12i	−0.228182	+	0.395222i
$395$	−1.84679e11	+	1.06624e11i	−0.0192058	+	0.0110885i
$396$		0			0
$397$	−8.36432e12	−	4.82915e12i	−0.848161	−	0.489686i	0.0118689	−	0.999930i	$-0.496222\pi$
$397$	−8.36432e12	−	4.82915e12i	−0.848161	−	0.489686i	−0.860030	+	0.510244i	$0.829555\pi$
$398$		−	3.64301e12i		−	0.364791i
$399$		0			0
$400$	2.55964e12			0.249965
$401$	−3.92306e12	+	6.79494e12i	−0.378358	+	0.655336i	−0.990824	−	0.135162i	$-0.956845\pi$
$401$	−3.92306e12	+	6.79494e12i	−0.378358	+	0.655336i	0.612465	+	0.790498i	$0.290178\pi$
$402$		0			0
$403$	−2.47778e12	−	4.29164e12i	−0.233098	−	0.403737i
$404$	−7.19244e12	−	4.15256e12i	−0.668297	−	0.385841i
$405$		0			0
$406$	5.36257e11	+	1.56149e12i	0.0486120	+	0.141550i
$407$	5.33011e12			0.477270
$408$		0			0
$409$	1.36678e13	−	7.89110e12i	1.19421	−	0.689479i	0.234953	−	0.972007i	$-0.424506\pi$
$409$	1.36678e13	−	7.89110e12i	1.19421	−	0.689479i	0.959259	+	0.282528i	$0.0911731\pi$
$410$	−7.14504e10	−	1.23756e11i	−0.00616716	−	0.0106818i
$411$		0			0
$412$		−	9.66324e12i		−	0.814023i
$413$	−1.54512e12	+	7.91492e12i	−0.128592	+	0.658713i
$414$		0			0
$415$	1.03134e11	−	1.78633e11i	0.00837841	−	0.0145118i
$416$	9.36345e11	−	5.40599e11i	0.0751570	−	0.0433919i
$417$		0			0
$418$	−4.27617e12	−	2.46885e12i	−0.335099	−	0.193470i
$419$		−	2.41325e12i		−	0.186867i	−0.995626	−	0.0934336i	$-0.970216\pi$
$419$		−	2.41325e12i		−	0.186867i	0.995626	−	0.0934336i	$-0.0297843\pi$
$420$		0			0
$421$	−2.06355e13			−1.56029			−0.780145	−	0.625599i	$-0.784855\pi$
$421$	−2.06355e13			−1.56029			−0.780145	+	0.625599i	$0.784855\pi$
$422$	1.22188e12	−	2.11635e12i	0.0912988	−	0.158134i
$423$		0			0
$424$	−1.03714e12	−	1.79638e12i	−0.0756847	−	0.131090i
$425$	−1.36422e13	−	7.87630e12i	−0.983872	−	0.568039i
$426$		0			0
$427$	−1.00306e13	+	3.44478e12i	−0.706623	+	0.242673i
$428$	9.27297e12			0.645654
$429$		0			0
$430$	1.36816e11	−	7.89906e10i	0.00930666	−	0.00537320i
$431$	−6.39961e12	−	1.10844e13i	−0.430296	−	0.745294i	0.566603	−	0.823991i	$-0.308257\pi$
$431$	−6.39961e12	−	1.10844e13i	−0.430296	−	0.745294i	−0.996899	+	0.0786971i	$0.974924\pi$
$432$		0			0
$433$		−	2.23235e13i		−	1.46664i	−0.679884	−	0.733320i	$-0.737970\pi$
$433$		−	2.23235e13i		−	1.46664i	0.679884	−	0.733320i	$-0.262030\pi$
$434$	7.79764e12	+	6.78942e12i	0.506424	+	0.440945i
$435$		0			0
$436$	7.57471e12	−	1.31198e13i	0.480766	−	0.832711i
$437$	8.27766e12	−	4.77911e12i	0.519398	−	0.299875i
$438$		0			0
$439$	1.44859e13	+	8.36345e12i	0.888431	+	0.512936i	0.873429	−	0.486952i	$-0.161891\pi$
$439$	1.44859e13	+	8.36345e12i	0.888431	+	0.512936i	0.0150020	+	0.999887i	$0.495225\pi$
$440$			5.77507e10i			0.00350182i
$441$		0			0
$442$	−6.65395e12			−0.394428
$443$	−1.20328e13	+	2.08414e13i	−0.705258	+	1.22154i	0.261340	+	0.965247i	$0.415836\pi$
$443$	−1.20328e13	+	2.08414e13i	−0.705258	+	1.22154i	−0.966598	+	0.256296i	$0.917498\pi$
$444$		0			0
$445$	1.46129e11	+	2.53102e11i	0.00837405	+	0.0145043i
$446$	3.33330e11	+	1.92448e11i	0.0188886	+	0.0109053i
$447$		0			0
$448$	−1.48131e12	+	1.70128e12i	−0.0820833	+	0.0942726i
$449$	−1.66231e13			−0.910919			−0.455460	−	0.890256i	$-0.650525\pi$
$449$	−1.66231e13			−0.910919			−0.455460	+	0.890256i	$0.650525\pi$
$450$		0			0
$451$	−1.97245e13	+	1.13879e13i	−1.05712	+	0.610326i
$452$	−3.23751e12	−	5.60753e12i	−0.171601	−	0.297221i
$453$		0			0
$454$			1.31775e13i			0.683210i
$455$	3.69942e10	+	1.07721e11i	0.00189704	+	0.00552386i
$456$		0			0
$457$	1.87000e12	−	3.23893e12i	0.0938124	−	0.162488i	−0.815300	−	0.579039i	$-0.803428\pi$
$457$	1.87000e12	−	3.23893e12i	0.0938124	−	0.162488i	0.909112	+	0.416551i	$0.136761\pi$
$458$	9.19677e12	−	5.30976e12i	0.456360	−	0.263480i
$459$		0			0
$460$	−9.68146e10	−	5.58959e10i	−0.00470058	−	0.00271388i
$461$		−	1.65515e13i		−	0.794936i	−0.917616	−	0.397468i	$-0.869889\pi$
$461$		−	1.65515e13i		−	0.794936i	0.917616	−	0.397468i	$-0.130111\pi$
$462$		0			0
$463$	−5.00015e12			−0.235006			−0.117503	−	0.993073i	$-0.537489\pi$
$463$	−5.00015e12			−0.235006			−0.117503	+	0.993073i	$0.537489\pi$
$464$	5.69028e11	−	9.85585e11i	0.0264572	−	0.0458252i
$465$		0			0
$466$	−1.06502e13	−	1.84466e13i	−0.484648	−	0.839435i
$467$	−2.84526e13	−	1.64271e13i	−1.28096	−	0.739565i	−0.303940	−	0.952691i	$-0.598302\pi$
$467$	−2.84526e13	−	1.64271e13i	−1.28096	−	0.739565i	−0.977025	+	0.213126i	$0.931636\pi$
$468$		0			0
$469$	−1.68682e13	−	3.29295e12i	−0.743370	−	0.145118i
$470$	−1.68928e10			−0.000736569
$471$		0			0
$472$	4.81408e12	−	2.77941e12i	0.205496	−	0.118643i
$473$	−1.25897e13	−	2.18060e13i	−0.531753	−	0.921023i
$474$		0			0
$475$			1.58915e13i			0.657197i
$476$	1.31300e13	−	4.50919e12i	0.537316	−	0.184529i
$477$		0			0
$478$	−3.32462e12	+	5.75841e12i	−0.133230	+	0.230762i
$479$	3.49951e13	−	2.02044e13i	1.38781	−	0.801252i	0.394741	−	0.918792i	$-0.370834\pi$
$479$	3.49951e13	−	2.02044e13i	1.38781	−	0.801252i	0.993068	+	0.117540i	$0.0375009\pi$
$480$		0			0
$481$	−6.27529e12	−	3.62304e12i	−0.243730	−	0.140717i
$482$		−	2.40380e13i		−	0.923980i
$483$		0			0
$484$	−4.07551e12			−0.153446
$485$	2.60977e11	−	4.52026e11i	0.00972511	−	0.0168444i
$486$		0			0
$487$	−1.90619e13	−	3.30161e13i	−0.695858	−	1.20526i	−0.969891	−	0.243540i	$-0.921691\pi$
$487$	−1.90619e13	−	3.30161e13i	−0.695858	−	1.20526i	0.274033	−	0.961720i	$-0.411642\pi$
$488$	6.33114e12	+	3.65529e12i	0.228762	+	0.132076i
$489$		0			0
$490$	−1.45999e11	−	1.87492e11i	−0.00516855	−	0.00663745i
$491$	−3.95192e12			−0.138484			−0.0692422	−	0.997600i	$-0.522058\pi$
$491$	−3.95192e12			−0.138484			−0.0692422	+	0.997600i	$0.522058\pi$
$492$		0			0
$493$	−6.06552e12	+	3.50193e12i	−0.208273	+	0.120247i
$494$	3.35630e12	+	5.81328e12i	0.114084	+	0.197600i
$495$		0			0
$496$		−	7.12693e12i		−	0.237407i
$497$	−2.15863e13	+	2.47919e13i	−0.711864	+	0.817574i
$498$		0			0
$499$	2.21713e13	−	3.84017e13i	0.716618	−	1.24122i	−0.245714	−	0.969342i	$-0.579023\pi$
$499$	2.21713e13	−	3.84017e13i	0.716618	−	1.24122i	0.962332	−	0.271876i	$-0.0876442\pi$
$500$	3.21950e11	−	1.85878e11i	0.0103024	−	0.00594810i
$501$		0			0
$502$	1.92786e13	+	1.11305e13i	0.604724	+	0.349138i
$503$			1.60566e13i			0.498670i	0.968417	+	0.249335i	$0.0802121\pi$
$503$			1.60566e13i			0.498670i	−0.968417	+	0.249335i	$0.919788\pi$
$504$		0			0
$505$	−6.03065e11			−0.0183615
$506$	−8.90882e12	+	1.54305e13i	−0.268576	+	0.465188i
$507$		0			0
$508$	−5.26577e12	−	9.12059e12i	−0.155648	−	0.269590i
$509$	5.85261e12	+	3.37901e12i	0.171301	+	0.0989009i	0.583199	−	0.812329i	$-0.301801\pi$
$509$	5.85261e12	+	3.37901e12i	0.171301	+	0.0989009i	−0.411898	+	0.911230i	$0.635134\pi$
$510$		0			0
$511$	7.59559e12	−	3.89086e13i	0.218000	−	1.11671i
$512$	1.55494e12			0.0441942
$513$		0			0
$514$	2.70729e13	−	1.56305e13i	0.754604	−	0.435671i
$515$	−3.50842e11	−	6.07676e11i	−0.00968446	−	0.0167740i
$516$		0			0
$517$			2.69242e12i			0.0728938i
$518$	1.48380e13	+	2.89663e12i	0.397857	+	0.0776682i
$519$		0			0
$520$	3.92549e10	−	6.79915e10i	0.00103247	−	0.00178829i
$521$	−9.78607e12	+	5.64999e12i	−0.254929	+	0.147183i	−0.622019	−	0.783002i	$-0.713687\pi$
$521$	−9.78607e12	+	5.64999e12i	−0.254929	+	0.147183i	0.367090	+	0.930185i	$0.380354\pi$
$522$		0			0
$523$	−2.83938e13	−	1.63932e13i	−0.725630	−	0.418943i	0.0911914	−	0.995833i	$-0.470933\pi$
$523$	−2.83938e13	−	1.63932e13i	−0.725630	−	0.418943i	−0.816821	+	0.576891i	$0.804266\pi$
$524$		−	3.10777e13i		−	0.786669i
$525$		0			0
$526$	1.80016e13			0.447076
$527$	−2.19304e13	+	3.79846e13i	−0.539503	+	0.934446i
$528$		0			0
$529$	3.46787e12	+	6.00653e12i	0.0837114	+	0.144992i
$530$	−1.30442e11	−	7.53106e10i	−0.00311916	−	0.00180085i
$531$		0			0
$532$	−1.05624e13	−	9.19667e12i	−0.247858	−	0.215810i
$533$	3.09629e13			0.719789
$534$		0			0
$535$	5.83134e11	−	3.36672e11i	0.0133045	−	0.00768137i
$536$	5.92346e12	+	1.02597e13i	0.133891	+	0.231906i
$537$		0			0
$538$			5.37739e13i			1.19305i
$539$	−2.98829e13	+	2.32696e13i	−0.656868	+	0.511500i
$540$		0			0
$541$	−4.31125e13	+	7.46731e13i	−0.930288	+	1.61131i	−0.147459	+	0.989068i	$0.547109\pi$
$541$	−4.31125e13	+	7.46731e13i	−0.930288	+	1.61131i	−0.782829	+	0.622237i	$0.786224\pi$
$542$	1.28907e12	−	7.44244e11i	0.0275600	−	0.0159118i
$543$		0			0
$544$	−8.28742e12	−	4.78475e12i	−0.173950	−	0.100430i
$545$		−	1.10006e12i		−	0.0228788i
$546$		0			0
$547$	2.71151e13			0.553701			0.276850	−	0.960913i	$-0.410709\pi$
$547$	2.71151e13			0.553701			0.276850	+	0.960913i	$0.410709\pi$
$548$	−8.84385e9	+	1.53180e10i	−0.000178953	+	0.000309955i
$549$		0			0
$550$	−1.48118e13	−	2.56548e13i	−0.294303	−	0.509747i
$551$	6.11899e12	+	3.53280e12i	0.120482	+	0.0695602i
$552$		0			0
$553$	3.13122e13	+	9.11756e13i	0.605463	+	1.76300i
$554$	8.79432e12			0.168521
$555$		0			0
$556$	8.86881e12	−	5.12041e12i	0.166913	−	0.0963675i
$557$	−1.29648e13	−	2.24557e13i	−0.241818	−	0.418842i	0.719414	−	0.694582i	$-0.244410\pi$
$557$	−1.29648e13	−	2.24557e13i	−0.241818	−	0.418842i	−0.961232	+	0.275740i	$0.911077\pi$
$558$		0			0
$559$			3.42304e13i			0.627124i
$560$	−3.13844e10	+	1.60767e11i	−0.000569867	+	0.00291915i
$561$		0			0
$562$	−1.72780e13	+	2.99265e13i	−0.308186	+	0.533794i
$563$	2.65559e13	−	1.53320e13i	0.469482	−	0.271055i	−0.246541	−	0.969132i	$-0.579294\pi$
$563$	2.65559e13	−	1.53320e13i	0.469482	−	0.271055i	0.716023	+	0.698077i	$0.245961\pi$
$564$		0			0
$565$	−4.07184e11	−	2.35088e11i	−0.00707210	−	0.00408308i
$566$			7.37183e13i			1.26909i
$567$		0			0
$568$	2.26594e13			0.383272
$569$	5.70593e12	−	9.88296e12i	0.0956676	−	0.165701i	−0.814219	−	0.580557i	$-0.802835\pi$
$569$	5.70593e12	−	9.88296e12i	0.0956676	−	0.165701i	0.909887	+	0.414856i	$0.136168\pi$
$570$		0			0
$571$	1.63873e13	+	2.83836e13i	0.269976	+	0.467613i	0.968855	−	0.247627i	$-0.0796508\pi$
$571$	1.63873e13	+	2.83836e13i	0.269976	+	0.467613i	−0.698879	+	0.715240i	$0.746317\pi$
$572$	−1.08366e13	−	6.25654e12i	−0.176976	−	0.102177i
$573$		0			0
$574$	−6.10979e13	+	2.09827e13i	−0.980543	+	0.336745i
$575$	5.73443e13			0.912328
$576$		0			0
$577$	8.59026e13	−	4.95959e13i	1.34316	−	0.775473i	0.355889	−	0.934528i	$-0.384178\pi$
$577$	8.59026e13	−	4.95959e13i	1.34316	−	0.775473i	0.987270	+	0.159056i	$0.0508449\pi$
$578$	6.63808e12	+	1.14975e13i	0.102897	+	0.178223i
$579$		0			0
$580$		−	8.26385e10i		−	0.00125905i
$581$	−7.03249e13	−	6.12320e13i	−1.06225	−	0.924907i
$582$		0			0
$583$	−1.20032e13	+	2.07901e13i	−0.178219	+	0.308684i
$584$	−2.36653e13	+	1.36632e13i	−0.348376	+	0.201135i
$585$		0			0
$586$	−5.17953e12	−	2.99040e12i	−0.0749553	−	0.0432755i
$587$			9.19804e13i			1.31979i	0.751358	+	0.659895i	$0.229399\pi$
$587$			9.19804e13i			1.31979i	−0.751358	+	0.659895i	$0.770601\pi$
$588$		0			0
$589$	4.42474e13			0.624182
$590$	2.01823e11	−	3.49568e11i	0.00282300	−	0.00488959i
$591$		0			0
$592$	−5.21054e12	−	9.02491e12i	−0.0716595	−	0.124118i
$593$	7.67548e13	+	4.43144e13i	1.04672	+	0.604327i	0.921731	−	0.387831i	$-0.126776\pi$
$593$	7.67548e13	+	4.43144e13i	1.04672	+	0.604327i	0.124994	+	0.992158i	$0.460109\pi$
$594$		0			0
$595$	6.61969e11	−	7.60271e11i	0.00887673	−	0.0101949i
$596$	−3.00294e13			−0.399315
$597$		0			0
$598$	2.09772e13	−	1.21112e13i	0.274310	−	0.158373i
$599$	2.37222e13	+	4.10880e13i	0.307624	+	0.532821i	0.977842	−	0.209344i	$-0.0671327\pi$
$599$	2.37222e13	+	4.10880e13i	0.307624	+	0.532821i	−0.670218	+	0.742164i	$0.733799\pi$
$600$		0			0
$601$			2.46584e12i			0.0314479i	0.999876	+	0.0157240i	$0.00500530\pi$
$601$			2.46584e12i			0.0314479i	−0.999876	+	0.0157240i	$0.994995\pi$
$602$	−2.31970e13	−	6.75456e13i	−0.293393	−	0.854309i
$603$		0			0
$604$	1.10057e13	−	1.90625e13i	0.136910	−	0.237135i
$605$	−2.56290e11	+	1.47969e11i	−0.00316195	+	0.00182555i
$606$		0			0
$607$	8.01186e13	+	4.62565e13i	0.972277	+	0.561344i	0.899930	−	0.436035i	$-0.143618\pi$
$607$	8.01186e13	+	4.62565e13i	0.972277	+	0.561344i	0.0723474	+	0.997379i	$0.476951\pi$
$608$			9.65384e12i			0.116194i
$609$		0			0
$610$	5.30848e11			0.00628523
$611$	1.83012e12	−	3.16986e12i	0.0214918	−	0.0372250i
$612$		0			0
$613$	−6.57118e13	−	1.13816e14i	−0.759174	−	1.31493i	−0.943273	−	0.332019i	$-0.892270\pi$
$613$	−6.57118e13	−	1.13816e14i	−0.759174	−	1.31493i	0.184099	−	0.982908i	$-0.441063\pi$
$614$	−9.19862e11	−	5.31083e11i	−0.0105410	−	0.00608584i
$615$		0			0
$616$	2.56234e13	+	5.00212e12i	0.288891	+	0.0563962i
$617$	−6.18670e12			−0.0691884			−0.0345942	−	0.999401i	$-0.511014\pi$
$617$	−6.18670e12			−0.0691884			−0.0345942	+	0.999401i	$0.511014\pi$
$618$		0			0
$619$	3.97783e13	−	2.29660e13i	0.437717	−	0.252716i	−0.264912	−	0.964273i	$-0.585343\pi$
$619$	3.97783e13	−	2.29660e13i	0.437717	−	0.252716i	0.702629	+	0.711557i	$0.252009\pi$
$620$	−2.58757e11	−	4.48179e11i	−0.00282444	−	0.00489208i
$621$		0			0
$622$			4.71888e13i			0.506859i
$623$	1.24956e14	−	4.29133e13i	1.33143	−	0.457247i
$624$		0			0
$625$	−4.76635e13	+	8.25556e13i	−0.499788	+	0.865658i
$626$	−7.02347e13	+	4.05501e13i	−0.730601	+	0.421813i
$627$		0			0
$628$	1.13830e12	+	6.57199e11i	0.0116536	+	0.00672820i
$629$			6.41337e13i			0.651378i
$630$		0			0
$631$	4.32442e13			0.432296			0.216148	−	0.976361i	$-0.430651\pi$
$631$	4.32442e13			0.432296			0.216148	+	0.976361i	$0.430651\pi$
$632$	3.32256e13	−	5.75485e13i	0.329525	−	0.570753i
$633$		0			0
$634$	5.21907e13	+	9.03969e13i	0.509503	+	0.882485i
$635$	−6.62280e11	−	3.82367e11i	−0.00641465	−	0.00370350i
$636$		0			0
$637$	5.09990e13	−	7.08368e12i	0.486255	−	0.0675401i
$638$	−1.31711e13			−0.124600
$639$		0			0
$640$	9.77832e10	−	5.64551e10i	0.000910677	−	0.000525780i
$641$	−3.07325e13	−	5.32303e13i	−0.283993	−	0.491891i	0.688371	−	0.725359i	$-0.258326\pi$
$641$	−3.07325e13	−	5.32303e13i	−0.283993	−	0.491891i	−0.972365	+	0.233468i	$0.924993\pi$
$642$		0			0
$643$			1.70194e14i			1.54842i	0.632930	+	0.774209i	$0.281852\pi$
$643$			1.70194e14i			1.54842i	−0.632930	+	0.774209i	$0.718148\pi$
$644$	−3.31861e13	+	3.81142e13i	−0.299590	+	0.344079i
$645$		0			0
$646$	2.97060e13	−	5.14523e13i	0.264047	−	0.457343i
$647$	4.23068e13	−	2.44258e13i	0.373155	−	0.215441i	−0.301681	−	0.953409i	$-0.597548\pi$
$647$	4.23068e13	−	2.44258e13i	0.373155	−	0.215441i	0.674836	+	0.737968i	$0.264214\pi$
$648$		0			0
$649$	−5.57150e13	−	3.21671e13i	−0.483893	−	0.279376i
$650$			4.02721e13i			0.347086i
$651$		0			0
$652$	2.69429e13			0.228668
$653$	7.92473e13	−	1.37260e14i	0.667450	−	1.15606i	−0.311165	−	0.950356i	$-0.600719\pi$
$653$	7.92473e13	−	1.37260e14i	0.667450	−	1.15606i	0.978615	−	0.205701i	$-0.0659476\pi$
$654$		0			0
$655$	−1.12833e12	−	1.95433e12i	−0.00935902	−	0.0162103i
$656$	3.85639e13	+	2.22649e13i	0.317440	+	0.183274i
$657$		0			0
$658$	−1.46318e12	+	7.49519e12i	−0.0118623	+	0.0607650i
$659$	1.22774e14			0.987823			0.493911	−	0.869512i	$-0.335567\pi$
$659$	1.22774e14			0.987823			0.493911	+	0.869512i	$0.335567\pi$
$660$		0			0
$661$	1.38210e14	−	7.97955e13i	1.09530	−	0.632370i	0.160315	−	0.987066i	$-0.448749\pi$
$661$	1.38210e14	−	7.97955e13i	1.09530	−	0.632370i	0.934982	+	0.354696i	$0.115416\pi$
$662$	−5.84631e13	−	1.01261e14i	−0.459824	−	0.796439i
$663$		0			0
$664$			6.42759e13i			0.497975i
$665$	−9.98120e11	−	1.94849e11i	−0.00767493	−	0.00149827i
$666$		0			0
$667$	1.27481e13	−	2.20803e13i	0.0965641	−	0.167254i
$668$	6.14790e13	−	3.54949e13i	0.462215	−	0.266860i
$669$		0			0
$670$	7.44998e11	+	4.30125e11i	0.00551799	+	0.00318581i
$671$		−	8.46078e13i		−	0.622011i
$672$		0			0
$673$	2.65164e13			0.192061			0.0960307	−	0.995378i	$-0.469385\pi$
$673$	2.65164e13			0.192061			0.0960307	+	0.995378i	$0.469385\pi$
$674$	−7.31441e13	+	1.26689e14i	−0.525872	+	0.910837i
$675$		0			0
$676$	−2.67863e13	−	4.63952e13i	−0.189749	−	0.328654i
$677$	5.86902e13	+	3.38848e13i	0.412688	+	0.238266i	0.691944	−	0.721951i	$-0.256754\pi$
$677$	5.86902e13	+	3.38848e13i	0.412688	+	0.238266i	−0.279256	+	0.960217i	$0.590088\pi$
$678$		0			0
$679$	−1.77955e14	−	1.54946e14i	−1.23299	−	1.07357i
$680$	−6.94876e11			−0.00477929
$681$		0			0
$682$	−7.14319e13	+	4.12412e13i	−0.484139	+	0.279518i
$683$	−1.29186e12	−	2.23757e12i	−0.00869184	−	0.0150547i	0.861647	−	0.507508i	$-0.169433\pi$
$683$	−1.29186e12	−	2.23757e12i	−0.00869184	−	0.0150547i	−0.870339	+	0.492454i	$0.836100\pi$
$684$		0			0
$685$			1.28437e9i			8.51603e-6i
$686$	−9.58340e13	+	4.85385e13i	−0.630811	+	0.319496i
$687$		0			0
$688$	−2.46145e13	+	4.26336e13i	−0.159680	+	0.276573i
$689$	2.82633e13	−	1.63179e13i	0.182024	−	0.105091i
$690$		0			0
$691$	2.23459e14	+	1.29014e14i	1.41843	+	0.818931i	0.996161	−	0.0875391i	$-0.0279003\pi$
$691$	2.23459e14	+	1.29014e14i	1.41843	+	0.818931i	0.422269	+	0.906470i	$0.361234\pi$
$692$		−	5.36718e13i		−	0.338232i
$693$		0			0
$694$	−1.01900e14			−0.632962
$695$	3.71812e11	−	6.43997e11i	0.00229297	−	0.00397155i
$696$		0			0
$697$	−1.37023e14	−	2.37331e14i	−0.832973	−	1.44275i
$698$	6.72777e12	+	3.88428e12i	0.0406063	+	0.0234441i
$699$		0			0
$700$	−2.72912e13	−	7.94674e13i	−0.162380	−	0.472823i
$701$	−2.95013e14			−1.74281			−0.871407	−	0.490561i	$-0.836792\pi$
$701$	−2.95013e14			−1.74281			−0.871407	+	0.490561i	$0.836792\pi$
$702$		0			0
$703$	5.60310e13	−	3.23495e13i	0.326326	−	0.188404i
$704$	−8.99796e12	−	1.55849e13i	−0.0520332	−	0.0901241i
$705$		0			0
$706$		−	1.97270e14i		−	1.12470i
$707$	−5.22349e13	+	2.67574e14i	−0.295708	+	1.51477i
$708$		0			0
$709$	8.28171e13	−	1.43443e14i	0.462263	−	0.800662i	−0.536811	−	0.843703i	$-0.680371\pi$
$709$	8.28171e13	−	1.43443e14i	0.462263	−	0.800662i	0.999073	+	0.0430404i	$0.0137044\pi$
$710$	1.42494e12	−	8.22692e11i	0.00789780	−	0.00455980i
$711$		0			0
$712$	−7.88701e13	−	4.55357e13i	−0.431035	−	0.248858i
$713$		−	1.59667e14i		−	0.866496i
$714$		0			0
$715$	−9.08622e11			−0.00486242
$716$	−7.60937e13	+	1.31798e14i	−0.404374	+	0.700397i
$717$		0			0
$718$	−2.23167e13	−	3.86537e13i	−0.116952	−	0.202567i
$719$	−6.56761e13	−	3.79181e13i	−0.341793	−	0.197334i	0.319272	−	0.947663i	$-0.396562\pi$
$719$	−6.56761e13	−	3.79181e13i	−0.341793	−	0.197334i	−0.661065	+	0.750329i	$0.729895\pi$
$720$		0			0
$721$	−3.00009e14	+	1.03031e14i	−1.53977	+	0.528800i
$722$	7.87945e13			0.401615
$723$		0			0
$724$	−1.32105e14	+	7.62706e13i	−0.664087	+	0.383411i
$725$	2.11949e13	+	3.67107e13i	0.105814	+	0.183275i
$726$		0			0
$727$			2.07361e14i			1.02107i	0.859858	+	0.510534i	$0.170552\pi$
$727$			2.07361e14i			1.02107i	−0.859858	+	0.510534i	$0.829448\pi$
$728$	−2.67671e13	−	2.33062e13i	−0.130901	−	0.113976i
$729$		0			0
$730$	−9.92134e11	+	1.71843e12i	−0.00478581	+	0.00828927i
$731$	2.62377e14	−	1.51484e14i	1.25701	−	0.725736i
$732$		0			0
$733$	1.83656e14	+	1.06034e14i	0.867931	+	0.501100i	0.866660	−	0.498899i	$-0.166262\pi$
$733$	1.83656e14	+	1.06034e14i	0.867931	+	0.501100i	0.00127063	+	0.999999i	$0.499596\pi$
$734$			8.19440e13i			0.384624i
$735$		0			0
$736$	3.48358e13			0.161301
$737$	6.85543e13	−	1.18740e14i	0.315281	−	0.546082i
$738$		0			0
$739$	−4.32095e13	−	7.48410e13i	−0.196046	−	0.339561i	0.751197	−	0.660078i	$-0.229477\pi$
$739$	−4.32095e13	−	7.48410e13i	−0.196046	−	0.339561i	−0.947243	+	0.320517i	$0.896143\pi$
$740$	−6.55333e11	−	3.78356e11i	−0.00295327	−	0.00170507i
$741$		0			0
$742$	−4.47129e13	+	5.13527e13i	−0.198799	+	0.228320i
$743$	1.26430e14			0.558350			0.279175	−	0.960240i	$-0.409939\pi$
$743$	1.26430e14			0.558350			0.279175	+	0.960240i	$0.409939\pi$
$744$		0			0
$745$	−1.88841e12	+	1.09028e12i	−0.00822840	+	0.00475067i
$746$	−1.04683e14	−	1.81316e14i	−0.453086	−	0.784768i
$747$		0			0
$748$			1.10751e14i			0.472977i
$749$	−9.88698e13	−	2.87892e14i	−0.419425	−	1.22129i
$750$		0			0
$751$	6.12441e13	−	1.06078e14i	0.256368	−	0.444043i	−0.708898	−	0.705311i	$-0.750807\pi$
$751$	6.12441e13	−	1.06078e14i	0.256368	−	0.444043i	0.965266	+	0.261268i	$0.0841406\pi$
$752$	4.55879e12	−	2.63202e12i	0.0189566	−	0.0109446i
$753$		0			0
$754$	1.55067e13	+	8.95280e12i	0.0636301	+	0.0367369i
$755$		−	1.59834e12i		−	0.00651528i
$756$		0			0
$757$	−1.47452e14			−0.593160			−0.296580	−	0.955008i	$-0.595846\pi$
$757$	−1.47452e14			−0.593160			−0.296580	+	0.955008i	$0.595846\pi$
$758$	2.86721e13	−	4.96615e13i	0.114581	−	0.198460i
$759$		0			0
$760$	3.50501e11	+	6.07085e11i	0.00138236	+	0.00239432i
$761$	9.23773e13	+	5.33341e13i	0.361945	+	0.208969i	0.669933	−	0.742421i	$-0.266323\pi$
$761$	9.23773e13	+	5.33341e13i	0.361945	+	0.208969i	−0.307989	+	0.951390i	$0.599656\pi$
$762$		0			0
$763$	−4.88084e14	−	9.52820e13i	−1.88744	−	0.368458i
$764$	−2.01940e14			−0.775811
$765$		0			0
$766$	7.39932e13	−	4.27200e13i	0.280574	−	0.161990i
$767$	4.37299e13	+	7.57424e13i	0.164741	+	0.285340i
$768$		0			0
$769$			6.05828e12i			0.0225278i	0.999937	+	0.0112639i	$0.00358548\pi$
$769$			6.05828e12i			0.0225278i	−0.999937	+	0.0112639i	$0.996415\pi$
$770$	1.79295e12	−	6.15747e11i	0.00662391	−	0.00227483i
$771$		0			0
$772$	−9.84422e12	+	1.70507e13i	−0.0359000	+	0.0621807i
$773$	−4.18822e14	+	2.41807e14i	−1.51751	+	0.876137i	−0.517725	+	0.855547i	$0.673221\pi$
$773$	−4.18822e14	+	2.41807e14i	−1.51751	+	0.876137i	−0.999788	+	0.0205897i	$0.993446\pi$
$774$		0			0
$775$	2.29896e14	+	1.32731e14i	0.822287	+	0.474747i
$776$			1.62648e14i			0.578017i
$777$		0			0
$778$	−9.65111e13			−0.338594
$779$	−1.38231e14	+	2.39423e14i	−0.481858	+	0.834602i
$780$		0			0
$781$	−1.31123e14	−	2.27111e14i	−0.451255	−	0.781597i
$782$	−1.85665e14	−	1.07194e14i	−0.634888	−	0.366553i
$783$		0			0
$784$	6.86124e13	+	2.78499e13i	0.231645	+	0.0940249i
$785$	9.54434e10			0.000320183
$786$		0			0
$787$	1.46131e14	−	8.43685e13i	0.484025	−	0.279452i	−0.238068	−	0.971249i	$-0.576514\pi$
$787$	1.46131e14	−	8.43685e13i	0.484025	−	0.279452i	0.722092	+	0.691797i	$0.243181\pi$
$788$	−4.90227e13	−	8.49098e13i	−0.161349	−	0.279464i
$789$		0			0
$790$		−	4.82527e12i		−	0.0156815i
$791$	−1.39575e14	+	1.60301e14i	−0.450738	+	0.517672i
$792$		0			0
$793$	−5.75105e13	+	9.96111e13i	−0.183392	+	0.317645i
$794$	1.89263e14	−	1.09271e14i	0.599740	−	0.346260i
$795$		0			0
$796$	7.13880e13	+	4.12159e13i	0.223388	+	0.128973i
$797$			4.34432e14i			1.35092i	0.737396	+	0.675461i	$0.236055\pi$
$797$			4.34432e14i			1.35092i	−0.737396	+	0.675461i	$0.763945\pi$
$798$		0			0
$799$	−3.23961e13			−0.0994854
$800$	−2.89590e13	+	5.01584e13i	−0.0883758	+	0.153071i
$801$		0			0
$802$	−8.87688e13	−	1.53752e14i	−0.267540	−	0.463392i
$803$	2.73887e14	+	1.58129e14i	0.820339	+	0.473623i
$804$		0			0
$805$	−7.03113e11	+	3.60171e12i	−0.00207991	+	0.0106544i
$806$	1.12132e14			0.329650
$807$		0			0
$808$	1.62746e14	−	9.39616e13i	0.472557	−	0.272831i
$809$	−2.17732e14	−	3.77123e14i	−0.628318	−	1.08828i	−0.987889	−	0.155161i	$-0.950410\pi$
$809$	−2.17732e14	−	3.77123e14i	−0.628318	−	1.08828i	0.359571	−	0.933118i	$-0.382923\pi$
$810$		0			0
$811$		−	3.27146e13i		−	0.0932475i	−0.998913	−	0.0466238i	$-0.985154\pi$
$811$		−	3.27146e13i		−	0.0932475i	0.998913	−	0.0466238i	$-0.0148462\pi$
$812$	−3.66659e13	−	7.15778e12i	−0.103868	−	0.0202767i
$813$		0			0
$814$	−6.03034e13	+	1.04448e14i	−0.168741	+	0.292267i
$815$	1.69431e12	−	9.78211e11i	0.00471200	−	0.00272047i
$816$		0			0
$817$	−2.64690e14	−	1.52819e14i	−0.727156	−	0.419824i
$818$			3.57110e14i			0.975070i
$819$		0			0
$820$	3.23347e12			0.00872168
$821$	3.47625e14	−	6.02105e14i	0.931957	−	1.61420i	0.151984	−	0.988383i	$-0.451434\pi$
$821$	3.47625e14	−	6.02105e14i	0.931957	−	1.61420i	0.779973	−	0.625814i	$-0.215233\pi$
$822$		0			0
$823$	−1.53594e14	−	2.66032e14i	−0.406794	−	0.704588i	0.587735	−	0.809054i	$-0.300020\pi$
$823$	−1.53594e14	−	2.66032e14i	−0.406794	−	0.704588i	−0.994528	+	0.104466i	$0.966687\pi$
$824$	1.89360e14	+	1.09327e14i	0.498486	+	0.287801i
$825$		0			0
$826$	−1.37619e14	−	1.19825e14i	−0.357914	−	0.311636i
$827$	−3.98069e13			−0.102904			−0.0514518	−	0.998675i	$-0.516385\pi$
$827$	−3.98069e13			−0.102904			−0.0514518	+	0.998675i	$0.516385\pi$
$828$		0			0
$829$	4.75066e14	−	2.74280e14i	1.21334	−	0.700521i	0.249853	−	0.968284i	$-0.419618\pi$
$829$	4.75066e14	−	2.74280e14i	1.21334	−	0.700521i	0.963485	+	0.267763i	$0.0862844\pi$
$830$	2.33366e12	+	4.04201e12i	0.00592443	+	0.0102614i
$831$		0			0
$832$			2.44647e13i			0.0613654i
$833$	−2.79988e14	−	3.59561e14i	−0.698095	−	0.896494i
$834$		0			0
$835$	2.57742e12	−	4.46422e12i	0.00634969	−	0.0109980i
$836$	9.67587e13	−	5.58636e13i	0.236951	−	0.136804i
$837$		0			0
$838$	4.72899e13	+	2.73029e13i	0.114432	+	0.0660675i
$839$			1.31654e14i			0.316683i	0.987384	+	0.158342i	$0.0506148\pi$
$839$			1.31654e14i			0.316683i	−0.987384	+	0.158342i	$0.949385\pi$
$840$		0			0
$841$	−4.01860e14			−0.955201
$842$	2.33464e14	−	4.04372e14i	0.551646	−	0.955479i
$843$		0			0
$844$	2.76479e13	+	4.78876e13i	0.0645580	+	0.111818i
$845$	−3.36892e12	−	1.94505e12i	−0.00782002	−	0.00451489i
$846$		0			0
$847$	4.34537e13	+	1.26530e14i	0.0996804	+	0.290252i
$848$	4.69356e13			0.107034
$849$		0			0
$850$	3.08687e14	−	1.78220e14i	0.695702	−	0.401664i
$851$	−1.16733e14	−	2.02188e14i	−0.261545	−	0.453009i
$852$		0			0
$853$			3.44248e14i			0.762300i	0.924513	+	0.381150i	$0.124472\pi$
$853$			3.44248e14i			0.762300i	−0.924513	+	0.381150i	$0.875528\pi$
$854$	4.59797e13	−	2.35532e14i	0.101223	−	0.518514i
$855$		0			0
$856$	−1.04912e14	+	1.81712e14i	−0.228273	+	0.395381i
$857$	1.96215e14	−	1.13285e14i	0.424451	−	0.245057i	−0.272529	−	0.962148i	$-0.587860\pi$
$857$	1.96215e14	−	1.13285e14i	0.424451	−	0.245057i	0.696980	+	0.717091i	$0.254527\pi$
$858$		0			0
$859$	2.32899e14	+	1.34464e14i	0.497969	+	0.287503i	0.727874	−	0.685710i	$-0.240508\pi$
$859$	2.32899e14	+	1.34464e14i	0.497969	+	0.287503i	−0.229905	+	0.973213i	$0.573842\pi$
$860$			3.57471e12i			0.00759886i
$861$		0			0
$862$	2.89613e14			0.608530
$863$	−1.15600e14	+	2.00226e14i	−0.241493	+	0.418279i	−0.961140	−	0.276062i	$-0.910971\pi$
$863$	−1.15600e14	+	2.00226e14i	−0.241493	+	0.418279i	0.719647	+	0.694341i	$0.244304\pi$
$864$		0			0
$865$	−1.94865e12	−	3.37517e12i	−0.00402396	−	0.00696971i
$866$	4.37450e14	+	2.52562e14i	0.898129	+	0.518535i
$867$		0			0
$868$	−2.21265e14	+	7.59884e13i	−0.449070	+	0.154223i
$869$	−7.69063e14			−1.55190
$870$		0			0
$871$	−1.61422e14	+	9.31968e13i	−0.322011	+	0.185913i
$872$	1.71396e14	+	2.96867e14i	0.339953	+	0.588816i
$873$		0			0
$874$			2.16278e14i			0.424087i
$875$	−9.20352e12	−	8.01352e12i	−0.0179438	−	0.0156237i
$876$		0			0
$877$	−3.41205e14	+	5.90985e14i	−0.657685	+	1.13914i	0.323529	+	0.946218i	$0.395131\pi$
$877$	−3.41205e14	+	5.90985e14i	−0.657685	+	1.13914i	−0.981213	+	0.192925i	$0.938203\pi$
$878$	−3.27779e14	+	1.89243e14i	−0.628216	+	0.362700i
$879$		0			0
$880$	−1.13168e12	−	6.53375e11i	−0.00214442	−	0.00123808i
$881$			2.22417e14i			0.419071i	0.977801	+	0.209536i	$0.0671952\pi$
$881$			2.22417e14i			0.419071i	−0.977801	+	0.209536i	$0.932805\pi$
$882$		0			0
$883$	8.58401e14			1.59914			0.799570	−	0.600573i	$-0.205061\pi$
$883$	8.58401e14			1.59914			0.799570	+	0.600573i	$0.205061\pi$
$884$	7.52808e13	−	1.30390e14i	0.139451	−	0.241537i
$885$		0			0
$886$	−2.72271e14	−	4.71588e14i	−0.498693	−	0.863761i
$887$	4.41610e14	+	2.54964e14i	0.804305	+	0.464366i	0.844974	−	0.534807i	$-0.179616\pi$
$887$	4.41610e14	+	2.54964e14i	0.804305	+	0.464366i	−0.0406690	+	0.999173i	$0.512949\pi$
$888$		0			0
$889$	−2.27016e14	+	2.60728e14i	−0.408835	+	0.469547i
$890$	−6.61303e12			−0.0118427
$891$		0			0
$892$	−7.54239e12	+	4.35460e12i	−0.0133563	+	0.00771124i
$893$	1.63408e13	+	2.83032e13i	0.0287751	+	0.0498400i
$894$		0			0
$895$			1.10509e13i			0.0192434i
$896$	−1.65791e13	−	4.82753e13i	−0.0287091	−	0.0835960i
$897$		0			0
$898$	1.88069e14	−	3.25745e14i	0.322059	−	0.557822i
$899$	1.02216e14	−	5.90141e13i	0.174068	−	0.100498i
$900$		0			0
$901$	−2.50154e14	−	1.44426e14i	−0.421292	−	0.243233i
$902$		−	5.15359e14i		−	0.863132i
$903$		0			0
$904$	1.46513e14			0.242680
$905$	−5.53829e12	+	9.59261e12i	−0.00912290	+	0.0158013i
$906$		0			0
$907$	−1.62995e14	−	2.82315e14i	−0.265544	−	0.459936i	0.702162	−	0.712017i	$-0.252218\pi$
$907$	−1.62995e14	−	2.82315e14i	−0.265544	−	0.459936i	−0.967706	+	0.252081i	$0.918885\pi$
$908$	−2.58225e14	−	1.49086e14i	−0.418379	−	0.241551i
$909$		0			0
$910$	−2.52943e12	−	4.93786e11i	−0.00405337	−	0.000791283i
$911$	4.29059e14			0.683795			0.341897	−	0.939737i	$-0.388931\pi$
$911$	4.29059e14			0.683795			0.341897	+	0.939737i	$0.388931\pi$
$912$		0			0
$913$	6.44226e14	−	3.71944e14i	1.01551	−	0.586305i
$914$	4.23132e13	+	7.32887e13i	0.0663354	+	0.114896i
$915$		0			0
$916$			2.40292e14i			0.372617i
$917$	−9.64848e14	+	3.31355e14i	−1.48803	+	0.511030i
$918$		0			0
$919$	−1.21667e14	+	2.10733e14i	−0.185607	+	0.321480i	−0.943781	−	0.330572i	$-0.892758\pi$
$919$	−1.21667e14	+	2.10733e14i	−0.185607	+	0.321480i	0.758174	+	0.652052i	$0.226092\pi$
$920$	2.19066e12	−	1.26478e12i	0.00332381	−	0.00191900i
$921$		0			0
$922$	3.24341e14	+	1.87259e14i	0.486797	+	0.281052i
$923$			3.56512e14i			0.532188i
$924$		0			0
$925$	3.88160e14			0.573195
$926$	5.65702e13	−	9.79825e13i	0.0830870	−	0.143911i
$927$		0			0
$928$	1.28756e13	+	2.23012e13i	0.0187081	+	0.0324033i
$929$	9.51490e14	+	5.49343e14i	1.37507	+	0.793898i	0.991561	−	0.129638i	$-0.0413815\pi$
$929$	9.51490e14	+	5.49343e14i	1.37507	+	0.793898i	0.383511	+	0.923536i	$0.374715\pi$
$930$		0			0
$931$	−1.72905e14	+	4.25979e14i	−0.247207	+	0.609032i
$932$	4.81971e14			0.685396
$933$		0			0
$934$	6.43808e14	−	3.71703e14i	0.905779	−	0.522952i
$935$	4.02102e12	+	6.96462e12i	0.00562702	+	0.00974629i
$936$		0			0
$937$			5.86960e12i			0.00812664i	0.999992	+	0.00406332i	$0.00129340\pi$
$937$			5.86960e12i			0.00812664i	−0.999992	+	0.00406332i	$0.998707\pi$
$938$	2.55371e14	−	2.93293e14i	0.351687	−	0.403912i
$939$		0			0
$940$	1.91121e11	−	3.31031e11i	0.000260417	−	0.000451055i
$941$	4.42242e14	−	2.55329e14i	0.599394	−	0.346060i	−0.169409	−	0.985546i	$-0.554186\pi$
$941$	4.42242e14	−	2.55329e14i	0.599394	−	0.346060i	0.768803	+	0.639486i	$0.220853\pi$
$942$		0			0
$943$	8.63958e14	+	4.98807e14i	1.15860	+	0.668919i
$944$			1.25782e14i			0.167787i
$945$		0			0
$946$	5.69745e14			0.752013
$947$	2.42990e13	−	4.20871e13i	0.0319035	−	0.0552585i	−0.849633	−	0.527375i	$-0.823176\pi$
$947$	2.42990e13	−	4.20871e13i	0.0319035	−	0.0552585i	0.881536	+	0.472116i	$0.156510\pi$
$948$		0			0
$949$	−2.14970e14	−	3.72338e14i	−0.279284	−	0.483734i
$950$	−3.11408e14	−	1.79791e14i	−0.402450	−	0.232354i
$951$		0			0
$952$	−6.01871e13	+	3.08310e14i	−0.0769695	+	0.394278i
$953$	−6.08156e14			−0.773660			−0.386830	−	0.922151i	$-0.626430\pi$
$953$	−6.08156e14			−0.773660			−0.386830	+	0.922151i	$0.626430\pi$
$954$		0			0
$955$	−1.26991e13	+	7.33181e12i	−0.0159866	+	0.00922985i
$956$	−7.52276e13	−	1.30298e14i	−0.0942080	−	0.163173i
$957$		0			0
$958$			9.14348e14i			1.13314i
$959$	5.69862e11	+	1.11246e11i	0.000702550	+	0.000137149i
$960$		0			0
$961$	−4.02454e13	+	6.97071e13i	−0.0491020	+	0.0850472i
$962$	1.41994e14	−	8.19800e13i	0.172343	−	0.0995022i
$963$		0			0
$964$	4.71046e14	+	2.71958e14i	0.565820	+	0.326676i
$965$			1.42965e12i			0.00170842i
$966$		0			0
$967$	−6.41646e14			−0.758863			−0.379431	−	0.925220i	$-0.623880\pi$
$967$	−6.41646e14			−0.758863			−0.379431	+	0.925220i	$0.623880\pi$
$968$	4.61091e13	−	7.98634e13i	0.0542513	−	0.0939660i
$969$		0			0
$970$	5.90525e12	+	1.02282e13i	0.00687669	+	0.0119108i
$971$	1.06433e14	+	6.14492e13i	0.123305	+	0.0711901i	0.560384	−	0.828233i	$-0.310654\pi$
$971$	1.06433e14	+	6.14492e13i	0.123305	+	0.0711901i	−0.437079	+	0.899423i	$0.643987\pi$
$972$		0			0
$973$	−2.53531e14	−	2.20750e14i	−0.290714	−	0.253125i
$974$	8.62641e14			0.984091
$975$		0			0
$976$	−1.43257e14	+	8.27097e13i	−0.161759	+	0.0933915i
$977$	−5.09182e14	−	8.81930e14i	−0.572006	−	0.990743i	−0.996360	−	0.0852468i	$-0.972832\pi$
$977$	−5.09182e14	−	8.81930e14i	−0.572006	−	0.990743i	0.424354	−	0.905496i	$-0.360501\pi$
$978$		0			0
$979$			1.05400e15i			1.17200i
$980$	5.32586e12	−	7.39753e11i	0.00589195	−	0.000818383i
$981$		0			0
$982$	4.47109e13	−	7.74415e13i	0.0489616	−	0.0848040i
$983$	8.27018e14	−	4.77479e14i	0.901047	−	0.520219i	0.0235070	−	0.999724i	$-0.492517\pi$
$983$	8.27018e14	−	4.77479e14i	0.901047	−	0.520219i	0.877540	+	0.479504i	$0.159183\pi$
$984$		0			0
$985$	−6.16562e12	−	3.55972e12i	−0.00664960	−	0.00383915i
$986$		−	1.58479e14i		−	0.170054i
$987$		0			0
$988$	−1.51889e14			−0.161340
$989$	−5.51446e14	+	9.55133e14i	−0.582803	+	1.00944i
$990$		0			0
$991$	7.74810e14	+	1.34201e15i	0.810638	+	1.40407i	0.912418	+	0.409259i	$0.134213\pi$
$991$	7.74810e14	+	1.34201e15i	0.810638	+	1.40407i	−0.101780	+	0.994807i	$0.532454\pi$
$992$	1.39659e14	+	8.06320e13i	0.145382	+	0.0839362i
$993$		0			0
$994$	−2.41598e14	−	7.03492e14i	−0.248978	−	0.724982i
$995$	5.98568e12			0.00613759
$996$		0			0
$997$	−5.91295e13	+	3.41384e13i	−0.0600244	+	0.0346551i	−0.529712	−	0.848178i	$-0.677700\pi$
$997$	−5.91295e13	+	3.41384e13i	−0.0600244	+	0.0346551i	0.469687	+	0.882833i	$0.344367\pi$
$998$	5.01678e14	+	8.68932e14i	0.506725	+	0.877674i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.11.n.b.19.2		12
3.2	odd	2		14.11.d.a.5.4	yes	12
7.3	odd	6	inner	126.11.n.b.73.2		12
12.11	even	2		112.11.s.a.33.5		12
21.2	odd	6		98.11.b.c.97.3		12
21.5	even	6		98.11.b.c.97.4		12
21.11	odd	6		98.11.d.a.31.6		12
21.17	even	6		14.11.d.a.3.4	✓	12
21.20	even	2		98.11.d.a.19.6		12
84.59	odd	6		112.11.s.a.17.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.11.d.a.3.4	✓	12	21.17	even	6
14.11.d.a.5.4	yes	12	3.2	odd	2
98.11.b.c.97.3		12	21.2	odd	6
98.11.b.c.97.4		12	21.5	even	6
98.11.d.a.19.6		12	21.20	even	2
98.11.d.a.31.6		12	21.11	odd	6
112.11.s.a.17.5		12	84.59	odd	6
112.11.s.a.33.5		12	12.11	even	2
126.11.n.b.19.2		12	1.1	even	1	trivial
126.11.n.b.73.2		12	7.3	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:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	126.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.3137 + 19.5959i) q^{2} +(-256.000 - 443.405i) q^{4} +(-32.1973 - 18.5891i) q^{5} +(-11036.6 + 12675.5i) q^{7} +11585.2 q^{8} +O(q^{10})\)	\(q+(-11.3137 + 19.5959i) q^{2} +(-256.000 - 443.405i) q^{4} +(-32.1973 - 18.5891i) q^{5} +(-11036.6 + 12675.5i) q^{7} +11585.2 q^{8} +(728.542 - 420.624i) q^{10} +(-67040.0 - 116117. i) q^{11} +182276. i q^{13} +(-123524. - 359679. i) q^{14} +(-131072. + 227023. i) q^{16} +(1.39715e6 - 806648. i) q^{17} +(-1.40947e6 - 813758. i) q^{19} +19035.3i q^{20} +3.03388e6 q^{22} +(-2.93644e6 + 5.08607e6i) q^{23} +(-4.88212e6 - 8.45608e6i) q^{25} +(-3.57187e6 - 2.06222e6i) q^{26} +(8.44576e6 + 1.64875e6i) q^{28} -4.34134e6 q^{29} +(-2.35447e7 + 1.35935e7i) q^{31} +(-2.96582e6 - 5.13695e6i) q^{32} +3.65047e7i q^{34} +(590975. - 202957. i) q^{35} +(-1.98766e7 + 3.44273e7i) q^{37} +(3.18927e7 - 1.84132e7i) q^{38} +(-373013. - 215359. i) q^{40} -1.69868e8i q^{41} +1.87794e8 q^{43} +(-3.43245e7 + 5.94517e7i) q^{44} +(-6.64441e7 - 1.15085e8i) q^{46} +(-1.73904e7 - 1.00404e7i) q^{47} +(-3.88623e7 - 2.79789e8i) q^{49} +2.20940e8 q^{50} +(8.08223e7 - 4.66628e7i) q^{52} +(-8.95226e7 - 1.55058e8i) q^{53} +4.98486e6i q^{55} +(-1.27862e8 + 1.46849e8i) q^{56} +(4.91166e7 - 8.50725e7i) q^{58} +(4.15536e8 - 2.39910e8i) q^{59} +(5.46484e8 + 3.15513e8i) q^{61} -6.15173e8i q^{62} +1.34218e8 q^{64} +(3.38836e6 - 5.86881e6i) q^{65} +(5.11294e8 + 8.85587e8i) q^{67} +(-7.15343e8 - 4.13004e8i) q^{68} +(-2.70900e6 + 1.38769e7i) q^{70} +1.95589e9 q^{71} +(-2.04271e9 + 1.17936e9i) q^{73} +(-4.49757e8 - 7.79001e8i) q^{74} +8.33288e8i q^{76} +(2.21173e9 + 4.31766e8i) q^{77} +(2.86793e9 - 4.96740e9i) q^{79} +(8.44033e6 - 4.87302e6i) q^{80} +(3.32871e9 + 1.92183e9i) q^{82} +5.54809e9i q^{83} -5.99795e7 q^{85} +(-2.12465e9 + 3.68000e9i) q^{86} +(-7.76674e8 - 1.34524e9i) q^{88} +(-6.80781e9 - 3.93049e9i) q^{89} +(-2.31045e9 - 2.01171e9i) q^{91} +3.00692e9 q^{92} +(3.93500e8 - 2.27187e8i) q^{94} +(3.02541e7 + 5.24016e7i) q^{95} +1.40393e10i q^{97} +(5.92240e9 + 2.40391e9i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3072 q^{4} + 6666 q^{5} + 30576 q^{7}+O(q^{10}) \) 12 * q - 3072 * q^4 + 6666 * q^5 + 30576 * q^7	\( 12 q - 3072 q^{4} + 6666 q^{5} + 30576 q^{7} + 130944 q^{10} + 111210 q^{11} + 38976 q^{14} - 1572864 q^{16} - 1439502 q^{17} - 452814 q^{19} - 1922688 q^{22} - 853074 q^{23} + 16905804 q^{25} + 8671872 q^{26} + 4064256 q^{28} - 60157248 q^{29} + 87231186 q^{31} - 153795138 q^{35} - 7666506 q^{37} + 21703872 q^{38} - 67043328 q^{40} + 1066803336 q^{43} + 56939520 q^{44} - 168245184 q^{46} + 985909398 q^{47} + 456183924 q^{49} - 1764094464 q^{50} - 538871808 q^{52} + 600022554 q^{53} + 243597312 q^{56} - 294598272 q^{58} + 2101762050 q^{59} - 2201391150 q^{61} + 1610612736 q^{64} - 1536128076 q^{65} - 1590058326 q^{67} + 737025024 q^{68} - 3745457856 q^{70} + 7739561160 q^{71} + 2008593834 q^{73} - 1042308096 q^{74} - 464655282 q^{77} + 2310562242 q^{79} - 1747451904 q^{80} + 9636272256 q^{82} - 39581743596 q^{85} + 4924086912 q^{86} + 492208128 q^{88} - 2541648690 q^{89} - 4866473640 q^{91} + 873547776 q^{92} + 28852652352 q^{94} - 29024266590 q^{95} + 11553118080 q^{98}+O(q^{100}) \) 12 * q - 3072 * q^4 + 6666 * q^5 + 30576 * q^7 + 130944 * q^10 + 111210 * q^11 + 38976 * q^14 - 1572864 * q^16 - 1439502 * q^17 - 452814 * q^19 - 1922688 * q^22 - 853074 * q^23 + 16905804 * q^25 + 8671872 * q^26 + 4064256 * q^28 - 60157248 * q^29 + 87231186 * q^31 - 153795138 * q^35 - 7666506 * q^37 + 21703872 * q^38 - 67043328 * q^40 + 1066803336 * q^43 + 56939520 * q^44 - 168245184 * q^46 + 985909398 * q^47 + 456183924 * q^49 - 1764094464 * q^50 - 538871808 * q^52 + 600022554 * q^53 + 243597312 * q^56 - 294598272 * q^58 + 2101762050 * q^59 - 2201391150 * q^61 + 1610612736 * q^64 - 1536128076 * q^65 - 1590058326 * q^67 + 737025024 * q^68 - 3745457856 * q^70 + 7739561160 * q^71 + 2008593834 * q^73 - 1042308096 * q^74 - 464655282 * q^77 + 2310562242 * q^79 - 1747451904 * q^80 + 9636272256 * q^82 - 39581743596 * q^85 + 4924086912 * q^86 + 492208128 * q^88 - 2541648690 * q^89 - 4866473640 * q^91 + 873547776 * q^92 + 28852652352 * q^94 - 29024266590 * q^95 + 11553118080 * q^98

Introduction

L-functions

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