LMFDB - Embedded newform 99.8.f.d.91.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,8,Mod(37,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, degree $4$, 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:	$30.9261175229$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.9
Character	$\chi$	$=$	99.91
Dual form			99.8.f.d.37.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.74849 - 3.44998i) q^{2} +(-28.9084 + 88.9708i) q^{4} +(314.728 + 228.663i) q^{5} +(-446.571 + 1374.41i) q^{7} +(401.838 + 1236.73i) q^{8} +O(q^{10})$	\(q+(4.74849 - 3.44998i) q^{2} +(-28.9084 + 88.9708i) q^{4} +(314.728 + 228.663i) q^{5} +(-446.571 + 1374.41i) q^{7} +(401.838 + 1236.73i) q^{8} +2283.36 q^{10} +(3723.63 - 2371.02i) q^{11} +(-9083.21 + 6599.34i) q^{13} +(2621.13 + 8067.01i) q^{14} +(-3512.62 - 2552.07i) q^{16} +(-19706.8 - 14317.9i) q^{17} +(-8562.19 - 26351.7i) q^{19} +(-29442.6 + 21391.3i) q^{20} +(9501.69 - 24105.2i) q^{22} +55212.9 q^{23} +(22624.8 + 69632.0i) q^{25} +(-20363.9 + 62673.8i) q^{26} +(-109372. - 79463.6i) q^{28} +(20468.2 - 62994.7i) q^{29} +(-45942.6 + 33379.3i) q^{31} -191932. q^{32} -142974. q^{34} +(-454824. + 330449. i) q^{35} +(-36180.8 + 111353. i) q^{37} +(-131570. - 95591.4i) q^{38} +(-156325. + 481119. i) q^{40} +(961.119 + 2958.02i) q^{41} +990987. q^{43} +(103307. + 399837. i) q^{44} +(262178. - 190483. i) q^{46} +(272681. + 839225. i) q^{47} +(-1.02330e6 - 743473. i) q^{49} +(347663. + 252592. i) q^{50} +(-324568. - 998917. i) q^{52} +(-1.36034e6 + 988347. i) q^{53} +(1.71410e6 + 105233. i) q^{55} -1.87922e6 q^{56} +(-120137. - 369744. i) q^{58} +(-107691. + 331440. i) q^{59} +(1.31928e6 + 958510. i) q^{61} +(-103000. + 317002. i) q^{62} +(-461773. + 335497. i) q^{64} -4.36776e6 q^{65} -378040. q^{67} +(1.84357e6 - 1.33943e6i) q^{68} +(-1.01969e6 + 3.13827e6i) q^{70} +(-1.99192e6 - 1.44722e6i) q^{71} +(88059.9 - 271020. i) q^{73} +(212361. + 653581. i) q^{74} +2.59205e6 q^{76} +(1.59587e6 + 6.17661e6i) q^{77} +(-5.74179e6 + 4.17166e6i) q^{79} +(-521956. - 1.60641e6i) q^{80} +(14769.0 + 10730.3i) q^{82} +(2.93363e6 + 2.13141e6i) q^{83} +(-2.92832e6 - 9.01246e6i) q^{85} +(4.70569e6 - 3.41889e6i) q^{86} +(4.42860e6 + 3.65237e6i) q^{88} +7.93014e6 q^{89} +(-5.01386e6 - 1.54311e7i) q^{91} +(-1.59612e6 + 4.91234e6i) q^{92} +(4.19013e6 + 3.04431e6i) q^{94} +(3.33090e6 - 1.02515e7i) q^{95} +(5.53528e6 - 4.02161e6i) q^{97} -7.42411e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 1260 q^{4} - 3902 q^{7}+O(q^{10}) $ 56 * q - 1260 * q^4 - 3902 * q^7	$ 56 q - 1260 q^{4} - 3902 q^{7} + 20008 q^{10} - 18158 q^{13} + 54064 q^{16} - 111812 q^{19} + 16106 q^{22} - 78708 q^{25} + 69378 q^{28} - 189868 q^{31} + 1561016 q^{34} - 795786 q^{37} - 1589918 q^{40} + 355744 q^{43} + 2273926 q^{46} - 4728752 q^{49} - 438038 q^{52} + 3414760 q^{55} + 4154034 q^{58} + 1604778 q^{61} + 9561960 q^{64} - 18424972 q^{67} - 5609964 q^{70} + 17372 q^{73} + 8053960 q^{76} - 15803082 q^{79} + 7756570 q^{82} - 21218378 q^{85} + 37593088 q^{88} + 18308922 q^{91} + 68235162 q^{94} + 34988922 q^{97}+O(q^{100}) $ 56 * q - 1260 * q^4 - 3902 * q^7 + 20008 * q^10 - 18158 * q^13 + 54064 * q^16 - 111812 * q^19 + 16106 * q^22 - 78708 * q^25 + 69378 * q^28 - 189868 * q^31 + 1561016 * q^34 - 795786 * q^37 - 1589918 * q^40 + 355744 * q^43 + 2273926 * q^46 - 4728752 * q^49 - 438038 * q^52 + 3414760 * q^55 + 4154034 * q^58 + 1604778 * q^61 + 9561960 * q^64 - 18424972 * q^67 - 5609964 * q^70 + 17372 * q^73 + 8053960 * q^76 - 15803082 * q^79 + 7756570 * q^82 - 21218378 * q^85 + 37593088 * q^88 + 18308922 * q^91 + 68235162 * q^94 + 34988922 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	4.74849	−	3.44998i	0.419711	−	0.304938i	−0.357810	−	0.933794i	$-0.616477\pi$
$2$	4.74849	−	3.44998i	0.419711	−	0.304938i	0.777522	+	0.628856i	$0.216477\pi$
$3$		0			0
$3$		0			0
$4$	−28.9084	+	88.9708i	−0.225847	+	0.695085i
$5$	314.728	+	228.663i	1.12600	+	0.818090i	0.985108	−	0.171934i	$-0.0550017\pi$
$5$	314.728	+	228.663i	1.12600	+	0.818090i	0.140896	+	0.990024i	$0.455002\pi$
$6$		0			0
$7$	−446.571	+	1374.41i	−0.492094	+	1.51451i	0.329344	+	0.944210i	$0.393172\pi$
$7$	−446.571	+	1374.41i	−0.492094	+	1.51451i	−0.821438	+	0.570298i	$0.806828\pi$
$8$	401.838	+	1236.73i	0.277483	+	0.854004i
$9$		0			0
$10$	2283.36			0.722063
$11$	3723.63	−	2371.02i	0.843515	−	0.537106i
$11$	3723.63	−	2371.02i	0.843515	−	0.537106i
$12$		0			0
$13$	−9083.21	+	6599.34i	−1.14667	+	0.833103i	−0.988034	−	0.154235i	$-0.950709\pi$
$13$	−9083.21	+	6599.34i	−1.14667	+	0.833103i	−0.158633	+	0.987338i	$0.550709\pi$
$14$	2621.13	+	8067.01i	0.255294	+	0.785714i
$15$		0			0
$16$	−3512.62	−	2552.07i	−0.214393	−	0.155766i
$17$	−19706.8	−	14317.9i	−0.972850	−	0.706817i	−0.0167507	−	0.999860i	$-0.505332\pi$
$17$	−19706.8	−	14317.9i	−0.972850	−	0.706817i	−0.956099	+	0.293043i	$0.905332\pi$
$18$		0			0
$19$	−8562.19	−	26351.7i	−0.286383	−	0.881396i	−0.985981	−	0.166859i	$-0.946637\pi$
$19$	−8562.19	−	26351.7i	−0.286383	−	0.881396i	0.699598	−	0.714537i	$-0.253363\pi$
$20$	−29442.6	+	21391.3i	−0.822946	+	0.597905i
$21$		0			0
$22$	9501.69	−	24105.2i	0.190249	−	0.482649i
$23$	55212.9			0.946223			0.473111	−	0.881003i	$-0.343131\pi$
$23$	55212.9			0.946223			0.473111	+	0.881003i	$0.343131\pi$
$24$		0			0
$25$	22624.8	+	69632.0i	0.289597	+	0.891289i
$26$	−20363.9	+	62673.8i	−0.227225	+	0.699325i
$27$		0			0
$28$	−109372.	−	79463.6i	−0.941574	−	0.684093i
$29$	20468.2	−	62994.7i	0.155843	−	0.479635i	−0.842403	−	0.538849i	$-0.818859\pi$
$29$	20468.2	−	62994.7i	0.155843	−	0.479635i	0.998245	+	0.0592140i	$0.0188594\pi$
$30$		0			0
$31$	−45942.6	+	33379.3i	−0.276981	+	0.201238i	−0.717599	−	0.696456i	$-0.754759\pi$
$31$	−45942.6	+	33379.3i	−0.276981	+	0.201238i	0.440619	+	0.897694i	$0.354759\pi$
$32$	−191932.			−1.03544
$33$		0			0
$34$	−142974.			−0.623851
$35$	−454824.	+	330449.i	−1.79310	+	1.30277i
$36$		0			0
$37$	−36180.8	+	111353.i	−0.117428	+	0.361406i	−0.992446	−	0.122685i	$-0.960850\pi$
$37$	−36180.8	+	111353.i	−0.117428	+	0.361406i	0.875018	+	0.484091i	$0.160850\pi$
$38$	−131570.	−	95591.4i	−0.388969	−	0.282603i
$39$		0			0
$40$	−156325.	+	481119.i	−0.386205	+	1.18862i
$41$	961.119	+	2958.02i	0.00217788	+	0.00670282i	0.952140	−	0.305664i	$-0.0988783\pi$
$41$	961.119	+	2958.02i	0.00217788	+	0.00670282i	−0.949962	+	0.312366i	$0.898878\pi$
$42$		0			0
$43$	990987.			1.90076			0.950382	−	0.311084i	$-0.100692\pi$
$43$	990987.			1.90076			0.950382	+	0.311084i	$0.100692\pi$
$44$	103307.	+	399837.i	0.182829	+	0.707618i
$45$		0			0
$46$	262178.	−	190483.i	0.397140	−	0.288539i
$47$	272681.	+	839225.i	0.383100	+	1.17906i	0.937849	+	0.347042i	$0.112814\pi$
$47$	272681.	+	839225.i	0.383100	+	1.17906i	−0.554750	+	0.832017i	$0.687186\pi$
$48$		0			0
$49$	−1.02330e6	−	743473.i	−1.24256	−	0.902774i
$50$	347663.	+	252592.i	0.393335	+	0.285775i
$51$		0			0
$52$	−324568.	−	998917.i	−0.320106	−	0.985185i
$53$	−1.36034e6	+	988347.i	−1.25511	+	0.911893i	−0.998507	−	0.0546231i	$-0.982604\pi$
$53$	−1.36034e6	+	988347.i	−1.25511	+	0.911893i	−0.256606	+	0.966516i	$0.582604\pi$
$54$		0			0
$55$	1.71410e6	+	105233.i	1.38920	+	0.0852873i
$56$	−1.87922e6			−1.42994
$57$		0			0
$58$	−120137.	−	369744.i	−0.0808499	−	0.248830i
$59$	−107691.	+	331440.i	−0.0682651	+	0.210098i	−0.979370	−	0.202077i	$-0.935231\pi$
$59$	−107691.	+	331440.i	−0.0682651	+	0.210098i	0.911105	+	0.412175i	$0.135231\pi$
$60$		0			0
$61$	1.31928e6	+	958510.i	0.744186	+	0.540683i	0.894019	−	0.448029i	$-0.147874\pi$
$61$	1.31928e6	+	958510.i	0.744186	+	0.540683i	−0.149833	+	0.988711i	$0.547874\pi$
$62$	−103000.	+	317002.i	−0.0548867	+	0.168924i
$63$		0			0
$64$	−461773.	+	335497.i	−0.220190	+	0.159978i
$65$	−4.36776e6			−1.97271
$66$		0			0
$67$	−378040.			−0.153559			−0.0767796	−	0.997048i	$-0.524464\pi$
$67$	−378040.			−0.153559			−0.0767796	+	0.997048i	$0.524464\pi$
$68$	1.84357e6	−	1.33943e6i	0.711013	−	0.516581i
$69$		0			0
$70$	−1.01969e6	+	3.13827e6i	−0.355323	+	1.09357i
$71$	−1.99192e6	−	1.44722e6i	−0.660494	−	0.479877i	0.206336	−	0.978481i	$-0.433846\pi$
$71$	−1.99192e6	−	1.44722e6i	−0.660494	−	0.479877i	−0.866830	+	0.498605i	$0.833846\pi$
$72$		0			0
$73$	88059.9	−	271020.i	0.0264940	−	0.0815402i	−0.936935	−	0.349503i	$-0.886350\pi$
$73$	88059.9	−	271020.i	0.0264940	−	0.0815402i	0.963429	+	0.267963i	$0.0863504\pi$
$74$	212361.	+	653581.i	0.0609207	+	0.187495i
$75$		0			0
$76$	2.59205e6			0.677324
$77$	1.59587e6	+	6.17661e6i	0.398363	+	1.54182i
$78$		0			0
$79$	−5.74179e6	+	4.17166e6i	−1.31025	+	0.951949i	−0.310246	+	0.950656i	$0.600412\pi$
$79$	−5.74179e6	+	4.17166e6i	−1.31025	+	0.951949i	−0.999999	+	0.00129285i	$0.999588\pi$
$80$	−521956.	−	1.60641e6i	−0.113977	−	0.350786i
$81$		0			0
$82$	14769.0	+	10730.3i	0.00295803	+	0.00214913i
$83$	2.93363e6	+	2.13141e6i	0.563161	+	0.409161i	0.832615	−	0.553853i	$-0.186843\pi$
$83$	2.93363e6	+	2.13141e6i	0.563161	+	0.409161i	−0.269453	+	0.963013i	$0.586843\pi$
$84$		0			0
$85$	−2.92832e6	−	9.01246e6i	−0.517193	−	1.59176i
$86$	4.70569e6	−	3.41889e6i	0.797772	−	0.579615i
$87$		0			0
$88$	4.42860e6	+	3.65237e6i	0.692752	+	0.571327i
$89$	7.93014e6			1.19238			0.596192	−	0.802842i	$-0.296680\pi$
$89$	7.93014e6			1.19238			0.596192	+	0.802842i	$0.296680\pi$
$90$		0			0
$91$	−5.01386e6	−	1.54311e7i	−0.697473	−	2.14660i
$92$	−1.59612e6	+	4.91234e6i	−0.213701	+	0.657705i
$93$		0			0
$94$	4.19013e6	+	3.04431e6i	0.520331	+	0.378043i
$95$	3.33090e6	−	1.02515e7i	0.398593	−	1.22674i
$96$		0			0
$97$	5.53528e6	−	4.02161e6i	0.615798	−	0.447403i	−0.235653	−	0.971837i	$-0.575723\pi$
$97$	5.53528e6	−	4.02161e6i	0.615798	−	0.447403i	0.851451	+	0.524434i	$0.175723\pi$
$98$	−7.42411e6			−0.796807
$99$		0			0
$100$	−6.84926e6			−0.684926
$101$	1.18963e7	−	8.64317e6i	1.14891	−	0.834734i	0.160577	−	0.987023i	$-0.448664\pi$
$101$	1.18963e7	−	8.64317e6i	1.14891	−	0.834734i	0.988336	+	0.152289i	$0.0486645\pi$
$102$		0			0
$103$	−5.79583e6	+	1.78377e7i	−0.522619	+	1.60846i	0.246357	+	0.969179i	$0.420766\pi$
$103$	−5.79583e6	+	1.78377e7i	−0.522619	+	1.60846i	−0.768976	+	0.639277i	$0.779234\pi$
$104$	−1.18116e7	−	8.58161e6i	−1.02965	−	0.748087i
$105$		0			0
$106$	−3.04980e6	+	9.38631e6i	−0.248714	+	0.765463i
$107$	−4.85577e6	−	1.49445e7i	−0.383190	−	1.17934i	−0.937785	−	0.347218i	$-0.887127\pi$
$107$	−4.85577e6	−	1.49445e7i	−0.383190	−	1.17934i	0.554594	−	0.832121i	$-0.312873\pi$
$108$		0			0
$109$	−6.90787e6			−0.510918			−0.255459	−	0.966820i	$-0.582227\pi$
$109$	−6.90787e6			−0.510918			−0.255459	+	0.966820i	$0.582227\pi$
$110$	8.50242e6	−	5.41389e6i	0.609071	−	0.387825i
$111$		0			0
$112$	5.07621e6	−	3.68808e6i	0.341410	−	0.248049i
$113$	7.95930e6	+	2.44962e7i	0.518920	+	1.59707i	0.776034	+	0.630690i	$0.217228\pi$
$113$	7.95930e6	+	2.44962e7i	0.518920	+	1.59707i	−0.257115	+	0.966381i	$0.582772\pi$
$114$		0			0
$115$	1.73770e7	+	1.26252e7i	1.06545	+	0.774095i
$116$	5.01298e6	+	3.64215e6i	0.298190	+	0.216648i
$117$		0			0
$118$	632089.	+	1.94537e6i	0.0354153	+	0.108997i
$119$	2.84791e7	−	2.06912e7i	1.54921	−	1.12557i
$120$		0			0
$121$	8.24374e6	−	1.76576e7i	0.423034	−	0.906114i
$122$	9.57141e6			0.477218
$123$		0			0
$124$	−1.64165e6	−	5.05249e6i	−0.0773225	−	0.237974i
$125$	590210.	−	1.81648e6i	0.0270285	−	0.0831851i
$126$		0			0
$127$	−7.88190e6	−	5.72653e6i	−0.341443	−	0.248073i	0.403828	−	0.914835i	$-0.367680\pi$
$127$	−7.88190e6	−	5.72653e6i	−0.341443	−	0.248073i	−0.745270	+	0.666762i	$0.767680\pi$
$128$	6.55646e6	−	2.01787e7i	0.276334	−	0.850469i
$129$		0			0
$130$	−2.07403e7	+	1.50687e7i	−0.827967	+	0.601553i
$131$	−3.39357e7			−1.31888			−0.659442	−	0.751755i	$-0.729208\pi$
$131$	−3.39357e7			−1.31888			−0.659442	+	0.751755i	$0.729208\pi$
$132$		0			0
$133$	4.00415e7			1.47581
$134$	−1.79512e6	+	1.30423e6i	−0.0644505	+	0.0468260i
$135$		0			0
$136$	9.78837e6	−	3.01255e7i	0.333675	−	1.02695i
$137$	4.14673e7	+	3.01277e7i	1.37779	+	1.00102i	0.997083	+	0.0763293i	$0.0243200\pi$
$137$	4.14673e7	+	3.01277e7i	1.37779	+	1.00102i	0.380709	+	0.924695i	$0.375680\pi$
$138$		0			0
$139$	−303706.	+	934712.i	−0.00959184	+	0.0295207i	−0.955738	−	0.294219i	$-0.904940\pi$
$139$	−303706.	+	934712.i	−0.00959184	+	0.0295207i	0.946146	+	0.323740i	$0.104940\pi$
$140$	−1.62521e7	−	5.00188e7i	−0.500566	−	1.54058i
$141$		0			0
$142$	−1.44515e7			−0.423549
$143$	−1.81754e7	+	4.61100e7i	−0.519767	+	1.31862i
$144$		0			0
$145$	2.08465e7	−	1.51458e7i	0.567864	−	0.412577i
$146$	−516864.	−	1.59074e6i	−0.0137449	−	0.0423024i
$147$		0			0
$148$	−8.86124e6	−	6.43807e6i	−0.224687	−	0.163245i
$149$	−6.66463e6	−	4.84214e6i	−0.165053	−	0.119918i	0.502192	−	0.864756i	$-0.332527\pi$
$149$	−6.66463e6	−	4.84214e6i	−0.165053	−	0.119918i	−0.667246	+	0.744838i	$0.732527\pi$
$150$		0			0
$151$	−1.19402e6	−	3.67480e6i	−0.0282222	−	0.0868590i	0.935953	−	0.352124i	$-0.114541\pi$
$151$	−1.19402e6	−	3.67480e6i	−0.0282222	−	0.0868590i	−0.964176	+	0.265265i	$0.914541\pi$
$152$	2.91493e7	−	2.11782e7i	0.673250	−	0.489144i
$153$		0			0
$154$	2.88871e7	+	2.38239e7i	0.637356	+	0.525641i
$155$	−2.20920e7			−0.476513
$156$		0			0
$157$	1.67457e7	+	5.15379e7i	0.345346	+	1.06287i	0.961398	+	0.275160i	$0.0887310\pi$
$157$	1.67457e7	+	5.15379e7i	0.345346	+	1.06287i	−0.616052	+	0.787705i	$0.711269\pi$
$158$	−1.28727e7	+	3.96181e7i	−0.259639	+	0.799087i
$159$		0			0
$160$	−6.04064e7	−	4.38878e7i	−1.16590	−	0.847079i
$161$	−2.46565e7	+	7.58849e7i	−0.465630	+	1.43306i
$162$		0			0
$163$	−5.19717e7	+	3.77596e7i	−0.939962	+	0.682922i	−0.948411	−	0.317042i	$-0.897310\pi$
$163$	−5.19717e7	+	3.77596e7i	−0.939962	+	0.682922i	0.00844982	+	0.999964i	$0.497310\pi$
$164$	−290962.			−0.00515090
$165$		0			0
$166$	2.12837e7			0.361134
$167$	−2.25605e7	+	1.63911e7i	−0.374835	+	0.272334i	−0.759213	−	0.650842i	$-0.774416\pi$
$167$	−2.25605e7	+	1.63911e7i	−0.374835	+	0.272334i	0.384378	+	0.923176i	$0.374416\pi$
$168$		0			0
$169$	1.95631e7	−	6.02089e7i	0.311769	−	0.959528i
$170$	−4.49979e7	−	3.26929e7i	−0.702459	−	0.510367i
$171$		0			0
$172$	−2.86478e7	+	8.81690e7i	−0.429281	+	1.32119i
$173$	2.38372e7	+	7.33633e7i	0.350020	+	1.07725i	0.958841	+	0.283944i	$0.0916429\pi$
$173$	2.38372e7	+	7.33633e7i	0.350020	+	1.07725i	−0.608821	+	0.793308i	$0.708357\pi$
$174$		0			0
$175$	−1.05806e8			−1.49237
$176$	−1.91307e7	−	1.17449e6i	−0.264507	−	0.0162389i
$177$		0			0
$178$	3.76562e7	−	2.73588e7i	0.500457	−	0.363603i
$179$	−7.08079e6	−	2.17924e7i	−0.0922776	−	0.284001i	0.894257	−	0.447554i	$-0.147705\pi$
$179$	−7.08079e6	−	2.17924e7i	−0.0922776	−	0.284001i	−0.986535	+	0.163553i	$0.947705\pi$
$180$		0			0
$181$	4.51894e7	+	3.28320e7i	0.566450	+	0.411550i	0.833814	−	0.552046i	$-0.186153\pi$
$181$	4.51894e7	+	3.28320e7i	0.566450	+	0.411550i	−0.267364	+	0.963596i	$0.586153\pi$
$182$	−7.70452e7	−	5.59766e7i	−0.947318	−	0.688267i
$183$		0			0
$184$	2.21866e7	+	6.82835e7i	0.262560	+	0.808078i
$185$	−3.68494e7	+	2.67727e7i	−0.427887	+	0.310878i
$186$		0			0
$187$	−1.07329e8	−	6.58925e6i	−1.20025	−	0.0736869i
$188$	−8.25493e7			−0.906068
$189$		0			0
$190$	−1.95506e7	−	6.01706e7i	−0.206787	−	0.636424i
$191$	−2.97865e7	+	9.16733e7i	−0.309316	+	0.951977i	0.668715	+	0.743519i	$0.266844\pi$
$191$	−2.97865e7	+	9.16733e7i	−0.309316	+	0.951977i	−0.978031	+	0.208458i	$0.933156\pi$
$192$		0			0
$193$	−4.85047e7	−	3.52407e7i	−0.485661	−	0.352854i	0.317852	−	0.948140i	$-0.397038\pi$
$193$	−4.85047e7	−	3.52407e7i	−0.485661	−	0.352854i	−0.803513	+	0.595287i	$0.797038\pi$
$194$	1.24097e7	−	3.81932e7i	0.122027	−	0.375560i
$195$		0			0
$196$	9.57295e7	−	6.95515e7i	0.908133	−	0.659797i
$197$	−3.72673e7			−0.347293			−0.173647	−	0.984808i	$-0.555555\pi$
$197$	−3.72673e7			−0.347293			−0.173647	+	0.984808i	$0.555555\pi$
$198$		0			0
$199$	1.66253e8			1.49549			0.747744	−	0.663987i	$-0.231137\pi$
$199$	1.66253e8			1.49549			0.747744	+	0.663987i	$0.231137\pi$
$200$	−7.70245e7	+	5.59615e7i	−0.680806	+	0.494635i
$201$		0			0
$202$	2.66707e7	−	8.20840e7i	0.227669	−	0.700695i
$203$	7.74397e7	+	5.62632e7i	0.649722	+	0.472050i
$204$		0			0
$205$	−373899.	+	1.15074e6i	−0.00303121	+	0.00932911i
$206$	3.40184e7	+	1.04698e8i	0.271130	+	0.834454i
$207$		0			0
$208$	4.87478e7			0.375607
$209$	−9.43628e7	−	7.78230e7i	−0.714971	−	0.589653i
$210$		0			0
$211$	−6.33018e7	+	4.59915e7i	−0.463904	+	0.337046i	−0.795061	−	0.606530i	$-0.792561\pi$
$211$	−6.33018e7	+	4.59915e7i	−0.463904	+	0.337046i	0.331157	+	0.943576i	$0.392561\pi$
$212$	−4.86088e7	−	1.49602e8i	−0.350380	−	1.07836i
$213$		0			0
$214$	−7.46158e7	−	5.42116e7i	−0.520454	−	0.378132i
$215$	3.11891e8	+	2.26602e8i	2.14027	+	1.55500i
$216$		0			0
$217$	−2.53600e7	−	7.80500e7i	−0.168477	−	0.518518i
$218$	−3.28020e7	+	2.38320e7i	−0.214438	+	0.155798i
$219$		0			0
$220$	−5.89144e7	+	1.49462e8i	−0.373029	+	0.946351i
$221$	2.73490e8			1.70439
$222$		0			0
$223$	−1.12496e7	−	3.46227e7i	−0.0679313	−	0.209071i	0.911328	−	0.411680i	$-0.135058\pi$
$223$	−1.12496e7	−	3.46227e7i	−0.0679313	−	0.209071i	−0.979260	+	0.202609i	$0.935058\pi$
$224$	8.57114e7	−	2.63793e8i	0.509531	−	1.56818i
$225$		0			0
$226$	1.22306e8	+	8.88606e7i	0.704804	+	0.512070i
$227$	−6.51171e6	+	2.00410e7i	−0.0369492	+	0.113718i	−0.967830	−	0.251605i	$-0.919042\pi$
$227$	−6.51171e6	+	2.00410e7i	−0.0369492	+	0.113718i	0.930881	+	0.365323i	$0.119042\pi$
$228$		0			0
$229$	−9.93691e6	+	7.21959e6i	−0.0546798	+	0.0397272i	−0.614789	−	0.788691i	$-0.710759\pi$
$229$	−9.93691e6	+	7.21959e6i	−0.0546798	+	0.0397272i	0.560110	+	0.828419i	$0.310759\pi$
$230$	1.26071e8			0.683233
$231$		0			0
$232$	8.61323e7			0.452854
$233$	−1.88905e8	+	1.37248e8i	−0.978359	+	0.710819i	−0.957341	−	0.288960i	$-0.906691\pi$
$233$	−1.88905e8	+	1.37248e8i	−0.978359	+	0.710819i	−0.0210176	+	0.999779i	$0.506691\pi$
$234$		0			0
$235$	−1.06080e8	+	3.26479e8i	−0.533205	+	1.64104i
$236$	−2.63753e7	−	1.91628e7i	−0.130619	−	0.0949000i
$237$		0			0
$238$	6.38481e7	−	1.96504e8i	0.306993	−	0.944828i
$239$	−8.62659e6	−	2.65499e7i	−0.0408739	−	0.125797i	0.928537	−	0.371239i	$-0.121067\pi$
$239$	−8.62659e6	−	2.65499e7i	−0.0408739	−	0.125797i	−0.969411	+	0.245442i	$0.921067\pi$
$240$		0			0
$241$	1.75971e8			0.809806			0.404903	−	0.914360i	$-0.367305\pi$
$241$	1.75971e8			0.809806			0.404903	+	0.914360i	$0.367305\pi$
$242$	−2.17730e7	−	1.12288e8i	−0.0987563	−	0.509305i
$243$		0			0
$244$	−1.23418e8	+	8.96682e7i	−0.543892	+	0.395161i
$245$	−1.52057e8	−	4.67983e8i	−0.660580	−	2.03305i
$246$		0			0
$247$	2.51676e8	+	1.82853e8i	1.06268	+	0.772082i
$248$	−5.97426e7	−	4.34055e7i	−0.248716	−	0.180703i
$249$		0			0
$250$	−3.46421e6	−	1.06617e7i	−0.0140221	−	0.0431557i
$251$	−2.36332e8	+	1.71705e8i	−0.943332	+	0.685371i	−0.949220	−	0.314612i	$-0.898126\pi$
$251$	−2.36332e8	+	1.71705e8i	−0.943332	+	0.685371i	0.00588840	+	0.999983i	$0.498126\pi$
$252$		0			0
$253$	2.05593e8	−	1.30911e8i	0.798153	−	0.508222i
$254$	−5.71835e7			−0.218954
$255$		0			0
$256$	−6.10597e7	−	1.87922e8i	−0.227465	−	0.700065i
$257$	8.91819e7	−	2.74474e8i	0.327726	−	1.00864i	−0.642469	−	0.766311i	$-0.722090\pi$
$257$	8.91819e7	−	2.74474e8i	0.327726	−	1.00864i	0.970195	−	0.242325i	$-0.0779100\pi$
$258$		0			0
$259$	−1.36887e8	−	9.94541e7i	−0.489567	−	0.355691i
$260$	1.26265e8	−	3.88604e8i	0.445529	−	1.37120i
$261$		0			0
$262$	−1.61143e8	+	1.17077e8i	−0.553551	+	0.402178i
$263$	4.97856e8			1.68756			0.843778	−	0.536692i	$-0.180326\pi$
$263$	4.97856e8			1.68756			0.843778	+	0.536692i	$0.180326\pi$
$264$		0			0
$265$	−6.54136e8			−2.15927
$266$	1.90137e8	−	1.38143e8i	0.619413	−	0.450030i
$267$		0			0
$268$	1.09285e7	−	3.36345e7i	0.0346808	−	0.106737i
$269$	3.99200e8	+	2.90036e8i	1.25042	+	0.908487i	0.998246	−	0.0591943i	$-0.0188531\pi$
$269$	3.99200e8	+	2.90036e8i	1.25042	+	0.908487i	0.252178	+	0.967681i	$0.418853\pi$
$270$		0			0
$271$	1.50339e8	−	4.62697e8i	0.458860	−	1.41223i	−0.407683	−	0.913124i	$-0.633663\pi$
$271$	1.50339e8	−	4.62697e8i	0.458860	−	1.41223i	0.866543	−	0.499102i	$-0.166337\pi$
$272$	3.26825e7	+	1.00586e8i	0.0984747	+	0.303074i
$273$		0			0
$274$	3.00847e8			0.883525
$275$	2.49345e8	+	2.05640e8i	0.722997	+	0.596271i
$276$		0			0
$277$	2.98666e8	−	2.16993e8i	0.844319	−	0.613433i	−0.0792551	−	0.996854i	$-0.525254\pi$
$277$	2.98666e8	−	2.16993e8i	0.844319	−	0.613433i	0.923574	+	0.383421i	$0.125254\pi$
$278$	1.78259e6	+	5.48625e6i	0.00497617	+	0.0153151i
$279$		0			0
$280$	−5.91442e8	−	4.29708e8i	−1.61012	−	1.16982i
$281$	2.82375e7	+	2.05157e7i	0.0759196	+	0.0551588i	0.625098	−	0.780547i	$-0.285059\pi$
$281$	2.82375e7	+	2.05157e7i	0.0759196	+	0.0551588i	−0.549178	+	0.835705i	$0.685059\pi$
$282$		0			0
$283$	5.82028e7	+	1.79130e8i	0.152648	+	0.469802i	0.997915	−	0.0645418i	$-0.0205586\pi$
$283$	5.82028e7	+	1.79130e8i	0.152648	+	0.469802i	−0.845267	+	0.534344i	$0.820559\pi$
$284$	1.86343e8	−	1.35386e8i	0.482725	−	0.350720i
$285$		0			0
$286$	7.27726e7	+	2.81657e8i	0.183945	+	0.711935i
$287$	−4.49473e6			−0.0112232
$288$		0			0
$289$	5.65570e7	+	1.74064e8i	0.137830	+	0.424197i
$290$	4.67364e7	−	1.43840e8i	0.112528	−	0.346327i
$291$		0			0
$292$	2.15672e7	+	1.56695e7i	0.0506938	+	0.0368312i
$293$	1.93588e7	−	5.95803e7i	0.0449616	−	0.138378i	−0.926056	−	0.377387i	$-0.876823\pi$
$293$	1.93588e7	−	5.95803e7i	0.0449616	−	0.138378i	0.971017	+	0.239009i	$0.0768227\pi$
$294$		0			0
$295$	−1.09681e8	+	7.96882e7i	−0.248746	+	0.180725i
$296$	−1.52252e8			−0.341227
$297$		0			0
$298$	−4.83522e7			−0.105842
$299$	−5.01510e8	+	3.64369e8i	−1.08500	+	0.788301i
$300$		0			0
$301$	−4.42546e8	+	1.36202e9i	−0.935354	+	2.87872i
$302$	−1.83478e7	−	1.33304e7i	−0.0383318	−	0.0278497i
$303$		0			0
$304$	−3.71756e7	+	1.14415e8i	−0.0758929	+	0.233574i
$305$	1.96037e8	+	6.03340e8i	0.395629	+	1.21762i
$306$		0			0
$307$	5.96776e8			1.17714			0.588569	−	0.808447i	$-0.299692\pi$
$307$	5.96776e8			1.17714			0.588569	+	0.808447i	$0.299692\pi$
$308$	−5.95672e8	−	3.65701e7i	−1.16166	−	0.0713179i
$309$		0			0
$310$	−1.04904e8	+	7.62170e7i	−0.199998	+	0.145307i
$311$	−3.06407e8	−	9.43025e8i	−0.577614	−	1.77771i	−0.627099	−	0.778939i	$-0.715758\pi$
$311$	−3.06407e8	−	9.43025e8i	−0.577614	−	1.77771i	0.0494851	−	0.998775i	$-0.484242\pi$
$312$		0			0
$313$	529600.	+	384777.i	0.000976209	+	0.000709257i	0.588273	−	0.808662i	$-0.299808\pi$
$313$	529600.	+	384777.i	0.000976209	+	0.000709257i	−0.587297	+	0.809371i	$0.699808\pi$
$314$	2.57322e8	+	1.86955e8i	0.469054	+	0.340787i
$315$		0			0
$316$	−2.05170e8	−	6.31448e8i	−0.365771	−	1.12573i
$317$	8.10987e8	−	5.89217e8i	1.42990	−	1.03889i	0.439869	−	0.898062i	$-0.355025\pi$
$317$	8.10987e8	−	5.89217e8i	1.42990	−	1.03889i	0.990035	−	0.140823i	$-0.0449750\pi$
$318$		0			0
$319$	−7.31452e7	−	2.83099e8i	−0.126159	−	0.488283i
$320$	−2.22049e8			−0.378811
$321$		0			0
$322$	1.44720e8	+	4.45403e8i	0.241565	+	0.743460i
$323$	−2.08566e8	+	6.41901e8i	−0.344378	+	1.05989i
$324$		0			0
$325$	−6.65031e8	−	4.83173e8i	−1.07461	−	0.780748i
$326$	−1.16517e8	+	3.58602e8i	−0.186263	+	0.573260i
$327$		0			0
$328$	−3.27206e6	+	2.37729e6i	−0.00511991	+	0.00371984i
$329$	−1.27521e9			−1.97422
$330$		0			0
$331$	1.23721e8			0.187518			0.0937592	−	0.995595i	$-0.470112\pi$
$331$	1.23721e8			0.187518			0.0937592	+	0.995595i	$0.470112\pi$
$332$	−2.74440e8	+	1.99392e8i	−0.411589	+	0.299037i
$333$		0			0
$334$	−5.05790e7	+	1.55666e8i	−0.0742776	+	0.228603i
$335$	−1.18980e8	−	8.64438e7i	−0.172908	−	0.125625i
$336$		0			0
$337$	4.31142e8	−	1.32692e9i	0.613643	−	1.88860i	0.193659	−	0.981069i	$-0.437965\pi$
$337$	4.31142e8	−	1.32692e9i	0.613643	−	1.88860i	0.419985	−	0.907531i	$-0.362035\pi$
$338$	−1.14825e8	−	3.53394e8i	−0.161743	−	0.497795i
$339$		0			0
$340$	8.86499e8			1.22321
$341$	−9.19307e7	+	2.33223e8i	−0.125551	+	0.318516i
$342$		0			0
$343$	5.15975e8	−	3.74878e8i	0.690397	−	0.501603i
$344$	3.98216e8	+	1.22558e9i	0.527429	+	1.62326i
$345$		0			0
$346$	3.66292e8	+	2.66127e8i	0.475402	+	0.345400i
$347$	−3.67372e8	−	2.66911e8i	−0.472011	−	0.342936i	0.326213	−	0.945296i	$-0.394227\pi$
$347$	−3.67372e8	−	2.66911e8i	−0.472011	−	0.342936i	−0.798225	+	0.602360i	$0.794227\pi$
$348$		0			0
$349$	2.65503e8	+	8.17133e8i	0.334334	+	1.02897i	0.967049	+	0.254589i	$0.0819401\pi$
$349$	2.65503e8	+	8.17133e8i	0.334334	+	1.02897i	−0.632716	+	0.774384i	$0.718060\pi$
$350$	−5.02419e8	+	3.65029e8i	−0.626366	+	0.455082i
$351$		0			0
$352$	−7.14686e8	+	4.55074e8i	−0.873405	+	0.556139i
$353$	4.48342e8			0.542498			0.271249	−	0.962509i	$-0.412563\pi$
$353$	4.48342e8			0.542498			0.271249	+	0.962509i	$0.412563\pi$
$354$		0			0
$355$	−2.95989e8	−	9.10959e8i	−0.351136	−	1.08069i
$356$	−2.29248e8	+	7.05551e8i	−0.269296	+	0.828807i
$357$		0			0
$358$	−1.08807e8	−	7.90526e7i	−0.125333	−	0.0910595i
$359$	−3.94373e8	+	1.21376e9i	−0.449859	+	1.38452i	0.427207	+	0.904154i	$0.359498\pi$
$359$	−3.94373e8	+	1.21376e9i	−0.449859	+	1.38452i	−0.877066	+	0.480370i	$0.840502\pi$
$360$		0			0
$361$	1.02056e8	−	7.41482e7i	0.114173	−	0.0829517i
$362$	3.27851e8			0.363243
$363$		0			0
$364$	1.51786e9			1.64959
$365$	8.96873e7	−	6.51616e7i	0.0965397	−	0.0701402i
$366$		0			0
$367$	3.64663e8	−	1.12232e9i	0.385088	−	1.18518i	−0.551328	−	0.834289i	$-0.685879\pi$
$367$	3.64663e8	−	1.12232e9i	0.385088	−	1.18518i	0.936416	−	0.350891i	$-0.114121\pi$
$368$	−1.93942e8	−	1.40907e8i	−0.202864	−	0.147389i
$369$		0			0
$370$	−8.26139e7	+	2.54259e8i	−0.0847905	+	0.260958i
$371$	−7.50899e8	−	2.31103e9i	−0.763436	−	2.34962i
$372$		0			0
$373$	−1.13904e9			−1.13647			−0.568236	−	0.822865i	$-0.692374\pi$
$373$	−1.13904e9			−1.13647			−0.568236	+	0.822865i	$0.692374\pi$
$374$	−5.32383e8	+	3.38994e8i	−0.526228	+	0.335074i
$375$		0			0
$376$	−9.28321e8	+	6.74465e8i	−0.900618	+	0.654338i
$377$	2.29806e8	+	7.07270e8i	0.220885	+	0.679815i
$378$		0			0
$379$	4.34939e8	+	3.16001e8i	0.410384	+	0.298162i	0.773757	−	0.633482i	$-0.218375\pi$
$379$	4.34939e8	+	3.16001e8i	0.410384	+	0.298162i	−0.363373	+	0.931644i	$0.618375\pi$
$380$	8.15791e8	+	5.92707e8i	0.762669	+	0.554112i
$381$		0			0
$382$	1.74830e8	+	5.38073e8i	0.160470	+	0.493877i
$383$	5.17941e8	−	3.76306e8i	0.471069	−	0.342252i	−0.326789	−	0.945097i	$-0.605967\pi$
$383$	5.17941e8	−	3.76306e8i	0.471069	−	0.342252i	0.797858	+	0.602846i	$0.205967\pi$
$384$		0			0
$385$	−9.10099e8	+	2.30887e9i	−0.812786	+	2.06199i
$386$	−3.51904e8			−0.311436
$387$		0			0
$388$	1.97791e8	+	6.08737e8i	0.171907	+	0.529076i
$389$	−4.56900e8	+	1.40619e9i	−0.393548	+	1.21121i	0.536539	+	0.843875i	$0.319731\pi$
$389$	−4.56900e8	+	1.40619e9i	−0.393548	+	1.21121i	−0.930087	+	0.367340i	$0.880269\pi$
$390$		0			0
$391$	−1.08807e9	−	7.90531e8i	−0.920533	−	0.668806i
$392$	5.08274e8	−	1.56431e9i	0.426183	−	1.31166i
$393$		0			0
$394$	−1.76963e8	+	1.28571e8i	−0.145763	+	0.105903i
$395$	−2.76101e9			−2.25412
$396$		0			0
$397$	1.10223e9			0.884112			0.442056	−	0.896988i	$-0.354249\pi$
$397$	1.10223e9			0.884112			0.442056	+	0.896988i	$0.354249\pi$
$398$	7.89450e8	−	5.73569e8i	0.627673	−	0.456031i
$399$		0			0
$400$	9.82333e7	−	3.02331e8i	0.0767447	−	0.236196i
$401$	5.94677e8	+	4.32058e8i	0.460549	+	0.334609i	0.793747	−	0.608248i	$-0.208128\pi$
$401$	5.94677e8	+	4.32058e8i	0.460549	+	0.334609i	−0.333197	+	0.942857i	$0.608128\pi$
$402$		0			0
$403$	1.97025e8	−	6.06381e8i	0.149953	−	0.461507i
$404$	4.25087e8	+	1.30828e9i	0.320733	+	0.987114i
$405$		0			0
$406$	5.61828e8			0.416641
$407$	1.29296e8	+	5.00423e8i	0.0950612	+	0.367923i
$408$		0			0
$409$	8.03627e8	−	5.83870e8i	0.580795	−	0.421973i	−0.258215	−	0.966087i	$-0.583134\pi$
$409$	8.03627e8	−	5.83870e8i	0.580795	−	0.421973i	0.839011	+	0.544115i	$0.183134\pi$
$410$	2.19459e6	+	6.75424e6i	0.00157257	+	0.00483986i
$411$		0			0
$412$	−1.41949e9	−	1.03132e9i	−0.999982	−	0.726529i
$413$	−4.07440e8	−	2.96023e8i	−0.284603	−	0.206776i
$414$		0			0
$415$	4.35921e8	+	1.34163e9i	0.299392	+	0.921433i
$416$	1.74336e9	−	1.26663e9i	1.18730	−	0.862624i
$417$		0			0
$418$	−7.16569e8	−	4.39923e7i	−0.479889	−	0.0294618i
$419$	1.49926e9			0.995699			0.497849	−	0.867264i	$-0.334123\pi$
$419$	1.49926e9			0.995699			0.497849	+	0.867264i	$0.334123\pi$
$420$		0			0
$421$	−7.35009e8	−	2.26213e9i	−0.480071	−	1.47751i	−0.838995	−	0.544140i	$-0.816856\pi$
$421$	−7.35009e8	−	2.26213e9i	−0.480071	−	1.47751i	0.358924	−	0.933367i	$-0.383144\pi$
$422$	−1.41918e8	+	4.36780e8i	−0.0919275	+	0.282924i
$423$		0			0
$424$	−1.76896e9	−	1.28522e9i	−1.12703	−	0.818837i
$425$	5.51118e8	−	1.69617e9i	0.348243	−	1.07178i
$426$		0			0
$427$	−1.90653e9	+	1.38518e9i	−1.18508	+	0.861009i
$428$	1.47000e9			0.906282
$429$		0			0
$430$	2.26278e9			1.37247
$431$	4.79718e8	−	3.48536e8i	0.288613	−	0.209690i	−0.434052	−	0.900888i	$-0.642917\pi$
$431$	4.79718e8	−	3.48536e8i	0.288613	−	0.209690i	0.722665	+	0.691198i	$0.242917\pi$
$432$		0			0
$433$	−4.64315e8	+	1.42902e9i	−0.274856	+	0.845920i	0.714401	+	0.699736i	$0.246699\pi$
$433$	−4.64315e8	+	1.42902e9i	−0.274856	+	0.845920i	−0.989257	+	0.146184i	$0.953301\pi$
$434$	−3.89692e8	−	2.83128e8i	−0.228827	−	0.166253i
$435$		0			0
$436$	1.99695e8	−	6.14599e8i	0.115389	−	0.355132i
$437$	−4.72743e8	−	1.45495e9i	−0.270982	−	0.833997i
$438$		0			0
$439$	−4.54836e8			−0.256584			−0.128292	−	0.991736i	$-0.540949\pi$
$439$	−4.54836e8			−0.256584			−0.128292	+	0.991736i	$0.540949\pi$
$440$	5.58643e8	+	2.16216e9i	0.312644	+	1.21005i
$441$		0			0
$442$	1.29866e9	−	9.43534e8i	0.715350	−	0.519732i
$443$	−4.52486e8	−	1.39261e9i	−0.247282	−	0.761055i	−0.995253	−	0.0973235i	$-0.968972\pi$
$443$	−4.52486e8	−	1.39261e9i	−0.247282	−	0.761055i	0.747971	−	0.663731i	$-0.231028\pi$
$444$		0			0
$445$	2.49584e9	+	1.81333e9i	1.34263	+	0.975477i
$446$	−1.72866e8	−	1.25595e8i	−0.0922653	−	0.0670347i
$447$		0			0
$448$	−2.54895e8	−	7.84486e8i	−0.133933	−	0.412204i
$449$	1.12367e8	−	8.16392e7i	0.0585835	−	0.0425634i	−0.558108	−	0.829768i	$-0.688473\pi$
$449$	1.12367e8	−	8.16392e7i	0.0585835	−	0.0425634i	0.616692	+	0.787205i	$0.288473\pi$
$450$		0			0
$451$	1.05924e7	+	8.73576e6i	0.00543720	+	0.00448418i
$452$	−2.40954e9			−1.22730
$453$		0			0
$454$	3.82202e7	+	1.17630e8i	0.0191689	+	0.0589959i
$455$	1.95052e9	−	6.00308e9i	0.970756	−	2.98768i
$456$		0			0
$457$	−2.75905e9	−	2.00457e9i	−1.35224	−	0.982457i	−0.998897	−	0.0469623i	$-0.985046\pi$
$457$	−2.75905e9	−	2.00457e9i	−1.35224	−	0.982457i	−0.353340	−	0.935495i	$-0.614954\pi$
$458$	−2.22779e7	+	6.85643e7i	−0.0108354	+	0.0333479i
$459$		0			0
$460$	−1.62561e9	+	1.18108e9i	−0.778690	+	0.565752i
$461$	−6.26858e8			−0.298000			−0.149000	−	0.988837i	$-0.547605\pi$
$461$	−6.26858e8			−0.298000			−0.149000	+	0.988837i	$0.547605\pi$
$462$		0			0
$463$	3.25784e9			1.52545			0.762723	−	0.646725i	$-0.223862\pi$
$463$	3.25784e9			1.52545			0.762723	+	0.646725i	$0.223862\pi$
$464$	−2.32664e8	+	1.69040e8i	−0.108122	+	0.0785556i
$465$		0			0
$466$	−4.23513e8	+	1.30344e9i	−0.193872	+	0.596678i
$467$	−1.32387e9	−	9.61847e8i	−0.601500	−	0.437015i	0.244911	−	0.969546i	$-0.421241\pi$
$467$	−1.32387e9	−	9.61847e8i	−0.601500	−	0.437015i	−0.846411	+	0.532530i	$0.821241\pi$
$468$		0			0
$469$	1.68822e8	−	5.19580e8i	0.0755655	−	0.232567i
$470$	6.22629e8	+	1.91626e9i	0.276622	+	0.851356i
$471$		0			0
$472$	−4.53176e8			−0.198367
$473$	3.69007e9	−	2.34965e9i	1.60332	−	1.02091i
$474$		0			0
$475$	1.64120e9	−	1.19240e9i	0.702643	−	0.510500i
$476$	1.01763e9	+	3.13196e9i	0.432481	+	1.33104i
$477$		0			0
$478$	−1.32560e8	−	9.63104e7i	−0.0555156	−	0.0403344i
$479$	3.21089e8	+	2.33285e8i	0.133491	+	0.0969866i	0.652527	−	0.757766i	$-0.273709\pi$
$479$	3.21089e8	+	2.33285e8i	0.133491	+	0.0969866i	−0.519036	+	0.854752i	$0.673709\pi$
$480$		0			0
$481$	−4.06218e8	−	1.25021e9i	−0.166438	−	0.512243i
$482$	8.35595e8	−	6.07096e8i	0.339885	−	0.246941i
$483$		0			0
$484$	1.33270e9	+	1.24390e9i	0.534285	+	0.498687i
$485$	2.66170e9			1.05941
$486$		0			0
$487$	9.06682e8	+	2.79048e9i	0.355716	+	1.09478i	0.955593	+	0.294689i	$0.0952162\pi$
$487$	9.06682e8	+	2.79048e9i	0.355716	+	1.09478i	−0.599877	+	0.800092i	$0.704784\pi$
$488$	−6.55283e8	+	2.01675e9i	−0.255246	+	0.785568i
$489$		0			0
$490$	−2.33657e9	−	1.69762e9i	−0.897208	−	0.651860i
$491$	−5.03127e8	+	1.54847e9i	−0.191819	+	0.590360i	0.808180	+	0.588936i	$0.200453\pi$
$491$	−5.03127e8	+	1.54847e9i	−0.191819	+	0.590360i	−0.999999	+	0.00142338i	$0.999547\pi$
$492$		0			0
$493$	−1.30531e9	+	9.48365e8i	−0.490626	+	0.356460i
$494$	1.82592e9			0.681456
$495$		0			0
$496$	2.46565e8			0.0907289
$497$	2.87860e9	−	2.09142e9i	1.05180	−	0.764179i
$498$		0			0
$499$	−1.42321e9	+	4.38018e9i	−0.512762	+	1.57812i	0.274554	+	0.961572i	$0.411470\pi$
$499$	−1.42321e9	+	4.38018e9i	−0.512762	+	1.57812i	−0.787317	+	0.616549i	$0.788530\pi$
$500$	1.44552e8	+	1.05023e8i	0.0517164	+	0.0375742i
$501$		0			0
$502$	−5.29841e8	+	1.63068e9i	−0.186931	+	0.575316i
$503$	3.20890e8	+	9.87598e8i	0.112426	+	0.346013i	0.991402	−	0.130855i	$-0.0417721\pi$
$503$	3.20890e8	+	9.87598e8i	0.112426	+	0.346013i	−0.878975	+	0.476868i	$0.841772\pi$
$504$		0			0
$505$	5.72047e9			1.97657
$506$	5.24616e8	−	1.33092e9i	0.180017	−	0.456693i
$507$		0			0
$508$	7.37347e8	−	5.35714e8i	0.249545	−	0.181305i
$509$	−8.77383e8	−	2.70031e9i	−0.294901	−	0.907613i	−0.983255	−	0.182238i	$-0.941666\pi$
$509$	−8.77383e8	−	2.70031e9i	−0.294901	−	0.907613i	0.688353	−	0.725376i	$-0.258334\pi$
$510$		0			0
$511$	3.33167e8	+	2.42060e8i	0.110456	+	0.0802508i
$512$	1.25885e9	+	9.14611e8i	0.414506	+	0.301156i
$513$		0			0
$514$	−5.23449e8	−	1.61101e9i	−0.170021	−	0.523272i
$515$	−5.90294e9	+	4.28874e9i	−1.90433	+	1.38358i
$516$		0			0
$517$	3.00518e9	+	2.47844e9i	0.956430	+	0.788789i
$518$	−9.93120e8			−0.313941
$519$		0			0
$520$	−1.75513e9	−	5.40174e9i	−0.547392	−	1.68470i
$521$	−4.95427e8	+	1.52477e9i	−0.153479	+	0.472358i	−0.998004	−	0.0631577i	$-0.979883\pi$
$521$	−4.95427e8	+	1.52477e9i	−0.153479	+	0.472358i	0.844525	+	0.535516i	$0.179883\pi$
$522$		0			0
$523$	−4.17666e9	−	3.03452e9i	−1.27665	−	0.927544i	−0.277208	−	0.960810i	$-0.589409\pi$
$523$	−4.17666e9	−	3.03452e9i	−1.27665	−	0.927544i	−0.999447	+	0.0332664i	$0.989409\pi$
$524$	9.81025e8	−	3.01929e9i	0.297866	−	0.916737i
$525$		0			0
$526$	2.36406e9	−	1.71759e9i	0.708286	−	0.514600i
$527$	1.38330e9			0.411699
$528$		0			0
$529$	−3.56359e8			−0.104663
$530$	−3.10616e9	+	2.25676e9i	−0.906271	+	0.658445i
$531$		0			0
$532$	−1.15754e9	+	3.56253e9i	−0.333307	+	1.02581i
$533$	−2.82510e7	−	2.05256e7i	−0.00808144	−	0.00587151i
$534$		0			0
$535$	1.88901e9	−	5.81379e9i	0.533331	−	1.64142i
$536$	−1.51911e8	−	4.67533e8i	−0.0426100	−	0.131140i
$537$		0			0
$538$	2.89621e9			0.801849
$539$	−5.57319e9	−	3.42155e8i	−1.53300	−	0.0941157i
$540$		0			0
$541$	−4.89760e8	+	3.55831e8i	−0.132982	+	0.0966170i	−0.652288	−	0.757972i	$-0.726191\pi$
$541$	−4.89760e8	+	3.55831e8i	−0.132982	+	0.0966170i	0.519306	+	0.854589i	$0.326191\pi$
$542$	−8.82410e8	−	2.71578e9i	−0.238053	−	0.732651i
$543$		0			0
$544$	3.78238e9	+	2.74806e9i	1.00732	+	0.731863i
$545$	−2.17410e9	−	1.57958e9i	−0.575296	−	0.417977i
$546$		0			0
$547$	−4.01503e8	−	1.23570e9i	−0.104890	−	0.322817i	0.884815	−	0.465943i	$-0.154285\pi$
$547$	−4.01503e8	−	1.23570e9i	−0.104890	−	0.322817i	−0.989705	+	0.143125i	$0.954285\pi$
$548$	−3.87924e9	+	2.81843e9i	−1.00697	+	0.731604i
$549$		0			0
$550$	1.89347e9	+	1.16246e8i	0.485275	+	0.0297925i
$551$	−1.83527e9			−0.467379
$552$		0			0
$553$	−3.16943e9	−	9.75449e9i	−0.796971	−	2.45283i
$554$	6.69589e8	−	2.06078e9i	0.167311	−	0.514930i
$555$		0			0
$556$	−7.43825e7	−	5.40420e7i	−0.0183531	−	0.0133343i
$557$	−2.06483e9	+	6.35491e9i	−0.506281	+	1.55817i	0.292324	+	0.956319i	$0.405571\pi$
$557$	−2.06483e9	+	6.35491e9i	−0.506281	+	1.55817i	−0.798606	+	0.601855i	$0.794429\pi$
$558$		0			0
$559$	−9.00134e9	+	6.53986e9i	−2.17955	+	1.58353i
$560$	2.44095e9			0.587356
$561$		0			0
$562$	2.04864e8			0.0486843
$563$	−2.80823e9	+	2.04030e9i	−0.663214	+	0.481853i	−0.867747	−	0.497007i	$-0.834432\pi$
$563$	−2.80823e9	+	2.04030e9i	−0.663214	+	0.481853i	0.204533	+	0.978860i	$0.434432\pi$
$564$		0			0
$565$	−3.09637e9	+	9.52964e9i	−0.722242	+	2.22283i
$566$	8.94370e8	+	6.49798e8i	0.207329	+	0.150633i
$567$		0			0
$568$	9.89387e8	−	3.04502e9i	0.226541	−	0.697222i
$569$	7.39161e7	+	2.27490e8i	0.0168208	+	0.0517690i	0.959115	−	0.283018i	$-0.0913356\pi$
$569$	7.39161e7	+	2.27490e8i	0.0168208	+	0.0517690i	−0.942294	+	0.334787i	$0.891336\pi$
$570$		0			0
$571$	3.64733e8			0.0819876			0.0409938	−	0.999159i	$-0.486948\pi$
$571$	3.64733e8			0.0819876			0.0409938	+	0.999159i	$0.486948\pi$
$572$	−3.57702e9	−	2.95005e9i	−0.799163	−	0.659087i
$573$		0			0
$574$	−2.13432e7	+	1.55067e7i	−0.00471050	+	0.00342238i
$575$	1.24918e9	+	3.84458e9i	0.274024	+	0.843358i
$576$		0			0
$577$	−6.66974e9	−	4.84585e9i	−1.44542	−	1.05016i	−0.986875	−	0.161485i	$-0.948372\pi$
$577$	−6.66974e9	−	4.84585e9i	−1.44542	−	1.05016i	−0.458543	−	0.888672i	$-0.651628\pi$
$578$	8.69079e8	+	6.31423e8i	0.187203	+	0.136011i
$579$		0			0
$580$	7.44901e8	+	2.29257e9i	0.158526	+	0.487893i
$581$	−4.23950e9	+	3.08018e9i	−0.896805	+	0.651567i
$582$		0			0
$583$	−2.72203e9	+	6.90564e9i	−0.568923	+	1.44332i
$584$	3.70565e8			0.0769873
$585$		0			0
$586$	−1.13626e8	−	3.49704e8i	−0.0233257	−	0.0717892i
$587$	−1.04081e9	+	3.20328e9i	−0.212392	+	0.653674i	0.786937	+	0.617033i	$0.211666\pi$
$587$	−1.04081e9	+	3.20328e9i	−0.212392	+	0.653674i	−0.999329	+	0.0366406i	$0.988334\pi$
$588$		0			0
$589$	1.27297e9	+	9.24866e8i	0.256693	+	0.186499i
$590$	−2.45898e8	+	7.56798e8i	−0.0492917	+	0.151704i
$591$		0			0
$592$	4.11270e8	−	2.98805e8i	0.0814706	−	0.0591919i
$593$	7.89612e9			1.55497			0.777486	−	0.628901i	$-0.216495\pi$
$593$	7.89612e9			1.55497			0.777486	+	0.628901i	$0.216495\pi$
$594$		0			0
$595$	1.36945e10			2.66524
$596$	6.23473e8	−	4.52980e8i	0.120630	−	0.0876429i
$597$		0			0
$598$	−1.12435e9	+	3.46040e9i	−0.215005	+	0.661717i
$599$	8.27828e8	+	6.01453e8i	0.157379	+	0.114342i	0.663688	−	0.748010i	$-0.268990\pi$
$599$	8.27828e8	+	6.01453e8i	0.157379	+	0.114342i	−0.506309	+	0.862352i	$0.668990\pi$
$600$		0			0
$601$	2.30620e8	−	7.09777e8i	0.0433348	−	0.133371i	−0.927048	−	0.374942i	$-0.877663\pi$
$601$	2.30620e8	−	7.09777e8i	0.0433348	−	0.133371i	0.970383	+	0.241571i	$0.0776627\pi$
$602$	2.59751e9	+	7.99430e9i	0.485254	+	1.49346i
$603$		0			0
$604$	3.61467e8			0.0667483
$605$	6.63217e9	−	3.67230e9i	1.21762	−	0.674208i
$606$		0			0
$607$	−6.39760e9	+	4.64813e9i	−1.16107	+	0.843563i	−0.989912	−	0.141681i	$-0.954749\pi$
$607$	−6.39760e9	+	4.64813e9i	−1.16107	+	0.843563i	−0.171153	+	0.985244i	$0.554749\pi$
$608$	1.64336e9	+	5.05774e9i	0.296531	+	0.912629i
$609$		0			0
$610$	3.01239e9	+	2.18863e9i	0.537349	+	0.390407i
$611$	−8.01514e9	−	5.82334e9i	−1.42157	−	1.03283i
$612$		0			0
$613$	−1.83635e9	−	5.65169e9i	−0.321990	−	0.990984i	−0.972781	−	0.231727i	$-0.925562\pi$
$613$	−1.83635e9	−	5.65169e9i	−0.321990	−	0.990984i	0.650790	−	0.759257i	$-0.274438\pi$
$614$	2.83379e9	−	2.05887e9i	0.494058	−	0.358954i
$615$		0			0
$616$	−6.99752e9	+	4.45565e9i	−1.20618	+	0.768031i
$617$	−4.03293e9			−0.691231			−0.345615	−	0.938376i	$-0.612330\pi$
$617$	−4.03293e9			−0.691231			−0.345615	+	0.938376i	$0.612330\pi$
$618$		0			0
$619$	1.06202e8	+	3.26855e8i	0.0179976	+	0.0553908i	0.959652	−	0.281191i	$-0.0907293\pi$
$619$	1.06202e8	+	3.26855e8i	0.0179976	+	0.0553908i	−0.941654	+	0.336581i	$0.890729\pi$
$620$	6.38644e8	−	1.96555e9i	0.107619	−	0.331217i
$621$		0			0
$622$	−4.70839e9	−	3.42085e9i	−0.784524	−	0.569990i
$623$	−3.54137e9	+	1.08992e10i	−0.586764	+	1.80587i
$624$		0			0
$625$	5.22866e9	−	3.79884e9i	0.856663	−	0.622402i
$626$	3.84227e6			0.000626005
$627$		0			0
$628$	−5.06947e9			−0.816777
$629$	2.30734e9	−	1.67638e9i	0.369688	−	0.268594i
$630$		0			0
$631$	1.50867e9	−	4.64320e9i	0.239051	−	0.735724i	−0.757507	−	0.652827i	$-0.773583\pi$
$631$	1.50867e9	−	4.64320e9i	0.239051	−	0.735724i	0.996558	−	0.0828967i	$-0.0264172\pi$
$632$	−7.46648e9	−	5.42472e9i	−1.17654	−	0.854806i
$633$		0			0
$634$	1.81818e9	−	5.59578e9i	0.283351	−	0.872064i
$635$	−1.17120e9	−	3.60460e9i	−0.181520	−	0.558662i
$636$		0			0
$637$	1.42013e10			2.17691
$638$	−1.32402e9	−	1.09195e9i	−0.201846	−	0.166467i
$639$		0			0
$640$	6.67762e9	−	4.85158e9i	1.00691	−	0.731565i
$641$	−8.50280e8	−	2.61689e9i	−0.127514	−	0.392449i	0.866836	−	0.498593i	$-0.166150\pi$
$641$	−8.50280e8	−	2.61689e9i	−0.127514	−	0.392449i	−0.994351	+	0.106144i	$0.966150\pi$
$642$		0			0
$643$	−4.04045e9	−	2.93556e9i	−0.599364	−	0.435464i	0.246289	−	0.969196i	$-0.420789\pi$
$643$	−4.04045e9	−	2.93556e9i	−0.599364	−	0.435464i	−0.845653	+	0.533733i	$0.820789\pi$
$644$	−6.03877e9	−	4.38742e9i	−0.890938	−	0.647305i
$645$		0			0
$646$	1.22417e9	+	3.76761e9i	0.178660	+	0.549860i
$647$	2.52629e9	−	1.83545e9i	0.366705	−	0.266427i	−0.389138	−	0.921179i	$-0.627227\pi$
$647$	2.52629e9	−	1.83545e9i	0.366705	−	0.266427i	0.755843	+	0.654752i	$0.227227\pi$
$648$		0			0
$649$	3.84846e8	+	1.48950e9i	0.0552624	+	0.213887i
$650$	−4.82483e9			−0.689105
$651$		0			0
$652$	−1.85709e9	−	5.71553e9i	−0.262401	−	0.807589i
$653$	1.04884e9	−	3.22801e9i	0.147406	−	0.453669i	−0.849907	−	0.526933i	$-0.823342\pi$
$653$	1.04884e9	−	3.22801e9i	0.147406	−	0.453669i	0.997313	+	0.0732646i	$0.0233418\pi$
$654$		0			0
$655$	−1.06805e10	−	7.75984e9i	−1.48507	−	1.07897i
$656$	4.17303e6	−	1.28433e7i	0.000577149	−	0.00177628i
$657$		0			0
$658$	−6.05530e9	+	4.39944e9i	−0.828601	+	0.602014i
$659$	2.75870e9			0.375496			0.187748	−	0.982217i	$-0.439881\pi$
$659$	2.75870e9			0.375496			0.187748	+	0.982217i	$0.439881\pi$
$660$		0			0
$661$	9.20263e9			1.23939			0.619693	−	0.784844i	$-0.287257\pi$
$661$	9.20263e9			1.23939			0.619693	+	0.784844i	$0.287257\pi$
$662$	5.87486e8	−	4.26834e8i	0.0787036	−	0.0571815i
$663$		0			0
$664$	−1.45713e9	+	4.48460e9i	−0.193157	+	0.594477i
$665$	1.26022e10	+	9.15602e9i	1.66177	+	1.20734i
$666$		0			0
$667$	1.13011e9	−	3.47812e9i	0.147462	−	0.453841i
$668$	−8.06147e8	−	2.48106e9i	−0.104640	−	0.322048i
$669$		0			0
$670$	−8.63203e8			−0.110879
$671$	7.18515e9	+	4.41118e8i	0.918136	+	0.0563671i
$672$		0			0
$673$	4.68786e9	−	3.40593e9i	0.592818	−	0.430708i	−0.250504	−	0.968116i	$-0.580596\pi$
$673$	4.68786e9	−	3.40593e9i	0.592818	−	0.430708i	0.843323	+	0.537408i	$0.180596\pi$
$674$	−2.53057e9	−	7.78830e9i	−0.318353	−	0.979790i
$675$		0			0
$676$	4.79130e9	+	3.48109e9i	0.596541	+	0.433412i
$677$	8.43742e9	+	6.13015e9i	1.04508	+	0.759295i	0.971271	−	0.237977i	$-0.0764844\pi$
$677$	8.43742e9	+	6.13015e9i	1.04508	+	0.759295i	0.0738092	+	0.997272i	$0.476484\pi$
$678$		0			0
$679$	3.05543e9	+	9.40365e9i	0.374566	+	1.15280i
$680$	9.96927e9	−	7.24310e9i	1.21586	−	0.883371i
$681$		0			0
$682$	3.68082e8	+	1.42462e9i	0.0444323	+	0.171970i
$683$	3.69042e9			0.443203			0.221602	−	0.975137i	$-0.428872\pi$
$683$	3.69042e9			0.443203			0.221602	+	0.975137i	$0.428872\pi$
$684$		0			0
$685$	6.16180e9	+	1.89641e10i	0.732471	+	2.25432i
$686$	1.15678e9	−	3.56021e9i	0.136810	−	0.421057i
$687$		0			0
$688$	−3.48096e9	−	2.52907e9i	−0.407511	−	0.296074i
$689$	5.83384e9	−	1.79547e10i	0.679497	−	2.09128i
$690$		0			0
$691$	1.39613e9	−	1.01435e9i	0.160973	−	0.116954i	−0.504383	−	0.863480i	$-0.668280\pi$
$691$	1.39613e9	−	1.01435e9i	0.160973	−	0.116954i	0.665356	+	0.746527i	$0.268280\pi$
$692$	−7.21628e9			−0.827832
$693$		0			0
$694$	−2.66530e9			−0.302683
$695$	−3.09319e8	+	2.24733e8i	−0.0349510	+	0.0253934i
$696$		0			0
$697$	2.34119e7	−	7.20544e7i	0.00261892	−	0.00806020i
$698$	4.07983e9	+	2.96417e9i	0.454096	+	0.329920i
$699$		0			0
$700$	3.05868e9	−	9.41366e9i	0.337048	−	1.03733i
$701$	−1.72135e9	−	5.29777e9i	−0.188737	−	0.580872i	0.811256	−	0.584691i	$-0.198784\pi$
$701$	−1.72135e9	−	5.29777e9i	−0.188737	−	0.580872i	−0.999993	+	0.00381937i	$0.998784\pi$
$702$		0			0
$703$	3.24413e9			0.352171
$704$	−9.24003e8	+	2.34414e9i	−0.0998089	+	0.253209i
$705$		0			0
$706$	2.12895e9	−	1.54677e9i	0.227693	−	0.165428i
$707$	6.56667e9	+	2.02101e10i	0.698839	+	2.15081i
$708$		0			0
$709$	4.31230e9	+	3.13307e9i	0.454409	+	0.330147i	0.791334	−	0.611384i	$-0.209387\pi$
$709$	4.31230e9	+	3.13307e9i	0.454409	+	0.330147i	−0.336925	+	0.941531i	$0.609387\pi$
$710$	−4.54829e9	−	3.30453e9i	−0.476918	−	0.346501i
$711$		0			0
$712$	3.18663e9	+	9.80744e9i	0.330866	+	1.01830i
$713$	−2.53663e9	+	1.84297e9i	−0.262085	+	0.190416i
$714$		0			0
$715$	−1.62640e10	+	1.03560e10i	−1.66401	+	1.05955i
$716$	2.14359e9			0.218245
$717$		0			0
$718$	2.31475e9	+	7.12408e9i	0.233383	+	0.718279i
$719$	−1.45199e9	+	4.46876e9i	−0.145684	+	0.448370i	−0.997098	−	0.0761243i	$-0.975745\pi$
$719$	−1.45199e9	+	4.46876e9i	−0.145684	+	0.448370i	0.851414	+	0.524494i	$0.175745\pi$
$720$		0			0
$721$	−2.19280e10	−	1.59316e10i	−2.17884	−	1.58302i
$722$	2.28803e8	−	7.04183e8i	0.0226246	−	0.0696315i
$723$		0			0
$724$	−4.22745e9	+	3.07142e9i	−0.413993	+	0.300784i
$725$	4.84953e9			0.472625
$726$		0			0
$727$	7.77660e9			0.750619			0.375309	−	0.926900i	$-0.377537\pi$
$727$	7.77660e9			0.750619			0.375309	+	0.926900i	$0.377537\pi$
$728$	1.70693e10	−	1.24016e10i	1.63967	−	1.19129i
$729$		0			0
$730$	2.01073e8	−	6.18838e8i	0.0191304	−	0.0588772i
$731$	−1.95292e10	−	1.41888e10i	−1.84916	−	1.34349i
$732$		0			0
$733$	7.03510e8	−	2.16518e9i	0.0659791	−	0.203063i	−0.912632	−	0.408782i	$-0.865953\pi$
$733$	7.03510e8	−	2.16518e9i	0.0659791	−	0.203063i	0.978611	+	0.205720i	$0.0659535\pi$
$734$	−2.14037e9	−	6.58739e9i	−0.199781	−	0.614861i
$735$		0			0
$736$	−1.05971e10			−0.979752
$737$	−1.40768e9	+	8.96339e8i	−0.129529	+	0.0824776i
$738$		0			0
$739$	1.25846e10	−	9.14322e9i	1.14705	−	0.833381i	0.158964	−	0.987284i	$-0.449185\pi$
$739$	1.25846e10	−	9.14322e9i	1.14705	−	0.833381i	0.988086	+	0.153904i	$0.0491845\pi$
$740$	−1.31673e9	−	4.05248e9i	−0.119450	−	0.367629i
$741$		0			0
$742$	−1.15386e10	−	8.38331e9i	−1.03691	−	0.753359i
$743$	3.01649e9	+	2.19161e9i	0.269800	+	0.196021i	0.714456	−	0.699680i	$-0.246674\pi$
$743$	3.01649e9	+	2.19161e9i	0.269800	+	0.196021i	−0.444656	+	0.895701i	$0.646674\pi$
$744$		0			0
$745$	−9.90327e8	−	3.04791e9i	−0.0877468	−	0.270057i
$746$	−5.40873e9	+	3.92967e9i	−0.476990	+	0.346554i
$747$		0			0
$748$	3.68896e9	−	9.35866e9i	0.322291	−	0.817633i
$749$	2.27083e10			1.97468
$750$		0			0
$751$	−1.42660e9	−	4.39061e9i	−0.122903	−	0.378255i	0.870611	−	0.491973i	$-0.163724\pi$
$751$	−1.42660e9	−	4.39061e9i	−0.122903	−	0.378255i	−0.993513	+	0.113718i	$0.963724\pi$
$752$	1.18394e9	−	3.64378e9i	0.101523	−	0.312457i
$753$		0			0
$754$	3.53130e9	+	2.56564e9i	0.300009	+	0.217970i
$755$	4.64502e8	−	1.42959e9i	0.0392802	−	0.120892i
$756$		0			0
$757$	−9.11863e9	+	6.62507e9i	−0.764001	+	0.555079i	−0.900135	−	0.435611i	$-0.856532\pi$
$757$	−9.11863e9	+	6.62507e9i	−0.764001	+	0.555079i	0.136134	+	0.990690i	$0.456532\pi$
$758$	3.15550e9			0.263164
$759$		0			0
$760$	1.40168e10			1.15825
$761$	3.30417e9	−	2.40062e9i	0.271779	−	0.197459i	−0.443545	−	0.896252i	$-0.646279\pi$
$761$	3.30417e9	−	2.40062e9i	0.271779	−	0.197459i	0.715324	+	0.698793i	$0.246279\pi$
$762$		0			0
$763$	3.08486e9	−	9.49421e9i	0.251420	−	0.773790i
$764$	−7.29518e9	−	5.30026e9i	−0.591846	−	0.430002i
$765$		0			0
$766$	1.16119e9	−	3.57377e9i	0.0933474	−	0.287294i
$767$	−1.20910e9	−	3.72123e9i	−0.0967561	−	0.297785i
$768$		0			0
$769$	7.37952e9			0.585175			0.292588	−	0.956239i	$-0.405484\pi$
$769$	7.37952e9			0.585175			0.292588	+	0.956239i	$0.405484\pi$
$770$	3.64395e9	+	1.41035e10i	0.287644	+	1.11329i
$771$		0			0
$772$	4.53759e9	−	3.29675e9i	0.354948	−	0.257885i
$773$	6.69132e9	+	2.05938e10i	0.521055	+	1.60364i	0.771987	+	0.635638i	$0.219263\pi$
$773$	6.69132e9	+	2.05938e10i	0.521055	+	1.60364i	−0.250932	+	0.968005i	$0.580737\pi$
$774$		0			0
$775$	−3.36371e9	−	2.44388e9i	−0.259574	−	0.188592i
$776$	7.19794e9	+	5.22961e9i	0.552958	+	0.401747i
$777$		0			0
$778$	2.68175e9	+	8.25359e9i	0.204169	+	0.628368i
$779$	6.97196e7	−	5.06543e7i	0.00528413	−	0.00383915i
$780$		0			0
$781$	−1.08486e10	−	6.66026e8i	−0.814881	−	0.0500280i
$782$	−7.89402e9			−0.590302
$783$		0			0
$784$	1.69708e9	+	5.22308e9i	0.125776	+	0.387098i
$785$	−6.51449e9	+	2.00495e10i	−0.480659	+	1.47932i
$786$		0			0
$787$	1.00260e10	+	7.28432e9i	0.733190	+	0.532694i	0.890571	−	0.454844i	$-0.150305\pi$
$787$	1.00260e10	+	7.28432e9i	0.733190	+	0.532694i	−0.157381	+	0.987538i	$0.550305\pi$
$788$	1.07734e9	−	3.31570e9i	0.0784350	−	0.241398i
$789$		0			0
$790$	−1.31106e10	+	9.52541e9i	−0.946080	+	0.687368i
$791$	−3.72221e10			−2.67413
$792$		0			0
$793$	−1.83088e10			−1.30378
$794$	5.23395e9	−	3.80269e9i	0.371072	−	0.269599i
$795$		0			0
$796$	−4.80610e9	+	1.47916e10i	−0.337751	+	1.03949i
$797$	−1.20453e9	−	8.75140e8i	−0.0842776	−	0.0612313i	0.544849	−	0.838534i	$-0.316587\pi$
$797$	−1.20453e9	−	8.75140e8i	−0.0842776	−	0.0612313i	−0.629126	+	0.777303i	$0.716587\pi$
$798$		0			0
$799$	6.64223e9	−	2.04427e10i	0.460681	−	1.41783i
$800$	−4.34243e9	−	1.33646e10i	−0.299859	−	0.922872i
$801$		0			0
$802$	4.31441e9			0.295333
$803$	−3.14691e8	−	1.21797e9i	−0.0214476	−	0.0830105i
$804$		0			0
$805$	−2.51122e10	+	1.82451e10i	−1.69667	+	1.23271i
$806$	−1.15643e9	−	3.55913e9i	−0.0777942	−	0.239426i
$807$		0			0
$808$	1.54697e10	+	1.12394e10i	1.03167	+	0.749552i
$809$	1.35445e10	+	9.84068e9i	0.899382	+	0.653439i	0.938307	−	0.345803i	$-0.112393\pi$
$809$	1.35445e10	+	9.84068e9i	0.899382	+	0.653439i	−0.0389253	+	0.999242i	$0.512393\pi$
$810$		0			0
$811$	1.08889e9	+	3.35124e9i	0.0716818	+	0.220614i	0.980479	−	0.196624i	$-0.0629980\pi$
$811$	1.08889e9	+	3.35124e9i	0.0716818	+	0.220614i	−0.908797	+	0.417238i	$0.862998\pi$
$812$	−7.24444e9	+	5.26339e9i	−0.474852	+	0.345001i
$813$		0			0
$814$	2.34041e9	+	1.93019e9i	0.152092	+	0.125434i
$815$	−2.49912e10			−1.61709
$816$		0			0
$817$	−8.48502e9	−	2.61142e10i	−0.544347	−	1.67533i
$818$	1.80168e9	−	5.54500e9i	0.115091	−	0.354213i
$819$		0			0
$820$	−9.15738e7	−	6.65323e7i	−0.00579993	−	0.00421390i
$821$	−8.56347e8	+	2.63557e9i	−0.0540068	+	0.166216i	−0.974422	−	0.224727i	$-0.927851\pi$
$821$	−8.56347e8	+	2.63557e9i	−0.0540068	+	0.166216i	0.920415	+	0.390943i	$0.127851\pi$
$822$		0			0
$823$	1.44628e10	−	1.05079e10i	0.904386	−	0.657075i	−0.0352026	−	0.999380i	$-0.511208\pi$
$823$	1.44628e10	−	1.05079e10i	0.904386	−	0.657075i	0.939589	+	0.342305i	$0.111208\pi$
$824$	−2.43894e10			−1.51865
$825$		0			0
$826$	−2.95600e9			−0.182505
$827$	−1.52615e10	+	1.10881e10i	−0.938270	+	0.681693i	−0.948004	−	0.318260i	$-0.896902\pi$
$827$	−1.52615e10	+	1.10881e10i	−0.938270	+	0.681693i	0.00973361	+	0.999953i	$0.496902\pi$
$828$		0			0
$829$	−7.31993e9	+	2.25284e10i	−0.446238	+	1.37338i	0.434883	+	0.900487i	$0.356790\pi$
$829$	−7.31993e9	+	2.25284e10i	−0.446238	+	1.37338i	−0.881121	+	0.472891i	$0.843210\pi$
$830$	6.69856e9	+	4.86679e9i	0.406638	+	0.295440i
$831$		0			0
$832$	1.98032e9	−	6.09479e9i	0.119207	−	0.366882i
$833$	9.52113e9	+	2.93030e10i	0.570730	+	1.75653i
$834$		0			0
$835$	−1.08484e10			−0.644859
$836$	9.65186e9	−	6.14580e9i	0.571332	−	0.363795i
$837$		0			0
$838$	7.11922e9	−	5.17242e9i	0.417906	−	0.303626i
$839$	−7.10072e9	−	2.18538e10i	−0.415084	−	1.27750i	−0.912176	−	0.409799i	$-0.865599\pi$
$839$	−7.10072e9	−	2.18538e10i	−0.415084	−	1.27750i	0.497092	−	0.867698i	$-0.334401\pi$
$840$		0			0
$841$	1.04061e10	+	7.56045e9i	0.603254	+	0.438290i
$842$	−1.12945e10	−	8.20591e9i	−0.652039	−	0.473734i
$843$		0			0
$844$	−2.26195e9	−	6.96156e9i	−0.129504	−	0.398573i
$845$	1.99246e10	−	1.44761e10i	1.13603	−	0.825377i
$846$		0			0
$847$	2.05873e10	+	1.92156e10i	1.16414	+	1.08658i
$848$	7.30070e9			0.411130
$849$		0			0
$850$	−3.23476e9	−	9.95557e9i	−0.180666	−	0.556032i
$851$	−1.99765e9	+	6.14812e9i	−0.111113	+	0.341971i
$852$		0			0
$853$	3.53423e9	+	2.56777e9i	0.194972	+	0.141656i	0.680988	−	0.732294i	$-0.261550\pi$
$853$	3.53423e9	+	2.56777e9i	0.194972	+	0.141656i	−0.486016	+	0.873950i	$0.661550\pi$
$854$	−4.27432e9	+	1.31550e10i	−0.234836	+	0.722750i
$855$		0			0
$856$	1.65311e10	−	1.20105e10i	0.900831	−	0.654492i
$857$	8.40312e7			0.00456045			0.00228023	−	0.999997i	$-0.499274\pi$
$857$	8.40312e7			0.00456045			0.00228023	+	0.999997i	$0.499274\pi$
$858$		0			0
$859$	7.04114e9			0.379024			0.189512	−	0.981878i	$-0.439309\pi$
$859$	7.04114e9			0.379024			0.189512	+	0.981878i	$0.439309\pi$
$860$	−2.91773e10	+	2.11985e10i	−1.56423	+	1.13648i
$861$		0			0
$862$	1.07550e9	−	3.31004e9i	0.0571918	−	0.176018i
$863$	−1.55502e10	−	1.12979e10i	−0.823565	−	0.598355i	0.0941666	−	0.995556i	$-0.469981\pi$
$863$	−1.55502e10	−	1.12979e10i	−0.823565	−	0.598355i	−0.917731	+	0.397202i	$0.869981\pi$
$864$		0			0
$865$	−9.27325e9	+	2.85401e10i	−0.487165	+	1.49934i
$866$	2.72528e9	+	8.38754e9i	0.142593	+	0.438856i
$867$		0			0
$868$	7.67729e9			0.398464
$869$	−1.14893e10	+	2.91476e10i	−0.593914	+	1.50672i
$870$		0			0
$871$	3.43382e9	−	2.49481e9i	0.176081	−	0.127931i
$872$	−2.77585e9	−	8.54317e9i	−0.141771	−	0.436326i
$873$		0			0
$874$	−7.26438e9	−	5.27788e9i	−0.368052	−	0.267405i
$875$	2.23301e9	+	1.62238e9i	0.112684	+	0.0818697i
$876$		0			0
$877$	−5.70601e9	−	1.75613e10i	−0.285650	−	0.879139i	−0.986203	−	0.165539i	$-0.947063\pi$
$877$	−5.70601e9	−	1.75613e10i	−0.285650	−	0.879139i	0.700553	−	0.713600i	$-0.252937\pi$
$878$	−2.15978e9	+	1.56918e9i	−0.107691	+	0.0782421i
$879$		0			0
$880$	−5.75241e9	−	4.74413e9i	−0.284551	−	0.234675i
$881$	7.05695e9			0.347697			0.173849	−	0.984772i	$-0.444380\pi$
$881$	7.05695e9			0.347697			0.173849	+	0.984772i	$0.444380\pi$
$882$		0			0
$883$	−2.46760e9	−	7.59448e9i	−0.120618	−	0.371224i	0.872459	−	0.488687i	$-0.162524\pi$
$883$	−2.46760e9	−	7.59448e9i	−0.120618	−	0.371224i	−0.993077	+	0.117463i	$0.962524\pi$
$884$	−7.90615e9	+	2.43326e10i	−0.384930	+	1.18469i
$885$		0			0
$886$	−6.95309e9	−	5.05172e9i	−0.335861	−	0.244018i
$887$	3.23489e9	−	9.95597e9i	0.155642	−	0.479017i	−0.842583	−	0.538566i	$-0.818966\pi$
$887$	3.23489e9	−	9.95597e9i	0.155642	−	0.479017i	0.998225	+	0.0595489i	$0.0189662\pi$
$888$		0			0
$889$	1.13904e10	−	8.27561e9i	0.543730	−	0.395043i
$890$	1.81074e10			0.860976
$891$		0			0
$892$	3.40562e9			0.160664
$893$	1.97803e10	−	1.43712e10i	0.929505	−	0.675325i
$894$		0			0
$895$	2.75460e9	−	8.47780e9i	0.128434	−	0.395278i
$896$	2.48058e10	+	1.80225e10i	1.15206	+	0.837020i
$897$		0			0
$898$	2.51918e8	−	7.75325e8i	0.0116089	−	0.0357287i
$899$	1.16235e9	+	3.57735e9i	0.0533554	+	0.164211i
$900$		0			0
$901$	4.09591e10			1.86558
$902$	8.04360e7	+	4.93821e6i	0.00364945	+	0.000224051i
$903$		0			0
$904$	−2.70969e10	+	1.96870e10i	−1.21991	+	0.886320i
$905$	6.71489e9	+	2.06663e10i	0.301140	+	0.926814i
$906$		0			0
$907$	−2.91408e9	−	2.11721e9i	−0.129681	−	0.0942188i	0.521054	−	0.853524i	$-0.325539\pi$
$907$	−2.91408e9	−	2.11721e9i	−0.129681	−	0.0942188i	−0.650735	+	0.759305i	$0.725539\pi$
$908$	−1.59482e9	−	1.15870e9i	−0.0706987	−	0.0513656i
$909$		0			0
$910$	−1.14485e10	−	3.52348e10i	−0.503620	−	1.54998i
$911$	−4.70022e9	+	3.41491e9i	−0.205970	+	0.149646i	−0.685988	−	0.727613i	$-0.740630\pi$
$911$	−4.70022e9	+	3.41491e9i	−0.205970	+	0.149646i	0.480019	+	0.877258i	$0.340630\pi$
$912$		0			0
$913$	1.59774e10	+	9.80900e8i	0.694797	+	0.0426557i
$914$	−2.00170e10			−0.867137
$915$		0			0
$916$	−3.55073e8	−	1.09280e9i	−0.0152645	−	0.0469794i
$917$	1.51547e10	−	4.66414e10i	0.649015	−	1.99746i
$918$		0			0
$919$	1.17516e10	+	8.53802e9i	0.499450	+	0.362871i	0.808807	−	0.588075i	$-0.200114\pi$
$919$	1.17516e10	+	8.53802e9i	0.499450	+	0.362871i	−0.309357	+	0.950946i	$0.600114\pi$
$920$	−8.63116e9	+	2.65640e10i	−0.365436	+	1.12470i
$921$		0			0
$922$	−2.97663e9	+	2.16265e9i	−0.125074	+	0.0908715i
$923$	2.76437e10			1.15715
$924$		0			0
$925$	−8.57231e9			−0.356124
$926$	1.54698e10	−	1.12395e10i	0.640247	−	0.465166i
$927$		0			0
$928$	−3.92851e9	+	1.20907e10i	−0.161365	+	0.496631i
$929$	1.59867e10	+	1.16150e10i	0.654189	+	0.475296i	0.864696	−	0.502296i	$-0.167511\pi$
$929$	1.59867e10	+	1.16150e10i	0.654189	+	0.475296i	−0.210506	+	0.977592i	$0.567511\pi$
$930$		0			0
$931$	−1.08301e10	+	3.33315e10i	−0.439853	+	1.35373i
$932$	−6.75010e9	−	2.07747e10i	−0.273121	−	0.840579i
$933$		0			0
$934$	−9.60473e9			−0.385719
$935$	−3.22727e10	−	2.66160e10i	−1.29120	−	1.06488i
$936$		0			0
$937$	2.58620e9	−	1.87898e9i	0.102701	−	0.0746164i	−0.535250	−	0.844694i	$-0.679782\pi$
$937$	2.58620e9	−	1.87898e9i	0.102701	−	0.0746164i	0.637950	+	0.770077i	$0.279782\pi$
$938$	−9.90892e8	−	3.04965e9i	−0.0392027	−	0.120654i
$939$		0			0
$940$	−2.59806e10	−	1.88760e10i	−1.02024	−	0.741245i
$941$	−2.71452e10	−	1.97222e10i	−1.06201	−	0.771598i	−0.0875539	−	0.996160i	$-0.527905\pi$
$941$	−2.71452e10	−	1.97222e10i	−1.06201	−	0.771598i	−0.974460	+	0.224562i	$0.927905\pi$
$942$		0			0
$943$	5.30662e7	+	1.63321e8i	0.00206076	+	0.00634236i
$944$	1.22414e9	−	8.89387e8i	0.0473617	−	0.0344103i
$945$		0			0
$946$	9.41605e9	−	2.38879e10i	0.361618	−	0.917402i
$947$	−8.16760e9			−0.312514			−0.156257	−	0.987716i	$-0.549943\pi$
$947$	−8.16760e9			−0.312514			−0.156257	+	0.987716i	$0.549943\pi$
$948$		0			0
$949$	9.88689e8	+	3.04287e9i	0.0375516	+	0.115572i
$950$	3.67947e9	−	1.13242e10i	0.139236	−	0.428525i
$951$		0			0
$952$	3.70334e10	+	2.69064e10i	1.39112	+	1.01071i
$953$	1.50091e10	−	4.61934e10i	0.561734	−	1.72884i	−0.115729	−	0.993281i	$-0.536920\pi$
$953$	1.50091e10	−	4.61934e10i	0.561734	−	1.72884i	0.677462	−	0.735557i	$-0.263080\pi$
$954$		0			0
$955$	−3.03369e10	+	2.20411e10i	−1.12709	+	0.818881i
$956$	2.61155e9			0.0966709
$957$		0			0
$958$	2.32951e9			0.0856024
$959$	−5.99258e10	+	4.35387e10i	−2.19406	+	1.59408i
$960$		0			0
$961$	−7.50532e9	+	2.30990e10i	−0.272796	+	0.839578i
$962$	−6.24213e9	−	4.53517e9i	−0.226058	−	0.164241i
$963$		0			0
$964$	−5.08703e9	+	1.56563e10i	−0.182892	+	0.562884i
$965$	−7.20752e9	−	2.21825e10i	−0.258191	−	0.794629i
$966$		0			0
$967$	−3.98415e10			−1.41691			−0.708455	−	0.705756i	$-0.750608\pi$
$967$	−3.98415e10			−1.41691			−0.708455	+	0.705756i	$0.750608\pi$
$968$	2.51503e10	+	3.09979e9i	0.891210	+	0.109842i
$969$		0			0
$970$	1.26391e10	−	9.18281e9i	0.444645	−	0.323054i
$971$	−1.71148e10	−	5.26740e10i	−0.599936	−	1.84641i	−0.528437	−	0.848972i	$-0.677222\pi$
$971$	−1.71148e10	−	5.26740e10i	−0.599936	−	1.84641i	−0.0714987	−	0.997441i	$-0.522778\pi$
$972$		0			0
$973$	−1.14905e9	−	8.34831e8i	−0.0399892	−	0.0290538i
$974$	1.39325e10	+	1.01225e10i	0.483139	+	0.351021i
$975$		0			0
$976$	−2.18793e9	−	6.73377e9i	−0.0753286	−	0.231838i
$977$	1.64293e9	−	1.19366e9i	0.0563622	−	0.0409495i	−0.559247	−	0.829001i	$-0.688910\pi$
$977$	1.64293e9	−	1.19366e9i	0.0563622	−	0.0409495i	0.615610	+	0.788051i	$0.288910\pi$
$978$		0			0
$979$	2.95289e10	−	1.88025e10i	1.00579	−	0.640436i
$980$	4.60326e10			1.56234
$981$		0			0
$982$	2.95308e9	+	9.08866e9i	0.0995143	+	0.306274i
$983$	−5.80713e9	+	1.78725e10i	−0.194995	+	0.600134i	0.804981	+	0.593300i	$0.202175\pi$
$983$	−5.80713e9	+	1.78725e10i	−0.194995	+	0.600134i	−0.999977	+	0.00683402i	$0.997825\pi$
$984$		0			0
$985$	−1.17291e10	−	8.52166e9i	−0.391054	−	0.284117i
$986$	−2.92642e9	+	9.00660e9i	−0.0972227	+	0.299221i
$987$		0			0
$988$	−2.35442e10	+	1.71058e10i	−0.776665	+	0.564280i
$989$	5.47153e10			1.79855
$990$		0			0
$991$	−4.68833e10			−1.53024			−0.765121	−	0.643886i	$-0.777321\pi$
$991$	−4.68833e10			−1.53024			−0.765121	+	0.643886i	$0.777321\pi$
$992$	8.81787e9	−	6.40655e9i	0.286796	−	0.208369i
$993$		0			0
$994$	6.45363e9	−	1.98622e10i	0.208426	−	0.641469i
$995$	5.23244e10	+	3.80159e10i	1.68393	+	1.22344i
$996$		0			0
$997$	−2.37071e9	+	7.29629e9i	−0.0757609	+	0.233168i	−0.981764	−	0.190102i	$-0.939118\pi$
$997$	−2.37071e9	+	7.29629e9i	−0.0757609	+	0.233168i	0.906003	+	0.423271i	$0.139118\pi$
$998$	8.35345e9	+	2.57093e10i	0.266017	+	0.818716i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.f.d.91.9	yes	56
3.2	odd	2	inner	99.8.f.d.91.6	yes	56
11.4	even	5	inner	99.8.f.d.37.9	yes	56
33.26	odd	10	inner	99.8.f.d.37.6	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.8.f.d.37.6	✓	56	33.26	odd	10	inner
99.8.f.d.37.9	yes	56	11.4	even	5	inner
99.8.f.d.91.6	yes	56	3.2	odd	2	inner
99.8.f.d.91.9	yes	56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(4.74849 - 3.44998i) q^{2} +(-28.9084 + 88.9708i) q^{4} +(314.728 + 228.663i) q^{5} +(-446.571 + 1374.41i) q^{7} +(401.838 + 1236.73i) q^{8} +O(q^{10})\)	\(q+(4.74849 - 3.44998i) q^{2} +(-28.9084 + 88.9708i) q^{4} +(314.728 + 228.663i) q^{5} +(-446.571 + 1374.41i) q^{7} +(401.838 + 1236.73i) q^{8} +2283.36 q^{10} +(3723.63 - 2371.02i) q^{11} +(-9083.21 + 6599.34i) q^{13} +(2621.13 + 8067.01i) q^{14} +(-3512.62 - 2552.07i) q^{16} +(-19706.8 - 14317.9i) q^{17} +(-8562.19 - 26351.7i) q^{19} +(-29442.6 + 21391.3i) q^{20} +(9501.69 - 24105.2i) q^{22} +55212.9 q^{23} +(22624.8 + 69632.0i) q^{25} +(-20363.9 + 62673.8i) q^{26} +(-109372. - 79463.6i) q^{28} +(20468.2 - 62994.7i) q^{29} +(-45942.6 + 33379.3i) q^{31} -191932. q^{32} -142974. q^{34} +(-454824. + 330449. i) q^{35} +(-36180.8 + 111353. i) q^{37} +(-131570. - 95591.4i) q^{38} +(-156325. + 481119. i) q^{40} +(961.119 + 2958.02i) q^{41} +990987. q^{43} +(103307. + 399837. i) q^{44} +(262178. - 190483. i) q^{46} +(272681. + 839225. i) q^{47} +(-1.02330e6 - 743473. i) q^{49} +(347663. + 252592. i) q^{50} +(-324568. - 998917. i) q^{52} +(-1.36034e6 + 988347. i) q^{53} +(1.71410e6 + 105233. i) q^{55} -1.87922e6 q^{56} +(-120137. - 369744. i) q^{58} +(-107691. + 331440. i) q^{59} +(1.31928e6 + 958510. i) q^{61} +(-103000. + 317002. i) q^{62} +(-461773. + 335497. i) q^{64} -4.36776e6 q^{65} -378040. q^{67} +(1.84357e6 - 1.33943e6i) q^{68} +(-1.01969e6 + 3.13827e6i) q^{70} +(-1.99192e6 - 1.44722e6i) q^{71} +(88059.9 - 271020. i) q^{73} +(212361. + 653581. i) q^{74} +2.59205e6 q^{76} +(1.59587e6 + 6.17661e6i) q^{77} +(-5.74179e6 + 4.17166e6i) q^{79} +(-521956. - 1.60641e6i) q^{80} +(14769.0 + 10730.3i) q^{82} +(2.93363e6 + 2.13141e6i) q^{83} +(-2.92832e6 - 9.01246e6i) q^{85} +(4.70569e6 - 3.41889e6i) q^{86} +(4.42860e6 + 3.65237e6i) q^{88} +7.93014e6 q^{89} +(-5.01386e6 - 1.54311e7i) q^{91} +(-1.59612e6 + 4.91234e6i) q^{92} +(4.19013e6 + 3.04431e6i) q^{94} +(3.33090e6 - 1.02515e7i) q^{95} +(5.53528e6 - 4.02161e6i) q^{97} -7.42411e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 1260 q^{4} - 3902 q^{7}+O(q^{10}) \) 56 * q - 1260 * q^4 - 3902 * q^7	\( 56 q - 1260 q^{4} - 3902 q^{7} + 20008 q^{10} - 18158 q^{13} + 54064 q^{16} - 111812 q^{19} + 16106 q^{22} - 78708 q^{25} + 69378 q^{28} - 189868 q^{31} + 1561016 q^{34} - 795786 q^{37} - 1589918 q^{40} + 355744 q^{43} + 2273926 q^{46} - 4728752 q^{49} - 438038 q^{52} + 3414760 q^{55} + 4154034 q^{58} + 1604778 q^{61} + 9561960 q^{64} - 18424972 q^{67} - 5609964 q^{70} + 17372 q^{73} + 8053960 q^{76} - 15803082 q^{79} + 7756570 q^{82} - 21218378 q^{85} + 37593088 q^{88} + 18308922 q^{91} + 68235162 q^{94} + 34988922 q^{97}+O(q^{100}) \) 56 * q - 1260 * q^4 - 3902 * q^7 + 20008 * q^10 - 18158 * q^13 + 54064 * q^16 - 111812 * q^19 + 16106 * q^22 - 78708 * q^25 + 69378 * q^28 - 189868 * q^31 + 1561016 * q^34 - 795786 * q^37 - 1589918 * q^40 + 355744 * q^43 + 2273926 * q^46 - 4728752 * q^49 - 438038 * q^52 + 3414760 * q^55 + 4154034 * q^58 + 1604778 * q^61 + 9561960 * q^64 - 18424972 * q^67 - 5609964 * q^70 + 17372 * q^73 + 8053960 * q^76 - 15803082 * q^79 + 7756570 * q^82 - 21218378 * q^85 + 37593088 * q^88 + 18308922 * q^91 + 68235162 * q^94 + 34988922 * q^97

Introduction

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