LMFDB - Embedded newform 5.11.c.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,11,Mod(2,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	5.c (of order $4$, 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:	$3.17678626337$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1334x^{6} + 456089x^{4} + 43159076x^{2} + 31360000 $ x^8 + 1334x^6 + 456089x^4 + 43159076*x^2 + 31360000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.1
Root			$-17.5804i$ of defining polynomial
Character	$\chi$	$=$	5.3
Dual form			5.11.c.a.2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-36.6454 + 36.6454i) q^{2} +(-13.8338 - 13.8338i) q^{3} -1661.78i q^{4} +(-721.162 - 3040.65i) q^{5} +1013.89 q^{6} +(-13891.7 + 13891.7i) q^{7} +(23371.7 + 23371.7i) q^{8} -58666.3i q^{9} +O(q^{10})$	\(q+(-36.6454 + 36.6454i) q^{2} +(-13.8338 - 13.8338i) q^{3} -1661.78i q^{4} +(-721.162 - 3040.65i) q^{5} +1013.89 q^{6} +(-13891.7 + 13891.7i) q^{7} +(23371.7 + 23371.7i) q^{8} -58666.3i q^{9} +(137853. + 84998.7i) q^{10} -257449. q^{11} +(-22988.7 + 22988.7i) q^{12} +(107046. + 107046. i) q^{13} -1.01813e6i q^{14} +(-32087.3 + 52040.1i) q^{15} -11269.0 q^{16} +(-439362. + 439362. i) q^{17} +(2.14985e6 + 2.14985e6i) q^{18} +1.46167e6i q^{19} +(-5.05288e6 + 1.19841e6i) q^{20} +384349. q^{21} +(9.43434e6 - 9.43434e6i) q^{22} +(-3.17515e6 - 3.17515e6i) q^{23} -646637. i q^{24} +(-8.72547e6 + 4.38560e6i) q^{25} -7.84552e6 q^{26} +(-1.62845e6 + 1.62845e6i) q^{27} +(2.30849e7 + 2.30849e7i) q^{28} -1.87044e7i q^{29} +(-731180. - 3.08289e6i) q^{30} +1.47179e7 q^{31} +(-2.35196e7 + 2.35196e7i) q^{32} +(3.56150e6 + 3.56150e6i) q^{33} -3.22012e7i q^{34} +(5.22579e7 + 3.22216e7i) q^{35} -9.74903e7 q^{36} +(1.77025e7 - 1.77025e7i) q^{37} +(-5.35635e7 - 5.35635e7i) q^{38} -2.96171e6i q^{39} +(5.42103e7 - 8.79198e7i) q^{40} +1.46701e8 q^{41} +(-1.40847e7 + 1.40847e7i) q^{42} +(-8.02116e7 - 8.02116e7i) q^{43} +4.27823e8i q^{44} +(-1.78384e8 + 4.23079e7i) q^{45} +2.32709e8 q^{46} +(-1.20806e8 + 1.20806e8i) q^{47} +(155893. + 155893. i) q^{48} -1.03483e8i q^{49} +(1.59037e8 - 4.80461e8i) q^{50} +1.21561e7 q^{51} +(1.77887e8 - 1.77887e8i) q^{52} +(-4.48776e8 - 4.48776e8i) q^{53} -1.19350e8i q^{54} +(1.85663e8 + 7.82812e8i) q^{55} -6.49343e8 q^{56} +(2.02204e7 - 2.02204e7i) q^{57} +(6.85433e8 + 6.85433e8i) q^{58} -2.00133e8i q^{59} +(8.64791e7 + 5.33220e7i) q^{60} -4.13408e7 q^{61} +(-5.39344e8 + 5.39344e8i) q^{62} +(8.14973e8 + 8.14973e8i) q^{63} -1.73531e9i q^{64} +(2.48293e8 - 4.02688e8i) q^{65} -2.61025e8 q^{66} +(1.80409e8 - 1.80409e8i) q^{67} +(7.30121e8 + 7.30121e8i) q^{68} +8.78486e7i q^{69} +(-3.09579e9 + 7.34240e8i) q^{70} -3.07760e8 q^{71} +(1.37113e9 - 1.37113e9i) q^{72} +(-1.88053e9 - 1.88053e9i) q^{73} +1.29743e9i q^{74} +(1.81376e8 + 6.00369e7i) q^{75} +2.42897e9 q^{76} +(3.57640e9 - 3.57640e9i) q^{77} +(1.08533e8 + 1.08533e8i) q^{78} +3.83202e9i q^{79} +(8.12679e6 + 3.42651e7i) q^{80} -3.41913e9 q^{81} +(-5.37591e9 + 5.37591e9i) q^{82} +(2.47618e9 + 2.47618e9i) q^{83} -6.38703e8i q^{84} +(1.65280e9 + 1.01909e9i) q^{85} +5.87878e9 q^{86} +(-2.58753e8 + 2.58753e8i) q^{87} +(-6.01701e9 - 6.01701e9i) q^{88} -3.22870e9i q^{89} +(4.98655e9 - 8.08734e9i) q^{90} -2.97411e9 q^{91} +(-5.27639e9 + 5.27639e9i) q^{92} +(-2.03605e8 - 2.03605e8i) q^{93} -8.85400e9i q^{94} +(4.44442e9 - 1.05410e9i) q^{95} +6.50731e8 q^{96} +(-2.24159e8 + 2.24159e8i) q^{97} +(3.79216e9 + 3.79216e9i) q^{98} +1.51036e10i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 30 q^{2} + 60 q^{3} - 5340 q^{5} + 17016 q^{6} - 14500 q^{7} + 22020 q^{8}+O(q^{10}) $ 8 * q + 30 * q^2 + 60 * q^3 - 5340 * q^5 + 17016 * q^6 - 14500 * q^7 + 22020 * q^8	\( 8 q + 30 q^{2} + 60 q^{3} - 5340 q^{5} + 17016 q^{6} - 14500 q^{7} + 22020 q^{8} - 161290 q^{10} - 233784 q^{11} + 863160 q^{12} + 433520 q^{13} - 3188580 q^{15} - 1193992 q^{16} + 1045440 q^{17} + 12804210 q^{18} - 16739820 q^{20} - 20777784 q^{21} + 25939360 q^{22} + 24737580 q^{23} - 35382400 q^{25} - 34440684 q^{26} + 27386640 q^{27} + 89876920 q^{28} - 115784880 q^{30} + 258616 q^{31} - 11664120 q^{32} + 11269320 q^{33} + 113638860 q^{35} + 66085308 q^{36} + 92216120 q^{37} - 435848520 q^{38} + 432590700 q^{40} + 115357416 q^{41} - 609152160 q^{42} - 262653700 q^{43} + 593742420 q^{45} + 1023085816 q^{46} - 669481140 q^{47} - 618046320 q^{48} + 944762850 q^{50} - 768258984 q^{51} - 70856500 q^{52} - 1321976040 q^{53} + 2597320 q^{55} + 852915600 q^{56} + 2367269280 q^{57} + 2687784720 q^{58} - 4237774440 q^{60} - 3143200184 q^{61} - 1373690040 q^{62} + 2578662540 q^{63} - 1924527480 q^{65} + 766734432 q^{66} + 4912566140 q^{67} + 6614874660 q^{68} - 8299690440 q^{70} - 4375053384 q^{71} + 808889220 q^{72} - 786968920 q^{73} + 5379002700 q^{75} - 5577898800 q^{76} + 7522045800 q^{77} + 4109901000 q^{78} + 47717760 q^{80} - 2499208992 q^{81} - 19442731040 q^{82} - 11064240660 q^{83} + 15814282160 q^{85} + 36286046616 q^{86} + 2020273920 q^{87} - 13252572960 q^{88} + 9489047670 q^{90} - 12917794184 q^{91} - 25757138760 q^{92} - 40141724280 q^{93} + 14671558800 q^{95} + 38082222816 q^{96} + 24688294760 q^{97} + 13744332030 q^{98}+O(q^{100}) \) 8 * q + 30 * q^2 + 60 * q^3 - 5340 * q^5 + 17016 * q^6 - 14500 * q^7 + 22020 * q^8 - 161290 * q^10 - 233784 * q^11 + 863160 * q^12 + 433520 * q^13 - 3188580 * q^15 - 1193992 * q^16 + 1045440 * q^17 + 12804210 * q^18 - 16739820 * q^20 - 20777784 * q^21 + 25939360 * q^22 + 24737580 * q^23 - 35382400 * q^25 - 34440684 * q^26 + 27386640 * q^27 + 89876920 * q^28 - 115784880 * q^30 + 258616 * q^31 - 11664120 * q^32 + 11269320 * q^33 + 113638860 * q^35 + 66085308 * q^36 + 92216120 * q^37 - 435848520 * q^38 + 432590700 * q^40 + 115357416 * q^41 - 609152160 * q^42 - 262653700 * q^43 + 593742420 * q^45 + 1023085816 * q^46 - 669481140 * q^47 - 618046320 * q^48 + 944762850 * q^50 - 768258984 * q^51 - 70856500 * q^52 - 1321976040 * q^53 + 2597320 * q^55 + 852915600 * q^56 + 2367269280 * q^57 + 2687784720 * q^58 - 4237774440 * q^60 - 3143200184 * q^61 - 1373690040 * q^62 + 2578662540 * q^63 - 1924527480 * q^65 + 766734432 * q^66 + 4912566140 * q^67 + 6614874660 * q^68 - 8299690440 * q^70 - 4375053384 * q^71 + 808889220 * q^72 - 786968920 * q^73 + 5379002700 * q^75 - 5577898800 * q^76 + 7522045800 * q^77 + 4109901000 * q^78 + 47717760 * q^80 - 2499208992 * q^81 - 19442731040 * q^82 - 11064240660 * q^83 + 15814282160 * q^85 + 36286046616 * q^86 + 2020273920 * q^87 - 13252572960 * q^88 + 9489047670 * q^90 - 12917794184 * q^91 - 25757138760 * q^92 - 40141724280 * q^93 + 14671558800 * q^95 + 38082222816 * q^96 + 24688294760 * q^97 + 13744332030 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−36.6454	+	36.6454i	−1.14517	+	1.14517i	−0.157680	+	0.987490i	$0.550401\pi$
$2$	−36.6454	+	36.6454i	−1.14517	+	1.14517i	−0.987490	+	0.157680i	$0.949599\pi$
$3$	−13.8338	−	13.8338i	−0.0569292	−	0.0569292i	0.678069	−	0.734998i	$-0.262817\pi$
$3$	−13.8338	−	13.8338i	−0.0569292	−	0.0569292i	−0.734998	+	0.678069i	$0.762817\pi$
$4$		−	1661.78i		−	1.62283i
$5$	−721.162	−	3040.65i	−0.230772	−	0.973008i
$5$	−721.162	−	3040.65i	−0.230772	−	0.973008i
$6$	1013.89			0.130387
$7$	−13891.7	+	13891.7i	−0.826542	+	0.826542i	−0.987037	−	0.160495i	$-0.948691\pi$
$7$	−13891.7	+	13891.7i	−0.826542	+	0.826542i	0.160495	+	0.987037i	$0.448691\pi$
$8$	23371.7	+	23371.7i	0.713246	+	0.713246i
$9$		−	58666.3i		−	0.993518i
$10$	137853.	+	84998.7i	1.37853	+	0.849987i
$11$	−257449.			−1.59856			−0.799278	−	0.600961i	$-0.794785\pi$
$11$	−257449.			−1.59856			−0.799278	+	0.600961i	$0.794785\pi$
$12$	−22988.7	+	22988.7i	−0.0923864	+	0.0923864i
$13$	107046.	+	107046.i	0.288307	+	0.288307i	0.836410	−	0.548104i	$-0.184650\pi$
$13$	107046.	+	107046.i	0.288307	+	0.288307i	−0.548104	+	0.836410i	$0.684650\pi$
$14$		−	1.01813e6i		−	1.89306i
$15$	−32087.3	+	52040.1i	−0.0422549	+	0.0685302i
$16$	−11269.0			−0.0107470
$17$	−439362.	+	439362.i	−0.309441	+	0.309441i	−0.844693	−	0.535252i	$-0.820217\pi$
$17$	−439362.	+	439362.i	−0.309441	+	0.309441i	0.535252	+	0.844693i	$0.320217\pi$
$18$	2.14985e6	+	2.14985e6i	1.13775	+	1.13775i
$19$			1.46167e6i			0.590311i	0.955449	+	0.295155i	$0.0953714\pi$
$19$			1.46167e6i			0.590311i	−0.955449	+	0.295155i	$0.904629\pi$
$20$	−5.05288e6	+	1.19841e6i	−1.57903	+	0.374504i
$21$	384349.			0.0941087
$22$	9.43434e6	−	9.43434e6i	1.83062	−	1.83062i
$23$	−3.17515e6	−	3.17515e6i	−0.493315	−	0.493315i	0.416034	−	0.909349i	$-0.363420\pi$
$23$	−3.17515e6	−	3.17515e6i	−0.493315	−	0.493315i	−0.909349	+	0.416034i	$0.863420\pi$
$24$		−	646637.i		−	0.0812091i
$25$	−8.72547e6	+	4.38560e6i	−0.893489	+	0.449086i
$26$	−7.84552e6			−0.660321
$27$	−1.62845e6	+	1.62845e6i	−0.113489	+	0.113489i
$28$	2.30849e7	+	2.30849e7i	1.34134	+	1.34134i
$29$		−	1.87044e7i		−	0.911916i	−0.890001	−	0.455958i	$-0.849297\pi$
$29$		−	1.87044e7i		−	0.911916i	0.890001	−	0.455958i	$-0.150703\pi$
$30$	−731180.	−	3.08289e6i	−0.0300897	−	0.126868i
$31$	1.47179e7			0.514088			0.257044	−	0.966400i	$-0.417251\pi$
$31$	1.47179e7			0.514088			0.257044	+	0.966400i	$0.417251\pi$
$32$	−2.35196e7	+	2.35196e7i	−0.700939	+	0.700939i
$33$	3.56150e6	+	3.56150e6i	0.0910045	+	0.0910045i
$34$		−	3.22012e7i		−	0.708725i
$35$	5.22579e7	+	3.22216e7i	0.994974	+	0.613489i
$36$	−9.74903e7			−1.61231
$37$	1.77025e7	−	1.77025e7i	0.255286	−	0.255286i	−0.567848	−	0.823134i	$-0.692224\pi$
$37$	1.77025e7	−	1.77025e7i	0.255286	−	0.255286i	0.823134	+	0.567848i	$0.192224\pi$
$38$	−5.35635e7	−	5.35635e7i	−0.676006	−	0.676006i
$39$		−	2.96171e6i		−	0.0328262i
$40$	5.42103e7	−	8.79198e7i	0.529397	−	0.858591i
$41$	1.46701e8			1.26623			0.633115	−	0.774058i	$-0.281776\pi$
$41$	1.46701e8			1.26623			0.633115	+	0.774058i	$0.281776\pi$
$42$	−1.40847e7	+	1.40847e7i	−0.107770	+	0.107770i
$43$	−8.02116e7	−	8.02116e7i	−0.545626	−	0.545626i	0.379547	−	0.925173i	$-0.376080\pi$
$43$	−8.02116e7	−	8.02116e7i	−0.545626	−	0.545626i	−0.925173	+	0.379547i	$0.876080\pi$
$44$			4.27823e8i			2.59418i
$45$	−1.78384e8	+	4.23079e7i	−0.966701	+	0.229276i
$46$	2.32709e8			1.12986
$47$	−1.20806e8	+	1.20806e8i	−0.526744	+	0.526744i	−0.919600	−	0.392856i	$-0.871487\pi$
$47$	−1.20806e8	+	1.20806e8i	−0.526744	+	0.526744i	0.392856	+	0.919600i	$0.371487\pi$
$48$	155893.	+	155893.i	0.000611817	+	0.000611817i
$49$		−	1.03483e8i		−	0.366342i
$50$	1.59037e8	−	4.80461e8i	0.508917	−	1.53748i
$51$	1.21561e7			0.0352324
$52$	1.77887e8	−	1.77887e8i	0.467873	−	0.467873i
$53$	−4.48776e8	−	4.48776e8i	−1.07312	−	1.07312i	−0.997106	−	0.0760175i	$-0.975779\pi$
$53$	−4.48776e8	−	4.48776e8i	−1.07312	−	1.07312i	−0.0760175	−	0.997106i	$-0.524221\pi$
$54$		−	1.19350e8i		−	0.259929i
$55$	1.85663e8	+	7.82812e8i	0.368902	+	1.55541i
$56$	−6.49343e8			−1.17906
$57$	2.02204e7	−	2.02204e7i	0.0336059	−	0.0336059i
$58$	6.85433e8	+	6.85433e8i	1.04430	+	1.04430i
$59$		−	2.00133e8i		−	0.279935i	−0.990156	−	0.139968i	$-0.955300\pi$
$59$		−	2.00133e8i		−	0.279935i	0.990156	−	0.139968i	$-0.0446999\pi$
$60$	8.64791e7	+	5.33220e7i	0.111213	+	0.0685725i
$61$	−4.13408e7			−0.0489474			−0.0244737	−	0.999700i	$-0.507791\pi$
$61$	−4.13408e7			−0.0489474			−0.0244737	+	0.999700i	$0.507791\pi$
$62$	−5.39344e8	+	5.39344e8i	−0.588719	+	0.588719i
$63$	8.14973e8	+	8.14973e8i	0.821184	+	0.821184i
$64$		−	1.73531e9i		−	1.61614i
$65$	2.48293e8	−	4.02688e8i	0.213992	−	0.347058i
$66$	−2.61025e8			−0.208431
$67$	1.80409e8	−	1.80409e8i	0.133624	−	0.133624i	−0.637131	−	0.770755i	$-0.719879\pi$
$67$	1.80409e8	−	1.80409e8i	0.133624	−	0.133624i	0.770755	+	0.637131i	$0.219879\pi$
$68$	7.30121e8	+	7.30121e8i	0.502170	+	0.502170i
$69$			8.78486e7i			0.0561681i
$70$	−3.09579e9	+	7.34240e8i	−1.84196	+	0.436866i
$71$	−3.07760e8			−0.170577			−0.0852884	−	0.996356i	$-0.527181\pi$
$71$	−3.07760e8			−0.170577			−0.0852884	+	0.996356i	$0.527181\pi$
$72$	1.37113e9	−	1.37113e9i	0.708623	−	0.708623i
$73$	−1.88053e9	−	1.88053e9i	−0.907124	−	0.907124i	0.0889156	−	0.996039i	$-0.471660\pi$
$73$	−1.88053e9	−	1.88053e9i	−0.907124	−	0.907124i	−0.996039	+	0.0889156i	$0.971660\pi$
$74$			1.29743e9i			0.584691i
$75$	1.81376e8	+	6.00369e7i	0.0764317	+	0.0252995i
$76$	2.42897e9			0.957974
$77$	3.57640e9	−	3.57640e9i	1.32127	−	1.32127i
$78$	1.08533e8	+	1.08533e8i	0.0375915	+	0.0375915i
$79$			3.83202e9i			1.24535i	0.782480	+	0.622676i	$0.213954\pi$
$79$			3.83202e9i			1.24535i	−0.782480	+	0.622676i	$0.786046\pi$
$80$	8.12679e6	+	3.42651e7i	0.00248010	+	0.0104569i
$81$	−3.41913e9			−0.980596
$82$	−5.37591e9	+	5.37591e9i	−1.45005	+	1.45005i
$83$	2.47618e9	+	2.47618e9i	0.628626	+	0.628626i	0.947722	−	0.319096i	$-0.103379\pi$
$83$	2.47618e9	+	2.47618e9i	0.628626	+	0.628626i	−0.319096	+	0.947722i	$0.603379\pi$
$84$		−	6.38703e8i		−	0.152722i
$85$	1.65280e9	+	1.01909e9i	0.372499	+	0.229678i
$86$	5.87878e9			1.24967
$87$	−2.58753e8	+	2.58753e8i	−0.0519146	+	0.0519146i
$88$	−6.01701e9	−	6.01701e9i	−1.14016	−	1.14016i
$89$		−	3.22870e9i		−	0.578200i	−0.957299	−	0.289100i	$-0.906644\pi$
$89$		−	3.22870e9i		−	0.578200i	0.957299	−	0.289100i	$-0.0933560\pi$
$90$	4.98655e9	−	8.08734e9i	0.844477	−	1.36960i
$91$	−2.97411e9			−0.476595
$92$	−5.27639e9	+	5.27639e9i	−0.800567	+	0.800567i
$93$	−2.03605e8	−	2.03605e8i	−0.0292666	−	0.0292666i
$94$		−	8.85400e9i		−	1.20642i
$95$	4.44442e9	−	1.05410e9i	0.574377	−	0.136227i
$96$	6.50731e8			0.0798078
$97$	−2.24159e8	+	2.24159e8i	−0.0261034	+	0.0261034i	−0.720038	−	0.693935i	$-0.755876\pi$
$97$	−2.24159e8	+	2.24159e8i	−0.0261034	+	0.0261034i	0.693935	+	0.720038i	$0.255876\pi$
$98$	3.79216e9	+	3.79216e9i	0.419524	+	0.419524i
$99$			1.51036e10i			1.58819i
$100$	7.28790e9	+	1.44998e10i	0.728790	+	1.44998i
$101$	−1.73001e10			−1.64605			−0.823024	−	0.568006i	$-0.807715\pi$
$101$	−1.73001e10			−1.64605			−0.823024	+	0.568006i	$0.807715\pi$
$102$	−4.45465e8	+	4.45465e8i	−0.0403471	+	0.0403471i
$103$	−9.54553e9	−	9.54553e9i	−0.823406	−	0.823406i	0.163189	−	0.986595i	$-0.447822\pi$
$103$	−9.54553e9	−	9.54553e9i	−0.823406	−	0.823406i	−0.986595	+	0.163189i	$0.947822\pi$
$104$			5.00370e9i			0.411268i
$105$	−2.77178e8	−	1.16867e9i	−0.0217176	−	0.0915685i
$106$	3.28912e10			2.45782
$107$	1.14387e10	−	1.14387e10i	0.815565	−	0.815565i	−0.169897	−	0.985462i	$-0.554343\pi$
$107$	1.14387e10	−	1.14387e10i	0.815565	−	0.815565i	0.985462	+	0.169897i	$0.0543435\pi$
$108$	2.70612e9	+	2.70612e9i	0.184174	+	0.184174i
$109$		−	2.35000e9i		−	0.152734i	−0.997080	−	0.0763670i	$-0.975668\pi$
$109$		−	2.35000e9i		−	0.152734i	0.997080	−	0.0763670i	$-0.0243321\pi$
$110$	−3.54902e10	−	2.18828e10i	−2.20366	−	1.35875i
$111$	−4.89786e8			−0.0290664
$112$	1.56546e8	−	1.56546e8i	0.00888282	−	0.00888282i
$113$	8.11951e9	+	8.11951e9i	0.440694	+	0.440694i	0.892245	−	0.451551i	$-0.149129\pi$
$113$	8.11951e9	+	8.11951e9i	0.440694	+	0.440694i	−0.451551	+	0.892245i	$0.649129\pi$
$114$			1.48197e9i			0.0769690i
$115$	−7.36471e9	+	1.19443e10i	−0.366156	+	0.593843i
$116$	−3.10826e10			−1.47988
$117$	6.28001e9	−	6.28001e9i	0.286438	−	0.286438i
$118$	7.33395e9	+	7.33395e9i	0.320574	+	0.320574i
$119$		−	1.22069e10i		−	0.511531i
$120$	−1.96620e9	+	4.66331e8i	−0.0790171	+	0.0187408i
$121$	4.03426e10			1.55538
$122$	1.51495e9	−	1.51495e9i	0.0560531	−	0.0560531i
$123$	−2.02943e9	−	2.02943e9i	−0.0720855	−	0.0720855i
$124$		−	2.44579e10i		−	0.834278i
$125$	1.96276e10	+	2.33684e10i	0.643156	+	0.765735i
$126$	−5.97301e10			−1.88079
$127$	3.27321e9	−	3.27321e9i	0.0990731	−	0.0990731i	−0.655833	−	0.754906i	$-0.727682\pi$
$127$	3.27321e9	−	3.27321e9i	0.0990731	−	0.0990731i	0.754906	+	0.655833i	$0.227682\pi$
$128$	3.95072e10	+	3.95072e10i	1.14981	+	1.14981i
$129$			2.21926e9i			0.0621241i
$130$	5.65790e9	+	2.38555e10i	0.152384	+	0.642498i
$131$	7.92542e8			0.0205431			0.0102716	−	0.999947i	$-0.496730\pi$
$131$	7.92542e8			0.0205431			0.0102716	+	0.999947i	$0.496730\pi$
$132$	5.91842e9	−	5.91842e9i	0.147685	−	0.147685i
$133$	−2.03050e10	−	2.03050e10i	−0.487916	−	0.487916i
$134$			1.32223e10i			0.306044i
$135$	6.12592e9	+	3.77717e9i	0.136616	+	0.0842359i
$136$	−2.05372e10			−0.441415
$137$	−5.07413e10	+	5.07413e10i	−1.05138	+	1.05138i	−0.0527700	+	0.998607i	$0.516805\pi$
$137$	−5.07413e10	+	5.07413e10i	−1.05138	+	1.05138i	−0.998607	+	0.0527700i	$0.983195\pi$
$138$	−3.21925e9	−	3.21925e9i	−0.0643220	−	0.0643220i
$139$		−	8.23117e10i		−	1.58631i	−0.609020	−	0.793155i	$-0.708437\pi$
$139$		−	8.23117e10i		−	1.58631i	0.609020	−	0.793155i	$-0.291563\pi$
$140$	5.35451e10	−	8.68410e10i	0.995588	−	1.61467i
$141$	3.34242e9			0.0599743
$142$	1.12780e10	−	1.12780e10i	0.195340	−	0.195340i
$143$	−2.75590e10	−	2.75590e10i	−0.460875	−	0.460875i
$144$			6.61111e8i			0.0106773i
$145$	−5.68736e10	+	1.34889e10i	−0.887301	+	0.210445i
$146$	1.37826e11			2.07762
$147$	−1.43156e9	+	1.43156e9i	−0.0208556	+	0.0208556i
$148$	−2.94176e10	−	2.94176e10i	−0.414285	−	0.414285i
$149$			1.12260e11i			1.52860i	0.644863	+	0.764298i	$0.276914\pi$
$149$			1.12260e11i			1.52860i	−0.644863	+	0.764298i	$0.723086\pi$
$150$	−8.84668e9	+	4.44653e9i	−0.116500	+	0.0585551i
$151$	−3.06257e10			−0.390122			−0.195061	−	0.980791i	$-0.562491\pi$
$151$	−3.06257e10			−0.390122			−0.195061	+	0.980791i	$0.562491\pi$
$152$	−3.41616e10	+	3.41616e10i	−0.421037	+	0.421037i
$153$	2.57757e10	+	2.57757e10i	0.307435	+	0.307435i
$154$			2.62118e11i			3.02617i
$155$	−1.06140e10	−	4.47520e10i	−0.118637	−	0.500212i
$156$	−4.92171e9			−0.0532713
$157$	5.91731e10	−	5.91731e10i	0.620334	−	0.620334i	−0.325283	−	0.945617i	$-0.605459\pi$
$157$	5.91731e10	−	5.91731e10i	0.620334	−	0.620334i	0.945617	+	0.325283i	$0.105459\pi$
$158$	−1.40426e11	−	1.40426e11i	−1.42614	−	1.42614i
$159$			1.24165e10i			0.122184i
$160$	8.84764e10	+	5.45534e10i	0.843776	+	0.520262i
$161$	8.82163e10			0.815491
$162$	1.25295e11	−	1.25295e11i	1.12295	−	1.12295i
$163$	1.96892e10	+	1.96892e10i	0.171116	+	0.171116i	0.787470	−	0.616354i	$-0.211391\pi$
$163$	1.96892e10	+	1.96892e10i	0.171116	+	0.171116i	−0.616354	+	0.787470i	$0.711391\pi$
$164$		−	2.43784e11i		−	2.05488i
$165$	8.26085e9	−	1.33977e10i	0.0675468	−	0.109549i
$166$	−1.81482e11			−1.43977
$167$	−1.40562e11	+	1.40562e11i	−1.08215	+	1.08215i	−0.0858387	+	0.996309i	$0.527357\pi$
$167$	−1.40562e11	+	1.40562e11i	−1.08215	+	1.08215i	−0.996309	+	0.0858387i	$0.972643\pi$
$168$	8.98288e9	+	8.98288e9i	0.0671227	+	0.0671227i
$169$		−	1.14941e11i		−	0.833758i
$170$	−9.79126e10	+	2.32223e10i	−0.689595	+	0.163554i
$171$	8.57506e10			0.586485
$172$	−1.33294e11	+	1.33294e11i	−0.885458	+	0.885458i
$173$	1.36495e11	+	1.36495e11i	0.880815	+	0.880815i	0.993617	−	0.112802i	$-0.0359827\pi$
$173$	1.36495e11	+	1.36495e11i	0.880815	+	0.880815i	−0.112802	+	0.993617i	$0.535983\pi$
$174$		−	1.89643e10i		−	0.118902i
$175$	6.02881e10	−	1.82135e11i	0.367317	−	1.10969i
$176$	2.90120e9			0.0171796
$177$	−2.76859e9	+	2.76859e9i	−0.0159365	+	0.0159365i
$178$	1.18317e11	+	1.18317e11i	0.662137	+	0.662137i
$179$		−	4.46176e10i		−	0.242796i	−0.992604	−	0.121398i	$-0.961262\pi$
$179$		−	4.46176e10i		−	0.242796i	0.992604	−	0.121398i	$-0.0387377\pi$
$180$	7.03063e10	+	2.96434e11i	0.372076	+	1.56879i
$181$	−2.28500e11			−1.17623			−0.588117	−	0.808776i	$-0.700130\pi$
$181$	−2.28500e11			−1.17623			−0.588117	+	0.808776i	$0.700130\pi$
$182$	1.08988e11	−	1.08988e11i	0.545783	−	0.545783i
$183$	5.71900e8	+	5.71900e8i	0.00278654	+	0.00278654i
$184$		−	1.48417e11i		−	0.703711i
$185$	−6.65935e10	−	4.10608e10i	−0.307308	−	0.189482i
$186$	1.49224e10			0.0670306
$187$	1.13113e11	−	1.13113e11i	0.494658	−	0.494658i
$188$	2.00753e11	+	2.00753e11i	0.854817	+	0.854817i
$189$		−	4.52438e10i		−	0.187607i
$190$	−1.24240e11	+	2.01496e11i	−0.501756	+	0.813763i
$191$	2.98408e10			0.117393			0.0586967	−	0.998276i	$-0.481306\pi$
$191$	2.98408e10			0.117393			0.0586967	+	0.998276i	$0.481306\pi$
$192$	−2.40060e10	+	2.40060e10i	−0.0920053	+	0.0920053i
$193$	−9.95871e8	−	9.95871e8i	−0.00371892	−	0.00371892i	0.705245	−	0.708964i	$-0.250837\pi$
$193$	−9.95871e8	−	9.95871e8i	−0.00371892	−	0.00371892i	−0.708964	+	0.705245i	$0.750837\pi$
$194$		−	1.64288e10i		−	0.0597857i
$195$	−9.00554e9	+	2.13588e9i	−0.0319401	+	0.00757536i
$196$	−1.71965e11			−0.594511
$197$	1.29244e9	−	1.29244e9i	0.00435590	−	0.00435590i	−0.704925	−	0.709281i	$-0.749020\pi$
$197$	1.29244e9	−	1.29244e9i	0.00435590	−	0.00435590i	0.709281	+	0.704925i	$0.249020\pi$
$198$	−5.53477e11	−	5.53477e11i	−1.81875	−	1.81875i
$199$			5.28508e11i			1.69350i	0.531987	+	0.846752i	$0.321445\pi$
$199$			5.28508e11i			1.69350i	−0.531987	+	0.846752i	$0.678555\pi$
$200$	−3.06428e11	−	1.01430e11i	−0.957586	−	0.316969i
$201$	−4.99148e9			−0.0152142
$202$	6.33971e11	−	6.33971e11i	1.88501	−	1.88501i
$203$	2.59836e11	+	2.59836e11i	0.753736	+	0.753736i
$204$		−	2.02007e10i		−	0.0571762i
$205$	−1.05795e11	−	4.46065e11i	−0.292210	−	1.23205i
$206$	6.99600e11			1.88588
$207$	−1.86274e11	+	1.86274e11i	−0.490118	+	0.490118i
$208$	−1.20631e9	−	1.20631e9i	−0.00309843	−	0.00309843i
$209$		−	3.76305e11i		−	0.943645i
$210$	5.29838e10	+	3.26692e10i	0.129732	+	0.0799911i
$211$	1.09556e11			0.261953			0.130977	−	0.991385i	$-0.458189\pi$
$211$	1.09556e11			0.261953			0.130977	+	0.991385i	$0.458189\pi$
$212$	−7.45765e11	+	7.45765e11i	−1.74150	+	1.74150i
$213$	4.25748e9	+	4.25748e9i	0.00971080	+	0.00971080i
$214$			8.38354e11i			1.86792i
$215$	−1.86050e11	+	3.01741e11i	−0.404983	+	0.656813i
$216$	−7.61191e10			−0.161892
$217$	−2.04457e11	+	2.04457e11i	−0.424915	+	0.424915i
$218$	8.61169e10	+	8.61169e10i	0.174906	+	0.174906i
$219$			5.20298e10i			0.103284i
$220$	1.30086e12	−	3.08530e11i	2.52416	−	0.598665i
$221$	−9.40641e10			−0.178428
$222$	1.79484e10	−	1.79484e10i	0.0332860	−	0.0332860i
$223$	−4.58052e11	−	4.58052e11i	−0.830597	−	0.830597i	0.157001	−	0.987598i	$-0.449817\pi$
$223$	−4.58052e11	−	4.58052e11i	−0.830597	−	0.830597i	−0.987598	+	0.157001i	$0.949817\pi$
$224$		−	6.53454e11i		−	1.15871i
$225$	2.57287e11	+	5.11891e11i	0.446175	+	0.887697i
$226$	−5.95086e11			−1.00934
$227$	1.19760e11	−	1.19760e11i	0.198693	−	0.198693i	−0.600746	−	0.799440i	$-0.705130\pi$
$227$	1.19760e11	−	1.19760e11i	0.198693	−	0.198693i	0.799440	+	0.600746i	$0.205130\pi$
$228$	−3.36018e10	−	3.36018e10i	−0.0545367	−	0.0545367i
$229$		−	5.26010e11i		−	0.835251i	−0.908619	−	0.417625i	$-0.862862\pi$
$229$		−	5.26010e11i		−	0.835251i	0.908619	−	0.417625i	$-0.137138\pi$
$230$	−1.67821e11	−	7.07588e11i	−0.260740	−	1.09936i
$231$	−9.89504e10			−0.150438
$232$	4.37154e11	−	4.37154e11i	0.650420	−	0.650420i
$233$	−5.71170e11	−	5.71170e11i	−0.831736	−	0.831736i	0.156018	−	0.987754i	$-0.450134\pi$
$233$	−5.71170e11	−	5.71170e11i	−0.831736	−	0.831736i	−0.987754	+	0.156018i	$0.950134\pi$
$234$			4.60267e11i			0.656041i
$235$	4.54450e11	+	2.80208e11i	0.634084	+	0.390969i
$236$	−3.32576e11			−0.454287
$237$	5.30113e10	−	5.30113e10i	0.0708968	−	0.0708968i
$238$	4.47329e11	+	4.47329e11i	0.585790	+	0.585790i
$239$			6.29535e10i			0.0807291i	0.999185	+	0.0403645i	$0.0128519\pi$
$239$			6.29535e10i			0.0807291i	−0.999185	+	0.0403645i	$0.987148\pi$
$240$	3.61593e8	−	5.86441e8i	0.000454112	−	0.000736493i
$241$	6.81163e11			0.837849			0.418925	−	0.908021i	$-0.362407\pi$
$241$	6.81163e11			0.837849			0.418925	+	0.908021i	$0.362407\pi$
$242$	−1.47837e12	+	1.47837e12i	−1.78118	+	1.78118i
$243$	1.43458e11	+	1.43458e11i	0.169314	+	0.169314i
$244$			6.86992e10i			0.0794333i
$245$	−3.14654e11	+	7.46277e10i	−0.356454	+	0.0845415i
$246$	1.48738e11			0.165100
$247$	−1.56466e11	+	1.56466e11i	−0.170191	+	0.170191i
$248$	3.43982e11	+	3.43982e11i	0.366672	+	0.366672i
$249$		−	6.85100e10i		−	0.0715744i
$250$	−1.57561e12	−	1.37084e11i	−1.61342	−	0.140374i
$251$	1.52582e12			1.53156			0.765780	−	0.643102i	$-0.222353\pi$
$251$	1.52582e12			1.53156			0.765780	+	0.643102i	$0.222353\pi$
$252$	1.35430e12	−	1.35430e12i	1.33264	−	1.33264i
$253$	8.17438e11	+	8.17438e11i	0.788592	+	0.788592i
$254$			2.39897e11i			0.226911i
$255$	−8.76651e9	−	3.69624e10i	−0.00813066	−	0.0342814i
$256$	−1.11856e12			−1.01733
$257$	1.42466e12	−	1.42466e12i	1.27071	−	1.27071i	0.324997	−	0.945715i	$-0.394637\pi$
$257$	1.42466e12	−	1.42466e12i	1.27071	−	1.27071i	0.945715	−	0.324997i	$-0.105363\pi$
$258$	−8.13258e10	−	8.13258e10i	−0.0711426	−	0.0711426i
$259$			4.91836e11i			0.422008i
$260$	−6.69178e11	−	4.12607e11i	−0.563216	−	0.347272i
$261$	−1.09732e12			−0.906005
$262$	−2.90431e10	+	2.90431e10i	−0.0235253	+	0.0235253i
$263$	−9.05820e11	−	9.05820e11i	−0.719885	−	0.719885i	0.248697	−	0.968581i	$-0.419998\pi$
$263$	−9.05820e11	−	9.05820e11i	−0.719885	−	0.719885i	−0.968581	+	0.248697i	$0.919998\pi$
$264$			1.66476e11i			0.129817i
$265$	−1.04093e12	+	1.68821e12i	−0.796511	+	1.29181i
$266$	1.48817e12			1.11749
$267$	−4.46652e10	+	4.46652e10i	−0.0329164	+	0.0329164i
$268$	−2.99800e11	−	2.99800e11i	−0.216849	−	0.216849i
$269$			6.44179e11i			0.457347i	0.973503	+	0.228673i	$0.0734387\pi$
$269$			6.44179e11i			0.457347i	−0.973503	+	0.228673i	$0.926561\pi$
$270$	−3.62903e11	+	8.60711e10i	−0.252913	+	0.0599844i
$271$	−1.73862e12			−1.18948			−0.594741	−	0.803917i	$-0.702746\pi$
$271$	−1.73862e12			−1.18948			−0.594741	+	0.803917i	$0.702746\pi$
$272$	4.95117e9	−	4.95117e9i	0.00332555	−	0.00332555i
$273$	4.11432e10	+	4.11432e10i	0.0271322	+	0.0271322i
$274$		−	3.71887e12i		−	2.40801i
$275$	2.24637e12	−	1.12907e12i	1.42829	−	0.717889i
$276$	1.45985e11			0.0911512
$277$	4.18449e11	−	4.18449e11i	0.256592	−	0.256592i	−0.567074	−	0.823667i	$-0.691925\pi$
$277$	4.18449e11	−	4.18449e11i	0.256592	−	0.256592i	0.823667	+	0.567074i	$0.191925\pi$
$278$	3.01635e12	+	3.01635e12i	1.81659	+	1.81659i
$279$		−	8.63445e11i		−	0.510756i
$280$	4.68282e11	+	1.97443e12i	0.272093	+	1.14723i
$281$	−2.35344e12			−1.34329			−0.671647	−	0.740871i	$-0.734413\pi$
$281$	−2.35344e12			−1.34329			−0.671647	+	0.740871i	$0.734413\pi$
$282$	−1.22484e11	+	1.22484e11i	−0.0686808	+	0.0686808i
$283$	−1.86874e12	−	1.86874e12i	−1.02948	−	1.02948i	−0.999552	−	0.0299242i	$-0.990473\pi$
$283$	−1.86874e12	−	1.86874e12i	−1.02948	−	1.02948i	−0.0299242	−	0.999552i	$-0.509527\pi$
$284$			5.11428e11i			0.276817i
$285$	−7.60654e10	−	4.69010e10i	−0.0404541	−	0.0249435i
$286$	2.01982e12			1.05556
$287$	−2.03792e12	+	2.03792e12i	−1.04659	+	1.04659i
$288$	1.37981e12	+	1.37981e12i	0.696396	+	0.696396i
$289$			1.62992e12i			0.808493i
$290$	1.58985e12	−	2.57847e12i	0.775116	−	1.25711i
$291$	6.20193e9			0.00297209
$292$	−3.12503e12	+	3.12503e12i	−1.47211	+	1.47211i
$293$	1.90601e12	+	1.90601e12i	0.882646	+	0.882646i	0.993803	−	0.111157i	$-0.0354557\pi$
$293$	1.90601e12	+	1.90601e12i	0.882646	+	0.882646i	−0.111157	+	0.993803i	$0.535456\pi$
$294$		−	1.04920e11i		−	0.0477663i
$295$	−6.08533e11	+	1.44328e11i	−0.272379	+	0.0646012i
$296$	8.27474e11			0.364163
$297$	4.19243e11	−	4.19243e11i	0.181419	−	0.181419i
$298$	−4.11381e12	−	4.11381e12i	−1.75050	−	1.75050i
$299$		−	6.79776e11i		−	0.284452i
$300$	9.97680e10	−	3.01407e11i	0.0410568	−	0.124036i
$301$	2.22855e12			0.901965
$302$	1.12229e12	−	1.12229e12i	0.446756	−	0.446756i
$303$	2.39327e11	+	2.39327e11i	0.0937082	+	0.0937082i
$304$		−	1.64716e10i		−	0.00634406i
$305$	2.98134e10	+	1.25703e11i	0.0112957	+	0.0476262i
$306$	−1.88912e12			−0.704131
$307$	3.61095e12	−	3.61095e12i	1.32413	−	1.32413i	0.413725	−	0.910402i	$-0.364228\pi$
$307$	3.61095e12	−	3.61095e12i	1.32413	−	1.32413i	0.910402	−	0.413725i	$-0.135772\pi$
$308$	−5.94318e12	−	5.94318e12i	−2.14420	−	2.14420i
$309$			2.64102e11i			0.0937516i
$310$	2.02891e12	+	1.25100e12i	0.708688	+	0.436968i
$311$	−3.11985e12			−1.07234			−0.536169	−	0.844110i	$-0.680129\pi$
$311$	−3.11985e12			−1.07234			−0.536169	+	0.844110i	$0.680129\pi$
$312$	6.92202e10	−	6.92202e10i	0.0234131	−	0.0234131i
$313$	2.31917e12	+	2.31917e12i	0.771990	+	0.771990i	0.978454	−	0.206464i	$-0.0661957\pi$
$313$	2.31917e12	+	2.31917e12i	0.771990	+	0.771990i	−0.206464	+	0.978454i	$0.566196\pi$
$314$			4.33685e12i			1.42078i
$315$	1.89032e12	−	3.06578e12i	0.609512	−	0.988525i
$316$	6.36796e12			2.02099
$317$	−2.55868e11	+	2.55868e11i	−0.0799317	+	0.0799317i	−0.745942	−	0.666011i	$-0.768001\pi$
$317$	−2.55868e11	+	2.55868e11i	−0.0799317	+	0.0799317i	0.666011	+	0.745942i	$0.268001\pi$
$318$	−4.55010e11	−	4.55010e11i	−0.139922	−	0.139922i
$319$			4.81544e12i			1.45775i
$320$	−5.27648e12	+	1.25144e12i	−1.57251	+	0.372959i
$321$	−3.16482e11			−0.0928589
$322$	−3.23272e12	+	3.23272e12i	−0.933876	+	0.933876i
$323$	−6.42201e11	−	6.42201e11i	−0.182666	−	0.182666i
$324$			5.68183e12i			1.59134i
$325$	−1.40349e12	−	4.64567e11i	−0.387074	−	0.128124i
$326$	−1.44304e12			−0.391914
$327$	−3.25094e10	+	3.25094e10i	−0.00869502	+	0.00869502i
$328$	3.42864e12	+	3.42864e12i	0.903134	+	0.903134i
$329$		−	3.35640e12i		−	0.870752i
$330$	1.88242e11	+	7.93687e11i	0.0481001	+	0.202805i
$331$	5.61795e12			1.41396			0.706981	−	0.707232i	$-0.250056\pi$
$331$	5.61795e12			1.41396			0.706981	+	0.707232i	$0.250056\pi$
$332$	4.11487e12	−	4.11487e12i	1.02015	−	1.02015i
$333$	−1.03854e12	−	1.03854e12i	−0.253631	−	0.253631i
$334$		−	1.03019e13i		−	2.47849i
$335$	−6.78665e11	−	4.18456e11i	−0.160854	−	0.0991805i
$336$	−4.33124e9			−0.00101138
$337$	−1.50329e12	+	1.50329e12i	−0.345854	+	0.345854i	−0.858563	−	0.512709i	$-0.828642\pi$
$337$	−1.50329e12	+	1.50329e12i	−0.345854	+	0.345854i	0.512709	+	0.858563i	$0.328642\pi$
$338$	4.21205e12	+	4.21205e12i	0.954795	+	0.954795i
$339$		−	2.24647e11i		−	0.0501767i
$340$	1.69351e12	−	2.74658e12i	0.372728	−	0.604502i
$341$	−3.78911e12			−0.821799
$342$	−3.14237e12	+	3.14237e12i	−0.671625	+	0.671625i
$343$	−2.48651e12	−	2.48651e12i	−0.523745	−	0.523745i
$344$		−	3.74936e12i		−	0.778331i
$345$	2.67117e11	−	6.33531e10i	0.0546520	−	0.0129620i
$346$	−1.00038e13			−2.01737
$347$	−3.03026e12	+	3.03026e12i	−0.602327	+	0.602327i	−0.940929	−	0.338603i	$-0.890046\pi$
$347$	−3.03026e12	+	3.03026e12i	−0.602327	+	0.602327i	0.338603	+	0.940929i	$0.390046\pi$
$348$	4.29991e11	+	4.29991e11i	0.0842486	+	0.0842486i
$349$		−	5.43229e12i		−	1.04919i	−0.851351	−	0.524597i	$-0.824216\pi$
$349$		−	5.43229e12i		−	1.04919i	0.851351	−	0.524597i	$-0.175784\pi$
$350$	4.46513e12	+	8.88370e12i	0.850147	+	1.69143i
$351$	−3.48639e11			−0.0654396
$352$	6.05510e12	−	6.05510e12i	1.12049	−	1.12049i
$353$	5.06267e12	+	5.06267e12i	0.923648	+	0.923648i	0.997285	−	0.0736374i	$-0.0234607\pi$
$353$	5.06267e12	+	5.06267e12i	0.923648	+	0.923648i	−0.0736374	+	0.997285i	$0.523461\pi$
$354$		−	2.02913e11i		−	0.0365000i
$355$	2.21945e11	+	9.35789e11i	0.0393643	+	0.165973i
$356$	−5.36538e12			−0.938320
$357$	−1.68868e11	+	1.68868e11i	−0.0291211	+	0.0291211i
$358$	1.63503e12	+	1.63503e12i	0.278043	+	0.278043i
$359$		−	3.43536e11i		−	0.0576103i	−0.999585	−	0.0288051i	$-0.990830\pi$
$359$		−	3.43536e11i		−	0.0576103i	0.999585	−	0.0288051i	$-0.00917023\pi$
$360$	−5.15792e12	−	3.18031e12i	−0.853026	−	0.525966i
$361$	3.99459e12			0.651533
$362$	8.37349e12	−	8.37349e12i	1.34699	−	1.34699i
$363$	−5.58091e11	−	5.58091e11i	−0.0885466	−	0.0885466i
$364$			4.94231e12i			0.773433i
$365$	−4.36187e12	+	7.07421e12i	−0.673300	+	1.09198i
$366$	−4.19151e10			−0.00638212
$367$	−7.27010e12	+	7.27010e12i	−1.09197	+	1.09197i	−0.0966506	+	0.995318i	$0.530813\pi$
$367$	−7.27010e12	+	7.27010e12i	−1.09197	+	1.09197i	−0.995318	+	0.0966506i	$0.969187\pi$
$368$	3.57808e10	+	3.57808e10i	0.00530165	+	0.00530165i
$369$		−	8.60638e12i		−	1.25802i
$370$	3.94504e12	−	9.35660e11i	0.568909	−	0.134930i
$371$	1.24685e13			1.77396
$372$	−3.38346e11	+	3.38346e11i	−0.0474948	+	0.0474948i
$373$	−5.31940e11	−	5.31940e11i	−0.0736748	−	0.0736748i	0.669309	−	0.742984i	$-0.266590\pi$
$373$	−5.31940e11	−	5.31940e11i	−0.0736748	−	0.0736748i	−0.742984	+	0.669309i	$0.766590\pi$
$374$			8.29017e12i			1.13294i
$375$	5.17496e10	−	5.94797e11i	0.00697832	−	0.0802070i
$376$	−5.64688e12			−0.751397
$377$	2.00224e12	−	2.00224e12i	0.262912	−	0.262912i
$378$	1.65798e12	+	1.65798e12i	0.214842	+	0.214842i
$379$			1.46221e13i			1.86988i	0.354809	+	0.934939i	$0.384546\pi$
$379$			1.46221e13i			1.86988i	−0.354809	+	0.934939i	$0.615454\pi$
$380$	−1.75168e12	−	7.38564e12i	−0.221074	−	0.932116i
$381$	−9.05619e10			−0.0112803
$382$	−1.09353e12	+	1.09353e12i	−0.134435	+	0.134435i
$383$	−5.12352e12	−	5.12352e12i	−0.621690	−	0.621690i	0.324273	−	0.945964i	$-0.394880\pi$
$383$	−5.12352e12	−	5.12352e12i	−0.621690	−	0.621690i	−0.945964	+	0.324273i	$0.894880\pi$
$384$		−	1.09307e12i		−	0.130916i
$385$	−1.34537e13	−	8.29542e12i	−1.59052	−	0.980696i
$386$	7.29883e10			0.00851759
$387$	−4.70571e12	+	4.70571e12i	−0.542089	+	0.542089i
$388$	3.72502e11	+	3.72502e11i	0.0423614	+	0.0423614i
$389$		−	9.85599e12i		−	1.10650i	−0.833015	−	0.553251i	$-0.813387\pi$
$389$		−	9.85599e12i		−	1.10650i	0.833015	−	0.553251i	$-0.186613\pi$
$390$	2.51742e11	−	4.08282e11i	0.0279018	−	0.0452519i
$391$	2.79007e12			0.305304
$392$	2.41856e12	−	2.41856e12i	0.261292	−	0.261292i
$393$	−1.09639e10	−	1.09639e10i	−0.00116950	−	0.00116950i
$394$			9.47237e10i			0.00997649i
$395$	1.16518e13	−	2.76351e12i	1.21174	−	0.287392i
$396$	2.50988e13			2.57737
$397$	9.24976e12	−	9.24976e12i	0.937946	−	0.937946i	−0.0602381	−	0.998184i	$-0.519186\pi$
$397$	9.24976e12	−	9.24976e12i	0.937946	−	0.937946i	0.998184	+	0.0602381i	$0.0191860\pi$
$398$	−1.93674e13	−	1.93674e13i	−1.93935	−	1.93935i
$399$			5.61791e11i			0.0555534i
$400$	9.83275e10	−	4.94215e10i	0.00960230	−	0.00482631i
$401$	−1.06441e13			−1.02657			−0.513284	−	0.858219i	$-0.671571\pi$
$401$	−1.06441e13			−1.02657			−0.513284	+	0.858219i	$0.671571\pi$
$402$	1.82915e11	−	1.82915e11i	0.0174229	−	0.0174229i
$403$	1.57550e12	+	1.57550e12i	0.148215	+	0.148215i
$404$			2.87490e13i			2.67126i
$405$	2.46575e12	+	1.03964e13i	0.226294	+	0.954128i
$406$	−1.90436e13			−1.72631
$407$	−4.55750e12	+	4.55750e12i	−0.408088	+	0.408088i
$408$	2.84108e11	+	2.84108e11i	0.0251294	+	0.0251294i
$409$			3.58194e12i			0.312969i	0.987680	+	0.156484i	$0.0500161\pi$
$409$			3.58194e12i			0.312969i	−0.987680	+	0.156484i	$0.949984\pi$
$410$	2.02232e13	+	1.24694e13i	1.74554	+	1.07628i
$411$	1.40389e12			0.119708
$412$	−1.58625e13	+	1.58625e13i	−1.33625	+	1.33625i
$413$	2.78018e12	+	2.78018e12i	0.231378	+	0.231378i
$414$		−	1.36522e13i		−	1.12254i
$415$	5.74348e12	−	9.31494e12i	0.466589	−	0.756727i
$416$	−5.03538e12			−0.404171
$417$	−1.13868e12	+	1.13868e12i	−0.0903073	+	0.0903073i
$418$	1.37899e13	+	1.37899e13i	1.08063	+	1.08063i
$419$		−	1.08482e13i		−	0.840018i	−0.907520	−	0.420009i	$-0.862027\pi$
$419$		−	1.08482e13i		−	0.840018i	0.907520	−	0.420009i	$-0.137973\pi$
$420$	−1.94207e12	+	4.60609e11i	−0.148600	+	0.0352440i
$421$	6.64651e12			0.502554			0.251277	−	0.967915i	$-0.419149\pi$
$421$	6.64651e12			0.502554			0.251277	+	0.967915i	$0.419149\pi$
$422$	−4.01473e12	+	4.01473e12i	−0.299981	+	0.299981i
$423$	7.08725e12	+	7.08725e12i	0.523330	+	0.523330i
$424$		−	2.09773e13i		−	1.53080i
$425$	1.90677e12	−	5.76050e12i	0.137516	−	0.415447i
$426$	−3.12035e11			−0.0222410
$427$	5.74293e11	−	5.74293e11i	0.0404571	−	0.0404571i
$428$	−1.90086e13	−	1.90086e13i	−1.32352	−	1.32352i
$429$			7.62491e11i			0.0524745i
$430$	−4.23955e12	−	1.78753e13i	−0.288389	−	1.21594i
$431$	2.81961e12			0.189585			0.0947923	−	0.995497i	$-0.469781\pi$
$431$	2.81961e12			0.189585			0.0947923	+	0.995497i	$0.469781\pi$
$432$	1.83510e10	−	1.83510e10i	0.00121967	−	0.00121967i
$433$	5.55274e12	+	5.55274e12i	0.364811	+	0.364811i	0.865580	−	0.500770i	$-0.166950\pi$
$433$	5.55274e12	+	5.55274e12i	0.364811	+	0.364811i	−0.500770	+	0.865580i	$0.666950\pi$
$434$		−	1.49848e13i		−	0.973201i
$435$	9.73381e11	+	6.00175e11i	0.0624938	+	0.0385329i
$436$	−3.90518e12			−0.247861
$437$	4.64101e12	−	4.64101e12i	0.291209	−	0.291209i
$438$	−1.90666e12	−	1.90666e12i	−0.118277	−	0.118277i
$439$			1.64442e13i			1.00853i	0.863548	+	0.504266i	$0.168237\pi$
$439$			1.64442e13i			1.00853i	−0.863548	+	0.504266i	$0.831763\pi$
$440$	−1.39564e13	+	2.26349e13i	−0.846271	+	1.37251i
$441$	−6.07093e12			−0.363967
$442$	3.44702e12	−	3.44702e12i	0.204330	−	0.204330i
$443$	−5.59823e12	−	5.59823e12i	−0.328119	−	0.328119i	0.523752	−	0.851871i	$-0.324532\pi$
$443$	−5.59823e12	−	5.59823e12i	−0.328119	−	0.328119i	−0.851871	+	0.523752i	$0.824532\pi$
$444$			8.13915e11i			0.0471698i
$445$	−9.81735e12	+	2.32842e12i	−0.562593	+	0.133432i
$446$	3.35710e13			1.90235
$447$	1.55298e12	−	1.55298e12i	0.0870218	−	0.0870218i
$448$	2.41064e13	+	2.41064e13i	1.33580	+	1.33580i
$449$			1.34775e13i			0.738547i	0.929321	+	0.369273i	$0.120393\pi$
$449$			1.34775e13i			0.738547i	−0.929321	+	0.369273i	$0.879607\pi$
$450$	−2.81869e13	−	9.33008e12i	−1.52751	−	0.505618i
$451$	−3.77679e13			−2.02414
$452$	1.34928e13	−	1.34928e13i	0.715172	−	0.715172i
$453$	4.23669e11	+	4.23669e11i	0.0222093	+	0.0222093i
$454$			8.77733e12i			0.455075i
$455$	2.14481e12	+	9.04322e12i	0.109985	+	0.463731i
$456$	9.45169e11			0.0479386
$457$	1.55855e13	−	1.55855e13i	0.781880	−	0.781880i	−0.198267	−	0.980148i	$-0.563531\pi$
$457$	1.55855e13	−	1.55855e13i	0.781880	−	0.781880i	0.980148	+	0.198267i	$0.0635315\pi$
$458$	1.92759e13	+	1.92759e13i	0.956505	+	0.956505i
$459$		−	1.43096e12i		−	0.0702365i
$460$	1.98488e13	+	1.22385e13i	0.963706	+	0.594209i
$461$	−1.55486e13			−0.746770			−0.373385	−	0.927676i	$-0.621803\pi$
$461$	−1.55486e13			−0.746770			−0.373385	+	0.927676i	$0.621803\pi$
$462$	3.62608e12	−	3.62608e12i	0.172277	−	0.172277i
$463$	−2.69336e13	−	2.69336e13i	−1.26587	−	1.26587i	−0.948203	−	0.317666i	$-0.897101\pi$
$463$	−2.69336e13	−	2.69336e13i	−1.26587	−	1.26587i	−0.317666	−	0.948203i	$-0.602899\pi$
$464$			2.10781e11i			0.00980033i
$465$	−4.72258e11	+	7.65922e11i	−0.0217227	+	0.0352306i
$466$	4.18615e13			1.90496
$467$	1.28890e13	−	1.28890e13i	0.580276	−	0.580276i	−0.354703	−	0.934979i	$-0.615418\pi$
$467$	1.28890e13	−	1.28890e13i	0.580276	−	0.580276i	0.934979	+	0.354703i	$0.115418\pi$
$468$	−1.04360e13	−	1.04360e13i	−0.464840	−	0.464840i
$469$			5.01237e12i			0.220891i
$470$	−2.69219e13	+	6.38517e12i	−1.17386	+	0.278409i
$471$	−1.63718e12			−0.0706303
$472$	4.67743e12	−	4.67743e12i	0.199663	−	0.199663i
$473$	2.06504e13	+	2.06504e13i	0.872213	+	0.872213i
$474$			3.88525e12i			0.162378i
$475$	−6.41030e12	−	1.27537e13i	−0.265100	−	0.527436i
$476$	−2.02852e13			−0.830128
$477$	−2.63280e13	+	2.63280e13i	−1.06617	+	1.06617i
$478$	−2.30696e12	−	2.30696e12i	−0.0924486	−	0.0924486i
$479$			4.73768e12i			0.187883i	0.995578	+	0.0939417i	$0.0299467\pi$
$479$			4.73768e12i			0.187883i	−0.995578	+	0.0939417i	$0.970053\pi$
$480$	−4.69283e11	−	1.97865e12i	−0.0184174	−	0.0776536i
$481$	3.78998e12			0.147201
$482$	−2.49615e13	+	2.49615e13i	−0.959480	+	0.959480i
$483$	−1.22037e12	−	1.22037e12i	−0.0464253	−	0.0464253i
$484$		−	6.70404e13i		−	2.52412i
$485$	8.43243e11	+	5.19933e11i	0.0314227	+	0.0193749i
$486$	−1.05141e13			−0.387787
$487$	1.21568e13	−	1.21568e13i	0.443788	−	0.443788i	−0.449495	−	0.893283i	$-0.648396\pi$
$487$	1.21568e13	−	1.21568e13i	0.443788	−	0.443788i	0.893283	+	0.449495i	$0.148396\pi$
$488$	−9.66203e11	−	9.66203e11i	−0.0349116	−	0.0349116i
$489$		−	5.44753e11i		−	0.0194830i
$490$	8.79588e12	−	1.42654e13i	0.311386	−	0.505015i
$491$	1.28353e13			0.449777			0.224889	−	0.974384i	$-0.427798\pi$
$491$	1.28353e13			0.449777			0.224889	+	0.974384i	$0.427798\pi$
$492$	−3.37246e12	+	3.37246e12i	−0.116982	+	0.116982i
$493$	8.21801e12	+	8.21801e12i	0.282184	+	0.282184i
$494$		−	1.14675e13i		−	0.389795i
$495$	4.59247e13	−	1.08921e13i	1.54533	−	0.366511i
$496$	−1.65856e11			−0.00552489
$497$	4.27530e12	−	4.27530e12i	0.140989	−	0.140989i
$498$	2.51058e12	+	2.51058e12i	0.0819648	+	0.0819648i
$499$		−	5.11808e12i		−	0.165426i	−0.996573	−	0.0827131i	$-0.973642\pi$
$499$		−	5.11808e12i		−	0.165426i	0.996573	−	0.0827131i	$-0.0263585\pi$
$500$	3.88331e13	−	3.26167e13i	1.24266	−	1.04373i
$501$	3.88902e12			0.123212
$502$	−5.59143e13	+	5.59143e13i	−1.75390	+	1.75390i
$503$	−1.03840e13	−	1.03840e13i	−0.322497	−	0.322497i	0.527227	−	0.849724i	$-0.323232\pi$
$503$	−1.03840e13	−	1.03840e13i	−0.322497	−	0.322497i	−0.849724	+	0.527227i	$0.823232\pi$
$504$			3.80945e13i			1.17141i
$505$	1.24762e13	+	5.26037e13i	0.379862	+	1.60162i
$506$	−5.99108e13			−1.80614
$507$	−1.59007e12	+	1.59007e12i	−0.0474652	+	0.0474652i
$508$	−5.43935e12	−	5.43935e12i	−0.160779	−	0.160779i
$509$		−	2.01882e13i		−	0.590893i	−0.955359	−	0.295447i	$-0.904532\pi$
$509$		−	2.01882e13i		−	0.590893i	0.955359	−	0.295447i	$-0.0954684\pi$
$510$	1.67576e12	+	1.03325e12i	0.0485691	+	0.0299471i
$511$	5.22475e13			1.49955
$512$	5.34740e11	−	5.34740e11i	0.0151982	−	0.0151982i
$513$	−2.38025e12	−	2.38025e12i	−0.0669940	−	0.0669940i
$514$			1.04415e14i			2.91036i
$515$	−2.21407e13	+	3.59085e13i	−0.611161	+	0.991199i
$516$	3.68792e12			0.100817
$517$	3.11014e13	−	3.11014e13i	0.842031	−	0.842031i
$518$	−1.80235e13	−	1.80235e13i	−0.483271	−	0.483271i
$519$		−	3.77647e12i		−	0.100288i
$520$	1.52145e13	−	3.60848e12i	0.400167	−	0.0949090i
$521$	−3.23334e13			−0.842293			−0.421146	−	0.906993i	$-0.638372\pi$
$521$	−3.23334e13			−0.842293			−0.421146	+	0.906993i	$0.638372\pi$
$522$	4.02118e13	−	4.02118e13i	1.03753	−	1.03753i
$523$	−4.70846e13	−	4.70846e13i	−1.20329	−	1.20329i	−0.973160	−	0.230130i	$-0.926085\pi$
$523$	−4.70846e13	−	4.70846e13i	−1.20329	−	1.20329i	−0.230130	−	0.973160i	$-0.573915\pi$
$524$		−	1.31703e12i		−	0.0333380i
$525$	−3.35363e12	+	1.68560e12i	−0.0840851	+	0.0422629i
$526$	6.63883e13			1.64878
$527$	−6.46649e12	+	6.46649e12i	−0.159080	+	0.159080i
$528$	−4.01346e10	−	4.01346e10i	−0.000978023	−	0.000978023i
$529$		−	2.12634e13i		−	0.513280i
$530$	−2.37199e13	−	1.00011e14i	−0.567196	−	2.39148i
$531$	−1.17410e13			−0.278121
$532$	−3.37425e13	+	3.37425e13i	−0.791805	+	0.791805i
$533$	1.57038e13	+	1.57038e13i	0.365063	+	0.365063i
$534$		−	3.27355e12i		−	0.0753899i
$535$	−4.30303e13	−	2.65320e13i	−0.981761	−	0.605342i
$536$	8.43292e12			0.190614
$537$	−6.17231e11	+	6.17231e11i	−0.0138222	+	0.0138222i
$538$	−2.36062e13	−	2.36062e13i	−0.523740	−	0.523740i
$539$			2.66415e13i			0.585618i
$540$	6.27681e12	−	1.01799e13i	0.136701	−	0.221705i
$541$	4.99974e13			1.07885			0.539426	−	0.842033i	$-0.318641\pi$
$541$	4.99974e13			1.07885			0.539426	+	0.842033i	$0.318641\pi$
$542$	6.37125e13	−	6.37125e13i	1.36216	−	1.36216i
$543$	3.16102e12	+	3.16102e12i	0.0669620	+	0.0669620i
$544$		−	2.06672e13i		−	0.433798i
$545$	−7.14553e12	+	1.69473e12i	−0.148611	+	0.0352467i
$546$	−3.01542e12			−0.0621420
$547$	−5.82818e13	+	5.82818e13i	−1.19014	+	1.19014i	−0.213106	+	0.977029i	$0.568358\pi$
$547$	−5.82818e13	+	5.82818e13i	−1.19014	+	1.19014i	−0.977029	+	0.213106i	$0.931642\pi$
$548$	8.43207e13	+	8.43207e13i	1.70621	+	1.70621i
$549$			2.42531e12i			0.0486301i
$550$	−4.09438e13	+	1.23694e14i	−0.813532	+	2.45774i
$551$	2.73397e13			0.538314
$552$	−2.05317e12	+	2.05317e12i	−0.0400617	+	0.0400617i
$553$	−5.32332e13	−	5.32332e13i	−1.02933	−	1.02933i
$554$			3.06685e13i			0.587684i
$555$	3.53215e11	+	1.48927e12i	0.00670771	+	0.0282818i
$556$	−1.36784e14			−2.57431
$557$	−4.26185e13	+	4.26185e13i	−0.794918	+	0.794918i	−0.982289	−	0.187371i	$-0.940003\pi$
$557$	−4.26185e13	+	4.26185e13i	−0.794918	+	0.794918i	0.187371	+	0.982289i	$0.440003\pi$
$558$	3.16413e13	+	3.16413e13i	0.584903	+	0.584903i
$559$		−	1.71727e13i		−	0.314615i
$560$	−5.88895e11	−	3.63106e11i	−0.0106930	−	0.00659315i
$561$	−3.12957e12			−0.0563210
$562$	8.62428e13	−	8.62428e13i	1.53830	−	1.53830i
$563$	5.61683e13	+	5.61683e13i	0.993000	+	0.993000i	0.999976	−	0.00697548i	$-0.00222038\pi$
$563$	5.61683e13	+	5.61683e13i	0.993000	+	0.993000i	−0.00697548	+	0.999976i	$0.502220\pi$
$564$		−	5.55435e12i		−	0.0973281i
$565$	1.88331e13	−	3.05441e13i	0.327099	−	0.530499i
$566$	1.36962e14			2.35785
$567$	4.74975e13	−	4.74975e13i	0.810504	−	0.810504i
$568$	−7.19285e12	−	7.19285e12i	−0.121663	−	0.121663i
$569$			6.58884e12i			0.110471i	0.998473	+	0.0552354i	$0.0175909\pi$
$569$			6.58884e12i			0.110471i	−0.998473	+	0.0552354i	$0.982409\pi$
$570$	4.50616e12	−	1.06874e12i	0.0748914	−	0.0177623i
$571$	−5.37135e13			−0.884917			−0.442459	−	0.896789i	$-0.645894\pi$
$571$	−5.37135e13			−0.884917			−0.442459	+	0.896789i	$0.645894\pi$
$572$	−4.57969e13	+	4.57969e13i	−0.747921	+	0.747921i
$573$	−4.12812e11	−	4.12812e11i	−0.00668312	−	0.00668312i
$574$		−	1.49361e14i		−	2.39705i
$575$	4.16296e13	+	1.37797e13i	0.662312	+	0.219231i
$576$	−1.01804e14			−1.60566
$577$	6.26053e12	−	6.26053e12i	0.0978885	−	0.0978885i	−0.656467	−	0.754355i	$-0.727950\pi$
$577$	6.26053e12	−	6.26053e12i	0.0978885	−	0.0978885i	0.754355	+	0.656467i	$0.227950\pi$
$578$	−5.97290e13	−	5.97290e13i	−0.925862	−	0.925862i
$579$			2.75533e10i			0.000423430i
$580$	2.24156e13	+	9.45114e13i	0.341516	+	1.43994i
$581$	−6.87967e13			−1.03917
$582$	−2.27273e11	+	2.27273e11i	−0.00340355	+	0.00340355i
$583$	1.15537e14	+	1.15537e14i	1.71545	+	1.71545i
$584$		−	8.79023e13i		−	1.29401i
$585$	−2.36242e13	−	1.45664e13i	−0.344808	−	0.212605i
$586$	−1.39693e14			−2.02156
$587$	−1.15834e13	+	1.15834e13i	−0.166205	+	0.166205i	−0.785309	−	0.619104i	$-0.787496\pi$
$587$	−1.15834e13	+	1.15834e13i	−0.166205	+	0.166205i	0.619104	+	0.785309i	$0.287496\pi$
$588$	2.37893e12	+	2.37893e12i	0.0338450	+	0.0338450i
$589$			2.15127e13i			0.303472i
$590$	1.70110e13	−	2.75889e13i	0.237941	−	0.385900i
$591$	−3.57586e10			−0.000495956
$592$	−1.99490e11	+	1.99490e11i	−0.00274355	+	0.00274355i
$593$	−3.57785e13	−	3.57785e13i	−0.487920	−	0.487920i	0.419729	−	0.907649i	$-0.362125\pi$
$593$	−3.57785e13	−	3.57785e13i	−0.487920	−	0.487920i	−0.907649	+	0.419729i	$0.862125\pi$
$594$			3.07267e13i			0.415512i
$595$	−3.71170e13	+	8.80319e12i	−0.497724	+	0.118047i
$596$	1.86551e14			2.48065
$597$	7.31127e12	−	7.31127e12i	0.0964099	−	0.0964099i
$598$	2.49107e13	+	2.49107e13i	0.325746	+	0.325746i
$599$		−	1.02657e14i		−	1.33123i	−0.746295	−	0.665615i	$-0.768169\pi$
$599$		−	1.02657e14i		−	1.33123i	0.746295	−	0.665615i	$-0.231831\pi$
$600$	2.83590e12	+	5.64222e12i	0.0364698	+	0.0725594i
$601$	1.17156e14			1.49415			0.747074	−	0.664741i	$-0.231458\pi$
$601$	1.17156e14			1.49415			0.747074	+	0.664741i	$0.231458\pi$
$602$	−8.16662e13	+	8.16662e13i	−1.03290	+	1.03290i
$603$	−1.05839e13	−	1.05839e13i	−0.132758	−	0.132758i
$604$			5.08930e13i			0.633102i
$605$	−2.90936e13	−	1.22668e14i	−0.358938	−	1.51340i
$606$	−1.75405e13			−0.214624
$607$	−1.79344e13	+	1.79344e13i	−0.217642	+	0.217642i	−0.807504	−	0.589862i	$-0.799182\pi$
$607$	−1.79344e13	+	1.79344e13i	−0.217642	+	0.217642i	0.589862	+	0.807504i	$0.299182\pi$
$608$	−3.43779e13	−	3.43779e13i	−0.413772	−	0.413772i
$609$		−	7.18904e12i		−	0.0858192i
$610$	−5.69897e12	−	3.51391e12i	−0.0674756	−	0.0416046i
$611$	−2.58637e13			−0.303728
$612$	4.28335e13	−	4.28335e13i	0.498915	−	0.498915i
$613$	−2.32799e13	−	2.32799e13i	−0.268954	−	0.268954i	0.559725	−	0.828679i	$-0.310907\pi$
$613$	−2.32799e13	−	2.32799e13i	−0.268954	−	0.268954i	−0.828679	+	0.559725i	$0.810907\pi$
$614$			2.64650e14i			3.03270i
$615$	−4.70723e12	+	7.63432e12i	−0.0535044	+	0.0867750i
$616$	1.67173e14			1.88479
$617$	−4.03449e12	+	4.03449e12i	−0.0451193	+	0.0451193i	−0.729306	−	0.684187i	$-0.760157\pi$
$617$	−4.03449e12	+	4.03449e12i	−0.0451193	+	0.0451193i	0.684187	+	0.729306i	$0.260157\pi$
$618$	−9.67813e12	−	9.67813e12i	−0.107362	−	0.107362i
$619$			1.31538e14i			1.44743i	0.690097	+	0.723717i	$0.257568\pi$
$619$			1.31538e14i			1.44743i	−0.690097	+	0.723717i	$0.742432\pi$
$620$	−7.43679e13	+	1.76381e13i	−0.811759	+	0.192528i
$621$	1.03411e13			0.111972
$622$	1.14328e14	−	1.14328e14i	1.22801	−	1.22801i
$623$	4.48521e13	+	4.48521e13i	0.477906	+	0.477906i
$624$			3.33756e10i			0.000352782i
$625$	5.69004e13	−	7.65330e13i	0.596644	−	0.802506i
$626$	−1.69974e14			−1.76812
$627$	−5.20573e12	+	5.20573e12i	−0.0537209	+	0.0537209i
$628$	−9.83325e13	−	9.83325e13i	−1.00670	−	1.00670i
$629$			1.55556e13i			0.157992i
$630$	4.30751e13	+	1.81618e14i	0.434034	+	1.83002i
$631$	−1.42695e13			−0.142647			−0.0713235	−	0.997453i	$-0.522722\pi$
$631$	−1.42695e13			−0.142647			−0.0713235	+	0.997453i	$0.522722\pi$
$632$	−8.95605e13	+	8.95605e13i	−0.888242	+	0.888242i
$633$	−1.51558e12	−	1.51558e12i	−0.0149128	−	0.0149128i
$634$		−	1.87528e13i		−	0.183071i
$635$	−1.23132e13	−	7.59217e12i	−0.119262	−	0.0735356i
$636$	2.06335e13			0.198284
$637$	1.10774e13	−	1.10774e13i	0.105619	−	0.105619i
$638$	−1.76464e14	−	1.76464e14i	−1.66937	−	1.66937i
$639$			1.80551e13i			0.169471i
$640$	9.16365e13	−	1.48619e14i	0.853432	−	1.38412i
$641$	5.69159e13			0.525949			0.262974	−	0.964803i	$-0.415297\pi$
$641$	5.69159e13			0.525949			0.262974	+	0.964803i	$0.415297\pi$
$642$	1.15976e13	−	1.15976e13i	0.106339	−	0.106339i
$643$	−2.85059e12	−	2.85059e12i	−0.0259346	−	0.0259346i	0.694021	−	0.719955i	$-0.255838\pi$
$643$	−2.85059e12	−	2.85059e12i	−0.0259346	−	0.0259346i	−0.719955	+	0.694021i	$0.755838\pi$
$644$		−	1.46596e14i		−	1.32340i
$645$	6.74800e12	−	1.60045e12i	0.0604472	−	0.0143365i
$646$	4.70675e13			0.418368
$647$	8.20235e13	−	8.20235e13i	0.723464	−	0.723464i	−0.245845	−	0.969309i	$-0.579066\pi$
$647$	8.20235e13	−	8.20235e13i	0.723464	−	0.723464i	0.969309	+	0.245845i	$0.0790655\pi$
$648$	−7.99107e13	−	7.99107e13i	−0.699407	−	0.699407i
$649$			5.15239e13i			0.447492i
$650$	6.84559e13	−	3.44074e13i	0.589989	−	0.296541i
$651$	5.65682e12			0.0483802
$652$	3.27191e13	−	3.27191e13i	0.277692	−	0.277692i
$653$	7.75115e13	+	7.75115e13i	0.652830	+	0.652830i	0.953673	−	0.300844i	$-0.0972682\pi$
$653$	7.75115e13	+	7.75115e13i	0.652830	+	0.652830i	−0.300844	+	0.953673i	$0.597268\pi$
$654$		−	2.38265e12i		−	0.0199146i
$655$	−5.71552e11	−	2.40984e12i	−0.00474077	−	0.0199886i
$656$	−1.65317e12			−0.0136081
$657$	−1.10324e14	+	1.10324e14i	−0.901244	+	0.901244i
$658$	1.22997e14	+	1.22997e14i	0.997160	+	0.997160i
$659$		−	1.61712e14i		−	1.30112i	−0.759456	−	0.650559i	$-0.774535\pi$
$659$		−	1.61712e14i		−	1.30112i	0.759456	−	0.650559i	$-0.225465\pi$
$660$	−2.22640e13	−	1.37277e13i	−0.177780	−	0.109617i
$661$	−1.35594e14			−1.07457			−0.537283	−	0.843402i	$-0.680549\pi$
$661$	−1.35594e14			−1.07457			−0.537283	+	0.843402i	$0.680549\pi$
$662$	−2.05872e14	+	2.05872e14i	−1.61923	+	1.61923i
$663$	1.30126e12	+	1.30126e12i	0.0101578	+	0.0101578i
$664$			1.15745e14i			0.896730i
$665$	−4.70973e13	+	7.63837e13i	−0.362149	+	0.587344i
$666$	7.61155e13			0.580901
$667$	−5.93893e13	+	5.93893e13i	−0.449862	+	0.449862i
$668$	2.33583e14	+	2.33583e14i	1.75614	+	1.75614i
$669$			1.26732e13i			0.0945705i
$670$	4.02045e13	−	9.53545e12i	0.297784	−	0.0706264i
$671$	1.06432e13			0.0782452
$672$	−9.03975e12	+	9.03975e12i	−0.0659645	+	0.0659645i
$673$	8.37535e12	+	8.37535e12i	0.0606635	+	0.0606635i	0.736788	−	0.676124i	$-0.236342\pi$
$673$	8.37535e12	+	8.37535e12i	0.0606635	+	0.0606635i	−0.676124	+	0.736788i	$0.736342\pi$
$674$		−	1.10177e14i		−	0.792123i
$675$	7.06726e12	−	2.13507e13i	0.0504350	−	0.152368i
$676$	−1.91006e14			−1.35305
$677$	−1.97192e12	+	1.97192e12i	−0.0138659	+	0.0138659i	−0.714006	−	0.700140i	$-0.753121\pi$
$677$	−1.97192e12	+	1.97192e12i	−0.0138659	+	0.0138659i	0.700140	+	0.714006i	$0.253121\pi$
$678$	8.23230e12	+	8.23230e12i	0.0574609	+	0.0574609i
$679$		−	6.22788e12i		−	0.0431511i
$680$	1.48107e13	+	6.24465e13i	0.101866	+	0.429500i
$681$	−3.31347e12			−0.0226229
$682$	1.38854e14	−	1.38854e14i	0.941100	−	0.941100i
$683$	−6.19350e13	−	6.19350e13i	−0.416709	−	0.416709i	0.467359	−	0.884068i	$-0.345206\pi$
$683$	−6.19350e13	−	6.19350e13i	−0.416709	−	0.416709i	−0.884068	+	0.467359i	$0.845206\pi$
$684$		−	1.42498e14i		−	0.951765i
$685$	1.90879e14	+	1.17694e14i	1.26563	+	0.780370i
$686$	1.82239e14			1.19955
$687$	−7.27672e12	+	7.27672e12i	−0.0475502	+	0.0475502i
$688$	9.03906e11	+	9.03906e11i	0.00586383	+	0.00586383i
$689$		−	9.60796e13i		−	0.618778i
$690$	−7.46702e12	+	1.21102e13i	−0.0477421	+	0.0774296i
$691$	−1.70456e14			−1.08198			−0.540992	−	0.841028i	$-0.681951\pi$
$691$	−1.70456e14			−1.08198			−0.540992	+	0.841028i	$0.681951\pi$
$692$	2.26824e14	−	2.26824e14i	1.42941	−	1.42941i
$693$	−2.09814e14	−	2.09814e14i	−1.31271	−	1.31271i
$694$		−	2.22090e14i		−	1.37953i
$695$	−2.50281e14	+	5.93601e13i	−1.54349	+	0.366076i
$696$	−1.20950e13			−0.0740558
$697$	−6.44546e13	+	6.44546e13i	−0.391823	+	0.391823i
$698$	1.99069e14	+	1.99069e14i	1.20151	+	1.20151i
$699$			1.58029e13i			0.0947002i
$700$	−3.02668e14	−	1.00185e14i	−1.80084	−	0.596094i
$701$	1.18379e14			0.699333			0.349667	−	0.936874i	$-0.386295\pi$
$701$	1.18379e14			0.699333			0.349667	+	0.936874i	$0.386295\pi$
$702$	1.27760e13	−	1.27760e13i	0.0749394	−	0.0749394i
$703$	2.58752e13	+	2.58752e13i	0.150698	+	0.150698i
$704$			4.46755e14i			2.58348i
$705$	−2.41043e12	−	1.01631e13i	−0.0138404	−	0.0583554i
$706$	−3.71048e14			−2.11547
$707$	2.40328e14	−	2.40328e14i	1.36053	−	1.36053i
$708$	4.60079e12	+	4.60079e12i	0.0258622	+	0.0258622i
$709$			1.42535e14i			0.795592i	0.917474	+	0.397796i	$0.130225\pi$
$709$			1.42535e14i			0.795592i	−0.917474	+	0.397796i	$0.869775\pi$
$710$	−4.24257e13	−	2.61592e13i	−0.235146	−	0.144988i
$711$	2.24810e14			1.23728
$712$	7.54601e13	−	7.54601e13i	0.412399	−	0.412399i
$713$	−4.67315e13	−	4.67315e13i	−0.253608	−	0.253608i
$714$		−	1.23765e13i		−	0.0666972i
$715$	−6.39227e13	+	1.03672e14i	−0.342078	+	0.554792i
$716$	−7.41446e13			−0.394016
$717$	8.70885e11	−	8.70885e11i	0.00459584	−	0.00459584i
$718$	1.25890e13	+	1.25890e13i	0.0659736	+	0.0659736i
$719$		−	1.84844e14i		−	0.961971i	−0.876729	−	0.480985i	$-0.840279\pi$
$719$		−	1.84844e14i		−	0.961971i	0.876729	−	0.480985i	$-0.159721\pi$
$720$	2.01021e12	−	4.76768e11i	0.0103891	−	0.00246402i
$721$	2.65207e14			1.36116
$722$	−1.46384e14	+	1.46384e14i	−0.746116	+	0.746116i
$723$	−9.42307e12	−	9.42307e12i	−0.0476981	−	0.0476981i
$724$			3.79716e14i			1.90883i
$725$	8.20303e13	+	1.63205e14i	0.409528	+	0.814786i
$726$	4.09030e13			0.202802
$727$	1.31222e12	−	1.31222e12i	0.00646154	−	0.00646154i	−0.703869	−	0.710330i	$-0.748546\pi$
$727$	1.31222e12	−	1.31222e12i	0.00646154	−	0.00646154i	0.710330	+	0.703869i	$0.248546\pi$
$728$	−6.95098e13	−	6.95098e13i	−0.339930	−	0.339930i
$729$			1.97927e14i			0.961319i
$730$	−9.93948e13	−	4.19080e14i	−0.479457	−	2.02154i
$731$	7.04838e13			0.337678
$732$	9.50371e11	−	9.50371e11i	0.00452208	−	0.00452208i
$733$	4.75943e13	+	4.75943e13i	0.224923	+	0.224923i	0.810568	−	0.585645i	$-0.199159\pi$
$733$	4.75943e13	+	4.75943e13i	0.224923	+	0.224923i	−0.585645	+	0.810568i	$0.699159\pi$
$734$		−	5.32832e14i		−	2.50098i
$735$	5.38525e12	+	3.32048e12i	0.0251055	+	0.0154797i
$736$	1.49356e14			0.691568
$737$	−4.64461e13	+	4.64461e13i	−0.213605	+	0.213605i
$738$	3.15384e14	+	3.15384e14i	1.44065	+	1.44065i
$739$		−	2.72621e14i		−	1.23691i	−0.785821	−	0.618454i	$-0.787759\pi$
$739$		−	2.72621e14i		−	1.23691i	0.785821	−	0.618454i	$-0.212241\pi$
$740$	−6.82339e13	+	1.10664e14i	−0.307497	+	0.498708i
$741$	4.32904e12			0.0193776
$742$	−4.56914e14	+	4.56914e14i	−2.03149	+	2.03149i
$743$	5.56171e13	+	5.56171e13i	0.245620	+	0.245620i	0.819170	−	0.573550i	$-0.194434\pi$
$743$	5.56171e13	+	5.56171e13i	0.245620	+	0.245620i	−0.573550	+	0.819170i	$0.694434\pi$
$744$		−	9.51715e12i		−	0.0417486i
$745$	3.41343e14	−	8.09575e13i	1.48734	−	0.352757i
$746$	3.89864e13			0.168740
$747$	1.45268e14	−	1.45268e14i	0.624551	−	0.624551i
$748$	−1.87969e14	−	1.87969e14i	−0.802746	−	0.802746i
$749$			3.17806e14i			1.34820i
$750$	1.99002e13	+	2.36930e13i	0.0838594	+	0.0998421i
$751$	−4.10425e14			−1.71804			−0.859022	−	0.511939i	$-0.828928\pi$
$751$	−4.10425e14			−1.71804			−0.859022	+	0.511939i	$0.828928\pi$
$752$	1.36137e12	−	1.36137e12i	0.00566091	−	0.00566091i
$753$	−2.11079e13	−	2.11079e13i	−0.0871905	−	0.0871905i
$754$			1.46746e14i			0.602157i
$755$	2.20861e13	+	9.31219e13i	0.0900293	+	0.379592i
$756$	−7.51851e13			−0.304455
$757$	7.95566e13	−	7.95566e13i	0.320034	−	0.320034i	−0.528746	−	0.848780i	$-0.677338\pi$
$757$	7.95566e13	−	7.95566e13i	0.320034	−	0.320034i	0.848780	+	0.528746i	$0.177338\pi$
$758$	−5.35833e14	−	5.35833e14i	−2.14133	−	2.14133i
$759$		−	2.26166e13i		−	0.0897878i
$760$	1.28510e14	+	7.92374e13i	0.506836	+	0.312509i
$761$	−3.44180e14			−1.34854			−0.674268	−	0.738487i	$-0.735541\pi$
$761$	−3.44180e14			−1.34854			−0.674268	+	0.738487i	$0.735541\pi$
$762$	3.31868e12	−	3.31868e12i	0.0129179	−	0.0129179i
$763$	3.26455e13	+	3.26455e13i	0.126241	+	0.126241i
$764$		−	4.95888e13i		−	0.190510i
$765$	5.97864e13	−	9.69633e13i	0.228189	−	0.370084i
$766$	3.75507e14			1.42388
$767$	2.14235e13	−	2.14235e13i	0.0807073	−	0.0807073i
$768$	1.54739e13	+	1.54739e13i	0.0579155	+	0.0579155i
$769$		−	1.60436e14i		−	0.596581i	−0.954475	−	0.298291i	$-0.903584\pi$
$769$		−	1.60436e14i		−	0.596581i	0.954475	−	0.298291i	$-0.0964165\pi$
$770$	7.97008e14	−	1.89029e14i	2.94448	−	0.698354i
$771$	−3.94170e13			−0.144681
$772$	−1.65492e12	+	1.65492e12i	−0.00603517	+	0.00603517i
$773$	−2.73906e14	−	2.73906e14i	−0.992438	−	0.992438i	0.00753359	−	0.999972i	$-0.497602\pi$
$773$	−2.73906e14	−	2.73906e14i	−0.992438	−	0.992438i	−0.999972	+	0.00753359i	$0.997602\pi$
$774$		−	3.44886e14i		−	1.24157i
$775$	−1.28421e14	+	6.45469e13i	−0.459332	+	0.230870i
$776$	−1.04779e13			−0.0372363
$777$	6.80395e12	−	6.80395e12i	0.0240246	−	0.0240246i
$778$	3.61177e14	+	3.61177e14i	1.26713	+	1.26713i
$779$			2.14428e14i			0.747469i
$780$	3.54935e12	+	1.49652e13i	0.0122935	+	0.0518334i
$781$	7.92324e13			0.272677
$782$	−1.02244e14	+	1.02244e14i	−0.349625	+	0.349625i
$783$	3.04592e13	+	3.04592e13i	0.103493	+	0.103493i
$784$			1.16615e12i			0.00393707i
$785$	−2.22598e14	−	1.37251e14i	−0.746746	−	0.460434i
$786$	8.03552e11			0.00267856
$787$	−1.39152e14	+	1.39152e14i	−0.460908	+	0.460908i	−0.898953	−	0.438045i	$-0.855671\pi$
$787$	−1.39152e14	+	1.39152e14i	−0.460908	+	0.460908i	0.438045	+	0.898953i	$0.355671\pi$
$788$	−2.14774e12	−	2.14774e12i	−0.00706888	−	0.00706888i
$789$			2.50618e13i			0.0819649i
$790$	−3.25716e14	+	5.28256e14i	−1.05853	+	1.71676i
$791$	−2.25587e14			−0.728504
$792$	−3.52995e14	+	3.52995e14i	−1.13277	+	1.13277i
$793$	−4.42538e12	−	4.42538e12i	−0.0141119	−	0.0141119i
$794$			6.77923e14i			2.14822i
$795$	3.77543e13	−	8.95434e12i	0.118886	−	0.0281967i
$796$	8.78263e14			2.74827
$797$	−1.18040e14	+	1.18040e14i	−0.367059	+	0.367059i	−0.866404	−	0.499345i	$-0.833574\pi$
$797$	−1.18040e14	+	1.18040e14i	−0.367059	+	0.367059i	0.499345	+	0.866404i	$0.333574\pi$
$798$	−2.05871e13	−	2.05871e13i	−0.0636181	−	0.0636181i
$799$		−	1.06155e14i		−	0.325992i
$800$	1.02072e14	−	3.08368e14i	0.311499	−	0.941063i
$801$	−1.89416e14			−0.574452
$802$	3.90059e14	−	3.90059e14i	1.17560	−	1.17560i
$803$	4.84141e14	+	4.84141e14i	1.45009	+	1.45009i
$804$			8.29474e12i			0.0246901i
$805$	−6.36182e13	−	2.68235e14i	−0.188192	−	0.793479i
$806$	−1.15470e14			−0.339463
$807$	8.91144e12	−	8.91144e12i	0.0260364	−	0.0260364i
$808$	−4.04333e14	−	4.04333e14i	−1.17404	−	1.17404i
$809$			4.81372e14i			1.38911i	0.719437	+	0.694557i	$0.244400\pi$
$809$			4.81372e14i			1.38911i	−0.719437	+	0.694557i	$0.755600\pi$
$810$	−4.71338e14	−	2.90621e14i	−1.35178	−	0.833494i
$811$	1.03601e14			0.295298			0.147649	−	0.989040i	$-0.452829\pi$
$811$	1.03601e14			0.295298			0.147649	+	0.989040i	$0.452829\pi$
$812$	4.31790e14	−	4.31790e14i	1.22319	−	1.22319i
$813$	2.40517e13	+	2.40517e13i	0.0677163	+	0.0677163i
$814$		−	3.34023e14i		−	0.934661i
$815$	4.56689e13	−	7.40671e13i	0.127008	−	0.205986i
$816$	−1.36987e11			−0.000378642
$817$	1.17243e14	−	1.17243e14i	0.322089	−	0.322089i
$818$	−1.31262e14	−	1.31262e14i	−0.358403	−	0.358403i
$819$			1.74480e14i			0.473506i
$820$	−7.41261e14	+	1.75808e14i	−1.99941	+	0.474208i
$821$	2.44974e14			0.656756			0.328378	−	0.944546i	$-0.393498\pi$
$821$	2.44974e14			0.656756			0.328378	+	0.944546i	$0.393498\pi$
$822$	−5.14461e13	+	5.14461e13i	−0.137086	+	0.137086i
$823$	−3.59716e14	−	3.59716e14i	−0.952708	−	0.952708i	0.0462228	−	0.998931i	$-0.485282\pi$
$823$	−3.59716e14	−	3.59716e14i	−0.952708	−	0.952708i	−0.998931	+	0.0462228i	$0.985282\pi$
$824$		−	4.46190e14i		−	1.17458i
$825$	−4.66951e13	−	1.54564e13i	−0.122180	−	0.0404427i
$826$	−2.03762e14			−0.529935
$827$	4.05136e14	−	4.05136e14i	1.04731	−	1.04731i	0.0484810	−	0.998824i	$-0.484562\pi$
$827$	4.05136e14	−	4.05136e14i	1.04731	−	1.04731i	0.998824	−	0.0484810i	$-0.0154380\pi$
$828$	3.09546e14	+	3.09546e14i	0.795378	+	0.795378i
$829$		−	5.36295e14i		−	1.36972i	−0.728676	−	0.684859i	$-0.759864\pi$
$829$		−	5.36295e14i		−	1.36972i	0.728676	−	0.684859i	$-0.240136\pi$
$830$	1.30878e14	+	5.51822e14i	0.332258	+	1.40091i
$831$	−1.15775e13			−0.0292152
$832$	1.85759e14	−	1.85759e14i	0.465943	−	0.465943i
$833$	4.54663e13	+	4.54663e13i	0.113361	+	0.113361i
$834$		−	8.34552e13i		−	0.206834i
$835$	5.28769e14	+	3.26033e14i	1.30267	+	0.803209i
$836$	−6.25335e14			−1.53138
$837$	−2.39674e13	+	2.39674e13i	−0.0583436	+	0.0583436i
$838$	3.97538e14	+	3.97538e14i	0.961964	+	0.961964i
$839$			5.11610e14i			1.23063i	0.788280	+	0.615317i	$0.210972\pi$
$839$			5.11610e14i			1.23063i	−0.788280	+	0.615317i	$0.789028\pi$
$840$	2.08357e13	−	3.37919e13i	0.0498209	−	0.0808009i
$841$	7.08512e13			0.168410
$842$	−2.43564e14	+	2.43564e14i	−0.575510	+	0.575510i
$843$	3.25570e13	+	3.25570e13i	0.0764727	+	0.0764727i
$844$		−	1.82058e14i		−	0.425106i
$845$	−3.49494e14	+	8.28909e13i	−0.811253	+	0.192408i
$846$	−5.19431e14			−1.19860
$847$	−5.60427e14	+	5.60427e14i	−1.28559	+	1.28559i
$848$	5.05726e12	+	5.05726e12i	0.0115328	+	0.0115328i
$849$			5.17035e13i			0.117215i
$850$	1.41222e14	+	2.80971e14i	0.318278	+	0.633237i
$851$	−1.12416e14			−0.251873
$852$	7.07499e12	−	7.07499e12i	0.0157590	−	0.0157590i
$853$	1.21410e14	+	1.21410e14i	0.268850	+	0.268850i	0.828637	−	0.559787i	$-0.189117\pi$
$853$	1.21410e14	+	1.21410e14i	0.268850	+	0.268850i	−0.559787	+	0.828637i	$0.689117\pi$
$854$			4.20905e13i			0.0926605i
$855$	−6.18401e13	−	2.60737e14i	−0.135344	−	0.570654i
$856$	5.34684e14			1.16340
$857$	4.36699e14	−	4.36699e14i	0.944666	−	0.944666i	−0.0538810	−	0.998547i	$-0.517159\pi$
$857$	4.36699e14	−	4.36699e14i	0.944666	−	0.944666i	0.998547	+	0.0538810i	$0.0171592\pi$
$858$	−2.79418e13	−	2.79418e13i	−0.0600922	−	0.0600922i
$859$		−	4.90000e14i		−	1.04768i	−0.851816	−	0.523841i	$-0.824498\pi$
$859$		−	4.90000e14i		−	1.04768i	0.851816	−	0.523841i	$-0.175502\pi$
$860$	5.01426e14	+	3.09173e14i	1.06590	+	0.657219i
$861$	5.63843e13			0.119163
$862$	−1.03326e14	+	1.03326e14i	−0.217107	+	0.217107i
$863$	5.28821e14	+	5.28821e14i	1.10473	+	1.10473i	0.993832	+	0.110894i	$0.0353714\pi$
$863$	5.28821e14	+	5.28821e14i	1.10473	+	1.10473i	0.110894	+	0.993832i	$0.464629\pi$
$864$		−	7.66010e13i		−	0.159098i
$865$	3.16597e14	−	5.13467e14i	0.653772	−	1.06031i
$866$	−4.06965e14			−0.835541
$867$	2.25479e13	−	2.25479e13i	0.0460268	−	0.0460268i
$868$	3.39761e14	+	3.39761e14i	0.689565	+	0.689565i
$869$		−	9.86549e14i		−	1.99076i
$870$	−5.76637e13	+	1.36763e13i	−0.115693	+	0.0274393i
$871$	3.86243e13			0.0770494
$872$	5.49234e13	−	5.49234e13i	0.108937	−	0.108937i
$873$	1.31506e13	+	1.31506e13i	0.0259342	+	0.0259342i
$874$			3.40144e14i			0.666969i
$875$	−5.97286e14	−	5.19661e13i	−1.16451	−	0.101317i
$876$	8.64620e13			0.167612
$877$	−5.69872e14	+	5.69872e14i	−1.09845	+	1.09845i	−0.103855	+	0.994592i	$0.533118\pi$
$877$	−5.69872e14	+	5.69872e14i	−1.09845	+	1.09845i	−0.994592	+	0.103855i	$0.966882\pi$
$878$	−6.02604e14	−	6.02604e14i	−1.15494	−	1.15494i
$879$		−	5.27346e13i		−	0.100497i
$880$	−2.09224e12	−	8.82153e12i	−0.00396458	−	0.0167159i
$881$	−2.09263e14			−0.394287			−0.197143	−	0.980375i	$-0.563166\pi$
$881$	−2.09263e14			−0.394287			−0.197143	+	0.980375i	$0.563166\pi$
$882$	2.22472e14	−	2.22472e14i	0.416805	−	0.416805i
$883$	−9.20423e13	−	9.20423e13i	−0.171468	−	0.171468i	0.616156	−	0.787624i	$-0.288689\pi$
$883$	−9.20423e13	−	9.20423e13i	−0.171468	−	0.171468i	−0.787624	+	0.616156i	$0.788689\pi$
$884$			1.56314e14i			0.289558i
$885$	1.04149e13	+	6.42172e12i	0.0191840	+	0.0118286i
$886$	4.10299e14			0.751505
$887$	−6.09121e14	+	6.09121e14i	−1.10939	+	1.10939i	−0.116164	+	0.993230i	$0.537060\pi$
$887$	−6.09121e14	+	6.09121e14i	−1.10939	+	1.10939i	−0.993230	+	0.116164i	$0.962940\pi$
$888$	−1.14471e13	−	1.14471e13i	−0.0207315	−	0.0207315i
$889$			9.09409e13i			0.163776i
$890$	2.74435e14	−	4.45087e14i	0.491462	−	0.797067i
$891$	8.80251e14			1.56754
$892$	−7.61181e14	+	7.61181e14i	−1.34792	+	1.34792i
$893$	−1.76579e14	−	1.76579e14i	−0.310943	−	0.310943i
$894$			1.13819e14i			0.199309i
$895$	−1.35667e14	+	3.21766e13i	−0.236242	+	0.0560305i
$896$	−1.09764e15			−1.90074
$897$	−9.40388e12	+	9.40388e12i	−0.0161936	+	0.0161936i
$898$	−4.93889e14	−	4.93889e14i	−0.845762	−	0.845762i
$899$		−	2.75290e14i		−	0.468805i
$900$	8.50649e14	−	4.27554e14i	1.44058	−	0.724066i
$901$	3.94350e14			0.664137
$902$	1.38402e15	−	1.38402e15i	2.31798	−	2.31798i
$903$	−3.08293e13	−	3.08293e13i	−0.0513481	−	0.0513481i
$904$			3.79533e14i			0.628647i
$905$	1.64786e14	+	6.94788e14i	0.271442	+	1.14448i
$906$	−3.10511e13			−0.0508670
$907$	7.00814e14	−	7.00814e14i	1.14174	−	1.14174i	0.153606	−	0.988132i	$-0.450911\pi$
$907$	7.00814e14	−	7.00814e14i	1.14174	−	1.14174i	0.988132	−	0.153606i	$-0.0490887\pi$
$908$	−1.99015e14	−	1.99015e14i	−0.322445	−	0.322445i
$909$			1.01493e15i			1.63538i
$910$	−4.09991e14	−	2.52795e14i	−0.657002	−	0.405100i
$911$	4.90813e14			0.782211			0.391105	−	0.920346i	$-0.372093\pi$
$911$	4.90813e14			0.782211			0.391105	+	0.920346i	$0.372093\pi$
$912$	−2.27864e11	+	2.27864e11i	−0.000361162	+	0.000361162i
$913$	−6.37491e14	−	6.37491e14i	−1.00489	−	1.00489i
$914$			1.14228e15i			1.79077i
$915$	1.32652e12	−	2.15138e12i	0.00206827	−	0.00335438i
$916$	−8.74113e14			−1.35547
$917$	−1.10097e13	+	1.10097e13i	−0.0169797	+	0.0169797i
$918$	5.24380e13	+	5.24380e13i	0.0804327	+	0.0804327i
$919$			7.23898e14i			1.10433i	0.833734	+	0.552166i	$0.186199\pi$
$919$			7.23898e14i			1.10433i	−0.833734	+	0.552166i	$0.813801\pi$
$920$	−4.51284e14	+	1.07033e14i	−0.684716	+	0.162397i
$921$	−9.99063e13			−0.150763
$922$	5.69786e14	−	5.69786e14i	0.855179	−	0.855179i
$923$	−3.29446e13	−	3.29446e13i	−0.0491785	−	0.0491785i
$924$			1.64434e14i			0.244135i
$925$	−7.68266e13	+	2.32099e14i	−0.113450	+	0.342740i
$926$	1.97398e15			2.89927
$927$	−5.60000e14	+	5.60000e14i	−0.818068	+	0.818068i
$928$	4.39921e14	+	4.39921e14i	0.639197	+	0.639197i
$929$		−	7.27356e14i		−	1.05116i	−0.850745	−	0.525579i	$-0.823849\pi$
$929$		−	7.27356e14i		−	1.05116i	0.850745	−	0.525579i	$-0.176151\pi$
$930$	−1.07614e13	−	4.53737e13i	−0.0154688	−	0.0652213i
$931$	1.51257e14			0.216256
$932$	−9.49157e14	+	9.49157e14i	−1.34977	+	1.34977i
$933$	4.31594e13	+	4.31594e13i	0.0610474	+	0.0610474i
$934$			9.44647e14i			1.32903i
$935$	−4.25511e14	−	2.62365e14i	−0.595460	−	0.367153i
$936$	2.93548e14			0.408602
$937$	−6.59549e14	+	6.59549e14i	−0.913164	+	0.913164i	−0.996520	−	0.0833556i	$-0.973436\pi$
$937$	−6.59549e14	+	6.59549e14i	−0.913164	+	0.913164i	0.0833556	+	0.996520i	$0.473436\pi$
$938$	−1.83681e14	−	1.83681e14i	−0.252958	−	0.252958i
$939$		−	6.41659e13i		−	0.0878975i
$940$	4.65644e14	−	7.55195e14i	0.634476	−	1.02901i
$941$	3.48623e14			0.472507			0.236253	−	0.971691i	$-0.424080\pi$
$941$	3.48623e14			0.472507			0.236253	+	0.971691i	$0.424080\pi$
$942$	5.99950e13	−	5.99950e13i	0.0808837	−	0.0808837i
$943$	−4.65796e14	−	4.65796e14i	−0.624651	−	0.624651i
$944$			2.25530e12i			0.00300846i
$945$	−1.37571e14	+	3.26281e13i	−0.182543	+	0.0432945i
$946$	−1.51349e15			−1.99767
$947$	1.70857e14	−	1.70857e14i	0.224328	−	0.224328i	−0.585990	−	0.810318i	$-0.699294\pi$
$947$	1.70857e14	−	1.70857e14i	0.224328	−	0.224328i	0.810318	+	0.585990i	$0.199294\pi$
$948$	−8.80930e13	−	8.80930e13i	−0.115054	−	0.115054i
$949$		−	4.02608e14i		−	0.523060i
$950$	7.02275e14	+	2.32459e14i	0.907589	+	0.300419i
$951$	7.07924e12			0.00910089
$952$	2.85297e14	−	2.85297e14i	0.364848	−	0.364848i
$953$	9.70810e14	+	9.70810e14i	1.23501	+	1.23501i	0.962017	+	0.272991i	$0.0880129\pi$
$953$	9.70810e14	+	9.70810e14i	1.23501	+	1.23501i	0.272991	+	0.962017i	$0.411987\pi$
$954$		−	1.92960e15i		−	2.44189i
$955$	−2.15201e13	−	9.07355e13i	−0.0270911	−	0.114225i
$956$	1.04615e14			0.131010
$957$	6.66158e13	−	6.66158e13i	0.0829884	−	0.0829884i
$958$	−1.73615e14	−	1.73615e14i	−0.215158	−	0.215158i
$959$		−	1.40976e15i		−	1.73801i
$960$	9.03059e13	+	5.56815e13i	0.110754	+	0.0682897i
$961$	−6.03011e14			−0.735713
$962$	−1.38885e14	+	1.38885e14i	−0.168570	+	0.168570i
$963$	−6.71067e14	−	6.71067e14i	−0.810279	−	0.810279i
$964$		−	1.13194e15i		−	1.35969i
$965$	−2.30991e12	+	3.74628e12i	−0.00276031	+	0.00447676i
$966$	8.94417e13			0.106330
$967$	7.75125e13	−	7.75125e13i	0.0916726	−	0.0916726i	−0.659783	−	0.751456i	$-0.729352\pi$
$967$	7.75125e13	−	7.75125e13i	0.0916726	−	0.0916726i	0.751456	+	0.659783i	$0.229352\pi$
$968$	9.42873e14	+	9.42873e14i	1.10937	+	1.10937i
$969$			1.77681e13i			0.0207981i
$970$	−4.99542e13	+	1.18478e13i	−0.0581719	+	0.0137969i
$971$	−9.14038e14			−1.05893			−0.529466	−	0.848331i	$-0.677608\pi$
$971$	−9.14038e14			−1.05893			−0.529466	+	0.848331i	$0.677608\pi$
$972$	2.38395e14	−	2.38395e14i	0.274768	−	0.274768i
$973$	1.14345e15	+	1.14345e15i	1.31115	+	1.31115i
$974$			8.90984e14i			1.01642i
$975$	1.29889e13	+	2.58424e13i	0.0147418	+	0.0293298i
$976$	4.65870e11			0.000526037
$977$	1.38081e14	−	1.38081e14i	0.155117	−	0.155117i	−0.625282	−	0.780399i	$-0.715016\pi$
$977$	1.38081e14	−	1.38081e14i	0.155117	−	0.155117i	0.780399	+	0.625282i	$0.215016\pi$
$978$	1.99627e13	+	1.99627e13i	0.0223113	+	0.0223113i
$979$			8.31226e14i			0.924285i
$980$	1.24015e14	+	5.22885e14i	0.137196	+	0.578464i
$981$	−1.37866e14			−0.151744
$982$	−4.70354e14	+	4.70354e14i	−0.515072	+	0.515072i
$983$	−2.93684e14	−	2.93684e14i	−0.319973	−	0.319973i	0.528784	−	0.848757i	$-0.322648\pi$
$983$	−2.93684e14	−	2.93684e14i	−0.319973	−	0.319973i	−0.848757	+	0.528784i	$0.822648\pi$
$984$		−	9.48621e13i		−	0.102829i
$985$	−4.86190e12	−	2.99779e12i	−0.00524354	−	0.00323310i
$986$	−6.02305e14			−0.646297
$987$	−4.64318e13	+	4.64318e13i	−0.0495712	+	0.0495712i
$988$	2.60012e14	+	2.60012e14i	0.276191	+	0.276191i
$989$			5.09367e14i			0.538331i
$990$	−1.28378e15	+	2.08208e15i	−1.34994	+	2.18938i
$991$	−4.64216e14			−0.485681			−0.242841	−	0.970066i	$-0.578079\pi$
$991$	−4.64216e14			−0.485681			−0.242841	+	0.970066i	$0.578079\pi$
$992$	−3.46160e14	+	3.46160e14i	−0.360345	+	0.360345i
$993$	−7.77176e13	−	7.77176e13i	−0.0804958	−	0.0804958i
$994$			3.13341e14i			0.322912i
$995$	1.60701e15	−	3.81140e14i	1.64779	−	0.390813i
$996$	−1.13848e14			−0.116153
$997$	1.05741e15	−	1.05741e15i	1.07341	−	1.07341i	0.0763320	−	0.997082i	$-0.475679\pi$
$997$	1.05741e15	−	1.05741e15i	1.07341	−	1.07341i	0.997082	−	0.0763320i	$-0.0243209\pi$
$998$	1.87554e14	+	1.87554e14i	0.189441	+	0.189441i
$999$			5.76553e13i			0.0579444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.11.c.a.3.1	yes	8
3.2	odd	2		45.11.g.a.28.4		8
4.3	odd	2		80.11.p.d.33.3		8
5.2	odd	4	inner	5.11.c.a.2.1	✓	8
5.3	odd	4		25.11.c.a.7.4		8
5.4	even	2		25.11.c.a.18.4		8
15.2	even	4		45.11.g.a.37.4		8
20.7	even	4		80.11.p.d.17.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.11.c.a.2.1	✓	8	5.2	odd	4	inner
5.11.c.a.3.1	yes	8	1.1	even	1	trivial
25.11.c.a.7.4		8	5.3	odd	4
25.11.c.a.18.4		8	5.4	even	2
45.11.g.a.28.4		8	3.2	odd	2
45.11.g.a.37.4		8	15.2	even	4
80.11.p.d.17.3		8	20.7	even	4
80.11.p.d.33.3		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-36.6454 + 36.6454i) q^{2} +(-13.8338 - 13.8338i) q^{3} -1661.78i q^{4} +(-721.162 - 3040.65i) q^{5} +1013.89 q^{6} +(-13891.7 + 13891.7i) q^{7} +(23371.7 + 23371.7i) q^{8} -58666.3i q^{9} +O(q^{10})\)	\(q+(-36.6454 + 36.6454i) q^{2} +(-13.8338 - 13.8338i) q^{3} -1661.78i q^{4} +(-721.162 - 3040.65i) q^{5} +1013.89 q^{6} +(-13891.7 + 13891.7i) q^{7} +(23371.7 + 23371.7i) q^{8} -58666.3i q^{9} +(137853. + 84998.7i) q^{10} -257449. q^{11} +(-22988.7 + 22988.7i) q^{12} +(107046. + 107046. i) q^{13} -1.01813e6i q^{14} +(-32087.3 + 52040.1i) q^{15} -11269.0 q^{16} +(-439362. + 439362. i) q^{17} +(2.14985e6 + 2.14985e6i) q^{18} +1.46167e6i q^{19} +(-5.05288e6 + 1.19841e6i) q^{20} +384349. q^{21} +(9.43434e6 - 9.43434e6i) q^{22} +(-3.17515e6 - 3.17515e6i) q^{23} -646637. i q^{24} +(-8.72547e6 + 4.38560e6i) q^{25} -7.84552e6 q^{26} +(-1.62845e6 + 1.62845e6i) q^{27} +(2.30849e7 + 2.30849e7i) q^{28} -1.87044e7i q^{29} +(-731180. - 3.08289e6i) q^{30} +1.47179e7 q^{31} +(-2.35196e7 + 2.35196e7i) q^{32} +(3.56150e6 + 3.56150e6i) q^{33} -3.22012e7i q^{34} +(5.22579e7 + 3.22216e7i) q^{35} -9.74903e7 q^{36} +(1.77025e7 - 1.77025e7i) q^{37} +(-5.35635e7 - 5.35635e7i) q^{38} -2.96171e6i q^{39} +(5.42103e7 - 8.79198e7i) q^{40} +1.46701e8 q^{41} +(-1.40847e7 + 1.40847e7i) q^{42} +(-8.02116e7 - 8.02116e7i) q^{43} +4.27823e8i q^{44} +(-1.78384e8 + 4.23079e7i) q^{45} +2.32709e8 q^{46} +(-1.20806e8 + 1.20806e8i) q^{47} +(155893. + 155893. i) q^{48} -1.03483e8i q^{49} +(1.59037e8 - 4.80461e8i) q^{50} +1.21561e7 q^{51} +(1.77887e8 - 1.77887e8i) q^{52} +(-4.48776e8 - 4.48776e8i) q^{53} -1.19350e8i q^{54} +(1.85663e8 + 7.82812e8i) q^{55} -6.49343e8 q^{56} +(2.02204e7 - 2.02204e7i) q^{57} +(6.85433e8 + 6.85433e8i) q^{58} -2.00133e8i q^{59} +(8.64791e7 + 5.33220e7i) q^{60} -4.13408e7 q^{61} +(-5.39344e8 + 5.39344e8i) q^{62} +(8.14973e8 + 8.14973e8i) q^{63} -1.73531e9i q^{64} +(2.48293e8 - 4.02688e8i) q^{65} -2.61025e8 q^{66} +(1.80409e8 - 1.80409e8i) q^{67} +(7.30121e8 + 7.30121e8i) q^{68} +8.78486e7i q^{69} +(-3.09579e9 + 7.34240e8i) q^{70} -3.07760e8 q^{71} +(1.37113e9 - 1.37113e9i) q^{72} +(-1.88053e9 - 1.88053e9i) q^{73} +1.29743e9i q^{74} +(1.81376e8 + 6.00369e7i) q^{75} +2.42897e9 q^{76} +(3.57640e9 - 3.57640e9i) q^{77} +(1.08533e8 + 1.08533e8i) q^{78} +3.83202e9i q^{79} +(8.12679e6 + 3.42651e7i) q^{80} -3.41913e9 q^{81} +(-5.37591e9 + 5.37591e9i) q^{82} +(2.47618e9 + 2.47618e9i) q^{83} -6.38703e8i q^{84} +(1.65280e9 + 1.01909e9i) q^{85} +5.87878e9 q^{86} +(-2.58753e8 + 2.58753e8i) q^{87} +(-6.01701e9 - 6.01701e9i) q^{88} -3.22870e9i q^{89} +(4.98655e9 - 8.08734e9i) q^{90} -2.97411e9 q^{91} +(-5.27639e9 + 5.27639e9i) q^{92} +(-2.03605e8 - 2.03605e8i) q^{93} -8.85400e9i q^{94} +(4.44442e9 - 1.05410e9i) q^{95} +6.50731e8 q^{96} +(-2.24159e8 + 2.24159e8i) q^{97} +(3.79216e9 + 3.79216e9i) q^{98} +1.51036e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 30 q^{2} + 60 q^{3} - 5340 q^{5} + 17016 q^{6} - 14500 q^{7} + 22020 q^{8}+O(q^{10}) \) 8 * q + 30 * q^2 + 60 * q^3 - 5340 * q^5 + 17016 * q^6 - 14500 * q^7 + 22020 * q^8	\( 8 q + 30 q^{2} + 60 q^{3} - 5340 q^{5} + 17016 q^{6} - 14500 q^{7} + 22020 q^{8} - 161290 q^{10} - 233784 q^{11} + 863160 q^{12} + 433520 q^{13} - 3188580 q^{15} - 1193992 q^{16} + 1045440 q^{17} + 12804210 q^{18} - 16739820 q^{20} - 20777784 q^{21} + 25939360 q^{22} + 24737580 q^{23} - 35382400 q^{25} - 34440684 q^{26} + 27386640 q^{27} + 89876920 q^{28} - 115784880 q^{30} + 258616 q^{31} - 11664120 q^{32} + 11269320 q^{33} + 113638860 q^{35} + 66085308 q^{36} + 92216120 q^{37} - 435848520 q^{38} + 432590700 q^{40} + 115357416 q^{41} - 609152160 q^{42} - 262653700 q^{43} + 593742420 q^{45} + 1023085816 q^{46} - 669481140 q^{47} - 618046320 q^{48} + 944762850 q^{50} - 768258984 q^{51} - 70856500 q^{52} - 1321976040 q^{53} + 2597320 q^{55} + 852915600 q^{56} + 2367269280 q^{57} + 2687784720 q^{58} - 4237774440 q^{60} - 3143200184 q^{61} - 1373690040 q^{62} + 2578662540 q^{63} - 1924527480 q^{65} + 766734432 q^{66} + 4912566140 q^{67} + 6614874660 q^{68} - 8299690440 q^{70} - 4375053384 q^{71} + 808889220 q^{72} - 786968920 q^{73} + 5379002700 q^{75} - 5577898800 q^{76} + 7522045800 q^{77} + 4109901000 q^{78} + 47717760 q^{80} - 2499208992 q^{81} - 19442731040 q^{82} - 11064240660 q^{83} + 15814282160 q^{85} + 36286046616 q^{86} + 2020273920 q^{87} - 13252572960 q^{88} + 9489047670 q^{90} - 12917794184 q^{91} - 25757138760 q^{92} - 40141724280 q^{93} + 14671558800 q^{95} + 38082222816 q^{96} + 24688294760 q^{97} + 13744332030 q^{98}+O(q^{100}) \) 8 * q + 30 * q^2 + 60 * q^3 - 5340 * q^5 + 17016 * q^6 - 14500 * q^7 + 22020 * q^8 - 161290 * q^10 - 233784 * q^11 + 863160 * q^12 + 433520 * q^13 - 3188580 * q^15 - 1193992 * q^16 + 1045440 * q^17 + 12804210 * q^18 - 16739820 * q^20 - 20777784 * q^21 + 25939360 * q^22 + 24737580 * q^23 - 35382400 * q^25 - 34440684 * q^26 + 27386640 * q^27 + 89876920 * q^28 - 115784880 * q^30 + 258616 * q^31 - 11664120 * q^32 + 11269320 * q^33 + 113638860 * q^35 + 66085308 * q^36 + 92216120 * q^37 - 435848520 * q^38 + 432590700 * q^40 + 115357416 * q^41 - 609152160 * q^42 - 262653700 * q^43 + 593742420 * q^45 + 1023085816 * q^46 - 669481140 * q^47 - 618046320 * q^48 + 944762850 * q^50 - 768258984 * q^51 - 70856500 * q^52 - 1321976040 * q^53 + 2597320 * q^55 + 852915600 * q^56 + 2367269280 * q^57 + 2687784720 * q^58 - 4237774440 * q^60 - 3143200184 * q^61 - 1373690040 * q^62 + 2578662540 * q^63 - 1924527480 * q^65 + 766734432 * q^66 + 4912566140 * q^67 + 6614874660 * q^68 - 8299690440 * q^70 - 4375053384 * q^71 + 808889220 * q^72 - 786968920 * q^73 + 5379002700 * q^75 - 5577898800 * q^76 + 7522045800 * q^77 + 4109901000 * q^78 + 47717760 * q^80 - 2499208992 * q^81 - 19442731040 * q^82 - 11064240660 * q^83 + 15814282160 * q^85 + 36286046616 * q^86 + 2020273920 * q^87 - 13252572960 * q^88 + 9489047670 * q^90 - 12917794184 * q^91 - 25757138760 * q^92 - 40141724280 * q^93 + 14671558800 * q^95 + 38082222816 * q^96 + 24688294760 * q^97 + 13744332030 * q^98

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