LMFDB - Embedded newform 5.11.c.a.2.2

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			2.2
Root			$-0.855727i$ of defining polynomial
Character	$\chi$	$=$	5.2
Dual form			5.11.c.a.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.63382 - 4.63382i) q^{2} +(70.6389 - 70.6389i) q^{3} -981.055i q^{4} +(1004.90 - 2959.02i) q^{5} -654.656 q^{6} +(2611.74 + 2611.74i) q^{7} +(-9291.07 + 9291.07i) q^{8} +49069.3i q^{9} +O(q^{10})$	\(q+(-4.63382 - 4.63382i) q^{2} +(70.6389 - 70.6389i) q^{3} -981.055i q^{4} +(1004.90 - 2959.02i) q^{5} -654.656 q^{6} +(2611.74 + 2611.74i) q^{7} +(-9291.07 + 9291.07i) q^{8} +49069.3i q^{9} +(-18368.1 + 9055.08i) q^{10} +15694.7 q^{11} +(-69300.6 - 69300.6i) q^{12} +(294351. - 294351. i) q^{13} -24204.7i q^{14} +(-138037. - 280007. i) q^{15} -918494. q^{16} +(1.23520e6 + 1.23520e6i) q^{17} +(227379. - 227379. i) q^{18} +2.66159e6i q^{19} +(-2.90296e6 - 985859. i) q^{20} +368981. q^{21} +(-72726.7 - 72726.7i) q^{22} +(7.36638e6 - 7.36638e6i) q^{23} +1.31262e6i q^{24} +(-7.74599e6 - 5.94702e6i) q^{25} -2.72795e6 q^{26} +(7.63735e6 + 7.63735e6i) q^{27} +(2.56226e6 - 2.56226e6i) q^{28} +1.66720e7i q^{29} +(-657861. + 1.93714e6i) q^{30} -2.74330e7 q^{31} +(1.37702e7 + 1.37702e7i) q^{32} +(1.10866e6 - 1.10866e6i) q^{33} -1.14474e7i q^{34} +(1.03527e7 - 5.10367e6i) q^{35} +4.81397e7 q^{36} +(-6.47670e7 - 6.47670e7i) q^{37} +(1.23333e7 - 1.23333e7i) q^{38} -4.15853e7i q^{39} +(1.81559e7 + 3.68291e7i) q^{40} +5.65192e7 q^{41} +(-1.70979e6 - 1.70979e6i) q^{42} +(-1.85471e8 + 1.85471e8i) q^{43} -1.53974e7i q^{44} +(1.45197e8 + 4.93095e7i) q^{45} -6.82690e7 q^{46} +(6.69481e7 + 6.69481e7i) q^{47} +(-6.48814e7 + 6.48814e7i) q^{48} -2.68833e8i q^{49} +(8.33614e6 + 6.34510e7i) q^{50} +1.74507e8 q^{51} +(-2.88775e8 - 2.88775e8i) q^{52} +(1.86243e8 - 1.86243e8i) q^{53} -7.07803e7i q^{54} +(1.57716e7 - 4.64411e7i) q^{55} -4.85318e7 q^{56} +(1.88012e8 + 1.88012e8i) q^{57} +(7.72550e7 - 7.72550e7i) q^{58} +7.53831e8i q^{59} +(-2.74702e8 + 1.35422e8i) q^{60} -3.22219e8 q^{61} +(1.27120e8 + 1.27120e8i) q^{62} +(-1.28156e8 + 1.28156e8i) q^{63} +8.12921e8i q^{64} +(-5.75200e8 - 1.16678e9i) q^{65} -1.02747e7 q^{66} +(9.46635e8 + 9.46635e8i) q^{67} +(1.21180e9 - 1.21180e9i) q^{68} -1.04071e9i q^{69} +(-7.16223e7 - 2.43232e7i) q^{70} -1.70508e9 q^{71} +(-4.55907e8 - 4.55907e8i) q^{72} +(8.54176e8 - 8.54176e8i) q^{73} +6.00238e8i q^{74} +(-9.67259e8 + 1.27078e8i) q^{75} +2.61117e9 q^{76} +(4.09906e7 + 4.09906e7i) q^{77} +(-1.92699e8 + 1.92699e8i) q^{78} +1.15355e9i q^{79} +(-9.22991e8 + 2.71784e9i) q^{80} -1.81851e9 q^{81} +(-2.61900e8 - 2.61900e8i) q^{82} +(-3.46702e9 + 3.46702e9i) q^{83} -3.61991e8i q^{84} +(4.89624e9 - 2.41374e9i) q^{85} +1.71888e9 q^{86} +(1.17769e9 + 1.17769e9i) q^{87} +(-1.45821e8 + 1.45821e8i) q^{88} -6.69639e9i q^{89} +(-4.44326e8 - 9.01310e8i) q^{90} +1.53754e9 q^{91} +(-7.22683e9 - 7.22683e9i) q^{92} +(-1.93784e9 + 1.93784e9i) q^{93} -6.20452e8i q^{94} +(7.87570e9 + 2.67462e9i) q^{95} +1.94542e9 q^{96} +(1.86215e9 + 1.86215e9i) q^{97} +(-1.24572e9 + 1.24572e9i) q^{98} +7.70130e8i 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 $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−4.63382	−	4.63382i	−0.144807	−	0.144807i	0.630987	−	0.775794i	$-0.282650\pi$
$2$	−4.63382	−	4.63382i	−0.144807	−	0.144807i	−0.775794	+	0.630987i	$0.782650\pi$
$3$	70.6389	−	70.6389i	0.290695	−	0.290695i	−0.546660	−	0.837355i	$-0.684101\pi$
$3$	70.6389	−	70.6389i	0.290695	−	0.290695i	0.837355	+	0.546660i	$0.184101\pi$
$4$		−	981.055i		−	0.958062i
$5$	1004.90	−	2959.02i	0.321567	−	0.946887i
$5$	1004.90	−	2959.02i	0.321567	−	0.946887i
$6$	−654.656			−0.0841893
$7$	2611.74	+	2611.74i	0.155396	+	0.155396i	0.780523	−	0.625127i	$-0.214953\pi$
$7$	2611.74	+	2611.74i	0.155396	+	0.155396i	−0.625127	+	0.780523i	$0.714953\pi$
$8$	−9291.07	+	9291.07i	−0.283541	+	0.283541i
$9$			49069.3i			0.830993i
$10$	−18368.1	+	9055.08i	−0.183681	+	0.0905508i
$11$	15694.7			0.0974520			0.0487260	−	0.998812i	$-0.484484\pi$
$11$	15694.7			0.0974520			0.0487260	+	0.998812i	$0.484484\pi$
$12$	−69300.6	−	69300.6i	−0.278504	−	0.278504i
$13$	294351.	−	294351.i	0.792774	−	0.792774i	−0.189170	−	0.981944i	$-0.560580\pi$
$13$	294351.	−	294351.i	0.792774	−	0.792774i	0.981944	+	0.189170i	$0.0605799\pi$
$14$		−	24204.7i		−	0.0450049i
$15$	−138037.	−	280007.i	−0.181777	−	0.368733i
$16$	−918494.			−0.875944
$17$	1.23520e6	+	1.23520e6i	0.869948	+	0.869948i	0.992466	−	0.122518i	$-0.0390969\pi$
$17$	1.23520e6	+	1.23520e6i	0.869948	+	0.869948i	−0.122518	+	0.992466i	$0.539097\pi$
$18$	227379.	−	227379.i	0.120334	−	0.120334i
$19$			2.66159e6i			1.07491i	0.843292	+	0.537456i	$0.180615\pi$
$19$			2.66159e6i			1.07491i	−0.843292	+	0.537456i	$0.819385\pi$
$20$	−2.90296e6	−	985859.i	−0.907176	−	0.308081i
$21$	368981.			0.0903457
$22$	−72726.7	−	72726.7i	−0.0141117	−	0.0141117i
$23$	7.36638e6	−	7.36638e6i	1.14450	−	1.14450i	0.156880	−	0.987618i	$-0.449856\pi$
$23$	7.36638e6	−	7.36638e6i	1.14450	−	1.14450i	0.987618	−	0.156880i	$-0.0501437\pi$
$24$			1.31262e6i			0.164848i
$25$	−7.74599e6	−	5.94702e6i	−0.793190	−	0.608975i
$26$	−2.72795e6			−0.229598
$27$	7.63735e6	+	7.63735e6i	0.532260	+	0.532260i
$28$	2.56226e6	−	2.56226e6i	0.148879	−	0.148879i
$29$			1.66720e7i			0.812824i	0.913690	+	0.406412i	$0.133220\pi$
$29$			1.66720e7i			0.812824i	−0.913690	+	0.406412i	$0.866780\pi$
$30$	−657861.	+	1.93714e6i	−0.0270725	+	0.0797178i
$31$	−2.74330e7			−0.958219			−0.479109	−	0.877755i	$-0.659040\pi$
$31$	−2.74330e7			−0.958219			−0.479109	+	0.877755i	$0.659040\pi$
$32$	1.37702e7	+	1.37702e7i	0.410384	+	0.410384i
$33$	1.10866e6	−	1.10866e6i	0.0283288	−	0.0283288i
$34$		−	1.14474e7i		−	0.251949i
$35$	1.03527e7	−	5.10367e6i	0.197113	−	0.0971723i
$36$	4.81397e7			0.796143
$37$	−6.47670e7	−	6.47670e7i	−0.933996	−	0.933996i	0.0639563	−	0.997953i	$-0.479628\pi$
$37$	−6.47670e7	−	6.47670e7i	−0.933996	−	0.933996i	−0.997953	+	0.0639563i	$0.979628\pi$
$38$	1.23333e7	−	1.23333e7i	0.155655	−	0.155655i
$39$		−	4.15853e7i		−	0.460911i
$40$	1.81559e7	+	3.68291e7i	0.177304	+	0.359659i
$41$	5.65192e7			0.487839			0.243920	−	0.969795i	$-0.421567\pi$
$41$	5.65192e7			0.487839			0.243920	+	0.969795i	$0.421567\pi$
$42$	−1.70979e6	−	1.70979e6i	−0.0130827	−	0.0130827i
$43$	−1.85471e8	+	1.85471e8i	−1.26163	+	1.26163i	−0.311335	+	0.950300i	$0.600776\pi$
$43$	−1.85471e8	+	1.85471e8i	−1.26163	+	1.26163i	−0.950300	+	0.311335i	$0.899224\pi$
$44$		−	1.53974e7i		−	0.0933651i
$45$	1.45197e8	+	4.93095e7i	0.786856	+	0.267220i
$46$	−6.82690e7			−0.331463
$47$	6.69481e7	+	6.69481e7i	0.291910	+	0.291910i	0.837834	−	0.545924i	$-0.183821\pi$
$47$	6.69481e7	+	6.69481e7i	0.291910	+	0.291910i	−0.545924	+	0.837834i	$0.683821\pi$
$48$	−6.48814e7	+	6.48814e7i	−0.254633	+	0.254633i
$49$		−	2.68833e8i		−	0.951704i
$50$	8.33614e6	+	6.34510e7i	0.0266756	+	0.203043i
$51$	1.74507e8			0.505779
$52$	−2.88775e8	−	2.88775e8i	−0.759526	−	0.759526i
$53$	1.86243e8	−	1.86243e8i	0.445349	−	0.445349i	−0.448456	−	0.893805i	$-0.648026\pi$
$53$	1.86243e8	−	1.86243e8i	0.445349	−	0.445349i	0.893805	+	0.448456i	$0.148026\pi$
$54$		−	7.07803e7i		−	0.154150i
$55$	1.57716e7	−	4.64411e7i	0.0313373	−	0.0922761i
$56$	−4.85318e7			−0.0881224
$57$	1.88012e8	+	1.88012e8i	0.312471	+	0.312471i
$58$	7.72550e7	−	7.72550e7i	0.117703	−	0.117703i
$59$			7.53831e8i			1.05442i	0.849735	+	0.527210i	$0.176762\pi$
$59$			7.53831e8i			1.05442i	−0.849735	+	0.527210i	$0.823238\pi$
$60$	−2.74702e8	+	1.35422e8i	−0.353269	+	0.174154i
$61$	−3.22219e8			−0.381507			−0.190753	−	0.981638i	$-0.561093\pi$
$61$	−3.22219e8			−0.381507			−0.190753	+	0.981638i	$0.561093\pi$
$62$	1.27120e8	+	1.27120e8i	0.138757	+	0.138757i
$63$	−1.28156e8	+	1.28156e8i	−0.129133	+	0.129133i
$64$			8.12921e8i			0.757091i
$65$	−5.75200e8	−	1.16678e9i	−0.495738	−	1.00560i
$66$	−1.02747e7			−0.00820442
$67$	9.46635e8	+	9.46635e8i	0.701146	+	0.701146i	0.964657	−	0.263510i	$-0.0848803\pi$
$67$	9.46635e8	+	9.46635e8i	0.701146	+	0.701146i	−0.263510	+	0.964657i	$0.584880\pi$
$68$	1.21180e9	−	1.21180e9i	0.833464	−	0.833464i
$69$		−	1.04071e9i		−	0.665399i
$70$	−7.16223e7	−	2.43232e7i	−0.0426145	−	0.0144721i
$71$	−1.70508e9			−0.945043			−0.472522	−	0.881319i	$-0.656656\pi$
$71$	−1.70508e9			−0.945043			−0.472522	+	0.881319i	$0.656656\pi$
$72$	−4.55907e8	−	4.55907e8i	−0.235621	−	0.235621i
$73$	8.54176e8	−	8.54176e8i	0.412034	−	0.412034i	−0.470413	−	0.882447i	$-0.655895\pi$
$73$	8.54176e8	−	8.54176e8i	0.412034	−	0.412034i	0.882447	+	0.470413i	$0.155895\pi$
$74$			6.00238e8i			0.270498i
$75$	−9.67259e8	+	1.27078e8i	−0.407602	+	0.0535504i
$76$	2.61117e9			1.02983
$77$	4.09906e7	+	4.09906e7i	0.0151437	+	0.0151437i
$78$	−1.92699e8	+	1.92699e8i	−0.0667431	+	0.0667431i
$79$			1.15355e9i			0.374888i	0.982275	+	0.187444i	$0.0600203\pi$
$79$			1.15355e9i			0.374888i	−0.982275	+	0.187444i	$0.939980\pi$
$80$	−9.22991e8	+	2.71784e9i	−0.281675	+	0.829420i
$81$	−1.81851e9			−0.521542
$82$	−2.61900e8	−	2.61900e8i	−0.0706426	−	0.0706426i
$83$	−3.46702e9	+	3.46702e9i	−0.880167	+	0.880167i	−0.993551	−	0.113384i	$-0.963831\pi$
$83$	−3.46702e9	+	3.46702e9i	−0.880167	+	0.880167i	0.113384	+	0.993551i	$0.463831\pi$
$84$		−	3.61991e8i		−	0.0865568i
$85$	4.89624e9	−	2.41374e9i	1.10349	−	0.543996i
$86$	1.71888e9			0.365387
$87$	1.17769e9	+	1.17769e9i	0.236284	+	0.236284i
$88$	−1.45821e8	+	1.45821e8i	−0.0276317	+	0.0276317i
$89$		−	6.69639e9i		−	1.19920i	−0.800301	−	0.599599i	$-0.795327\pi$
$89$		−	6.69639e9i		−	1.19920i	0.800301	−	0.599599i	$-0.204673\pi$
$90$	−4.44326e8	−	9.01310e8i	−0.0752470	−	0.152638i
$91$	1.53754e9			0.246388
$92$	−7.22683e9	−	7.22683e9i	−1.09650	−	1.09650i
$93$	−1.93784e9	+	1.93784e9i	−0.278549	+	0.278549i
$94$		−	6.20452e8i		−	0.0845413i
$95$	7.87570e9	+	2.67462e9i	1.01782	+	0.345656i
$96$	1.94542e9			0.238593
$97$	1.86215e9	+	1.86215e9i	0.216849	+	0.216849i	0.807169	−	0.590320i	$-0.200999\pi$
$97$	1.86215e9	+	1.86215e9i	0.216849	+	0.216849i	−0.590320	+	0.807169i	$0.700999\pi$
$98$	−1.24572e9	+	1.24572e9i	−0.137813	+	0.137813i
$99$			7.70130e8i			0.0809820i
$100$	−5.83435e9	+	7.59925e9i	−0.583435	+	0.759925i
$101$	−2.20341e7			−0.00209647			−0.00104824	−	0.999999i	$-0.500334\pi$
$101$	−2.20341e7			−0.00209647			−0.00104824	+	0.999999i	$0.500334\pi$
$102$	−8.08633e8	−	8.08633e8i	−0.0732403	−	0.0732403i
$103$	−4.11705e9	+	4.11705e9i	−0.355141	+	0.355141i	−0.862018	−	0.506877i	$-0.830800\pi$
$103$	−4.11705e9	+	4.11705e9i	−0.355141	+	0.355141i	0.506877	+	0.862018i	$0.330800\pi$
$104$			5.46968e9i			0.449568i
$105$	3.70787e8	−	1.09182e9i	0.0290522	−	0.0855472i
$106$	−1.72603e9			−0.128979
$107$	4.55710e9	+	4.55710e9i	0.324915	+	0.324915i	0.850649	−	0.525734i	$-0.176209\pi$
$107$	4.55710e9	+	4.55710e9i	0.324915	+	0.324915i	−0.525734	+	0.850649i	$0.676209\pi$
$108$	7.49267e9	−	7.49267e9i	0.509938	−	0.509938i
$109$		−	4.51896e9i		−	0.293701i	−0.989159	−	0.146851i	$-0.953086\pi$
$109$		−	4.51896e9i		−	0.293701i	0.989159	−	0.146851i	$-0.0469137\pi$
$110$	−2.88283e8	+	1.42117e8i	−0.0179001	+	0.00882436i
$111$	−9.15013e9			−0.543016
$112$	−2.39887e9	−	2.39887e9i	−0.136118	−	0.136118i
$113$	6.46147e9	−	6.46147e9i	0.350703	−	0.350703i	−0.509668	−	0.860371i	$-0.670232\pi$
$113$	6.46147e9	−	6.46147e9i	0.350703	−	0.350703i	0.860371	+	0.509668i	$0.170232\pi$
$114$		−	1.74243e9i		−	0.0904961i
$115$	−1.43948e10	−	2.91997e10i	−0.715678	−	1.45174i
$116$	1.63561e10			0.778736
$117$	1.44436e10	+	1.44436e10i	0.658789	+	0.658789i
$118$	3.49312e9	−	3.49312e9i	0.152687	−	0.152687i
$119$			6.45206e9i			0.270373i
$120$	3.88408e9	+	1.31905e9i	0.156092	+	0.0530096i
$121$	−2.56911e10			−0.990503
$122$	1.49311e9	+	1.49311e9i	0.0552448	+	0.0552448i
$123$	3.99245e9	−	3.99245e9i	0.141812	−	0.141812i
$124$			2.69133e10i			0.918033i
$125$	−2.53813e10	+	1.69444e10i	−0.831693	+	0.555235i
$126$	1.18771e9			0.0373987
$127$	−3.05294e9	−	3.05294e9i	−0.0924060	−	0.0924060i	0.659393	−	0.751799i	$-0.270813\pi$
$127$	−3.05294e9	−	3.05294e9i	−0.0924060	−	0.0924060i	−0.751799	+	0.659393i	$0.770813\pi$
$128$	1.78676e10	−	1.78676e10i	0.520016	−	0.520016i
$129$			2.62029e10i			0.733502i
$130$	−2.74130e9	+	8.07205e9i	−0.0738312	+	0.217404i
$131$	1.32702e10			0.343971			0.171986	−	0.985099i	$-0.444982\pi$
$131$	1.32702e10			0.343971			0.171986	+	0.985099i	$0.444982\pi$
$132$	−1.08766e9	−	1.08766e9i	−0.0271407	−	0.0271407i
$133$	−6.95138e9	+	6.95138e9i	−0.167037	+	0.167037i
$134$		−	8.77308e9i		−	0.203062i
$135$	3.02738e10	−	1.49243e10i	0.675147	−	0.332833i
$136$	−2.29527e10			−0.493332
$137$	−6.77863e9	−	6.77863e9i	−0.140456	−	0.140456i	0.633383	−	0.773839i	$-0.281666\pi$
$137$	−6.77863e9	−	6.77863e9i	−0.140456	−	0.140456i	−0.773839	+	0.633383i	$0.781666\pi$
$138$	−4.82245e9	+	4.82245e9i	−0.0963545	+	0.0963545i
$139$		−	6.78011e10i		−	1.30666i	−0.757073	−	0.653330i	$-0.773371\pi$
$139$		−	6.78011e10i		−	1.30666i	0.757073	−	0.653330i	$-0.226629\pi$
$140$	−5.00699e9	−	1.01566e10i	−0.0930971	−	0.188846i
$141$	9.45828e9			0.169714
$142$	7.90102e9	+	7.90102e9i	0.136849	+	0.136849i
$143$	4.61977e9	−	4.61977e9i	0.0772574	−	0.0772574i
$144$		−	4.50699e10i		−	0.727904i
$145$	4.93327e10	+	1.67536e10i	0.769653	+	0.261377i
$146$	−7.91620e9			−0.119331
$147$	−1.89900e10	−	1.89900e10i	−0.276655	−	0.276655i
$148$	−6.35400e10	+	6.35400e10i	−0.894826	+	0.894826i
$149$			5.59484e10i			0.761827i	0.924611	+	0.380913i	$0.124390\pi$
$149$			5.59484e10i			0.761827i	−0.924611	+	0.380913i	$0.875610\pi$
$150$	5.07096e9	+	3.89325e9i	0.0667781	+	0.0512692i
$151$	1.02237e11			1.30233			0.651167	−	0.758934i	$-0.274280\pi$
$151$	1.02237e11			1.30233			0.651167	+	0.758934i	$0.274280\pi$
$152$	−2.47290e10	−	2.47290e10i	−0.304782	−	0.304782i
$153$	−6.06105e10	+	6.06105e10i	−0.722921	+	0.722921i
$154$		−	3.79887e8i		−	0.00438582i
$155$	−2.75673e10	+	8.11748e10i	−0.308131	+	0.907325i
$156$	−4.07975e10			−0.441581
$157$	−1.18836e9	−	1.18836e9i	−0.0124580	−	0.0124580i	0.700850	−	0.713308i	$-0.252804\pi$
$157$	−1.18836e9	−	1.18836e9i	−0.0124580	−	0.0124580i	−0.713308	+	0.700850i	$0.752804\pi$
$158$	5.34535e9	−	5.34535e9i	0.0542864	−	0.0542864i
$159$		−	2.63120e10i		−	0.258921i
$160$	5.45839e10	−	2.69087e10i	0.520553	−	0.256621i
$161$	3.84782e10			0.355701
$162$	8.42664e9	+	8.42664e9i	0.0755230	+	0.0755230i
$163$	4.34968e10	−	4.34968e10i	0.378024	−	0.378024i	−0.492365	−	0.870389i	$-0.663867\pi$
$163$	4.34968e10	−	4.34968e10i	0.378024	−	0.378024i	0.870389	+	0.492365i	$0.163867\pi$
$164$		−	5.54485e10i		−	0.467380i
$165$	−2.16646e9	−	4.39463e9i	−0.0177146	−	0.0359338i
$166$	3.21311e10			0.254909
$167$	−1.31695e11	−	1.31695e11i	−1.01388	−	1.01388i	−0.999902	−	0.0139823i	$-0.995549\pi$
$167$	−1.31695e11	−	1.31695e11i	−1.01388	−	1.01388i	−0.0139823	−	0.999902i	$-0.504451\pi$
$168$	−3.42823e9	+	3.42823e9i	−0.0256167	+	0.0256167i
$169$		−	3.54270e10i		−	0.256981i
$170$	−3.38732e10	−	1.15035e10i	−0.238567	−	0.0810185i
$171$	−1.30602e11			−0.893245
$172$	1.81957e11	+	1.81957e11i	1.20872	+	1.20872i
$173$	1.11305e11	−	1.11305e11i	0.718267	−	0.718267i	−0.249983	−	0.968250i	$-0.580425\pi$
$173$	1.11305e11	−	1.11305e11i	0.718267	−	0.718267i	0.968250	+	0.249983i	$0.0804252\pi$
$174$		−	1.09144e10i		−	0.0684311i
$175$	−4.69846e9	−	3.57626e10i	−0.0286263	−	0.217891i
$176$	−1.44155e10			−0.0853626
$177$	5.32497e10	+	5.32497e10i	0.306515	+	0.306515i
$178$	−3.10299e10	+	3.10299e10i	−0.173652	+	0.173652i
$179$			2.45459e11i			1.33572i	0.744289	+	0.667858i	$0.232789\pi$
$179$			2.45459e11i			1.33572i	−0.744289	+	0.667858i	$0.767211\pi$
$180$	4.83754e10	−	1.42446e11i	0.256013	−	0.753857i
$181$	−1.52111e11			−0.783009			−0.391504	−	0.920176i	$-0.628045\pi$
$181$	−1.52111e11			−0.783009			−0.391504	+	0.920176i	$0.628045\pi$
$182$	−7.12469e9	−	7.12469e9i	−0.0356787	−	0.0356787i
$183$	−2.27612e10	+	2.27612e10i	−0.110902	+	0.110902i
$184$			1.36883e11i			0.649024i
$185$	−2.56731e11	+	1.26563e11i	−1.18473	+	0.584047i
$186$	1.79592e10			0.0806718
$187$	1.93862e10	+	1.93862e10i	0.0847782	+	0.0847782i
$188$	6.56798e10	−	6.56798e10i	0.279668	−	0.279668i
$189$			3.98936e10i			0.165422i
$190$	−2.41009e10	−	4.88883e10i	−0.0973341	−	0.197441i
$191$	3.04332e11			1.19724			0.598619	−	0.801034i	$-0.295716\pi$
$191$	3.04332e11			1.19724			0.598619	+	0.801034i	$0.295716\pi$
$192$	5.74238e10	+	5.74238e10i	0.220083	+	0.220083i
$193$	2.42004e11	−	2.42004e11i	0.903726	−	0.903726i	−0.0920301	−	0.995756i	$-0.529336\pi$
$193$	2.42004e11	−	2.42004e11i	0.903726	−	0.903726i	0.995756	+	0.0920301i	$0.0293356\pi$
$194$		−	1.72578e10i		−	0.0628024i
$195$	−1.23052e11	−	4.17889e10i	−0.436430	−	0.148213i
$196$	−2.63740e11			−0.911791
$197$	−1.95726e11	−	1.95726e11i	−0.659655	−	0.659655i	0.295643	−	0.955298i	$-0.404466\pi$
$197$	−1.95726e11	−	1.95726e11i	−0.659655	−	0.659655i	−0.955298	+	0.295643i	$0.904466\pi$
$198$	3.56865e9	−	3.56865e9i	0.0117268	−	0.0117268i
$199$		−	1.32708e11i		−	0.425238i	−0.977135	−	0.212619i	$-0.931801\pi$
$199$		−	1.32708e11i		−	0.425238i	0.977135	−	0.212619i	$-0.0681993\pi$
$200$	1.27223e11	−	1.67144e10i	0.397571	−	0.0522326i
$201$	1.33738e11			0.407639
$202$	1.02102e8	+	1.02102e8i	0.000303584	+	0.000303584i
$203$	−4.35429e10	+	4.35429e10i	−0.126310	+	0.126310i
$204$		−	1.71201e11i		−	0.484568i
$205$	5.67959e10	−	1.67242e11i	0.156873	−	0.461929i
$206$	3.81554e10			0.102854
$207$	3.61463e11	+	3.61463e11i	0.951070	+	0.951070i
$208$	−2.70360e11	+	2.70360e11i	−0.694426	+	0.694426i
$209$			4.17730e10i			0.104752i
$210$	−6.77748e9	+	3.34115e9i	−0.0165948	+	0.00818087i
$211$	−2.87300e11			−0.686948			−0.343474	−	0.939162i	$-0.611604\pi$
$211$	−2.87300e11			−0.686948			−0.343474	+	0.939162i	$0.611604\pi$
$212$	−1.82715e11	−	1.82715e11i	−0.426672	−	0.426672i
$213$	−1.20445e11	+	1.20445e11i	−0.274719	+	0.274719i
$214$		−	4.22336e10i		−	0.0940999i
$215$	3.62434e11	+	7.35192e11i	0.788926	+	1.60033i
$216$	−1.41918e11			−0.301835
$217$	−7.16479e10	−	7.16479e10i	−0.148903	−	0.148903i
$218$	−2.09401e10	+	2.09401e10i	−0.0425300	+	0.0425300i
$219$		−	1.20676e11i		−	0.239552i
$220$	−4.55613e10	−	1.54728e10i	−0.0884062	−	0.0300231i
$221$	7.27167e11			1.37934
$222$	4.24001e10	+	4.24001e10i	0.0786325	+	0.0786325i
$223$	−4.39899e11	+	4.39899e11i	−0.797680	+	0.797680i	−0.982729	−	0.185049i	$-0.940755\pi$
$223$	−4.39899e11	+	4.39899e11i	−0.797680	+	0.797680i	0.185049	+	0.982729i	$0.440755\pi$
$224$			7.19284e10i			0.127544i
$225$	2.91816e11	−	3.80091e11i	0.506054	−	0.659135i
$226$	−5.98827e10			−0.101568
$227$	−6.77659e11	−	6.77659e11i	−1.12430	−	1.12430i	−0.991088	−	0.133211i	$-0.957471\pi$
$227$	−6.77659e11	−	6.77659e11i	−1.12430	−	1.12430i	−0.133211	−	0.991088i	$-0.542529\pi$
$228$	1.84450e11	−	1.84450e11i	0.299367	−	0.299367i
$229$		−	4.76659e11i		−	0.756887i	−0.925624	−	0.378443i	$-0.876460\pi$
$229$		−	4.76659e11i		−	0.756887i	0.925624	−	0.378443i	$-0.123540\pi$
$230$	−6.86033e10	+	2.02010e11i	−0.106587	+	0.313858i
$231$	5.79106e9			0.00880437
$232$	−1.54900e11	−	1.54900e11i	−0.230469	−	0.230469i
$233$	2.19919e11	−	2.19919e11i	0.320246	−	0.320246i	−0.528615	−	0.848862i	$-0.677289\pi$
$233$	2.19919e11	−	2.19919e11i	0.320246	−	0.320246i	0.848862	+	0.528615i	$0.177289\pi$
$234$		−	1.33858e11i		−	0.190795i
$235$	2.65377e11	−	1.30825e11i	0.370275	−	0.182537i
$236$	7.39550e11			1.01020
$237$	8.14855e10	+	8.14855e10i	0.108978	+	0.108978i
$238$	2.98977e10	−	2.98977e10i	0.0391519	−	0.0391519i
$239$			1.40281e11i			0.179891i	0.995947	+	0.0899454i	$0.0286692\pi$
$239$			1.40281e11i			0.179891i	−0.995947	+	0.0899454i	$0.971331\pi$
$240$	1.26786e11	+	2.57184e11i	0.159227	+	0.322990i
$241$	−7.40125e11			−0.910374			−0.455187	−	0.890396i	$-0.650428\pi$
$241$	−7.40125e11			−0.910374			−0.455187	+	0.890396i	$0.650428\pi$
$242$	1.19048e11	+	1.19048e11i	0.143432	+	0.143432i
$243$	−5.79435e11	+	5.79435e11i	−0.683870	+	0.683870i
$244$			3.16115e11i			0.365507i
$245$	−7.95482e11	−	2.70149e11i	−0.901156	−	0.306036i
$246$	−3.70006e10			−0.0410709
$247$	7.83442e11	+	7.83442e11i	0.852162	+	0.852162i
$248$	2.54882e11	−	2.54882e11i	0.271694	−	0.271694i
$249$			4.89812e11i			0.511720i
$250$	1.96130e11	+	3.90949e10i	0.200837	+	0.0400331i
$251$	−9.97549e11			−1.00130			−0.500652	−	0.865649i	$-0.666906\pi$
$251$	−9.97549e11			−1.00130			−0.500652	+	0.865649i	$0.666906\pi$
$252$	1.25728e11	+	1.25728e11i	0.123717	+	0.123717i
$253$	1.15613e11	−	1.15613e11i	0.111534	−	0.111534i
$254$			2.82936e10i			0.0267621i
$255$	1.75361e11	−	5.16369e11i	0.162642	−	0.478915i
$256$	6.66840e11			0.606487
$257$	4.29300e11	+	4.29300e11i	0.382909	+	0.382909i	0.872149	−	0.489240i	$-0.162726\pi$
$257$	4.29300e11	+	4.29300e11i	0.382909	+	0.382909i	−0.489240	+	0.872149i	$0.662726\pi$
$258$	1.21420e11	−	1.21420e11i	0.106216	−	0.106216i
$259$		−	3.38309e11i		−	0.290279i
$260$	−1.14468e12	+	5.64303e11i	−0.963424	+	0.474947i
$261$	−8.18082e11			−0.675451
$262$	−6.14919e10	−	6.14919e10i	−0.0498094	−	0.0498094i
$263$	1.26771e12	−	1.26771e12i	1.00749	−	1.00749i	0.00751567	−	0.999972i	$-0.497608\pi$
$263$	1.26771e12	−	1.26771e12i	1.00749	−	1.00749i	0.999972	−	0.00751567i	$-0.00239233\pi$
$264$			2.06013e10i			0.0160648i
$265$	−3.63942e11	−	7.38251e11i	−0.278486	−	0.564904i
$266$	6.44230e10			0.0483763
$267$	−4.73026e11	−	4.73026e11i	−0.348601	−	0.348601i
$268$	9.28701e11	−	9.28701e11i	0.671741	−	0.671741i
$269$			1.33804e12i			0.949966i	0.879995	+	0.474983i	$0.157546\pi$
$269$			1.33804e12i			0.949966i	−0.879995	+	0.474983i	$0.842454\pi$
$270$	−2.09440e11	−	7.11268e10i	−0.145963	−	0.0495695i
$271$	1.64105e12			1.12273			0.561364	−	0.827569i	$-0.310277\pi$
$271$	1.64105e12			1.12273			0.561364	+	0.827569i	$0.310277\pi$
$272$	−1.13453e12	−	1.13453e12i	−0.762026	−	0.762026i
$273$	1.08610e11	−	1.08610e11i	0.0716237	−	0.0716237i
$274$			6.28219e10i			0.0406779i
$275$	−1.21571e11	−	9.33369e10i	−0.0772979	−	0.0593458i
$276$	−1.02099e12			−0.637494
$277$	1.88551e12	+	1.88551e12i	1.15619	+	1.15619i	0.985287	+	0.170905i	$0.0546692\pi$
$277$	1.88551e12	+	1.88551e12i	1.15619	+	1.15619i	0.170905	+	0.985287i	$0.445331\pi$
$278$	−3.14178e11	+	3.14178e11i	−0.189213	+	0.189213i
$279$		−	1.34612e12i		−	0.796273i
$280$	−4.87694e10	+	1.43607e11i	−0.0283372	+	0.0834419i
$281$	−8.00428e11			−0.456868			−0.228434	−	0.973559i	$-0.573360\pi$
$281$	−8.00428e11			−0.456868			−0.228434	+	0.973559i	$0.573360\pi$
$282$	−4.38280e10	−	4.38280e10i	−0.0245757	−	0.0245757i
$283$	−1.51030e12	+	1.51030e12i	−0.832013	+	0.832013i	−0.987792	−	0.155779i	$-0.950211\pi$
$283$	−1.51030e12	+	1.51030e12i	−0.832013	+	0.832013i	0.155779	+	0.987792i	$0.450211\pi$
$284$			1.67277e12i			0.905410i
$285$	7.45262e11	−	3.67398e11i	0.396356	−	0.195395i
$286$	−4.28144e10			−0.0223748
$287$	1.47614e11	+	1.47614e11i	0.0758083	+	0.0758083i
$288$	−6.75694e11	+	6.75694e11i	−0.341026	+	0.341026i
$289$			1.03545e12i			0.513620i
$290$	−1.50966e11	−	3.06232e11i	−0.0736019	−	0.149300i
$291$	2.63081e11			0.126074
$292$	−8.37993e11	−	8.37993e11i	−0.394754	−	0.394754i
$293$	−2.02228e11	+	2.02228e11i	−0.0936489	+	0.0936489i	−0.752379	−	0.658730i	$-0.771094\pi$
$293$	−2.02228e11	+	2.02228e11i	−0.0936489	+	0.0936489i	0.658730	+	0.752379i	$0.271094\pi$
$294$			1.75993e11i			0.0801233i
$295$	2.23060e12	+	7.57521e11i	0.998417	+	0.339066i
$296$	1.20351e12			0.529653
$297$	1.19866e11	+	1.19866e11i	0.0518698	+	0.0518698i
$298$	2.59255e11	−	2.59255e11i	0.110318	−	0.110318i
$299$		−	4.33661e12i		−	1.81466i
$300$	1.24670e11	+	9.48934e11i	0.0513046	+	0.390508i
$301$	−9.68805e11			−0.392106
$302$	−4.73747e11	−	4.73747e11i	−0.188587	−	0.188587i
$303$	−1.55647e9	+	1.55647e9i	−0.000609433	+	0.000609433i
$304$		−	2.44465e12i		−	0.941563i
$305$	−3.23797e11	+	9.53453e11i	−0.122680	+	0.361244i
$306$	5.61717e11			0.209368
$307$	−2.37230e12	−	2.37230e12i	−0.869915	−	0.869915i	0.122548	−	0.992463i	$-0.460894\pi$
$307$	−2.37230e12	−	2.37230e12i	−0.869915	−	0.869915i	−0.992463	+	0.122548i	$0.960894\pi$
$308$	4.02141e10	−	4.02141e10i	0.0145086	−	0.0145086i
$309$			5.81648e11i			0.206475i
$310$	5.03892e11	−	2.48408e11i	0.176007	−	0.0867675i
$311$	1.53573e12			0.527853			0.263926	−	0.964543i	$-0.414982\pi$
$311$	1.53573e12			0.527853			0.263926	+	0.964543i	$0.414982\pi$
$312$	3.86372e11	+	3.86372e11i	0.130687	+	0.130687i
$313$	−8.40022e11	+	8.40022e11i	−0.279621	+	0.279621i	−0.832958	−	0.553337i	$-0.813354\pi$
$313$	−8.40022e11	+	8.40022e11i	−0.279621	+	0.279621i	0.553337	+	0.832958i	$0.313354\pi$
$314$			1.10133e10i			0.00360801i
$315$	2.50434e11	+	5.08001e11i	0.0807495	+	0.163799i
$316$	1.13170e12			0.359166
$317$	3.01880e11	+	3.01880e11i	0.0943057	+	0.0943057i	0.752686	−	0.658380i	$-0.228758\pi$
$317$	3.01880e11	+	3.01880e11i	0.0943057	+	0.0943057i	−0.658380	+	0.752686i	$0.728758\pi$
$318$	−1.21925e11	+	1.21925e11i	−0.0374936	+	0.0374936i
$319$			2.61662e11i			0.0792114i
$320$	2.40545e12	+	8.16901e11i	0.716880	+	0.243455i
$321$	6.43817e11			0.188902
$322$	−1.78301e11	−	1.78301e11i	−0.0515080	−	0.0515080i
$323$	−3.28760e12	+	3.28760e12i	−0.935118	+	0.935118i
$324$			1.78405e12i			0.499670i
$325$	−4.03056e12	+	5.29531e11i	−1.11160	+	0.146041i
$326$	−4.03113e11			−0.109481
$327$	−3.19214e11	−	3.19214e11i	−0.0853775	−	0.0853775i
$328$	−5.25124e11	+	5.25124e11i	−0.138322	+	0.138322i
$329$			3.49703e11i			0.0907234i
$330$	−1.03250e10	+	3.04029e10i	−0.00263827	+	0.00776866i
$331$	−2.77221e12			−0.697727			−0.348863	−	0.937174i	$-0.613432\pi$
$331$	−2.77221e12			−0.697727			−0.348863	+	0.937174i	$0.613432\pi$
$332$	3.40133e12	+	3.40133e12i	0.843255	+	0.843255i
$333$	3.17807e12	−	3.17807e12i	0.776144	−	0.776144i
$334$			1.22051e12i			0.293635i
$335$	3.75238e12	−	1.84984e12i	0.889371	−	0.438441i
$336$	−3.38907e11			−0.0791378
$337$	−5.71886e11	−	5.71886e11i	−0.131571	−	0.131571i	0.638254	−	0.769825i	$-0.279657\pi$
$337$	−5.71886e11	−	5.71886e11i	−0.131571	−	0.131571i	−0.769825	+	0.638254i	$0.779657\pi$
$338$	−1.64162e11	+	1.64162e11i	−0.0372126	+	0.0372126i
$339$		−	9.12862e11i		−	0.203895i
$340$	−2.36801e12	−	4.80348e12i	−0.521182	−	1.05721i
$341$	−4.30554e11			−0.0933804
$342$	6.05188e11	+	6.05188e11i	0.129348	+	0.129348i
$343$	1.43987e12	−	1.43987e12i	0.303287	−	0.303287i
$344$		−	3.44645e12i		−	0.715451i
$345$	−3.07947e12	−	1.04580e12i	−0.630058	−	0.213970i
$346$	−1.03154e12			−0.208020
$347$	−1.13487e12	−	1.13487e12i	−0.225580	−	0.225580i	0.585263	−	0.810843i	$-0.300991\pi$
$347$	−1.13487e12	−	1.13487e12i	−0.225580	−	0.225580i	−0.810843	+	0.585263i	$0.800991\pi$
$348$	1.15538e12	−	1.15538e12i	0.226375	−	0.226375i
$349$			5.63803e12i			1.08893i	0.838783	+	0.544465i	$0.183267\pi$
$349$			5.63803e12i			1.08893i	−0.838783	+	0.544465i	$0.816733\pi$
$350$	−1.43946e11	+	1.87490e11i	−0.0274068	+	0.0356974i
$351$	4.49613e12			0.843924
$352$	2.16120e11	+	2.16120e11i	0.0399928	+	0.0399928i
$353$	7.43074e12	−	7.43074e12i	1.35568	−	1.35568i	0.476520	−	0.879164i	$-0.341898\pi$
$353$	7.43074e12	−	7.43074e12i	1.35568	−	1.35568i	0.879164	−	0.476520i	$-0.158102\pi$
$354$		−	4.93500e11i		−	0.0887709i
$355$	−1.71342e12	+	5.04535e12i	−0.303894	+	0.894849i
$356$	−6.56953e12			−1.14891
$357$	4.55766e11	+	4.55766e11i	0.0785961	+	0.0785961i
$358$	1.13742e12	−	1.13742e12i	0.193421	−	0.193421i
$359$			7.02776e12i			1.17854i	0.807936	+	0.589270i	$0.200585\pi$
$359$			7.02776e12i			1.17854i	−0.807936	+	0.589270i	$0.799415\pi$
$360$	−1.80718e12	+	8.90899e11i	−0.298874	+	0.147338i
$361$	−9.52990e11			−0.155436
$362$	7.04854e11	+	7.04854e11i	0.113385	+	0.113385i
$363$	−1.81479e12	+	1.81479e12i	−0.287934	+	0.287934i
$364$		−	1.50841e12i		−	0.236055i
$365$	−1.66917e12	−	3.38588e12i	−0.257653	−	0.522646i
$366$	2.10943e11			0.0321188
$367$	4.10757e11	+	4.10757e11i	0.0616956	+	0.0616956i	0.737281	−	0.675586i	$-0.236109\pi$
$367$	4.10757e11	+	4.10757e11i	0.0616956	+	0.0616956i	−0.675586	+	0.737281i	$0.736109\pi$
$368$	−6.76598e12	+	6.76598e12i	−1.00252	+	1.00252i
$369$			2.77336e12i			0.405391i
$370$	1.77612e12	+	6.03177e11i	0.256131	+	0.0869833i
$371$	9.72837e11			0.138411
$372$	1.90112e12	+	1.90112e12i	0.266867	+	0.266867i
$373$	5.37175e12	−	5.37175e12i	0.743998	−	0.743998i	−0.229347	−	0.973345i	$-0.573659\pi$
$373$	5.37175e12	−	5.37175e12i	0.743998	−	0.743998i	0.973345	+	0.229347i	$0.0736589\pi$
$374$		−	1.79664e11i		−	0.0245530i
$375$	−5.95969e11	+	2.98984e12i	−0.0803651	+	0.403173i
$376$	−1.24404e12			−0.165537
$377$	4.90742e12	+	4.90742e12i	0.644386	+	0.644386i
$378$	1.84860e11	−	1.84860e11i	0.0239543	−	0.0239543i
$379$		−	3.45301e12i		−	0.441573i	−0.975322	−	0.220786i	$-0.929138\pi$
$379$		−	3.45301e12i		−	0.441573i	0.975322	−	0.220786i	$-0.0708624\pi$
$380$	2.62395e12	−	7.72650e12i	0.331160	−	0.975135i
$381$	−4.31313e11			−0.0537239
$382$	−1.41022e12	−	1.41022e12i	−0.173368	−	0.173368i
$383$	−7.95493e12	+	7.95493e12i	−0.965256	+	0.965256i	−0.999416	−	0.0341606i	$-0.989124\pi$
$383$	−7.95493e12	+	7.95493e12i	−0.965256	+	0.965256i	0.0341606	+	0.999416i	$0.489124\pi$
$384$		−	2.52430e12i		−	0.302332i
$385$	1.62483e11	−	8.01008e10i	0.0192090	−	0.00946964i
$386$	−2.24281e12			−0.261732
$387$	−9.10093e12	−	9.10093e12i	−1.04841	−	1.04841i
$388$	1.82687e12	−	1.82687e12i	0.207754	−	0.207754i
$389$		−	1.31059e13i		−	1.47136i	−0.677329	−	0.735680i	$-0.736863\pi$
$389$		−	1.31059e13i		−	1.47136i	0.677329	−	0.735680i	$-0.263137\pi$
$390$	3.76558e11	+	7.63843e11i	0.0417358	+	0.0846605i
$391$	1.81979e13			1.99131
$392$	2.49775e12	+	2.49775e12i	0.269847	+	0.269847i
$393$	9.37394e11	−	9.37394e11i	0.0999906	−	0.0999906i
$394$			1.81392e12i			0.191045i
$395$	3.41338e12	+	1.15920e12i	0.354976	+	0.120551i
$396$	7.55540e11			0.0775857
$397$	−5.77637e12	−	5.77637e12i	−0.585736	−	0.585736i	0.350738	−	0.936474i	$-0.385931\pi$
$397$	−5.77637e12	−	5.77637e12i	−0.585736	−	0.585736i	−0.936474	+	0.350738i	$0.885931\pi$
$398$	−6.14946e11	+	6.14946e11i	−0.0615774	+	0.0615774i
$399$			9.82076e11i			0.0971137i
$400$	7.11465e12	+	5.46230e12i	0.694790	+	0.533428i
$401$	−1.00597e13			−0.970202			−0.485101	−	0.874458i	$-0.661217\pi$
$401$	−1.00597e13			−0.970202			−0.485101	+	0.874458i	$0.661217\pi$
$402$	−6.19720e11	−	6.19720e11i	−0.0590290	−	0.0590290i
$403$	−8.07494e12	+	8.07494e12i	−0.759651	+	0.759651i
$404$			2.16167e10i			0.00200855i
$405$	−1.82741e12	+	5.38100e12i	−0.167711	+	0.493842i
$406$	4.03540e11			0.0365811
$407$	−1.01650e12	−	1.01650e12i	−0.0910198	−	0.0910198i
$408$	−1.62135e12	+	1.62135e12i	−0.143409	+	0.143409i
$409$			5.81279e12i			0.507888i	0.967219	+	0.253944i	$0.0817279\pi$
$409$			5.81279e12i			0.507888i	−0.967219	+	0.253944i	$0.918272\pi$
$410$	−1.03815e12	+	5.11786e11i	−0.0896068	+	0.0441742i
$411$	−9.57669e11			−0.0816594
$412$	4.03906e12	+	4.03906e12i	0.340247	+	0.340247i
$413$	−1.96881e12	+	1.96881e12i	−0.163853	+	0.163853i
$414$		−	3.34991e12i		−	0.275443i
$415$	6.77498e12	+	1.37430e13i	0.550387	+	1.11645i
$416$	8.10656e12			0.650683
$417$	−4.78939e12	−	4.78939e12i	−0.379839	−	0.379839i
$418$	1.93569e11	−	1.93569e11i	0.0151689	−	0.0151689i
$419$		−	4.24519e12i		−	0.328721i	−0.986400	−	0.164360i	$-0.947444\pi$
$419$		−	4.24519e12i		−	0.328721i	0.986400	−	0.164360i	$-0.0525560\pi$
$420$	−1.07114e12	−	3.63763e11i	−0.0819595	−	0.0278338i
$421$	2.54080e12			0.192115			0.0960574	−	0.995376i	$-0.469377\pi$
$421$	2.54080e12			0.192115			0.0960574	+	0.995376i	$0.469377\pi$
$422$	1.33130e12	+	1.33130e12i	0.0994749	+	0.0994749i
$423$	−3.28510e12	+	3.28510e12i	−0.242575	+	0.242575i
$424$			3.46079e12i			0.252549i
$425$	−2.22210e12	−	1.69136e13i	−0.160258	−	1.21981i
$426$	1.11624e12			0.0795626
$427$	−8.41553e11	−	8.41553e11i	−0.0592846	−	0.0592846i
$428$	4.47077e12	−	4.47077e12i	0.311289	−	0.311289i
$429$		−	6.52671e11i		−	0.0449167i
$430$	1.72730e12	−	5.08620e12i	0.117496	−	0.345980i
$431$	−2.15279e13			−1.44749			−0.723743	−	0.690070i	$-0.757580\pi$
$431$	−2.15279e13			−1.44749			−0.723743	+	0.690070i	$0.757580\pi$
$432$	−7.01486e12	−	7.01486e12i	−0.466230	−	0.466230i
$433$	9.99110e12	−	9.99110e12i	0.656408	−	0.656408i	−0.298121	−	0.954528i	$-0.596360\pi$
$433$	9.99110e12	−	9.99110e12i	0.656408	−	0.656408i	0.954528	+	0.298121i	$0.0963598\pi$
$434$			6.64008e11i			0.0431245i
$435$	4.66826e12	−	2.30135e12i	0.299715	−	0.147753i
$436$	−4.43335e12			−0.281384
$437$	1.96063e13	+	1.96063e13i	1.23023	+	1.23023i
$438$	−5.59191e11	+	5.59191e11i	−0.0346888	+	0.0346888i
$439$		−	2.33293e13i		−	1.43080i	−0.698714	−	0.715401i	$-0.746244\pi$
$439$		−	2.33293e13i		−	1.43080i	0.698714	−	0.715401i	$-0.253756\pi$
$440$	2.84953e11	+	5.78023e11i	0.0172786	+	0.0350495i
$441$	1.31914e13			0.790859
$442$	−3.36956e12	−	3.36956e12i	−0.199739	−	0.199739i
$443$	2.92902e12	−	2.92902e12i	0.171673	−	0.171673i	−0.616041	−	0.787714i	$-0.711264\pi$
$443$	2.92902e12	−	2.92902e12i	0.171673	−	0.171673i	0.787714	+	0.616041i	$0.211264\pi$
$444$			8.97679e12i			0.520243i
$445$	−1.98148e13	−	6.72918e12i	−1.13550	−	0.385622i
$446$	4.07683e12			0.231019
$447$	3.95213e12	+	3.95213e12i	0.221459	+	0.221459i
$448$	−2.12314e12	+	2.12314e12i	−0.117649	+	0.117649i
$449$			3.40161e13i			1.86403i	0.362419	+	0.932015i	$0.381951\pi$
$449$			3.40161e13i			1.86403i	−0.362419	+	0.932015i	$0.618049\pi$
$450$	−3.11350e12	+	4.09049e11i	−0.168728	+	0.0221673i
$451$	8.87055e11			0.0475409
$452$	−6.33906e12	−	6.33906e12i	−0.335995	−	0.335995i
$453$	7.22189e12	−	7.22189e12i	0.378582	−	0.378582i
$454$			6.28030e12i			0.325613i
$455$	1.54507e12	−	4.54961e12i	0.0792301	−	0.233301i
$456$	−3.49366e12			−0.177197
$457$	4.38241e12	+	4.38241e12i	0.219853	+	0.219853i	0.808436	−	0.588584i	$-0.200314\pi$
$457$	4.38241e12	+	4.38241e12i	0.219853	+	0.219853i	−0.588584	+	0.808436i	$0.700314\pi$
$458$	−2.20876e12	+	2.20876e12i	−0.109602	+	0.109602i
$459$			1.88673e13i			0.926078i
$460$	−2.86466e13	+	1.41221e13i	−1.39086	+	0.685664i
$461$	−6.09175e12			−0.292575			−0.146288	−	0.989242i	$-0.546732\pi$
$461$	−6.09175e12			−0.292575			−0.146288	+	0.989242i	$0.546732\pi$
$462$	−2.68348e10	−	2.68348e10i	−0.00127493	−	0.00127493i
$463$	5.30861e12	−	5.30861e12i	0.249503	−	0.249503i	−0.571264	−	0.820767i	$-0.693547\pi$
$463$	5.30861e12	−	5.30861e12i	0.249503	−	0.249503i	0.820767	+	0.571264i	$0.193547\pi$
$464$		−	1.53131e13i		−	0.711989i
$465$	3.78677e12	+	7.68142e12i	0.174183	+	0.353327i
$466$	−2.03814e12			−0.0927478
$467$	1.33139e13	+	1.33139e13i	0.599407	+	0.599407i	0.940155	−	0.340747i	$-0.110680\pi$
$467$	1.33139e13	+	1.33139e13i	0.599407	+	0.599407i	−0.340747	+	0.940155i	$0.610680\pi$
$468$	1.41700e13	−	1.41700e13i	0.631161	−	0.631161i
$469$			4.94473e12i			0.217911i
$470$	−1.83593e12	−	6.23490e11i	−0.0800510	−	0.0271857i
$471$	−1.67888e11			−0.00724295
$472$	−7.00390e12	−	7.00390e12i	−0.298972	−	0.298972i
$473$	−2.91092e12	+	2.91092e12i	−0.122949	+	0.122949i
$474$		−	7.55179e11i		−	0.0315615i
$475$	1.58285e13	−	2.06167e13i	0.654594	−	0.852609i
$476$	6.32983e12			0.259034
$477$	9.13881e12	+	9.13881e12i	0.370082	+	0.370082i
$478$	6.50037e11	−	6.50037e11i	0.0260494	−	0.0260494i
$479$		−	4.52816e13i		−	1.79574i	−0.440257	−	0.897872i	$-0.645113\pi$
$479$		−	4.52816e13i		−	1.79574i	0.440257	−	0.897872i	$-0.354887\pi$
$480$	1.95495e12	−	5.75655e12i	0.0767236	−	0.225921i
$481$	−3.81285e13			−1.48090
$482$	3.42961e12	+	3.42961e12i	0.131828	+	0.131828i
$483$	2.71805e12	−	2.71805e12i	0.103400	−	0.103400i
$484$			2.52044e13i			0.948963i
$485$	7.38142e12	−	3.63888e12i	0.275062	−	0.135600i
$486$	5.37000e12			0.198058
$487$	−1.68828e13	−	1.68828e13i	−0.616309	−	0.616309i	0.328273	−	0.944583i	$-0.393533\pi$
$487$	−1.68828e13	−	1.68828e13i	−0.616309	−	0.616309i	−0.944583	+	0.328273i	$0.893533\pi$
$488$	2.99376e12	−	2.99376e12i	0.108173	−	0.108173i
$489$		−	6.14513e12i		−	0.219779i
$490$	2.43430e12	+	4.93795e12i	0.0861775	+	0.174810i
$491$	2.30176e13			0.806590			0.403295	−	0.915070i	$-0.367865\pi$
$491$	2.30176e13			0.806590			0.403295	+	0.915070i	$0.367865\pi$
$492$	−3.91682e12	−	3.91682e12i	−0.135865	−	0.135865i
$493$	−2.05932e13	+	2.05932e13i	−0.707115	+	0.707115i
$494$		−	7.26067e12i		−	0.246798i
$495$	2.27883e12	+	7.73901e11i	0.0766808	+	0.0260411i
$496$	2.51970e13			0.839346
$497$	−4.45322e12	−	4.45322e12i	−0.146856	−	0.146856i
$498$	2.26970e12	−	2.26970e12i	0.0741007	−	0.0741007i
$499$		−	9.09915e12i		−	0.294102i	−0.989129	−	0.147051i	$-0.953022\pi$
$499$		−	9.09915e12i		−	0.294102i	0.989129	−	0.147051i	$-0.0469782\pi$
$500$	1.66234e13	+	2.49004e13i	0.531949	+	0.796814i
$501$	−1.86056e13			−0.589462
$502$	4.62247e12	+	4.62247e12i	0.144996	+	0.144996i
$503$	−2.81006e13	+	2.81006e13i	−0.872721	+	0.872721i	−0.992768	−	0.120048i	$-0.961695\pi$
$503$	−2.81006e13	+	2.81006e13i	−0.872721	+	0.872721i	0.120048	+	0.992768i	$0.461695\pi$
$504$		−	2.38142e12i		−	0.0732291i
$505$	−2.21420e10	+	6.51994e10i	−0.000674155	+	0.00198512i
$506$	−1.07147e12			−0.0323017
$507$	−2.50252e12	−	2.50252e12i	−0.0747030	−	0.0747030i
$508$	−2.99511e12	+	2.99511e12i	−0.0885306	+	0.0885306i
$509$			4.20563e13i			1.23095i	0.788155	+	0.615477i	$0.211037\pi$
$509$			4.20563e13i			1.23095i	−0.788155	+	0.615477i	$0.788963\pi$
$510$	−3.20535e12	+	1.58017e12i	−0.0929020	+	0.0457987i
$511$	4.46177e12			0.128057
$512$	−2.13865e13	−	2.13865e13i	−0.607840	−	0.607840i
$513$	−2.03275e13	+	2.03275e13i	−0.572133	+	0.572133i
$514$		−	3.97860e12i		−	0.110896i
$515$	8.04524e12	+	1.63197e13i	0.222077	+	0.450479i
$516$	2.57065e13			0.702740
$517$	1.05073e12	+	1.05073e12i	0.0284472	+	0.0284472i
$518$	−1.56767e12	+	1.56767e12i	−0.0420344	+	0.0420344i
$519$		−	1.57250e13i		−	0.417593i
$520$	1.61849e13	+	5.49646e12i	0.425690	+	0.144566i
$521$	3.53219e13			0.920143			0.460072	−	0.887882i	$-0.347824\pi$
$521$	3.53219e13			0.920143			0.460072	+	0.887882i	$0.347824\pi$
$522$	3.79085e12	+	3.79085e12i	0.0978101	+	0.0978101i
$523$	1.01996e13	−	1.01996e13i	0.260661	−	0.260661i	−0.564662	−	0.825322i	$-0.690993\pi$
$523$	1.01996e13	−	1.01996e13i	0.260661	−	0.260661i	0.825322	+	0.564662i	$0.190993\pi$
$524$		−	1.30188e13i		−	0.329546i
$525$	−2.85812e12	−	2.19434e12i	−0.0716613	−	0.0550182i
$526$	−1.17487e13			−0.291783
$527$	−3.38853e13	−	3.38853e13i	−0.833601	−	0.833601i
$528$	−1.01830e12	+	1.01830e12i	−0.0248145	+	0.0248145i
$529$		−	6.71007e13i		−	1.61975i
$530$	−1.73448e12	+	5.10737e12i	−0.0414754	+	0.122129i
$531$	−3.69900e13			−0.876216
$532$	6.81969e12	+	6.81969e12i	0.160032	+	0.160032i
$533$	1.66365e13	−	1.66365e13i	0.386746	−	0.386746i
$534$			4.38383e12i			0.100960i
$535$	1.80640e13	−	8.90515e12i	0.412140	−	0.203176i
$536$	−1.75905e13			−0.397608
$537$	1.73390e13	+	1.73390e13i	0.388286	+	0.388286i
$538$	6.20025e12	−	6.20025e12i	0.137562	−	0.137562i
$539$		−	4.21926e12i		−	0.0927455i
$540$	−1.46416e13	−	2.97003e13i	−0.318875	−	0.646833i
$541$	5.17386e13			1.11642			0.558211	−	0.829699i	$-0.311488\pi$
$541$	5.17386e13			1.11642			0.558211	+	0.829699i	$0.311488\pi$
$542$	−7.60433e12	−	7.60433e12i	−0.162579	−	0.162579i
$543$	−1.07449e13	+	1.07449e13i	−0.227617	+	0.227617i
$544$			3.40180e13i			0.714026i
$545$	−1.33717e13	−	4.54109e12i	−0.278102	−	0.0944446i
$546$	−1.00656e12			−0.0207432
$547$	5.40393e13	+	5.40393e13i	1.10350	+	1.10350i	0.993985	+	0.109516i	$0.0349302\pi$
$547$	5.40393e13	+	5.40393e13i	1.10350	+	1.10350i	0.109516	+	0.993985i	$0.465070\pi$
$548$	−6.65021e12	+	6.65021e12i	−0.134565	+	0.134565i
$549$		−	1.58111e13i		−	0.317029i
$550$	1.30834e11	+	9.95848e11i	0.00259960	+	0.0197870i
$551$	−4.43739e13			−0.873715
$552$	9.66927e12	+	9.66927e12i	0.188668	+	0.188668i
$553$	−3.01278e12	+	3.01278e12i	−0.0582561	+	0.0582561i
$554$		−	1.74743e13i		−	0.334850i
$555$	−9.19493e12	+	2.70754e13i	−0.174616	+	0.514175i
$556$	−6.65166e13			−1.25186
$557$	−2.64732e12	−	2.64732e12i	−0.0493777	−	0.0493777i	0.681987	−	0.731365i	$-0.261116\pi$
$557$	−2.64732e12	−	2.64732e12i	−0.0493777	−	0.0493777i	−0.731365	+	0.681987i	$0.761116\pi$
$558$	−6.23767e12	+	6.23767e12i	−0.115306	+	0.115306i
$559$			1.09187e14i			2.00038i
$560$	−9.50892e12	+	4.68769e12i	−0.172660	+	0.0851175i
$561$	2.73884e12			0.0492892
$562$	3.70904e12	+	3.70904e12i	0.0661577	+	0.0661577i
$563$	5.45245e13	−	5.45245e13i	0.963940	−	0.963940i	−0.0354321	−	0.999372i	$-0.511281\pi$
$563$	5.45245e13	−	5.45245e13i	0.963940	−	0.963940i	0.999372	+	0.0354321i	$0.0112808\pi$
$564$		−	9.27910e12i		−	0.162596i
$565$	−1.26265e13	−	2.56128e13i	−0.219302	−	0.444850i
$566$	1.39969e13			0.240963
$567$	−4.74947e12	−	4.74947e12i	−0.0810456	−	0.0810456i
$568$	1.58420e13	−	1.58420e13i	0.267959	−	0.267959i
$569$			8.15865e13i			1.36791i	0.729525	+	0.683955i	$0.239741\pi$
$569$			8.15865e13i			1.36791i	−0.729525	+	0.683955i	$0.760259\pi$
$570$	−5.15587e12	−	1.75096e12i	−0.0856896	−	0.0291005i
$571$	9.85629e13			1.62380			0.811901	−	0.583795i	$-0.198433\pi$
$571$	9.85629e13			1.62380			0.811901	+	0.583795i	$0.198433\pi$
$572$	−4.53225e12	−	4.53225e12i	−0.0740174	−	0.0740174i
$573$	2.14977e13	−	2.14977e13i	0.348031	−	0.348031i
$574$		−	1.36803e12i		−	0.0219552i
$575$	−1.00868e14	+	1.32519e13i	−1.60477	+	0.210834i
$576$	−3.98895e13			−0.629138
$577$	−3.53230e13	−	3.53230e13i	−0.552305	−	0.552305i	0.374801	−	0.927105i	$-0.377711\pi$
$577$	−3.53230e13	−	3.53230e13i	−0.552305	−	0.552305i	−0.927105	+	0.374801i	$0.877711\pi$
$578$	4.79811e12	−	4.79811e12i	0.0743758	−	0.0743758i
$579$		−	3.41898e13i		−	0.525417i
$580$	1.64362e13	−	4.83981e13i	0.250416	−	0.737375i
$581$	−1.81099e13			−0.273549
$582$	−1.21907e12	−	1.21907e12i	−0.0182563	−	0.0182563i
$583$	2.92303e12	−	2.92303e12i	0.0434001	−	0.0434001i
$584$			1.58724e13i			0.233657i
$585$	5.72533e13	−	2.82246e13i	0.835644	−	0.411954i
$586$	1.87418e12			0.0271220
$587$	4.08411e12	+	4.08411e12i	0.0586012	+	0.0586012i	0.735800	−	0.677199i	$-0.236806\pi$
$587$	4.08411e12	+	4.08411e12i	0.0586012	+	0.0586012i	−0.677199	+	0.735800i	$0.736806\pi$
$588$	−1.86303e13	+	1.86303e13i	−0.265053	+	0.265053i
$589$		−	7.30154e13i		−	1.03000i
$590$	−6.82600e12	−	1.38464e13i	−0.0954786	−	0.193677i
$591$	−2.76517e13			−0.383517
$592$	5.94881e13	+	5.94881e13i	0.818129	+	0.818129i
$593$	8.89286e13	−	8.89286e13i	1.21274	−	1.21274i	0.242619	−	0.970122i	$-0.421994\pi$
$593$	8.89286e13	−	8.89286e13i	1.21274	−	1.21274i	0.970122	−	0.242619i	$-0.0780064\pi$
$594$		−	1.11088e12i		−	0.0150222i
$595$	1.90918e13	+	6.48365e12i	0.256013	+	0.0869430i
$596$	5.48885e13			0.729877
$597$	−9.37434e12	−	9.37434e12i	−0.123614	−	0.123614i
$598$	−2.00951e13	+	2.00951e13i	−0.262775	+	0.262775i
$599$			8.84354e13i			1.14681i	0.819272	+	0.573406i	$0.194378\pi$
$599$			8.84354e13i			1.14681i	−0.819272	+	0.573406i	$0.805622\pi$
$600$	7.80618e12	−	1.01676e13i	0.100388	−	0.130756i
$601$	−1.24727e14			−1.59070			−0.795352	−	0.606148i	$-0.792714\pi$
$601$	−1.24727e14			−1.59070			−0.795352	+	0.606148i	$0.792714\pi$
$602$	4.48927e12	+	4.48927e12i	0.0567797	+	0.0567797i
$603$	−4.64507e13	+	4.64507e13i	−0.582648	+	0.582648i
$604$		−	1.00300e14i		−	1.24772i
$605$	−2.58169e13	+	7.60205e13i	−0.318513	+	0.937894i
$606$	1.44248e10			0.000176500
$607$	−7.90250e12	−	7.90250e12i	−0.0959005	−	0.0959005i	0.657529	−	0.753429i	$-0.271602\pi$
$607$	−7.90250e12	−	7.90250e12i	−0.0959005	−	0.0959005i	−0.753429	+	0.657529i	$0.771602\pi$
$608$	−3.66506e13	+	3.66506e13i	−0.441127	+	0.441127i
$609$			6.15164e12i			0.0734352i
$610$	5.91855e12	−	2.91772e12i	0.0700755	−	0.0345457i
$611$	3.94126e13			0.462837
$612$	5.94623e13	+	5.94623e13i	0.692603	+	0.692603i
$613$	−7.87997e13	+	7.87997e13i	−0.910378	+	0.910378i	−0.996302	−	0.0859234i	$-0.972616\pi$
$613$	−7.87997e13	+	7.87997e13i	−0.910378	+	0.910378i	0.0859234	+	0.996302i	$0.472616\pi$
$614$			2.19856e13i			0.251940i
$615$	−7.80175e12	−	1.58258e13i	−0.0886782	−	0.179882i
$616$	−7.61694e11			−0.00858770
$617$	−8.06967e13	−	8.06967e13i	−0.902464	−	0.902464i	0.0931846	−	0.995649i	$-0.470295\pi$
$617$	−8.06967e13	−	8.06967e13i	−0.902464	−	0.902464i	−0.995649	+	0.0931846i	$0.970295\pi$
$618$	2.69525e12	−	2.69525e12i	0.0298990	−	0.0298990i
$619$			1.91232e13i			0.210430i	0.994450	+	0.105215i	$0.0335530\pi$
$619$			1.91232e13i			0.210430i	−0.994450	+	0.105215i	$0.966447\pi$
$620$	7.96370e13	+	2.70451e13i	0.869273	+	0.295209i
$621$	1.12519e14			1.21834
$622$	−7.11630e12	−	7.11630e12i	−0.0764368	−	0.0764368i
$623$	1.74893e13	−	1.74893e13i	0.186351	−	0.186351i
$624$			3.81958e13i			0.403732i
$625$	2.46334e13	+	9.21311e13i	0.258300	+	0.966065i
$626$	7.78503e12			0.0809821
$627$	2.95079e12	+	2.95079e12i	0.0304510	+	0.0304510i
$628$	−1.16584e12	+	1.16584e12i	−0.0119355	+	0.0119355i
$629$		−	1.60001e14i		−	1.62506i
$630$	1.19352e12	−	3.51445e12i	0.0120262	−	0.0354124i
$631$	−7.38246e13			−0.737997			−0.368998	−	0.929430i	$-0.620299\pi$
$631$	−7.38246e13			−0.737997			−0.368998	+	0.929430i	$0.620299\pi$
$632$	−1.07177e13	−	1.07177e13i	−0.106296	−	0.106296i
$633$	−2.02946e13	+	2.02946e13i	−0.199692	+	0.199692i
$634$		−	2.79772e12i		−	0.0273123i
$635$	−1.21016e13	+	5.96583e12i	−0.117213	+	0.0577833i
$636$	−2.58135e13			−0.248063
$637$	−7.91313e13	−	7.91313e13i	−0.754486	−	0.754486i
$638$	1.21250e12	−	1.21250e12i	0.0114704	−	0.0114704i
$639$		−	8.36668e13i		−	0.785324i
$640$	−3.49156e13	−	7.08258e13i	−0.325177	−	0.659616i
$641$	2.06509e14			1.90831			0.954154	−	0.299317i	$-0.0967587\pi$
$641$	2.06509e14			1.90831			0.954154	+	0.299317i	$0.0967587\pi$
$642$	−2.98333e12	−	2.98333e12i	−0.0273544	−	0.0273544i
$643$	−4.65598e13	+	4.65598e13i	−0.423600	+	0.423600i	−0.886441	−	0.462841i	$-0.846830\pi$
$643$	−4.65598e13	+	4.65598e13i	−0.423600	+	0.423600i	0.462841	+	0.886441i	$0.346830\pi$
$644$		−	3.77492e13i		−	0.340784i
$645$	7.75350e13	+	2.63312e13i	0.694543	+	0.235870i
$646$	3.04683e13			0.270823
$647$	−3.93706e13	−	3.93706e13i	−0.347257	−	0.347257i	0.511830	−	0.859087i	$-0.328968\pi$
$647$	−3.93706e13	−	3.93706e13i	−0.347257	−	0.347257i	−0.859087	+	0.511830i	$0.828968\pi$
$648$	1.68959e13	−	1.68959e13i	0.147879	−	0.147879i
$649$			1.18312e13i			0.102755i
$650$	2.11306e13	+	1.62231e13i	0.182115	+	0.139820i
$651$	−1.01223e13			−0.0865710
$652$	−4.26728e13	−	4.26728e13i	−0.362171	−	0.362171i
$653$	−2.83045e12	+	2.83045e12i	−0.0238391	+	0.0238391i	−0.718926	−	0.695087i	$-0.755366\pi$
$653$	−2.83045e12	+	2.83045e12i	−0.0238391	+	0.0238391i	0.695087	+	0.718926i	$0.255366\pi$
$654$			2.95837e12i			0.0247265i
$655$	1.33352e13	−	3.92669e13i	0.110610	−	0.325702i
$656$	−5.19126e13			−0.427320
$657$	4.19138e13	+	4.19138e13i	0.342397	+	0.342397i
$658$	1.62046e12	−	1.62046e12i	0.0131374	−	0.0131374i
$659$			1.73272e14i			1.39412i	0.717011	+	0.697062i	$0.245510\pi$
$659$			1.73272e14i			1.39412i	−0.717011	+	0.697062i	$0.754490\pi$
$660$	−4.31138e12	+	2.12542e12i	−0.0344268	+	0.0169717i
$661$	−8.78289e13			−0.696034			−0.348017	−	0.937488i	$-0.613145\pi$
$661$	−8.78289e13			−0.696034			−0.348017	+	0.937488i	$0.613145\pi$
$662$	1.28459e13	+	1.28459e13i	0.101036	+	0.101036i
$663$	5.13662e13	−	5.13662e13i	0.400968	−	0.400968i
$664$		−	6.44246e13i		−	0.499127i
$665$	1.35839e13	+	2.75547e13i	0.104452	+	0.211879i
$666$	−2.94533e13			−0.224782
$667$	1.22812e14	+	1.22812e14i	0.930276	+	0.930276i
$668$	−1.29201e14	+	1.29201e14i	−0.971364	+	0.971364i
$669$			6.21479e13i			0.463763i
$670$	−2.59597e13	−	8.81603e12i	−0.192277	−	0.0652979i
$671$	−5.05715e12			−0.0371786
$672$	5.08094e12	+	5.08094e12i	0.0370764	+	0.0370764i
$673$	−5.27984e13	+	5.27984e13i	−0.382424	+	0.382424i	−0.871975	−	0.489551i	$-0.837161\pi$
$673$	−5.27984e13	+	5.27984e13i	−0.382424	+	0.382424i	0.489551	+	0.871975i	$0.337161\pi$
$674$			5.30004e12i			0.0381048i
$675$	−1.37394e13	−	1.04578e14i	−0.0980504	−	0.746316i
$676$	−3.47558e13			−0.246203
$677$	6.90074e13	+	6.90074e13i	0.485235	+	0.485235i	0.906799	−	0.421563i	$-0.138519\pi$
$677$	6.90074e13	+	6.90074e13i	0.485235	+	0.485235i	−0.421563	+	0.906799i	$0.638519\pi$
$678$	−4.23004e12	+	4.23004e12i	−0.0295254	+	0.0295254i
$679$			9.72692e12i			0.0673948i
$680$	−2.30651e13	+	6.79176e13i	−0.158639	+	0.467130i
$681$	−9.57381e13			−0.653656
$682$	1.99511e12	+	1.99511e12i	0.0135221	+	0.0135221i
$683$	1.63496e14	−	1.63496e14i	1.10003	−	1.10003i	0.105625	−	0.994406i	$-0.466316\pi$
$683$	1.63496e14	−	1.63496e14i	1.10003	−	1.10003i	0.994406	−	0.105625i	$-0.0336842\pi$
$684$			1.28128e14i			0.855783i
$685$	−2.68699e13	+	1.32463e13i	−0.178161	+	0.0878297i
$686$	−1.33443e13			−0.0878362
$687$	−3.36707e13	−	3.36707e13i	−0.220023	−	0.220023i
$688$	1.70354e14	−	1.70354e14i	1.10512	−	1.10512i
$689$		−	1.09642e14i		−	0.706122i
$690$	9.42367e12	+	1.91158e13i	0.0602524	+	0.122221i
$691$	1.36873e14			0.868818			0.434409	−	0.900716i	$-0.356957\pi$
$691$	1.36873e14			0.868818			0.434409	+	0.900716i	$0.356957\pi$
$692$	−1.09197e14	−	1.09197e14i	−0.688144	−	0.688144i
$693$	−2.01138e12	+	2.01138e12i	−0.0125843	+	0.0125843i
$694$			1.05176e13i			0.0653311i
$695$	−2.00625e14	−	6.81330e13i	−1.23726	−	0.420178i
$696$	−2.18840e13			−0.133992
$697$	6.98126e13	+	6.98126e13i	0.424395	+	0.424395i
$698$	2.61256e13	−	2.61256e13i	0.157685	−	0.157685i
$699$		−	3.10697e13i		−	0.186188i
$700$	−3.50851e13	+	4.60945e12i	−0.208753	+	0.0274258i
$701$	−1.67987e13			−0.0992398			−0.0496199	−	0.998768i	$-0.515801\pi$
$701$	−1.67987e13			−0.0992398			−0.0496199	+	0.998768i	$0.515801\pi$
$702$	−2.08343e13	−	2.08343e13i	−0.122206	−	0.122206i
$703$	1.72383e14	−	1.72383e14i	1.00396	−	1.00396i
$704$			1.27586e13i			0.0737801i
$705$	9.50459e12	−	2.79873e13i	0.0545742	−	0.160700i
$706$	−6.88655e13			−0.392625
$707$	−5.75474e10	−	5.75474e10i	−0.000325783	−	0.000325783i
$708$	5.22409e13	−	5.22409e13i	0.293660	−	0.293660i
$709$			1.26548e14i			0.706356i	0.935556	+	0.353178i	$0.114899\pi$
$709$			1.26548e14i			0.706356i	−0.935556	+	0.353178i	$0.885101\pi$
$710$	3.13190e13	−	1.54396e13i	0.173587	−	0.0855744i
$711$	−5.66039e13			−0.311529
$712$	6.22167e13	+	6.22167e13i	0.340022	+	0.340022i
$713$	−2.02082e14	+	2.02082e14i	−1.09668	+	1.09668i
$714$		−	4.22388e12i		−	0.0227625i
$715$	−9.02761e12	−	1.83124e13i	−0.0483106	−	0.0979975i
$716$	2.40809e14			1.27970
$717$	9.90927e12	+	9.90927e12i	0.0522933	+	0.0522933i
$718$	3.25654e13	−	3.25654e13i	0.170661	−	0.170661i
$719$			8.16574e11i			0.00424963i	0.999998	+	0.00212481i	$0.000676350\pi$
$719$			8.16574e11i			0.00424963i	−0.999998	+	0.00212481i	$0.999324\pi$
$720$	−1.33363e14	−	4.52905e13i	−0.689242	−	0.234070i
$721$	−2.15054e13			−0.110375
$722$	4.41599e12	+	4.41599e12i	0.0225083	+	0.0225083i
$723$	−5.22816e13	+	5.22816e13i	−0.264641	+	0.264641i
$724$			1.49229e14i			0.750171i
$725$	9.91485e13	−	1.29141e14i	0.494989	−	0.644724i
$726$	1.68188e13			0.0833898
$727$	1.34638e14	+	1.34638e14i	0.662974	+	0.662974i	0.956080	−	0.293106i	$-0.0946889\pi$
$727$	1.34638e14	+	1.34638e14i	0.662974	+	0.662974i	−0.293106	+	0.956080i	$0.594689\pi$
$728$	−1.42854e13	+	1.42854e13i	−0.0698611	+	0.0698611i
$729$		−	2.55197e13i		−	0.123947i
$730$	−7.95496e12	+	2.34242e13i	−0.0383728	+	0.112993i
$731$	−4.58188e14			−2.19511
$732$	2.23300e13	+	2.23300e13i	0.106251	+	0.106251i
$733$	−1.94919e14	+	1.94919e14i	−0.921157	+	0.921157i	−0.997111	−	0.0759543i	$-0.975800\pi$
$733$	−1.94919e14	+	1.94919e14i	−0.921157	+	0.921157i	0.0759543	+	0.997111i	$0.475800\pi$
$734$		−	3.80675e12i		−	0.0178679i
$735$	−7.52750e13	+	3.71089e13i	−0.350925	+	0.172998i
$736$	2.02873e14			0.939367
$737$	1.48572e13	+	1.48572e13i	0.0683281	+	0.0683281i
$738$	1.28513e13	−	1.28513e13i	0.0587035	−	0.0587035i
$739$		−	1.67761e14i		−	0.761146i	−0.924751	−	0.380573i	$-0.875727\pi$
$739$		−	1.67761e14i		−	0.761146i	0.924751	−	0.380573i	$-0.124273\pi$
$740$	1.24165e14	+	2.51867e14i	0.559553	+	1.13505i
$741$	1.10683e14			0.495438
$742$	−4.50795e12	−	4.50795e12i	−0.0200429	−	0.0200429i
$743$	6.39674e13	−	6.39674e13i	0.282497	−	0.282497i	−0.551607	−	0.834104i	$-0.685985\pi$
$743$	6.39674e13	−	6.39674e13i	0.282497	−	0.282497i	0.834104	+	0.551607i	$0.185985\pi$
$744$		−	3.60091e13i		−	0.157960i
$745$	1.65552e14	+	5.62223e13i	0.721364	+	0.244978i
$746$	−4.97835e13			−0.215472
$747$	−1.70124e14	−	1.70124e14i	−0.731413	−	0.731413i
$748$	1.90189e13	−	1.90189e13i	0.0812228	−	0.0812228i
$749$			2.38039e13i			0.100981i
$750$	1.66160e13	−	1.10928e13i	0.0700197	−	0.0467449i
$751$	1.82829e14			0.765323			0.382661	−	0.923889i	$-0.375008\pi$
$751$	1.82829e14			0.765323			0.382661	+	0.923889i	$0.375008\pi$
$752$	−6.14915e13	−	6.14915e13i	−0.255697	−	0.255697i
$753$	−7.04657e13	+	7.04657e13i	−0.291074	+	0.291074i
$754$		−	4.54802e13i		−	0.186623i
$755$	1.02737e14	−	3.02521e14i	0.418787	−	1.23316i
$756$	3.91378e13			0.158485
$757$	−2.32023e14	−	2.32023e14i	−0.933363	−	0.933363i	0.0645511	−	0.997914i	$-0.479438\pi$
$757$	−2.32023e14	−	2.32023e14i	−0.933363	−	0.933363i	−0.997914	+	0.0645511i	$0.979438\pi$
$758$	−1.60007e13	+	1.60007e13i	−0.0639428	+	0.0639428i
$759$		−	1.63336e13i		−	0.0648445i
$760$	−9.80238e13	+	4.83236e13i	−0.386602	+	0.190586i
$761$	−6.14463e13			−0.240753			−0.120377	−	0.992728i	$-0.538410\pi$
$761$	−6.14463e13			−0.240753			−0.120377	+	0.992728i	$0.538410\pi$
$762$	1.99863e12	+	1.99863e12i	0.00777959	+	0.00777959i
$763$	1.18024e13	−	1.18024e13i	0.0456401	−	0.0456401i
$764$		−	2.98566e14i		−	1.14703i
$765$	1.18441e14	+	2.40255e14i	0.452057	+	0.916992i
$766$	7.37235e13			0.279552
$767$	2.21891e14	+	2.21891e14i	0.835917	+	0.835917i
$768$	4.71048e13	−	4.71048e13i	0.176303	−	0.176303i
$769$		−	2.33449e14i		−	0.868080i	−0.900894	−	0.434040i	$-0.857088\pi$
$769$		−	2.33449e14i		−	0.868080i	0.900894	−	0.434040i	$-0.142912\pi$
$770$	−1.12409e12	−	3.81747e11i	−0.00415287	−	0.00141033i
$771$	6.06505e13			0.222619
$772$	−2.37420e14	−	2.37420e14i	−0.865826	−	0.865826i
$773$	1.25932e13	−	1.25932e13i	0.0456288	−	0.0456288i	−0.683924	−	0.729553i	$-0.739728\pi$
$773$	1.25932e13	−	1.25932e13i	0.0456288	−	0.0456288i	0.729553	+	0.683924i	$0.239728\pi$
$774$			8.43443e13i			0.303634i
$775$	2.12496e14	+	1.63145e14i	0.760049	+	0.583531i
$776$	−3.46028e13			−0.122971
$777$	−2.38978e13	−	2.38978e13i	−0.0843826	−	0.0843826i
$778$	−6.07305e13	+	6.07305e13i	−0.213063	+	0.213063i
$779$			1.50431e14i			0.524384i
$780$	−4.09972e13	+	1.20721e14i	−0.141998	+	0.418127i
$781$	−2.67607e13			−0.0920964
$782$	−8.43261e13	−	8.43261e13i	−0.288355	−	0.288355i
$783$	−1.27330e14	+	1.27330e14i	−0.432634	+	0.432634i
$784$			2.46921e14i			0.833640i
$785$	−4.71055e12	+	2.32220e12i	−0.0158024	+	0.00779024i
$786$	−8.68743e12			−0.0289587
$787$	9.94162e12	+	9.94162e12i	0.0329294	+	0.0329294i	0.723380	−	0.690450i	$-0.242588\pi$
$787$	9.94162e12	+	9.94162e12i	0.0329294	+	0.0329294i	−0.690450	+	0.723380i	$0.742588\pi$
$788$	−1.92018e14	+	1.92018e14i	−0.631990	+	0.631990i
$789$		−	1.79099e14i		−	0.585743i
$790$	−1.04455e13	−	2.11885e13i	−0.0339464	−	0.0688597i
$791$	3.37514e13			0.108996
$792$	−7.15534e12	−	7.15534e12i	−0.0229617	−	0.0229617i
$793$	−9.48456e13	+	9.48456e13i	−0.302448	+	0.302448i
$794$			5.35333e13i			0.169637i
$795$	−7.78577e13	−	2.64408e13i	−0.245169	−	0.0832604i
$796$	−1.30194e14			−0.407404
$797$	3.81477e14	+	3.81477e14i	1.18625	+	1.18625i	0.978096	+	0.208155i	$0.0667457\pi$
$797$	3.81477e14	+	3.81477e14i	1.18625	+	1.18625i	0.208155	+	0.978096i	$0.433254\pi$
$798$	4.55077e12	−	4.55077e12i	0.0140627	−	0.0140627i
$799$			1.65389e14i			0.507893i
$800$	−2.47723e13	−	1.88556e14i	−0.0755989	−	0.575426i
$801$	3.28587e14			0.996525
$802$	4.66148e13	+	4.66148e13i	0.140492	+	0.140492i
$803$	1.34061e13	−	1.34061e13i	0.0401535	−	0.0401535i
$804$		−	1.31205e14i		−	0.390544i
$805$	3.86666e13	−	1.13858e14i	0.114382	−	0.336809i
$806$	7.48357e13			0.220006
$807$	9.45177e13	+	9.45177e13i	0.276150	+	0.276150i
$808$	2.04721e11	−	2.04721e11i	0.000594436	−	0.000594436i
$809$		−	7.59808e13i		−	0.219261i	−0.993972	−	0.109630i	$-0.965033\pi$
$809$		−	7.59808e13i		−	0.219261i	0.993972	−	0.109630i	$-0.0349668\pi$
$810$	3.34025e13	−	1.64667e13i	0.0957974	−	0.0472261i
$811$	−3.51474e14			−1.00182			−0.500909	−	0.865500i	$-0.667001\pi$
$811$	−3.51474e14			−1.00182			−0.500909	+	0.865500i	$0.667001\pi$
$812$	4.27180e13	+	4.27180e13i	0.121013	+	0.121013i
$813$	1.15922e14	−	1.15922e14i	0.326371	−	0.326371i
$814$			9.42058e12i			0.0263606i
$815$	−8.49983e13	−	1.72418e14i	−0.236386	−	0.479506i
$816$	−1.60283e14			−0.443034
$817$	−4.93648e14	−	4.93648e14i	−1.35615	−	1.35615i
$818$	2.69354e13	−	2.69354e13i	0.0735457	−	0.0735457i
$819$			7.54460e13i			0.204747i
$820$	−1.64073e14	−	5.57199e13i	−0.442556	−	0.150294i
$821$	−5.87456e13			−0.157492			−0.0787462	−	0.996895i	$-0.525092\pi$
$821$	−5.87456e13			−0.157492			−0.0787462	+	0.996895i	$0.525092\pi$
$822$	4.43767e12	+	4.43767e12i	0.0118249	+	0.0118249i
$823$	2.06649e14	−	2.06649e14i	0.547311	−	0.547311i	−0.378351	−	0.925662i	$-0.623509\pi$
$823$	2.06649e14	−	2.06649e14i	0.547311	−	0.547311i	0.925662	+	0.378351i	$0.123509\pi$
$824$		−	7.65037e13i		−	0.201394i
$825$	−1.51809e13	+	1.99445e12i	−0.0397216	+	0.00521859i
$826$	1.82463e13			0.0474541
$827$	2.86687e14	+	2.86687e14i	0.741107	+	0.741107i	0.972791	−	0.231684i	$-0.0744236\pi$
$827$	2.86687e14	+	2.86687e14i	0.741107	+	0.741107i	−0.231684	+	0.972791i	$0.574424\pi$
$828$	3.54615e14	−	3.54615e14i	0.911184	−	0.911184i
$829$		−	9.04765e13i		−	0.231080i	−0.993303	−	0.115540i	$-0.963140\pi$
$829$		−	9.04765e13i		−	0.231080i	0.993303	−	0.115540i	$-0.0368599\pi$
$830$	3.22884e13	−	9.50766e13i	0.0819702	−	0.241370i
$831$	2.66381e14			0.672199
$832$	2.39284e14	+	2.39284e14i	0.600202	+	0.600202i
$833$	3.32063e14	−	3.32063e14i	0.827933	−	0.827933i
$834$			4.43864e13i			0.110007i
$835$	−5.22030e14	+	2.57350e14i	−1.28607	+	0.634003i
$836$	4.09816e13			0.100359
$837$	−2.09515e14	−	2.09515e14i	−0.510022	−	0.510022i
$838$	−1.96715e13	+	1.96715e13i	−0.0476011	+	0.0476011i
$839$			3.57580e14i			0.860128i	0.902798	+	0.430064i	$0.141509\pi$
$839$			3.57580e14i			0.860128i	−0.902798	+	0.430064i	$0.858491\pi$
$840$	6.69919e12	+	1.35892e13i	0.0160187	+	0.0324936i
$841$	1.42753e14			0.339316
$842$	−1.17736e13	−	1.17736e13i	−0.0278196	−	0.0278196i
$843$	−5.65413e13	+	5.65413e13i	−0.132809	+	0.132809i
$844$			2.81858e14i			0.658139i
$845$	−1.04829e14	−	3.56004e13i	−0.243332	−	0.0826364i
$846$	3.04451e13			0.0702532
$847$	−6.70985e13	−	6.70985e13i	−0.153920	−	0.153920i
$848$	−1.71063e14	+	1.71063e14i	−0.390101	+	0.390101i
$849$			2.13371e14i			0.483724i
$850$	−6.80780e13	+	8.86716e13i	−0.153431	+	0.199844i
$851$	−9.54197e14			−2.13791
$852$	1.18163e14	+	1.18163e14i	0.263198	+	0.263198i
$853$	7.28675e13	−	7.28675e13i	0.161357	−	0.161357i	−0.621810	−	0.783168i	$-0.713603\pi$
$853$	7.28675e13	−	7.28675e13i	0.161357	−	0.161357i	0.783168	+	0.621810i	$0.213603\pi$
$854$			7.79922e12i			0.0171697i
$855$	−1.31242e14	+	3.86455e14i	−0.287238	+	0.845802i
$856$	−8.46807e13			−0.184253
$857$	3.16590e14	+	3.16590e14i	0.684847	+	0.684847i	0.961088	−	0.276242i	$-0.0890890\pi$
$857$	3.16590e14	+	3.16590e14i	0.684847	+	0.684847i	−0.276242	+	0.961088i	$0.589089\pi$
$858$	−3.02436e12	+	3.02436e12i	−0.00650425	+	0.00650425i
$859$		−	1.37150e13i		−	0.0293244i	−0.999893	−	0.0146622i	$-0.995333\pi$
$859$		−	1.37150e13i		−	0.0293244i	0.999893	−	0.0146622i	$-0.00466729\pi$
$860$	7.21264e14	−	3.55567e14i	1.53321	−	0.755840i
$861$	2.08545e13			0.0440742
$862$	9.97563e13	+	9.97563e13i	0.209606	+	0.209606i
$863$	2.41396e13	−	2.41396e13i	0.0504286	−	0.0504286i	−0.681443	−	0.731871i	$-0.738647\pi$
$863$	2.41396e13	−	2.41396e13i	0.0504286	−	0.0504286i	0.731871	+	0.681443i	$0.238647\pi$
$864$			2.10336e14i			0.436862i
$865$	−2.17505e14	−	4.41205e14i	−0.449147	−	0.911088i
$866$	−9.25940e13			−0.190105
$867$	7.31433e13	+	7.31433e13i	0.149307	+	0.149307i
$868$	−7.02906e13	+	7.02906e13i	−0.142659	+	0.142659i
$869$			1.81047e13i			0.0365336i
$870$	−3.22960e13	−	1.09678e13i	−0.0647965	−	0.0220052i
$871$	5.57287e14			1.11170
$872$	4.19860e13	+	4.19860e13i	0.0832764	+	0.0832764i
$873$	−9.13745e13	+	9.13745e13i	−0.180200	+	0.180200i
$874$		−	1.81704e14i		−	0.356293i
$875$	−1.10544e14	−	2.20349e13i	−0.215523	−	0.0429606i
$876$	−1.18390e14			−0.229506
$877$	−3.68225e14	−	3.68225e14i	−0.709766	−	0.709766i	0.256720	−	0.966486i	$-0.417358\pi$
$877$	−3.68225e14	−	3.68225e14i	−0.709766	−	0.709766i	−0.966486	+	0.256720i	$0.917358\pi$
$878$	−1.08104e14	+	1.08104e14i	−0.207190	+	0.207190i
$879$			2.85703e13i			0.0544465i
$880$	−1.44861e13	+	4.26559e13i	−0.0274498	+	0.0808287i
$881$	1.21911e14			0.229700			0.114850	−	0.993383i	$-0.463361\pi$
$881$	1.21911e14			0.229700			0.114850	+	0.993383i	$0.463361\pi$
$882$	−6.11268e13	−	6.11268e13i	−0.114522	−	0.114522i
$883$	7.38601e13	−	7.38601e13i	0.137596	−	0.137596i	−0.634954	−	0.772550i	$-0.718981\pi$
$883$	7.38601e13	−	7.38601e13i	0.137596	−	0.137596i	0.772550	+	0.634954i	$0.218981\pi$
$884$		−	7.13391e14i		−	1.32150i
$885$	2.11078e14	−	1.04057e14i	0.388800	−	0.191670i
$886$	−2.71451e13			−0.0497190
$887$	−4.03967e14	−	4.03967e14i	−0.735746	−	0.735746i	0.236005	−	0.971752i	$-0.424162\pi$
$887$	−4.03967e14	−	4.03967e14i	−0.735746	−	0.735746i	−0.971752	+	0.236005i	$0.924162\pi$
$888$	8.50146e13	−	8.50146e13i	0.153967	−	0.153967i
$889$		−	1.59470e13i		−	0.0287191i
$890$	6.06363e13	+	1.23000e14i	0.108588	+	0.220270i
$891$	−2.85410e13			−0.0508254
$892$	4.31565e14	+	4.31565e14i	0.764227	+	0.764227i
$893$	−1.78188e14	+	1.78188e14i	−0.313778	+	0.313778i
$894$		−	3.66269e13i		−	0.0641377i
$895$	7.26319e14	+	2.46661e14i	1.26477	+	0.429522i
$896$	9.33312e13			0.161617
$897$	−3.06333e14	−	3.06333e14i	−0.527511	−	0.527511i
$898$	1.57625e14	−	1.57625e14i	0.269925	−	0.269925i
$899$		−	4.57362e14i		−	0.778864i
$900$	−3.72890e14	−	2.86288e14i	−0.631492	−	0.484831i
$901$	4.60095e14			0.774861
$902$	−4.11046e12	−	4.11046e12i	−0.00688426	−	0.00688426i
$903$	−6.84353e13	+	6.84353e13i	−0.113983	+	0.113983i
$904$			1.20068e14i			0.198877i
$905$	−1.52855e14	+	4.50098e14i	−0.251789	+	0.741421i
$906$	−6.69300e13			−0.109643
$907$	−1.93179e14	−	1.93179e14i	−0.314719	−	0.314719i	0.532016	−	0.846734i	$-0.321435\pi$
$907$	−1.93179e14	−	1.93179e14i	−0.314719	−	0.314719i	−0.846734	+	0.532016i	$0.821435\pi$
$908$	−6.64821e14	+	6.64821e14i	−1.07715	+	1.07715i
$909$		−	1.08120e12i		−	0.00174215i
$910$	−2.82417e13	+	1.39225e13i	−0.0452568	+	0.0223106i
$911$	8.80416e14			1.40312			0.701562	−	0.712608i	$-0.252486\pi$
$911$	8.80416e14			1.40312			0.701562	+	0.712608i	$0.252486\pi$
$912$	−1.72688e14	−	1.72688e14i	−0.273708	−	0.273708i
$913$	−5.44139e13	+	5.44139e13i	−0.0857741	+	0.0857741i
$914$		−	4.06147e13i		−	0.0636725i
$915$	4.44782e13	+	9.02234e13i	0.0693493	+	0.140674i
$916$	−4.67629e14			−0.725144
$917$	3.46584e13	+	3.46584e13i	0.0534518	+	0.0534518i
$918$	8.74280e13	−	8.74280e13i	0.134103	−	0.134103i
$919$			2.50083e14i			0.381510i	0.981638	+	0.190755i	$0.0610937\pi$
$919$			2.50083e14i			0.381510i	−0.981638	+	0.190755i	$0.938906\pi$
$920$	4.05040e14	+	1.37553e14i	0.614553	+	0.208705i
$921$	−3.35152e14			−0.505760
$922$	2.82281e13	+	2.82281e13i	0.0423669	+	0.0423669i
$923$	−5.01891e14	+	5.01891e14i	−0.749206	+	0.749206i
$924$		−	5.68135e12i		−	0.00843513i
$925$	1.16514e14	+	8.86855e14i	0.172056	+	1.30962i
$926$	−4.91984e13			−0.0722596
$927$	−2.02021e14	−	2.02021e14i	−0.295119	−	0.295119i
$928$	−2.29576e14	+	2.29576e14i	−0.333570	+	0.333570i
$929$			4.22608e12i			0.00610744i	0.999995	+	0.00305372i	$0.000972031\pi$
$929$			4.22608e12i			0.00610744i	−0.999995	+	0.00305372i	$0.999028\pi$
$930$	1.80471e13	−	5.31416e13i	0.0259414	−	0.0763871i
$931$	7.15523e14			1.02300
$932$	−2.15753e14	−	2.15753e14i	−0.306816	−	0.306816i
$933$	1.08482e14	−	1.08482e14i	0.153444	−	0.153444i
$934$		−	1.23389e14i		−	0.173597i
$935$	7.68452e13	−	3.78830e13i	0.107537	−	0.0530135i
$936$	−2.68393e14			−0.373588
$937$	8.53049e14	+	8.53049e14i	1.18107	+	1.18107i	0.979467	+	0.201604i	$0.0646154\pi$
$937$	8.53049e14	+	8.53049e14i	1.18107	+	1.18107i	0.201604	+	0.979467i	$0.435385\pi$
$938$	2.29130e13	−	2.29130e13i	0.0315550	−	0.0315550i
$939$			1.18676e14i			0.162569i
$940$	−1.28347e14	−	2.60349e14i	−0.174882	−	0.354746i
$941$	−7.60983e14			−1.03140			−0.515699	−	0.856770i	$-0.672468\pi$
$941$	−7.60983e14			−1.03140			−0.515699	+	0.856770i	$0.672468\pi$
$942$	7.77965e11	+	7.77965e11i	0.00104883	+	0.00104883i
$943$	4.16342e14	−	4.16342e14i	0.558331	−	0.558331i
$944$		−	6.92389e14i		−	0.923614i
$945$	1.18046e14	+	4.00889e13i	0.156636	+	0.0531943i
$946$	2.69774e13			0.0356077
$947$	−2.06394e14	−	2.06394e14i	−0.270987	−	0.270987i	0.558511	−	0.829497i	$-0.311373\pi$
$947$	−2.06394e14	−	2.06394e14i	−0.270987	−	0.270987i	−0.829497	+	0.558511i	$0.811373\pi$
$948$	7.99418e13	−	7.99418e13i	0.104408	−	0.104408i
$949$		−	5.02855e14i		−	0.653299i
$950$	−1.68881e14	+	2.21874e13i	−0.218254	+	0.0286740i
$951$	4.26489e13			0.0548284
$952$	−5.99466e13	−	5.99466e13i	−0.0766619	−	0.0766619i
$953$	3.44966e14	−	3.44966e14i	0.438845	−	0.438845i	−0.452778	−	0.891623i	$-0.649567\pi$
$953$	3.44966e14	−	3.44966e14i	0.438845	−	0.438845i	0.891623	+	0.452778i	$0.149567\pi$
$954$		−	8.46953e13i		−	0.107181i
$955$	3.05822e14	−	9.00524e14i	0.384992	−	1.13365i
$956$	1.37623e14			0.172346
$957$	1.84835e13	+	1.84835e13i	0.0230263	+	0.0230263i
$958$	−2.09827e14	+	2.09827e14i	−0.260036	+	0.260036i
$959$		−	3.54081e13i		−	0.0436525i
$960$	2.27623e14	−	1.12213e14i	0.279165	−	0.137622i
$961$	−6.70591e13			−0.0818165
$962$	1.76681e14	+	1.76681e14i	0.214444	+	0.214444i
$963$	−2.23614e14	+	2.23614e14i	−0.270002	+	0.270002i
$964$			7.26103e14i			0.872194i
$965$	−4.72907e14	−	9.59286e14i	−0.565118	−	1.14633i
$966$	−2.51900e13			−0.0299462
$967$	−5.84321e14	−	5.84321e14i	−0.691065	−	0.691065i	0.271401	−	0.962466i	$-0.412513\pi$
$967$	−5.84321e14	−	5.84321e14i	−0.691065	−	0.691065i	−0.962466	+	0.271401i	$0.912513\pi$
$968$	2.38698e14	−	2.38698e14i	0.280848	−	0.280848i
$969$			4.64465e14i			0.543668i
$970$	−5.10661e13	−	1.73423e13i	−0.0594668	−	0.0201952i
$971$	−1.97850e14			−0.229213			−0.114606	−	0.993411i	$-0.536561\pi$
$971$	−1.97850e14			−0.229213			−0.114606	+	0.993411i	$0.536561\pi$
$972$	5.68458e14	+	5.68458e14i	0.655190	+	0.655190i
$973$	1.77079e14	−	1.77079e14i	0.203050	−	0.203050i
$974$			1.56464e14i			0.178492i
$975$	−2.47308e14	+	3.22119e14i	−0.280683	+	0.365590i
$976$	2.95956e14			0.334178
$977$	2.11691e14	+	2.11691e14i	0.237809	+	0.237809i	0.815942	−	0.578133i	$-0.196219\pi$
$977$	2.11691e14	+	2.11691e14i	0.237809	+	0.237809i	−0.578133	+	0.815942i	$0.696219\pi$
$978$	−2.84755e13	+	2.84755e13i	−0.0318256	+	0.0318256i
$979$		−	1.05098e14i		−	0.116864i
$980$	−2.65031e14	+	7.80412e14i	−0.293202	+	0.863363i
$981$	2.21742e14			0.244064
$982$	−1.06660e14	−	1.06660e14i	−0.116800	−	0.116800i
$983$	6.31966e14	−	6.31966e14i	0.688535	−	0.688535i	−0.273373	−	0.961908i	$-0.588139\pi$
$983$	6.31966e14	−	6.31966e14i	0.688535	−	0.688535i	0.961908	+	0.273373i	$0.0881394\pi$
$984$			7.41883e13i			0.0804193i
$985$	−7.75841e14	+	3.82473e14i	−0.836742	+	0.412496i
$986$	1.90851e14			0.204790
$987$	2.47026e13	+	2.47026e13i	0.0263728	+	0.0263728i
$988$	7.68600e14	−	7.68600e14i	0.816424	−	0.816424i
$989$			2.73250e15i			2.88788i
$990$	−6.97359e12	−	1.41458e13i	−0.00733298	−	0.0148748i
$991$	−1.45360e15			−1.52082			−0.760409	−	0.649445i	$-0.775001\pi$
$991$	−1.45360e15			−1.52082			−0.760409	+	0.649445i	$0.775001\pi$
$992$	−3.77758e14	−	3.77758e14i	−0.393238	−	0.393238i
$993$	−1.95825e14	+	1.95825e14i	−0.202826	+	0.202826i
$994$			4.12708e13i			0.0425316i
$995$	−3.92686e14	−	1.33358e14i	−0.402652	−	0.136742i
$996$	4.80533e14			0.490260
$997$	4.52019e14	+	4.52019e14i	0.458861	+	0.458861i	0.898282	−	0.439420i	$-0.144816\pi$
$997$	4.52019e14	+	4.52019e14i	0.458861	+	0.458861i	−0.439420	+	0.898282i	$0.644816\pi$
$998$	−4.21639e13	+	4.21639e13i	−0.0425881	+	0.0425881i
$999$		−	9.89297e14i		−	0.994258i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.11.c.a.2.2	✓	8
3.2	odd	2		45.11.g.a.37.3		8
4.3	odd	2		80.11.p.d.17.2		8
5.2	odd	4		25.11.c.a.18.3		8
5.3	odd	4	inner	5.11.c.a.3.2	yes	8
5.4	even	2		25.11.c.a.7.3		8
15.8	even	4		45.11.g.a.28.3		8
20.3	even	4		80.11.p.d.33.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.11.c.a.2.2	✓	8	1.1	even	1	trivial
5.11.c.a.3.2	yes	8	5.3	odd	4	inner
25.11.c.a.7.3		8	5.4	even	2
25.11.c.a.18.3		8	5.2	odd	4
45.11.g.a.28.3		8	15.8	even	4
45.11.g.a.37.3		8	3.2	odd	2
80.11.p.d.17.2		8	4.3	odd	2
80.11.p.d.33.2		8	20.3	even	4

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)

\(f(q)\)	\(=\)	\(q+(-4.63382 - 4.63382i) q^{2} +(70.6389 - 70.6389i) q^{3} -981.055i q^{4} +(1004.90 - 2959.02i) q^{5} -654.656 q^{6} +(2611.74 + 2611.74i) q^{7} +(-9291.07 + 9291.07i) q^{8} +49069.3i q^{9} +O(q^{10})\)	\(q+(-4.63382 - 4.63382i) q^{2} +(70.6389 - 70.6389i) q^{3} -981.055i q^{4} +(1004.90 - 2959.02i) q^{5} -654.656 q^{6} +(2611.74 + 2611.74i) q^{7} +(-9291.07 + 9291.07i) q^{8} +49069.3i q^{9} +(-18368.1 + 9055.08i) q^{10} +15694.7 q^{11} +(-69300.6 - 69300.6i) q^{12} +(294351. - 294351. i) q^{13} -24204.7i q^{14} +(-138037. - 280007. i) q^{15} -918494. q^{16} +(1.23520e6 + 1.23520e6i) q^{17} +(227379. - 227379. i) q^{18} +2.66159e6i q^{19} +(-2.90296e6 - 985859. i) q^{20} +368981. q^{21} +(-72726.7 - 72726.7i) q^{22} +(7.36638e6 - 7.36638e6i) q^{23} +1.31262e6i q^{24} +(-7.74599e6 - 5.94702e6i) q^{25} -2.72795e6 q^{26} +(7.63735e6 + 7.63735e6i) q^{27} +(2.56226e6 - 2.56226e6i) q^{28} +1.66720e7i q^{29} +(-657861. + 1.93714e6i) q^{30} -2.74330e7 q^{31} +(1.37702e7 + 1.37702e7i) q^{32} +(1.10866e6 - 1.10866e6i) q^{33} -1.14474e7i q^{34} +(1.03527e7 - 5.10367e6i) q^{35} +4.81397e7 q^{36} +(-6.47670e7 - 6.47670e7i) q^{37} +(1.23333e7 - 1.23333e7i) q^{38} -4.15853e7i q^{39} +(1.81559e7 + 3.68291e7i) q^{40} +5.65192e7 q^{41} +(-1.70979e6 - 1.70979e6i) q^{42} +(-1.85471e8 + 1.85471e8i) q^{43} -1.53974e7i q^{44} +(1.45197e8 + 4.93095e7i) q^{45} -6.82690e7 q^{46} +(6.69481e7 + 6.69481e7i) q^{47} +(-6.48814e7 + 6.48814e7i) q^{48} -2.68833e8i q^{49} +(8.33614e6 + 6.34510e7i) q^{50} +1.74507e8 q^{51} +(-2.88775e8 - 2.88775e8i) q^{52} +(1.86243e8 - 1.86243e8i) q^{53} -7.07803e7i q^{54} +(1.57716e7 - 4.64411e7i) q^{55} -4.85318e7 q^{56} +(1.88012e8 + 1.88012e8i) q^{57} +(7.72550e7 - 7.72550e7i) q^{58} +7.53831e8i q^{59} +(-2.74702e8 + 1.35422e8i) q^{60} -3.22219e8 q^{61} +(1.27120e8 + 1.27120e8i) q^{62} +(-1.28156e8 + 1.28156e8i) q^{63} +8.12921e8i q^{64} +(-5.75200e8 - 1.16678e9i) q^{65} -1.02747e7 q^{66} +(9.46635e8 + 9.46635e8i) q^{67} +(1.21180e9 - 1.21180e9i) q^{68} -1.04071e9i q^{69} +(-7.16223e7 - 2.43232e7i) q^{70} -1.70508e9 q^{71} +(-4.55907e8 - 4.55907e8i) q^{72} +(8.54176e8 - 8.54176e8i) q^{73} +6.00238e8i q^{74} +(-9.67259e8 + 1.27078e8i) q^{75} +2.61117e9 q^{76} +(4.09906e7 + 4.09906e7i) q^{77} +(-1.92699e8 + 1.92699e8i) q^{78} +1.15355e9i q^{79} +(-9.22991e8 + 2.71784e9i) q^{80} -1.81851e9 q^{81} +(-2.61900e8 - 2.61900e8i) q^{82} +(-3.46702e9 + 3.46702e9i) q^{83} -3.61991e8i q^{84} +(4.89624e9 - 2.41374e9i) q^{85} +1.71888e9 q^{86} +(1.17769e9 + 1.17769e9i) q^{87} +(-1.45821e8 + 1.45821e8i) q^{88} -6.69639e9i q^{89} +(-4.44326e8 - 9.01310e8i) q^{90} +1.53754e9 q^{91} +(-7.22683e9 - 7.22683e9i) q^{92} +(-1.93784e9 + 1.93784e9i) q^{93} -6.20452e8i q^{94} +(7.87570e9 + 2.67462e9i) q^{95} +1.94542e9 q^{96} +(1.86215e9 + 1.86215e9i) q^{97} +(-1.24572e9 + 1.24572e9i) q^{98} +7.70130e8i 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more