LMFDB - Embedded newform 5.21.c.a.2.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,21,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, 21, names="a")

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 21);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 21 $
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:	$12.6756882551$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 7326009 x^{16} + 21914129354136 x^{14} + \cdots + 79\!\cdots\!76 $ x^18 + 7326009x^16 + 21914129354136x^14 + 34716886079362208784x^12 + 31708037646565185778430976x^10 + 17074068956994774485619232997376x^8 + 5289719974975064649188570034899779584x^6 + 860456443567863287787024826102919920091136x^4 + 56032264901085762369236000491606259366923075584x^2 + 797517854172776133766249661927470942176176766976
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{48}\cdot 3^{16}\cdot 5^{32} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.5
Root			$-3.77310i$ of defining polynomial
Character	$\chi$	$=$	5.2
Dual form			5.21.c.a.3.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.77310 + 3.77310i) q^{2} +(38858.9 - 38858.9i) q^{3} -1.04855e6i q^{4} +(-8.90462e6 - 4.00939e6i) q^{5} +293237. q^{6} +(4.46902e7 + 4.46902e7i) q^{7} +(7.91266e6 - 7.91266e6i) q^{8} +4.66753e8i q^{9} +O(q^{10})$	\(q+(3.77310 + 3.77310i) q^{2} +(38858.9 - 38858.9i) q^{3} -1.04855e6i q^{4} +(-8.90462e6 - 4.00939e6i) q^{5} +293237. q^{6} +(4.46902e7 + 4.46902e7i) q^{7} +(7.91266e6 - 7.91266e6i) q^{8} +4.66753e8i q^{9} +(-1.84702e7 - 4.87259e7i) q^{10} -1.60852e10 q^{11} +(-4.07454e10 - 4.07454e10i) q^{12} +(-3.76718e10 + 3.76718e10i) q^{13} +3.37242e8i q^{14} +(-5.01824e11 + 1.90223e11i) q^{15} -1.09942e12 q^{16} +(-2.08022e12 - 2.08022e12i) q^{17} +(-1.76111e9 + 1.76111e9i) q^{18} -2.99942e11i q^{19} +(-4.20404e12 + 9.33691e12i) q^{20} +3.47323e12 q^{21} +(-6.06910e10 - 6.06910e10i) q^{22} +(4.11357e13 - 4.11357e13i) q^{23} -6.14955e11i q^{24} +(6.32170e13 + 7.14042e13i) q^{25} -2.84279e11 q^{26} +(1.53630e14 + 1.53630e14i) q^{27} +(4.68598e13 - 4.68598e13i) q^{28} -3.65291e14i q^{29} +(-2.61117e12 - 1.17570e12i) q^{30} -1.33214e15 q^{31} +(-1.24453e13 - 1.24453e13i) q^{32} +(-6.25053e14 + 6.25053e14i) q^{33} -1.56978e13i q^{34} +(-2.18769e14 - 5.77130e14i) q^{35} +4.89412e14 q^{36} +(-1.48105e15 - 1.48105e15i) q^{37} +(1.13171e12 - 1.13171e12i) q^{38} +2.92777e15i q^{39} +(-1.02184e14 + 3.87343e13i) q^{40} +2.38548e16 q^{41} +(1.31048e13 + 1.31048e13i) q^{42} +(5.02697e15 - 5.02697e15i) q^{43} +1.68661e16i q^{44} +(1.87139e15 - 4.15625e15i) q^{45} +3.10419e14 q^{46} +(-1.96675e16 - 1.96675e16i) q^{47} +(-4.27224e16 + 4.27224e16i) q^{48} -7.57978e16i q^{49} +(-3.08912e13 + 5.07940e14i) q^{50} -1.61670e17 q^{51} +(3.95006e16 + 3.95006e16i) q^{52} +(-6.48453e15 + 6.48453e15i) q^{53} +1.15932e15i q^{54} +(1.43232e17 + 6.44918e16i) q^{55} +7.07237e14 q^{56} +(-1.16554e16 - 1.16554e16i) q^{57} +(1.37828e15 - 1.37828e15i) q^{58} -5.84951e17i q^{59} +(1.99458e17 + 5.26187e17i) q^{60} +9.66810e17 q^{61} +(-5.02630e15 - 5.02630e15i) q^{62} +(-2.08593e16 + 2.08593e16i) q^{63} +1.15273e18i q^{64} +(4.86494e17 - 1.84412e17i) q^{65} -4.71678e15 q^{66} +(-2.23353e18 - 2.23353e18i) q^{67} +(-2.18121e18 + 2.18121e18i) q^{68} -3.19698e18i q^{69} +(1.35213e15 - 3.00301e15i) q^{70} +1.33306e18 q^{71} +(3.69326e15 + 3.69326e15i) q^{72} +(-4.76853e18 + 4.76853e18i) q^{73} -1.11763e16i q^{74} +(5.23123e18 + 3.18146e17i) q^{75} -3.14504e17 q^{76} +(-7.18850e17 - 7.18850e17i) q^{77} +(-1.10468e16 + 1.10468e16i) q^{78} -1.15172e19i q^{79} +(9.78993e18 + 4.40801e18i) q^{80} +1.03123e19 q^{81} +(9.00068e16 + 9.00068e16i) q^{82} +(-6.54386e18 + 6.54386e18i) q^{83} -3.64184e18i q^{84} +(1.01831e19 + 2.68640e19i) q^{85} +3.79345e16 q^{86} +(-1.41948e19 - 1.41948e19i) q^{87} +(-1.27277e17 + 1.27277e17i) q^{88} -2.48209e19i q^{89} +(2.27429e16 - 8.62101e15i) q^{90} -3.36712e18 q^{91} +(-4.31328e19 - 4.31328e19i) q^{92} +(-5.17655e19 + 5.17655e19i) q^{93} -1.48415e17i q^{94} +(-1.20259e18 + 2.67087e18i) q^{95} -9.67219e17 q^{96} +(4.02655e19 + 4.02655e19i) q^{97} +(2.85993e17 - 2.85993e17i) q^{98} -7.50780e18i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + 29448 q^{3} - 7302140 q^{5} + 19792536 q^{6} - 585532752 q^{7} + 930113700 q^{8}+O(q^{10}) $ 18 * q - 2 * q^2 + 29448 * q^3 - 7302140 * q^5 + 19792536 * q^6 - 585532752 * q^7 + 930113700 * q^8	$ 18 q - 2 q^{2} + 29448 q^{3} - 7302140 q^{5} + 19792536 q^{6} - 585532752 q^{7} + 930113700 q^{8} - 17138778090 q^{10} - 6506343064 q^{11} + 140311795848 q^{12} - 369354655602 q^{13} + 998626204320 q^{15} - 6345876020232 q^{16} + 6508314764998 q^{17} - 11265991705902 q^{18} + 38356516779780 q^{20} - 97402974719064 q^{21} + 161054386758096 q^{22} - 81655963656152 q^{23} + 33913283845350 q^{25} + 234104101103636 q^{26} - 511935279143400 q^{27} + 772213614545352 q^{28} - 877127470680480 q^{30} + 17\!\cdots\!36 q^{31}+ \cdots - 27\!\cdots\!98 q^{98}+O(q^{100}) $ 18 * q - 2 * q^2 + 29448 * q^3 - 7302140 * q^5 + 19792536 * q^6 - 585532752 * q^7 + 930113700 * q^8 - 17138778090 * q^10 - 6506343064 * q^11 + 140311795848 * q^12 - 369354655602 * q^13 + 998626204320 * q^15 - 6345876020232 * q^16 + 6508314764998 * q^17 - 11265991705902 * q^18 + 38356516779780 * q^20 - 97402974719064 * q^21 + 161054386758096 * q^22 - 81655963656152 * q^23 + 33913283845350 * q^25 + 234104101103636 * q^26 - 511935279143400 * q^27 + 772213614545352 * q^28 - 877127470680480 * q^30 + 1742256896900736 * q^31 - 4072699683722552 * q^32 + 1579138514189496 * q^33 - 4817791288113440 * q^35 + 2214548622647868 * q^36 + 6383289895587498 * q^37 - 14134212502378200 * q^38 + 43297629431150700 * q^40 - 30602304597564664 * q^41 + 48810732785962896 * q^42 - 46399469942287752 * q^43 + 67947826451186070 * q^45 + 17467214047538136 * q^46 - 137109249757437752 * q^47 - 103698596104819152 * q^48 - 40012852869983150 * q^50 + 686047946059669536 * q^51 - 745026624616846452 * q^52 - 184102027021671302 * q^53 + 752956242406989720 * q^55 + 685775432394721200 * q^56 - 785021725278622800 * q^57 - 2701246502184220800 * q^58 + 6219197632829342760 * q^60 + 49879194030044136 * q^61 - 1190554579738283704 * q^62 - 7082176979112100152 * q^63 + 6907070599410641170 * q^65 + 11227963704975799872 * q^66 - 5597336519263153752 * q^67 - 25617328014464685148 * q^68 + 31706333959370270760 * q^70 + 10983277495574224736 * q^71 - 41525052650392592700 * q^72 - 19072400700441139902 * q^73 + 36766882672050433200 * q^75 + 75630007803532292400 * q^76 - 47766064678699704904 * q^77 - 109239984515466629304 * q^78 + 134231700802559812960 * q^80 + 74219234884008322518 * q^81 - 83501540658117625104 * q^82 - 119739383617210903952 * q^83 + 169044713294843560110 * q^85 + 33497378050769887736 * q^86 - 28944830404542403200 * q^87 - 337125565675837197600 * q^88 + 396784292056608506070 * q^90 + 86281377644254817136 * q^91 - 206921051460419061752 * q^92 - 285487695991878257304 * q^93 + 118106834336527303800 * q^95 + 377091713708556287136 * q^96 - 318608382222604685502 * q^97 - 27697031317753120498 * 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 $

$2$	3.77310	+	3.77310i	0.00368467	+	0.00368467i	0.708947	−	0.705262i	$-0.249171\pi$
$2$	3.77310	+	3.77310i	0.00368467	+	0.00368467i	−0.705262	+	0.708947i	$0.749171\pi$
$3$	38858.9	−	38858.9i	0.658079	−	0.658079i	−0.296846	−	0.954925i	$-0.595935\pi$
$3$	38858.9	−	38858.9i	0.658079	−	0.658079i	0.954925	+	0.296846i	$0.0959348\pi$
$4$		−	1.04855e6i		−	0.999973i
$5$	−8.90462e6	−	4.00939e6i	−0.911833	−	0.410562i
$5$	−8.90462e6	−	4.00939e6i	−0.911833	−	0.410562i
$6$	293237.			0.00484961
$7$	4.46902e7	+	4.46902e7i	0.158209	+	0.158209i	0.781773	−	0.623563i	$-0.214316\pi$
$7$	4.46902e7	+	4.46902e7i	0.158209	+	0.158209i	−0.623563	+	0.781773i	$0.714316\pi$
$8$	7.91266e6	−	7.91266e6i	0.00736924	−	0.00736924i
$9$			4.66753e8i			0.133863i
$10$	−1.84702e7	−	4.87259e7i	−0.00184702	−	0.00487259i
$11$	−1.60852e10			−0.620153			−0.310077	−	0.950712i	$-0.600355\pi$
$11$	−1.60852e10			−0.620153			−0.310077	+	0.950712i	$0.600355\pi$
$12$	−4.07454e10	−	4.07454e10i	−0.658061	−	0.658061i
$13$	−3.76718e10	+	3.76718e10i	−0.273264	+	0.273264i	−0.830413	−	0.557149i	$-0.811895\pi$
$13$	−3.76718e10	+	3.76718e10i	−0.273264	+	0.273264i	0.557149	+	0.830413i	$0.311895\pi$
$14$			3.37242e8i			0.00116590i
$15$	−5.01824e11	+	1.90223e11i	−0.870240	+	0.329876i
$16$	−1.09942e12			−0.999919
$17$	−2.08022e12	−	2.08022e12i	−1.03186	−	1.03186i	−0.999476	−	0.0323821i	$-0.989691\pi$
$17$	−2.08022e12	−	2.08022e12i	−1.03186	−	1.03186i	−0.0323821	−	0.999476i	$-0.510309\pi$
$18$	−1.76111e9	+	1.76111e9i	−0.000493242	+	0.000493242i
$19$		−	2.99942e11i		−	0.0489217i	−0.999701	−	0.0244609i	$-0.992213\pi$
$19$		−	2.99942e11i		−	0.0489217i	0.999701	−	0.0244609i	$-0.00778691\pi$
$20$	−4.20404e12	+	9.33691e12i	−0.410551	+	0.911808i
$21$	3.47323e12			0.208229
$22$	−6.06910e10	−	6.06910e10i	−0.00228506	−	0.00228506i
$23$	4.11357e13	−	4.11357e13i	0.992981	−	0.992981i	−0.00699448	−	0.999976i	$-0.502226\pi$
$23$	4.11357e13	−	4.11357e13i	0.992981	−	0.992981i	0.999976	+	0.00699448i	$0.00222643\pi$
$24$		−	6.14955e11i		−	0.00969909i
$25$	6.32170e13	+	7.14042e13i	0.662878	+	0.748727i
$26$	−2.84279e11			−0.00201378
$27$	1.53630e14	+	1.53630e14i	0.746172	+	0.746172i
$28$	4.68598e13	−	4.68598e13i	0.158205	−	0.158205i
$29$		−	3.65291e14i		−	0.868279i	−0.900846	−	0.434140i	$-0.857052\pi$
$29$		−	3.65291e14i		−	0.868279i	0.900846	−	0.434140i	$-0.142948\pi$
$30$	−2.61117e12	−	1.17570e12i	−0.00442203	−	0.00199106i
$31$	−1.33214e15			−1.62530			−0.812649	−	0.582754i	$-0.801975\pi$
$31$	−1.33214e15			−1.62530			−0.812649	+	0.582754i	$0.801975\pi$
$32$	−1.24453e13	−	1.24453e13i	−0.0110536	−	0.0110536i
$33$	−6.25053e14	+	6.25053e14i	−0.408110	+	0.408110i
$34$		−	1.56978e13i		−	0.00760411i
$35$	−2.18769e14	−	5.77130e14i	−0.0793058	−	0.209215i
$36$	4.89412e14			0.133860
$37$	−1.48105e15	−	1.48105e15i	−0.308002	−	0.308002i	0.536132	−	0.844134i	$-0.319885\pi$
$37$	−1.48105e15	−	1.48105e15i	−0.308002	−	0.308002i	−0.844134	+	0.536132i	$0.819885\pi$
$38$	1.13171e12	−	1.13171e12i	0.000180260	−	0.000180260i
$39$			2.92777e15i			0.359659i
$40$	−1.02184e14	+	3.87343e13i	−0.00974504	+	0.00369399i
$41$	2.38548e16			1.77721			0.888603	−	0.458676i	$-0.151676\pi$
$41$	2.38548e16			1.77721			0.888603	+	0.458676i	$0.151676\pi$
$42$	1.31048e13	+	1.31048e13i	0.000767254	+	0.000767254i
$43$	5.02697e15	−	5.02697e15i	0.232606	−	0.232606i	−0.581173	−	0.813780i	$-0.697406\pi$
$43$	5.02697e15	−	5.02697e15i	0.232606	−	0.232606i	0.813780	+	0.581173i	$0.197406\pi$
$44$			1.68661e16i			0.620136i
$45$	1.87139e15	−	4.15625e15i	0.0549592	−	0.122061i
$46$	3.10419e14			0.00731762
$47$	−1.96675e16	−	1.96675e16i	−0.373913	−	0.373913i	0.494987	−	0.868900i	$-0.335173\pi$
$47$	−1.96675e16	−	1.96675e16i	−0.373913	−	0.373913i	−0.868900	+	0.494987i	$0.835173\pi$
$48$	−4.27224e16	+	4.27224e16i	−0.658026	+	0.658026i
$49$		−	7.57978e16i		−	0.949940i
$50$	−3.08912e13	+	5.07940e14i	−0.000316326	+	0.00520130i
$51$	−1.61670e17			−1.35809
$52$	3.95006e16	+	3.95006e16i	0.273257	+	0.273257i
$53$	−6.48453e15	+	6.48453e15i	−0.0370783	+	0.0370783i	−0.725403	−	0.688325i	$-0.758347\pi$
$53$	−6.48453e15	+	6.48453e15i	−0.0370783	+	0.0370783i	0.688325	+	0.725403i	$0.258347\pi$
$54$			1.15932e15i			0.00549880i
$55$	1.43232e17	+	6.44918e16i	0.565476	+	0.254611i
$56$	7.07237e14			0.00233177
$57$	−1.16554e16	−	1.16554e16i	−0.0321944	−	0.0321944i
$58$	1.37828e15	−	1.37828e15i	0.00319932	−	0.00319932i
$59$		−	5.84951e17i		−	1.14446i	−0.820094	−	0.572229i	$-0.806079\pi$
$59$		−	5.84951e17i		−	1.14446i	0.820094	−	0.572229i	$-0.193921\pi$
$60$	1.99458e17	+	5.26187e17i	0.329867	+	0.870217i
$61$	9.66810e17			1.35532			0.677662	−	0.735374i	$-0.262993\pi$
$61$	9.66810e17			1.35532			0.677662	+	0.735374i	$0.262993\pi$
$62$	−5.02630e15	−	5.02630e15i	−0.00598869	−	0.00598869i
$63$	−2.08593e16	+	2.08593e16i	−0.0211784	+	0.0211784i
$64$			1.15273e18i			0.999837i
$65$	4.86494e17	−	1.84412e17i	0.361363	−	0.136979i
$66$	−4.71678e15			−0.00300750
$67$	−2.23353e18	−	2.23353e18i	−1.22530	−	1.22530i	−0.965721	−	0.259581i	$-0.916416\pi$
$67$	−2.23353e18	−	2.23353e18i	−1.22530	−	1.22530i	−0.259581	−	0.965721i	$-0.583584\pi$
$68$	−2.18121e18	+	2.18121e18i	−1.03183	+	1.03183i
$69$		−	3.19698e18i		−	1.30692i
$70$	1.35213e15	−	3.00301e15i	0.000478673	−	0.00106310i
$71$	1.33306e18			0.409513			0.204757	−	0.978813i	$-0.434360\pi$
$71$	1.33306e18			0.409513			0.204757	+	0.978813i	$0.434360\pi$
$72$	3.69326e15	+	3.69326e15i	0.000986471	+	0.000986471i
$73$	−4.76853e18	+	4.76853e18i	−1.10957	+	1.10957i	−0.116367	+	0.993206i	$0.537125\pi$
$73$	−4.76853e18	+	4.76853e18i	−1.10957	+	1.10957i	−0.993206	+	0.116367i	$0.962875\pi$
$74$		−	1.11763e16i		−	0.00226977i
$75$	5.23123e18	+	3.18146e17i	0.928948	+	0.0564956i
$76$	−3.14504e17			−0.0489204
$77$	−7.18850e17	−	7.18850e17i	−0.0981141	−	0.0981141i
$78$	−1.10468e16	+	1.10468e16i	−0.00132522	+	0.00132522i
$79$		−	1.15172e19i		−	1.21639i	−0.793786	−	0.608197i	$-0.791893\pi$
$79$		−	1.15172e19i		−	1.21639i	0.793786	−	0.608197i	$-0.208107\pi$
$80$	9.78993e18	+	4.40801e18i	0.911759	+	0.410528i
$81$	1.03123e19			0.848217
$82$	9.00068e16	+	9.00068e16i	0.00654842	+	0.00654842i
$83$	−6.54386e18	+	6.54386e18i	−0.421748	+	0.421748i	−0.885805	−	0.464057i	$-0.846393\pi$
$83$	−6.54386e18	+	6.54386e18i	−0.421748	+	0.421748i	0.464057	+	0.885805i	$0.346393\pi$
$84$		−	3.64184e18i		−	0.208223i
$85$	1.01831e19	+	2.68640e19i	0.517240	+	1.36452i
$86$	3.79345e16			0.00171415
$87$	−1.41948e19	−	1.41948e19i	−0.571397	−	0.571397i
$88$	−1.27277e17	+	1.27277e17i	−0.00457006	+	0.00457006i
$89$		−	2.48209e19i		−	0.796008i	−0.917384	−	0.398004i	$-0.869703\pi$
$89$		−	2.48209e19i		−	0.796008i	0.917384	−	0.398004i	$-0.130297\pi$
$90$	2.27429e16	−	8.62101e15i	0.000652261	−	0.000247248i
$91$	−3.36712e18			−0.0864659
$92$	−4.31328e19	−	4.31328e19i	−0.992954	−	0.992954i
$93$	−5.17655e19	+	5.17655e19i	−1.06957	+	1.06957i
$94$		−	1.48415e17i		−	0.00275549i
$95$	−1.20259e18	+	2.67087e18i	−0.0200854	+	0.0446084i
$96$	−9.67219e17			−0.0145483
$97$	4.02655e19	+	4.02655e19i	0.546030	+	0.546030i	0.925290	−	0.379260i	$-0.123822\pi$
$97$	4.02655e19	+	4.02655e19i	0.546030	+	0.546030i	−0.379260	+	0.925290i	$0.623822\pi$
$98$	2.85993e17	−	2.85993e17i	0.00350021	−	0.00350021i
$99$		−	7.50780e18i		−	0.0830158i
$100$	7.48707e19	−	6.62860e19i	0.748707	−	0.662860i
$101$	1.10526e20			1.00058			0.500288	−	0.865859i	$-0.333228\pi$
$101$	1.10526e20			1.00058			0.500288	+	0.865859i	$0.333228\pi$
$102$	−6.09998e17	−	6.09998e17i	−0.00500411	−	0.00500411i
$103$	−5.79262e19	+	5.79262e19i	−0.431025	+	0.431025i	−0.888977	−	0.457952i	$-0.848583\pi$
$103$	−5.79262e19	+	5.79262e19i	−0.431025	+	0.431025i	0.457952	+	0.888977i	$0.348583\pi$
$104$			5.96168e17i			0.00402750i
$105$	−3.09278e19	−	1.39255e19i	−0.189870	−	0.0854907i
$106$	−4.89336e16			−0.000273243
$107$	8.04515e19	+	8.04515e19i	0.408975	+	0.408975i	0.881381	−	0.472406i	$-0.156614\pi$
$107$	8.04515e19	+	8.04515e19i	0.408975	+	0.408975i	−0.472406	+	0.881381i	$0.656614\pi$
$108$	1.61089e20	−	1.61089e20i	0.746152	−	0.746152i
$109$			1.45257e20i			0.613581i	0.951777	+	0.306790i	$0.0992551\pi$
$109$			1.45257e20i			0.613581i	−0.951777	+	0.306790i	$0.900745\pi$
$110$	2.97096e17	+	7.83765e17i	0.00114543	+	0.00302175i
$111$	−1.15104e20			−0.405379
$112$	−4.91334e19	−	4.91334e19i	−0.158196	−	0.158196i
$113$	1.43712e20	−	1.43712e20i	0.423359	−	0.423359i	−0.463000	−	0.886358i	$-0.653227\pi$
$113$	1.43712e20	−	1.43712e20i	0.423359	−	0.423359i	0.886358	+	0.463000i	$0.153227\pi$
$114$		−	8.79543e16i		−	0.000237251i
$115$	−5.31227e20	+	2.01369e20i	−1.31311	+	0.497753i
$116$	−3.83025e20			−0.868256
$117$	−1.75834e19	−	1.75834e19i	−0.0365800	−	0.0365800i
$118$	2.20708e18	−	2.20708e18i	0.00421695	−	0.00421695i
$119$		−	1.85931e20i		−	0.326499i
$120$	−2.46560e18	+	5.47594e18i	−0.00398207	+	0.00884395i
$121$	−4.14017e20			−0.615410
$122$	3.64787e18	+	3.64787e18i	0.00499392	+	0.00499392i
$123$	9.26973e20	−	9.26973e20i	1.16954	−	1.16954i
$124$			1.39681e21i			1.62525i
$125$	−2.76636e20	−	8.89289e20i	−0.297035	−	0.954867i
$126$	−1.57408e17			−0.000156071
$127$	1.28344e21	+	1.28344e21i	1.17582	+	1.17582i	0.980800	+	0.195016i	$0.0624760\pi$
$127$	1.28344e21	+	1.28344e21i	1.17582	+	1.17582i	0.195016	+	0.980800i	$0.437524\pi$
$128$	−1.73992e19	+	1.73992e19i	−0.0147377	+	0.0147377i
$129$		−	3.90685e20i		−	0.306147i
$130$	2.53139e18	+	1.13979e18i	0.00183623	+	0.000826779i
$131$	9.63942e20			0.647647			0.323823	−	0.946118i	$-0.395032\pi$
$131$	9.63942e20			0.647647			0.323823	+	0.946118i	$0.395032\pi$
$132$	6.55398e20	+	6.55398e20i	0.408099	+	0.408099i
$133$	1.34045e19	−	1.34045e19i	0.00773987	−	0.00773987i
$134$		−	1.68547e19i		−	0.00902967i
$135$	−7.52054e20	−	1.98398e21i	−0.374034	−	0.986734i
$136$	−3.29201e19			−0.0152080
$137$	−1.38810e21	−	1.38810e21i	−0.595958	−	0.595958i	0.343276	−	0.939234i	$-0.388463\pi$
$137$	−1.38810e21	−	1.38810e21i	−0.595958	−	0.595958i	−0.939234	+	0.343276i	$0.888463\pi$
$138$	1.20625e19	−	1.20625e19i	0.00481557	−	0.00481557i
$139$			2.98122e21i			1.10725i	0.832766	+	0.553626i	$0.186756\pi$
$139$			2.98122e21i			1.10725i	−0.832766	+	0.553626i	$0.813244\pi$
$140$	−6.05148e20	+	2.29389e20i	−0.209210	+	0.0793036i
$141$	−1.52852e21			−0.492129
$142$	5.02979e18	+	5.02979e18i	0.00150892	+	0.00150892i
$143$	6.05957e20	−	6.05957e20i	0.169466	−	0.169466i
$144$		−	5.13158e20i		−	0.133852i
$145$	−1.46460e21	+	3.25278e21i	−0.356482	+	0.791726i
$146$	−3.59843e19			−0.00817682
$147$	−2.94542e21	−	2.94542e21i	−0.625136	−	0.625136i
$148$	−1.55295e21	+	1.55295e21i	−0.307993	+	0.307993i
$149$		−	5.77191e21i		−	1.07018i	−0.844795	−	0.535090i	$-0.820278\pi$
$149$		−	5.77191e21i		−	1.07018i	0.844795	−	0.535090i	$-0.179722\pi$
$150$	1.85376e19	+	2.09384e19i	0.00321470	+	0.00363104i
$151$	−2.64955e20			−0.0429934			−0.0214967	−	0.999769i	$-0.506843\pi$
$151$	−2.64955e20			−0.0429934			−0.0214967	+	0.999769i	$0.506843\pi$
$152$	−2.37334e18	−	2.37334e18i	−0.000360516	−	0.000360516i
$153$	9.70948e20	−	9.70948e20i	0.138128	−	0.138128i
$154$		−	5.42459e18i		−	0.000723036i
$155$	1.18622e22	+	5.34107e21i	1.48200	+	0.667285i
$156$	3.06990e21			0.359649
$157$	6.41131e21	+	6.41131e21i	0.704612	+	0.704612i	0.965397	−	0.260785i	$-0.0839813\pi$
$157$	6.41131e21	+	6.41131e21i	0.704612	+	0.704612i	−0.260785	+	0.965397i	$0.583981\pi$
$158$	4.34554e19	−	4.34554e19i	0.00448201	−	0.00448201i
$159$			5.03964e20i			0.0488009i
$160$	6.09223e19	+	1.60718e20i	0.00554086	+	0.0146172i
$161$	3.67673e21			0.314198
$162$	3.89095e19	+	3.89095e19i	0.00312540	+	0.00312540i
$163$	−1.36800e22	+	1.36800e22i	−1.03326	+	1.03326i	−0.0338306	+	0.999428i	$0.510771\pi$
$163$	−1.36800e22	+	1.36800e22i	−1.03326	+	1.03326i	−0.999428	+	0.0338306i	$0.989229\pi$
$164$		−	2.50129e22i		−	1.77716i
$165$	8.07194e21	−	3.05977e21i	0.539682	−	0.204574i
$166$	−4.93813e19			−0.00310801
$167$	−1.38963e22	−	1.38963e22i	−0.823634	−	0.823634i	0.162993	−	0.986627i	$-0.447885\pi$
$167$	−1.38963e22	−	1.38963e22i	−0.823634	−	0.823634i	−0.986627	+	0.162993i	$0.947885\pi$
$168$	2.74825e19	−	2.74825e19i	0.00153449	−	0.00153449i
$169$			1.61666e22i			0.850654i
$170$	−6.29385e19	+	1.39783e20i	−0.00312196	+	0.00693368i
$171$	1.39999e20			0.00654883
$172$	−5.27101e21	−	5.27101e21i	−0.232600	−	0.232600i
$173$	−2.74845e22	+	2.74845e22i	−1.14453	+	1.14453i	−0.156915	+	0.987612i	$0.550155\pi$
$173$	−2.74845e22	+	2.74845e22i	−1.14453	+	1.14453i	−0.987612	+	0.156915i	$0.949845\pi$
$174$		−	1.07117e20i		−	0.00421082i
$175$	−3.65888e20	+	6.01625e21i	−0.0135821	+	0.223329i
$176$	1.76844e22			0.620103
$177$	−2.27306e22	−	2.27306e22i	−0.753144	−	0.753144i
$178$	9.36518e19	−	9.36518e19i	0.00293303	−	0.00293303i
$179$		−	7.43674e21i		−	0.220218i	−0.993920	−	0.110109i	$-0.964880\pi$
$179$		−	7.43674e21i		−	0.220218i	0.993920	−	0.110109i	$-0.0351200\pi$
$180$	−4.35803e21	−	1.96225e21i	−0.122058	−	0.0549577i
$181$	9.99277e21			0.264789			0.132395	−	0.991197i	$-0.457733\pi$
$181$	9.99277e21			0.264789			0.132395	+	0.991197i	$0.457733\pi$
$182$	−1.27045e19	−	1.27045e19i	−0.000318598	−	0.000318598i
$183$	3.75692e22	−	3.75692e22i	0.891910	−	0.891910i
$184$		−	6.50986e20i		−	0.0146350i
$185$	7.25009e21	+	1.91263e22i	0.154392	+	0.407300i
$186$	−3.90633e20			−0.00788206
$187$	3.34607e22	+	3.34607e22i	0.639910	+	0.639910i
$188$	−2.06223e22	+	2.06223e22i	−0.373903	+	0.373903i
$189$			1.37315e22i			0.236103i
$190$	−1.46150e19	+	5.53999e18i	−0.000238375	+	9.03593e-5i
$191$	1.85330e22			0.286822			0.143411	−	0.989663i	$-0.454193\pi$
$191$	1.85330e22			0.286822			0.143411	+	0.989663i	$0.454193\pi$
$192$	4.47940e22	+	4.47940e22i	0.657972	+	0.657972i
$193$	5.77240e22	−	5.77240e22i	0.804976	−	0.804976i	−0.178892	−	0.983869i	$-0.557251\pi$
$193$	5.77240e22	−	5.77240e22i	0.804976	−	0.804976i	0.983869	+	0.178892i	$0.0572514\pi$
$194$			3.03852e20i			0.00402388i
$195$	1.17386e22	−	2.60707e22i	0.147662	−	0.327949i
$196$	−7.94776e22			−0.949914
$197$	3.85613e21	+	3.85613e21i	0.0438015	+	0.0438015i	0.728668	−	0.684867i	$-0.240140\pi$
$197$	3.85613e21	+	3.85613e21i	0.0438015	+	0.0438015i	−0.684867	+	0.728668i	$0.740140\pi$
$198$	2.83277e19	−	2.83277e19i	0.000305886	−	0.000305886i
$199$		−	5.84096e22i		−	0.599727i	−0.953982	−	0.299863i	$-0.903059\pi$
$199$		−	5.84096e22i		−	0.599727i	0.953982	−	0.299863i	$-0.0969411\pi$
$200$	1.06521e21	+	6.47827e19i	0.0104025	+	0.000632643i
$201$	−1.73585e23			−1.61269
$202$	4.17025e20	+	4.17025e20i	0.00368679	+	0.00368679i
$203$	1.63250e22	−	1.63250e22i	0.137370	−	0.137370i
$204$			1.69519e23i			1.35805i
$205$	−2.12418e23	−	9.56434e22i	−1.62052	−	0.729653i
$206$	−4.37123e20			−0.00317637
$207$	1.92002e22	+	1.92002e22i	0.132924	+	0.132924i
$208$	4.14172e22	−	4.14172e22i	0.273242	−	0.273242i
$209$			4.82463e21i			0.0303390i
$210$	−6.41512e19	−	1.69236e20i	−0.000384602	−	0.00101461i
$211$	1.97241e23			1.12765			0.563824	−	0.825895i	$-0.309330\pi$
$211$	1.97241e23			1.12765			0.563824	+	0.825895i	$0.309330\pi$
$212$	6.79934e21	+	6.79934e21i	0.0370773	+	0.0370773i
$213$	5.18015e22	−	5.18015e22i	0.269492	−	0.269492i
$214$			6.07104e20i			0.00301387i
$215$	−6.49183e22	+	2.46081e22i	−0.307597	+	0.116599i
$216$	2.43125e21			0.0109974
$217$	−5.95336e22	−	5.95336e22i	−0.257137	−	0.257137i
$218$	−5.48069e20	+	5.48069e20i	−0.00226084	+	0.00226084i
$219$			3.70600e23i			1.46037i
$220$	6.76227e22	−	1.50186e23i	0.254604	−	0.565461i
$221$	1.56731e23			0.563939
$222$	−4.34300e20	−	4.34300e20i	−0.00149369	−	0.00149369i
$223$	2.39987e23	−	2.39987e23i	0.789112	−	0.789112i	−0.192237	−	0.981349i	$-0.561574\pi$
$223$	2.39987e23	−	2.39987e23i	0.789112	−	0.789112i	0.981349	+	0.192237i	$0.0615741\pi$
$224$		−	1.11236e21i		−	0.00349757i
$225$	−3.33281e22	+	2.95067e22i	−0.100227	+	0.0887351i
$226$	1.08448e21			0.00311987
$227$	3.10473e23	+	3.10473e23i	0.854605	+	0.854605i	0.990696	−	0.136092i	$-0.0434542\pi$
$227$	3.10473e23	+	3.10473e23i	0.854605	+	0.854605i	−0.136092	+	0.990696i	$0.543454\pi$
$228$	−1.22213e22	+	1.22213e22i	−0.0321935	+	0.0321935i
$229$		−	4.24623e23i		−	1.07065i	−0.844645	−	0.535327i	$-0.820189\pi$
$229$		−	4.24623e23i		−	1.07065i	0.844645	−	0.535327i	$-0.179811\pi$
$230$	−2.76416e21	−	1.24459e21i	−0.00667244	−	0.00300433i
$231$	−5.58675e22			−0.129134
$232$	−2.89043e21	−	2.89043e21i	−0.00639856	−	0.00639856i
$233$	−4.79808e23	+	4.79808e23i	−1.01744	+	1.01744i	−0.0175940	+	0.999845i	$0.505601\pi$
$233$	−4.79808e23	+	4.79808e23i	−1.01744	+	1.01744i	−0.999845	+	0.0175940i	$0.994399\pi$
$234$		−	1.32688e20i		−	0.000269571i
$235$	9.62768e22	+	2.53986e23i	0.187432	+	0.494460i
$236$	−6.13349e23			−1.14443
$237$	−4.47544e23	−	4.47544e23i	−0.800484	−	0.800484i
$238$	7.01536e20	−	7.01536e20i	0.00120304	−	0.00120304i
$239$		−	1.58870e23i		−	0.261254i	−0.991432	−	0.130627i	$-0.958301\pi$
$239$		−	1.58870e23i		−	0.261254i	0.991432	−	0.130627i	$-0.0416991\pi$
$240$	5.51717e23	−	2.09136e23i	0.870170	−	0.329849i
$241$	−3.90298e23			−0.590509			−0.295254	−	0.955419i	$-0.595404\pi$
$241$	−3.90298e23			−0.590509			−0.295254	+	0.955419i	$0.595404\pi$
$242$	−1.56213e21	−	1.56213e21i	−0.00226758	−	0.00226758i
$243$	−1.34949e23	+	1.34949e23i	−0.187978	+	0.187978i
$244$		−	1.01375e24i		−	1.35529i
$245$	−3.03903e23	+	6.74951e23i	−0.390009	+	0.866186i
$246$	6.99513e21			0.00861876
$247$	1.12994e22	+	1.12994e22i	0.0133685	+	0.0133685i
$248$	−1.05408e22	+	1.05408e22i	−0.0119772	+	0.0119772i
$249$			5.08575e23i			0.555087i
$250$	2.31160e21	−	4.39915e21i	0.00242389	−	0.00461285i
$251$	1.59459e24			1.60661			0.803307	−	0.595565i	$-0.203072\pi$
$251$	1.59459e24			1.60661			0.803307	+	0.595565i	$0.203072\pi$
$252$	2.18720e22	+	2.18720e22i	0.0211779	+	0.0211779i
$253$	−6.61676e23	+	6.61676e23i	−0.615800	+	0.615800i
$254$			9.68513e21i			0.00866499i
$255$	1.43961e24	+	6.48199e23i	1.23835	+	0.557579i
$256$	1.20860e24			0.999728
$257$	−9.80272e23	−	9.80272e23i	−0.779858	−	0.779858i	0.199948	−	0.979806i	$-0.435923\pi$
$257$	−9.80272e23	−	9.80272e23i	−0.779858	−	0.779858i	−0.979806	+	0.199948i	$0.935923\pi$
$258$	1.47409e21	−	1.47409e21i	0.00112805	−	0.00112805i
$259$		−	1.32377e23i		−	0.0974575i
$260$	−1.93365e23	−	5.10112e23i	−0.136976	−	0.361353i
$261$	1.70501e23			0.116231
$262$	3.63705e21	+	3.63705e21i	0.00238636	+	0.00238636i
$263$	7.09161e23	−	7.09161e23i	0.447907	−	0.447907i	−0.446752	−	0.894658i	$-0.647419\pi$
$263$	7.09161e23	−	7.09161e23i	0.447907	−	0.447907i	0.894658	+	0.446752i	$0.147419\pi$
$264$			9.89166e21i			0.00601492i
$265$	8.37413e22	−	3.17432e22i	0.0490321	−	0.0185863i
$266$	1.01153e20			5.70378e−5
$267$	−9.64513e23	−	9.64513e23i	−0.523836	−	0.523836i
$268$	−2.34196e24	+	2.34196e24i	−1.22527	+	1.22527i
$269$		−	3.36094e23i		−	0.169409i	−0.996406	−	0.0847047i	$-0.973005\pi$
$269$		−	3.36094e23i		−	0.169409i	0.996406	−	0.0847047i	$-0.0269947\pi$
$270$	4.64819e21	−	1.03233e22i	0.00225759	−	0.00501398i
$271$	8.77461e23			0.410710			0.205355	−	0.978688i	$-0.434165\pi$
$271$	8.77461e23			0.410710			0.205355	+	0.978688i	$0.434165\pi$
$272$	2.28704e24	+	2.28704e24i	1.03177	+	1.03177i
$273$	−1.30843e23	+	1.30843e23i	−0.0569014	+	0.0569014i
$274$		−	1.04749e22i		−	0.00439182i
$275$	−1.01686e24	−	1.14855e24i	−0.411086	−	0.464326i
$276$	−3.35219e24			−1.30688
$277$	−1.37066e24	−	1.37066e24i	−0.515385	−	0.515385i	0.400786	−	0.916172i	$-0.368737\pi$
$277$	−1.37066e24	−	1.37066e24i	−0.515385	−	0.515385i	−0.916172	+	0.400786i	$0.868737\pi$
$278$	−1.12485e22	+	1.12485e22i	−0.00407986	+	0.00407986i
$279$		−	6.21780e23i		−	0.217568i
$280$	−6.29768e21	−	2.83559e21i	−0.00212618	−	0.000957334i
$281$	−3.31689e24			−1.08061			−0.540304	−	0.841470i	$-0.681691\pi$
$281$	−3.31689e24			−1.08061			−0.540304	+	0.841470i	$0.681691\pi$
$282$	−5.76724e21	−	5.76724e21i	−0.00181333	−	0.00181333i
$283$	2.37935e24	−	2.37935e24i	0.722094	−	0.722094i	−0.246937	−	0.969031i	$-0.579424\pi$
$283$	2.37935e24	−	2.37935e24i	0.722094	−	0.722094i	0.969031	+	0.246937i	$0.0794242\pi$
$284$		−	1.39778e24i		−	0.409502i
$285$	5.70560e22	+	1.50518e23i	0.0161381	+	0.0425737i
$286$	4.57268e21			0.00124885
$287$	1.06608e24	+	1.06608e24i	0.281171	+	0.281171i
$288$	5.80886e21	−	5.80886e21i	0.00147967	−	0.00147967i
$289$			4.59039e24i			1.12946i
$290$	−1.77991e22	+	6.74700e21i	−0.00423077	+	0.00160373i
$291$	3.12935e24			0.718662
$292$	5.00003e24	+	5.00003e24i	1.10954	+	1.10954i
$293$	5.85441e24	−	5.85441e24i	1.25547	−	1.25547i	0.302240	−	0.953232i	$-0.402266\pi$
$293$	5.85441e24	−	5.85441e24i	1.25547	−	1.25547i	0.953232	−	0.302240i	$-0.0977343\pi$
$294$		−	2.22268e22i		−	0.00460684i
$295$	−2.34530e24	+	5.20877e24i	−0.469870	+	1.04355i
$296$	−2.34381e22			−0.00453948
$297$	−2.47117e24	−	2.47117e24i	−0.462741	−	0.462741i
$298$	2.17780e22	−	2.17780e22i	0.00394326	−	0.00394326i
$299$			3.09931e24i			0.542692i
$300$	3.33592e23	−	5.48520e24i	0.0564940	−	0.928923i
$301$	4.49313e23			0.0736010
$302$	−9.99701e20	−	9.99701e20i	−0.000158417	−	0.000158417i
$303$	4.29491e24	−	4.29491e24i	0.658458	−	0.658458i
$304$			3.29763e23i			0.0489177i
$305$	−8.60908e24	−	3.87632e24i	−1.23583	−	0.556444i
$306$	7.32697e21			0.00101791
$307$	1.15304e24	+	1.15304e24i	0.155046	+	0.155046i	0.780367	−	0.625321i	$-0.215032\pi$
$307$	1.15304e24	+	1.15304e24i	0.155046	+	0.155046i	−0.625321	+	0.780367i	$0.715032\pi$
$308$	−7.53749e23	+	7.53749e23i	−0.0981114	+	0.0981114i
$309$			4.50190e24i			0.567298i
$310$	2.46049e22	+	6.49097e22i	0.00300196	+	0.00791941i
$311$	−2.21080e23			−0.0261183			−0.0130592	−	0.999915i	$-0.504157\pi$
$311$	−2.21080e23			−0.0261183			−0.0130592	+	0.999915i	$0.504157\pi$
$312$	2.31664e22	+	2.31664e22i	0.00265041	+	0.00265041i
$313$	−6.86614e24	+	6.86614e24i	−0.760798	+	0.760798i	−0.976467	−	0.215668i	$-0.930807\pi$
$313$	−6.86614e24	+	6.86614e24i	−0.760798	+	0.760798i	0.215668	+	0.976467i	$0.430807\pi$
$314$			4.83810e22i			0.00519253i
$315$	2.69377e23	−	1.02111e23i	0.0280062	−	0.0106161i
$316$	−1.20763e25			−1.21636
$317$	−3.58531e24	−	3.58531e24i	−0.349892	−	0.349892i	0.510177	−	0.860069i	$-0.329580\pi$
$317$	−3.58531e24	−	3.58531e24i	−0.349892	−	0.349892i	−0.860069	+	0.510177i	$0.829580\pi$
$318$	−1.90151e21	+	1.90151e21i	−0.000179815	+	0.000179815i
$319$			5.87578e24i			0.538466i
$320$	4.62176e24	−	1.02647e25i	0.410495	−	0.911684i
$321$	6.25252e24			0.538276
$322$	1.38727e22	+	1.38727e22i	0.00115772	+	0.00115772i
$323$	−6.23946e23	+	6.23946e23i	−0.0504803	+	0.0504803i
$324$		−	1.08130e25i		−	0.848194i
$325$	−5.07142e24	−	3.08427e23i	−0.385741	−	0.0234595i
$326$	−1.03232e23			−0.00761443
$327$	5.64453e24	+	5.64453e24i	0.403785	+	0.403785i
$328$	1.88755e23	−	1.88755e23i	0.0130967	−	0.0130967i
$329$		−	1.75789e24i		−	0.118313i
$330$	4.20011e22	+	1.89114e22i	0.00274234	+	0.00123477i
$331$	6.60953e24			0.418688			0.209344	−	0.977842i	$-0.432867\pi$
$331$	6.60953e24			0.418688			0.209344	+	0.977842i	$0.432867\pi$
$332$	6.86155e24	+	6.86155e24i	0.421737	+	0.421737i
$333$	6.91285e23	−	6.91285e23i	0.0412302	−	0.0412302i
$334$		−	1.04864e23i		−	0.00606964i
$335$	1.09336e25	+	2.88438e25i	0.614209	+	1.62033i
$336$	−3.81854e24			−0.208212
$337$	−7.50720e24	−	7.50720e24i	−0.397355	−	0.397355i	0.479944	−	0.877299i	$-0.340657\pi$
$337$	−7.50720e24	−	7.50720e24i	−0.397355	−	0.397355i	−0.877299	+	0.479944i	$0.840657\pi$
$338$	−6.09984e22	+	6.09984e22i	−0.00313438	+	0.00313438i
$339$		−	1.11690e25i		−	0.557207i
$340$	2.81681e25	−	1.06775e25i	1.36449	−	0.517226i
$341$	2.14277e25			1.00793
$342$	5.28230e20	+	5.28230e20i	2.41303e−5	+	2.41303e-5i
$343$	6.95336e24	−	6.95336e24i	0.308499	−	0.308499i
$344$		−	7.95534e22i		−	0.00342826i
$345$	−1.28180e25	+	2.84679e25i	−0.536572	+	1.19169i
$346$	−2.07403e23			−0.00843441
$347$	−2.47822e25	−	2.47822e25i	−0.979141	−	0.979141i	0.0206460	−	0.999787i	$-0.493428\pi$
$347$	−2.47822e25	−	2.47822e25i	−0.979141	−	0.979141i	−0.999787	+	0.0206460i	$0.993428\pi$
$348$	−1.48840e25	+	1.48840e25i	−0.571381	+	0.571381i
$349$		−	1.86774e25i		−	0.696725i	−0.937360	−	0.348363i	$-0.886738\pi$
$349$		−	1.86774e25i		−	0.696725i	0.937360	−	0.348363i	$-0.113262\pi$
$350$	−2.40805e22	+	2.13194e22i	−0.000872940	+	0.000772849i
$351$	−1.15750e25			−0.407804
$352$	2.00184e23	+	2.00184e23i	0.00685493	+	0.00685493i
$353$	−1.93968e25	+	1.93968e25i	−0.645631	+	0.645631i	−0.951934	−	0.306303i	$-0.900908\pi$
$353$	−1.93968e25	+	1.93968e25i	−0.645631	+	0.645631i	0.306303	+	0.951934i	$0.400908\pi$
$354$		−	1.71530e23i		−	0.00555017i
$355$	−1.18704e25	−	5.34478e24i	−0.373407	−	0.168130i
$356$	−2.60259e25			−0.795986
$357$	−7.22507e24	−	7.22507e24i	−0.214862	−	0.214862i
$358$	2.80596e22	−	2.80596e22i	0.000811430	−	0.000811430i
$359$		−	1.14804e25i		−	0.322859i	−0.986884	−	0.161430i	$-0.948389\pi$
$359$		−	1.14804e25i		−	0.322859i	0.986884	−	0.161430i	$-0.0516105\pi$
$360$	−1.80793e22	−	4.76947e22i	−0.000494490	−	0.00130450i
$361$	3.75000e25			0.997607
$362$	3.77038e22	+	3.77038e22i	0.000975661	+	0.000975661i
$363$	−1.60883e25	+	1.60883e25i	−0.404988	+	0.404988i
$364$			3.53058e24i			0.0864635i
$365$	6.15809e25	−	2.33430e25i	1.46729	−	0.556197i
$366$	2.83505e23			0.00657279
$367$	−3.13881e25	−	3.13881e25i	−0.708117	−	0.708117i	0.258022	−	0.966139i	$-0.416929\pi$
$367$	−3.13881e25	−	3.13881e25i	−0.708117	−	0.708117i	−0.966139	+	0.258022i	$0.916929\pi$
$368$	−4.52255e25	+	4.52255e25i	−0.992900	+	0.992900i
$369$			1.11343e25i			0.237903i
$370$	−4.48103e22	+	9.95209e22i	−0.000931881	+	0.00206965i
$371$	−5.79590e23			−0.0117323
$372$	5.42786e25	+	5.42786e25i	1.06955	+	1.06955i
$373$	3.66873e25	−	3.66873e25i	0.703765	−	0.703765i	−0.261452	−	0.965217i	$-0.584201\pi$
$373$	3.66873e25	−	3.66873e25i	0.703765	−	0.703765i	0.965217	+	0.261452i	$0.0842013\pi$
$374$			2.52501e23i			0.00471571i
$375$	−4.53066e25	−	2.38070e25i	−0.823851	−	0.432905i
$376$	−3.11244e23			−0.00551091
$377$	1.37612e25	+	1.37612e25i	0.237270	+	0.237270i
$378$	−5.18105e22	+	5.18105e22i	−0.000869961	+	0.000869961i
$379$		−	2.11918e25i		−	0.346558i	−0.984873	−	0.173279i	$-0.944564\pi$
$379$		−	2.11918e25i		−	0.346558i	0.984873	−	0.173279i	$-0.0554362\pi$
$380$	2.80054e24	+	1.26097e24i	0.0446072	+	0.0200848i
$381$	9.97464e25			1.54756
$382$	6.99269e22	+	6.99269e22i	0.00105684	+	0.00105684i
$383$	2.94906e25	−	2.94906e25i	0.434207	−	0.434207i	−0.455850	−	0.890057i	$-0.650665\pi$
$383$	2.94906e25	−	2.94906e25i	0.434207	−	0.434207i	0.890057	+	0.455850i	$0.150665\pi$
$384$			1.35223e24i			0.0193971i
$385$	3.51893e24	+	9.28324e24i	0.0491817	+	0.129745i
$386$	4.35597e23			0.00593215
$387$	2.34635e24	+	2.34635e24i	0.0311375	+	0.0311375i
$388$	4.22203e25	−	4.22203e25i	0.546015	−	0.546015i
$389$			1.10150e26i			1.38831i	0.719825	+	0.694156i	$0.244222\pi$
$389$			1.10150e26i			1.38831i	−0.719825	+	0.694156i	$0.755778\pi$
$390$	1.42658e23	−	5.40764e22i	0.00175247	−	0.000664296i
$391$	−1.71143e26			−2.04923
$392$	−5.99763e23	−	5.99763e23i	−0.00700033	−	0.00700033i
$393$	3.74578e25	−	3.74578e25i	0.426203	−	0.426203i
$394$			2.90991e22i			0.000322788i
$395$	−4.61768e25	+	1.02556e26i	−0.499405	+	1.10915i
$396$	−7.87229e24			−0.0830136
$397$	−2.67646e25	−	2.67646e25i	−0.275204	−	0.275204i	0.555987	−	0.831191i	$-0.312341\pi$
$397$	−2.67646e25	−	2.67646e25i	−0.275204	−	0.275204i	−0.831191	+	0.555987i	$0.812341\pi$
$398$	2.20385e23	−	2.20385e23i	0.00220979	−	0.00220979i
$399$		−	1.04177e24i		−	0.0101869i
$400$	−6.95021e25	−	7.85034e25i	−0.662824	−	0.748666i
$401$	−5.13198e25			−0.477355			−0.238677	−	0.971099i	$-0.576714\pi$
$401$	−5.13198e25			−0.477355			−0.238677	+	0.971099i	$0.576714\pi$
$402$	−6.54954e23	−	6.54954e23i	−0.00594224	−	0.00594224i
$403$	5.01841e25	−	5.01841e25i	0.444135	−	0.444135i
$404$		−	1.15892e26i		−	1.00055i
$405$	−9.18275e25	−	4.13462e25i	−0.773432	−	0.348246i
$406$	1.23191e23			0.00101233
$407$	2.38230e25	+	2.38230e25i	0.191008	+	0.191008i
$408$	−1.27924e24	+	1.27924e24i	−0.0100081	+	0.0100081i
$409$			1.45081e26i			1.10759i	0.832654	+	0.553794i	$0.186820\pi$
$409$			1.45081e26i			1.10759i	−0.832654	+	0.553794i	$0.813180\pi$
$410$	−4.40603e23	−	1.16235e24i	−0.00328253	−	0.00865960i
$411$	−1.07880e26			−0.784375
$412$	6.07384e25	+	6.07384e25i	0.431014	+	0.431014i
$413$	2.61416e25	−	2.61416e25i	0.181064	−	0.181064i
$414$			1.44889e23i			0.000979561i
$415$	8.45075e25	−	3.20337e25i	0.557717	−	0.211410i
$416$	9.37670e23			0.00604111
$417$	1.15847e26	+	1.15847e26i	0.728659	+	0.728659i
$418$	−1.82038e22	+	1.82038e22i	−0.000111789	+	0.000111789i
$419$			9.76407e25i			0.585451i	0.956196	+	0.292726i	$0.0945622\pi$
$419$			9.76407e25i			0.585451i	−0.956196	+	0.292726i	$0.905438\pi$
$420$	−1.46016e25	+	3.24292e25i	−0.0854884	+	0.189865i
$421$	2.34366e26			1.33990			0.669952	−	0.742404i	$-0.266315\pi$
$421$	2.34366e26			1.33990			0.669952	+	0.742404i	$0.266315\pi$
$422$	7.44212e23	+	7.44212e23i	0.00415501	+	0.00415501i
$423$	9.17986e24	−	9.17986e24i	0.0500532	−	0.0500532i
$424$			1.02620e23i			0.000546478i
$425$	1.70312e25	−	2.80042e26i	0.0885841	−	1.45658i
$426$	3.90904e23			0.00198598
$427$	4.32070e25	+	4.32070e25i	0.214425	+	0.214425i
$428$	8.43573e25	−	8.43573e25i	0.408964	−	0.408964i
$429$		−	4.70937e25i		−	0.223044i
$430$	−3.37792e23	−	1.52094e23i	−0.00156302	−	0.000703766i
$431$	−1.95945e25			−0.0885853			−0.0442926	−	0.999019i	$-0.514103\pi$
$431$	−1.95945e25			−0.0885853			−0.0442926	+	0.999019i	$0.514103\pi$
$432$	−1.68904e26	−	1.68904e26i	−0.746111	−	0.746111i
$433$	−2.06182e26	+	2.06182e26i	−0.889965	+	0.889965i	−0.994519	−	0.104555i	$-0.966658\pi$
$433$	−2.06182e26	+	2.06182e26i	−0.889965	+	0.889965i	0.104555	+	0.994519i	$0.466658\pi$
$434$		−	4.49253e23i		−	0.00189493i
$435$	6.94869e25	+	1.83312e26i	0.286425	+	0.755612i
$436$	1.52309e26			0.613564
$437$	−1.23383e25	−	1.23383e25i	−0.0485783	−	0.0485783i
$438$	−1.39831e24	+	1.39831e24i	−0.00538100	+	0.00538100i
$439$			7.67531e24i			0.0288702i	0.999896	+	0.0144351i	$0.00459500\pi$
$439$			7.67531e24i			0.0288702i	−0.999896	+	0.0144351i	$0.995405\pi$
$440$	1.64365e24	−	6.23048e23i	0.00604342	−	0.00229084i
$441$	3.53788e25			0.127162
$442$	5.91362e23	+	5.91362e23i	0.00207793	+	0.00207793i
$443$	−6.26585e25	+	6.26585e25i	−0.215250	+	0.215250i	−0.806493	−	0.591243i	$-0.798637\pi$
$443$	−6.26585e25	+	6.26585e25i	−0.215250	+	0.215250i	0.591243	+	0.806493i	$0.298637\pi$
$444$			1.20692e26i			0.405368i
$445$	−9.95167e25	+	2.21021e26i	−0.326810	+	0.725826i
$446$	1.81099e24			0.00581523
$447$	−2.24290e26	−	2.24290e26i	−0.704263	−	0.704263i
$448$	−5.15159e25	+	5.15159e25i	−0.158184	+	0.158184i
$449$		−	3.72189e26i		−	1.11763i	−0.829291	−	0.558817i	$-0.811255\pi$
$449$		−	3.72189e26i		−	1.11763i	0.829291	−	0.558817i	$-0.188745\pi$
$450$	−2.37082e23	−	1.44186e22i	−0.000696264	−	4.23444e-5i
$451$	−3.83709e26			−1.10214
$452$	−1.50689e26	−	1.50689e26i	−0.423347	−	0.423347i
$453$	−1.02958e25	+	1.02958e25i	−0.0282931	+	0.0282931i
$454$			2.34289e24i			0.00629787i
$455$	2.99829e25	+	1.35001e25i	0.0788424	+	0.0354996i
$456$	−1.84451e23			−0.000474496
$457$	−1.07465e26	−	1.07465e26i	−0.270461	−	0.270461i	0.558825	−	0.829286i	$-0.311252\pi$
$457$	−1.07465e26	−	1.07465e26i	−0.270461	−	0.270461i	−0.829286	+	0.558825i	$0.811252\pi$
$458$	1.60215e24	−	1.60215e24i	0.00394500	−	0.00394500i
$459$		−	6.39169e26i		−	1.53989i
$460$	2.11145e26	+	5.57017e26i	0.497739	+	1.31308i
$461$	1.93725e26			0.446865			0.223433	−	0.974719i	$-0.428274\pi$
$461$	1.93725e26			0.446865			0.223433	+	0.974719i	$0.428274\pi$
$462$	−2.10794e23	−	2.10794e23i	−0.000475815	−	0.000475815i
$463$	−2.75418e26	+	2.75418e26i	−0.608391	+	0.608391i	−0.942525	−	0.334135i	$-0.891556\pi$
$463$	−2.75418e26	+	2.75418e26i	−0.608391	+	0.608391i	0.334135	+	0.942525i	$0.391556\pi$
$464$			4.01609e26i			0.868209i
$465$	6.68501e26	−	2.53404e26i	1.41440	−	0.536147i
$466$	−3.62073e24			−0.00749786
$467$	5.17420e26	+	5.17420e26i	1.04876	+	1.04876i	0.998749	+	0.0500079i	$0.0159246\pi$
$467$	5.17420e26	+	5.17420e26i	1.04876	+	1.04876i	0.0500079	+	0.998749i	$0.484075\pi$
$468$	−1.84370e25	+	1.84370e25i	−0.0365790	+	0.0365790i
$469$		−	1.99634e26i		−	0.387709i
$470$	−5.95054e23	+	1.32158e24i	−0.00113130	+	0.00251255i
$471$	4.98273e26			0.927381
$472$	−4.62852e24	−	4.62852e24i	−0.00843378	−	0.00843378i
$473$	−8.08597e25	+	8.08597e25i	−0.144252	+	0.144252i
$474$		−	3.37726e24i		−	0.00589904i
$475$	2.14171e25	−	1.89614e25i	0.0366290	−	0.0324291i
$476$	−1.94957e26			−0.326490
$477$	−3.02667e24	−	3.02667e24i	−0.00496343	−	0.00496343i
$478$	5.99433e23	−	5.99433e23i	0.000962636	−	0.000962636i
$479$		−	7.65347e26i		−	1.20366i	−0.798625	−	0.601829i	$-0.794439\pi$
$479$		−	7.65347e26i		−	1.20366i	0.798625	−	0.601829i	$-0.205561\pi$
$480$	8.61271e24	+	3.87796e24i	0.0132656	+	0.00597298i
$481$	1.11588e26			0.168332
$482$	−1.47264e24	−	1.47264e24i	−0.00217583	−	0.00217583i
$483$	1.42874e26	−	1.42874e26i	0.206767	−	0.206767i
$484$			4.34116e26i			0.615393i
$485$	−1.97109e26	−	5.19990e26i	−0.273709	−	0.722067i
$486$	−1.01835e24			−0.00138527
$487$	1.26890e25	+	1.26890e25i	0.0169097	+	0.0169097i	0.715511	−	0.698601i	$-0.246194\pi$
$487$	1.26890e25	+	1.26890e25i	0.0169097	+	0.0169097i	−0.698601	+	0.715511i	$0.746194\pi$
$488$	7.65004e24	−	7.65004e24i	0.00998770	−	0.00998770i
$489$			1.06318e27i			1.35993i
$490$	−3.69332e24	+	1.40000e24i	−0.00462866	+	0.00175456i
$491$	−5.45011e26			−0.669253			−0.334626	−	0.942351i	$-0.608610\pi$
$491$	−5.45011e26			−0.669253			−0.334626	+	0.942351i	$0.608610\pi$
$492$	−9.71976e26	−	9.71976e26i	−1.16951	−	1.16951i
$493$	−7.59886e26	+	7.59886e26i	−0.895941	+	0.895941i
$494$			8.52673e22i			9.85174e-5i
$495$	−3.01017e25	+	6.68541e25i	−0.0340831	+	0.0756965i
$496$	1.46458e27			1.62517
$497$	5.95750e25	+	5.95750e25i	0.0647888	+	0.0647888i
$498$	−1.91890e24	+	1.91890e24i	−0.00204531	+	0.00204531i
$499$		−	3.36680e26i		−	0.351732i	−0.984414	−	0.175866i	$-0.943727\pi$
$499$		−	3.36680e26i		−	0.351732i	0.984414	−	0.175866i	$-0.0562725\pi$
$500$	−9.32462e26	+	2.90066e26i	−0.954841	+	0.297027i
$501$	−1.07999e27			−1.08403
$502$	6.01655e24	+	6.01655e24i	0.00591984	+	0.00591984i
$503$	4.74966e26	−	4.74966e26i	0.458123	−	0.458123i	−0.439916	−	0.898039i	$-0.644992\pi$
$503$	4.74966e26	−	4.74966e26i	0.458123	−	0.458123i	0.898039	+	0.439916i	$0.144992\pi$
$504$			3.30105e23i			0.000312138i
$505$	−9.84190e26	−	4.43141e26i	−0.912358	−	0.410798i
$506$	−4.99314e24			−0.00453804
$507$	6.28218e26	+	6.28218e26i	0.559797	+	0.559797i
$508$	1.34575e27	−	1.34575e27i	1.17578	−	1.17578i
$509$			6.84432e26i			0.586344i	0.956060	+	0.293172i	$0.0947108\pi$
$509$			6.84432e26i			0.586344i	−0.956060	+	0.293172i	$0.905289\pi$
$510$	2.98608e24	+	7.87752e24i	0.00250841	+	0.00661740i
$511$	−4.26214e26			−0.351090
$512$	2.28045e25	+	2.28045e25i	0.0184214	+	0.0184214i
$513$	4.60802e25	−	4.60802e25i	0.0365040	−	0.0365040i
$514$		−	7.39734e24i		−	0.00574704i
$515$	7.48060e26	−	2.83562e26i	0.569986	−	0.216061i
$516$	−4.09652e26			−0.306138
$517$	3.16355e26	+	3.16355e26i	0.231883	+	0.231883i
$518$	4.99472e23	−	4.99472e23i	0.000359099	−	0.000359099i
$519$			2.13603e27i			1.50638i
$520$	2.39027e24	−	5.30865e24i	0.00165354	−	0.00367240i
$521$	−3.25861e26			−0.221134			−0.110567	−	0.993869i	$-0.535267\pi$
$521$	−3.25861e26			−0.221134			−0.110567	+	0.993869i	$0.535267\pi$
$522$	6.43317e23	+	6.43317e23i	0.000428272	+	0.000428272i
$523$	1.32995e27	−	1.32995e27i	0.868596	−	0.868596i	−0.123721	−	0.992317i	$-0.539483\pi$
$523$	1.32995e27	−	1.32995e27i	0.868596	−	0.868596i	0.992317	+	0.123721i	$0.0394829\pi$
$524$		−	1.01074e27i		−	0.647629i
$525$	2.19567e26	+	2.48003e26i	0.138030	+	0.155906i
$526$	5.35147e24			0.00330078
$527$	2.77114e27	+	2.77114e27i	1.67708	+	1.67708i
$528$	6.87197e26	−	6.87197e26i	0.408077	−	0.408077i
$529$		−	1.66814e27i		−	0.972023i
$530$	4.35735e23	+	1.96194e23i	0.000249152	+	0.000112183i
$531$	2.73028e26			0.153201
$532$	−1.40552e25	−	1.40552e25i	−0.00773966	−	0.00773966i
$533$	−8.98654e26	+	8.98654e26i	−0.485647	+	0.485647i
$534$		−	7.27842e24i		−	0.00386033i
$535$	−3.93828e26	−	1.03895e27i	−0.205007	−	0.540826i
$536$	−3.53463e25			−0.0180591
$537$	−2.88984e26	−	2.88984e26i	−0.144921	−	0.144921i
$538$	1.26812e24	−	1.26812e24i	0.000624218	−	0.000624218i
$539$			1.21922e27i			0.589108i
$540$	−2.08030e27	+	7.88565e26i	−0.986707	+	0.374024i
$541$	−3.00958e27			−1.40130			−0.700652	−	0.713503i	$-0.747108\pi$
$541$	−3.00958e27			−1.40130			−0.700652	+	0.713503i	$0.747108\pi$
$542$	3.31075e24	+	3.31075e24i	0.00151333	+	0.00151333i
$543$	3.88308e26	−	3.88308e26i	0.174252	−	0.174252i
$544$			5.17777e25i			0.0228115i
$545$	5.82392e26	−	1.29346e27i	0.251913	−	0.559483i
$546$	−9.87365e23			−0.000419326
$547$	−2.39169e27	−	2.39169e27i	−0.997311	−	0.997311i	0.00268498	−	0.999996i	$-0.499145\pi$
$547$	−2.39169e27	−	2.39169e27i	−0.997311	−	0.997311i	−0.999996	+	0.00268498i	$0.999145\pi$
$548$	−1.45549e27	+	1.45549e27i	−0.595942	+	0.595942i
$549$			4.51261e26i			0.181428i
$550$	4.96891e23	−	8.17030e24i	0.000196171	−	0.00322560i
$551$	−1.09566e26			−0.0424777
$552$	−2.52966e25	−	2.52966e25i	−0.00963101	−	0.00963101i
$553$	5.14704e26	−	5.14704e26i	0.192445	−	0.192445i
$554$		−	1.03433e25i		−	0.00379805i
$555$	1.02496e27	+	4.61498e26i	0.369638	+	0.166433i
$556$	3.12595e27			1.10722
$557$	−1.94071e27	−	1.94071e27i	−0.675162	−	0.675162i	0.283739	−	0.958901i	$-0.408425\pi$
$557$	−1.94071e27	−	1.94071e27i	−0.675162	−	0.675162i	−0.958901	+	0.283739i	$0.908425\pi$
$558$	2.34604e24	−	2.34604e24i	0.000801666	−	0.000801666i
$559$			3.78749e26i			0.127126i
$560$	2.40519e26	+	6.34509e26i	0.0792993	+	0.209198i
$561$	2.60049e27			0.842223
$562$	−1.25150e25	−	1.25150e25i	−0.00398168	−	0.00398168i
$563$	−3.04528e27	+	3.04528e27i	−0.951794	+	0.951794i	−0.998890	−	0.0470961i	$-0.985003\pi$
$563$	−3.04528e27	+	3.04528e27i	−0.951794	+	0.951794i	0.0470961	+	0.998890i	$0.485003\pi$
$564$			1.60272e27i			0.492115i
$565$	−1.85590e27	+	7.03502e26i	−0.559847	+	0.212217i
$566$	1.79551e25			0.00532136
$567$	4.60861e26	+	4.60861e26i	0.134196	+	0.134196i
$568$	1.05481e25	−	1.05481e25i	0.00301780	−	0.00301780i
$569$		−	3.26586e27i		−	0.918068i	−0.888419	−	0.459034i	$-0.848196\pi$
$569$		−	3.26586e27i		−	0.918068i	0.888419	−	0.459034i	$-0.151804\pi$
$570$	−3.52643e23	+	7.83199e23i	−9.74063e−5	+	0.000216333i
$571$	3.57523e27			0.970383			0.485191	−	0.874408i	$-0.338750\pi$
$571$	3.57523e27			0.970383			0.485191	+	0.874408i	$0.338750\pi$
$572$	−6.35375e26	−	6.35375e26i	−0.169461	−	0.169461i
$573$	7.20173e26	−	7.20173e26i	0.188752	−	0.188752i
$574$			8.04484e24i			0.00207204i
$575$	5.53774e27	+	3.36787e26i	1.40170	+	0.0852466i
$576$	−5.38042e26			−0.133842
$577$	2.63542e26	+	2.63542e26i	0.0644306	+	0.0644306i	0.738588	−	0.674157i	$-0.235493\pi$
$577$	2.63542e26	+	2.63542e26i	0.0644306	+	0.0644306i	−0.674157	+	0.738588i	$0.735493\pi$
$578$	−1.73200e25	+	1.73200e25i	−0.00416169	+	0.00416169i
$579$		−	4.48618e27i		−	1.05948i
$580$	3.41069e27	+	1.53570e27i	0.791704	+	0.356473i
$581$	−5.84893e26			−0.133449
$582$	1.18074e25	+	1.18074e25i	0.00264803	+	0.00264803i
$583$	1.04305e26	−	1.04305e26i	0.0229942	−	0.0229942i
$584$			7.54636e25i			0.0163534i
$585$	8.60747e25	+	2.27072e26i	0.0183365	+	0.0483732i
$586$	4.41786e25			0.00925200
$587$	1.83539e27	+	1.83539e27i	0.377873	+	0.377873i	0.870334	−	0.492461i	$-0.163903\pi$
$587$	1.83539e27	+	1.83539e27i	0.377873	+	0.377873i	−0.492461	+	0.870334i	$0.663903\pi$
$588$	−3.08842e27	+	3.08842e27i	−0.625119	+	0.625119i
$589$			3.99565e26i			0.0795124i
$590$	−2.85023e25	+	1.08042e25i	−0.00557647	+	0.00211383i
$591$	2.99690e26			0.0576497
$592$	1.62830e27	+	1.62830e27i	0.307977	+	0.307977i
$593$	−2.89387e27	+	2.89387e27i	−0.538185	+	0.538185i	−0.922996	−	0.384811i	$-0.874267\pi$
$593$	−2.89387e27	+	2.89387e27i	−0.538185	+	0.538185i	0.384811	+	0.922996i	$0.374267\pi$
$594$		−	1.86479e25i		−	0.00341010i
$595$	−7.45470e26	+	1.65564e27i	−0.134048	+	0.297713i
$596$	−6.05212e27			−1.07015
$597$	−2.26973e27	−	2.26973e27i	−0.394668	−	0.394668i
$598$	−1.16940e25	+	1.16940e25i	−0.00199964	+	0.00199964i
$599$		−	7.86676e27i		−	1.32290i	−0.749988	−	0.661451i	$-0.769941\pi$
$599$		−	7.86676e27i		−	1.32290i	0.749988	−	0.661451i	$-0.230059\pi$
$600$	4.39104e25	−	3.88756e25i	0.00726197	−	0.00642931i
$601$	−4.80387e27			−0.781351			−0.390676	−	0.920528i	$-0.627759\pi$
$601$	−4.80387e27			−0.781351			−0.390676	+	0.920528i	$0.627759\pi$
$602$	1.69530e24	+	1.69530e24i	0.000271195	+	0.000271195i
$603$	1.04250e27	−	1.04250e27i	0.164023	−	0.164023i
$604$			2.77817e26i			0.0429922i
$605$	3.68666e27	+	1.65996e27i	0.561151	+	0.252664i
$606$	3.24103e25			0.00485240
$607$	−8.30490e27	−	8.30490e27i	−1.22306	−	1.22306i	−0.966539	−	0.256520i	$-0.917424\pi$
$607$	−8.30490e27	−	8.30490e27i	−1.22306	−	1.22306i	−0.256520	−	0.966539i	$-0.582576\pi$
$608$	−3.73286e24	+	3.73286e24i	−0.000540762	+	0.000540762i
$609$		−	1.26874e27i		−	0.180801i
$610$	−1.78572e25	−	4.71087e25i	−0.00250331	−	0.00660393i
$611$	1.48182e27			0.204354
$612$	−1.01808e27	−	1.01808e27i	−0.138124	−	0.138124i
$613$	−2.69070e26	+	2.69070e26i	−0.0359138	+	0.0359138i	−0.724836	−	0.688922i	$-0.758084\pi$
$613$	−2.69070e26	+	2.69070e26i	−0.0359138	+	0.0359138i	0.688922	+	0.724836i	$0.258084\pi$
$614$			8.70106e24i			0.00114259i
$615$	−1.19709e28	+	4.53774e27i	−1.54660	+	0.586258i
$616$	−1.13760e25			−0.00144605
$617$	7.68618e27	+	7.68618e27i	0.961300	+	0.961300i	0.999279	−	0.0379785i	$-0.0120918\pi$
$617$	7.68618e27	+	7.68618e27i	0.961300	+	0.961300i	−0.0379785	+	0.999279i	$0.512092\pi$
$618$	−1.69861e25	+	1.69861e25i	−0.00209030	+	0.00209030i
$619$			1.64811e28i			1.99563i	0.0660814	+	0.997814i	$0.478950\pi$
$619$			1.64811e28i			1.99563i	−0.0660814	+	0.997814i	$0.521050\pi$
$620$	5.60037e27	−	1.24381e28i	0.667267	−	1.48196i
$621$	1.26394e28			1.48187
$622$	−8.34158e23	−	8.34158e23i	−9.62375e−5	−	9.62375e-5i
$623$	1.10925e27	−	1.10925e27i	0.125936	−	0.125936i
$624$		−	3.21885e27i		−	0.359629i
$625$	−1.10217e27	+	9.02792e27i	−0.121185	+	0.992630i
$626$	−5.18133e25			−0.00560658
$627$	1.87480e26	+	1.87480e26i	0.0199654	+	0.0199654i
$628$	6.72256e27	−	6.72256e27i	0.704593	−	0.704593i
$629$			6.16183e27i			0.635628i
$630$	1.40166e24	+	6.31112e23i	0.000142311	+	6.40768e-5i
$631$	4.08536e27			0.408260			0.204130	−	0.978944i	$-0.434563\pi$
$631$	4.08536e27			0.408260			0.204130	+	0.978944i	$0.434563\pi$
$632$	−9.11313e25	−	9.11313e25i	−0.00896390	−	0.00896390i
$633$	7.66458e27	−	7.66458e27i	0.742081	−	0.742081i
$634$		−	2.70555e25i		−	0.00257847i
$635$	−6.28274e27	−	1.65744e28i	−0.589403	−	1.55489i
$636$	5.28430e26			0.0487996
$637$	2.85544e27	+	2.85544e27i	0.259584	+	0.259584i
$638$	−2.21699e25	+	2.21699e25i	−0.00198407	+	0.00198407i
$639$			6.22212e26i			0.0548188i
$640$	2.24693e26	−	8.51729e25i	0.0194890	−	0.00738757i
$641$	−2.99650e27			−0.255878			−0.127939	−	0.991782i	$-0.540836\pi$
$641$	−2.99650e27			−0.255878			−0.127939	+	0.991782i	$0.540836\pi$
$642$	2.35914e25	+	2.35914e25i	0.00198337	+	0.00198337i
$643$	−1.09767e28	+	1.09767e28i	−0.908577	+	0.908577i	−0.996157	−	0.0875802i	$-0.972087\pi$
$643$	−1.09767e28	+	1.09767e28i	−0.908577	+	0.908577i	0.0875802	+	0.996157i	$0.472087\pi$
$644$		−	3.85523e27i		−	0.314189i
$645$	−1.56641e27	+	3.47890e27i	−0.125692	+	0.279155i
$646$	−4.70842e24			−0.000372006
$647$	2.13474e27	+	2.13474e27i	0.166074	+	0.166074i	0.785251	−	0.619177i	$-0.212534\pi$
$647$	2.13474e27	+	2.13474e27i	0.166074	+	0.166074i	−0.619177	+	0.785251i	$0.712534\pi$
$648$	8.15981e25	−	8.15981e25i	0.00625072	−	0.00625072i
$649$			9.40905e27i			0.709739i
$650$	−1.79713e25	−	2.02987e25i	−0.00133489	−	0.00150777i
$651$	−4.62683e27			−0.338434
$652$	1.43441e28	+	1.43441e28i	1.03323	+	1.03323i
$653$	1.51870e28	−	1.51870e28i	1.07731	−	1.07731i	0.0805577	−	0.996750i	$-0.474330\pi$
$653$	1.51870e28	−	1.51870e28i	1.07731	−	1.07731i	0.996750	−	0.0805577i	$-0.0256701\pi$
$654$			4.25948e25i			0.00297563i
$655$	−8.58354e27	−	3.86482e27i	−0.590545	−	0.265899i
$656$	−2.62265e28			−1.77706
$657$	−2.22573e27	−	2.22573e27i	−0.148531	−	0.148531i
$658$	6.63270e24	−	6.63270e24i	0.000435945	−	0.000435945i
$659$			7.70752e27i			0.498954i	0.968381	+	0.249477i	$0.0802587\pi$
$659$			7.70752e27i			0.498954i	−0.968381	+	0.249477i	$0.919741\pi$
$660$	−3.20832e27	−	8.46381e27i	−0.204568	−	0.539668i
$661$	−1.06771e28			−0.670561			−0.335280	−	0.942118i	$-0.608831\pi$
$661$	−1.06771e28			−0.670561			−0.335280	+	0.942118i	$0.608831\pi$
$662$	2.49384e25	+	2.49384e25i	0.00154273	+	0.00154273i
$663$	6.09040e27	−	6.09040e27i	0.371117	−	0.371117i
$664$			1.03559e26i			0.00621593i
$665$	−1.73106e26	+	6.56180e25i	−0.0102352	+	0.00387977i
$666$	5.21658e24			0.000303839
$667$	−1.50265e28	−	1.50265e28i	−0.862185	−	0.862185i
$668$	−1.45709e28	+	1.45709e28i	−0.823612	+	0.823612i
$669$		−	1.86513e28i		−	1.03860i
$670$	−6.75769e25	+	1.50084e26i	−0.00370724	+	0.00823355i
$671$	−1.55513e28			−0.840508
$672$	−4.32252e25	−	4.32252e25i	−0.00230168	−	0.00230168i
$673$	1.34303e28	−	1.34303e28i	0.704590	−	0.704590i	−0.260802	−	0.965392i	$-0.583987\pi$
$673$	1.34303e28	−	1.34303e28i	0.704590	−	0.704590i	0.965392	+	0.260802i	$0.0839871\pi$
$674$		−	5.66509e25i		−	0.00292825i
$675$	−1.25780e27	+	2.06819e28i	−0.0640582	+	1.05330i
$676$	1.69515e28			0.850630
$677$	1.97993e28	+	1.97993e28i	0.978955	+	0.978955i	0.999783	−	0.0208277i	$-0.00663015\pi$
$677$	1.97993e28	+	1.97993e28i	0.978955	+	0.978955i	−0.0208277	+	0.999783i	$0.506630\pi$
$678$	4.21417e25	−	4.21417e25i	0.00205312	−	0.00205312i
$679$			3.59895e27i			0.172774i
$680$	2.93141e26	+	1.31990e26i	0.0138672	+	0.00624383i
$681$	2.41293e28			1.12480
$682$	8.08490e25	+	8.08490e25i	0.00371390	+	0.00371390i
$683$	6.17987e27	−	6.17987e27i	0.279752	−	0.279752i	−0.553258	−	0.833010i	$-0.686616\pi$
$683$	6.17987e27	−	6.17987e27i	0.279752	−	0.279752i	0.833010	+	0.553258i	$0.186616\pi$
$684$		−	1.46795e26i		−	0.00654865i
$685$	6.79507e27	+	1.79260e28i	0.298736	+	0.788091i
$686$	5.24715e25			0.00227343
$687$	−1.65004e28	−	1.65004e28i	−0.704575	−	0.704575i
$688$	−5.52676e27	+	5.52676e27i	−0.232587	+	0.232587i
$689$		−	4.88567e26i		−	0.0202643i
$690$	−1.55776e26	+	5.90488e25i	−0.00636808	+	0.00241391i
$691$	2.87344e28			1.15777			0.578884	−	0.815410i	$-0.303489\pi$
$691$	2.87344e28			1.15777			0.578884	+	0.815410i	$0.303489\pi$
$692$	2.88188e28	+	2.88188e28i	1.14450	+	1.14450i
$693$	3.35525e26	−	3.35525e26i	0.0131339	−	0.0131339i
$694$		−	1.87012e26i		−	0.00721562i
$695$	1.19529e28	−	2.65466e28i	0.454595	−	1.00963i
$696$	−2.24638e26			−0.00842152
$697$	−4.96233e28	−	4.96233e28i	−1.83382	−	1.83382i
$698$	7.04716e25	−	7.04716e25i	0.00256720	−	0.00256720i
$699$			3.72897e28i			1.33911i
$700$	6.30833e27	+	3.83651e26i	0.223323	+	0.0135818i
$701$	1.27524e27			0.0445053			0.0222527	−	0.999752i	$-0.492916\pi$
$701$	1.27524e27			0.0445053			0.0222527	+	0.999752i	$0.492916\pi$
$702$	−4.36738e25	−	4.36738e25i	−0.00150262	−	0.00150262i
$703$	−4.44230e26	+	4.44230e26i	−0.0150680	+	0.0150680i
$704$		−	1.85419e28i		−	0.620052i
$705$	1.36108e28	+	6.12842e27i	0.448739	+	0.202049i
$706$	−1.46373e26			−0.00475787
$707$	4.93942e27	+	4.93942e27i	0.158300	+	0.158300i
$708$	−2.38341e28	+	2.38341e28i	−0.753123	+	0.753123i
$709$		−	3.99111e28i		−	1.24346i	−0.783232	−	0.621729i	$-0.786430\pi$
$709$		−	3.99111e28i		−	1.24346i	0.783232	−	0.621729i	$-0.213570\pi$
$710$	−2.46220e25	−	6.49548e25i	−0.000756378	−	0.00199539i
$711$	5.37566e27			0.162831
$712$	−1.96399e26	−	1.96399e26i	−0.00586598	−	0.00586598i
$713$	−5.47986e28	+	5.47986e28i	−1.61389	+	1.61389i
$714$		−	5.45219e25i		−	0.00158339i
$715$	−7.82534e27	+	2.96630e27i	−0.224100	+	0.0849482i
$716$	−7.79778e27			−0.220212
$717$	−6.17352e27	−	6.17352e27i	−0.171926	−	0.171926i
$718$	4.33168e25	−	4.33168e25i	0.00118963	−	0.00118963i
$719$		−	3.78806e28i		−	1.02595i	−0.858402	−	0.512977i	$-0.828543\pi$
$719$		−	3.78806e28i		−	1.02595i	0.858402	−	0.512977i	$-0.171457\pi$
$720$	−2.05745e27	+	4.56948e27i	−0.0549547	+	0.122051i
$721$	−5.17747e27			−0.136384
$722$	1.41491e26	+	1.41491e26i	0.00367585	+	0.00367585i
$723$	−1.51666e28	+	1.51666e28i	−0.388601	+	0.388601i
$724$		−	1.04779e28i		−	0.264782i
$725$	2.60833e28	−	2.30926e28i	0.650104	−	0.575563i
$726$	−1.21405e26			−0.00298450
$727$	−6.81066e26	−	6.81066e26i	−0.0165137	−	0.0165137i	0.698802	−	0.715315i	$-0.253717\pi$
$727$	−6.81066e26	−	6.81066e26i	−0.0165137	−	0.0165137i	−0.715315	+	0.698802i	$0.753717\pi$
$728$	−2.66429e25	+	2.66429e25i	−0.000637188	+	0.000637188i
$729$			4.64448e28i			1.09563i
$730$	3.20427e26	+	1.44275e26i	0.00745590	+	0.00335709i
$731$	−2.09144e28			−0.480033
$732$	−3.93931e28	−	3.93931e28i	−0.891886	−	0.891886i
$733$	3.19735e28	−	3.19735e28i	0.714087	−	0.714087i	−0.253301	−	0.967388i	$-0.581516\pi$
$733$	3.19735e28	−	3.19735e28i	0.714087	−	0.714087i	0.967388	+	0.253301i	$0.0815163\pi$
$734$		−	2.36861e26i		−	0.00521835i
$735$	1.44185e28	+	3.80372e28i	0.313362	+	0.826676i
$736$	−1.02389e27			−0.0219521
$737$	3.59267e28	+	3.59267e28i	0.759875	+	0.759875i
$738$	−4.20109e25	+	4.20109e25i	−0.000876594	+	0.000876594i
$739$		−	5.44973e28i		−	1.12184i	−0.827871	−	0.560919i	$-0.810448\pi$
$739$		−	5.44973e28i		−	1.12184i	0.827871	−	0.560919i	$-0.189552\pi$
$740$	2.00549e28	−	7.60206e27i	0.407289	−	0.154388i
$741$	8.78162e26			0.0175951
$742$	−2.18685e24	−	2.18685e24i	−4.32295e−5	−	4.32295e-5i
$743$	−3.02473e28	+	3.02473e28i	−0.589928	+	0.589928i	−0.937612	−	0.347684i	$-0.886968\pi$
$743$	−3.02473e28	+	3.02473e28i	−0.589928	+	0.589928i	0.347684	+	0.937612i	$0.386968\pi$
$744$			8.19206e26i			0.0157639i
$745$	−2.31419e28	+	5.13967e28i	−0.439375	+	0.975825i
$746$	2.76850e26			0.00518628
$747$	−3.05436e27	−	3.05436e27i	−0.0564566	−	0.0564566i
$748$	3.50851e28	−	3.50851e28i	0.639893	−	0.639893i
$749$			7.19079e27i			0.129407i
$750$	−8.11199e25	−	2.60773e26i	−0.00144051	−	0.00463073i
$751$	7.71306e28			1.35153			0.675767	−	0.737115i	$-0.263812\pi$
$751$	7.71306e28			1.35153			0.675767	+	0.737115i	$0.263812\pi$
$752$	2.16229e28	+	2.16229e28i	0.373882	+	0.373882i
$753$	6.19640e28	−	6.19640e28i	1.05728	−	1.05728i
$754$			1.03845e26i			0.00174852i
$755$	2.35932e27	+	1.06231e27i	0.0392028	+	0.0176514i
$756$	1.43982e28			0.236096
$757$	7.96584e27	+	7.96584e27i	0.128906	+	0.128906i	0.768616	−	0.639710i	$-0.220946\pi$
$757$	7.96584e27	+	7.96584e27i	0.128906	+	0.128906i	−0.639710	+	0.768616i	$0.720946\pi$
$758$	7.99588e25	−	7.99588e25i	0.00127695	−	0.00127695i
$759$			5.14240e28i			0.810491i
$760$	1.16180e25	+	3.06494e25i	0.000180716	+	0.000476744i
$761$	−4.63585e28			−0.711677			−0.355839	−	0.934547i	$-0.615805\pi$
$761$	−4.63585e28			−0.711677			−0.355839	+	0.934547i	$0.615805\pi$
$762$	3.76354e26	+	3.76354e26i	0.00570225	+	0.00570225i
$763$	−6.49156e27	+	6.49156e27i	−0.0970742	+	0.0970742i
$764$		−	1.94327e28i		−	0.286814i
$765$	−1.25388e28	+	4.75301e27i	−0.182660	+	0.0692395i
$766$	2.22542e26			0.00319982
$767$	2.20362e28	+	2.20362e28i	0.312739	+	0.312739i
$768$	4.69648e28	−	4.69648e28i	0.657901	−	0.657901i
$769$			5.21119e28i			0.720565i	0.932843	+	0.360283i	$0.117320\pi$
$769$			5.21119e28i			0.720565i	−0.932843	+	0.360283i	$0.882680\pi$
$770$	−2.17493e25	+	4.83039e25i	−0.000296851	+	0.000659288i
$771$	−7.61847e28			−1.02642
$772$	−6.05263e28	−	6.05263e28i	−0.804955	−	0.804955i
$773$	−8.28103e28	+	8.28103e28i	−1.08715	+	1.08715i	−0.0913294	+	0.995821i	$0.529112\pi$
$773$	−8.28103e28	+	8.28103e28i	−1.08715	+	1.08715i	−0.995821	+	0.0913294i	$0.970888\pi$
$774$			1.77060e25i			0.000229463i
$775$	−8.42139e28	−	9.51204e28i	−1.07737	−	1.21690i
$776$	6.37215e26			0.00804765
$777$	−5.14403e27	−	5.14403e27i	−0.0641348	−	0.0641348i
$778$	−4.15606e26	+	4.15606e26i	−0.00511547	+	0.00511547i
$779$		−	7.15508e27i		−	0.0869440i
$780$	−2.73363e28	−	1.23085e28i	−0.327940	−	0.147658i
$781$	−2.14426e28			−0.253961
$782$	−6.45739e26	−	6.45739e26i	−0.00755074	−	0.00755074i
$783$	5.61198e28	−	5.61198e28i	0.647886	−	0.647886i
$784$			8.33338e28i			0.949862i
$785$	−3.13848e28	−	8.27957e28i	−0.353202	−	0.931775i
$786$	2.82664e26			0.00314083
$787$	8.66634e28	+	8.66634e28i	0.950798	+	0.950798i	0.998845	−	0.0480469i	$-0.0152997\pi$
$787$	8.66634e28	+	8.66634e28i	0.950798	+	0.950798i	−0.0480469	+	0.998845i	$0.515300\pi$
$788$	4.04333e27	−	4.04333e27i	0.0438003	−	0.0438003i
$789$		−	5.51145e28i		−	0.589516i
$790$	−5.61183e26	+	2.12724e26i	−0.00592699	+	0.00224670i
$791$	1.28450e28			0.133959
$792$	−5.94067e25	−	5.94067e25i	−0.000611763	−	0.000611763i
$793$	−3.64215e28	+	3.64215e28i	−0.370361	+	0.370361i
$794$		−	2.01971e26i		−	0.00202808i
$795$	2.02059e27	−	4.48760e27i	0.0200358	−	0.0444983i
$796$	−6.12452e28			−0.599710
$797$	5.24123e28	+	5.24123e28i	0.506815	+	0.506815i	0.913547	−	0.406732i	$-0.133332\pi$
$797$	5.24123e28	+	5.24123e28i	0.506815	+	0.506815i	−0.406732	+	0.913547i	$0.633332\pi$
$798$	3.93070e24	−	3.93070e24i	3.75354e−5	−	3.75354e-5i
$799$			8.18254e28i			0.771650i
$800$	1.01892e26	−	1.67540e27i	0.000948943	−	0.0156033i
$801$	1.15852e28			0.106556
$802$	−1.93635e26	−	1.93635e26i	−0.00175889	−	0.00175889i
$803$	7.67027e28	−	7.67027e28i	0.688106	−	0.688106i
$804$			1.82012e29i			1.61265i
$805$	−3.27399e28	−	1.47415e28i	−0.286496	−	0.128998i
$806$	3.78699e26			0.00327299
$807$	−1.30602e28	−	1.30602e28i	−0.111485	−	0.111485i
$808$	8.74553e26	−	8.74553e26i	0.00737348	−	0.00737348i
$809$		−	2.16772e29i		−	1.80517i	−0.430509	−	0.902586i	$-0.641666\pi$
$809$		−	2.16772e29i		−	1.80517i	0.430509	−	0.902586i	$-0.358334\pi$
$810$	−1.90471e26	−	5.02478e26i	−0.00156667	−	0.00413301i
$811$	6.24252e28			0.507167			0.253584	−	0.967313i	$-0.418391\pi$
$811$	6.24252e28			0.507167			0.253584	+	0.967313i	$0.418391\pi$
$812$	−1.71175e28	−	1.71175e28i	−0.137366	−	0.137366i
$813$	3.40972e28	−	3.40972e28i	0.270279	−	0.270279i
$814$			1.79773e26i			0.00140761i
$815$	1.76663e29	−	6.69665e28i	1.36638	−	0.517942i
$816$	1.77744e29			1.35798
$817$	−1.50780e27	−	1.50780e27i	−0.0113795	−	0.0113795i
$818$	−5.47406e26	+	5.47406e26i	−0.00408109	+	0.00408109i
$819$		−	1.57161e27i		−	0.0115746i
$820$	−1.00287e29	+	2.22731e29i	−0.729633	+	1.62047i
$821$	−1.45291e29			−1.04425			−0.522127	−	0.852868i	$-0.674861\pi$
$821$	−1.45291e29			−1.04425			−0.522127	+	0.852868i	$0.674861\pi$
$822$	−4.07043e26	−	4.07043e26i	−0.00289016	−	0.00289016i
$823$	1.58958e29	−	1.58958e29i	1.11502	−	1.11502i	0.122560	−	0.992461i	$-0.460890\pi$
$823$	1.58958e29	−	1.58958e29i	1.11502	−	1.11502i	0.992461	−	0.122560i	$-0.0391103\pi$
$824$			9.16701e26i			0.00635266i
$825$	−8.41453e28	−	5.11744e27i	−0.576090	−	0.0350359i
$826$	1.97270e26			0.00133432
$827$	1.28860e29	+	1.28860e29i	0.861122	+	0.861122i	0.991468	−	0.130347i	$-0.0416090\pi$
$827$	1.28860e29	+	1.28860e29i	0.861122	+	0.861122i	−0.130347	+	0.991468i	$0.541609\pi$
$828$	2.01323e28	−	2.01323e28i	0.132920	−	0.132920i
$829$			1.27029e29i			0.828624i	0.910135	+	0.414312i	$0.135978\pi$
$829$			1.27029e29i			0.828624i	−0.910135	+	0.414312i	$0.864022\pi$
$830$	4.39722e26	+	1.97989e26i	0.00283398	+	0.00127603i
$831$	−1.06525e29			−0.678329
$832$	−4.34255e28	−	4.34255e28i	−0.273220	−	0.273220i
$833$	−1.57676e29	+	1.57676e29i	−0.980202	+	0.980202i
$834$			8.74205e26i			0.00536974i
$835$	6.80255e28	+	1.79457e29i	0.412864	+	1.08917i
$836$	5.05885e27			0.0303381
$837$	−2.04657e29	−	2.04657e29i	−1.21275	−	1.21275i
$838$	−3.68408e26	+	3.68408e26i	−0.00215719	+	0.00215719i
$839$		−	1.51592e29i		−	0.877114i	−0.898703	−	0.438557i	$-0.855490\pi$
$839$		−	1.51592e29i		−	0.877114i	0.898703	−	0.438557i	$-0.144510\pi$
$840$	−3.54909e26	+	1.34533e26i	−0.00202920	+	0.000769194i
$841$	4.35568e28			0.246091
$842$	8.84287e26	+	8.84287e26i	0.00493710	+	0.00493710i
$843$	−1.28891e29	+	1.28891e29i	−0.711125	+	0.711125i
$844$		−	2.06817e29i		−	1.12762i
$845$	6.48184e28	−	1.43958e29i	0.349246	−	0.775654i
$846$	6.92731e25			0.000368859
$847$	−1.85025e28	−	1.85025e28i	−0.0973636	−	0.0973636i
$848$	7.12923e27	−	7.12923e27i	0.0370753	−	0.0370753i
$849$		−	1.84918e29i		−	0.950390i
$850$	1.12089e27	−	9.92365e26i	0.00569341	−	0.00504060i
$851$	−1.21848e29			−0.611680
$852$	−5.43163e28	−	5.43163e28i	−0.269485	−	0.269485i
$853$	−2.18327e29	+	2.18327e29i	−1.07058	+	1.07058i	−0.0732623	+	0.997313i	$0.523341\pi$
$853$	−2.18327e29	+	2.18327e29i	−1.07058	+	1.07058i	−0.997313	+	0.0732623i	$0.976659\pi$
$854$			3.26049e26i			0.00158017i
$855$	−1.24664e27	−	5.61310e26i	−0.00597143	−	0.00268870i
$856$	1.27317e27			0.00602767
$857$	−4.94404e28	−	4.94404e28i	−0.231352	−	0.231352i	0.581905	−	0.813257i	$-0.302308\pi$
$857$	−4.94404e28	−	4.94404e28i	−0.231352	−	0.231352i	−0.813257	+	0.581905i	$0.802308\pi$
$858$	1.77689e26	−	1.77689e26i	0.000821842	−	0.000821842i
$859$			2.18722e29i			0.999910i	0.866052	+	0.499955i	$0.166650\pi$
$859$			2.18722e29i			0.999910i	−0.866052	+	0.499955i	$0.833350\pi$
$860$	2.58028e28	+	6.80699e28i	0.116596	+	0.307589i
$861$	8.28533e28			0.370065
$862$	−7.39321e25	−	7.39321e25i	−0.000326408	−	0.000326408i
$863$	−3.26266e28	+	3.26266e28i	−0.142385	+	0.142385i	−0.774706	−	0.632321i	$-0.782102\pi$
$863$	−3.26266e28	+	3.26266e28i	−0.142385	+	0.142385i	0.632321	+	0.774706i	$0.282102\pi$
$864$		−	3.82394e27i		−	0.0164958i
$865$	3.54935e29	−	1.34543e29i	1.51352	−	0.573718i
$866$	−1.55589e27			−0.00655845
$867$	1.78378e29	+	1.78378e29i	0.743275	+	0.743275i
$868$	−6.24239e28	+	6.24239e28i	−0.257130	+	0.257130i
$869$			1.85255e29i			0.754351i
$870$	−4.29474e26	+	9.53837e26i	−0.00172880	+	0.00383956i
$871$	1.68282e29			0.669662
$872$	1.14937e27	+	1.14937e27i	0.00452162	+	0.00452162i
$873$	−1.87940e28	+	1.87940e28i	−0.0730934	+	0.0730934i
$874$		−	9.31077e25i		−	0.000357990i
$875$	2.73796e28	−	5.21054e28i	0.104075	−	0.198063i
$876$	3.88592e29			1.46033
$877$	−6.53451e28	−	6.53451e28i	−0.242782	−	0.242782i	0.575218	−	0.818000i	$-0.304917\pi$
$877$	−6.53451e28	−	6.53451e28i	−0.242782	−	0.242782i	−0.818000	+	0.575218i	$0.804917\pi$
$878$	−2.89597e25	+	2.89597e25i	−0.000106377	+	0.000106377i
$879$		−	4.54992e29i		−	1.65240i
$880$	−1.57473e29	−	7.09037e28i	−0.565430	−	0.254590i
$881$	1.64158e29			0.582779			0.291390	−	0.956604i	$-0.405882\pi$
$881$	1.64158e29			0.582779			0.291390	+	0.956604i	$0.405882\pi$
$882$	1.33488e26	+	1.33488e26i	0.000468550	+	0.000468550i
$883$	−3.18805e28	+	3.18805e28i	−0.110642	+	0.110642i	−0.760260	−	0.649619i	$-0.774929\pi$
$883$	−3.18805e28	+	3.18805e28i	−0.110642	+	0.110642i	0.649619	+	0.760260i	$0.274929\pi$
$884$		−	1.64340e29i		−	0.563924i
$885$	1.11271e29	+	2.93543e29i	0.377529	+	0.995953i
$886$	−4.72834e26			−0.00158625
$887$	−3.31815e28	−	3.31815e28i	−0.110068	−	0.110068i	0.649928	−	0.759996i	$-0.274799\pi$
$887$	−3.31815e28	−	3.31815e28i	−0.110068	−	0.110068i	−0.759996	+	0.649928i	$0.774799\pi$
$888$	−9.10781e26	+	9.10781e26i	−0.00298734	+	0.00298734i
$889$			1.14715e29i			0.372050i
$890$	−1.20942e27	+	4.58447e26i	−0.00387862	+	0.00147024i
$891$	−1.65876e29			−0.526025
$892$	−2.51637e29	−	2.51637e29i	−0.789091	−	0.789091i
$893$	−5.89911e27	+	5.89911e27i	−0.0182925	+	0.0182925i
$894$		−	1.69254e27i		−	0.00518996i
$895$	−2.98168e28	+	6.62214e28i	−0.0904130	+	0.200802i
$896$	−1.55515e27			−0.00466328
$897$	1.20436e29	+	1.20436e29i	0.357134	+	0.357134i
$898$	1.40431e27	−	1.40431e27i	0.00411811	−	0.00411811i
$899$			4.86619e29i			1.41121i
$900$	3.09392e28	+	3.49461e28i	0.0887327	+	0.100224i
$901$	2.69785e28			0.0765190
$902$	−1.44777e27	−	1.44777e27i	−0.00406102	−	0.00406102i
$903$	1.74598e28	−	1.74598e28i	0.0484353	−	0.0484353i
$904$		−	2.27429e27i		−	0.00623966i
$905$	−8.89818e28	−	4.00649e28i	−0.241443	−	0.108712i
$906$	−7.76946e25			−0.000208501
$907$	−5.55720e28	−	5.55720e28i	−0.147497	−	0.147497i	0.629502	−	0.776999i	$-0.283259\pi$
$907$	−5.55720e28	−	5.55720e28i	−0.147497	−	0.147497i	−0.776999	+	0.629502i	$0.783259\pi$
$908$	3.25546e29	−	3.25546e29i	0.854581	−	0.854581i
$909$			5.15882e28i			0.133940i
$910$	6.21913e25	+	1.64066e26i	0.000159704	+	0.000421312i
$911$	−6.81980e29			−1.73216			−0.866080	−	0.499906i	$-0.833368\pi$
$911$	−6.81980e29			−1.73216			−0.866080	+	0.499906i	$0.833368\pi$
$912$	1.28142e28	+	1.28142e28i	0.0321917	+	0.0321917i
$913$	1.05259e29	−	1.05259e29i	0.261548	−	0.261548i
$914$		−	8.10953e26i		−	0.00199312i
$915$	−4.85169e29	+	1.83910e29i	−1.17946	+	0.447089i
$916$	−4.45238e29			−1.07062
$917$	4.30788e28	+	4.30788e28i	0.102464	+	0.102464i
$918$	2.41165e27	−	2.41165e27i	0.00567397	−	0.00567397i
$919$		−	6.49458e29i		−	1.51146i	−0.654885	−	0.755728i	$-0.727283\pi$
$919$		−	6.49458e29i		−	1.51146i	0.654885	−	0.755728i	$-0.272717\pi$
$920$	−2.61006e27	+	5.79678e27i	−0.00600858	+	0.0133447i
$921$	8.96117e28			0.204065
$922$	7.30944e26	+	7.30944e26i	0.00164655	+	0.00164655i
$923$	−5.02189e28	+	5.02189e28i	−0.111905	+	0.111905i
$924$			5.85797e28i			0.129130i
$925$	1.21257e28	−	1.99381e29i	0.0264417	−	0.434777i
$926$	−2.07836e27			−0.00448344
$927$	−2.70372e28	−	2.70372e28i	−0.0576985	−	0.0576985i
$928$	−4.54615e27	+	4.54615e27i	−0.00959762	+	0.00959762i
$929$			2.76287e29i			0.577037i	0.957474	+	0.288518i	$0.0931627\pi$
$929$			2.76287e29i			0.577037i	−0.957474	+	0.288518i	$0.906837\pi$
$930$	3.47844e27	+	1.56620e27i	0.00718712	+	0.00323607i
$931$	−2.27350e28			−0.0464727
$932$	5.03102e29	+	5.03102e29i	1.01741	+	1.01741i
$933$	−8.59093e27	+	8.59093e27i	−0.0171879	+	0.0171879i
$934$			3.90456e27i			0.00772865i
$935$	−1.63798e29	−	4.32112e29i	−0.320768	−	0.846213i
$936$	−2.78263e26			−0.000539134
$937$	2.92472e29	+	2.92472e29i	0.560646	+	0.560646i	0.929491	−	0.368845i	$-0.120247\pi$
$937$	2.92472e29	+	2.92472e29i	0.560646	+	0.560646i	−0.368845	+	0.929491i	$0.620247\pi$
$938$	7.53238e26	−	7.53238e26i	0.00142858	−	0.00142858i
$939$			5.33622e29i			1.00133i
$940$	2.66317e29	−	1.00951e29i	0.494447	−	0.187427i
$941$	4.28555e29			0.787246			0.393623	−	0.919272i	$-0.371222\pi$
$941$	4.28555e29			0.787246			0.393623	+	0.919272i	$0.371222\pi$
$942$	1.88003e27	+	1.88003e27i	0.00341709	+	0.00341709i
$943$	9.81287e29	−	9.81287e29i	1.76473	−	1.76473i
$944$			6.43108e29i			1.14436i
$945$	5.50551e28	−	1.22274e29i	0.0969348	−	0.215286i
$946$	−6.10183e26			−0.00106304
$947$	1.53144e29	+	1.53144e29i	0.263998	+	0.263998i	0.826676	−	0.562678i	$-0.190229\pi$
$947$	1.53144e29	+	1.53144e29i	0.263998	+	0.263998i	−0.562678	+	0.826676i	$0.690229\pi$
$948$	−4.69271e29	+	4.69271e29i	−0.800462	+	0.800462i
$949$		−	3.59278e29i		−	0.606413i
$950$	1.52353e26	+	9.26558e24i	0.000254457	+	1.54752e-5i
$951$	−2.78642e29			−0.460513
$952$	−1.47121e27	−	1.47121e27i	−0.00240605	−	0.00240605i
$953$	1.42012e29	−	1.42012e29i	0.229825	−	0.229825i	−0.582795	−	0.812620i	$-0.698041\pi$
$953$	1.42012e29	−	1.42012e29i	0.229825	−	0.229825i	0.812620	+	0.582795i	$0.198041\pi$
$954$		−	2.28399e25i		−	3.65772e-5i
$955$	−1.65029e29	−	7.43061e28i	−0.261534	−	0.117758i
$956$	−1.66583e29			−0.261247
$957$	2.28326e29	+	2.28326e29i	0.354354	+	0.354354i
$958$	2.88773e27	−	2.88773e27i	0.00443509	−	0.00443509i
$959$		−	1.24069e29i		−	0.188572i
$960$	−2.19277e29	−	5.78470e29i	−0.329822	−	0.870099i
$961$	1.10281e30			1.64159
$962$	4.21032e26	+	4.21032e26i	0.000620246	+	0.000620246i
$963$	−3.75510e28	+	3.75510e28i	−0.0547467	+	0.0547467i
$964$			4.09246e29i			0.590492i
$965$	−7.45448e29	+	2.82572e29i	−1.06450	+	0.403511i
$966$	1.07816e27			0.00152374
$967$	−5.27619e29	−	5.27619e29i	−0.737999	−	0.737999i	0.234191	−	0.972191i	$-0.424756\pi$
$967$	−5.27619e29	−	5.27619e29i	−0.737999	−	0.737999i	−0.972191	+	0.234191i	$0.924756\pi$
$968$	−3.27598e27	+	3.27598e27i	−0.00453510	+	0.00453510i
$969$			4.84917e28i			0.0664400i
$970$	1.21826e27	−	2.70569e27i	0.00165205	−	0.00366910i
$971$	1.97947e29			0.265679			0.132840	−	0.991138i	$-0.457590\pi$
$971$	1.97947e29			0.265679			0.132840	+	0.991138i	$0.457590\pi$
$972$	1.41500e29	+	1.41500e29i	0.187973	+	0.187973i
$973$	−1.33231e29	+	1.33231e29i	−0.175177	+	0.175177i
$974$			9.57535e25i			0.000124614i
$975$	−2.09055e29	+	1.85085e29i	−0.269286	+	0.238410i
$976$	−1.06293e30			−1.35521
$977$	−9.76815e29	−	9.76815e29i	−1.23273	−	1.23273i	−0.962913	−	0.269813i	$-0.913038\pi$
$977$	−9.76815e29	−	9.76815e29i	−1.23273	−	1.23273i	−0.269813	−	0.962913i	$-0.586962\pi$
$978$	−4.01148e27	+	4.01148e27i	−0.00501090	+	0.00501090i
$979$			3.99249e29i			0.493647i
$980$	7.07718e29	+	3.18657e29i	0.866163	+	0.389998i
$981$	−6.77991e28			−0.0821360
$982$	−2.05638e27	−	2.05638e27i	−0.00246598	−	0.00246598i
$983$	−1.45347e29	+	1.45347e29i	−0.172532	+	0.172532i	−0.788091	−	0.615559i	$-0.788930\pi$
$983$	−1.45347e29	+	1.45347e29i	−0.172532	+	0.172532i	0.615559	+	0.788091i	$0.288930\pi$
$984$		−	1.46697e28i		−	0.0172373i
$985$	−1.88766e28	−	4.97981e28i	−0.0219564	−	0.0579229i
$986$	−5.73426e27			−0.00660249
$987$	−6.83097e28	−	6.83097e28i	−0.0778594	−	0.0778594i
$988$	1.18479e28	−	1.18479e28i	0.0133682	−	0.0133682i
$989$		−	4.13576e29i		−	0.461947i
$990$	−3.65824e26	+	1.38670e26i	−0.000404502	+	0.000153332i
$991$	−3.82280e29			−0.418452			−0.209226	−	0.977867i	$-0.567094\pi$
$991$	−3.82280e29			−0.418452			−0.209226	+	0.977867i	$0.567094\pi$
$992$	1.65788e28	+	1.65788e28i	0.0179654	+	0.0179654i
$993$	2.56839e29	−	2.56839e29i	0.275530	−	0.275530i
$994$			4.49565e26i			0.000477451i
$995$	−2.34187e29	+	5.20115e29i	−0.246225	+	0.546850i
$996$	5.33265e29			0.555072
$997$	2.89012e29	+	2.89012e29i	0.297827	+	0.297827i	0.840162	−	0.542335i	$-0.182460\pi$
$997$	2.89012e29	+	2.89012e29i	0.297827	+	0.297827i	−0.542335	+	0.840162i	$0.682460\pi$
$998$	1.27033e27	−	1.27033e27i	0.00129602	−	0.00129602i
$999$		−	4.55069e29i		−	0.459645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.21.c.a.2.5	✓	18
3.2	odd	2		45.21.g.a.37.5		18
5.2	odd	4		25.21.c.b.18.5		18
5.3	odd	4	inner	5.21.c.a.3.5	yes	18
5.4	even	2		25.21.c.b.7.5		18
15.8	even	4		45.21.g.a.28.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.21.c.a.2.5	✓	18	1.1	even	1	trivial
5.21.c.a.3.5	yes	18	5.3	odd	4	inner
25.21.c.b.7.5		18	5.4	even	2
25.21.c.b.18.5		18	5.2	odd	4
45.21.g.a.28.5		18	15.8	even	4
45.21.g.a.37.5		18	3.2	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:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.77310 + 3.77310i) q^{2} +(38858.9 - 38858.9i) q^{3} -1.04855e6i q^{4} +(-8.90462e6 - 4.00939e6i) q^{5} +293237. q^{6} +(4.46902e7 + 4.46902e7i) q^{7} +(7.91266e6 - 7.91266e6i) q^{8} +4.66753e8i q^{9} +O(q^{10})\)	\(q+(3.77310 + 3.77310i) q^{2} +(38858.9 - 38858.9i) q^{3} -1.04855e6i q^{4} +(-8.90462e6 - 4.00939e6i) q^{5} +293237. q^{6} +(4.46902e7 + 4.46902e7i) q^{7} +(7.91266e6 - 7.91266e6i) q^{8} +4.66753e8i q^{9} +(-1.84702e7 - 4.87259e7i) q^{10} -1.60852e10 q^{11} +(-4.07454e10 - 4.07454e10i) q^{12} +(-3.76718e10 + 3.76718e10i) q^{13} +3.37242e8i q^{14} +(-5.01824e11 + 1.90223e11i) q^{15} -1.09942e12 q^{16} +(-2.08022e12 - 2.08022e12i) q^{17} +(-1.76111e9 + 1.76111e9i) q^{18} -2.99942e11i q^{19} +(-4.20404e12 + 9.33691e12i) q^{20} +3.47323e12 q^{21} +(-6.06910e10 - 6.06910e10i) q^{22} +(4.11357e13 - 4.11357e13i) q^{23} -6.14955e11i q^{24} +(6.32170e13 + 7.14042e13i) q^{25} -2.84279e11 q^{26} +(1.53630e14 + 1.53630e14i) q^{27} +(4.68598e13 - 4.68598e13i) q^{28} -3.65291e14i q^{29} +(-2.61117e12 - 1.17570e12i) q^{30} -1.33214e15 q^{31} +(-1.24453e13 - 1.24453e13i) q^{32} +(-6.25053e14 + 6.25053e14i) q^{33} -1.56978e13i q^{34} +(-2.18769e14 - 5.77130e14i) q^{35} +4.89412e14 q^{36} +(-1.48105e15 - 1.48105e15i) q^{37} +(1.13171e12 - 1.13171e12i) q^{38} +2.92777e15i q^{39} +(-1.02184e14 + 3.87343e13i) q^{40} +2.38548e16 q^{41} +(1.31048e13 + 1.31048e13i) q^{42} +(5.02697e15 - 5.02697e15i) q^{43} +1.68661e16i q^{44} +(1.87139e15 - 4.15625e15i) q^{45} +3.10419e14 q^{46} +(-1.96675e16 - 1.96675e16i) q^{47} +(-4.27224e16 + 4.27224e16i) q^{48} -7.57978e16i q^{49} +(-3.08912e13 + 5.07940e14i) q^{50} -1.61670e17 q^{51} +(3.95006e16 + 3.95006e16i) q^{52} +(-6.48453e15 + 6.48453e15i) q^{53} +1.15932e15i q^{54} +(1.43232e17 + 6.44918e16i) q^{55} +7.07237e14 q^{56} +(-1.16554e16 - 1.16554e16i) q^{57} +(1.37828e15 - 1.37828e15i) q^{58} -5.84951e17i q^{59} +(1.99458e17 + 5.26187e17i) q^{60} +9.66810e17 q^{61} +(-5.02630e15 - 5.02630e15i) q^{62} +(-2.08593e16 + 2.08593e16i) q^{63} +1.15273e18i q^{64} +(4.86494e17 - 1.84412e17i) q^{65} -4.71678e15 q^{66} +(-2.23353e18 - 2.23353e18i) q^{67} +(-2.18121e18 + 2.18121e18i) q^{68} -3.19698e18i q^{69} +(1.35213e15 - 3.00301e15i) q^{70} +1.33306e18 q^{71} +(3.69326e15 + 3.69326e15i) q^{72} +(-4.76853e18 + 4.76853e18i) q^{73} -1.11763e16i q^{74} +(5.23123e18 + 3.18146e17i) q^{75} -3.14504e17 q^{76} +(-7.18850e17 - 7.18850e17i) q^{77} +(-1.10468e16 + 1.10468e16i) q^{78} -1.15172e19i q^{79} +(9.78993e18 + 4.40801e18i) q^{80} +1.03123e19 q^{81} +(9.00068e16 + 9.00068e16i) q^{82} +(-6.54386e18 + 6.54386e18i) q^{83} -3.64184e18i q^{84} +(1.01831e19 + 2.68640e19i) q^{85} +3.79345e16 q^{86} +(-1.41948e19 - 1.41948e19i) q^{87} +(-1.27277e17 + 1.27277e17i) q^{88} -2.48209e19i q^{89} +(2.27429e16 - 8.62101e15i) q^{90} -3.36712e18 q^{91} +(-4.31328e19 - 4.31328e19i) q^{92} +(-5.17655e19 + 5.17655e19i) q^{93} -1.48415e17i q^{94} +(-1.20259e18 + 2.67087e18i) q^{95} -9.67219e17 q^{96} +(4.02655e19 + 4.02655e19i) q^{97} +(2.85993e17 - 2.85993e17i) q^{98} -7.50780e18i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 29448 q^{3} - 7302140 q^{5} + 19792536 q^{6} - 585532752 q^{7} + 930113700 q^{8}+O(q^{10}) \) 18 * q - 2 * q^2 + 29448 * q^3 - 7302140 * q^5 + 19792536 * q^6 - 585532752 * q^7 + 930113700 * q^8	\( 18 q - 2 q^{2} + 29448 q^{3} - 7302140 q^{5} + 19792536 q^{6} - 585532752 q^{7} + 930113700 q^{8} - 17138778090 q^{10} - 6506343064 q^{11} + 140311795848 q^{12} - 369354655602 q^{13} + 998626204320 q^{15} - 6345876020232 q^{16} + 6508314764998 q^{17} - 11265991705902 q^{18} + 38356516779780 q^{20} - 97402974719064 q^{21} + 161054386758096 q^{22} - 81655963656152 q^{23} + 33913283845350 q^{25} + 234104101103636 q^{26} - 511935279143400 q^{27} + 772213614545352 q^{28} - 877127470680480 q^{30} + 17\!\cdots\!36 q^{31}+ \cdots - 27\!\cdots\!98 q^{98}+O(q^{100}) \) 18 * q - 2 * q^2 + 29448 * q^3 - 7302140 * q^5 + 19792536 * q^6 - 585532752 * q^7 + 930113700 * q^8 - 17138778090 * q^10 - 6506343064 * q^11 + 140311795848 * q^12 - 369354655602 * q^13 + 998626204320 * q^15 - 6345876020232 * q^16 + 6508314764998 * q^17 - 11265991705902 * q^18 + 38356516779780 * q^20 - 97402974719064 * q^21 + 161054386758096 * q^22 - 81655963656152 * q^23 + 33913283845350 * q^25 + 234104101103636 * q^26 - 511935279143400 * q^27 + 772213614545352 * q^28 - 877127470680480 * q^30 + 1742256896900736 * q^31 - 4072699683722552 * q^32 + 1579138514189496 * q^33 - 4817791288113440 * q^35 + 2214548622647868 * q^36 + 6383289895587498 * q^37 - 14134212502378200 * q^38 + 43297629431150700 * q^40 - 30602304597564664 * q^41 + 48810732785962896 * q^42 - 46399469942287752 * q^43 + 67947826451186070 * q^45 + 17467214047538136 * q^46 - 137109249757437752 * q^47 - 103698596104819152 * q^48 - 40012852869983150 * q^50 + 686047946059669536 * q^51 - 745026624616846452 * q^52 - 184102027021671302 * q^53 + 752956242406989720 * q^55 + 685775432394721200 * q^56 - 785021725278622800 * q^57 - 2701246502184220800 * q^58 + 6219197632829342760 * q^60 + 49879194030044136 * q^61 - 1190554579738283704 * q^62 - 7082176979112100152 * q^63 + 6907070599410641170 * q^65 + 11227963704975799872 * q^66 - 5597336519263153752 * q^67 - 25617328014464685148 * q^68 + 31706333959370270760 * q^70 + 10983277495574224736 * q^71 - 41525052650392592700 * q^72 - 19072400700441139902 * q^73 + 36766882672050433200 * q^75 + 75630007803532292400 * q^76 - 47766064678699704904 * q^77 - 109239984515466629304 * q^78 + 134231700802559812960 * q^80 + 74219234884008322518 * q^81 - 83501540658117625104 * q^82 - 119739383617210903952 * q^83 + 169044713294843560110 * q^85 + 33497378050769887736 * q^86 - 28944830404542403200 * q^87 - 337125565675837197600 * q^88 + 396784292056608506070 * q^90 + 86281377644254817136 * q^91 - 206921051460419061752 * q^92 - 285487695991878257304 * q^93 + 118106834336527303800 * q^95 + 377091713708556287136 * q^96 - 318608382222604685502 * q^97 - 27697031317753120498 * q^98

Introduction

L-functions

Modular forms

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