LMFDB - Embedded newform 4.33.b.b.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,33,Mod(3,4)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 33, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 33);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 33 $
Character orbit:	$[\chi]$	$=$	4.b (of order $2$, degree $1$, 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:	$25.9466620569$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 72511313626452 x^{12} + \cdots + 62\!\cdots\!00 $ x^14 + 72511313626452x^12 + 2025191977179903324811336518x^10 + 27922884728028663894750078705223437415644x^8 + 203010662886800095440071970440402438747266446160157745x^6 + 758734102549599282271818004575465783845093632382487984186969965640x^4 + 1269648449115368448095465842606476325720277486461580161887038301255933321354000x^2 + 624216522131873762678666934520680301449631616035103441585151846396220724278849706601312000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{182}\cdot 3^{20}\cdot 5^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.8
Root			$-4.36932e6i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.33.b.b.3.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15224.0 + 63743.2i) q^{2} -6.99091e7i q^{3} +(-3.83143e9 - 1.94085e9i) q^{4} -1.46681e11 q^{5} +(4.45623e12 + 1.06430e12i) q^{6} -5.71644e13i q^{7} +(1.82046e14 - 2.14680e14i) q^{8} -3.03426e15 q^{9} +O(q^{10})$	\(q+(-15224.0 + 63743.2i) q^{2} -6.99091e7i q^{3} +(-3.83143e9 - 1.94085e9i) q^{4} -1.46681e11 q^{5} +(4.45623e12 + 1.06430e12i) q^{6} -5.71644e13i q^{7} +(1.82046e14 - 2.14680e14i) q^{8} -3.03426e15 q^{9} +(2.23307e15 - 9.34993e15i) q^{10} -6.39967e16i q^{11} +(-1.35683e17 + 2.67852e17i) q^{12} +3.82332e17 q^{13} +(3.64385e18 + 8.70272e17i) q^{14} +1.02543e19i q^{15} +(1.09129e19 + 1.48725e19i) q^{16} -4.07694e19 q^{17} +(4.61937e19 - 1.93414e20i) q^{18} +6.13984e19i q^{19} +(5.61998e20 + 2.84687e20i) q^{20} -3.99632e21 q^{21} +(4.07936e21 + 9.74287e20i) q^{22} +2.81087e20i q^{23} +(-1.50081e22 - 1.27267e22i) q^{24} -1.76771e21 q^{25} +(-5.82063e21 + 2.43711e22i) q^{26} +8.25797e22i q^{27} +(-1.10948e23 + 2.19021e23i) q^{28} +9.24035e22 q^{29} +(-6.53645e23 - 1.56112e23i) q^{30} -4.23845e23i q^{31} +(-1.11416e24 + 4.69206e23i) q^{32} -4.47396e24 q^{33} +(6.20674e23 - 2.59877e24i) q^{34} +8.38495e24i q^{35} +(1.16256e25 + 5.88906e24i) q^{36} -4.96114e23 q^{37} +(-3.91373e24 - 9.34729e23i) q^{38} -2.67285e25i q^{39} +(-2.67027e25 + 3.14895e25i) q^{40} +7.78015e25 q^{41} +(6.08399e25 - 2.54738e26i) q^{42} -5.67810e24i q^{43} +(-1.24208e26 + 2.45199e26i) q^{44} +4.45069e26 q^{45} +(-1.79174e25 - 4.27927e24i) q^{46} +2.70622e26i q^{47} +(1.03972e27 - 7.62912e26i) q^{48} -2.16335e27 q^{49} +(2.69116e25 - 1.12679e26i) q^{50} +2.85015e27i q^{51} +(-1.46488e27 - 7.42051e26i) q^{52} +1.23036e27 q^{53} +(-5.26390e27 - 1.25719e27i) q^{54} +9.38712e27i q^{55} +(-1.22721e28 - 1.04066e28i) q^{56} +4.29231e27 q^{57} +(-1.40675e27 + 5.89010e27i) q^{58} +3.43224e27i q^{59} +(1.99022e28 - 3.92888e28i) q^{60} +4.92044e28 q^{61} +(2.70172e28 + 6.45261e27i) q^{62} +1.73452e29i q^{63} +(-1.29467e28 - 7.81632e28i) q^{64} -5.60809e28 q^{65} +(6.81115e28 - 2.85184e29i) q^{66} -1.86282e29i q^{67} +(1.56205e29 + 7.91275e28i) q^{68} +1.96506e28 q^{69} +(-5.34483e29 - 1.27652e29i) q^{70} +7.39887e29i q^{71} +(-5.52375e29 + 6.51395e29i) q^{72} +1.01270e30 q^{73} +(7.55284e27 - 3.16239e28i) q^{74} +1.23579e29i q^{75} +(1.19165e29 - 2.35243e29i) q^{76} -3.65834e30 q^{77} +(1.70376e30 + 4.06915e29i) q^{78} -2.63707e30i q^{79} +(-1.60072e30 - 2.18151e30i) q^{80} +1.50522e29 q^{81} +(-1.18445e30 + 4.95932e30i) q^{82} -5.56904e30i q^{83} +(1.53116e31 + 7.75627e30i) q^{84} +5.98011e30 q^{85} +(3.61940e29 + 8.64434e28i) q^{86} -6.45985e30i q^{87} +(-1.37388e31 - 1.16503e31i) q^{88} +1.36383e31 q^{89} +(-6.77574e30 + 2.83701e31i) q^{90} -2.18558e31i q^{91} +(5.45549e29 - 1.07697e30i) q^{92} -2.96306e31 q^{93} +(-1.72503e31 - 4.11995e30i) q^{94} -9.00598e30i q^{95} +(3.28017e31 + 7.78898e31i) q^{96} -9.37964e31 q^{97} +(3.29348e31 - 1.37899e32i) q^{98} +1.94183e32i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 23780 q^{2} - 2922848368 q^{4} + 138121491740 q^{5} + 1262734959552 q^{6} - 191366550113600 q^{8} - 11\!\cdots\!50 q^{9}+O(q^{10}) $ 14 * q - 23780 * q^2 - 2922848368 * q^4 + 138121491740 * q^5 + 1262734959552 * q^6 - 191366550113600 * q^8 - 11183509932817650 * q^9	$ 14 q - 23780 q^{2} - 2922848368 q^{4} + 138121491740 q^{5} + 1262734959552 q^{6} - 191366550113600 q^{8} - 11\!\cdots\!50 q^{9}+ \cdots - 46\!\cdots\!00 q^{98}+O(q^{100}) $ 14 * q - 23780 * q^2 - 2922848368 * q^4 + 138121491740 * q^5 + 1262734959552 * q^6 - 191366550113600 * q^8 - 11183509932817650 * q^9 + 31775605694457400 * q^10 - 356375853407619840 * q^12 - 1640418469677858020 * q^13 + 7731597686180285568 * q^14 - 30570843123186593536 * q^16 + 31570967905797256220 * q^17 - 356724239595483290340 * q^18 + 2022222335397731344160 * q^20 - 2117057333603414716416 * q^21 + 5453282318362187158080 * q^22 - 25676387438412555666432 * q^24 + 10252879651857697291050 * q^25 - 100487287286439222842824 * q^26 + 287406099989137745118720 * q^28 - 383350228001906510553316 * q^29 - 58105690536229485525120 * q^30 - 3049085458330908760601600 * q^32 + 300337698474624477849600 * q^33 + 2968198158688225453161016 * q^34 + 4059126291383069998225296 * q^36 - 10743727036349878681805540 * q^37 - 23674230631082905997232960 * q^38 + 46284510399605997225174400 * q^40 + 36301708465641824663518748 * q^41 + 115560171253757823362918400 * q^42 - 341183497187317069095824640 * q^44 + 807084693575724158345591580 * q^45 - 292611965791335032977170048 * q^46 + 2221472331677427727192412160 * q^48 - 4831123780514350255580603890 * q^49 - 510591072029103065039587500 * q^50 - 9698318635805895955111735520 * q^52 + 18428895934780252746021636380 * q^53 + 5640914457354711920825943936 * q^54 + 6374003242890184756165527552 * q^56 - 45021698676819804378731120640 * q^57 - 38529567312130296955877295560 * q^58 + 47104092918034241778705984000 * q^60 + 106402038936127775684939892508 * q^61 + 21568431972603200921875622400 * q^62 - 196737301243248539525687308288 * q^64 + 113178238686492542374351007800 * q^65 + 127488965971714418642064552960 * q^66 + 354271480525935415641826176800 * q^68 - 518263207562337876647092752384 * q^69 - 514873634674652910315035354880 * q^70 + 114107440511865769651514823360 * q^72 + 1432707125192338982920850898460 * q^73 - 984194129445064624850959434184 * q^74 - 782627770945775078204519980800 * q^76 - 3080015547766001613074070589440 * q^77 + 87768417039576149684305430400 * q^78 + 6279147555674556254006737379840 * q^80 - 42644471558968013664770433522 * q^81 - 4557892929168088074284564686280 * q^82 + 18798568063225498187446552682496 * q^84 + 6758108895547933966316548575800 * q^85 - 23458263349697798020331664550848 * q^86 + 11102138256776653733497151431680 * q^88 - 18473812211636703183423448507876 * q^89 - 25496421058026878088516916614600 * q^90 + 60798444498044060215697222361600 * q^92 + 43431545808036949970541566115840 * q^93 - 130643574777689548682138472237312 * q^94 + 345792875639857602943412371832832 * q^96 - 201795139515948373218799959195620 * q^97 - 460006462884606019803763245136100 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$	−15224.0	+	63743.2i	−0.232300	+	0.972644i
$2$	−15224.0	+	63743.2i	−0.232300	+	0.972644i
$3$		−	6.99091e7i		−	1.62403i	−0.583637	−	0.812014i	$-0.698371\pi$
$3$		−	6.99091e7i		−	1.62403i	0.583637	−	0.812014i	$-0.301629\pi$
$4$	−3.83143e9	−	1.94085e9i	−0.892074	−	0.451890i
$5$	−1.46681e11			−0.961290			−0.480645	−	0.876915i	$-0.659597\pi$
$5$	−1.46681e11			−0.961290			−0.480645	+	0.876915i	$0.659597\pi$
$6$	4.45623e12	+	1.06430e12i	1.57960	+	0.377262i
$7$		−	5.71644e13i		−	1.72011i	−0.510198	−	0.860057i	$-0.670428\pi$
$7$		−	5.71644e13i		−	1.72011i	0.510198	−	0.860057i	$-0.329572\pi$
$8$	1.82046e14	−	2.14680e14i	0.646757	−	0.762696i
$9$	−3.03426e15			−1.63747
$10$	2.23307e15	−	9.34993e15i	0.223307	−	0.934993i
$11$		−	6.39967e16i		−	1.39276i	−0.717675	−	0.696378i	$-0.754794\pi$
$11$		−	6.39967e16i		−	1.39276i	0.717675	−	0.696378i	$-0.245206\pi$
$12$	−1.35683e17	+	2.67852e17i	−0.733883	+	1.44875i
$13$	3.82332e17			0.574576			0.287288	−	0.957844i	$-0.407246\pi$
$13$	3.82332e17			0.574576			0.287288	+	0.957844i	$0.407246\pi$
$14$	3.64385e18	+	8.70272e17i	1.67306	+	0.399582i
$15$			1.02543e19i			1.56116i
$16$	1.09129e19	+	1.48725e19i	0.591590	+	0.806239i
$17$	−4.07694e19			−0.837822			−0.418911	−	0.908027i	$-0.637588\pi$
$17$	−4.07694e19			−0.837822			−0.418911	+	0.908027i	$0.637588\pi$
$18$	4.61937e19	−	1.93414e20i	0.380384	−	1.59268i
$19$			6.13984e19i			0.212863i	0.994320	+	0.106431i	$0.0339424\pi$
$19$			6.13984e19i			0.212863i	−0.994320	+	0.106431i	$0.966058\pi$
$20$	5.61998e20	+	2.84687e20i	0.857541	+	0.434397i
$21$	−3.99632e21			−2.79352
$22$	4.07936e21	+	9.74287e20i	1.35466	+	0.323537i
$23$			2.81087e20i			0.0458348i	0.999737	+	0.0229174i	$0.00729548\pi$
$23$			2.81087e20i			0.0458348i	−0.999737	+	0.0229174i	$0.992705\pi$
$24$	−1.50081e22	−	1.27267e22i	−1.23864	−	1.05035i
$25$	−1.76771e21			−0.0759224
$26$	−5.82063e21	+	2.43711e22i	−0.133474	+	0.558858i
$27$			8.25797e22i			1.03527i
$28$	−1.10948e23	+	2.19021e23i	−0.777303	+	1.53447i
$29$	9.24035e22			0.369250			0.184625	−	0.982809i	$-0.440893\pi$
$29$	9.24035e22			0.369250			0.184625	+	0.982809i	$0.440893\pi$
$30$	−6.53645e23	−	1.56112e23i	−1.51846	−	0.362658i
$31$		−	4.23845e23i		−	0.582666i	−0.956622	−	0.291333i	$-0.905901\pi$
$31$		−	4.23845e23i		−	0.582666i	0.956622	−	0.291333i	$-0.0940987\pi$
$32$	−1.11416e24	+	4.69206e23i	−0.921610	+	0.388118i
$33$	−4.47396e24			−2.26188
$34$	6.20674e23	−	2.59877e24i	0.194626	−	0.814903i
$35$			8.38495e24i			1.65353i
$36$	1.16256e25	+	5.88906e24i	1.46074	+	0.739957i
$37$	−4.96114e23			−0.0402118			−0.0201059	−	0.999798i	$-0.506400\pi$
$37$	−4.96114e23			−0.0402118			−0.0201059	+	0.999798i	$0.506400\pi$
$38$	−3.91373e24	−	9.34729e23i	−0.207040	−	0.0494480i
$39$		−	2.67285e25i		−	0.933127i
$40$	−2.67027e25	+	3.14895e25i	−0.621721	+	0.733172i
$41$	7.78015e25			1.22024			0.610121	−	0.792308i	$-0.291121\pi$
$41$	7.78015e25			1.22024			0.610121	+	0.792308i	$0.291121\pi$
$42$	6.08399e25	−	2.54738e26i	0.648933	−	2.71710i
$43$		−	5.67810e24i		−	0.0415631i	−0.999784	−	0.0207815i	$-0.993385\pi$
$43$		−	5.67810e24i		−	0.0415631i	0.999784	−	0.0207815i	$-0.00661544\pi$
$44$	−1.24208e26	+	2.45199e26i	−0.629373	+	1.24244i
$45$	4.45069e26			1.57408
$46$	−1.79174e25	−	4.27927e24i	−0.0445810	−	0.0106474i
$47$			2.70622e26i			0.477307i	0.971105	+	0.238653i	$0.0767059\pi$
$47$			2.70622e26i			0.477307i	−0.971105	+	0.238653i	$0.923294\pi$
$48$	1.03972e27	−	7.62912e26i	1.30935	−	0.960760i
$49$	−2.16335e27			−1.95879
$50$	2.69116e25	−	1.12679e26i	0.0176368	−	0.0738454i
$51$			2.85015e27i			1.36065i
$52$	−1.46488e27	−	7.42051e26i	−0.512564	−	0.259645i
$53$	1.23036e27			0.317408			0.158704	−	0.987326i	$-0.449268\pi$
$53$	1.23036e27			0.317408			0.158704	+	0.987326i	$0.449268\pi$
$54$	−5.26390e27	−	1.25719e27i	−1.00695	−	0.240493i
$55$			9.38712e27i			1.33884i
$56$	−1.22721e28	−	1.04066e28i	−1.31192	−	1.11250i
$57$	4.29231e27			0.345695
$58$	−1.40675e27	+	5.89010e27i	−0.0857768	+	0.359149i
$59$			3.43224e27i			0.159201i	0.996827	+	0.0796005i	$0.0253645\pi$
$59$			3.43224e27i			0.159201i	−0.996827	+	0.0796005i	$0.974636\pi$
$60$	1.99022e28	−	3.92888e28i	0.705474	−	1.39267i
$61$	4.92044e28			1.33883			0.669416	−	0.742888i	$-0.266544\pi$
$61$	4.92044e28			1.33883			0.669416	+	0.742888i	$0.266544\pi$
$62$	2.70172e28	+	6.45261e27i	0.566726	+	0.135353i
$63$			1.73452e29i			2.81663i
$64$	−1.29467e28	−	7.81632e28i	−0.163411	−	0.986558i
$65$	−5.60809e28			−0.552333
$66$	6.81115e28	−	2.85184e29i	0.525433	−	2.20000i
$67$		−	1.86282e29i		−	1.12973i	−0.825184	−	0.564864i	$-0.808929\pi$
$67$		−	1.86282e29i		−	1.12973i	0.825184	−	0.564864i	$-0.191071\pi$
$68$	1.56205e29	+	7.91275e28i	0.747399	+	0.378604i
$69$	1.96506e28			0.0744371
$70$	−5.34483e29	−	1.27652e29i	−1.60829	−	0.384114i
$71$			7.39887e29i			1.77432i	0.461463	+	0.887159i	$0.347325\pi$
$71$			7.39887e29i			1.77432i	−0.461463	+	0.887159i	$0.652675\pi$
$72$	−5.52375e29	+	6.51395e29i	−1.05904	+	1.24889i
$73$	1.01270e30			1.55710			0.778549	−	0.627583i	$-0.215956\pi$
$73$	1.01270e30			1.55710			0.778549	+	0.627583i	$0.215956\pi$
$74$	7.55284e27	−	3.16239e28i	0.00934120	−	0.0391118i
$75$			1.23579e29i			0.123300i
$76$	1.19165e29	−	2.35243e29i	0.0961905	−	0.189889i
$77$	−3.65834e30			−2.39570
$78$	1.70376e30	+	4.06915e29i	0.907601	+	0.216765i
$79$		−	2.63707e30i		−	1.14575i	−0.819644	−	0.572874i	$-0.805829\pi$
$79$		−	2.63707e30i		−	1.14575i	0.819644	−	0.572874i	$-0.194171\pi$
$80$	−1.60072e30	−	2.18151e30i	−0.568690	−	0.775029i
$81$	1.50522e29			0.0438367
$82$	−1.18445e30	+	4.95932e30i	−0.283462	+	1.18686i
$83$		−	5.56904e30i		−	1.09782i	−0.835882	−	0.548910i	$-0.815043\pi$
$83$		−	5.56904e30i		−	1.09782i	0.835882	−	0.548910i	$-0.184957\pi$
$84$	1.53116e31	+	7.75627e30i	2.49202	+	1.26236i
$85$	5.98011e30			0.805390
$86$	3.61940e29	+	8.64434e28i	0.0404261	+	0.00965510i
$87$		−	6.45985e30i		−	0.599673i
$88$	−1.37388e31	−	1.16503e31i	−1.06225	−	0.900775i
$89$	1.36383e31			0.880073			0.440037	−	0.897980i	$-0.354965\pi$
$89$	1.36383e31			0.880073			0.440037	+	0.897980i	$0.354965\pi$
$90$	−6.77574e30	+	2.83701e31i	−0.365659	+	1.53102i
$91$		−	2.18558e31i		−	0.988336i
$92$	5.45549e29	−	1.07697e30i	0.0207123	−	0.0408880i
$93$	−2.96306e31			−0.946266
$94$	−1.72503e31	−	4.11995e30i	−0.464249	−	0.110878i
$95$		−	9.00598e30i		−	0.204623i
$96$	3.28017e31	+	7.78898e31i	0.630314	+	1.49672i
$97$	−9.37964e31			−1.52700			−0.763499	−	0.645809i	$-0.776520\pi$
$97$	−9.37964e31			−1.52700			−0.763499	+	0.645809i	$0.776520\pi$
$98$	3.29348e31	−	1.37899e32i	0.455028	−	1.90521i
$99$			1.94183e32i			2.28059i
$100$	6.77283e30	+	3.43086e30i	0.0677283	+	0.0343086i
$101$	5.72813e30			0.0488507			0.0244253	−	0.999702i	$-0.492224\pi$
$101$	5.72813e30			0.0488507			0.0244253	+	0.999702i	$0.492224\pi$
$102$	−1.81678e32	−	4.33908e31i	−1.32343	−	0.316078i
$103$		−	9.76491e31i		−	0.608517i	−0.952590	−	0.304258i	$-0.901591\pi$
$103$		−	9.76491e31i		−	0.608517i	0.952590	−	0.304258i	$-0.0984087\pi$
$104$	6.96020e31	−	8.20790e31i	0.371611	−	0.438227i
$105$	5.86184e32			2.68538
$106$	−1.87310e31	+	7.84271e31i	−0.0737339	+	0.308725i
$107$			2.83419e32i			0.960038i	0.877258	+	0.480019i	$0.159370\pi$
$107$			2.83419e32i			0.960038i	−0.877258	+	0.480019i	$0.840630\pi$
$108$	1.60275e32	−	3.16398e32i	0.467828	−	0.923536i
$109$	−2.57765e32			−0.649232			−0.324616	−	0.945846i	$-0.605235\pi$
$109$	−2.57765e32			−0.649232			−0.324616	+	0.945846i	$0.605235\pi$
$110$	−5.98365e32	−	1.42910e32i	−1.30222	−	0.311013i
$111$			3.46829e31i			0.0653051i
$112$	8.50177e32	−	6.23831e32i	1.38682	−	1.01760i
$113$	2.01143e32			0.284610			0.142305	−	0.989823i	$-0.454549\pi$
$113$	2.01143e32			0.284610			0.142305	+	0.989823i	$0.454549\pi$
$114$	−6.53461e31	+	2.73605e32i	−0.0803049	+	0.336238i
$115$		−	4.12302e31i		−	0.0440606i
$116$	−3.54037e32	−	1.79342e32i	−0.329398	−	0.166861i
$117$	−1.16010e33			−0.940850
$118$	−2.18782e32	−	5.22525e31i	−0.154846	−	0.0369824i
$119$			2.33056e33i			1.44115i
$120$	2.20140e33	+	1.86676e33i	1.19069	+	1.00969i
$121$	−1.98421e33			−0.939768
$122$	−7.49087e32	+	3.13644e33i	−0.311011	+	1.30221i
$123$		−	5.43903e33i		−	1.98171i
$124$	−8.22620e32	+	1.62393e33i	−0.263301	+	0.519781i
$125$	3.67448e33			1.03427
$126$	−1.10564e34	−	2.64063e33i	−2.73958	−	0.654304i
$127$		−	7.58615e33i		−	1.65639i	−0.560442	−	0.828194i	$-0.689369\pi$
$127$		−	7.58615e33i		−	1.65639i	0.560442	−	0.828194i	$-0.310631\pi$
$128$	5.17947e33	+	3.64691e32i	0.997530	+	0.0702370i
$129$	−3.96951e32			−0.0674996
$130$	8.53776e32	−	3.57478e33i	0.128307	−	0.537224i
$131$			7.08226e33i			0.941523i	0.882261	+	0.470761i	$0.156021\pi$
$131$			7.08226e33i			0.941523i	−0.882261	+	0.470761i	$0.843979\pi$
$132$	1.71416e34	+	8.68329e33i	2.01776	+	1.02212i
$133$	3.50980e33			0.366148
$134$	1.18742e34	+	2.83596e33i	1.09882	+	0.262436i
$135$		−	1.21129e34i		−	0.995193i
$136$	−7.42191e33	+	8.75238e33i	−0.541868	+	0.639004i
$137$	−1.56966e34			−1.01924			−0.509620	−	0.860399i	$-0.670214\pi$
$137$	−1.56966e34			−1.01924			−0.509620	+	0.860399i	$0.670214\pi$
$138$	−2.99160e32	+	1.25259e33i	−0.0172917	+	0.0724008i
$139$			1.66363e34i			0.856680i	0.903618	+	0.428340i	$0.140901\pi$
$139$			1.66363e34i			0.856680i	−0.903618	+	0.428340i	$0.859099\pi$
$140$	1.62740e34	−	3.21263e34i	0.747213	−	1.47507i
$141$	1.89189e34			0.775160
$142$	−4.71628e34	−	1.12640e34i	−1.72578	−	0.412174i
$143$		−	2.44680e34i		−	0.800243i
$144$	−3.31127e34	−	4.51270e34i	−0.968711	−	1.32019i
$145$	−1.35539e34			−0.354956
$146$	−1.54174e34	+	6.45529e34i	−0.361714	+	1.51450i
$147$			1.51238e35i			3.18114i
$148$	1.90082e33	+	9.62884e32i	0.0358719	+	0.0181713i
$149$	3.15083e33			0.0533881			0.0266941	−	0.999644i	$-0.491502\pi$
$149$	3.15083e33			0.0533881			0.0266941	+	0.999644i	$0.491502\pi$
$150$	−7.87730e33	−	1.88136e33i	−0.119927	−	0.0286426i
$151$		−	6.49171e34i		−	0.888644i	−0.895867	−	0.444322i	$-0.853445\pi$
$151$		−	6.49171e34i		−	0.888644i	0.895867	−	0.444322i	$-0.146555\pi$
$152$	1.31810e34	+	1.11773e34i	0.162349	+	0.137670i
$153$	1.23705e35			1.37191
$154$	5.56946e34	−	2.33194e35i	0.556521	−	2.33016i
$155$			6.21700e34i			0.560111i
$156$	−5.18761e34	+	1.02408e35i	−0.421671	+	0.832418i
$157$	−2.59905e35			−1.90731			−0.953653	−	0.300908i	$-0.902710\pi$
$157$	−2.59905e35			−1.90731			−0.953653	+	0.300908i	$0.902710\pi$
$158$	1.68096e35	+	4.01468e34i	1.11440	+	0.266157i
$159$		−	8.60134e34i		−	0.515480i
$160$	1.63426e35	−	6.88236e34i	0.885934	−	0.373093i
$161$	1.60682e34			0.0788412
$162$	−2.29154e33	+	9.59472e33i	−0.0101833	+	0.0426376i
$163$			1.38465e34i			0.0557619i	0.999611	+	0.0278809i	$0.00887593\pi$
$163$			1.38465e34i			0.0557619i	−0.999611	+	0.0278809i	$0.991124\pi$
$164$	−2.98091e35	−	1.51001e35i	−1.08855	−	0.551416i
$165$	6.56245e35			2.17432
$166$	3.54989e35	+	8.47831e34i	1.06779	+	0.255023i
$167$		−	6.26917e35i		−	1.71296i	−0.516182	−	0.856479i	$-0.672647\pi$
$167$		−	6.26917e35i		−	1.71296i	0.516182	−	0.856479i	$-0.327353\pi$
$168$	−7.27513e35	+	8.57928e35i	−1.80673	+	2.13060i
$169$	−2.96601e35			−0.669863
$170$	−9.10412e34	+	3.81191e35i	−0.187092	+	0.783358i
$171$		−	1.86299e35i		−	0.348556i
$172$	−1.10204e34	+	2.17552e34i	−0.0187819	+	0.0370773i
$173$	−1.09058e36			−1.69403			−0.847014	−	0.531570i	$-0.821602\pi$
$173$	−1.09058e36			−1.69403			−0.847014	+	0.531570i	$0.821602\pi$
$174$	4.11772e35	+	9.83448e34i	0.583268	+	0.139304i
$175$			1.01050e35i			0.130595i
$176$	9.51790e35	−	6.98391e35i	1.12289	−	0.823941i
$177$	2.39945e35			0.258547
$178$	−2.07629e35	+	8.69346e35i	−0.204441	+	0.855998i
$179$			1.61896e36i			1.45743i	0.684815	+	0.728717i	$0.259883\pi$
$179$			1.61896e36i			1.45743i	−0.684815	+	0.728717i	$0.740117\pi$
$180$	−1.70525e36	−	8.63815e35i	−1.40420	−	0.711313i
$181$	−8.32130e35			−0.627096			−0.313548	−	0.949572i	$-0.601518\pi$
$181$	−8.32130e35			−0.627096			−0.313548	+	0.949572i	$0.601518\pi$
$182$	1.39316e36	+	3.32733e35i	0.961299	+	0.229590i
$183$		−	3.43983e36i		−	2.17430i
$184$	6.03438e34	+	5.11708e34i	0.0349581	+	0.0296440i
$185$	7.27705e34			0.0386552
$186$	4.51096e35	−	1.88875e36i	0.219817	−	0.920380i
$187$			2.60911e36i			1.16688i
$188$	5.25238e35	−	1.03687e36i	0.215690	−	0.425793i
$189$	4.72062e36			1.78078
$190$	5.74070e35	+	1.37107e35i	0.199025	+	0.0475338i
$191$			2.12110e36i			0.676127i	0.941123	+	0.338063i	$0.109772\pi$
$191$			2.12110e36i			0.676127i	−0.941123	+	0.338063i	$0.890228\pi$
$192$	−5.46432e36	+	9.05094e35i	−1.60220	+	0.265383i
$193$	5.32606e36			1.43711			0.718553	−	0.695472i	$-0.244805\pi$
$193$	5.32606e36			1.43711			0.718553	+	0.695472i	$0.244805\pi$
$194$	1.42796e36	−	5.97888e36i	0.354721	−	1.48523i
$195$			3.92057e36i			0.897005i
$196$	8.28870e36	+	4.19874e36i	1.74739	+	0.885160i
$197$	−3.57225e36			−0.694195			−0.347098	−	0.937829i	$-0.612833\pi$
$197$	−3.57225e36			−0.694195			−0.347098	+	0.937829i	$0.612833\pi$
$198$	−1.23778e37	−	2.95624e36i	−2.21821	−	0.529782i
$199$			2.75249e36i			0.455069i	0.973770	+	0.227534i	$0.0730664\pi$
$199$			2.75249e36i			0.455069i	−0.973770	+	0.227534i	$0.926934\pi$
$200$	−3.21804e35	+	3.79491e35i	−0.0491033	+	0.0579057i
$201$	−1.30228e37			−1.83471
$202$	−8.72050e34	+	3.65129e35i	−0.0113480	+	0.0475143i
$203$		−	5.28220e36i		−	0.635152i
$204$	5.53173e36	−	1.09202e37i	0.614863	−	1.21380i
$205$	−1.14120e37			−1.17301
$206$	6.22447e36	+	1.48661e36i	0.591871	+	0.141358i
$207$		−	8.52893e35i		−	0.0750532i
$208$	4.17236e36	+	5.68623e36i	0.339913	+	0.463245i
$209$	3.92930e36			0.296466
$210$	−8.92407e36	+	3.73653e37i	−0.623813	+	2.61192i
$211$		−	2.17197e36i		−	0.140713i	−0.997522	−	0.0703567i	$-0.977586\pi$
$211$		−	2.17197e36i		−	0.140713i	0.997522	−	0.0703567i	$-0.0224137\pi$
$212$	−4.71403e36	−	2.38795e36i	−0.283151	−	0.143434i
$213$	5.17248e37			2.88154
$214$	−1.80660e37	−	4.31477e36i	−0.933775	−	0.223017i
$215$			8.32870e35i			0.0399541i
$216$	1.77282e37	+	1.50333e37i	0.789595	+	0.669567i
$217$	−2.42288e37			−1.00225
$218$	3.92422e36	−	1.64308e37i	0.150817	−	0.631472i
$219$		−	7.07971e37i		−	2.52877i
$220$	1.82190e37	−	3.59660e37i	0.605009	−	1.19434i
$221$	−1.55875e37			−0.481392
$222$	−2.21080e36	−	5.28012e35i	−0.0635186	−	0.0151704i
$223$			2.64062e36i			0.0706038i	0.999377	+	0.0353019i	$0.0112393\pi$
$223$			2.64062e36i			0.0706038i	−0.999377	+	0.0353019i	$0.988761\pi$
$224$	2.68219e37	+	6.36902e37i	0.667607	+	1.58527i
$225$	5.36368e36			0.124321
$226$	−3.06220e36	+	1.28215e37i	−0.0661148	+	0.276824i
$227$		−	4.82575e37i		−	0.970847i	−0.874279	−	0.485423i	$-0.838665\pi$
$227$		−	4.82575e37i		−	0.970847i	0.874279	−	0.485423i	$-0.161335\pi$
$228$	−1.64457e37	−	8.33074e36i	−0.308385	−	0.156216i
$229$	−6.43637e37			−1.12531			−0.562656	−	0.826691i	$-0.690221\pi$
$229$	−6.43637e37			−1.12531			−0.562656	+	0.826691i	$0.690221\pi$
$230$	2.62815e36	+	6.27689e35i	0.0428552	+	0.0102353i
$231$			2.55751e38i			3.89068i
$232$	1.68217e37	−	1.98372e37i	0.238815	−	0.281626i
$233$	9.66736e37			1.28119			0.640594	−	0.767880i	$-0.278688\pi$
$233$	9.66736e37			1.28119			0.640594	+	0.767880i	$0.278688\pi$
$234$	1.76613e37	−	7.39483e37i	0.218559	−	0.915112i
$235$		−	3.96951e37i		−	0.458830i
$236$	6.66148e36	−	1.31504e37i	0.0719414	−	0.142019i
$237$	−1.84355e38			−1.86073
$238$	−1.48558e38	−	3.54805e37i	−1.40173	−	0.334779i
$239$		−	9.30138e37i		−	0.820694i	−0.911930	−	0.410347i	$-0.865408\pi$
$239$		−	9.30138e37i		−	0.820694i	0.911930	−	0.410347i	$-0.134592\pi$
$240$	−1.52508e38	+	1.11905e38i	−1.25867	+	0.923568i
$241$	1.83413e38			1.41631			0.708155	−	0.706057i	$-0.249528\pi$
$241$	1.83413e38			1.41631			0.708155	+	0.706057i	$0.249528\pi$
$242$	3.02076e37	−	1.26480e38i	0.218308	−	0.914060i
$243$			1.42499e38i			0.964077i
$244$	−1.88523e38	−	9.54985e37i	−1.19434	−	0.605005i
$245$	3.17322e38			1.88297
$246$	3.46701e38	+	8.28039e37i	1.92750	+	0.460351i
$247$			2.34746e37i			0.122306i
$248$	−9.09909e37	−	7.71592e37i	−0.444397	−	0.376843i
$249$	−3.89327e38			−1.78289
$250$	−5.59402e37	+	2.34223e38i	−0.240262	+	1.00598i
$251$			1.81978e38i			0.733229i	0.930373	+	0.366614i	$0.119483\pi$
$251$			1.81978e38i			0.733229i	−0.930373	+	0.366614i	$0.880517\pi$
$252$	3.36645e38	−	6.64569e38i	1.27281	−	2.51265i
$253$	1.79887e37			0.0638367
$254$	4.83566e38	+	1.15492e38i	1.61108	+	0.384779i
$255$		−	4.18064e38i		−	1.30798i
$256$	−1.02099e38	+	3.24604e38i	−0.300042	+	0.953926i
$257$	1.81708e38			0.501700			0.250850	−	0.968026i	$-0.419290\pi$
$257$	1.81708e38			0.501700			0.250850	+	0.968026i	$0.419290\pi$
$258$	6.04318e36	−	2.53029e37i	0.0156802	−	0.0656531i
$259$			2.83601e37i			0.0691689i
$260$	2.14870e38	+	1.08845e38i	0.492722	+	0.249594i
$261$	−2.80377e38			−0.604636
$262$	−4.51446e38	−	1.07820e38i	−0.915767	−	0.218716i
$263$		−	1.03099e38i		−	0.196772i	−0.995148	−	0.0983859i	$-0.968632\pi$
$263$		−	1.03099e38i		−	0.196772i	0.995148	−	0.0983859i	$-0.0313680\pi$
$264$	−8.14465e38	+	9.60468e38i	−1.46288	+	1.72512i
$265$	−1.80471e38			−0.305121
$266$	−5.34333e37	+	2.23726e38i	−0.0850561	+	0.356132i
$267$		−	9.53439e38i		−	1.42926i
$268$	−3.61546e38	+	7.13726e38i	−0.510513	+	1.00780i
$269$	7.79655e38			1.03721			0.518604	−	0.855014i	$-0.326452\pi$
$269$	7.79655e38			1.03721			0.518604	+	0.855014i	$0.326452\pi$
$270$	7.72114e38	+	1.84407e38i	0.967969	+	0.231183i
$271$		−	1.53349e38i		−	0.181206i	−0.995887	−	0.0906032i	$-0.971121\pi$
$271$		−	1.53349e38i		−	0.181206i	0.995887	−	0.0906032i	$-0.0288795\pi$
$272$	−4.44913e38	−	6.06343e38i	−0.495648	−	0.675485i
$273$	−1.52792e39			−1.60509
$274$	2.38965e38	−	1.00055e39i	0.236770	−	0.991359i
$275$			1.13127e38i			0.105741i
$276$	−7.52897e37	−	3.81389e37i	−0.0664034	−	0.0336374i
$277$	−4.47583e38			−0.372561			−0.186280	−	0.982497i	$-0.559643\pi$
$277$	−4.47583e38			−0.372561			−0.186280	+	0.982497i	$0.559643\pi$
$278$	−1.06045e39	−	2.53270e38i	−0.833245	−	0.199007i
$279$			1.28606e39i			0.954097i
$280$	1.80008e39	+	1.52645e39i	1.26114	+	1.06943i
$281$	2.40210e39			1.58961			0.794804	−	0.606867i	$-0.207574\pi$
$281$	2.40210e39			1.58961			0.794804	+	0.606867i	$0.207574\pi$
$282$	−2.88022e38	+	1.20595e39i	−0.180069	+	0.753954i
$283$			1.34695e39i			0.795736i	0.917443	+	0.397868i	$0.130250\pi$
$283$			1.34695e39i			0.795736i	−0.917443	+	0.397868i	$0.869750\pi$
$284$	1.43601e39	−	2.83482e39i	0.801798	−	1.58282i
$285$	−6.29600e38			−0.332313
$286$	1.55967e39	+	3.72501e38i	0.778352	+	0.185896i
$287$		−	4.44748e39i		−	2.09896i
$288$	3.38065e39	−	1.42369e39i	1.50911	−	0.635531i
$289$	−7.05765e38			−0.298054
$290$	2.06344e38	−	8.63966e38i	0.0824563	−	0.345246i
$291$			6.55722e39i			2.47989i
$292$	−3.88010e39	−	1.96551e39i	−1.38905	−	0.703638i
$293$	1.19107e39			0.403696			0.201848	−	0.979417i	$-0.435305\pi$
$293$	1.19107e39			0.403696			0.201848	+	0.979417i	$0.435305\pi$
$294$	−9.64037e39	−	2.30244e39i	−3.09411	−	0.738978i
$295$		−	5.03445e38i		−	0.153038i
$296$	−9.03155e37	+	1.06506e38i	−0.0260073	+	0.0306694i
$297$	5.28483e39			1.44188
$298$	−4.79683e37	+	2.00844e38i	−0.0124021	+	0.0519276i
$299$			1.07469e38i			0.0263356i
$300$	2.39848e38	−	4.73483e38i	0.0557181	−	0.109993i
$301$	−3.24585e38			−0.0714932
$302$	4.13802e39	+	9.88298e38i	0.864335	+	0.206432i
$303$		−	4.00448e38i		−	0.0793349i
$304$	−9.13146e38	+	6.70035e38i	−0.171618	+	0.125927i
$305$	−7.21735e39			−1.28701
$306$	−1.88329e39	+	7.88537e39i	−0.318694	+	1.33438i
$307$			9.61787e39i			1.54477i	0.635152	+	0.772387i	$0.280937\pi$
$307$			9.61787e39i			1.54477i	−0.635152	+	0.772387i	$0.719063\pi$
$308$	1.40167e40	+	7.10030e39i	2.13714	+	1.08259i
$309$	−6.82656e39			−0.988249
$310$	−3.96292e39	−	9.46477e38i	−0.544788	−	0.130114i
$311$		−	1.94296e39i		−	0.253687i	−0.991923	−	0.126844i	$-0.959515\pi$
$311$		−	1.94296e39i		−	0.253687i	0.991923	−	0.126844i	$-0.0404846\pi$
$312$	−5.73807e39	−	4.86581e39i	−0.711692	−	0.603507i
$313$	−5.24329e39			−0.617866			−0.308933	−	0.951084i	$-0.599972\pi$
$313$	−5.24329e39			−0.617866			−0.308933	+	0.951084i	$0.599972\pi$
$314$	3.95680e39	−	1.65672e40i	0.443067	−	1.85513i
$315$		−	2.54421e40i		−	2.70760i
$316$	−5.11818e39	+	1.01038e40i	−0.517752	+	1.02209i
$317$	3.19617e39			0.307384			0.153692	−	0.988119i	$-0.450884\pi$
$317$	3.19617e39			0.307384			0.153692	+	0.988119i	$0.450884\pi$
$318$	5.48277e39	+	1.30947e39i	0.501379	+	0.119746i
$319$		−	5.91353e39i		−	0.514275i
$320$	1.89904e39	+	1.14651e40i	0.157085	+	0.948368i
$321$	1.98136e40			1.55913
$322$	−2.44622e38	+	1.02424e39i	−0.0183148	+	0.0766844i
$323$		−	2.50318e39i		−	0.178341i
$324$	−5.76712e38	−	2.92140e38i	−0.0391056	−	0.0198094i
$325$	−6.75851e38			−0.0436231
$326$	−8.82619e38	−	2.10799e38i	−0.0542365	−	0.0129535i
$327$			1.80201e40i			1.05437i
$328$	1.41634e40	−	1.67024e40i	0.789201	−	0.930674i
$329$	1.54700e40			0.821022
$330$	−9.99068e39	+	4.18312e40i	−0.505094	+	2.11484i
$331$		−	3.13828e40i		−	1.51163i	−0.654788	−	0.755813i	$-0.727242\pi$
$331$		−	3.13828e40i		−	1.51163i	0.654788	−	0.755813i	$-0.272758\pi$
$332$	−1.08087e40	+	2.13374e40i	−0.496094	+	0.979336i
$333$	1.50534e39			0.0658456
$334$	3.99617e40	+	9.54419e39i	1.66610	+	0.397920i
$335$			2.73240e40i			1.08600i
$336$	−4.36115e40	−	5.94351e40i	−1.65262	−	2.25224i
$337$	−4.25178e40			−1.53636			−0.768178	−	0.640236i	$-0.778836\pi$
$337$	−4.25178e40			−1.53636			−0.768178	+	0.640236i	$0.778836\pi$
$338$	4.51546e39	−	1.89063e40i	0.155609	−	0.651538i
$339$		−	1.40617e40i		−	0.462214i
$340$	−2.29123e40	−	1.16065e40i	−0.718467	−	0.363948i
$341$	−2.71247e40			−0.811511
$342$	1.18753e40	+	2.83622e39i	0.339021	+	0.0809695i
$343$			6.05325e40i			1.64923i
$344$	−1.21897e39	−	1.03367e39i	−0.0317000	−	0.0268812i
$345$	−2.88237e39			−0.0715556
$346$	1.66030e40	−	6.95172e40i	0.393523	−	1.64769i
$347$			6.07154e40i			1.37413i	0.726597	+	0.687064i	$0.241101\pi$
$347$			6.07154e40i			1.37413i	−0.726597	+	0.687064i	$0.758899\pi$
$348$	−1.25376e40	+	2.47504e40i	−0.270986	+	0.534952i
$349$	−1.47031e40			−0.303530			−0.151765	−	0.988417i	$-0.548496\pi$
$349$	−1.47031e40			−0.303530			−0.151765	+	0.988417i	$0.548496\pi$
$350$	−6.44124e39	−	1.53838e39i	−0.127023	−	0.0303372i
$351$			3.15729e40i			0.594840i
$352$	3.00276e40	+	7.13025e40i	0.540553	+	1.28358i
$353$	4.72487e40			0.812821			0.406410	−	0.913691i	$-0.366780\pi$
$353$	4.72487e40			0.812821			0.406410	+	0.913691i	$0.366780\pi$
$354$	−3.65293e39	+	1.52949e40i	−0.0600605	+	0.251474i
$355$		−	1.08527e41i		−	1.70563i
$356$	−5.22540e40	−	2.64699e40i	−0.785090	−	0.397697i
$357$	1.62928e41			2.34047
$358$	−1.03198e41	−	2.46471e40i	−1.41756	−	0.338562i
$359$		−	7.34931e40i		−	0.965463i	−0.875769	−	0.482731i	$-0.839645\pi$
$359$		−	7.34931e40i		−	0.965463i	0.875769	−	0.482731i	$-0.160355\pi$
$360$	8.10231e40	−	9.55474e40i	1.01805	−	1.20055i
$361$	7.94287e40			0.954690
$362$	1.26684e40	−	5.30427e40i	0.145674	−	0.609941i
$363$			1.38714e41i			1.52621i
$364$	−4.24189e40	+	8.37389e40i	−0.446619	+	0.881668i
$365$	−1.48544e41			−1.49682
$366$	2.19266e41	+	5.23680e40i	2.11482	+	0.505090i
$367$		−	2.06487e40i		−	0.190649i	−0.995446	−	0.0953245i	$-0.969611\pi$
$367$		−	2.06487e40i		−	0.190649i	0.995446	−	0.0953245i	$-0.0303889\pi$
$368$	−4.18046e39	+	3.06748e39i	−0.0369538	+	0.0271154i
$369$	−2.36070e41			−1.99811
$370$	−1.10786e39	+	4.63863e39i	−0.00897959	+	0.0375977i
$371$		−	7.03328e40i		−	0.545979i
$372$	1.13527e41	+	5.75087e40i	0.844139	+	0.427608i
$373$	1.13423e41			0.807907			0.403954	−	0.914780i	$-0.367636\pi$
$373$	1.13423e41			0.807907			0.403954	+	0.914780i	$0.367636\pi$
$374$	−1.66313e41	−	3.97211e40i	−1.13496	−	0.271067i
$375$		−	2.56879e41i		−	1.67969i
$376$	5.80971e40	+	4.92656e40i	0.364040	+	0.308701i
$377$	3.53288e40			0.212162
$378$	−7.18668e40	+	3.00908e41i	−0.413675	+	1.73207i
$379$			3.63335e40i			0.200484i	0.994963	+	0.100242i	$0.0319617\pi$
$379$			3.63335e40i			0.200484i	−0.994963	+	0.100242i	$0.968038\pi$
$380$	−1.74793e40	+	3.45058e40i	−0.0924670	+	0.182538i
$381$	−5.30341e41			−2.69002
$382$	−1.35206e41	−	3.22917e40i	−0.657631	−	0.157064i
$383$			1.98232e40i			0.0924686i	0.998931	+	0.0462343i	$0.0147221\pi$
$383$			1.98232e40i			0.0924686i	−0.998931	+	0.0462343i	$0.985278\pi$
$384$	2.54953e40	−	3.62092e41i	0.114067	−	1.62002i
$385$	5.36609e41			2.30296
$386$	−8.10839e40	+	3.39500e41i	−0.333840	+	1.39779i
$387$			1.72288e40i			0.0680583i
$388$	3.59374e41	+	1.82045e41i	1.36219	+	0.690035i
$389$	−1.68951e41			−0.614563			−0.307282	−	0.951619i	$-0.599419\pi$
$389$	−1.68951e41			−0.614563			−0.307282	+	0.951619i	$0.599419\pi$
$390$	−2.49910e41	−	5.96867e40i	−0.872467	−	0.208374i
$391$		−	1.14598e40i		−	0.0384015i
$392$	−3.93828e41	+	4.64427e41i	−1.26686	+	1.49396i
$393$	4.95114e41			1.52906
$394$	5.43839e40	−	2.27706e41i	0.161262	−	0.675205i
$395$			3.86809e41i			1.10139i
$396$	3.76881e41	−	7.43998e41i	1.03058	−	2.03446i
$397$	2.48937e40			0.0653794			0.0326897	−	0.999466i	$-0.489593\pi$
$397$	2.48937e40			0.0653794			0.0326897	+	0.999466i	$0.489593\pi$
$398$	−1.75453e41	−	4.19040e40i	−0.442620	−	0.105712i
$399$		−	2.45367e41i		−	0.594635i
$400$	−1.92908e40	−	2.62902e40i	−0.0449149	−	0.0612116i
$401$	−1.93121e41			−0.432035			−0.216017	−	0.976389i	$-0.569307\pi$
$401$	−1.93121e41			−0.432035			−0.216017	+	0.976389i	$0.569307\pi$
$402$	1.98259e41	−	8.30115e41i	0.426203	−	1.78452i
$403$		−	1.62049e41i		−	0.334786i
$404$	−2.19469e40	−	1.11175e40i	−0.0435784	−	0.0220751i
$405$	−2.20787e40			−0.0421398
$406$	3.36704e41	+	8.04162e40i	0.617777	+	0.147546i
$407$			3.17496e40i			0.0560052i
$408$	6.11871e41	+	5.18859e41i	1.03776	+	0.880008i
$409$	−6.28224e41			−1.02457			−0.512285	−	0.858816i	$-0.671201\pi$
$409$	−6.28224e41			−1.02457			−0.512285	+	0.858816i	$0.671201\pi$
$410$	1.73737e41	−	7.27438e41i	0.272489	−	1.14092i
$411$			1.09734e42i			1.65528i
$412$	−1.89523e41	+	3.74135e41i	−0.274983	+	0.542842i
$413$	1.96202e41			0.273844
$414$	5.43661e40	+	1.29844e40i	0.0730000	+	0.0174348i
$415$			8.16874e41i			1.05532i
$416$	−4.25978e41	+	1.79392e41i	−0.529534	+	0.223003i
$417$	1.16303e42			1.39127
$418$	−5.98196e40	+	2.50466e41i	−0.0688689	+	0.288355i
$419$			5.12219e41i			0.567586i	0.958886	+	0.283793i	$0.0915928\pi$
$419$			5.12219e41i			0.567586i	−0.958886	+	0.283793i	$0.908407\pi$
$420$	−2.24592e42	−	1.13770e42i	−2.39555	−	1.21350i
$421$	1.70891e41			0.175471			0.0877355	−	0.996144i	$-0.472037\pi$
$421$	1.70891e41			0.175471			0.0877355	+	0.996144i	$0.472037\pi$
$422$	1.38449e41	+	3.30661e40i	0.136864	+	0.0326877i
$423$		−	8.21139e41i		−	0.781575i
$424$	2.23982e41	−	2.64133e41i	0.205286	−	0.242086i
$425$	7.20683e40			0.0636095
$426$	−7.87459e41	+	3.29711e42i	−0.669383	+	2.80272i
$427$		−	2.81274e42i		−	2.30294i
$428$	5.50075e41	−	1.08590e42i	0.433832	−	0.856424i
$429$	−1.71054e42			−1.29962
$430$	−5.30898e40	−	1.26796e40i	−0.0388612	−	0.00928134i
$431$		−	2.81567e41i		−	0.198584i	−0.995058	−	0.0992922i	$-0.968342\pi$
$431$		−	2.81567e41i		−	0.198584i	0.995058	−	0.0992922i	$-0.0316579\pi$
$432$	−1.22816e42	+	9.01185e41i	−0.834674	+	0.612455i
$433$	−2.65364e42			−1.73795			−0.868973	−	0.494859i	$-0.835220\pi$
$433$	−2.65364e42			−1.73795			−0.868973	+	0.494859i	$0.835220\pi$
$434$	3.68860e41	−	1.54442e42i	0.232823	−	0.974834i
$435$			9.47538e41i			0.576459i
$436$	9.87608e41	+	5.00284e41i	0.579163	+	0.293382i
$437$	−1.72583e40			−0.00975652
$438$	4.51284e42	+	1.07782e42i	2.45960	+	0.587434i
$439$		−	1.28733e42i		−	0.676482i	−0.941059	−	0.338241i	$-0.890168\pi$
$439$		−	1.28733e42i		−	0.676482i	0.941059	−	0.338241i	$-0.109832\pi$
$440$	2.01522e42	+	1.70889e42i	1.02113	+	0.865905i
$441$	6.56416e42			3.20746
$442$	2.37304e41	−	9.93595e41i	0.111827	−	0.468223i
$443$			1.10165e42i			0.500708i	0.968154	+	0.250354i	$0.0805471\pi$
$443$			1.10165e42i			0.500708i	−0.968154	+	0.250354i	$0.919453\pi$
$444$	6.73144e40	−	1.32885e41i	0.0295107	−	0.0582570i
$445$	−2.00048e42			−0.846005
$446$	−1.68322e41	−	4.02008e40i	−0.0686724	−	0.0164013i
$447$		−	2.20272e41i		−	0.0867038i
$448$	−4.46816e42	+	7.40092e41i	−1.69699	+	0.281085i
$449$	−1.09716e42			−0.402093			−0.201047	−	0.979582i	$-0.564434\pi$
$449$	−1.09716e42			−0.402093			−0.201047	+	0.979582i	$0.564434\pi$
$450$	−8.16568e40	+	3.41898e41i	−0.0288797	+	0.120920i
$451$		−	4.97904e42i		−	1.69950i
$452$	−7.70664e41	−	3.90389e41i	−0.253893	−	0.128612i
$453$	−4.53830e42			−1.44318
$454$	3.07609e42	+	7.34672e41i	0.944289	+	0.225528i
$455$			3.20583e42i			0.950077i
$456$	7.81397e41	−	9.21472e41i	0.223581	−	0.263660i
$457$	6.91623e42			1.91078			0.955389	−	0.295351i	$-0.0954364\pi$
$457$	6.91623e42			1.91078			0.955389	+	0.295351i	$0.0954364\pi$
$458$	9.79873e41	−	4.10275e42i	0.261410	−	1.09453i
$459$		−	3.36673e42i		−	0.867371i
$460$	−8.00218e40	+	1.57970e41i	−0.0199105	+	0.0393053i
$461$	2.42051e40			0.00581690			0.00290845	−	0.999996i	$-0.499074\pi$
$461$	2.42051e40			0.00581690			0.00290845	+	0.999996i	$0.499074\pi$
$462$	−1.63024e43	−	3.89356e42i	−3.78425	−	0.903806i
$463$			7.32467e42i			1.64245i	0.570604	+	0.821225i	$0.306709\pi$
$463$			7.32467e42i			1.64245i	−0.570604	+	0.821225i	$0.693291\pi$
$464$	1.00839e42	+	1.37427e42i	0.218445	+	0.297704i
$465$	4.34625e42			0.909636
$466$	−1.47176e42	+	6.16228e42i	−0.297620	+	1.24614i
$467$		−	5.77631e41i		−	0.112870i	−0.998406	−	0.0564352i	$-0.982027\pi$
$467$		−	5.77631e41i		−	0.112870i	0.998406	−	0.0564352i	$-0.0179734\pi$
$468$	4.44482e42	+	2.25158e42i	0.839307	+	0.425161i
$469$	−1.06487e43			−1.94326
$470$	2.53030e42	+	6.04319e41i	0.446278	+	0.106586i
$471$			1.81697e43i			3.09752i
$472$	7.36834e41	+	6.24826e41i	0.121422	+	0.102964i
$473$	−3.63380e41			−0.0578872
$474$	2.80663e42	−	1.17514e43i	0.432247	−	1.80982i
$475$		−	1.08534e41i		−	0.0161610i
$476$	4.52328e42	−	8.92938e42i	0.651242	−	1.28561i
$477$	−3.73324e42			−0.519746
$478$	5.92900e42	+	1.41604e42i	0.798243	+	0.190647i
$479$		−	9.75812e42i		−	1.27057i	−0.772278	−	0.635284i	$-0.780883\pi$
$479$		−	9.75812e42i		−	1.27057i	0.772278	−	0.635284i	$-0.219117\pi$
$480$	−4.81140e42	−	1.14250e43i	−0.605915	−	1.43878i
$481$	−1.89680e41			−0.0231047
$482$	−2.79229e42	+	1.16914e43i	−0.329009	+	1.37757i
$483$		−	1.12331e42i		−	0.128040i
$484$	7.60234e42	+	3.85105e42i	0.838342	+	0.424672i
$485$	1.37582e43			1.46789
$486$	−9.08335e42	−	2.16941e42i	−0.937704	−	0.223955i
$487$		−	8.73926e42i		−	0.872994i	−0.899706	−	0.436497i	$-0.856219\pi$
$487$		−	8.73926e42i		−	0.872994i	0.899706	−	0.436497i	$-0.143781\pi$
$488$	8.95745e42	−	1.05632e43i	0.865899	−	1.02112i
$489$	9.67995e41			0.0905589
$490$	−4.83091e42	+	2.02271e43i	−0.437413	+	1.83146i
$491$			6.41960e42i			0.562606i	0.959619	+	0.281303i	$0.0907665\pi$
$491$			6.41960e42i			0.562606i	−0.959619	+	0.281303i	$0.909233\pi$
$492$	−1.05564e43	+	2.08393e43i	−0.895515	+	1.76783i
$493$	−3.76724e42			−0.309366
$494$	−1.49634e42	−	3.57377e41i	−0.118960	−	0.0284116i
$495$		−	2.84830e43i		−	2.19231i
$496$	6.30362e42	−	4.62538e42i	0.469768	−	0.344699i
$497$	4.22952e43			3.05203
$498$	5.92711e42	−	2.48169e43i	0.414165	−	1.73412i
$499$			1.60910e43i			1.08886i	0.838805	+	0.544432i	$0.183255\pi$
$499$			1.60910e43i			1.08886i	−0.838805	+	0.544432i	$0.816745\pi$
$500$	−1.40785e43	−	7.13162e42i	−0.922647	−	0.467378i
$501$	−4.38272e43			−2.78189
$502$	−1.15999e43	−	2.77043e42i	−0.713171	−	0.170329i
$503$		−	9.65906e42i		−	0.575238i	−0.957745	−	0.287619i	$-0.907136\pi$
$503$		−	9.65906e42i		−	0.575238i	0.957745	−	0.287619i	$-0.0928636\pi$
$504$	3.72367e43	+	3.15762e43i	2.14824	+	1.82168i
$505$	−8.40208e41			−0.0469597
$506$	−2.73860e41	+	1.14666e42i	−0.0148293	+	0.0620904i
$507$			2.07351e43i			1.08788i
$508$	−1.47236e43	+	2.90658e43i	−0.748506	+	1.47762i
$509$	−3.22003e43			−1.58626			−0.793132	−	0.609050i	$-0.791551\pi$
$509$	−3.22003e43			−1.58626			−0.793132	+	0.609050i	$0.791551\pi$
$510$	2.66487e43	+	6.36461e42i	1.27220	+	0.303843i
$511$		−	5.78906e43i		−	2.67839i
$512$	−1.91370e43	−	1.14499e43i	−0.858131	−	0.513431i
$513$	−5.07026e42			−0.220370
$514$	−2.76633e42	+	1.15827e43i	−0.116545	+	0.487976i
$515$			1.43233e43i			0.584961i
$516$	1.52089e42	+	7.70424e41i	0.0602146	+	0.0305024i
$517$	1.73189e43			0.664771
$518$	−1.80776e42	−	4.31754e41i	−0.0672767	−	0.0160679i
$519$			7.62416e43i			2.75115i
$520$	−1.02093e43	+	1.20394e43i	−0.357226	+	0.421263i
$521$	−2.63327e43			−0.893494			−0.446747	−	0.894660i	$-0.647418\pi$
$521$	−2.63327e43			−0.893494			−0.446747	+	0.894660i	$0.647418\pi$
$522$	4.26846e42	−	1.78721e43i	0.140457	−	0.588096i
$523$		−	5.37407e43i		−	1.71505i	−0.514444	−	0.857524i	$-0.672002\pi$
$523$		−	5.37407e43i		−	1.71505i	0.514444	−	0.857524i	$-0.327998\pi$
$524$	1.37456e43	−	2.71351e43i	0.425465	−	0.839908i
$525$	7.06431e42			0.212090
$526$	6.57187e42	+	1.56958e42i	0.191389	+	0.0457101i
$527$			1.72799e43i			0.488170i
$528$	−4.88239e43	−	6.65388e43i	−1.33810	−	1.82361i
$529$	3.75299e43			0.997899
$530$	2.74749e42	−	1.15038e43i	0.0708796	−	0.296774i
$531$		−	1.04143e43i		−	0.260687i
$532$	−1.34476e43	−	6.81202e42i	−0.326631	−	0.165459i
$533$	2.97460e43			0.701122
$534$	6.07752e43	+	1.45152e43i	1.39017	+	0.332018i
$535$		−	4.15722e43i		−	0.922874i
$536$	−3.99910e43	−	3.39119e43i	−0.861639	−	0.730660i
$537$	1.13180e44			2.36691
$538$	−1.18695e43	+	4.96977e43i	−0.240943	+	1.00883i
$539$			1.38447e44i			2.72812i
$540$	−2.35093e43	+	4.64096e43i	−0.449718	+	0.887785i
$541$	−4.14984e43			−0.770682			−0.385341	−	0.922774i	$-0.625916\pi$
$541$	−4.14984e43			−0.770682			−0.385341	+	0.922774i	$0.625916\pi$
$542$	9.77498e42	+	2.33459e42i	0.176249	+	0.0420942i
$543$			5.81735e43i			1.01842i
$544$	4.54236e43	−	1.91292e43i	0.772145	−	0.325174i
$545$	3.78093e43			0.624100
$546$	2.32611e43	−	9.73945e43i	0.372861	−	1.56118i
$547$		−	8.89957e43i		−	1.38539i	−0.721231	−	0.692694i	$-0.756424\pi$
$547$		−	8.89957e43i		−	1.38539i	0.721231	−	0.692694i	$-0.243576\pi$
$548$	6.01404e43	+	3.04648e43i	0.909238	+	0.460585i
$549$	−1.49299e44			−2.19230
$550$	−7.21110e42	−	1.72225e42i	−0.102849	−	0.0245637i
$551$			5.67343e42i			0.0785995i
$552$	3.57730e42	−	4.21858e42i	0.0481427	−	0.0567729i
$553$	−1.50747e44			−1.97082
$554$	6.81401e42	−	2.85304e43i	0.0865459	−	0.362369i
$555$		−	5.08732e42i		−	0.0627771i
$556$	3.22885e43	−	6.37406e43i	0.387125	−	0.764222i
$557$	−4.03548e43			−0.470123			−0.235062	−	0.971980i	$-0.575529\pi$
$557$	−4.03548e43			−0.470123			−0.235062	+	0.971980i	$0.575529\pi$
$558$	−8.19774e43	−	1.95789e43i	−0.927997	−	0.221637i
$559$		−	2.17092e42i		−	0.0238811i
$560$	−1.24705e44	+	9.15042e43i	−1.33314	+	0.978211i
$561$	1.82401e44			1.89505
$562$	−3.65696e43	+	1.53118e44i	−0.369266	+	1.54612i
$563$		−	5.34292e43i		−	0.524378i	−0.965017	−	0.262189i	$-0.915556\pi$
$563$		−	5.34292e43i		−	0.524378i	0.965017	−	0.262189i	$-0.0844444\pi$
$564$	−7.24865e43	−	3.67189e43i	−0.691499	−	0.350287i
$565$	−2.95039e43			−0.273592
$566$	−8.58590e43	−	2.05060e43i	−0.773968	−	0.184849i
$567$		−	8.60448e42i		−	0.0754042i
$568$	1.58839e44	+	1.34693e44i	1.35327	+	1.14755i
$569$	9.27836e42			0.0768555			0.0384277	−	0.999261i	$-0.487765\pi$
$569$	9.27836e42			0.0768555			0.0384277	+	0.999261i	$0.487765\pi$
$570$	9.58504e42	−	4.01328e43i	0.0771963	−	0.323222i
$571$		−	2.36677e43i		−	0.185344i	−0.995697	−	0.0926719i	$-0.970459\pi$
$571$		−	2.36677e43i		−	0.185344i	0.995697	−	0.0926719i	$-0.0295408\pi$
$572$	−4.74888e43	+	9.37474e43i	−0.361622	+	0.713876i
$573$	1.48285e44			1.09805
$574$	2.83497e44	+	6.77084e43i	2.04154	+	0.487588i
$575$		−	4.96879e41i		−	0.00347989i
$576$	3.92838e43	+	2.37168e44i	0.267580	+	1.61546i
$577$	1.03883e44			0.688225			0.344113	−	0.938928i	$-0.388180\pi$
$577$	1.03883e44			0.688225			0.344113	+	0.938928i	$0.388180\pi$
$578$	1.07446e43	−	4.49877e43i	0.0692379	−	0.289900i
$579$		−	3.72340e44i		−	2.33390i
$580$	5.19306e43	+	2.63061e43i	0.316647	+	0.160401i
$581$	−3.18351e44			−1.88838
$582$	−4.17978e44	−	9.98272e43i	−2.41205	−	0.576078i
$583$		−	7.87390e43i		−	0.442072i
$584$	1.84358e44	−	2.17407e44i	1.00706	−	1.18759i
$585$	1.70164e44			0.904429
$586$	−1.81328e43	+	7.59224e43i	−0.0937785	+	0.392652i
$587$			2.34372e44i			1.17949i	0.807588	+	0.589747i	$0.200772\pi$
$587$			2.34372e44i			1.17949i	−0.807588	+	0.589747i	$0.799228\pi$
$588$	2.93530e44	−	5.79456e44i	1.43753	−	2.83781i
$589$	2.60234e43			0.124028
$590$	3.20912e43	+	7.66446e42i	0.148852	+	0.0355508i
$591$			2.49733e44i			1.12739i
$592$	−5.41404e42	−	7.37844e42i	−0.0237889	−	0.0324203i
$593$	−3.76769e44			−1.61139			−0.805695	−	0.592331i	$-0.798208\pi$
$593$	−3.76769e44			−1.61139			−0.805695	+	0.592331i	$0.798208\pi$
$594$	−8.04563e43	+	3.36872e44i	−0.334948	+	1.40243i
$595$		−	3.41850e44i		−	1.38536i
$596$	−1.20722e43	−	6.11530e42i	−0.0476261	−	0.0241256i
$597$	1.92424e44			0.739045
$598$	−6.85040e42	−	1.63610e42i	−0.0256151	−	0.00611775i
$599$			3.22426e44i			1.17382i	0.809652	+	0.586910i	$0.199656\pi$
$599$			3.22426e44i			1.17382i	−0.809652	+	0.586910i	$0.800344\pi$
$600$	2.65299e43	+	2.24970e43i	0.0940405	+	0.0797452i
$601$	−2.80517e43			−0.0968206			−0.0484103	−	0.998828i	$-0.515416\pi$
$601$	−2.80517e43			−0.0968206			−0.0484103	+	0.998828i	$0.515416\pi$
$602$	4.94149e42	−	2.06901e43i	0.0166079	−	0.0695375i
$603$			5.65229e44i			1.84990i
$604$	−1.25995e44	+	2.48725e44i	−0.401570	+	0.792736i
$605$	2.91046e44			0.903389
$606$	2.55259e43	+	6.09643e42i	0.0771646	+	0.0184295i
$607$		−	3.35287e44i		−	0.987184i	−0.869694	−	0.493592i	$-0.835684\pi$
$607$		−	3.35287e44i		−	0.987184i	0.869694	−	0.493592i	$-0.164316\pi$
$608$	−2.88085e43	−	6.84075e43i	−0.0826157	−	0.196176i
$609$	−3.69274e44			−1.03151
$610$	1.09877e44	−	4.60057e44i	0.298971	−	1.25180i
$611$			1.03467e44i			0.274249i
$612$	−4.73967e44	−	2.40094e44i	−1.22384	−	0.619952i
$613$	5.01061e44			1.26044			0.630221	−	0.776416i	$-0.282964\pi$
$613$	5.01061e44			1.26044			0.630221	+	0.776416i	$0.282964\pi$
$614$	−6.13074e44	−	1.46423e44i	−1.50252	−	0.358851i
$615$			7.97804e44i			1.90500i
$616$	−6.65986e44	+	7.85372e44i	−1.54944	+	1.82719i
$617$	9.93241e43			0.225161			0.112580	−	0.993643i	$-0.464088\pi$
$617$	9.93241e43			0.225161			0.112580	+	0.993643i	$0.464088\pi$
$618$	1.03928e44	−	4.35147e44i	0.229570	−	0.961215i
$619$		−	1.77023e44i		−	0.381048i	−0.981683	−	0.190524i	$-0.938981\pi$
$619$		−	1.77023e44i		−	0.381048i	0.981683	−	0.190524i	$-0.0610187\pi$
$620$	1.20663e44	−	2.38200e44i	0.253109	−	0.499660i
$621$	−2.32121e43			−0.0474514
$622$	1.23851e44	+	2.95797e43i	0.246747	+	0.0589315i
$623$		−	7.79624e44i		−	1.51383i
$624$	3.97519e44	−	2.91686e44i	0.752323	−	0.552029i
$625$	−4.97819e44			−0.918313
$626$	7.98239e43	−	3.34224e44i	0.143530	−	0.600964i
$627$		−	2.74694e44i		−	0.481469i
$628$	9.95808e44	+	5.04438e44i	1.70146	+	0.861893i
$629$	2.02263e43			0.0336903
$630$	1.62176e45	+	3.87331e44i	2.63353	+	0.628976i
$631$			4.90233e44i			0.776128i	0.921633	+	0.388064i	$0.126856\pi$
$631$			4.90233e44i			0.776128i	−0.921633	+	0.388064i	$0.873144\pi$
$632$	−5.66127e44	−	4.80069e44i	−0.873857	−	0.741020i
$633$	−1.51841e44			−0.228523
$634$	−4.86585e43	+	2.03734e44i	−0.0714054	+	0.298976i
$635$			1.11275e45i			1.59227i
$636$	−1.66939e44	+	3.29554e44i	−0.232940	+	0.459846i
$637$	−8.27117e44			−1.12548
$638$	3.76947e44	+	9.00276e43i	0.500207	+	0.119466i
$639$		−	2.24501e45i		−	2.90539i
$640$	−7.59731e44	−	5.34934e43i	−0.958916	−	0.0675181i
$641$	1.44698e45			1.78128			0.890641	−	0.454706i	$-0.150256\pi$
$641$	1.44698e45			1.78128			0.890641	+	0.454706i	$0.150256\pi$
$642$	−3.01642e44	+	1.26298e45i	−0.362186	+	1.51648i
$643$		−	1.18107e45i		−	1.38325i	−0.722258	−	0.691623i	$-0.756896\pi$
$643$		−	1.18107e45i		−	1.38325i	0.722258	−	0.691623i	$-0.243104\pi$
$644$	−6.15641e43	−	3.11860e43i	−0.0703321	−	0.0356276i
$645$	5.82252e43			0.0648867
$646$	1.59561e44	+	3.81084e43i	0.173462	+	0.0414286i
$647$		−	4.17210e44i		−	0.442472i	−0.975220	−	0.221236i	$-0.928991\pi$
$647$		−	4.17210e44i		−	0.442472i	0.975220	−	0.221236i	$-0.0710091\pi$
$648$	2.74018e43	−	3.23139e43i	0.0283517	−	0.0334341i
$649$	2.19652e44			0.221728
$650$	1.02892e43	−	4.30809e43i	0.0101336	−	0.0424298i
$651$			1.69382e45i			1.62769i
$652$	2.68740e43	−	5.30517e43i	0.0251983	−	0.0497437i
$653$	1.61773e45			1.48011			0.740057	−	0.672544i	$-0.234799\pi$
$653$	1.61773e45			1.48011			0.740057	+	0.672544i	$0.234799\pi$
$654$	−1.14866e45	−	2.74339e44i	−1.02553	−	0.244930i
$655$		−	1.03883e45i		−	0.905076i
$656$	8.49041e44	+	1.15710e45i	0.721884	+	0.983807i
$657$	−3.07281e45			−2.54970
$658$	−2.35515e44	+	9.86105e44i	−0.190723	+	0.798562i
$659$			9.04904e44i			0.715214i	0.933872	+	0.357607i	$0.116407\pi$
$659$			9.04904e44i			0.715214i	−0.933872	+	0.357607i	$0.883593\pi$
$660$	−2.51435e45	−	1.27368e45i	−1.93965	−	0.982553i
$661$	−5.46004e44			−0.411124			−0.205562	−	0.978644i	$-0.565902\pi$
$661$	−5.46004e44			−0.411124			−0.205562	+	0.978644i	$0.565902\pi$
$662$	2.00044e45	+	4.77772e44i	1.47027	+	0.351150i
$663$			1.08971e45i			0.781795i
$664$	−1.19556e45	−	1.01382e45i	−0.837303	−	0.710023i
$665$	−5.14822e44			−0.351974
$666$	−2.29173e43	+	9.59552e43i	−0.0152959	+	0.0640443i
$667$			2.59735e43i			0.0169245i
$668$	−1.21675e45	+	2.40199e45i	−0.774069	+	1.52808i
$669$	1.84603e44			0.114663
$670$	−1.74172e45	−	4.15981e44i	−1.05629	−	0.252277i
$671$		−	3.14892e45i		−	1.86467i
$672$	4.45253e45	−	1.87509e45i	2.57453	−	1.08421i
$673$	6.50078e44			0.367050			0.183525	−	0.983015i	$-0.441249\pi$
$673$	6.50078e44			0.367050			0.183525	+	0.983015i	$0.441249\pi$
$674$	6.47291e44	−	2.71022e45i	0.356895	−	1.49433i
$675$		−	1.45977e44i		−	0.0786000i
$676$	1.13641e45	+	5.75660e44i	0.597567	+	0.302705i
$677$	1.51141e45			0.776181			0.388091	−	0.921621i	$-0.373135\pi$
$677$	1.51141e45			0.776181			0.388091	+	0.921621i	$0.373135\pi$
$678$	8.96339e44	+	2.14076e44i	0.449570	+	0.107372i
$679$			5.36182e45i			2.62661i
$680$	1.08865e45	−	1.28381e45i	0.520892	−	0.614268i
$681$	−3.37364e45			−1.57668
$682$	4.12946e44	−	1.72901e45i	0.188514	−	0.789311i
$683$			1.57870e45i			0.703992i	0.936001	+	0.351996i	$0.114497\pi$
$683$			1.57870e45i			0.703992i	−0.936001	+	0.351996i	$0.885503\pi$
$684$	−3.61579e44	+	7.13791e44i	−0.157509	+	0.310938i
$685$	2.30240e45			0.979786
$686$	−3.85853e45	−	9.21547e44i	−1.60412	−	0.383117i
$687$			4.49961e45i			1.82754i
$688$	8.44474e43	−	6.19646e43i	0.0335098	−	0.0245883i
$689$	4.70406e44			0.182375
$690$	4.38812e43	−	1.83731e44i	0.0166224	−	0.0695981i
$691$		−	2.81812e45i		−	1.04306i	−0.853232	−	0.521532i	$-0.825361\pi$
$691$		−	2.81812e45i		−	1.04306i	0.853232	−	0.521532i	$-0.174639\pi$
$692$	4.17848e45	+	2.11666e45i	1.51120	+	0.765515i
$693$	1.11004e46			3.92288
$694$	−3.87019e45	−	9.24332e44i	−1.33654	−	0.319210i
$695$		−	2.44022e45i		−	0.823518i
$696$	−1.38680e45	−	1.17599e45i	−0.457368	−	0.387843i
$697$	−3.17192e45			−1.02235
$698$	2.23840e44	−	9.37223e44i	0.0705101	−	0.295227i
$699$		−	6.75836e45i		−	2.08069i
$700$	1.96123e44	−	3.87165e44i	0.0590147	−	0.116500i
$701$	−5.77620e45			−1.69884			−0.849422	−	0.527714i	$-0.823049\pi$
$701$	−5.77620e45			−1.69884			−0.849422	+	0.527714i	$0.823049\pi$
$702$	−2.01256e45	−	4.80666e44i	−0.578568	−	0.138181i
$703$		−	3.04606e43i		−	0.00855959i
$704$	−5.00219e45	+	8.28548e44i	−1.37403	+	0.227591i
$705$	−2.77505e45			−0.745153
$706$	−7.19315e44	+	3.01179e45i	−0.188818	+	0.790585i
$707$		−	3.27445e44i		−	0.0840288i
$708$	−9.19332e44	−	4.65698e44i	−0.230643	−	0.116835i
$709$	3.05399e44			0.0749080			0.0374540	−	0.999298i	$-0.488075\pi$
$709$	3.05399e44			0.0749080			0.0374540	+	0.999298i	$0.488075\pi$
$710$	6.91789e45	+	1.65222e45i	1.65898	+	0.396219i
$711$			8.00158e45i			1.87613i
$712$	2.48279e45	−	2.92786e45i	0.569194	−	0.671228i
$713$	1.19137e44			0.0267064
$714$	−2.48041e45	+	1.03855e46i	−0.543691	+	2.27644i
$715$			3.58900e45i			0.769266i
$716$	3.14217e45	−	6.20294e45i	0.658600	−	1.30014i
$717$	−6.50251e45			−1.33283
$718$	4.68469e45	+	1.11886e45i	0.939052	+	0.224277i
$719$		−	2.10378e45i		−	0.412418i	−0.978508	−	0.206209i	$-0.933887\pi$
$719$		−	2.10378e45i		−	0.412418i	0.978508	−	0.206209i	$-0.0661127\pi$
$720$	4.85700e45	+	6.61928e45i	0.931212	+	1.26909i
$721$	−5.58206e45			−1.04672
$722$	−1.20922e45	+	5.06304e45i	−0.221774	+	0.928573i
$723$		−	1.28223e46i		−	2.30013i
$724$	3.18825e45	+	1.61504e45i	0.559416	+	0.283379i
$725$	−1.63342e44			−0.0280343
$726$	−8.84208e45	−	2.11178e45i	−1.48446	−	0.354539i
$727$			5.93359e45i			0.974466i	0.873272	+	0.487233i	$0.161994\pi$
$727$			5.93359e45i			0.974466i	−0.873272	+	0.487233i	$0.838006\pi$
$728$	−4.69200e45	−	3.97876e45i	−0.753800	−	0.639213i
$729$	1.02409e46			1.60952
$730$	2.26144e45	−	9.46869e45i	0.347712	−	1.45588i
$731$			2.31493e44i			0.0348225i
$732$	−6.67621e45	+	1.31795e46i	−0.982546	+	1.93964i
$733$	1.14451e46			1.64800			0.824000	−	0.566590i	$-0.191738\pi$
$733$	1.14451e46			1.64800			0.824000	+	0.566590i	$0.191738\pi$
$734$	1.31621e45	+	3.14355e44i	0.185434	+	0.0442878i
$735$		−	2.21837e46i		−	3.05799i
$736$	−1.31888e44	−	3.13176e44i	−0.0177893	−	0.0422418i
$737$	−1.19214e46			−1.57343
$738$	3.59394e45	−	1.50479e46i	0.464161	−	1.94345i
$739$			2.33426e45i			0.295011i	0.989061	+	0.147505i	$0.0471244\pi$
$739$			2.33426e45i			0.295011i	−0.989061	+	0.147505i	$0.952876\pi$
$740$	−2.78815e44	−	1.41237e44i	−0.0344833	−	0.0174679i
$741$	1.64109e45			0.198628
$742$	4.48324e45	+	1.07075e45i	0.531043	+	0.126831i
$743$		−	2.99487e45i		−	0.347182i	−0.984818	−	0.173591i	$-0.944463\pi$
$743$		−	2.99487e45i		−	0.347182i	0.984818	−	0.173591i	$-0.0555371\pi$
$744$	−5.39413e45	+	6.36109e45i	−0.612004	+	0.721713i
$745$	−4.62167e44			−0.0513214
$746$	−1.72676e45	+	7.22997e45i	−0.187677	+	0.785806i
$747$			1.68979e46i			1.79765i
$748$	5.06390e45	−	9.99662e45i	0.527303	−	1.04094i
$749$	1.62015e46			1.65138
$750$	1.63743e46	+	3.91073e45i	1.63374	+	0.390192i
$751$			1.07059e46i			1.04564i	0.852442	+	0.522822i	$0.175121\pi$
$751$			1.07059e46i			1.04564i	−0.852442	+	0.522822i	$0.824879\pi$
$752$	−4.02482e45	+	2.95327e45i	−0.384823	+	0.282370i
$753$	1.27219e46			1.19078
$754$	−5.37847e44	+	2.25197e45i	−0.0492852	+	0.206358i
$755$			9.52211e45i			0.854244i
$756$	−1.80867e46	−	9.16204e45i	−1.58859	−	0.804718i
$757$	−9.65089e45			−0.829915			−0.414957	−	0.909841i	$-0.636203\pi$
$757$	−9.65089e45			−0.829915			−0.414957	+	0.909841i	$0.636203\pi$
$758$	−2.31601e45	−	5.53141e44i	−0.195000	−	0.0465724i
$759$		−	1.25757e45i		−	0.103673i
$760$	−1.93340e45	−	1.63950e45i	−0.156065	−	0.132341i
$761$	−1.39608e46			−1.10346			−0.551729	−	0.834023i	$-0.686032\pi$
$761$	−1.39608e46			−1.10346			−0.551729	+	0.834023i	$0.686032\pi$
$762$	8.07392e45	−	3.38057e46i	0.624892	−	2.61643i
$763$			1.47350e46i			1.11675i
$764$	4.11675e45	−	8.12686e45i	0.305535	−	0.603155i
$765$	−1.81452e46			−1.31880
$766$	−1.26360e45	−	3.01789e44i	−0.0899391	−	0.0214804i
$767$			1.31226e45i			0.0914730i
$768$	2.26928e46	+	7.13765e45i	1.54920	+	0.487277i
$769$	−1.40709e45			−0.0940808			−0.0470404	−	0.998893i	$-0.514979\pi$
$769$	−1.40709e45			−0.0940808			−0.0470404	+	0.998893i	$0.514979\pi$
$770$	−8.16934e45	+	3.42052e46i	−0.534977	+	2.23996i
$771$		−	1.27031e46i		−	0.814776i
$772$	−2.04064e46	−	1.03371e46i	−1.28200	−	0.649414i
$773$	−2.99265e46			−1.84155			−0.920775	−	0.390093i	$-0.872443\pi$
$773$	−2.99265e46			−1.84155			−0.920775	+	0.390093i	$0.872443\pi$
$774$	−1.09822e45	−	2.62292e44i	−0.0661965	−	0.0158099i
$775$			7.49232e44i			0.0442374i
$776$	−1.70752e46	+	2.01362e46i	−0.987596	+	1.16463i
$777$	1.98263e45			0.112332
$778$	2.57211e45	−	1.07695e46i	0.142763	−	0.597751i
$779$			4.77689e45i			0.259744i
$780$	7.60925e45	−	1.50214e46i	0.405348	−	0.800195i
$781$	4.73503e46			2.47119
$782$	7.30482e44	+	1.74464e44i	0.0373510	+	0.00892065i
$783$			7.63066e45i			0.382273i
$784$	−2.36084e46	−	3.21743e46i	−1.15880	−	1.57926i
$785$	3.81232e46			1.83347
$786$	−7.53762e45	+	3.15602e46i	−0.355201	+	1.48723i
$787$		−	1.65954e46i		−	0.766290i	−0.923688	−	0.383145i	$-0.874841\pi$
$787$		−	1.65954e46i		−	0.766290i	0.923688	−	0.383145i	$-0.125159\pi$
$788$	1.36868e46	+	6.93321e45i	0.619273	+	0.313700i
$789$	−7.20757e45			−0.319563
$790$	−2.46564e46	−	5.88878e45i	−1.07127	−	0.255854i
$791$		−	1.14982e46i		−	0.489561i
$792$	4.16872e46	+	3.53502e46i	1.73940	+	1.47499i
$793$	1.88124e46			0.769260
$794$	−3.78981e44	+	1.58680e45i	−0.0151876	+	0.0635909i
$795$			1.26165e46i			0.495526i
$796$	5.34219e45	−	1.05460e46i	0.205641	−	0.405955i
$797$	−2.40047e46			−0.905655			−0.452827	−	0.891598i	$-0.649585\pi$
$797$	−2.40047e46			−0.905655			−0.452827	+	0.891598i	$0.649585\pi$
$798$	1.56405e46	+	3.73547e45i	0.578368	+	0.138134i
$799$		−	1.10331e46i		−	0.399898i
$800$	1.96950e45	−	8.29417e44i	0.0699708	−	0.0294668i
$801$	−4.13821e46			−1.44109
$802$	2.94007e45	−	1.23101e46i	0.100362	−	0.420216i
$803$		−	6.48097e46i		−	2.16866i
$804$	4.98959e46	+	2.52754e46i	1.63670	+	0.829088i
$805$	−2.35690e45			−0.0757892
$806$	1.03295e46	+	2.46704e45i	0.325627	+	0.0777706i
$807$		−	5.45050e46i		−	1.68446i
$808$	1.04278e45	−	1.22971e45i	0.0315945	−	0.0372582i
$809$	−1.46290e45			−0.0434549			−0.0217275	−	0.999764i	$-0.506917\pi$
$809$	−1.46290e45			−0.0434549			−0.0217275	+	0.999764i	$0.506917\pi$
$810$	3.36126e44	−	1.40737e45i	0.00978907	−	0.0409870i
$811$			6.60062e46i			1.88474i	0.334574	+	0.942369i	$0.391408\pi$
$811$			6.60062e46i			1.88474i	−0.334574	+	0.942369i	$0.608592\pi$
$812$	−1.02520e46	+	2.02384e46i	−0.287019	+	0.566603i
$813$	−1.07205e46			−0.294284
$814$	−2.02382e45	−	4.83357e44i	−0.0544731	−	0.0130100i
$815$		−	2.03102e45i		−	0.0536033i
$816$	−4.23889e46	+	3.11035e46i	−1.09701	+	0.804946i
$817$	3.48626e44			0.00884722
$818$	9.56409e45	−	4.00450e46i	0.238008	−	0.996542i
$819$			6.63163e46i			1.61837i
$820$	4.37243e46	+	2.21490e46i	1.04641	+	0.530070i
$821$	−8.81734e45			−0.206941			−0.103471	−	0.994633i	$-0.532995\pi$
$821$	−8.81734e45			−0.206941			−0.103471	+	0.994633i	$0.532995\pi$
$822$	−6.99477e46	−	1.67059e46i	−1.61000	−	0.384521i
$823$		−	3.84058e46i		−	0.866961i	−0.901163	−	0.433480i	$-0.857285\pi$
$823$		−	3.84058e46i		−	0.866961i	0.901163	−	0.433480i	$-0.142715\pi$
$824$	−2.09633e46	−	1.77766e46i	−0.464113	−	0.393563i
$825$	7.90863e45			0.171727
$826$	−2.98698e45	+	1.25066e46i	−0.0636139	+	0.266353i
$827$		−	5.40170e46i		−	1.12835i	−0.825656	−	0.564174i	$-0.809195\pi$
$827$		−	5.40170e46i		−	1.12835i	0.825656	−	0.564174i	$-0.190805\pi$
$828$	−1.65534e45	+	3.26780e45i	−0.0339158	+	0.0669529i
$829$	−5.31805e46			−1.06876			−0.534380	−	0.845244i	$-0.679455\pi$
$829$	−5.31805e46			−1.06876			−0.534380	+	0.845244i	$0.679455\pi$
$830$	−5.20701e46	−	1.24361e46i	−1.02645	−	0.245151i
$831$			3.12901e46i			0.605050i
$832$	−4.94995e45	−	2.98843e46i	−0.0938917	−	0.566852i
$833$	8.81984e46			1.64112
$834$	−1.77059e46	+	7.41350e46i	−0.323193	+	1.35321i
$835$			9.19569e46i			1.64665i
$836$	−1.50548e46	−	7.62619e45i	−0.264469	−	0.133970i
$837$	3.50010e46			0.603216
$838$	−3.26505e46	−	7.79803e45i	−0.552059	−	0.131850i
$839$			1.08388e47i			1.79801i	0.437943	+	0.899003i	$0.355707\pi$
$839$			1.08388e47i			1.79801i	−0.437943	+	0.899003i	$0.644293\pi$
$840$	1.06712e47	−	1.25842e47i	1.73679	−	2.04813i
$841$	−5.40849e46			−0.863654
$842$	−2.60164e45	+	1.08931e46i	−0.0407619	+	0.170671i
$843$		−	1.67929e47i		−	2.58157i
$844$	−4.21548e45	+	8.32176e45i	−0.0635870	+	0.125527i
$845$	4.35058e46			0.643932
$846$	5.23420e46	+	1.25010e46i	0.760194	+	0.181560i
$847$			1.13426e47i			1.61651i
$848$	1.34268e46	+	1.82985e46i	0.187776	+	0.255907i
$849$	9.41642e46			1.29230
$850$	−1.09717e45	+	4.59387e45i	−0.0147765	+	0.0618694i
$851$		−	1.39451e44i		−	0.00184310i
$852$	−1.98180e47	−	1.00390e47i	−2.57055	−	1.30214i
$853$	−3.06780e46			−0.390520			−0.195260	−	0.980752i	$-0.562555\pi$
$853$	−3.06780e46			−0.390520			−0.195260	+	0.980752i	$0.562555\pi$
$854$	1.79293e47	+	4.28212e46i	2.23995	+	0.534974i
$855$			2.73265e46i			0.335063i
$856$	6.08443e46	+	5.15953e46i	0.732217	+	0.620911i
$857$	1.81471e46			0.214345			0.107172	−	0.994240i	$-0.465820\pi$
$857$	1.81471e46			0.214345			0.107172	+	0.994240i	$0.465820\pi$
$858$	2.60412e46	−	1.09035e47i	0.301901	−	1.26407i
$859$		−	1.25824e47i		−	1.43177i	−0.698216	−	0.715887i	$-0.746023\pi$
$859$		−	1.25824e47i		−	1.43177i	0.698216	−	0.715887i	$-0.253977\pi$
$860$	1.61648e45	−	3.19108e45i	0.0180549	−	0.0356420i
$861$	−3.10919e47			−3.40877
$862$	1.79480e46	+	4.28658e45i	0.193152	+	0.0461311i
$863$			1.26832e47i			1.33984i	0.742431	+	0.669922i	$0.233673\pi$
$863$			1.26832e47i			1.33984i	−0.742431	+	0.669922i	$0.766327\pi$
$864$	−3.87469e46	−	9.20068e46i	−0.401806	−	0.954114i
$865$	1.59968e47			1.62845
$866$	4.03991e46	−	1.69152e47i	0.403725	−	1.69040i
$867$			4.93394e46i			0.484048i
$868$	9.28310e46	+	4.70246e46i	0.894082	+	0.452908i
$869$	−1.68764e47			−1.59575
$870$	−6.03991e46	−	1.44253e46i	−0.560690	−	0.133911i
$871$		−	7.12216e46i		−	0.649114i
$872$	−4.69251e46	+	5.53370e46i	−0.419896	+	0.495167i
$873$	2.84603e47			2.50041
$874$	2.62740e44	−	1.10010e45i	0.00226644	−	0.00948962i
$875$		−	2.10049e47i		−	1.77907i
$876$	−1.37407e47	+	2.71254e47i	−1.14273	+	2.25585i
$877$	1.96939e47			1.60820			0.804098	−	0.594497i	$-0.202649\pi$
$877$	1.96939e47			1.60820			0.804098	+	0.594497i	$0.202649\pi$
$878$	8.20584e46	+	1.95983e46i	0.657977	+	0.157147i
$879$		−	8.32664e46i		−	0.655613i
$880$	−1.39610e47	+	1.02441e47i	−1.07943	+	0.792046i
$881$	−2.44488e46			−0.185628			−0.0928141	−	0.995683i	$-0.529586\pi$
$881$	−2.44488e46			−0.185628			−0.0928141	+	0.995683i	$0.529586\pi$
$882$	−9.99329e46	+	4.18421e47i	−0.745094	+	3.11972i
$883$			2.15626e47i			1.57881i	0.613874	+	0.789404i	$0.289610\pi$
$883$			2.15626e47i			1.57881i	−0.613874	+	0.789404i	$0.710390\pi$
$884$	5.97222e46	+	3.02530e46i	0.429437	+	0.217536i
$885$	−3.51954e46			−0.248539
$886$	−7.02228e46	−	1.67716e46i	−0.487011	−	0.116315i
$887$		−	3.56722e46i		−	0.242970i	−0.992593	−	0.121485i	$-0.961234\pi$
$887$		−	3.56722e46i		−	0.242970i	0.992593	−	0.121485i	$-0.0387656\pi$
$888$	7.44571e45	+	6.31387e45i	0.0498080	+	0.0422365i
$889$	−4.33658e47			−2.84918
$890$	3.04553e46	−	1.27517e47i	0.196527	−	0.822862i
$891$		−	9.63289e45i		−	0.0610539i
$892$	5.12506e45	−	1.01173e46i	0.0319052	−	0.0629838i
$893$	−1.66158e46			−0.101601
$894$	1.40408e46	+	3.35342e45i	0.0843320	+	0.0201413i
$895$		−	2.37471e47i		−	1.40102i
$896$	2.08474e46	−	2.96082e47i	0.120816	−	1.71587i
$897$	7.51304e45			0.0427697
$898$	1.67031e46	−	6.99362e46i	0.0934062	−	0.391094i
$899$		−	3.91647e46i		−	0.215149i
$900$	−2.05506e46	−	1.04101e46i	−0.110903	−	0.0561793i
$901$	−5.01611e46			−0.265932
$902$	3.17380e47	+	7.58010e46i	1.65301	+	0.394794i
$903$			2.26915e46i			0.116107i
$904$	3.66172e46	−	4.31813e46i	0.184073	−	0.217071i
$905$	1.22058e47			0.602821
$906$	6.90910e46	−	2.89286e47i	0.335251	−	1.40370i
$907$		−	1.18540e47i		−	0.565129i	−0.959248	−	0.282565i	$-0.908815\pi$
$907$		−	1.18540e47i		−	0.565129i	0.959248	−	0.282565i	$-0.0911851\pi$
$908$	−9.36607e46	+	1.84895e47i	−0.438716	+	0.866067i
$909$	−1.73806e46			−0.0799915
$910$	−2.04350e47	−	4.88056e46i	−0.924087	−	0.220703i
$911$			2.37322e46i			0.105450i	0.998609	+	0.0527248i	$0.0167906\pi$
$911$			2.37322e46i			0.105450i	−0.998609	+	0.0527248i	$0.983209\pi$
$912$	4.68416e46	+	6.38372e46i	0.204510	+	0.278713i
$913$	−3.56401e47			−1.52899
$914$	−1.05293e47	+	4.40863e47i	−0.443874	+	1.85851i
$915$			5.04559e47i			2.09013i
$916$	2.46605e47	+	1.24921e47i	1.00386	+	0.508518i
$917$	4.04853e47			1.61953
$918$	2.14606e47	+	5.12551e46i	0.843644	+	0.201490i
$919$		−	3.14225e47i		−	1.21393i	−0.794730	−	0.606963i	$-0.792388\pi$
$919$		−	3.14225e47i		−	1.21393i	0.794730	−	0.606963i	$-0.207612\pi$
$920$	−8.85129e45	−	7.50579e45i	−0.0336048	−	0.0284965i
$921$	6.72377e47			2.50876
$922$	−3.68498e44	+	1.54291e45i	−0.00135127	+	0.00565777i
$923$			2.82882e47i			1.01948i
$924$	4.96376e47	−	9.79892e47i	1.75816	−	3.47078i
$925$	8.76983e44			0.00305297
$926$	−4.66898e47	−	1.11511e47i	−1.59752	−	0.381541i
$927$			2.96293e47i			0.996428i
$928$	−1.02952e47	+	4.33563e46i	−0.340305	+	0.143313i
$929$	−2.38969e46			−0.0776409			−0.0388205	−	0.999246i	$-0.512360\pi$
$929$	−2.38969e46			−0.0776409			−0.0388205	+	0.999246i	$0.512360\pi$
$930$	−6.61673e46	+	2.77044e47i	−0.211308	+	0.884752i
$931$		−	1.32826e47i		−	0.416954i
$932$	−3.70398e47	−	1.87629e47i	−1.14291	−	0.578957i
$933$	−1.35831e47			−0.411995
$934$	3.68200e46	+	8.79385e45i	0.109783	+	0.0262198i
$935$		−	3.82707e47i		−	1.12171i
$936$	−2.11191e47	+	2.49049e47i	−0.608501	+	0.717583i
$937$	5.26937e46			0.149254			0.0746268	−	0.997212i	$-0.476223\pi$
$937$	5.26937e46			0.149254			0.0746268	+	0.997212i	$0.476223\pi$
$938$	1.62116e47	−	6.78783e47i	0.451419	−	1.89010i
$939$			3.66554e47i			1.00343i
$940$	−7.70425e46	+	1.52089e47i	−0.207341	+	0.409310i
$941$	−1.10297e47			−0.291829			−0.145915	−	0.989297i	$-0.546612\pi$
$941$	−1.10297e47			−0.291829			−0.145915	+	0.989297i	$0.546612\pi$
$942$	−1.15820e48	−	2.76616e47i	−3.01279	−	0.719554i
$943$			2.18690e46i			0.0559296i
$944$	−5.10460e46	+	3.74558e46i	−0.128354	+	0.0941818i
$945$	−6.92426e47			−1.71185
$946$	5.53210e45	−	2.31630e46i	0.0134472	−	0.0563036i
$947$			7.59630e47i			1.81552i	0.419485	+	0.907762i	$0.362211\pi$
$947$			7.59630e47i			1.81552i	−0.419485	+	0.907762i	$0.637789\pi$
$948$	7.06345e47	+	3.57807e47i	1.65990	+	0.840844i
$949$	3.87189e47			0.894671
$950$	6.91832e45	+	1.65233e45i	0.0157189	+	0.00375421i
$951$		−	2.23442e47i		−	0.499201i
$952$	5.00325e47	+	4.24269e47i	1.09916	+	0.932074i
$953$	−2.69647e47			−0.582517			−0.291259	−	0.956644i	$-0.594074\pi$
$953$	−2.69647e47			−0.582517			−0.291259	+	0.956644i	$0.594074\pi$
$954$	5.68348e46	−	2.37968e47i	0.120737	−	0.505528i
$955$		−	3.11126e47i		−	0.649954i
$956$	−1.80526e47	+	3.56376e47i	−0.370863	+	0.732119i
$957$	−4.13409e47			−0.835198
$958$	6.22014e47	+	1.48558e47i	1.23581	+	0.295153i
$959$			8.97288e47i			1.75321i
$960$	8.01513e47	−	1.32760e47i	1.54018	−	0.255110i
$961$	3.49500e47			0.660501
$962$	2.88769e45	−	1.20908e46i	0.00536722	−	0.0224727i
$963$		−	8.59968e47i		−	1.57203i
$964$	−7.02735e47	−	3.55979e47i	−1.26345	−	0.640017i
$965$	−7.81232e47			−1.38148
$966$	7.16036e46	+	1.71013e46i	0.124538	+	0.0297438i
$967$		−	8.68662e47i		−	1.48603i	−0.669276	−	0.743014i	$-0.733396\pi$
$967$		−	8.68662e47i		−	1.48603i	0.669276	−	0.743014i	$-0.266604\pi$
$968$	−3.61217e47	+	4.25969e47i	−0.607802	+	0.716757i
$969$	−1.74995e47			−0.289631
$970$	−2.09454e47	+	8.76989e47i	−0.340990	+	1.42773i
$971$		−	3.07628e47i		−	0.492627i	−0.969190	−	0.246314i	$-0.920781\pi$
$971$		−	3.07628e47i		−	0.492627i	0.969190	−	0.246314i	$-0.0792193\pi$
$972$	2.76570e47	−	5.45975e47i	0.435657	−	0.860027i
$973$	9.51002e47			1.47359
$974$	5.57069e47	+	1.33047e47i	0.849113	+	0.202797i
$975$			4.72481e46i			0.0708452i
$976$	5.36963e47	+	7.31791e47i	0.792040	+	1.07942i
$977$	1.00138e48			1.45306			0.726531	−	0.687134i	$-0.241131\pi$
$977$	1.00138e48			1.45306			0.726531	+	0.687134i	$0.241131\pi$
$978$	−1.47368e46	+	6.17031e46i	−0.0210368	+	0.0880816i
$979$		−	8.72804e47i		−	1.22573i
$980$	−1.21580e48	−	6.15876e47i	−1.67975	−	0.850895i
$981$	7.82127e47			1.06310
$982$	−4.09206e47	−	9.77320e46i	−0.547215	−	0.130693i
$983$			5.92610e47i			0.779674i	0.920884	+	0.389837i	$0.127469\pi$
$983$			5.92610e47i			0.779674i	−0.920884	+	0.389837i	$0.872531\pi$
$984$	−1.16765e48	−	9.90154e47i	−1.51144	−	1.28168i
$985$	5.23981e47			0.667323
$986$	5.73525e46	−	2.40136e47i	0.0718657	−	0.300903i
$987$		−	1.08149e48i		−	1.33336i
$988$	4.55607e46	−	8.99411e46i	0.0552687	−	0.109106i
$989$	1.59604e45			0.00190504
$990$	1.81560e48	+	4.33625e47i	2.13234	+	0.509274i
$991$			7.60458e47i			0.878813i	0.898288	+	0.439407i	$0.144811\pi$
$991$			7.60458e47i			0.878813i	−0.898288	+	0.439407i	$0.855189\pi$
$992$	1.98870e47	+	4.72230e47i	0.226143	+	0.536991i
$993$	−2.19395e48			−2.45492
$994$	−6.43903e47	+	2.69603e48i	−0.708987	+	2.96854i
$995$		−	4.03739e47i		−	0.437453i
$996$	1.49168e48	+	7.55627e47i	1.59047	+	0.805671i
$997$	−4.12064e47			−0.432356			−0.216178	−	0.976354i	$-0.569359\pi$
$997$	−4.12064e47			−0.432356			−0.216178	+	0.976354i	$0.569359\pi$
$998$	−1.02569e48	−	2.44969e47i	−1.05908	−	0.252943i
$999$		−	4.09689e46i		−	0.0416300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.33.b.b.3.8	yes	14
3.2	odd	2		36.33.d.b.19.7		14
4.3	odd	2	inner	4.33.b.b.3.7	✓	14
12.11	even	2		36.33.d.b.19.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.33.b.b.3.7	✓	14	4.3	odd	2	inner
4.33.b.b.3.8	yes	14	1.1	even	1	trivial
36.33.d.b.19.7		14	3.2	odd	2
36.33.d.b.19.8		14	12.11	even	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:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 33 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-15224.0 + 63743.2i) q^{2} -6.99091e7i q^{3} +(-3.83143e9 - 1.94085e9i) q^{4} -1.46681e11 q^{5} +(4.45623e12 + 1.06430e12i) q^{6} -5.71644e13i q^{7} +(1.82046e14 - 2.14680e14i) q^{8} -3.03426e15 q^{9} +O(q^{10})\)	\(q+(-15224.0 + 63743.2i) q^{2} -6.99091e7i q^{3} +(-3.83143e9 - 1.94085e9i) q^{4} -1.46681e11 q^{5} +(4.45623e12 + 1.06430e12i) q^{6} -5.71644e13i q^{7} +(1.82046e14 - 2.14680e14i) q^{8} -3.03426e15 q^{9} +(2.23307e15 - 9.34993e15i) q^{10} -6.39967e16i q^{11} +(-1.35683e17 + 2.67852e17i) q^{12} +3.82332e17 q^{13} +(3.64385e18 + 8.70272e17i) q^{14} +1.02543e19i q^{15} +(1.09129e19 + 1.48725e19i) q^{16} -4.07694e19 q^{17} +(4.61937e19 - 1.93414e20i) q^{18} +6.13984e19i q^{19} +(5.61998e20 + 2.84687e20i) q^{20} -3.99632e21 q^{21} +(4.07936e21 + 9.74287e20i) q^{22} +2.81087e20i q^{23} +(-1.50081e22 - 1.27267e22i) q^{24} -1.76771e21 q^{25} +(-5.82063e21 + 2.43711e22i) q^{26} +8.25797e22i q^{27} +(-1.10948e23 + 2.19021e23i) q^{28} +9.24035e22 q^{29} +(-6.53645e23 - 1.56112e23i) q^{30} -4.23845e23i q^{31} +(-1.11416e24 + 4.69206e23i) q^{32} -4.47396e24 q^{33} +(6.20674e23 - 2.59877e24i) q^{34} +8.38495e24i q^{35} +(1.16256e25 + 5.88906e24i) q^{36} -4.96114e23 q^{37} +(-3.91373e24 - 9.34729e23i) q^{38} -2.67285e25i q^{39} +(-2.67027e25 + 3.14895e25i) q^{40} +7.78015e25 q^{41} +(6.08399e25 - 2.54738e26i) q^{42} -5.67810e24i q^{43} +(-1.24208e26 + 2.45199e26i) q^{44} +4.45069e26 q^{45} +(-1.79174e25 - 4.27927e24i) q^{46} +2.70622e26i q^{47} +(1.03972e27 - 7.62912e26i) q^{48} -2.16335e27 q^{49} +(2.69116e25 - 1.12679e26i) q^{50} +2.85015e27i q^{51} +(-1.46488e27 - 7.42051e26i) q^{52} +1.23036e27 q^{53} +(-5.26390e27 - 1.25719e27i) q^{54} +9.38712e27i q^{55} +(-1.22721e28 - 1.04066e28i) q^{56} +4.29231e27 q^{57} +(-1.40675e27 + 5.89010e27i) q^{58} +3.43224e27i q^{59} +(1.99022e28 - 3.92888e28i) q^{60} +4.92044e28 q^{61} +(2.70172e28 + 6.45261e27i) q^{62} +1.73452e29i q^{63} +(-1.29467e28 - 7.81632e28i) q^{64} -5.60809e28 q^{65} +(6.81115e28 - 2.85184e29i) q^{66} -1.86282e29i q^{67} +(1.56205e29 + 7.91275e28i) q^{68} +1.96506e28 q^{69} +(-5.34483e29 - 1.27652e29i) q^{70} +7.39887e29i q^{71} +(-5.52375e29 + 6.51395e29i) q^{72} +1.01270e30 q^{73} +(7.55284e27 - 3.16239e28i) q^{74} +1.23579e29i q^{75} +(1.19165e29 - 2.35243e29i) q^{76} -3.65834e30 q^{77} +(1.70376e30 + 4.06915e29i) q^{78} -2.63707e30i q^{79} +(-1.60072e30 - 2.18151e30i) q^{80} +1.50522e29 q^{81} +(-1.18445e30 + 4.95932e30i) q^{82} -5.56904e30i q^{83} +(1.53116e31 + 7.75627e30i) q^{84} +5.98011e30 q^{85} +(3.61940e29 + 8.64434e28i) q^{86} -6.45985e30i q^{87} +(-1.37388e31 - 1.16503e31i) q^{88} +1.36383e31 q^{89} +(-6.77574e30 + 2.83701e31i) q^{90} -2.18558e31i q^{91} +(5.45549e29 - 1.07697e30i) q^{92} -2.96306e31 q^{93} +(-1.72503e31 - 4.11995e30i) q^{94} -9.00598e30i q^{95} +(3.28017e31 + 7.78898e31i) q^{96} -9.37964e31 q^{97} +(3.29348e31 - 1.37899e32i) q^{98} +1.94183e32i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 23780 q^{2} - 2922848368 q^{4} + 138121491740 q^{5} + 1262734959552 q^{6} - 191366550113600 q^{8} - 11\!\cdots\!50 q^{9}+O(q^{10}) \) 14 * q - 23780 * q^2 - 2922848368 * q^4 + 138121491740 * q^5 + 1262734959552 * q^6 - 191366550113600 * q^8 - 11183509932817650 * q^9	\( 14 q - 23780 q^{2} - 2922848368 q^{4} + 138121491740 q^{5} + 1262734959552 q^{6} - 191366550113600 q^{8} - 11\!\cdots\!50 q^{9}+ \cdots - 46\!\cdots\!00 q^{98}+O(q^{100}) \) 14 * q - 23780 * q^2 - 2922848368 * q^4 + 138121491740 * q^5 + 1262734959552 * q^6 - 191366550113600 * q^8 - 11183509932817650 * q^9 + 31775605694457400 * q^10 - 356375853407619840 * q^12 - 1640418469677858020 * q^13 + 7731597686180285568 * q^14 - 30570843123186593536 * q^16 + 31570967905797256220 * q^17 - 356724239595483290340 * q^18 + 2022222335397731344160 * q^20 - 2117057333603414716416 * q^21 + 5453282318362187158080 * q^22 - 25676387438412555666432 * q^24 + 10252879651857697291050 * q^25 - 100487287286439222842824 * q^26 + 287406099989137745118720 * q^28 - 383350228001906510553316 * q^29 - 58105690536229485525120 * q^30 - 3049085458330908760601600 * q^32 + 300337698474624477849600 * q^33 + 2968198158688225453161016 * q^34 + 4059126291383069998225296 * q^36 - 10743727036349878681805540 * q^37 - 23674230631082905997232960 * q^38 + 46284510399605997225174400 * q^40 + 36301708465641824663518748 * q^41 + 115560171253757823362918400 * q^42 - 341183497187317069095824640 * q^44 + 807084693575724158345591580 * q^45 - 292611965791335032977170048 * q^46 + 2221472331677427727192412160 * q^48 - 4831123780514350255580603890 * q^49 - 510591072029103065039587500 * q^50 - 9698318635805895955111735520 * q^52 + 18428895934780252746021636380 * q^53 + 5640914457354711920825943936 * q^54 + 6374003242890184756165527552 * q^56 - 45021698676819804378731120640 * q^57 - 38529567312130296955877295560 * q^58 + 47104092918034241778705984000 * q^60 + 106402038936127775684939892508 * q^61 + 21568431972603200921875622400 * q^62 - 196737301243248539525687308288 * q^64 + 113178238686492542374351007800 * q^65 + 127488965971714418642064552960 * q^66 + 354271480525935415641826176800 * q^68 - 518263207562337876647092752384 * q^69 - 514873634674652910315035354880 * q^70 + 114107440511865769651514823360 * q^72 + 1432707125192338982920850898460 * q^73 - 984194129445064624850959434184 * q^74 - 782627770945775078204519980800 * q^76 - 3080015547766001613074070589440 * q^77 + 87768417039576149684305430400 * q^78 + 6279147555674556254006737379840 * q^80 - 42644471558968013664770433522 * q^81 - 4557892929168088074284564686280 * q^82 + 18798568063225498187446552682496 * q^84 + 6758108895547933966316548575800 * q^85 - 23458263349697798020331664550848 * q^86 + 11102138256776653733497151431680 * q^88 - 18473812211636703183423448507876 * q^89 - 25496421058026878088516916614600 * q^90 + 60798444498044060215697222361600 * q^92 + 43431545808036949970541566115840 * q^93 - 130643574777689548682138472237312 * q^94 + 345792875639857602943412371832832 * q^96 - 201795139515948373218799959195620 * q^97 - 460006462884606019803763245136100 * q^98

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