LMFDB - Embedded newform 4.33.b.b.3.3

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			3.3
Root			$-2.55660e6i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.33.b.b.3.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-56022.2 - 34007.1i) q^{2} -4.09055e7i q^{3} +(1.98200e9 + 3.81031e9i) q^{4} -2.17196e11 q^{5} +(-1.39108e12 + 2.29162e12i) q^{6} -2.81808e12i q^{7} +(1.85418e13 - 2.80864e14i) q^{8} +1.79757e14 q^{9} +O(q^{10})$	\(q+(-56022.2 - 34007.1i) q^{2} -4.09055e7i q^{3} +(1.98200e9 + 3.81031e9i) q^{4} -2.17196e11 q^{5} +(-1.39108e12 + 2.29162e12i) q^{6} -2.81808e12i q^{7} +(1.85418e13 - 2.80864e14i) q^{8} +1.79757e14 q^{9} +(1.21678e16 + 7.38622e15i) q^{10} +6.95526e16i q^{11} +(1.55863e17 - 8.10747e16i) q^{12} -7.08184e17 q^{13} +(-9.58347e16 + 1.57875e17i) q^{14} +8.88453e18i q^{15} +(-1.05901e19 + 1.51040e19i) q^{16} +6.55998e19 q^{17} +(-1.00704e19 - 6.11302e18i) q^{18} +1.83995e20i q^{19} +(-4.30482e20 - 8.27584e20i) q^{20} -1.15275e20 q^{21} +(2.36528e21 - 3.89649e21i) q^{22} -7.92873e20i q^{23} +(-1.14889e22 - 7.58463e20i) q^{24} +2.38911e22 q^{25} +(3.96740e22 + 2.40833e22i) q^{26} -8.31519e22i q^{27} +(1.07377e22 - 5.58542e21i) q^{28} -1.45523e23 q^{29} +(3.02137e23 - 4.97731e23i) q^{30} -1.34887e24i q^{31} +(1.10693e24 - 4.86021e23i) q^{32} +2.84509e24 q^{33} +(-3.67504e24 - 2.23086e24i) q^{34} +6.12075e23i q^{35} +(3.56278e23 + 6.84930e23i) q^{36} -2.62567e24 q^{37} +(6.25715e24 - 1.03078e25i) q^{38} +2.89686e25i q^{39} +(-4.02721e24 + 6.10025e25i) q^{40} -1.80745e25 q^{41} +(6.45795e24 + 3.92017e24i) q^{42} -1.56149e26i q^{43} +(-2.65017e26 + 1.37853e26i) q^{44} -3.90426e25 q^{45} +(-2.69633e25 + 4.44185e25i) q^{46} +8.64218e26i q^{47} +(6.17839e26 + 4.33194e26i) q^{48} +1.09649e27 q^{49} +(-1.33843e27 - 8.12470e26i) q^{50} -2.68339e27i q^{51} +(-1.40362e27 - 2.69840e27i) q^{52} +5.50243e27 q^{53} +(-2.82776e27 + 4.65835e27i) q^{54} -1.51066e28i q^{55} +(-7.91495e26 - 5.22522e25i) q^{56} +7.52642e27 q^{57} +(8.15252e27 + 4.94882e27i) q^{58} +9.48554e27i q^{59} +(-3.38528e28 + 1.76091e28i) q^{60} +3.04221e28 q^{61} +(-4.58712e28 + 7.55666e28i) q^{62} -5.06569e26i q^{63} +(-7.85406e28 - 1.04154e28i) q^{64} +1.53815e29 q^{65} +(-1.59388e29 - 9.67532e28i) q^{66} -7.40203e28i q^{67} +(1.30019e29 + 2.49955e29i) q^{68} -3.24329e28 q^{69} +(2.08149e28 - 3.42898e28i) q^{70} -2.60149e29i q^{71} +(3.33302e27 - 5.04872e28i) q^{72} +3.70906e29 q^{73} +(1.47095e29 + 8.92914e28i) q^{74} -9.77280e29i q^{75} +(-7.01078e29 + 3.64678e29i) q^{76} +1.96004e29 q^{77} +(9.85140e29 - 1.62289e30i) q^{78} +2.10671e30i q^{79} +(2.30013e30 - 3.28054e30i) q^{80} -3.06828e30 q^{81} +(1.01257e30 + 6.14660e29i) q^{82} +6.24724e30i q^{83} +(-2.28475e29 - 4.39233e29i) q^{84} -1.42480e31 q^{85} +(-5.31019e30 + 8.74783e30i) q^{86} +5.95270e30i q^{87} +(1.95348e31 + 1.28963e30i) q^{88} +1.03445e31 q^{89} +(2.18725e30 + 1.32773e30i) q^{90} +1.99572e30i q^{91} +(3.02109e30 - 1.57147e30i) q^{92} -5.51763e31 q^{93} +(2.93896e31 - 4.84153e31i) q^{94} -3.99630e31i q^{95} +(-1.98809e31 - 4.52794e31i) q^{96} +1.05656e32 q^{97} +(-6.14275e31 - 3.72883e31i) q^{98} +1.25026e31i 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 $

$2$	−56022.2	−	34007.1i	−0.854830	−	0.518908i
$2$	−56022.2	−	34007.1i	−0.854830	−	0.518908i
$3$		−	4.09055e7i		−	0.950259i	−0.879916	−	0.475130i	$-0.842401\pi$
$3$		−	4.09055e7i		−	0.950259i	0.879916	−	0.475130i	$-0.157599\pi$
$4$	1.98200e9	+	3.81031e9i	0.461470	+	0.887156i
$5$	−2.17196e11			−1.42342			−0.711709	−	0.702475i	$-0.752078\pi$
$5$	−2.17196e11			−1.42342			−0.711709	+	0.702475i	$0.752078\pi$
$6$	−1.39108e12	+	2.29162e12i	−0.493097	+	0.812310i
$7$		−	2.81808e12i		−	0.0847977i	−0.999101	−	0.0423988i	$-0.986500\pi$
$7$		−	2.81808e12i		−	0.0847977i	0.999101	−	0.0423988i	$-0.0135000\pi$
$8$	1.85418e13	−	2.80864e14i	0.0658738	−	0.997828i
$9$	1.79757e14			0.0970076
$10$	1.21678e16	+	7.38622e15i	1.21678	+	0.738622i
$11$			6.95526e16i			1.51367i	0.653607	+	0.756834i	$0.273255\pi$
$11$			6.95526e16i			1.51367i	−0.653607	+	0.756834i	$0.726745\pi$
$12$	1.55863e17	−	8.10747e16i	0.843028	−	0.438516i
$13$	−7.08184e17			−1.06427			−0.532136	−	0.846659i	$-0.678610\pi$
$13$	−7.08184e17			−1.06427			−0.532136	+	0.846659i	$0.678610\pi$
$14$	−9.58347e16	+	1.57875e17i	−0.0440022	+	0.0724876i
$15$			8.88453e18i			1.35262i
$16$	−1.05901e19	+	1.51040e19i	−0.574091	+	0.818791i
$17$	6.55998e19			1.34809			0.674046	−	0.738689i	$-0.264555\pi$
$17$	6.55998e19			1.34809			0.674046	+	0.738689i	$0.264555\pi$
$18$	−1.00704e19	−	6.11302e18i	−0.0829251	−	0.0503380i
$19$			1.83995e20i			0.637894i	0.947773	+	0.318947i	$0.103329\pi$
$19$			1.83995e20i			0.637894i	−0.947773	+	0.318947i	$0.896671\pi$
$20$	−4.30482e20	−	8.27584e20i	−0.656864	−	1.26279i
$21$	−1.15275e20			−0.0805798
$22$	2.36528e21	−	3.89649e21i	0.785454	−	1.29393i
$23$		−	7.92873e20i		−	0.129288i	−0.997908	−	0.0646440i	$-0.979409\pi$
$23$		−	7.92873e20i		−	0.129288i	0.997908	−	0.0646440i	$-0.0205912\pi$
$24$	−1.14889e22	−	7.58463e20i	−0.948195	−	0.0625972i
$25$	2.38911e22			1.02612
$26$	3.96740e22	+	2.40833e22i	0.909771	+	0.552259i
$27$		−	8.31519e22i		−	1.04244i
$28$	1.07377e22	−	5.58542e21i	0.0752288	−	0.0391316i
$29$	−1.45523e23			−0.581519			−0.290760	−	0.956796i	$-0.593908\pi$
$29$	−1.45523e23			−0.581519			−0.290760	+	0.956796i	$0.593908\pi$
$30$	3.02137e23	−	4.97731e23i	0.701882	−	1.15626i
$31$		−	1.34887e24i		−	1.85431i	−0.374673	−	0.927157i	$-0.622245\pi$
$31$		−	1.34887e24i		−	1.85431i	0.374673	−	0.927157i	$-0.377755\pi$
$32$	1.10693e24	−	4.86021e23i	0.915628	−	0.402027i
$33$	2.84509e24			1.43838
$34$	−3.67504e24	−	2.23086e24i	−1.15239	−	0.699535i
$35$			6.12075e23i			0.120702i
$36$	3.56278e23	+	6.84930e23i	0.0447661	+	0.0860609i
$37$	−2.62567e24			−0.212820			−0.106410	−	0.994322i	$-0.533936\pi$
$37$	−2.62567e24			−0.212820			−0.106410	+	0.994322i	$0.533936\pi$
$38$	6.25715e24	−	1.03078e25i	0.331008	−	0.545291i
$39$			2.89686e25i			1.01133i
$40$	−4.02721e24	+	6.10025e25i	−0.0937659	+	1.42033i
$41$	−1.80745e25			−0.283481			−0.141740	−	0.989904i	$-0.545270\pi$
$41$	−1.80745e25			−0.283481			−0.141740	+	0.989904i	$0.545270\pi$
$42$	6.45795e24	+	3.92017e24i	0.0688820	+	0.0418135i
$43$		−	1.56149e26i		−	1.14300i	−0.820603	−	0.571498i	$-0.806362\pi$
$43$		−	1.56149e26i		−	1.14300i	0.820603	−	0.571498i	$-0.193638\pi$
$44$	−2.65017e26	+	1.37853e26i	−1.34286	+	0.698512i
$45$	−3.90426e25			−0.138082
$46$	−2.69633e25	+	4.44185e25i	−0.0670885	+	0.110519i
$47$			8.64218e26i			1.52425i	0.647427	+	0.762127i	$0.275845\pi$
$47$			8.64218e26i			1.52425i	−0.647427	+	0.762127i	$0.724155\pi$
$48$	6.17839e26	+	4.33194e26i	0.778064	+	0.545536i
$49$	1.09649e27			0.992809
$50$	−1.33843e27	−	8.12470e26i	−0.877156	−	0.532460i
$51$		−	2.68339e27i		−	1.28104i
$52$	−1.40362e27	−	2.69840e27i	−0.491129	−	0.944175i
$53$	5.50243e27			1.41952			0.709759	−	0.704444i	$-0.248804\pi$
$53$	5.50243e27			1.41952			0.709759	+	0.704444i	$0.248804\pi$
$54$	−2.82776e27	+	4.65835e27i	−0.540931	+	0.891111i
$55$		−	1.51066e28i		−	2.15458i
$56$	−7.91495e26	−	5.22522e25i	−0.0846135	−	0.00558594i
$57$	7.52642e27			0.606165
$58$	8.15252e27	+	4.94882e27i	0.497100	+	0.301755i
$59$			9.48554e27i			0.439977i	0.975502	+	0.219988i	$0.0706020\pi$
$59$			9.48554e27i			0.439977i	−0.975502	+	0.219988i	$0.929398\pi$
$60$	−3.38528e28	+	1.76091e28i	−1.19998	+	0.624191i
$61$	3.04221e28			0.827774			0.413887	−	0.910328i	$-0.364171\pi$
$61$	3.04221e28			0.827774			0.413887	+	0.910328i	$0.364171\pi$
$62$	−4.58712e28	+	7.55666e28i	−0.962218	+	1.58512i
$63$		−	5.06569e26i		−	0.00822602i
$64$	−7.85406e28	−	1.04154e28i	−0.991321	−	0.131461i
$65$	1.53815e29			1.51490
$66$	−1.59388e29	−	9.67532e28i	−1.22957	−	0.746384i
$67$		−	7.40203e28i		−	0.448905i	−0.974485	−	0.224452i	$-0.927941\pi$
$67$		−	7.40203e28i		−	0.448905i	0.974485	−	0.224452i	$-0.0720593\pi$
$68$	1.30019e29	+	2.49955e29i	0.622103	+	1.19597i
$69$	−3.24329e28			−0.122857
$70$	2.08149e28	−	3.42898e28i	0.0626334	−	0.103180i
$71$		−	2.60149e29i		−	0.623863i	−0.950105	−	0.311932i	$-0.899024\pi$
$71$		−	2.60149e29i		−	0.623863i	0.950105	−	0.311932i	$-0.100976\pi$
$72$	3.33302e27	−	5.04872e28i	0.00639026	−	0.0967969i
$73$	3.70906e29			0.570293			0.285147	−	0.958484i	$-0.407958\pi$
$73$	3.70906e29			0.570293			0.285147	+	0.958484i	$0.407958\pi$
$74$	1.47095e29	+	8.92914e28i	0.181925	+	0.110434i
$75$		−	9.77280e29i		−	0.975077i
$76$	−7.01078e29	+	3.64678e29i	−0.565912	+	0.294369i
$77$	1.96004e29			0.128355
$78$	9.85140e29	−	1.62289e30i	0.524789	−	0.864519i
$79$			2.10671e30i			0.915317i	0.889128	+	0.457659i	$0.151312\pi$
$79$			2.10671e30i			0.915317i	−0.889128	+	0.457659i	$0.848688\pi$
$80$	2.30013e30	−	3.28054e30i	0.817172	−	1.16548i
$81$	−3.06828e30			−0.893582
$82$	1.01257e30	+	6.14660e29i	0.242328	+	0.147100i
$83$			6.24724e30i			1.23151i	0.787937	+	0.615756i	$0.211149\pi$
$83$			6.24724e30i			1.23151i	−0.787937	+	0.615756i	$0.788851\pi$
$84$	−2.28475e29	−	4.39233e29i	−0.0371851	−	0.0714868i
$85$	−1.42480e31			−1.91890
$86$	−5.31019e30	+	8.74783e30i	−0.593110	+	0.977068i
$87$			5.95270e30i			0.552594i
$88$	1.95348e31	+	1.28963e30i	1.51038	+	0.0997110i
$89$	1.03445e31			0.667526			0.333763	−	0.942657i	$-0.391682\pi$
$89$	1.03445e31			0.667526			0.333763	+	0.942657i	$0.391682\pi$
$90$	2.18725e30	+	1.32773e30i	0.118037	+	0.0716520i
$91$			1.99572e30i			0.0902477i
$92$	3.02109e30	−	1.57147e30i	0.114699	−	0.0596625i
$93$	−5.51763e31			−1.76208
$94$	2.93896e31	−	4.84153e31i	0.790947	−	1.30298i
$95$		−	3.99630e31i		−	0.907990i
$96$	−1.98809e31	−	4.52794e31i	−0.382030	−	0.870084i
$97$	1.05656e32			1.72007			0.860036	−	0.510233i	$-0.170441\pi$
$97$	1.05656e32			1.72007			0.860036	+	0.510233i	$0.170441\pi$
$98$	−6.14275e31	−	3.72883e31i	−0.848684	−	0.515176i
$99$			1.25026e31i			0.146837i
$100$	4.73522e31	+	9.10326e31i	0.473522	+	0.910326i
$101$	9.75597e31			0.832010			0.416005	−	0.909362i	$-0.363430\pi$
$101$	9.75597e31			0.832010			0.416005	+	0.909362i	$0.363430\pi$
$102$	−9.12545e31	+	1.50329e32i	−0.664740	+	1.09507i
$103$		−	1.75898e31i		−	0.109614i	−0.998497	−	0.0548068i	$-0.982546\pi$
$103$		−	1.75898e31i		−	0.109614i	0.998497	−	0.0548068i	$-0.0174543\pi$
$104$	−1.31310e31	+	1.98903e32i	−0.0701076	+	1.06196i
$105$	2.50373e31			0.114699
$106$	−3.08258e32	−	1.87122e32i	−1.21345	−	0.736599i
$107$		−	2.30757e32i		−	0.781653i	−0.920464	−	0.390827i	$-0.872189\pi$
$107$		−	2.30757e32i		−	0.781653i	0.920464	−	0.390827i	$-0.127811\pi$
$108$	3.16834e32	−	1.64807e32i	0.924808	−	0.481055i
$109$	−3.17192e32			−0.798910			−0.399455	−	0.916753i	$-0.630801\pi$
$109$	−3.17192e32			−0.798910			−0.399455	+	0.916753i	$0.630801\pi$
$110$	−5.13731e32	+	8.46302e32i	−1.11803	+	1.84180i
$111$			1.07404e32i			0.202234i
$112$	4.25643e31	+	2.98438e31i	0.0694316	+	0.0486816i
$113$	1.38155e33			1.95485			0.977424	−	0.211288i	$-0.0677658\pi$
$113$	1.38155e33			1.95485			0.977424	+	0.211288i	$0.0677658\pi$
$114$	−4.21646e32	−	2.55952e32i	−0.518168	−	0.314544i
$115$			1.72209e32i			0.184031i
$116$	−2.88426e32	−	5.54488e32i	−0.268353	−	0.515898i
$117$	−1.27301e32			−0.103242
$118$	3.22576e32	−	5.31400e32i	0.228307	−	0.376105i
$119$		−	1.84865e32i		−	0.114315i
$120$	2.49534e33	+	1.64735e32i	1.34968	+	0.0891019i
$121$	−2.72619e33			−1.29119
$122$	−1.70431e33	−	1.03457e33i	−0.707606	−	0.429538i
$123$			7.39345e32i			0.269380i
$124$	5.13961e33	−	2.67346e33i	1.64507	−	0.855710i
$125$	−1.32074e32			−0.0371755
$126$	−1.72270e31	+	2.83791e31i	−0.00426855	+	0.00703185i
$127$		−	5.38941e33i		−	1.17674i	−0.808590	−	0.588372i	$-0.799769\pi$
$127$		−	5.38941e33i		−	1.17674i	0.808590	−	0.588372i	$-0.200231\pi$
$128$	4.04581e33	+	3.25444e33i	0.779195	+	0.626781i
$129$	−6.38737e33			−1.08614
$130$	−8.61704e33	−	5.23080e33i	−1.29498	−	0.786094i
$131$			1.38685e34i			1.84370i	0.387550	+	0.921849i	$0.373321\pi$
$131$			1.38685e34i			1.84370i	−0.387550	+	0.921849i	$0.626679\pi$
$132$	5.63895e33	+	1.08407e34i	0.663767	+	1.27606i
$133$	5.18512e32			0.0540919
$134$	−2.51722e33	+	4.14678e33i	−0.232940	+	0.383737i
$135$			1.80603e34i			1.48383i
$136$	1.21634e33	−	1.84246e34i	0.0888039	−	1.34516i
$137$	−1.41446e34			−0.918461			−0.459231	−	0.888317i	$-0.651875\pi$
$137$	−1.41446e34			−0.918461			−0.459231	+	0.888317i	$0.651875\pi$
$138$	1.81696e33	+	1.10295e33i	0.105022	+	0.0637515i
$139$		−	1.36246e34i		−	0.701596i	−0.936451	−	0.350798i	$-0.885910\pi$
$139$		−	1.36246e34i		−	0.701596i	0.936451	−	0.350798i	$-0.114090\pi$
$140$	−2.33219e33	+	1.21313e33i	−0.107082	+	0.0557005i
$141$	3.53513e34			1.44844
$142$	−8.84694e33	+	1.45741e34i	−0.323727	+	0.533297i
$143$		−	4.92560e34i		−	1.61095i
$144$	−1.90365e33	+	2.71506e33i	−0.0556913	+	0.0794290i
$145$	3.16071e34			0.827745
$146$	−2.07790e34	−	1.26134e34i	−0.487504	−	0.295929i
$147$		−	4.48524e34i		−	0.943426i
$148$	−5.20406e33	−	1.00046e34i	−0.0982098	−	0.188804i
$149$	1.20034e34			0.203388			0.101694	−	0.994816i	$-0.467574\pi$
$149$	1.20034e34			0.203388			0.101694	+	0.994816i	$0.467574\pi$
$150$	−3.32345e34	+	5.47494e34i	−0.505975	+	0.833525i
$151$		−	4.78649e34i		−	0.655219i	−0.944813	−	0.327609i	$-0.893757\pi$
$151$		−	4.78649e34i		−	0.655219i	0.944813	−	0.327609i	$-0.106243\pi$
$152$	5.16775e34	+	3.41160e33i	0.636509	+	0.0420205i
$153$	1.17920e34			0.130775
$154$	−1.09806e34	−	6.66555e33i	−0.109722	−	0.0666046i
$155$			2.92970e35i			2.63946i
$156$	−1.10379e35	+	5.74158e34i	−0.897211	+	0.466700i
$157$	7.13932e34			0.523917			0.261959	−	0.965079i	$-0.415632\pi$
$157$	7.13932e34			0.523917			0.261959	+	0.965079i	$0.415632\pi$
$158$	7.16432e34	−	1.18023e35i	0.474965	−	0.782441i
$159$		−	2.25080e35i		−	1.34891i
$160$	−2.40420e35	+	1.05562e35i	−1.30332	+	0.572252i
$161$	−2.23438e33			−0.0109633
$162$	1.71892e35	+	1.04343e35i	0.763861	+	0.463686i
$163$			9.56621e34i			0.385246i	0.981273	+	0.192623i	$0.0616995\pi$
$163$			9.56621e34i			0.385246i	−0.981273	+	0.192623i	$0.938301\pi$
$164$	−3.58235e34	−	6.88692e34i	−0.130818	−	0.251492i
$165$	−6.17942e35			−2.04741
$166$	2.12451e35	−	3.49984e35i	0.639041	−	1.05273i
$167$			1.85412e35i			0.506609i	0.967387	+	0.253305i	$0.0815175\pi$
$167$			1.85412e35i			0.506609i	−0.967387	+	0.253305i	$0.918482\pi$
$168$	−2.13741e33	+	3.23765e34i	−0.00530809	+	0.0804047i
$169$	5.87451e34			0.132674
$170$	7.98205e35	+	4.84534e35i	1.64033	+	0.995731i
$171$			3.30744e34i			0.0618806i
$172$	5.94977e35	−	3.09488e35i	1.01402	−	0.527458i
$173$	−2.05267e35			−0.318846			−0.159423	−	0.987210i	$-0.550963\pi$
$173$	−2.05267e35			−0.318846			−0.159423	+	0.987210i	$0.550963\pi$
$174$	2.02434e35	−	3.33483e35i	0.286745	−	0.472374i
$175$		−	6.73271e34i		−	0.0870123i
$176$	−1.05052e36	−	7.36570e35i	−1.23938	−	0.868984i
$177$	3.88011e35			0.418092
$178$	−5.79519e35	−	3.51786e35i	−0.570621	−	0.346384i
$179$		−	1.25998e35i		−	0.113426i	−0.998391	−	0.0567132i	$-0.981938\pi$
$179$		−	1.25998e35i		−	0.113426i	0.998391	−	0.0567132i	$-0.0180621\pi$
$180$	−7.73823e34	−	1.48764e35i	−0.0637208	−	0.122501i
$181$	−1.20858e35			−0.0910789			−0.0455394	−	0.998963i	$-0.514501\pi$
$181$	−1.20858e35			−0.0910789			−0.0455394	+	0.998963i	$0.514501\pi$
$182$	6.78686e34	−	1.11804e35i	0.0468302	−	0.0771465i
$183$		−	1.24443e36i		−	0.786600i
$184$	−2.22689e35	−	1.47013e34i	−0.129007	−	0.00851669i
$185$	5.70285e35			0.302931
$186$	3.09109e36	+	1.87639e36i	1.50628	+	0.914356i
$187$			4.56263e36i			2.04056i
$188$	−3.29293e36	+	1.71288e36i	−1.35225	+	0.703397i
$189$	−2.34328e35			−0.0883966
$190$	−1.35903e36	+	2.23882e36i	−0.471163	+	0.776177i
$191$		−	2.97958e36i		−	0.949776i	−0.880046	−	0.474888i	$-0.842489\pi$
$191$		−	2.97958e36i		−	0.949776i	0.880046	−	0.474888i	$-0.157511\pi$
$192$	−4.26049e35	+	3.21274e36i	−0.124922	+	0.942012i
$193$	−1.00262e35			−0.0270532			−0.0135266	−	0.999909i	$-0.504306\pi$
$193$	−1.00262e35			−0.0270532			−0.0135266	+	0.999909i	$0.504306\pi$
$194$	−5.91908e36	−	3.59306e36i	−1.47037	−	0.892559i
$195$		−	6.29188e36i		−	1.43955i
$196$	2.17323e36	+	4.17795e36i	0.458151	+	0.880777i
$197$	9.62694e36			1.87081			0.935403	−	0.353585i	$-0.115037\pi$
$197$	9.62694e36			1.87081			0.935403	+	0.353585i	$0.115037\pi$
$198$	4.25177e35	−	7.00421e35i	0.0761950	−	0.125521i
$199$			1.60787e36i			0.265828i	0.991128	+	0.132914i	$0.0424335\pi$
$199$			1.60787e36i			0.265828i	−0.991128	+	0.132914i	$0.957567\pi$
$200$	4.42985e35	−	6.71015e36i	0.0675942	−	1.02389i
$201$	−3.02784e36			−0.426576
$202$	−5.46551e36	−	3.31773e36i	−0.711228	−	0.431736i
$203$			4.10095e35i			0.0493115i
$204$	1.02245e37	−	5.31848e36i	1.13648	−	0.591159i
$205$	3.92570e36			0.403511
$206$	−5.98178e35	+	9.85417e35i	−0.0568794	+	0.0937011i
$207$		−	1.42525e35i		−	0.0125419i
$208$	7.49975e36	−	1.06964e37i	0.610989	−	0.871416i
$209$	−1.27973e37			−0.965560
$210$	−1.40264e36	−	8.51446e35i	−0.0980479	−	0.0595180i
$211$		−	3.10011e36i		−	0.200843i	−0.994945	−	0.100422i	$-0.967981\pi$
$211$		−	3.10011e36i		−	0.200843i	0.994945	−	0.100422i	$-0.0320192\pi$
$212$	1.09058e37	+	2.09660e37i	0.655065	+	1.25933i
$213$	−1.06416e37			−0.592832
$214$	−7.84738e36	+	1.29275e37i	−0.405606	+	0.668181i
$215$			3.39151e37i			1.62696i
$216$	−2.33543e37	−	1.54179e36i	−1.04018	−	0.0686696i
$217$	−3.80122e36			−0.157242
$218$	1.77698e37	+	1.07868e37i	0.682933	+	0.414561i
$219$		−	1.51721e37i		−	0.541926i
$220$	5.75606e37	−	2.99412e37i	1.91145	−	0.994274i
$221$	−4.64567e37			−1.43474
$222$	3.65251e36	−	6.01702e36i	0.104941	−	0.172876i
$223$			1.15242e37i			0.308129i	0.988061	+	0.154065i	$0.0492364\pi$
$223$			1.15242e37i			0.308129i	−0.988061	+	0.154065i	$0.950764\pi$
$224$	−1.36964e36	−	3.11940e36i	−0.0340910	−	0.0776431i
$225$	4.29460e36			0.0995412
$226$	−7.73977e37	−	4.69827e37i	−1.67106	−	1.01439i
$227$			4.61854e37i			0.929160i	0.885531	+	0.464580i	$0.153795\pi$
$227$			4.61854e37i			0.929160i	−0.885531	+	0.464580i	$0.846205\pi$
$228$	1.49173e37	+	2.86780e37i	0.279727	+	0.537763i
$229$	3.72281e37			0.650883			0.325441	−	0.945562i	$-0.394487\pi$
$229$	3.72281e37			0.650883			0.325441	+	0.945562i	$0.394487\pi$
$230$	5.85634e36	−	9.64752e36i	0.0954950	−	0.157315i
$231$		−	8.01767e36i		−	0.121971i
$232$	−2.69826e36	+	4.08722e37i	−0.0383069	+	0.580256i
$233$	7.06883e37			0.936813			0.468407	−	0.883513i	$-0.344828\pi$
$233$	7.06883e37			0.936813			0.468407	+	0.883513i	$0.344828\pi$
$234$	7.13168e36	+	4.32915e36i	0.0882548	+	0.0535733i
$235$		−	1.87705e38i		−	2.16965i
$236$	−3.61428e37	+	1.88003e37i	−0.390328	+	0.203036i
$237$	8.61762e37			0.869789
$238$	−6.28673e36	+	1.03565e37i	−0.0593190	+	0.0977200i
$239$			1.27048e37i			0.112099i	0.998428	+	0.0560493i	$0.0178504\pi$
$239$			1.27048e37i			0.112099i	−0.998428	+	0.0560493i	$0.982150\pi$
$240$	−1.34192e38	−	9.40882e37i	−1.10751	−	0.776525i
$241$	4.54592e37			0.351034			0.175517	−	0.984476i	$-0.443840\pi$
$241$	4.54592e37			0.351034			0.175517	+	0.984476i	$0.443840\pi$
$242$	1.52727e38	+	9.27098e37i	1.10375	+	0.670008i
$243$		−	2.85725e37i		−	0.193307i
$244$	6.02965e37	+	1.15917e38i	0.381993	+	0.734365i
$245$	−2.38153e38			−1.41318
$246$	2.51430e37	−	4.14197e37i	0.139783	−	0.230274i
$247$		−	1.30302e38i		−	0.678892i
$248$	−3.78849e38	−	2.50105e37i	−1.85029	−	0.122151i
$249$	2.55547e38			1.17026
$250$	7.39907e36	+	4.49146e36i	0.0317787	+	0.0192907i
$251$			1.86541e38i			0.751612i	0.926698	+	0.375806i	$0.122634\pi$
$251$			1.86541e38i			0.751612i	−0.926698	+	0.375806i	$0.877366\pi$
$252$	1.93018e36	−	1.00402e36i	0.00729777	−	0.00379606i
$253$	5.51464e37			0.195699
$254$	−1.83279e38	+	3.01927e38i	−0.610622	+	1.00592i
$255$			5.82823e38i			1.82345i
$256$	−1.15981e38	−	3.19907e38i	−0.340838	−	0.940122i
$257$	−1.69751e38			−0.468687			−0.234344	−	0.972154i	$-0.575294\pi$
$257$	−1.69751e38			−0.468687			−0.234344	+	0.972154i	$0.575294\pi$
$258$	3.57834e38	+	2.17216e38i	0.928468	+	0.563608i
$259$			7.39932e36i			0.0180466i
$260$	3.04861e38	+	5.86082e38i	0.699082	+	1.34395i
$261$	−2.61588e37			−0.0564118
$262$	4.71629e38	−	7.76945e38i	0.956709	−	1.57605i
$263$		−	2.65236e38i		−	0.506221i	−0.967437	−	0.253110i	$-0.918546\pi$
$263$		−	2.65236e38i		−	0.506221i	0.967437	−	0.253110i	$-0.0814536\pi$
$264$	5.27531e37	−	7.99081e38i	0.0947513	−	1.43525i
$265$	−1.19511e39			−2.02057
$266$	−2.90482e37	−	1.76331e37i	−0.0462394	−	0.0280687i
$267$		−	4.23146e38i		−	0.634322i
$268$	2.82040e38	−	1.46708e38i	0.398249	−	0.207156i
$269$	1.81625e38			0.241624			0.120812	−	0.992675i	$-0.461450\pi$
$269$	1.81625e38			0.241624			0.120812	+	0.992675i	$0.461450\pi$
$270$	6.14178e38	−	1.01178e39i	0.769970	−	1.26842i
$271$		−	1.02031e39i		−	1.20566i	−0.797870	−	0.602829i	$-0.794040\pi$
$271$		−	1.02031e39i		−	1.20566i	0.797870	−	0.602829i	$-0.205960\pi$
$272$	−6.94709e38	+	9.90821e38i	−0.773928	+	1.10381i
$273$	8.16358e37			0.0857587
$274$	7.92410e38	+	4.81017e38i	0.785129	+	0.476597i
$275$			1.66169e39i			1.55320i
$276$	−6.42819e37	−	1.23579e38i	−0.0566948	−	0.108993i
$277$	1.47642e39			1.22895			0.614475	−	0.788937i	$-0.289368\pi$
$277$	1.47642e39			1.22895			0.614475	+	0.788937i	$0.289368\pi$
$278$	−4.63334e38	+	7.63280e38i	−0.364064	+	0.599745i
$279$		−	2.42469e38i		−	0.179883i
$280$	1.71910e38	+	1.13490e37i	0.120440	+	0.00795113i
$281$	−5.86616e38			−0.388197			−0.194099	−	0.980982i	$-0.562178\pi$
$281$	−5.86616e38			−0.388197			−0.194099	+	0.980982i	$0.562178\pi$
$282$	−1.98046e39	−	1.20220e39i	−1.23817	−	0.751605i
$283$			2.31347e39i			1.36673i	0.730078	+	0.683363i	$0.239484\pi$
$283$			2.31347e39i			1.36673i	−0.730078	+	0.683363i	$0.760516\pi$
$284$	9.91249e38	−	5.15615e38i	0.553464	−	0.287894i
$285$	−1.63471e39			−0.862825
$286$	−1.67506e39	+	2.75943e39i	−0.835936	+	1.37709i
$287$			5.09352e37i			0.0240385i
$288$	1.98978e38	−	8.73657e37i	0.0888229	−	0.0389997i
$289$	1.93542e39			0.817351
$290$	−1.77070e39	−	1.07487e39i	−0.707581	−	0.429523i
$291$		−	4.32192e39i		−	1.63451i
$292$	7.35135e38	+	1.41327e39i	0.263173	+	0.505939i
$293$	9.55731e38			0.323932			0.161966	−	0.986796i	$-0.448217\pi$
$293$	9.55731e38			0.323932			0.161966	+	0.986796i	$0.448217\pi$
$294$	−1.52530e39	+	2.51273e39i	−0.489551	+	0.806469i
$295$		−	2.06022e39i		−	0.626271i
$296$	−4.86846e37	+	7.37454e38i	−0.0140192	+	0.212357i
$297$	5.78343e39			1.57791
$298$	−6.72457e38	−	4.08202e38i	−0.173862	−	0.105539i
$299$			5.61500e38i			0.137598i
$300$	3.72374e39	−	1.93697e39i	0.865045	−	0.449969i
$301$	−4.40041e38			−0.0969235
$302$	−1.62775e39	+	2.68150e39i	−0.339998	+	0.560101i
$303$		−	3.99073e39i		−	0.790625i
$304$	−2.77907e39	−	1.94853e39i	−0.522302	−	0.366210i
$305$	−6.60756e39			−1.17827
$306$	−6.60615e38	−	4.01013e38i	−0.111791	−	0.0678603i
$307$			1.81430e39i			0.291404i	0.989329	+	0.145702i	$0.0465440\pi$
$307$			1.81430e39i			0.291404i	−0.989329	+	0.145702i	$0.953456\pi$
$308$	3.88480e38	+	7.46837e38i	0.0592322	+	0.113871i
$309$	−7.19519e38			−0.104161
$310$	9.96306e39	−	1.64128e40i	1.36964	−	2.25629i
$311$			1.20307e40i			1.57082i	0.618976	+	0.785410i	$0.287548\pi$
$311$			1.20307e40i			1.57082i	−0.618976	+	0.785410i	$0.712452\pi$
$312$	8.13624e39	+	5.37131e38i	1.00914	+	0.0666204i
$313$	9.36962e39			1.10411			0.552055	−	0.833808i	$-0.313844\pi$
$313$	9.36962e39			1.10411			0.552055	+	0.833808i	$0.313844\pi$
$314$	−3.99960e39	−	2.42788e39i	−0.447860	−	0.271865i
$315$			1.10025e38i			0.0117091i
$316$	−8.02722e39	+	4.17550e39i	−0.812029	+	0.422391i
$317$	−1.26999e40			−1.22138			−0.610692	−	0.791868i	$-0.709109\pi$
$317$	−1.26999e40			−1.22138			−0.610692	+	0.791868i	$0.709109\pi$
$318$	−7.65433e39	+	1.26095e40i	−0.699960	+	1.15309i
$319$		−	1.01215e40i		−	0.880227i
$320$	1.70587e40	+	2.26220e39i	1.41106	+	0.187124i
$321$	−9.43923e39			−0.742773
$322$	1.25175e38	+	7.59847e37i	0.00937178	+	0.00568895i
$323$			1.20700e40i			0.859940i
$324$	−6.08132e39	−	1.16911e40i	−0.412361	−	0.792747i
$325$	−1.69193e40			−1.09207
$326$	3.25320e39	−	5.35920e39i	0.199907	−	0.329320i
$327$			1.29749e40i			0.759172i
$328$	−3.35133e38	+	5.07646e39i	−0.0186739	+	0.282865i
$329$	2.43543e39			0.129253
$330$	3.46185e40	+	2.10144e40i	1.75019	+	1.06242i
$331$		−	1.76393e39i		−	0.0849637i	−0.999097	−	0.0424818i	$-0.986474\pi$
$331$		−	1.76393e39i		−	0.0849637i	0.999097	−	0.0424818i	$-0.0135265\pi$
$332$	−2.38039e40	+	1.23820e40i	−1.09254	+	0.568305i
$333$	−4.71982e38			−0.0206451
$334$	6.30531e39	−	1.03872e40i	0.262883	−	0.433065i
$335$			1.60769e40i			0.638979i
$336$	1.22077e39	−	1.74112e39i	0.0462602	−	0.0659780i
$337$	8.12789e38			0.0293697			0.0146848	−	0.999892i	$-0.495326\pi$
$337$	8.12789e38			0.0293697			0.0146848	+	0.999892i	$0.495326\pi$
$338$	−3.29103e39	−	1.99775e39i	−0.113413	−	0.0688453i
$339$		−	5.65132e40i		−	1.85761i
$340$	−2.82395e40	−	5.42893e40i	−0.885513	−	1.70236i
$341$	9.38175e40			2.80681
$342$	1.12477e39	−	1.85290e39i	0.0321103	−	0.0528974i
$343$		−	6.20234e39i		−	0.168986i
$344$	−4.38567e40	−	2.89529e39i	−1.14051	−	0.0752935i
$345$	7.04430e39			0.174877
$346$	1.14995e40	+	6.98054e39i	0.272559	+	0.165452i
$347$		−	7.06291e40i		−	1.59850i	−0.601000	−	0.799249i	$-0.705231\pi$
$347$		−	7.06291e40i		−	1.59850i	0.601000	−	0.799249i	$-0.294769\pi$
$348$	−2.26816e40	+	1.17982e40i	−0.490237	+	0.255005i
$349$	−1.82205e40			−0.376143			−0.188071	−	0.982155i	$-0.560224\pi$
$349$	−1.82205e40			−0.376143			−0.188071	+	0.982155i	$0.560224\pi$
$350$	−2.28960e39	+	3.77181e39i	−0.0451514	+	0.0743808i
$351$			5.88868e40i			1.10944i
$352$	3.38040e40	+	7.69896e40i	0.608535	+	1.38596i
$353$	−2.49744e40			−0.429636			−0.214818	−	0.976654i	$-0.568916\pi$
$353$	−2.49744e40			−0.429636			−0.214818	+	0.976654i	$0.568916\pi$
$354$	−2.17372e40	−	1.31951e40i	−0.357398	−	0.216951i
$355$			5.65035e40i			0.888018i
$356$	2.05027e40	+	3.94156e40i	0.308043	+	0.592199i
$357$	−7.56200e39			−0.108629
$358$	−4.28482e39	+	7.05866e39i	−0.0588578	+	0.0969603i
$359$		−	8.95589e40i		−	1.17651i	−0.808674	−	0.588257i	$-0.799814\pi$
$359$		−	8.95589e40i		−	1.17651i	0.808674	−	0.588257i	$-0.200186\pi$
$360$	−7.23920e38	+	1.09656e40i	−0.00909601	+	0.137782i
$361$	4.93443e40			0.593091
$362$	6.77072e39	+	4.11003e39i	0.0778570	+	0.0472615i
$363$			1.11516e41i			1.22696i
$364$	−7.60429e39	+	3.95550e39i	−0.0800638	+	0.0416466i
$365$	−8.05594e40			−0.811765
$366$	−4.23196e40	+	6.97158e40i	−0.408173	+	0.672409i
$367$			1.14387e40i			0.105614i	0.998605	+	0.0528069i	$0.0168168\pi$
$367$			1.14387e40i			0.105614i	−0.998605	+	0.0528069i	$0.983183\pi$
$368$	1.19756e40	+	8.39662e39i	0.105860	+	0.0742232i
$369$	−3.24901e39			−0.0274998
$370$	−3.19486e40	−	1.93937e40i	−0.258955	−	0.157193i
$371$		−	1.55063e40i		−	0.120372i
$372$	−1.09359e41	−	2.10239e41i	−0.813146	−	1.56324i
$373$	−1.08315e41			−0.771519			−0.385760	−	0.922599i	$-0.626061\pi$
$373$	−1.08315e41			−0.771519			−0.385760	+	0.922599i	$0.626061\pi$
$374$	1.55162e41	−	2.55609e41i	1.05886	−	1.74433i
$375$			5.40255e39i			0.0353264i
$376$	2.42727e41	+	1.60242e40i	1.52094	+	0.100408i
$377$	1.03057e41			0.618894
$378$	1.31276e40	+	7.96883e39i	0.0755641	+	0.0458697i
$379$			9.31410e40i			0.513941i	0.966419	+	0.256971i	$0.0827244\pi$
$379$			9.31410e40i			0.513941i	−0.966419	+	0.256971i	$0.917276\pi$
$380$	1.52271e41	−	7.92066e40i	0.805528	−	0.419010i
$381$	−2.20457e41			−1.11821
$382$	−1.01327e41	+	1.66923e41i	−0.492846	+	0.811897i
$383$		−	7.96910e39i		−	0.0371731i	−0.999827	−	0.0185866i	$-0.994083\pi$
$383$		−	7.96910e39i		−	0.0371731i	0.999827	−	0.0185866i	$-0.00591663\pi$
$384$	1.33124e41	−	1.65496e41i	0.595605	−	0.740437i
$385$	−4.25714e40			−0.182703
$386$	5.61688e39	+	3.40962e39i	0.0231259	+	0.0140381i
$387$		−	2.80690e40i		−	0.110879i
$388$	2.09410e41	+	4.02582e41i	0.793761	+	1.52597i
$389$	9.70371e39			0.0352975			0.0176488	−	0.999844i	$-0.494382\pi$
$389$	9.70371e39			0.0352975			0.0176488	+	0.999844i	$0.494382\pi$
$390$	−2.13969e41	+	3.52485e41i	−0.746993	+	1.23057i
$391$		−	5.20123e40i		−	0.174292i
$392$	2.03308e40	−	3.07963e41i	0.0654001	−	0.990653i
$393$	5.67300e41			1.75199
$394$	−5.39322e41	−	3.27385e41i	−1.59922	−	0.970775i
$395$		−	4.57570e41i		−	1.30288i
$396$	−4.76386e40	+	2.47801e40i	−0.130268	+	0.0677610i
$397$	−5.94309e41			−1.56086			−0.780430	−	0.625243i	$-0.785000\pi$
$397$	−5.94309e41			−1.56086			−0.780430	+	0.625243i	$0.785000\pi$
$398$	5.46790e40	−	9.00762e40i	0.137940	−	0.227238i
$399$		−	2.12100e40i		−	0.0514014i
$400$	−2.53010e41	+	3.60853e41i	−0.589085	+	0.840176i
$401$	−8.19907e40			−0.183423			−0.0917117	−	0.995786i	$-0.529234\pi$
$401$	−8.19907e40			−0.183423			−0.0917117	+	0.995786i	$0.529234\pi$
$402$	1.69626e41	+	1.02968e41i	0.364650	+	0.221353i
$403$			9.55248e41i			1.97349i
$404$	1.93363e41	+	3.71732e41i	0.383947	+	0.738123i
$405$	6.66418e41			1.27194
$406$	1.39462e40	−	2.29744e40i	0.0255881	−	0.0421529i
$407$		−	1.82622e41i		−	0.322138i
$408$	−7.53667e41	−	4.97550e40i	−1.27825	−	0.0843867i
$409$	7.15084e41			1.16623			0.583115	−	0.812390i	$-0.301834\pi$
$409$	7.15084e41			1.16623			0.583115	+	0.812390i	$0.301834\pi$
$410$	−2.19926e41	−	1.33502e41i	−0.344934	−	0.209385i
$411$			5.78592e41i			0.872776i
$412$	6.70224e40	−	3.48629e40i	0.0972444	−	0.0505834i
$413$	2.67310e40			0.0373090
$414$	−4.84685e39	+	7.98453e39i	−0.00650810	+	0.0107212i
$415$		−	1.35688e42i		−	1.75296i
$416$	−7.83907e41	+	3.44192e41i	−0.974476	+	0.427866i
$417$	−5.57322e41			−0.666698
$418$	7.16935e41	+	4.35201e41i	0.825390	+	0.501036i
$419$		−	1.14174e42i		−	1.26515i	−0.774498	−	0.632576i	$-0.781997\pi$
$419$		−	1.14174e42i		−	1.26515i	0.774498	−	0.632576i	$-0.218003\pi$
$420$	4.96238e40	+	9.53997e40i	0.0529299	+	0.101756i
$421$	2.75721e39			0.00283110			0.00141555	−	0.999999i	$-0.499549\pi$
$421$	2.75721e39			0.00283110			0.00141555	+	0.999999i	$0.499549\pi$
$422$	−1.05426e41	+	1.73675e41i	−0.104219	+	0.171687i
$423$			1.55349e41i			0.147864i
$424$	1.02025e41	−	1.54543e42i	0.0935090	−	1.41644i
$425$	1.56725e42			1.38330
$426$	5.96163e41	+	3.61889e41i	0.506770	+	0.307625i
$427$		−	8.57317e40i		−	0.0701933i
$428$	8.79254e41	−	4.57359e41i	0.693448	−	0.360709i
$429$	−2.01484e42			−1.53082
$430$	1.15335e42	−	1.89999e42i	0.844243	−	1.39078i
$431$			1.37954e42i			0.972967i	0.873690	+	0.486484i	$0.161721\pi$
$431$			1.37954e42i			0.972967i	−0.873690	+	0.486484i	$0.838279\pi$
$432$	1.25593e42	+	8.80588e41i	0.853542	+	0.598457i
$433$	−1.83219e42			−1.19995			−0.599976	−	0.800018i	$-0.704823\pi$
$433$	−1.83219e42			−1.19995			−0.599976	+	0.800018i	$0.704823\pi$
$434$	2.12953e41	+	1.29269e41i	0.134415	+	0.0815938i
$435$		−	1.29290e42i		−	0.786572i
$436$	−6.28673e41	−	1.20860e42i	−0.368673	−	0.708758i
$437$	1.45885e41			0.0824721
$438$	−5.15960e41	+	8.49974e41i	−0.281210	+	0.463255i
$439$			3.54955e42i			1.86527i	0.360827	+	0.932633i	$0.382494\pi$
$439$			3.54955e42i			1.86527i	−0.360827	+	0.932633i	$0.617506\pi$
$440$	−4.24288e42	−	2.80103e41i	−2.14990	−	0.141930i
$441$	1.97101e41			0.0963101
$442$	2.60260e42	+	1.57986e42i	1.22646	+	0.744495i
$443$			3.06452e42i			1.39285i	0.717631	+	0.696423i	$0.245226\pi$
$443$			3.06452e42i			1.39285i	−0.717631	+	0.696423i	$0.754774\pi$
$444$	−4.09243e41	+	2.12875e41i	−0.179413	+	0.0933248i
$445$	−2.24678e42			−0.950168
$446$	3.91905e41	−	6.45610e41i	0.159890	−	0.263398i
$447$		−	4.91006e41i		−	0.193271i
$448$	−2.93515e40	+	2.21333e41i	−0.0111476	+	0.0840617i
$449$	2.68427e42			0.983749			0.491875	−	0.870666i	$-0.336312\pi$
$449$	2.68427e42			0.983749			0.491875	+	0.870666i	$0.336312\pi$
$450$	−2.40593e41	−	1.46047e41i	−0.0850908	−	0.0516527i
$451$		−	1.25713e42i		−	0.429095i
$452$	2.73824e42	+	5.26415e42i	0.902103	+	1.73425i
$453$	−1.95794e42			−0.622628
$454$	1.57063e42	−	2.58740e42i	0.482148	−	0.794274i
$455$		−	4.33462e41i		−	0.128460i
$456$	1.39553e41	−	2.11390e42i	0.0399304	−	0.604848i
$457$	1.28397e42			0.354729			0.177365	−	0.984145i	$-0.443243\pi$
$457$	1.28397e42			0.354729			0.177365	+	0.984145i	$0.443243\pi$
$458$	−2.08560e42	−	1.26602e42i	−0.556394	−	0.337748i
$459$		−	5.45474e42i		−	1.40531i
$460$	−6.56169e41	+	3.41318e41i	−0.163264	+	0.0849246i
$461$	−5.93149e42			−1.42544			−0.712721	−	0.701448i	$-0.752537\pi$
$461$	−5.93149e42			−1.42544			−0.712721	+	0.701448i	$0.752537\pi$
$462$	−2.72658e41	+	4.49167e41i	−0.0632917	+	0.104264i
$463$		−	2.14282e42i		−	0.480495i	−0.970712	−	0.240248i	$-0.922771\pi$
$463$		−	2.14282e42i		−	0.480495i	0.970712	−	0.240248i	$-0.0772286\pi$
$464$	1.54111e42	−	2.19799e42i	0.333845	−	0.476143i
$465$	1.19841e43			2.50817
$466$	−3.96011e42	−	2.40391e42i	−0.800816	−	0.486120i
$467$		−	2.77518e42i		−	0.542278i	−0.962540	−	0.271139i	$-0.912600\pi$
$467$		−	2.77518e42i		−	0.542278i	0.962540	−	0.271139i	$-0.0874003\pi$
$468$	−2.52310e41	−	4.85056e41i	−0.0476433	−	0.0915922i
$469$	−2.08595e41			−0.0380661
$470$	−6.38330e42	+	1.05156e43i	−1.12585	+	1.85468i
$471$		−	2.92038e42i		−	0.497857i
$472$	2.66414e42	+	1.75879e41i	0.439021	+	0.0289829i
$473$	1.08606e43			1.73012
$474$	−4.82778e42	−	2.93061e42i	−0.743522	−	0.451340i
$475$			4.39585e42i			0.654554i
$476$	7.04392e41	−	3.66402e41i	0.101415	−	0.0527529i
$477$	9.89102e41			0.137704
$478$	4.32052e41	−	7.11748e41i	0.0581688	−	0.0958252i
$479$			9.77483e42i			1.27274i	0.771383	+	0.636372i	$0.219566\pi$
$479$			9.77483e42i			1.27274i	−0.771383	+	0.636372i	$0.780434\pi$
$480$	4.31807e42	+	9.83452e42i	0.543788	+	1.23849i
$481$	1.85945e42			0.226498
$482$	−2.54672e42	−	1.54594e42i	−0.300074	−	0.182154i
$483$			9.13984e40i			0.0104180i
$484$	−5.40330e42	−	1.03876e43i	−0.595845	−	1.14549i
$485$	−2.29481e43			−2.44838
$486$	−9.71669e41	+	1.60069e42i	−0.100309	+	0.165245i
$487$		−	4.78815e42i		−	0.478304i	−0.970982	−	0.239152i	$-0.923131\pi$
$487$		−	4.78815e42i		−	0.478304i	0.970982	−	0.239152i	$-0.0768695\pi$
$488$	5.64081e41	−	8.54446e42i	0.0545286	−	0.825976i
$489$	3.91311e42			0.366084
$490$	1.33418e43	+	8.09889e42i	1.20803	+	0.733311i
$491$		−	4.17934e42i		−	0.366272i	−0.983088	−	0.183136i	$-0.941375\pi$
$491$		−	4.17934e42i		−	0.366272i	0.983088	−	0.183136i	$-0.0586248\pi$
$492$	−2.81713e42	+	1.46538e42i	−0.238982	+	0.124311i
$493$	−9.54628e42			−0.783941
$494$	−4.43121e42	+	7.29982e42i	−0.352283	+	0.580338i
$495$		−	2.71551e42i		−	0.209011i
$496$	2.03734e43	+	1.42847e43i	1.51830	+	1.06455i
$497$	−7.33121e41			−0.0529021
$498$	−1.43163e43	−	8.69041e42i	−1.00037	−	0.607254i
$499$			2.18612e43i			1.47933i	0.672975	+	0.739665i	$0.265016\pi$
$499$			2.18612e43i			1.47933i	−0.672975	+	0.739665i	$0.734984\pi$
$500$	−2.61770e41	−	5.03242e41i	−0.0171554	−	0.0329805i
$501$	7.58436e42			0.481410
$502$	6.34371e42	−	1.04504e43i	0.390017	−	0.642501i
$503$		−	8.88151e41i		−	0.0528931i	−0.999650	−	0.0264466i	$-0.991581\pi$
$503$		−	8.88151e41i		−	0.0528931i	0.999650	−	0.0264466i	$-0.00841918\pi$
$504$	−1.42277e41	−	9.39271e39i	−0.00820816	−	0.000541879i
$505$	−2.11896e43			−1.18430
$506$	−3.08942e42	−	1.87537e42i	−0.167289	−	0.101550i
$507$		−	2.40300e42i		−	0.126074i
$508$	2.05353e43	−	1.06818e43i	1.04396	−	0.543032i
$509$	1.41679e43			0.697946			0.348973	−	0.937133i	$-0.386530\pi$
$509$	1.41679e43			0.697946			0.348973	+	0.937133i	$0.386530\pi$
$510$	1.98201e43	−	3.26510e43i	0.946202	−	1.55874i
$511$		−	1.04524e42i		−	0.0483595i
$512$	−4.38160e42	+	2.18661e43i	−0.196478	+	0.980508i
$513$	1.52995e43			0.664967
$514$	9.50984e42	+	5.77276e42i	0.400648	+	0.243205i
$515$			3.82043e42i			0.156026i
$516$	−1.26598e43	−	2.43379e43i	−0.501222	−	0.963578i
$517$	−6.01086e43			−2.30721
$518$	2.51630e41	−	4.14526e41i	0.00936453	−	0.0154268i
$519$			8.39655e42i			0.302987i
$520$	2.85201e42	−	4.32010e43i	0.0997923	−	1.51161i
$521$	4.87247e43			1.65328			0.826639	−	0.562733i	$-0.190250\pi$
$521$	4.87247e43			1.65328			0.826639	+	0.562733i	$0.190250\pi$
$522$	1.46547e42	+	8.89586e41i	0.0482225	+	0.0292725i
$523$			1.24274e42i			0.0396601i	0.999803	+	0.0198300i	$0.00631251\pi$
$523$			1.24274e42i			0.0396601i	−0.999803	+	0.0198300i	$0.993687\pi$
$524$	−5.28433e43	+	2.74874e43i	−1.63565	+	0.850810i
$525$	−2.75405e42			−0.0826843
$526$	−9.01990e42	+	1.48591e43i	−0.262682	+	0.432733i
$527$		−	8.84856e43i		−	2.49979i
$528$	−3.01298e43	+	4.29723e43i	−0.825760	+	1.17773i
$529$	3.69803e43			0.983285
$530$	6.69525e43	+	4.06422e43i	1.72724	+	1.04849i
$531$			1.70509e42i			0.0426811i
$532$	1.02769e42	+	1.97569e42i	0.0249618	+	0.0479880i
$533$	1.28000e43			0.301700
$534$	−1.43900e43	+	2.37055e43i	−0.329155	+	0.542238i
$535$			5.01195e43i			1.11262i
$536$	−2.07896e43	−	1.37247e42i	−0.447930	−	0.0295710i
$537$	−5.15400e42			−0.107784
$538$	−1.01750e43	−	6.17656e42i	−0.206548	−	0.125381i
$539$			7.62635e43i			1.50278i
$540$	−6.88152e43	+	3.57954e43i	−1.31639	+	0.684742i
$541$	−5.93941e43			−1.10303			−0.551515	−	0.834165i	$-0.685950\pi$
$541$	−5.93941e43			−1.10303			−0.551515	+	0.834165i	$0.685950\pi$
$542$	−3.46979e43	+	5.71601e43i	−0.625625	+	1.03063i
$543$			4.94376e42i			0.0865485i
$544$	7.26141e43	−	3.18828e43i	1.23435	−	0.541969i
$545$	6.88929e43			1.13718
$546$	−4.57341e42	−	2.77620e42i	−0.0733092	−	0.0445009i
$547$		−	1.03500e44i		−	1.61118i	−0.592476	−	0.805588i	$-0.701850\pi$
$547$		−	1.03500e44i		−	1.61118i	0.592476	−	0.805588i	$-0.298150\pi$
$548$	−2.80345e43	−	5.38952e43i	−0.423842	−	0.814819i
$549$	5.46859e42			0.0803004
$550$	5.65094e43	−	9.30916e43i	0.805967	−	1.32772i
$551$		−	2.67755e43i		−	0.370948i
$552$	−6.01365e41	+	9.10922e42i	−0.00809306	+	0.122590i
$553$	5.93687e42			0.0776168
$554$	−8.27123e43	−	5.02089e43i	−1.05054	−	0.637711i
$555$		−	2.33278e43i		−	0.287863i
$556$	5.19139e43	−	2.70039e43i	0.622425	−	0.323765i
$557$	3.46931e43			0.404166			0.202083	−	0.979368i	$-0.435229\pi$
$557$	3.46931e43			0.404166			0.202083	+	0.979368i	$0.435229\pi$
$558$	−8.24568e42	+	1.35836e43i	−0.0933425	+	0.153769i
$559$			1.10582e44i			1.21646i
$560$	−9.24481e42	−	6.48195e42i	−0.0988301	−	0.0692943i
$561$	1.86637e44			1.93906
$562$	3.28635e43	+	1.99491e43i	0.331843	+	0.201439i
$563$		−	1.44724e44i		−	1.42038i	−0.704008	−	0.710192i	$-0.748608\pi$
$563$		−	1.44724e44i		−	1.42038i	0.704008	−	0.710192i	$-0.251392\pi$
$564$	7.00662e43	+	1.34699e44i	0.668410	+	1.28499i
$565$	−3.00068e44			−2.78256
$566$	7.86746e43	−	1.29606e44i	0.709205	−	1.16832i
$567$			8.64664e42i			0.0757737i
$568$	−7.30665e43	−	4.82364e42i	−0.622508	−	0.0410962i
$569$	−8.69359e43			−0.720117			−0.360059	−	0.932930i	$-0.617243\pi$
$569$	−8.69359e43			−0.720117			−0.360059	+	0.932930i	$0.617243\pi$
$570$	9.15800e43	+	5.55918e43i	0.737569	+	0.447727i
$571$			1.65234e44i			1.29396i	0.762506	+	0.646981i	$0.223969\pi$
$571$			1.65234e44i			1.29396i	−0.762506	+	0.646981i	$0.776031\pi$
$572$	1.87681e44	−	9.76253e43i	1.42917	−	0.743406i
$573$	−1.21881e44			−0.902533
$574$	1.73216e42	−	2.85350e42i	0.0124738	−	0.0205488i
$575$		−	1.89426e43i		−	0.132665i
$576$	−1.41182e43	−	1.87225e42i	−0.0961657	−	0.0127528i
$577$	−8.34544e43			−0.552887			−0.276443	−	0.961030i	$-0.589156\pi$
$577$	−8.34544e43			−0.552887			−0.276443	+	0.961030i	$0.589156\pi$
$578$	−1.08426e44	−	6.58180e43i	−0.698697	−	0.424130i
$579$			4.10126e42i			0.0257075i
$580$	6.26451e43	+	1.20433e44i	0.381979	+	0.734339i
$581$	1.76052e43			0.104429
$582$	−1.46976e44	+	2.42123e44i	−0.848162	+	1.39723i
$583$			3.82709e44i			2.14868i
$584$	6.87727e42	−	1.04174e44i	0.0375674	−	0.569054i
$585$	2.76493e43			0.146957
$586$	−5.35421e43	−	3.25017e43i	−0.276907	−	0.168091i
$587$		−	6.43456e42i		−	0.0323824i	−0.999869	−	0.0161912i	$-0.994846\pi$
$587$		−	6.43456e42i		−	0.0323824i	0.999869	−	0.0161912i	$-0.00515405\pi$
$588$	1.70901e44	−	8.88972e43i	0.836966	−	0.435363i
$589$	2.48186e44			1.18286
$590$	−7.00623e43	+	1.15418e44i	−0.324977	+	0.535355i
$591$		−	3.93795e44i		−	1.77775i
$592$	2.78061e43	−	3.96581e43i	0.122178	−	0.174255i
$593$	6.27744e43			0.268477			0.134239	−	0.990949i	$-0.457141\pi$
$593$	6.27744e43			0.268477			0.134239	+	0.990949i	$0.457141\pi$
$594$	−3.24000e44	−	1.96678e44i	−1.34885	−	0.818789i
$595$			4.01520e43i			0.162718i
$596$	2.37907e43	+	4.57367e43i	0.0938572	+	0.180437i
$597$	6.57707e43			0.252606
$598$	1.90950e43	−	3.14564e43i	0.0714004	−	0.117623i
$599$		−	5.41478e43i		−	0.197129i	−0.995131	−	0.0985647i	$-0.968575\pi$
$599$		−	5.41478e43i		−	0.197129i	0.995131	−	0.0985647i	$-0.0314251\pi$
$600$	−2.74482e44	−	1.81206e43i	−0.972959	−	0.0642320i
$601$	−4.48094e44			−1.54660			−0.773299	−	0.634042i	$-0.781395\pi$
$601$	−4.48094e44			−1.54660			−0.773299	+	0.634042i	$0.781395\pi$
$602$	2.46520e43	+	1.49645e43i	0.0828531	+	0.0502943i
$603$		−	1.33057e43i		−	0.0435472i
$604$	1.82380e44	−	9.48682e43i	0.581281	−	0.302364i
$605$	5.92118e44			1.83790
$606$	−1.35713e44	+	2.23570e44i	−0.410262	+	0.675850i
$607$			1.09513e44i			0.322440i	0.986919	+	0.161220i	$0.0515428\pi$
$607$			1.09513e44i			0.322440i	−0.986919	+	0.161220i	$0.948457\pi$
$608$	8.94255e43	+	2.03669e44i	0.256451	+	0.584074i
$609$	1.67752e43			0.0468587
$610$	3.70170e44	+	2.24704e44i	1.00722	+	0.611412i
$611$		−	6.12025e44i		−	1.62222i
$612$	2.33718e43	+	4.49312e43i	0.0603488	+	0.116018i
$613$	1.27103e44			0.319734			0.159867	−	0.987139i	$-0.448894\pi$
$613$	1.27103e44			0.319734			0.159867	+	0.987139i	$0.448894\pi$
$614$	6.16991e43	−	1.01641e44i	0.151212	−	0.249101i
$615$		−	1.60583e44i		−	0.383440i
$616$	3.63428e42	−	5.50505e43i	0.00845526	−	0.128077i
$617$	6.26067e44			1.41925			0.709624	−	0.704581i	$-0.248865\pi$
$617$	6.26067e44			1.41925			0.709624	+	0.704581i	$0.248865\pi$
$618$	4.03090e43	+	2.44688e43i	0.0890403	+	0.0540501i
$619$		−	2.94769e44i		−	0.634500i	−0.948342	−	0.317250i	$-0.897241\pi$
$619$		−	2.94769e44i		−	0.634500i	0.948342	−	0.317250i	$-0.102759\pi$
$620$	−1.11630e45	+	5.80665e44i	−2.34161	+	1.21803i
$621$	−6.59289e43			−0.134775
$622$	4.09131e44	−	6.73989e44i	0.815111	−	1.34278i
$623$		−	2.91515e43i		−	0.0566046i
$624$	−4.37543e44	−	3.06781e44i	−0.828071	−	0.580598i
$625$	−5.27573e44			−0.973201
$626$	−5.24906e44	−	3.18634e44i	−0.943827	−	0.572931i
$627$			5.23482e44i			0.917532i
$628$	1.41501e44	+	2.72030e44i	0.241772	+	0.464796i
$629$	−1.72243e44			−0.286900
$630$	3.74163e42	−	6.16383e42i	0.00607592	−	0.0100093i
$631$			3.61763e44i			0.572736i	0.958120	+	0.286368i	$0.0924479\pi$
$631$			3.61763e44i			0.572736i	−0.958120	+	0.286368i	$0.907552\pi$
$632$	5.91699e44	+	3.90623e43i	0.913329	+	0.0602954i
$633$	−1.26812e44			−0.190853
$634$	7.11476e44	+	4.31887e44i	1.04408	+	0.633786i
$635$			1.17056e45i			1.67500i
$636$	8.57624e44	−	4.46108e44i	1.19669	−	0.622481i
$637$	−7.76514e44			−1.05662
$638$	−3.44204e44	+	5.67029e44i	−0.456756	+	0.752444i
$639$		−	4.67637e43i		−	0.0605195i
$640$	−8.78735e44	−	7.06851e44i	−1.10912	−	0.892172i
$641$	−7.60593e44			−0.936319			−0.468159	−	0.883644i	$-0.655083\pi$
$641$	−7.60593e44			−0.936319			−0.468159	+	0.883644i	$0.655083\pi$
$642$	5.28806e44	+	3.21001e44i	0.634945	+	0.385431i
$643$			1.05982e45i			1.24124i	0.784112	+	0.620619i	$0.213119\pi$
$643$			1.05982e45i			1.24124i	−0.784112	+	0.620619i	$0.786881\pi$
$644$	−4.42853e42	−	8.51366e42i	−0.00505924	−	0.00972618i
$645$	1.38731e45			1.54603
$646$	4.10467e44	−	6.76189e44i	0.446229	−	0.735103i
$647$		−	4.77969e44i		−	0.506911i	−0.967347	−	0.253455i	$-0.918433\pi$
$647$		−	4.77969e44i		−	0.506911i	0.967347	−	0.253455i	$-0.0815671\pi$
$648$	−5.68914e43	+	8.61768e44i	−0.0588636	+	0.891641i
$649$	−6.59744e44			−0.665979
$650$	9.47857e44	+	5.75378e44i	0.933532	+	0.566682i
$651$			1.55491e44i			0.149420i
$652$	−3.64502e44	+	1.89602e44i	−0.341774	+	0.177779i
$653$	−1.50534e45			−1.37729			−0.688643	−	0.725101i	$-0.741793\pi$
$653$	−1.50534e45			−1.37729			−0.688643	+	0.725101i	$0.741793\pi$
$654$	4.41239e44	−	7.26882e44i	0.393940	−	0.648963i
$655$		−	3.01219e45i		−	2.62435i
$656$	1.91411e44	−	2.72997e44i	0.162744	−	0.232111i
$657$	6.66730e43			0.0553228
$658$	−1.36438e44	−	8.28220e43i	−0.110490	−	0.0670705i
$659$		−	1.35593e45i		−	1.07169i	−0.844315	−	0.535847i	$-0.819992\pi$
$659$		−	1.35593e45i		−	1.07169i	0.844315	−	0.535847i	$-0.180008\pi$
$660$	−1.22476e45	−	2.35455e45i	−0.944818	−	1.81637i
$661$	1.79337e45			1.35035			0.675176	−	0.737657i	$-0.264068\pi$
$661$	1.79337e45			1.35035			0.675176	+	0.737657i	$0.264068\pi$
$662$	−5.99862e43	+	9.88191e43i	−0.0440883	+	0.0726295i
$663$			1.90034e45i			1.36337i
$664$	1.75462e45	+	1.15835e44i	1.22884	+	0.0811243i
$665$	−1.12619e44			−0.0769954
$666$	2.64415e43	+	1.60508e43i	0.0176481	+	0.0107129i
$667$			1.15381e44i			0.0751835i
$668$	−7.06475e44	+	3.67485e44i	−0.449441	+	0.233785i
$669$	4.71403e44			0.292802
$670$	5.46731e44	−	9.00665e44i	0.331571	−	0.546218i
$671$			2.11594e45i			1.25297i
$672$	−1.27601e44	+	5.60260e43i	−0.0737811	+	0.0323952i
$673$	−1.07392e45			−0.606361			−0.303181	−	0.952933i	$-0.598049\pi$
$673$	−1.07392e45			−0.606361			−0.303181	+	0.952933i	$0.598049\pi$
$674$	−4.55342e43	−	2.76406e43i	−0.0251061	−	0.0152401i
$675$		−	1.98659e45i		−	1.06967i
$676$	1.16433e44	+	2.23837e44i	0.0612248	+	0.117702i
$677$	1.73726e45			0.892165			0.446083	−	0.894992i	$-0.352819\pi$
$677$	1.73726e45			0.892165			0.446083	+	0.894992i	$0.352819\pi$
$678$	−1.92185e45	+	3.16599e45i	−0.963929	+	1.58794i
$679$		−	2.97747e44i		−	0.145858i
$680$	−2.64184e44	+	4.00175e45i	−0.126405	+	1.91473i
$681$	1.88924e45			0.882943
$682$	−5.25586e45	−	3.19046e45i	−2.39935	−	1.45648i
$683$			3.65073e45i			1.62798i	0.580882	+	0.813988i	$0.302708\pi$
$683$			3.65073e45i			1.62798i	−0.580882	+	0.813988i	$0.697292\pi$
$684$	−1.26024e44	+	6.55534e43i	−0.0548978	+	0.0285560i
$685$	3.07215e45			1.30735
$686$	−2.10924e44	+	3.47469e44i	−0.0876879	+	0.144454i
$687$		−	1.52283e45i		−	0.618507i
$688$	2.35849e45	+	1.65364e45i	0.935876	+	0.656185i
$689$	−3.89674e45			−1.51075
$690$	−3.94637e44	−	2.39557e44i	−0.149490	−	0.0907450i
$691$		−	4.60791e45i		−	1.70551i	−0.522309	−	0.852756i	$-0.674929\pi$
$691$		−	4.60791e45i		−	1.70551i	0.522309	−	0.852756i	$-0.325071\pi$
$692$	−4.06838e44	−	7.82130e44i	−0.147138	−	0.282866i
$693$	3.52332e43			0.0124515
$694$	−2.40189e45	+	3.95680e45i	−0.829473	+	1.36644i
$695$			2.95921e45i			0.998664i
$696$	1.67190e45	+	1.10374e44i	0.551394	+	0.0364014i
$697$	−1.18568e45			−0.382158
$698$	1.02075e45	+	6.19626e44i	0.321538	+	0.195183i
$699$		−	2.89154e45i		−	0.890215i
$700$	2.56537e44	−	1.33442e44i	0.0771935	−	0.0401536i
$701$	2.86431e45			0.842425			0.421212	−	0.906962i	$-0.361605\pi$
$701$	2.86431e45			0.842425			0.421212	+	0.906962i	$0.361605\pi$
$702$	2.00257e45	−	3.29897e45i	0.575697	−	0.948383i
$703$		−	4.83110e44i		−	0.135756i
$704$	7.24421e44	−	5.46270e45i	0.198989	−	1.50053i
$705$	−7.67817e45			−2.06173
$706$	1.39912e45	+	8.49309e44i	0.367265	+	0.222941i
$707$		−	2.74931e44i		−	0.0705525i
$708$	7.69037e44	+	1.47844e45i	0.192937	+	0.370913i
$709$	6.73611e45			1.65223			0.826113	−	0.563504i	$-0.190547\pi$
$709$	6.73611e45			1.65223			0.826113	+	0.563504i	$0.190547\pi$
$710$	1.92152e45	−	3.16545e45i	0.460799	−	0.759104i
$711$			3.78696e44i			0.0887928i
$712$	1.91805e44	−	2.90538e45i	0.0439724	−	0.666076i
$713$	−1.06948e45			−0.239741
$714$	4.23640e44	+	2.57162e44i	0.0928593	+	0.0563684i
$715$			1.06982e46i			2.29306i
$716$	4.80090e44	−	2.49727e44i	0.100627	−	0.0523428i
$717$	5.19695e44			0.106523
$718$	−3.04564e45	+	5.01728e45i	−0.610502	+	1.00572i
$719$		−	6.36501e45i		−	1.24778i	−0.781514	−	0.623888i	$-0.785552\pi$
$719$		−	6.36501e45i		−	1.24778i	0.781514	−	0.623888i	$-0.214448\pi$
$720$	4.13465e44	−	5.89700e44i	0.0792719	−	0.113061i
$721$	−4.95693e43			−0.00929498
$722$	−2.76437e45	−	1.67806e45i	−0.506992	−	0.307760i
$723$		−	1.85953e45i		−	0.333573i
$724$	−2.39540e44	−	4.60505e44i	−0.0420301	−	0.0808012i
$725$	−3.47672e45			−0.596707
$726$	3.79235e45	−	6.24738e45i	0.636681	−	1.04885i
$727$			8.93864e45i			1.46798i	0.679159	+	0.733991i	$0.262345\pi$
$727$			8.93864e45i			1.46798i	−0.679159	+	0.733991i	$0.737655\pi$
$728$	5.60524e44	+	3.70042e43i	0.0900517	+	0.00594496i
$729$	−6.85435e45			−1.07727
$730$	4.51311e45	+	2.73959e45i	0.693921	+	0.421231i
$731$		−	1.02434e46i		−	1.54086i
$732$	4.74167e45	−	2.46646e45i	0.697837	−	0.362992i
$733$	−3.50667e45			−0.504930			−0.252465	−	0.967606i	$-0.581241\pi$
$733$	−3.50667e45			−0.504930			−0.252465	+	0.967606i	$0.581241\pi$
$734$	3.88998e44	−	6.40822e44i	0.0548038	−	0.0902818i
$735$			9.74176e45i			1.34289i
$736$	−3.85353e44	−	8.77652e44i	−0.0519773	−	0.118380i
$737$	5.14831e45			0.679492
$738$	1.82017e44	+	1.10490e44i	0.0235077	+	0.0142699i
$739$		−	3.33091e45i		−	0.420971i	−0.977597	−	0.210486i	$-0.932496\pi$
$739$		−	3.33091e45i		−	0.420971i	0.977597	−	0.210486i	$-0.0675045\pi$
$740$	1.13030e45	+	2.17296e45i	0.139794	+	0.268747i
$741$	−5.33009e45			−0.645124
$742$	−5.27324e44	+	8.68695e44i	−0.0624619	+	0.102898i
$743$			5.60428e45i			0.649679i	0.945769	+	0.324840i	$0.105310\pi$
$743$			5.60428e45i			0.649679i	−0.945769	+	0.324840i	$0.894690\pi$
$744$	−1.02307e45	+	1.54970e46i	−0.116075	+	1.75825i
$745$	−2.60710e45			−0.289505
$746$	6.06803e45	+	3.68348e45i	0.659518	+	0.400347i
$747$			1.12299e45i			0.119466i
$748$	−1.73850e46	+	9.04313e45i	−1.81030	+	0.941658i
$749$	−6.50290e44			−0.0662824
$750$	1.83725e44	−	3.02663e44i	0.0183311	−	0.0301980i
$751$		−	1.89091e46i		−	1.84685i	−0.383775	−	0.923427i	$-0.625376\pi$
$751$		−	1.89091e46i		−	1.84685i	0.383775	−	0.923427i	$-0.374624\pi$
$752$	−1.30532e46	−	9.15217e45i	−1.24805	−	0.875061i
$753$	7.63054e45			0.714226
$754$	−5.77348e45	−	3.50468e45i	−0.529050	−	0.321149i
$755$			1.03961e46i			0.932650i
$756$	−4.64438e44	−	8.92862e44i	−0.0407924	−	0.0784216i
$757$	2.00538e46			1.72450			0.862250	−	0.506483i	$-0.169055\pi$
$757$	2.00538e46			1.72450			0.862250	+	0.506483i	$0.169055\pi$
$758$	3.16746e45	−	5.21796e45i	0.266688	−	0.439333i
$759$		−	2.25579e45i		−	0.185965i
$760$	−1.12242e46	−	7.40987e44i	−0.906017	−	0.0598127i
$761$	1.36781e46			1.08112			0.540558	−	0.841307i	$-0.318213\pi$
$761$	1.36781e46			1.08112			0.540558	+	0.841307i	$0.318213\pi$
$762$	1.23505e46	+	7.49711e45i	0.955881	+	0.580249i
$763$			8.93871e44i			0.0677457i
$764$	1.13531e46	−	5.90552e45i	0.842600	−	0.438293i
$765$	−2.56118e45			−0.186148
$766$	−2.71006e44	+	4.46446e44i	−0.0192894	+	0.0317767i
$767$		−	6.71750e45i		−	0.468255i
$768$	−1.30860e46	+	4.74427e45i	−0.893360	+	0.323884i
$769$	1.11734e46			0.747071			0.373536	−	0.927616i	$-0.378145\pi$
$769$	1.11734e46			0.747071			0.373536	+	0.927616i	$0.378145\pi$
$770$	2.38494e45	+	1.44773e45i	0.156180	+	0.0948062i
$771$			6.94377e45i			0.445374i
$772$	−1.98719e44	−	3.82028e44i	−0.0124842	−	0.0240004i
$773$	−2.18678e46			−1.34565			−0.672827	−	0.739800i	$-0.734920\pi$
$773$	−2.18678e46			−1.34565			−0.672827	+	0.739800i	$0.734920\pi$
$774$	−9.54545e44	+	1.57248e45i	−0.0575362	+	0.0947831i
$775$		−	3.22261e46i		−	1.90274i
$776$	1.95906e45	−	2.96749e46i	0.113308	−	1.71634i
$777$	3.02673e44			0.0171490
$778$	−5.43623e44	−	3.29996e44i	−0.0301734	−	0.0183162i
$779$		−	3.32561e45i		−	0.180831i
$780$	2.39740e46	−	1.24705e46i	1.27711	−	0.664309i
$781$	1.80941e46			0.944321
$782$	−1.76879e45	+	2.91384e45i	−0.0904415	+	0.148990i
$783$			1.21005e46i			0.606200i
$784$	−1.16119e46	+	1.65614e46i	−0.569963	+	0.812904i
$785$	−1.55063e46			−0.745753
$786$	−3.17813e46	−	1.92922e46i	−1.49765	−	0.909121i
$787$		−	1.68275e46i		−	0.777007i	−0.921447	−	0.388503i	$-0.872992\pi$
$787$		−	1.68275e46i		−	0.777007i	0.921447	−	0.388503i	$-0.127008\pi$
$788$	1.90806e46	+	3.66816e46i	0.863320	+	1.65970i
$789$	−1.08496e46			−0.481041
$790$	−1.55606e46	+	2.56341e46i	−0.676074	+	1.11374i
$791$		−	3.89332e45i		−	0.165767i
$792$	3.51152e45	+	2.31821e44i	0.146518	+	0.00967273i
$793$	−2.15444e46			−0.880976
$794$	3.32945e46	+	2.02107e46i	1.33427	+	0.809942i
$795$			4.88865e46i			1.92006i
$796$	−6.12647e45	+	3.18679e45i	−0.235831	+	0.122672i
$797$	−3.48117e45			−0.131339			−0.0656693	−	0.997841i	$-0.520918\pi$
$797$	−3.48117e45			−0.131339			−0.0656693	+	0.997841i	$0.520918\pi$
$798$	−7.21292e44	+	1.18823e45i	−0.0266726	+	0.0439394i
$799$			5.66925e46i			2.05483i
$800$	2.64457e46	−	1.16116e46i	0.939541	−	0.412527i
$801$	1.85949e45			0.0647551
$802$	4.59330e45	+	2.78827e45i	0.156796	+	0.0951798i
$803$			2.57975e46i			0.863234i
$804$	−6.00117e45	−	1.15370e46i	−0.196852	−	0.378439i
$805$	4.85298e44			0.0156054
$806$	3.24853e46	−	5.35151e46i	1.02406	−	1.68700i
$807$		−	7.42948e45i		−	0.229605i
$808$	1.80893e45	−	2.74010e46i	0.0548076	−	0.830203i
$809$	−2.87821e46			−0.854961			−0.427481	−	0.904025i	$-0.640599\pi$
$809$	−2.87821e46			−0.854961			−0.427481	+	0.904025i	$0.640599\pi$
$810$	−3.73342e46	−	2.26630e46i	−1.08729	−	0.660019i
$811$		−	4.47972e46i		−	1.27914i	−0.768733	−	0.639569i	$-0.779113\pi$
$811$		−	4.47972e46i		−	1.27914i	0.768733	−	0.639569i	$-0.220887\pi$
$812$	−1.56259e45	+	8.12807e44i	−0.0437470	+	0.0227558i
$813$	−4.17364e46			−1.14569
$814$	−6.21045e45	+	1.02309e46i	−0.167160	+	0.275374i
$815$		−	2.07775e46i		−	0.548366i
$816$	4.05301e46	+	2.84175e46i	1.04890	+	0.735432i
$817$	2.87307e46			0.729111
$818$	−4.00606e46	−	2.43180e46i	−0.996929	−	0.605166i
$819$			3.58744e44i			0.00875472i
$820$	7.78073e45	+	1.49581e46i	0.186208	+	0.357977i
$821$	−2.72426e46			−0.639378			−0.319689	−	0.947523i	$-0.603578\pi$
$821$	−2.72426e46			−0.639378			−0.319689	+	0.947523i	$0.603578\pi$
$822$	1.96762e46	−	3.24140e46i	0.452890	−	0.746076i
$823$			1.08853e46i			0.245721i	0.992424	+	0.122861i	$0.0392068\pi$
$823$			1.08853e46i			0.245721i	−0.992424	+	0.122861i	$0.960793\pi$
$824$	−4.94033e45	−	3.26146e44i	−0.109376	−	0.00722066i
$825$	6.79724e46			1.47594
$826$	−1.49753e45	−	9.09043e44i	−0.0318929	−	0.0193599i
$827$		−	3.00168e46i		−	0.627013i	−0.949586	−	0.313507i	$-0.898496\pi$
$827$		−	3.00168e46i		−	0.627013i	0.949586	−	0.313507i	$-0.101504\pi$
$828$	5.43062e44	−	2.82483e44i	0.0111266	−	0.00578772i
$829$	7.52687e46			1.51266			0.756331	−	0.654189i	$-0.226990\pi$
$829$	7.52687e46			1.51266			0.756331	+	0.654189i	$0.226990\pi$
$830$	−4.61435e46	+	7.60152e46i	−0.909622	+	1.49848i
$831$		−	6.03938e46i		−	1.16782i
$832$	5.56212e46	+	7.37605e45i	1.05503	+	0.139911i
$833$	7.19292e46			1.33840
$834$	3.12224e46	+	1.89529e46i	0.569914	+	0.345955i
$835$		−	4.02707e46i		−	0.721117i
$836$	−2.53643e46	−	4.87618e46i	−0.445576	−	0.856602i
$837$	−1.12161e47			−1.93301
$838$	−3.88273e46	+	6.39628e46i	−0.656497	+	1.08149i
$839$			5.53407e46i			0.918023i	0.888430	+	0.459011i	$0.151796\pi$
$839$			5.53407e46i			0.918023i	−0.888430	+	0.459011i	$0.848204\pi$
$840$	4.64237e44	−	7.03206e45i	0.00755563	−	0.114450i
$841$	−4.14463e46			−0.661835
$842$	−1.54465e44	−	9.37647e43i	−0.00242011	−	0.00146908i
$843$			2.39958e46i			0.368888i
$844$	1.18124e46	−	6.14440e45i	0.178179	−	0.0926831i
$845$	−1.27592e46			−0.188850
$846$	5.28298e45	−	8.70300e45i	0.0767279	−	0.126399i
$847$			7.68260e45i			0.109490i
$848$	−5.82714e46	+	8.31089e46i	−0.814933	+	1.16229i
$849$	9.46339e46			1.29874
$850$	−8.78009e46	−	5.32978e46i	−1.18249	−	0.717805i
$851$			2.08182e45i			0.0275150i
$852$	−2.10915e46	−	4.05476e46i	−0.273574	−	0.525934i
$853$	−5.02319e45			−0.0639433			−0.0319717	−	0.999489i	$-0.510179\pi$
$853$	−5.02319e45			−0.0639433			−0.0319717	+	0.999489i	$0.510179\pi$
$854$	−2.91549e45	+	4.80288e45i	−0.0364238	+	0.0600034i
$855$		−	7.18364e45i		−	0.0880819i
$856$	−6.48112e46	−	4.27865e45i	−0.779955	−	0.0514904i
$857$	9.46054e46			1.11744			0.558718	−	0.829357i	$-0.311293\pi$
$857$	9.46054e46			1.11744			0.558718	+	0.829357i	$0.311293\pi$
$858$	1.12876e47	+	6.85191e46i	1.30859	+	0.794356i
$859$		−	1.91602e46i		−	0.218026i	−0.994040	−	0.109013i	$-0.965231\pi$
$859$		−	1.91602e46i		−	0.218026i	0.994040	−	0.109013i	$-0.0347691\pi$
$860$	−1.29227e47	+	6.72196e46i	−1.44337	+	0.750793i
$861$	2.08353e45			0.0228428
$862$	4.69142e46	−	7.72848e46i	0.504880	−	0.831722i
$863$			9.20747e46i			0.972675i	0.873771	+	0.486338i	$0.161667\pi$
$863$			9.20747e46i			0.972675i	−0.873771	+	0.486338i	$0.838333\pi$
$864$	−4.04135e46	−	9.20430e46i	−0.419090	−	0.954488i
$865$	4.45832e46			0.453851
$866$	1.02643e47	+	6.23075e46i	1.02575	+	0.622664i
$867$		−	7.91692e46i		−	0.776696i
$868$	−7.53401e45	−	1.44838e46i	−0.0725622	−	0.139498i
$869$	−1.46527e47			−1.38549
$870$	−4.39680e46	+	7.24313e46i	−0.408158	+	0.672385i
$871$			5.24200e46i			0.477756i
$872$	−5.88131e45	+	8.90876e46i	−0.0526272	+	0.797175i
$873$	1.89924e46			0.166860
$874$	−8.17278e45	−	4.96112e45i	−0.0704996	−	0.0427954i
$875$			3.72194e44i			0.00315240i
$876$	5.78104e46	−	3.00711e46i	0.480773	−	0.250082i
$877$	−1.63787e47			−1.33748			−0.668739	−	0.743497i	$-0.733166\pi$
$877$	−1.63787e47			−1.33748			−0.668739	+	0.743497i	$0.733166\pi$
$878$	1.20710e47	−	1.98853e47i	0.967901	−	1.59449i
$879$		−	3.90947e46i		−	0.307819i
$880$	2.28170e47	+	1.59980e47i	1.76415	+	1.23693i
$881$	3.60559e46			0.273755			0.136877	−	0.990588i	$-0.456293\pi$
$881$	3.60559e46			0.273755			0.136877	+	0.990588i	$0.456293\pi$
$882$	−1.10420e46	−	6.70285e45i	−0.0823288	−	0.0499760i
$883$			1.54388e47i			1.13042i	0.824945	+	0.565212i	$0.191206\pi$
$883$			1.54388e47i			1.13042i	−0.824945	+	0.565212i	$0.808794\pi$
$884$	−9.20770e46	−	1.77014e47i	−0.662087	−	1.27283i
$885$	−8.42745e46			−0.595119
$886$	1.04216e47	−	1.71681e47i	0.722759	−	1.19065i
$887$		−	1.06318e47i		−	0.724150i	−0.932149	−	0.362075i	$-0.882068\pi$
$887$		−	1.06318e47i		−	0.724150i	0.932149	−	0.362075i	$-0.117932\pi$
$888$	3.01659e46	+	1.99147e45i	0.201795	+	0.0133219i
$889$	−1.51878e46			−0.0997852
$890$	1.25869e47	+	7.64065e46i	0.812232	+	0.493049i
$891$		−	2.13407e47i		−	1.35259i
$892$	−4.39107e46	+	2.28409e46i	−0.273358	+	0.142192i
$893$	−1.59012e47			−0.972313
$894$	−1.66977e46	+	2.75072e46i	−0.100290	+	0.165214i
$895$			2.73662e46i			0.161453i
$896$	9.17124e45	−	1.14014e46i	0.0531496	−	0.0660739i
$897$	2.29685e46			0.130753
$898$	−1.50378e47	−	9.12843e46i	−0.840939	−	0.510475i
$899$			1.96292e47i			1.07832i
$900$	8.51189e45	+	1.63638e46i	0.0459352	+	0.0883086i
$901$	3.60958e47			1.91364
$902$	−4.27512e46	+	7.04269e46i	−0.222661	+	0.366804i
$903$			1.80001e46i			0.0921024i
$904$	2.56165e46	−	3.88028e47i	0.128773	−	1.95060i
$905$	2.62499e46			0.129643
$906$	1.09688e47	+	6.65840e46i	0.532241	+	0.323086i
$907$		−	1.29696e47i		−	0.618314i	−0.951011	−	0.309157i	$-0.899953\pi$
$907$		−	1.29696e47i		−	0.618314i	0.951011	−	0.309157i	$-0.100047\pi$
$908$	−1.75980e47	+	9.15393e46i	−0.824310	+	0.428779i
$909$	1.75371e46			0.0807113
$910$	−1.47408e46	+	2.42835e46i	−0.0666590	+	0.109812i
$911$			3.45293e47i			1.53424i	0.641503	+	0.767120i	$0.278311\pi$
$911$			3.45293e47i			1.53424i	−0.641503	+	0.767120i	$0.721689\pi$
$912$	−7.97057e46	+	1.13679e47i	−0.347994	+	0.496322i
$913$	−4.34512e47			−1.86410
$914$	−7.19310e46	−	4.36643e46i	−0.303233	−	0.184072i
$915$			2.70286e47i			1.11966i
$916$	7.37859e46	+	1.41850e47i	0.300363	+	0.577434i
$917$	3.90826e46			0.156341
$918$	−1.85500e47	+	3.05586e47i	−0.729224	+	1.20130i
$919$		−	4.17823e47i		−	1.61415i	−0.590447	−	0.807076i	$-0.701049\pi$
$919$		−	4.17823e47i		−	1.61415i	0.590447	−	0.807076i	$-0.298951\pi$
$920$	4.83673e46	+	3.19307e45i	0.183631	+	0.0121228i
$921$	7.42149e46			0.276909
$922$	3.32295e47	+	2.01713e47i	1.21851	+	0.739672i
$923$			1.84234e47i			0.663960i
$924$	3.05498e46	−	1.58910e46i	0.108207	−	0.0562859i
$925$	−6.27302e46			−0.218378
$926$	−7.28710e46	+	1.20045e47i	−0.249333	+	0.410742i
$927$		−	3.16189e45i		−	0.0106334i
$928$	−1.61083e47	+	7.07273e46i	−0.532455	+	0.233786i
$929$	1.68290e47			0.546772			0.273386	−	0.961904i	$-0.411856\pi$
$929$	1.68290e47			0.546772			0.273386	+	0.961904i	$0.411856\pi$
$930$	−6.71374e47	−	4.07544e47i	−2.14406	−	1.30151i
$931$			2.01748e47i			0.633307i
$932$	1.40104e47	+	2.69344e47i	0.432311	+	0.831099i
$933$	4.92124e47			1.49269
$934$	−9.43761e46	+	1.55472e47i	−0.281392	+	0.463555i
$935$		−	9.90987e47i		−	2.90457i
$936$	−2.36039e45	+	3.57542e46i	−0.00680097	+	0.103018i
$937$	9.90873e46			0.280663			0.140331	−	0.990105i	$-0.455183\pi$
$937$	9.90873e46			0.280663			0.140331	+	0.990105i	$0.455183\pi$
$938$	1.16859e46	+	7.09371e45i	0.0325400	+	0.0197528i
$939$		−	3.83269e47i		−	1.04919i
$940$	7.15213e47	−	3.72031e47i	1.92482	−	1.00123i
$941$	1.96858e47			0.520858			0.260429	−	0.965493i	$-0.416136\pi$
$941$	1.96858e47			0.520858			0.260429	+	0.965493i	$0.416136\pi$
$942$	−9.93137e46	+	1.63606e47i	−0.258342	+	0.425583i
$943$			1.43307e46i			0.0366507i
$944$	−1.43270e47	−	1.00453e47i	−0.360249	−	0.252587i
$945$	5.08952e46			0.125825
$946$	−6.08434e47	−	3.69338e47i	−1.47896	−	0.897771i
$947$		−	3.79998e47i		−	0.908200i	−0.890951	−	0.454100i	$-0.849961\pi$
$947$		−	3.79998e47i		−	0.908200i	0.890951	−	0.454100i	$-0.150039\pi$
$948$	1.70801e47	+	3.28358e47i	0.401381	+	0.771638i
$949$	−2.62670e47			−0.606947
$950$	1.49490e47	−	2.46265e47i	0.339653	−	0.559533i
$951$			5.19497e47i			1.16063i
$952$	−5.19219e46	−	3.42773e45i	−0.114067	−	0.00753036i
$953$	7.54445e47			1.62982			0.814912	−	0.579584i	$-0.196785\pi$
$953$	7.54445e47			1.62982			0.814912	+	0.579584i	$0.196785\pi$
$954$	−5.54116e46	−	3.36365e46i	−0.117714	−	0.0714557i
$955$			6.47154e47i			1.35193i
$956$	−4.84090e46	+	2.51808e46i	−0.0994489	+	0.0517301i
$957$	−4.14026e47			−0.836443
$958$	3.32414e47	−	5.47607e47i	0.660436	−	1.08798i
$959$			3.98605e46i			0.0778834i
$960$	9.25363e46	−	6.97796e47i	0.177817	−	1.34088i
$961$	−1.29031e48			−2.43848
$962$	−1.04171e47	−	6.32347e46i	−0.193617	−	0.117531i
$963$		−	4.14802e46i		−	0.0758263i
$964$	9.00999e46	+	1.73213e47i	0.161991	+	0.311422i
$965$	2.17765e46			0.0385080
$966$	3.10820e45	−	5.12033e45i	0.00540598	−	0.00890562i
$967$			8.33368e47i			1.42565i	0.701342	+	0.712825i	$0.252585\pi$
$967$			8.33368e47i			1.42565i	−0.701342	+	0.712825i	$0.747415\pi$
$968$	−5.05485e46	+	7.65687e47i	−0.0850555	+	1.28838i
$969$	4.93731e47			0.817166
$970$	1.28560e48	+	7.80399e47i	2.09295	+	1.27048i
$971$		−	8.37495e47i		−	1.34114i	−0.741846	−	0.670571i	$-0.766049\pi$
$971$		−	8.37495e47i		−	1.34114i	0.741846	−	0.670571i	$-0.233951\pi$
$972$	1.08870e47	−	5.66306e46i	0.171494	−	0.0892054i
$973$	−3.83952e46			−0.0594937
$974$	−1.62831e47	+	2.68243e47i	−0.248196	+	0.408869i
$975$			6.92094e47i			1.03775i
$976$	−3.22174e47	+	4.59496e47i	−0.475218	+	0.677774i
$977$	−7.41388e45			−0.0107580			−0.00537901	−	0.999986i	$-0.501712\pi$
$977$	−7.41388e45			−0.0107580			−0.00537901	+	0.999986i	$0.501712\pi$
$978$	−2.19221e47	−	1.33074e47i	−0.312940	−	0.189964i
$979$			7.19485e47i			1.01041i
$980$	−4.72018e47	−	9.07435e47i	−0.652141	−	1.25371i
$981$	−5.70175e46			−0.0775004
$982$	−1.42127e47	+	2.34136e47i	−0.190061	+	0.313100i
$983$		−	5.93909e47i		−	0.781382i	−0.920522	−	0.390691i	$-0.872236\pi$
$983$		−	5.93909e47i		−	0.781382i	0.920522	−	0.390691i	$-0.127764\pi$
$984$	2.07655e47	+	1.37088e46i	0.268795	+	0.0177451i
$985$	−2.09093e48			−2.66294
$986$	5.34803e47	+	3.24642e47i	0.670137	+	0.406793i
$987$		−	9.96226e46i		−	0.122824i
$988$	4.96492e47	−	2.58259e47i	0.602284	−	0.313288i
$989$	−1.23807e47			−0.147776
$990$	−9.23468e46	+	1.52129e47i	−0.108457	+	0.178669i
$991$		−	5.19983e47i		−	0.600911i	−0.953796	−	0.300456i	$-0.902861\pi$
$991$		−	5.19983e47i		−	0.600911i	0.953796	−	0.300456i	$-0.0971388\pi$
$992$	−6.55579e47	−	1.49310e48i	−0.745484	−	1.69786i
$993$	−7.21545e46			−0.0807375
$994$	4.10710e46	+	2.49313e46i	0.0452224	+	0.0274513i
$995$		−	3.49223e47i		−	0.378385i
$996$	5.06493e47	+	9.73711e47i	0.540037	+	1.03820i
$997$	1.07840e48			1.13150			0.565752	−	0.824575i	$-0.308586\pi$
$997$	1.07840e48			1.13150			0.565752	+	0.824575i	$0.308586\pi$
$998$	7.43436e47	−	1.22471e48i	0.767636	−	1.26458i
$999$			2.18329e47i			0.221852i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.33.b.b.3.3	✓	14
3.2	odd	2		36.33.d.b.19.12		14
4.3	odd	2	inner	4.33.b.b.3.4	yes	14
12.11	even	2		36.33.d.b.19.11		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.33.b.b.3.3	✓	14	1.1	even	1	trivial
4.33.b.b.3.4	yes	14	4.3	odd	2	inner
36.33.d.b.19.11		14	12.11	even	2
36.33.d.b.19.12		14	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:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 33 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-56022.2 - 34007.1i) q^{2} -4.09055e7i q^{3} +(1.98200e9 + 3.81031e9i) q^{4} -2.17196e11 q^{5} +(-1.39108e12 + 2.29162e12i) q^{6} -2.81808e12i q^{7} +(1.85418e13 - 2.80864e14i) q^{8} +1.79757e14 q^{9} +O(q^{10})\)	\(q+(-56022.2 - 34007.1i) q^{2} -4.09055e7i q^{3} +(1.98200e9 + 3.81031e9i) q^{4} -2.17196e11 q^{5} +(-1.39108e12 + 2.29162e12i) q^{6} -2.81808e12i q^{7} +(1.85418e13 - 2.80864e14i) q^{8} +1.79757e14 q^{9} +(1.21678e16 + 7.38622e15i) q^{10} +6.95526e16i q^{11} +(1.55863e17 - 8.10747e16i) q^{12} -7.08184e17 q^{13} +(-9.58347e16 + 1.57875e17i) q^{14} +8.88453e18i q^{15} +(-1.05901e19 + 1.51040e19i) q^{16} +6.55998e19 q^{17} +(-1.00704e19 - 6.11302e18i) q^{18} +1.83995e20i q^{19} +(-4.30482e20 - 8.27584e20i) q^{20} -1.15275e20 q^{21} +(2.36528e21 - 3.89649e21i) q^{22} -7.92873e20i q^{23} +(-1.14889e22 - 7.58463e20i) q^{24} +2.38911e22 q^{25} +(3.96740e22 + 2.40833e22i) q^{26} -8.31519e22i q^{27} +(1.07377e22 - 5.58542e21i) q^{28} -1.45523e23 q^{29} +(3.02137e23 - 4.97731e23i) q^{30} -1.34887e24i q^{31} +(1.10693e24 - 4.86021e23i) q^{32} +2.84509e24 q^{33} +(-3.67504e24 - 2.23086e24i) q^{34} +6.12075e23i q^{35} +(3.56278e23 + 6.84930e23i) q^{36} -2.62567e24 q^{37} +(6.25715e24 - 1.03078e25i) q^{38} +2.89686e25i q^{39} +(-4.02721e24 + 6.10025e25i) q^{40} -1.80745e25 q^{41} +(6.45795e24 + 3.92017e24i) q^{42} -1.56149e26i q^{43} +(-2.65017e26 + 1.37853e26i) q^{44} -3.90426e25 q^{45} +(-2.69633e25 + 4.44185e25i) q^{46} +8.64218e26i q^{47} +(6.17839e26 + 4.33194e26i) q^{48} +1.09649e27 q^{49} +(-1.33843e27 - 8.12470e26i) q^{50} -2.68339e27i q^{51} +(-1.40362e27 - 2.69840e27i) q^{52} +5.50243e27 q^{53} +(-2.82776e27 + 4.65835e27i) q^{54} -1.51066e28i q^{55} +(-7.91495e26 - 5.22522e25i) q^{56} +7.52642e27 q^{57} +(8.15252e27 + 4.94882e27i) q^{58} +9.48554e27i q^{59} +(-3.38528e28 + 1.76091e28i) q^{60} +3.04221e28 q^{61} +(-4.58712e28 + 7.55666e28i) q^{62} -5.06569e26i q^{63} +(-7.85406e28 - 1.04154e28i) q^{64} +1.53815e29 q^{65} +(-1.59388e29 - 9.67532e28i) q^{66} -7.40203e28i q^{67} +(1.30019e29 + 2.49955e29i) q^{68} -3.24329e28 q^{69} +(2.08149e28 - 3.42898e28i) q^{70} -2.60149e29i q^{71} +(3.33302e27 - 5.04872e28i) q^{72} +3.70906e29 q^{73} +(1.47095e29 + 8.92914e28i) q^{74} -9.77280e29i q^{75} +(-7.01078e29 + 3.64678e29i) q^{76} +1.96004e29 q^{77} +(9.85140e29 - 1.62289e30i) q^{78} +2.10671e30i q^{79} +(2.30013e30 - 3.28054e30i) q^{80} -3.06828e30 q^{81} +(1.01257e30 + 6.14660e29i) q^{82} +6.24724e30i q^{83} +(-2.28475e29 - 4.39233e29i) q^{84} -1.42480e31 q^{85} +(-5.31019e30 + 8.74783e30i) q^{86} +5.95270e30i q^{87} +(1.95348e31 + 1.28963e30i) q^{88} +1.03445e31 q^{89} +(2.18725e30 + 1.32773e30i) q^{90} +1.99572e30i q^{91} +(3.02109e30 - 1.57147e30i) q^{92} -5.51763e31 q^{93} +(2.93896e31 - 4.84153e31i) q^{94} -3.99630e31i q^{95} +(-1.98809e31 - 4.52794e31i) q^{96} +1.05656e32 q^{97} +(-6.14275e31 - 3.72883e31i) q^{98} +1.25026e31i 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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