LMFDB - Embedded newform 4.33.b.b.3.6

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			3.6
Root			$1.78456e6i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.33.b.b.3.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-18058.8 + 62998.8i) q^{2} +2.85529e7i q^{3} +(-3.64273e9 - 2.27536e9i) q^{4} +1.21258e11 q^{5} +(-1.79880e12 - 5.15631e11i) q^{6} -3.17263e10i q^{7} +(2.09128e14 - 1.88397e14i) q^{8} +1.03775e15 q^{9} +O(q^{10})$	\(q+(-18058.8 + 62998.8i) q^{2} +2.85529e7i q^{3} +(-3.64273e9 - 2.27536e9i) q^{4} +1.21258e11 q^{5} +(-1.79880e12 - 5.15631e11i) q^{6} -3.17263e10i q^{7} +(2.09128e14 - 1.88397e14i) q^{8} +1.03775e15 q^{9} +(-2.18978e15 + 7.63913e15i) q^{10} +6.68515e16i q^{11} +(6.49683e16 - 1.04011e17i) q^{12} +5.92013e17 q^{13} +(1.99872e15 + 5.72939e14i) q^{14} +3.46228e18i q^{15} +(8.09220e18 + 1.65771e19i) q^{16} +4.82732e19 q^{17} +(-1.87405e19 + 6.53770e19i) q^{18} -9.57586e19i q^{19} +(-4.41711e20 - 2.75907e20i) q^{20} +9.05881e17 q^{21} +(-4.21156e21 - 1.20726e21i) q^{22} -5.33527e20i q^{23} +(5.37930e21 + 5.97123e21i) q^{24} -8.57947e21 q^{25} +(-1.06910e22 + 3.72961e22i) q^{26} +8.25400e22i q^{27} +(-7.21889e19 + 1.15570e20i) q^{28} -4.06224e23 q^{29} +(-2.18120e23 - 6.25246e22i) q^{30} +4.12012e23i q^{31} +(-1.19047e24 + 2.10438e23i) q^{32} -1.90881e24 q^{33} +(-8.71755e23 + 3.04116e24i) q^{34} -3.84709e21i q^{35} +(-3.78024e24 - 2.36126e24i) q^{36} +1.13492e25 q^{37} +(6.03268e24 + 1.72928e24i) q^{38} +1.69037e25i q^{39} +(2.53586e25 - 2.28447e25i) q^{40} -2.76466e23 q^{41} +(-1.63591e22 + 5.70694e22i) q^{42} -1.68374e26i q^{43} +(1.52111e26 - 2.43522e26i) q^{44} +1.25836e26 q^{45} +(3.36116e25 + 9.63485e24i) q^{46} +7.88873e26i q^{47} +(-4.73324e26 + 2.31056e26i) q^{48} +1.10443e27 q^{49} +(1.54935e26 - 5.40496e26i) q^{50} +1.37834e27i q^{51} +(-2.15654e27 - 1.34704e27i) q^{52} -5.53595e27 q^{53} +(-5.19992e27 - 1.49057e27i) q^{54} +8.10630e27i q^{55} +(-5.97716e24 - 6.63488e24i) q^{56} +2.73419e27 q^{57} +(7.33590e27 - 2.55916e28i) q^{58} +4.25442e28i q^{59} +(7.87795e27 - 1.26122e28i) q^{60} +5.00768e28 q^{61} +(-2.59563e28 - 7.44043e27i) q^{62} -3.29240e25i q^{63} +(8.24109e27 - 7.87984e28i) q^{64} +7.17866e28 q^{65} +(3.44707e28 - 1.20253e29i) q^{66} +1.33261e29i q^{67} +(-1.75846e29 - 1.09839e29i) q^{68} +1.52338e28 q^{69} +(2.42362e26 + 6.94736e25i) q^{70} +5.68414e29i q^{71} +(2.17023e29 - 1.95509e29i) q^{72} -6.17148e29 q^{73} +(-2.04953e29 + 7.14989e29i) q^{74} -2.44969e29i q^{75} +(-2.17885e29 + 3.48823e29i) q^{76} +2.12095e27 q^{77} +(-1.06491e30 - 3.05261e29i) q^{78} -1.44347e30i q^{79} +(9.81247e29 + 2.01011e30i) q^{80} -4.33789e29 q^{81} +(4.99263e27 - 1.74170e28i) q^{82} -6.98874e30i q^{83} +(-3.29988e27 - 2.06121e27i) q^{84} +5.85353e30 q^{85} +(1.06074e31 + 3.04063e30i) q^{86} -1.15989e31i q^{87} +(1.25946e31 + 1.39805e31i) q^{88} -1.07508e31 q^{89} +(-2.27244e30 + 7.92750e30i) q^{90} -1.87824e28i q^{91} +(-1.21397e30 + 1.94350e30i) q^{92} -1.17642e31 q^{93} +(-4.96981e31 - 1.42461e31i) q^{94} -1.16115e31i q^{95} +(-6.00862e30 - 3.39914e31i) q^{96} -3.35405e31 q^{97} +(-1.99446e31 + 6.95775e31i) q^{98} +6.93751e31i 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 $

$2$	−18058.8	+	62998.8i	−0.275555	+	0.961285i
$2$	−18058.8	+	62998.8i	−0.275555	+	0.961285i
$3$			2.85529e7i			0.663301i	0.943402	+	0.331651i	$0.107606\pi$
$3$			2.85529e7i			0.663301i	−0.943402	+	0.331651i	$0.892394\pi$
$4$	−3.64273e9	−	2.27536e9i	−0.848139	−	0.529774i
$5$	1.21258e11			0.794679			0.397339	−	0.917672i	$-0.369934\pi$
$5$	1.21258e11			0.794679			0.397339	+	0.917672i	$0.369934\pi$
$6$	−1.79880e12	−	5.15631e11i	−0.637622	−	0.182776i
$7$		−	3.17263e10i		−	0.000954666i	−1.00000		0.000477333i	$-0.999848\pi$
$7$		−	3.17263e10i		−	0.000954666i	1.00000		0.000477333i	$-0.000151940\pi$
$8$	2.09128e14	−	1.88397e14i	0.742973	−	0.669322i
$9$	1.03775e15			0.560031
$10$	−2.18978e15	+	7.63913e15i	−0.218978	+	0.763913i
$11$			6.68515e16i			1.45488i	0.686169	+	0.727442i	$0.259291\pi$
$11$			6.68515e16i			1.45488i	−0.686169	+	0.727442i	$0.740709\pi$
$12$	6.49683e16	−	1.04011e17i	0.351400	−	0.562572i
$13$	5.92013e17			0.889688			0.444844	−	0.895608i	$-0.353259\pi$
$13$	5.92013e17			0.889688			0.444844	+	0.895608i	$0.353259\pi$
$14$	1.99872e15	+	5.72939e14i	0.000917706	+	0.000263063i
$15$			3.46228e18i			0.527112i
$16$	8.09220e18	+	1.65771e19i	0.438679	+	0.898644i
$17$	4.82732e19			0.992027			0.496014	−	0.868315i	$-0.334797\pi$
$17$	4.82732e19			0.992027			0.496014	+	0.868315i	$0.334797\pi$
$18$	−1.87405e19	+	6.53770e19i	−0.154319	+	0.538350i
$19$		−	9.57586e19i		−	0.331986i	−0.986127	−	0.165993i	$-0.946917\pi$
$19$		−	9.57586e19i		−	0.331986i	0.986127	−	0.165993i	$-0.0530830\pi$
$20$	−4.41711e20	−	2.75907e20i	−0.673998	−	0.421000i
$21$	9.05881e17			0.000633231
$22$	−4.21156e21	−	1.20726e21i	−1.39856	−	0.400900i
$23$		−	5.33527e20i		−	0.0869984i	−0.999053	−	0.0434992i	$-0.986149\pi$
$23$		−	5.33527e20i		−	0.0869984i	0.999053	−	0.0434992i	$-0.0138506\pi$
$24$	5.37930e21	+	5.97123e21i	0.443962	+	0.492815i
$25$	−8.57947e21			−0.368485
$26$	−1.06910e22	+	3.72961e22i	−0.245158	+	0.855244i
$27$			8.25400e22i			1.03477i
$28$	−7.21889e19	+	1.15570e20i	−0.000505757	+	0.000809689i
$29$	−4.06224e23			−1.62330			−0.811648	−	0.584147i	$-0.801429\pi$
$29$	−4.06224e23			−1.62330			−0.811648	+	0.584147i	$0.801429\pi$
$30$	−2.18120e23	−	6.25246e22i	−0.506705	−	0.145248i
$31$			4.12012e23i			0.566399i	0.959061	+	0.283200i	$0.0913959\pi$
$31$			4.12012e23i			0.566399i	−0.959061	+	0.283200i	$0.908604\pi$
$32$	−1.19047e24	+	2.10438e23i	−0.984733	+	0.174070i
$33$	−1.90881e24			−0.965026
$34$	−8.71755e23	+	3.04116e24i	−0.273358	+	0.953621i
$35$		−	3.84709e21i		−	0.000758653i
$36$	−3.78024e24	−	2.36126e24i	−0.474984	−	0.296690i
$37$	1.13492e25			0.919897			0.459949	−	0.887946i	$-0.347868\pi$
$37$	1.13492e25			0.919897			0.459949	+	0.887946i	$0.347868\pi$
$38$	6.03268e24	+	1.72928e24i	0.319134	+	0.0914805i
$39$			1.69037e25i			0.590131i
$40$	2.53586e25	−	2.28447e25i	0.590425	−	0.531896i
$41$	−2.76466e23			−0.00433610			−0.00216805	−	0.999998i	$-0.500690\pi$
$41$	−2.76466e23			−0.00433610			−0.00216805	+	0.999998i	$0.500690\pi$
$42$	−1.63591e22	+	5.70694e22i	−0.000174490	+	0.000608716i
$43$		−	1.68374e26i		−	1.23248i	−0.787559	−	0.616239i	$-0.788655\pi$
$43$		−	1.68374e26i		−	1.23248i	0.787559	−	0.616239i	$-0.211345\pi$
$44$	1.52111e26	−	2.43522e26i	0.770759	−	1.23394i
$45$	1.25836e26			0.445045
$46$	3.36116e25	+	9.63485e24i	0.0836303	+	0.0239728i
$47$			7.88873e26i			1.39137i	0.718349	+	0.695683i	$0.244898\pi$
$47$			7.88873e26i			1.39137i	−0.718349	+	0.695683i	$0.755102\pi$
$48$	−4.73324e26	+	2.31056e26i	−0.596072	+	0.290976i
$49$	1.10443e27			0.999999
$50$	1.54935e26	−	5.40496e26i	0.101538	−	0.354220i
$51$			1.37834e27i			0.658013i
$52$	−2.15654e27	−	1.34704e27i	−0.754579	−	0.471334i
$53$	−5.53595e27			−1.42816			−0.714082	−	0.700062i	$-0.753156\pi$
$53$	−5.53595e27			−1.42816			−0.714082	+	0.700062i	$0.753156\pi$
$54$	−5.19992e27	−	1.49057e27i	−0.994710	−	0.285136i
$55$			8.10630e27i			1.15617i
$56$	−5.97716e24	−	6.63488e24i	−0.000638979	−	0.000709291i
$57$	2.73419e27			0.220207
$58$	7.33590e27	−	2.55916e28i	0.447307	−	1.56045i
$59$			4.25442e28i			1.97337i	0.162647	+	0.986684i	$0.447997\pi$
$59$			4.25442e28i			1.97337i	−0.162647	+	0.986684i	$0.552003\pi$
$60$	7.87795e27	−	1.26122e28i	0.279250	−	0.447064i
$61$	5.00768e28			1.36257			0.681286	−	0.732018i	$-0.261421\pi$
$61$	5.00768e28			1.36257			0.681286	+	0.732018i	$0.261421\pi$
$62$	−2.59563e28	−	7.44043e27i	−0.544472	−	0.156074i
$63$		−	3.29240e25i		−	0.000534643i
$64$	8.24109e27	−	7.87984e28i	0.104017	−	0.994576i
$65$	7.17866e28			0.707017
$66$	3.44707e28	−	1.20253e29i	0.265918	−	0.927665i
$67$			1.33261e29i			0.808175i	0.914720	+	0.404087i	$0.132411\pi$
$67$			1.33261e29i			0.808175i	−0.914720	+	0.404087i	$0.867589\pi$
$68$	−1.75846e29	−	1.09839e29i	−0.841377	−	0.525550i
$69$	1.52338e28			0.0577062
$70$	2.42362e26	+	6.94736e25i	0.000729282	+	0.000209051i
$71$			5.68414e29i			1.36311i	0.731767	+	0.681555i	$0.238696\pi$
$71$			5.68414e29i			1.36311i	−0.731767	+	0.681555i	$0.761304\pi$
$72$	2.17023e29	−	1.95509e29i	0.416088	−	0.374841i
$73$	−6.17148e29			−0.948906			−0.474453	−	0.880281i	$-0.657354\pi$
$73$	−6.17148e29			−0.948906			−0.474453	+	0.880281i	$0.657354\pi$
$74$	−2.04953e29	+	7.14989e29i	−0.253482	+	0.884284i
$75$		−	2.44969e29i		−	0.244417i
$76$	−2.17885e29	+	3.48823e29i	−0.175878	+	0.281571i
$77$	2.12095e27			0.00138893
$78$	−1.06491e30	−	3.05261e29i	−0.567285	−	0.162614i
$79$		−	1.44347e30i		−	0.627152i	−0.949563	−	0.313576i	$-0.898473\pi$
$79$		−	1.44347e30i		−	0.627152i	0.949563	−	0.313576i	$-0.101527\pi$
$80$	9.81247e29	+	2.01011e30i	0.348609	+	0.714133i
$81$	−4.33789e29			−0.126333
$82$	4.99263e27	−	1.74170e28i	0.00119484	−	0.00416823i
$83$		−	6.98874e30i		−	1.37768i	−0.724912	−	0.688841i	$-0.758120\pi$
$83$		−	6.98874e30i		−	1.37768i	0.724912	−	0.688841i	$-0.241880\pi$
$84$	−3.29988e27	−	2.06121e27i	−0.000537068	−	0.000335469i
$85$	5.85353e30			0.788343
$86$	1.06074e31	+	3.04063e30i	1.18476	+	0.339616i
$87$		−	1.15989e31i		−	1.07673i
$88$	1.25946e31	+	1.39805e31i	0.973785	+	1.08094i
$89$	−1.07508e31			−0.693744			−0.346872	−	0.937912i	$-0.612756\pi$
$89$	−1.07508e31			−0.693744			−0.346872	+	0.937912i	$0.612756\pi$
$90$	−2.27244e30	+	7.92750e30i	−0.122634	+	0.427815i
$91$		−	1.87824e28i		−	0.000849355i
$92$	−1.21397e30	+	1.94350e30i	−0.0460895	+	0.0737867i
$93$	−1.17642e31			−0.375694
$94$	−4.96981e31	−	1.42461e31i	−1.33750	−	0.383398i
$95$		−	1.16115e31i		−	0.263823i
$96$	−6.00862e30	−	3.39914e31i	−0.115461	−	0.653175i
$97$	−3.35405e31			−0.546036			−0.273018	−	0.962009i	$-0.588022\pi$
$97$	−3.35405e31			−0.546036			−0.273018	+	0.962009i	$0.588022\pi$
$98$	−1.99446e31	+	6.95775e31i	−0.275555	+	0.961284i
$99$			6.93751e31i			0.814780i
$100$	3.12527e31	+	1.95214e31i	0.312527	+	0.195214i
$101$	1.12793e32			0.961922			0.480961	−	0.876742i	$-0.340288\pi$
$101$	1.12793e32			0.961922			0.480961	+	0.876742i	$0.340288\pi$
$102$	−8.68340e31	−	2.48912e31i	−0.632538	−	0.181319i
$103$			1.88551e32i			1.17499i	0.809228	+	0.587495i	$0.199886\pi$
$103$			1.88551e32i			1.17499i	−0.809228	+	0.587495i	$0.800114\pi$
$104$	1.23807e32	−	1.11534e32i	0.661014	−	0.595488i
$105$	1.09846e29			0.000503215
$106$	9.99725e31	−	3.48758e32i	0.393538	−	1.37287i
$107$		−	2.35968e31i		−	0.0799306i	−0.999201	−	0.0399653i	$-0.987275\pi$
$107$		−	2.35968e31i		−	0.0799306i	0.999201	−	0.0399653i	$-0.0127247\pi$
$108$	1.87808e32	−	3.00671e32i	0.548195	−	0.877629i
$109$	1.86142e32			0.468835			0.234417	−	0.972136i	$-0.424682\pi$
$109$	1.86142e32			0.468835			0.234417	+	0.972136i	$0.424682\pi$
$110$	−5.10687e32	−	1.46390e32i	−1.11140	−	0.318587i
$111$			3.24054e32i			0.610169i
$112$	5.25929e29	−	2.56736e29i	0.000857905	−	0.000418792i
$113$	6.55553e31			0.0927583			0.0463791	−	0.998924i	$-0.485232\pi$
$113$	6.55553e31			0.0927583			0.0463791	+	0.998924i	$0.485232\pi$
$114$	−4.93761e31	+	1.72251e32i	−0.0606791	+	0.211682i
$115$		−	6.46947e31i		−	0.0691358i
$116$	1.47976e33	+	9.24306e32i	1.37678	+	0.859979i
$117$	6.14362e32			0.498253
$118$	−2.68023e33	−	7.68296e32i	−1.89697	−	0.543772i
$119$		−	1.53153e30i		−	0.000947055i
$120$	6.52285e32	+	7.24061e32i	0.352807	+	0.391630i
$121$	−2.35775e33			−1.11669
$122$	−9.04326e32	+	3.15478e33i	−0.375463	+	1.30982i
$123$		−	7.89391e30i		−	0.00287614i
$124$	9.37476e32	−	1.50085e33i	0.300064	−	0.480385i
$125$	−3.86360e33			−1.08751
$126$	2.07417e30	+	5.94567e29i	0.000513944	+	0.000147324i
$127$		−	7.32371e33i		−	1.59908i	−0.600610	−	0.799542i	$-0.705075\pi$
$127$		−	7.32371e33i		−	1.59908i	0.600610	−	0.799542i	$-0.294925\pi$
$128$	4.81538e33	+	1.94218e33i	0.927408	+	0.374050i
$129$	4.80757e33			0.817505
$130$	−1.29638e33	+	4.52247e33i	−0.194822	+	0.679645i
$131$		−	7.71918e33i		−	1.02620i	−0.858330	−	0.513098i	$-0.828498\pi$
$131$		−	7.71918e33i		−	1.02620i	0.858330	−	0.513098i	$-0.171502\pi$
$132$	6.95327e33	+	4.34323e33i	0.818476	+	0.511246i
$133$	−3.03807e30			−0.000316936
$134$	−8.39526e33	−	2.40652e33i	−0.776887	−	0.222697i
$135$			1.00087e34i			0.822311i
$136$	1.00953e34	−	9.09455e33i	0.737049	−	0.663985i
$137$	2.27924e34			1.47999			0.739997	−	0.672610i	$-0.234827\pi$
$137$	2.27924e34			1.47999			0.739997	+	0.672610i	$0.234827\pi$
$138$	−2.75103e32	+	9.59710e32i	−0.0159012	+	0.0554721i
$139$		−	1.27157e34i		−	0.654791i	−0.944887	−	0.327396i	$-0.893829\pi$
$139$		−	1.27157e34i		−	0.654791i	0.944887	−	0.327396i	$-0.106171\pi$
$140$	−8.75351e30	+	1.40139e31i	−0.000401915	+	0.000643443i
$141$	−2.25247e34			−0.922895
$142$	−3.58094e34	−	1.02649e34i	−1.31034	−	0.375612i
$143$			3.95770e34i			1.29439i
$144$	8.39768e33	+	1.72028e34i	0.245674	+	0.503269i
$145$	−4.92580e34			−1.29000
$146$	1.11449e34	−	3.88796e34i	0.261476	−	0.912170i
$147$			3.15346e34i			0.663301i
$148$	−4.13422e34	−	2.58236e34i	−0.780201	−	0.487338i
$149$	3.99267e34			0.676524			0.338262	−	0.941052i	$-0.390161\pi$
$149$	3.99267e34			0.676524			0.338262	+	0.941052i	$0.390161\pi$
$150$	1.54328e34	+	4.42384e33i	0.234954	+	0.0673503i
$151$			7.15918e34i			0.980014i	0.871719	+	0.490007i	$0.163006\pi$
$151$			7.15918e34i			0.980014i	−0.871719	+	0.490007i	$0.836994\pi$
$152$	−1.80407e34	−	2.00258e34i	−0.222206	−	0.246657i
$153$	5.00955e34			0.555567
$154$	−3.83018e31	+	1.33618e32i	−0.000382726	+	0.00133516i
$155$			4.99599e34i			0.450106i
$156$	3.84621e34	−	6.15757e34i	0.312636	−	0.500513i
$157$	9.50355e34			0.697415			0.348707	−	0.937232i	$-0.386621\pi$
$157$	9.50355e34			0.697415			0.348707	+	0.937232i	$0.386621\pi$
$158$	9.09366e34	+	2.60672e34i	0.602872	+	0.172815i
$159$		−	1.58068e35i		−	0.947304i
$160$	−1.44354e35	+	2.55174e34i	−0.782547	+	0.138330i
$161$	−1.69269e31			−8.30544e−5
$162$	7.83370e33	−	2.73282e34i	0.0348118	−	0.121442i
$163$		−	4.30635e35i		−	1.73423i	−0.498106	−	0.867116i	$-0.665971\pi$
$163$		−	4.30635e35i		−	1.73423i	0.498106	−	0.867116i	$-0.334029\pi$
$164$	1.00709e33	+	6.29060e32i	0.00367762	+	0.00229716i
$165$	−2.31459e35			−0.766886
$166$	4.40282e35	+	1.26208e35i	1.32435	+	0.379627i
$167$			2.79090e35i			0.762572i	0.924457	+	0.381286i	$0.124519\pi$
$167$			2.79090e35i			0.762572i	−0.924457	+	0.381286i	$0.875481\pi$
$168$	1.89445e32	−	1.70665e32i	0.000470474	−	0.000423835i
$169$	−9.22994e34			−0.208455
$170$	−1.05708e35	+	3.68766e35i	−0.217232	+	0.757823i
$171$		−	9.93735e34i		−	0.185923i
$172$	−3.83111e35	+	6.13340e35i	−0.652935	+	1.04531i
$173$	5.12088e34			0.0795439			0.0397719	−	0.999209i	$-0.487337\pi$
$173$	5.12088e34			0.0795439			0.0397719	+	0.999209i	$0.487337\pi$
$174$	7.30716e35	+	2.09462e35i	1.03505	+	0.296699i
$175$			2.72195e32i			0.000351781i
$176$	−1.10820e36	+	5.40976e35i	−1.30742	+	0.638227i
$177$	−1.21476e36			−1.30894
$178$	1.94146e35	−	6.77285e35i	0.191165	−	0.666886i
$179$		−	1.91323e36i		−	1.72234i	−0.508315	−	0.861172i	$-0.669731\pi$
$179$		−	1.91323e36i		−	1.72234i	0.508315	−	0.861172i	$-0.330269\pi$
$180$	−4.58386e35	−	2.86322e35i	−0.377460	−	0.235773i
$181$	1.04359e36			0.786450			0.393225	−	0.919442i	$-0.371359\pi$
$181$	1.04359e36			0.786450			0.393225	+	0.919442i	$0.371359\pi$
$182$	1.18327e33	+	3.39187e32i	0.000816473	+	0.000234044i
$183$			1.42984e36i			0.903795i
$184$	−1.00515e35	−	1.11576e35i	−0.0582299	−	0.0646374i
$185$	1.37619e36			0.731023
$186$	2.12446e35	−	7.41128e35i	0.103524	−	0.361149i
$187$			3.22714e36i			1.44328i
$188$	1.79497e36	−	2.87365e36i	0.737110	−	1.18007i
$189$	2.61869e33			0.000987860
$190$	7.31513e35	+	2.09690e35i	0.253609	+	0.0726976i
$191$		−	1.14601e36i		−	0.365304i	−0.983178	−	0.182652i	$-0.941532\pi$
$191$		−	1.14601e36i		−	0.365304i	0.983178	−	0.182652i	$-0.0584681\pi$
$192$	2.24993e36	+	2.35307e35i	0.659703	+	0.0689947i
$193$	3.03069e36			0.817757			0.408878	−	0.912589i	$-0.365920\pi$
$193$	3.03069e36			0.817757			0.408878	+	0.912589i	$0.365920\pi$
$194$	6.05700e35	−	2.11301e36i	0.150463	−	0.524897i
$195$			2.04972e36i			0.468965i
$196$	−4.02313e36	−	2.51297e36i	−0.848138	−	0.529773i
$197$	−2.82588e36			−0.549154			−0.274577	−	0.961565i	$-0.588538\pi$
$197$	−2.82588e36			−0.549154			−0.274577	+	0.961565i	$0.588538\pi$
$198$	−4.37055e36	−	1.25283e36i	−0.783236	−	0.224517i
$199$			4.12362e36i			0.681757i	0.940107	+	0.340879i	$0.110725\pi$
$199$			4.12362e36i			0.681757i	−0.940107	+	0.340879i	$0.889275\pi$
$200$	−1.79421e36	+	1.61635e36i	−0.273775	+	0.246635i
$201$	−3.80499e36			−0.536063
$202$	−2.03690e36	+	7.10582e36i	−0.265062	+	0.924681i
$203$			1.28880e34i			0.00154970i
$204$	3.13623e36	−	5.02093e36i	0.348598	−	0.558087i
$205$	−3.35238e34			−0.00344581
$206$	−1.18785e37	−	3.40501e36i	−1.12950	−	0.323774i
$207$		−	5.53668e35i		−	0.0487218i
$208$	4.79069e36	+	9.81384e36i	0.390288	+	0.799513i
$209$	6.40161e36			0.483001
$210$	−1.98368e33	+	6.92014e33i	−0.000138664	+	0.000483734i
$211$		−	8.72796e36i		−	0.565449i	−0.959201	−	0.282725i	$-0.908762\pi$
$211$		−	8.72796e36i		−	0.565449i	0.959201	−	0.282725i	$-0.0912382\pi$
$212$	2.01660e37	+	1.25963e37i	1.21128	+	0.756605i
$213$	−1.62299e37			−0.904153
$214$	1.48657e36	+	4.26130e35i	0.0768361	+	0.0220253i
$215$		−	2.04167e37i		−	0.979425i
$216$	1.55503e37	+	1.72614e37i	0.692594	+	0.768807i
$217$	1.30716e34			0.000540722
$218$	−3.36149e36	+	1.17267e37i	−0.129190	+	0.450684i
$219$		−	1.76214e37i		−	0.629411i
$220$	1.84448e37	−	2.95291e37i	0.612506	−	0.980589i
$221$	2.85784e37			0.882595
$222$	−2.04150e37	−	5.85202e36i	−0.586547	−	0.168135i
$223$		−	3.46341e37i		−	0.926033i	−0.886350	−	0.463016i	$-0.846767\pi$
$223$		−	3.46341e37i		−	0.926033i	0.886350	−	0.463016i	$-0.153233\pi$
$224$	6.67642e33	+	3.77692e34i	0.000166179	+	0.000940091i
$225$	−8.90334e36			−0.206363
$226$	−1.18385e36	+	4.12990e36i	−0.0255600	+	0.0891671i
$227$			4.61174e37i			0.927794i	0.885889	+	0.463897i	$0.153549\pi$
$227$			4.61174e37i			0.927794i	−0.885889	+	0.463897i	$0.846451\pi$
$228$	−9.95992e36	−	6.22127e36i	−0.186766	−	0.116660i
$229$	−2.33950e37			−0.409030			−0.204515	−	0.978863i	$-0.565562\pi$
$229$	−2.33950e37			−0.409030			−0.204515	+	0.978863i	$0.565562\pi$
$230$	4.07569e36	+	1.16831e36i	0.0664592	+	0.0190507i
$231$			6.05595e34i			0.000921278i
$232$	−8.49529e37	+	7.65315e37i	−1.20606	+	1.08651i
$233$	2.24295e37			0.297252			0.148626	−	0.988893i	$-0.452515\pi$
$233$	2.24295e37			0.297252			0.148626	+	0.988893i	$0.452515\pi$
$234$	−1.10946e37	+	3.87040e37i	−0.137296	+	0.478964i
$235$			9.56575e37i			1.10569i
$236$	9.68035e37	−	1.54977e38i	1.04544	−	1.67369i
$237$	4.12152e37			0.415991
$238$	9.64848e34	+	2.76576e34i	0.000910390	+	0.000260966i
$239$			7.63924e37i			0.674037i	0.941498	+	0.337018i	$0.109418\pi$
$239$			7.63924e37i			0.674037i	−0.941498	+	0.337018i	$0.890582\pi$
$240$	−5.73945e37	+	2.80175e37i	−0.473685	+	0.231233i
$241$	−2.15781e38			−1.66625			−0.833124	−	0.553086i	$-0.813450\pi$
$241$	−2.15781e38			−1.66625			−0.833124	+	0.553086i	$0.813450\pi$
$242$	4.25780e37	−	1.48535e38i	0.307708	−	1.07345i
$243$			1.40562e38i			0.950974i
$244$	−1.82416e38	−	1.13943e38i	−1.15565	−	0.721855i
$245$	1.33921e38			0.794678
$246$	4.97307e35	+	1.42554e35i	0.00276479	+	0.000792536i
$247$		−	5.66904e37i		−	0.295364i
$248$	7.76220e37	+	8.61634e37i	0.379103	+	0.420819i
$249$	1.99549e38			0.913819
$250$	6.97719e37	−	2.43402e38i	0.299668	−	1.04540i
$251$		−	3.23115e38i		−	1.30190i	−0.759121	−	0.650949i	$-0.774371\pi$
$251$		−	3.23115e38i		−	1.30190i	0.759121	−	0.650949i	$-0.225629\pi$
$252$	−7.49140e34	+	1.19933e35i	−0.000283240	+	0.000453451i
$253$	3.56671e37			0.126573
$254$	4.61385e38	+	1.32257e38i	1.53718	+	0.440636i
$255$			1.67136e38i			0.522909i
$256$	−2.09315e38	+	2.68290e38i	−0.615121	+	0.788433i
$257$	3.79367e38			1.04744			0.523721	−	0.851890i	$-0.324543\pi$
$257$	3.79367e38			1.04744			0.523721	+	0.851890i	$0.324543\pi$
$258$	−8.68188e37	+	3.02871e38i	−0.225268	+	0.785855i
$259$		−	3.60070e35i		−	0.000878195i
$260$	−2.61499e38	−	1.63340e38i	−0.599648	−	0.374559i
$261$	−4.21559e38			−0.909096
$262$	4.86299e38	+	1.39399e38i	0.986467	+	0.282774i
$263$		−	5.28506e38i		−	1.00869i	−0.863502	−	0.504345i	$-0.831734\pi$
$263$		−	5.28506e38i		−	1.00869i	0.863502	−	0.504345i	$-0.168266\pi$
$264$	−3.99186e38	+	3.59614e38i	−0.716988	+	0.645913i
$265$	−6.71281e38			−1.13493
$266$	5.48638e34	−	1.91395e35i	8.73333e−5	−	0.000304666i
$267$		−	3.06966e38i		−	0.460161i
$268$	3.03216e38	−	4.85433e38i	0.428150	−	0.685444i
$269$	−7.48552e38			−0.995831			−0.497916	−	0.867226i	$-0.665901\pi$
$269$	−7.48552e38			−0.995831			−0.497916	+	0.867226i	$0.665901\pi$
$270$	−6.30534e38	−	1.80744e38i	−0.790475	−	0.226592i
$271$			1.81220e38i			0.214140i	0.994251	+	0.107070i	$0.0341469\pi$
$271$			1.81220e38i			0.214140i	−0.994251	+	0.107070i	$0.965853\pi$
$272$	3.90637e38	+	8.00228e38i	0.435182	+	0.891479i
$273$	5.36293e35			0.000563378
$274$	−4.11602e38	+	1.43589e39i	−0.407820	+	1.42270i
$275$		−	5.73551e38i		−	0.536103i
$276$	−5.54925e37	−	3.46624e37i	−0.0489428	−	0.0305712i
$277$	5.50087e38			0.457884			0.228942	−	0.973440i	$-0.426473\pi$
$277$	5.50087e38			0.457884			0.228942	+	0.973440i	$0.426473\pi$
$278$	8.01073e38	+	2.29630e38i	0.629441	+	0.180431i
$279$			4.27565e38i			0.317201i
$280$	−7.24780e35	−	8.04534e35i	−0.000507783	−	0.000563658i
$281$	2.00956e39			1.32984			0.664921	−	0.746914i	$-0.268465\pi$
$281$	2.00956e39			1.32984			0.664921	+	0.746914i	$0.268465\pi$
$282$	4.06768e38	−	1.41903e39i	0.254308	−	0.887166i
$283$			1.10638e39i			0.653613i	0.945091	+	0.326806i	$0.105973\pi$
$283$			1.10638e39i			0.653613i	−0.945091	+	0.326806i	$0.894027\pi$
$284$	1.29335e39	−	2.07058e39i	0.722140	−	1.15611i
$285$	3.31544e38			0.174994
$286$	−2.49330e39	−	7.14712e38i	−1.24428	−	0.356676i
$287$			8.77125e33i			4.13953e-6i
$288$	−1.23541e39	+	2.18382e38i	−0.551482	+	0.0974847i
$289$	−3.76060e37			−0.0158815
$290$	8.89540e38	−	3.10320e39i	0.355465	−	1.24006i
$291$		−	9.57680e38i		−	0.362187i
$292$	2.24810e39	+	1.40423e39i	0.804804	+	0.502706i
$293$	1.58688e39			0.537851			0.268926	−	0.963161i	$-0.413331\pi$
$293$	1.58688e39			0.537851			0.268926	+	0.963161i	$0.413331\pi$
$294$	−1.98664e39	−	5.69477e38i	−0.637621	−	0.182776i
$295$			5.15884e39i			1.56819i
$296$	2.37345e39	−	2.13817e39i	0.683459	−	0.615707i
$297$	−5.51792e39			−1.50547
$298$	−7.21028e38	+	2.51534e39i	−0.186420	+	0.650333i
$299$		−	3.15855e38i		−	0.0774015i
$300$	−5.57393e38	+	8.92356e38i	−0.129486	+	0.207299i
$301$	−5.34189e36			−0.00117661
$302$	−4.51020e39	−	1.29286e39i	−0.942073	−	0.270048i
$303$			3.22057e39i			0.638044i
$304$	1.58740e39	−	7.74898e38i	0.298337	−	0.145636i
$305$	6.07223e39			1.08281
$306$	−9.04664e38	+	3.15596e39i	−0.153089	+	0.534058i
$307$		−	5.18035e38i		−	0.0832042i	−0.999134	−	0.0416021i	$-0.986754\pi$
$307$		−	5.18035e38i		−	0.0832042i	0.999134	−	0.0416021i	$-0.0132462\pi$
$308$	−7.72606e36	−	4.82594e36i	−0.00117800	−	0.000735818i
$309$	−5.38370e39			−0.779373
$310$	−3.14741e39	−	9.02215e38i	−0.432680	−	0.124029i
$311$		−	4.91084e39i		−	0.641194i	−0.947216	−	0.320597i	$-0.896117\pi$
$311$		−	4.91084e39i		−	0.641194i	0.947216	−	0.320597i	$-0.103883\pi$
$312$	3.18462e39	+	3.53505e39i	0.394988	+	0.438452i
$313$	−3.57734e39			−0.421552			−0.210776	−	0.977534i	$-0.567599\pi$
$313$	−3.57734e39			−0.421552			−0.210776	+	0.977534i	$0.567599\pi$
$314$	−1.71622e39	+	5.98712e39i	−0.192176	+	0.670415i
$315$		−	3.99231e36i		−	0.000424869i
$316$	−3.28441e39	+	5.25816e39i	−0.332249	+	0.531912i
$317$	5.68505e39			0.546746			0.273373	−	0.961908i	$-0.411861\pi$
$317$	5.68505e39			0.546746			0.273373	+	0.961908i	$0.411861\pi$
$318$	9.95808e39	+	2.85451e39i	0.910629	+	0.261034i
$319$		−	2.71567e40i		−	2.36171i
$320$	9.99301e38	−	9.55496e39i	0.0826602	−	0.790368i
$321$	6.73759e38			0.0530181
$322$	3.05679e35	−	1.06637e36i	2.28861e−5	−	7.98390e-5i
$323$		−	4.62258e39i		−	0.329340i
$324$	1.58018e39	+	9.87027e38i	0.107148	+	0.0669282i
$325$	−5.07916e39			−0.327837
$326$	2.71295e40	+	7.77673e39i	1.66709	+	0.477876i
$327$			5.31490e39i			0.310979i
$328$	−5.78168e37	+	5.20854e37i	−0.00322161	+	0.00290225i
$329$	2.50281e37			0.00132829
$330$	4.17986e39	−	1.45816e40i	0.211319	−	0.737196i
$331$			1.18264e40i			0.569643i	0.958581	+	0.284822i	$0.0919344\pi$
$331$			1.18264e40i			0.569643i	−0.958581	+	0.284822i	$0.908066\pi$
$332$	−1.59019e40	+	2.54581e40i	−0.729860	+	1.16847i
$333$	1.17777e40			0.515171
$334$	−1.75823e40	−	5.04002e39i	−0.733049	−	0.210130i
$335$			1.61590e40i			0.642239i
$336$	7.33057e36	+	1.50168e37i	0.000277785	+	0.000569049i
$337$	2.80251e39			0.101267			0.0506336	−	0.998717i	$-0.483876\pi$
$337$	2.80251e39			0.101267			0.0506336	+	0.998717i	$0.483876\pi$
$338$	1.66681e39	−	5.81475e39i	0.0574407	−	0.200384i
$339$			1.87180e39i			0.0615267i
$340$	−2.13228e40	−	1.33189e40i	−0.668625	−	0.417644i
$341$	−2.75436e40			−0.824045
$342$	6.26041e39	+	1.79456e39i	0.178725	+	0.0512320i
$343$		−	7.00789e37i		−	0.00190933i
$344$	−3.17212e40	−	3.52117e40i	−0.824925	−	0.915698i
$345$	1.84722e39			0.0458579
$346$	−9.24768e38	+	3.22609e39i	−0.0219187	+	0.0764644i
$347$			2.15434e40i			0.487577i	0.969828	+	0.243789i	$0.0783903\pi$
$347$			2.15434e40i			0.487577i	−0.969828	+	0.243789i	$0.921610\pi$
$348$	−2.63917e40	+	4.22516e40i	−0.570425	+	0.913220i
$349$	−2.12404e40			−0.438486			−0.219243	−	0.975670i	$-0.570359\pi$
$349$	−2.12404e40			−0.438486			−0.219243	+	0.975670i	$0.570359\pi$
$350$	−1.71480e37	−	4.91551e36i	−0.000338161	−	9.69349e-5i
$351$			4.88648e40i			0.920623i
$352$	−1.40681e40	−	7.95847e40i	−0.253252	−	1.43267i
$353$	6.57081e40			1.13038			0.565189	−	0.824961i	$-0.308803\pi$
$353$	6.57081e40			1.13038			0.565189	+	0.824961i	$0.308803\pi$
$354$	2.19371e40	−	7.65286e40i	0.360684	−	1.25826i
$355$			6.89249e40i			1.08324i
$356$	3.91621e40	+	2.44619e40i	0.588391	+	0.367528i
$357$	4.37298e37			0.000628183
$358$	1.20531e41	+	3.45507e40i	1.65566	+	0.474600i
$359$		−	5.03977e40i		−	0.662064i	−0.943620	−	0.331032i	$-0.892603\pi$
$359$		−	5.03977e40i		−	0.662064i	0.943620	−	0.331032i	$-0.107397\pi$
$360$	2.63158e40	−	2.37071e40i	0.330656	−	0.297878i
$361$	7.40287e40			0.889785
$362$	−1.88459e40	+	6.57447e40i	−0.216710	+	0.756003i
$363$		−	6.73206e40i		−	0.740699i
$364$	−4.27368e37	+	6.84193e37i	−0.000449966	+	0.000720371i
$365$	−7.48343e40			−0.754076
$366$	−9.00782e40	−	2.58212e40i	−0.868805	−	0.249045i
$367$		−	1.14455e41i		−	1.05676i	−0.849008	−	0.528380i	$-0.822800\pi$
$367$		−	1.14455e41i		−	1.05676i	0.849008	−	0.528380i	$-0.177200\pi$
$368$	8.84431e39	−	4.31741e39i	0.0781806	−	0.0381644i
$369$	−2.86902e38			−0.00242835
$370$	−2.48523e40	+	8.66984e40i	−0.201437	+	0.702722i
$371$			1.75636e38i			0.00136342i
$372$	4.28536e40	+	2.67677e40i	0.318640	+	0.199033i
$373$	1.14383e40			0.0814742			0.0407371	−	0.999170i	$-0.487029\pi$
$373$	1.14383e40			0.0814742			0.0407371	+	0.999170i	$0.487029\pi$
$374$	−2.03306e41	−	5.82782e40i	−1.38741	−	0.397704i
$375$		−	1.10317e41i		−	0.721344i
$376$	1.48622e41	+	1.64976e41i	0.931272	+	1.03375i
$377$	−2.40490e41			−1.44423
$378$	−4.72904e37	+	1.64974e38i	−0.000272210	+	0.000949616i
$379$		−	1.18219e41i		−	0.652321i	−0.945314	−	0.326161i	$-0.894245\pi$
$379$		−	1.18219e41i		−	0.652321i	0.945314	−	0.326161i	$-0.105755\pi$
$380$	−2.64204e40	+	4.22977e40i	−0.139766	+	0.223758i
$381$	2.09113e41			1.06067
$382$	7.21972e40	+	2.06955e40i	0.351161	+	0.100661i
$383$			3.95929e41i			1.84687i	0.383751	+	0.923437i	$0.374632\pi$
$383$			3.95929e41i			1.84687i	−0.383751	+	0.923437i	$0.625368\pi$
$384$	−5.54550e40	+	1.37493e41i	−0.248108	+	0.615151i
$385$	2.57183e38			0.00110375
$386$	−5.47305e40	+	1.90930e41i	−0.225337	+	0.786098i
$387$		−	1.74730e41i		−	0.690227i
$388$	1.22179e41	+	7.63167e40i	0.463115	+	0.289276i
$389$	−5.23472e41			−1.90414			−0.952072	−	0.305874i	$-0.901052\pi$
$389$	−5.23472e41			−1.90414			−0.952072	+	0.305874i	$0.901052\pi$
$390$	−1.29130e41	−	3.70154e40i	−0.450809	−	0.129226i
$391$		−	2.57551e40i		−	0.0863048i
$392$	2.30967e41	−	2.08071e41i	0.742972	−	0.669321i
$393$	2.20405e41			0.680677
$394$	5.10319e40	−	1.78027e41i	0.151322	−	0.527893i
$395$		−	1.75032e41i		−	0.498385i
$396$	1.57853e41	−	2.52715e41i	0.431649	−	0.691047i
$397$	2.03759e41			0.535143			0.267571	−	0.963538i	$-0.413779\pi$
$397$	2.03759e41			0.535143			0.267571	+	0.963538i	$0.413779\pi$
$398$	−2.59783e41	−	7.44676e40i	−0.655363	−	0.187862i
$399$		−	8.67459e37i		−	0.000210224i
$400$	−6.94268e40	−	1.42222e41i	−0.161647	−	0.331137i
$401$	5.34108e41			1.19487			0.597433	−	0.801919i	$-0.296187\pi$
$401$	5.34108e41			1.19487			0.597433	+	0.801919i	$0.296187\pi$
$402$	6.87134e40	−	2.39710e41i	0.147715	−	0.515310i
$403$			2.43917e41i			0.503919i
$404$	−4.10874e41	−	2.56645e41i	−0.815843	−	0.509601i
$405$	−5.26006e40			−0.100395
$406$	−8.11928e38	−	2.32741e38i	−0.00148971	−	0.000427029i
$407$			7.58714e41i			1.33834i
$408$	2.59676e41	+	2.88250e41i	0.440422	+	0.488886i
$409$	3.50235e41			0.571199			0.285599	−	0.958349i	$-0.407807\pi$
$409$	3.50235e41			0.571199			0.285599	+	0.958349i	$0.407807\pi$
$410$	6.05399e38	−	2.11196e39i	0.000949510	−	0.00331241i
$411$			6.50789e41i			0.981683i
$412$	4.29023e41	−	6.86842e41i	0.622479	−	0.996555i
$413$	1.34977e39			0.00188391
$414$	3.48804e40	+	9.99856e39i	0.0468356	+	0.0134255i
$415$		−	8.47443e41i		−	1.09482i
$416$	−7.04774e41	+	1.24582e41i	−0.876106	+	0.154868i
$417$	3.63070e41			0.434324
$418$	−1.15605e41	+	4.03294e41i	−0.133093	+	0.464302i
$419$		−	9.79209e40i		−	0.108505i	−0.998527	−	0.0542526i	$-0.982722\pi$
$419$		−	9.79209e40i		−	0.108505i	0.998527	−	0.0542526i	$-0.0172776\pi$
$420$	−4.00138e38	−	2.49939e38i	−0.000426797	−	0.000266590i
$421$	−1.90222e42			−1.95321			−0.976603	−	0.215052i	$-0.931008\pi$
$421$	−1.90222e42			−1.95321			−0.976603	+	0.215052i	$0.931008\pi$
$422$	5.49851e41	+	1.57616e41i	0.543558	+	0.155812i
$423$			8.18653e41i			0.779209i
$424$	−1.15772e42	+	1.04296e42i	−1.06109	+	0.955902i
$425$	−4.14159e41			−0.365548
$426$	2.93092e41	−	1.02246e42i	0.249144	−	0.869149i
$427$		−	1.58875e39i		−	0.00130080i
$428$	−5.36913e40	+	8.59568e40i	−0.0423452	+	0.0677923i
$429$	−1.13004e42			−0.858572
$430$	1.28623e42	+	3.68701e41i	0.941507	+	0.269885i
$431$		−	5.57257e41i		−	0.393024i	−0.980501	−	0.196512i	$-0.937039\pi$
$431$		−	5.57257e41i		−	0.393024i	0.980501	−	0.196512i	$-0.0629615\pi$
$432$	−1.36827e42	+	6.67930e41i	−0.929890	+	0.453932i
$433$	2.19637e42			1.43846			0.719231	−	0.694771i	$-0.244494\pi$
$433$	2.19637e42			1.43846			0.719231	+	0.694771i	$0.244494\pi$
$434$	−2.36058e38	+	8.23497e38i	−0.000148999	+	0.000519788i
$435$		−	1.40646e42i		−	0.855658i
$436$	−6.78064e41	−	4.23540e41i	−0.397637	−	0.248376i
$437$	−5.10898e40			−0.0288823
$438$	1.11013e42	+	3.18221e41i	0.605043	+	0.173437i
$439$		−	2.85773e42i		−	1.50172i	−0.660462	−	0.750859i	$-0.729640\pi$
$439$		−	2.85773e42i		−	1.50172i	0.660462	−	0.750859i	$-0.270360\pi$
$440$	1.52721e42	+	1.69526e42i	0.773846	+	0.858999i
$441$	1.14612e42			0.560031
$442$	−5.16091e41	+	1.80040e42i	−0.243204	+	0.848426i
$443$		−	9.08746e41i		−	0.413031i	−0.978443	−	0.206516i	$-0.933788\pi$
$443$		−	9.08746e41i		−	0.413031i	0.978443	−	0.206516i	$-0.0662124\pi$
$444$	7.37341e41	−	1.18044e42i	0.323252	−	0.517508i
$445$	−1.30362e42			−0.551304
$446$	2.18191e42	+	6.25450e41i	0.890182	+	0.255173i
$447$			1.14003e42i			0.448740i
$448$	−2.49999e39	−	2.61460e38i	−0.000949487	−	9.93016e-5i
$449$	4.17788e42			1.53114			0.765570	−	0.643353i	$-0.222457\pi$
$449$	4.17788e42			1.53114			0.765570	+	0.643353i	$0.222457\pi$
$450$	1.60783e41	−	5.60900e41i	0.0568645	−	0.198374i
$451$		−	1.84822e40i		−	0.00630853i
$452$	−2.38800e41	−	1.49162e41i	−0.0786719	−	0.0491409i
$453$	−2.04416e42			−0.650044
$454$	−2.90534e42	−	8.32824e41i	−0.891874	−	0.255658i
$455$		−	2.27753e39i		−	0.000674965i
$456$	5.71796e41	−	5.15114e41i	0.163608	−	0.147389i
$457$	−3.75807e42			−1.03826			−0.519130	−	0.854695i	$-0.673744\pi$
$457$	−3.75807e42			−1.03826			−0.519130	+	0.854695i	$0.673744\pi$
$458$	4.22484e41	−	1.47386e42i	0.112710	−	0.393194i
$459$			3.98447e42i			1.02652i
$460$	−1.47204e41	+	2.35665e41i	−0.0366263	+	0.0586368i
$461$	−1.39943e42			−0.336307			−0.168153	−	0.985761i	$-0.553780\pi$
$461$	−1.39943e42			−0.336307			−0.168153	+	0.985761i	$0.553780\pi$
$462$	−3.81517e39	−	1.09363e39i	−0.000885611	−	0.000253863i
$463$		−	1.36252e42i		−	0.305525i	−0.988263	−	0.152762i	$-0.951183\pi$
$463$		−	1.36252e42i		−	0.305525i	0.988263	−	0.152762i	$-0.0488169\pi$
$464$	−3.28725e42	−	6.73399e42i	−0.712106	−	1.45876i
$465$	−1.42650e42			−0.298556
$466$	−4.05050e41	+	1.41303e42i	−0.0819094	+	0.285744i
$467$			7.19617e42i			1.40615i	0.711116	+	0.703074i	$0.248190\pi$
$467$			7.19617e42i			1.40615i	−0.711116	+	0.703074i	$0.751810\pi$
$468$	−2.23795e42	−	1.39789e42i	−0.422588	−	0.263962i
$469$	4.22788e39			0.000771537
$470$	−6.02631e42	−	1.72746e42i	−1.06288	−	0.304678i
$471$			2.71354e42i			0.462596i
$472$	8.01521e42	+	8.89719e42i	1.32082	+	1.46616i
$473$	1.12560e43			1.79311
$474$	−7.44296e41	+	2.59651e42i	−0.114628	+	0.399886i
$475$			8.21558e41i			0.122332i
$476$	−3.48479e39	+	5.57896e39i	−0.000501725	+	0.000803234i
$477$	−5.74493e42			−0.799817
$478$	−4.81263e42	−	1.37955e42i	−0.647941	−	0.185734i
$479$			3.01680e42i			0.392806i	0.980523	+	0.196403i	$0.0629261\pi$
$479$			3.01680e42i			0.392806i	−0.980523	+	0.196403i	$0.937074\pi$
$480$	−7.28596e41	−	4.12174e42i	−0.0917544	−	0.519064i
$481$	6.71890e42			0.818422
$482$	3.89673e42	−	1.35939e43i	0.459143	−	1.60174i
$483$		−	4.83312e38i		−	5.50901e-5i
$484$	8.58863e42	+	5.36472e42i	0.947105	+	0.591591i
$485$	−4.06706e42			−0.433924
$486$	−8.85526e42	−	2.53838e42i	−0.914157	−	0.262046i
$487$		−	7.87682e42i		−	0.786842i	−0.919358	−	0.393421i	$-0.871292\pi$
$487$		−	7.87682e42i		−	0.786842i	0.919358	−	0.393421i	$-0.128708\pi$
$488$	1.04725e43	−	9.43434e42i	1.01235	−	0.911999i
$489$	1.22959e43			1.15032
$490$	−2.41845e42	+	8.43686e42i	−0.218978	+	0.763912i
$491$		−	1.58573e43i		−	1.38971i	−0.719150	−	0.694855i	$-0.755469\pi$
$491$		−	1.58573e43i		−	1.38971i	0.719150	−	0.694855i	$-0.244531\pi$
$492$	−1.79615e40	+	2.87554e40i	−0.00152371	+	0.00243937i
$493$	−1.96097e43			−1.61035
$494$	3.57143e42	+	1.02376e42i	0.283929	+	0.0813891i
$495$			8.41231e42i			0.647489i
$496$	−6.82995e42	+	3.33409e42i	−0.508991	+	0.248468i
$497$	1.80337e40			0.00130132
$498$	−3.60361e42	+	1.25713e43i	−0.251807	+	0.878440i
$499$		−	1.31326e43i		−	0.888670i	−0.895861	−	0.444335i	$-0.853440\pi$
$499$		−	1.31326e43i		−	0.888670i	0.895861	−	0.444335i	$-0.146560\pi$
$500$	1.40740e43	+	8.79109e42i	0.922357	+	0.576133i
$501$	−7.96884e42			−0.505815
$502$	2.03558e43	+	5.83506e42i	1.25150	+	0.358745i
$503$		−	4.56337e42i		−	0.271767i	−0.990725	−	0.135884i	$-0.956613\pi$
$503$		−	4.56337e42i		−	0.271767i	0.990725	−	0.135884i	$-0.0433874\pi$
$504$	−6.20279e39	−	6.88534e39i	−0.000357848	−	0.000397225i
$505$	1.36771e43			0.764419
$506$	−6.44104e41	+	2.24698e42i	−0.0348777	+	0.121672i
$507$		−	2.63542e42i		−	0.138268i
$508$	−1.66641e43	+	2.66783e43i	−0.847153	+	1.35625i
$509$	−1.03750e42			−0.0511097			−0.0255549	−	0.999673i	$-0.508135\pi$
$509$	−1.03750e42			−0.0511097			−0.0255549	+	0.999673i	$0.508135\pi$
$510$	−1.05293e43	−	3.01826e42i	−0.502665	−	0.144090i
$511$			1.95798e40i			0.000905889i
$512$	−1.31220e43	−	1.80316e43i	−0.588409	−	0.808563i
$513$	7.90392e42			0.343530
$514$	−6.85091e42	+	2.38997e43i	−0.288628	+	1.00689i
$515$			2.28634e43i			0.933740i
$516$	−1.75127e43	−	1.09390e43i	−0.693358	−	0.433093i
$517$	−5.27374e43			−2.02428
$518$	2.26840e40	+	6.50242e39i	0.000844196	+	0.000241991i
$519$			1.46216e42i			0.0527616i
$520$	1.50126e43	−	1.35244e43i	0.525294	−	0.473221i
$521$	1.65964e43			0.563132			0.281566	−	0.959542i	$-0.409146\pi$
$521$	1.65964e43			0.563132			0.281566	+	0.959542i	$0.409146\pi$
$522$	7.61283e42	−	2.65577e43i	0.250506	−	0.873901i
$523$		−	4.85049e43i		−	1.54795i	−0.633213	−	0.773977i	$-0.718264\pi$
$523$		−	4.85049e43i		−	1.54795i	0.633213	−	0.773977i	$-0.281736\pi$
$524$	−1.75639e43	+	2.81189e43i	−0.543652	+	0.870357i
$525$	−7.77198e39			−0.000233336
$526$	3.32952e43	+	9.54416e42i	0.969639	+	0.277950i
$527$			1.98892e43i			0.561884i
$528$	−1.54465e43	−	3.16424e43i	−0.423337	−	0.867215i
$529$	3.73243e43			0.992431
$530$	1.21225e43	−	4.22899e43i	0.312736	−	1.09099i
$531$			4.41502e43i			1.10515i
$532$	1.10669e40	+	6.91271e39i	0.000268806	+	0.000167904i
$533$	−1.63671e41			−0.00385778
$534$	1.93385e43	+	5.54343e42i	0.442346	+	0.126800i
$535$		−	2.86131e42i		−	0.0635192i
$536$	2.51060e43	+	2.78686e43i	0.540929	+	0.600452i
$537$	5.46285e43			1.14243
$538$	1.35179e43	−	4.71579e43i	0.274406	−	0.957278i
$539$			7.38326e43i			1.45488i
$540$	2.27733e43	−	3.64589e43i	0.435639	−	0.697434i
$541$	−4.36755e43			−0.811114			−0.405557	−	0.914070i	$-0.632922\pi$
$541$	−4.36755e43			−0.811114			−0.405557	+	0.914070i	$0.632922\pi$
$542$	−1.14166e43	−	3.27261e42i	−0.205849	−	0.0590073i
$543$			2.97975e43i			0.521653i
$544$	−5.74678e43	+	1.01585e43i	−0.976882	+	0.172682i
$545$	2.25712e43			0.372573
$546$	−9.68480e39	+	3.37858e40i	−0.000155242	+	0.000541567i
$547$		−	1.01722e44i		−	1.58351i	−0.610842	−	0.791753i	$-0.709169\pi$
$547$		−	1.01722e44i		−	1.58351i	0.610842	−	0.791753i	$-0.290831\pi$
$548$	−8.30264e43	−	5.18609e43i	−1.25524	−	0.784063i
$549$	5.19672e43			0.763083
$550$	3.61330e43	+	1.03576e43i	0.515348	+	0.147726i
$551$			3.88994e43i			0.538912i
$552$	3.18581e42	−	2.87000e42i	0.0428741	−	0.0386240i
$553$	−4.57959e40			−0.000598721
$554$	−9.93390e42	+	3.46548e43i	−0.126172	+	0.440157i
$555$			3.92943e43i			0.484888i
$556$	−2.89328e43	+	4.63198e43i	−0.346891	+	0.555354i
$557$	−1.35627e44			−1.58002			−0.790009	−	0.613096i	$-0.789924\pi$
$557$	−1.35627e44			−1.58002			−0.790009	+	0.613096i	$0.789924\pi$
$558$	−2.69361e43	−	7.72130e42i	−0.304921	−	0.0874065i
$559$		−	9.96796e43i		−	1.09652i
$560$	6.37733e40	−	3.11314e40i	0.000681759	−	0.000332805i
$561$	−9.21443e43			−0.957332
$562$	−3.62902e43	+	1.26600e44i	−0.366445	+	1.27836i
$563$			2.89870e43i			0.284492i	0.989831	+	0.142246i	$0.0454323\pi$
$563$			2.89870e43i			0.284492i	−0.989831	+	0.142246i	$0.954568\pi$
$564$	8.20512e43	+	5.12517e43i	0.782743	+	0.488926i
$565$	7.94913e42			0.0737130
$566$	−6.97005e43	−	1.99798e43i	−0.628309	−	0.180106i
$567$			1.37625e40i			0.000120606i
$568$	1.07088e44	+	1.18871e44i	0.912359	+	1.01275i
$569$	5.38772e43			0.446281			0.223141	−	0.974786i	$-0.428369\pi$
$569$	5.38772e43			0.446281			0.223141	+	0.974786i	$0.428369\pi$
$570$	−5.98727e42	+	2.08868e43i	−0.0482204	+	0.168219i
$571$		−	1.44273e44i		−	1.12982i	−0.825153	−	0.564909i	$-0.808911\pi$
$571$		−	1.44273e44i		−	1.12982i	0.825153	−	0.564909i	$-0.191089\pi$
$572$	9.00520e43	−	1.44168e44i	0.685736	−	1.09782i
$573$	3.27219e43			0.242306
$574$	−5.52578e38	−	1.58398e38i	−3.97927e−6	−	1.14067e-6i
$575$			4.57738e42i			0.0320576i
$576$	8.55218e42	−	8.17730e43i	0.0582529	−	0.556994i
$577$	−9.92412e42			−0.0657474			−0.0328737	−	0.999460i	$-0.510466\pi$
$577$	−9.92412e42			−0.0657474			−0.0328737	+	0.999460i	$0.510466\pi$
$578$	6.79118e41	−	2.36913e42i	0.00437623	−	0.0152666i
$579$			8.65351e43i			0.542419i
$580$	1.79434e44	+	1.12080e44i	1.09410	+	0.683407i
$581$	−2.21727e41			−0.00131523
$582$	6.03327e43	+	1.72945e43i	0.348165	+	0.0998023i
$583$		−	3.70087e44i		−	2.07781i
$584$	−1.29063e44	+	1.16269e44i	−0.705012	+	0.635123i
$585$	7.44965e43			0.395951
$586$	−2.86571e43	+	9.99715e43i	−0.148208	+	0.517028i
$587$			1.21624e44i			0.612083i	0.952018	+	0.306042i	$0.0990046\pi$
$587$			1.21624e44i			0.612083i	−0.952018	+	0.306042i	$0.900995\pi$
$588$	7.17527e43	−	1.14872e44i	0.351399	−	0.562571i
$589$	3.94537e43			0.188037
$590$	−3.25001e44	−	9.31623e43i	−1.50748	−	0.432124i
$591$		−	8.06871e43i		−	0.364254i
$592$	9.18404e43	+	1.88137e44i	0.403540	+	0.826660i
$593$	1.18094e44			0.505071			0.252536	−	0.967588i	$-0.418736\pi$
$593$	1.18094e44			0.505071			0.252536	+	0.967588i	$0.418736\pi$
$594$	9.96469e43	−	3.47622e44i	0.414840	−	1.44719i
$595$		−	1.85711e41i		−	0.000752604i
$596$	−1.45442e44	−	9.08478e43i	−0.573787	−	0.358405i
$597$	−1.17742e44			−0.452211
$598$	1.98985e43	+	5.70396e42i	0.0744049	+	0.0213284i
$599$			2.39488e44i			0.871877i	0.899977	+	0.435938i	$0.143583\pi$
$599$			2.39488e44i			0.871877i	−0.899977	+	0.435938i	$0.856417\pi$
$600$	−4.61515e43	−	5.12300e43i	−0.163594	−	0.181595i
$601$	1.10890e44			0.382737			0.191368	−	0.981518i	$-0.438708\pi$
$601$	1.10890e44			0.382737			0.191368	+	0.981518i	$0.438708\pi$
$602$	9.64679e40	−	3.36533e41i	0.000324220	−	0.00113105i
$603$			1.38291e44i			0.452603i
$604$	1.62897e44	−	2.60790e44i	0.519186	−	0.831188i
$605$	−2.85896e44			−0.887407
$606$	−2.02892e44	−	5.81595e43i	−0.613342	−	0.175816i
$607$			6.73326e44i			1.98247i	0.132121	+	0.991234i	$0.457821\pi$
$607$			6.73326e44i			1.98247i	−0.132121	+	0.991234i	$0.542179\pi$
$608$	2.01512e43	+	1.13998e44i	0.0577889	+	0.326918i
$609$	−3.67990e41			−0.00102792
$610$	−1.09657e44	+	3.82543e44i	−0.298373	+	1.04089i
$611$			4.67024e44i			1.23788i
$612$	−1.82484e44	−	1.13985e44i	−0.471198	−	0.294325i
$613$	1.55932e44			0.392254			0.196127	−	0.980579i	$-0.437164\pi$
$613$	1.55932e44			0.392254			0.196127	+	0.980579i	$0.437164\pi$
$614$	3.26356e43	+	9.35508e42i	0.0799830	+	0.0229273i
$615$		−	9.57203e41i		−	0.00228561i
$616$	4.43551e41	−	3.99582e41i	0.00103194	−	0.000929639i
$617$	−2.42947e44			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$617$	−2.42947e44			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$618$	9.72230e43	−	3.39167e44i	0.214760	−	0.749199i
$619$		−	8.44075e44i		−	1.81690i	−0.417996	−	0.908449i	$-0.637267\pi$
$619$		−	8.44075e44i		−	1.81690i	0.417996	−	0.908449i	$-0.362733\pi$
$620$	1.13677e44	−	1.81990e44i	0.238454	−	0.381752i
$621$	4.40373e43			0.0900234
$622$	3.09377e44	+	8.86837e43i	0.616370	+	0.176684i
$623$			3.41083e41i			0.000662294i
$624$	−2.80214e44	+	1.36788e44i	−0.530318	+	0.258878i
$625$	−2.68737e44			−0.495733
$626$	6.46024e43	−	2.25368e44i	0.116161	−	0.405231i
$627$			1.82785e44i			0.320376i
$628$	−3.46188e44	−	2.16240e44i	−0.591505	−	0.369472i
$629$	5.47865e44			0.912563
$630$	2.51511e41	+	7.20962e40i	0.000408421	+	0.000117075i
$631$		−	5.16712e44i		−	0.818048i	−0.912524	−	0.409024i	$-0.865869\pi$
$631$		−	5.16712e44i		−	0.818048i	0.912524	−	0.409024i	$-0.134131\pi$
$632$	−2.71945e44	−	3.01870e44i	−0.419767	−	0.465957i
$633$	2.49209e44			0.375063
$634$	−1.02665e44	+	3.58151e44i	−0.150659	+	0.525579i
$635$		−	8.88061e44i		−	1.27076i
$636$	−3.59661e44	+	5.75798e44i	−0.501857	+	0.803445i
$637$	6.53835e44			0.889687
$638$	1.71084e45	+	4.90416e44i	2.27027	+	0.650780i
$639$			5.89871e44i			0.763385i
$640$	5.83905e44	+	2.35506e44i	0.736992	+	0.297250i
$641$	−1.90781e44			−0.234859			−0.117429	−	0.993081i	$-0.537465\pi$
$641$	−1.90781e44			−0.234859			−0.117429	+	0.993081i	$0.537465\pi$
$642$	−1.21673e43	+	4.24460e43i	−0.0146094	+	0.0509655i
$643$			2.24114e44i			0.262478i	0.991351	+	0.131239i	$0.0418956\pi$
$643$			2.24114e44i			0.262478i	−0.991351	+	0.131239i	$0.958104\pi$
$644$	6.16600e40	+	3.85148e40i	7.04417e−5	+	4.40001e-5i
$645$	5.82958e44			0.649654
$646$	2.91217e44	+	8.34781e43i	0.316589	+	0.0907512i
$647$		−	1.04450e45i		−	1.10775i	−0.832601	−	0.553873i	$-0.813149\pi$
$647$		−	1.04450e45i		−	1.10775i	0.832601	−	0.553873i	$-0.186851\pi$
$648$	−9.07176e43	+	8.17247e43i	−0.0938623	+	0.0845577i
$649$	−2.84414e45			−2.87102
$650$	9.17234e43	−	3.19981e44i	0.0903372	−	0.315145i
$651$			3.73234e41i			0.000358662i
$652$	−9.79850e44	+	1.56869e45i	−0.918751	+	1.47087i
$653$	1.37316e45			1.25635			0.628174	−	0.778073i	$-0.283803\pi$
$653$	1.37316e45			1.25635			0.628174	+	0.778073i	$0.283803\pi$
$654$	−3.34832e44	−	9.59805e43i	−0.298939	−	0.0856917i
$655$		−	9.36015e44i		−	0.815497i
$656$	−2.23722e42	−	4.58299e42i	−0.00190216	−	0.00389661i
$657$	−6.40445e44			−0.531417
$658$	−4.51976e41	+	1.57674e42i	−0.000366017	+	0.00127687i
$659$		−	4.41987e43i		−	0.0349336i	−0.999847	−	0.0174668i	$-0.994440\pi$
$659$		−	4.41987e43i		−	0.0349336i	0.999847	−	0.0174668i	$-0.00556014\pi$
$660$	8.43142e44	+	5.26653e44i	0.650426	+	0.406276i
$661$	−2.19392e45			−1.65195			−0.825974	−	0.563708i	$-0.809374\pi$
$661$	−2.19392e45			−1.65195			−0.825974	+	0.563708i	$0.809374\pi$
$662$	−7.45046e44	−	2.13569e44i	−0.547590	−	0.156968i
$663$			8.15998e44i			0.585427i
$664$	−1.31666e45	−	1.46154e45i	−0.922113	−	1.02358i
$665$	−3.68392e41			−0.000251862
$666$	−2.12690e44	+	7.41979e44i	−0.141958	+	0.495227i
$667$			2.16732e44i			0.141224i
$668$	6.35031e44	−	1.01665e45i	0.403991	−	0.646767i
$669$	9.88906e44			0.614239
$670$	−1.01800e45	−	2.91811e44i	−0.617375	−	0.176972i
$671$			3.34771e45i			1.98238i
$672$	−1.07842e42	+	1.90632e41i	−0.000623564	+	0.000110227i
$673$	2.14147e45			1.20912			0.604562	−	0.796558i	$-0.293348\pi$
$673$	2.14147e45			1.20912			0.604562	+	0.796558i	$0.293348\pi$
$674$	−5.06099e43	+	1.76555e44i	−0.0279047	+	0.0973467i
$675$		−	7.08149e44i		−	0.381298i
$676$	3.36222e44	+	2.10015e44i	0.176799	+	0.110434i
$677$	2.65983e45			1.36595			0.682975	−	0.730441i	$-0.260686\pi$
$677$	2.65983e45			1.36595			0.682975	+	0.730441i	$0.260686\pi$
$678$	−1.17921e44	−	3.38023e43i	−0.0591447	−	0.0169540i
$679$			1.06412e42i			0.000521282i
$680$	1.22414e45	−	1.10279e45i	0.585718	−	0.527655i
$681$	−1.31679e45			−0.615407
$682$	4.97404e44	−	1.73522e45i	0.227070	−	0.792143i
$683$		−	4.16209e44i		−	0.185601i	−0.995685	−	0.0928005i	$-0.970418\pi$
$683$		−	4.16209e44i		−	0.185601i	0.995685	−	0.0928005i	$-0.0295819\pi$
$684$	−2.26111e44	+	3.61991e44i	−0.0984970	+	0.157688i
$685$	2.76376e45			1.17612
$686$	4.41488e42	+	1.26554e42i	0.00183541	+	0.000526126i
$687$		−	6.67995e44i		−	0.271310i
$688$	2.79114e45	−	1.36252e45i	1.10756	−	0.540663i
$689$	−3.27736e45			−1.27062
$690$	−3.33586e43	+	1.16373e44i	−0.0126364	+	0.0440825i
$691$			3.56018e45i			1.31772i	0.752265	+	0.658860i	$0.228961\pi$
$691$			3.56018e45i			1.31772i	−0.752265	+	0.658860i	$0.771039\pi$
$692$	−1.86540e44	−	1.16518e44i	−0.0674643	−	0.0421403i
$693$	2.20102e42			0.000777843
$694$	−1.35721e45	−	3.89048e44i	−0.468701	−	0.134354i
$695$		−	1.54188e45i		−	0.520349i
$696$	−2.18520e45	−	2.42566e45i	−0.720681	−	0.799984i
$697$	−1.33459e43			−0.00430154
$698$	3.83575e44	−	1.33812e45i	0.120827	−	0.421510i
$699$			6.40429e44i			0.197168i
$700$	6.19343e41	−	9.91534e41i	0.000186364	−	0.000298359i
$701$	1.22041e45			0.358936			0.179468	−	0.983764i	$-0.442562\pi$
$701$	1.22041e45			0.358936			0.179468	+	0.983764i	$0.442562\pi$
$702$	−3.07842e45	−	8.82438e44i	−0.884982	−	0.253682i
$703$		−	1.08679e45i		−	0.305393i
$704$	5.26779e45	+	5.50929e44i	1.44699	+	0.151333i
$705$	−2.73130e45			−0.733405
$706$	−1.18661e45	+	4.13953e45i	−0.311481	+	1.08662i
$707$		−	3.57851e42i		−	0.000918314i
$708$	4.42505e45	+	2.76402e45i	1.11016	+	0.693441i
$709$	−1.04935e45			−0.257383			−0.128691	−	0.991685i	$-0.541078\pi$
$709$	−1.04935e45			−0.257383			−0.128691	+	0.991685i	$0.541078\pi$
$710$	−4.34219e45	−	1.24470e45i	−1.04130	−	0.298491i
$711$		−	1.49796e45i		−	0.351225i
$712$	−2.24829e45	+	2.02542e45i	−0.515433	+	0.464338i
$713$	2.19820e44			0.0492759
$714$	−7.89706e41	+	2.75492e42i	−0.000173099	+	0.000603863i
$715$			4.79904e45i			1.02863i
$716$	−4.35330e45	+	6.96939e45i	−0.912452	+	1.46079i
$717$	−2.18123e45			−0.447089
$718$	3.17500e45	+	9.10121e44i	0.636432	+	0.182435i
$719$		−	6.79956e45i		−	1.33296i	−0.745521	−	0.666482i	$-0.767799\pi$
$719$		−	6.79956e45i		−	1.33296i	0.745521	−	0.666482i	$-0.232201\pi$
$720$	1.01829e45	+	2.08599e45i	0.195232	+	0.399937i
$721$	5.98205e42			0.00112172
$722$	−1.33687e45	+	4.66372e45i	−0.245185	+	0.855337i
$723$		−	6.16117e45i		−	1.10522i
$724$	−3.80150e45	−	2.37454e45i	−0.667019	−	0.416641i
$725$	3.48519e45			0.598161
$726$	4.24112e45	+	1.21573e45i	0.712023	+	0.204103i
$727$			1.35491e45i			0.222515i	0.993792	+	0.111257i	$0.0354878\pi$
$727$			1.35491e45i			0.222515i	−0.993792	+	0.111257i	$0.964512\pi$
$728$	−3.53856e42	−	3.92793e42i	−0.000568492	−	0.000631048i
$729$	−4.81729e45			−0.757116
$730$	1.35142e45	−	4.71447e45i	0.207789	−	0.724882i
$731$		−	8.12795e45i		−	1.22265i
$732$	3.25340e45	−	5.20852e45i	0.478807	−	0.766544i
$733$	6.94890e45			1.00058			0.500291	−	0.865857i	$-0.333226\pi$
$733$	6.94890e45			1.00058			0.500291	+	0.865857i	$0.333226\pi$
$734$	7.21051e45	+	2.06691e45i	1.01585	+	0.291196i
$735$			3.82384e45i			0.527111i
$736$	1.12274e44	+	6.35148e44i	0.0151438	+	0.0856702i
$737$	−8.90868e45			−1.17580
$738$	5.18110e42	−	1.80745e43i	0.000669145	−	0.00233434i
$739$			7.67315e45i			0.969757i	0.874582	+	0.484879i	$0.161136\pi$
$739$			7.67315e45i			0.969757i	−0.874582	+	0.484879i	$0.838864\pi$
$740$	−5.01309e45	−	3.13133e45i	−0.620009	−	0.387277i
$741$	1.61868e45			0.195916
$742$	−1.10648e43	−	3.17176e42i	−0.00131064	−	0.000375697i
$743$		−	5.23761e45i		−	0.607173i	−0.952804	−	0.303587i	$-0.901816\pi$
$743$		−	5.23761e45i		−	0.607173i	0.952804	−	0.303587i	$-0.0981842\pi$
$744$	−2.46022e45	+	2.21634e45i	−0.279130	+	0.251460i
$745$	4.84145e45			0.537620
$746$	−2.06562e44	+	7.20599e44i	−0.0224506	+	0.0783200i
$747$		−	7.25256e45i		−	0.771545i
$748$	7.34291e45	−	1.17556e46i	0.764614	−	1.22411i
$749$	−7.48641e41			−7.63070e−5
$750$	6.94985e45	+	1.99219e45i	0.693418	+	0.198770i
$751$			1.05662e46i			1.03200i	0.856587	+	0.516002i	$0.172580\pi$
$751$			1.05662e46i			1.03200i	−0.856587	+	0.516002i	$0.827420\pi$
$752$	−1.30772e46	+	6.38372e45i	−1.25034	+	0.610364i
$753$	9.22588e45			0.863551
$754$	4.34295e45	−	1.51506e46i	0.397964	−	1.38831i
$755$			8.68111e45i			0.778796i
$756$	−9.53919e42	−	5.95847e42i	−0.000837843	−	0.000523343i
$757$	9.35152e45			0.804171			0.402085	−	0.915602i	$-0.368286\pi$
$757$	9.35152e45			0.804171			0.402085	+	0.915602i	$0.368286\pi$
$758$	7.44768e45	+	2.13490e45i	0.627067	+	0.179750i
$759$			1.01840e45i			0.0839557i
$760$	−2.18758e45	−	2.42830e45i	−0.176582	−	0.196013i
$761$	−1.90393e46			−1.50486			−0.752429	−	0.658673i	$-0.771118\pi$
$761$	−1.90393e46			−1.50486			−0.752429	+	0.658673i	$0.771118\pi$
$762$	−3.77633e45	+	1.31739e46i	−0.292274	+	1.01961i
$763$		−	5.90560e42i		−	0.000447581i
$764$	−2.60758e45	+	4.17460e45i	−0.193528	+	0.309828i
$765$	6.07450e45			0.441497
$766$	−2.49431e46	−	7.14999e45i	−1.77537	−	0.508915i
$767$			2.51867e46i			1.75568i
$768$	−7.66046e45	−	5.97656e45i	−0.522968	−	0.408011i
$769$	6.00273e45			0.401354			0.200677	−	0.979657i	$-0.435686\pi$
$769$	6.00273e45			0.401354			0.200677	+	0.979657i	$0.435686\pi$
$770$	−4.64442e42	+	1.62022e43i	−0.000304144	+	0.00106102i
$771$			1.08321e46i			0.694770i
$772$	−1.10400e46	−	6.89591e45i	−0.693571	−	0.433226i
$773$	−8.64477e45			−0.531963			−0.265981	−	0.963978i	$-0.585696\pi$
$773$	−8.64477e45			−0.531963			−0.265981	+	0.963978i	$0.585696\pi$
$774$	1.10078e46	+	3.15541e45i	0.663505	+	0.190195i
$775$		−	3.53485e45i		−	0.208710i
$776$	−7.01426e45	+	6.31894e45i	−0.405690	+	0.365474i
$777$	1.02811e43			0.000582508
$778$	9.45326e45	−	3.29781e46i	0.524696	−	1.83043i
$779$			2.64740e43i			0.00143953i
$780$	4.66385e45	−	7.46657e45i	0.248445	−	0.397747i
$781$	−3.79993e46			−1.98317
$782$	1.62254e45	+	4.65105e44i	0.0829635	+	0.0237817i
$783$		−	3.35297e46i		−	1.67974i
$784$	8.93724e45	+	1.83081e46i	0.438679	+	0.898643i
$785$	1.15238e46			0.554221
$786$	−3.98025e45	+	1.38853e46i	−0.187564	+	0.654325i
$787$		−	7.42361e45i		−	0.342783i	−0.985203	−	0.171392i	$-0.945174\pi$
$787$		−	7.42361e45i		−	0.342783i	0.985203	−	0.171392i	$-0.0548263\pi$
$788$	1.02939e46	+	6.42989e45i	0.465758	+	0.290927i
$789$	1.50904e46			0.669065
$790$	1.10268e46	+	3.16087e45i	0.479090	+	0.137332i
$791$		−	2.07983e42i		−	8.85531e-5i
$792$	1.30701e46	+	1.45083e46i	0.545350	+	0.605360i
$793$	2.96461e46			1.21226
$794$	−3.67964e45	+	1.28366e46i	−0.147461	+	0.514425i
$795$		−	1.91670e46i		−	0.752802i
$796$	9.38274e45	−	1.50212e46i	0.361177	−	0.578225i
$797$	−2.06105e45			−0.0777597			−0.0388798	−	0.999244i	$-0.512379\pi$
$797$	−2.06105e45			−0.0777597			−0.0388798	+	0.999244i	$0.512379\pi$
$798$	5.46489e42	+	1.56652e42i	0.000202085	+	5.79283e-5i
$799$			3.80815e46i			1.38027i
$800$	1.02136e46	−	1.80545e45i	0.362860	−	0.0641423i
$801$	−1.11566e46			−0.388519
$802$	−9.64534e45	+	3.36482e46i	−0.329251	+	1.14861i
$803$		−	4.12572e46i		−	1.38055i
$804$	1.38605e46	+	8.65772e45i	0.454656	+	0.283992i
$805$	−2.05253e42			−6.60016e−5
$806$	−1.53665e46	−	4.40484e45i	−0.484410	−	0.138857i
$807$		−	2.13734e46i		−	0.660536i
$808$	2.35882e46	−	2.12499e46i	0.714682	−	0.643835i
$809$	2.54117e46			0.754843			0.377422	−	0.926042i	$-0.376811\pi$
$809$	2.54117e46			0.754843			0.377422	+	0.926042i	$0.376811\pi$
$810$	9.49902e44	−	3.31377e45i	0.0276642	−	0.0965078i
$811$		−	4.73692e45i		−	0.135258i	−0.997711	−	0.0676288i	$-0.978457\pi$
$811$		−	4.73692e45i		−	0.135258i	0.997711	−	0.0676288i	$-0.0215434\pi$
$812$	2.93249e43	−	4.69475e43i	0.000820993	−	0.00131436i
$813$	−5.17436e45			−0.142039
$814$	−4.77981e46	−	1.37014e46i	−1.28653	−	0.368787i
$815$		−	5.22181e46i		−	1.37816i
$816$	−2.28489e46	+	1.11538e46i	−0.591319	+	0.288657i
$817$	−1.61233e46			−0.409166
$818$	−6.32482e45	+	2.20644e46i	−0.157397	+	0.549085i
$819$		−	1.94914e43i		−	0.000475666i
$820$	1.22118e44	+	7.62788e43i	0.00292253	+	0.00182550i
$821$	−7.74502e46			−1.81774			−0.908870	−	0.417079i	$-0.863054\pi$
$821$	−7.74502e46			−1.81774			−0.908870	+	0.417079i	$0.863054\pi$
$822$	−4.09989e46	−	1.17525e46i	−0.943677	−	0.270508i
$823$			5.33360e46i			1.20399i	0.798500	+	0.601995i	$0.205627\pi$
$823$			5.33360e46i			1.20399i	−0.798500	+	0.601995i	$0.794373\pi$
$824$	3.55226e46	+	3.94314e46i	0.786446	+	0.872986i
$825$	1.63766e46			0.355598
$826$	−2.43752e43	+	8.50340e43i	−0.000519120	+	0.00181097i
$827$			5.53001e46i			1.15515i	0.816338	+	0.577574i	$0.196001\pi$
$827$			5.53001e46i			1.15515i	−0.816338	+	0.577574i	$0.803999\pi$
$828$	−1.25979e45	+	2.01686e45i	−0.0258116	+	0.0413229i
$829$	−3.21975e46			−0.647067			−0.323534	−	0.946217i	$-0.604871\pi$
$829$	−3.21975e46			−0.647067			−0.323534	+	0.946217i	$0.604871\pi$
$830$	5.33879e46	+	1.53038e46i	1.05243	+	0.301682i
$831$			1.57066e46i			0.303715i
$832$	4.87883e45	−	4.66497e46i	0.0925428	−	0.884862i
$833$	5.33143e46			0.992027
$834$	−6.55660e45	+	2.28730e46i	−0.119680	+	0.417509i
$835$			3.38420e46i			0.606000i
$836$	−2.33193e46	−	1.45660e46i	−0.409652	−	0.255882i
$837$	−3.40075e46			−0.586094
$838$	6.16890e45	+	1.76833e45i	0.104305	+	0.0298992i
$839$		−	4.42433e45i		−	0.0733932i	−0.999326	−	0.0366966i	$-0.988316\pi$
$839$		−	4.42433e45i		−	0.0733932i	0.999326	−	0.0366966i	$-0.0116835\pi$
$840$	2.29718e43	−	2.06946e43i	0.000373875	−	0.000336813i
$841$	1.02395e47			1.63509
$842$	3.43518e46	−	1.19838e47i	0.538215	−	1.87759i
$843$			5.73789e46i			0.882086i
$844$	−1.98593e46	+	3.17936e46i	−0.299560	+	0.479579i
$845$	−1.11921e46			−0.165655
$846$	−5.15741e46	−	1.47839e46i	−0.749042	−	0.214715i
$847$			7.48027e43i			0.00106606i
$848$	−4.47980e46	−	9.17698e46i	−0.626506	−	1.28341i
$849$	−3.15904e46			−0.433542
$850$	7.47920e45	−	2.60915e46i	0.100728	−	0.351396i
$851$		−	6.05513e45i		−	0.0800296i
$852$	5.91211e46	+	3.69289e46i	0.766847	+	0.478997i
$853$	6.02455e46			0.766902			0.383451	−	0.923561i	$-0.374735\pi$
$853$	6.02455e46			0.766902			0.383451	+	0.923561i	$0.374735\pi$
$854$	1.00090e44	+	2.86910e43i	0.00125044	+	0.000358442i
$855$		−	1.20499e46i		−	0.147749i
$856$	−4.44558e45	−	4.93476e45i	−0.0534993	−	0.0593863i
$857$	2.46922e46			0.291653			0.145826	−	0.989310i	$-0.453416\pi$
$857$	2.46922e46			0.291653			0.145826	+	0.989310i	$0.453416\pi$
$858$	2.04071e46	−	7.11911e46i	0.236584	−	0.825333i
$859$			2.00215e46i			0.227828i	0.993491	+	0.113914i	$0.0363388\pi$
$859$			2.00215e46i			0.227828i	−0.993491	+	0.113914i	$0.963661\pi$
$860$	−4.64555e46	+	7.43727e46i	−0.518874	+	0.830688i
$861$	−2.50445e41			−2.74576e−6
$862$	3.51065e46	+	1.00634e46i	0.377808	+	0.108300i
$863$		−	1.52936e47i		−	1.61561i	−0.589450	−	0.807805i	$-0.700655\pi$
$863$		−	1.52936e47i		−	1.61561i	0.589450	−	0.807805i	$-0.299345\pi$
$864$	−1.73695e46	−	9.82613e46i	−0.180123	−	1.01897i
$865$	6.20949e45			0.0632118
$866$	−3.96637e46	+	1.38368e47i	−0.396375	+	1.38277i
$867$		−	1.07376e45i		−	0.0105342i
$868$	−4.76164e43	−	2.97427e43i	−0.000458608	−	0.000286461i
$869$	9.64979e46			0.912434
$870$	8.86054e46	+	2.53990e46i	0.822531	+	0.235781i
$871$			7.88921e46i			0.719024i
$872$	3.89275e46	−	3.50686e46i	0.348331	−	0.313801i
$873$	−3.48066e46			−0.305797
$874$	9.22620e44	−	3.21860e45i	0.00795866	−	0.0277641i
$875$			1.22578e44i			0.00103821i
$876$	−4.00950e46	+	6.41899e46i	−0.333445	+	0.533828i
$877$	−2.36139e47			−1.92830			−0.964148	−	0.265367i	$-0.914507\pi$
$877$	−2.36139e47			−1.92830			−0.964148	+	0.265367i	$0.914507\pi$
$878$	1.80033e47	+	5.16071e46i	1.44358	+	0.413806i
$879$			4.53101e46i			0.356757i
$880$	−1.34379e47	+	6.55979e46i	−1.03898	+	0.507186i
$881$	3.98305e46			0.302413			0.151207	−	0.988502i	$-0.451684\pi$
$881$	3.98305e46			0.302413			0.151207	+	0.988502i	$0.451684\pi$
$882$	−2.06975e46	+	7.22041e46i	−0.154319	+	0.538349i
$883$		−	1.08523e47i		−	0.794606i	−0.917688	−	0.397303i	$-0.869946\pi$
$883$		−	1.08523e47i		−	0.794606i	0.917688	−	0.397303i	$-0.130054\pi$
$884$	−1.04103e47	−	6.50262e46i	−0.748563	−	0.467576i
$885$	−1.47300e47			−1.04019
$886$	5.72499e46	+	1.64108e46i	0.397041	+	0.113813i
$887$			7.95605e46i			0.541900i	0.962593	+	0.270950i	$0.0873379\pi$
$887$			7.95605e46i			0.541900i	−0.962593	+	0.270950i	$0.912662\pi$
$888$	6.10510e46	+	6.77689e46i	0.408399	+	0.453339i
$889$	−2.32354e44			−0.00152659
$890$	2.35418e46	−	8.21265e46i	0.151915	−	0.529960i
$891$		−	2.89995e46i		−	0.183800i
$892$	−7.88052e46	+	1.26163e47i	−0.490588	+	0.785404i
$893$	7.55414e46			0.461915
$894$	−7.18203e46	−	2.05875e46i	−0.431367	−	0.123652i
$895$		−	2.31996e47i		−	1.36871i
$896$	6.16183e43	−	1.52774e44i	0.000357093	−	0.000885365i
$897$	9.01860e45			0.0513405
$898$	−7.54474e46	+	2.63201e47i	−0.421913	+	1.47186i
$899$		−	1.67369e47i		−	0.919434i
$900$	3.24325e46	+	2.02583e46i	0.175025	+	0.109326i
$901$	−2.67238e47			−1.41678
$902$	1.16435e45	+	3.33765e44i	0.00606429	+	0.00173835i
$903$		−	1.52527e44i		−	0.000780444i
$904$	1.37095e46	−	1.23504e46i	0.0689169	−	0.0620851i
$905$	1.26544e47			0.624975
$906$	3.69150e46	−	1.28779e47i	0.179123	−	0.624878i
$907$		−	8.27618e46i		−	0.394560i	−0.980347	−	0.197280i	$-0.936789\pi$
$907$		−	8.27618e46i		−	0.394560i	0.980347	−	0.197280i	$-0.0632108\pi$
$908$	1.04934e47	−	1.67993e47i	0.491521	−	0.786898i
$909$	1.17051e47			0.538706
$910$	1.43481e44	+	4.11293e43i	0.000648834	+	0.000185990i
$911$			2.58323e47i			1.14781i	0.818922	+	0.573904i	$0.194572\pi$
$911$			2.58323e47i			1.14781i	−0.818922	+	0.573904i	$0.805428\pi$
$912$	2.21256e46	+	4.53248e46i	0.0966002	+	0.197888i
$913$	4.67208e47			2.00437
$914$	6.78662e46	−	2.36754e47i	0.286098	−	0.998064i
$915$			1.73380e47i			0.718227i
$916$	8.52215e46	+	5.32320e46i	0.346914	+	0.216693i
$917$	−2.44901e44			−0.000979675
$918$	−2.51017e47	−	7.19547e46i	−0.986780	−	0.282863i
$919$		−	2.31481e47i		−	0.894267i	−0.894467	−	0.447134i	$-0.852445\pi$
$919$		−	2.31481e47i		−	0.894267i	0.894467	−	0.447134i	$-0.147555\pi$
$920$	−1.21883e46	−	1.35295e46i	−0.0462741	−	0.0513660i
$921$	1.47914e46			0.0551894
$922$	2.52719e46	−	8.81622e46i	0.0926709	−	0.323287i
$923$			3.36509e47i			1.21274i
$924$	1.37795e44	−	2.20602e44i	0.000488069	−	0.000781371i
$925$	−9.73705e46			−0.338969
$926$	8.58370e46	+	2.46054e46i	0.293697	+	0.0841889i
$927$			1.95669e47i			0.658031i
$928$	4.83597e47	−	8.54849e46i	1.59851	−	0.282567i
$929$	−1.59295e47			−0.517547			−0.258773	−	0.965938i	$-0.583318\pi$
$929$	−1.59295e47			−0.517547			−0.258773	+	0.965938i	$0.583318\pi$
$930$	2.57609e46	−	8.98680e46i	0.0822685	−	0.286997i
$931$		−	1.05758e47i		−	0.331986i
$932$	−8.17047e46	−	5.10353e46i	−0.252111	−	0.157477i
$933$	1.40219e47			0.425305
$934$	−4.53350e47	−	1.29954e47i	−1.35171	−	0.387471i
$935$			3.91318e47i			1.14695i
$936$	1.28480e47	−	1.15744e47i	0.370189	−	0.333492i
$937$	−2.80245e47			−0.793788			−0.396894	−	0.917864i	$-0.629912\pi$
$937$	−2.80245e47			−0.793788			−0.396894	+	0.917864i	$0.629912\pi$
$938$	−7.63502e43	+	2.66351e44i	−0.000212601	+	0.000741667i
$939$		−	1.02144e47i		−	0.279616i
$940$	2.17655e47	−	3.48454e47i	0.585766	−	0.937778i
$941$	1.45598e47			0.385232			0.192616	−	0.981274i	$-0.438303\pi$
$941$	1.45598e47			0.385232			0.192616	+	0.981274i	$0.438303\pi$
$942$	−1.70950e47	−	4.90032e46i	−0.444687	−	0.127471i
$943$			1.47502e44i			0.000377234i
$944$	−7.05257e47	+	3.44276e47i	−1.77336	+	0.865676i
$945$	3.17538e44			0.000785032
$946$	−2.03270e47	+	7.09117e47i	−0.494101	+	1.72369i
$947$			8.61762e46i			0.205962i	0.994683	+	0.102981i	$0.0328381\pi$
$947$			8.61762e46i			0.205962i	−0.994683	+	0.102981i	$0.967162\pi$
$948$	−1.50136e47	−	9.37795e46i	−0.352818	−	0.220381i
$949$	−3.65360e47			−0.844231
$950$	−5.17572e46	−	1.48363e46i	−0.117596	−	0.0337092i
$951$			1.62325e47i			0.362657i
$952$	−2.88537e44	−	3.20287e44i	−0.000633884	−	0.000703636i
$953$	−7.16117e47			−1.54703			−0.773513	−	0.633780i	$-0.781502\pi$
$953$	−7.16117e47			−1.54703			−0.773513	+	0.633780i	$0.781502\pi$
$954$	1.03746e47	−	3.61924e47i	0.220394	−	0.768853i
$955$		−	1.38963e47i		−	0.290299i
$956$	1.73820e47	−	2.78277e47i	0.357087	−	0.571677i
$957$	7.75403e47			1.56652
$958$	−1.90055e47	−	5.44797e46i	−0.377598	−	0.108240i
$959$		−	7.23118e44i		−	0.00141290i
$960$	2.72822e47	+	2.85330e46i	0.524252	+	0.0548286i
$961$	3.59390e47			0.679192
$962$	−1.21335e47	+	4.23283e47i	−0.225520	+	0.786737i
$963$		−	2.44876e46i		−	0.0447636i
$964$	7.86030e47	+	4.90979e47i	1.41321	+	0.882735i
$965$	3.67496e47			0.649854
$966$	3.04481e43	+	8.72802e42i	5.29573e−5	+	1.51804e-5i
$967$		−	4.01544e47i		−	0.686925i	−0.939166	−	0.343463i	$-0.888400\pi$
$967$		−	4.01544e47i		−	0.686925i	0.939166	−	0.343463i	$-0.111600\pi$
$968$	−4.93071e47	+	4.44193e47i	−0.829667	+	0.747422i
$969$	1.31988e47			0.218451
$970$	7.34462e46	−	2.56220e47i	0.119570	−	0.417124i
$971$		−	3.71191e47i		−	0.594415i	−0.954813	−	0.297208i	$-0.903945\pi$
$971$		−	3.71191e47i		−	0.594415i	0.954813	−	0.297208i	$-0.0960553\pi$
$972$	3.19830e47	−	5.12030e47i	0.503801	−	0.806558i
$973$	−4.03422e44			−0.000625107
$974$	4.96230e47	+	1.42246e47i	0.756380	+	0.216818i
$975$		−	1.45025e47i		−	0.217455i
$976$	4.05232e47	+	8.30126e47i	0.597732	+	1.22447i
$977$	−1.04108e48			−1.51068			−0.755341	−	0.655332i	$-0.772529\pi$
$977$	−1.04108e48			−1.51068			−0.755341	+	0.655332i	$0.772529\pi$
$978$	−2.22049e47	+	7.74626e47i	−0.316976	+	1.10578i
$979$		−	7.18705e47i		−	1.00932i
$980$	−4.87838e47	−	3.04719e47i	−0.673997	−	0.421000i
$981$	1.93169e47			0.262562
$982$	9.98988e47	+	2.86363e47i	1.33591	+	0.382941i
$983$		−	2.41310e47i		−	0.317481i	−0.987320	−	0.158741i	$-0.949257\pi$
$983$		−	2.41310e47i		−	0.317481i	0.987320	−	0.158741i	$-0.0507434\pi$
$984$	−1.48719e45	−	1.65084e45i	−0.00192507	−	0.00213690i
$985$	−3.42661e47			−0.436401
$986$	3.54128e47	−	1.23539e48i	0.443741	−	1.54801i
$987$			7.14625e44i			0.000881057i
$988$	−1.28991e47	+	2.06508e47i	−0.156476	+	0.250510i
$989$	−8.98321e46			−0.107224
$990$	−5.29966e47	−	1.51916e47i	−0.622421	−	0.178419i
$991$		−	1.70900e48i		−	1.97498i	−0.157683	−	0.987490i	$-0.550402\pi$
$991$		−	1.70900e48i		−	1.97498i	0.157683	−	0.987490i	$-0.449598\pi$
$992$	−8.67029e46	−	4.90488e47i	−0.0985932	−	0.557752i
$993$	−3.37677e47			−0.377845
$994$	−3.25666e44	+	1.13610e45i	−0.000358584	+	0.00125094i
$995$			5.00024e47i			0.541778i
$996$	−7.26903e47	−	4.54046e47i	−0.775045	−	0.484117i
$997$	1.51218e48			1.58665			0.793326	−	0.608797i	$-0.208347\pi$
$997$	1.51218e48			1.58665			0.793326	+	0.608797i	$0.208347\pi$
$998$	8.27335e47	+	2.37158e47i	0.854265	+	0.244877i
$999$			9.36766e47i			0.951883i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.33.b.b.3.6	yes	14
3.2	odd	2		36.33.d.b.19.9		14
4.3	odd	2	inner	4.33.b.b.3.5	✓	14
12.11	even	2		36.33.d.b.19.10		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.33.b.b.3.5	✓	14	4.3	odd	2	inner
4.33.b.b.3.6	yes	14	1.1	even	1	trivial
36.33.d.b.19.9		14	3.2	odd	2
36.33.d.b.19.10		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)

\(f(q)\)	\(=\)	\(q+(-18058.8 + 62998.8i) q^{2} +2.85529e7i q^{3} +(-3.64273e9 - 2.27536e9i) q^{4} +1.21258e11 q^{5} +(-1.79880e12 - 5.15631e11i) q^{6} -3.17263e10i q^{7} +(2.09128e14 - 1.88397e14i) q^{8} +1.03775e15 q^{9} +O(q^{10})\)	\(q+(-18058.8 + 62998.8i) q^{2} +2.85529e7i q^{3} +(-3.64273e9 - 2.27536e9i) q^{4} +1.21258e11 q^{5} +(-1.79880e12 - 5.15631e11i) q^{6} -3.17263e10i q^{7} +(2.09128e14 - 1.88397e14i) q^{8} +1.03775e15 q^{9} +(-2.18978e15 + 7.63913e15i) q^{10} +6.68515e16i q^{11} +(6.49683e16 - 1.04011e17i) q^{12} +5.92013e17 q^{13} +(1.99872e15 + 5.72939e14i) q^{14} +3.46228e18i q^{15} +(8.09220e18 + 1.65771e19i) q^{16} +4.82732e19 q^{17} +(-1.87405e19 + 6.53770e19i) q^{18} -9.57586e19i q^{19} +(-4.41711e20 - 2.75907e20i) q^{20} +9.05881e17 q^{21} +(-4.21156e21 - 1.20726e21i) q^{22} -5.33527e20i q^{23} +(5.37930e21 + 5.97123e21i) q^{24} -8.57947e21 q^{25} +(-1.06910e22 + 3.72961e22i) q^{26} +8.25400e22i q^{27} +(-7.21889e19 + 1.15570e20i) q^{28} -4.06224e23 q^{29} +(-2.18120e23 - 6.25246e22i) q^{30} +4.12012e23i q^{31} +(-1.19047e24 + 2.10438e23i) q^{32} -1.90881e24 q^{33} +(-8.71755e23 + 3.04116e24i) q^{34} -3.84709e21i q^{35} +(-3.78024e24 - 2.36126e24i) q^{36} +1.13492e25 q^{37} +(6.03268e24 + 1.72928e24i) q^{38} +1.69037e25i q^{39} +(2.53586e25 - 2.28447e25i) q^{40} -2.76466e23 q^{41} +(-1.63591e22 + 5.70694e22i) q^{42} -1.68374e26i q^{43} +(1.52111e26 - 2.43522e26i) q^{44} +1.25836e26 q^{45} +(3.36116e25 + 9.63485e24i) q^{46} +7.88873e26i q^{47} +(-4.73324e26 + 2.31056e26i) q^{48} +1.10443e27 q^{49} +(1.54935e26 - 5.40496e26i) q^{50} +1.37834e27i q^{51} +(-2.15654e27 - 1.34704e27i) q^{52} -5.53595e27 q^{53} +(-5.19992e27 - 1.49057e27i) q^{54} +8.10630e27i q^{55} +(-5.97716e24 - 6.63488e24i) q^{56} +2.73419e27 q^{57} +(7.33590e27 - 2.55916e28i) q^{58} +4.25442e28i q^{59} +(7.87795e27 - 1.26122e28i) q^{60} +5.00768e28 q^{61} +(-2.59563e28 - 7.44043e27i) q^{62} -3.29240e25i q^{63} +(8.24109e27 - 7.87984e28i) q^{64} +7.17866e28 q^{65} +(3.44707e28 - 1.20253e29i) q^{66} +1.33261e29i q^{67} +(-1.75846e29 - 1.09839e29i) q^{68} +1.52338e28 q^{69} +(2.42362e26 + 6.94736e25i) q^{70} +5.68414e29i q^{71} +(2.17023e29 - 1.95509e29i) q^{72} -6.17148e29 q^{73} +(-2.04953e29 + 7.14989e29i) q^{74} -2.44969e29i q^{75} +(-2.17885e29 + 3.48823e29i) q^{76} +2.12095e27 q^{77} +(-1.06491e30 - 3.05261e29i) q^{78} -1.44347e30i q^{79} +(9.81247e29 + 2.01011e30i) q^{80} -4.33789e29 q^{81} +(4.99263e27 - 1.74170e28i) q^{82} -6.98874e30i q^{83} +(-3.29988e27 - 2.06121e27i) q^{84} +5.85353e30 q^{85} +(1.06074e31 + 3.04063e30i) q^{86} -1.15989e31i q^{87} +(1.25946e31 + 1.39805e31i) q^{88} -1.07508e31 q^{89} +(-2.27244e30 + 7.92750e30i) q^{90} -1.87824e28i q^{91} +(-1.21397e30 + 1.94350e30i) q^{92} -1.17642e31 q^{93} +(-4.96981e31 - 1.42461e31i) q^{94} -1.16115e31i q^{95} +(-6.00862e30 - 3.39914e31i) q^{96} -3.35405e31 q^{97} +(-1.99446e31 + 6.95775e31i) q^{98} +6.93751e31i 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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