LMFDB - Embedded newform 4.33.b.b.3.11

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			3.11
Root			$-5.00408e6i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.33.b.b.3.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(46092.7 - 46587.9i) q^{2} -8.00653e7i q^{3} +(-4.59006e7 - 4.29472e9i) q^{4} -3.25403e10 q^{5} +(-3.73007e12 - 3.69042e12i) q^{6} +4.74477e13i q^{7} +(-2.02198e14 - 1.95817e14i) q^{8} -4.55743e15 q^{9} +O(q^{10})$	\(q+(46092.7 - 46587.9i) q^{2} -8.00653e7i q^{3} +(-4.59006e7 - 4.29472e9i) q^{4} -3.25403e10 q^{5} +(-3.73007e12 - 3.69042e12i) q^{6} +4.74477e13i q^{7} +(-2.02198e14 - 1.95817e14i) q^{8} -4.55743e15 q^{9} +(-1.49987e15 + 1.51599e15i) q^{10} +1.35259e16i q^{11} +(-3.43858e17 + 3.67504e15i) q^{12} +9.45442e16 q^{13} +(2.21049e18 + 2.18699e18i) q^{14} +2.60535e18i q^{15} +(-1.84425e19 + 3.94261e17i) q^{16} +6.35019e18 q^{17} +(-2.10064e20 + 2.12321e20i) q^{18} -4.93031e20i q^{19} +(1.49362e18 + 1.39752e20i) q^{20} +3.79891e21 q^{21} +(6.30141e20 + 6.23443e20i) q^{22} -4.92552e21i q^{23} +(-1.56781e22 + 1.61890e22i) q^{24} -2.22242e22 q^{25} +(4.35779e21 - 4.40461e21i) q^{26} +2.16529e23i q^{27} +(2.03775e23 - 2.17788e21i) q^{28} -2.04879e23 q^{29} +(1.21378e23 + 1.20087e23i) q^{30} +8.15726e23i q^{31} +(-8.31698e23 + 8.77372e23i) q^{32} +1.08295e24 q^{33} +(2.92697e23 - 2.95842e23i) q^{34} -1.54396e24i q^{35} +(2.09189e23 + 1.95729e25i) q^{36} +8.64253e24 q^{37} +(-2.29693e25 - 2.27251e25i) q^{38} -7.56970e24i q^{39} +(6.57958e24 + 6.37194e24i) q^{40} -9.37253e25 q^{41} +(1.75102e26 - 1.76983e26i) q^{42} -9.13599e25i q^{43} +(5.80898e25 - 6.20845e23i) q^{44} +1.48300e26 q^{45} +(-2.29470e26 - 2.27030e26i) q^{46} -4.69294e26i q^{47} +(3.15666e25 + 1.47661e27i) q^{48} -1.14686e27 q^{49} +(-1.02437e27 + 1.03538e27i) q^{50} -5.08430e26i q^{51} +(-4.33963e24 - 4.06041e26i) q^{52} +3.40698e27 q^{53} +(1.00876e28 + 9.98040e27i) q^{54} -4.40135e26i q^{55} +(9.29106e27 - 9.59382e27i) q^{56} -3.94747e28 q^{57} +(-9.44342e27 + 9.54489e27i) q^{58} +2.87556e27i q^{59} +(1.11892e28 - 1.19587e26i) q^{60} +7.72100e27 q^{61} +(3.80030e28 + 3.75990e28i) q^{62} -2.16239e29i q^{63} +(2.53976e27 + 7.91874e28i) q^{64} -3.07650e27 q^{65} +(4.99161e28 - 5.04524e28i) q^{66} -8.28696e28i q^{67} +(-2.91478e26 - 2.72723e28i) q^{68} -3.94363e29 q^{69} +(-7.19300e28 - 7.11654e28i) q^{70} +2.37111e29i q^{71} +(9.21502e29 + 8.92420e29i) q^{72} -4.61844e27 q^{73} +(3.98357e29 - 4.02637e29i) q^{74} +1.77939e30i q^{75} +(-2.11743e30 + 2.26304e28i) q^{76} -6.41771e29 q^{77} +(-3.52657e29 - 3.48908e29i) q^{78} -3.06260e30i q^{79} +(6.00126e29 - 1.28294e28i) q^{80} +8.89145e30 q^{81} +(-4.32005e30 + 4.36647e30i) q^{82} +3.67153e29i q^{83} +(-1.74372e29 - 1.63153e31i) q^{84} -2.06637e29 q^{85} +(-4.25627e30 - 4.21102e30i) q^{86} +1.64037e31i q^{87} +(2.64859e30 - 2.73490e30i) q^{88} -2.12166e31 q^{89} +(6.83554e30 - 6.90899e30i) q^{90} +4.48590e30i q^{91} +(-2.11537e31 + 2.26084e29i) q^{92} +6.53113e31 q^{93} +(-2.18634e31 - 2.16310e31i) q^{94} +1.60434e31i q^{95} +(7.02470e31 + 6.65901e31i) q^{96} +2.45829e30 q^{97} +(-5.28617e31 + 5.34297e31i) q^{98} -6.16431e31i 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 $

$2$	46092.7	−	46587.9i	0.703318	−	0.710875i
$2$	46092.7	−	46587.9i	0.703318	−	0.710875i
$3$		−	8.00653e7i		−	1.85996i	−0.367608	−	0.929981i	$-0.619823\pi$
$3$		−	8.00653e7i		−	1.85996i	0.367608	−	0.929981i	$-0.380177\pi$
$4$	−4.59006e7	−	4.29472e9i	−0.0106871	−	0.999943i
$5$	−3.25403e10			−0.213256			−0.106628	−	0.994299i	$-0.534005\pi$
$5$	−3.25403e10			−0.213256			−0.106628	+	0.994299i	$0.534005\pi$
$6$	−3.73007e12	−	3.69042e12i	−1.32220	−	1.30815i
$7$			4.74477e13i			1.42773i	0.700283	+	0.713866i	$0.253057\pi$
$7$			4.74477e13i			1.42773i	−0.700283	+	0.713866i	$0.746943\pi$
$8$	−2.02198e14	−	1.95817e14i	−0.718351	−	0.695681i
$9$	−4.55743e15			−2.45946
$10$	−1.49987e15	+	1.51599e15i	−0.149987	+	0.151599i
$11$			1.35259e16i			0.294362i	0.989110	+	0.147181i	$0.0470200\pi$
$11$			1.35259e16i			0.294362i	−0.989110	+	0.147181i	$0.952980\pi$
$12$	−3.43858e17	+	3.67504e15i	−1.85986	+	0.0198775i
$13$	9.45442e16			0.142083			0.0710413	−	0.997473i	$-0.477368\pi$
$13$	9.45442e16			0.142083			0.0710413	+	0.997473i	$0.477368\pi$
$14$	2.21049e18	+	2.18699e18i	1.01494	+	1.00415i
$15$			2.60535e18i			0.396648i
$16$	−1.84425e19	+	3.94261e17i	−0.999772	+	0.0213729i
$17$	6.35019e18			0.130498			0.0652491	−	0.997869i	$-0.479216\pi$
$17$	6.35019e18			0.130498			0.0652491	+	0.997869i	$0.479216\pi$
$18$	−2.10064e20	+	2.12321e20i	−1.72978	+	1.74837i
$19$		−	4.93031e20i		−	1.70929i	−0.519210	−	0.854647i	$-0.673774\pi$
$19$		−	4.93031e20i		−	1.70929i	0.519210	−	0.854647i	$-0.326226\pi$
$20$	1.49362e18	+	1.39752e20i	0.00227908	+	0.213244i
$21$	3.79891e21			2.65553
$22$	6.30141e20	+	6.23443e20i	0.209255	+	0.207030i
$23$		−	4.92552e21i		−	0.803168i	−0.915822	−	0.401584i	$-0.868460\pi$
$23$		−	4.92552e21i		−	0.803168i	0.915822	−	0.401584i	$-0.131540\pi$
$24$	−1.56781e22	+	1.61890e22i	−1.29394	+	1.33611i
$25$	−2.22242e22			−0.954522
$26$	4.35779e21	−	4.40461e21i	0.0999293	−	0.101003i
$27$			2.16529e23i			2.71454i
$28$	2.03775e23	−	2.17788e21i	1.42765	−	0.0152583i
$29$	−2.04879e23			−0.818709			−0.409355	−	0.912375i	$-0.634246\pi$
$29$	−2.04879e23			−0.818709			−0.409355	+	0.912375i	$0.634246\pi$
$30$	1.21378e23	+	1.20087e23i	0.281967	+	0.278970i
$31$			8.15726e23i			1.12139i	0.828022	+	0.560696i	$0.189466\pi$
$31$			8.15726e23i			1.12139i	−0.828022	+	0.560696i	$0.810534\pi$
$32$	−8.31698e23	+	8.77372e23i	−0.687964	+	0.725745i
$33$	1.08295e24			0.547502
$34$	2.92697e23	−	2.95842e23i	0.0917817	−	0.0927679i
$35$		−	1.54396e24i		−	0.304473i
$36$	2.09189e23	+	1.95729e25i	0.0262844	+	2.45932i
$37$	8.64253e24			0.700508			0.350254	−	0.936655i	$-0.386095\pi$
$37$	8.64253e24			0.700508			0.350254	+	0.936655i	$0.386095\pi$
$38$	−2.29693e25	−	2.27251e25i	−1.21509	−	1.20218i
$39$		−	7.56970e24i		−	0.264268i
$40$	6.57958e24	+	6.37194e24i	0.153193	+	0.148358i
$41$	−9.37253e25			−1.46999			−0.734996	−	0.678071i	$-0.762816\pi$
$41$	−9.37253e25			−1.46999			−0.734996	+	0.678071i	$0.762816\pi$
$42$	1.75102e26	−	1.76983e26i	1.86768	−	1.88775i
$43$		−	9.13599e25i		−	0.668744i	−0.942441	−	0.334372i	$-0.891476\pi$
$43$		−	9.13599e25i		−	0.668744i	0.942441	−	0.334372i	$-0.108524\pi$
$44$	5.80898e25	−	6.20845e23i	0.294345	−	0.00314587i
$45$	1.48300e26			0.524495
$46$	−2.29470e26	−	2.27030e26i	−0.570952	−	0.564883i
$47$		−	4.69294e26i		−	0.827712i	−0.910342	−	0.413856i	$-0.864182\pi$
$47$		−	4.69294e26i		−	0.827712i	0.910342	−	0.413856i	$-0.135818\pi$
$48$	3.15666e25	+	1.47661e27i	0.0397528	+	1.85954i
$49$	−1.14686e27			−1.03842
$50$	−1.02437e27	+	1.03538e27i	−0.671333	+	0.678546i
$51$		−	5.08430e26i		−	0.242722i
$52$	−4.33963e24	−	4.06041e26i	−0.00151845	−	0.142075i
$53$	3.40698e27			0.878932			0.439466	−	0.898259i	$-0.355168\pi$
$53$	3.40698e27			0.878932			0.439466	+	0.898259i	$0.355168\pi$
$54$	1.00876e28	+	9.98040e27i	1.92970	+	1.90918i
$55$		−	4.40135e26i		−	0.0627745i
$56$	9.29106e27	−	9.59382e27i	0.993246	−	1.02561i
$57$	−3.94747e28			−3.17922
$58$	−9.44342e27	+	9.54489e27i	−0.575813	+	0.582000i
$59$			2.87556e27i			0.133380i	0.997774	+	0.0666898i	$0.0212438\pi$
$59$			2.87556e27i			0.133380i	−0.997774	+	0.0666898i	$0.978756\pi$
$60$	1.11892e28	−	1.19587e26i	0.396626	−	0.00423901i
$61$	7.72100e27			0.210086			0.105043	−	0.994468i	$-0.466502\pi$
$61$	7.72100e27			0.210086			0.105043	+	0.994468i	$0.466502\pi$
$62$	3.80030e28	+	3.75990e28i	0.797169	+	0.788695i
$63$		−	2.16239e29i		−	3.51145i
$64$	2.53976e27	+	7.91874e28i	0.0320563	+	0.999486i
$65$	−3.07650e27			−0.0303000
$66$	4.99161e28	−	5.04524e28i	0.385068	−	0.389206i
$67$		−	8.28696e28i		−	0.502572i	−0.967913	−	0.251286i	$-0.919147\pi$
$67$		−	8.28696e28i		−	0.502572i	0.967913	−	0.251286i	$-0.0808534\pi$
$68$	−2.91478e26	−	2.72723e28i	−0.00139464	−	0.130491i
$69$	−3.94363e29			−1.49386
$70$	−7.19300e28	−	7.11654e28i	−0.216442	−	0.214141i
$71$			2.37111e29i			0.568615i	0.958733	+	0.284307i	$0.0917637\pi$
$71$			2.37111e29i			0.568615i	−0.958733	+	0.284307i	$0.908236\pi$
$72$	9.21502e29	+	8.92420e29i	1.76675	+	1.71100i
$73$	−4.61844e27			−0.00710117			−0.00355058	−	0.999994i	$-0.501130\pi$
$73$	−4.61844e27			−0.00710117			−0.00355058	+	0.999994i	$0.501130\pi$
$74$	3.98357e29	−	4.02637e29i	0.492680	−	0.497974i
$75$			1.77939e30i			1.77537i
$76$	−2.11743e30	+	2.26304e28i	−1.70920	+	0.0182673i
$77$	−6.41771e29			−0.420270
$78$	−3.52657e29	−	3.48908e29i	−0.187862	−	0.185865i
$79$		−	3.06260e30i		−	1.33063i	−0.746563	−	0.665315i	$-0.768297\pi$
$79$		−	3.06260e30i		−	1.33063i	0.746563	−	0.665315i	$-0.231703\pi$
$80$	6.00126e29	−	1.28294e28i	0.213207	−	0.00455791i
$81$	8.89145e30			2.58948
$82$	−4.32005e30	+	4.36647e30i	−1.03387	+	1.04498i
$83$			3.67153e29i			0.0723764i	0.999345	+	0.0361882i	$0.0115216\pi$
$83$			3.67153e29i			0.0723764i	−0.999345	+	0.0361882i	$0.988478\pi$
$84$	−1.74372e29	−	1.63153e31i	−0.0283798	−	2.65537i
$85$	−2.06637e29			−0.0278295
$86$	−4.25627e30	−	4.21102e30i	−0.475394	−	0.470340i
$87$			1.64037e31i			1.52277i
$88$	2.64859e30	−	2.73490e30i	0.204782	−	0.211455i
$89$	−2.12166e31			−1.36910			−0.684550	−	0.728966i	$-0.740001\pi$
$89$	−2.12166e31			−1.36910			−0.684550	+	0.728966i	$0.740001\pi$
$90$	6.83554e30	−	6.90899e30i	0.368887	−	0.372850i
$91$			4.48590e30i			0.202856i
$92$	−2.11537e31	+	2.26084e29i	−0.803122	+	0.00858351i
$93$	6.53113e31			2.08574
$94$	−2.18634e31	−	2.16310e31i	−0.588400	−	0.582145i
$95$			1.60434e31i			0.364517i
$96$	7.02470e31	+	6.65901e31i	1.34986	+	1.27959i
$97$	2.45829e30			0.0400208			0.0200104	−	0.999800i	$-0.493630\pi$
$97$	2.45829e30			0.0400208			0.0200104	+	0.999800i	$0.493630\pi$
$98$	−5.28617e31	+	5.34297e31i	−0.730338	+	0.738185i
$99$		−	6.16431e31i		−	0.723971i
$100$	1.02010e30	+	9.54467e31i	0.0102010	+	0.954467i
$101$	−1.51581e32			−1.29271			−0.646356	−	0.763036i	$-0.723708\pi$
$101$	−1.51581e32			−1.29271			−0.646356	+	0.763036i	$0.723708\pi$
$102$	−2.36867e31	−	2.34349e31i	−0.172545	−	0.170710i
$103$		−	2.50065e30i		−	0.0155833i	−0.999970	−	0.00779163i	$-0.997520\pi$
$103$		−	2.50065e30i		−	0.0155833i	0.999970	−	0.00779163i	$-0.00248018\pi$
$104$	−1.91166e31	−	1.85133e31i	−0.102065	−	0.0988442i
$105$	−1.23618e32			−0.566307
$106$	1.57037e32	−	1.58724e32i	0.618169	−	0.624811i
$107$		−	2.37982e32i		−	0.806129i	−0.915172	−	0.403064i	$-0.867945\pi$
$107$		−	2.37982e32i		−	0.806129i	0.915172	−	0.403064i	$-0.132055\pi$
$108$	9.29932e32	−	9.93881e30i	2.71438	−	0.0290104i
$109$	−3.79577e32			−0.956040			−0.478020	−	0.878349i	$-0.658645\pi$
$109$	−3.79577e32			−0.956040			−0.478020	+	0.878349i	$0.658645\pi$
$110$	−2.05050e31	−	2.02870e31i	−0.0446248	−	0.0441505i
$111$		−	6.91966e32i		−	1.30292i
$112$	−1.87068e31	−	8.75056e32i	−0.0305148	−	1.42741i
$113$	5.36449e32			0.759055			0.379527	−	0.925181i	$-0.376087\pi$
$113$	5.36449e32			0.759055			0.379527	+	0.925181i	$0.376087\pi$
$114$	−1.81949e33	+	1.83904e33i	−2.23600	+	2.26003i
$115$			1.60278e32i			0.171281i
$116$	9.40407e30	+	8.79899e32i	0.00874960	+	0.818662i
$117$	−4.30878e32			−0.349446
$118$	1.33966e32	+	1.32542e32i	0.0948163	+	0.0938084i
$119$			3.01302e32i			0.186316i
$120$	5.10171e32	−	5.26796e32i	0.275941	−	0.284933i
$121$	1.92843e33			0.913351
$122$	3.55882e32	−	3.59705e32i	0.147757	−	0.149345i
$123$			7.50414e33i			2.73413i
$124$	3.50332e33	−	3.74423e31i	1.12133	−	0.0119844i
$125$	1.48082e33			0.416814
$126$	−1.00741e34	−	9.96705e33i	−2.49620	−	2.46966i
$127$		−	4.53645e33i		−	0.990505i	−0.868749	−	0.495252i	$-0.835076\pi$
$127$		−	4.53645e33i		−	0.990505i	0.868749	−	0.495252i	$-0.164924\pi$
$128$	3.80624e33	+	3.53164e33i	0.733056	+	0.680169i
$129$	−7.31475e33			−1.24384
$130$	−1.41804e32	+	1.43328e32i	−0.0213105	+	0.0215395i
$131$			3.62488e33i			0.481896i	0.970538	+	0.240948i	$0.0774583\pi$
$131$			3.62488e33i			0.481896i	−0.970538	+	0.240948i	$0.922542\pi$
$132$	−4.97081e31	−	4.65097e33i	−0.00585119	−	0.547471i
$133$	2.33932e34			2.44041
$134$	−3.86072e33	−	3.81968e33i	−0.357266	−	0.353468i
$135$		−	7.04592e33i		−	0.578892i
$136$	−1.28400e33	−	1.24347e33i	−0.0937435	−	0.0907851i
$137$	−1.09766e33			−0.0712753			−0.0356376	−	0.999365i	$-0.511346\pi$
$137$	−1.09766e33			−0.0712753			−0.0356376	+	0.999365i	$0.511346\pi$
$138$	−1.81772e34	+	1.83725e34i	−1.05066	+	1.06195i
$139$		−	1.65733e34i		−	0.853439i	−0.904384	−	0.426719i	$-0.859669\pi$
$139$		−	1.65733e34i		−	0.853439i	0.904384	−	0.426719i	$-0.140331\pi$
$140$	−6.63089e33	+	7.08688e31i	−0.304455	+	0.00325392i
$141$	−3.75741e34			−1.53951
$142$	1.10465e34	+	1.09291e34i	0.404214	+	0.399917i
$143$			1.27879e33i			0.0418237i
$144$	8.40505e34	−	1.79681e33i	2.45890	−	0.0525658i
$145$	6.66683e33			0.174595
$146$	−2.12876e32	+	2.15164e32i	−0.00499438	+	0.00504804i
$147$			9.18234e34i			1.93142i
$148$	−3.96697e32	−	3.71172e34i	−0.00748638	−	0.700468i
$149$	−6.72732e34			−1.13989			−0.569944	−	0.821684i	$-0.693035\pi$
$149$	−6.72732e34			−1.13989			−0.569944	+	0.821684i	$0.693035\pi$
$150$	8.28979e34	+	8.20166e34i	1.26207	+	1.24865i
$151$		−	1.31684e35i		−	1.80262i	−0.433178	−	0.901308i	$-0.642608\pi$
$151$		−	1.31684e35i		−	1.80262i	0.433178	−	0.901308i	$-0.357392\pi$
$152$	−9.65437e34	+	9.96898e34i	−1.18912	+	1.22787i
$153$	−2.89405e34			−0.320955
$154$	−2.95809e34	+	2.98988e34i	−0.295583	+	0.298759i
$155$		−	2.65440e34i		−	0.239144i
$156$	−3.25098e34	+	3.47454e32i	−0.264253	+	0.00282425i
$157$	6.25240e34			0.458831			0.229415	−	0.973329i	$-0.426319\pi$
$157$	6.25240e34			0.458831			0.229415	+	0.973329i	$0.426319\pi$
$158$	−1.42680e35	−	1.41164e35i	−0.945912	−	0.935856i
$159$		−	2.72781e35i		−	1.63478i
$160$	2.70637e34	−	2.85499e34i	0.146713	−	0.154770i
$161$	2.33705e35			1.14671
$162$	4.09830e35	−	4.14234e35i	1.82123	−	1.84080i
$163$			3.41681e35i			1.37600i	0.725709	+	0.688001i	$0.241512\pi$
$163$			3.41681e35i			1.37600i	−0.725709	+	0.688001i	$0.758488\pi$
$164$	4.30205e33	+	4.02524e35i	0.0157099	+	1.46991i
$165$	−3.52396e34			−0.116758
$166$	1.71049e34	+	1.69230e34i	0.0514506	+	0.0509037i
$167$		−	2.40656e35i		−	0.657557i	−0.944407	−	0.328779i	$-0.893363\pi$
$167$		−	2.40656e35i		−	0.657557i	0.944407	−	0.328779i	$-0.106637\pi$
$168$	−7.68132e35	−	7.43891e35i	−1.90760	−	1.84740i
$169$	−4.33841e35			−0.979813
$170$	−9.52446e33	+	9.62680e33i	−0.0195730	+	0.0197833i
$171$			2.24695e36i			4.20394i
$172$	−3.92365e35	+	4.19347e33i	−0.668706	+	0.00714692i
$173$	6.96522e35			1.08192			0.540962	−	0.841047i	$-0.318060\pi$
$173$	6.96522e35			1.08192			0.540962	+	0.841047i	$0.318060\pi$
$174$	7.64214e35	+	7.56090e35i	1.08250	+	1.07099i
$175$		−	1.05449e36i		−	1.36280i
$176$	−5.33271e33	−	2.49451e35i	−0.00629137	−	0.294295i
$177$	2.30232e35			0.248081
$178$	−9.77929e35	+	9.88436e35i	−0.962913	+	0.973260i
$179$		−	9.85163e35i		−	0.886869i	−0.896307	−	0.443435i	$-0.853760\pi$
$179$		−	9.85163e35i		−	0.886869i	0.896307	−	0.443435i	$-0.146240\pi$
$180$	−6.80706e33	−	6.36907e35i	−0.00560531	−	0.524465i
$181$	1.91175e36			1.44070			0.720349	−	0.693611i	$-0.243982\pi$
$181$	1.91175e36			1.44070			0.720349	+	0.693611i	$0.243982\pi$
$182$	2.08989e35	+	2.06767e35i	0.144205	+	0.142672i
$183$		−	6.18184e35i		−	0.390751i
$184$	−9.64499e35	+	9.95929e35i	−0.558749	+	0.576957i
$185$	−2.81230e35			−0.149388
$186$	3.01037e36	−	3.04272e36i	1.46694	−	1.48270i
$187$			8.58918e34i			0.0384137i
$188$	−2.01549e36	+	2.15409e34i	−0.827664	+	0.00884581i
$189$	−1.02738e37			−3.87563
$190$	7.47428e35	+	7.39482e35i	0.259126	+	0.256372i
$191$		−	2.21443e36i		−	0.705876i	−0.935647	−	0.352938i	$-0.885183\pi$
$191$		−	2.21443e36i		−	0.705876i	0.935647	−	0.352938i	$-0.114817\pi$
$192$	6.34016e36	−	2.03347e35i	1.85901	−	0.0596235i
$193$	3.14662e36			0.849037			0.424519	−	0.905419i	$-0.360443\pi$
$193$	3.14662e36			0.849037			0.424519	+	0.905419i	$0.360443\pi$
$194$	1.13309e35	−	1.14527e35i	0.0281473	−	0.0284498i
$195$			2.46320e35i			0.0563568i
$196$	5.26414e34	+	4.92543e36i	0.0110976	+	1.03836i
$197$	6.11775e36			1.18886			0.594432	−	0.804146i	$-0.297377\pi$
$197$	6.11775e36			1.18886			0.594432	+	0.804146i	$0.297377\pi$
$198$	−2.87182e36	−	2.84129e36i	−0.514653	−	0.509182i
$199$		−	1.63495e36i		−	0.270306i	−0.990825	−	0.135153i	$-0.956847\pi$
$199$		−	1.63495e36i		−	0.270306i	0.990825	−	0.135153i	$-0.0431525\pi$
$200$	4.49368e36	+	4.35187e36i	0.685682	+	0.664043i
$201$	−6.63497e36			−0.934765
$202$	−6.98675e36	+	7.06182e36i	−0.909187	+	0.918956i
$203$		−	9.72104e36i		−	1.16890i
$204$	−2.18357e36	+	2.33372e34i	−0.242708	+	0.00259398i
$205$	3.04985e36			0.313485
$206$	−1.16500e35	−	1.15262e35i	−0.0110777	−	0.0109600i
$207$			2.24477e37i			1.97536i
$208$	−1.74363e36	+	3.72750e34i	−0.142050	+	0.00303672i
$209$	6.66867e36			0.503151
$210$	−5.69787e36	+	5.75910e36i	−0.398294	+	0.402574i
$211$			7.39921e36i			0.479364i	0.970851	+	0.239682i	$0.0770432\pi$
$211$			7.39921e36i			0.479364i	−0.970851	+	0.239682i	$0.922957\pi$
$212$	−1.56382e35	−	1.46320e37i	−0.00939321	−	0.878882i
$213$	1.89844e37			1.05760
$214$	−1.10871e37	−	1.09692e37i	−0.573057	−	0.566965i
$215$			2.97288e36i			0.142614i
$216$	4.24000e37	−	4.37817e37i	1.88845	−	1.94999i
$217$	−3.87043e37			−1.60105
$218$	−1.74957e37	+	1.76837e37i	−0.672400	+	0.679625i
$219$			3.69777e35i			0.0132079i
$220$	−1.89026e36	+	2.02025e34i	−0.0627709	+	0.000670875i
$221$	6.00374e35			0.0185415
$222$	−3.22373e37	−	3.18946e37i	−0.926212	−	0.916366i
$223$			5.90826e36i			0.157973i	0.996876	+	0.0789863i	$0.0251683\pi$
$223$			5.90826e36i			0.157973i	−0.996876	+	0.0789863i	$0.974832\pi$
$224$	−4.16293e37	−	3.94621e37i	−1.03617	−	0.982228i
$225$	1.01285e38			2.34761
$226$	2.47263e37	−	2.49920e37i	0.533857	−	0.539593i
$227$		−	8.07545e37i		−	1.62462i	−0.583223	−	0.812312i	$-0.698209\pi$
$227$		−	8.07545e37i		−	1.62462i	0.583223	−	0.812312i	$-0.301791\pi$
$228$	1.81191e36	+	1.69533e38i	0.0339765	+	3.17904i
$229$	2.52873e37			0.442115			0.221058	−	0.975261i	$-0.429049\pi$
$229$	2.52873e37			0.442115			0.221058	+	0.975261i	$0.429049\pi$
$230$	7.46701e36	+	7.38763e36i	0.121759	+	0.120465i
$231$			5.13835e37i			0.781686i
$232$	4.14261e37	+	4.01188e37i	0.588121	+	0.569560i
$233$	−9.45644e37			−1.25324			−0.626618	−	0.779326i	$-0.715561\pi$
$233$	−9.45644e37			−1.25324			−0.626618	+	0.779326i	$0.715561\pi$
$234$	−1.98603e37	+	2.00737e37i	−0.245772	+	0.248413i
$235$			1.52710e37i			0.176515i
$236$	1.23497e37	−	1.31990e35i	0.133372	−	0.00142544i
$237$	−2.45208e38			−2.47492
$238$	1.40370e37	+	1.38878e37i	0.132448	+	0.131040i
$239$			1.78296e38i			1.57317i	0.617484	+	0.786584i	$0.288152\pi$
$239$			1.78296e38i			1.57317i	−0.617484	+	0.786584i	$0.711848\pi$
$240$	−1.02719e36	−	4.80492e37i	−0.00847753	−	0.396558i
$241$	8.20511e37			0.633595			0.316797	−	0.948493i	$-0.397392\pi$
$241$	8.20511e37			0.633595			0.316797	+	0.948493i	$0.397392\pi$
$242$	8.88864e37	−	8.98415e37i	0.642376	−	0.649279i
$243$		−	3.10664e38i		−	2.10179i
$244$	−3.54399e35	−	3.31596e37i	−0.00224520	−	0.210074i
$245$	3.73191e37			0.221449
$246$	3.49602e38	+	3.45886e38i	1.94363	+	1.92296i
$247$		−	4.66132e37i		−	0.242861i
$248$	1.59733e38	−	1.64938e38i	0.780130	−	0.805552i
$249$	2.93962e37			0.134617
$250$	6.82549e37	−	6.89883e37i	0.293153	−	0.296303i
$251$		−	2.58885e38i		−	1.04310i	−0.853220	−	0.521551i	$-0.825354\pi$
$251$		−	2.58885e38i		−	1.04310i	0.853220	−	0.521551i	$-0.174646\pi$
$252$	−9.28688e38	+	9.92552e36i	−3.51125	+	0.0375271i
$253$	6.66218e37			0.236422
$254$	−2.11344e38	−	2.09097e38i	−0.704125	−	0.696640i
$255$			1.65445e37i			0.0517619i
$256$	3.39971e38	−	1.45423e37i	0.999086	−	0.0427361i
$257$	−3.36333e38			−0.928622			−0.464311	−	0.885672i	$-0.653698\pi$
$257$	−3.36333e38			−0.928622			−0.464311	+	0.885672i	$0.653698\pi$
$258$	−3.37156e38	+	3.40779e38i	−0.874815	+	0.884214i
$259$			4.10068e38i			1.00014i
$260$	1.41213e35	+	1.32127e37i	0.000323818	+	0.0302983i
$261$	9.33721e38			2.01358
$262$	1.68876e38	+	1.67080e38i	0.342568	+	0.338926i
$263$		−	3.51698e38i		−	0.671239i	−0.941998	−	0.335620i	$-0.891054\pi$
$263$		−	3.51698e38i		−	0.671239i	0.941998	−	0.335620i	$-0.108946\pi$
$264$	−2.18970e38	−	2.12060e38i	−0.393299	−	0.380887i
$265$	−1.10864e38			−0.187438
$266$	1.07825e39	−	1.08984e39i	1.71639	−	1.73483i
$267$			1.69871e39i			2.54647i
$268$	−3.55902e38	+	3.80376e36i	−0.502543	+	0.00537102i
$269$	−5.77334e37			−0.0768052			−0.0384026	−	0.999262i	$-0.512227\pi$
$269$	−5.77334e37			−0.0768052			−0.0384026	+	0.999262i	$0.512227\pi$
$270$	−3.28255e38	−	3.24765e38i	−0.411520	−	0.407145i
$271$			1.07532e39i			1.27066i	0.772242	+	0.635328i	$0.219135\pi$
$271$			1.07532e39i			1.27066i	−0.772242	+	0.635328i	$0.780865\pi$
$272$	−1.17114e38	+	2.50363e36i	−0.130468	+	0.00278913i
$273$	3.59165e38			0.377304
$274$	−5.05941e37	+	5.11377e37i	−0.0501292	+	0.0506678i
$275$		−	3.00601e38i		−	0.280975i
$276$	1.81015e37	+	1.69368e39i	0.0159650	+	1.49378i
$277$	−1.81603e39			−1.51164			−0.755819	−	0.654781i	$-0.772761\pi$
$277$	−1.81603e39			−1.51164			−0.755819	+	0.654781i	$0.772761\pi$
$278$	−7.72116e38	−	7.63908e38i	−0.606688	−	0.600239i
$279$		−	3.71761e39i		−	2.75802i
$280$	−3.02334e38	+	3.12186e38i	−0.211816	+	0.218718i
$281$	2.38762e39			1.58003			0.790014	−	0.613089i	$-0.210073\pi$
$281$	2.38762e39			1.58003			0.790014	+	0.613089i	$0.210073\pi$
$282$	−1.73189e39	+	1.75050e39i	−1.08277	+	1.09440i
$283$			2.42757e39i			1.43413i	0.697006	+	0.717065i	$0.254515\pi$
$283$			2.42757e39i			1.43413i	−0.697006	+	0.717065i	$0.745485\pi$
$284$	1.01833e39	−	1.08835e37i	0.568583	−	0.00607683i
$285$	1.28452e39			0.677988
$286$	5.95762e37	+	5.89428e37i	0.0297315	+	0.0294154i
$287$		−	4.44705e39i		−	2.09875i
$288$	3.79040e39	−	3.99856e39i	1.69202	−	1.78494i
$289$	−2.32759e39			−0.982970
$290$	3.07292e38	−	3.10594e38i	0.122796	−	0.124115i
$291$		−	1.96824e38i		−	0.0744371i
$292$	2.11989e35	+	1.98349e37i	7.58907e−5	+	0.00710076i
$293$	−4.98153e39			−1.68842			−0.844210	−	0.536012i	$-0.819930\pi$
$293$	−4.98153e39			−1.68842			−0.844210	+	0.536012i	$0.819930\pi$
$294$	4.27786e39	+	4.23239e39i	1.37300	+	1.35840i
$295$		−	9.35715e37i		−	0.0284440i
$296$	−1.74750e39	−	1.69235e39i	−0.503211	−	0.487330i
$297$	−2.92874e39			−0.799057
$298$	−3.10080e39	+	3.13412e39i	−0.801704	+	0.810318i
$299$		−	4.65679e38i		−	0.114116i
$300$	7.64197e39	−	8.16749e37i	1.77527	−	0.0189735i
$301$	4.33482e39			0.954787
$302$	−6.13490e39	−	6.06969e39i	−1.28144	−	1.26781i
$303$			1.21363e40i			2.40439i
$304$	1.94383e38	+	9.09274e39i	0.0365326	+	1.70890i
$305$	−2.51244e38			−0.0448021
$306$	−1.33395e39	+	1.34828e39i	−0.225733	+	0.228159i
$307$		−	4.44575e39i		−	0.714055i	−0.934094	−	0.357027i	$-0.883790\pi$
$307$		−	4.44575e39i		−	0.714055i	0.934094	−	0.357027i	$-0.116210\pi$
$308$	2.94577e37	+	2.75623e39i	0.00449145	+	0.420246i
$309$	−2.00216e38			−0.0289843
$310$	−1.23663e39	−	1.22348e39i	−0.170001	−	0.168194i
$311$		−	8.05331e39i		−	1.05150i	−0.850640	−	0.525749i	$-0.823785\pi$
$311$		−	8.05331e39i		−	1.05150i	0.850640	−	0.525749i	$-0.176215\pi$
$312$	−1.48227e39	+	1.53058e39i	−0.183846	+	0.189837i
$313$	1.22081e40			1.43859			0.719297	−	0.694703i	$-0.244464\pi$
$313$	1.22081e40			1.43859			0.719297	+	0.694703i	$0.244464\pi$
$314$	2.88190e39	−	2.91286e39i	0.322704	−	0.326171i
$315$			7.03650e39i			0.748838i
$316$	−1.31530e40	+	1.40575e38i	−1.33055	+	0.0142205i
$317$	1.31141e40			1.26122			0.630608	−	0.776101i	$-0.282806\pi$
$317$	1.31141e40			1.26122			0.630608	+	0.776101i	$0.282806\pi$
$318$	−1.27083e40	−	1.25732e40i	−1.16212	−	1.14977i
$319$		−	2.77116e39i		−	0.240997i
$320$	−8.26447e37	−	2.57678e39i	−0.00683621	−	0.213147i
$321$	−1.90541e40			−1.49937
$322$	1.07721e40	−	1.08878e40i	0.806501	−	0.815167i
$323$		−	3.13084e39i		−	0.223060i
$324$	−4.08123e38	−	3.81863e40i	−0.0276739	−	2.58933i
$325$	−2.10117e39			−0.135621
$326$	1.59182e40	+	1.57490e40i	0.978166	+	0.967768i
$327$			3.03909e40i			1.77820i
$328$	1.89511e40	+	1.83530e40i	1.05597	+	1.02265i
$329$	2.22669e40			1.18175
$330$	−1.62429e39	+	1.64174e39i	−0.0821182	+	0.0830005i
$331$		−	4.77499e39i		−	0.229998i	−0.993366	−	0.114999i	$-0.963313\pi$
$331$		−	4.77499e39i		−	0.229998i	0.993366	−	0.114999i	$-0.0366866\pi$
$332$	1.57682e39	−	1.68525e37i	0.0723723	−	0.000773492i
$333$	−3.93877e40			−1.72287
$334$	−1.12117e40	−	1.10925e40i	−0.467441	−	0.462472i
$335$			2.69660e39i			0.107177i
$336$	−7.00616e40	+	1.49776e39i	−2.65492	+	0.0567563i
$337$	2.78352e40			1.00581			0.502906	−	0.864341i	$-0.332264\pi$
$337$	2.78352e40			1.00581			0.502906	+	0.864341i	$0.332264\pi$
$338$	−1.99969e40	+	2.02117e40i	−0.689120	+	0.696524i
$339$		−	4.29509e40i		−	1.41181i
$340$	9.48478e36	+	8.87450e38i	0.000297416	+	0.0278279i
$341$	−1.10334e40			−0.330095
$342$	1.04681e41	+	1.03568e41i	2.98847	+	2.95670i
$343$		−	2.01317e39i		−	0.0548498i
$344$	−1.78898e40	+	1.84728e40i	−0.465233	+	0.480393i
$345$	1.28327e40			0.318575
$346$	3.21045e40	−	3.24495e40i	0.760937	−	0.769114i
$347$		−	2.07944e40i		−	0.470625i	−0.971920	−	0.235312i	$-0.924389\pi$
$347$		−	2.07944e40i		−	0.470625i	0.971920	−	0.235312i	$-0.0756113\pi$
$348$	7.04493e40	−	7.52940e38i	1.52268	−	0.0162739i
$349$	2.76042e39			0.0569861			0.0284931	−	0.999594i	$-0.490929\pi$
$349$	2.76042e39			0.0569861			0.0284931	+	0.999594i	$0.490929\pi$
$350$	−4.91263e40	−	4.86041e40i	−0.968781	−	0.958483i
$351$			2.04715e40i			0.385689i
$352$	−1.18672e40	−	1.12494e40i	−0.213632	−	0.202510i
$353$	−9.59897e40			−1.65131			−0.825656	−	0.564174i	$-0.809195\pi$
$353$	−9.59897e40			−1.65131			−0.825656	+	0.564174i	$0.809195\pi$
$354$	1.06120e40	−	1.07260e40i	0.174480	−	0.176355i
$355$		−	7.71567e39i		−	0.121261i
$356$	9.73854e38	+	9.11193e40i	0.0146317	+	1.36902i
$357$	2.41238e40			0.346541
$358$	−4.58967e40	−	4.54088e40i	−0.630453	−	0.623751i
$359$			6.27660e40i			0.824543i	0.911061	+	0.412271i	$0.135264\pi$
$359$			6.27660e40i			0.824543i	−0.911061	+	0.412271i	$0.864736\pi$
$360$	−2.99859e40	−	2.90396e40i	−0.376771	−	0.364881i
$361$	−1.59881e41			−1.92168
$362$	8.81175e40	−	8.90643e40i	1.01327	−	1.02416i
$363$		−	1.54400e41i		−	1.69880i
$364$	1.92657e40	−	2.05906e38i	0.202844	−	0.00216793i
$365$	1.50286e38			0.00151437
$366$	−2.87999e40	−	2.84938e40i	−0.277775	−	0.274823i
$367$		−	8.57201e39i		−	0.0791454i	−0.999217	−	0.0395727i	$-0.987400\pi$
$367$		−	8.57201e39i		−	0.0791454i	0.999217	−	0.0395727i	$-0.0125997\pi$
$368$	1.94194e39	+	9.08390e40i	0.0171660	+	0.802985i
$369$	4.27146e41			3.61539
$370$	−1.29627e40	+	1.31019e40i	−0.105067	+	0.106196i
$371$			1.61653e41i			1.25488i
$372$	−2.99783e39	−	2.80494e41i	−0.0222905	−	2.08563i
$373$	1.37825e41			0.981716			0.490858	−	0.871240i	$-0.336683\pi$
$373$	1.37825e41			0.981716			0.490858	+	0.871240i	$0.336683\pi$
$374$	4.00152e39	+	3.95898e39i	0.0273073	+	0.0270170i
$375$		−	1.18562e41i		−	0.775258i
$376$	−9.18956e40	+	9.48902e40i	−0.575823	+	0.594588i
$377$	−1.93701e40			−0.116324
$378$	−4.73547e41	+	4.78635e41i	−2.72580	+	2.75509i
$379$			1.50229e41i			0.828946i	0.910062	+	0.414473i	$0.136034\pi$
$379$			1.50229e41i			0.828946i	−0.910062	+	0.414473i	$0.863966\pi$
$380$	6.89019e40	−	7.36401e38i	0.364497	−	0.00389562i
$381$	−3.63212e41			−1.84230
$382$	−1.03166e41	−	1.02069e41i	−0.501790	−	0.496455i
$383$			2.19628e41i			1.02449i	0.858840	+	0.512244i	$0.171186\pi$
$383$			2.19628e41i			1.02449i	−0.858840	+	0.512244i	$0.828814\pi$
$384$	2.82762e41	−	3.04748e41i	1.26509	−	1.36346i
$385$	2.08834e40			0.0896251
$386$	1.45036e41	−	1.46594e41i	0.597143	−	0.603560i
$387$			4.16366e41i			1.64475i
$388$	−1.12837e38	−	1.05577e40i	−0.000427705	−	0.0400185i
$389$	2.11359e40			0.0768826			0.0384413	−	0.999261i	$-0.487761\pi$
$389$	2.11359e40			0.0768826			0.0384413	+	0.999261i	$0.487761\pi$
$390$	1.14756e40	+	1.13536e40i	0.0400627	+	0.0396368i
$391$		−	3.12780e40i		−	0.104812i
$392$	2.31892e41	+	2.24574e41i	0.745948	+	0.722407i
$393$	2.90227e41			0.896308
$394$	2.81983e41	−	2.85013e41i	0.836150	−	0.845134i
$395$			9.96581e40i			0.283765i
$396$	−2.64740e41	+	2.82945e39i	−0.723930	+	0.00773713i
$397$	−4.90660e41			−1.28864			−0.644322	−	0.764754i	$-0.722860\pi$
$397$	−4.90660e41			−1.28864			−0.644322	+	0.764754i	$0.722860\pi$
$398$	−7.61689e40	−	7.53592e40i	−0.192154	−	0.190111i
$399$		−	1.87298e42i		−	4.53907i
$400$	4.09870e41	−	8.76213e39i	0.954304	−	0.0204009i
$401$	1.99805e41			0.446989			0.223494	−	0.974705i	$-0.428254\pi$
$401$	1.99805e41			0.446989			0.223494	+	0.974705i	$0.428254\pi$
$402$	−3.05824e41	+	3.09110e41i	−0.657437	+	0.664501i
$403$			7.71221e40i			0.159330i
$404$	6.95764e39	+	6.50996e41i	0.0138153	+	1.29264i
$405$	−2.89330e41			−0.552222
$406$	−4.52883e41	−	4.48069e41i	−0.830940	−	0.822106i
$407$			1.16898e41i			0.206203i
$408$	−9.95591e40	+	1.02803e41i	−0.168857	+	0.174359i
$409$	3.16160e41			0.515625			0.257812	−	0.966195i	$-0.416998\pi$
$409$	3.16160e41			0.515625			0.257812	+	0.966195i	$0.416998\pi$
$410$	1.40576e41	−	1.42086e41i	0.220480	−	0.222849i
$411$			8.78845e40i			0.132569i
$412$	−1.07396e40	+	1.14782e38i	−0.0155824	+	0.000166539i
$413$	−1.36439e41			−0.190430
$414$	1.04579e42	+	1.03467e42i	1.40423	+	1.38931i
$415$		−	1.19473e40i		−	0.0154347i
$416$	−7.86321e40	+	8.29504e40i	−0.0977478	+	0.103116i
$417$	−1.32695e42			−1.58736
$418$	3.07377e41	−	3.10679e41i	0.353875	−	0.357678i
$419$		−	2.27724e41i		−	0.252338i	−0.992009	−	0.126169i	$-0.959732\pi$
$419$		−	2.27724e41i		−	0.252338i	0.992009	−	0.126169i	$-0.0402682\pi$
$420$	5.67413e39	+	5.30904e41i	0.00605216	+	0.566275i
$421$	5.81964e41			0.597561			0.298781	−	0.954322i	$-0.403420\pi$
$421$	5.81964e41			0.597561			0.298781	+	0.954322i	$0.403420\pi$
$422$	3.44714e41	+	3.41049e41i	0.340768	+	0.337146i
$423$			2.13877e42i			2.03572i
$424$	−6.88883e41	−	6.67143e41i	−0.631382	−	0.611456i
$425$	−1.41128e41			−0.124563
$426$	8.75040e41	−	8.84442e41i	0.743831	−	0.751823i
$427$			3.66344e41i			0.299946i
$428$	−1.02207e42	+	1.09235e40i	−0.806083	+	0.00861515i
$429$	1.02387e41			0.0777905
$430$	1.38500e41	+	1.37028e41i	0.101381	+	0.100303i
$431$			6.23287e41i			0.439594i	0.975546	+	0.219797i	$0.0705395\pi$
$431$			6.23287e41i			0.439594i	−0.975546	+	0.219797i	$0.929461\pi$
$432$	−8.53689e40	−	3.99334e42i	−0.0580176	−	2.71392i
$433$	2.42979e42			1.59134			0.795669	−	0.605732i	$-0.207120\pi$
$433$	2.42979e42			1.59134			0.795669	+	0.605732i	$0.207120\pi$
$434$	−1.78399e42	+	1.80315e42i	−1.12604	+	1.13814i
$435$		−	5.33781e41i		−	0.324740i
$436$	1.74228e40	+	1.63018e42i	0.0102173	+	0.955985i
$437$	−2.42843e42			−1.37285
$438$	1.72271e40	+	1.70440e40i	0.00938917	+	0.00928936i
$439$		−	1.23596e42i		−	0.649489i	−0.945802	−	0.324744i	$-0.894722\pi$
$439$		−	1.23596e42i		−	0.649489i	0.945802	−	0.324744i	$-0.105278\pi$
$440$	−8.61859e40	+	8.89944e40i	−0.0436710	+	0.0450941i
$441$	5.22672e42			2.55394
$442$	2.76728e40	−	2.79702e40i	0.0130406	−	0.0131807i
$443$		−	3.70666e42i		−	1.68470i	−0.538928	−	0.842352i	$-0.681170\pi$
$443$		−	3.70666e42i		−	1.68470i	0.538928	−	0.842352i	$-0.318830\pi$
$444$	−2.97180e42	+	3.17617e40i	−1.30284	+	0.0139244i
$445$	6.90394e41			0.291969
$446$	2.75254e41	+	2.72327e41i	0.112299	+	0.111105i
$447$			5.38625e42i			2.12015i
$448$	−3.75726e42	+	1.20506e41i	−1.42700	+	0.0457678i
$449$	1.53593e42			0.562898			0.281449	−	0.959576i	$-0.409185\pi$
$449$	1.53593e42			0.562898			0.281449	+	0.959576i	$0.409185\pi$
$450$	4.66850e42	−	4.71866e42i	1.65111	−	1.66886i
$451$		−	1.26771e42i		−	0.432710i
$452$	−2.46233e40	−	2.30390e42i	−0.00811207	−	0.759011i
$453$	−1.05434e43			−3.35280
$454$	−3.76218e42	−	3.72219e42i	−1.15491	−	1.14263i
$455$		−	1.45973e41i		−	0.0432603i
$456$	7.98169e42	+	7.72980e42i	2.28380	+	2.21172i
$457$	9.11690e41			0.251877			0.125938	−	0.992038i	$-0.459806\pi$
$457$	9.11690e41			0.251877			0.125938	+	0.992038i	$0.459806\pi$
$458$	1.16556e42	−	1.17808e42i	0.310948	−	0.314289i
$459$			1.37500e42i			0.354242i
$460$	6.88349e41	−	7.35685e39i	0.171271	−	0.00183049i
$461$	2.18901e42			0.526057			0.263029	−	0.964788i	$-0.415279\pi$
$461$	2.18901e42			0.526057			0.263029	+	0.964788i	$0.415279\pi$
$462$	2.39385e42	+	2.36840e42i	0.555681	+	0.549774i
$463$			2.51512e42i			0.563980i	0.959417	+	0.281990i	$0.0909945\pi$
$463$			2.51512e42i			0.563980i	−0.959417	+	0.281990i	$0.909006\pi$
$464$	3.77849e42	−	8.07758e40i	0.818522	−	0.0174982i
$465$	−2.12525e42			−0.444798
$466$	−4.35873e42	+	4.40556e42i	−0.881424	+	0.890895i
$467$		−	4.49771e42i		−	0.878864i	−0.898276	−	0.439432i	$-0.855180\pi$
$467$		−	4.49771e42i		−	0.878864i	0.898276	−	0.439432i	$-0.144820\pi$
$468$	1.97776e40	+	1.85050e42i	0.00373456	+	0.349426i
$469$	3.93197e42			0.717538
$470$	7.11442e41	+	7.03879e41i	0.125480	+	0.124146i
$471$		−	5.00600e42i		−	0.853408i
$472$	5.63082e41	−	5.81431e41i	0.0927897	−	0.0958134i
$473$	1.23572e42			0.196853
$474$	−1.13023e43	+	1.14237e43i	−1.74066	+	1.75936i
$475$			1.09572e43i			1.63156i
$476$	1.29401e42	−	1.38300e40i	0.186306	−	0.00199117i
$477$	−1.55270e43			−2.16170
$478$	8.30644e42	+	8.21813e42i	1.11833	+	1.10644i
$479$		−	1.36411e43i		−	1.77616i	−0.459689	−	0.888080i	$-0.652039\pi$
$479$		−	1.36411e43i		−	1.77616i	0.459689	−	0.888080i	$-0.347961\pi$
$480$	−2.28586e42	−	2.16686e42i	−0.287865	−	0.272880i
$481$	8.17100e41			0.0995300
$482$	3.78195e42	−	3.82259e42i	0.445619	−	0.450407i
$483$		−	1.87116e43i		−	2.13283i
$484$	−8.85161e40	−	8.28207e42i	−0.00976104	−	0.913299i
$485$	−7.99935e40			−0.00853468
$486$	−1.44732e43	−	1.43193e43i	−1.49411	−	1.47823i
$487$			1.93772e43i			1.93565i	0.251618	+	0.967827i	$0.419037\pi$
$487$			1.93772e43i			1.93565i	−0.251618	+	0.967827i	$0.580963\pi$
$488$	−1.56117e42	−	1.51190e42i	−0.150915	−	0.146153i
$489$	2.73568e43			2.55931
$490$	1.72014e42	−	1.73862e42i	0.155749	−	0.157423i
$491$			1.38022e41i			0.0120960i	0.999982	+	0.00604802i	$0.00192516\pi$
$491$			1.38022e41i			0.0120960i	−0.999982	+	0.00604802i	$0.998075\pi$
$492$	3.22282e43	−	3.44445e41i	2.73397	−	0.0292198i
$493$	−1.30102e42			−0.106840
$494$	−2.17161e42	−	2.14853e42i	−0.172644	−	0.170809i
$495$			2.00588e42i			0.154391i
$496$	−3.21609e41	−	1.50440e43i	−0.0239674	−	1.12114i
$497$	−1.12504e43			−0.811830
$498$	1.35495e42	−	1.36951e42i	0.0946789	−	0.0956962i
$499$			1.55609e43i			1.05299i	0.850177	+	0.526497i	$0.176495\pi$
$499$			1.55609e43i			1.05299i	−0.850177	+	0.526497i	$0.823505\pi$
$500$	−6.79705e40	−	6.35971e42i	−0.00445452	−	0.416790i
$501$	−1.92682e43			−1.22303
$502$	−1.20609e43	−	1.19327e43i	−0.741515	−	0.733632i
$503$		−	6.36940e42i		−	0.379325i	−0.981849	−	0.189662i	$-0.939261\pi$
$503$		−	6.36940e42i		−	0.379325i	0.981849	−	0.189662i	$-0.0607393\pi$
$504$	−4.23433e43	+	4.37231e43i	−2.44285	+	2.52245i
$505$	4.93248e42			0.275679
$506$	3.07078e42	−	3.10377e42i	0.166280	−	0.168067i
$507$			3.47356e43i			1.82241i
$508$	−1.94828e43	+	2.08226e41i	−0.990448	+	0.0105856i
$509$	−1.11048e43			−0.547048			−0.273524	−	0.961865i	$-0.588189\pi$
$509$	−1.11048e43			−0.547048			−0.273524	+	0.961865i	$0.588189\pi$
$510$	7.70772e41	+	7.62579e41i	0.0367962	+	0.0364051i
$511$		−	2.19134e41i		−	0.0101386i
$512$	1.49927e43	−	1.65089e43i	0.672296	−	0.740283i
$513$	1.06756e44			4.63994
$514$	−1.55025e43	+	1.56690e43i	−0.653117	+	0.660134i
$515$			8.13721e40i			0.00332322i
$516$	3.35751e41	+	3.14148e43i	0.0132930	+	1.24377i
$517$	6.34760e42			0.243647
$518$	1.91042e43	+	1.89011e43i	0.710973	+	0.703415i
$519$		−	5.57672e43i		−	2.01234i
$520$	6.22061e41	+	6.02429e41i	0.0217660	+	0.0210791i
$521$	−4.50656e43			−1.52912			−0.764560	−	0.644552i	$-0.777044\pi$
$521$	−4.50656e43			−1.52912			−0.764560	+	0.644552i	$0.777044\pi$
$522$	4.30377e43	−	4.35001e43i	1.41619	−	1.43141i
$523$			2.33715e43i			0.745864i	0.927859	+	0.372932i	$0.121648\pi$
$523$			2.33715e43i			0.745864i	−0.927859	+	0.372932i	$0.878352\pi$
$524$	1.55679e43	−	1.66384e41i	0.481868	−	0.00515005i
$525$	−8.44278e43			−2.53476
$526$	−1.63849e43	−	1.62107e43i	−0.477167	−	0.472095i
$527$			5.18002e42i			0.146339i
$528$	−1.99724e43	+	4.26965e41i	−0.547377	+	0.0117017i
$529$	1.33482e43			0.354921
$530$	−5.11002e42	+	5.16493e42i	−0.131828	+	0.133245i
$531$		−	1.31051e43i		−	0.328042i
$532$	−1.07376e42	−	1.00467e44i	−0.0260808	−	2.44027i
$533$	−8.86118e42			−0.208860
$534$	7.91394e43	+	7.82981e43i	1.81023	+	1.79098i
$535$			7.74402e42i			0.171912i
$536$	−1.62272e43	+	1.67560e43i	−0.349630	+	0.361023i
$537$	−7.88773e43			−1.64954
$538$	−2.66108e42	+	2.68968e42i	−0.0540185	+	0.0545989i
$539$		−	1.55122e43i		−	0.305671i
$540$	−3.02603e43	+	3.23412e41i	−0.578859	+	0.00618666i
$541$	6.53826e43			1.21424			0.607122	−	0.794609i	$-0.292324\pi$
$541$	6.53826e43			1.21424			0.607122	+	0.794609i	$0.292324\pi$
$542$	5.00968e43	+	4.95642e43i	0.903278	+	0.893676i
$543$		−	1.53065e44i		−	2.67964i
$544$	−5.28144e42	+	5.57148e42i	−0.0897780	+	0.0947083i
$545$	1.23516e43			0.203881
$546$	1.65549e43	−	1.67327e43i	0.265365	−	0.268216i
$547$			2.02527e43i			0.315273i	0.987497	+	0.157636i	$0.0503874\pi$
$547$			2.02527e43i			0.315273i	−0.987497	+	0.157636i	$0.949613\pi$
$548$	5.03833e40	+	4.71415e42i	0.000761724	+	0.0712712i
$549$	−3.51879e43			−0.516697
$550$	−1.40044e43	−	1.38555e43i	−0.199738	−	0.197615i
$551$			1.01012e44i			1.39941i
$552$	7.97393e43	+	7.72229e43i	1.07312	+	1.03925i
$553$	1.45314e44			1.89978
$554$	−8.37058e43	+	8.46052e43i	−1.06316	+	1.07459i
$555$			2.25168e43i			0.277855i
$556$	−7.11777e43	+	7.60725e41i	−0.853390	+	0.00912075i
$557$	−8.56431e43			−0.997722			−0.498861	−	0.866682i	$-0.666248\pi$
$557$	−8.56431e43			−0.997722			−0.498861	+	0.866682i	$0.666248\pi$
$558$	−1.73196e44	−	1.71355e44i	−1.96060	−	1.93976i
$559$		−	8.63754e42i		−	0.0950170i
$560$	6.08724e41	+	2.84746e43i	0.00650747	+	0.304403i
$561$	6.87695e42			0.0714480
$562$	1.10052e44	−	1.11234e44i	1.11126	−	1.12320i
$563$		−	1.69794e44i		−	1.66644i	−0.552945	−	0.833218i	$-0.686496\pi$
$563$		−	1.69794e44i		−	1.66644i	0.552945	−	0.833218i	$-0.313504\pi$
$564$	1.72468e42	+	1.61370e44i	0.0164529	+	1.53942i
$565$	−1.74562e43			−0.161873
$566$	1.13095e44	+	1.11893e44i	1.01949	+	1.00865i
$567$			4.21879e44i			3.69708i
$568$	4.64303e43	−	4.79433e43i	0.395575	−	0.408465i
$569$	1.73820e44			1.43981			0.719904	−	0.694074i	$-0.244186\pi$
$569$	1.73820e44			1.43981			0.719904	+	0.694074i	$0.244186\pi$
$570$	5.92068e43	−	5.98430e43i	0.476842	−	0.481965i
$571$			9.06850e43i			0.710162i	0.934835	+	0.355081i	$0.115547\pi$
$571$			9.06850e43i			0.710162i	−0.934835	+	0.355081i	$0.884453\pi$
$572$	5.49205e42	−	5.86972e40i	0.0418213	−	0.000446973i
$573$	−1.77299e44			−1.31290
$574$	−2.07179e44	−	2.04976e44i	−1.49195	−	1.47609i
$575$			1.09466e44i			0.766642i
$576$	−1.15748e43	−	3.60891e44i	−0.0788412	−	2.45819i
$577$	5.56570e43			0.368728			0.184364	−	0.982858i	$-0.440977\pi$
$577$	5.56570e43			0.368728			0.184364	+	0.982858i	$0.440977\pi$
$578$	−1.07285e44	+	1.08437e44i	−0.691341	+	0.698769i
$579$		−	2.51935e44i		−	1.57918i
$580$	−3.06011e41	−	2.86322e43i	−0.00186591	−	0.174585i
$581$	−1.74206e43			−0.103334
$582$	−9.16961e42	−	9.07213e42i	−0.0529155	−	0.0523530i
$583$			4.60823e43i			0.258724i
$584$	9.33839e41	+	9.04368e41i	0.00510113	+	0.00494015i
$585$	1.40209e43			0.0745216
$586$	−2.29612e44	+	2.32079e44i	−1.18750	+	1.20026i
$587$		−	2.62247e44i		−	1.31978i	−0.751362	−	0.659890i	$-0.770603\pi$
$587$		−	2.62247e44i		−	1.31978i	0.751362	−	0.659890i	$-0.229397\pi$
$588$	3.94356e44	−	4.21475e42i	1.93131	−	0.0206412i
$589$	4.02178e44			1.91679
$590$	−4.35930e42	−	4.31296e42i	−0.0202202	−	0.0200052i
$591$		−	4.89819e44i		−	2.21124i
$592$	−1.59390e44	+	3.40741e42i	−0.700348	+	0.0149719i
$593$	−9.29311e43			−0.397453			−0.198727	−	0.980055i	$-0.563681\pi$
$593$	−9.29311e43			−0.397453			−0.198727	+	0.980055i	$0.563681\pi$
$594$	−1.34993e44	+	1.36444e44i	−0.561991	+	0.568030i
$595$		−	9.80447e42i		−	0.0397331i
$596$	3.08788e42	+	2.88920e44i	0.0121821	+	1.13982i
$597$	−1.30903e44			−0.502758
$598$	−2.16950e43	−	2.14644e43i	−0.0811224	−	0.0802600i
$599$			4.04496e44i			1.47260i	0.676655	+	0.736301i	$0.263429\pi$
$599$			4.04496e44i			1.47260i	−0.676655	+	0.736301i	$0.736571\pi$
$600$	3.48434e44	−	3.59788e44i	1.23509	−	1.27534i
$601$	−3.28279e43			−0.113305			−0.0566527	−	0.998394i	$-0.518043\pi$
$601$	−3.28279e43			−0.113305			−0.0566527	+	0.998394i	$0.518043\pi$
$602$	1.99803e44	−	2.01950e44i	0.671519	−	0.678735i
$603$			3.77672e44i			1.23605i
$604$	−5.65548e44	+	6.04440e42i	−1.80251	+	0.0192647i
$605$	−6.27517e43			−0.194778
$606$	5.65407e44	+	5.59396e44i	1.70922	+	1.69105i
$607$		−	2.42531e43i		−	0.0714081i	−0.999362	−	0.0357041i	$-0.988633\pi$
$607$		−	2.42531e43i		−	0.0714081i	0.999362	−	0.0357041i	$-0.0113674\pi$
$608$	4.32571e44	+	4.10053e44i	1.24051	+	1.17593i
$609$	−7.78318e44			−2.17410
$610$	−1.15805e43	+	1.17049e43i	−0.0315101	+	0.0318487i
$611$		−	4.43690e43i		−	0.117603i
$612$	1.32839e42	+	1.24292e44i	0.00343007	+	0.320936i
$613$	−3.90547e44			−0.982440			−0.491220	−	0.871035i	$-0.663449\pi$
$613$	−3.90547e44			−0.982440			−0.491220	+	0.871035i	$0.663449\pi$
$614$	−2.07118e44	−	2.04917e44i	−0.507604	−	0.502208i
$615$		−	2.44187e44i		−	0.583070i
$616$	1.29765e44	+	1.25669e44i	0.301901	+	0.292374i
$617$	−3.70500e44			−0.839895			−0.419948	−	0.907548i	$-0.637952\pi$
$617$	−3.70500e44			−0.839895			−0.419948	+	0.907548i	$0.637952\pi$
$618$	−9.22847e42	+	9.32763e42i	−0.0203852	+	0.0206042i
$619$			6.45166e44i			1.38874i	0.719618	+	0.694370i	$0.244317\pi$
$619$			6.45166e44i			1.38874i	−0.719618	+	0.694370i	$0.755683\pi$
$620$	−1.13999e44	+	1.21838e42i	−0.239130	+	0.00255574i
$621$	1.06652e45			2.18023
$622$	−3.75187e44	−	3.71198e44i	−0.747483	−	0.739537i
$623$		−	1.00668e45i		−	1.95471i
$624$	2.98444e42	+	1.39604e44i	0.00564818	+	0.264208i
$625$	4.69261e44			0.865634
$626$	5.62703e44	−	5.68750e44i	1.01179	−	1.02266i
$627$		−	5.33928e44i		−	0.935842i
$628$	−2.86989e42	−	2.68523e44i	−0.00490355	−	0.458804i
$629$	5.48817e43			0.0914150
$630$	3.27816e44	+	3.24331e44i	0.532330	+	0.526671i
$631$			3.80541e44i			0.602465i	0.953551	+	0.301233i	$0.0973980\pi$
$631$			3.80541e44i			0.602465i	−0.953551	+	0.301233i	$0.902602\pi$
$632$	−5.99709e44	+	6.19252e44i	−0.925694	+	0.955860i
$633$	5.92419e44			0.891600
$634$	6.04463e44	−	6.10958e44i	0.887036	−	0.896567i
$635$			1.47617e44i			0.211231i
$636$	−1.17152e45	+	1.25208e43i	−1.63469	+	0.0174710i
$637$	−1.08429e44			−0.147541
$638$	−1.29103e44	−	1.27730e44i	−0.171319	−	0.169497i
$639$		−	1.08062e45i		−	1.39848i
$640$	−1.23856e44	−	1.14921e44i	−0.156329	−	0.145050i
$641$	−3.15290e44			−0.388134			−0.194067	−	0.980988i	$-0.562168\pi$
$641$	−3.15290e44			−0.388134			−0.194067	+	0.980988i	$0.562168\pi$
$642$	−8.78256e44	+	8.87692e44i	−1.05453	+	1.06586i
$643$			6.19810e44i			0.725910i	0.931807	+	0.362955i	$0.118232\pi$
$643$			6.19810e44i			0.725910i	−0.931807	+	0.362955i	$0.881768\pi$
$644$	−1.07272e43	−	1.00370e45i	−0.0122550	−	1.14664i
$645$	2.38024e44			0.265256
$646$	−1.45859e44	−	1.44309e44i	−0.158568	−	0.156882i
$647$			1.08329e45i			1.14888i	0.818545	+	0.574442i	$0.194781\pi$
$647$			1.08329e45i			1.14888i	−0.818545	+	0.574442i	$0.805219\pi$
$648$	−1.79783e45	−	1.74109e45i	−1.86015	−	1.80145i
$649$	−3.88944e43			−0.0392619
$650$	−9.68484e43	+	9.78890e43i	−0.0953847	+	0.0964096i
$651$			3.09887e45i			2.97788i
$652$	1.46743e45	−	1.56834e43i	1.37592	−	0.0147054i
$653$	−8.28187e44			−0.757735			−0.378868	−	0.925451i	$-0.623686\pi$
$653$	−8.28187e44			−0.757735			−0.378868	+	0.925451i	$0.623686\pi$
$654$	1.41585e45	+	1.40080e45i	1.26408	+	1.25064i
$655$		−	1.17955e44i		−	0.102767i
$656$	1.72853e45	−	3.69522e43i	1.46966	−	0.0314180i
$657$	2.10482e43			0.0174650
$658$	1.02634e45	−	1.03737e45i	0.831146	−	0.840077i
$659$		−	1.81794e45i		−	1.43686i	−0.695600	−	0.718429i	$-0.744862\pi$
$659$		−	1.81794e45i		−	1.43686i	0.695600	−	0.718429i	$-0.255138\pi$
$660$	1.61752e42	+	1.51344e44i	0.00124780	+	0.116752i
$661$	2.20937e45			1.66359			0.831794	−	0.555085i	$-0.187314\pi$
$661$	2.20937e45			1.66359			0.831794	+	0.555085i	$0.187314\pi$
$662$	−2.22457e44	−	2.20092e44i	−0.163500	−	0.161762i
$663$		−	4.80691e43i		−	0.0344865i
$664$	7.18946e43	−	7.42375e43i	0.0503509	−	0.0519917i
$665$	−7.61222e44			−0.520433
$666$	−1.81548e45	+	1.83499e45i	−1.21173	+	1.22475i
$667$			1.00914e45i			0.657561i
$668$	−1.03355e45	+	1.10463e43i	−0.657520	+	0.00702736i
$669$	4.73046e44			0.293823
$670$	1.25629e44	+	1.24294e44i	0.0761891	+	0.0753792i
$671$			1.04433e44i			0.0618412i
$672$	−3.15955e45	+	3.33306e45i	−1.82691	+	1.92723i
$673$	−2.06677e45			−1.16695			−0.583473	−	0.812132i	$-0.698307\pi$
$673$	−2.06677e45			−1.16695			−0.583473	+	0.812132i	$0.698307\pi$
$674$	1.28300e45	−	1.29679e45i	0.707405	−	0.715006i
$675$		−	4.81218e45i		−	2.59109i
$676$	1.99135e43	+	1.86323e45i	0.0104713	+	0.979757i
$677$	3.45773e45			1.77571			0.887856	−	0.460121i	$-0.152194\pi$
$677$	3.45773e45			1.77571			0.887856	+	0.460121i	$0.152194\pi$
$678$	−2.00099e45	−	1.97972e45i	−1.00362	−	0.992954i
$679$			1.16640e44i			0.0571389i
$680$	4.17816e43	+	4.04630e43i	0.0199914	+	0.0193605i
$681$	−6.46563e45			−3.02174
$682$	−5.08558e44	+	5.14023e44i	−0.232162	+	0.234656i
$683$		−	3.98486e43i		−	0.0177698i	−0.999961	−	0.00888488i	$-0.997172\pi$
$683$		−	3.98486e43i		−	0.0177698i	0.999961	−	0.00888488i	$-0.00282818\pi$
$684$	9.65004e45	−	1.03136e44i	4.20370	−	0.0449278i
$685$	3.57182e43			0.0151999
$686$	−9.37895e43	−	9.27924e43i	−0.0389914	−	0.0385769i
$687$		−	2.02464e45i		−	0.822317i
$688$	3.60196e43	+	1.68491e45i	0.0142930	+	0.668592i
$689$	3.22110e44			0.124881
$690$	5.91493e44	−	5.97848e44i	0.224060	−	0.226467i
$691$		−	1.35175e45i		−	0.500319i	−0.968205	−	0.250159i	$-0.919517\pi$
$691$		−	1.35175e45i		−	0.500319i	0.968205	−	0.250159i	$-0.0804830\pi$
$692$	−3.19708e43	−	2.99137e45i	−0.0115626	−	1.08186i
$693$	2.92482e45			1.03364
$694$	−9.68768e44	−	9.58469e44i	−0.334555	−	0.330999i
$695$			5.39300e44i			0.182001i
$696$	3.21212e45	−	3.31679e45i	1.05936	−	1.09388i
$697$	−5.95174e44			−0.191831
$698$	1.27235e44	−	1.28602e44i	0.0400794	−	0.0405100i
$699$			7.57132e45i			2.33097i
$700$	−4.52873e45	+	4.84016e43i	−1.36272	+	0.0145643i
$701$	−5.09328e45			−1.49799			−0.748995	−	0.662575i	$-0.769464\pi$
$701$	−5.09328e45			−1.49799			−0.748995	+	0.662575i	$0.769464\pi$
$702$	9.53727e44	+	9.43588e44i	0.274176	+	0.271262i
$703$		−	4.26103e45i		−	1.19737i
$704$	−1.07108e45	+	3.43525e43i	−0.294211	+	0.00943616i
$705$	1.22267e45			0.328310
$706$	−4.42442e45	+	4.47196e45i	−1.16140	+	1.17388i
$707$		−	7.19215e45i		−	1.84564i
$708$	−1.05678e43	−	9.88783e44i	−0.00265126	−	0.248067i
$709$	−3.07778e45			−0.754915			−0.377458	−	0.926027i	$-0.623202\pi$
$709$	−3.07778e45			−0.754915			−0.377458	+	0.926027i	$0.623202\pi$
$710$	−3.59457e44	−	3.55636e44i	−0.0862012	−	0.0852848i
$711$			1.39576e46i			3.27263i
$712$	4.28995e45	+	4.15456e45i	0.983495	+	0.952457i
$713$	4.01787e45			0.900666
$714$	1.11193e45	−	1.12388e45i	0.243729	−	0.246348i
$715$		−	4.16122e43i		−	0.00891917i
$716$	−4.23100e45	+	4.52196e43i	−0.886818	+	0.00947803i
$717$	1.42753e46			2.92603
$718$	2.92414e45	+	2.89305e45i	0.586147	+	0.579916i
$719$			5.99920e45i			1.17607i	0.808837	+	0.588033i	$0.200097\pi$
$719$			5.99920e45i			1.17607i	−0.808837	+	0.588033i	$0.799903\pi$
$720$	−2.73503e45	+	5.84689e43i	−0.524375	+	0.0112100i
$721$	1.18650e44			0.0222487
$722$	−7.36935e45	+	7.44853e45i	−1.35156	+	1.36608i
$723$		−	6.56944e45i		−	1.17846i
$724$	−8.77503e43	−	8.21042e45i	−0.0153968	−	1.44062i
$725$	4.55327e45			0.781476
$726$	−7.19318e45	−	7.11671e45i	−1.20763	−	1.19480i
$727$			8.37590e44i			0.137556i	0.997632	+	0.0687782i	$0.0219101\pi$
$727$			8.37590e44i			0.137556i	−0.997632	+	0.0687782i	$0.978090\pi$
$728$	8.78415e44	−	9.07040e44i	0.141123	−	0.145722i
$729$	−8.39733e45			−1.31978
$730$	6.92706e42	−	7.00149e42i	0.00106508	−	0.00107653i
$731$		−	5.80153e44i		−	0.0872699i
$732$	−2.65493e45	+	2.83750e43i	−0.390729	+	0.00417599i
$733$	−6.02634e45			−0.867740			−0.433870	−	0.900975i	$-0.642852\pi$
$733$	−6.02634e45			−0.867740			−0.433870	+	0.900975i	$0.642852\pi$
$734$	−3.99352e44	−	3.95107e44i	−0.0562625	−	0.0556644i
$735$		−	2.98796e45i		−	0.411887i
$736$	4.32151e45	+	4.09654e45i	0.582895	+	0.552551i
$737$	1.12088e45			0.147938
$738$	1.96883e46	−	1.98999e46i	2.54277	−	2.57009i
$739$			2.20478e45i			0.278648i	0.990247	+	0.139324i	$0.0444929\pi$
$739$			2.20478e45i			0.278648i	−0.990247	+	0.139324i	$0.955507\pi$
$740$	1.29086e43	+	1.20781e45i	0.00159652	+	0.149379i
$741$	−3.73210e45			−0.451712
$742$	7.53109e45	+	7.45103e45i	0.892062	+	0.882579i
$743$			6.54848e45i			0.759135i	0.925164	+	0.379568i	$0.123927\pi$
$743$			6.54848e45i			0.759135i	−0.925164	+	0.379568i	$0.876073\pi$
$744$	−1.32058e46	−	1.27890e46i	−1.49830	−	1.45101i
$745$	2.18909e45			0.243088
$746$	6.35271e45	−	6.42097e45i	0.690459	−	0.697877i
$747$		−	1.67327e45i		−	0.178007i
$748$	3.68881e44	−	3.94249e42i	0.0384115	−	0.000410530i
$749$	1.12917e46			1.15094
$750$	−5.52357e45	−	5.46485e45i	−0.551112	−	0.545253i
$751$		−	1.64814e46i		−	1.60974i	−0.593450	−	0.804871i	$-0.702235\pi$
$751$		−	1.64814e46i		−	1.60974i	0.593450	−	0.804871i	$-0.297765\pi$
$752$	1.85024e44	+	8.65497e45i	0.0176906	+	0.827523i
$753$	−2.07277e46			−1.94013
$754$	−8.92820e44	+	9.02414e44i	−0.0818130	+	0.0826921i
$755$			4.28505e45i			0.384419i
$756$	4.71574e44	+	4.41231e46i	0.0414191	+	3.87541i
$757$	3.89000e44			0.0334515			0.0167258	−	0.999860i	$-0.494676\pi$
$757$	3.89000e44			0.0334515			0.0167258	+	0.999860i	$0.494676\pi$
$758$	6.99885e45	+	6.92445e45i	0.589277	+	0.583013i
$759$		−	5.33409e45i		−	0.439736i
$760$	3.14156e45	−	3.24394e45i	0.253588	−	0.261851i
$761$	6.29711e45			0.497722			0.248861	−	0.968539i	$-0.419944\pi$
$761$	6.29711e45			0.497722			0.248861	+	0.968539i	$0.419944\pi$
$762$	−1.67414e46	+	1.69213e46i	−1.29572	+	1.30965i
$763$		−	1.80101e46i		−	1.36497i
$764$	−9.51037e45	+	1.01644e44i	−0.705835	+	0.00754374i
$765$	9.41734e44			0.0684456
$766$	1.02320e46	+	1.01232e46i	0.728283	+	0.720541i
$767$			2.71867e44i			0.0189509i
$768$	−1.16434e45	−	2.72199e46i	−0.0794875	−	1.85826i
$769$	−1.79196e46			−1.19814			−0.599070	−	0.800696i	$-0.704463\pi$
$769$	−1.79196e46			−1.19814			−0.599070	+	0.800696i	$0.704463\pi$
$770$	9.62572e44	−	9.72915e44i	0.0630350	−	0.0637123i
$771$			2.69286e46i			1.72720i
$772$	−1.44432e44	−	1.35138e46i	−0.00907372	−	0.848989i
$773$	−7.75856e45			−0.477430			−0.238715	−	0.971090i	$-0.576726\pi$
$773$	−7.75856e45			−0.477430			−0.238715	+	0.971090i	$0.576726\pi$
$774$	1.93976e46	+	1.91914e46i	1.16921	+	1.15678i
$775$		−	1.81288e46i		−	1.07039i
$776$	−4.97061e44	−	4.81374e44i	−0.0287490	−	0.0278417i
$777$	3.28322e46			1.86022
$778$	9.74211e44	−	9.84679e44i	0.0540729	−	0.0546539i
$779$			4.62095e46i			2.51265i
$780$	1.05788e45	−	1.13063e43i	0.0563536	−	0.000602289i
$781$	−3.20713e45			−0.167379
$782$	−1.45718e45	−	1.44169e45i	−0.0745082	−	0.0737162i
$783$		−	4.43623e46i		−	2.22242i
$784$	2.11509e46	−	4.52161e44i	1.03818	−	0.0221940i
$785$	−2.03455e45			−0.0978485
$786$	1.33773e46	−	1.35211e46i	0.630390	−	0.637163i
$787$			9.43901e43i			0.00435844i	0.999998	+	0.00217922i	$0.000693668\pi$
$787$			9.43901e43i			0.00435844i	−0.999998	+	0.00217922i	$0.999306\pi$
$788$	−2.80808e44	−	2.62740e46i	−0.0127055	−	1.18880i
$789$	−2.81588e46			−1.24848
$790$	4.64286e45	+	4.59351e45i	0.201722	+	0.199577i
$791$			2.54533e46i			1.08373i
$792$	−1.20707e46	+	1.24641e46i	−0.503653	+	0.520065i
$793$	7.29976e44			0.0298495
$794$	−2.26158e46	+	2.28588e46i	−0.906327	+	0.916065i
$795$			8.87636e45i			0.348627i
$796$	−7.02165e45	+	7.50452e43i	−0.270290	+	0.00288878i
$797$	−3.19696e46			−1.20616			−0.603079	−	0.797681i	$-0.706060\pi$
$797$	−3.19696e46			−1.20616			−0.603079	+	0.797681i	$0.706060\pi$
$798$	−8.72583e46	−	8.63307e46i	−3.22672	−	3.19241i
$799$		−	2.98011e45i		−	0.108015i
$800$	1.84838e46	−	1.94989e46i	0.656677	−	0.692739i
$801$	9.66930e46			3.36725
$802$	9.20955e45	−	9.30850e45i	0.314375	−	0.317753i
$803$		−	6.24684e43i		−	0.00209031i
$804$	3.04549e44	+	2.84954e46i	0.00998989	+	0.934711i
$805$	−7.60482e45			−0.244543
$806$	3.59296e45	+	3.55476e45i	0.113264	+	0.112060i
$807$			4.62244e45i			0.142855i
$808$	3.06493e46	+	2.96820e46i	0.928621	+	0.899315i
$809$	−9.61726e45			−0.285677			−0.142838	−	0.989746i	$-0.545623\pi$
$809$	−9.61726e45			−0.285677			−0.142838	+	0.989746i	$0.545623\pi$
$810$	−1.33360e46	+	1.34793e46i	−0.388388	+	0.392561i
$811$		−	3.33522e46i		−	0.952337i	−0.879354	−	0.476169i	$-0.842025\pi$
$811$		−	3.33522e46i		−	0.952337i	0.879354	−	0.476169i	$-0.157975\pi$
$812$	−4.17492e46	+	4.46202e44i	−1.16883	+	0.0124921i
$813$	8.60956e46			2.36337
$814$	5.44601e45	+	5.38812e45i	0.146585	+	0.145026i
$815$		−	1.11184e46i		−	0.293441i
$816$	2.00454e44	+	9.37674e45i	0.00518767	+	0.242666i
$817$	−4.50432e46			−1.14308
$818$	1.45726e46	−	1.47292e46i	0.362648	−	0.366545i
$819$		−	2.04442e46i		−	0.498916i
$820$	−1.39990e44	−	1.30983e46i	−0.00335024	−	0.313467i
$821$	4.76322e46			1.11792			0.558959	−	0.829195i	$-0.311201\pi$
$821$	4.76322e46			1.11792			0.558959	+	0.829195i	$0.311201\pi$
$822$	4.09435e45	+	4.05083e45i	0.0942402	+	0.0932384i
$823$			4.85340e46i			1.09559i	0.836612	+	0.547796i	$0.184533\pi$
$823$			4.85340e46i			1.09559i	−0.836612	+	0.547796i	$0.815467\pi$
$824$	−4.89670e44	+	5.05627e44i	−0.0108410	+	0.0111942i
$825$	−2.40677e46			−0.522603
$826$	−6.28882e45	+	6.35639e45i	−0.133933	+	0.135372i
$827$			3.23463e46i			0.675674i	0.941205	+	0.337837i	$0.109695\pi$
$827$			3.23463e46i			0.675674i	−0.941205	+	0.337837i	$0.890305\pi$
$828$	9.64066e46	−	1.03036e45i	1.97525	−	0.0211108i
$829$	−8.22952e46			−1.65387			−0.826936	−	0.562296i	$-0.809918\pi$
$829$	−8.22952e46			−1.65387			−0.826936	+	0.562296i	$0.809918\pi$
$830$	−5.56598e44	−	5.50681e44i	−0.0109722	−	0.0108555i
$831$			1.45401e47i			2.81159i
$832$	2.40120e44	+	7.48671e45i	0.00455465	+	0.142010i
$833$	−7.28277e45			−0.135512
$834$	−6.11625e46	+	6.18196e46i	−1.11642	+	1.12842i
$835$			7.83103e45i			0.140228i
$836$	−3.06096e44	−	2.86401e46i	−0.00537721	−	0.503122i
$837$	−1.76628e47			−3.04406
$838$	−1.06092e46	−	1.04964e46i	−0.179381	−	0.177474i
$839$		−	1.12025e47i		−	1.85834i	−0.369656	−	0.929169i	$-0.620525\pi$
$839$		−	1.12025e47i		−	1.85834i	0.369656	−	0.929169i	$-0.379475\pi$
$840$	2.49952e46	+	2.42064e46i	0.406807	+	0.393969i
$841$	−2.06479e46			−0.329715
$842$	2.68243e46	−	2.71125e46i	0.420276	−	0.424791i
$843$		−	1.91166e47i		−	2.93879i
$844$	3.17775e46	−	3.39628e44i	0.479337	−	0.00512300i
$845$	1.41173e46			0.208951
$846$	9.96409e46	+	9.85817e46i	1.44714	+	1.43176i
$847$			9.14995e46i			1.30402i
$848$	−6.28333e46	+	1.34324e45i	−0.878731	+	0.0187853i
$849$	1.94364e47			2.66743
$850$	−6.50496e45	+	6.57486e45i	−0.0876076	+	0.0885490i
$851$		−	4.25689e46i		−	0.562626i
$852$	−8.71394e44	−	8.15326e46i	−0.0113027	−	1.05754i
$853$	1.49776e47			1.90659			0.953295	−	0.302040i	$-0.0976677\pi$
$853$	1.49776e47			1.90659			0.953295	+	0.302040i	$0.0976677\pi$
$854$	1.70672e46	+	1.68858e46i	0.213224	+	0.210957i
$855$		−	7.31165e46i		−	0.896515i
$856$	−4.66010e46	+	4.81195e46i	−0.560808	+	0.579084i
$857$	6.71938e46			0.793662			0.396831	−	0.917892i	$-0.370110\pi$
$857$	6.71938e46			0.793662			0.396831	+	0.917892i	$0.370110\pi$
$858$	4.71927e45	−	4.76998e45i	0.0547115	−	0.0552994i
$859$		−	1.13231e47i		−	1.28847i	−0.764828	−	0.644235i	$-0.777176\pi$
$859$		−	1.13231e47i		−	1.28847i	0.764828	−	0.644235i	$-0.222824\pi$
$860$	1.27677e46	−	1.36457e44i	0.142606	−	0.00152412i
$861$	−3.56054e47			−3.90360
$862$	2.90376e46	+	2.87290e46i	0.312496	+	0.309174i
$863$		−	1.18796e47i		−	1.25495i	−0.778635	−	0.627477i	$-0.784088\pi$
$863$		−	1.18796e47i		−	1.25495i	0.778635	−	0.627477i	$-0.215912\pi$
$864$	−1.89976e47	−	1.80087e47i	−1.97006	−	1.86750i
$865$	−2.26650e46			−0.230727
$866$	1.11995e47	−	1.13199e47i	1.11922	−	1.13124i
$867$			1.86359e47i			1.82829i
$868$	1.77655e45	+	1.66224e47i	0.0171105	+	1.60095i
$869$	4.14243e46			0.391687
$870$	−2.48678e46	−	2.46034e46i	−0.230849	−	0.228395i
$871$		−	7.83483e45i		−	0.0714067i
$872$	7.67496e46	+	7.43275e46i	0.686772	+	0.665098i
$873$	−1.12035e46			−0.0984294
$874$	−1.11933e47	+	1.13136e47i	−0.965550	+	0.975925i
$875$			7.02615e46i			0.595098i
$876$	1.58809e45	−	1.69730e43i	0.0132071	−	0.000141154i
$877$	4.86612e46			0.397365			0.198682	−	0.980064i	$-0.436334\pi$
$877$	4.86612e46			0.397365			0.198682	+	0.980064i	$0.436334\pi$
$878$	−5.75807e46	−	5.69686e46i	−0.461705	−	0.456797i
$879$			3.98847e47i			3.14040i
$880$	1.73528e44	+	8.11721e45i	0.00134167	+	0.0627602i
$881$	1.38653e47			1.05273			0.526364	−	0.850259i	$-0.323555\pi$
$881$	1.38653e47			1.05273			0.526364	+	0.850259i	$0.323555\pi$
$882$	2.40913e47	−	2.43502e47i	1.79624	−	1.81554i
$883$			4.21902e46i			0.308916i	0.987999	+	0.154458i	$0.0493631\pi$
$883$			4.21902e46i			0.308916i	−0.987999	+	0.154458i	$0.950637\pi$
$884$	−2.75575e43	−	2.57844e45i	−0.000198154	−	0.0185405i
$885$	−7.49183e45			−0.0529048
$886$	−1.72686e47	−	1.70850e47i	−1.19761	−	1.18488i
$887$		−	1.47559e46i		−	0.100505i	−0.998737	−	0.0502524i	$-0.983997\pi$
$887$		−	1.47559e46i		−	0.100505i	0.998737	−	0.0502524i	$-0.0160026\pi$
$888$	−1.35499e47	+	1.39914e47i	−0.906415	+	0.935953i
$889$	2.15244e47			1.41417
$890$	3.18221e46	−	3.21640e46i	0.205347	−	0.207554i
$891$			1.20264e47i			0.762244i
$892$	2.53743e46	−	2.71193e44i	0.157964	−	0.00168826i
$893$	−2.31376e47			−1.41480
$894$	2.50934e47	+	2.48267e47i	1.50716	+	1.49114i
$895$			3.20575e46i			0.189130i
$896$	−1.67568e47	+	1.80597e47i	−0.971098	+	1.04661i
$897$	−3.72847e46			−0.212252
$898$	7.07951e46	−	7.15557e46i	0.395896	−	0.400150i
$899$		−	1.67125e47i		−	0.918093i
$900$	−4.64905e45	−	4.34991e47i	−0.0250890	−	2.34747i
$901$	2.16350e46			0.114699
$902$	−5.90602e46	−	5.84323e46i	−0.307603	−	0.304333i
$903$		−	3.47068e47i		−	1.77587i
$904$	−1.08469e47	−	1.05046e47i	−0.545268	−	0.528060i
$905$	−6.22088e46			−0.307238
$906$	−4.85971e47	+	4.91193e47i	−2.35808	+	2.38342i
$907$			7.24496e46i			0.345398i	0.984975	+	0.172699i	$0.0552487\pi$
$907$			7.24496e46i			0.345398i	−0.984975	+	0.172699i	$0.944751\pi$
$908$	−3.46818e47	+	3.70668e45i	−1.62453	+	0.0173625i
$909$	6.90817e47			3.17937
$910$	−6.80056e45	−	6.72827e45i	−0.0307526	−	0.0304257i
$911$		−	9.68720e46i		−	0.430432i	−0.976566	−	0.215216i	$-0.930954\pi$
$911$		−	9.68720e46i		−	0.430432i	0.976566	−	0.215216i	$-0.0690455\pi$
$912$	7.28013e47	−	1.55633e46i	3.17849	−	0.0679492i
$913$	−4.96605e45			−0.0213049
$914$	4.20222e46	−	4.24737e46i	0.177149	−	0.179053i
$915$			2.01159e46i			0.0833301i
$916$	−1.16070e45	−	1.08602e47i	−0.00472491	−	0.442090i
$917$	−1.71992e47			−0.688018
$918$	6.40584e46	+	6.33775e46i	0.251822	+	0.249145i
$919$		−	3.03055e47i		−	1.17077i	−0.810754	−	0.585386i	$-0.800943\pi$
$919$		−	3.03055e47i		−	1.17077i	0.810754	−	0.585386i	$-0.199057\pi$
$920$	3.13851e46	−	3.24078e46i	0.119157	−	0.123040i
$921$	−3.55951e47			−1.32811
$922$	1.00897e47	−	1.01981e47i	0.369986	−	0.373961i
$923$			2.24175e46i			0.0807903i
$924$	2.20678e47	−	2.35854e45i	0.781641	−	0.00835393i
$925$	−1.92073e47			−0.668650
$926$	1.17174e47	+	1.15929e47i	0.400919	+	0.396657i
$927$			1.13966e46i			0.0383264i
$928$	1.70397e47	−	1.79755e47i	0.563242	−	0.594174i
$929$	−5.44330e47			−1.76852			−0.884261	−	0.466993i	$-0.845337\pi$
$929$	−5.44330e47			−1.76852			−0.884261	+	0.466993i	$0.845337\pi$
$930$	−9.79584e46	+	9.90110e46i	−0.312834	+	0.316196i
$931$			5.65436e47i			1.77496i
$932$	4.34056e45	+	4.06128e47i	0.0133934	+	1.25316i
$933$	−6.44790e47			−1.95575
$934$	−2.09539e47	−	2.07311e47i	−0.624762	−	0.618121i
$935$		−	2.79495e45i		−	0.00819196i
$936$	8.71226e46	+	8.43731e46i	0.251025	+	0.243103i
$937$	3.91148e47			1.10792			0.553958	−	0.832544i	$-0.313117\pi$
$937$	3.91148e47			1.10792			0.553958	+	0.832544i	$0.313117\pi$
$938$	1.81235e47	−	1.83182e47i	0.504657	−	0.510080i
$939$		−	9.77444e47i		−	2.67573i
$940$	6.55846e46	−	7.00947e44i	0.176505	−	0.00188642i
$941$	3.45260e47			0.913507			0.456753	−	0.889593i	$-0.349012\pi$
$941$	3.45260e47			0.913507			0.456753	+	0.889593i	$0.349012\pi$
$942$	−2.33219e47	−	2.30740e47i	−0.606666	−	0.600217i
$943$			4.61646e47i			1.18065i
$944$	−1.13372e45	−	5.30325e46i	−0.00285071	−	0.133349i
$945$	3.34313e47			0.826502
$946$	5.69576e46	−	5.75696e46i	0.138450	−	0.139938i
$947$			6.77649e47i			1.61959i	0.586713	+	0.809795i	$0.300422\pi$
$947$			6.77649e47i			1.61959i	−0.586713	+	0.809795i	$0.699578\pi$
$948$	1.12552e46	+	1.05310e48i	0.0264497	+	2.47478i
$949$	−4.36647e44			−0.00100895
$950$	5.10474e47	+	5.05047e47i	1.15983	+	1.14750i
$951$		−	1.04998e48i		−	2.34581i
$952$	5.90000e46	−	6.09226e46i	0.129617	−	0.133841i
$953$	6.43964e47			1.39115			0.695577	−	0.718452i	$-0.255149\pi$
$953$	6.43964e47			1.39115			0.695577	+	0.718452i	$0.255149\pi$
$954$	−7.15683e47	+	7.23373e47i	−1.52036	+	1.53670i
$955$			7.20583e46i			0.150532i
$956$	7.65731e47	−	8.18389e45i	1.57308	−	0.0168125i
$957$	−2.21874e47			−0.448245
$958$	−6.35512e47	−	6.28756e47i	−1.26263	−	1.24921i
$959$		−	5.20815e46i		−	0.101762i
$960$	−2.06311e47	+	6.61697e45i	−0.396444	+	0.0127151i
$961$	−1.36264e47			−0.257518
$962$	3.76623e46	−	3.80670e46i	0.0700013	−	0.0707534i
$963$			1.08459e48i			1.98264i
$964$	−3.76619e45	−	3.52387e47i	−0.00677127	−	0.633559i
$965$	−1.02392e47			−0.181062
$966$	−8.71735e47	−	8.62468e47i	−1.51618	−	1.50006i
$967$		−	1.27943e46i		−	0.0218874i	−0.999940	−	0.0109437i	$-0.996516\pi$
$967$		−	1.27943e46i		−	0.0218874i	0.999940	−	0.0109437i	$-0.00348355\pi$
$968$	−3.89924e47	−	3.77619e47i	−0.656107	−	0.635401i
$969$	−2.50672e47			−0.414882
$970$	−3.68711e45	+	3.72673e45i	−0.00600259	+	0.00606709i
$971$		−	1.02864e47i		−	0.164724i	−0.996602	−	0.0823620i	$-0.973754\pi$
$971$		−	1.02864e47i		−	0.164724i	0.996602	−	0.0823620i	$-0.0262464\pi$
$972$	−1.33421e48	+	1.42596e46i	−2.10167	+	0.0224620i
$973$	7.86365e47			1.21848
$974$	9.02743e47	+	8.93147e47i	1.37601	+	1.36138i
$975$			1.68231e47i			0.252250i
$976$	−1.42395e47	+	3.04409e45i	−0.210038	+	0.00449014i
$977$	−1.19273e48			−1.73073			−0.865363	−	0.501145i	$-0.832912\pi$
$977$	−1.19273e48			−1.73073			−0.865363	+	0.501145i	$0.832912\pi$
$978$	1.26095e48	−	1.27450e48i	1.80001	−	1.81935i
$979$		−	2.86972e47i		−	0.403011i
$980$	−1.71297e45	−	1.60275e47i	−0.00236664	−	0.221436i
$981$	1.72989e48			2.35134
$982$	6.43014e45	+	6.36178e45i	0.00859878	+	0.00850737i
$983$			7.70423e47i			1.01362i	0.862059	+	0.506808i	$0.169175\pi$
$983$			7.70423e47i			1.01362i	−0.862059	+	0.506808i	$0.830825\pi$
$984$	1.46944e48	−	1.51732e48i	1.90208	−	1.96407i
$985$	−1.99073e47			−0.253533
$986$	−5.99676e46	+	6.06119e46i	−0.0751425	+	0.0759499i
$987$		−	1.78281e48i		−	2.19801i
$988$	−2.00191e47	+	2.13957e45i	−0.242847	+	0.00259547i
$989$	−4.49995e47			−0.537114
$990$	9.34500e46	+	9.24566e46i	0.109753	+	0.108586i
$991$			1.05952e48i			1.22442i	0.790696	+	0.612209i	$0.209719\pi$
$991$			1.05952e48i			1.22442i	−0.790696	+	0.612209i	$0.790281\pi$
$992$	−7.15695e47	−	6.78437e47i	−0.813844	−	0.771477i
$993$	−3.82311e47			−0.427788
$994$	−5.18560e47	+	5.24132e47i	−0.570974	+	0.577109i
$995$			5.32018e46i			0.0576444i
$996$	−1.34930e45	−	1.26248e47i	−0.00143867	−	0.134610i
$997$	1.16358e48			1.22088			0.610441	−	0.792062i	$-0.290992\pi$
$997$	1.16358e48			1.22088			0.610441	+	0.792062i	$0.290992\pi$
$998$	7.24950e47	+	7.17243e47i	0.748548	+	0.740590i
$999$			1.87136e48i			1.90156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.33.b.b.3.11	✓	14
3.2	odd	2		36.33.d.b.19.4		14
4.3	odd	2	inner	4.33.b.b.3.12	yes	14
12.11	even	2		36.33.d.b.19.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.33.b.b.3.11	✓	14	1.1	even	1	trivial
4.33.b.b.3.12	yes	14	4.3	odd	2	inner
36.33.d.b.19.3		14	12.11	even	2
36.33.d.b.19.4		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)

\(f(q)\)	\(=\)	\(q+(46092.7 - 46587.9i) q^{2} -8.00653e7i q^{3} +(-4.59006e7 - 4.29472e9i) q^{4} -3.25403e10 q^{5} +(-3.73007e12 - 3.69042e12i) q^{6} +4.74477e13i q^{7} +(-2.02198e14 - 1.95817e14i) q^{8} -4.55743e15 q^{9} +O(q^{10})\)	\(q+(46092.7 - 46587.9i) q^{2} -8.00653e7i q^{3} +(-4.59006e7 - 4.29472e9i) q^{4} -3.25403e10 q^{5} +(-3.73007e12 - 3.69042e12i) q^{6} +4.74477e13i q^{7} +(-2.02198e14 - 1.95817e14i) q^{8} -4.55743e15 q^{9} +(-1.49987e15 + 1.51599e15i) q^{10} +1.35259e16i q^{11} +(-3.43858e17 + 3.67504e15i) q^{12} +9.45442e16 q^{13} +(2.21049e18 + 2.18699e18i) q^{14} +2.60535e18i q^{15} +(-1.84425e19 + 3.94261e17i) q^{16} +6.35019e18 q^{17} +(-2.10064e20 + 2.12321e20i) q^{18} -4.93031e20i q^{19} +(1.49362e18 + 1.39752e20i) q^{20} +3.79891e21 q^{21} +(6.30141e20 + 6.23443e20i) q^{22} -4.92552e21i q^{23} +(-1.56781e22 + 1.61890e22i) q^{24} -2.22242e22 q^{25} +(4.35779e21 - 4.40461e21i) q^{26} +2.16529e23i q^{27} +(2.03775e23 - 2.17788e21i) q^{28} -2.04879e23 q^{29} +(1.21378e23 + 1.20087e23i) q^{30} +8.15726e23i q^{31} +(-8.31698e23 + 8.77372e23i) q^{32} +1.08295e24 q^{33} +(2.92697e23 - 2.95842e23i) q^{34} -1.54396e24i q^{35} +(2.09189e23 + 1.95729e25i) q^{36} +8.64253e24 q^{37} +(-2.29693e25 - 2.27251e25i) q^{38} -7.56970e24i q^{39} +(6.57958e24 + 6.37194e24i) q^{40} -9.37253e25 q^{41} +(1.75102e26 - 1.76983e26i) q^{42} -9.13599e25i q^{43} +(5.80898e25 - 6.20845e23i) q^{44} +1.48300e26 q^{45} +(-2.29470e26 - 2.27030e26i) q^{46} -4.69294e26i q^{47} +(3.15666e25 + 1.47661e27i) q^{48} -1.14686e27 q^{49} +(-1.02437e27 + 1.03538e27i) q^{50} -5.08430e26i q^{51} +(-4.33963e24 - 4.06041e26i) q^{52} +3.40698e27 q^{53} +(1.00876e28 + 9.98040e27i) q^{54} -4.40135e26i q^{55} +(9.29106e27 - 9.59382e27i) q^{56} -3.94747e28 q^{57} +(-9.44342e27 + 9.54489e27i) q^{58} +2.87556e27i q^{59} +(1.11892e28 - 1.19587e26i) q^{60} +7.72100e27 q^{61} +(3.80030e28 + 3.75990e28i) q^{62} -2.16239e29i q^{63} +(2.53976e27 + 7.91874e28i) q^{64} -3.07650e27 q^{65} +(4.99161e28 - 5.04524e28i) q^{66} -8.28696e28i q^{67} +(-2.91478e26 - 2.72723e28i) q^{68} -3.94363e29 q^{69} +(-7.19300e28 - 7.11654e28i) q^{70} +2.37111e29i q^{71} +(9.21502e29 + 8.92420e29i) q^{72} -4.61844e27 q^{73} +(3.98357e29 - 4.02637e29i) q^{74} +1.77939e30i q^{75} +(-2.11743e30 + 2.26304e28i) q^{76} -6.41771e29 q^{77} +(-3.52657e29 - 3.48908e29i) q^{78} -3.06260e30i q^{79} +(6.00126e29 - 1.28294e28i) q^{80} +8.89145e30 q^{81} +(-4.32005e30 + 4.36647e30i) q^{82} +3.67153e29i q^{83} +(-1.74372e29 - 1.63153e31i) q^{84} -2.06637e29 q^{85} +(-4.25627e30 - 4.21102e30i) q^{86} +1.64037e31i q^{87} +(2.64859e30 - 2.73490e30i) q^{88} -2.12166e31 q^{89} +(6.83554e30 - 6.90899e30i) q^{90} +4.48590e30i q^{91} +(-2.11537e31 + 2.26084e29i) q^{92} +6.53113e31 q^{93} +(-2.18634e31 - 2.16310e31i) q^{94} +1.60434e31i q^{95} +(7.02470e31 + 6.65901e31i) q^{96} +2.45829e30 q^{97} +(-5.28617e31 + 5.34297e31i) q^{98} -6.16431e31i 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more