LMFDB - Embedded newform 4.33.b.b.3.13

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			3.13
Root			$3.18854e6i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.33.b.b.3.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(60712.0 - 24678.5i) q^{2} +5.10167e7i q^{3} +(3.07691e9 - 2.99655e9i) q^{4} +2.49571e11 q^{5} +(1.25901e12 + 3.09732e12i) q^{6} +4.65014e13i q^{7} +(1.12855e14 - 2.57860e14i) q^{8} -7.49683e14 q^{9} +O(q^{10})$	\(q+(60712.0 - 24678.5i) q^{2} +5.10167e7i q^{3} +(3.07691e9 - 2.99655e9i) q^{4} +2.49571e11 q^{5} +(1.25901e12 + 3.09732e12i) q^{6} +4.65014e13i q^{7} +(1.12855e14 - 2.57860e14i) q^{8} -7.49683e14 q^{9} +(1.51520e16 - 6.15903e15i) q^{10} -4.19273e16i q^{11} +(1.52874e17 + 1.56974e17i) q^{12} -6.87705e17 q^{13} +(1.14758e18 + 2.82319e18i) q^{14} +1.27323e19i q^{15} +(4.88063e17 - 1.84403e19i) q^{16} +4.91747e19 q^{17} +(-4.55147e19 + 1.85010e19i) q^{18} +3.14168e20i q^{19} +(7.67909e20 - 7.47854e20i) q^{20} -2.37235e21 q^{21} +(-1.03470e21 - 2.54549e21i) q^{22} +4.04400e21i q^{23} +(1.31552e22 + 5.75750e21i) q^{24} +3.90027e22 q^{25} +(-4.17519e22 + 1.69715e22i) q^{26} +5.62886e22i q^{27} +(1.39344e23 + 1.43081e23i) q^{28} +1.16515e23 q^{29} +(3.14213e23 + 7.73002e23i) q^{30} -3.53780e23i q^{31} +(-4.25447e23 - 1.13159e24i) q^{32} +2.13899e24 q^{33} +(2.98549e24 - 1.21356e24i) q^{34} +1.16054e25i q^{35} +(-2.30671e24 + 2.24647e24i) q^{36} -7.58489e24 q^{37} +(7.75318e24 + 1.90737e25i) q^{38} -3.50844e25i q^{39} +(2.81654e25 - 6.43545e25i) q^{40} -2.78643e25 q^{41} +(-1.44030e26 + 5.85459e25i) q^{42} -1.82822e26i q^{43} +(-1.25637e26 - 1.29007e26i) q^{44} -1.87099e26 q^{45} +(9.97996e25 + 2.45519e26i) q^{46} +6.77015e25i q^{47} +(9.40763e26 + 2.48994e25i) q^{48} -1.05795e27 q^{49} +(2.36793e27 - 9.62526e26i) q^{50} +2.50873e27i q^{51} +(-2.11601e27 + 2.06075e27i) q^{52} +1.13783e27 q^{53} +(1.38912e27 + 3.41739e27i) q^{54} -1.04638e28i q^{55} +(1.19909e28 + 5.24792e27i) q^{56} -1.60278e28 q^{57} +(7.07388e27 - 2.87542e27i) q^{58} -5.33270e27i q^{59} +(3.81530e28 + 3.91762e28i) q^{60} -5.47348e28 q^{61} +(-8.73075e27 - 2.14787e28i) q^{62} -3.48613e28i q^{63} +(-5.37556e28 - 5.82017e28i) q^{64} -1.71631e29 q^{65} +(1.29862e29 - 5.27871e28i) q^{66} -6.20754e28i q^{67} +(1.51306e29 - 1.47355e29i) q^{68} -2.06311e29 q^{69} +(2.86403e29 + 7.04587e29i) q^{70} -4.47902e29i q^{71} +(-8.46056e28 + 1.93313e29i) q^{72} +5.03491e29 q^{73} +(-4.60494e29 + 1.87183e29i) q^{74} +1.98979e30i q^{75} +(9.41421e29 + 9.66668e29i) q^{76} +1.94968e30 q^{77} +(-8.65830e29 - 2.13004e30i) q^{78} -1.79837e30i q^{79} +(1.21806e29 - 4.60216e30i) q^{80} -4.26084e30 q^{81} +(-1.69170e30 + 6.87649e29i) q^{82} +2.17738e30i q^{83} +(-7.29951e30 + 7.10887e30i) q^{84} +1.22726e31 q^{85} +(-4.51175e30 - 1.10995e31i) q^{86} +5.94423e30i q^{87} +(-1.08114e31 - 4.73171e30i) q^{88} +1.19112e31 q^{89} +(-1.13592e31 + 4.61732e30i) q^{90} -3.19792e31i q^{91} +(1.21181e31 + 1.24430e31i) q^{92} +1.80487e31 q^{93} +(1.67077e30 + 4.11029e30i) q^{94} +7.84072e31i q^{95} +(5.77300e31 - 2.17049e31i) q^{96} -9.02666e31 q^{97} +(-6.42303e31 + 2.61086e31i) q^{98} +3.14322e31i 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 $

$2$	60712.0	−	24678.5i	0.926391	−	0.376563i
$2$	60712.0	−	24678.5i	0.926391	−	0.376563i
$3$			5.10167e7i			1.18515i	0.805516	+	0.592574i	$0.201888\pi$
$3$			5.10167e7i			1.18515i	−0.805516	+	0.592574i	$0.798112\pi$
$4$	3.07691e9	−	2.99655e9i	0.716400	−	0.697690i
$5$	2.49571e11			1.63559			0.817795	−	0.575510i	$-0.195196\pi$
$5$	2.49571e11			1.63559			0.817795	+	0.575510i	$0.195196\pi$
$6$	1.25901e12	+	3.09732e12i	0.446283	+	1.09791i
$7$			4.65014e13i			1.39926i	0.714507	+	0.699628i	$0.246651\pi$
$7$			4.65014e13i			1.39926i	−0.714507	+	0.699628i	$0.753349\pi$
$8$	1.12855e14	−	2.57860e14i	0.400942	−	0.916103i
$9$	−7.49683e14			−0.404574
$10$	1.51520e16	−	6.15903e15i	1.51520	−	0.615903i
$11$		−	4.19273e16i		−	0.912461i	−0.889862	−	0.456230i	$-0.849199\pi$
$11$		−	4.19273e16i		−	0.912461i	0.889862	−	0.456230i	$-0.150801\pi$
$12$	1.52874e17	+	1.56974e17i	0.826865	+	0.849039i
$13$	−6.87705e17			−1.03350			−0.516748	−	0.856138i	$-0.672857\pi$
$13$	−6.87705e17			−1.03350			−0.516748	+	0.856138i	$0.672857\pi$
$14$	1.14758e18	+	2.82319e18i	0.526909	+	1.29626i
$15$			1.27323e19i			1.93841i
$16$	4.88063e17	−	1.84403e19i	0.0264580	−	0.999650i
$17$	4.91747e19			1.01055			0.505277	−	0.862957i	$-0.331390\pi$
$17$	4.91747e19			1.01055			0.505277	+	0.862957i	$0.331390\pi$
$18$	−4.55147e19	+	1.85010e19i	−0.374793	+	0.152348i
$19$			3.14168e20i			1.08919i	0.838699	+	0.544596i	$0.183317\pi$
$19$			3.14168e20i			1.08919i	−0.838699	+	0.544596i	$0.816683\pi$
$20$	7.67909e20	−	7.47854e20i	1.17174	−	1.14113i
$21$	−2.37235e21			−1.65832
$22$	−1.03470e21	−	2.54549e21i	−0.343599	−	0.845295i
$23$			4.04400e21i			0.659425i	0.944081	+	0.329713i	$0.106952\pi$
$23$			4.04400e21i			0.659425i	−0.944081	+	0.329713i	$0.893048\pi$
$24$	1.31552e22	+	5.75750e21i	1.08572	+	0.475175i
$25$	3.90027e22			1.67515
$26$	−4.17519e22	+	1.69715e22i	−0.957420	+	0.389176i
$27$			5.62886e22i			0.705668i
$28$	1.39344e23	+	1.43081e23i	0.976247	+	1.00243i
$29$	1.16515e23			0.465603			0.232801	−	0.972524i	$-0.425211\pi$
$29$	1.16515e23			0.465603			0.232801	+	0.972524i	$0.425211\pi$
$30$	3.14213e23	+	7.73002e23i	0.729936	+	1.79573i
$31$		−	3.53780e23i		−	0.486347i	−0.969983	−	0.243174i	$-0.921812\pi$
$31$		−	3.53780e23i		−	0.486347i	0.969983	−	0.243174i	$-0.0781885\pi$
$32$	−4.25447e23	−	1.13159e24i	−0.351921	−	0.936030i
$33$	2.13899e24			1.08140
$34$	2.98549e24	−	1.21356e24i	0.936167	−	0.380537i
$35$			1.16054e25i			2.28861i
$36$	−2.30671e24	+	2.24647e24i	−0.289837	+	0.282267i
$37$	−7.58489e24			−0.614783			−0.307392	−	0.951583i	$-0.599456\pi$
$37$	−7.58489e24			−0.614783			−0.307392	+	0.951583i	$0.599456\pi$
$38$	7.75318e24	+	1.90737e25i	0.410150	+	1.00902i
$39$		−	3.50844e25i		−	1.22484i
$40$	2.81654e25	−	6.43545e25i	0.655776	−	1.49837i
$41$	−2.78643e25			−0.437026			−0.218513	−	0.975834i	$-0.570121\pi$
$41$	−2.78643e25			−0.437026			−0.218513	+	0.975834i	$0.570121\pi$
$42$	−1.44030e26	+	5.85459e25i	−1.53626	+	0.624464i
$43$		−	1.82822e26i		−	1.33823i	−0.743157	−	0.669117i	$-0.766672\pi$
$43$		−	1.82822e26i		−	1.33823i	0.743157	−	0.669117i	$-0.233328\pi$
$44$	−1.25637e26	−	1.29007e26i	−0.636614	−	0.653687i
$45$	−1.87099e26			−0.661716
$46$	9.97996e25	+	2.45519e26i	0.248315	+	0.610885i
$47$			6.77015e25i			0.119408i	0.998216	+	0.0597039i	$0.0190157\pi$
$47$			6.77015e25i			0.119408i	−0.998216	+	0.0597039i	$0.980984\pi$
$48$	9.40763e26	+	2.48994e25i	1.18473	+	0.0313566i
$49$	−1.05795e27			−0.957918
$50$	2.36793e27	−	9.62526e26i	1.55185	−	0.630801i
$51$			2.50873e27i			1.19765i
$52$	−2.11601e27	+	2.06075e27i	−0.740396	+	0.721059i
$53$	1.13783e27			0.293537			0.146769	−	0.989171i	$-0.453113\pi$
$53$	1.13783e27			0.293537			0.146769	+	0.989171i	$0.453113\pi$
$54$	1.38912e27	+	3.41739e27i	0.265729	+	0.653724i
$55$		−	1.04638e28i		−	1.49241i
$56$	1.19909e28	+	5.24792e27i	1.28186	+	0.561021i
$57$	−1.60278e28			−1.29085
$58$	7.07388e27	−	2.87542e27i	0.431330	−	0.175329i
$59$		−	5.33270e27i		−	0.247352i	−0.992323	−	0.123676i	$-0.960532\pi$
$59$		−	5.33270e27i		−	0.247352i	0.992323	−	0.123676i	$-0.0394683\pi$
$60$	3.81530e28	+	3.91762e28i	1.35241	+	1.38868i
$61$	−5.47348e28			−1.48931			−0.744657	−	0.667448i	$-0.767387\pi$
$61$	−5.47348e28			−1.48931			−0.744657	+	0.667448i	$0.767387\pi$
$62$	−8.73075e27	−	2.14787e28i	−0.183141	−	0.450548i
$63$		−	3.48613e28i		−	0.566102i
$64$	−5.37556e28	−	5.82017e28i	−0.678491	−	0.734609i
$65$	−1.71631e29			−1.69037
$66$	1.29862e29	−	5.27871e28i	1.00180	−	0.407216i
$67$		−	6.20754e28i		−	0.376464i	−0.982125	−	0.188232i	$-0.939724\pi$
$67$		−	6.20754e28i		−	0.376464i	0.982125	−	0.188232i	$-0.0602756\pi$
$68$	1.51306e29	−	1.47355e29i	0.723960	−	0.705053i
$69$	−2.06311e29			−0.781516
$70$	2.86403e29	+	7.04587e29i	0.861806	+	2.12015i
$71$		−	4.47902e29i		−	1.07411i	−0.843546	−	0.537056i	$-0.819536\pi$
$71$		−	4.47902e29i		−	1.07411i	0.843546	−	0.537056i	$-0.180464\pi$
$72$	−8.46056e28	+	1.93313e29i	−0.162211	+	0.370631i
$73$	5.03491e29			0.774151			0.387076	−	0.922048i	$-0.373485\pi$
$73$	5.03491e29			0.774151			0.387076	+	0.922048i	$0.373485\pi$
$74$	−4.60494e29	+	1.87183e29i	−0.569529	+	0.231505i
$75$			1.98979e30i			1.98530i
$76$	9.41421e29	+	9.66668e29i	0.759918	+	0.780297i
$77$	1.94968e30			1.27677
$78$	−8.65830e29	−	2.13004e30i	−0.461231	−	1.13468i
$79$		−	1.79837e30i		−	0.781349i	−0.920529	−	0.390674i	$-0.872242\pi$
$79$		−	1.79837e30i		−	0.781349i	0.920529	−	0.390674i	$-0.127758\pi$
$80$	1.21806e29	−	4.60216e30i	0.0432743	−	1.63502i
$81$	−4.26084e30			−1.24089
$82$	−1.69170e30	+	6.87649e29i	−0.404857	+	0.164568i
$83$			2.17738e30i			0.429224i	0.976699	+	0.214612i	$0.0688487\pi$
$83$			2.17738e30i			0.429224i	−0.976699	+	0.214612i	$0.931151\pi$
$84$	−7.29951e30	+	7.10887e30i	−1.18802	+	1.15700i
$85$	1.22726e31			1.65285
$86$	−4.51175e30	−	1.10995e31i	−0.503930	−	1.23973i
$87$			5.94423e30i			0.551808i
$88$	−1.08114e31	−	4.73171e30i	−0.835908	−	0.365844i
$89$	1.19112e31			0.768627			0.384314	−	0.923203i	$-0.374438\pi$
$89$	1.19112e31			0.768627			0.384314	+	0.923203i	$0.374438\pi$
$90$	−1.13592e31	+	4.61732e30i	−0.613008	+	0.249178i
$91$		−	3.19792e31i		−	1.44612i
$92$	1.21181e31	+	1.24430e31i	0.460074	+	0.472412i
$93$	1.80487e31			0.576393
$94$	1.67077e30	+	4.11029e30i	0.0449646	+	0.110618i
$95$			7.84072e31i			1.78147i
$96$	5.77300e31	−	2.17049e31i	1.10933	−	0.417078i
$97$	−9.02666e31			−1.46953			−0.734767	−	0.678320i	$-0.762708\pi$
$97$	−9.02666e31			−1.46953			−0.734767	+	0.678320i	$0.762708\pi$
$98$	−6.42303e31	+	2.61086e31i	−0.887406	+	0.360717i
$99$			3.14322e31i			0.369157i
$100$	1.20008e32	−	1.16874e32i	1.20008	−	1.16874i
$101$	2.25353e32			1.92186			0.960929	−	0.276794i	$-0.0892719\pi$
$101$	2.25353e32			1.92186			0.960929	+	0.276794i	$0.0892719\pi$
$102$	6.19116e31	+	1.52310e32i	0.450993	+	1.10950i
$103$		−	1.26169e32i		−	0.786242i	−0.919487	−	0.393121i	$-0.871395\pi$
$103$		−	1.26169e32i		−	0.786242i	0.919487	−	0.393121i	$-0.128605\pi$
$104$	−7.76110e31	+	1.77332e32i	−0.414372	+	0.946788i
$105$	−5.92069e32			−2.71234
$106$	6.90799e31	−	2.80799e31i	0.271930	−	0.110535i
$107$		−	4.06321e32i		−	1.37635i	−0.725545	−	0.688175i	$-0.758412\pi$
$107$		−	4.06321e32i		−	1.37635i	0.725545	−	0.688175i	$-0.241588\pi$
$108$	1.68672e32	+	1.73195e32i	0.492337	+	0.505540i
$109$	−5.20609e32			−1.31126			−0.655629	−	0.755083i	$-0.727596\pi$
$109$	−5.20609e32			−1.31126			−0.655629	+	0.755083i	$0.727596\pi$
$110$	−2.58232e32	−	6.35281e32i	−0.561987	−	1.38256i
$111$		−	3.86956e32i		−	0.728608i
$112$	8.57499e32	+	2.26956e31i	1.39877	+	0.0370215i
$113$	4.51919e32			0.639448			0.319724	−	0.947511i	$-0.396410\pi$
$113$	4.51919e32			0.639448			0.319724	+	0.947511i	$0.396410\pi$
$114$	−9.73079e32	+	3.95542e32i	−1.19583	+	0.486088i
$115$			1.00927e33i			1.07855i
$116$	3.58508e32	−	3.49145e32i	0.333558	−	0.324846i
$117$	5.15561e32			0.418125
$118$	−1.31603e32	−	3.23759e32i	−0.0931436	−	0.229144i
$119$			2.28669e33i			1.41402i
$120$	3.28315e33	+	1.43690e33i	1.77579	+	0.777192i
$121$	3.53478e32			0.167416
$122$	−3.32306e33	+	1.35077e33i	−1.37969	+	0.560821i
$123$		−	1.42155e33i		−	0.517940i
$124$	−1.06012e33	−	1.08855e33i	−0.339320	−	0.348419i
$125$	3.92316e33			1.10427
$126$	−8.60323e32	−	2.11650e33i	−0.213173	−	0.524432i
$127$		−	5.08881e33i		−	1.11111i	−0.831480	−	0.555555i	$-0.812506\pi$
$127$		−	5.08881e33i		−	1.11111i	0.831480	−	0.555555i	$-0.187494\pi$
$128$	−4.69994e33	−	2.20693e33i	−0.905175	−	0.425040i
$129$	9.32695e33			1.58600
$130$	−1.04201e34	+	4.23560e33i	−1.56595	+	0.636533i
$131$			7.19059e33i			0.955925i	0.878380	+	0.477962i	$0.158624\pi$
$131$			7.19059e33i			0.955925i	−0.878380	+	0.477962i	$0.841376\pi$
$132$	6.58150e33	−	6.40961e33i	0.774715	−	0.754482i
$133$	−1.46092e34			−1.52406
$134$	−1.53193e33	−	3.76872e33i	−0.141762	−	0.348752i
$135$			1.40480e34i			1.15418i
$136$	5.54962e33	−	1.26802e34i	0.405173	−	0.925771i
$137$	−2.68810e33			−0.174548			−0.0872741	−	0.996184i	$-0.527816\pi$
$137$	−2.68810e33			−0.174548			−0.0872741	+	0.996184i	$0.527816\pi$
$138$	−1.25256e34	+	5.09145e33i	−0.723989	+	0.294290i
$139$		−	3.58167e34i		−	1.84437i	−0.386744	−	0.922187i	$-0.626400\pi$
$139$		−	3.58167e34i		−	1.84437i	0.386744	−	0.922187i	$-0.373600\pi$
$140$	3.47762e34	+	3.57088e34i	1.59674	+	1.63956i
$141$	−3.45391e33			−0.141516
$142$	−1.10535e34	−	2.71930e34i	−0.404471	−	0.995048i
$143$			2.88336e34i			0.943024i
$144$	−3.65893e32	+	1.38244e34i	−0.0107042	+	0.404432i
$145$	2.90789e34			0.761535
$146$	3.05679e34	−	1.24254e34i	0.717167	−	0.291517i
$147$		−	5.39732e34i		−	1.13527i
$148$	−2.33381e34	+	2.27285e34i	−0.440431	+	0.428928i
$149$	−8.57097e34			−1.45228			−0.726139	−	0.687548i	$-0.758687\pi$
$149$	−8.57097e34			−1.45228			−0.726139	+	0.687548i	$0.758687\pi$
$150$	4.91049e34	+	1.20804e35i	0.747592	+	1.83917i
$151$			7.17265e34i			0.981857i	0.871200	+	0.490929i	$0.163342\pi$
$151$			7.17265e34i			0.981857i	−0.871200	+	0.490929i	$0.836658\pi$
$152$	8.10114e34	+	3.54555e34i	0.997812	+	0.436702i
$153$	−3.68655e34			−0.408843
$154$	1.18369e35	−	4.81151e34i	1.18278	−	0.480783i
$155$		−	8.82933e34i		−	0.795464i
$156$	−1.05132e35	−	1.07952e35i	−0.854561	−	0.877478i
$157$	−1.95517e33			−0.0143480			−0.00717399	−	0.999974i	$-0.502284\pi$
$157$	−1.95517e33			−0.0143480			−0.00717399	+	0.999974i	$0.502284\pi$
$158$	−4.43809e34	−	1.09182e35i	−0.294227	−	0.723835i
$159$			5.80483e34i			0.347885i
$160$	−1.06179e35	−	2.82412e35i	−0.575599	−	1.53096i
$161$	−1.88052e35			−0.922705
$162$	−2.58684e35	+	1.05151e35i	−1.14955	+	0.467275i
$163$		−	8.07068e34i		−	0.325019i	−0.986707	−	0.162509i	$-0.948041\pi$
$163$		−	8.07068e34i		−	0.325019i	0.986707	−	0.162509i	$-0.0519588\pi$
$164$	−8.57362e34	+	8.34970e34i	−0.313085	+	0.304908i
$165$	5.33831e35			1.76873
$166$	5.37343e34	+	1.32193e35i	0.161630	+	0.397629i
$167$			6.85162e33i			0.0187210i	0.999956	+	0.00936052i	$0.00297959\pi$
$167$			6.85162e33i			0.0187210i	−0.999956	+	0.00936052i	$0.997020\pi$
$168$	−2.67732e35	+	6.11734e35i	−0.664892	+	1.51920i
$169$	3.01587e34			0.0681123
$170$	7.45093e35	−	3.02869e35i	1.53119	−	0.622403i
$171$		−	2.35526e35i		−	0.440658i
$172$	−5.47835e35	−	5.62526e35i	−0.933672	−	0.958711i
$173$	9.99732e35			1.55291			0.776454	−	0.630174i	$-0.217016\pi$
$173$	9.99732e35			1.55291			0.776454	+	0.630174i	$0.217016\pi$
$174$	1.46695e35	+	3.60886e35i	0.207791	+	0.511190i
$175$			1.81368e36i			2.34397i
$176$	−7.73152e35	−	2.04632e34i	−0.912141	−	0.0241418i
$177$	2.72057e35			0.293148
$178$	7.23153e35	−	2.93950e35i	0.712049	−	0.289437i
$179$			4.70514e35i			0.423569i	0.977316	+	0.211785i	$0.0679275\pi$
$179$			4.70514e35i			0.423569i	−0.977316	+	0.211785i	$0.932072\pi$
$180$	−5.75689e35	+	5.60653e35i	−0.474054	+	0.461673i
$181$	−7.45049e35			−0.561471			−0.280736	−	0.959785i	$-0.590578\pi$
$181$	−7.45049e35			−0.561471			−0.280736	+	0.959785i	$0.590578\pi$
$182$	−7.89198e35	−	1.94152e36i	−0.544558	−	1.33968i
$183$		−	2.79239e36i		−	1.76506i
$184$	1.04279e36	+	4.56386e35i	0.604102	+	0.264391i
$185$	−1.89297e36			−1.00553
$186$	1.09577e36	−	4.45414e35i	0.533965	−	0.217049i
$187$		−	2.06176e36i		−	0.922090i
$188$	2.02871e35	+	2.08312e35i	0.0833096	+	0.0855438i
$189$	−2.61750e36			−0.987410
$190$	1.93497e36	+	4.76026e36i	0.670836	+	1.65034i
$191$			3.68249e36i			1.17384i	0.809646	+	0.586919i	$0.199659\pi$
$191$			3.68249e36i			1.17384i	−0.809646	+	0.586919i	$0.800341\pi$
$192$	2.96926e36	−	2.74243e36i	0.870619	−	0.804112i
$193$	8.17250e35			0.220515			0.110258	−	0.993903i	$-0.464832\pi$
$193$	8.17250e35			0.220515			0.110258	+	0.993903i	$0.464832\pi$
$194$	−5.48026e36	+	2.22764e36i	−1.36136	+	0.553372i
$195$		−	8.75606e36i		−	2.00334i
$196$	−3.25523e36	+	3.17021e36i	−0.686252	+	0.668330i
$197$	−3.31320e36			−0.643855			−0.321928	−	0.946764i	$-0.604331\pi$
$197$	−3.31320e36			−0.643855			−0.321928	+	0.946764i	$0.604331\pi$
$198$	7.75698e35	+	1.90831e36i	0.139011	+	0.341984i
$199$			6.72031e36i			1.11107i	0.831495	+	0.555533i	$0.187486\pi$
$199$			6.72031e36i			1.11107i	−0.831495	+	0.555533i	$0.812514\pi$
$200$	4.40165e36	−	1.00572e37i	0.671639	−	1.53461i
$201$	3.16688e36			0.446165
$202$	1.36816e37	−	5.56137e36i	1.78039	−	0.723702i
$203$			5.41813e36i			0.651498i
$204$	7.51755e36	+	7.71915e36i	0.835591	+	0.858000i
$205$	−6.95414e36			−0.714795
$206$	−3.11365e36	−	7.65995e36i	−0.296070	−	0.728367i
$207$		−	3.03172e36i		−	0.266786i
$208$	−3.35643e35	+	1.26815e37i	−0.0273442	+	1.03313i
$209$	1.31722e37			0.993844
$210$	−3.59457e37	+	1.46114e37i	−2.51269	+	1.02137i
$211$			2.52226e37i			1.63407i	0.576586	+	0.817036i	$0.304385\pi$
$211$			2.52226e37i			1.63407i	−0.576586	+	0.817036i	$0.695615\pi$
$212$	3.50100e36	−	3.40957e36i	0.210290	−	0.204798i
$213$	2.28505e37			1.27298
$214$	−1.00274e37	−	2.46685e37i	−0.518283	−	1.27504i
$215$		−	4.56270e37i		−	2.18880i
$216$	1.45146e37	+	6.35246e36i	0.646465	+	0.282932i
$217$	1.64513e37			0.680524
$218$	−3.16072e37	+	1.28478e37i	−1.21474	+	0.493771i
$219$			2.56864e37i			0.917483i
$220$	−3.13555e37	−	3.21964e37i	−1.04124	−	1.06916i
$221$	−3.38177e37			−1.04440
$222$	−9.54948e36	−	2.34929e37i	−0.274367	−	0.674976i
$223$		−	3.57438e37i		−	0.955703i	−0.878441	−	0.477851i	$-0.841416\pi$
$223$		−	3.57438e37i		−	0.955703i	0.878441	−	0.477851i	$-0.158584\pi$
$224$	5.26205e37	−	1.97839e37i	1.30975	−	0.492428i
$225$	−2.92397e37			−0.677723
$226$	2.74369e37	−	1.11527e37i	0.592379	−	0.240793i
$227$			2.14630e37i			0.431794i	0.976416	+	0.215897i	$0.0692675\pi$
$227$			2.14630e37i			0.431794i	−0.976416	+	0.215897i	$0.930733\pi$
$228$	−4.93162e37	+	4.80282e37i	−0.924766	+	0.900614i
$229$	6.83961e37			1.19581			0.597907	−	0.801565i	$-0.295999\pi$
$229$	6.83961e37			1.19581			0.597907	+	0.801565i	$0.295999\pi$
$230$	2.49071e37	+	6.12745e37i	0.406142	+	0.999158i
$231$			9.94661e37i			1.51316i
$232$	1.31494e37	−	3.00447e37i	0.186680	−	0.426540i
$233$	−5.97446e37			−0.791778			−0.395889	−	0.918298i	$-0.629564\pi$
$233$	−5.97446e37			−0.791778			−0.395889	+	0.918298i	$0.629564\pi$
$234$	3.13007e37	−	1.27232e37i	0.387347	−	0.157451i
$235$			1.68964e37i			0.195302i
$236$	−1.59797e37	−	1.64083e37i	−0.172575	−	0.177203i
$237$	9.17468e37			0.926013
$238$	5.64321e37	+	1.38830e38i	0.532469	+	1.30994i
$239$		−	1.48844e38i		−	1.31330i	−0.754195	−	0.656651i	$-0.771973\pi$
$239$		−	1.48844e38i		−	1.31330i	0.754195	−	0.656651i	$-0.228027\pi$
$240$	2.34787e38	+	6.21416e36i	1.93774	+	0.0512865i
$241$	−1.20182e38			−0.928040			−0.464020	−	0.885825i	$-0.653593\pi$
$241$	−1.20182e38			−0.928040			−0.464020	+	0.885825i	$0.653593\pi$
$242$	2.14603e37	−	8.72329e36i	0.155092	−	0.0630427i
$243$		−	1.13070e38i		−	0.764974i
$244$	−1.68414e38	+	1.64016e38i	−1.06694	+	1.03908i
$245$	−2.64034e38			−1.56676
$246$	−3.50816e37	−	8.63049e37i	−0.195037	−	0.479815i
$247$		−	2.16055e38i		−	1.12567i
$248$	−9.12258e37	−	3.99259e37i	−0.445544	−	0.194997i
$249$	−1.11083e38			−0.508694
$250$	2.38183e38	−	9.68176e37i	1.02299	−	0.415829i
$251$			2.24908e38i			0.906201i	0.891459	+	0.453100i	$0.149682\pi$
$251$			2.24908e38i			0.906201i	−0.891459	+	0.453100i	$0.850318\pi$
$252$	−1.04464e38	−	1.07265e38i	−0.394964	−	0.405556i
$253$	1.69554e38			0.601699
$254$	−1.25584e38	−	3.08952e38i	−0.418403	−	1.02932i
$255$			6.26107e38i			1.95887i
$256$	−3.39806e38	−	1.80000e37i	−0.998600	−	0.0528974i
$257$	3.64164e38			1.00547			0.502733	−	0.864442i	$-0.332328\pi$
$257$	3.64164e38			1.00547			0.502733	+	0.864442i	$0.332328\pi$
$258$	5.66257e38	−	2.30175e38i	1.46926	−	0.597231i
$259$		−	3.52708e38i		−	0.860239i
$260$	−5.28095e38	+	5.14303e38i	−1.21098	+	1.17936i
$261$	−8.73497e37			−0.188371
$262$	1.77453e38	+	4.36555e38i	0.359966	+	0.885560i
$263$		−	6.65323e38i		−	1.26981i	−0.772588	−	0.634907i	$-0.781038\pi$
$263$		−	6.65323e38i		−	1.26981i	0.772588	−	0.634907i	$-0.218962\pi$
$264$	2.41396e38	−	5.51561e38i	0.433579	−	0.990674i
$265$	2.83969e38			0.480107
$266$	−8.86955e38	+	3.60534e38i	−1.41187	+	0.573904i
$267$			6.07671e38i			0.910937i
$268$	−1.86012e38	−	1.91001e38i	−0.262655	−	0.269699i
$269$	4.52066e38			0.601403			0.300701	−	0.953718i	$-0.402779\pi$
$269$	4.52066e38			0.601403			0.300701	+	0.953718i	$0.402779\pi$
$270$	3.46683e38	+	8.52882e38i	0.434623	+	1.06922i
$271$			1.41567e39i			1.67284i	0.548092	+	0.836418i	$0.315354\pi$
$271$			1.41567e39i			1.67284i	−0.548092	+	0.836418i	$0.684646\pi$
$272$	2.40004e37	−	9.06796e38i	0.0267372	−	1.01020i
$273$	1.63147e39			1.71387
$274$	−1.63199e38	+	6.63380e37i	−0.161700	+	0.0657285i
$275$		−	1.63528e39i		−	1.52851i
$276$	−6.34803e38	+	6.18223e38i	−0.559878	+	0.545256i
$277$	−3.33834e36			−0.00277878			−0.00138939	−	0.999999i	$-0.500442\pi$
$277$	−3.33834e36			−0.00277878			−0.00138939	+	0.999999i	$0.500442\pi$
$278$	−8.83902e38	−	2.17450e39i	−0.694524	−	1.70861i
$279$			2.65223e38i			0.196763i
$280$	2.99257e39	+	1.30973e39i	2.09660	+	0.917599i
$281$	−1.77763e39			−1.17636			−0.588179	−	0.808731i	$-0.700155\pi$
$281$	−1.77763e39			−1.17636			−0.588179	+	0.808731i	$0.700155\pi$
$282$	−2.09694e38	+	8.52372e37i	−0.131099	+	0.0532897i
$283$			1.97454e39i			1.16650i	0.812294	+	0.583248i	$0.198218\pi$
$283$			1.97454e39i			1.16650i	−0.812294	+	0.583248i	$0.801782\pi$
$284$	−1.34216e39	−	1.37816e39i	−0.749397	−	0.769494i
$285$	−4.00008e39			−2.11130
$286$	7.11569e38	+	1.75055e39i	0.355108	+	0.873608i
$287$		−	1.29573e39i		−	0.611511i
$288$	3.18950e38	+	8.48334e38i	0.142378	+	0.378693i
$289$	5.02422e37			0.0212179
$290$	1.76544e39	−	7.17622e38i	0.705479	−	0.286766i
$291$		−	4.60510e39i		−	1.74161i
$292$	1.54920e39	−	1.50874e39i	0.554602	−	0.540117i
$293$	−2.15799e39			−0.731422			−0.365711	−	0.930729i	$-0.619174\pi$
$293$	−2.15799e39			−0.731422			−0.365711	+	0.930729i	$0.619174\pi$
$294$	−1.33197e39	−	3.27682e39i	−0.427503	−	1.05171i
$295$		−	1.33089e39i		−	0.404566i
$296$	−8.55994e38	+	1.95584e39i	−0.246492	+	0.563205i
$297$	2.36003e39			0.643894
$298$	−5.20360e39	+	2.11518e39i	−1.34538	+	0.546874i
$299$		−	2.78108e39i		−	0.681513i
$300$	5.96251e39	+	6.12241e39i	1.38513	+	1.42227i
$301$	8.50145e39			1.87253
$302$	1.77010e39	+	4.35466e39i	0.369732	+	0.909584i
$303$			1.14968e40i			2.27769i
$304$	5.79335e39	+	1.53334e38i	1.08881	+	0.0288178i
$305$	−1.36602e40			−2.43591
$306$	−2.23817e39	+	9.09783e38i	−0.378749	+	0.153955i
$307$			4.21465e39i			0.676936i	0.940978	+	0.338468i	$0.109909\pi$
$307$			4.21465e39i			0.676936i	−0.940978	+	0.338468i	$0.890091\pi$
$308$	5.99899e39	−	5.84232e39i	0.914675	−	0.890787i
$309$	6.43671e39			0.931812
$310$	−2.17894e39	−	5.36046e39i	−0.299543	−	0.736911i
$311$			8.06001e38i			0.105237i	0.998615	+	0.0526186i	$0.0167568\pi$
$311$			8.06001e38i			0.105237i	−0.998615	+	0.0526186i	$0.983243\pi$
$312$	−9.04688e39	−	3.95946e39i	−1.12208	−	0.491091i
$313$	9.82093e38			0.115729			0.0578646	−	0.998324i	$-0.481571\pi$
$313$	9.82093e38			0.115729			0.0578646	+	0.998324i	$0.481571\pi$
$314$	−1.18702e38	+	4.82506e37i	−0.0132918	+	0.00540292i
$315$		−	8.70038e39i		−	0.925911i
$316$	−5.38891e39	−	5.53342e39i	−0.545139	−	0.559758i
$317$	9.87696e39			0.949894			0.474947	−	0.880014i	$-0.342467\pi$
$317$	9.87696e39			0.949894			0.474947	+	0.880014i	$0.342467\pi$
$318$	1.43254e39	+	3.52423e39i	0.131001	+	0.322277i
$319$		−	4.88518e39i		−	0.424844i
$320$	−1.34158e40	−	1.45255e40i	−1.10973	−	1.20152i
$321$	2.07291e40			1.63118
$322$	−1.14170e40	+	4.64082e39i	−0.854785	+	0.347457i
$323$			1.54491e40i			1.10069i
$324$	−1.31102e40	+	1.27678e40i	−0.888976	+	0.865759i
$325$	−2.68223e40			−1.73126
$326$	−1.99172e39	−	4.89987e39i	−0.122390	−	0.301094i
$327$		−	2.65598e40i		−	1.55403i
$328$	−3.14463e39	+	7.18510e39i	−0.175222	+	0.400361i
$329$	−3.14822e39			−0.167082
$330$	3.24099e40	−	1.31741e40i	1.63853	−	0.666038i
$331$			2.26441e40i			1.09071i	0.838207	+	0.545353i	$0.183604\pi$
$331$			2.26441e40i			1.09071i	−0.838207	+	0.545353i	$0.816396\pi$
$332$	6.52463e39	+	6.69960e39i	0.299465	+	0.307496i
$333$	5.68627e39			0.248725
$334$	1.69087e38	+	4.15975e38i	0.00704966	+	0.0173430i
$335$		−	1.54922e40i		−	0.615740i
$336$	−1.15785e39	+	4.37468e40i	−0.0438759	+	1.65774i
$337$	2.83693e40			1.02511			0.512555	−	0.858655i	$-0.328699\pi$
$337$	2.83693e40			1.02511			0.512555	+	0.858655i	$0.328699\pi$
$338$	1.83099e39	−	7.44270e38i	0.0630986	−	0.0256486i
$339$			2.30554e40i			0.757840i
$340$	3.77617e40	−	3.67755e40i	1.18410	−	1.15318i
$341$	−1.48331e40			−0.443773
$342$	−5.81243e39	−	1.42993e40i	−0.165936	−	0.408222i
$343$			2.16122e39i			0.0588835i
$344$	−4.71424e40	−	2.06323e40i	−1.22596	−	0.536554i
$345$	−5.14894e40			−1.27824
$346$	6.06957e40	−	2.46718e40i	1.43860	−	0.584768i
$347$			3.40376e40i			0.770349i	0.922844	+	0.385175i	$0.125859\pi$
$347$			3.40376e40i			0.770349i	−0.922844	+	0.385175i	$0.874141\pi$
$348$	1.78122e40	+	1.82899e40i	0.384991	+	0.395315i
$349$	−5.22160e40			−1.07795			−0.538973	−	0.842323i	$-0.681187\pi$
$349$	−5.22160e40			−1.07795			−0.538973	+	0.842323i	$0.681187\pi$
$350$	4.47588e40	+	1.10112e41i	0.882652	+	2.17143i
$351$		−	3.87099e40i		−	0.729304i
$352$	−4.74445e40	+	1.78378e40i	−0.854090	+	0.321114i
$353$	8.73532e40			1.50274			0.751369	−	0.659882i	$-0.229394\pi$
$353$	8.73532e40			1.50274			0.751369	+	0.659882i	$0.229394\pi$
$354$	1.65171e40	−	6.71394e39i	0.271570	−	0.110389i
$355$		−	1.11783e41i		−	1.75681i
$356$	3.66498e40	−	3.56926e40i	0.550645	−	0.536264i
$357$	−1.16660e41			−1.67583
$358$	1.16116e40	+	2.85658e40i	0.159501	+	0.392391i
$359$		−	1.80854e39i		−	0.0237584i	−0.999929	−	0.0118792i	$-0.996219\pi$
$359$		−	1.80854e39i		−	0.0237584i	0.999929	−	0.0118792i	$-0.00378135\pi$
$360$	−2.11151e40	+	4.82455e40i	−0.265310	+	0.606201i
$361$	−1.55030e40			−0.186337
$362$	−4.52334e40	+	1.83867e40i	−0.520142	+	0.211430i
$363$			1.80333e40i			0.198412i
$364$	−9.58275e40	−	9.83974e40i	−1.00895	−	1.03600i
$365$	1.25657e41			1.26619
$366$	−6.89119e40	−	1.69531e41i	−0.664655	−	1.63513i
$367$			4.27904e40i			0.395084i	0.980294	+	0.197542i	$0.0632959\pi$
$367$			4.27904e40i			0.395084i	−0.980294	+	0.197542i	$0.936704\pi$
$368$	7.45725e40	+	1.97373e39i	0.659194	+	0.0174470i
$369$	2.08894e40			0.176809
$370$	−1.14926e41	+	4.67156e40i	−0.931516	+	0.378647i
$371$			5.29107e40i			0.410734i
$372$	5.55343e40	−	5.40839e40i	0.412928	−	0.402144i
$373$	2.44105e40			0.173875			0.0869373	−	0.996214i	$-0.472292\pi$
$373$	2.44105e40			0.173875			0.0869373	+	0.996214i	$0.472292\pi$
$374$	−5.08812e40	−	1.25174e41i	−0.347225	−	0.854216i
$375$			2.00147e41i			1.30873i
$376$	1.74575e40	+	7.64047e39i	0.109390	+	0.0478756i
$377$	−8.01282e40			−0.481198
$378$	−1.58913e41	+	6.45958e40i	−0.914728	+	0.371822i
$379$		−	1.39770e41i		−	0.771236i	−0.922658	−	0.385618i	$-0.873988\pi$
$379$		−	1.39770e41i		−	0.771236i	0.922658	−	0.385618i	$-0.126012\pi$
$380$	2.34952e41	+	2.41252e41i	1.24291	+	1.27624i
$381$	2.59615e41			1.31683
$382$	9.08782e40	+	2.23571e41i	0.442024	+	1.08743i
$383$			4.23797e40i			0.197687i	0.995103	+	0.0988433i	$0.0315143\pi$
$383$			4.23797e40i			0.197687i	−0.995103	+	0.0988433i	$0.968486\pi$
$384$	1.12590e41	−	2.39775e41i	0.503735	−	1.07277i
$385$	4.86583e41			2.08827
$386$	4.96169e40	−	2.01685e40i	0.204283	−	0.0830379i
$387$			1.37058e41i			0.541414i
$388$	−2.77743e41	+	2.70489e41i	−1.05277	+	1.02528i
$389$	−1.85666e41			−0.675366			−0.337683	−	0.941260i	$-0.609643\pi$
$389$	−1.85666e41			−0.675366			−0.337683	+	0.941260i	$0.609643\pi$
$390$	−2.16086e41	−	5.31598e41i	−0.754385	−	1.85588i
$391$			1.98862e41i			0.666384i
$392$	−1.19395e41	+	2.72803e41i	−0.384070	+	0.877552i
$393$	−3.66840e41			−1.13291
$394$	−2.01151e41	+	8.17647e40i	−0.596462	+	0.242452i
$395$		−	4.48821e41i		−	1.27797i
$396$	9.41883e40	+	9.67142e40i	0.257557	+	0.264464i
$397$	−7.51305e40			−0.197319			−0.0986594	−	0.995121i	$-0.531455\pi$
$397$	−7.51305e40			−0.197319			−0.0986594	+	0.995121i	$0.531455\pi$
$398$	1.65847e41	+	4.08003e41i	0.418387	+	1.02928i
$399$		−	7.45315e41i		−	1.80623i
$400$	1.90358e40	−	7.19221e41i	0.0443211	−	1.67457i
$401$	−1.59206e41			−0.356164			−0.178082	−	0.984016i	$-0.556989\pi$
$401$	−1.59206e41			−0.356164			−0.178082	+	0.984016i	$0.556989\pi$
$402$	1.92268e41	−	7.81538e40i	0.413323	−	0.168009i
$403$			2.43296e41i			0.502638i
$404$	6.93392e41	−	6.75283e41i	1.37682	−	1.34086i
$405$	−1.06338e42			−2.02959
$406$	1.33711e41	+	3.28945e41i	0.245330	+	0.603541i
$407$			3.18014e41i			0.560965i
$408$	6.46902e41	+	2.83123e41i	1.09718	+	0.480190i
$409$	−5.39300e41			−0.879543			−0.439772	−	0.898110i	$-0.644941\pi$
$409$	−5.39300e41			−0.879543			−0.439772	+	0.898110i	$0.644941\pi$
$410$	−4.22199e41	+	1.71617e41i	−0.662179	+	0.269166i
$411$		−	1.37138e41i		−	0.206865i
$412$	−3.78071e41	−	3.88210e41i	−0.548553	−	0.563263i
$413$	2.47978e41			0.346109
$414$	−7.48181e40	−	1.84061e41i	−0.100462	−	0.247148i
$415$			5.43411e41i			0.702035i
$416$	2.92582e41	+	7.78200e41i	0.363709	+	0.967382i
$417$	1.82725e42			2.18586
$418$	7.99711e41	−	3.25070e41i	0.920688	−	0.374245i
$419$			2.11602e41i			0.234474i	0.993104	+	0.117237i	$0.0374037\pi$
$419$			2.11602e41i			0.234474i	−0.993104	+	0.117237i	$0.962596\pi$
$420$	−1.82175e42	+	1.77417e42i	−1.94312	+	1.89237i
$421$	−1.06108e42			−1.08951			−0.544757	−	0.838594i	$-0.683378\pi$
$421$	−1.06108e42			−1.08951			−0.544757	+	0.838594i	$0.683378\pi$
$422$	6.22456e41	+	1.53132e42i	0.615332	+	1.51379i
$423$		−	5.07547e40i		−	0.0483093i
$424$	1.28410e41	−	2.93401e41i	0.117691	−	0.268911i
$425$	1.91795e42			1.69283
$426$	1.38730e42	−	5.63915e41i	1.17928	−	0.479358i
$427$		−	2.54524e42i		−	2.08393i
$428$	−1.21756e42	−	1.25021e42i	−0.960265	−	0.986016i
$429$	−1.47100e42			−1.11762
$430$	−1.12600e42	−	2.77010e42i	−0.824222	−	2.02769i
$431$			1.51417e42i			1.06792i	0.845510	+	0.533960i	$0.179297\pi$
$431$			1.51417e42i			1.06792i	−0.845510	+	0.533960i	$0.820703\pi$
$432$	1.03798e42	+	2.74724e40i	0.705421	+	0.0186705i
$433$	1.62637e42			1.06516			0.532579	−	0.846380i	$-0.321223\pi$
$433$	1.62637e42			1.06516			0.532579	+	0.846380i	$0.321223\pi$
$434$	9.98789e41	−	4.05992e41i	0.630432	−	0.256261i
$435$			1.48351e42i			0.902531i
$436$	−1.60187e42	+	1.56003e42i	−0.939385	+	0.914851i
$437$	−1.27049e42			−0.718240
$438$	6.33902e41	+	1.55947e42i	0.345491	+	0.849948i
$439$			5.61498e41i			0.295064i	0.989057	+	0.147532i	$0.0471329\pi$
$439$			5.61498e41i			0.295064i	−0.989057	+	0.147532i	$0.952867\pi$
$440$	−2.69821e42	−	1.18090e42i	−1.36720	−	0.598370i
$441$	7.93128e41			0.387548
$442$	−2.05314e42	+	8.34569e41i	−0.967524	+	0.393284i
$443$			3.65040e42i			1.65913i	0.558408	+	0.829566i	$0.311412\pi$
$443$			3.65040e42i			1.65913i	−0.558408	+	0.829566i	$0.688588\pi$
$444$	−1.15954e42	−	1.19063e42i	−0.508343	−	0.521975i
$445$	2.97269e42			1.25716
$446$	−8.82102e41	−	2.17008e42i	−0.359883	−	0.885354i
$447$		−	4.37262e42i		−	1.72116i
$448$	2.70646e42	−	2.49971e42i	1.02791	−	0.949383i
$449$	−1.04369e41			−0.0382500			−0.0191250	−	0.999817i	$-0.506088\pi$
$449$	−1.04369e41			−0.0382500			−0.0191250	+	0.999817i	$0.506088\pi$
$450$	−1.77520e42	+	7.21590e41i	−0.627836	+	0.255206i
$451$			1.16828e42i			0.398769i
$452$	1.39052e42	−	1.35420e42i	0.458101	−	0.446137i
$453$	−3.65925e42			−1.16365
$454$	5.29673e41	+	1.30306e42i	0.162598	+	0.400010i
$455$		−	7.98109e42i		−	2.36527i
$456$	−1.80882e42	+	4.13293e42i	−0.517557	+	1.18255i
$457$	1.25344e42			0.346293			0.173147	−	0.984896i	$-0.444607\pi$
$457$	1.25344e42			0.346293			0.173147	+	0.984896i	$0.444607\pi$
$458$	4.15246e42	−	1.68791e42i	1.10779	−	0.450300i
$459$			2.76798e42i			0.713115i
$460$	3.02432e42	+	3.10542e42i	0.752493	+	0.772672i
$461$	−5.99142e42			−1.43984			−0.719921	−	0.694056i	$-0.755822\pi$
$461$	−5.99142e42			−1.43984			−0.719921	+	0.694056i	$0.755822\pi$
$462$	2.45467e42	+	6.03878e42i	0.569799	+	1.40177i
$463$			5.84792e42i			1.31131i	0.755060	+	0.655656i	$0.227608\pi$
$463$			5.84792e42i			1.31131i	−0.755060	+	0.655656i	$0.772392\pi$
$464$	5.68669e40	−	2.14858e42i	0.0123189	−	0.465440i
$465$	4.50443e42			0.942742
$466$	−3.62721e42	+	1.47440e42i	−0.733496	+	0.298155i
$467$		−	6.14480e42i		−	1.20071i	−0.799734	−	0.600354i	$-0.795026\pi$
$467$		−	6.14480e42i		−	1.20071i	0.799734	−	0.600354i	$-0.204974\pi$
$468$	1.58634e42	−	1.54491e42i	0.299545	−	0.291721i
$469$	2.88659e42			0.526769
$470$	4.16976e41	+	1.02581e42i	0.0735437	+	0.180926i
$471$		−	9.97464e40i		−	0.0170045i
$472$	−1.37509e42	−	6.01823e41i	−0.226600	−	0.0991737i
$473$	−7.66522e42			−1.22109
$474$	5.57013e42	−	2.26417e42i	0.857850	−	0.348703i
$475$			1.22534e43i			1.82456i
$476$	6.85220e42	+	7.03596e42i	0.986549	+	1.01301i
$477$	−8.53012e41			−0.118757
$478$	−3.67324e42	−	9.03660e42i	−0.494541	−	1.21663i
$479$			3.58791e42i			0.467168i	0.972337	+	0.233584i	$0.0750454\pi$
$479$			3.58791e42i			0.467168i	−0.972337	+	0.233584i	$0.924955\pi$
$480$	1.44077e43	−	5.41691e42i	1.81441	−	0.682169i
$481$	5.21617e42			0.635375
$482$	−7.29648e42	+	2.96591e42i	−0.859728	+	0.349466i
$483$		−	9.59377e42i		−	1.09354i
$484$	1.08762e42	−	1.05922e42i	0.119937	−	0.116804i
$485$	−2.25279e43			−2.40355
$486$	−2.79039e42	−	6.86469e42i	−0.288061	−	0.708665i
$487$		−	1.26614e43i		−	1.26479i	−0.774644	−	0.632397i	$-0.782071\pi$
$487$		−	1.26614e43i		−	1.26479i	0.774644	−	0.632397i	$-0.217929\pi$
$488$	−6.17710e42	+	1.41139e43i	−0.597128	+	1.36437i
$489$	4.11739e42			0.385195
$490$	−1.60300e43	+	6.51595e42i	−1.45143	+	0.589985i
$491$		−	1.91062e43i		−	1.67445i	−0.546861	−	0.837224i	$-0.684177\pi$
$491$		−	1.91062e43i		−	1.67445i	0.546861	−	0.837224i	$-0.315823\pi$
$492$	−4.25974e42	−	4.37398e42i	−0.361361	−	0.371052i
$493$	5.72961e42			0.470516
$494$	−5.33190e42	−	1.31171e43i	−0.423888	−	1.04281i
$495$			7.84457e42i			0.603790i
$496$	−6.52381e42	−	1.72667e41i	−0.486177	−	0.0128678i
$497$	2.08281e43			1.50296
$498$	−6.74404e42	+	2.74135e42i	−0.471249	+	0.191555i
$499$			2.27907e43i			1.54223i	0.636695	+	0.771116i	$0.280301\pi$
$499$			2.27907e43i			1.54223i	−0.636695	+	0.771116i	$0.719699\pi$
$500$	1.20712e43	−	1.17560e43i	0.791101	−	0.770440i
$501$	−3.49547e41			−0.0221872
$502$	5.55037e42	+	1.36546e43i	0.341242	+	0.839496i
$503$			1.26686e43i			0.754465i	0.926119	+	0.377233i	$0.123124\pi$
$503$			1.26686e43i			0.754465i	−0.926119	+	0.377233i	$0.876876\pi$
$504$	−8.98934e42	−	3.93428e42i	−0.518608	−	0.226974i
$505$	5.62416e43			3.14337
$506$	1.02940e43	−	4.18433e42i	0.557409	−	0.226578i
$507$			1.53860e42i			0.0807230i
$508$	−1.52489e43	−	1.56578e43i	−0.775210	−	0.795999i
$509$	−3.59379e43			−1.77039			−0.885193	−	0.465224i	$-0.845974\pi$
$509$	−3.59379e43			−1.77039			−0.885193	+	0.465224i	$0.845974\pi$
$510$	1.54514e43	+	3.80122e43i	0.737639	+	1.81468i
$511$			2.34130e43i			1.08324i
$512$	−2.10745e43	+	7.29307e42i	−0.945013	+	0.327033i
$513$	−1.76841e43			−0.768607
$514$	2.21091e43	−	8.98702e42i	0.931455	−	0.378622i
$515$		−	3.14881e43i		−	1.28597i
$516$	2.86982e43	−	2.79487e43i	1.13621	−	1.10654i
$517$	2.83854e42			0.108955
$518$	−8.70429e42	−	2.14136e43i	−0.323935	−	0.796918i
$519$			5.10030e43i			1.84042i
$520$	−1.93695e43	+	4.42569e43i	−0.677742	+	1.54856i
$521$	5.25643e43			1.78356			0.891778	−	0.452473i	$-0.149458\pi$
$521$	5.25643e43			1.78356			0.891778	+	0.452473i	$0.149458\pi$
$522$	−5.30317e42	+	2.15566e42i	−0.174505	+	0.0709335i
$523$		−	4.65945e43i		−	1.48699i	−0.668743	−	0.743494i	$-0.733167\pi$
$523$		−	4.65945e43i		−	1.48699i	0.668743	−	0.743494i	$-0.266833\pi$
$524$	2.15470e43	+	2.21248e43i	0.666939	+	0.684825i
$525$	−9.25279e43			−2.77795
$526$	−1.64191e43	−	4.03930e43i	−0.478166	−	1.17634i
$527$		−	1.73970e43i		−	0.491480i
$528$	1.04396e42	−	3.94436e43i	0.0286116	−	1.08102i
$529$	2.12550e43			0.565158
$530$	1.72403e43	−	7.00793e42i	0.444766	−	0.180791i
$531$			3.99784e42i			0.100072i
$532$	−4.49514e43	+	4.37774e43i	−1.09183	+	1.06332i
$533$	1.91624e43			0.451664
$534$	1.49964e43	+	3.68929e43i	0.343025	+	0.843883i
$535$		−	1.01406e44i		−	2.25114i
$536$	−1.60068e43	−	7.00553e42i	−0.344880	−	0.150940i
$537$	−2.40041e43			−0.501992
$538$	2.74458e43	−	1.11563e43i	0.557134	−	0.226466i
$539$			4.43570e43i			0.874062i
$540$	4.20956e43	+	4.32245e43i	0.805262	+	0.826857i
$541$	−6.40627e43			−1.18973			−0.594865	−	0.803825i	$-0.702795\pi$
$541$	−6.40627e43			−1.18973			−0.594865	+	0.803825i	$0.702795\pi$
$542$	3.49366e43	+	8.59481e43i	0.629929	+	1.54970i
$543$		−	3.80099e43i		−	0.665426i
$544$	−2.09212e43	−	5.56456e43i	−0.355635	−	0.945908i
$545$	−1.29929e44			−2.14468
$546$	9.90500e43	−	4.02623e43i	1.58771	−	0.645381i
$547$			1.05284e44i			1.63895i	0.573118	+	0.819473i	$0.305734\pi$
$547$			1.05284e44i			1.63895i	−0.573118	+	0.819473i	$0.694266\pi$
$548$	−8.27104e42	+	8.05502e42i	−0.125046	+	0.121781i
$549$	4.10338e43			0.602537
$550$	−4.03561e43	−	9.92809e43i	−0.575581	−	1.41600i
$551$			3.66054e43i			0.507130i
$552$	−2.32833e43	+	5.31995e43i	−0.313343	+	0.715949i
$553$	8.36266e43			1.09331
$554$	−2.02677e41	+	8.23852e40i	−0.00257424	+	0.00104639i
$555$		−	9.65731e43i		−	1.19170i
$556$	−1.07327e44	−	1.10205e44i	−1.28680	−	1.32131i
$557$	6.38377e43			0.743694			0.371847	−	0.928294i	$-0.378725\pi$
$557$	6.38377e43			0.743694			0.371847	+	0.928294i	$0.378725\pi$
$558$	6.54530e42	+	1.61022e43i	0.0740939	+	0.182280i
$559$			1.25727e44i			1.38306i
$560$	2.14007e44	+	5.66417e42i	2.28781	+	0.0605519i
$561$	1.05184e44			1.09281
$562$	−1.07923e44	+	4.38691e43i	−1.08977	+	0.442974i
$563$			5.33900e43i			0.523993i	0.965069	+	0.261997i	$0.0843809\pi$
$563$			5.33900e43i			0.523993i	−0.965069	+	0.261997i	$0.915619\pi$
$564$	−1.06274e43	+	1.03498e43i	−0.101382	+	0.0987342i
$565$	1.12786e44			1.04587
$566$	4.87286e43	+	1.19878e44i	0.439260	+	1.08063i
$567$		−	1.98135e44i		−	1.73633i
$568$	−1.15496e44	−	5.05481e43i	−0.983998	−	0.430657i
$569$	−1.24668e43			−0.103267			−0.0516333	−	0.998666i	$-0.516443\pi$
$569$	−1.24668e43			−0.103267			−0.0516333	+	0.998666i	$0.516443\pi$
$570$	−2.42853e44	+	9.87158e43i	−1.95589	+	0.795040i
$571$			4.73606e43i			0.370885i	0.982655	+	0.185443i	$0.0593719\pi$
$571$			4.73606e43i			0.370885i	−0.982655	+	0.185443i	$0.940628\pi$
$572$	8.64015e43	+	8.87186e43i	0.657938	+	0.675582i
$573$	−1.87869e44			−1.39117
$574$	−3.19766e43	−	7.86663e43i	−0.230273	−	0.566498i
$575$			1.57727e44i			1.10464i
$576$	4.02997e43	+	4.36328e43i	0.274500	+	0.297203i
$577$	1.91505e44			1.26872			0.634361	−	0.773037i	$-0.281263\pi$
$577$	1.91505e44			1.26872			0.634361	+	0.773037i	$0.281263\pi$
$578$	3.05030e42	−	1.23990e42i	0.0196561	−	0.00798989i
$579$			4.16934e43i			0.261343i
$580$	8.94733e43	−	8.71365e43i	0.545564	−	0.531315i
$581$	−1.01251e44			−0.600595
$582$	−1.13647e44	−	2.79585e44i	−0.655828	−	1.61341i
$583$		−	4.77061e43i		−	0.267841i
$584$	5.68215e43	−	1.29830e44i	0.310390	−	0.709203i
$585$	1.28669e44			0.683881
$586$	−1.31016e44	+	5.32559e43i	−0.677582	+	0.275427i
$587$		−	3.61550e44i		−	1.81953i	−0.415125	−	0.909764i	$-0.636262\pi$
$587$		−	3.61550e44i		−	1.81953i	0.415125	−	0.909764i	$-0.363738\pi$
$588$	−1.61734e44	−	1.66071e44i	−0.792069	−	0.813310i
$589$	1.11146e44			0.529725
$590$	−3.28443e43	−	8.08008e43i	−0.152345	−	0.374786i
$591$		−	1.69029e44i		−	0.763063i
$592$	−3.70191e42	+	1.39868e44i	−0.0162659	+	0.614568i
$593$	−3.22195e44			−1.37798			−0.688992	−	0.724769i	$-0.741947\pi$
$593$	−3.22195e44			−1.37798			−0.688992	+	0.724769i	$0.741947\pi$
$594$	1.43282e44	−	5.82419e43i	0.596498	−	0.242467i
$595$			5.70693e44i			2.31276i
$596$	−2.63721e44	+	2.56834e44i	−1.04041	+	1.01324i
$597$	−3.42848e44			−1.31678
$598$	−6.86327e43	−	1.68845e44i	−0.256633	−	0.631347i
$599$			1.11435e44i			0.405688i	0.979211	+	0.202844i	$0.0650185\pi$
$599$			1.11435e44i			0.405688i	−0.979211	+	0.202844i	$0.934982\pi$
$600$	5.13087e44	+	2.24558e44i	1.81874	+	0.795991i
$601$	1.21014e44			0.417679			0.208839	−	0.977950i	$-0.433031\pi$
$601$	1.21014e44			0.417679			0.208839	+	0.977950i	$0.433031\pi$
$602$	5.16140e44	−	2.09803e44i	1.73470	−	0.705127i
$603$			4.65369e43i			0.152307i
$604$	2.14932e44	+	2.20696e44i	0.685032	+	0.703403i
$605$	8.82179e43			0.273824
$606$	2.83723e44	+	6.97991e44i	0.857693	+	2.11003i
$607$		−	3.55121e44i		−	1.04558i	−0.852462	−	0.522790i	$-0.824891\pi$
$607$		−	3.55121e44i		−	1.04558i	0.852462	−	0.522790i	$-0.175109\pi$
$608$	3.55509e44	−	1.33662e44i	1.01952	−	0.383309i
$609$	−2.76415e44			−0.772120
$610$	−8.29339e44	+	3.37113e44i	−2.25660	+	0.917273i
$611$		−	4.65587e43i		−	0.123407i
$612$	−1.13432e44	+	1.10469e44i	−0.292895	+	0.285246i
$613$	1.29016e44			0.324546			0.162273	−	0.986746i	$-0.448118\pi$
$613$	1.29016e44			0.324546			0.162273	+	0.986746i	$0.448118\pi$
$614$	1.04011e44	+	2.55880e44i	0.254909	+	0.627107i
$615$		−	3.54777e44i		−	0.847137i
$616$	2.20031e44	−	5.02744e44i	0.511909	−	1.16965i
$617$	3.97498e44			0.901099			0.450550	−	0.892751i	$-0.351228\pi$
$617$	3.97498e44			0.901099			0.450550	+	0.892751i	$0.351228\pi$
$618$	3.90785e44	−	1.58848e44i	0.863222	−	0.350886i
$619$		−	4.19604e44i		−	0.903212i	−0.892218	−	0.451606i	$-0.850851\pi$
$619$		−	4.19604e44i		−	0.903212i	0.892218	−	0.451606i	$-0.149149\pi$
$620$	−2.64576e44	−	2.71671e44i	−0.554987	−	0.569871i
$621$	−2.27631e44			−0.465335
$622$	1.98909e43	+	4.89339e43i	0.0396285	+	0.0974908i
$623$			5.53888e44i			1.07551i
$624$	−6.46967e44	−	1.71234e43i	−1.22442	−	0.0324069i
$625$	7.10064e43			0.130984
$626$	5.96248e43	−	2.42365e43i	0.107211	−	0.0435794i
$627$			6.72003e44i			1.17785i
$628$	−6.01590e42	+	5.85878e42i	−0.0102789	+	0.0100104i
$629$	−3.72985e44			−0.621271
$630$	−2.14712e44	−	5.28217e44i	−0.348664	−	0.857755i
$631$			4.07277e44i			0.644792i	0.946605	+	0.322396i	$0.104488\pi$
$631$			4.07277e44i			0.644792i	−0.946605	+	0.322396i	$0.895512\pi$
$632$	−4.63727e44	−	2.02955e44i	−0.715796	−	0.313276i
$633$	−1.28678e45			−1.93662
$634$	5.99650e44	−	2.43748e44i	0.879973	−	0.357695i
$635$		−	1.27002e45i		−	1.81732i
$636$	1.73945e44	+	1.78610e44i	0.242716	+	0.249225i
$637$	7.27558e44			0.990004
$638$	−1.20559e44	−	2.96589e44i	−0.159981	−	0.393572i
$639$			3.35785e44i			0.434558i
$640$	−1.17297e45	−	5.50787e44i	−1.48049	−	0.695191i
$641$	2.63607e44			0.324510			0.162255	−	0.986749i	$-0.448123\pi$
$641$	2.63607e44			0.324510			0.162255	+	0.986749i	$0.448123\pi$
$642$	1.25851e45	−	5.11563e44i	1.51111	−	0.614241i
$643$		−	5.14623e44i		−	0.602717i	−0.953511	−	0.301359i	$-0.902560\pi$
$643$		−	5.14623e44i		−	0.602717i	0.953511	−	0.301359i	$-0.0974401\pi$
$644$	−5.78618e44	+	5.63507e44i	−0.661026	+	0.643762i
$645$	2.32774e45			2.59405
$646$	3.81260e44	+	9.37946e44i	0.414478	+	1.01967i
$647$			5.16937e44i			0.548238i	0.961696	+	0.274119i	$0.0883862\pi$
$647$			5.16937e44i			0.548238i	−0.961696	+	0.274119i	$0.911614\pi$
$648$	−4.80857e44	+	1.09870e45i	−0.497526	+	1.13679i
$649$	−2.23586e44			−0.225699
$650$	−1.62844e45	+	6.61934e44i	−1.60383	+	0.651930i
$651$			8.39290e44i			0.806522i
$652$	−2.41842e44	−	2.48328e44i	−0.226762	−	0.232843i
$653$	1.24102e45			1.13545			0.567723	−	0.823220i	$-0.307825\pi$
$653$	1.24102e45			1.13545			0.567723	+	0.823220i	$0.307825\pi$
$654$	−6.55454e44	−	1.61250e45i	−0.585192	−	1.43964i
$655$			1.79456e45i			1.56350i
$656$	−1.35996e43	+	5.13826e44i	−0.0115628	+	0.436873i
$657$	−3.77459e44			−0.313201
$658$	−1.91134e44	+	7.76931e43i	−0.154783	+	0.0629170i
$659$		−	2.03659e45i		−	1.60967i	−0.593499	−	0.804835i	$-0.702254\pi$
$659$		−	2.03659e45i		−	1.60967i	0.593499	−	0.804835i	$-0.297746\pi$
$660$	1.64255e45	−	1.59965e45i	1.26712	−	1.23402i
$661$	7.03489e44			0.529705			0.264852	−	0.964289i	$-0.414677\pi$
$661$	7.03489e44			0.529705			0.264852	+	0.964289i	$0.414677\pi$
$662$	5.58822e44	+	1.37477e45i	0.410720	+	1.01042i
$663$		−	1.72527e45i		−	1.23777i
$664$	5.61459e44	+	2.45728e44i	0.393214	+	0.172094i
$665$	−3.64604e45			−2.49273
$666$	3.45224e44	−	1.40328e44i	0.230417	−	0.0936607i
$667$			4.71188e44i			0.307030i
$668$	2.05313e43	+	2.10819e43i	0.0130615	+	0.0134117i
$669$	1.82353e45			1.13265
$670$	−3.82325e44	−	9.40564e44i	−0.231865	−	0.570416i
$671$			2.29488e45i			1.35894i
$672$	1.00931e45	+	2.68453e45i	0.583599	+	1.55224i
$673$	5.51542e44			0.311413			0.155707	−	0.987803i	$-0.450235\pi$
$673$	5.51542e44			0.311413			0.155707	+	0.987803i	$0.450235\pi$
$674$	1.72236e45	−	7.00111e44i	0.949652	−	0.386019i
$675$			2.19541e45i			1.18210i
$676$	9.27957e43	−	9.03722e43i	0.0487956	−	0.0475212i
$677$	−3.04089e45			−1.56165			−0.780823	−	0.624753i	$-0.785200\pi$
$677$	−3.04089e45			−1.56165			−0.780823	+	0.624753i	$0.785200\pi$
$678$	5.68972e44	+	1.39974e45i	0.285375	+	0.702056i
$679$		−	4.19752e45i		−	2.05625i
$680$	1.38503e45	−	3.16461e45i	0.662697	−	1.51418i
$681$	−1.09497e45			−0.511739
$682$	−9.00544e44	+	3.66057e44i	−0.411107	+	0.167109i
$683$		−	1.65046e45i		−	0.735993i	−0.929827	−	0.367996i	$-0.880044\pi$
$683$		−	1.65046e45i		−	0.735993i	0.929827	−	0.367996i	$-0.119956\pi$
$684$	−7.05768e44	−	7.24694e44i	−0.307443	−	0.315687i
$685$	−6.70871e44			−0.285489
$686$	5.33357e43	+	1.31212e44i	0.0221734	+	0.0545492i
$687$			3.48934e45i			1.41722i
$688$	−3.37128e45	−	8.92284e43i	−1.33777	−	0.0354069i
$689$	−7.82491e44			−0.303369
$690$	−3.12602e45	+	1.27068e45i	−1.18415	+	0.481338i
$691$			1.42722e45i			0.528252i	0.964488	+	0.264126i	$0.0850834\pi$
$691$			1.42722e45i			0.528252i	−0.964488	+	0.264126i	$0.914917\pi$
$692$	3.07609e45	−	2.99575e45i	1.11250	−	1.08345i
$693$	−1.46164e45			−0.516546
$694$	8.39996e44	+	2.06649e45i	0.290085	+	0.713645i
$695$		−	8.93882e45i		−	3.01664i
$696$	1.53278e45	+	6.70837e44i	0.505513	+	0.221243i
$697$	−1.37022e45			−0.441638
$698$	−3.17014e45	+	1.28861e45i	−0.998599	+	0.405915i
$699$		−	3.04797e45i		−	0.938374i
$700$	5.43479e45	+	5.58054e45i	1.63536	+	1.67922i
$701$	5.21518e45			1.53384			0.766922	−	0.641741i	$-0.221787\pi$
$701$	5.21518e45			1.53384			0.766922	+	0.641741i	$0.221787\pi$
$702$	−9.55302e44	−	2.35016e45i	−0.274629	−	0.675621i
$703$		−	2.38293e45i		−	0.669616i
$704$	−2.44024e45	+	2.25383e45i	−0.670301	+	0.619096i
$705$	−8.61996e44			−0.231462
$706$	5.30338e45	−	2.15574e45i	1.39212	−	0.565876i
$707$			1.04792e46i			2.68917i
$708$	8.37096e44	−	8.15233e44i	0.210011	−	0.204527i
$709$	−9.80217e44			−0.240426			−0.120213	−	0.992748i	$-0.538358\pi$
$709$	−9.80217e44			−0.240426			−0.120213	+	0.992748i	$0.538358\pi$
$710$	−2.75864e45	−	6.78659e45i	−0.661549	−	1.62749i
$711$			1.34821e45i			0.316113i
$712$	1.34424e45	−	3.07143e45i	0.308175	−	0.704142i
$713$	1.43069e45			0.320710
$714$	−7.08263e45	+	2.87898e45i	−1.55247	+	0.631054i
$715$			7.19604e45i			1.54240i
$716$	1.40992e45	+	1.44773e45i	0.295520	+	0.303445i
$717$	7.59352e45			1.55646
$718$	−4.46320e43	−	1.09800e44i	−0.00894654	−	0.0220095i
$719$			8.51901e45i			1.67004i	0.550220	+	0.835020i	$0.314544\pi$
$719$			8.51901e45i			1.67004i	−0.550220	+	0.835020i	$0.685456\pi$
$720$	−9.13162e43	+	3.45016e45i	−0.0175077	+	0.661485i
$721$	5.86702e45			1.10015
$722$	−9.41217e44	+	3.82590e44i	−0.172621	+	0.0701679i
$723$		−	6.13129e45i		−	1.09986i
$724$	−2.29245e45	+	2.23258e45i	−0.402238	+	0.391733i
$725$	4.54442e45			0.779956
$726$	4.45034e44	+	1.09484e45i	0.0747148	+	0.183807i
$727$			4.72807e45i			0.776486i	0.921557	+	0.388243i	$0.126918\pi$
$727$			4.72807e45i			0.776486i	−0.921557	+	0.388243i	$0.873082\pi$
$728$	−8.24617e45	−	3.60902e45i	−1.32480	−	0.579812i
$729$	−2.12696e45			−0.334287
$730$	7.62887e45	−	3.10102e45i	1.17299	−	0.476802i
$731$		−	8.99020e45i		−	1.35236i
$732$	−8.36755e45	−	8.59194e45i	−1.23146	−	1.26449i
$733$	−1.17970e46			−1.69866			−0.849330	−	0.527862i	$-0.822994\pi$
$733$	−1.17970e46			−1.69866			−0.849330	+	0.527862i	$0.822994\pi$
$734$	1.05600e45	+	2.59789e45i	0.148774	+	0.366002i
$735$		−	1.34701e46i		−	1.85684i
$736$	4.57615e45	−	1.72051e45i	0.617242	−	0.232066i
$737$	−2.60266e45			−0.343508
$738$	1.26824e45	−	5.15519e44i	0.163794	−	0.0665798i
$739$		−	4.15446e45i		−	0.525054i	−0.964925	−	0.262527i	$-0.915444\pi$
$739$		−	4.15446e45i		−	0.525054i	0.964925	−	0.262527i	$-0.0845559\pi$
$740$	−5.82451e45	+	5.67239e45i	−0.720364	+	0.701550i
$741$	1.10224e46			1.33409
$742$	1.30575e45	+	3.21231e45i	0.154667	+	0.380500i
$743$			3.14116e45i			0.364141i	0.983285	+	0.182070i	$0.0582799\pi$
$743$			3.14116e45i			0.364141i	−0.983285	+	0.182070i	$0.941720\pi$
$744$	2.03689e45	−	4.65404e45i	0.231100	−	0.528036i
$745$	−2.13907e46			−2.37533
$746$	1.48201e45	−	6.02414e44i	0.161076	−	0.0654748i
$747$		−	1.63234e45i		−	0.173653i
$748$	−6.17819e45	−	6.34387e45i	−0.643333	−	0.660585i
$749$	1.88945e46			1.92586
$750$	4.93932e45	+	1.21513e46i	0.492818	+	1.21239i
$751$			6.57015e44i			0.0641707i	0.999485	+	0.0320853i	$0.0102148\pi$
$751$			6.57015e44i			0.0641707i	−0.999485	+	0.0320853i	$0.989785\pi$
$752$	1.24844e45	+	3.30426e43i	0.119366	+	0.00315929i
$753$	−1.14740e46			−1.07398
$754$	−4.86474e45	+	1.97744e45i	−0.445778	+	0.181202i
$755$			1.79009e46i			1.60592i
$756$	−8.05382e45	+	7.84348e45i	−0.707381	+	0.688906i
$757$	−7.25472e45			−0.623859			−0.311930	−	0.950105i	$-0.600975\pi$
$757$	−7.25472e45			−0.623859			−0.311930	+	0.950105i	$0.600975\pi$
$758$	−3.44931e45	−	8.48572e45i	−0.290419	−	0.714466i
$759$			8.65008e45i			0.713102i
$760$	2.02181e46	+	8.84866e45i	1.63201	+	0.714266i
$761$	9.43510e45			0.745748			0.372874	−	0.927882i	$-0.378372\pi$
$761$	9.43510e45			0.745748			0.372874	+	0.927882i	$0.378372\pi$
$762$	1.57617e46	−	6.40689e45i	1.21990	−	0.495870i
$763$		−	2.42091e46i		−	1.83478i
$764$	1.10348e46	+	1.13307e46i	0.818974	+	0.840937i
$765$	−9.20056e45			−0.668700
$766$	1.04587e45	+	2.57295e45i	0.0744415	+	0.183135i
$767$			3.66732e45i			0.255637i
$768$	9.18303e44	−	1.73358e46i	0.0626912	−	1.18349i
$769$	−8.57108e45			−0.573078			−0.286539	−	0.958069i	$-0.592505\pi$
$769$	−8.57108e45			−0.573078			−0.286539	+	0.958069i	$0.592505\pi$
$770$	2.95414e46	−	1.20081e46i	1.93455	−	0.786364i
$771$			1.85785e46i			1.19163i
$772$	2.51461e45	−	2.44894e45i	0.157977	−	0.153851i
$773$	−9.45230e45			−0.581655			−0.290828	−	0.956775i	$-0.593931\pi$
$773$	−9.45230e45			−0.581655			−0.290828	+	0.956775i	$0.593931\pi$
$774$	3.38239e45	+	8.32107e45i	0.203877	+	0.501561i
$775$		−	1.37984e46i		−	0.814706i
$776$	−1.01870e46	+	2.32762e46i	−0.589197	+	1.34624i
$777$	1.79940e46			1.01951
$778$	−1.12722e46	+	4.58196e45i	−0.625653	+	0.254318i
$779$		−	8.75408e45i		−	0.476005i
$780$	−2.62380e46	−	2.69417e46i	−1.39771	−	1.43519i
$781$	−1.87793e46			−0.980085
$782$	4.90762e45	+	1.20733e46i	0.250936	+	0.617332i
$783$			6.55849e45i			0.328561i
$784$	−5.16347e44	+	1.95089e46i	−0.0253445	+	0.957583i
$785$	−4.87955e44			−0.0234674
$786$	−2.22716e46	+	9.05305e45i	−1.04952	+	0.426613i
$787$		−	3.25122e46i		−	1.50124i	−0.660733	−	0.750621i	$-0.729755\pi$
$787$		−	3.25122e46i		−	1.50124i	0.660733	−	0.750621i	$-0.270245\pi$
$788$	−1.01944e46	+	9.92819e45i	−0.461258	+	0.449211i
$789$	3.39426e46			1.50492
$790$	−1.10762e46	−	2.72488e46i	−0.481235	−	1.18390i
$791$			2.10149e46i			0.894752i
$792$	8.10511e45	+	3.54729e45i	0.338186	+	0.148011i
$793$	3.76414e46			1.53920
$794$	−4.56132e45	+	1.85411e45i	−0.182794	+	0.0743030i
$795$			1.44872e46i			0.568997i
$796$	2.01378e46	+	2.06778e46i	0.775179	+	0.795968i
$797$	−2.94599e45			−0.111147			−0.0555735	−	0.998455i	$-0.517699\pi$
$797$	−2.94599e45			−0.111147			−0.0555735	+	0.998455i	$0.517699\pi$
$798$	−1.83932e46	−	4.52495e46i	−0.680161	−	1.67328i
$799$			3.32920e45i			0.120668i
$800$	−1.65936e46	−	4.41351e46i	−0.589522	−	1.56799i
$801$	−8.92964e45			−0.310966
$802$	−9.66573e45	+	3.92897e45i	−0.329947	+	0.134118i
$803$		−	2.11100e46i		−	0.706382i
$804$	9.74423e45	−	9.48974e45i	0.319632	−	0.311285i
$805$	−4.69322e46			−1.50917
$806$	6.00418e45	+	1.47710e46i	0.189275	+	0.465639i
$807$			2.30629e46i			0.712751i
$808$	2.54322e46	−	5.81096e46i	0.770554	−	1.76062i
$809$	3.70181e46			1.09961			0.549804	−	0.835294i	$-0.314702\pi$
$809$	3.70181e46			1.09961			0.549804	+	0.835294i	$0.314702\pi$
$810$	−6.45600e46	+	2.62426e46i	−1.88020	+	0.764270i
$811$			3.30022e46i			0.942344i	0.882041	+	0.471172i	$0.156169\pi$
$811$			3.30022e46i			0.942344i	−0.882041	+	0.471172i	$0.843831\pi$
$812$	1.62357e46	+	1.66711e46i	0.454543	+	0.466733i
$813$	−7.22228e46			−1.98256
$814$	7.84810e45	+	1.93073e46i	0.211239	+	0.519673i
$815$		−	2.01421e46i		−	0.531597i
$816$	4.62617e46	+	1.22442e45i	1.19724	+	0.0316875i
$817$	5.74366e46			1.45759
$818$	−3.27419e46	+	1.33091e46i	−0.814801	+	0.331204i
$819$			2.39743e46i			0.585064i
$820$	−2.13973e46	+	2.08384e46i	−0.512079	+	0.498705i
$821$	6.39550e46			1.50101			0.750506	−	0.660864i	$-0.229810\pi$
$821$	6.39550e46			1.50101			0.750506	+	0.660864i	$0.229810\pi$
$822$	−3.38435e45	−	8.32590e45i	−0.0778979	−	0.191638i
$823$		−	3.58417e46i		−	0.809080i	−0.914520	−	0.404540i	$-0.867432\pi$
$823$		−	3.58417e46i		−	0.809080i	0.914520	−	0.404540i	$-0.132568\pi$
$824$	−3.25339e46	−	1.42388e46i	−0.720279	−	0.315237i
$825$	8.34265e46			1.81151
$826$	1.50552e46	−	6.11971e45i	0.320632	−	0.130332i
$827$			1.31958e46i			0.275643i	0.990457	+	0.137821i	$0.0440100\pi$
$827$			1.31958e46i			0.275643i	−0.990457	+	0.137821i	$0.955990\pi$
$828$	−9.08471e45	−	9.32834e45i	−0.186134	−	0.191126i
$829$	−7.76124e46			−1.55976			−0.779881	−	0.625927i	$-0.784721\pi$
$829$	−7.76124e46			−1.55976			−0.779881	+	0.625927i	$0.784721\pi$
$830$	1.34105e46	+	3.29915e46i	0.264361	+	0.650358i
$831$		−	1.70311e44i		−	0.00329327i
$832$	3.69680e46	+	4.00256e46i	0.701217	+	0.759214i
$833$	−5.20245e46			−0.968027
$834$	1.10936e47	−	4.50937e46i	2.02496	−	0.823113i
$835$			1.70997e45i			0.0306199i
$836$	4.05298e46	−	3.94713e46i	0.711990	−	0.693395i
$837$	1.99138e46			0.343200
$838$	5.22201e45	+	1.28468e46i	0.0882944	+	0.217215i
$839$			1.83814e46i			0.304921i	0.988310	+	0.152460i	$0.0487196\pi$
$839$			1.83814e46i			0.304921i	−0.988310	+	0.152460i	$0.951280\pi$
$840$	−6.68181e46	+	1.52671e47i	−1.08749	+	2.48478i
$841$	−4.90474e46			−0.783214
$842$	−6.44199e46	+	2.61857e46i	−1.00932	+	0.410271i
$843$		−	9.06887e46i		−	1.39416i
$844$	7.55811e46	+	7.76079e46i	1.14008	+	1.17065i
$845$	7.52674e45			0.111404
$846$	−1.25255e45	−	3.08142e45i	−0.0181915	−	0.0447533i
$847$			1.64372e46i			0.234258i
$848$	5.55333e44	−	2.09819e46i	0.00776640	−	0.293435i
$849$	−1.00735e47			−1.38247
$850$	1.16442e47	−	4.73320e46i	1.56822	−	0.637458i
$851$		−	3.06733e46i		−	0.405403i
$852$	7.03090e46	−	6.84728e46i	0.911964	−	0.888146i
$853$	−1.27256e47			−1.61992			−0.809958	−	0.586488i	$-0.800510\pi$
$853$	−1.27256e47			−1.61992			−0.809958	+	0.586488i	$0.800510\pi$
$854$	−6.28127e46	−	1.54527e47i	−0.784732	−	1.93054i
$855$		−	5.87806e46i		−	0.720736i
$856$	−1.04774e47	−	4.58554e46i	−1.26088	−	0.551836i
$857$	−8.49613e46			−1.00352			−0.501762	−	0.865006i	$-0.667315\pi$
$857$	−8.49613e46			−1.00352			−0.501762	+	0.865006i	$0.667315\pi$
$858$	−8.93070e46	+	3.63019e46i	−1.03535	+	0.420855i
$859$			1.38903e47i			1.58060i	0.612723	+	0.790298i	$0.290074\pi$
$859$			1.38903e47i			1.58060i	−0.612723	+	0.790298i	$0.709926\pi$
$860$	−1.36724e47	−	1.40390e47i	−1.52710	−	1.56806i
$861$	6.61039e46			0.724731
$862$	3.73674e46	+	9.19283e46i	0.402140	+	0.989312i
$863$		−	1.18295e47i		−	1.24967i	−0.780759	−	0.624833i	$-0.785167\pi$
$863$		−	1.18295e47i		−	1.24967i	0.780759	−	0.624833i	$-0.214833\pi$
$864$	6.36957e46	−	2.39478e46i	0.660526	−	0.248339i
$865$	2.49504e47			2.53992
$866$	9.87403e46	−	4.01364e46i	0.986753	−	0.401100i
$867$			2.56319e45i			0.0251464i
$868$	5.06192e46	−	4.92971e46i	0.487528	−	0.474795i
$869$	−7.54007e46			−0.712950
$870$	3.66107e46	+	9.00667e46i	0.339860	+	0.836096i
$871$			4.26896e46i			0.389073i
$872$	−5.87534e46	+	1.34244e47i	−0.525738	+	1.20125i
$873$	6.76714e46			0.594534
$874$	−7.71342e46	+	3.13538e46i	−0.665371	+	0.270463i
$875$			1.82433e47i			1.54516i
$876$	7.69708e46	+	7.90350e46i	0.640118	+	0.657285i
$877$	−1.57931e46			−0.128965			−0.0644827	−	0.997919i	$-0.520540\pi$
$877$	−1.57931e46			−0.128965			−0.0644827	+	0.997919i	$0.520540\pi$
$878$	1.38569e46	+	3.40896e46i	0.111110	+	0.273344i
$879$		−	1.10094e47i		−	0.866842i
$880$	−1.92956e47	−	5.10702e45i	−1.49189	−	0.0394861i
$881$	2.23327e46			0.169561			0.0847806	−	0.996400i	$-0.472981\pi$
$881$	2.23327e46			0.169561			0.0847806	+	0.996400i	$0.472981\pi$
$882$	4.81524e46	−	1.95732e46i	0.359021	−	0.145937i
$883$		−	5.28087e44i		−	0.00386665i	−0.999998	−	0.00193332i	$-0.999385\pi$
$883$		−	5.28087e44i		−	0.00386665i	0.999998	−	0.00193332i	$-0.000615397\pi$
$884$	−1.04054e47	+	1.01337e47i	−0.748210	+	0.728669i
$885$	6.78975e46			0.479470
$886$	9.00863e46	+	2.21623e47i	0.624769	+	1.53701i
$887$		−	1.36689e47i		−	0.931011i	−0.885045	−	0.465505i	$-0.845873\pi$
$887$		−	1.36689e47i		−	0.931011i	0.885045	−	0.465505i	$-0.154127\pi$
$888$	−9.97806e46	−	4.36700e46i	−0.667481	−	0.292130i
$889$	2.36637e47			1.55473
$890$	1.80478e47	−	7.33615e46i	1.16462	−	0.473400i
$891$			1.78645e47i			1.13227i
$892$	−1.07108e47	−	1.09981e47i	−0.666784	−	0.684666i
$893$	−2.12696e46			−0.130058
$894$	−1.07910e47	−	2.65471e47i	−0.648127	−	1.59447i
$895$			1.17427e47i			0.692785i
$896$	1.02625e47	−	2.18554e47i	0.594740	−	1.26657i
$897$	1.41881e47			0.807693
$898$	−6.33647e45	+	2.57568e45i	−0.0354345	+	0.0144036i
$899$		−	4.12209e46i		−	0.226445i
$900$	−8.99679e46	+	8.76182e46i	−0.485521	+	0.472840i
$901$	5.59525e46			0.296635
$902$	2.88313e46	+	7.09284e46i	0.150162	+	0.369416i
$903$			4.33716e47i			2.21923i
$904$	5.10014e46	−	1.16532e47i	0.256382	−	0.585801i
$905$	−1.85943e47			−0.918337
$906$	−2.22160e47	+	9.03046e46i	−1.07799	+	0.438186i
$907$		−	3.79202e47i		−	1.80782i	−0.427726	−	0.903908i	$-0.640685\pi$
$907$		−	3.79202e47i		−	1.80782i	0.427726	−	0.903908i	$-0.359315\pi$
$908$	6.43150e46	+	6.60398e46i	0.301258	+	0.309337i
$909$	−1.68943e47			−0.777533
$910$	−1.96961e47	−	4.84548e47i	−0.890673	−	2.19116i
$911$			2.01538e46i			0.0895493i	0.998997	+	0.0447746i	$0.0142570\pi$
$911$			2.01538e46i			0.0895493i	−0.998997	+	0.0447746i	$0.985743\pi$
$912$	−7.82258e45	+	2.95557e47i	−0.0341533	+	1.29040i
$913$	9.12916e46			0.391650
$914$	7.60987e46	−	3.09329e46i	0.320803	−	0.130401i
$915$		−	6.96900e47i		−	2.88691i
$916$	2.10449e47	−	2.04953e47i	0.856682	−	0.834308i
$917$	−3.34372e47			−1.33758
$918$	6.83094e46	+	1.68049e47i	0.268533	+	0.660623i
$919$			3.04402e47i			1.17598i	0.808869	+	0.587989i	$0.200080\pi$
$919$			3.04402e47i			1.17598i	−0.808869	+	0.587989i	$0.799920\pi$
$920$	2.60249e47	+	1.13901e47i	0.988062	+	0.432436i
$921$	−2.15017e47			−0.802268
$922$	−3.63751e47	+	1.47859e47i	−1.33386	+	0.542192i
$923$			3.08025e47i			1.11009i
$924$	2.98056e47	+	3.06049e47i	1.05571	+	1.08402i
$925$	−2.95831e47			−1.02986
$926$	1.44318e47	+	3.55039e47i	0.493792	+	1.21479i
$927$			9.45865e46i			0.318093i
$928$	−4.95711e46	−	1.31848e47i	−0.163855	−	0.435818i
$929$	9.58853e46			0.311531			0.155765	−	0.987794i	$-0.450216\pi$
$929$	9.58853e46			0.311531			0.155765	+	0.987794i	$0.450216\pi$
$930$	2.73473e47	−	1.11163e47i	0.873348	−	0.355002i
$931$		−	3.32374e47i		−	1.04336i
$932$	−1.83829e47	+	1.79028e47i	−0.567230	+	0.552416i
$933$	−4.11195e46			−0.124722
$934$	−1.51644e47	−	3.73063e47i	−0.452143	−	1.11233i
$935$		−	5.14557e47i		−	1.50816i
$936$	5.81837e46	−	1.32943e47i	0.167644	−	0.383046i
$937$	4.66513e47			1.32139			0.660694	−	0.750655i	$-0.270262\pi$
$937$	4.66513e47			1.32139			0.660694	+	0.750655i	$0.270262\pi$
$938$	1.75251e47	−	7.12367e46i	0.487994	−	0.198362i
$939$			5.01031e46i			0.137156i
$940$	5.06308e46	+	5.19886e46i	0.136260	+	0.139914i
$941$	5.79901e47			1.53433			0.767167	−	0.641447i	$-0.221666\pi$
$941$	5.79901e47			1.53433			0.767167	+	0.641447i	$0.221666\pi$
$942$	−2.46159e45	−	6.05580e45i	−0.00640326	−	0.0157528i
$943$		−	1.12683e47i		−	0.288186i
$944$	−9.83365e46	−	2.60269e45i	−0.247265	−	0.00654442i
$945$	−6.53252e47			−1.61500
$946$	−4.65370e47	+	1.89166e47i	−1.13120	+	0.459816i
$947$			4.08962e46i			0.0977425i	0.998805	+	0.0488713i	$0.0155624\pi$
$947$			4.08962e46i			0.0977425i	−0.998805	+	0.0488713i	$0.984438\pi$
$948$	2.82297e47	−	2.74924e47i	0.663396	−	0.646070i
$949$	−3.46253e47			−0.800081
$950$	3.02395e47	+	7.43927e47i	0.687063	+	1.69026i
$951$			5.03890e47i			1.12576i
$952$	5.89647e47	+	2.58065e47i	1.29539	+	0.566941i
$953$	−2.93440e47			−0.633917			−0.316958	−	0.948439i	$-0.602662\pi$
$953$	−2.93440e47			−0.633917			−0.316958	+	0.948439i	$0.602662\pi$
$954$	−5.17880e46	+	2.10510e46i	−0.110016	+	0.0447197i
$955$			9.19044e47i			1.91992i
$956$	−4.46019e47	−	4.57980e47i	−0.916277	−	0.940849i
$957$	2.49226e47			0.503503
$958$	8.85441e46	+	2.17829e47i	0.175918	+	0.432780i
$959$		−	1.25000e47i		−	0.244238i
$960$	7.41041e47	−	6.84432e47i	1.42398	−	1.31520i
$961$	4.03984e47			0.763466
$962$	3.16684e47	−	1.28727e47i	0.588606	−	0.239259i
$963$			3.04612e47i			0.556835i
$964$	−3.69790e47	+	3.60132e47i	−0.664848	+	0.647484i
$965$	2.03962e47			0.360672
$966$	−2.36759e47	−	5.82456e47i	−0.411788	−	1.01305i
$967$			1.52616e47i			0.261081i	0.991443	+	0.130541i	$0.0416713\pi$
$967$			1.52616e47i			0.261081i	−0.991443	+	0.130541i	$0.958329\pi$
$968$	3.98918e46	−	9.11479e46i	0.0671240	−	0.153370i
$969$	−7.88163e47			−1.30447
$970$	−1.36772e48	+	5.55955e47i	−2.22663	+	0.905090i
$971$		−	4.62624e47i		−	0.740833i	−0.928866	−	0.370417i	$-0.879215\pi$
$971$		−	4.62624e47i		−	0.740833i	0.928866	−	0.370417i	$-0.120785\pi$
$972$	−3.38820e47	−	3.47906e47i	−0.533714	−	0.548027i
$973$	1.66553e48			2.58075
$974$	−3.12465e47	−	7.68701e47i	−0.476275	−	1.17169i
$975$		−	1.36839e48i		−	2.05180i
$976$	−2.67140e46	+	1.00933e48i	−0.0394042	+	1.48879i
$977$	2.90967e47			0.422212			0.211106	−	0.977463i	$-0.432293\pi$
$977$	2.90967e47			0.422212			0.211106	+	0.977463i	$0.432293\pi$
$978$	2.49975e47	−	1.01611e47i	0.356841	−	0.145050i
$979$		−	4.99405e47i		−	0.701342i
$980$	−8.12410e47	+	7.91193e47i	−1.12243	+	1.09311i
$981$	3.90292e47			0.530500
$982$	−4.71513e47	−	1.15998e48i	−0.630535	−	1.55119i
$983$			1.04874e48i			1.37979i	0.723909	+	0.689896i	$0.242344\pi$
$983$			1.04874e48i			1.37979i	−0.723909	+	0.689896i	$0.757656\pi$
$984$	−3.66560e47	−	1.60429e47i	−0.474486	−	0.207664i
$985$	−8.26879e47			−1.05308
$986$	3.47856e47	−	1.41398e47i	0.435882	−	0.177179i
$987$		−	1.60612e47i		−	0.198017i
$988$	−6.47420e47	−	6.64782e47i	−0.785371	−	0.806433i
$989$	7.39330e47			0.882465
$990$	1.93592e47	+	4.76259e47i	0.227365	+	0.559346i
$991$		−	7.53420e47i		−	0.870680i	−0.900266	−	0.435340i	$-0.856628\pi$
$991$		−	7.53420e47i		−	0.870680i	0.900266	−	0.435340i	$-0.143372\pi$
$992$	−4.00334e47	+	1.50515e47i	−0.455235	+	0.171156i
$993$	−1.15523e48			−1.29265
$994$	1.26451e48	−	5.14005e47i	1.39233	−	0.565959i
$995$			1.67719e48i			1.81725i
$996$	−3.41792e47	+	3.32865e47i	−0.364428	+	0.354911i
$997$	−2.59410e47			−0.272185			−0.136092	−	0.990696i	$-0.543454\pi$
$997$	−2.59410e47			−0.272185			−0.136092	+	0.990696i	$0.543454\pi$
$998$	5.62440e47	+	1.38367e48i	0.580748	+	1.42871i
$999$		−	4.26943e47i		−	0.433833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.33.b.b.3.13	✓	14
3.2	odd	2		36.33.d.b.19.2		14
4.3	odd	2	inner	4.33.b.b.3.14	yes	14
12.11	even	2		36.33.d.b.19.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.33.b.b.3.13	✓	14	1.1	even	1	trivial
4.33.b.b.3.14	yes	14	4.3	odd	2	inner
36.33.d.b.19.1		14	12.11	even	2
36.33.d.b.19.2		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)

\(f(q)\)	\(=\)	\(q+(60712.0 - 24678.5i) q^{2} +5.10167e7i q^{3} +(3.07691e9 - 2.99655e9i) q^{4} +2.49571e11 q^{5} +(1.25901e12 + 3.09732e12i) q^{6} +4.65014e13i q^{7} +(1.12855e14 - 2.57860e14i) q^{8} -7.49683e14 q^{9} +O(q^{10})\)	\(q+(60712.0 - 24678.5i) q^{2} +5.10167e7i q^{3} +(3.07691e9 - 2.99655e9i) q^{4} +2.49571e11 q^{5} +(1.25901e12 + 3.09732e12i) q^{6} +4.65014e13i q^{7} +(1.12855e14 - 2.57860e14i) q^{8} -7.49683e14 q^{9} +(1.51520e16 - 6.15903e15i) q^{10} -4.19273e16i q^{11} +(1.52874e17 + 1.56974e17i) q^{12} -6.87705e17 q^{13} +(1.14758e18 + 2.82319e18i) q^{14} +1.27323e19i q^{15} +(4.88063e17 - 1.84403e19i) q^{16} +4.91747e19 q^{17} +(-4.55147e19 + 1.85010e19i) q^{18} +3.14168e20i q^{19} +(7.67909e20 - 7.47854e20i) q^{20} -2.37235e21 q^{21} +(-1.03470e21 - 2.54549e21i) q^{22} +4.04400e21i q^{23} +(1.31552e22 + 5.75750e21i) q^{24} +3.90027e22 q^{25} +(-4.17519e22 + 1.69715e22i) q^{26} +5.62886e22i q^{27} +(1.39344e23 + 1.43081e23i) q^{28} +1.16515e23 q^{29} +(3.14213e23 + 7.73002e23i) q^{30} -3.53780e23i q^{31} +(-4.25447e23 - 1.13159e24i) q^{32} +2.13899e24 q^{33} +(2.98549e24 - 1.21356e24i) q^{34} +1.16054e25i q^{35} +(-2.30671e24 + 2.24647e24i) q^{36} -7.58489e24 q^{37} +(7.75318e24 + 1.90737e25i) q^{38} -3.50844e25i q^{39} +(2.81654e25 - 6.43545e25i) q^{40} -2.78643e25 q^{41} +(-1.44030e26 + 5.85459e25i) q^{42} -1.82822e26i q^{43} +(-1.25637e26 - 1.29007e26i) q^{44} -1.87099e26 q^{45} +(9.97996e25 + 2.45519e26i) q^{46} +6.77015e25i q^{47} +(9.40763e26 + 2.48994e25i) q^{48} -1.05795e27 q^{49} +(2.36793e27 - 9.62526e26i) q^{50} +2.50873e27i q^{51} +(-2.11601e27 + 2.06075e27i) q^{52} +1.13783e27 q^{53} +(1.38912e27 + 3.41739e27i) q^{54} -1.04638e28i q^{55} +(1.19909e28 + 5.24792e27i) q^{56} -1.60278e28 q^{57} +(7.07388e27 - 2.87542e27i) q^{58} -5.33270e27i q^{59} +(3.81530e28 + 3.91762e28i) q^{60} -5.47348e28 q^{61} +(-8.73075e27 - 2.14787e28i) q^{62} -3.48613e28i q^{63} +(-5.37556e28 - 5.82017e28i) q^{64} -1.71631e29 q^{65} +(1.29862e29 - 5.27871e28i) q^{66} -6.20754e28i q^{67} +(1.51306e29 - 1.47355e29i) q^{68} -2.06311e29 q^{69} +(2.86403e29 + 7.04587e29i) q^{70} -4.47902e29i q^{71} +(-8.46056e28 + 1.93313e29i) q^{72} +5.03491e29 q^{73} +(-4.60494e29 + 1.87183e29i) q^{74} +1.98979e30i q^{75} +(9.41421e29 + 9.66668e29i) q^{76} +1.94968e30 q^{77} +(-8.65830e29 - 2.13004e30i) q^{78} -1.79837e30i q^{79} +(1.21806e29 - 4.60216e30i) q^{80} -4.26084e30 q^{81} +(-1.69170e30 + 6.87649e29i) q^{82} +2.17738e30i q^{83} +(-7.29951e30 + 7.10887e30i) q^{84} +1.22726e31 q^{85} +(-4.51175e30 - 1.10995e31i) q^{86} +5.94423e30i q^{87} +(-1.08114e31 - 4.73171e30i) q^{88} +1.19112e31 q^{89} +(-1.13592e31 + 4.61732e30i) q^{90} -3.19792e31i q^{91} +(1.21181e31 + 1.24430e31i) q^{92} +1.80487e31 q^{93} +(1.67077e30 + 4.11029e30i) q^{94} +7.84072e31i q^{95} +(5.77300e31 - 2.17049e31i) q^{96} -9.02666e31 q^{97} +(-6.42303e31 + 2.61086e31i) q^{98} +3.14322e31i 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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