LMFDB - Embedded newform 4.35.b.a.3.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,35,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, 35, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 35);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 35 $
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:	$29.2902616171$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 72626617369828 x^{14} - 508386321588656 x^{13} + \cdots + 10\!\cdots\!04 $ x^16 - 8x^15 + 72626617369828x^14 - 508386321588656x^13 + 2070719277905647749353609238x^12 - 12424315667427277473941003264x^11 + 29149279164108071001422670079476973946124x^10 - 145746395820426465446828612470414408396048x^9 + 208496096173568297991996731996084596831140332539876641x^8 - 833984384693398713593064505859129757329019844492402808x^7 + 698875044281632666404075222255491833772167721683562957908849313992x^6 - 2096625132841979053865799383403762221200483615238531437571184911168x^5 + 875349684493967266675808505113830711763013718564229702361030689486070549970192x^4 - 1750699368984440158130214684786333899894027567027597503857227657836248590530944x^3 + 58492108779558800474886843372761385704540074687283929338876917776255190499572053123416832x^2 - 58492108778683450790394972731218418552991821255044754502302019047778482600406279068669952*x + 1002905835814255424301301646724378424153530387112307506080792395282136017819372496998790246522159104
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{240}\cdot 3^{26}\cdot 5^{6}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.5
Root			$0.500000 - 2.05624e6i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.35.b.a.3.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-83785.2 - 100796. i) q^{2} +9.86995e7i q^{3} +(-3.13996e9 + 1.68905e10i) q^{4} -1.17209e12 q^{5} +(9.94856e12 - 8.26956e12i) q^{6} -2.80726e14i q^{7} +(1.96558e15 - 1.09867e15i) q^{8} +6.93558e15 q^{9} +O(q^{10})$	\(q+(-83785.2 - 100796. i) q^{2} +9.86995e7i q^{3} +(-3.13996e9 + 1.68905e10i) q^{4} -1.17209e12 q^{5} +(9.94856e12 - 8.26956e12i) q^{6} -2.80726e14i q^{7} +(1.96558e15 - 1.09867e15i) q^{8} +6.93558e15 q^{9} +(9.82041e16 + 1.18143e17i) q^{10} -6.38615e17i q^{11} +(-1.66708e18 - 3.09913e17i) q^{12} +9.36212e18 q^{13} +(-2.82961e19 + 2.35206e19i) q^{14} -1.15685e20i q^{15} +(-2.75429e20 - 1.06071e20i) q^{16} -1.12609e21 q^{17} +(-5.81099e20 - 6.99082e20i) q^{18} +4.37344e21i q^{19} +(3.68033e21 - 1.97972e22i) q^{20} +2.77075e22 q^{21} +(-6.43701e22 + 5.35065e22i) q^{22} +7.31443e22i q^{23} +(1.08439e23 + 1.94002e23i) q^{24} +7.91727e23 q^{25} +(-7.84407e23 - 9.43668e23i) q^{26} +2.33057e24i q^{27} +(4.74159e24 + 8.81469e23i) q^{28} -1.01373e25 q^{29} +(-1.16606e25 + 9.69270e24i) q^{30} -4.87911e23i q^{31} +(1.23853e25 + 3.66495e25i) q^{32} +6.30311e25 q^{33} +(9.43498e25 + 1.13506e26i) q^{34} +3.29037e26i q^{35} +(-2.17775e25 + 1.17145e26i) q^{36} -6.91349e25 q^{37} +(4.40827e26 - 3.66430e26i) q^{38} +9.24037e26i q^{39} +(-2.30385e27 + 1.28775e27i) q^{40} +1.16510e27 q^{41} +(-2.32148e27 - 2.79282e27i) q^{42} -5.88982e27i q^{43} +(1.07865e28 + 2.00523e27i) q^{44} -8.12915e27 q^{45} +(7.37269e27 - 6.12841e27i) q^{46} -1.68523e27i q^{47} +(1.04692e28 - 2.71847e28i) q^{48} -2.46899e28 q^{49} +(-6.63350e28 - 7.98033e28i) q^{50} -1.11145e29i q^{51} +(-2.93967e28 + 1.58131e29i) q^{52} +3.41859e28 q^{53} +(2.34913e29 - 1.95267e29i) q^{54} +7.48517e29i q^{55} +(-3.08426e29 - 5.51789e29i) q^{56} -4.31657e29 q^{57} +(8.49357e29 + 1.02181e30i) q^{58} +2.08495e30i q^{59} +(1.95398e30 + 3.63247e29i) q^{60} -5.31573e29 q^{61} +(-4.91796e28 + 4.08797e28i) q^{62} -1.94700e30i q^{63} +(2.65643e30 - 4.31907e30i) q^{64} -1.09733e31 q^{65} +(-5.28107e30 - 6.35330e30i) q^{66} +2.05716e31i q^{67} +(3.53589e30 - 1.90202e31i) q^{68} -7.21931e30 q^{69} +(3.31657e31 - 2.75684e31i) q^{70} -8.65876e30i q^{71} +(1.36325e31 - 7.61995e30i) q^{72} -2.42765e30 q^{73} +(5.79248e30 + 6.96855e30i) q^{74} +7.81431e31i q^{75} +(-7.38696e31 - 1.37325e31i) q^{76} -1.79276e32 q^{77} +(9.31396e31 - 7.74206e31i) q^{78} +9.47008e31i q^{79} +(3.22829e32 + 1.24325e32i) q^{80} -1.14360e32 q^{81} +(-9.76178e31 - 1.17438e32i) q^{82} +4.82929e32i q^{83} +(-8.70005e31 + 4.67993e32i) q^{84} +1.31989e33 q^{85} +(-5.93672e32 + 4.93479e32i) q^{86} -1.00055e33i q^{87} +(-7.01631e32 - 1.25525e33i) q^{88} -8.20306e32 q^{89} +(6.81102e32 + 8.19389e32i) q^{90} -2.62819e33i q^{91} +(-1.23544e33 - 2.29671e32i) q^{92} +4.81565e31 q^{93} +(-1.69865e32 + 1.41197e32i) q^{94} -5.12609e33i q^{95} +(-3.61728e33 + 1.22242e33i) q^{96} +3.81131e33 q^{97} +(2.06865e33 + 2.48865e33i) q^{98} -4.42917e33i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 27372 q^{2} - 20032875248 q^{4} - 21372255840 q^{5} + 20836736461728 q^{6} + 22\!\cdots\!12 q^{8}+ \cdots - 67\!\cdots\!80 q^{9}+O(q^{10}) $ 16 * q - 27372 * q^2 - 20032875248 * q^4 - 21372255840 * q^5 + 20836736461728 * q^6 + 2284358011394112 * q^8 - 67828545645364080 * q^9	$ 16 q - 27372 q^{2} - 20032875248 q^{4} - 21372255840 q^{5} + 20836736461728 q^{6} + 22\!\cdots\!12 q^{8}+ \cdots + 16\!\cdots\!32 q^{98}+O(q^{100}) $ 16 * q - 27372 * q^2 - 20032875248 * q^4 - 21372255840 * q^5 + 20836736461728 * q^6 + 2284358011394112 * q^8 - 67828545645364080 * q^9 - 45113792455239160 * q^10 + 2389205919902175360 * q^12 - 5233507036411659616 * q^13 - 78584294183795706432 * q^14 + 495182112183820124416 * q^16 - 603670905919309938144 * q^17 - 3049682100893194226508 * q^18 - 33058393758449688290400 * q^20 + 51436061805005728413696 * q^21 + 71660876143050404765280 * q^22 + 216144869785928938234368 * q^24 + 1224730607199300816400560 * q^25 - 2068583291215840445568696 * q^26 + 891252510406495618671360 * q^28 - 4086289565288128397679456 * q^29 + 29601064663371600024444480 * q^30 + 20026414012547463259849728 * q^32 + 73954448514753271238568960 * q^33 + 46288216238217191722231976 * q^34 + 569062048300724903070378384 * q^36 + 950385175701396416644593056 * q^37 - 123498782719680108073563360 * q^38 - 3250024485723791435879459200 * q^40 + 469238845433510127731349792 * q^41 + 2352670327884382399711157760 * q^42 + 7327222247557584897899214720 * q^44 - 24427097188106605438098250080 * q^45 - 19562783684402230406331003072 * q^46 + 10576141603633237485164267520 * q^48 - 5662649722408510114314091760 * q^49 + 20191932196464263485504736220 * q^50 - 299155663662273783907276503904 * q^52 - 287274278887575172234950512736 * q^53 + 6047252470624543429578889536 * q^54 + 957626384837555513184792726528 * q^56 + 2791286265941381406754467578880 * q^57 - 314499391713380785247660833336 * q^58 + 1103184540481814815474103512320 * q^60 - 7360215904797065436447249778528 * q^61 + 6668101684324825273374014288640 * q^62 - 4672502276277215477475812569088 * q^64 + 7390500022468645317433010287680 * q^65 - 12460359580334220374288279205120 * q^66 + 3201090312765007118305938045984 * q^68 - 20909099675706939600670541666304 * q^69 - 13302319794857519494110175324800 * q^70 - 776423968147266229824274003392 * q^72 - 21322365514881309087265291408096 * q^73 + 60200090281780873185690769101576 * q^74 - 104909582027053727863743869884800 * q^76 + 31510097566037837419459121448960 * q^77 + 173718506967281862717403400063040 * q^78 + 360511559214548868760655536888320 * q^80 - 262819454584631237298859074129648 * q^81 - 127799686177535642546403976474264 * q^82 - 481860976739335096182940424300544 * q^84 + 2066519418228326883252673443837760 * q^85 + 680164732953303409567751182232928 * q^86 - 1868588957981221169228370505105920 * q^88 - 2487774705888249186282098457137376 * q^89 + 2710136859758550244207319911170120 * q^90 - 5719642193953545223478177490435840 * q^92 - 4648987096869411453766406983557120 * q^93 - 174301665834847119752293250078592 * q^94 - 1356265248520894619800195113541632 * q^96 + 7119191713926779638291321673063456 * q^97 + 16929214407930779244441537548523732 * 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 $

$2$	−83785.2	−	100796.i	−0.639230	−	0.769016i
$2$	−83785.2	−	100796.i	−0.639230	−	0.769016i
$3$			9.86995e7i			0.764282i	0.924104	+	0.382141i	$0.124813\pi$
$3$			9.86995e7i			0.764282i	−0.924104	+	0.382141i	$0.875187\pi$
$4$	−3.13996e9	+	1.68905e10i	−0.182770	+	0.983156i
$5$	−1.17209e12			−1.53629			−0.768143	−	0.640278i	$-0.778819\pi$
$5$	−1.17209e12			−1.53629			−0.768143	+	0.640278i	$0.778819\pi$
$6$	9.94856e12	−	8.26956e12i	0.587745	−	0.488552i
$7$		−	2.80726e14i		−	1.20674i	−0.797460	−	0.603372i	$-0.793823\pi$
$7$		−	2.80726e14i		−	1.20674i	0.797460	−	0.603372i	$-0.206177\pi$
$8$	1.96558e15	−	1.09867e15i	0.872894	−	0.487910i
$9$	6.93558e15			0.415873
$10$	9.82041e16	+	1.18143e17i	0.982041	+	1.18143i
$11$		−	6.38615e17i		−	1.26347i	−0.775186	−	0.631733i	$-0.782344\pi$
$11$		−	6.38615e17i		−	1.26347i	0.775186	−	0.631733i	$-0.217656\pi$
$12$	−1.66708e18	−	3.09913e17i	−0.751409	−	0.139688i
$13$	9.36212e18			1.08227			0.541137	−	0.840934i	$-0.317994\pi$
$13$	9.36212e18			1.08227			0.541137	+	0.840934i	$0.317994\pi$
$14$	−2.82961e19	+	2.35206e19i	−0.928005	+	0.771387i
$15$		−	1.15685e20i		−	1.17416i
$16$	−2.75429e20	−	1.06071e20i	−0.933190	−	0.359383i
$17$	−1.12609e21			−1.36126			−0.680632	−	0.732625i	$-0.738295\pi$
$17$	−1.12609e21			−1.36126			−0.680632	+	0.732625i	$0.738295\pi$
$18$	−5.81099e20	−	6.99082e20i	−0.265838	−	0.319812i
$19$			4.37344e21i			0.798017i	0.916947	+	0.399009i	$0.130646\pi$
$19$			4.37344e21i			0.798017i	−0.916947	+	0.399009i	$0.869354\pi$
$20$	3.68033e21	−	1.97972e22i	0.280787	−	1.51041i
$21$	2.77075e22			0.922293
$22$	−6.43701e22	+	5.35065e22i	−0.971626	+	0.807646i
$23$			7.31443e22i			0.518570i	0.965801	+	0.259285i	$0.0834869\pi$
$23$			7.31443e22i			0.518570i	−0.965801	+	0.259285i	$0.916513\pi$
$24$	1.08439e23	+	1.94002e23i	0.372901	+	0.667138i
$25$	7.91727e23			1.36018
$26$	−7.84407e23	−	9.43668e23i	−0.691822	−	0.832286i
$27$			2.33057e24i			1.08213i
$28$	4.74159e24	+	8.81469e23i	1.18642	+	0.220557i
$29$	−1.01373e25			−1.39687			−0.698437	−	0.715672i	$-0.746121\pi$
$29$	−1.01373e25			−1.39687			−0.698437	+	0.715672i	$0.746121\pi$
$30$	−1.16606e25	+	9.69270e24i	−0.902945	+	0.750556i
$31$		−	4.87911e23i		−	0.0216367i	−0.999941	−	0.0108184i	$-0.996556\pi$
$31$		−	4.87911e23i		−	0.0216367i	0.999941	−	0.0108184i	$-0.00344366\pi$
$32$	1.23853e25	+	3.66495e25i	0.320152	+	0.947366i
$33$	6.30311e25			0.965645
$34$	9.43498e25	+	1.13506e26i	0.870161	+	1.04683i
$35$			3.29037e26i			1.85391i
$36$	−2.17775e25	+	1.17145e26i	−0.0760090	+	0.408867i
$37$	−6.91349e25			−0.151450			−0.0757248	−	0.997129i	$-0.524127\pi$
$37$	−6.91349e25			−0.151450			−0.0757248	+	0.997129i	$0.524127\pi$
$38$	4.40827e26	−	3.66430e26i	0.613688	−	0.510117i
$39$			9.24037e26i			0.827163i
$40$	−2.30385e27	+	1.28775e27i	−1.34102	+	0.749569i
$41$	1.16510e27			0.445694			0.222847	−	0.974853i	$-0.428465\pi$
$41$	1.16510e27			0.445694			0.222847	+	0.974853i	$0.428465\pi$
$42$	−2.32148e27	−	2.79282e27i	−0.589558	−	0.709258i
$43$		−	5.88982e27i		−	1.00262i	−0.865267	−	0.501312i	$-0.832851\pi$
$43$		−	5.88982e27i		−	1.00262i	0.865267	−	0.501312i	$-0.167149\pi$
$44$	1.07865e28	+	2.00523e27i	1.24218	+	0.230924i
$45$	−8.12915e27			−0.638900
$46$	7.37269e27	−	6.12841e27i	0.398789	−	0.331486i
$47$		−	1.68523e27i		−	0.0632404i	−0.999500	−	0.0316202i	$-0.989933\pi$
$47$		−	1.68523e27i		−	0.0632404i	0.999500	−	0.0316202i	$-0.0100667\pi$
$48$	1.04692e28	−	2.71847e28i	0.274670	−	0.713221i
$49$	−2.46899e28			−0.456232
$50$	−6.63350e28	−	7.98033e28i	−0.869466	−	1.04600i
$51$		−	1.11145e29i		−	1.04039i
$52$	−2.93967e28	+	1.58131e29i	−0.197807	+	1.06404i
$53$	3.41859e28			0.166401			0.0832006	−	0.996533i	$-0.473486\pi$
$53$	3.41859e28			0.166401			0.0832006	+	0.996533i	$0.473486\pi$
$54$	2.34913e29	−	1.95267e29i	0.832172	−	0.691728i
$55$			7.48517e29i			1.94105i
$56$	−3.08426e29	−	5.51789e29i	−0.588782	−	1.05336i
$57$	−4.31657e29			−0.609911
$58$	8.49357e29	+	1.02181e30i	0.892923	+	1.07422i
$59$			2.08495e30i			1.63912i	0.572991	+	0.819561i	$0.305783\pi$
$59$			2.08495e30i			1.63912i	−0.572991	+	0.819561i	$0.694217\pi$
$60$	1.95398e30	+	3.63247e29i	1.15438	+	0.214601i
$61$	−5.31573e29			−0.237113			−0.118557	−	0.992947i	$-0.537827\pi$
$61$	−5.31573e29			−0.237113			−0.118557	+	0.992947i	$0.537827\pi$
$62$	−4.91796e28	+	4.08797e28i	−0.0166390	+	0.0138308i
$63$		−	1.94700e30i		−	0.501852i
$64$	2.65643e30	−	4.31907e30i	0.523888	−	0.851787i
$65$	−1.09733e31			−1.66268
$66$	−5.28107e30	−	6.35330e30i	−0.617269	−	0.742596i
$67$			2.05716e31i			1.86207i	0.364931	+	0.931035i	$0.381093\pi$
$67$			2.05716e31i			1.86207i	−0.364931	+	0.931035i	$0.618907\pi$
$68$	3.53589e30	−	1.90202e31i	0.248798	−	1.33833i
$69$	−7.21931e30			−0.396334
$70$	3.31657e31	−	2.75684e31i	1.42568	−	1.18507i
$71$		−	8.65876e30i		−	0.292458i	−0.989251	−	0.146229i	$-0.953286\pi$
$71$		−	8.65876e30i		−	0.292458i	0.989251	−	0.146229i	$-0.0467137\pi$
$72$	1.36325e31	−	7.61995e30i	0.363013	−	0.202908i
$73$	−2.42765e30			−0.0511326			−0.0255663	−	0.999673i	$-0.508139\pi$
$73$	−2.42765e30			−0.0511326			−0.0255663	+	0.999673i	$0.508139\pi$
$74$	5.79248e30	+	6.96855e30i	0.0968111	+	0.116467i
$75$			7.81431e31i			1.03956i
$76$	−7.38696e31	−	1.37325e31i	−0.784575	−	0.145854i
$77$	−1.79276e32			−1.52468
$78$	9.31396e31	−	7.74206e31i	0.636101	−	0.528747i
$79$			9.47008e31i			0.520827i	0.965497	+	0.260413i	$0.0838588\pi$
$79$			9.47008e31i			0.520827i	−0.965497	+	0.260413i	$0.916141\pi$
$80$	3.22829e32	+	1.24325e32i	1.43365	+	0.552115i
$81$	−1.14360e32			−0.411177
$82$	−9.76178e31	−	1.17438e32i	−0.284901	−	0.342745i
$83$			4.82929e32i			1.14698i	0.819213	+	0.573489i	$0.194411\pi$
$83$			4.82929e32i			1.14698i	−0.819213	+	0.573489i	$0.805589\pi$
$84$	−8.70005e31	+	4.67993e32i	−0.168568	+	0.906758i
$85$	1.31989e33			2.09129
$86$	−5.93672e32	+	4.93479e32i	−0.771033	+	0.640907i
$87$		−	1.00055e33i		−	1.06761i
$88$	−7.01631e32	−	1.25525e33i	−0.616458	−	1.10287i
$89$	−8.20306e32			−0.594766			−0.297383	−	0.954758i	$-0.596114\pi$
$89$	−8.20306e32			−0.594766			−0.297383	+	0.954758i	$0.596114\pi$
$90$	6.81102e32	+	8.19389e32i	0.408404	+	0.491324i
$91$		−	2.62819e33i		−	1.30603i
$92$	−1.23544e33	−	2.29671e32i	−0.509835	−	0.0947791i
$93$	4.81565e31			0.0165366
$94$	−1.69865e32	+	1.41197e32i	−0.0486328	+	0.0404251i
$95$		−	5.12609e33i		−	1.22598i
$96$	−3.61728e33	+	1.22242e33i	−0.724055	+	0.244687i
$97$	3.81131e33			0.639668			0.319834	−	0.947474i	$-0.396373\pi$
$97$	3.81131e33			0.639668			0.319834	+	0.947474i	$0.396373\pi$
$98$	2.06865e33	+	2.48865e33i	0.291637	+	0.350850i
$99$		−	4.42917e33i		−	0.525441i
$100$	−2.48600e33	+	1.33727e34i	−0.248600	+	1.33727i
$101$	1.95994e34			1.65493			0.827464	−	0.561518i	$-0.189783\pi$
$101$	1.95994e34			1.65493			0.827464	+	0.561518i	$0.189783\pi$
$102$	−1.12030e34	+	9.31229e33i	−0.800076	+	0.665049i
$103$			1.86262e34i			1.12691i	0.826145	+	0.563457i	$0.190529\pi$
$103$			1.86262e34i			1.12691i	−0.826145	+	0.563457i	$0.809471\pi$
$104$	1.84020e34	−	1.02859e34i	0.944711	−	0.528052i
$105$	−3.24758e34			−1.41691
$106$	−2.86427e33	−	3.44581e33i	−0.106369	−	0.127965i
$107$			1.89032e34i			0.598428i	0.954186	+	0.299214i	$0.0967244\pi$
$107$			1.89032e34i			0.598428i	−0.954186	+	0.299214i	$0.903276\pi$
$108$	−3.93644e34	−	7.31790e33i	−1.06390	−	0.197780i
$109$	3.95334e34			0.913510			0.456755	−	0.889593i	$-0.349012\pi$
$109$	3.95334e34			0.913510			0.456755	+	0.889593i	$0.349012\pi$
$110$	7.54479e34	−	6.27146e34i	1.49270	−	1.24078i
$111$		−	6.82358e33i		−	0.115750i
$112$	−2.97769e34	+	7.73200e34i	−0.433683	+	1.12612i
$113$	−1.56756e35			−1.96287			−0.981434	−	0.191798i	$-0.938568\pi$
$113$	−1.56756e35			−1.96287			−0.981434	+	0.191798i	$0.938568\pi$
$114$	3.61664e34	+	4.35095e34i	0.389873	+	0.469031i
$115$		−	8.57320e34i		−	0.796673i
$116$	3.18308e34	−	1.71224e35i	0.255307	−	1.37334i
$117$	6.49318e34			0.450088
$118$	2.10156e35	−	1.74688e35i	1.26051	−	1.04778i
$119$			3.16123e35i			1.64270i
$120$	−1.27100e35	−	2.27389e35i	−0.572882	−	1.02491i
$121$	−1.52353e35			−0.596348
$122$	4.45379e34	+	5.35806e34i	0.151570	+	0.182344i
$123$			1.14995e35i			0.340636i
$124$	8.24105e33	+	1.53202e33i	0.0212723	+	0.00395454i
$125$	−2.45730e35			−0.553336
$126$	−1.96250e35	+	1.63129e35i	−0.385932	+	0.320799i
$127$		−	3.62673e35i		−	0.623522i	−0.950161	−	0.311761i	$-0.899081\pi$
$127$		−	3.62673e35i		−	0.623522i	0.950161	−	0.311761i	$-0.100919\pi$
$128$	−6.57916e35	+	9.41156e34i	−0.989923	+	0.141609i
$129$	5.81322e35			0.766288
$130$	9.19398e35	+	1.10607e36i	1.06284	+	1.27863i
$131$			1.44389e36i			1.46529i	0.680611	+	0.732645i	$0.261714\pi$
$131$			1.44389e36i			1.46529i	−0.680611	+	0.732645i	$0.738286\pi$
$132$	−1.97915e35	+	1.06463e36i	−0.176491	+	0.949380i
$133$	1.22774e36			0.963003
$134$	2.07354e36	−	1.72359e36i	1.43196	−	1.19029i
$135$		−	2.73165e36i		−	1.66246i
$136$	−2.21343e36	+	1.23721e36i	−1.18824	+	0.664174i
$137$	−1.44308e36			−0.683976			−0.341988	−	0.939704i	$-0.611100\pi$
$137$	−1.44308e36			−0.683976			−0.341988	+	0.939704i	$0.611100\pi$
$138$	6.04871e35	+	7.27681e35i	0.253349	+	0.304787i
$139$		−	1.46694e36i		−	0.543452i	−0.962375	−	0.271726i	$-0.912406\pi$
$139$		−	1.46694e36i		−	0.543452i	0.962375	−	0.271726i	$-0.0875944\pi$
$140$	−5.55759e36	−	1.03316e36i	−1.82268	−	0.338838i
$141$	1.66331e35			0.0483335
$142$	−8.72772e35	+	7.25476e35i	−0.224905	+	0.186948i
$143$		−	5.97880e36i		−	1.36742i
$144$	−1.91026e36	−	7.35665e35i	−0.388088	−	0.149457i
$145$	1.18819e37			2.14600
$146$	2.03401e35	+	2.44699e35i	0.0326855	+	0.0393218i
$147$		−	2.43688e36i		−	0.348690i
$148$	2.17081e35	−	1.16772e36i	0.0276804	−	0.148898i
$149$	−1.03647e37			−1.17867			−0.589334	−	0.807890i	$-0.700610\pi$
$149$	−1.03647e37			−1.17867			−0.589334	+	0.807890i	$0.700610\pi$
$150$	7.87655e36	−	6.54723e36i	0.799437	−	0.664518i
$151$			2.07568e37i			1.88171i	0.338813	+	0.940854i	$0.389974\pi$
$151$			2.07568e37i			1.88171i	−0.338813	+	0.940854i	$0.610026\pi$
$152$	4.80499e36	+	8.59637e36i	0.389360	+	0.696585i
$153$	−7.81011e36			−0.566112
$154$	1.50206e37	+	1.80703e37i	0.974622	+	1.17250i
$155$			5.71877e35i			0.0332402i
$156$	−1.56074e37	−	2.90144e36i	−0.813230	−	0.151181i
$157$	−9.87626e36			−0.461635			−0.230817	−	0.972997i	$-0.574140\pi$
$157$	−9.87626e36			−0.461635			−0.230817	+	0.972997i	$0.574140\pi$
$158$	9.54550e36	−	7.93452e36i	0.400524	−	0.332928i
$159$			3.37413e36i			0.127178i
$160$	−1.45167e37	−	4.29566e37i	−0.491846	−	1.45543i
$161$	2.05335e37			0.625782
$162$	9.58168e36	+	1.15271e37i	0.262837	+	0.316202i
$163$			5.64670e37i			1.39510i	0.716536	+	0.697550i	$0.245726\pi$
$163$			5.64670e37i			1.39510i	−0.716536	+	0.697550i	$0.754274\pi$
$164$	−3.65836e36	+	1.96791e37i	−0.0814594	+	0.438186i
$165$	−7.38783e37			−1.48351
$166$	4.86775e37	−	4.04622e37i	0.882045	−	0.733183i
$167$		−	2.69494e37i		−	0.440929i	−0.975395	−	0.220465i	$-0.929243\pi$
$167$		−	2.69494e37i		−	0.440929i	0.975395	−	0.220465i	$-0.0707574\pi$
$168$	5.44614e37	−	3.04415e37i	0.805065	−	0.449996i
$169$	1.28196e37			0.171318
$170$	−1.10587e38	−	1.33040e38i	−1.33682	−	1.60824i
$171$			3.03324e37i			0.331873i
$172$	9.94819e37	+	1.84938e37i	0.985735	+	0.183250i
$173$	1.23458e38			1.10850			0.554251	−	0.832349i	$-0.313005\pi$
$173$	1.23458e38			1.10850			0.554251	+	0.832349i	$0.313005\pi$
$174$	−1.00852e38	+	8.38311e37i	−0.821005	+	0.682446i
$175$		−	2.22258e38i		−	1.64139i
$176$	−6.77386e37	+	1.75893e38i	−0.454068	+	1.17905i
$177$	−2.05784e38			−1.25275
$178$	6.87295e37	+	8.26839e37i	0.380192	+	0.457384i
$179$		−	5.38708e37i		−	0.270927i	−0.990782	−	0.135463i	$-0.956748\pi$
$179$		−	5.38708e37i		−	0.270927i	0.990782	−	0.135463i	$-0.0432523\pi$
$180$	2.55253e37	−	1.37305e38i	0.116772	−	0.628138i
$181$	2.35455e38			0.980329			0.490165	−	0.871630i	$-0.336937\pi$
$181$	2.35455e38			0.980329			0.490165	+	0.871630i	$0.336937\pi$
$182$	−2.64912e38	+	2.20203e38i	−1.00436	+	0.834853i
$183$		−	5.24660e37i		−	0.181221i
$184$	8.03619e37	+	1.43771e38i	0.253015	+	0.452657i
$185$	8.10326e37			0.232670
$186$	−4.03480e36	−	4.85401e36i	−0.0105707	−	0.0127169i
$187$			7.19140e38i			1.71991i
$188$	2.84643e37	+	5.29155e36i	0.0621751	+	0.0115584i
$189$	6.54250e38			1.30585
$190$	−5.16691e38	+	4.29490e38i	−0.942800	+	0.783685i
$191$		−	5.19509e38i		−	0.867013i	−0.901150	−	0.433507i	$-0.857276\pi$
$191$		−	5.19509e38i		−	0.867013i	0.901150	−	0.433507i	$-0.142724\pi$
$192$	4.26291e38	+	2.62188e38i	0.651006	+	0.400399i
$193$	5.94004e37			0.0830453			0.0415226	−	0.999138i	$-0.486779\pi$
$193$	5.94004e37			0.0830453			0.0415226	+	0.999138i	$0.486779\pi$
$194$	−3.19331e38	−	3.84166e38i	−0.408895	−	0.491914i
$195$		−	1.08306e39i		−	1.27076i
$196$	7.75254e37	−	4.17025e38i	0.0833856	−	0.448547i
$197$	−5.77652e38			−0.569824			−0.284912	−	0.958554i	$-0.591964\pi$
$197$	−5.77652e38			−0.569824			−0.284912	+	0.958554i	$0.591964\pi$
$198$	−4.46444e38	+	3.71099e38i	−0.404072	+	0.335878i
$199$		−	7.72846e38i		−	0.642082i	−0.947065	−	0.321041i	$-0.895967\pi$
$199$		−	7.72846e38i		−	0.642082i	0.947065	−	0.321041i	$-0.104033\pi$
$200$	1.55621e39	−	8.69851e38i	1.18729	−	0.663644i
$201$	−2.03040e39			−1.42315
$202$	−1.64214e39	−	1.97555e39i	−1.05788	−	1.27267i
$203$			2.84580e39i			1.68567i
$204$	1.87729e39	+	3.48991e38i	1.02287	+	0.190152i
$205$	−1.36560e39			−0.684713
$206$	1.87745e39	−	1.56060e39i	0.866615	−	0.720358i
$207$			5.07299e38i			0.215659i
$208$	−2.57860e39	−	9.93050e38i	−1.00997	−	0.388951i
$209$	2.79295e39			1.00827
$210$	2.72099e39	+	3.27344e39i	0.905730	+	1.08962i
$211$			6.05613e38i			0.185949i	0.995669	+	0.0929744i	$0.0296375\pi$
$211$			6.05613e38i			0.185949i	−0.995669	+	0.0929744i	$0.970363\pi$
$212$	−1.07342e38	+	5.77416e38i	−0.0304132	+	0.163598i
$213$	8.54616e38			0.223521
$214$	1.90538e39	−	1.58381e39i	0.460200	−	0.382533i
$215$			6.90342e39i			1.54032i
$216$	2.56054e39	+	4.58093e39i	0.527980	+	0.944582i
$217$	−1.36969e38			−0.0261100
$218$	−3.31231e39	−	3.98482e39i	−0.583943	−	0.702503i
$219$		−	2.39608e38i		−	0.0390798i
$220$	−1.26428e40	−	2.35032e39i	−1.90835	−	0.354765i
$221$	−1.05426e40			−1.47326
$222$	−6.87792e38	+	5.71715e38i	−0.0890137	+	0.0739910i
$223$		−	3.32117e39i		−	0.398207i	−0.979978	−	0.199103i	$-0.936197\pi$
$223$		−	3.32117e39i		−	0.398207i	0.979978	−	0.199103i	$-0.0638029\pi$
$224$	1.02884e40	−	3.47687e39i	1.14323	−	0.386342i
$225$	5.49109e39			0.565660
$226$	1.31338e40	+	1.58005e40i	1.25472	+	1.50948i
$227$		−	1.60578e40i		−	1.42314i	−0.702616	−	0.711569i	$-0.747985\pi$
$227$		−	1.60578e40i		−	1.42314i	0.702616	−	0.711569i	$-0.252015\pi$
$228$	1.35539e39	−	7.29089e39i	0.111473	−	0.599637i
$229$	9.35890e39			0.714532			0.357266	−	0.934003i	$-0.383709\pi$
$229$	9.35890e39			0.714532			0.357266	+	0.934003i	$0.383709\pi$
$230$	−8.64148e39	+	7.18307e39i	−0.612654	+	0.509257i
$231$		−	1.76944e40i		−	1.16529i
$232$	−1.99257e40	+	1.11376e40i	−1.21932	+	0.681548i
$233$	2.58942e40			1.47283			0.736414	−	0.676531i	$-0.236517\pi$
$233$	2.58942e40			1.47283			0.736414	+	0.676531i	$0.236517\pi$
$234$	−5.44032e39	−	6.54489e39i	−0.287710	−	0.346125i
$235$			1.97524e39i			0.0971553i
$236$	−3.52158e40	−	6.54667e39i	−1.61151	−	0.299583i
$237$	−9.34693e39			−0.398059
$238$	3.18641e40	−	2.64864e40i	1.26326	−	1.05006i
$239$		−	9.77868e39i		−	0.361007i	−0.983574	−	0.180504i	$-0.942227\pi$
$239$		−	9.77868e39i		−	0.361007i	0.983574	−	0.180504i	$-0.0577728\pi$
$240$	−1.22708e40	+	3.18631e40i	−0.421972	+	1.09571i
$241$	−2.12330e40			−0.680333			−0.340167	−	0.940365i	$-0.610483\pi$
$241$	−2.12330e40			−0.680333			−0.340167	+	0.940365i	$0.610483\pi$
$242$	1.27649e40	+	1.53566e40i	0.381203	+	0.458601i
$243$			2.75800e40i			0.767871i
$244$	1.66912e39	−	8.97853e39i	0.0433372	−	0.233119i
$245$	2.89389e40			0.700904
$246$	1.15910e40	−	9.63483e39i	0.261954	−	0.217745i
$247$			4.09447e40i			0.863674i
$248$	−5.36055e38	−	9.59029e38i	−0.0105568	−	0.0188866i
$249$	−4.76648e40			−0.876616
$250$	2.05886e40	+	2.47687e40i	0.353709	+	0.425524i
$251$		−	5.08018e40i		−	0.815504i	−0.913093	−	0.407752i	$-0.866313\pi$
$251$		−	5.08018e40i		−	0.815504i	0.913093	−	0.407752i	$-0.133687\pi$
$252$	3.28857e40	+	6.11350e39i	0.493399	+	0.0917235i
$253$	4.67111e40			0.655196
$254$	−3.65561e40	+	3.03866e40i	−0.479498	+	0.398574i
$255$			1.30272e41i			1.59834i
$256$	6.46101e40	+	5.84301e40i	0.741688	+	0.670745i
$257$	−8.63889e40			−0.928100			−0.464050	−	0.885809i	$-0.653604\pi$
$257$	−8.63889e40			−0.928100			−0.464050	+	0.885809i	$0.653604\pi$
$258$	−4.87062e40	−	5.85952e40i	−0.489834	−	0.589287i
$259$			1.94079e40i			0.182761i
$260$	3.44557e40	−	1.85344e41i	0.303889	−	1.63468i
$261$	−7.03082e40			−0.580921
$262$	1.45539e41	−	1.20977e41i	1.12683	−	0.936657i
$263$		−	6.39582e40i		−	0.464139i	−0.972699	−	0.232070i	$-0.925450\pi$
$263$		−	6.39582e40i		−	0.464139i	0.972699	−	0.232070i	$-0.0745497\pi$
$264$	1.23893e41	−	6.92506e40i	0.842906	−	0.471148i
$265$	−4.00690e40			−0.255640
$266$	−1.02866e41	−	1.23752e41i	−0.615580	−	0.740564i
$267$		−	8.09638e40i		−	0.454569i
$268$	−3.47464e41	−	6.45940e40i	−1.83070	−	0.340330i
$269$	−3.05387e40			−0.151029			−0.0755147	−	0.997145i	$-0.524060\pi$
$269$	−3.05387e40			−0.151029			−0.0755147	+	0.997145i	$0.524060\pi$
$270$	−2.75340e41	+	2.28871e41i	−1.27845	+	1.06269i
$271$			2.46931e41i			1.07671i	0.842719	+	0.538354i	$0.180954\pi$
$271$			2.46931e41i			1.07671i	−0.842719	+	0.538354i	$0.819046\pi$
$272$	3.10159e41	+	1.19446e41i	1.27032	+	0.489215i
$273$	2.59401e41			0.998175
$274$	1.20909e41	+	1.45457e41i	0.437218	+	0.525989i
$275$		−	5.05609e41i		−	1.71854i
$276$	2.26684e40	−	1.21938e41i	0.0724380	−	0.389658i
$277$	1.96296e41			0.589867			0.294934	−	0.955518i	$-0.404702\pi$
$277$	1.96296e41			0.589867			0.294934	+	0.955518i	$0.404702\pi$
$278$	−1.47862e41	+	1.22908e41i	−0.417923	+	0.347391i
$279$		−	3.38394e39i		−	0.00899812i
$280$	3.61504e41	+	6.46749e41i	0.904538	+	1.61826i
$281$	−4.01904e41			−0.946488			−0.473244	−	0.880931i	$-0.656917\pi$
$281$	−4.01904e41			−0.946488			−0.473244	+	0.880931i	$0.656917\pi$
$282$	−1.39361e40	−	1.67656e40i	−0.0308962	−	0.0371692i
$283$			4.82815e41i			1.00789i	0.863737	+	0.503943i	$0.168118\pi$
$283$			4.82815e41i			1.00789i	−0.863737	+	0.503943i	$0.831882\pi$
$284$	1.46251e41	+	2.71882e40i	0.287532	+	0.0534526i
$285$	5.05942e41			0.936997
$286$	−6.02641e41	+	5.00934e41i	−1.05157	+	0.874094i
$287$		−	3.27073e41i		−	0.537838i
$288$	8.58992e40	+	2.54185e41i	0.133143	+	0.393984i
$289$	5.83758e41			0.853040
$290$	−9.95526e41	−	1.19765e42i	−1.37179	−	1.65031i
$291$			3.76174e41i			0.488887i
$292$	7.62275e39	−	4.10043e40i	0.00934551	−	0.0502713i
$293$	−9.17834e41			−1.06173			−0.530866	−	0.847456i	$-0.678133\pi$
$293$	−9.17834e41			−1.06173			−0.530866	+	0.847456i	$0.678133\pi$
$294$	−2.45629e41	+	2.04175e41i	−0.268148	+	0.222893i
$295$		−	2.44376e42i		−	2.51816i
$296$	−1.35890e41	+	7.59567e40i	−0.132199	+	0.0738937i
$297$	1.48834e42			1.36723
$298$	8.68411e41	+	1.04473e42i	0.753440	+	0.906414i
$299$			6.84786e41i			0.561235i
$300$	−1.31988e42	−	2.45367e41i	−1.02205	−	0.190000i
$301$	−1.65342e42			−1.20991
$302$	2.09221e42	−	1.73911e42i	1.44706	−	1.20284i
$303$			1.93445e42i			1.26483i
$304$	4.63896e41	−	1.20457e42i	0.286794	−	0.744702i
$305$	6.23053e41			0.364274
$306$	6.54371e41	+	7.87231e41i	0.361876	+	0.435349i
$307$			6.90950e41i			0.361488i	0.983530	+	0.180744i	$0.0578506\pi$
$307$			6.90950e41i			0.361488i	−0.983530	+	0.180744i	$0.942149\pi$
$308$	5.62919e41	−	3.02805e42i	0.278666	−	1.49900i
$309$	−1.83840e42			−0.861281
$310$	5.76431e40	−	4.79148e40i	0.0255622	−	0.0212481i
$311$		−	1.80957e42i		−	0.759711i	−0.925046	−	0.379855i	$-0.875974\pi$
$311$		−	1.80957e42i		−	0.759711i	0.925046	−	0.379855i	$-0.124026\pi$
$312$	1.01522e42	+	1.81627e42i	0.403581	+	0.722026i
$313$	−4.01954e42			−1.51329			−0.756645	−	0.653826i	$-0.773163\pi$
$313$	−4.01954e42			−1.51329			−0.756645	+	0.653826i	$0.773163\pi$
$314$	8.27484e41	+	9.95492e41i	0.295091	+	0.355004i
$315$			2.28206e42i			0.770988i
$316$	−1.59954e42	−	2.97357e41i	−0.512054	−	0.0951915i
$317$	3.08795e42			0.936836			0.468418	−	0.883507i	$-0.344824\pi$
$317$	3.08795e42			0.936836			0.468418	+	0.883507i	$0.344824\pi$
$318$	3.40100e41	−	2.82702e41i	0.0978015	−	0.0812957i
$319$			6.47385e42i			1.76490i
$320$	−3.11359e42	+	5.06236e42i	−0.804843	+	1.30859i
$321$	−1.86574e42			−0.457368
$322$	−1.72040e42	−	2.06970e42i	−0.400018	−	0.481236i
$323$		−	4.92490e42i		−	1.08631i
$324$	3.59087e41	−	1.93160e42i	0.0751509	−	0.404251i
$325$	7.41225e42			1.47208
$326$	5.69167e42	−	4.73109e42i	1.07285	−	0.891789i
$327$			3.90192e42i			0.698180i
$328$	2.29009e42	−	1.28006e42i	0.389043	−	0.217458i
$329$	−4.73086e41			−0.0763150
$330$	6.18991e42	+	7.44667e42i	0.948303	+	1.14084i
$331$			7.38390e42i			1.07451i	0.843420	+	0.537254i	$0.180539\pi$
$331$			7.38390e42i			1.07451i	−0.843420	+	0.537254i	$0.819461\pi$
$332$	−8.15690e42	−	1.51638e42i	−1.12766	−	0.209633i
$333$	−4.79491e41			−0.0629837
$334$	−2.71640e42	+	2.25796e42i	−0.339082	+	0.281855i
$335$		−	2.41118e43i		−	2.86067i
$336$	−7.63145e42	−	2.93896e42i	−0.860675	−	0.331456i
$337$	−4.38743e42			−0.470438			−0.235219	−	0.971942i	$-0.575581\pi$
$337$	−4.38743e42			−0.470438			−0.235219	+	0.971942i	$0.575581\pi$
$338$	−1.07410e42	−	1.29217e42i	−0.109511	−	0.131746i
$339$		−	1.54718e43i		−	1.50019i
$340$	−4.14440e42	+	2.22935e43i	−0.382225	+	2.05607i
$341$	−3.11587e41			−0.0273373
$342$	3.05739e42	−	2.54140e42i	0.255216	−	0.212143i
$343$		−	8.26093e42i		−	0.656189i
$344$	−6.47099e42	−	1.15769e43i	−0.489190	−	0.875185i
$345$	8.46171e42			0.608883
$346$	−1.03440e43	−	1.24442e43i	−0.708588	−	0.852456i
$347$			7.60531e42i			0.496039i	0.968755	+	0.248020i	$0.0797797\pi$
$347$			7.60531e42i			0.496039i	−0.968755	+	0.248020i	$0.920220\pi$
$348$	1.68998e43	+	3.14169e42i	1.04962	+	0.195126i
$349$	2.14482e43			1.26870			0.634350	−	0.773046i	$-0.281268\pi$
$349$	2.14482e43			1.26870			0.634350	+	0.773046i	$0.281268\pi$
$350$	−2.24028e43	+	1.86219e43i	−1.26225	+	1.04922i
$351$			2.18191e43i			1.17116i
$352$	2.34049e43	−	7.90944e42i	1.19697	−	0.404502i
$353$	−4.37695e42			−0.213305			−0.106653	−	0.994296i	$-0.534013\pi$
$353$	−4.37695e42			−0.213305			−0.106653	+	0.994296i	$0.534013\pi$
$354$	1.72416e43	+	2.07423e43i	0.800797	+	0.963386i
$355$			1.01489e43i			0.449300i
$356$	2.57573e42	−	1.38554e43i	0.108705	−	0.584747i
$357$	−3.12012e43			−1.25549
$358$	−5.42998e42	+	4.51357e42i	−0.208347	+	0.173185i
$359$			3.34404e43i			1.22367i	0.790984	+	0.611836i	$0.209569\pi$
$359$			3.34404e43i			1.22367i	−0.790984	+	0.611836i	$0.790431\pi$
$360$	−1.59785e43	+	8.93130e42i	−0.557692	+	0.311725i
$361$	1.09076e43			0.363168
$362$	−1.97276e43	−	2.37330e43i	−0.626656	−	0.753888i
$363$		−	1.50372e43i		−	0.455778i
$364$	4.43914e43	+	8.25242e42i	1.28403	+	0.238703i
$365$	2.84544e42			0.0785544
$366$	−5.28839e42	+	4.39587e42i	−0.139362	+	0.115842i
$367$			8.39401e42i			0.211177i	0.994410	+	0.105588i	$0.0336726\pi$
$367$			8.39401e42i			0.211177i	−0.994410	+	0.105588i	$0.966327\pi$
$368$	7.75850e42	−	2.01461e43i	0.186365	−	0.483925i
$369$	8.08062e42			0.185352
$370$	−6.78933e42	−	8.16779e42i	−0.148730	−	0.178927i
$371$		−	9.59684e42i		−	0.200804i
$372$	−1.51210e41	+	8.13387e41i	−0.00302239	+	0.0162580i
$373$	−8.82976e43			−1.68616			−0.843080	−	0.537788i	$-0.819260\pi$
$373$	−8.82976e43			−1.68616			−0.843080	+	0.537788i	$0.819260\pi$
$374$	7.24867e43	−	6.02533e43i	1.32264	−	1.09942i
$375$		−	2.42535e43i		−	0.422905i
$376$	−1.85151e42	−	3.31245e42i	−0.0308556	−	0.0552021i
$377$	−9.49068e43			−1.51180
$378$	−5.48165e43	−	6.59461e43i	−0.834739	−	1.00422i
$379$			1.34296e43i			0.195522i	0.995210	+	0.0977609i	$0.0311680\pi$
$379$			1.34296e43i			0.195522i	−0.995210	+	0.0977609i	$0.968832\pi$
$380$	8.65821e43	+	1.60957e43i	1.20533	+	0.224073i
$381$	3.57957e43			0.476547
$382$	−5.23646e43	+	4.35271e43i	−0.666747	+	0.554221i
$383$			7.30133e43i			0.889248i	0.895717	+	0.444624i	$0.146663\pi$
$383$			7.30133e43i			0.889248i	−0.895717	+	0.444624i	$0.853337\pi$
$384$	−9.28916e42	−	6.49361e43i	−0.108230	−	0.756580i
$385$	2.10128e44			2.34235
$386$	−4.97687e42	−	5.98735e42i	−0.0530850	−	0.0638631i
$387$		−	4.08493e43i		−	0.416964i
$388$	−1.19674e43	+	6.43748e43i	−0.116912	+	0.628893i
$389$	1.01539e44			0.949488			0.474744	−	0.880124i	$-0.342541\pi$
$389$	1.01539e44			0.949488			0.474744	+	0.880124i	$0.342541\pi$
$390$	−1.09168e44	+	9.07442e43i	−0.977234	+	0.812308i
$391$		−	8.23673e43i		−	0.705911i
$392$	−4.85301e43	+	2.71262e43i	−0.398243	+	0.222600i
$393$	−1.42512e44			−1.11990
$394$	4.83987e43	+	5.82253e43i	0.364249	+	0.438204i
$395$		−	1.10998e44i		−	0.800139i
$396$	7.48108e43	+	1.39074e43i	0.516590	+	0.0960349i
$397$	−1.01279e43			−0.0670009			−0.0335005	−	0.999439i	$-0.510666\pi$
$397$	−1.01279e43			−0.0670009			−0.0335005	+	0.999439i	$0.510666\pi$
$398$	−7.79001e43	+	6.47530e43i	−0.493771	+	0.410438i
$399$			1.21177e44i			0.736006i
$400$	−2.18065e44	−	8.39794e43i	−1.26930	−	0.488824i
$401$	−2.04635e43			−0.114163			−0.0570816	−	0.998370i	$-0.518180\pi$
$401$	−2.04635e43			−0.114163			−0.0570816	+	0.998370i	$0.518180\pi$
$402$	1.70118e44	+	2.04657e44i	0.909718	+	1.09442i
$403$		−	4.56788e42i		−	0.0234169i
$404$	−6.15414e43	+	3.31043e44i	−0.302471	+	1.62705i
$405$	1.34041e44			0.631687
$406$	2.86847e44	−	2.38436e44i	1.29631	−	1.07753i
$407$			4.41506e43i			0.191351i
$408$	−1.22112e44	−	2.18464e44i	−0.507616	−	0.908150i
$409$	−2.18467e44			−0.871144			−0.435572	−	0.900154i	$-0.643454\pi$
$409$	−2.18467e44			−0.871144			−0.435572	+	0.900154i	$0.643454\pi$
$410$	1.14417e44	+	1.37648e44i	0.437689	+	0.526555i
$411$		−	1.42431e44i		−	0.522751i
$412$	−3.14605e44	−	5.84856e43i	−1.10793	−	0.205966i
$413$	5.85299e44			1.97800
$414$	5.11339e43	−	4.25041e43i	0.165845	−	0.137856i
$415$		−	5.66038e44i		−	1.76209i
$416$	1.15953e44	+	3.43117e44i	0.346493	+	1.02531i
$417$	1.44786e44			0.415351
$418$	−2.34008e44	−	2.81519e44i	−0.644515	−	0.775374i
$419$			5.81389e44i			1.53755i	0.639520	+	0.768774i	$0.279133\pi$
$419$			5.81389e44i			1.53755i	−0.639520	+	0.768774i	$0.720867\pi$
$420$	1.01973e44	−	5.48532e44i	0.258968	−	1.39304i
$421$	−6.20640e44			−1.51372			−0.756858	−	0.653580i	$-0.773266\pi$
$421$	−6.20640e44			−1.51372			−0.756858	+	0.653580i	$0.773266\pi$
$422$	6.10436e43	−	5.07414e43i	0.142997	−	0.118864i
$423$		−	1.16880e43i		−	0.0262999i
$424$	6.71951e43	−	3.75591e43i	0.145251	−	0.0811888i
$425$	−8.91558e44			−1.85156
$426$	−7.16041e43	−	8.61422e43i	−0.142881	−	0.171891i
$427$			1.49226e44i			0.286135i
$428$	−3.19285e44	−	5.93555e43i	−0.588348	−	0.109375i
$429$	5.90104e44			1.04509
$430$	6.95840e44	−	5.78404e44i	1.18453	−	0.984617i
$431$			6.51059e43i			0.106539i	0.998580	+	0.0532693i	$0.0169642\pi$
$431$			6.51059e43i			0.106539i	−0.998580	+	0.0532693i	$0.983036\pi$
$432$	2.47206e44	−	6.41907e44i	0.388898	−	1.00983i
$433$	−3.05450e44			−0.462005			−0.231002	−	0.972953i	$-0.574200\pi$
$433$	−3.05450e44			−0.462005			−0.231002	+	0.972953i	$0.574200\pi$
$434$	1.14760e43	+	1.38060e43i	0.0166903	+	0.0200790i
$435$			1.17274e45i			1.64015i
$436$	−1.24133e44	+	6.67738e44i	−0.166962	+	0.898123i
$437$	−3.19893e44			−0.413828
$438$	−2.41517e43	+	2.00756e43i	−0.0300530	+	0.0249810i
$439$			1.30447e44i			0.156148i	0.996948	+	0.0780741i	$0.0248771\pi$
$439$			1.30447e44i			0.156148i	−0.996948	+	0.0780741i	$0.975123\pi$
$440$	8.22377e44	+	1.47127e45i	0.947056	+	1.69433i
$441$	−1.71239e44			−0.189735
$442$	8.83315e44	+	1.06266e45i	0.941753	+	1.13296i
$443$			1.81171e42i			0.00185877i	1.00000		0.000929384i	$0.000295832\pi$
$443$			1.81171e42i			0.00185877i	−1.00000		0.000929384i	$0.999704\pi$
$444$	1.15254e44	+	2.14258e43i	0.113800	+	0.0211557i
$445$	9.61476e44			0.913730
$446$	−3.34762e44	+	2.78265e44i	−0.306227	+	0.254546i
$447$		−	1.02299e45i		−	0.900835i
$448$	−1.21247e45	−	7.45728e44i	−1.02789	−	0.632199i
$449$	1.54218e45			1.25877			0.629386	−	0.777093i	$-0.283306\pi$
$449$	1.54218e45			1.25877			0.629386	+	0.777093i	$0.283306\pi$
$450$	−4.60072e44	−	5.53482e44i	−0.361587	−	0.435002i
$451$		−	7.44049e44i		−	0.563119i
$452$	4.92209e44	−	2.64769e45i	0.358754	−	1.92981i
$453$	−2.04869e45			−1.43816
$454$	−1.61857e45	+	1.34541e45i	−1.09441	+	0.909712i
$455$			3.08048e45i			2.00643i
$456$	−8.48457e44	+	4.74251e44i	−0.532387	+	0.297581i
$457$	9.29433e43			0.0561879			0.0280939	−	0.999605i	$-0.491056\pi$
$457$	9.29433e43			0.0561879			0.0280939	+	0.999605i	$0.491056\pi$
$458$	−7.84137e44	−	9.43343e44i	−0.456750	−	0.549486i
$459$		−	2.62444e45i		−	1.47306i
$460$	1.44806e45	+	2.69196e44i	0.783253	+	0.145608i
$461$	7.79916e44			0.406567			0.203283	−	0.979120i	$-0.434839\pi$
$461$	7.79916e44			0.406567			0.203283	+	0.979120i	$0.434839\pi$
$462$	−1.78354e45	+	1.48253e45i	−0.896124	+	0.744886i
$463$		−	3.21873e45i		−	1.55886i	−0.626489	−	0.779430i	$-0.715509\pi$
$463$		−	3.21873e45i		−	1.55886i	0.626489	−	0.779430i	$-0.284491\pi$
$464$	2.79211e45	+	1.07528e45i	1.30355	+	0.502012i
$465$	−5.64440e43			−0.0254049
$466$	−2.16955e45	−	2.61004e45i	−0.941476	−	1.13263i
$467$		−	3.35073e45i		−	1.40201i	−0.713155	−	0.701006i	$-0.752734\pi$
$467$		−	3.35073e45i		−	1.40201i	0.713155	−	0.701006i	$-0.247266\pi$
$468$	−2.03883e44	+	1.09673e45i	−0.0822626	+	0.442507i
$469$	5.77497e45			2.24704
$470$	1.99097e44	−	1.65496e44i	0.0747140	−	0.0621046i
$471$		−	9.74783e44i		−	0.352819i
$472$	2.29068e45	+	4.09814e45i	0.799744	+	1.43078i
$473$	−3.76133e45			−1.26678
$474$	7.83134e44	+	9.42137e44i	0.254451	+	0.306113i
$475$			3.46257e45i			1.08544i
$476$	−5.33947e45	−	9.92615e44i	−1.61503	−	0.300236i
$477$	2.37099e44			0.0692017
$478$	−9.85656e44	+	8.19308e44i	−0.277620	+	0.230767i
$479$			4.36061e45i			1.18534i	0.805445	+	0.592671i	$0.201926\pi$
$479$			4.36061e45i			1.18534i	−0.805445	+	0.592671i	$0.798074\pi$
$480$	4.23980e45	−	1.43279e45i	1.11236	−	0.375909i
$481$	−6.47249e44			−0.163910
$482$	1.77901e45	+	2.14021e45i	0.434889	+	0.523187i
$483$			2.02665e45i			0.478274i
$484$	4.78383e44	−	2.57332e45i	0.108995	−	0.586303i
$485$	−4.46721e45			−0.982713
$486$	2.77997e45	−	2.31080e45i	0.590505	−	0.490846i
$487$		−	1.91444e42i		−	0.000392689i	−1.00000		0.000196344i	$-0.999938\pi$
$487$		−	1.91444e42i		−	0.000392689i	1.00000		0.000196344i	$-6.24984e-5\pi$
$488$	−1.04485e45	+	5.84026e44i	−0.206975	+	0.115690i
$489$	−5.57326e45			−1.06625
$490$	−2.42465e45	−	2.91694e45i	−0.448039	−	0.539006i
$491$			2.96683e45i			0.529550i	0.964310	+	0.264775i	$0.0852977\pi$
$491$			2.96683e45i			0.529550i	−0.964310	+	0.264775i	$0.914702\pi$
$492$	−1.94231e45	−	3.61079e44i	−0.334898	−	0.0622580i
$493$	1.14156e46			1.90151
$494$	4.12708e45	−	3.43056e45i	0.664178	−	0.552086i
$495$			5.19140e45i			0.807228i
$496$	−5.17532e43	+	1.34385e44i	−0.00777586	+	0.0201912i
$497$	−2.43074e45			−0.352922
$498$	3.99361e45	+	4.80444e45i	0.560359	+	0.674131i
$499$			1.09533e45i			0.148537i	0.997238	+	0.0742684i	$0.0236622\pi$
$499$			1.09533e45i			0.148537i	−0.997238	+	0.0742684i	$0.976338\pi$
$500$	7.71585e44	−	4.15050e45i	0.101133	−	0.544015i
$501$	2.65989e45			0.336995
$502$	−5.12064e45	+	4.25644e45i	−0.627135	+	0.521295i
$503$		−	7.05457e45i		−	0.835247i	−0.908620	−	0.417624i	$-0.862863\pi$
$503$		−	7.05457e45i		−	0.835247i	0.908620	−	0.417624i	$-0.137137\pi$
$504$	−2.13911e45	−	3.82698e45i	−0.244858	−	0.438064i
$505$	−2.29723e46			−2.54245
$506$	−3.91370e45	−	4.70831e45i	−0.418821	−	0.503856i
$507$			1.26529e45i			0.130935i
$508$	6.12572e45	+	1.13878e45i	0.613019	+	0.113961i
$509$	1.70188e46			1.64712			0.823560	−	0.567229i	$-0.191984\pi$
$509$	1.70188e46			1.64712			0.823560	+	0.567229i	$0.191984\pi$
$510$	1.31310e46	−	1.09149e46i	1.22915	−	1.02171i
$511$			6.81505e44i			0.0617040i
$512$	4.76177e44	−	1.14080e46i	0.0417041	−	0.999130i
$513$	−1.01926e46			−0.863556
$514$	7.23811e45	+	8.70769e45i	0.593270	+	0.713724i
$515$		−	2.18316e46i		−	1.73126i
$516$	−1.82533e45	+	9.81882e45i	−0.140054	+	0.753380i
$517$	−1.07621e45			−0.0799021
$518$	1.95625e45	−	1.62610e45i	0.140546	−	0.116826i
$519$			1.21853e46i			0.847209i
$520$	−2.15689e46	+	1.20561e46i	−1.45135	+	0.811239i
$521$	1.31042e45			0.0853435			0.0426718	−	0.999089i	$-0.486413\pi$
$521$	1.31042e45			0.0853435			0.0426718	+	0.999089i	$0.486413\pi$
$522$	5.89078e45	+	7.08681e45i	0.371342	+	0.446738i
$523$		−	8.48378e45i		−	0.517679i	−0.965920	−	0.258839i	$-0.916660\pi$
$523$		−	8.48378e45i		−	0.517679i	0.965920	−	0.258839i	$-0.0833401\pi$
$524$	−2.43881e46	−	4.53378e45i	−1.44061	−	0.267811i
$525$	2.19368e46			1.25448
$526$	−6.44675e45	+	5.35874e45i	−0.356930	+	0.296692i
$527$			5.49432e44i			0.0294533i
$528$	−1.73606e46	−	6.68577e45i	−0.901131	−	0.347036i
$529$	1.45450e46			0.731085
$530$	3.35719e45	+	4.03881e45i	0.163413	+	0.196591i
$531$			1.44603e46i			0.681666i
$532$	−3.85505e45	+	2.07371e46i	−0.176008	+	0.946782i
$533$	1.09078e46			0.482363
$534$	−8.16086e45	+	6.78357e45i	−0.349570	+	0.290574i
$535$		−	2.21564e46i		−	0.919357i
$536$	2.26015e46	+	4.04351e46i	0.908521	+	1.62539i
$537$	5.31702e45			0.207065
$538$	2.55869e45	+	3.07819e45i	0.0965425	+	0.116144i
$539$			1.57674e46i			0.576434i
$540$	4.61388e46	+	8.57727e45i	1.63445	+	0.303847i
$541$	6.74768e45			0.231633			0.115817	−	0.993271i	$-0.463052\pi$
$541$	6.74768e45			0.231633			0.115817	+	0.993271i	$0.463052\pi$
$542$	2.48898e46	−	2.06892e46i	0.828006	−	0.688264i
$543$			2.32393e46i			0.749248i
$544$	−1.39470e46	−	4.12707e46i	−0.435812	−	1.28962i
$545$	−4.63368e46			−1.40341
$546$	−2.17339e46	−	2.61467e46i	−0.638063	−	0.767612i
$547$		−	2.49173e46i		−	0.709116i	−0.935034	−	0.354558i	$-0.884631\pi$
$547$		−	2.49173e46i		−	0.709116i	0.935034	−	0.354558i	$-0.115369\pi$
$548$	4.53122e45	−	2.43743e46i	0.125010	−	0.672455i
$549$	−3.68677e45			−0.0986089
$550$	−5.09636e46	+	4.23626e46i	−1.32158	+	1.09854i
$551$		−	4.43350e46i		−	1.11473i
$552$	−1.41902e46	+	7.93168e45i	−0.345958	+	0.193375i
$553$	2.65849e46			0.628505
$554$	−1.64467e46	−	1.97859e46i	−0.377061	−	0.453617i
$555$			7.99788e45i			0.177825i
$556$	2.47773e46	+	4.60614e45i	0.534298	+	0.0993267i
$557$	−7.80423e46			−1.63227			−0.816135	−	0.577861i	$-0.803887\pi$
$557$	−7.80423e46			−1.63227			−0.816135	+	0.577861i	$0.803887\pi$
$558$	−3.41089e44	+	2.83524e44i	−0.00691969	+	0.00575187i
$559$		−	5.51412e46i		−	1.08511i
$560$	3.49013e46	−	9.06263e46i	0.666262	−	1.73005i
$561$	−7.09788e46			−1.31450
$562$	3.36736e46	+	4.05105e46i	0.605024	+	0.727864i
$563$			9.25186e46i			1.61282i	0.591356	+	0.806411i	$0.298593\pi$
$563$			9.25186e46i			1.61282i	−0.591356	+	0.806411i	$0.701407\pi$
$564$	−5.22273e44	+	2.80941e45i	−0.00883391	+	0.0475194i
$565$	1.83733e47			3.01553
$566$	4.86660e46	−	4.04527e46i	0.775080	−	0.644271i
$567$			3.21038e46i			0.496186i
$568$	−9.51316e45	−	1.70195e46i	−0.142693	−	0.255285i
$569$	−1.06443e47			−1.54956			−0.774780	−	0.632231i	$-0.782139\pi$
$569$	−1.06443e47			−1.54956			−0.774780	+	0.632231i	$0.782139\pi$
$570$	−4.23905e46	−	5.09972e46i	−0.598957	−	0.720566i
$571$			1.01443e47i			1.39125i	0.718403	+	0.695627i	$0.244873\pi$
$571$			1.01443e47i			1.39125i	−0.718403	+	0.695627i	$0.755127\pi$
$572$	1.00985e47	+	1.87732e46i	1.34438	+	0.249923i
$573$	5.12753e46			0.662643
$574$	−3.29677e46	+	2.74038e46i	−0.413606	+	0.343802i
$575$			5.79104e46i			0.705347i
$576$	1.84239e46	−	2.99553e46i	0.217871	−	0.354235i
$577$	−1.23033e47			−1.41265			−0.706323	−	0.707890i	$-0.749647\pi$
$577$	−1.23033e47			−1.41265			−0.706323	+	0.707890i	$0.749647\pi$
$578$	−4.89102e46	−	5.88407e46i	−0.545289	−	0.656001i
$579$			5.86279e45i			0.0634700i
$580$	−3.73087e46	+	2.00691e47i	−0.392224	+	2.10985i
$581$	1.35570e47			1.38411
$582$	3.79170e46	−	3.15178e46i	0.375961	−	0.312511i
$583$		−	2.18316e46i		−	0.210242i
$584$	−4.77176e45	+	2.66720e45i	−0.0446334	+	0.0249481i
$585$	−7.61061e46			−0.691464
$586$	7.69009e46	+	9.25144e46i	0.678691	+	0.816488i
$587$		−	1.17161e47i		−	1.00447i	−0.864731	−	0.502235i	$-0.832511\pi$
$587$		−	1.17161e47i		−	1.00447i	0.864731	−	0.502235i	$-0.167489\pi$
$588$	4.11601e46	+	7.65173e45i	0.342817	+	0.0637301i
$589$	2.13385e45			0.0172665
$590$	−2.46322e47	+	2.04751e47i	−1.93651	+	1.60969i
$591$		−	5.70140e46i		−	0.435506i
$592$	1.90418e46	+	7.33321e45i	0.141331	+	0.0544283i
$593$	−3.71586e46			−0.267997			−0.133998	−	0.990982i	$-0.542782\pi$
$593$	−3.71586e46			−0.267997			−0.133998	+	0.990982i	$0.542782\pi$
$594$	−1.24701e47	−	1.50019e47i	−0.873975	−	1.05142i
$595$		−	3.70526e47i		−	2.52366i
$596$	3.25449e46	−	1.75065e47i	0.215425	−	1.15881i
$597$	7.62795e46			0.490732
$598$	6.90240e46	−	5.73749e46i	0.431599	−	0.358758i
$599$			2.84494e47i			1.72909i	0.502559	+	0.864543i	$0.332392\pi$
$599$			2.84494e47i			1.72909i	−0.502559	+	0.864543i	$0.667608\pi$
$600$	8.58539e46	+	1.53597e47i	0.507211	+	0.907425i
$601$	1.94119e47			1.11481			0.557406	−	0.830240i	$-0.311797\pi$
$601$	1.94119e47			1.11481			0.557406	+	0.830240i	$0.311797\pi$
$602$	1.38532e47	+	1.66659e47i	0.773411	+	0.930440i
$603$			1.42676e47i			0.774383i
$604$	−3.50592e47	−	6.51756e46i	−1.85001	−	0.343920i
$605$	1.78572e47			0.916161
$606$	1.94986e47	−	1.62078e47i	0.972676	−	0.808519i
$607$		−	3.02880e47i		−	1.46914i	−0.678533	−	0.734570i	$-0.737384\pi$
$607$		−	3.02880e47i		−	1.46914i	0.678533	−	0.734570i	$-0.262616\pi$
$608$	−1.60284e47	+	5.41664e46i	−0.756015	+	0.255487i
$609$	−2.80880e47			−1.28833
$610$	−5.22026e46	−	6.28015e46i	−0.232855	−	0.280132i
$611$		−	1.57773e46i		−	0.0684434i
$612$	2.45235e46	−	1.31916e47i	0.103468	−	0.556577i
$613$	3.36826e47			1.38222			0.691110	−	0.722749i	$-0.257122\pi$
$613$	3.36826e47			1.38222			0.691110	+	0.722749i	$0.257122\pi$
$614$	6.96453e46	−	5.78914e46i	0.277990	−	0.231074i
$615$		−	1.34784e47i		−	0.523314i
$616$	−3.52381e47	+	1.96966e47i	−1.33089	+	0.743907i
$617$	−1.74755e47			−0.642068			−0.321034	−	0.947068i	$-0.604030\pi$
$617$	−1.74755e47			−0.642068			−0.321034	+	0.947068i	$0.604030\pi$
$618$	1.54030e47	+	1.85304e47i	0.550557	+	0.662338i
$619$		−	2.04063e47i		−	0.709614i	−0.934940	−	0.354807i	$-0.884547\pi$
$619$		−	2.04063e47i		−	0.709614i	0.934940	−	0.354807i	$-0.115453\pi$
$620$	−9.65928e45	−	1.79567e45i	−0.0326803	−	0.00607531i
$621$	−1.70468e47			−0.561158
$622$	−1.82398e47	+	1.51615e47i	−0.584230	+	0.485630i
$623$			2.30281e47i			0.717730i
$624$	9.80136e46	−	2.54507e47i	0.297268	−	0.771901i
$625$	−1.72827e47			−0.510095
$626$	3.36777e47	+	4.05155e47i	0.967340	+	1.16374i
$627$			2.75663e47i			0.770602i
$628$	3.10111e46	−	1.66815e47i	0.0843730	−	0.453859i
$629$	7.78523e46			0.206163
$630$	2.30024e47	−	1.91203e47i	0.592902	−	0.492839i
$631$			6.25751e47i			1.57001i	0.619490	+	0.785005i	$0.287340\pi$
$631$			6.25751e47i			1.57001i	−0.619490	+	0.785005i	$0.712660\pi$
$632$	1.04045e47	+	1.86142e47i	0.254116	+	0.454626i
$633$	−5.97737e46			−0.142117
$634$	−2.58725e47	−	3.11255e47i	−0.598853	−	0.720441i
$635$			4.25087e47i			0.957909i
$636$	−5.69907e46	−	1.05946e46i	−0.125035	−	0.0232442i
$637$	−2.31150e47			−0.493769
$638$	6.52541e47	−	5.42412e47i	1.35724	−	1.12818i
$639$		−	6.00536e46i		−	0.121625i
$640$	7.71140e47	−	1.10312e47i	1.52081	−	0.217553i
$641$	−2.26126e47			−0.434275			−0.217137	−	0.976141i	$-0.569672\pi$
$641$	−2.26126e47			−0.434275			−0.217137	+	0.976141i	$0.569672\pi$
$642$	1.56321e47	+	1.88060e47i	0.292363	+	0.351723i
$643$		−	5.96760e47i		−	1.08696i	−0.839422	−	0.543480i	$-0.817106\pi$
$643$		−	5.96760e47i		−	1.08696i	0.839422	−	0.543480i	$-0.182894\pi$
$644$	−6.44744e46	+	3.46821e47i	−0.114374	+	0.615241i
$645$	−6.81364e47			−1.17724
$646$	−4.96412e47	+	4.12634e47i	−0.835391	+	0.694403i
$647$			9.75428e47i			1.59890i	0.600730	+	0.799452i	$0.294877\pi$
$647$			9.75428e47i			1.59890i	−0.600730	+	0.799452i	$0.705123\pi$
$648$	−2.24784e47	+	1.25645e47i	−0.358914	+	0.200617i
$649$	1.33148e48			2.07098
$650$	−6.21036e47	−	7.47128e47i	−0.941001	−	1.13206i
$651$		−	1.35188e46i		−	0.0199554i
$652$	−9.53754e47	−	1.77304e47i	−1.37160	−	0.254982i
$653$	−5.32611e45			−0.00746253			−0.00373127	−	0.999993i	$-0.501188\pi$
$653$	−5.32611e45			−0.00746253			−0.00373127	+	0.999993i	$0.501188\pi$
$654$	3.93300e47	−	3.26923e47i	0.536911	−	0.446297i
$655$		−	1.69238e48i		−	2.25111i
$656$	−3.20902e47	−	1.23583e47i	−0.415917	−	0.160175i
$657$	−1.68372e46			−0.0212647
$658$	3.96376e46	+	4.76854e46i	0.0487828	+	0.0586874i
$659$			6.32908e47i			0.759082i	0.925175	+	0.379541i	$0.123918\pi$
$659$			6.32908e47i			0.759082i	−0.925175	+	0.379541i	$0.876082\pi$
$660$	2.31975e47	−	1.24784e48i	0.271141	−	1.45852i
$661$	2.06659e47			0.235412			0.117706	−	0.993048i	$-0.462446\pi$
$661$	2.06659e47			0.235412			0.117706	+	0.993048i	$0.462446\pi$
$662$	7.44271e47	−	6.18661e47i	0.826314	−	0.686858i
$663$		−	1.04055e48i		−	1.12599i
$664$	5.30581e47	+	9.49236e47i	0.559622	+	1.00119i
$665$	−1.43902e48			−1.47945
$666$	4.01742e46	+	4.83309e46i	0.0402611	+	0.0484354i
$667$		−	7.41488e47i		−	0.724377i
$668$	4.55188e47	+	8.46202e46i	0.433502	+	0.0805887i
$669$	3.27798e47			0.304342
$670$	−2.43038e48	+	2.02021e48i	−2.19990	+	1.82863i
$671$			3.39471e47i			0.299585i
$672$	3.43165e47	+	1.01546e48i	0.295274	+	0.873750i
$673$	−1.69672e47			−0.142349			−0.0711743	−	0.997464i	$-0.522675\pi$
$673$	−1.69672e47			−0.142349			−0.0711743	+	0.997464i	$0.522675\pi$
$674$	3.67602e47	+	4.42238e47i	0.300718	+	0.361774i
$675$			1.84518e48i			1.47188i
$676$	−4.02532e46	+	2.16530e47i	−0.0313117	+	0.168432i
$677$	1.37236e48			1.04103			0.520513	−	0.853854i	$-0.325741\pi$
$677$	1.37236e48			1.04103			0.520513	+	0.853854i	$0.325741\pi$
$678$	−1.55950e48	+	1.29630e48i	−1.15367	+	0.958964i
$679$		−	1.06993e48i		−	0.771915i
$680$	2.59435e48	−	1.45013e48i	1.82548	−	1.02036i
$681$	1.58490e48			1.08768
$682$	2.61064e46	+	3.14069e46i	0.0174748	+	0.0210228i
$683$		−	1.56733e48i		−	1.02332i	−0.859189	−	0.511658i	$-0.829031\pi$
$683$		−	1.56733e48i		−	1.02332i	0.859189	−	0.511658i	$-0.170969\pi$
$684$	−5.12329e47	−	9.52426e46i	−0.326283	−	0.0606565i
$685$	1.69143e48			1.05078
$686$	−8.32672e47	+	6.92143e47i	−0.504619	+	0.419455i
$687$			9.23719e47i			0.546104i
$688$	−6.24739e47	+	1.62223e48i	−0.360326	+	0.935639i
$689$	3.20052e47			0.180092
$690$	−7.08966e47	−	8.52910e47i	−0.389216	−	0.468240i
$691$		−	6.73298e47i		−	0.360646i	−0.983607	−	0.180323i	$-0.942286\pi$
$691$		−	6.73298e47i		−	0.360646i	0.983607	−	0.180323i	$-0.0577142\pi$
$692$	−3.87655e47	+	2.08527e48i	−0.202601	+	1.08983i
$693$	−1.24338e48			−0.634073
$694$	7.66588e47	−	6.37212e47i	0.381462	−	0.317083i
$695$			1.71939e48i			0.834898i
$696$	−1.09928e48	−	1.96666e48i	−0.520895	−	0.931907i
$697$	−1.31201e48			−0.606707
$698$	−1.79704e48	−	2.16190e48i	−0.810991	−	0.975650i
$699$			2.55575e48i			1.12566i
$700$	3.75405e48	+	6.97883e47i	1.61374	+	0.299996i
$701$	−4.16255e48			−1.74644			−0.873218	−	0.487329i	$-0.837971\pi$
$701$	−4.16255e48			−1.74644			−0.873218	+	0.487329i	$0.837971\pi$
$702$	2.19928e48	−	1.82811e48i	0.900638	−	0.748639i
$703$		−	3.02357e47i		−	0.120859i
$704$	−2.75823e48	−	1.69644e48i	−1.07620	−	0.661916i
$705$	−1.94955e47			−0.0742541
$706$	3.66724e47	+	4.41181e47i	0.136351	+	0.164035i
$707$		−	5.50205e48i		−	1.99708i
$708$	6.46153e47	−	3.47579e48i	0.228966	−	1.23165i
$709$	8.65297e47			0.299350			0.149675	−	0.988735i	$-0.452177\pi$
$709$	8.65297e47			0.299350			0.149675	+	0.988735i	$0.452177\pi$
$710$	1.02297e48	−	8.50326e47i	0.345519	−	0.287206i
$711$			6.56805e47i			0.216597i
$712$	−1.61238e48	+	9.01250e47i	−0.519167	+	0.290192i
$713$	3.56879e46			0.0112202
$714$	2.61420e48	+	3.14497e48i	0.802544	+	0.965488i
$715$			7.00771e48i			2.10075i
$716$	9.09904e47	+	1.69152e47i	0.266363	+	0.0495173i
$717$	9.65151e47			0.275912
$718$	3.37067e48	−	2.80181e48i	0.941024	−	0.782208i
$719$		−	3.97141e48i		−	1.08281i	−0.840761	−	0.541407i	$-0.817892\pi$
$719$		−	3.97141e48i		−	1.08281i	0.840761	−	0.541407i	$-0.182108\pi$
$720$	2.23901e48	+	8.62268e47i	0.596215	+	0.229609i
$721$	5.22885e48			1.35990
$722$	−9.13898e47	−	1.09945e48i	−0.232148	−	0.279282i
$723$		−	2.09569e48i		−	0.519967i
$724$	−7.39320e47	+	3.97695e48i	−0.179175	+	0.963816i
$725$	−8.02599e48			−1.90000
$726$	−1.51569e48	+	1.25989e48i	−0.350500	+	0.291347i
$727$			1.13264e48i			0.255863i	0.991783	+	0.127932i	$0.0408338\pi$
$727$			1.13264e48i			0.255863i	−0.991783	+	0.127932i	$0.959166\pi$
$728$	−2.88752e48	−	5.16592e48i	−0.637224	−	1.14002i
$729$	−4.62934e48			−0.998047
$730$	−2.38405e47	−	2.86810e47i	−0.0502143	−	0.0604096i
$731$			6.63248e48i			1.36484i
$732$	8.86176e47	+	1.64741e47i	0.178169	+	0.0331218i
$733$	−5.58812e48			−1.09774			−0.548869	−	0.835909i	$-0.684941\pi$
$733$	−5.58812e48			−1.09774			−0.548869	+	0.835909i	$0.684941\pi$
$734$	8.46086e47	−	7.03293e47i	0.162398	−	0.134991i
$735$			2.85625e48i			0.535688i
$736$	−2.68070e48	+	9.05914e47i	−0.491276	+	0.166021i
$737$	1.31373e49			2.35266
$738$	−6.77036e47	−	8.14498e47i	−0.118482	−	0.142538i
$739$			1.03011e48i			0.176168i	0.996113	+	0.0880841i	$0.0280744\pi$
$739$			1.03011e48i			0.176168i	−0.996113	+	0.0880841i	$0.971926\pi$
$740$	−2.54439e47	+	1.36868e48i	−0.0425251	+	0.228751i
$741$	−4.04122e48			−0.660090
$742$	−9.67328e47	+	8.04073e47i	−0.154421	+	0.128360i
$743$		−	1.29275e48i		−	0.201700i	−0.994902	−	0.100850i	$-0.967844\pi$
$743$		−	1.29275e48i		−	0.201700i	0.994902	−	0.100850i	$-0.0321562\pi$
$744$	9.46557e46	−	5.29084e46i	0.0144347	−	0.00806835i
$745$	1.21484e49			1.81077
$746$	7.39803e48	+	8.90009e48i	1.07784	+	1.29668i
$747$			3.34939e48i			0.476997i
$748$	−1.21466e49	−	2.25807e48i	−1.69094	−	0.314348i
$749$	5.30662e48			0.722149
$750$	−2.44466e48	+	2.03208e48i	−0.325220	+	0.270333i
$751$		−	8.19156e48i		−	1.06534i	−0.846324	−	0.532669i	$-0.821189\pi$
$751$		−	8.19156e48i		−	1.06534i	0.846324	−	0.532669i	$-0.178811\pi$
$752$	−1.78754e47	+	4.64160e47i	−0.0227275	+	0.0590153i
$753$	5.01412e48			0.623275
$754$	7.95178e48	+	9.56627e48i	0.966388	+	1.16260i
$755$		−	2.43289e49i		−	2.89084i
$756$	−2.05432e48	+	1.10506e49i	−0.238670	+	1.28385i
$757$	−1.67350e49			−1.90106			−0.950529	−	0.310635i	$-0.899458\pi$
$757$	−1.67350e49			−1.90106			−0.950529	+	0.310635i	$0.899458\pi$
$758$	1.35365e48	−	1.12520e48i	0.150359	−	0.124983i
$759$			4.61037e48i			0.500755i
$760$	−5.63190e48	−	1.00757e49i	−0.598169	−	1.07015i
$761$	−1.02834e48			−0.106807			−0.0534033	−	0.998573i	$-0.517007\pi$
$761$	−1.02834e48			−0.106807			−0.0534033	+	0.998573i	$0.517007\pi$
$762$	−2.99914e48	−	3.60807e48i	−0.304623	−	0.366472i
$763$		−	1.10980e49i		−	1.10237i
$764$	8.77476e48	+	1.63124e48i	0.852409	+	0.158464i
$765$	9.15418e48			0.869711
$766$	7.35948e48	−	6.11743e48i	0.683846	−	0.568434i
$767$			1.95196e49i			1.77398i
$768$	−5.76703e48	+	6.37699e48i	−0.512639	+	0.566859i
$769$	1.43251e48			0.124552			0.0622760	−	0.998059i	$-0.480164\pi$
$769$	1.43251e48			0.124552			0.0622760	+	0.998059i	$0.480164\pi$
$770$	−1.76056e49	−	2.11801e49i	−1.49730	−	1.80130i
$771$		−	8.52655e48i		−	0.709331i
$772$	−1.86515e47	+	1.00330e48i	−0.0151782	+	0.0816464i
$773$	−1.03551e49			−0.824333			−0.412166	−	0.911109i	$-0.635228\pi$
$773$	−1.03551e49			−0.824333			−0.412166	+	0.911109i	$0.635228\pi$
$774$	−4.11746e48	+	3.42257e48i	−0.320652	+	0.266536i
$775$		−	3.86292e47i		−	0.0294298i
$776$	7.49144e48	−	4.18739e48i	0.558362	−	0.312100i
$777$	−1.91555e48			−0.139681
$778$	−8.50745e48	−	1.02348e49i	−0.606941	−	0.730171i
$779$			5.09549e48i			0.355671i
$780$	1.82934e49	+	3.40077e48i	1.24935	+	0.232257i
$781$	−5.52962e48			−0.369511
$782$	−8.30233e48	+	6.90116e48i	−0.542857	+	0.451239i
$783$		−	2.36257e49i		−	1.51159i
$784$	6.80032e48	+	2.61888e48i	0.425752	+	0.163962i
$785$	1.15759e49			0.709204
$786$	1.19404e49	+	1.43647e49i	0.715871	+	0.861217i
$787$			3.31777e49i			1.94659i	0.229551	+	0.973297i	$0.426274\pi$
$787$			3.31777e49i			1.94659i	−0.229551	+	0.973297i	$0.573726\pi$
$788$	1.81381e48	−	9.75683e48i	0.104147	−	0.560226i
$789$	6.31264e48			0.354733
$790$	−1.11882e49	+	9.30000e48i	−0.615319	+	0.511473i
$791$			4.40055e49i			2.36868i
$792$	−4.86622e48	−	8.70590e48i	−0.256368	−	0.458654i
$793$	−4.97665e48			−0.256621
$794$	8.48568e47	+	1.02086e48i	0.0428290	+	0.0515247i
$795$		−	3.95480e48i		−	0.195381i
$796$	1.30537e49	+	2.42671e48i	0.631267	+	0.117353i
$797$	2.81545e48			0.133277			0.0666387	−	0.997777i	$-0.478773\pi$
$797$	2.81545e48			0.133277			0.0666387	+	0.997777i	$0.478773\pi$
$798$	1.22142e49	−	1.01528e49i	0.566000	−	0.470477i
$799$			1.89772e48i			0.0860868i
$800$	9.80577e48	+	2.90164e49i	0.435464	+	1.28859i
$801$	−5.68930e48			−0.247347
$802$	1.71454e48	+	2.06265e48i	0.0729765	+	0.0877933i
$803$			1.55034e48i			0.0646044i
$804$	6.37540e48	−	3.42945e49i	0.260109	−	1.39917i
$805$	−2.40672e49			−0.961380
$806$	−4.60426e47	+	3.82720e47i	−0.0180079	+	0.0149688i
$807$		−	3.01415e48i		−	0.115429i
$808$	3.85242e49	−	2.15334e49i	1.44458	−	0.807456i
$809$	−3.57881e49			−1.31405			−0.657027	−	0.753867i	$-0.728186\pi$
$809$	−3.57881e49			−1.31405			−0.657027	+	0.753867i	$0.728186\pi$
$810$	−1.12306e49	−	1.35108e49i	−0.403793	−	0.485777i
$811$			4.08011e49i			1.43654i	0.695766	+	0.718269i	$0.255065\pi$
$811$			4.08011e49i			1.43654i	−0.695766	+	0.718269i	$0.744935\pi$
$812$	−4.80670e49	−	8.93573e48i	−1.65728	−	0.308090i
$813$	−2.43720e49			−0.822909
$814$	4.45022e48	−	3.69916e48i	0.147152	−	0.122318i
$815$		−	6.61846e49i		−	2.14327i
$816$	−1.17892e49	+	3.06125e49i	−0.373898	+	0.970882i
$817$	2.57588e49			0.800111
$818$	1.83043e49	+	2.20207e49i	0.556862	+	0.669924i
$819$		−	1.82280e49i		−	0.543141i
$820$	4.28795e48	−	2.30657e49i	0.125145	−	0.673180i
$821$	4.63923e49			1.32621			0.663105	−	0.748526i	$-0.269238\pi$
$821$	4.63923e49			1.32621			0.663105	+	0.748526i	$0.269238\pi$
$822$	−1.43566e49	+	1.19336e49i	−0.402004	+	0.334158i
$823$		−	4.71637e49i		−	1.29363i	−0.762646	−	0.646816i	$-0.776100\pi$
$823$		−	4.71637e49i		−	1.29363i	0.762646	−	0.646816i	$-0.223900\pi$
$824$	2.04641e49	+	3.66113e49i	0.549832	+	0.983677i
$825$	4.99034e49			1.31345
$826$	−4.90394e49	−	5.89960e49i	−1.26440	−	1.52111i
$827$		−	1.56590e49i		−	0.395521i	−0.980250	−	0.197760i	$-0.936633\pi$
$827$		−	1.56590e49i		−	0.395521i	0.980250	−	0.197760i	$-0.0633668\pi$
$828$	−8.56852e48	−	1.59290e48i	−0.212026	−	0.0394160i
$829$	−3.06337e49			−0.742630			−0.371315	−	0.928507i	$-0.621093\pi$
$829$	−3.06337e49			−0.742630			−0.371315	+	0.928507i	$0.621093\pi$
$830$	−5.70546e49	+	4.74256e49i	−1.35507	+	1.12638i
$831$			1.93743e49i			0.450825i
$832$	2.48698e49	−	4.04357e49i	0.566991	−	0.921867i
$833$	2.78031e49			0.621053
$834$	−1.21309e49	−	1.45939e49i	−0.265505	−	0.319411i
$835$			3.15872e49i			0.677394i
$836$	−8.76976e48	+	4.71743e49i	−0.184281	+	0.991285i
$837$	1.13711e48			0.0234137
$838$	5.86020e49	−	4.87118e49i	1.18240	−	0.982847i
$839$			1.72854e48i			0.0341764i	0.999854	+	0.0170882i	$0.00543960\pi$
$839$			1.72854e48i			0.0341764i	−0.999854	+	0.0170882i	$0.994560\pi$
$840$	−6.38338e49	+	3.56803e49i	−1.23681	+	0.691323i
$841$	5.00990e49			0.951256
$842$	5.20004e49	+	6.25583e49i	0.967612	+	1.16407i
$843$		−	3.96678e49i		−	0.723384i
$844$	−1.02291e49	−	1.90160e48i	−0.182817	−	0.0339859i
$845$	−1.50258e49			−0.263193
$846$	−1.17811e48	+	9.79282e47i	−0.0202251	+	0.0168117i
$847$			4.27694e49i			0.719639i
$848$	−9.41578e48	−	3.62613e48i	−0.155284	−	0.0598018i
$849$	−4.76536e49			−0.770309
$850$	7.46993e49	+	8.98659e49i	1.18357	+	1.42388i
$851$		−	5.05683e48i		−	0.0785372i
$852$	−2.68346e48	+	1.44349e49i	−0.0408529	+	0.219756i
$853$	−6.80113e49			−1.01496			−0.507478	−	0.861665i	$-0.669422\pi$
$853$	−6.80113e49			−1.01496			−0.507478	+	0.861665i	$0.669422\pi$
$854$	1.50415e49	−	1.25029e49i	0.220042	−	0.182906i
$855$		−	3.55524e49i		−	0.509853i
$856$	2.07685e49	+	3.71559e49i	0.291979	+	0.522364i
$857$	1.11497e50			1.53669			0.768347	−	0.640033i	$-0.221079\pi$
$857$	1.11497e50			1.53669			0.768347	+	0.640033i	$0.221079\pi$
$858$	−4.94420e49	−	5.94804e49i	−0.668055	−	0.803693i
$859$		−	3.82108e49i		−	0.506177i	−0.967443	−	0.253089i	$-0.918554\pi$
$859$		−	3.82108e49i		−	0.506177i	0.967443	−	0.253089i	$-0.0814464\pi$
$860$	−1.16602e50	−	2.16765e49i	−1.51437	−	0.281524i
$861$	3.22819e49			0.411060
$862$	6.56244e48	−	5.45491e48i	0.0819298	−	0.0681026i
$863$		−	2.23558e49i		−	0.273657i	−0.990595	−	0.136829i	$-0.956309\pi$
$863$		−	2.23558e49i		−	0.273657i	0.990595	−	0.136829i	$-0.0436910\pi$
$864$	−8.54141e49	+	2.88648e49i	−1.02517	+	0.346445i
$865$	−1.44705e50			−1.70298
$866$	2.55922e49	+	3.07883e49i	0.295327	+	0.355289i
$867$			5.76166e49i			0.651963i
$868$	4.30078e47	−	2.31347e48i	0.00477212	−	0.0256702i
$869$	6.04774e49			0.658047
$870$	1.18208e50	−	9.82579e49i	1.26130	−	1.04843i
$871$			1.92594e50i			2.01527i
$872$	7.77061e49	−	4.34343e49i	0.797398	−	0.445710i
$873$	2.64336e49			0.266020
$874$	2.68023e49	+	3.22440e49i	0.264531	+	0.318240i
$875$			6.89828e49i			0.667735i
$876$	4.04710e48	+	7.52362e47i	0.0384215	+	0.00714261i
$877$	−6.05441e49			−0.563740			−0.281870	−	0.959453i	$-0.590955\pi$
$877$	−6.05441e49			−0.563740			−0.281870	+	0.959453i	$0.590955\pi$
$878$	1.31486e49	−	1.09295e49i	0.120080	−	0.0998146i
$879$		−	9.05898e49i		−	0.811463i
$880$	7.93960e49	−	2.06163e50i	0.697579	−	1.81137i
$881$	−2.00729e50			−1.72989			−0.864947	−	0.501862i	$-0.832648\pi$
$881$	−2.00729e50			−1.72989			−0.864947	+	0.501862i	$0.832648\pi$
$882$	1.43473e49	+	1.72603e49i	0.121284	+	0.145909i
$883$		−	1.34874e50i		−	1.11839i	−0.829034	−	0.559197i	$-0.811109\pi$
$883$		−	1.34874e50i		−	1.11839i	0.829034	−	0.559197i	$-0.188891\pi$
$884$	3.31034e49	−	1.78070e50i	0.269268	−	1.44845i
$885$	2.41198e50			1.92459
$886$	1.82614e47	−	1.51794e47i	0.00142942	−	0.00118818i
$887$			3.53288e49i			0.271286i	0.990758	+	0.135643i	$0.0433100\pi$
$887$			3.53288e49i			0.271286i	−0.990758	+	0.135643i	$0.956690\pi$
$888$	−7.49690e48	−	1.34123e49i	−0.0564756	−	0.101038i
$889$	−1.01812e50			−0.752432
$890$	−8.05574e49	−	9.69133e49i	−0.584084	−	0.702673i
$891$			7.30321e49i			0.519509i
$892$	5.60962e49	+	1.04284e49i	0.391499	+	0.0727802i
$893$	7.37024e48			0.0504669
$894$	−1.03114e50	+	8.57117e49i	−0.692756	+	0.575841i
$895$			6.31416e49i			0.416221i
$896$	2.64207e49	+	1.84694e50i	0.170886	+	1.19458i
$897$	−6.75881e49			−0.428942
$898$	−1.29212e50	−	1.55446e50i	−0.804645	−	0.968016i
$899$			4.94610e48i			0.0302238i
$900$	−1.72418e49	+	9.27472e49i	−0.103386	+	0.556132i
$901$	−3.84964e49			−0.226516
$902$	−7.49975e49	+	6.23402e49i	−0.433047	+	0.359963i
$903$		−	1.63192e50i		−	0.924714i
$904$	−3.08117e50	+	1.72224e50i	−1.71338	+	0.957703i
$905$	−2.75975e50			−1.50607
$906$	1.71649e50	+	2.06500e50i	0.919312	+	1.10596i
$907$		−	5.94947e49i		−	0.312719i	−0.987700	−	0.156359i	$-0.950024\pi$
$907$		−	5.94947e49i		−	0.312719i	0.987700	−	0.156359i	$-0.0499758\pi$
$908$	2.71224e50	+	5.04210e49i	1.39917	+	0.260107i
$909$	1.35933e50			0.688239
$910$	3.10502e50	−	2.58099e50i	1.54298	−	1.28257i
$911$		−	6.59320e49i		−	0.321576i	−0.986989	−	0.160788i	$-0.948596\pi$
$911$		−	6.59320e49i		−	0.321576i	0.986989	−	0.160788i	$-0.0514036\pi$
$912$	1.18891e50	+	4.57863e49i	0.569163	+	0.219191i
$913$	3.08406e50			1.44917
$914$	−7.78727e48	−	9.36835e48i	−0.0359170	−	0.0432094i
$915$			6.14951e49i			0.278408i
$916$	−2.93866e49	+	1.58076e50i	−0.130595	+	0.702496i
$917$	4.05338e50			1.76823
$918$	−2.64534e50	+	2.19889e50i	−1.13281	+	0.941624i
$919$			4.09737e50i			1.72243i	0.508243	+	0.861214i	$0.330295\pi$
$919$			4.09737e50i			1.72243i	−0.508243	+	0.861214i	$0.669705\pi$
$920$	−9.41916e49	−	1.68513e50i	−0.388704	−	0.695411i
$921$	−6.81965e49			−0.276279
$922$	−6.53454e49	−	7.86127e49i	−0.259890	−	0.312656i
$923$		−	8.10644e49i		−	0.316520i
$924$	2.98868e50	+	5.55599e49i	1.14566	+	0.212980i
$925$	−5.47360e49			−0.205998
$926$	−3.24436e50	+	2.69681e50i	−1.19879	+	0.996470i
$927$			1.29183e50i			0.468653i
$928$	−1.25554e50	−	3.71527e50i	−0.447212	−	1.32335i
$929$	−5.05635e49			−0.176836			−0.0884179	−	0.996083i	$-0.528181\pi$
$929$	−5.05635e49			−0.176836			−0.0884179	+	0.996083i	$0.528181\pi$
$930$	4.72917e48	+	5.68935e48i	0.0162396	+	0.0195368i
$931$		−	1.07980e50i		−	0.364081i
$932$	−8.13070e49	+	4.37366e50i	−0.269189	+	1.44802i
$933$	1.78604e50			0.580634
$934$	−3.37741e50	+	2.80741e50i	−1.07817	+	0.896209i
$935$		−	8.42900e50i		−	2.64228i
$936$	1.27629e50	−	7.13389e49i	0.392879	−	0.219602i
$937$	−1.72737e50			−0.522171			−0.261085	−	0.965316i	$-0.584080\pi$
$937$	−1.72737e50			−0.522171			−0.261085	+	0.965316i	$0.584080\pi$
$938$	−4.83856e50	−	5.82096e50i	−1.43638	−	1.72801i
$939$		−	3.96726e50i		−	1.15658i
$940$	−3.33628e49	−	6.20219e48i	−0.0955188	−	0.0177571i
$941$	6.04821e50			1.70060			0.850302	−	0.526295i	$-0.176419\pi$
$941$	6.04821e50			1.70060			0.850302	+	0.526295i	$0.176419\pi$
$942$	−9.82546e49	+	8.16723e49i	−0.271324	+	0.225533i
$943$			8.52203e49i			0.231123i
$944$	2.21153e50	−	5.74256e50i	0.589073	−	1.52961i
$945$	−7.66843e50			−2.00616
$946$	3.15143e50	+	3.79128e50i	0.809765	+	0.974175i
$947$		−	2.47731e50i		−	0.625216i	−0.949882	−	0.312608i	$-0.898797\pi$
$947$		−	2.47731e50i		−	0.625216i	0.949882	−	0.312608i	$-0.101203\pi$
$948$	2.93490e49	−	1.57874e50i	0.0727532	−	0.391353i
$949$	−2.27280e49			−0.0553395
$950$	3.49015e50	−	2.90112e50i	0.834724	−	0.693849i
$951$			3.04780e50i			0.716007i
$952$	3.47316e50	+	6.21366e50i	0.801488	+	1.43390i
$953$	−9.96420e49			−0.225872			−0.112936	−	0.993602i	$-0.536026\pi$
$953$	−9.96420e49			−0.225872			−0.112936	+	0.993602i	$0.536026\pi$
$954$	−1.98654e49	−	2.38987e49i	−0.0442358	−	0.0532172i
$955$			6.08913e50i			1.33198i
$956$	1.65167e50	+	3.07047e49i	0.354926	+	0.0659813i
$957$	−6.38966e50			−1.34888
$958$	4.39534e50	−	3.65354e50i	0.911546	−	0.757706i
$959$			4.05110e50i			0.825385i
$960$	−4.99652e50	−	3.07309e50i	−1.00013	−	0.615127i
$961$	5.08270e50			0.999532
$962$	5.42299e49	+	6.52404e49i	0.104776	+	0.126049i
$963$			1.31105e50i			0.248870i
$964$	6.66709e49	−	3.58636e50i	0.124345	−	0.668873i
$965$	−6.96228e49			−0.127581
$966$	2.04279e50	−	1.69803e50i	0.367800	−	0.305727i
$967$		−	2.51824e50i		−	0.445499i	−0.974876	−	0.222749i	$-0.928497\pi$
$967$		−	2.51824e50i		−	0.445499i	0.974876	−	0.222749i	$-0.0715032\pi$
$968$	−2.99462e50	+	1.67386e50i	−0.520549	+	0.290964i
$969$	4.86086e50			0.830249
$970$	3.74286e50	+	4.50279e50i	0.628180	+	0.755722i
$971$			5.48017e50i			0.903790i	0.892071	+	0.451895i	$0.149252\pi$
$971$			5.48017e50i			0.903790i	−0.892071	+	0.451895i	$0.850748\pi$
$972$	−4.65840e50	−	8.66003e49i	−0.754936	−	0.140344i
$973$	−4.11808e50			−0.655807
$974$	−1.92968e47	+	1.60401e47i	−0.000301984	+	0.000251018i
$975$			7.31586e50i			1.12509i
$976$	1.46411e50	+	5.63845e49i	0.221272	+	0.0852144i
$977$	−8.32203e50			−1.23601			−0.618005	−	0.786174i	$-0.712059\pi$
$977$	−8.32203e50			−1.23601			−0.618005	+	0.786174i	$0.712059\pi$
$978$	4.66957e50	+	5.61765e50i	0.681579	+	0.819963i
$979$			5.23860e50i			0.751466i
$980$	−9.08671e49	+	4.88792e50i	−0.128104	+	0.689098i
$981$	2.74187e50			0.379904
$982$	2.99046e50	−	2.48576e50i	0.407232	−	0.338504i
$983$		−	9.05659e50i		−	1.21215i	−0.795409	−	0.606073i	$-0.792744\pi$
$983$		−	9.05659e50i		−	1.21215i	0.795409	−	0.606073i	$-0.207256\pi$
$984$	1.26342e50	+	2.26031e50i	0.166199	+	0.297339i
$985$	6.77063e50			0.875413
$986$	−9.56454e50	−	1.15065e51i	−1.21550	−	1.46229i
$987$		−	4.66934e49i		−	0.0583262i
$988$	−6.91576e50	−	1.28565e50i	−0.849126	−	0.157854i
$989$	4.30807e50			0.519931
$990$	5.23275e50	−	4.34962e50i	0.620771	−	0.516004i
$991$		−	1.06929e49i		−	0.0124693i	−0.999981	−	0.00623466i	$-0.998015\pi$
$991$		−	1.06929e49i		−	0.0124693i	0.999981	−	0.00623466i	$-0.00198457\pi$
$992$	1.78817e49	−	6.04291e48i	0.0204979	−	0.00692704i
$993$	−7.28788e50			−0.821228
$994$	2.03660e50	+	2.45009e50i	0.225599	+	0.271403i
$995$			9.05848e50i			0.986422i
$996$	1.49666e50	−	8.05082e50i	0.160219	−	0.861850i
$997$	−4.83582e50			−0.508924			−0.254462	−	0.967083i	$-0.581898\pi$
$997$	−4.83582e50			−0.508924			−0.254462	+	0.967083i	$0.581898\pi$
$998$	1.10405e50	−	9.17721e49i	0.114227	−	0.0949492i
$999$		−	1.61124e50i		−	0.163888i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.35.b.a.3.5	✓	16
4.3	odd	2	inner	4.35.b.a.3.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.35.b.a.3.5	✓	16	1.1	even	1	trivial
4.35.b.a.3.6	yes	16	4.3	odd	2	inner

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:	\( k \)	\(=\)	\( 35 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-83785.2 - 100796. i) q^{2} +9.86995e7i q^{3} +(-3.13996e9 + 1.68905e10i) q^{4} -1.17209e12 q^{5} +(9.94856e12 - 8.26956e12i) q^{6} -2.80726e14i q^{7} +(1.96558e15 - 1.09867e15i) q^{8} +6.93558e15 q^{9} +O(q^{10})\)	\(q+(-83785.2 - 100796. i) q^{2} +9.86995e7i q^{3} +(-3.13996e9 + 1.68905e10i) q^{4} -1.17209e12 q^{5} +(9.94856e12 - 8.26956e12i) q^{6} -2.80726e14i q^{7} +(1.96558e15 - 1.09867e15i) q^{8} +6.93558e15 q^{9} +(9.82041e16 + 1.18143e17i) q^{10} -6.38615e17i q^{11} +(-1.66708e18 - 3.09913e17i) q^{12} +9.36212e18 q^{13} +(-2.82961e19 + 2.35206e19i) q^{14} -1.15685e20i q^{15} +(-2.75429e20 - 1.06071e20i) q^{16} -1.12609e21 q^{17} +(-5.81099e20 - 6.99082e20i) q^{18} +4.37344e21i q^{19} +(3.68033e21 - 1.97972e22i) q^{20} +2.77075e22 q^{21} +(-6.43701e22 + 5.35065e22i) q^{22} +7.31443e22i q^{23} +(1.08439e23 + 1.94002e23i) q^{24} +7.91727e23 q^{25} +(-7.84407e23 - 9.43668e23i) q^{26} +2.33057e24i q^{27} +(4.74159e24 + 8.81469e23i) q^{28} -1.01373e25 q^{29} +(-1.16606e25 + 9.69270e24i) q^{30} -4.87911e23i q^{31} +(1.23853e25 + 3.66495e25i) q^{32} +6.30311e25 q^{33} +(9.43498e25 + 1.13506e26i) q^{34} +3.29037e26i q^{35} +(-2.17775e25 + 1.17145e26i) q^{36} -6.91349e25 q^{37} +(4.40827e26 - 3.66430e26i) q^{38} +9.24037e26i q^{39} +(-2.30385e27 + 1.28775e27i) q^{40} +1.16510e27 q^{41} +(-2.32148e27 - 2.79282e27i) q^{42} -5.88982e27i q^{43} +(1.07865e28 + 2.00523e27i) q^{44} -8.12915e27 q^{45} +(7.37269e27 - 6.12841e27i) q^{46} -1.68523e27i q^{47} +(1.04692e28 - 2.71847e28i) q^{48} -2.46899e28 q^{49} +(-6.63350e28 - 7.98033e28i) q^{50} -1.11145e29i q^{51} +(-2.93967e28 + 1.58131e29i) q^{52} +3.41859e28 q^{53} +(2.34913e29 - 1.95267e29i) q^{54} +7.48517e29i q^{55} +(-3.08426e29 - 5.51789e29i) q^{56} -4.31657e29 q^{57} +(8.49357e29 + 1.02181e30i) q^{58} +2.08495e30i q^{59} +(1.95398e30 + 3.63247e29i) q^{60} -5.31573e29 q^{61} +(-4.91796e28 + 4.08797e28i) q^{62} -1.94700e30i q^{63} +(2.65643e30 - 4.31907e30i) q^{64} -1.09733e31 q^{65} +(-5.28107e30 - 6.35330e30i) q^{66} +2.05716e31i q^{67} +(3.53589e30 - 1.90202e31i) q^{68} -7.21931e30 q^{69} +(3.31657e31 - 2.75684e31i) q^{70} -8.65876e30i q^{71} +(1.36325e31 - 7.61995e30i) q^{72} -2.42765e30 q^{73} +(5.79248e30 + 6.96855e30i) q^{74} +7.81431e31i q^{75} +(-7.38696e31 - 1.37325e31i) q^{76} -1.79276e32 q^{77} +(9.31396e31 - 7.74206e31i) q^{78} +9.47008e31i q^{79} +(3.22829e32 + 1.24325e32i) q^{80} -1.14360e32 q^{81} +(-9.76178e31 - 1.17438e32i) q^{82} +4.82929e32i q^{83} +(-8.70005e31 + 4.67993e32i) q^{84} +1.31989e33 q^{85} +(-5.93672e32 + 4.93479e32i) q^{86} -1.00055e33i q^{87} +(-7.01631e32 - 1.25525e33i) q^{88} -8.20306e32 q^{89} +(6.81102e32 + 8.19389e32i) q^{90} -2.62819e33i q^{91} +(-1.23544e33 - 2.29671e32i) q^{92} +4.81565e31 q^{93} +(-1.69865e32 + 1.41197e32i) q^{94} -5.12609e33i q^{95} +(-3.61728e33 + 1.22242e33i) q^{96} +3.81131e33 q^{97} +(2.06865e33 + 2.48865e33i) q^{98} -4.42917e33i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 27372 q^{2} - 20032875248 q^{4} - 21372255840 q^{5} + 20836736461728 q^{6} + 22\!\cdots\!12 q^{8}+ \cdots - 67\!\cdots\!80 q^{9}+O(q^{10}) \) 16 * q - 27372 * q^2 - 20032875248 * q^4 - 21372255840 * q^5 + 20836736461728 * q^6 + 2284358011394112 * q^8 - 67828545645364080 * q^9	\( 16 q - 27372 q^{2} - 20032875248 q^{4} - 21372255840 q^{5} + 20836736461728 q^{6} + 22\!\cdots\!12 q^{8}+ \cdots + 16\!\cdots\!32 q^{98}+O(q^{100}) \) 16 * q - 27372 * q^2 - 20032875248 * q^4 - 21372255840 * q^5 + 20836736461728 * q^6 + 2284358011394112 * q^8 - 67828545645364080 * q^9 - 45113792455239160 * q^10 + 2389205919902175360 * q^12 - 5233507036411659616 * q^13 - 78584294183795706432 * q^14 + 495182112183820124416 * q^16 - 603670905919309938144 * q^17 - 3049682100893194226508 * q^18 - 33058393758449688290400 * q^20 + 51436061805005728413696 * q^21 + 71660876143050404765280 * q^22 + 216144869785928938234368 * q^24 + 1224730607199300816400560 * q^25 - 2068583291215840445568696 * q^26 + 891252510406495618671360 * q^28 - 4086289565288128397679456 * q^29 + 29601064663371600024444480 * q^30 + 20026414012547463259849728 * q^32 + 73954448514753271238568960 * q^33 + 46288216238217191722231976 * q^34 + 569062048300724903070378384 * q^36 + 950385175701396416644593056 * q^37 - 123498782719680108073563360 * q^38 - 3250024485723791435879459200 * q^40 + 469238845433510127731349792 * q^41 + 2352670327884382399711157760 * q^42 + 7327222247557584897899214720 * q^44 - 24427097188106605438098250080 * q^45 - 19562783684402230406331003072 * q^46 + 10576141603633237485164267520 * q^48 - 5662649722408510114314091760 * q^49 + 20191932196464263485504736220 * q^50 - 299155663662273783907276503904 * q^52 - 287274278887575172234950512736 * q^53 + 6047252470624543429578889536 * q^54 + 957626384837555513184792726528 * q^56 + 2791286265941381406754467578880 * q^57 - 314499391713380785247660833336 * q^58 + 1103184540481814815474103512320 * q^60 - 7360215904797065436447249778528 * q^61 + 6668101684324825273374014288640 * q^62 - 4672502276277215477475812569088 * q^64 + 7390500022468645317433010287680 * q^65 - 12460359580334220374288279205120 * q^66 + 3201090312765007118305938045984 * q^68 - 20909099675706939600670541666304 * q^69 - 13302319794857519494110175324800 * q^70 - 776423968147266229824274003392 * q^72 - 21322365514881309087265291408096 * q^73 + 60200090281780873185690769101576 * q^74 - 104909582027053727863743869884800 * q^76 + 31510097566037837419459121448960 * q^77 + 173718506967281862717403400063040 * q^78 + 360511559214548868760655536888320 * q^80 - 262819454584631237298859074129648 * q^81 - 127799686177535642546403976474264 * q^82 - 481860976739335096182940424300544 * q^84 + 2066519418228326883252673443837760 * q^85 + 680164732953303409567751182232928 * q^86 - 1868588957981221169228370505105920 * q^88 - 2487774705888249186282098457137376 * q^89 + 2710136859758550244207319911170120 * q^90 - 5719642193953545223478177490435840 * q^92 - 4648987096869411453766406983557120 * q^93 - 174301665834847119752293250078592 * q^94 - 1356265248520894619800195113541632 * q^96 + 7119191713926779638291321673063456 * q^97 + 16929214407930779244441537548523732 * q^98

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