LMFDB - Embedded newform 4.35.b.a.3.10

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			3.10
Root			$0.500000 + 4.39438e6i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.35.b.a.3.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13540.0 + 130371. i) q^{2} -2.10930e8i q^{3} +(-1.68132e10 + 3.53043e9i) q^{4} +1.26172e12 q^{5} +(2.74991e13 - 2.85599e12i) q^{6} +2.66990e14i q^{7} +(-6.87916e14 - 2.14415e15i) q^{8} -2.78144e16 q^{9} +O(q^{10})$	\(q+(13540.0 + 130371. i) q^{2} -2.10930e8i q^{3} +(-1.68132e10 + 3.53043e9i) q^{4} +1.26172e12 q^{5} +(2.74991e13 - 2.85599e12i) q^{6} +2.66990e14i q^{7} +(-6.87916e14 - 2.14415e15i) q^{8} -2.78144e16 q^{9} +(1.70837e16 + 1.64492e17i) q^{10} +3.69323e16i q^{11} +(7.44675e17 + 3.54641e18i) q^{12} +5.25274e18 q^{13} +(-3.48076e19 + 3.61503e18i) q^{14} -2.66135e20i q^{15} +(2.70220e20 - 1.18716e20i) q^{16} +7.43326e20 q^{17} +(-3.76606e20 - 3.62618e21i) q^{18} +5.11603e21i q^{19} +(-2.12136e22 + 4.45442e21i) q^{20} +5.63162e22 q^{21} +(-4.81489e21 + 5.00062e20i) q^{22} -3.98684e22i q^{23} +(-4.52266e23 + 1.45102e23i) q^{24} +1.00986e24 q^{25} +(7.11220e22 + 6.84804e23i) q^{26} +2.34917e24i q^{27} +(-9.42589e23 - 4.48895e24i) q^{28} -1.21423e23 q^{29} +(3.46962e25 - 3.60346e24i) q^{30} -3.15805e25i q^{31} +(1.91358e25 + 3.36214e25i) q^{32} +7.79014e24 q^{33} +(1.00646e25 + 9.69079e25i) q^{34} +3.36866e26i q^{35} +(4.67649e26 - 9.81968e25i) q^{36} +8.45310e26 q^{37} +(-6.66981e26 + 6.92709e25i) q^{38} -1.10796e27i q^{39} +(-8.67957e26 - 2.70532e27i) q^{40} +3.33779e27 q^{41} +(7.62519e26 + 7.34198e27i) q^{42} +1.26703e26i q^{43} +(-1.30387e26 - 6.20951e26i) q^{44} -3.50940e28 q^{45} +(5.19768e27 - 5.39817e26i) q^{46} +6.15750e27i q^{47} +(-2.50408e28 - 5.69976e28i) q^{48} -1.71664e28 q^{49} +(1.36735e28 + 1.31657e29i) q^{50} -1.56790e29i q^{51} +(-8.83155e28 + 1.85445e28i) q^{52} +1.72901e29 q^{53} +(-3.06263e29 + 3.18077e28i) q^{54} +4.65983e28i q^{55} +(5.72465e29 - 1.83666e29i) q^{56} +1.07913e30 q^{57} +(-1.64406e27 - 1.58300e28i) q^{58} -4.94695e29i q^{59} +(9.39572e29 + 4.47458e30i) q^{60} -3.28307e30 q^{61} +(4.11717e30 - 4.27598e29i) q^{62} -7.42615e30i q^{63} +(-4.12415e30 + 2.94999e30i) q^{64} +6.62750e30 q^{65} +(1.05478e29 + 1.01561e30i) q^{66} -1.65385e31i q^{67} +(-1.24977e31 + 2.62426e30i) q^{68} -8.40945e30 q^{69} +(-4.39175e31 + 4.56116e30i) q^{70} +5.10292e30i q^{71} +(1.91339e31 + 5.96382e31i) q^{72} +3.84823e29 q^{73} +(1.14455e31 + 1.10204e32i) q^{74} -2.13011e32i q^{75} +(-1.80618e31 - 8.60169e31i) q^{76} -9.86054e30 q^{77} +(1.44446e32 - 1.50018e31i) q^{78} +9.83778e31i q^{79} +(3.40942e32 - 1.49786e32i) q^{80} +3.16460e31 q^{81} +(4.51936e31 + 4.35151e32i) q^{82} +2.13922e32i q^{83} +(-9.46855e32 + 1.98820e32i) q^{84} +9.37869e32 q^{85} +(-1.65184e31 + 1.71556e30i) q^{86} +2.56117e31i q^{87} +(7.91884e31 - 2.54063e31i) q^{88} -6.24982e32 q^{89} +(-4.75172e32 - 4.57523e33i) q^{90} +1.40243e33i q^{91} +(1.40753e32 + 6.70316e32i) q^{92} -6.66127e33 q^{93} +(-8.02758e32 + 8.33724e31i) q^{94} +6.45500e33i q^{95} +(7.09177e33 - 4.03633e33i) q^{96} +4.77972e33 q^{97} +(-2.32433e32 - 2.23800e33i) q^{98} -1.02725e33i 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 $

$2$	13540.0	+	130371.i	0.103302	+	0.994650i
$2$	13540.0	+	130371.i	0.103302	+	0.994650i
$3$		−	2.10930e8i		−	1.63334i	−0.577103	−	0.816672i	$-0.695817\pi$
$3$		−	2.10930e8i		−	1.63334i	0.577103	−	0.816672i	$-0.304183\pi$
$4$	−1.68132e10	+	3.53043e9i	−0.978657	+	0.205498i
$5$	1.26172e12			1.65376			0.826881	−	0.562376i	$-0.190113\pi$
$5$	1.26172e12			1.65376			0.826881	+	0.562376i	$0.190113\pi$
$6$	2.74991e13	−	2.85599e12i	1.62461	−	0.168727i
$7$			2.66990e14i			1.14770i	0.818961	+	0.573849i	$0.194550\pi$
$7$			2.66990e14i			1.14770i	−0.818961	+	0.573849i	$0.805450\pi$
$8$	−6.87916e14	−	2.14415e15i	−0.305496	−	0.952193i
$9$	−2.78144e16			−1.66781
$10$	1.70837e16	+	1.64492e17i	0.170837	+	1.64492i
$11$			3.69323e16i			0.0730686i	0.999332	+	0.0365343i	$0.0116318\pi$
$11$			3.69323e16i			0.0730686i	−0.999332	+	0.0365343i	$0.988368\pi$
$12$	7.44675e17	+	3.54641e18i	0.335649	+	1.59848i
$13$	5.25274e18			0.607225			0.303612	−	0.952796i	$-0.401807\pi$
$13$	5.25274e18			0.607225			0.303612	+	0.952796i	$0.401807\pi$
$14$	−3.48076e19	+	3.61503e18i	−1.14156	+	0.118559i
$15$		−	2.66135e20i		−	2.70116i
$16$	2.70220e20	−	1.18716e20i	0.915541	−	0.402225i
$17$	7.43326e20			0.898561			0.449280	−	0.893391i	$-0.351680\pi$
$17$	7.43326e20			0.898561			0.449280	+	0.893391i	$0.351680\pi$
$18$	−3.76606e20	−	3.62618e21i	−0.172288	−	1.65889i
$19$			5.11603e21i			0.933516i	0.884385	+	0.466758i	$0.154578\pi$
$19$			5.11603e21i			0.933516i	−0.884385	+	0.466758i	$0.845422\pi$
$20$	−2.12136e22	+	4.45442e21i	−1.61847	+	0.339845i
$21$	5.63162e22			1.87458
$22$	−4.81489e21	+	5.00062e20i	−0.0726777	+	0.00754812i
$23$		−	3.98684e22i		−	0.282654i	−0.989963	−	0.141327i	$-0.954863\pi$
$23$		−	3.98684e22i		−	0.282654i	0.989963	−	0.141327i	$-0.0451370\pi$
$24$	−4.52266e23	+	1.45102e23i	−1.55526	+	0.498980i
$25$	1.00986e24			1.73493
$26$	7.11220e22	+	6.84804e23i	0.0627274	+	0.603976i
$27$			2.34917e24i			1.09076i
$28$	−9.42589e23	−	4.48895e24i	−0.235850	−	1.12320i
$29$	−1.21423e23			−0.0167315			−0.00836574	−	0.999965i	$-0.502663\pi$
$29$	−1.21423e23			−0.0167315			−0.00836574	+	0.999965i	$0.502663\pi$
$30$	3.46962e25	−	3.60346e24i	2.68671	−	0.279035i
$31$		−	3.15805e25i		−	1.40046i	−0.713919	−	0.700228i	$-0.753082\pi$
$31$		−	3.15805e25i		−	1.40046i	0.713919	−	0.700228i	$-0.246918\pi$
$32$	1.91358e25	+	3.36214e25i	0.494650	+	0.869092i
$33$	7.79014e24			0.119346
$34$	1.00646e25	+	9.69079e25i	0.0928229	+	0.893754i
$35$			3.36866e26i			1.89802i
$36$	4.67649e26	−	9.81968e25i	1.63222	−	0.342732i
$37$	8.45310e26			1.85177			0.925884	−	0.377807i	$-0.123322\pi$
$37$	8.45310e26			1.85177			0.925884	+	0.377807i	$0.123322\pi$
$38$	−6.66981e26	+	6.92709e25i	−0.928522	+	0.0964339i
$39$		−	1.10796e27i		−	0.991806i
$40$	−8.67957e26	−	2.70532e27i	−0.505218	−	1.57470i
$41$	3.33779e27			1.27683			0.638416	−	0.769692i	$-0.279590\pi$
$41$	3.33779e27			1.27683			0.638416	+	0.769692i	$0.279590\pi$
$42$	7.62519e26	+	7.34198e27i	0.193648	+	1.86456i
$43$			1.26703e26i			0.0215687i	0.999942	+	0.0107843i	$0.00343283\pi$
$43$			1.26703e26i			0.0215687i	−0.999942	+	0.0107843i	$0.996567\pi$
$44$	−1.30387e26	−	6.20951e26i	−0.0150155	−	0.0715091i
$45$	−3.50940e28			−2.75816
$46$	5.19768e27	−	5.39817e26i	0.281142	−	0.0291987i
$47$			6.15750e27i			0.231069i	0.993303	+	0.115534i	$0.0368580\pi$
$47$			6.15750e27i			0.231069i	−0.993303	+	0.115534i	$0.963142\pi$
$48$	−2.50408e28	−	5.69976e28i	−0.656971	−	1.49539i
$49$	−1.71664e28			−0.317210
$50$	1.36735e28	+	1.31657e29i	0.179221	+	1.72565i
$51$		−	1.56790e29i		−	1.46766i
$52$	−8.83155e28	+	1.85445e28i	−0.594265	+	0.124784i
$53$	1.72901e29			0.841605			0.420802	−	0.907152i	$-0.361749\pi$
$53$	1.72901e29			0.841605			0.420802	+	0.907152i	$0.361749\pi$
$54$	−3.06263e29	+	3.18077e28i	−1.08493	+	0.112678i
$55$			4.65983e28i			0.120838i
$56$	5.72465e29	−	1.83666e29i	1.09283	−	0.350617i
$57$	1.07913e30			1.52475
$58$	−1.64406e27	−	1.58300e28i	−0.00172839	−	0.0166420i
$59$		−	4.94695e29i		−	0.388914i	−0.980911	−	0.194457i	$-0.937706\pi$
$59$		−	4.94695e29i		−	0.388914i	0.980911	−	0.194457i	$-0.0622944\pi$
$60$	9.39572e29	+	4.47458e30i	0.555084	+	2.64351i
$61$	−3.28307e30			−1.46444			−0.732221	−	0.681067i	$-0.761516\pi$
$61$	−3.28307e30			−1.46444			−0.732221	+	0.681067i	$0.761516\pi$
$62$	4.11717e30	−	4.27598e29i	1.39296	−	0.144670i
$63$		−	7.42615e30i		−	1.91414i
$64$	−4.12415e30	+	2.94999e30i	−0.813345	+	0.581782i
$65$	6.62750e30			1.00421
$66$	1.05478e29	+	1.01561e30i	0.0123287	+	0.118708i
$67$		−	1.65385e31i		−	1.49701i	−0.663129	−	0.748505i	$-0.730772\pi$
$67$		−	1.65385e31i		−	1.49701i	0.663129	−	0.748505i	$-0.269228\pi$
$68$	−1.24977e31	+	2.62426e30i	−0.879383	+	0.184653i
$69$	−8.40945e30			−0.461672
$70$	−4.39175e31	+	4.56116e30i	−1.88787	+	0.196069i
$71$			5.10292e30i			0.172356i	0.996280	+	0.0861780i	$0.0274654\pi$
$71$			5.10292e30i			0.172356i	−0.996280	+	0.0861780i	$0.972535\pi$
$72$	1.91339e31	+	5.96382e31i	0.509509	+	1.58808i
$73$	3.84823e29			0.00810536			0.00405268	−	0.999992i	$-0.498710\pi$
$73$	3.84823e29			0.00810536			0.00405268	+	0.999992i	$0.498710\pi$
$74$	1.14455e31	+	1.10204e32i	0.191291	+	1.84186i
$75$		−	2.13011e32i		−	2.83374i
$76$	−1.80618e31	−	8.60169e31i	−0.191836	−	0.913593i
$77$	−9.86054e30			−0.0838607
$78$	1.44446e32	−	1.50018e31i	0.986500	−	0.102455i
$79$			9.83778e31i			0.541049i	0.962713	+	0.270524i	$0.0871971\pi$
$79$			9.83778e31i			0.541049i	−0.962713	+	0.270524i	$0.912803\pi$
$80$	3.40942e32	−	1.49786e32i	1.51409	−	0.665184i
$81$	3.16460e31			0.113782
$82$	4.51936e31	+	4.35151e32i	0.131899	+	1.27000i
$83$			2.13922e32i			0.508075i	0.967194	+	0.254037i	$0.0817586\pi$
$83$			2.13922e32i			0.508075i	−0.967194	+	0.254037i	$0.918241\pi$
$84$	−9.46855e32	+	1.98820e32i	−1.83458	+	0.385224i
$85$	9.37869e32			1.48601
$86$	−1.65184e31	+	1.71556e30i	−0.0214533	+	0.00222808i
$87$			2.56117e31i			0.0273282i
$88$	7.91884e31	−	2.54063e31i	0.0695754	−	0.0223222i
$89$	−6.24982e32			−0.453146			−0.226573	−	0.973994i	$-0.572752\pi$
$89$	−6.24982e32			−0.453146			−0.226573	+	0.973994i	$0.572752\pi$
$90$	−4.75172e32	−	4.57523e33i	−0.284923	−	2.74341i
$91$			1.40243e33i			0.696910i
$92$	1.40753e32	+	6.70316e32i	0.0580850	+	0.276622i
$93$	−6.66127e33			−2.28743
$94$	−8.02758e32	+	8.33724e31i	−0.229832	+	0.0238698i
$95$			6.45500e33i			1.54381i
$96$	7.09177e33	−	4.03633e33i	1.41953	−	0.807933i
$97$	4.77972e33			0.802201			0.401101	−	0.916034i	$-0.368628\pi$
$97$	4.77972e33			0.802201			0.401101	+	0.916034i	$0.368628\pi$
$98$	−2.32433e32	−	2.23800e33i	−0.0327684	−	0.315513i
$99$		−	1.02725e33i		−	0.121865i
$100$	−1.69790e34	+	3.56525e33i	−1.69790	+	0.356525i
$101$	−6.70756e33			−0.566371			−0.283186	−	0.959065i	$-0.591391\pi$
$101$	−6.70756e33			−0.566371			−0.283186	+	0.959065i	$0.591391\pi$
$102$	2.04408e34	−	2.12293e33i	1.45981	−	0.151612i
$103$			8.68750e33i			0.525608i	0.964849	+	0.262804i	$0.0846473\pi$
$103$			8.68750e33i			0.525608i	−0.964849	+	0.262804i	$0.915353\pi$
$104$	−3.61345e33	−	1.12627e34i	−0.185505	−	0.578195i
$105$	7.10553e34			3.10012
$106$	2.34108e33	+	2.25413e34i	0.0869393	+	0.837102i
$107$			4.12540e34i			1.30600i	0.757359	+	0.652998i	$0.226489\pi$
$107$			4.12540e34i			1.30600i	−0.757359	+	0.652998i	$0.773511\pi$
$108$	−8.29360e33	−	3.94971e34i	−0.224150	−	1.06748i
$109$	−7.03145e34			−1.62478			−0.812390	−	0.583114i	$-0.801834\pi$
$109$	−7.03145e34			−1.62478			−0.812390	+	0.583114i	$0.801834\pi$
$110$	−6.07505e33	+	6.30939e32i	−0.120192	+	0.0124828i
$111$		−	1.78301e35i		−	3.02457i
$112$	3.16959e34	+	7.21459e34i	0.461632	+	1.05076i
$113$	−4.93474e34			−0.617918			−0.308959	−	0.951075i	$-0.599981\pi$
$113$	−4.93474e34			−0.617918			−0.308959	+	0.951075i	$0.599981\pi$
$114$	1.46113e34	+	1.40686e35i	0.157510	+	1.51660i
$115$		−	5.03028e34i		−	0.467443i
$116$	2.04151e33	−	4.28675e32i	0.0163744	−	0.00343829i
$117$	−1.46102e35			−1.01274
$118$	6.44938e34	−	6.69816e33i	0.386833	−	0.0401755i
$119$			1.98460e35i			1.03128i
$120$	−5.70633e35	+	1.83078e35i	−2.57203	+	0.825194i
$121$	2.54113e35			0.994661
$122$	−4.44526e34	−	4.28016e35i	−0.151280	−	1.45661i
$123$		−	7.04041e35i		−	2.08551i
$124$	1.11493e35	+	5.30969e35i	0.287791	+	1.37057i
$125$	5.39746e35			1.21540
$126$	9.68153e35	−	1.00550e35i	1.90390	−	0.197734i
$127$		−	3.16970e34i		−	0.0544947i	−0.999629	−	0.0272474i	$-0.991326\pi$
$127$		−	3.16970e34i		−	0.0544947i	0.999629	−	0.0272474i	$-0.00867418\pi$
$128$	−4.40433e35	−	4.97725e35i	−0.662690	−	0.748894i
$129$	2.67255e34			0.0352291
$130$	8.97361e34	+	8.64032e35i	0.103736	+	0.998833i
$131$			1.15819e36i			1.17535i	0.809096	+	0.587677i	$0.199957\pi$
$131$			1.15819e36i			1.17535i	−0.809096	+	0.587677i	$0.800043\pi$
$132$	−1.30977e35	+	2.75026e34i	−0.116799	+	0.0245254i
$133$	−1.36593e36			−1.07139
$134$	2.15614e36	−	2.23931e35i	1.48900	−	0.154644i
$135$			2.96400e36i			1.80387i
$136$	−5.11345e35	−	1.59380e36i	−0.274507	−	0.855604i
$137$	−7.40331e35			−0.350894			−0.175447	−	0.984489i	$-0.556137\pi$
$137$	−7.40331e35			−0.350894			−0.175447	+	0.984489i	$0.556137\pi$
$138$	−1.13864e35	−	1.09635e36i	−0.0476915	−	0.459202i
$139$		−	1.83519e36i		−	0.679876i	−0.940448	−	0.339938i	$-0.889594\pi$
$139$		−	1.83519e36i		−	0.679876i	0.940448	−	0.339938i	$-0.110406\pi$
$140$	−1.18928e36	−	5.66380e36i	−0.390040	−	1.85751i
$141$	1.29880e36			0.377414
$142$	−6.65271e35	+	6.90933e34i	−0.171434	+	0.0178047i
$143$			1.93996e35i			0.0443691i
$144$	−7.51600e36	+	3.30201e36i	−1.52695	+	0.670835i
$145$	−1.53202e35			−0.0276699
$146$	5.21049e33	+	5.01696e34i	0.000837298	+	0.00806199i
$147$			3.62092e36i			0.518113i
$148$	−1.42124e37	+	2.98431e36i	−1.81225	+	0.380535i
$149$	3.10513e36			0.353113			0.176556	−	0.984291i	$-0.443504\pi$
$149$	3.10513e36			0.353113			0.176556	+	0.984291i	$0.443504\pi$
$150$	2.77704e37	−	2.88416e36i	2.81858	−	0.292730i
$151$			1.75965e37i			1.59521i	0.603180	+	0.797605i	$0.293900\pi$
$151$			1.75965e37i			1.59521i	−0.603180	+	0.797605i	$0.706100\pi$
$152$	1.09695e37	−	3.51940e36i	0.888888	−	0.285185i
$153$	−2.06751e37			−1.49863
$154$	−1.33511e35	−	1.28553e36i	−0.00866296	−	0.0834120i
$155$		−	3.98457e37i		−	2.31602i
$156$	3.91159e36	+	1.86284e37i	0.203814	+	0.970639i
$157$	3.35264e37			1.56709			0.783543	−	0.621338i	$-0.213411\pi$
$157$	3.35264e37			1.56709			0.783543	+	0.621338i	$0.213411\pi$
$158$	−1.28256e37	+	1.33203e36i	−0.538154	+	0.0558913i
$159$		−	3.64701e37i		−	1.37463i
$160$	2.41441e37	+	4.24208e37i	0.818034	+	1.43727i
$161$	1.06444e37			0.324402
$162$	4.28486e35	+	4.12571e36i	0.0117539	+	0.113173i
$163$			1.91669e37i			0.473547i	0.971565	+	0.236773i	$0.0760899\pi$
$163$			1.91669e37i			0.473547i	−0.971565	+	0.236773i	$0.923910\pi$
$164$	−5.61190e37	+	1.17839e37i	−1.24958	+	0.262387i
$165$	9.82898e36			0.197370
$166$	−2.78891e37	+	2.89649e36i	−0.505356	+	0.0524850i
$167$			1.41530e37i			0.231563i	0.993275	+	0.115781i	$0.0369372\pi$
$167$			1.41530e37i			0.231563i	−0.993275	+	0.115781i	$0.963063\pi$
$168$	−3.87408e37	−	1.20750e38i	−0.572678	−	1.78497i
$169$	−4.72384e37			−0.631278
$170$	1.26987e37	+	1.22271e38i	0.153507	+	1.47806i
$171$		−	1.42299e38i		−	1.55693i
$172$	−4.47317e35	−	2.13029e36i	−0.00443233	−	0.0211084i
$173$	−4.74756e37			−0.426272			−0.213136	−	0.977023i	$-0.568368\pi$
$173$	−4.74756e37			−0.426272			−0.213136	+	0.977023i	$0.568368\pi$
$174$	−3.33902e36	+	3.46782e35i	−0.0271820	+	0.00282306i
$175$			2.69623e38i			1.99118i
$176$	4.38445e36	+	9.97985e36i	0.0293900	+	0.0668973i
$177$	−1.04346e38			−0.635230
$178$	−8.46224e36	−	8.14794e37i	−0.0468107	−	0.450721i
$179$		−	3.07231e38i		−	1.54513i	−0.634938	−	0.772563i	$-0.718974\pi$
$179$		−	3.07231e38i		−	1.54513i	0.634938	−	0.772563i	$-0.281026\pi$
$180$	5.90042e38	−	1.23897e38i	2.69930	−	0.566798i
$181$	−1.48431e38			−0.618001			−0.309000	−	0.951062i	$-0.599994\pi$
$181$	−1.48431e38			−0.618001			−0.309000	+	0.951062i	$0.599994\pi$
$182$	−1.82836e38	+	1.89888e37i	−0.693182	+	0.0719921i
$183$			6.92498e38i			2.39194i
$184$	−8.54838e37	+	2.74261e37i	−0.269142	+	0.0863498i
$185$	1.06655e39			3.06239
$186$	−9.01934e37	−	8.68435e38i	−0.236295	−	2.27519i
$187$			2.74527e37i			0.0656566i
$188$	−2.17386e37	−	1.03527e38i	−0.0474842	−	0.226137i
$189$	−6.27204e38			−1.25187
$190$	−8.41544e38	+	8.74005e37i	−1.53556	+	0.159479i
$191$			1.04732e39i			1.74788i	0.486032	+	0.873941i	$0.338444\pi$
$191$			1.04732e39i			1.74788i	−0.486032	+	0.873941i	$0.661556\pi$
$192$	6.22241e38	+	8.69907e38i	0.950250	+	1.32847i
$193$	6.34075e38			0.886475			0.443237	−	0.896404i	$-0.353830\pi$
$193$	6.34075e38			0.886475			0.443237	+	0.896404i	$0.353830\pi$
$194$	6.47173e37	+	6.23136e38i	0.0828688	+	0.797910i
$195$		−	1.39794e39i		−	1.64021i
$196$	2.88623e38	−	6.06050e37i	0.310440	−	0.0651861i
$197$	−1.11274e39			−1.09766			−0.548832	−	0.835933i	$-0.684927\pi$
$197$	−1.11274e39			−1.09766			−0.548832	+	0.835933i	$0.684927\pi$
$198$	1.33923e38	−	1.39089e37i	0.121213	−	0.0125888i
$199$		−	1.42127e39i		−	1.18080i	−0.807112	−	0.590398i	$-0.798971\pi$
$199$		−	1.42127e39i		−	1.18080i	0.807112	−	0.590398i	$-0.201029\pi$
$200$	−6.94700e38	−	2.16530e39i	−0.530014	−	1.65199i
$201$	−3.48847e39			−2.44513
$202$	−9.08201e37	−	8.74469e38i	−0.0585071	−	0.563341i
$203$		−	3.24186e37i		−	0.0192027i
$204$	5.53536e38	+	2.63614e39i	0.301601	+	1.43633i
$205$	4.21136e39			2.11158
$206$	−1.13260e39	+	1.17629e38i	−0.522796	+	0.0542963i
$207$			1.10892e39i			0.471414i
$208$	1.41940e39	−	6.23584e38i	0.555939	−	0.244241i
$209$	−1.88947e38			−0.0682107
$210$	9.62086e38	+	9.26353e39i	0.320248	+	3.08353i
$211$		−	4.78878e39i		−	1.47036i	−0.677873	−	0.735179i	$-0.737098\pi$
$211$		−	4.78878e39i		−	1.47036i	0.677873	−	0.735179i	$-0.262902\pi$
$212$	−2.90702e39	+	6.10416e38i	−0.823643	+	0.172948i
$213$	1.07636e39			0.281517
$214$	−5.37832e39	+	5.58578e38i	−1.29901	+	0.134912i
$215$			1.59864e38i			0.0356695i
$216$	5.03698e39	−	1.61603e39i	1.03862	−	0.333224i
$217$	8.43165e39			1.60730
$218$	−9.52057e38	−	9.16696e39i	−0.167843	−	1.61609i
$219$		−	8.11707e37i		−	0.0132388i
$220$	−1.64512e38	−	7.83466e38i	−0.0248320	−	0.118259i
$221$	3.90450e39			0.545628
$222$	2.32453e40	−	2.41420e39i	3.00839	−	0.312444i
$223$		−	5.39721e38i		−	0.0647123i	−0.999476	−	0.0323561i	$-0.989699\pi$
$223$		−	5.39721e38i		−	0.0647123i	0.999476	−	0.0323561i	$-0.0103011\pi$
$224$	−8.97656e39	+	5.10907e39i	−0.997455	+	0.567709i
$225$	−2.80887e40			−2.89354
$226$	−6.68163e38	−	6.43346e39i	−0.0638321	−	0.614612i
$227$			1.80384e40i			1.59867i	0.600884	+	0.799336i	$0.294815\pi$
$227$			1.80384e40i			1.59867i	−0.600884	+	0.799336i	$0.705185\pi$
$228$	−1.81436e40	+	3.80978e39i	−1.49221	+	0.313334i
$229$	−1.33372e40			−1.01826			−0.509132	−	0.860689i	$-0.670033\pi$
$229$	−1.33372e40			−1.01826			−0.509132	+	0.860689i	$0.670033\pi$
$230$	6.55802e39	−	6.81098e38i	0.464942	−	0.0482877i
$231$			2.07989e39i			0.136973i
$232$	8.35286e37	+	2.60348e38i	0.00511140	+	0.0159316i
$233$	1.89032e40			1.07519			0.537595	−	0.843203i	$-0.319333\pi$
$233$	1.89032e40			1.07519			0.537595	+	0.843203i	$0.319333\pi$
$234$	−1.97821e39	−	1.90474e40i	−0.104617	−	1.00732i
$235$			7.76905e39i			0.382133i
$236$	1.74649e39	+	8.31741e39i	0.0799211	+	0.380613i
$237$	2.07508e40			0.883718
$238$	−2.58734e40	+	2.68714e39i	−1.02576	+	0.106533i
$239$		−	1.09441e40i		−	0.404032i	−0.979382	−	0.202016i	$-0.935251\pi$
$239$		−	1.09441e40i		−	0.404032i	0.979382	−	0.202016i	$-0.0647493\pi$
$240$	−3.15944e40	−	7.19150e40i	−1.08647	−	2.47302i
$241$	3.17221e39			0.101642			0.0508209	−	0.998708i	$-0.483816\pi$
$241$	3.17221e39			0.101642			0.0508209	+	0.998708i	$0.483816\pi$
$242$	3.44068e39	+	3.31289e40i	0.102750	+	0.989340i
$243$			3.25025e40i			0.904919i
$244$	5.51989e40	−	1.15906e40i	1.43319	−	0.300940i
$245$	−2.16593e40			−0.524590
$246$	9.17864e40	−	9.53270e39i	2.07435	−	0.215436i
$247$			2.68732e40i			0.566854i
$248$	−6.77132e40	+	2.17247e40i	−1.33351	+	0.427834i
$249$	4.51226e40			0.829860
$250$	7.30815e39	+	7.03672e40i	0.125553	+	1.20890i
$251$		−	8.57401e40i		−	1.37636i	−0.725542	−	0.688178i	$-0.758411\pi$
$251$		−	8.57401e40i		−	1.37636i	0.725542	−	0.688178i	$-0.241589\pi$
$252$	2.62175e40	+	1.24857e41i	0.393353	+	1.87329i
$253$	1.47243e39			0.0206532
$254$	4.13236e39	−	4.29176e38i	0.0542032	−	0.00562940i
$255$		−	1.97825e41i		−	2.42716i
$256$	5.89254e40	−	6.41588e40i	0.676430	−	0.736507i
$257$	−1.14975e41			−1.23521			−0.617605	−	0.786489i	$-0.711897\pi$
$257$	−1.14975e41			−1.23521			−0.617605	+	0.786489i	$0.711897\pi$
$258$	3.61863e38	+	3.48423e39i	0.00363923	+	0.0350406i
$259$			2.25689e41i			2.12527i
$260$	−1.11429e41	+	2.33979e40i	−0.982773	+	0.206362i
$261$	3.37730e39			0.0279049
$262$	−1.50994e41	+	1.56819e40i	−1.16907	+	0.121416i
$263$		−	1.99068e41i		−	1.44462i	−0.691568	−	0.722311i	$-0.743080\pi$
$263$		−	1.99068e41i		−	1.44462i	0.691568	−	0.722311i	$-0.256920\pi$
$264$	−5.35896e39	−	1.67032e40i	−0.0364598	−	0.113641i
$265$	2.18153e41			1.39181
$266$	−1.84946e40	−	1.78077e41i	−0.110677	−	1.06566i
$267$			1.31828e41i			0.740142i
$268$	5.83881e40	+	2.78065e41i	0.307633	+	1.46506i
$269$	−2.09332e41			−1.03526			−0.517628	−	0.855606i	$-0.673185\pi$
$269$	−2.09332e41			−1.03526			−0.517628	+	0.855606i	$0.673185\pi$
$270$	−3.86419e41	+	4.01325e40i	−1.79421	+	0.186342i
$271$		−	3.60826e41i		−	1.57333i	−0.617380	−	0.786665i	$-0.711806\pi$
$271$		−	3.60826e41i		−	1.57333i	0.617380	−	0.786665i	$-0.288194\pi$
$272$	2.00861e41	−	8.82445e40i	0.822669	−	0.361423i
$273$	2.95814e41			1.13829
$274$	−1.00241e40	−	9.65175e40i	−0.0362480	−	0.349017i
$275$			3.72966e40i			0.126769i
$276$	1.41390e41	−	2.96890e40i	0.451818	−	0.0948727i
$277$	−4.51616e41			−1.35710			−0.678552	−	0.734552i	$-0.737392\pi$
$277$	−4.51616e41			−1.35710			−0.678552	+	0.734552i	$0.737392\pi$
$278$	2.39255e41	−	2.48484e40i	0.676239	−	0.0702324i
$279$			8.78391e41i			2.33570i
$280$	7.22291e41	−	2.31736e41i	1.80728	−	0.579837i
$281$	−5.75868e41			−1.35617			−0.678087	−	0.734982i	$-0.737191\pi$
$281$	−5.75868e41			−1.35617			−0.678087	+	0.734982i	$0.737191\pi$
$282$	1.75858e40	+	1.69326e41i	0.0389876	+	0.375395i
$283$			1.78979e41i			0.373623i	0.982396	+	0.186811i	$0.0598154\pi$
$283$			1.78979e41i			0.373623i	−0.982396	+	0.186811i	$0.940185\pi$
$284$	−1.80155e40	−	8.57964e40i	−0.0354189	−	0.168677i
$285$	1.36156e42			2.52158
$286$	−2.52914e40	+	2.62670e39i	−0.0441317	+	0.00458340i
$287$			8.91156e41i			1.46542i
$288$	−5.32252e41	−	9.35158e41i	−0.824982	−	1.44948i
$289$	−1.31793e41			−0.192588
$290$	−2.07435e39	−	1.99730e40i	−0.00285835	−	0.0275219i
$291$		−	1.00819e42i		−	1.31027i
$292$	−6.47010e39	+	1.35859e39i	−0.00793237	+	0.00166564i
$293$	1.10807e41			0.128179			0.0640897	−	0.997944i	$-0.479586\pi$
$293$	1.10807e41			0.128179			0.0640897	+	0.997944i	$0.479586\pi$
$294$	−4.72062e41	+	4.90272e40i	−0.515341	+	0.0535220i
$295$		−	6.24167e41i		−	0.643171i
$296$	−5.81502e41	−	1.81247e42i	−0.565708	−	1.76324i
$297$	−8.67604e40			−0.0797006
$298$	4.20434e40	+	4.04818e41i	0.0364772	+	0.351223i
$299$		−	2.09419e41i		−	0.171635i
$300$	7.52020e41	+	3.58139e42i	0.582328	+	2.77326i
$301$	−3.38284e40			−0.0247543
$302$	−2.29407e42	+	2.38256e41i	−1.58668	+	0.164788i
$303$			1.41483e42i			0.925078i
$304$	6.07354e41	+	1.38245e42i	0.375483	+	0.854672i
$305$	−4.14231e42			−2.42184
$306$	−2.79941e41	−	2.69543e42i	−0.154811	−	1.49061i
$307$		−	3.26983e41i		−	0.171070i	−0.996335	−	0.0855348i	$-0.972740\pi$
$307$		−	3.26983e41i		−	0.171070i	0.996335	−	0.0855348i	$-0.0272599\pi$
$308$	1.65787e41	−	3.48120e40i	0.0820709	−	0.0172332i
$309$	1.83246e42			0.858499
$310$	5.19472e42	−	5.39510e41i	2.30363	−	0.239249i
$311$		−	8.13026e41i		−	0.341333i	−0.985329	−	0.170666i	$-0.945408\pi$
$311$		−	8.13026e41i		−	0.341333i	0.985329	−	0.170666i	$-0.0545920\pi$
$312$	−2.37564e42	+	7.62185e41i	−0.944391	+	0.302993i
$313$	2.44411e42			0.920169			0.460085	−	0.887875i	$-0.347819\pi$
$313$	2.44411e42			0.920169			0.460085	+	0.887875i	$0.347819\pi$
$314$	4.53946e41	+	4.37086e42i	0.161883	+	1.55870i
$315$		−	9.36973e42i		−	3.16554i
$316$	−3.47316e41	−	1.65405e42i	−0.111185	−	0.529501i
$317$	−2.90983e42			−0.882797			−0.441398	−	0.897311i	$-0.645517\pi$
$317$	−2.90983e42			−0.882797			−0.441398	+	0.897311i	$0.645517\pi$
$318$	4.75463e42	−	4.93804e41i	1.36728	−	0.142002i
$319$		−	4.48442e39i		−	0.00122255i
$320$	−5.20352e42	+	3.72206e42i	−1.34508	+	0.962130i
$321$	8.70172e42			2.13314
$322$	1.44126e41	+	1.38772e42i	0.0335113	+	0.322666i
$323$			3.80288e42i			0.838821i
$324$	−5.32071e41	+	1.11724e41i	−0.111354	+	0.0233820i
$325$	5.30455e42			1.05349
$326$	−2.49880e42	+	2.59519e41i	−0.471013	+	0.0489182i
$327$			1.48315e43i			2.65382i
$328$	−2.29612e42	−	7.15672e42i	−0.390067	−	1.21579i
$329$	−1.64399e42			−0.265197
$330$	1.33084e41	+	1.28141e42i	0.0203887	+	0.196314i
$331$			2.42690e42i			0.353164i	0.984286	+	0.176582i	$0.0565040\pi$
$331$			2.42690e42i			0.353164i	−0.984286	+	0.176582i	$0.943496\pi$
$332$	−7.55236e41	−	3.59671e42i	−0.104408	−	0.497231i
$333$	−2.35118e43			−3.08840
$334$	−1.84514e42	+	1.91631e41i	−0.230324	+	0.0239208i
$335$		−	2.08670e43i		−	2.47570i
$336$	1.52178e43	−	6.68562e42i	1.71626	−	0.754004i
$337$	3.19895e42			0.343004			0.171502	−	0.985184i	$-0.445138\pi$
$337$	3.19895e42			0.343004			0.171502	+	0.985184i	$0.445138\pi$
$338$	−6.39606e41	−	6.15850e42i	−0.0652122	−	0.627901i
$339$			1.04089e43i			1.00927i
$340$	−1.57686e43	+	3.31109e42i	−1.45429	+	0.305372i
$341$	1.16634e42			0.102329
$342$	1.85517e43	−	1.92673e42i	1.54860	−	0.160833i
$343$			9.86540e42i			0.783636i
$344$	2.71671e41	−	8.71611e40i	0.0205376	−	0.00658915i
$345$	−1.06104e43			−0.763495
$346$	−6.42819e41	−	6.18944e42i	−0.0440347	−	0.423992i
$347$			3.61215e42i			0.235594i	0.993038	+	0.117797i	$0.0375833\pi$
$347$			3.61215e42i			0.235594i	−0.993038	+	0.117797i	$0.962417\pi$
$348$	−9.04205e40	−	4.30615e41i	−0.00561591	−	0.0267450i
$349$	1.15456e43			0.682944			0.341472	−	0.939892i	$-0.389075\pi$
$349$	1.15456e43			0.682944			0.341472	+	0.939892i	$0.389075\pi$
$350$	−3.51509e43	+	3.65068e42i	−1.98052	+	0.205692i
$351$			1.23396e43i			0.662339i
$352$	−1.24172e42	+	7.06731e41i	−0.0635034	+	0.0361434i
$353$	8.70904e42			0.424425			0.212212	−	0.977224i	$-0.431933\pi$
$353$	8.70904e42			0.424425			0.212212	+	0.977224i	$0.431933\pi$
$354$	−1.41284e42	−	1.36037e43i	−0.0656204	−	0.631831i
$355$			6.43845e42i			0.285036i
$356$	1.05080e43	−	2.20646e42i	0.443474	−	0.0931206i
$357$	4.18612e43			1.68443
$358$	4.00540e43	−	4.15990e42i	1.53686	−	0.159614i
$359$		−	1.14073e42i		−	0.0417423i	−0.999782	−	0.0208712i	$-0.993356\pi$
$359$		−	1.14073e42i		−	0.0417423i	0.999782	−	0.0208712i	$-0.00664398\pi$
$360$	2.41417e43	+	7.52467e43i	0.842608	+	2.62630i
$361$	3.86087e42			0.128547
$362$	−2.00975e42	−	1.93511e43i	−0.0638406	−	0.614695i
$363$		−	5.36001e43i		−	1.62462i
$364$	−4.95118e42	−	2.35793e43i	−0.143214	−	0.682036i
$365$	4.85539e41			0.0134043
$366$	−9.02815e43	+	9.37640e42i	−2.37914	+	0.247091i
$367$		−	6.00896e43i		−	1.51174i	−0.654723	−	0.755869i	$-0.727215\pi$
$367$		−	6.00896e43i		−	1.51174i	0.654723	−	0.755869i	$-0.272785\pi$
$368$	−4.73301e42	−	1.07732e43i	−0.113691	−	0.258782i
$369$	−9.28386e43			−2.12951
$370$	1.44410e43	+	1.39046e44i	0.316350	+	3.04600i
$371$			4.61628e43i			0.965908i
$372$	1.11997e44	−	2.35172e43i	2.23861	−	0.470062i
$373$	2.47052e42			0.0471779			0.0235890	−	0.999722i	$-0.492491\pi$
$373$	2.47052e42			0.0471779			0.0235890	+	0.999722i	$0.492491\pi$
$374$	−3.57903e42	+	3.71709e41i	−0.0653053	+	0.00678244i
$375$		−	1.13849e44i		−	1.98517i
$376$	1.32026e43	−	4.23584e42i	0.220022	−	0.0705905i
$377$	−6.37803e41			−0.0101598
$378$	−8.49233e42	−	8.17691e43i	−0.129320	−	1.24517i
$379$			1.32050e44i			1.92252i	0.275638	+	0.961262i	$0.411111\pi$
$379$			1.32050e44i			1.92252i	−0.275638	+	0.961262i	$0.588889\pi$
$380$	−2.27890e43	−	1.08529e44i	−0.317251	−	1.51087i
$381$	−6.68585e42			−0.0890086
$382$	−1.36540e44	+	1.41807e43i	−1.73853	+	0.180559i
$383$		−	2.07993e43i		−	0.253321i	−0.991946	−	0.126660i	$-0.959574\pi$
$383$		−	2.07993e43i		−	0.253321i	0.991946	−	0.126660i	$-0.0404258\pi$
$384$	−1.04985e44	+	9.29006e43i	−1.22320	+	1.08240i
$385$	−1.24412e43			−0.138686
$386$	8.58536e42	+	8.26648e43i	0.0915744	+	0.881732i
$387$		−	3.52417e42i		−	0.0359725i
$388$	−8.03625e43	+	1.68745e43i	−0.785080	+	0.164851i
$389$	9.03500e43			0.844861			0.422430	−	0.906395i	$-0.361177\pi$
$389$	9.03500e43			0.844861			0.422430	+	0.906395i	$0.361177\pi$
$390$	1.82250e44	−	1.89281e43i	1.63144	−	0.169437i
$391$		−	2.96352e43i		−	0.253982i
$392$	1.18091e43	+	3.68074e43i	0.0969064	+	0.302045i
$393$	2.44298e44			1.91976
$394$	−1.50665e43	−	1.45069e44i	−0.113391	−	1.09179i
$395$			1.24125e44i			0.894766i
$396$	3.62664e42	+	1.72714e43i	0.0250430	+	0.119264i
$397$	−1.62654e44			−1.07603			−0.538016	−	0.842935i	$-0.680826\pi$
$397$	−1.62654e44			−1.07603			−0.538016	+	0.842935i	$0.680826\pi$
$398$	1.85292e44	−	1.92440e43i	1.17448	−	0.121978i
$399$			2.88115e44i			1.74996i
$400$	2.72885e44	−	1.19887e44i	1.58840	−	0.697832i
$401$	−2.42530e44			−1.35304			−0.676520	−	0.736424i	$-0.736513\pi$
$401$	−2.42530e44			−1.35304			−0.676520	+	0.736424i	$0.736513\pi$
$402$	−4.72338e43	−	4.54795e44i	−0.252587	−	2.43205i
$403$		−	1.65884e44i		−	0.850392i
$404$	1.12776e44	−	2.36806e43i	0.554283	−	0.116388i
$405$	3.99284e43			0.188168
$406$	4.22644e42	−	4.38947e41i	0.0190999	−	0.00198367i
$407$			3.12193e43i			0.135306i
$408$	−3.36181e44	+	1.07858e44i	−1.39749	+	0.448364i
$409$	4.56218e43			0.181918			0.0909592	−	0.995855i	$-0.471007\pi$
$409$	4.56218e43			0.181918			0.0909592	+	0.995855i	$0.471007\pi$
$410$	5.70217e43	+	5.49038e44i	0.218130	+	2.10028i
$411$			1.56158e44i			0.573130i
$412$	−3.06706e43	−	1.46065e44i	−0.108012	−	0.514390i
$413$	1.32078e44			0.446355
$414$	−1.44570e44	+	1.50147e43i	−0.468892	+	0.0486979i
$415$			2.69910e44i			0.840235i
$416$	1.00516e44	+	1.76605e44i	0.300364	+	0.527734i
$417$	−3.87097e44			−1.11047
$418$	−2.55833e42	−	2.46331e43i	−0.00704629	−	0.0678458i
$419$		−	6.27056e44i		−	1.65832i	−0.559012	−	0.829159i	$-0.688820\pi$
$419$		−	6.27056e44i		−	1.65832i	0.559012	−	0.829159i	$-0.311180\pi$
$420$	−1.19467e45	+	2.50856e44i	−3.03395	+	0.637069i
$421$	−2.75086e43			−0.0670922			−0.0335461	−	0.999437i	$-0.510680\pi$
$421$	−2.75086e43			−0.0670922			−0.0335461	+	0.999437i	$0.510680\pi$
$422$	6.24317e44	−	6.48399e43i	1.46249	−	0.151891i
$423$		−	1.71267e44i		−	0.385379i
$424$	−1.18941e44	−	3.70726e44i	−0.257107	−	0.801371i
$425$	7.50657e44			1.55894
$426$	1.45739e43	+	1.40326e44i	0.0290812	+	0.280010i
$427$		−	8.76544e44i		−	1.68074i
$428$	−1.45645e44	−	6.93612e44i	−0.268380	−	1.27812i
$429$	4.09196e43			0.0724699
$430$	−2.08416e43	+	2.16455e42i	−0.0354787	+	0.00368472i
$431$			1.80452e44i			0.295289i	0.989041	+	0.147644i	$0.0471691\pi$
$431$			1.80452e44i			0.295289i	−0.989041	+	0.147644i	$0.952831\pi$
$432$	2.78884e44	+	6.34793e44i	0.438732	+	0.998639i
$433$	−8.56237e44			−1.29509			−0.647545	−	0.762027i	$-0.724204\pi$
$433$	−8.56237e44			−1.29509			−0.647545	+	0.762027i	$0.724204\pi$
$434$	1.14164e44	+	1.09924e45i	0.166037	+	1.59870i
$435$			3.23149e43i			0.0451944i
$436$	1.18221e45	−	2.48241e44i	1.59010	−	0.333890i
$437$	2.03968e44			0.263862
$438$	1.05823e43	−	1.09905e42i	0.0131680	−	0.00136759i
$439$			8.25296e44i			0.987899i	0.869491	+	0.493950i	$0.164447\pi$
$439$			8.25296e44i			0.987899i	−0.869491	+	0.493950i	$0.835553\pi$
$440$	9.99136e43	−	3.20557e43i	0.115061	−	0.0369156i
$441$	4.77474e44			0.529046
$442$	5.28668e43	+	5.09033e44i	0.0563644	+	0.542709i
$443$		−	7.97531e44i		−	0.818247i	−0.912479	−	0.409123i	$-0.865835\pi$
$443$		−	7.97531e44i		−	0.818247i	0.912479	−	0.409123i	$-0.134165\pi$
$444$	6.29481e44	+	2.99782e45i	0.621545	+	2.96002i
$445$	−7.88553e44			−0.749395
$446$	7.03638e43	−	7.30781e42i	0.0643661	−	0.00668489i
$447$		−	6.54966e44i		−	0.576754i
$448$	−7.87616e44	−	1.10110e45i	−0.667710	−	0.933474i
$449$	−1.36824e44			−0.111679			−0.0558397	−	0.998440i	$-0.517784\pi$
$449$	−1.36824e44			−0.111679			−0.0558397	+	0.998440i	$0.517784\pi$
$450$	−3.80320e44	−	3.66195e45i	−0.298907	−	2.87806i
$451$			1.23272e44i			0.0932963i
$452$	8.29689e44	−	1.74218e44i	0.604730	−	0.126981i
$453$	3.71163e45			2.60553
$454$	−2.35169e45	+	2.44240e44i	−1.59012	+	0.165146i
$455$			1.76947e45i			1.15252i
$456$	−7.42347e44	−	2.31381e45i	−0.465806	−	1.45186i
$457$	−1.30271e45			−0.787541			−0.393771	−	0.919209i	$-0.628830\pi$
$457$	−1.30271e45			−0.787541			−0.393771	+	0.919209i	$0.628830\pi$
$458$	−1.80585e44	−	1.73878e45i	−0.105188	−	1.01282i
$459$			1.74620e45i			0.980118i
$460$	1.77591e44	+	8.45751e44i	0.0960588	+	0.457467i
$461$	5.55467e44			0.289563			0.144781	−	0.989464i	$-0.453752\pi$
$461$	5.55467e44			0.289563			0.144781	+	0.989464i	$0.453752\pi$
$462$	−2.71156e44	+	2.81616e43i	−0.136240	+	0.0141496i
$463$			7.65090e44i			0.370540i	0.982688	+	0.185270i	$0.0593160\pi$
$463$			7.65090e44i			0.370540i	−0.982688	+	0.185270i	$0.940684\pi$
$464$	−3.28109e43	+	1.44148e43i	−0.0153183	+	0.00672981i
$465$	−8.40467e45			−3.78286
$466$	2.55949e44	+	2.46443e45i	0.111069	+	1.06944i
$467$			2.24354e45i			0.938744i	0.883001	+	0.469372i	$0.155520\pi$
$467$			2.24354e45i			0.938744i	−0.883001	+	0.469372i	$0.844480\pi$
$468$	2.45644e45	−	5.15803e44i	0.991121	−	0.208115i
$469$	4.41561e45			1.71812
$470$	−1.01286e45	+	1.05193e44i	−0.380088	+	0.0394750i
$471$		−	7.07173e45i		−	2.55959i
$472$	−1.06070e45	+	3.40308e44i	−0.370321	+	0.118812i
$473$	−4.67944e42			−0.00157599
$474$	2.80966e44	+	2.70530e45i	0.0912897	+	0.878991i
$475$			5.16649e45i			1.61959i
$476$	−7.00650e44	−	3.33675e45i	−0.211925	−	1.00927i
$477$	−4.80914e45			−1.40364
$478$	1.42679e45	−	1.48183e44i	0.401870	−	0.0417372i
$479$			1.65174e45i			0.448991i	0.974475	+	0.224496i	$0.0720734\pi$
$479$			1.65174e45i			0.448991i	−0.974475	+	0.224496i	$0.927927\pi$
$480$	8.94783e45	−	5.09272e45i	2.34756	−	1.33613i
$481$	4.44020e45			1.12444
$482$	4.29516e43	+	4.13563e44i	0.0104998	+	0.101098i
$483$		−	2.24524e45i		−	0.529860i
$484$	−4.27245e45	+	8.97128e44i	−0.973432	+	0.204401i
$485$	6.03068e45			1.32665
$486$	−4.23737e45	+	4.40083e44i	−0.900078	+	0.0934798i
$487$			8.49985e44i			0.174349i	0.996193	+	0.0871744i	$0.0277837\pi$
$487$			8.49985e44i			0.174349i	−0.996193	+	0.0871744i	$0.972216\pi$
$488$	2.25847e45	+	7.03938e45i	0.447381	+	1.39443i
$489$	4.04288e45			0.773464
$490$	−2.93266e44	−	2.82373e45i	−0.0541911	−	0.521784i
$491$		−	8.82246e45i		−	1.57472i	−0.616491	−	0.787362i	$-0.711446\pi$
$491$		−	8.82246e45i		−	1.57472i	0.616491	−	0.787362i	$-0.288554\pi$
$492$	2.48557e45	+	1.18372e46i	0.428568	+	2.04100i
$493$	−9.02567e43			−0.0150342
$494$	−3.50348e45	+	3.63862e44i	−0.563821	+	0.0585570i
$495$		−	1.29610e45i		−	0.201535i
$496$	−3.74910e45	−	8.53367e45i	−0.563298	−	1.28218i
$497$	−1.36242e45			−0.197813
$498$	6.10958e44	+	5.88266e45i	0.0857260	+	0.825420i
$499$			2.36768e44i			0.0321080i	0.999871	+	0.0160540i	$0.00511037\pi$
$499$			2.36768e44i			0.0321080i	−0.999871	+	0.0160540i	$0.994890\pi$
$500$	−9.07487e45	+	1.90554e45i	−1.18946	+	0.249763i
$501$	2.98530e45			0.378221
$502$	1.11780e46	−	1.16092e45i	1.36899	−	0.142180i
$503$		−	1.55121e46i		−	1.83661i	−0.395877	−	0.918303i	$-0.629559\pi$
$503$		−	1.55121e46i		−	1.83661i	0.395877	−	0.918303i	$-0.370441\pi$
$504$	−1.59228e46	+	5.10856e45i	−1.82263	+	0.584763i
$505$	−8.46306e45			−0.936643
$506$	1.99367e43	+	1.91962e44i	0.00213351	+	0.0205427i
$507$			9.96400e45i			1.03109i
$508$	1.11904e44	+	5.32928e44i	0.0111986	+	0.0533317i
$509$	−1.31229e46			−1.27007			−0.635033	−	0.772485i	$-0.719014\pi$
$509$	−1.31229e46			−1.27007			−0.635033	+	0.772485i	$0.719014\pi$
$510$	2.57906e46	−	2.67855e45i	2.41417	−	0.250730i
$511$			1.02744e44i			0.00930250i
$512$	9.16228e45	+	6.81344e45i	0.802443	+	0.596729i
$513$	−1.20184e46			−1.01825
$514$	−1.55676e45	−	1.49894e46i	−0.127599	−	1.22860i
$515$			1.09612e46i			0.869231i
$516$	−4.49342e44	+	9.43527e43i	−0.0344772	+	0.00723952i
$517$	−2.27411e44			−0.0168839
$518$	−2.94232e46	+	3.05582e45i	−2.11390	+	0.219544i
$519$			1.00140e46i			0.696249i
$520$	−4.55916e45	−	1.42103e46i	−0.306781	−	0.956198i
$521$	−8.37325e45			−0.545321			−0.272661	−	0.962110i	$-0.587904\pi$
$521$	−8.37325e45			−0.545321			−0.272661	+	0.962110i	$0.587904\pi$
$522$	4.57285e43	+	4.40301e44i	0.00288263	+	0.0277556i
$523$		−	7.95006e44i		−	0.0485111i	−0.999706	−	0.0242556i	$-0.992278\pi$
$523$		−	7.95006e44i		−	0.0485111i	0.999706	−	0.0242556i	$-0.00772154\pi$
$524$	−4.08892e45	−	1.94729e46i	−0.241533	−	1.15027i
$525$	5.68716e46			3.25227
$526$	2.59527e46	−	2.69538e45i	1.43689	−	0.149232i
$527$		−	2.34746e46i		−	1.25840i
$528$	2.10505e45	−	9.24813e44i	0.109266	−	0.0480040i
$529$	1.83056e46			0.920107
$530$	2.95379e45	+	2.84408e46i	0.143777	+	1.38437i
$531$			1.37596e46i			0.648635i
$532$	2.29656e46	−	4.82231e45i	1.04853	−	0.220170i
$533$	1.75326e46			0.775324
$534$	−1.71865e46	+	1.78494e45i	−0.736183	+	0.0764580i
$535$			5.20511e46i			2.15981i
$536$	−3.54610e46	+	1.13771e46i	−1.42544	+	0.457331i
$537$	−6.48044e46			−2.52372
$538$	−2.83435e45	−	2.72908e46i	−0.106944	−	1.02972i
$539$		−	6.33996e44i		−	0.0231781i
$540$	−1.04642e46	−	4.98343e46i	−0.370691	−	1.76537i
$541$	2.35719e46			0.809172			0.404586	−	0.914500i	$-0.367416\pi$
$541$	2.35719e46			0.809172			0.404586	+	0.914500i	$0.367416\pi$
$542$	4.70412e46	−	4.88557e45i	1.56491	−	0.162528i
$543$			3.13086e46i			1.00941i
$544$	1.42242e46	+	2.49916e46i	0.444473	+	0.780932i
$545$	−8.87173e46			−2.68700
$546$	4.00532e45	+	3.85656e46i	0.117588	+	1.13220i
$547$		−	2.01154e45i		−	0.0572458i	−0.999590	−	0.0286229i	$-0.990888\pi$
$547$		−	2.01154e45i		−	0.0572458i	0.999590	−	0.0286229i	$-0.00911220\pi$
$548$	1.24473e46	−	2.61369e45i	0.343405	−	0.0721081i
$549$	9.13164e46			2.44241
$550$	−4.86238e45	+	5.04994e44i	−0.126091	+	0.0130955i
$551$		−	6.21203e44i		−	0.0156191i
$552$	5.78499e45	+	1.80311e46i	0.141039	+	0.439601i
$553$	−2.62658e46			−0.620960
$554$	−6.11487e45	−	5.88775e46i	−0.140191	−	1.34984i
$555$		−	2.24967e47i		−	5.00193i
$556$	6.47902e45	+	3.08555e46i	0.139713	+	0.665366i
$557$	−5.78141e46			−1.20919			−0.604596	−	0.796532i	$-0.706666\pi$
$557$	−5.78141e46			−1.20919			−0.604596	+	0.796532i	$0.706666\pi$
$558$	−1.14517e47	+	1.18934e46i	−2.32320	+	0.241282i
$559$			6.65540e44i			0.0130970i
$560$	3.99913e46	+	9.10280e46i	0.763431	+	1.73771i
$561$	5.79061e45			0.107240
$562$	−7.79723e45	−	7.50763e46i	−0.140095	−	1.34892i
$563$			6.83448e46i			1.19141i	0.803202	+	0.595707i	$0.203128\pi$
$563$			6.83448e46i			1.19141i	−0.803202	+	0.595707i	$0.796872\pi$
$564$	−2.18370e46	+	4.58534e45i	−0.369359	+	0.0775580i
$565$	−6.22627e46			−1.02189
$566$	−2.33337e46	+	2.42338e45i	−0.371624	+	0.0385959i
$567$			8.44915e45i			0.130587i
$568$	1.09414e46	−	3.51037e45i	0.164116	−	0.0526541i
$569$	1.34395e47			1.95648			0.978238	−	0.207487i	$-0.0665285\pi$
$569$	1.34395e47			1.95648			0.978238	+	0.207487i	$0.0665285\pi$
$570$	1.84354e46	+	1.77507e47i	0.260484	+	2.50809i
$571$			1.33995e47i			1.83770i	0.394613	+	0.918848i	$0.370879\pi$
$571$			1.33995e47i			1.83770i	−0.394613	+	0.918848i	$0.629121\pi$
$572$	−6.84890e44	−	3.26169e45i	−0.00911776	−	0.0434221i
$573$	2.20911e47			2.85489
$574$	−1.16181e47	+	1.20662e46i	−1.45758	+	0.151380i
$575$		−	4.02616e46i		−	0.490386i
$576$	1.14711e47	−	8.20521e46i	1.35650	−	0.970303i
$577$	−1.11421e47			−1.27932			−0.639658	−	0.768660i	$-0.720924\pi$
$577$	−1.11421e47			−1.27932			−0.639658	+	0.768660i	$0.720924\pi$
$578$	−1.78448e45	−	1.71820e46i	−0.0198947	−	0.191558i
$579$		−	1.33746e47i		−	1.44792i
$580$	2.57581e45	−	5.40868e44i	0.0270793	−	0.00568611i
$581$	−5.71149e46			−0.583116
$582$	1.31438e47	−	1.36508e46i	1.30326	−	0.135353i
$583$			6.38564e45i			0.0614949i
$584$	−2.64726e44	−	8.25117e44i	−0.00247615	−	0.00771787i
$585$	−1.84340e47			−1.67482
$586$	1.50033e45	+	1.44460e46i	0.0132412	+	0.127494i
$587$		−	2.05485e47i		−	1.76170i	−0.473396	−	0.880850i	$-0.656972\pi$
$587$		−	2.05485e47i		−	1.76170i	0.473396	−	0.880850i	$-0.343028\pi$
$588$	−1.27834e46	−	6.08793e46i	−0.106471	−	0.507055i
$589$	1.61567e47			1.30735
$590$	8.13731e46	−	8.45120e45i	0.639730	−	0.0664407i
$591$			2.34711e47i			1.79286i
$592$	2.28420e47	−	1.00352e47i	1.69537	−	0.744827i
$593$	9.27065e46			0.668622			0.334311	−	0.942463i	$-0.391496\pi$
$593$	9.27065e46			0.668622			0.334311	+	0.942463i	$0.391496\pi$
$594$	−1.17473e45	−	1.13110e46i	−0.00823322	−	0.0792742i
$595$			2.50401e47i			1.70549i
$596$	−5.22072e46	+	1.09625e46i	−0.345576	+	0.0725640i
$597$	−2.99789e47			−1.92865
$598$	2.73021e46	−	2.83552e45i	0.170716	−	0.0177302i
$599$		−	2.31249e47i		−	1.40548i	−0.711447	−	0.702739i	$-0.751960\pi$
$599$		−	2.31249e47i		−	1.40548i	0.711447	−	0.702739i	$-0.248040\pi$
$600$	−4.56726e47	+	1.46533e47i	−2.69827	+	0.865695i
$601$	−1.47577e47			−0.847524			−0.423762	−	0.905774i	$-0.639291\pi$
$601$	−1.47577e47			−0.847524			−0.423762	+	0.905774i	$0.639291\pi$
$602$	−4.58036e44	−	4.41024e45i	−0.00255717	−	0.0246219i
$603$			4.60009e47i			2.49673i
$604$	−6.21232e46	−	2.95853e47i	−0.327813	−	1.56116i
$605$	3.20619e47			1.64493
$606$	−1.84452e47	+	1.91567e46i	−0.920129	+	0.0955622i
$607$			2.56506e47i			1.24420i	0.782937	+	0.622101i	$0.213721\pi$
$607$			2.56506e47i			1.24420i	−0.782937	+	0.622101i	$0.786279\pi$
$608$	−1.72008e47	+	9.78996e46i	−0.811312	+	0.461764i
$609$	−6.83806e45			−0.0313646
$610$	−5.60868e46	−	5.40036e47i	−0.250180	−	2.40888i
$611$			3.23438e46i			0.140310i
$612$	3.47616e47	−	7.29922e46i	1.46664	−	0.307966i
$613$	7.32476e46			0.300584			0.150292	−	0.988642i	$-0.451979\pi$
$613$	7.32476e46			0.300584			0.150292	+	0.988642i	$0.451979\pi$
$614$	4.26290e46	−	4.42734e45i	0.170154	−	0.0176718i
$615$		−	8.88304e47i		−	3.44893i
$616$	6.78322e45	+	2.11425e46i	0.0256191	+	0.0798516i
$617$	−2.56029e47			−0.940677			−0.470339	−	0.882486i	$-0.655868\pi$
$617$	−2.56029e47			−0.940677			−0.470339	+	0.882486i	$0.655868\pi$
$618$	2.48114e46	+	2.38899e47i	0.0886845	+	0.853906i
$619$			2.07532e47i			0.721679i	0.932628	+	0.360840i	$0.117510\pi$
$619$			2.07532e47i			0.721679i	−0.932628	+	0.360840i	$0.882490\pi$
$620$	1.40673e47	+	6.69934e47i	0.475939	+	2.26659i
$621$	9.36578e46			0.308309
$622$	1.05995e47	−	1.10083e46i	0.339506	−	0.0352603i
$623$		−	1.66864e47i		−	0.520074i
$624$	−1.31533e47	−	2.99394e47i	−0.398929	−	0.908039i
$625$	9.31919e46			0.275054
$626$	3.30932e46	+	3.18641e47i	0.0950551	+	0.915246i
$627$			3.98546e46i			0.111412i
$628$	−5.63686e47	+	1.18363e47i	−1.53364	+	0.322033i
$629$	6.28341e47			1.66393
$630$	1.22154e48	−	1.26866e47i	3.14860	−	0.327006i
$631$			1.97025e47i			0.494336i	0.968973	+	0.247168i	$0.0794999\pi$
$631$			1.97025e47i			0.494336i	−0.968973	+	0.247168i	$0.920500\pi$
$632$	2.10937e47	−	6.76756e46i	0.515183	−	0.165288i
$633$	−1.01010e48			−2.40160
$634$	−3.93991e46	−	3.79357e47i	−0.0911945	−	0.878074i
$635$		−	3.99927e46i		−	0.0901213i
$636$	1.28755e47	+	6.13179e47i	0.282484	+	1.34529i
$637$	−9.01709e46			−0.192618
$638$	5.84638e44	−	6.07190e43i	0.00121600	−	0.000126291i
$639$		−	1.41934e47i		−	0.287457i
$640$	−5.55703e47	−	6.27991e47i	−1.09593	−	1.23849i
$641$	8.14855e47			1.56493			0.782463	−	0.622697i	$-0.213963\pi$
$641$	8.14855e47			1.56493			0.782463	+	0.622697i	$0.213963\pi$
$642$	1.17821e47	+	1.13445e48i	0.220357	+	2.12173i
$643$		−	4.12336e47i		−	0.751042i	−0.926814	−	0.375521i	$-0.877464\pi$
$643$		−	4.12336e47i		−	0.751042i	0.926814	−	0.375521i	$-0.122536\pi$
$644$	−1.78967e47	+	3.75795e46i	−0.317478	+	0.0666640i
$645$	3.37202e46			0.0582605
$646$	−4.95784e47	+	5.14908e46i	−0.834334	+	0.0866517i
$647$		−	1.64441e47i		−	0.269549i	−0.990876	−	0.134774i	$-0.956969\pi$
$647$		−	1.64441e47i		−	0.269549i	0.990876	−	0.134774i	$-0.0430309\pi$
$648$	−2.17698e46	−	6.78537e46i	−0.0347599	−	0.108342i
$649$	1.82702e46			0.0284174
$650$	7.18235e46	+	6.91558e47i	0.108828	+	1.04786i
$651$		−	1.77849e48i		−	2.62527i
$652$	−6.76675e46	−	3.22257e47i	−0.0973130	−	0.463440i
$653$	1.41867e47			0.198772			0.0993862	−	0.995049i	$-0.468312\pi$
$653$	1.41867e47			0.198772			0.0993862	+	0.995049i	$0.468312\pi$
$654$	−1.93359e48	+	2.00818e47i	−2.63963	+	0.274145i
$655$			1.46132e48i			1.94376i
$656$	9.01938e47	−	3.96249e47i	1.16899	−	0.513573i
$657$	−1.07036e46			−0.0135182
$658$	−2.22595e46	−	2.14328e47i	−0.0273953	−	0.263778i
$659$			1.44200e48i			1.72947i	0.502229	+	0.864735i	$0.332513\pi$
$659$			1.44200e48i			1.72947i	−0.502229	+	0.864735i	$0.667487\pi$
$660$	−1.65257e47	+	3.47006e46i	−0.193158	+	0.0405592i
$661$	1.47944e46			0.0168528			0.00842640	−	0.999964i	$-0.497318\pi$
$661$	1.47944e46			0.0168528			0.00842640	+	0.999964i	$0.497318\pi$
$662$	−3.16397e47	+	3.28602e46i	−0.351274	+	0.0364825i
$663$		−	8.23577e47i		−	0.891198i
$664$	4.58680e47	−	1.47160e47i	0.483785	−	0.155215i
$665$	−1.72342e48			−1.77183
$666$	−3.18349e47	−	3.06525e48i	−0.319037	−	3.07188i
$667$			4.84093e45i			0.00472922i
$668$	−4.99662e46	−	2.37957e47i	−0.0475857	−	0.226620i
$669$	−1.13843e47			−0.105697
$670$	2.72045e48	−	2.82538e47i	2.46246	−	0.255744i
$671$		−	1.21251e47i		−	0.107005i
$672$	1.07766e48	+	1.89343e48i	0.927263	+	1.62919i
$673$	−8.72346e47			−0.731868			−0.365934	−	0.930641i	$-0.619250\pi$
$673$	−8.72346e47			−0.731868			−0.365934	+	0.930641i	$0.619250\pi$
$674$	4.33137e46	+	4.17050e47i	0.0354330	+	0.341169i
$675$			2.37234e48i			1.89240i
$676$	7.94228e47	−	1.66772e47i	0.617805	−	0.129727i
$677$	−1.56860e47			−0.118989			−0.0594944	−	0.998229i	$-0.518949\pi$
$677$	−1.56860e47			−0.118989			−0.0594944	+	0.998229i	$0.518949\pi$
$678$	−1.35701e48	+	1.40936e47i	−1.00387	+	0.104260i
$679$			1.27614e48i			0.920685i
$680$	−6.45175e47	−	2.01093e48i	−0.453969	−	1.41497i
$681$	3.80485e48			2.61118
$682$	1.57922e46	+	1.52057e47i	0.0105708	+	0.101782i
$683$		−	2.11776e48i		−	1.38269i	−0.722526	−	0.691344i	$-0.757019\pi$
$683$		−	2.11776e48i		−	1.38269i	0.722526	−	0.691344i	$-0.242981\pi$
$684$	5.02378e47	+	2.39251e48i	0.319946	+	1.52370i
$685$	−9.34090e47			−0.580295
$686$	−1.28616e48	+	1.33577e47i	−0.779444	+	0.0809510i
$687$			2.81321e48i			1.66317i
$688$	1.50417e46	+	3.42377e46i	0.00867546	+	0.0197470i
$689$	9.08206e47			0.511043
$690$	−1.43664e47	−	1.38328e48i	−0.0788704	−	0.759411i
$691$			6.94015e46i			0.0371742i	0.999827	+	0.0185871i	$0.00591681\pi$
$691$			6.94015e46i			0.0371742i	−0.999827	+	0.0185871i	$0.994083\pi$
$692$	7.98218e47	−	1.67610e47i	0.417175	−	0.0875982i
$693$	2.74265e47			0.139864
$694$	−4.70919e47	+	4.89084e46i	−0.234334	+	0.0243373i
$695$		−	2.31550e48i		−	1.12435i
$696$	5.49154e46	−	1.76187e46i	0.0260218	−	0.00834867i
$697$	2.48107e48			1.14731
$698$	1.56327e47	+	1.50521e48i	0.0705493	+	0.679290i
$699$		−	3.98726e48i		−	1.75616i
$700$	−9.51885e47	−	4.53322e48i	−0.409183	−	1.94868i
$701$	−3.25258e48			−1.36465			−0.682326	−	0.731048i	$-0.739031\pi$
$701$	−3.25258e48			−1.36465			−0.682326	+	0.731048i	$0.739031\pi$
$702$	−1.60872e48	+	1.67078e47i	−0.658795	+	0.0684208i
$703$			4.32463e48i			1.72866i
$704$	−1.08950e47	−	1.52314e47i	−0.0425100	−	0.0594300i
$705$	1.63873e48			0.624154
$706$	1.17920e47	+	1.13540e48i	0.0438438	+	0.422154i
$707$		−	1.79085e48i		−	0.650023i
$708$	1.75439e48	−	3.68387e47i	0.621672	−	0.130539i
$709$	−4.59663e48			−1.59021			−0.795103	−	0.606475i	$-0.792583\pi$
$709$	−4.59663e48			−1.59021			−0.795103	+	0.606475i	$0.792583\pi$
$710$	−8.39386e47	+	8.71765e46i	−0.283511	+	0.0294447i
$711$		−	2.73632e48i		−	0.902367i
$712$	4.29935e47	+	1.34006e48i	0.138434	+	0.431482i
$713$	−1.25906e48			−0.395845
$714$	5.66800e47	+	5.45748e48i	0.174004	+	1.67542i
$715$			2.44769e47i			0.0733759i
$716$	1.08466e48	+	5.16554e48i	0.317521	+	1.51215i
$717$	−2.30844e48			−0.659923
$718$	1.48718e47	−	1.54454e46i	0.0415190	−	0.00431206i
$719$		−	3.42063e48i		−	0.932642i	−0.884616	−	0.466321i	$-0.845579\pi$
$719$		−	3.42063e48i		−	0.932642i	0.884616	−	0.466321i	$-0.154421\pi$
$720$	−9.48310e48	+	4.16621e48i	−2.52521	+	1.10940i
$721$	−2.31947e48			−0.603239
$722$	5.22761e46	+	5.03345e47i	0.0132792	+	0.127860i
$723$		−	6.69115e47i		−	0.166016i
$724$	2.49560e48	−	5.24026e47i	0.604811	−	0.126998i
$725$	−1.22620e47			−0.0290279
$726$	6.98788e48	−	7.25743e47i	1.61593	−	0.167826i
$727$		−	2.77485e48i		−	0.626838i	−0.949615	−	0.313419i	$-0.898526\pi$
$727$		−	2.77485e48i		−	0.626838i	0.949615	−	0.313419i	$-0.101474\pi$
$728$	3.00701e48	−	9.64752e47i	0.663593	−	0.212903i
$729$	7.38352e48			1.59183
$730$	6.57418e45	+	6.33001e46i	0.00138469	+	0.0133326i
$731$			9.41817e46i			0.0193808i
$732$	−2.44482e48	−	1.16431e49i	−0.491539	−	2.34089i
$733$	7.96409e48			1.56448			0.782238	−	0.622980i	$-0.214078\pi$
$733$	7.96409e48			1.56448			0.782238	+	0.622980i	$0.214078\pi$
$734$	7.83393e48	−	8.13612e47i	1.50365	−	0.156165i
$735$			4.56859e48i			0.856836i
$736$	1.34043e48	−	7.62916e47i	0.245653	−	0.139815i
$737$	6.10806e47			0.109384
$738$	−1.25703e48	−	1.21034e49i	−0.219983	−	2.11812i
$739$			9.63345e48i			1.64750i	0.566950	+	0.823752i	$0.308123\pi$
$739$			9.63345e48i			1.64750i	−0.566950	+	0.823752i	$0.691877\pi$
$740$	−1.79320e49	+	3.76537e48i	−2.99703	+	0.629315i
$741$	5.66837e48			0.925867
$742$	−6.01828e48	+	6.25043e47i	−0.960741	+	0.0997800i
$743$		−	4.64951e48i		−	0.725434i	−0.931899	−	0.362717i	$-0.881849\pi$
$743$		−	4.64951e48i		−	0.725434i	0.931899	−	0.362717i	$-0.118151\pi$
$744$	4.58239e48	+	1.42828e49i	0.698799	+	2.17807i
$745$	3.91781e48			0.583964
$746$	3.34508e46	+	3.22084e47i	0.00487356	+	0.0469255i
$747$		−	5.95010e48i		−	0.847372i
$748$	−9.69200e46	−	4.61569e47i	−0.0134923	−	0.0642553i
$749$	−1.10144e49			−1.49889
$750$	1.48426e49	−	1.54151e48i	1.97455	−	0.205071i
$751$			6.73060e48i			0.875335i	0.899137	+	0.437668i	$0.144195\pi$
$751$			6.73060e48i			0.875335i	−0.899137	+	0.437668i	$0.855805\pi$
$752$	7.30993e47	+	1.66388e48i	0.0929415	+	0.211553i
$753$	−1.80852e49			−2.24806
$754$	−8.63583e45	−	8.31508e46i	−0.00104952	−	0.0101054i
$755$			2.22018e49i			2.63810i
$756$	1.05453e49	−	2.21430e48i	1.22515	−	0.257257i
$757$	9.43888e48			1.07224			0.536118	−	0.844143i	$-0.319890\pi$
$757$	9.43888e48			1.07224			0.536118	+	0.844143i	$0.319890\pi$
$758$	−1.72155e49	+	1.78795e48i	−1.91224	+	0.198600i
$759$		−	3.10581e47i		−	0.0337337i
$760$	1.38405e49	−	4.44050e48i	1.47001	−	0.471629i
$761$	5.37047e48			0.557793			0.278897	−	0.960321i	$-0.410031\pi$
$761$	5.37047e48			0.557793			0.278897	+	0.960321i	$0.410031\pi$
$762$	−9.05262e46	−	8.71639e47i	−0.00919475	−	0.0885324i
$763$		−	1.87732e49i		−	1.86476i
$764$	−3.69749e48	−	1.76088e49i	−0.359187	−	1.71058i
$765$	−2.60863e49			−2.47838
$766$	2.71163e48	−	2.81623e47i	0.251965	−	0.0261685i
$767$		−	2.59851e48i		−	0.236158i
$768$	−1.35330e49	−	1.24291e49i	−1.20297	−	1.10484i
$769$	−3.12310e48			−0.271542			−0.135771	−	0.990740i	$-0.543351\pi$
$769$	−3.12310e48			−0.271542			−0.135771	+	0.990740i	$0.543351\pi$
$770$	−1.68454e47	−	1.62198e48i	−0.0143265	−	0.137944i
$771$			2.42517e49i			2.01752i
$772$	−1.06608e49	+	2.23856e48i	−0.867555	+	0.182169i
$773$	−1.47289e49			−1.17251			−0.586257	−	0.810125i	$-0.699399\pi$
$773$	−1.47289e49			−1.17251			−0.586257	+	0.810125i	$0.699399\pi$
$774$	4.59449e47	−	4.77172e46i	0.0357800	−	0.00371602i
$775$		−	3.18919e49i		−	2.42970i
$776$	−3.28805e48	−	1.02484e49i	−0.245069	−	0.763851i
$777$	4.76046e49			3.47130
$778$	1.22334e48	+	1.17790e49i	0.0872756	+	0.840341i
$779$			1.70762e49i			1.19194i
$780$	4.93533e48	+	2.35038e49i	0.337061	+	1.60521i
$781$	−1.88462e47			−0.0125938
$782$	3.86357e48	−	4.01260e47i	0.252623	−	0.0262368i
$783$		−	2.85243e47i		−	0.0182501i
$784$	−4.63872e48	+	2.03793e48i	−0.290419	+	0.127590i
$785$	4.23009e49			2.59159
$786$	3.30779e48	+	3.18493e49i	0.198314	+	1.90949i
$787$			1.51959e48i			0.0891574i	0.999006	+	0.0445787i	$0.0141945\pi$
$787$			1.51959e48i			0.0891574i	−0.999006	+	0.0445787i	$0.985805\pi$
$788$	1.87088e49	−	3.92847e48i	1.07424	−	0.225568i
$789$	−4.19895e49			−2.35956
$790$	−1.61823e49	+	1.68065e48i	−0.889979	+	0.0924309i
$791$		−	1.31752e49i		−	0.709183i
$792$	−2.20258e48	+	7.06661e47i	−0.116039	+	0.0372291i
$793$	−1.72451e49			−0.889246
$794$	−2.20233e48	−	2.12053e49i	−0.111156	−	1.07028i
$795$		−	4.60151e49i		−	2.27331i
$796$	5.01771e48	+	2.38962e49i	0.242652	+	1.15560i
$797$	2.54943e49			1.20684			0.603422	−	0.797422i	$-0.293804\pi$
$797$	2.54943e49			1.20684			0.603422	+	0.797422i	$0.293804\pi$
$798$	−3.75618e49	+	3.90107e48i	−1.74059	+	0.180773i
$799$			4.57703e48i			0.207629i
$800$	1.93246e49	+	3.39530e49i	0.858183	+	1.50782i
$801$	1.73835e49			0.755761
$802$	−3.28384e48	−	3.16188e49i	−0.139771	−	1.34580i
$803$			1.42124e46i			0.000592247i
$804$	5.86524e49	−	1.23158e49i	2.39295	−	0.502470i
$805$	1.34303e49			0.536484
$806$	2.16264e49	−	2.24607e48i	0.845842	−	0.0878470i
$807$			4.41545e49i			1.69093i
$808$	4.61423e48	+	1.43820e49i	0.173024	+	0.539295i
$809$	−2.94551e49			−1.08152			−0.540761	−	0.841177i	$-0.681864\pi$
$809$	−2.94551e49			−1.08152			−0.540761	+	0.841177i	$0.681864\pi$
$810$	5.40629e47	+	5.20550e48i	0.0194381	+	0.187162i
$811$		−	2.58606e49i		−	0.910509i	−0.890361	−	0.455254i	$-0.849548\pi$
$811$		−	2.58606e49i		−	0.910509i	0.890361	−	0.455254i	$-0.150452\pi$
$812$	1.14452e47	+	5.45061e47i	0.00394612	+	0.0187928i
$813$	−7.61091e49			−2.56979
$814$	−4.07008e48	+	4.22708e47i	−0.134582	+	0.0139774i
$815$			2.41833e49i			0.783134i
$816$	−1.86134e49	−	4.23678e49i	−0.590329	−	1.34370i
$817$	−6.48217e47			−0.0201347
$818$	6.17718e47	+	5.94775e48i	0.0187925	+	0.180945i
$819$		−	3.90077e49i		−	1.16231i
$820$	−7.08065e49	+	1.48679e49i	−2.06651	+	0.433925i
$821$	3.69414e49			1.05604			0.528019	−	0.849232i	$-0.322935\pi$
$821$	3.69414e49			1.05604			0.528019	+	0.849232i	$0.322935\pi$
$822$	−2.03585e49	+	2.11438e48i	−0.570064	+	0.0592054i
$823$		−	1.96548e49i		−	0.539103i	−0.962986	−	0.269551i	$-0.913125\pi$
$823$		−	1.96548e49i		−	0.539103i	0.962986	−	0.269551i	$-0.0868754\pi$
$824$	1.86273e49	−	5.97627e48i	0.500481	−	0.160571i
$825$	7.86697e48			0.207057
$826$	1.78834e48	+	1.72192e49i	0.0461093	+	0.443967i
$827$		−	2.57300e49i		−	0.649898i	−0.945731	−	0.324949i	$-0.894653\pi$
$827$		−	2.57300e49i		−	0.649898i	0.945731	−	0.324949i	$-0.105347\pi$
$828$	−3.91495e48	−	1.86444e49i	−0.0968748	−	0.461353i
$829$	2.52920e49			0.613134			0.306567	−	0.951849i	$-0.400820\pi$
$829$	2.52920e49			0.613134			0.306567	+	0.951849i	$0.400820\pi$
$830$	−3.51883e49	+	3.65457e48i	−0.835739	+	0.0867977i
$831$			9.52595e49i			2.21662i
$832$	−2.16631e49	+	1.54955e49i	−0.493883	+	0.353273i
$833$	−1.27603e49			−0.285033
$834$	−5.24129e48	−	5.04662e49i	−0.114714	−	1.10453i
$835$			1.78571e49i			0.382950i
$836$	3.17680e48	−	6.67064e47i	0.0667550	−	0.0140172i
$837$	7.41879e49			1.52757
$838$	8.17498e49	−	8.49032e48i	1.64945	−	0.171307i
$839$			1.36285e49i			0.269460i	0.990882	+	0.134730i	$0.0430168\pi$
$839$			1.36285e49i			0.269460i	−0.990882	+	0.134730i	$0.956983\pi$
$840$	−4.88800e49	−	1.52353e50i	−0.947073	−	2.95191i
$841$	−5.26514e49			−0.999720
$842$	−3.72465e47	−	3.58631e48i	−0.00693075	−	0.0667333i
$843$			1.21468e50i			2.21510i
$844$	1.69065e49	+	8.05147e49i	0.302156	+	1.43898i
$845$	−5.96016e49			−1.04398
$846$	2.23282e49	−	2.31895e48i	0.383317	−	0.0398103i
$847$			6.78454e49i			1.14157i
$848$	4.67214e49	−	2.05261e49i	0.770524	−	0.338514i
$849$	3.77522e49			0.610255
$850$	1.01639e49	+	9.78637e49i	0.161041	+	1.55060i
$851$		−	3.37012e49i		−	0.523411i
$852$	−1.80970e49	+	3.80001e48i	−0.275508	+	0.0578512i
$853$	−8.43705e49			−1.25909			−0.629545	−	0.776964i	$-0.716759\pi$
$853$	−8.43705e49			−1.25909			−0.629545	+	0.776964i	$0.716759\pi$
$854$	1.14276e50	−	1.18684e49i	1.67175	−	0.173623i
$855$		−	1.79542e50i		−	2.57479i
$856$	8.84548e49	−	2.83793e49i	1.24356	−	0.398977i
$857$	2.31459e49			0.319007			0.159504	−	0.987197i	$-0.449011\pi$
$857$	2.31459e49			0.319007			0.159504	+	0.987197i	$0.449011\pi$
$858$	5.54050e47	+	5.33472e48i	0.00748627	+	0.0720822i
$859$		−	1.14122e50i		−	1.51177i	−0.654706	−	0.755883i	$-0.727208\pi$
$859$		−	1.14122e50i		−	1.51177i	0.654706	−	0.755883i	$-0.272792\pi$
$860$	−5.64389e47	−	2.68783e48i	−0.00733002	−	0.0349082i
$861$	1.87972e50			2.39353
$862$	−2.35256e49	+	2.44331e48i	−0.293709	+	0.0305039i
$863$			6.96883e49i			0.853054i	0.904475	+	0.426527i	$0.140263\pi$
$863$			6.96883e49i			0.853054i	−0.904475	+	0.426527i	$0.859737\pi$
$864$	−7.89824e49	+	4.49534e49i	−0.947975	+	0.539546i
$865$	−5.99010e49			−0.704953
$866$	−1.15934e49	−	1.11628e50i	−0.133785	−	1.28816i
$867$			2.77992e49i			0.314563i
$868$	−1.41763e50	+	2.97674e49i	−1.57300	+	0.330297i
$869$	−3.63332e48			−0.0395337
$870$	−4.21291e48	+	4.37542e47i	−0.0449526	+	0.00466866i
$871$		−	8.68726e49i		−	0.909021i
$872$	4.83705e49	+	1.50765e50i	0.496364	+	1.54711i
$873$	−1.32945e50			−1.33792
$874$	2.76172e48	+	2.65915e49i	0.0272575	+	0.262451i
$875$			1.44107e50i			1.39491i
$876$	2.86568e47	+	1.36474e48i	0.00272056	+	0.0129563i
$877$	5.52415e49			0.514367			0.257183	−	0.966363i	$-0.417206\pi$
$877$	5.52415e49			0.514367			0.257183	+	0.966363i	$0.417206\pi$
$878$	−1.07594e50	+	1.11745e49i	−0.982614	+	0.102052i
$879$		−	2.33726e49i		−	0.209361i
$880$	5.53195e48	+	1.25918e49i	0.0486041	+	0.110632i
$881$	1.27118e50			1.09551			0.547757	−	0.836638i	$-0.315482\pi$
$881$	1.27118e50			1.09551			0.547757	+	0.836638i	$0.315482\pi$
$882$	6.46498e48	+	6.22487e49i	0.0546514	+	0.526216i
$883$		−	1.68236e50i		−	1.39504i	−0.716566	−	0.697520i	$-0.754287\pi$
$883$		−	1.68236e50i		−	1.39504i	0.716566	−	0.697520i	$-0.245713\pi$
$884$	−6.56472e49	+	1.37846e49i	−0.533983	+	0.112126i
$885$	−1.31656e50			−1.05052
$886$	1.03975e50	−	1.07985e49i	0.813869	−	0.0845263i
$887$			1.02987e50i			0.790825i	0.918504	+	0.395413i	$0.129398\pi$
$887$			1.02987e50i			0.790825i	−0.918504	+	0.395413i	$0.870602\pi$
$888$	−3.82305e50	+	1.22656e50i	−2.87998	+	0.923995i
$889$	8.46276e48			0.0625435
$890$	−1.06770e49	−	1.02804e50i	−0.0774139	−	0.745386i
$891$			1.16876e48i			0.00831389i
$892$	1.90545e48	+	9.07444e48i	0.0132983	+	0.0633311i
$893$	−3.15020e49			−0.215706
$894$	8.53884e49	−	8.86822e48i	0.573668	−	0.0595797i
$895$		−	3.87640e50i		−	2.55527i
$896$	1.32887e50	−	1.17591e50i	0.859504	−	0.760568i
$897$	−4.41727e49			−0.280338
$898$	−1.85259e48	−	1.78378e49i	−0.0115367	−	0.111082i
$899$			3.83459e48i			0.0234317i
$900$	4.72261e50	−	9.91653e49i	2.83178	−	0.594617i
$901$	1.28522e50			0.756233
$902$	−1.60711e49	+	1.66910e48i	−0.0927972	+	0.00963768i
$903$			7.13544e48i			0.0404323i
$904$	3.39469e49	+	1.05808e50i	0.188771	+	0.588378i
$905$	−1.87279e50			−1.02203
$906$	5.02554e49	+	4.83888e50i	0.269155	+	2.59159i
$907$		−	6.83501e49i		−	0.359265i	−0.983734	−	0.179633i	$-0.942509\pi$
$907$		−	6.83501e49i		−	0.359265i	0.983734	−	0.179633i	$-0.0574909\pi$
$908$	−6.36835e49	−	3.03284e50i	−0.328524	−	1.56455i
$909$	1.86567e50			0.944600
$910$	−2.30687e50	+	2.39586e49i	−1.14636	+	0.119058i
$911$			4.17917e48i			0.0203834i	0.999948	+	0.0101917i	$0.00324418\pi$
$911$			4.17917e48i			0.0203834i	−0.999948	+	0.0101917i	$0.996756\pi$
$912$	2.91601e50	−	1.28109e50i	1.39597	−	0.613293i
$913$	−7.90063e48			−0.0371243
$914$	−1.76387e49	−	1.69836e50i	−0.0813544	−	0.783328i
$915$			8.73739e50i			3.95570i
$916$	2.24240e50	−	4.70859e49i	0.996531	−	0.209251i
$917$	−3.09225e50			−1.34895
$918$	−2.27653e50	+	2.36435e49i	−0.974874	+	0.101248i
$919$			3.61673e50i			1.52038i	0.649701	+	0.760190i	$0.274894\pi$
$919$			3.61673e50i			1.52038i	−0.649701	+	0.760190i	$0.725106\pi$
$920$	−1.07857e50	+	3.46041e49i	−0.445096	+	0.142802i
$921$	−6.89706e49			−0.279416
$922$	7.52101e48	+	7.24167e49i	0.0299123	+	0.288014i
$923$			2.68043e49i			0.104659i
$924$	−7.34290e48	−	3.49696e49i	−0.0281478	−	0.134050i
$925$	8.53647e50			3.21269
$926$	−9.97453e49	+	1.03593e49i	−0.368558	+	0.0382775i
$927$		−	2.41638e50i		−	0.876615i
$928$	−2.32353e48	−	4.08240e48i	−0.00827622	−	0.0145412i
$929$	2.16353e50			0.756650			0.378325	−	0.925673i	$-0.376500\pi$
$929$	2.16353e50			0.756650			0.378325	+	0.925673i	$0.376500\pi$
$930$	−1.13799e50	−	1.09572e51i	−0.390776	−	3.76262i
$931$		−	8.78240e49i		−	0.296121i
$932$	−3.17824e50	+	6.67366e49i	−1.05224	+	0.220950i
$933$	−1.71492e50			−0.557513
$934$	−2.92492e50	+	3.03775e49i	−0.933722	+	0.0969739i
$935$			3.46377e49i			0.108580i
$936$	1.00506e50	+	3.13264e50i	0.309387	+	0.964320i
$937$	−2.59868e50			−0.785560			−0.392780	−	0.919633i	$-0.628487\pi$
$937$	−2.59868e50			−0.785560			−0.392780	+	0.919633i	$0.628487\pi$
$938$	5.97872e49	+	5.75666e50i	0.177484	+	1.70892i
$939$		−	5.15538e50i		−	1.50295i
$940$	−2.74281e49	−	1.30623e50i	−0.0785276	−	0.373977i
$941$	−1.55744e50			−0.437913			−0.218957	−	0.975735i	$-0.570265\pi$
$941$	−1.55744e50			−0.437913			−0.218957	+	0.975735i	$0.570265\pi$
$942$	9.21947e50	−	9.57510e49i	2.54590	−	0.264410i
$943$		−	1.33072e50i		−	0.360902i
$944$	−5.87281e49	−	1.33676e50i	−0.156431	−	0.356066i
$945$	−7.91357e50			−2.07029
$946$	−6.33595e46	−	6.10062e47i	−0.000162803	−	0.00156756i
$947$		−	4.61434e50i		−	1.16455i	−0.812990	−	0.582277i	$-0.802162\pi$
$947$		−	4.61434e50i		−	1.16455i	0.812990	−	0.582277i	$-0.197838\pi$
$948$	−3.48888e50	+	7.32595e49i	−0.864858	+	0.181603i
$949$	2.02138e48			0.00492177
$950$	−6.73559e50	+	6.99541e49i	−1.61092	+	0.167306i
$951$			6.13772e50i			1.44191i
$952$	4.25528e50	−	1.36524e50i	0.981974	−	0.315051i
$953$	−5.61633e49			−0.127313			−0.0636566	−	0.997972i	$-0.520276\pi$
$953$	−5.61633e49			−0.127313			−0.0636566	+	0.997972i	$0.520276\pi$
$954$	−6.51156e49	−	6.26971e50i	−0.144998	−	1.39613i
$955$			1.32142e51i			2.89058i
$956$	3.86374e49	+	1.84005e50i	0.0830278	+	0.395409i
$957$	−9.45900e47			−0.00199684
$958$	−2.15339e50	+	2.23645e49i	−0.446589	+	0.0463816i
$959$		−	1.97660e50i		−	0.402720i
$960$	7.85095e50	+	1.09758e51i	1.57149	+	2.19698i
$961$	−4.88817e50			−0.961278
$962$	6.01201e49	+	5.78872e50i	0.116157	+	1.11842i
$963$		−	1.14746e51i		−	2.17816i
$964$	−5.33350e49	+	1.11993e49i	−0.0994724	+	0.0208872i
$965$	8.00026e50			1.46602
$966$	2.92713e50	−	3.04004e49i	0.527025	−	0.0547354i
$967$		−	4.01898e50i		−	0.710995i	−0.934677	−	0.355497i	$-0.884312\pi$
$967$		−	4.01898e50i		−	0.710995i	0.934677	−	0.355497i	$-0.115688\pi$
$968$	−1.74808e50	−	5.44855e50i	−0.303865	−	0.947110i
$969$	8.02142e50			1.37008
$970$	8.16552e49	+	7.86224e50i	0.137045	+	1.31955i
$971$		−	3.44213e50i		−	0.567676i	−0.958872	−	0.283838i	$-0.908392\pi$
$971$		−	3.44213e50i		−	0.567676i	0.958872	−	0.283838i	$-0.0916078\pi$
$972$	−1.14748e50	−	5.46471e50i	−0.185959	−	0.885606i
$973$	4.89977e50			0.780292
$974$	−1.10813e50	+	1.15088e49i	−0.173416	+	0.0180105i
$975$		−	1.11889e51i		−	1.72072i
$976$	−8.87150e50	+	3.89752e50i	−1.34076	+	0.589035i
$977$	−6.75292e50			−1.00296			−0.501481	−	0.865169i	$-0.667211\pi$
$977$	−6.75292e50			−1.00296			−0.501481	+	0.865169i	$0.667211\pi$
$978$	5.47405e49	+	5.27073e50i	0.0799002	+	0.769326i
$979$		−	2.30820e49i		−	0.0331107i
$980$	3.64162e50	−	7.64666e49i	0.513394	−	0.107802i
$981$	1.95576e51			2.70983
$982$	1.15019e51	−	1.19456e50i	1.56630	−	0.162672i
$983$			7.17658e50i			0.960522i	0.877126	+	0.480261i	$0.159458\pi$
$983$			7.17658e50i			0.960522i	−0.877126	+	0.480261i	$0.840542\pi$
$984$	−1.50957e51	+	4.84321e50i	−1.98580	+	0.637113i
$985$	−1.40397e51			−1.81528
$986$	−1.22207e48	−	1.17668e49i	−0.00155306	−	0.0149538i
$987$			3.46767e50i			0.433158i
$988$	−9.48740e49	−	4.51825e50i	−0.116488	−	0.554756i
$989$	5.05146e48			0.00609649
$990$	1.68974e50	−	1.75492e49i	0.200457	−	0.0208189i
$991$			1.02389e51i			1.19400i	0.802243	+	0.596998i	$0.203640\pi$
$991$			1.02389e51i			1.19400i	−0.802243	+	0.596998i	$0.796360\pi$
$992$	1.06178e51	−	6.04319e50i	1.21713	−	0.692736i
$993$	5.11907e50			0.576838
$994$	−1.84472e49	−	1.77620e50i	−0.0204344	−	0.196754i
$995$		−	1.79325e51i		−	1.95276i
$996$	−7.58655e50	+	1.59302e50i	−0.812149	+	0.170535i
$997$	4.97693e50			0.523773			0.261887	−	0.965099i	$-0.415655\pi$
$997$	4.97693e50			0.523773			0.261887	+	0.965099i	$0.415655\pi$
$998$	−3.08676e49	+	3.20583e48i	−0.0319362	+	0.00331681i
$999$			1.98578e51i			2.01984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.35.b.a.3.10	yes	16
4.3	odd	2	inner	4.35.b.a.3.9	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.35.b.a.3.9	✓	16	4.3	odd	2	inner
4.35.b.a.3.10	yes	16	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(13540.0 + 130371. i) q^{2} -2.10930e8i q^{3} +(-1.68132e10 + 3.53043e9i) q^{4} +1.26172e12 q^{5} +(2.74991e13 - 2.85599e12i) q^{6} +2.66990e14i q^{7} +(-6.87916e14 - 2.14415e15i) q^{8} -2.78144e16 q^{9} +O(q^{10})\)	\(q+(13540.0 + 130371. i) q^{2} -2.10930e8i q^{3} +(-1.68132e10 + 3.53043e9i) q^{4} +1.26172e12 q^{5} +(2.74991e13 - 2.85599e12i) q^{6} +2.66990e14i q^{7} +(-6.87916e14 - 2.14415e15i) q^{8} -2.78144e16 q^{9} +(1.70837e16 + 1.64492e17i) q^{10} +3.69323e16i q^{11} +(7.44675e17 + 3.54641e18i) q^{12} +5.25274e18 q^{13} +(-3.48076e19 + 3.61503e18i) q^{14} -2.66135e20i q^{15} +(2.70220e20 - 1.18716e20i) q^{16} +7.43326e20 q^{17} +(-3.76606e20 - 3.62618e21i) q^{18} +5.11603e21i q^{19} +(-2.12136e22 + 4.45442e21i) q^{20} +5.63162e22 q^{21} +(-4.81489e21 + 5.00062e20i) q^{22} -3.98684e22i q^{23} +(-4.52266e23 + 1.45102e23i) q^{24} +1.00986e24 q^{25} +(7.11220e22 + 6.84804e23i) q^{26} +2.34917e24i q^{27} +(-9.42589e23 - 4.48895e24i) q^{28} -1.21423e23 q^{29} +(3.46962e25 - 3.60346e24i) q^{30} -3.15805e25i q^{31} +(1.91358e25 + 3.36214e25i) q^{32} +7.79014e24 q^{33} +(1.00646e25 + 9.69079e25i) q^{34} +3.36866e26i q^{35} +(4.67649e26 - 9.81968e25i) q^{36} +8.45310e26 q^{37} +(-6.66981e26 + 6.92709e25i) q^{38} -1.10796e27i q^{39} +(-8.67957e26 - 2.70532e27i) q^{40} +3.33779e27 q^{41} +(7.62519e26 + 7.34198e27i) q^{42} +1.26703e26i q^{43} +(-1.30387e26 - 6.20951e26i) q^{44} -3.50940e28 q^{45} +(5.19768e27 - 5.39817e26i) q^{46} +6.15750e27i q^{47} +(-2.50408e28 - 5.69976e28i) q^{48} -1.71664e28 q^{49} +(1.36735e28 + 1.31657e29i) q^{50} -1.56790e29i q^{51} +(-8.83155e28 + 1.85445e28i) q^{52} +1.72901e29 q^{53} +(-3.06263e29 + 3.18077e28i) q^{54} +4.65983e28i q^{55} +(5.72465e29 - 1.83666e29i) q^{56} +1.07913e30 q^{57} +(-1.64406e27 - 1.58300e28i) q^{58} -4.94695e29i q^{59} +(9.39572e29 + 4.47458e30i) q^{60} -3.28307e30 q^{61} +(4.11717e30 - 4.27598e29i) q^{62} -7.42615e30i q^{63} +(-4.12415e30 + 2.94999e30i) q^{64} +6.62750e30 q^{65} +(1.05478e29 + 1.01561e30i) q^{66} -1.65385e31i q^{67} +(-1.24977e31 + 2.62426e30i) q^{68} -8.40945e30 q^{69} +(-4.39175e31 + 4.56116e30i) q^{70} +5.10292e30i q^{71} +(1.91339e31 + 5.96382e31i) q^{72} +3.84823e29 q^{73} +(1.14455e31 + 1.10204e32i) q^{74} -2.13011e32i q^{75} +(-1.80618e31 - 8.60169e31i) q^{76} -9.86054e30 q^{77} +(1.44446e32 - 1.50018e31i) q^{78} +9.83778e31i q^{79} +(3.40942e32 - 1.49786e32i) q^{80} +3.16460e31 q^{81} +(4.51936e31 + 4.35151e32i) q^{82} +2.13922e32i q^{83} +(-9.46855e32 + 1.98820e32i) q^{84} +9.37869e32 q^{85} +(-1.65184e31 + 1.71556e30i) q^{86} +2.56117e31i q^{87} +(7.91884e31 - 2.54063e31i) q^{88} -6.24982e32 q^{89} +(-4.75172e32 - 4.57523e33i) q^{90} +1.40243e33i q^{91} +(1.40753e32 + 6.70316e32i) q^{92} -6.66127e33 q^{93} +(-8.02758e32 + 8.33724e31i) q^{94} +6.45500e33i q^{95} +(7.09177e33 - 4.03633e33i) q^{96} +4.77972e33 q^{97} +(-2.32433e32 - 2.23800e33i) q^{98} -1.02725e33i 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more