LMFDB - Embedded newform 4.35.b.a.3.2

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			3.2
Root			$0.500000 - 3.36022e6i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.35.b.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-130415. + 13105.5i) q^{2} +1.61291e8i q^{3} +(1.68364e10 - 3.41831e9i) q^{4} -2.13902e10 q^{5} +(-2.11380e12 - 2.10348e13i) q^{6} +7.96031e13i q^{7} +(-2.15092e15 + 6.66449e14i) q^{8} -9.33752e15 q^{9} +O(q^{10})$	\(q+(-130415. + 13105.5i) q^{2} +1.61291e8i q^{3} +(1.68364e10 - 3.41831e9i) q^{4} -2.13902e10 q^{5} +(-2.11380e12 - 2.10348e13i) q^{6} +7.96031e13i q^{7} +(-2.15092e15 + 6.66449e14i) q^{8} -9.33752e15 q^{9} +(2.78961e15 - 2.80330e14i) q^{10} +6.81233e17i q^{11} +(5.51342e17 + 2.71555e18i) q^{12} +4.12366e18 q^{13} +(-1.04324e18 - 1.03815e19i) q^{14} -3.45004e18i q^{15} +(2.71778e20 - 1.15104e20i) q^{16} +9.62590e20 q^{17} +(1.21775e21 - 1.22373e20i) q^{18} +8.20698e21i q^{19} +(-3.60133e20 + 7.31184e19i) q^{20} -1.28392e22 q^{21} +(-8.92790e21 - 8.88431e22i) q^{22} +1.41698e23i q^{23} +(-1.07492e23 - 3.46923e23i) q^{24} -5.81619e23 q^{25} +(-5.37788e23 + 5.40426e22i) q^{26} +1.18382e24i q^{27} +(2.72108e23 + 1.34023e24i) q^{28} +4.99716e23 q^{29} +(4.52146e22 + 4.49938e23i) q^{30} -3.80384e25i q^{31} +(-3.39355e25 + 1.85731e25i) q^{32} -1.09877e26 q^{33} +(-1.25536e26 + 1.26152e25i) q^{34} -1.70273e24i q^{35} +(-1.57210e26 + 3.19185e25i) q^{36} -5.54802e26 q^{37} +(-1.07557e26 - 1.07031e27i) q^{38} +6.65108e26i q^{39} +(4.60086e25 - 1.42555e25i) q^{40} +1.30171e27 q^{41} +(1.67443e27 - 1.68265e26i) q^{42} +1.77563e27i q^{43} +(2.32867e27 + 1.14695e28i) q^{44} +1.99732e26 q^{45} +(-1.85702e27 - 1.84795e28i) q^{46} -3.99406e28i q^{47} +(1.85652e28 + 4.38353e28i) q^{48} +4.77803e28 q^{49} +(7.58519e28 - 7.62241e27i) q^{50} +1.55257e29i q^{51} +(6.94274e28 - 1.40960e28i) q^{52} -1.11744e29 q^{53} +(-1.55145e28 - 1.54388e29i) q^{54} -1.45717e28i q^{55} +(-5.30514e28 - 1.71220e29i) q^{56} -1.32371e30 q^{57} +(-6.51706e28 + 6.54903e27i) q^{58} -1.19557e30i q^{59} +(-1.17933e28 - 5.80862e28i) q^{60} -3.77721e30 q^{61} +(4.98513e29 + 4.96079e30i) q^{62} -7.43296e29i q^{63} +(4.18230e30 - 2.86695e30i) q^{64} -8.82060e28 q^{65} +(1.43296e31 - 1.43999e30i) q^{66} +3.98674e29i q^{67} +(1.62065e31 - 3.29043e30i) q^{68} -2.28545e31 q^{69} +(2.23151e28 + 2.22062e29i) q^{70} +3.35054e31i q^{71} +(2.00842e31 - 6.22298e30i) q^{72} -4.87079e31 q^{73} +(7.23546e31 - 7.27096e30i) q^{74} -9.38098e31i q^{75} +(2.80540e31 + 1.38176e32i) q^{76} -5.42283e31 q^{77} +(-8.71658e30 - 8.67402e31i) q^{78} -1.05689e32i q^{79} +(-5.81340e30 + 2.46210e30i) q^{80} -3.46663e32 q^{81} +(-1.69763e32 + 1.70596e31i) q^{82} +3.41797e32i q^{83} +(-2.16166e32 + 4.38885e31i) q^{84} -2.05900e31 q^{85} +(-2.32705e31 - 2.31569e32i) q^{86} +8.05996e31i q^{87} +(-4.54007e32 - 1.46528e33i) q^{88} +1.98737e33 q^{89} +(-2.60480e31 + 2.61758e30i) q^{90} +3.28256e32i q^{91} +(4.84367e32 + 2.38567e33i) q^{92} +6.13525e33 q^{93} +(5.23442e32 + 5.20886e33i) q^{94} -1.75549e32i q^{95} +(-2.99567e33 - 5.47348e33i) q^{96} +3.77538e33 q^{97} +(-6.23128e33 + 6.26185e32i) q^{98} -6.36103e33i 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 $

$2$	−130415.	+	13105.5i	−0.994989	+	0.0999870i
$2$	−130415.	+	13105.5i	−0.994989	+	0.0999870i
$3$			1.61291e8i			1.24896i	0.781041	+	0.624479i	$0.214689\pi$
$3$			1.61291e8i			1.24896i	−0.781041	+	0.624479i	$0.785311\pi$
$4$	1.68364e10	−	3.41831e9i	0.980005	−	0.198972i
$5$	−2.13902e10			−0.0280366			−0.0140183	−	0.999902i	$-0.504462\pi$
$5$	−2.13902e10			−0.0280366			−0.0140183	+	0.999902i	$0.504462\pi$
$6$	−2.11380e12	−	2.10348e13i	−0.124880	−	1.24270i
$7$			7.96031e13i			0.342187i	0.985255	+	0.171093i	$0.0547300\pi$
$7$			7.96031e13i			0.342187i	−0.985255	+	0.171093i	$0.945270\pi$
$8$	−2.15092e15	+	6.66449e14i	−0.955200	+	0.295963i
$9$	−9.33752e15			−0.559898
$10$	2.78961e15	−	2.80330e14i	0.0278961	−	0.00280330i
$11$			6.81233e17i			1.34778i	0.738830	+	0.673892i	$0.235379\pi$
$11$			6.81233e17i			1.34778i	−0.738830	+	0.673892i	$0.764621\pi$
$12$	5.51342e17	+	2.71555e18i	0.248508	+	1.22399i
$13$	4.12366e18			0.476701			0.238350	−	0.971179i	$-0.423393\pi$
$13$	4.12366e18			0.476701			0.238350	+	0.971179i	$0.423393\pi$
$14$	−1.04324e18	−	1.03815e19i	−0.0342142	−	0.340472i
$15$		−	3.45004e18i		−	0.0350165i
$16$	2.71778e20	−	1.15104e20i	0.920820	−	0.389987i
$17$	9.62590e20			1.16362			0.581808	−	0.813326i	$-0.302345\pi$
$17$	9.62590e20			1.16362			0.581808	+	0.813326i	$0.302345\pi$
$18$	1.21775e21	−	1.22373e20i	0.557092	−	0.0559825i
$19$			8.20698e21i			1.49752i	0.662842	+	0.748759i	$0.269350\pi$
$19$			8.20698e21i			1.49752i	−0.662842	+	0.748759i	$0.730650\pi$
$20$	−3.60133e20	+	7.31184e19i	−0.0274760	+	0.00557849i
$21$	−1.28392e22			−0.427377
$22$	−8.92790e21	−	8.88431e22i	−0.134761	−	1.34103i
$23$			1.41698e23i			1.00459i	0.864696	+	0.502296i	$0.167511\pi$
$23$			1.41698e23i			1.00459i	−0.864696	+	0.502296i	$0.832489\pi$
$24$	−1.07492e23	−	3.46923e23i	−0.369645	−	1.19300i
$25$	−5.81619e23			−0.999214
$26$	−5.37788e23	+	5.40426e22i	−0.474312	+	0.0476639i
$27$			1.18382e24i			0.549669i
$28$	2.72108e23	+	1.34023e24i	0.0680856	+	0.335345i
$29$	4.99716e23			0.0688585			0.0344293	−	0.999407i	$-0.489039\pi$
$29$	4.99716e23			0.0688585			0.0344293	+	0.999407i	$0.489039\pi$
$30$	4.52146e22	+	4.49938e23i	0.00350120	+	0.0348411i
$31$		−	3.80384e25i		−	1.68684i	−0.537254	−	0.843420i	$-0.680539\pi$
$31$		−	3.80384e25i		−	1.68684i	0.537254	−	0.843420i	$-0.319461\pi$
$32$	−3.39355e25	+	1.85731e25i	−0.877212	+	0.480103i
$33$	−1.09877e26			−1.68333
$34$	−1.25536e26	+	1.26152e25i	−1.15779	+	0.116347i
$35$		−	1.70273e24i		−	0.00959375i
$36$	−1.57210e26	+	3.19185e25i	−0.548703	+	0.111404i
$37$	−5.54802e26			−1.21537			−0.607685	−	0.794178i	$-0.707902\pi$
$37$	−5.54802e26			−1.21537			−0.607685	+	0.794178i	$0.707902\pi$
$38$	−1.07557e26	−	1.07031e27i	−0.149732	−	1.49001i
$39$			6.65108e26i			0.595380i
$40$	4.60086e25	−	1.42555e25i	0.0267805	−	0.00829778i
$41$	1.30171e27			0.497954			0.248977	−	0.968509i	$-0.419906\pi$
$41$	1.30171e27			0.497954			0.248977	+	0.968509i	$0.419906\pi$
$42$	1.67443e27	−	1.68265e26i	0.425236	−	0.0427322i
$43$			1.77563e27i			0.302266i	0.988513	+	0.151133i	$0.0482921\pi$
$43$			1.77563e27i			0.302266i	−0.988513	+	0.151133i	$0.951708\pi$
$44$	2.32867e27	+	1.14695e28i	0.268171	+	1.32083i
$45$	1.99732e26			0.0156976
$46$	−1.85702e27	−	1.84795e28i	−0.100446	−	0.999558i
$47$		−	3.99406e28i		−	1.49883i	−0.662103	−	0.749413i	$-0.730336\pi$
$47$		−	3.99406e28i		−	1.49883i	0.662103	−	0.749413i	$-0.269664\pi$
$48$	1.85652e28	+	4.38353e28i	0.487078	+	1.15007i
$49$	4.77803e28			0.882908
$50$	7.58519e28	−	7.62241e27i	0.994207	−	0.0999084i
$51$			1.55257e29i			1.45331i
$52$	6.94274e28	−	1.40960e28i	0.467169	−	0.0948501i
$53$	−1.11744e29			−0.543921			−0.271960	−	0.962308i	$-0.587672\pi$
$53$	−1.11744e29			−0.543921			−0.271960	+	0.962308i	$0.587672\pi$
$54$	−1.55145e28	−	1.54388e29i	−0.0549598	−	0.546915i
$55$		−	1.45717e28i		−	0.0377872i
$56$	−5.30514e28	−	1.71220e29i	−0.101275	−	0.326857i
$57$	−1.32371e30			−1.87034
$58$	−6.51706e28	+	6.54903e27i	−0.0685135	+	0.00688496i
$59$		−	1.19557e30i		−	0.939923i	−0.882687	−	0.469962i	$-0.844268\pi$
$59$		−	1.19557e30i		−	0.939923i	0.882687	−	0.469962i	$-0.155732\pi$
$60$	−1.17933e28	−	5.80862e28i	−0.00696731	−	0.0343164i
$61$	−3.77721e30			−1.68486			−0.842430	−	0.538805i	$-0.818876\pi$
$61$	−3.77721e30			−1.68486			−0.842430	+	0.538805i	$0.818876\pi$
$62$	4.98513e29	+	4.96079e30i	0.168662	+	1.67839i
$63$		−	7.43296e29i		−	0.191590i
$64$	4.18230e30	−	2.86695e30i	0.824812	−	0.565407i
$65$	−8.82060e28			−0.0133651
$66$	1.43296e31	−	1.43999e30i	1.67489	−	0.168311i
$67$			3.98674e29i			0.0360866i	0.999837	+	0.0180433i	$0.00574368\pi$
$67$			3.98674e29i			0.0360866i	−0.999837	+	0.0180433i	$0.994256\pi$
$68$	1.62065e31	−	3.29043e30i	1.14035	−	0.231527i
$69$	−2.28545e31			−1.25469
$70$	2.23151e28	+	2.22062e29i	0.000959251	+	0.00954568i
$71$			3.35054e31i			1.13168i	0.824515	+	0.565840i	$0.191448\pi$
$71$			3.35054e31i			1.13168i	−0.824515	+	0.565840i	$0.808552\pi$
$72$	2.00842e31	−	6.22298e30i	0.534814	−	0.165709i
$73$	−4.87079e31			−1.02591			−0.512956	−	0.858415i	$-0.671450\pi$
$73$	−4.87079e31			−1.02591			−0.512956	+	0.858415i	$0.671450\pi$
$74$	7.23546e31	−	7.27096e30i	1.20928	−	0.121521i
$75$		−	9.38098e31i		−	1.24798i
$76$	2.80540e31	+	1.38176e32i	0.297964	+	1.46758i
$77$	−5.42283e31			−0.461194
$78$	−8.71658e30	−	8.67402e31i	−0.0595302	−	0.592396i
$79$		−	1.05689e32i		−	0.581258i	−0.956836	−	0.290629i	$-0.906136\pi$
$79$		−	1.05689e32i		−	0.581258i	0.956836	−	0.290629i	$-0.0938645\pi$
$80$	−5.81340e30	+	2.46210e30i	−0.0258167	+	0.0109339i
$81$	−3.46663e32			−1.24641
$82$	−1.69763e32	+	1.70596e31i	−0.495458	+	0.0497889i
$83$			3.41797e32i			0.811784i	0.913921	+	0.405892i	$0.133039\pi$
$83$			3.41797e32i			0.811784i	−0.913921	+	0.405892i	$0.866961\pi$
$84$	−2.16166e32	+	4.38885e31i	−0.418832	+	0.0850361i
$85$	−2.05900e31			−0.0326238
$86$	−2.32705e31	−	2.31569e32i	−0.0302227	−	0.300751i
$87$			8.05996e31i			0.0860015i
$88$	−4.54007e32	−	1.46528e33i	−0.398893	−	1.28740i
$89$	1.98737e33			1.44095			0.720476	−	0.693480i	$-0.243924\pi$
$89$	1.98737e33			1.44095			0.720476	+	0.693480i	$0.243924\pi$
$90$	−2.60480e31	+	2.61758e30i	−0.0156190	+	0.00156956i
$91$			3.28256e32i			0.163121i
$92$	4.84367e32	+	2.38567e33i	0.199886	+	0.984506i
$93$	6.13525e33			2.10679
$94$	5.23442e32	+	5.20886e33i	0.149863	+	1.49132i
$95$		−	1.75549e32i		−	0.0419853i
$96$	−2.99567e33	−	5.47348e33i	−0.599629	−	1.09560i
$97$	3.77538e33			0.633639			0.316819	−	0.948486i	$-0.397385\pi$
$97$	3.77538e33			0.633639			0.316819	+	0.948486i	$0.397385\pi$
$98$	−6.23128e33	+	6.26185e32i	−0.878484	+	0.0882794i
$99$		−	6.36103e33i		−	0.754621i
$100$	−9.79235e33	+	1.98816e33i	−0.979235	+	0.198816i
$101$	−8.63161e33			−0.728834			−0.364417	−	0.931236i	$-0.618732\pi$
$101$	−8.63161e33			−0.728834			−0.364417	+	0.931236i	$0.618732\pi$
$102$	−2.03472e33	−	2.02479e34i	−0.145312	−	1.44603i
$103$			1.58373e34i			0.958181i	0.877765	+	0.479091i	$0.159034\pi$
$103$			1.58373e34i			0.958181i	−0.877765	+	0.479091i	$0.840966\pi$
$104$	−8.86966e33	+	2.74821e33i	−0.455344	+	0.141086i
$105$	2.74634e32			0.0119822
$106$	1.45731e34	−	1.46446e33i	0.541195	−	0.0543850i
$107$			2.09513e34i			0.663264i	0.943409	+	0.331632i	$0.107599\pi$
$107$			2.09513e34i			0.663264i	−0.943409	+	0.331632i	$0.892401\pi$
$108$	4.04666e33	+	1.99312e34i	0.109369	+	0.538679i
$109$	−1.71142e34			−0.395464			−0.197732	−	0.980256i	$-0.563358\pi$
$109$	−1.71142e34			−0.395464			−0.197732	+	0.980256i	$0.563358\pi$
$110$	1.90970e32	+	1.90037e33i	0.00377823	+	0.0375979i
$111$		−	8.94844e34i		−	1.51795i
$112$	9.16263e33	+	2.16344e34i	0.133448	+	0.315093i
$113$	−4.25971e34			−0.533392			−0.266696	−	0.963781i	$-0.585932\pi$
$113$	−4.25971e34			−0.533392			−0.266696	+	0.963781i	$0.585932\pi$
$114$	1.72632e35	−	1.73479e34i	1.86097	−	0.187010i
$115$		−	3.03095e33i		−	0.0281653i
$116$	8.41341e33	−	1.70819e33i	0.0674817	−	0.0137009i
$117$	−3.85048e34			−0.266904
$118$	1.56686e34	+	1.55921e35i	0.0939801	+	0.935213i
$119$			7.66252e34i			0.398174i
$120$	2.29928e33	+	7.42076e33i	0.0103636	+	0.0334478i
$121$	−2.08602e35			−0.816519
$122$	4.92605e35	−	4.95022e34i	1.67642	−	0.168464i
$123$			2.09954e35i			0.621924i
$124$	−1.30027e35	−	6.40429e35i	−0.335634	−	1.65311i
$125$	2.48917e34			0.0560511
$126$	9.74126e33	+	9.69370e34i	0.0191565	+	0.190630i
$127$		−	1.31350e35i		−	0.225823i	−0.993605	−	0.112911i	$-0.963982\pi$
$127$		−	1.31350e35i		−	0.225823i	0.993605	−	0.112911i	$-0.0360176\pi$
$128$	−5.07862e35	+	4.28705e35i	−0.764146	+	0.645044i
$129$	−2.86393e35			−0.377517
$130$	1.15034e34	−	1.15598e33i	0.0132981	−	0.00133633i
$131$		−	7.60398e35i		−	0.771666i	−0.922569	−	0.385833i	$-0.873914\pi$
$131$		−	7.60398e35i		−	0.771666i	0.922569	−	0.385833i	$-0.126086\pi$
$132$	−1.84992e36	+	3.75592e35i	−1.64967	+	0.334934i
$133$	−6.53301e35			−0.512431
$134$	−5.22482e33	−	5.19932e34i	−0.00360820	−	0.0359058i
$135$		−	2.53222e34i		−	0.0154109i
$136$	−2.07045e36	+	6.41517e35i	−1.11149	+	0.344387i
$137$	3.85899e36			1.82904			0.914521	−	0.404539i	$-0.132568\pi$
$137$	3.85899e36			1.82904			0.914521	+	0.404539i	$0.132568\pi$
$138$	2.98058e36	−	2.99520e35i	1.24841	−	0.125453i
$139$			6.91077e35i			0.256021i	0.991773	+	0.128010i	$0.0408591\pi$
$139$			6.91077e35i			0.256021i	−0.991773	+	0.128010i	$0.959141\pi$
$140$	−5.82046e33	−	2.86677e34i	−0.00190889	−	0.00940193i
$141$	6.44205e36			1.87197
$142$	−4.39105e35	−	4.36962e36i	−0.113153	−	1.12601i
$143$			2.80917e36i			0.642489i
$144$	−2.53773e36	+	1.07478e36i	−0.515565	+	0.218353i
$145$	−1.06890e34			−0.00193056
$146$	6.35224e36	−	6.38341e35i	1.02077	−	0.102578i
$147$			7.70652e36i			1.10272i
$148$	−9.34085e36	+	1.89649e36i	−1.19107	+	0.241825i
$149$	−3.97310e36			−0.451818			−0.225909	−	0.974148i	$-0.572535\pi$
$149$	−3.97310e36			−0.451818			−0.225909	+	0.974148i	$0.572535\pi$
$150$	1.22942e36	+	1.22342e37i	0.124782	+	1.24172i
$151$		−	2.07968e37i		−	1.88533i	−0.333737	−	0.942666i	$-0.608310\pi$
$151$		−	2.07968e37i		−	1.88533i	0.333737	−	0.942666i	$-0.391690\pi$
$152$	−5.46953e36	−	1.76525e37i	−0.443209	−	1.43043i
$153$	−8.98821e36			−0.651506
$154$	7.07219e36	−	7.10688e35i	0.458883	−	0.0461134i
$155$			8.13651e35i			0.0472933i
$156$	2.27355e36	+	1.11980e37i	0.118464	+	0.583475i
$157$	−3.00995e37			−1.40691			−0.703454	−	0.710741i	$-0.748360\pi$
$157$	−3.00995e37			−1.40691			−0.703454	+	0.710741i	$0.748360\pi$
$158$	1.38511e36	+	1.37834e37i	0.0581182	+	0.578345i
$159$		−	1.80233e37i		−	0.679334i
$160$	7.25888e35	−	3.97282e35i	0.0245940	−	0.0134604i
$161$	−1.12796e37			−0.343758
$162$	4.52101e37	−	4.54319e36i	1.24017	−	0.124625i
$163$			6.55042e37i			1.61838i	0.587548	+	0.809189i	$0.300093\pi$
$163$			6.55042e37i			1.61838i	−0.587548	+	0.809189i	$0.699907\pi$
$164$	2.19161e37	−	4.44965e36i	0.487997	−	0.0990788i
$165$	2.35028e36			0.0471947
$166$	−4.47942e36	−	4.45755e37i	−0.0811678	−	0.807716i
$167$		−	1.13921e35i		−	0.00186391i	−1.00000		0.000931955i	$-0.999703\pi$
$167$		−	1.13921e35i		−	0.00186391i	1.00000		0.000931955i	$-0.000296651\pi$
$168$	2.76162e37	−	8.55670e36i	0.408231	−	0.126488i
$169$	−5.78251e37			−0.772756
$170$	2.68525e36	−	2.69842e35i	0.0324604	−	0.00326196i
$171$		−	7.66328e37i		−	0.838457i
$172$	6.06966e36	+	2.98952e37i	0.0601424	+	0.296222i
$173$	1.06140e38			0.953004			0.476502	−	0.879173i	$-0.341904\pi$
$173$	1.06140e38			0.953004			0.476502	+	0.879173i	$0.341904\pi$
$174$	−1.05630e36	−	1.05114e37i	−0.00859903	−	0.0855705i
$175$		−	4.62987e37i		−	0.341918i
$176$	7.84125e37	+	1.85144e38i	0.525618	+	1.24107i
$177$	1.92835e38			1.17393
$178$	−2.59184e38	+	2.60455e37i	−1.43373	+	0.144076i
$179$			2.86297e38i			1.43984i	0.694055	+	0.719922i	$0.255822\pi$
$179$			2.86297e38i			1.43984i	−0.694055	+	0.719922i	$0.744178\pi$
$180$	3.36275e36	−	6.82745e35i	0.0153838	−	0.00312339i
$181$	−2.84467e37			−0.118440			−0.0592198	−	0.998245i	$-0.518861\pi$
$181$	−2.84467e37			−0.118440			−0.0592198	+	0.998245i	$0.518861\pi$
$182$	−4.30196e36	−	4.28096e37i	−0.0163100	−	0.162303i
$183$		−	6.09229e38i		−	2.10432i
$184$	−9.44343e37	−	3.04780e38i	−0.297322	−	0.959586i
$185$	1.18673e37			0.0340748
$186$	−8.00130e38	+	8.04055e37i	−2.09624	+	0.210652i
$187$			6.55748e38i			1.56830i
$188$	−1.36530e38	−	6.72455e38i	−0.298224	−	1.46886i
$189$	−9.42357e37			−0.188090
$190$	2.30066e36	+	2.28943e37i	0.00419798	+	0.0417749i
$191$			2.04580e38i			0.341426i	0.985321	+	0.170713i	$0.0546071\pi$
$191$			2.04580e38i			0.341426i	−0.985321	+	0.170713i	$0.945393\pi$
$192$	4.62413e38	+	6.74565e38i	0.706170	+	1.03016i
$193$	4.04976e38			0.566181			0.283090	−	0.959093i	$-0.408640\pi$
$193$	4.04976e38			0.566181			0.283090	+	0.959093i	$0.408640\pi$
$194$	−4.92367e38	+	4.94783e37i	−0.630463	+	0.0633556i
$195$		−	1.42268e37i		−	0.0166924i
$196$	8.04446e38	−	1.63328e38i	0.865255	−	0.175674i
$197$	5.02741e38			0.495928			0.247964	−	0.968769i	$-0.420239\pi$
$197$	5.02741e38			0.495928			0.247964	+	0.968769i	$0.420239\pi$
$198$	8.33644e37	+	8.29574e38i	0.0754523	+	0.750839i
$199$		−	1.12630e39i		−	0.935730i	−0.883800	−	0.467865i	$-0.845023\pi$
$199$		−	1.12630e39i		−	0.935730i	0.883800	−	0.467865i	$-0.154977\pi$
$200$	1.25101e39	−	3.87619e38i	0.954449	−	0.295730i
$201$	−6.43025e37			−0.0450707
$202$	1.12569e39	−	1.13122e38i	0.725181	−	0.0728739i
$203$			3.97790e37i			0.0235625i
$204$	5.30716e38	+	2.61396e39i	0.289168	+	1.42425i
$205$	−2.78439e37			−0.0139609
$206$	−2.07555e38	−	2.06542e39i	−0.0958057	−	0.953380i
$207$		−	1.32311e39i		−	0.562469i
$208$	1.12072e39	−	4.74649e38i	0.438956	−	0.185907i
$209$	−5.59086e39			−2.01833
$210$	−3.58165e37	+	3.59922e36i	−0.0119222	+	0.00119806i
$211$			5.01369e39i			1.53942i	0.638396	+	0.769708i	$0.279598\pi$
$211$			5.01369e39i			1.53942i	−0.638396	+	0.769708i	$0.720402\pi$
$212$	−1.88137e39	+	3.81977e38i	−0.533045	+	0.108225i
$213$	−5.40412e39			−1.41342
$214$	−2.74577e38	−	2.73237e39i	−0.0663178	−	0.659940i
$215$		−	3.79811e37i		−	0.00847450i
$216$	−7.88955e38	−	2.54630e39i	−0.162682	−	0.525044i
$217$	3.02798e39			0.577215
$218$	2.23196e39	−	2.24291e38i	0.393482	−	0.0395413i
$219$		−	7.85613e39i		−	1.28132i
$220$	−4.98107e37	−	2.45335e38i	−0.00751860	−	0.0370317i
$221$	3.96940e39			0.554697
$222$	1.17274e39	+	1.16701e40i	0.151775	+	1.51034i
$223$			1.55876e39i			0.186894i	0.995624	+	0.0934472i	$0.0297886\pi$
$223$			1.55876e39i			0.186894i	−0.995624	+	0.0934472i	$0.970211\pi$
$224$	−1.47847e39	−	2.70137e39i	−0.164285	−	0.300171i
$225$	5.43088e39			0.559458
$226$	5.55530e39	−	5.58256e38i	0.530719	−	0.0533322i
$227$			5.95610e39i			0.527865i	0.964541	+	0.263932i	$0.0850196\pi$
$227$			5.95610e39i			0.527865i	−0.964541	+	0.263932i	$0.914980\pi$
$228$	−2.22864e40	+	4.52485e39i	−1.83294	+	0.372145i
$229$	5.73463e39			0.437827			0.218913	−	0.975744i	$-0.429749\pi$
$229$	5.73463e39			0.437827			0.218913	+	0.975744i	$0.429749\pi$
$230$	3.97221e37	+	3.95281e38i	0.00281617	+	0.0280242i
$231$		−	8.74652e39i		−	0.576012i
$232$	−1.07485e39	+	3.33035e38i	−0.0657736	+	0.0203795i
$233$	2.35154e40			1.33752			0.668761	−	0.743477i	$-0.266825\pi$
$233$	2.35154e40			1.33752			0.668761	+	0.743477i	$0.266825\pi$
$234$	5.02160e39	−	5.04624e38i	0.265566	−	0.0266869i
$235$			8.54339e38i			0.0420220i
$236$	−4.08685e39	−	2.01291e40i	−0.187018	−	0.921130i
$237$	1.70466e40			0.725967
$238$	−1.00421e39	−	9.99309e39i	−0.0398123	−	0.396179i
$239$			4.51182e40i			1.66566i	0.553525	+	0.832832i	$0.313282\pi$
$239$			4.51182e40i			1.66566i	−0.553525	+	0.832832i	$0.686718\pi$
$240$	−3.97113e38	−	9.37647e38i	−0.0136560	−	0.0322439i
$241$	−1.58276e40			−0.507136			−0.253568	−	0.967318i	$-0.581604\pi$
$241$	−1.58276e40			−0.507136			−0.253568	+	0.967318i	$0.581604\pi$
$242$	2.72048e40	−	2.73383e39i	0.812427	−	0.0816413i
$243$		−	3.61707e40i		−	1.00705i
$244$	−6.35945e40	+	1.29117e40i	−1.65117	+	0.335240i
$245$	−1.02203e39			−0.0247537
$246$	−2.75155e39	−	2.73812e40i	−0.0621843	−	0.618807i
$247$			3.38428e40i			0.713868i
$248$	2.53507e40	+	8.18176e40i	0.499242	+	1.61127i
$249$	−5.51287e40			−1.01388
$250$	−3.24626e39	+	3.26218e38i	−0.0557703	+	0.00560439i
$251$		−	1.04709e41i		−	1.68086i	−0.541923	−	0.840428i	$-0.682304\pi$
$251$		−	1.04709e41i		−	1.68086i	0.541923	−	0.840428i	$-0.317696\pi$
$252$	−2.54082e39	−	1.25144e40i	−0.0381210	−	0.187759i
$253$	−9.65292e40			−1.35397
$254$	1.72141e39	+	1.71301e40i	0.0225794	+	0.224691i
$255$		−	3.32098e39i		−	0.0407458i
$256$	6.06145e40	−	6.25654e40i	0.695820	−	0.718216i
$257$	−7.96095e39			−0.0855268			−0.0427634	−	0.999085i	$-0.513616\pi$
$257$	−7.96095e39			−0.0855268			−0.0427634	+	0.999085i	$0.513616\pi$
$258$	3.73500e40	−	3.75332e39i	0.375626	−	0.0377468i
$259$		−	4.41640e40i		−	0.415884i
$260$	−1.48507e39	+	3.01516e38i	−0.0130978	+	0.00265927i
$261$	−4.66611e39			−0.0385537
$262$	9.96540e39	+	9.91675e40i	0.0771565	+	0.767799i
$263$			1.71022e41i			1.24109i	0.784171	+	0.620545i	$0.213089\pi$
$263$			1.71022e41i			1.24109i	−0.784171	+	0.620545i	$0.786911\pi$
$264$	2.36335e41	−	7.32271e40i	1.60791	−	0.498201i
$265$	2.39023e39			0.0152497
$266$	8.52004e40	−	8.56184e39i	0.509863	−	0.0512365i
$267$			3.20545e41i			1.79969i
$268$	1.36279e39	+	6.71222e39i	0.00718023	+	0.0353651i
$269$	2.51077e41			1.24171			0.620853	−	0.783927i	$-0.286786\pi$
$269$	2.51077e41			1.24171			0.620853	+	0.783927i	$0.286786\pi$
$270$	3.31860e38	+	3.30239e39i	0.00154089	+	0.0153336i
$271$		−	3.41671e41i		−	1.48981i	−0.667171	−	0.744904i	$-0.732495\pi$
$271$		−	3.41671e41i		−	1.48981i	0.667171	−	0.744904i	$-0.267505\pi$
$272$	2.61611e41	−	1.10798e41i	1.07148	−	0.453795i
$273$	−5.29447e40			−0.203731
$274$	−5.03270e41	+	5.05739e40i	−1.81988	+	0.182880i
$275$		−	3.96218e41i		−	1.34672i
$276$	−3.84787e41	+	7.81239e40i	−1.22961	+	0.249649i
$277$	−3.52934e41			−1.06057			−0.530283	−	0.847821i	$-0.677914\pi$
$277$	−3.52934e41			−1.06057			−0.530283	+	0.847821i	$0.677914\pi$
$278$	−9.05691e39	−	9.01269e40i	−0.0255987	−	0.254738i
$279$			3.55185e41i			0.944458i
$280$	1.13478e39	+	3.66243e39i	0.00283939	+	0.00916395i
$281$	4.53388e41			1.06773			0.533867	−	0.845568i	$-0.320738\pi$
$281$	4.53388e41			1.06773			0.533867	+	0.845568i	$0.320738\pi$
$282$	−8.40142e41	+	8.44263e40i	−1.86259	+	0.187173i
$283$		−	2.65623e41i		−	0.554493i	−0.960799	−	0.277246i	$-0.910578\pi$
$283$		−	2.65623e41i		−	0.554493i	0.960799	−	0.277246i	$-0.0894218\pi$
$284$	1.14532e41	+	5.64110e41i	0.225172	+	1.10905i
$285$	2.83144e40			0.0524379
$286$	−3.68156e40	−	3.66359e41i	−0.0642406	−	0.639270i
$287$			1.03620e41i			0.170393i
$288$	3.16873e41	−	1.73426e41i	0.491149	−	0.268809i
$289$	2.42254e41			0.354003
$290$	1.39401e39	−	1.40085e38i	0.00192088	−	0.000193031i
$291$			6.08934e41i			0.791388i
$292$	−8.20063e41	+	1.66499e41i	−1.00540	+	0.204128i
$293$	1.24988e42			1.44583			0.722917	−	0.690935i	$-0.242801\pi$
$293$	1.24988e42			1.44583			0.722917	+	0.690935i	$0.242801\pi$
$294$	−1.00998e41	−	1.00505e42i	−0.110257	−	1.09719i
$295$			2.55736e40i			0.0263522i
$296$	1.19333e42	−	3.69747e41i	1.16092	−	0.359704i
$297$	−8.06457e41			−0.740835
$298$	5.18153e41	−	5.20695e40i	0.449553	−	0.0451759i
$299$			5.84314e41i			0.478890i
$300$	−3.20671e41	−	1.57942e42i	−0.248312	−	1.22302i
$301$	−1.41346e41			−0.103431
$302$	2.72552e41	+	2.71222e42i	0.188509	+	1.87588i
$303$		−	1.39220e42i		−	0.910283i
$304$	9.44655e41	+	2.23048e42i	0.584013	+	1.37894i
$305$	8.07954e40			0.0472377
$306$	1.17220e42	−	1.17795e41i	0.648242	−	0.0651422i
$307$			9.95270e41i			0.520701i	0.965514	+	0.260351i	$0.0838381\pi$
$307$			9.95270e41i			0.520701i	−0.965514	+	0.260351i	$0.916162\pi$
$308$	−9.13007e41	+	1.85369e41i	−0.451972	+	0.0917646i
$309$	−2.55441e42			−1.19673
$310$	−1.06633e40	−	1.06112e41i	−0.00472871	−	0.0470563i
$311$		−	3.16772e42i		−	1.32990i	−0.746886	−	0.664952i	$-0.768452\pi$
$311$		−	3.16772e42i		−	1.32990i	0.746886	−	0.664952i	$-0.231548\pi$
$312$	−4.43260e41	−	1.43059e42i	−0.176210	−	0.568706i
$313$	−1.12965e42			−0.425295			−0.212647	−	0.977129i	$-0.568209\pi$
$313$	−1.12965e42			−0.425295			−0.212647	+	0.977129i	$0.568209\pi$
$314$	3.92543e42	−	3.94469e41i	1.39986	−	0.140672i
$315$			1.58993e40i			0.00537152i
$316$	−3.61277e41	−	1.77942e42i	−0.115654	−	0.569635i
$317$	−6.77521e41			−0.205549			−0.102775	−	0.994705i	$-0.532772\pi$
$317$	−6.77521e41			−0.205549			−0.102775	+	0.994705i	$0.532772\pi$
$318$	2.36205e41	+	2.35051e42i	0.0679246	+	0.675930i
$319$			3.40423e41i			0.0928064i
$320$	−8.94602e40	+	6.13248e40i	−0.0231249	+	0.0158521i
$321$	−3.37925e42			−0.828390
$322$	1.47103e42	−	1.47825e41i	0.342036	−	0.0343714i
$323$			7.89996e42i			1.74254i
$324$	−5.83654e42	+	1.18500e42i	−1.22149	+	0.248001i
$325$	−2.39840e42			−0.476326
$326$	−8.58466e41	−	8.54275e42i	−0.161817	−	1.61027i
$327$		−	2.76037e42i		−	0.493918i
$328$	−2.79987e42	+	8.67523e41i	−0.475645	+	0.147376i
$329$	3.17940e42			0.512879
$330$	−3.06513e41	+	3.08016e40i	−0.0469582	+	0.00471886i
$331$		−	3.84713e42i		−	0.559836i	−0.960024	−	0.279918i	$-0.909693\pi$
$331$		−	3.84713e42i		−	0.559836i	0.960024	−	0.279918i	$-0.0903072\pi$
$332$	1.16837e42	+	5.75461e42i	0.161522	+	0.795552i
$333$	5.18047e42			0.680483
$334$	1.49300e39	+	1.48571e40i	0.000186367	+	0.00185457i
$335$		−	8.52773e39i		−	0.00101175i
$336$	−3.48943e42	+	1.47785e42i	−0.393538	+	0.166672i
$337$	1.11877e43			1.19959			0.599796	−	0.800153i	$-0.295248\pi$
$337$	1.11877e43			1.19959			0.599796	+	0.800153i	$0.295248\pi$
$338$	7.54127e42	−	7.57827e41i	0.768884	−	0.0772656i
$339$		−	6.87051e42i		−	0.666184i
$340$	−3.46661e41	+	7.03831e40i	−0.0319715	+	0.00649123i
$341$	2.59130e43			2.27349
$342$	1.00431e42	+	9.99408e42i	0.0838348	+	0.834255i
$343$			8.11134e42i			0.644307i
$344$	−1.18337e42	−	3.81924e42i	−0.0894594	−	0.288724i
$345$	4.88864e41			0.0351773
$346$	−1.38423e43	+	1.39102e42i	−0.948229	+	0.0952881i
$347$			2.94708e42i			0.192216i	0.995371	+	0.0961082i	$0.0306395\pi$
$347$			2.94708e42i			0.192216i	−0.995371	+	0.0961082i	$0.969361\pi$
$348$	2.75515e41	+	1.35700e42i	0.0171119	+	0.0842819i
$349$	−2.41210e43			−1.42680			−0.713399	−	0.700758i	$-0.752845\pi$
$349$	−2.41210e43			−1.42680			−0.713399	+	0.700758i	$0.752845\pi$
$350$	6.06767e41	+	6.03805e42i	0.0341874	+	0.340204i
$351$			4.88167e42i			0.262028i
$352$	−1.26526e43	−	2.31180e43i	−0.647074	−	1.18229i
$353$	−3.36439e42			−0.163959			−0.0819797	−	0.996634i	$-0.526124\pi$
$353$	−3.36439e42			−0.163959			−0.0819797	+	0.996634i	$0.526124\pi$
$354$	−2.51486e43	+	2.52720e42i	−1.16804	+	0.117377i
$355$		−	7.16689e41i		−	0.0317284i
$356$	3.34601e43	−	6.79346e42i	1.41214	−	0.286709i
$357$	−1.23589e43			−0.497303
$358$	−3.75207e42	−	3.73375e43i	−0.143966	−	1.43263i
$359$			9.41272e42i			0.344437i	0.985059	+	0.172218i	$0.0550935\pi$
$359$			9.41272e42i			0.344437i	−0.985059	+	0.172218i	$0.944907\pi$
$360$	−4.29606e41	+	1.33111e41i	−0.0149944	+	0.00464591i
$361$	−3.73198e43			−1.24256
$362$	3.70989e42	−	3.72809e41i	0.117846	−	0.0118424i
$363$		−	3.36455e43i		−	1.01980i
$364$	1.12208e42	+	5.52664e42i	0.0324565	+	0.159859i
$365$	1.04187e42			0.0287631
$366$	7.98425e42	+	7.94527e43i	0.210405	+	2.09378i
$367$			7.76876e42i			0.195447i	0.995214	+	0.0977234i	$0.0311560\pi$
$367$			7.76876e42i			0.195447i	−0.995214	+	0.0977234i	$0.968844\pi$
$368$	1.63100e43	+	3.85104e43i	0.391778	+	0.925049i
$369$	−1.21548e43			−0.278803
$370$	−1.54768e42	+	1.55527e41i	−0.0339041	+	0.00340704i
$371$		−	8.89519e42i		−	0.186122i
$372$	1.03295e44	−	2.09722e43i	2.06467	−	0.419193i
$373$	1.32973e43			0.253930			0.126965	−	0.991907i	$-0.459476\pi$
$373$	1.32973e43			0.253930			0.126965	+	0.991907i	$0.459476\pi$
$374$	−8.59391e42	−	8.55195e43i	−0.156810	−	1.56044i
$375$			4.01480e42i			0.0700056i
$376$	2.66184e43	+	8.59090e43i	0.443597	+	1.43168i
$377$	2.06066e42			0.0328249
$378$	1.22898e43	−	1.23501e42i	0.187147	−	0.0188065i
$379$		−	3.55713e43i		−	0.517885i	−0.965893	−	0.258943i	$-0.916626\pi$
$379$		−	3.55713e43i		−	0.517885i	0.965893	−	0.258943i	$-0.0833741\pi$
$380$	−6.00081e41	−	2.95561e42i	−0.00835390	−	0.0411458i
$381$	2.11856e43			0.282044
$382$	−2.68113e42	−	2.66804e43i	−0.0341382	−	0.339715i
$383$			6.04026e43i			0.735659i	0.929893	+	0.367830i	$0.119899\pi$
$383$			6.04026e43i			0.735659i	−0.929893	+	0.367830i	$0.880101\pi$
$384$	−6.91462e43	−	8.19134e43i	−0.805633	−	0.954386i
$385$	1.15995e42			0.0129303
$386$	−5.28150e43	+	5.30741e42i	−0.563343	+	0.0566107i
$387$		−	1.65800e43i		−	0.169238i
$388$	6.35637e43	−	1.29054e43i	0.620969	−	0.126076i
$389$	−1.05760e44			−0.988961			−0.494481	−	0.869189i	$-0.664642\pi$
$389$	−1.05760e44			−0.988961			−0.494481	+	0.869189i	$0.664642\pi$
$390$	1.86449e41	+	1.85539e42i	0.00166903	+	0.0166088i
$391$			1.36397e44i			1.16896i
$392$	−1.02772e44	+	3.18431e43i	−0.843353	+	0.261308i
$393$	1.22645e44			0.963778
$394$	−6.55651e43	+	6.58867e42i	−0.493443	+	0.0495864i
$395$			2.26071e42i			0.0162965i
$396$	−2.17440e43	−	1.07097e44i	−0.150148	−	0.739532i
$397$	2.37534e44			1.57140			0.785701	−	0.618606i	$-0.212302\pi$
$397$	2.37534e44			1.57140			0.785701	+	0.618606i	$0.212302\pi$
$398$	1.47607e43	+	1.46886e44i	0.0935608	+	0.931040i
$399$		−	1.05371e44i		−	0.640005i
$400$	−1.58071e44	+	6.69466e43i	−0.920097	+	0.389680i
$401$	−9.78652e43			−0.545977			−0.272988	−	0.962017i	$-0.588012\pi$
$401$	−9.78652e43			−0.545977			−0.272988	+	0.962017i	$0.588012\pi$
$402$	8.38601e42	−	8.42716e41i	0.0448449	−	0.00450649i
$403$		−	1.56858e44i		−	0.804118i
$404$	−1.45325e44	+	2.95055e43i	−0.714261	+	0.145017i
$405$	7.41519e42			0.0349451
$406$	−5.21323e41	−	5.18778e42i	−0.00235594	−	0.0234444i
$407$		−	3.77949e44i		−	1.63806i
$408$	−1.03471e44	−	3.33945e44i	−0.430125	−	1.38820i
$409$	−2.26029e43			−0.0901296			−0.0450648	−	0.998984i	$-0.514349\pi$
$409$	−2.26029e43			−0.0901296			−0.0450648	+	0.998984i	$0.514349\pi$
$410$	3.63126e42	−	3.64908e41i	0.0138910	−	0.00139591i
$411$			6.22419e44i			2.28440i
$412$	5.41368e43	+	2.66642e44i	0.190651	+	0.939023i
$413$	9.51714e43			0.321629
$414$	1.73400e43	+	1.72553e44i	0.0562396	+	0.559650i
$415$		−	7.31111e42i		−	0.0227597i
$416$	−1.39939e44	+	7.65891e43i	−0.418168	+	0.228865i
$417$	−1.11464e44			−0.319759
$418$	7.29133e44	−	7.32711e43i	2.00821	−	0.201807i
$419$			9.69330e43i			0.256350i	0.991752	+	0.128175i	$0.0409119\pi$
$419$			9.69330e43i			0.256350i	−0.991752	+	0.128175i	$0.959088\pi$
$420$	4.62384e42	−	9.38786e41i	0.0117426	−	0.00238412i
$421$	5.33590e44			1.30140			0.650702	−	0.759333i	$-0.274475\pi$
$421$	5.33590e44			1.30140			0.650702	+	0.759333i	$0.274475\pi$
$422$	−6.57070e43	−	6.53862e44i	−0.153922	−	1.53170i
$423$			3.72946e44i			0.839190i
$424$	2.40353e44	−	7.44718e43i	0.519553	−	0.160980i
$425$	−5.59861e44			−1.16270
$426$	7.04779e44	−	7.08236e43i	1.40634	−	0.141324i
$427$		−	3.00678e44i		−	0.576537i
$428$	7.16180e43	+	3.52743e44i	0.131971	+	0.650002i
$429$	−4.53094e44			−0.802443
$430$	4.97762e41	+	4.95332e42i	0.000847340	+	0.00843203i
$431$		−	6.06761e44i		−	0.992897i	−0.868066	−	0.496448i	$-0.834637\pi$
$431$		−	6.06761e44i		−	0.992897i	0.868066	−	0.496448i	$-0.165363\pi$
$432$	1.36262e44	+	3.21736e44i	0.214364	+	0.506147i
$433$	1.10913e44			0.167759			0.0838796	−	0.996476i	$-0.473269\pi$
$433$	1.10913e44			0.167759			0.0838796	+	0.996476i	$0.473269\pi$
$434$	−3.94894e44	+	3.96832e43i	−0.574322	+	0.0577140i
$435$		−	1.72404e42i		−	0.00241119i
$436$	−2.88141e44	+	5.85018e43i	−0.387557	+	0.0786862i
$437$	−1.16291e45			−1.50439
$438$	1.02958e44	+	1.02456e45i	0.128116	+	1.27490i
$439$		−	2.57551e44i		−	0.308295i	−0.988048	−	0.154147i	$-0.950737\pi$
$439$		−	2.57551e44i		−	0.308295i	0.988048	−	0.154147i	$-0.0492631\pi$
$440$	9.71130e42	+	3.13426e43i	0.0111836	+	0.0360944i
$441$	−4.46149e44			−0.494338
$442$	−5.17669e44	+	5.20209e43i	−0.551917	+	0.0554625i
$443$			2.48387e44i			0.254839i	0.991849	+	0.127420i	$0.0406695\pi$
$443$			2.48387e44i			0.254839i	−0.991849	+	0.127420i	$0.959331\pi$
$444$	−3.05886e44	−	1.50659e45i	−0.302029	−	1.48760i
$445$	−4.25104e43			−0.0403994
$446$	−2.04283e43	−	2.03286e44i	−0.0186870	−	0.185958i
$447$		−	6.40825e44i		−	0.564302i
$448$	2.28218e44	+	3.32924e44i	0.193475	+	0.282240i
$449$	−1.11425e45			−0.909484			−0.454742	−	0.890623i	$-0.650269\pi$
$449$	−1.11425e45			−0.909484			−0.454742	+	0.890623i	$0.650269\pi$
$450$	−7.08269e44	+	7.11744e43i	−0.556654	+	0.0559385i
$451$			8.86768e44i			0.671134i
$452$	−7.17180e44	+	1.45610e44i	−0.522727	+	0.106130i
$453$	3.35433e45			2.35470
$454$	−7.80577e43	−	7.76766e44i	−0.0527796	−	0.525219i
$455$		−	7.02147e42i		−	0.00457335i
$456$	2.84719e45	−	8.82184e44i	1.78655	−	0.553550i
$457$	1.36105e45			0.822810			0.411405	−	0.911453i	$-0.365038\pi$
$457$	1.36105e45			0.822810			0.411405	+	0.911453i	$0.365038\pi$
$458$	−7.47882e44	+	7.51552e43i	−0.435632	+	0.0437770i
$459$			1.13953e45i			0.639604i
$460$	−1.03607e43	−	5.10301e43i	−0.00560411	−	0.0276022i
$461$	2.80519e45			1.46234			0.731168	−	0.682198i	$-0.238976\pi$
$461$	2.80519e45			1.46234			0.731168	+	0.682198i	$0.238976\pi$
$462$	1.14627e44	+	1.14068e45i	0.0575937	+	0.573125i
$463$			2.45959e45i			1.19120i	0.803280	+	0.595601i	$0.203086\pi$
$463$			2.45959e45i			1.19120i	−0.803280	+	0.595601i	$0.796914\pi$
$464$	1.35812e44	−	5.75193e43i	0.0634063	−	0.0268539i
$465$	−1.31234e44			−0.0590673
$466$	−3.06676e45	+	3.08181e44i	−1.33082	+	0.133735i
$467$		−	3.93242e43i		−	0.0164541i	−0.999966	−	0.00822703i	$-0.997381\pi$
$467$		−	3.93242e43i		−	0.0164541i	0.999966	−	0.00822703i	$-0.00261878\pi$
$468$	−6.48280e44	+	1.31621e44i	−0.261567	+	0.0531064i
$469$	−3.17357e43			−0.0123484
$470$	−1.11965e43	−	1.11419e44i	−0.00420165	−	0.0418114i
$471$		−	4.85477e45i		−	1.75717i
$472$	7.96789e44	+	2.57158e45i	0.278182	+	0.897814i
$473$	−1.20962e45			−0.407389
$474$	−2.22314e45	+	2.23405e44i	−0.722329	+	0.0725872i
$475$		−	4.77333e45i		−	1.49634i
$476$	2.61929e44	+	1.29009e45i	0.0792255	+	0.390213i
$477$	1.04341e45			0.304540
$478$	−5.91297e44	−	5.88410e45i	−0.166545	−	1.65732i
$479$			4.82849e45i			1.31252i	0.754533	+	0.656262i	$0.227864\pi$
$479$			4.82849e45i			1.31252i	−0.754533	+	0.656262i	$0.772136\pi$
$480$	6.40779e43	+	1.17079e44i	0.0168115	+	0.0307169i
$481$	−2.28782e45			−0.579368
$482$	2.06416e45	−	2.07428e44i	0.504595	−	0.0507070i
$483$		−	1.81929e45i		−	0.429340i
$484$	−3.51209e45	+	7.13065e44i	−0.800193	+	0.162464i
$485$	−8.07563e43			−0.0177651
$486$	4.74035e44	+	4.71721e45i	0.100692	+	1.00200i
$487$			6.90284e45i			1.41591i	0.706258	+	0.707954i	$0.250382\pi$
$487$			6.90284e45i			1.41591i	−0.706258	+	0.707954i	$0.749618\pi$
$488$	8.12447e45	−	2.51732e45i	1.60938	−	0.498656i
$489$	−1.05652e46			−2.02129
$490$	1.33288e44	−	1.33942e43i	0.0246297	−	0.00247505i
$491$			5.06561e43i			0.00904162i	0.999990	+	0.00452081i	$0.00143902\pi$
$491$			5.06561e43i			0.00904162i	−0.999990	+	0.00452081i	$0.998561\pi$
$492$	7.17688e44	+	3.53486e45i	0.123745	+	0.609488i
$493$	4.81022e44			0.0801249
$494$	−4.43527e44	−	4.41361e45i	−0.0713775	−	0.710291i
$495$			1.36064e44i			0.0211570i
$496$	−4.37837e45	−	1.03380e46i	−0.657846	−	1.55328i
$497$	−2.66714e45			−0.387246
$498$	7.18961e45	−	7.22488e44i	1.00880	−	0.101375i
$499$		−	3.58701e45i		−	0.486433i	−0.969972	−	0.243217i	$-0.921797\pi$
$499$		−	3.58701e45i		−	0.486433i	0.969972	−	0.243217i	$-0.0782026\pi$
$500$	4.19086e44	−	8.50876e43i	0.0549304	−	0.0111526i
$501$	1.83745e43			0.00232795
$502$	1.37226e45	+	1.36556e46i	0.168064	+	1.67243i
$503$			1.70281e45i			0.201609i	0.994906	+	0.100804i	$0.0321416\pi$
$503$			1.70281e45i			0.201609i	−0.994906	+	0.100804i	$0.967858\pi$
$504$	4.95368e44	+	1.59877e45i	0.0567034	+	0.183006i
$505$	1.84632e44			0.0204340
$506$	1.25889e46	−	1.26506e45i	1.34719	−	0.135380i
$507$		−	9.32666e45i		−	0.965141i
$508$	−4.48997e44	−	2.21146e45i	−0.0449324	−	0.221308i
$509$	6.82407e45			0.660452			0.330226	−	0.943902i	$-0.392875\pi$
$509$	6.82407e45			0.660452			0.330226	+	0.943902i	$0.392875\pi$
$510$	4.35231e43	+	4.33106e44i	0.00407405	+	0.0405416i
$511$		−	3.87730e45i		−	0.351054i
$512$	−7.08510e45	+	8.95386e45i	−0.620521	+	0.784190i
$513$	−9.71558e45			−0.823140
$514$	1.03823e45	−	1.04332e44i	0.0850982	−	0.00855157i
$515$		−	3.38763e44i		−	0.0268641i
$516$	−4.82181e45	+	9.78980e44i	−0.369969	+	0.0751154i
$517$	2.72089e46			2.02009
$518$	5.78791e44	+	5.75965e45i	0.0415830	+	0.413800i
$519$			1.71194e46i			1.19026i
$520$	1.89724e44	−	5.87848e43i	0.0127663	−	0.00395556i
$521$	−2.70956e45			−0.176465			−0.0882323	−	0.996100i	$-0.528122\pi$
$521$	−2.70956e45			−0.176465			−0.0882323	+	0.996100i	$0.528122\pi$
$522$	6.08532e44	−	6.11517e43i	0.0383605	−	0.00385487i
$523$			1.96928e46i			1.20165i	0.799380	+	0.600826i	$0.205162\pi$
$523$			1.96928e46i			1.20165i	−0.799380	+	0.600826i	$0.794838\pi$
$524$	−2.59928e45	−	1.28023e46i	−0.153540	−	0.756236i
$525$	7.46755e45			0.427041
$526$	−2.24132e45	−	2.23038e46i	−0.124093	−	1.23487i
$527$		−	3.66154e46i		−	1.96284i
$528$	−2.98621e46	+	1.26472e46i	−1.55004	+	0.656475i
$529$	−1.83143e44			−0.00920545
$530$	−3.11723e44	+	3.13252e43i	−0.0151733	+	0.00152477i
$531$			1.11637e46i			0.526261i
$532$	−1.09992e46	+	2.23319e45i	−0.502185	+	0.101959i
$533$	5.36781e45			0.237375
$534$	−4.20090e45	−	4.18039e46i	−0.179946	−	1.79067i
$535$		−	4.48153e44i		−	0.0185957i
$536$	−2.65696e44	−	8.57516e44i	−0.0106803	−	0.0344699i
$537$	−4.61771e46			−1.79831
$538$	−3.27443e46	+	3.29049e45i	−1.23548	+	0.124154i
$539$			3.25495e46i			1.18997i
$540$	−8.65590e43	−	4.26333e44i	−0.00306633	−	0.0151027i
$541$	3.23329e46			1.10992			0.554959	−	0.831877i	$-0.312734\pi$
$541$	3.23329e46			1.10992			0.554959	+	0.831877i	$0.312734\pi$
$542$	4.47777e45	+	4.45591e46i	0.148962	+	1.48234i
$543$		−	4.58819e45i		−	0.147926i
$544$	−3.26660e46	+	1.78783e46i	−1.02074	+	0.558655i
$545$	3.66077e44			0.0110875
$546$	6.90479e45	−	6.93867e44i	0.202710	−	0.0203705i
$547$		−	6.14375e46i		−	1.74843i	−0.485536	−	0.874217i	$-0.661375\pi$
$547$		−	6.14375e46i		−	1.74843i	0.485536	−	0.874217i	$-0.338625\pi$
$548$	6.49713e46	−	1.31912e46i	1.79247	−	0.363928i
$549$	3.52698e46			0.943350
$550$	5.19264e45	+	5.16728e46i	0.134655	+	1.33997i
$551$			4.10116e45i			0.103117i
$552$	4.91582e46	−	1.52314e46i	1.19848	−	0.371343i
$553$	8.41316e45			0.198899
$554$	4.60280e46	−	4.62538e45i	1.05525	−	0.106043i
$555$			1.91409e45i			0.0425581i
$556$	2.36232e45	+	1.16352e46i	0.0509409	+	0.250902i
$557$	2.46554e46			0.515673			0.257836	−	0.966189i	$-0.416990\pi$
$557$	2.46554e46			0.515673			0.257836	+	0.966189i	$0.416990\pi$
$558$	−4.65487e45	−	4.63215e46i	−0.0944336	−	0.939725i
$559$			7.32210e45i			0.144090i
$560$	−1.95991e44	−	4.62764e44i	−0.00374144	−	0.00883412i
$561$	−1.05766e47			−1.95875
$562$	−5.91287e46	+	5.94188e45i	−1.06238	+	0.106760i
$563$			5.12878e46i			0.894070i	0.894516	+	0.447035i	$0.147520\pi$
$563$			5.12878e46i			0.894070i	−0.894516	+	0.447035i	$0.852480\pi$
$564$	1.08461e47	−	2.20209e46i	1.83454	−	0.372470i
$565$	9.11161e44			0.0149545
$566$	3.48112e45	+	3.46412e46i	0.0554421	+	0.551714i
$567$		−	2.75954e46i		−	0.426506i
$568$	−2.23296e46	−	7.20674e46i	−0.334935	−	1.08098i
$569$	−6.54696e46			−0.953085			−0.476542	−	0.879152i	$-0.658110\pi$
$569$	−6.54696e46			−0.953085			−0.476542	+	0.879152i	$0.658110\pi$
$570$	−3.69263e45	+	3.71075e44i	−0.0521751	+	0.00524311i
$571$			8.14239e46i			1.11670i	0.829604	+	0.558352i	$0.188566\pi$
$571$			8.14239e46i			1.11670i	−0.829604	+	0.558352i	$0.811434\pi$
$572$	9.60263e45	+	4.72963e46i	0.127837	+	0.629643i
$573$	−3.29969e46			−0.426427
$574$	−1.35800e45	−	1.35137e46i	−0.0170371	−	0.169539i
$575$		−	8.24141e46i		−	1.00380i
$576$	−3.90523e46	+	2.67702e46i	−0.461811	+	0.316570i
$577$	−5.94016e46			−0.682039			−0.341020	−	0.940056i	$-0.610772\pi$
$577$	−5.94016e46			−0.682039			−0.341020	+	0.940056i	$0.610772\pi$
$578$	−3.15936e46	+	3.17486e45i	−0.352229	+	0.0353957i
$579$			6.53189e46i			0.707136i
$580$	−1.79965e44	+	3.65385e43i	−0.00189196	+	0.000384127i
$581$	−2.72081e46			−0.277782
$582$	−7.98039e45	−	7.94143e46i	−0.0791286	−	0.787423i
$583$		−	7.61239e46i		−	0.733087i
$584$	1.04767e47	−	3.24613e46i	0.979952	−	0.303632i
$585$	8.23625e44			0.00748307
$586$	−1.63003e47	+	1.63803e46i	−1.43859	+	0.144565i
$587$		−	2.03399e47i		−	1.74382i	−0.489666	−	0.871910i	$-0.662881\pi$
$587$		−	2.03399e47i		−	1.74382i	0.489666	−	0.871910i	$-0.337119\pi$
$588$	2.63433e46	+	1.29750e47i	0.219409	+	1.08067i
$589$	3.12181e47			2.52607
$590$	−3.35155e44	−	3.33519e45i	−0.00263488	−	0.0262202i
$591$			8.10875e46i			0.619394i
$592$	−1.50783e47	+	6.38598e46i	−1.11914	+	0.473979i
$593$	−1.41984e47			−1.02402			−0.512012	−	0.858978i	$-0.671100\pi$
$593$	−1.41984e47			−1.02402			−0.512012	+	0.858978i	$0.671100\pi$
$594$	1.05174e47	−	1.05690e46i	0.737123	−	0.0740739i
$595$		−	1.63903e45i		−	0.0111635i
$596$	−6.68926e46	+	1.35813e46i	−0.442784	+	0.0898990i
$597$	1.81661e47			1.16869
$598$	−7.65772e45	−	7.62033e46i	−0.0478828	−	0.476490i
$599$			2.93795e47i			1.78561i	0.450439	+	0.892807i	$0.351268\pi$
$599$			2.93795e47i			1.78561i	−0.450439	+	0.892807i	$0.648732\pi$
$600$	6.25194e46	+	2.01777e47i	0.369355	+	1.19207i
$601$	1.24621e47			0.715693			0.357846	−	0.933780i	$-0.383511\pi$
$601$	1.24621e47			0.715693			0.357846	+	0.933780i	$0.383511\pi$
$602$	1.84336e46	−	1.85241e45i	0.102913	−	0.0103418i
$603$		−	3.72263e45i		−	0.0202048i
$604$	−7.10899e46	−	3.50142e47i	−0.375128	−	1.84764i
$605$	4.46203e45			0.0228924
$606$	1.82455e46	+	1.81564e47i	0.0910165	+	0.905721i
$607$		−	1.72419e46i		−	0.0836330i	−0.999125	−	0.0418165i	$-0.986686\pi$
$607$		−	1.72419e46i		−	0.0836330i	0.999125	−	0.0418165i	$-0.0133145\pi$
$608$	−1.52429e47	−	2.78508e47i	−0.718963	−	1.31364i
$609$	−6.41598e45			−0.0294286
$610$	−1.05369e46	+	1.05886e45i	−0.0470010	+	0.00472316i
$611$		−	1.64702e47i		−	0.714492i
$612$	−1.51329e47	+	3.07245e46i	−0.638480	+	0.129631i
$613$	4.18675e47			1.71810			0.859052	−	0.511889i	$-0.171054\pi$
$613$	4.18675e47			1.71810			0.859052	+	0.511889i	$0.171054\pi$
$614$	−1.30435e46	−	1.29798e47i	−0.0520634	−	0.518092i
$615$		−	4.49096e45i		−	0.0174366i
$616$	1.16641e47	−	3.61403e46i	0.440532	−	0.136496i
$617$	−3.40439e47			−1.25081			−0.625406	−	0.780300i	$-0.715067\pi$
$617$	−3.40439e47			−1.25081			−0.625406	+	0.780300i	$0.715067\pi$
$618$	3.33133e47	−	3.34768e46i	1.19073	−	0.119657i
$619$			3.76747e47i			1.31011i	0.755580	+	0.655057i	$0.227355\pi$
$619$			3.76747e47i			1.31011i	−0.755580	+	0.655057i	$0.772645\pi$
$620$	2.78131e45	+	1.36989e46i	0.00941003	+	0.0463476i
$621$	−1.67745e47			−0.552194
$622$	4.15146e46	+	4.13119e47i	0.132973	+	1.32324i
$623$			1.58201e47i			0.493075i
$624$	7.65565e46	+	1.80762e47i	0.232190	+	0.548238i
$625$	3.38014e47			0.997642
$626$	1.47323e47	−	1.48046e46i	0.423163	−	0.0425239i
$627$		−	9.01754e47i		−	2.52081i
$628$	−5.06766e47	+	1.02890e47i	−1.37878	+	0.279935i
$629$	−5.34047e47			−1.41423
$630$	−2.08368e44	−	2.07350e45i	−0.000537083	−	0.00534460i
$631$			8.82171e46i			0.221337i	0.993857	+	0.110668i	$0.0352992\pi$
$631$			8.82171e46i			0.221337i	−0.993857	+	0.110668i	$0.964701\pi$
$632$	7.04362e46	+	2.27328e47i	0.172031	+	0.555217i
$633$	−8.08662e47			−1.92267
$634$	8.83591e46	−	8.87926e45i	0.204519	−	0.0205522i
$635$			2.80961e45i			0.00633131i
$636$	−6.16093e46	−	3.03447e47i	−0.135168	−	0.665751i
$637$	1.97030e47			0.420883
$638$	−4.46142e45	−	4.43964e46i	−0.00927943	−	0.0923413i
$639$		−	3.12858e47i		−	0.633625i
$640$	1.08633e46	−	9.17010e45i	0.0214240	−	0.0180848i
$641$	−8.63808e47			−1.65894			−0.829470	−	0.558552i	$-0.811357\pi$
$641$	−8.63808e47			−1.65894			−0.829470	+	0.558552i	$0.811357\pi$
$642$	4.40705e47	−	4.42867e46i	0.824238	−	0.0828282i
$643$			2.09498e47i			0.381586i	0.981630	+	0.190793i	$0.0611060\pi$
$643$			2.09498e47i			0.381586i	−0.981630	+	0.190793i	$0.938894\pi$
$644$	−1.89907e47	+	3.85571e46i	−0.336885	+	0.0683982i
$645$	6.12601e45			0.0105843
$646$	−1.03533e47	−	1.03027e48i	−0.174231	−	1.73380i
$647$			4.18484e47i			0.685971i	0.939341	+	0.342986i	$0.111438\pi$
$647$			4.18484e47i			0.685971i	−0.939341	+	0.342986i	$0.888562\pi$
$648$	7.45643e47	−	2.31033e47i	1.19057	−	0.368891i
$649$	8.14465e47			1.26681
$650$	3.12788e47	−	3.14322e46i	0.473939	−	0.0476264i
$651$			4.88385e47i			0.720917i
$652$	2.23914e47	+	1.10285e48i	0.322012	+	1.58602i
$653$	−1.37008e46			−0.0191965			−0.00959824	−	0.999954i	$-0.503055\pi$
$653$	−1.37008e46			−0.0191965			−0.00959824	+	0.999954i	$0.503055\pi$
$654$	3.61760e46	+	3.59994e47i	0.0493854	+	0.491443i
$655$			1.62651e46i			0.0216349i
$656$	3.53777e47	−	1.49832e47i	0.458526	−	0.194196i
$657$	4.54811e47			0.574407
$658$	−4.14642e47	+	4.16676e46i	−0.510309	+	0.0512812i
$659$		−	8.16368e46i		−	0.0979116i	−0.998801	−	0.0489558i	$-0.984411\pi$
$659$		−	8.16368e46i		−	0.0979116i	0.998801	−	0.0489558i	$-0.0155893\pi$
$660$	3.95702e46	−	8.03400e45i	0.0462511	−	0.00939042i
$661$	1.09275e48			1.24478			0.622392	−	0.782705i	$-0.286161\pi$
$661$	1.09275e48			1.24478			0.622392	+	0.782705i	$0.286161\pi$
$662$	5.04185e46	+	5.01724e47i	0.0559763	+	0.557030i
$663$			6.40227e47i			0.692794i
$664$	−2.27790e47	−	7.35177e47i	−0.240258	−	0.775416i
$665$	1.39743e46			0.0143668
$666$	−6.75612e47	+	6.78927e46i	−0.677073	+	0.0680395i
$667$			7.08087e46i			0.0691747i
$668$	−3.89419e44	−	1.91802e45i	−0.000370866	−	0.00182664i
$669$	−2.51413e47			−0.233423
$670$	1.11760e44	+	1.11215e45i	0.000101162	+	0.00100668i
$671$		−	2.57316e48i		−	2.27083i
$672$	4.35706e47	−	2.38464e47i	0.374901	−	0.205185i
$673$	1.35442e48			1.13631			0.568155	−	0.822921i	$-0.307657\pi$
$673$	1.35442e48			1.13631			0.568155	+	0.822921i	$0.307657\pi$
$674$	−1.45905e48	+	1.46621e47i	−1.19358	+	0.119944i
$675$		−	6.88532e47i		−	0.549237i
$676$	−9.73565e47	+	1.97664e47i	−0.757305	+	0.153757i
$677$	−4.45192e47			−0.337707			−0.168854	−	0.985641i	$-0.554006\pi$
$677$	−4.45192e47			−0.337707			−0.168854	+	0.985641i	$0.554006\pi$
$678$	9.00415e46	+	8.96019e47i	0.0666098	+	0.662846i
$679$			3.00532e47i			0.216823i
$680$	4.42874e46	−	1.37222e46i	0.0311623	−	0.00965544i
$681$	−9.60664e47			−0.659281
$682$	−3.37945e48	+	3.39603e47i	−2.26210	+	0.227320i
$683$			2.15097e48i			1.40437i	0.711994	+	0.702186i	$0.247792\pi$
$683$			2.15097e48i			1.40437i	−0.711994	+	0.702186i	$0.752208\pi$
$684$	−2.61955e47	−	1.29022e48i	−0.166829	−	0.821692i
$685$	−8.25446e46			−0.0512801
$686$	−1.06303e47	−	1.05784e48i	−0.0644223	−	0.641078i
$687$			9.24942e47i			0.546827i
$688$	2.04382e47	+	4.82578e47i	0.117880	+	0.278332i
$689$	−4.60795e47			−0.259287
$690$	−6.37552e46	+	6.40680e45i	−0.0350011	+	0.00351728i
$691$		−	7.03708e47i		−	0.376934i	−0.982079	−	0.188467i	$-0.939648\pi$
$691$		−	7.03708e47i		−	0.376934i	0.982079	−	0.188467i	$-0.0603519\pi$
$692$	1.78701e48	−	3.62819e47i	0.933949	−	0.189621i
$693$	5.06357e47			0.258221
$694$	−3.86229e46	−	3.84344e47i	−0.0192192	−	0.191253i
$695$		−	1.47823e46i		−	0.00717795i
$696$	−5.37155e46	−	1.73363e47i	−0.0254532	−	0.0821485i
$697$	1.25301e48			0.579427
$698$	3.14574e48	−	3.16117e47i	1.41965	−	0.142661i
$699$			3.79281e48i			1.67051i
$700$	−1.58263e47	−	7.79501e47i	−0.0680321	−	0.335081i
$701$	7.17291e47			0.300946			0.150473	−	0.988614i	$-0.451920\pi$
$701$	7.17291e47			0.300946			0.150473	+	0.988614i	$0.451920\pi$
$702$	−6.39767e46	−	6.36644e47i	−0.0261994	−	0.260715i
$703$		−	4.55325e48i		−	1.82004i
$704$	1.95306e48	+	2.84912e48i	0.762046	+	1.11167i
$705$	−1.37797e47			−0.0524837
$706$	4.38767e47	−	4.40920e46i	0.163138	−	0.0163938i
$707$		−	6.87103e47i		−	0.249397i
$708$	3.24664e48	−	6.59170e47i	1.15045	−	0.233578i
$709$	−5.07521e48			−1.75577			−0.877886	−	0.478871i	$-0.841046\pi$
$709$	−5.07521e48			−1.75577			−0.877886	+	0.478871i	$0.841046\pi$
$710$	9.39256e45	+	9.34671e46i	0.00317243	+	0.0315694i
$711$			9.86872e47i			0.325445i
$712$	−4.27468e48	+	1.32448e48i	−1.37640	+	0.426468i
$713$	5.38996e48			1.69459
$714$	1.61179e48	−	1.61970e47i	0.494811	−	0.0497239i
$715$		−	6.00888e46i		−	0.0180132i
$716$	9.78652e47	+	4.82020e48i	0.286488	+	1.41105i
$717$	−7.27715e48			−2.08035
$718$	−1.23358e47	−	1.22756e48i	−0.0344392	−	0.342711i
$719$		−	3.96894e48i		−	1.08214i	−0.840977	−	0.541070i	$-0.818019\pi$
$719$		−	3.96894e48i		−	1.08214i	0.840977	−	0.541070i	$-0.181981\pi$
$720$	5.42827e46	−	2.29899e46i	0.0144547	−	0.00612187i
$721$	−1.26070e48			−0.327877
$722$	4.86707e48	−	4.89095e47i	1.23633	−	0.124240i
$723$		−	2.55284e48i		−	0.633392i
$724$	−4.78939e47	+	9.72398e46i	−0.116071	+	0.0235661i
$725$	−2.90645e47			−0.0688044
$726$	4.40941e47	+	4.38788e48i	0.101967	+	1.01469i
$727$			7.53308e48i			1.70172i	0.525395	+	0.850859i	$0.323918\pi$
$727$			7.53308e48i			1.70172i	−0.525395	+	0.850859i	$0.676082\pi$
$728$	−2.18766e47	−	7.06052e47i	−0.0482777	−	0.155813i
$729$	5.26424e46			0.0113493
$730$	−1.35876e47	+	1.36543e46i	−0.0286190	+	0.00287594i
$731$			1.70921e48i			0.351721i
$732$	−2.08253e48	−	1.02572e49i	−0.418701	−	2.06225i
$733$	4.14786e48			0.814809			0.407405	−	0.913248i	$-0.366434\pi$
$733$	4.14786e48			0.814809			0.407405	+	0.913248i	$0.366434\pi$
$734$	−1.01813e47	−	1.01316e48i	−0.0195421	−	0.194467i
$735$		−	1.64844e47i		−	0.0309164i
$736$	−2.63176e48	−	4.80859e48i	−0.482308	−	0.881241i
$737$	−2.71590e47			−0.0486370
$738$	1.58516e48	−	1.59294e47i	0.277406	−	0.0278767i
$739$		−	8.02853e48i		−	1.37303i	−0.727115	−	0.686516i	$-0.759139\pi$
$739$		−	8.02853e48i		−	1.37303i	0.727115	−	0.686516i	$-0.240861\pi$
$740$	1.99803e47	−	4.05663e46i	0.0333935	−	0.00677994i
$741$	−5.45853e48			−0.891592
$742$	1.16576e47	+	1.16007e48i	0.0186098	+	0.185190i
$743$			9.76643e48i			1.52379i	0.647699	+	0.761897i	$0.275732\pi$
$743$			9.76643e48i			1.52379i	−0.647699	+	0.761897i	$0.724268\pi$
$744$	−1.31964e49	+	4.08883e48i	−2.01241	+	0.623532i
$745$	8.49855e46			0.0126674
$746$	−1.73418e48	+	1.74268e47i	−0.252658	+	0.0253897i
$747$		−	3.19153e48i		−	0.454516i
$748$	2.24155e48	+	1.10404e49i	0.312048	+	1.53694i
$749$	−1.66779e48			−0.226960
$750$	−5.26160e46	−	5.23591e47i	−0.00699965	−	0.0696547i
$751$			6.95844e48i			0.904968i	0.891773	+	0.452484i	$0.149462\pi$
$751$			6.95844e48i			0.904968i	−0.891773	+	0.452484i	$0.850538\pi$
$752$	−4.59732e48	−	1.08550e49i	−0.584523	−	1.38015i
$753$	1.68886e49			2.09932
$754$	−2.68741e47	+	2.70060e46i	−0.0326604	+	0.00328207i
$755$			4.44848e47i			0.0528583i
$756$	−1.58659e48	+	3.22127e47i	−0.184329	+	0.0374246i
$757$	2.55139e48			0.289832			0.144916	−	0.989444i	$-0.453709\pi$
$757$	2.55139e48			0.289832			0.144916	+	0.989444i	$0.453709\pi$
$758$	4.66180e47	+	4.63904e48i	0.0517818	+	0.515290i
$759$		−	1.55693e49i		−	1.69106i
$760$	1.16994e47	+	3.77592e47i	0.0124261	+	0.0401043i
$761$	6.18484e48			0.642376			0.321188	−	0.947015i	$-0.395918\pi$
$761$	6.18484e48			0.642376			0.321188	+	0.947015i	$0.395918\pi$
$762$	−2.76292e48	+	2.77648e47i	−0.280630	+	0.0282007i
$763$		−	1.36235e48i		−	0.135323i
$764$	6.99319e47	+	3.44439e48i	0.0679342	+	0.334599i
$765$	1.92260e47			0.0182660
$766$	−7.91606e47	−	7.87742e48i	−0.0735564	−	0.731972i
$767$		−	4.93014e48i		−	0.448062i
$768$	1.00912e49	+	9.77656e48i	0.897022	+	0.869051i
$769$	1.18918e49			1.03395			0.516975	−	0.856001i	$-0.327058\pi$
$769$	1.18918e49			1.03395			0.516975	+	0.856001i	$0.327058\pi$
$770$	−1.51276e47	+	1.52018e46i	−0.0128655	+	0.00129286i
$771$		−	1.28403e48i		−	0.106819i
$772$	6.81832e48	−	1.38433e48i	0.554860	−	0.112654i
$773$	−1.63017e48			−0.129772			−0.0648859	−	0.997893i	$-0.520668\pi$
$773$	−1.63017e48			−0.129772			−0.0648859	+	0.997893i	$0.520668\pi$
$774$	2.17289e47	+	2.16228e48i	0.0169216	+	0.168390i
$775$			2.21239e49i			1.68551i
$776$	−8.12054e48	+	2.51610e48i	−0.605251	+	0.187533i
$777$	7.12324e48			0.519422
$778$	1.37927e49	−	1.38604e48i	0.984006	−	0.0988833i
$779$			1.06831e49i			0.745695i
$780$	−4.86317e46	−	2.39528e47i	−0.00332132	−	0.0163587i
$781$	−2.28250e49			−1.52526
$782$	−1.78755e48	−	1.77882e49i	−0.116881	−	1.16310i
$783$			5.91574e47i			0.0378494i
$784$	1.29856e49	−	5.49970e48i	0.813000	−	0.344323i
$785$	6.43835e47			0.0394449
$786$	−1.59948e49	+	1.60733e48i	−0.958949	+	0.0963653i
$787$		−	2.95480e48i		−	0.173364i	−0.996236	−	0.0866818i	$-0.972374\pi$
$787$		−	2.95480e48i		−	0.173364i	0.996236	−	0.0866818i	$-0.0276264\pi$
$788$	8.46433e48	−	1.71853e48i	0.486012	−	0.0986757i
$789$	−2.75842e49			−1.55007
$790$	−2.96277e46	−	2.94831e47i	−0.00162944	−	0.0162148i
$791$		−	3.39086e48i		−	0.182520i
$792$	4.23930e48	+	1.36820e49i	0.223340	+	0.720814i
$793$	−1.55759e49			−0.803174
$794$	−3.09781e49	+	3.11300e48i	−1.56353	+	0.157120i
$795$			3.85523e47i			0.0190462i
$796$	−3.85003e48	−	1.89627e49i	−0.186184	−	0.917020i
$797$	−2.35944e49			−1.11691			−0.558454	−	0.829535i	$-0.688605\pi$
$797$	−2.35944e49			−1.11691			−0.558454	+	0.829535i	$0.688605\pi$
$798$	1.38094e48	+	1.37420e49i	0.0639922	+	0.636798i
$799$		−	3.84465e49i		−	1.74406i
$800$	1.97375e49	−	1.08025e49i	0.876523	−	0.479725i
$801$	−1.85571e49			−0.806786
$802$	1.27631e49	−	1.28257e48i	0.543241	−	0.0545906i
$803$		−	3.31814e49i		−	1.38271i
$804$	−1.08262e48	+	2.19806e47i	−0.0441695	+	0.00896781i
$805$	2.41273e47			0.00963781
$806$	2.05570e48	+	2.04566e49i	0.0804014	+	0.800089i
$807$			4.04964e49i			1.55084i
$808$	1.85659e49	−	5.75252e48i	0.696182	−	0.215708i
$809$	2.58804e49			0.950269			0.475134	−	0.879913i	$-0.342399\pi$
$809$	2.58804e49			0.950269			0.475134	+	0.879913i	$0.342399\pi$
$810$	−9.67053e47	+	9.71798e46i	−0.0347700	+	0.00349406i
$811$			1.73401e49i			0.610515i	0.952270	+	0.305257i	$0.0987425\pi$
$811$			1.73401e49i			0.610515i	−0.952270	+	0.305257i	$0.901258\pi$
$812$	1.35977e47	+	6.69733e47i	0.00468827	+	0.0230914i
$813$	5.51084e49			1.86071
$814$	4.95322e48	+	4.92903e49i	0.163784	+	1.62985i
$815$		−	1.40115e48i		−	0.0453738i
$816$	1.78707e49	+	4.21954e49i	0.566772	+	1.33824i
$817$	−1.45726e49			−0.452648
$818$	2.94776e48	−	2.96222e47i	0.0896779	−	0.00901179i
$819$		−	3.06510e48i		−	0.0913310i
$820$	−4.68790e47	+	9.51791e46i	−0.0136818	+	0.00277783i
$821$	−1.36660e49			−0.390667			−0.195334	−	0.980737i	$-0.562579\pi$
$821$	−1.36660e49			−0.390667			−0.195334	+	0.980737i	$0.562579\pi$
$822$	−8.15711e48	−	8.11728e49i	−0.228410	−	2.27295i
$823$		−	8.50577e48i		−	0.233301i	−0.993173	−	0.116650i	$-0.962784\pi$
$823$		−	8.50577e48i		−	0.233301i	0.993173	−	0.116650i	$-0.0372157\pi$
$824$	−1.05547e49	−	3.40647e49i	−0.283586	−	0.915254i
$825$	6.39063e49			1.68200
$826$	−1.24118e49	+	1.24727e48i	−0.320018	+	0.0321588i
$827$			7.61108e49i			1.92244i	0.275782	+	0.961220i	$0.411063\pi$
$827$			7.61108e49i			1.92244i	−0.275782	+	0.961220i	$0.588937\pi$
$828$	−4.52279e48	−	2.22763e49i	−0.111916	−	0.551223i
$829$	−3.58811e49			−0.869838			−0.434919	−	0.900470i	$-0.643223\pi$
$829$	−3.58811e49			−0.869838			−0.434919	+	0.900470i	$0.643223\pi$
$830$	9.58157e46	+	9.53479e47i	0.00227567	+	0.0226456i
$831$		−	5.69250e49i		−	1.32460i
$832$	1.72464e49	−	1.18223e49i	0.393189	−	0.269530i
$833$	4.59929e49			1.02737
$834$	1.45366e49	−	1.46080e48i	0.318157	−	0.0319718i
$835$			2.43680e45i			5.22577e-5i
$836$	−9.41298e49	+	1.91113e49i	−1.97797	+	0.401591i
$837$	4.50307e49			0.927204
$838$	−1.27036e48	−	1.26415e49i	−0.0256317	−	0.255065i
$839$		−	6.27690e48i		−	0.124106i	−0.998073	−	0.0620529i	$-0.980235\pi$
$839$		−	6.27690e48i		−	0.124106i	0.998073	−	0.0620529i	$-0.0197647\pi$
$840$	−5.90716e47	+	1.83030e47i	−0.0114454	+	0.00354628i
$841$	−5.24165e49			−0.995259
$842$	−6.95883e49	+	6.99297e48i	−1.29488	+	0.130124i
$843$			7.31274e49i			1.33356i
$844$	1.71384e49	+	8.44124e49i	0.306301	+	1.50864i
$845$	1.23689e48			0.0216655
$846$	−4.88765e48	−	4.86379e49i	−0.0839081	−	0.834984i
$847$		−	1.66053e49i		−	0.279402i
$848$	−3.03697e49	+	1.28622e49i	−0.500853	+	0.212122i
$849$	4.28425e49			0.692538
$850$	7.30144e49	−	7.33726e48i	1.15688	−	0.116255i
$851$		−	7.86142e49i		−	1.22095i
$852$	−9.09856e49	+	1.84730e49i	−1.38516	+	0.281231i
$853$	6.20009e48			0.0925261			0.0462630	−	0.998929i	$-0.485269\pi$
$853$	6.20009e48			0.0925261			0.0462630	+	0.998929i	$0.485269\pi$
$854$	3.94053e48	+	3.92129e49i	0.0576462	+	0.573648i
$855$			1.63919e48i			0.0235075i
$856$	−1.39630e49	−	4.50645e49i	−0.196301	−	0.633550i
$857$	−8.20433e49			−1.13076			−0.565378	−	0.824832i	$-0.691270\pi$
$857$	−8.20433e49			−1.13076			−0.565378	+	0.824832i	$0.691270\pi$
$858$	5.90903e49	−	5.93802e48i	0.798421	−	0.0802339i
$859$		−	2.69757e49i		−	0.357346i	−0.983909	−	0.178673i	$-0.942820\pi$
$859$		−	2.69757e49i		−	0.357346i	0.983909	−	0.178673i	$-0.0571804\pi$
$860$	−1.29831e47	−	6.39464e47i	−0.00168619	−	0.00830506i
$861$	−1.67130e49			−0.212814
$862$	7.95191e48	+	7.91309e49i	0.0992768	+	0.987921i
$863$		−	5.23317e49i		−	0.640592i	−0.947318	−	0.320296i	$-0.896218\pi$
$863$		−	5.23317e49i		−	0.640592i	0.947318	−	0.320296i	$-0.103782\pi$
$864$	−2.19872e49	−	4.01735e49i	−0.263898	−	0.482177i
$865$	−2.27036e48			−0.0267190
$866$	−1.44647e49	+	1.45356e48i	−0.166919	+	0.0167738i
$867$			3.90733e49i			0.442135i
$868$	5.09801e49	−	1.03506e49i	0.565673	−	0.114850i
$869$	7.19987e49			0.783409
$870$	2.25945e46	+	2.24841e47i	0.000241087	+	0.00239910i
$871$			1.64400e48i			0.0172025i
$872$	3.68113e49	−	1.14058e49i	0.377747	−	0.117043i
$873$	−3.52527e49			−0.354773
$874$	1.51661e50	−	1.52405e49i	1.49686	−	0.150420i
$875$			1.98146e48i			0.0191800i
$876$	−2.68547e49	−	1.32269e50i	−0.254947	−	1.25570i
$877$	−1.42675e50			−1.32848			−0.664239	−	0.747520i	$-0.731244\pi$
$877$	−1.42675e50			−1.32848			−0.664239	+	0.747520i	$0.731244\pi$
$878$	3.37533e48	+	3.35886e49i	0.0308255	+	0.306750i
$879$			2.01594e50i			1.80579i
$880$	−1.67726e48	−	3.96028e48i	−0.0147365	−	0.0347953i
$881$	−1.15719e50			−0.997275			−0.498638	−	0.866811i	$-0.666166\pi$
$881$	−1.15719e50			−0.997275			−0.498638	+	0.866811i	$0.666166\pi$
$882$	5.81847e49	−	5.84701e48i	0.491861	−	0.0494274i
$883$			6.21753e49i			0.515568i	0.966203	+	0.257784i	$0.0829923\pi$
$883$			6.21753e49i			0.515568i	−0.966203	+	0.257784i	$0.917008\pi$
$884$	6.68302e49	−	1.35686e49i	0.543606	−	0.110369i
$885$	−4.12478e48			−0.0329129
$886$	−3.25524e48	−	3.23935e49i	−0.0254806	−	0.253562i
$887$		−	5.32005e48i		−	0.0408520i	−0.999791	−	0.0204260i	$-0.993498\pi$
$887$		−	5.32005e48i		−	0.0408520i	0.999791	−	0.0204260i	$-0.00650226\pi$
$888$	5.96368e49	+	1.92474e50i	0.449256	+	1.44994i
$889$	1.04559e49			0.0772737
$890$	5.54399e48	−	5.57119e47i	0.0401969	−	0.00403941i
$891$		−	2.36158e50i		−	1.67989i
$892$	5.32832e48	+	2.62438e49i	0.0371867	+	0.183157i
$893$	3.27792e50			2.24452
$894$	8.39832e48	+	8.35732e49i	0.0564228	+	0.561474i
$895$		−	6.12396e48i		−	0.0403683i
$896$	−3.41263e49	−	4.04274e49i	−0.220726	−	0.261481i
$897$	−9.42444e49			−0.598114
$898$	1.45315e50	−	1.46028e49i	0.904927	−	0.0909366i
$899$		−	1.90084e49i		−	0.116153i
$900$	9.14362e49	−	1.85644e49i	0.548272	−	0.111316i
$901$	−1.07564e50			−0.632915
$902$	−1.16215e49	−	1.15648e50i	−0.0671047	−	0.667770i
$903$		−	2.27978e49i		−	0.129182i
$904$	9.16228e49	−	2.83888e49i	0.509495	−	0.157864i
$905$	6.08482e47			0.00332064
$906$	−4.37455e50	+	4.39601e49i	−2.34290	+	0.235440i
$907$		−	2.45948e50i		−	1.29277i	−0.763013	−	0.646383i	$-0.776281\pi$
$907$		−	2.45948e50i		−	1.29277i	0.763013	−	0.646383i	$-0.223719\pi$
$908$	2.03598e49	+	1.00279e50i	0.105030	+	0.517310i
$909$	8.05978e49			0.408072
$910$	9.20199e46	+	9.15707e47i	0.000457276	+	0.00455043i
$911$			2.50811e50i			1.22330i	0.791127	+	0.611652i	$0.209495\pi$
$911$			2.50811e50i			1.22330i	−0.791127	+	0.611652i	$0.790505\pi$
$912$	−3.59755e50	+	1.52364e50i	−1.72225	+	0.729408i
$913$	−2.32843e50			−1.09411
$914$	−1.77502e50	+	1.78373e49i	−0.818687	+	0.0822703i
$915$			1.30315e49i			0.0589980i
$916$	9.65503e49	−	1.96027e49i	0.429072	−	0.0871152i
$917$	6.05301e49			0.264054
$918$	−1.49342e49	−	1.48612e50i	−0.0639521	−	0.636399i
$919$			1.38386e49i			0.0581737i	0.999577	+	0.0290869i	$0.00925995\pi$
$919$			1.38386e49i			0.0581737i	−0.999577	+	0.0290869i	$0.990740\pi$
$920$	2.01997e48	+	6.51932e48i	0.00833589	+	0.0269035i
$921$	−1.60528e50			−0.650334
$922$	−3.65840e50	+	3.67634e49i	−1.45501	+	0.146215i
$923$			1.38165e50i			0.539472i
$924$	−2.98983e49	−	1.47260e50i	−0.114610	−	0.564495i
$925$	3.22683e50			1.21442
$926$	−3.22341e49	−	3.20768e50i	−0.119105	−	1.18523i
$927$		−	1.47881e50i		−	0.536484i
$928$	−1.69581e49	+	9.28127e48i	−0.0604035	+	0.0330592i
$929$	1.53810e50			0.537920			0.268960	−	0.963151i	$-0.413320\pi$
$929$	1.53810e50			0.537920			0.268960	+	0.963151i	$0.413320\pi$
$930$	1.71149e49	−	1.71989e48i	0.0587713	−	0.00590597i
$931$			3.92132e50i			1.32217i
$932$	3.95913e50	−	8.03829e49i	1.31078	−	0.266129i
$933$	5.10924e50			1.66100
$934$	5.15364e47	+	5.12848e48i	0.00164519	+	0.0163716i
$935$		−	1.40266e49i		−	0.0439699i
$936$	8.28206e49	−	2.56614e49i	0.254946	−	0.0789936i
$937$	4.23663e49			0.128070			0.0640351	−	0.997948i	$-0.479603\pi$
$937$	4.23663e49			0.128070			0.0640351	+	0.997948i	$0.479603\pi$
$938$	4.13882e48	−	4.15912e47i	0.0122865	−	0.00123468i
$939$		−	1.82202e50i		−	0.531175i
$940$	2.92040e48	+	1.43840e49i	0.00836120	+	0.0411818i
$941$	1.02489e50			0.288173			0.144087	−	0.989565i	$-0.453976\pi$
$941$	1.02489e50			0.288173			0.144087	+	0.989565i	$0.453976\pi$
$942$	6.36242e49	+	6.33136e50i	0.175694	+	1.74836i
$943$			1.84450e50i			0.500240i
$944$	−1.37615e50	−	3.24931e50i	−0.366558	−	0.865500i
$945$	2.01572e48			0.00527339
$946$	1.57753e50	−	1.58527e49i	0.405347	−	0.0407336i
$947$		−	3.27985e50i		−	0.827760i	−0.910332	−	0.413880i	$-0.864173\pi$
$947$		−	3.27985e50i		−	0.827760i	0.910332	−	0.413880i	$-0.135827\pi$
$948$	2.87003e50	−	5.82707e49i	0.711451	−	0.144447i
$949$	−2.00855e50			−0.489054
$950$	6.25569e49	+	6.22515e50i	0.149615	+	1.48884i
$951$		−	1.09278e50i		−	0.256722i
$952$	−5.10668e49	−	1.64815e50i	−0.117845	−	0.380336i
$953$	2.67687e50			0.606804			0.303402	−	0.952863i	$-0.401877\pi$
$953$	2.67687e50			0.606804			0.303402	+	0.952863i	$0.401877\pi$
$954$	−1.36077e50	+	1.36745e49i	−0.303014	+	0.0304500i
$955$		−	4.37602e48i		−	0.00957242i
$956$	1.54228e50	+	7.59627e50i	0.331421	+	1.63236i
$957$	−5.49071e49			−0.115911
$958$	−6.32798e49	−	6.29708e50i	−0.131235	−	1.30595i
$959$			3.07187e50i			0.625874i
$960$	−9.89111e48	−	1.44291e49i	−0.0197986	−	0.0288821i
$961$	−9.38416e50			−1.84543
$962$	2.98366e50	−	2.99830e49i	0.576465	−	0.0579293i
$963$		−	1.95633e50i		−	0.371360i
$964$	−2.66479e50	+	5.41036e49i	−0.496996	+	0.100906i
$965$	−8.66253e48			−0.0158738
$966$	2.38427e49	+	2.37263e50i	0.0429284	+	0.427188i
$967$		−	8.04212e50i		−	1.42272i	−0.702827	−	0.711361i	$-0.748079\pi$
$967$		−	8.04212e50i		−	1.42272i	0.702827	−	0.711361i	$-0.251921\pi$
$968$	4.48685e50	−	1.39022e50i	0.779939	−	0.241659i
$969$	−1.27419e51			−2.17636
$970$	1.05318e49	−	1.05835e48i	0.0176760	−	0.00177628i
$971$			1.91446e50i			0.315733i	0.987460	+	0.157866i	$0.0504615\pi$
$971$			1.91446e50i			0.315733i	−0.987460	+	0.157866i	$0.949539\pi$
$972$	−1.23643e50	−	6.08983e50i	−0.200374	−	0.986912i
$973$	−5.50119e49			−0.0876069
$974$	−9.04651e49	−	9.00235e50i	−0.141572	−	1.40881i
$975$		−	3.86840e50i		−	0.594912i
$976$	−1.02656e51	+	4.34771e50i	−1.55145	+	0.657074i
$977$	−1.75630e50			−0.260851			−0.130425	−	0.991458i	$-0.541634\pi$
$977$	−1.75630e50			−0.260851			−0.130425	+	0.991458i	$0.541634\pi$
$978$	1.37787e51	−	1.38463e50i	2.01116	−	0.202103i
$979$			1.35386e51i			1.94209i
$980$	−1.72073e49	+	3.49362e48i	−0.0242588	+	0.00492530i
$981$	1.59804e50			0.221419
$982$	−6.63873e47	−	6.60632e48i	−0.000904045	−	0.00899631i
$983$			4.64592e50i			0.621816i	0.950440	+	0.310908i	$0.100633\pi$
$983$			4.64592e50i			0.621816i	−0.950440	+	0.310908i	$0.899367\pi$
$984$	−1.39923e50	−	4.51594e50i	−0.184066	−	0.594061i
$985$	−1.07537e49			−0.0139041
$986$	−6.27326e49	+	6.30404e48i	−0.0797234	+	0.00801145i
$987$			5.12808e50i			0.640564i
$988$	1.15685e50	+	5.69789e50i	0.142040	+	0.699594i
$989$	−2.51603e50			−0.303654
$990$	−1.78318e48	−	1.77448e49i	−0.00211543	−	0.0210510i
$991$		−	7.47899e50i		−	0.872150i	−0.899910	−	0.436075i	$-0.856368\pi$
$991$		−	7.47899e50i		−	0.872150i	0.899910	−	0.436075i	$-0.143632\pi$
$992$	7.06491e50	+	1.29085e51i	0.809857	+	1.47972i
$993$	6.20506e50			0.699212
$994$	3.47835e50	−	3.49542e49i	0.385305	−	0.0387195i
$995$			2.40917e49i			0.0262347i
$996$	−9.28166e50	+	1.88447e50i	−0.993612	+	0.201735i
$997$	1.23522e51			1.29994			0.649972	−	0.759958i	$-0.274780\pi$
$997$	1.23522e51			1.29994			0.649972	+	0.759958i	$0.274780\pi$
$998$	4.70095e49	+	4.67800e50i	0.0486370	+	0.483996i
$999$		−	6.56785e50i		−	0.668052i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.35.b.a.3.2	yes	16
4.3	odd	2	inner	4.35.b.a.3.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.35.b.a.3.1	✓	16	4.3	odd	2	inner
4.35.b.a.3.2	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)

\(f(q)\)	\(=\)	\(q+(-130415. + 13105.5i) q^{2} +1.61291e8i q^{3} +(1.68364e10 - 3.41831e9i) q^{4} -2.13902e10 q^{5} +(-2.11380e12 - 2.10348e13i) q^{6} +7.96031e13i q^{7} +(-2.15092e15 + 6.66449e14i) q^{8} -9.33752e15 q^{9} +O(q^{10})\)	\(q+(-130415. + 13105.5i) q^{2} +1.61291e8i q^{3} +(1.68364e10 - 3.41831e9i) q^{4} -2.13902e10 q^{5} +(-2.11380e12 - 2.10348e13i) q^{6} +7.96031e13i q^{7} +(-2.15092e15 + 6.66449e14i) q^{8} -9.33752e15 q^{9} +(2.78961e15 - 2.80330e14i) q^{10} +6.81233e17i q^{11} +(5.51342e17 + 2.71555e18i) q^{12} +4.12366e18 q^{13} +(-1.04324e18 - 1.03815e19i) q^{14} -3.45004e18i q^{15} +(2.71778e20 - 1.15104e20i) q^{16} +9.62590e20 q^{17} +(1.21775e21 - 1.22373e20i) q^{18} +8.20698e21i q^{19} +(-3.60133e20 + 7.31184e19i) q^{20} -1.28392e22 q^{21} +(-8.92790e21 - 8.88431e22i) q^{22} +1.41698e23i q^{23} +(-1.07492e23 - 3.46923e23i) q^{24} -5.81619e23 q^{25} +(-5.37788e23 + 5.40426e22i) q^{26} +1.18382e24i q^{27} +(2.72108e23 + 1.34023e24i) q^{28} +4.99716e23 q^{29} +(4.52146e22 + 4.49938e23i) q^{30} -3.80384e25i q^{31} +(-3.39355e25 + 1.85731e25i) q^{32} -1.09877e26 q^{33} +(-1.25536e26 + 1.26152e25i) q^{34} -1.70273e24i q^{35} +(-1.57210e26 + 3.19185e25i) q^{36} -5.54802e26 q^{37} +(-1.07557e26 - 1.07031e27i) q^{38} +6.65108e26i q^{39} +(4.60086e25 - 1.42555e25i) q^{40} +1.30171e27 q^{41} +(1.67443e27 - 1.68265e26i) q^{42} +1.77563e27i q^{43} +(2.32867e27 + 1.14695e28i) q^{44} +1.99732e26 q^{45} +(-1.85702e27 - 1.84795e28i) q^{46} -3.99406e28i q^{47} +(1.85652e28 + 4.38353e28i) q^{48} +4.77803e28 q^{49} +(7.58519e28 - 7.62241e27i) q^{50} +1.55257e29i q^{51} +(6.94274e28 - 1.40960e28i) q^{52} -1.11744e29 q^{53} +(-1.55145e28 - 1.54388e29i) q^{54} -1.45717e28i q^{55} +(-5.30514e28 - 1.71220e29i) q^{56} -1.32371e30 q^{57} +(-6.51706e28 + 6.54903e27i) q^{58} -1.19557e30i q^{59} +(-1.17933e28 - 5.80862e28i) q^{60} -3.77721e30 q^{61} +(4.98513e29 + 4.96079e30i) q^{62} -7.43296e29i q^{63} +(4.18230e30 - 2.86695e30i) q^{64} -8.82060e28 q^{65} +(1.43296e31 - 1.43999e30i) q^{66} +3.98674e29i q^{67} +(1.62065e31 - 3.29043e30i) q^{68} -2.28545e31 q^{69} +(2.23151e28 + 2.22062e29i) q^{70} +3.35054e31i q^{71} +(2.00842e31 - 6.22298e30i) q^{72} -4.87079e31 q^{73} +(7.23546e31 - 7.27096e30i) q^{74} -9.38098e31i q^{75} +(2.80540e31 + 1.38176e32i) q^{76} -5.42283e31 q^{77} +(-8.71658e30 - 8.67402e31i) q^{78} -1.05689e32i q^{79} +(-5.81340e30 + 2.46210e30i) q^{80} -3.46663e32 q^{81} +(-1.69763e32 + 1.70596e31i) q^{82} +3.41797e32i q^{83} +(-2.16166e32 + 4.38885e31i) q^{84} -2.05900e31 q^{85} +(-2.32705e31 - 2.31569e32i) q^{86} +8.05996e31i q^{87} +(-4.54007e32 - 1.46528e33i) q^{88} +1.98737e33 q^{89} +(-2.60480e31 + 2.61758e30i) q^{90} +3.28256e32i q^{91} +(4.84367e32 + 2.38567e33i) q^{92} +6.13525e33 q^{93} +(5.23442e32 + 5.20886e33i) q^{94} -1.75549e32i q^{95} +(-2.99567e33 - 5.47348e33i) q^{96} +3.77538e33 q^{97} +(-6.23128e33 + 6.26185e32i) q^{98} -6.36103e33i 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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