LMFDB - Embedded newform 4.35.b.a.3.3

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			3.3
Root			$0.500000 + 182748. i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.35.b.a.3.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-88896.6 - 96318.6i) q^{2} -8.77192e6i q^{3} +(-1.37468e9 + 1.71248e10i) q^{4} +8.59192e11 q^{5} +(-8.44899e11 + 7.79793e11i) q^{6} +3.22173e14i q^{7} +(1.77164e15 - 1.38993e15i) q^{8} +1.66002e16 q^{9} +O(q^{10})$	\(q+(-88896.6 - 96318.6i) q^{2} -8.77192e6i q^{3} +(-1.37468e9 + 1.71248e10i) q^{4} +8.59192e11 q^{5} +(-8.44899e11 + 7.79793e11i) q^{6} +3.22173e14i q^{7} +(1.77164e15 - 1.38993e15i) q^{8} +1.66002e16 q^{9} +(-7.63792e16 - 8.27562e16i) q^{10} +3.83523e17i q^{11} +(1.50217e17 + 1.20585e16i) q^{12} -1.34109e19 q^{13} +(3.10313e19 - 2.86401e19i) q^{14} -7.53676e18i q^{15} +(-2.91368e20 - 4.70820e19i) q^{16} -5.50763e20 q^{17} +(-1.47570e21 - 1.59891e21i) q^{18} -5.93674e21i q^{19} +(-1.18111e21 + 1.47135e22i) q^{20} +2.82608e21 q^{21} +(3.69404e22 - 3.40938e22i) q^{22} +1.68339e23i q^{23} +(-1.21923e22 - 1.55407e22i) q^{24} +1.56134e23 q^{25} +(1.19218e24 + 1.29172e24i) q^{26} -2.91907e23i q^{27} +(-5.51714e24 - 4.42883e23i) q^{28} -1.59166e24 q^{29} +(-7.25930e23 + 6.69992e23i) q^{30} +2.89141e25i q^{31} +(2.13668e25 + 3.22496e25i) q^{32} +3.36423e24 q^{33} +(4.89609e25 + 5.30487e25i) q^{34} +2.76809e26i q^{35} +(-2.28199e25 + 2.84275e26i) q^{36} +3.42727e26 q^{37} +(-5.71819e26 + 5.27756e26i) q^{38} +1.17639e26i q^{39} +(1.52218e27 - 1.19421e27i) q^{40} -3.35617e27 q^{41} +(-2.51228e26 - 2.72204e26i) q^{42} +1.07019e26i q^{43} +(-6.56774e27 - 5.27219e26i) q^{44} +1.42628e28 q^{45} +(1.62142e28 - 1.49647e28i) q^{46} -2.74408e28i q^{47} +(-4.13000e26 + 2.55586e27i) q^{48} -4.96785e28 q^{49} +(-1.38798e28 - 1.50386e28i) q^{50} +4.83125e27i q^{51} +(1.84356e28 - 2.29659e29i) q^{52} -9.06021e28 q^{53} +(-2.81161e28 + 2.59495e28i) q^{54} +3.29520e29i q^{55} +(4.47797e29 + 5.70774e29i) q^{56} -5.20766e28 q^{57} +(1.41493e29 + 1.53307e29i) q^{58} +1.96904e30i q^{59} +(1.29065e29 + 1.03606e28i) q^{60} -1.15432e30 q^{61} +(2.78496e30 - 2.57036e30i) q^{62} +5.34815e30i q^{63} +(1.20681e30 - 4.92490e30i) q^{64} -1.15225e31 q^{65} +(-2.99068e29 - 3.24038e29i) q^{66} -1.07279e31i q^{67} +(7.57120e29 - 9.43170e30i) q^{68} +1.47665e30 q^{69} +(2.66618e31 - 2.46073e31i) q^{70} +5.04398e31i q^{71} +(2.94096e31 - 2.30731e31i) q^{72} -5.26267e31 q^{73} +(-3.04673e31 - 3.30110e31i) q^{74} -1.36960e30i q^{75} +(1.01665e32 + 8.16109e30i) q^{76} -1.23561e32 q^{77} +(1.13308e31 - 1.04577e31i) q^{78} +2.42129e32i q^{79} +(-2.50341e32 - 4.04525e31i) q^{80} +2.74285e32 q^{81} +(2.98352e32 + 3.23262e32i) q^{82} +5.99024e31i q^{83} +(-3.88494e30 + 4.83959e31i) q^{84} -4.73211e32 q^{85} +(1.03079e31 - 9.51359e30i) q^{86} +1.39619e31i q^{87} +(5.33069e32 + 6.79464e32i) q^{88} +1.75205e33 q^{89} +(-1.26791e33 - 1.37377e33i) q^{90} -4.32063e33i q^{91} +(-2.88277e33 - 2.31411e32i) q^{92} +2.53632e32 q^{93} +(-2.64306e33 + 2.43939e33i) q^{94} -5.10080e33i q^{95} +(2.82891e32 - 1.87428e32i) q^{96} +3.66838e33 q^{97} +(4.41625e33 + 4.78497e33i) q^{98} +6.36657e33i 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 $

$2$	−88896.6	−	96318.6i	−0.678227	−	0.734853i
$2$	−88896.6	−	96318.6i	−0.678227	−	0.734853i
$3$		−	8.77192e6i		−	0.0679256i	−0.999423	−	0.0339628i	$-0.989187\pi$
$3$		−	8.77192e6i		−	0.0679256i	0.999423	−	0.0339628i	$-0.0108128\pi$
$4$	−1.37468e9	+	1.71248e10i	−0.0800166	+	0.996794i
$5$	8.59192e11			1.12616			0.563080	−	0.826402i	$-0.309616\pi$
$5$	8.59192e11			1.12616			0.563080	+	0.826402i	$0.309616\pi$
$6$	−8.44899e11	+	7.79793e11i	−0.0499153	+	0.0460689i
$7$			3.22173e14i			1.38491i	0.721460	+	0.692457i	$0.243472\pi$
$7$			3.22173e14i			1.38491i	−0.721460	+	0.692457i	$0.756528\pi$
$8$	1.77164e15	−	1.38993e15i	0.786766	−	0.617252i
$9$	1.66002e16			0.995386
$10$	−7.63792e16	−	8.27562e16i	−0.763792	−	0.827562i
$11$			3.83523e17i			0.758779i	0.925237	+	0.379390i	$0.123866\pi$
$11$			3.83523e17i			0.758779i	−0.925237	+	0.379390i	$0.876134\pi$
$12$	1.50217e17	+	1.20585e16i	0.0677078	+	0.00543518i
$13$	−1.34109e19			−1.55032			−0.775159	−	0.631767i	$-0.782330\pi$
$13$	−1.34109e19			−1.55032			−0.775159	+	0.631767i	$0.782330\pi$
$14$	3.10313e19	−	2.86401e19i	1.01771	−	0.939285i
$15$		−	7.53676e18i		−	0.0764951i
$16$	−2.91368e20	−	4.70820e19i	−0.987195	−	0.159520i
$17$	−5.50763e20			−0.665784			−0.332892	−	0.942965i	$-0.608024\pi$
$17$	−5.50763e20			−0.665784			−0.332892	+	0.942965i	$0.608024\pi$
$18$	−1.47570e21	−	1.59891e21i	−0.675098	−	0.731462i
$19$		−	5.93674e21i		−	1.08327i	−0.840614	−	0.541635i	$-0.817805\pi$
$19$		−	5.93674e21i		−	1.08327i	0.840614	−	0.541635i	$-0.182195\pi$
$20$	−1.18111e21	+	1.47135e22i	−0.0901116	+	1.12255i
$21$	2.82608e21			0.0940710
$22$	3.69404e22	−	3.40938e22i	0.557591	−	0.514624i
$23$			1.68339e23i			1.19347i	0.802439	+	0.596735i	$0.203535\pi$
$23$			1.68339e23i			1.19347i	−0.802439	+	0.596735i	$0.796465\pi$
$24$	−1.21923e22	−	1.55407e22i	−0.0419272	−	0.0534415i
$25$	1.56134e23			0.268237
$26$	1.19218e24	+	1.29172e24i	1.05147	+	1.13925i
$27$		−	2.91907e23i		−	0.135538i
$28$	−5.51714e24	−	4.42883e23i	−1.38047	−	0.110816i
$29$	−1.59166e24			−0.219323			−0.109662	−	0.993969i	$-0.534977\pi$
$29$	−1.59166e24			−0.219323			−0.109662	+	0.993969i	$0.534977\pi$
$30$	−7.25930e23	+	6.69992e23i	−0.0562126	+	0.0518810i
$31$			2.89141e25i			1.28221i	0.767451	+	0.641107i	$0.221525\pi$
$31$			2.89141e25i			1.28221i	−0.767451	+	0.641107i	$0.778475\pi$
$32$	2.13668e25	+	3.22496e25i	0.552318	+	0.833633i
$33$	3.36423e24			0.0515405
$34$	4.89609e25	+	5.30487e25i	0.451552	+	0.489253i
$35$			2.76809e26i			1.55963i
$36$	−2.28199e25	+	2.84275e26i	−0.0796475	+	0.992194i
$37$	3.42727e26			0.750791			0.375396	−	0.926865i	$-0.377507\pi$
$37$	3.42727e26			0.750791			0.375396	+	0.926865i	$0.377507\pi$
$38$	−5.71819e26	+	5.27756e26i	−0.796044	+	0.734703i
$39$			1.17639e26i			0.105306i
$40$	1.52218e27	−	1.19421e27i	0.886024	−	0.695124i
$41$	−3.35617e27			−1.28386			−0.641932	−	0.766762i	$-0.721867\pi$
$41$	−3.35617e27			−1.28386			−0.641932	+	0.766762i	$0.721867\pi$
$42$	−2.51228e26	−	2.72204e26i	−0.0638015	−	0.0691283i
$43$			1.07019e26i			0.0182178i	0.999959	+	0.00910890i	$0.00289949\pi$
$43$			1.07019e26i			0.0182178i	−0.999959	+	0.00910890i	$0.997101\pi$
$44$	−6.56774e27	−	5.27219e26i	−0.756346	−	0.0607150i
$45$	1.42628e28			1.12096
$46$	1.62142e28	−	1.49647e28i	0.877024	−	0.809443i
$47$		−	2.74408e28i		−	1.02975i	−0.857264	−	0.514877i	$-0.827838\pi$
$47$		−	2.74408e28i		−	1.02975i	0.857264	−	0.514877i	$-0.172162\pi$
$48$	−4.13000e26	+	2.55586e27i	−0.0108355	+	0.0670558i
$49$	−4.96785e28			−0.917985
$50$	−1.38798e28	−	1.50386e28i	−0.181925	−	0.197114i
$51$			4.83125e27i			0.0452237i
$52$	1.84356e28	−	2.29659e29i	0.124051	−	1.54535i
$53$	−9.06021e28			−0.441010			−0.220505	−	0.975386i	$-0.570771\pi$
$53$	−9.06021e28			−0.441010			−0.220505	+	0.975386i	$0.570771\pi$
$54$	−2.81161e28	+	2.59495e28i	−0.0996003	+	0.0919253i
$55$			3.29520e29i			0.854507i
$56$	4.47797e29	+	5.70774e29i	0.854840	+	1.08960i
$57$	−5.20766e28			−0.0735818
$58$	1.41493e29	+	1.53307e29i	0.148751	+	0.161170i
$59$			1.96904e30i			1.54800i	0.633185	+	0.774001i	$0.281747\pi$
$59$			1.96904e30i			1.54800i	−0.633185	+	0.774001i	$0.718253\pi$
$60$	1.29065e29	+	1.03606e28i	0.0762498	+	0.00612088i
$61$	−1.15432e30			−0.514893			−0.257447	−	0.966292i	$-0.582881\pi$
$61$	−1.15432e30			−0.514893			−0.257447	+	0.966292i	$0.582881\pi$
$62$	2.78496e30	−	2.57036e30i	0.942239	−	0.869632i
$63$			5.34815e30i			1.37852i
$64$	1.20681e30	−	4.92490e30i	0.238001	−	0.971265i
$65$	−1.15225e31			−1.74591
$66$	−2.99068e29	−	3.24038e29i	−0.0349562	−	0.0378747i
$67$		−	1.07279e31i		−	0.971051i	−0.874223	−	0.485525i	$-0.838628\pi$
$67$		−	1.07279e31i		−	0.971051i	0.874223	−	0.485525i	$-0.161372\pi$
$68$	7.57120e29	−	9.43170e30i	0.0532738	−	0.663649i
$69$	1.47665e30			0.0810671
$70$	2.66618e31	−	2.46073e31i	1.14610	−	1.05779i
$71$			5.04398e31i			1.70365i	0.523823	+	0.851827i	$0.324505\pi$
$71$			5.04398e31i			1.70365i	−0.523823	+	0.851827i	$0.675495\pi$
$72$	2.94096e31	−	2.30731e31i	0.783136	−	0.614404i
$73$	−5.26267e31			−1.10845			−0.554226	−	0.832366i	$-0.686986\pi$
$73$	−5.26267e31			−1.10845			−0.554226	+	0.832366i	$0.686986\pi$
$74$	−3.04673e31	−	3.30110e31i	−0.509207	−	0.551721i
$75$		−	1.36960e30i		−	0.0182201i
$76$	1.01665e32	+	8.16109e30i	1.07980	+	0.0866797i
$77$	−1.23561e32			−1.05084
$78$	1.13308e31	−	1.04577e31i	0.0773845	−	0.0714215i
$79$			2.42129e32i			1.33164i	0.746113	+	0.665820i	$0.231918\pi$
$79$			2.42129e32i			1.33164i	−0.746113	+	0.665820i	$0.768082\pi$
$80$	−2.50341e32	−	4.04525e31i	−1.11174	−	0.179645i
$81$	2.74285e32			0.986180
$82$	2.98352e32	+	3.23262e32i	0.870751	+	0.943451i
$83$			5.99024e31i			0.142271i	0.997467	+	0.0711356i	$0.0226623\pi$
$83$			5.99024e31i			0.142271i	−0.997467	+	0.0711356i	$0.977338\pi$
$84$	−3.88494e30	+	4.83959e31i	−0.00752725	+	0.0937694i
$85$	−4.73211e32			−0.749779
$86$	1.03079e31	−	9.51359e30i	0.0133874	−	0.0123558i
$87$			1.39619e31i			0.0148977i
$88$	5.33069e32	+	6.79464e32i	0.468358	+	0.596981i
$89$	1.75205e33			1.27033			0.635163	−	0.772378i	$-0.280933\pi$
$89$	1.75205e33			1.27033			0.635163	+	0.772378i	$0.280933\pi$
$90$	−1.26791e33	−	1.37377e33i	−0.760268	−	0.823743i
$91$		−	4.32063e33i		−	2.14705i
$92$	−2.88277e33	−	2.31411e32i	−1.18964	−	0.0954974i
$93$	2.53632e32			0.0870952
$94$	−2.64306e33	+	2.43939e33i	−0.756717	+	0.698406i
$95$		−	5.10080e33i		−	1.21994i
$96$	2.82891e32	−	1.87428e32i	0.0566250	−	0.0375165i
$97$	3.66838e33			0.615679			0.307840	−	0.951438i	$-0.400394\pi$
$97$	3.66838e33			0.615679			0.307840	+	0.951438i	$0.400394\pi$
$98$	4.41625e33	+	4.78497e33i	0.622602	+	0.674583i
$99$			6.36657e33i			0.755278i
$100$	−2.14634e32	+	2.67376e33i	−0.0214634	+	0.267376i
$101$	8.55625e33			0.722471			0.361235	−	0.932475i	$-0.382355\pi$
$101$	8.55625e33			0.722471			0.361235	+	0.932475i	$0.382355\pi$
$102$	4.65339e32	−	4.29481e32i	0.0332328	−	0.0306719i
$103$			1.01803e33i			0.0615926i	0.999526	+	0.0307963i	$0.00980432\pi$
$103$			1.01803e33i			0.0615926i	−0.999526	+	0.0307963i	$0.990196\pi$
$104$	−2.37593e34	+	1.86402e34i	−1.21974	+	0.956936i
$105$	2.42814e33			0.105939
$106$	8.05421e33	+	8.72667e33i	0.299105	+	0.324077i
$107$			7.43181e33i			0.235272i	0.993057	+	0.117636i	$0.0375316\pi$
$107$			7.43181e33i			0.235272i	−0.993057	+	0.117636i	$0.962468\pi$
$108$	4.99884e33	+	4.01277e32i	0.135103	+	0.0108453i
$109$	−5.85009e34			−1.35180			−0.675899	−	0.736994i	$-0.736245\pi$
$109$	−5.85009e34			−1.35180			−0.675899	+	0.736994i	$0.736245\pi$
$110$	3.17389e34	−	2.92932e34i	0.627937	−	0.579549i
$111$		−	3.00638e33i		−	0.0509979i
$112$	1.51686e34	−	9.38711e34i	0.220922	−	1.36718i
$113$	5.62766e34			0.704684			0.352342	−	0.935871i	$-0.385385\pi$
$113$	5.62766e34			0.704684			0.352342	+	0.935871i	$0.385385\pi$
$114$	4.62943e33	+	5.01595e33i	0.0499051	+	0.0540718i
$115$			1.44635e35i			1.34404i
$116$	2.18802e33	−	2.72569e34i	0.0175495	−	0.218620i
$117$	−2.22624e35			−1.54316
$118$	1.89656e35	−	1.75041e35i	1.13755	−	1.04990i
$119$		−	1.77441e35i		−	0.922052i
$120$	−1.04756e34	−	1.33524e34i	−0.0472167	−	0.0601837i
$121$	1.08387e35			0.424254
$122$	1.02615e35	+	1.11182e35i	0.349215	+	0.378371i
$123$			2.94401e34i			0.0872072i
$124$	−4.95147e35	−	3.97475e34i	−1.27810	−	0.102599i
$125$	−3.65966e35			−0.824083
$126$	5.15126e35	−	4.75432e35i	1.01301	−	0.934952i
$127$			1.13854e36i			1.95743i	0.205226	+	0.978715i	$0.434207\pi$
$127$			1.13854e36i			1.95743i	−0.205226	+	0.978715i	$0.565793\pi$
$128$	−5.81640e35	+	3.21569e35i	−0.875155	+	0.483843i
$129$	9.38759e32			0.00123745
$130$	1.02431e36	+	1.10983e36i	1.18412	+	1.28298i
$131$		−	9.76216e35i		−	0.990682i	−0.868699	−	0.495341i	$-0.835043\pi$
$131$		−	9.76216e35i		−	0.990682i	0.868699	−	0.495341i	$-0.164957\pi$
$132$	−4.62472e33	+	5.76117e34i	−0.00412410	+	0.0513752i
$133$	1.91266e36			1.50024
$134$	−1.03329e36	+	9.53671e35i	−0.713579	+	0.658593i
$135$		−	2.50804e35i		−	0.152637i
$136$	−9.75753e35	+	7.65520e35i	−0.523816	+	0.410956i
$137$	5.34317e35			0.253250			0.126625	−	0.991951i	$-0.459585\pi$
$137$	5.34317e35			0.253250			0.126625	+	0.991951i	$0.459585\pi$
$138$	−1.31270e35	−	1.42229e35i	−0.0549819	−	0.0595723i
$139$		−	3.34653e36i		−	1.23977i	−0.784691	−	0.619887i	$-0.787178\pi$
$139$		−	3.34653e36i		−	1.23977i	0.784691	−	0.619887i	$-0.212822\pi$
$140$	−4.74029e36	−	3.80522e35i	−1.55463	−	0.124797i
$141$	−2.40709e35			−0.0699466
$142$	4.85829e36	−	4.48392e36i	1.25193	−	1.15546i
$143$		−	5.14338e36i		−	1.17635i
$144$	−4.83678e36	−	7.81573e35i	−0.982640	−	0.158784i
$145$	−1.36754e36			−0.246993
$146$	4.67833e36	+	5.06893e36i	0.751782	+	0.814549i
$147$			4.35776e35i			0.0623546i
$148$	−4.71139e35	+	5.86913e36i	−0.0600758	+	0.748384i
$149$	1.02791e37			1.16893			0.584465	−	0.811419i	$-0.301305\pi$
$149$	1.02791e37			1.16893			0.584465	+	0.811419i	$0.301305\pi$
$150$	−1.31918e35	+	1.21752e35i	−0.0133891	+	0.0123574i
$151$			6.00190e36i			0.544102i	0.962283	+	0.272051i	$0.0877020\pi$
$151$			6.00190e36i			0.544102i	−0.962283	+	0.272051i	$0.912298\pi$
$152$	−8.25164e36	−	1.05178e37i	−0.668651	−	0.852280i
$153$	−9.14279e36			−0.662712
$154$	1.09841e37	+	1.19012e37i	0.712710	+	0.772215i
$155$			2.48428e37i			1.44398i
$156$	−2.01455e36	−	1.61716e35i	−0.104969	−	0.00842625i
$157$	−4.97324e36			−0.232458			−0.116229	−	0.993222i	$-0.537081\pi$
$157$	−4.97324e36			−0.232458			−0.116229	+	0.993222i	$0.537081\pi$
$158$	2.33215e37	−	2.15245e37i	0.978559	−	0.903154i
$159$			7.94754e35i			0.0299559i
$160$	1.83582e37	+	2.77086e37i	0.621999	+	0.938805i
$161$	−5.42342e37			−1.65285
$162$	−2.43830e37	−	2.64187e37i	−0.668854	−	0.724697i
$163$			3.48764e37i			0.861672i	0.902430	+	0.430836i	$0.141781\pi$
$163$			3.48764e37i			0.861672i	−0.902430	+	0.430836i	$0.858219\pi$
$164$	4.61365e36	−	5.74738e37i	0.102730	−	1.27975i
$165$	2.89052e36			0.0580429
$166$	5.76972e36	−	5.32512e36i	0.104548	−	0.0964921i
$167$		−	1.37544e37i		−	0.225041i	−0.993649	−	0.112520i	$-0.964108\pi$
$167$		−	1.37544e37i		−	0.225041i	0.993649	−	0.112520i	$-0.0358924\pi$
$168$	5.00679e36	−	3.92804e36i	0.0740119	−	0.0580655i
$169$	1.05022e38			1.40348
$170$	4.20668e37	+	4.55790e37i	0.508520	+	0.550977i
$171$		−	9.85513e37i		−	1.07827i
$172$	−1.83267e36	−	1.47116e35i	−0.0181594	−	0.00145773i
$173$	−1.47558e38			−1.32489			−0.662444	−	0.749111i	$-0.730481\pi$
$173$	−1.47558e38			−1.32489			−0.662444	+	0.749111i	$0.730481\pi$
$174$	1.34479e36	−	1.24117e36i	0.0109476	−	0.0101040i
$175$			5.03022e37i			0.371484i
$176$	1.80570e37	−	1.11746e38i	0.121041	−	0.749063i
$177$	1.72723e37			0.105149
$178$	−1.55751e38	−	1.68755e38i	−0.861570	−	0.933503i
$179$		−	9.17523e37i		−	0.461440i	−0.973020	−	0.230720i	$-0.925892\pi$
$179$		−	9.17523e37i		−	0.461440i	0.973020	−	0.230720i	$-0.0741082\pi$
$180$	−1.96067e37	+	2.44247e38i	−0.0896958	+	1.11737i
$181$	2.30089e38			0.957987			0.478994	−	0.877818i	$-0.341002\pi$
$181$	2.30089e38			0.957987			0.478994	+	0.877818i	$0.341002\pi$
$182$	−4.16157e38	+	3.84089e38i	−1.57777	+	1.45619i
$183$			1.01256e37i			0.0349744i
$184$	2.33979e38	+	2.98236e38i	0.736671	+	0.938981i
$185$	2.94468e38			0.845511
$186$	−2.25470e37	−	2.44295e37i	−0.0590703	−	0.0640021i
$187$		−	2.11230e38i		−	0.505183i
$188$	4.69918e38	+	3.77222e37i	1.02645	+	0.0823974i
$189$	9.40445e37			0.187708
$190$	−4.91302e38	+	4.53444e38i	−0.896473	+	0.827394i
$191$			2.14829e38i			0.358530i	0.983801	+	0.179265i	$0.0573719\pi$
$191$			2.14829e38i			0.358530i	−0.983801	+	0.179265i	$0.942628\pi$
$192$	−4.32008e37	−	1.05860e37i	−0.0659737	−	0.0161663i
$193$	−1.71092e38			−0.239197			−0.119599	−	0.992822i	$-0.538161\pi$
$193$	−1.71092e38			−0.239197			−0.119599	+	0.992822i	$0.538161\pi$
$194$	−3.26106e38	−	3.53333e38i	−0.417570	−	0.452434i
$195$			1.01075e38i			0.118592i
$196$	6.82919e37	−	8.50734e38i	0.0734541	−	0.915041i
$197$	−2.25273e38			−0.222220			−0.111110	−	0.993808i	$-0.535441\pi$
$197$	−2.25273e38			−0.222220			−0.111110	+	0.993808i	$0.535441\pi$
$198$	6.13219e38	−	5.65966e38i	0.555018	−	0.512250i
$199$		−	1.25361e39i		−	1.04150i	−0.853710	−	0.520749i	$-0.825653\pi$
$199$		−	1.25361e39i		−	1.04150i	0.853710	−	0.520749i	$-0.174347\pi$
$200$	2.76613e38	−	2.17015e38i	0.211039	−	0.165569i
$201$	−9.41040e37			−0.0659592
$202$	−7.60621e38	−	8.24126e38i	−0.489999	−	0.530910i
$203$		−	5.12791e38i		−	0.303744i
$204$	−8.27341e37	−	6.64140e36i	−0.0450787	−	0.00361865i
$205$	−2.88360e39			−1.44584
$206$	9.80554e37	−	9.04995e37i	0.0452615	−	0.0417738i
$207$			2.79446e39i			1.18796i
$208$	3.90751e39	+	6.31412e38i	1.53046	+	0.247307i
$209$	2.27688e39			0.821963
$210$	−2.15853e38	−	2.33875e38i	−0.0718507	−	0.0778496i
$211$			5.52416e39i			1.69615i	0.529876	+	0.848075i	$0.322239\pi$
$211$			5.52416e39i			1.69615i	−0.529876	+	0.848075i	$0.677761\pi$
$212$	1.24548e38	−	1.55154e39i	0.0352881	−	0.439596i
$213$	4.42454e38			0.115722
$214$	7.15821e38	−	6.60662e38i	0.172890	−	0.159568i
$215$			9.19496e37i			0.0205162i
$216$	−4.05729e38	−	5.17153e38i	−0.0836609	−	0.106636i
$217$	−9.31534e39			−1.77576
$218$	5.20053e39	+	5.63472e39i	0.916826	+	0.993373i
$219$			4.61637e38i			0.0752923i
$220$	−5.64295e39	−	4.52983e38i	−0.851767	−	0.0683748i
$221$	7.38622e39			1.03218
$222$	−2.89570e38	+	2.67256e38i	−0.0374760	+	0.0345882i
$223$		−	7.96231e39i		−	0.954677i	−0.878719	−	0.477339i	$-0.841601\pi$
$223$		−	7.96231e39i		−	0.954677i	0.878719	−	0.477339i	$-0.158399\pi$
$224$	−1.03900e40	+	6.88380e39i	−1.15451	+	0.764913i
$225$	2.59186e39			0.266999
$226$	−5.00280e39	−	5.42049e39i	−0.477936	−	0.517839i
$227$		−	7.49858e39i		−	0.664568i	−0.943179	−	0.332284i	$-0.892181\pi$
$227$		−	7.49858e39i		−	0.664568i	0.943179	−	0.332284i	$-0.107819\pi$
$228$	7.15885e37	−	8.91801e38i	0.00588777	−	0.0733458i
$229$	1.82422e40			1.39275			0.696375	−	0.717678i	$-0.254795\pi$
$229$	1.82422e40			1.39275			0.696375	+	0.717678i	$0.254795\pi$
$230$	1.39311e40	−	1.28576e40i	0.987669	−	0.911562i
$231$			1.08386e39i			0.0713791i
$232$	−2.81985e39	+	2.21229e39i	−0.172556	+	0.135378i
$233$	−1.44542e40			−0.822138			−0.411069	−	0.911604i	$-0.634844\pi$
$233$	−1.44542e40			−0.822138			−0.411069	+	0.911604i	$0.634844\pi$
$234$	1.97905e40	+	2.14428e40i	1.04662	+	1.13400i
$235$		−	2.35769e40i		−	1.15967i
$236$	−3.37195e40	−	2.70680e39i	−1.54304	−	0.123866i
$237$	2.12394e39			0.0904524
$238$	−1.70909e40	+	1.57739e40i	−0.677573	+	0.625361i
$239$		−	1.12431e40i		−	0.415070i	−0.978228	−	0.207535i	$-0.933456\pi$
$239$		−	1.12431e40i		−	0.415070i	0.978228	−	0.207535i	$-0.0665442\pi$
$240$	−3.54846e38	+	2.19597e39i	−0.0122025	+	0.0755155i
$241$	4.26272e40			1.36583			0.682915	−	0.730498i	$-0.260712\pi$
$241$	4.26272e40			1.36583			0.682915	+	0.730498i	$0.260712\pi$
$242$	−9.63524e39	−	1.04397e40i	−0.287741	−	0.311764i
$243$		−	7.27418e39i		−	0.202525i
$244$	1.58681e39	−	1.97674e40i	0.0412001	−	0.513242i
$245$	−4.26834e40			−1.03380
$246$	2.83563e39	−	2.61712e39i	0.0640844	−	0.0591463i
$247$			7.96170e40i			1.67941i
$248$	4.01885e40	+	5.12253e40i	0.791449	+	1.00880i
$249$	5.25459e38			0.00966385
$250$	3.25331e40	+	3.52494e40i	0.558915	+	0.605579i
$251$			4.22323e40i			0.677940i	0.940797	+	0.338970i	$0.110078\pi$
$251$			4.22323e40i			0.677940i	−0.940797	+	0.338970i	$0.889922\pi$
$252$	−9.15859e40	−	7.35197e39i	−1.37410	−	0.110305i
$253$	−6.45618e40			−0.905579
$254$	1.09663e41	−	1.01213e41i	1.43842	−	1.32758i
$255$			4.15097e39i			0.0509292i
$256$	8.26788e40	+	2.74364e40i	0.949107	+	0.314955i
$257$	3.16541e40			0.340069			0.170034	−	0.985438i	$-0.445612\pi$
$257$	3.16541e40			0.340069			0.170034	+	0.985438i	$0.445612\pi$
$258$	−8.34525e37	−	9.04200e37i	−0.000839275	−	0.000909347i
$259$			1.10417e41i			1.03978i
$260$	1.58397e40	−	1.97321e41i	0.139701	−	1.74031i
$261$	−2.64220e40			−0.218311
$262$	−9.40278e40	+	8.67823e40i	−0.728005	+	0.671907i
$263$		−	2.04171e41i		−	1.48165i	−0.671696	−	0.740827i	$-0.734434\pi$
$263$		−	2.04171e41i		−	1.48165i	0.671696	−	0.740827i	$-0.265566\pi$
$264$	5.96020e39	−	4.67603e39i	0.0405503	−	0.0318135i
$265$	−7.78446e40			−0.496648
$266$	−1.70029e41	−	1.84225e41i	−1.01750	−	1.10245i
$267$		−	1.53688e40i		−	0.0862877i
$268$	1.83712e41	+	1.47473e40i	0.967937	+	0.0777002i
$269$	−1.27350e41			−0.629812			−0.314906	−	0.949123i	$-0.601973\pi$
$269$	−1.27350e41			−0.629812			−0.314906	+	0.949123i	$0.601973\pi$
$270$	−2.41571e40	+	2.22956e40i	−0.112166	+	0.103523i
$271$		−	7.60109e40i		−	0.331435i	−0.986173	−	0.165717i	$-0.947006\pi$
$271$		−	7.60109e40i		−	0.331435i	0.986173	−	0.165717i	$-0.0529939\pi$
$272$	1.60475e41	+	2.59310e40i	0.657258	+	0.106206i
$273$	−3.79002e40			−0.145840
$274$	−4.74990e40	−	5.14647e40i	−0.171761	−	0.186102i
$275$			5.98810e40i			0.203532i
$276$	−2.02992e39	+	2.52874e40i	−0.00648671	+	0.0808071i
$277$	5.53831e41			1.66426			0.832131	−	0.554580i	$-0.187121\pi$
$277$	5.53831e41			1.66426			0.832131	+	0.554580i	$0.187121\pi$
$278$	−3.22333e41	+	2.97495e41i	−0.911051	+	0.840848i
$279$			4.79981e41i			1.27630i
$280$	3.84744e41	+	4.90405e41i	0.962687	+	1.22707i
$281$	3.17285e41			0.747209			0.373604	−	0.927588i	$-0.378122\pi$
$281$	3.17285e41			0.747209			0.373604	+	0.927588i	$0.378122\pi$
$282$	2.13982e40	+	2.31847e40i	0.0474397	+	0.0514004i
$283$		−	2.85714e41i		−	0.596433i	−0.954498	−	0.298216i	$-0.903608\pi$
$283$		−	2.85714e41i		−	0.596433i	0.954498	−	0.298216i	$-0.0963917\pi$
$284$	−8.63770e41	−	6.93383e40i	−1.69819	−	0.136321i
$285$	−4.47438e40			−0.0828649
$286$	−4.95403e41	+	4.57229e41i	−0.864443	+	0.797831i
$287$		−	1.08127e42i		−	1.77804i
$288$	3.54693e41	+	5.35351e41i	0.549770	+	0.829787i
$289$	−3.80987e41			−0.556732
$290$	1.21570e41	+	1.31720e41i	0.167517	+	0.181504i
$291$		−	3.21787e40i		−	0.0418204i
$292$	7.23446e40	−	9.01220e41i	0.0886947	−	1.10490i
$293$	3.35542e41			0.388148			0.194074	−	0.980987i	$-0.437830\pi$
$293$	3.35542e41			0.388148			0.194074	+	0.980987i	$0.437830\pi$
$294$	4.19733e40	−	3.87390e40i	0.0458215	−	0.0422906i
$295$			1.69179e42i			1.74330i
$296$	6.07189e41	−	4.76366e41i	0.590697	−	0.463427i
$297$	1.11953e41			0.102843
$298$	−9.13776e41	−	9.90068e41i	−0.792799	−	0.858991i
$299$		−	2.25757e42i		−	1.85026i
$300$	2.34540e40	+	1.88275e39i	0.0181617	+	0.00145791i
$301$	−3.44785e40			−0.0252301
$302$	5.78095e41	−	5.33548e41i	0.399835	−	0.369025i
$303$		−	7.50548e40i		−	0.0490742i
$304$	−2.79514e41	+	1.72978e42i	−0.172804	+	1.06940i
$305$	−9.91779e41			−0.579852
$306$	8.12763e41	+	8.80621e41i	0.449469	+	0.486995i
$307$			1.76284e42i			0.922277i	0.887328	+	0.461138i	$0.152559\pi$
$307$			1.76284e42i			0.922277i	−0.887328	+	0.461138i	$0.847441\pi$
$308$	1.69856e41	−	2.11595e42i	0.0840850	−	1.04747i
$309$	8.93009e39			0.00418371
$310$	2.39282e42	−	2.20844e42i	1.06111	−	0.979345i
$311$			1.36879e41i			0.0574661i	0.999587	+	0.0287330i	$0.00914727\pi$
$311$			1.36879e41i			0.0574661i	−0.999587	+	0.0287330i	$0.990853\pi$
$312$	1.63510e41	+	2.08414e41i	0.0650004	+	0.0828513i
$313$	−1.70699e42			−0.642653			−0.321326	−	0.946969i	$-0.604129\pi$
$313$	−1.70699e42			−0.642653			−0.321326	+	0.946969i	$0.604129\pi$
$314$	4.42104e41	+	4.79015e41i	0.157660	+	0.170823i
$315$			4.59509e42i			1.55244i
$316$	−4.14641e42	−	3.32849e41i	−1.32737	−	0.106553i
$317$	−1.90990e42			−0.579433			−0.289716	−	0.957113i	$-0.593561\pi$
$317$	−1.90990e42			−0.579433			−0.289716	+	0.957113i	$0.593561\pi$
$318$	7.65496e40	−	7.06509e40i	0.0220131	−	0.0203169i
$319$		−	6.10439e41i		−	0.166418i
$320$	1.03688e42	−	4.23143e42i	0.268027	−	1.09380i
$321$	6.51912e40			0.0159810
$322$	4.82124e42	+	5.22377e42i	1.12101	+	1.21460i
$323$			3.26974e42i			0.721224i
$324$	−3.77052e41	+	4.69706e42i	−0.0789108	+	0.983017i
$325$	−2.09390e42			−0.415852
$326$	3.35924e42	−	3.10039e42i	0.633202	−	0.584409i
$327$			5.13165e41i			0.0918217i
$328$	−5.94593e42	+	4.66484e42i	−1.01010	+	0.792467i
$329$	8.84069e42			1.42612
$330$	−2.56957e41	−	2.78411e41i	−0.0393662	−	0.0426529i
$331$		−	9.57525e42i		−	1.39340i	−0.717365	−	0.696698i	$-0.754652\pi$
$331$		−	9.57525e42i		−	1.39340i	0.717365	−	0.696698i	$-0.245348\pi$
$332$	−1.02582e42	−	8.23464e40i	−0.141815	−	0.0113841i
$333$	5.68935e42			0.747327
$334$	−1.32480e42	+	1.22272e42i	−0.165372	+	0.152629i
$335$		−	9.21730e42i		−	1.09356i
$336$	−8.23429e41	−	1.33057e41i	−0.0928664	−	0.0150062i
$337$	−3.76582e41			−0.0403787			−0.0201893	−	0.999796i	$-0.506427\pi$
$337$	−3.76582e41			−0.0403787			−0.0201893	+	0.999796i	$0.506427\pi$
$338$	−9.33611e42	−	1.01156e43i	−0.951880	−	1.03135i
$339$		−	4.93654e41i		−	0.0478661i
$340$	6.50512e41	−	8.10364e42i	0.0599948	−	0.747375i
$341$	−1.10892e43			−0.972918
$342$	−9.49233e42	+	8.76087e42i	−0.792371	+	0.731313i
$343$			1.42994e42i			0.113584i
$344$	1.48748e41	+	1.89599e41i	0.0112450	+	0.0143331i
$345$	1.26873e42			0.0912945
$346$	1.31174e43	+	1.42126e43i	0.898575	+	0.973598i
$347$		−	2.56557e43i		−	1.67333i	−0.547711	−	0.836667i	$-0.684501\pi$
$347$		−	2.56557e43i		−	1.67333i	0.547711	−	0.836667i	$-0.315499\pi$
$348$	−2.39095e41	−	1.91931e40i	−0.0148499	−	0.00119206i
$349$	2.32374e43			1.37453			0.687266	−	0.726406i	$-0.258811\pi$
$349$	2.32374e43			1.37453			0.687266	+	0.726406i	$0.258811\pi$
$350$	4.84504e42	−	4.47170e42i	0.272986	−	0.251951i
$351$			3.91473e42i			0.210126i
$352$	−1.23685e43	+	8.19464e42i	−0.632544	+	0.419087i
$353$	2.38187e41			0.0116077			0.00580387	−	0.999983i	$-0.498153\pi$
$353$	2.38187e41			0.0116077			0.00580387	+	0.999983i	$0.498153\pi$
$354$	−1.53545e42	−	1.66364e42i	−0.0713148	−	0.0772689i
$355$			4.33375e43i			1.91859i
$356$	−2.40849e42	+	3.00034e43i	−0.101647	+	1.26625i
$357$	−1.55650e42			−0.0626309
$358$	−8.83745e42	+	8.15646e42i	−0.339091	+	0.312961i
$359$			2.10845e43i			0.771539i	0.922595	+	0.385769i	$0.126064\pi$
$359$			2.10845e43i			0.771539i	−0.922595	+	0.385769i	$0.873936\pi$
$360$	2.52685e43	−	1.98242e43i	0.881936	−	0.691917i
$361$	−5.21027e42			−0.173475
$362$	−2.04541e43	−	2.21618e43i	−0.649733	−	0.703979i
$363$		−	9.50763e41i		−	0.0288177i
$364$	7.39898e43	+	5.93946e42i	2.14017	+	0.171800i
$365$	−4.52164e43			−1.24830
$366$	9.75280e41	−	9.00128e41i	0.0257011	−	0.0237206i
$367$			1.51246e43i			0.380506i	0.981735	+	0.190253i	$0.0609308\pi$
$367$			1.51246e43i			0.380506i	−0.981735	+	0.190253i	$0.939069\pi$
$368$	7.92574e42	−	4.90486e43i	0.190382	−	1.17819i
$369$	−5.57133e43			−1.27794
$370$	−2.61772e43	−	2.83628e43i	−0.573448	−	0.621326i
$371$		−	2.91896e43i		−	0.610761i
$372$	−3.48662e41	+	4.34339e42i	−0.00696906	+	0.0868159i
$373$	4.32574e43			0.826057			0.413028	−	0.910718i	$-0.364471\pi$
$373$	4.32574e43			0.826057			0.413028	+	0.910718i	$0.364471\pi$
$374$	−2.03454e43	+	1.87776e43i	−0.371235	+	0.342628i
$375$			3.21023e42i			0.0559763i
$376$	−3.81407e43	−	4.86152e43i	−0.635617	−	0.810175i
$377$	2.13456e43			0.340021
$378$	−8.36023e42	−	9.05824e42i	−0.127309	−	0.137938i
$379$			2.61111e43i			0.380152i	0.981769	+	0.190076i	$0.0608735\pi$
$379$			2.61111e43i			0.380152i	−0.981769	+	0.190076i	$0.939126\pi$
$380$	8.73501e43	+	7.01195e42i	1.21602	+	0.0976152i
$381$	9.98720e42			0.132959
$382$	2.06920e43	−	1.90975e43i	0.263466	−	0.243164i
$383$		−	5.65877e43i		−	0.689196i	−0.938750	−	0.344598i	$-0.888015\pi$
$383$		−	5.65877e43i		−	0.689196i	0.938750	−	0.344598i	$-0.111985\pi$
$384$	2.82077e42	+	5.10210e42i	0.0328653	+	0.0594454i
$385$	−1.06162e44			−1.18342
$386$	1.52095e43	+	1.64794e43i	0.162230	+	0.175775i
$387$			1.77654e42i			0.0181337i
$388$	−5.04283e42	+	6.28202e43i	−0.0492646	+	0.613705i
$389$	1.76875e44			1.65395			0.826977	−	0.562236i	$-0.190059\pi$
$389$	1.76875e44			1.65395			0.826977	+	0.562236i	$0.190059\pi$
$390$	9.73537e42	−	8.98519e42i	0.0871473	−	0.0804320i
$391$		−	9.27148e43i		−	0.794592i
$392$	−8.80124e43	+	6.90495e43i	−0.722239	+	0.566628i
$393$	−8.56329e42			−0.0672926
$394$	2.00260e43	+	2.16980e43i	0.150716	+	0.163299i
$395$			2.08035e44i			1.49964i
$396$	−1.09026e44	−	8.75196e42i	−0.752856	−	0.0604348i
$397$	−9.64511e43			−0.638070			−0.319035	−	0.947743i	$-0.603359\pi$
$397$	−9.64511e43			−0.638070			−0.319035	+	0.947743i	$0.603359\pi$
$398$	−1.20746e44	+	1.11441e44i	−0.765348	+	0.706372i
$399$		−	1.67777e43i		−	0.101904i
$400$	−4.54926e43	−	7.35112e42i	−0.264802	−	0.0427891i
$401$	1.02246e44			0.570418			0.285209	−	0.958465i	$-0.407937\pi$
$401$	1.02246e44			0.570418			0.285209	+	0.958465i	$0.407937\pi$
$402$	8.36552e42	+	9.06397e42i	0.0447353	+	0.0484703i
$403$		−	3.87764e44i		−	1.98784i
$404$	−1.17621e43	+	1.46524e44i	−0.0578097	+	0.720154i
$405$	2.35663e44			1.11060
$406$	−4.93913e43	+	4.55853e43i	−0.223207	+	0.206007i
$407$			1.31444e44i			0.569685i
$408$	6.71508e42	+	8.55923e42i	0.0279144	+	0.0355805i
$409$	3.26884e44			1.30346			0.651729	−	0.758452i	$-0.274044\pi$
$409$	3.26884e44			1.30346			0.651729	+	0.758452i	$0.274044\pi$
$410$	2.56342e44	+	2.77744e44i	0.980605	+	1.06248i
$411$		−	4.68699e42i		−	0.0172022i
$412$	−1.74336e43	−	1.39946e42i	−0.0613951	−	0.00492843i
$413$	−6.34373e44			−2.14385
$414$	2.69159e44	−	2.48418e44i	0.872977	−	0.805708i
$415$			5.14677e43i			0.160220i
$416$	−2.86547e44	−	4.32496e44i	−0.856268	−	1.29240i
$417$	−2.93555e43			−0.0842124
$418$	−2.02406e44	−	2.19305e44i	−0.557478	−	0.604022i
$419$			2.33058e44i			0.616348i	0.951330	+	0.308174i	$0.0997178\pi$
$419$			2.33058e44i			0.616348i	−0.951330	+	0.308174i	$0.900282\pi$
$420$	−3.33791e42	+	4.15814e43i	−0.00847689	+	0.105599i
$421$	2.93200e43			0.0715103			0.0357551	−	0.999361i	$-0.488616\pi$
$421$	2.93200e43			0.0715103			0.0357551	+	0.999361i	$0.488616\pi$
$422$	5.32079e44	−	4.91079e44i	1.24642	−	1.15038i
$423$		−	4.55524e44i		−	1.02500i
$424$	−1.60514e44	+	1.25930e44i	−0.346972	+	0.272214i
$425$	−8.59929e43			−0.178587
$426$	−3.93326e43	−	4.26165e43i	−0.0784855	−	0.0850384i
$427$		−	3.71889e44i		−	0.713083i
$428$	−1.27268e44	−	1.02163e43i	−0.234518	−	0.0188257i
$429$	−4.51173e43			−0.0799041
$430$	8.85646e42	−	8.17400e42i	0.0150764	−	0.0139146i
$431$			1.09190e45i			1.78678i	0.449287	+	0.893388i	$0.351678\pi$
$431$			1.09190e45i			1.78678i	−0.449287	+	0.893388i	$0.648322\pi$
$432$	−1.37436e43	+	8.50524e43i	−0.0216210	+	0.133802i
$433$	−1.15339e45			−1.74454			−0.872271	−	0.489022i	$-0.837354\pi$
$433$	−1.15339e45			−1.74454			−0.872271	+	0.489022i	$0.837354\pi$
$434$	8.28102e44	+	8.97241e44i	1.20437	+	1.30492i
$435$			1.19960e43i			0.0167772i
$436$	8.04197e43	−	1.00182e45i	0.108166	−	1.34746i
$437$	9.99384e44			1.29285
$438$	4.44642e43	−	4.10379e43i	0.0553287	−	0.0510652i
$439$			8.38009e44i			1.00312i	0.865124	+	0.501559i	$0.167240\pi$
$439$			8.38009e44i			1.00312i	−0.865124	+	0.501559i	$0.832760\pi$
$440$	4.58008e44	+	5.83790e44i	0.527446	+	0.672297i
$441$	−8.24675e44			−0.913749
$442$	−6.56610e44	−	7.11430e44i	−0.700049	−	0.758497i
$443$			1.37469e45i			1.41039i	0.709012	+	0.705197i	$0.249141\pi$
$443$			1.37469e45i			1.41039i	−0.709012	+	0.705197i	$0.750859\pi$
$444$	5.14835e43	+	4.13279e42i	0.0508344	+	0.00408068i
$445$	1.50534e45			1.43059
$446$	−7.66919e44	+	7.07822e44i	−0.701547	+	0.647488i
$447$		−	9.01674e43i		−	0.0794002i
$448$	1.58667e45	+	3.88801e44i	1.34512	+	0.329610i
$449$	−6.97377e44			−0.569220			−0.284610	−	0.958643i	$-0.591864\pi$
$449$	−6.97377e44			−0.569220			−0.284610	+	0.958643i	$0.591864\pi$
$450$	−2.30408e44	−	2.49645e44i	−0.181086	−	0.196205i
$451$		−	1.28717e45i		−	0.974169i
$452$	−7.73621e43	+	9.63725e44i	−0.0563865	+	0.702425i
$453$	5.26482e43			0.0369585
$454$	−7.22252e44	+	6.66598e44i	−0.488359	+	0.450728i
$455$		−	3.71225e45i		−	2.41793i
$456$	−9.22610e43	+	7.23827e43i	−0.0578916	+	0.0454185i
$457$	3.68009e44			0.222476			0.111238	−	0.993794i	$-0.464518\pi$
$457$	3.68009e44			0.222476			0.111238	+	0.993794i	$0.464518\pi$
$458$	−1.62167e45	−	1.75706e45i	−0.944601	−	1.02347i
$459$			1.60771e44i			0.0902388i
$460$	−2.47685e45	−	1.98827e44i	−1.33973	−	0.107545i
$461$	3.93360e44			0.205057			0.102529	−	0.994730i	$-0.467307\pi$
$461$	3.93360e44			0.205057			0.102529	+	0.994730i	$0.467307\pi$
$462$	1.04396e44	−	9.63518e43i	0.0524531	−	0.0484112i
$463$		−	1.18479e45i		−	0.573804i	−0.957960	−	0.286902i	$-0.907375\pi$
$463$		−	1.18479e45i		−	0.573804i	0.957960	−	0.286902i	$-0.0926253\pi$
$464$	4.63760e44	+	7.49387e43i	0.216515	+	0.0349865i
$465$	2.17919e44			0.0980831
$466$	1.28493e45	+	1.39221e45i	0.557596	+	0.604150i
$467$			5.09109e44i			0.213022i	0.994312	+	0.106511i	$0.0339679\pi$
$467$			5.09109e44i			0.213022i	−0.994312	+	0.106511i	$0.966032\pi$
$468$	3.06036e44	−	3.81239e45i	0.123479	−	1.53822i
$469$	3.45623e45			1.34482
$470$	−2.27090e45	+	2.09591e45i	−0.852184	+	0.786517i
$471$			4.36248e43i			0.0157899i
$472$	2.73683e45	+	3.48844e45i	0.955506	+	1.21791i
$473$	−4.10441e43			−0.0138233
$474$	−1.88811e44	−	2.04575e44i	−0.0613472	−	0.0664692i
$475$		−	9.26929e44i		−	0.290573i
$476$	3.03864e45	+	2.43924e44i	0.919096	+	0.0737795i
$477$	−1.50402e45			−0.438975
$478$	−1.08292e45	+	9.99473e44i	−0.305016	+	0.281512i
$479$			2.58878e45i			0.703707i	0.936055	+	0.351854i	$0.114449\pi$
$479$			2.58878e45i			0.703707i	−0.936055	+	0.351854i	$0.885551\pi$
$480$	2.43058e44	−	1.61036e44i	0.0637688	−	0.0422496i
$481$	−4.59628e45			−1.16396
$482$	−3.78941e45	−	4.10579e45i	−0.926343	−	1.00368i
$483$			4.75738e44i			0.112271i
$484$	−1.48997e44	+	1.85610e45i	−0.0339474	+	0.422894i
$485$	3.15184e45			0.693353
$486$	−7.00639e44	+	6.46650e44i	−0.148826	+	0.137358i
$487$			5.08666e45i			1.04337i	0.853137	+	0.521687i	$0.174697\pi$
$487$			5.08666e45i			1.04337i	−0.853137	+	0.521687i	$0.825303\pi$
$488$	−2.04503e45	+	1.60441e45i	−0.405101	+	0.317819i
$489$	3.05933e44			0.0585296
$490$	3.79441e45	+	4.11120e45i	0.701149	+	0.759689i
$491$		−	9.54813e44i		−	0.170425i	−0.996363	−	0.0852125i	$-0.972843\pi$
$491$		−	9.54813e44i		−	0.170425i	0.996363	−	0.0852125i	$-0.0271569\pi$
$492$	−5.04155e44	−	4.04706e43i	−0.0869276	−	0.00697803i
$493$	8.76629e44			0.146022
$494$	7.66860e45	−	7.07768e45i	1.23412	−	1.13902i
$495$			5.47010e45i			0.850564i
$496$	1.36133e45	−	8.42465e45i	0.204539	−	1.26580i
$497$	−1.62503e46			−2.35941
$498$	−4.67115e43	−	5.06115e43i	−0.00655428	−	0.00710150i
$499$			7.82876e44i			0.106166i	0.998590	+	0.0530828i	$0.0169047\pi$
$499$			7.82876e44i			0.106166i	−0.998590	+	0.0530828i	$0.983095\pi$
$500$	5.03085e44	−	6.26709e45i	0.0659403	−	0.821440i
$501$	−1.20652e44			−0.0152860
$502$	4.06775e45	−	3.75430e45i	0.498186	−	0.459797i
$503$			1.57279e45i			0.186215i	0.995656	+	0.0931075i	$0.0296800\pi$
$503$			1.57279e45i			0.186215i	−0.995656	+	0.0931075i	$0.970320\pi$
$504$	7.43354e45	+	9.47499e45i	0.850896	+	1.08457i
$505$	7.35146e45			0.813618
$506$	5.73932e45	+	6.21850e45i	0.614188	+	0.665467i
$507$		−	9.21246e44i		−	0.0953324i
$508$	−1.94973e46	−	1.56513e45i	−1.95115	−	0.156627i
$509$	5.29994e45			0.512943			0.256471	−	0.966552i	$-0.417440\pi$
$509$	5.29994e45			0.512943			0.256471	+	0.966552i	$0.417440\pi$
$510$	3.99816e44	−	3.69007e44i	0.0374254	−	0.0345415i
$511$		−	1.69549e46i		−	1.53511i
$512$	−4.70723e45	−	1.04025e46i	−0.412264	−	0.911064i
$513$	−1.73298e45			−0.146824
$514$	−2.81394e45	−	3.04888e45i	−0.230644	−	0.249900i
$515$			8.74685e44i			0.0693631i
$516$	−1.29049e42	+	1.60761e43i	−9.90170e−5	+	0.00123349i
$517$	1.05242e46			0.781355
$518$	1.06353e46	−	9.81573e45i	0.764086	−	0.705207i
$519$			1.29437e45i			0.0899938i
$520$	−2.04138e46	+	1.60155e46i	−1.37362	+	1.07766i
$521$	−1.34358e46			−0.875027			−0.437514	−	0.899212i	$-0.644141\pi$
$521$	−1.34358e46			−0.875027			−0.437514	+	0.899212i	$0.644141\pi$
$522$	2.34882e45	+	2.54493e45i	0.148065	+	0.160427i
$523$		−	5.21448e45i		−	0.318187i	−0.987264	−	0.159093i	$-0.949143\pi$
$523$		−	5.21448e45i		−	0.318187i	0.987264	−	0.159093i	$-0.0508571\pi$
$524$	1.67175e46	+	1.34198e45i	0.987505	+	0.0792710i
$525$	4.41247e44			0.0252333
$526$	−1.96655e46	+	1.81501e46i	−1.08880	+	1.00490i
$527$		−	1.59248e46i		−	0.853677i
$528$	−9.80230e44	−	1.58395e44i	−0.0508805	−	0.00822175i
$529$	−8.44286e45			−0.424368
$530$	6.92012e45	+	7.49788e45i	0.336840	+	0.364963i
$531$			3.26866e46i			1.54086i
$532$	−2.62928e45	+	3.27539e46i	−0.120044	+	1.49543i
$533$	4.50093e46			1.99040
$534$	−1.48030e45	+	1.36623e45i	−0.0634087	+	0.0585226i
$535$			6.38535e45i			0.264954i
$536$	−1.49110e46	−	1.90059e46i	−0.599383	−	0.763990i
$537$	−8.04844e44			−0.0313436
$538$	1.13210e46	+	1.22662e46i	0.427155	+	0.462819i
$539$		−	1.90528e46i		−	0.696548i
$540$	4.29496e45	+	3.44774e44i	0.152148	+	0.0122135i
$541$	5.25544e46			1.80408			0.902039	−	0.431654i	$-0.142070\pi$
$541$	5.25544e46			1.80408			0.902039	+	0.431654i	$0.142070\pi$
$542$	−7.32126e45	+	6.75710e45i	−0.243556	+	0.224788i
$543$		−	2.01832e45i		−	0.0650718i
$544$	−1.17680e46	−	1.77619e46i	−0.367724	−	0.555019i
$545$	−5.02635e46			−1.52234
$546$	3.36920e45	+	3.65049e45i	0.0989125	+	0.107171i
$547$		−	3.01094e46i		−	0.856877i	−0.903571	−	0.428438i	$-0.859064\pi$
$547$		−	3.01094e46i		−	0.856877i	0.903571	−	0.428438i	$-0.140936\pi$
$548$	−7.34513e44	+	9.15007e45i	−0.0202642	+	0.252438i
$549$	−1.91619e46			−0.512518
$550$	5.76766e45	−	5.32322e45i	0.149566	−	0.138041i
$551$			9.44929e45i			0.237587i
$552$	2.61610e45	−	2.05244e45i	0.0637808	−	0.0500388i
$553$	−7.80075e46			−1.84421
$554$	−4.92337e46	−	5.33443e46i	−1.12875	−	1.22299i
$555$		−	2.58305e45i		−	0.0574318i
$556$	5.73085e46	+	4.60039e45i	1.23580	+	0.0992026i
$557$	3.92692e46			0.821323			0.410662	−	0.911788i	$-0.365298\pi$
$557$	3.92692e46			0.821323			0.410662	+	0.911788i	$0.365298\pi$
$558$	4.62311e46	−	4.26686e46i	0.937891	−	0.865620i
$559$		−	1.43522e45i		−	0.0282434i
$560$	1.30327e46	−	8.06533e46i	0.248793	−	1.53966i
$561$	−1.85289e45			−0.0343148
$562$	−2.82055e46	−	3.05604e46i	−0.506777	−	0.549088i
$563$			2.09753e46i			0.365650i	0.983145	+	0.182825i	$0.0585242\pi$
$563$			2.09753e46i			0.365650i	−0.983145	+	0.182825i	$0.941476\pi$
$564$	3.30896e44	−	4.12208e45i	0.00559689	−	0.0697223i
$565$	4.83524e46			0.793587
$566$	−2.75195e46	+	2.53990e46i	−0.438290	+	0.404517i
$567$			8.83671e46i			1.36577i
$568$	7.01076e46	+	8.93611e46i	1.05158	+	1.34038i
$569$	−1.25771e47			−1.83093			−0.915466	−	0.402396i	$-0.868178\pi$
$569$	−1.25771e47			−1.83093			−0.915466	+	0.402396i	$0.868178\pi$
$570$	3.97757e45	+	4.30966e45i	0.0562012	+	0.0608935i
$571$		−	6.61952e45i		−	0.0907847i	−0.998969	−	0.0453924i	$-0.985546\pi$
$571$		−	6.61952e45i		−	0.0907847i	0.998969	−	0.0453924i	$-0.0144538\pi$
$572$	8.80793e46	+	7.07048e45i	1.17258	+	0.0941275i
$573$	1.88446e45			0.0243533
$574$	−1.04146e47	+	9.61211e46i	−1.30660	+	1.20591i
$575$			2.62835e46i			0.320132i
$576$	2.00333e46	−	8.17545e46i	0.236903	−	0.966784i
$577$	1.23615e47			1.41932			0.709662	−	0.704543i	$-0.248848\pi$
$577$	1.23615e47			1.41932			0.709662	+	0.704543i	$0.248848\pi$
$578$	3.38684e46	+	3.66961e46i	0.377591	+	0.409116i
$579$			1.50081e45i			0.0162476i
$580$	1.87993e45	−	2.34189e46i	0.0197636	−	0.246201i
$581$	−1.92989e46			−0.197033
$582$	−3.09941e45	+	2.86058e45i	−0.0307318	+	0.0283637i
$583$		−	3.47480e46i		−	0.334629i
$584$	−9.32354e46	+	7.31472e46i	−0.872093	+	0.684194i
$585$	−1.91277e47			−1.73785
$586$	−2.98285e46	−	3.23189e46i	−0.263252	−	0.285232i
$587$			1.26567e47i			1.08511i	0.840020	+	0.542555i	$0.182543\pi$
$587$			1.26567e47i			1.08511i	−0.840020	+	0.542555i	$0.817457\pi$
$588$	−7.46257e45	−	5.99051e44i	−0.0621547	−	0.00498941i
$589$	1.71655e47			1.38899
$590$	1.62951e47	−	1.50394e47i	1.28107	−	1.18235i
$591$			1.97608e45i			0.0150944i
$592$	−9.98599e46	−	1.61363e46i	−0.741177	−	0.119766i
$593$	3.45233e46			0.248990			0.124495	−	0.992220i	$-0.460269\pi$
$593$	3.45233e46			0.248990			0.124495	+	0.992220i	$0.460269\pi$
$594$	−9.95222e45	−	1.07831e46i	−0.0697510	−	0.0755746i
$595$		−	1.52456e47i		−	1.03838i
$596$	−1.41304e46	+	1.76027e47i	−0.0935338	+	1.16518i
$597$	−1.09965e46			−0.0707444
$598$	−2.17446e47	+	2.00691e47i	−1.35967	+	1.25489i
$599$		−	2.40618e47i		−	1.46242i	−0.682153	−	0.731209i	$-0.738956\pi$
$599$		−	2.40618e47i		−	1.46242i	0.682153	−	0.731209i	$-0.261044\pi$
$600$	−1.90364e45	−	2.42643e45i	−0.0112464	−	0.0143350i
$601$	1.42970e47			0.821066			0.410533	−	0.911846i	$-0.365343\pi$
$601$	1.42970e47			0.821066			0.410533	+	0.911846i	$0.365343\pi$
$602$	3.06502e45	+	3.32093e45i	0.0171117	+	0.0185404i
$603$		−	1.78085e47i		−	0.966571i
$604$	−1.02781e47	−	8.25066e45i	−0.542358	−	0.0435372i
$605$	9.31253e46			0.477778
$606$	−7.22917e45	+	6.67211e45i	−0.0360623	+	0.0332835i
$607$		−	2.04005e47i		−	0.989541i	−0.869024	−	0.494771i	$-0.835252\pi$
$607$		−	2.04005e47i		−	0.989541i	0.869024	−	0.494771i	$-0.164748\pi$
$608$	1.91458e47	−	1.26849e47i	0.903051	−	0.598310i
$609$	−4.49816e45			−0.0206320
$610$	8.81657e46	+	9.55267e46i	0.393272	+	0.426106i
$611$			3.68006e47i			1.59644i
$612$	1.25684e46	−	1.56568e47i	0.0530280	−	0.660587i
$613$	2.25081e47			0.923655			0.461828	−	0.886970i	$-0.347194\pi$
$613$	2.25081e47			0.923655			0.461828	+	0.886970i	$0.347194\pi$
$614$	1.69795e47	−	1.56711e47i	0.677737	−	0.625513i
$615$			2.52947e46i			0.0982093i
$616$	−2.18905e47	+	1.71740e47i	−0.826767	+	0.648635i
$617$	−3.35902e47			−1.23414			−0.617070	−	0.786908i	$-0.711680\pi$
$617$	−3.35902e47			−1.23414			−0.617070	+	0.786908i	$0.711680\pi$
$618$	−7.93854e44	−	8.60134e44i	−0.00283751	−	0.00307441i
$619$		−	2.78856e47i		−	0.969704i	−0.874596	−	0.484852i	$-0.838873\pi$
$619$		−	2.78856e47i		−	0.969704i	0.874596	−	0.484852i	$-0.161127\pi$
$620$	−4.25427e47	−	3.41507e46i	−1.43935	−	0.115542i
$621$	4.91393e46			0.161760
$622$	1.31840e46	−	1.21681e46i	0.0422291	−	0.0389750i
$623$			5.64462e47i			1.75929i
$624$	5.53869e45	−	3.42764e46i	0.0167985	−	0.103958i
$625$	−4.05317e47			−1.19629
$626$	1.51745e47	+	1.64415e47i	0.435864	+	0.472255i
$627$		−	1.99726e46i		−	0.0558323i
$628$	6.83659e45	−	8.51656e46i	0.0186005	−	0.231713i
$629$	−1.88761e47			−0.499865
$630$	4.42592e47	−	4.08487e47i	1.14081	−	1.05291i
$631$		−	4.14149e47i		−	1.03910i	−0.854440	−	0.519550i	$-0.826100\pi$
$631$		−	4.14149e47i		−	1.03910i	0.854440	−	0.519550i	$-0.173900\pi$
$632$	3.36542e47	+	4.28966e47i	0.821957	+	1.04769i
$633$	4.84575e46			0.115212
$634$	1.69784e47	+	1.83959e47i	0.392987	+	0.425798i
$635$			9.78227e47i			2.20438i
$636$	−1.36100e46	−	1.09253e45i	−0.0298598	−	0.00239697i
$637$	6.66233e47			1.42317
$638$	−5.87966e46	+	5.42659e46i	−0.122293	+	0.112869i
$639$			8.37312e47i			1.69579i
$640$	−4.99741e47	+	2.76289e47i	−0.985565	+	0.544884i
$641$	−3.18515e47			−0.611707			−0.305854	−	0.952079i	$-0.598942\pi$
$641$	−3.18515e47			−0.611707			−0.305854	+	0.952079i	$0.598942\pi$
$642$	−5.79527e45	−	6.27913e45i	−0.0108387	−	0.0117437i
$643$		−	7.53348e47i		−	1.37217i	−0.727520	−	0.686087i	$-0.759327\pi$
$643$		−	7.53348e47i		−	1.37217i	0.727520	−	0.686087i	$-0.240673\pi$
$644$	7.45545e46	−	9.28750e47i	0.132256	−	1.64755i
$645$	8.06575e44			0.00139357
$646$	3.14937e47	−	2.90668e47i	0.529993	−	0.489153i
$647$			1.49462e47i			0.244995i	0.992469	+	0.122497i	$0.0390903\pi$
$647$			1.49462e47i			0.244995i	−0.992469	+	0.122497i	$0.960910\pi$
$648$	4.85933e47	−	3.81236e47i	0.775892	−	0.608721i
$649$	−7.55173e47			−1.17459
$650$	1.86140e47	+	2.01681e47i	0.282042	+	0.305590i
$651$			8.17134e46i			0.120619i
$652$	−5.97251e47	−	4.79437e46i	−0.858910	−	0.0689481i
$653$	2.72330e46			0.0381568			0.0190784	−	0.999818i	$-0.493927\pi$
$653$	2.72330e46			0.0381568			0.0190784	+	0.999818i	$0.493927\pi$
$654$	4.94273e46	−	4.56186e46i	0.0674754	−	0.0622759i
$655$		−	8.38757e47i		−	1.11567i
$656$	9.77883e47	+	1.58016e47i	1.26742	+	0.204802i
$657$	−8.73615e47			−1.10334
$658$	−7.85907e47	−	8.51523e47i	−0.967232	−	1.04799i
$659$		−	7.39342e47i		−	0.886734i	−0.896340	−	0.443367i	$-0.853784\pi$
$659$		−	7.39342e47i		−	0.886734i	0.896340	−	0.443367i	$-0.146216\pi$
$660$	−3.97353e45	+	4.94995e46i	−0.00464439	+	0.0578567i
$661$	4.21709e47			0.480383			0.240191	−	0.970726i	$-0.422790\pi$
$661$	4.21709e47			0.480383			0.240191	+	0.970726i	$0.422790\pi$
$662$	−9.22275e47	+	8.51207e47i	−1.02394	+	0.945038i
$663$		−	6.47913e46i		−	0.0701111i
$664$	8.32600e46	+	1.06125e47i	0.0878171	+	0.111934i
$665$	1.64334e48			1.68951
$666$	−5.05764e47	−	5.47990e47i	−0.506857	−	0.549175i
$667$		−	2.67939e47i		−	0.261756i
$668$	2.35541e47	+	1.89078e46i	0.224319	+	0.0180070i
$669$	−6.98448e46			−0.0648470
$670$	−8.87798e47	+	8.19386e47i	−0.803604	+	0.741681i
$671$		−	4.42706e47i		−	0.390690i
$672$	6.03841e46	+	9.11399e46i	0.0519571	+	0.0784207i
$673$	2.08164e48			1.74642			0.873211	−	0.487342i	$-0.162034\pi$
$673$	2.08164e48			1.74642			0.873211	+	0.487342i	$0.162034\pi$
$674$	3.34769e46	+	3.62719e46i	0.0273859	+	0.0296724i
$675$		−	4.55766e46i		−	0.0363562i
$676$	−1.44371e47	+	1.79848e48i	−0.112302	+	1.39898i
$677$	−1.55180e48			−1.17714			−0.588571	−	0.808445i	$-0.700309\pi$
$677$	−1.55180e48			−1.17714			−0.588571	+	0.808445i	$0.700309\pi$
$678$	−4.75481e46	+	4.38841e46i	−0.0351745	+	0.0324641i
$679$			1.18185e48i			0.852662i
$680$	−8.38359e47	+	6.57729e47i	−0.589900	+	0.462802i
$681$	−6.57769e46			−0.0451411
$682$	9.85792e47	+	1.06810e48i	0.659859	+	0.714951i
$683$			5.34392e47i			0.348906i	0.984666	+	0.174453i	$0.0558157\pi$
$683$			5.34392e47i			0.348906i	−0.984666	+	0.174453i	$0.944184\pi$
$684$	1.68767e48	+	1.35476e47i	1.07482	+	0.0862798i
$685$	4.59081e47			0.285200
$686$	1.37730e47	−	1.27117e47i	0.0834676	−	0.0770358i
$687$		−	1.60019e47i		−	0.0946033i
$688$	5.03866e45	−	3.11819e46i	0.00290611	−	0.0179845i
$689$	1.21505e48			0.683705
$690$	−1.12786e47	−	1.22202e47i	−0.0619184	−	0.0670880i
$691$			1.18730e48i			0.635963i	0.948097	+	0.317982i	$0.103005\pi$
$691$			1.18730e48i			0.635963i	−0.948097	+	0.317982i	$0.896995\pi$
$692$	2.02845e47	−	2.52690e48i	0.106013	−	1.32064i
$693$	−2.05114e48			−1.04599
$694$	−2.47112e48	+	2.28070e48i	−1.22965	+	1.13490i
$695$		−	2.87531e48i		−	1.39618i
$696$	1.94061e46	+	2.47355e46i	0.00919561	+	0.0117210i
$697$	1.84846e48			0.854776
$698$	−2.06572e48	−	2.23819e48i	−0.932244	−	1.01008i
$699$			1.26791e47i			0.0558442i
$700$	−8.61415e47	−	6.91493e46i	−0.370293	−	0.0297249i
$701$	−3.02810e48			−1.27047			−0.635233	−	0.772320i	$-0.719096\pi$
$701$	−3.02810e48			−1.27047			−0.635233	+	0.772320i	$0.719096\pi$
$702$	3.77061e47	−	3.48006e47i	0.154412	−	0.142513i
$703$		−	2.03468e48i		−	0.813310i
$704$	1.88881e48	+	4.62838e47i	0.736976	+	0.180590i
$705$	−2.06815e47			−0.0787711
$706$	−2.11740e46	−	2.29418e46i	−0.00787268	−	0.00852998i
$707$			2.75659e48i			1.00056i
$708$	−2.37438e46	+	2.95784e47i	−0.00841366	+	0.104812i
$709$	2.45091e48			0.847892			0.423946	−	0.905687i	$-0.360645\pi$
$709$	2.45091e48			0.847892			0.423946	+	0.905687i	$0.360645\pi$
$710$	4.17420e48	−	3.85255e48i	1.40988	−	1.30124i
$711$			4.01940e48i			1.32550i
$712$	3.10399e48	−	2.43522e48i	0.999450	−	0.784111i
$713$	−4.86736e48			−1.53028
$714$	1.38367e47	+	1.49920e47i	0.0424780	+	0.0460245i
$715$		−	4.41915e48i		−	1.32476i
$716$	1.57124e48	+	1.26130e47i	0.459961	+	0.0369229i
$717$	−9.86236e46			−0.0281939
$718$	2.03083e48	−	1.87434e48i	0.566967	−	0.523278i
$719$			2.48716e48i			0.678130i	0.940763	+	0.339065i	$0.110111\pi$
$719$			2.48716e48i			0.678130i	−0.940763	+	0.339065i	$0.889889\pi$
$720$	−4.15573e48	−	6.71521e47i	−1.10661	−	0.178816i
$721$	−3.27982e47			−0.0853004
$722$	4.63175e47	+	5.01846e47i	0.117656	+	0.127479i
$723$		−	3.73922e47i		−	0.0927748i
$724$	−3.16297e47	+	3.94022e48i	−0.0766549	+	0.954916i
$725$	−2.48513e47			−0.0588305
$726$	−9.15761e46	+	8.45195e46i	−0.0211768	+	0.0195449i
$727$			5.86256e48i			1.32435i	0.749350	+	0.662175i	$0.230366\pi$
$727$			5.86256e48i			1.32435i	−0.749350	+	0.662175i	$0.769634\pi$
$728$	−6.00536e48	−	7.65459e48i	−1.32527	−	1.68923i
$729$	4.51048e48			0.972423
$730$	4.01958e48	+	4.35518e48i	0.846627	+	0.917313i
$731$		−	5.89419e46i		−	0.0121291i
$732$	−1.73398e47	−	1.39194e46i	−0.0348623	−	0.00279854i
$733$	−9.10245e48			−1.78810			−0.894048	−	0.447972i	$-0.852147\pi$
$733$	−9.10245e48			−1.78810			−0.894048	+	0.447972i	$0.852147\pi$
$734$	1.45678e48	−	1.34453e48i	0.279616	−	0.258069i
$735$			3.74415e47i			0.0702213i
$736$	−5.42887e48	+	3.59686e48i	−0.994916	+	0.659175i
$737$	4.11438e48			0.736813
$738$	4.95272e48	+	5.36623e48i	0.866734	+	0.939098i
$739$		−	7.09028e47i		−	0.121257i	−0.998160	−	0.0606286i	$-0.980689\pi$
$739$		−	7.09028e47i		−	0.121257i	0.998160	−	0.0606286i	$-0.0193105\pi$
$740$	−4.04799e47	+	5.04271e48i	−0.0676550	+	0.842800i
$741$	6.98394e47			0.114075
$742$	−2.81150e48	+	2.59485e48i	−0.448819	+	0.414234i
$743$		−	1.19926e49i		−	1.87112i	−0.353162	−	0.935562i	$-0.614893\pi$
$743$		−	1.19926e49i		−	1.87112i	0.353162	−	0.935562i	$-0.385107\pi$
$744$	4.49344e47	−	3.52530e47i	0.0685235	−	0.0537596i
$745$	8.83171e48			1.31640
$746$	−3.84543e48	−	4.16649e48i	−0.560254	−	0.607030i
$747$			9.94394e47i			0.141615i
$748$	3.61727e48	+	2.90373e47i	0.503563	+	0.0404230i
$749$	−2.39433e48			−0.325831
$750$	3.09205e47	−	2.85378e47i	0.0411343	−	0.0379646i
$751$			7.61613e48i			0.990502i	0.868750	+	0.495251i	$0.164924\pi$
$751$			7.61613e48i			0.990502i	−0.868750	+	0.495251i	$0.835076\pi$
$752$	−1.29197e48	+	7.99538e48i	−0.164266	+	1.01657i
$753$	3.70458e47			0.0460494
$754$	−1.89755e48	−	2.05598e48i	−0.230611	−	0.249865i
$755$			5.15678e48i			0.612746i
$756$	−1.29281e47	+	1.61049e48i	−0.0150198	+	0.187106i
$757$	1.23873e48			0.140717			0.0703583	−	0.997522i	$-0.477586\pi$
$757$	1.23873e48			0.140717			0.0703583	+	0.997522i	$0.477586\pi$
$758$	2.51498e48	−	2.32118e48i	0.279356	−	0.257830i
$759$			5.66331e47i			0.0615120i
$760$	−7.08974e48	−	9.03678e48i	−0.753008	−	0.959804i
$761$	1.55956e49			1.61981			0.809905	−	0.586561i	$-0.199518\pi$
$761$	1.55956e49			1.61981			0.809905	+	0.586561i	$0.199518\pi$
$762$	−8.87828e47	−	9.61954e47i	−0.0901767	−	0.0977056i
$763$		−	1.88474e49i		−	1.87212i
$764$	−3.67889e48	−	2.95320e47i	−0.357380	−	0.0286883i
$765$	−7.85542e48			−0.746319
$766$	−5.45045e48	+	5.03045e48i	−0.506458	+	0.467431i
$767$		−	2.64066e49i		−	2.39989i
$768$	2.40670e47	−	7.25252e47i	0.0213935	−	0.0644686i
$769$	−6.58631e48			−0.572657			−0.286329	−	0.958132i	$-0.592435\pi$
$769$	−6.58631e48			−0.572657			−0.286329	+	0.958132i	$0.592435\pi$
$770$	9.43747e48	+	1.02254e49i	0.802626	+	0.869638i
$771$		−	2.77667e47i		−	0.0230993i
$772$	2.35196e47	−	2.92992e48i	0.0191398	−	0.238430i
$773$	6.53179e48			0.519973			0.259986	−	0.965612i	$-0.416282\pi$
$773$	6.53179e48			0.519973			0.259986	+	0.965612i	$0.416282\pi$
$774$	1.71113e47	−	1.57928e47i	0.0133256	−	0.0122988i
$775$			4.51448e48i			0.343937i
$776$	6.49904e48	−	5.09878e48i	0.484395	−	0.380029i
$777$	9.68573e47			0.0706277
$778$	−1.57236e49	−	1.70364e49i	−1.12176	−	1.21541i
$779$			1.99247e49i			1.39077i
$780$	−1.73088e48	−	1.38945e47i	−0.118211	−	0.00948930i
$781$	−1.93448e49			−1.29270
$782$	−8.93016e48	+	8.24203e48i	−0.583908	+	0.538914i
$783$			4.64617e47i			0.0297266i
$784$	1.44748e49	+	2.33897e48i	0.906230	+	0.146437i
$785$	−4.27297e48			−0.261785
$786$	7.61247e47	+	8.24804e47i	0.0456397	+	0.0494501i
$787$			2.77646e49i			1.62900i	0.580165	+	0.814499i	$0.302988\pi$
$787$			2.77646e49i			1.62900i	−0.580165	+	0.814499i	$0.697012\pi$
$788$	3.09678e47	−	3.85775e48i	0.0177813	−	0.221508i
$789$	−1.79097e48			−0.100642
$790$	2.00377e49	−	1.84936e49i	1.10201	−	1.01710i
$791$			1.81308e49i			0.975926i
$792$	8.84906e48	+	1.12793e49i	0.466197	+	0.594227i
$793$	1.54804e49			0.798248
$794$	8.57417e48	+	9.29003e48i	0.432756	+	0.468888i
$795$			6.82847e47i			0.0337351i
$796$	2.14677e49	+	1.72330e48i	1.03816	+	0.0833372i
$797$	−2.13583e49			−1.01105			−0.505527	−	0.862811i	$-0.668702\pi$
$797$	−2.13583e49			−1.01105			−0.505527	+	0.862811i	$0.668702\pi$
$798$	−1.61600e48	+	1.49148e48i	−0.0748847	+	0.0691143i
$799$			1.51134e49i			0.685593i
$800$	3.33608e48	+	5.03527e48i	0.148152	+	0.223611i
$801$	2.90844e49			1.26447
$802$	−9.08935e48	−	9.84823e48i	−0.386873	−	0.419173i
$803$		−	2.01835e49i		−	0.841071i
$804$	1.29363e47	−	1.61151e48i	0.00527783	−	0.0657477i
$805$	−4.65976e49			−1.86137
$806$	−3.73488e49	+	3.44708e49i	−1.46077	+	1.34821i
$807$			1.11711e48i			0.0427803i
$808$	1.51586e49	−	1.18926e49i	0.568415	−	0.445946i
$809$	1.13701e49			0.417483			0.208742	−	0.977971i	$-0.433063\pi$
$809$	1.13701e49			0.417483			0.208742	+	0.977971i	$0.433063\pi$
$810$	−2.09496e49	−	2.26987e49i	−0.753236	−	0.816124i
$811$		−	5.65751e46i		−	0.00199191i	−1.00000		0.000995957i	$-0.999683\pi$
$811$		−	5.65751e46i		−	0.00199191i	1.00000		0.000995957i	$-0.000317023\pi$
$812$	8.78143e48	+	7.04921e47i	0.302770	+	0.0243046i
$813$	−6.66761e47			−0.0225129
$814$	1.26605e49	−	1.16849e49i	0.418634	−	0.386376i
$815$			2.99655e49i			0.970381i
$816$	2.27465e47	−	1.40767e48i	0.00721410	−	0.0446446i
$817$	6.35343e47			0.0197348
$818$	−2.90588e49	−	3.14850e49i	−0.884040	−	0.957849i
$819$		−	7.17234e49i		−	2.13715i
$820$	3.96401e48	−	4.93810e49i	0.115691	−	1.44120i
$821$	−1.31939e49			−0.377171			−0.188585	−	0.982057i	$-0.560390\pi$
$821$	−1.31939e49			−0.377171			−0.188585	+	0.982057i	$0.560390\pi$
$822$	−4.51444e47	+	4.16657e47i	−0.0126410	+	0.0116670i
$823$		−	3.08643e49i		−	0.846563i	−0.905998	−	0.423281i	$-0.860878\pi$
$823$		−	3.08643e49i		−	0.846563i	0.905998	−	0.423281i	$-0.139122\pi$
$824$	1.41499e48	+	1.80358e48i	0.0380181	+	0.0484589i
$825$	5.25271e47			0.0138250
$826$	5.63936e49	+	6.11019e49i	1.45401	+	1.57541i
$827$			1.97274e49i			0.498282i	0.968467	+	0.249141i	$0.0801483\pi$
$827$			1.97274e49i			0.498282i	−0.968467	+	0.249141i	$0.919852\pi$
$828$	−4.78546e49	−	3.84148e48i	−1.18415	−	0.0950568i
$829$	5.19182e49			1.25861			0.629307	−	0.777157i	$-0.283339\pi$
$829$	5.19182e49			1.25861			0.629307	+	0.777157i	$0.283339\pi$
$830$	4.95730e48	−	4.57530e48i	0.117738	−	0.108666i
$831$		−	4.85816e48i		−	0.113046i
$832$	−1.61844e49	+	6.60473e49i	−0.368977	+	1.50577i
$833$	2.73611e49			0.611179
$834$	2.60960e48	+	2.82748e48i	0.0571151	+	0.0618837i
$835$		−	1.18177e49i		−	0.253432i
$836$	−3.12996e48	+	3.89910e49i	−0.0657707	+	0.819328i
$837$	8.44022e48			0.173788
$838$	2.24478e49	−	2.07181e49i	0.452925	−	0.418024i
$839$		−	4.31308e49i		−	0.852774i	−0.904541	−	0.426387i	$-0.859786\pi$
$839$		−	4.31308e49i		−	0.852774i	0.904541	−	0.426387i	$-0.140214\pi$
$840$	4.30179e48	−	3.37494e48i	0.0833492	−	0.0653910i
$841$	−5.01328e49			−0.951897
$842$	−2.60645e48	−	2.82406e48i	−0.0485002	−	0.0525495i
$843$		−	2.78320e48i		−	0.0507546i
$844$	−9.46000e49	−	7.59393e48i	−1.69071	−	0.135720i
$845$	9.02343e49			1.58055
$846$	−4.38754e49	+	4.04945e49i	−0.753226	+	0.695184i
$847$			3.49194e49i			0.587555i
$848$	2.63986e49	+	4.26573e48i	0.435363	+	0.0703500i
$849$	−2.50626e48			−0.0405130
$850$	7.64448e48	+	8.28272e48i	0.121123	+	0.131235i
$851$			5.76943e49i			0.896046i
$852$	−6.08230e47	+	7.57692e48i	−0.00925966	+	0.115351i
$853$	1.73520e49			0.258950			0.129475	−	0.991583i	$-0.458671\pi$
$853$	1.73520e49			0.258950			0.129475	+	0.991583i	$0.458671\pi$
$854$	−3.58199e49	+	3.30597e49i	−0.524011	+	0.483632i
$855$		−	8.46745e49i		−	1.21431i
$856$	1.03297e49	+	1.31665e49i	0.145222	+	0.185104i
$857$	−3.02409e49			−0.416794			−0.208397	−	0.978044i	$-0.566825\pi$
$857$	−3.02409e49			−0.416794			−0.208397	+	0.978044i	$0.566825\pi$
$858$	4.01077e48	+	4.34564e48i	0.0541931	+	0.0587178i
$859$			9.45492e49i			1.25249i	0.779627	+	0.626245i	$0.215409\pi$
$859$			9.45492e49i			1.25249i	−0.779627	+	0.626245i	$0.784591\pi$
$860$	−1.57462e48	−	1.26401e47i	−0.0204504	−	0.00164163i
$861$	−9.48481e48			−0.120774
$862$	1.05170e50	−	9.70663e49i	1.31302	−	1.21184i
$863$		−	1.75300e49i		−	0.214585i	−0.994227	−	0.107293i	$-0.965782\pi$
$863$		−	1.75300e49i		−	0.214585i	0.994227	−	0.107293i	$-0.0342181\pi$
$864$	9.41389e48	−	6.23711e48i	0.112989	−	0.0748599i
$865$	−1.26781e50			−1.49204
$866$	1.02532e50	+	1.11093e50i	1.18320	+	1.28198i
$867$			3.34198e48i			0.0378164i
$868$	1.28056e49	−	1.59523e50i	0.142090	−	1.77006i
$869$	−9.28620e49			−1.01042
$870$	1.15544e48	−	1.06640e48i	0.0123287	−	0.0113787i
$871$			1.43870e50i			1.50544i
$872$	−1.03642e50	+	8.13120e49i	−1.06355	+	0.834400i
$873$	6.08959e49			0.612839
$874$	−8.88418e49	−	9.62593e49i	−0.876846	−	0.950054i
$875$		−	1.17904e50i		−	1.14128i
$876$	−7.90543e48	−	6.34601e47i	−0.0750508	−	0.00602463i
$877$	1.01569e50			0.945730			0.472865	−	0.881135i	$-0.343220\pi$
$877$	1.01569e50			0.945730			0.472865	+	0.881135i	$0.343220\pi$
$878$	8.07158e49	−	7.44961e49i	0.737143	−	0.680341i
$879$		−	2.94335e48i		−	0.0263652i
$880$	1.55145e49	−	9.60116e49i	0.136311	−	0.843565i
$881$	1.51097e50			1.30217			0.651083	−	0.759007i	$-0.274315\pi$
$881$	1.51097e50			1.30217			0.651083	+	0.759007i	$0.274315\pi$
$882$	7.33108e49	+	7.94316e49i	0.619729	+	0.671471i
$883$		−	2.64807e49i		−	0.219582i	−0.993955	−	0.109791i	$-0.964982\pi$
$883$		−	2.64807e49i		−	0.219582i	0.993955	−	0.109791i	$-0.0350182\pi$
$884$	−1.01537e49	+	1.26487e50i	−0.0825912	+	1.02887i
$885$	1.48402e49			0.118414
$886$	1.32408e50	−	1.22205e50i	1.03643	−	0.956567i
$887$			9.38691e48i			0.0720811i	0.999350	+	0.0360405i	$0.0114745\pi$
$887$			9.38691e48i			0.0720811i	−0.999350	+	0.0360405i	$0.988525\pi$
$888$	−4.17864e48	−	5.32621e48i	−0.0314786	−	0.0401234i
$889$	−3.66808e50			−2.71087
$890$	−1.33820e50	−	1.44993e50i	−0.970265	−	1.05127i
$891$			1.05194e50i			0.748293i
$892$	1.36353e50	+	1.09456e49i	0.951616	+	0.0763901i
$893$	−1.62909e50			−1.11550
$894$	−8.68479e48	+	8.01557e48i	−0.0583474	+	0.0538513i
$895$		−	7.88328e49i		−	0.519656i
$896$	−1.03601e50	−	1.87389e50i	−0.670080	−	1.21201i
$897$	−1.98033e49			−0.125680
$898$	6.19944e49	+	6.71704e49i	0.386060	+	0.418293i
$899$		−	4.60215e49i		−	0.281220i
$900$	−3.56297e48	+	4.43851e49i	−0.0213644	+	0.266143i
$901$	4.99003e49			0.293617
$902$	−1.23978e50	+	1.14425e50i	−0.715871	+	0.660708i
$903$			3.02443e47i			0.00171377i
$904$	9.97019e49	−	7.82204e49i	0.554421	−	0.434967i
$905$	1.97690e50			1.07885
$906$	−4.68024e48	−	5.07100e48i	−0.0250662	−	0.0271590i
$907$			1.37668e50i			0.723616i	0.932253	+	0.361808i	$0.117840\pi$
$907$			1.37668e50i			0.723616i	−0.932253	+	0.361808i	$0.882160\pi$
$908$	1.28411e50	+	1.03081e49i	0.662437	+	0.0531765i
$909$	1.42036e50			0.719137
$910$	−3.57559e50	+	3.30006e50i	−1.77682	+	1.63990i
$911$			1.87382e50i			0.913936i	0.889483	+	0.456968i	$0.151065\pi$
$911$			1.87382e50i			0.913936i	−0.889483	+	0.456968i	$0.848935\pi$
$912$	1.51735e49	+	2.45187e48i	0.0726395	+	0.0117378i
$913$	−2.29739e49			−0.107952
$914$	−3.27147e49	−	3.54461e49i	−0.150889	−	0.163487i
$915$			8.69980e48i			0.0393868i
$916$	−2.50771e49	+	3.12393e50i	−0.111443	+	1.38828i
$917$	3.14511e50			1.37201
$918$	1.54853e49	−	1.42920e49i	0.0663122	−	0.0612024i
$919$		−	5.89483e47i		−	0.00247803i	−0.999999	−	0.00123902i	$-0.999606\pi$
$919$		−	5.89483e47i		−	0.00247803i	0.999999	−	0.00123902i	$-0.000394391\pi$
$920$	2.01033e50	+	2.56242e50i	0.829609	+	1.05744i
$921$	1.54635e49			0.0626462
$922$	−3.49684e49	−	3.78879e49i	−0.139075	−	0.150687i
$923$		−	6.76442e50i		−	2.64120i
$924$	−1.85609e49	−	1.48996e48i	−0.0711502	−	0.00571152i
$925$	5.35114e49			0.201390
$926$	−1.14117e50	+	1.05323e50i	−0.421661	+	0.389169i
$927$			1.68996e49i			0.0613084i
$928$	−3.40087e49	−	5.13305e49i	−0.121136	−	0.182835i
$929$	−7.83571e49			−0.274038			−0.137019	−	0.990568i	$-0.543752\pi$
$929$	−7.83571e49			−0.274038			−0.137019	+	0.990568i	$0.543752\pi$
$930$	−1.93722e49	−	2.09896e49i	−0.0665226	−	0.0720766i
$931$			2.94929e50i			0.994426i
$932$	1.98699e49	−	2.47526e50i	0.0657847	−	0.819502i
$933$	1.20069e48			0.00390341
$934$	4.90367e49	−	4.52580e49i	0.156540	−	0.144477i
$935$		−	1.81487e50i		−	0.568917i
$936$	−3.94409e50	+	3.09431e50i	−1.21411	+	0.952521i
$937$	−4.16173e50			−1.25806			−0.629029	−	0.777382i	$-0.716547\pi$
$937$	−4.16173e50			−1.25806			−0.629029	+	0.777382i	$0.716547\pi$
$938$	−3.07247e50	−	3.32899e50i	−0.912094	−	0.988245i
$939$			1.49735e49i			0.0436526i
$940$	4.03750e50	+	3.24106e49i	1.15595	+	0.0927927i
$941$	1.94047e50			0.545610			0.272805	−	0.962069i	$-0.412049\pi$
$941$	1.94047e50			0.545610			0.272805	+	0.962069i	$0.412049\pi$
$942$	4.20188e48	−	3.87810e48i	0.0116032	−	0.0107091i
$943$		−	5.64975e50i		−	1.53225i
$944$	9.27066e49	−	5.73717e50i	0.246937	−	1.52818i
$945$	8.08023e49			0.211389
$946$	3.64868e48	+	3.95331e48i	0.00937533	+	0.0101581i
$947$			3.81706e49i			0.0963338i	0.998839	+	0.0481669i	$0.0153379\pi$
$947$			3.81706e49i			0.0963338i	−0.998839	+	0.0481669i	$0.984662\pi$
$948$	−2.91973e48	+	3.63720e49i	−0.00723770	+	0.0901623i
$949$	7.05770e50			1.71845
$950$	−8.92805e49	+	8.24008e49i	−0.213528	+	0.197074i
$951$			1.67535e49i			0.0393583i
$952$	−2.46630e50	−	3.14361e50i	−0.569138	−	0.725439i
$953$	−8.22701e50			−1.86493			−0.932465	−	0.361260i	$-0.882347\pi$
$953$	−8.22701e50			−1.86493			−0.932465	+	0.361260i	$0.882347\pi$
$954$	1.33702e50	+	1.44865e50i	0.297725	+	0.322582i
$955$			1.84579e50i			0.403762i
$956$	1.92536e50	+	1.54556e49i	0.413740	+	0.0332125i
$957$	−5.35472e48			−0.0113040
$958$	2.49348e50	−	2.30134e50i	0.517121	−	0.477273i
$959$			1.72143e50i			0.350729i
$960$	−3.71178e49	−	9.09542e48i	−0.0742970	−	0.0182059i
$961$	−3.27517e50			−0.644074
$962$	4.08593e50	+	4.42707e50i	0.789432	+	0.855343i
$963$			1.23370e50i			0.234186i
$964$	−5.85985e49	+	7.29981e50i	−0.109289	+	1.36145i
$965$	−1.47001e50			−0.269374
$966$	4.58225e49	−	4.22915e49i	0.0825025	−	0.0761451i
$967$			8.12088e50i			1.43666i	0.695704	+	0.718328i	$0.255092\pi$
$967$			8.12088e50i			1.43666i	−0.695704	+	0.718328i	$0.744908\pi$
$968$	1.92023e50	−	1.50650e50i	0.333789	−	0.261872i
$969$	2.86819e49			0.0489895
$970$	−2.80188e50	−	3.03581e50i	−0.470251	−	0.509513i
$971$			4.02928e50i			0.664509i	0.943190	+	0.332255i	$0.107809\pi$
$971$			4.02928e50i			0.664509i	−0.943190	+	0.332255i	$0.892191\pi$
$972$	1.24569e50	+	9.99964e48i	0.201875	+	0.0162053i
$973$	1.07816e51			1.71698
$974$	4.89940e50	−	4.52186e50i	0.766726	−	0.707644i
$975$			1.83675e49i			0.0282470i
$976$	3.36331e50	+	5.43475e49i	0.508300	+	0.0821359i
$977$	−8.92528e50			−1.32561			−0.662803	−	0.748794i	$-0.730633\pi$
$977$	−8.92528e50			−1.32561			−0.662803	+	0.748794i	$0.730633\pi$
$978$	−2.71964e49	−	2.94670e49i	−0.0396963	−	0.0430106i
$979$			6.71949e50i			0.963897i
$980$	5.86758e49	−	7.30944e50i	0.0827210	−	1.03048i
$981$	−9.71129e50			−1.34556
$982$	−9.19663e49	+	8.48796e49i	−0.125237	+	0.115587i
$983$			3.52439e50i			0.471709i	0.971788	+	0.235855i	$0.0757889\pi$
$983$			3.52439e50i			0.471709i	−0.971788	+	0.235855i	$0.924211\pi$
$984$	4.09196e49	+	5.21572e49i	0.0538288	+	0.0686116i
$985$	−1.93553e50			−0.250256
$986$	−7.79293e49	−	8.44356e49i	−0.0990360	−	0.107305i
$987$		−	7.75498e49i		−	0.0968699i
$988$	−1.36342e51	−	1.09448e50i	−1.67403	−	0.134381i
$989$	−1.80154e49			−0.0217424
$990$	5.26873e50	−	4.86273e50i	0.625039	−	0.576875i
$991$		−	9.55321e50i		−	1.11403i	−0.830502	−	0.557015i	$-0.811946\pi$
$991$		−	9.55321e50i		−	1.11403i	0.830502	−	0.557015i	$-0.188054\pi$
$992$	−9.32469e50	+	6.17801e50i	−1.06890	+	0.708190i
$993$	−8.39933e49			−0.0946471
$994$	1.44460e51	+	1.56521e51i	1.60022	+	1.73382i
$995$		−	1.07709e51i		−	1.17289i
$996$	−7.22336e47	+	8.99837e48i	−0.000773269	+	0.00963286i
$997$	6.07599e50			0.639439			0.319719	−	0.947512i	$-0.396411\pi$
$997$	6.07599e50			0.639439			0.319719	+	0.947512i	$0.396411\pi$
$998$	7.54055e49	−	6.95950e49i	0.0780161	−	0.0720044i
$999$		−	1.00044e50i		−	0.101761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.35.b.a.3.3	✓	16
4.3	odd	2	inner	4.35.b.a.3.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.35.b.a.3.3	✓	16	1.1	even	1	trivial
4.35.b.a.3.4	yes	16	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 35 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-88896.6 - 96318.6i) q^{2} -8.77192e6i q^{3} +(-1.37468e9 + 1.71248e10i) q^{4} +8.59192e11 q^{5} +(-8.44899e11 + 7.79793e11i) q^{6} +3.22173e14i q^{7} +(1.77164e15 - 1.38993e15i) q^{8} +1.66002e16 q^{9} +O(q^{10})\)	\(q+(-88896.6 - 96318.6i) q^{2} -8.77192e6i q^{3} +(-1.37468e9 + 1.71248e10i) q^{4} +8.59192e11 q^{5} +(-8.44899e11 + 7.79793e11i) q^{6} +3.22173e14i q^{7} +(1.77164e15 - 1.38993e15i) q^{8} +1.66002e16 q^{9} +(-7.63792e16 - 8.27562e16i) q^{10} +3.83523e17i q^{11} +(1.50217e17 + 1.20585e16i) q^{12} -1.34109e19 q^{13} +(3.10313e19 - 2.86401e19i) q^{14} -7.53676e18i q^{15} +(-2.91368e20 - 4.70820e19i) q^{16} -5.50763e20 q^{17} +(-1.47570e21 - 1.59891e21i) q^{18} -5.93674e21i q^{19} +(-1.18111e21 + 1.47135e22i) q^{20} +2.82608e21 q^{21} +(3.69404e22 - 3.40938e22i) q^{22} +1.68339e23i q^{23} +(-1.21923e22 - 1.55407e22i) q^{24} +1.56134e23 q^{25} +(1.19218e24 + 1.29172e24i) q^{26} -2.91907e23i q^{27} +(-5.51714e24 - 4.42883e23i) q^{28} -1.59166e24 q^{29} +(-7.25930e23 + 6.69992e23i) q^{30} +2.89141e25i q^{31} +(2.13668e25 + 3.22496e25i) q^{32} +3.36423e24 q^{33} +(4.89609e25 + 5.30487e25i) q^{34} +2.76809e26i q^{35} +(-2.28199e25 + 2.84275e26i) q^{36} +3.42727e26 q^{37} +(-5.71819e26 + 5.27756e26i) q^{38} +1.17639e26i q^{39} +(1.52218e27 - 1.19421e27i) q^{40} -3.35617e27 q^{41} +(-2.51228e26 - 2.72204e26i) q^{42} +1.07019e26i q^{43} +(-6.56774e27 - 5.27219e26i) q^{44} +1.42628e28 q^{45} +(1.62142e28 - 1.49647e28i) q^{46} -2.74408e28i q^{47} +(-4.13000e26 + 2.55586e27i) q^{48} -4.96785e28 q^{49} +(-1.38798e28 - 1.50386e28i) q^{50} +4.83125e27i q^{51} +(1.84356e28 - 2.29659e29i) q^{52} -9.06021e28 q^{53} +(-2.81161e28 + 2.59495e28i) q^{54} +3.29520e29i q^{55} +(4.47797e29 + 5.70774e29i) q^{56} -5.20766e28 q^{57} +(1.41493e29 + 1.53307e29i) q^{58} +1.96904e30i q^{59} +(1.29065e29 + 1.03606e28i) q^{60} -1.15432e30 q^{61} +(2.78496e30 - 2.57036e30i) q^{62} +5.34815e30i q^{63} +(1.20681e30 - 4.92490e30i) q^{64} -1.15225e31 q^{65} +(-2.99068e29 - 3.24038e29i) q^{66} -1.07279e31i q^{67} +(7.57120e29 - 9.43170e30i) q^{68} +1.47665e30 q^{69} +(2.66618e31 - 2.46073e31i) q^{70} +5.04398e31i q^{71} +(2.94096e31 - 2.30731e31i) q^{72} -5.26267e31 q^{73} +(-3.04673e31 - 3.30110e31i) q^{74} -1.36960e30i q^{75} +(1.01665e32 + 8.16109e30i) q^{76} -1.23561e32 q^{77} +(1.13308e31 - 1.04577e31i) q^{78} +2.42129e32i q^{79} +(-2.50341e32 - 4.04525e31i) q^{80} +2.74285e32 q^{81} +(2.98352e32 + 3.23262e32i) q^{82} +5.99024e31i q^{83} +(-3.88494e30 + 4.83959e31i) q^{84} -4.73211e32 q^{85} +(1.03079e31 - 9.51359e30i) q^{86} +1.39619e31i q^{87} +(5.33069e32 + 6.79464e32i) q^{88} +1.75205e33 q^{89} +(-1.26791e33 - 1.37377e33i) q^{90} -4.32063e33i q^{91} +(-2.88277e33 - 2.31411e32i) q^{92} +2.53632e32 q^{93} +(-2.64306e33 + 2.43939e33i) q^{94} -5.10080e33i q^{95} +(2.82891e32 - 1.87428e32i) q^{96} +3.66838e33 q^{97} +(4.41625e33 + 4.78497e33i) q^{98} +6.36657e33i 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