LMFDB - Embedded newform 4.35.b.a.3.11

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			3.11
Root			$0.500000 - 190511. i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.35.b.a.3.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(49362.6 - 121422. i) q^{2} +9.14451e6i q^{3} +(-1.23065e10 - 1.19874e10i) q^{4} -6.20904e11 q^{5} +(1.11034e12 + 4.51397e11i) q^{6} +3.03953e14i q^{7} +(-2.06301e15 + 9.02552e14i) q^{8} +1.65936e16 q^{9} +O(q^{10})$	\(q+(49362.6 - 121422. i) q^{2} +9.14451e6i q^{3} +(-1.23065e10 - 1.19874e10i) q^{4} -6.20904e11 q^{5} +(1.11034e12 + 4.51397e11i) q^{6} +3.03953e14i q^{7} +(-2.06301e15 + 9.02552e14i) q^{8} +1.65936e16 q^{9} +(-3.06494e16 + 7.53911e16i) q^{10} -4.34141e17i q^{11} +(1.09619e17 - 1.12537e17i) q^{12} -1.62713e18 q^{13} +(3.69064e19 + 1.50039e19i) q^{14} -5.67786e18i q^{15} +(7.75384e18 + 2.95046e20i) q^{16} +1.14730e21 q^{17} +(8.19101e20 - 2.01482e21i) q^{18} +4.29240e21i q^{19} +(7.64118e21 + 7.44301e21i) q^{20} -2.77950e21 q^{21} +(-5.27141e22 - 2.14303e22i) q^{22} -1.36588e23i q^{23} +(-8.25339e21 - 1.88652e22i) q^{24} -1.96555e23 q^{25} +(-8.03194e22 + 1.97569e23i) q^{26} +3.04245e23i q^{27} +(3.64359e24 - 3.74061e24i) q^{28} +1.10326e25 q^{29} +(-6.89415e23 - 2.80274e23i) q^{30} -1.99725e25i q^{31} +(3.62077e25 + 1.36228e25i) q^{32} +3.97001e24 q^{33} +(5.66336e25 - 1.39307e26i) q^{34} -1.88725e26i q^{35} +(-2.04209e26 - 1.98913e26i) q^{36} +5.08323e26 q^{37} +(5.21190e26 + 2.11884e26i) q^{38} -1.48793e25i q^{39} +(1.28093e27 - 5.60398e26i) q^{40} +5.95843e26 q^{41} +(-1.37203e26 + 3.37491e26i) q^{42} -2.03855e26i q^{43} +(-5.20421e27 + 5.34277e27i) q^{44} -1.03030e28 q^{45} +(-1.65848e28 - 6.74235e27i) q^{46} +3.56118e28i q^{47} +(-2.69805e27 + 7.09051e25i) q^{48} -3.82703e28 q^{49} +(-9.70246e27 + 2.38660e28i) q^{50} +1.04915e28i q^{51} +(2.00243e28 + 1.95050e28i) q^{52} +2.36155e29 q^{53} +(3.69419e28 + 1.50183e28i) q^{54} +2.69560e29i q^{55} +(-2.74333e29 - 6.27057e29i) q^{56} -3.92519e28 q^{57} +(5.44600e29 - 1.33960e30i) q^{58} -3.03266e29i q^{59} +(-6.80626e28 + 6.98748e28i) q^{60} +2.73318e30 q^{61} +(-2.42509e30 - 9.85893e29i) q^{62} +5.04366e30i q^{63} +(3.44140e30 - 3.72394e30i) q^{64} +1.01029e30 q^{65} +(1.95970e29 - 4.82044e29i) q^{66} +1.85805e31i q^{67} +(-1.41193e31 - 1.37531e31i) q^{68} +1.24903e30 q^{69} +(-2.29153e31 - 9.31598e30i) q^{70} +5.00172e31i q^{71} +(-3.42326e31 + 1.49765e31i) q^{72} -1.57987e31 q^{73} +(2.50922e31 - 6.17214e31i) q^{74} -1.79740e30i q^{75} +(5.14546e31 - 5.28246e31i) q^{76} +1.31958e32 q^{77} +(-1.80667e30 - 7.34481e29i) q^{78} +2.44172e32i q^{79} +(-4.81439e30 - 1.83195e32i) q^{80} +2.73952e32 q^{81} +(2.94124e31 - 7.23482e31i) q^{82} -6.99260e32i q^{83} +(3.42060e31 + 3.33189e31i) q^{84} -7.12362e32 q^{85} +(-2.47524e31 - 1.00628e31i) q^{86} +1.00888e32i q^{87} +(3.91835e32 + 8.95636e32i) q^{88} -3.74683e32 q^{89} +(-5.08583e32 + 1.25101e33i) q^{90} -4.94571e32i q^{91} +(-1.63733e33 + 1.68093e33i) q^{92} +1.82638e32 q^{93} +(4.32404e33 + 1.75789e33i) q^{94} -2.66517e33i q^{95} +(-1.24573e32 + 3.31102e32i) q^{96} -1.01929e34 q^{97} +(-1.88912e33 + 4.64684e33i) q^{98} -7.20394e33i 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 $

$2$	49362.6	−	121422.i	0.376607	−	0.926373i
$2$	49362.6	−	121422.i	0.376607	−	0.926373i
$3$			9.14451e6i			0.0708107i	0.999373	+	0.0354054i	$0.0112722\pi$
$3$			9.14451e6i			0.0708107i	−0.999373	+	0.0354054i	$0.988728\pi$
$4$	−1.23065e10	−	1.19874e10i	−0.716335	−	0.697757i
$5$	−6.20904e11			−0.813831			−0.406916	−	0.913466i	$-0.633396\pi$
$5$	−6.20904e11			−0.813831			−0.406916	+	0.913466i	$0.633396\pi$
$6$	1.11034e12	+	4.51397e11i	0.0655972	+	0.0266678i
$7$			3.03953e14i			1.30659i	0.757103	+	0.653295i	$0.226614\pi$
$7$			3.03953e14i			1.30659i	−0.757103	+	0.653295i	$0.773386\pi$
$8$	−2.06301e15	+	9.02552e14i	−0.916160	+	0.400814i
$9$	1.65936e16			0.994986
$10$	−3.06494e16	+	7.53911e16i	−0.306494	+	0.753911i
$11$		−	4.34141e17i		−	0.858925i	−0.903085	−	0.429462i	$-0.858703\pi$
$11$		−	4.34141e17i		−	0.858925i	0.903085	−	0.429462i	$-0.141297\pi$
$12$	1.09619e17	−	1.12537e17i	0.0494087	−	0.0507242i
$13$	−1.62713e18			−0.188098			−0.0940492	−	0.995568i	$-0.529981\pi$
$13$	−1.62713e18			−0.188098			−0.0940492	+	0.995568i	$0.529981\pi$
$14$	3.69064e19	+	1.50039e19i	1.21039	+	0.492071i
$15$		−	5.67786e18i		−	0.0576280i
$16$	7.75384e18	+	2.95046e20i	0.0262710	+	0.999655i
$17$	1.14730e21			1.38690			0.693449	−	0.720506i	$-0.256090\pi$
$17$	1.14730e21			1.38690			0.693449	+	0.720506i	$0.256090\pi$
$18$	8.19101e20	−	2.01482e21i	0.374718	−	0.921728i
$19$			4.29240e21i			0.783230i	0.920129	+	0.391615i	$0.128083\pi$
$19$			4.29240e21i			0.783230i	−0.920129	+	0.391615i	$0.871917\pi$
$20$	7.64118e21	+	7.44301e21i	0.582976	+	0.567856i
$21$	−2.77950e21			−0.0925206
$22$	−5.27141e22	−	2.14303e22i	−0.795685	−	0.323477i
$23$		−	1.36588e23i		−	0.968367i	−0.874966	−	0.484183i	$-0.839117\pi$
$23$		−	1.36588e23i		−	0.968367i	0.874966	−	0.484183i	$-0.160883\pi$
$24$	−8.25339e21	−	1.88652e22i	−0.0283819	−	0.0648739i
$25$	−1.96555e23			−0.337679
$26$	−8.03194e22	+	1.97569e23i	−0.0708391	+	0.174249i
$27$			3.04245e23i			0.141266i
$28$	3.64359e24	−	3.74061e24i	0.911682	−	0.935956i
$29$	1.10326e25			1.52024			0.760122	−	0.649780i	$-0.225139\pi$
$29$	1.10326e25			1.52024			0.760122	+	0.649780i	$0.225139\pi$
$30$	−6.89415e23	−	2.80274e23i	−0.0533850	−	0.0217031i
$31$		−	1.99725e25i		−	0.885692i	−0.896598	−	0.442846i	$-0.853969\pi$
$31$		−	1.99725e25i		−	0.885692i	0.896598	−	0.442846i	$-0.146031\pi$
$32$	3.62077e25	+	1.36228e25i	0.935947	+	0.352140i
$33$	3.97001e24			0.0608211
$34$	5.66336e25	−	1.39307e26i	0.522315	−	1.28479i
$35$		−	1.88725e26i		−	1.06334i
$36$	−2.04209e26	−	1.98913e26i	−0.712743	−	0.694258i
$37$	5.08323e26			1.11355			0.556776	−	0.830662i	$-0.312038\pi$
$37$	5.08323e26			1.11355			0.556776	+	0.830662i	$0.312038\pi$
$38$	5.21190e26	+	2.11884e26i	0.725563	+	0.294970i
$39$		−	1.48793e25i		−	0.0133194i
$40$	1.28093e27	−	5.60398e26i	0.745599	−	0.326195i
$41$	5.95843e26			0.227933			0.113966	−	0.993485i	$-0.463644\pi$
$41$	5.95843e26			0.227933			0.113966	+	0.993485i	$0.463644\pi$
$42$	−1.37203e26	+	3.37491e26i	−0.0348439	+	0.0857086i
$43$		−	2.03855e26i		−	0.0347022i	−0.999849	−	0.0173511i	$-0.994477\pi$
$43$		−	2.03855e26i		−	0.0347022i	0.999849	−	0.0173511i	$-0.00552331\pi$
$44$	−5.20421e27	+	5.34277e27i	−0.599320	+	0.615278i
$45$	−1.03030e28			−0.809751
$46$	−1.65848e28	−	6.74235e27i	−0.897069	−	0.364694i
$47$			3.56118e28i			1.33638i	0.743990	+	0.668191i	$0.232931\pi$
$47$			3.56118e28i			1.33638i	−0.743990	+	0.668191i	$0.767069\pi$
$48$	−2.69805e27	+	7.09051e25i	−0.0707863	+	0.00186027i
$49$	−3.82703e28			−0.707177
$50$	−9.70246e27	+	2.38660e28i	−0.127172	+	0.312817i
$51$			1.04915e28i			0.0982073i
$52$	2.00243e28	+	1.95050e28i	0.134741	+	0.131247i
$53$	2.36155e29			1.14949			0.574747	−	0.818331i	$-0.305100\pi$
$53$	2.36155e29			1.14949			0.574747	+	0.818331i	$0.305100\pi$
$54$	3.69419e28	+	1.50183e28i	0.130865	+	0.0532019i
$55$			2.69560e29i			0.699020i
$56$	−2.74333e29	−	6.27057e29i	−0.523699	−	1.19705i
$57$	−3.92519e28			−0.0554611
$58$	5.44600e29	−	1.33960e30i	0.572534	−	1.40831i
$59$		−	3.03266e29i		−	0.238418i	−0.992869	−	0.119209i	$-0.961964\pi$
$59$		−	3.03266e29i		−	0.238418i	0.992869	−	0.119209i	$-0.0380359\pi$
$60$	−6.80626e28	+	6.98748e28i	−0.0402103	+	0.0412809i
$61$	2.73318e30			1.21916			0.609580	−	0.792724i	$-0.291338\pi$
$61$	2.73318e30			1.21916			0.609580	+	0.792724i	$0.291338\pi$
$62$	−2.42509e30	−	9.85893e29i	−0.820482	−	0.333558i
$63$			5.04366e30i			1.30004i
$64$	3.44140e30	−	3.72394e30i	0.678697	−	0.734418i
$65$	1.01029e30			0.153080
$66$	1.95970e29	−	4.82044e29i	0.0229056	−	0.0563430i
$67$			1.85805e31i			1.68185i	0.541154	+	0.840923i	$0.317987\pi$
$67$			1.85805e31i			1.68185i	−0.541154	+	0.840923i	$0.682013\pi$
$68$	−1.41193e31	−	1.37531e31i	−0.993483	−	0.967717i
$69$	1.24903e30			0.0685708
$70$	−2.29153e31	−	9.31598e30i	−0.985053	−	0.400462i
$71$			5.00172e31i			1.68938i	0.535255	+	0.844690i	$0.320215\pi$
$71$			5.00172e31i			1.68938i	−0.535255	+	0.844690i	$0.679785\pi$
$72$	−3.42326e31	+	1.49765e31i	−0.911566	+	0.398804i
$73$	−1.57987e31			−0.332761			−0.166381	−	0.986062i	$-0.553208\pi$
$73$	−1.57987e31			−0.332761			−0.166381	+	0.986062i	$0.553208\pi$
$74$	2.50922e31	−	6.17214e31i	0.419371	−	1.03157i
$75$		−	1.79740e30i		−	0.0239113i
$76$	5.14546e31	−	5.28246e31i	0.546504	−	0.561055i
$77$	1.31958e32			1.12226
$78$	−1.80667e30	−	7.34481e29i	−0.0123387	−	0.00501617i
$79$			2.44172e32i			1.34287i	0.741061	+	0.671437i	$0.234323\pi$
$79$			2.44172e32i			1.34287i	−0.741061	+	0.671437i	$0.765677\pi$
$80$	−4.81439e30	−	1.83195e32i	−0.0213802	−	0.813550i
$81$	2.73952e32			0.984983
$82$	2.94124e31	−	7.23482e31i	0.0858409	−	0.211151i
$83$		−	6.99260e32i		−	1.66078i	−0.557186	−	0.830388i	$-0.688119\pi$
$83$		−	6.99260e32i		−	1.66078i	0.557186	−	0.830388i	$-0.311881\pi$
$84$	3.42060e31	+	3.33189e31i	0.0662757	+	0.0645569i
$85$	−7.12362e32			−1.12870
$86$	−2.47524e31	−	1.00628e31i	−0.0321472	−	0.0130691i
$87$			1.00888e32i			0.107650i
$88$	3.91835e32	+	8.95636e32i	0.344269	+	0.786912i
$89$	−3.74683e32			−0.271665			−0.135833	−	0.990732i	$-0.543371\pi$
$89$	−3.74683e32			−0.271665			−0.135833	+	0.990732i	$0.543371\pi$
$90$	−5.08583e32	+	1.25101e33i	−0.304957	+	0.750131i
$91$		−	4.94571e32i		−	0.245768i
$92$	−1.63733e33	+	1.68093e33i	−0.675685	+	0.693675i
$93$	1.82638e32			0.0627165
$94$	4.32404e33	+	1.75789e33i	1.23799	+	0.503290i
$95$		−	2.66517e33i		−	0.637417i
$96$	−1.24573e32	+	3.31102e32i	−0.0249353	+	0.0662751i
$97$	−1.01929e34			−1.71071			−0.855356	−	0.518040i	$-0.826662\pi$
$97$	−1.01929e34			−1.71071			−0.855356	+	0.518040i	$0.826662\pi$
$98$	−1.88912e33	+	4.64684e33i	−0.266328	+	0.655110i
$99$		−	7.20394e33i		−	0.854618i
$100$	2.41891e33	+	2.35618e33i	0.241891	+	0.235618i
$101$	1.20668e34			1.01889			0.509445	−	0.860503i	$-0.329851\pi$
$101$	1.20668e34			1.01889			0.509445	+	0.860503i	$0.329851\pi$
$102$	1.27389e33	+	5.17886e32i	0.0909766	+	0.0369855i
$103$		−	2.46275e34i		−	1.49000i	−0.667062	−	0.745002i	$-0.732448\pi$
$103$		−	2.46275e34i		−	1.49000i	0.667062	−	0.745002i	$-0.267552\pi$
$104$	3.35678e33	−	1.46857e33i	0.172328	−	0.0753924i
$105$	1.72580e33			0.0752961
$106$	1.16572e34	−	2.86743e34i	0.432907	−	1.06486i
$107$			4.54571e34i			1.43905i	0.694464	+	0.719527i	$0.255641\pi$
$107$			4.54571e34i			1.43905i	−0.694464	+	0.719527i	$0.744359\pi$
$108$	3.64709e33	−	3.74420e33i	0.0985696	−	0.101194i
$109$	3.80748e34			0.879806			0.439903	−	0.898045i	$-0.355013\pi$
$109$	3.80748e34			0.879806			0.439903	+	0.898045i	$0.355013\pi$
$110$	3.27304e34	+	1.33062e34i	0.647553	+	0.263256i
$111$			4.64837e33i			0.0788515i
$112$	−8.96800e34	+	2.35680e33i	−1.30614	+	0.0343255i
$113$	−5.92069e34			−0.741377			−0.370688	−	0.928757i	$-0.620878\pi$
$113$	−5.92069e34			−0.741377			−0.370688	+	0.928757i	$0.620878\pi$
$114$	−1.93758e33	+	4.76603e33i	−0.0208870	+	0.0513777i
$115$			8.48082e34i			0.788087i
$116$	−1.35774e35	−	1.32252e35i	−1.08900	−	1.06076i
$117$	−2.69999e34			−0.187155
$118$	−3.68230e34	−	1.49700e34i	−0.220864	−	0.0897899i
$119$			3.48724e35i			1.81211i
$120$	5.12456e33	+	1.17135e34i	0.0230981	+	0.0527964i
$121$	6.69984e34			0.262249
$122$	1.34917e35	−	3.31867e35i	0.459144	−	1.12940i
$123$			5.44869e33i			0.0161401i
$124$	−2.39417e35	+	2.45792e35i	−0.617998	+	0.634452i
$125$	4.83455e35			1.08864
$126$	6.12409e35	+	2.48968e35i	1.20432	+	0.489603i
$127$		−	4.67222e35i		−	0.803267i	−0.915800	−	0.401634i	$-0.868443\pi$
$127$		−	4.67222e35i		−	0.803267i	0.915800	−	0.401634i	$-0.131557\pi$
$128$	−2.82291e35	−	6.01684e35i	−0.424744	−	0.905314i
$129$	1.86415e33			0.00245729
$130$	4.98706e34	−	1.22671e35i	0.0576511	−	0.141810i
$131$		−	7.98034e35i		−	0.809859i	−0.914348	−	0.404930i	$-0.867296\pi$
$131$		−	7.98034e35i		−	0.809859i	0.914348	−	0.404930i	$-0.132704\pi$
$132$	−4.88570e34	−	4.75899e34i	−0.0435683	−	0.0424383i
$133$	−1.30469e36			−1.02336
$134$	2.25608e36	+	9.17183e35i	1.55802	+	0.633395i
$135$		−	1.88907e35i		−	0.114967i
$136$	−2.36688e36	+	1.03550e36i	−1.27062	+	0.555887i
$137$	3.84307e35			0.182150			0.0910748	−	0.995844i	$-0.470970\pi$
$137$	3.84307e35			0.182150			0.0910748	+	0.995844i	$0.470970\pi$
$138$	6.16555e34	−	1.51659e35i	0.0258242	−	0.0635221i
$139$		−	2.30268e36i		−	0.853065i	−0.904472	−	0.426533i	$-0.859735\pi$
$139$		−	2.30268e36i		−	0.853065i	0.904472	−	0.426533i	$-0.140265\pi$
$140$	−2.26232e36	+	2.32256e36i	−0.741955	+	0.761710i
$141$	−3.25652e35			−0.0946301
$142$	6.07317e36	+	2.46898e36i	1.56500	+	0.636232i
$143$			7.06404e35i			0.161562i
$144$	1.28664e35	+	4.89586e36i	0.0261393	+	0.994642i
$145$	−6.85021e36			−1.23722
$146$	−7.79865e35	+	1.91830e36i	−0.125320	+	0.308261i
$147$		−	3.49963e35i		−	0.0500757i
$148$	−6.25570e36	−	6.09346e36i	−0.797677	−	0.776989i
$149$	6.22141e35			0.0707494			0.0353747	−	0.999374i	$-0.488738\pi$
$149$	6.22141e35			0.0707494			0.0353747	+	0.999374i	$0.488738\pi$
$150$	−2.18243e35	−	8.87242e34i	−0.0221508	−	0.00900515i
$151$		−	4.80007e36i		−	0.435151i	−0.976044	−	0.217575i	$-0.930185\pi$
$151$		−	4.80007e36i		−	0.435151i	0.976044	−	0.217575i	$-0.0698148\pi$
$152$	−3.87411e36	−	8.85526e36i	−0.313929	−	0.717563i
$153$	1.90378e37			1.37994
$154$	6.51380e36	−	1.60226e37i	0.422651	−	1.03963i
$155$			1.24010e37i			0.720804i
$156$	−1.78364e35	+	1.83113e35i	−0.00929369	+	0.00954114i
$157$	−1.02909e37			−0.481017			−0.240509	−	0.970647i	$-0.577314\pi$
$157$	−1.02909e37			−0.481017			−0.240509	+	0.970647i	$0.577314\pi$
$158$	2.96478e37	+	1.20530e37i	1.24400	+	0.505736i
$159$			2.15952e36i			0.0813966i
$160$	−2.24815e37	−	8.45842e36i	−0.761703	−	0.286582i
$161$	4.15164e37			1.26526
$162$	1.35230e37	−	3.32636e37i	0.370951	−	0.912462i
$163$			4.13537e37i			1.02170i	0.859669	+	0.510852i	$0.170670\pi$
$163$			4.13537e37i			1.02170i	−0.859669	+	0.510852i	$0.829330\pi$
$164$	−7.33277e36	−	7.14259e36i	−0.163276	−	0.159041i
$165$	−2.46499e36			−0.0494981
$166$	−8.49052e37	−	3.45173e37i	−1.53850	−	0.625459i
$167$			2.15925e37i			0.353284i	0.984275	+	0.176642i	$0.0565234\pi$
$167$			2.15925e37i			0.353284i	−0.984275	+	0.176642i	$0.943477\pi$
$168$	5.73413e36	−	2.50864e36i	0.0847636	−	0.0370835i
$169$	−7.21821e37			−0.964619
$170$	−3.51640e37	+	8.64961e37i	−0.425076	+	1.04560i
$171$			7.12262e37i			0.779302i
$172$	−2.44368e36	+	2.50875e36i	−0.0242137	+	0.0248584i
$173$	−4.35115e37			−0.390679			−0.195339	−	0.980736i	$-0.562581\pi$
$173$	−4.35115e37			−0.390679			−0.195339	+	0.980736i	$0.562581\pi$
$174$	1.22500e37	+	4.98010e36i	0.0997237	+	0.0405416i
$175$		−	5.97434e37i		−	0.441208i
$176$	1.28092e38	−	3.36626e36i	0.858628	−	0.0225648i
$177$	2.77322e36			0.0168826
$178$	−1.84953e37	+	4.54947e37i	−0.102311	+	0.251664i
$179$		−	3.09126e38i		−	1.55466i	−0.629096	−	0.777328i	$-0.716575\pi$
$179$		−	3.09126e38i		−	1.55466i	0.629096	−	0.777328i	$-0.283425\pi$
$180$	1.26794e38	+	1.23506e38i	0.580052	+	0.565009i
$181$	2.81380e38			1.17154			0.585770	−	0.810477i	$-0.300792\pi$
$181$	2.81380e38			1.17154			0.585770	+	0.810477i	$0.300792\pi$
$182$	−6.00515e37	−	2.44133e37i	−0.227673	−	0.0925577i
$183$			2.49936e37i			0.0863297i
$184$	1.23278e38	+	2.81783e38i	0.388135	+	0.887179i
$185$	−3.15620e38			−0.906244
$186$	9.01551e36	−	2.21762e37i	0.0236195	−	0.0580989i
$187$		−	4.98089e38i		−	1.19124i
$188$	4.26892e38	−	4.38258e38i	0.932469	−	0.957296i
$189$	−9.24760e37			−0.184577
$190$	−3.23609e38	−	1.31560e38i	−0.590486	−	0.240055i
$191$		−	2.50270e38i		−	0.417677i	−0.977950	−	0.208839i	$-0.933032\pi$
$191$		−	2.50270e38i		−	0.417677i	0.977950	−	0.208839i	$-0.0669683\pi$
$192$	3.40536e37	+	3.14699e37i	0.0520047	+	0.0480590i
$193$	−1.33712e38			−0.186937			−0.0934687	−	0.995622i	$-0.529796\pi$
$193$	−1.33712e38			−0.186937			−0.0934687	+	0.995622i	$0.529796\pi$
$194$	−5.03147e38	+	1.23763e39i	−0.644266	+	1.58476i
$195$			9.23862e36i			0.0108397i
$196$	4.70975e38	+	4.58760e38i	0.506576	+	0.493438i
$197$	2.67616e38			0.263989			0.131995	−	0.991250i	$-0.457862\pi$
$197$	2.67616e38			0.263989			0.131995	+	0.991250i	$0.457862\pi$
$198$	−8.74714e38	−	3.55605e38i	−0.791695	−	0.321855i
$199$			1.34085e39i			1.11398i	0.830518	+	0.556991i	$0.188044\pi$
$199$			1.34085e39i			1.11398i	−0.830518	+	0.556991i	$0.811956\pi$
$200$	4.05494e38	−	1.77401e38i	0.309368	−	0.135346i
$201$	−1.69910e38			−0.119093
$202$	5.95646e38	−	1.46516e39i	0.383721	−	0.943872i
$203$			3.35340e39i			1.98634i
$204$	1.25765e38	−	1.29114e38i	0.0685248	−	0.0703493i
$205$	−3.69961e38			−0.185499
$206$	−2.99031e39	−	1.21568e39i	−1.38030	−	0.561146i
$207$		−	2.26648e39i		−	0.963511i
$208$	−1.26165e37	−	4.80078e38i	−0.00494154	−	0.188034i
$209$	1.86351e39			0.672735
$210$	8.51900e37	−	2.09550e38i	0.0283570	−	0.0697523i
$211$			9.78808e38i			0.300536i	0.988645	+	0.150268i	$0.0480136\pi$
$211$			9.78808e38i			0.300536i	−0.988645	+	0.150268i	$0.951986\pi$
$212$	−2.90625e39	−	2.83088e39i	−0.823423	−	0.802068i
$213$	−4.57383e38			−0.119626
$214$	5.51947e39	+	2.24388e39i	1.33310	+	0.541957i
$215$			1.26574e38i			0.0282418i
$216$	−2.74597e38	−	6.27659e38i	−0.0566215	−	0.129423i
$217$	6.07069e39			1.15724
$218$	1.87947e39	−	4.62310e39i	0.331341	−	0.815029i
$219$		−	1.44471e38i		−	0.0235631i
$220$	3.23131e39	−	3.31735e39i	0.487746	−	0.500732i
$221$	−1.86680e39			−0.260873
$222$	5.64412e38	+	2.29456e38i	0.0730459	+	0.0296960i
$223$			1.69807e38i			0.0203598i	0.999948	+	0.0101799i	$0.00324042\pi$
$223$			1.69807e38i			0.0203598i	−0.999948	+	0.0101799i	$0.996760\pi$
$224$	−4.14067e39	+	1.10054e40i	−0.460103	+	1.22290i
$225$	−3.26154e39			−0.335986
$226$	−2.92261e39	+	7.18900e39i	−0.279207	+	0.686791i
$227$		−	8.49225e39i		−	0.752633i	−0.926491	−	0.376316i	$-0.877191\pi$
$227$		−	8.49225e39i		−	0.752633i	0.926491	−	0.376316i	$-0.122809\pi$
$228$	4.83055e38	+	4.70527e38i	0.0397287	+	0.0386983i
$229$	−3.70477e39			−0.282851			−0.141426	−	0.989949i	$-0.545169\pi$
$229$	−3.70477e39			−0.282851			−0.141426	+	0.989949i	$0.545169\pi$
$230$	1.02975e40	+	4.18635e39i	0.730063	+	0.296799i
$231$			1.20669e39i			0.0794682i
$232$	−2.27604e40	+	9.95753e39i	−1.39279	+	0.609334i
$233$	−3.15797e40			−1.79621			−0.898106	−	0.439779i	$-0.855057\pi$
$233$	−3.15797e40			−1.79621			−0.898106	+	0.439779i	$0.855057\pi$
$234$	−1.33278e39	+	3.27837e39i	−0.0704839	+	0.173376i
$235$		−	2.21115e40i		−	1.08759i
$236$	−3.63536e39	+	3.73215e39i	−0.166358	+	0.170787i
$237$	−2.23283e39			−0.0950899
$238$	4.23427e40	+	1.72139e40i	1.67869	+	0.682452i
$239$			3.46110e39i			0.127776i	0.997957	+	0.0638881i	$0.0203501\pi$
$239$			3.46110e39i			0.127776i	−0.997957	+	0.0638881i	$0.979650\pi$
$240$	1.67523e39	−	4.40252e37i	0.0576081	−	0.00151395i
$241$	4.22422e40			1.35350			0.676748	−	0.736214i	$-0.263389\pi$
$241$	4.22422e40			1.35350			0.676748	+	0.736214i	$0.263389\pi$
$242$	3.30721e39	−	8.13505e39i	0.0987646	−	0.242940i
$243$			7.57910e39i			0.211014i
$244$	−3.36360e40	−	3.27636e40i	−0.873327	−	0.850678i
$245$	2.37622e40			0.575523
$246$	6.61589e38	+	2.68962e38i	0.0149517	+	0.00607846i
$247$		−	6.98430e39i		−	0.147324i
$248$	1.80262e40	+	4.12034e40i	0.354997	+	0.811436i
$249$	6.39439e39			0.117601
$250$	2.38646e40	−	5.87019e40i	0.409991	−	1.00849i
$251$		−	4.84791e39i		−	0.0778219i	−0.999243	−	0.0389109i	$-0.987611\pi$
$251$		−	4.84791e39i		−	0.0778219i	0.999243	−	0.0389109i	$-0.0123889\pi$
$252$	6.04602e40	−	6.20700e40i	0.907111	−	0.931263i
$253$	−5.92985e40			−0.831754
$254$	−5.67308e40	−	2.30633e40i	−0.744125	−	0.302516i
$255$		−	6.51420e39i		−	0.0799241i
$256$	−8.69920e40	+	4.57548e39i	−0.998620	+	0.0525239i
$257$	8.50841e39			0.0914082			0.0457041	−	0.998955i	$-0.485447\pi$
$257$	8.50841e39			0.0914082			0.0457041	+	0.998955i	$0.485447\pi$
$258$	9.20194e37	−	2.26348e38i	0.000925432	−	0.00227637i
$259$			1.54506e41i			1.45496i
$260$	−1.24332e40	−	1.21107e40i	−0.109657	−	0.106813i
$261$	1.83071e41			1.51262
$262$	−9.68986e40	−	3.93930e40i	−0.750232	−	0.304998i
$263$			2.04018e41i			1.48054i	0.672309	+	0.740271i	$0.265303\pi$
$263$			2.04018e41i			1.48054i	−0.672309	+	0.740271i	$0.734697\pi$
$264$	−8.19015e39	+	3.58314e39i	−0.0557218	+	0.0243779i
$265$	−1.46629e41			−0.935495
$266$	−6.44027e40	+	1.58417e41i	−0.385404	+	0.948013i
$267$		−	3.42630e39i		−	0.0192368i
$268$	2.22732e41	−	2.28662e41i	1.17352	−	1.20477i
$269$	−7.27162e40			−0.359619			−0.179809	−	0.983701i	$-0.557548\pi$
$269$	−7.27162e40			−0.359619			−0.179809	+	0.983701i	$0.557548\pi$
$270$	−2.29374e40	−	9.32492e39i	−0.106502	−	0.0432973i
$271$		−	2.52650e41i		−	1.10165i	−0.834622	−	0.550823i	$-0.814314\pi$
$271$		−	2.52650e41i		−	1.10165i	0.834622	−	0.550823i	$-0.185686\pi$
$272$	8.89596e39	+	3.38506e41i	0.0364352	+	1.38642i
$273$	4.52261e39			0.0174030
$274$	1.89704e40	−	4.66631e40i	0.0685988	−	0.168739i
$275$			8.53325e40i			0.290041i
$276$	−1.53713e40	−	1.49726e40i	−0.0491196	−	0.0478457i
$277$	2.89946e40			0.0871286			0.0435643	−	0.999051i	$-0.486129\pi$
$277$	2.89946e40			0.0871286			0.0435643	+	0.999051i	$0.486129\pi$
$278$	−2.79595e41	−	1.13666e41i	−0.790257	−	0.321270i
$279$		−	3.31414e41i		−	0.881251i
$280$	1.70334e41	+	3.89342e41i	0.426203	+	0.974193i
$281$	−1.14056e41			−0.268604			−0.134302	−	0.990940i	$-0.542879\pi$
$281$	−1.14056e41			−0.268604			−0.134302	+	0.990940i	$0.542879\pi$
$282$	−1.60750e40	+	3.95412e40i	−0.0356383	+	0.0876628i
$283$		−	8.18564e41i		−	1.70877i	−0.519642	−	0.854384i	$-0.673935\pi$
$283$		−	8.18564e41i		−	1.70877i	0.519642	−	0.854384i	$-0.326065\pi$
$284$	5.99575e41	−	6.15539e41i	1.17878	−	1.21016i
$285$	2.43717e40			0.0451360
$286$	8.57727e40	+	3.48699e40i	0.149667	+	0.0608455i
$287$			1.81108e41i			0.297814i
$288$	6.00815e41	+	2.26050e41i	0.931254	+	0.350374i
$289$	6.31966e41			0.923486
$290$	−3.38144e41	+	8.31763e41i	−0.465946	+	1.14613i
$291$		−	9.32088e40i		−	0.121137i
$292$	1.94427e41	+	1.89385e41i	0.238369	+	0.232186i
$293$	−1.01502e42			−1.17415			−0.587076	−	0.809532i	$-0.699721\pi$
$293$	−1.01502e42			−1.17415			−0.587076	+	0.809532i	$0.699721\pi$
$294$	−4.24931e40	−	1.72751e40i	−0.0463888	−	0.0188589i
$295$			1.88299e41i			0.194032i
$296$	−1.04868e42	+	4.58788e41i	−1.02019	+	0.446327i
$297$	1.32085e41			0.121337
$298$	3.07105e40	−	7.55414e40i	0.0266447	−	0.0655403i
$299$			2.22247e41i			0.182148i
$300$	−2.15461e40	+	2.21197e40i	−0.0166843	+	0.0171285i
$301$	6.19622e40			0.0453416
$302$	−5.82833e41	−	2.36944e41i	−0.403112	−	0.163881i
$303$			1.10345e41i			0.0721483i
$304$	−1.26646e42	+	3.32826e40i	−0.782959	+	0.0205763i
$305$	−1.69704e42			−0.992191
$306$	9.39753e41	−	2.31159e42i	0.519696	−	1.27834i
$307$			2.39156e42i			1.25121i	0.780141	+	0.625604i	$0.215147\pi$
$307$			2.39156e42i			1.25121i	−0.780141	+	0.625604i	$0.784853\pi$
$308$	−1.62395e42	−	1.58183e42i	−0.803915	−	0.783066i
$309$	2.25206e41			0.105508
$310$	1.50575e42	+	6.12145e41i	0.667734	+	0.271460i
$311$			3.93969e42i			1.65400i	0.562203	+	0.826999i	$0.309954\pi$
$311$			3.93969e42i			1.65400i	−0.562203	+	0.826999i	$0.690046\pi$
$312$	1.34293e40	+	3.06961e40i	0.00533859	+	0.0122027i
$313$	4.98442e42			1.87655			0.938276	−	0.345887i	$-0.112422\pi$
$313$	4.98442e42			1.87655			0.938276	+	0.345887i	$0.112422\pi$
$314$	−5.07987e41	+	1.24954e42i	−0.181154	+	0.445602i
$315$		−	3.13163e42i		−	1.05801i
$316$	2.92698e42	−	3.00491e42i	0.937000	−	0.961948i
$317$	1.53460e42			0.465574			0.232787	−	0.972528i	$-0.425216\pi$
$317$	1.53460e42			0.465574			0.232787	+	0.972528i	$0.425216\pi$
$318$	2.62212e41	+	1.06600e41i	0.0754036	+	0.0306545i
$319$		−	4.78972e42i		−	1.30578i
$320$	−2.13678e42	+	2.31221e42i	−0.552345	+	0.597693i
$321$	−4.15683e41			−0.101900
$322$	2.04935e42	−	5.04098e42i	0.476505	−	1.17210i
$323$			4.92466e42i			1.08626i
$324$	−3.37140e42	−	3.28396e42i	−0.705577	−	0.687278i
$325$	3.19820e41			0.0635168
$326$	5.02123e42	+	2.04133e42i	0.946480	+	0.384781i
$327$			3.48175e41i			0.0622997i
$328$	−1.22923e42	+	5.37779e41i	−0.208823	+	0.0913585i
$329$	−1.08243e43			−1.74610
$330$	−1.21678e41	+	2.99303e41i	−0.0186413	+	0.0458537i
$331$			1.35229e41i			0.0196786i	0.999952	+	0.00983928i	$0.00313199\pi$
$331$			1.35229e41i			0.0196786i	−0.999952	+	0.00983928i	$0.996868\pi$
$332$	−8.38228e42	+	8.60547e42i	−1.15882	+	1.18967i
$333$	8.43490e42			1.10797
$334$	2.62180e42	+	1.06586e42i	0.327272	+	0.133049i
$335$		−	1.15367e43i		−	1.36874i
$336$	−2.15518e40	−	8.20080e41i	−0.00243061	−	0.0924887i
$337$	−5.44175e42			−0.583485			−0.291743	−	0.956497i	$-0.594235\pi$
$337$	−5.44175e42			−0.583485			−0.291743	+	0.956497i	$0.594235\pi$
$338$	−3.56310e42	+	8.76447e42i	−0.363282	+	0.893597i
$339$		−	5.41418e41i		−	0.0524974i
$340$	8.76671e42	+	8.53934e42i	0.808528	+	0.787559i
$341$	−8.67086e42			−0.760743
$342$	8.64840e42	+	3.51591e42i	0.721925	+	0.293491i
$343$			4.81664e42i			0.382599i
$344$	1.83990e41	+	4.20554e41i	0.0139091	+	0.0317928i
$345$	−7.75529e41			−0.0558050
$346$	−2.14784e42	+	5.28323e42i	−0.147132	+	0.361914i
$347$		−	6.28542e42i		−	0.409952i	−0.978767	−	0.204976i	$-0.934288\pi$
$347$		−	6.28542e42i		−	0.409952i	0.978767	−	0.204976i	$-0.0657116\pi$
$348$	1.20938e42	−	1.24158e42i	0.0751132	−	0.0771132i
$349$	−2.62369e42			−0.155196			−0.0775978	−	0.996985i	$-0.524725\pi$
$349$	−2.62369e42			−0.155196			−0.0775978	+	0.996985i	$0.524725\pi$
$350$	−7.25414e42	−	2.94909e42i	−0.408723	−	0.166162i
$351$		−	4.95046e41i		−	0.0265720i
$352$	5.91419e42	−	1.57192e43i	0.302462	−	0.803908i
$353$	1.89188e43			0.921986			0.460993	−	0.887404i	$-0.347493\pi$
$353$	1.89188e43			0.921986			0.460993	+	0.887404i	$0.347493\pi$
$354$	1.36893e41	−	3.36729e41i	0.00635809	−	0.0156396i
$355$		−	3.10559e43i		−	1.37487i
$356$	4.61106e42	+	4.49147e42i	0.194603	+	0.189556i
$357$	−3.18891e42			−0.128317
$358$	−3.75346e43	−	1.52593e43i	−1.44019	−	0.585494i
$359$			3.36230e43i			1.23035i	0.788389	+	0.615177i	$0.210916\pi$
$359$			3.36230e43i			1.23035i	−0.788389	+	0.615177i	$0.789084\pi$
$360$	2.12552e43	−	9.29900e42i	0.741861	−	0.324559i
$361$	1.16099e43			0.386551
$362$	1.38896e43	−	3.41656e43i	0.441210	−	1.08528i
$363$			6.12667e41i			0.0185700i
$364$	−5.92860e42	+	6.08645e42i	−0.171486	+	0.176052i
$365$	9.80948e42			0.270812
$366$	3.03476e42	+	1.23375e42i	0.0799735	+	0.0325123i
$367$			1.39483e43i			0.350911i	0.984487	+	0.175456i	$0.0561398\pi$
$367$			1.39483e43i			0.350911i	−0.984487	+	0.175456i	$0.943860\pi$
$368$	4.02998e43	−	1.05908e42i	0.968033	−	0.0254400i
$369$	9.88716e42			0.226790
$370$	−1.55798e43	+	3.83231e43i	−0.341298	+	0.839520i
$371$			7.17799e43i			1.50192i
$372$	−2.24765e42	−	2.18935e42i	−0.0449260	−	0.0437609i
$373$	−6.69798e41			−0.0127907			−0.00639534	−	0.999980i	$-0.502036\pi$
$373$	−6.69798e41			−0.0127907			−0.00639534	+	0.999980i	$0.502036\pi$
$374$	−6.04787e43	−	2.45870e43i	−1.10353	−	0.448629i
$375$			4.42096e42i			0.0770877i
$376$	−3.21415e43	−	7.34674e43i	−0.535640	−	1.22434i
$377$	−1.79515e43			−0.285956
$378$	−4.56485e42	+	1.12286e43i	−0.0695130	+	0.170987i
$379$			3.72526e43i			0.542364i	0.962528	+	0.271182i	$0.0874145\pi$
$379$			3.72526e43i			0.542364i	−0.962528	+	0.271182i	$0.912586\pi$
$380$	−3.19484e43	+	3.27990e43i	−0.444762	+	0.456604i
$381$	4.27252e42			0.0568799
$382$	−3.03881e43	−	1.23540e43i	−0.386925	−	0.157300i
$383$		−	1.10518e43i		−	0.134603i	−0.997733	−	0.0673016i	$-0.978561\pi$
$383$		−	1.10518e43i		−	0.134603i	0.997733	−	0.0673016i	$-0.0214390\pi$
$384$	5.50211e42	−	2.58141e42i	0.0641059	−	0.0300764i
$385$	−8.19334e43			−0.913332
$386$	−6.60037e42	+	1.62355e43i	−0.0704019	+	0.173174i
$387$		−	3.38268e42i		−	0.0345282i
$388$	1.25439e44	+	1.22186e44i	1.22544	+	1.19366i
$389$	−1.42396e43			−0.133155			−0.0665773	−	0.997781i	$-0.521208\pi$
$389$	−1.42396e43			−0.133155			−0.0665773	+	0.997781i	$0.521208\pi$
$390$	1.12177e42	+	4.56042e41i	0.0100416	+	0.00408232i
$391$		−	1.56707e44i		−	1.34303i
$392$	7.89519e43	−	3.45409e43i	0.647887	−	0.283446i
$393$	7.29763e42			0.0573467
$394$	1.32102e43	−	3.24944e43i	0.0994201	−	0.244553i
$395$		−	1.51607e44i		−	1.09287i
$396$	−8.63563e43	+	8.86556e43i	−0.596315	+	0.612192i
$397$	1.57466e44			1.04171			0.520856	−	0.853644i	$-0.325613\pi$
$397$	1.57466e44			1.04171			0.520856	+	0.853644i	$0.325613\pi$
$398$	1.62808e44	+	6.61879e43i	1.03196	+	0.419533i
$399$		−	1.19307e43i		−	0.0724649i
$400$	−1.52406e42	−	5.79927e43i	−0.00887117	−	0.337562i
$401$	1.81831e44			1.01441			0.507204	−	0.861826i	$-0.330679\pi$
$401$	1.81831e44			1.01441			0.507204	+	0.861826i	$0.330679\pi$
$402$	−8.38719e42	+	2.06307e43i	−0.0448511	+	0.110324i
$403$			3.24978e43i			0.166597i
$404$	−1.48500e44	−	1.44649e44i	−0.729866	−	0.710937i
$405$	−1.70098e44			−0.801610
$406$	4.07175e44	+	1.65533e44i	1.84009	+	0.748067i
$407$		−	2.20684e44i		−	0.956458i
$408$	−9.46910e42	−	2.16440e43i	−0.0393628	−	0.0899735i
$409$	−4.94587e44			−1.97218			−0.986090	−	0.166213i	$-0.946846\pi$
$409$	−4.94587e44			−1.97218			−0.986090	+	0.166213i	$0.946846\pi$
$410$	−1.82623e43	+	4.49213e43i	−0.0698600	+	0.171841i
$411$			3.51430e42i			0.0128981i
$412$	−2.95219e44	+	3.03079e44i	−1.03966	+	1.06734i
$413$	9.21785e43			0.311515
$414$	−2.75200e44	−	1.11880e44i	−0.892571	−	0.362865i
$415$			4.34173e44i			1.35159i
$416$	−5.89147e43	−	2.21660e43i	−0.176050	−	0.0662370i
$417$	2.10569e43			0.0604062
$418$	9.19875e43	−	2.26270e44i	0.253357	−	0.623204i
$419$		−	4.66286e44i		−	1.23314i	−0.787298	−	0.616572i	$-0.788521\pi$
$419$		−	4.66286e44i		−	1.23314i	0.787298	−	0.616572i	$-0.211479\pi$
$420$	−2.12386e43	−	2.06878e43i	−0.0539372	−	0.0525384i
$421$	4.26948e44			1.04131			0.520655	−	0.853767i	$-0.325688\pi$
$421$	4.26948e44			1.04131			0.520655	+	0.853767i	$0.325688\pi$
$422$	1.18848e44	+	4.83165e43i	0.278408	+	0.113184i
$423$			5.90926e44i			1.32968i
$424$	−4.87189e44	+	2.13142e44i	−1.05312	+	0.460733i
$425$	−2.25507e44			−0.468326
$426$	−2.25776e43	+	5.55362e43i	−0.0450521	+	0.110819i
$427$			8.30757e44i			1.59294i
$428$	5.44911e44	−	5.59419e44i	1.00411	−	1.03084i
$429$	−6.45972e42			−0.0114404
$430$	1.53689e43	+	6.24804e42i	0.0261624	+	0.0106360i
$431$			3.36518e44i			0.550674i	0.961348	+	0.275337i	$0.0887895\pi$
$431$			3.36518e44i			0.550674i	−0.961348	+	0.275337i	$0.911211\pi$
$432$	−8.97662e43	+	2.35906e42i	−0.141218	+	0.00371121i
$433$	4.59142e44			0.694469			0.347234	−	0.937778i	$-0.387121\pi$
$433$	4.59142e44			0.694469			0.347234	+	0.937778i	$0.387121\pi$
$434$	2.99665e44	−	7.37112e44i	0.435823	−	1.07203i
$435$		−	6.26418e43i		−	0.0876086i
$436$	−4.68569e44	−	4.56416e44i	−0.630235	−	0.613890i
$437$	5.86291e44			0.758454
$438$	−1.75419e43	−	7.13148e42i	−0.0218282	−	0.00887401i
$439$		−	1.46509e45i		−	1.75375i	−0.480719	−	0.876875i	$-0.659624\pi$
$439$		−	1.46509e45i		−	1.75375i	0.480719	−	0.876875i	$-0.340376\pi$
$440$	−2.43292e44	−	5.56104e44i	−0.280177	−	0.640414i
$441$	−6.35040e44			−0.703631
$442$	−9.21502e43	+	2.26670e44i	−0.0982467	+	0.241666i
$443$			2.86620e44i			0.294064i	0.989132	+	0.147032i	$0.0469721\pi$
$443$			2.86620e44i			0.294064i	−0.989132	+	0.147032i	$0.953028\pi$
$444$	5.57217e43	−	5.72053e43i	0.0550192	−	0.0564841i
$445$	2.32642e44			0.221090
$446$	2.06183e43	+	8.38213e42i	0.0188608	+	0.00766764i
$447$			5.68918e42i			0.00500981i
$448$	1.13190e45	+	1.04602e45i	0.959584	+	0.886779i
$449$	1.19675e44			0.0976826			0.0488413	−	0.998807i	$-0.484447\pi$
$449$	1.19675e44			0.0976826			0.0488413	+	0.998807i	$0.484447\pi$
$450$	−1.60998e44	+	3.96022e44i	−0.126534	+	0.311248i
$451$		−	2.58680e44i		−	0.195777i
$452$	7.28632e44	+	7.09735e44i	0.531074	+	0.517301i
$453$	4.38943e43			0.0308133
$454$	−1.03114e45	−	4.19199e44i	−0.697219	−	0.283447i
$455$			3.07081e44i			0.200013i
$456$	8.09770e43	−	3.54269e43i	0.0508112	−	0.0222295i
$457$	−2.01430e45			−1.21772			−0.608861	−	0.793277i	$-0.708373\pi$
$457$	−2.01430e45			−1.21772			−0.608861	+	0.793277i	$0.708373\pi$
$458$	−1.82877e44	+	4.49839e44i	−0.106524	+	0.262026i
$459$			3.49059e44i			0.195922i
$460$	1.01663e45	−	1.04369e45i	0.549893	−	0.564534i
$461$	1.76802e45			0.921663			0.460832	−	0.887488i	$-0.347551\pi$
$461$	1.76802e45			0.921663			0.460832	+	0.887488i	$0.347551\pi$
$462$	1.46519e44	+	5.95655e43i	0.0736172	+	0.0299283i
$463$		−	1.69842e45i		−	0.822563i	−0.911508	−	0.411282i	$-0.865081\pi$
$463$		−	1.69842e45i		−	0.822563i	0.911508	−	0.411282i	$-0.134919\pi$
$464$	8.55453e43	+	3.25514e45i	0.0399384	+	1.51972i
$465$	−1.13401e44			−0.0510407
$466$	−1.55886e45	+	3.83446e45i	−0.676465	+	1.66396i
$467$		−	1.55014e45i		−	0.648609i	−0.945953	−	0.324304i	$-0.894870\pi$
$467$		−	1.55014e45i		−	0.648609i	0.945953	−	0.324304i	$-0.105130\pi$
$468$	3.32275e44	+	3.23658e44i	0.134066	+	0.130589i
$469$	−5.64760e45			−2.19748
$470$	−2.68481e45	−	1.09148e45i	−1.00751	−	0.409593i
$471$		−	9.41056e43i		−	0.0340612i
$472$	2.73713e44	+	6.25640e44i	0.0955613	+	0.218429i
$473$	−8.85017e43			−0.0298066
$474$	−1.10218e44	+	2.71114e44i	−0.0358115	+	0.0880888i
$475$		−	8.43692e44i		−	0.264480i
$476$	4.18029e45	−	4.29159e45i	1.26441	−	1.29808i
$477$	3.91865e45			1.14373
$478$	4.20253e44	+	1.70849e44i	0.118369	+	0.0481214i
$479$			1.05670e45i			0.287242i	0.989633	+	0.143621i	$0.0458746\pi$
$479$			1.05670e45i			0.287242i	−0.989633	+	0.143621i	$0.954125\pi$
$480$	7.73481e43	−	2.05582e44i	0.0202931	−	0.0539368i
$481$	−8.27108e44			−0.209458
$482$	2.08519e45	−	5.12912e45i	0.509736	−	1.25384i
$483$			3.79647e44i			0.0895939i
$484$	−8.24518e44	−	8.03134e44i	−0.187858	−	0.182986i
$485$	6.32879e45			1.39223
$486$	9.20266e44	+	3.74124e44i	0.195477	+	0.0794692i
$487$			8.02364e44i			0.164581i	0.996608	+	0.0822904i	$0.0262235\pi$
$487$			8.02364e44i			0.164581i	−0.996608	+	0.0822904i	$0.973776\pi$
$488$	−5.63857e45	+	2.46684e45i	−1.11695	+	0.488656i
$489$	−3.78159e44			−0.0723476
$490$	1.17296e45	−	2.88524e45i	0.216746	−	0.533149i
$491$			2.35961e45i			0.421168i	0.977576	+	0.210584i	$0.0675365\pi$
$491$			2.35961e45i			0.421168i	−0.977576	+	0.210584i	$0.932463\pi$
$492$	6.53155e43	−	6.70546e43i	0.0112618	−	0.0115617i
$493$	1.26577e46			2.10842
$494$	−8.48044e44	−	3.44763e44i	−0.136477	−	0.0554833i
$495$			4.47296e45i			0.695515i
$496$	5.89280e45	−	1.54863e44i	0.885387	−	0.0232681i
$497$	−1.52029e46			−2.20733
$498$	3.15644e44	−	7.76417e44i	0.0442892	−	0.108942i
$499$		−	7.08769e44i		−	0.0961160i	−0.998845	−	0.0480580i	$-0.984697\pi$
$499$		−	7.08769e44i		−	0.0961160i	0.998845	−	0.0480580i	$-0.0153032\pi$
$500$	−5.94966e45	−	5.79536e45i	−0.779834	−	0.759609i
$501$	−1.97453e44			−0.0250163
$502$	−5.88641e44	−	2.39306e44i	−0.0720921	−	0.0293082i
$503$			8.39076e45i			0.993449i	0.867908	+	0.496724i	$0.165464\pi$
$503$			8.39076e45i			0.993449i	−0.867908	+	0.496724i	$0.834536\pi$
$504$	−4.55216e45	−	1.04051e46i	−0.521073	−	1.19104i
$505$	−7.49230e45			−0.829204
$506$	−2.92713e45	+	7.20012e45i	−0.313244	+	0.770515i
$507$		−	6.60070e44i		−	0.0683054i
$508$	−5.60076e45	+	5.74989e45i	−0.560485	+	0.575408i
$509$	3.72541e45			0.360555			0.180278	−	0.983616i	$-0.442300\pi$
$509$	3.72541e45			0.360555			0.180278	+	0.983616i	$0.442300\pi$
$510$	−7.90964e44	−	3.21558e44i	−0.0740396	−	0.0301000i
$511$		−	4.80206e45i		−	0.434783i
$512$	−3.73859e45	+	1.07886e46i	−0.327430	+	0.944875i
$513$	−1.30594e45			−0.110644
$514$	4.19997e44	−	1.03310e45i	0.0344250	−	0.0846782i
$515$			1.52913e46i			1.21261i
$516$	−2.29413e43	−	2.23463e43i	−0.00176024	−	0.00171459i
$517$	1.54605e46			1.14785
$518$	1.87604e46	+	7.62683e45i	1.34783	+	0.547947i
$519$		−	3.97891e44i		−	0.0276643i
$520$	−2.08424e45	+	9.11840e44i	−0.140246	+	0.0613567i
$521$	−1.59460e46			−1.03851			−0.519254	−	0.854620i	$-0.673790\pi$
$521$	−1.59460e46			−1.03851			−0.519254	+	0.854620i	$0.673790\pi$
$522$	9.03685e45	−	2.22287e46i	0.569663	−	1.40125i
$523$		−	2.73828e46i		−	1.67090i	−0.549570	−	0.835448i	$-0.685208\pi$
$523$		−	2.73828e46i		−	1.67090i	0.549570	−	0.835448i	$-0.314792\pi$
$524$	−9.56633e45	+	9.82104e45i	−0.565085	+	0.580130i
$525$	5.46324e44			0.0312422
$526$	2.47722e46	+	1.00709e46i	1.37153	+	0.557582i
$527$		−	2.29144e46i		−	1.22836i
$528$	3.07828e43	+	1.17133e45i	0.00159783	+	0.0608001i
$529$	1.23878e45			0.0622654
$530$	−7.23801e45	+	1.78040e46i	−0.352314	+	0.866617i
$531$		−	5.03226e45i		−	0.237223i
$532$	1.60562e46	+	1.56398e46i	0.733068	+	0.714056i
$533$	−9.69514e44			−0.0428738
$534$	−4.16026e44	−	1.69131e44i	−0.0178205	−	0.00724472i
$535$		−	2.82245e46i		−	1.17115i
$536$	−1.67699e46	−	3.83318e46i	−0.674107	−	1.54084i
$537$	2.82681e45			0.110086
$538$	−3.58946e45	+	8.82931e45i	−0.135435	+	0.333141i
$539$			1.66147e46i			0.607412i
$540$	−2.26449e45	+	2.32479e45i	−0.0802190	+	0.0823549i
$541$	1.91364e45			0.0656910			0.0328455	−	0.999460i	$-0.489543\pi$
$541$	1.91364e45			0.0656910			0.0328455	+	0.999460i	$0.489543\pi$
$542$	−3.06772e46	−	1.24715e46i	−1.02053	−	0.414887i
$543$			2.57308e45i			0.0829576i
$544$	4.15410e46	+	1.56294e46i	1.29806	+	0.488382i
$545$	−2.36408e46			−0.716013
$546$	2.23248e44	−	5.49142e44i	0.00655408	−	0.0161217i
$547$			9.65466e45i			0.274759i	0.990518	+	0.137380i	$0.0438680\pi$
$547$			9.65466e45i			0.274759i	−0.990518	+	0.137380i	$0.956132\pi$
$548$	−4.72948e45	−	4.60683e45i	−0.130480	−	0.127096i
$549$	4.53532e46			1.21305
$550$	1.03612e46	+	4.21223e45i	0.268686	+	0.109231i
$551$			4.73565e46i			1.19070i
$552$	−2.57676e45	+	1.12732e45i	−0.0628218	+	0.0274841i
$553$	−7.42168e46			−1.75459
$554$	1.43125e45	−	3.52057e45i	0.0328132	−	0.0807136i
$555$		−	2.88619e45i		−	0.0641718i
$556$	−2.76031e46	+	2.83380e46i	−0.595232	+	0.611080i
$557$	4.10537e46			0.858646			0.429323	−	0.903151i	$-0.358752\pi$
$557$	4.10537e46			0.858646			0.429323	+	0.903151i	$0.358752\pi$
$558$	−4.02409e46	−	1.63595e46i	−0.816368	−	0.331885i
$559$			3.31698e44i			0.00652744i
$560$	5.56827e46	−	1.46335e45i	1.06298	−	0.0279351i
$561$	4.55478e45			0.0843526
$562$	−5.63012e45	+	1.38489e46i	−0.101158	+	0.248827i
$563$			7.07753e46i			1.23378i	0.787048	+	0.616892i	$0.211609\pi$
$563$			7.07753e46i			1.23378i	−0.787048	+	0.616892i	$0.788391\pi$
$564$	4.00765e45	+	3.90372e45i	0.0677868	+	0.0660288i
$565$	3.67618e46			0.603355
$566$	−9.93913e46	−	4.04064e46i	−1.58296	−	0.643533i
$567$			8.32683e46i			1.28697i
$568$	−4.51431e46	−	1.03186e47i	−0.677127	−	1.54774i
$569$	−2.27536e45			−0.0331239			−0.0165620	−	0.999863i	$-0.505272\pi$
$569$	−2.27536e45			−0.0331239			−0.0165620	+	0.999863i	$0.505272\pi$
$570$	1.20305e45	−	2.95925e45i	0.0169985	−	0.0418127i
$571$		−	1.09044e47i		−	1.49550i	−0.663978	−	0.747752i	$-0.731133\pi$
$571$		−	1.09044e47i		−	1.49550i	0.663978	−	0.747752i	$-0.268867\pi$
$572$	8.46792e45	−	8.69338e45i	0.112731	−	0.115733i
$573$	2.28859e45			0.0295760
$574$	2.19904e46	+	8.93997e45i	0.275887	+	0.112159i
$575$			2.68471e46i			0.326997i
$576$	5.71051e46	−	6.17935e46i	0.675294	−	0.730736i
$577$	−1.23848e47			−1.42200			−0.710999	−	0.703193i	$-0.751757\pi$
$577$	−1.23848e47			−1.42200			−0.710999	+	0.703193i	$0.751757\pi$
$578$	3.11955e46	−	7.67343e46i	0.347791	−	0.855492i
$579$		−	1.22273e45i		−	0.0132372i
$580$	8.43023e46	+	8.21160e46i	0.886265	+	0.863280i
$581$	2.12542e47			2.16995
$582$	−1.13176e46	−	4.60103e45i	−0.112218	−	0.0456209i
$583$		−	1.02524e47i		−	0.987329i
$584$	3.25929e46	−	1.42592e46i	0.304863	−	0.133375i
$585$	1.67643e46			0.152313
$586$	−5.01039e46	+	1.23245e47i	−0.442193	+	1.08770i
$587$			5.32247e46i			0.456316i	0.973624	+	0.228158i	$0.0732702\pi$
$587$			5.32247e46i			0.456316i	−0.973624	+	0.228158i	$0.926730\pi$
$588$	−4.19514e45	+	4.30683e45i	−0.0349407	+	0.0358710i
$589$	8.57299e46			0.693701
$590$	2.28636e46	+	9.29493e45i	0.179746	+	0.0730738i
$591$			2.44722e45i			0.0186933i
$592$	3.94146e45	+	1.49979e47i	0.0292542	+	1.11317i
$593$	−1.90194e47			−1.37172			−0.685861	−	0.727733i	$-0.740574\pi$
$593$	−1.90194e47			−1.37172			−0.685861	+	0.727733i	$0.740574\pi$
$594$	6.52006e45	−	1.60380e46i	0.0456964	−	0.112404i
$595$		−	2.16524e47i		−	1.47475i
$596$	−7.65641e45	−	7.45784e45i	−0.0506802	−	0.0493659i
$597$	−1.22614e46			−0.0788819
$598$	2.69856e46	+	1.09707e46i	0.168737	+	0.0685983i
$599$		−	1.17386e47i		−	0.713444i	−0.934211	−	0.356722i	$-0.883894\pi$
$599$		−	1.17386e47i		−	0.713444i	0.934211	−	0.356722i	$-0.116106\pi$
$600$	1.62224e45	+	3.70805e45i	0.00958396	+	0.0219065i
$601$	−2.61329e47			−1.50079			−0.750396	−	0.660988i	$-0.770137\pi$
$601$	−2.61329e47			−1.50079			−0.750396	+	0.660988i	$0.770137\pi$
$602$	3.05862e45	−	7.52355e45i	0.0170759	−	0.0420032i
$603$			3.08317e47i			1.67341i
$604$	−5.75402e46	+	5.90723e46i	−0.303629	+	0.311714i
$605$	−4.15996e46			−0.213426
$606$	1.33982e46	+	5.44689e45i	0.0668363	+	0.0271715i
$607$		−	1.24244e47i		−	0.602655i	−0.953521	−	0.301327i	$-0.902570\pi$
$607$		−	1.24244e47i		−	0.602655i	0.953521	−	0.301327i	$-0.0974297\pi$
$608$	−5.84743e46	+	1.55418e47i	−0.275806	+	0.733062i
$609$	−3.06652e46			−0.140654
$610$	−8.37704e46	+	2.06058e47i	−0.373666	+	0.919139i
$611$		−	5.79450e46i		−	0.251371i
$612$	−2.34289e47	−	2.28213e47i	−0.988502	−	0.962865i
$613$	1.32241e46			0.0542673			0.0271336	−	0.999632i	$-0.491362\pi$
$613$	1.32241e46			0.0542673			0.0271336	+	0.999632i	$0.491362\pi$
$614$	2.90388e47	+	1.18054e47i	1.15909	+	0.471213i
$615$		−	3.38312e45i		−	0.0131353i
$616$	−2.72231e47	+	1.19099e47i	−1.02817	+	0.449818i
$617$	2.46524e47			0.905755			0.452878	−	0.891573i	$-0.350397\pi$
$617$	2.46524e47			0.905755			0.452878	+	0.891573i	$0.350397\pi$
$618$	1.11168e46	−	2.73449e46i	0.0397351	−	0.0977401i
$619$		−	1.28216e46i		−	0.0445863i	−0.999751	−	0.0222931i	$-0.992903\pi$
$619$		−	1.28216e46i		−	0.0445863i	0.999751	−	0.0222931i	$-0.00709671\pi$
$620$	1.48655e47	−	1.52613e47i	0.502946	−	0.516337i
$621$	4.15562e46			0.136798
$622$	4.78363e47	+	1.94473e47i	1.53222	+	0.622907i
$623$		−	1.13886e47i		−	0.354955i
$624$	4.39008e45	−	1.15372e44i	0.0133148	−	0.000349914i
$625$	−1.85769e47			−0.548294
$626$	2.46044e47	−	6.05216e47i	0.706722	−	1.73839i
$627$			1.70409e46i			0.0476369i
$628$	1.26646e47	+	1.23361e47i	0.344570	+	0.335633i
$629$	5.83198e47			1.54438
$630$	−3.80247e47	−	1.54585e47i	−0.980114	−	0.398454i
$631$			2.63150e47i			0.660244i	0.943938	+	0.330122i	$0.107090\pi$
$631$			2.63150e47i			0.660244i	−0.943938	+	0.330122i	$0.892910\pi$
$632$	−2.20378e47	−	5.03729e47i	−0.538242	−	1.23029i
$633$	−8.95072e45			−0.0212811
$634$	7.57519e46	−	1.86334e47i	0.175338	−	0.431295i
$635$			2.90100e47i			0.653724i
$636$	2.58870e46	−	2.65762e46i	0.0567950	−	0.0583072i
$637$	6.22707e46			0.133019
$638$	−5.81575e47	−	2.36433e47i	−1.20964	−	0.491764i
$639$			8.29964e47i			1.68091i
$640$	1.75275e47	+	3.73588e47i	0.345670	+	0.736773i
$641$	−6.71426e46			−0.128947			−0.0644736	−	0.997919i	$-0.520537\pi$
$641$	−6.71426e46			−0.128947			−0.0644736	+	0.997919i	$0.520537\pi$
$642$	−2.05192e46	+	5.04728e46i	−0.0383764	+	0.0943979i
$643$		−	8.17403e47i		−	1.48885i	−0.667708	−	0.744423i	$-0.732725\pi$
$643$		−	8.17403e47i		−	1.48885i	0.667708	−	0.744423i	$-0.267275\pi$
$644$	−5.10923e47	−	4.97672e47i	−0.906349	−	0.882843i
$645$	−1.15746e45			−0.00199982
$646$	5.97960e47	+	2.43094e47i	1.00628	+	0.409093i
$647$		−	1.35487e47i		−	0.222088i	−0.993816	−	0.111044i	$-0.964581\pi$
$647$		−	1.35487e47i		−	0.222088i	0.993816	−	0.111044i	$-0.0354194\pi$
$648$	−5.65164e47	+	2.47256e47i	−0.902401	+	0.394794i
$649$	−1.31660e47			−0.204783
$650$	1.57872e46	−	3.88331e46i	0.0239209	−	0.0588403i
$651$			5.55134e46i			0.0819448i
$652$	4.95722e47	−	5.08921e47i	0.712901	−	0.731882i
$653$	−7.17987e46			−0.100599			−0.0502994	−	0.998734i	$-0.516018\pi$
$653$	−7.17987e46			−0.100599			−0.0502994	+	0.998734i	$0.516018\pi$
$654$	4.22760e46	+	1.71868e46i	0.0577128	+	0.0234625i
$655$			4.95503e47i			0.659089i
$656$	4.62007e45	+	1.75801e47i	0.00598802	+	0.227854i
$657$	−2.62157e47			−0.331093
$658$	−5.34316e47	+	1.31430e48i	−0.657594	+	1.61754i
$659$			1.22313e48i			1.46697i	0.679707	+	0.733484i	$0.262107\pi$
$659$			1.22313e48i			1.46697i	−0.679707	+	0.733484i	$0.737893\pi$
$660$	3.03355e46	+	2.95488e46i	0.0354572	+	0.0345376i
$661$	−6.15228e47			−0.700828			−0.350414	−	0.936595i	$-0.613959\pi$
$661$	−6.15228e47			−0.700828			−0.350414	+	0.936595i	$0.613959\pi$
$662$	1.64197e46	+	6.67524e45i	0.0182297	+	0.00741108i
$663$		−	1.70710e46i		−	0.0184726i
$664$	6.31118e47	+	1.44258e48i	0.665661	+	1.52154i
$665$	8.10085e47			0.832842
$666$	4.16368e47	−	1.02418e48i	0.417269	−	1.02639i
$667$		−	1.50693e48i		−	1.47215i
$668$	2.58838e47	−	2.65729e47i	0.246506	−	0.253069i
$669$	−1.55280e45			−0.00144169
$670$	−1.40081e48	−	5.69483e47i	−1.26796	−	0.515476i
$671$		−	1.18659e48i		−	1.04717i
$672$	−1.00639e47	−	3.78644e46i	−0.0865944	−	0.0325802i
$673$	−1.90585e47			−0.159894			−0.0799470	−	0.996799i	$-0.525475\pi$
$673$	−1.90585e47			−0.159894			−0.0799470	+	0.996799i	$0.525475\pi$
$674$	−2.68619e47	+	6.60746e47i	−0.219745	+	0.540525i
$675$		−	5.98008e46i		−	0.0477027i
$676$	8.88312e47	+	8.65274e47i	0.690990	+	0.673069i
$677$	−8.94804e47			−0.678767			−0.339383	−	0.940648i	$-0.610218\pi$
$677$	−8.94804e47			−0.678767			−0.339383	+	0.940648i	$0.610218\pi$
$678$	−6.57399e46	−	2.67258e46i	−0.0486322	−	0.0197709i
$679$		−	3.09815e48i		−	2.23520i
$680$	1.46961e48	−	6.42943e47i	1.03407	−	0.452399i
$681$	7.76574e46			0.0532945
$682$	−4.28016e47	+	1.05283e48i	−0.286501	+	0.704732i
$683$			1.78816e48i			1.16750i	0.811935	+	0.583748i	$0.198414\pi$
$683$			1.78816e48i			1.16750i	−0.811935	+	0.583748i	$0.801586\pi$
$684$	8.53815e47	−	8.76548e47i	0.543764	−	0.558241i
$685$	−2.38618e47			−0.148239
$686$	5.84844e47	+	2.37762e47i	0.354430	+	0.144089i
$687$		−	3.38783e46i		−	0.0200289i
$688$	6.01466e46	−	1.58066e45i	0.0346903	−	0.000911664i
$689$	−3.84255e47			−0.216218
$690$	−3.82821e46	+	9.41660e46i	−0.0210166	+	0.0516963i
$691$		−	1.83766e48i		−	0.984323i	−0.870504	−	0.492162i	$-0.836207\pi$
$691$		−	1.83766e48i		−	0.984323i	0.870504	−	0.492162i	$-0.163793\pi$
$692$	5.35475e47	+	5.21588e47i	0.279857	+	0.272599i
$693$	2.18966e48			1.11664
$694$	−7.63185e47	−	3.10264e47i	−0.379769	−	0.154391i
$695$			1.42974e48i			0.694251i
$696$	−9.10567e46	−	2.08133e47i	−0.0431474	−	0.0986242i
$697$	6.83610e47			0.316119
$698$	−1.29512e47	+	3.18572e47i	−0.0584477	+	0.143769i
$699$		−	2.88781e47i		−	0.127191i
$700$	−7.16166e47	+	7.35234e47i	−0.307856	+	0.316052i
$701$	1.73557e48			0.728173			0.364087	−	0.931365i	$-0.381381\pi$
$701$	1.73557e48			0.728173			0.364087	+	0.931365i	$0.381381\pi$
$702$	−6.01092e46	−	2.44367e46i	−0.0246156	−	0.0100072i
$703$			2.18193e48i			0.872168i
$704$	−1.61672e48	−	1.49405e48i	−0.630810	−	0.582950i
$705$	2.02199e47			0.0770129
$706$	9.33882e47	−	2.29715e48i	0.347226	−	0.854103i
$707$			3.66772e48i			1.33127i
$708$	−3.41287e46	−	3.32436e46i	−0.0120936	−	0.0117799i
$709$	−5.64217e48			−1.95191			−0.975955	−	0.217971i	$-0.930056\pi$
$709$	−5.64217e48			−1.95191			−0.975955	+	0.217971i	$0.930056\pi$
$710$	−3.77085e48	−	1.53300e48i	−1.27364	−	0.517786i
$711$			4.05168e48i			1.33614i
$712$	7.72975e47	−	3.38171e47i	0.248889	−	0.108887i
$713$	−2.72800e48			−0.857675
$714$	−1.57413e47	+	3.87203e47i	−0.0483249	+	0.118869i
$715$		−	4.38609e47i		−	0.131485i
$716$	−3.70561e48	+	3.80427e48i	−1.08477	+	1.11365i
$717$	−3.16501e46			−0.00904793
$718$	4.08255e48	+	1.65972e48i	1.13977	+	0.463360i
$719$		−	3.72634e48i		−	1.01600i	−0.861359	−	0.507998i	$-0.830386\pi$
$719$		−	3.72634e48i		−	1.01600i	0.861359	−	0.507998i	$-0.169614\pi$
$720$	−7.98879e46	−	3.03986e48i	−0.0212730	−	0.809471i
$721$	7.48560e48			1.94683
$722$	5.73096e47	−	1.40970e48i	0.145578	−	0.358091i
$723$			3.86285e47i			0.0958421i
$724$	−3.46281e48	−	3.37300e48i	−0.839215	−	0.817450i
$725$	−2.16852e48			−0.513354
$726$	7.43910e46	+	3.02429e46i	0.0172028	+	0.00699359i
$727$			2.53261e48i			0.572115i	0.958212	+	0.286058i	$0.0923449\pi$
$727$			2.53261e48i			0.572115i	−0.958212	+	0.286058i	$0.907655\pi$
$728$	4.46376e47	+	1.02030e48i	0.0985070	+	0.225162i
$729$	4.49943e48			0.970041
$730$	4.84221e47	−	1.19108e48i	0.101989	−	0.250873i
$731$		−	2.33882e47i		−	0.0481285i
$732$	2.99607e47	−	3.07585e47i	0.0602371	−	0.0618409i
$733$	−3.90024e48			−0.766167			−0.383083	−	0.923714i	$-0.625138\pi$
$733$	−3.90024e48			−0.766167			−0.383083	+	0.923714i	$0.625138\pi$
$734$	1.69362e48	+	6.88523e47i	0.325075	+	0.132155i
$735$			2.17293e47i			0.0407532i
$736$	1.86071e48	−	4.94555e48i	0.341001	−	0.906341i
$737$	8.06657e48			1.44458
$738$	4.88056e47	−	1.20051e48i	0.0854105	−	0.210092i
$739$		−	2.84901e48i		−	0.487235i	−0.969871	−	0.243617i	$-0.921666\pi$
$739$		−	2.84901e48i		−	0.487235i	0.969871	−	0.243617i	$-0.0783341\pi$
$740$	3.88419e48	+	3.78345e48i	0.649174	+	0.632338i
$741$	6.38680e46			0.0104321
$742$	8.71563e48	+	3.54324e48i	1.39134	+	0.565633i
$743$			3.32263e48i			0.518408i	0.965823	+	0.259204i	$0.0834602\pi$
$743$			3.32263e48i			0.518408i	−0.965823	+	0.259204i	$0.916540\pi$
$744$	−3.76785e47	+	1.64841e47i	−0.0574584	+	0.0251376i
$745$	−3.86290e47			−0.0575780
$746$	−3.30630e46	+	8.13280e46i	−0.00481706	+	0.0118490i
$747$		−	1.16032e49i		−	1.65245i
$748$	−5.97078e48	+	6.12975e48i	−0.831196	+	0.853327i
$749$	−1.38168e49			−1.88025
$750$	5.36800e47	+	2.18230e47i	0.0714120	+	0.0290318i
$751$		−	1.39345e49i		−	1.81223i	−0.423031	−	0.906115i	$-0.639034\pi$
$751$		−	1.39345e49i		−	1.81223i	0.423031	−	0.906115i	$-0.360966\pi$
$752$	−1.05071e49	+	2.76128e47i	−1.33592	+	0.0351081i
$753$	4.43318e46			0.00551062
$754$	−8.86134e47	+	2.17970e48i	−0.107693	+	0.264902i
$755$			2.98038e48i			0.354139i
$756$	1.13806e48	+	1.10854e48i	0.132219	+	0.128790i
$757$	−6.26459e47			−0.0711644			−0.0355822	−	0.999367i	$-0.511329\pi$
$757$	−6.26459e47			−0.0711644			−0.0355822	+	0.999367i	$0.511329\pi$
$758$	4.52328e48	+	1.83889e48i	0.502431	+	0.204258i
$759$		−	5.42256e47i		−	0.0588971i
$760$	2.40545e48	+	5.49827e48i	0.255485	+	0.583976i
$761$	1.74459e47			0.0181198			0.00905990	−	0.999959i	$-0.497116\pi$
$761$	1.74459e47			0.0181198			0.00905990	+	0.999959i	$0.497116\pi$
$762$	2.10903e47	−	5.18776e47i	0.0214214	−	0.0526921i
$763$			1.15729e49i			1.14955i
$764$	−3.00007e48	+	3.07995e48i	−0.291437	+	0.299197i
$765$	−1.18206e49			−1.12304
$766$	−1.34193e48	−	5.45547e47i	−0.124693	−	0.0506925i
$767$			4.93453e47i			0.0448461i
$768$	−4.18405e46	−	7.95500e47i	−0.00371926	−	0.0707130i
$769$	1.41354e49			1.22903			0.614514	−	0.788906i	$-0.289352\pi$
$769$	1.41354e49			1.22903			0.614514	+	0.788906i	$0.289352\pi$
$770$	−4.04445e48	+	9.94849e48i	−0.343967	+	0.846086i
$771$			7.78052e46i			0.00647269i
$772$	1.64553e48	+	1.60286e48i	0.133910	+	0.130437i
$773$	−1.27804e49			−1.01741			−0.508703	−	0.860942i	$-0.669875\pi$
$773$	−1.27804e49			−1.01741			−0.508703	+	0.860942i	$0.669875\pi$
$774$	−4.10730e47	−	1.66978e47i	−0.0319860	−	0.0130036i
$775$			3.92569e48i			0.299079i
$776$	2.10280e49	−	9.19960e48i	1.56729	−	0.685677i
$777$	−1.41288e48			−0.103027
$778$	−7.02906e47	+	1.72900e48i	−0.0501469	+	0.123351i
$779$			2.55760e48i			0.178524i
$780$	1.10747e47	−	1.13695e47i	0.00756350	−	0.00776488i
$781$	2.17145e49			1.45105
$782$	−1.90277e49	−	7.73548e48i	−1.24414	−	0.505793i
$783$			3.35662e48i			0.214759i
$784$	−2.96742e47	−	1.12915e49i	−0.0185783	−	0.706933i
$785$	6.38968e48			0.391467
$786$	3.60230e47	−	8.86090e47i	0.0215972	−	0.0531245i
$787$		−	1.95005e48i		−	0.114413i	−0.998362	−	0.0572065i	$-0.981781\pi$
$787$		−	1.95005e48i		−	0.114413i	0.998362	−	0.0572065i	$-0.0182193\pi$
$788$	−3.29343e48	−	3.20801e48i	−0.189105	−	0.184200i
$789$	−1.86564e48			−0.104838
$790$	−1.84084e49	−	7.48374e48i	−1.01241	−	0.411583i
$791$		−	1.79961e49i		−	0.968675i
$792$	6.50193e48	+	1.48618e49i	0.342542	+	0.782966i
$793$	−4.44724e48			−0.229322
$794$	7.77293e48	−	1.91198e49i	0.392316	−	0.965015i
$795$		−	1.34085e48i		−	0.0662431i
$796$	1.60733e49	−	1.65012e49i	0.777289	−	0.797984i
$797$	1.70069e49			0.805070			0.402535	−	0.915405i	$-0.368129\pi$
$797$	1.70069e49			0.805070			0.402535	+	0.915405i	$0.368129\pi$
$798$	−1.44865e48	−	5.88931e47i	−0.0671295	−	0.0272908i
$799$			4.08573e49i			1.85342i
$800$	−7.11680e48	−	2.67762e48i	−0.316049	−	0.118910i
$801$	−6.21733e48			−0.270303
$802$	8.97564e48	−	2.20782e49i	0.382033	−	0.939721i
$803$			6.85886e48i			0.285817i
$804$	2.09100e48	+	2.03677e48i	0.0853103	+	0.0830978i
$805$	−2.57777e49			−1.02971
$806$	3.94593e48	+	1.60418e48i	0.154331	+	0.0627417i
$807$		−	6.64954e47i		−	0.0254649i
$808$	−2.48938e49	+	1.08909e49i	−0.933466	+	0.408385i
$809$	4.65753e49			1.71014			0.855068	−	0.518516i	$-0.173515\pi$
$809$	4.65753e49			1.71014			0.855068	+	0.518516i	$0.173515\pi$
$810$	−8.39646e48	+	2.06535e49i	−0.301892	+	0.742590i
$811$			2.02824e49i			0.714108i	0.934084	+	0.357054i	$0.116219\pi$
$811$			2.02824e49i			0.714108i	−0.934084	+	0.357054i	$0.883781\pi$
$812$	4.01984e49	−	4.12687e49i	1.38598	−	1.42288i
$813$	2.31036e48			0.0780083
$814$	−2.67958e49	−	1.08935e49i	−0.886037	−	0.360208i
$815$		−	2.56767e49i		−	0.831495i
$816$	−3.09547e48	+	8.13492e46i	−0.0981734	+	0.00258001i
$817$	8.75027e47			0.0271798
$818$	−2.44141e49	+	6.00535e49i	−0.742736	+	1.82697i
$819$		−	8.20669e48i		−	0.244535i
$820$	4.55294e48	+	4.43486e48i	0.132879	+	0.129433i
$821$	−2.14727e49			−0.613836			−0.306918	−	0.951736i	$-0.599298\pi$
$821$	−2.14727e49			−0.613836			−0.306918	+	0.951736i	$0.599298\pi$
$822$	4.26711e47	+	1.73475e47i	0.0119485	+	0.00485753i
$823$			3.45556e49i			0.947811i	0.880576	+	0.473905i	$0.157156\pi$
$823$			3.45556e49i			0.947811i	−0.880576	+	0.473905i	$0.842844\pi$
$824$	2.22276e49	+	5.08067e49i	0.597214	+	1.36508i
$825$	−7.80324e47			−0.0205380
$826$	4.55017e48	−	1.11925e49i	0.117319	−	0.288579i
$827$		−	4.38594e49i		−	1.10782i	−0.832577	−	0.553909i	$-0.813135\pi$
$827$		−	4.38594e49i		−	1.10782i	0.832577	−	0.553909i	$-0.186865\pi$
$828$	−2.71692e49	+	2.78926e49i	−0.672297	+	0.690197i
$829$	−7.66632e49			−1.85849			−0.929244	−	0.369467i	$-0.879540\pi$
$829$	−7.66632e49			−1.85849			−0.929244	+	0.369467i	$0.879540\pi$
$830$	5.27180e49	+	2.14319e49i	1.25208	+	0.509018i
$831$			2.65141e47i			0.00616964i
$832$	−5.59961e48	+	6.05934e48i	−0.127662	+	0.138143i
$833$	−4.39074e49			−0.980783
$834$	1.03942e48	−	2.55676e48i	0.0227494	−	0.0559587i
$835$		−	1.34069e49i		−	0.287513i
$836$	−2.29333e49	−	2.23385e49i	−0.481904	−	0.469406i
$837$	6.07652e48			0.125119
$838$	−5.66172e49	−	2.30171e49i	−1.14235	−	0.464411i
$839$		−	6.59836e49i		−	1.30462i	−0.757954	−	0.652308i	$-0.773801\pi$
$839$		−	6.59836e49i		−	1.30462i	0.757954	−	0.652308i	$-0.226199\pi$
$840$	−3.56034e48	+	1.55763e48i	−0.0689833	+	0.0301797i
$841$	6.90529e49			1.31114
$842$	2.10753e49	−	5.18407e49i	0.392164	−	0.964641i
$843$		−	1.04299e48i		−	0.0190200i
$844$	1.17333e49	−	1.20457e49i	0.209701	−	0.215284i
$845$	4.48182e49			0.785037
$846$	7.17512e49	+	2.91697e49i	1.23178	+	0.500766i
$847$			2.03643e49i			0.342651i
$848$	1.83111e48	+	6.96765e49i	0.0301984	+	1.14910i
$849$	7.48536e48			0.120999
$850$	−1.11316e49	+	2.73814e49i	−0.176375	+	0.433845i
$851$		−	6.94310e49i		−	1.07833i
$852$	5.62880e48	+	5.48282e48i	0.0856925	+	0.0834700i
$853$	6.62877e48			0.0989235			0.0494617	−	0.998776i	$-0.484249\pi$
$853$	6.62877e48			0.0989235			0.0494617	+	0.998776i	$0.484249\pi$
$854$	1.00872e50	+	4.10083e49i	1.47566	+	0.599913i
$855$		−	4.42246e49i		−	0.634221i
$856$	−4.10273e49	−	9.37783e49i	−0.576792	−	1.31840i
$857$	−3.82145e49			−0.526690			−0.263345	−	0.964702i	$-0.584826\pi$
$857$	−3.82145e49			−0.526690			−0.263345	+	0.964702i	$0.584826\pi$
$858$	−3.18868e47	+	7.84349e47i	−0.00430851	+	0.0105980i
$859$			8.54696e49i			1.13221i	0.824332	+	0.566106i	$0.191551\pi$
$859$			8.54696e49i			1.13221i	−0.824332	+	0.566106i	$0.808449\pi$
$860$	1.51729e48	−	1.55769e48i	0.0197059	−	0.0202306i
$861$	−1.65615e48			−0.0210885
$862$	4.08606e49	+	1.66114e49i	0.510130	+	0.207388i
$863$			1.86775e49i			0.228631i	0.993444	+	0.114315i	$0.0364675\pi$
$863$			1.86775e49i			0.228631i	−0.993444	+	0.114315i	$0.963533\pi$
$864$	−4.14465e48	+	1.10160e49i	−0.0497455	+	0.132218i
$865$	2.70164e49			0.317947
$866$	2.26644e49	−	5.57498e49i	0.261542	−	0.643337i
$867$			5.77902e48i			0.0653927i
$868$	−7.47091e49	−	7.27715e49i	−0.828969	−	0.807470i
$869$	1.06005e50			1.15343
$870$	−7.60607e48	−	3.09216e48i	−0.0811583	−	0.0329940i
$871$		−	3.02329e49i		−	0.316353i
$872$	−7.85486e49	+	3.43644e49i	−0.806043	+	0.352638i
$873$	−1.69136e50			−1.70214
$874$	2.89409e49	−	7.11884e49i	0.285639	−	0.702611i
$875$			1.46948e50i			1.42241i
$876$	−1.73183e48	+	1.77794e48i	−0.0164413	+	0.0168791i
$877$	4.14203e49			0.385674			0.192837	−	0.981231i	$-0.438231\pi$
$877$	4.14203e49			0.385674			0.192837	+	0.981231i	$0.438231\pi$
$878$	−1.77894e50	−	7.23207e49i	−1.62463	−	0.660474i
$879$		−	9.28184e48i		−	0.0831425i
$880$	−7.95326e49	+	2.09012e48i	−0.698778	+	0.0183640i
$881$	−4.14674e49			−0.357369			−0.178684	−	0.983906i	$-0.557184\pi$
$881$	−4.14674e49			−0.357369			−0.178684	+	0.983906i	$0.557184\pi$
$882$	−3.13472e49	+	7.71076e49i	−0.264992	+	0.651825i
$883$			1.94669e50i			1.61423i	0.590395	+	0.807114i	$0.298972\pi$
$883$			1.94669e50i			1.61423i	−0.590395	+	0.807114i	$0.701028\pi$
$884$	2.29739e49	+	2.23781e49i	0.186873	+	0.182026i
$885$	−1.72190e48			−0.0137396
$886$	3.48018e49	+	1.41483e49i	0.272413	+	0.110747i
$887$			1.00003e50i			0.767913i	0.923351	+	0.383956i	$0.125439\pi$
$887$			1.00003e50i			0.767913i	−0.923351	+	0.383956i	$0.874561\pi$
$888$	−4.19539e48	−	9.58962e48i	−0.0316047	−	0.0722406i
$889$	1.42013e50			1.04954
$890$	1.14838e49	−	2.82478e49i	0.0832639	−	0.204812i
$891$		−	1.18934e50i		−	0.846026i
$892$	2.03554e48	−	2.08974e48i	0.0142062	−	0.0145844i
$893$	−1.52860e50			−1.04669
$894$	6.90789e47	+	2.80833e47i	0.00464096	+	0.00188673i
$895$			1.91938e50i			1.26523i
$896$	1.82884e50	−	8.58030e49i	1.18287	−	0.554966i
$897$	−2.03234e48			−0.0128981
$898$	5.90749e48	−	1.45312e49i	0.0367879	−	0.0904906i
$899$		−	2.20349e50i		−	1.34647i
$900$	4.01383e49	+	3.90973e49i	0.240678	+	0.234436i
$901$	2.70940e50			1.59423
$902$	−3.14093e49	−	1.27691e49i	−0.181362	−	0.0737309i
$903$			5.66614e47i			0.00321067i
$904$	1.22144e50	−	5.34373e49i	0.679219	−	0.297154i
$905$	−1.74710e50			−0.953436
$906$	2.16674e48	−	5.32972e48i	0.0116045	−	0.0285447i
$907$		−	1.73078e50i		−	0.909741i	−0.890558	−	0.454870i	$-0.849686\pi$
$907$		−	1.73078e50i		−	0.909741i	0.890558	−	0.454870i	$-0.150314\pi$
$908$	−1.01800e50	+	1.04510e50i	−0.525155	+	0.539137i
$909$	2.00230e50			1.01378
$910$	3.72862e49	+	1.51583e49i	0.185287	+	0.0753264i
$911$		−	1.76425e50i		−	0.860493i	−0.902712	−	0.430246i	$-0.858427\pi$
$911$		−	1.76425e50i		−	0.860493i	0.902712	−	0.430246i	$-0.141573\pi$
$912$	−3.04353e47	−	1.15811e49i	−0.00145702	−	0.0554419i
$913$	−3.03577e50			−1.42648
$914$	−9.94309e49	+	2.44579e50i	−0.458602	+	1.12807i
$915$		−	1.55186e49i		−	0.0702578i
$916$	4.55929e49	+	4.44105e49i	0.202616	+	0.197361i
$917$	2.42565e50			1.05815
$918$	4.23833e49	+	1.72305e49i	0.181497	+	0.0737856i
$919$			8.00927e49i			0.336689i	0.985728	+	0.168345i	$0.0538422\pi$
$919$			8.00927e49i			0.336689i	−0.985728	+	0.168345i	$0.946158\pi$
$920$	−7.65438e49	−	1.74960e50i	−0.315876	−	0.722014i
$921$	−2.18697e49			−0.0885990
$922$	8.72742e49	−	2.14676e50i	0.347105	−	0.853804i
$923$		−	8.13845e49i		−	0.317770i
$924$	1.44651e49	−	1.48502e49i	0.0554495	−	0.0569258i
$925$	−9.99134e49			−0.376023
$926$	−2.06225e50	−	8.38386e49i	−0.762001	−	0.309783i
$927$		−	4.08658e50i		−	1.48253i
$928$	3.99467e50	+	1.50295e50i	1.42287	+	0.535339i
$929$	−3.92684e50			−1.37333			−0.686667	−	0.726972i	$-0.740927\pi$
$929$	−3.92684e50			−1.37333			−0.686667	+	0.726972i	$0.740927\pi$
$930$	−5.59776e48	+	1.37693e49i	−0.0192223	+	0.0472827i
$931$		−	1.64271e50i		−	0.553882i
$932$	3.88637e50	+	3.78558e50i	1.28669	+	1.25332i
$933$	−3.60265e49			−0.117121
$934$	−1.88220e50	−	7.65187e49i	−0.600854	−	0.244270i
$935$			3.09265e50i			0.969469i
$936$	5.57010e49	−	2.43688e49i	0.171464	−	0.0750144i
$937$	7.82422e49			0.236520			0.118260	−	0.992983i	$-0.462268\pi$
$937$	7.82422e49			0.236520			0.118260	+	0.992983i	$0.462268\pi$
$938$	−2.78780e50	+	6.85741e50i	−0.827587	+	2.03569i
$939$			4.55801e49i			0.132880i
$940$	−2.65059e50	+	2.72116e50i	−0.758872	+	0.779078i
$941$	2.49039e50			0.700235			0.350117	−	0.936706i	$-0.386142\pi$
$941$	2.49039e50			0.700235			0.350117	+	0.936706i	$0.386142\pi$
$942$	−1.14264e49	−	4.64530e48i	−0.0315534	−	0.0128277i
$943$		−	8.13851e49i		−	0.220722i
$944$	8.94774e49	−	2.35148e48i	0.238336	−	0.00626349i
$945$	5.74187e49			0.150215
$946$	−4.36868e48	+	1.07460e49i	−0.0112254	+	0.0276120i
$947$			4.30190e50i			1.08570i	0.839829	+	0.542852i	$0.182655\pi$
$947$			4.30190e50i			1.08570i	−0.839829	+	0.542852i	$0.817345\pi$
$948$	2.74785e49	+	2.67658e49i	0.0681162	+	0.0663496i
$949$	2.57065e49			0.0625919
$950$	−1.02442e50	−	4.16468e49i	−0.245007	−	0.0996049i
$951$			1.40332e49i			0.0329676i
$952$	−3.14742e50	−	7.19421e50i	−0.726317	−	1.66018i
$953$	−5.09134e50			−1.15412			−0.577062	−	0.816700i	$-0.695801\pi$
$953$	−5.09134e50			−1.15412			−0.577062	+	0.816700i	$0.695801\pi$
$954$	1.93435e50	−	4.75809e50i	0.430737	−	1.05952i
$955$			1.55393e50i			0.339919i
$956$	4.14895e49	−	4.25942e49i	0.0891568	−	0.0915306i
$957$	4.37996e49			0.0924629
$958$	1.28306e50	+	5.21614e49i	0.266093	+	0.108177i
$959$			1.16811e50i			0.237995i
$960$	−2.11440e49	−	1.95398e49i	−0.0423230	−	0.0391119i
$961$	1.09608e50			0.215549
$962$	−4.08282e49	+	1.00429e50i	−0.0788831	+	0.194036i
$963$			7.54294e50i			1.43184i
$964$	−5.19856e50	−	5.06373e50i	−0.969557	−	0.944412i
$965$	8.30223e49			0.152135
$966$	4.60973e49	+	1.87403e49i	0.0829974	+	0.0337417i
$967$		−	5.96244e50i		−	1.05481i	−0.849614	−	0.527404i	$-0.823165\pi$
$967$		−	5.96244e50i		−	1.05481i	0.849614	−	0.527404i	$-0.176835\pi$
$968$	−1.38218e50	+	6.04695e49i	−0.240262	+	0.105113i
$969$	−4.50336e49			−0.0769188
$970$	3.12406e50	−	7.68452e50i	0.524324	−	1.28973i
$971$		−	3.60777e50i		−	0.594993i	−0.954723	−	0.297496i	$-0.903848\pi$
$971$		−	3.60777e50i		−	0.594993i	0.954723	−	0.297496i	$-0.0961516\pi$
$972$	9.08534e49	−	9.32724e49i	0.147236	−	0.151156i
$973$	6.99906e50			1.11461
$974$	9.74243e49	+	3.96068e49i	0.152463	+	0.0619822i
$975$			2.92460e48i			0.00449767i
$976$	2.11926e49	+	8.06414e50i	0.0320286	+	1.21874i
$977$	4.28087e50			0.635805			0.317903	−	0.948123i	$-0.397022\pi$
$977$	4.28087e50			0.635805			0.317903	+	0.948123i	$0.397022\pi$
$978$	−1.86669e49	+	4.59167e49i	−0.0272466	+	0.0670209i
$979$			1.62665e50i			0.233340i
$980$	−2.92430e50	−	2.84846e50i	−0.412267	−	0.401575i
$981$	6.31796e50			0.875394
$982$	2.86508e50	+	1.16477e50i	0.390159	+	0.158615i
$983$			8.22664e50i			1.10106i	0.834814	+	0.550532i	$0.185575\pi$
$983$			8.22664e50i			1.10106i	−0.834814	+	0.550532i	$0.814425\pi$
$984$	−4.91773e48	−	1.12407e49i	−0.00646916	−	0.0147869i
$985$	−1.66164e50			−0.214843
$986$	6.24818e50	−	1.53692e51i	0.794046	−	1.95319i
$987$		−	9.89829e49i		−	0.123643i
$988$	−8.37233e49	+	8.59525e49i	−0.102797	+	0.105534i
$989$	−2.78442e49			−0.0336045
$990$	5.43114e50	+	2.20797e50i	0.644306	+	0.261935i
$991$			1.40043e50i			0.163308i	0.996661	+	0.0816542i	$0.0260203\pi$
$991$			1.40043e50i			0.163308i	−0.996661	+	0.0816542i	$0.973980\pi$
$992$	2.72080e50	−	7.23157e50i	0.311888	−	0.828961i
$993$	−1.23660e48			−0.00139345
$994$	−7.50453e50	+	1.84596e51i	−0.831294	+	2.04481i
$995$		−	8.32540e50i		−	0.906594i
$996$	−7.86928e49	−	7.66519e49i	−0.0842415	−	0.0820567i
$997$	−1.55310e51			−1.63448			−0.817242	−	0.576295i	$-0.804498\pi$
$997$	−1.55310e51			−1.63448			−0.817242	+	0.576295i	$0.804498\pi$
$998$	−8.60599e49	−	3.49867e49i	−0.0890393	−	0.0361979i
$999$			1.54655e50i			0.157308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.35.b.a.3.11	✓	16
4.3	odd	2	inner	4.35.b.a.3.12	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.35.b.a.3.11	✓	16	1.1	even	1	trivial
4.35.b.a.3.12	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)

\(f(q)\)	\(=\)	\(q+(49362.6 - 121422. i) q^{2} +9.14451e6i q^{3} +(-1.23065e10 - 1.19874e10i) q^{4} -6.20904e11 q^{5} +(1.11034e12 + 4.51397e11i) q^{6} +3.03953e14i q^{7} +(-2.06301e15 + 9.02552e14i) q^{8} +1.65936e16 q^{9} +O(q^{10})\)	\(q+(49362.6 - 121422. i) q^{2} +9.14451e6i q^{3} +(-1.23065e10 - 1.19874e10i) q^{4} -6.20904e11 q^{5} +(1.11034e12 + 4.51397e11i) q^{6} +3.03953e14i q^{7} +(-2.06301e15 + 9.02552e14i) q^{8} +1.65936e16 q^{9} +(-3.06494e16 + 7.53911e16i) q^{10} -4.34141e17i q^{11} +(1.09619e17 - 1.12537e17i) q^{12} -1.62713e18 q^{13} +(3.69064e19 + 1.50039e19i) q^{14} -5.67786e18i q^{15} +(7.75384e18 + 2.95046e20i) q^{16} +1.14730e21 q^{17} +(8.19101e20 - 2.01482e21i) q^{18} +4.29240e21i q^{19} +(7.64118e21 + 7.44301e21i) q^{20} -2.77950e21 q^{21} +(-5.27141e22 - 2.14303e22i) q^{22} -1.36588e23i q^{23} +(-8.25339e21 - 1.88652e22i) q^{24} -1.96555e23 q^{25} +(-8.03194e22 + 1.97569e23i) q^{26} +3.04245e23i q^{27} +(3.64359e24 - 3.74061e24i) q^{28} +1.10326e25 q^{29} +(-6.89415e23 - 2.80274e23i) q^{30} -1.99725e25i q^{31} +(3.62077e25 + 1.36228e25i) q^{32} +3.97001e24 q^{33} +(5.66336e25 - 1.39307e26i) q^{34} -1.88725e26i q^{35} +(-2.04209e26 - 1.98913e26i) q^{36} +5.08323e26 q^{37} +(5.21190e26 + 2.11884e26i) q^{38} -1.48793e25i q^{39} +(1.28093e27 - 5.60398e26i) q^{40} +5.95843e26 q^{41} +(-1.37203e26 + 3.37491e26i) q^{42} -2.03855e26i q^{43} +(-5.20421e27 + 5.34277e27i) q^{44} -1.03030e28 q^{45} +(-1.65848e28 - 6.74235e27i) q^{46} +3.56118e28i q^{47} +(-2.69805e27 + 7.09051e25i) q^{48} -3.82703e28 q^{49} +(-9.70246e27 + 2.38660e28i) q^{50} +1.04915e28i q^{51} +(2.00243e28 + 1.95050e28i) q^{52} +2.36155e29 q^{53} +(3.69419e28 + 1.50183e28i) q^{54} +2.69560e29i q^{55} +(-2.74333e29 - 6.27057e29i) q^{56} -3.92519e28 q^{57} +(5.44600e29 - 1.33960e30i) q^{58} -3.03266e29i q^{59} +(-6.80626e28 + 6.98748e28i) q^{60} +2.73318e30 q^{61} +(-2.42509e30 - 9.85893e29i) q^{62} +5.04366e30i q^{63} +(3.44140e30 - 3.72394e30i) q^{64} +1.01029e30 q^{65} +(1.95970e29 - 4.82044e29i) q^{66} +1.85805e31i q^{67} +(-1.41193e31 - 1.37531e31i) q^{68} +1.24903e30 q^{69} +(-2.29153e31 - 9.31598e30i) q^{70} +5.00172e31i q^{71} +(-3.42326e31 + 1.49765e31i) q^{72} -1.57987e31 q^{73} +(2.50922e31 - 6.17214e31i) q^{74} -1.79740e30i q^{75} +(5.14546e31 - 5.28246e31i) q^{76} +1.31958e32 q^{77} +(-1.80667e30 - 7.34481e29i) q^{78} +2.44172e32i q^{79} +(-4.81439e30 - 1.83195e32i) q^{80} +2.73952e32 q^{81} +(2.94124e31 - 7.23482e31i) q^{82} -6.99260e32i q^{83} +(3.42060e31 + 3.33189e31i) q^{84} -7.12362e32 q^{85} +(-2.47524e31 - 1.00628e31i) q^{86} +1.00888e32i q^{87} +(3.91835e32 + 8.95636e32i) q^{88} -3.74683e32 q^{89} +(-5.08583e32 + 1.25101e33i) q^{90} -4.94571e32i q^{91} +(-1.63733e33 + 1.68093e33i) q^{92} +1.82638e32 q^{93} +(4.32404e33 + 1.75789e33i) q^{94} -2.66517e33i q^{95} +(-1.24573e32 + 3.31102e32i) q^{96} -1.01929e34 q^{97} +(-1.88912e33 + 4.64684e33i) q^{98} -7.20394e33i 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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