LMFDB - Embedded newform 4.39.b.a.3.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,39,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, 39, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 39);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 39 $
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:	$36.5853876134$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 9 x^{17} + \cdots + 98\!\cdots\!00 $ x^18 - 9x^17 + 62197466427874200x^16 - 497579731422993396x^15 + 1533330651456954523834224606283158x^14 - 10733314560198672959194272341598390x^13 + 19481782443651984882412391050385129300654889992244x^12 - 116890694661911769761385063719584946156168645371260x^11 + 139136237606150959215813468176435276664250794192016778233210479201x^10 - 695681188030753724581032940024542714621854609744310005116371215353x^9 + 568497808401670574980605551637816112488442166027324531949553103951206327341764748x^8 - 2273991233606678125835294022030202761397409545881853066054780853036284586514186696x^7 + 1283345352716388020512119899733143277332875078305115652503919007522645061900921255799901780340080x^6 - 3850036058149156102567042075828911269459277293563124763645420508567574714938226584752670924974864x^5 + 1439289344267733945837233684997856126673028793147138744042225979486721504292452534506308895244176799020170408512x^4 - 2878578688535461474947703788071527631381805661197607189586491117390555337819668654857160404811027247469352955136x^3 + 595941113794922164474527754149079025845074143571524485346938332375224698791062016413718632611595715188157806349620071647759360x^2 - 595941113794920725185183486418983224669538300112471429188966406515013857315416680428086116138384986393156714104315884501606400*x + 9817075370481683892061162300824582856496888117704407266492938605020758056089024085664206842636148929977821744687833149264494609112760320000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{306}\cdot 3^{34}\cdot 5^{10}\cdot 19^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.11
Root			$0.500000 + 7.59483e7i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.39.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)

$f(q)$	$=$	$q+(130787. - 507713. i) q^{2} -1.21517e9i q^{3} +(-2.40667e11 - 1.32805e11i) q^{4} -7.30752e12 q^{5} +(-6.16959e14 - 1.58929e14i) q^{6} +7.26783e15i q^{7} +(-9.89028e16 + 1.04821e17i) q^{8} -1.25791e17 q^{9} +O(q^{10})$	\(q+(130787. - 507713. i) q^{2} -1.21517e9i q^{3} +(-2.40667e11 - 1.32805e11i) q^{4} -7.30752e12 q^{5} +(-6.16959e14 - 1.58929e14i) q^{6} +7.26783e15i q^{7} +(-9.89028e16 + 1.04821e17i) q^{8} -1.25791e17 q^{9} +(-9.55728e17 + 3.71012e18i) q^{10} +4.95016e19i q^{11} +(-1.61380e20 + 2.92452e20i) q^{12} +1.33417e21 q^{13} +(3.68997e21 + 9.50538e20i) q^{14} +8.87989e21i q^{15} +(4.02837e22 + 6.39235e22i) q^{16} -1.14555e22 q^{17} +(-1.64519e22 + 6.38660e22i) q^{18} +5.70300e22i q^{19} +(1.75868e24 + 9.70472e23i) q^{20} +8.83167e24 q^{21} +(2.51326e25 + 6.47416e24i) q^{22} +1.17299e26i q^{23} +(1.27375e26 + 1.20184e26i) q^{24} -3.10398e26 q^{25} +(1.74493e26 - 6.77378e26i) q^{26} -1.48866e27i q^{27} +(9.65202e26 - 1.74913e27i) q^{28} -1.11611e28 q^{29} +(4.50844e27 + 1.16137e27i) q^{30} +1.05042e28i q^{31} +(3.77234e28 - 1.20922e28i) q^{32} +6.01529e28 q^{33} +(-1.49823e27 + 5.81611e27i) q^{34} -5.31098e28i q^{35} +(3.02739e28 + 1.67057e28i) q^{36} +9.56044e29 q^{37} +(2.89549e28 + 7.45878e27i) q^{38} -1.62125e30i q^{39} +(7.22734e29 - 7.65980e29i) q^{40} +5.59134e30 q^{41} +(1.15507e30 - 4.48395e30i) q^{42} -7.10284e30i q^{43} +(6.57404e30 - 1.19134e31i) q^{44} +9.19223e29 q^{45} +(5.95544e31 + 1.53412e31i) q^{46} +1.17187e31i q^{47} +(7.76780e31 - 4.89517e31i) q^{48} +7.71134e31 q^{49} +(-4.05960e31 + 1.57593e32i) q^{50} +1.39204e31i q^{51} +(-3.21092e32 - 1.77185e32i) q^{52} -3.89822e32 q^{53} +(-7.55812e32 - 1.94697e32i) q^{54} -3.61734e32i q^{55} +(-7.61821e32 - 7.18809e32i) q^{56} +6.93013e31 q^{57} +(-1.45973e33 + 5.66665e33i) q^{58} +6.64750e33i q^{59} +(1.17929e33 - 2.13710e33i) q^{60} -6.57417e33 q^{61} +(5.33313e33 + 1.37382e33i) q^{62} -9.14232e32i q^{63} +(-1.20565e33 - 2.07342e34i) q^{64} -9.74950e33 q^{65} +(7.86722e33 - 3.05404e34i) q^{66} +3.38641e33i q^{67} +(2.75697e33 + 1.52134e33i) q^{68} +1.42539e35 q^{69} +(-2.69645e34 - 6.94607e33i) q^{70} +4.35113e34i q^{71} +(1.24411e34 - 1.31856e34i) q^{72} +2.83225e35 q^{73} +(1.25038e35 - 4.85396e35i) q^{74} +3.77187e35i q^{75} +(7.57385e33 - 1.37253e34i) q^{76} -3.59769e35 q^{77} +(-8.23131e35 - 2.12039e35i) q^{78} +2.18449e36i q^{79} +(-2.94374e35 - 4.67122e35i) q^{80} -1.97890e36 q^{81} +(7.31275e35 - 2.83880e36i) q^{82} +1.82062e36i q^{83} +(-2.12549e36 - 1.17289e36i) q^{84} +8.37113e34 q^{85} +(-3.60620e36 - 9.28959e35i) q^{86} +1.35627e37i q^{87} +(-5.18880e36 - 4.89585e36i) q^{88} +2.05963e37 q^{89} +(1.20222e35 - 4.66702e35i) q^{90} +9.69656e36i q^{91} +(1.55779e37 - 2.82301e37i) q^{92} +1.27644e37 q^{93} +(5.94972e36 + 1.53265e36i) q^{94} -4.16748e35i q^{95} +(-1.46941e37 - 4.58404e37i) q^{96} -5.02029e37 q^{97} +(1.00854e37 - 3.91515e37i) q^{98} -6.22688e36i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 364228 q^{2} + 200567335824 q^{4} - 8991287507020 q^{5} + 817599417526752 q^{6} + 90\!\cdots\!32 q^{8}+ \cdots - 75\!\cdots\!14 q^{9}+O(q^{10}) $ 18 * q + 364228 * q^2 + 200567335824 * q^4 - 8991287507020 * q^5 + 817599417526752 * q^6 + 90410803724813632 * q^8 - 7529771892957713214 * q^9	$ 18 q + 364228 q^{2} + 200567335824 q^{4} - 8991287507020 q^{5} + 817599417526752 q^{6} + 90\!\cdots\!32 q^{8}+ \cdots + 79\!\cdots\!72 q^{98}+O(q^{100}) $ 18 * q + 364228 * q^2 + 200567335824 * q^4 - 8991287507020 * q^5 + 817599417526752 * q^6 + 90410803724813632 * q^8 - 7529771892957713214 * q^9 - 3330064307292995160 * q^10 + 214196660016355524480 * q^12 - 1351697142828804018156 * q^13 - 7517302305589491995328 * q^14 + 146524491404032531730688 * q^16 - 108377436655642595433244 * q^17 - 2269182475834354952235228 * q^18 + 14024643346150499263916960 * q^20 - 3613555902040956758482176 * q^21 - 48893102429006434191867360 * q^22 - 507867326842846671102786048 * q^24 + 441821122409714044642015590 * q^25 + 1408725703649472883667066984 * q^26 - 248593478439946838208756480 * q^28 + 12039386014829706600024980948 * q^29 - 36685926266894937628070825280 * q^30 + 40815302174771571873068643328 * q^32 - 25787267222238191864238656640 * q^33 + 36261374450642004292958003976 * q^34 - 580544496119856571348909156080 * q^36 - 1267140929573154455938088740044 * q^37 + 1030706182877614317326332452960 * q^38 + 3677775331309955303335927125120 * q^40 - 4228447688719256876424323554684 * q^41 - 14054054841750269128772739402240 * q^42 - 10408853597054255998042527960960 * q^44 + 5968962977750993515218889928340 * q^45 + 22407092921477343211835072559552 * q^46 - 235299721005018637688575231641600 * q^48 - 31615512188019323981649417734094 * q^49 + 24292124186551164152560477361580 * q^50 + 1002079305454954374889708255510176 * q^52 + 9170251390510729272958214802164 * q^53 - 787051683509089599494415837112896 * q^54 + 1152829073224199082248229376115712 * q^56 + 1668394969897754054685444684739200 * q^57 + 6129531800884682398669731348277224 * q^58 - 11636557112389656620532244922123520 * q^60 - 3962895304807674280127771339766444 * q^61 - 8994819235653434082008553861768960 * q^62 + 24667562443996411690757328278360064 * q^64 + 95108472178397576493345013351708360 * q^65 - 59643686483535838768039195759223040 * q^66 - 37428614071533769215405413189346016 * q^68 - 378107798255717180855219732084825856 * q^69 + 185830274294359588352082139216848000 * q^70 - 260290846480495236441760743958748352 * q^72 + 769773517671824524924524644742901764 * q^73 - 250034850108007402381953386687905624 * q^74 + 347277300516185248422743813412796800 * q^76 - 1122048032159971455828617866562814720 * q^77 - 1450998872578214468135780206011466560 * q^78 + 391473453760426152176293685484792320 * q^80 + 8894227269421968655762303906241837682 * q^81 + 344096947623408239895482884304277576 * q^82 - 6791395692770555756905407625225660416 * q^84 - 3198312652592605820819998423888978200 * q^85 + 8678996853442312035283130731028012832 * q^86 - 815671442380761053869289210355156480 * q^88 - 6268329434682461663886854261019826492 * q^89 - 23166185157487343623484458734705269400 * q^90 + 11421593562829281515681866911017506560 * q^92 + 41748150138354461655386813609302195200 * q^93 - 33742046901195882761657274622561154688 * q^94 - 31638035665740952392118263378397667328 * q^96 - 62817319233285161836922640968633412444 * q^97 + 79415378721147757612981391241727219972 * 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 $

$2$	130787.	−	507713.i	0.249456	−	0.968386i
$2$	130787.	−	507713.i	0.249456	−	0.968386i
$3$		−	1.21517e9i		−	1.04552i	−0.852479	−	0.522762i	$-0.824902\pi$
$3$		−	1.21517e9i		−	1.04552i	0.852479	−	0.522762i	$-0.175098\pi$
$4$	−2.40667e11	−	1.32805e11i	−0.875543	−	0.483140i
$5$	−7.30752e12			−0.383124			−0.191562	−	0.981480i	$-0.561355\pi$
$5$	−7.30752e12			−0.383124			−0.191562	+	0.981480i	$0.561355\pi$
$6$	−6.16959e14	−	1.58929e14i	−1.01247	−	0.260813i
$7$			7.26783e15i			0.637591i	0.947824	+	0.318796i	$0.103278\pi$
$7$			7.26783e15i			0.637591i	−0.947824	+	0.318796i	$0.896722\pi$
$8$	−9.89028e16	+	1.04821e17i	−0.686276	+	0.727341i
$9$	−1.25791e17			−0.0931201
$10$	−9.55728e17	+	3.71012e18i	−0.0955728	+	0.371012i
$11$			4.95016e19i			0.809390i	0.914452	+	0.404695i	$0.132622\pi$
$11$			4.95016e19i			0.809390i	−0.914452	+	0.404695i	$0.867378\pi$
$12$	−1.61380e20	+	2.92452e20i	−0.505135	+	0.915401i
$13$	1.33417e21			0.912618			0.456309	−	0.889821i	$-0.349171\pi$
$13$	1.33417e21			0.912618			0.456309	+	0.889821i	$0.349171\pi$
$14$	3.68997e21	+	9.50538e20i	0.617434	+	0.159051i
$15$			8.87989e21i			0.400566i
$16$	4.02837e22	+	6.39235e22i	0.533151	+	0.846020i
$17$	−1.14555e22			−0.0479165			−0.0239582	−	0.999713i	$-0.507627\pi$
$17$	−1.14555e22			−0.0479165			−0.0239582	+	0.999713i	$0.507627\pi$
$18$	−1.64519e22	+	6.38660e22i	−0.0232294	+	0.0901762i
$19$			5.70300e22i			0.0288260i	0.999896	+	0.0144130i	$0.00458797\pi$
$19$			5.70300e22i			0.0288260i	−0.999896	+	0.0144130i	$0.995412\pi$
$20$	1.75868e24	+	9.70472e23i	0.335442	+	0.185103i
$21$	8.83167e24			0.666617
$22$	2.51326e25	+	6.47416e24i	0.783802	+	0.201908i
$23$			1.17299e26i			1.57205i	0.618195	+	0.786025i	$0.287864\pi$
$23$			1.17299e26i			1.57205i	−0.618195	+	0.786025i	$0.712136\pi$
$24$	1.27375e26	+	1.20184e26i	0.760452	+	0.717518i
$25$	−3.10398e26			−0.853216
$26$	1.74493e26	−	6.77378e26i	0.227658	−	0.883766i
$27$		−	1.48866e27i		−	0.948165i
$28$	9.65202e26	−	1.74913e27i	0.308046	−	0.558238i
$29$	−1.11611e28			−1.82871			−0.914357	−	0.404908i	$-0.867303\pi$
$29$	−1.11611e28			−1.82871			−0.914357	+	0.404908i	$0.867303\pi$
$30$	4.50844e27	+	1.16137e27i	0.387902	+	0.0999237i
$31$			1.05042e28i			0.484721i	0.970186	+	0.242360i	$0.0779217\pi$
$31$			1.05042e28i			0.484721i	−0.970186	+	0.242360i	$0.922078\pi$
$32$	3.77234e28	−	1.20922e28i	0.952272	−	0.305251i
$33$	6.01529e28			0.846237
$34$	−1.49823e27	+	5.81611e27i	−0.0119531	+	0.0464017i
$35$		−	5.31098e28i		−	0.244277i
$36$	3.02739e28	+	1.67057e28i	0.0815307	+	0.0449901i
$37$	9.56044e29			1.52984			0.764918	−	0.644127i	$-0.222779\pi$
$37$	9.56044e29			1.52984			0.764918	+	0.644127i	$0.222779\pi$
$38$	2.89549e28	+	7.45878e27i	0.0279147	+	0.00719084i
$39$		−	1.62125e30i		−	0.954164i
$40$	7.22734e29	−	7.65980e29i	0.262929	−	0.278662i
$41$	5.59134e30			1.27240			0.636199	−	0.771525i	$-0.280506\pi$
$41$	5.59134e30			1.27240			0.636199	+	0.771525i	$0.280506\pi$
$42$	1.15507e30	−	4.48395e30i	0.166292	−	0.645542i
$43$		−	7.10284e30i		−	0.653930i	−0.945036	−	0.326965i	$-0.893974\pi$
$43$		−	7.10284e30i		−	0.653930i	0.945036	−	0.326965i	$-0.106026\pi$
$44$	6.57404e30	−	1.19134e31i	0.391049	−	0.708656i
$45$	9.19223e29			0.0356766
$46$	5.95544e31	+	1.53412e31i	1.52235	+	0.392158i
$47$			1.17187e31i			0.199076i	0.995034	+	0.0995380i	$0.0317365\pi$
$47$			1.17187e31i			0.199076i	−0.995034	+	0.0995380i	$0.968264\pi$
$48$	7.76780e31	−	4.89517e31i	0.884534	−	0.557422i
$49$	7.71134e31			0.593478
$50$	−4.05960e31	+	1.57593e32i	−0.212840	+	0.826242i
$51$			1.39204e31i			0.0500978i
$52$	−3.21092e32	−	1.77185e32i	−0.799036	−	0.440922i
$53$	−3.89822e32			−0.675499			−0.337749	−	0.941236i	$-0.609666\pi$
$53$	−3.89822e32			−0.675499			−0.337749	+	0.941236i	$0.609666\pi$
$54$	−7.55812e32	−	1.94697e32i	−0.918189	−	0.236526i
$55$		−	3.61734e32i		−	0.310097i
$56$	−7.61821e32	−	7.18809e32i	−0.463746	−	0.437563i
$57$	6.93013e31			0.0301383
$58$	−1.45973e33	+	5.66665e33i	−0.456185	+	1.77090i
$59$			6.64750e33i			1.50131i	0.660695	+	0.750654i	$0.270262\pi$
$59$			6.64750e33i			1.50131i	−0.660695	+	0.750654i	$0.729738\pi$
$60$	1.17929e33	−	2.13710e33i	0.193529	−	0.350712i
$61$	−6.57417e33			−0.788086			−0.394043	−	0.919092i	$-0.628924\pi$
$61$	−6.57417e33			−0.788086			−0.394043	+	0.919092i	$0.628924\pi$
$62$	5.33313e33	+	1.37382e33i	0.469397	+	0.120917i
$63$		−	9.14232e32i		−	0.0593726i
$64$	−1.20565e33	−	2.07342e34i	−0.0580501	−	0.998314i
$65$	−9.74950e33			−0.349646
$66$	7.86722e33	−	3.05404e34i	0.211099	−	0.819484i
$67$			3.38641e33i			0.0682838i	0.999417	+	0.0341419i	$0.0108698\pi$
$67$			3.38641e33i			0.0682838i	−0.999417	+	0.0341419i	$0.989130\pi$
$68$	2.75697e33	+	1.52134e33i	0.0419529	+	0.0231504i
$69$	1.42539e35			1.64362
$70$	−2.69645e34	−	6.94607e33i	−0.236554	−	0.0609364i
$71$			4.35113e34i			0.291537i	0.989319	+	0.145768i	$0.0465655\pi$
$71$			4.35113e34i			0.291537i	−0.989319	+	0.145768i	$0.953435\pi$
$72$	1.24411e34	−	1.31856e34i	0.0639061	−	0.0677301i
$73$	2.83225e35			1.11943			0.559715	−	0.828685i	$-0.310911\pi$
$73$	2.83225e35			1.11943			0.559715	+	0.828685i	$0.310911\pi$
$74$	1.25038e35	−	4.85396e35i	0.381628	−	1.48147i
$75$			3.77187e35i			0.892057i
$76$	7.57385e33	−	1.37253e34i	0.0139270	−	0.0252384i
$77$	−3.59769e35			−0.516060
$78$	−8.23131e35	−	2.12039e35i	−0.923999	−	0.238022i
$79$			2.18449e36i			1.92502i	0.271252	+	0.962508i	$0.412562\pi$
$79$			2.18449e36i			1.92502i	−0.271252	+	0.962508i	$0.587438\pi$
$80$	−2.94374e35	−	4.67122e35i	−0.204263	−	0.324131i
$81$	−1.97890e36			−1.08445
$82$	7.31275e35	−	2.83880e36i	0.317408	−	1.23217i
$83$			1.82062e36i			0.627677i	0.949476	+	0.313839i	$0.101615\pi$
$83$			1.82062e36i			0.627677i	−0.949476	+	0.313839i	$0.898385\pi$
$84$	−2.12549e36	−	1.17289e36i	−0.583651	−	0.322069i
$85$	8.37113e34			0.0183580
$86$	−3.60620e36	−	9.28959e35i	−0.633257	−	0.163127i
$87$			1.35627e37i			1.91196i
$88$	−5.18880e36	−	4.89585e36i	−0.588703	−	0.555465i
$89$	2.05963e37			1.88529			0.942646	−	0.333795i	$-0.108329\pi$
$89$	2.05963e37			1.88529			0.942646	+	0.333795i	$0.108329\pi$
$90$	1.20222e35	−	4.66702e35i	0.00889976	−	0.0345487i
$91$			9.69656e36i			0.581877i
$92$	1.55779e37	−	2.82301e37i	0.759521	−	1.37640i
$93$	1.27644e37			0.506787
$94$	5.94972e36	+	1.53265e36i	0.192782	+	0.0496608i
$95$		−	4.16748e35i		−	0.0110440i
$96$	−1.46941e37	−	4.58404e37i	−0.319147	−	0.995623i
$97$	−5.02029e37			−0.895501			−0.447750	−	0.894159i	$-0.647775\pi$
$97$	−5.02029e37			−0.895501			−0.447750	+	0.894159i	$0.647775\pi$
$98$	1.00854e37	−	3.91515e37i	0.148047	−	0.574716i
$99$		−	6.22688e36i		−	0.0753705i
$100$	7.47027e37	+	4.12223e37i	0.747027	+	0.412223i
$101$	6.20394e37			0.513525			0.256762	−	0.966475i	$-0.417344\pi$
$101$	6.20394e37			0.513525			0.256762	+	0.966475i	$0.417344\pi$
$102$	7.06758e36	+	1.82061e36i	0.0485140	+	0.0124972i
$103$			1.63183e38i			0.930611i	0.885150	+	0.465305i	$0.154055\pi$
$103$			1.63183e38i			0.930611i	−0.885150	+	0.465305i	$0.845945\pi$
$104$	−1.31954e38	+	1.39849e38i	−0.626308	+	0.663784i
$105$	−6.45376e37			−0.255397
$106$	−5.09836e37	+	1.97918e38i	−0.168507	+	0.654143i
$107$		−	2.75178e38i		−	0.760889i	−0.924804	−	0.380444i	$-0.875771\pi$
$107$		−	2.75178e38i		−	0.760889i	0.924804	−	0.380444i	$-0.124229\pi$
$108$	−1.97701e38	+	3.58272e38i	−0.458096	+	0.830159i
$109$	−3.45759e38			−0.672466			−0.336233	−	0.941779i	$-0.609153\pi$
$109$	−3.45759e38			−0.672466			−0.336233	+	0.941779i	$0.609153\pi$
$110$	−1.83657e38	−	4.73101e37i	−0.300294	−	0.0773557i
$111$		−	1.16176e39i		−	1.59948i
$112$	−4.64585e38	+	2.92776e38i	−0.539415	+	0.339932i
$113$	−3.27947e38			−0.321598			−0.160799	−	0.986987i	$-0.551407\pi$
$113$	−3.27947e38			−0.321598			−0.160799	+	0.986987i	$0.551407\pi$
$114$	9.06371e36	−	3.51852e37i	0.00751820	−	0.0291855i
$115$		−	8.57166e38i		−	0.602290i
$116$	2.68612e39	+	1.48225e39i	1.60112	+	0.883526i
$117$	−1.67828e38			−0.0849831
$118$	3.37502e39	+	8.69407e38i	1.45385	+	0.374511i
$119$		−	8.32567e37i		−	0.0305511i
$120$	−9.30798e38	−	8.78246e38i	−0.291348	−	0.274899i
$121$	1.29003e39			0.344887
$122$	−8.59816e38	+	3.33779e39i	−0.196593	+	0.763172i
$123$		−	6.79444e39i		−	1.33032i
$124$	1.39501e39	−	2.52802e39i	0.234188	−	0.424394i
$125$	4.92670e39			0.710012
$126$	−4.64167e38	−	1.19570e38i	−0.0574956	−	0.0148109i
$127$		−	3.39805e39i		−	0.362208i	−0.983464	−	0.181104i	$-0.942033\pi$
$127$		−	3.39805e39i		−	0.362208i	0.983464	−	0.181104i	$-0.0579671\pi$
$128$	−1.06847e40	−	2.09963e39i	−0.981234	−	0.192821i
$129$	−8.63117e39			−0.683699
$130$	−1.27511e39	+	4.94995e39i	−0.0872215	+	0.338592i
$131$			3.17297e40i			1.87634i	0.346173	+	0.938171i	$0.387481\pi$
$131$			3.17297e40i			1.87634i	−0.346173	+	0.938171i	$0.612519\pi$
$132$	−1.44769e40	−	7.98859e39i	−0.740917	−	0.408851i
$133$	−4.14485e38			−0.0183792
$134$	1.71932e39	+	4.42898e38i	0.0661251	+	0.0170338i
$135$			1.08784e40i			0.363265i
$136$	1.13298e39	−	1.20078e39i	0.0328839	−	0.0348516i
$137$	−1.96261e40			−0.495613			−0.247806	−	0.968810i	$-0.579710\pi$
$137$	−1.96261e40			−0.495613			−0.247806	+	0.968810i	$0.579710\pi$
$138$	1.86422e40	−	7.23688e40i	0.410010	−	1.59165i
$139$			5.67513e40i			1.08817i	0.839032	+	0.544083i	$0.183122\pi$
$139$			5.67513e40i			1.08817i	−0.839032	+	0.544083i	$0.816878\pi$
$140$	−7.05323e39	+	1.27818e40i	−0.118020	+	0.213875i
$141$	1.42402e40			0.208139
$142$	2.20913e40	+	5.69072e39i	0.282320	+	0.0727258i
$143$			6.60437e40i			0.738664i
$144$	−5.06735e39	−	8.04103e39i	−0.0496471	−	0.0787815i
$145$	8.15601e40			0.700625
$146$	3.70421e40	−	1.43797e41i	0.279249	−	1.08404i
$147$		−	9.37061e40i		−	0.620495i
$148$	−2.30089e41	−	1.26967e41i	−1.33944	−	0.739126i
$149$	2.15975e41			1.10628			0.553139	−	0.833089i	$-0.313430\pi$
$149$	2.15975e41			1.10628			0.553139	+	0.833089i	$0.313430\pi$
$150$	1.91503e41	+	4.93312e40i	0.863856	+	0.222529i
$151$		−	8.25689e40i		−	0.328288i	−0.986436	−	0.164144i	$-0.947514\pi$
$151$		−	8.25689e40i		−	0.328288i	0.986436	−	0.164144i	$-0.0524861\pi$
$152$	−5.97794e39	−	5.64043e39i	−0.0209664	−	0.0197826i
$153$	1.44101e39			0.00446199
$154$	−4.70531e40	+	1.82660e41i	−0.128735	+	0.499745i
$155$		−	7.67598e40i		−	0.185708i
$156$	−2.15310e41	+	3.90182e41i	−0.460995	+	0.835411i
$157$	−5.49352e41			−1.04174			−0.520868	−	0.853637i	$-0.674392\pi$
$157$	−5.49352e41			−1.04174			−0.520868	+	0.853637i	$0.674392\pi$
$158$	1.10909e42	+	2.85702e41i	1.86416	+	0.480208i
$159$			4.73700e41i			0.706250i
$160$	−2.75664e41	+	8.83641e40i	−0.364839	+	0.116949i
$161$	−8.52511e41			−1.00232
$162$	−2.58815e41	+	1.00471e42i	−0.270523	+	1.05017i
$163$		−	1.84282e42i		−	1.71364i	−0.515618	−	0.856819i	$-0.672438\pi$
$163$		−	1.84282e42i		−	1.71364i	0.515618	−	0.856819i	$-0.327562\pi$
$164$	−1.34565e42	−	7.42556e41i	−1.11404	−	0.614746i
$165$	−4.39569e41			−0.324214
$166$	9.24355e41	+	2.38114e41i	0.607834	+	0.156578i
$167$		−	1.08923e42i		−	0.639008i	−0.947585	−	0.319504i	$-0.896484\pi$
$167$		−	1.08923e42i		−	0.639008i	0.947585	−	0.319504i	$-0.103516\pi$
$168$	−8.73477e41	+	9.25743e41i	−0.457483	+	0.484858i
$169$	−3.57189e41			−0.167129
$170$	1.09484e40	−	4.25013e40i	0.00457951	−	0.0177776i
$171$		−	7.17389e39i		−	0.00268428i
$172$	−9.43289e41	+	1.70942e42i	−0.315940	+	0.572544i
$173$	4.09054e42			1.22717			0.613584	−	0.789629i	$-0.289727\pi$
$173$	4.09054e42			1.22717			0.613584	+	0.789629i	$0.289727\pi$
$174$	6.88595e42	+	1.77382e42i	1.85152	+	0.476952i
$175$		−	2.25592e42i		−	0.544003i
$176$	−3.16431e42	+	1.99411e42i	−0.684761	+	0.431527i
$177$	8.07786e42			1.56965
$178$	2.69372e42	−	1.04570e43i	0.470298	−	1.82569i
$179$			3.65462e42i			0.573634i	0.957985	+	0.286817i	$0.0925972\pi$
$179$			3.65462e42i			0.573634i	−0.957985	+	0.286817i	$0.907403\pi$
$180$	−2.21227e41	−	1.22077e41i	−0.0312364	−	0.0172368i
$181$	−1.33452e43			−1.69603			−0.848015	−	0.529972i	$-0.822202\pi$
$181$	−1.33452e43			−1.69603			−0.848015	+	0.529972i	$0.822202\pi$
$182$	4.92307e42	+	1.26818e42i	0.563481	+	0.145153i
$183$			7.98874e42i			0.823963i
$184$	−1.22954e43	−	1.16012e43i	−1.14342	−	1.07886i
$185$	−6.98631e42			−0.586118
$186$	1.66942e42	−	6.48067e42i	0.126421	−	0.490766i
$187$		−	5.67066e41i		−	0.0387831i
$188$	1.55629e42	−	2.82030e42i	0.0961816	−	0.174300i
$189$	1.08193e43			0.604541
$190$	−2.11588e41	−	5.45052e40i	−0.0106948	−	0.00275499i
$191$			3.77753e43i			1.72812i	0.503387	+	0.864061i	$0.332087\pi$
$191$			3.77753e43i			1.72812i	−0.503387	+	0.864061i	$0.667913\pi$
$192$	−2.51956e43	+	1.46508e42i	−1.04376	+	0.0606928i
$193$	3.40504e42			0.127801			0.0639005	−	0.997956i	$-0.479646\pi$
$193$	3.40504e42			0.127801			0.0639005	+	0.997956i	$0.479646\pi$
$194$	−6.56589e42	+	2.54887e43i	−0.223388	+	0.867190i
$195$			1.18473e43i			0.365563i
$196$	−1.85587e43	−	1.02410e43i	−0.519615	−	0.286733i
$197$	1.50175e43			0.381716			0.190858	−	0.981618i	$-0.438873\pi$
$197$	1.50175e43			0.381716			0.190858	+	0.981618i	$0.438873\pi$
$198$	−3.16147e42	−	8.14395e41i	−0.0729878	−	0.0188017i
$199$			3.32525e41i			0.00697616i	0.999994	+	0.00348808i	$0.00111029\pi$
$199$			3.32525e41i			0.00697616i	−0.999994	+	0.00348808i	$0.998890\pi$
$200$	3.06992e43	−	3.25362e43i	0.585542	−	0.620579i
$201$	4.11507e42			0.0713924
$202$	8.11395e42	−	3.14982e43i	0.128102	−	0.497290i
$203$		−	8.11172e43i		−	1.16597i
$204$	1.84870e42	−	3.35019e42i	0.0242043	−	0.0438628i
$205$	−4.08588e43			−0.487486
$206$	8.28502e43	+	2.13422e43i	0.901191	+	0.232147i
$207$		−	1.47552e43i		−	0.146389i
$208$	5.37455e43	+	8.52851e43i	0.486563	+	0.772093i
$209$	−2.82308e42			−0.0233315
$210$	−8.44068e42	+	3.27666e43i	−0.0637104	+	0.247323i
$211$		−	1.86502e44i		−	1.28622i	−0.765772	−	0.643112i	$-0.777643\pi$
$211$		−	1.86502e44i		−	1.28622i	0.765772	−	0.643112i	$-0.222357\pi$
$212$	9.38174e43	+	5.17701e43i	0.591428	+	0.326361i
$213$	5.28737e43			0.304809
$214$	−1.39711e44	−	3.59897e43i	−0.736834	−	0.189809i
$215$			5.19041e43i			0.250536i
$216$	1.56043e44	+	1.47233e44i	0.689639	+	0.650703i
$217$	−7.63429e43			−0.309054
$218$	−4.52208e43	+	1.75546e44i	−0.167751	+	0.651206i
$219$		−	3.44167e44i		−	1.17039i
$220$	−4.80399e43	+	8.70575e43i	−0.149820	+	0.271503i
$221$	−1.52837e43			−0.0437294
$222$	−5.89840e44	−	1.51943e44i	−1.54891	−	0.399001i
$223$			4.46316e44i			1.07609i	0.842915	+	0.538047i	$0.180838\pi$
$223$			4.46316e44i			1.07609i	−0.842915	+	0.538047i	$0.819162\pi$
$224$	8.78843e43	+	2.74167e44i	0.194625	+	0.607160i
$225$	3.90454e43			0.0794516
$226$	−4.28912e43	+	1.66503e44i	−0.0802247	+	0.311431i
$227$		−	2.49004e44i		−	0.428267i	−0.976804	−	0.214134i	$-0.931307\pi$
$227$		−	2.49004e44i		−	0.428267i	0.976804	−	0.214134i	$-0.0686928\pi$
$228$	−1.66786e43	−	9.20353e42i	−0.0263874	−	0.0145610i
$229$	−6.19255e44			−0.901562			−0.450781	−	0.892635i	$-0.648854\pi$
$229$	−6.19255e44			−0.901562			−0.450781	+	0.892635i	$0.648854\pi$
$230$	−4.35194e44	−	1.12106e44i	−0.583250	−	0.150245i
$231$			4.37181e44i			0.539553i
$232$	1.10387e45	−	1.16992e45i	1.25500	−	1.33010i
$233$	−8.69248e44			−0.910712			−0.455356	−	0.890309i	$-0.650488\pi$
$233$	−8.69248e44			−0.910712			−0.455356	+	0.890309i	$0.650488\pi$
$234$	−2.19497e43	+	8.52084e43i	−0.0211996	+	0.0822964i
$235$		−	8.56344e43i		−	0.0762709i
$236$	8.82818e44	−	1.59984e45i	0.725343	−	1.31446i
$237$	2.65453e45			2.01265
$238$	−4.22705e43	−	1.08889e43i	−0.0295853	−	0.00762117i
$239$			2.46178e45i			1.59107i	0.605908	+	0.795534i	$0.292810\pi$
$239$			2.46178e45i			1.59107i	−0.605908	+	0.795534i	$0.707190\pi$
$240$	−5.67633e44	+	3.57715e44i	−0.338887	+	0.213562i
$241$	1.61182e45			0.889188			0.444594	−	0.895732i	$-0.353348\pi$
$241$	1.61182e45			0.889188			0.444594	+	0.895732i	$0.353348\pi$
$242$	1.68719e44	−	6.54964e44i	0.0860343	−	0.333984i
$243$			3.93750e44i			0.185653i
$244$	1.58219e45	+	8.73079e44i	0.690003	+	0.380756i
$245$	−5.63508e44			−0.227376
$246$	−3.44963e45	−	8.88625e44i	−1.28826	−	0.331857i
$247$			7.60880e43i			0.0263072i
$248$	−1.10106e45	−	1.03890e45i	−0.352557	−	0.332652i
$249$	2.21237e45			0.656252
$250$	6.44348e44	−	2.50135e45i	0.177117	−	0.687566i
$251$		−	3.21678e45i		−	0.819635i	−0.912168	−	0.409817i	$-0.865592\pi$
$251$		−	3.21678e45i		−	0.819635i	0.912168	−	0.409817i	$-0.134408\pi$
$252$	−1.21414e44	+	2.20026e44i	−0.0286853	+	0.0519832i
$253$	−5.80650e45			−1.27240
$254$	−1.72523e45	−	4.44420e44i	−0.350758	−	0.0903552i
$255$		−	1.01724e44i		−	0.0191937i
$256$	−2.46343e45	+	5.15015e45i	−0.431500	+	0.902113i
$257$	−6.42474e45			−1.04502			−0.522512	−	0.852632i	$-0.675005\pi$
$257$	−6.42474e45			−1.04502			−0.522512	+	0.852632i	$0.675005\pi$
$258$	−1.12885e45	+	4.38216e45i	−0.170553	+	0.662085i
$259$			6.94837e45i			0.975410i
$260$	2.34639e45	+	1.29478e45i	0.306130	+	0.168928i
$261$	1.40397e45			0.170290
$262$	1.61096e46	+	4.14984e45i	1.81702	+	0.468065i
$263$		−	3.42099e44i		−	0.0358916i	−0.999839	−	0.0179458i	$-0.994287\pi$
$263$		−	3.42099e44i		−	0.0358916i	0.999839	−	0.0179458i	$-0.00571263\pi$
$264$	−5.94929e45	+	6.30528e45i	−0.580752	+	0.615503i
$265$	2.84863e45			0.258800
$266$	−5.42092e43	+	2.10439e44i	−0.00458482	+	0.0177982i
$267$		−	2.50280e46i		−	1.97112i
$268$	4.49730e44	−	8.14998e44i	0.0329907	−	0.0597854i
$269$	−6.96422e45			−0.475970			−0.237985	−	0.971269i	$-0.576487\pi$
$269$	−6.96422e45			−0.475970			−0.237985	+	0.971269i	$0.576487\pi$
$270$	5.52311e45	+	1.42275e45i	0.351781	+	0.0906188i
$271$		−	1.11990e46i		−	0.664912i	−0.943119	−	0.332456i	$-0.892123\pi$
$271$		−	1.11990e46i		−	0.664912i	0.943119	−	0.332456i	$-0.107877\pi$
$272$	−4.61471e44	−	7.32276e44i	−0.0255467	−	0.0405383i
$273$	1.17830e46			0.608366
$274$	−2.56684e45	+	9.96441e45i	−0.123634	+	0.479945i
$275$		−	1.53652e46i		−	0.690585i
$276$	−3.43044e46	−	1.89298e46i	−1.43906	−	0.794097i
$277$	2.45032e46			0.959637			0.479819	−	0.877368i	$-0.340702\pi$
$277$	2.45032e46			0.959637			0.479819	+	0.877368i	$0.340702\pi$
$278$	2.88134e46	+	7.42234e45i	1.05376	+	0.271450i
$279$		−	1.32134e45i		−	0.0451373i
$280$	5.56702e45	+	5.25271e45i	0.177672	+	0.167641i
$281$	−3.47809e45			−0.103734			−0.0518669	−	0.998654i	$-0.516517\pi$
$281$	−3.47809e45			−0.103734			−0.0518669	+	0.998654i	$0.516517\pi$
$282$	1.86243e45	−	7.22994e45i	0.0519215	−	0.201559i
$283$			4.65075e46i			1.21222i	0.795381	+	0.606109i	$0.207271\pi$
$283$			4.65075e46i			1.21222i	−0.795381	+	0.606109i	$0.792729\pi$
$284$	5.77850e45	−	1.04718e46i	0.140853	−	0.255253i
$285$	−5.06420e44			−0.0115467
$286$	3.35313e46	+	8.63767e45i	0.715312	+	0.184265i
$287$			4.06369e46i			0.811269i
$288$	−4.74528e45	+	1.52110e45i	−0.0886757	+	0.0284250i
$289$	−5.70244e46			−0.997704
$290$	1.06670e46	−	4.14091e46i	0.174775	−	0.678475i
$291$			6.10052e46i			0.936267i
$292$	−6.81630e46	−	3.76136e46i	−0.980109	−	0.540842i
$293$	−6.29809e46			−0.848641			−0.424321	−	0.905512i	$-0.639487\pi$
$293$	−6.29809e46			−0.848641			−0.424321	+	0.905512i	$0.639487\pi$
$294$	−4.75758e46	−	1.22555e46i	−0.600879	−	0.154787i
$295$		−	4.85767e46i		−	0.575188i
$296$	−9.45554e46	+	1.00213e47i	−1.04989	+	1.11271i
$297$	7.36910e46			0.767435
$298$	2.82467e46	−	1.09653e47i	0.275968	−	1.07130i
$299$			1.56498e47i			1.43468i
$300$	5.00922e46	−	9.07766e46i	0.430989	−	0.781035i
$301$	5.16222e46			0.416940
$302$	−4.19213e46	−	1.07989e46i	−0.317909	−	0.0818935i
$303$		−	7.53885e46i		−	0.536902i
$304$	−3.64556e45	+	2.29738e45i	−0.0243874	+	0.0153686i
$305$	4.80408e46			0.301935
$306$	1.88465e44	−	7.31618e44i	0.00111307	−	0.00432093i
$307$			4.16955e46i			0.231452i	0.993281	+	0.115726i	$0.0369194\pi$
$307$			4.16955e46i			0.231452i	−0.993281	+	0.115726i	$0.963081\pi$
$308$	8.65847e46	+	4.77790e46i	0.451833	+	0.249329i
$309$	1.98296e47			0.972976
$310$	−3.89720e46	−	1.00392e46i	−0.179837	−	0.0463261i
$311$		−	2.03179e47i		−	0.881923i	−0.897526	−	0.440962i	$-0.854638\pi$
$311$		−	2.03179e47i		−	0.881923i	0.897526	−	0.440962i	$-0.145362\pi$
$312$	1.69941e47	+	1.60346e47i	0.694002	+	0.654820i
$313$	−8.98855e46			−0.345420			−0.172710	−	0.984973i	$-0.555252\pi$
$313$	−8.98855e46			−0.345420			−0.172710	+	0.984973i	$0.555252\pi$
$314$	−7.18482e46	+	2.78913e47i	−0.259868	+	1.00880i
$315$			6.68076e45i			0.0227471i
$316$	2.90110e47	−	5.25735e47i	0.930053	−	1.68543i
$317$	−5.01925e46			−0.151535			−0.0757675	−	0.997126i	$-0.524141\pi$
$317$	−5.01925e46			−0.151535			−0.0757675	+	0.997126i	$0.524141\pi$
$318$	2.40504e47	+	6.19539e46i	0.683922	+	0.176179i
$319$		−	5.52493e47i		−	1.48014i
$320$	8.81034e45	+	1.51515e47i	0.0222404	+	0.382478i
$321$	−3.34388e47			−0.795528
$322$	−1.11497e47	+	4.32831e47i	−0.250036	+	0.970637i
$323$		−	6.53308e44i		−	0.00138124i
$324$	4.76257e47	+	2.62807e47i	0.949481	+	0.523941i
$325$	−4.14125e47			−0.778660
$326$	−9.35625e47	−	2.41017e47i	−1.65946	−	0.427478i
$327$			4.20157e47i			0.703079i
$328$	−5.52999e47	+	5.86089e47i	−0.873216	+	0.925467i
$329$	−8.51693e46			−0.126929
$330$	−5.74899e46	+	2.23175e47i	−0.0808773	+	0.313964i
$331$		−	9.10673e47i		−	1.20957i	−0.796389	−	0.604784i	$-0.793259\pi$
$331$		−	9.10673e47i		−	1.20957i	0.796389	−	0.604784i	$-0.206741\pi$
$332$	2.41787e47	−	4.38165e47i	0.303256	−	0.549558i
$333$	−1.20262e47			−0.142459
$334$	−5.53016e47	−	1.42457e47i	−0.618806	−	0.159405i
$335$		−	2.47462e46i		−	0.0261612i
$336$	3.55773e47	+	5.64551e47i	0.355407	+	0.563971i
$337$	1.64288e48			1.55109			0.775547	−	0.631289i	$-0.217474\pi$
$337$	1.64288e48			1.55109			0.775547	+	0.631289i	$0.217474\pi$
$338$	−4.67157e46	+	1.81350e47i	−0.0416913	+	0.161845i
$339$			3.98512e47i			0.336238i
$340$	−2.01466e46	−	1.11172e46i	−0.0160732	−	0.00886947i
$341$	−5.19976e47			−0.392328
$342$	−3.64228e45	−	9.38252e44i	−0.00259942	−	0.000669612i
$343$			1.50479e48i			1.01599i
$344$	7.44526e47	+	7.02491e47i	0.475630	+	0.448777i
$345$	−1.04160e48			−0.629709
$346$	5.34989e47	−	2.07682e48i	0.306125	−	1.18837i
$347$			1.70075e48i			0.921258i	0.887593	+	0.460629i	$0.152376\pi$
$347$			1.70075e48i			0.921258i	−0.887593	+	0.460629i	$0.847624\pi$
$348$	1.80119e48	−	3.26410e48i	0.923747	−	1.67401i
$349$	2.04634e48			0.993791			0.496896	−	0.867810i	$-0.334473\pi$
$349$	2.04634e48			0.993791			0.496896	+	0.867810i	$0.334473\pi$
$350$	−1.14536e48	−	2.95045e47i	−0.526805	−	0.135705i
$351$		−	1.98613e48i		−	0.865312i
$352$	5.98584e47	+	1.86737e48i	0.247067	+	0.770760i
$353$	−8.30359e47			−0.324748			−0.162374	−	0.986729i	$-0.551915\pi$
$353$	−8.30359e47			−0.324748			−0.162374	+	0.986729i	$0.551915\pi$
$354$	1.05648e48	−	4.10123e48i	0.391560	−	1.52003i
$355$		−	3.17960e47i		−	0.111695i
$356$	−4.95685e48	−	2.73528e48i	−1.65065	−	0.910860i
$357$	−1.01171e47			−0.0319419
$358$	1.85550e48	+	4.77977e47i	0.555499	+	0.143097i
$359$			4.59767e48i			1.30540i	0.757617	+	0.652700i	$0.226364\pi$
$359$			4.59767e48i			1.30540i	−0.757617	+	0.652700i	$0.773636\pi$
$360$	−9.09138e46	+	9.63538e46i	−0.0244840	+	0.0259490i
$361$	3.91089e48			0.999169
$362$	−1.74538e48	+	6.77556e48i	−0.423086	+	1.64241i
$363$		−	1.56761e48i		−	0.360588i
$364$	1.28775e48	−	2.33365e48i	0.281128	−	0.509458i
$365$	−2.06967e48			−0.428881
$366$	4.05599e48	+	1.04482e48i	0.797914	+	0.205543i
$367$			6.04449e48i			1.12903i	0.825424	+	0.564513i	$0.190936\pi$
$367$			6.04449e48i			1.12903i	−0.825424	+	0.564513i	$0.809064\pi$
$368$	−7.49817e48	+	4.72525e48i	−1.32999	+	0.838140i
$369$	−7.03343e47			−0.118486
$370$	−9.13718e47	+	3.54704e48i	−0.146211	+	0.567588i
$371$		−	2.83316e48i		−	0.430692i
$372$	−3.07198e48	−	1.69518e48i	−0.443714	−	0.244849i
$373$	1.85397e48			0.254470			0.127235	−	0.991873i	$-0.459390\pi$
$373$	1.85397e48			0.254470			0.127235	+	0.991873i	$0.459390\pi$
$374$	−2.87907e47	−	7.41649e46i	−0.0375571	−	0.00967470i
$375$		−	5.98679e48i		−	0.742334i
$376$	−1.22836e48	−	1.15901e48i	−0.144796	−	0.136621i
$377$	−1.48909e49			−1.66892
$378$	1.41503e48	−	5.49311e48i	0.150807	−	0.585429i
$379$		−	1.44280e49i		−	1.46238i	−0.682172	−	0.731192i	$-0.738964\pi$
$379$		−	1.44280e49i		−	1.46238i	0.682172	−	0.731192i	$-0.261036\pi$
$380$	−5.53460e46	+	1.00298e47i	−0.00533578	+	0.00966946i
$381$	−4.12921e48			−0.378698
$382$	1.91790e49	+	4.94052e48i	1.67349	+	0.431091i
$383$		−	2.57290e48i		−	0.213622i	−0.994279	−	0.106811i	$-0.965936\pi$
$383$		−	2.57290e48i		−	0.213622i	0.994279	−	0.106811i	$-0.0340640\pi$
$384$	−2.55142e48	+	1.29837e49i	−0.201599	+	1.02590i
$385$	2.62902e48			0.197715
$386$	4.45336e47	−	1.72879e48i	0.0318808	−	0.123761i
$387$			8.93477e47i			0.0608940i
$388$	1.20822e49	+	6.66718e48i	0.784049	+	0.432652i
$389$	4.82829e47			0.0298367			0.0149184	−	0.999889i	$-0.495251\pi$
$389$	4.82829e47			0.0298367			0.0149184	+	0.999889i	$0.495251\pi$
$390$	6.01504e48	+	1.54948e48i	0.354006	+	0.0911921i
$391$		−	1.34372e48i		−	0.0753271i
$392$	−7.62673e48	+	8.08310e48i	−0.407290	+	0.431661i
$393$	3.85571e49			1.96176
$394$	1.96410e48	−	7.62459e48i	0.0952214	−	0.369648i
$395$		−	1.59632e49i		−	0.737521i
$396$	−8.26958e47	+	1.49861e48i	−0.0364145	+	0.0659901i
$397$	1.63366e49			0.685714			0.342857	−	0.939388i	$-0.388605\pi$
$397$	1.63366e49			0.685714			0.342857	+	0.939388i	$0.388605\pi$
$398$	1.68828e47	+	4.34900e46i	0.00675562	+	0.00174025i
$399$			5.03670e47i			0.0192159i
$400$	−1.25040e49	−	1.98417e49i	−0.454893	−	0.721838i
$401$	−3.91043e49			−1.35669			−0.678347	−	0.734742i	$-0.737303\pi$
$401$	−3.91043e49			−1.35669			−0.678347	+	0.734742i	$0.737303\pi$
$402$	5.38197e47	−	2.08927e48i	0.0178093	−	0.0691354i
$403$			1.40145e49i			0.442365i
$404$	−1.49309e49	−	8.23911e48i	−0.449613	−	0.248104i
$405$	1.44609e49			0.415479
$406$	−4.11843e49	−	1.06091e49i	−1.12911	−	0.290859i
$407$			4.73257e49i			1.23824i
$408$	−1.45915e48	−	1.37677e48i	−0.0364382	−	0.0343809i
$409$	−4.46584e49			−1.06454			−0.532269	−	0.846576i	$-0.678660\pi$
$409$	−4.46584e49			−1.06454			−0.532269	+	0.846576i	$0.678660\pi$
$410$	−5.34380e48	+	2.07446e49i	−0.121607	+	0.472075i
$411$			2.38491e49i			0.518175i
$412$	2.16715e49	−	3.92729e49i	0.449616	−	0.814790i
$413$	−4.83129e49			−0.957221
$414$	−7.49143e48	−	1.92979e48i	−0.141762	−	0.0365178i
$415$		−	1.33042e49i		−	0.240478i
$416$	5.03296e49	−	1.61331e49i	0.869060	−	0.278577i
$417$	6.89626e49			1.13770
$418$	−3.69222e47	+	1.43331e48i	−0.00582020	+	0.0225939i
$419$			1.14898e50i			1.73080i	0.501084	+	0.865399i	$0.332935\pi$
$419$			1.14898e50i			1.73080i	−0.501084	+	0.865399i	$0.667065\pi$
$420$	1.55321e49	+	8.57088e48i	0.223611	+	0.123393i
$421$	−1.26109e49			−0.173535			−0.0867676	−	0.996229i	$-0.527654\pi$
$421$	−1.26109e49			−0.173535			−0.0867676	+	0.996229i	$0.527654\pi$
$422$	−9.46895e49	−	2.43920e49i	−1.24556	−	0.320857i
$423$		−	1.47411e48i		−	0.0185380i
$424$	3.85545e49	−	4.08615e49i	0.463579	−	0.491318i
$425$	3.55577e48			0.0408831
$426$	6.91520e48	−	2.68447e49i	0.0760365	−	0.295173i
$427$		−	4.77799e49i		−	0.502477i
$428$	−3.65448e49	+	6.62263e49i	−0.367616	+	0.666191i
$429$	8.02545e49			0.772291
$430$	2.63524e49	+	6.78838e48i	0.242616	+	0.0624979i
$431$		−	3.89274e49i		−	0.342916i	−0.985191	−	0.171458i	$-0.945152\pi$
$431$		−	3.89274e49i		−	0.342916i	0.985191	−	0.171458i	$-0.0548477\pi$
$432$	9.51603e49	−	5.99688e49i	0.802166	−	0.505515i
$433$	1.05308e50			0.849554			0.424777	−	0.905298i	$-0.360352\pi$
$433$	1.05308e50			0.849554			0.424777	+	0.905298i	$0.360352\pi$
$434$	−9.98467e48	+	3.87603e49i	−0.0770954	+	0.299283i
$435$		−	9.91095e49i		−	0.732520i
$436$	8.32129e49	+	4.59184e49i	0.588773	+	0.324895i
$437$	−6.68958e48			−0.0453160
$438$	−1.74738e50	−	4.50126e49i	−1.13339	−	0.291962i
$439$		−	2.51668e50i		−	1.56316i	−0.623808	−	0.781578i	$-0.714415\pi$
$439$		−	2.51668e50i		−	1.56316i	0.623808	−	0.781578i	$-0.285585\pi$
$440$	3.79172e49	+	3.57765e49i	0.225546	+	0.212812i
$441$	−9.70021e48			−0.0552647
$442$	−1.99890e48	+	7.75971e48i	−0.0109086	+	0.0423470i
$443$			1.36698e50i			0.714648i	0.933981	+	0.357324i	$0.116311\pi$
$443$			1.36698e50i			0.714648i	−0.933981	+	0.357324i	$0.883689\pi$
$444$	−1.54287e50	+	2.79597e50i	−0.772774	+	1.40041i
$445$	−1.50508e50			−0.722301
$446$	2.26601e50	+	5.83724e49i	1.04207	+	0.268439i
$447$		−	2.62447e50i		−	1.15664i
$448$	1.50692e50	−	8.76249e48i	0.636516	−	0.0370122i
$449$	−3.22282e50			−1.30484			−0.652418	−	0.757860i	$-0.726245\pi$
$449$	−3.22282e50			−1.30484			−0.652418	+	0.757860i	$0.726245\pi$
$450$	5.10664e48	−	1.98239e49i	0.0198197	−	0.0769398i
$451$			2.76780e50i			1.02987i
$452$	7.89262e49	+	4.35529e49i	0.281573	+	0.155377i
$453$	−1.00335e50			−0.343233
$454$	−1.26423e50	−	3.25665e49i	−0.414728	−	0.106834i
$455$		−	7.08578e49i		−	0.222931i
$456$	−6.85409e48	+	7.26422e48i	−0.0206832	+	0.0219208i
$457$	−1.25133e50			−0.362212			−0.181106	−	0.983464i	$-0.557968\pi$
$457$	−1.25133e50			−0.362212			−0.181106	+	0.983464i	$0.557968\pi$
$458$	−8.09906e49	+	3.14404e50i	−0.224900	+	0.873060i
$459$			1.70533e49i			0.0454327i
$460$	−1.13836e50	+	2.06292e50i	−0.290991	+	0.527331i
$461$	5.41554e50			1.32839			0.664193	−	0.747561i	$-0.268775\pi$
$461$	5.41554e50			1.32839			0.664193	+	0.747561i	$0.268775\pi$
$462$	2.21963e50	+	5.71777e49i	0.522496	+	0.134595i
$463$			2.68721e50i			0.607104i	0.952815	+	0.303552i	$0.0981727\pi$
$463$			2.68721e50i			0.607104i	−0.952815	+	0.303552i	$0.901827\pi$
$464$	−4.49612e50	−	7.13458e50i	−0.974981	−	1.54713i
$465$	−9.32763e49			−0.194163
$466$	−1.13686e50	+	4.41329e50i	−0.227183	+	0.881921i
$467$		−	6.79338e50i		−	1.30336i	−0.758493	−	0.651681i	$-0.774064\pi$
$467$		−	6.79338e50i		−	1.30336i	0.758493	−	0.651681i	$-0.225936\pi$
$468$	4.03907e49	+	2.22883e49i	0.0744064	+	0.0410588i
$469$	−2.46118e49			−0.0435372
$470$	−4.34777e49	−	1.11999e49i	−0.0738596	−	0.0190263i
$471$			6.67558e50i			1.08916i
$472$	−6.96797e50	−	6.57456e50i	−1.09196	−	1.03031i
$473$	3.51602e50			0.529285
$474$	3.47178e50	−	1.34774e51i	0.502069	−	1.94902i
$475$		−	1.77020e49i		−	0.0245948i
$476$	−1.10569e49	+	2.00372e49i	−0.0147605	+	0.0267488i
$477$	4.90362e49			0.0629025
$478$	1.24988e51	+	3.21969e50i	1.54077	+	0.396902i
$479$		−	4.54455e49i		−	0.0538413i	−0.999638	−	0.0269207i	$-0.991430\pi$
$479$		−	4.54455e49i		−	0.0538413i	0.999638	−	0.0269207i	$-0.00857015\pi$
$480$	1.07378e50	+	3.34979e50i	0.122273	+	0.381447i
$481$	1.27553e51			1.39616
$482$	2.10806e50	−	8.18344e50i	0.221814	−	0.861077i
$483$			1.03595e51i			1.04795i
$484$	−3.10468e50	−	1.71322e50i	−0.301964	−	0.166629i
$485$	3.66859e50			0.343088
$486$	1.99912e50	+	5.14973e49i	0.179783	+	0.0463122i
$487$			1.48221e51i			1.28191i	0.767577	+	0.640957i	$0.221462\pi$
$487$			1.48221e51i			1.28191i	−0.767577	+	0.640957i	$0.778538\pi$
$488$	6.50203e50	−	6.89110e50i	0.540845	−	0.573208i
$489$	−2.23935e51			−1.79165
$490$	−7.36995e49	+	2.86100e50i	−0.0567203	+	0.220187i
$491$			6.80414e49i			0.0503761i	0.999683	+	0.0251881i	$0.00801846\pi$
$491$			6.80414e49i			0.0503761i	−0.999683	+	0.0251881i	$0.991982\pi$
$492$	−9.02333e50	+	1.63520e51i	−0.642732	+	1.16475i
$493$	1.27856e50			0.0876256
$494$	3.86309e49	+	9.95132e48i	0.0254755	+	0.00656249i
$495$			4.55030e49i			0.0288763i
$496$	−6.71466e50	+	4.23149e50i	−0.410084	+	0.258429i
$497$	−3.16233e50			−0.185881
$498$	2.89349e50	−	1.12325e51i	0.163706	−	0.635505i
$499$		−	3.16884e51i		−	1.72580i	−0.505378	−	0.862898i	$-0.668647\pi$
$499$		−	3.16884e51i		−	1.72580i	0.505378	−	0.862898i	$-0.331353\pi$
$500$	−1.18570e51	−	6.54288e50i	−0.621646	−	0.343035i
$501$	−1.32360e51			−0.668098
$502$	−1.63320e51	−	4.20713e50i	−0.793723	−	0.204463i
$503$		−	1.30008e51i		−	0.608386i	−0.952610	−	0.304193i	$-0.901613\pi$
$503$		−	1.30008e51i		−	0.608386i	0.952610	−	0.304193i	$-0.0983867\pi$
$504$	9.58306e49	+	9.04201e49i	0.0431841	+	0.0407460i
$505$	−4.53354e50			−0.196744
$506$	−7.59414e50	+	2.94803e51i	−0.317409	+	1.23218i
$507$			4.34046e50i			0.174737i
$508$	−4.51276e50	+	8.17799e50i	−0.174998	+	0.317129i
$509$	2.56938e51			0.959821			0.479911	−	0.877317i	$-0.340669\pi$
$509$	2.56938e51			0.959821			0.479911	+	0.877317i	$0.340669\pi$
$510$	−5.16464e49	−	1.33041e49i	−0.0185869	−	0.00478799i
$511$			2.05843e51i			0.713739i
$512$	2.29262e51	+	1.92429e51i	0.765953	+	0.642897i
$513$	8.48982e49			0.0273318
$514$	−8.40272e50	+	3.26192e51i	−0.260688	+	1.01199i
$515$		−	1.19246e51i		−	0.356540i
$516$	2.07724e51	+	1.14626e51i	0.598608	+	0.330323i
$517$	−5.80093e50			−0.161130
$518$	3.52778e51	+	9.08756e50i	0.944574	+	0.243322i
$519$		−	4.97071e51i		−	1.28303i
$520$	9.64253e50	−	1.02195e51i	0.239954	−	0.254312i
$521$	2.86439e51			0.687250			0.343625	−	0.939107i	$-0.388345\pi$
$521$	2.86439e51			0.687250			0.343625	+	0.939107i	$0.388345\pi$
$522$	1.83622e50	−	7.12816e50i	0.0424800	−	0.164907i
$523$		−	2.62713e51i		−	0.586069i	−0.956102	−	0.293035i	$-0.905335\pi$
$523$		−	2.62713e51i		−	0.586069i	0.956102	−	0.293035i	$-0.0946651\pi$
$524$	4.21385e51	−	7.63631e51i	0.906536	−	1.64282i
$525$	−2.74133e51			−0.568768
$526$	−1.73688e50	−	4.47421e49i	−0.0347569	−	0.00895339i
$527$		−	1.20331e50i		−	0.0232261i
$528$	2.42319e51	+	3.84518e51i	0.451172	+	0.715933i
$529$	−8.19164e51			−1.47134
$530$	3.72564e50	−	1.44629e51i	0.0645593	−	0.250618i
$531$		−	8.36199e50i		−	0.139802i
$532$	9.97529e49	+	5.50454e49i	0.0160918	+	0.00887974i
$533$	7.45982e51			1.16121
$534$	−1.27071e52	−	3.27334e51i	−1.90880	−	0.491708i
$535$			2.01086e51i			0.291515i
$536$	−3.54966e50	−	3.34925e50i	−0.0496656	−	0.0468616i
$537$	4.44100e51			0.599748
$538$	−9.10830e50	+	3.53583e51i	−0.118734	+	0.460922i
$539$			3.81724e51i			0.480355i
$540$	1.44470e51	−	2.61808e51i	0.175508	−	0.318054i
$541$	−2.10965e50			−0.0247436			−0.0123718	−	0.999923i	$-0.503938\pi$
$541$	−2.10965e50			−0.0247436			−0.0123718	+	0.999923i	$0.503938\pi$
$542$	−5.68590e51	−	1.46469e51i	−0.643891	−	0.165867i
$543$			1.62168e52i			1.77324i
$544$	−4.32141e50	+	1.38523e50i	−0.0456295	+	0.0146265i
$545$	2.52664e51			0.257638
$546$	1.54106e51	−	5.98238e51i	0.151761	−	0.589133i
$547$			3.56277e51i			0.338866i	0.985542	+	0.169433i	$0.0541937\pi$
$547$			3.56277e51i			0.338866i	−0.985542	+	0.169433i	$0.945806\pi$
$548$	4.72336e51	+	2.60643e51i	0.433930	+	0.239451i
$549$	8.26974e50			0.0733867
$550$	−7.80111e51	−	2.00957e51i	−0.668752	−	0.172271i
$551$		−	6.36519e50i		−	0.0527146i
$552$	−1.40975e52	+	1.49410e52i	−1.12797	+	1.19547i
$553$	−1.58765e52			−1.22737
$554$	3.20470e51	−	1.24406e52i	0.239388	−	0.929299i
$555$			8.48956e51i			0.612800i
$556$	7.53684e51	−	1.36582e52i	0.525736	−	0.952735i
$557$	1.02176e52			0.688809			0.344404	−	0.938821i	$-0.388081\pi$
$557$	1.02176e52			0.688809			0.344404	+	0.938821i	$0.388081\pi$
$558$	−6.70863e50	−	1.72814e50i	−0.0437103	−	0.0112598i
$559$		−	9.47642e51i		−	0.596788i
$560$	3.39496e51	−	2.13946e51i	0.206663	−	0.130236i
$561$	−6.89083e50			−0.0405487
$562$	−4.54889e50	+	1.76587e51i	−0.0258771	+	0.100454i
$563$			1.97371e52i			1.08549i	0.839899	+	0.542743i	$0.182614\pi$
$563$			1.97371e52i			1.08549i	−0.839899	+	0.542743i	$0.817386\pi$
$564$	−3.42715e51	−	1.89116e51i	−0.182234	−	0.100560i
$565$	2.39648e51			0.123212
$566$	2.36125e52	+	6.08258e51i	1.17390	+	0.302396i
$567$		−	1.43823e52i		−	0.691435i
$568$	−4.56090e51	−	4.30339e51i	−0.212047	−	0.200075i
$569$	−3.96984e52			−1.78501			−0.892505	−	0.451038i	$-0.851054\pi$
$569$	−3.96984e52			−1.78501			−0.892505	+	0.451038i	$0.851054\pi$
$570$	−6.62332e49	+	2.57116e50i	−0.00288040	+	0.0111817i
$571$		−	9.79434e51i		−	0.411992i	−0.978553	−	0.205996i	$-0.933957\pi$
$571$		−	9.79434e51i		−	0.411992i	0.978553	−	0.205996i	$-0.0660435\pi$
$572$	8.77091e51	−	1.58946e52i	0.356878	−	0.646732i
$573$	4.59035e52			1.80679
$574$	2.06319e52	+	5.31478e51i	0.785621	+	0.202376i
$575$		−	3.64095e52i		−	1.34130i
$576$	1.51661e50	+	2.60818e51i	0.00540564	+	0.0929631i
$577$	2.89703e52			0.999107			0.499553	−	0.866283i	$-0.333497\pi$
$577$	2.89703e52			0.999107			0.499553	+	0.866283i	$0.333497\pi$
$578$	−7.45805e51	+	2.89520e52i	−0.248884	+	0.966163i
$579$		−	4.13772e51i		−	0.133619i
$580$	−1.96289e52	−	1.08316e52i	−0.613427	−	0.338500i
$581$	−1.32320e52			−0.400201
$582$	3.09731e52	+	7.97868e51i	0.906668	+	0.233558i
$583$		−	1.92968e52i		−	0.546742i
$584$	−2.80117e52	+	2.96879e52i	−0.768238	+	0.814208i
$585$	1.22640e51			0.0325591
$586$	−8.23708e51	+	3.19762e52i	−0.211699	+	0.821812i
$587$			2.04019e51i			0.0507628i	0.999678	+	0.0253814i	$0.00808002\pi$
$587$			2.04019e51i			0.0507628i	−0.999678	+	0.0253814i	$0.991920\pi$
$588$	−1.24446e52	+	2.25520e52i	−0.299786	+	0.543270i
$589$	−5.99056e50			−0.0139726
$590$	−2.46630e52	−	6.35320e51i	−0.557004	−	0.143484i
$591$		−	1.82489e52i		−	0.399093i
$592$	3.85130e52	+	6.11136e52i	0.815634	+	1.29427i
$593$	−4.25499e52			−0.872688			−0.436344	−	0.899780i	$-0.643727\pi$
$593$	−4.25499e52			−0.872688			−0.436344	+	0.899780i	$0.643727\pi$
$594$	9.63782e51	−	3.74139e52i	0.191442	−	0.743174i
$595$			6.08400e50i			0.0117049i
$596$	−5.19782e52	−	2.86825e52i	−0.968595	−	0.534488i
$597$	4.04076e50			0.00729374
$598$	7.94559e52	+	2.04679e52i	1.38932	+	0.357890i
$599$			3.17123e52i			0.537178i	0.963255	+	0.268589i	$0.0865573\pi$
$599$			3.17123e52i			0.537178i	−0.963255	+	0.268589i	$0.913443\pi$
$600$	−3.95371e52	−	3.73049e52i	−0.648830	−	0.612198i
$601$	−7.87931e52			−1.25278			−0.626388	−	0.779512i	$-0.715467\pi$
$601$	−7.87931e52			−1.25278			−0.626388	+	0.779512i	$0.715467\pi$
$602$	6.75152e51	−	2.62093e52i	0.104008	−	0.403759i
$603$		−	4.25981e50i		−	0.00635860i
$604$	−1.09655e52	+	1.98717e52i	−0.158609	+	0.287430i
$605$	−9.42690e51			−0.132135
$606$	−3.82757e52	−	9.85984e51i	−0.519929	−	0.133934i
$607$			1.64239e52i			0.216217i	0.994139	+	0.108109i	$0.0344794\pi$
$607$			1.64239e52i			0.216217i	−0.994139	+	0.108109i	$0.965521\pi$
$608$	6.89620e50	+	2.15136e51i	0.00879917	+	0.0274502i
$609$	−9.85713e52			−1.21905
$610$	6.28312e51	−	2.43910e52i	0.0753196	−	0.292390i
$611$			1.56347e52i			0.181680i
$612$	−3.46803e50	−	1.91372e50i	−0.00390666	−	0.00215577i
$613$	1.37490e53			1.50149			0.750743	−	0.660594i	$-0.229696\pi$
$613$	1.37490e53			1.50149			0.750743	+	0.660594i	$0.229696\pi$
$614$	2.11694e52	+	5.45323e51i	0.224135	+	0.0577371i
$615$			4.96505e52i			0.509678i
$616$	3.55822e52	−	3.77113e52i	0.354160	−	0.375352i
$617$	1.15288e53			1.11267			0.556335	−	0.830958i	$-0.312207\pi$
$617$	1.15288e53			1.11267			0.556335	+	0.830958i	$0.312207\pi$
$618$	2.59345e52	−	1.00677e53i	0.242715	−	0.942216i
$619$		−	2.79562e52i		−	0.253721i	−0.991921	−	0.126860i	$-0.959510\pi$
$619$		−	2.79562e52i		−	0.253721i	0.991921	−	0.126860i	$-0.0404900\pi$
$620$	−1.01941e52	+	1.84736e52i	−0.0897232	+	0.162596i
$621$	1.74619e53			1.49056
$622$	−1.03156e53	−	2.65731e52i	−0.854042	−	0.220001i
$623$			1.49690e53i			1.20204i
$624$	1.03636e53	−	6.53101e52i	0.807242	−	0.508713i
$625$	7.69202e52			0.581193
$626$	−1.17559e52	+	4.56360e52i	−0.0861672	+	0.334500i
$627$			3.43052e51i			0.0243937i
$628$	1.32211e53	+	7.29565e52i	0.912084	+	0.503304i
$629$	−1.09520e52			−0.0733044
$630$	3.39191e51	+	8.73757e50i	0.0220279	+	0.00567440i
$631$			1.04936e52i			0.0661254i	0.999453	+	0.0330627i	$0.0105261\pi$
$631$			1.04936e52i			0.0661254i	−0.999453	+	0.0330627i	$0.989474\pi$
$632$	−2.28980e53	−	2.16052e53i	−1.40014	−	1.32109i
$633$	−2.26632e53			−1.34478
$634$	−6.56453e51	+	2.54834e52i	−0.0378014	+	0.146744i
$635$			2.48313e52i			0.138771i
$636$	6.29096e52	−	1.14004e53i	0.341218	−	0.618352i
$637$	1.02883e53			0.541618
$638$	−2.80508e53	−	7.22589e52i	−1.43335	−	0.369231i
$639$		−	5.47335e51i		−	0.0271480i
$640$	7.80786e52	+	1.53431e52i	0.375935	+	0.0738744i
$641$	−2.70023e53			−1.26211			−0.631056	−	0.775737i	$-0.717378\pi$
$641$	−2.70023e53			−1.26211			−0.631056	+	0.775737i	$0.717378\pi$
$642$	−4.37336e52	+	1.69773e53i	−0.198449	+	0.770378i
$643$		−	3.40744e53i		−	1.50114i	−0.660793	−	0.750568i	$-0.729780\pi$
$643$		−	3.40744e53i		−	1.50114i	0.660793	−	0.750568i	$-0.270220\pi$
$644$	2.05172e53	+	1.13217e53i	0.877578	+	0.484263i
$645$	6.30724e52			0.261942
$646$	−3.31693e50	−	8.54442e49i	−0.00133758	−	0.000344560i
$647$			2.23016e53i			0.873283i	0.899636	+	0.436641i	$0.143832\pi$
$647$			2.23016e53i			0.873283i	−0.899636	+	0.436641i	$0.856168\pi$
$648$	1.95719e53	−	2.07430e53i	0.744231	−	0.788764i
$649$	−3.29062e53			−1.21515
$650$	−5.41622e52	+	2.10257e53i	−0.194242	+	0.754043i
$651$			9.27698e52i			0.323123i
$652$	−2.44735e53	+	4.43507e53i	−0.827927	+	1.50036i
$653$	−9.12263e52			−0.299757			−0.149879	−	0.988704i	$-0.547888\pi$
$653$	−9.12263e52			−0.299757			−0.149879	+	0.988704i	$0.547888\pi$
$654$	2.13319e53	+	5.49510e52i	0.680852	+	0.175388i
$655$		−	2.31866e53i		−	0.718872i
$656$	2.25240e53	+	3.57418e53i	0.678380	+	1.07647i
$657$	−3.56273e52			−0.104241
$658$	−1.11390e52	+	4.32416e52i	−0.0316633	+	0.122916i
$659$			2.26086e53i			0.624384i	0.950019	+	0.312192i	$0.101063\pi$
$659$			2.26086e53i			0.624384i	−0.950019	+	0.312192i	$0.898937\pi$
$660$	1.05790e53	+	5.83767e52i	0.283863	+	0.156641i
$661$	5.08886e53			1.32676			0.663381	−	0.748282i	$-0.269121\pi$
$661$	5.08886e53			1.32676			0.663381	+	0.748282i	$0.269121\pi$
$662$	−4.62361e53	−	1.19104e53i	−1.17133	−	0.301735i
$663$			1.85723e52i			0.0457202i
$664$	−1.90839e53	−	1.80065e53i	−0.456536	−	0.430760i
$665$	3.02885e51			0.00704153
$666$	−1.57287e52	+	6.10587e52i	−0.0355372	+	0.137955i
$667$		−	1.30919e54i		−	2.87483i
$668$	−1.44655e53	+	2.62142e53i	−0.308730	+	0.559479i
$669$	5.42351e53			1.12508
$670$	−1.25640e52	−	3.23649e51i	−0.0253341	−	0.00652608i
$671$		−	3.25432e53i		−	0.637869i
$672$	3.33160e53	−	1.06795e53i	0.634800	−	0.203485i
$673$	−9.70945e53			−1.79849			−0.899246	−	0.437443i	$-0.855884\pi$
$673$	−9.70945e53			−1.79849			−0.899246	+	0.437443i	$0.855884\pi$
$674$	2.14868e53	−	8.34113e53i	0.386931	−	1.50206i
$675$			4.62077e53i			0.808989i
$676$	8.59638e52	+	4.74364e52i	0.146328	+	0.0807466i
$677$	9.12822e53			1.51078			0.755391	−	0.655275i	$-0.227447\pi$
$677$	9.12822e53			1.51078			0.755391	+	0.655275i	$0.227447\pi$
$678$	2.02330e53	+	5.21202e52i	0.325609	+	0.0838768i
$679$		−	3.64866e53i		−	0.570963i
$680$	−8.27929e51	+	8.77470e51i	−0.0125986	+	0.0133525i
$681$	−3.02582e53			−0.447763
$682$	−6.80061e52	+	2.63998e53i	−0.0978689	+	0.379925i
$683$			5.74161e53i			0.803601i	0.915727	+	0.401801i	$0.131616\pi$
$683$			5.74161e53i			0.803601i	−0.915727	+	0.401801i	$0.868384\pi$
$684$	−9.52725e50	+	1.72652e51i	−0.00129689	+	0.00235021i
$685$	1.43418e53			0.189881
$686$	7.64003e53	+	1.96807e53i	0.983868	+	0.253445i
$687$			7.52502e53i			0.942605i
$688$	4.54038e53	−	2.86129e53i	0.553238	−	0.348643i
$689$	−5.20090e53			−0.616472
$690$	−1.36228e53	+	5.28836e53i	−0.157085	+	0.609801i
$691$			1.18177e54i			1.32572i	0.748744	+	0.662860i	$0.230657\pi$
$691$			1.18177e54i			1.32572i	−0.748744	+	0.662860i	$0.769343\pi$
$692$	−9.84459e53	−	5.43242e53i	−1.07444	−	0.592895i
$693$	4.52559e52			0.0480556
$694$	8.63495e53	+	2.22436e53i	0.892133	+	0.229814i
$695$		−	4.14711e53i		−	0.416903i
$696$	−1.42165e54	−	1.34139e54i	−1.39065	−	1.31214i
$697$	−6.40517e52			−0.0609688
$698$	2.67635e53	−	1.03895e54i	0.247908	−	0.962374i
$699$			1.05629e54i			0.952171i
$700$	−2.99597e53	+	5.42927e53i	−0.262830	+	0.476298i
$701$	4.63765e53			0.395964			0.197982	−	0.980206i	$-0.436561\pi$
$701$	4.63765e53			0.395964			0.197982	+	0.980206i	$0.436561\pi$
$702$	−1.00838e54	−	2.59760e53i	−0.837956	−	0.215858i
$703$			5.45232e52i			0.0440991i
$704$	1.02637e54	−	5.96818e52i	0.808025	−	0.0469852i
$705$	−1.04060e53			−0.0797430
$706$	−1.08600e53	+	4.21584e53i	−0.0810105	+	0.314481i
$707$			4.50892e53i			0.327419i
$708$	−1.94408e54	−	1.07278e54i	−1.37430	−	0.758363i
$709$	−6.87957e53			−0.473460			−0.236730	−	0.971576i	$-0.576076\pi$
$709$	−6.87957e53			−0.473460			−0.236730	+	0.971576i	$0.576076\pi$
$710$	−1.61432e53	−	4.15850e52i	−0.108164	−	0.0278630i
$711$		−	2.74790e53i		−	0.179258i
$712$	−2.03703e54	+	2.15892e54i	−1.29383	+	1.37125i
$713$	−1.23214e54			−0.762005
$714$	−1.32319e52	+	5.13660e52i	−0.00796812	+	0.0309321i
$715$		−	4.82616e53i		−	0.283000i
$716$	4.85351e53	−	8.79549e53i	0.277146	−	0.502241i
$717$	2.99149e54			1.66350
$718$	2.33430e54	+	6.01316e53i	1.26413	+	0.325640i
$719$			1.88968e54i			0.996642i	0.866993	+	0.498321i	$0.166050\pi$
$719$			1.88968e54i			0.996642i	−0.866993	+	0.498321i	$0.833950\pi$
$720$	3.70298e52	+	5.87600e52i	0.0190210	+	0.0301831i
$721$	−1.18599e54			−0.593349
$722$	5.11494e53	−	1.98561e54i	0.249249	−	0.967581i
$723$		−	1.95864e54i		−	0.929667i
$724$	3.21177e54	+	1.77231e54i	1.48495	+	0.819421i
$725$	3.46439e54			1.56029
$726$	−7.95894e53	−	2.05023e53i	−0.349188	−	0.0899510i
$727$		−	3.93284e54i		−	1.68094i	−0.541857	−	0.840471i	$-0.682279\pi$
$727$		−	3.93284e54i		−	1.68094i	0.541857	−	0.840471i	$-0.317721\pi$
$728$	−1.01640e54	−	9.59017e53i	−0.423223	−	0.399328i
$729$	−2.19473e54			−0.890345
$730$	−2.70686e53	+	1.05080e54i	−0.106987	+	0.415322i
$731$			8.13666e52i			0.0313340i
$732$	1.06094e54	−	1.92263e54i	0.398090	−	0.721415i
$733$	−1.59209e54			−0.582094			−0.291047	−	0.956709i	$-0.594004\pi$
$733$	−1.59209e54			−0.582094			−0.291047	+	0.956709i	$0.594004\pi$
$734$	3.06887e54	+	7.90540e53i	1.09333	+	0.281643i
$735$			6.84759e53i			0.237727i
$736$	1.41841e54	+	4.42492e54i	0.479869	+	1.49702i
$737$	−1.67632e53			−0.0552683
$738$	−9.19881e52	+	3.57097e53i	−0.0295570	+	0.114740i
$739$			2.11977e53i			0.0663810i	0.999449	+	0.0331905i	$0.0105668\pi$
$739$			2.11977e53i			0.0663810i	−0.999449	+	0.0331905i	$0.989433\pi$
$740$	1.68138e54	+	9.27814e53i	0.513171	+	0.283177i
$741$	9.24600e52			0.0275048
$742$	−1.43843e54	−	3.70540e53i	−0.417076	−	0.107439i
$743$		−	2.29917e54i		−	0.649807i	−0.945747	−	0.324903i	$-0.894668\pi$
$743$		−	2.29917e54i		−	0.649807i	0.945747	−	0.324903i	$-0.105332\pi$
$744$	−1.26244e54	+	1.33798e54i	−0.347796	+	0.368607i
$745$	−1.57824e54			−0.423842
$746$	2.42476e53	−	9.41287e53i	0.0634791	−	0.246425i
$747$		−	2.29019e53i		−	0.0584494i
$748$	−7.53089e52	+	1.36474e53i	−0.0187377	+	0.0339563i
$749$	1.99994e54			0.485136
$750$	−3.03957e54	−	7.82994e53i	−0.718866	−	0.185180i
$751$		−	7.06622e54i		−	1.62940i	−0.579882	−	0.814701i	$-0.696901\pi$
$751$		−	7.06622e54i		−	1.62940i	0.579882	−	0.814701i	$-0.303099\pi$
$752$	−7.49098e53	+	4.72072e53i	−0.168422	+	0.106138i
$753$	−3.90894e54			−0.856948
$754$	−1.94753e54	+	7.56030e54i	−0.416322	+	1.61616i
$755$			6.03374e53i			0.125775i
$756$	−2.60386e54	−	1.43686e54i	−0.529302	−	0.292078i
$757$	3.95297e54			0.783614			0.391807	−	0.920047i	$-0.371850\pi$
$757$	3.95297e54			0.783614			0.391807	+	0.920047i	$0.371850\pi$
$758$	−7.32529e54	−	1.88700e54i	−1.41615	−	0.364801i
$759$			7.05589e54i			1.33033i
$760$	4.36839e52	+	4.12175e52i	0.00803272	+	0.00757920i
$761$	−1.92105e54			−0.344533			−0.172266	−	0.985050i	$-0.555109\pi$
$761$	−1.92105e54			−0.344533			−0.172266	+	0.985050i	$0.555109\pi$
$762$	−5.40047e53	+	2.09645e54i	−0.0944686	+	0.366725i
$763$		−	2.51292e54i		−	0.428758i
$764$	5.01674e54	−	9.09129e54i	0.834925	−	1.51304i
$765$	−1.05302e52			−0.00170950
$766$	−1.30630e54	−	3.36502e53i	−0.206869	−	0.0532895i
$767$			8.86892e54i			1.37012i
$768$	6.25832e54	+	2.99349e54i	0.943181	+	0.451144i
$769$	−7.19087e54			−1.05726			−0.528629	−	0.848853i	$-0.677294\pi$
$769$	−7.19087e54			−1.05726			−0.528629	+	0.848853i	$0.677294\pi$
$770$	3.43842e53	−	1.33479e54i	0.0493213	−	0.191465i
$771$			7.80716e54i			1.09260i
$772$	−8.19483e53	−	4.52206e53i	−0.111895	−	0.0617458i
$773$	5.65460e54			0.753341			0.376671	−	0.926347i	$-0.377069\pi$
$773$	5.65460e54			0.753341			0.376671	+	0.926347i	$0.377069\pi$
$774$	4.53630e53	+	1.16855e53i	0.0589689	+	0.0151904i
$775$		−	3.26049e54i		−	0.413572i
$776$	4.96521e54	−	5.26231e54i	0.614561	−	0.651334i
$777$	8.44346e54			1.01981
$778$	6.31478e52	−	2.45139e53i	0.00744296	−	0.0288935i
$779$			3.18874e53i			0.0366782i
$780$	1.57338e54	−	2.85126e54i	0.176618	−	0.320066i
$781$	−2.15388e54			−0.235967
$782$	−6.82226e53	−	1.75741e53i	−0.0729457	−	0.0187908i
$783$			1.66151e55i			1.73392i
$784$	3.10642e54	+	4.92936e54i	0.316413	+	0.502094i
$785$	4.01440e54			0.399114
$786$	5.04277e54	−	1.95759e55i	0.489374	−	1.89974i
$787$		−	1.74093e55i		−	1.64915i	−0.565750	−	0.824577i	$-0.691413\pi$
$787$		−	1.74093e55i		−	1.64915i	0.565750	−	0.824577i	$-0.308587\pi$
$788$	−3.61423e54	−	1.99440e54i	−0.334208	−	0.184422i
$789$	−4.15709e53			−0.0375255
$790$	−8.10471e54	−	2.08777e54i	−0.714205	−	0.183979i
$791$		−	2.38346e54i		−	0.205048i
$792$	6.52707e53	+	6.15856e53i	0.0548201	+	0.0517250i
$793$	−8.77108e54			−0.719222
$794$	2.13662e54	−	8.29433e54i	0.171056	−	0.664036i
$795$		−	3.46157e54i		−	0.270581i
$796$	4.41609e52	−	8.00280e52i	0.00337046	−	0.00610793i
$797$	1.50341e55			1.12039			0.560195	−	0.828361i	$-0.310726\pi$
$797$	1.50341e55			1.12039			0.560195	+	0.828361i	$0.310726\pi$
$798$	2.55720e53	+	6.58735e52i	0.0186084	+	0.00479353i
$799$		−	1.34243e53i		−	0.00953902i
$800$	−1.17093e55	+	3.75340e54i	−0.812493	+	0.260445i
$801$	−2.59084e54			−0.175559
$802$	−5.11434e54	+	1.98538e55i	−0.338436	+	1.31380i
$803$			1.40201e55i			0.906056i
$804$	−9.90363e53	−	5.46500e53i	−0.0625071	−	0.0344925i
$805$	6.22974e54			0.384015
$806$	7.11533e54	+	1.83291e54i	0.428380	+	0.110351i
$807$			8.46273e54i			0.497638i
$808$	−6.13587e54	+	6.50302e54i	−0.352420	+	0.373508i
$809$	3.16925e54			0.177801			0.0889006	−	0.996040i	$-0.471665\pi$
$809$	3.16925e54			0.177801			0.0889006	+	0.996040i	$0.471665\pi$
$810$	1.89129e54	−	7.34197e54i	0.103644	−	0.402344i
$811$		−	2.98626e55i		−	1.59857i	−0.600954	−	0.799283i	$-0.705213\pi$
$811$		−	2.98626e55i		−	1.59857i	0.600954	−	0.799283i	$-0.294787\pi$
$812$	−1.07727e55	+	1.95223e55i	−0.563328	+	1.02086i
$813$	−1.36088e55			−0.695181
$814$	2.40279e55	+	6.18959e54i	1.19909	+	0.308886i
$815$			1.34665e55i			0.656536i
$816$	−8.89841e53	+	5.60767e53i	−0.0423838	+	0.0267097i
$817$	4.05075e53			0.0188502
$818$	−5.84075e54	+	2.26737e55i	−0.265556	+	1.03088i
$819$		−	1.21974e54i		−	0.0541845i
$820$	9.83338e54	+	5.42624e54i	0.426815	+	0.235524i
$821$	−3.08324e55			−1.30764			−0.653818	−	0.756652i	$-0.726834\pi$
$821$	−3.08324e55			−1.30764			−0.653818	+	0.756652i	$0.726834\pi$
$822$	1.21085e55	+	3.11915e54i	0.501793	+	0.129262i
$823$		−	3.32552e55i		−	1.34667i	−0.739336	−	0.673337i	$-0.764860\pi$
$823$		−	3.32552e55i		−	1.34667i	0.739336	−	0.673337i	$-0.235140\pi$
$824$	−1.71050e55	−	1.61393e55i	−0.676871	−	0.638656i
$825$	−1.86714e55			−0.722023
$826$	−6.31870e54	+	2.45291e55i	−0.238785	+	0.926960i
$827$			6.70226e54i			0.247524i	0.992312	+	0.123762i	$0.0394959\pi$
$827$			6.70226e54i			0.247524i	−0.992312	+	0.123762i	$0.960504\pi$
$828$	−1.95956e54	+	3.55111e54i	−0.0707267	+	0.128170i
$829$	−2.74877e55			−0.969620			−0.484810	−	0.874619i	$-0.661111\pi$
$829$	−2.74877e55			−0.969620			−0.484810	+	0.874619i	$0.661111\pi$
$830$	−6.75474e54	−	1.74002e54i	−0.232876	−	0.0599889i
$831$		−	2.97756e55i		−	1.00332i
$832$	−1.60855e54	−	2.76630e55i	−0.0529776	−	0.911079i
$833$	−8.83374e53			−0.0284374
$834$	9.01942e54	−	3.50132e55i	0.283807	−	1.10174i
$835$			7.95956e54i			0.244819i
$836$	6.79422e53	+	3.74917e53i	0.0204277	+	0.0112724i
$837$	1.56372e55			0.459595
$838$	5.83353e55	+	1.50272e55i	1.67608	+	0.431759i
$839$		−	3.36217e55i		−	0.944371i	−0.881499	−	0.472185i	$-0.843465\pi$
$839$		−	3.36217e55i		−	0.944371i	0.881499	−	0.472185i	$-0.156535\pi$
$840$	6.38295e54	−	6.76488e54i	0.175273	−	0.185761i
$841$	8.73209e55			2.34420
$842$	−1.64935e54	+	6.40274e54i	−0.0432895	+	0.168049i
$843$			4.22647e54i			0.108456i
$844$	−2.47683e55	+	4.48849e55i	−0.621427	+	1.12614i
$845$	2.61017e54			0.0640311
$846$	−7.48424e53	−	1.92794e53i	−0.0179519	−	0.00462442i
$847$			9.37571e54i			0.219897i
$848$	−1.57035e55	−	2.49188e55i	−0.360143	−	0.571485i
$849$	5.65146e55			1.26740
$850$	4.65048e53	−	1.80531e54i	0.0101986	−	0.0395906i
$851$			1.12143e56i			2.40498i
$852$	−1.27250e55	−	7.02188e54i	−0.266873	−	0.147265i
$853$	6.69387e54			0.137292			0.0686461	−	0.997641i	$-0.478132\pi$
$853$	6.69387e54			0.137292			0.0686461	+	0.997641i	$0.478132\pi$
$854$	−2.42585e55	−	6.24900e54i	−0.486591	−	0.125346i
$855$			5.24233e52i			0.00102841i
$856$	2.88444e55	+	2.72158e55i	0.553426	+	0.522180i
$857$	−6.80760e55			−1.27749			−0.638747	−	0.769417i	$-0.720547\pi$
$857$	−6.80760e55			−1.27749			−0.638747	+	0.769417i	$0.720547\pi$
$858$	1.04962e55	−	4.07463e55i	0.192653	−	0.747876i
$859$		−	9.19214e55i		−	1.65024i	−0.564959	−	0.825119i	$-0.691108\pi$
$859$		−	9.19214e55i		−	1.65024i	0.564959	−	0.825119i	$-0.308892\pi$
$860$	6.89310e54	−	1.24916e55i	0.121044	−	0.219355i
$861$	4.93809e55			0.848201
$862$	−1.97640e55	−	5.09120e54i	−0.332075	−	0.0855425i
$863$			4.40945e55i			0.724734i	0.932035	+	0.362367i	$0.118031\pi$
$863$			4.40945e55i			0.724734i	−0.932035	+	0.362367i	$0.881969\pi$
$864$	−1.80012e55	−	5.61573e55i	−0.289428	−	0.902911i
$865$	−2.98917e55			−0.470158
$866$	1.37729e55	−	5.34662e55i	0.211927	−	0.822696i
$867$			6.92945e55i			1.04312i
$868$	1.83733e55	+	1.01387e55i	0.270590	+	0.149316i
$869$	−1.08135e56			−1.55809
$870$	−5.03192e55	−	1.29622e55i	−0.709362	−	0.182732i
$871$			4.51806e54i			0.0623170i
$872$	3.41965e55	−	3.62428e55i	0.461497	−	0.489112i
$873$	6.31510e54			0.0833891
$874$	−8.74910e53	+	3.39639e54i	−0.0113044	+	0.0438833i
$875$			3.58064e55i			0.452697i
$876$	−4.57069e55	+	8.28298e55i	−0.565463	+	1.02473i
$877$	−7.01400e55			−0.849129			−0.424564	−	0.905398i	$-0.639573\pi$
$877$	−7.01400e55			−0.849129			−0.424564	+	0.905398i	$0.639573\pi$
$878$	−1.27775e56	−	3.29149e55i	−1.51374	−	0.389939i
$879$			7.65326e55i			0.887274i
$880$	2.31233e55	−	1.45720e55i	0.262348	−	0.165329i
$881$	9.27731e55			1.03010			0.515051	−	0.857160i	$-0.327773\pi$
$881$	9.27731e55			1.03010			0.515051	+	0.857160i	$0.327773\pi$
$882$	−1.26866e54	+	4.92493e54i	−0.0137861	+	0.0535176i
$883$			1.16178e56i			1.23558i	0.786342	+	0.617792i	$0.211972\pi$
$883$			1.16178e56i			1.23558i	−0.786342	+	0.617792i	$0.788028\pi$
$884$	3.67828e54	+	2.02974e54i	0.0382870	+	0.0211275i
$885$	−5.90291e55			−0.601373
$886$	6.94035e55	+	1.78784e55i	0.692055	+	0.178273i
$887$		−	1.34404e56i		−	1.31179i	−0.754853	−	0.655894i	$-0.772292\pi$
$887$		−	1.34404e56i		−	1.31179i	0.754853	−	0.655894i	$-0.227708\pi$
$888$	1.21777e56	+	1.14901e56i	1.16337	+	1.09769i
$889$	2.46964e55			0.230941
$890$	−1.96844e55	+	7.64147e55i	−0.180183	+	0.699466i
$891$		−	9.79588e55i		−	0.877742i
$892$	5.92728e55	−	1.07414e56i	0.519904	−	0.942166i
$893$	−6.68316e53			−0.00573857
$894$	−1.33248e56	−	3.43247e55i	−1.12007	−	0.288532i
$895$		−	2.67062e55i		−	0.219773i
$896$	1.52598e55	−	7.76546e55i	0.122941	−	0.625626i
$897$	1.90172e56			1.49999
$898$	−4.21503e55	+	1.63627e56i	−0.325500	+	1.26358i
$899$		−	1.17239e56i		−	0.886416i
$900$	−9.39696e54	−	5.18541e54i	−0.0695633	−	0.0383863i
$901$	4.46561e54			0.0323675
$902$	1.40525e56	+	3.61993e55i	0.997308	+	0.256907i
$903$		−	6.27299e55i		−	0.435921i
$904$	3.24349e55	−	3.43757e55i	0.220705	−	0.233911i
$905$	9.75206e55			0.649790
$906$	−1.31226e55	+	5.09416e55i	−0.0856216	+	0.332382i
$907$		−	1.97114e56i		−	1.25944i	−0.776820	−	0.629722i	$-0.783169\pi$
$907$		−	1.97114e56i		−	1.25944i	0.776820	−	0.629722i	$-0.216831\pi$
$908$	−3.30688e55	+	5.99271e55i	−0.206913	+	0.374966i
$909$	−7.80403e54			−0.0478195
$910$	−3.59754e55	−	9.26727e54i	−0.215883	−	0.0556116i
$911$			1.01191e56i			0.594692i	0.954770	+	0.297346i	$0.0961015\pi$
$911$			1.01191e56i			0.594692i	−0.954770	+	0.297346i	$0.903899\pi$
$912$	2.79171e54	+	4.42998e54i	0.0160683	+	0.0254976i
$913$	−9.01237e55			−0.508036
$914$	−1.63657e55	+	6.35314e55i	−0.0903560	+	0.350761i
$915$		−	5.83779e55i		−	0.315680i
$916$	1.49035e56	+	8.22400e55i	0.789356	+	0.435581i
$917$	−2.30606e56			−1.19634
$918$	8.65821e54	+	2.23036e54i	0.0439964	+	0.0113335i
$919$		−	6.29072e55i		−	0.313116i	−0.987669	−	0.156558i	$-0.949960\pi$
$919$		−	6.29072e55i		−	0.313116i	0.987669	−	0.156558i	$-0.0500399\pi$
$920$	8.98489e55	+	8.47761e55i	0.438071	+	0.413338i
$921$	5.06672e55			0.241988
$922$	7.08283e55	−	2.74954e56i	0.331375	−	1.28639i
$923$			5.80517e55i			0.266062i
$924$	5.80597e55	−	1.05215e56i	0.260680	−	0.472402i
$925$	−2.96754e56			−1.30528
$926$	1.36433e56	+	3.51453e55i	0.587911	+	0.151446i
$927$		−	2.05271e55i		−	0.0866586i
$928$	−4.21035e56	+	1.34963e56i	−1.74143	+	0.558216i
$929$	1.94099e56			0.786548			0.393274	−	0.919421i	$-0.371342\pi$
$929$	1.94099e56			0.786548			0.393274	+	0.919421i	$0.371342\pi$
$930$	−1.21993e55	+	4.73576e55i	−0.0484351	+	0.188024i
$931$			4.39778e54i			0.0171076i
$932$	2.09200e56	+	1.15440e56i	0.797368	+	0.440002i
$933$	−2.46897e56			−0.922072
$934$	−3.44909e56	−	8.88485e55i	−1.26216	−	0.325132i
$935$			4.14384e54i			0.0148588i
$936$	1.65986e55	−	1.75919e55i	0.0583219	−	0.0618117i
$937$	1.42702e56			0.491334			0.245667	−	0.969354i	$-0.420993\pi$
$937$	1.42702e56			0.491334			0.245667	+	0.969354i	$0.420993\pi$
$938$	−3.21891e54	+	1.24958e55i	−0.0108606	+	0.0421608i
$939$			1.09226e56i			0.361145i
$940$	−1.13726e55	+	2.06094e55i	−0.0368495	+	0.0667784i
$941$	1.05206e56			0.334069			0.167035	−	0.985951i	$-0.446581\pi$
$941$	1.05206e56			0.334069			0.167035	+	0.985951i	$0.446581\pi$
$942$	3.38928e56	+	8.73079e55i	1.05473	+	0.271698i
$943$			6.55860e56i			2.00027i
$944$	−4.24931e56	+	2.67786e56i	−1.27014	+	0.800424i
$945$	−7.90624e55			−0.231614
$946$	4.59849e55	−	1.78513e56i	0.132033	−	0.512552i
$947$			1.85655e56i			0.522466i	0.965276	+	0.261233i	$0.0841290\pi$
$947$			1.85655e56i			0.522466i	−0.965276	+	0.261233i	$0.915871\pi$
$948$	−6.38858e56	−	3.52533e56i	−1.76216	−	0.972393i
$949$	3.77871e56			1.02161
$950$	−8.98754e54	−	2.31519e54i	−0.0238173	−	0.00613534i
$951$			6.09925e55i			0.158433i
$952$	8.72705e54	+	8.23433e54i	0.0222211	+	0.0209665i
$953$	5.16017e56			1.28795			0.643975	−	0.765046i	$-0.277284\pi$
$953$	5.16017e56			1.28795			0.643975	+	0.765046i	$0.277284\pi$
$954$	6.41331e54	−	2.48963e55i	0.0156914	−	0.0609139i
$955$		−	2.76044e56i		−	0.662085i
$956$	3.26936e56	−	5.92470e56i	0.768709	−	1.39305i
$957$	−6.71374e56			−1.54753
$958$	−2.30733e55	−	5.94368e54i	−0.0521392	−	0.0134311i
$959$		−	1.42639e56i		−	0.315998i
$960$	1.84117e56	−	1.07061e55i	0.399890	−	0.0232529i
$961$	3.59279e56			0.765046
$962$	1.66823e56	−	6.47603e56i	0.348280	−	1.35202i
$963$			3.46150e55i			0.0708541i
$964$	−3.87913e56	−	2.14057e56i	−0.778522	−	0.429602i
$965$	−2.48824e55			−0.0489636
$966$	5.25964e56	+	1.35489e56i	1.01482	+	0.261419i
$967$			3.90929e56i			0.739597i	0.929112	+	0.369799i	$0.120573\pi$
$967$			3.90929e56i			0.739597i	−0.929112	+	0.369799i	$0.879427\pi$
$968$	−1.27587e56	+	1.35222e56i	−0.236688	+	0.250851i
$969$	−7.93881e53			−0.00144412
$970$	4.79803e55	−	1.86259e56i	0.0855855	−	0.332242i
$971$		−	8.16200e56i		−	1.42768i	−0.700308	−	0.713841i	$-0.746954\pi$
$971$		−	8.16200e56i		−	1.42768i	0.700308	−	0.713841i	$-0.253046\pi$
$972$	5.22917e55	−	9.47627e55i	0.0896962	−	0.162547i
$973$	−4.12459e56			−0.693804
$974$	7.52536e56	+	1.93853e56i	1.24139	+	0.319781i
$975$			5.03233e56i			0.814108i
$976$	−2.64832e56	−	4.20243e56i	−0.420169	−	0.666737i
$977$	4.37423e56			0.680620			0.340310	−	0.940313i	$-0.389468\pi$
$977$	4.37423e56			0.680620			0.340310	+	0.940313i	$0.389468\pi$
$978$	−2.92877e56	+	1.13695e57i	−0.446938	+	1.73501i
$979$			1.01955e57i			1.52594i
$980$	1.35618e56	+	7.48364e55i	0.199077	+	0.109854i
$981$	4.34935e55			0.0626201
$982$	3.45455e55	+	8.89893e54i	0.0487835	+	0.0125667i
$983$		−	1.32709e57i		−	1.83816i	−0.394074	−	0.919079i	$-0.628934\pi$
$983$		−	1.32709e57i		−	1.83816i	0.394074	−	0.919079i	$-0.371066\pi$
$984$	7.12199e56	+	6.71989e56i	0.967597	+	0.912968i
$985$	−1.09741e56			−0.146245
$986$	1.67220e55	−	6.49144e55i	0.0218588	−	0.0848554i
$987$			1.03495e56i			0.132707i
$988$	1.01048e55	−	1.83119e55i	0.0127100	−	0.0230330i
$989$	8.33157e56			1.02801
$990$	2.31025e55	+	5.95120e54i	0.0279634	+	0.00720338i
$991$			6.86443e55i			0.0815089i	0.999169	+	0.0407545i	$0.0129761\pi$
$991$			6.86443e55i			0.0815089i	−0.999169	+	0.0407545i	$0.987024\pi$
$992$	1.27019e56	+	3.96255e56i	0.147961	+	0.461586i
$993$	−1.10662e57			−1.26463
$994$	−4.13592e55	+	1.60556e56i	−0.0463693	+	0.180005i
$995$		−	2.42994e54i		−	0.00267274i
$996$	−5.32446e56	−	2.93813e56i	−0.574576	−	0.317062i
$997$	−8.32531e56			−0.881439			−0.440719	−	0.897645i	$-0.645277\pi$
$997$	−8.32531e56			−0.881439			−0.440719	+	0.897645i	$0.645277\pi$
$998$	−1.60886e57	−	4.14443e56i	−1.67124	−	0.430511i
$999$		−	1.42322e57i		−	1.45054i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.39.b.a.3.11	✓	18
4.3	odd	2	inner	4.39.b.a.3.12	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.39.b.a.3.11	✓	18	1.1	even	1	trivial
4.39.b.a.3.12	yes	18	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:	\( k \)	\(=\)	\( 39 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(130787. - 507713. i) q^{2} -1.21517e9i q^{3} +(-2.40667e11 - 1.32805e11i) q^{4} -7.30752e12 q^{5} +(-6.16959e14 - 1.58929e14i) q^{6} +7.26783e15i q^{7} +(-9.89028e16 + 1.04821e17i) q^{8} -1.25791e17 q^{9} +O(q^{10})\)	\(q+(130787. - 507713. i) q^{2} -1.21517e9i q^{3} +(-2.40667e11 - 1.32805e11i) q^{4} -7.30752e12 q^{5} +(-6.16959e14 - 1.58929e14i) q^{6} +7.26783e15i q^{7} +(-9.89028e16 + 1.04821e17i) q^{8} -1.25791e17 q^{9} +(-9.55728e17 + 3.71012e18i) q^{10} +4.95016e19i q^{11} +(-1.61380e20 + 2.92452e20i) q^{12} +1.33417e21 q^{13} +(3.68997e21 + 9.50538e20i) q^{14} +8.87989e21i q^{15} +(4.02837e22 + 6.39235e22i) q^{16} -1.14555e22 q^{17} +(-1.64519e22 + 6.38660e22i) q^{18} +5.70300e22i q^{19} +(1.75868e24 + 9.70472e23i) q^{20} +8.83167e24 q^{21} +(2.51326e25 + 6.47416e24i) q^{22} +1.17299e26i q^{23} +(1.27375e26 + 1.20184e26i) q^{24} -3.10398e26 q^{25} +(1.74493e26 - 6.77378e26i) q^{26} -1.48866e27i q^{27} +(9.65202e26 - 1.74913e27i) q^{28} -1.11611e28 q^{29} +(4.50844e27 + 1.16137e27i) q^{30} +1.05042e28i q^{31} +(3.77234e28 - 1.20922e28i) q^{32} +6.01529e28 q^{33} +(-1.49823e27 + 5.81611e27i) q^{34} -5.31098e28i q^{35} +(3.02739e28 + 1.67057e28i) q^{36} +9.56044e29 q^{37} +(2.89549e28 + 7.45878e27i) q^{38} -1.62125e30i q^{39} +(7.22734e29 - 7.65980e29i) q^{40} +5.59134e30 q^{41} +(1.15507e30 - 4.48395e30i) q^{42} -7.10284e30i q^{43} +(6.57404e30 - 1.19134e31i) q^{44} +9.19223e29 q^{45} +(5.95544e31 + 1.53412e31i) q^{46} +1.17187e31i q^{47} +(7.76780e31 - 4.89517e31i) q^{48} +7.71134e31 q^{49} +(-4.05960e31 + 1.57593e32i) q^{50} +1.39204e31i q^{51} +(-3.21092e32 - 1.77185e32i) q^{52} -3.89822e32 q^{53} +(-7.55812e32 - 1.94697e32i) q^{54} -3.61734e32i q^{55} +(-7.61821e32 - 7.18809e32i) q^{56} +6.93013e31 q^{57} +(-1.45973e33 + 5.66665e33i) q^{58} +6.64750e33i q^{59} +(1.17929e33 - 2.13710e33i) q^{60} -6.57417e33 q^{61} +(5.33313e33 + 1.37382e33i) q^{62} -9.14232e32i q^{63} +(-1.20565e33 - 2.07342e34i) q^{64} -9.74950e33 q^{65} +(7.86722e33 - 3.05404e34i) q^{66} +3.38641e33i q^{67} +(2.75697e33 + 1.52134e33i) q^{68} +1.42539e35 q^{69} +(-2.69645e34 - 6.94607e33i) q^{70} +4.35113e34i q^{71} +(1.24411e34 - 1.31856e34i) q^{72} +2.83225e35 q^{73} +(1.25038e35 - 4.85396e35i) q^{74} +3.77187e35i q^{75} +(7.57385e33 - 1.37253e34i) q^{76} -3.59769e35 q^{77} +(-8.23131e35 - 2.12039e35i) q^{78} +2.18449e36i q^{79} +(-2.94374e35 - 4.67122e35i) q^{80} -1.97890e36 q^{81} +(7.31275e35 - 2.83880e36i) q^{82} +1.82062e36i q^{83} +(-2.12549e36 - 1.17289e36i) q^{84} +8.37113e34 q^{85} +(-3.60620e36 - 9.28959e35i) q^{86} +1.35627e37i q^{87} +(-5.18880e36 - 4.89585e36i) q^{88} +2.05963e37 q^{89} +(1.20222e35 - 4.66702e35i) q^{90} +9.69656e36i q^{91} +(1.55779e37 - 2.82301e37i) q^{92} +1.27644e37 q^{93} +(5.94972e36 + 1.53265e36i) q^{94} -4.16748e35i q^{95} +(-1.46941e37 - 4.58404e37i) q^{96} -5.02029e37 q^{97} +(1.00854e37 - 3.91515e37i) q^{98} -6.22688e36i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 364228 q^{2} + 200567335824 q^{4} - 8991287507020 q^{5} + 817599417526752 q^{6} + 90\!\cdots\!32 q^{8}+ \cdots - 75\!\cdots\!14 q^{9}+O(q^{10}) \) 18 * q + 364228 * q^2 + 200567335824 * q^4 - 8991287507020 * q^5 + 817599417526752 * q^6 + 90410803724813632 * q^8 - 7529771892957713214 * q^9	\( 18 q + 364228 q^{2} + 200567335824 q^{4} - 8991287507020 q^{5} + 817599417526752 q^{6} + 90\!\cdots\!32 q^{8}+ \cdots + 79\!\cdots\!72 q^{98}+O(q^{100}) \) 18 * q + 364228 * q^2 + 200567335824 * q^4 - 8991287507020 * q^5 + 817599417526752 * q^6 + 90410803724813632 * q^8 - 7529771892957713214 * q^9 - 3330064307292995160 * q^10 + 214196660016355524480 * q^12 - 1351697142828804018156 * q^13 - 7517302305589491995328 * q^14 + 146524491404032531730688 * q^16 - 108377436655642595433244 * q^17 - 2269182475834354952235228 * q^18 + 14024643346150499263916960 * q^20 - 3613555902040956758482176 * q^21 - 48893102429006434191867360 * q^22 - 507867326842846671102786048 * q^24 + 441821122409714044642015590 * q^25 + 1408725703649472883667066984 * q^26 - 248593478439946838208756480 * q^28 + 12039386014829706600024980948 * q^29 - 36685926266894937628070825280 * q^30 + 40815302174771571873068643328 * q^32 - 25787267222238191864238656640 * q^33 + 36261374450642004292958003976 * q^34 - 580544496119856571348909156080 * q^36 - 1267140929573154455938088740044 * q^37 + 1030706182877614317326332452960 * q^38 + 3677775331309955303335927125120 * q^40 - 4228447688719256876424323554684 * q^41 - 14054054841750269128772739402240 * q^42 - 10408853597054255998042527960960 * q^44 + 5968962977750993515218889928340 * q^45 + 22407092921477343211835072559552 * q^46 - 235299721005018637688575231641600 * q^48 - 31615512188019323981649417734094 * q^49 + 24292124186551164152560477361580 * q^50 + 1002079305454954374889708255510176 * q^52 + 9170251390510729272958214802164 * q^53 - 787051683509089599494415837112896 * q^54 + 1152829073224199082248229376115712 * q^56 + 1668394969897754054685444684739200 * q^57 + 6129531800884682398669731348277224 * q^58 - 11636557112389656620532244922123520 * q^60 - 3962895304807674280127771339766444 * q^61 - 8994819235653434082008553861768960 * q^62 + 24667562443996411690757328278360064 * q^64 + 95108472178397576493345013351708360 * q^65 - 59643686483535838768039195759223040 * q^66 - 37428614071533769215405413189346016 * q^68 - 378107798255717180855219732084825856 * q^69 + 185830274294359588352082139216848000 * q^70 - 260290846480495236441760743958748352 * q^72 + 769773517671824524924524644742901764 * q^73 - 250034850108007402381953386687905624 * q^74 + 347277300516185248422743813412796800 * q^76 - 1122048032159971455828617866562814720 * q^77 - 1450998872578214468135780206011466560 * q^78 + 391473453760426152176293685484792320 * q^80 + 8894227269421968655762303906241837682 * q^81 + 344096947623408239895482884304277576 * q^82 - 6791395692770555756905407625225660416 * q^84 - 3198312652592605820819998423888978200 * q^85 + 8678996853442312035283130731028012832 * q^86 - 815671442380761053869289210355156480 * q^88 - 6268329434682461663886854261019826492 * q^89 - 23166185157487343623484458734705269400 * q^90 + 11421593562829281515681866911017506560 * q^92 + 41748150138354461655386813609302195200 * q^93 - 33742046901195882761657274622561154688 * q^94 - 31638035665740952392118263378397667328 * q^96 - 62817319233285161836922640968633412444 * q^97 + 79415378721147757612981391241727219972 * q^98

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