LMFDB - Embedded newform 4.39.b.a.3.14

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			3.14
Root			$0.500000 + 2.95082e7i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.39.b.a.3.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(383569. + 357425. i) q^{2} -4.72132e8i q^{3} +(1.93720e10 + 2.74194e11i) q^{4} +2.09077e13 q^{5} +(1.68752e14 - 1.81095e14i) q^{6} +1.08901e16i q^{7} +(-9.05736e16 + 1.12096e17i) q^{8} +1.12794e18 q^{9} +O(q^{10})$	\(q+(383569. + 357425. i) q^{2} -4.72132e8i q^{3} +(1.93720e10 + 2.74194e11i) q^{4} +2.09077e13 q^{5} +(1.68752e14 - 1.81095e14i) q^{6} +1.08901e16i q^{7} +(-9.05736e16 + 1.12096e17i) q^{8} +1.12794e18 q^{9} +(8.01953e18 + 7.47293e18i) q^{10} -5.05873e19i q^{11} +(1.29456e20 - 9.14616e18i) q^{12} -7.96735e20 q^{13} +(-3.89239e21 + 4.17709e21i) q^{14} -9.87118e21i q^{15} +(-7.48073e22 + 1.06234e22i) q^{16} +3.83882e23 q^{17} +(4.32644e23 + 4.03156e23i) q^{18} +6.36661e23i q^{19} +(4.05024e23 + 5.73277e24i) q^{20} +5.14155e24 q^{21} +(1.80812e25 - 1.94037e25i) q^{22} +1.18366e26i q^{23} +(5.29243e25 + 4.27627e25i) q^{24} +7.33327e25 q^{25} +(-3.05603e26 - 2.84774e26i) q^{26} -1.17032e27i q^{27} +(-2.98600e27 + 2.10963e26i) q^{28} +1.59257e27 q^{29} +(3.52821e27 - 3.78628e27i) q^{30} +1.54910e28i q^{31} +(-3.24908e28 - 2.26632e28i) q^{32} -2.38839e28 q^{33} +(1.47245e29 + 1.37209e29i) q^{34} +2.27686e29i q^{35} +(2.18506e28 + 3.09276e29i) q^{36} +4.02079e29 q^{37} +(-2.27559e29 + 2.44203e29i) q^{38} +3.76164e29i q^{39} +(-1.89368e30 + 2.34368e30i) q^{40} -5.97871e30 q^{41} +(1.97214e30 + 1.83772e30i) q^{42} +1.62015e31i q^{43} +(1.38708e31 - 9.79979e29i) q^{44} +2.35827e31 q^{45} +(-4.23071e31 + 4.54016e31i) q^{46} +7.30265e31i q^{47} +(5.01565e30 + 3.53189e31i) q^{48} +1.13411e31 q^{49} +(2.81281e31 + 2.62110e31i) q^{50} -1.81243e32i q^{51} +(-1.54344e31 - 2.18460e32i) q^{52} -3.06110e32 q^{53} +(4.18302e32 - 4.48898e32i) q^{54} -1.05766e33i q^{55} +(-1.22074e33 - 9.86353e32i) q^{56} +3.00588e32 q^{57} +(6.10860e32 + 5.69225e32i) q^{58} -5.23574e33i q^{59} +(2.70662e33 - 1.91225e32i) q^{60} +8.85956e33 q^{61} +(-5.53688e33 + 5.94187e33i) q^{62} +1.22834e34i q^{63} +(-4.36205e33 - 2.03060e34i) q^{64} -1.66579e34 q^{65} +(-9.16111e33 - 8.53671e33i) q^{66} -2.65331e34i q^{67} +(7.43658e33 + 1.05258e35i) q^{68} +5.58845e34 q^{69} +(-8.13808e34 + 8.73332e34i) q^{70} +4.15949e34i q^{71} +(-1.02162e35 + 1.26438e35i) q^{72} +1.69330e35 q^{73} +(1.54225e35 + 1.43713e35i) q^{74} -3.46227e34i q^{75} +(-1.74569e35 + 1.23334e34i) q^{76} +5.50900e35 q^{77} +(-1.34451e35 + 1.44285e35i) q^{78} -1.90317e36i q^{79} +(-1.56405e36 + 2.22111e35i) q^{80} +9.71139e35 q^{81} +(-2.29325e36 - 2.13694e36i) q^{82} -5.71624e36i q^{83} +(9.96023e34 + 1.40978e36i) q^{84} +8.02609e36 q^{85} +(-5.79082e36 + 6.21438e36i) q^{86} -7.51903e35i q^{87} +(5.67066e36 + 4.58187e36i) q^{88} +1.56670e36 q^{89} +(9.04557e36 + 8.42904e36i) q^{90} -8.67651e36i q^{91} +(-3.24553e37 + 2.29299e36i) q^{92} +7.31380e36 q^{93} +(-2.61015e37 + 2.80107e37i) q^{94} +1.33111e37i q^{95} +(-1.07000e37 + 1.53400e37i) q^{96} +7.60398e37 q^{97} +(4.35010e36 + 4.05361e36i) q^{98} -5.70596e37i 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 $

$2$	383569.	+	357425.i	0.731599	+	0.681735i
$2$	383569.	+	357425.i	0.731599	+	0.681735i
$3$		−	4.72132e8i		−	0.406218i	−0.979156	−	0.203109i	$-0.934895\pi$
$3$		−	4.72132e8i		−	0.406218i	0.979156	−	0.203109i	$-0.0651046\pi$
$4$	1.93720e10	+	2.74194e11i	0.0704750	+	0.997514i
$5$	2.09077e13			1.09616			0.548082	−	0.836425i	$-0.315358\pi$
$5$	2.09077e13			1.09616			0.548082	+	0.836425i	$0.315358\pi$
$6$	1.68752e14	−	1.81095e14i	0.276933	−	0.297189i
$7$			1.08901e16i			0.955362i	0.878533	+	0.477681i	$0.158523\pi$
$7$			1.08901e16i			0.955362i	−0.878533	+	0.477681i	$0.841477\pi$
$8$	−9.05736e16	+	1.12096e17i	−0.628480	+	0.777825i
$9$	1.12794e18			0.834987
$10$	8.01953e18	+	7.47293e18i	0.801953	+	0.747293i
$11$		−	5.05873e19i		−	0.827143i	−0.910472	−	0.413572i	$-0.864281\pi$
$11$		−	5.05873e19i		−	0.827143i	0.910472	−	0.413572i	$-0.135719\pi$
$12$	1.29456e20	−	9.14616e18i	0.405208	−	0.0286283i
$13$	−7.96735e20			−0.544992			−0.272496	−	0.962157i	$-0.587849\pi$
$13$	−7.96735e20			−0.544992			−0.272496	+	0.962157i	$0.587849\pi$
$14$	−3.89239e21	+	4.17709e21i	−0.651304	+	0.698942i
$15$		−	9.87118e21i		−	0.445282i
$16$	−7.48073e22	+	1.06234e22i	−0.990067	+	0.140600i
$17$	3.83882e23			1.60572			0.802858	−	0.596170i	$-0.203312\pi$
$17$	3.83882e23			1.60572			0.802858	+	0.596170i	$0.203312\pi$
$18$	4.32644e23	+	4.03156e23i	0.610876	+	0.569240i
$19$			6.36661e23i			0.321803i	0.986970	+	0.160901i	$0.0514401\pi$
$19$			6.36661e23i			0.321803i	−0.986970	+	0.160901i	$0.948560\pi$
$20$	4.05024e23	+	5.73277e24i	0.0772522	+	1.09344i
$21$	5.14155e24			0.388086
$22$	1.80812e25	−	1.94037e25i	0.563892	−	0.605137i
$23$			1.18366e26i			1.58635i	0.608994	+	0.793175i	$0.291573\pi$
$23$			1.18366e26i			1.58635i	−0.608994	+	0.793175i	$0.708427\pi$
$24$	5.29243e25	+	4.27627e25i	0.315967	+	0.255300i
$25$	7.33327e25			0.201575
$26$	−3.05603e26	−	2.84774e26i	−0.398716	−	0.371540i
$27$		−	1.17032e27i		−	0.745405i
$28$	−2.98600e27	+	2.10963e26i	−0.952987	+	0.0673292i
$29$	1.59257e27			0.260937			0.130469	−	0.991452i	$-0.458352\pi$
$29$	1.59257e27			0.260937			0.130469	+	0.991452i	$0.458352\pi$
$30$	3.52821e27	−	3.78628e27i	0.303564	−	0.325768i
$31$			1.54910e28i			0.714838i	0.933944	+	0.357419i	$0.116343\pi$
$31$			1.54910e28i			0.714838i	−0.933944	+	0.357419i	$0.883657\pi$
$32$	−3.24908e28	−	2.26632e28i	−0.820184	−	0.572100i
$33$	−2.38839e28			−0.336001
$34$	1.47245e29	+	1.37209e29i	1.17474	+	1.09467i
$35$			2.27686e29i			1.04723i
$36$	2.18506e28	+	3.09276e29i	0.0588457	+	0.832910i
$37$	4.02079e29			0.643396			0.321698	−	0.946842i	$-0.395746\pi$
$37$	4.02079e29			0.643396			0.321698	+	0.946842i	$0.395746\pi$
$38$	−2.27559e29	+	2.44203e29i	−0.219384	+	0.235431i
$39$			3.76164e29i			0.221386i
$40$	−1.89368e30	+	2.34368e30i	−0.688917	+	0.852624i
$41$	−5.97871e30			−1.36055			−0.680275	−	0.732957i	$-0.738139\pi$
$41$	−5.97871e30			−1.36055			−0.680275	+	0.732957i	$0.738139\pi$
$42$	1.97214e30	+	1.83772e30i	0.283923	+	0.264572i
$43$			1.62015e31i			1.49160i	0.666167	+	0.745802i	$0.267934\pi$
$43$			1.62015e31i			1.49160i	−0.666167	+	0.745802i	$0.732066\pi$
$44$	1.38708e31	−	9.79979e29i	0.825086	−	0.0582929i
$45$	2.35827e31			0.915282
$46$	−4.23071e31	+	4.54016e31i	−1.08147	+	1.16057i
$47$			7.30265e31i			1.24057i	0.784377	+	0.620284i	$0.212983\pi$
$47$			7.30265e31i			1.24057i	−0.784377	+	0.620284i	$0.787017\pi$
$48$	5.01565e30	+	3.53189e31i	0.0571142	+	0.402183i
$49$	1.13411e31			0.0872832
$50$	2.81281e31	+	2.62110e31i	0.147472	+	0.137421i
$51$		−	1.81243e32i		−	0.652271i
$52$	−1.54344e31	−	2.18460e32i	−0.0384084	−	0.543637i
$53$	−3.06110e32			−0.530439			−0.265219	−	0.964188i	$-0.585444\pi$
$53$	−3.06110e32			−0.530439			−0.265219	+	0.964188i	$0.585444\pi$
$54$	4.18302e32	−	4.48898e32i	0.508169	−	0.545338i
$55$		−	1.05766e33i		−	0.906685i
$56$	−1.22074e33	−	9.86353e32i	−0.743105	−	0.600426i
$57$	3.00588e32			0.130722
$58$	6.10860e32	+	5.69225e32i	0.190902	+	0.177890i
$59$		−	5.23574e33i		−	1.18247i	−0.806499	−	0.591235i	$-0.798641\pi$
$59$		−	5.23574e33i		−	1.18247i	0.806499	−	0.591235i	$-0.201359\pi$
$60$	2.70662e33	−	1.91225e32i	0.444175	−	0.0313813i
$61$	8.85956e33			1.06205			0.531025	−	0.847356i	$-0.321807\pi$
$61$	8.85956e33			1.06205			0.531025	+	0.847356i	$0.321807\pi$
$62$	−5.53688e33	+	5.94187e33i	−0.487330	+	0.522975i
$63$			1.22834e34i			0.797715i
$64$	−4.36205e33	−	2.03060e34i	−0.210025	−	0.977696i
$65$	−1.66579e34			−0.597401
$66$	−9.16111e33	−	8.53671e33i	−0.245818	−	0.229063i
$67$		−	2.65331e34i		−	0.535016i	−0.963556	−	0.267508i	$-0.913800\pi$
$67$		−	2.65331e34i		−	0.535016i	0.963556	−	0.267508i	$-0.0862001\pi$
$68$	7.43658e33	+	1.05258e35i	0.113163	+	1.60172i
$69$	5.58845e34			0.644404
$70$	−8.13808e34	+	8.73332e34i	−0.713936	+	0.766155i
$71$			4.15949e34i			0.278696i	0.990243	+	0.139348i	$0.0445007\pi$
$71$			4.15949e34i			0.278696i	−0.990243	+	0.139348i	$0.955499\pi$
$72$	−1.02162e35	+	1.26438e35i	−0.524773	+	0.649474i
$73$	1.69330e35			0.669268			0.334634	−	0.942348i	$-0.391387\pi$
$73$	1.69330e35			0.669268			0.334634	+	0.942348i	$0.391387\pi$
$74$	1.54225e35	+	1.43713e35i	0.470708	+	0.438625i
$75$		−	3.46227e34i		−	0.0818837i
$76$	−1.74569e35	+	1.23334e34i	−0.321003	+	0.0226791i
$77$	5.50900e35			0.790221
$78$	−1.34451e35	+	1.44285e35i	−0.150927	+	0.161966i
$79$		−	1.90317e36i		−	1.67711i	−0.544816	−	0.838556i	$-0.683400\pi$
$79$		−	1.90317e36i		−	1.67711i	0.544816	−	0.838556i	$-0.316600\pi$
$80$	−1.56405e36	+	2.22111e35i	−1.08528	+	0.154120i
$81$	9.71139e35			0.532189
$82$	−2.29325e36	−	2.13694e36i	−0.995377	−	0.927534i
$83$		−	5.71624e36i		−	1.97073i	−0.170467	−	0.985363i	$-0.554528\pi$
$83$		−	5.71624e36i		−	1.97073i	0.170467	−	0.985363i	$-0.445472\pi$
$84$	9.96023e34	+	1.40978e36i	0.0273504	+	0.387121i
$85$	8.02609e36			1.76013
$86$	−5.79082e36	+	6.21438e36i	−1.01688	+	1.09126i
$87$		−	7.51903e35i		−	0.105998i
$88$	5.67066e36	+	4.58187e36i	0.643373	+	0.519843i
$89$	1.56670e36			0.143409			0.0717046	−	0.997426i	$-0.477156\pi$
$89$	1.56670e36			0.143409			0.0717046	+	0.997426i	$0.477156\pi$
$90$	9.04557e36	+	8.42904e36i	0.669620	+	0.623980i
$91$		−	8.67651e36i		−	0.520665i
$92$	−3.24553e37	+	2.29299e36i	−1.58240	+	0.111798i
$93$	7.31380e36			0.290380
$94$	−2.61015e37	+	2.80107e37i	−0.845739	+	0.907599i
$95$			1.33111e37i			0.352749i
$96$	−1.07000e37	+	1.53400e37i	−0.232398	+	0.333174i
$97$	7.60398e37			1.35637			0.678185	−	0.734891i	$-0.262767\pi$
$97$	7.60398e37			1.35637			0.678185	+	0.734891i	$0.262767\pi$
$98$	4.35010e36	+	4.05361e36i	0.0638563	+	0.0595040i
$99$		−	5.70596e37i		−	0.690653i
$100$	1.42060e36	+	2.01074e37i	0.0142060	+	0.201074i
$101$	−1.38872e38			−1.14950			−0.574750	−	0.818329i	$-0.694901\pi$
$101$	−1.38872e38			−1.14950			−0.574750	+	0.818329i	$0.694901\pi$
$102$	6.47809e37	−	6.95192e37i	0.444676	−	0.477201i
$103$			2.02261e38i			1.15346i	0.816934	+	0.576732i	$0.195672\pi$
$103$			2.02261e38i			1.15346i	−0.816934	+	0.576732i	$0.804328\pi$
$104$	7.21632e37	−	8.93112e37i	0.342517	−	0.423909i
$105$	1.07498e38			0.425406
$106$	−1.17414e38	−	1.09411e38i	−0.388069	−	0.361619i
$107$		−	3.85604e38i		−	1.06623i	−0.846044	−	0.533114i	$-0.821022\pi$
$107$		−	3.85604e38i		−	1.06623i	0.846044	−	0.533114i	$-0.178978\pi$
$108$	3.20895e38	−	2.26714e37i	0.743552	−	0.0525325i
$109$	−3.72464e38			−0.724404			−0.362202	−	0.932100i	$-0.617975\pi$
$109$	−3.72464e38			−0.724404			−0.362202	+	0.932100i	$0.617975\pi$
$110$	3.78036e38	−	4.05686e38i	0.618118	−	0.663330i
$111$		−	1.89834e38i		−	0.261359i
$112$	−1.15690e38	−	8.14657e38i	−0.134324	−	0.945872i
$113$	−1.17442e39			−1.15168			−0.575841	−	0.817562i	$-0.695325\pi$
$113$	−1.17442e39			−1.15168			−0.575841	+	0.817562i	$0.695325\pi$
$114$	1.15296e38	+	1.07438e38i	0.0956363	+	0.0891179i
$115$			2.47476e39i			1.73890i
$116$	3.08513e37	+	4.36674e38i	0.0183896	+	0.260289i
$117$	−8.98672e38			−0.455061
$118$	1.87139e39	−	2.00827e39i	0.806131	−	0.865094i
$119$			4.18051e39i			1.53404i
$120$	1.10652e39	+	8.94068e38i	0.346352	+	0.279851i
$121$	1.18136e39			0.315834
$122$	3.39825e39	+	3.16663e39i	0.776996	+	0.724037i
$123$			2.82274e39i			0.552680i
$124$	−4.24755e39	+	3.00092e38i	−0.713060	+	0.0503782i
$125$	−6.07295e39			−0.875204
$126$	−4.39039e39	+	4.71152e39i	−0.543830	+	0.583607i
$127$		−	1.45149e40i		−	1.54719i	−0.633682	−	0.773593i	$-0.718457\pi$
$127$		−	1.45149e40i		−	1.54719i	0.633682	−	0.773593i	$-0.281543\pi$
$128$	5.58472e39	−	9.34784e39i	0.512875	−	0.858463i
$129$	7.64923e39			0.605917
$130$	−6.38944e39	−	5.95395e39i	−0.437058	−	0.407269i
$131$		−	1.65764e39i		−	0.0980247i	−0.998798	−	0.0490123i	$-0.984393\pi$
$131$		−	1.65764e39i		−	0.0980247i	0.998798	−	0.0490123i	$-0.0156074\pi$
$132$	−4.62680e38	−	6.54883e39i	−0.0236797	−	0.335165i
$133$	−6.93328e39			−0.307438
$134$	9.48360e39	−	1.01773e40i	0.364739	−	0.391417i
$135$		−	2.44686e40i		−	0.817086i
$136$	−3.47696e40	+	4.30319e40i	−1.00916	+	1.24897i
$137$	7.05321e40			1.78113			0.890566	−	0.454853i	$-0.150308\pi$
$137$	7.05321e40			1.78113			0.890566	+	0.454853i	$0.150308\pi$
$138$	2.14355e40	+	1.99745e40i	0.471446	+	0.439313i
$139$		−	4.86577e40i		−	0.932976i	−0.884528	−	0.466488i	$-0.845519\pi$
$139$		−	4.86577e40i		−	0.932976i	0.884528	−	0.466488i	$-0.154481\pi$
$140$	−6.24302e40	+	4.41074e39i	−1.04463	+	0.0738038i
$141$	3.44781e40			0.503942
$142$	−1.48671e40	+	1.59545e40i	−0.189997	+	0.203894i
$143$			4.03047e40i			0.450787i
$144$	−8.43784e40	+	1.19826e40i	−0.826692	+	0.117399i
$145$	3.32969e40			0.286030
$146$	6.49498e40	+	6.05230e40i	0.489636	+	0.456264i
$147$		−	5.35451e39i		−	0.0354560i
$148$	7.78908e39	+	1.10248e41i	0.0453433	+	0.641796i
$149$	−3.04583e41			−1.56015			−0.780075	−	0.625686i	$-0.784819\pi$
$149$	−3.04583e41			−1.56015			−0.780075	+	0.625686i	$0.784819\pi$
$150$	1.23750e40	−	1.32802e40i	0.0558229	−	0.0599060i
$151$		−	2.44695e40i		−	0.0972888i	−0.998816	−	0.0486444i	$-0.984510\pi$
$151$		−	2.44695e40i		−	0.0972888i	0.998816	−	0.0486444i	$-0.0154901\pi$
$152$	−7.13675e40	−	5.76647e40i	−0.250306	−	0.202247i
$153$	4.32998e41			1.34075
$154$	2.11308e41	+	1.96906e41i	0.578125	+	0.538721i
$155$			3.23881e41i			0.783580i
$156$	−1.03142e41	+	7.28707e39i	−0.220835	+	0.0156022i
$157$	2.74970e40			0.0521424			0.0260712	−	0.999660i	$-0.491700\pi$
$157$	2.74970e40			0.0521424			0.0260712	+	0.999660i	$0.491700\pi$
$158$	6.80240e41	−	7.29995e41i	1.14335	−	1.22697i
$159$			1.44524e41i			0.215474i
$160$	−6.79307e41	−	4.73835e41i	−0.899056	−	0.627116i
$161$	−1.28902e42			−1.51554
$162$	3.72499e41	+	3.47110e41i	0.389349	+	0.362812i
$163$		−	1.07391e42i		−	0.998629i	−0.866421	−	0.499315i	$-0.833585\pi$
$163$		−	1.07391e42i		−	0.998629i	0.866421	−	0.499315i	$-0.166415\pi$
$164$	−1.15820e41	−	1.63933e42i	−0.0958848	−	1.35717i
$165$	−4.99357e41			−0.368312
$166$	2.04313e42	−	2.19257e42i	1.34351	−	1.44178i
$167$			2.06172e42i			1.20953i	0.796405	+	0.604764i	$0.206733\pi$
$167$			2.06172e42i			1.20953i	−0.796405	+	0.604764i	$0.793267\pi$
$168$	−4.65689e41	+	5.76350e41i	−0.243904	+	0.301863i
$169$	−1.50242e42			−0.702983
$170$	3.07856e42	+	2.86873e42i	1.28771	+	1.19994i
$171$			7.18117e41i			0.268701i
$172$	−4.44235e42	+	3.13855e41i	−1.48790	+	0.105121i
$173$	2.78835e42			0.836509			0.418255	−	0.908330i	$-0.362642\pi$
$173$	2.78835e42			0.836509			0.418255	+	0.908330i	$0.362642\pi$
$174$	2.68749e41	−	2.88406e41i	0.0722622	−	0.0775477i
$175$			7.98599e41i			0.192578i
$176$	5.37410e41	+	3.78430e42i	0.116296	+	0.818927i
$177$	−2.47196e42			−0.480341
$178$	6.00939e41	+	5.59980e41i	0.104918	+	0.0977670i
$179$			4.60894e42i			0.723425i	0.932290	+	0.361713i	$0.117808\pi$
$179$			4.60894e42i			0.723425i	−0.932290	+	0.361713i	$0.882192\pi$
$180$	4.56844e41	+	6.46623e42i	0.0645046	+	0.913006i
$181$	2.68060e42			0.340674			0.170337	−	0.985386i	$-0.445514\pi$
$181$	2.68060e42			0.340674			0.170337	+	0.985386i	$0.445514\pi$
$182$	3.10120e42	−	3.32804e42i	0.354956	−	0.380918i
$183$		−	4.18288e42i		−	0.431425i
$184$	−1.32684e43	−	1.07208e43i	−1.23390	−	0.996989i
$185$	8.40653e42			0.705267
$186$	2.80535e42	+	2.61414e42i	0.212442	+	0.197962i
$187$		−	1.94196e43i		−	1.32816i
$188$	−2.00234e43	+	1.41467e42i	−1.23748	+	0.0874291i
$189$	1.27449e43			0.712132
$190$	−4.75772e42	+	5.10572e42i	−0.240481	+	0.258071i
$191$		−	3.38592e43i		−	1.54897i	−0.632593	−	0.774484i	$-0.718009\pi$
$191$		−	3.38592e43i		−	1.54897i	0.632593	−	0.774484i	$-0.281991\pi$
$192$	−9.58709e42	+	2.05946e42i	−0.397158	+	0.0853160i
$193$	−5.60166e42			−0.210246			−0.105123	−	0.994459i	$-0.533524\pi$
$193$	−5.60166e42			−0.210246			−0.105123	+	0.994459i	$0.533524\pi$
$194$	2.91665e43	+	2.71786e43i	0.992319	+	0.924684i
$195$			7.86472e42i			0.242675i
$196$	2.19701e41	+	3.10967e42i	0.00615129	+	0.0870662i
$197$	3.74560e43			0.952057			0.476029	−	0.879430i	$-0.342076\pi$
$197$	3.74560e43			0.952057			0.476029	+	0.879430i	$0.342076\pi$
$198$	2.03946e43	−	2.18863e43i	0.470843	−	0.505282i
$199$			1.44674e43i			0.303517i	0.988418	+	0.151759i	$0.0484936\pi$
$199$			1.44674e43i			0.303517i	−0.988418	+	0.151759i	$0.951506\pi$
$200$	−6.64201e42	+	8.22034e42i	−0.126686	+	0.156791i
$201$	−1.25271e43			−0.217333
$202$	−5.32670e43	−	4.96364e43i	−0.840973	−	0.783654i
$203$			1.73432e43i			0.249290i
$204$	4.96959e43	−	3.51105e42i	0.650650	−	0.0459689i
$205$	−1.25001e44			−1.49138
$206$	−7.22931e43	+	7.75808e43i	−0.786356	+	0.843873i
$207$			1.33510e44i			1.32458i
$208$	5.96016e43	−	8.46404e42i	0.539579	−	0.0766257i
$209$	3.22070e43			0.266177
$210$	4.12328e43	+	3.84225e43i	0.311226	+	0.290014i
$211$		−	6.54428e43i		−	0.451331i	−0.974205	−	0.225666i	$-0.927544\pi$
$211$		−	6.54428e43i		−	0.451331i	0.974205	−	0.225666i	$-0.0724557\pi$
$212$	−5.92996e42	−	8.39335e43i	−0.0373827	−	0.529120i
$213$	1.96383e43			0.113212
$214$	1.37825e44	−	1.47906e44i	0.726885	−	0.780051i
$215$			3.38735e44i			1.63504i
$216$	1.31189e44	+	1.06000e44i	0.579795	+	0.468473i
$217$	−1.68698e44			−0.682929
$218$	−1.42865e44	−	1.33128e44i	−0.529973	−	0.493851i
$219$		−	7.99463e43i		−	0.271869i
$220$	2.90005e44	−	2.04891e43i	0.904430	−	0.0638986i
$221$	−3.05853e44			−0.875103
$222$	6.78516e43	−	7.28144e43i	0.178178	−	0.191210i
$223$		−	2.33526e44i		−	0.563045i	−0.959555	−	0.281522i	$-0.909161\pi$
$223$		−	2.33526e44i		−	0.563045i	0.959555	−	0.281522i	$-0.0908394\pi$
$224$	2.46804e44	−	3.53827e44i	0.546563	−	0.783572i
$225$	8.27151e43			0.168313
$226$	−4.50470e44	−	4.19767e44i	−0.842569	−	0.785141i
$227$		−	7.34501e44i		−	1.26328i	−0.775260	−	0.631642i	$-0.782381\pi$
$227$		−	7.34501e44i		−	1.26328i	0.775260	−	0.631642i	$-0.217619\pi$
$228$	5.82300e42	+	8.24196e43i	0.00921265	+	0.130397i
$229$	2.77326e44			0.403754			0.201877	−	0.979411i	$-0.435296\pi$
$229$	2.77326e44			0.403754			0.201877	+	0.979411i	$0.435296\pi$
$230$	−8.84542e44	+	9.49241e44i	−1.18547	+	1.27218i
$231$		−	2.60097e44i		−	0.321002i
$232$	−1.44245e44	+	1.78521e44i	−0.163994	+	0.202964i
$233$	1.17182e45			1.22772			0.613860	−	0.789415i	$-0.289616\pi$
$233$	1.17182e45			1.22772			0.613860	+	0.789415i	$0.289616\pi$
$234$	−3.44703e44	−	3.21208e44i	−0.332923	−	0.310231i
$235$			1.52681e45i			1.35987i
$236$	1.43561e45	−	1.01427e44i	1.17953	−	0.0833346i
$237$	−8.98546e44			−0.681274
$238$	−1.49422e45	+	1.60351e45i	−1.04581	+	1.12230i
$239$			3.52214e44i			0.227639i	0.993501	+	0.113819i	$0.0363085\pi$
$239$			3.52214e44i			0.227639i	−0.993501	+	0.113819i	$0.963692\pi$
$240$	1.04866e44	+	7.38436e44i	0.0626065	+	0.440859i
$241$	2.19326e45			1.20995			0.604973	−	0.796246i	$-0.293184\pi$
$241$	2.19326e45			1.20995			0.604973	+	0.796246i	$0.293184\pi$
$242$	4.53132e44	+	4.22247e44i	0.231064	+	0.215315i
$243$		−	2.03943e45i		−	0.961590i
$244$	1.71628e44	+	2.42924e45i	0.0748481	+	1.05941i
$245$	2.37117e44			0.0956767
$246$	−1.00892e45	+	1.08271e45i	−0.376781	+	0.404340i
$247$		−	5.07250e44i		−	0.175380i
$248$	−1.73649e45	−	1.40308e45i	−0.556019	−	0.449262i
$249$	−2.69882e45			−0.800545
$250$	−2.32939e45	−	2.17063e45i	−0.640299	−	0.596657i
$251$		−	2.03962e45i		−	0.519696i	−0.965650	−	0.259848i	$-0.916328\pi$
$251$		−	2.03962e45i		−	0.519696i	0.965650	−	0.259848i	$-0.0836724\pi$
$252$	−3.36804e45	+	2.37954e44i	−0.795731	+	0.0562190i
$253$	5.98783e45			1.31214
$254$	5.18799e45	−	5.56745e45i	1.05477	−	1.13192i
$255$		−	3.78937e45i		−	0.714996i
$256$	5.48328e45	−	1.58942e45i	0.960463	−	0.278406i
$257$	−8.53814e45			−1.38878			−0.694391	−	0.719598i	$-0.744326\pi$
$257$	−8.53814e45			−1.38878			−0.694391	+	0.719598i	$0.744326\pi$
$258$	2.93401e45	+	2.73403e45i	0.443289	+	0.413075i
$259$			4.37867e45i			0.614676i
$260$	−3.22697e44	−	4.56750e45i	−0.0421019	−	0.595916i
$261$	1.79633e45			0.217879
$262$	5.92482e44	−	6.35818e44i	0.0668268	−	0.0717148i
$263$			1.31745e46i			1.38221i	0.722754	+	0.691105i	$0.242876\pi$
$263$			1.31745e46i			1.38221i	−0.722754	+	0.691105i	$0.757124\pi$
$264$	2.16325e45	−	2.67730e45i	0.211170	−	0.261350i
$265$	−6.40004e45			−0.581448
$266$	−2.65939e45	−	2.47813e45i	−0.224922	−	0.209591i
$267$		−	7.39691e44i		−	0.0582554i
$268$	7.27522e45	−	5.14000e44i	0.533685	−	0.0377052i
$269$	−3.49902e45			−0.239141			−0.119570	−	0.992826i	$-0.538152\pi$
$269$	−3.49902e45			−0.239141			−0.119570	+	0.992826i	$0.538152\pi$
$270$	8.74571e45	−	9.38540e45i	0.557036	−	0.597780i
$271$			7.54533e45i			0.447983i	0.974591	+	0.223992i	$0.0719088\pi$
$271$			7.54533e45i			0.447983i	−0.974591	+	0.223992i	$0.928091\pi$
$272$	−2.87172e46	+	4.07814e45i	−1.58977	+	0.225763i
$273$	−4.09646e45			−0.211504
$274$	2.70539e46	+	2.52100e46i	1.30308	+	1.21426i
$275$		−	3.70971e45i		−	0.166732i
$276$	1.08260e45	+	1.53232e46i	0.0454144	+	0.642802i
$277$	−1.89988e46			−0.744063			−0.372031	−	0.928220i	$-0.621339\pi$
$277$	−1.89988e46			−0.744063			−0.372031	+	0.928220i	$0.621339\pi$
$278$	1.73915e46	−	1.86636e46i	0.636042	−	0.682564i
$279$			1.74730e46i			0.596880i
$280$	−2.55228e46	−	2.06223e46i	−0.814565	−	0.658166i
$281$	4.69370e45			0.139989			0.0699947	−	0.997547i	$-0.477702\pi$
$281$	4.69370e45			0.139989			0.0699947	+	0.997547i	$0.477702\pi$
$282$	1.32247e46	+	1.23234e46i	0.368684	+	0.343555i
$283$			2.58100e46i			0.672738i	0.941730	+	0.336369i	$0.109199\pi$
$283$			2.58100e46i			0.672738i	−0.941730	+	0.336369i	$0.890801\pi$
$284$	−1.14051e46	+	8.05777e44i	−0.278003	+	0.0196411i
$285$	6.28459e45			0.143293
$286$	−1.44059e46	+	1.54596e46i	−0.307317	+	0.329795i
$287$		−	6.51086e46i		−	1.29982i
$288$	−3.66478e46	−	2.55628e46i	−0.684842	−	0.477696i
$289$	9.02101e46			1.57832
$290$	1.27717e46	+	1.19012e46i	0.209259	+	0.194997i
$291$		−	3.59008e46i		−	0.550982i
$292$	3.28027e45	+	4.64294e46i	0.0471667	+	0.667604i
$293$	8.61122e46			1.16033			0.580163	−	0.814500i	$-0.302989\pi$
$293$	8.61122e46			1.16033			0.580163	+	0.814500i	$0.302989\pi$
$294$	1.91384e45	−	2.05382e45i	0.0241716	−	0.0259396i
$295$		−	1.09467e47i		−	1.29618i
$296$	−3.64177e46	+	4.50716e46i	−0.404362	+	0.500450i
$297$	−5.92033e46			−0.616557
$298$	−1.16829e47	−	1.08866e47i	−1.14141	−	1.06361i
$299$		−	9.43065e46i		−	0.864548i
$300$	9.49336e45	−	6.70713e44i	0.0816801	−	0.00577075i
$301$	−1.76435e47			−1.42502
$302$	8.74601e45	−	9.38573e45i	0.0663251	−	0.0711764i
$303$			6.55659e46i			0.466948i
$304$	−6.76351e45	−	4.76269e46i	−0.0452454	−	0.318606i
$305$	1.85233e47			1.16418
$306$	1.66084e47	+	1.54764e47i	0.980893	+	0.914037i
$307$			2.32516e47i			1.29070i	0.763888	+	0.645348i	$0.223288\pi$
$307$			2.32516e47i			1.29070i	−0.763888	+	0.645348i	$0.776712\pi$
$308$	1.06720e46	+	1.51054e47i	0.0556909	+	0.788256i
$309$	9.54937e46			0.468558
$310$	−1.15763e47	+	1.24231e47i	−0.534194	+	0.573266i
$311$			2.89673e46i			0.125736i	0.998022	+	0.0628682i	$0.0200248\pi$
$311$			2.89673e46i			0.125736i	−0.998022	+	0.0628682i	$0.979975\pi$
$312$	−4.21667e46	−	3.40705e46i	−0.172200	−	0.139137i
$313$	−7.03048e46			−0.270174			−0.135087	−	0.990834i	$-0.543131\pi$
$313$	−7.03048e46			−0.270174			−0.135087	+	0.990834i	$0.543131\pi$
$314$	1.05470e46	+	9.82811e45i	0.0381474	+	0.0355473i
$315$			2.56817e47i			0.874426i
$316$	5.21838e47	−	3.68682e46i	1.67294	−	0.118195i
$317$	−2.66860e47			−0.805670			−0.402835	−	0.915273i	$-0.631975\pi$
$317$	−2.66860e47			−0.805670			−0.402835	+	0.915273i	$0.631975\pi$
$318$	−5.16566e46	+	5.54349e46i	−0.146896	+	0.157641i
$319$		−	8.05638e46i		−	0.215833i
$320$	−9.12003e46	−	4.24550e47i	−0.230222	−	1.07172i
$321$	−1.82056e47			−0.433121
$322$	−4.94426e47	−	4.60727e47i	−1.10877	−	1.03320i
$323$			2.44403e47i			0.516724i
$324$	1.88129e46	+	2.66281e47i	0.0375061	+	0.530866i
$325$	−5.84268e46			−0.109857
$326$	3.83844e47	−	4.11919e47i	0.680800	−	0.730596i
$327$			1.75852e47i			0.294266i
$328$	5.41513e47	−	6.70192e47i	0.855078	−	1.05827i
$329$	−7.95263e47			−1.18519
$330$	−1.91538e47	−	1.78483e47i	−0.269457	−	0.251091i
$331$		−	8.32944e47i		−	1.10633i	−0.833072	−	0.553164i	$-0.813420\pi$
$331$		−	8.32944e47i		−	1.10633i	0.833072	−	0.553164i	$-0.186580\pi$
$332$	1.56736e48	−	1.10735e47i	1.96583	−	0.138887i
$333$	4.53522e47			0.537227
$334$	−7.36910e47	+	7.90810e47i	−0.824578	+	0.884890i
$335$		−	5.54745e47i		−	0.586465i
$336$	−3.84626e47	+	5.46208e46i	−0.384231	+	0.0545647i
$337$	1.74781e47			0.165016			0.0825078	−	0.996590i	$-0.473707\pi$
$337$	1.74781e47			0.165016			0.0825078	+	0.996590i	$0.473707\pi$
$338$	−5.76283e47	−	5.37004e47i	−0.514302	−	0.479248i
$339$			5.54480e47i			0.467834i
$340$	1.55482e47	+	2.20071e48i	0.124045	+	1.75575i
$341$	7.83649e47			0.591273
$342$	−2.56673e47	+	2.75447e47i	−0.183183	+	0.196581i
$343$			1.53851e48i			1.03875i
$344$	−1.81613e48	−	1.46742e48i	−1.16021	−	0.937444i
$345$	1.16841e48			0.706373
$346$	1.06952e48	+	9.96626e47i	0.611990	+	0.570278i
$347$		−	2.25920e48i		−	1.22376i	−0.790952	−	0.611878i	$-0.790414\pi$
$347$		−	2.25920e48i		−	1.22376i	0.790952	−	0.611878i	$-0.209586\pi$
$348$	2.06168e47	−	1.45659e46i	0.105734	−	0.00747018i
$349$	−4.68675e47			−0.227609			−0.113804	−	0.993503i	$-0.536304\pi$
$349$	−4.68675e47			−0.227609			−0.113804	+	0.993503i	$0.536304\pi$
$350$	−2.85439e47	+	3.06318e47i	−0.131287	+	0.140890i
$351$			9.32434e47i			0.406240i
$352$	−1.14647e48	+	1.64362e48i	−0.473209	+	0.678409i
$353$	−1.08094e48			−0.422749			−0.211375	−	0.977405i	$-0.567794\pi$
$353$	−1.08094e48			−0.422749			−0.211375	+	0.977405i	$0.567794\pi$
$354$	−9.48168e47	−	8.83542e47i	−0.351417	−	0.327465i
$355$			8.69652e47i			0.305497i
$356$	3.03502e46	+	4.29582e47i	0.0101068	+	0.143053i
$357$	1.97375e48			0.623155
$358$	−1.64735e48	+	1.76785e48i	−0.493184	+	0.529257i
$359$		−	4.37055e48i		−	1.24091i	−0.784240	−	0.620457i	$-0.786947\pi$
$359$		−	4.37055e48i		−	1.24091i	0.784240	−	0.620457i	$-0.213053\pi$
$360$	−2.13597e48	+	2.64353e48i	−0.575237	+	0.711930i
$361$	3.50881e48			0.896443
$362$	1.02819e48	+	9.58113e47i	0.249237	+	0.232249i
$363$		−	5.57757e47i		−	0.128298i
$364$	2.37905e48	−	1.68082e47i	0.519370	−	0.0366939i
$365$	3.54030e48			0.733628
$366$	1.49507e48	−	1.60442e48i	0.294117	−	0.315630i
$367$			3.55045e47i			0.0663175i	0.999450	+	0.0331588i	$0.0105567\pi$
$367$			3.55045e47i			0.0663175i	−0.999450	+	0.0331588i	$0.989443\pi$
$368$	−1.25745e48	−	8.85466e48i	−0.223040	−	1.57059i
$369$	−6.74364e48			−1.13604
$370$	3.22448e48	+	3.00471e48i	0.515973	+	0.480805i
$371$		−	3.33356e48i		−	0.506761i
$372$	1.41683e47	+	2.00540e48i	0.0204646	+	0.289658i
$373$	−6.83509e48			−0.938159			−0.469079	−	0.883156i	$-0.655414\pi$
$373$	−6.83509e48			−0.938159			−0.469079	+	0.883156i	$0.655414\pi$
$374$	6.94105e48	−	7.44875e48i	0.905451	−	0.971679i
$375$			2.86723e48i			0.355524i
$376$	−8.18601e48	−	6.61427e48i	−0.964946	−	0.779673i
$377$	−1.26886e48			−0.142209
$378$	4.88853e48	+	4.55533e48i	0.520995	+	0.485485i
$379$			1.02030e49i			1.03415i	0.855941	+	0.517073i	$0.172979\pi$
$379$			1.02030e49i			1.03415i	−0.855941	+	0.517073i	$0.827021\pi$
$380$	−3.64983e48	+	2.57863e47i	−0.351872	+	0.0248600i
$381$	−6.85294e48			−0.628496
$382$	1.21021e49	−	1.29873e49i	1.05599	−	1.13322i
$383$		−	1.06014e49i		−	0.880214i	−0.897945	−	0.440107i	$-0.854941\pi$
$383$		−	1.06014e49i		−	0.880214i	0.897945	−	0.440107i	$-0.145059\pi$
$384$	−4.41341e48	−	2.63672e48i	−0.348723	−	0.208339i
$385$	1.15180e49			0.866212
$386$	−2.14862e48	−	2.00218e48i	−0.153816	−	0.143332i
$387$			1.82743e49i			1.24547i
$388$	1.47305e48	+	2.08497e49i	0.0955902	+	1.35300i
$389$	−1.15747e49			−0.715264			−0.357632	−	0.933863i	$-0.616416\pi$
$389$	−1.15747e49			−0.715264			−0.357632	+	0.933863i	$0.616416\pi$
$390$	−2.81105e48	+	3.01666e48i	−0.165440	+	0.177541i
$391$			4.54387e49i			2.54723i
$392$	−1.02721e48	+	1.27130e48i	−0.0548558	+	0.0678911i
$393$	−7.82624e47			−0.0398194
$394$	1.43669e49	+	1.33877e49i	0.696524	+	0.649051i
$395$		−	3.97908e49i		−	1.83839i
$396$	1.56454e49	−	1.10536e48i	0.688936	−	0.0486738i
$397$	−1.42293e49			−0.597260			−0.298630	−	0.954369i	$-0.596530\pi$
$397$	−1.42293e49			−0.597260			−0.298630	+	0.954369i	$0.596530\pi$
$398$	−5.17103e48	+	5.54926e48i	−0.206918	+	0.222053i
$399$			3.27343e48i			0.124887i
$400$	−5.48582e48	+	7.79043e47i	−0.199573	+	0.0283414i
$401$	1.12813e49			0.391396			0.195698	−	0.980664i	$-0.437303\pi$
$401$	1.12813e49			0.391396			0.195698	+	0.980664i	$0.437303\pi$
$402$	−4.80501e48	−	4.47751e48i	−0.159001	−	0.148164i
$403$		−	1.23422e49i		−	0.389581i
$404$	−2.69023e48	−	3.80779e49i	−0.0810110	−	1.14664i
$405$	2.03043e49			0.583367
$406$	−6.19890e48	+	6.65231e48i	−0.169949	+	0.182380i
$407$		−	2.03401e49i		−	0.532180i
$408$	2.03167e49	+	1.64158e49i	0.507353	+	0.409940i
$409$	2.78981e48			0.0665016			0.0332508	−	0.999447i	$-0.489414\pi$
$409$	2.78981e48			0.0665016			0.0332508	+	0.999447i	$0.489414\pi$
$410$	−4.79464e49	−	4.46785e49i	−1.09110	−	1.01673i
$411$		−	3.33005e49i		−	0.723529i
$412$	−5.54587e49	+	3.91820e48i	−1.15060	+	0.0812904i
$413$	5.70176e49			1.12969
$414$	−4.77200e49	+	5.12104e49i	−0.903013	+	0.969062i
$415$		−	1.19513e50i		−	2.16024i
$416$	2.58866e49	+	1.80566e49i	0.446994	+	0.311790i
$417$	−2.29729e49			−0.378992
$418$	1.23536e49	+	1.15116e49i	0.194735	+	0.181462i
$419$			3.56437e49i			0.536928i	0.963290	+	0.268464i	$0.0865161\pi$
$419$			3.56437e49i			0.536928i	−0.963290	+	0.268464i	$0.913484\pi$
$420$	2.08245e48	+	2.94753e49i	0.0299805	+	0.424348i
$421$	5.14183e49			0.707551			0.353776	−	0.935330i	$-0.384898\pi$
$421$	5.14183e49			0.707551			0.353776	+	0.935330i	$0.384898\pi$
$422$	2.33909e49	−	2.51018e49i	0.307688	−	0.330194i
$423$			8.23697e49i			1.03586i
$424$	2.77254e49	−	3.43138e49i	0.333370	−	0.412589i
$425$	2.81511e49			0.323673
$426$	7.53262e48	+	7.01922e48i	0.0828255	+	0.0771803i
$427$			9.64813e49i			1.01464i
$428$	1.05731e50	−	7.46994e48i	1.06358	−	0.0751424i
$429$	1.90291e49			0.183118
$430$	−1.21072e50	+	1.29928e50i	−1.11467	+	1.19620i
$431$		−	3.78128e48i		−	0.0333097i	−0.999861	−	0.0166548i	$-0.994698\pi$
$431$		−	3.78128e48i		−	0.0333097i	0.999861	−	0.0166548i	$-0.00530165\pi$
$432$	1.24328e49	+	8.75484e49i	0.104804	+	0.738001i
$433$	−1.94791e50			−1.57145			−0.785724	−	0.618578i	$-0.787709\pi$
$433$	−1.94791e50			−1.57145			−0.785724	+	0.618578i	$0.787709\pi$
$434$	−6.47074e49	−	6.02970e49i	−0.499630	−	0.465577i
$435$		−	1.57205e49i		−	0.116191i
$436$	−7.21538e48	−	1.02128e50i	−0.0510524	−	0.722602i
$437$	−7.53591e49			−0.510492
$438$	2.85748e49	−	3.06649e49i	0.185343	−	0.198899i
$439$		−	8.56681e49i		−	0.532100i	−0.963959	−	0.266050i	$-0.914281\pi$
$439$		−	8.56681e49i		−	0.532100i	0.963959	−	0.266050i	$-0.0857186\pi$
$440$	1.18560e50	+	9.57963e49i	0.705242	+	0.569833i
$441$	1.27921e49			0.0728803
$442$	−1.17316e50	−	1.09320e50i	−0.640225	−	0.596588i
$443$			1.27735e50i			0.667787i	0.942611	+	0.333893i	$0.108363\pi$
$443$			1.27735e50i			0.667787i	−0.942611	+	0.333893i	$0.891637\pi$
$444$	5.20515e49	−	3.67747e48i	0.260709	−	0.0184193i
$445$	3.27561e49			0.157200
$446$	8.34681e49	−	8.95733e49i	0.383847	−	0.411923i
$447$			1.43803e50i			0.633762i
$448$	2.21133e50	−	4.75030e49i	0.934054	−	0.200650i
$449$	−1.19966e50			−0.485709			−0.242855	−	0.970063i	$-0.578084\pi$
$449$	−1.19966e50			−0.485709			−0.242855	+	0.970063i	$0.578084\pi$
$450$	3.17269e49	+	2.95645e49i	0.123138	+	0.114745i
$451$			3.02447e50i			1.12537i
$452$	−2.27509e49	−	3.22019e50i	−0.0811648	−	1.14882i
$453$	−1.15528e49			−0.0395205
$454$	2.62529e50	−	2.81731e50i	0.861225	−	0.924218i
$455$		−	1.81406e50i		−	0.570734i
$456$	−2.72253e49	+	3.36949e49i	−0.0821563	+	0.101679i
$457$	2.04703e50			0.592537			0.296269	−	0.955105i	$-0.404258\pi$
$457$	2.04703e50			0.592537			0.296269	+	0.955105i	$0.404258\pi$
$458$	1.06374e50	+	9.91233e49i	0.295386	+	0.275253i
$459$		−	4.49265e50i		−	1.19691i
$460$	−6.78566e50	+	4.79411e49i	−1.73457	+	0.122549i
$461$	−5.51105e50			−1.35181			−0.675906	−	0.736988i	$-0.736248\pi$
$461$	−5.51105e50			−1.35181			−0.675906	+	0.736988i	$0.736248\pi$
$462$	9.29654e49	−	9.97652e49i	0.218839	−	0.234845i
$463$			1.39874e50i			0.316007i	0.987439	+	0.158004i	$0.0505058\pi$
$463$			1.39874e50i			0.316007i	−0.987439	+	0.158004i	$0.949494\pi$
$464$	−1.19136e50	+	1.69185e49i	−0.258345	+	0.0366877i
$465$	1.52915e50			0.318304
$466$	4.49474e50	+	4.18839e50i	0.898198	+	0.836979i
$467$		−	4.50874e50i		−	0.865036i	−0.901625	−	0.432518i	$-0.857625\pi$
$467$		−	4.50874e50i		−	0.865036i	0.901625	−	0.432518i	$-0.142375\pi$
$468$	−1.74091e49	−	2.46411e50i	−0.0320705	−	0.453930i
$469$	2.88947e50			0.511134
$470$	−5.45722e50	+	5.85638e50i	−0.927069	+	0.994878i
$471$		−	1.29822e49i		−	0.0211812i
$472$	5.86908e50	+	4.74220e50i	0.919756	+	0.743159i
$473$	8.19589e50			1.23377
$474$	−3.44654e50	−	3.21163e50i	−0.498419	−	0.464448i
$475$			4.66881e49i			0.0648676i
$476$	−1.14627e51	+	8.09849e49i	−1.53023	+	0.108112i
$477$	−3.45274e50			−0.442909
$478$	−1.25890e50	+	1.35098e50i	−0.155189	+	0.166540i
$479$			4.76752e50i			0.564830i	0.959292	+	0.282415i	$0.0911354\pi$
$479$			4.76752e50i			0.564830i	−0.959292	+	0.282415i	$0.908865\pi$
$480$	−2.23713e50	+	3.20723e50i	−0.254746	+	0.365213i
$481$	−3.20350e50			−0.350646
$482$	8.41265e50	+	7.83926e50i	0.885195	+	0.824862i
$483$			6.08586e50i			0.615639i
$484$	2.28853e49	+	3.23922e50i	0.0222584	+	0.315049i
$485$	1.58981e51			1.48680
$486$	7.28945e50	−	7.82262e50i	0.655550	−	0.703499i
$487$		−	5.31475e50i		−	0.459655i	−0.973231	−	0.229828i	$-0.926184\pi$
$487$		−	5.31475e50i		−	0.459655i	0.973231	−	0.229828i	$-0.0738163\pi$
$488$	−8.02442e50	+	9.93125e50i	−0.667478	+	0.826090i
$489$	−5.07028e50			−0.405662
$490$	9.09505e49	+	8.47515e49i	0.0699970	+	0.0652261i
$491$		−	2.92285e50i		−	0.216400i	−0.994129	−	0.108200i	$-0.965491\pi$
$491$		−	2.92285e50i		−	0.216400i	0.994129	−	0.108200i	$-0.0345088\pi$
$492$	−7.73980e50	+	5.46822e49i	−0.551306	+	0.0389501i
$493$	6.11359e50			0.418991
$494$	1.81304e50	−	1.94565e50i	0.119563	−	0.128308i
$495$		−	1.19298e51i		−	0.757069i
$496$	−1.64567e50	−	1.15884e51i	−0.100506	−	0.707737i
$497$	−4.52971e50			−0.266256
$498$	−1.03518e51	−	9.64626e50i	−0.585679	−	0.545760i
$499$		−	2.63381e51i		−	1.43441i	−0.696860	−	0.717207i	$-0.745420\pi$
$499$		−	2.63381e51i		−	1.43441i	0.696860	−	0.717207i	$-0.254580\pi$
$500$	−1.17645e50	−	1.66517e51i	−0.0616801	−	0.873028i
$501$	9.73402e50			0.491333
$502$	7.29013e50	−	7.82335e50i	0.354295	−	0.380209i
$503$			1.68584e51i			0.788907i	0.918916	+	0.394454i	$0.129066\pi$
$503$			1.68584e51i			0.788907i	−0.918916	+	0.394454i	$0.870934\pi$
$504$	−1.37692e51	−	1.11255e51i	−0.620483	−	0.501348i
$505$	−2.90349e51			−1.26004
$506$	2.29674e51	+	2.14020e51i	0.959959	+	0.894530i
$507$			7.09342e50i			0.285565i
$508$	3.97990e51	−	2.81183e50i	1.54334	−	0.109038i
$509$	−4.84627e51			−1.81038			−0.905190	−	0.425006i	$-0.860272\pi$
$509$	−4.84627e51			−1.81038			−0.905190	+	0.425006i	$0.860272\pi$
$510$	1.35442e51	−	1.45348e51i	0.487438	−	0.523091i
$511$			1.84402e51i			0.639394i
$512$	2.67131e51	+	1.35021e51i	0.892473	+	0.451100i
$513$	7.45096e50			0.239874
$514$	−3.27496e51	−	3.05175e51i	−1.01603	−	0.946781i
$515$			4.22880e51i			1.26439i
$516$	1.48181e50	+	2.09738e51i	0.0427020	+	0.604411i
$517$	3.69421e51			1.02613
$518$	−1.56505e51	+	1.67952e51i	−0.419046	+	0.449696i
$519$		−	1.31647e51i		−	0.339805i
$520$	1.50876e51	−	1.86729e51i	0.375455	−	0.464674i
$521$	3.73899e50			0.0897093			0.0448547	−	0.998994i	$-0.485718\pi$
$521$	3.73899e50			0.0897093			0.0448547	+	0.998994i	$0.485718\pi$
$522$	6.89015e50	+	6.42053e50i	0.159400	+	0.148536i
$523$			4.26927e51i			0.952404i	0.879336	+	0.476202i	$0.157987\pi$
$523$			4.26927e51i			0.952404i	−0.879336	+	0.476202i	$0.842013\pi$
$524$	4.54515e50	−	3.21118e49i	0.0977809	−	0.00690829i
$525$	3.77044e50			0.0782285
$526$	−4.70889e51	+	5.05332e51i	−0.942301	+	1.01122i
$527$			5.94673e51i			1.14783i
$528$	1.78669e51	−	2.53728e50i	0.332663	−	0.0472416i
$529$	−8.44308e51			−1.51650
$530$	−2.45485e51	−	2.28754e51i	−0.425387	−	0.396393i
$531$		−	5.90562e51i		−	0.987347i
$532$	−1.34312e50	−	1.90107e51i	−0.0216667	−	0.306674i
$533$	4.76345e51			0.741489
$534$	2.64384e50	−	2.83722e50i	0.0397148	−	0.0426196i
$535$		−	8.06208e51i		−	1.16876i
$536$	2.97426e51	+	2.40320e51i	0.416149	+	0.336247i
$537$	2.17603e51			0.293869
$538$	−1.34212e51	−	1.25064e51i	−0.174955	−	0.163031i
$539$		−	5.73717e50i		−	0.0721957i
$540$	6.70916e51	−	4.74007e50i	0.815055	−	0.0575842i
$541$	4.52519e51			0.530749			0.265374	−	0.964145i	$-0.414504\pi$
$541$	4.52519e51			0.530749			0.265374	+	0.964145i	$0.414504\pi$
$542$	−2.69689e51	+	2.89415e51i	−0.305406	+	0.327744i
$543$		−	1.26560e51i		−	0.138388i
$544$	−1.24727e52	−	8.70002e51i	−1.31698	−	0.918631i
$545$	−7.78735e51			−0.794065
$546$	−1.57127e51	−	1.46418e51i	−0.154736	−	0.144189i
$547$		−	1.30304e52i		−	1.23936i	−0.784854	−	0.619681i	$-0.787262\pi$
$547$		−	1.30304e52i		−	1.23936i	0.784854	−	0.619681i	$-0.212738\pi$
$548$	1.36635e51	+	1.93395e52i	0.125525	+	1.77670i
$549$	9.99308e51			0.886798
$550$	1.32594e51	−	1.42293e51i	0.113667	−	0.121981i
$551$			1.01393e51i			0.0839704i
$552$	−5.06165e51	+	6.26445e51i	−0.404995	+	0.501234i
$553$	2.07256e52			1.60225
$554$	−7.28733e51	−	6.79064e51i	−0.544356	−	0.507253i
$555$		−	3.96899e51i		−	0.286493i
$556$	1.33417e52	−	9.42599e50i	0.930656	−	0.0657515i
$557$	7.16739e51			0.483184			0.241592	−	0.970378i	$-0.422330\pi$
$557$	7.16739e51			0.483184			0.241592	+	0.970378i	$0.422330\pi$
$558$	−6.24529e51	+	6.70209e51i	−0.406914	+	0.436677i
$559$		−	1.29083e52i		−	0.812913i
$560$	−2.41880e51	−	1.70326e52i	−0.147241	−	1.03683i
$561$	−9.16861e51			−0.539522
$562$	1.80036e51	+	1.67765e51i	0.102416	+	0.0954356i
$563$			2.88572e51i			0.158706i	0.996847	+	0.0793532i	$0.0252855\pi$
$563$			2.88572e51i			0.158706i	−0.996847	+	0.0793532i	$0.974715\pi$
$564$	6.67911e50	+	9.45371e51i	0.0355153	+	0.502689i
$565$	−2.45543e52			−1.26243
$566$	−9.22516e51	+	9.89992e51i	−0.458629	+	0.492175i
$567$			1.05758e52i			0.508433i
$568$	−4.66264e51	−	3.76739e51i	−0.216777	−	0.175155i
$569$	9.00115e51			0.404730			0.202365	−	0.979310i	$-0.435137\pi$
$569$	9.00115e51			0.404730			0.202365	+	0.979310i	$0.435137\pi$
$570$	2.41057e51	+	2.24627e51i	0.104833	+	0.0976878i
$571$			4.31267e52i			1.81410i	0.421028	+	0.907048i	$0.361669\pi$
$571$			4.31267e52i			1.81410i	−0.421028	+	0.907048i	$0.638331\pi$
$572$	−1.10513e52	+	7.80784e50i	−0.449666	+	0.0317692i
$573$	−1.59860e52			−0.629220
$574$	2.32715e52	−	2.49736e52i	0.886131	−	0.950945i
$575$			8.68011e51i			0.319769i
$576$	−4.92014e51	−	2.29040e52i	−0.175368	−	0.816363i
$577$	−3.81069e52			−1.31421			−0.657103	−	0.753801i	$-0.728218\pi$
$577$	−3.81069e52			−1.31421			−0.657103	+	0.753801i	$0.728218\pi$
$578$	3.46018e52	+	3.22434e52i	1.15470	+	1.07600i
$579$			2.64472e51i			0.0854058i
$580$	6.45029e50	+	9.12983e51i	0.0201580	+	0.285319i
$581$	6.22502e52			1.88276
$582$	1.28319e52	−	1.37704e52i	0.375624	−	0.403098i
$583$			1.54853e52i			0.438749i
$584$	−1.53368e52	+	1.89813e52i	−0.420622	+	0.520574i
$585$	−1.87891e52			−0.498822
$586$	3.30300e52	+	3.07787e52i	0.848894	+	0.791035i
$587$		−	3.38931e52i		−	0.843311i	−0.906756	−	0.421655i	$-0.861449\pi$
$587$		−	3.38931e52i		−	0.843311i	0.906756	−	0.421655i	$-0.138551\pi$
$588$	1.46818e51	−	1.03728e50i	0.0353679	−	0.00249877i
$589$	−9.86252e51			−0.230037
$590$	3.91264e52	−	4.19882e52i	0.883652	−	0.948285i
$591$		−	1.76842e52i		−	0.386743i
$592$	−3.00784e52	+	4.27144e51i	−0.637005	+	0.0904612i
$593$	−7.13251e52			−1.46286			−0.731430	−	0.681916i	$-0.761147\pi$
$593$	−7.13251e52			−1.46286			−0.731430	+	0.681916i	$0.761147\pi$
$594$	−2.27085e52	−	2.11608e52i	−0.451073	−	0.420328i
$595$			8.74047e52i			1.68156i
$596$	−5.90039e51	−	8.35150e52i	−0.109952	−	1.55627i
$597$	6.83054e51			0.123294
$598$	3.37076e52	−	3.61730e52i	0.589393	−	0.632503i
$599$		−	8.06132e52i		−	1.36552i	−0.730645	−	0.682758i	$-0.760780\pi$
$599$		−	8.06132e52i		−	1.36552i	0.730645	−	0.682758i	$-0.239220\pi$
$600$	3.88109e51	+	3.13590e51i	0.0636912	+	0.0514623i
$601$	6.33670e50			0.0100751			0.00503753	−	0.999987i	$-0.498396\pi$
$601$	6.33670e50			0.0100751			0.00503753	+	0.999987i	$0.498396\pi$
$602$	−6.76750e52	−	6.30624e52i	−1.04255	−	0.971488i
$603$		−	2.99278e52i		−	0.446731i
$604$	6.70939e51	−	4.74023e50i	0.0970469	−	0.00685643i
$605$	2.46994e52			0.346206
$606$	−2.34349e52	+	2.51490e52i	−0.318335	+	0.341619i
$607$			8.02934e51i			0.105705i	0.998602	+	0.0528524i	$0.0168313\pi$
$607$			8.02934e51i			0.105705i	−0.998602	+	0.0528524i	$0.983169\pi$
$608$	1.44288e52	−	2.06856e52i	0.184103	−	0.263937i
$609$	8.18828e51			0.101266
$610$	7.10495e52	+	6.62069e52i	0.851715	+	0.793663i
$611$		−	5.81828e52i		−	0.676101i
$612$	8.38804e51	+	1.18726e53i	0.0944895	+	1.33742i
$613$	1.75777e53			1.91961			0.959806	−	0.280663i	$-0.0905542\pi$
$613$	1.75777e53			1.91961			0.959806	+	0.280663i	$0.0905542\pi$
$614$	−8.31072e52	+	8.91860e52i	−0.879913	+	0.944273i
$615$			5.90169e52i			0.605828i
$616$	−4.98969e52	+	6.17539e52i	−0.496638	+	0.614654i
$617$	−9.81502e52			−0.947268			−0.473634	−	0.880722i	$-0.657058\pi$
$617$	−9.81502e52			−0.947268			−0.473634	+	0.880722i	$0.657058\pi$
$618$	3.66284e52	+	3.41319e52i	0.342797	+	0.319432i
$619$		−	1.47542e52i		−	0.133904i	−0.997756	−	0.0669520i	$-0.978673\pi$
$619$		−	1.47542e52i		−	0.133904i	0.997756	−	0.0669520i	$-0.0213274\pi$
$620$	−8.88063e52	+	6.27423e51i	−0.781631	+	0.0552228i
$621$	1.38526e53			1.18247
$622$	−1.03537e52	+	1.11110e52i	−0.0857189	+	0.0919887i
$623$			1.70615e52i			0.137008i
$624$	−3.99615e51	−	2.81398e52i	−0.0311268	−	0.219187i
$625$	−1.53650e53			−1.16094
$626$	−2.69667e52	−	2.51287e52i	−0.197659	−	0.184187i
$627$		−	1.52059e52i		−	0.108126i
$628$	5.32672e50	+	7.53951e51i	0.00367474	+	0.0520128i
$629$	1.54351e53			1.03311
$630$	−9.17929e52	+	9.85069e52i	−0.596127	+	0.639729i
$631$			1.37006e53i			0.863342i	0.902031	+	0.431671i	$0.142076\pi$
$631$			1.37006e53i			0.863342i	−0.902031	+	0.431671i	$0.857924\pi$
$632$	2.13338e53	+	1.72377e53i	1.30450	+	1.05403i
$633$	−3.08976e52			−0.183339
$634$	−1.02359e53	−	9.53825e52i	−0.589428	−	0.549254i
$635$		−	3.03472e53i		−	1.69597i
$636$	−3.96277e52	+	2.79973e51i	−0.214938	+	0.0151855i
$637$	−9.03588e51			−0.0475687
$638$	2.87956e52	−	3.09018e52i	0.147141	−	0.157903i
$639$			4.69166e52i			0.232708i
$640$	1.16763e53	−	1.95441e53i	0.562195	−	0.941016i
$641$	−1.33117e53			−0.622199			−0.311100	−	0.950377i	$-0.600697\pi$
$641$	−1.33117e53			−0.622199			−0.311100	+	0.950377i	$0.600697\pi$
$642$	−6.98310e52	−	6.50715e52i	−0.316871	−	0.295274i
$643$			1.54720e51i			0.00681614i	0.999994	+	0.00340807i	$0.00108482\pi$
$643$			1.54720e51i			0.00681614i	−0.999994	+	0.00340807i	$0.998915\pi$
$644$	−2.49709e52	−	3.53441e53i	−0.106808	−	1.51177i
$645$	1.59928e53			0.664185
$646$	−8.73558e52	+	9.37453e52i	−0.352269	+	0.378035i
$647$		−	1.34852e53i		−	0.528052i	−0.964516	−	0.264026i	$-0.914950\pi$
$647$		−	1.34852e53i		−	0.528052i	0.964516	−	0.264026i	$-0.0850505\pi$
$648$	−8.79595e52	+	1.08861e53i	−0.334470	+	0.413950i
$649$	−2.64862e53			−0.978072
$650$	−2.24107e52	−	2.08832e52i	−0.0803714	−	0.0748934i
$651$			7.96478e52i			0.277418i
$652$	2.94461e53	−	2.08039e52i	0.996146	−	0.0703784i
$653$	2.32730e53			0.764719			0.382359	−	0.924014i	$-0.375112\pi$
$653$	2.32730e53			0.764719			0.382359	+	0.924014i	$0.375112\pi$
$654$	−6.28540e52	+	6.74514e52i	−0.200611	+	0.215285i
$655$		−	3.46574e52i		−	0.107451i
$656$	4.47251e53	−	6.35143e52i	1.34703	−	0.191293i
$657$	1.90995e53			0.558830
$658$	−3.05038e53	−	2.84247e53i	−0.867086	−	0.807987i
$659$			5.75603e53i			1.58965i	0.606842	+	0.794823i	$0.292436\pi$
$659$			5.75603e53i			1.58965i	−0.606842	+	0.794823i	$0.707564\pi$
$660$	−9.67355e51	−	1.36921e53i	−0.0259568	−	0.367396i
$661$	−7.06863e53			−1.84292			−0.921462	−	0.388469i	$-0.873004\pi$
$661$	−7.06863e53			−1.84292			−0.921462	+	0.388469i	$0.873004\pi$
$662$	2.97715e53	−	3.19491e53i	0.754223	−	0.809389i
$663$			1.44403e53i			0.355483i
$664$	6.40770e53	+	5.17740e53i	1.53288	+	1.23856i
$665$	−1.44959e53			−0.337003
$666$	1.73957e53	+	1.62100e53i	0.393035	+	0.366246i
$667$			1.88506e53i			0.413938i
$668$	−5.65311e53	+	3.99396e52i	−1.20652	+	0.0852416i
$669$	−1.10255e53			−0.228719
$670$	1.98280e53	−	2.12783e53i	0.399814	−	0.429057i
$671$		−	4.48181e53i		−	0.878468i
$672$	−1.67053e53	−	1.16524e53i	−0.318302	−	0.222024i
$673$	−7.44199e53			−1.37849			−0.689244	−	0.724529i	$-0.742057\pi$
$673$	−7.44199e53			−1.37849			−0.689244	+	0.724529i	$0.742057\pi$
$674$	6.70403e52	+	6.24710e52i	0.120725	+	0.112497i
$675$		−	8.58226e52i		−	0.150255i
$676$	−2.91050e52	−	4.11956e53i	−0.0495428	−	0.701235i
$677$	8.46471e53			1.40097			0.700483	−	0.713669i	$-0.252968\pi$
$677$	8.46471e53			1.40097			0.700483	+	0.713669i	$0.252968\pi$
$678$	−1.98185e53	+	2.12681e53i	−0.318939	+	0.342267i
$679$			8.28079e53i			1.29582i
$680$	−7.26951e53	+	8.99696e53i	−1.10621	+	1.36907i
$681$	−3.46781e53			−0.513169
$682$	3.00583e53	+	2.80096e53i	0.432575	+	0.403092i
$683$		−	8.95780e52i		−	0.125374i	−0.998033	−	0.0626871i	$-0.980033\pi$
$683$		−	8.95780e52i		−	0.125374i	0.998033	−	0.0626871i	$-0.0199670\pi$
$684$	−1.96904e53	+	1.39114e52i	−0.268033	+	0.0189367i
$685$	1.47466e54			1.95241
$686$	−5.49901e53	+	5.90123e53i	−0.708152	+	0.759948i
$687$		−	1.30934e53i		−	0.164012i
$688$	−1.72115e53	−	1.21199e54i	−0.209719	−	1.47679i
$689$	2.43888e53			0.289085
$690$	4.48167e53	+	4.17621e53i	0.516782	+	0.481559i
$691$		−	2.09102e53i		−	0.234572i	−0.993098	−	0.117286i	$-0.962581\pi$
$691$		−	2.09102e53i		−	0.234572i	0.993098	−	0.117286i	$-0.0374194\pi$
$692$	5.40159e52	+	7.64549e53i	0.0589530	+	0.834429i
$693$	6.21383e53			0.659824
$694$	8.07496e53	−	8.66559e53i	0.834277	−	0.895299i
$695$		−	1.01732e54i		−	1.02269i
$696$	8.42856e52	+	6.81025e52i	0.0824476	+	0.0666174i
$697$	−2.29512e54			−2.18466
$698$	−1.79769e53	−	1.67516e53i	−0.166518	−	0.155169i
$699$		−	5.53254e53i		−	0.498722i
$700$	−2.18971e53	+	1.54705e52i	−0.192099	+	0.0135719i
$701$	1.33189e54			1.13717			0.568587	−	0.822623i	$-0.307490\pi$
$701$	1.33189e54			1.13717			0.568587	+	0.822623i	$0.307490\pi$
$702$	−3.33276e53	+	3.57653e53i	−0.276948	+	0.297205i
$703$			2.55988e53i			0.207047i
$704$	−1.02722e54	+	2.20664e53i	−0.808695	+	0.173721i
$705$	7.20857e53			0.552403
$706$	−4.14615e53	−	3.86356e53i	−0.309283	−	0.288203i
$707$		−	1.51233e54i		−	1.09819i
$708$	−4.78869e52	−	6.77798e53i	−0.0338521	−	0.479147i
$709$	2.08719e54			1.43643			0.718213	−	0.695823i	$-0.244960\pi$
$709$	2.08719e54			1.43643			0.718213	+	0.695823i	$0.244960\pi$
$710$	−3.10836e53	+	3.33571e53i	−0.208268	+	0.223501i
$711$		−	2.14666e54i		−	1.40037i
$712$	−1.41902e53	+	1.75622e53i	−0.0901298	+	0.111547i
$713$	−1.83361e54			−1.13398
$714$	7.57069e53	+	7.05469e53i	0.455900	+	0.424827i
$715$			8.42678e53i			0.494136i
$716$	−1.26375e54	+	8.92846e52i	−0.721626	+	0.0509834i
$717$	1.66291e53			0.0924710
$718$	1.56215e54	−	1.67641e54i	0.845975	−	0.907852i
$719$			1.57319e54i			0.829721i	0.909885	+	0.414861i	$0.136170\pi$
$719$			1.57319e54i			0.829721i	−0.909885	+	0.414861i	$0.863830\pi$
$720$	−1.76416e54	+	2.50528e53i	−0.906190	+	0.128688i
$721$	−2.20263e54			−1.10198
$722$	1.34587e54	+	1.25414e54i	0.655837	+	0.611136i
$723$		−	1.03551e54i		−	0.491502i
$724$	5.19286e52	+	7.35005e53i	0.0240090	+	0.339827i
$725$	1.16787e53			0.0525986
$726$	1.99356e53	−	2.13938e53i	0.0874650	−	0.0938625i
$727$			2.87479e54i			1.22872i	0.789027	+	0.614359i	$0.210585\pi$
$727$			2.87479e54i			1.22872i	−0.789027	+	0.614359i	$0.789415\pi$
$728$	9.72606e53	+	7.85862e53i	0.404987	+	0.327228i
$729$	3.48984e53			0.141574
$730$	1.35795e54	+	1.26539e54i	0.536722	+	0.500140i
$731$			6.21946e54i			2.39509i
$732$	1.14692e54	−	8.10309e52i	0.430352	−	0.0304047i
$733$	7.86070e53			0.287399			0.143700	−	0.989621i	$-0.454100\pi$
$733$	7.86070e53			0.287399			0.143700	+	0.989621i	$0.454100\pi$
$734$	−1.26902e53	+	1.36184e53i	−0.0452110	+	0.0485179i
$735$		−	1.11950e53i		−	0.0388656i
$736$	2.68256e54	−	3.84581e54i	0.907551	−	1.30110i
$737$	−1.34224e54			−0.442534
$738$	−2.58665e54	−	2.41035e54i	−0.831126	−	0.774478i
$739$			3.69931e54i			1.15845i	0.815169	+	0.579224i	$0.196644\pi$
$739$			3.69931e54i			1.15845i	−0.815169	+	0.579224i	$0.803356\pi$
$740$	1.62851e53	+	2.30502e54i	0.0497037	+	0.703514i
$741$	−2.39489e53			−0.0712426
$742$	1.19150e54	−	1.27865e54i	0.345477	−	0.370746i
$743$		−	2.52661e54i		−	0.714085i	−0.934088	−	0.357043i	$-0.883785\pi$
$743$		−	2.52661e54i		−	0.714085i	0.934088	−	0.357043i	$-0.116215\pi$
$744$	−6.62437e53	+	8.19851e53i	−0.182498	+	0.225865i
$745$	−6.36812e54			−1.71018
$746$	−2.62173e54	−	2.44303e54i	−0.686356	−	0.639575i
$747$		−	6.44759e54i		−	1.64553i
$748$	5.32474e54	−	3.76197e53i	1.32485	−	0.0936019i
$749$	4.19926e54			1.01863
$750$	−1.02482e54	+	1.09978e54i	−0.242373	+	0.260101i
$751$		−	5.62779e52i		−	0.0129771i	−0.999979	−	0.00648857i	$-0.997935\pi$
$751$		−	5.62779e52i		−	0.0129771i	0.999979	−	0.00648857i	$-0.00206539\pi$
$752$	−7.75790e53	−	5.46291e54i	−0.174424	−	1.22825i
$753$	−9.62971e53			−0.211110
$754$	−4.86694e53	−	4.53521e53i	−0.104040	−	0.0969488i
$755$		−	5.11600e53i		−	0.106644i
$756$	2.46894e53	+	3.49457e54i	0.0501875	+	0.710361i
$757$	−6.65977e54			−1.32019			−0.660096	−	0.751181i	$-0.729485\pi$
$757$	−6.65977e54			−1.32019			−0.660096	+	0.751181i	$0.729485\pi$
$758$	−3.64680e54	+	3.91354e54i	−0.705014	+	0.756581i
$759$		−	2.82705e54i		−	0.533014i
$760$	−1.49213e54	−	1.20563e54i	−0.274377	−	0.221696i
$761$	3.83544e54			0.687870			0.343935	−	0.938993i	$-0.388240\pi$
$761$	3.83544e54			0.687870			0.343935	+	0.938993i	$0.388240\pi$
$762$	−2.62857e54	−	2.44941e54i	−0.459807	−	0.428467i
$763$		−	4.05616e54i		−	0.692068i
$764$	9.28400e54	−	6.55922e53i	1.54512	−	0.109164i
$765$	9.05297e54			1.46968
$766$	3.78922e54	−	4.06638e54i	0.600073	−	0.643964i
$767$			4.17150e54i			0.644437i
$768$	−7.50415e53	−	2.58883e54i	−0.113094	−	0.390158i
$769$	1.07625e54			0.158239			0.0791194	−	0.996865i	$-0.474789\pi$
$769$	1.07625e54			0.158239			0.0791194	+	0.996865i	$0.474789\pi$
$770$	4.41795e54	+	4.11684e54i	0.633720	+	0.590527i
$771$			4.03113e54i			0.564149i
$772$	−1.08516e53	−	1.53594e54i	−0.0148171	−	0.209723i
$773$	6.46623e53			0.0861471			0.0430735	−	0.999072i	$-0.486285\pi$
$773$	6.46623e53			0.0861471			0.0430735	+	0.999072i	$0.486285\pi$
$774$	−6.53171e54	+	7.00946e54i	−0.849080	+	0.911185i
$775$			1.13600e54i			0.144094i
$776$	−6.88720e54	+	8.52379e54i	−0.852451	+	1.05502i
$777$	2.06731e54			0.249693
$778$	−4.43969e54	−	4.13708e54i	−0.523287	−	0.487621i
$779$		−	3.80641e54i		−	0.437829i
$780$	−2.15646e54	+	1.52356e53i	−0.242072	+	0.0171026i
$781$	2.10417e54			0.230522
$782$	−1.62409e55	+	1.74289e55i	−1.73653	+	1.86355i
$783$		−	1.86381e54i		−	0.194504i
$784$	−8.48399e53	+	1.20481e53i	−0.0864162	+	0.0122720i
$785$	5.74897e53			0.0571567
$786$	−3.00190e53	−	2.79730e53i	−0.0291319	−	0.0271463i
$787$		−	3.54695e54i		−	0.335996i	−0.985787	−	0.167998i	$-0.946270\pi$
$787$		−	3.54695e54i		−	0.335996i	0.985787	−	0.167998i	$-0.0537303\pi$
$788$	7.25599e53	+	1.02702e55i	0.0670963	+	0.949690i
$789$	6.22009e54			0.561479
$790$	1.42222e55	−	1.52625e55i	1.25329	−	1.34496i
$791$		−	1.27895e55i		−	1.10027i
$792$	6.39618e54	+	5.16809e54i	0.537208	+	0.434062i
$793$	−7.05873e54			−0.578810
$794$	−5.45791e54	−	5.08591e54i	−0.436955	−	0.407173i
$795$			3.02166e54i			0.236195i
$796$	−3.96689e54	+	2.80264e53i	−0.302762	+	0.0213904i
$797$	9.82426e54			0.732136			0.366068	−	0.930588i	$-0.380704\pi$
$797$	9.82426e54			0.732136			0.366068	+	0.930588i	$0.380704\pi$
$798$	−1.17001e54	+	1.25558e54i	−0.0851399	+	0.0913673i
$799$			2.80336e55i			1.99200i
$800$	−2.38264e54	−	1.66196e54i	−0.165329	−	0.115321i
$801$	1.76715e54			0.119745
$802$	4.32716e54	+	4.03223e54i	0.286345	+	0.266829i
$803$		−	8.56597e54i		−	0.553581i
$804$	−2.42676e53	−	3.43487e54i	−0.0153166	−	0.216793i
$805$	−2.69503e55			−1.66128
$806$	4.41143e54	−	4.73410e54i	0.265591	−	0.285017i
$807$			1.65200e54i			0.0971433i
$808$	1.25781e55	−	1.55671e55i	0.722438	−	0.894110i
$809$	−2.21908e54			−0.124495			−0.0622475	−	0.998061i	$-0.519827\pi$
$809$	−2.21908e54			−0.124495			−0.0622475	+	0.998061i	$0.519827\pi$
$810$	7.78808e54	+	7.25726e54i	0.426791	+	0.397701i
$811$			5.68992e53i			0.0304586i	0.999884	+	0.0152293i	$0.00484782\pi$
$811$			5.68992e53i			0.0304586i	−0.999884	+	0.0152293i	$0.995152\pi$
$812$	−4.75541e54	+	3.35973e53i	−0.248670	+	0.0175687i
$813$	3.56239e54			0.181979
$814$	7.27006e54	−	7.80182e54i	0.362806	−	0.389343i
$815$		−	2.24530e55i		−	1.09466i
$816$	1.92542e54	+	1.35583e55i	0.0917091	+	0.645792i
$817$	−1.03148e55			−0.480003
$818$	1.07008e54	+	9.97149e53i	0.0486525	+	0.0453364i
$819$		−	9.78661e54i		−	0.434748i
$820$	−2.42152e54	−	3.42745e55i	−0.105105	−	1.48768i
$821$	2.50665e55			1.06310			0.531550	−	0.847027i	$-0.321610\pi$
$821$	2.50665e55			1.06310			0.531550	+	0.847027i	$0.321610\pi$
$822$	1.19024e55	−	1.27730e55i	0.493255	−	0.529333i
$823$			2.89582e55i			1.17267i	0.810070	+	0.586333i	$0.199429\pi$
$823$			2.89582e55i			1.17267i	−0.810070	+	0.586333i	$0.800571\pi$
$824$	−2.26727e55	−	1.83195e55i	−0.897193	−	0.724929i
$825$	−1.75147e54			−0.0677295
$826$	2.18702e55	+	2.03796e55i	0.826478	+	0.770147i
$827$			8.07277e54i			0.298138i	0.988827	+	0.149069i	$0.0476277\pi$
$827$			8.07277e54i			0.298138i	−0.988827	+	0.149069i	$0.952372\pi$
$828$	−3.66078e55	+	2.58637e54i	−1.32129	+	0.0933499i
$829$	−4.68868e55			−1.65392			−0.826959	−	0.562262i	$-0.809931\pi$
$829$	−4.68868e55			−1.65392			−0.826959	+	0.562262i	$0.809931\pi$
$830$	4.27170e55	−	4.58415e55i	1.47271	−	1.58043i
$831$			8.96992e54i			0.302252i
$832$	3.47540e54	+	1.61785e55i	0.114462	+	0.532837i
$833$	4.35366e54			0.140152
$834$	−8.81167e54	−	8.21108e54i	−0.277270	−	0.258372i
$835$			4.31057e55i			1.32584i
$836$	6.23915e53	+	8.83097e54i	0.0187588	+	0.265515i
$837$	1.81294e55			0.532844
$838$	−1.27400e55	+	1.36718e55i	−0.366043	+	0.392817i
$839$		−	4.12427e55i		−	1.15843i	−0.815175	−	0.579215i	$-0.803359\pi$
$839$		−	4.12427e55i		−	1.15843i	0.815175	−	0.579215i	$-0.196641\pi$
$840$	−9.73646e54	+	1.20501e55i	−0.267359	+	0.330891i
$841$	−3.47135e55			−0.931912
$842$	1.97225e55	+	1.83782e55i	0.517644	+	0.482362i
$843$		−	2.21604e54i		−	0.0568662i
$844$	1.79441e55	−	1.26776e54i	0.450209	−	0.0318076i
$845$	−3.14122e55			−0.770585
$846$	−2.94410e55	+	3.15944e55i	−0.706181	+	0.757833i
$847$			1.28651e55i			0.301736i
$848$	2.28992e55	−	3.25193e54i	0.525170	−	0.0745795i
$849$	1.21857e55			0.273279
$850$	1.07979e55	+	1.00619e55i	0.236799	+	0.220659i
$851$			4.75925e55i			1.02065i
$852$	3.80433e53	+	5.38470e54i	0.00797859	+	0.112930i
$853$	8.55540e55			1.75472			0.877362	−	0.479830i	$-0.159302\pi$
$853$	8.55540e55			1.75472			0.877362	+	0.479830i	$0.159302\pi$
$854$	−3.44849e55	+	3.70072e55i	−0.691718	+	0.742312i
$855$			1.50142e55i			0.294540i
$856$	4.32249e55	+	3.49255e55i	0.829339	+	0.670103i
$857$	7.20266e55			1.35163			0.675814	−	0.737072i	$-0.263792\pi$
$857$	7.20266e55			1.35163			0.675814	+	0.737072i	$0.263792\pi$
$858$	7.29898e54	+	6.80150e54i	0.133969	+	0.124838i
$859$		−	4.54832e55i		−	0.816546i	−0.912860	−	0.408273i	$-0.866131\pi$
$859$		−	4.54832e55i		−	0.816546i	0.912860	−	0.408273i	$-0.133869\pi$
$860$	−9.28792e55	+	6.56198e54i	−1.63098	+	0.115230i
$861$	−3.07398e55			−0.528010
$862$	1.35153e54	−	1.45038e54i	0.0227084	−	0.0243693i
$863$		−	1.19707e56i		−	1.96749i	−0.179564	−	0.983746i	$-0.557469\pi$
$863$		−	1.19707e56i		−	1.96749i	0.179564	−	0.983746i	$-0.442531\pi$
$864$	−2.65232e55	+	3.80246e55i	−0.426447	+	0.611369i
$865$	5.82978e55			0.916951
$866$	−7.47159e55	−	6.96234e55i	−1.14967	−	1.07131i
$867$		−	4.25911e55i		−	0.641144i
$868$	−3.26803e54	−	4.62561e55i	−0.0481295	−	0.681231i
$869$	−9.62761e55			−1.38721
$870$	5.61892e54	−	6.02991e54i	0.0792113	−	0.0850050i
$871$			2.11398e55i			0.291579i
$872$	3.37354e55	−	4.17519e55i	0.455273	−	0.563460i
$873$	8.57686e55			1.13255
$874$	−2.89054e55	−	2.69353e55i	−0.373475	−	0.348020i
$875$		−	6.61349e55i		−	0.836137i
$876$	2.19208e55	−	1.54872e54i	0.271193	−	0.0191600i
$877$	−1.01372e56			−1.22723			−0.613614	−	0.789606i	$-0.710285\pi$
$877$	−1.01372e56			−1.22723			−0.613614	+	0.789606i	$0.710285\pi$
$878$	3.06200e55	−	3.28596e55i	0.362751	−	0.389284i
$879$		−	4.06563e55i		−	0.471346i
$880$	1.12360e55	+	7.91209e55i	0.127479	+	0.897678i
$881$	6.27766e55			0.697036			0.348518	−	0.937302i	$-0.386685\pi$
$881$	6.27766e55			0.697036			0.348518	+	0.937302i	$0.386685\pi$
$882$	4.90667e54	+	4.57224e54i	0.0533192	+	0.0496850i
$883$			1.03931e56i			1.10533i	0.833404	+	0.552665i	$0.186389\pi$
$883$			1.03931e56i			1.10533i	−0.833404	+	0.552665i	$0.813611\pi$
$884$	−5.92499e54	−	8.38631e55i	−0.0616729	−	0.872927i
$885$	−5.16830e55			−0.526533
$886$	−4.56556e55	+	4.89950e55i	−0.455254	+	0.488552i
$887$			1.42465e55i			0.139046i	0.997580	+	0.0695230i	$0.0221477\pi$
$887$			1.42465e55i			0.139046i	−0.997580	+	0.0695230i	$0.977852\pi$
$888$	2.12797e55	+	1.71940e55i	0.203292	+	0.164259i
$889$	1.58068e56			1.47812
$890$	1.25642e55	+	1.17079e55i	0.115007	+	0.107169i
$891$		−	4.91273e55i		−	0.440197i
$892$	6.40315e55	−	4.52387e54i	0.561645	−	0.0396806i
$893$	−4.64931e55			−0.399219
$894$	−5.13990e55	+	5.51585e55i	−0.432058	+	0.463660i
$895$			9.63622e55i			0.792993i
$896$	1.01799e56	+	6.08180e55i	0.820143	+	0.489982i
$897$	−4.45251e55			−0.351195
$898$	−4.60151e55	−	4.28788e55i	−0.355345	−	0.331125i
$899$			2.46705e55i			0.186528i
$900$	1.60236e54	+	2.26800e55i	0.0118619	+	0.167894i
$901$	−1.17510e56			−0.851734
$902$	−1.08102e56	+	1.16009e56i	−0.767203	+	0.823319i
$903$			8.33007e55i			0.578870i
$904$	1.06371e56	−	1.31648e56i	0.723809	−	0.895807i
$905$	5.60450e55			0.373434
$906$	−4.43130e54	−	4.12927e54i	−0.0289132	−	0.0269425i
$907$			9.75834e55i			0.623502i	0.950164	+	0.311751i	$0.100915\pi$
$907$			9.75834e55i			0.623502i	−0.950164	+	0.311751i	$0.899085\pi$
$908$	2.01396e56	−	1.42288e55i	1.26014	−	0.0890300i
$909$	−1.56640e56			−0.959817
$910$	6.48389e55	−	6.95815e55i	0.389090	−	0.417549i
$911$			2.84255e56i			1.67055i	0.549832	+	0.835275i	$0.314692\pi$
$911$			2.84255e56i			1.67055i	−0.549832	+	0.835275i	$0.685308\pi$
$912$	−2.24862e55	+	3.19327e54i	−0.129424	+	0.0183795i
$913$	−2.89169e56			−1.63007
$914$	7.85175e55	+	7.31659e55i	0.433500	+	0.403953i
$915$		−	8.74543e55i		−	0.472912i
$916$	5.37237e54	+	7.60412e55i	0.0284545	+	0.402750i
$917$	1.80518e55			0.0936490
$918$	1.60579e56	−	1.72324e56i	0.815975	−	0.875658i
$919$		−	1.86426e56i		−	0.927924i	−0.885855	−	0.463962i	$-0.846427\pi$
$919$		−	1.86426e56i		−	0.927924i	0.885855	−	0.463962i	$-0.153573\pi$
$920$	−2.77412e56	−	2.24148e56i	−1.35256	−	1.09286i
$921$	1.09778e56			0.524305
$922$	−2.11386e56	−	1.96979e56i	−0.988985	−	0.921578i
$923$		−	3.31401e55i		−	0.151887i
$924$	7.13172e55	−	5.03861e54i	0.320204	−	0.0226227i
$925$	2.94855e55			0.129693
$926$	−4.99944e55	+	5.36512e55i	−0.215433	+	0.231191i
$927$			2.28138e56i			0.963127i
$928$	−5.17439e55	−	3.60928e55i	−0.214017	−	0.149282i
$929$	1.83875e56			0.745118			0.372559	−	0.928009i	$-0.378480\pi$
$929$	1.83875e56			0.745118			0.372559	+	0.928009i	$0.378480\pi$
$930$	5.86532e55	+	5.46555e55i	0.232871	+	0.216999i
$931$			7.22045e54i			0.0280880i
$932$	2.27006e55	+	3.21307e56i	0.0865236	+	1.22467i
$933$	1.36764e55			0.0510764
$934$	1.61154e56	−	1.72941e56i	0.589725	−	0.632860i
$935$		−	4.06018e56i		−	1.45588i
$936$	8.13959e55	−	1.00738e56i	0.285997	−	0.353958i
$937$	2.04279e56			0.703350			0.351675	−	0.936122i	$-0.385612\pi$
$937$	2.04279e56			0.703350			0.351675	+	0.936122i	$0.385612\pi$
$938$	1.10831e56	+	1.03277e56i	0.373945	+	0.348458i
$939$			3.31932e55i			0.109749i
$940$	−4.18644e56	+	2.95775e55i	−1.35649	+	0.0958367i
$941$	−1.06823e56			−0.339205			−0.169603	−	0.985513i	$-0.554248\pi$
$941$	−1.06823e56			−0.339205			−0.169603	+	0.985513i	$0.554248\pi$
$942$	4.64017e54	−	4.97956e54i	0.0144400	−	0.0154962i
$943$		−	7.07677e56i		−	2.15831i
$944$	5.56214e55	+	3.91672e56i	0.166255	+	1.17072i
$945$	2.66465e56			0.780613
$946$	3.14369e56	+	2.92942e56i	0.902626	+	0.841104i
$947$			3.52842e56i			0.992958i	0.868049	+	0.496479i	$0.165374\pi$
$947$			3.52842e56i			0.992958i	−0.868049	+	0.496479i	$0.834626\pi$
$948$	−1.74067e55	−	2.46376e56i	−0.0480128	−	0.679580i
$949$	−1.34911e56			−0.364746
$950$	−1.66875e55	+	1.79081e55i	−0.0442225	+	0.0474571i
$951$			1.25993e56i			0.327278i
$952$	−4.68620e56	−	3.78643e56i	−1.19322	−	0.964114i
$953$	−3.35786e55			−0.0838102			−0.0419051	−	0.999122i	$-0.513343\pi$
$953$	−3.35786e55			−0.0838102			−0.0419051	+	0.999122i	$0.513343\pi$
$954$	−1.32436e56	−	1.23410e56i	−0.324032	−	0.301947i
$955$		−	7.07917e56i		−	1.69792i
$956$	−9.65750e55	+	6.82309e54i	−0.227073	+	0.0160428i
$957$	−3.80367e55			−0.0876752
$958$	−1.70403e56	+	1.82867e56i	−0.385064	+	0.413229i
$959$			7.68100e56i			1.70163i
$960$	−2.00444e56	+	4.30586e55i	−0.435350	+	0.0935203i
$961$	2.29646e56			0.489007
$962$	−1.22876e56	−	1.14501e56i	−0.256532	−	0.239047i
$963$		−	4.34940e56i		−	0.890286i
$964$	4.24878e55	+	6.01379e56i	0.0852709	+	1.20694i
$965$	−1.17118e56			−0.230464
$966$	−2.17524e56	+	2.33434e56i	−0.419703	+	0.450401i
$967$			7.50504e55i			0.141987i	0.997477	+	0.0709937i	$0.0226170\pi$
$967$			7.50504e55i			0.141987i	−0.997477	+	0.0709937i	$0.977383\pi$
$968$	−1.07000e56	+	1.32426e56i	−0.198496	+	0.245664i
$969$	1.15390e56			0.209903
$970$	6.09803e56	+	5.68240e56i	1.08774	+	1.01361i
$971$			6.78010e56i			1.18596i	0.805216	+	0.592981i	$0.202049\pi$
$971$			6.78010e56i			1.18596i	−0.805216	+	0.592981i	$0.797951\pi$
$972$	5.59201e56	−	3.95080e55i	0.959199	−	0.0677681i
$973$	5.29886e56			0.891330
$974$	1.89963e56	−	2.03857e56i	0.313363	−	0.336284i
$975$			2.75852e55i			0.0446260i
$976$	−6.62760e56	+	9.41187e55i	−1.05150	+	0.149324i
$977$	2.94582e56			0.458363			0.229181	−	0.973384i	$-0.426395\pi$
$977$	2.94582e56			0.458363			0.229181	+	0.973384i	$0.426395\pi$
$978$	−1.94480e56	−	1.81225e56i	−0.296782	−	0.276554i
$979$		−	7.92554e55i		−	0.118620i
$980$	4.59343e54	+	6.50160e55i	0.00674282	+	0.0954388i
$981$	−4.20118e56			−0.604867
$982$	1.04470e56	−	1.12111e56i	0.147528	−	0.158318i
$983$		−	4.91924e56i		−	0.681368i	−0.940178	−	0.340684i	$-0.889341\pi$
$983$		−	4.91924e56i		−	0.681368i	0.940178	−	0.340684i	$-0.110659\pi$
$984$	−3.16419e56	−	2.55666e56i	−0.429889	−	0.347349i
$985$	7.83118e56			1.04361
$986$	2.34498e56	+	2.18515e56i	0.306534	+	0.285641i
$987$			3.75469e56i			0.481447i
$988$	1.39085e56	−	9.82647e54i	0.174944	−	0.0123599i
$989$	−1.91771e57			−2.36621
$990$	4.26403e56	−	4.57591e56i	0.516121	−	0.553871i
$991$			1.16876e57i			1.38779i	0.720074	+	0.693897i	$0.244108\pi$
$991$			1.16876e57i			1.38779i	−0.720074	+	0.693897i	$0.755892\pi$
$992$	3.51076e56	−	5.03316e56i	0.408959	−	0.586298i
$993$	−3.93260e56			−0.449411
$994$	−1.73746e56	−	1.61903e56i	−0.194793	−	0.181516i
$995$			3.02480e56i			0.332705i
$996$	−5.22816e55	−	7.40001e56i	−0.0564185	−	0.798555i
$997$	−3.67989e56			−0.389608			−0.194804	−	0.980842i	$-0.562407\pi$
$997$	−3.67989e56			−0.389608			−0.194804	+	0.980842i	$0.562407\pi$
$998$	9.41392e56	−	1.01025e57i	0.977890	−	1.04942i
$999$		−	4.70560e56i		−	0.479591i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.39.b.a.3.14	yes	18
4.3	odd	2	inner	4.39.b.a.3.13	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.39.b.a.3.13	✓	18	4.3	odd	2	inner
4.39.b.a.3.14	yes	18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 39 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(383569. + 357425. i) q^{2} -4.72132e8i q^{3} +(1.93720e10 + 2.74194e11i) q^{4} +2.09077e13 q^{5} +(1.68752e14 - 1.81095e14i) q^{6} +1.08901e16i q^{7} +(-9.05736e16 + 1.12096e17i) q^{8} +1.12794e18 q^{9} +O(q^{10})\)	\(q+(383569. + 357425. i) q^{2} -4.72132e8i q^{3} +(1.93720e10 + 2.74194e11i) q^{4} +2.09077e13 q^{5} +(1.68752e14 - 1.81095e14i) q^{6} +1.08901e16i q^{7} +(-9.05736e16 + 1.12096e17i) q^{8} +1.12794e18 q^{9} +(8.01953e18 + 7.47293e18i) q^{10} -5.05873e19i q^{11} +(1.29456e20 - 9.14616e18i) q^{12} -7.96735e20 q^{13} +(-3.89239e21 + 4.17709e21i) q^{14} -9.87118e21i q^{15} +(-7.48073e22 + 1.06234e22i) q^{16} +3.83882e23 q^{17} +(4.32644e23 + 4.03156e23i) q^{18} +6.36661e23i q^{19} +(4.05024e23 + 5.73277e24i) q^{20} +5.14155e24 q^{21} +(1.80812e25 - 1.94037e25i) q^{22} +1.18366e26i q^{23} +(5.29243e25 + 4.27627e25i) q^{24} +7.33327e25 q^{25} +(-3.05603e26 - 2.84774e26i) q^{26} -1.17032e27i q^{27} +(-2.98600e27 + 2.10963e26i) q^{28} +1.59257e27 q^{29} +(3.52821e27 - 3.78628e27i) q^{30} +1.54910e28i q^{31} +(-3.24908e28 - 2.26632e28i) q^{32} -2.38839e28 q^{33} +(1.47245e29 + 1.37209e29i) q^{34} +2.27686e29i q^{35} +(2.18506e28 + 3.09276e29i) q^{36} +4.02079e29 q^{37} +(-2.27559e29 + 2.44203e29i) q^{38} +3.76164e29i q^{39} +(-1.89368e30 + 2.34368e30i) q^{40} -5.97871e30 q^{41} +(1.97214e30 + 1.83772e30i) q^{42} +1.62015e31i q^{43} +(1.38708e31 - 9.79979e29i) q^{44} +2.35827e31 q^{45} +(-4.23071e31 + 4.54016e31i) q^{46} +7.30265e31i q^{47} +(5.01565e30 + 3.53189e31i) q^{48} +1.13411e31 q^{49} +(2.81281e31 + 2.62110e31i) q^{50} -1.81243e32i q^{51} +(-1.54344e31 - 2.18460e32i) q^{52} -3.06110e32 q^{53} +(4.18302e32 - 4.48898e32i) q^{54} -1.05766e33i q^{55} +(-1.22074e33 - 9.86353e32i) q^{56} +3.00588e32 q^{57} +(6.10860e32 + 5.69225e32i) q^{58} -5.23574e33i q^{59} +(2.70662e33 - 1.91225e32i) q^{60} +8.85956e33 q^{61} +(-5.53688e33 + 5.94187e33i) q^{62} +1.22834e34i q^{63} +(-4.36205e33 - 2.03060e34i) q^{64} -1.66579e34 q^{65} +(-9.16111e33 - 8.53671e33i) q^{66} -2.65331e34i q^{67} +(7.43658e33 + 1.05258e35i) q^{68} +5.58845e34 q^{69} +(-8.13808e34 + 8.73332e34i) q^{70} +4.15949e34i q^{71} +(-1.02162e35 + 1.26438e35i) q^{72} +1.69330e35 q^{73} +(1.54225e35 + 1.43713e35i) q^{74} -3.46227e34i q^{75} +(-1.74569e35 + 1.23334e34i) q^{76} +5.50900e35 q^{77} +(-1.34451e35 + 1.44285e35i) q^{78} -1.90317e36i q^{79} +(-1.56405e36 + 2.22111e35i) q^{80} +9.71139e35 q^{81} +(-2.29325e36 - 2.13694e36i) q^{82} -5.71624e36i q^{83} +(9.96023e34 + 1.40978e36i) q^{84} +8.02609e36 q^{85} +(-5.79082e36 + 6.21438e36i) q^{86} -7.51903e35i q^{87} +(5.67066e36 + 4.58187e36i) q^{88} +1.56670e36 q^{89} +(9.04557e36 + 8.42904e36i) q^{90} -8.67651e36i q^{91} +(-3.24553e37 + 2.29299e36i) q^{92} +7.31380e36 q^{93} +(-2.61015e37 + 2.80107e37i) q^{94} +1.33111e37i q^{95} +(-1.07000e37 + 1.53400e37i) q^{96} +7.60398e37 q^{97} +(4.35010e36 + 4.05361e36i) q^{98} -5.70596e37i 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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