LMFDB - Embedded newform 4.39.b.a.3.6

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			3.6
Root			$0.500000 - 7.90224e7i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.39.b.a.3.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-306058. + 425684. i) q^{2} +1.26436e9i q^{3} +(-8.75354e10 - 2.60567e11i) q^{4} -4.90299e12 q^{5} +(-5.38217e14 - 3.86966e14i) q^{6} +1.75338e16i q^{7} +(1.37710e17 + 4.24863e16i) q^{8} -2.47749e17 q^{9} +O(q^{10})$	\(q+(-306058. + 425684. i) q^{2} +1.26436e9i q^{3} +(-8.75354e10 - 2.60567e11i) q^{4} -4.90299e12 q^{5} +(-5.38217e14 - 3.86966e14i) q^{6} +1.75338e16i q^{7} +(1.37710e17 + 4.24863e16i) q^{8} -2.47749e17 q^{9} +(1.50060e18 - 2.08712e18i) q^{10} +5.84750e19i q^{11} +(3.29451e20 - 1.10676e20i) q^{12} -2.66415e21 q^{13} +(-7.46387e21 - 5.36636e21i) q^{14} -6.19913e21i q^{15} +(-6.02330e22 + 4.56178e22i) q^{16} +3.72111e22 q^{17} +(7.58254e22 - 1.05463e23i) q^{18} +1.66958e24i q^{19} +(4.29185e23 + 1.27756e24i) q^{20} -2.21690e25 q^{21} +(-2.48918e25 - 1.78967e25i) q^{22} +1.32941e25i q^{23} +(-5.37179e25 + 1.74115e26i) q^{24} -3.39759e26 q^{25} +(8.15382e26 - 1.13408e27i) q^{26} +1.39472e27i q^{27} +(4.56875e27 - 1.53483e27i) q^{28} +4.91284e26 q^{29} +(2.63887e27 + 1.89729e27i) q^{30} -3.21732e27i q^{31} +(-9.83973e26 - 3.96019e28i) q^{32} -7.39333e28 q^{33} +(-1.13887e28 + 1.58402e28i) q^{34} -8.59681e28i q^{35} +(2.16868e28 + 6.45553e28i) q^{36} +9.26858e29 q^{37} +(-7.10714e29 - 5.10989e29i) q^{38} -3.36843e30i q^{39} +(-6.75191e29 - 2.08310e29i) q^{40} +2.76483e30 q^{41} +(6.78500e30 - 9.43700e30i) q^{42} -8.54057e30i q^{43} +(1.52367e31 - 5.11863e30i) q^{44} +1.21471e30 q^{45} +(-5.65910e30 - 4.06877e30i) q^{46} -1.63375e31i q^{47} +(-5.76772e31 - 7.61560e31i) q^{48} -1.77501e32 q^{49} +(1.03986e32 - 1.44630e32i) q^{50} +4.70482e31i q^{51} +(2.33207e32 + 6.94190e32i) q^{52} +1.08629e33 q^{53} +(-5.93708e32 - 4.26864e32i) q^{54} -2.86702e32i q^{55} +(-7.44947e32 + 2.41459e33i) q^{56} -2.11095e33 q^{57} +(-1.50361e32 + 2.09132e32i) q^{58} +6.34821e33i q^{59} +(-1.61529e33 + 5.42643e32i) q^{60} -9.47917e33 q^{61} +(1.36956e33 + 9.84686e32i) q^{62} -4.34398e33i q^{63} +(1.71590e34 + 1.17016e34i) q^{64} +1.30623e34 q^{65} +(2.26278e34 - 3.14722e34i) q^{66} -5.59969e34i q^{67} +(-3.25729e33 - 9.69601e33i) q^{68} -1.68085e34 q^{69} +(3.65952e34 + 2.63112e34i) q^{70} -2.26917e35i q^{71} +(-3.41175e34 - 1.05259e34i) q^{72} +7.29274e34 q^{73} +(-2.83672e35 + 3.94548e35i) q^{74} -4.29576e35i q^{75} +(4.35039e35 - 1.46148e35i) q^{76} -1.02529e36 q^{77} +(1.43389e36 + 1.03093e36i) q^{78} +7.48717e35i q^{79} +(2.95321e35 - 2.23663e35i) q^{80} -2.09809e36 q^{81} +(-8.46197e35 + 1.17694e36i) q^{82} -3.83632e36i q^{83} +(1.94058e36 + 5.77653e36i) q^{84} -1.82446e35 q^{85} +(3.63558e36 + 2.61391e36i) q^{86} +6.21159e35i q^{87} +(-2.48438e36 + 8.05260e36i) q^{88} -1.37441e37 q^{89} +(-3.71771e35 + 5.17082e35i) q^{90} -4.67127e37i q^{91} +(3.46402e36 - 1.16371e36i) q^{92} +4.06784e36 q^{93} +(6.95460e36 + 5.00021e36i) q^{94} -8.18594e36i q^{95} +(5.00709e37 - 1.24409e36i) q^{96} +2.37702e37 q^{97} +(5.43254e37 - 7.55591e37i) q^{98} -1.44871e37i 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 $

$2$	−306058.	+	425684.i	−0.583759	+	0.811927i
$2$	−306058.	+	425684.i	−0.583759	+	0.811927i
$3$			1.26436e9i			1.08784i	0.839136	+	0.543921i	$0.183061\pi$
$3$			1.26436e9i			1.08784i	−0.839136	+	0.543921i	$0.816939\pi$
$4$	−8.75354e10	−	2.60567e11i	−0.318452	−	0.947939i
$5$	−4.90299e12			−0.257058			−0.128529	−	0.991706i	$-0.541025\pi$
$5$	−4.90299e12			−0.257058			−0.128529	+	0.991706i	$0.541025\pi$
$6$	−5.38217e14	−	3.86966e14i	−0.883249	−	0.635038i
$7$			1.75338e16i			1.53820i	0.639126	+	0.769102i	$0.279296\pi$
$7$			1.75338e16i			1.53820i	−0.639126	+	0.769102i	$0.720704\pi$
$8$	1.37710e17	+	4.24863e16i	0.955557	+	0.294808i
$9$	−2.47749e17			−0.183402
$10$	1.50060e18	−	2.08712e18i	0.150060	−	0.208712i
$11$			5.84750e19i			0.956113i	0.878329	+	0.478056i	$0.158659\pi$
$11$			5.84750e19i			0.956113i	−0.878329	+	0.478056i	$0.841341\pi$
$12$	3.29451e20	−	1.10676e20i	1.03121	−	0.346426i
$13$	−2.66415e21			−1.82236			−0.911181	−	0.412007i	$-0.864828\pi$
$13$	−2.66415e21			−1.82236			−0.911181	+	0.412007i	$0.864828\pi$
$14$	−7.46387e21	−	5.36636e21i	−1.24891	−	0.897940i
$15$		−	6.19913e21i		−	0.279638i
$16$	−6.02330e22	+	4.56178e22i	−0.797177	+	0.603746i
$17$	3.72111e22			0.155648			0.0778239	−	0.996967i	$-0.475203\pi$
$17$	3.72111e22			0.155648			0.0778239	+	0.996967i	$0.475203\pi$
$18$	7.58254e22	−	1.05463e23i	0.107062	−	0.148909i
$19$			1.66958e24i			0.843897i	0.906620	+	0.421949i	$0.138654\pi$
$19$			1.66958e24i			0.843897i	−0.906620	+	0.421949i	$0.861346\pi$
$20$	4.29185e23	+	1.27756e24i	0.0818605	+	0.243675i
$21$	−2.21690e25			−1.67332
$22$	−2.48918e25	−	1.78967e25i	−0.776294	−	0.558139i
$23$			1.32941e25i			0.178169i	0.996024	+	0.0890843i	$0.0283940\pi$
$23$			1.32941e25i			0.178169i	−0.996024	+	0.0890843i	$0.971606\pi$
$24$	−5.37179e25	+	1.74115e26i	−0.320704	+	1.03950i
$25$	−3.39759e26			−0.933921
$26$	8.15382e26	−	1.13408e27i	1.06382	−	1.47962i
$27$			1.39472e27i			0.888330i
$28$	4.56875e27	−	1.53483e27i	1.45812	−	0.489844i
$29$	4.91284e26			0.0804954			0.0402477	−	0.999190i	$-0.487185\pi$
$29$	4.91284e26			0.0804954			0.0402477	+	0.999190i	$0.487185\pi$
$30$	2.63887e27	+	1.89729e27i	0.227046	+	0.163241i
$31$		−	3.21732e27i		−	0.148464i	−0.997241	−	0.0742322i	$-0.976349\pi$
$31$		−	3.21732e27i		−	0.148464i	0.997241	−	0.0742322i	$-0.0236506\pi$
$32$	−9.83973e26	−	3.96019e28i	−0.0248390	−	0.999691i
$33$	−7.39333e28			−1.04010
$34$	−1.13887e28	+	1.58402e28i	−0.0908608	+	0.126375i
$35$		−	8.59681e28i		−	0.395407i
$36$	2.16868e28	+	6.45553e28i	0.0584047	+	0.173854i
$37$	9.26858e29			1.48313			0.741567	−	0.670879i	$-0.234083\pi$
$37$	9.26858e29			1.48313			0.741567	+	0.670879i	$0.234083\pi$
$38$	−7.10714e29	−	5.10989e29i	−0.685183	−	0.492632i
$39$		−	3.36843e30i		−	1.98244i
$40$	−6.75191e29	−	2.08310e29i	−0.245633	−	0.0757826i
$41$	2.76483e30			0.629180			0.314590	−	0.949228i	$-0.398133\pi$
$41$	2.76483e30			0.629180			0.314590	+	0.949228i	$0.398133\pi$
$42$	6.78500e30	−	9.43700e30i	0.976818	−	1.35862i
$43$		−	8.54057e30i		−	0.786296i	−0.919475	−	0.393148i	$-0.871386\pi$
$43$		−	8.54057e30i		−	0.786296i	0.919475	−	0.393148i	$-0.128614\pi$
$44$	1.52367e31	−	5.11863e30i	0.906336	−	0.304476i
$45$	1.21471e30			0.0471448
$46$	−5.65910e30	−	4.06877e30i	−0.144660	−	0.104007i
$47$		−	1.63375e31i		−	0.277540i	−0.990325	−	0.138770i	$-0.955685\pi$
$47$		−	1.63375e31i		−	0.277540i	0.990325	−	0.138770i	$-0.0443149\pi$
$48$	−5.76772e31	−	7.61560e31i	−0.656781	−	0.867203i
$49$	−1.77501e32			−1.36607
$50$	1.03986e32	−	1.44630e32i	0.545185	−	0.758276i
$51$			4.70482e31i			0.169320i
$52$	2.33207e32	+	6.94190e32i	0.580334	+	1.72749i
$53$	1.08629e33			1.88237			0.941187	−	0.337887i	$-0.109712\pi$
$53$	1.08629e33			1.88237			0.941187	+	0.337887i	$0.109712\pi$
$54$	−5.93708e32	−	4.26864e32i	−0.721260	−	0.518570i
$55$		−	2.86702e32i		−	0.245776i
$56$	−7.44947e32	+	2.41459e33i	−0.453475	+	1.46984i
$57$	−2.11095e33			−0.918028
$58$	−1.50361e32	+	2.09132e32i	−0.0469899	+	0.0653564i
$59$			6.34821e33i			1.43371i	0.697220	+	0.716857i	$0.254420\pi$
$59$			6.34821e33i			1.43371i	−0.697220	+	0.716857i	$0.745580\pi$
$60$	−1.61529e33	+	5.42643e32i	−0.265080	+	0.0890513i
$61$	−9.47917e33			−1.13633			−0.568164	−	0.822916i	$-0.692346\pi$
$61$	−9.47917e33			−1.13633			−0.568164	+	0.822916i	$0.692346\pi$
$62$	1.36956e33	+	9.84686e32i	0.120542	+	0.0866673i
$63$		−	4.34398e33i		−	0.282110i
$64$	1.71590e34	+	1.17016e34i	0.826177	+	0.563411i
$65$	1.30623e34			0.468452
$66$	2.26278e34	−	3.14722e34i	0.607167	−	0.844486i
$67$		−	5.59969e34i		−	1.12913i	−0.825389	−	0.564564i	$-0.809044\pi$
$67$		−	5.59969e34i		−	1.12913i	0.825389	−	0.564564i	$-0.190956\pi$
$68$	−3.25729e33	−	9.69601e33i	−0.0495663	−	0.147545i
$69$	−1.68085e34			−0.193819
$70$	3.65952e34	+	2.63112e34i	0.321042	+	0.230822i
$71$		−	2.26917e35i		−	1.52040i	−0.649689	−	0.760200i	$-0.725101\pi$
$71$		−	2.26917e35i		−	1.52040i	0.649689	−	0.760200i	$-0.274899\pi$
$72$	−3.41175e34	−	1.05259e34i	−0.175251	−	0.0540683i
$73$	7.29274e34			0.288241			0.144121	−	0.989560i	$-0.453965\pi$
$73$	7.29274e34			0.288241			0.144121	+	0.989560i	$0.453965\pi$
$74$	−2.83672e35	+	3.94548e35i	−0.865792	+	1.20420i
$75$		−	4.29576e35i		−	1.01596i
$76$	4.35039e35	−	1.46148e35i	0.799963	−	0.268741i
$77$	−1.02529e36			−1.47070
$78$	1.43389e36	+	1.03093e36i	1.60960	+	1.15727i
$79$			7.48717e35i			0.659786i	0.944018	+	0.329893i	$0.107013\pi$
$79$			7.48717e35i			0.659786i	−0.944018	+	0.329893i	$0.892987\pi$
$80$	2.95321e35	−	2.23663e35i	0.204920	−	0.155198i
$81$	−2.09809e36			−1.14977
$82$	−8.46197e35	+	1.17694e36i	−0.367289	+	0.510848i
$83$		−	3.83632e36i		−	1.32261i	−0.750118	−	0.661304i	$-0.770003\pi$
$83$		−	3.83632e36i		−	1.32261i	0.750118	−	0.661304i	$-0.229997\pi$
$84$	1.94058e36	+	5.77653e36i	0.532873	+	1.58621i
$85$	−1.82446e35			−0.0400105
$86$	3.63558e36	+	2.61391e36i	0.638415	+	0.459007i
$87$			6.21159e35i			0.0875663i
$88$	−2.48438e36	+	8.05260e36i	−0.281869	+	0.913620i
$89$	−1.37441e37			−1.25807			−0.629036	−	0.777376i	$-0.716550\pi$
$89$	−1.37441e37			−1.25807			−0.629036	+	0.777376i	$0.716550\pi$
$90$	−3.71771e35	+	5.17082e35i	−0.0275212	+	0.0382782i
$91$		−	4.67127e37i		−	2.80316i
$92$	3.46402e36	−	1.16371e36i	0.168893	−	0.0567381i
$93$	4.06784e36			0.161506
$94$	6.95460e36	+	5.00021e36i	0.225343	+	0.162017i
$95$		−	8.18594e36i		−	0.216930i
$96$	5.00709e37	−	1.24409e36i	1.08751	−	0.0270209i
$97$	2.37702e37			0.424005			0.212002	−	0.977269i	$-0.432002\pi$
$97$	2.37702e37			0.424005			0.212002	+	0.977269i	$0.432002\pi$
$98$	5.43254e37	−	7.55591e37i	0.797457	−	1.10915i
$99$		−	1.44871e37i		−	0.175353i
$100$	2.97409e37	+	8.85301e37i	0.297409	+	0.885301i
$101$	−1.83709e38			−1.52064			−0.760318	−	0.649551i	$-0.774957\pi$
$101$	−1.83709e38			−1.52064			−0.760318	+	0.649551i	$0.774957\pi$
$102$	−2.00276e37	−	1.43994e37i	−0.137476	−	0.0988422i
$103$			1.43454e38i			0.818097i	0.912513	+	0.409049i	$0.134139\pi$
$103$			1.43454e38i			0.818097i	−0.912513	+	0.409049i	$0.865861\pi$
$104$	−3.66880e38	−	1.13190e38i	−1.74137	−	0.537246i
$105$	1.08694e38			0.430141
$106$	−3.32469e38	+	4.62418e38i	−1.09885	+	1.52835i
$107$			1.34510e38i			0.371932i	0.982556	+	0.185966i	$0.0595414\pi$
$107$			1.34510e38i			0.371932i	−0.982556	+	0.185966i	$0.940459\pi$
$108$	3.63418e38	−	1.22087e38i	0.842083	−	0.282890i
$109$	9.17365e38			1.78418			0.892090	−	0.451857i	$-0.149238\pi$
$109$	9.17365e38			1.78418			0.892090	+	0.451857i	$0.149238\pi$
$110$	1.22044e38	+	8.77473e37i	0.199552	+	0.143474i
$111$			1.17188e39i			1.61342i
$112$	−7.99854e38	−	1.05612e39i	−0.928685	−	1.22622i
$113$	−2.82851e38			−0.277375			−0.138687	−	0.990336i	$-0.544288\pi$
$113$	−2.82851e38			−0.277375			−0.138687	+	0.990336i	$0.544288\pi$
$114$	6.46072e38	−	8.98597e38i	0.535906	−	0.745372i
$115$		−	6.51809e37i		−	0.0457996i
$116$	−4.30048e37	−	1.28013e38i	−0.0256339	−	0.0763047i
$117$	6.60039e38			0.334224
$118$	−2.70233e39	−	1.94292e39i	−1.16407	−	0.836943i
$119$			6.52453e38i			0.239418i
$120$	2.63378e38	−	8.53683e38i	0.0824395	−	0.267210i
$121$	3.21112e38			0.0858487
$122$	2.90117e39	−	4.03513e39i	0.663341	−	0.922615i
$123$			3.49573e39i			0.684449i
$124$	−8.38329e38	+	2.81629e38i	−0.140735	+	0.0472787i
$125$	3.44953e39			0.497129
$126$	1.84916e39	+	1.32951e39i	0.229052	+	0.164684i
$127$		−	1.29401e40i		−	1.37932i	−0.724131	−	0.689662i	$-0.757759\pi$
$127$		−	1.29401e40i		−	1.37932i	0.724131	−	0.689662i	$-0.242241\pi$
$128$	−1.02328e40	+	3.72296e39i	−0.939737	+	0.341899i
$129$	1.07983e40			0.855367
$130$	−3.99781e39	+	5.56040e39i	−0.273463	+	0.380349i
$131$			1.09909e40i			0.649949i	0.945723	+	0.324974i	$0.105356\pi$
$131$			1.09909e40i			0.649949i	−0.945723	+	0.324974i	$0.894644\pi$
$132$	6.47178e39	+	1.92646e40i	0.331222	+	0.985952i
$133$	−2.92742e40			−1.29809
$134$	2.38370e40	+	1.71383e40i	0.916769	+	0.659138i
$135$		−	6.83828e39i		−	0.228352i
$136$	5.12435e39	+	1.58096e39i	0.148730	+	0.0458862i
$137$	−6.79802e40			−1.71669			−0.858345	−	0.513073i	$-0.828507\pi$
$137$	−6.79802e40			−1.71669			−0.858345	+	0.513073i	$0.828507\pi$
$138$	5.14438e39	−	7.15512e39i	0.113144	−	0.157367i
$139$			2.04964e40i			0.393004i	0.980503	+	0.196502i	$0.0629582\pi$
$139$			2.04964e40i			0.393004i	−0.980503	+	0.196502i	$0.937042\pi$
$140$	−2.24005e40	+	7.52525e39i	−0.374822	+	0.125918i
$141$	2.06564e40			0.301920
$142$	9.65948e40	+	6.94496e40i	1.23445	+	0.887547i
$143$		−	1.55786e41i		−	1.74238i
$144$	1.49226e40	−	1.13017e40i	0.146204	−	0.110728i
$145$	−2.40876e39			−0.0206919
$146$	−2.23200e40	+	3.10440e40i	−0.168263	+	0.234031i
$147$		−	2.24424e41i		−	1.48607i
$148$	−8.11329e40	−	2.41509e41i	−0.472307	−	1.40592i
$149$	1.44807e41			0.741737			0.370869	−	0.928685i	$-0.379060\pi$
$149$	1.44807e41			0.741737			0.370869	+	0.928685i	$0.379060\pi$
$150$	1.82864e41	+	1.31475e41i	0.824885	+	0.593075i
$151$			1.49687e41i			0.595145i	0.954699	+	0.297572i	$0.0961769\pi$
$151$			1.49687e41i			0.595145i	−0.954699	+	0.297572i	$0.903823\pi$
$152$	−7.09344e40	+	2.29919e41i	−0.248788	+	0.806392i
$153$	−9.21900e39			−0.0285461
$154$	3.13798e41	−	4.36450e41i	0.858532	−	1.19410i
$155$			1.57745e40i			0.0381639i
$156$	−8.77705e41	+	2.94857e41i	−1.87923	+	0.631312i
$157$	−1.37059e41			−0.259905			−0.129952	−	0.991520i	$-0.541482\pi$
$157$	−1.37059e41			−0.259905			−0.129952	+	0.991520i	$0.541482\pi$
$158$	−3.18717e41	−	2.29151e41i	−0.535698	−	0.385156i
$159$			1.37346e42i			2.04773i
$160$	4.82441e39	+	1.94167e41i	0.00638505	+	0.256978i
$161$	−2.33097e41			−0.274060
$162$	6.42137e41	−	8.93124e41i	0.671186	−	0.933526i
$163$			7.67808e41i			0.713984i	0.934107	+	0.356992i	$0.116198\pi$
$163$			7.67808e41i			0.713984i	−0.934107	+	0.356992i	$0.883802\pi$
$164$	−2.42020e41	−	7.20424e41i	−0.200364	−	0.596424i
$165$	3.62494e41			0.267366
$166$	1.63306e42	+	1.17414e42i	1.07386	+	0.772084i
$167$			7.43939e41i			0.436440i	0.975900	+	0.218220i	$0.0700250\pi$
$167$			7.43939e41i			0.436440i	−0.975900	+	0.218220i	$0.929975\pi$
$168$	−3.05290e42	−	9.41880e41i	−1.59896	−	0.493309i
$169$	4.96047e42			2.32100
$170$	5.58388e40	−	7.76641e40i	0.0233565	−	0.0324856i
$171$		−	4.13637e41i		−	0.154772i
$172$	−2.22539e42	+	7.47602e41i	−0.745361	+	0.250397i
$173$	−1.86001e42			−0.558005			−0.279003	−	0.960290i	$-0.590004\pi$
$173$	−1.86001e42			−0.558005			−0.279003	+	0.960290i	$0.590004\pi$
$174$	−2.64417e41	−	1.90110e41i	−0.0710975	−	0.0511176i
$175$		−	5.95727e42i		−	1.43656i
$176$	−2.66750e42	−	3.52212e42i	−0.577249	−	0.762191i
$177$	−8.02640e42			−1.55966
$178$	4.20648e42	−	5.85063e42i	0.734410	−	1.02146i
$179$			5.61184e42i			0.880842i	0.897791	+	0.440421i	$0.145171\pi$
$179$			5.61184e42i			0.880842i	−0.897791	+	0.440421i	$0.854829\pi$
$180$	−1.06330e41	−	3.16513e41i	−0.0150134	−	0.0446904i
$181$	8.57246e42			1.08946			0.544732	−	0.838610i	$-0.316632\pi$
$181$	8.57246e42			1.08946			0.544732	+	0.838610i	$0.316632\pi$
$182$	1.98848e43	+	1.42968e43i	2.27597	+	1.63637i
$183$		−	1.19851e43i		−	1.23615i
$184$	−5.64818e41	+	1.83074e42i	−0.0525255	+	0.170250i
$185$	−4.54437e42			−0.381251
$186$	−1.24499e42	+	1.73162e42i	−0.0942804	+	0.131131i
$187$			2.17592e42i			0.148817i
$188$	−4.25702e42	+	1.43011e42i	−0.263091	+	0.0883832i
$189$	−2.44547e43			−1.36643
$190$	3.48462e42	+	2.50537e42i	0.176132	+	0.126635i
$191$		−	8.48625e42i		−	0.388223i	−0.980979	−	0.194112i	$-0.937818\pi$
$191$		−	8.48625e42i		−	0.388223i	0.980979	−	0.194112i	$-0.0621824\pi$
$192$	−1.47950e43	+	2.16951e43i	−0.612903	+	0.898750i
$193$	−2.67677e42			−0.100467			−0.0502333	−	0.998738i	$-0.515996\pi$
$193$	−2.67677e42			−0.100467			−0.0502333	+	0.998738i	$0.515996\pi$
$194$	−7.27506e42	+	1.01186e43i	−0.247516	+	0.344261i
$195$			1.65154e43i			0.509602i
$196$	1.55376e43	+	4.62509e43i	0.435029	+	1.29495i
$197$	−9.67188e42			−0.245840			−0.122920	−	0.992417i	$-0.539226\pi$
$197$	−9.67188e42			−0.245840			−0.122920	+	0.992417i	$0.539226\pi$
$198$	6.16692e42	+	4.43389e42i	0.142374	+	0.102364i
$199$		−	4.54881e43i		−	0.954309i	−0.878819	−	0.477155i	$-0.841668\pi$
$199$		−	4.54881e43i		−	0.954309i	0.878819	−	0.477155i	$-0.158332\pi$
$200$	−4.67882e43	−	1.44351e43i	−0.892415	−	0.275327i
$201$	7.08002e43			1.22831
$202$	5.62257e43	−	7.82021e43i	0.887685	−	1.23465i
$203$			8.61410e42i			0.123818i
$204$	1.22592e43	−	4.11838e42i	0.160505	−	0.0539204i
$205$	−1.35559e43			−0.161736
$206$	−6.10660e43	−	4.39052e43i	−0.664236	−	0.477571i
$207$		−	3.29360e42i		−	0.0326764i
$208$	1.60469e44	−	1.21532e44i	1.45274	−	1.10024i
$209$	−9.76288e43			−0.806861
$210$	−3.32668e43	+	4.62695e43i	−0.251098	+	0.349243i
$211$			1.63132e44i			1.12505i	0.826779	+	0.562526i	$0.190171\pi$
$211$			1.63132e44i			1.12505i	−0.826779	+	0.562526i	$0.809829\pi$
$212$	−9.50891e43	−	2.83053e44i	−0.599445	−	1.78438i
$213$	2.86904e44			1.65396
$214$	−5.72588e43	−	4.11679e43i	−0.301982	−	0.217118i
$215$			4.18743e43i			0.202123i
$216$	−5.92563e43	+	1.92067e44i	−0.261887	+	0.848850i
$217$	5.64120e43			0.228369
$218$	−2.80767e44	+	3.90508e44i	−1.04153	+	1.44863i
$219$			9.22063e43i			0.313561i
$220$	−7.47052e43	+	2.50966e43i	−0.232981	+	0.0782678i
$221$	−9.91359e43			−0.283647
$222$	−4.98850e44	−	3.58663e44i	−1.30998	−	0.941846i
$223$			1.45800e44i			0.351532i	0.984432	+	0.175766i	$0.0562403\pi$
$223$			1.45800e44i			0.351532i	−0.984432	+	0.175766i	$0.943760\pi$
$224$	6.94372e44	−	1.72528e43i	1.53773	−	0.0382074i
$225$	8.41747e43			0.171283
$226$	8.65686e43	−	1.20405e44i	0.161920	−	0.225208i
$227$			6.75172e44i			1.16124i	0.814174	+	0.580622i	$0.197190\pi$
$227$			6.75172e44i			1.16124i	−0.814174	+	0.580622i	$0.802810\pi$
$228$	1.84783e44	+	5.50045e44i	0.292348	+	0.870234i
$229$	−1.19571e44			−0.174082			−0.0870408	−	0.996205i	$-0.527741\pi$
$229$	−1.19571e44			−0.174082			−0.0870408	+	0.996205i	$0.527741\pi$
$230$	2.77465e43	+	1.99491e43i	0.0371859	+	0.0267359i
$231$		−	1.29633e45i		−	1.59989i
$232$	6.76549e43	+	2.08728e43i	0.0769179	+	0.0237307i
$233$	−2.07166e44			−0.217048			−0.108524	−	0.994094i	$-0.534612\pi$
$233$	−2.07166e44			−0.217048			−0.108524	+	0.994094i	$0.534612\pi$
$234$	−2.02010e44	+	2.80968e44i	−0.195106	+	0.271366i
$235$			8.01025e43i			0.0713439i
$236$	1.65414e45	−	5.55693e44i	1.35907	−	0.456569i
$237$	−9.46646e44			−0.717743
$238$	−2.77739e44	−	1.99688e44i	−0.194390	−	0.139762i
$239$		−	1.97531e45i		−	1.27666i	−0.769762	−	0.638331i	$-0.779625\pi$
$239$		−	1.97531e45i		−	1.27666i	0.769762	−	0.638331i	$-0.220375\pi$
$240$	2.82790e44	+	3.73392e44i	0.168830	+	0.222921i
$241$	−1.80484e45			−0.995670			−0.497835	−	0.867272i	$-0.665871\pi$
$241$	−1.80484e45			−0.995670			−0.497835	+	0.867272i	$0.665871\pi$
$242$	−9.82786e43	+	1.36692e44i	−0.0501149	+	0.0697029i
$243$		−	7.68684e44i		−	0.362434i
$244$	8.29763e44	+	2.46996e45i	0.361866	+	1.07717i
$245$	8.70283e44			0.351160
$246$	−1.48808e45	−	1.06990e45i	−0.555723	−	0.399553i
$247$		−	4.44801e45i		−	1.53789i
$248$	1.36692e44	−	4.43058e44i	0.0437684	−	0.141866i
$249$	4.85048e45			1.43879
$250$	−1.05575e45	+	1.46841e45i	−0.290203	+	0.403633i
$251$			4.76316e45i			1.21365i	0.794834	+	0.606827i	$0.207558\pi$
$251$			4.76316e45i			1.21365i	−0.794834	+	0.606827i	$0.792442\pi$
$252$	−1.13190e45	+	3.80252e44i	−0.267423	+	0.0898383i
$253$	−7.77374e44			−0.170349
$254$	5.50838e45	+	3.96041e45i	1.11991	+	0.805192i
$255$		−	2.30676e44i		−	0.0435251i
$256$	1.54703e45	−	5.49539e45i	0.270982	−	0.962584i
$257$	−6.75988e45			−1.09954			−0.549768	−	0.835317i	$-0.685284\pi$
$257$	−6.75988e45			−1.09954			−0.549768	+	0.835317i	$0.685284\pi$
$258$	−3.30491e45	+	4.59668e45i	−0.499328	+	0.694496i
$259$			1.62514e46i			2.28136i
$260$	−1.14341e45	−	3.40360e45i	−0.149179	−	0.444064i
$261$	−1.21715e44			−0.0147630
$262$	−4.67865e45	−	3.36385e45i	−0.527711	−	0.379413i
$263$			6.31600e45i			0.662648i	0.943517	+	0.331324i	$0.107495\pi$
$263$			6.31600e45i			0.662648i	−0.943517	+	0.331324i	$0.892505\pi$
$264$	−1.01814e46	−	3.14115e45i	−0.993875	−	0.306630i
$265$	−5.32608e45			−0.483879
$266$	8.95959e45	−	1.24615e46i	0.757769	−	1.05395i
$267$		−	1.73774e46i		−	1.36858i
$268$	−1.45910e46	+	4.90171e45i	−1.07034	+	0.359573i
$269$	1.61772e46			1.10563			0.552817	−	0.833303i	$-0.313553\pi$
$269$	1.61772e46			1.10563			0.552817	+	0.833303i	$0.313553\pi$
$270$	2.91094e45	+	2.09291e45i	0.185405	+	0.133303i
$271$			1.77512e46i			1.05393i	0.849888	+	0.526963i	$0.176669\pi$
$271$			1.77512e46i			1.05393i	−0.849888	+	0.526963i	$0.823331\pi$
$272$	−2.24134e45	+	1.69749e45i	−0.124079	+	0.0939718i
$273$	5.90616e46			3.04940
$274$	2.08059e46	−	2.89381e46i	1.00213	−	1.39383i
$275$		−	1.98674e46i		−	0.892934i
$276$	1.47134e45	+	4.37976e45i	0.0617221	+	0.183729i
$277$	−3.30297e46			−1.29357			−0.646783	−	0.762674i	$-0.723886\pi$
$277$	−3.30297e46			−1.29357			−0.646783	+	0.762674i	$0.723886\pi$
$278$	−8.72499e45	−	6.27309e45i	−0.319091	−	0.229419i
$279$			7.97087e44i			0.0272286i
$280$	3.65247e45	−	1.18387e46i	0.116569	−	0.377834i
$281$	−4.17143e46			−1.24413			−0.622063	−	0.782967i	$-0.713705\pi$
$281$	−4.17143e46			−1.24413			−0.622063	+	0.782967i	$0.713705\pi$
$282$	−6.32206e45	+	8.79311e45i	−0.176248	+	0.245137i
$283$		−	3.96827e46i		−	1.03433i	−0.855886	−	0.517165i	$-0.826987\pi$
$283$		−	3.96827e46i		−	1.03433i	0.855886	−	0.517165i	$-0.173013\pi$
$284$	−5.91271e46	+	1.98632e46i	−1.44125	+	0.484174i
$285$	1.03500e46			0.235986
$286$	6.63155e46	+	4.76795e46i	1.41469	+	1.01713i
$287$			4.84780e46i			0.967808i
$288$	2.43778e44	+	9.81131e45i	0.00455551	+	0.183345i
$289$	−5.57710e46			−0.975774
$290$	7.37219e44	−	1.02537e45i	0.0120791	−	0.0168004i
$291$			3.00541e46i			0.461250i
$292$	−6.38373e45	−	1.90025e46i	−0.0917910	−	0.273235i
$293$	−1.90543e46			−0.256748			−0.128374	−	0.991726i	$-0.540976\pi$
$293$	−1.90543e46			−0.256748			−0.128374	+	0.991726i	$0.540976\pi$
$294$	9.55337e46	+	6.86867e46i	1.20658	+	0.867508i
$295$		−	3.11252e46i		−	0.368547i
$296$	1.27638e47	+	3.93788e46i	1.41722	+	0.437240i
$297$	−8.15560e46			−0.849344
$298$	−4.43193e46	+	6.16419e46i	−0.432996	+	0.602237i
$299$		−	3.54175e46i		−	0.324687i
$300$	−1.11934e47	+	3.76031e46i	−0.963068	+	0.323534i
$301$	1.49749e47			1.20948
$302$	−6.37194e46	−	4.58129e46i	−0.483214	−	0.347421i
$303$		−	2.32274e47i		−	1.65421i
$304$	−7.61626e46	−	1.00564e47i	−0.509500	−	0.672735i
$305$	4.64762e46			0.292102
$306$	2.82155e45	−	3.92438e45i	0.0166640	−	0.0231774i
$307$		−	1.32974e47i		−	0.738138i	−0.929402	−	0.369069i	$-0.879677\pi$
$307$		−	1.32974e47i		−	0.738138i	0.929402	−	0.369069i	$-0.120323\pi$
$308$	8.97492e46	+	2.67157e47i	0.468346	+	1.39413i
$309$	−1.81377e47			−0.889961
$310$	−6.71494e45	−	4.82790e45i	−0.0309863	−	0.0222785i
$311$			4.05175e47i			1.75871i	0.476164	+	0.879357i	$0.342027\pi$
$311$			4.05175e47i			1.75871i	−0.476164	+	0.879357i	$0.657973\pi$
$312$	1.43112e47	−	4.63868e47i	0.584439	−	1.89434i
$313$	3.46826e47			1.33281			0.666407	−	0.745589i	$-0.267832\pi$
$313$	3.46826e47			1.33281			0.666407	+	0.745589i	$0.267832\pi$
$314$	4.19480e46	−	5.83438e46i	0.151722	−	0.211024i
$315$			2.12985e46i			0.0725184i
$316$	1.95091e47	−	6.55392e46i	0.625437	−	0.210110i
$317$	−2.88485e47			−0.870958			−0.435479	−	0.900199i	$-0.643421\pi$
$317$	−2.88485e47			−0.870958			−0.435479	+	0.900199i	$0.643421\pi$
$318$	−5.84661e47	−	4.20359e47i	−1.66260	−	1.19538i
$319$			2.87278e46i			0.0769626i
$320$	−8.41304e46	−	5.73727e46i	−0.212375	−	0.144829i
$321$	−1.70069e47			−0.404604
$322$	7.13411e46	−	9.92256e46i	0.159985	−	0.222517i
$323$			6.21270e46i			0.131351i
$324$	1.83657e47	+	5.46695e47i	0.366145	+	1.08991i
$325$	9.05167e47			1.70194
$326$	−3.26844e47	−	2.34994e47i	−0.579703	−	0.416794i
$327$			1.15988e48i			1.94091i
$328$	3.80745e47	+	1.17467e47i	0.601217	+	0.185487i
$329$	2.86459e47			0.426914
$330$	−1.10944e47	+	1.54308e47i	−0.156077	+	0.217082i
$331$		−	2.85500e47i		−	0.379206i	−0.981861	−	0.189603i	$-0.939280\pi$
$331$		−	2.85500e47i		−	0.379206i	0.981861	−	0.189603i	$-0.0607200\pi$
$332$	−9.99621e47	+	3.35814e47i	−1.25375	+	0.421187i
$333$	−2.29628e47			−0.272010
$334$	−3.16683e47	−	2.27688e47i	−0.354358	−	0.254776i
$335$			2.74552e47i			0.290251i
$336$	1.33531e48	−	1.01130e48i	1.33394	−	1.01026i
$337$	−8.12808e47			−0.767397			−0.383698	−	0.923458i	$-0.625350\pi$
$337$	−8.12808e47			−0.767397			−0.383698	+	0.923458i	$0.625350\pi$
$338$	−1.51819e48	+	2.11159e48i	−1.35490	+	1.88448i
$339$		−	3.57624e47i		−	0.301740i
$340$	1.59704e46	+	4.75394e46i	0.0127414	+	0.0379275i
$341$	1.88133e47			0.141949
$342$	1.76079e47	+	1.26597e47i	0.125664	+	0.0903497i
$343$		−	8.34010e47i		−	0.563096i
$344$	3.62857e47	−	1.17612e48i	0.231806	−	0.751351i
$345$	8.24120e46			0.0498228
$346$	5.69269e47	−	7.91774e47i	0.325740	−	0.453060i
$347$		−	1.12522e48i		−	0.609505i	−0.952432	−	0.304752i	$-0.901426\pi$
$347$		−	1.12522e48i		−	0.609505i	0.952432	−	0.304752i	$-0.0985737\pi$
$348$	1.61854e47	−	5.43734e46i	0.0830075	−	0.0278856i
$349$	−1.77642e48			−0.862707			−0.431353	−	0.902183i	$-0.641964\pi$
$349$	−1.77642e48			−0.862707			−0.431353	+	0.902183i	$0.641964\pi$
$350$	2.53591e48	+	1.82327e48i	1.16638	+	0.838606i
$351$		−	3.71573e48i		−	1.61886i
$352$	2.31572e48	−	5.75378e46i	0.955818	−	0.0237489i
$353$	−3.18465e46			−0.0124549			−0.00622747	−	0.999981i	$-0.501982\pi$
$353$	−3.18465e46			−0.0124549			−0.00622747	+	0.999981i	$0.501982\pi$
$354$	2.45654e48	−	3.41671e48i	0.910463	−	1.26633i
$355$			1.11257e48i			0.390831i
$356$	1.20309e48	+	3.58126e48i	0.400635	+	1.19258i
$357$	−8.24935e47			−0.260449
$358$	−2.38887e48	−	1.71755e48i	−0.715180	−	0.514199i
$359$			3.97930e46i			0.0112983i	0.999984	+	0.00564914i	$0.00179819\pi$
$359$			3.97930e46i			0.0112983i	−0.999984	+	0.00564914i	$0.998202\pi$
$360$	1.67278e47	+	5.16084e46i	0.0450496	+	0.0138987i
$361$	1.12664e48			0.287837
$362$	−2.62367e48	+	3.64916e48i	−0.635983	+	0.884565i
$363$			4.06000e47i			0.0933899i
$364$	−1.21718e49	+	4.08901e48i	−2.65723	+	0.892673i
$365$	−3.57562e47			−0.0740947
$366$	5.10185e48	+	3.66812e48i	1.00366	+	0.721610i
$367$		−	8.45967e48i		−	1.58015i	−0.613011	−	0.790075i	$-0.710042\pi$
$367$		−	8.45967e48i		−	1.58015i	0.613011	−	0.790075i	$-0.289958\pi$
$368$	−6.06448e47	−	8.00745e47i	−0.107569	−	0.142032i
$369$	−6.84983e47			−0.115393
$370$	1.39084e48	−	1.93447e48i	0.222559	−	0.309548i
$371$			1.90469e49i			2.89548i
$372$	−3.56080e47	−	1.05995e48i	−0.0514318	−	0.153098i
$373$	−4.35741e47			−0.0598082			−0.0299041	−	0.999553i	$-0.509520\pi$
$373$	−4.35741e47			−0.0598082			−0.0299041	+	0.999553i	$0.509520\pi$
$374$	−9.26253e47	−	6.65957e47i	−0.120828	−	0.0868731i
$375$			4.36144e48i			0.540798i
$376$	6.94119e47	−	2.24984e48i	0.0818210	−	0.265205i
$377$	−1.30885e48			−0.146692
$378$	7.48456e48	−	1.04100e49i	0.797668	−	1.10945i
$379$		−	3.70147e48i		−	0.375171i	−0.982248	−	0.187586i	$-0.939934\pi$
$379$		−	3.70147e48i		−	0.375171i	0.982248	−	0.187586i	$-0.0600662\pi$
$380$	−2.13299e48	+	7.16560e47i	−0.205637	+	0.0690818i
$381$	1.63609e49			1.50049
$382$	3.61246e48	+	2.59728e48i	0.315209	+	0.226629i
$383$			4.28701e48i			0.355941i	0.984036	+	0.177971i	$0.0569532\pi$
$383$			4.28701e48i			0.355941i	−0.984036	+	0.177971i	$0.943047\pi$
$384$	−4.70715e48	−	1.29380e49i	−0.371933	−	1.02229i
$385$	5.02698e48			0.378054
$386$	8.19245e47	−	1.13946e48i	0.0586483	−	0.0815716i
$387$			2.11591e48i			0.144208i
$388$	−2.08074e48	−	6.19375e48i	−0.135025	−	0.401931i
$389$	−6.95989e48			−0.430091			−0.215045	−	0.976604i	$-0.568990\pi$
$389$	−6.95989e48			−0.430091			−0.215045	+	0.976604i	$0.568990\pi$
$390$	−7.03033e48	−	5.05466e48i	−0.413760	−	0.297485i
$391$			4.94689e47i			0.0277316i
$392$	−2.44436e49	−	7.54134e48i	−1.30536	−	0.402729i
$393$	−1.38964e49			−0.707042
$394$	2.96015e48	−	4.11716e48i	0.143511	−	0.199604i
$395$		−	3.67095e48i		−	0.169603i
$396$	−3.77487e48	+	1.26813e48i	−0.166224	+	0.0558414i
$397$	9.66079e48			0.405502			0.202751	−	0.979230i	$-0.435012\pi$
$397$	9.66079e48			0.405502			0.202751	+	0.979230i	$0.435012\pi$
$398$	1.93635e49	+	1.39220e49i	0.774830	+	0.557086i
$399$		−	3.70131e49i		−	1.41211i
$400$	2.04647e49	−	1.54990e49i	0.744500	−	0.563851i
$401$	2.47391e49			0.858302			0.429151	−	0.903233i	$-0.358813\pi$
$401$	2.47391e49			0.858302			0.429151	+	0.903233i	$0.358813\pi$
$402$	−2.16689e49	+	3.01385e49i	−0.717038	+	0.997301i
$403$			8.57141e48i			0.270556i
$404$	1.60811e49	+	4.78687e49i	0.484250	+	1.44147i
$405$	1.02869e49			0.295556
$406$	−3.66688e48	−	2.63641e48i	−0.100531	−	0.0722800i
$407$			5.41980e49i			1.41804i
$408$	−1.99890e48	+	6.47901e48i	−0.0499170	+	0.161795i
$409$	−1.71268e49			−0.408257			−0.204128	−	0.978944i	$-0.565436\pi$
$409$	−1.71268e49			−0.408257			−0.204128	+	0.978944i	$0.565436\pi$
$410$	4.14889e48	−	5.77053e48i	0.0944145	−	0.131317i
$411$		−	8.59513e49i		−	1.86749i
$412$	3.73794e49	−	1.25573e49i	0.775507	−	0.260525i
$413$	−1.11308e50			−2.20535
$414$	1.40203e48	+	1.00803e48i	0.0265309	+	0.0190752i
$415$			1.88094e49i			0.339987i
$416$	2.62145e48	+	1.05505e50i	0.0452656	+	1.82180i
$417$	−2.59148e49			−0.427526
$418$	2.98800e49	−	4.15590e49i	0.471012	−	0.655112i
$419$			6.12828e49i			0.923150i	0.887101	+	0.461575i	$0.152716\pi$
$419$			6.12828e49i			0.923150i	−0.887101	+	0.461575i	$0.847284\pi$
$420$	−9.51461e48	−	2.83222e49i	−0.136979	−	0.407747i
$421$	−1.14147e49			−0.157074			−0.0785371	−	0.996911i	$-0.525025\pi$
$421$	−1.14147e49			−0.157074			−0.0785371	+	0.996911i	$0.525025\pi$
$422$	−6.94427e49	−	4.99278e49i	−0.913461	−	0.656759i
$423$			4.04759e48i			0.0509014i
$424$	1.49594e50	+	4.61526e49i	1.79871	+	0.554938i
$425$	−1.26428e49			−0.145363
$426$	−8.78091e49	+	1.22130e50i	−0.965511	+	1.34289i
$427$		−	1.66206e50i		−	1.74790i
$428$	3.50490e49	−	1.17744e49i	0.352569	−	0.118442i
$429$	1.96969e50			1.89544
$430$	−1.78252e49	−	1.28159e49i	−0.164110	−	0.117991i
$431$		−	6.33263e49i		−	0.557848i	−0.960313	−	0.278924i	$-0.910022\pi$
$431$		−	6.33263e49i		−	0.557848i	0.960313	−	0.278924i	$-0.0899778\pi$
$432$	−6.36238e49	−	8.40079e49i	−0.536326	−	0.708156i
$433$	2.92411e49			0.235898			0.117949	−	0.993020i	$-0.462368\pi$
$433$	2.92411e49			0.235898			0.117949	+	0.993020i	$0.462368\pi$
$434$	−1.72653e49	+	2.40137e49i	−0.133312	+	0.185419i
$435$		−	3.04553e48i		−	0.0225096i
$436$	−8.03019e49	−	2.39036e50i	−0.568176	−	1.69129i
$437$	−2.21957e49			−0.150356
$438$	−3.92507e49	−	2.82204e49i	−0.254589	−	0.183044i
$439$			5.86332e49i			0.364181i	0.983282	+	0.182091i	$0.0582864\pi$
$439$			5.86332e49i			0.364181i	−0.983282	+	0.182091i	$0.941714\pi$
$440$	1.21809e49	−	3.94818e49i	0.0724567	−	0.234853i
$441$	4.39755e49			0.250540
$442$	3.03413e49	−	4.22005e49i	0.165581	−	0.230300i
$443$			2.23210e50i			1.16693i	0.812139	+	0.583464i	$0.198303\pi$
$443$			2.23210e50i			1.16693i	−0.812139	+	0.583464i	$0.801697\pi$
$444$	3.05354e50	−	1.02581e50i	1.52942	−	0.513796i
$445$	6.73870e49			0.323397
$446$	−6.20647e49	−	4.46232e49i	−0.285419	−	0.205210i
$447$			1.83088e50i			0.806894i
$448$	−2.05174e50	+	3.00863e50i	−0.866641	+	1.27083i
$449$	6.21641e49			0.251686			0.125843	−	0.992050i	$-0.459836\pi$
$449$	6.21641e49			0.251686			0.125843	+	0.992050i	$0.459836\pi$
$450$	−2.57623e49	+	3.58318e49i	−0.0999879	+	0.139069i
$451$			1.61673e50i			0.601567i
$452$	2.47594e49	+	7.37017e49i	0.0883304	+	0.262934i
$453$	−1.89258e50			−0.647424
$454$	−2.87410e50	−	2.06642e50i	−0.942845	−	0.677886i
$455$			2.29032e50i			0.720575i
$456$	−2.90699e50	−	8.96864e49i	−0.877227	−	0.270642i
$457$	−6.07259e49			−0.175779			−0.0878893	−	0.996130i	$-0.528012\pi$
$457$	−6.07259e49			−0.175779			−0.0878893	+	0.996130i	$0.528012\pi$
$458$	3.65957e49	−	5.08995e49i	0.101622	−	0.141342i
$459$			5.18990e49i			0.138267i
$460$	−1.69840e49	+	5.70564e48i	−0.0434152	+	0.0145850i
$461$	−2.79239e50			−0.684948			−0.342474	−	0.939527i	$-0.611265\pi$
$461$	−2.79239e50			−0.684948			−0.342474	+	0.939527i	$0.611265\pi$
$462$	5.51828e50	+	3.96753e50i	1.29899	+	0.933948i
$463$			9.66146e49i			0.218275i	0.994027	+	0.109138i	$0.0348089\pi$
$463$			9.66146e49i			0.218275i	−0.994027	+	0.109138i	$0.965191\pi$
$464$	−2.95915e49	+	2.24113e49i	−0.0641690	+	0.0485987i
$465$	−1.99446e49			−0.0415163
$466$	6.34048e49	−	8.81873e49i	0.126704	−	0.176227i
$467$		−	9.06956e50i		−	1.74007i	−0.492994	−	0.870033i	$-0.664098\pi$
$467$		−	9.06956e50i		−	1.74007i	0.492994	−	0.870033i	$-0.335902\pi$
$468$	−5.77767e49	−	1.71985e50i	−0.106434	−	0.316824i
$469$	9.81841e50			1.73683
$470$	−3.40983e49	−	2.45160e49i	−0.0579260	−	0.0416476i
$471$		−	1.73292e50i		−	0.282735i
$472$	−2.69712e50	+	8.74213e50i	−0.422670	+	1.37000i
$473$	4.99410e50			0.751788
$474$	2.89728e50	−	4.02972e50i	0.418989	−	0.582755i
$475$		−	5.67255e50i		−	0.788134i
$476$	1.70008e50	−	5.71128e49i	0.226954	−	0.0762432i
$477$	−2.69128e50			−0.345231
$478$	8.40858e50	+	6.04559e50i	1.03656	+	0.745262i
$479$		−	8.82583e50i		−	1.04564i	−0.852444	−	0.522819i	$-0.824881\pi$
$479$		−	8.82583e50i		−	1.04564i	0.852444	−	0.522819i	$-0.175119\pi$
$480$	−2.45497e50	+	6.09978e48i	−0.279552	+	0.00694593i
$481$	−2.46929e51			−2.70281
$482$	5.52386e50	−	7.68292e50i	0.581231	−	0.808412i
$483$		−	2.94718e50i		−	0.298134i
$484$	−2.81086e49	−	8.36712e49i	−0.0273387	−	0.0813794i
$485$	−1.16545e50			−0.108994
$486$	3.27216e50	+	2.35262e50i	0.294270	+	0.211574i
$487$			5.11024e50i			0.441968i	0.975277	+	0.220984i	$0.0709268\pi$
$487$			5.11024e50i			0.441968i	−0.975277	+	0.220984i	$0.929073\pi$
$488$	−1.30538e51	−	4.02735e50i	−1.08583	−	0.334998i
$489$	−9.70784e50			−0.776702
$490$	−2.66357e50	+	3.70465e50i	−0.204992	+	0.285116i
$491$			1.05732e51i			0.782810i	0.920218	+	0.391405i	$0.128011\pi$
$491$			1.05732e51i			0.782810i	−0.920218	+	0.391405i	$0.871989\pi$
$492$	9.10874e50	−	3.06000e50i	0.648816	−	0.217964i
$493$	1.82812e49			0.0125289
$494$	1.89345e51	+	1.36135e51i	1.24865	+	0.897754i
$495$			7.10300e49i			0.0450758i
$496$	1.46767e50	+	1.93789e50i	0.0896347	+	0.118352i
$497$	3.97872e51			2.33869
$498$	−1.48453e51	+	2.06477e51i	−0.839906	+	1.16819i
$499$			1.29283e51i			0.704095i	0.935982	+	0.352048i	$0.114514\pi$
$499$			1.29283e51i			0.704095i	−0.935982	+	0.352048i	$0.885486\pi$
$500$	−3.01956e50	−	8.98835e50i	−0.158312	−	0.471248i
$501$	−9.40605e50			−0.474778
$502$	−2.02760e51	−	1.45780e51i	−0.985399	−	0.708481i
$503$		−	3.84626e51i		−	1.79989i	−0.436002	−	0.899946i	$-0.643606\pi$
$503$		−	3.84626e51i		−	1.79989i	0.436002	−	0.899946i	$-0.356394\pi$
$504$	1.84560e50	−	5.98211e50i	0.0831681	−	0.269572i
$505$	9.00725e50			0.390891
$506$	2.37921e50	−	3.30915e50i	0.0994428	−	0.138311i
$507$			6.27180e51i			2.52488i
$508$	−3.37176e51	+	1.13271e51i	−1.30751	+	0.439248i
$509$	1.54984e51			0.578960			0.289480	−	0.957184i	$-0.406518\pi$
$509$	1.54984e51			0.578960			0.289480	+	0.957184i	$0.406518\pi$
$510$	9.81952e49	+	7.06003e49i	0.0353392	+	0.0254082i
$511$			1.27870e51i			0.443374i
$512$	1.86582e51	+	2.34045e51i	0.623361	+	0.781934i
$513$	−2.32860e51			−0.749660
$514$	2.06891e51	−	2.87757e51i	0.641864	−	0.892744i
$515$		−	7.03352e50i		−	0.210298i
$516$	−9.45236e50	−	2.81370e51i	−0.272393	−	0.810835i
$517$	9.55334e50			0.265360
$518$	−6.91795e51	−	4.97386e51i	−1.85230	−	1.33177i
$519$		−	2.35171e51i		−	0.607022i
$520$	1.79881e51	+	5.54967e50i	0.447632	+	0.138103i
$521$	−3.81868e51			−0.916214			−0.458107	−	0.888897i	$-0.651472\pi$
$521$	−3.81868e51			−0.916214			−0.458107	+	0.888897i	$0.651472\pi$
$522$	3.72518e49	−	5.18121e49i	0.00861803	−	0.0119865i
$523$			2.36519e51i			0.527636i	0.964572	+	0.263818i	$0.0849818\pi$
$523$			2.36519e51i			0.527636i	−0.964572	+	0.263818i	$0.915018\pi$
$524$	2.86388e51	−	9.62094e50i	0.616112	−	0.206977i
$525$	7.53212e51			1.56275
$526$	−2.68862e51	−	1.93306e51i	−0.538022	−	0.386826i
$527$		−	1.19720e50i		−	0.0231082i
$528$	4.45322e51	−	3.37267e51i	0.829144	−	0.627956i
$529$	5.39073e51			0.968256
$530$	1.63009e51	−	2.26723e51i	0.282468	−	0.392874i
$531$		−	1.57276e51i		−	0.262946i
$532$	2.56253e51	+	7.62790e51i	0.413378	+	1.23051i
$533$	−7.36591e51			−1.14659
$534$	7.39729e51	+	5.31849e51i	1.11119	+	0.798923i
$535$		−	6.59502e50i		−	0.0956080i
$536$	2.37910e51	−	7.71135e51i	0.332876	−	1.07895i
$537$	−7.09538e51			−0.958218
$538$	−4.95117e51	+	6.88639e51i	−0.645423	+	0.897694i
$539$		−	1.03793e52i		−	1.30612i
$540$	−1.78183e51	+	5.98591e50i	−0.216464	+	0.0727192i
$541$	5.02770e51			0.589687			0.294843	−	0.955546i	$-0.404733\pi$
$541$	5.02770e51			0.589687			0.294843	+	0.955546i	$0.404733\pi$
$542$	−7.55638e51	−	5.43288e51i	−0.855711	−	0.615238i
$543$			1.08387e52i			1.18516i
$544$	−3.66147e49	−	1.47363e51i	−0.00386613	−	0.155600i
$545$	−4.49783e51			−0.458637
$546$	−1.80762e52	+	2.51416e52i	−1.78011	+	2.47589i
$547$		−	1.20514e52i		−	1.14625i	−0.819468	−	0.573125i	$-0.805731\pi$
$547$		−	1.20514e52i		−	1.14625i	0.819468	−	0.573125i	$-0.194269\pi$
$548$	5.95067e51	+	1.77134e52i	0.546683	+	1.62732i
$549$	2.34845e51			0.208405
$550$	8.45722e51	+	6.08056e51i	0.724997	+	0.521258i
$551$			8.20240e50i			0.0679298i
$552$	−2.31471e51	−	7.14132e50i	−0.185205	−	0.0571395i
$553$	−1.31279e52			−1.01489
$554$	1.01090e52	−	1.40602e52i	0.755130	−	1.05028i
$555$		−	5.74571e51i		−	0.414741i
$556$	5.34070e51	−	1.79416e51i	0.372544	−	0.125153i
$557$	−4.26713e51			−0.287665			−0.143833	−	0.989602i	$-0.545943\pi$
$557$	−4.26713e51			−0.287665			−0.143833	+	0.989602i	$0.545943\pi$
$558$	−3.39307e50	−	2.43955e50i	−0.0221077	−	0.0158949i
$559$			2.27533e52i			1.43292i
$560$	3.92167e51	+	5.17812e51i	0.238726	+	0.315210i
$561$	−2.75114e51			−0.161889
$562$	1.27670e52	−	1.77571e52i	0.726270	−	1.01014i
$563$			2.39954e51i			0.131968i	0.997821	+	0.0659841i	$0.0210187\pi$
$563$			2.39954e51i			0.131968i	−0.997821	+	0.0659841i	$0.978981\pi$
$564$	−1.80817e51	−	5.38239e51i	−0.0961470	−	0.286202i
$565$	1.38681e51			0.0713012
$566$	1.68923e52	+	1.21452e52i	0.839801	+	0.603799i
$567$		−	3.67876e52i		−	1.76857i
$568$	9.64085e51	−	3.12488e52i	0.448226	−	1.45283i
$569$	1.00752e52			0.453023			0.226512	−	0.974008i	$-0.427268\pi$
$569$	1.00752e52			0.453023			0.226512	+	0.974008i	$0.427268\pi$
$570$	−3.16768e51	+	4.40581e51i	−0.137759	+	0.191603i
$571$			3.72705e50i			0.0156776i	0.999969	+	0.00783880i	$0.00249519\pi$
$571$			3.72705e50i			0.0156776i	−0.999969	+	0.00783880i	$0.997505\pi$
$572$	−4.05927e52	+	1.36368e52i	−1.65167	+	0.554865i
$573$	1.07297e52			0.422326
$574$	−2.06363e52	−	1.48371e52i	−0.785789	−	0.564966i
$575$		−	4.51680e51i		−	0.166395i
$576$	−4.25112e51	−	2.89905e51i	−0.151522	−	0.103331i
$577$	−9.17812e51			−0.316529			−0.158264	−	0.987397i	$-0.550590\pi$
$577$	−9.17812e51			−0.316529			−0.158264	+	0.987397i	$0.550590\pi$
$578$	1.70691e52	−	2.37408e52i	0.569616	−	0.792257i
$579$		−	3.38439e51i		−	0.109292i
$580$	2.10852e50	+	6.27644e50i	0.00658939	+	0.0196147i
$581$	6.72654e52			2.03444
$582$	−1.27935e52	−	9.19828e51i	−0.374502	−	0.269259i
$583$			6.35210e52i			1.79976i
$584$	1.00428e52	+	3.09841e51i	0.275431	+	0.0849758i
$585$	−3.23616e51			−0.0859149
$586$	5.83171e51	−	8.11110e51i	0.149879	−	0.208461i
$587$			2.86552e52i			0.712983i	0.934299	+	0.356491i	$0.116027\pi$
$587$			2.86552e52i			0.712983i	−0.934299	+	0.356491i	$0.883973\pi$
$588$	−5.84776e52	+	1.96451e52i	−1.40871	+	0.473243i
$589$	5.37158e51			0.125289
$590$	1.32495e52	+	9.52609e51i	0.299234	+	0.215143i
$591$		−	1.22287e52i		−	0.267435i
$592$	−5.58274e52	+	4.22812e52i	−1.18232	+	0.895436i
$593$	−8.79157e52			−1.80313			−0.901565	−	0.432643i	$-0.857581\pi$
$593$	−8.79157e52			−1.80313			−0.901565	+	0.432643i	$0.857581\pi$
$594$	2.49608e52	−	3.47171e52i	0.495812	−	0.689605i
$595$		−	3.19897e51i		−	0.0615443i
$596$	−1.26757e52	−	3.77320e52i	−0.236208	−	0.703122i
$597$	5.75132e52			1.03814
$598$	1.50767e52	+	1.08398e52i	0.263623	+	0.189539i
$599$			5.80821e52i			0.983858i	0.870635	+	0.491929i	$0.163708\pi$
$599$			5.80821e52i			0.983858i	−0.870635	+	0.491929i	$0.836292\pi$
$600$	1.82511e52	−	5.91571e52i	0.299513	−	0.970807i
$601$	1.87927e51			0.0298796			0.0149398	−	0.999888i	$-0.495244\pi$
$601$	1.87927e51			0.0298796			0.0149398	+	0.999888i	$0.495244\pi$
$602$	−4.58318e52	+	6.37457e52i	−0.706047	+	0.982014i
$603$			1.38732e52i			0.207084i
$604$	3.90036e52	−	1.31029e52i	0.564161	−	0.189525i
$605$	−1.57441e51			−0.0220681
$606$	9.88755e52	+	7.10894e52i	1.34310	+	0.965661i
$607$		−	5.89099e52i		−	0.775538i	−0.921757	−	0.387769i	$-0.873246\pi$
$607$		−	5.89099e52i		−	0.775538i	0.921757	−	0.387769i	$-0.126754\pi$
$608$	6.61186e52	−	1.64283e51i	0.843637	−	0.0209615i
$609$	−1.08913e52			−0.134695
$610$	−1.42244e52	+	1.97842e52i	−0.170517	+	0.237165i
$611$			4.35255e52i			0.505779i
$612$	8.06989e50	+	2.40217e51i	0.00909056	+	0.0270600i
$613$	−4.69520e52			−0.512749			−0.256374	−	0.966578i	$-0.582528\pi$
$613$	−4.69520e52			−0.512749			−0.256374	+	0.966578i	$0.582528\pi$
$614$	5.66049e52	+	4.06977e52i	0.599315	+	0.430895i
$615$		−	1.71395e52i		−	0.175943i
$616$	−1.41193e53	−	4.35608e52i	−1.40533	−	0.433573i
$617$	−8.74221e52			−0.843730			−0.421865	−	0.906659i	$-0.638624\pi$
$617$	−8.74221e52			−0.843730			−0.421865	+	0.906659i	$0.638624\pi$
$618$	5.55118e52	−	7.72093e52i	0.519523	−	0.722584i
$619$		−	1.44865e53i		−	1.31474i	−0.753568	−	0.657370i	$-0.771669\pi$
$619$		−	1.44865e53i		−	1.31474i	0.753568	−	0.657370i	$-0.228331\pi$
$620$	4.11032e51	−	1.38082e51i	0.0361770	−	0.0121534i
$621$	−1.85415e52			−0.158273
$622$	−1.72476e53	−	1.24007e53i	−1.42795	−	1.02666i
$623$		−	2.40986e53i		−	1.93517i
$624$	1.53660e53	+	2.02891e53i	1.19689	+	1.58036i
$625$	1.06690e53			0.806130
$626$	−1.06149e53	+	1.47638e53i	−0.778041	+	1.08215i
$627$		−	1.23438e53i		−	0.877738i
$628$	1.19975e52	+	3.57131e52i	0.0827671	+	0.246374i
$629$	3.44894e52			0.230847
$630$	−9.06642e51	−	6.51857e51i	−0.0588797	−	0.0423332i
$631$			5.15579e52i			0.324891i	0.986718	+	0.162445i	$0.0519381\pi$
$631$			5.15579e52i			0.324891i	−0.986718	+	0.162445i	$0.948062\pi$
$632$	−3.18102e52	+	1.03106e53i	−0.194510	+	0.630463i
$633$	−2.06257e53			−1.22388
$634$	8.82930e52	−	1.22803e53i	0.508429	−	0.707155i
$635$			6.34450e52i			0.354566i
$636$	3.57880e53	−	1.20227e53i	1.94112	−	0.652102i
$637$	4.72887e53			2.48948
$638$	−1.22290e52	−	8.79237e51i	−0.0624881	−	0.0449276i
$639$			5.62183e52i			0.278844i
$640$	5.01714e52	−	1.82536e52i	0.241566	−	0.0878879i
$641$	−3.57878e53			−1.67275			−0.836377	−	0.548154i	$-0.815331\pi$
$641$	−3.57878e53			−1.67275			−0.836377	+	0.548154i	$0.815331\pi$
$642$	5.20509e52	−	7.23956e52i	0.236191	−	0.328509i
$643$			3.39613e53i			1.49615i	0.663612	+	0.748077i	$0.269023\pi$
$643$			3.39613e53i			1.49615i	−0.663612	+	0.748077i	$0.730977\pi$
$644$	2.04042e52	+	6.07375e52i	0.0872748	+	0.259792i
$645$	−5.29441e52			−0.219879
$646$	−2.64465e52	−	1.90145e52i	−0.106647	−	0.0766772i
$647$			1.31557e53i			0.515147i	0.966259	+	0.257573i	$0.0829229\pi$
$647$			1.31557e53i			0.515147i	−0.966259	+	0.257573i	$0.917077\pi$
$648$	−2.88929e53	−	8.91401e52i	−1.09867	−	0.338960i
$649$	−3.71211e53			−1.37079
$650$	−2.77033e53	+	3.85315e53i	−0.993523	+	1.38185i
$651$			7.13249e52i			0.248429i
$652$	2.00066e53	−	6.72104e52i	0.676813	−	0.227369i
$653$	4.19492e53			1.37839			0.689196	−	0.724575i	$-0.257964\pi$
$653$	4.19492e53			1.37839			0.689196	+	0.724575i	$0.257964\pi$
$654$	−4.93741e53	−	3.54989e53i	−1.57588	−	1.13302i
$655$		−	5.38883e52i		−	0.167074i
$656$	−1.66534e53	+	1.26125e53i	−0.501568	+	0.379865i
$657$	−1.80677e52			−0.0528640
$658$	−8.76729e52	+	1.21941e53i	−0.249215	+	0.346623i
$659$			5.59855e53i			1.54615i	0.634313	+	0.773076i	$0.281283\pi$
$659$			5.59855e53i			1.54615i	−0.634313	+	0.773076i	$0.718717\pi$
$660$	−3.17310e52	−	9.44541e52i	−0.0851431	−	0.253446i
$661$	3.67571e53			0.958326			0.479163	−	0.877726i	$-0.340940\pi$
$661$	3.67571e53			0.958326			0.479163	+	0.877726i	$0.340940\pi$
$662$	1.21533e53	+	8.73796e52i	0.307887	+	0.221365i
$663$		−	1.25343e53i		−	0.308563i
$664$	1.62991e53	−	5.28301e53i	0.389915	−	1.26383i
$665$	1.43531e53			0.333683
$666$	7.02794e52	−	9.77488e52i	0.158788	−	0.220852i
$667$			6.53120e51i			0.0143417i
$668$	1.93846e53	−	6.51210e52i	0.413718	−	0.138985i
$669$	−1.84343e53			−0.382412
$670$	−1.16872e53	−	8.40288e52i	−0.235663	−	0.169436i
$671$		−	5.54294e53i		−	1.08646i
$672$	2.18137e52	+	8.77935e53i	0.0415637	+	1.67281i
$673$	6.30791e53			1.16842			0.584210	−	0.811602i	$-0.301404\pi$
$673$	6.30791e53			1.16842			0.584210	+	0.811602i	$0.301404\pi$
$674$	2.48766e53	−	3.45999e53i	0.447974	−	0.623070i
$675$		−	4.73867e53i		−	0.829631i
$676$	−4.34216e53	−	1.29254e54i	−0.739127	−	2.20017i
$677$	8.12445e53			1.34465			0.672325	−	0.740256i	$-0.265296\pi$
$677$	8.12445e53			1.34465			0.672325	+	0.740256i	$0.265296\pi$
$678$	1.52235e53	+	1.09454e53i	0.244991	+	0.176143i
$679$			4.16783e53i			0.652206i
$680$	−2.51246e52	−	7.75143e51i	−0.0382323	−	0.0117954i
$681$	−8.53659e53			−1.26325
$682$	−5.75795e52	+	8.00851e52i	−0.0828637	+	0.115252i
$683$		−	2.65341e53i		−	0.371373i	−0.982609	−	0.185687i	$-0.940549\pi$
$683$		−	2.65341e53i		−	0.371373i	0.982609	−	0.185687i	$-0.0594509\pi$
$684$	−1.07780e53	+	3.62079e52i	−0.146715	+	0.0492875i
$685$	3.33306e53			0.441288
$686$	3.55024e53	+	2.55255e53i	0.457193	+	0.328712i
$687$		−	1.51181e53i		−	0.189373i
$688$	3.89602e53	+	5.14424e53i	0.474723	+	0.626817i
$689$	−2.89405e54			−3.43036
$690$	−2.52228e52	+	3.50815e52i	−0.0290845	+	0.0404525i
$691$			3.44958e53i			0.386976i	0.981103	+	0.193488i	$0.0619800\pi$
$691$			3.44958e53i			0.386976i	−0.981103	+	0.193488i	$0.938020\pi$
$692$	1.62816e53	+	4.84657e53i	0.177698	+	0.528955i
$693$	2.54014e53			0.269728
$694$	4.78987e53	+	3.44382e53i	0.494873	+	0.355804i
$695$		−	1.00494e53i		−	0.101025i
$696$	−2.63907e52	+	8.55399e52i	−0.0258152	+	0.0836745i
$697$	1.02882e53			0.0979305
$698$	5.43688e53	−	7.56194e53i	0.503613	−	0.700455i
$699$		−	2.61932e53i		−	0.236114i
$700$	−1.55227e54	+	5.21472e53i	−1.36177	+	0.457476i
$701$	2.07439e52			0.0177112			0.00885560	−	0.999961i	$-0.497181\pi$
$701$	2.07439e52			0.0177112			0.00885560	+	0.999961i	$0.497181\pi$
$702$	1.58173e54	+	1.13723e54i	1.31440	+	0.945023i
$703$			1.54747e54i			1.25161i
$704$	−6.84250e53	+	1.00337e54i	−0.538684	+	0.789918i
$705$	−1.01278e53			−0.0776109
$706$	9.74685e51	−	1.35565e52i	0.00727068	−	0.0101125i
$707$		−	3.22113e54i		−	2.33905i
$708$	7.02594e53	+	2.09142e54i	0.496675	+	1.47846i
$709$	9.61703e53			0.661854			0.330927	−	0.943656i	$-0.392639\pi$
$709$	9.61703e53			0.661854			0.330927	+	0.943656i	$0.392639\pi$
$710$	−4.73603e53	−	3.40510e53i	−0.317326	−	0.228151i
$711$		−	1.85494e53i		−	0.121006i
$712$	−1.89270e54	−	5.83934e53i	−1.20216	−	0.370889i
$713$	4.27715e52			0.0264517
$714$	2.52478e53	−	3.51161e53i	0.152040	−	0.211466i
$715$			7.63816e53i			0.447893i
$716$	1.46226e54	−	4.91235e53i	0.834985	−	0.280506i
$717$	2.49750e54			1.38881
$718$	−1.69392e52	−	1.21789e52i	−0.00917337	−	0.00659546i
$719$			9.39009e53i			0.495246i	0.968856	+	0.247623i	$0.0796494\pi$
$719$			9.39009e53i			0.495246i	−0.968856	+	0.247623i	$0.920351\pi$
$720$	−7.31655e52	+	5.54123e52i	−0.0375828	+	0.0284635i
$721$	−2.51530e54			−1.25840
$722$	−3.44816e53	+	4.79591e53i	−0.168027	+	0.233703i
$723$		−	2.28197e54i		−	1.08313i
$724$	−7.50394e53	−	2.23370e54i	−0.346942	−	1.03274i
$725$	−1.66918e53			−0.0751763
$726$	−1.72828e53	−	1.24259e53i	−0.0758258	−	0.0545172i
$727$			2.50321e54i			1.06990i	0.844884	+	0.534950i	$0.179669\pi$
$727$			2.50321e54i			1.06990i	−0.844884	+	0.534950i	$0.820331\pi$
$728$	1.98465e54	−	6.43282e54i	0.826395	−	2.67858i
$729$	−1.86232e54			−0.755495
$730$	1.09435e53	−	1.52208e53i	0.0432534	−	0.0601595i
$731$		−	3.17804e53i		−	0.122385i
$732$	−3.12292e54	+	1.04912e54i	−1.17179	+	0.393653i
$733$	−1.03311e53			−0.0377719			−0.0188860	−	0.999822i	$-0.506012\pi$
$733$	−1.03311e53			−0.0377719			−0.0188860	+	0.999822i	$0.506012\pi$
$734$	3.60114e54	+	2.58915e54i	1.28297	+	0.922426i
$735$			1.10035e54i			0.382007i
$736$	5.26472e53	−	1.30811e52i	0.178114	−	0.00442553i
$737$	3.27442e54			1.07957
$738$	2.09644e53	−	2.91586e53i	0.0673615	−	0.0936905i
$739$			4.25818e54i			1.33346i	0.745300	+	0.666729i	$0.232306\pi$
$739$			4.25818e54i			1.33346i	−0.745300	+	0.666729i	$0.767694\pi$
$740$	3.97793e53	+	1.18412e54i	0.121410	+	0.361403i
$741$	5.62388e54			1.67298
$742$	−8.10795e54	−	5.82945e54i	−2.35092	−	1.69026i
$743$		−	3.69716e54i		−	1.04491i	−0.852666	−	0.522457i	$-0.825016\pi$
$743$		−	3.69716e54i		−	1.04491i	0.852666	−	0.522457i	$-0.174984\pi$
$744$	5.60184e53	+	1.72828e53i	0.154328	+	0.0476132i
$745$	−7.09986e53			−0.190669
$746$	1.33362e53	−	1.85488e53i	0.0349135	−	0.0485599i
$747$			9.50444e53i			0.242569i
$748$	5.66974e53	−	1.90470e53i	0.141069	−	0.0473910i
$749$	−2.35848e54			−0.572108
$750$	−1.85659e54	−	1.33485e54i	−0.439089	−	0.315696i
$751$			3.10593e54i			0.716197i	0.933684	+	0.358098i	$0.116575\pi$
$751$			3.10593e54i			0.716197i	−0.933684	+	0.358098i	$0.883425\pi$
$752$	7.45280e53	+	9.84056e53i	0.167564	+	0.221249i
$753$	−6.02234e54			−1.32026
$754$	4.00584e53	−	5.57158e53i	0.0856325	−	0.119103i
$755$		−	7.33914e53i		−	0.152986i
$756$	2.14065e54	+	6.37211e54i	0.435143	+	1.29530i
$757$	8.97740e54			1.77963			0.889814	−	0.456324i	$-0.150834\pi$
$757$	8.97740e54			1.77963			0.889814	+	0.456324i	$0.150834\pi$
$758$	1.57566e54	+	1.13286e54i	0.304612	+	0.219010i
$759$		−	9.82879e53i		−	0.185313i
$760$	3.47790e53	−	1.12729e54i	0.0639527	−	0.207289i
$761$	2.14256e54			0.384260			0.192130	−	0.981369i	$-0.438460\pi$
$761$	2.14256e54			0.384260			0.192130	+	0.981369i	$0.438460\pi$
$762$	−5.00737e54	+	6.96456e54i	−0.875922	+	1.21829i
$763$			1.60849e55i			2.74444i
$764$	−2.21124e54	+	7.42847e53i	−0.368012	+	0.123630i
$765$	4.52006e52			0.00733799
$766$	−1.82491e54	−	1.31207e54i	−0.288998	−	0.207784i
$767$		−	1.69125e55i		−	2.61275i
$768$	6.94813e54	+	1.95600e54i	1.04714	+	0.294786i
$769$	−4.13582e54			−0.608081			−0.304041	−	0.952659i	$-0.598336\pi$
$769$	−4.13582e54			−0.608081			−0.304041	+	0.952659i	$0.598336\pi$
$770$	−1.53855e54	+	2.13991e54i	−0.220692	+	0.306952i
$771$		−	8.54691e54i		−	1.19612i
$772$	2.34312e53	+	6.97479e53i	0.0319938	+	0.0952363i
$773$	−9.18697e54			−1.22395			−0.611973	−	0.790879i	$-0.709624\pi$
$773$	−9.18697e54			−1.22395			−0.611973	+	0.790879i	$0.709624\pi$
$774$	−9.00710e53	−	6.47592e53i	−0.117087	−	0.0841827i
$775$			1.09311e54i			0.138654i
$776$	3.27340e54	+	1.00991e54i	0.405160	+	0.125000i
$777$	−2.05476e55			−2.48177
$778$	2.13013e54	−	2.96271e54i	0.251069	−	0.349202i
$779$			4.61611e54i			0.530963i
$780$	4.30337e54	−	1.44568e54i	0.483072	−	0.162284i
$781$	1.32690e55			1.45367
$782$	−2.10581e53	−	1.51403e53i	−0.0225160	−	0.0161885i
$783$			6.85202e53i			0.0715065i
$784$	1.06914e55	−	8.09718e54i	1.08900	−	0.824761i
$785$	6.71998e53			0.0668105
$786$	4.25311e54	−	5.91549e54i	0.412742	−	0.574067i
$787$		−	1.88649e55i		−	1.78704i	−0.449019	−	0.893522i	$-0.648226\pi$
$787$		−	1.88649e55i		−	1.78704i	0.449019	−	0.893522i	$-0.351774\pi$
$788$	8.46632e53	+	2.52018e54i	0.0782882	+	0.233041i
$789$	−7.98568e54			−0.720856
$790$	1.56266e54	+	1.12352e54i	0.137705	+	0.0990072i
$791$		−	4.95945e54i		−	0.426659i
$792$	6.15503e53	−	1.99502e54i	0.0516954	−	0.167560i
$793$	2.52539e55			2.07080
$794$	−2.95676e54	+	4.11244e54i	−0.236715	+	0.329238i
$795$		−	6.73407e54i		−	0.526384i
$796$	−1.18527e55	+	3.98182e54i	−0.904627	+	0.303901i
$797$	4.64822e54			0.346401			0.173200	−	0.984887i	$-0.444589\pi$
$797$	4.64822e54			0.346401			0.173200	+	0.984887i	$0.444589\pi$
$798$	1.57559e55	+	1.13281e55i	1.14653	+	0.824334i
$799$		−	6.07936e53i		−	0.0431986i
$800$	3.34313e53	+	1.34551e55i	0.0231977	+	0.933633i
$801$	3.40508e54			0.230733
$802$	−7.57157e54	+	1.05310e55i	−0.501041	+	0.696879i
$803$			4.26443e54i			0.275591i
$804$	−6.19752e54	−	1.84482e55i	−0.391159	−	1.16437i
$805$	1.14287e54			0.0704492
$806$	−3.64871e54	−	2.62335e54i	−0.219672	−	0.157939i
$807$			2.04538e55i			1.20276i
$808$	−2.52987e55	−	7.80513e54i	−1.45305	−	0.448295i
$809$	−2.35673e55			−1.32217			−0.661087	−	0.750309i	$-0.729905\pi$
$809$	−2.35673e55			−1.32217			−0.661087	+	0.750309i	$0.729905\pi$
$810$	−3.14839e54	+	4.37897e54i	−0.172533	+	0.239970i
$811$			1.74153e55i			0.932256i	0.884717	+	0.466128i	$0.154351\pi$
$811$			1.74153e55i			0.932256i	−0.884717	+	0.466128i	$0.845649\pi$
$812$	2.24455e54	−	7.54038e53i	0.117372	−	0.0394302i
$813$	−2.24438e55			−1.14651
$814$	−2.30712e55	−	1.65877e55i	−1.15135	−	0.827795i
$815$		−	3.76455e54i		−	0.183535i
$816$	−2.14623e54	−	2.83385e54i	−0.102226	−	0.134978i
$817$	1.42592e55			0.663553
$818$	5.24179e54	−	7.29060e54i	0.238323	−	0.331475i
$819$			1.15730e55i			0.514105i
$820$	1.18662e54	+	3.53223e54i	0.0515050	+	0.153315i
$821$	5.44852e54			0.231078			0.115539	−	0.993303i	$-0.463140\pi$
$821$	5.44852e54			0.231078			0.115539	+	0.993303i	$0.463140\pi$
$822$	3.65881e55	+	2.63061e55i	1.51626	+	1.09016i
$823$			4.31927e55i			1.74910i	0.484938	+	0.874548i	$0.338842\pi$
$823$			4.31927e55i			1.74910i	−0.484938	+	0.874548i	$0.661158\pi$
$824$	−6.09482e54	+	1.97551e55i	−0.241181	+	0.781738i
$825$	2.51195e55			0.971372
$826$	3.40668e55	−	4.73822e55i	1.28739	−	1.79058i
$827$			3.19468e55i			1.17984i	0.807462	+	0.589919i	$0.200840\pi$
$827$			3.19468e55i			1.17984i	−0.807462	+	0.589919i	$0.799160\pi$
$828$	−8.58206e53	+	2.88307e53i	−0.0309753	+	0.0104059i
$829$	3.55499e55			1.25401			0.627007	−	0.779013i	$-0.284280\pi$
$829$	3.55499e55			1.25401			0.627007	+	0.779013i	$0.284280\pi$
$830$	−8.00687e54	−	5.75677e54i	−0.276044	−	0.198470i
$831$		−	4.17613e55i		−	1.40720i
$832$	−4.57141e55	−	3.11747e55i	−1.50559	−	1.02674i
$833$	−6.60499e54			−0.212626
$834$	7.93142e54	−	1.10315e55i	0.249572	−	0.347120i
$835$		−	3.64752e54i		−	0.112190i
$836$	8.54598e54	+	2.54389e55i	0.256946	+	0.764855i
$837$	4.48725e54			0.131885
$838$	−2.60871e55	−	1.87561e55i	−0.749531	−	0.538897i
$839$		−	2.45001e55i		−	0.688162i	−0.938940	−	0.344081i	$-0.888191\pi$
$839$		−	2.45001e55i		−	0.688162i	0.938940	−	0.344081i	$-0.111809\pi$
$840$	1.49683e55	+	4.61802e54i	0.411024	+	0.126809i
$841$	−3.70084e55			−0.993520
$842$	3.49356e54	−	4.85906e54i	0.0916934	−	0.127533i
$843$		−	5.27418e55i		−	1.35341i
$844$	4.25069e55	−	1.42798e55i	1.06648	−	0.358275i
$845$	−2.43211e55			−0.596631
$846$	−1.72299e54	−	1.23880e54i	−0.0413282	−	0.0297141i
$847$			5.63032e54i			0.132053i
$848$	−6.54307e55	+	4.95543e55i	−1.50058	+	1.13648i
$849$	5.01732e55			1.12519
$850$	3.86942e54	−	5.38183e54i	0.0848568	−	0.118024i
$851$			1.23218e55i			0.264248i
$852$	−2.51142e55	−	7.47578e55i	−0.526706	−	1.56785i
$853$	−4.60031e55			−0.943530			−0.471765	−	0.881724i	$-0.656383\pi$
$853$	−4.60031e55			−0.943530			−0.471765	+	0.881724i	$0.656383\pi$
$854$	7.07513e55	+	5.08687e55i	1.41917	+	1.02035i
$855$			2.02806e54i			0.0397854i
$856$	−5.71484e54	+	1.85234e55i	−0.109648	+	0.355402i
$857$	6.69827e55			1.25698			0.628488	−	0.777819i	$-0.283674\pi$
$857$	6.69827e55			1.25698			0.628488	+	0.777819i	$0.283674\pi$
$858$	−6.02839e55	+	8.38466e55i	−1.10648	+	1.53896i
$859$		−	5.14374e55i		−	0.923441i	−0.887025	−	0.461720i	$-0.847232\pi$
$859$		−	5.14374e55i		−	0.923441i	0.887025	−	0.461720i	$-0.152768\pi$
$860$	1.09111e55	−	3.66548e54i	0.191601	−	0.0643666i
$861$	−6.12936e55			−1.05282
$862$	2.69570e55	+	1.93815e55i	0.452932	+	0.325649i
$863$		−	3.93612e55i		−	0.646940i	−0.946239	−	0.323470i	$-0.895151\pi$
$863$		−	3.93612e55i		−	0.646940i	0.946239	−	0.323470i	$-0.104849\pi$
$864$	5.52334e55	−	1.37236e54i	0.888056	−	0.0220652i
$865$	9.11958e54			0.143440
$866$	−8.94948e54	+	1.24475e55i	−0.137708	+	0.191532i
$867$		−	7.05144e55i		−	1.06149i
$868$	−4.93804e54	−	1.46991e55i	−0.0727244	−	0.216479i
$869$	−4.37812e55			−0.630830
$870$	1.29643e54	+	9.32109e53i	0.0182761	+	0.0131402i
$871$			1.49184e56i			2.05768i
$872$	1.26331e56	+	3.89754e55i	1.70489	+	0.525990i
$873$	−5.88904e54			−0.0777632
$874$	6.79315e54	−	9.44833e54i	0.0877716	−	0.122078i
$875$			6.04834e55i			0.764687i
$876$	2.40260e55	−	8.07132e54i	0.297237	−	0.0998542i
$877$	−9.57785e55			−1.15951			−0.579757	−	0.814790i	$-0.696852\pi$
$877$	−9.57785e55			−1.15951			−0.579757	+	0.814790i	$0.696852\pi$
$878$	−2.49592e55	−	1.79451e55i	−0.295689	−	0.212594i
$879$		−	2.40914e55i		−	0.279302i
$880$	1.30787e55	+	1.72689e55i	0.148386	+	0.195927i
$881$	−1.25845e56			−1.39731			−0.698656	−	0.715458i	$-0.746218\pi$
$881$	−1.25845e56			−1.39731			−0.698656	+	0.715458i	$0.746218\pi$
$882$	−1.34590e55	+	1.87197e55i	−0.146255	+	0.203421i
$883$		−	3.62248e55i		−	0.385259i	−0.981272	−	0.192629i	$-0.938299\pi$
$883$		−	3.62248e55i		−	0.385259i	0.981272	−	0.192629i	$-0.0617015\pi$
$884$	8.67790e54	+	2.58316e55i	0.0903278	+	0.268880i
$885$	3.93533e55			0.400922
$886$	−9.50171e55	−	6.83153e55i	−0.947460	−	0.681204i
$887$			7.17047e55i			0.699840i	0.936780	+	0.349920i	$0.113791\pi$
$887$			7.17047e55i			0.699840i	−0.936780	+	0.349920i	$0.886209\pi$
$888$	−4.97888e55	+	1.61380e56i	−0.475648	+	1.54171i
$889$	2.26889e56			2.12168
$890$	−2.06243e55	+	2.86855e55i	−0.188786	+	0.262575i
$891$		−	1.22686e56i		−	1.09931i
$892$	3.79908e55	−	1.27627e55i	0.333231	−	0.111946i
$893$	2.72768e55			0.234216
$894$	−7.79375e55	−	5.60354e55i	−0.655139	−	0.471031i
$895$		−	2.75148e55i		−	0.226427i
$896$	−6.52777e55	−	1.79421e56i	−0.525911	−	1.44551i
$897$	4.47804e55			0.353209
$898$	−1.90258e55	+	2.64622e55i	−0.146924	+	0.204351i
$899$		−	1.58062e54i		−	0.0119507i
$900$	−7.36827e54	−	2.19332e55i	−0.0545454	−	0.162366i
$901$	4.04222e55			0.292987
$902$	−6.88217e55	−	4.94813e55i	−0.488429	−	0.351170i
$903$			1.89336e56i			1.31573i
$904$	−3.89514e55	−	1.20173e55i	−0.265047	−	0.0817722i
$905$	−4.20306e55			−0.280055
$906$	5.79239e55	−	8.05641e55i	0.377939	−	0.525661i
$907$			8.50893e55i			0.543671i	0.962344	+	0.271836i	$0.0876307\pi$
$907$			8.50893e55i			0.543671i	−0.962344	+	0.271836i	$0.912369\pi$
$908$	1.75928e56	−	5.91015e55i	1.10079	−	0.369800i
$909$	4.55138e55			0.278888
$910$	−9.74951e55	−	7.00969e55i	−0.585054	−	0.420642i
$911$		−	3.16761e56i		−	1.86158i	−0.365550	−	0.930792i	$-0.619119\pi$
$911$		−	3.16761e56i		−	1.86158i	0.365550	−	0.930792i	$-0.380881\pi$
$912$	1.27149e56	−	9.62968e55i	0.731830	−	0.554255i
$913$	2.24329e56			1.26456
$914$	1.85856e55	−	2.58500e55i	0.102612	−	0.142719i
$915$			5.87626e55i			0.317761i
$916$	1.04667e55	+	3.11564e55i	0.0554366	+	0.165019i
$917$	−1.92713e56			−0.999755
$918$	−2.20925e55	−	1.58841e55i	−0.112263	−	0.0807144i
$919$		−	1.03826e55i		−	0.0516787i	−0.999666	−	0.0258394i	$-0.991774\pi$
$919$		−	1.03826e55i		−	0.0516787i	0.999666	−	0.0258394i	$-0.00822584\pi$
$920$	2.76930e54	−	8.97608e54i	0.0135021	−	0.0437641i
$921$	1.68127e56			0.802978
$922$	8.54631e55	−	1.18867e56i	0.399844	−	0.556128i
$923$			6.04540e56i			2.77072i
$924$	−3.37783e56	+	1.13475e56i	−1.51660	+	0.509487i
$925$	−3.14908e56			−1.38513
$926$	−4.11273e55	−	2.95696e55i	−0.177223	−	0.127420i
$927$		−	3.55405e55i		−	0.150041i
$928$	−4.83411e53	−	1.94558e55i	−0.00199942	−	0.0804705i
$929$	4.61993e56			1.87213			0.936066	−	0.351824i	$-0.114439\pi$
$929$	4.61993e56			1.87213			0.936066	+	0.351824i	$0.114439\pi$
$930$	6.10419e54	−	8.49008e54i	0.0242355	−	0.0337082i
$931$		−	2.96352e56i		−	1.15283i
$932$	1.81344e55	+	5.39808e55i	0.0691194	+	0.205749i
$933$	−5.12286e56			−1.91320
$934$	3.86076e56	+	2.77581e56i	1.41281	+	1.01578i
$935$		−	1.06685e55i		−	0.0382545i
$936$	9.08941e55	+	2.80426e55i	0.319370	+	0.0985319i
$937$	−3.24881e56			−1.11859			−0.559297	−	0.828967i	$-0.688929\pi$
$937$	−3.24881e56			−1.11859			−0.559297	+	0.828967i	$0.688929\pi$
$938$	−3.00500e56	+	4.17954e56i	−1.01389	+	1.41018i
$939$			4.38512e56i			1.44989i
$940$	2.08721e55	−	7.01180e54i	0.0676296	−	0.0227196i
$941$	2.13347e56			0.677461			0.338730	−	0.940884i	$-0.390003\pi$
$941$	2.13347e56			0.677461			0.338730	+	0.940884i	$0.390003\pi$
$942$	7.37674e55	+	5.30372e55i	0.229561	+	0.165049i
$943$			3.67560e55i			0.112100i
$944$	−2.89591e56	−	3.82371e56i	−0.865599	−	1.14292i
$945$	1.19901e56			0.351252
$946$	−1.52848e56	+	2.12591e56i	−0.438863	+	0.610397i
$947$		−	4.92826e56i		−	1.38690i	−0.720507	−	0.693448i	$-0.756091\pi$
$947$		−	4.92826e56i		−	1.38690i	0.720507	−	0.693448i	$-0.243909\pi$
$948$	8.28650e55	+	2.46665e56i	0.228567	+	0.680377i
$949$	−1.94289e56			−0.525280
$950$	2.41471e56	+	1.73613e56i	0.639907	+	0.460080i
$951$		−	3.64748e56i		−	0.947465i
$952$	−2.77203e55	+	8.98495e55i	−0.0705824	+	0.228778i
$953$	−4.13229e55			−0.103140			−0.0515699	−	0.998669i	$-0.516422\pi$
$953$	−4.13229e55			−0.103140			−0.0515699	+	0.998669i	$0.516422\pi$
$954$	8.23686e55	−	1.14563e56i	0.201531	−	0.280302i
$955$			4.16080e55i			0.0997958i
$956$	−5.14702e56	+	1.72910e56i	−1.21020	+	0.406555i
$957$	−3.63223e55			−0.0837232
$958$	3.75701e56	+	2.70121e56i	0.848981	+	0.610400i
$959$		−	1.19195e57i		−	2.64062i
$960$	7.25396e55	−	1.06371e56i	0.157551	−	0.231031i
$961$	4.59266e56			0.977958
$962$	7.55744e56	−	1.05113e57i	1.57779	−	2.19448i
$963$		−	3.33247e55i		−	0.0682130i
$964$	1.57988e56	+	4.70283e56i	0.317073	+	0.943834i
$965$	1.31242e55			0.0258257
$966$	1.25457e56	+	9.02007e55i	0.242063	+	0.174038i
$967$			1.86519e56i			0.352874i	0.984312	+	0.176437i	$0.0564571\pi$
$967$			1.86519e56i			0.352874i	−0.984312	+	0.176437i	$0.943543\pi$
$968$	4.42203e55	+	1.36428e55i	0.0820333	+	0.0253089i
$969$	−7.85508e55			−0.142889
$970$	3.56695e55	−	4.96114e55i	0.0636260	−	0.0884949i
$971$			2.84061e56i			0.496873i	0.968648	+	0.248437i	$0.0799168\pi$
$971$			2.84061e56i			0.496873i	−0.968648	+	0.248437i	$0.920083\pi$
$972$	−2.00294e56	+	6.72870e55i	−0.343565	+	0.115418i
$973$	−3.59381e56			−0.604520
$974$	−2.17534e56	−	1.56403e56i	−0.358846	−	0.258003i
$975$			1.14445e57i			1.85145i
$976$	5.70959e56	−	4.32418e56i	0.905854	−	0.686053i
$977$	−5.09703e56			−0.793087			−0.396544	−	0.918016i	$-0.629790\pi$
$977$	−5.09703e56			−0.793087			−0.396544	+	0.918016i	$0.629790\pi$
$978$	2.97116e56	−	4.13247e56i	0.453407	−	0.630626i
$979$		−	8.03684e56i		−	1.20286i
$980$	−7.61805e55	−	2.26767e56i	−0.111827	−	0.332878i
$981$	−2.27276e56			−0.327222
$982$	−4.50082e56	−	3.23600e56i	−0.635585	−	0.456972i
$983$			1.19102e56i			0.164969i	0.996592	+	0.0824845i	$0.0262855\pi$
$983$			1.19102e56i			0.164969i	−0.996592	+	0.0824845i	$0.973715\pi$
$984$	−1.48521e56	+	4.81398e56i	−0.201781	+	0.654030i
$985$	4.74211e55			0.0631951
$986$	−5.59511e54	+	7.78202e54i	−0.00731387	+	0.0101726i
$987$			3.62186e56i			0.464415i
$988$	−1.15901e57	+	3.89359e56i	−1.45782	+	0.489743i
$989$	1.13539e56			0.140093
$990$	−3.02363e55	−	2.17393e55i	−0.0365983	−	0.0263134i
$991$		−	2.37717e56i		−	0.282268i	−0.989991	−	0.141134i	$-0.954925\pi$
$991$		−	2.37717e56i		−	0.282268i	0.989991	−	0.141134i	$-0.0450748\pi$
$992$	−1.27412e56	+	3.16576e54i	−0.148419	+	0.00368770i
$993$	3.60975e56			0.412516
$994$	−1.21772e57	+	1.69368e57i	−1.36523	+	1.89884i
$995$			2.23027e56i			0.245312i
$996$	−4.24589e56	−	1.26388e57i	−0.458185	−	1.36389i
$997$	6.97114e56			0.738067			0.369034	−	0.929416i	$-0.379689\pi$
$997$	6.97114e56			0.738067			0.369034	+	0.929416i	$0.379689\pi$
$998$	−5.50337e56	−	3.95681e56i	−0.571674	−	0.411022i
$999$			1.29270e57i			1.31751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.39.b.a.3.6	yes	18
4.3	odd	2	inner	4.39.b.a.3.5	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.39.b.a.3.5	✓	18	4.3	odd	2	inner
4.39.b.a.3.6	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)

\(f(q)\)	\(=\)	\(q+(-306058. + 425684. i) q^{2} +1.26436e9i q^{3} +(-8.75354e10 - 2.60567e11i) q^{4} -4.90299e12 q^{5} +(-5.38217e14 - 3.86966e14i) q^{6} +1.75338e16i q^{7} +(1.37710e17 + 4.24863e16i) q^{8} -2.47749e17 q^{9} +O(q^{10})\)	\(q+(-306058. + 425684. i) q^{2} +1.26436e9i q^{3} +(-8.75354e10 - 2.60567e11i) q^{4} -4.90299e12 q^{5} +(-5.38217e14 - 3.86966e14i) q^{6} +1.75338e16i q^{7} +(1.37710e17 + 4.24863e16i) q^{8} -2.47749e17 q^{9} +(1.50060e18 - 2.08712e18i) q^{10} +5.84750e19i q^{11} +(3.29451e20 - 1.10676e20i) q^{12} -2.66415e21 q^{13} +(-7.46387e21 - 5.36636e21i) q^{14} -6.19913e21i q^{15} +(-6.02330e22 + 4.56178e22i) q^{16} +3.72111e22 q^{17} +(7.58254e22 - 1.05463e23i) q^{18} +1.66958e24i q^{19} +(4.29185e23 + 1.27756e24i) q^{20} -2.21690e25 q^{21} +(-2.48918e25 - 1.78967e25i) q^{22} +1.32941e25i q^{23} +(-5.37179e25 + 1.74115e26i) q^{24} -3.39759e26 q^{25} +(8.15382e26 - 1.13408e27i) q^{26} +1.39472e27i q^{27} +(4.56875e27 - 1.53483e27i) q^{28} +4.91284e26 q^{29} +(2.63887e27 + 1.89729e27i) q^{30} -3.21732e27i q^{31} +(-9.83973e26 - 3.96019e28i) q^{32} -7.39333e28 q^{33} +(-1.13887e28 + 1.58402e28i) q^{34} -8.59681e28i q^{35} +(2.16868e28 + 6.45553e28i) q^{36} +9.26858e29 q^{37} +(-7.10714e29 - 5.10989e29i) q^{38} -3.36843e30i q^{39} +(-6.75191e29 - 2.08310e29i) q^{40} +2.76483e30 q^{41} +(6.78500e30 - 9.43700e30i) q^{42} -8.54057e30i q^{43} +(1.52367e31 - 5.11863e30i) q^{44} +1.21471e30 q^{45} +(-5.65910e30 - 4.06877e30i) q^{46} -1.63375e31i q^{47} +(-5.76772e31 - 7.61560e31i) q^{48} -1.77501e32 q^{49} +(1.03986e32 - 1.44630e32i) q^{50} +4.70482e31i q^{51} +(2.33207e32 + 6.94190e32i) q^{52} +1.08629e33 q^{53} +(-5.93708e32 - 4.26864e32i) q^{54} -2.86702e32i q^{55} +(-7.44947e32 + 2.41459e33i) q^{56} -2.11095e33 q^{57} +(-1.50361e32 + 2.09132e32i) q^{58} +6.34821e33i q^{59} +(-1.61529e33 + 5.42643e32i) q^{60} -9.47917e33 q^{61} +(1.36956e33 + 9.84686e32i) q^{62} -4.34398e33i q^{63} +(1.71590e34 + 1.17016e34i) q^{64} +1.30623e34 q^{65} +(2.26278e34 - 3.14722e34i) q^{66} -5.59969e34i q^{67} +(-3.25729e33 - 9.69601e33i) q^{68} -1.68085e34 q^{69} +(3.65952e34 + 2.63112e34i) q^{70} -2.26917e35i q^{71} +(-3.41175e34 - 1.05259e34i) q^{72} +7.29274e34 q^{73} +(-2.83672e35 + 3.94548e35i) q^{74} -4.29576e35i q^{75} +(4.35039e35 - 1.46148e35i) q^{76} -1.02529e36 q^{77} +(1.43389e36 + 1.03093e36i) q^{78} +7.48717e35i q^{79} +(2.95321e35 - 2.23663e35i) q^{80} -2.09809e36 q^{81} +(-8.46197e35 + 1.17694e36i) q^{82} -3.83632e36i q^{83} +(1.94058e36 + 5.77653e36i) q^{84} -1.82446e35 q^{85} +(3.63558e36 + 2.61391e36i) q^{86} +6.21159e35i q^{87} +(-2.48438e36 + 8.05260e36i) q^{88} -1.37441e37 q^{89} +(-3.71771e35 + 5.17082e35i) q^{90} -4.67127e37i q^{91} +(3.46402e36 - 1.16371e36i) q^{92} +4.06784e36 q^{93} +(6.95460e36 + 5.00021e36i) q^{94} -8.18594e36i q^{95} +(5.00709e37 - 1.24409e36i) q^{96} +2.37702e37 q^{97} +(5.43254e37 - 7.55591e37i) q^{98} -1.44871e37i 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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