LMFDB - Embedded newform 4.39.b.a.3.17

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			3.17
Root			$0.500000 + 1.42659e8i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.39.b.a.3.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(518652. - 76670.9i) q^{2} -2.28254e9i q^{3} +(2.63121e11 - 7.95309e10i) q^{4} +1.45926e13 q^{5} +(-1.75005e14 - 1.18385e15i) q^{6} -8.90761e15i q^{7} +(1.30370e17 - 6.14226e16i) q^{8} -3.85916e18 q^{9} +O(q^{10})$	\(q+(518652. - 76670.9i) q^{2} -2.28254e9i q^{3} +(2.63121e11 - 7.95309e10i) q^{4} +1.45926e13 q^{5} +(-1.75005e14 - 1.18385e15i) q^{6} -8.90761e15i q^{7} +(1.30370e17 - 6.14226e16i) q^{8} -3.85916e18 q^{9} +(7.56849e18 - 1.11883e18i) q^{10} -4.38272e19i q^{11} +(-1.81533e20 - 6.00586e20i) q^{12} +1.87649e21 q^{13} +(-6.82954e20 - 4.61995e21i) q^{14} -3.33083e22i q^{15} +(6.29075e22 - 4.18525e22i) q^{16} +4.37216e22 q^{17} +(-2.00156e24 + 2.95885e23i) q^{18} +2.11999e24i q^{19} +(3.83963e24 - 1.16057e24i) q^{20} -2.03320e25 q^{21} +(-3.36027e24 - 2.27310e25i) q^{22} -2.46227e25i q^{23} +(-1.40200e26 - 2.97576e26i) q^{24} -1.50853e26 q^{25} +(9.73246e26 - 1.43872e26i) q^{26} +5.72532e27i q^{27} +(-7.08431e26 - 2.34378e27i) q^{28} +3.71574e27 q^{29} +(-2.55378e27 - 1.72754e28i) q^{30} +1.46587e28i q^{31} +(2.94182e28 - 2.65301e28i) q^{32} -1.00037e29 q^{33} +(2.26763e28 - 3.35217e27i) q^{34} -1.29986e29i q^{35} +(-1.01543e30 + 3.06922e29i) q^{36} -3.14590e29 q^{37} +(1.62541e29 + 1.09953e30i) q^{38} -4.28318e30i q^{39} +(1.90245e30 - 8.96317e29i) q^{40} -1.59147e30 q^{41} +(-1.05452e31 + 1.55887e30i) q^{42} +1.13757e31i q^{43} +(-3.48561e30 - 1.15318e31i) q^{44} -5.63153e31 q^{45} +(-1.88784e30 - 1.27706e31i) q^{46} +3.60466e31i q^{47} +(-9.55302e31 - 1.43589e32i) q^{48} +5.05892e31 q^{49} +(-7.82401e31 + 1.15660e31i) q^{50} -9.97964e31i q^{51} +(4.93745e32 - 1.49239e32i) q^{52} +1.01267e32 q^{53} +(4.38965e32 + 2.96945e33i) q^{54} -6.39554e32i q^{55} +(-5.47129e32 - 1.16129e33i) q^{56} +4.83896e33 q^{57} +(1.92717e33 - 2.84889e32i) q^{58} -1.33527e33i q^{59} +(-2.64904e33 - 8.76412e33i) q^{60} -7.35637e33 q^{61} +(1.12389e33 + 7.60274e33i) q^{62} +3.43759e34i q^{63} +(1.32237e34 - 1.60154e34i) q^{64} +2.73830e34 q^{65} +(-5.18846e34 + 7.66996e33i) q^{66} -3.46090e34i q^{67} +(1.15041e34 - 3.47722e33i) q^{68} -5.62024e34 q^{69} +(-9.96610e33 - 6.74172e34i) q^{70} -2.59319e35i q^{71} +(-5.03120e35 + 2.37039e35i) q^{72} +3.29372e35 q^{73} +(-1.63163e35 + 2.41199e34i) q^{74} +3.44329e35i q^{75} +(1.68604e35 + 5.57813e35i) q^{76} -3.90395e35 q^{77} +(-3.28395e35 - 2.22148e36i) q^{78} +9.78414e35i q^{79} +(9.17986e35 - 6.10739e35i) q^{80} +7.85514e36 q^{81} +(-8.25420e35 + 1.22020e35i) q^{82} +3.96638e36i q^{83} +(-5.34978e36 + 1.61702e36i) q^{84} +6.38013e35 q^{85} +(8.72187e35 + 5.90004e36i) q^{86} -8.48133e36i q^{87} +(-2.69198e36 - 5.71377e36i) q^{88} +7.10862e36 q^{89} +(-2.92080e37 + 4.31774e36i) q^{90} -1.67151e37i q^{91} +(-1.95827e36 - 6.47875e36i) q^{92} +3.34590e37 q^{93} +(2.76372e36 + 1.86956e37i) q^{94} +3.09362e37i q^{95} +(-6.05560e37 - 6.71484e37i) q^{96} -6.10990e37 q^{97} +(2.62382e37 - 3.87872e36i) q^{98} +1.69136e38i 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 $

$2$	518652.	−	76670.9i	0.989249	−	0.146238i
$2$	518652.	−	76670.9i	0.989249	−	0.146238i
$3$		−	2.28254e9i		−	1.96388i	−0.189187	−	0.981941i	$-0.560585\pi$
$3$		−	2.28254e9i		−	1.96388i	0.189187	−	0.981941i	$-0.439415\pi$
$4$	2.63121e11	−	7.95309e10i	0.957229	−	0.289332i
$5$	1.45926e13			0.765074			0.382537	−	0.923940i	$-0.375050\pi$
$5$	1.45926e13			0.765074			0.382537	+	0.923940i	$0.375050\pi$
$6$	−1.75005e14	−	1.18385e15i	−0.287194	−	1.94277i
$7$		−	8.90761e15i		−	0.781445i	−0.920508	−	0.390723i	$-0.872225\pi$
$7$		−	8.90761e15i		−	0.781445i	0.920508	−	0.390723i	$-0.127775\pi$
$8$	1.30370e17	−	6.14226e16i	0.904627	−	0.426205i
$9$	−3.85916e18			−2.85683
$10$	7.56849e18	−	1.11883e18i	0.756849	−	0.111883i
$11$		−	4.38272e19i		−	0.716609i	−0.933605	−	0.358304i	$-0.883355\pi$
$11$		−	4.38272e19i		−	0.716609i	0.933605	−	0.358304i	$-0.116645\pi$
$12$	−1.81533e20	−	6.00586e20i	−0.568214	−	1.87988i
$13$	1.87649e21			1.28358			0.641791	−	0.766880i	$-0.278192\pi$
$13$	1.87649e21			1.28358			0.641791	+	0.766880i	$0.278192\pi$
$14$	−6.82954e20	−	4.61995e21i	−0.114277	−	0.773044i
$15$		−	3.33083e22i		−	1.50252i
$16$	6.29075e22	−	4.18525e22i	0.832574	−	0.553914i
$17$	4.37216e22			0.182880			0.0914400	−	0.995811i	$-0.470853\pi$
$17$	4.37216e22			0.182880			0.0914400	+	0.995811i	$0.470853\pi$
$18$	−2.00156e24	+	2.95885e23i	−2.82612	+	0.417778i
$19$			2.11999e24i			1.07156i	0.844359	+	0.535778i	$0.179981\pi$
$19$			2.11999e24i			1.07156i	−0.844359	+	0.535778i	$0.820019\pi$
$20$	3.83963e24	−	1.16057e24i	0.732351	−	0.221360i
$21$	−2.03320e25			−1.53467
$22$	−3.36027e24	−	2.27310e25i	−0.104796	−	0.708905i
$23$		−	2.46227e25i		−	0.329995i	−0.986294	−	0.164997i	$-0.947238\pi$
$23$		−	2.46227e25i		−	0.329995i	0.986294	−	0.164997i	$-0.0527615\pi$
$24$	−1.40200e26	−	2.97576e26i	−0.837016	−	1.77658i
$25$	−1.50853e26			−0.414661
$26$	9.73246e26	−	1.43872e26i	1.26978	−	0.187708i
$27$			5.72532e27i			3.64660i
$28$	−7.08431e26	−	2.34378e27i	−0.226097	−	0.748022i
$29$	3.71574e27			0.608812			0.304406	−	0.952542i	$-0.401542\pi$
$29$	3.71574e27			0.608812			0.304406	+	0.952542i	$0.401542\pi$
$30$	−2.55378e27	−	1.72754e28i	−0.219725	−	1.48636i
$31$			1.46587e28i			0.676429i	0.941069	+	0.338214i	$0.109823\pi$
$31$			1.46587e28i			0.676429i	−0.941069	+	0.338214i	$0.890177\pi$
$32$	2.94182e28	−	2.65301e28i	0.742620	−	0.669713i
$33$	−1.00037e29			−1.40734
$34$	2.26763e28	−	3.35217e27i	0.180914	−	0.0267440i
$35$		−	1.29986e29i		−	0.597864i
$36$	−1.01543e30	+	3.06922e29i	−2.73464	+	0.826573i
$37$	−3.14590e29			−0.503399			−0.251700	−	0.967805i	$-0.580990\pi$
$37$	−3.14590e29			−0.503399			−0.251700	+	0.967805i	$0.580990\pi$
$38$	1.62541e29	+	1.09953e30i	0.156702	+	1.06004i
$39$		−	4.28318e30i		−	2.52080i
$40$	1.90245e30	−	8.96317e29i	0.692107	−	0.326078i
$41$	−1.59147e30			−0.362164			−0.181082	−	0.983468i	$-0.557960\pi$
$41$	−1.59147e30			−0.362164			−0.181082	+	0.983468i	$0.557960\pi$
$42$	−1.05452e31	+	1.55887e30i	−1.51817	+	0.224427i
$43$			1.13757e31i			1.04732i	0.851928	+	0.523659i	$0.175433\pi$
$43$			1.13757e31i			1.04732i	−0.851928	+	0.523659i	$0.824567\pi$
$44$	−3.48561e30	−	1.15318e31i	−0.207338	−	0.685959i
$45$	−5.63153e31			−2.18569
$46$	−1.88784e30	−	1.27706e31i	−0.0482578	−	0.326447i
$47$			3.60466e31i			0.612358i	0.951974	+	0.306179i	$0.0990505\pi$
$47$			3.60466e31i			0.612358i	−0.951974	+	0.306179i	$0.900949\pi$
$48$	−9.55302e31	−	1.43589e32i	−1.08782	−	1.63508i
$49$	5.05892e31			0.389343
$50$	−7.82401e31	+	1.15660e31i	−0.410204	+	0.0606393i
$51$		−	9.97964e31i		−	0.359155i
$52$	4.93745e32	−	1.49239e32i	1.22868	−	0.371381i
$53$	1.01267e32			0.175480			0.0877402	−	0.996143i	$-0.472035\pi$
$53$	1.01267e32			0.175480			0.0877402	+	0.996143i	$0.472035\pi$
$54$	4.38965e32	+	2.96945e33i	0.533272	+	3.60740i
$55$		−	6.39554e32i		−	0.548259i
$56$	−5.47129e32	−	1.16129e33i	−0.333056	−	0.706917i
$57$	4.83896e33			2.10441
$58$	1.92717e33	−	2.84889e32i	0.602266	−	0.0890314i
$59$		−	1.33527e33i		−	0.301565i	−0.988567	−	0.150782i	$-0.951821\pi$
$59$		−	1.33527e33i		−	0.301565i	0.988567	−	0.150782i	$-0.0481793\pi$
$60$	−2.64904e33	−	8.76412e33i	−0.434726	−	1.43825i
$61$	−7.35637e33			−0.881854			−0.440927	−	0.897543i	$-0.645350\pi$
$61$	−7.35637e33			−0.881854			−0.440927	+	0.897543i	$0.645350\pi$
$62$	1.12389e33	+	7.60274e33i	0.0989196	+	0.669157i
$63$			3.43759e34i			2.23246i
$64$	1.32237e34	−	1.60154e34i	0.636699	−	0.771112i
$65$	2.73830e34			0.982035
$66$	−5.18846e34	+	7.66996e33i	−1.39221	+	0.205806i
$67$		−	3.46090e34i		−	0.697859i	−0.937149	−	0.348929i	$-0.886545\pi$
$67$		−	3.46090e34i		−	0.697859i	0.937149	−	0.348929i	$-0.113455\pi$
$68$	1.15041e34	−	3.47722e33i	0.175058	−	0.0529130i
$69$	−5.62024e34			−0.648070
$70$	−9.96610e33	−	6.74172e34i	−0.0874304	−	0.591436i
$71$		−	2.59319e35i		−	1.73750i	−0.495249	−	0.868751i	$-0.664923\pi$
$71$		−	2.59319e35i		−	1.73750i	0.495249	−	0.868751i	$-0.335077\pi$
$72$	−5.03120e35	+	2.37039e35i	−2.58437	+	1.21760i
$73$	3.29372e35			1.30182			0.650912	−	0.759154i	$-0.274387\pi$
$73$	3.29372e35			1.30182			0.650912	+	0.759154i	$0.274387\pi$
$74$	−1.63163e35	+	2.41199e34i	−0.497988	+	0.0736162i
$75$			3.44329e35i			0.814346i
$76$	1.68604e35	+	5.57813e35i	0.310035	+	1.02572i
$77$	−3.90395e35			−0.559991
$78$	−3.28395e35	−	2.22148e36i	−0.368637	−	2.49370i
$79$			9.78414e35i			0.862200i	0.902304	+	0.431100i	$0.141874\pi$
$79$			9.78414e35i			0.862200i	−0.902304	+	0.431100i	$0.858126\pi$
$80$	9.17986e35	−	6.10739e35i	0.636981	−	0.423785i
$81$	7.85514e36			4.30466
$82$	−8.25420e35	+	1.22020e35i	−0.358271	+	0.0529622i
$83$			3.96638e36i			1.36745i	0.729741	+	0.683723i	$0.239640\pi$
$83$			3.96638e36i			1.36745i	−0.729741	+	0.683723i	$0.760360\pi$
$84$	−5.34978e36	+	1.61702e36i	−1.46903	+	0.444028i
$85$	6.38013e35			0.139917
$86$	8.72187e35	+	5.90004e36i	0.153158	+	1.03606i
$87$		−	8.48133e36i		−	1.19563i
$88$	−2.69198e36	−	5.71377e36i	−0.305422	−	0.648264i
$89$	7.10862e36			0.650691			0.325346	−	0.945595i	$-0.394519\pi$
$89$	7.10862e36			0.650691			0.325346	+	0.945595i	$0.394519\pi$
$90$	−2.92080e37	+	4.31774e36i	−2.16219	+	0.319631i
$91$		−	1.67151e37i		−	1.00305i
$92$	−1.95827e36	−	6.47875e36i	−0.0954779	−	0.315880i
$93$	3.34590e37			1.32843
$94$	2.76372e36	+	1.86956e37i	0.0895500	+	0.605774i
$95$			3.09362e37i			0.819819i
$96$	−6.05560e37	−	6.71484e37i	−1.31524	−	1.45842i
$97$	−6.10990e37			−1.08986			−0.544930	−	0.838481i	$-0.683444\pi$
$97$	−6.10990e37			−1.08986			−0.544930	+	0.838481i	$0.683444\pi$
$98$	2.62382e37	−	3.87872e36i	0.385157	−	0.0569368i
$99$			1.69136e38i			2.04723i
$100$	−3.96926e37	+	1.19975e37i	−0.396926	+	0.119975i
$101$	1.26223e38			1.04479			0.522397	−	0.852702i	$-0.325038\pi$
$101$	1.26223e38			1.04479			0.522397	+	0.852702i	$0.325038\pi$
$102$	−7.65148e36	−	5.17596e37i	−0.0525221	−	0.355294i
$103$		−	3.14830e38i		−	1.79543i	−0.440574	−	0.897716i	$-0.645225\pi$
$103$		−	3.14830e38i		−	1.79543i	0.440574	−	0.897716i	$-0.354775\pi$
$104$	2.44639e38	−	1.15259e38i	1.16116	−	0.547068i
$105$	−2.96698e38			−1.17413
$106$	5.25225e37	−	7.76426e36i	0.173594	−	0.0256619i
$107$		−	2.88847e38i		−	0.798685i	−0.916802	−	0.399343i	$-0.869238\pi$
$107$		−	2.88847e38i		−	0.798685i	0.916802	−	0.399343i	$-0.130762\pi$
$108$	4.55340e38	+	1.50645e39i	1.05508	+	3.49063i
$109$	3.59798e38			0.699770			0.349885	−	0.936793i	$-0.386221\pi$
$109$	3.59798e38			0.699770			0.349885	+	0.936793i	$0.386221\pi$
$110$	−4.90351e37	−	3.31705e38i	−0.0801763	−	0.542365i
$111$			7.18067e38i			0.988617i
$112$	−3.72806e38	−	5.60356e38i	−0.432853	−	0.650611i
$113$	−1.38882e38			−0.136194			−0.0680968	−	0.997679i	$-0.521693\pi$
$113$	−1.38882e38			−0.136194			−0.0680968	+	0.997679i	$0.521693\pi$
$114$	2.50974e39	−	3.71007e38i	2.08178	−	0.307745i
$115$		−	3.59310e38i		−	0.252470i
$116$	9.77688e38	−	2.95516e38i	0.582772	−	0.176149i
$117$	−7.24168e39			−3.66698
$118$	−1.02376e38	−	6.92539e38i	−0.0441002	−	0.298323i
$119$		−	3.89455e38i		−	0.142911i
$120$	−2.04588e39	−	4.34242e39i	−0.640379	−	1.35922i
$121$	1.81961e39			0.486472
$122$	−3.81539e39	+	5.64019e38i	−0.872373	+	0.128961i
$123$			3.63261e39i			0.711248i
$124$	1.16582e39	+	3.85700e39i	0.195712	+	0.647497i
$125$	−7.51011e39			−1.08232
$126$	2.63563e39	+	1.78291e40i	0.326470	+	2.20846i
$127$		−	1.18917e40i		−	1.26758i	−0.773507	−	0.633788i	$-0.781499\pi$
$127$		−	1.18917e40i		−	1.26758i	0.773507	−	0.633788i	$-0.218501\pi$
$128$	5.63059e39	−	9.32027e39i	0.517088	−	0.855932i
$129$	2.59656e40			2.05681
$130$	1.42022e40	−	2.09948e39i	0.971478	−	0.143611i
$131$		−	2.14287e40i		−	1.26719i	−0.773666	−	0.633593i	$-0.781579\pi$
$131$		−	2.14287e40i		−	1.26719i	0.773666	−	0.633593i	$-0.218421\pi$
$132$	−2.63220e40	+	7.95607e39i	−1.34714	+	0.407187i
$133$	1.88840e40			0.837362
$134$	−2.65350e39	−	1.79500e40i	−0.102053	−	0.690356i
$135$			8.35475e40i			2.78992i
$136$	5.70000e39	−	2.68549e39i	0.165438	−	0.0779443i
$137$	−3.18667e38			−0.00804723			−0.00402362	−	0.999992i	$-0.501281\pi$
$137$	−3.18667e38			−0.00804723			−0.00402362	+	0.999992i	$0.501281\pi$
$138$	−2.91495e40	+	4.30909e39i	−0.641103	+	0.0947725i
$139$			2.48667e40i			0.476800i	0.971167	+	0.238400i	$0.0766229\pi$
$139$			2.48667e40i			0.476800i	−0.971167	+	0.238400i	$0.923377\pi$
$140$	−1.03379e40	−	3.42019e40i	−0.172981	−	0.572292i
$141$	8.22780e40			1.20260
$142$	−1.98822e40	−	1.34496e41i	−0.254089	−	1.71882i
$143$		−	8.22414e40i		−	0.919826i
$144$	−2.42770e41	+	1.61515e41i	−2.37853	+	1.58244i
$145$	5.42224e40			0.465786
$146$	1.70829e41	−	2.52532e40i	1.28783	−	0.190376i
$147$		−	1.15472e41i		−	0.764624i
$148$	−8.27754e40	+	2.50197e40i	−0.481868	+	0.145649i
$149$	−1.44384e41			−0.739572			−0.369786	−	0.929117i	$-0.620569\pi$
$149$	−1.44384e41			−0.739572			−0.369786	+	0.929117i	$0.620569\pi$
$150$	2.64000e40	+	1.78587e41i	0.119088	+	0.805591i
$151$		−	4.13386e40i		−	0.164359i	−0.996618	−	0.0821796i	$-0.973812\pi$
$151$		−	4.13386e40i		−	0.164359i	0.996618	−	0.0821796i	$-0.0261881\pi$
$152$	1.30215e41	+	2.76384e41i	0.456702	+	0.969358i
$153$	−1.68728e41			−0.522458
$154$	−2.02479e41	+	2.99320e40i	−0.553971	+	0.0818920i
$155$			2.13908e41i			0.517518i
$156$	−3.40645e41	−	1.12699e42i	−0.729348	−	2.41298i
$157$	6.70769e40			0.127198			0.0635989	−	0.997976i	$-0.479742\pi$
$157$	6.70769e40			0.127198			0.0635989	+	0.997976i	$0.479742\pi$
$158$	7.50158e40	+	5.07456e41i	0.126086	+	0.852930i
$159$		−	2.31147e41i		−	0.344623i
$160$	4.29289e41	−	3.87143e41i	0.568160	−	0.512380i
$161$	−2.19330e41			−0.257873
$162$	4.07408e42	−	6.02261e41i	4.25838	−	0.629505i
$163$			1.57199e42i			1.46179i	0.682490	+	0.730895i	$0.260897\pi$
$163$			1.57199e42i			1.46179i	−0.682490	+	0.730895i	$0.739103\pi$
$164$	−4.18750e41	+	1.26571e41i	−0.346674	+	0.104786i
$165$	−1.45981e42			−1.07672
$166$	3.04106e41	+	2.05717e42i	0.199973	+	1.35275i
$167$			5.86398e41i			0.344017i	0.985095	+	0.172008i	$0.0550256\pi$
$167$			5.86398e41i			0.344017i	−0.985095	+	0.172008i	$0.944974\pi$
$168$	−2.65070e42	+	1.24885e42i	−1.38830	+	0.654082i
$169$	1.38402e42			0.647581
$170$	3.30906e41	−	4.89170e40i	0.138413	−	0.0204612i
$171$		−	8.18136e42i		−	3.06125i
$172$	9.04722e41	+	2.99319e42i	0.303022	+	1.00252i
$173$	−4.64403e42			−1.39322			−0.696609	−	0.717451i	$-0.745309\pi$
$173$	−4.64403e42			−1.39322			−0.696609	+	0.717451i	$0.745309\pi$
$174$	−6.50271e41	−	4.39886e42i	−0.174847	−	1.18278i
$175$			1.34374e42i			0.324035i
$176$	−1.83428e42	−	2.75706e42i	−0.396939	−	0.596630i
$177$	−3.04781e42			−0.592238
$178$	3.68689e42	−	5.45024e41i	0.643696	−	0.0951558i
$179$			3.70299e42i			0.581226i	0.956841	+	0.290613i	$0.0938592\pi$
$179$			3.70299e42i			0.581226i	−0.956841	+	0.290613i	$0.906141\pi$
$180$	−1.48177e43	+	4.47881e42i	−2.09220	+	0.632389i
$181$	9.61745e42			1.22227			0.611135	−	0.791527i	$-0.290713\pi$
$181$	9.61745e42			1.22227			0.611135	+	0.791527i	$0.290713\pi$
$182$	−1.28156e42	−	8.66930e42i	−0.146684	−	0.992266i
$183$			1.67912e43i			1.73186i
$184$	−1.51239e42	−	3.21007e42i	−0.140645	−	0.298522i
$185$	−4.59070e42			−0.385138
$186$	1.73536e43	−	2.56533e42i	1.31415	−	0.194266i
$187$		−	1.91619e42i		−	0.131053i
$188$	2.86682e42	+	9.48462e42i	0.177175	+	0.586166i
$189$	5.09989e43			2.84962
$190$	2.37190e42	+	1.60451e43i	0.119889	+	0.811006i
$191$		−	5.35328e42i		−	0.244898i	−0.992475	−	0.122449i	$-0.960925\pi$
$191$		−	5.35328e42i		−	0.244898i	0.992475	−	0.122449i	$-0.0390748\pi$
$192$	−3.65558e43	−	3.01837e43i	−1.51437	−	1.25040i
$193$	1.22524e43			0.459867			0.229934	−	0.973206i	$-0.426149\pi$
$193$	1.22524e43			0.459867			0.229934	+	0.973206i	$0.426149\pi$
$194$	−3.16891e43	+	4.68451e42i	−1.07814	+	0.159379i
$195$		−	6.25029e43i		−	1.92860i
$196$	1.33111e43	−	4.02341e42i	0.372690	−	0.112649i
$197$	2.06408e42			0.0524648			0.0262324	−	0.999656i	$-0.491649\pi$
$197$	2.06408e42			0.0524648			0.0262324	+	0.999656i	$0.491649\pi$
$198$	1.29678e43	+	8.77226e43i	0.299383	+	2.02522i
$199$			7.29919e43i			1.53132i	0.643246	+	0.765660i	$0.277587\pi$
$199$			7.29919e43i			1.53132i	−0.643246	+	0.765660i	$0.722413\pi$
$200$	−1.96668e43	+	9.26577e42i	−0.375114	+	0.176731i
$201$	−7.89965e43			−1.37051
$202$	6.54655e43	−	9.67759e42i	1.03356	−	0.152789i
$203$		−	3.30983e43i		−	0.475753i
$204$	−7.93690e42	−	2.62585e43i	−0.103915	−	0.343793i
$205$	−2.32238e43			−0.277083
$206$	−2.41383e43	−	1.63287e44i	−0.262561	−	1.77613i
$207$			9.50229e43i			0.942739i
$208$	1.18046e44	−	7.85360e43i	1.06868	−	0.710993i
$209$	9.29130e43			0.767886
$210$	−1.53883e44	+	2.27481e43i	−1.16151	+	0.171703i
$211$		−	7.46929e43i		−	0.515125i	−0.966262	−	0.257563i	$-0.917081\pi$
$211$		−	7.46929e43i		−	0.515125i	0.966262	−	0.257563i	$-0.0829194\pi$
$212$	2.66456e43	−	8.05390e42i	0.167975	−	0.0507720i
$213$	−5.91906e44			−3.41225
$214$	−2.21461e43	−	1.49811e44i	−0.116798	−	0.790099i
$215$			1.66002e44i			0.801276i
$216$	3.51664e44	+	7.46412e44i	1.55420	+	3.29881i
$217$	1.30574e44			0.528592
$218$	1.86610e44	−	2.75860e43i	0.692247	−	0.102333i
$219$		−	7.51806e44i		−	2.55663i
$220$	−5.08643e43	−	1.68280e44i	−0.158629	−	0.524809i
$221$	8.20432e43			0.234741
$222$	5.50548e43	+	3.72426e44i	0.144573	+	0.977989i
$223$			3.77394e44i			0.909919i	0.890512	+	0.454959i	$0.150346\pi$
$223$			3.77394e44i			0.909919i	−0.890512	+	0.454959i	$0.849654\pi$
$224$	−2.36319e44	−	2.62046e44i	−0.523344	−	0.580317i
$225$	5.82165e44			1.18462
$226$	−7.20315e43	+	1.06482e43i	−0.134729	+	0.0199167i
$227$		−	6.83403e43i		−	0.117540i	−0.998272	−	0.0587699i	$-0.981282\pi$
$227$		−	6.83403e43i		−	0.117540i	0.998272	−	0.0587699i	$-0.0187178\pi$
$228$	1.27323e45	−	3.84847e44i	2.01440	−	0.608872i
$229$	3.66784e44			0.533994			0.266997	−	0.963697i	$-0.413969\pi$
$229$	3.66784e44			0.533994			0.266997	+	0.963697i	$0.413969\pi$
$230$	−2.75486e43	−	1.86357e44i	−0.0369208	−	0.249756i
$231$			8.91095e44i			1.09976i
$232$	4.84422e44	−	2.28230e44i	0.550747	−	0.259478i
$233$	−1.01331e45			−1.06165			−0.530823	−	0.847483i	$-0.678117\pi$
$233$	−1.01331e45			−1.06165			−0.530823	+	0.847483i	$0.678117\pi$
$234$	−3.75591e45	+	5.55226e44i	−3.62756	+	0.536252i
$235$			5.26015e44i			0.468499i
$236$	−1.06195e44	−	3.51337e44i	−0.0872523	−	0.288666i
$237$	2.23327e45			1.69326
$238$	−2.98598e43	−	2.01991e44i	−0.0208990	−	0.141374i
$239$			2.66930e45i			1.72519i	0.505892	+	0.862597i	$0.331163\pi$
$239$			2.66930e45i			1.72519i	−0.505892	+	0.862597i	$0.668837\pi$
$240$	−1.39404e45	−	2.09534e45i	−0.832264	−	1.25096i
$241$	−2.98744e45			−1.64807			−0.824035	−	0.566538i	$-0.808282\pi$
$241$	−2.98744e45			−1.64807			−0.824035	+	0.566538i	$0.808282\pi$
$242$	9.43746e44	−	1.39511e44i	0.481242	−	0.0711407i
$243$		−	1.01957e46i		−	4.80724i
$244$	−1.93562e45	+	5.85059e44i	−0.844136	+	0.255148i
$245$	7.38230e44			0.297876
$246$	2.78515e44	+	1.88406e45i	0.104012	+	0.703602i
$247$			3.97814e45i			1.37543i
$248$	9.00372e44	+	1.91106e45i	0.288297	+	0.611916i
$249$	9.05343e45			2.68550
$250$	−3.89513e45	+	5.75807e44i	−1.07069	+	0.158277i
$251$			4.81645e45i			1.22723i	0.789605	+	0.613616i	$0.210285\pi$
$251$			4.81645e45i			1.22723i	−0.789605	+	0.613616i	$0.789715\pi$
$252$	2.73395e45	+	9.04502e45i	0.645921	+	2.13697i
$253$	−1.07914e45			−0.236477
$254$	−9.11748e44	−	6.16766e45i	−0.185368	−	1.25395i
$255$		−	1.45629e45i		−	0.274780i
$256$	2.20572e45	−	5.26568e45i	0.386360	−	0.922348i
$257$	−4.53209e45			−0.737173			−0.368586	−	0.929594i	$-0.620158\pi$
$257$	−4.53209e45			−0.737173			−0.368586	+	0.929594i	$0.620158\pi$
$258$	1.34671e46	−	1.99080e45i	2.03470	−	0.300784i
$259$			2.80225e45i			0.393379i
$260$	7.20504e45	−	2.17779e45i	0.940032	−	0.284134i
$261$	−1.43396e46			−1.73927
$262$	−1.64295e45	−	1.11140e46i	−0.185311	−	1.25356i
$263$			7.57752e45i			0.795001i	0.917602	+	0.397500i	$0.130122\pi$
$263$			7.57752e45i			0.795001i	−0.917602	+	0.397500i	$0.869878\pi$
$264$	−1.30419e46	+	6.14455e45i	−1.27311	+	0.599813i
$265$	1.47776e45			0.134255
$266$	9.79423e45	−	1.44785e45i	0.828360	−	0.122454i
$267$		−	1.62257e46i		−	1.27788i
$268$	−2.75248e45	−	9.10635e45i	−0.201913	−	0.668010i
$269$	9.75268e45			0.666547			0.333273	−	0.942830i	$-0.391847\pi$
$269$	9.75268e45			0.666547			0.333273	+	0.942830i	$0.391847\pi$
$270$	6.40566e45	+	4.33320e46i	0.407992	+	2.75993i
$271$		−	3.37324e45i		−	0.200277i	−0.994974	−	0.100138i	$-0.968071\pi$
$271$		−	3.37324e45i		−	0.200277i	0.994974	−	0.100138i	$-0.0319285\pi$
$272$	2.75042e45	−	1.82986e45i	0.152261	−	0.101300i
$273$	−3.81529e46			−1.96987
$274$	−1.65277e44	+	2.44325e43i	−0.00796072	+	0.00117681i
$275$			6.61145e45i			0.297150i
$276$	−1.47880e46	+	4.46983e45i	−0.620352	+	0.187507i
$277$	−1.89104e46			−0.740603			−0.370301	−	0.928912i	$-0.620746\pi$
$277$	−1.89104e46			−0.740603			−0.370301	+	0.928912i	$0.620746\pi$
$278$	1.90655e45	+	1.28971e46i	0.0697263	+	0.471674i
$279$		−	5.65701e46i		−	1.93244i
$280$	−7.98405e45	−	1.69463e46i	−0.254812	−	0.540844i
$281$	2.46698e46			0.735775			0.367888	−	0.929870i	$-0.380081\pi$
$281$	2.46698e46			0.735775			0.367888	+	0.929870i	$0.380081\pi$
$282$	4.26736e46	−	6.30832e45i	1.18967	−	0.175866i
$283$			4.22253e46i			1.10060i	0.834966	+	0.550302i	$0.185487\pi$
$283$			4.22253e46i			1.10060i	−0.834966	+	0.550302i	$0.814513\pi$
$284$	−2.06239e46	−	6.82322e46i	−0.502715	−	1.66319i
$285$	7.06132e46			1.61003
$286$	−6.30552e45	−	4.26546e46i	−0.134514	−	0.909937i
$287$			1.41762e46i			0.283012i
$288$	−1.13530e47	+	1.02384e47i	−2.12154	+	1.91326i
$289$	−5.52441e46			−0.966555
$290$	2.81225e46	−	4.15728e45i	0.460779	−	0.0681156i
$291$			1.39461e47i			2.14036i
$292$	8.66646e46	−	2.61952e46i	1.24614	−	0.376659i
$293$	4.89119e46			0.659067			0.329534	−	0.944144i	$-0.393109\pi$
$293$	4.89119e46			0.659067			0.329534	+	0.944144i	$0.393109\pi$
$294$	−8.85335e45	−	5.98898e46i	−0.111817	−	0.756404i
$295$		−	1.94851e46i		−	0.230719i
$296$	−4.10133e46	+	1.93229e46i	−0.455389	+	0.214551i
$297$	2.50924e47			2.61319
$298$	−7.48850e46	+	1.10701e46i	−0.731621	+	0.108153i
$299$		−	4.62043e46i		−	0.423575i
$300$	2.73848e46	+	9.06001e46i	0.235616	+	0.779516i
$301$	1.01331e47			0.818422
$302$	−3.16947e45	−	2.14403e46i	−0.0240356	−	0.162592i
$303$		−	2.88109e47i		−	2.05185i
$304$	8.87268e46	+	1.33363e47i	0.593549	+	0.892149i
$305$	−1.07349e47			−0.674684
$306$	−8.75113e46	+	1.29366e46i	−0.516841	+	0.0764032i
$307$		−	3.11195e46i		−	0.172744i	−0.996263	−	0.0863722i	$-0.972473\pi$
$307$		−	3.11195e46i		−	0.172744i	0.996263	−	0.0863722i	$-0.0275274\pi$
$308$	−1.02721e47	+	3.10485e46i	−0.536039	+	0.162023i
$309$	−7.18614e47			−3.52602
$310$	1.64005e46	+	1.10944e47i	0.0756809	+	0.511955i
$311$			1.10257e47i			0.478587i	0.970947	+	0.239293i	$0.0769158\pi$
$311$			1.10257e47i			0.478587i	−0.970947	+	0.239293i	$0.923084\pi$
$312$	−2.63084e47	−	5.58400e47i	−1.07438	−	2.28039i
$313$	2.97136e47			1.14186			0.570931	−	0.820998i	$-0.306582\pi$
$313$	2.97136e47			1.14186			0.570931	+	0.820998i	$0.306582\pi$
$314$	3.47895e46	−	5.14284e45i	0.125830	−	0.0186012i
$315$			5.01635e47i			1.70800i
$316$	7.78141e46	+	2.57441e47i	0.249462	+	0.825322i
$317$	1.49952e47			0.452716			0.226358	−	0.974044i	$-0.427318\pi$
$317$	1.49952e47			0.452716			0.226358	+	0.974044i	$0.427318\pi$
$318$	−1.77223e46	−	1.19885e47i	−0.0503969	−	0.340918i
$319$		−	1.62850e47i		−	0.436280i
$320$	1.92969e47	−	2.33706e47i	0.487122	−	0.589958i
$321$	−6.59305e47			−1.56852
$322$	−1.13756e47	+	1.68162e46i	−0.255100	+	0.0377108i
$323$			9.26891e46i			0.195966i
$324$	2.06685e48	−	6.24727e47i	4.12054	−	1.24547i
$325$	−2.83075e47			−0.532252
$326$	1.20526e47	+	8.15314e47i	0.213769	+	1.44607i
$327$		−	8.21255e47i		−	1.37427i
$328$	−2.07481e47	+	9.77523e46i	−0.327624	+	0.154356i
$329$	3.21089e47			0.478524
$330$	−7.57133e47	+	1.11925e47i	−1.06514	+	0.157457i
$331$			6.23454e47i			0.828080i	0.910259	+	0.414040i	$0.135883\pi$
$331$			6.23454e47i			0.828080i	−0.910259	+	0.414040i	$0.864117\pi$
$332$	3.15450e47	+	1.04364e48i	0.395646	+	1.30896i
$333$	1.21405e48			1.43813
$334$	4.49597e46	+	3.04136e47i	0.0503083	+	0.340318i
$335$		−	5.05036e47i		−	0.533914i
$336$	−1.27904e48	+	8.50947e47i	−1.27772	+	0.850073i
$337$	−1.21282e48			−1.14506			−0.572532	−	0.819882i	$-0.694039\pi$
$337$	−1.21282e48			−1.14506			−0.572532	+	0.819882i	$0.694039\pi$
$338$	7.17823e47	−	1.06114e47i	0.640619	−	0.0947010i
$339$			3.17005e47i			0.267468i
$340$	1.67875e47	−	5.07417e46i	0.133932	−	0.0404824i
$341$	6.42447e47			0.484735
$342$	−6.27272e47	−	4.24328e48i	−0.447672	−	3.02834i
$343$		−	1.60804e48i		−	1.08570i
$344$	6.98726e47	+	1.48306e48i	0.446372	+	0.947432i
$345$	−8.20141e47			−0.495822
$346$	−2.40863e48	+	3.56062e47i	−1.37824	+	0.203741i
$347$		−	1.46129e48i		−	0.791546i	−0.918348	−	0.395773i	$-0.870477\pi$
$347$		−	1.46129e48i		−	0.791546i	0.918348	−	0.395773i	$-0.129523\pi$
$348$	−6.74528e47	−	2.23162e48i	−0.345935	−	1.14450i
$349$	1.40124e48			0.680500			0.340250	−	0.940335i	$-0.389488\pi$
$349$	1.40124e48			0.680500			0.340250	+	0.940335i	$0.389488\pi$
$350$	1.03026e47	+	6.96933e47i	0.0473863	+	0.320552i
$351$			1.07435e49i			4.68071i
$352$	−1.16274e48	−	1.28932e48i	−0.479922	−	0.532168i
$353$	2.27405e48			0.889365			0.444682	−	0.895688i	$-0.353317\pi$
$353$	2.27405e48			0.889365			0.444682	+	0.895688i	$0.353317\pi$
$354$	−1.58075e48	+	2.33678e47i	−0.585871	+	0.0866077i
$355$		−	3.78414e48i		−	1.32932i
$356$	1.87043e48	−	5.65355e47i	0.622860	−	0.188266i
$357$	−8.88948e47			−0.280660
$358$	2.83912e47	+	1.92056e48i	0.0849974	+	0.574978i
$359$		−	2.51644e48i		−	0.714482i	−0.934012	−	0.357241i	$-0.883717\pi$
$359$		−	2.51644e48i		−	0.714482i	0.934012	−	0.357241i	$-0.116283\pi$
$360$	−7.34185e48	+	3.45903e48i	−1.97723	+	0.931551i
$361$	−5.80198e47			−0.148231
$362$	4.98811e48	−	7.37378e47i	1.20913	−	0.178742i
$363$		−	4.15335e48i		−	0.955373i
$364$	−1.32937e48	−	4.39809e48i	−0.290214	−	0.960147i
$365$	4.80640e48			0.995991
$366$	1.28740e48	+	8.70880e48i	0.253263	+	1.71324i
$367$		−	6.41579e48i		−	1.19838i	−0.800607	−	0.599190i	$-0.795489\pi$
$367$		−	6.41579e48i		−	1.19838i	0.800607	−	0.599190i	$-0.204511\pi$
$368$	−1.03052e48	−	1.54895e48i	−0.182788	−	0.274745i
$369$	6.14174e48			1.03464
$370$	−2.38098e48	+	3.51973e47i	−0.380997	+	0.0563218i
$371$		−	9.02052e47i		−	0.137128i
$372$	8.80378e48	−	2.66103e48i	1.27161	−	0.384356i
$373$	−1.20897e49			−1.65939			−0.829693	−	0.558219i	$-0.811485\pi$
$373$	−1.20897e49			−1.65939			−0.829693	+	0.558219i	$0.811485\pi$
$374$	−1.46916e47	−	9.93836e47i	−0.0191650	−	0.129645i
$375$			1.71422e49i			2.12555i
$376$	2.21407e48	+	4.69941e48i	0.260990	+	0.553955i
$377$	6.97256e48			0.781459
$378$	2.64507e49	−	3.91013e48i	2.81898	−	0.416723i
$379$			3.23372e48i			0.327761i	0.986480	+	0.163881i	$0.0524012\pi$
$379$			3.23372e48i			0.327761i	−0.986480	+	0.163881i	$0.947599\pi$
$380$	2.46038e48	+	8.13996e48i	0.237200	+	0.784755i
$381$	−2.71434e49			−2.48937
$382$	−4.10440e47	−	2.77649e48i	−0.0358135	−	0.242266i
$383$			1.94131e49i			1.61182i	0.592036	+	0.805912i	$0.298324\pi$
$383$			1.94131e49i			1.61182i	−0.592036	+	0.805912i	$0.701676\pi$
$384$	−2.12739e49	−	1.28521e49i	−1.68095	−	1.01550i
$385$	−5.69690e48			−0.428435
$386$	6.35473e48	−	9.39402e47i	0.454923	−	0.0672501i
$387$		−	4.39007e49i		−	2.99201i
$388$	−1.60764e49	+	4.85926e48i	−1.04325	+	0.315331i
$389$	3.15655e49			1.95061			0.975305	−	0.220863i	$-0.0708873\pi$
$389$	3.15655e49			1.95061			0.975305	+	0.220863i	$0.0708873\pi$
$390$	−4.79215e48	−	3.24172e49i	−0.282035	−	1.90787i
$391$		−	1.07654e48i		−	0.0603494i
$392$	6.59534e48	−	3.10732e48i	0.352210	−	0.165940i
$393$	−4.89119e49			−2.48860
$394$	1.07054e48	−	1.58255e47i	0.0519007	−	0.00767235i
$395$			1.42776e49i			0.659647i
$396$	1.34515e49	+	4.45032e49i	0.592329	+	1.95967i
$397$	−3.08835e49			−1.29630			−0.648152	−	0.761511i	$-0.724458\pi$
$397$	−3.08835e49			−1.29630			−0.648152	+	0.761511i	$0.724458\pi$
$398$	5.59635e48	+	3.78573e49i	0.223937	+	1.51486i
$399$		−	4.31036e49i		−	1.64448i
$400$	−9.48979e48	+	6.31358e48i	−0.345236	+	0.229687i
$401$	1.42475e49			0.494307			0.247153	−	0.968976i	$-0.420505\pi$
$401$	1.42475e49			0.494307			0.247153	+	0.968976i	$0.420505\pi$
$402$	−4.09717e49	+	6.05673e48i	−1.35578	+	0.200421i
$403$			2.75069e49i			0.868252i
$404$	3.32118e49	−	1.00386e49i	1.00011	−	0.302292i
$405$	1.14627e50			3.29338
$406$	−2.53768e48	−	1.71665e49i	−0.0695732	−	0.470638i
$407$			1.37876e49i			0.360741i
$408$	−6.12975e48	−	1.30105e49i	−0.153073	−	0.324901i
$409$	3.21318e49			0.765936			0.382968	−	0.923762i	$-0.374902\pi$
$409$	3.21318e49			0.765936			0.382968	+	0.923762i	$0.374902\pi$
$410$	−1.20450e49	+	1.78059e48i	−0.274104	+	0.0405200i
$411$			7.27372e47i			0.0158038i
$412$	−2.50387e49	−	8.28384e49i	−0.519476	−	1.71864i
$413$	−1.18941e49			−0.235656
$414$	7.28548e48	+	4.92838e49i	0.137864	+	0.932604i
$415$			5.78799e49i			1.04620i
$416$	5.52031e49	−	4.97835e49i	0.953214	−	0.859631i
$417$	5.67593e49			0.936379
$418$	4.81895e49	−	7.12372e48i	0.759631	−	0.112294i
$419$			1.02125e50i			1.53839i	0.639014	+	0.769195i	$0.279342\pi$
$419$			1.02125e50i			1.53839i	−0.639014	+	0.769195i	$0.720658\pi$
$420$	−7.80674e49	+	2.35967e49i	−1.12391	+	0.339714i
$421$	−1.69218e49			−0.232855			−0.116428	−	0.993199i	$-0.537144\pi$
$421$	−1.69218e49			−0.232855			−0.116428	+	0.993199i	$0.537144\pi$
$422$	−5.72677e48	−	3.87396e49i	−0.0753309	−	0.509587i
$423$		−	1.39110e50i		−	1.74940i
$424$	1.32023e49	−	6.22011e48i	0.158744	−	0.0747905i
$425$	−6.59553e48			−0.0758333
$426$	−3.06993e50	+	4.53820e49i	−3.37556	+	0.499001i
$427$			6.55277e49i			0.689121i
$428$	−2.29722e49	−	7.60016e49i	−0.231085	−	0.764524i
$429$	−1.87720e50			−1.80643
$430$	1.27275e49	+	8.60971e49i	0.117177	+	0.792662i
$431$		−	1.84118e50i		−	1.62192i	−0.585105	−	0.810958i	$-0.698947\pi$
$431$		−	1.84118e50i		−	1.62192i	0.585105	−	0.810958i	$-0.301053\pi$
$432$	2.39619e50	+	3.60166e50i	2.01990	+	3.03606i
$433$	6.80095e49			0.548655			0.274327	−	0.961636i	$-0.411545\pi$
$433$	6.80095e49			0.548655			0.274327	+	0.961636i	$0.411545\pi$
$434$	6.77223e49	−	1.00112e49i	0.522910	−	0.0773003i
$435$		−	1.23765e50i		−	0.914749i
$436$	9.46704e49	−	2.86151e49i	0.669840	−	0.202466i
$437$	5.21998e49			0.353607
$438$	−5.76416e49	−	3.89925e50i	−0.373876	−	2.52914i
$439$		−	7.69130e49i		−	0.477720i	−0.971054	−	0.238860i	$-0.923226\pi$
$439$		−	7.69130e49i		−	0.477720i	0.971054	−	0.238860i	$-0.0767738\pi$
$440$	−3.92830e49	−	8.33789e49i	−0.233671	−	0.495970i
$441$	−1.95232e50			−1.11229
$442$	4.25519e49	−	6.29033e48i	0.232218	−	0.0343281i
$443$			2.32649e50i			1.21627i	0.793833	+	0.608136i	$0.208082\pi$
$443$			2.32649e50i			1.21627i	−0.793833	+	0.608136i	$0.791918\pi$
$444$	5.71085e49	+	1.88938e50i	0.286038	+	0.946333i
$445$	1.03733e50			0.497827
$446$	2.89351e49	+	1.95736e50i	0.133065	+	0.900137i
$447$			3.29563e50i			1.45243i
$448$	−1.42659e50	−	1.17792e50i	−0.602582	−	0.497546i
$449$	−3.93199e50			−1.59196			−0.795981	−	0.605322i	$-0.793044\pi$
$449$	−3.93199e50			−1.59196			−0.795981	+	0.605322i	$0.793044\pi$
$450$	3.01941e50	−	4.46351e49i	1.17188	−	0.173236i
$451$			6.97497e49i			0.259530i
$452$	−3.65429e49	+	1.10454e49i	−0.130368	+	0.0394051i
$453$	−9.43573e49			−0.322782
$454$	−5.23971e48	−	3.54448e49i	−0.0171888	−	0.116276i
$455$		−	2.43917e50i		−	0.767407i
$456$	6.30858e50	−	2.97221e50i	1.90370	−	0.896909i
$457$	−1.81880e50			−0.526475			−0.263237	−	0.964731i	$-0.584790\pi$
$457$	−1.81880e50			−0.526475			−0.263237	+	0.964731i	$0.584790\pi$
$458$	1.90233e50	−	2.81216e49i	0.528253	−	0.0780902i
$459$			2.50320e50i			0.666890i
$460$	−2.85763e49	−	9.45420e49i	−0.0730477	−	0.241672i
$461$	7.53980e50			1.84945			0.924724	−	0.380638i	$-0.124296\pi$
$461$	7.53980e50			1.84945			0.924724	+	0.380638i	$0.124296\pi$
$462$	6.83210e49	+	4.62168e50i	0.160826	+	1.08793i
$463$		−	6.29632e50i		−	1.42249i	−0.702946	−	0.711243i	$-0.748133\pi$
$463$		−	6.29632e50i		−	1.42249i	0.702946	−	0.711243i	$-0.251867\pi$
$464$	2.33748e50	−	1.55513e50i	0.506881	−	0.337229i
$465$	4.88256e50			1.01634
$466$	−5.25555e50	+	7.76914e49i	−1.05023	+	0.155253i
$467$		−	1.81850e48i		−	0.00348893i	−0.999998	−	0.00174446i	$-0.999445\pi$
$467$		−	1.81850e48i		−	0.00348893i	0.999998	−	0.00174446i	$-0.000555280\pi$
$468$	−1.90544e51	+	5.75938e50i	−3.51014	+	1.06097i
$469$	−3.08283e50			−0.545339
$470$	4.03300e49	+	2.72818e50i	0.0685124	+	0.463462i
$471$		−	1.53106e50i		−	0.249801i
$472$	−8.20156e49	−	1.74080e50i	−0.128528	−	0.272804i
$473$	4.98566e50			0.750517
$474$	1.15829e51	−	1.71227e50i	1.67505	−	0.247619i
$475$		−	3.19806e50i		−	0.444333i
$476$	−3.09737e49	−	1.02474e50i	−0.0413486	−	0.136798i
$477$	−3.90807e50			−0.501318
$478$	2.04658e50	+	1.38444e51i	0.252289	+	1.70665i
$479$			7.60161e50i			0.900597i	0.892878	+	0.450299i	$0.148682\pi$
$479$			7.60161e50i			0.900597i	−0.892878	+	0.450299i	$0.851318\pi$
$480$	−8.83672e50	−	9.79872e50i	−1.00625	−	1.11580i
$481$	−5.90327e50			−0.646154
$482$	−1.54944e51	+	2.29050e50i	−1.63035	+	0.241011i
$483$			5.00629e50i			0.506432i
$484$	4.78779e50	−	1.44716e50i	0.465665	−	0.140752i
$485$	−8.91595e50			−0.833824
$486$	−7.81710e50	−	5.28799e51i	−0.703002	−	4.75556i
$487$			1.04970e51i			0.907848i	0.891041	+	0.453924i	$0.149976\pi$
$487$			1.04970e51i			0.907848i	−0.891041	+	0.453924i	$0.850024\pi$
$488$	−9.59053e50	+	4.51847e50i	−0.797748	+	0.375850i
$489$	3.58813e51			2.87078
$490$	3.82884e50	−	5.66007e49i	0.294674	−	0.0435608i
$491$		−	2.37081e51i		−	1.75529i	−0.479315	−	0.877643i	$-0.659115\pi$
$491$		−	2.37081e51i		−	1.75529i	0.479315	−	0.877643i	$-0.340885\pi$
$492$	2.88905e50	+	9.55815e50i	0.205787	+	0.680827i
$493$	1.62458e50			0.111339
$494$	3.05007e50	+	2.06327e51i	0.201140	+	1.36064i
$495$			2.46814e51i			1.56628i
$496$	6.13502e50	+	9.22140e50i	0.374683	+	0.563177i
$497$	−2.30991e51			−1.35776
$498$	4.69558e51	−	6.94135e50i	2.65663	−	0.392723i
$499$		−	6.02439e49i		−	0.0328098i	−0.999865	−	0.0164049i	$-0.994778\pi$
$499$		−	6.02439e49i		−	0.0328098i	0.999865	−	0.0164049i	$-0.00522207\pi$
$500$	−1.97607e51	+	5.97286e50i	−1.03603	+	0.313150i
$501$	1.33848e51			0.675608
$502$	3.69281e50	+	2.49806e51i	0.179468	+	1.21404i
$503$			2.63005e50i			0.123076i	0.998105	+	0.0615378i	$0.0196005\pi$
$503$			2.63005e50i			0.123076i	−0.998105	+	0.0615378i	$0.980400\pi$
$504$	2.11145e51	+	4.48160e51i	0.951484	+	2.01954i
$505$	1.84192e51			0.799345
$506$	−5.59699e50	+	8.27388e49i	−0.233935	+	0.0345819i
$507$		−	3.15908e51i		−	1.27177i
$508$	−9.45759e50	−	3.12896e51i	−0.366750	−	1.21336i
$509$	1.66263e51			0.621096			0.310548	−	0.950558i	$-0.399488\pi$
$509$	1.66263e51			0.621096			0.310548	+	0.950558i	$0.399488\pi$
$510$	−1.11655e50	−	7.55308e50i	−0.0401833	−	0.271826i
$511$		−	2.93392e51i		−	1.01730i
$512$	7.40278e50	−	2.90017e51i	0.247324	−	0.968933i
$513$	−1.21376e52			−3.90753
$514$	−2.35058e51	+	3.47479e50i	−0.729248	+	0.107803i
$515$		−	4.59420e51i		−	1.37364i
$516$	6.83210e51	−	2.06507e51i	1.96884	−	0.595100i
$517$	1.57982e51			0.438821
$518$	2.14851e50	+	1.45339e51i	0.0575270	+	0.389150i
$519$			1.06002e52i			2.73612i
$520$	3.56993e51	−	1.68193e51i	0.888375	−	0.418548i
$521$	−7.40204e51			−1.77597			−0.887983	−	0.459876i	$-0.847894\pi$
$521$	−7.40204e51			−1.77597			−0.887983	+	0.459876i	$0.847894\pi$
$522$	−7.43726e51	+	1.09943e51i	−1.72057	+	0.254348i
$523$			8.88656e50i			0.198245i	0.995075	+	0.0991223i	$0.0316035\pi$
$523$			8.88656e50i			0.198245i	−0.995075	+	0.0991223i	$0.968396\pi$
$524$	−1.70424e51	−	5.63833e51i	−0.366637	−	1.21299i
$525$	3.06715e51			0.636367
$526$	5.80975e50	+	3.93009e51i	0.116259	+	0.786454i
$527$			6.40900e50i			0.123705i
$528$	−6.29311e51	+	4.18682e51i	−1.17171	+	0.779542i
$529$	4.96119e51			0.891104
$530$	7.66442e50	−	1.13301e50i	0.132812	−	0.0196333i
$531$			5.15301e51i			0.861520i
$532$	4.96878e51	−	1.50186e51i	0.801547	−	0.242276i
$533$	−2.98639e51			−0.464868
$534$	−1.24404e51	−	8.41550e51i	−0.186875	−	1.26414i
$535$		−	4.21503e51i		−	0.611053i
$536$	−2.12577e51	−	4.51199e51i	−0.297431	−	0.631302i
$537$	8.45224e51			1.14146
$538$	5.05824e51	−	7.47746e50i	0.659381	−	0.0974745i
$539$		−	2.21718e51i		−	0.279007i
$540$	6.64461e51	+	2.19831e52i	0.807213	+	2.67059i
$541$	−3.73036e51			−0.437524			−0.218762	−	0.975778i	$-0.570202\pi$
$541$	−3.73036e51			−0.437524			−0.218762	+	0.975778i	$0.570202\pi$
$542$	−2.58629e50	−	1.74953e51i	−0.0292881	−	0.198124i
$543$		−	2.19523e52i		−	2.40039i
$544$	1.28621e51	−	1.15994e51i	0.135810	−	0.122477i
$545$	5.25040e51			0.535376
$546$	−1.97881e52	+	2.92522e51i	−1.94869	+	0.288070i
$547$			5.24333e51i			0.498710i	0.968412	+	0.249355i	$0.0802187\pi$
$547$			5.24333e51i			0.498710i	−0.968412	+	0.249355i	$0.919781\pi$
$548$	−8.38480e49	+	2.53439e49i	−0.00770304	+	0.00232832i
$549$	2.83894e52			2.51931
$550$	5.06906e50	+	3.42904e51i	0.0434547	+	0.293956i
$551$			7.87731e51i			0.652375i
$552$	−7.32713e51	+	3.45210e51i	−0.586262	+	0.276211i
$553$	8.71533e51			0.673762
$554$	−9.80791e51	+	1.44988e51i	−0.732641	+	0.108304i
$555$			1.04785e52i			0.756365i
$556$	1.97767e51	+	6.54294e51i	0.137953	+	0.456407i
$557$	−1.57359e52			−1.06082			−0.530411	−	0.847741i	$-0.677962\pi$
$557$	−1.57359e52			−1.06082			−0.530411	+	0.847741i	$0.677962\pi$
$558$	−4.33728e51	−	2.93402e52i	−0.282597	−	1.91167i
$559$			2.13465e52i			1.34432i
$560$	−5.44022e51	−	8.17707e51i	−0.331165	−	0.497766i
$561$	−4.37379e51			−0.257374
$562$	1.27950e52	−	1.89145e51i	0.727865	−	0.107598i
$563$			2.51773e52i			1.38468i	0.721571	+	0.692340i	$0.243420\pi$
$563$			2.51773e52i			1.38468i	−0.721571	+	0.692340i	$0.756580\pi$
$564$	2.16491e52	−	6.54364e51i	1.15116	−	0.347950i
$565$	−2.02666e51			−0.104198
$566$	3.23745e51	+	2.19002e52i	0.160950	+	1.08877i
$567$		−	6.99706e52i		−	3.36386i
$568$	−1.59280e52	−	3.38075e52i	−0.740531	−	1.57179i
$569$	−8.21227e51			−0.369258			−0.184629	−	0.982808i	$-0.559108\pi$
$569$	−8.21227e51			−0.369258			−0.184629	+	0.982808i	$0.559108\pi$
$570$	3.66237e52	−	5.41398e51i	1.59272	−	0.235447i
$571$			2.98136e52i			1.25409i	0.778983	+	0.627045i	$0.215736\pi$
$571$			2.98136e52i			1.25409i	−0.778983	+	0.627045i	$0.784264\pi$
$572$	−6.54073e51	−	2.16394e52i	−0.266135	−	0.880484i
$573$	−1.22191e52			−0.480951
$574$	1.08690e51	+	7.35252e51i	0.0413871	+	0.279969i
$575$			3.71441e51i			0.136836i
$576$	−5.10324e52	+	6.18058e52i	−1.81894	+	2.20294i
$577$	−3.08063e52			−1.06243			−0.531213	−	0.847238i	$-0.678264\pi$
$577$	−3.08063e52			−1.06243			−0.531213	+	0.847238i	$0.678264\pi$
$578$	−2.86524e52	+	4.23561e51i	−0.956164	+	0.141347i
$579$		−	2.79667e52i		−	0.903125i
$580$	1.42670e52	−	4.31236e51i	0.445864	−	0.134767i
$581$	3.53310e52			1.06858
$582$	1.06926e52	+	7.23317e52i	0.313002	+	2.11735i
$583$		−	4.43826e51i		−	0.125751i
$584$	4.29403e52	−	2.02309e52i	1.17766	−	0.554843i
$585$	−1.05675e53			−2.80551
$586$	2.53682e52	−	3.75012e51i	0.651982	−	0.0963807i
$587$		−	4.00798e52i		−	0.997244i	−0.866819	−	0.498622i	$-0.833840\pi$
$587$		−	4.00798e52i		−	0.997244i	0.866819	−	0.498622i	$-0.166160\pi$
$588$	−9.18360e51	−	3.03831e52i	−0.221230	−	0.731920i
$589$	−3.10762e52			−0.724831
$590$	−1.49394e51	−	1.01060e52i	−0.0337400	−	0.228239i
$591$		−	4.71135e51i		−	0.103035i
$592$	−1.97901e52	+	1.31664e52i	−0.419117	+	0.278840i
$593$	6.24440e52			1.28071			0.640356	−	0.768078i	$-0.278787\pi$
$593$	6.24440e52			1.28071			0.640356	+	0.768078i	$0.278787\pi$
$594$	1.30142e53	−	1.92386e52i	2.58509	−	0.382147i
$595$		−	5.68317e51i		−	0.109337i
$596$	−3.79905e52	+	1.14830e52i	−0.707939	+	0.213982i
$597$	1.66607e53			3.00733
$598$	−3.54253e51	−	2.39640e52i	−0.0619428	−	0.419021i
$599$			7.16880e52i			1.21433i	0.794576	+	0.607165i	$0.207693\pi$
$599$			7.16880e52i			1.21433i	−0.794576	+	0.607165i	$0.792307\pi$
$600$	2.11495e52	+	4.48903e52i	0.347078	+	0.736679i
$601$	−9.82291e52			−1.56180			−0.780900	−	0.624656i	$-0.785239\pi$
$601$	−9.82291e52			−1.56180			−0.780900	+	0.624656i	$0.785239\pi$
$602$	5.25553e52	−	7.76910e51i	0.809623	−	0.119684i
$603$			1.33561e53i			1.99367i
$604$	−3.28770e51	−	1.08771e52i	−0.0475544	−	0.157329i
$605$	2.65530e52			0.372187
$606$	−2.20895e52	−	1.49428e53i	−0.300059	−	2.02979i
$607$		−	8.84512e52i		−	1.16444i	−0.813030	−	0.582222i	$-0.802183\pi$
$607$		−	8.84512e52i		−	1.16444i	0.813030	−	0.582222i	$-0.197817\pi$
$608$	5.62433e52	+	6.23662e52i	0.717634	+	0.795759i
$609$	−7.55484e52			−0.934323
$610$	−5.56766e52	+	8.23052e51i	−0.667430	+	0.0986644i
$611$			6.76412e52i			0.786011i
$612$	−4.43960e52	+	1.34191e52i	−0.500111	+	0.151164i
$613$	−4.73801e52			−0.517424			−0.258712	−	0.965954i	$-0.583298\pi$
$613$	−4.73801e52			−0.517424			−0.258712	+	0.965954i	$0.583298\pi$
$614$	−2.38596e51	−	1.61402e52i	−0.0252618	−	0.170887i
$615$			5.30093e52i			0.544158i
$616$	−5.08960e52	+	2.39791e52i	−0.506583	+	0.238671i
$617$	1.61910e53			1.56263			0.781313	−	0.624139i	$-0.214550\pi$
$617$	1.61910e53			1.56263			0.781313	+	0.624139i	$0.214550\pi$
$618$	−3.72710e53	+	5.50967e52i	−3.48811	+	0.515638i
$619$		−	1.92411e53i		−	1.74625i	−0.487494	−	0.873126i	$-0.662089\pi$
$619$		−	1.92411e53i		−	1.74625i	0.487494	−	0.873126i	$-0.337911\pi$
$620$	1.70123e52	+	5.62838e52i	0.149735	+	0.495383i
$621$	1.40973e53			1.20336
$622$	8.45354e51	+	5.71852e52i	0.0699876	+	0.473442i
$623$		−	6.33208e52i		−	0.508480i
$624$	−1.79262e53	−	2.69444e53i	−1.39631	−	2.09876i
$625$	−5.47123e52			−0.413395
$626$	1.54110e53	−	2.27817e52i	1.12959	−	0.166984i
$627$		−	2.12078e53i		−	1.50804i
$628$	1.76493e52	−	5.33469e51i	0.121757	−	0.0368024i
$629$	−1.37544e52			−0.0920617
$630$	3.84608e52	+	2.60174e53i	0.249774	+	1.68963i
$631$		−	1.89132e52i		−	0.119181i	−0.998223	−	0.0595905i	$-0.981021\pi$
$631$		−	1.89132e52i		−	0.119181i	0.998223	−	0.0595905i	$-0.0189795\pi$
$632$	6.00967e52	+	1.27556e53i	0.367473	+	0.779969i
$633$	−1.70490e53			−1.01165
$634$	7.77728e52	−	1.14969e52i	0.447849	−	0.0662043i
$635$		−	1.73531e53i		−	0.969789i
$636$	−1.83834e52	−	6.08198e52i	−0.0997103	−	0.329883i
$637$	9.49303e52			0.499753
$638$	−1.24859e52	−	8.44625e52i	−0.0638007	−	0.431590i
$639$			1.00075e54i			4.96375i
$640$	8.21652e52	−	1.36007e53i	0.395611	−	0.654852i
$641$	2.93730e52			0.137292			0.0686461	−	0.997641i	$-0.478132\pi$
$641$	2.93730e52			0.137292			0.0686461	+	0.997641i	$0.478132\pi$
$642$	−3.41950e53	+	5.05495e52i	−1.55166	+	0.229378i
$643$			2.14021e53i			0.942861i	0.881903	+	0.471430i	$0.156262\pi$
$643$			2.14021e53i			0.942861i	−0.881903	+	0.471430i	$0.843738\pi$
$644$	−5.77102e52	+	1.74435e52i	−0.246843	+	0.0746108i
$645$	3.78906e53			1.57361
$646$	7.10655e51	+	4.80734e52i	0.0286577	+	0.193859i
$647$		−	3.12905e53i		−	1.22527i	−0.790366	−	0.612635i	$-0.790110\pi$
$647$		−	3.12905e53i		−	1.22527i	0.790366	−	0.612635i	$-0.209890\pi$
$648$	1.02408e54	−	4.82483e53i	3.89411	−	1.83467i
$649$	−5.85210e52			−0.216104
$650$	−1.46817e53	+	2.17036e52i	−0.526530	+	0.0778354i
$651$		−	2.98040e53i		−	1.03809i
$652$	1.25022e53	+	4.13623e53i	0.422942	+	1.39927i
$653$	2.09397e53			0.688051			0.344025	−	0.938960i	$-0.388209\pi$
$653$	2.09397e53			0.688051			0.344025	+	0.938960i	$0.388209\pi$
$654$	−6.29663e52	−	4.25945e53i	−0.200970	−	1.35949i
$655$		−	3.12701e53i		−	0.969492i
$656$	−1.00116e53	+	6.66071e52i	−0.301529	+	0.200608i
$657$	−1.27110e54			−3.71909
$658$	1.66533e53	−	2.46182e52i	0.473380	−	0.0699784i
$659$			1.07866e53i			0.297895i	0.988845	+	0.148947i	$0.0475885\pi$
$659$			1.07866e53i			0.297895i	−0.988845	+	0.148947i	$0.952411\pi$
$660$	−3.84107e53	+	1.16100e53i	−1.03066	+	0.311528i
$661$	−3.83365e53			−0.999505			−0.499752	−	0.866168i	$-0.666576\pi$
$661$	−3.83365e53			−0.999505			−0.499752	+	0.866168i	$0.666576\pi$
$662$	4.78007e52	+	3.23355e53i	0.121097	+	0.819178i
$663$		−	1.87267e53i		−	0.461004i
$664$	2.43625e53	+	5.17099e53i	0.582812	+	1.23703i
$665$	2.75568e53			0.640644
$666$	6.29671e53	−	9.30825e52i	1.42267	−	0.210309i
$667$		−	9.14914e52i		−	0.200904i
$668$	4.66368e52	+	1.54294e53i	0.0995350	+	0.329303i
$669$	8.61419e53			1.78697
$670$	−3.87215e52	−	2.61938e53i	−0.0780785	−	0.528174i
$671$			3.22409e53i			0.631944i
$672$	−5.98132e53	+	5.39410e53i	−1.13967	+	1.02779i
$673$	−7.68413e53			−1.42334			−0.711669	−	0.702514i	$-0.752061\pi$
$673$	−7.68413e53			−1.42334			−0.711669	+	0.702514i	$0.752061\pi$
$674$	−6.29033e53	+	9.29883e52i	−1.13275	+	0.167452i
$675$		−	8.63681e53i		−	1.51210i
$676$	3.64164e53	−	1.10072e53i	0.619883	−	0.187366i
$677$	−1.93220e53			−0.319792			−0.159896	−	0.987134i	$-0.551116\pi$
$677$	−1.93220e53			−0.319792			−0.159896	+	0.987134i	$0.551116\pi$
$678$	2.43050e52	+	1.64415e53i	0.0391140	+	0.264593i
$679$			5.44246e53i			0.851667i
$680$	8.31780e52	−	3.91884e52i	0.126572	−	0.0596332i
$681$	−1.55990e53			−0.230834
$682$	3.33206e53	−	4.92570e52i	0.479524	−	0.0708867i
$683$			6.78686e53i			0.949895i	0.880014	+	0.474947i	$0.157533\pi$
$683$			6.78686e53i			0.949895i	−0.880014	+	0.474947i	$0.842467\pi$
$684$	−6.50671e53	−	2.15269e54i	−0.885718	−	2.93032i
$685$	−4.65019e51			−0.00615673
$686$	−1.23290e53	−	8.34012e53i	−0.158770	−	1.07402i
$687$		−	8.37200e53i		−	1.04870i
$688$	4.76103e53	+	7.15619e53i	0.580123	+	0.871970i
$689$	1.90028e53			0.225243
$690$	−4.25367e53	+	6.28809e52i	−0.490492	+	0.0725080i
$691$			6.69604e53i			0.751165i	0.926789	+	0.375583i	$0.122557\pi$
$691$			6.69604e53i			0.751165i	−0.926789	+	0.375583i	$0.877443\pi$
$692$	−1.22194e54	+	3.69344e53i	−1.33363	+	0.403102i
$693$	1.50660e54			1.59980
$694$	−1.12038e53	−	7.57900e53i	−0.115754	−	0.783037i
$695$			3.62870e53i			0.364787i
$696$	−5.20945e53	−	1.10572e54i	−0.509585	−	1.08160i
$697$	−6.95817e52			−0.0662326
$698$	7.26753e53	−	1.07434e53i	0.673184	−	0.0995150i
$699$			2.31293e54i			2.08495i
$700$	1.06869e53	+	3.53566e53i	0.0937537	+	0.310176i
$701$	1.25735e54			1.07353			0.536763	−	0.843733i	$-0.319647\pi$
$701$	1.25735e54			1.07353			0.536763	+	0.843733i	$0.319647\pi$
$702$	8.23715e53	+	5.57215e54i	0.684498	+	4.63039i
$703$		−	6.66927e53i		−	0.539420i
$704$	−7.01908e53	−	5.79558e53i	−0.552586	−	0.456264i
$705$	1.20065e54			0.920077
$706$	1.17944e54	−	1.74353e53i	0.879804	−	0.130059i
$707$		−	1.12434e54i		−	0.816450i
$708$	−8.01943e53	+	2.42395e53i	−0.566907	+	0.171353i
$709$	−1.55166e54			−1.06787			−0.533935	−	0.845525i	$-0.679287\pi$
$709$	−1.55166e54			−1.06787			−0.533935	+	0.845525i	$0.679287\pi$
$710$	−2.90133e53	−	1.96265e54i	−0.194397	−	1.31503i
$711$		−	3.77585e54i		−	2.46316i
$712$	9.26753e53	−	4.36629e53i	0.588633	−	0.277328i
$713$	3.60936e53			0.223218
$714$	−4.61054e53	+	6.81564e52i	−0.277643	+	0.0410431i
$715$		−	1.20012e54i		−	0.703735i
$716$	2.94502e53	+	9.74335e53i	0.168167	+	0.556366i
$717$	6.09280e54			3.38808
$718$	−1.92937e53	−	1.30515e54i	−0.104484	−	0.706801i
$719$			5.03007e53i			0.265293i	0.991163	+	0.132646i	$0.0423475\pi$
$719$			5.03007e53i			0.265293i	−0.991163	+	0.132646i	$0.957653\pi$
$720$	−3.54265e54	+	2.35694e54i	−1.81975	+	1.21068i
$721$	−2.80439e54			−1.40303
$722$	−3.00921e53	+	4.44843e52i	−0.146637	+	0.0216770i
$723$			6.81897e54i			3.23662i
$724$	2.53055e54	−	7.64885e53i	1.16999	−	0.353642i
$725$	−5.60530e53			−0.252451
$726$	−3.18441e53	−	2.15414e54i	−0.139712	−	0.945102i
$727$		−	2.18479e54i		−	0.933805i	−0.884309	−	0.466903i	$-0.845370\pi$
$727$		−	2.18479e54i		−	0.933805i	0.884309	−	0.466903i	$-0.154630\pi$
$728$	−1.02668e54	−	2.17915e54i	−0.427504	−	0.907385i
$729$	−1.26609e55			−5.13620
$730$	2.49285e54	−	3.68511e53i	0.985284	−	0.145652i
$731$			4.97365e53i			0.191533i
$732$	1.33542e54	+	4.41813e54i	0.501081	+	1.65778i
$733$	−1.79061e54			−0.654675			−0.327338	−	0.944907i	$-0.606151\pi$
$733$	−1.79061e54			−0.654675			−0.327338	+	0.944907i	$0.606151\pi$
$734$	−4.91904e53	−	3.32756e54i	−0.175249	−	1.18550i
$735$		−	1.68504e54i		−	0.584994i
$736$	−6.53242e53	−	7.24356e53i	−0.221002	−	0.245061i
$737$	−1.51681e54			−0.500092
$738$	3.18542e54	−	4.70893e53i	1.02352	−	0.151304i
$739$			3.36658e54i			1.05425i	0.849787	+	0.527125i	$0.176730\pi$
$739$			3.36658e54i			1.05425i	−0.849787	+	0.527125i	$0.823270\pi$
$740$	−1.20791e54	+	3.65103e53i	−0.368665	+	0.111433i
$741$	9.08028e54			2.70118
$742$	−6.91611e52	−	4.67851e53i	−0.0200534	−	0.135654i
$743$			2.39939e54i			0.678131i	0.940763	+	0.339065i	$0.110111\pi$
$743$			2.39939e54i			0.678131i	−0.940763	+	0.339065i	$0.889889\pi$
$744$	4.36207e54	−	2.05514e54i	1.20173	−	0.566181i
$745$	−2.10694e54			−0.565827
$746$	−6.27034e54	+	9.26927e53i	−1.64155	+	0.242665i
$747$		−	1.53069e55i		−	3.90657i
$748$	−1.52397e53	−	5.04190e53i	−0.0379179	−	0.125448i
$749$	−2.57293e54			−0.624129
$750$	1.31430e54	+	8.89081e54i	0.310836	+	2.10270i
$751$			7.21481e54i			1.66367i	0.555026	+	0.831833i	$0.312708\pi$
$751$			7.21481e54i			1.66367i	−0.555026	+	0.831833i	$0.687292\pi$
$752$	1.50864e54	+	2.26760e54i	0.339193	+	0.509833i
$753$	1.09938e55			2.41014
$754$	3.61633e54	−	5.34592e53i	0.773058	−	0.114279i
$755$		−	6.03239e53i		−	0.125747i
$756$	1.34189e55	−	4.05599e54i	2.72774	−	0.824485i
$757$	−4.59282e54			−0.910454			−0.455227	−	0.890375i	$-0.650442\pi$
$757$	−4.59282e54			−0.910454			−0.455227	+	0.890375i	$0.650442\pi$
$758$	2.47932e53	+	1.67717e54i	0.0479312	+	0.324238i
$759$			2.46319e54i			0.464413i
$760$	1.90018e54	+	4.03316e54i	0.349411	+	0.741631i
$761$	−1.06143e54			−0.190363			−0.0951816	−	0.995460i	$-0.530343\pi$
$761$	−1.06143e54			−0.190363			−0.0951816	+	0.995460i	$0.530343\pi$
$762$	−1.40780e55	+	2.08111e54i	−2.46261	+	0.364040i
$763$		−	3.20494e54i		−	0.546832i
$764$	−4.25751e53	−	1.40856e54i	−0.0708569	−	0.234424i
$765$	−2.46219e54			−0.399719
$766$	1.48842e54	+	1.00686e55i	0.235710	+	1.59450i
$767$		−	2.50562e54i		−	0.387083i
$768$	−1.20191e55	−	5.03466e54i	−1.81138	−	0.758765i
$769$	5.30962e54			0.780662			0.390331	−	0.920675i	$-0.372361\pi$
$769$	5.30962e54			0.780662			0.390331	+	0.920675i	$0.372361\pi$
$770$	−2.95470e54	+	4.36786e53i	−0.423829	+	0.0626534i
$771$			1.03447e55i			1.44772i
$772$	3.22387e54	−	9.74445e53i	0.440198	−	0.133054i
$773$	4.72332e54			0.629270			0.314635	−	0.949213i	$-0.398118\pi$
$773$	4.72332e54			0.629270			0.314635	+	0.949213i	$0.398118\pi$
$774$	−3.36591e54	−	2.27692e55i	−0.437546	−	2.95985i
$775$		−	2.21130e54i		−	0.280489i
$776$	−7.96550e54	+	3.75286e54i	−0.985917	+	0.464504i
$777$	6.39626e54			0.772550
$778$	1.63715e55	−	2.42015e54i	1.92964	−	0.285253i
$779$		−	3.37390e54i		−	0.388079i
$780$	−4.97091e54	−	1.64458e55i	−0.558006	−	1.84611i
$781$	−1.13652e55			−1.24511
$782$	−8.25395e52	−	5.58351e53i	−0.00882538	−	0.0597006i
$783$			2.12738e55i			2.22009i
$784$	3.18244e54	−	2.11729e54i	0.324157	−	0.215662i
$785$	9.78829e53			0.0973158
$786$	−2.53682e55	+	3.75012e54i	−2.46185	+	0.363929i
$787$		−	1.27863e55i		−	1.21123i	−0.795758	−	0.605615i	$-0.792927\pi$
$787$		−	1.27863e55i		−	1.21123i	0.795758	−	0.605615i	$-0.207073\pi$
$788$	5.43102e53	−	1.64158e53i	0.0502208	−	0.0151797i
$789$	1.72960e55			1.56129
$790$	1.09468e54	+	7.40512e54i	0.0964654	+	0.652555i
$791$			1.23711e54i			0.106428i
$792$	1.03888e55	+	2.20503e55i	0.872540	+	1.85198i
$793$	−1.38042e55			−1.13193
$794$	−1.60178e55	+	2.36786e54i	−1.28237	+	0.189569i
$795$		−	3.37305e54i		−	0.263662i
$796$	5.80511e54	+	1.92057e55i	0.443060	+	1.46582i
$797$	2.39742e55			1.78663			0.893317	−	0.449428i	$-0.148372\pi$
$797$	2.39742e55			1.78663			0.893317	+	0.449428i	$0.148372\pi$
$798$	−3.30479e54	−	2.23558e55i	−0.240486	−	1.62680i
$799$			1.57601e54i			0.111988i
$800$	−4.43783e54	+	4.00214e54i	−0.307936	+	0.277704i
$801$	−2.74333e55			−1.85892
$802$	7.38950e54	−	1.09237e54i	0.488993	−	0.0722864i
$803$		−	1.44354e55i		−	0.932898i
$804$	−2.07856e55	+	6.28267e54i	−1.31189	+	0.396533i
$805$	−3.20060e54			−0.197292
$806$	2.10898e54	+	1.42665e55i	0.126971	+	0.858917i
$807$		−	2.22609e55i		−	1.30902i
$808$	1.64557e55	−	7.75291e54i	0.945149	−	0.445296i
$809$	1.05520e55			0.591990			0.295995	−	0.955190i	$-0.404349\pi$
$809$	1.05520e55			0.591990			0.295995	+	0.955190i	$0.404349\pi$
$810$	5.94516e55	−	8.78857e54i	3.25798	−	0.481618i
$811$		−	2.04697e55i		−	1.09576i	−0.836557	−	0.547879i	$-0.815435\pi$
$811$		−	2.04697e55i		−	1.09576i	0.836557	−	0.547879i	$-0.184565\pi$
$812$	−2.63234e54	−	8.70887e54i	−0.137650	−	0.455405i
$813$	−7.69956e54			−0.393320
$814$	1.05711e54	+	7.15096e54i	0.0527540	+	0.356862i
$815$			2.29395e55i			1.11838i
$816$	−4.17673e54	−	6.27795e54i	−0.198941	−	0.299023i
$817$	−2.41164e55			−1.12226
$818$	1.66652e55	−	2.46357e54i	0.757701	−	0.112009i
$819$			6.45061e55i			2.86554i
$820$	−6.11066e54	+	1.84701e54i	−0.265232	+	0.0801688i
$821$	1.31108e55			0.556045			0.278023	−	0.960575i	$-0.410321\pi$
$821$	1.31108e55			0.556045			0.278023	+	0.960575i	$0.410321\pi$
$822$	5.57682e52	+	3.77253e53i	0.00231112	+	0.0156339i
$823$		−	1.52379e55i		−	0.617061i	−0.951214	−	0.308531i	$-0.900163\pi$
$823$		−	1.52379e55i		−	0.617061i	0.951214	−	0.308531i	$-0.0998372\pi$
$824$	−1.93377e55	−	4.10446e55i	−0.765222	−	1.62420i
$825$	1.50909e55			0.583568
$826$	−6.16887e54	+	9.11928e53i	−0.233123	+	0.0344619i
$827$		−	7.79385e54i		−	0.287837i	−0.989590	−	0.143919i	$-0.954030\pi$
$827$		−	7.79385e54i		−	0.287837i	0.989590	−	0.143919i	$-0.0459704\pi$
$828$	7.55726e54	+	2.50025e55i	0.272764	+	0.902417i
$829$	−7.84920e54			−0.276879			−0.138439	−	0.990371i	$-0.544209\pi$
$829$	−7.84920e54			−0.276879			−0.138439	+	0.990371i	$0.544209\pi$
$830$	4.43770e54	+	3.00195e55i	0.152994	+	1.03495i
$831$			4.31638e55i			1.45446i
$832$	2.48142e55	−	3.00527e55i	0.817255	−	0.989785i
$833$	2.21184e54			0.0712030
$834$	2.94383e55	−	4.35178e54i	0.926312	−	0.136934i
$835$			8.55709e54i			0.263198i
$836$	2.44474e55	−	7.38945e54i	0.735043	−	0.222174i
$837$	−8.39255e55			−2.46667
$838$	7.83002e54	+	5.29674e55i	0.224971	+	1.52185i
$839$		−	5.17960e55i		−	1.45485i	−0.686186	−	0.727426i	$-0.740716\pi$
$839$		−	5.17960e55i		−	1.45485i	0.686186	−	0.727426i	$-0.259284\pi$
$840$	−3.86806e55	+	1.82239e55i	−1.06215	+	0.500421i
$841$	−2.34431e55			−0.629349
$842$	−8.77651e54	+	1.29741e54i	−0.230352	+	0.0340523i
$843$		−	5.63099e55i		−	1.44498i
$844$	−5.94040e54	−	1.96533e55i	−0.149042	−	0.493093i
$845$	2.01965e55			0.495448
$846$	−1.06656e55	−	7.21494e55i	−0.255829	−	1.73060i
$847$		−	1.62084e55i		−	0.380151i
$848$	6.37049e54	−	4.23830e54i	0.146100	−	0.0972009i
$849$	9.63812e55			2.16146
$850$	−3.42078e54	+	5.05685e53i	−0.0750180	+	0.0110897i
$851$			7.74607e54i			0.166119i
$852$	−1.55743e56	+	4.70749e55i	−3.26630	+	0.987272i
$853$	−7.94807e55			−1.63016			−0.815080	−	0.579349i	$-0.803307\pi$
$853$	−7.94807e55			−1.63016			−0.815080	+	0.579349i	$0.803307\pi$
$854$	5.02406e54	+	3.39860e55i	0.100776	+	0.681712i
$855$		−	1.19388e56i		−	2.34209i
$856$	−1.77417e55	−	3.76571e55i	−0.340403	−	0.722512i
$857$	8.22446e55			1.54338			0.771688	−	0.636002i	$-0.219413\pi$
$857$	8.22446e55			1.54338			0.771688	+	0.636002i	$0.219413\pi$
$858$	−9.73611e55	+	1.43926e55i	−1.78701	+	0.264169i
$859$			7.27918e55i			1.30681i	0.757008	+	0.653405i	$0.226660\pi$
$859$			7.27918e55i			1.30681i	−0.757008	+	0.653405i	$0.773340\pi$
$860$	1.32023e55	+	4.36786e55i	0.231835	+	0.767004i
$861$	3.23579e55			0.555802
$862$	−1.41165e55	−	9.54931e55i	−0.237186	−	1.60448i
$863$			1.16155e56i			1.90911i	0.298032	+	0.954556i	$0.403670\pi$
$863$			1.16155e56i			1.90911i	−0.298032	+	0.954556i	$0.596330\pi$
$864$	1.51893e56	+	1.68429e56i	2.44217	+	2.70804i
$865$	−6.77686e55			−1.06592
$866$	3.52732e55	−	5.21434e54i	0.542757	−	0.0802342i
$867$			1.26097e56i			1.89820i
$868$	3.43567e55	−	1.03846e55i	0.505984	−	0.152939i
$869$	4.28811e55			0.617860
$870$	−9.48917e54	−	6.41909e55i	−0.133771	−	0.904915i
$871$		−	6.49435e55i		−	0.895758i
$872$	4.69070e55	−	2.20997e55i	0.633031	−	0.298245i
$873$	2.35791e56			3.11355
$874$	2.70735e55	−	4.00220e54i	0.349806	−	0.0517109i
$875$			6.68972e55i			0.845775i
$876$	−5.97918e55	−	1.97816e56i	−0.739714	−	2.44728i
$877$	1.78105e55			0.215618			0.107809	−	0.994172i	$-0.465617\pi$
$877$	1.78105e55			0.215618			0.107809	+	0.994172i	$0.465617\pi$
$878$	−5.89698e54	−	3.98910e55i	−0.0698609	−	0.472585i
$879$		−	1.11644e56i		−	1.29433i
$880$	−2.67669e55	−	4.02327e55i	−0.303688	−	0.456466i
$881$	−3.22754e55			−0.358368			−0.179184	−	0.983816i	$-0.557346\pi$
$881$	−3.22754e55			−0.358368			−0.179184	+	0.983816i	$0.557346\pi$
$882$	−1.01257e56	+	1.49686e55i	−1.10033	+	0.162659i
$883$			9.47388e55i			1.00757i	0.863830	+	0.503784i	$0.168059\pi$
$883$			9.47388e55i			1.00757i	−0.863830	+	0.503784i	$0.831941\pi$
$884$	2.15873e55	−	6.52498e54i	0.224701	−	0.0679181i
$885$	−4.44756e55			−0.453106
$886$	1.78374e55	+	1.20664e56i	0.177865	+	1.20320i
$887$			8.28656e55i			0.808771i	0.914589	+	0.404386i	$0.132515\pi$
$887$			8.28656e55i			0.808771i	−0.914589	+	0.404386i	$0.867485\pi$
$888$	4.41055e55	+	9.36147e55i	0.421353	+	0.894330i
$889$	−1.05927e56			−0.990541
$890$	5.38015e55	−	7.95333e54i	0.492475	−	0.0728013i
$891$		−	3.44269e56i		−	3.08476i
$892$	3.00145e55	+	9.93003e55i	0.263268	+	0.871001i
$893$	−7.64183e55			−0.656175
$894$	2.52679e55	+	1.70928e56i	0.212401	+	1.43682i
$895$			5.40364e55i			0.444681i
$896$	−8.30214e55	−	5.01552e55i	−0.668864	−	0.404076i
$897$	−1.05463e56			−0.831851
$898$	−2.03934e56	+	3.01469e55i	−1.57485	+	0.232805i
$899$			5.44677e55i			0.411818i
$900$	1.53180e56	−	4.63001e55i	1.13395	−	0.342748i
$901$	4.42757e54			0.0320918
$902$	5.34777e54	+	3.61758e55i	0.0379532	+	0.256740i
$903$		−	2.31292e56i		−	1.60728i
$904$	−1.81061e55	+	8.53050e54i	−0.123204	+	0.0580463i
$905$	1.40344e56			0.935127
$906$	−4.89385e55	+	7.23445e54i	−0.319312	+	0.0472030i
$907$			3.74844e55i			0.239504i	0.992804	+	0.119752i	$0.0382099\pi$
$907$			3.74844e55i			0.239504i	−0.992804	+	0.119752i	$0.961790\pi$
$908$	−5.43516e54	−	1.79818e55i	−0.0340080	−	0.112513i
$909$	−4.87113e56			−2.98480
$910$	−1.87013e55	−	1.26508e56i	−0.112224	−	0.759157i
$911$			6.42369e55i			0.377516i	0.982024	+	0.188758i	$0.0604462\pi$
$911$			6.42369e55i			0.377516i	−0.982024	+	0.188758i	$0.939554\pi$
$912$	3.04407e56	−	2.02523e56i	1.75208	−	1.16566i
$913$	1.73835e56			0.979925
$914$	−9.43324e55	+	1.39449e55i	−0.520815	+	0.0769906i
$915$			2.45028e56i			1.32500i
$916$	9.65086e55	−	2.91707e55i	0.511154	−	0.154501i
$917$	−1.90878e56			−0.990237
$918$	1.91922e55	+	1.29829e56i	0.0975247	+	0.659721i
$919$		−	2.37138e56i		−	1.18034i	−0.807280	−	0.590169i	$-0.799061\pi$
$919$		−	2.37138e56i		−	1.18034i	0.807280	−	0.590169i	$-0.200939\pi$
$920$	−2.20697e55	−	4.68434e55i	−0.107604	−	0.228391i
$921$	−7.10317e55			−0.339250
$922$	3.91053e56	−	5.78083e55i	1.82957	−	0.270460i
$923$		−	4.86610e56i		−	2.23022i
$924$	7.08696e55	+	2.34466e56i	0.318194	+	1.05272i
$925$	4.74569e55			0.208740
$926$	−4.82744e55	−	3.26560e56i	−0.208022	−	1.40719i
$927$			1.21498e57i			5.12925i
$928$	1.09310e56	−	9.85787e55i	0.452116	−	0.407729i
$929$	2.13714e56			0.866032			0.433016	−	0.901386i	$-0.357449\pi$
$929$	2.13714e56			0.866032			0.433016	+	0.901386i	$0.357449\pi$
$930$	2.53235e56	−	3.74350e55i	1.00542	−	0.148628i
$931$			1.07248e56i			0.417203i
$932$	−2.66623e56	+	8.05895e55i	−1.01624	+	0.307168i
$933$	2.51668e56			0.939888
$934$	−1.39426e53	−	9.43166e53i	−0.000510214	−	0.00345142i
$935$		−	2.79623e55i		−	0.100266i
$936$	−9.44102e56	+	4.44803e56i	−3.31725	+	1.56288i
$937$	1.68115e56			0.578834			0.289417	−	0.957203i	$-0.406539\pi$
$937$	1.68115e56			0.578834			0.289417	+	0.957203i	$0.406539\pi$
$938$	−1.59892e56	+	2.36364e55i	−0.539476	+	0.0797492i
$939$		−	6.78227e56i		−	2.24248i
$940$	4.18344e55	+	1.38406e56i	0.135552	+	0.448461i
$941$	−5.50586e56			−1.74832			−0.874162	−	0.485634i	$-0.838589\pi$
$941$	−5.50586e56			−1.74832			−0.874162	+	0.485634i	$0.838589\pi$
$942$	−1.17388e55	−	7.94087e55i	−0.0365305	−	0.247116i
$943$			3.91863e55i			0.119512i
$944$	−5.58844e55	−	8.39985e55i	−0.167041	−	0.251075i
$945$	7.44209e56			2.18017
$946$	2.58582e56	−	3.82255e55i	0.742449	−	0.109754i
$947$		−	3.71320e56i		−	1.04496i	−0.852652	−	0.522480i	$-0.825007\pi$
$947$		−	3.71320e56i		−	1.04496i	0.852652	−	0.522480i	$-0.174993\pi$
$948$	5.87621e56	−	1.77614e56i	1.62084	−	0.489913i
$949$	6.18064e56			1.67100
$950$	−2.45198e55	−	1.65868e56i	−0.0649783	−	0.439556i
$951$		−	3.42272e56i		−	0.889081i
$952$	−2.39213e55	−	5.07734e55i	−0.0609092	−	0.129281i
$953$	−2.83958e56			−0.708743			−0.354371	−	0.935105i	$-0.615305\pi$
$953$	−2.83958e56			−0.708743			−0.354371	+	0.935105i	$0.615305\pi$
$954$	−2.02693e56	+	2.99635e55i	−0.495928	+	0.0733118i
$955$		−	7.81184e55i		−	0.187365i
$956$	2.12292e56	+	7.02350e56i	0.499153	+	1.65140i
$957$	−3.71713e56			−0.856802
$958$	5.82822e55	+	3.94259e56i	0.131702	+	0.890915i
$959$			2.83856e54i			0.00628847i
$960$	−5.33445e56	−	4.40460e56i	−1.15861	−	0.956650i
$961$	2.54741e56			0.542444
$962$	−3.06174e56	+	4.52609e55i	−0.639208	+	0.0944923i
$963$			1.11470e57i			2.28171i
$964$	−7.86059e56	+	2.37594e56i	−1.57758	+	0.476839i
$965$	1.78795e56			0.351833
$966$	3.83837e55	+	2.59652e56i	0.0740596	+	0.500987i
$967$			2.40616e56i			0.455221i	0.973752	+	0.227610i	$0.0730913\pi$
$967$			2.40616e56i			0.455221i	−0.973752	+	0.227610i	$0.926909\pi$
$968$	2.37224e56	−	1.11765e56i	0.440075	−	0.207336i
$969$	2.11567e56			0.384854
$970$	−4.62427e56	+	6.83594e55i	−0.824860	+	0.121937i
$971$		−	7.55418e55i		−	0.132136i	−0.997815	−	0.0660681i	$-0.978955\pi$
$971$		−	7.55418e55i		−	0.132136i	0.997815	−	0.0660681i	$-0.0210455\pi$
$972$	−8.10870e56	−	2.68269e57i	−1.39089	−	4.60163i
$973$	2.21503e56			0.372593
$974$	8.04810e55	+	5.44426e56i	0.132762	+	0.898088i
$975$			6.46130e56i			1.04528i
$976$	−4.62771e56	+	3.07883e56i	−0.734209	+	0.488471i
$977$	−1.07830e57			−1.67781			−0.838905	−	0.544278i	$-0.816804\pi$
$977$	−1.07830e57			−1.67781			−0.838905	+	0.544278i	$0.816804\pi$
$978$	1.86099e57	−	2.75105e56i	2.83992	−	0.419818i
$979$		−	3.11550e56i		−	0.466291i
$980$	1.94244e56	−	5.87121e55i	0.285136	−	0.0861851i
$981$	−1.38852e57			−1.99913
$982$	−1.81772e56	−	1.22962e57i	−0.256690	−	1.73642i
$983$		−	4.14254e56i		−	0.573786i	−0.957963	−	0.286893i	$-0.907378\pi$
$983$		−	4.14254e56i		−	0.573786i	0.957963	−	0.286893i	$-0.0926224\pi$
$984$	2.23124e56	+	4.73584e56i	0.303137	+	0.643414i
$985$	3.01203e55			0.0401394
$986$	8.42590e55	−	1.24558e55i	0.110142	−	0.0162821i
$987$		−	7.32901e56i		−	0.939765i
$988$	3.16385e56	+	1.04673e57i	0.397955	+	1.31660i
$989$	2.80101e56			0.345609
$990$	1.89234e56	+	1.28010e57i	0.229050	+	1.54945i
$991$		−	4.03281e56i		−	0.478860i	−0.970914	−	0.239430i	$-0.923039\pi$
$991$		−	4.03281e56i		−	0.478860i	0.970914	−	0.239430i	$-0.0769606\pi$
$992$	3.88895e56	+	4.31232e56i	0.453013	+	0.502330i
$993$	1.42306e57			1.62625
$994$	−1.19804e57	+	1.77103e56i	−1.34317	+	0.198557i
$995$			1.06514e57i			1.17157i
$996$	2.38215e57	−	7.20028e56i	2.57064	−	0.777002i
$997$	5.30858e56			0.562044			0.281022	−	0.959701i	$-0.409327\pi$
$997$	5.30858e56			0.562044			0.281022	+	0.959701i	$0.409327\pi$
$998$	−4.61896e54	−	3.12456e55i	−0.00479804	−	0.0324570i
$999$		−	1.80113e57i		−	1.83570i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.39.b.a.3.17	✓	18
4.3	odd	2	inner	4.39.b.a.3.18	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.39.b.a.3.17	✓	18	1.1	even	1	trivial
4.39.b.a.3.18	yes	18	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(518652. - 76670.9i) q^{2} -2.28254e9i q^{3} +(2.63121e11 - 7.95309e10i) q^{4} +1.45926e13 q^{5} +(-1.75005e14 - 1.18385e15i) q^{6} -8.90761e15i q^{7} +(1.30370e17 - 6.14226e16i) q^{8} -3.85916e18 q^{9} +O(q^{10})\)	\(q+(518652. - 76670.9i) q^{2} -2.28254e9i q^{3} +(2.63121e11 - 7.95309e10i) q^{4} +1.45926e13 q^{5} +(-1.75005e14 - 1.18385e15i) q^{6} -8.90761e15i q^{7} +(1.30370e17 - 6.14226e16i) q^{8} -3.85916e18 q^{9} +(7.56849e18 - 1.11883e18i) q^{10} -4.38272e19i q^{11} +(-1.81533e20 - 6.00586e20i) q^{12} +1.87649e21 q^{13} +(-6.82954e20 - 4.61995e21i) q^{14} -3.33083e22i q^{15} +(6.29075e22 - 4.18525e22i) q^{16} +4.37216e22 q^{17} +(-2.00156e24 + 2.95885e23i) q^{18} +2.11999e24i q^{19} +(3.83963e24 - 1.16057e24i) q^{20} -2.03320e25 q^{21} +(-3.36027e24 - 2.27310e25i) q^{22} -2.46227e25i q^{23} +(-1.40200e26 - 2.97576e26i) q^{24} -1.50853e26 q^{25} +(9.73246e26 - 1.43872e26i) q^{26} +5.72532e27i q^{27} +(-7.08431e26 - 2.34378e27i) q^{28} +3.71574e27 q^{29} +(-2.55378e27 - 1.72754e28i) q^{30} +1.46587e28i q^{31} +(2.94182e28 - 2.65301e28i) q^{32} -1.00037e29 q^{33} +(2.26763e28 - 3.35217e27i) q^{34} -1.29986e29i q^{35} +(-1.01543e30 + 3.06922e29i) q^{36} -3.14590e29 q^{37} +(1.62541e29 + 1.09953e30i) q^{38} -4.28318e30i q^{39} +(1.90245e30 - 8.96317e29i) q^{40} -1.59147e30 q^{41} +(-1.05452e31 + 1.55887e30i) q^{42} +1.13757e31i q^{43} +(-3.48561e30 - 1.15318e31i) q^{44} -5.63153e31 q^{45} +(-1.88784e30 - 1.27706e31i) q^{46} +3.60466e31i q^{47} +(-9.55302e31 - 1.43589e32i) q^{48} +5.05892e31 q^{49} +(-7.82401e31 + 1.15660e31i) q^{50} -9.97964e31i q^{51} +(4.93745e32 - 1.49239e32i) q^{52} +1.01267e32 q^{53} +(4.38965e32 + 2.96945e33i) q^{54} -6.39554e32i q^{55} +(-5.47129e32 - 1.16129e33i) q^{56} +4.83896e33 q^{57} +(1.92717e33 - 2.84889e32i) q^{58} -1.33527e33i q^{59} +(-2.64904e33 - 8.76412e33i) q^{60} -7.35637e33 q^{61} +(1.12389e33 + 7.60274e33i) q^{62} +3.43759e34i q^{63} +(1.32237e34 - 1.60154e34i) q^{64} +2.73830e34 q^{65} +(-5.18846e34 + 7.66996e33i) q^{66} -3.46090e34i q^{67} +(1.15041e34 - 3.47722e33i) q^{68} -5.62024e34 q^{69} +(-9.96610e33 - 6.74172e34i) q^{70} -2.59319e35i q^{71} +(-5.03120e35 + 2.37039e35i) q^{72} +3.29372e35 q^{73} +(-1.63163e35 + 2.41199e34i) q^{74} +3.44329e35i q^{75} +(1.68604e35 + 5.57813e35i) q^{76} -3.90395e35 q^{77} +(-3.28395e35 - 2.22148e36i) q^{78} +9.78414e35i q^{79} +(9.17986e35 - 6.10739e35i) q^{80} +7.85514e36 q^{81} +(-8.25420e35 + 1.22020e35i) q^{82} +3.96638e36i q^{83} +(-5.34978e36 + 1.61702e36i) q^{84} +6.38013e35 q^{85} +(8.72187e35 + 5.90004e36i) q^{86} -8.48133e36i q^{87} +(-2.69198e36 - 5.71377e36i) q^{88} +7.10862e36 q^{89} +(-2.92080e37 + 4.31774e36i) q^{90} -1.67151e37i q^{91} +(-1.95827e36 - 6.47875e36i) q^{92} +3.34590e37 q^{93} +(2.76372e36 + 1.86956e37i) q^{94} +3.09362e37i q^{95} +(-6.05560e37 - 6.71484e37i) q^{96} -6.10990e37 q^{97} +(2.62382e37 - 3.87872e36i) q^{98} +1.69136e38i 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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