LMFDB - Embedded newform 4.39.b.a.3.2

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			3.2
Root			$0.500000 - 9.26410e7i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.39.b.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-521279. + 56087.1i) q^{2} +1.48226e9i q^{3} +(2.68586e11 - 5.84741e10i) q^{4} +1.90217e13 q^{5} +(-8.31355e13 - 7.72670e14i) q^{6} -1.45250e16i q^{7} +(-1.36729e17 + 4.55456e16i) q^{8} -8.46232e17 q^{9} +O(q^{10})$	\(q+(-521279. + 56087.1i) q^{2} +1.48226e9i q^{3} +(2.68586e11 - 5.84741e10i) q^{4} +1.90217e13 q^{5} +(-8.31355e13 - 7.72670e14i) q^{6} -1.45250e16i q^{7} +(-1.36729e17 + 4.55456e16i) q^{8} -8.46232e17 q^{9} +(-9.91563e18 + 1.06687e18i) q^{10} -3.87139e19i q^{11} +(8.66736e19 + 3.98114e20i) q^{12} -8.59840e20 q^{13} +(8.14663e20 + 7.57156e21i) q^{14} +2.81951e22i q^{15} +(6.87194e22 - 3.14107e22i) q^{16} -1.60298e23 q^{17} +(4.41123e23 - 4.74627e22i) q^{18} -1.01555e24i q^{19} +(5.10898e24 - 1.11228e24i) q^{20} +2.15297e25 q^{21} +(2.17135e24 + 2.01807e25i) q^{22} +1.41511e26i q^{23} +(-6.75102e25 - 2.02667e26i) q^{24} -1.97170e24 q^{25} +(4.48217e26 - 4.82260e25i) q^{26} +7.47975e26i q^{27} +(-8.49334e26 - 3.90121e27i) q^{28} -9.93962e27 q^{29} +(-1.58138e27 - 1.46975e28i) q^{30} +3.69457e28i q^{31} +(-3.40603e28 + 2.02280e28i) q^{32} +5.73839e28 q^{33} +(8.35602e28 - 8.99067e27i) q^{34} -2.76290e29i q^{35} +(-2.27286e29 + 4.94827e28i) q^{36} -7.42006e29 q^{37} +(5.69592e28 + 5.29385e29i) q^{38} -1.27450e30i q^{39} +(-2.60082e30 + 8.66355e29i) q^{40} -6.52818e30 q^{41} +(-1.12230e31 + 1.20754e30i) q^{42} -5.95952e30i q^{43} +(-2.26376e30 - 1.03980e31i) q^{44} -1.60968e31 q^{45} +(-7.93693e30 - 7.37666e31i) q^{46} +9.29922e31i q^{47} +(4.65587e31 + 1.01860e32i) q^{48} -8.10395e31 q^{49} +(1.02781e30 - 1.10587e29i) q^{50} -2.37603e32i q^{51} +(-2.30941e32 + 5.02784e31i) q^{52} +3.86726e32 q^{53} +(-4.19518e31 - 3.89904e32i) q^{54} -7.36405e32i q^{55} +(6.61547e32 + 1.98598e33i) q^{56} +1.50530e33 q^{57} +(5.18132e33 - 5.57484e32i) q^{58} +2.63935e33i q^{59} +(1.64868e33 + 7.57281e33i) q^{60} +2.89103e33 q^{61} +(-2.07218e33 - 1.92590e34i) q^{62} +1.22915e34i q^{63} +(1.66204e34 - 1.24548e34i) q^{64} -1.63557e34 q^{65} +(-2.99130e34 + 3.21849e33i) q^{66} -2.95727e34i q^{67} +(-4.30540e34 + 9.37330e33i) q^{68} -2.09755e35 q^{69} +(1.54963e34 + 1.44024e35i) q^{70} -1.32591e35i q^{71} +(1.15704e35 - 3.85421e34i) q^{72} -1.42953e34 q^{73} +(3.86792e35 - 4.16170e34i) q^{74} -2.92256e33i q^{75} +(-5.93833e34 - 2.72763e35i) q^{76} -5.62317e35 q^{77} +(7.14832e34 + 6.64372e35i) q^{78} +5.08832e35i q^{79} +(1.30716e36 - 5.97486e35i) q^{80} -2.25183e36 q^{81} +(3.40300e36 - 3.66147e35i) q^{82} +2.79965e36i q^{83} +(5.78259e36 - 1.25893e36i) q^{84} -3.04915e36 q^{85} +(3.34252e35 + 3.10657e36i) q^{86} -1.47331e37i q^{87} +(1.76324e36 + 5.29330e36i) q^{88} -4.53475e36 q^{89} +(8.39093e36 - 9.02823e35i) q^{90} +1.24891e37i q^{91} +(8.27471e36 + 3.80078e37i) q^{92} -5.47630e37 q^{93} +(-5.21566e36 - 4.84749e37i) q^{94} -1.93175e37i q^{95} +(-2.99831e37 - 5.04861e37i) q^{96} -9.50070e37 q^{97} +(4.22442e37 - 4.54527e36i) q^{98} +3.27609e37i 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 $

$2$	−521279.	+	56087.1i	−0.994261	+	0.106978i
$2$	−521279.	+	56087.1i	−0.994261	+	0.106978i
$3$			1.48226e9i			1.27532i	0.770318	+	0.637660i	$0.220098\pi$
$3$			1.48226e9i			1.27532i	−0.770318	+	0.637660i	$0.779902\pi$
$4$	2.68586e11	−	5.84741e10i	0.977112	−	0.212728i
$5$	1.90217e13			0.997286			0.498643	−	0.866807i	$-0.333832\pi$
$5$	1.90217e13			0.997286			0.498643	+	0.866807i	$0.333832\pi$
$6$	−8.31355e13	−	7.72670e14i	−0.136431	−	1.26800i
$7$		−	1.45250e16i		−	1.27424i	−0.770764	−	0.637121i	$-0.780125\pi$
$7$		−	1.45250e16i		−	1.27424i	0.770764	−	0.637121i	$-0.219875\pi$
$8$	−1.36729e17	+	4.55456e16i	−0.948747	+	0.316036i
$9$	−8.46232e17			−0.626443
$10$	−9.91563e18	+	1.06687e18i	−0.991563	+	0.106687i
$11$		−	3.87139e19i		−	0.633003i	−0.948592	−	0.316501i	$-0.897492\pi$
$11$		−	3.87139e19i		−	0.633003i	0.948592	−	0.316501i	$-0.102508\pi$
$12$	8.66736e19	+	3.98114e20i	0.271296	+	1.24613i
$13$	−8.59840e20			−0.588158			−0.294079	−	0.955781i	$-0.595013\pi$
$13$	−8.59840e20			−0.588158			−0.294079	+	0.955781i	$0.595013\pi$
$14$	8.14663e20	+	7.57156e21i	0.136315	+	1.26693i
$15$			2.81951e22i			1.27186i
$16$	6.87194e22	−	3.14107e22i	0.909494	−	0.415717i
$17$	−1.60298e23			−0.670501			−0.335251	−	0.942129i	$-0.608821\pi$
$17$	−1.60298e23			−0.670501			−0.335251	+	0.942129i	$0.608821\pi$
$18$	4.41123e23	−	4.74627e22i	0.622849	−	0.0670155i
$19$		−	1.01555e24i		−	0.513313i	−0.966503	−	0.256657i	$-0.917379\pi$
$19$		−	1.01555e24i		−	0.513313i	0.966503	−	0.256657i	$-0.0826209\pi$
$20$	5.10898e24	−	1.11228e24i	0.974460	−	0.212150i
$21$	2.15297e25			1.62507
$22$	2.17135e24	+	2.01807e25i	0.0677171	+	0.629370i
$23$			1.41511e26i			1.89653i	0.317475	+	0.948267i	$0.397165\pi$
$23$			1.41511e26i			1.89653i	−0.317475	+	0.948267i	$0.602835\pi$
$24$	−6.75102e25	−	2.02667e26i	−0.403047	−	1.20996i
$25$	−1.97170e24			−0.00541976
$26$	4.48217e26	−	4.82260e25i	0.584783	−	0.0629198i
$27$			7.47975e26i			0.476404i
$28$	−8.49334e26	−	3.90121e27i	−0.271066	−	1.24508i
$29$	−9.93962e27			−1.62858			−0.814288	−	0.580462i	$-0.802872\pi$
$29$	−9.93962e27			−1.62858			−0.814288	+	0.580462i	$0.802872\pi$
$30$	−1.58138e27	−	1.46975e28i	−0.136061	−	1.26456i
$31$			3.69457e28i			1.70487i	0.522831	+	0.852437i	$0.324876\pi$
$31$			3.69457e28i			1.70487i	−0.522831	+	0.852437i	$0.675124\pi$
$32$	−3.40603e28	+	2.02280e28i	−0.859802	+	0.510627i
$33$	5.73839e28			0.807281
$34$	8.35602e28	−	8.99067e27i	0.666654	−	0.0717287i
$35$		−	2.76290e29i		−	1.27078i
$36$	−2.27286e29	+	4.94827e28i	−0.612105	+	0.133262i
$37$	−7.42006e29			−1.18734			−0.593669	−	0.804709i	$-0.702321\pi$
$37$	−7.42006e29			−1.18734			−0.593669	+	0.804709i	$0.702321\pi$
$38$	5.69592e28	+	5.29385e29i	0.0549130	+	0.510368i
$39$		−	1.27450e30i		−	0.750090i
$40$	−2.60082e30	+	8.66355e29i	−0.946173	+	0.315178i
$41$	−6.52818e30			−1.48559			−0.742794	−	0.669520i	$-0.766500\pi$
$41$	−6.52818e30			−1.48559			−0.742794	+	0.669520i	$0.766500\pi$
$42$	−1.12230e31	+	1.20754e30i	−1.61574	+	0.173846i
$43$		−	5.95952e30i		−	0.548669i	−0.961634	−	0.274334i	$-0.911542\pi$
$43$		−	5.95952e30i		−	0.548669i	0.961634	−	0.274334i	$-0.0884575\pi$
$44$	−2.26376e30	−	1.03980e31i	−0.134657	−	0.618514i
$45$	−1.60968e31			−0.624744
$46$	−7.93693e30	−	7.37666e31i	−0.202887	−	1.88565i
$47$			9.29922e31i			1.57975i	0.613271	+	0.789873i	$0.289853\pi$
$47$			9.29922e31i			1.57975i	−0.613271	+	0.789873i	$0.710147\pi$
$48$	4.65587e31	+	1.01860e32i	0.530173	+	1.15990i
$49$	−8.10395e31			−0.623694
$50$	1.02781e30	−	1.10587e29i	0.00538866	−	0.000579794i
$51$		−	2.37603e32i		−	0.855104i
$52$	−2.30941e32	+	5.02784e31i	−0.574696	+	0.125117i
$53$	3.86726e32			0.670134			0.335067	−	0.942194i	$-0.391241\pi$
$53$	3.86726e32			0.670134			0.335067	+	0.942194i	$0.391241\pi$
$54$	−4.19518e31	−	3.89904e32i	−0.0509646	−	0.473671i
$55$		−	7.36405e32i		−	0.631285i
$56$	6.61547e32	+	1.98598e33i	0.402706	+	1.20893i
$57$	1.50530e33			0.654639
$58$	5.18132e33	−	5.57484e32i	1.61923	−	0.174221i
$59$			2.63935e33i			0.596086i	0.954552	+	0.298043i	$0.0963339\pi$
$59$			2.63935e33i			0.596086i	−0.954552	+	0.298043i	$0.903666\pi$
$60$	1.64868e33	+	7.57281e33i	0.270560	+	1.24275i
$61$	2.89103e33			0.346566			0.173283	−	0.984872i	$-0.444562\pi$
$61$	2.89103e33			0.346566			0.173283	+	0.984872i	$0.444562\pi$
$62$	−2.07218e33	−	1.92590e34i	−0.182383	−	1.69509i
$63$			1.22915e34i			0.798241i
$64$	1.66204e34	−	1.24548e34i	0.800243	−	0.599676i
$65$	−1.63557e34			−0.586562
$66$	−2.99130e34	+	3.21849e33i	−0.802649	+	0.0863611i
$67$		−	2.95727e34i		−	0.596306i	−0.954518	−	0.298153i	$-0.903629\pi$
$67$		−	2.95727e34i		−	0.596306i	0.954518	−	0.298153i	$-0.0963706\pi$
$68$	−4.30540e34	+	9.37330e33i	−0.655155	+	0.142634i
$69$	−2.09755e35			−2.41869
$70$	1.54963e34	+	1.44024e35i	0.135946	+	1.26349i
$71$		−	1.32591e35i		−	0.888394i	−0.895929	−	0.444197i	$-0.853489\pi$
$71$		−	1.32591e35i		−	0.888394i	0.895929	−	0.444197i	$-0.146511\pi$
$72$	1.15704e35	−	3.85421e34i	0.594336	−	0.197979i
$73$	−1.42953e34			−0.0565013			−0.0282506	−	0.999601i	$-0.508994\pi$
$73$	−1.42953e34			−0.0565013			−0.0282506	+	0.999601i	$0.508994\pi$
$74$	3.86792e35	−	4.16170e34i	1.18053	−	0.127019i
$75$		−	2.92256e33i		−	0.00691194i
$76$	−5.93833e34	−	2.72763e35i	−0.109196	−	0.501564i
$77$	−5.62317e35			−0.806599
$78$	7.14832e34	+	6.64372e35i	0.0802429	+	0.745786i
$79$			5.08832e35i			0.448394i	0.974544	+	0.224197i	$0.0719759\pi$
$79$			5.08832e35i			0.448394i	−0.974544	+	0.224197i	$0.928024\pi$
$80$	1.30716e36	−	5.97486e35i	0.907026	−	0.414589i
$81$	−2.25183e36			−1.23401
$82$	3.40300e36	−	3.66147e35i	1.47706	−	0.158925i
$83$			2.79965e36i			0.965208i	0.875839	+	0.482604i	$0.160309\pi$
$83$			2.79965e36i			0.965208i	−0.875839	+	0.482604i	$0.839691\pi$
$84$	5.78259e36	−	1.25893e36i	1.58787	−	0.345697i
$85$	−3.04915e36			−0.668682
$86$	3.34252e35	+	3.10657e36i	0.0586953	+	0.545520i
$87$		−	1.47331e37i		−	2.07696i
$88$	1.76324e36	+	5.29330e36i	0.200052	+	0.600559i
$89$	−4.53475e36			−0.415091			−0.207546	−	0.978225i	$-0.566548\pi$
$89$	−4.53475e36			−0.415091			−0.207546	+	0.978225i	$0.566548\pi$
$90$	8.39093e36	−	9.02823e35i	0.621158	−	0.0668336i
$91$			1.24891e37i			0.749456i
$92$	8.27471e36	+	3.80078e37i	0.403445	+	1.85312i
$93$	−5.47630e37			−2.17426
$94$	−5.21566e36	−	4.84749e37i	−0.168997	−	1.57068i
$95$		−	1.93175e37i		−	0.511920i
$96$	−2.99831e37	−	5.04861e37i	−0.651213	−	1.09652i
$97$	−9.50070e37			−1.69470			−0.847350	−	0.531035i	$-0.821803\pi$
$97$	−9.50070e37			−1.69470			−0.847350	+	0.531035i	$0.821803\pi$
$98$	4.22442e37	−	4.54527e36i	0.620114	−	0.0667213i
$99$			3.27609e37i			0.396540i
$100$	−5.29571e35	+	1.15293e35i	−0.00529571	+	0.00115293i
$101$	1.51020e38			1.25005			0.625025	−	0.780605i	$-0.285089\pi$
$101$	1.51020e38			1.25005			0.625025	+	0.780605i	$0.285089\pi$
$102$	1.33265e37	+	1.23858e38i	0.0914771	+	0.850197i
$103$			8.62556e37i			0.491904i	0.969282	+	0.245952i	$0.0791005\pi$
$103$			8.62556e37i			0.491904i	−0.969282	+	0.245952i	$0.920899\pi$
$104$	1.17565e38	−	3.91619e37i	0.558013	−	0.185879i
$105$	4.09532e38			1.62066
$106$	−2.01592e38	+	2.16903e37i	−0.666289	+	0.0716894i
$107$		−	6.84920e37i		−	0.189386i	−0.995507	−	0.0946930i	$-0.969813\pi$
$107$		−	6.84920e37i		−	0.189386i	0.995507	−	0.0946930i	$-0.0301869\pi$
$108$	4.37372e37	+	2.00896e38i	0.101344	+	0.465500i
$109$	1.28382e38			0.249690			0.124845	−	0.992176i	$-0.460157\pi$
$109$	1.28382e38			0.249690			0.124845	+	0.992176i	$0.460157\pi$
$110$	4.13028e37	+	3.83873e38i	0.0675334	+	0.627662i
$111$		−	1.09984e39i		−	1.51424i
$112$	−4.56239e38	−	9.98147e38i	−0.529724	−	1.15892i
$113$	1.08233e39			1.06138			0.530688	−	0.847567i	$-0.321934\pi$
$113$	1.08233e39			1.06138			0.530688	+	0.847567i	$0.321934\pi$
$114$	−7.84684e38	+	8.44281e37i	−0.650882	+	0.0700318i
$115$			2.69178e39i			1.89139i
$116$	−2.66965e39	+	5.81210e38i	−1.59130	+	0.346443i
$117$	7.27625e38			0.368448
$118$	−1.48034e38	−	1.37584e39i	−0.0637679	−	0.592665i
$119$			2.32833e39i			0.854381i
$120$	−1.28416e39	−	3.85508e39i	−0.401953	−	1.20667i
$121$	2.24167e39			0.599308
$122$	−1.50704e39	+	1.62150e38i	−0.344577	+	0.0370748i
$123$		−	9.67643e39i		−	1.89460i
$124$	2.16037e39	+	9.92312e39i	0.362673	+	1.66585i
$125$	−6.95757e39			−1.00269
$126$	−6.89394e38	−	6.40730e39i	−0.0853939	−	0.793660i
$127$			4.25573e39i			0.453631i	0.973938	+	0.226816i	$0.0728315\pi$
$127$			4.25573e39i			0.453631i	−0.973938	+	0.226816i	$0.927169\pi$
$128$	−7.96531e39	+	7.42461e39i	−0.731498	+	0.681843i
$129$	8.83353e39			0.699729
$130$	8.52586e39	−	9.17341e38i	0.583196	−	0.0627490i
$131$		−	3.80318e39i		−	0.224902i	−0.993657	−	0.112451i	$-0.964130\pi$
$131$		−	3.80318e39i		−	0.224902i	0.993657	−	0.112451i	$-0.0358701\pi$
$132$	1.54125e40	−	3.35547e39i	0.788804	−	0.171731i
$133$	−1.47508e40			−0.654085
$134$	1.65865e39	+	1.54156e40i	0.0637914	+	0.592884i
$135$			1.42278e40i			0.475112i
$136$	2.19174e40	−	7.30088e39i	0.636136	−	0.211902i
$137$	2.88810e40			0.729325			0.364662	−	0.931140i	$-0.381184\pi$
$137$	2.88810e40			0.729325			0.364662	+	0.931140i	$0.381184\pi$
$138$	1.09341e41	−	1.17646e40i	2.40481	−	0.258746i
$139$			5.82010e39i			0.111596i	0.998442	+	0.0557981i	$0.0177703\pi$
$139$			5.82010e39i			0.111596i	−0.998442	+	0.0557981i	$0.982230\pi$
$140$	−1.61558e40	−	7.42077e40i	−0.270331	−	1.24170i
$141$	−1.37838e41			−2.01468
$142$	7.43665e39	+	6.91170e40i	0.0950383	+	0.883296i
$143$			3.32877e40i			0.372306i
$144$	−5.81526e40	+	2.65807e40i	−0.569747	+	0.260423i
$145$	−1.89069e41			−1.62416
$146$	7.45184e39	−	8.01781e38i	0.0561771	−	0.00604438i
$147$		−	1.20121e41i		−	0.795409i
$148$	−1.99293e41	+	4.33881e40i	−1.16016	+	0.252580i
$149$	9.09811e40			0.466028			0.233014	−	0.972473i	$-0.425141\pi$
$149$	9.09811e40			0.466028			0.233014	+	0.972473i	$0.425141\pi$
$150$	1.63918e38	+	1.52347e39i	0.000739423	+	0.00687227i
$151$		−	4.25600e41i		−	1.69215i	−0.533061	−	0.846077i	$-0.678958\pi$
$151$		−	4.25600e41i		−	1.69215i	0.533061	−	0.846077i	$-0.321042\pi$
$152$	4.62538e40	+	1.38855e41i	0.162225	+	0.487004i
$153$	1.35650e41			0.420031
$154$	2.93124e41	−	3.15387e40i	0.801970	−	0.0862880i
$155$			7.02772e41i			1.70025i
$156$	−7.45255e40	−	3.42314e41i	−0.159565	−	0.732922i
$157$	−4.28263e40			−0.0812114			−0.0406057	−	0.999175i	$-0.512929\pi$
$157$	−4.28263e40			−0.0812114			−0.0406057	+	0.999175i	$0.512929\pi$
$158$	−2.85389e40	−	2.65243e41i	−0.0479681	−	0.445821i
$159$			5.73227e41i			0.854636i
$160$	−6.47885e41	+	3.84772e41i	−0.857469	+	0.509241i
$161$	2.05544e42			2.41664
$162$	1.17383e42	−	1.26298e41i	1.22693	−	0.132012i
$163$			2.17593e41i			0.202340i	0.994869	+	0.101170i	$0.0322585\pi$
$163$			2.17593e41i			0.202340i	−0.994869	+	0.101170i	$0.967741\pi$
$164$	−1.75338e42	+	3.81729e41i	−1.45159	+	0.316026i
$165$	1.09154e42			0.805091
$166$	−1.57025e41	−	1.45940e42i	−0.103256	−	0.959669i
$167$		−	2.18212e42i		−	1.28016i	−0.768308	−	0.640081i	$-0.778901\pi$
$167$		−	2.18212e42i		−	1.28016i	0.768308	−	0.640081i	$-0.221099\pi$
$168$	−2.94373e42	+	9.80583e41i	−1.54178	+	0.513580i
$169$	−1.39789e42			−0.654070
$170$	1.58946e42	−	1.71018e41i	0.664845	−	0.0715340i
$171$			8.59390e41i			0.321562i
$172$	−3.48477e41	−	1.60064e42i	−0.116717	−	0.536111i
$173$	1.95778e42			0.587338			0.293669	−	0.955907i	$-0.405124\pi$
$173$	1.95778e42			0.587338			0.293669	+	0.955907i	$0.405124\pi$
$174$	8.26335e41	+	7.68004e42i	0.222188	+	2.06504i
$175$			2.86388e40i			0.00690609i
$176$	−1.21603e42	−	2.66039e42i	−0.263150	−	0.575712i
$177$	−3.91219e42			−0.760201
$178$	2.36387e42	−	2.54341e41i	0.412709	−	0.0444055i
$179$		−	1.93234e42i		−	0.303302i	−0.988434	−	0.151651i	$-0.951541\pi$
$179$		−	1.93234e42i		−	0.303302i	0.988434	−	0.151651i	$-0.0484590\pi$
$180$	−4.32338e42	+	9.41246e41i	−0.610444	+	0.132900i
$181$	−5.26990e42			−0.669744			−0.334872	−	0.942264i	$-0.608693\pi$
$181$	−5.26990e42			−0.669744			−0.334872	+	0.942264i	$0.608693\pi$
$182$	−7.00480e41	−	6.51033e42i	−0.0801750	−	0.745155i
$183$			4.28525e42i			0.441983i
$184$	−6.44519e42	−	1.93486e43i	−0.599372	−	1.79933i
$185$	−1.41142e43			−1.18412
$186$	2.85468e43	−	3.07150e42i	2.16178	−	0.232597i
$187$			6.20577e42i			0.424429i
$188$	5.43763e42	+	2.49764e43i	0.336055	+	1.54359i
$189$	1.08643e43			0.607055
$190$	1.08346e42	+	1.00698e43i	0.0547640	+	0.508983i
$191$		−	4.37537e42i		−	0.200161i	−0.994979	−	0.100081i	$-0.968090\pi$
$191$		−	4.37537e42i		−	0.200161i	0.994979	−	0.100081i	$-0.0319101\pi$
$192$	1.84612e43	+	2.46357e43i	0.764780	+	1.02057i
$193$	−2.22592e43			−0.835450			−0.417725	−	0.908574i	$-0.637172\pi$
$193$	−2.22592e43			−0.835450			−0.417725	+	0.908574i	$0.637172\pi$
$194$	4.95252e43	−	5.32867e42i	1.68497	−	0.181295i
$195$		−	2.42433e43i		−	0.748055i
$196$	−2.17661e43	+	4.73871e42i	−0.609418	+	0.132677i
$197$	2.14613e43			0.545503			0.272751	−	0.962085i	$-0.412066\pi$
$197$	2.14613e43			0.545503			0.272751	+	0.962085i	$0.412066\pi$
$198$	−1.83746e42	−	1.70776e43i	−0.0424210	−	0.394265i
$199$		−	4.36019e43i		−	0.914737i	−0.889277	−	0.457369i	$-0.848792\pi$
$199$		−	4.36019e43i		−	0.914737i	0.889277	−	0.457369i	$-0.151208\pi$
$200$	2.69588e41	−	8.98021e40i	0.00514198	−	0.00171284i
$201$	4.38343e43			0.760482
$202$	−7.87235e43	+	8.47026e42i	−1.24288	+	0.133727i
$203$			1.44373e44i			2.07520i
$204$	−1.38936e43	−	6.38170e43i	−0.181904	−	0.835532i
$205$	−1.24177e44			−1.48156
$206$	−4.83783e42	−	4.49633e43i	−0.0526227	−	0.489081i
$207$		−	1.19751e44i		−	1.18807i
$208$	−5.90877e43	+	2.70082e43i	−0.534926	+	0.244507i
$209$	−3.93158e43			−0.324929
$210$	−2.13481e44	+	2.29695e43i	−1.61136	+	0.173374i
$211$			1.61611e44i			1.11456i	0.830324	+	0.557281i	$0.188156\pi$
$211$			1.61611e44i			1.11456i	−0.830324	+	0.557281i	$0.811844\pi$
$212$	1.03869e44	−	2.26135e43i	0.654796	−	0.142556i
$213$	1.96534e44			1.13299
$214$	3.84152e42	+	3.57035e43i	0.0202601	+	0.188299i
$215$		−	1.13360e44i		−	0.547180i
$216$	−3.40670e43	−	1.02270e44i	−0.150561	−	0.451987i
$217$	5.36635e44			2.17242
$218$	−6.69229e43	+	7.20058e42i	−0.248257	+	0.0267112i
$219$		−	2.11893e43i		−	0.0720573i
$220$	−4.30606e43	−	1.97788e44i	−0.134292	−	0.616836i
$221$	1.37831e44			0.394361
$222$	6.16870e43	+	5.73326e44i	0.161990	+	1.50555i
$223$		−	3.64937e44i		−	0.879885i	−0.898026	−	0.439943i	$-0.854999\pi$
$223$		−	3.64937e44i		−	0.879885i	0.898026	−	0.439943i	$-0.145001\pi$
$224$	2.93811e44	+	4.94724e44i	0.650662	+	1.09560i
$225$	1.66851e42			0.00339517
$226$	−5.64196e44	+	6.07047e43i	−1.05528	+	0.113543i
$227$			8.19663e44i			1.40976i	0.709328	+	0.704879i	$0.248999\pi$
$227$			8.19663e44i			1.40976i	−0.709328	+	0.704879i	$0.751001\pi$
$228$	4.04304e44	−	8.80213e43i	0.639655	−	0.139260i
$229$	−8.36405e44			−1.21771			−0.608853	−	0.793283i	$-0.708370\pi$
$229$	−8.36405e44			−1.21771			−0.608853	+	0.793283i	$0.708370\pi$
$230$	−1.50974e44	−	1.40317e45i	−0.202336	−	1.88053i
$231$		−	8.33498e44i		−	1.02867i
$232$	1.35903e45	−	4.52706e44i	1.54511	−	0.514688i
$233$	−3.29214e44			−0.344917			−0.172459	−	0.985017i	$-0.555171\pi$
$233$	−3.29214e44			−0.344917			−0.172459	+	0.985017i	$0.555171\pi$
$234$	−3.79296e44	+	4.08104e43i	−0.366333	+	0.0394157i
$235$			1.76887e45i			1.57546i
$236$	1.54334e44	+	7.08894e44i	0.126804	+	0.582443i
$237$	−7.54219e44			−0.571846
$238$	−1.30589e44	−	1.21371e45i	−0.0913997	−	0.849478i
$239$		−	1.12428e45i		−	0.726632i	−0.931666	−	0.363316i	$-0.881644\pi$
$239$		−	1.12428e45i		−	0.726632i	0.931666	−	0.363316i	$-0.118356\pi$
$240$	8.85627e44	+	1.93755e45i	0.528734	+	1.15675i
$241$	−1.35363e45			−0.746751			−0.373375	−	0.927680i	$-0.621800\pi$
$241$	−1.35363e45			−0.746751			−0.373375	+	0.927680i	$0.621800\pi$
$242$	−1.16854e45	+	1.25729e44i	−0.595869	+	0.0641125i
$243$		−	2.32738e45i		−	1.09736i
$244$	7.76492e44	−	1.69050e44i	0.338634	−	0.0737241i
$245$	−1.54151e45			−0.622001
$246$	5.42723e44	+	5.04412e45i	0.202680	+	1.88373i
$247$			8.73210e44i			0.301909i
$248$	−1.68271e45	−	5.05155e45i	−0.538801	−	1.61749i
$249$	−4.14981e45			−1.23095
$250$	3.62684e45	−	3.90230e44i	0.996937	−	0.107266i
$251$		−	3.64288e43i		−	0.00928204i	−0.999989	−	0.00464102i	$-0.998523\pi$
$251$		−	3.64288e43i		−	0.00928204i	0.999989	−	0.00464102i	$-0.00147729\pi$
$252$	7.18733e44	+	3.30133e45i	0.169808	+	0.779970i
$253$	5.47843e45			1.20051
$254$	−2.38691e44	−	2.21842e45i	−0.0485284	−	0.451028i
$255$		−	4.51963e45i		−	0.852784i
$256$	3.73573e45	−	4.31705e45i	0.654359	−	0.756184i
$257$	7.62471e45			1.24021			0.620103	−	0.784520i	$-0.287091\pi$
$257$	7.62471e45			1.24021			0.620103	+	0.784520i	$0.287091\pi$
$258$	−4.60474e45	+	4.95447e44i	−0.695713	+	0.0748553i
$259$			1.07776e46i			1.51296i
$260$	−4.39290e45	+	9.56382e44i	−0.573137	+	0.124778i
$261$	8.41123e45			1.02021
$262$	2.13309e44	+	1.98252e45i	0.0240594	+	0.223611i
$263$			1.22073e46i			1.28073i	0.768069	+	0.640367i	$0.221218\pi$
$263$			1.22073e46i			1.28073i	−0.768069	+	0.640367i	$0.778782\pi$
$264$	−7.84603e45	+	2.61358e45i	−0.765906	+	0.255130i
$265$	7.35620e45			0.668316
$266$	7.68929e45	−	8.27330e44i	0.650332	−	0.0699725i
$267$		−	6.72167e45i		−	0.529375i
$268$	−1.72924e45	−	7.94282e45i	−0.126851	−	0.582658i
$269$	−1.62480e45			−0.111047			−0.0555234	−	0.998457i	$-0.517683\pi$
$269$	−1.62480e45			−0.111047			−0.0555234	+	0.998457i	$0.517683\pi$
$270$	−7.97995e44	−	7.41665e45i	−0.0508263	−	0.472385i
$271$		−	2.49493e46i		−	1.48130i	−0.671894	−	0.740648i	$-0.734519\pi$
$271$		−	2.49493e46i		−	1.48130i	0.671894	−	0.740648i	$-0.265481\pi$
$272$	−1.10156e46	+	5.03508e45i	−0.609817	+	0.278739i
$273$	−1.85121e46			−0.955797
$274$	−1.50550e46	+	1.61985e45i	−0.725139	+	0.0780214i
$275$			7.63321e43i			0.00343072i
$276$	−5.63374e46	+	1.22652e46i	−2.36333	+	0.514522i
$277$	−2.25070e45			−0.0881457			−0.0440728	−	0.999028i	$-0.514033\pi$
$277$	−2.25070e45			−0.0881457			−0.0440728	+	0.999028i	$0.514033\pi$
$278$	−3.26433e44	−	3.03390e45i	−0.0119383	−	0.110956i
$279$		−	3.12647e46i		−	1.06801i
$280$	1.25838e46	+	3.77768e46i	0.401614	+	1.20565i
$281$	5.94139e45			0.177202			0.0886009	−	0.996067i	$-0.471760\pi$
$281$	5.94139e45			0.177202			0.0886009	+	0.996067i	$0.471760\pi$
$282$	7.18522e46	−	7.73095e45i	2.00312	−	0.215526i
$283$			5.89716e46i			1.53709i	0.639793	+	0.768547i	$0.279020\pi$
$283$			5.89716e46i			1.53709i	−0.639793	+	0.768547i	$0.720980\pi$
$284$	−7.75314e45	−	3.56122e46i	−0.188986	−	0.868060i
$285$	2.86335e46			0.652863
$286$	−1.86701e45	−	1.73522e46i	−0.0398284	−	0.370169i
$287$			9.48215e46i			1.89300i
$288$	2.88229e46	−	1.71176e46i	0.538618	−	0.319879i
$289$	−3.14601e46			−0.550428
$290$	9.85576e46	−	1.06043e46i	1.61484	−	0.173748i
$291$		−	1.40825e47i		−	2.16129i
$292$	−3.83952e45	+	8.35904e44i	−0.0552081	+	0.0120194i
$293$	−9.14649e46			−1.23245			−0.616225	−	0.787570i	$-0.711339\pi$
$293$	−9.14649e46			−1.23245			−0.616225	+	0.787570i	$0.711339\pi$
$294$	6.73726e45	+	6.26168e46i	0.0850910	+	0.790845i
$295$			5.02050e46i			0.594469i
$296$	1.01454e47	−	3.37951e46i	1.12648	−	0.375242i
$297$	2.89570e46			0.301565
$298$	−4.74266e46	+	5.10287e45i	−0.463354	+	0.0498546i
$299$		−	1.21677e47i		−	1.11546i
$300$	−1.70894e44	−	7.84960e44i	−0.00147036	−	0.00675373i
$301$	−8.65617e46			−0.699137
$302$	2.38707e46	+	2.21857e47i	0.181023	+	1.68244i
$303$			2.23850e47i			1.59422i
$304$	−3.18991e46	−	6.97879e46i	−0.213393	−	0.466855i
$305$	5.49924e46			0.345626
$306$	−7.07114e46	+	7.60820e45i	−0.417621	+	0.0449339i
$307$		−	2.55999e47i		−	1.42105i	−0.703673	−	0.710524i	$-0.748458\pi$
$307$		−	2.55999e47i		−	1.42105i	0.703673	−	0.710524i	$-0.251542\pi$
$308$	−1.51031e47	+	3.28810e46i	−0.788137	+	0.171586i
$309$	−1.27853e47			−0.627335
$310$	−3.94164e46	−	3.66340e47i	−0.181888	−	1.69049i
$311$		−	1.48731e47i		−	0.645585i	−0.946470	−	0.322792i	$-0.895378\pi$
$311$		−	1.48731e47i		−	0.645585i	0.946470	−	0.322792i	$-0.104622\pi$
$312$	5.80480e46	+	1.74261e47i	0.237055	+	0.711646i
$313$	−1.03852e46			−0.0399092			−0.0199546	−	0.999801i	$-0.506352\pi$
$313$	−1.03852e46			−0.0399092			−0.0199546	+	0.999801i	$0.506352\pi$
$314$	2.23245e46	−	2.40200e45i	0.0807454	−	0.00868781i
$315$			2.33805e47i			0.796075i
$316$	2.97535e46	+	1.36665e47i	0.0953857	+	0.438131i
$317$	3.32562e47			1.00403			0.502015	−	0.864859i	$-0.332592\pi$
$317$	3.32562e47			1.00403			0.502015	+	0.864859i	$0.332592\pi$
$318$	−3.21506e46	−	2.98811e47i	−0.0914270	−	0.849732i
$319$			3.84801e47i			1.03089i
$320$	3.16149e47	−	2.36912e47i	0.798071	−	0.598049i
$321$	1.01523e47			0.241528
$322$	−1.07146e48	+	1.15283e47i	−2.40277	+	0.258527i
$323$			1.62791e47i			0.344177i
$324$	−6.04810e47	+	1.31673e47i	−1.20577	+	0.262508i
$325$	1.69535e45			0.00318768
$326$	−1.22042e46	−	1.13427e47i	−0.0216458	−	0.201178i
$327$			1.90295e47i			0.318435i
$328$	8.92590e47	−	2.97330e47i	1.40945	−	0.469499i
$329$	1.35071e48			2.01298
$330$	−5.68997e47	+	6.12213e46i	−0.800471	+	0.0861267i
$331$		−	1.35003e48i		−	1.79313i	−0.442909	−	0.896567i	$-0.646053\pi$
$331$		−	1.35003e48i		−	1.79313i	0.442909	−	0.896567i	$-0.353947\pi$
$332$	1.63707e47	+	7.51949e47i	0.205326	+	0.943115i
$333$	6.27909e47			0.743801
$334$	1.22389e47	+	1.13749e48i	0.136949	+	1.27282i
$335$		−	5.62523e47i		−	0.594688i
$336$	1.47951e48	−	6.76263e47i	1.47799	−	0.675568i
$337$	−1.40009e48			−1.32187			−0.660933	−	0.750445i	$-0.729839\pi$
$337$	−1.40009e48			−1.32187			−0.660933	+	0.750445i	$0.729839\pi$
$338$	7.28689e47	−	7.84033e46i	0.650317	−	0.0699709i
$339$			1.60429e48i			1.35359i
$340$	−8.18961e47	+	1.78296e47i	−0.653377	+	0.142247i
$341$	1.43031e48			1.07919
$342$	−4.82007e46	−	4.47982e47i	−0.0343999	−	0.319716i
$343$		−	7.10202e47i		−	0.479506i
$344$	2.71430e47	+	8.14838e47i	0.173399	+	0.520548i
$345$	−3.98991e48			−2.41212
$346$	−1.02055e48	+	1.09806e47i	−0.583967	+	0.0628320i
$347$			2.20459e48i			1.19418i	0.802175	+	0.597088i	$0.203676\pi$
$347$			2.20459e48i			1.19418i	−0.802175	+	0.597088i	$0.796324\pi$
$348$	−8.61503e47	−	3.95710e48i	−0.441826	−	2.02942i
$349$	−1.96796e48			−0.955727			−0.477863	−	0.878434i	$-0.658589\pi$
$349$	−1.96796e48			−0.955727			−0.477863	+	0.878434i	$0.658589\pi$
$350$	−1.60627e45	−	1.49288e46i	−0.000738797	−	0.00686646i
$351$		−	6.43139e47i		−	0.280201i
$352$	7.83105e47	+	1.31861e48i	0.323228	+	0.544257i
$353$	−5.50281e47			−0.215211			−0.107606	−	0.994194i	$-0.534318\pi$
$353$	−5.50281e47			−0.215211			−0.107606	+	0.994194i	$0.534318\pi$
$354$	2.03935e48	−	2.19424e47i	0.755838	−	0.0813245i
$355$		−	2.52211e48i		−	0.885983i
$356$	−1.21797e48	+	2.65166e47i	−0.405591	+	0.0883014i
$357$	−3.45118e48			−1.08961
$358$	1.08379e47	+	1.00729e48i	0.0324466	+	0.301562i
$359$		−	2.63214e48i		−	0.747334i	−0.927563	−	0.373667i	$-0.878100\pi$
$359$		−	2.63214e48i		−	0.747334i	0.927563	−	0.373667i	$-0.121900\pi$
$360$	2.20090e48	−	7.33138e47i	0.592724	−	0.197441i
$361$	2.88280e48			0.736510
$362$	2.74709e48	−	2.95573e47i	0.665901	−	0.0716477i
$363$			3.32273e48i			0.764310i
$364$	7.30291e47	+	3.35441e48i	0.159430	+	0.732302i
$365$	−2.71921e47			−0.0563480
$366$	−2.40347e47	−	2.23381e48i	−0.0472823	−	0.439447i
$367$			4.67445e48i			0.873122i	0.899675	+	0.436561i	$0.143804\pi$
$367$			4.67445e48i			0.873122i	−0.899675	+	0.436561i	$0.856196\pi$
$368$	4.44495e48	+	9.72453e48i	0.788421	+	1.72489i
$369$	5.52435e48			0.930637
$370$	7.35746e48	−	7.91627e47i	1.17732	−	0.126674i
$371$		−	5.61718e48i		−	0.853913i
$372$	−1.47086e49	+	3.20222e48i	−2.12449	+	0.462525i
$373$	8.33802e48			1.14445			0.572223	−	0.820098i	$-0.306081\pi$
$373$	8.33802e48			1.14445			0.572223	+	0.820098i	$0.306081\pi$
$374$	−3.48064e47	−	3.23494e48i	−0.0454044	−	0.421993i
$375$		−	1.03129e49i		−	1.27875i
$376$	−4.23538e48	−	1.27147e49i	−0.499256	−	1.49878i
$377$	8.54649e48			0.957860
$378$	−5.66334e48	+	6.09348e47i	−0.603571	+	0.0649413i
$379$			1.67174e49i			1.69443i	0.531250	+	0.847215i	$0.321723\pi$
$379$			1.67174e49i			1.69443i	−0.531250	+	0.847215i	$0.678277\pi$
$380$	−1.12957e48	−	5.18842e48i	−0.108900	−	0.500203i
$381$	−6.30808e48			−0.578525
$382$	2.45402e47	+	2.28079e48i	0.0214128	+	0.199013i
$383$			8.37544e48i			0.695394i	0.937607	+	0.347697i	$0.113036\pi$
$383$			8.37544e48i			0.695394i	−0.937607	+	0.347697i	$0.886964\pi$
$384$	−1.10052e49	−	1.18066e49i	−0.869569	−	0.932895i
$385$	−1.06962e49			−0.804410
$386$	1.16033e49	−	1.24845e48i	0.830656	−	0.0893745i
$387$			5.04313e48i			0.343710i
$388$	−2.55176e49	+	5.55545e48i	−1.65591	+	0.360509i
$389$	7.43652e48			0.459544			0.229772	−	0.973244i	$-0.426202\pi$
$389$	7.43652e48			0.459544			0.229772	+	0.973244i	$0.426202\pi$
$390$	1.35973e48	+	1.26375e49i	0.0800252	+	0.743762i
$391$		−	2.26839e49i		−	1.27163i
$392$	1.10804e49	−	3.69099e48i	0.591728	−	0.197110i
$393$	5.63729e48			0.286822
$394$	−1.11873e49	+	1.20370e48i	−0.542373	+	0.0583566i
$395$			9.67886e48i			0.447177i
$396$	1.91566e48	+	8.79914e48i	0.0843550	+	0.387464i
$397$	−9.64903e47			−0.0405009			−0.0202504	−	0.999795i	$-0.506446\pi$
$397$	−9.64903e47			−0.0405009			−0.0202504	+	0.999795i	$0.506446\pi$
$398$	2.44550e48	+	2.27287e49i	0.0978565	+	0.909488i
$399$		−	2.18645e49i		−	0.834169i
$400$	−1.35494e47	+	6.19324e46i	−0.00492924	+	0.00225309i
$401$	3.33372e49			1.15661			0.578304	−	0.815821i	$-0.303715\pi$
$401$	3.33372e49			1.15661			0.578304	+	0.815821i	$0.303715\pi$
$402$	−2.28499e49	+	2.45854e48i	−0.756118	+	0.0813546i
$403$		−	3.17674e49i		−	1.00273i
$404$	4.05618e49	−	8.83074e48i	1.22144	−	0.265920i
$405$	−4.28336e49			−1.23066
$406$	−8.09744e48	−	7.52584e49i	−0.222000	−	2.06329i
$407$			2.87259e49i			0.751589i
$408$	1.08218e49	+	3.24872e49i	0.270244	+	0.811278i
$409$	−7.74923e49			−1.84721			−0.923604	−	0.383348i	$-0.874771\pi$
$409$	−7.74923e49			−1.84721			−0.923604	+	0.383348i	$0.874771\pi$
$410$	6.47310e49	−	6.96474e48i	1.47306	−	0.158494i
$411$			4.28090e49i			0.930123i
$412$	5.04372e48	+	2.31671e49i	0.104641	+	0.480645i
$413$	3.83365e49			0.759558
$414$	6.71648e48	+	6.24237e49i	0.127097	+	1.18125i
$415$			5.32543e49i			0.962588i
$416$	2.92864e49	−	1.73929e49i	0.505700	−	0.300329i
$417$	−8.62688e48			−0.142321
$418$	2.04945e49	−	2.20511e48i	0.323064	−	0.0347601i
$419$		−	2.73512e49i		−	0.412013i	−0.978551	−	0.206006i	$-0.933953\pi$
$419$		−	2.73512e49i		−	0.412013i	0.978551	−	0.206006i	$-0.0660468\pi$
$420$	1.09995e50	−	2.39470e49i	1.58356	−	0.344759i
$421$	1.25744e49			0.173032			0.0865160	−	0.996250i	$-0.472427\pi$
$421$	1.25744e49			0.173032			0.0865160	+	0.996250i	$0.472427\pi$
$422$	−9.06430e48	−	8.42445e49i	−0.119233	−	1.10817i
$423$		−	7.86930e49i		−	0.989621i
$424$	−5.28766e49	+	1.76137e49i	−0.635788	+	0.211786i
$425$	3.16060e47			0.00363396
$426$	−1.02449e50	+	1.10230e49i	−1.12649	+	0.121204i
$427$		−	4.19921e49i		−	0.441609i
$428$	−4.00501e48	−	1.83960e49i	−0.0402876	−	0.185051i
$429$	−4.93410e49			−0.474809
$430$	6.35805e48	+	5.90924e49i	0.0585360	+	0.544040i
$431$			1.63530e50i			1.44055i	0.693686	+	0.720277i	$0.255985\pi$
$431$			1.63530e50i			1.44055i	−0.693686	+	0.720277i	$0.744015\pi$
$432$	2.34944e49	+	5.14004e49i	0.198049	+	0.433287i
$433$	−1.34096e50			−1.08179			−0.540897	−	0.841089i	$-0.681915\pi$
$433$	−1.34096e50			−1.08179			−0.540897	+	0.841089i	$0.681915\pi$
$434$	−2.79737e50	+	3.00983e49i	−2.15995	+	0.232401i
$435$		−	2.80248e50i		−	2.07132i
$436$	3.44817e49	−	7.50702e48i	0.243975	−	0.0531159i
$437$	1.43711e50			0.973515
$438$	1.18844e48	+	1.10455e49i	0.00770852	+	0.0716438i
$439$			1.04622e50i			0.649829i	0.945743	+	0.324914i	$0.105336\pi$
$439$			1.04622e50i			0.649829i	−0.945743	+	0.324914i	$0.894664\pi$
$440$	3.35400e49	+	1.00688e50i	0.199509	+	0.598930i
$441$	6.85782e49			0.390709
$442$	−7.18485e49	+	7.73054e48i	−0.392098	+	0.0421878i
$443$		−	4.66785e49i		−	0.244032i	−0.992528	−	0.122016i	$-0.961064\pi$
$443$		−	4.66785e49i		−	0.244032i	0.992528	−	0.122016i	$-0.0389359\pi$
$444$	−6.43123e49	−	2.95403e50i	−0.322120	−	1.47958i
$445$	−8.62589e49			−0.413965
$446$	2.04683e49	+	1.90234e50i	0.0941281	+	0.874836i
$447$			1.34857e50i			0.594335i
$448$	−1.80905e50	−	2.41410e50i	−0.764133	−	1.01970i
$449$	2.54850e50			1.03182			0.515910	−	0.856643i	$-0.327454\pi$
$449$	2.54850e50			1.03182			0.515910	+	0.856643i	$0.327454\pi$
$450$	−8.69762e47	+	9.35821e46i	−0.00337569	+	0.000363208i
$451$			2.52731e50i			0.940382i
$452$	2.90699e50	−	6.32882e49i	1.03708	−	0.225784i
$453$	6.30848e50			2.15804
$454$	−4.59725e49	−	4.27274e50i	−0.150813	−	1.40167i
$455$			2.37565e50i			0.747422i
$456$	−2.05819e50	+	6.85599e49i	−0.621087	+	0.206889i
$457$	5.57953e50			1.61507			0.807533	−	0.589823i	$-0.200802\pi$
$457$	5.57953e50			1.61507			0.807533	+	0.589823i	$0.200802\pi$
$458$	4.36001e50	−	4.69115e49i	1.21072	−	0.130267i
$459$		−	1.19899e50i		−	0.319430i
$460$	1.57399e50	+	7.22975e50i	0.402350	+	1.84810i
$461$	−4.09629e50			−1.00478			−0.502392	−	0.864640i	$-0.667547\pi$
$461$	−4.09629e50			−1.00478			−0.502392	+	0.864640i	$0.667547\pi$
$462$	4.67485e49	+	4.34485e50i	0.110045	+	1.02277i
$463$		−	2.84574e50i		−	0.642919i	−0.946923	−	0.321460i	$-0.895827\pi$
$463$		−	2.84574e50i		−	0.642919i	0.946923	−	0.321460i	$-0.104173\pi$
$464$	−6.83045e50	+	3.12210e50i	−1.48118	+	0.677026i
$465$	−1.04169e51			−2.16836
$466$	1.71612e50	−	1.84646e49i	0.342938	−	0.0368985i
$467$		−	5.27136e50i		−	1.01135i	−0.862724	−	0.505676i	$-0.831243\pi$
$467$		−	5.27136e50i		−	1.01135i	0.862724	−	0.505676i	$-0.168757\pi$
$468$	1.95430e50	−	4.25472e49i	0.360015	−	0.0783790i
$469$	−4.29542e50			−0.759839
$470$	−9.92109e49	−	9.22077e50i	−0.168539	−	1.56642i
$471$		−	6.34795e49i		−	0.103571i
$472$	−1.20211e50	−	3.60876e50i	−0.188385	−	0.565535i
$473$	−2.30716e50			−0.347309
$474$	3.93159e50	−	4.23020e49i	0.568564	−	0.0611747i
$475$			2.00236e48i			0.00278204i
$476$	1.36147e50	+	6.25357e50i	0.181750	+	0.834826i
$477$	−3.27260e50			−0.419801
$478$	6.30577e49	+	5.86064e50i	0.0777334	+	0.722463i
$479$		−	1.02379e51i		−	1.21293i	−0.795111	−	0.606464i	$-0.792588\pi$
$479$		−	1.02379e51i		−	1.21293i	0.795111	−	0.606464i	$-0.207412\pi$
$480$	−5.70331e50	−	9.60332e50i	−0.649446	−	1.09355i
$481$	6.38007e50			0.698343
$482$	7.05619e50	−	7.59211e49i	0.742466	−	0.0798857i
$483$			3.04668e51i			3.08199i
$484$	6.02082e50	−	1.31080e50i	0.585591	−	0.127489i
$485$	−1.80720e51			−1.69010
$486$	1.30536e50	+	1.21321e51i	0.117393	+	1.09106i
$487$		−	1.04852e51i		−	0.906828i	−0.891300	−	0.453414i	$-0.850206\pi$
$487$		−	1.04852e51i		−	0.906828i	0.891300	−	0.453414i	$-0.149794\pi$
$488$	−3.95288e50	+	1.31674e50i	−0.328804	+	0.109527i
$489$	−3.22529e50			−0.258048
$490$	8.03558e50	−	8.64589e49i	0.618432	−	0.0665402i
$491$		−	1.72849e50i		−	0.127973i	−0.997951	−	0.0639866i	$-0.979619\pi$
$491$		−	1.72849e50i		−	0.127973i	0.997951	−	0.0639866i	$-0.0203815\pi$
$492$	−5.65821e50	−	2.59896e51i	−0.403034	−	1.85124i
$493$	1.59330e51			1.09196
$494$	−4.89758e49	−	4.55186e50i	−0.0322976	−	0.300177i
$495$			6.23169e50i			0.395464i
$496$	1.16049e51	+	2.53889e51i	0.708745	+	1.55057i
$497$	−1.92588e51			−1.13203
$498$	2.16321e51	−	2.32751e50i	1.22389	−	0.131684i
$499$		−	1.00275e51i		−	0.546111i	−0.961998	−	0.273056i	$-0.911966\pi$
$499$		−	1.00275e51i		−	0.546111i	0.961998	−	0.273056i	$-0.0880343\pi$
$500$	−1.86871e51	+	4.06838e50i	−0.979741	+	0.213300i
$501$	3.23446e51			1.63262
$502$	2.04318e48	+	1.89896e49i	0.000992971	+	0.00922878i
$503$		−	2.34914e50i		−	0.109930i	−0.998488	−	0.0549651i	$-0.982495\pi$
$503$		−	2.34914e50i		−	0.109930i	0.998488	−	0.0549651i	$-0.0175047\pi$
$504$	−5.59823e50	−	1.68060e51i	−0.252273	−	0.757329i
$505$	2.87266e51			1.24666
$506$	−2.85579e51	+	3.07269e50i	−1.19362	+	0.128428i
$507$		−	2.07202e51i		−	0.834149i
$508$	2.48850e50	+	1.14303e51i	0.0964998	+	0.443248i
$509$	1.50917e50			0.0563768			0.0281884	−	0.999603i	$-0.491026\pi$
$509$	1.50917e50			0.0563768			0.0281884	+	0.999603i	$0.491026\pi$
$510$	2.53493e50	+	2.35599e51i	0.0912288	+	0.847890i
$511$			2.07638e50i			0.0719963i
$512$	−1.70523e51	+	2.45991e51i	−0.569709	+	0.821847i
$513$	7.59606e50			0.244545
$514$	−3.97460e51	+	4.27648e50i	−1.23309	+	0.132674i
$515$			1.64073e51i			0.490569i
$516$	2.37257e51	−	5.16533e50i	0.683713	−	0.148852i
$517$	3.60009e51			0.999983
$518$	−6.04485e50	−	5.61814e51i	−0.161853	−	1.50428i
$519$			2.90193e51i			0.749044i
$520$	2.23629e51	−	7.44927e50i	0.556499	−	0.185375i
$521$	−1.62828e51			−0.390673			−0.195336	−	0.980736i	$-0.562580\pi$
$521$	−1.62828e51			−0.390673			−0.195336	+	0.980736i	$0.562580\pi$
$522$	−4.38460e51	+	4.71761e50i	−1.01436	+	0.109140i
$523$			4.95932e51i			1.10634i	0.833067	+	0.553172i	$0.186583\pi$
$523$			4.95932e51i			1.10634i	−0.833067	+	0.553172i	$0.813417\pi$
$524$	−2.22388e50	−	1.02148e51i	−0.0478428	−	0.219754i
$525$	−4.24501e49			−0.00880748
$526$	−6.84670e50	−	6.36339e51i	−0.137010	−	1.27338i
$527$		−	5.92234e51i		−	1.14312i
$528$	3.94339e51	−	1.80247e51i	0.734218	−	0.335601i
$529$	−1.44578e52			−2.59684
$530$	−3.83463e51	+	4.12588e50i	−0.664481	+	0.0714949i
$531$		−	2.23350e51i		−	0.373414i
$532$	−3.96186e51	+	8.62540e50i	−0.639114	+	0.139142i
$533$	5.61319e51			0.873761
$534$	3.76999e50	+	3.50387e51i	0.0566313	+	0.526337i
$535$		−	1.30284e51i		−	0.188872i
$536$	1.34690e51	+	4.04344e51i	0.188454	+	0.565744i
$537$	2.86422e51			0.386808
$538$	8.46974e50	−	9.11303e49i	0.110410	−	0.0118795i
$539$			3.13735e51i			0.394800i
$540$	8.31957e50	+	3.82139e51i	0.101069	+	0.464237i
$541$	−2.05605e51			−0.241149			−0.120574	−	0.992704i	$-0.538474\pi$
$541$	−2.05605e51			−0.241149			−0.120574	+	0.992704i	$0.538474\pi$
$542$	1.39933e51	+	1.30056e52i	0.158466	+	1.47279i
$543$		−	7.81134e51i		−	0.854139i
$544$	5.45981e51	−	3.24252e51i	0.576499	−	0.342376i
$545$	2.44205e51			0.249012
$546$	9.64998e51	−	1.03829e51i	0.950312	−	0.102249i
$547$			3.96530e51i			0.377152i	0.982059	+	0.188576i	$0.0603873\pi$
$547$			3.96530e51i			0.377152i	−0.982059	+	0.188576i	$0.939613\pi$
$548$	7.75703e51	−	1.68879e51i	0.712631	−	0.155147i
$549$	−2.44648e51			−0.217104
$550$	−4.28124e48	−	3.97903e49i	−0.000367011	−	0.00341104i
$551$			1.00942e52i			0.835969i
$552$	2.86796e52	−	9.55342e51i	2.29472	−	0.764392i
$553$	7.39076e51			0.571362
$554$	1.17324e51	−	1.26235e50i	0.0876399	−	0.00942962i
$555$		−	2.09209e52i		−	1.51013i
$556$	3.40325e50	+	1.56320e51i	0.0237396	+	0.109042i
$557$	−2.49633e52			−1.68288			−0.841441	−	0.540350i	$-0.818292\pi$
$557$	−2.49633e52			−1.68288			−0.841441	+	0.540350i	$0.818292\pi$
$558$	1.75354e51	+	1.62976e52i	0.114253	+	1.06188i
$559$			5.12423e51i			0.322704i
$560$	−8.67845e51	−	1.89865e52i	−0.528287	−	1.15577i
$561$	−9.19854e51			−0.541283
$562$	−3.09713e51	+	3.33236e50i	−0.176185	+	0.0189566i
$563$			5.15392e51i			0.283451i	0.989906	+	0.141726i	$0.0452650\pi$
$563$			5.15392e51i			0.283451i	−0.989906	+	0.141726i	$0.954735\pi$
$564$	−3.70215e52	+	8.05997e51i	−1.96857	+	0.428578i
$565$	2.05878e52			1.05850
$566$	−3.30755e51	−	3.07407e52i	−0.164435	−	1.52827i
$567$			3.27077e52i			1.57243i
$568$	6.03894e51	+	1.81290e52i	0.280764	+	0.842862i
$569$	−2.78426e52			−1.25192			−0.625961	−	0.779855i	$-0.715293\pi$
$569$	−2.78426e52			−1.25192			−0.625961	+	0.779855i	$0.715293\pi$
$570$	−1.49260e52	+	1.60597e51i	−0.649116	+	0.0698417i
$571$		−	1.13401e52i		−	0.477014i	−0.971141	−	0.238507i	$-0.923342\pi$
$571$		−	1.13401e52i		−	0.477014i	0.971141	−	0.238507i	$-0.0766579\pi$
$572$	1.94647e51	+	8.94063e51i	0.0791997	+	0.363784i
$573$	6.48542e51			0.255270
$574$	−5.31826e51	−	4.94285e52i	−0.202509	−	1.88214i
$575$		−	2.79016e50i		−	0.0102788i
$576$	−1.40647e52	+	1.05396e52i	−0.501307	+	0.375663i
$577$	9.57231e51			0.330123			0.165062	−	0.986283i	$-0.447218\pi$
$577$	9.57231e51			0.330123			0.165062	+	0.986283i	$0.447218\pi$
$578$	1.63995e52	−	1.76450e51i	0.547269	−	0.0588835i
$579$		−	3.29938e52i		−	1.06547i
$580$	−5.07813e52	+	1.10556e52i	−1.58698	+	0.345503i
$581$	4.06649e52			1.22991
$582$	7.89845e51	+	7.34090e52i	0.231209	+	2.14888i
$583$		−	1.49717e52i		−	0.424197i
$584$	1.95458e51	−	6.51087e50i	0.0536054	−	0.0178564i
$585$	1.38407e52			0.367448
$586$	4.76788e52	−	5.13000e51i	1.22538	−	0.131845i
$587$		−	3.27860e52i		−	0.815764i	−0.913035	−	0.407882i	$-0.866267\pi$
$587$		−	3.27860e52i		−	0.815764i	0.913035	−	0.407882i	$-0.133733\pi$
$588$	−7.02398e51	−	3.22629e52i	−0.169205	−	0.777204i
$589$	3.75202e52			0.875134
$590$	−2.81585e51	−	2.61708e52i	−0.0635948	−	0.591057i
$591$			3.18111e52i			0.695691i
$592$	−5.09902e52	+	2.33069e52i	−1.07988	+	0.493597i
$593$	−1.87234e52			−0.384013			−0.192006	−	0.981394i	$-0.561499\pi$
$593$	−1.87234e52			−0.384013			−0.192006	+	0.981394i	$0.561499\pi$
$594$	−1.50947e52	+	1.62412e51i	−0.299835	+	0.0322607i
$595$			4.42888e52i			0.852063i
$596$	2.44363e52	−	5.32004e51i	0.455361	−	0.0991370i
$597$	6.46291e52			1.16658
$598$	6.82449e51	+	6.34275e52i	0.119329	+	1.10906i
$599$			6.44824e52i			1.09227i	0.837696	+	0.546137i	$0.183902\pi$
$599$			6.44824e52i			1.09227i	−0.837696	+	0.546137i	$0.816098\pi$
$600$	1.33110e50	+	3.99599e50i	0.00218442	+	0.00655768i
$601$	8.37720e51			0.133194			0.0665969	−	0.997780i	$-0.478786\pi$
$601$	8.37720e51			0.133194			0.0665969	+	0.997780i	$0.478786\pi$
$602$	4.51228e52	−	4.85499e51i	0.695125	−	0.0747920i
$603$			2.50253e52i			0.373552i
$604$	−2.48866e52	−	1.14310e53i	−0.359968	−	1.65342i
$605$	4.26405e52			0.597681
$606$	−1.25551e52	−	1.16688e53i	−0.170545	−	1.58507i
$607$		−	1.62298e52i		−	0.213662i	−0.994277	−	0.106831i	$-0.965930\pi$
$607$		−	1.62298e52i		−	0.213662i	0.994277	−	0.106831i	$-0.0340704\pi$
$608$	2.05425e52	+	3.45899e52i	0.262112	+	0.441348i
$609$	−2.13997e53			−2.64655
$610$	−2.86664e52	+	3.08437e51i	−0.343642	+	0.0369742i
$611$		−	7.99584e52i		−	0.929140i
$612$	3.64336e52	−	7.93199e51i	0.410417	−	0.0893522i
$613$	2.77165e52			0.302684			0.151342	−	0.988481i	$-0.451641\pi$
$613$	2.77165e52			0.302684			0.151342	+	0.988481i	$0.451641\pi$
$614$	1.43582e52	+	1.33447e53i	0.152020	+	1.41289i
$615$		−	1.84062e53i		−	1.88946i
$616$	7.68850e52	−	2.56111e52i	0.765258	−	0.254914i
$617$	−3.43615e52			−0.331630			−0.165815	−	0.986157i	$-0.553025\pi$
$617$	−3.43615e52			−0.331630			−0.165815	+	0.986157i	$0.553025\pi$
$618$	6.66471e52	−	7.17090e51i	0.623735	−	0.0671108i
$619$			1.85801e53i			1.68627i	0.537704	+	0.843134i	$0.319292\pi$
$619$			1.85801e53i			1.68627i	−0.537704	+	0.843134i	$0.680708\pi$
$620$	4.10939e52	+	1.88755e53i	0.361689	+	1.66133i
$621$	−1.05847e53			−0.903517
$622$	8.34187e51	+	7.75302e52i	0.0690631	+	0.641880i
$623$			6.58671e52i			0.528927i
$624$	−4.00330e52	−	8.75832e52i	−0.311825	−	0.682203i
$625$	−1.31628e53			−0.994551
$626$	5.41360e51	−	5.82477e50i	0.0396802	−	0.00426939i
$627$		−	5.82761e52i		−	0.414388i
$628$	−1.15026e52	+	2.50423e51i	−0.0793526	+	0.0172759i
$629$	1.18942e53			0.796112
$630$	−1.31135e52	−	1.21878e53i	−0.0851622	−	0.791506i
$631$		−	2.72301e53i		−	1.71590i	−0.513735	−	0.857949i	$-0.671739\pi$
$631$		−	2.72301e53i		−	1.71590i	0.513735	−	0.857949i	$-0.328261\pi$
$632$	−2.31750e52	−	6.95720e52i	−0.141708	−	0.425412i
$633$	−2.39549e53			−1.42143
$634$	−1.73358e53	+	1.86524e52i	−0.998267	+	0.107409i
$635$			8.09513e52i			0.452400i
$636$	3.35189e52	+	1.53961e53i	0.181805	+	0.835075i
$637$	6.96810e52			0.366830
$638$	−2.15824e52	−	2.00589e53i	−0.110282	−	1.02498i
$639$			1.12203e53i			0.556529i
$640$	−1.51514e53	+	1.41229e53i	−0.729513	+	0.679993i
$641$	6.04692e52			0.282639			0.141319	−	0.989964i	$-0.454866\pi$
$641$	6.04692e52			0.282639			0.141319	+	0.989964i	$0.454866\pi$
$642$	−5.29217e52	+	5.69411e51i	−0.240142	+	0.0258381i
$643$			5.90817e52i			0.260282i	0.991495	+	0.130141i	$0.0415430\pi$
$643$			5.90817e52i			0.260282i	−0.991495	+	0.130141i	$0.958457\pi$
$644$	5.52062e53	−	1.20190e53i	2.36133	−	0.514086i
$645$	1.68029e53			0.697830
$646$	−9.13047e51	−	8.48595e52i	−0.0368193	−	0.342202i
$647$		−	1.96965e53i		−	0.771271i	−0.922651	−	0.385635i	$-0.873982\pi$
$647$		−	1.96965e53i		−	0.771271i	0.922651	−	0.385635i	$-0.126018\pi$
$648$	3.07890e53	−	1.02561e53i	1.17077	−	0.389992i
$649$	1.02179e53			0.377324
$650$	−8.83749e50	+	9.50870e49i	−0.00316938	+	0.000341010i
$651$			7.95431e53i			2.77053i
$652$	1.27236e52	+	5.84426e52i	0.0430432	+	0.197708i
$653$	5.40162e53			1.77490			0.887449	−	0.460906i	$-0.152475\pi$
$653$	5.40162e53			1.77490			0.887449	+	0.460906i	$0.152475\pi$
$654$	−1.06731e52	−	9.91969e52i	−0.0340654	−	0.316607i
$655$		−	7.23431e52i		−	0.224291i
$656$	−4.48613e53	+	2.05055e53i	−1.35113	+	0.617585i
$657$	1.20971e52			0.0353949
$658$	−7.04096e53	+	7.57573e52i	−2.00143	+	0.215344i
$659$		−	2.00451e53i		−	0.553587i	−0.960929	−	0.276794i	$-0.910728\pi$
$659$		−	2.00451e53i		−	0.553587i	0.960929	−	0.276794i	$-0.0892718\pi$
$660$	2.93173e53	−	6.38268e52i	0.786664	−	0.171265i
$661$	3.12269e53			0.814144			0.407072	−	0.913396i	$-0.366550\pi$
$661$	3.12269e53			0.814144			0.407072	+	0.913396i	$0.366550\pi$
$662$	7.57195e52	+	7.03745e53i	0.191825	+	1.78284i
$663$			2.04301e53i			0.502937i
$664$	−1.27512e53	−	3.82794e53i	−0.305040	−	0.915738i
$665$	−2.80586e53			−0.652311
$666$	−3.27316e53	+	3.52176e52i	−0.739532	+	0.0795701i
$667$		−	1.40656e54i		−	3.08865i
$668$	−1.27597e53	−	5.86087e53i	−0.272326	−	1.25086i
$669$	5.40931e53			1.12214
$670$	3.15503e52	+	2.93232e53i	0.0636183	+	0.591275i
$671$		−	1.11923e53i		−	0.219377i
$672$	−7.33308e53	+	4.35503e53i	−1.39724	+	0.829803i
$673$	−1.40702e53			−0.260624			−0.130312	−	0.991473i	$-0.541598\pi$
$673$	−1.40702e53			−0.260624			−0.130312	+	0.991473i	$0.541598\pi$
$674$	7.29837e53	−	7.85269e52i	1.31428	−	0.141410i
$675$		−	1.47478e51i		−	0.00258200i
$676$	−3.75453e53	+	8.17401e52i	−0.639099	+	0.139139i
$677$	−9.24747e53			−1.53052			−0.765258	−	0.643723i	$-0.777389\pi$
$677$	−9.24747e53			−1.53052			−0.765258	+	0.643723i	$0.777389\pi$
$678$	−8.99799e52	−	8.36283e53i	−0.144804	−	1.34583i
$679$			1.37997e54i			2.15946i
$680$	4.16907e53	−	1.38875e53i	0.634410	−	0.211327i
$681$	−1.21495e54			−1.79789
$682$	−7.45592e53	+	8.02220e52i	−1.07300	+	0.115449i
$683$			7.94333e53i			1.11176i	0.831264	+	0.555878i	$0.187618\pi$
$683$			7.94333e53i			1.11176i	−0.831264	+	0.555878i	$0.812382\pi$
$684$	5.02521e52	+	2.30821e53i	0.0684050	+	0.314202i
$685$	5.49366e53			0.727345
$686$	3.98332e52	+	3.70214e53i	0.0512964	+	0.476754i
$687$		−	1.23977e54i		−	1.55297i
$688$	−1.87192e53	−	4.09534e53i	−0.228091	−	0.499011i
$689$	−3.32523e53			−0.394145
$690$	2.07986e54	−	2.23782e53i	2.39828	−	0.258043i
$691$			5.60269e53i			0.628512i	0.949338	+	0.314256i	$0.101755\pi$
$691$			5.60269e53i			0.628512i	−0.949338	+	0.314256i	$0.898245\pi$
$692$	5.25833e53	−	1.14479e53i	0.573894	−	0.124943i
$693$	4.75851e53			0.505288
$694$	−1.23649e53	−	1.14921e54i	−0.127750	−	1.18732i
$695$			1.10708e53i			0.111293i
$696$	6.71026e53	+	2.01444e54i	0.656393	+	1.97051i
$697$	1.04646e54			0.996089
$698$	1.02586e54	−	1.10377e53i	0.950242	−	0.102241i
$699$		−	4.87979e53i		−	0.439880i
$700$	1.67463e51	+	7.69200e51i	0.00146912	+	0.00674802i
$701$	3.82771e53			0.326811			0.163405	−	0.986559i	$-0.447752\pi$
$701$	3.82771e53			0.326811			0.163405	+	0.986559i	$0.447752\pi$
$702$	3.60718e52	+	3.35255e53i	0.0299753	+	0.278593i
$703$			7.53543e53i			0.609477i
$704$	−4.82173e53	−	6.43439e53i	−0.379597	−	0.506556i
$705$	−2.62192e54			−2.00922
$706$	2.86850e53	−	3.08636e52i	0.213976	−	0.0230228i
$707$		−	2.19355e54i		−	1.59287i
$708$	−1.05076e54	+	2.28762e53i	−0.742801	+	0.161716i
$709$	2.39700e54			1.64964			0.824822	−	0.565392i	$-0.191275\pi$
$709$	2.39700e54			1.64964			0.824822	+	0.565392i	$0.191275\pi$
$710$	1.41458e53	+	1.31472e54i	0.0947804	+	0.880899i
$711$		−	4.30590e53i		−	0.280893i
$712$	6.20032e53	−	2.06538e53i	0.393817	−	0.131184i
$713$	−5.22822e54			−3.23335
$714$	1.79903e54	−	1.93567e53i	1.08336	−	0.116564i
$715$			6.33190e53i			0.371295i
$716$	−1.12992e53	−	5.19000e53i	−0.0645207	−	0.296360i
$717$	1.66647e54			0.926690
$718$	1.47629e53	+	1.37208e54i	0.0799481	+	0.743045i
$719$			1.91513e54i			1.01007i	0.863100	+	0.505033i	$0.168520\pi$
$719$			1.91513e54i			1.01007i	−0.863100	+	0.505033i	$0.831480\pi$
$720$	−1.10616e54	+	5.05612e53i	−0.568201	+	0.259717i
$721$	1.25286e54			0.626805
$722$	−1.50275e54	+	1.61688e53i	−0.732283	+	0.0787901i
$723$		−	2.00642e54i		−	0.952347i
$724$	−1.41542e54	+	3.08152e53i	−0.654415	+	0.142473i
$725$	1.95979e52			0.00882649
$726$	−1.86362e53	−	1.73207e54i	−0.0817641	−	0.759924i
$727$			7.02587e53i			0.300294i	0.988664	+	0.150147i	$0.0479747\pi$
$727$			7.02587e53i			0.300294i	−0.988664	+	0.150147i	$0.952025\pi$
$728$	−5.68825e53	−	1.70763e54i	−0.236855	−	0.711044i
$729$	4.07890e53			0.165470
$730$	1.41747e53	−	1.52513e52i	0.0560246	−	0.00602797i
$731$			9.55301e53i			0.367883i
$732$	2.50576e53	+	1.15096e54i	0.0940219	+	0.431867i
$733$	4.89872e54			1.79105			0.895524	−	0.445012i	$-0.146801\pi$
$733$	4.89872e54			1.79105			0.895524	+	0.445012i	$0.146801\pi$
$734$	−2.62176e53	−	2.43669e54i	−0.0934046	−	0.868112i
$735$		−	2.28492e54i		−	0.793251i
$736$	−2.86248e54	−	4.81989e54i	−0.968421	−	1.63064i
$737$	−1.14487e54			−0.377463
$738$	−2.87973e54	+	3.09845e53i	−0.925297	+	0.0995574i
$739$			5.19784e54i			1.62772i	0.581064	+	0.813858i	$0.302636\pi$
$739$			5.19784e54i			1.62772i	−0.581064	+	0.813858i	$0.697364\pi$
$740$	−3.79089e54	+	8.25317e53i	−1.15701	+	0.251894i
$741$	−1.29432e54			−0.385031
$742$	3.15051e53	+	2.92812e54i	0.0913497	+	0.849013i
$743$			3.61825e54i			1.02261i	0.859398	+	0.511307i	$0.170838\pi$
$743$			3.61825e54i			1.02261i	−0.859398	+	0.511307i	$0.829162\pi$
$744$	7.48769e54	−	2.49421e54i	2.06282	−	0.687144i
$745$	1.73062e54			0.464763
$746$	−4.34644e54	+	4.67656e53i	−1.13788	+	0.122430i
$747$		−	2.36916e54i		−	0.604648i
$748$	3.62877e53	+	1.66679e54i	0.0902877	+	0.414715i
$749$	−9.94843e53			−0.241324
$750$	5.78421e53	+	5.37590e54i	0.136798	+	1.27142i
$751$		−	6.21252e54i		−	1.43255i	−0.697819	−	0.716274i	$-0.745846\pi$
$751$		−	6.21252e54i		−	1.43255i	0.697819	−	0.716274i	$-0.254154\pi$
$752$	2.92095e54	+	6.39037e54i	0.656727	+	1.43677i
$753$	5.39968e52			0.0118376
$754$	−4.45511e54	+	4.79348e53i	−0.952363	+	0.102470i
$755$		−	8.09565e54i		−	1.68756i
$756$	2.91801e54	−	6.35281e53i	0.593160	−	0.129137i
$757$	9.25923e54			1.83549			0.917747	−	0.397165i	$-0.130006\pi$
$757$	9.25923e54			1.83549			0.917747	+	0.397165i	$0.130006\pi$
$758$	−9.37631e53	−	8.71444e54i	−0.181266	−	1.68471i
$759$			8.12043e54i			1.53104i
$760$	8.79826e53	+	2.64126e54i	0.161785	+	0.485683i
$761$	−4.61983e54			−0.828548			−0.414274	−	0.910152i	$-0.635964\pi$
$761$	−4.61983e54			−0.828548			−0.414274	+	0.910152i	$0.635964\pi$
$762$	3.28827e54	−	3.53802e53i	0.575206	−	0.0618893i
$763$		−	1.86474e54i		−	0.318165i
$764$	−2.55846e53	−	1.17516e54i	−0.0425799	−	0.195580i
$765$	2.58029e54			0.418891
$766$	−4.69754e53	−	4.36594e54i	−0.0743916	−	0.691404i
$767$		−	2.26942e54i		−	0.350593i
$768$	6.39897e54	+	5.53731e54i	0.964378	+	0.834517i
$769$	6.21880e54			0.914337			0.457168	−	0.889380i	$-0.348864\pi$
$769$	6.21880e54			0.914337			0.457168	+	0.889380i	$0.348864\pi$
$770$	5.57573e54	−	5.99921e53i	0.799794	−	0.0860539i
$771$			1.13018e55i			1.58166i
$772$	−5.97851e54	+	1.30159e54i	−0.816328	+	0.177723i
$773$	−9.51269e54			−1.26734			−0.633670	−	0.773604i	$-0.718452\pi$
$773$	−9.51269e54			−1.26734			−0.633670	+	0.773604i	$0.718452\pi$
$774$	−2.82855e53	−	2.62888e54i	−0.0367693	−	0.341738i
$775$		−	7.28458e52i		−	0.00924001i
$776$	1.29902e55	−	4.32715e54i	1.60784	−	0.535586i
$777$	−1.59752e55			−1.92951
$778$	−3.87651e54	+	4.17093e53i	−0.456907	+	0.0491610i
$779$			6.62968e54i			0.762572i
$780$	−1.41760e54	−	6.51141e54i	−0.159132	−	0.730933i
$781$	−5.13311e54			−0.562356
$782$	1.27228e54	+	1.18247e55i	0.136036	+	1.26433i
$783$		−	7.43459e54i		−	0.775861i
$784$	−5.56899e54	+	2.54551e54i	−0.567246	+	0.259280i
$785$	−8.14630e53			−0.0809910
$786$	−2.93860e54	+	3.16179e53i	−0.285176	+	0.0306835i
$787$		−	1.00037e54i		−	0.0947636i	−0.998877	−	0.0473818i	$-0.984912\pi$
$787$		−	1.00037e54i		−	0.0947636i	0.998877	−	0.0473818i	$-0.0150878\pi$
$788$	5.76420e54	−	1.25493e54i	0.533017	−	0.116043i
$789$	−1.80943e55			−1.63335
$790$	−5.42859e53	−	5.04539e54i	−0.0478379	−	0.444611i
$791$		−	1.57208e55i		−	1.35245i
$792$	−1.49211e54	−	4.47936e54i	−0.125321	−	0.376217i
$793$	−2.48583e54			−0.203836
$794$	5.02984e53	−	5.41186e52i	0.0402684	−	0.00433269i
$795$			1.09038e55i			0.852317i
$796$	−2.54958e54	−	1.17109e55i	−0.194590	−	0.893801i
$797$	−2.22747e54			−0.165998			−0.0829992	−	0.996550i	$-0.526450\pi$
$797$	−2.22747e54			−0.165998			−0.0829992	+	0.996550i	$0.526450\pi$
$798$	1.22631e54	+	1.13975e55i	0.0892374	+	0.829382i
$799$		−	1.49065e55i		−	1.05922i
$800$	6.71566e52	−	3.98835e52i	0.00465992	−	0.00276748i
$801$	3.83746e54			0.260031
$802$	−1.73780e55	+	1.86979e54i	−1.14997	+	0.123731i
$803$			5.53426e53i			0.0357655i
$804$	1.17733e55	−	2.56317e54i	0.743076	−	0.161775i
$805$	3.90980e55			2.41008
$806$	1.78174e54	+	1.65597e55i	0.107270	+	0.996981i
$807$		−	2.40837e54i		−	0.141620i
$808$	−2.06488e55	+	6.87828e54i	−1.18598	+	0.395061i
$809$	5.36292e54			0.300870			0.150435	−	0.988620i	$-0.451933\pi$
$809$	5.36292e54			0.300870			0.150435	+	0.988620i	$0.451933\pi$
$810$	2.23283e55	−	2.40241e54i	1.22360	−	0.131653i
$811$			2.26902e55i			1.21463i	0.794462	+	0.607314i	$0.207753\pi$
$811$			2.26902e55i			1.21463i	−0.794462	+	0.607314i	$0.792247\pi$
$812$	8.44205e54	+	3.87765e55i	0.441452	+	2.02770i
$813$	3.69812e55			1.88913
$814$	−1.61115e54	−	1.49742e55i	−0.0804032	−	0.747276i
$815$			4.13900e54i			0.201790i
$816$	−7.46328e54	−	1.63280e55i	−0.355481	−	0.777712i
$817$	−6.05218e54			−0.281639
$818$	4.03951e55	−	4.34632e54i	1.83661	−	0.197610i
$819$		−	1.05687e55i		−	0.469492i
$820$	−3.33523e55	+	7.26115e54i	−1.44765	+	0.315168i
$821$	−8.38021e54			−0.355414			−0.177707	−	0.984083i	$-0.556868\pi$
$821$	−8.38021e54			−0.355414			−0.177707	+	0.984083i	$0.556868\pi$
$822$	−2.40103e54	−	2.23154e55i	−0.0995024	−	0.924785i
$823$			3.09277e55i			1.25242i	0.779653	+	0.626212i	$0.215396\pi$
$823$			3.09277e55i			1.25242i	−0.779653	+	0.626212i	$0.784604\pi$
$824$	−3.92856e54	−	1.17936e55i	−0.155459	−	0.466692i
$825$	−1.13144e53			−0.00437527
$826$	−1.99840e55	+	2.15018e54i	−0.755199	+	0.0812557i
$827$		−	5.17202e54i		−	0.191010i	−0.995429	−	0.0955048i	$-0.969553\pi$
$827$		−	5.17202e54i		−	0.191010i	0.995429	−	0.0955048i	$-0.0304465\pi$
$828$	−7.00233e54	−	3.21635e55i	−0.252735	−	1.16088i
$829$	7.71739e53			0.0272229			0.0136114	−	0.999907i	$-0.495667\pi$
$829$	7.71739e53			0.0272229			0.0136114	+	0.999907i	$0.495667\pi$
$830$	−2.98688e54	−	2.77604e55i	−0.102975	−	0.957064i
$831$		−	3.33611e54i		−	0.112414i
$832$	−1.42909e55	+	1.07091e55i	−0.470669	+	0.352705i
$833$	1.29905e55			0.418187
$834$	4.49702e54	−	4.83857e53i	0.141504	−	0.0152252i
$835$		−	4.15076e55i		−	1.27669i
$836$	−1.05597e55	+	2.29896e54i	−0.317491	+	0.0691212i
$837$	−2.76345e55			−0.812209
$838$	1.53405e54	+	1.42576e55i	0.0440761	+	0.409648i
$839$			5.50494e55i			1.54624i	0.634263	+	0.773118i	$0.281304\pi$
$839$			5.50494e55i			1.54624i	−0.634263	+	0.773118i	$0.718696\pi$
$840$	−5.59949e55	+	1.86524e55i	−1.53759	+	0.512186i
$841$	6.15462e55			1.65226
$842$	−6.55476e54	+	7.05260e53i	−0.172039	+	0.0185106i
$843$			8.80667e54i			0.225989i
$844$	9.45006e54	+	4.34065e55i	0.237098	+	1.08905i
$845$	−2.65902e55			−0.652295
$846$	4.41366e54	+	4.10210e55i	0.105867	+	0.983942i
$847$		−	3.25602e55i		−	0.763663i
$848$	2.65756e55	−	1.21473e55i	0.609483	−	0.278586i
$849$	−8.74110e55			−1.96029
$850$	−1.64756e53	+	1.77269e52i	−0.00361310	+	0.000388752i
$851$		−	1.05002e56i		−	2.25183i
$852$	5.27864e55	−	1.14921e55i	1.10706	−	0.241018i
$853$	−8.25808e53			−0.0169374			−0.00846872	−	0.999964i	$-0.502696\pi$
$853$	−8.25808e53			−0.0169374			−0.00846872	+	0.999964i	$0.502696\pi$
$854$	2.35522e54	+	2.18896e55i	0.0472423	+	0.439075i
$855$			1.63471e55i			0.320689i
$856$	3.11951e54	+	9.36483e54i	0.0598528	+	0.179679i
$857$	3.68402e55			0.691331			0.345666	−	0.938358i	$-0.387653\pi$
$857$	3.68402e55			0.691331			0.345666	+	0.938358i	$0.387653\pi$
$858$	2.57204e55	−	2.76739e54i	0.472084	−	0.0507940i
$859$			3.04325e55i			0.546345i	0.961965	+	0.273172i	$0.0880730\pi$
$859$			3.04325e55i			0.546345i	−0.961965	+	0.273172i	$0.911927\pi$
$860$	−6.62864e54	−	3.04470e55i	−0.116400	−	0.534656i
$861$	−1.40550e56			−2.41418
$862$	−9.17193e54	−	8.52449e55i	−0.154107	−	1.43229i
$863$			7.58901e55i			1.24733i	0.781693	+	0.623663i	$0.214356\pi$
$863$			7.58901e55i			1.24733i	−0.781693	+	0.623663i	$0.785644\pi$
$864$	−1.51301e55	−	2.54763e55i	−0.243265	−	0.409614i
$865$	3.72403e55			0.585744
$866$	6.99012e55	−	7.52103e54i	1.07559	−	0.115728i
$867$		−	4.66319e55i		−	0.701972i
$868$	1.44133e56	−	3.13792e55i	2.12270	−	0.462134i
$869$	1.96988e55			0.283834
$870$	1.57183e55	+	1.46088e56i	0.221585	+	2.05943i
$871$			2.54278e55i			0.350722i
$872$	−1.75535e55	+	5.84723e54i	−0.236892	+	0.0789109i
$873$	8.03980e55			1.06163
$874$	−7.49136e55	+	8.06034e54i	−0.967929	+	0.104144i
$875$			1.01058e56i			1.27767i
$876$	−1.23902e54	−	5.69115e54i	−0.0153286	−	0.0704080i
$877$	−7.68908e55			−0.930855			−0.465427	−	0.885086i	$-0.654099\pi$
$877$	−7.68908e55			−0.930855			−0.465427	+	0.885086i	$0.654099\pi$
$878$	−5.86797e54	−	5.45375e55i	−0.0695172	−	0.646100i
$879$		−	1.35574e56i		−	1.57177i
$880$	−2.31310e55	−	5.06053e55i	−0.262436	−	0.574150i
$881$	5.04962e54			0.0560681			0.0280341	−	0.999607i	$-0.491075\pi$
$881$	5.04962e54			0.0560681			0.0280341	+	0.999607i	$0.491075\pi$
$882$	−3.57484e55	+	3.84635e54i	−0.388467	+	0.0417971i
$883$			2.61388e55i			0.277992i	0.990293	+	0.138996i	$0.0443875\pi$
$883$			2.61388e55i			0.277992i	−0.990293	+	0.138996i	$0.955612\pi$
$884$	3.70195e55	−	8.05954e54i	0.385334	−	0.0838914i
$885$	−7.44167e55			−0.758138
$886$	2.61806e54	+	2.43325e55i	0.0261059	+	0.242631i
$887$			8.03525e55i			0.784243i	0.919913	+	0.392122i	$0.128259\pi$
$887$			8.03525e55i			0.784243i	−0.919913	+	0.392122i	$0.871741\pi$
$888$	5.00930e55	+	1.50380e56i	0.478554	+	1.43663i
$889$	6.18142e55			0.578036
$890$	4.49650e55	−	4.83801e54i	0.411589	−	0.0442850i
$891$			8.71769e55i			0.781133i
$892$	−2.13394e55	−	9.80172e55i	−0.187176	−	0.859746i
$893$	9.44381e55			0.810904
$894$	−7.56376e54	−	7.02983e55i	−0.0635806	−	0.590925i
$895$		−	3.67564e55i		−	0.302479i
$896$	1.07842e56	+	1.15696e56i	0.868833	+	0.932106i
$897$	1.80356e56			1.42257
$898$	−1.32848e56	+	1.42938e55i	−1.02590	+	0.110382i
$899$		−	3.67227e56i		−	2.77651i
$900$	4.48140e53	−	9.75649e52i	0.00331746	−	0.000722247i
$901$	−6.19915e55			−0.449326
$902$	−1.41749e55	−	1.31743e56i	−0.100600	−	0.934985i
$903$		−	1.28307e56i		−	0.891624i
$904$	−1.47986e56	+	4.92953e55i	−1.00698	+	0.335433i
$905$	−1.00243e56			−0.667927
$906$	−3.28848e56	+	3.53825e55i	−2.14565	+	0.230862i
$907$			2.22949e56i			1.42452i	0.701918	+	0.712258i	$0.252327\pi$
$907$			2.22949e56i			1.42452i	−0.701918	+	0.712258i	$0.747673\pi$
$908$	4.79291e55	+	2.20150e56i	0.299894	+	1.37749i
$909$	−1.27798e56			−0.783086
$910$	−1.33243e55	−	1.23838e56i	−0.0799575	−	0.743133i
$911$			1.13569e56i			0.667440i	0.942672	+	0.333720i	$0.108304\pi$
$911$			1.13569e56i			0.667440i	−0.942672	+	0.333720i	$0.891696\pi$
$912$	1.03444e56	−	4.72826e55i	0.595390	−	0.272145i
$913$	1.08385e56			0.610979
$914$	−2.90850e56	+	3.12940e55i	−1.60580	+	0.172776i
$915$			8.15129e55i			0.440784i
$916$	−2.24647e56	+	4.89080e55i	−1.18983	+	0.259040i
$917$	−5.52411e55			−0.286579
$918$	6.72480e54	+	6.25010e55i	0.0341719	+	0.317597i
$919$			5.09000e55i			0.253351i	0.991944	+	0.126676i	$0.0404307\pi$
$919$			5.09000e55i			0.253351i	−0.991944	+	0.126676i	$0.959569\pi$
$920$	−1.22599e56	−	3.68044e56i	−0.597746	−	1.79445i
$921$	3.79456e56			1.81229
$922$	2.13531e56	−	2.29749e55i	0.999018	−	0.107489i
$923$			1.14007e56i			0.522516i
$924$	−4.87380e55	−	2.23866e56i	−0.218827	−	1.00513i
$925$	1.46301e54			0.00643510
$926$	1.59609e55	+	1.48343e56i	0.0687780	+	0.639230i
$927$		−	7.29923e55i		−	0.308150i
$928$	3.38546e56	−	2.01059e56i	1.40025	−	0.831594i
$929$	−3.46567e55			−0.140439			−0.0702197	−	0.997532i	$-0.522370\pi$
$929$	−3.46567e55			−0.140439			−0.0702197	+	0.997532i	$0.522370\pi$
$930$	5.43010e56	−	5.84252e55i	2.15592	−	0.231966i
$931$			8.22996e55i			0.320150i
$932$	−8.84223e55	+	1.92505e55i	−0.337023	+	0.0733734i
$933$	2.20457e56			0.823327
$934$	2.95655e55	+	2.74785e56i	0.108192	+	1.00555i
$935$			1.18044e56i			0.423277i
$936$	−9.94873e55	+	3.31401e55i	−0.349564	+	0.116443i
$937$	−6.42395e55			−0.221182			−0.110591	−	0.993866i	$-0.535274\pi$
$937$	−6.42395e55			−0.221182			−0.110591	+	0.993866i	$0.535274\pi$
$938$	2.23911e56	−	2.40918e55i	0.755478	−	0.0812858i
$939$		−	1.53936e55i		−	0.0508971i
$940$	1.03433e56	+	4.75095e56i	0.335143	+	1.53940i
$941$	−5.20051e56			−1.65136			−0.825682	−	0.564135i	$-0.809210\pi$
$941$	−5.20051e56			−1.65136			−0.825682	+	0.564135i	$0.809210\pi$
$942$	3.56038e54	+	3.30906e55i	0.0110797	+	0.102976i
$943$		−	9.23807e56i		−	2.81747i
$944$	8.29038e55	+	1.81375e56i	0.247803	+	0.542137i
$945$	2.06658e56			0.605407
$946$	1.20267e56	−	1.29402e55i	0.345316	−	0.0371543i
$947$			2.24906e56i			0.632923i	0.948605	+	0.316462i	$0.102495\pi$
$947$			2.24906e56i			0.632923i	−0.948605	+	0.316462i	$0.897505\pi$
$948$	−2.02573e56	+	4.41023e55i	−0.558757	+	0.121647i
$949$	1.22917e55			0.0332317
$950$	−1.12306e53	−	1.04379e54i	−0.000297616	−	0.00276607i
$951$			4.92942e56i			1.28046i
$952$	−1.06045e56	−	3.18349e56i	−0.270015	−	0.810592i
$953$	2.70444e56			0.675012			0.337506	−	0.941323i	$-0.390417\pi$
$953$	2.70444e56			0.675012			0.337506	+	0.941323i	$0.390417\pi$
$954$	1.70594e56	−	1.83551e55i	0.417392	−	0.0449093i
$955$		−	8.32271e55i		−	0.199618i
$956$	−6.57413e55	−	3.01967e56i	−0.154575	−	0.710001i
$957$	−5.70374e56			−1.31472
$958$	5.74212e55	+	5.33679e56i	0.129756	+	1.20597i
$959$		−	4.19495e56i		−	0.929336i
$960$	3.51164e56	+	4.68613e56i	0.762704	+	1.01780i
$961$	−8.95369e56			−1.90659
$962$	−3.32580e56	+	3.57839e55i	−0.694336	+	0.0747071i
$963$			5.79601e55i			0.118640i
$964$	−3.63566e56	+	7.91522e55i	−0.729659	+	0.158854i
$965$	−4.23408e56			−0.833183
$966$	−1.70880e56	−	1.58817e57i	−0.329705	−	3.06431i
$967$			6.06480e56i			1.14740i	0.819066	+	0.573699i	$0.194492\pi$
$967$			6.06480e56i			1.14740i	−0.819066	+	0.573699i	$0.805508\pi$
$968$	−3.06501e56	+	1.02098e56i	−0.568592	+	0.189403i
$969$	−2.41298e56			−0.438936
$970$	9.42055e56	−	1.01360e56i	1.68040	−	0.180803i
$971$		−	8.08233e56i		−	1.41375i	−0.707340	−	0.706873i	$-0.750105\pi$
$971$		−	8.08233e56i		−	1.41375i	0.707340	−	0.706873i	$-0.249895\pi$
$972$	−1.36091e56	−	6.25102e56i	−0.233438	−	1.07224i
$973$	8.45367e55			0.142201
$974$	5.88082e55	+	5.46570e56i	0.0970103	+	0.901624i
$975$			2.51294e54i			0.00406531i
$976$	1.98670e56	−	9.08093e55i	0.315200	−	0.144073i
$977$	5.76887e56			0.897623			0.448811	−	0.893627i	$-0.351848\pi$
$977$	5.76887e56			0.897623			0.448811	+	0.893627i	$0.351848\pi$
$978$	1.68128e56	−	1.80897e55i	0.256567	−	0.0276054i
$979$			1.75558e56i			0.262754i
$980$	−4.14029e56	+	9.01385e55i	−0.607764	+	0.132317i
$981$	−1.08641e56			−0.156417
$982$	9.69460e54	+	9.01026e55i	0.0136903	+	0.127239i
$983$			5.52329e56i			0.765034i	0.923948	+	0.382517i	$0.124943\pi$
$983$			5.52329e56i			0.765034i	−0.923948	+	0.382517i	$0.875057\pi$
$984$	4.40719e56	+	1.32305e57i	0.598762	+	1.79750i
$985$	4.08230e56			0.544023
$986$	−8.30557e56	+	8.93639e55i	−1.08570	+	0.116816i
$987$			2.00209e57i			2.56719i
$988$	5.10602e55	+	2.34532e56i	0.0642244	+	0.294999i
$989$	8.43335e56			1.04057
$990$	−3.49518e55	−	3.24845e56i	−0.0423058	−	0.393195i
$991$		−	1.19721e57i		−	1.42158i	−0.703406	−	0.710788i	$-0.748338\pi$
$991$		−	1.19721e57i		−	1.42158i	0.703406	−	0.710788i	$-0.251662\pi$
$992$	−7.47339e56	−	1.25838e57i	−0.870554	−	1.46585i
$993$	2.00110e57			2.28682
$994$	1.00392e57	−	1.08017e56i	1.12553	−	0.121102i
$995$		−	8.29383e56i		−	0.912255i
$996$	−1.11458e57	+	2.42656e56i	−1.20277	+	0.261857i
$997$	−1.00088e57			−1.05968			−0.529841	−	0.848097i	$-0.677749\pi$
$997$	−1.00088e57			−1.05968			−0.529841	+	0.848097i	$0.677749\pi$
$998$	5.62412e55	+	5.22711e56i	0.0584217	+	0.542977i
$999$		−	5.55002e56i		−	0.565654i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.39.b.a.3.2	yes	18
4.3	odd	2	inner	4.39.b.a.3.1	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.39.b.a.3.1	✓	18	4.3	odd	2	inner
4.39.b.a.3.2	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)

\(f(q)\)	\(=\)	\(q+(-521279. + 56087.1i) q^{2} +1.48226e9i q^{3} +(2.68586e11 - 5.84741e10i) q^{4} +1.90217e13 q^{5} +(-8.31355e13 - 7.72670e14i) q^{6} -1.45250e16i q^{7} +(-1.36729e17 + 4.55456e16i) q^{8} -8.46232e17 q^{9} +O(q^{10})\)	\(q+(-521279. + 56087.1i) q^{2} +1.48226e9i q^{3} +(2.68586e11 - 5.84741e10i) q^{4} +1.90217e13 q^{5} +(-8.31355e13 - 7.72670e14i) q^{6} -1.45250e16i q^{7} +(-1.36729e17 + 4.55456e16i) q^{8} -8.46232e17 q^{9} +(-9.91563e18 + 1.06687e18i) q^{10} -3.87139e19i q^{11} +(8.66736e19 + 3.98114e20i) q^{12} -8.59840e20 q^{13} +(8.14663e20 + 7.57156e21i) q^{14} +2.81951e22i q^{15} +(6.87194e22 - 3.14107e22i) q^{16} -1.60298e23 q^{17} +(4.41123e23 - 4.74627e22i) q^{18} -1.01555e24i q^{19} +(5.10898e24 - 1.11228e24i) q^{20} +2.15297e25 q^{21} +(2.17135e24 + 2.01807e25i) q^{22} +1.41511e26i q^{23} +(-6.75102e25 - 2.02667e26i) q^{24} -1.97170e24 q^{25} +(4.48217e26 - 4.82260e25i) q^{26} +7.47975e26i q^{27} +(-8.49334e26 - 3.90121e27i) q^{28} -9.93962e27 q^{29} +(-1.58138e27 - 1.46975e28i) q^{30} +3.69457e28i q^{31} +(-3.40603e28 + 2.02280e28i) q^{32} +5.73839e28 q^{33} +(8.35602e28 - 8.99067e27i) q^{34} -2.76290e29i q^{35} +(-2.27286e29 + 4.94827e28i) q^{36} -7.42006e29 q^{37} +(5.69592e28 + 5.29385e29i) q^{38} -1.27450e30i q^{39} +(-2.60082e30 + 8.66355e29i) q^{40} -6.52818e30 q^{41} +(-1.12230e31 + 1.20754e30i) q^{42} -5.95952e30i q^{43} +(-2.26376e30 - 1.03980e31i) q^{44} -1.60968e31 q^{45} +(-7.93693e30 - 7.37666e31i) q^{46} +9.29922e31i q^{47} +(4.65587e31 + 1.01860e32i) q^{48} -8.10395e31 q^{49} +(1.02781e30 - 1.10587e29i) q^{50} -2.37603e32i q^{51} +(-2.30941e32 + 5.02784e31i) q^{52} +3.86726e32 q^{53} +(-4.19518e31 - 3.89904e32i) q^{54} -7.36405e32i q^{55} +(6.61547e32 + 1.98598e33i) q^{56} +1.50530e33 q^{57} +(5.18132e33 - 5.57484e32i) q^{58} +2.63935e33i q^{59} +(1.64868e33 + 7.57281e33i) q^{60} +2.89103e33 q^{61} +(-2.07218e33 - 1.92590e34i) q^{62} +1.22915e34i q^{63} +(1.66204e34 - 1.24548e34i) q^{64} -1.63557e34 q^{65} +(-2.99130e34 + 3.21849e33i) q^{66} -2.95727e34i q^{67} +(-4.30540e34 + 9.37330e33i) q^{68} -2.09755e35 q^{69} +(1.54963e34 + 1.44024e35i) q^{70} -1.32591e35i q^{71} +(1.15704e35 - 3.85421e34i) q^{72} -1.42953e34 q^{73} +(3.86792e35 - 4.16170e34i) q^{74} -2.92256e33i q^{75} +(-5.93833e34 - 2.72763e35i) q^{76} -5.62317e35 q^{77} +(7.14832e34 + 6.64372e35i) q^{78} +5.08832e35i q^{79} +(1.30716e36 - 5.97486e35i) q^{80} -2.25183e36 q^{81} +(3.40300e36 - 3.66147e35i) q^{82} +2.79965e36i q^{83} +(5.78259e36 - 1.25893e36i) q^{84} -3.04915e36 q^{85} +(3.34252e35 + 3.10657e36i) q^{86} -1.47331e37i q^{87} +(1.76324e36 + 5.29330e36i) q^{88} -4.53475e36 q^{89} +(8.39093e36 - 9.02823e35i) q^{90} +1.24891e37i q^{91} +(8.27471e36 + 3.80078e37i) q^{92} -5.47630e37 q^{93} +(-5.21566e36 - 4.84749e37i) q^{94} -1.93175e37i q^{95} +(-2.99831e37 - 5.04861e37i) q^{96} -9.50070e37 q^{97} +(4.22442e37 - 4.54527e36i) q^{98} +3.27609e37i 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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