LMFDB - Embedded newform 4.43.b.a.3.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,43,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, 43, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 43);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 43 $
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:	$44.6910828688$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 10 x^{19} + \cdots + 58\!\cdots\!00 $ x^20 - 10x^19 + 5706153082570973323x^18 - 51355377743138759622x^17 + 13343173699766809979413665939112009554x^16 - 106745389598134478671254098668417526292x^15 + 16693561135686664895777023363809349450836742088201197926x^14 - 116854927949806652402394845579312073483103768875776598924x^13 + 12284098900487592120525252537511749903693989702365519944116294471974842357x^12 - 73704593402925551204037451877584023047946172398254928793692285881529570994x^11 + 5516336147855606858523686089551925620872550605204284237709228096232716802903002973392852815x^10 - 27581680739278033616992990920942078185728560285226412785624452693072488043503225695971731566x^9 + 1517878455648890489695001684494985450863656907930075530716193787298253181082685160982376785780193706273465608x^8 - 6071513822595561793289922302311740912247209538248891478546899284872728565602870282822535480605440763098529168x^7 + 247927346162348834423749451228358273830598680827645592402766959253902686957544779014145143897629177833020849983266016607613296x^6 - 743782038487046482020949974600608660820127089359583964963101929666258034682878431219929402460388250614556570989709464530610144x^5 + 21882859534466294287228939036881852886736567554233410610686187918042890793111187503539197126144459328207808614661966382731946870926901879113984x^4 - 43765719068932587334821147262019576155322637135607756862708434377743408992078827726727780310966542756561373742782816017120711348834657134242304x^3 + 797986861806247403230610551033523340880583800155549360507218139622165905339813235339233274528940034896016490666809497848765871357094638184408888034812433039360x^2 - 797986861806247381347751016567229797433683250320173941085258239326107003523949004518061241874365252424389220229742074846265472846643782528368645538242847539200*x + 582776938526821481202155286064003991435776530121314093258912761316091268879815440298128652209601652301637461916981612534140214354747684373258396815504158589037626247741440000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{380}\cdot 3^{41}\cdot 5^{10}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.5
Root			$0.500000 + 4.95367e8i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.43.b.a.3.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.51618e6 - 1.44888e6i) q^{2} -7.92587e9i q^{3} +(1.99543e11 + 4.39352e12i) q^{4} +1.59403e13 q^{5} +(-1.14836e16 + 1.20170e16i) q^{6} +6.57146e16i q^{7} +(6.06313e18 - 6.95047e18i) q^{8} +4.65995e19 q^{9} +O(q^{10})$	\(q+(-1.51618e6 - 1.44888e6i) q^{2} -7.92587e9i q^{3} +(1.99543e11 + 4.39352e12i) q^{4} +1.59403e13 q^{5} +(-1.14836e16 + 1.20170e16i) q^{6} +6.57146e16i q^{7} +(6.06313e18 - 6.95047e18i) q^{8} +4.65995e19 q^{9} +(-2.41683e19 - 2.30956e19i) q^{10} +2.70695e21i q^{11} +(3.48225e22 - 1.58155e21i) q^{12} +1.13176e23 q^{13} +(9.52125e22 - 9.96350e22i) q^{14} -1.26341e23i q^{15} +(-1.92632e25 + 1.75339e24i) q^{16} -8.31192e25 q^{17} +(-7.06531e25 - 6.75171e25i) q^{18} -1.43601e26i q^{19} +(3.18077e24 + 7.00340e25i) q^{20} +5.20846e26 q^{21} +(3.92204e27 - 4.10422e27i) q^{22} -2.76394e28i q^{23} +(-5.50885e28 - 4.80556e28i) q^{24} -2.27120e29 q^{25} +(-1.71595e29 - 1.63978e29i) q^{26} -1.23658e30i q^{27} +(-2.88718e29 + 1.31129e28i) q^{28} -4.03591e30 q^{29} +(-1.83053e29 + 1.91555e29i) q^{30} -3.93704e30i q^{31} +(3.17469e31 + 2.52516e31i) q^{32} +2.14549e31 q^{33} +(1.26023e32 + 1.20430e32i) q^{34} +1.04751e30i q^{35} +(9.29860e30 + 2.04736e32i) q^{36} -7.75523e32 q^{37} +(-2.08061e32 + 2.17725e32i) q^{38} -8.97018e32i q^{39} +(9.66482e31 - 1.10793e32i) q^{40} +1.59095e33 q^{41} +(-7.89694e32 - 7.54642e32i) q^{42} +1.63708e34i q^{43} +(-1.18930e34 + 5.40153e32i) q^{44} +7.42810e32 q^{45} +(-4.00462e34 + 4.19063e34i) q^{46} +2.52833e35i q^{47} +(1.38972e34 + 1.52678e35i) q^{48} +3.07655e35 q^{49} +(3.44354e35 + 3.29069e35i) q^{50} +6.58792e35i q^{51} +(2.25834e34 + 4.97240e35i) q^{52} -2.13176e36 q^{53} +(-1.79166e36 + 1.87488e36i) q^{54} +4.31496e34i q^{55} +(4.56747e35 + 3.98436e35i) q^{56} -1.13817e36 q^{57} +(6.11916e36 + 5.84755e36i) q^{58} +1.16148e37i q^{59} +(5.55081e35 - 2.52104e34i) q^{60} +2.47633e37 q^{61} +(-5.70429e36 + 5.96925e36i) q^{62} +3.06227e36i q^{63} +(-1.15474e37 - 8.42832e37i) q^{64} +1.80406e36 q^{65} +(-3.25295e37 - 3.10856e37i) q^{66} -2.41338e38i q^{67} +(-1.65858e37 - 3.65186e38i) q^{68} -2.19067e38 q^{69} +(1.51772e36 - 1.58821e36i) q^{70} -8.94928e38i q^{71} +(2.82539e38 - 3.23888e38i) q^{72} -1.03772e38 q^{73} +(1.17583e39 + 1.12364e39i) q^{74} +1.80012e39i q^{75} +(6.30915e38 - 2.86546e37i) q^{76} -1.77886e38 q^{77} +(-1.29967e39 + 1.36004e39i) q^{78} +7.18896e39i q^{79} +(-3.07061e38 + 2.79496e37i) q^{80} -4.70213e39 q^{81} +(-2.41216e39 - 2.30509e39i) q^{82} +2.07230e40i q^{83} +(1.03931e38 + 2.28834e39i) q^{84} -1.32494e39 q^{85} +(2.37193e40 - 2.48210e40i) q^{86} +3.19882e40i q^{87} +(1.88146e40 + 1.64126e40i) q^{88} -1.14220e41 q^{89} +(-1.12623e39 - 1.07624e39i) q^{90} +7.43730e39i q^{91} +(1.21434e41 - 5.51525e39i) q^{92} -3.12045e40 q^{93} +(3.66324e41 - 3.83339e41i) q^{94} -2.28905e39i q^{95} +(2.00141e41 - 2.51622e41i) q^{96} -4.95617e41 q^{97} +(-4.66460e41 - 4.45755e41i) q^{98} +1.26143e41i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 802164 q^{2} + 1311168818192 q^{4} + 139235684997000 q^{5} + 68\!\cdots\!12 q^{6}+ \cdots - 73\!\cdots\!76 q^{9}+O(q^{10}) $ 20 * q + 802164 * q^2 + 1311168818192 * q^4 + 139235684997000 * q^5 + 6838718638036512 * q^6 - 27661415389266953664 * q^8 - 733170595646091132876 * q^9	$ 20 q + 802164 q^{2} + 1311168818192 q^{4} + 139235684997000 q^{5} + 68\!\cdots\!12 q^{6}+ \cdots + 18\!\cdots\!96 q^{98}+O(q^{100}) $ 20 * q + 802164 * q^2 + 1311168818192 * q^4 + 139235684997000 * q^5 + 6838718638036512 * q^6 - 27661415389266953664 * q^8 - 733170595646091132876 * q^9 + 42625185369378343240 * q^10 - 25848729272513843675520 * q^12 - 144898631886191567496248 * q^13 - 306990738295992471121728 * q^14 + 27792040878005009897120000 * q^16 + 81746542725793625328399528 * q^17 - 217831601203830755951030124 * q^18 + 6344592401135696008447573920 * q^20 + 7651089590961386749851047424 * q^21 - 46254109397133274566238240800 * q^22 + 506607644284406956508290140672 * q^24 + 844166434154191999887370985820 * q^25 + 305910330554143989456096580488 * q^26 - 1621415041794921570009743366400 * q^28 + 8494173617816210057524981535304 * q^29 + 32483836243012295467926394800960 * q^30 - 117067340157863901568162598132736 * q^32 - 195434629079924022845409037850880 * q^33 - 435728002928020507520645688017048 * q^34 + 905808650859207966395798479569552 * q^36 + 320827308804868360600766816935048 * q^37 - 834801746373065199942054885540960 * q^38 - 2080347678511686114819737054821760 * q^40 + 12238592465130696350192985088255080 * q^41 + 39180793491987624842407723014766080 * q^42 - 40147560736600746149658671246198400 * q^44 - 57674168870802092374169153418160440 * q^45 - 133593585977858896021440512714708928 * q^46 + 223617847456028179696661192651827200 * q^48 - 763663932888918132103393205670102316 * q^49 - 1073296820241355924814923786366326660 * q^50 - 580677968103327319151855528386839392 * q^52 + 3592528655430046000719727125882705672 * q^53 + 8087462166590362832897538370358812224 * q^54 - 4056862272141293872664295528725971968 * q^56 + 1376964140105307936676325853454767360 * q^57 - 17787847411919404506009575679670206968 * q^58 + 27803845757503537955964429994460432640 * q^60 - 72876803820111699199759396563493728440 * q^61 - 83779848218915601601226708273126396160 * q^62 - 51258837764961549702163120437185671168 * q^64 + 143337782114217802520090675036041365840 * q^65 + 479881795533282188176080436671310498560 * q^66 - 201679039132028748396903074185205050848 * q^68 + 496255895990320623770556878095159325184 * q^69 + 244550326432622351468933399511720393600 * q^70 + 1389470702024602675984554222025462031424 * q^72 + 675217186810136917874725959945538619752 * q^73 - 5048325762233564608985375515346235670968 * q^74 - 727730227778639944706768217921060021120 * q^76 - 13945771646073577607404274150247166932480 * q^77 + 2630485389052859541031650397045824087360 * q^78 - 14080069438753558698176635521889841825280 * q^80 + 50326416439524122225413610454605570342484 * q^81 + 38442316210858292795461617709768475559208 * q^82 + 21041665749991691364416236667734761560064 * q^84 - 100747029416581567610441680879732008651760 * q^85 - 109399875737541346773887857542693387248928 * q^86 + 61542411942227832459784035156153652876800 * q^88 + 298677519739918601751826215340976530195944 * q^89 + 5248331693055749298139854308097091987080 * q^90 - 311056321102768653749854891753699429405440 * q^92 - 902946967697899772252214392286633142732800 * q^93 - 120754391334239789606838050760853185629568 * q^94 - 369891338439189821551415861997759233875968 * q^96 + 2729077788738058742150638081801454021515048 * q^97 + 1829330555781863715528793474157579946873396 * 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 $

$2$	−1.51618e6	−	1.44888e6i	−0.722970	−	0.690880i
$2$	−1.51618e6	−	1.44888e6i	−0.722970	−	0.690880i
$3$		−	7.92587e9i		−	0.757706i	−0.925457	−	0.378853i	$-0.876319\pi$
$3$		−	7.92587e9i		−	0.757706i	0.925457	−	0.378853i	$-0.123681\pi$
$4$	1.99543e11	+	4.39352e12i	0.0453708	+	0.998970i
$5$	1.59403e13			0.0334292			0.0167146	−	0.999860i	$-0.494679\pi$
$5$	1.59403e13			0.0334292			0.0167146	+	0.999860i	$0.494679\pi$
$6$	−1.14836e16	+	1.20170e16i	−0.523484	+	0.547799i
$7$			6.57146e16i			0.117653i	0.998268	+	0.0588265i	$0.0187359\pi$
$7$			6.57146e16i			0.117653i	−0.998268	+	0.0588265i	$0.981264\pi$
$8$	6.06313e18	−	6.95047e18i	0.657366	−	0.753571i
$9$	4.65995e19			0.425881
$10$	−2.41683e19	−	2.30956e19i	−0.0241683	−	0.0230956i
$11$			2.70695e21i			0.365792i	0.983132	+	0.182896i	$0.0585471\pi$
$11$			2.70695e21i			0.365792i	−0.983132	+	0.182896i	$0.941453\pi$
$12$	3.48225e22	−	1.58155e21i	0.756926	−	0.0343777i
$13$	1.13176e23			0.458082			0.229041	−	0.973417i	$-0.426441\pi$
$13$	1.13176e23			0.458082			0.229041	+	0.973417i	$0.426441\pi$
$14$	9.52125e22	−	9.96350e22i	0.0812840	−	0.0850595i
$15$		−	1.26341e23i		−	0.0253295i
$16$	−1.92632e25	+	1.75339e24i	−0.995883	+	0.0906482i
$17$	−8.31192e25			−1.20302			−0.601512	−	0.798864i	$-0.705435\pi$
$17$	−8.31192e25			−1.20302			−0.601512	+	0.798864i	$0.705435\pi$
$18$	−7.06531e25	−	6.75171e25i	−0.307899	−	0.294233i
$19$		−	1.43601e26i		−	0.201063i	−0.994934	−	0.100532i	$-0.967946\pi$
$19$		−	1.43601e26i		−	0.201063i	0.994934	−	0.100532i	$-0.0320544\pi$
$20$	3.18077e24	+	7.00340e25i	0.00151671	+	0.0333948i
$21$	5.20846e26			0.0891464
$22$	3.92204e27	−	4.10422e27i	0.252718	−	0.264456i
$23$		−	2.76394e28i		−	0.700236i	−0.936706	−	0.350118i	$-0.886141\pi$
$23$		−	2.76394e28i		−	0.700236i	0.936706	−	0.350118i	$-0.113859\pi$
$24$	−5.50885e28	−	4.80556e28i	−0.570986	−	0.498091i
$25$	−2.27120e29			−0.998882
$26$	−1.71595e29	−	1.63978e29i	−0.331180	−	0.316480i
$27$		−	1.23658e30i		−	1.08040i
$28$	−2.88718e29	+	1.31129e28i	−0.117532	+	0.00533801i
$29$	−4.03591e30			−0.786292			−0.393146	−	0.919476i	$-0.628613\pi$
$29$	−4.03591e30			−0.786292			−0.393146	+	0.919476i	$0.628613\pi$
$30$	−1.83053e29	+	1.91555e29i	−0.0174997	+	0.0183125i
$31$		−	3.93704e30i		−	0.189049i	−0.995523	−	0.0945244i	$-0.969867\pi$
$31$		−	3.93704e30i		−	0.189049i	0.995523	−	0.0945244i	$-0.0301330\pi$
$32$	3.17469e31	+	2.52516e31i	0.782620	+	0.622499i
$33$	2.14549e31			0.277163
$34$	1.26023e32	+	1.20430e32i	0.869750	+	0.831144i
$35$			1.04751e30i			0.00393305i
$36$	9.29860e30	+	2.04736e32i	0.0193226	+	0.425443i
$37$	−7.75523e32			−0.906480			−0.453240	−	0.891388i	$-0.649732\pi$
$37$	−7.75523e32			−0.906480			−0.453240	+	0.891388i	$0.649732\pi$
$38$	−2.08061e32	+	2.17725e32i	−0.138911	+	0.145363i
$39$		−	8.97018e32i		−	0.347092i
$40$	9.66482e31	−	1.10793e32i	0.0219753	−	0.0251913i
$41$	1.59095e33			0.215375			0.107687	−	0.994185i	$-0.465655\pi$
$41$	1.59095e33			0.215375			0.107687	+	0.994185i	$0.465655\pi$
$42$	−7.89694e32	−	7.54642e32i	−0.0644501	−	0.0615894i
$43$			1.63708e34i			0.815140i	0.913174	+	0.407570i	$0.133624\pi$
$43$			1.63708e34i			0.815140i	−0.913174	+	0.407570i	$0.866376\pi$
$44$	−1.18930e34	+	5.40153e32i	−0.365415	+	0.0165963i
$45$	7.42810e32			0.0142369
$46$	−4.00462e34	+	4.19063e34i	−0.483779	+	0.506250i
$47$			2.52833e35i			1.94437i	0.234224	+	0.972183i	$0.424745\pi$
$47$			2.52833e35i			1.94437i	−0.234224	+	0.972183i	$0.575255\pi$
$48$	1.38972e34	+	1.52678e35i	0.0686847	+	0.754587i
$49$	3.07655e35			0.986158
$50$	3.44354e35	+	3.29069e35i	0.722162	+	0.690108i
$51$			6.58792e35i			0.911538i
$52$	2.25834e34	+	4.97240e35i	0.0207836	+	0.457610i
$53$	−2.13176e36			−1.31506			−0.657530	−	0.753428i	$-0.728399\pi$
$53$	−2.13176e36			−1.31506			−0.657530	+	0.753428i	$0.728399\pi$
$54$	−1.79166e36	+	1.87488e36i	−0.746426	+	0.781096i
$55$			4.31496e34i			0.0122281i
$56$	4.56747e35	+	3.98436e35i	0.0886599	+	0.0773411i
$57$	−1.13817e36			−0.152347
$58$	6.11916e36	+	5.84755e36i	0.568466	+	0.543233i
$59$			1.16148e37i			0.753563i	0.926302	+	0.376781i	$0.122969\pi$
$59$			1.16148e37i			0.753563i	−0.926302	+	0.376781i	$0.877031\pi$
$60$	5.55081e35	−	2.52104e34i	0.0253035	−	0.00114922i
$61$	2.47633e37			0.797776			0.398888	−	0.917000i	$-0.369396\pi$
$61$	2.47633e37			0.797776			0.398888	+	0.917000i	$0.369396\pi$
$62$	−5.70429e36	+	5.96925e36i	−0.130610	+	0.136677i
$63$			3.06227e36i			0.0501062i
$64$	−1.15474e37	−	8.42832e37i	−0.135739	−	0.990745i
$65$	1.80406e36			0.0153133
$66$	−3.25295e37	−	3.10856e37i	−0.200380	−	0.191486i
$67$		−	2.41338e38i		−	1.08406i	−0.840358	−	0.542032i	$-0.817655\pi$
$67$		−	2.41338e38i		−	1.08406i	0.840358	−	0.542032i	$-0.182345\pi$
$68$	−1.65858e37	−	3.65186e38i	−0.0545821	−	1.20178i
$69$	−2.19067e38			−0.530573
$70$	1.51772e36	−	1.58821e36i	0.00271726	−	0.00284348i
$71$		−	8.94928e38i		−	1.18950i	−0.803912	−	0.594748i	$-0.797252\pi$
$71$		−	8.94928e38i		−	1.18950i	0.803912	−	0.594748i	$-0.202748\pi$
$72$	2.82539e38	−	3.23888e38i	0.279960	−	0.320932i
$73$	−1.03772e38			−0.0769662			−0.0384831	−	0.999259i	$-0.512253\pi$
$73$	−1.03772e38			−0.0769662			−0.0384831	+	0.999259i	$0.512253\pi$
$74$	1.17583e39	+	1.12364e39i	0.655358	+	0.626269i
$75$			1.80012e39i			0.756859i
$76$	6.30915e38	−	2.86546e37i	0.200856	−	0.00912240i
$77$	−1.77886e38			−0.0430365
$78$	−1.29967e39	+	1.36004e39i	−0.239799	+	0.250937i
$79$			7.18896e39i			1.01507i	0.861630	+	0.507536i	$0.169444\pi$
$79$			7.18896e39i			1.01507i	−0.861630	+	0.507536i	$0.830556\pi$
$80$	−3.07061e38	+	2.79496e37i	−0.0332916	+	0.00303030i
$81$	−4.70213e39			−0.392744
$82$	−2.41216e39	−	2.30509e39i	−0.155709	−	0.148798i
$83$			2.07230e40i			1.03708i	0.855053	+	0.518541i	$0.173525\pi$
$83$			2.07230e40i			1.03708i	−0.855053	+	0.518541i	$0.826475\pi$
$84$	1.03931e38	+	2.28834e39i	0.00404464	+	0.0890546i
$85$	−1.32494e39			−0.0402161
$86$	2.37193e40	−	2.48210e40i	0.563163	−	0.589321i
$87$			3.19882e40i			0.595779i
$88$	1.88146e40	+	1.64126e40i	0.275650	+	0.240459i
$89$	−1.14220e41			−1.31994			−0.659968	−	0.751293i	$-0.729430\pi$
$89$	−1.14220e41			−1.31994			−0.659968	+	0.751293i	$0.729430\pi$
$90$	−1.12623e39	−	1.07624e39i	−0.0102928	−	0.00983597i
$91$			7.43730e39i			0.0538947i
$92$	1.21434e41	−	5.51525e39i	0.699515	−	0.0317703i
$93$	−3.12045e40			−0.143243
$94$	3.66324e41	−	3.83339e41i	1.34332	−	1.40572i
$95$		−	2.28905e39i		−	0.00672139i
$96$	2.00141e41	−	2.51622e41i	0.471672	−	0.592996i
$97$	−4.95617e41			−0.939592			−0.469796	−	0.882775i	$-0.655673\pi$
$97$	−4.95617e41			−0.939592			−0.469796	+	0.882775i	$0.655673\pi$
$98$	−4.66460e41	−	4.45755e41i	−0.712962	−	0.681316i
$99$			1.26143e41i			0.155784i
$100$	−4.53201e40	−	9.97854e41i	−0.0453201	−	0.997854i
$101$	−1.56129e42			−1.26688			−0.633438	−	0.773793i	$-0.718357\pi$
$101$	−1.56129e42			−1.26688			−0.633438	+	0.773793i	$0.718357\pi$
$102$	9.54511e41	−	9.98846e41i	0.629763	−	0.659015i
$103$			3.06912e42i			1.64980i	0.565277	+	0.824901i	$0.308769\pi$
$103$			3.06912e42i			1.64980i	−0.565277	+	0.824901i	$0.691231\pi$
$104$	6.86200e41	−	7.86625e41i	0.301128	−	0.345197i
$105$	8.30243e39			0.00298009
$106$	3.23213e42	+	3.08867e42i	0.950749	+	0.908548i
$107$			6.57399e42i			1.58770i	0.608111	+	0.793852i	$0.291928\pi$
$107$			6.57399e42i			1.58770i	−0.608111	+	0.793852i	$0.708072\pi$
$108$	5.43295e42	−	2.46751e41i	1.07929	−	0.0490186i
$109$	−5.10158e42			−0.835118			−0.417559	−	0.908650i	$-0.637114\pi$
$109$	−5.10158e42			−0.835118			−0.417559	+	0.908650i	$0.637114\pi$
$110$	6.25186e40	−	6.54225e40i	0.00844817	−	0.00884057i
$111$			6.14670e42i			0.686846i
$112$	−1.15223e41	−	1.26587e42i	−0.0106650	−	0.117169i
$113$	−2.12408e43			−1.63126			−0.815632	−	0.578571i	$-0.803610\pi$
$113$	−2.12408e43			−1.63126			−0.815632	+	0.578571i	$0.803610\pi$
$114$	1.72566e42	+	1.64907e42i	0.110142	+	0.105253i
$115$		−	4.40581e41i		−	0.0234084i
$116$	−8.05338e41	−	1.77319e43i	−0.0356747	−	0.785483i
$117$	5.27394e42			0.195089
$118$	1.68284e43	−	1.76101e43i	0.520621	−	0.544803i
$119$		−	5.46214e42i		−	0.141539i
$120$	−8.78128e41	−	7.66021e41i	−0.0190876	−	0.0166508i
$121$	4.74361e43			0.866196
$122$	−3.75455e43	−	3.58790e43i	−0.576768	−	0.551167i
$123$		−	1.26097e43i		−	0.163191i
$124$	1.72974e43	−	7.85608e41i	0.188854	−	0.00857729i
$125$	−7.24476e42			−0.0668211
$126$	4.43685e42	−	4.64294e42i	0.0346173	−	0.0362253i
$127$		−	1.19587e44i		−	0.790325i	−0.918611	−	0.395163i	$-0.870688\pi$
$127$		−	1.19587e44i		−	0.790325i	0.918611	−	0.395163i	$-0.129312\pi$
$128$	−1.04608e44	+	1.44519e44i	−0.586350	+	0.810058i
$129$	1.29753e44			0.617636
$130$	−2.73527e42	−	2.61386e42i	−0.0110711	−	0.0105797i
$131$		−	3.04854e44i		−	1.05050i	−0.850949	−	0.525249i	$-0.823972\pi$
$131$		−	3.04854e44i		−	1.05050i	0.850949	−	0.525249i	$-0.176028\pi$
$132$	4.28118e42	+	9.42627e43i	0.0125751	+	0.276877i
$133$	9.43670e42			0.0236557
$134$	−3.49670e44	+	3.65911e44i	−0.748958	+	0.783745i
$135$		−	1.97115e43i		−	0.0361169i
$136$	−5.03963e44	+	5.77717e44i	−0.790827	+	0.906564i
$137$	4.16870e44			0.560878			0.280439	−	0.959872i	$-0.409520\pi$
$137$	4.16870e44			0.560878			0.280439	+	0.959872i	$0.409520\pi$
$138$	3.32144e44	+	3.17401e44i	0.383589	+	0.366562i
$139$			3.35499e44i			0.332951i	0.986046	+	0.166476i	$0.0532387\pi$
$139$			3.35499e44i			0.332951i	−0.986046	+	0.166476i	$0.946761\pi$
$140$	−4.60225e42	+	2.09023e41i	−0.00392900	+	0.000178446i
$141$	2.00392e45			1.47326
$142$	−1.29664e45	+	1.35687e45i	−0.821798	+	0.859969i
$143$			3.06361e44i			0.167563i
$144$	−8.97654e44	+	8.17071e43i	−0.424128	+	0.0386054i
$145$	−6.43337e43			−0.0262851
$146$	1.57337e44	+	1.50353e44i	0.0556442	+	0.0531743i
$147$		−	2.43844e45i		−	0.747218i
$148$	−1.54750e44	−	3.40727e45i	−0.0411277	−	0.905547i
$149$	−5.05450e44			−0.116618			−0.0583091	−	0.998299i	$-0.518571\pi$
$149$	−5.05450e44			−0.116618			−0.0583091	+	0.998299i	$0.518571\pi$
$150$	2.60816e45	−	2.72930e45i	0.522899	−	0.547187i
$151$		−	6.77621e45i		−	1.18160i	−0.806818	−	0.590800i	$-0.798812\pi$
$151$		−	6.77621e45i		−	1.18160i	0.806818	−	0.590800i	$-0.201188\pi$
$152$	−9.98096e44	−	8.70674e44i	−0.151516	−	0.132172i
$153$	−3.87331e45			−0.512345
$154$	2.69707e44	+	2.57736e44i	0.0311141	+	0.0297330i
$155$		−	6.27575e43i		−	0.00631975i
$156$	3.94106e45	−	1.78993e44i	0.346734	−	0.0157478i
$157$	−1.23696e46			−0.951618			−0.475809	−	0.879549i	$-0.657845\pi$
$157$	−1.23696e46			−0.951618			−0.475809	+	0.879549i	$0.657845\pi$
$158$	1.04159e46	−	1.08997e46i	0.701293	−	0.733867i
$159$			1.68961e46i			0.996429i
$160$	5.06054e44	+	4.02518e44i	0.0261624	+	0.0208097i
$161$	1.81631e45			0.0823849
$162$	7.12927e45	+	6.81282e45i	0.283942	+	0.271339i
$163$			4.96590e46i			1.73803i	0.494782	+	0.869017i	$0.335248\pi$
$163$			4.96590e46i			1.73803i	−0.494782	+	0.869017i	$0.664752\pi$
$164$	3.17462e44	+	6.98986e45i	0.00977173	+	0.215153i
$165$	3.41998e44			0.00926533
$166$	3.00252e46	−	3.14198e46i	0.716499	−	0.749779i
$167$			4.03371e46i			0.848513i	0.905542	+	0.424257i	$0.139465\pi$
$167$			4.03371e46i			0.848513i	−0.905542	+	0.424257i	$0.860535\pi$
$168$	3.15796e45	−	3.62012e45i	0.0586018	−	0.0671781i
$169$	−4.82321e46			−0.790161
$170$	2.00885e45	+	1.91969e45i	0.0290751	+	0.0277845i
$171$		−	6.69175e45i		−	0.0856291i
$172$	−7.19253e46	+	3.26667e45i	−0.814300	+	0.0369835i
$173$	−1.16859e47			−1.17137			−0.585683	−	0.810540i	$-0.699174\pi$
$173$	−1.16859e47			−1.17137			−0.585683	+	0.810540i	$0.699174\pi$
$174$	4.63470e46	−	4.84997e46i	0.411611	−	0.430730i
$175$		−	1.49251e46i		−	0.117521i
$176$	−4.74634e45	−	5.21445e46i	−0.0331583	−	0.364286i
$177$	9.20575e46			0.570979
$178$	1.73178e47	+	1.65491e47i	0.954275	+	0.911917i
$179$		−	1.79650e47i		−	0.880063i	−0.897982	−	0.440031i	$-0.854967\pi$
$179$		−	1.79650e47i		−	0.880063i	0.897982	−	0.440031i	$-0.145033\pi$
$180$	1.48222e44	+	3.26355e45i	0.000645939	+	0.0142222i
$181$	2.96510e47			1.15024			0.575122	−	0.818068i	$-0.304955\pi$
$181$	2.96510e47			1.15024			0.575122	+	0.818068i	$0.304955\pi$
$182$	1.07758e46	−	1.12763e46i	0.0372348	−	0.0389643i
$183$		−	1.96270e47i		−	0.604480i
$184$	−1.92107e47	−	1.67582e47i	−0.527678	−	0.460312i
$185$	−1.23621e46			−0.0303029
$186$	4.73115e46	+	4.52115e46i	0.103561	+	0.0989639i
$187$		−	2.25000e47i		−	0.440056i
$188$	−1.11082e48	+	5.04509e46i	−1.94236	+	0.0882174i
$189$	8.12615e46			0.127112
$190$	−3.31655e45	+	3.47060e45i	−0.00464367	+	0.00485936i
$191$		−	3.52544e47i		−	0.442091i	−0.975263	−	0.221046i	$-0.929053\pi$
$191$		−	3.52544e47i		−	0.442091i	0.975263	−	0.221046i	$-0.0709470\pi$
$192$	−6.68018e47	+	9.15231e46i	−0.750693	+	0.102850i
$193$	1.02097e48			1.02875			0.514374	−	0.857566i	$-0.328024\pi$
$193$	1.02097e48			1.02875			0.514374	+	0.857566i	$0.328024\pi$
$194$	7.51443e47	+	7.18089e47i	0.679297	+	0.649145i
$195$		−	1.42987e46i		−	0.0116030i
$196$	6.13904e46	+	1.35169e48i	0.0447428	+	0.985142i
$197$	9.65808e47			0.632557			0.316279	−	0.948666i	$-0.397567\pi$
$197$	9.65808e47			0.632557			0.316279	+	0.948666i	$0.397567\pi$
$198$	1.82765e47	−	1.91254e47i	0.107628	−	0.112627i
$199$			1.27680e48i			0.676408i	0.941073	+	0.338204i	$0.109819\pi$
$199$			1.27680e48i			0.676408i	−0.941073	+	0.338204i	$0.890181\pi$
$200$	−1.37706e48	+	1.57859e48i	−0.656632	+	0.752729i
$201$	−1.91281e48			−0.821402
$202$	2.36719e48	+	2.26212e48i	0.915914	+	0.875259i
$203$		−	2.65218e47i		−	0.0925096i
$204$	−2.89442e48	+	1.31457e47i	−0.910600	+	0.0413572i
$205$	2.53602e46			0.00719981
$206$	4.44678e48	−	4.65333e48i	1.13981	−	1.19276i
$207$		−	1.28798e48i		−	0.298218i
$208$	−2.18013e48	+	1.98441e47i	−0.456196	+	0.0415243i
$209$	3.88722e47			0.0735473
$210$	−1.25880e46	−	1.20292e46i	−0.00215452	−	0.00205889i
$211$			9.98177e47i			0.154624i	0.997007	+	0.0773119i	$0.0246337\pi$
$211$			9.98177e47i			0.154624i	−0.997007	+	0.0773119i	$0.975366\pi$
$212$	−4.25378e47	−	9.36594e48i	−0.0596653	−	1.31371i
$213$	−7.09309e48			−0.901288
$214$	9.52491e48	−	9.96733e48i	1.09691	−	1.14786i
$215$			2.60955e47i			0.0272495i
$216$	−8.59483e48	−	7.49757e48i	−0.814158	−	0.710218i
$217$	2.58721e47			0.0222421
$218$	7.73490e48	+	7.39157e48i	0.603765	+	0.576966i
$219$			8.22483e47i			0.0583177i
$220$	−1.89578e47	+	8.61019e45i	−0.0122155	+	0.000554800i
$221$	−9.40709e48			−0.551083
$222$	8.90582e48	−	9.31949e48i	0.474528	−	0.496569i
$223$			3.16542e49i			1.53472i	0.641215	+	0.767361i	$0.278431\pi$
$223$			3.16542e49i			1.53472i	−0.641215	+	0.767361i	$0.721569\pi$
$224$	−1.65940e48	+	2.08623e48i	−0.0732389	+	0.0920776i
$225$	−1.05837e49			−0.425405
$226$	3.22049e49	+	3.07754e49i	1.17935	+	1.12701i
$227$		−	3.21737e48i		−	0.107389i	−0.998557	−	0.0536943i	$-0.982900\pi$
$227$		−	3.21737e48i		−	0.107389i	0.998557	−	0.0536943i	$-0.0170996\pi$
$228$	−2.27113e47	−	5.00055e48i	−0.00691210	−	0.152190i
$229$	7.12036e48			0.197677			0.0988386	−	0.995103i	$-0.468487\pi$
$229$	7.12036e48			0.197677			0.0988386	+	0.995103i	$0.468487\pi$
$230$	−6.38349e47	+	6.67999e47i	−0.0161724	+	0.0169235i
$231$			1.40990e48i			0.0326090i
$232$	−2.44703e49	+	2.80515e49i	−0.516882	+	0.592527i
$233$	−3.54816e49			−0.684746			−0.342373	−	0.939564i	$-0.611231\pi$
$233$	−3.54816e49			−0.684746			−0.342373	+	0.939564i	$0.611231\pi$
$234$	−7.99623e48	−	7.64130e48i	−0.141043	−	0.134783i
$235$			4.03023e48i			0.0649986i
$236$	−5.10298e49	+	2.31765e48i	−0.752787	+	0.0341898i
$237$	5.69788e49			0.769127
$238$	−7.91399e48	+	8.28158e48i	−0.0977866	+	0.102329i
$239$		−	3.22824e49i		−	0.365266i	−0.983181	−	0.182633i	$-0.941538\pi$
$239$		−	3.22824e49i		−	0.365266i	0.983181	−	0.182633i	$-0.0584620\pi$
$240$	2.21525e47	+	2.43373e48i	0.00229608	+	0.0252253i
$241$	1.21286e50			1.15200			0.575999	−	0.817450i	$-0.304613\pi$
$241$	1.21286e50			1.15200			0.575999	+	0.817450i	$0.304613\pi$
$242$	−7.19216e49	−	6.87292e49i	−0.626234	−	0.598437i
$243$		−	9.80372e49i		−	0.782815i
$244$	4.94133e48	+	1.08798e50i	0.0361958	+	0.796955i
$245$	4.90411e48			0.0329665
$246$	−1.82699e49	+	1.91185e49i	−0.112745	+	0.117982i
$247$		−	1.62522e49i		−	0.0921035i
$248$	−2.73642e49	−	2.38708e49i	−0.142462	−	0.124274i
$249$	1.64248e50			0.785804
$250$	1.09843e49	+	1.04968e49i	0.0483096	+	0.0461653i
$251$		−	4.29149e50i		−	1.73564i	−0.496877	−	0.867821i	$-0.665520\pi$
$251$		−	4.29149e50i		−	1.73564i	0.496877	−	0.867821i	$-0.334480\pi$
$252$	−1.34541e49	+	6.11053e47i	−0.0500546	+	0.00227336i
$253$	7.48186e49			0.256141
$254$	−1.73267e50	+	1.81315e50i	−0.546020	+	0.571381i
$255$			1.05013e49i			0.0304720i
$256$	3.67996e50	−	6.75517e49i	0.983566	−	0.180550i
$257$	−3.64830e50			−0.898453			−0.449226	−	0.893418i	$-0.648300\pi$
$257$	−3.64830e50			−0.898453			−0.449226	+	0.893418i	$0.648300\pi$
$258$	−1.96728e50	−	1.87996e50i	−0.446532	−	0.426712i
$259$		−	5.09632e49i		−	0.106650i
$260$	3.59987e47	+	7.92615e48i	0.000694778	+	0.0152976i
$261$	−1.88072e50			−0.334867
$262$	−4.41697e50	+	4.62213e50i	−0.725768	+	0.759478i
$263$			8.28360e50i			1.25646i	0.778028	+	0.628230i	$0.216220\pi$
$263$			8.28360e50i			1.25646i	−0.778028	+	0.628230i	$0.783780\pi$
$264$	1.30084e50	−	1.49122e50i	0.182197	−	0.208862i
$265$	−3.39809e49			−0.0439615
$266$	−1.43077e49	−	1.36726e49i	−0.0171024	−	0.0163432i
$267$			9.05296e50i			1.00012i
$268$	1.06032e51	−	4.81573e49i	1.08295	−	0.0491848i
$269$	4.35985e50			0.411788			0.205894	−	0.978574i	$-0.433990\pi$
$269$	4.35985e50			0.411788			0.205894	+	0.978574i	$0.433990\pi$
$270$	−2.85596e49	+	2.98861e49i	−0.0249524	+	0.0261114i
$271$			1.70956e51i			1.38206i	0.722824	+	0.691032i	$0.242844\pi$
$271$			1.70956e51i			1.38206i	−0.722824	+	0.691032i	$0.757156\pi$
$272$	1.60114e51	−	1.45740e50i	1.19807	−	0.109052i
$273$	5.89471e49			0.0408364
$274$	−6.32048e50	−	6.03994e50i	−0.405498	−	0.387499i
$275$		−	6.14801e50i		−	0.365383i
$276$	−4.37132e49	−	9.62473e50i	−0.0240725	−	0.530027i
$277$	−2.98764e51			−1.52494			−0.762470	−	0.647023i	$-0.776014\pi$
$277$	−2.98764e51			−1.52494			−0.762470	+	0.647023i	$0.776014\pi$
$278$	4.86098e50	−	5.08677e50i	0.230029	−	0.240714i
$279$		−	1.83464e50i		−	0.0805123i
$280$	7.28068e48	+	6.35119e48i	0.00296383	+	0.00258545i
$281$	−1.79016e51			−0.676176			−0.338088	−	0.941115i	$-0.609780\pi$
$281$	−1.79016e51			−0.676176			−0.338088	+	0.941115i	$0.609780\pi$
$282$	−3.03830e51	−	2.90344e51i	−1.06512	−	1.01784i
$283$		−	5.22388e51i		−	1.70011i	−0.526691	−	0.850057i	$-0.676567\pi$
$283$		−	5.22388e51i		−	1.70011i	0.526691	−	0.850057i	$-0.323433\pi$
$284$	3.93188e51	−	1.78577e50i	1.18827	−	0.0539684i
$285$	−1.81427e49			−0.00509284
$286$	4.43881e50	−	4.64498e50i	0.115766	−	0.121143i
$287$			1.04548e50i			0.0253395i
$288$	1.47939e51	+	1.17671e51i	0.333303	+	0.265111i
$289$	2.13511e51			0.447265
$290$	9.75413e49	+	9.32117e49i	0.0190034	+	0.0181599i
$291$			3.92820e51i			0.711935i
$292$	−2.07069e49	−	4.55924e50i	−0.00349202	−	0.0768869i
$293$	6.97207e51			1.09431			0.547156	−	0.837030i	$-0.315710\pi$
$293$	6.97207e51			1.09431			0.547156	+	0.837030i	$0.315710\pi$
$294$	−3.53300e51	+	3.69710e51i	−0.516238	+	0.540216i
$295$			1.85143e50i			0.0251910i
$296$	−4.70210e51	+	5.39025e51i	−0.595890	+	0.683097i
$297$	3.34737e51			0.395201
$298$	7.66352e50	+	7.32336e50i	0.0843115	+	0.0805692i
$299$		−	3.12812e51i		−	0.320766i
$300$	−7.90886e51	+	3.59201e50i	−0.756080	+	0.0343393i
$301$	−1.07580e51			−0.0959036
$302$	−9.81791e51	+	1.02739e52i	−0.816344	+	0.854262i
$303$			1.23746e52i			0.959920i
$304$	2.51789e50	+	2.76622e51i	0.0182260	+	0.200236i
$305$	3.94734e50			0.0266691
$306$	5.87263e51	+	5.61196e51i	0.370410	+	0.353969i
$307$		−	2.37488e52i		−	1.39874i	−0.714761	−	0.699368i	$-0.753465\pi$
$307$		−	2.37488e52i		−	1.39874i	0.714761	−	0.699368i	$-0.246535\pi$
$308$	−3.54959e49	−	7.81546e50i	−0.00195260	−	0.0429922i
$309$	2.43254e52			1.25007
$310$	−9.09281e49	+	9.51516e49i	−0.00436619	+	0.00456899i
$311$		−	1.16027e52i		−	0.520705i	−0.965514	−	0.260352i	$-0.916161\pi$
$311$		−	1.16027e52i		−	0.520705i	0.965514	−	0.260352i	$-0.0838387\pi$
$312$	−6.23469e51	−	5.43874e51i	−0.261558	−	0.228166i
$313$	−1.61642e52			−0.634048			−0.317024	−	0.948418i	$-0.602684\pi$
$313$	−1.61642e52			−0.634048			−0.317024	+	0.948418i	$0.602684\pi$
$314$	1.87545e52	+	1.79220e52i	0.687991	+	0.657453i
$315$			4.88134e49i			0.00167501i
$316$	−3.15848e52	+	1.43451e51i	−1.01403	+	0.0460547i
$317$	−3.56759e52			−1.07184			−0.535920	−	0.844269i	$-0.680035\pi$
$317$	−3.56759e52			−1.07184			−0.535920	+	0.844269i	$0.680035\pi$
$318$	2.44804e52	−	2.56175e52i	0.688413	−	0.720388i
$319$		−	1.09250e52i		−	0.287619i
$320$	−1.84069e50	−	1.34350e51i	−0.00453764	−	0.0331198i
$321$	5.21046e52			1.20301
$322$	−2.75385e51	−	2.63162e51i	−0.0595618	−	0.0569180i
$323$			1.19360e52i			0.241884i
$324$	−9.38277e50	−	2.06589e52i	−0.0178191	−	0.392339i
$325$	−2.57044e52			−0.457570
$326$	7.19499e52	−	7.52919e52i	1.20077	−	1.25655i
$327$			4.04345e52i			0.632774i
$328$	9.64613e51	−	1.10578e52i	0.141580	−	0.162300i
$329$	−1.66148e52			−0.228760
$330$	−5.18530e50	−	4.95514e50i	−0.00669856	−	0.00640123i
$331$			3.38332e52i			0.410161i	0.978745	+	0.205081i	$0.0657457\pi$
$331$			3.38332e52i			0.410161i	−0.978745	+	0.205081i	$0.934254\pi$
$332$	−9.10470e52	+	4.13513e51i	−1.03601	+	0.0470532i
$333$	−3.61390e52			−0.386053
$334$	5.84436e52	−	6.11582e52i	0.586220	−	0.613449i
$335$		−	3.84700e51i		−	0.0362394i
$336$	−1.00331e52	+	9.13246e50i	−0.0887794	+	0.00808096i
$337$	−1.63677e53			−1.36069			−0.680344	−	0.732893i	$-0.738170\pi$
$337$	−1.63677e53			−1.36069			−0.680344	+	0.732893i	$0.738170\pi$
$338$	7.31284e52	+	6.98825e52i	0.571262	+	0.545906i
$339$			1.68352e53i			1.23602i
$340$	−2.64383e50	−	5.82117e51i	−0.00182464	−	0.0401747i
$341$	1.06574e52			0.0691525
$342$	−9.69554e51	+	1.01459e52i	−0.0591594	+	0.0619073i
$343$			4.07186e52i			0.233677i
$344$	1.13785e53	+	9.92583e52i	0.614266	+	0.535845i
$345$	−3.49199e51			−0.0177367
$346$	1.77179e53	+	1.69314e53i	0.846863	+	0.809273i
$347$			2.00064e52i			0.0900017i	0.998987	+	0.0450008i	$0.0143290\pi$
$347$			2.00064e52i			0.0900017i	−0.998987	+	0.0450008i	$0.985671\pi$
$348$	−1.40541e53	+	6.38301e51i	−0.595165	+	0.0270309i
$349$	1.73434e53			0.691513			0.345757	−	0.938324i	$-0.387622\pi$
$349$	1.73434e53			0.691513			0.345757	+	0.938324i	$0.387622\pi$
$350$	−2.16246e52	+	2.26291e52i	−0.0811932	+	0.0849645i
$351$		−	1.39951e53i		−	0.494912i
$352$	−6.83547e52	+	8.59371e52i	−0.227705	+	0.286276i
$353$	1.20414e53			0.377927			0.188963	−	0.981984i	$-0.439487\pi$
$353$	1.20414e53			0.377927			0.188963	+	0.981984i	$0.439487\pi$
$354$	−1.39575e53	−	1.33380e53i	−0.412801	−	0.394478i
$355$		−	1.42654e52i		−	0.0397639i
$356$	−2.27918e52	−	5.01829e53i	−0.0598866	−	1.31858i
$357$	−4.32923e52			−0.107245
$358$	−2.60291e53	+	2.72381e53i	−0.608017	+	0.636259i
$359$		−	7.26488e53i		−	1.60046i	−0.599693	−	0.800230i	$-0.704711\pi$
$359$		−	7.26488e53i		−	1.60046i	0.599693	−	0.800230i	$-0.295289\pi$
$360$	4.50376e51	−	5.16288e51i	0.00935885	−	0.0107285i
$361$	4.89474e53			0.959574
$362$	−4.49562e53	−	4.29608e53i	−0.831591	−	0.794680i
$363$		−	3.75973e53i		−	0.656322i
$364$	−3.26759e52	+	1.48406e51i	−0.0538392	+	0.00244525i
$365$	−1.65416e51			−0.00257292
$366$	−2.84372e53	+	2.97581e53i	−0.417623	+	0.437021i
$367$		−	1.35458e53i		−	0.187853i	−0.995579	−	0.0939265i	$-0.970058\pi$
$367$		−	1.35458e53i		−	0.187853i	0.995579	−	0.0939265i	$-0.0299419\pi$
$368$	4.84627e52	+	5.32423e53i	0.0634751	+	0.697353i
$369$	7.41374e52			0.0917241
$370$	1.87431e52	+	1.79111e52i	0.0219081	+	0.0209357i
$371$		−	1.40088e53i		−	0.154721i
$372$	−6.22663e51	−	1.37097e53i	−0.00649907	−	0.143096i
$373$	8.16209e53			0.805223			0.402611	−	0.915371i	$-0.368103\pi$
$373$	8.16209e53			0.805223			0.402611	+	0.915371i	$0.368103\pi$
$374$	−3.25997e53	+	3.41139e53i	−0.304026	+	0.318147i
$375$			5.74210e52i			0.0506308i
$376$	1.75730e54	+	1.53296e54i	1.46522	+	1.27816i
$377$	−4.56768e53			−0.360186
$378$	−1.23207e53	−	1.17738e53i	−0.0918983	−	0.0878192i
$379$			2.09757e54i			1.48011i	0.672547	+	0.740055i	$0.265200\pi$
$379$			2.09757e54i			1.48011i	−0.672547	+	0.740055i	$0.734800\pi$
$380$	1.00570e52	−	4.56763e50i	0.00671447	−	0.000304955i
$381$	−9.47832e53			−0.598834
$382$	−5.10793e53	+	5.34519e53i	−0.305432	+	0.319619i
$383$		−	5.80536e53i		−	0.328591i	−0.986411	−	0.164295i	$-0.947465\pi$
$383$		−	5.80536e53i		−	0.328591i	0.986411	−	0.164295i	$-0.0525350\pi$
$384$	1.14544e54	+	8.29113e53i	0.613786	+	0.444281i
$385$	−2.83556e51			−0.00143868
$386$	−1.54797e54	−	1.47926e54i	−0.743754	−	0.710741i
$387$			7.62870e53i			0.347153i
$388$	−9.88968e52	−	2.17750e54i	−0.0426301	−	0.938625i
$389$	−1.33629e54			−0.545707			−0.272853	−	0.962056i	$-0.587967\pi$
$389$	−1.33629e54			−0.545707			−0.272853	+	0.962056i	$0.587967\pi$
$390$	−2.07171e52	+	2.16794e52i	−0.00801628	+	0.00838862i
$391$			2.29737e54i			0.842401i
$392$	1.86535e54	−	2.13835e54i	0.648267	−	0.743140i
$393$	−2.41624e54			−0.795969
$394$	−1.46434e54	−	1.39934e54i	−0.457320	−	0.437021i
$395$			1.14594e53i			0.0339331i
$396$	−5.54209e53	+	2.51708e52i	−0.155623	+	0.00706804i
$397$	−2.83450e53			−0.0754875			−0.0377438	−	0.999287i	$-0.512017\pi$
$397$	−2.83450e53			−0.0754875			−0.0377438	+	0.999287i	$0.512017\pi$
$398$	1.84993e54	−	1.93586e54i	0.467316	−	0.489023i
$399$		−	7.47941e52i		−	0.0179241i
$400$	4.37505e54	−	3.98229e53i	0.994770	−	0.0905469i
$401$	3.94358e54			0.850860			0.425430	−	0.904991i	$-0.360123\pi$
$401$	3.94358e54			0.850860			0.425430	+	0.904991i	$0.360123\pi$
$402$	2.90017e54	+	2.77144e54i	0.593849	+	0.567490i
$403$		−	4.45577e53i		−	0.0865998i
$404$	−3.11544e53	−	6.85955e54i	−0.0574792	−	1.26557i
$405$	−7.49534e52			−0.0131291
$406$	−3.84270e53	+	4.02118e53i	−0.0639130	+	0.0668817i
$407$		−	2.09930e54i		−	0.331583i
$408$	4.57891e54	+	3.99435e54i	0.686909	+	0.599215i
$409$	−8.99142e54			−1.28126			−0.640632	−	0.767848i	$-0.721328\pi$
$409$	−8.99142e54			−1.28126			−0.640632	+	0.767848i	$0.721328\pi$
$410$	−3.84505e52	−	3.67438e52i	−0.00520525	−	0.00497420i
$411$		−	3.30406e54i		−	0.424981i
$412$	−1.34842e55	+	6.12421e53i	−1.64810	+	0.0748528i
$413$	−7.63262e53			−0.0886589
$414$	−1.86613e54	+	1.95281e54i	−0.206032	+	0.215602i
$415$			3.30331e53i			0.0346689i
$416$	3.59298e54	+	2.85787e54i	0.358504	+	0.285156i
$417$	2.65913e54			0.252279
$418$	−5.89371e53	−	5.63211e53i	−0.0531725	−	0.0508123i
$419$		−	7.21855e54i		−	0.619378i	−0.950838	−	0.309689i	$-0.899775\pi$
$419$		−	7.21855e54i		−	0.619378i	0.950838	−	0.309689i	$-0.100225\pi$
$420$	1.65669e51	+	3.64769e52i	0.000135209	+	0.00297703i
$421$	1.13827e55			0.883735			0.441867	−	0.897080i	$-0.354316\pi$
$421$	1.13827e55			0.883735			0.441867	+	0.897080i	$0.354316\pi$
$422$	1.44624e54	−	1.51341e54i	0.106826	−	0.111788i
$423$			1.17819e55i			0.828069i
$424$	−1.29252e55	+	1.48167e55i	−0.864477	+	0.990992i
$425$	1.88780e55			1.20168
$426$	1.07544e55	+	1.02770e55i	0.651604	+	0.622682i
$427$			1.62731e54i			0.0938608i
$428$	−2.88829e55	+	1.31179e54i	−1.58607	+	0.0720354i
$429$	2.42818e54			0.126963
$430$	3.78093e53	−	3.95654e53i	0.0188261	−	0.0197006i
$431$		−	2.34802e54i		−	0.111347i	−0.998449	−	0.0556735i	$-0.982269\pi$
$431$		−	2.34802e54i		−	0.111347i	0.998449	−	0.0556735i	$-0.0177306\pi$
$432$	2.16821e54	+	2.38205e55i	0.0979362	+	1.07595i
$433$	−1.65367e54			−0.0711546			−0.0355773	−	0.999367i	$-0.511327\pi$
$433$	−1.65367e54			−0.0711546			−0.0355773	+	0.999367i	$0.511327\pi$
$434$	−3.92266e53	−	3.74855e53i	−0.0160804	−	0.0153666i
$435$			5.09901e53i			0.0199164i
$436$	−1.01798e54	−	2.24139e55i	−0.0378900	−	0.834258i
$437$	−3.96906e54			−0.140792
$438$	1.19168e54	−	1.24703e54i	0.0402905	−	0.0421620i
$439$		−	5.82484e54i		−	0.187728i	−0.995585	−	0.0938639i	$-0.970078\pi$
$439$		−	5.82484e54i		−	0.187728i	0.995585	−	0.0938639i	$-0.0299219\pi$
$440$	2.99910e53	+	2.61622e53i	0.00921477	+	0.00803837i
$441$	1.43366e55			0.419986
$442$	1.42628e55	+	1.36297e55i	0.398417	+	0.380732i
$443$		−	6.75701e55i		−	1.80002i	−0.435874	−	0.900008i	$-0.643561\pi$
$443$		−	6.75701e55i		−	1.80002i	0.435874	−	0.900008i	$-0.356439\pi$
$444$	−2.70056e55	+	1.22653e54i	−0.686139	+	0.0311627i
$445$	−1.82071e54			−0.0441245
$446$	4.58632e55	−	4.79935e55i	1.06031	−	1.10956i
$447$			4.00613e54i			0.0883624i
$448$	5.53864e54	−	7.58831e53i	0.116564	−	0.0159701i
$449$	−3.66006e55			−0.735047			−0.367524	−	0.930014i	$-0.619794\pi$
$449$	−3.66006e55			−0.735047			−0.367524	+	0.930014i	$0.619794\pi$
$450$	1.60467e55	+	1.53344e55i	0.307555	+	0.293904i
$451$			4.30662e54i			0.0787823i
$452$	−4.23846e54	−	9.33219e55i	−0.0740117	−	1.62958i
$453$	−5.37074e55			−0.895306
$454$	−4.66158e54	+	4.87810e54i	−0.0741925	+	0.0776387i
$455$			1.18553e53i			0.00180166i
$456$	−6.90085e54	+	7.91079e54i	−0.100148	+	0.114804i
$457$	−2.65918e55			−0.368559			−0.184279	−	0.982874i	$-0.558995\pi$
$457$	−2.65918e55			−0.368559			−0.184279	+	0.982874i	$0.558995\pi$
$458$	−1.07957e55	−	1.03165e55i	−0.142915	−	0.136571i
$459$			1.02784e56i			1.29975i
$460$	1.93570e54	−	8.79148e52i	0.0233843	−	0.00106206i
$461$	4.10799e55			0.474144			0.237072	−	0.971492i	$-0.423812\pi$
$461$	4.10799e55			0.474144			0.237072	+	0.971492i	$0.423812\pi$
$462$	2.04278e54	−	2.13766e54i	0.0225289	−	0.0235753i
$463$			1.71681e56i			1.80935i	0.426102	+	0.904675i	$0.359886\pi$
$463$			1.71681e56i			1.80935i	−0.426102	+	0.904675i	$0.640114\pi$
$464$	7.77445e55	−	7.07653e54i	0.783055	−	0.0712759i
$465$	−4.97408e53			−0.00478852
$466$	5.37965e55	+	5.14086e55i	0.495050	+	0.473077i
$467$		−	9.73605e54i		−	0.0856502i	−0.999083	−	0.0428251i	$-0.986364\pi$
$467$		−	9.73605e54i		−	0.0856502i	0.999083	−	0.0428251i	$-0.0136358\pi$
$468$	1.05238e54	+	2.31711e55i	0.00885133	+	0.194888i
$469$	1.58594e55			0.127543
$470$	5.83931e54	−	6.11054e54i	0.0449062	−	0.0469921i
$471$			9.80398e55i			0.721047i
$472$	8.07283e55	+	7.04221e55i	0.567863	+	0.495367i
$473$	−4.43149e55			−0.298171
$474$	−8.63900e55	−	8.25554e55i	−0.556056	−	0.531374i
$475$			3.26147e55i			0.200839i
$476$	2.39980e55	−	1.08993e54i	0.141394	−	0.00642175i
$477$	−9.93391e55			−0.560060
$478$	−4.67733e55	+	4.89458e55i	−0.252355	+	0.264076i
$479$		−	3.55102e56i		−	1.83361i	−0.399332	−	0.916806i	$-0.630758\pi$
$479$		−	3.55102e56i		−	1.83361i	0.399332	−	0.916806i	$-0.369242\pi$
$480$	3.19030e54	−	4.01092e54i	0.0157676	−	0.0198234i
$481$	−8.77705e55			−0.415242
$482$	−1.83891e56	−	1.75729e56i	−0.832860	−	0.795893i
$483$		−	1.43959e55i		−	0.0624235i
$484$	9.46554e54	+	2.08411e56i	0.0393000	+	0.865304i
$485$	−7.90028e54			−0.0314099
$486$	−1.42044e56	+	1.48642e56i	−0.540831	+	0.565951i
$487$		−	1.38017e56i		−	0.503298i	−0.967819	−	0.251649i	$-0.919027\pi$
$487$		−	1.38017e56i		−	0.503298i	0.967819	−	0.251649i	$-0.0809729\pi$
$488$	1.50143e56	−	1.72116e56i	0.524431	−	0.601181i
$489$	3.93591e56			1.31692
$490$	−7.43551e54	−	7.10547e54i	−0.0238338	−	0.0227759i
$491$		−	3.96809e56i		−	1.21863i	−0.792930	−	0.609313i	$-0.791445\pi$
$491$		−	3.96809e56i		−	1.21863i	0.792930	−	0.609313i	$-0.208555\pi$
$492$	5.54007e55	−	2.51617e54i	0.163023	−	0.00740410i
$493$	3.35462e56			0.945928
$494$	−2.35475e55	+	2.46412e55i	−0.0636324	+	0.0665881i
$495$			2.01075e54i			0.00520773i
$496$	6.90316e54	+	7.58398e55i	0.0171369	+	0.188270i
$497$	5.88098e55			0.139948
$498$	−2.49029e56	−	2.37976e56i	−0.568112	−	0.542896i
$499$			4.45340e56i			0.974047i	0.873389	+	0.487024i	$0.161917\pi$
$499$			4.45340e56i			0.974047i	−0.873389	+	0.487024i	$0.838083\pi$
$500$	−1.44564e54	−	3.18300e55i	−0.00303173	−	0.0667523i
$501$	3.19707e56			0.642924
$502$	−6.21785e56	+	6.50666e56i	−1.19912	+	1.25482i
$503$		−	6.94983e56i		−	1.28542i	−0.766108	−	0.642712i	$-0.777809\pi$
$503$		−	6.94983e56i		−	1.28542i	0.766108	−	0.642712i	$-0.222191\pi$
$504$	2.12842e55	+	1.85669e55i	0.0377586	+	0.0329381i
$505$	−2.48874e55			−0.0423507
$506$	−1.13438e56	−	1.08403e56i	−0.185182	−	0.176962i
$507$			3.82282e56i			0.598710i
$508$	5.25408e56	−	2.38627e55i	0.789511	−	0.0358577i
$509$	−2.51933e56			−0.363255			−0.181627	−	0.983367i	$-0.558136\pi$
$509$	−2.51933e56			−0.363255			−0.181627	+	0.983367i	$0.558136\pi$
$510$	1.52152e55	−	1.59219e55i	0.0210525	−	0.0220304i
$511$		−	6.81933e54i		−	0.00905530i
$512$	−6.55821e56	−	4.30761e56i	−0.835827	−	0.548993i
$513$	−1.77575e56			−0.217229
$514$	5.53147e56	+	5.28595e56i	0.649554	+	0.620723i
$515$			4.89227e55i			0.0551516i
$516$	2.58912e55	+	5.70071e56i	0.0280227	+	0.617000i
$517$	−6.84405e56			−0.711233
$518$	−7.38395e55	+	7.72692e55i	−0.0736824	+	0.0771048i
$519$			9.26207e56i			0.887552i
$520$	1.09382e55	−	1.25390e55i	0.0100665	−	0.0115397i
$521$	−7.30470e56			−0.645669			−0.322835	−	0.946455i	$-0.604636\pi$
$521$	−7.30470e56			−0.645669			−0.322835	+	0.946455i	$0.604636\pi$
$522$	2.85150e56	+	2.72493e56i	0.242099	+	0.231353i
$523$			4.77962e56i			0.389815i	0.980822	+	0.194907i	$0.0624406\pi$
$523$			4.77962e56i			0.389815i	−0.980822	+	0.194907i	$0.937559\pi$
$524$	1.33938e57	−	6.08315e55i	1.04942	−	0.0476619i
$525$	−1.18294e56			−0.0890468
$526$	1.20019e57	−	1.25594e57i	0.868062	−	0.908382i
$527$			3.27243e56i			0.227430i
$528$	−4.13290e56	+	3.76189e55i	−0.276022	+	0.0251243i
$529$	7.94067e56			0.509669
$530$	5.15211e55	+	4.92343e55i	0.0317828	+	0.0303721i
$531$			5.41244e56i			0.320928i
$532$	1.88303e54	+	4.14603e55i	0.00107328	+	0.0236313i
$533$	1.80057e56			0.0986593
$534$	1.31166e57	−	1.37259e57i	0.690965	−	0.723060i
$535$			1.04791e56i			0.0530757i
$536$	−1.67741e57	−	1.46326e57i	−0.816919	−	0.712627i
$537$	−1.42388e57			−0.666829
$538$	−6.61030e56	−	6.31689e56i	−0.297710	−	0.284496i
$539$			8.32807e56i			0.360728i
$540$	8.66028e55	−	3.93329e54i	0.0360797	−	0.00163865i
$541$	−1.50294e57			−0.602282			−0.301141	−	0.953580i	$-0.597367\pi$
$541$	−1.50294e57			−0.602282			−0.301141	+	0.953580i	$0.597367\pi$
$542$	2.47694e57	−	2.59199e57i	0.954840	−	0.999191i
$543$		−	2.35010e57i		−	0.871547i
$544$	−2.63877e57	−	2.09889e57i	−0.941511	−	0.748881i
$545$	−8.13207e55			−0.0279174
$546$	−8.93743e55	−	8.54073e55i	−0.0295235	−	0.0282130i
$547$		−	2.57378e57i		−	0.818159i	−0.912499	−	0.409079i	$-0.865850\pi$
$547$		−	2.57378e57i		−	0.818159i	0.912499	−	0.409079i	$-0.134150\pi$
$548$	8.31833e55	+	1.83152e57i	0.0254475	+	0.560300i
$549$	1.15396e57			0.339758
$550$	−8.90773e56	+	9.32148e56i	−0.252436	+	0.264161i
$551$			5.79563e56i			0.158095i
$552$	−1.32823e57	+	1.52262e57i	−0.348781	+	0.399825i
$553$	−4.72420e56			−0.119426
$554$	4.52979e57	+	4.32873e57i	1.10249	+	1.05355i
$555$			9.79802e55i			0.0229607i
$556$	−1.47402e57	+	6.69465e55i	−0.332608	+	0.0151063i
$557$	5.81481e57			1.26350			0.631752	−	0.775171i	$-0.282336\pi$
$557$	5.81481e57			1.26350			0.631752	+	0.775171i	$0.282336\pi$
$558$	−2.65817e56	+	2.78164e56i	−0.0556243	+	0.0582080i
$559$			1.85278e57i			0.373401i
$560$	−1.83669e54	−	2.01784e55i	−0.000356524	−	0.00391686i
$561$	−1.78332e57			−0.333433
$562$	2.71420e57	+	2.59373e57i	0.488855	+	0.467156i
$563$			1.05561e57i			0.183158i	0.995798	+	0.0915790i	$0.0291914\pi$
$563$			1.05561e57i			0.183158i	−0.995798	+	0.0915790i	$0.970809\pi$
$564$	3.99868e56	+	8.80425e57i	0.0668429	+	1.47174i
$565$	−3.38585e56			−0.0545319
$566$	−7.56877e57	+	7.92033e57i	−1.17457	+	1.22913i
$567$		−	3.08999e56i		−	0.0462075i
$568$	−6.22017e57	−	5.42607e57i	−0.896370	−	0.781934i
$569$	6.51005e57			0.904122			0.452061	−	0.891987i	$-0.350689\pi$
$569$	6.51005e57			0.904122			0.452061	+	0.891987i	$0.350689\pi$
$570$	2.75076e55	+	2.62866e55i	0.00368197	+	0.00351854i
$571$		−	6.32329e57i		−	0.815803i	−0.913026	−	0.407901i	$-0.866261\pi$
$571$		−	6.32329e57i		−	0.815803i	0.913026	−	0.407901i	$-0.133739\pi$
$572$	−1.34600e57	+	6.11322e55i	−0.167390	+	0.00760245i
$573$	−2.79422e57			−0.334975
$574$	1.51478e56	−	1.58514e56i	0.0175065	−	0.0183197i
$575$			6.27746e57i			0.699454i
$576$	−5.38102e56	−	3.92756e57i	−0.0578086	−	0.421940i
$577$	9.58365e57			0.992747			0.496374	−	0.868109i	$-0.334665\pi$
$577$	9.58365e57			0.992747			0.496374	+	0.868109i	$0.334665\pi$
$578$	−3.23720e57	−	3.09351e57i	−0.323359	−	0.309006i
$579$		−	8.09207e57i		−	0.779489i
$580$	−1.28373e55	−	2.82651e56i	−0.00119258	−	0.0262581i
$581$	−1.36180e57			−0.122016
$582$	5.69148e57	−	5.95584e57i	0.491861	−	0.514708i
$583$		−	5.77058e57i		−	0.481038i
$584$	−6.29183e56	+	7.21263e56i	−0.0505950	+	0.0579995i
$585$	8.40681e55			0.00652166
$586$	−1.05709e58	−	1.01017e58i	−0.791155	−	0.756038i
$587$			1.32139e57i			0.0954183i	0.998861	+	0.0477091i	$0.0151921\pi$
$587$			1.32139e57i			0.0954183i	−0.998861	+	0.0477091i	$0.984808\pi$
$588$	1.07133e58	−	4.86573e56i	0.746448	−	0.0339019i
$589$	−5.65364e56			−0.0380108
$590$	2.68250e56	−	2.80710e56i	0.0174040	−	0.0182124i
$591$		−	7.65487e57i		−	0.479293i
$592$	1.49390e58	−	1.35979e57i	0.902748	−	0.0821708i
$593$	−2.98318e58			−1.73993			−0.869963	−	0.493116i	$-0.835858\pi$
$593$	−2.98318e58			−1.73993			−0.869963	+	0.493116i	$0.835858\pi$
$594$	−5.07521e57	−	4.84993e57i	−0.285718	−	0.273036i
$595$		−	8.70682e55i		−	0.00473155i
$596$	−1.00859e56	−	2.22070e57i	−0.00529106	−	0.116498i
$597$	1.01198e58			0.512519
$598$	−4.53226e57	+	4.74278e57i	−0.221610	+	0.231904i
$599$			3.01989e58i			1.42570i	0.701317	+	0.712850i	$0.252596\pi$
$599$			3.01989e58i			1.42570i	−0.701317	+	0.712850i	$0.747404\pi$
$600$	1.25117e58	+	1.09144e58i	0.570347	+	0.497534i
$601$	−1.27916e58			−0.563067			−0.281533	−	0.959551i	$-0.590843\pi$
$601$	−1.27916e58			−0.563067			−0.281533	+	0.959551i	$0.590843\pi$
$602$	1.63110e57	+	1.55870e57i	0.0693354	+	0.0662578i
$603$		−	1.12462e58i		−	0.461682i
$604$	2.97714e58	−	1.35214e57i	1.18038	−	0.0536102i
$605$	7.56146e56			0.0289563
$606$	1.79293e58	−	1.87621e58i	0.663189	−	0.693993i
$607$			2.17658e58i			0.777700i	0.921301	+	0.388850i	$0.127128\pi$
$607$			2.17658e58i			0.777700i	−0.921301	+	0.388850i	$0.872872\pi$
$608$	3.62616e57	−	4.55889e57i	0.125162	−	0.157356i
$609$	−2.10209e57			−0.0700951
$610$	−5.98486e56	−	5.71922e56i	−0.0192809	−	0.0184251i
$611$			2.86145e58i			0.890679i
$612$	−7.72892e56	−	1.70175e58i	−0.0232455	−	0.511817i
$613$	−3.40102e57			−0.0988414			−0.0494207	−	0.998778i	$-0.515738\pi$
$613$	−3.40102e57			−0.0988414			−0.0494207	+	0.998778i	$0.515738\pi$
$614$	−3.44092e58	+	3.60074e58i	−0.966359	+	1.01124i
$615$		−	2.01002e56i		−	0.00545534i
$616$	−1.07855e57	+	1.23639e57i	−0.0282907	+	0.0324310i
$617$	−2.44309e58			−0.619372			−0.309686	−	0.950839i	$-0.600224\pi$
$617$	−2.44309e58			−0.619372			−0.309686	+	0.950839i	$0.600224\pi$
$618$	−3.68817e58	−	3.52446e58i	−0.903760	−	0.863645i
$619$			2.88767e58i			0.683981i	0.939703	+	0.341990i	$0.111101\pi$
$619$			2.88767e58i			0.683981i	−0.939703	+	0.341990i	$0.888899\pi$
$620$	2.75726e56	−	1.25228e55i	0.00631325	−	0.000286732i
$621$	−3.41785e58			−0.756535
$622$	−1.68109e58	+	1.75918e58i	−0.359744	+	0.376454i
$623$		−	7.50594e57i		−	0.155294i
$624$	1.57282e57	+	1.72794e58i	0.0314632	+	0.345663i
$625$	5.15255e58			0.996649
$626$	2.45077e58	+	2.34199e58i	0.458398	+	0.438051i
$627$		−	3.08096e57i		−	0.0557272i
$628$	−2.46826e57	−	5.43460e58i	−0.0431757	−	0.950638i
$629$	6.44608e58			1.09052
$630$	7.07248e55	−	7.40098e55i	0.00115723	−	0.00121098i
$631$		−	6.93780e58i		−	1.09801i	−0.835820	−	0.549004i	$-0.815007\pi$
$631$		−	6.93780e58i		−	1.09801i	0.835820	−	0.549004i	$-0.184993\pi$
$632$	4.99666e58	+	4.35876e58i	0.764930	+	0.667275i
$633$	7.91143e57			0.117159
$634$	5.40910e58	+	5.16900e58i	0.774908	+	0.740512i
$635$		−	1.90625e57i		−	0.0264200i
$636$	−7.42333e58	+	3.37149e57i	−0.995403	+	0.0452088i
$637$	3.48191e58			0.451741
$638$	−1.58290e58	+	1.65643e58i	−0.198710	+	0.207940i
$639$		−	4.17032e58i		−	0.506584i
$640$	−1.66749e57	+	2.30368e57i	−0.0196012	+	0.0270796i
$641$	−6.03172e57			−0.0686155			−0.0343078	−	0.999411i	$-0.510923\pi$
$641$	−6.03172e57			−0.0686155			−0.0343078	+	0.999411i	$0.510923\pi$
$642$	−7.89998e58	−	7.54933e58i	−0.869742	−	0.831137i
$643$		−	1.54137e59i		−	1.64239i	−0.570647	−	0.821196i	$-0.693308\pi$
$643$		−	1.54137e59i		−	1.64239i	0.570647	−	0.821196i	$-0.306692\pi$
$644$	3.62433e56	+	7.98001e57i	0.00373787	+	0.0823000i
$645$	2.06830e57			0.0206471
$646$	1.72939e58	−	1.80971e58i	0.167113	−	0.174875i
$647$		−	7.90460e58i		−	0.739418i	−0.929148	−	0.369709i	$-0.879457\pi$
$647$		−	7.90460e58i		−	0.739418i	0.929148	−	0.369709i	$-0.120543\pi$
$648$	−2.85097e58	+	3.26820e58i	−0.258177	+	0.295960i
$649$	−3.14407e58			−0.275647
$650$	3.89725e58	+	3.72427e58i	0.330809	+	0.316126i
$651$		−	2.05059e57i		−	0.0168530i
$652$	−2.18178e59	+	9.90910e57i	−1.73624	+	0.0788560i
$653$	3.37848e58			0.260342			0.130171	−	0.991492i	$-0.458447\pi$
$653$	3.37848e58			0.260342			0.130171	+	0.991492i	$0.458447\pi$
$654$	5.85847e58	−	6.13058e58i	0.437171	−	0.457477i
$655$		−	4.85947e57i		−	0.0351173i
$656$	−3.06467e58	+	2.78955e57i	−0.214488	+	0.0195233i
$657$	−4.83572e57			−0.0327784
$658$	2.51910e58	+	2.40728e58i	0.165387	+	0.158046i
$659$			2.58519e59i			1.64399i	0.569494	+	0.821996i	$0.307139\pi$
$659$			2.58519e59i			1.64399i	−0.569494	+	0.821996i	$0.692861\pi$
$660$	6.82433e55	+	1.50258e57i	0.000420376	+	0.00925579i
$661$	8.64392e58			0.515798			0.257899	−	0.966172i	$-0.416970\pi$
$661$	8.64392e58			0.515798			0.257899	+	0.966172i	$0.416970\pi$
$662$	4.90202e58	−	5.12971e58i	0.283372	−	0.296534i
$663$			7.45594e58i			0.417559i
$664$	1.44035e59	+	1.25646e59i	0.781515	+	0.681743i
$665$	1.50424e56			0.000790792
$666$	5.47931e58	+	5.23610e58i	0.279105	+	0.266716i
$667$			1.11550e59i			0.550590i
$668$	−1.77222e59	+	8.04898e57i	−0.847639	+	0.0384977i
$669$	2.50888e59			1.16287
$670$	−5.57384e57	+	5.83273e57i	−0.0250371	+	0.0262000i
$671$			6.70329e58i			0.291820i
$672$	1.65352e58	+	1.31522e58i	0.0697678	+	0.0554936i
$673$	−4.09831e59			−1.67606			−0.838028	−	0.545627i	$-0.816292\pi$
$673$	−4.09831e59			−1.67606			−0.838028	+	0.545627i	$0.816292\pi$
$674$	2.48163e59	+	2.37148e59i	0.983737	+	0.940072i
$675$			2.80852e59i			1.07919i
$676$	−9.62437e57	−	2.11909e59i	−0.0358502	−	0.789347i
$677$	−3.65667e59			−1.32045			−0.660227	−	0.751066i	$-0.729540\pi$
$677$	−3.65667e59			−1.32045			−0.660227	+	0.751066i	$0.729540\pi$
$678$	2.43922e59	−	2.55252e59i	0.853940	−	0.893604i
$679$		−	3.25692e58i		−	0.110546i
$680$	−8.03332e57	+	9.20899e57i	−0.0264367	+	0.0303057i
$681$	−2.55005e58			−0.0813690
$682$	−1.61585e58	−	1.54412e58i	−0.0499951	−	0.0477760i
$683$		−	2.27291e59i		−	0.681942i	−0.940074	−	0.340971i	$-0.889244\pi$
$683$		−	2.27291e59i		−	0.681942i	0.940074	−	0.340971i	$-0.110756\pi$
$684$	2.94003e58	−	1.33529e57i	0.0855409	−	0.00388506i
$685$	6.64502e57			0.0187497
$686$	5.89964e58	−	6.17367e58i	0.161443	−	0.168942i
$687$		−	5.64351e58i		−	0.149781i
$688$	−2.87044e58	−	3.15353e59i	−0.0738909	−	0.811784i
$689$	−2.41264e59			−0.602406
$690$	5.29448e57	+	5.05947e57i	0.0128231	+	0.0122539i
$691$		−	4.18131e59i		−	0.982365i	−0.871057	−	0.491183i	$-0.836565\pi$
$691$		−	4.18131e59i		−	0.982365i	0.871057	−	0.491183i	$-0.163435\pi$
$692$	−2.33183e58	−	5.13421e59i	−0.0531459	−	1.17016i
$693$	−8.28940e57			−0.0183284
$694$	2.89869e58	−	3.03333e58i	0.0621803	−	0.0650685i
$695$			5.34796e57i			0.0111303i
$696$	2.22333e59	+	1.93948e59i	0.448961	+	0.391645i
$697$	−1.32238e59			−0.259101
$698$	−2.62957e59	−	2.51285e59i	−0.499943	−	0.477752i
$699$			2.81223e59i			0.518836i
$700$	6.55735e58	−	2.97819e57i	0.117400	−	0.00533204i
$701$	5.84394e59			1.01538			0.507688	−	0.861541i	$-0.330500\pi$
$701$	5.84394e59			1.01538			0.507688	+	0.861541i	$0.330500\pi$
$702$	−2.02773e59	+	2.12191e59i	−0.341924	+	0.357806i
$703$			1.11366e59i			0.182260i
$704$	2.28151e59	−	3.12582e58i	0.362406	−	0.0496521i
$705$	3.19431e58			0.0492499
$706$	−1.82569e59	−	1.74465e59i	−0.273230	−	0.261102i
$707$		−	1.02599e59i		−	0.149052i
$708$	1.83694e58	+	4.04456e59i	0.0259058	+	0.570391i
$709$	9.90676e59			1.35632			0.678158	−	0.734917i	$-0.262779\pi$
$709$	9.90676e59			1.35632			0.678158	+	0.734917i	$0.262779\pi$
$710$	−2.06689e58	+	2.16289e58i	−0.0274721	+	0.0287481i
$711$			3.35002e59i			0.432301i
$712$	−6.92533e59	+	7.93884e59i	−0.867682	+	0.994666i
$713$	−1.08817e59			−0.132379
$714$	6.56388e58	+	6.27253e58i	0.0775350	+	0.0740935i
$715$			4.88349e57i			0.00560149i
$716$	7.89295e59	−	3.58479e58i	0.879156	−	0.0399291i
$717$	−2.55866e59			−0.276764
$718$	−1.05259e60	+	1.10148e60i	−1.10573	+	1.15708i
$719$		−	4.61888e59i		−	0.471227i	−0.971847	−	0.235614i	$-0.924290\pi$
$719$		−	4.61888e59i		−	0.471227i	0.971847	−	0.235614i	$-0.0757100\pi$
$720$	−1.43089e58	+	1.30244e57i	−0.0141783	+	0.00129055i
$721$	−2.01686e59			−0.194104
$722$	−7.42129e59	−	7.09189e59i	−0.693743	−	0.662950i
$723$		−	9.61296e59i		−	0.872877i
$724$	5.91665e58	+	1.30272e60i	0.0521875	+	1.14906i
$725$	9.16635e59			0.785414
$726$	−5.44739e59	+	5.70041e59i	−0.453440	+	0.474501i
$727$			8.28045e59i			0.669625i	0.942285	+	0.334812i	$0.108673\pi$
$727$			8.28045e59i			0.669625i	−0.942285	+	0.334812i	$0.891327\pi$
$728$	5.16927e58	+	4.50934e58i	0.0406135	+	0.0354286i
$729$	−1.29153e60			−0.985887
$730$	2.50799e57	+	2.39667e57i	0.00186014	+	0.00177758i
$731$		−	1.36073e60i		−	0.980632i
$732$	8.62318e59	−	3.91644e58i	0.603858	−	0.0274258i
$733$	1.18634e60			0.807286			0.403643	−	0.914917i	$-0.367744\pi$
$733$	1.18634e60			0.807286			0.403643	+	0.914917i	$0.367744\pi$
$734$	−1.96263e59	+	2.05379e59i	−0.129784	+	0.135812i
$735$		−	3.88694e58i		−	0.0249789i
$736$	6.97939e59	−	8.77465e59i	0.435897	−	0.548019i
$737$	6.53290e59			0.396542
$738$	−1.12405e59	−	1.07416e59i	−0.0663138	−	0.0633703i
$739$			4.03960e59i			0.231636i	0.993270	+	0.115818i	$0.0369489\pi$
$739$			4.03960e59i			0.231636i	−0.993270	+	0.115818i	$0.963051\pi$
$740$	−2.46676e57	−	5.43130e58i	−0.00137487	−	0.0302717i
$741$	−1.28813e59			−0.0697874
$742$	−2.02971e59	+	2.12398e59i	−0.106893	+	0.111858i
$743$		−	7.38373e59i		−	0.378017i	−0.981975	−	0.189008i	$-0.939473\pi$
$743$		−	7.38373e59i		−	0.378017i	0.981975	−	0.189008i	$-0.0605273\pi$
$744$	−1.89197e59	+	2.16886e59i	−0.0941634	+	0.107944i
$745$	−8.05702e57			−0.00389846
$746$	−1.23752e60	−	1.18259e60i	−0.582152	−	0.556312i
$747$			9.65682e59i			0.441674i
$748$	9.88539e59	−	4.48971e58i	0.439603	−	0.0199657i
$749$	−4.32007e59			−0.186798
$750$	8.31962e58	−	8.70605e58i	0.0349798	−	0.0366045i
$751$			1.60774e60i			0.657321i	0.944448	+	0.328660i	$0.106597\pi$
$751$			1.60774e60i			0.657321i	−0.944448	+	0.328660i	$0.893403\pi$
$752$	−4.43314e59	−	4.87036e60i	−0.176253	−	1.93636i
$753$	−3.40138e60			−1.31511
$754$	6.92541e59	+	6.61802e59i	0.260404	+	0.248845i
$755$		−	1.08015e59i		−	0.0395000i
$756$	1.62152e58	+	3.57024e59i	0.00576718	+	0.126981i
$757$	5.73788e60			1.98490			0.992449	−	0.122660i	$-0.0391423\pi$
$757$	5.73788e60			1.98490			0.992449	+	0.122660i	$0.0391423\pi$
$758$	3.03913e60	−	3.18029e60i	1.02258	−	1.07007i
$759$		−	5.93003e59i		−	0.194079i
$760$	−1.59100e58	−	1.38788e58i	−0.00506505	−	0.00441842i
$761$	−5.46630e60			−1.69284			−0.846420	−	0.532516i	$-0.821247\pi$
$761$	−5.46630e60			−1.69284			−0.846420	+	0.532516i	$0.821247\pi$
$762$	1.43708e60	+	1.37329e60i	0.432939	+	0.413722i
$763$		−	3.35248e59i		−	0.0982541i
$764$	1.54891e60	−	7.03476e58i	0.441636	−	0.0200580i
$765$	−6.17418e58			−0.0171273
$766$	−8.41127e59	+	8.80196e59i	−0.227016	+	0.237561i
$767$			1.31451e60i			0.345194i
$768$	−5.35407e59	−	2.91669e60i	−0.136804	−	0.745254i
$769$	−4.22678e60			−1.05089			−0.525444	−	0.850828i	$-0.676101\pi$
$769$	−4.22678e60			−1.05089			−0.525444	+	0.850828i	$0.676101\pi$
$770$	4.29921e57	+	4.10838e57i	0.00104012	+	0.000993952i
$771$			2.89160e60i			0.680763i
$772$	2.03727e59	+	4.48565e60i	0.0466751	+	1.02769i
$773$	−2.42828e60			−0.541413			−0.270707	−	0.962662i	$-0.587257\pi$
$773$	−2.42828e60			−0.541413			−0.270707	+	0.962662i	$0.587257\pi$
$774$	1.10531e60	−	1.15665e60i	0.239841	−	0.250981i
$775$			8.94178e59i			0.188837i
$776$	−3.00499e60	+	3.44477e60i	−0.617656	+	0.708050i
$777$	−4.03928e59			−0.0808094
$778$	2.02605e60	+	1.93612e60i	0.394529	+	0.377018i
$779$		−	2.28462e59i		−	0.0433040i
$780$	6.28217e58	−	2.85321e57i	0.0115911	−	0.000526438i
$781$	2.42253e60			0.435108
$782$	3.32861e60	−	3.48322e60i	0.581997	−	0.609030i
$783$			4.99074e60i			0.849509i
$784$	−5.92641e60	+	5.39439e59i	−0.982098	+	0.0893934i
$785$	−1.97175e59			−0.0318119
$786$	3.66345e60	+	3.50084e60i	0.575462	+	0.549919i
$787$			2.39485e60i			0.366276i	0.983087	+	0.183138i	$0.0586255\pi$
$787$			2.39485e60i			0.366276i	−0.983087	+	0.183138i	$0.941374\pi$
$788$	1.92720e59	+	4.24329e60i	0.0286996	+	0.631906i
$789$	6.56548e60			0.952027
$790$	1.66033e59	−	1.73745e59i	0.0234437	−	0.0245326i
$791$		−	1.39583e60i		−	0.191923i
$792$	8.76749e59	+	7.64819e59i	0.117394	+	0.102407i
$793$	2.80260e60			0.365447
$794$	4.29760e59	+	4.10684e59i	0.0545752	+	0.0521528i
$795$			2.69329e59i			0.0333099i
$796$	−5.60965e60	+	2.54777e59i	−0.675711	+	0.0306892i
$797$	1.48763e61			1.74531			0.872653	−	0.488341i	$-0.162398\pi$
$797$	1.48763e61			1.74531			0.872653	+	0.488341i	$0.162398\pi$
$798$	−1.08368e59	+	1.13401e59i	−0.0123834	+	0.0129586i
$799$		−	2.10152e61i		−	2.33912i
$800$	−7.21033e60	−	5.73513e60i	−0.781746	−	0.621804i
$801$	−5.32261e60			−0.562136
$802$	−5.97916e60	−	5.71377e60i	−0.615146	−	0.587842i
$803$		−	2.80905e59i		−	0.0281536i
$804$	−3.81689e59	−	8.40398e60i	−0.0372677	−	0.820556i
$805$	2.89526e58			0.00275406
$806$	−6.45588e59	+	6.75574e59i	−0.0598301	+	0.0626091i
$807$		−	3.45556e60i		−	0.312014i
$808$	−9.46630e60	+	1.08517e61i	−0.832802	+	0.954682i
$809$	−2.03352e61			−1.74313			−0.871566	−	0.490278i	$-0.836895\pi$
$809$	−2.03352e61			−1.74313			−0.871566	+	0.490278i	$0.836895\pi$
$810$	1.13643e59	+	1.08598e59i	0.00949196	+	0.00907064i
$811$		−	1.53565e61i		−	1.24984i	−0.780690	−	0.624918i	$-0.785132\pi$
$811$		−	1.53565e61i		−	1.24984i	0.780690	−	0.624918i	$-0.214868\pi$
$812$	1.16524e60	−	5.29224e58i	0.0924143	−	0.00419724i
$813$	1.35497e61			1.04720
$814$	−3.04164e60	+	3.18291e60i	−0.229084	+	0.239725i
$815$			7.91579e59i			0.0581011i
$816$	−1.15512e60	−	1.26904e61i	−0.0826293	−	0.907785i
$817$	2.35087e60			0.163895
$818$	1.36326e61	+	1.30275e61i	0.926315	+	0.885199i
$819$			3.46575e59i			0.0229528i
$820$	5.06044e57	+	1.11420e59i	0.000326661	+	0.00719240i
$821$	1.81566e61			1.14243			0.571213	−	0.820802i	$-0.306473\pi$
$821$	1.81566e61			1.14243			0.571213	+	0.820802i	$0.306473\pi$
$822$	−4.78718e60	+	5.00954e60i	−0.293610	+	0.307248i
$823$		−	1.44335e61i		−	0.862926i	−0.902131	−	0.431463i	$-0.857998\pi$
$823$		−	1.44335e61i		−	0.862926i	0.902131	−	0.431463i	$-0.142002\pi$
$824$	2.13318e61	+	1.86085e61i	1.24324	+	1.08452i
$825$	−4.87284e60			−0.276853
$826$	1.15724e60	+	1.10587e60i	0.0640977	+	0.0612526i
$827$			3.36003e61i			1.81438i	0.420723	+	0.907189i	$0.361776\pi$
$827$			3.36003e61i			1.81438i	−0.420723	+	0.907189i	$0.638224\pi$
$828$	5.65878e60	−	2.57008e59i	0.297910	−	0.0135304i
$829$	3.70062e60			0.189946			0.0949728	−	0.995480i	$-0.469724\pi$
$829$	3.70062e60			0.189946			0.0949728	+	0.995480i	$0.469724\pi$
$830$	4.78610e59	−	5.00841e59i	0.0239520	−	0.0250645i
$831$			2.36796e61i			1.15546i
$832$	−1.30688e60	−	9.53883e60i	−0.0621795	−	0.453842i
$833$	−2.55720e61			−1.18637
$834$	−4.03171e60	−	3.85275e60i	−0.182390	−	0.174295i
$835$			6.42985e59i			0.0283651i
$836$	7.75666e58	+	1.70786e60i	0.00333690	+	0.0734716i
$837$	−4.86847e60			−0.204248
$838$	−1.04588e61	+	1.09446e61i	−0.427915	+	0.447791i
$839$			1.11644e61i			0.445485i	0.974877	+	0.222743i	$0.0715010\pi$
$839$			1.11644e61i			0.445485i	−0.974877	+	0.222743i	$0.928499\pi$
$840$	5.03388e58	−	5.77058e58i	0.00195901	−	0.00224571i
$841$	−1.00575e61			−0.381745
$842$	−1.72582e61	−	1.64922e61i	−0.638914	−	0.610554i
$843$			1.41886e61i			0.512343i
$844$	−4.38551e60	+	1.99179e59i	−0.154464	+	0.00701540i
$845$	−7.68834e59			−0.0264145
$846$	1.70705e61	−	1.78634e61i	0.572096	−	0.598669i
$847$			3.11724e60i			0.101911i
$848$	4.10645e61	−	3.73781e60i	1.30965	−	0.119208i
$849$	−4.14038e61			−1.28819
$850$	−2.86224e61	−	2.73519e61i	−0.868778	−	0.830215i
$851$			2.14350e61i			0.634750i
$852$	−1.41538e60	−	3.11636e61i	−0.0408922	−	0.900360i
$853$	5.94368e61			1.67543			0.837714	−	0.546110i	$-0.183892\pi$
$853$	5.94368e61			1.67543			0.837714	+	0.546110i	$0.183892\pi$
$854$	2.35777e60	−	2.46729e60i	0.0648465	−	0.0678585i
$855$		−	1.06668e59i		−	0.00286251i
$856$	4.56923e61	+	3.98590e61i	1.19645	+	1.04370i
$857$	−4.31421e61			−1.10231			−0.551155	−	0.834403i	$-0.685813\pi$
$857$	−4.31421e61			−1.10231			−0.551155	+	0.834403i	$0.685813\pi$
$858$	−3.68155e60	−	3.51814e60i	−0.0917906	−	0.0877163i
$859$		−	7.01571e61i		−	1.70693i	−0.521153	−	0.853463i	$-0.674498\pi$
$859$		−	7.01571e61i		−	1.70693i	0.521153	−	0.853463i	$-0.325502\pi$
$860$	−1.14651e60	+	5.20718e58i	−0.0272214	+	0.00123633i
$861$	8.28638e59			0.0191999
$862$	−3.40199e60	+	3.56001e60i	−0.0769273	+	0.0805005i
$863$			3.88175e61i			0.856646i	0.903626	+	0.428323i	$0.140895\pi$
$863$			3.88175e61i			0.856646i	−0.903626	+	0.428323i	$0.859105\pi$
$864$	3.12257e61	−	3.92576e61i	0.672548	−	0.845542i
$865$	−1.86276e60			−0.0391579
$866$	2.50726e60	+	2.39597e60i	0.0514426	+	0.0491593i
$867$		−	1.69226e61i		−	0.338896i
$868$	5.16259e58	+	1.13669e60i	0.00100914	+	0.0222192i
$869$	−1.94602e61			−0.371305
$870$	7.38785e59	−	7.73100e59i	0.0137598	−	0.0143990i
$871$		−	2.73136e61i		−	0.496590i
$872$	−3.09316e61	+	3.54583e61i	−0.548979	+	0.629321i
$873$	−2.30955e61			−0.400155
$874$	6.01780e60	+	5.75069e60i	0.101788	+	0.0972702i
$875$		−	4.76086e59i		−	0.00786170i
$876$	−3.61359e60	+	1.64121e59i	−0.0582577	+	0.00264592i
$877$	1.20481e62			1.89638			0.948190	−	0.317704i	$-0.102912\pi$
$877$	1.20481e62			1.89638			0.948190	+	0.317704i	$0.102912\pi$
$878$	−8.43949e60	+	8.83149e60i	−0.129697	+	0.135722i
$879$		−	5.52597e61i		−	0.829167i
$880$	−7.56581e58	−	8.31198e59i	−0.00110846	−	0.0121778i
$881$	−1.28803e61			−0.184260			−0.0921300	−	0.995747i	$-0.529368\pi$
$881$	−1.28803e61			−0.184260			−0.0921300	+	0.995747i	$0.529368\pi$
$882$	−2.17368e61	−	2.07720e61i	−0.303637	−	0.290160i
$883$		−	4.02178e61i		−	0.548584i	−0.961646	−	0.274292i	$-0.911557\pi$
$883$		−	4.02178e61i		−	0.548584i	0.961646	−	0.274292i	$-0.0884435\pi$
$884$	−1.87712e60	−	4.13302e61i	−0.0250031	−	0.550516i
$885$	1.46742e60			0.0190874
$886$	−9.79009e61	+	1.02448e62i	−1.24359	+	1.30136i
$887$			8.18220e61i			1.01502i	0.861646	+	0.507509i	$0.169434\pi$
$887$			8.18220e61i			1.01502i	−0.861646	+	0.507509i	$0.830566\pi$
$888$	4.27224e61	+	3.72683e61i	0.517587	+	0.451509i
$889$	7.85861e60			0.0929841
$890$	2.76051e60	+	2.63798e60i	0.0319007	+	0.0304847i
$891$		−	1.27284e61i		−	0.143662i
$892$	−1.39073e62	+	6.31638e60i	−1.53314	+	0.0696316i
$893$	3.63071e61			0.390941
$894$	5.80440e60	−	6.07401e60i	0.0610478	−	0.0638833i
$895$		−	2.86367e60i		−	0.0294198i
$896$	−9.49701e60	−	6.87429e60i	−0.0953057	−	0.0689858i
$897$	−2.47931e61			−0.243046
$898$	5.54930e61	+	5.30299e61i	0.531417	+	0.507829i
$899$			1.58895e61i			0.148648i
$900$	−2.11189e60	−	4.64995e61i	−0.0193010	−	0.424967i
$901$	1.77190e62			1.58205
$902$	6.23977e60	−	6.52960e60i	0.0544291	−	0.0569572i
$903$			8.52665e60i			0.0726667i
$904$	−1.28786e62	+	1.47634e62i	−1.07234	+	1.22927i
$905$	4.72646e60			0.0384517
$906$	8.14299e61	+	7.78155e61i	0.647279	+	0.618549i
$907$		−	3.58390e60i		−	0.0278357i	−0.999903	−	0.0139179i	$-0.995570\pi$
$907$		−	3.58390e60i		−	0.0278357i	0.999903	−	0.0139179i	$-0.00443034\pi$
$908$	1.41356e61	−	6.42003e59i	0.107278	−	0.00487230i
$909$	−7.27553e61			−0.539539
$910$	1.71769e59	−	1.79747e59i	0.00124473	−	0.00130255i
$911$			8.84583e61i			0.626402i	0.949687	+	0.313201i	$0.101401\pi$
$911$			8.84583e61i			0.626402i	−0.949687	+	0.313201i	$0.898599\pi$
$912$	2.19247e61	−	1.99565e60i	0.151720	−	0.0138100i
$913$	−5.60962e61			−0.379356
$914$	4.03178e61	+	3.85283e61i	0.266457	+	0.254630i
$915$		−	3.12861e60i		−	0.0202073i
$916$	1.42082e60	+	3.12834e61i	0.00896877	+	0.197474i
$917$	2.00334e61			0.123594
$918$	1.48921e62	−	1.55838e62i	0.897968	−	0.939677i
$919$		−	2.09830e62i		−	1.23664i	−0.785928	−	0.618318i	$-0.787814\pi$
$919$		−	2.09830e62i		−	1.23664i	0.785928	−	0.618318i	$-0.212186\pi$
$920$	−3.06224e60	−	2.67130e60i	−0.0176399	−	0.0153879i
$921$	−1.88230e62			−1.05983
$922$	−6.22845e61	−	5.95199e61i	−0.342792	−	0.327576i
$923$		−	1.01284e62i		−	0.544887i
$924$	−6.19443e60	+	2.81336e59i	−0.0325754	+	0.00147950i
$925$	1.76136e62			0.905467
$926$	2.48746e62	−	2.60300e62i	1.25004	−	1.30811i
$927$			1.43019e62i			0.702620i
$928$	−1.28128e62	−	1.01913e62i	−0.615368	−	0.489466i
$929$	−3.21600e62			−1.51003			−0.755016	−	0.655706i	$-0.772371\pi$
$929$	−3.21600e62			−1.51003			−0.755016	+	0.655706i	$0.772371\pi$
$930$	7.54159e59	+	7.20685e59i	0.00346195	+	0.00330829i
$931$		−	4.41797e61i		−	0.198280i
$932$	−7.08011e60	−	1.55889e62i	−0.0310675	−	0.684041i
$933$	−9.19616e61			−0.394541
$934$	−1.41064e61	+	1.47616e61i	−0.0591739	+	0.0619225i
$935$		−	3.58656e60i		−	0.0147107i
$936$	3.19766e61	−	3.66563e61i	0.128245	−	0.147013i
$937$	1.32864e62			0.521046			0.260523	−	0.965468i	$-0.416105\pi$
$937$	1.32864e62			0.521046			0.260523	+	0.965468i	$0.416105\pi$
$938$	−2.40457e61	−	2.29784e61i	−0.0922100	−	0.0881171i
$939$			1.28115e62i			0.480422i
$940$	−1.77069e61	+	8.04203e59i	−0.0649317	+	0.00294904i
$941$	−2.93928e61			−0.105404			−0.0527022	−	0.998610i	$-0.516783\pi$
$941$	−2.93928e61			−0.105404			−0.0527022	+	0.998610i	$0.516783\pi$
$942$	1.42048e62	−	1.48646e62i	0.498156	−	0.521295i
$943$		−	4.39729e61i		−	0.150813i
$944$	−2.03653e61	−	2.23738e62i	−0.0683091	−	0.750460i
$945$	1.29533e60			0.00424926
$946$	6.71893e61	+	6.42070e61i	0.215569	+	0.206000i
$947$			4.90269e62i			1.53846i	0.638975	+	0.769228i	$0.279359\pi$
$947$			4.90269e62i			1.53846i	−0.638975	+	0.769228i	$0.720641\pi$
$948$	1.13697e61	+	2.50337e62i	0.0348959	+	0.768335i
$949$	−1.17445e61			−0.0352568
$950$	4.72547e61	−	4.94496e61i	0.138755	−	0.145200i
$951$			2.82762e62i			0.812140i
$952$	−3.79644e61	−	3.31177e61i	−0.106660	−	0.0930432i
$953$	−2.11237e62			−0.580523			−0.290262	−	0.956947i	$-0.593742\pi$
$953$	−2.11237e62			−0.580523			−0.290262	+	0.956947i	$0.593742\pi$
$954$	1.50616e62	+	1.43930e62i	0.404906	+	0.386934i
$955$		−	5.61965e60i		−	0.0147788i
$956$	1.41833e62	−	6.44172e60i	0.364890	−	0.0165724i
$957$	−8.65903e61			−0.217931
$958$	−5.14500e62	+	5.38398e62i	−1.26681	+	1.32565i
$959$			2.73944e61i			0.0659889i
$960$	−1.06484e61	+	1.45891e60i	−0.0250951	+	0.00343820i
$961$	4.18201e62			0.964261
$962$	1.33076e62	+	1.27169e62i	0.300208	+	0.286883i
$963$			3.06344e62i			0.676173i
$964$	2.42017e61	+	5.32871e62i	0.0522671	+	1.15081i
$965$	1.62746e61			0.0343903
$966$	−2.08579e61	+	2.18267e61i	−0.0431271	+	0.0451303i
$967$		−	6.87865e62i		−	1.39171i	−0.718184	−	0.695853i	$-0.755027\pi$
$967$		−	6.87865e62i		−	1.39171i	0.718184	−	0.695853i	$-0.244973\pi$
$968$	2.87612e62	−	3.29703e62i	0.569408	−	0.652741i
$969$	9.46035e61			0.183277
$970$	1.19782e61	+	1.14466e61i	0.0227084	+	0.0217004i
$971$		−	4.29558e62i		−	0.796926i	−0.917184	−	0.398463i	$-0.869544\pi$
$971$		−	4.29558e62i		−	0.796926i	0.917184	−	0.398463i	$-0.130456\pi$
$972$	4.30728e62	−	1.95626e61i	0.782009	−	0.0355169i
$973$	−2.20472e61			−0.0391727
$974$	−1.99970e62	+	2.09259e62i	−0.347718	+	0.363869i
$975$			2.03730e62i			0.346704i
$976$	−4.77019e62	+	4.34197e61i	−0.794492	+	0.0723170i
$977$	1.97346e62			0.321693			0.160846	−	0.986979i	$-0.448578\pi$
$977$	1.97346e62			0.321693			0.160846	+	0.986979i	$0.448578\pi$
$978$	−5.96754e62	−	5.70266e62i	−0.952093	−	0.909832i
$979$		−	3.09189e62i		−	0.482822i
$980$	9.78581e59	+	2.15463e61i	0.00149572	+	0.0329325i
$981$	−2.37731e62			−0.355661
$982$	−5.74929e62	+	6.01634e62i	−0.841924	+	0.881030i
$983$		−	1.19008e63i		−	1.70589i	−0.522002	−	0.852944i	$-0.674815\pi$
$983$		−	1.19008e63i		−	1.70589i	0.522002	−	0.852944i	$-0.325185\pi$
$984$	−8.76430e61	−	7.64540e61i	−0.122976	−	0.107276i
$985$	1.53953e61			0.0211459
$986$	−5.08620e62	−	4.86044e62i	−0.683877	−	0.653522i
$987$			1.31687e62i			0.173333i
$988$	7.14043e61	−	3.24301e60i	0.0920087	−	0.00417881i
$989$	4.52479e62			0.570790
$990$	2.91333e60	−	3.04865e60i	0.00359792	−	0.00376503i
$991$		−	3.46585e62i		−	0.419047i	−0.977804	−	0.209524i	$-0.932809\pi$
$991$		−	3.46585e62i		−	0.419047i	0.977804	−	0.209524i	$-0.0671913\pi$
$992$	9.94163e61	−	1.24988e62i	0.117683	−	0.147953i
$993$	2.68157e62			0.310782
$994$	−8.91661e61	−	8.52083e61i	−0.101178	−	0.0966870i
$995$			2.03526e61i			0.0226118i
$996$	3.27745e61	+	7.21627e62i	0.0356525	+	0.784994i
$997$	1.39534e63			1.48622			0.743109	−	0.669171i	$-0.233351\pi$
$997$	1.39534e63			1.48622			0.743109	+	0.669171i	$0.233351\pi$
$998$	6.45244e62	−	6.75214e62i	0.672949	−	0.704207i
$999$			9.58998e62i			0.979361i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.43.b.a.3.5	✓	20
4.3	odd	2	inner	4.43.b.a.3.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.43.b.a.3.5	✓	20	1.1	even	1	trivial
4.43.b.a.3.6	yes	20	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:	\( k \)	\(=\)	\( 43 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.51618e6 - 1.44888e6i) q^{2} -7.92587e9i q^{3} +(1.99543e11 + 4.39352e12i) q^{4} +1.59403e13 q^{5} +(-1.14836e16 + 1.20170e16i) q^{6} +6.57146e16i q^{7} +(6.06313e18 - 6.95047e18i) q^{8} +4.65995e19 q^{9} +O(q^{10})\)	\(q+(-1.51618e6 - 1.44888e6i) q^{2} -7.92587e9i q^{3} +(1.99543e11 + 4.39352e12i) q^{4} +1.59403e13 q^{5} +(-1.14836e16 + 1.20170e16i) q^{6} +6.57146e16i q^{7} +(6.06313e18 - 6.95047e18i) q^{8} +4.65995e19 q^{9} +(-2.41683e19 - 2.30956e19i) q^{10} +2.70695e21i q^{11} +(3.48225e22 - 1.58155e21i) q^{12} +1.13176e23 q^{13} +(9.52125e22 - 9.96350e22i) q^{14} -1.26341e23i q^{15} +(-1.92632e25 + 1.75339e24i) q^{16} -8.31192e25 q^{17} +(-7.06531e25 - 6.75171e25i) q^{18} -1.43601e26i q^{19} +(3.18077e24 + 7.00340e25i) q^{20} +5.20846e26 q^{21} +(3.92204e27 - 4.10422e27i) q^{22} -2.76394e28i q^{23} +(-5.50885e28 - 4.80556e28i) q^{24} -2.27120e29 q^{25} +(-1.71595e29 - 1.63978e29i) q^{26} -1.23658e30i q^{27} +(-2.88718e29 + 1.31129e28i) q^{28} -4.03591e30 q^{29} +(-1.83053e29 + 1.91555e29i) q^{30} -3.93704e30i q^{31} +(3.17469e31 + 2.52516e31i) q^{32} +2.14549e31 q^{33} +(1.26023e32 + 1.20430e32i) q^{34} +1.04751e30i q^{35} +(9.29860e30 + 2.04736e32i) q^{36} -7.75523e32 q^{37} +(-2.08061e32 + 2.17725e32i) q^{38} -8.97018e32i q^{39} +(9.66482e31 - 1.10793e32i) q^{40} +1.59095e33 q^{41} +(-7.89694e32 - 7.54642e32i) q^{42} +1.63708e34i q^{43} +(-1.18930e34 + 5.40153e32i) q^{44} +7.42810e32 q^{45} +(-4.00462e34 + 4.19063e34i) q^{46} +2.52833e35i q^{47} +(1.38972e34 + 1.52678e35i) q^{48} +3.07655e35 q^{49} +(3.44354e35 + 3.29069e35i) q^{50} +6.58792e35i q^{51} +(2.25834e34 + 4.97240e35i) q^{52} -2.13176e36 q^{53} +(-1.79166e36 + 1.87488e36i) q^{54} +4.31496e34i q^{55} +(4.56747e35 + 3.98436e35i) q^{56} -1.13817e36 q^{57} +(6.11916e36 + 5.84755e36i) q^{58} +1.16148e37i q^{59} +(5.55081e35 - 2.52104e34i) q^{60} +2.47633e37 q^{61} +(-5.70429e36 + 5.96925e36i) q^{62} +3.06227e36i q^{63} +(-1.15474e37 - 8.42832e37i) q^{64} +1.80406e36 q^{65} +(-3.25295e37 - 3.10856e37i) q^{66} -2.41338e38i q^{67} +(-1.65858e37 - 3.65186e38i) q^{68} -2.19067e38 q^{69} +(1.51772e36 - 1.58821e36i) q^{70} -8.94928e38i q^{71} +(2.82539e38 - 3.23888e38i) q^{72} -1.03772e38 q^{73} +(1.17583e39 + 1.12364e39i) q^{74} +1.80012e39i q^{75} +(6.30915e38 - 2.86546e37i) q^{76} -1.77886e38 q^{77} +(-1.29967e39 + 1.36004e39i) q^{78} +7.18896e39i q^{79} +(-3.07061e38 + 2.79496e37i) q^{80} -4.70213e39 q^{81} +(-2.41216e39 - 2.30509e39i) q^{82} +2.07230e40i q^{83} +(1.03931e38 + 2.28834e39i) q^{84} -1.32494e39 q^{85} +(2.37193e40 - 2.48210e40i) q^{86} +3.19882e40i q^{87} +(1.88146e40 + 1.64126e40i) q^{88} -1.14220e41 q^{89} +(-1.12623e39 - 1.07624e39i) q^{90} +7.43730e39i q^{91} +(1.21434e41 - 5.51525e39i) q^{92} -3.12045e40 q^{93} +(3.66324e41 - 3.83339e41i) q^{94} -2.28905e39i q^{95} +(2.00141e41 - 2.51622e41i) q^{96} -4.95617e41 q^{97} +(-4.66460e41 - 4.45755e41i) q^{98} +1.26143e41i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 802164 q^{2} + 1311168818192 q^{4} + 139235684997000 q^{5} + 68\!\cdots\!12 q^{6}+ \cdots - 73\!\cdots\!76 q^{9}+O(q^{10}) \) 20 * q + 802164 * q^2 + 1311168818192 * q^4 + 139235684997000 * q^5 + 6838718638036512 * q^6 - 27661415389266953664 * q^8 - 733170595646091132876 * q^9	\( 20 q + 802164 q^{2} + 1311168818192 q^{4} + 139235684997000 q^{5} + 68\!\cdots\!12 q^{6}+ \cdots + 18\!\cdots\!96 q^{98}+O(q^{100}) \) 20 * q + 802164 * q^2 + 1311168818192 * q^4 + 139235684997000 * q^5 + 6838718638036512 * q^6 - 27661415389266953664 * q^8 - 733170595646091132876 * q^9 + 42625185369378343240 * q^10 - 25848729272513843675520 * q^12 - 144898631886191567496248 * q^13 - 306990738295992471121728 * q^14 + 27792040878005009897120000 * q^16 + 81746542725793625328399528 * q^17 - 217831601203830755951030124 * q^18 + 6344592401135696008447573920 * q^20 + 7651089590961386749851047424 * q^21 - 46254109397133274566238240800 * q^22 + 506607644284406956508290140672 * q^24 + 844166434154191999887370985820 * q^25 + 305910330554143989456096580488 * q^26 - 1621415041794921570009743366400 * q^28 + 8494173617816210057524981535304 * q^29 + 32483836243012295467926394800960 * q^30 - 117067340157863901568162598132736 * q^32 - 195434629079924022845409037850880 * q^33 - 435728002928020507520645688017048 * q^34 + 905808650859207966395798479569552 * q^36 + 320827308804868360600766816935048 * q^37 - 834801746373065199942054885540960 * q^38 - 2080347678511686114819737054821760 * q^40 + 12238592465130696350192985088255080 * q^41 + 39180793491987624842407723014766080 * q^42 - 40147560736600746149658671246198400 * q^44 - 57674168870802092374169153418160440 * q^45 - 133593585977858896021440512714708928 * q^46 + 223617847456028179696661192651827200 * q^48 - 763663932888918132103393205670102316 * q^49 - 1073296820241355924814923786366326660 * q^50 - 580677968103327319151855528386839392 * q^52 + 3592528655430046000719727125882705672 * q^53 + 8087462166590362832897538370358812224 * q^54 - 4056862272141293872664295528725971968 * q^56 + 1376964140105307936676325853454767360 * q^57 - 17787847411919404506009575679670206968 * q^58 + 27803845757503537955964429994460432640 * q^60 - 72876803820111699199759396563493728440 * q^61 - 83779848218915601601226708273126396160 * q^62 - 51258837764961549702163120437185671168 * q^64 + 143337782114217802520090675036041365840 * q^65 + 479881795533282188176080436671310498560 * q^66 - 201679039132028748396903074185205050848 * q^68 + 496255895990320623770556878095159325184 * q^69 + 244550326432622351468933399511720393600 * q^70 + 1389470702024602675984554222025462031424 * q^72 + 675217186810136917874725959945538619752 * q^73 - 5048325762233564608985375515346235670968 * q^74 - 727730227778639944706768217921060021120 * q^76 - 13945771646073577607404274150247166932480 * q^77 + 2630485389052859541031650397045824087360 * q^78 - 14080069438753558698176635521889841825280 * q^80 + 50326416439524122225413610454605570342484 * q^81 + 38442316210858292795461617709768475559208 * q^82 + 21041665749991691364416236667734761560064 * q^84 - 100747029416581567610441680879732008651760 * q^85 - 109399875737541346773887857542693387248928 * q^86 + 61542411942227832459784035156153652876800 * q^88 + 298677519739918601751826215340976530195944 * q^89 + 5248331693055749298139854308097091987080 * q^90 - 311056321102768653749854891753699429405440 * q^92 - 902946967697899772252214392286633142732800 * q^93 - 120754391334239789606838050760853185629568 * q^94 - 369891338439189821551415861997759233875968 * q^96 + 2729077788738058742150638081801454021515048 * q^97 + 1829330555781863715528793474157579946873396 * q^98

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