LMFDB - Embedded newform 4.43.b.a.3.3

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			3.3
Root			$0.500000 - 5.41536e8i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.43.b.a.3.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.05360e6 - 425178. i) q^{2} +8.66457e9i q^{3} +(4.03649e12 + 1.74629e12i) q^{4} -5.87785e14 q^{5} +(3.68399e15 - 1.77936e16i) q^{6} -1.08401e18i q^{7} +(-7.54686e18 - 5.30241e18i) q^{8} +3.43442e19 q^{9} +O(q^{10})$	\(q+(-2.05360e6 - 425178. i) q^{2} +8.66457e9i q^{3} +(4.03649e12 + 1.74629e12i) q^{4} -5.87785e14 q^{5} +(3.68399e15 - 1.77936e16i) q^{6} -1.08401e18i q^{7} +(-7.54686e18 - 5.30241e18i) q^{8} +3.43442e19 q^{9} +(1.20707e21 + 2.49913e20i) q^{10} -1.54708e21i q^{11} +(-1.51309e22 + 3.49745e22i) q^{12} -2.11810e23 q^{13} +(-4.60896e23 + 2.22612e24i) q^{14} -5.09290e24i q^{15} +(1.32437e25 + 1.40978e25i) q^{16} +9.80292e25 q^{17} +(-7.05292e25 - 1.46024e25i) q^{18} +6.85144e26i q^{19} +(-2.37259e27 - 1.02644e27i) q^{20} +9.39246e27 q^{21} +(-6.57783e26 + 3.17707e27i) q^{22} -7.24896e28i q^{23} +(4.59431e28 - 6.53903e28i) q^{24} +1.18117e29 q^{25} +(4.34974e29 + 9.00572e28i) q^{26} +1.24565e30i q^{27} +(1.89299e30 - 4.37559e30i) q^{28} +5.49253e29 q^{29} +(-2.16539e30 + 1.04588e31i) q^{30} -3.73986e30i q^{31} +(-2.12033e31 - 3.45822e31i) q^{32} +1.34048e31 q^{33} +(-2.01313e32 - 4.16799e31i) q^{34} +6.37163e32i q^{35} +(1.38630e32 + 5.99749e31i) q^{36} -5.40076e32 q^{37} +(2.91308e32 - 1.40701e33i) q^{38} -1.83525e33i q^{39} +(4.43593e33 + 3.11668e33i) q^{40} +6.20060e32 q^{41} +(-1.92883e34 - 3.99347e33i) q^{42} +1.07740e33i q^{43} +(2.70165e33 - 6.24476e33i) q^{44} -2.01870e34 q^{45} +(-3.08210e34 + 1.48865e35i) q^{46} -2.86955e34i q^{47} +(-1.22151e35 + 1.14751e35i) q^{48} -8.63099e35 q^{49} +(-2.42565e35 - 5.02208e34i) q^{50} +8.49381e35i q^{51} +(-8.54971e35 - 3.69883e35i) q^{52} +1.08405e36 q^{53} +(5.29622e35 - 2.55806e36i) q^{54} +9.09348e35i q^{55} +(-5.74785e36 + 8.18085e36i) q^{56} -5.93648e36 q^{57} +(-1.12795e36 - 2.33530e35i) q^{58} +7.58262e36i q^{59} +(8.89369e36 - 2.05575e37i) q^{60} -2.45473e37 q^{61} +(-1.59011e36 + 7.68017e36i) q^{62} -3.72293e37i q^{63} +(2.88395e37 + 8.00331e37i) q^{64} +1.24499e38 q^{65} +(-2.75280e37 - 5.69941e36i) q^{66} -2.23091e38i q^{67} +(3.95694e38 + 1.71187e38i) q^{68} +6.28092e38 q^{69} +(2.70908e38 - 1.30848e39i) q^{70} +4.36094e38i q^{71} +(-2.59191e38 - 1.82107e38i) q^{72} -1.36538e39 q^{73} +(1.10910e39 + 2.29629e38i) q^{74} +1.02343e39i q^{75} +(-1.19646e39 + 2.76558e39i) q^{76} -1.67704e39 q^{77} +(-7.80307e38 + 3.76886e39i) q^{78} +5.82641e38i q^{79} +(-7.78447e39 - 8.28646e39i) q^{80} -7.03509e39 q^{81} +(-1.27335e39 - 2.63636e38i) q^{82} -6.65169e39i q^{83} +(3.79126e40 + 1.64020e40i) q^{84} -5.76200e40 q^{85} +(4.58086e38 - 2.21254e39i) q^{86} +4.75904e39i q^{87} +(-8.20323e39 + 1.16756e40i) q^{88} -3.51819e40 q^{89} +(4.14560e40 + 8.58306e39i) q^{90} +2.29604e41i q^{91} +(1.26588e41 - 2.92604e41i) q^{92} +3.24043e40 q^{93} +(-1.22007e40 + 5.89291e40i) q^{94} -4.02717e41i q^{95} +(2.99640e41 - 1.83717e41i) q^{96} -6.45753e41 q^{97} +(1.77246e42 + 3.66971e41i) q^{98} -5.31331e40i 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 $

$2$	−2.05360e6	−	425178.i	−0.979232	−	0.202741i
$2$	−2.05360e6	−	425178.i	−0.979232	−	0.202741i
$3$			8.66457e9i			0.828325i	0.910203	+	0.414163i	$0.135925\pi$
$3$			8.66457e9i			0.828325i	−0.910203	+	0.414163i	$0.864075\pi$
$4$	4.03649e12	+	1.74629e12i	0.917792	+	0.397061i
$5$	−5.87785e14			−1.23267			−0.616337	−	0.787483i	$-0.711384\pi$
$5$	−5.87785e14			−1.23267			−0.616337	+	0.787483i	$0.711384\pi$
$6$	3.68399e15	−	1.77936e16i	0.167935	−	0.811123i
$7$		−	1.08401e18i		−	1.94077i	−0.241570	−	0.970384i	$-0.577662\pi$
$7$		−	1.08401e18i		−	1.94077i	0.241570	−	0.970384i	$-0.422338\pi$
$8$	−7.54686e18	−	5.30241e18i	−0.818232	−	0.574889i
$9$	3.43442e19			0.313878
$10$	1.20707e21	+	2.49913e20i	1.20707	+	0.249913i
$11$		−	1.54708e21i		−	0.209057i	−0.994522	−	0.104529i	$-0.966667\pi$
$11$		−	1.54708e21i		−	0.209057i	0.994522	−	0.104529i	$-0.0333334\pi$
$12$	−1.51309e22	+	3.49745e22i	−0.328895	+	0.760230i
$13$	−2.11810e23			−0.857308			−0.428654	−	0.903469i	$-0.641012\pi$
$13$	−2.11810e23			−0.857308			−0.428654	+	0.903469i	$0.641012\pi$
$14$	−4.60896e23	+	2.22612e24i	−0.393473	+	1.90046i
$15$		−	5.09290e24i		−	1.02105i
$16$	1.32437e25	+	1.40978e25i	0.684686	+	0.728838i
$17$	9.80292e25			1.41882			0.709411	−	0.704795i	$-0.248961\pi$
$17$	9.80292e25			1.41882			0.709411	+	0.704795i	$0.248961\pi$
$18$	−7.05292e25	−	1.46024e25i	−0.307359	−	0.0636358i
$19$			6.85144e26i			0.959303i	0.877459	+	0.479652i	$0.159237\pi$
$19$			6.85144e26i			0.959303i	−0.877459	+	0.479652i	$0.840763\pi$
$20$	−2.37259e27	−	1.02644e27i	−1.13134	−	0.489446i
$21$	9.39246e27			1.60759
$22$	−6.57783e26	+	3.17707e27i	−0.0423844	+	0.204716i
$23$		−	7.24896e28i		−	1.83650i	−0.395999	−	0.918251i	$-0.629602\pi$
$23$		−	7.24896e28i		−	1.83650i	0.395999	−	0.918251i	$-0.370398\pi$
$24$	4.59431e28	−	6.53903e28i	0.476195	−	0.677762i
$25$	1.18117e29			0.519484
$26$	4.34974e29	+	9.00572e28i	0.839504	+	0.173811i
$27$			1.24565e30i			1.08832i
$28$	1.89299e30	−	4.37559e30i	0.770602	−	1.78122i
$29$	5.49253e29			0.107008			0.0535038	−	0.998568i	$-0.482961\pi$
$29$	5.49253e29			0.107008			0.0535038	+	0.998568i	$0.482961\pi$
$30$	−2.16539e30	+	1.04588e31i	−0.207009	+	0.999850i
$31$		−	3.73986e30i		−	0.179581i	−0.995961	−	0.0897903i	$-0.971380\pi$
$31$		−	3.73986e30i		−	0.179581i	0.995961	−	0.0897903i	$-0.0286197\pi$
$32$	−2.12033e31	−	3.45822e31i	−0.522701	−	0.852516i
$33$	1.34048e31			0.173167
$34$	−2.01313e32	−	4.16799e31i	−1.38936	−	0.287653i
$35$			6.37163e32i			2.39233i
$36$	1.38630e32	+	5.99749e31i	0.288075	+	0.124628i
$37$	−5.40076e32			−0.631275			−0.315638	−	0.948880i	$-0.602218\pi$
$37$	−5.40076e32			−0.631275			−0.315638	+	0.948880i	$0.602218\pi$
$38$	2.91308e32	−	1.40701e33i	0.194490	−	0.939381i
$39$		−	1.83525e33i		−	0.710130i
$40$	4.43593e33	+	3.11668e33i	1.00861	+	0.708650i
$41$	6.20060e32			0.0839407			0.0419703	−	0.999119i	$-0.486636\pi$
$41$	6.20060e32			0.0839407			0.0419703	+	0.999119i	$0.486636\pi$
$42$	−1.92883e34	−	3.99347e33i	−1.57420	−	0.325923i
$43$			1.07740e33i			0.0536461i	0.999640	+	0.0268231i	$0.00853907\pi$
$43$			1.07740e33i			0.0536461i	−0.999640	+	0.0268231i	$0.991461\pi$
$44$	2.70165e33	−	6.24476e33i	0.0830084	−	0.191871i
$45$	−2.01870e34			−0.386909
$46$	−3.08210e34	+	1.48865e35i	−0.372334	+	1.79836i
$47$		−	2.86955e34i		−	0.220678i	−0.993894	−	0.110339i	$-0.964806\pi$
$47$		−	2.86955e34i		−	0.220678i	0.993894	−	0.110339i	$-0.0351937\pi$
$48$	−1.22151e35	+	1.14751e35i	−0.603715	+	0.567142i
$49$	−8.63099e35			−2.76658
$50$	−2.42565e35	−	5.02208e34i	−0.508696	−	0.105321i
$51$			8.49381e35i			1.17525i
$52$	−8.54971e35	−	3.69883e35i	−0.786831	−	0.340403i
$53$	1.08405e36			0.668738			0.334369	−	0.942442i	$-0.391477\pi$
$53$	1.08405e36			0.668738			0.334369	+	0.942442i	$0.391477\pi$
$54$	5.29622e35	−	2.55806e36i	0.220646	−	1.06572i
$55$			9.09348e35i			0.257699i
$56$	−5.74785e36	+	8.18085e36i	−1.11572	+	1.58800i
$57$	−5.93648e36			−0.794615
$58$	−1.12795e36	−	2.33530e35i	−0.104785	−	0.0216948i
$59$			7.58262e36i			0.491957i	0.969275	+	0.245978i	$0.0791093\pi$
$59$			7.58262e36i			0.491957i	−0.969275	+	0.245978i	$0.920891\pi$
$60$	8.89369e36	−	2.05575e37i	0.405420	−	0.937116i
$61$	−2.45473e37			−0.790820			−0.395410	−	0.918505i	$-0.629397\pi$
$61$	−2.45473e37			−0.790820			−0.395410	+	0.918505i	$0.629397\pi$
$62$	−1.59011e36	+	7.68017e36i	−0.0364083	+	0.175851i
$63$		−	3.72293e37i		−	0.609163i
$64$	2.88395e37	+	8.00331e37i	0.339006	+	0.940784i
$65$	1.24499e38			1.05678
$66$	−2.75280e37	−	5.69941e36i	−0.169571	−	0.0351081i
$67$		−	2.23091e38i		−	1.00210i	−0.865419	−	0.501050i	$-0.832947\pi$
$67$		−	2.23091e38i		−	1.00210i	0.865419	−	0.501050i	$-0.167053\pi$
$68$	3.95694e38	+	1.71187e38i	1.30218	+	0.563358i
$69$	6.28092e38			1.52122
$70$	2.70908e38	−	1.30848e39i	0.485023	−	2.34265i
$71$			4.36094e38i			0.579635i	0.957082	+	0.289817i	$0.0935946\pi$
$71$			4.36094e38i			0.579635i	−0.957082	+	0.289817i	$0.906405\pi$
$72$	−2.59191e38	−	1.82107e38i	−0.256825	−	0.180445i
$73$	−1.36538e39			−1.01268			−0.506341	−	0.862334i	$-0.669002\pi$
$73$	−1.36538e39			−1.01268			−0.506341	+	0.862334i	$0.669002\pi$
$74$	1.10910e39	+	2.29629e38i	0.618165	+	0.127985i
$75$			1.02343e39i			0.430302i
$76$	−1.19646e39	+	2.76558e39i	−0.380902	+	0.880441i
$77$	−1.67704e39			−0.405731
$78$	−7.80307e38	+	3.76886e39i	−0.143972	+	0.695382i
$79$			5.82641e38i			0.0822683i	0.999154	+	0.0411341i	$0.0130971\pi$
$79$			5.82641e38i			0.0822683i	−0.999154	+	0.0411341i	$0.986903\pi$
$80$	−7.78447e39	−	8.28646e39i	−0.843994	−	0.898420i
$81$	−7.03509e39			−0.587603
$82$	−1.27335e39	−	2.63636e38i	−0.0821975	−	0.0170182i
$83$		−	6.65169e39i		−	0.332883i	−0.986051	−	0.166442i	$-0.946772\pi$
$83$		−	6.65169e39i		−	0.332883i	0.986051	−	0.166442i	$-0.0532278\pi$
$84$	3.79126e40	+	1.64020e40i	1.47543	+	0.638309i
$85$	−5.76200e40			−1.74895
$86$	4.58086e38	−	2.21254e39i	0.0108763	−	0.0525320i
$87$			4.75904e39i			0.0886370i
$88$	−8.20323e39	+	1.16756e40i	−0.120185	+	0.171057i
$89$	−3.51819e40			−0.406565			−0.203282	−	0.979120i	$-0.565161\pi$
$89$	−3.51819e40			−0.406565			−0.203282	+	0.979120i	$0.565161\pi$
$90$	4.14560e40	+	8.58306e39i	0.378874	+	0.0784422i
$91$			2.29604e41i			1.66384i
$92$	1.26588e41	−	2.92604e41i	0.729203	−	1.68553i
$93$	3.24043e40			0.148751
$94$	−1.22007e40	+	5.89291e40i	−0.0447405	+	0.216095i
$95$		−	4.02717e41i		−	1.18251i
$96$	2.99640e41	−	1.83717e41i	0.706160	−	0.432967i
$97$	−6.45753e41			−1.22422			−0.612111	−	0.790772i	$-0.709679\pi$
$97$	−6.45753e41			−1.22422			−0.612111	+	0.790772i	$0.709679\pi$
$98$	1.77246e42	+	3.66971e41i	2.70912	+	0.560898i
$99$		−	5.31331e40i		−	0.0656184i
$100$	4.76779e41	+	2.06267e41i	0.476779	+	0.206267i
$101$	−6.44421e41			−0.522903			−0.261451	−	0.965217i	$-0.584201\pi$
$101$	−6.44421e41			−0.522903			−0.261451	+	0.965217i	$0.584201\pi$
$102$	3.61138e41	−	1.74429e42i	0.238270	−	1.15084i
$103$			3.14771e41i			0.169205i	0.996415	+	0.0846024i	$0.0269620\pi$
$103$			3.14771e41i			0.169205i	−0.996415	+	0.0846024i	$0.973038\pi$
$104$	1.59850e42	+	1.12311e42i	0.701477	+	0.492857i
$105$	−5.52074e42			−1.98163
$106$	−2.22620e42	−	4.60914e41i	−0.654850	−	0.135580i
$107$			5.00693e42i			1.20924i	0.796514	+	0.604620i	$0.206675\pi$
$107$			5.00693e42i			1.20924i	−0.796514	+	0.604620i	$0.793325\pi$
$108$	−2.17526e42	+	5.02804e42i	−0.432128	+	0.998850i
$109$	−1.11163e43			−1.81971			−0.909855	−	0.414927i	$-0.863807\pi$
$109$	−1.11163e43			−1.81971			−0.909855	+	0.414927i	$0.863807\pi$
$110$	3.86635e41	−	1.86744e42i	0.0522462	−	0.252348i
$111$		−	4.67953e42i		−	0.522901i
$112$	1.52821e43	−	1.43563e43i	1.41451	−	1.32882i
$113$	−6.59469e42			−0.506462			−0.253231	−	0.967406i	$-0.581493\pi$
$113$	−6.59469e42			−0.506462			−0.253231	+	0.967406i	$0.581493\pi$
$114$	1.21911e43	+	2.52406e42i	0.778113	+	0.161101i
$115$			4.26083e43i			2.26381i
$116$	2.21706e42	+	9.59155e41i	0.0982107	+	0.0424885i
$117$	−7.27445e42			−0.269090
$118$	3.22396e42	−	1.55717e43i	0.0997397	−	0.481740i
$119$		−	1.06264e44i		−	2.75360i
$120$	−2.70047e43	+	3.84354e43i	−0.586992	+	0.835459i
$121$	5.23703e43			0.956295
$122$	5.04103e43	+	1.04370e43i	0.774396	+	0.160331i
$123$			5.37255e42i			0.0695302i
$124$	6.53088e42	−	1.50959e43i	0.0713044	−	0.164818i
$125$	6.42194e43			0.592319
$126$	−1.58291e43	+	7.64541e43i	−0.123502	+	0.596513i
$127$			1.39241e44i			0.920218i	0.887863	+	0.460109i	$0.152190\pi$
$127$			1.39241e44i			0.920218i	−0.887863	+	0.460109i	$0.847810\pi$
$128$	−2.51964e43	−	1.76618e44i	−0.141231	−	0.989977i
$129$	−9.33519e42			−0.0444364
$130$	−2.55671e44	−	5.29342e43i	−1.03483	−	0.214253i
$131$		−	4.81877e42i		−	0.0166050i	−0.999966	−	0.00830251i	$-0.997357\pi$
$131$		−	4.81877e42i		−	0.0166050i	0.999966	−	0.00830251i	$-0.00264280\pi$
$132$	5.41082e43	+	2.34086e43i	0.158932	+	0.0687579i
$133$	7.42701e44			1.86178
$134$	−9.48533e43	+	4.58139e44i	−0.203166	+	0.981288i
$135$		−	7.32172e44i		−	1.34154i
$136$	−7.39812e44	−	5.19791e44i	−1.16093	−	0.815665i
$137$	−9.94168e43			−0.133760			−0.0668802	−	0.997761i	$-0.521305\pi$
$137$	−9.94168e43			−0.133760			−0.0668802	+	0.997761i	$0.521305\pi$
$138$	−1.28985e45	−	2.67051e44i	−1.48963	−	0.308413i
$139$			1.31815e45i			1.30814i	0.756434	+	0.654070i	$0.226940\pi$
$139$			1.31815e45i			1.30814i	−0.756434	+	0.654070i	$0.773060\pi$
$140$	−1.11267e45	+	2.57190e45i	−0.949901	+	2.19566i
$141$	2.48635e44			0.182793
$142$	1.85417e44	−	8.95562e44i	0.117516	−	0.567597i
$143$			3.27687e44i			0.179227i
$144$	4.54846e44	+	4.84177e44i	0.214908	+	0.228766i
$145$	−3.22842e44			−0.131905
$146$	2.80394e45	+	5.80529e44i	0.991650	+	0.205312i
$147$		−	7.47838e45i		−	2.29162i
$148$	−2.18001e45	−	9.43130e44i	−0.579380	−	0.250655i
$149$	5.49879e45			1.26869			0.634345	−	0.773050i	$-0.281270\pi$
$149$	5.49879e45			1.26869			0.634345	+	0.773050i	$0.281270\pi$
$150$	4.35142e44	−	2.10172e45i	0.0872397	−	0.421366i
$151$			7.49267e45i			1.30653i	0.757128	+	0.653267i	$0.226602\pi$
$151$			7.49267e45i			1.30653i	−0.757128	+	0.653267i	$0.773398\pi$
$152$	3.63291e45	−	5.17068e45i	0.551492	−	0.784932i
$153$	3.36673e45			0.445337
$154$	3.44397e45	+	7.13042e44i	0.397305	+	0.0822583i
$155$			2.19823e45i			0.221364i
$156$	3.20487e45	−	7.40796e45i	0.281965	−	0.651752i
$157$	1.13107e45			0.0870152			0.0435076	−	0.999053i	$-0.486147\pi$
$157$	1.13107e45			0.0870152			0.0435076	+	0.999053i	$0.486147\pi$
$158$	2.47726e44	−	1.19651e45i	0.0166791	−	0.0805598i
$159$			9.39283e45i			0.553932i
$160$	1.24630e46	+	2.03269e46i	0.644320	+	1.05087i
$161$	−7.85793e46			−3.56422
$162$	1.44473e46	+	2.99117e45i	0.575400	+	0.119131i
$163$		−	2.95250e46i		−	1.03336i	−0.856180	−	0.516678i	$-0.827169\pi$
$163$		−	2.95250e46i		−	1.03336i	0.856180	−	0.516678i	$-0.172831\pi$
$164$	2.50287e45	+	1.08280e45i	0.0770401	+	0.0333295i
$165$	−7.87911e45			−0.213459
$166$	−2.82815e45	+	1.36599e46i	−0.0674890	+	0.325970i
$167$			4.80433e46i			1.01062i	0.862939	+	0.505309i	$0.168621\pi$
$167$			4.80433e46i			1.01062i	−0.862939	+	0.505309i	$0.831379\pi$
$168$	−7.08835e46	−	4.98027e46i	−1.31538	−	0.924183i
$169$	−1.61772e46			−0.265023
$170$	1.18328e47	+	2.44988e46i	1.71262	+	0.354582i
$171$			2.35307e46i			0.301104i
$172$	−1.88145e45	+	4.34891e45i	−0.0213008	+	0.0492360i
$173$	9.16703e45			0.0918884			0.0459442	−	0.998944i	$-0.485370\pi$
$173$	9.16703e45			0.0918884			0.0459442	+	0.998944i	$0.485370\pi$
$174$	2.02344e45	−	9.77316e45i	0.0179703	−	0.0867962i
$175$		−	1.28040e47i		−	1.00820i
$176$	2.18103e46	−	2.04891e46i	0.152369	−	0.143139i
$177$	−6.57002e46			−0.407500
$178$	7.22496e46	+	1.49586e46i	0.398121	+	0.0824272i
$179$			2.71077e47i			1.32794i	0.747758	+	0.663971i	$0.231130\pi$
$179$			2.71077e47i			1.32794i	−0.747758	+	0.663971i	$0.768870\pi$
$180$	−8.14846e46	−	3.52523e46i	−0.355102	−	0.153626i
$181$	2.31401e47			0.897666			0.448833	−	0.893616i	$-0.351840\pi$
$181$	2.31401e47			0.897666			0.448833	+	0.893616i	$0.351840\pi$
$182$	9.76226e46	−	4.71515e47i	0.337327	−	1.62928i
$183$		−	2.12692e47i		−	0.655056i
$184$	−3.84370e47	+	5.47069e47i	−1.05578	+	1.50268i
$185$	3.17448e47			0.778156
$186$	−6.65454e46	−	1.37776e46i	−0.145662	−	0.0301579i
$187$		−	1.51659e47i		−	0.296615i
$188$	5.01108e46	−	1.15829e47i	0.0876226	−	0.202537i
$189$	1.35029e48			2.11217
$190$	−1.71226e47	+	8.27019e47i	−0.239743	+	1.15795i
$191$		−	1.32439e48i		−	1.66079i	−0.557173	−	0.830396i	$-0.688114\pi$
$191$		−	1.32439e48i		−	1.66079i	0.557173	−	0.830396i	$-0.311886\pi$
$192$	−6.93452e47	+	2.49882e47i	−0.779275	+	0.280807i
$193$	−3.17945e47			−0.320367			−0.160184	−	0.987087i	$-0.551209\pi$
$193$	−3.17945e47			−0.320367			−0.160184	+	0.987087i	$0.551209\pi$
$194$	1.32612e48	+	2.74560e47i	1.19880	+	0.248199i
$195$			1.07873e48i			0.875358i
$196$	−3.48389e48	−	1.50722e48i	−2.53914	−	1.09850i
$197$	−2.16363e48			−1.41707			−0.708537	−	0.705673i	$-0.750645\pi$
$197$	−2.16363e48			−1.41707			−0.708537	+	0.705673i	$0.750645\pi$
$198$	−2.25910e46	+	1.09114e47i	−0.0133035	+	0.0642557i
$199$			2.66363e48i			1.41110i	0.708658	+	0.705552i	$0.249301\pi$
$199$			2.66363e48i			1.41110i	−0.708658	+	0.705552i	$0.750699\pi$
$200$	−8.91412e47	−	6.26305e47i	−0.425059	−	0.298646i
$201$	1.93299e48			0.830064
$202$	1.32338e48	+	2.73994e47i	0.512043	+	0.106014i
$203$		−	5.95394e47i		−	0.207677i
$204$	−1.48327e48	+	3.42852e48i	−0.466644	+	1.07863i
$205$	−3.64462e47			−0.103471
$206$	1.33834e47	−	6.46413e47i	0.0343047	−	0.165691i
$207$		−	2.48960e48i		−	0.576437i
$208$	−2.80516e48	−	2.98606e48i	−0.586987	−	0.624839i
$209$	1.05997e48			0.200549
$210$	1.13374e49	+	2.34730e48i	1.94048	+	0.401757i
$211$		−	9.33608e47i		−	0.144622i	−0.997382	−	0.0723108i	$-0.976963\pi$
$211$		−	9.33608e47i		−	0.144622i	0.997382	−	0.0723108i	$-0.0230373\pi$
$212$	4.37576e48	+	1.89307e48i	0.613762	+	0.265529i
$213$	−3.77856e48			−0.480126
$214$	2.12884e48	−	1.02822e49i	0.245162	−	1.18413i
$215$		−	6.33277e47i		−	0.0661281i
$216$	6.60493e48	−	9.40071e48i	0.625661	−	0.890496i
$217$	−4.05403e48			−0.348524
$218$	2.28283e49	+	4.72639e48i	1.78192	+	0.368929i
$219$		−	1.18304e49i		−	0.838829i
$220$	−1.58799e48	+	3.67058e48i	−0.102322	+	0.236515i
$221$	−2.07636e49			−1.21637
$222$	−1.98963e48	+	9.60988e48i	−0.106013	+	0.512042i
$223$			3.17809e49i			1.54086i	0.637524	+	0.770431i	$0.279959\pi$
$223$			3.17809e49i			1.54086i	−0.637524	+	0.770431i	$0.720041\pi$
$224$	−3.74873e49	+	2.29845e49i	−1.65453	+	1.01444i
$225$	4.05663e48			0.163055
$226$	1.35429e49	+	2.80392e48i	0.495944	+	0.102681i
$227$			1.61934e49i			0.540498i	0.962790	+	0.270249i	$0.0871061\pi$
$227$			1.61934e49i			0.540498i	−0.962790	+	0.270249i	$0.912894\pi$
$228$	−2.39625e49	−	1.03668e49i	−0.729292	−	0.315510i
$229$	−4.95887e49			−1.37669			−0.688347	−	0.725382i	$-0.741663\pi$
$229$	−4.95887e49			−1.37669			−0.688347	+	0.725382i	$0.741663\pi$
$230$	1.81161e49	−	8.75004e49i	0.458966	−	2.21679i
$231$		−	1.45309e49i		−	0.336078i
$232$	−4.14513e48	−	2.91236e48i	−0.0875569	−	0.0615174i
$233$	6.24810e49			1.20579			0.602897	−	0.797819i	$-0.294013\pi$
$233$	6.24810e49			1.20579			0.602897	+	0.797819i	$0.294013\pi$
$234$	1.49388e49	+	3.09294e48i	0.263502	+	0.0545555i
$235$			1.68668e49i			0.272024i
$236$	−1.32415e49	+	3.06072e49i	−0.195337	+	0.451514i
$237$	−5.04834e48			−0.0681449
$238$	−4.51813e49	+	2.18224e50i	−0.558268	+	2.69642i
$239$		−	1.29383e50i		−	1.46394i	−0.681338	−	0.731969i	$-0.738602\pi$
$239$		−	1.29383e50i		−	1.46394i	0.681338	−	0.731969i	$-0.261398\pi$
$240$	7.17986e49	−	6.74491e49i	0.744184	−	0.699101i
$241$	−7.11393e49			−0.675696			−0.337848	−	0.941201i	$-0.609699\pi$
$241$	−7.11393e49			−0.675696			−0.337848	+	0.941201i	$0.609699\pi$
$242$	−1.07548e50	−	2.22667e49i	−0.936435	−	0.193880i
$243$			7.53413e49i			0.601591i
$244$	−9.90851e49	−	4.28668e49i	−0.725808	−	0.314003i
$245$	5.07316e50			3.41029
$246$	2.28429e48	−	1.10331e49i	0.0140966	−	0.0680862i
$247$		−	1.45121e50i		−	0.822419i
$248$	−1.98303e49	+	2.82242e49i	−0.103239	+	0.146939i
$249$	5.76341e49			0.275736
$250$	−1.31881e50	−	2.73047e49i	−0.580018	−	0.120087i
$251$			2.72687e50i			1.10285i	0.834225	+	0.551424i	$0.185915\pi$
$251$			2.72687e50i			1.10285i	−0.834225	+	0.551424i	$0.814085\pi$
$252$	6.50133e49	−	1.50276e50i	0.241875	−	0.559086i
$253$	−1.12147e50			−0.383934
$254$	5.92024e49	−	2.85946e50i	0.186566	−	0.901107i
$255$		−	4.99253e50i		−	1.44869i
$256$	−2.33507e49	+	3.73415e50i	−0.0624109	+	0.998051i
$257$	3.67615e49			0.0905312			0.0452656	−	0.998975i	$-0.485587\pi$
$257$	3.67615e49			0.0905312			0.0452656	+	0.998975i	$0.485587\pi$
$258$	1.91707e49	+	3.96912e48i	0.0435136	+	0.00900907i
$259$			5.85447e50i			1.22516i
$260$	5.02539e50	+	2.17411e50i	0.969906	+	0.419606i
$261$	1.88636e49			0.0335873
$262$	−2.04884e48	+	9.89583e48i	−0.00336651	+	0.0162602i
$263$			8.27592e49i			0.125529i	0.998028	+	0.0627647i	$0.0199918\pi$
$263$			8.27592e49i			0.125529i	−0.998028	+	0.0627647i	$0.980008\pi$
$264$	−1.01164e50	−	7.10775e49i	−0.141691	−	0.0995519i
$265$	−6.37188e50			−0.824335
$266$	−1.52521e51	−	3.15780e50i	−1.82312	−	0.377459i
$267$		−	3.04836e50i		−	0.336768i
$268$	3.89581e50	−	9.00504e50i	0.397894	−	0.919719i
$269$	−1.55602e51			−1.46966			−0.734830	−	0.678251i	$-0.762738\pi$
$269$	−1.55602e51			−1.46966			−0.734830	+	0.678251i	$0.762738\pi$
$270$	−3.11303e50	+	1.50359e51i	−0.271985	+	1.31368i
$271$			3.11268e50i			0.251640i	0.992053	+	0.125820i	$0.0401562\pi$
$271$			3.11268e50i			0.251640i	−0.992053	+	0.125820i	$0.959844\pi$
$272$	1.29827e51	+	1.38199e51i	0.971447	+	1.03409i
$273$	−1.98942e51			−1.37820
$274$	2.04162e50	+	4.22698e49i	0.130983	+	0.0271187i
$275$		−	1.82736e50i		−	0.108602i
$276$	2.53529e51	+	1.09683e51i	1.39616	+	0.604017i
$277$	1.54021e51			0.786151			0.393075	−	0.919506i	$-0.371411\pi$
$277$	1.54021e51			0.786151			0.393075	+	0.919506i	$0.371411\pi$
$278$	5.60449e50	−	2.70696e51i	0.265213	−	1.28097i
$279$		−	1.28442e50i		−	0.0563663i
$280$	3.37850e51	−	4.80858e51i	1.37532	−	1.95748i
$281$	−6.19321e50			−0.233929			−0.116964	−	0.993136i	$-0.537316\pi$
$281$	−6.19321e50			−0.233929			−0.116964	+	0.993136i	$0.537316\pi$
$282$	−5.10596e50	−	1.05714e50i	−0.178997	−	0.0370596i
$283$			2.68194e51i			0.872838i	0.899744	+	0.436419i	$0.143753\pi$
$283$			2.68194e51i			0.872838i	−0.899744	+	0.436419i	$0.856247\pi$
$284$	−7.61546e50	+	1.76029e51i	−0.230150	+	0.531984i
$285$	3.48937e51			0.979501
$286$	1.39325e50	−	6.72938e50i	0.0363365	−	0.175504i
$287$		−	6.72149e50i		−	0.162909i
$288$	−7.28209e50	−	1.18770e51i	−0.164064	−	0.267586i
$289$	4.83603e51			1.01306
$290$	6.62989e50	+	1.37265e50i	0.129166	+	0.0267426i
$291$		−	5.59517e51i		−	1.01405i
$292$	−5.51134e51	−	2.38435e51i	−0.929431	−	0.402096i
$293$	−8.07761e51			−1.26784			−0.633918	−	0.773400i	$-0.718554\pi$
$293$	−8.07761e51			−1.26784			−0.633918	+	0.773400i	$0.718554\pi$
$294$	−3.17964e51	+	1.53576e52i	−0.464606	+	2.24403i
$295$		−	4.45695e51i		−	0.606422i
$296$	4.07588e51	+	2.86371e51i	0.516530	+	0.362913i
$297$	1.92711e51			0.227521
$298$	−1.12923e52	−	2.33796e51i	−1.24234	−	0.257215i
$299$			1.53541e52i			1.57445i
$300$	−1.78721e51	+	4.13108e51i	−0.170856	+	0.394928i
$301$	1.16791e51			0.104115
$302$	3.18572e51	−	1.53869e52i	0.264888	−	1.27940i
$303$		−	5.58363e51i		−	0.433134i
$304$	−9.65901e51	+	9.07387e51i	−0.699177	+	0.656821i
$305$	1.44285e52			0.974823
$306$	−6.91392e51	−	1.43146e51i	−0.436088	−	0.0902879i
$307$		−	3.32729e51i		−	0.195968i	−0.995188	−	0.0979840i	$-0.968761\pi$
$307$		−	3.32729e51i		−	0.195968i	0.995188	−	0.0979840i	$-0.0312394\pi$
$308$	−6.76937e51	−	2.92860e51i	−0.372377	−	0.161100i
$309$	−2.72735e51			−0.140157
$310$	9.34639e50	−	4.51428e51i	0.0448795	−	0.216767i
$311$		−	1.89346e52i		−	0.849743i	−0.905254	−	0.424872i	$-0.860319\pi$
$311$		−	1.89346e52i		−	0.849743i	0.905254	−	0.424872i	$-0.139681\pi$
$312$	−9.73123e51	+	1.38503e52i	−0.408245	+	0.581051i
$313$	3.37141e52			1.32245			0.661227	−	0.750186i	$-0.270036\pi$
$313$	3.37141e52			1.32245			0.661227	+	0.750186i	$0.270036\pi$
$314$	−2.32276e51	−	4.80905e50i	−0.0852081	−	0.0176415i
$315$			2.18828e52i			0.750900i
$316$	−1.01746e51	+	2.35183e51i	−0.0326655	+	0.0755052i
$317$	4.95438e51			0.148849			0.0744243	−	0.997227i	$-0.476288\pi$
$317$	4.95438e51			0.148849			0.0744243	+	0.997227i	$0.476288\pi$
$318$	3.99362e51	−	1.92891e52i	0.112305	−	0.542428i
$319$		−	8.49736e50i		−	0.0223707i
$320$	−1.69514e52	−	4.70422e52i	−0.417884	−	1.15968i
$321$	−4.33829e52			−1.00164
$322$	1.61370e53	+	3.34102e52i	3.49020	+	0.722613i
$323$			6.71641e52i			1.36108i
$324$	−2.83971e52	−	1.22853e52i	−0.539298	−	0.233314i
$325$	−2.50184e52			−0.445358
$326$	−1.25534e52	+	6.06324e52i	−0.209503	+	1.01189i
$327$		−	9.63176e52i		−	1.50731i
$328$	−4.67950e51	−	3.28781e51i	−0.0686829	−	0.0482565i
$329$	−3.11062e52			−0.428285
$330$	1.61805e52	+	3.35002e51i	0.209026	+	0.0432768i
$331$		−	1.13436e53i		−	1.37519i	−0.726095	−	0.687595i	$-0.758667\pi$
$331$		−	1.13436e53i		−	1.37519i	0.726095	−	0.687595i	$-0.241333\pi$
$332$	1.16158e52	−	2.68495e52i	0.132175	−	0.305518i
$333$	−1.85485e52			−0.198143
$334$	2.04270e52	−	9.86617e52i	0.204893	−	0.989630i
$335$			1.31129e53i			1.23526i
$336$	1.24391e53	+	1.32413e53i	1.10069	+	1.17167i
$337$	−5.61997e52			−0.467203			−0.233602	−	0.972332i	$-0.575051\pi$
$337$	−5.61997e52			−0.467203			−0.233602	+	0.972332i	$0.575051\pi$
$338$	3.32215e52	+	6.87820e51i	0.259519	+	0.0537309i
$339$		−	5.71402e52i		−	0.419516i
$340$	−2.32583e53	−	1.00621e53i	−1.60517	−	0.694437i
$341$	−5.78584e51			−0.0375426
$342$	1.00047e52	−	4.83226e52i	0.0610460	−	0.294851i
$343$			5.97424e53i			3.42851i
$344$	5.71280e51	−	8.13096e51i	0.0308405	−	0.0438950i
$345$	−3.69183e53			−1.87517
$346$	−1.88254e52	−	3.89762e51i	−0.0899801	−	0.0186295i
$347$		−	2.72575e53i		−	1.22622i	−0.789999	−	0.613108i	$-0.789919\pi$
$347$		−	2.72575e53i		−	1.22622i	0.789999	−	0.613108i	$-0.210081\pi$
$348$	−8.31067e51	+	1.92098e52i	−0.0351943	+	0.0813504i
$349$	−1.39161e53			−0.554860			−0.277430	−	0.960746i	$-0.589483\pi$
$349$	−1.39161e53			−0.554860			−0.277430	+	0.960746i	$0.589483\pi$
$350$	−5.44397e52	+	2.62942e53i	−0.204403	+	0.987260i
$351$		−	2.63841e53i		−	0.933024i
$352$	−5.35012e52	+	3.28031e52i	−0.178225	+	0.109275i
$353$	5.16516e53			1.62112			0.810560	−	0.585656i	$-0.199163\pi$
$353$	5.16516e53			1.62112			0.810560	+	0.585656i	$0.199163\pi$
$354$	1.34922e53	+	2.79343e52i	0.399037	+	0.0826169i
$355$		−	2.56329e53i		−	0.714500i
$356$	−1.42012e53	−	6.14379e52i	−0.373142	−	0.161431i
$357$	9.20735e53			2.28088
$358$	1.15256e53	−	5.56684e53i	0.269228	−	1.30036i
$359$		−	3.35232e53i		−	0.738520i	−0.929326	−	0.369260i	$-0.879611\pi$
$359$		−	3.35232e53i		−	0.738520i	0.929326	−	0.369260i	$-0.120389\pi$
$360$	1.52348e53	+	1.07040e53i	0.316581	+	0.222429i
$361$	4.06736e52			0.0797372
$362$	−4.75204e53	−	9.83865e52i	−0.879023	−	0.181993i
$363$			4.53766e53i			0.792123i
$364$	−4.00956e53	+	9.26795e53i	−0.660643	+	1.52706i
$365$	8.02548e53			1.24831
$366$	−9.04320e52	+	4.36784e53i	−0.132806	+	0.641452i
$367$			1.51444e53i			0.210023i	0.994471	+	0.105011i	$0.0334879\pi$
$367$			1.51444e53i			0.210023i	−0.994471	+	0.105011i	$0.966512\pi$
$368$	1.02194e54	−	9.60034e53i	1.33851	−	1.25743i
$369$	2.12954e52			0.0263471
$370$	−6.51912e53	−	1.34972e53i	−0.761996	−	0.157764i
$371$		−	1.17512e54i		−	1.29786i
$372$	1.30800e53	+	5.65873e52i	0.136523	+	0.0590632i
$373$	−1.11885e54			−1.10379			−0.551894	−	0.833914i	$-0.686095\pi$
$373$	−1.11885e54			−1.10379			−0.551894	+	0.833914i	$0.686095\pi$
$374$	−6.44819e52	+	3.11446e53i	−0.0601360	+	0.290455i
$375$			5.56433e53i			0.490633i
$376$	−1.52156e53	+	2.16561e53i	−0.126865	+	0.180566i
$377$	−1.16337e53			−0.0917384
$378$	−2.77295e54	−	5.74114e53i	−2.06831	−	0.428223i
$379$			1.56635e54i			1.10526i	0.833427	+	0.552630i	$0.186376\pi$
$379$			1.56635e54i			1.10526i	−0.833427	+	0.552630i	$0.813624\pi$
$380$	7.03261e53	−	1.62556e54i	0.469527	−	1.08530i
$381$	−1.20647e54			−0.762239
$382$	−5.63102e53	+	2.71977e54i	−0.336710	+	1.62630i
$383$			1.95761e54i			1.10803i	0.832506	+	0.554017i	$0.186906\pi$
$383$			1.95761e54i			1.10803i	−0.832506	+	0.554017i	$0.813094\pi$
$384$	1.53032e54	−	2.18316e53i	0.820022	−	0.116985i
$385$	9.85739e53			0.500135
$386$	6.52931e53	+	1.35183e53i	0.313714	+	0.0649515i
$387$			3.70023e52i			0.0168383i
$388$	−2.60658e54	−	1.12767e54i	−1.12358	−	0.486090i
$389$	−1.92750e54			−0.787141			−0.393570	−	0.919294i	$-0.628760\pi$
$389$	−1.92750e54			−0.787141			−0.393570	+	0.919294i	$0.628760\pi$
$390$	4.58652e53	−	2.21528e54i	0.177471	−	0.857179i
$391$		−	7.10610e54i		−	2.60567i
$392$	6.51368e54	+	4.57650e54i	2.26370	+	1.59047i
$393$	4.17526e52			0.0137543
$394$	4.44323e54	+	9.19929e53i	1.38765	+	0.287299i
$395$		−	3.42468e53i		−	0.101410i
$396$	9.27858e52	−	2.14471e53i	0.0260545	−	0.0602241i
$397$	−5.41836e54			−1.44300			−0.721502	−	0.692413i	$-0.756548\pi$
$397$	−5.41836e54			−1.44300			−0.721502	+	0.692413i	$0.756548\pi$
$398$	1.13252e54	−	5.47002e54i	0.286088	−	1.38180i
$399$			6.43518e54i			1.54216i
$400$	1.56431e54	+	1.66519e54i	0.355684	+	0.378620i
$401$	−2.28448e54			−0.492896			−0.246448	−	0.969156i	$-0.579263\pi$
$401$	−2.28448e54			−0.492896			−0.246448	+	0.969156i	$0.579263\pi$
$402$	−3.96958e54	−	8.21863e53i	−0.812825	−	0.168288i
$403$			7.92141e53i			0.153956i
$404$	−2.60120e54	−	1.12535e54i	−0.479916	−	0.207624i
$405$	4.13512e54			0.724323
$406$	−2.53149e53	+	1.22270e54i	−0.0421045	+	0.203364i
$407$			8.35539e53i			0.131973i
$408$	4.50377e54	−	6.41016e54i	0.675636	−	0.961624i
$409$	6.96579e54			0.992615			0.496307	−	0.868147i	$-0.334689\pi$
$409$	6.96579e54			0.992615			0.496307	+	0.868147i	$0.334689\pi$
$410$	7.48458e53	+	1.54961e53i	0.101323	+	0.0209779i
$411$		−	8.61404e53i		−	0.110797i
$412$	−5.49681e53	+	1.27057e54i	−0.0671846	+	0.155295i
$413$	8.21962e54			0.954774
$414$	−1.05852e54	+	5.11263e54i	−0.116867	+	0.564466i
$415$			3.90976e54i			0.410337i
$416$	4.49108e54	+	7.32486e54i	0.448116	+	0.730869i
$417$	−1.14212e55			−1.08357
$418$	−2.17675e54	−	4.50676e53i	−0.196384	−	0.0406595i
$419$		−	1.80564e55i		−	1.54930i	−0.632389	−	0.774651i	$-0.717926\pi$
$419$		−	1.80564e55i		−	1.54930i	0.632389	−	0.774651i	$-0.282074\pi$
$420$	−2.22844e55	−	9.64083e54i	−1.81872	−	0.786827i
$421$	−3.56797e54			−0.277011			−0.138505	−	0.990362i	$-0.544230\pi$
$421$	−3.56797e54			−0.277011			−0.138505	+	0.990362i	$0.544230\pi$
$422$	−3.96950e53	+	1.91726e54i	−0.0293207	+	0.141618i
$423$		−	9.85525e53i		−	0.0692660i
$424$	−8.18117e54	−	5.74808e54i	−0.547182	−	0.384450i
$425$	1.15789e55			0.737056
$426$	7.75966e54	+	1.60656e54i	0.470155	+	0.0973411i
$427$			2.66095e55i			1.53480i
$428$	−8.74357e54	+	2.02105e55i	−0.480142	+	1.10983i
$429$	−2.83927e54			−0.148458
$430$	−2.69256e53	+	1.30050e54i	−0.0134069	+	0.0647548i
$431$		−	1.15366e55i		−	0.547086i	−0.961860	−	0.273543i	$-0.911804\pi$
$431$		−	1.15366e55i		−	0.547086i	0.961860	−	0.273543i	$-0.0881956\pi$
$432$	−1.75609e55	+	1.64970e55i	−0.793208	+	0.745156i
$433$	2.78395e54			0.119789			0.0598943	−	0.998205i	$-0.480924\pi$
$433$	2.78395e54			0.119789			0.0598943	+	0.998205i	$0.480924\pi$
$434$	8.32536e54	+	1.72369e54i	0.341286	+	0.0706600i
$435$		−	2.79729e54i		−	0.109260i
$436$	−4.48707e55	−	1.94122e55i	−1.67012	−	0.722535i
$437$	4.96658e55			1.76176
$438$	−5.03003e54	+	2.42949e55i	−0.170065	+	0.821409i
$439$		−	4.53209e55i		−	1.46064i	−0.683104	−	0.730321i	$-0.739370\pi$
$439$		−	4.53209e55i		−	1.46064i	0.683104	−	0.730321i	$-0.260630\pi$
$440$	4.82173e54	−	6.86271e54i	0.148148	−	0.210858i
$441$	−2.96424e55			−0.868367
$442$	4.26401e55	+	8.82823e54i	1.19111	+	0.246607i
$443$			3.65755e55i			0.974344i	0.873306	+	0.487172i	$0.161971\pi$
$443$			3.65755e55i			0.974344i	−0.873306	+	0.487172i	$0.838029\pi$
$444$	8.17182e54	−	1.88889e55i	0.207623	−	0.479915i
$445$	2.06794e55			0.501162
$446$	1.35125e55	−	6.52652e55i	0.312395	−	1.50886i
$447$			4.76446e55i			1.05089i
$448$	8.67564e55	−	3.12622e55i	1.82584	−	0.657932i
$449$	4.22670e55			0.848844			0.424422	−	0.905465i	$-0.360477\pi$
$449$	4.22670e55			0.848844			0.424422	+	0.905465i	$0.360477\pi$
$450$	−8.33070e54	−	1.72479e54i	−0.159668	−	0.0330578i
$451$		−	9.59280e53i		−	0.0175484i
$452$	−2.66194e55	−	1.15163e55i	−0.464827	−	0.201096i
$453$	−6.49207e55			−1.08223
$454$	6.88507e54	−	3.32547e55i	0.109581	−	0.529273i
$455$		−	1.34958e56i		−	2.05097i
$456$	4.48017e55	+	3.14776e55i	0.650179	+	0.456815i
$457$	−1.09422e56			−1.51658			−0.758290	−	0.651918i	$-0.773965\pi$
$457$	−1.09422e56			−1.51658			−0.758290	+	0.651918i	$0.773965\pi$
$458$	1.01835e56	+	2.10840e55i	1.34810	+	0.279112i
$459$			1.22110e56i			1.54413i
$460$	−7.44065e55	+	1.71988e56i	−0.898869	+	2.07771i
$461$	4.12503e54			0.0476111			0.0238055	−	0.999717i	$-0.492422\pi$
$461$	4.12503e54			0.0476111			0.0238055	+	0.999717i	$0.492422\pi$
$462$	−6.17820e54	+	2.98405e55i	−0.0681366	+	0.329098i
$463$		−	3.56077e54i		−	0.0375270i	−0.999824	−	0.0187635i	$-0.994027\pi$
$463$		−	3.56077e54i		−	0.0375270i	0.999824	−	0.0187635i	$-0.00597295\pi$
$464$	7.27417e54	+	7.74325e54i	0.0732665	+	0.0779912i
$465$	−1.90467e55			−0.183362
$466$	−1.28311e56	−	2.65655e55i	−1.18075	−	0.244464i
$467$		−	1.50309e55i		−	0.132230i	−0.997812	−	0.0661150i	$-0.978940\pi$
$467$		−	1.50309e55i		−	0.132230i	0.997812	−	0.0661150i	$-0.0210604\pi$
$468$	−2.93633e55	−	1.27033e55i	−0.246969	−	0.106845i
$469$	−2.41832e56			−1.94484
$470$	7.17139e54	−	3.46376e55i	0.0551504	−	0.266375i
$471$			9.80020e54i			0.0720769i
$472$	4.02062e55	−	5.72249e55i	0.282820	−	0.402535i
$473$	1.66682e54			0.0112151
$474$	1.03673e55	+	2.14644e54i	0.0667297	+	0.0138157i
$475$			8.09271e55i			0.498343i
$476$	1.85568e56	−	4.28935e56i	1.09335	−	2.52724i
$477$	3.72308e55			0.209902
$478$	−5.50110e55	+	2.65702e56i	−0.296800	+	1.43353i
$479$			3.11081e56i			1.60630i	0.595775	+	0.803151i	$0.296845\pi$
$479$			3.11081e56i			1.60630i	−0.595775	+	0.803151i	$0.703155\pi$
$480$	−1.76124e56	+	1.07986e56i	−0.870465	+	0.533706i
$481$	1.14394e56			0.541197
$482$	1.46092e56	+	3.02469e55i	0.661664	+	0.136991i
$483$		−	6.80856e56i		−	2.95233i
$484$	2.11392e56	+	9.14537e55i	0.877680	+	0.379707i
$485$	3.79564e56			1.50907
$486$	3.20335e55	−	1.54721e56i	0.121967	−	0.589098i
$487$			2.23753e56i			0.815946i	0.912994	+	0.407973i	$0.133764\pi$
$487$			2.23753e56i			0.815946i	−0.912994	+	0.407973i	$0.866236\pi$
$488$	1.85255e56	+	1.30160e56i	0.647074	+	0.454633i
$489$	2.55821e56			0.855954
$490$	−1.04182e57	−	2.15700e56i	−3.33946	−	0.691404i
$491$			5.03493e55i			0.154626i	0.997007	+	0.0773129i	$0.0246340\pi$
$491$			5.03493e55i			0.154626i	−0.997007	+	0.0773129i	$0.975366\pi$
$492$	−9.38204e54	+	2.16863e55i	−0.0276077	+	0.0638143i
$493$	5.38428e55			0.151825
$494$	−6.17021e55	+	2.98019e56i	−0.166738	+	0.805339i
$495$			3.12308e55i			0.0808861i
$496$	5.27237e55	−	4.95297e55i	0.130885	−	0.122956i
$497$	4.72729e56			1.12494
$498$	−1.18357e56	−	2.45047e55i	−0.270009	−	0.0559028i
$499$		−	1.03886e56i		−	0.227220i	−0.993525	−	0.113610i	$-0.963759\pi$
$499$		−	1.03886e56i		−	0.227220i	0.993525	−	0.113610i	$-0.0362414\pi$
$500$	2.59221e56	+	1.12146e56i	0.543626	+	0.235187i
$501$	−4.16275e56			−0.837120
$502$	1.15940e56	−	5.59989e56i	0.223592	−	1.07995i
$503$		−	8.22303e56i		−	1.52091i	−0.649390	−	0.760456i	$-0.724976\pi$
$503$		−	8.22303e56i		−	1.52091i	0.649390	−	0.760456i	$-0.275024\pi$
$504$	−1.97405e56	+	2.80964e56i	−0.350201	+	0.498437i
$505$	3.78781e56			0.644569
$506$	2.30305e56	+	4.76824e55i	0.375961	+	0.0778391i
$507$		−	1.40169e56i		−	0.219525i
$508$	−2.43156e56	+	5.62047e56i	−0.365382	+	0.844569i
$509$	−1.64693e56			−0.237466			−0.118733	−	0.992926i	$-0.537883\pi$
$509$	−1.64693e56			−0.237466			−0.118733	+	0.992926i	$0.537883\pi$
$510$	−2.12271e56	+	1.02527e57i	−0.293709	+	1.41861i
$511$			1.48008e57i			1.96538i
$512$	2.06721e56	−	7.56917e56i	0.263460	−	0.964670i
$513$	−8.53447e56			−1.04403
$514$	−7.54935e55	−	1.56302e55i	−0.0886511	−	0.0183544i
$515$		−	1.85017e56i		−	0.208574i
$516$	−3.76814e55	−	1.63020e55i	−0.0407834	−	0.0176440i
$517$	−4.43942e55			−0.0461344
$518$	2.48919e56	−	1.20227e57i	0.248390	−	1.19971i
$519$			7.94284e55i			0.0761134i
$520$	−9.39575e56	−	6.60144e56i	−0.864692	−	0.607531i
$521$	−3.63980e56			−0.321726			−0.160863	−	0.986977i	$-0.551428\pi$
$521$	−3.63980e56			−0.321726			−0.160863	+	0.986977i	$0.551428\pi$
$522$	−3.87383e55	−	8.02040e54i	−0.0328897	−	0.00680951i
$523$			1.01989e57i			0.831797i	0.909411	+	0.415898i	$0.136533\pi$
$523$			1.01989e57i			0.831797i	−0.909411	+	0.415898i	$0.863467\pi$
$524$	8.41498e54	−	1.94509e55i	0.00659320	−	0.0152400i
$525$	1.10941e57			0.835116
$526$	3.51874e55	−	1.69954e56i	0.0254499	−	0.122923i
$527$		−	3.66615e56i		−	0.254793i
$528$	1.77529e56	+	1.88977e56i	0.118565	+	0.126211i
$529$	−3.69674e57			−2.37274
$530$	1.30853e57	+	2.70918e56i	0.807216	+	0.167126i
$531$			2.60419e56i			0.154414i
$532$	2.99791e57	+	1.29697e57i	1.70873	+	0.739241i
$533$	−1.31335e56			−0.0719630
$534$	−1.29610e56	+	6.26012e56i	−0.0682765	+	0.329774i
$535$		−	2.94300e57i		−	1.49060i
$536$	−1.18292e57	+	1.68363e57i	−0.576095	+	0.819949i
$537$	−2.34877e57			−1.09997
$538$	3.19544e57	+	6.61585e56i	1.43914	+	0.297960i
$539$			1.33528e57i			0.578373i
$540$	1.27858e57	−	2.95541e57i	0.532673	−	1.23126i
$541$	2.17089e57			0.869953			0.434976	−	0.900442i	$-0.356757\pi$
$541$	2.17089e57			0.869953			0.434976	+	0.900442i	$0.356757\pi$
$542$	1.32345e56	−	6.39221e56i	0.0510177	−	0.246414i
$543$			2.00499e57i			0.743559i
$544$	−2.07854e57	−	3.39006e57i	−0.741620	−	1.20957i
$545$	6.53396e57			2.24311
$546$	4.08547e57	+	8.45858e56i	1.34957	+	0.279417i
$547$		−	4.67785e57i		−	1.48700i	−0.668734	−	0.743502i	$-0.733163\pi$
$547$		−	4.67785e57i		−	1.48700i	0.668734	−	0.743502i	$-0.266837\pi$
$548$	−4.01295e56	−	1.73611e56i	−0.122764	−	0.0531110i
$549$	−8.43057e56			−0.248221
$550$	−7.76954e55	+	3.75267e56i	−0.0220180	+	0.106347i
$551$			3.76317e56i			0.102653i
$552$	−4.74012e57	−	3.33040e57i	−1.24471	−	0.874532i
$553$	6.31587e56			0.159664
$554$	−3.16298e57	−	6.54865e56i	−0.769824	−	0.159385i
$555$			2.75056e57i			0.644566i
$556$	−2.30188e57	+	5.32071e57i	−0.519411	+	1.20060i
$557$	−5.57398e57			−1.21117			−0.605586	−	0.795780i	$-0.707061\pi$
$557$	−5.57398e57			−1.21117			−0.605586	+	0.795780i	$0.707061\pi$
$558$	−5.46108e55	+	2.63769e56i	−0.0114277	+	0.0551957i
$559$		−	2.28204e56i		−	0.0459912i
$560$	−8.98259e57	+	8.43842e57i	−1.74362	+	1.63800i
$561$	1.31406e57			0.245694
$562$	1.27184e57	+	2.63322e56i	0.229071	+	0.0474269i
$563$			4.22462e57i			0.733013i	0.930415	+	0.366507i	$0.119446\pi$
$563$			4.22462e57i			0.733013i	−0.930415	+	0.366507i	$0.880554\pi$
$564$	1.00361e57	+	4.34188e56i	0.167766	+	0.0725800i
$565$	3.87626e57			0.624303
$566$	1.14030e57	−	5.50763e57i	0.176960	−	0.854711i
$567$			7.62609e57i			1.14040i
$568$	2.31235e57	−	3.29114e57i	0.333225	−	0.474276i
$569$	−7.99340e57			−1.11013			−0.555065	−	0.831807i	$-0.687307\pi$
$569$	−7.99340e57			−1.11013			−0.555065	+	0.831807i	$0.687307\pi$
$570$	−7.16577e57	−	1.48360e57i	−0.959159	−	0.198585i
$571$		−	9.00976e57i		−	1.16240i	−0.813761	−	0.581199i	$-0.802584\pi$
$571$		−	9.00976e57i		−	1.16240i	0.813761	−	0.581199i	$-0.197416\pi$
$572$	−5.72237e56	+	1.32271e57i	−0.0711638	+	0.164493i
$573$	1.14753e58			1.37568
$574$	−2.85783e56	+	1.38033e57i	−0.0330284	+	0.159526i
$575$		−	8.56226e57i		−	0.954034i
$576$	9.90468e56	+	2.74867e57i	0.106407	+	0.295291i
$577$	1.41994e58			1.47089			0.735443	−	0.677587i	$-0.236974\pi$
$577$	1.41994e58			1.47089			0.735443	+	0.677587i	$0.236974\pi$
$578$	−9.93126e57	−	2.05617e57i	−0.992018	−	0.205388i
$579$		−	2.75486e57i		−	0.265368i
$580$	−1.30315e57	−	5.63777e56i	−0.121062	−	0.0523744i
$581$	−7.21048e57			−0.646049
$582$	−2.37894e57	+	1.14902e58i	−0.205590	+	0.992994i
$583$		−	1.67711e57i		−	0.139805i
$584$	1.03043e58	+	7.23979e57i	0.828608	+	0.582179i
$585$	4.27581e57			0.331700
$586$	1.65882e58	+	3.43442e57i	1.24151	+	0.257042i
$587$		−	8.43477e57i		−	0.609078i	−0.952500	−	0.304539i	$-0.901498\pi$
$587$		−	8.43477e57i		−	0.609078i	0.952500	−	0.304539i	$-0.0985024\pi$
$588$	1.30594e58	−	3.01864e58i	0.909914	−	2.10324i
$589$	2.56234e57			0.172272
$590$	−1.89500e57	+	9.15279e57i	−0.122947	+	0.593829i
$591$		−	1.87469e58i		−	1.17380i
$592$	−7.15263e57	−	7.61388e57i	−0.432225	−	0.460098i
$593$	3.63304e57			0.211895			0.105948	−	0.994372i	$-0.466212\pi$
$593$	3.63304e57			0.211895			0.105948	+	0.994372i	$0.466212\pi$
$594$	−3.95751e57	−	8.19365e56i	−0.222796	−	0.0461277i
$595$			6.24606e58i			3.39429i
$596$	2.21958e58	+	9.60248e57i	1.16439	+	0.503747i
$597$	−2.30792e58			−1.16885
$598$	6.52821e57	−	3.15311e58i	0.319205	−	1.54175i
$599$			2.03262e58i			0.959606i	0.877376	+	0.479803i	$0.159292\pi$
$599$			2.03262e58i			0.959606i	−0.877376	+	0.479803i	$0.840708\pi$
$600$	5.42667e57	−	7.72371e57i	0.247376	−	0.352087i
$601$	−2.56439e58			−1.12881			−0.564403	−	0.825499i	$-0.690894\pi$
$601$	−2.56439e58			−1.12881			−0.564403	+	0.825499i	$0.690894\pi$
$602$	−2.39841e57	−	4.96568e56i	−0.101952	−	0.0211083i
$603$		−	7.66187e57i		−	0.314537i
$604$	−1.30844e58	+	3.02441e58i	−0.518773	+	1.19913i
$605$	−3.07824e58			−1.17880
$606$	−2.37404e57	+	1.14665e58i	−0.0878138	+	0.424138i
$607$		−	5.09834e58i		−	1.82166i	−0.412787	−	0.910828i	$-0.635444\pi$
$607$		−	5.09834e58i		−	1.82166i	0.412787	−	0.910828i	$-0.364556\pi$
$608$	2.36937e58	−	1.45273e58i	0.817821	−	0.501429i
$609$	5.15883e57			0.172024
$610$	−2.96304e58	−	6.13470e57i	−0.954578	−	0.197636i
$611$			6.07802e57i			0.189189i
$612$	1.35898e58	+	5.87929e57i	0.408727	+	0.176826i
$613$	1.75492e58			0.510021			0.255010	−	0.966938i	$-0.417921\pi$
$613$	1.75492e58			0.510021			0.255010	+	0.966938i	$0.417921\pi$
$614$	−1.41469e57	+	6.83292e57i	−0.0397307	+	0.191898i
$615$		−	3.15790e57i		−	0.0857080i
$616$	1.26564e58	+	8.89237e57i	0.331982	+	0.233250i
$617$	−5.32101e58			−1.34898			−0.674490	−	0.738284i	$-0.735636\pi$
$617$	−5.32101e58			−1.34898			−0.674490	+	0.738284i	$0.735636\pi$
$618$	5.60089e57	+	1.15961e57i	0.137246	+	0.0284155i
$619$		−	4.65842e57i		−	0.110340i	−0.998477	−	0.0551702i	$-0.982430\pi$
$619$		−	4.65842e57i		−	0.110340i	0.998477	−	0.0551702i	$-0.0175701\pi$
$620$	−3.83875e57	+	8.87314e57i	−0.0878950	+	0.203166i
$621$	9.02964e58			1.99870
$622$	−8.05057e57	+	3.88841e58i	−0.172278	+	0.832096i
$623$			3.81375e58i			0.789047i
$624$	2.58729e58	−	2.43055e58i	0.517570	−	0.486216i
$625$	−6.46039e58			−1.24962
$626$	−6.92353e58	−	1.43345e58i	−1.29499	−	0.268115i
$627$			9.18418e57i			0.166120i
$628$	4.56554e57	+	1.97517e57i	0.0798619	+	0.0345503i
$629$	−5.29432e58			−0.895668
$630$	9.30410e57	−	4.49386e58i	0.152238	−	0.735305i
$631$			2.55894e58i			0.404990i	0.979283	+	0.202495i	$0.0649050\pi$
$631$			2.55894e58i			0.404990i	−0.979283	+	0.202495i	$0.935095\pi$
$632$	3.08940e57	−	4.39711e57i	0.0472951	−	0.0673145i
$633$	8.08932e57			0.119794
$634$	−1.01743e58	−	2.10649e57i	−0.145757	−	0.0301777i
$635$		−	8.18440e58i		−	1.13433i
$636$	−1.64026e58	+	3.79141e58i	−0.219945	+	0.508395i
$637$	1.82813e59			2.37181
$638$	−3.61289e56	+	1.74502e57i	−0.00453545	+	0.0219061i
$639$			1.49773e58i			0.181934i
$640$	1.48101e58	+	1.03813e59i	0.174091	+	1.22032i
$641$	1.49856e59			1.70473			0.852366	−	0.522945i	$-0.175167\pi$
$641$	1.49856e59			1.70473			0.852366	+	0.522945i	$0.175167\pi$
$642$	8.90912e58	+	1.84455e58i	0.980842	+	0.203074i
$643$		−	1.34495e59i		−	1.43310i	−0.697538	−	0.716548i	$-0.745721\pi$
$643$		−	1.34495e59i		−	1.43310i	0.697538	−	0.716548i	$-0.254279\pi$
$644$	−3.17185e59	−	1.37222e59i	−3.27122	−	1.41521i
$645$	5.48708e57			0.0547756
$646$	2.85567e58	−	1.37928e59i	0.275947	−	1.33281i
$647$			1.62557e59i			1.52060i	0.649571	+	0.760301i	$0.274948\pi$
$647$			1.62557e59i			1.52060i	−0.649571	+	0.760301i	$0.725052\pi$
$648$	5.30928e58	+	3.73029e58i	0.480796	+	0.337806i
$649$	1.17309e58			0.102847
$650$	5.13778e58	+	1.06373e58i	0.436109	+	0.0902922i
$651$		−	3.51264e58i		−	0.288691i
$652$	5.15592e58	−	1.19177e59i	0.410305	−	0.948406i
$653$	1.53065e59			1.17950			0.589750	−	0.807586i	$-0.299226\pi$
$653$	1.53065e59			1.17950			0.589750	+	0.807586i	$0.299226\pi$
$654$	−4.09521e58	+	1.97798e59i	−0.305593	+	1.47601i
$655$			2.83240e57i			0.0204686i
$656$	8.21192e57	+	8.74147e57i	0.0574730	+	0.0611792i
$657$	−4.68928e58			−0.317858
$658$	6.38796e58	+	1.32257e58i	0.419391	+	0.0868308i
$659$			3.68968e58i			0.234636i	0.993094	+	0.117318i	$0.0374297\pi$
$659$			3.68968e58i			0.234636i	−0.993094	+	0.117318i	$0.962570\pi$
$660$	−3.18040e58	−	1.37592e58i	−0.195911	−	0.0847561i
$661$	−1.82239e59			−1.08745			−0.543727	−	0.839262i	$-0.682987\pi$
$661$	−1.82239e59			−1.08745			−0.543727	+	0.839262i	$0.682987\pi$
$662$	−4.82304e58	+	2.32952e59i	−0.278807	+	1.34663i
$663$		−	1.79908e59i		−	1.00755i
$664$	−3.52700e58	+	5.01994e58i	−0.191371	+	0.272376i
$665$	−4.36548e59			−2.29497
$666$	3.80911e58	+	7.88640e57i	0.194028	+	0.0401717i
$667$		−	3.98151e58i		−	0.196519i
$668$	−8.38976e58	+	1.93926e59i	−0.401276	+	0.927537i
$669$	−2.75368e59			−1.27633
$670$	5.57533e58	−	2.69287e59i	0.250438	−	1.20961i
$671$			3.79766e58i			0.165327i
$672$	−1.99151e59	−	3.24812e59i	−0.840287	−	1.37049i
$673$	2.56658e59			1.04964			0.524818	−	0.851215i	$-0.324133\pi$
$673$	2.56658e59			1.04964			0.524818	+	0.851215i	$0.324133\pi$
$674$	1.15412e59	+	2.38949e58i	0.457501	+	0.0947211i
$675$			1.47132e59i			0.565364i
$676$	−6.52993e58	−	2.82501e58i	−0.243236	−	0.105230i
$677$	1.41793e59			0.512028			0.256014	−	0.966673i	$-0.417591\pi$
$677$	1.41793e59			0.512028			0.256014	+	0.966673i	$0.417591\pi$
$678$	−2.42948e58	+	1.17343e59i	−0.0850529	+	0.410803i
$679$			7.00001e59i			2.37593i
$680$	4.34850e59	+	3.05525e59i	1.43104	+	1.00545i
$681$	−1.40309e59			−0.447708
$682$	1.18818e58	+	2.46001e57i	0.0367630	+	0.00761142i
$683$		−	6.65472e58i		−	0.199662i	−0.995004	−	0.0998310i	$-0.968170\pi$
$683$		−	6.65472e58i		−	0.199662i	0.995004	−	0.0998310i	$-0.0318302\pi$
$684$	−4.10914e58	+	9.49815e58i	−0.119556	+	0.276351i
$685$	5.84356e58			0.164883
$686$	2.54011e59	−	1.22687e60i	0.695099	−	3.35731i
$687$		−	4.29665e59i		−	1.14035i
$688$	−1.51889e58	+	1.42688e58i	−0.0390993	+	0.0367307i
$689$	−2.29613e59			−0.573314
$690$	7.58153e59	+	1.56968e59i	1.83623	+	0.380173i
$691$		−	1.12604e59i		−	0.264554i	−0.991213	−	0.132277i	$-0.957771\pi$
$691$		−	1.12604e59i		−	0.264554i	0.991213	−	0.132277i	$-0.0422288\pi$
$692$	3.70027e58	+	1.60083e58i	0.0843344	+	0.0364852i
$693$	−5.75966e58			−0.127350
$694$	−1.15893e59	+	5.59760e59i	−0.248604	+	1.20075i
$695$		−	7.74789e59i		−	1.61251i
$696$	2.52344e58	−	3.59158e58i	0.0509564	−	0.0725256i
$697$	6.07840e58			0.119097
$698$	2.85781e59	+	5.91682e58i	0.543337	+	0.112493i
$699$			5.41371e59i			0.998790i
$700$	2.23595e59	−	5.16832e59i	0.400316	−	0.925317i
$701$	4.60943e59			0.800883			0.400441	−	0.916322i	$-0.368857\pi$
$701$	4.60943e59			0.800883			0.400441	+	0.916322i	$0.368857\pi$
$702$	−1.12179e59	+	5.41823e59i	−0.189162	+	0.913647i
$703$		−	3.70030e59i		−	0.605585i
$704$	1.23817e59	−	4.46169e58i	0.196678	−	0.0708717i
$705$	−1.46144e59			−0.225324
$706$	−1.06072e60	−	2.19611e59i	−1.58745	−	0.328667i
$707$			6.98557e59i			1.01483i
$708$	−2.65198e59	−	1.14732e59i	−0.374001	−	0.161802i
$709$	1.21483e59			0.166321			0.0831603	−	0.996536i	$-0.473499\pi$
$709$	1.21483e59			0.166321			0.0831603	+	0.996536i	$0.473499\pi$
$710$	−1.08986e59	+	5.26397e59i	−0.144858	+	0.699662i
$711$			2.00103e58i			0.0258222i
$712$	2.65513e59	+	1.86549e59i	0.332664	+	0.233729i
$713$	−2.71101e59			−0.329800
$714$	−1.89082e60	−	3.91476e59i	−2.23351	−	0.462427i
$715$		−	1.92609e59i		−	0.220928i
$716$	−4.73380e59	+	1.09420e60i	−0.527274	+	1.21878i
$717$	1.12105e60			1.21262
$718$	−1.42533e59	+	6.88433e59i	−0.149728	+	0.723183i
$719$			5.76394e59i			0.588048i	0.955798	+	0.294024i	$0.0949945\pi$
$719$			5.76394e59i			0.588048i	−0.955798	+	0.294024i	$0.905005\pi$
$720$	−2.67351e59	−	2.84592e59i	−0.264911	−	0.281994i
$721$	3.41214e59			0.328387
$722$	−8.35272e58	−	1.72935e58i	−0.0780812	−	0.0161660i
$723$		−	6.16391e59i		−	0.559696i
$724$	9.34047e59	+	4.04093e59i	0.823871	+	0.356428i
$725$	6.48761e58			0.0555887
$726$	1.92931e59	−	9.31853e59i	0.160596	−	0.775673i
$727$		−	1.65198e60i		−	1.33592i	−0.744195	−	0.667962i	$-0.767167\pi$
$727$		−	1.65198e60i		−	1.33592i	0.744195	−	0.667962i	$-0.232833\pi$
$728$	1.21746e60	−	1.73279e60i	0.956520	−	1.36140i
$729$	−1.42257e60			−1.08592
$730$	−1.64811e60	−	3.41226e59i	−1.22238	−	0.253082i
$731$			1.05616e59i			0.0761143i
$732$	3.71422e59	−	8.58530e59i	0.260097	−	0.601205i
$733$	1.90093e60			1.29355			0.646773	−	0.762682i	$-0.276118\pi$
$733$	1.90093e60			1.29355			0.646773	+	0.762682i	$0.276118\pi$
$734$	6.43908e58	−	3.11006e59i	0.0425801	−	0.205661i
$735$			4.39568e60i			2.82483i
$736$	−2.50685e60	+	1.53702e60i	−1.56565	+	0.959942i
$737$	−3.45138e59			−0.209496
$738$	−4.37323e58	−	9.05436e57i	−0.0257999	−	0.00534163i
$739$		−	8.40558e59i		−	0.481986i	−0.970527	−	0.240993i	$-0.922527\pi$
$739$		−	8.40558e59i		−	0.481986i	0.970527	−	0.240993i	$-0.0774731\pi$
$740$	1.28138e60	+	5.54357e59i	0.714186	+	0.308975i
$741$	1.25741e60			0.681230
$742$	−4.99634e59	+	2.41322e60i	−0.263130	+	1.27091i
$743$		−	1.77585e60i		−	0.909161i	−0.890706	−	0.454581i	$-0.849789\pi$
$743$		−	1.77585e60i		−	0.909161i	0.890706	−	0.454581i	$-0.150211\pi$
$744$	−2.44550e59	−	1.71821e59i	−0.121713	−	0.0855153i
$745$	−3.23210e60			−1.56388
$746$	2.29767e60	+	4.75710e59i	1.08087	+	0.223783i
$747$		−	2.28447e59i		−	0.104485i
$748$	2.64840e59	−	6.12169e59i	0.117774	−	0.272231i
$749$	5.42755e60			2.34685
$750$	2.36583e59	−	1.14269e60i	0.0994712	−	0.480443i
$751$		−	1.55020e60i		−	0.633794i	−0.948460	−	0.316897i	$-0.897359\pi$
$751$		−	1.55020e60i		−	0.633794i	0.948460	−	0.316897i	$-0.102641\pi$
$752$	4.04544e59	−	3.80037e59i	0.160839	−	0.151095i
$753$	−2.36271e60			−0.913517
$754$	2.38911e59	+	4.94641e58i	0.0898332	+	0.0185991i
$755$		−	4.40407e60i		−	1.61053i
$756$	5.45044e60	+	2.35800e60i	1.93853	+	0.838660i
$757$	−3.08357e60			−1.06669			−0.533347	−	0.845896i	$-0.679066\pi$
$757$	−3.08357e60			−1.06669			−0.533347	+	0.845896i	$0.679066\pi$
$758$	6.65976e59	−	3.21665e60i	0.224081	−	1.08231i
$759$		−	9.71706e59i		−	0.318022i
$760$	−2.13537e60	+	3.03925e60i	−0.679810	+	0.967565i
$761$	−2.60458e60			−0.806604			−0.403302	−	0.915067i	$-0.632137\pi$
$761$	−2.60458e60			−0.806604			−0.403302	+	0.915067i	$0.632137\pi$
$762$	2.47760e60	+	5.12964e59i	0.746409	+	0.154537i
$763$			1.20501e61i			3.53163i
$764$	2.31277e60	−	5.34589e60i	0.659435	−	1.52426i
$765$	−1.97891e60			−0.548955
$766$	8.32335e59	−	4.02015e60i	0.224643	−	1.08502i
$767$		−	1.60608e60i		−	0.421759i
$768$	−3.23548e60	−	2.02324e59i	−0.826710	−	0.0516965i
$769$	−1.63038e60			−0.405354			−0.202677	−	0.979246i	$-0.564964\pi$
$769$	−1.63038e60			−0.405354			−0.202677	+	0.979246i	$0.564964\pi$
$770$	−2.02431e60	−	4.19115e59i	−0.489748	−	0.101398i
$771$			3.18523e59i			0.0749892i
$772$	−1.28338e60	−	5.55224e59i	−0.294031	−	0.127205i
$773$	3.32906e60			0.742253			0.371126	−	0.928582i	$-0.378972\pi$
$773$	3.32906e60			0.742253			0.371126	+	0.928582i	$0.378972\pi$
$774$	1.57326e58	−	7.59879e58i	0.00341381	−	0.0164886i
$775$		−	4.41741e59i		−	0.0932893i
$776$	4.87340e60	+	3.42405e60i	1.00170	+	0.703791i
$777$	−5.07264e60			−1.01483
$778$	3.95831e60	+	8.19530e59i	0.770794	+	0.159586i
$779$			4.24830e59i			0.0805246i
$780$	−1.88378e60	+	4.35429e60i	−0.347570	+	0.803397i
$781$	6.74670e59			0.121177
$782$	−3.02136e60	+	1.45931e61i	−0.528275	+	2.55156i
$783$			6.84175e59i			0.116458i
$784$	−1.14307e61	−	1.21678e61i	−1.89424	−	2.01639i
$785$	−6.64823e59			−0.107261
$786$	−8.57431e58	−	1.77523e58i	−0.0134687	−	0.00278857i
$787$		−	5.44543e60i		−	0.832842i	−0.909172	−	0.416421i	$-0.863284\pi$
$787$		−	5.44543e60i		−	0.832842i	0.909172	−	0.416421i	$-0.136716\pi$
$788$	−8.73349e60	−	3.77833e60i	−1.30058	−	0.562664i
$789$	−7.17073e59			−0.103979
$790$	−1.45610e59	+	7.03291e59i	−0.0205599	+	0.0993039i
$791$			7.14870e60i			0.982926i
$792$	−2.81733e59	+	4.00988e59i	−0.0377233	+	0.0536911i
$793$	5.19938e60			0.677976
$794$	1.11271e61	+	2.30377e60i	1.41304	+	0.292556i
$795$		−	5.52096e60i		−	0.682818i
$796$	−4.65147e60	+	1.07517e61i	−0.560294	+	1.29510i
$797$	−4.21316e60			−0.494292			−0.247146	−	0.968978i	$-0.579493\pi$
$797$	−4.21316e60			−0.494292			−0.247146	+	0.968978i	$0.579493\pi$
$798$	2.73610e60	−	1.32153e61i	0.312659	−	1.51014i
$799$		−	2.81300e60i		−	0.313103i
$800$	−2.50447e60	−	4.08474e60i	−0.271535	−	0.442869i
$801$	−1.20829e60			−0.127612
$802$	4.69140e60	+	9.71311e59i	0.482660	+	0.0999301i
$803$			2.11234e60i			0.211708i
$804$	7.80249e60	+	3.37556e60i	0.761826	+	0.329586i
$805$	4.61877e61			4.39352
$806$	3.36801e59	−	1.62674e60i	0.0312131	−	0.150759i
$807$		−	1.34822e61i		−	1.21736i
$808$	4.86335e60	+	3.41699e60i	0.427856	+	0.300611i
$809$	−1.04703e60			−0.0897516			−0.0448758	−	0.998993i	$-0.514289\pi$
$809$	−1.04703e60			−0.0897516			−0.0448758	+	0.998993i	$0.514289\pi$
$810$	−8.49187e60	−	1.75816e60i	−0.709281	−	0.146850i
$811$		−	1.61702e61i		−	1.31607i	−0.752988	−	0.658034i	$-0.771388\pi$
$811$		−	1.61702e61i		−	1.31607i	0.752988	−	0.658034i	$-0.228612\pi$
$812$	1.03973e60	−	2.40330e60i	0.0824602	−	0.190604i
$813$	−2.69701e60			−0.208440
$814$	3.55253e59	−	1.71586e60i	0.0267562	−	0.129232i
$815$			1.73543e61i			1.27379i
$816$	−1.19744e61	+	1.12490e61i	−0.856565	+	0.804674i
$817$	−7.38172e59			−0.0514629
$818$	−1.43049e61	−	2.96170e60i	−0.972001	−	0.201243i
$819$			7.88556e60i			0.522241i
$820$	−1.47115e60	−	6.36456e59i	−0.0949653	−	0.0410845i
$821$	−6.98608e60			−0.439569			−0.219785	−	0.975548i	$-0.570535\pi$
$821$	−6.98608e60			−0.439569			−0.219785	+	0.975548i	$0.570535\pi$
$822$	−3.66250e59	+	1.76898e60i	−0.0224631	+	0.108496i
$823$			2.14602e61i			1.28303i	0.767109	+	0.641517i	$0.221694\pi$
$823$			2.14602e61i			1.28303i	−0.767109	+	0.641517i	$0.778306\pi$
$824$	1.66904e60	−	2.37553e60i	0.0972739	−	0.138449i
$825$	1.58333e60			0.0899577
$826$	−1.68798e61	−	3.49480e60i	−0.934946	−	0.193572i
$827$		−	9.18523e60i		−	0.495991i	−0.968761	−	0.247996i	$-0.920228\pi$
$827$		−	9.18523e60i		−	0.495991i	0.968761	−	0.247996i	$-0.0797719\pi$
$828$	4.34756e60	−	1.00492e61i	0.228880	−	0.529049i
$829$	2.05552e61			1.05506			0.527530	−	0.849537i	$-0.323118\pi$
$829$	2.05552e61			1.05506			0.527530	+	0.849537i	$0.323118\pi$
$830$	1.66235e60	−	8.02908e60i	0.0831919	−	0.401815i
$831$			1.33453e61i			0.651188i
$832$	−6.10850e60	−	1.69518e61i	−0.290633	−	0.806542i
$833$	−8.46088e61			−3.92528
$834$	2.34546e61	+	4.85605e60i	1.06106	+	0.219683i
$835$		−	2.82391e61i		−	1.24576i
$836$	4.27856e60	+	1.85101e60i	0.184063	+	0.0796302i
$837$	4.65854e60			0.195441
$838$	−7.67717e60	+	3.70805e61i	−0.314107	+	1.51713i
$839$			2.85476e61i			1.13912i	0.821951	+	0.569559i	$0.192886\pi$
$839$			2.85476e61i			1.13912i	−0.821951	+	0.569559i	$0.807114\pi$
$840$	4.16643e61	+	2.92733e61i	1.62143	+	1.13922i
$841$	−2.60444e61			−0.988549
$842$	7.32718e60	+	1.51702e60i	0.271258	+	0.0561614i
$843$		−	5.36616e60i		−	0.193769i
$844$	1.63035e60	−	3.76850e60i	0.0574235	−	0.132733i
$845$	9.50872e60			0.326687
$846$	−4.19024e59	+	2.02387e60i	−0.0140430	+	0.0678275i
$847$		−	5.67697e61i		−	1.85595i
$848$	1.43569e61	+	1.52827e61i	0.457875	+	0.487402i
$849$	−2.32378e61			−0.722993
$850$	−2.37785e61	−	4.92310e60i	−0.721749	−	0.149431i
$851$			3.91499e61i			1.15934i
$852$	−1.52522e61	−	6.59847e60i	−0.440656	−	0.190639i
$853$	6.01665e61			1.69600			0.847999	−	0.529998i	$-0.177807\pi$
$853$	6.01665e61			1.69600			0.847999	+	0.529998i	$0.177807\pi$
$854$	1.13138e61	−	5.46452e61i	0.311166	−	1.50292i
$855$		−	1.38310e61i		−	0.371163i
$856$	2.65488e61	−	3.77866e61i	0.695178	−	0.989439i
$857$	−2.53160e61			−0.646842			−0.323421	−	0.946255i	$-0.604833\pi$
$857$	−2.53160e61			−0.646842			−0.323421	+	0.946255i	$0.604833\pi$
$858$	5.83072e60	+	1.20719e60i	0.145375	+	0.0300984i
$859$			5.21842e61i			1.26965i	0.772658	+	0.634823i	$0.218927\pi$
$859$			5.21842e61i			1.26965i	−0.772658	+	0.634823i	$0.781073\pi$
$860$	1.10589e60	−	2.55622e60i	0.0262569	−	0.0606919i
$861$	5.82389e60			0.134942
$862$	−4.90511e60	+	2.36916e61i	−0.110917	+	0.535724i
$863$		−	4.94082e61i		−	1.09037i	−0.838317	−	0.545183i	$-0.816460\pi$
$863$		−	4.94082e61i		−	1.09037i	0.838317	−	0.545183i	$-0.183540\pi$
$864$	4.30771e61	−	2.64118e61i	0.927808	−	0.568865i
$865$	−5.38824e60			−0.113268
$866$	−5.71711e60	−	1.18367e60i	−0.117301	−	0.0242860i
$867$			4.19021e61i			0.839140i
$868$	−1.63641e61	−	7.07952e60i	−0.319873	−	0.138385i
$869$	9.01390e59			0.0171988
$870$	−1.18935e60	+	5.74451e60i	−0.0221516	+	0.106991i
$871$			4.72529e61i			0.859108i
$872$	8.38928e61	+	5.89429e61i	1.48894	+	1.04613i
$873$	−2.21778e61			−0.384256
$874$	−1.01994e62	−	2.11168e61i	−1.72517	−	0.357181i
$875$		−	6.96143e61i		−	1.14955i
$876$	2.06593e61	−	4.77534e61i	0.333066	−	0.769871i
$877$	7.34404e61			1.15596			0.577981	−	0.816050i	$-0.303841\pi$
$877$	7.34404e61			1.15596			0.577981	+	0.816050i	$0.303841\pi$
$878$	−1.92695e61	+	9.30711e61i	−0.296132	+	1.43031i
$879$		−	6.99891e61i		−	1.05018i
$880$	−1.28198e61	+	1.20432e61i	−0.187821	+	0.176443i
$881$	−2.56710e61			−0.367239			−0.183620	−	0.982997i	$-0.558781\pi$
$881$	−2.56710e61			−0.367239			−0.183620	+	0.982997i	$0.558781\pi$
$882$	6.08736e61	+	1.26033e61i	0.850333	+	0.176053i
$883$			7.48890e61i			1.02151i	0.859726	+	0.510756i	$0.170634\pi$
$883$			7.48890e61i			1.02151i	−0.859726	+	0.510756i	$0.829366\pi$
$884$	−8.38122e61	−	3.62593e61i	−1.11637	−	0.482972i
$885$	3.86175e61			0.502315
$886$	1.55511e61	−	7.51115e61i	0.197539	−	0.954109i
$887$			1.35315e61i			0.167862i	0.996472	+	0.0839308i	$0.0267475\pi$
$887$			1.35315e61i			0.167862i	−0.996472	+	0.0839308i	$0.973253\pi$
$888$	−2.48128e61	+	3.53157e61i	−0.300610	+	0.427854i
$889$	1.50939e62			1.78593
$890$	−4.24672e61	−	8.79243e60i	−0.490754	−	0.101606i
$891$			1.08838e61i			0.122843i
$892$	−5.54986e61	+	1.28283e62i	−0.611815	+	1.41419i
$893$	1.96606e61			0.211697
$894$	2.02575e61	−	9.78430e61i	0.213058	−	1.02906i
$895$		−	1.59335e62i		−	1.63692i
$896$	−1.91455e62	+	2.73131e61i	−1.92131	+	0.274096i
$897$	−1.33036e62			−1.30415
$898$	−8.67994e61	−	1.79710e61i	−0.831216	−	0.172095i
$899$		−	2.05413e60i		−	0.0192165i
$900$	1.63746e61	+	7.08406e60i	0.149650	+	0.0647425i
$901$	1.06268e62			0.948820
$902$	−4.07865e59	+	1.96998e60i	−0.00355778	+	0.0171840i
$903$			1.01194e61i			0.0862407i
$904$	4.97692e61	+	3.49678e61i	0.414404	+	0.291159i
$905$	−1.36014e62			−1.10653
$906$	1.33321e62	+	2.76029e61i	1.05976	+	0.219413i
$907$		−	3.31973e61i		−	0.257840i	−0.991655	−	0.128920i	$-0.958849\pi$
$907$		−	3.31973e61i		−	0.257840i	0.991655	−	0.128920i	$-0.0411510\pi$
$908$	−2.82783e61	+	6.53644e61i	−0.214611	+	0.496065i
$909$	−2.21321e61			−0.164128
$910$	−5.73811e61	+	2.77149e62i	−0.415814	+	2.00837i
$911$			2.12808e62i			1.50696i	0.657469	+	0.753482i	$0.271627\pi$
$911$			2.12808e62i			1.50696i	−0.657469	+	0.753482i	$0.728373\pi$
$912$	−7.86212e61	−	8.36912e61i	−0.544062	−	0.579146i
$913$	−1.02907e61			−0.0695917
$914$	2.24709e62	+	4.65239e61i	1.48508	+	0.307472i
$915$			1.25017e62i			0.807470i
$916$	−2.00164e62	−	8.65962e61i	−1.26352	−	0.546631i
$917$	−5.22359e60			−0.0322265
$918$	5.19184e61	−	2.50764e62i	0.313058	−	1.51206i
$919$			7.90202e61i			0.465707i	0.972512	+	0.232853i	$0.0748062\pi$
$919$			7.90202e61i			0.465707i	−0.972512	+	0.232853i	$0.925194\pi$
$920$	2.25927e62	−	3.21559e62i	1.30144	−	1.85232i
$921$	2.88296e61			0.162325
$922$	−8.47116e60	−	1.75387e60i	−0.0466223	−	0.00965270i
$923$		−	9.23692e61i		−	0.496926i
$924$	2.53751e61	−	5.86537e61i	0.133443	−	0.308449i
$925$	−6.37922e61			−0.327938
$926$	−1.51396e60	+	7.31240e60i	−0.00760824	+	0.0367476i
$927$			1.08105e61i			0.0531096i
$928$	−1.16460e61	−	1.89943e61i	−0.0559330	−	0.0912256i
$929$	1.72221e62			0.808640			0.404320	−	0.914618i	$-0.367508\pi$
$929$	1.72221e62			0.808640			0.404320	+	0.914618i	$0.367508\pi$
$930$	3.91143e61	+	8.09825e60i	0.179554	+	0.0371748i
$931$		−	5.91346e62i		−	2.65399i
$932$	2.52204e62	+	1.09110e62i	1.10667	+	0.478774i
$933$	1.64060e62			0.703864
$934$	−6.39081e60	+	3.08674e61i	−0.0268084	+	0.129484i
$935$			8.91426e61i			0.365630i
$936$	5.48993e61	+	3.85721e61i	0.220178	+	0.154697i
$937$	1.47047e62			0.576666			0.288333	−	0.957530i	$-0.406899\pi$
$937$	1.47047e62			0.576666			0.288333	+	0.957530i	$0.406899\pi$
$938$	4.96626e62	+	1.02822e62i	1.90445	+	0.394298i
$939$			2.92118e62i			1.09542i
$940$	−2.94543e61	+	6.80827e61i	−0.108010	+	0.249662i
$941$	−4.59603e62			−1.64817			−0.824083	−	0.566469i	$-0.808309\pi$
$941$	−4.59603e62			−1.64817			−0.824083	+	0.566469i	$0.808309\pi$
$942$	4.16683e60	−	2.01257e61i	0.0146129	−	0.0705800i
$943$		−	4.49479e61i		−	0.154157i
$944$	−1.06898e62	+	1.00422e62i	−0.358557	+	0.336836i
$945$	−7.93680e62			−2.60362
$946$	−3.42297e60	−	7.08693e59i	−0.0109822	−	0.00227376i
$947$		−	2.18002e62i		−	0.684087i	−0.939684	−	0.342043i	$-0.888881\pi$
$947$		−	2.18002e62i		−	0.684087i	0.939684	−	0.342043i	$-0.111119\pi$
$948$	−2.03776e61	−	8.81587e60i	−0.0625428	−	0.0270576i
$949$	2.89201e62			0.868180
$950$	3.44085e61	−	1.66192e62i	0.101034	−	0.487994i
$951$			4.29276e61i			0.123295i
$952$	−5.63457e62	+	8.01962e62i	−1.58302	+	2.25309i
$953$	−5.45529e62			−1.49922			−0.749612	−	0.661877i	$-0.769760\pi$
$953$	−5.45529e62			−1.49922			−0.749612	+	0.661877i	$0.769760\pi$
$954$	−7.64571e61	−	1.58297e61i	−0.205543	−	0.0425557i
$955$			7.78456e62i			2.04721i
$956$	2.25941e62	−	5.22255e62i	0.581272	−	1.34359i
$957$	7.36260e60			0.0185302
$958$	1.32265e62	−	6.38835e62i	0.325663	−	1.57294i
$959$			1.07769e62i			0.259598i
$960$	4.07601e62	−	1.46877e62i	0.960592	−	0.346144i
$961$	4.19715e62			0.967751
$962$	−2.34919e62	−	4.86377e61i	−0.529958	−	0.109723i
$963$			1.71959e62i			0.379554i
$964$	−2.87153e62	−	1.24230e62i	−0.620149	−	0.268292i
$965$	1.86883e62			0.394908
$966$	−2.89485e62	+	1.39821e63i	−0.598558	+	2.89102i
$967$		−	5.74148e62i		−	1.16163i	−0.814036	−	0.580815i	$-0.802734\pi$
$967$		−	5.74148e62i		−	1.16163i	0.814036	−	0.580815i	$-0.197266\pi$
$968$	−3.95231e62	−	2.77689e62i	−0.782471	−	0.549763i
$969$	−5.81948e62			−1.12742
$970$	−7.79471e62	−	1.61382e62i	−1.47773	−	0.305949i
$971$		−	4.50241e62i		−	0.835297i	−0.908609	−	0.417649i	$-0.862854\pi$
$971$		−	4.50241e62i		−	0.835297i	0.908609	−	0.417649i	$-0.137146\pi$
$972$	−1.31568e62	+	3.04115e62i	−0.238868	+	0.552136i
$973$	1.42889e63			2.53880
$974$	9.51351e61	−	4.59500e62i	0.165426	−	0.799001i
$975$		−	2.16774e62i		−	0.368901i
$976$	−3.25098e62	−	3.46063e62i	−0.541463	−	0.576380i
$977$	3.05071e62			0.497295			0.248648	−	0.968594i	$-0.420014\pi$
$977$	3.05071e62			0.497295			0.248648	+	0.968594i	$0.420014\pi$
$978$	−5.25354e62	−	1.08770e62i	−0.838178	−	0.173537i
$979$			5.44291e61i			0.0849953i
$980$	2.04778e63	+	8.85921e62i	3.12993	+	1.35409i
$981$	−3.81779e62			−0.571166
$982$	2.14074e61	−	1.03397e62i	0.0313489	−	0.151415i
$983$			9.01690e62i			1.29251i	0.763122	+	0.646254i	$0.223666\pi$
$983$			9.01690e62i			1.29251i	−0.763122	+	0.646254i	$0.776334\pi$
$984$	2.84875e61	−	4.05459e61i	0.0399721	−	0.0568918i
$985$	1.27175e63			1.74679
$986$	−1.10572e62	−	2.28928e61i	−0.148672	−	0.0307810i
$987$		−	2.69522e62i		−	0.354759i
$988$	2.53423e62	−	5.85778e62i	0.326550	−	0.754809i
$989$	7.81001e61			0.0985212
$990$	1.32786e61	−	6.41355e61i	0.0163989	−	0.0792063i
$991$			7.37526e61i			0.0891725i	0.999006	+	0.0445862i	$0.0141969\pi$
$991$			7.37526e61i			0.0891725i	−0.999006	+	0.0445862i	$0.985803\pi$
$992$	−1.29332e62	+	7.92972e61i	−0.153095	+	0.0938670i
$993$	9.82873e62			1.13910
$994$	−9.70795e62	−	2.00994e62i	−1.10157	−	0.228070i
$995$		−	1.56564e63i		−	1.73943i
$996$	2.32640e62	+	1.00646e62i	0.253068	+	0.109484i
$997$	−1.30953e63			−1.39481			−0.697407	−	0.716675i	$-0.745663\pi$
$997$	−1.30953e63			−1.39481			−0.697407	+	0.716675i	$0.745663\pi$
$998$	−4.41701e61	+	2.13340e62i	−0.0460667	+	0.222501i
$999$		−	6.72744e62i		−	0.687028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.43.b.a.3.3	✓	20
4.3	odd	2	inner	4.43.b.a.3.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.43.b.a.3.3	✓	20	1.1	even	1	trivial
4.43.b.a.3.4	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)

\(f(q)\)	\(=\)	\(q+(-2.05360e6 - 425178. i) q^{2} +8.66457e9i q^{3} +(4.03649e12 + 1.74629e12i) q^{4} -5.87785e14 q^{5} +(3.68399e15 - 1.77936e16i) q^{6} -1.08401e18i q^{7} +(-7.54686e18 - 5.30241e18i) q^{8} +3.43442e19 q^{9} +O(q^{10})\)	\(q+(-2.05360e6 - 425178. i) q^{2} +8.66457e9i q^{3} +(4.03649e12 + 1.74629e12i) q^{4} -5.87785e14 q^{5} +(3.68399e15 - 1.77936e16i) q^{6} -1.08401e18i q^{7} +(-7.54686e18 - 5.30241e18i) q^{8} +3.43442e19 q^{9} +(1.20707e21 + 2.49913e20i) q^{10} -1.54708e21i q^{11} +(-1.51309e22 + 3.49745e22i) q^{12} -2.11810e23 q^{13} +(-4.60896e23 + 2.22612e24i) q^{14} -5.09290e24i q^{15} +(1.32437e25 + 1.40978e25i) q^{16} +9.80292e25 q^{17} +(-7.05292e25 - 1.46024e25i) q^{18} +6.85144e26i q^{19} +(-2.37259e27 - 1.02644e27i) q^{20} +9.39246e27 q^{21} +(-6.57783e26 + 3.17707e27i) q^{22} -7.24896e28i q^{23} +(4.59431e28 - 6.53903e28i) q^{24} +1.18117e29 q^{25} +(4.34974e29 + 9.00572e28i) q^{26} +1.24565e30i q^{27} +(1.89299e30 - 4.37559e30i) q^{28} +5.49253e29 q^{29} +(-2.16539e30 + 1.04588e31i) q^{30} -3.73986e30i q^{31} +(-2.12033e31 - 3.45822e31i) q^{32} +1.34048e31 q^{33} +(-2.01313e32 - 4.16799e31i) q^{34} +6.37163e32i q^{35} +(1.38630e32 + 5.99749e31i) q^{36} -5.40076e32 q^{37} +(2.91308e32 - 1.40701e33i) q^{38} -1.83525e33i q^{39} +(4.43593e33 + 3.11668e33i) q^{40} +6.20060e32 q^{41} +(-1.92883e34 - 3.99347e33i) q^{42} +1.07740e33i q^{43} +(2.70165e33 - 6.24476e33i) q^{44} -2.01870e34 q^{45} +(-3.08210e34 + 1.48865e35i) q^{46} -2.86955e34i q^{47} +(-1.22151e35 + 1.14751e35i) q^{48} -8.63099e35 q^{49} +(-2.42565e35 - 5.02208e34i) q^{50} +8.49381e35i q^{51} +(-8.54971e35 - 3.69883e35i) q^{52} +1.08405e36 q^{53} +(5.29622e35 - 2.55806e36i) q^{54} +9.09348e35i q^{55} +(-5.74785e36 + 8.18085e36i) q^{56} -5.93648e36 q^{57} +(-1.12795e36 - 2.33530e35i) q^{58} +7.58262e36i q^{59} +(8.89369e36 - 2.05575e37i) q^{60} -2.45473e37 q^{61} +(-1.59011e36 + 7.68017e36i) q^{62} -3.72293e37i q^{63} +(2.88395e37 + 8.00331e37i) q^{64} +1.24499e38 q^{65} +(-2.75280e37 - 5.69941e36i) q^{66} -2.23091e38i q^{67} +(3.95694e38 + 1.71187e38i) q^{68} +6.28092e38 q^{69} +(2.70908e38 - 1.30848e39i) q^{70} +4.36094e38i q^{71} +(-2.59191e38 - 1.82107e38i) q^{72} -1.36538e39 q^{73} +(1.10910e39 + 2.29629e38i) q^{74} +1.02343e39i q^{75} +(-1.19646e39 + 2.76558e39i) q^{76} -1.67704e39 q^{77} +(-7.80307e38 + 3.76886e39i) q^{78} +5.82641e38i q^{79} +(-7.78447e39 - 8.28646e39i) q^{80} -7.03509e39 q^{81} +(-1.27335e39 - 2.63636e38i) q^{82} -6.65169e39i q^{83} +(3.79126e40 + 1.64020e40i) q^{84} -5.76200e40 q^{85} +(4.58086e38 - 2.21254e39i) q^{86} +4.75904e39i q^{87} +(-8.20323e39 + 1.16756e40i) q^{88} -3.51819e40 q^{89} +(4.14560e40 + 8.58306e39i) q^{90} +2.29604e41i q^{91} +(1.26588e41 - 2.92604e41i) q^{92} +3.24043e40 q^{93} +(-1.22007e40 + 5.89291e40i) q^{94} -4.02717e41i q^{95} +(2.99640e41 - 1.83717e41i) q^{96} -6.45753e41 q^{97} +(1.77246e42 + 3.66971e41i) q^{98} -5.31331e40i 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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