LMFDB - Embedded newform 4.43.b.a.3.8

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			3.8
Root			$0.500000 + 8.71475e8i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.43.b.a.3.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-766250. + 1.95215e6i) q^{2} -1.39436e10i q^{3} +(-3.22377e12 - 2.99168e12i) q^{4} -2.28561e14 q^{5} +(2.72200e16 + 1.06843e16i) q^{6} -3.10753e17i q^{7} +(8.31043e18 - 4.00092e18i) q^{8} -8.50048e19 q^{9} +O(q^{10})$	\(q+(-766250. + 1.95215e6i) q^{2} -1.39436e10i q^{3} +(-3.22377e12 - 2.99168e12i) q^{4} -2.28561e14 q^{5} +(2.72200e16 + 1.06843e16i) q^{6} -3.10753e17i q^{7} +(8.31043e18 - 4.00092e18i) q^{8} -8.50048e19 q^{9} +(1.75135e20 - 4.46186e20i) q^{10} +1.16581e22i q^{11} +(-4.17147e22 + 4.49509e22i) q^{12} +2.36357e23 q^{13} +(6.06638e23 + 2.38115e23i) q^{14} +3.18696e24i q^{15} +(1.44254e24 + 1.92889e25i) q^{16} +7.33330e25 q^{17} +(6.51350e25 - 1.65942e26i) q^{18} +7.36625e26i q^{19} +(7.36827e26 + 6.83781e26i) q^{20} -4.33301e27 q^{21} +(-2.27584e28 - 8.93301e27i) q^{22} -4.03280e28i q^{23} +(-5.57871e28 - 1.15877e29i) q^{24} -1.75134e29 q^{25} +(-1.81109e29 + 4.61405e29i) q^{26} -3.40421e29i q^{27} +(-9.29673e29 + 1.00179e30i) q^{28} +2.73947e30 q^{29} +(-6.22144e30 - 2.44201e30i) q^{30} -1.62058e31i q^{31} +(-3.87603e31 - 1.19641e31i) q^{32} +1.62556e32 q^{33} +(-5.61914e31 + 1.43157e32i) q^{34} +7.10260e31i q^{35} +(2.74036e32 + 2.54307e32i) q^{36} +1.40763e33 q^{37} +(-1.43801e33 - 5.64439e32i) q^{38} -3.29567e33i q^{39} +(-1.89944e33 + 9.14453e32i) q^{40} -8.91817e33 q^{41} +(3.32017e33 - 8.45871e33i) q^{42} +5.01280e33i q^{43} +(3.48772e34 - 3.75830e34i) q^{44} +1.94288e34 q^{45} +(7.87266e34 + 3.09014e34i) q^{46} -1.59065e34i q^{47} +(2.68957e35 - 2.01141e34i) q^{48} +2.15406e35 q^{49} +(1.34196e35 - 3.41888e35i) q^{50} -1.02253e36i q^{51} +(-7.61960e35 - 7.07104e35i) q^{52} +1.96886e36 q^{53} +(6.64555e35 + 2.60848e35i) q^{54} -2.66458e36i q^{55} +(-1.24330e36 - 2.58249e36i) q^{56} +1.02712e37 q^{57} +(-2.09912e36 + 5.34787e36i) q^{58} -2.95570e36i q^{59} +(9.53436e36 - 1.02740e37i) q^{60} -3.70699e37 q^{61} +(3.16363e37 + 1.24177e37i) q^{62} +2.64155e37i q^{63} +(5.30559e37 - 6.64987e37i) q^{64} -5.40220e37 q^{65} +(-1.24558e38 + 3.17334e38i) q^{66} +3.45272e38i q^{67} +(-2.36409e38 - 2.19389e38i) q^{68} -5.62318e38 q^{69} +(-1.38654e38 - 5.44237e37i) q^{70} -1.20803e39i q^{71} +(-7.06427e38 + 3.40097e38i) q^{72} +1.30745e39 q^{73} +(-1.07860e39 + 2.74791e39i) q^{74} +2.44199e39i q^{75} +(2.20374e39 - 2.37471e39i) q^{76} +3.62278e39 q^{77} +(6.43365e39 + 2.52531e39i) q^{78} -7.83976e39i q^{79} +(-3.29707e38 - 4.40870e39i) q^{80} -1.40478e40 q^{81} +(6.83355e39 - 1.74096e40i) q^{82} -1.91214e40i q^{83} +(1.39686e40 + 1.29630e40i) q^{84} -1.67611e40 q^{85} +(-9.78576e39 - 3.84106e39i) q^{86} -3.81981e40i q^{87} +(4.66430e40 + 9.68837e40i) q^{88} +1.27292e41 q^{89} +(-1.48873e40 + 3.79280e40i) q^{90} -7.34486e40i q^{91} +(-1.20649e41 + 1.30008e41i) q^{92} -2.25968e41 q^{93} +(3.10520e40 + 1.21884e40i) q^{94} -1.68364e41i q^{95} +(-1.66823e41 + 5.40459e41i) q^{96} -6.15040e41 q^{97} +(-1.65055e41 + 4.20506e41i) q^{98} -9.90993e41i 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 $

$2$	−766250.	+	1.95215e6i	−0.365377	+	0.930860i
$2$	−766250.	+	1.95215e6i	−0.365377	+	0.930860i
$3$		−	1.39436e10i		−	1.33299i	−0.745507	−	0.666497i	$-0.767793\pi$
$3$		−	1.39436e10i		−	1.33299i	0.745507	−	0.666497i	$-0.232207\pi$
$4$	−3.22377e12	−	2.99168e12i	−0.733000	−	0.680229i
$5$	−2.28561e14			−0.479327			−0.239664	−	0.970856i	$-0.577037\pi$
$5$	−2.28561e14			−0.479327			−0.239664	+	0.970856i	$0.577037\pi$
$6$	2.72200e16	+	1.06843e16i	1.24083	+	0.487045i
$7$		−	3.10753e17i		−	0.556360i	−0.960529	−	0.278180i	$-0.910269\pi$
$7$		−	3.10753e17i		−	0.556360i	0.960529	−	0.278180i	$-0.0897313\pi$
$8$	8.31043e18	−	4.00092e18i	0.901019	−	0.433780i
$9$	−8.50048e19			−0.776874
$10$	1.75135e20	−	4.46186e20i	0.175135	−	0.446186i
$11$			1.16581e22i			1.57536i	0.616082	+	0.787682i	$0.288719\pi$
$11$			1.16581e22i			1.57536i	−0.616082	+	0.787682i	$0.711281\pi$
$12$	−4.17147e22	+	4.49509e22i	−0.906741	+	0.977085i
$13$	2.36357e23			0.956661			0.478330	−	0.878180i	$-0.341242\pi$
$13$	2.36357e23			0.956661			0.478330	+	0.878180i	$0.341242\pi$
$14$	6.06638e23	+	2.38115e23i	0.517894	+	0.203281i
$15$			3.18696e24i			0.638940i
$16$	1.44254e24	+	1.92889e25i	0.0745773	+	0.997215i
$17$	7.33330e25			1.06138			0.530692	−	0.847565i	$-0.321932\pi$
$17$	7.33330e25			1.06138			0.530692	+	0.847565i	$0.321932\pi$
$18$	6.51350e25	−	1.65942e26i	0.283852	−	0.723161i
$19$			7.36625e26i			1.03138i	0.856774	+	0.515692i	$0.172465\pi$
$19$			7.36625e26i			1.03138i	−0.856774	+	0.515692i	$0.827535\pi$
$20$	7.36827e26	+	6.83781e26i	0.351347	+	0.326052i
$21$	−4.33301e27			−0.741625
$22$	−2.27584e28	−	8.93301e27i	−1.46644	−	0.575601i
$23$		−	4.03280e28i		−	1.02170i	−0.859670	−	0.510849i	$-0.829331\pi$
$23$		−	4.03280e28i		−	1.02170i	0.859670	−	0.510849i	$-0.170669\pi$
$24$	−5.57871e28	−	1.15877e29i	−0.578227	−	1.20105i
$25$	−1.75134e29			−0.770246
$26$	−1.81109e29	+	4.61405e29i	−0.349542	+	0.890517i
$27$		−	3.40421e29i		−	0.297425i
$28$	−9.29673e29	+	1.00179e30i	−0.378452	+	0.407812i
$29$	2.73947e30			0.533714			0.266857	−	0.963736i	$-0.414015\pi$
$29$	2.73947e30			0.533714			0.266857	+	0.963736i	$0.414015\pi$
$30$	−6.22144e30	−	2.44201e30i	−0.594764	−	0.233454i
$31$		−	1.62058e31i		−	0.778172i	−0.921201	−	0.389086i	$-0.872791\pi$
$31$		−	1.62058e31i		−	0.778172i	0.921201	−	0.389086i	$-0.127209\pi$
$32$	−3.87603e31	−	1.19641e31i	−0.955516	−	0.294938i
$33$	1.62556e32			2.09995
$34$	−5.61914e31	+	1.43157e32i	−0.387805	+	0.987999i
$35$			7.10260e31i			0.266679i
$36$	2.74036e32	+	2.54307e32i	0.569449	+	0.528452i
$37$	1.40763e33			1.64533			0.822664	−	0.568528i	$-0.192487\pi$
$37$	1.40763e33			1.64533			0.822664	+	0.568528i	$0.192487\pi$
$38$	−1.43801e33	−	5.64439e32i	−0.960075	−	0.376844i
$39$		−	3.29567e33i		−	1.27522i
$40$	−1.89944e33	+	9.14453e32i	−0.431883	+	0.207923i
$41$	−8.91817e33			−1.20730			−0.603649	−	0.797250i	$-0.706287\pi$
$41$	−8.91817e33			−1.20730			−0.603649	+	0.797250i	$0.706287\pi$
$42$	3.32017e33	−	8.45871e33i	0.270973	−	0.690349i
$43$			5.01280e33i			0.249599i	0.992182	+	0.124800i	$0.0398288\pi$
$43$			5.01280e33i			0.249599i	−0.992182	+	0.124800i	$0.960171\pi$
$44$	3.48772e34	−	3.75830e34i	1.07161	−	1.15474i
$45$	1.94288e34			0.372377
$46$	7.87266e34	+	3.09014e34i	0.951058	+	0.373305i
$47$		−	1.59065e34i		−	0.122326i	−0.998128	−	0.0611632i	$-0.980519\pi$
$47$		−	1.59065e34i		−	0.122326i	0.998128	−	0.0611632i	$-0.0194810\pi$
$48$	2.68957e35	−	2.01141e34i	1.32928	−	0.0994111i
$49$	2.15406e35			0.690463
$50$	1.34196e35	−	3.41888e35i	0.281430	−	0.716991i
$51$		−	1.02253e36i		−	1.41482i
$52$	−7.61960e35	−	7.07104e35i	−0.701232	−	0.650748i
$53$	1.96886e36			1.21457			0.607285	−	0.794484i	$-0.292259\pi$
$53$	1.96886e36			1.21457			0.607285	+	0.794484i	$0.292259\pi$
$54$	6.64555e35	+	2.60848e35i	0.276861	+	0.108672i
$55$		−	2.66458e36i		−	0.755115i
$56$	−1.24330e36	−	2.58249e36i	−0.241338	−	0.501291i
$57$	1.02712e37			1.37483
$58$	−2.09912e36	+	5.34787e36i	−0.195007	+	0.496813i
$59$		−	2.95570e36i		−	0.191764i	−0.995393	−	0.0958822i	$-0.969433\pi$
$59$		−	2.95570e36i		−	0.191764i	0.995393	−	0.0958822i	$-0.0305672\pi$
$60$	9.53436e36	−	1.02740e37i	0.434626	−	0.468343i
$61$	−3.70699e37			−1.19425			−0.597124	−	0.802149i	$-0.703690\pi$
$61$	−3.70699e37			−1.19425			−0.597124	+	0.802149i	$0.703690\pi$
$62$	3.16363e37	+	1.24177e37i	0.724369	+	0.284326i
$63$			2.64155e37i			0.432222i
$64$	5.30559e37	−	6.64987e37i	0.623669	−	0.781688i
$65$	−5.40220e37			−0.458554
$66$	−1.24558e38	+	3.17334e38i	−0.767273	+	1.95476i
$67$			3.45272e38i			1.55093i	0.631393	+	0.775463i	$0.282483\pi$
$67$			3.45272e38i			1.55093i	−0.631393	+	0.775463i	$0.717517\pi$
$68$	−2.36409e38	−	2.19389e38i	−0.777993	−	0.721983i
$69$	−5.62318e38			−1.36192
$70$	−1.38654e38	−	5.44237e37i	−0.248240	−	0.0974382i
$71$		−	1.20803e39i		−	1.60565i	−0.596212	−	0.802827i	$-0.703328\pi$
$71$		−	1.20803e39i		−	1.60565i	0.596212	−	0.802827i	$-0.296672\pi$
$72$	−7.06427e38	+	3.40097e38i	−0.699978	+	0.336993i
$73$	1.30745e39			0.969715			0.484857	−	0.874593i	$-0.338871\pi$
$73$	1.30745e39			0.969715			0.484857	+	0.874593i	$0.338871\pi$
$74$	−1.07860e39	+	2.74791e39i	−0.601165	+	1.53157i
$75$			2.44199e39i			1.02673i
$76$	2.20374e39	−	2.37471e39i	0.701578	−	0.756005i
$77$	3.62278e39			0.876470
$78$	6.43365e39	+	2.52531e39i	1.18705	+	0.465937i
$79$		−	7.83976e39i		−	1.10696i	−0.832861	−	0.553482i	$-0.813299\pi$
$79$		−	7.83976e39i		−	1.10696i	0.832861	−	0.553482i	$-0.186701\pi$
$80$	−3.29707e38	−	4.40870e39i	−0.0357469	−	0.477992i
$81$	−1.40478e40			−1.17334
$82$	6.83355e39	−	1.74096e40i	0.441119	−	1.12383i
$83$		−	1.91214e40i		−	0.956930i	−0.878107	−	0.478465i	$-0.841193\pi$
$83$		−	1.91214e40i		−	0.956930i	0.878107	−	0.478465i	$-0.158807\pi$
$84$	1.39686e40	+	1.29630e40i	0.543611	+	0.504475i
$85$	−1.67611e40			−0.508750
$86$	−9.78576e39	−	3.84106e39i	−0.232342	−	0.0911977i
$87$		−	3.81981e40i		−	0.711438i
$88$	4.66430e40	+	9.68837e40i	0.683362	+	1.41943i
$89$	1.27292e41			1.47100			0.735499	−	0.677526i	$-0.236948\pi$
$89$	1.27292e41			1.47100			0.735499	+	0.677526i	$0.236948\pi$
$90$	−1.48873e40	+	3.79280e40i	−0.136058	+	0.346631i
$91$		−	7.34486e40i		−	0.532248i
$92$	−1.20649e41	+	1.30008e41i	−0.694989	+	0.748904i
$93$	−2.25968e41			−1.03730
$94$	3.10520e40	+	1.21884e40i	0.113869	+	0.0446952i
$95$		−	1.68364e41i		−	0.494371i
$96$	−1.66823e41	+	5.40459e41i	−0.393151	+	1.27370i
$97$	−6.15040e41			−1.16599			−0.582997	−	0.812474i	$-0.698120\pi$
$97$	−6.15040e41			−1.16599			−0.582997	+	0.812474i	$0.698120\pi$
$98$	−1.65055e41	+	4.20506e41i	−0.252279	+	0.642724i
$99$		−	9.90993e41i		−	1.22386i
$100$	5.64590e41	+	5.23943e41i	0.564590	+	0.523943i
$101$	−1.90615e42			−1.54670			−0.773352	−	0.633977i	$-0.781421\pi$
$101$	−1.90615e42			−1.54670			−0.773352	+	0.633977i	$0.781421\pi$
$102$	1.99613e42	+	7.83511e41i	1.31700	+	0.516941i
$103$		−	9.46851e41i		−	0.508979i	−0.967076	−	0.254489i	$-0.918093\pi$
$103$		−	9.46851e41i		−	0.508979i	0.967076	−	0.254489i	$-0.0819074\pi$
$104$	1.96423e42	−	9.45645e41i	0.861969	−	0.414981i
$105$	9.90357e41			0.355481
$106$	−1.50864e42	+	3.84353e42i	−0.443776	+	1.13059i
$107$		−	6.40954e42i		−	1.54799i	−0.633193	−	0.773994i	$-0.718256\pi$
$107$		−	6.40954e42i		−	1.54799i	0.633193	−	0.773994i	$-0.281744\pi$
$108$	−1.01843e42	+	1.09744e42i	−0.202317	+	0.218013i
$109$	7.05029e42			1.15412			0.577059	−	0.816702i	$-0.304200\pi$
$109$	7.05029e42			1.15412			0.577059	+	0.816702i	$0.304200\pi$
$110$	5.20168e42	+	2.04174e42i	0.702906	+	0.275901i
$111$		−	1.96274e43i		−	2.19321i
$112$	5.99410e42	−	4.48272e41i	0.554811	−	0.0414919i
$113$	−1.90187e42			−0.146060			−0.0730302	−	0.997330i	$-0.523267\pi$
$113$	−1.90187e42			−0.146060			−0.0730302	+	0.997330i	$0.523267\pi$
$114$	−7.87031e42	+	2.00510e43i	−0.502331	+	1.27977i
$115$			9.21742e42i			0.489728i
$116$	−8.83142e42	−	8.19562e42i	−0.391212	−	0.363048i
$117$	−2.00915e43			−0.743205
$118$	5.76998e42	+	2.26481e42i	0.178506	+	0.0700662i
$119$		−	2.27884e43i		−	0.590512i
$120$	1.27508e43	+	2.64850e43i	0.277160	+	0.575697i
$121$	−8.11473e43			−1.48177
$122$	2.84048e43	−	7.23661e43i	0.436351	−	1.11168i
$123$			1.24351e44i			1.60932i
$124$	−4.84826e43	+	5.22438e43i	−0.529335	+	0.570400i
$125$	9.19974e43			0.848527
$126$	−5.15671e43	−	2.02409e43i	−0.402338	−	0.157924i
$127$			1.22729e44i			0.811091i	0.914075	+	0.405545i	$0.132918\pi$
$127$			1.22729e44i			0.811091i	−0.914075	+	0.405545i	$0.867082\pi$
$128$	8.91616e43	+	1.54528e44i	0.499768	+	0.866159i
$129$	6.98965e43			0.332714
$130$	4.13944e43	−	1.05459e44i	0.167545	−	0.426849i
$131$		−	7.40114e43i		−	0.255036i	−0.991836	−	0.127518i	$-0.959299\pi$
$131$		−	7.40114e43i		−	0.255036i	0.991836	−	0.127518i	$-0.0407011\pi$
$132$	−5.24041e44	−	4.86314e44i	−1.53926	−	1.42845i
$133$	2.28908e44			0.573822
$134$	−6.74025e44	−	2.64565e44i	−1.44369	−	0.566672i
$135$			7.78071e43i			0.142564i
$136$	6.09429e44	−	2.93399e44i	0.956326	−	0.460407i
$137$	9.09590e44			1.22381			0.611905	−	0.790931i	$-0.290403\pi$
$137$	9.09590e44			1.22381			0.611905	+	0.790931i	$0.290403\pi$
$138$	4.30876e44	−	1.09773e45i	0.497613	−	1.26775i
$139$			1.02949e45i			1.02168i	0.859677	+	0.510838i	$0.170665\pi$
$139$			1.02949e45i			1.02168i	−0.859677	+	0.510838i	$0.829335\pi$
$140$	2.12487e44	−	2.28971e44i	0.181403	−	0.195475i
$141$	−2.21794e44			−0.163060
$142$	2.35826e45	+	9.25653e44i	1.49464	+	0.586669i
$143$			2.75547e45i			1.50709i
$144$	−1.22622e44	−	1.63965e45i	−0.0579372	−	0.774711i
$145$	−6.26136e44			−0.255824
$146$	−1.00183e45	+	2.55234e45i	−0.354311	+	0.902668i
$147$		−	3.00354e45i		−	0.920383i
$148$	−4.53787e45	−	4.21118e45i	−1.20603	−	1.11920i
$149$	−1.34778e45			−0.310961			−0.155480	−	0.987839i	$-0.549693\pi$
$149$	−1.34778e45			−0.310961			−0.155480	+	0.987839i	$0.549693\pi$
$150$	−4.76714e45	−	1.87118e45i	−0.955744	−	0.375144i
$151$			1.83551e45i			0.320067i	0.987112	+	0.160034i	$0.0511603\pi$
$151$			1.83551e45i			0.320067i	−0.987112	+	0.160034i	$0.948840\pi$
$152$	2.94717e45	+	6.12167e45i	0.447394	+	0.929297i
$153$	−6.23366e45			−0.824561
$154$	−2.77596e45	+	7.07223e45i	−0.320242	+	0.815871i
$155$			3.70402e45i			0.372999i
$156$	−9.85957e45	+	1.06245e46i	−0.867444	+	0.934739i
$157$	1.66848e46			1.28359			0.641797	−	0.766874i	$-0.278189\pi$
$157$	1.66848e46			1.28359			0.641797	+	0.766874i	$0.278189\pi$
$158$	1.53044e46	+	6.00722e45i	1.03043	+	0.404459i
$159$		−	2.74530e46i		−	1.61902i
$160$	8.85910e45	+	2.73453e45i	0.458005	+	0.141372i
$161$	−1.25321e46			−0.568432
$162$	1.07642e46	−	2.74235e46i	0.428711	−	1.09222i
$163$		−	2.02147e46i		−	0.707503i	−0.935339	−	0.353751i	$-0.884906\pi$
$163$		−	2.02147e46i		−	0.707503i	0.935339	−	0.353751i	$-0.115094\pi$
$164$	2.87501e46	+	2.66803e46i	0.884949	+	0.821239i
$165$	−3.71539e46			−1.00656
$166$	3.73280e46	+	1.46518e46i	0.890767	+	0.349640i
$167$		−	3.28248e46i		−	0.690489i	−0.938513	−	0.345244i	$-0.887796\pi$
$167$		−	3.28248e46i		−	0.690489i	0.938513	−	0.345244i	$-0.112204\pi$
$168$	−3.60092e46	+	1.73360e46i	−0.668218	+	0.321702i
$169$	−5.17626e45			−0.0847998
$170$	1.28432e46	−	3.27202e46i	0.185885	−	0.473575i
$171$		−	6.26166e46i		−	0.801256i
$172$	1.49967e46	−	1.61601e46i	0.169785	−	0.182956i
$173$	8.02340e46			0.804249			0.402124	−	0.915585i	$-0.368272\pi$
$173$	8.02340e46			0.804249			0.402124	+	0.915585i	$0.368272\pi$
$174$	7.45685e46	+	2.92693e46i	0.662249	+	0.259943i
$175$			5.44232e46i			0.428534i
$176$	−2.24872e47	+	1.68172e46i	−1.57098	+	0.117486i
$177$	−4.12131e46			−0.255621
$178$	−9.75378e46	+	2.48494e47i	−0.537469	+	1.36929i
$179$		−	9.89658e46i		−	0.484810i	−0.970175	−	0.242405i	$-0.922064\pi$
$179$		−	9.89658e46i		−	0.484810i	0.970175	−	0.242405i	$-0.0779363\pi$
$180$	−6.26339e46	−	5.81247e46i	−0.272952	−	0.253302i
$181$	1.30213e47			0.505130			0.252565	−	0.967580i	$-0.418726\pi$
$181$	1.30213e47			0.505130			0.252565	+	0.967580i	$0.418726\pi$
$182$	1.43383e47	+	5.62800e46i	0.495449	+	0.194471i
$183$			5.16887e47i			1.59193i
$184$	−1.61349e47	−	3.35143e47i	−0.443192	−	0.920569i
$185$	−3.21730e47			−0.788651
$186$	1.73148e47	−	4.41124e47i	0.379005	−	0.965580i
$187$			8.54922e47i			1.67206i
$188$	−4.75872e46	+	5.12789e46i	−0.0832100	+	0.0896653i
$189$	−1.05787e47			−0.165476
$190$	3.28672e47	+	1.29009e47i	0.460190	+	0.180632i
$191$		−	4.73031e47i		−	0.593184i	−0.955004	−	0.296592i	$-0.904150\pi$
$191$		−	4.73031e47i		−	0.593184i	0.955004	−	0.296592i	$-0.0958501\pi$
$192$	−9.27230e47	−	7.39790e47i	−1.04199	−	0.831348i
$193$	5.47266e47			0.551436			0.275718	−	0.961239i	$-0.411084\pi$
$193$	5.47266e47			0.551436			0.275718	+	0.961239i	$0.411084\pi$
$194$	4.71274e47	−	1.20065e48i	0.426027	−	1.08538i
$195$			7.53261e47i			0.611249i
$196$	−6.94419e47	−	6.44426e47i	−0.506109	−	0.469673i
$197$	−9.94931e46			−0.0651632			−0.0325816	−	0.999469i	$-0.510373\pi$
$197$	−9.94931e46			−0.0651632			−0.0325816	+	0.999469i	$0.510373\pi$
$198$	1.93457e48	+	7.59349e47i	1.13924	+	0.447170i
$199$		−	8.84757e47i		−	0.468716i	−0.972150	−	0.234358i	$-0.924701\pi$
$199$		−	8.84757e47i		−	0.468716i	0.972150	−	0.234358i	$-0.0752988\pi$
$200$	−1.45544e48	+	7.00695e47i	−0.694006	+	0.334117i
$201$	4.81434e48			2.06738
$202$	1.46058e48	−	3.72109e48i	0.565129	−	1.43976i
$203$		−	8.51299e47i		−	0.296938i
$204$	−3.05907e48	+	3.29638e48i	−0.962400	+	1.03706i
$205$	2.03834e48			0.578691
$206$	1.84840e48	+	7.25525e47i	0.473788	+	0.185969i
$207$			3.42808e48i			0.793731i
$208$	3.40953e47	+	4.55908e48i	0.0713452	+	0.953997i
$209$	−8.58763e48			−1.62481
$210$	−7.58862e47	+	1.93333e48i	−0.129885	+	0.330903i
$211$		−	5.69142e48i		−	0.881636i	−0.897596	−	0.440818i	$-0.854688\pi$
$211$		−	5.69142e48i		−	0.881636i	0.897596	−	0.440818i	$-0.145312\pi$
$212$	−6.34716e48	−	5.89021e48i	−0.890280	−	0.826186i
$213$	−1.68443e49			−2.14033
$214$	1.25124e49	+	4.91131e48i	1.44096	+	0.565599i
$215$		−	1.14573e48i		−	0.119640i
$216$	−1.36200e48	−	2.82905e48i	−0.129017	−	0.267986i
$217$	−5.03601e48			−0.432944
$218$	−5.40228e48	+	1.37632e49i	−0.421688	+	1.07432i
$219$		−	1.82305e49i		−	1.29262i
$220$	−7.97158e48	+	8.59000e48i	−0.513651	+	0.553499i
$221$	1.73328e49			1.01538
$222$	3.83158e49	+	1.50395e49i	2.04157	+	0.801349i
$223$			2.20112e49i			1.06719i	0.845740	+	0.533596i	$0.179160\pi$
$223$			2.20112e49i			1.06719i	−0.845740	+	0.533596i	$0.820840\pi$
$224$	−3.71788e48	+	1.20449e49i	−0.164092	+	0.531612i
$225$	1.48872e49			0.598384
$226$	1.45731e48	−	3.71274e48i	0.0533671	−	0.135962i
$227$		−	3.56289e49i		−	1.18921i	−0.804017	−	0.594606i	$-0.797308\pi$
$227$		−	3.56289e49i		−	1.18921i	0.804017	−	0.594606i	$-0.202692\pi$
$228$	−3.31119e49	−	3.07281e49i	−1.00775	−	0.935199i
$229$	3.17647e49			0.881860			0.440930	−	0.897541i	$-0.354649\pi$
$229$	3.17647e49			0.881860			0.440930	+	0.897541i	$0.354649\pi$
$230$	−1.79938e49	−	7.06285e48i	−0.455868	−	0.178935i
$231$		−	5.05146e49i		−	1.16833i
$232$	2.27662e49	−	1.09604e49i	0.480887	−	0.231515i
$233$	−1.77955e49			−0.343427			−0.171714	−	0.985147i	$-0.554930\pi$
$233$	−1.77955e49			−0.343427			−0.171714	+	0.985147i	$0.554930\pi$
$234$	1.53951e49	−	3.92217e49i	0.271550	−	0.691820i
$235$			3.63561e48i			0.0586344i
$236$	−8.84250e48	+	9.52848e48i	−0.130444	+	0.140563i
$237$	−1.09314e50			−1.47558
$238$	4.44866e49	+	1.74617e49i	0.549683	+	0.215759i
$239$			1.50173e50i			1.69917i	0.527450	+	0.849586i	$0.323148\pi$
$239$			1.50173e50i			1.69917i	−0.527450	+	0.849586i	$0.676852\pi$
$240$	−6.14731e49	+	4.59730e48i	−0.637161	+	0.0476505i
$241$	1.76728e50			1.67860			0.839301	−	0.543668i	$-0.182965\pi$
$241$	1.76728e50			1.67860			0.839301	+	0.543668i	$0.182965\pi$
$242$	6.21791e49	−	1.58412e50i	0.541405	−	1.37932i
$243$			1.58629e50i			1.26663i
$244$	1.19505e50	+	1.10901e50i	0.875384	+	0.812362i
$245$	−4.92334e49			−0.330958
$246$	−2.42753e50	−	9.52842e49i	−1.49805	−	0.588009i
$247$			1.74106e50i			0.986685i
$248$	−6.48382e49	−	1.34677e50i	−0.337556	−	0.701148i
$249$	−2.66621e50			−1.27558
$250$	−7.04931e49	+	1.79593e50i	−0.310032	+	0.789859i
$251$		−	1.47092e50i		−	0.594895i	−0.954738	−	0.297447i	$-0.903865\pi$
$251$		−	1.47092e50i		−	0.594895i	0.954738	−	0.297447i	$-0.0961353\pi$
$252$	7.90266e49	−	8.51574e49i	0.294010	−	0.316819i
$253$	4.70148e50			1.60955
$254$	−2.39586e50	−	9.40412e49i	−0.755012	−	0.296354i
$255$			2.33709e50i			0.678161i
$256$	−3.69983e50	+	5.56500e49i	−0.988876	+	0.148739i
$257$	1.76471e50			0.434588			0.217294	−	0.976106i	$-0.430277\pi$
$257$	1.76471e50			0.434588			0.217294	+	0.976106i	$0.430277\pi$
$258$	−5.35582e49	+	1.36449e50i	−0.121566	+	0.309710i
$259$		−	4.37425e50i		−	0.915396i
$260$	1.74154e50	+	1.61616e50i	0.336120	+	0.311921i
$261$	−2.32868e50			−0.414629
$262$	1.44482e50	+	5.67113e49i	0.237403	+	0.0931842i
$263$			2.31166e50i			0.350633i	0.984512	+	0.175316i	$0.0560948\pi$
$263$			2.31166e50i			0.350633i	−0.984512	+	0.175316i	$0.943905\pi$
$264$	1.35091e51	−	6.50371e50i	1.89210	−	0.910917i
$265$	−4.50006e50			−0.582176
$266$	−1.75401e50	+	4.46864e50i	−0.209661	+	0.534148i
$267$		−	1.77491e51i		−	1.96083i
$268$	1.03294e51	−	1.11308e51i	1.05498	−	1.13683i
$269$	5.86845e50			0.554275			0.277138	−	0.960830i	$-0.410614\pi$
$269$	5.86845e50			0.554275			0.277138	+	0.960830i	$0.410614\pi$
$270$	−1.51891e50	−	5.96197e49i	−0.132707	−	0.0520896i
$271$			9.75042e50i			0.788257i	0.919055	+	0.394129i	$0.128954\pi$
$271$			9.75042e50i			0.788257i	−0.919055	+	0.394129i	$0.871046\pi$
$272$	1.05785e50	+	1.41452e51i	0.0791551	+	1.05843i
$273$	−1.02414e51			−0.709484
$274$	−6.96974e50	+	1.77566e51i	−0.447152	+	1.13920i
$275$		−	2.04172e51i		−	1.21342i
$276$	1.81278e51	+	1.68227e51i	0.998286	+	0.926416i
$277$	−5.21615e50			−0.266241			−0.133120	−	0.991100i	$-0.542500\pi$
$277$	−5.21615e50			−0.266241			−0.133120	+	0.991100i	$0.542500\pi$
$278$	−2.00973e51	−	7.88850e50i	−0.951037	−	0.373296i
$279$			1.37757e51i			0.604542i
$280$	2.84169e50	+	5.90256e50i	0.115680	+	0.240282i
$281$	5.45840e50			0.206173			0.103087	−	0.994672i	$-0.467128\pi$
$281$	5.45840e50			0.206173			0.103087	+	0.994672i	$0.467128\pi$
$282$	1.69950e50	−	4.32976e50i	0.0595785	−	0.151786i
$283$		−	4.84642e51i		−	1.57727i	−0.614862	−	0.788635i	$-0.710788\pi$
$283$		−	4.84642e51i		−	1.57727i	0.614862	−	0.788635i	$-0.289212\pi$
$284$	−3.61403e51	+	3.89440e51i	−1.09221	+	1.17694i
$285$	−2.34759e51			−0.658993
$286$	−5.37910e51	−	2.11138e51i	−1.40289	−	0.550655i
$287$			2.77135e51i			0.671693i
$288$	3.29482e51	+	1.01701e51i	0.742316	+	0.229130i
$289$	6.04034e50			0.126534
$290$	4.79777e50	−	1.22231e51i	0.0934720	−	0.238136i
$291$			8.57586e51i			1.55426i
$292$	−4.21490e51	−	3.91146e51i	−0.710801	−	0.659628i
$293$	1.32973e51			0.208711			0.104355	−	0.994540i	$-0.466722\pi$
$293$	1.32973e51			0.208711			0.104355	+	0.994540i	$0.466722\pi$
$294$	5.86337e51	+	2.30146e51i	0.856748	+	0.336287i
$295$			6.75557e50i			0.0919179i
$296$	1.16980e52	−	5.63181e51i	1.48247	−	0.713711i
$297$	3.96866e51			0.468553
$298$	1.03273e51	−	2.63107e51i	0.113618	−	0.289461i
$299$		−	9.53181e51i		−	0.977419i
$300$	7.30565e51	−	7.87241e51i	0.698413	−	0.752595i
$301$	1.55774e51			0.138867
$302$	−3.58320e51	−	1.40646e51i	−0.297938	−	0.116945i
$303$			2.65785e52i			2.06175i
$304$	−1.42087e52	+	1.06261e51i	−1.02851	+	0.0769179i
$305$	8.47273e51			0.572436
$306$	4.77654e51	−	1.21691e52i	0.301275	−	0.767551i
$307$		−	9.36165e51i		−	0.551374i	−0.961247	−	0.275687i	$-0.911095\pi$
$307$		−	9.36165e51i		−	0.551374i	0.961247	−	0.275687i	$-0.0889053\pi$
$308$	−1.16790e52	−	1.08382e52i	−0.642452	−	0.596200i
$309$	−1.32025e52			−0.678466
$310$	−7.23082e51	−	2.83821e51i	−0.347210	−	0.136285i
$311$		−	5.67020e51i		−	0.254466i	−0.991873	−	0.127233i	$-0.959390\pi$
$311$		−	5.67020e51i		−	0.254466i	0.991873	−	0.127233i	$-0.0406096\pi$
$312$	−1.31857e52	−	2.73884e52i	−0.553167	−	1.14900i
$313$	2.46923e52			0.968568			0.484284	−	0.874911i	$-0.339080\pi$
$313$	2.46923e52			0.968568			0.484284	+	0.874911i	$0.339080\pi$
$314$	−1.27847e52	+	3.25713e52i	−0.468996	+	1.19485i
$315$		−	6.03755e51i		−	0.207176i
$316$	−2.34540e52	+	2.52736e52i	−0.752989	+	0.811405i
$317$	4.46714e52			1.34210			0.671050	−	0.741412i	$-0.265844\pi$
$317$	4.46714e52			1.34210			0.671050	+	0.741412i	$0.265844\pi$
$318$	5.35926e52	+	2.10359e52i	1.50708	+	0.591550i
$319$			3.19370e52i			0.840794i
$320$	−1.21265e52	+	1.51990e52i	−0.298942	+	0.374684i
$321$	−8.93720e52			−2.06346
$322$	9.60269e51	−	2.44645e52i	0.207692	−	0.529131i
$323$			5.40189e52i			1.09469i
$324$	4.52870e52	+	4.20266e52i	0.860058	+	0.798140i
$325$	−4.13940e52			−0.736864
$326$	3.94623e52	+	1.54895e52i	0.658586	+	0.258505i
$327$		−	9.83063e52i		−	1.53843i
$328$	−7.41138e52	+	3.56808e52i	−1.08780	+	0.523702i
$329$	−4.94300e51			−0.0680576
$330$	2.84692e52	−	7.25301e52i	0.367775	−	0.936970i
$331$		−	8.72561e52i		−	1.05781i	−0.848681	−	0.528905i	$-0.822603\pi$
$331$		−	8.72561e52i		−	1.05781i	0.848681	−	0.528905i	$-0.177397\pi$
$332$	−5.72051e52	+	6.16430e52i	−0.650931	+	0.701429i
$333$	−1.19655e53			−1.27821
$334$	6.40792e52	+	2.51520e52i	0.642748	+	0.252289i
$335$		−	7.89158e52i		−	0.743401i
$336$	−6.25052e51	−	8.35792e52i	−0.0553084	−	0.739560i
$337$	8.80027e52			0.731591			0.365795	−	0.930695i	$-0.380797\pi$
$337$	8.80027e52			0.731591			0.365795	+	0.930695i	$0.380797\pi$
$338$	3.96631e51	−	1.01049e52i	0.0309839	−	0.0789368i
$339$			2.65188e52i			0.194698i
$340$	5.40338e52	+	5.01437e52i	0.372913	+	0.346066i
$341$	1.88929e53			1.22590
$342$	1.22237e53	+	4.79800e52i	0.745857	+	0.292760i
$343$		−	1.63885e53i		−	0.940507i
$344$	2.00558e52	+	4.16585e52i	0.108271	+	0.224893i
$345$	1.28524e53			0.652804
$346$	−6.14794e52	+	1.56629e53i	−0.293854	+	0.748643i
$347$			7.20602e52i			0.324173i	0.986777	+	0.162086i	$0.0518223\pi$
$347$			7.20602e52i			0.324173i	−0.986777	+	0.162086i	$0.948178\pi$
$348$	−1.14276e53	+	1.23142e53i	−0.483941	+	0.521484i
$349$	2.19071e53			0.873477			0.436739	−	0.899589i	$-0.356134\pi$
$349$	2.19071e53			0.873477			0.436739	+	0.899589i	$0.356134\pi$
$350$	−1.06243e53	−	4.17018e52i	−0.398905	−	0.156576i
$351$		−	8.04610e52i		−	0.284535i
$352$	1.39479e53	−	4.51871e53i	0.464635	−	1.50529i
$353$	−4.83415e53			−1.51723			−0.758615	−	0.651539i	$-0.774124\pi$
$353$	−4.83415e53			−1.51723			−0.758615	+	0.651539i	$0.774124\pi$
$354$	3.15795e52	−	8.04542e52i	0.0933979	−	0.237947i
$355$			2.76108e53i			0.769634i
$356$	−4.10361e53	−	3.80818e53i	−1.07824	−	1.00062i
$357$	−3.17753e53			−0.787149
$358$	1.93197e53	+	7.58326e52i	0.451290	+	0.177138i
$359$			5.65495e53i			1.24579i	0.782305	+	0.622896i	$0.214044\pi$
$359$			5.65495e53i			1.24579i	−0.782305	+	0.622896i	$0.785956\pi$
$360$	1.61462e53	−	7.77329e52i	0.335519	−	0.161530i
$361$	−3.25208e52			−0.0637544
$362$	−9.97754e52	+	2.54195e53i	−0.184563	+	0.470205i
$363$			1.13148e54i			1.97519i
$364$	−2.19735e53	+	2.36781e53i	−0.362051	+	0.390138i
$365$	−2.98831e53			−0.464811
$366$	−1.00904e54	−	3.96065e53i	−1.48186	−	0.581653i
$367$		−	7.59620e52i		−	0.105344i	−0.998612	−	0.0526719i	$-0.983226\pi$
$367$		−	7.59620e52i		−	0.105344i	0.998612	−	0.0526719i	$-0.0167737\pi$
$368$	7.77885e53	−	5.81746e52i	1.01885	−	0.0761955i
$369$	7.58087e53			0.937919
$370$	2.46525e53	−	6.28066e53i	0.288155	−	0.734123i
$371$		−	6.11830e53i		−	0.675739i
$372$	7.28467e53	+	6.76022e53i	0.760340	+	0.705601i
$373$	7.03820e53			0.694346			0.347173	−	0.937801i	$-0.387142\pi$
$373$	7.03820e53			0.694346			0.347173	+	0.937801i	$0.387142\pi$
$374$	−1.66894e54	−	6.55085e53i	−1.55646	−	0.610933i
$375$		−	1.28278e54i		−	1.13108i
$376$	−6.36407e52	−	1.32190e53i	−0.0530628	−	0.110218i
$377$	6.47493e53			0.510584
$378$	8.10593e52	−	2.06512e53i	0.0604610	−	0.154035i
$379$			1.89796e54i			1.33926i	0.742696	+	0.669628i	$0.233547\pi$
$379$			1.89796e54i			1.33926i	−0.742696	+	0.669628i	$0.766453\pi$
$380$	−5.03690e53	+	5.42765e53i	−0.336285	+	0.362374i
$381$	1.71128e54			1.08118
$382$	9.23430e53	+	3.62461e53i	0.552171	+	0.216736i
$383$		−	2.18705e54i		−	1.23790i	−0.785432	−	0.618948i	$-0.787559\pi$
$383$		−	2.18705e54i		−	1.23790i	0.785432	−	0.618948i	$-0.212441\pi$
$384$	2.15468e54	−	1.24323e54i	1.15459	−	0.666188i
$385$	−8.28027e53			−0.420116
$386$	−4.19343e53	+	1.06835e54i	−0.201482	+	0.513309i
$387$		−	4.26112e53i		−	0.193907i
$388$	1.98274e54	+	1.84000e54i	0.854674	+	0.793143i
$389$	−4.42637e54			−1.80762			−0.903808	−	0.427938i	$-0.859240\pi$
$389$	−4.42637e54			−1.80762			−0.903808	+	0.427938i	$0.859240\pi$
$390$	−1.47048e54	−	5.77186e53i	−0.568987	−	0.223336i
$391$		−	2.95738e54i		−	1.08441i
$392$	1.79012e54	−	8.61822e53i	0.622120	−	0.299509i
$393$	−1.03199e54			−0.339962
$394$	7.62366e52	−	1.94226e53i	0.0238091	−	0.0606578i
$395$			1.79186e54i			0.530598i
$396$	−2.96473e54	+	3.19473e54i	−0.832505	+	0.897089i
$397$	−2.55510e53			−0.0680467			−0.0340233	−	0.999421i	$-0.510832\pi$
$397$	−2.55510e53			−0.0680467			−0.0340233	+	0.999421i	$0.510832\pi$
$398$	1.72718e54	+	6.77946e53i	0.436309	+	0.171258i
$399$		−	3.19180e54i		−	0.764901i
$400$	−2.52636e53	−	3.37814e54i	−0.0574428	−	0.768101i
$401$	−4.79440e54			−1.03443			−0.517217	−	0.855854i	$-0.673032\pi$
$401$	−4.79440e54			−1.03443			−0.517217	+	0.855854i	$0.673032\pi$
$402$	−3.68899e54	+	9.39833e54i	−0.755371	+	1.92444i
$403$		−	3.83036e54i		−	0.744447i
$404$	6.14497e54	+	5.70257e54i	1.13373	+	1.05211i
$405$	3.21079e54			0.562414
$406$	1.66187e54	+	6.52308e53i	0.276407	+	0.108494i
$407$			1.64103e55i			2.59199i
$408$	−4.09104e54	−	8.49763e54i	−0.613720	−	1.27478i
$409$	7.40890e54			1.05576			0.527879	−	0.849320i	$-0.322987\pi$
$409$	7.40890e54			1.05576			0.527879	+	0.849320i	$0.322987\pi$
$410$	−1.56188e54	+	3.97916e54i	−0.211440	+	0.538680i
$411$		−	1.26830e55i		−	1.63133i
$412$	−2.83267e54	+	3.05243e54i	−0.346222	+	0.373081i
$413$	−9.18492e53			−0.106690
$414$	−6.69214e54	−	2.62677e54i	−0.738852	−	0.290011i
$415$			4.37041e54i			0.458682i
$416$	−9.16128e54	−	2.82780e54i	−0.914105	−	0.282156i
$417$	1.43548e55			1.36189
$418$	6.58028e54	−	1.67644e55i	0.593666	−	1.51247i
$419$		−	4.63995e54i		−	0.398124i	−0.979987	−	0.199062i	$-0.936210\pi$
$419$		−	4.63995e54i		−	0.398124i	0.979987	−	0.199062i	$-0.0637896\pi$
$420$	−3.19268e54	−	2.96283e54i	−0.260568	−	0.241809i
$421$	−2.26595e55			−1.75924			−0.879622	−	0.475673i	$-0.842205\pi$
$421$	−2.26595e55			−1.75924			−0.879622	+	0.475673i	$0.842205\pi$
$422$	1.11105e55	+	4.36106e54i	0.820680	+	0.322129i
$423$			1.35213e54i			0.0950323i
$424$	1.63621e55	−	7.87726e54i	1.09435	−	0.526857i
$425$	−1.28431e55			−0.817525
$426$	1.29069e55	−	3.28826e55i	0.782026	−	1.99235i
$427$			1.15196e55i			0.664433i
$428$	−1.91753e55	+	2.06629e55i	−1.05299	+	1.13467i
$429$	3.84212e55			2.00894
$430$	2.23664e54	+	8.77917e53i	0.111368	+	0.0437135i
$431$			3.00442e55i			1.42475i	0.701800	+	0.712374i	$0.252380\pi$
$431$			3.00442e55i			1.42475i	−0.701800	+	0.712374i	$0.747620\pi$
$432$	6.56637e54	−	4.91070e53i	0.296597	−	0.0221812i
$433$	−6.63899e53			−0.0285664			−0.0142832	−	0.999898i	$-0.504547\pi$
$433$	−6.63899e53			−0.0285664			−0.0142832	+	0.999898i	$0.504547\pi$
$434$	3.85884e54	−	9.83107e54i	0.158188	−	0.403011i
$435$			8.73059e54i			0.341012i
$436$	−2.27285e55	−	2.10922e55i	−0.845968	−	0.785065i
$437$	2.97066e55			1.05376
$438$	3.55888e55	+	1.39691e55i	1.20325	+	0.472295i
$439$		−	1.59156e55i		−	0.512941i	−0.966552	−	0.256471i	$-0.917440\pi$
$439$		−	1.59156e55i		−	0.512941i	0.966552	−	0.256471i	$-0.0825597\pi$
$440$	−1.06608e55	−	2.21438e55i	−0.327554	−	0.680372i
$441$	−1.83106e55			−0.536403
$442$	−1.32812e55	+	3.38362e55i	−0.370998	+	0.945180i
$443$			5.18710e54i			0.138180i	0.997610	+	0.0690902i	$0.0220096\pi$
$443$			5.18710e54i			0.138180i	−0.997610	+	0.0690902i	$0.977990\pi$
$444$	−5.87190e55	+	6.32743e55i	−1.49189	+	1.60763i
$445$	−2.90941e55			−0.705090
$446$	−4.29694e55	−	1.68661e55i	−0.993406	−	0.389927i
$447$			1.87928e55i			0.414509i
$448$	−2.06647e55	−	1.64873e55i	−0.434900	−	0.346985i
$449$	−6.21436e55			−1.24802			−0.624012	−	0.781415i	$-0.714499\pi$
$449$	−6.21436e55			−1.24802			−0.624012	+	0.781415i	$0.714499\pi$
$450$	−1.14073e55	+	2.90621e55i	−0.218636	+	0.557012i
$451$		−	1.03969e56i		−	1.90193i
$452$	6.13117e54	+	5.68977e54i	0.107062	+	0.0993545i
$453$	2.55936e55			0.426648
$454$	6.95531e55	+	2.73007e55i	1.10699	+	0.434510i
$455$			1.67875e55i			0.255121i
$456$	8.53581e55	−	4.10942e55i	1.23875	−	0.596374i
$457$	6.07800e55			0.842404			0.421202	−	0.906967i	$-0.361608\pi$
$457$	6.07800e55			0.842404			0.421202	+	0.906967i	$0.361608\pi$
$458$	−2.43397e55	+	6.20096e55i	−0.322211	+	0.820888i
$459$		−	2.49641e55i		−	0.315682i
$460$	2.75755e55	−	2.97148e55i	0.333127	−	0.358970i
$461$	−1.40672e56			−1.62363			−0.811817	−	0.583912i	$-0.801521\pi$
$461$	−1.40672e56			−1.62363			−0.811817	+	0.583912i	$0.801521\pi$
$462$	9.86123e55	+	3.87068e55i	1.08755	+	0.426880i
$463$			3.36911e55i			0.355071i	0.984114	+	0.177535i	$0.0568124\pi$
$463$			3.36911e55i			0.355071i	−0.984114	+	0.177535i	$0.943188\pi$
$464$	3.95178e54	+	5.28415e55i	0.0398030	+	0.532228i
$465$	5.16474e55			0.497206
$466$	1.36358e55	−	3.47395e55i	0.125480	−	0.319683i
$467$		−	2.24964e55i		−	0.197906i	−0.995092	−	0.0989531i	$-0.968451\pi$
$467$		−	2.24964e55i		−	0.197906i	0.995092	−	0.0989531i	$-0.0315494\pi$
$468$	6.47702e55	+	6.01072e55i	0.544769	+	0.505550i
$469$	1.07294e56			0.862874
$470$	−7.09728e54	−	2.78579e54i	−0.0545804	−	0.0214236i
$471$		−	2.32646e56i		−	1.71102i
$472$	−1.18255e55	−	2.45631e55i	−0.0831836	−	0.172783i
$473$	−5.84397e55			−0.393209
$474$	8.37622e55	−	2.13399e56i	0.539142	−	1.37356i
$475$		−	1.29008e56i		−	0.794419i
$476$	−6.81757e55	+	7.34646e55i	−0.401683	+	0.432845i
$477$	−1.67363e56			−0.943568
$478$	−2.93162e56	−	1.15070e56i	−1.58169	−	0.620838i
$479$			1.49862e56i			0.773830i	0.922115	+	0.386915i	$0.126459\pi$
$479$			1.49862e56i			0.773830i	−0.922115	+	0.386915i	$0.873541\pi$
$480$	3.81292e55	−	1.23528e56i	0.188448	−	0.610518i
$481$	3.32703e56			1.57402
$482$	−1.35418e56	+	3.45000e56i	−0.613322	+	1.56254i
$483$			1.74742e56i			0.757717i
$484$	2.61600e56	+	2.42767e56i	1.08614	+	1.00794i
$485$	1.40574e56			0.558893
$486$	−3.09668e56	−	1.21549e56i	−1.17906	−	0.462798i
$487$			4.40905e55i			0.160782i	0.996763	+	0.0803909i	$0.0256169\pi$
$487$			4.40905e55i			0.160782i	−0.996763	+	0.0803909i	$0.974383\pi$
$488$	−3.08067e56	+	1.48313e56i	−1.07604	+	0.518041i
$489$	−2.81866e56			−0.943097
$490$	3.77251e55	−	9.61113e55i	0.120924	−	0.308075i
$491$			5.27811e56i			1.62094i	0.585780	+	0.810470i	$0.300788\pi$
$491$			5.27811e56i			1.62094i	−0.585780	+	0.810470i	$0.699212\pi$
$492$	3.72019e56	−	4.00880e56i	1.09471	−	1.17963i
$493$	2.00894e56			0.566475
$494$	−3.39883e56	−	1.33409e56i	−0.918466	−	0.360512i
$495$			2.26502e56i			0.586629i
$496$	3.12594e56	−	2.33775e55i	0.776005	−	0.0580340i
$497$	−3.75398e56			−0.893323
$498$	2.04299e56	−	5.20486e56i	0.466068	−	1.18739i
$499$			5.39960e56i			1.18100i	0.807037	+	0.590501i	$0.201070\pi$
$499$			5.39960e56i			1.18100i	−0.807037	+	0.590501i	$0.798930\pi$
$500$	−2.96578e56	−	2.75227e56i	−0.621970	−	0.577192i
$501$	−4.57696e56			−0.920418
$502$	2.87146e56	+	1.12709e56i	0.553764	+	0.217361i
$503$		−	5.44769e56i		−	1.00759i	−0.863823	−	0.503796i	$-0.831936\pi$
$503$		−	5.44769e56i		−	1.00759i	0.863823	−	0.503796i	$-0.168064\pi$
$504$	1.05686e56	+	2.19524e56i	0.187489	+	0.389440i
$505$	4.35670e56			0.741377
$506$	−3.60251e56	+	9.17801e56i	−0.588091	+	1.49826i
$507$			7.21756e55i			0.113038i
$508$	3.67166e56	−	3.95650e56i	0.551727	−	0.594529i
$509$	5.71657e56			0.824255			0.412128	−	0.911126i	$-0.364786\pi$
$509$	5.71657e56			0.824255			0.412128	+	0.911126i	$0.364786\pi$
$510$	−4.56237e56	−	1.79080e56i	−0.631272	−	0.247784i
$511$		−	4.06293e56i		−	0.539511i
$512$	1.74862e56	−	7.64905e56i	0.222857	−	0.974851i
$513$	2.50763e56			0.306760
$514$	−1.35221e56	+	3.44499e56i	−0.158788	+	0.404541i
$515$			2.16413e56i			0.243967i
$516$	−2.25330e56	−	2.09108e56i	−0.243879	−	0.226322i
$517$	1.85440e56			0.192709
$518$	8.53922e56	+	3.35177e56i	0.852105	+	0.334464i
$519$		−	1.11875e57i		−	1.07206i
$520$	−4.48946e56	+	2.16137e56i	−0.413165	+	0.198911i
$521$	−2.42727e56			−0.214549			−0.107274	−	0.994229i	$-0.534212\pi$
$521$	−2.42727e56			−0.214549			−0.107274	+	0.994229i	$0.534212\pi$
$522$	1.78435e56	−	4.54595e56i	0.151496	−	0.385961i
$523$		−	1.11302e57i		−	0.907750i	−0.891065	−	0.453875i	$-0.850041\pi$
$523$		−	1.11302e57i		−	0.907750i	0.891065	−	0.453875i	$-0.149959\pi$
$524$	−2.21418e56	+	2.38596e56i	−0.173483	+	0.186941i
$525$	7.58856e56			0.571234
$526$	−4.51271e56	−	1.77131e56i	−0.326390	−	0.128113i
$527$		−	1.18842e57i		−	0.825939i
$528$	2.34492e56	+	3.13553e57i	0.156609	+	2.09410i
$529$	−6.83450e55			−0.0438670
$530$	3.44817e56	−	8.78481e56i	0.212714	−	0.541925i
$531$			2.51249e56i			0.148977i
$532$	−7.37947e56	−	6.84820e56i	−0.420611	−	0.390330i
$533$	−2.10787e57			−1.15497
$534$	3.46490e57	+	1.36003e57i	1.82526	+	0.716443i
$535$			1.46497e57i			0.741993i
$536$	1.38141e57	+	2.86936e57i	0.672761	+	1.39741i
$537$	−1.37994e57			−0.646249
$538$	−4.49670e56	+	1.14561e57i	−0.202519	+	0.515953i
$539$			2.51122e57i			1.08773i
$540$	2.32774e56	−	2.50832e56i	0.0969762	−	0.104499i
$541$	−2.54193e57			−1.01864			−0.509320	−	0.860577i	$-0.670103\pi$
$541$	−2.54193e57			−1.01864			−0.509320	+	0.860577i	$0.670103\pi$
$542$	−1.90343e57	−	7.47126e56i	−0.733757	−	0.288011i
$543$		−	1.81563e57i		−	0.673335i
$544$	−2.84241e57	−	8.77364e56i	−1.01417	−	0.313042i
$545$	−1.61142e57			−0.553200
$546$	7.84746e56	−	1.99927e57i	0.259229	−	0.660430i
$547$		−	4.81433e57i		−	1.53039i	−0.643800	−	0.765194i	$-0.722643\pi$
$547$		−	4.81433e57i		−	1.53039i	0.643800	−	0.765194i	$-0.277357\pi$
$548$	−2.93231e57	−	2.72120e57i	−0.897052	−	0.832471i
$549$	3.15112e57			0.927781
$550$	3.98576e57	+	1.56447e57i	1.12952	+	0.443354i
$551$			2.01796e57i			0.550465i
$552$	−4.67310e57	+	2.24979e57i	−1.22711	+	0.590773i
$553$	−2.43623e57			−0.615871
$554$	3.99688e56	−	1.01827e57i	0.0972782	−	0.247833i
$555$			4.48607e57i			1.05127i
$556$	3.07991e57	−	3.31885e57i	0.694973	−	0.748888i
$557$	6.90720e57			1.50087			0.750435	−	0.660944i	$-0.229844\pi$
$557$	6.90720e57			1.50087			0.750435	+	0.660944i	$0.229844\pi$
$558$	−2.68924e57	−	1.05557e57i	−0.562744	−	0.220886i
$559$			1.18481e57i			0.238782i
$560$	−1.37002e57	+	1.02457e56i	−0.265936	+	0.0198882i
$561$	1.19207e58			2.22885
$562$	−4.18250e56	+	1.06556e57i	−0.0753310	+	0.191919i
$563$		−	2.31993e57i		−	0.402530i	−0.979537	−	0.201265i	$-0.935495\pi$
$563$		−	2.31993e57i		−	0.402530i	0.979537	−	0.201265i	$-0.0645053\pi$
$564$	7.15013e56	+	6.63537e56i	0.119523	+	0.110918i
$565$	4.34692e56			0.0700107
$566$	9.46096e57	+	3.71357e57i	1.46822	+	0.576298i
$567$			4.36541e57i			0.652800i
$568$	−4.83322e57	−	1.00392e58i	−0.696501	−	1.44672i
$569$	1.82639e57			0.253650			0.126825	−	0.991925i	$-0.459521\pi$
$569$	1.82639e57			0.253650			0.126825	+	0.991925i	$0.459521\pi$
$570$	1.79885e57	−	4.58287e57i	0.240781	−	0.613430i
$571$		−	1.25001e56i		−	0.0161271i	−0.999967	−	0.00806353i	$-0.997433\pi$
$571$		−	1.25001e56i		−	0.0161271i	0.999967	−	0.00806353i	$-0.00256673\pi$
$572$	8.24348e57	−	8.88299e57i	1.02517	−	1.10470i
$573$	−6.59576e57			−0.790711
$574$	−5.41009e57	−	2.12354e57i	−0.625252	−	0.245421i
$575$			7.06279e57i			0.786958i
$576$	−4.51001e57	+	5.65271e57i	−0.484513	+	0.607273i
$577$	−1.75036e58			−1.81316			−0.906578	−	0.422038i	$-0.861315\pi$
$577$	−1.75036e58			−1.81316			−0.906578	+	0.422038i	$0.861315\pi$
$578$	−4.62842e56	+	1.17917e57i	−0.0462325	+	0.117785i
$579$		−	7.63086e57i		−	0.735061i
$580$	2.01852e57	+	1.87320e57i	0.187519	+	0.174019i
$581$	−5.94203e57			−0.532398
$582$	−1.67414e58	−	6.57126e57i	−1.44680	−	0.567892i
$583$			2.29532e58i			1.91339i
$584$	1.08654e58	−	5.23099e57i	0.873731	−	0.420643i
$585$	4.59213e57			0.356238
$586$	−1.01891e57	+	2.59584e57i	−0.0762580	+	0.194280i
$587$		−	1.59701e58i		−	1.15320i	−0.817025	−	0.576602i	$-0.804378\pi$
$587$		−	1.59701e58i		−	1.15320i	0.817025	−	0.576602i	$-0.195622\pi$
$588$	−8.98561e57	+	9.68270e57i	−0.626071	+	0.674641i
$589$	1.19376e58			0.802595
$590$	−1.31879e57	−	5.17646e56i	−0.0855626	−	0.0335846i
$591$			1.38729e57i			0.0868622i
$592$	2.03056e57	+	2.71517e58i	0.122704	+	1.64075i
$593$	−4.91075e56			−0.0286417			−0.0143209	−	0.999897i	$-0.504559\pi$
$593$	−4.91075e56			−0.0286417			−0.0143209	+	0.999897i	$0.504559\pi$
$594$	−3.04099e57	+	7.74744e57i	−0.171198	+	0.436157i
$595$			5.20855e57i			0.283048i
$596$	4.34491e57	+	4.03211e57i	0.227934	+	0.211525i
$597$	−1.23367e58			−0.624796
$598$	1.86076e58	+	7.30376e57i	0.909840	+	0.357126i
$599$		−	2.61128e58i		−	1.23279i	−0.787437	−	0.616396i	$-0.788592\pi$
$599$		−	2.61128e58i		−	1.23279i	0.787437	−	0.616396i	$-0.211408\pi$
$600$	9.77020e57	+	2.02940e58i	0.445376	+	0.925106i
$601$	1.16358e58			0.512191			0.256096	−	0.966651i	$-0.417564\pi$
$601$	1.16358e58			0.512191			0.256096	+	0.966651i	$0.417564\pi$
$602$	−1.19362e57	+	3.04095e57i	−0.0507388	+	0.129266i
$603$		−	2.93498e58i		−	1.20487i
$604$	5.49126e57	−	5.91727e57i	0.217719	−	0.234609i
$605$	1.85471e58			0.710253
$606$	−5.18854e58	−	2.03658e58i	−1.91920	−	0.753314i
$607$		−	2.26085e57i		−	0.0807810i	−0.999184	−	0.0403905i	$-0.987140\pi$
$607$		−	2.26085e57i		−	0.0807810i	0.999184	−	0.0403905i	$-0.0128602\pi$
$608$	8.81306e57	−	2.85518e58i	0.304195	−	0.985505i
$609$	−1.18702e58			−0.395816
$610$	−6.49223e57	+	1.65401e58i	−0.209155	+	0.532857i
$611$		−	3.75962e57i		−	0.117025i
$612$	2.00959e58	+	1.86491e58i	0.604403	+	0.560890i
$613$	−2.52625e58			−0.734186			−0.367093	−	0.930184i	$-0.619647\pi$
$613$	−2.52625e58			−0.734186			−0.367093	+	0.930184i	$0.619647\pi$
$614$	1.82754e58	+	7.17337e57i	0.513252	+	0.201459i
$615$		−	2.84218e58i		−	0.771392i
$616$	3.01069e58	−	1.44945e58i	0.789716	−	0.380195i
$617$	−2.30219e58			−0.583650			−0.291825	−	0.956472i	$-0.594263\pi$
$617$	−2.30219e58			−0.583650			−0.291825	+	0.956472i	$0.594263\pi$
$618$	1.01164e58	−	2.57733e58i	0.247896	−	0.631557i
$619$			9.93765e57i			0.235386i	0.993050	+	0.117693i	$0.0375498\pi$
$619$			9.93765e57i			0.235386i	−0.993050	+	0.117693i	$0.962450\pi$
$620$	1.10812e58	−	1.19409e58i	0.253725	−	0.273408i
$621$	−1.37285e58			−0.303879
$622$	1.10691e58	+	4.34479e57i	0.236872	+	0.0929760i
$623$		−	3.95565e58i		−	0.818405i
$624$	6.35699e58	−	4.75411e57i	1.27167	−	0.0951028i
$625$	1.87937e58			0.363524
$626$	−1.89205e58	+	4.82032e58i	−0.353892	+	0.901601i
$627$			1.19742e59i			2.16586i
$628$	−5.37879e58	−	4.99155e58i	−0.940875	−	0.873138i
$629$	1.03226e59			1.74632
$630$	1.17862e58	+	4.62627e57i	0.192852	+	0.0756972i
$631$			1.29291e58i			0.204621i	0.994752	+	0.102311i	$0.0326236\pi$
$631$			1.29291e58i			0.204621i	−0.994752	+	0.102311i	$0.967376\pi$
$632$	−3.13662e58	−	6.51518e58i	−0.480179	−	0.997396i
$633$	−7.93589e58			−1.17522
$634$	−3.42295e58	+	8.72054e58i	−0.490372	+	1.24931i
$635$		−	2.80511e58i		−	0.388778i
$636$	−8.21307e58	+	8.85022e58i	−1.10130	+	1.18674i
$637$	5.09127e58			0.660539
$638$	−6.23459e58	−	2.44717e58i	−0.782661	−	0.307207i
$639$			1.02688e59i			1.24739i
$640$	−2.03789e58	−	3.53191e58i	−0.239552	−	0.415174i
$641$	1.02269e58			0.116339			0.0581694	−	0.998307i	$-0.481474\pi$
$641$	1.02269e58			0.116339			0.0581694	+	0.998307i	$0.481474\pi$
$642$	6.84814e58	−	1.74468e59i	0.753940	−	1.92079i
$643$		−	1.54238e57i		−	0.0164347i	−0.999966	−	0.00821735i	$-0.997384\pi$
$643$		−	1.54238e57i		−	0.0164347i	0.999966	−	0.00821735i	$-0.00261569\pi$
$644$	4.04004e58	+	3.74919e58i	0.416661	+	0.386664i
$645$	−1.59756e58			−0.159479
$646$	−1.05453e59	−	4.13920e58i	−1.01901	−	0.399976i
$647$			4.27331e58i			0.399738i	0.979823	+	0.199869i	$0.0640516\pi$
$647$			4.27331e58i			0.399738i	−0.979823	+	0.199869i	$0.935948\pi$
$648$	−1.16744e59	+	5.62042e58i	−1.05720	+	0.508972i
$649$	3.44578e58			0.302099
$650$	3.17182e58	−	8.08076e58i	0.269233	−	0.685917i
$651$			7.02201e58i			0.577112i
$652$	−6.04760e58	+	6.51676e58i	−0.481264	+	0.518599i
$653$	2.56981e58			0.198027			0.0990133	−	0.995086i	$-0.468431\pi$
$653$	2.56981e58			0.198027			0.0990133	+	0.995086i	$0.468431\pi$
$654$	1.91909e59	+	7.53273e58i	1.43207	+	0.562108i
$655$			1.69161e58i			0.122246i
$656$	−1.28648e58	−	1.72022e59i	−0.0900370	−	1.20394i
$657$	−1.11139e59			−0.753347
$658$	3.78757e57	−	9.64950e57i	0.0248667	−	0.0633521i
$659$			1.15122e59i			0.732090i	0.930597	+	0.366045i	$0.119288\pi$
$659$			1.15122e59i			0.732090i	−0.930597	+	0.366045i	$0.880712\pi$
$660$	1.19775e59	+	1.11152e59i	0.737811	+	0.684694i
$661$	−1.31530e59			−0.784863			−0.392432	−	0.919781i	$-0.628366\pi$
$661$	−1.31530e59			−0.784863			−0.392432	+	0.919781i	$0.628366\pi$
$662$	1.70337e59	+	6.68600e58i	0.984673	+	0.386499i
$663$		−	2.41681e59i		−	1.35350i
$664$	−7.65032e58	−	1.58907e59i	−0.415097	−	0.862212i
$665$	−5.23195e58			−0.275048
$666$	9.16860e58	−	2.33586e59i	0.467029	−	1.18984i
$667$		−	1.10478e59i		−	0.545295i
$668$	−9.82014e58	+	1.05820e59i	−0.469691	+	0.506128i
$669$	3.06916e59			1.42256
$670$	1.54056e59	+	6.04693e58i	0.692002	+	0.271621i
$671$		−	4.32164e59i		−	1.88138i
$672$	1.67949e59	+	5.18406e58i	0.708635	+	0.218734i
$673$	1.68239e59			0.688033			0.344017	−	0.938964i	$-0.388212\pi$
$673$	1.68239e59			0.688033			0.344017	+	0.938964i	$0.388212\pi$
$674$	−6.74321e58	+	1.71795e59i	−0.267306	+	0.681008i
$675$			5.96192e58i			0.229091i
$676$	1.66870e58	+	1.54857e58i	0.0621583	+	0.0576833i
$677$	1.70595e59			0.616032			0.308016	−	0.951381i	$-0.400335\pi$
$677$	1.70595e59			0.616032			0.308016	+	0.951381i	$0.400335\pi$
$678$	−5.17689e58	−	2.03201e58i	−0.181236	−	0.0711380i
$679$			1.91125e59i			0.648713i
$680$	−1.39292e59	+	6.70596e58i	−0.458393	+	0.220686i
$681$	−4.96795e59			−1.58521
$682$	−1.44767e59	+	3.68819e59i	−0.447917	+	1.14115i
$683$			2.42791e59i			0.728448i	0.931311	+	0.364224i	$0.118666\pi$
$683$			2.42791e59i			0.728448i	−0.931311	+	0.364224i	$0.881334\pi$
$684$	−1.87329e59	+	2.01861e59i	−0.545038	+	0.587321i
$685$	−2.07897e59			−0.586605
$686$	3.19928e59	+	1.25577e59i	0.875480	+	0.343639i
$687$		−	4.42914e59i		−	1.17551i
$688$	−9.66917e58	+	7.23114e57i	−0.248904	+	0.0186144i
$689$	4.65355e59			1.16193
$690$	−9.84815e58	+	2.50899e59i	−0.238519	+	0.607669i
$691$		−	5.15590e59i		−	1.21134i	−0.795717	−	0.605669i	$-0.792906\pi$
$691$		−	5.15590e59i		−	1.21134i	0.795717	−	0.605669i	$-0.207094\pi$
$692$	−2.58656e59	−	2.40034e59i	−0.589514	−	0.547073i
$693$	−3.07954e59			−0.680907
$694$	−1.40673e59	−	5.52161e58i	−0.301759	−	0.118445i
$695$		−	2.35302e59i		−	0.489717i
$696$	−1.52827e59	−	3.17442e59i	−0.308608	−	0.641019i
$697$	−6.53996e59			−1.28141
$698$	−1.67863e59	+	4.27661e59i	−0.319148	+	0.813085i
$699$			2.48133e59i			0.457787i
$700$	1.62817e59	−	1.75448e59i	0.291501	−	0.314115i
$701$	−5.33819e59			−0.927504			−0.463752	−	0.885965i	$-0.653497\pi$
$701$	−5.33819e59			−0.927504			−0.463752	+	0.885965i	$0.653497\pi$
$702$	1.57072e59	+	6.16533e58i	0.264862	+	0.103963i
$703$			1.03690e60i			1.69697i
$704$	7.75247e59	+	6.18531e59i	1.23144	+	0.982506i
$705$	5.06935e58			0.0781593
$706$	3.70417e59	−	9.43701e59i	0.554360	−	1.41233i
$707$			5.92340e59i			0.860525i
$708$	1.32861e59	+	1.23296e59i	0.187370	+	0.173881i
$709$	1.35108e60			1.84973			0.924866	−	0.380293i	$-0.124177\pi$
$709$	1.35108e60			1.84973			0.924866	+	0.380293i	$0.124177\pi$
$710$	−5.39006e59	−	2.11568e59i	−0.716421	−	0.281206i
$711$			6.66417e59i			0.859972i
$712$	1.05785e60	−	5.09286e59i	1.32540	−	0.638090i
$713$	−6.53550e59			−0.795057
$714$	2.43478e59	−	6.20302e59i	0.287606	−	0.732725i
$715$		−	6.29793e59i		−	0.722389i
$716$	−2.96074e59	+	3.19043e59i	−0.329782	+	0.355366i
$717$	2.09396e60			2.26499
$718$	−1.10393e60	−	4.33311e59i	−1.15966	−	0.455183i
$719$			5.87568e59i			0.599448i	0.954026	+	0.299724i	$0.0968946\pi$
$719$			5.87568e59i			0.599448i	−0.954026	+	0.299724i	$0.903105\pi$
$720$	2.80267e58	+	3.74761e59i	0.0277709	+	0.371340i
$721$	−2.94237e59			−0.283176
$722$	2.49191e58	−	6.34857e58i	0.0232944	−	0.0593464i
$723$		−	2.46422e60i		−	2.23757i
$724$	−4.19775e59	−	3.89554e59i	−0.370260	−	0.343604i
$725$	−4.79773e59			−0.411091
$726$	−2.20883e60	−	8.67000e59i	−1.83863	−	0.721689i
$727$			1.13674e60i			0.919264i	0.888109	+	0.459632i	$0.152019\pi$
$727$			1.13674e60i			0.919264i	−0.888109	+	0.459632i	$0.847981\pi$
$728$	−2.93862e59	−	6.10390e59i	−0.230879	−	0.479566i
$729$	6.74755e59			0.515072
$730$	2.28980e59	−	5.83365e59i	0.169831	−	0.432673i
$731$			3.67604e59i			0.264920i
$732$	1.54636e60	−	1.66632e60i	1.08287	−	1.16688i
$733$	1.81948e60			1.23813			0.619063	−	0.785341i	$-0.287513\pi$
$733$	1.81948e60			1.23813			0.619063	+	0.785341i	$0.287513\pi$
$734$	1.48289e59	+	5.82059e58i	0.0980603	+	0.0384902i
$735$			6.86491e59i			0.441165i
$736$	−4.82489e59	+	1.56313e60i	−0.301338	+	0.976249i
$737$	−4.02522e60			−2.44327
$738$	−5.80884e59	+	1.47990e60i	−0.342694	+	0.873071i
$739$			1.28414e59i			0.0736341i	0.999322	+	0.0368170i	$0.0117219\pi$
$739$			1.28414e59i			0.0736341i	−0.999322	+	0.0368170i	$0.988278\pi$
$740$	1.03718e60	+	9.62511e59i	0.578081	+	0.536463i
$741$	2.42767e60			1.31525
$742$	1.19439e60	+	4.68815e59i	0.629018	+	0.246899i
$743$			6.32406e59i			0.323766i	0.986810	+	0.161883i	$0.0517567\pi$
$743$			6.32406e59i			0.323766i	−0.986810	+	0.161883i	$0.948243\pi$
$744$	−1.87789e60	+	9.04077e59i	−0.934626	+	0.449960i
$745$	3.08049e59			0.149052
$746$	−5.39302e59	+	1.37397e60i	−0.253698	+	0.646339i
$747$			1.62541e60i			0.743414i
$748$	2.55765e60	−	2.75607e60i	1.13739	−	1.22562i
$749$	−1.99178e60			−0.861239
$750$	2.50417e60	+	9.82927e59i	1.05288	+	0.413271i
$751$			5.83930e59i			0.238738i	0.992850	+	0.119369i	$0.0380872\pi$
$751$			5.83930e59i			0.238738i	−0.992850	+	0.119369i	$0.961913\pi$
$752$	3.06820e59	−	2.29457e58i	0.121986	−	0.00912278i
$753$	−2.05099e60			−0.792991
$754$	−4.96142e59	+	1.26401e60i	−0.186555	+	0.475282i
$755$		−	4.19527e59i		−	0.153417i
$756$	3.41032e59	+	3.16481e59i	0.121294	+	0.112561i
$757$	−4.05544e60			−1.40289			−0.701447	−	0.712722i	$-0.747462\pi$
$757$	−4.05544e60			−1.40289			−0.701447	+	0.712722i	$0.747462\pi$
$758$	−3.70511e60	−	1.45431e60i	−1.24666	−	0.489333i
$759$		−	6.55555e60i		−	2.14552i
$760$	−6.73609e59	−	1.39917e60i	−0.214448	−	0.445437i
$761$	−1.86163e59			−0.0576522			−0.0288261	−	0.999584i	$-0.509177\pi$
$761$	−1.86163e59			−0.0576522			−0.0288261	+	0.999584i	$0.509177\pi$
$762$	−1.31127e60	+	3.34069e60i	−0.395038	+	1.00643i
$763$		−	2.19090e60i		−	0.642106i
$764$	−1.41516e60	+	1.52494e60i	−0.403501	+	0.434804i
$765$	1.42477e60			0.395235
$766$	4.26945e60	+	1.67583e60i	1.15231	+	0.452298i
$767$		−	6.98600e59i		−	0.183453i
$768$	7.75960e59	+	5.15889e60i	0.198269	+	1.31817i
$769$	1.08285e60			0.269224			0.134612	−	0.990898i	$-0.457021\pi$
$769$	1.08285e60			0.269224			0.134612	+	0.990898i	$0.457021\pi$
$770$	6.34476e59	−	1.61644e60i	0.153501	−	0.391069i
$771$		−	2.46064e60i		−	0.579303i
$772$	−1.76426e60	−	1.63724e60i	−0.404202	−	0.375103i
$773$	7.12854e60			1.58939			0.794696	−	0.607008i	$-0.207630\pi$
$773$	7.12854e60			1.58939			0.794696	+	0.607008i	$0.207630\pi$
$774$	8.31837e59	+	3.26509e59i	0.180500	+	0.0708491i
$775$			2.83819e60i			0.599384i
$776$	−5.11124e60	+	2.46072e60i	−1.05058	+	0.505786i
$777$	−6.09928e60			−1.22022
$778$	3.39171e60	−	8.64096e60i	0.660461	−	1.68264i
$779$		−	6.56934e60i		−	1.24519i
$780$	2.25351e60	−	2.42834e60i	0.415789	−	0.448046i
$781$	1.40833e61			2.52949
$782$	5.77326e60	+	2.26609e60i	1.00944	+	0.396219i
$783$		−	9.32575e59i		−	0.158740i
$784$	3.10731e59	+	4.15496e60i	0.0514929	+	0.688540i
$785$	−3.81349e60			−0.615262
$786$	7.90759e59	−	2.01459e60i	0.124214	−	0.316457i
$787$			9.67242e60i			1.47933i	0.672974	+	0.739666i	$0.265017\pi$
$787$			9.67242e60i			1.47933i	−0.672974	+	0.739666i	$0.734983\pi$
$788$	3.20743e59	+	2.97651e59i	0.0477646	+	0.0443259i
$789$	3.22328e60			0.467391
$790$	−3.49799e60	−	1.37302e60i	−0.493912	−	0.193868i
$791$			5.91010e59i			0.0812622i
$792$	−3.96488e60	−	8.23558e60i	−0.530886	−	1.10272i
$793$	−8.76173e60			−1.14249
$794$	1.95785e59	−	4.98795e59i	0.0248627	−	0.0633419i
$795$			6.27470e60i			0.776038i
$796$	−2.64691e60	+	2.85225e60i	−0.318834	+	0.343569i
$797$	−9.31498e60			−1.09284			−0.546421	−	0.837511i	$-0.684010\pi$
$797$	−9.31498e60			−1.09284			−0.546421	+	0.837511i	$0.684010\pi$
$798$	6.23089e60	+	2.44572e60i	0.712016	+	0.279477i
$799$		−	1.16647e60i		−	0.129835i
$800$	6.78824e60	+	2.09532e60i	0.735982	+	0.227175i
$801$	−1.08205e61			−1.14278
$802$	3.67371e60	−	9.35941e60i	0.377958	−	0.962912i
$803$			1.52423e61i			1.52765i
$804$	−1.55203e61	−	1.44030e61i	−1.51539	−	1.40629i
$805$	2.86434e60			0.272465
$806$	7.47746e60	+	2.93502e60i	0.692976	+	0.272004i
$807$		−	8.18273e60i		−	0.738846i
$808$	−1.58409e61	+	7.62633e60i	−1.39361	+	0.670929i
$809$	1.20201e61			1.03036			0.515180	−	0.857082i	$-0.327725\pi$
$809$	1.20201e61			1.03036			0.515180	+	0.857082i	$0.327725\pi$
$810$	−2.46027e60	+	6.26795e60i	−0.205493	+	0.523529i
$811$			1.64280e61i			1.33705i	0.743691	+	0.668524i	$0.233073\pi$
$811$			1.64280e61i			1.33705i	−0.743691	+	0.668524i	$0.766927\pi$
$812$	−2.54681e60	+	2.74439e60i	−0.201985	+	0.217655i
$813$	1.35956e61			1.05074
$814$	−3.20354e61	−	1.25744e61i	−2.41278	−	0.947053i
$815$			4.62030e60i			0.339125i
$816$	1.97234e61	−	1.47503e60i	1.41088	−	0.105513i
$817$	−3.69255e60			−0.257433
$818$	−5.67707e60	+	1.44633e61i	−0.385749	+	0.982763i
$819$			6.24348e60i			0.413490i
$820$	−6.57115e60	−	6.09807e60i	−0.424180	−	0.393642i
$821$	1.76853e61			1.11277			0.556385	−	0.830925i	$-0.312188\pi$
$821$	1.76853e61			1.11277			0.556385	+	0.830925i	$0.312188\pi$
$822$	2.47591e61	+	9.71832e60i	1.51854	+	0.596051i
$823$		−	1.06664e61i		−	0.637710i	−0.947803	−	0.318855i	$-0.896702\pi$
$823$		−	1.06664e61i		−	0.637710i	0.947803	−	0.318855i	$-0.103298\pi$
$824$	−3.78827e60	−	7.86874e60i	−0.220785	−	0.458599i
$825$	−2.84689e61			−1.61748
$826$	7.03795e59	−	1.79304e60i	0.0389821	−	0.0993135i
$827$		−	3.20580e61i		−	1.73109i	−0.500828	−	0.865547i	$-0.666971\pi$
$827$		−	3.20580e61i		−	1.73109i	0.500828	−	0.865547i	$-0.333029\pi$
$828$	1.02557e61	−	1.10513e61i	0.539919	−	0.581805i
$829$	1.84101e61			0.944956			0.472478	−	0.881342i	$-0.343360\pi$
$829$	1.84101e61			0.944956			0.472478	+	0.881342i	$0.343360\pi$
$830$	−8.53171e60	−	3.34883e60i	−0.426969	−	0.167592i
$831$			7.27319e60i			0.354898i
$832$	1.25401e61	−	1.57174e61i	0.596640	−	0.747811i
$833$	1.57964e61			0.732846
$834$	−1.09994e61	+	2.80229e61i	−0.497602	+	1.26773i
$835$			7.50248e60i			0.330970i
$836$	2.76845e61	+	2.56914e61i	1.19098	+	1.10524i
$837$	−5.51681e60			−0.231448
$838$	9.05790e60	+	3.55536e60i	0.370598	+	0.145465i
$839$		−	4.04532e61i		−	1.61418i	−0.590428	−	0.807090i	$-0.701041\pi$
$839$		−	4.04532e61i		−	1.61418i	0.590428	−	0.807090i	$-0.298959\pi$
$840$	8.23030e60	−	3.96234e60i	0.320295	−	0.154201i
$841$	−1.88414e61			−0.715149
$842$	1.73628e61	−	4.42348e61i	0.642787	−	1.63761i
$843$		−	7.61097e60i		−	0.274828i
$844$	−1.70269e61	+	1.83478e61i	−0.599714	+	0.646239i
$845$	1.18309e60			0.0406469
$846$	−2.63957e60	−	1.03607e60i	−0.0884617	−	0.0347226i
$847$			2.52167e61i			0.824399i
$848$	2.84016e60	+	3.79773e61i	0.0905794	+	1.21119i
$849$	−6.75765e61			−2.10249
$850$	9.84101e60	−	2.50717e61i	0.298705	−	0.761002i
$851$		−	5.67670e61i		−	1.68103i
$852$	5.43020e61	+	5.03926e61i	1.56886	+	1.45591i
$853$	3.97779e61			1.12128			0.560638	−	0.828061i	$-0.310556\pi$
$853$	3.97779e61			1.12128			0.560638	+	0.828061i	$0.310556\pi$
$854$	−2.24880e61	−	8.82688e60i	−0.618494	−	0.242768i
$855$			1.43117e61i			0.384064i
$856$	−2.56440e61	−	5.32661e61i	−0.671487	−	1.39477i
$857$	−5.87790e61			−1.50185			−0.750923	−	0.660390i	$-0.770391\pi$
$857$	−5.87790e61			−1.50185			−0.750923	+	0.660390i	$0.770391\pi$
$858$	−2.94402e61	+	7.50040e61i	−0.734020	+	1.87004i
$859$			3.04985e61i			0.742030i	0.928627	+	0.371015i	$0.120990\pi$
$859$			3.04985e61i			0.742030i	−0.928627	+	0.371015i	$0.879010\pi$
$860$	−3.42766e60	+	3.69357e60i	−0.0813823	+	0.0876958i
$861$	3.86425e61			0.895363
$862$	−5.86509e61	−	2.30214e61i	−1.32624	−	0.520570i
$863$		−	3.93939e61i		−	0.869365i	−0.900584	−	0.434682i	$-0.856861\pi$
$863$		−	3.93939e61i		−	0.869365i	0.900584	−	0.434682i	$-0.143139\pi$
$864$	−4.07284e60	+	1.31949e61i	−0.0877221	+	0.284195i
$865$	−1.83384e61			−0.385498
$866$	5.08713e59	−	1.29603e60i	0.0104375	−	0.0265914i
$867$		−	8.42241e60i		−	0.168669i
$868$	1.62349e61	+	1.50661e61i	0.317348	+	0.294501i
$869$	9.13966e61			1.74387
$870$	−1.70435e61	−	6.68982e60i	−0.317434	−	0.124598i
$871$			8.16075e61i			1.48371i
$872$	5.85909e61	−	2.82076e61i	1.03988	−	0.500634i
$873$	5.22813e61			0.905831
$874$	−2.27627e61	+	5.79919e61i	−0.385021	+	0.980906i
$875$		−	2.85885e61i		−	0.472087i
$876$	−5.45398e61	+	5.87709e61i	−0.879281	+	0.947493i
$877$	−5.29245e61			−0.833039			−0.416519	−	0.909127i	$-0.636750\pi$
$877$	−5.29245e61			−0.833039			−0.416519	+	0.909127i	$0.636750\pi$
$878$	3.10697e61	+	1.21953e61i	0.477477	+	0.187417i
$879$		−	1.85413e61i		−	0.278210i
$880$	5.13970e61	−	3.84376e60i	0.753012	−	0.0563144i
$881$	−7.02812e61			−1.00541			−0.502707	−	0.864457i	$-0.667662\pi$
$881$	−7.02812e61			−1.00541			−0.502707	+	0.864457i	$0.667662\pi$
$882$	1.40305e61	−	3.57450e61i	0.195989	−	0.499316i
$883$			1.17244e62i			1.59924i	0.600505	+	0.799621i	$0.294966\pi$
$883$			1.17244e62i			1.59924i	−0.600505	+	0.799621i	$0.705034\pi$
$884$	−5.58768e61	−	5.18541e61i	−0.744276	−	0.690693i
$885$	9.41970e60			0.122526
$886$	−1.01260e61	−	3.97462e60i	−0.128627	−	0.0504879i
$887$			1.26075e62i			1.56398i	0.623290	+	0.781990i	$0.285795\pi$
$887$			1.26075e62i			1.56398i	−0.623290	+	0.781990i	$0.714205\pi$
$888$	−7.85277e61	−	1.63112e62i	−0.951373	−	1.97613i
$889$	3.81384e61			0.451259
$890$	2.22933e61	−	5.67961e61i	0.257623	−	0.656339i
$891$		−	1.63771e62i		−	1.84844i
$892$	6.58506e61	−	7.09591e61i	0.725935	−	0.782251i
$893$	1.17171e61			0.126166
$894$	−3.66865e61	−	1.44000e61i	−0.385850	−	0.151452i
$895$			2.26197e61i			0.232383i
$896$	4.80200e61	−	2.77072e61i	0.481897	−	0.278051i
$897$	−1.32908e62			−1.30289
$898$	4.76176e61	−	1.21314e62i	0.455999	−	1.16174i
$899$		−	4.43954e61i		−	0.415322i
$900$	−4.79928e61	−	4.45377e61i	−0.438615	−	0.407038i
$901$	1.44383e62			1.28912
$902$	2.02963e62	+	7.96661e61i	1.77043	+	0.694922i
$903$		−	2.17205e61i		−	0.185109i
$904$	−1.58053e61	+	7.60920e60i	−0.131603	+	0.0633581i
$905$	−2.97615e61			−0.242122
$906$	−1.96111e61	+	4.99627e61i	−0.155887	+	0.397150i
$907$			2.37513e62i			1.84474i	0.386307	+	0.922370i	$0.373750\pi$
$907$			2.37513e62i			1.84474i	−0.386307	+	0.922370i	$0.626250\pi$
$908$	−1.06590e62	+	1.14859e62i	−0.808937	+	0.871692i
$909$	1.62032e62			1.20159
$910$	−3.27718e61	−	1.28634e61i	−0.237482	−	0.0932153i
$911$			4.03034e61i			0.285401i	0.989766	+	0.142701i	$0.0455786\pi$
$911$			4.03034e61i			0.285401i	−0.989766	+	0.142701i	$0.954421\pi$
$912$	1.48166e61	+	1.98121e62i	0.102531	+	1.37100i
$913$	2.22919e62			1.50751
$914$	−4.65727e61	+	1.18652e62i	−0.307795	+	0.784160i
$915$		−	1.18140e62i		−	0.763054i
$916$	−1.02402e62	−	9.50298e61i	−0.646403	−	0.599867i
$917$	−2.29993e61			−0.141892
$918$	4.87338e61	+	1.91288e61i	0.293856	+	0.115343i
$919$		−	4.00963e61i		−	0.236308i	−0.992995	−	0.118154i	$-0.962302\pi$
$919$		−	4.00963e61i		−	0.236308i	0.992995	−	0.118154i	$-0.0376977\pi$
$920$	3.68781e61	+	7.66007e61i	0.212434	+	0.441254i
$921$	−1.30535e62			−0.734979
$922$	1.07790e62	−	2.74613e62i	0.593238	−	1.51137i
$923$		−	2.85526e62i		−	1.53607i
$924$	−1.51123e62	+	1.62847e62i	−0.794732	+	0.856386i
$925$	−2.46523e62			−1.26731
$926$	−6.57703e61	−	2.58158e61i	−0.330521	−	0.129735i
$927$			8.04868e61i			0.395413i
$928$	−1.06183e62	−	3.27753e61i	−0.509973	−	0.157413i
$929$	−2.11072e62			−0.991062			−0.495531	−	0.868590i	$-0.665027\pi$
$929$	−2.11072e62			−0.991062			−0.495531	+	0.868590i	$0.665027\pi$
$930$	−3.95748e61	+	1.00824e62i	−0.181667	+	0.462829i
$931$			1.58674e62i			0.712133i
$932$	5.73684e61	+	5.32383e61i	0.251732	+	0.233609i
$933$	−7.90630e61			−0.339202
$934$	4.39165e61	+	1.72379e61i	0.184223	+	0.0723103i
$935$		−	1.95402e62i		−	0.801466i
$936$	−1.66969e62	+	8.03843e61i	−0.669642	+	0.322388i
$937$	−2.10078e62			−0.823852			−0.411926	−	0.911217i	$-0.635144\pi$
$937$	−2.10078e62			−0.823852			−0.411926	+	0.911217i	$0.635144\pi$
$938$	−8.22144e61	+	2.09455e62i	−0.315274	+	0.803214i
$939$		−	3.44299e62i		−	1.29110i
$940$	1.08766e61	−	1.17204e61i	0.0398848	−	0.0429790i
$941$	2.60859e61			0.0935455			0.0467728	−	0.998906i	$-0.485106\pi$
$941$	2.60859e61			0.0935455			0.0467728	+	0.998906i	$0.485106\pi$
$942$	4.54161e62	+	1.78265e62i	1.59272	+	0.625169i
$943$			3.59652e62i			1.23349i
$944$	5.70123e61	−	4.26370e60i	0.191230	−	0.0143013i
$945$	2.41788e61			0.0793170
$946$	4.47794e61	−	1.14083e62i	0.143670	−	0.366023i
$947$			1.96367e62i			0.616195i	0.951355	+	0.308097i	$0.0996922\pi$
$947$			1.96367e62i			0.616195i	−0.951355	+	0.308097i	$0.900308\pi$
$948$	3.52404e62	+	3.27033e62i	1.08160	+	1.00373i
$949$	3.09024e62			0.927688
$950$	2.51843e62	+	9.88522e61i	0.739493	+	0.290262i
$951$		−	6.22880e62i		−	1.78901i
$952$	−9.11746e61	−	1.89382e62i	−0.256152	−	0.532062i
$953$	−2.88427e62			−0.792656			−0.396328	−	0.918109i	$-0.629716\pi$
$953$	−2.88427e62			−0.792656			−0.396328	+	0.918109i	$0.629716\pi$
$954$	1.28242e62	−	3.26718e62i	0.344758	−	0.878330i
$955$			1.08117e62i			0.284329i
$956$	4.49271e62	−	4.84124e62i	1.15583	−	1.24549i
$957$	4.45316e62			1.12077
$958$	−2.92554e62	−	1.14832e62i	−0.720327	−	0.282740i
$959$		−	2.82658e62i		−	0.680879i
$960$	2.11929e62	+	1.69087e62i	0.499452	+	0.398488i
$961$	1.71073e62			0.394448
$962$	−2.54934e62	+	6.49488e62i	−0.575111	+	1.46519i
$963$			5.44842e62i			1.20259i
$964$	−5.69730e62	−	5.28713e62i	−1.23041	−	1.14183i
$965$	−1.25084e62			−0.264318
$966$	−3.41123e62	−	1.33896e62i	−0.705329	−	0.276852i
$967$		−	8.99130e62i		−	1.81914i	−0.415549	−	0.909571i	$-0.636410\pi$
$967$		−	8.99130e62i		−	1.81914i	0.415549	−	0.909571i	$-0.363590\pi$
$968$	−6.74369e62	+	3.24663e62i	−1.33510	+	0.642763i
$969$	7.53218e62			1.45922
$970$	−1.07715e62	+	2.74422e62i	−0.204206	+	0.520251i
$971$			1.04558e62i			0.193978i	0.995285	+	0.0969892i	$0.0309212\pi$
$971$			1.04558e62i			0.193978i	−0.995285	+	0.0969892i	$0.969079\pi$
$972$	4.74566e62	−	5.11382e62i	0.861599	−	0.928440i
$973$	3.19918e62			0.568420
$974$	−8.60714e61	−	3.37844e61i	−0.149665	−	0.0587459i
$975$			5.77182e62i			0.982235i
$976$	−5.34746e61	−	7.15039e62i	−0.0890638	−	1.19092i
$977$	−3.80411e62			−0.620108			−0.310054	−	0.950719i	$-0.600347\pi$
$977$	−3.80411e62			−0.620108			−0.310054	+	0.950719i	$0.600347\pi$
$978$	2.15980e62	−	5.50246e62i	0.344586	−	0.877891i
$979$			1.48399e63i			2.31736i
$980$	1.58717e62	+	1.47291e62i	0.242592	+	0.225127i
$981$	−5.99308e62			−0.896605
$982$	−1.03037e63	−	4.04435e62i	−1.50887	−	0.592254i
$983$		−	2.79320e62i		−	0.400386i	−0.979757	−	0.200193i	$-0.935843\pi$
$983$		−	2.79320e62i		−	0.400386i	0.979757	−	0.200193i	$-0.0641568\pi$
$984$	4.97519e62	+	1.03341e63i	0.698092	+	1.45003i
$985$	2.27402e61			0.0312345
$986$	−1.53935e62	+	3.92175e62i	−0.206977	+	0.527309i
$987$			6.89232e61i			0.0907204i
$988$	5.20870e62	−	5.61278e62i	0.671172	−	0.723240i
$989$	2.02156e62			0.255015
$990$	−4.42168e62	−	1.73558e62i	−0.546069	−	0.214341i
$991$			1.00599e63i			1.21632i	0.793815	+	0.608159i	$0.208092\pi$
$991$			1.00599e63i			1.21632i	−0.793815	+	0.608159i	$0.791908\pi$
$992$	−1.93888e62	+	6.28144e62i	−0.229513	+	0.743556i
$993$	−1.21666e63			−1.41006
$994$	2.87649e62	−	7.32836e62i	0.326399	−	0.831558i
$995$			2.02221e62i			0.224668i
$996$	8.59525e62	+	7.97645e62i	0.935001	+	0.867688i
$997$	−2.40574e62			−0.256242			−0.128121	−	0.991759i	$-0.540895\pi$
$997$	−2.40574e62			−0.256242			−0.128121	+	0.991759i	$0.540895\pi$
$998$	−1.05409e63	−	4.13745e62i	−1.09935	−	0.431510i
$999$		−	4.79188e62i		−	0.489362i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.43.b.a.3.8	yes	20
4.3	odd	2	inner	4.43.b.a.3.7	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.43.b.a.3.7	✓	20	4.3	odd	2	inner
4.43.b.a.3.8	yes	20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 43 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-766250. + 1.95215e6i) q^{2} -1.39436e10i q^{3} +(-3.22377e12 - 2.99168e12i) q^{4} -2.28561e14 q^{5} +(2.72200e16 + 1.06843e16i) q^{6} -3.10753e17i q^{7} +(8.31043e18 - 4.00092e18i) q^{8} -8.50048e19 q^{9} +O(q^{10})\)	\(q+(-766250. + 1.95215e6i) q^{2} -1.39436e10i q^{3} +(-3.22377e12 - 2.99168e12i) q^{4} -2.28561e14 q^{5} +(2.72200e16 + 1.06843e16i) q^{6} -3.10753e17i q^{7} +(8.31043e18 - 4.00092e18i) q^{8} -8.50048e19 q^{9} +(1.75135e20 - 4.46186e20i) q^{10} +1.16581e22i q^{11} +(-4.17147e22 + 4.49509e22i) q^{12} +2.36357e23 q^{13} +(6.06638e23 + 2.38115e23i) q^{14} +3.18696e24i q^{15} +(1.44254e24 + 1.92889e25i) q^{16} +7.33330e25 q^{17} +(6.51350e25 - 1.65942e26i) q^{18} +7.36625e26i q^{19} +(7.36827e26 + 6.83781e26i) q^{20} -4.33301e27 q^{21} +(-2.27584e28 - 8.93301e27i) q^{22} -4.03280e28i q^{23} +(-5.57871e28 - 1.15877e29i) q^{24} -1.75134e29 q^{25} +(-1.81109e29 + 4.61405e29i) q^{26} -3.40421e29i q^{27} +(-9.29673e29 + 1.00179e30i) q^{28} +2.73947e30 q^{29} +(-6.22144e30 - 2.44201e30i) q^{30} -1.62058e31i q^{31} +(-3.87603e31 - 1.19641e31i) q^{32} +1.62556e32 q^{33} +(-5.61914e31 + 1.43157e32i) q^{34} +7.10260e31i q^{35} +(2.74036e32 + 2.54307e32i) q^{36} +1.40763e33 q^{37} +(-1.43801e33 - 5.64439e32i) q^{38} -3.29567e33i q^{39} +(-1.89944e33 + 9.14453e32i) q^{40} -8.91817e33 q^{41} +(3.32017e33 - 8.45871e33i) q^{42} +5.01280e33i q^{43} +(3.48772e34 - 3.75830e34i) q^{44} +1.94288e34 q^{45} +(7.87266e34 + 3.09014e34i) q^{46} -1.59065e34i q^{47} +(2.68957e35 - 2.01141e34i) q^{48} +2.15406e35 q^{49} +(1.34196e35 - 3.41888e35i) q^{50} -1.02253e36i q^{51} +(-7.61960e35 - 7.07104e35i) q^{52} +1.96886e36 q^{53} +(6.64555e35 + 2.60848e35i) q^{54} -2.66458e36i q^{55} +(-1.24330e36 - 2.58249e36i) q^{56} +1.02712e37 q^{57} +(-2.09912e36 + 5.34787e36i) q^{58} -2.95570e36i q^{59} +(9.53436e36 - 1.02740e37i) q^{60} -3.70699e37 q^{61} +(3.16363e37 + 1.24177e37i) q^{62} +2.64155e37i q^{63} +(5.30559e37 - 6.64987e37i) q^{64} -5.40220e37 q^{65} +(-1.24558e38 + 3.17334e38i) q^{66} +3.45272e38i q^{67} +(-2.36409e38 - 2.19389e38i) q^{68} -5.62318e38 q^{69} +(-1.38654e38 - 5.44237e37i) q^{70} -1.20803e39i q^{71} +(-7.06427e38 + 3.40097e38i) q^{72} +1.30745e39 q^{73} +(-1.07860e39 + 2.74791e39i) q^{74} +2.44199e39i q^{75} +(2.20374e39 - 2.37471e39i) q^{76} +3.62278e39 q^{77} +(6.43365e39 + 2.52531e39i) q^{78} -7.83976e39i q^{79} +(-3.29707e38 - 4.40870e39i) q^{80} -1.40478e40 q^{81} +(6.83355e39 - 1.74096e40i) q^{82} -1.91214e40i q^{83} +(1.39686e40 + 1.29630e40i) q^{84} -1.67611e40 q^{85} +(-9.78576e39 - 3.84106e39i) q^{86} -3.81981e40i q^{87} +(4.66430e40 + 9.68837e40i) q^{88} +1.27292e41 q^{89} +(-1.48873e40 + 3.79280e40i) q^{90} -7.34486e40i q^{91} +(-1.20649e41 + 1.30008e41i) q^{92} -2.25968e41 q^{93} +(3.10520e40 + 1.21884e40i) q^{94} -1.68364e41i q^{95} +(-1.66823e41 + 5.40459e41i) q^{96} -6.15040e41 q^{97} +(-1.65055e41 + 4.20506e41i) q^{98} -9.90993e41i 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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