LMFDB - Embedded newform 4.43.b.a.3.16

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			3.16
Root			$0.500000 - 4.69874e8i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.43.b.a.3.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.57912e6 + 1.38001e6i) q^{2} +7.51798e9i q^{3} +(5.89205e11 + 4.35840e12i) q^{4} +5.33275e14 q^{5} +(-1.03749e16 + 1.18718e16i) q^{6} -7.46884e17i q^{7} +(-5.08420e18 + 7.69555e18i) q^{8} +5.28989e19 q^{9} +O(q^{10})$	\(q+(1.57912e6 + 1.38001e6i) q^{2} +7.51798e9i q^{3} +(5.89205e11 + 4.35840e12i) q^{4} +5.33275e14 q^{5} +(-1.03749e16 + 1.18718e16i) q^{6} -7.46884e17i q^{7} +(-5.08420e18 + 7.69555e18i) q^{8} +5.28989e19 q^{9} +(8.42107e20 + 7.35924e20i) q^{10} +6.22915e21i q^{11} +(-3.27664e22 + 4.42963e21i) q^{12} +4.81446e23 q^{13} +(1.03071e24 - 1.17942e24i) q^{14} +4.00915e24i q^{15} +(-1.86485e25 + 5.13598e24i) q^{16} +7.46133e25 q^{17} +(8.35338e25 + 7.30009e25i) q^{18} -7.57016e26i q^{19} +(3.14208e26 + 2.32423e27i) q^{20} +5.61506e27 q^{21} +(-8.59628e27 + 9.83659e27i) q^{22} +2.53407e28i q^{23} +(-5.78550e28 - 3.82229e28i) q^{24} +5.70088e28 q^{25} +(7.60262e29 + 6.64400e29i) q^{26} +1.22030e30i q^{27} +(3.25522e30 - 4.40067e29i) q^{28} -1.54350e30 q^{29} +(-5.53266e30 + 6.33094e30i) q^{30} -1.96158e31i q^{31} +(-3.65359e31 - 1.76247e31i) q^{32} -4.68307e31 q^{33} +(1.17823e32 + 1.02967e32i) q^{34} -3.98295e32i q^{35} +(3.11683e31 + 2.30555e32i) q^{36} -6.73293e32 q^{37} +(1.04469e33 - 1.19542e33i) q^{38} +3.61950e33i q^{39} +(-2.71128e33 + 4.10385e33i) q^{40} +3.14869e33 q^{41} +(8.86686e33 + 7.74882e33i) q^{42} +7.71866e33i q^{43} +(-2.71491e34 + 3.67024e33i) q^{44} +2.82097e34 q^{45} +(-3.49704e34 + 4.00161e34i) q^{46} +1.95126e35i q^{47} +(-3.86122e34 - 1.40199e35i) q^{48} -2.45862e35 q^{49} +(9.00238e34 + 7.86726e34i) q^{50} +5.60941e35i q^{51} +(2.83670e35 + 2.09834e36i) q^{52} -3.91250e35 q^{53} +(-1.68403e36 + 1.92701e36i) q^{54} +3.32185e36i q^{55} +(5.74768e36 + 3.79731e36i) q^{56} +5.69123e36 q^{57} +(-2.43738e36 - 2.13005e36i) q^{58} +2.85242e36i q^{59} +(-1.74735e37 + 2.36221e36i) q^{60} -5.39160e37 q^{61} +(2.70699e37 - 3.09757e37i) q^{62} -3.95093e37i q^{63} +(-3.33724e37 - 7.82514e37i) q^{64} +2.56743e38 q^{65} +(-7.39513e37 - 6.46267e37i) q^{66} -4.98954e37i q^{67} +(4.39625e37 + 3.25195e38i) q^{68} -1.90511e38 q^{69} +(5.49649e38 - 6.28956e38i) q^{70} -1.04801e39i q^{71} +(-2.68949e38 + 4.07086e38i) q^{72} -1.07660e39 q^{73} +(-1.06321e39 - 9.29150e38i) q^{74} +4.28591e38i q^{75} +(3.29938e39 - 4.46037e38i) q^{76} +4.65245e39 q^{77} +(-4.99494e39 + 5.71564e39i) q^{78} -1.50373e39i q^{79} +(-9.94478e39 + 2.73889e39i) q^{80} -3.38607e39 q^{81} +(4.97217e39 + 4.34522e39i) q^{82} +3.31555e40i q^{83} +(3.30842e39 + 2.44727e40i) q^{84} +3.97894e40 q^{85} +(-1.06518e40 + 1.21887e40i) q^{86} -1.16040e40i q^{87} +(-4.79368e40 - 3.16703e40i) q^{88} -1.74834e40 q^{89} +(4.45465e40 + 3.89296e40i) q^{90} -3.59584e41i q^{91} +(-1.10445e41 + 1.49309e40i) q^{92} +1.47471e41 q^{93} +(-2.69276e41 + 3.08128e41i) q^{94} -4.03698e41i q^{95} +(1.32502e41 - 2.74676e41i) q^{96} +7.69142e41 q^{97} +(-3.88245e41 - 3.39291e41i) q^{98} +3.29515e41i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 802164 q^{2} + 1311168818192 q^{4} + 139235684997000 q^{5} + 68\!\cdots\!12 q^{6}+ \cdots - 73\!\cdots\!76 q^{9}+O(q^{10}) $ 20 * q + 802164 * q^2 + 1311168818192 * q^4 + 139235684997000 * q^5 + 6838718638036512 * q^6 - 27661415389266953664 * q^8 - 733170595646091132876 * q^9	$ 20 q + 802164 q^{2} + 1311168818192 q^{4} + 139235684997000 q^{5} + 68\!\cdots\!12 q^{6}+ \cdots + 18\!\cdots\!96 q^{98}+O(q^{100}) $ 20 * q + 802164 * q^2 + 1311168818192 * q^4 + 139235684997000 * q^5 + 6838718638036512 * q^6 - 27661415389266953664 * q^8 - 733170595646091132876 * q^9 + 42625185369378343240 * q^10 - 25848729272513843675520 * q^12 - 144898631886191567496248 * q^13 - 306990738295992471121728 * q^14 + 27792040878005009897120000 * q^16 + 81746542725793625328399528 * q^17 - 217831601203830755951030124 * q^18 + 6344592401135696008447573920 * q^20 + 7651089590961386749851047424 * q^21 - 46254109397133274566238240800 * q^22 + 506607644284406956508290140672 * q^24 + 844166434154191999887370985820 * q^25 + 305910330554143989456096580488 * q^26 - 1621415041794921570009743366400 * q^28 + 8494173617816210057524981535304 * q^29 + 32483836243012295467926394800960 * q^30 - 117067340157863901568162598132736 * q^32 - 195434629079924022845409037850880 * q^33 - 435728002928020507520645688017048 * q^34 + 905808650859207966395798479569552 * q^36 + 320827308804868360600766816935048 * q^37 - 834801746373065199942054885540960 * q^38 - 2080347678511686114819737054821760 * q^40 + 12238592465130696350192985088255080 * q^41 + 39180793491987624842407723014766080 * q^42 - 40147560736600746149658671246198400 * q^44 - 57674168870802092374169153418160440 * q^45 - 133593585977858896021440512714708928 * q^46 + 223617847456028179696661192651827200 * q^48 - 763663932888918132103393205670102316 * q^49 - 1073296820241355924814923786366326660 * q^50 - 580677968103327319151855528386839392 * q^52 + 3592528655430046000719727125882705672 * q^53 + 8087462166590362832897538370358812224 * q^54 - 4056862272141293872664295528725971968 * q^56 + 1376964140105307936676325853454767360 * q^57 - 17787847411919404506009575679670206968 * q^58 + 27803845757503537955964429994460432640 * q^60 - 72876803820111699199759396563493728440 * q^61 - 83779848218915601601226708273126396160 * q^62 - 51258837764961549702163120437185671168 * q^64 + 143337782114217802520090675036041365840 * q^65 + 479881795533282188176080436671310498560 * q^66 - 201679039132028748396903074185205050848 * q^68 + 496255895990320623770556878095159325184 * q^69 + 244550326432622351468933399511720393600 * q^70 + 1389470702024602675984554222025462031424 * q^72 + 675217186810136917874725959945538619752 * q^73 - 5048325762233564608985375515346235670968 * q^74 - 727730227778639944706768217921060021120 * q^76 - 13945771646073577607404274150247166932480 * q^77 + 2630485389052859541031650397045824087360 * q^78 - 14080069438753558698176635521889841825280 * q^80 + 50326416439524122225413610454605570342484 * q^81 + 38442316210858292795461617709768475559208 * q^82 + 21041665749991691364416236667734761560064 * q^84 - 100747029416581567610441680879732008651760 * q^85 - 109399875737541346773887857542693387248928 * q^86 + 61542411942227832459784035156153652876800 * q^88 + 298677519739918601751826215340976530195944 * q^89 + 5248331693055749298139854308097091987080 * q^90 - 311056321102768653749854891753699429405440 * q^92 - 902946967697899772252214392286633142732800 * q^93 - 120754391334239789606838050760853185629568 * q^94 - 369891338439189821551415861997759233875968 * q^96 + 2729077788738058742150638081801454021515048 * q^97 + 1829330555781863715528793474157579946873396 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.57912e6	+	1.38001e6i	0.752984	+	0.658039i
$2$	1.57912e6	+	1.38001e6i	0.752984	+	0.658039i
$3$			7.51798e9i			0.718712i	0.933201	+	0.359356i	$0.117004\pi$
$3$			7.51798e9i			0.718712i	−0.933201	+	0.359356i	$0.882996\pi$
$4$	5.89205e11	+	4.35840e12i	0.133970	+	0.990985i
$5$	5.33275e14			1.11836			0.559180	−	0.829047i	$-0.311116\pi$
$5$	5.33275e14			1.11836			0.559180	+	0.829047i	$0.311116\pi$
$6$	−1.03749e16	+	1.18718e16i	−0.472941	+	0.541179i
$7$		−	7.46884e17i		−	1.33719i	−0.743625	−	0.668596i	$-0.766895\pi$
$7$		−	7.46884e17i		−	1.33719i	0.743625	−	0.668596i	$-0.233105\pi$
$8$	−5.08420e18	+	7.69555e18i	−0.551230	+	0.834353i
$9$	5.28989e19			0.483453
$10$	8.42107e20	+	7.35924e20i	0.842107	+	0.735924i
$11$			6.22915e21i			0.841749i	0.907119	+	0.420874i	$0.138277\pi$
$11$			6.22915e21i			0.841749i	−0.907119	+	0.420874i	$0.861723\pi$
$12$	−3.27664e22	+	4.42963e21i	−0.712233	+	0.0962856i
$13$	4.81446e23			1.94867			0.974333	−	0.225111i	$-0.0722746\pi$
$13$	4.81446e23			1.94867			0.974333	+	0.225111i	$0.0722746\pi$
$14$	1.03071e24	−	1.17942e24i	0.879925	−	1.00688i
$15$			4.00915e24i			0.803778i
$16$	−1.86485e25	+	5.13598e24i	−0.964104	+	0.265524i
$17$	7.46133e25			1.07991			0.539957	−	0.841693i	$-0.318441\pi$
$17$	7.46133e25			1.07991			0.539957	+	0.841693i	$0.318441\pi$
$18$	8.35338e25	+	7.30009e25i	0.364032	+	0.318131i
$19$		−	7.57016e26i		−	1.05993i	−0.848018	−	0.529967i	$-0.822204\pi$
$19$		−	7.57016e26i		−	1.05993i	0.848018	−	0.529967i	$-0.177796\pi$
$20$	3.14208e26	+	2.32423e27i	0.149826	+	1.10828i
$21$	5.61506e27			0.961057
$22$	−8.59628e27	+	9.83659e27i	−0.553904	+	0.633823i
$23$			2.53407e28i			0.642000i	0.947079	+	0.321000i	$0.104019\pi$
$23$			2.53407e28i			0.642000i	−0.947079	+	0.321000i	$0.895981\pi$
$24$	−5.78550e28	−	3.82229e28i	−0.599660	−	0.396176i
$25$	5.70088e28			0.250727
$26$	7.60262e29	+	6.64400e29i	1.46731	+	1.28230i
$27$			1.22030e30i			1.06618i
$28$	3.25522e30	−	4.40067e29i	1.32514	−	0.179143i
$29$	−1.54350e30			−0.300711			−0.150356	−	0.988632i	$-0.548042\pi$
$29$	−1.54350e30			−0.300711			−0.150356	+	0.988632i	$0.548042\pi$
$30$	−5.53266e30	+	6.33094e30i	−0.528917	+	0.605232i
$31$		−	1.96158e31i		−	0.941911i	−0.882157	−	0.470956i	$-0.843909\pi$
$31$		−	1.96158e31i		−	0.941911i	0.882157	−	0.470956i	$-0.156091\pi$
$32$	−3.65359e31	−	1.76247e31i	−0.900680	−	0.434483i
$33$	−4.68307e31			−0.604975
$34$	1.17823e32	+	1.02967e32i	0.813157	+	0.710625i
$35$		−	3.98295e32i		−	1.49546i
$36$	3.11683e31	+	2.30555e32i	0.0647680	+	0.479095i
$37$	−6.73293e32			−0.786988			−0.393494	−	0.919327i	$-0.628734\pi$
$37$	−6.73293e32			−0.786988			−0.393494	+	0.919327i	$0.628734\pi$
$38$	1.04469e33	−	1.19542e33i	0.697478	−	0.798114i
$39$			3.61950e33i			1.40053i
$40$	−2.71128e33	+	4.10385e33i	−0.616473	+	0.933107i
$41$	3.14869e33			0.426254			0.213127	−	0.977024i	$-0.431635\pi$
$41$	3.14869e33			0.426254			0.213127	+	0.977024i	$0.431635\pi$
$42$	8.86686e33	+	7.74882e33i	0.723660	+	0.632413i
$43$			7.71866e33i			0.384330i	0.981363	+	0.192165i	$0.0615509\pi$
$43$			7.71866e33i			0.384330i	−0.981363	+	0.192165i	$0.938449\pi$
$44$	−2.71491e34	+	3.67024e33i	−0.834161	+	0.112769i
$45$	2.82097e34			0.540674
$46$	−3.49704e34	+	4.00161e34i	−0.422461	+	0.483415i
$47$			1.95126e35i			1.50059i	0.661106	+	0.750293i	$0.270088\pi$
$47$			1.95126e35i			1.50059i	−0.661106	+	0.750293i	$0.729912\pi$
$48$	−3.86122e34	−	1.40199e35i	−0.190835	−	0.692913i
$49$	−2.45862e35			−0.788085
$50$	9.00238e34	+	7.86726e34i	0.188794	+	0.164988i
$51$			5.60941e35i			0.776147i
$52$	2.83670e35	+	2.09834e36i	0.261062	+	1.93110i
$53$	−3.91250e35			−0.241358			−0.120679	−	0.992692i	$-0.538507\pi$
$53$	−3.91250e35			−0.241358			−0.120679	+	0.992692i	$0.538507\pi$
$54$	−1.68403e36	+	1.92701e36i	−0.701585	+	0.802813i
$55$			3.32185e36i			0.941378i
$56$	5.74768e36	+	3.79731e36i	1.11569	+	0.737101i
$57$	5.69123e36			0.761788
$58$	−2.43738e36	−	2.13005e36i	−0.226431	−	0.197880i
$59$			2.85242e36i			0.185064i	0.995710	+	0.0925319i	$0.0294960\pi$
$59$			2.85242e36i			0.185064i	−0.995710	+	0.0925319i	$0.970504\pi$
$60$	−1.74735e37	+	2.36221e36i	−0.796533	+	0.107682i
$61$	−5.39160e37			−1.73697			−0.868483	−	0.495719i	$-0.834905\pi$
$61$	−5.39160e37			−1.73697			−0.868483	+	0.495719i	$0.834905\pi$
$62$	2.70699e37	−	3.09757e37i	0.619814	−	0.709244i
$63$		−	3.95093e37i		−	0.646470i
$64$	−3.33724e37	−	7.82514e37i	−0.392291	−	0.919841i
$65$	2.56743e38			2.17931
$66$	−7.39513e37	−	6.46267e37i	−0.455537	−	0.398097i
$67$		−	4.98954e37i		−	0.224125i	−0.993701	−	0.112062i	$-0.964254\pi$
$67$		−	4.98954e37i		−	0.224125i	0.993701	−	0.112062i	$-0.0357456\pi$
$68$	4.39625e37	+	3.25195e38i	0.144676	+	1.07018i
$69$	−1.90511e38			−0.461413
$70$	5.49649e38	−	6.28956e38i	0.984072	−	1.12606i
$71$		−	1.04801e39i		−	1.39296i	−0.717575	−	0.696481i	$-0.754748\pi$
$71$		−	1.04801e39i		−	1.39296i	0.717575	−	0.696481i	$-0.245252\pi$
$72$	−2.68949e38	+	4.07086e38i	−0.266494	+	0.403370i
$73$	−1.07660e39			−0.798497			−0.399249	−	0.916843i	$-0.630729\pi$
$73$	−1.07660e39			−0.798497			−0.399249	+	0.916843i	$0.630729\pi$
$74$	−1.06321e39	−	9.29150e38i	−0.592589	−	0.517868i
$75$			4.28591e38i			0.180201i
$76$	3.29938e39	−	4.46037e38i	1.05038	−	0.141999i
$77$	4.65245e39			1.12558
$78$	−4.99494e39	+	5.71564e39i	−0.921603	+	1.05458i
$79$		−	1.50373e39i		−	0.212325i	−0.994349	−	0.106163i	$-0.966144\pi$
$79$		−	1.50373e39i		−	0.212325i	0.994349	−	0.106163i	$-0.0338564\pi$
$80$	−9.94478e39	+	2.73889e39i	−1.07821	+	0.296951i
$81$	−3.38607e39			−0.282821
$82$	4.97217e39	+	4.34522e39i	0.320963	+	0.280492i
$83$			3.31555e40i			1.65927i	0.558310	+	0.829633i	$0.311450\pi$
$83$			3.31555e40i			1.65927i	−0.558310	+	0.829633i	$0.688550\pi$
$84$	3.30842e39	+	2.44727e40i	0.128752	+	0.952393i
$85$	3.97894e40			1.20773
$86$	−1.06518e40	+	1.21887e40i	−0.252904	+	0.289394i
$87$		−	1.16040e40i		−	0.216125i
$88$	−4.79368e40	−	3.16703e40i	−0.702316	−	0.463997i
$89$	−1.74834e40			−0.202039			−0.101019	−	0.994884i	$-0.532210\pi$
$89$	−1.74834e40			−0.202039			−0.101019	+	0.994884i	$0.532210\pi$
$90$	4.45465e40	+	3.89296e40i	0.407119	+	0.355784i
$91$		−	3.59584e41i		−	2.60574i
$92$	−1.10445e41	+	1.49309e40i	−0.636212	+	0.0860084i
$93$	1.47471e41			0.676963
$94$	−2.69276e41	+	3.08128e41i	−0.987444	+	1.12992i
$95$		−	4.03698e41i		−	1.18539i
$96$	1.32502e41	−	2.74676e41i	0.312268	−	0.647330i
$97$	7.69142e41			1.45814			0.729071	−	0.684438i	$-0.239952\pi$
$97$	7.69142e41			1.45814			0.729071	+	0.684438i	$0.239952\pi$
$98$	−3.88245e41	−	3.39291e41i	−0.593415	−	0.518591i
$99$			3.29515e41i			0.406946i
$100$	3.35898e40	+	2.48467e41i	0.0335898	+	0.248467i
$101$	1.00224e42			0.813246			0.406623	−	0.913596i	$-0.366706\pi$
$101$	1.00224e42			0.813246			0.406623	+	0.913596i	$0.366706\pi$
$102$	−7.74103e41	+	8.85795e41i	−0.510735	+	0.584426i
$103$		−	2.77198e42i		−	1.49008i	−0.667021	−	0.745039i	$-0.732431\pi$
$103$		−	2.77198e42i		−	1.49008i	0.667021	−	0.745039i	$-0.267569\pi$
$104$	−2.44777e42	+	3.70499e42i	−1.07416	+	1.62588i
$105$	2.99437e42			1.07481
$106$	−6.17832e41	−	5.39928e41i	−0.181739	−	0.158823i
$107$		−	3.31740e41i		−	0.0801196i	−0.999197	−	0.0400598i	$-0.987245\pi$
$107$		−	3.31740e41i		−	0.0801196i	0.999197	−	0.0400598i	$-0.0127548\pi$
$108$	−5.31857e42	+	7.19008e41i	−1.05656	+	0.142835i
$109$	1.47309e42			0.241142			0.120571	−	0.992705i	$-0.461527\pi$
$109$	1.47309e42			0.241142			0.120571	+	0.992705i	$0.461527\pi$
$110$	−4.58418e42	+	5.24561e42i	−0.619463	+	0.708842i
$111$		−	5.06181e42i		−	0.565618i
$112$	3.83598e42	+	1.39283e43i	0.355057	+	1.28919i
$113$	1.60332e42			0.123132			0.0615662	−	0.998103i	$-0.480390\pi$
$113$	1.60332e42			0.123132			0.0615662	+	0.998103i	$0.480390\pi$
$114$	8.98714e42	+	7.85394e42i	0.573614	+	0.501286i
$115$			1.35136e43i			0.717986i
$116$	−9.09440e41	−	6.72721e42i	−0.0402862	−	0.298001i
$117$	2.54680e43			0.942088
$118$	−3.93636e42	+	4.50432e42i	−0.121779	+	0.139350i
$119$		−	5.57274e43i		−	1.44405i
$120$	−3.08526e43	−	2.03833e43i	−0.670635	−	0.443067i
$121$	1.59614e43			0.291459
$122$	−8.51400e43	−	7.44045e43i	−1.30791	−	1.14299i
$123$			2.36718e43i			0.306354i
$124$	8.54934e43	−	1.15577e43i	0.933421	−	0.126187i
$125$	−9.08514e43			−0.837956
$126$	5.45232e43	−	6.23901e43i	0.425402	−	0.486781i
$127$		−	1.42876e44i		−	0.944240i	−0.881534	−	0.472120i	$-0.843489\pi$
$127$		−	1.42876e44i		−	0.944240i	0.881534	−	0.472120i	$-0.156511\pi$
$128$	5.52885e43	−	1.69623e44i	0.309903	−	0.950768i
$129$	−5.80288e43			−0.276223
$130$	4.05429e44	+	3.54308e44i	1.64098	+	1.43407i
$131$			5.31516e44i			1.83155i	0.401692	+	0.915775i	$0.368422\pi$
$131$			5.31516e44i			1.83155i	−0.401692	+	0.915775i	$0.631578\pi$
$132$	−2.75928e43	−	2.04107e44i	−0.0810483	−	0.599522i
$133$	−5.65402e44			−1.41734
$134$	6.88560e43	−	7.87909e43i	0.147483	−	0.168762i
$135$			6.50758e44i			1.19237i
$136$	−3.79349e44	+	5.74190e44i	−0.595281	+	0.901029i
$137$	1.91399e44			0.257519			0.128759	−	0.991676i	$-0.458901\pi$
$137$	1.91399e44			0.257519			0.128759	+	0.991676i	$0.458901\pi$
$138$	−3.00840e44	−	2.62907e44i	−0.347436	−	0.303628i
$139$		−	1.48190e44i		−	0.147065i	−0.997293	−	0.0735323i	$-0.976573\pi$
$139$		−	1.48190e44i		−	0.147065i	0.997293	−	0.0735323i	$-0.0234272\pi$
$140$	1.73593e45	−	2.34677e44i	1.48198	−	0.200346i
$141$	−1.46696e45			−1.07849
$142$	1.44626e45	−	1.65493e45i	0.916623	−	1.04888i
$143$			2.99900e45i			1.64029i
$144$	−9.86485e44	+	2.71688e44i	−0.466099	+	0.128368i
$145$	−8.23113e44			−0.336303
$146$	−1.70008e45	−	1.48571e45i	−0.601256	−	0.525442i
$147$		−	1.84838e45i		−	0.566406i
$148$	−3.96707e44	−	2.93448e45i	−0.105432	−	0.779893i
$149$	1.56939e45			0.362092			0.181046	−	0.983475i	$-0.442052\pi$
$149$	1.56939e45			0.362092			0.181046	+	0.983475i	$0.442052\pi$
$150$	−5.91459e44	+	6.76798e44i	−0.118579	+	0.135688i
$151$		−	5.27304e45i		−	0.919486i	−0.888052	−	0.459743i	$-0.847941\pi$
$151$		−	5.27304e45i		−	0.919486i	0.888052	−	0.459743i	$-0.152059\pi$
$152$	5.82565e45	+	3.84882e45i	0.884360	+	0.584268i
$153$	3.94696e45			0.522087
$154$	7.34679e45	+	6.42042e45i	0.847544	+	0.740676i
$155$		−	1.04606e46i		−	1.05340i
$156$	−1.57753e46	+	2.13263e45i	−1.38790	+	0.187628i
$157$	8.59406e44			0.0661158			0.0330579	−	0.999453i	$-0.489475\pi$
$157$	8.59406e44			0.0661158			0.0330579	+	0.999453i	$0.489475\pi$
$158$	2.07516e45	−	2.37457e45i	0.139718	−	0.159877i
$159$		−	2.94141e45i		−	0.173467i
$160$	−1.94837e46	−	9.39883e45i	−1.00728	−	0.485908i
$161$	1.89266e46			0.858477
$162$	−5.34702e45	−	4.67281e45i	−0.212959	−	0.186107i
$163$			1.72880e45i			0.0605070i	0.999542	+	0.0302535i	$0.00963146\pi$
$163$			1.72880e45i			0.0605070i	−0.999542	+	0.0302535i	$0.990369\pi$
$164$	1.85522e45	+	1.37233e46i	0.0571051	+	0.422412i
$165$	−2.49736e46			−0.676580
$166$	−4.57549e46	+	5.23566e46i	−1.09186	+	1.24940i
$167$			3.03185e46i			0.637766i	0.947794	+	0.318883i	$0.103308\pi$
$167$			3.03185e46i			0.637766i	−0.947794	+	0.318883i	$0.896692\pi$
$168$	−2.85481e46	+	4.32110e46i	−0.529763	+	0.801861i
$169$	1.70750e47			2.79730
$170$	6.28323e46	+	5.49097e46i	0.909402	+	0.794734i
$171$		−	4.00453e46i		−	0.512428i
$172$	−3.36410e46	+	4.54787e45i	−0.380866	+	0.0514886i
$173$	−1.18082e47			−1.18362			−0.591812	−	0.806076i	$-0.701587\pi$
$173$	−1.18082e47			−1.18362			−0.591812	+	0.806076i	$0.701587\pi$
$174$	1.60137e46	−	1.83242e46i	0.142219	−	0.162739i
$175$		−	4.25789e46i		−	0.335271i
$176$	−3.19928e46	−	1.16164e47i	−0.223504	−	0.811534i
$177$	−2.14445e46			−0.133008
$178$	−2.76084e46	−	2.41272e46i	−0.152132	−	0.132949i
$179$		−	6.75465e45i		−	0.0330894i	−0.999863	−	0.0165447i	$-0.994733\pi$
$179$		−	6.75465e45i		−	0.0330894i	0.999863	−	0.0165447i	$-0.00526659\pi$
$180$	1.66213e46	+	1.22949e47i	0.0724339	+	0.535800i
$181$	−1.59754e47			−0.619730			−0.309865	−	0.950780i	$-0.600284\pi$
$181$	−1.59754e47			−0.619730			−0.309865	+	0.950780i	$0.600284\pi$
$182$	4.96229e47	−	5.67827e47i	1.71468	−	1.96208i
$183$		−	4.05340e47i		−	1.24838i
$184$	−1.95011e47	−	1.28837e47i	−0.535654	−	0.353889i
$185$	−3.59050e47			−0.880135
$186$	2.32875e47	+	2.03511e47i	0.509742	+	0.445468i
$187$			4.64778e47i			0.909016i
$188$	−8.50439e47	+	1.14969e47i	−1.48706	+	0.201033i
$189$	9.11425e47			1.42568
$190$	5.57106e47	−	6.37488e47i	0.780031	−	0.892578i
$191$			1.30074e48i			1.63114i	0.578658	+	0.815570i	$0.303577\pi$
$191$			1.30074e48i			1.63114i	−0.578658	+	0.815570i	$0.696423\pi$
$192$	5.88293e47	−	2.50893e47i	0.661101	−	0.281944i
$193$	−8.78035e47			−0.884726			−0.442363	−	0.896836i	$-0.645860\pi$
$193$	−8.78035e47			−0.884726			−0.442363	+	0.896836i	$0.645860\pi$
$194$	1.21457e48	+	1.06142e48i	1.09796	+	0.959515i
$195$			1.93019e48i			1.56630i
$196$	−1.44863e47	−	1.07156e48i	−0.105579	−	0.780981i
$197$	−2.97593e48			−1.94909			−0.974545	−	0.224191i	$-0.928026\pi$
$197$	−2.97593e48			−1.94909			−0.974545	+	0.224191i	$0.928026\pi$
$198$	−4.54734e47	+	5.20345e47i	−0.267786	+	0.306424i
$199$		−	2.69254e48i		−	1.42642i	−0.700949	−	0.713211i	$-0.747240\pi$
$199$		−	2.69254e48i		−	1.42642i	0.700949	−	0.713211i	$-0.252760\pi$
$200$	−2.89844e47	+	4.38714e47i	−0.138208	+	0.209195i
$201$	3.75113e47			0.161081
$202$	1.58265e48	+	1.38310e48i	0.612361	+	0.535147i
$203$			1.15282e48i			0.402109i
$204$	−2.44481e48	+	3.30509e47i	−0.769150	+	0.103980i
$205$	1.67912e48			0.476706
$206$	3.82536e48	−	4.37730e48i	0.980529	−	1.12200i
$207$			1.34050e48i			0.310377i
$208$	−8.97825e48	+	2.47270e48i	−1.87872	+	0.517417i
$209$	4.71557e48			0.892199
$210$	4.72848e48	+	4.13226e48i	0.809312	+	0.707265i
$211$		−	1.21220e49i		−	1.87776i	−0.344239	−	0.938882i	$-0.611863\pi$
$211$		−	1.21220e49i		−	1.87776i	0.344239	−	0.938882i	$-0.388137\pi$
$212$	−2.30526e47	−	1.70523e48i	−0.0323346	−	0.239182i
$213$	7.87891e48			1.00114
$214$	4.57804e47	−	5.23858e47i	0.0527218	−	0.0603288i
$215$			4.11617e48i			0.429819i
$216$	−9.39091e48	−	6.20427e48i	−0.889567	−	0.587708i
$217$	−1.46507e49			−1.25952
$218$	2.32619e48	+	2.03288e48i	0.181576	+	0.158681i
$219$		−	8.09384e48i		−	0.573890i
$220$	−1.44780e49	+	1.95725e48i	−0.932892	+	0.126116i
$221$	3.59223e49			2.10439
$222$	6.98533e48	−	7.99321e48i	0.372198	−	0.425901i
$223$		−	1.96421e49i		−	0.952325i	−0.879357	−	0.476162i	$-0.842027\pi$
$223$		−	1.96421e49i		−	0.952325i	0.879357	−	0.476162i	$-0.157973\pi$
$224$	−1.31636e49	+	2.72881e49i	−0.580988	+	1.20438i
$225$	3.01570e48			0.121215
$226$	2.53183e48	+	2.21259e48i	0.0927167	+	0.0810259i
$227$		−	7.80948e48i		−	0.260663i	−0.991470	−	0.130332i	$-0.958396\pi$
$227$		−	7.80948e48i		−	0.260663i	0.991470	−	0.130332i	$-0.0416042\pi$
$228$	3.35330e48	+	2.48047e49i	0.102056	+	0.754921i
$229$	−3.39479e49			−0.942470			−0.471235	−	0.882008i	$-0.656192\pi$
$229$	−3.39479e49			−0.942470			−0.471235	+	0.882008i	$0.656192\pi$
$230$	−1.86489e49	+	2.13396e49i	−0.472463	+	0.540632i
$231$			3.49771e49i			0.808969i
$232$	7.84749e48	−	1.18781e49i	0.165761	−	0.250900i
$233$	−2.49217e49			−0.480953			−0.240477	−	0.970655i	$-0.577304\pi$
$233$	−2.49217e49			−0.480953			−0.240477	+	0.970655i	$0.577304\pi$
$234$	4.02171e49	+	3.51460e49i	0.709377	+	0.619931i
$235$			1.04056e50i			1.67819i
$236$	−1.24320e49	+	1.68066e48i	−0.183396	+	0.0247929i
$237$	1.13050e49			0.152601
$238$	7.69043e49	−	8.80004e49i	0.950243	−	1.08735i
$239$		−	2.26981e49i		−	0.256823i	−0.991721	−	0.128412i	$-0.959012\pi$
$239$		−	2.26981e49i		−	0.256823i	0.991721	−	0.128412i	$-0.0409878\pi$
$240$	−2.05909e49	−	7.47647e49i	−0.213422	−	0.774926i
$241$	5.53855e49			0.526064			0.263032	−	0.964787i	$-0.415278\pi$
$241$	5.53855e49			0.526064			0.263032	+	0.964787i	$0.415278\pi$
$242$	2.52049e49	+	2.20268e49i	0.219464	+	0.191791i
$243$			1.08068e50i			0.862909i
$244$	−3.17676e49	−	2.34988e50i	−0.232701	−	1.72131i
$245$	−1.31112e50			−0.881362
$246$	−3.26673e49	+	3.73807e49i	−0.201593	+	0.230680i
$247$		−	3.64462e50i		−	2.06546i
$248$	1.50954e50	+	9.97306e49i	0.785887	+	0.519210i
$249$	−2.49263e50			−1.19253
$250$	−1.43465e50	−	1.25376e50i	−0.630967	−	0.551408i
$251$			6.78032e49i			0.274222i	0.990556	+	0.137111i	$0.0437817\pi$
$251$			6.78032e49i			0.274222i	−0.990556	+	0.137111i	$0.956218\pi$
$252$	1.72197e50	−	2.32791e49i	0.640642	−	0.0866073i
$253$	−1.57851e50			−0.540402
$254$	1.97171e50	−	2.25619e50i	0.621347	−	0.710998i
$255$			2.99136e50i			0.868011i
$256$	3.21388e50	−	1.91556e50i	0.858994	−	0.511985i
$257$	4.98099e50			1.22665			0.613324	−	0.789831i	$-0.289832\pi$
$257$	4.98099e50			1.22665			0.613324	+	0.789831i	$0.289832\pi$
$258$	−9.16345e49	−	8.00801e49i	−0.207991	−	0.181765i
$259$			5.02872e50i			1.05235i
$260$	1.51274e50	+	1.11899e51i	0.291961	+	2.15966i
$261$	−8.16497e49			−0.145380
$262$	−7.33495e50	+	8.39328e50i	−1.20523	+	1.37913i
$263$		−	4.90484e50i		−	0.743968i	−0.928239	−	0.371984i	$-0.878678\pi$
$263$		−	4.90484e50i		−	0.743968i	0.928239	−	0.371984i	$-0.121322\pi$
$264$	2.38096e50	−	3.60388e50i	0.333481	−	0.504763i
$265$	−2.08644e50			−0.269925
$266$	−8.92839e50	−	7.80260e50i	−1.06723	−	0.932663i
$267$		−	1.31440e50i		−	0.145208i
$268$	2.17464e50	−	2.93986e49i	0.222104	−	0.0300259i
$269$	4.60002e50			0.434472			0.217236	−	0.976119i	$-0.430296\pi$
$269$	4.60002e50			0.434472			0.217236	+	0.976119i	$0.430296\pi$
$270$	−8.98050e50	+	1.02763e51i	−0.784624	+	0.897833i
$271$		−	5.34679e50i		−	0.432253i	−0.976365	−	0.216126i	$-0.930658\pi$
$271$		−	5.34679e50i		−	0.432253i	0.976365	−	0.216126i	$-0.0693423\pi$
$272$	−1.39143e51	+	3.83212e50i	−1.04115	+	0.286743i
$273$	2.70335e51			1.87278
$274$	3.02243e50	+	2.64133e50i	0.193907	+	0.169457i
$275$			3.55116e50i			0.211049i
$276$	−1.12250e50	−	8.30324e50i	−0.0618153	−	0.457253i
$277$	−1.30079e51			−0.663943			−0.331972	−	0.943289i	$-0.607714\pi$
$277$	−1.30079e51			−0.663943			−0.331972	+	0.943289i	$0.607714\pi$
$278$	2.04503e50	−	2.34010e50i	0.0967742	−	0.110737i
$279$		−	1.03765e51i		−	0.455370i
$280$	3.06510e51	+	2.02501e51i	1.24774	+	0.824344i
$281$	−9.36843e50			−0.353862			−0.176931	−	0.984223i	$-0.556617\pi$
$281$	−9.36843e50			−0.353862			−0.176931	+	0.984223i	$0.556617\pi$
$282$	−2.31650e51	−	2.02441e51i	−0.812085	−	0.709688i
$283$		−	4.65787e51i		−	1.51591i	−0.652309	−	0.757953i	$-0.726199\pi$
$283$		−	4.65787e51i		−	1.51591i	0.652309	−	0.757953i	$-0.273801\pi$
$284$	4.56764e51	−	6.17491e50i	1.38041	−	0.186615i
$285$	3.03499e51			0.851953
$286$	−4.13865e51	+	4.73579e51i	−1.07937	+	1.23511i
$287$		−	2.35171e51i		−	0.569984i
$288$	−1.93271e51	−	9.32329e50i	−0.435436	−	0.210052i
$289$	7.93447e50			0.166212
$290$	−1.29980e51	−	1.13590e51i	−0.253231	−	0.221301i
$291$			5.78240e51i			1.04798i
$292$	−6.34336e50	−	4.69224e51i	−0.106974	−	0.791299i
$293$	−4.50012e51			−0.706324			−0.353162	−	0.935562i	$-0.614893\pi$
$293$	−4.50012e51			−0.706324			−0.353162	+	0.935562i	$0.614893\pi$
$294$	2.55078e51	−	2.91882e51i	0.372717	−	0.426495i
$295$			1.52113e51i			0.206968i
$296$	3.42316e51	−	5.18136e51i	0.433811	−	0.656626i
$297$	−7.60146e51			−0.897452
$298$	2.47826e51	+	2.16577e51i	0.272650	+	0.238271i
$299$			1.22002e52i			1.25104i
$300$	−1.86797e51	+	2.52528e50i	−0.178576	+	0.0241414i
$301$	5.76494e51			0.513924
$302$	7.27684e51	−	8.32678e51i	0.605058	−	0.692359i
$303$			7.53480e51i			0.584490i
$304$	3.88801e51	+	1.41172e52i	0.281438	+	1.02189i
$305$	−2.87521e52			−1.94255
$306$	6.23273e51	+	5.44684e51i	0.393123	+	0.343554i
$307$			2.88468e52i			1.69899i	0.527593	+	0.849497i	$0.323095\pi$
$307$			2.88468e52i			1.69899i	−0.527593	+	0.849497i	$0.676905\pi$
$308$	2.74125e51	+	2.02772e52i	0.150794	+	1.11543i
$309$	2.08397e52			1.07094
$310$	1.44357e52	−	1.65186e52i	0.693175	−	0.793190i
$311$		−	2.68748e52i		−	1.20608i	−0.797710	−	0.603041i	$-0.793956\pi$
$311$		−	2.68748e52i		−	1.20608i	0.797710	−	0.603041i	$-0.206044\pi$
$312$	−2.78541e52	−	1.84023e52i	−1.16854	−	0.772014i
$313$	3.94075e51			0.154578			0.0772890	−	0.997009i	$-0.475374\pi$
$313$	3.94075e51			0.154578			0.0772890	+	0.997009i	$0.475374\pi$
$314$	1.35711e51	+	1.18599e51i	0.0497842	+	0.0435068i
$315$		−	2.10694e52i		−	0.722985i
$316$	6.55386e51	−	8.86005e50i	0.210411	−	0.0284451i
$317$	−3.19883e52			−0.961052			−0.480526	−	0.876980i	$-0.659554\pi$
$317$	−3.19883e52			−0.961052			−0.480526	+	0.876980i	$0.659554\pi$
$318$	4.05917e51	−	4.64485e51i	0.114148	−	0.130618i
$319$		−	9.61473e51i		−	0.253124i
$320$	−1.77967e52	−	4.17296e52i	−0.438722	−	1.02871i
$321$	2.49402e51			0.0575830
$322$	2.98874e52	+	2.61188e52i	0.646420	+	0.564911i
$323$		−	5.64834e52i		−	1.14464i
$324$	−1.99509e51	−	1.47579e52i	−0.0378894	−	0.280271i
$325$	2.74467e52			0.488584
$326$	−2.38576e51	+	2.72999e51i	−0.0398160	+	0.0455608i
$327$			1.10747e52i			0.173312i
$328$	−1.60086e52	+	2.42309e52i	−0.234964	+	0.355647i
$329$	1.45737e53			2.00657
$330$	−3.94364e52	−	3.44638e52i	−0.509454	−	0.445216i
$331$			3.01946e52i			0.366051i	0.983108	+	0.183025i	$0.0585891\pi$
$331$			3.01946e52i			0.366051i	−0.983108	+	0.183025i	$0.941411\pi$
$332$	−1.44505e53	+	1.95354e52i	−1.64431	+	0.222291i
$333$	−3.56165e52			−0.380471
$334$	−4.18397e52	+	4.78765e52i	−0.419675	+	0.480227i
$335$		−	2.66080e52i		−	0.250652i
$336$	−1.04712e53	+	2.88388e52i	−0.926559	+	0.255184i
$337$	5.65477e51			0.0470097			0.0235048	−	0.999724i	$-0.492517\pi$
$337$	5.65477e51			0.0470097			0.0235048	+	0.999724i	$0.492517\pi$
$338$	2.69634e53	+	2.35636e53i	2.10632	+	1.84073i
$339$			1.20537e52i			0.0884968i
$340$	2.34441e52	+	1.73418e53i	0.161799	+	1.19684i
$341$	1.22190e53			0.792853
$342$	5.52628e52	−	6.32364e52i	0.337198	−	0.385850i
$343$		−	4.93778e52i		−	0.283371i
$344$	−5.93994e52	−	3.92432e52i	−0.320667	−	0.211854i
$345$	−1.01595e53			−0.516025
$346$	−1.86465e53	−	1.62953e53i	−0.891250	−	0.778871i
$347$		−	1.32477e53i		−	0.595967i	−0.954571	−	0.297983i	$-0.903686\pi$
$347$		−	1.32477e53i		−	0.595967i	0.954571	−	0.297983i	$-0.0963140\pi$
$348$	5.05751e52	−	6.83715e51i	0.214177	−	0.0289542i
$349$	−3.71222e53			−1.48013			−0.740064	−	0.672536i	$-0.765205\pi$
$349$	−3.71222e53			−1.48013			−0.740064	+	0.672536i	$0.765205\pi$
$350$	5.87592e52	−	6.72373e52i	0.220621	−	0.252454i
$351$			5.87510e53i			2.07762i
$352$	1.09787e53	−	2.27588e53i	0.365726	−	0.758147i
$353$	1.54798e52			0.0485844			0.0242922	−	0.999705i	$-0.492267\pi$
$353$	1.54798e52			0.0485844			0.0242922	+	0.999705i	$0.492267\pi$
$354$	−3.38634e52	−	2.95935e52i	−0.100153	−	0.0875242i
$355$		−	5.58877e53i		−	1.55783i
$356$	−1.03013e52	−	7.61995e52i	−0.0270671	−	0.200218i
$357$	4.18958e53			1.03786
$358$	9.32147e51	−	1.06664e52i	0.0217741	−	0.0249158i
$359$			2.27556e53i			0.501308i	0.968077	+	0.250654i	$0.0806456\pi$
$359$			2.27556e53i			0.501308i	−0.968077	+	0.250654i	$0.919354\pi$
$360$	−1.43424e53	+	2.17089e53i	−0.298036	+	0.451113i
$361$	−6.29773e52			−0.123462
$362$	−2.52272e53	−	2.20462e53i	−0.466647	−	0.407807i
$363$			1.19997e53i			0.209475i
$364$	1.56721e54	−	2.11869e53i	2.58225	−	0.349090i
$365$	−5.74123e53			−0.893007
$366$	5.59372e53	−	6.40081e53i	0.821482	−	0.940009i
$367$			3.78230e53i			0.524527i	0.964996	+	0.262264i	$0.0844690\pi$
$367$			3.78230e53i			0.524527i	−0.964996	+	0.262264i	$0.915531\pi$
$368$	−1.30149e53	−	4.72567e53i	−0.170466	−	0.618955i
$369$	1.66562e53			0.206074
$370$	−5.66984e53	−	4.95492e53i	−0.662727	−	0.579163i
$371$			2.92218e53i			0.322742i
$372$	8.68906e52	+	6.42738e53i	0.0906925	+	0.670861i
$373$	−1.48546e54			−1.46546			−0.732732	−	0.680517i	$-0.761755\pi$
$373$	−1.48546e54			−1.46546			−0.732732	+	0.680517i	$0.761755\pi$
$374$	−6.41397e53	+	7.33940e53i	−0.598168	+	0.684474i
$375$		−	6.83019e53i		−	0.602249i
$376$	−1.50160e54	−	9.92061e53i	−1.25202	−	0.827168i
$377$	−7.43115e53			−0.585986
$378$	1.43925e54	+	1.25777e54i	1.07352	+	0.938155i
$379$			9.57606e53i			0.675715i	0.941197	+	0.337857i	$0.109702\pi$
$379$			9.57606e53i			0.675715i	−0.941197	+	0.337857i	$0.890298\pi$
$380$	1.75948e54	−	2.37860e53i	1.17470	−	0.158806i
$381$	1.07414e54			0.678637
$382$	−1.79504e54	+	2.05403e54i	−1.07335	+	1.22822i
$383$		−	1.07845e54i		−	0.610416i	−0.952286	−	0.305208i	$-0.901274\pi$
$383$		−	1.07845e54i		−	0.610416i	0.952286	−	0.305208i	$-0.0987259\pi$
$384$	1.27522e54	+	4.15658e53i	0.683329	+	0.222731i
$385$	2.48104e54			1.25880
$386$	−1.38652e54	−	1.21170e54i	−0.666184	−	0.582184i
$387$			4.08309e53i			0.185805i
$388$	4.53182e53	+	3.35223e54i	0.195347	+	1.44500i
$389$	3.04929e54			1.24525			0.622627	−	0.782519i	$-0.286065\pi$
$389$	3.04929e54			1.24525			0.622627	+	0.782519i	$0.286065\pi$
$390$	−2.66368e54	+	3.04801e54i	−1.03068	+	1.17940i
$391$			1.89076e54i			0.693304i
$392$	1.25001e54	−	1.89204e54i	0.434416	−	0.657541i
$393$	−3.99592e54			−1.31636
$394$	−4.69936e54	−	4.10681e54i	−1.46763	−	1.28258i
$395$		−	8.01902e53i		−	0.237456i
$396$	−1.43616e54	+	1.94152e53i	−0.403277	+	0.0545184i
$397$	6.05630e54			1.61290			0.806449	−	0.591303i	$-0.201386\pi$
$397$	6.05630e54			1.61290			0.806449	+	0.591303i	$0.201386\pi$
$398$	3.71573e54	−	4.25185e54i	0.938641	−	1.07407i
$399$		−	4.25069e54i		−	1.01866i
$400$	−1.06313e54	+	2.92796e53i	−0.241727	+	0.0665741i
$401$	−1.98234e54			−0.427707			−0.213854	−	0.976866i	$-0.568602\pi$
$401$	−1.98234e54			−0.427707			−0.213854	+	0.976866i	$0.568602\pi$
$402$	5.92349e53	+	5.17659e53i	0.121292	+	0.105998i
$403$		−	9.44395e54i		−	1.83547i
$404$	5.90523e53	+	4.36815e54i	0.108950	+	0.805915i
$405$	−1.80571e54			−0.316295
$406$	−1.59090e54	+	1.82044e54i	−0.264604	+	0.302782i
$407$		−	4.19405e54i		−	0.662446i
$408$	−4.31675e54	−	2.85194e54i	−0.647581	−	0.427835i
$409$	1.90826e54			0.271924			0.135962	−	0.990714i	$-0.456588\pi$
$409$	1.90826e54			0.271924			0.135962	+	0.990714i	$0.456588\pi$
$410$	2.65153e54	+	2.31720e54i	0.358952	+	0.313691i
$411$			1.43894e54i			0.185082i
$412$	1.20814e55	−	1.63327e54i	1.47665	−	0.199625i
$413$	2.13043e54			0.247466
$414$	−1.84990e54	+	2.11681e54i	−0.204240	+	0.233709i
$415$			1.76810e55i			1.85565i
$416$	−1.75901e55	−	8.48536e54i	−1.75512	−	0.846662i
$417$	1.11409e54			0.105697
$418$	7.44645e54	+	6.50752e54i	0.671812	+	0.587102i
$419$			7.27140e53i			0.0623912i	0.999513	+	0.0311956i	$0.00993148\pi$
$419$			7.27140e53i			0.0623912i	−0.999513	+	0.0311956i	$0.990069\pi$
$420$	1.76430e54	+	1.30507e55i	0.143991	+	1.06512i
$421$	−2.07884e55			−1.61397			−0.806987	−	0.590569i	$-0.798903\pi$
$421$	−2.07884e55			−1.61397			−0.806987	+	0.590569i	$0.798903\pi$
$422$	1.67284e55	−	1.91420e55i	1.23564	−	1.41393i
$423$			1.03220e55i			0.725462i
$424$	1.98919e54	−	3.01089e54i	0.133044	−	0.201378i
$425$	4.25361e54			0.270764
$426$	1.24418e55	+	1.08730e55i	0.753841	+	0.658788i
$427$			4.02690e55i			2.32266i
$428$	1.44586e54	−	1.95463e53i	0.0793974	−	0.0107336i
$429$	−2.25464e55			−1.17889
$430$	−5.68035e54	+	6.49993e54i	−0.282838	+	0.323647i
$431$		−	2.20526e55i		−	1.04577i	−0.852403	−	0.522885i	$-0.824856\pi$
$431$		−	2.20526e55i		−	1.04577i	0.852403	−	0.522885i	$-0.175144\pi$
$432$	−6.26745e54	−	2.27568e55i	−0.283095	−	1.02790i
$433$	6.62429e54			0.285032			0.142516	−	0.989792i	$-0.454481\pi$
$433$	6.62429e54			0.285032			0.142516	+	0.989792i	$0.454481\pi$
$434$	−2.31352e55	−	2.02181e55i	−0.948396	−	0.828811i
$435$		−	6.18815e54i		−	0.241705i
$436$	8.67951e53	+	6.42032e54i	0.0323057	+	0.238968i
$437$	1.91833e55			0.680478
$438$	1.11696e55	−	1.27812e55i	0.377642	−	0.432130i
$439$		−	2.63874e55i		−	0.850435i	−0.905091	−	0.425217i	$-0.860198\pi$
$439$		−	2.63874e55i		−	0.850435i	0.905091	−	0.425217i	$-0.139802\pi$
$440$	−2.55635e55	−	1.68890e55i	−0.785442	−	0.518916i
$441$	−1.30058e55			−0.381002
$442$	5.67257e55	+	4.95730e55i	1.58457	+	1.38477i
$443$		−	8.61061e54i		−	0.229380i	−0.993401	−	0.114690i	$-0.963413\pi$
$443$		−	8.61061e54i		−	0.229380i	0.993401	−	0.114690i	$-0.0365875\pi$
$444$	2.20614e55	−	2.98244e54i	0.560519	−	0.0757756i
$445$	−9.32345e54			−0.225952
$446$	2.71062e55	−	3.10172e55i	0.626667	−	0.717085i
$447$			1.17986e55i			0.260240i
$448$	−5.84447e55	+	2.49253e55i	−1.23001	+	0.524569i
$449$	−2.26658e55			−0.455196			−0.227598	−	0.973755i	$-0.573087\pi$
$449$	−2.26658e55			−0.455196			−0.227598	+	0.973755i	$0.573087\pi$
$450$	4.76216e54	+	4.16169e54i	0.0912728	+	0.0797641i
$451$			1.96137e55i			0.358799i
$452$	9.44682e53	+	6.98790e54i	0.0164960	+	0.122022i
$453$	3.96426e55			0.660846
$454$	1.07771e55	−	1.23321e55i	0.171526	−	0.196275i
$455$		−	1.91757e56i		−	2.91416i
$456$	−2.89353e55	+	4.37971e55i	−0.419920	+	0.635600i
$457$	1.02108e56			1.41521			0.707605	−	0.706608i	$-0.249776\pi$
$457$	1.02108e56			1.41521			0.707605	+	0.706608i	$0.249776\pi$
$458$	−5.36079e55	−	4.68483e55i	−0.709665	−	0.620182i
$459$			9.10508e55i			1.15138i
$460$	−5.88976e55	+	7.96227e54i	−0.711514	+	0.0961883i
$461$	9.25084e54			0.106773			0.0533865	−	0.998574i	$-0.482998\pi$
$461$	9.25084e54			0.106773			0.0533865	+	0.998574i	$0.482998\pi$
$462$	−4.82686e55	+	5.52330e55i	−0.532333	+	0.609140i
$463$			1.47039e56i			1.54965i	0.632178	+	0.774823i	$0.282161\pi$
$463$			1.47039e56i			1.54965i	−0.632178	+	0.774823i	$0.717839\pi$
$464$	2.87840e55	−	7.92741e54i	0.289917	−	0.0798461i
$465$	7.86427e55			0.757088
$466$	−3.93543e55	−	3.43921e55i	−0.362150	−	0.316486i
$467$		−	1.55618e56i		−	1.36901i	−0.729010	−	0.684503i	$-0.760019\pi$
$467$		−	1.55618e56i		−	1.36901i	0.729010	−	0.684503i	$-0.239981\pi$
$468$	1.50059e55	+	1.11000e56i	0.126211	+	0.933596i
$469$	−3.72661e55			−0.299698
$470$	−1.43598e56	+	1.64317e56i	−1.10432	+	1.26365i
$471$			6.46100e54i			0.0475183i
$472$	−2.19510e55	−	1.45023e55i	−0.154409	−	0.102013i
$473$	−4.80807e55			−0.323509
$474$	1.78520e55	+	1.56010e55i	0.114906	+	0.100417i
$475$		−	4.31565e55i		−	0.265755i
$476$	2.42882e56	−	3.28349e55i	1.43103	−	0.193459i
$477$	−2.06967e55			−0.116685
$478$	3.13236e55	−	3.58431e55i	0.169000	−	0.193384i
$479$			2.37266e56i			1.22515i	0.790412	+	0.612575i	$0.209866\pi$
$479$			2.37266e56i			1.22515i	−0.790412	+	0.612575i	$0.790134\pi$
$480$	7.06602e55	−	1.46478e56i	0.349228	−	0.723947i
$481$	−3.24154e56			−1.53358
$482$	8.74605e55	+	7.64325e55i	0.396118	+	0.346170i
$483$			1.42290e56i			0.616998i
$484$	9.40450e54	+	6.95660e55i	0.0390466	+	0.288831i
$485$	4.10164e56			1.63073
$486$	−1.49135e56	+	1.70652e56i	−0.567828	+	0.649757i
$487$		−	2.28960e56i		−	0.834931i	−0.908693	−	0.417465i	$-0.862918\pi$
$487$		−	2.28960e56i		−	0.834931i	0.908693	−	0.417465i	$-0.137082\pi$
$488$	2.74120e56	−	4.14913e56i	0.957468	−	1.44924i
$489$	−1.29971e55			−0.0434871
$490$	−2.07042e56	−	1.80935e56i	−0.663652	−	0.579971i
$491$		−	2.89726e56i		−	0.889766i	−0.895589	−	0.444883i	$-0.853245\pi$
$491$		−	2.89726e56i		−	0.889766i	0.895589	−	0.444883i	$-0.146755\pi$
$492$	−1.03171e56	+	1.39475e55i	−0.303593	+	0.0410422i
$493$	−1.15166e56			−0.324742
$494$	5.02961e56	−	5.75530e56i	1.35915	−	1.55526i
$495$			1.75722e56i			0.455112i
$496$	1.00746e56	+	3.65805e56i	0.250100	+	0.908101i
$497$	−7.82740e56			−1.86266
$498$	−3.93616e56	−	3.43984e56i	−0.897959	−	0.784734i
$499$		−	4.36402e56i		−	0.954497i	−0.878768	−	0.477249i	$-0.841634\pi$
$499$		−	4.36402e56i		−	0.954497i	0.878768	−	0.477249i	$-0.158366\pi$
$500$	−5.35300e55	−	3.95967e56i	−0.112261	−	0.830402i
$501$	−2.27934e56			−0.458370
$502$	−9.35689e55	+	1.07069e56i	−0.180449	+	0.206485i
$503$			6.10709e56i			1.12955i	0.825244	+	0.564777i	$0.191038\pi$
$503$			6.10709e56i			1.12955i	−0.825244	+	0.564777i	$0.808962\pi$
$504$	3.04046e56	+	2.00873e56i	0.539384	+	0.356354i
$505$	5.34468e56			0.909501
$506$	−2.49266e56	−	2.17836e56i	−0.406914	−	0.355606i
$507$			1.28369e57i			2.01045i
$508$	6.22713e56	−	8.41835e55i	0.935728	−	0.126500i
$509$	5.22818e55			0.0753837			0.0376918	−	0.999289i	$-0.487999\pi$
$509$	5.22818e55			0.0753837			0.0376918	+	0.999289i	$0.487999\pi$
$510$	−4.12810e56	+	4.72372e56i	−0.571185	+	0.653598i
$511$			8.04093e56i			1.06774i
$512$	7.71860e56	+	1.41027e56i	0.983715	+	0.179735i
$513$	9.23789e56			1.13008
$514$	7.86559e56	+	6.87381e56i	0.923647	+	0.807183i
$515$		−	1.47823e57i		−	1.66644i
$516$	−3.41908e55	−	2.52913e56i	−0.0370054	−	0.273733i
$517$	−1.21547e57			−1.26312
$518$	−6.93967e56	+	7.94095e56i	−0.692490	+	0.792406i
$519$		−	8.87735e56i		−	0.850685i
$520$	−1.30533e57	+	1.97578e57i	−1.20130	+	1.81831i
$521$	1.33475e56			0.117980			0.0589901	−	0.998259i	$-0.481212\pi$
$521$	1.33475e56			0.117980			0.0589901	+	0.998259i	$0.481212\pi$
$522$	−1.28935e56	−	1.12677e56i	−0.109469	−	0.0956656i
$523$			2.78450e56i			0.227098i	0.993532	+	0.113549i	$0.0362218\pi$
$523$			2.78450e56i			0.227098i	−0.993532	+	0.113549i	$0.963778\pi$
$524$	−2.31656e57	+	3.13171e56i	−1.81504	+	0.245372i
$525$	3.20108e56			0.240963
$526$	6.76872e56	−	7.74534e56i	0.489560	−	0.560196i
$527$		−	1.46360e57i		−	1.01718i
$528$	8.73321e56	−	2.40521e56i	0.583259	−	0.160635i
$529$	9.15853e56			0.587837
$530$	−3.29474e56	−	2.87930e56i	−0.203249	−	0.177621i
$531$			1.50890e56i			0.0894696i
$532$	−3.33138e56	−	2.46425e57i	−0.189880	−	1.40456i
$533$	1.51593e57			0.830628
$534$	1.81388e56	−	2.07559e56i	0.0955524	−	0.109339i
$535$		−	1.76909e56i		−	0.0896025i
$536$	3.83973e56	+	2.53678e56i	0.186999	+	0.123544i
$537$	5.07814e55			0.0237818
$538$	7.26399e56	+	6.34806e56i	0.327150	+	0.285899i
$539$		−	1.53151e57i		−	0.663370i
$540$	−2.83626e57	+	3.83429e56i	−1.18162	+	0.159741i
$541$	1.78358e57			0.714742			0.357371	−	0.933962i	$-0.383673\pi$
$541$	1.78358e57			0.714742			0.357371	+	0.933962i	$0.383673\pi$
$542$	7.37861e56	−	8.44323e56i	0.284439	−	0.325479i
$543$		−	1.20103e57i		−	0.445408i
$544$	−2.72607e57	−	1.31504e57i	−0.972656	−	0.469204i
$545$	7.85563e56			0.269683
$546$	4.26892e57	+	3.73064e57i	1.41017	+	1.23236i
$547$			1.43548e57i			0.456315i	0.973624	+	0.228157i	$0.0732701\pi$
$547$			1.43548e57i			0.456315i	−0.973624	+	0.228157i	$0.926730\pi$
$548$	1.12773e56	+	8.34195e56i	0.0344997	+	0.255197i
$549$	−2.85210e57			−0.839741
$550$	−4.90063e56	+	5.60772e56i	−0.138879	+	0.158917i
$551$			1.16846e57i			0.318735i
$552$	9.68597e56	−	1.46609e57i	0.254345	−	0.384981i
$553$	−1.12311e57			−0.283920
$554$	−2.05410e57	−	1.79509e57i	−0.499938	−	0.436900i
$555$		−	2.69934e57i		−	0.632564i
$556$	6.45871e56	−	8.73142e55i	0.145739	−	0.0197022i
$557$	−1.17398e57			−0.255095			−0.127548	−	0.991832i	$-0.540711\pi$
$557$	−1.17398e57			−0.255095			−0.127548	+	0.991832i	$0.540711\pi$
$558$	1.43197e57	−	1.63858e57i	0.299651	−	0.342886i
$559$			3.71612e57i			0.748931i
$560$	2.04563e57	+	7.42759e57i	0.397081	+	1.44178i
$561$	−3.49419e57			−0.653321
$562$	−1.47939e57	−	1.29285e57i	−0.266452	−	0.232855i
$563$			6.40650e57i			1.11159i	0.831319	+	0.555795i	$0.187586\pi$
$563$			6.40650e57i			1.11159i	−0.831319	+	0.555795i	$0.812414\pi$
$564$	−8.64337e56	−	6.39358e57i	−0.144485	−	1.06877i
$565$	8.55010e56			0.137706
$566$	6.42790e57	−	7.35535e57i	0.997526	−	1.14145i
$567$			2.52900e57i			0.378186i
$568$	8.06500e57	+	5.32828e57i	1.16222	+	0.767843i
$569$	−8.87740e57			−1.23290			−0.616451	−	0.787393i	$-0.711430\pi$
$569$	−8.87740e57			−1.23290			−0.616451	+	0.787393i	$0.711430\pi$
$570$	4.79262e57	+	4.18831e57i	0.641507	+	0.560618i
$571$			6.67045e57i			0.860591i	0.902688	+	0.430295i	$0.141591\pi$
$571$			6.67045e57i			0.860591i	−0.902688	+	0.430295i	$0.858409\pi$
$572$	−1.30709e58	+	1.76703e57i	−1.62550	+	0.219749i
$573$	−9.77898e57			−1.17232
$574$	3.24537e57	−	3.71363e57i	0.375072	−	0.429189i
$575$			1.44464e57i			0.160967i
$576$	−1.76537e57	−	4.13942e57i	−0.189654	−	0.444700i
$577$	3.75671e57			0.389148			0.194574	−	0.980888i	$-0.437667\pi$
$577$	3.75671e57			0.389148			0.194574	+	0.980888i	$0.437667\pi$
$578$	1.25295e57	+	1.09496e57i	0.125155	+	0.109374i
$579$		−	6.60106e57i		−	0.635863i
$580$	−4.84982e56	−	3.58746e57i	−0.0450544	−	0.333272i
$581$	2.47633e58			2.21876
$582$	−7.97975e57	+	9.13111e57i	−0.689615	+	0.789116i
$583$		−	2.43716e57i		−	0.203163i
$584$	5.47364e57	−	8.28501e57i	0.440156	−	0.666229i
$585$	1.35814e58			1.05359
$586$	−7.10623e57	−	6.21019e57i	−0.531850	−	0.464788i
$587$			1.13033e58i			0.816219i	0.912933	+	0.408109i	$0.133812\pi$
$587$			1.13033e58i			0.816219i	−0.912933	+	0.408109i	$0.866188\pi$
$588$	8.05600e57	−	1.08908e57i	0.561300	−	0.0758812i
$589$	−1.48495e58			−0.998365
$590$	−2.09917e57	+	2.40204e57i	−0.136193	+	0.155843i
$591$		−	2.23730e58i		−	1.40083i
$592$	1.25559e58	−	3.45802e57i	0.758738	−	0.208964i
$593$	−3.29525e58			−1.92194			−0.960969	−	0.276656i	$-0.910774\pi$
$593$	−3.29525e58			−1.92194			−0.960969	+	0.276656i	$0.910774\pi$
$594$	−1.20036e58	−	1.04901e58i	−0.675767	−	0.590558i
$595$		−	2.97181e58i		−	1.61497i
$596$	9.24691e56	+	6.84003e57i	0.0485093	+	0.358828i
$597$	2.02425e58			1.02519
$598$	−1.68364e58	+	1.92656e58i	−0.823235	+	0.942015i
$599$		−	5.10173e57i		−	0.240854i	−0.992722	−	0.120427i	$-0.961574\pi$
$599$		−	5.10173e57i		−	0.240854i	0.992722	−	0.120427i	$-0.0384264\pi$
$600$	−3.29824e57	−	2.17904e57i	−0.150351	−	0.0993321i
$601$	1.55884e58			0.686178			0.343089	−	0.939303i	$-0.388527\pi$
$601$	1.55884e58			0.686178			0.343089	+	0.939303i	$0.388527\pi$
$602$	9.10354e57	+	7.95566e57i	0.386976	+	0.338182i
$603$		−	2.63941e57i		−	0.108354i
$604$	2.29820e58	−	3.10690e57i	0.911198	−	0.123183i
$605$	8.51179e57			0.325955
$606$	−1.03981e58	+	1.18984e58i	−0.384617	+	0.440111i
$607$		−	2.55219e58i		−	0.911905i	−0.890004	−	0.455953i	$-0.849299\pi$
$607$		−	2.55219e58i		−	0.911905i	0.890004	−	0.455953i	$-0.150701\pi$
$608$	−1.33422e58	+	2.76583e58i	−0.460524	+	0.954662i
$609$	−8.66687e57			−0.289001
$610$	−4.54030e58	−	3.96781e58i	−1.46271	−	1.27827i
$611$			9.39428e58i			2.92414i
$612$	2.32557e57	+	1.72024e58i	0.0699438	+	0.517381i
$613$	5.28802e58			1.53682			0.768410	−	0.639958i	$-0.221048\pi$
$613$	5.28802e58			1.53682			0.768410	+	0.639958i	$0.221048\pi$
$614$	−3.98088e58	+	4.55526e58i	−1.11800	+	1.27932i
$615$			1.26236e58i			0.342614i
$616$	−2.36540e58	+	3.58032e58i	−0.620454	+	0.939132i
$617$	3.28812e58			0.833602			0.416801	−	0.908998i	$-0.363151\pi$
$617$	3.28812e58			0.833602			0.416801	+	0.908998i	$0.363151\pi$
$618$	3.29085e58	+	2.87590e58i	0.806398	+	0.704718i
$619$		−	5.81480e58i		−	1.37731i	−0.725090	−	0.688654i	$-0.758202\pi$
$619$		−	5.81480e58i		−	1.37731i	0.725090	−	0.688654i	$-0.241798\pi$
$620$	4.55915e58	−	6.16344e57i	1.04390	−	0.141123i
$621$	−3.09234e58			−0.684484
$622$	3.70874e58	−	4.24385e58i	0.793649	−	0.908160i
$623$			1.30580e58i			0.270165i
$624$	−1.85897e58	−	6.74983e58i	−0.371874	−	1.35026i
$625$	−6.14111e58			−1.18786
$626$	6.22292e57	+	5.43827e57i	0.116395	+	0.101718i
$627$			3.54515e58i			0.641234i
$628$	5.06366e56	+	3.74563e57i	0.00885751	+	0.0655198i
$629$	−5.02366e58			−0.849878
$630$	2.90759e58	−	3.32711e58i	0.475753	−	0.544396i
$631$			3.70156e58i			0.585825i	0.956139	+	0.292913i	$0.0946245\pi$
$631$			3.70156e58i			0.585825i	−0.956139	+	0.292913i	$0.905375\pi$
$632$	1.15720e58	+	7.64527e57i	0.177154	+	0.117040i
$633$	9.11326e58			1.34957
$634$	−5.05135e58	−	4.41441e58i	−0.723657	−	0.632410i
$635$		−	7.61925e58i		−	1.05600i
$636$	1.28199e58	−	1.73309e57i	0.171903	−	0.0232393i
$637$	−1.18369e59			−1.53571
$638$	1.32684e58	−	1.51828e58i	0.166565	−	0.190598i
$639$		−	5.54385e58i		−	0.673431i
$640$	2.94840e58	−	9.04556e58i	0.346582	−	1.06330i
$641$	−3.15478e58			−0.358881			−0.179440	−	0.983769i	$-0.557429\pi$
$641$	−3.15478e58			−0.358881			−0.179440	+	0.983769i	$0.557429\pi$
$642$	3.93836e57	+	3.44176e57i	0.0433590	+	0.0378918i
$643$		−	7.19598e57i		−	0.0766760i	−0.999265	−	0.0383380i	$-0.987794\pi$
$643$		−	7.19598e57i		−	0.0766760i	0.999265	−	0.0383380i	$-0.0122064\pi$
$644$	1.11516e58	+	8.24896e58i	0.115010	+	0.850739i
$645$	−3.09453e58			−0.308916
$646$	7.79475e58	−	8.91942e58i	0.753216	−	0.861894i
$647$			8.89244e58i			0.831823i	0.909405	+	0.415912i	$0.136537\pi$
$647$			8.89244e58i			0.831823i	−0.909405	+	0.415912i	$0.863463\pi$
$648$	1.72155e58	−	2.60577e58i	0.155899	−	0.235972i
$649$	−1.77682e58			−0.155777
$650$	4.33416e58	+	3.78766e58i	0.367896	+	0.321507i
$651$		−	1.10144e59i		−	0.905230i
$652$	−7.53481e57	+	1.01862e57i	−0.0599616	+	0.00810610i
$653$	1.50401e59			1.15898			0.579488	−	0.814981i	$-0.303253\pi$
$653$	1.50401e59			1.15898			0.579488	+	0.814981i	$0.303253\pi$
$654$	−1.52831e58	+	1.74882e58i	−0.114046	+	0.130501i
$655$			2.83444e59i			2.04833i
$656$	−5.87183e58	+	1.61716e58i	−0.410954	+	0.113181i
$657$	−5.69509e58			−0.386036
$658$	2.30136e59	+	2.01118e59i	1.51092	+	1.32040i
$659$		−	5.37852e58i		−	0.342034i	−0.985268	−	0.171017i	$-0.945295\pi$
$659$		−	5.37852e58i		−	0.342034i	0.985268	−	0.171017i	$-0.0547053\pi$
$660$	−1.47146e58	−	1.08845e59i	−0.0906411	−	0.670481i
$661$	9.15978e58			0.546581			0.273290	−	0.961932i	$-0.411888\pi$
$661$	9.15978e58			0.546581			0.273290	+	0.961932i	$0.411888\pi$
$662$	−4.16688e58	+	4.76809e58i	−0.240876	+	0.275630i
$663$			2.70063e59i			1.51245i
$664$	−2.55150e59	−	1.68569e59i	−1.38441	−	0.914637i
$665$	−3.01515e59			−1.58509
$666$	−5.62428e58	−	4.91510e58i	−0.286489	−	0.250365i
$667$		−	3.91136e58i		−	0.193057i
$668$	−1.32140e59	+	1.78638e58i	−0.632017	+	0.0854412i
$669$	1.47669e59			0.684448
$670$	3.67192e58	−	4.20172e58i	0.164939	−	0.188737i
$671$		−	3.35851e59i		−	1.46209i
$672$	−2.05151e59	−	9.89638e58i	−0.865605	−	0.417563i
$673$	−4.69261e58			−0.191910			−0.0959552	−	0.995386i	$-0.530591\pi$
$673$	−4.69261e58			−0.191910			−0.0959552	+	0.995386i	$0.530591\pi$
$674$	8.92958e57	+	7.80363e57i	0.0353975	+	0.0309342i
$675$			6.95680e58i			0.267319i
$676$	1.00606e59	+	7.44195e59i	0.374753	+	2.77208i
$677$	4.75164e59			1.71586			0.857929	−	0.513768i	$-0.171751\pi$
$677$	4.75164e59			1.71586			0.857929	+	0.513768i	$0.171751\pi$
$678$	−1.66342e58	+	1.90343e58i	−0.0582343	+	0.0666367i
$679$		−	5.74459e59i		−	1.94982i
$680$	−2.02297e59	+	3.06201e59i	−0.665737	+	1.00767i
$681$	5.87116e58			0.187342
$682$	1.92952e59	+	1.68623e59i	0.597006	+	0.521728i
$683$			2.38223e59i			0.714740i	0.933963	+	0.357370i	$0.116326\pi$
$683$			2.38223e59i			0.714740i	−0.933963	+	0.357370i	$0.883674\pi$
$684$	1.74533e59	−	2.35949e58i	0.507809	−	0.0686498i
$685$	1.02069e59			0.287998
$686$	6.81418e58	−	7.79736e58i	0.186469	−	0.213374i
$687$		−	2.55220e59i		−	0.677365i
$688$	−3.96429e58	−	1.43941e59i	−0.102049	−	0.370534i
$689$	−1.88366e59			−0.470326
$690$	−1.60431e59	−	1.40202e59i	−0.388559	−	0.339565i
$691$			4.10554e58i			0.0964565i	0.998836	+	0.0482282i	$0.0153575\pi$
$691$			4.10554e58i			0.0964565i	−0.998836	+	0.0482282i	$0.984643\pi$
$692$	−6.95742e58	−	5.14646e59i	−0.158570	−	1.17295i
$693$	2.46110e59			0.544165
$694$	1.82819e59	−	2.09198e59i	0.392169	−	0.448753i
$695$		−	7.90260e58i		−	0.164471i
$696$	8.92995e58	+	5.89973e58i	0.180325	+	0.119135i
$697$	2.34934e59			0.460318
$698$	−5.86204e59	−	5.12289e59i	−1.11451	−	0.973982i
$699$		−	1.87361e59i		−	0.345667i
$700$	1.85576e59	−	2.50877e58i	0.332248	−	0.0449161i
$701$	−3.63509e59			−0.631593			−0.315796	−	0.948827i	$-0.602272\pi$
$701$	−3.63509e59			−0.631593			−0.315796	+	0.948827i	$0.602272\pi$
$702$	−8.10769e59	+	9.27751e59i	−1.36715	+	1.56441i
$703$			5.09693e59i			0.834156i
$704$	4.87440e59	−	2.07882e59i	0.774275	−	0.330210i
$705$	−7.82291e59			−1.20614
$706$	2.44445e58	+	2.13623e58i	0.0365833	+	0.0319704i
$707$		−	7.48555e59i		−	1.08747i
$708$	−1.26352e58	−	9.34636e58i	−0.0178190	−	0.131809i
$709$	4.75727e59			0.651308			0.325654	−	0.945489i	$-0.394416\pi$
$709$	4.75727e59			0.651308			0.325654	+	0.945489i	$0.394416\pi$
$710$	7.71254e59	−	8.82534e59i	1.02511	−	1.17302i
$711$		−	7.95457e58i		−	0.102649i
$712$	8.88889e58	−	1.34544e59i	0.111370	−	0.168572i
$713$	4.97078e59			0.604707
$714$	6.61586e59	+	5.78165e59i	0.781490	+	0.682951i
$715$			1.59929e60i			1.83443i
$716$	2.94395e58	−	3.97987e57i	0.0327912	−	0.00443298i
$717$	1.70644e59			0.184582
$718$	−3.14029e59	+	3.59338e59i	−0.329880	+	0.377477i
$719$			4.79953e59i			0.489657i	0.969566	+	0.244829i	$0.0787317\pi$
$719$			4.79953e59i			0.489657i	−0.969566	+	0.244829i	$0.921268\pi$
$720$	−5.26068e59	+	1.44884e59i	−0.521266	+	0.143562i
$721$	−2.07035e60			−1.99252
$722$	−9.94488e58	−	8.69091e58i	−0.0929648	−	0.0812427i
$723$			4.16387e59i			0.378088i
$724$	−9.41280e58	−	6.96274e59i	−0.0830250	−	0.614144i
$725$	−8.79933e58			−0.0753966
$726$	−1.65597e59	+	1.89490e59i	−0.137843	+	0.157731i
$727$			1.68327e60i			1.36123i	0.732643	+	0.680613i	$0.238287\pi$
$727$			1.68327e60i			1.36123i	−0.732643	+	0.680613i	$0.761713\pi$
$728$	2.76720e60	+	1.82820e60i	2.17411	+	1.43636i
$729$	−1.18295e60			−0.903004
$730$	−9.06610e59	−	7.92294e59i	−0.672420	−	0.587633i
$731$			5.75915e59i			0.415043i
$732$	1.76663e60	−	2.38828e59i	1.23712	−	0.167245i
$733$	−6.39885e59			−0.435430			−0.217715	−	0.976012i	$-0.569860\pi$
$733$	−6.39885e59			−0.435430			−0.217715	+	0.976012i	$0.569860\pi$
$734$	−5.21960e59	+	5.97271e59i	−0.345159	+	0.394961i
$735$		−	9.85697e59i		−	0.633446i
$736$	4.46624e59	−	9.25847e59i	0.278938	−	0.578236i
$737$	3.10806e59			0.188657
$738$	2.63022e59	+	2.29857e59i	0.155170	+	0.135605i
$739$		−	1.71279e60i		−	0.982132i	−0.871122	−	0.491066i	$-0.836607\pi$
$739$		−	1.71279e60i		−	0.982132i	0.871122	−	0.491066i	$-0.163393\pi$
$740$	−2.11554e59	−	1.56489e60i	−0.117911	−	0.872201i
$741$	2.74002e60			1.48447
$742$	−4.03264e59	+	4.61449e59i	−0.212377	+	0.243020i
$743$		−	3.39513e60i		−	1.73816i	−0.494668	−	0.869082i	$-0.664710\pi$
$743$		−	3.39513e60i		−	1.73816i	0.494668	−	0.869082i	$-0.335290\pi$
$744$	−7.49773e59	+	1.13487e60i	−0.373162	+	0.564826i
$745$	8.36916e59			0.404949
$746$	−2.34572e60	−	2.04994e60i	−1.10347	−	0.964332i
$747$			1.75389e60i			0.802177i
$748$	−2.02569e60	+	2.73849e59i	−0.900821	+	0.121780i
$749$	−2.47771e59			−0.107135
$750$	9.42572e59	−	1.07857e60i	0.396303	−	0.453484i
$751$			6.43064e59i			0.262915i	0.991322	+	0.131458i	$0.0419657\pi$
$751$			6.43064e59i			0.262915i	−0.991322	+	0.131458i	$0.958034\pi$
$752$	−1.00216e60	−	3.63881e60i	−0.398441	−	1.44672i
$753$	−5.09743e59			−0.197086
$754$	−1.17347e60	−	1.02550e60i	−0.441238	−	0.385602i
$755$		−	2.81198e60i		−	1.02832i
$756$	5.37015e59	+	3.97235e60i	0.190998	+	1.41283i
$757$	1.59596e60			0.552088			0.276044	−	0.961145i	$-0.410977\pi$
$757$	1.59596e60			0.552088			0.276044	+	0.961145i	$0.410977\pi$
$758$	−1.32150e60	+	1.51218e60i	−0.444647	+	0.508802i
$759$		−	1.18672e60i		−	0.388394i
$760$	3.10668e60	+	2.05248e60i	0.989032	+	0.653421i
$761$	3.03237e60			0.939083			0.469541	−	0.882910i	$-0.344419\pi$
$761$	3.03237e60			0.939083			0.469541	+	0.882910i	$0.344419\pi$
$762$	1.69620e60	+	1.48233e60i	0.511003	+	0.446570i
$763$		−	1.10023e60i		−	0.322453i
$764$	−5.66917e60	+	7.66405e59i	−1.61644	+	0.218523i
$765$	2.10482e60			0.583881
$766$	1.48827e60	−	1.70300e60i	0.401677	−	0.459633i
$767$			1.37329e60i			0.360628i
$768$	1.44012e60	+	2.41619e60i	0.367970	+	0.617370i
$769$	−7.39821e60			−1.83939			−0.919694	−	0.392636i	$-0.871563\pi$
$769$	−7.39821e60			−1.83939			−0.919694	+	0.392636i	$0.871563\pi$
$770$	3.91786e60	+	3.42385e60i	0.947859	+	0.828342i
$771$			3.74470e60i			0.881607i
$772$	−5.17342e59	−	3.82683e60i	−0.118526	−	0.876750i
$773$	5.30130e60			1.18199			0.590993	−	0.806676i	$-0.298736\pi$
$773$	5.30130e60			1.18199			0.590993	+	0.806676i	$0.298736\pi$
$774$	−5.63469e59	+	6.44769e59i	−0.122267	+	0.139909i
$775$		−	1.11827e60i		−	0.236163i
$776$	−3.91047e60	+	5.91897e60i	−0.803772	+	1.21661i
$777$	−3.78058e60			−0.756340
$778$	4.81521e60	+	4.20805e60i	0.937656	+	0.819425i
$779$		−	2.38361e60i		−	0.451802i
$780$	−8.41255e60	+	1.13728e60i	−1.55218	+	0.209836i
$781$	6.52820e60			1.17252
$782$	−2.60926e60	+	2.98573e60i	−0.456221	+	0.522047i
$783$		−	1.88354e60i		−	0.320611i
$784$	4.58495e60	−	1.26274e60i	0.759796	−	0.209255i
$785$	4.58300e59			0.0739413
$786$	−6.31005e60	−	5.51441e60i	−0.991196	−	0.866214i
$787$			6.74513e60i			1.03162i	0.856702	+	0.515811i	$0.172509\pi$
$787$			6.74513e60i			1.03162i	−0.856702	+	0.515811i	$0.827491\pi$
$788$	−1.75343e60	−	1.29703e61i	−0.261119	−	1.93152i
$789$	3.68745e60			0.534699
$790$	1.10663e60	−	1.26630e60i	0.156255	−	0.178800i
$791$		−	1.19749e60i		−	0.164652i
$792$	−2.53580e60	−	1.67532e60i	−0.339537	−	0.224321i
$793$	−2.59577e61			−3.38477
$794$	9.56364e60	+	8.35775e60i	1.21449	+	1.06135i
$795$		−	1.56858e60i		−	0.193998i
$796$	1.17352e61	−	1.58646e60i	1.41356	−	0.191097i
$797$	6.46199e60			0.758126			0.379063	−	0.925371i	$-0.376246\pi$
$797$	6.46199e60			0.758126			0.379063	+	0.925371i	$0.376246\pi$
$798$	5.86598e60	−	6.71235e60i	0.670316	−	0.767033i
$799$			1.45590e61i			1.62050i
$800$	−2.08287e60	−	1.00476e60i	−0.225825	−	0.108937i
$801$	−9.24851e59			−0.0976763
$802$	−3.13036e60	−	2.73565e60i	−0.322057	−	0.281448i
$803$		−	6.70629e60i		−	0.672134i
$804$	2.21018e59	+	1.63489e60i	0.0215800	+	0.159629i
$805$	1.00931e61			0.960086
$806$	1.30327e61	−	1.49131e61i	1.20781	−	1.38208i
$807$			3.45828e60i			0.312260i
$808$	−5.09557e60	+	7.71277e60i	−0.448285	+	0.678534i
$809$	−1.09013e61			−0.934455			−0.467227	−	0.884137i	$-0.654747\pi$
$809$	−1.09013e61			−0.934455			−0.467227	+	0.884137i	$0.654747\pi$
$810$	−2.85143e60	−	2.49189e60i	−0.238165	−	0.208134i
$811$			7.79618e59i			0.0634518i	0.999497	+	0.0317259i	$0.0101004\pi$
$811$			7.79618e59i			0.0634518i	−0.999497	+	0.0317259i	$0.989900\pi$
$812$	−5.02444e60	+	6.79246e59i	−0.398484	+	0.0538704i
$813$	4.01970e60			0.310665
$814$	5.78781e60	−	6.62291e60i	0.435915	−	0.498811i
$815$			9.21928e59i			0.0676686i
$816$	−2.88098e60	−	1.04607e61i	−0.206085	−	0.748286i
$817$	5.84315e60			0.407365
$818$	3.01337e60	+	2.63341e60i	0.204754	+	0.178936i
$819$		−	1.90216e61i		−	1.25975i
$820$	9.89344e59	+	7.31827e60i	0.0638641	+	0.472408i
$821$	−2.21652e61			−1.39465			−0.697326	−	0.716754i	$-0.745627\pi$
$821$	−2.21652e61			−1.39465			−0.697326	+	0.716754i	$0.745627\pi$
$822$	−1.98575e60	+	2.27226e60i	−0.121791	+	0.139364i
$823$			6.02862e59i			0.0360430i	0.999838	+	0.0180215i	$0.00573674\pi$
$823$			6.02862e59i			0.0360430i	−0.999838	+	0.0180215i	$0.994263\pi$
$824$	2.13319e61	+	1.40933e61i	1.24325	+	0.821376i
$825$	−2.66976e60			−0.151684
$826$	3.36420e60	+	2.94001e60i	0.186338	+	0.162842i
$827$			1.02519e60i			0.0553589i	0.999617	+	0.0276794i	$0.00881176\pi$
$827$			1.02519e60i			0.0553589i	−0.999617	+	0.0276794i	$0.991188\pi$
$828$	−5.84243e60	+	7.89827e59i	−0.307579	+	0.0415810i
$829$	1.03234e61			0.529880			0.264940	−	0.964265i	$-0.414648\pi$
$829$	1.03234e61			0.529880			0.264940	+	0.964265i	$0.414648\pi$
$830$	−2.43999e61	+	2.79205e61i	−1.22109	+	1.39728i
$831$		−	9.77929e60i		−	0.477184i
$832$	−1.60670e61	−	3.76739e61i	−0.764444	−	1.79246i
$833$	−1.83445e61			−0.851063
$834$	1.75928e60	+	1.53745e60i	0.0795882	+	0.0695528i
$835$			1.61681e61i			0.713251i
$836$	2.77843e60	+	2.05523e61i	0.119528	+	0.884156i
$837$	2.39372e61			1.00424
$838$	−1.00346e60	+	1.14824e60i	−0.0410559	+	0.0469796i
$839$			4.48263e61i			1.78868i	0.447392	+	0.894338i	$0.352353\pi$
$839$			4.48263e61i			1.78868i	−0.447392	+	0.894338i	$0.647647\pi$
$840$	−1.52240e61	+	2.30433e61i	−0.592466	+	0.896769i
$841$	−2.39637e61			−0.909573
$842$	−3.28274e61	−	2.86881e61i	−1.21530	−	1.06206i
$843$		−	7.04317e60i		−	0.254325i
$844$	5.28323e61	−	7.14231e60i	1.86084	−	0.251563i
$845$	9.10565e61			3.12839
$846$	−1.42444e61	+	1.62997e61i	−0.477383	+	0.546262i
$847$		−	1.19213e61i		−	0.389736i
$848$	7.29623e60	−	2.00945e60i	0.232694	−	0.0640863i
$849$	3.50178e61			1.08950
$850$	6.71697e60	+	5.87002e60i	0.203881	+	0.178173i
$851$		−	1.70617e61i		−	0.505246i
$852$	4.64229e60	+	3.43394e61i	0.134122	+	0.992114i
$853$	−1.74705e61			−0.492467			−0.246233	−	0.969211i	$-0.579193\pi$
$853$	−1.74705e61			−0.492467			−0.246233	+	0.969211i	$0.579193\pi$
$854$	−5.55715e61	+	6.35896e61i	−1.52840	+	1.74892i
$855$		−	2.13552e61i		−	0.573079i
$856$	2.55292e60	+	1.68663e60i	0.0668481	+	0.0441643i
$857$	−3.89100e61			−0.994177			−0.497088	−	0.867700i	$-0.665598\pi$
$857$	−3.89100e61			−0.994177			−0.497088	+	0.867700i	$0.665598\pi$
$858$	−3.56036e61	−	3.11143e61i	−0.887689	−	0.775759i
$859$		−	2.54821e61i		−	0.619982i	−0.950739	−	0.309991i	$-0.899674\pi$
$859$		−	2.54821e61i		−	0.619982i	0.950739	−	0.309991i	$-0.100326\pi$
$860$	−1.79399e61	+	2.42527e60i	−0.425944	+	0.0575827i
$861$	1.76801e61			0.409655
$862$	3.04327e61	−	3.48237e61i	0.688157	−	0.787448i
$863$		−	7.90313e61i		−	1.74410i	−0.489413	−	0.872052i	$-0.662789\pi$
$863$		−	7.90313e61i		−	1.74410i	0.489413	−	0.872052i	$-0.337211\pi$
$864$	2.15075e61	−	4.45849e61i	0.463235	−	0.960283i
$865$	−6.29699e61			−1.32372
$866$	1.04606e61	+	9.14158e60i	0.214625	+	0.187562i
$867$			5.96512e60i			0.119459i
$868$	−8.63226e60	−	6.38536e61i	−0.168737	−	1.24816i
$869$	9.36697e60			0.178724
$870$	8.53969e60	−	9.77184e60i	0.159052	−	0.182000i
$871$		−	2.40220e61i		−	0.436744i
$872$	−7.48949e60	+	1.13362e61i	−0.132925	+	0.201198i
$873$	4.06868e61			0.704943
$874$	3.02928e61	+	2.64731e61i	0.512389	+	0.447781i
$875$			6.78554e61i			1.12051i
$876$	3.52762e61	−	4.76893e60i	0.568716	−	0.0768838i
$877$	−3.55428e61			−0.559449			−0.279725	−	0.960080i	$-0.590243\pi$
$877$	−3.55428e61			−0.559449			−0.279725	+	0.960080i	$0.590243\pi$
$878$	3.64148e61	−	4.16689e61i	0.559619	−	0.640364i
$879$		−	3.38318e61i		−	0.507643i
$880$	−1.70610e61	−	6.19475e61i	−0.249958	−	0.907586i
$881$	−7.63111e60			−0.109168			−0.0545838	−	0.998509i	$-0.517383\pi$
$881$	−7.63111e60			−0.109168			−0.0545838	+	0.998509i	$0.517383\pi$
$882$	−2.05378e61	−	1.79481e61i	−0.286888	−	0.250714i
$883$			1.26270e62i			1.72236i	0.508298	+	0.861181i	$0.330275\pi$
$883$			1.26270e62i			1.72236i	−0.508298	+	0.861181i	$0.669725\pi$
$884$	2.11656e61	+	1.56564e62i	0.281924	+	2.08542i
$885$	−1.14358e61			−0.148750
$886$	1.18827e61	−	1.35972e61i	0.150941	−	0.172719i
$887$			1.06440e62i			1.32041i	0.751085	+	0.660206i	$0.229531\pi$
$887$			1.06440e62i			1.32041i	−0.751085	+	0.660206i	$0.770469\pi$
$888$	3.89534e61	+	2.57352e61i	0.471925	+	0.311785i
$889$	−1.06712e62			−1.26263
$890$	−1.47229e61	−	1.28664e61i	−0.170138	−	0.148685i
$891$		−	2.10924e61i		−	0.238064i
$892$	8.56080e61	−	1.15732e61i	0.943740	−	0.127583i
$893$	1.47714e62			1.59052
$894$	−1.62822e61	+	1.86315e61i	−0.171248	+	0.195957i
$895$		−	3.60209e60i		−	0.0370059i
$896$	−1.26688e62	−	4.12940e61i	−1.27136	−	0.414400i
$897$	−9.17209e61			−0.899140
$898$	−3.57921e61	−	3.12790e61i	−0.342755	−	0.299537i
$899$			3.02771e61i			0.283244i
$900$	1.77687e60	+	1.31436e61i	0.0162391	+	0.120122i
$901$	−2.91925e61			−0.260646
$902$	−2.70670e61	+	3.09724e61i	−0.236104	+	0.270170i
$903$			4.33407e61i			0.369363i
$904$	−8.15159e60	+	1.23384e61i	−0.0678743	+	0.102736i
$905$	−8.51931e61			−0.693081
$906$	6.26006e61	+	5.47071e61i	0.497606	+	0.434862i
$907$			1.94296e62i			1.50908i	0.656256	+	0.754538i	$0.272139\pi$
$907$			1.94296e62i			1.50908i	−0.656256	+	0.754538i	$0.727861\pi$
$908$	3.40369e61	−	4.60138e60i	0.258313	−	0.0349209i
$909$	5.30173e61			0.393166
$910$	2.64627e62	−	3.02808e62i	1.91763	−	2.19431i
$911$			3.70463e60i			0.0262337i	0.999914	+	0.0131168i	$0.00417534\pi$
$911$			3.70463e60i			0.0262337i	−0.999914	+	0.0131168i	$0.995825\pi$
$912$	−1.06133e62	+	2.92300e61i	−0.734443	+	0.202273i
$913$	−2.06531e62			−1.39668
$914$	1.61241e62	+	1.40910e62i	1.06563	+	0.931263i
$915$		−	2.16158e62i		−	1.39614i
$916$	−2.00023e61	−	1.47958e62i	−0.126262	−	0.933974i
$917$	3.96980e62			2.44914
$918$	−1.25651e62	+	1.43780e62i	−0.757651	+	0.866968i
$919$		−	6.62041e61i		−	0.390175i	−0.980786	−	0.195087i	$-0.937501\pi$
$919$		−	6.62041e61i		−	0.390175i	0.980786	−	0.195087i	$-0.0624990\pi$
$920$	−1.03995e62	−	6.87058e61i	−0.599054	−	0.395776i
$921$	−2.16870e62			−1.22109
$922$	1.46082e61	+	1.27662e61i	0.0803984	+	0.0702608i
$923$		−	5.04560e62i		−	2.71442i
$924$	−1.52444e62	+	2.06086e61i	−0.801676	+	0.108377i
$925$	−3.83836e61			−0.197319
$926$	−2.02915e62	+	2.32193e62i	−1.01973	+	1.16686i
$927$		−	1.46635e62i		−	0.720382i
$928$	5.63934e61	+	2.72038e61i	0.270845	+	0.130654i
$929$	6.43967e61			0.302366			0.151183	−	0.988506i	$-0.451692\pi$
$929$	6.43967e61			0.302366			0.151183	+	0.988506i	$0.451692\pi$
$930$	1.24186e62	+	1.08528e62i	0.570075	+	0.498193i
$931$			1.86121e62i			0.835319i
$932$	−1.46840e61	−	1.08619e62i	−0.0644331	−	0.476617i
$933$	2.02044e62			0.866825
$934$	2.14754e62	−	2.45740e62i	0.900859	−	1.03084i
$935$			2.47854e62i			1.01661i
$936$	−1.29484e62	+	1.95990e62i	−0.519307	+	0.786034i
$937$	4.19397e62			1.64473			0.822364	−	0.568962i	$-0.192655\pi$
$937$	4.19397e62			1.64473			0.822364	+	0.568962i	$0.192655\pi$
$938$	−5.88477e61	−	5.14275e61i	−0.225668	−	0.197213i
$939$			2.96265e61i			0.111097i
$940$	−4.53518e62	+	6.13103e61i	−1.66307	+	0.224827i
$941$	1.00265e62			0.359555			0.179778	−	0.983707i	$-0.442462\pi$
$941$	1.00265e62			0.359555			0.179778	+	0.983707i	$0.442462\pi$
$942$	−8.91623e60	+	1.02027e61i	−0.0312689	+	0.0357805i
$943$			7.97901e61i			0.273655i
$944$	−1.46500e61	−	5.31934e61i	−0.0491389	−	0.178421i
$945$	4.86040e62			1.59443
$946$	−7.59253e61	−	6.63518e61i	−0.243597	−	0.212882i
$947$		−	4.46412e62i		−	1.40083i	−0.713734	−	0.700417i	$-0.752997\pi$
$947$		−	4.46412e62i		−	1.40083i	0.713734	−	0.700417i	$-0.247003\pi$
$948$	6.66097e60	+	4.92718e61i	0.0204438	+	0.151225i
$949$	−5.18324e62			−1.55600
$950$	5.95563e61	−	6.81494e61i	0.174877	−	0.200109i
$951$		−	2.40488e62i		−	0.690720i
$952$	4.28853e62	+	2.83329e62i	1.20485	+	0.796005i
$953$	−6.33284e62			−1.74039			−0.870197	−	0.492704i	$-0.836008\pi$
$953$	−6.33284e62			−1.74039			−0.870197	+	0.492704i	$0.836008\pi$
$954$	−3.26826e61	−	2.85616e61i	−0.0878620	−	0.0767834i
$955$			6.93655e62i			1.82420i
$956$	9.89275e61	−	1.33738e61i	0.254508	−	0.0344065i
$957$	7.22834e61			0.181923
$958$	−3.27429e62	+	3.74672e62i	−0.806197	+	0.922519i
$959$		−	1.42953e62i		−	0.344352i
$960$	3.13722e62	−	1.33795e62i	0.739348	−	0.315315i
$961$	4.89228e61			0.112803
$962$	−5.11879e62	−	4.47336e62i	−1.15476	−	1.00915i
$963$		−	1.75487e61i		−	0.0387341i
$964$	3.26334e61	+	2.41392e62i	0.0704766	+	0.521322i
$965$	−4.68235e62			−0.989441
$966$	−1.96361e62	+	2.24693e62i	−0.406009	+	0.464590i
$967$			5.23915e62i			1.06000i	0.847998	+	0.529999i	$0.177808\pi$
$967$			5.23915e62i			1.06000i	−0.847998	+	0.529999i	$0.822192\pi$
$968$	−8.11507e61	+	1.22831e62i	−0.160661	+	0.243180i
$969$	4.24641e62			0.822665
$970$	6.47699e62	+	5.66030e62i	1.22791	+	1.07308i
$971$		−	4.94294e61i		−	0.0917026i	−0.998948	−	0.0458513i	$-0.985400\pi$
$971$		−	4.94294e61i		−	0.0917026i	0.998948	−	0.0458513i	$-0.0146000\pi$
$972$	−4.71003e62	+	6.36741e61i	−0.855130	+	0.115604i
$973$	−1.10681e62			−0.196654
$974$	3.15966e62	−	3.61555e62i	0.549417	−	0.628690i
$975$			2.06344e62i			0.351151i
$976$	1.00545e63	−	2.76911e62i	1.67462	−	0.461206i
$977$	5.52585e62			0.900769			0.450384	−	0.892835i	$-0.351287\pi$
$977$	5.52585e62			0.900769			0.450384	+	0.892835i	$0.351287\pi$
$978$	−2.05240e61	−	1.79361e61i	−0.0327451	−	0.0286162i
$979$		−	1.08907e62i		−	0.170066i
$980$	−7.72517e61	−	5.71438e62i	−0.118076	−	0.873417i
$981$	7.79249e61			0.116581
$982$	3.99824e62	−	4.57512e62i	0.585501	−	0.669979i
$983$		−	6.10031e62i		−	0.874436i	−0.899355	−	0.437218i	$-0.855964\pi$
$983$		−	6.10031e62i		−	0.874436i	0.899355	−	0.437218i	$-0.144036\pi$
$984$	−1.82168e62	−	1.20352e62i	−0.255608	−	0.168872i
$985$	−1.58699e63			−2.17978
$986$	−1.81861e62	−	1.58930e62i	−0.244526	−	0.213693i
$987$			1.09565e63i			1.44215i
$988$	1.58847e63	−	2.14743e62i	2.04684	−	0.276709i
$989$	−1.95597e62			−0.246740
$990$	−2.42498e62	+	2.77487e62i	−0.299481	+	0.342692i
$991$			8.93543e62i			1.08036i	0.841549	+	0.540181i	$0.181644\pi$
$991$			8.93543e62i			1.08036i	−0.841549	+	0.540181i	$0.818356\pi$
$992$	−3.45723e62	+	7.16681e62i	−0.409244	+	0.848361i
$993$	−2.27002e62			−0.263085
$994$	−1.23604e63	−	1.08019e63i	−1.40255	−	1.22570i
$995$		−	1.43587e63i		−	1.59525i
$996$	−1.46867e62	−	1.08639e63i	−0.159763	−	1.18178i
$997$	−8.66565e62			−0.923003			−0.461501	−	0.887140i	$-0.652689\pi$
$997$	−8.66565e62			−0.923003			−0.461501	+	0.887140i	$0.652689\pi$
$998$	6.02237e62	−	6.89131e62i	0.628096	−	0.718721i
$999$		−	8.21622e62i		−	0.839067i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.43.b.a.3.16	yes	20
4.3	odd	2	inner	4.43.b.a.3.15	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.43.b.a.3.15	✓	20	4.3	odd	2	inner
4.43.b.a.3.16	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)

\(f(q)\)	\(=\)	\(q+(1.57912e6 + 1.38001e6i) q^{2} +7.51798e9i q^{3} +(5.89205e11 + 4.35840e12i) q^{4} +5.33275e14 q^{5} +(-1.03749e16 + 1.18718e16i) q^{6} -7.46884e17i q^{7} +(-5.08420e18 + 7.69555e18i) q^{8} +5.28989e19 q^{9} +O(q^{10})\)	\(q+(1.57912e6 + 1.38001e6i) q^{2} +7.51798e9i q^{3} +(5.89205e11 + 4.35840e12i) q^{4} +5.33275e14 q^{5} +(-1.03749e16 + 1.18718e16i) q^{6} -7.46884e17i q^{7} +(-5.08420e18 + 7.69555e18i) q^{8} +5.28989e19 q^{9} +(8.42107e20 + 7.35924e20i) q^{10} +6.22915e21i q^{11} +(-3.27664e22 + 4.42963e21i) q^{12} +4.81446e23 q^{13} +(1.03071e24 - 1.17942e24i) q^{14} +4.00915e24i q^{15} +(-1.86485e25 + 5.13598e24i) q^{16} +7.46133e25 q^{17} +(8.35338e25 + 7.30009e25i) q^{18} -7.57016e26i q^{19} +(3.14208e26 + 2.32423e27i) q^{20} +5.61506e27 q^{21} +(-8.59628e27 + 9.83659e27i) q^{22} +2.53407e28i q^{23} +(-5.78550e28 - 3.82229e28i) q^{24} +5.70088e28 q^{25} +(7.60262e29 + 6.64400e29i) q^{26} +1.22030e30i q^{27} +(3.25522e30 - 4.40067e29i) q^{28} -1.54350e30 q^{29} +(-5.53266e30 + 6.33094e30i) q^{30} -1.96158e31i q^{31} +(-3.65359e31 - 1.76247e31i) q^{32} -4.68307e31 q^{33} +(1.17823e32 + 1.02967e32i) q^{34} -3.98295e32i q^{35} +(3.11683e31 + 2.30555e32i) q^{36} -6.73293e32 q^{37} +(1.04469e33 - 1.19542e33i) q^{38} +3.61950e33i q^{39} +(-2.71128e33 + 4.10385e33i) q^{40} +3.14869e33 q^{41} +(8.86686e33 + 7.74882e33i) q^{42} +7.71866e33i q^{43} +(-2.71491e34 + 3.67024e33i) q^{44} +2.82097e34 q^{45} +(-3.49704e34 + 4.00161e34i) q^{46} +1.95126e35i q^{47} +(-3.86122e34 - 1.40199e35i) q^{48} -2.45862e35 q^{49} +(9.00238e34 + 7.86726e34i) q^{50} +5.60941e35i q^{51} +(2.83670e35 + 2.09834e36i) q^{52} -3.91250e35 q^{53} +(-1.68403e36 + 1.92701e36i) q^{54} +3.32185e36i q^{55} +(5.74768e36 + 3.79731e36i) q^{56} +5.69123e36 q^{57} +(-2.43738e36 - 2.13005e36i) q^{58} +2.85242e36i q^{59} +(-1.74735e37 + 2.36221e36i) q^{60} -5.39160e37 q^{61} +(2.70699e37 - 3.09757e37i) q^{62} -3.95093e37i q^{63} +(-3.33724e37 - 7.82514e37i) q^{64} +2.56743e38 q^{65} +(-7.39513e37 - 6.46267e37i) q^{66} -4.98954e37i q^{67} +(4.39625e37 + 3.25195e38i) q^{68} -1.90511e38 q^{69} +(5.49649e38 - 6.28956e38i) q^{70} -1.04801e39i q^{71} +(-2.68949e38 + 4.07086e38i) q^{72} -1.07660e39 q^{73} +(-1.06321e39 - 9.29150e38i) q^{74} +4.28591e38i q^{75} +(3.29938e39 - 4.46037e38i) q^{76} +4.65245e39 q^{77} +(-4.99494e39 + 5.71564e39i) q^{78} -1.50373e39i q^{79} +(-9.94478e39 + 2.73889e39i) q^{80} -3.38607e39 q^{81} +(4.97217e39 + 4.34522e39i) q^{82} +3.31555e40i q^{83} +(3.30842e39 + 2.44727e40i) q^{84} +3.97894e40 q^{85} +(-1.06518e40 + 1.21887e40i) q^{86} -1.16040e40i q^{87} +(-4.79368e40 - 3.16703e40i) q^{88} -1.74834e40 q^{89} +(4.45465e40 + 3.89296e40i) q^{90} -3.59584e41i q^{91} +(-1.10445e41 + 1.49309e40i) q^{92} +1.47471e41 q^{93} +(-2.69276e41 + 3.08128e41i) q^{94} -4.03698e41i q^{95} +(1.32502e41 - 2.74676e41i) q^{96} +7.69142e41 q^{97} +(-3.88245e41 - 3.39291e41i) q^{98} +3.29515e41i 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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