LMFDB - Embedded newform 4.43.b.a.3.18

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			3.18
Root			$0.500000 + 1.16651e9i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.43.b.a.3.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70189e6 + 1.22541e6i) q^{2} -1.86642e10i q^{3} +(1.39480e12 + 4.17101e12i) q^{4} +4.71964e14 q^{5} +(2.28712e16 - 3.17644e16i) q^{6} +6.63278e17i q^{7} +(-2.73739e18 + 8.80780e18i) q^{8} -2.38933e20 q^{9} +O(q^{10})$	\(q+(1.70189e6 + 1.22541e6i) q^{2} -1.86642e10i q^{3} +(1.39480e12 + 4.17101e12i) q^{4} +4.71964e14 q^{5} +(2.28712e16 - 3.17644e16i) q^{6} +6.63278e17i q^{7} +(-2.73739e18 + 8.80780e18i) q^{8} -2.38933e20 q^{9} +(8.03231e20 + 5.78348e20i) q^{10} +9.22168e21i q^{11} +(7.78486e22 - 2.60329e22i) q^{12} -1.95221e23 q^{13} +(-8.12785e23 + 1.12883e24i) q^{14} -8.80883e24i q^{15} +(-1.54519e25 + 1.16355e25i) q^{16} -1.12157e26 q^{17} +(-4.06637e26 - 2.92790e26i) q^{18} -4.52385e25i q^{19} +(6.58297e26 + 1.96857e27i) q^{20} +1.23795e28 q^{21} +(-1.13003e28 + 1.56943e28i) q^{22} +2.77301e28i q^{23} +(1.64390e29 + 5.10911e28i) q^{24} -4.62328e27 q^{25} +(-3.32245e29 - 2.39225e29i) q^{26} +2.41727e30i q^{27} +(-2.76654e30 + 9.25142e29i) q^{28} +1.47725e30 q^{29} +(1.07944e31 - 1.49917e31i) q^{30} +1.58291e31i q^{31} +(-4.05555e31 + 8.67457e29i) q^{32} +1.72115e32 q^{33} +(-1.90878e32 - 1.37438e32i) q^{34} +3.13044e32i q^{35} +(-3.33264e32 - 9.96592e32i) q^{36} -5.75921e32 q^{37} +(5.54356e31 - 7.69909e31i) q^{38} +3.64365e33i q^{39} +(-1.29195e33 + 4.15697e33i) q^{40} +8.30103e33 q^{41} +(2.10686e34 + 1.51700e34i) q^{42} -9.98962e32i q^{43} +(-3.84637e34 + 1.28624e34i) q^{44} -1.12768e35 q^{45} +(-3.39807e34 + 4.71935e34i) q^{46} -1.65183e35i q^{47} +(2.17167e35 + 2.88397e35i) q^{48} -1.27964e35 q^{49} +(-7.86831e33 - 5.66540e33i) q^{50} +2.09332e36i q^{51} +(-2.72295e35 - 8.14270e35i) q^{52} +1.24931e36 q^{53} +(-2.96214e36 + 4.11393e36i) q^{54} +4.35230e36i q^{55} +(-5.84202e36 - 1.81565e36i) q^{56} -8.44340e35 q^{57} +(2.51411e36 + 1.81023e36i) q^{58} +1.26149e37i q^{59} +(3.67417e37 - 1.22866e37i) q^{60} -7.25751e36 q^{61} +(-1.93971e37 + 2.69394e37i) q^{62} -1.58479e38i q^{63} +(-7.00840e37 - 4.82207e37i) q^{64} -9.21374e37 q^{65} +(2.92921e38 + 2.10911e38i) q^{66} -1.18317e38i q^{67} +(-1.56437e38 - 4.67807e38i) q^{68} +5.17560e38 q^{69} +(-3.83606e38 + 5.32765e38i) q^{70} +5.09944e38i q^{71} +(6.54052e38 - 2.10447e39i) q^{72} +1.45038e39 q^{73} +(-9.80154e38 - 7.05738e38i) q^{74} +8.62899e37i q^{75} +(1.88690e38 - 6.30988e37i) q^{76} -6.11653e39 q^{77} +(-4.46495e39 + 6.20108e39i) q^{78} -6.50257e39i q^{79} +(-7.29273e39 + 5.49153e39i) q^{80} +1.89726e40 q^{81} +(1.41274e40 + 1.01721e40i) q^{82} +2.20429e40i q^{83} +(1.72670e40 + 5.16352e40i) q^{84} -5.29340e40 q^{85} +(1.22414e39 - 1.70012e39i) q^{86} -2.75716e40i q^{87} +(-8.12227e40 - 2.52433e40i) q^{88} +1.68386e41 q^{89} +(-1.91918e41 - 1.38187e41i) q^{90} -1.29486e41i q^{91} +(-1.15663e41 + 3.86780e40i) q^{92} +2.95437e41 q^{93} +(2.02417e41 - 2.81123e41i) q^{94} -2.13510e40i q^{95} +(1.61904e40 + 7.56936e41i) q^{96} +7.67811e41 q^{97} +(-2.17781e41 - 1.56808e41i) q^{98} -2.20336e42i 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 $

$2$	1.70189e6	+	1.22541e6i	0.811524	+	0.584320i
$2$	1.70189e6	+	1.22541e6i	0.811524	+	0.584320i
$3$		−	1.86642e10i		−	1.78428i	−0.451760	−	0.892140i	$-0.649204\pi$
$3$		−	1.86642e10i		−	1.78428i	0.451760	−	0.892140i	$-0.350796\pi$
$4$	1.39480e12	+	4.17101e12i	0.317141	+	0.948378i
$5$	4.71964e14			0.989781			0.494891	−	0.868955i	$-0.335208\pi$
$5$	4.71964e14			0.989781			0.494891	+	0.868955i	$0.335208\pi$
$6$	2.28712e16	−	3.17644e16i	1.04259	−	1.44798i
$7$			6.63278e17i			1.18751i	0.804646	+	0.593754i	$0.202355\pi$
$7$			6.63278e17i			1.18751i	−0.804646	+	0.593754i	$0.797645\pi$
$8$	−2.73739e18	+	8.80780e18i	−0.296788	+	0.954943i
$9$	−2.38933e20			−2.18365
$10$	8.03231e20	+	5.78348e20i	0.803231	+	0.578348i
$11$			9.22168e21i			1.24613i	0.782170	+	0.623065i	$0.214113\pi$
$11$			9.22168e21i			1.24613i	−0.782170	+	0.623065i	$0.785887\pi$
$12$	7.78486e22	−	2.60329e22i	1.69217	−	0.565869i
$13$	−1.95221e23			−0.790163			−0.395081	−	0.918646i	$-0.629284\pi$
$13$	−1.95221e23			−0.790163			−0.395081	+	0.918646i	$0.629284\pi$
$14$	−8.12785e23	+	1.12883e24i	−0.693884	+	0.963691i
$15$		−	8.80883e24i		−	1.76605i
$16$	−1.54519e25	+	1.16355e25i	−0.798843	+	0.601540i
$17$	−1.12157e26			−1.62330			−0.811649	−	0.584146i	$-0.801430\pi$
$17$	−1.12157e26			−1.62330			−0.811649	+	0.584146i	$0.801430\pi$
$18$	−4.06637e26	−	2.92790e26i	−1.77209	−	1.27595i
$19$		−	4.52385e25i		−	0.0633407i	−0.999498	−	0.0316703i	$-0.989917\pi$
$19$		−	4.52385e25i		−	0.0633407i	0.999498	−	0.0316703i	$-0.0100827\pi$
$20$	6.58297e26	+	1.96857e27i	0.313901	+	0.938687i
$21$	1.23795e28			2.11885
$22$	−1.13003e28	+	1.56943e28i	−0.728138	+	1.01126i
$23$			2.77301e28i			0.702533i	0.936275	+	0.351267i	$0.114249\pi$
$23$			2.77301e28i			0.702533i	−0.936275	+	0.351267i	$0.885751\pi$
$24$	1.64390e29	+	5.10911e28i	1.70389	+	0.529553i
$25$	−4.62328e27			−0.0203334
$26$	−3.32245e29	−	2.39225e29i	−0.641236	−	0.461708i
$27$			2.41727e30i			2.11197i
$28$	−2.76654e30	+	9.25142e29i	−1.12621	+	0.376608i
$29$	1.47725e30			0.287803			0.143901	−	0.989592i	$-0.454035\pi$
$29$	1.47725e30			0.287803			0.143901	+	0.989592i	$0.454035\pi$
$30$	1.07944e31	−	1.49917e31i	1.03193	−	1.43319i
$31$			1.58291e31i			0.760082i	0.924970	+	0.380041i	$0.124090\pi$
$31$			1.58291e31i			0.760082i	−0.924970	+	0.380041i	$0.875910\pi$
$32$	−4.05555e31	+	8.67457e29i	−0.999771	+	0.0213845i
$33$	1.72115e32			2.22344
$34$	−1.90878e32	−	1.37438e32i	−1.31734	−	0.948525i
$35$			3.13044e32i			1.17537i
$36$	−3.33264e32	−	9.96592e32i	−0.692526	−	2.07093i
$37$	−5.75921e32			−0.673173			−0.336587	−	0.941653i	$-0.609272\pi$
$37$	−5.75921e32			−0.673173			−0.336587	+	0.941653i	$0.609272\pi$
$38$	5.54356e31	−	7.69909e31i	0.0370112	−	0.0514024i
$39$			3.64365e33i			1.40987i
$40$	−1.29195e33	+	4.15697e33i	−0.293755	+	0.945185i
$41$	8.30103e33			1.12375			0.561876	−	0.827221i	$-0.310080\pi$
$41$	8.30103e33			1.12375			0.561876	+	0.827221i	$0.310080\pi$
$42$	2.10686e34	+	1.51700e34i	1.71949	+	1.23808i
$43$		−	9.98962e32i		−	0.0497406i	−0.999691	−	0.0248703i	$-0.992083\pi$
$43$		−	9.98962e32i		−	0.0497406i	0.999691	−	0.0248703i	$-0.00791729\pi$
$44$	−3.84637e34	+	1.28624e34i	−1.18180	+	0.395199i
$45$	−1.12768e35			−2.16134
$46$	−3.39807e34	+	4.71935e34i	−0.410504	+	0.570122i
$47$		−	1.65183e35i		−	1.27031i	−0.772384	−	0.635156i	$-0.780936\pi$
$47$		−	1.65183e35i		−	1.27031i	0.772384	−	0.635156i	$-0.219064\pi$
$48$	2.17167e35	+	2.88397e35i	1.07332	+	1.42536i
$49$	−1.27964e35			−0.410176
$50$	−7.86831e33	−	5.66540e33i	−0.0165011	−	0.0118812i
$51$			2.09332e36i			2.89642i
$52$	−2.72295e35	−	8.14270e35i	−0.250593	−	0.749373i
$53$	1.24931e36			0.770683			0.385341	−	0.922774i	$-0.374084\pi$
$53$	1.24931e36			0.770683			0.385341	+	0.922774i	$0.374084\pi$
$54$	−2.96214e36	+	4.11393e36i	−1.23406	+	1.71391i
$55$			4.35230e36i			1.23340i
$56$	−5.84202e36	−	1.81565e36i	−1.13400	−	0.352439i
$57$	−8.44340e35			−0.113017
$58$	2.51411e36	+	1.81023e36i	0.233559	+	0.168169i
$59$			1.26149e37i			0.818449i	0.912434	+	0.409225i	$0.134201\pi$
$59$			1.26149e37i			0.818449i	−0.912434	+	0.409225i	$0.865799\pi$
$60$	3.67417e37	−	1.22866e37i	1.67488	−	0.560086i
$61$	−7.25751e36			−0.233809			−0.116904	−	0.993143i	$-0.537297\pi$
$61$	−7.25751e36			−0.233809			−0.116904	+	0.993143i	$0.537297\pi$
$62$	−1.93971e37	+	2.69394e37i	−0.444131	+	0.616825i
$63$		−	1.58479e38i		−	2.59310i
$64$	−7.00840e37	−	4.82207e37i	−0.823833	−	0.566832i
$65$	−9.21374e37			−0.782088
$66$	2.92921e38	+	2.10911e38i	1.80438	+	1.29920i
$67$		−	1.18317e38i		−	0.531469i	−0.964046	−	0.265735i	$-0.914386\pi$
$67$		−	1.18317e38i		−	0.531469i	0.964046	−	0.265735i	$-0.0856145\pi$
$68$	−1.56437e38	−	4.67807e38i	−0.514815	−	1.53950i
$69$	5.17560e38			1.25352
$70$	−3.83606e38	+	5.32765e38i	−0.686794	+	0.953843i
$71$			5.09944e38i			0.677792i	0.940824	+	0.338896i	$0.110054\pi$
$71$			5.09944e38i			0.677792i	−0.940824	+	0.338896i	$0.889946\pi$
$72$	6.54052e38	−	2.10447e39i	0.648082	−	2.08526i
$73$	1.45038e39			1.07572			0.537862	−	0.843033i	$-0.319232\pi$
$73$	1.45038e39			1.07572			0.537862	+	0.843033i	$0.319232\pi$
$74$	−9.80154e38	−	7.05738e38i	−0.546296	−	0.393348i
$75$			8.62899e37i			0.0362805i
$76$	1.88690e38	−	6.30988e37i	0.0600709	−	0.0200879i
$77$	−6.11653e39			−1.47979
$78$	−4.46495e39	+	6.20108e39i	−0.823815	+	1.14414i
$79$		−	6.50257e39i		−	0.918155i	−0.888396	−	0.459077i	$-0.848180\pi$
$79$		−	6.50257e39i		−	0.918155i	0.888396	−	0.459077i	$-0.151820\pi$
$80$	−7.29273e39	+	5.49153e39i	−0.790679	+	0.595393i
$81$	1.89726e40			1.58468
$82$	1.41274e40	+	1.01721e40i	0.911952	+	0.656631i
$83$			2.20429e40i			1.10313i	0.834130	+	0.551567i	$0.185970\pi$
$83$			2.20429e40i			1.10313i	−0.834130	+	0.551567i	$0.814030\pi$
$84$	1.72670e40	+	5.16352e40i	0.671974	+	2.00947i
$85$	−5.29340e40			−1.60671
$86$	1.22414e39	−	1.70012e39i	0.0290644	−	0.0403657i
$87$		−	2.75716e40i		−	0.513521i
$88$	−8.12227e40	−	2.52433e40i	−1.18998	−	0.369837i
$89$	1.68386e41			1.94587			0.972937	−	0.231070i	$-0.0742227\pi$
$89$	1.68386e41			1.94587			0.972937	+	0.231070i	$0.0742227\pi$
$90$	−1.91918e41	−	1.38187e41i	−1.75398	−	1.26291i
$91$		−	1.29486e41i		−	0.938325i
$92$	−1.15663e41	+	3.86780e40i	−0.666267	+	0.222802i
$93$	2.95437e41			1.35620
$94$	2.02417e41	−	2.81123e41i	0.742269	−	1.03089i
$95$		−	2.13510e40i		−	0.0626934i
$96$	1.61904e40	+	7.56936e41i	0.0381559	+	1.78387i
$97$	7.67811e41			1.45562			0.727810	−	0.685779i	$-0.240538\pi$
$97$	7.67811e41			1.45562			0.727810	+	0.685779i	$0.240538\pi$
$98$	−2.17781e41	−	1.56808e41i	−0.332868	−	0.239674i
$99$		−	2.20336e42i		−	2.72111i
$100$	−6.44857e39	−	1.92838e40i	−0.00644857	−	0.0192838i
$101$	−1.45110e42			−1.17747			−0.588733	−	0.808327i	$-0.700373\pi$
$101$	−1.45110e42			−1.17747			−0.588733	+	0.808327i	$0.700373\pi$
$102$	−2.56516e42	+	3.56259e42i	−1.69243	+	2.35051i
$103$			4.57011e41i			0.245666i	0.992427	+	0.122833i	$0.0391980\pi$
$103$			4.57011e41i			0.245666i	−0.992427	+	0.122833i	$0.960802\pi$
$104$	5.34396e41	−	1.71947e42i	0.234511	−	0.754561i
$105$	5.84270e42			2.09719
$106$	2.12618e42	+	1.53091e42i	0.625427	+	0.450325i
$107$		−	4.15440e42i		−	1.00334i	−0.865058	−	0.501671i	$-0.832719\pi$
$107$		−	4.15440e42i		−	1.00334i	0.865058	−	0.501671i	$-0.167281\pi$
$108$	−1.00825e43	+	3.37162e42i	−2.00294	+	0.669791i
$109$	8.83335e42			1.44600			0.723001	−	0.690847i	$-0.242762\pi$
$109$	8.83335e42			1.44600			0.723001	+	0.690847i	$0.242762\pi$
$110$	−5.33334e42	+	7.40713e42i	−0.720697	+	1.00093i
$111$			1.07491e43i			1.20113i
$112$	−7.71755e42	−	1.02489e43i	−0.714334	−	0.948632i
$113$	−1.23262e43			−0.946637			−0.473319	−	0.880891i	$-0.656944\pi$
$113$	−1.23262e43			−0.946637			−0.473319	+	0.880891i	$0.656944\pi$
$114$	−1.43697e42	−	1.03466e42i	−0.0917163	−	0.0660383i
$115$			1.30876e43i			0.695354i
$116$	2.06047e42	+	6.16161e42i	0.0912742	+	0.272946i
$117$	4.66448e43			1.72544
$118$	−1.54584e43	+	2.14692e43i	−0.478236	+	0.664191i
$119$		−	7.43911e43i		−	1.92768i
$120$	7.75864e43	+	2.41132e43i	1.68647	+	0.524142i
$121$	−3.02756e43			−0.552841
$122$	−1.23515e43	−	8.89340e42i	−0.189741	−	0.136619i
$123$		−	1.54932e44i		−	2.00509i
$124$	−6.60233e43	+	2.20785e43i	−0.720845	+	0.241053i
$125$	−1.09494e44			−1.00991
$126$	1.94201e44	−	2.69714e44i	1.51520	−	2.10437i
$127$			2.59927e44i			1.71780i	0.512139	+	0.858902i	$0.328853\pi$
$127$			2.59927e44i			1.71780i	−0.512139	+	0.858902i	$0.671147\pi$
$128$	−6.01851e43	−	1.67948e44i	−0.337349	−	0.941380i
$129$	−1.86448e43			−0.0887512
$130$	−1.56808e44	−	1.12906e44i	−0.634683	−	0.456989i
$131$			2.99544e44i			1.03220i	0.856528	+	0.516100i	$0.172617\pi$
$131$			2.99544e44i			1.03220i	−0.856528	+	0.516100i	$0.827383\pi$
$132$	2.40067e44	+	7.17894e44i	0.705146	+	2.10867i
$133$	3.00057e43			0.0752176
$134$	1.44987e44	−	2.01363e44i	0.310548	−	0.431300i
$135$			1.14087e45i			2.09038i
$136$	3.07017e44	−	9.87854e44i	0.481776	−	1.55016i
$137$	−5.66219e44			−0.761820			−0.380910	−	0.924612i	$-0.624389\pi$
$137$	−5.66219e44			−0.761820			−0.380910	+	0.924612i	$0.624389\pi$
$138$	8.80829e44	+	6.34222e44i	1.01726	+	0.732454i
$139$		−	2.80347e44i		−	0.278218i	−0.990277	−	0.139109i	$-0.955576\pi$
$139$		−	2.80347e44i		−	0.278218i	0.990277	−	0.139109i	$-0.0444238\pi$
$140$	−1.30571e45	+	4.36634e44i	−1.11470	+	0.372759i
$141$	−3.08301e45			−2.26659
$142$	−6.24888e44	+	8.67867e44i	−0.396047	+	0.550045i
$143$		−	1.80027e45i		−	0.984646i
$144$	3.69196e45	−	2.78010e45i	1.74439	−	1.31355i
$145$	6.97208e44			0.284862
$146$	2.46838e45	+	1.77730e45i	0.872976	+	0.628567i
$147$			2.38835e45i			0.731869i
$148$	−8.03296e44	−	2.40217e45i	−0.213491	−	0.638423i
$149$	−2.88987e45			−0.666756			−0.333378	−	0.942793i	$-0.608188\pi$
$149$	−2.88987e45			−0.666756			−0.333378	+	0.942793i	$0.608188\pi$
$150$	−1.05740e44	+	1.46856e44i	−0.0211994	+	0.0294425i
$151$		−	3.60516e45i		−	0.628650i	−0.949315	−	0.314325i	$-0.898222\pi$
$151$		−	3.60516e45i		−	0.628650i	0.949315	−	0.314325i	$-0.101778\pi$
$152$	3.98452e44	+	1.23835e44i	0.0604867	+	0.0187988i
$153$	2.67980e46			3.54472
$154$	−1.04097e46	−	7.49524e45i	−1.20088	−	0.864670i
$155$			7.47077e45i			0.752315i
$156$	−1.51977e46	+	5.08216e45i	−1.33709	+	0.447128i
$157$	−1.48559e46			−1.14290			−0.571448	−	0.820638i	$-0.693618\pi$
$157$	−1.48559e46			−1.14290			−0.571448	+	0.820638i	$0.693618\pi$
$158$	7.96829e45	−	1.10666e46i	0.536496	−	0.745104i
$159$		−	2.33173e46i		−	1.37511i
$160$	−1.91408e46	+	4.09409e44i	−0.989555	+	0.0211659i
$161$	−1.83928e46			−0.834264
$162$	3.22893e46	+	2.32492e46i	1.28601	+	0.925962i
$163$		−	2.21326e46i		−	0.774627i	−0.921948	−	0.387313i	$-0.873403\pi$
$163$		−	2.21326e46i		−	0.774627i	0.921948	−	0.387313i	$-0.126597\pi$
$164$	1.15783e46	+	3.46237e46i	0.356388	+	1.06574i
$165$	8.12322e46			2.20072
$166$	−2.70115e46	+	3.75145e46i	−0.644583	+	0.895220i
$167$			1.79668e46i			0.377942i	0.981983	+	0.188971i	$0.0605152\pi$
$167$			1.79668e46i			0.377942i	−0.981983	+	0.188971i	$0.939485\pi$
$168$	−3.38876e46	+	1.09037e47i	−0.628849	+	2.02338i
$169$	−2.29296e46			−0.375643
$170$	−9.00878e46	−	6.48657e46i	−1.30388	−	0.938832i
$171$			1.08090e46i			0.138314i
$172$	4.16668e45	−	1.39335e45i	0.0471730	−	0.0157748i
$173$	−5.25036e46			−0.526285			−0.263142	−	0.964757i	$-0.584759\pi$
$173$	−5.25036e46			−0.526285			−0.263142	+	0.964757i	$0.584759\pi$
$174$	3.37864e46	−	4.69238e46i	0.300060	−	0.416734i
$175$		−	3.06652e45i		−	0.0241461i
$176$	−1.07299e47	−	1.42492e47i	−0.749597	−	0.995462i
$177$	2.35447e47			1.46034
$178$	2.86573e47	+	2.06341e47i	1.57912	+	1.13701i
$179$			2.39933e46i			0.117537i	0.998272	+	0.0587687i	$0.0187174\pi$
$179$			2.39933e46i			0.117537i	−0.998272	+	0.0587687i	$0.981283\pi$
$180$	−1.57289e47	−	4.70356e47i	−0.685449	−	2.04977i
$181$	−2.70113e46			−0.104784			−0.0523921	−	0.998627i	$-0.516685\pi$
$181$	−2.70113e46			−0.104784			−0.0523921	+	0.998627i	$0.516685\pi$
$182$	1.58673e47	−	2.20371e47i	0.548282	−	0.761473i
$183$			1.35456e47i			0.417180i
$184$	−2.44241e47	−	7.59081e46i	−0.670880	−	0.208504i
$185$	−2.71814e47			−0.666294
$186$	5.02801e47	+	3.62031e47i	1.10059	+	0.792453i
$187$		−	1.03427e48i		−	2.02284i
$188$	6.88981e47	−	2.30398e47i	1.20474	−	0.402869i
$189$	−1.60332e48			−2.50798
$190$	2.61636e46	−	3.63370e46i	0.0366330	−	0.0508772i
$191$			1.15634e48i			1.45006i	0.688718	+	0.725029i	$0.258174\pi$
$191$			1.15634e48i			1.45006i	−0.688718	+	0.725029i	$0.741826\pi$
$192$	−9.00001e47	+	1.30806e48i	−1.01139	+	1.46995i
$193$	8.91915e47			0.898710			0.449355	−	0.893353i	$-0.351654\pi$
$193$	8.91915e47			0.898710			0.449355	+	0.893353i	$0.351654\pi$
$194$	1.30673e48	+	9.40881e47i	1.18127	+	0.850547i
$195$			1.71967e48i			1.39546i
$196$	−1.78485e47	−	5.33740e47i	−0.130084	−	0.389002i
$197$	−4.67268e47			−0.306038			−0.153019	−	0.988223i	$-0.548900\pi$
$197$	−4.67268e47			−0.306038			−0.153019	+	0.988223i	$0.548900\pi$
$198$	2.70002e48	−	3.74988e48i	1.59000	−	2.20825i
$199$			1.77170e48i			0.938589i	0.883042	+	0.469295i	$0.155492\pi$
$199$			1.77170e48i			0.938589i	−0.883042	+	0.469295i	$0.844508\pi$
$200$	1.26557e46	−	4.07210e46i	0.00603472	−	0.0194173i
$201$	−2.20830e48			−0.948289
$202$	−2.46961e48	−	1.77819e48i	−0.955542	−	0.688017i
$203$			9.79825e47i			0.341768i
$204$	−8.73124e48	+	2.91976e48i	−2.74690	+	0.918573i
$205$	3.91779e48			1.11227
$206$	−5.60025e47	+	7.77782e47i	−0.143548	+	0.199364i
$207$		−	6.62564e48i		−	1.53409i
$208$	3.01653e48	−	2.27149e48i	0.631216	−	0.475314i
$209$	4.17175e47			0.0789307
$210$	9.94363e48	+	7.15969e48i	1.70192	+	1.22543i
$211$		−	3.44183e48i		−	0.533160i	−0.963813	−	0.266580i	$-0.914106\pi$
$211$		−	3.44183e48i		−	0.533160i	0.963813	−	0.266580i	$-0.0858936\pi$
$212$	1.74254e48	+	5.21087e48i	0.244415	+	0.730899i
$213$	9.51768e48			1.20937
$214$	5.09083e48	−	7.07033e48i	0.586273	−	0.814236i
$215$		−	4.71475e47i		−	0.0492324i
$216$	−2.12909e49	−	6.61702e48i	−2.01681	−	0.626806i
$217$	−1.04991e49			−0.902604
$218$	1.50334e49	+	1.08244e49i	1.17346	+	0.844927i
$219$		−	2.70701e49i		−	1.91939i
$220$	−1.81535e49	+	6.07060e48i	−1.16973	+	0.391161i
$221$	2.18954e49			1.28267
$222$	−1.31720e49	+	1.82938e49i	−0.701843	+	0.974745i
$223$		−	7.59882e48i		−	0.368420i	−0.982887	−	0.184210i	$-0.941027\pi$
$223$		−	7.59882e48i		−	0.368420i	0.982887	−	0.184210i	$-0.0589727\pi$
$224$	−5.75365e47	−	2.68996e49i	−0.0253942	−	1.18724i
$225$	1.10466e48			0.0444011
$226$	−2.09779e49	−	1.51047e49i	−0.768219	−	0.553139i
$227$			3.43122e49i			1.14526i	0.819813	+	0.572631i	$0.194077\pi$
$227$			3.43122e49i			1.14526i	−0.819813	+	0.572631i	$0.805923\pi$
$228$	−1.17769e48	−	3.52175e48i	−0.0358425	−	0.107183i
$229$	2.42258e49			0.672563			0.336282	−	0.941761i	$-0.390831\pi$
$229$	2.42258e49			0.672563			0.336282	+	0.941761i	$0.390831\pi$
$230$	−1.60377e49	+	2.22737e49i	−0.406309	+	0.564296i
$231$			1.14160e50i			2.64036i
$232$	−4.04380e48	+	1.30113e49i	−0.0854165	+	0.274835i
$233$	2.08311e49			0.402012			0.201006	−	0.979590i	$-0.435579\pi$
$233$	2.08311e49			0.402012			0.201006	+	0.979590i	$0.435579\pi$
$234$	7.93842e49	+	5.71588e49i	1.40024	+	1.00821i
$235$		−	7.79606e49i		−	1.25733i
$236$	−5.26169e49	+	1.75953e49i	−0.776199	+	0.259564i
$237$	−1.21365e50			−1.63824
$238$	9.11594e49	−	1.26605e50i	1.12638	−	1.56436i
$239$		−	9.88983e48i		−	0.111901i	−0.998434	−	0.0559504i	$-0.982181\pi$
$239$		−	9.88983e48i		−	0.111901i	0.998434	−	0.0559504i	$-0.0178189\pi$
$240$	1.02495e50	+	1.36113e50i	1.06235	+	1.41079i
$241$	−1.67569e50			−1.59160			−0.795802	−	0.605556i	$-0.792951\pi$
$241$	−1.67569e50			−1.59160			−0.795802	+	0.605556i	$0.792951\pi$
$242$	−5.15257e49	−	3.70999e49i	−0.448643	−	0.323036i
$243$		−	8.96135e49i		−	0.715552i
$244$	−1.01228e49	−	3.02712e49i	−0.0741505	−	0.221739i
$245$	−6.03945e49			−0.405985
$246$	1.89855e50	−	2.63677e50i	1.17161	−	1.62718i
$247$			8.83151e48i			0.0500494i
$248$	−1.39419e50	−	4.33304e49i	−0.725835	−	0.225583i
$249$	4.11413e50			1.96830
$250$	−1.86347e50	−	1.34175e50i	−0.819563	−	0.590108i
$251$		−	1.33413e50i		−	0.539575i	−0.962920	−	0.269787i	$-0.913047\pi$
$251$		−	1.33413e50i		−	0.539575i	0.962920	−	0.269787i	$-0.0869534\pi$
$252$	6.61018e50	−	2.21047e50i	2.45924	−	0.822381i
$253$	−2.55718e50			−0.875448
$254$	−3.18517e50	+	4.42367e50i	−1.00375	+	1.39404i
$255$			9.87970e50i			2.86682i
$256$	1.03376e50	−	3.59580e50i	0.276299	−	0.961072i
$257$	−1.20065e50			−0.295679			−0.147840	−	0.989011i	$-0.547232\pi$
$257$	−1.20065e50			−0.295679			−0.147840	+	0.989011i	$0.547232\pi$
$258$	−3.17314e49	−	2.28475e49i	−0.0720237	−	0.0518591i
$259$		−	3.81996e50i		−	0.799399i
$260$	−1.28514e50	−	3.84306e50i	−0.248032	−	0.741715i
$261$	−3.52963e50			−0.628461
$262$	−3.67064e50	+	5.09791e50i	−0.603135	+	0.837655i
$263$			8.26891e50i			1.25423i	0.778926	+	0.627116i	$0.215765\pi$
$263$			8.26891e50i			1.25423i	−0.778926	+	0.627116i	$0.784235\pi$
$264$	−4.71146e50	+	1.51595e51i	−0.659892	+	2.12326i
$265$	5.89628e50			0.762807
$266$	5.10664e49	+	3.67692e49i	0.0610408	+	0.0439511i
$267$		−	3.14278e51i		−	3.47198i
$268$	4.93504e50	−	1.65029e50i	0.504034	−	0.168551i
$269$	1.56577e51			1.47887			0.739437	−	0.673226i	$-0.235092\pi$
$269$	1.56577e51			1.47887			0.739437	+	0.673226i	$0.235092\pi$
$270$	−1.39803e51	+	1.94163e51i	−1.22145	+	1.69640i
$271$			1.45309e51i			1.17473i	0.809321	+	0.587366i	$0.199835\pi$
$271$			1.45309e51i			1.17473i	−0.809321	+	0.587366i	$0.800165\pi$
$272$	1.73303e51	−	1.30500e51i	1.29676	−	0.976478i
$273$	−2.41675e51			−1.67423
$274$	−9.63642e50	−	6.93849e50i	−0.618235	−	0.445146i
$275$		−	4.26344e49i		−	0.0253381i
$276$	7.21894e50	+	2.15875e51i	0.397542	+	1.18881i
$277$	1.63532e51			0.834693			0.417346	−	0.908748i	$-0.362960\pi$
$277$	1.63532e51			0.834693			0.417346	+	0.908748i	$0.362960\pi$
$278$	3.43539e50	−	4.77119e50i	0.162568	−	0.225780i
$279$		−	3.78209e51i		−	1.65975i
$280$	−2.75722e51	−	8.56922e50i	−1.12241	−	0.348837i
$281$	3.98886e51			1.50666			0.753331	−	0.657642i	$-0.228446\pi$
$281$	3.98886e51			1.50666			0.753331	+	0.657642i	$0.228446\pi$
$282$	−5.24694e51	−	3.77794e51i	−1.83939	−	1.32441i
$283$			3.62215e51i			1.17883i	0.807830	+	0.589416i	$0.200642\pi$
$283$			3.62215e51i			1.17883i	−0.807830	+	0.589416i	$0.799358\pi$
$284$	−2.12698e51	+	7.11270e50i	−0.642804	+	0.214956i
$285$	−3.98498e50			−0.111862
$286$	2.20606e51	−	3.06385e51i	0.575348	−	0.799063i
$287$			5.50589e51i			1.33447i
$288$	9.69006e51	−	2.07264e50i	2.18315	−	0.0466962i
$289$	7.80545e51			1.63510
$290$	1.18657e51	+	8.54363e50i	0.231172	+	0.166450i
$291$		−	1.43306e52i		−	2.59723i
$292$	2.02299e51	+	6.04954e51i	0.341157	+	1.02019i
$293$	−1.05367e52			−1.65381			−0.826905	−	0.562342i	$-0.809900\pi$
$293$	−1.05367e52			−1.65381			−0.826905	+	0.562342i	$0.809900\pi$
$294$	−2.92670e51	+	4.06470e51i	−0.427645	+	0.593929i
$295$			5.95379e51i			0.810085i
$296$	1.57652e51	−	5.07260e51i	0.199790	−	0.642842i
$297$	−2.22913e52			−2.63178
$298$	−4.91824e51	−	3.54127e51i	−0.541088	−	0.389598i
$299$		−	5.41350e51i		−	0.555116i
$300$	−3.59916e50	+	1.20357e50i	−0.0344076	+	0.0115060i
$301$	6.62590e50			0.0590674
$302$	4.41779e51	−	6.13558e51i	0.367332	−	0.510164i
$303$			2.70836e52i			2.10093i
$304$	5.26371e50	+	6.99019e50i	0.0381019	+	0.0505992i
$305$	−3.42529e51			−0.231420
$306$	4.56071e52	+	3.28384e52i	2.87662	+	2.07125i
$307$			1.92950e52i			1.13642i	0.822884	+	0.568210i	$0.192364\pi$
$307$			1.92950e52i			1.13642i	−0.822884	+	0.568210i	$0.807636\pi$
$308$	−8.53136e51	−	2.55121e52i	−0.469303	−	1.40340i
$309$	8.52975e51			0.438337
$310$	−9.15473e51	+	1.27144e52i	−0.439592	+	0.610521i
$311$			2.70627e52i			1.21451i	0.794506	+	0.607257i	$0.207730\pi$
$311$			2.70627e52i			1.21451i	−0.794506	+	0.607257i	$0.792270\pi$
$312$	−3.20925e52	−	9.97407e51i	−1.34635	−	0.418433i
$313$	1.63393e52			0.640917			0.320459	−	0.947263i	$-0.396163\pi$
$313$	1.63393e52			0.640917			0.320459	+	0.947263i	$0.396163\pi$
$314$	−2.52831e52	−	1.82045e52i	−0.927488	−	0.667817i
$315$		−	7.47964e52i		−	2.56661i
$316$	2.71223e52	−	9.06980e51i	0.870758	−	0.291185i
$317$	2.58531e52			0.776726			0.388363	−	0.921506i	$-0.373041\pi$
$317$	2.58531e52			0.776726			0.388363	+	0.921506i	$0.373041\pi$
$318$	2.85732e52	−	3.96834e52i	0.803505	−	1.11594i
$319$			1.36227e52i			0.358640i
$320$	−3.30772e52	−	2.27585e52i	−0.815415	−	0.561040i
$321$	−7.75386e52			−1.79024
$322$	−3.13024e52	−	2.25386e52i	−0.677025	−	0.487477i
$323$			5.07380e51i			0.102821i
$324$	2.64631e52	+	7.91351e52i	0.502569	+	1.50288i
$325$	9.02563e50			0.0160667
$326$	2.71214e52	−	3.76672e52i	0.452630	−	0.628628i
$327$		−	1.64867e53i		−	2.58007i
$328$	−2.27231e52	+	7.31137e52i	−0.333517	+	1.07312i
$329$	1.09562e53			1.50851
$330$	1.38248e53	+	9.95425e52i	1.78594	+	1.28593i
$331$			3.85892e52i			0.467819i	0.972258	+	0.233910i	$0.0751520\pi$
$331$			3.85892e52i			0.467819i	−0.972258	+	0.233910i	$0.924848\pi$
$332$	−9.19411e52	+	3.07455e52i	−1.04619	+	0.349850i
$333$	1.37607e53			1.46998
$334$	−2.20167e52	+	3.05775e52i	−0.220839	+	0.306709i
$335$		−	5.58416e52i		−	0.526038i
$336$	−1.91287e53	+	1.44042e53i	−1.69263	+	1.27457i
$337$	−7.11300e52			−0.591323			−0.295662	−	0.955293i	$-0.595540\pi$
$337$	−7.11300e52			−0.591323			−0.295662	+	0.955293i	$0.595540\pi$
$338$	−3.90236e52	−	2.80981e52i	−0.304843	−	0.219495i
$339$			2.30059e53i			1.68907i
$340$	−7.38325e52	−	2.20788e53i	−0.509554	−	1.52377i
$341$	−1.45971e53			−0.947161
$342$	−1.32454e52	+	1.83957e52i	−0.0808195	+	0.112245i
$343$			1.22049e53i			0.700421i
$344$	8.79866e51	+	2.73455e51i	0.0474995	+	0.0147624i
$345$	2.44270e53			1.24071
$346$	−8.93553e52	−	6.43383e52i	−0.427093	−	0.307519i
$347$			9.09319e52i			0.409070i	0.978859	+	0.204535i	$0.0655681\pi$
$347$			9.09319e52i			0.409070i	−0.978859	+	0.204535i	$0.934432\pi$
$348$	1.15002e53	−	3.84569e52i	0.487012	−	0.162859i
$349$	−3.62874e52			−0.144684			−0.0723421	−	0.997380i	$-0.523047\pi$
$349$	−3.62874e52			−0.144684			−0.0723421	+	0.997380i	$0.523047\pi$
$350$	3.75774e51	−	5.21888e51i	0.0141090	−	0.0195951i
$351$		−	4.71903e53i		−	1.66880i
$352$	−7.99941e51	−	3.73990e53i	−0.0266478	−	1.24585i
$353$	2.62134e53			0.822725			0.411362	−	0.911472i	$-0.365053\pi$
$353$	2.62134e53			0.822725			0.411362	+	0.911472i	$0.365053\pi$
$354$	4.00704e53	+	2.88518e53i	1.18510	+	0.853306i
$355$			2.40675e53i			0.670866i
$356$	2.34865e53	+	7.02338e53i	0.617117	+	1.84542i
$357$	−1.38845e54			−3.43952
$358$	−2.94015e52	+	4.08339e52i	−0.0686794	+	0.0953844i
$359$		−	3.44766e53i		−	0.759523i	−0.925084	−	0.379762i	$-0.876006\pi$
$359$		−	3.44766e53i		−	0.759523i	0.925084	−	0.379762i	$-0.123994\pi$
$360$	3.08689e53	−	9.93236e53i	0.641460	−	2.06395i
$361$	5.08049e53			0.995988
$362$	−4.59703e52	−	3.30999e52i	−0.0850349	−	0.0612275i
$363$			5.65070e53i			0.986422i
$364$	5.40087e53	−	1.80607e53i	0.889887	−	0.297582i
$365$	6.84527e53			1.06473
$366$	−1.65988e53	+	2.30530e53i	−0.243767	+	0.338552i
$367$		−	1.07810e54i		−	1.49511i	−0.664200	−	0.747555i	$-0.731227\pi$
$367$		−	1.07810e54i		−	1.49511i	0.664200	−	0.747555i	$-0.268773\pi$
$368$	−3.22653e53	−	4.28482e53i	−0.422602	−	0.561214i
$369$	−1.98339e54			−2.45388
$370$	−4.62598e53	−	3.33083e53i	−0.540713	−	0.389329i
$371$			8.28637e53i			0.915192i
$372$	4.12077e53	+	1.23227e54i	0.430107	+	1.28619i
$373$	3.72880e53			0.367861			0.183930	−	0.982939i	$-0.441118\pi$
$373$	3.72880e53			0.367861			0.183930	+	0.982939i	$0.441118\pi$
$374$	1.26741e54	−	1.76022e54i	1.18199	−	1.64158i
$375$			2.04362e54i			1.80196i
$376$	1.45490e54	+	4.52170e53i	1.21308	+	0.377014i
$377$	−2.88390e53			−0.227411
$378$	−2.72868e54	−	1.96472e54i	−2.03528	−	1.46546i
$379$			5.89093e53i			0.415682i	0.978163	+	0.207841i	$0.0666436\pi$
$379$			5.89093e53i			0.415682i	−0.978163	+	0.207841i	$0.933356\pi$
$380$	8.90551e52	−	2.97804e52i	0.0594570	−	0.0198827i
$381$	4.85133e54			3.06504
$382$	−1.41699e54	+	1.96796e54i	−0.847297	+	1.17676i
$383$		−	1.19630e54i		−	0.677120i	−0.940945	−	0.338560i	$-0.890060\pi$
$383$		−	1.19630e54i		−	0.677120i	0.940945	−	0.338560i	$-0.109940\pi$
$384$	−3.13461e54	+	1.12331e54i	−1.67968	+	0.601925i
$385$	−2.88679e54			−1.46467
$386$	1.51794e54	+	1.09296e54i	0.729325	+	0.525134i
$387$			2.38685e53i			0.108616i
$388$	1.07094e54	+	3.20255e54i	0.461637	+	1.38048i
$389$	−3.61854e54			−1.47772			−0.738859	−	0.673860i	$-0.764635\pi$
$389$	−3.61854e54			−1.47772			−0.738859	+	0.673860i	$0.764635\pi$
$390$	−2.10730e54	+	2.92669e54i	−0.815397	+	1.13245i
$391$		−	3.11012e54i		−	1.14042i
$392$	3.50288e53	−	1.12708e54i	0.121736	−	0.391695i
$393$	5.59075e54			1.84173
$394$	−7.95238e53	−	5.72593e53i	−0.248357	−	0.178824i
$395$		−	3.06898e54i		−	0.908772i
$396$	9.19025e54	−	3.07326e54i	2.58065	−	0.862978i
$397$	−1.54103e54			−0.410404			−0.205202	−	0.978720i	$-0.565785\pi$
$397$	−1.54103e54			−0.410404			−0.205202	+	0.978720i	$0.565785\pi$
$398$	−2.17105e54	+	3.01524e54i	−0.548436	+	0.761688i
$399$		−	5.60032e53i		−	0.134209i
$400$	7.14384e52	−	5.37941e52i	0.0162432	−	0.0122314i
$401$	3.37182e54			0.727499			0.363750	−	0.931497i	$-0.381496\pi$
$401$	3.37182e54			0.727499			0.363750	+	0.931497i	$0.381496\pi$
$402$	−3.75828e54	−	2.70607e54i	−0.769559	−	0.554104i
$403$		−	3.09017e54i		−	0.600589i
$404$	−2.02400e54	−	6.05255e54i	−0.373423	−	1.11668i
$405$	8.95441e54			1.56849
$406$	−1.20068e54	+	1.66755e54i	−0.199702	+	0.277353i
$407$		−	5.31096e54i		−	0.838862i
$408$	−1.84375e55	−	5.73022e54i	−2.76591	−	0.859622i
$409$	−1.19968e54			−0.170953			−0.0854767	−	0.996340i	$-0.527241\pi$
$409$	−1.19968e54			−0.170953			−0.0854767	+	0.996340i	$0.527241\pi$
$410$	6.66764e54	+	4.80088e54i	0.902633	+	0.649921i
$411$			1.05680e55i			1.35930i
$412$	−1.90620e54	+	6.37441e53i	−0.232984	+	0.0779109i
$413$	−8.36719e54			−0.971915
$414$	8.11910e54	−	1.12761e55i	0.896398	−	1.24495i
$415$			1.04035e55i			1.09186i
$416$	7.91730e54	−	1.69346e53i	0.789982	−	0.0168972i
$417$	−5.23245e54			−0.496418
$418$	7.09985e53	+	5.11209e53i	0.0640541	+	0.0461208i
$419$		−	1.21816e55i		−	1.04522i	−0.852571	−	0.522612i	$-0.824958\pi$
$419$		−	1.21816e55i		−	1.04522i	0.852571	−	0.522612i	$-0.175042\pi$
$420$	8.14942e54	+	2.43700e55i	0.665107	+	1.98893i
$421$	−5.71257e53			−0.0443514			−0.0221757	−	0.999754i	$-0.507059\pi$
$421$	−5.71257e53			−0.0443514			−0.0221757	+	0.999754i	$0.507059\pi$
$422$	4.21764e54	−	5.85761e54i	0.311536	−	0.432672i
$423$			3.94677e55i			2.77392i
$424$	−3.41984e54	+	1.10036e55i	−0.228730	+	0.735958i
$425$	5.18533e53			0.0330072
$426$	1.61980e55	+	1.16630e55i	0.981433	+	0.706659i
$427$		−	4.81375e54i		−	0.277650i
$428$	1.73281e55	−	5.79457e54i	0.951548	−	0.318201i
$429$	−3.36005e55			−1.75688
$430$	5.77748e53	−	8.02397e53i	0.0287674	−	0.0399532i
$431$		−	3.21891e55i		−	1.52646i	−0.646125	−	0.763231i	$-0.723612\pi$
$431$		−	3.21891e55i		−	1.52646i	0.646125	−	0.763231i	$-0.276388\pi$
$432$	−2.81261e55	−	3.73514e55i	−1.27043	−	1.68713i
$433$	−2.91234e55			−1.25313			−0.626566	−	0.779369i	$-0.715540\pi$
$433$	−2.91234e55			−1.25313			−0.626566	+	0.779369i	$0.715540\pi$
$434$	−1.78683e55	−	1.28657e55i	−0.732485	−	0.527409i
$435$		−	1.30128e55i		−	0.508273i
$436$	1.23208e55	+	3.68440e55i	0.458587	+	1.37136i
$437$	1.25447e54			0.0444989
$438$	3.31719e55	−	4.60703e55i	1.12154	−	1.55763i
$439$			5.42141e55i			1.74726i	0.486591	+	0.873630i	$0.338240\pi$
$439$			5.42141e55i			1.74726i	−0.486591	+	0.873630i	$0.661760\pi$
$440$	−3.83342e55	−	1.19139e55i	−1.17782	−	0.366058i
$441$	3.05748e55			0.895682
$442$	3.72635e55	+	2.68307e55i	1.04092	+	0.749489i
$443$		−	6.22654e55i		−	1.65870i	−0.558727	−	0.829351i	$-0.688710\pi$
$443$		−	6.22654e55i		−	1.65870i	0.558727	−	0.829351i	$-0.311290\pi$
$444$	−4.48346e55	+	1.49929e55i	−1.13912	+	0.380928i
$445$	7.94720e55			1.92599
$446$	9.31164e54	−	1.29323e55i	0.215275	−	0.298982i
$447$			5.39371e55i			1.18968i
$448$	3.19837e55	−	4.64852e55i	0.673118	−	0.978309i
$449$	6.90166e55			1.38606			0.693028	−	0.720911i	$-0.256276\pi$
$449$	6.90166e55			1.38606			0.693028	+	0.720911i	$0.256276\pi$
$450$	1.88000e54	+	1.35365e54i	0.0360325	+	0.0259444i
$451$			7.65494e55i			1.40034i
$452$	−1.71927e55	−	5.14129e55i	−0.300218	−	0.897770i
$453$	−6.72874e55			−1.12169
$454$	−4.20464e55	+	5.83955e55i	−0.669200	+	0.929408i
$455$		−	6.11127e55i		−	0.928736i
$456$	2.31129e54	−	7.43677e54i	0.0335422	−	0.107925i
$457$	−1.18829e56			−1.64696			−0.823480	−	0.567345i	$-0.807971\pi$
$457$	−1.18829e56			−1.64696			−0.823480	+	0.567345i	$0.807971\pi$
$458$	4.12296e55	+	2.96865e55i	0.545801	+	0.392992i
$459$		−	2.71114e56i		−	3.42835i
$460$	−5.45886e55	+	1.82546e55i	−0.659459	+	0.220526i
$461$	4.35130e55			0.502227			0.251114	−	0.967958i	$-0.419203\pi$
$461$	4.35130e55			0.502227			0.251114	+	0.967958i	$0.419203\pi$
$462$	−1.39893e56	+	1.94288e56i	−1.54281	+	2.14271i
$463$		−	4.73535e55i		−	0.499059i	−0.968367	−	0.249529i	$-0.919724\pi$
$463$		−	4.73535e55i		−	0.499059i	0.968367	−	0.249529i	$-0.0802759\pi$
$464$	−2.28262e55	+	1.71885e55i	−0.229909	+	0.173125i
$465$	1.39436e56			1.34234
$466$	3.54523e55	+	2.55266e55i	0.326242	+	0.234903i
$467$			7.58670e55i			0.667419i	0.942676	+	0.333709i	$0.108300\pi$
$467$			7.58670e55i			0.667419i	−0.942676	+	0.333709i	$0.891700\pi$
$468$	6.50602e55	+	1.94556e56i	0.547208	+	1.63637i
$469$	7.84774e55			0.631124
$470$	9.55334e55	−	1.32680e56i	0.734683	−	1.02035i
$471$			2.77274e56i			2.03925i
$472$	−1.11110e56	−	3.45319e55i	−0.781573	−	0.242906i
$473$	9.21210e54			0.0619833
$474$	−2.06550e56	−	1.48722e56i	−1.32947	−	0.957258i
$475$			2.09150e53i			0.00128793i
$476$	3.10286e56	−	1.03761e56i	1.82817	−	0.611347i
$477$	−2.98500e56			−1.68290
$478$	1.21191e55	−	1.68314e55i	0.0653858	−	0.0908101i
$479$		−	2.16482e55i		−	0.111783i	−0.998437	−	0.0558915i	$-0.982200\pi$
$479$		−	2.16482e55i		−	0.111783i	0.998437	−	0.0558915i	$-0.0178001\pi$
$480$	7.64129e54	+	3.57247e56i	0.0377660	+	1.76564i
$481$	1.12432e56			0.531916
$482$	−2.85183e56	−	2.05340e56i	−1.29162	−	0.930006i
$483$			3.43286e56i			1.48856i
$484$	−4.22285e55	−	1.26280e56i	−0.175329	−	0.524302i
$485$	3.62380e56			1.44075
$486$	1.09813e56	−	1.52512e56i	0.418111	−	0.580688i
$487$		−	3.17328e56i		−	1.15718i	−0.815619	−	0.578589i	$-0.803604\pi$
$487$		−	3.17328e56i		−	1.15718i	0.815619	−	0.578589i	$-0.196396\pi$
$488$	1.98666e55	−	6.39227e55i	0.0693917	−	0.223274i
$489$	−4.13087e56			−1.38215
$490$	−1.02785e56	−	7.40079e55i	−0.329466	−	0.237225i
$491$			2.05187e56i			0.630142i	0.949068	+	0.315071i	$0.102028\pi$
$491$			2.05187e56i			0.630142i	−0.949068	+	0.315071i	$0.897972\pi$
$492$	6.46223e56	−	2.16099e56i	1.90158	−	0.635896i
$493$	−1.65683e56			−0.467190
$494$	−1.08222e55	+	1.50303e55i	−0.0292449	+	0.0406163i
$495$		−	1.03991e57i		−	2.69331i
$496$	−1.84179e56	−	2.44589e56i	−0.457220	−	0.607186i
$497$	−3.38234e56			−0.804884
$498$	7.00178e56	+	5.04148e56i	1.59732	+	1.15012i
$499$			7.49527e56i			1.63936i	0.572818	+	0.819682i	$0.305850\pi$
$499$			7.49527e56i			1.63936i	−0.572818	+	0.819682i	$0.694150\pi$
$500$	−1.52723e56	−	4.56702e56i	−0.320283	−	0.957774i
$501$	3.35336e56			0.674354
$502$	1.63486e56	−	2.27055e56i	0.315284	−	0.437878i
$503$		−	4.80155e56i		−	0.888083i	−0.896006	−	0.444042i	$-0.853544\pi$
$503$		−	4.80155e56i		−	0.888083i	0.896006	−	0.444042i	$-0.146456\pi$
$504$	1.39585e57	+	4.33819e56i	2.47627	+	0.769603i
$505$	−6.84867e56			−1.16543
$506$	−4.35204e56	−	3.13359e56i	−0.710447	−	0.511541i
$507$			4.27962e56i			0.670252i
$508$	−1.08416e57	+	3.62547e56i	−1.62913	+	0.544787i
$509$	−7.30807e56			−1.05373			−0.526865	−	0.849949i	$-0.676633\pi$
$509$	−7.30807e56			−1.05373			−0.526865	+	0.849949i	$0.676633\pi$
$510$	−1.21067e57	+	1.68142e57i	−1.67514	+	2.32649i
$511$			9.62004e56i			1.27743i
$512$	6.16566e56	−	4.85287e56i	0.785796	−	0.618485i
$513$	1.09354e56			0.133773
$514$	−2.04337e56	−	1.47129e56i	−0.239951	−	0.172771i
$515$			2.15693e56i			0.243156i
$516$	−2.60058e55	−	7.77678e55i	−0.0281467	−	0.0841697i
$517$	1.52327e57			1.58298
$518$	4.68100e56	−	6.50114e56i	0.467104	−	0.648731i
$519$			9.79937e56i			0.939039i
$520$	2.52216e56	−	8.11528e56i	0.232115	−	0.746850i
$521$	1.76234e57			1.55775			0.778876	−	0.627177i	$-0.215790\pi$
$521$	1.76234e57			1.55775			0.778876	+	0.627177i	$0.215790\pi$
$522$	−6.00704e56	−	4.32523e56i	−0.510011	−	0.367222i
$523$			2.71370e56i			0.221323i	0.993858	+	0.110661i	$0.0352969\pi$
$523$			2.71370e56i			0.221323i	−0.993858	+	0.110661i	$0.964703\pi$
$524$	−1.24940e57	+	4.17805e56i	−0.978916	+	0.327353i
$525$	−5.72342e55			−0.0430834
$526$	−1.01328e57	+	1.40728e57i	−0.732872	+	1.01784i
$527$		−	1.77534e57i		−	1.23384i
$528$	−2.65950e57	+	2.00264e57i	−1.77618	+	1.33749i
$529$	7.89047e56			0.506447
$530$	1.00348e57	+	7.22534e56i	0.619036	+	0.445723i
$531$		−	3.01412e57i		−	1.78721i
$532$	4.18520e55	+	1.25154e56i	0.0238546	+	0.0713347i
$533$	−1.62054e57			−0.887947
$534$	3.85118e57	−	5.34866e57i	2.02875	−	2.81760i
$535$		−	1.96073e57i		−	0.993089i
$536$	1.04212e57	+	3.23881e56i	0.507523	+	0.157734i
$537$	4.47815e56			0.209719
$538$	2.66477e57	+	1.91871e57i	1.20014	+	0.864135i
$539$		−	1.18004e57i		−	0.511133i
$540$	−4.75857e57	+	1.59128e57i	−1.98247	+	0.662947i
$541$	−3.53065e57			−1.41486			−0.707428	−	0.706786i	$-0.750144\pi$
$541$	−3.53065e57			−1.41486			−0.707428	+	0.706786i	$0.750144\pi$
$542$	−1.78063e57	+	2.47300e57i	−0.686419	+	0.953323i
$543$			5.04145e56i			0.186964i
$544$	4.54858e57	−	9.72912e55i	1.62293	−	0.0347134i
$545$	4.16902e57			1.43123
$546$	−4.11304e57	−	2.96150e57i	−1.35868	−	0.978287i
$547$			2.04025e57i			0.648560i	0.945961	+	0.324280i	$0.105122\pi$
$547$			2.04025e57i			0.648560i	−0.945961	+	0.324280i	$0.894878\pi$
$548$	−7.89764e56	−	2.36171e57i	−0.241605	−	0.722494i
$549$	1.73406e57			0.510557
$550$	5.22445e55	−	7.25590e55i	0.0148055	−	0.0205625i
$551$		−	6.68284e55i		−	0.0182296i
$552$	−1.41676e57	+	4.55856e57i	−0.372029	+	1.19704i
$553$	4.31301e57			1.09032
$554$	2.78313e57	+	2.00393e57i	0.677373	+	0.487727i
$555$			5.07319e57i			1.18885i
$556$	1.16933e57	−	3.91028e56i	0.263856	−	0.0882344i
$557$	3.25294e57			0.706834			0.353417	−	0.935466i	$-0.385020\pi$
$557$	3.25294e57			0.706834			0.353417	+	0.935466i	$0.385020\pi$
$558$	4.63460e57	−	6.43670e57i	0.969827	−	1.34693i
$559$			1.95019e56i			0.0393032i
$560$	−3.64241e57	−	4.83711e57i	−0.707034	−	0.938938i
$561$	−1.93039e58			−3.60931
$562$	6.78859e57	+	4.88797e57i	1.22269	+	0.880372i
$563$			4.52928e57i			0.785874i	0.919565	+	0.392937i	$0.128541\pi$
$563$			4.52928e57i			0.785874i	−0.919565	+	0.392937i	$0.871459\pi$
$564$	−4.30019e57	−	1.28593e58i	−0.718830	−	2.14959i
$565$	−5.81755e57			−0.936964
$566$	−4.43861e57	+	6.16450e57i	−0.688814	+	0.956650i
$567$			1.25841e58i			1.88183i
$568$	−4.49148e57	−	1.39591e57i	−0.647253	−	0.201161i
$569$	−6.95182e57			−0.965475			−0.482737	−	0.875765i	$-0.660357\pi$
$569$	−6.95182e57			−0.965475			−0.482737	+	0.875765i	$0.660357\pi$
$570$	−6.78200e56	−	4.88323e56i	−0.0907791	−	0.0653634i
$571$		−	8.38391e57i		−	1.08165i	−0.841134	−	0.540827i	$-0.818111\pi$
$571$		−	8.38391e57i		−	1.08165i	0.841134	−	0.540827i	$-0.181889\pi$
$572$	7.50893e57	−	2.51102e57i	0.933817	−	0.312272i
$573$	2.15822e58			2.58731
$574$	−6.74695e57	+	9.37041e57i	−0.779754	+	1.08295i
$575$		−	1.28204e56i		−	0.0142849i
$576$	1.67454e58	+	1.15215e58i	1.79897	+	1.23776i
$577$	−9.19099e57			−0.952073			−0.476036	−	0.879426i	$-0.657927\pi$
$577$	−9.19099e57			−0.952073			−0.476036	+	0.879426i	$0.657927\pi$
$578$	1.32840e58	+	9.56485e57i	1.32692	+	0.955418i
$579$		−	1.66469e58i		−	1.60355i
$580$	9.72467e56	+	2.90806e57i	0.0903414	+	0.270157i
$581$	−1.46206e58			−1.30998
$582$	1.75608e58	−	2.43890e58i	1.51761	−	2.10772i
$583$			1.15207e58i			0.960371i
$584$	−3.97025e57	+	1.27746e58i	−0.319262	+	1.02726i
$585$	2.20147e58			1.70781
$586$	−1.79323e58	−	1.29118e58i	−1.34211	−	0.966353i
$587$		−	1.08896e58i		−	0.786342i	−0.919465	−	0.393171i	$-0.871378\pi$
$587$		−	1.08896e58i		−	0.786342i	0.919465	−	0.393171i	$-0.128622\pi$
$588$	−9.96182e57	+	3.33127e57i	−0.694089	+	0.232106i
$589$	7.16085e56			0.0481441
$590$	−7.29581e57	+	1.01327e58i	−0.473349	+	0.657404i
$591$			8.72118e57i			0.546057i
$592$	8.89906e57	−	6.70112e57i	0.537760	−	0.404941i
$593$	−2.15769e58			−1.25846			−0.629231	−	0.777218i	$-0.716630\pi$
$593$	−2.15769e58			−1.25846			−0.629231	+	0.777218i	$0.716630\pi$
$594$	−3.79373e58	−	2.73159e58i	−2.13575	−	1.53780i
$595$		−	3.51100e58i		−	1.90798i
$596$	−4.03080e57	−	1.20537e58i	−0.211456	−	0.632337i
$597$	3.30674e58			1.67471
$598$	6.63375e57	−	9.21318e57i	0.324365	−	0.450490i
$599$			2.18127e57i			0.102978i	0.998674	+	0.0514892i	$0.0163968\pi$
$599$			2.18127e57i			0.102978i	−0.998674	+	0.0514892i	$0.983603\pi$
$600$	−7.60024e56	−	2.36209e56i	−0.0346458	−	0.0107676i
$601$	3.60288e58			1.58594			0.792969	−	0.609262i	$-0.208534\pi$
$601$	3.60288e58			1.58594			0.792969	+	0.609262i	$0.208534\pi$
$602$	1.12765e57	+	8.11942e56i	0.0479346	+	0.0345143i
$603$			2.82699e58i			1.16054i
$604$	1.50372e58	−	5.02849e57i	0.596198	−	0.199371i
$605$	−1.42890e58			−0.547191
$606$	−3.31884e58	+	4.60933e58i	−1.22761	+	1.70495i
$607$			9.46723e57i			0.338268i	0.985593	+	0.169134i	$0.0540970\pi$
$607$			9.46723e57i			0.338268i	−0.985593	+	0.169134i	$0.945903\pi$
$608$	3.92425e55	+	1.83467e57i	0.00135451	+	0.0633262i
$609$	1.82876e58			0.609810
$610$	−5.82946e57	−	4.19737e57i	−0.187803	−	0.135223i
$611$			3.22472e58i			1.00375i
$612$	3.73778e58	+	1.11775e59i	1.12418	+	3.36173i
$613$	−3.61251e57			−0.104988			−0.0524939	−	0.998621i	$-0.516717\pi$
$613$	−3.61251e57			−0.104988			−0.0524939	+	0.998621i	$0.516717\pi$
$614$	−2.36442e58	+	3.28379e58i	−0.664032	+	0.922231i
$615$		−	7.31223e58i		−	1.98460i
$616$	1.67433e58	−	5.38732e58i	0.439184	−	1.41312i
$617$	6.79996e57			0.172392			0.0861962	−	0.996278i	$-0.472529\pi$
$617$	6.79996e57			0.172392			0.0861962	+	0.996278i	$0.472529\pi$
$618$	1.45167e58	+	1.04524e58i	0.355721	+	0.256129i
$619$		−	6.97631e58i		−	1.65243i	−0.563357	−	0.826214i	$-0.690490\pi$
$619$		−	6.97631e58i		−	1.65243i	0.563357	−	0.826214i	$-0.309510\pi$
$620$	−3.11607e58	+	1.04202e58i	−0.713479	+	0.238590i
$621$	−6.70313e58			−1.48373
$622$	−3.31628e58	+	4.60576e58i	−0.709664	+	0.985606i
$623$			1.11686e59i			2.31074i
$624$	−4.23955e58	−	5.63011e58i	−0.848094	−	1.12627i
$625$	−5.06262e58			−0.979253
$626$	2.78076e58	+	2.00223e58i	0.520120	+	0.374500i
$627$		−	7.78623e57i		−	0.140834i
$628$	−2.07211e58	−	6.19642e58i	−0.362460	−	1.08390i
$629$	6.45935e58			1.09276
$630$	9.16561e58	−	1.27295e59i	1.49972	−	2.08286i
$631$		−	2.87701e58i		−	0.455328i	−0.973740	−	0.227664i	$-0.926891\pi$
$631$		−	2.87701e58i		−	0.455328i	0.973740	−	0.227664i	$-0.0731088\pi$
$632$	5.72733e58	+	1.78001e58i	0.876786	+	0.272498i
$633$	−6.42389e58			−0.951306
$634$	4.39991e58	+	3.16806e58i	0.630332	+	0.453856i
$635$			1.22676e59i			1.70025i
$636$	9.72567e58	−	3.25230e58i	1.30413	−	0.436105i
$637$	2.49813e58			0.324106
$638$	−1.66933e58	+	2.31843e58i	−0.209560	+	0.291045i
$639$		−	1.21842e59i		−	1.48006i
$640$	−2.84052e58	−	7.92653e58i	−0.333902	−	0.931760i
$641$	1.12544e59			1.28028			0.640138	−	0.768260i	$-0.278877\pi$
$641$	1.12544e59			1.28028			0.640138	+	0.768260i	$0.278877\pi$
$642$	−1.31962e59	−	9.50163e58i	−1.45282	−	1.04607i
$643$			7.85354e58i			0.836826i	0.908257	+	0.418413i	$0.137414\pi$
$643$			7.85354e58i			0.836826i	−0.908257	+	0.418413i	$0.862586\pi$
$644$	−2.56543e58	−	7.67164e58i	−0.264580	−	0.791198i
$645$	−8.79969e57			−0.0878443
$646$	−6.21747e57	+	8.63505e57i	−0.0600802	+	0.0834415i
$647$		−	1.28763e59i		−	1.20449i	−0.798313	−	0.602243i	$-0.794274\pi$
$647$		−	1.28763e59i		−	1.20449i	0.798313	−	0.602243i	$-0.205726\pi$
$648$	−5.19355e58	+	1.67107e59i	−0.470315	+	1.51328i
$649$	−1.16331e59			−1.01989
$650$	1.53606e57	+	1.10601e57i	0.0130385	+	0.00938809i
$651$			1.95957e59i			1.61050i
$652$	9.23153e58	−	3.08706e58i	0.734639	−	0.245666i
$653$	−4.15957e58			−0.320532			−0.160266	−	0.987074i	$-0.551235\pi$
$653$	−4.15957e58			−0.320532			−0.160266	+	0.987074i	$0.551235\pi$
$654$	2.02029e59	−	2.80586e59i	1.50759	−	2.09379i
$655$			1.41374e59i			1.02165i
$656$	−1.28266e59	+	9.65864e58i	−0.897702	+	0.675982i
$657$	−3.46543e59			−2.34901
$658$	1.86463e59	+	1.34258e59i	1.22419	+	0.881450i
$659$			1.18903e58i			0.0756133i	0.999285	+	0.0378066i	$0.0120371\pi$
$659$			1.18903e58i			0.0756133i	−0.999285	+	0.0378066i	$0.987963\pi$
$660$	1.13303e59	+	3.38820e59i	0.697940	+	2.08712i
$661$	2.81967e59			1.68255			0.841276	−	0.540607i	$-0.181805\pi$
$661$	2.81967e59			1.68255			0.841276	+	0.540607i	$0.181805\pi$
$662$	−4.72875e58	+	6.56746e58i	−0.273356	+	0.379647i
$663$		−	4.08659e59i		−	2.28864i
$664$	−1.94149e59	−	6.03399e58i	−1.05343	−	0.327397i
$665$	1.41616e58			0.0744489
$666$	2.34191e59	+	1.68624e59i	1.19292	+	0.858936i
$667$			4.09642e58i			0.202191i
$668$	−7.49398e58	+	2.50602e58i	−0.358432	+	0.119861i
$669$	−1.41826e59			−0.657365
$670$	6.84287e58	−	9.50362e58i	0.307374	−	0.426892i
$671$		−	6.69264e58i		−	0.291356i
$672$	−5.02059e59	+	1.07387e58i	−2.11836	+	0.0453104i
$673$	2.79520e59			1.14313			0.571566	−	0.820556i	$-0.306336\pi$
$673$	2.79520e59			1.14313			0.571566	+	0.820556i	$0.306336\pi$
$674$	−1.21055e59	−	8.71632e58i	−0.479873	−	0.345522i
$675$		−	1.11757e58i		−	0.0429435i
$676$	−3.19822e58	−	9.56395e58i	−0.119132	−	0.356252i
$677$	4.64338e58			0.167676			0.0838382	−	0.996479i	$-0.473282\pi$
$677$	4.64338e58			0.167676			0.0838382	+	0.996479i	$0.473282\pi$
$678$	−2.81916e59	+	3.91536e59i	−0.986954	+	1.37072i
$679$			5.09272e59i			1.72856i
$680$	1.44901e59	−	4.66232e59i	0.476852	−	1.53432i
$681$	6.40409e59			2.04347
$682$	−2.48426e59	−	1.78874e59i	−0.768644	−	0.553445i
$683$		−	5.55319e57i		−	0.0166613i	−0.999965	−	0.00833064i	$-0.997348\pi$
$683$		−	5.55319e57i		−	0.0166613i	0.999965	−	0.00833064i	$-0.00265175\pi$
$684$	−4.50843e58	+	1.50764e58i	−0.131174	+	0.0438651i
$685$	−2.67235e59			−0.754035
$686$	−1.49560e59	+	2.07714e59i	−0.409269	+	0.568408i
$687$		−	4.52155e59i		−	1.20004i
$688$	1.16234e58	+	1.54358e58i	0.0299210	+	0.0397350i
$689$	−2.43891e59			−0.608965
$690$	4.15720e59	+	2.99330e59i	1.00686	+	0.724969i
$691$		−	1.40309e59i		−	0.329644i	−0.986323	−	0.164822i	$-0.947295\pi$
$691$		−	1.40309e59i		−	0.329644i	0.986323	−	0.164822i	$-0.0527049\pi$
$692$	−7.32321e58	−	2.18993e59i	−0.166907	−	0.499117i
$693$	1.46144e60			3.23135
$694$	−1.11429e59	+	1.54756e59i	−0.239027	+	0.331970i
$695$		−	1.32314e59i		−	0.275375i
$696$	2.42845e59	+	7.54742e58i	0.490383	+	0.152407i
$697$	−9.31016e59			−1.82419
$698$	−6.17570e58	−	4.44668e58i	−0.117415	−	0.0845418i
$699$		−	3.88796e59i		−	0.717301i
$700$	1.27905e58	−	4.27719e57i	0.0228996	−	0.00765773i
$701$	6.43047e58			0.111729			0.0558643	−	0.998438i	$-0.482209\pi$
$701$	6.43047e58			0.111729			0.0558643	+	0.998438i	$0.482209\pi$
$702$	5.78273e59	−	8.03126e59i	0.975110	−	1.35427i
$703$			2.60538e58i			0.0426392i
$704$	4.44676e59	−	6.46292e59i	0.706346	−	1.02660i
$705$	−1.45507e60			−2.24343
$706$	4.46123e59	+	3.21221e59i	0.667660	+	0.480734i
$707$		−	9.62482e59i		−	1.39825i
$708$	3.28402e59	+	9.82052e59i	0.463135	+	1.38496i
$709$	4.81928e59			0.659799			0.329899	−	0.944016i	$-0.392985\pi$
$709$	4.81928e59			0.659799			0.329899	+	0.944016i	$0.392985\pi$
$710$	−2.94925e59	+	4.09602e59i	−0.392000	+	0.544424i
$711$			1.55368e60i			2.00493i
$712$	−4.60937e59	+	1.48311e60i	−0.577513	+	1.85820i
$713$	−4.38943e59			−0.533983
$714$	−2.36299e60	−	1.70142e60i	−2.79125	−	2.00978i
$715$		−	8.49662e59i		−	0.974584i
$716$	−1.00076e59	+	3.34659e58i	−0.111470	+	0.0372760i
$717$	−1.84586e59			−0.199662
$718$	4.22479e59	−	5.86753e59i	0.443804	−	0.616371i
$719$			1.51990e59i			0.155063i	0.996990	+	0.0775314i	$0.0247038\pi$
$719$			1.51990e59i			0.155063i	−0.996990	+	0.0775314i	$0.975296\pi$
$720$	1.74247e60	−	1.31211e60i	1.72657	−	1.30013i
$721$	−3.03126e59			−0.291731
$722$	8.64642e59	+	6.22566e59i	0.808268	+	0.581975i
$723$			3.12754e60i			2.83987i
$724$	−3.76755e58	−	1.12665e59i	−0.0332314	−	0.0993751i
$725$	−6.82973e57			−0.00585201
$726$	−6.92440e59	+	9.61685e59i	−0.576386	+	0.800505i
$727$			2.04919e60i			1.65714i	0.559885	+	0.828570i	$0.310845\pi$
$727$			2.04919e60i			1.65714i	−0.559885	+	0.828570i	$0.689155\pi$
$728$	1.14049e60	+	3.54453e59i	0.896047	+	0.278484i
$729$	4.03405e59			0.307938
$730$	1.16499e60	+	8.38824e59i	0.864055	+	0.622144i
$731$			1.12040e59i			0.0807439i
$732$	−5.64987e59	+	1.88934e59i	−0.395645	+	0.132305i
$733$	−1.16769e60			−0.794594			−0.397297	−	0.917690i	$-0.630052\pi$
$733$	−1.16769e60			−0.794594			−0.397297	+	0.917690i	$0.630052\pi$
$734$	1.32112e60	−	1.83481e60i	0.873622	−	1.21332i
$735$			1.12721e60i			0.724390i
$736$	−2.40547e58	−	1.12461e60i	−0.0150233	−	0.702373i
$737$	1.09109e60			0.662280
$738$	−3.37551e60	−	2.43046e60i	−1.99139	−	1.43385i
$739$		−	2.12442e60i		−	1.21817i	−0.793106	−	0.609084i	$-0.791537\pi$
$739$		−	2.12442e60i		−	1.21817i	0.793106	−	0.609084i	$-0.208463\pi$
$740$	−3.79127e59	−	1.13374e60i	−0.211309	−	0.631899i
$741$	1.64833e59			0.0893021
$742$	−1.01542e60	+	1.41025e60i	−0.534765	+	0.742700i
$743$		−	3.08505e60i		−	1.57942i	−0.613483	−	0.789708i	$-0.710232\pi$
$743$		−	3.08505e60i		−	1.57942i	0.613483	−	0.789708i	$-0.289768\pi$
$744$	−8.08727e59	+	2.60215e60i	−0.402504	+	1.29509i
$745$	−1.36392e60			−0.659942
$746$	6.34600e59	+	4.56929e59i	0.298528	+	0.214948i
$747$		−	5.26677e60i		−	2.40886i
$748$	4.31397e60	−	1.44261e60i	1.91842	−	0.641526i
$749$	2.75552e60			1.19148
$750$	−2.50427e60	+	3.47802e60i	−1.05292	+	1.46233i
$751$		−	2.49132e60i		−	1.01857i	−0.860598	−	0.509285i	$-0.829910\pi$
$751$		−	2.49132e60i		−	1.01857i	0.860598	−	0.509285i	$-0.170090\pi$
$752$	1.92198e60	+	2.55239e60i	0.764144	+	1.01478i
$753$	−2.49005e60			−0.962752
$754$	−4.90807e59	−	3.53395e59i	−0.184549	−	0.132881i
$755$		−	1.70151e60i		−	0.622226i
$756$	−2.23632e60	−	6.68748e60i	−0.795383	−	2.37851i
$757$	−1.84385e60			−0.637839			−0.318919	−	0.947782i	$-0.603320\pi$
$757$	−1.84385e60			−0.637839			−0.318919	+	0.947782i	$0.603320\pi$
$758$	−7.21879e59	+	1.00257e60i	−0.242891	+	0.337335i
$759$			4.77277e60i			1.56204i
$760$	1.88055e59	+	5.84459e58i	0.0598686	+	0.0186067i
$761$	2.32448e60			0.719861			0.359931	−	0.932979i	$-0.382800\pi$
$761$	2.32448e60			0.719861			0.359931	+	0.932979i	$0.382800\pi$
$762$	8.25643e60	+	5.94486e60i	2.48736	+	1.79096i
$763$			5.85896e60i			1.71714i
$764$	−4.82311e60	+	1.61287e60i	−1.37520	+	0.459873i
$765$	1.26477e61			3.50849
$766$	1.46595e60	−	2.03597e60i	0.395654	−	0.549499i
$767$		−	2.46270e60i		−	0.646708i
$768$	−6.71126e60	−	1.92943e60i	−1.71482	−	0.492995i
$769$	4.18397e59			0.104024			0.0520122	−	0.998646i	$-0.483437\pi$
$769$	4.18397e59			0.104024			0.0520122	+	0.998646i	$0.483437\pi$
$770$	−4.91299e60	−	3.53749e60i	−1.18861	−	0.855834i
$771$			2.24092e60i			0.527575i
$772$	1.24404e60	+	3.72019e60i	0.285018	+	0.852317i
$773$	−1.15011e60			−0.256432			−0.128216	−	0.991746i	$-0.540925\pi$
$773$	−1.15011e60			−0.256432			−0.128216	+	0.991746i	$0.540925\pi$
$774$	−2.92486e59	+	4.06215e59i	−0.0634666	+	0.0881447i
$775$		−	7.31824e58i		−	0.0154551i
$776$	−2.10180e60	+	6.76273e60i	−0.432011	+	1.39003i
$777$	−7.12964e60			−1.42635
$778$	−6.15835e60	−	4.43418e60i	−1.19920	−	0.863460i
$779$		−	3.75526e59i		−	0.0711792i
$780$	−7.17277e60	+	2.39860e60i	−1.32343	+	0.442559i
$781$	−4.70253e60			−0.844618
$782$	3.81116e60	−	5.29308e60i	0.666370	−	0.925479i
$783$			3.57091e60i			0.607830i
$784$	1.97728e60	−	1.48892e60i	0.327666	−	0.246737i
$785$	−7.01147e60			−1.13122
$786$	9.51484e60	+	6.85095e60i	1.49461	+	1.07616i
$787$		−	1.86998e59i		−	0.0286001i	−0.999898	−	0.0143001i	$-0.995448\pi$
$787$		−	1.86998e59i		−	0.0286001i	0.999898	−	0.0143001i	$-0.00455201\pi$
$788$	−6.51746e59	−	1.94898e60i	−0.0970573	−	0.290240i
$789$	1.54333e61			2.23790
$790$	3.76075e60	−	5.22306e60i	0.531013	−	0.737490i
$791$		−	8.17573e60i		−	1.12414i
$792$	1.94068e61	+	6.03146e60i	2.59851	+	0.807595i
$793$	1.41682e60			0.184747
$794$	−2.62267e60	−	1.88839e60i	−0.333053	−	0.239807i
$795$		−	1.10049e61i		−	1.36106i
$796$	−7.38978e60	+	2.47117e60i	−0.890138	+	0.297666i
$797$	8.43988e60			0.990174			0.495087	−	0.868843i	$-0.335136\pi$
$797$	8.43988e60			0.990174			0.495087	+	0.868843i	$0.335136\pi$
$798$	6.86267e59	−	9.53112e59i	0.0784210	−	0.108914i
$799$			1.85264e61i			2.06210i
$800$	1.87500e59	−	4.01050e57i	0.0203288	−	0.000434819i
$801$	−4.02329e61			−4.24911
$802$	5.73846e60	+	4.13185e60i	0.590383	+	0.425092i
$803$			1.33749e61i			1.34049i
$804$	−3.08014e60	−	9.21084e60i	−0.300742	−	0.899337i
$805$	−8.68073e60			−0.825739
$806$	3.78672e60	−	5.25913e60i	0.350936	−	0.487392i
$807$		−	2.92239e61i		−	2.63872i
$808$	3.97222e60	−	1.27810e61i	0.349458	−	1.12441i
$809$	−2.87682e60			−0.246600			−0.123300	−	0.992369i	$-0.539348\pi$
$809$	−2.87682e60			−0.246600			−0.123300	+	0.992369i	$0.539348\pi$
$810$	1.52394e61	+	1.09728e61i	1.27287	+	0.916499i
$811$			1.38058e61i			1.12363i	0.827264	+	0.561814i	$0.189896\pi$
$811$			1.38058e61i			1.12363i	−0.827264	+	0.561814i	$0.810104\pi$
$812$	−4.08686e60	+	1.36666e60i	−0.324126	+	0.108389i
$813$	2.71208e61			2.09605
$814$	6.50809e60	−	9.03866e60i	0.490163	−	0.680756i
$815$		−	1.04458e61i		−	0.766711i
$816$	−2.43567e61	−	3.23456e61i	−1.74231	−	2.31378i
$817$	−4.51915e58			−0.00315061
$818$	−2.04173e60	−	1.47010e60i	−0.138733	−	0.0998914i
$819$			3.09385e61i			2.04897i
$820$	5.46454e60	+	1.63411e61i	0.352747	+	1.05485i
$821$	2.01488e61			1.26778			0.633888	−	0.773425i	$-0.281458\pi$
$821$	2.01488e61			1.26778			0.633888	+	0.773425i	$0.281458\pi$
$822$	−1.29501e61	+	1.79856e61i	−0.794266	+	1.10310i
$823$		−	1.08566e61i		−	0.649078i	−0.945872	−	0.324539i	$-0.894791\pi$
$823$		−	1.08566e61i		−	0.649078i	0.945872	−	0.324539i	$-0.105209\pi$
$824$	−4.02526e60	−	1.25102e60i	−0.234597	−	0.0729108i
$825$	−7.95737e59			−0.0452102
$826$	−1.42400e61	−	1.02532e61i	−0.788732	−	0.567909i
$827$			2.23442e61i			1.20656i	0.797530	+	0.603280i	$0.206140\pi$
$827$			2.23442e61i			1.20656i	−0.797530	+	0.603280i	$0.793860\pi$
$828$	2.76356e61	−	9.24145e60i	1.45490	−	0.486523i
$829$	−9.19006e60			−0.471708			−0.235854	−	0.971789i	$-0.575789\pi$
$829$	−9.19006e60			−0.471708			−0.235854	+	0.971789i	$0.575789\pi$
$830$	−1.27485e61	+	1.77055e61i	−0.637996	+	0.886072i
$831$		−	3.05219e61i		−	1.48932i
$832$	1.36819e61	+	9.41371e60i	0.650962	+	0.447889i
$833$	1.43520e61			0.665838
$834$	−8.90504e60	−	6.41188e60i	−0.402855	−	0.290067i
$835$			8.47970e60i			0.374080i
$836$	5.81876e59	+	1.74004e60i	0.0250322	+	0.0748562i
$837$	−3.82633e61			−1.60527
$838$	1.49274e61	−	2.07317e61i	0.610745	−	0.848224i
$839$			4.22854e61i			1.68729i	0.536904	+	0.843644i	$0.319594\pi$
$839$			4.22854e61i			1.68729i	−0.536904	+	0.843644i	$0.680406\pi$
$840$	−1.59938e61	+	5.14614e61i	−0.622423	+	2.00270i
$841$	−2.41638e61			−0.917170
$842$	−9.72215e59	−	7.00022e59i	−0.0359922	−	0.0259154i
$843$		−	7.44488e61i		−	2.68831i
$844$	1.43559e61	−	4.80067e60i	0.505637	−	0.169087i
$845$	−1.08219e61			−0.371804
$846$	−4.83640e61	+	6.71696e61i	−1.62086	+	2.25110i
$847$		−	2.00811e61i		−	0.656503i
$848$	−1.93041e61	+	1.45363e61i	−0.615654	+	0.463596i
$849$	6.76046e61			2.10336
$850$	8.82485e59	+	6.35414e59i	0.0267861	+	0.0192867i
$851$		−	1.59704e61i		−	0.472927i
$852$	1.32753e61	+	3.96984e61i	0.383542	+	1.14694i
$853$	6.97269e61			1.96549			0.982744	−	0.184970i	$-0.0592189\pi$
$853$	6.97269e61			1.96549			0.982744	+	0.184970i	$0.0592189\pi$
$854$	5.89880e60	−	8.19246e60i	0.162236	−	0.225320i
$855$			5.10145e60i			0.136901i
$856$	3.65911e61	+	1.13722e61i	0.958135	+	0.297780i
$857$	−5.91769e61			−1.51201			−0.756005	−	0.654566i	$-0.772851\pi$
$857$	−5.91769e61			−1.51201			−0.756005	+	0.654566i	$0.772851\pi$
$858$	−5.71843e61	−	4.11743e61i	−1.42575	−	1.02658i
$859$			4.91598e61i			1.19606i	0.801473	+	0.598031i	$0.204050\pi$
$859$			4.91598e61i			1.19606i	−0.801473	+	0.598031i	$0.795950\pi$
$860$	1.96653e60	−	6.57614e59i	0.0466909	−	0.0156136i
$861$	1.02763e62			2.38106
$862$	3.94448e61	−	5.47823e61i	0.891942	−	1.23876i
$863$			5.01711e61i			1.10720i	0.832782	+	0.553601i	$0.186747\pi$
$863$			5.01711e61i			1.10720i	−0.832782	+	0.553601i	$0.813253\pi$
$864$	−2.09688e60	−	9.80338e61i	−0.0451633	−	2.11148i
$865$	−2.47798e61			−0.520907
$866$	−4.95648e61	−	3.56880e61i	−1.01695	−	0.732229i
$867$		−	1.45682e62i		−	2.91747i
$868$	−1.46442e61	−	4.37918e61i	−0.286253	−	0.856010i
$869$	5.99646e61			1.14414
$870$	1.59460e61	−	2.21464e61i	0.296994	−	0.412475i
$871$			2.30981e61i			0.419947i
$872$	−2.41803e61	+	7.78023e61i	−0.429156	+	1.38085i
$873$	−1.83455e62			−3.17857
$874$	2.13497e60	+	1.53723e60i	0.0361119	+	0.0260016i
$875$		−	7.26252e61i		−	1.19927i
$876$	1.12910e62	−	3.77575e61i	1.82031	−	0.608719i
$877$	−7.92808e61			−1.24789			−0.623945	−	0.781468i	$-0.714471\pi$
$877$	−7.92808e61			−1.24789			−0.623945	+	0.781468i	$0.714471\pi$
$878$	−6.64343e61	+	9.22664e61i	−1.02096	+	1.41794i
$879$			1.96659e62i			2.95086i
$880$	−5.06411e61	−	6.72512e61i	−0.741937	−	0.985290i
$881$	1.03200e62			1.47634			0.738169	−	0.674616i	$-0.235691\pi$
$881$	1.03200e62			1.47634			0.738169	+	0.674616i	$0.235691\pi$
$882$	5.20350e61	+	3.74666e61i	0.726867	+	0.523365i
$883$			1.68628e61i			0.230014i	0.993365	+	0.115007i	$0.0366891\pi$
$883$			1.68628e61i			0.230014i	−0.993365	+	0.115007i	$0.963311\pi$
$884$	3.05397e61	+	9.13259e61i	0.406787	+	1.21646i
$885$	1.11123e62			1.44542
$886$	7.63005e61	−	1.05969e62i	0.969212	−	1.34608i
$887$		−	1.27405e62i		−	1.58049i	−0.612794	−	0.790243i	$-0.709954\pi$
$887$		−	1.27405e62i		−	1.58049i	0.612794	−	0.790243i	$-0.290046\pi$
$888$	−9.46759e61	−	2.94245e61i	−1.14701	−	0.356481i
$889$	−1.72404e62			−2.03991
$890$	1.35252e62	+	9.73855e61i	1.56299	+	1.12539i
$891$			1.74960e62i			1.97472i
$892$	3.16947e61	−	1.05988e61i	0.349402	−	0.116841i
$893$	−7.47264e60			−0.0804624
$894$	−6.60949e61	+	9.17949e61i	−0.695152	+	0.965452i
$895$			1.13240e61i			0.116336i
$896$	1.11396e62	−	3.99195e61i	1.11790	−	0.400605i
$897$	−1.01039e62			−0.990481
$898$	1.17459e62	+	8.45735e61i	1.12482	+	0.809899i
$899$			2.33835e61i			0.218754i
$900$	1.54078e60	+	4.60753e60i	0.0140814	+	0.0421090i
$901$	−1.40118e62			−1.25105
$902$	−9.38041e61	+	1.30278e62i	−0.818247	+	1.13641i
$903$		−	1.23667e61i		−	0.105393i
$904$	3.37417e61	−	1.08567e62i	0.280951	−	0.903985i
$905$	−1.27484e61			−0.103713
$906$	−1.14516e62	−	8.24545e61i	−0.910275	−	0.655423i
$907$		−	1.81984e62i		−	1.41345i	−0.707491	−	0.706723i	$-0.750173\pi$
$907$		−	1.81984e62i		−	1.41345i	0.707491	−	0.706723i	$-0.249827\pi$
$908$	−1.43116e62	+	4.78587e61i	−1.08614	+	0.363210i
$909$	3.46716e62			2.57118
$910$	7.48880e61	−	1.04007e62i	0.542679	−	0.753691i
$911$			1.85555e62i			1.31398i	0.753901	+	0.656988i	$0.228170\pi$
$911$			1.85555e62i			1.31398i	−0.753901	+	0.656988i	$0.771830\pi$
$912$	1.30466e61	−	9.82430e60i	0.0902831	−	0.0679845i
$913$	−2.03272e62			−1.37465
$914$	−2.02234e62	−	1.45614e62i	−1.33655	−	0.962351i
$915$			6.39302e61i			0.412917i
$916$	3.37902e61	+	1.01046e62i	0.213298	+	0.637844i
$917$	−1.98681e62			−1.22575
$918$	3.32225e62	−	4.61405e62i	2.00325	−	2.78219i
$919$			5.54278e61i			0.326665i	0.986571	+	0.163332i	$0.0522243\pi$
$919$			5.54278e61i			0.326665i	−0.986571	+	0.163332i	$0.947776\pi$
$920$	−1.15273e62	−	3.58259e61i	−0.664024	−	0.206373i
$921$	3.60125e62			2.02769
$922$	7.40544e61	+	5.33212e61i	0.407569	+	0.293461i
$923$		−	9.95518e61i		−	0.535566i
$924$	−4.76163e62	+	1.59231e62i	−2.50406	+	0.837367i
$925$	2.66265e60			0.0136879
$926$	5.80274e61	−	8.05905e61i	0.291610	−	0.404998i
$927$		−	1.09195e62i		−	0.536449i
$928$	−5.99105e61	+	1.28145e60i	−0.287737	+	0.00615451i
$929$	3.25169e62			1.52679			0.763394	−	0.645934i	$-0.223532\pi$
$929$	3.25169e62			1.52679			0.763394	+	0.645934i	$0.223532\pi$
$930$	2.37304e62	+	1.70866e62i	1.08934	+	0.784355i
$931$			5.78890e60i			0.0259808i
$932$	2.90553e61	+	8.68870e61i	0.127495	+	0.381259i
$933$	5.05103e62			2.16703
$934$	−9.29680e61	+	1.29117e62i	−0.389986	+	0.541626i
$935$		−	4.88140e62i		−	2.00217i
$936$	−1.27685e62	+	4.10838e62i	−0.512090	+	1.64770i
$937$	−1.80951e62			−0.709626			−0.354813	−	0.934937i	$-0.615455\pi$
$937$	−1.80951e62			−0.709626			−0.354813	+	0.934937i	$0.615455\pi$
$938$	1.33560e62	+	9.61667e61i	0.512172	+	0.368778i
$939$		−	3.04960e62i		−	1.14358i
$940$	3.25174e62	−	1.08740e62i	1.19243	−	0.398752i
$941$	−1.71987e61			−0.0616757			−0.0308379	−	0.999524i	$-0.509818\pi$
$941$	−1.71987e61			−0.0616757			−0.0308379	+	0.999524i	$0.509818\pi$
$942$	−3.39773e62	+	4.71889e62i	−1.19157	+	1.65490i
$943$			2.30188e62i			0.789474i
$944$	−1.46780e62	−	1.94924e62i	−0.492330	−	0.653812i
$945$	−7.56712e62			−2.48235
$946$	1.56780e61	+	1.12886e61i	0.0503009	+	0.0362181i
$947$			1.29392e62i			0.406028i	0.979176	+	0.203014i	$0.0650737\pi$
$947$			1.29392e62i			0.406028i	−0.979176	+	0.203014i	$0.934926\pi$
$948$	−1.69280e62	−	5.06215e62i	−0.519555	−	1.55368i
$949$	−2.83145e62			−0.849998
$950$	−2.56294e59	+	3.55951e59i	−0.000752564	+	0.00104519i
$951$		−	4.82527e62i		−	1.38590i
$952$	6.55222e62	+	2.03637e62i	1.84082	+	0.572113i
$953$	2.05231e62			0.564017			0.282008	−	0.959412i	$-0.408999\pi$
$953$	2.05231e62			0.564017			0.282008	+	0.959412i	$0.408999\pi$
$954$	−5.08014e62	−	3.65784e62i	−1.36572	−	0.983353i
$955$			5.45752e62i			1.43524i
$956$	4.12506e61	−	1.37944e61i	0.106124	−	0.0354883i
$957$	2.54256e62			0.639913
$958$	2.65278e61	−	3.68428e61i	0.0653169	−	0.0907145i
$959$		−	3.75561e62i		−	0.904668i
$960$	−4.24768e62	+	6.17358e62i	−1.00105	+	1.45493i
$961$	1.83141e62			0.422275
$962$	1.91347e62	+	1.37775e62i	0.431663	+	0.310809i
$963$			9.92624e62i			2.19095i
$964$	−2.33725e62	−	6.98931e62i	−0.504764	−	1.50944i
$965$	4.20952e62			0.889527
$966$	−4.20665e62	+	5.84235e62i	−0.869795	+	1.20800i
$967$			7.59327e62i			1.53629i	0.640276	+	0.768145i	$0.278820\pi$
$967$			7.59327e62i			1.53629i	−0.640276	+	0.768145i	$0.721180\pi$
$968$	8.28761e61	−	2.66661e62i	0.164077	−	0.527932i
$969$	9.46984e61			0.183461
$970$	6.16730e62	+	4.44062e62i	1.16920	+	0.841856i
$971$		−	4.92894e62i		−	0.914428i	−0.889357	−	0.457214i	$-0.848847\pi$
$971$		−	4.92894e62i		−	0.914428i	0.889357	−	0.457214i	$-0.151153\pi$
$972$	3.73779e62	−	1.24993e62i	0.678614	−	0.226931i
$973$	1.85948e62			0.330386
$974$	3.88856e62	−	5.40057e62i	0.676162	−	0.939077i
$975$		−	1.68456e61i		−	0.0286675i
$976$	1.12142e62	−	8.44446e61i	0.186777	−	0.140645i
$977$	−2.02919e62			−0.330778			−0.165389	−	0.986228i	$-0.552888\pi$
$977$	−2.02919e62			−0.330778			−0.165389	+	0.986228i	$0.552888\pi$
$978$	−7.03028e62	−	5.06199e62i	−1.12165	−	0.807618i
$979$			1.55280e63i			2.42481i
$980$	−8.42384e61	−	2.51906e62i	−0.128755	−	0.385027i
$981$	−2.11058e63			−3.15756
$982$	−2.51438e62	+	3.49206e62i	−0.368204	+	0.511375i
$983$		−	8.59332e62i		−	1.23179i	−0.787828	−	0.615896i	$-0.788794\pi$
$983$		−	8.59332e62i		−	1.23179i	0.787828	−	0.615896i	$-0.211206\pi$
$984$	1.36461e63	+	4.24109e62i	1.91475	+	0.595087i
$985$	−2.20534e62			−0.302910
$986$	−2.81974e62	−	2.03029e62i	−0.379135	−	0.272988i
$987$		−	2.04489e63i		−	2.69160i
$988$	−3.68363e61	+	1.23182e61i	−0.0474658	+	0.0158727i
$989$	2.77013e61			0.0349445
$990$	1.27431e63	−	1.76981e63i	1.57375	−	2.18568i
$991$			7.57765e62i			0.916194i	0.888902	+	0.458097i	$0.151469\pi$
$991$			7.57765e62i			0.916194i	−0.888902	+	0.458097i	$0.848531\pi$
$992$	−1.37311e61	−	6.41958e62i	−0.0162540	−	0.759908i
$993$	7.20237e62			0.834721
$994$	−5.75637e62	−	4.14475e62i	−0.653183	−	0.470310i
$995$			8.36180e62i			0.928998i
$996$	5.73839e62	+	1.71601e63i	0.624229	+	1.86669i
$997$	−6.10757e62			−0.650534			−0.325267	−	0.945622i	$-0.605454\pi$
$997$	−6.10757e62			−0.650534			−0.325267	+	0.945622i	$0.605454\pi$
$998$	−9.18475e62	+	1.27561e63i	−0.957913	+	1.33038i
$999$		−	1.39216e63i		−	1.42172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.43.b.a.3.18	yes	20
4.3	odd	2	inner	4.43.b.a.3.17	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.43.b.a.3.17	✓	20	4.3	odd	2	inner
4.43.b.a.3.18	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)

\(f(q)\)	\(=\)	\(q+(1.70189e6 + 1.22541e6i) q^{2} -1.86642e10i q^{3} +(1.39480e12 + 4.17101e12i) q^{4} +4.71964e14 q^{5} +(2.28712e16 - 3.17644e16i) q^{6} +6.63278e17i q^{7} +(-2.73739e18 + 8.80780e18i) q^{8} -2.38933e20 q^{9} +O(q^{10})\)	\(q+(1.70189e6 + 1.22541e6i) q^{2} -1.86642e10i q^{3} +(1.39480e12 + 4.17101e12i) q^{4} +4.71964e14 q^{5} +(2.28712e16 - 3.17644e16i) q^{6} +6.63278e17i q^{7} +(-2.73739e18 + 8.80780e18i) q^{8} -2.38933e20 q^{9} +(8.03231e20 + 5.78348e20i) q^{10} +9.22168e21i q^{11} +(7.78486e22 - 2.60329e22i) q^{12} -1.95221e23 q^{13} +(-8.12785e23 + 1.12883e24i) q^{14} -8.80883e24i q^{15} +(-1.54519e25 + 1.16355e25i) q^{16} -1.12157e26 q^{17} +(-4.06637e26 - 2.92790e26i) q^{18} -4.52385e25i q^{19} +(6.58297e26 + 1.96857e27i) q^{20} +1.23795e28 q^{21} +(-1.13003e28 + 1.56943e28i) q^{22} +2.77301e28i q^{23} +(1.64390e29 + 5.10911e28i) q^{24} -4.62328e27 q^{25} +(-3.32245e29 - 2.39225e29i) q^{26} +2.41727e30i q^{27} +(-2.76654e30 + 9.25142e29i) q^{28} +1.47725e30 q^{29} +(1.07944e31 - 1.49917e31i) q^{30} +1.58291e31i q^{31} +(-4.05555e31 + 8.67457e29i) q^{32} +1.72115e32 q^{33} +(-1.90878e32 - 1.37438e32i) q^{34} +3.13044e32i q^{35} +(-3.33264e32 - 9.96592e32i) q^{36} -5.75921e32 q^{37} +(5.54356e31 - 7.69909e31i) q^{38} +3.64365e33i q^{39} +(-1.29195e33 + 4.15697e33i) q^{40} +8.30103e33 q^{41} +(2.10686e34 + 1.51700e34i) q^{42} -9.98962e32i q^{43} +(-3.84637e34 + 1.28624e34i) q^{44} -1.12768e35 q^{45} +(-3.39807e34 + 4.71935e34i) q^{46} -1.65183e35i q^{47} +(2.17167e35 + 2.88397e35i) q^{48} -1.27964e35 q^{49} +(-7.86831e33 - 5.66540e33i) q^{50} +2.09332e36i q^{51} +(-2.72295e35 - 8.14270e35i) q^{52} +1.24931e36 q^{53} +(-2.96214e36 + 4.11393e36i) q^{54} +4.35230e36i q^{55} +(-5.84202e36 - 1.81565e36i) q^{56} -8.44340e35 q^{57} +(2.51411e36 + 1.81023e36i) q^{58} +1.26149e37i q^{59} +(3.67417e37 - 1.22866e37i) q^{60} -7.25751e36 q^{61} +(-1.93971e37 + 2.69394e37i) q^{62} -1.58479e38i q^{63} +(-7.00840e37 - 4.82207e37i) q^{64} -9.21374e37 q^{65} +(2.92921e38 + 2.10911e38i) q^{66} -1.18317e38i q^{67} +(-1.56437e38 - 4.67807e38i) q^{68} +5.17560e38 q^{69} +(-3.83606e38 + 5.32765e38i) q^{70} +5.09944e38i q^{71} +(6.54052e38 - 2.10447e39i) q^{72} +1.45038e39 q^{73} +(-9.80154e38 - 7.05738e38i) q^{74} +8.62899e37i q^{75} +(1.88690e38 - 6.30988e37i) q^{76} -6.11653e39 q^{77} +(-4.46495e39 + 6.20108e39i) q^{78} -6.50257e39i q^{79} +(-7.29273e39 + 5.49153e39i) q^{80} +1.89726e40 q^{81} +(1.41274e40 + 1.01721e40i) q^{82} +2.20429e40i q^{83} +(1.72670e40 + 5.16352e40i) q^{84} -5.29340e40 q^{85} +(1.22414e39 - 1.70012e39i) q^{86} -2.75716e40i q^{87} +(-8.12227e40 - 2.52433e40i) q^{88} +1.68386e41 q^{89} +(-1.91918e41 - 1.38187e41i) q^{90} -1.29486e41i q^{91} +(-1.15663e41 + 3.86780e40i) q^{92} +2.95437e41 q^{93} +(2.02417e41 - 2.81123e41i) q^{94} -2.13510e40i q^{95} +(1.61904e40 + 7.56936e41i) q^{96} +7.67811e41 q^{97} +(-2.17781e41 - 1.56808e41i) q^{98} -2.20336e42i 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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