LMFDB - Embedded newform 4.43.b.a.3.11

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			3.11
Root			$0.500000 + 1.25309e9i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.43.b.a.3.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(232318. - 2.08424e6i) q^{2} -2.00495e10i q^{3} +(-4.29010e12 - 9.68414e11i) q^{4} -5.01114e14 q^{5} +(-4.17880e16 - 4.65785e15i) q^{6} -9.07936e16i q^{7} +(-3.01508e18 + 8.71664e18i) q^{8} -2.92563e20 q^{9} +O(q^{10})$	\(q+(232318. - 2.08424e6i) q^{2} -2.00495e10i q^{3} +(-4.29010e12 - 9.68414e11i) q^{4} -5.01114e14 q^{5} +(-4.17880e16 - 4.65785e15i) q^{6} -9.07936e16i q^{7} +(-3.01508e18 + 8.71664e18i) q^{8} -2.92563e20 q^{9} +(-1.16418e20 + 1.04444e21i) q^{10} -1.06683e22i q^{11} +(-1.94162e22 + 8.60144e22i) q^{12} -1.14000e23 q^{13} +(-1.89236e23 - 2.10930e22i) q^{14} +1.00471e25i q^{15} +(1.74672e25 + 8.30920e24i) q^{16} +4.41888e25 q^{17} +(-6.79676e25 + 6.09773e26i) q^{18} -9.90347e25i q^{19} +(2.14983e27 + 4.85286e26i) q^{20} -1.82036e27 q^{21} +(-2.22353e28 - 2.47843e27i) q^{22} -3.40290e28i q^{23} +(1.74764e29 + 6.04508e28i) q^{24} +2.37415e28 q^{25} +(-2.64843e28 + 2.37605e29i) q^{26} +3.67195e30i q^{27} +(-8.79258e28 + 3.89514e29i) q^{28} -5.31418e30 q^{29} +(2.09406e31 + 2.33412e30i) q^{30} -3.57390e31i q^{31} +(2.13763e31 - 3.44755e31i) q^{32} -2.13893e32 q^{33} +(1.02659e31 - 9.21003e31i) q^{34} +4.54979e31i q^{35} +(1.25513e33 + 2.83322e32i) q^{36} -9.70417e32 q^{37} +(-2.06412e32 - 2.30075e31i) q^{38} +2.28565e33i q^{39} +(1.51090e33 - 4.36803e33i) q^{40} +5.96887e33 q^{41} +(-4.22903e32 + 3.79409e33i) q^{42} -1.94992e34i q^{43} +(-1.03313e34 + 4.57680e34i) q^{44} +1.46607e35 q^{45} +(-7.09247e34 - 7.90554e33i) q^{46} +2.30373e34i q^{47} +(1.66595e35 - 3.50208e35i) q^{48} +3.03730e35 q^{49} +(5.51557e33 - 4.94830e34i) q^{50} -8.85963e35i q^{51} +(4.89074e35 + 1.10400e35i) q^{52} +1.67526e35 q^{53} +(7.65323e36 + 8.53059e35i) q^{54} +5.34602e36i q^{55} +(7.91415e35 + 2.73750e35i) q^{56} -1.98559e36 q^{57} +(-1.23458e36 + 1.10760e37i) q^{58} -2.06438e37i q^{59} +(9.72974e36 - 4.31030e37i) q^{60} +2.37447e37 q^{61} +(-7.44887e37 - 8.30280e36i) q^{62} +2.65628e37i q^{63} +(-6.68892e37 - 5.25628e37i) q^{64} +5.71272e37 q^{65} +(-4.96913e37 + 4.45806e38i) q^{66} +4.39373e37i q^{67} +(-1.89575e38 - 4.27931e37i) q^{68} -6.82263e38 q^{69} +(9.48288e37 + 1.05700e37i) q^{70} +5.38649e38i q^{71} +(8.82101e38 - 2.55017e39i) q^{72} -1.46894e39 q^{73} +(-2.25445e38 + 2.02259e39i) q^{74} -4.76005e38i q^{75} +(-9.59066e37 + 4.24869e38i) q^{76} -9.68610e38 q^{77} +(4.76386e39 + 5.30998e38i) q^{78} +1.90750e39i q^{79} +(-8.75304e39 - 4.16385e39i) q^{80} +4.16087e40 q^{81} +(1.38668e39 - 1.24406e40i) q^{82} -3.93683e39i q^{83} +(7.80955e39 + 1.76287e39i) q^{84} -2.21436e40 q^{85} +(-4.06411e40 - 4.53002e39i) q^{86} +1.06547e41i q^{87} +(9.29915e40 + 3.21657e40i) q^{88} +4.67965e40 q^{89} +(3.40595e40 - 3.05566e41i) q^{90} +1.03505e40i q^{91} +(-3.29541e40 + 1.45988e41i) q^{92} -7.16548e41 q^{93} +(4.80154e40 + 5.35198e39i) q^{94} +4.96276e40i q^{95} +(-6.91215e41 - 4.28584e41i) q^{96} +8.04950e41 q^{97} +(7.05619e40 - 6.33048e41i) q^{98} +3.12114e42i 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 $

$2$	232318.	−	2.08424e6i	0.110778	−	0.993845i
$2$	232318.	−	2.08424e6i	0.110778	−	0.993845i
$3$		−	2.00495e10i		−	1.91671i	−0.285575	−	0.958356i	$-0.592185\pi$
$3$		−	2.00495e10i		−	1.91671i	0.285575	−	0.958356i	$-0.407815\pi$
$4$	−4.29010e12	−	9.68414e11i	−0.975457	−	0.220192i
$5$	−5.01114e14			−1.05091			−0.525456	−	0.850821i	$-0.676105\pi$
$5$	−5.01114e14			−1.05091			−0.525456	+	0.850821i	$0.676105\pi$
$6$	−4.17880e16	−	4.65785e15i	−1.90492	−	0.212329i
$7$		−	9.07936e16i		−	0.162553i	−0.996692	−	0.0812767i	$-0.974100\pi$
$7$		−	9.07936e16i		−	0.162553i	0.996692	−	0.0812767i	$-0.0258998\pi$
$8$	−3.01508e18	+	8.71664e18i	−0.326896	+	0.945060i
$9$	−2.92563e20			−2.67379
$10$	−1.16418e20	+	1.04444e21i	−0.116418	+	1.04444i
$11$		−	1.06683e22i		−	1.44161i	−0.693138	−	0.720805i	$-0.743772\pi$
$11$		−	1.06683e22i		−	1.44161i	0.693138	−	0.720805i	$-0.256228\pi$
$12$	−1.94162e22	+	8.60144e22i	−0.422045	+	1.86967i
$13$	−1.14000e23			−0.461420			−0.230710	−	0.973023i	$-0.574105\pi$
$13$	−1.14000e23			−0.461420			−0.230710	+	0.973023i	$0.574105\pi$
$14$	−1.89236e23	−	2.10930e22i	−0.161553	−	0.0180073i
$15$			1.00471e25i			2.01430i
$16$	1.74672e25	+	8.30920e24i	0.903031	+	0.429575i
$17$	4.41888e25			0.639566			0.319783	−	0.947491i	$-0.396390\pi$
$17$	4.41888e25			0.639566			0.319783	+	0.947491i	$0.396390\pi$
$18$	−6.79676e25	+	6.09773e26i	−0.296196	+	2.65733i
$19$		−	9.90347e25i		−	0.138663i	−0.997594	−	0.0693317i	$-0.977913\pi$
$19$		−	9.90347e25i		−	0.138663i	0.997594	−	0.0693317i	$-0.0220867\pi$
$20$	2.14983e27	+	4.85286e26i	1.02512	+	0.231402i
$21$	−1.82036e27			−0.311568
$22$	−2.22353e28	−	2.47843e27i	−1.43274	−	0.159698i
$23$		−	3.40290e28i		−	0.862113i	−0.902325	−	0.431056i	$-0.858141\pi$
$23$		−	3.40290e28i		−	0.862113i	0.902325	−	0.431056i	$-0.141859\pi$
$24$	1.74764e29	+	6.04508e28i	1.81141	+	0.626565i
$25$	2.37415e28			0.104416
$26$	−2.64843e28	+	2.37605e29i	−0.0511151	+	0.458580i
$27$			3.67195e30i			3.20817i
$28$	−8.79258e28	+	3.89514e29i	−0.0357930	+	0.158564i
$29$	−5.31418e30			−1.03533			−0.517664	−	0.855584i	$-0.673198\pi$
$29$	−5.31418e30			−1.03533			−0.517664	+	0.855584i	$0.673198\pi$
$30$	2.09406e31	+	2.33412e30i	2.00190	+	0.223139i
$31$		−	3.57390e31i		−	1.71612i	−0.513553	−	0.858058i	$-0.671671\pi$
$31$		−	3.57390e31i		−	1.71612i	0.513553	−	0.858058i	$-0.328329\pi$
$32$	2.13763e31	−	3.44755e31i	0.526967	−	0.849886i
$33$	−2.13893e32			−2.76315
$34$	1.02659e31	−	9.21003e31i	0.0708497	−	0.635629i
$35$			4.54979e31i			0.170829i
$36$	1.25513e33	+	2.83322e32i	2.60816	+	0.588746i
$37$	−9.70417e32			−1.13429			−0.567143	−	0.823620i	$-0.691951\pi$
$37$	−9.70417e32			−1.13429			−0.567143	+	0.823620i	$0.691951\pi$
$38$	−2.06412e32	−	2.30075e31i	−0.137810	−	0.0153608i
$39$			2.28565e33i			0.884409i
$40$	1.51090e33	−	4.36803e33i	0.343539	−	0.993175i
$41$	5.96887e33			0.808037			0.404019	−	0.914751i	$-0.367613\pi$
$41$	5.96887e33			0.808037			0.404019	+	0.914751i	$0.367613\pi$
$42$	−4.22903e32	+	3.79409e33i	−0.0345148	+	0.309651i
$43$		−	1.94992e34i		−	0.970912i	−0.874261	−	0.485456i	$-0.838654\pi$
$43$		−	1.94992e34i		−	0.970912i	0.874261	−	0.485456i	$-0.161346\pi$
$44$	−1.03313e34	+	4.57680e34i	−0.317431	+	1.40623i
$45$	1.46607e35			2.80992
$46$	−7.09247e34	−	7.90554e33i	−0.856807	−	0.0955030i
$47$			2.30373e34i			0.177165i	0.996069	+	0.0885823i	$0.0282336\pi$
$47$			2.30373e34i			0.177165i	−0.996069	+	0.0885823i	$0.971766\pi$
$48$	1.66595e35	−	3.50208e35i	0.823372	−	1.73085i
$49$	3.03730e35			0.973576
$50$	5.51557e33	−	4.94830e34i	0.0115670	−	0.103773i
$51$		−	8.85963e35i		−	1.22586i
$52$	4.89074e35	+	1.10400e35i	0.450095	+	0.101601i
$53$	1.67526e35			0.103345			0.0516723	−	0.998664i	$-0.483545\pi$
$53$	1.67526e35			0.103345			0.0516723	+	0.998664i	$0.483545\pi$
$54$	7.65323e36	+	8.53059e35i	3.18842	+	0.355394i
$55$			5.34602e36i			1.51500i
$56$	7.91415e35	+	2.73750e35i	0.153623	+	0.0531380i
$57$	−1.98559e36			−0.265778
$58$	−1.23458e36	+	1.10760e37i	−0.114691	+	1.02896i
$59$		−	2.06438e37i		−	1.33936i	−0.742651	−	0.669679i	$-0.766432\pi$
$59$		−	2.06438e37i		−	1.33936i	0.742651	−	0.669679i	$-0.233568\pi$
$60$	9.72974e36	−	4.31030e37i	0.443532	−	1.96486i
$61$	2.37447e37			0.764962			0.382481	−	0.923963i	$-0.375070\pi$
$61$	2.37447e37			0.764962			0.382481	+	0.923963i	$0.375070\pi$
$62$	−7.44887e37	−	8.30280e36i	−1.70555	−	0.190107i
$63$			2.65628e37i			0.434633i
$64$	−6.68892e37	−	5.25628e37i	−0.786279	−	0.617872i
$65$	5.71272e37			0.484912
$66$	−4.96913e37	+	4.45806e38i	−0.306096	+	2.74614i
$67$			4.39373e37i			0.197362i	0.995119	+	0.0986808i	$0.0314623\pi$
$67$			4.39373e37i			0.197362i	−0.995119	+	0.0986808i	$0.968538\pi$
$68$	−1.89575e38	−	4.27931e37i	−0.623868	−	0.140827i
$69$	−6.82263e38			−1.65242
$70$	9.48288e37	+	1.05700e37i	0.169778	+	0.0189241i
$71$			5.38649e38i			0.715946i	0.933732	+	0.357973i	$0.116532\pi$
$71$			5.38649e38i			0.715946i	−0.933732	+	0.357973i	$0.883468\pi$
$72$	8.82101e38	−	2.55017e39i	0.874049	−	2.52689i
$73$	−1.46894e39			−1.08949			−0.544744	−	0.838602i	$-0.683373\pi$
$73$	−1.46894e39			−1.08949			−0.544744	+	0.838602i	$0.683373\pi$
$74$	−2.25445e38	+	2.02259e39i	−0.125654	+	1.12730i
$75$		−	4.76005e38i		−	0.200136i
$76$	−9.59066e37	+	4.24869e38i	−0.0305325	+	0.135260i
$77$	−9.68610e38			−0.234339
$78$	4.76386e39	+	5.30998e38i	0.878966	+	0.0979729i
$79$			1.90750e39i			0.269337i	0.990891	+	0.134669i	$0.0429970\pi$
$79$			1.90750e39i			0.269337i	−0.990891	+	0.134669i	$0.957003\pi$
$80$	−8.75304e39	−	4.16385e39i	−0.949006	−	0.451446i
$81$	4.16087e40			3.47535
$82$	1.38668e39	−	1.24406e40i	0.0895125	−	0.803064i
$83$		−	3.93683e39i		−	0.197018i	−0.995136	−	0.0985092i	$-0.968593\pi$
$83$		−	3.93683e39i		−	0.197018i	0.995136	−	0.0985092i	$-0.0314074\pi$
$84$	7.80955e39	+	1.76287e39i	0.303921	+	0.0686048i
$85$	−2.21436e40			−0.672127
$86$	−4.06411e40	−	4.53002e39i	−0.964936	−	0.107555i
$87$			1.06547e41i			1.98443i
$88$	9.29915e40	+	3.21657e40i	1.36241	+	0.471256i
$89$	4.67965e40			0.540784			0.270392	−	0.962750i	$-0.412847\pi$
$89$	4.67965e40			0.540784			0.270392	+	0.962750i	$0.412847\pi$
$90$	3.40595e40	−	3.05566e41i	0.311276	−	2.79262i
$91$			1.03505e40i			0.0750054i
$92$	−3.29541e40	+	1.45988e41i	−0.189830	+	0.840954i
$93$	−7.16548e41			−3.28930
$94$	4.80154e40	+	5.35198e39i	0.176074	+	0.0196259i
$95$			4.96276e40i			0.145723i
$96$	−6.91215e41	−	4.28584e41i	−1.62899	−	1.01004i
$97$	8.04950e41			1.52603			0.763014	−	0.646382i	$-0.223719\pi$
$97$	8.04950e41			1.52603			0.763014	+	0.646382i	$0.223719\pi$
$98$	7.05619e40	−	6.33048e41i	0.107851	−	0.967584i
$99$			3.12114e42i			3.85456i
$100$	−1.01853e41	−	2.29916e40i	−0.101853	−	0.0229916i
$101$	1.16934e42			0.948835			0.474418	−	0.880300i	$-0.342659\pi$
$101$	1.16934e42			0.948835			0.474418	+	0.880300i	$0.342659\pi$
$102$	−1.84656e42	−	2.05825e41i	−1.21832	−	0.135798i
$103$		−	5.76793e41i		−	0.310055i	−0.987910	−	0.155027i	$-0.950453\pi$
$103$		−	5.76793e41i		−	0.310055i	0.987910	−	0.155027i	$-0.0495466\pi$
$104$	3.43721e41	−	9.93702e41i	0.150836	−	0.436070i
$105$	9.12210e41			0.327431
$106$	3.89192e40	−	3.49164e41i	0.0114483	−	0.102709i
$107$		−	6.93458e41i		−	0.167479i	−0.996488	−	0.0837395i	$-0.973314\pi$
$107$		−	6.93458e41i		−	0.167479i	0.996488	−	0.0837395i	$-0.0266864\pi$
$108$	3.55597e42	−	1.57530e43i	0.706413	−	3.12943i
$109$	−8.22711e41			−0.134676			−0.0673381	−	0.997730i	$-0.521451\pi$
$109$	−8.22711e41			−0.134676			−0.0673381	+	0.997730i	$0.521451\pi$
$110$	1.11424e43	+	1.24198e42i	1.50568	+	0.167829i
$111$			1.94564e43i			2.17410i
$112$	7.54422e41	−	1.58591e42i	0.0698290	−	0.146791i
$113$	−6.47037e42			−0.496915			−0.248457	−	0.968643i	$-0.579924\pi$
$113$	−6.47037e42			−0.496915			−0.248457	+	0.968643i	$0.579924\pi$
$114$	−4.61289e41	+	4.13846e42i	−0.0294423	+	0.264142i
$115$			1.70524e43i			0.906005i
$116$	2.27984e43	+	5.14632e42i	1.00992	+	0.227971i
$117$	3.33523e43			1.23374
$118$	−4.30267e43	−	4.79592e42i	−1.33111	−	0.148371i
$119$		−	4.01206e42i		−	0.103964i
$120$	−8.75768e43	−	3.02927e43i	−1.90363	−	0.658465i
$121$	−5.90483e43			−1.07824
$122$	5.51632e42	−	4.94898e43i	0.0847408	−	0.760254i
$123$		−	1.19673e44i		−	1.54877i
$124$	−3.46101e43	+	1.53324e44i	−0.377875	+	1.67400i
$125$	1.02043e44			0.941180
$126$	5.53635e43	+	6.17102e42i	0.431958	+	0.0481477i
$127$			7.41564e43i			0.490084i	0.969512	+	0.245042i	$0.0788018\pi$
$127$			7.41564e43i			0.490084i	−0.969512	+	0.245042i	$0.921198\pi$
$128$	−1.25093e44	+	1.27202e44i	−0.701172	+	0.712993i
$129$	−3.90950e44			−1.86096
$130$	1.32717e43	−	1.19067e44i	0.0537174	−	0.481927i
$131$			1.72311e44i			0.593767i	0.954914	+	0.296883i	$0.0959472\pi$
$131$			1.72311e44i			0.593767i	−0.954914	+	0.296883i	$0.904053\pi$
$132$	9.17625e44	+	2.07137e44i	2.69533	+	0.608424i
$133$	−8.99171e42			−0.0225402
$134$	9.15761e43	+	1.02074e43i	0.196147	+	0.0218633i
$135$		−	1.84006e45i		−	3.37150i
$136$	−1.33233e44	+	3.85178e44i	−0.209071	+	0.604428i
$137$	8.30206e44			1.11700			0.558501	−	0.829504i	$-0.311377\pi$
$137$	8.30206e44			1.11700			0.558501	+	0.829504i	$0.311377\pi$
$138$	−1.58502e44	+	1.42200e45i	−0.183052	+	1.64225i
$139$		−	2.54122e44i		−	0.252192i	−0.992018	−	0.126096i	$-0.959755\pi$
$139$		−	2.54122e44i		−	0.252192i	0.992018	−	0.126096i	$-0.0402448\pi$
$140$	4.40608e43	−	1.95191e44i	0.0376153	−	0.166637i
$141$	4.61887e44			0.339574
$142$	1.12268e45	+	1.25138e44i	0.711540	+	0.0793109i
$143$			1.21619e45i			0.665187i
$144$	−5.11025e45	−	2.43096e45i	−2.41451	−	1.14859i
$145$	2.66301e45			1.08804
$146$	−3.41260e44	+	3.06162e45i	−0.120691	+	1.08278i
$147$		−	6.08963e45i		−	1.86607i
$148$	4.16319e45	+	9.39766e44i	1.10645	+	0.249760i
$149$	−6.75311e45			−1.55809			−0.779044	−	0.626969i	$-0.784295\pi$
$149$	−6.75311e45			−1.55809			−0.779044	+	0.626969i	$0.784295\pi$
$150$	−9.92110e44	−	1.10584e44i	−0.198904	−	0.0221706i
$151$			5.62745e45i			0.981286i	0.871361	+	0.490643i	$0.163238\pi$
$151$			5.62745e45i			0.981286i	−0.871361	+	0.490643i	$0.836762\pi$
$152$	8.63250e44	+	2.98597e44i	0.131045	+	0.0453284i
$153$	−1.29280e46			−1.71006
$154$	−2.25025e44	+	2.01882e45i	−0.0259595	+	0.232896i
$155$			1.79093e46i			1.80349i
$156$	2.21346e45	−	9.80568e45i	0.194740	−	0.862703i
$157$	8.41119e45			0.647090			0.323545	−	0.946213i	$-0.395125\pi$
$157$	8.41119e45			0.647090			0.323545	+	0.946213i	$0.395125\pi$
$158$	3.97570e45	+	4.43147e44i	0.267679	+	0.0298366i
$159$		−	3.35880e45i		−	0.198082i
$160$	−1.07120e46	+	1.72761e46i	−0.553796	+	0.893155i
$161$	−3.08961e45			−0.140139
$162$	9.66644e45	−	8.67227e46i	0.384992	−	3.45396i
$163$		−	3.69588e45i		−	0.129354i	−0.997906	−	0.0646768i	$-0.979398\pi$
$163$		−	3.69588e45i		−	0.129354i	0.997906	−	0.0646768i	$-0.0206016\pi$
$164$	−2.56071e46	−	5.78034e45i	−0.788205	−	0.177923i
$165$	1.07185e47			2.90383
$166$	−8.20531e45	−	9.14596e44i	−0.195806	−	0.0218253i
$167$			7.00626e46i			1.47381i	0.675999	+	0.736903i	$0.263713\pi$
$167$			7.00626e46i			1.47381i	−0.675999	+	0.736903i	$0.736287\pi$
$168$	5.48855e45	−	1.58675e46i	0.101850	−	0.294451i
$169$	−4.80448e46			−0.787092
$170$	−5.14436e45	+	4.61527e46i	−0.0744568	+	0.667990i
$171$			2.89739e46i			0.370756i
$172$	−1.88833e46	+	8.36537e46i	−0.213787	+	0.947082i
$173$	1.00803e47			1.01043			0.505214	−	0.862994i	$-0.331414\pi$
$173$	1.00803e47			1.01043			0.505214	+	0.862994i	$0.331414\pi$
$174$	2.22069e47	+	2.47527e46i	1.97221	+	0.219830i
$175$		−	2.15557e45i		−	0.0169732i
$176$	8.86448e46	−	1.86344e47i	0.619280	−	1.30182i
$177$	−4.13897e47			−2.56716
$178$	1.08717e46	−	9.75354e46i	0.0599068	−	0.537455i
$179$			7.07171e46i			0.346426i	0.984884	+	0.173213i	$0.0554150\pi$
$179$			7.07171e46i			0.346426i	−0.984884	+	0.173213i	$0.944585\pi$
$180$	−6.28961e47	−	1.41977e47i	−2.74095	−	0.618721i
$181$	−2.70962e47			−1.05113			−0.525567	−	0.850752i	$-0.676147\pi$
$181$	−2.70962e47			−1.05113			−0.525567	+	0.850752i	$0.676147\pi$
$182$	2.15730e46	+	2.40461e45i	0.0745438	+	0.00830893i
$183$		−	4.76069e47i		−	1.46621i
$184$	2.96618e47	+	1.02600e47i	0.814749	+	0.281821i
$185$	4.86290e47			1.19203
$186$	−1.66467e47	+	1.49346e48i	−0.364381	+	3.26905i
$187$		−	4.71418e47i		−	0.922004i
$188$	2.23097e46	−	9.88325e46i	0.0390102	−	0.172816i
$189$	3.33389e47			0.521499
$190$	1.03436e47	+	1.15294e46i	0.144826	+	0.0161429i
$191$			5.08885e47i			0.638145i	0.947730	+	0.319072i	$0.103371\pi$
$191$			5.08885e47i			0.638145i	−0.947730	+	0.319072i	$0.896629\pi$
$192$	−1.05386e48	+	1.34109e48i	−1.18428	+	1.50707i
$193$	1.06856e48			1.07671			0.538353	−	0.842720i	$-0.319047\pi$
$193$	1.06856e48			1.07671			0.538353	+	0.842720i	$0.319047\pi$
$194$	1.87004e47	−	1.67771e48i	0.169050	−	1.51664i
$195$		−	1.14537e48i		−	0.929436i
$196$	−1.30303e48	−	2.94137e47i	−0.949681	−	0.214374i
$197$	−1.83912e48			−1.20453			−0.602267	−	0.798295i	$-0.705736\pi$
$197$	−1.83912e48			−1.20453			−0.602267	+	0.798295i	$0.705736\pi$
$198$	6.50522e48	+	7.25097e47i	3.83083	+	0.426999i
$199$		−	2.99003e48i		−	1.58402i	−0.610507	−	0.792011i	$-0.709034\pi$
$199$		−	2.99003e48i		−	1.58402i	0.610507	−	0.792011i	$-0.290966\pi$
$200$	−7.15825e46	+	2.06946e47i	−0.0341332	+	0.0986796i
$201$	8.80921e47			0.378285
$202$	2.71658e47	−	2.43718e48i	0.105110	−	0.942995i
$203$			4.82493e47i			0.168296i
$204$	−8.57980e47	+	3.80087e48i	−0.269925	+	1.19578i
$205$	−2.99108e48			−0.849176
$206$	−1.20218e48	−	1.33999e47i	−0.308147	−	0.0343472i
$207$			9.95562e48i			2.30511i
$208$	−1.99126e48	−	9.47252e47i	−0.416676	−	0.198215i
$209$	−1.05653e48			−0.199898
$210$	2.11923e47	−	1.90127e48i	0.0362721	−	0.325416i
$211$		−	8.39996e48i		−	1.30120i	−0.759419	−	0.650602i	$-0.774517\pi$
$211$		−	8.39996e48i		−	1.30120i	0.759419	−	0.650602i	$-0.225483\pi$
$212$	−7.18702e47	−	1.62234e47i	−0.100808	−	0.0227556i
$213$	1.07996e49			1.37226
$214$	−1.44534e48	−	1.61103e47i	−0.166448	−	0.0185530i
$215$			9.77133e48i			1.02034i
$216$	−3.20071e49	−	1.10712e49i	−3.03191	−	1.04874i
$217$	−3.24487e48			−0.278960
$218$	−1.91131e47	+	1.71473e48i	−0.0149191	+	0.133847i
$219$			2.94514e49i			2.08824i
$220$	5.17716e48	−	2.29350e49i	0.333592	−	1.47782i
$221$	−5.03755e48			−0.295108
$222$	4.05518e49	+	4.52006e48i	2.16072	+	0.240842i
$223$		−	5.23935e48i		−	0.254024i	−0.991901	−	0.127012i	$-0.959461\pi$
$223$		−	5.23935e48i		−	0.254024i	0.991901	−	0.127012i	$-0.0405387\pi$
$224$	−3.13015e48	−	1.94083e48i	−0.138152	−	0.0856603i
$225$	−6.94588e48			−0.279187
$226$	−1.50318e48	+	1.34858e49i	−0.0550471	+	0.493856i
$227$		−	3.25773e49i		−	1.08736i	−0.839294	−	0.543678i	$-0.817031\pi$
$227$		−	3.25773e49i		−	1.08736i	0.839294	−	0.543678i	$-0.182969\pi$
$228$	8.51841e48	+	1.92288e48i	0.259255	+	0.0585221i
$229$	−2.80755e49			−0.779440			−0.389720	−	0.920933i	$-0.627428\pi$
$229$	−2.80755e49			−0.779440			−0.389720	+	0.920933i	$0.627428\pi$
$230$	3.55413e49	+	3.96157e48i	0.900429	+	0.100365i
$231$			1.94201e49i			0.449160i
$232$	1.60227e49	−	4.63218e49i	0.338444	−	0.978448i
$233$	7.31107e49			1.41093			0.705467	−	0.708743i	$-0.250737\pi$
$233$	7.31107e49			1.41093			0.705467	+	0.708743i	$0.250737\pi$
$234$	7.74834e48	−	6.95144e49i	0.136671	−	1.22615i
$235$		−	1.15443e49i		−	0.186184i
$236$	−1.99917e49	+	8.85639e49i	−0.294916	+	1.30649i
$237$	3.82445e49			0.516242
$238$	−8.36212e48	−	9.32073e47i	−0.103324	−	0.0115169i
$239$			1.20229e50i			1.36036i	0.733044	+	0.680181i	$0.238099\pi$
$239$			1.20229e50i			1.36036i	−0.733044	+	0.680181i	$0.761901\pi$
$240$	−8.34831e49	+	1.75494e50i	−0.865292	+	1.81897i
$241$	4.41627e49			0.419467			0.209734	−	0.977759i	$-0.432740\pi$
$241$	4.41627e49			0.419467			0.209734	+	0.977759i	$0.432740\pi$
$242$	−1.37180e49	+	1.23071e50i	−0.119445	+	1.07160i
$243$		−	4.32453e50i		−	3.45308i
$244$	−1.01867e50	−	2.29947e49i	−0.746188	−	0.168439i
$245$	−1.52203e50			−1.02314
$246$	−2.49427e50	−	2.78021e49i	−1.53924	−	0.171570i
$247$			1.12900e49i			0.0639820i
$248$	3.11524e50	+	1.07756e50i	1.62183	+	0.560991i
$249$	−7.89314e49			−0.377628
$250$	2.37064e49	−	2.12682e50i	0.104262	−	0.935387i
$251$		−	2.23778e50i		−	0.905044i	−0.891753	−	0.452522i	$-0.850524\pi$
$251$		−	2.23778e50i		−	0.905044i	0.891753	−	0.452522i	$-0.149476\pi$
$252$	2.57238e49	−	1.13957e50i	0.0957028	−	0.423966i
$253$	−3.63030e50			−1.24283
$254$	1.54560e50	+	1.72279e49i	0.487068	+	0.0542904i
$255$			4.43969e50i			1.28827i
$256$	2.36059e50	+	2.90276e50i	0.630930	+	0.775840i
$257$	−4.76780e50			−1.17415			−0.587074	−	0.809533i	$-0.699720\pi$
$257$	−4.76780e50			−1.17415			−0.587074	+	0.809533i	$0.699720\pi$
$258$	−9.08245e49	+	8.14834e50i	−0.206153	+	1.84950i
$259$			8.81076e49i			0.184382i
$260$	−2.45082e50	−	5.53228e49i	−0.473010	−	0.106774i
$261$	1.55473e51			2.76825
$262$	3.59138e50	+	4.00309e49i	0.590112	+	0.0657761i
$263$			4.31487e50i			0.654481i	0.944941	+	0.327240i	$0.106119\pi$
$263$			4.31487e50i			0.654481i	−0.944941	+	0.327240i	$0.893881\pi$
$264$	6.44906e50	−	1.86443e51i	0.903262	−	2.61135i
$265$	−8.39494e49			−0.108606
$266$	−2.08893e48	+	1.87409e49i	−0.00249695	+	0.0224015i
$267$		−	9.38247e50i		−	1.03653i
$268$	4.25495e49	−	1.88496e50i	0.0434574	−	0.192518i
$269$	1.32027e51			1.24700			0.623499	−	0.781824i	$-0.285710\pi$
$269$	1.32027e51			1.24700			0.623499	+	0.781824i	$0.285710\pi$
$270$	−3.83514e51	−	4.27480e50i	−3.35075	−	0.373488i
$271$			1.45627e50i			0.117730i	0.998266	+	0.0588648i	$0.0187481\pi$
$271$			1.45627e50i			0.117730i	−0.998266	+	0.0588648i	$0.981252\pi$
$272$	7.71853e50	+	3.67174e50i	0.577548	+	0.274742i
$273$	2.07522e50			0.143764
$274$	1.92872e50	−	1.73035e51i	0.123739	−	1.11013i
$275$		−	2.53281e50i		−	0.150527i
$276$	2.92698e51	+	6.60714e50i	1.61187	+	0.363850i
$277$	−1.50520e51			−0.768277			−0.384138	−	0.923276i	$-0.625501\pi$
$277$	−1.50520e51			−0.768277			−0.384138	+	0.923276i	$0.625501\pi$
$278$	−5.29653e50	−	5.90371e49i	−0.250640	−	0.0279373i
$279$			1.04559e52i			4.58853i
$280$	−3.96589e50	−	1.37180e50i	−0.161444	−	0.0558434i
$281$	−4.06078e51			−1.53383			−0.766913	−	0.641751i	$-0.778208\pi$
$281$	−4.06078e51			−1.53383			−0.766913	+	0.641751i	$0.778208\pi$
$282$	1.07305e50	−	9.62685e50i	0.0376172	−	0.337484i
$283$		−	4.23627e51i		−	1.37870i	−0.724430	−	0.689348i	$-0.757897\pi$
$283$		−	4.23627e51i		−	1.37870i	0.724430	−	0.689348i	$-0.242103\pi$
$284$	5.21635e50	−	2.31086e51i	0.157646	−	0.698375i
$285$	9.95009e50			0.279309
$286$	2.53483e51	+	2.82542e50i	0.661093	+	0.0736880i
$287$		−	5.41935e50i		−	0.131349i
$288$	−6.25392e51	+	1.00862e52i	−1.40900	+	2.27241i
$289$	−2.82104e51			−0.590956
$290$	6.18664e50	−	5.55036e51i	0.120531	−	1.08134i
$291$		−	1.61388e52i		−	2.92496i
$292$	6.30188e51	+	1.42254e51i	1.06275	+	0.239897i
$293$	−1.06303e52			−1.66850			−0.834249	−	0.551388i	$-0.814098\pi$
$293$	−1.06303e52			−1.66850			−0.834249	+	0.551388i	$0.814098\pi$
$294$	−1.26923e52	−	1.41473e51i	−1.85458	−	0.206719i
$295$			1.03449e52i			1.40755i
$296$	2.92589e51	−	8.45878e51i	0.370793	−	1.07197i
$297$	3.91733e52			4.62493
$298$	−1.56887e51	+	1.40751e52i	−0.172602	+	1.54850i
$299$			3.87932e51i			0.397796i
$300$	−4.60970e50	+	2.04211e51i	−0.0440683	+	0.195224i
$301$	−1.77040e51			−0.157825
$302$	1.17290e52	+	1.30736e51i	0.975247	+	0.108705i
$303$		−	2.34446e52i		−	1.81864i
$304$	8.22898e50	−	1.72985e51i	0.0595663	−	0.125217i
$305$	−1.18988e52			−0.803908
$306$	−3.00341e51	+	2.69452e52i	−0.189437	+	1.69954i
$307$		−	9.76203e51i		−	0.574956i	−0.957787	−	0.287478i	$-0.907183\pi$
$307$		−	9.76203e51i		−	0.574956i	0.957787	−	0.287478i	$-0.0928168\pi$
$308$	4.15544e51	+	9.38016e50i	0.228587	+	0.0515995i
$309$	−1.15644e52			−0.594286
$310$	3.73273e52	+	4.16065e51i	1.79239	+	0.199786i
$311$		−	2.43319e50i		−	0.0109196i	−0.999985	−	0.00545981i	$-0.998262\pi$
$311$		−	2.43319e50i		−	0.0109196i	0.999985	−	0.00545981i	$-0.00173792\pi$
$312$	−1.99232e52	−	6.89142e51i	−0.835820	−	0.289110i
$313$	−3.06916e52			−1.20389			−0.601947	−	0.798536i	$-0.705608\pi$
$313$	−3.06916e52			−1.20389			−0.601947	+	0.798536i	$0.705608\pi$
$314$	1.95407e51	−	1.75310e52i	0.0716832	−	0.643107i
$315$		−	1.33110e52i		−	0.456761i
$316$	1.84725e51	−	8.18338e51i	0.0593059	−	0.262727i
$317$	1.02516e52			0.307997			0.153998	−	0.988071i	$-0.450785\pi$
$317$	1.02516e52			0.307997			0.153998	+	0.988071i	$0.450785\pi$
$318$	−7.00057e51	−	7.80310e50i	−0.196863	−	0.0219431i
$319$			5.66931e52i			1.49254i
$320$	3.35191e52	+	2.63399e52i	0.826310	+	0.649329i
$321$	−1.39035e52			−0.321009
$322$	−7.17772e50	+	6.43950e51i	−0.0155243	+	0.139277i
$323$		−	4.37623e51i		−	0.0886843i
$324$	−1.78506e53	−	4.02945e52i	−3.39005	−	0.765244i
$325$	−2.70654e51			−0.0481797
$326$	−7.70313e51	−	8.58620e50i	−0.128557	−	0.0143295i
$327$			1.64949e52i			0.258136i
$328$	−1.79966e52	+	5.20285e52i	−0.264144	+	0.763644i
$329$	2.09164e51			0.0287987
$330$	2.49010e52	−	2.23400e53i	0.321680	−	2.88596i
$331$			8.40636e52i			1.01911i	0.860439	+	0.509554i	$0.170190\pi$
$331$			8.40636e52i			1.01911i	−0.860439	+	0.509554i	$0.829810\pi$
$332$	−3.81248e51	+	1.68894e52i	−0.0433818	+	0.192183i
$333$	2.83908e53			3.03284
$334$	1.46028e53	+	1.62768e52i	1.46473	+	0.163265i
$335$		−	2.20176e52i		−	0.207410i
$336$	−3.17966e52	−	1.51258e52i	−0.281356	−	0.133842i
$337$	−1.09100e53			−0.906975			−0.453488	−	0.891263i	$-0.649820\pi$
$337$	−1.09100e53			−0.906975			−0.453488	+	0.891263i	$0.649820\pi$
$338$	−1.11617e52	+	1.00137e53i	−0.0871923	+	0.782247i
$339$			1.29728e53i			0.952443i
$340$	9.49985e52	+	2.14442e52i	0.655631	+	0.147997i
$341$	−3.81273e53			−2.47397
$342$	6.03887e52	+	6.73115e51i	0.368474	+	0.0410716i
$343$		−	5.59019e52i		−	0.320812i
$344$	1.69968e53	+	5.87917e52i	0.917570	+	0.317387i
$345$	3.41892e53			1.73655
$346$	2.34183e52	−	2.10098e53i	0.111933	−	1.00421i
$347$			2.35925e53i			1.06134i	0.847578	+	0.530671i	$0.178060\pi$
$347$			2.35925e53i			1.06134i	−0.847578	+	0.530671i	$0.821940\pi$
$348$	1.03181e53	−	4.57096e53i	0.436955	−	1.93572i
$349$	2.01321e52			0.0802704			0.0401352	−	0.999194i	$-0.487221\pi$
$349$	2.01321e52			0.0802704			0.0401352	+	0.999194i	$0.487221\pi$
$350$	−4.49274e51	−	5.00778e50i	−0.0168687	−	0.00188025i
$351$		−	4.18604e53i		−	1.48031i
$352$	−3.67794e53	−	2.28048e53i	−1.22520	−	0.759681i
$353$	−2.95364e53			−0.927018			−0.463509	−	0.886092i	$-0.653410\pi$
$353$	−2.95364e53			−0.927018			−0.463509	+	0.886092i	$0.653410\pi$
$354$	−9.61557e52	+	8.62663e53i	−0.284385	+	2.55136i
$355$		−	2.69924e53i		−	0.752397i
$356$	−2.00762e53	−	4.53184e52i	−0.527511	−	0.119076i
$357$	−8.04398e52			−0.199268
$358$	1.47392e53	+	1.64289e52i	0.344294	+	0.0383763i
$359$		−	6.96302e53i		−	1.53396i	−0.641671	−	0.766980i	$-0.721759\pi$
$359$		−	6.96302e53i		−	1.53396i	0.641671	−	0.766980i	$-0.278241\pi$
$360$	−4.42033e53	+	1.27792e54i	−0.918549	+	2.65554i
$361$	5.00287e53			0.980772
$362$	−6.29493e52	+	5.64751e53i	−0.116442	+	1.04466i
$363$			1.18389e54i			2.06667i
$364$	1.00236e52	−	4.44048e52i	0.0165156	−	0.0731645i
$365$	7.36104e53			1.14496
$366$	−9.92244e53	−	1.10599e53i	−1.45719	−	0.162424i
$367$		−	5.65502e53i		−	0.784236i	−0.919915	−	0.392118i	$-0.871742\pi$
$367$		−	5.65502e53i		−	0.784236i	0.919915	−	0.392118i	$-0.128258\pi$
$368$	2.82753e53	−	5.94389e53i	0.370342	−	0.778515i
$369$	−1.74627e54			−2.16052
$370$	1.12974e53	−	1.01355e54i	0.132051	−	1.18470i
$371$		−	1.52102e52i		−	0.0167990i
$372$	3.07407e54	+	6.93915e53i	3.20857	+	0.724277i
$373$	−1.04035e54			−1.02634			−0.513172	−	0.858286i	$-0.671530\pi$
$373$	−1.04035e54			−1.02634			−0.513172	+	0.858286i	$0.671530\pi$
$374$	−9.82551e53	−	1.09519e53i	−0.916329	−	0.102138i
$375$		−	2.04591e54i		−	1.80397i
$376$	−2.00808e53	−	6.94594e52i	−0.167431	−	0.0579143i
$377$	6.05819e53			0.477721
$378$	7.74522e52	−	6.94864e53i	0.0577705	−	0.518289i
$379$		−	1.05506e54i		−	0.744485i	−0.928136	−	0.372242i	$-0.878589\pi$
$379$		−	1.05506e54i		−	0.744485i	0.928136	−	0.372242i	$-0.121411\pi$
$380$	4.80601e52	−	2.12908e53i	0.0320870	−	0.142146i
$381$	1.48680e54			0.939351
$382$	1.06064e54	+	1.18223e53i	0.634217	+	0.0706923i
$383$			2.43091e54i			1.37593i	0.725745	+	0.687963i	$0.241495\pi$
$383$			2.43091e54i			1.37593i	−0.725745	+	0.687963i	$0.758505\pi$
$384$	2.55034e54	+	2.50805e54i	1.36660	+	1.34394i
$385$	4.85384e53			0.246269
$386$	2.48246e53	−	2.22715e54i	0.119275	−	1.07008i
$387$			5.70475e54i			2.59601i
$388$	−3.45332e54	−	7.79525e53i	−1.48857	−	0.336019i
$389$	6.59971e53			0.269515			0.134758	−	0.990879i	$-0.456974\pi$
$389$	6.59971e53			0.269515			0.134758	+	0.990879i	$0.456974\pi$
$390$	−2.38723e54	−	2.66090e53i	−0.923716	−	0.102961i
$391$		−	1.50370e54i		−	0.551378i
$392$	−9.15770e53	+	2.64751e54i	−0.318258	+	0.920089i
$393$	3.45475e54			1.13808
$394$	−4.27260e53	+	3.83317e54i	−0.133436	+	1.19712i
$395$		−	9.55876e53i		−	0.283050i
$396$	3.02256e54	−	1.33900e55i	0.848742	−	3.75995i
$397$	2.59913e54			0.692194			0.346097	−	0.938199i	$-0.387507\pi$
$397$	2.59913e54			0.692194			0.346097	+	0.938199i	$0.387507\pi$
$398$	−6.23196e54	−	6.94638e53i	−1.57427	−	0.175474i
$399$			1.80279e53i			0.0432031i
$400$	4.14696e53	+	1.97273e53i	0.0942910	+	0.0448546i
$401$	−4.81985e54			−1.03993			−0.519963	−	0.854189i	$-0.674054\pi$
$401$	−4.81985e54			−1.03993			−0.519963	+	0.854189i	$0.674054\pi$
$402$	2.04654e53	−	1.83605e54i	0.0419056	−	0.375957i
$403$			4.07426e54i			0.791850i
$404$	−5.01657e54	−	1.13240e54i	−0.925547	−	0.208926i
$405$	−2.08507e55			−3.65229
$406$	1.00563e54	+	1.12092e53i	0.167260	+	0.0186435i
$407$			1.03527e55i			1.63520i
$408$	7.72263e54	+	2.67125e54i	1.15852	+	0.400729i
$409$	1.31322e55			1.87132			0.935661	−	0.352899i	$-0.114804\pi$
$409$	1.31322e55			1.87132			0.935661	+	0.352899i	$0.114804\pi$
$410$	−6.94882e53	+	6.23415e54i	−0.0940698	+	0.843949i
$411$		−	1.66452e55i		−	2.14097i
$412$	−5.58575e53	+	2.47450e54i	−0.0682716	+	0.302445i
$413$	−1.87432e54			−0.217717
$414$	2.07499e55	+	2.31287e54i	2.29092	+	0.255355i
$415$			1.97280e54i			0.207049i
$416$	−2.43691e54	+	3.93022e54i	−0.243153	+	0.392154i
$417$	−5.09502e54			−0.483380
$418$	−2.45450e53	+	2.20206e54i	−0.0221443	+	0.198668i
$419$		−	2.86152e54i		−	0.245529i	−0.992436	−	0.122764i	$-0.960824\pi$
$419$		−	2.86152e54i		−	0.245529i	0.992436	−	0.122764i	$-0.0391760\pi$
$420$	−3.91348e54	−	8.83397e53i	−0.319395	−	0.0720976i
$421$	2.20771e55			1.71403			0.857013	−	0.515295i	$-0.172318\pi$
$421$	2.20771e55			1.71403			0.857013	+	0.515295i	$0.172318\pi$
$422$	−1.75076e55	−	1.95146e54i	−1.29320	−	0.144145i
$423$		−	6.73987e54i		−	0.473701i
$424$	−5.05103e53	+	1.46026e54i	−0.0337829	+	0.0976669i
$425$	1.04911e54			0.0667810
$426$	2.50895e54	−	2.25091e55i	0.152016	−	1.36382i
$427$		−	2.15587e54i		−	0.124347i
$428$	−6.71554e53	+	2.97500e54i	−0.0368775	+	0.163369i
$429$	2.43840e55			1.27497
$430$	2.03658e55	+	2.27005e54i	1.01406	+	0.113031i
$431$		−	2.23228e55i		−	1.05859i	−0.848439	−	0.529293i	$-0.822457\pi$
$431$		−	2.23228e55i		−	1.05859i	0.848439	−	0.529293i	$-0.177543\pi$
$432$	−3.05109e55	+	6.41385e55i	−1.37815	+	2.89708i
$433$	1.16815e54			0.0502634			0.0251317	−	0.999684i	$-0.491999\pi$
$433$	1.16815e54			0.0502634			0.0251317	+	0.999684i	$0.491999\pi$
$434$	−7.53841e53	+	6.76310e54i	−0.0309026	+	0.277244i
$435$		−	5.33919e55i		−	2.08546i
$436$	3.52952e54	+	7.96726e53i	0.131371	+	0.0296546i
$437$	−3.37005e54			−0.119543
$438$	6.13839e55	+	6.84209e54i	2.07538	+	0.231330i
$439$			5.62221e55i			1.81197i	0.423306	+	0.905987i	$0.360869\pi$
$439$			5.62221e55i			1.81197i	−0.423306	+	0.905987i	$0.639131\pi$
$440$	−4.65993e55	−	1.61187e55i	−1.43177	−	0.495248i
$441$	−8.88602e55			−2.60314
$442$	−1.17031e54	+	1.04995e55i	−0.0326914	+	0.293292i
$443$		−	3.30478e55i		−	0.880369i	−0.897907	−	0.440185i	$-0.854913\pi$
$443$		−	3.30478e55i		−	0.880369i	0.897907	−	0.440185i	$-0.145087\pi$
$444$	1.88418e55	−	8.34698e55i	0.478719	−	2.12074i
$445$	−2.34504e55			−0.568316
$446$	−1.09201e55	−	1.21719e54i	−0.252461	−	0.0281402i
$447$			1.35396e56i			2.98641i
$448$	−4.77236e54	+	6.07311e54i	−0.100437	+	0.127812i
$449$	−4.46249e55			−0.896198			−0.448099	−	0.893984i	$-0.647899\pi$
$449$	−4.46249e55			−0.896198			−0.448099	+	0.893984i	$0.647899\pi$
$450$	−1.61365e54	+	1.44769e55i	−0.0309277	+	0.277468i
$451$		−	6.36775e55i		−	1.16487i
$452$	2.77586e55	+	6.26600e54i	0.484719	+	0.109417i
$453$	1.12828e56			1.88084
$454$	−6.78990e55	−	7.56828e54i	−1.08066	−	0.120455i
$455$		−	5.18678e54i		−	0.0788241i
$456$	5.98673e54	−	1.73077e55i	0.0868816	−	0.251176i
$457$	4.64937e55			0.644398			0.322199	−	0.946672i	$-0.395578\pi$
$457$	4.64937e55			0.644398			0.322199	+	0.946672i	$0.395578\pi$
$458$	−6.52244e54	+	5.85162e55i	−0.0863446	+	0.774643i
$459$			1.62259e56i			2.05183i
$460$	1.65138e55	−	7.31565e55i	0.199495	−	0.883768i
$461$	−1.28726e56			−1.48575			−0.742877	−	0.669427i	$-0.766540\pi$
$461$	−1.28726e56			−1.48575			−0.742877	+	0.669427i	$0.766540\pi$
$462$	4.04763e55	+	4.51165e54i	0.446395	+	0.0497569i
$463$		−	5.41494e55i		−	0.570680i	−0.958426	−	0.285340i	$-0.907893\pi$
$463$		−	5.41494e55i		−	0.570680i	0.958426	−	0.285340i	$-0.0921066\pi$
$464$	−9.28236e55	−	4.41565e55i	−0.934933	−	0.444751i
$465$	3.59072e56			3.45676
$466$	1.69849e55	−	1.52381e56i	0.156300	−	1.40225i
$467$			2.30411e55i			0.202698i	0.994851	+	0.101349i	$0.0323159\pi$
$467$			2.30411e55i			0.202698i	−0.994851	+	0.101349i	$0.967684\pi$
$468$	−1.43085e56	−	3.22989e55i	−1.20346	−	0.271659i
$469$	3.98923e54			0.0320818
$470$	−2.40612e55	−	2.68195e54i	−0.185039	−	0.0206251i
$471$		−	1.68640e56i		−	1.24029i
$472$	1.79944e56	+	6.22426e55i	1.26577	+	0.437830i
$473$	−2.08023e56			−1.39968
$474$	8.88487e54	−	7.97108e55i	0.0571881	−	0.513065i
$475$		−	2.35123e54i		−	0.0144787i
$476$	−3.88534e54	+	1.72122e55i	−0.0228919	+	0.101412i
$477$	−4.90118e55			−0.276322
$478$	2.50587e56	+	2.79314e55i	1.35199	+	0.150698i
$479$			3.25556e56i			1.68105i	0.541773	+	0.840525i	$0.317753\pi$
$479$			3.25556e56i			1.68105i	−0.541773	+	0.840525i	$0.682247\pi$
$480$	3.46378e56	+	2.14770e56i	1.71192	+	1.06147i
$481$	1.10628e56			0.523382
$482$	1.02598e55	−	9.20459e55i	0.0464676	−	0.416885i
$483$			6.19451e55i			0.268607i
$484$	2.53323e56	+	5.71832e55i	1.05177	+	0.237419i
$485$	−4.03372e56			−1.60372
$486$	−9.01337e56	−	1.00466e56i	−3.43183	−	0.382525i
$487$		−	9.03410e55i		−	0.329440i	−0.986340	−	0.164720i	$-0.947328\pi$
$487$		−	9.03410e55i		−	0.329440i	0.986340	−	0.164720i	$-0.0526721\pi$
$488$	−7.15922e55	+	2.06974e56i	−0.250063	+	0.722936i
$489$	−7.41006e55			−0.247934
$490$	−3.53596e55	+	3.17229e56i	−0.113342	+	1.01685i
$491$		−	2.45159e53i		−	0.000752898i	−1.00000		0.000376449i	$-0.999880\pi$
$491$		−	2.45159e53i		−	0.000752898i	1.00000		0.000376449i	$-0.000119827\pi$
$492$	−1.15893e56	+	5.13409e56i	−0.341028	+	1.51076i
$493$	−2.34827e56			−0.662160
$494$	2.35311e55	+	2.62287e54i	0.0635882	+	0.00708778i
$495$		−	1.56405e57i		−	4.05080i
$496$	2.96962e56	−	6.24258e56i	0.737201	−	1.54971i
$497$	4.89059e55			0.116380
$498$	−1.83372e55	+	1.64512e56i	−0.0418327	+	0.375303i
$499$		−	4.50764e56i		−	0.985910i	−0.870055	−	0.492955i	$-0.835917\pi$
$499$		−	4.50764e56i		−	0.985910i	0.870055	−	0.492955i	$-0.164083\pi$
$500$	−4.37775e56	−	9.88198e55i	−0.918080	−	0.207240i
$501$	1.40472e57			2.82486
$502$	−4.66409e56	−	5.19877e55i	−0.899474	−	0.100259i
$503$			9.17401e56i			1.69680i	0.529354	+	0.848401i	$0.322434\pi$
$503$			9.17401e56i			1.69680i	−0.529354	+	0.848401i	$0.677566\pi$
$504$	−2.31539e56	−	8.00891e55i	−0.410755	−	0.142080i
$505$	−5.85971e56			−0.997142
$506$	−8.43384e55	+	7.56644e56i	−0.137678	+	1.23518i
$507$			9.63273e56i			1.50863i
$508$	7.18142e55	−	3.18139e56i	0.107913	−	0.478056i
$509$	−2.90868e56			−0.419394			−0.209697	−	0.977766i	$-0.567248\pi$
$509$	−2.90868e56			−0.419394			−0.209697	+	0.977766i	$0.567248\pi$
$510$	9.25339e56	+	1.03142e56i	1.28035	+	0.142712i
$511$			1.33370e56i			0.177100i
$512$	6.59847e56	−	4.24568e56i	0.840958	−	0.541101i
$513$	3.63650e56			0.444855
$514$	−1.10765e56	+	9.93727e56i	−0.130070	+	1.16692i
$515$			2.89039e56i			0.325840i
$516$	1.67721e57	+	3.78601e56i	1.81528	+	0.409768i
$517$	2.45768e56			0.255402
$518$	1.83638e56	+	2.04690e55i	0.183247	+	0.0204254i
$519$		−	2.02105e57i		−	1.93670i
$520$	−1.72243e56	+	4.97958e56i	−0.158516	+	0.458271i
$521$	−1.08917e57			−0.962724			−0.481362	−	0.876522i	$-0.659858\pi$
$521$	−1.08917e57			−0.962724			−0.481362	+	0.876522i	$0.659858\pi$
$522$	3.61192e56	−	3.24044e57i	0.306660	−	2.75121i
$523$			1.14867e57i			0.936832i	0.883508	+	0.468416i	$0.155175\pi$
$523$			1.14867e57i			0.936832i	−0.883508	+	0.468416i	$0.844825\pi$
$524$	1.66868e56	−	7.39232e56i	0.130743	−	0.579193i
$525$	−4.32182e55			−0.0325328
$526$	8.99324e56	+	1.00242e56i	0.650452	+	0.0725019i
$527$		−	1.57926e57i		−	1.09757i
$528$	−3.73611e57	−	1.77728e57i	−2.49521	−	1.18698i
$529$	4.00036e56			0.256761
$530$	−1.95029e55	+	1.74971e56i	−0.0120311	+	0.107938i
$531$			6.03960e57i			3.58116i
$532$	3.85754e55	+	8.70770e54i	0.0219870	+	0.00496317i
$533$	−6.80454e56			−0.372844
$534$	−1.95554e57	−	2.17971e56i	−1.03015	−	0.114824i
$535$			3.47501e56i			0.176006i
$536$	−3.82986e56	−	1.32475e56i	−0.186519	−	0.0645166i
$537$	1.41784e57			0.664000
$538$	3.06723e56	−	2.75177e57i	0.138140	−	1.23932i
$539$		−	3.24027e57i		−	1.40352i
$540$	−1.78194e57	+	7.89406e57i	−0.742378	+	3.28876i
$541$	2.50169e57			1.00251			0.501257	−	0.865298i	$-0.332871\pi$
$541$	2.50169e57			1.00251			0.501257	+	0.865298i	$0.332871\pi$
$542$	3.03522e56	+	3.38317e55i	0.117005	+	0.0130418i
$543$			5.43265e57i			2.01472i
$544$	9.44595e56	−	1.52343e57i	0.337030	−	0.543558i
$545$	4.12272e56			0.141533
$546$	4.82112e55	−	4.32528e56i	0.0159258	−	0.142879i
$547$		−	2.49088e57i		−	0.791807i	−0.918292	−	0.395904i	$-0.870431\pi$
$547$		−	2.49088e57i		−	0.791807i	0.918292	−	0.395904i	$-0.129569\pi$
$548$	−3.56167e57	−	8.03984e56i	−1.08959	−	0.245955i
$549$	−6.94682e57			−2.04535
$550$	−5.27899e56	−	5.88416e55i	−0.149601	−	0.0166751i
$551$			5.26288e56i			0.143562i
$552$	2.05708e57	−	5.94705e57i	0.540170	−	1.56164i
$553$	1.73189e56			0.0437817
$554$	−3.49684e56	+	3.13719e57i	−0.0851080	+	0.763548i
$555$		−	9.74986e57i		−	2.28479i
$556$	−2.46096e56	+	1.09021e57i	−0.0555307	+	0.246003i
$557$	3.87716e57			0.842471			0.421235	−	0.906951i	$-0.361597\pi$
$557$	3.87716e57			0.842471			0.421235	+	0.906951i	$0.361597\pi$
$558$	2.17927e58	+	2.42909e57i	4.56029	+	0.508307i
$559$			2.22292e57i			0.447998i
$560$	−3.78051e56	+	7.94719e56i	−0.0733841	+	0.154264i
$561$	−9.45170e57			−1.76722
$562$	−9.43391e56	+	8.46365e57i	−0.169914	+	1.52439i
$563$		−	3.22760e57i		−	0.560019i	−0.959997	−	0.280010i	$-0.909662\pi$
$563$		−	3.22760e57i		−	0.560019i	0.959997	−	0.280010i	$-0.0903377\pi$
$564$	−1.98154e57	−	4.47298e56i	−0.331239	−	0.0747714i
$565$	3.24239e57			0.522214
$566$	−8.82943e57	−	9.84161e56i	−1.37021	−	0.152729i
$567$		−	3.77780e57i		−	0.564930i
$568$	−4.69521e57	−	1.62407e57i	−0.676613	−	0.234040i
$569$	9.08852e57			1.26222			0.631110	−	0.775693i	$-0.282599\pi$
$569$	9.08852e57			1.26222			0.631110	+	0.775693i	$0.282599\pi$
$570$	2.31158e56	−	2.07384e57i	0.0309412	−	0.277590i
$571$			6.34725e57i			0.818893i	0.912334	+	0.409447i	$0.134278\pi$
$571$			6.34725e57i			0.818893i	−0.912334	+	0.409447i	$0.865722\pi$
$572$	1.17777e57	−	5.21757e57i	0.146469	−	0.648861i
$573$	1.02029e58			1.22314
$574$	−1.12953e57	−	1.25901e56i	−0.130541	−	0.0145506i
$575$		−	8.07898e56i		−	0.0900185i
$576$	1.95693e58	+	1.53779e58i	2.10234	+	1.65206i
$577$	−1.41714e57			−0.146798			−0.0733990	−	0.997303i	$-0.523385\pi$
$577$	−1.41714e57			−0.146798			−0.0733990	+	0.997303i	$0.523385\pi$
$578$	−6.55379e56	+	5.87974e57i	−0.0654648	+	0.587319i
$579$		−	2.14242e58i		−	2.06373i
$580$	−1.14246e58	−	2.57889e57i	−1.06133	−	0.239577i
$581$	−3.57439e56			−0.0320260
$582$	−3.36373e58	−	3.74934e57i	−2.90695	−	0.324020i
$583$		−	1.78721e57i		−	0.148983i
$584$	4.42896e57	−	1.28042e58i	0.356149	−	1.02963i
$585$	−1.67133e58			−1.29655
$586$	−2.46961e57	+	2.21561e58i	−0.184832	+	1.65823i
$587$			6.78157e57i			0.489700i	0.969561	+	0.244850i	$0.0787387\pi$
$587$			6.78157e57i			0.489700i	−0.969561	+	0.244850i	$0.921261\pi$
$588$	−5.89729e57	+	2.61252e58i	−0.410893	+	1.82027i
$589$	−3.53940e57			−0.237962
$590$	2.15613e58	+	2.40330e57i	1.39888	+	0.155925i
$591$			3.68734e58i			2.30874i
$592$	−1.69504e58	−	8.06339e57i	−1.02429	−	0.487261i
$593$	1.90720e58			1.11237			0.556184	−	0.831059i	$-0.312265\pi$
$593$	1.90720e58			1.11237			0.556184	+	0.831059i	$0.312265\pi$
$594$	9.10066e57	−	8.16468e58i	0.512339	−	4.59646i
$595$			2.01050e57i			0.109257i
$596$	2.89715e58	+	6.53981e57i	1.51985	+	0.343078i
$597$	−5.99486e58			−3.03612
$598$	8.08545e57	+	9.01235e56i	0.395348	+	0.0440670i
$599$			2.55855e58i			1.20790i	0.797022	+	0.603950i	$0.206407\pi$
$599$			2.55855e58i			1.20790i	−0.797022	+	0.603950i	$0.793593\pi$
$600$	4.14916e57	+	1.43519e57i	0.189140	+	0.0654235i
$601$	5.28475e57			0.232627			0.116314	−	0.993213i	$-0.462892\pi$
$601$	5.28475e57			0.232627			0.116314	+	0.993213i	$0.462892\pi$
$602$	−4.11296e56	+	3.68995e57i	−0.0174835	+	0.156854i
$603$		−	1.28544e58i		−	0.527703i
$604$	5.44970e57	−	2.41423e58i	0.216071	−	0.957202i
$605$	2.95899e58			1.13313
$606$	−4.88643e58	−	5.44660e57i	−1.80745	−	0.201465i
$607$		−	3.04614e58i		−	1.08840i	−0.838956	−	0.544199i	$-0.816834\pi$
$607$		−	3.04614e58i		−	1.08840i	0.838956	−	0.544199i	$-0.183166\pi$
$608$	−3.41427e57	−	2.11700e57i	−0.117848	−	0.0730710i
$609$	9.67374e57			0.322575
$610$	−2.76430e57	+	2.48000e58i	−0.0890552	+	0.798960i
$611$		−	2.62627e57i		−	0.0817473i
$612$	5.54625e58	+	1.25197e58i	1.66809	+	0.376542i
$613$	−4.50881e57			−0.131036			−0.0655182	−	0.997851i	$-0.520870\pi$
$613$	−4.50881e57			−0.131036			−0.0655182	+	0.997851i	$0.520870\pi$
$614$	−2.03465e58	−	2.26789e57i	−0.571417	−	0.0636923i
$615$			5.99697e58i			1.62763i
$616$	2.92044e57	−	8.44303e57i	0.0766043	−	0.221464i
$617$	6.11538e58			1.55037			0.775184	−	0.631736i	$-0.217657\pi$
$617$	6.11538e58			1.55037			0.775184	+	0.631736i	$0.217657\pi$
$618$	−2.68662e57	+	2.41031e58i	−0.0658337	+	0.590628i
$619$			1.56809e58i			0.371421i	0.982604	+	0.185711i	$0.0594587\pi$
$619$			1.56809e58i			0.371421i	−0.982604	+	0.185711i	$0.940541\pi$
$620$	1.73436e58	−	7.68327e58i	0.397113	−	1.75922i
$621$	1.24953e59			2.76580
$622$	−5.07136e56	−	5.65273e55i	−0.0108524	−	0.00120965i
$623$		−	4.24882e57i		−	0.0879062i
$624$	−1.89919e58	+	3.99238e58i	−0.379920	+	0.798649i
$625$	−5.65333e58			−1.09351
$626$	−7.13020e57	+	6.39687e58i	−0.133365	+	1.19648i
$627$			2.11829e58i			0.383148i
$628$	−3.60849e58	−	8.14552e57i	−0.631208	−	0.142484i
$629$	−4.28816e58			−0.725450
$630$	−2.77434e58	−	3.09239e57i	−0.453950	−	0.0505990i
$631$		−	1.20668e59i		−	1.90975i	−0.297015	−	0.954873i	$-0.595991\pi$
$631$		−	1.20668e59i		−	1.90975i	0.297015	−	0.954873i	$-0.404009\pi$
$632$	−1.66270e58	−	5.75127e57i	−0.254540	−	0.0880451i
$633$	−1.68415e59			−2.49403
$634$	2.38163e57	−	2.13668e58i	0.0341192	−	0.306101i
$635$		−	3.71608e58i		−	0.515035i
$636$	−3.25271e57	+	1.44096e58i	−0.0436160	+	0.193220i
$637$	−3.46254e58			−0.449227
$638$	1.18162e59	+	1.31708e58i	1.48335	+	0.165340i
$639$		−	1.57589e59i		−	1.91429i
$640$	6.26859e58	−	6.37428e58i	0.736870	−	0.749293i
$641$	−1.06420e59			−1.21061			−0.605307	−	0.795992i	$-0.706950\pi$
$641$	−1.06420e59			−1.21061			−0.605307	+	0.795992i	$0.706950\pi$
$642$	−3.23002e57	+	2.89782e58i	−0.0355607	+	0.319034i
$643$			1.46456e59i			1.56055i	0.625440	+	0.780273i	$0.284920\pi$
$643$			1.46456e59i			1.56055i	−0.625440	+	0.780273i	$0.715080\pi$
$644$	1.32548e58	+	2.99202e57i	0.136700	+	0.0308576i
$645$	1.95910e59			1.95570
$646$	−9.12112e57	−	1.01668e57i	−0.0881385	−	0.00982425i
$647$		−	1.31825e58i		−	0.123313i	−0.998097	−	0.0616563i	$-0.980362\pi$
$647$		−	1.31825e58i		−	0.123313i	0.998097	−	0.0616563i	$-0.0196383\pi$
$648$	−1.25454e59	+	3.62688e59i	−1.13608	+	3.28442i
$649$	−2.20233e59			−1.93083
$650$	−6.28778e56	+	5.64109e57i	−0.00533724	+	0.0478831i
$651$			6.50580e58i			0.534687i
$652$	−3.57915e57	+	1.58557e58i	−0.0284826	+	0.126179i
$653$	2.30675e58			0.177756			0.0888780	−	0.996043i	$-0.471672\pi$
$653$	2.30675e58			0.177756			0.0888780	+	0.996043i	$0.471672\pi$
$654$	3.43795e58	+	3.83207e57i	0.256547	+	0.0285957i
$655$		−	8.63474e58i		−	0.623996i
$656$	1.04259e59	+	4.95965e58i	0.729683	+	0.347113i
$657$	4.29756e59			2.91306
$658$	4.85926e56	−	4.35949e57i	0.00319026	−	0.0286215i
$659$		−	1.27850e59i		−	0.813029i	−0.913644	−	0.406514i	$-0.866744\pi$
$659$		−	1.27850e59i		−	0.813029i	0.913644	−	0.406514i	$-0.133256\pi$
$660$	−4.59835e59	−	1.03799e59i	−2.83256	−	0.639400i
$661$	2.65202e58			0.158251			0.0791254	−	0.996865i	$-0.474787\pi$
$661$	2.65202e58			0.158251			0.0791254	+	0.996865i	$0.474787\pi$
$662$	1.75209e59	+	1.95295e58i	1.01284	+	0.112895i
$663$			1.01000e59i			0.565638i
$664$	3.43159e58	+	1.18699e58i	0.186194	+	0.0644044i
$665$	4.50587e57			0.0236878
$666$	6.59570e58	−	5.91734e59i	0.335971	−	3.01417i
$667$			1.80836e59i			0.892570i
$668$	6.78496e58	−	3.00576e59i	0.324520	−	1.43763i
$669$	−1.05046e59			−0.486892
$670$	−4.58901e58	−	5.11508e57i	−0.206133	−	0.0229764i
$671$		−	2.53315e59i		−	1.10278i
$672$	−3.89127e58	+	6.27579e58i	−0.164186	+	0.264797i
$673$	4.00339e59			1.63724			0.818619	−	0.574337i	$-0.194740\pi$
$673$	4.00339e59			1.63724			0.818619	+	0.574337i	$0.194740\pi$
$674$	−2.53458e58	+	2.27390e59i	−0.100473	+	0.901393i
$675$			8.71774e58i			0.334985i
$676$	2.06117e59	+	4.65272e58i	0.767774	+	0.173311i
$677$	−6.90456e58			−0.249330			−0.124665	−	0.992199i	$-0.539786\pi$
$677$	−6.90456e58			−0.249330			−0.124665	+	0.992199i	$0.539786\pi$
$678$	2.70384e59	+	3.01380e58i	0.946581	+	0.105509i
$679$		−	7.30843e58i		−	0.248061i
$680$	6.67648e58	−	1.93018e59i	0.219715	−	0.635201i
$681$	−6.53158e59			−2.08415
$682$	−8.85765e58	+	7.94666e59i	−0.274061	+	2.45874i
$683$			6.41644e59i			1.92513i	0.271059	+	0.962563i	$0.412626\pi$
$683$			6.41644e59i			1.92513i	−0.271059	+	0.962563i	$0.587374\pi$
$684$	2.80587e58	−	1.24301e59i	0.0816375	−	0.361657i
$685$	−4.16028e59			−1.17387
$686$	−1.16513e59	−	1.29870e58i	−0.318837	−	0.0355388i
$687$			5.62900e59i			1.49396i
$688$	1.62023e59	−	3.40596e59i	0.417080	−	0.876763i
$689$	−1.90980e58			−0.0476853
$690$	7.94275e58	−	7.12586e59i	0.192371	−	1.72586i
$691$			3.42914e59i			0.805651i	0.915277	+	0.402825i	$0.131972\pi$
$691$			3.42914e59i			0.805651i	−0.915277	+	0.402825i	$0.868028\pi$
$692$	−4.32455e59	−	9.76191e58i	−0.985628	−	0.222488i
$693$	2.83380e59			0.626572
$694$	4.91726e59	+	5.48097e58i	1.05481	+	0.117573i
$695$			1.27344e59i			0.265032i
$696$	−9.28728e59	−	3.21246e59i	−1.87540	−	0.648700i
$697$	2.63757e59			0.516793
$698$	4.67705e57	−	4.19602e58i	0.00889217	−	0.0797763i
$699$		−	1.46583e60i		−	2.70435i
$700$	−2.08749e57	+	9.24763e57i	−0.00373736	+	0.0165566i
$701$	2.98694e59			0.518977			0.259488	−	0.965746i	$-0.416446\pi$
$701$	2.98694e59			0.518977			0.259488	+	0.965746i	$0.416446\pi$
$702$	−8.72472e59	−	9.72491e58i	−1.47120	−	0.163986i
$703$			9.61049e58i			0.157284i
$704$	−5.60754e59	+	7.13592e59i	−0.890731	+	1.13351i
$705$	−2.31458e59			−0.356862
$706$	−6.86182e58	+	6.15610e59i	−0.102693	+	0.921312i
$707$		−	1.06168e59i		−	0.154236i
$708$	1.77566e60	+	4.00824e59i	2.50416	+	0.565269i
$709$	4.15997e59			0.569533			0.284766	−	0.958597i	$-0.408084\pi$
$709$	4.15997e59			0.569533			0.284766	+	0.958597i	$0.408084\pi$
$710$	−5.62589e59	−	6.27083e58i	−0.747766	−	0.0833488i
$711$		−	5.58065e59i		−	0.720150i
$712$	−1.41095e59	+	4.07909e59i	−0.176780	+	0.511073i
$713$	−1.21616e60			−1.47949
$714$	−1.86876e58	+	1.67656e59i	−0.0220745	+	0.198042i
$715$		−	6.09449e59i		−	0.699053i
$716$	6.84835e58	−	3.03384e59i	0.0762803	−	0.337924i
$717$	2.41054e60			2.60742
$718$	−1.45126e60	−	1.61763e59i	−1.52452	−	0.169929i
$719$			1.48006e60i			1.50999i	0.655732	+	0.754993i	$0.272360\pi$
$719$			1.48006e60i			1.50999i	−0.655732	+	0.754993i	$0.727640\pi$
$720$	2.56082e60	+	1.21819e60i	2.53744	+	1.20707i
$721$	−5.23691e58			−0.0504005
$722$	1.16226e59	−	1.04272e60i	0.108648	−	0.974736i
$723$		−	8.85440e59i		−	0.803998i
$724$	1.16245e60	+	2.62403e59i	1.02534	+	0.231451i
$725$	−1.26166e59			−0.108105
$726$	2.46751e60	+	2.75038e59i	2.05395	+	0.228941i
$727$		−	2.23220e60i		−	1.80514i	−0.430543	−	0.902570i	$-0.641678\pi$
$727$		−	2.23220e60i		−	1.80514i	0.430543	−	0.902570i	$-0.358322\pi$
$728$	−9.02217e58	−	3.12076e58i	−0.0708846	−	0.0245189i
$729$	−4.11767e60			−3.14321
$730$	1.71010e59	−	1.53422e60i	0.126836	−	1.13791i
$731$		−	8.61648e59i		−	0.620962i
$732$	−4.61032e59	+	2.04239e60i	−0.322848	+	1.43023i
$733$	1.06594e60			0.725350			0.362675	−	0.931916i	$-0.381864\pi$
$733$	1.06594e60			0.725350			0.362675	+	0.931916i	$0.381864\pi$
$734$	−1.17864e60	−	1.31376e59i	−0.779409	−	0.0868759i
$735$			3.05160e60i			1.96107i
$736$	−1.17316e60	−	7.27414e59i	−0.732697	−	0.454305i
$737$	4.68735e59			0.284518
$738$	−4.05690e59	+	3.63966e60i	−0.239338	+	2.14722i
$739$		−	1.42564e60i		−	0.817479i	−0.912651	−	0.408739i	$-0.865969\pi$
$739$		−	1.42564e60i		−	0.817479i	0.912651	−	0.408739i	$-0.134031\pi$
$740$	−2.08623e60	−	4.70930e59i	−1.16278	−	0.262476i
$741$	2.26359e59			0.122635
$742$	−3.17019e58	−	3.53361e57i	−0.0166956	−	0.00186096i
$743$			1.50905e60i			0.772570i	0.922379	+	0.386285i	$0.126242\pi$
$743$			1.50905e60i			0.772570i	−0.922379	+	0.386285i	$0.873758\pi$
$744$	2.16045e60	−	6.24589e60i	1.07526	−	3.10859i
$745$	3.38408e60			1.63741
$746$	−2.41691e59	+	2.16834e60i	−0.113696	+	1.02003i
$747$			1.15177e60i			0.526785i
$748$	−4.56528e59	+	2.02243e60i	−0.203018	+	0.899375i
$749$	−6.29615e58			−0.0272243
$750$	−4.26417e60	−	4.75301e59i	−1.79287	−	0.199840i
$751$		−	2.05038e60i		−	0.838292i	−0.907919	−	0.419146i	$-0.862330\pi$
$751$		−	2.05038e60i		−	0.838292i	0.907919	−	0.419146i	$-0.137670\pi$
$752$	−1.91422e59	+	4.02397e59i	−0.0761056	+	0.159985i
$753$	−4.48664e60			−1.73471
$754$	1.40742e59	−	1.26267e60i	0.0529209	−	0.474781i
$755$		−	2.81999e60i		−	1.03125i
$756$	−1.43027e60	−	3.22859e59i	−0.508700	−	0.114830i
$757$	−3.68995e59			−0.127646			−0.0638229	−	0.997961i	$-0.520329\pi$
$757$	−3.68995e59			−0.127646			−0.0638229	+	0.997961i	$0.520329\pi$
$758$	−2.19901e60	−	2.45110e59i	−0.739903	−	0.0824724i
$759$			7.27857e60i			2.38215i
$760$	−4.32587e59	−	1.49631e59i	−0.137717	−	0.0476362i
$761$	1.81491e60			0.562054			0.281027	−	0.959700i	$-0.409325\pi$
$761$	1.81491e60			0.562054			0.281027	+	0.959700i	$0.409325\pi$
$762$	3.45410e59	−	3.09885e60i	0.104059	−	0.933569i
$763$			7.46969e58i			0.0218921i
$764$	4.92812e59	−	2.18317e60i	0.140514	−	0.622483i
$765$	6.47841e60			1.79713
$766$	5.06662e60	+	5.64745e59i	1.36746	+	0.152422i
$767$			2.35340e60i			0.618006i
$768$	5.81989e60	−	4.73286e60i	1.48706	−	1.20931i
$769$	−6.24685e60			−1.55313			−0.776565	−	0.630037i	$-0.783040\pi$
$769$	−6.24685e60			−1.55313			−0.776565	+	0.630037i	$0.783040\pi$
$770$	1.12763e59	−	1.01166e60i	0.0272812	−	0.244754i
$771$			9.55921e60i			2.25050i
$772$	−4.58425e60	−	1.03481e60i	−1.05028	−	0.237082i
$773$	−4.60999e60			−1.02785			−0.513926	−	0.857835i	$-0.671809\pi$
$773$	−4.60999e60			−1.02785			−0.513926	+	0.857835i	$0.671809\pi$
$774$	1.18901e61	+	1.32532e60i	2.58003	+	0.287580i
$775$		−	8.48496e59i		−	0.179190i
$776$	−2.42699e60	+	7.01646e60i	−0.498852	+	1.44219i
$777$	1.76651e60			0.353407
$778$	1.53323e59	−	1.37554e60i	0.0298563	−	0.267856i
$779$		−	5.91125e59i		−	0.112045i
$780$	−1.10919e60	+	4.91376e60i	−0.204654	+	0.906625i
$781$	5.74645e60			1.03212
$782$	−3.13408e60	−	3.49336e59i	−0.547984	−	0.0610804i
$783$		−	1.95134e61i		−	3.32151i
$784$	5.30530e60	+	2.52375e60i	0.879170	+	0.418224i
$785$	−4.21497e60			−0.680035
$786$	8.02599e59	−	7.20054e60i	0.126074	−	1.13108i
$787$		−	1.83379e60i		−	0.280467i	−0.990118	−	0.140233i	$-0.955215\pi$
$787$		−	1.83379e60i		−	0.280467i	0.990118	−	0.140233i	$-0.0447853\pi$
$788$	7.89001e60	+	1.78103e60i	1.17497	+	0.265229i
$789$	8.65109e60			1.25445
$790$	−1.99228e60	−	2.22067e59i	−0.281308	−	0.0313556i
$791$			5.87468e59i			0.0807752i
$792$	−2.72059e61	−	9.41049e60i	−3.64279	−	1.26004i
$793$	−2.70691e60			−0.352969
$794$	6.03825e59	−	5.41722e60i	0.0766797	−	0.687933i
$795$			1.68314e60i			0.208167i
$796$	−2.89559e60	+	1.28275e61i	−0.348789	+	1.54514i
$797$	1.27706e61			1.49826			0.749131	−	0.662422i	$-0.230471\pi$
$797$	1.27706e61			1.49826			0.749131	+	0.662422i	$0.230471\pi$
$798$	3.75746e59	+	4.18821e58i	0.0429372	+	0.00478594i
$799$			1.01799e60i			0.113308i
$800$	5.07506e59	−	8.18498e59i	0.0550239	−	0.0887418i
$801$	−1.36909e61			−1.44594
$802$	−1.11974e60	+	1.00458e61i	−0.115201	+	1.03352i
$803$			1.56710e61i			1.57062i
$804$	−3.77924e60	−	8.53096e59i	−0.369001	−	0.0832954i
$805$	1.54825e60			0.147274
$806$	8.49175e60	+	9.46523e59i	0.786976	+	0.0877193i
$807$		−	2.64708e61i		−	2.39014i
$808$	−3.52564e60	+	1.01927e61i	−0.310170	+	0.896706i
$809$	−1.47711e61			−1.26618			−0.633089	−	0.774079i	$-0.718213\pi$
$809$	−1.47711e61			−1.26618			−0.633089	+	0.774079i	$0.718213\pi$
$810$	−4.84399e60	+	4.34580e61i	−0.404592	+	3.62981i
$811$			1.59635e60i			0.129924i	0.997888	+	0.0649622i	$0.0206927\pi$
$811$			1.59635e60i			0.129924i	−0.997888	+	0.0649622i	$0.979307\pi$
$812$	4.67253e59	−	2.06994e60i	0.0370575	−	0.164166i
$813$	2.91974e60			0.225654
$814$	2.15775e61	+	2.40511e60i	1.62513	+	0.181143i
$815$			1.85206e60i			0.135939i
$816$	7.36164e60	−	1.54753e61i	0.526601	−	1.10699i
$817$	−1.93110e60			−0.134630
$818$	3.05085e60	−	2.73708e61i	0.207301	−	1.85981i
$819$		−	3.02818e60i		−	0.200548i
$820$	1.28321e61	+	2.89661e60i	0.828334	+	0.186982i
$821$	−1.45072e61			−0.912806			−0.456403	−	0.889773i	$-0.650863\pi$
$821$	−1.45072e61			−0.912806			−0.456403	+	0.889773i	$0.650863\pi$
$822$	−3.46927e61	−	3.86698e60i	−2.12780	−	0.237172i
$823$		−	1.10912e61i		−	0.663105i	−0.943437	−	0.331552i	$-0.892428\pi$
$823$		−	1.10912e61i		−	0.663105i	0.943437	−	0.331552i	$-0.107572\pi$
$824$	5.02770e60	+	1.73908e60i	0.293021	+	0.101356i
$825$	−5.07815e60			−0.288518
$826$	−4.35438e59	+	3.90654e60i	−0.0241182	+	0.216377i
$827$		−	8.97394e60i		−	0.484582i	−0.970204	−	0.242291i	$-0.922101\pi$
$827$		−	8.97394e60i		−	0.484582i	0.970204	−	0.242291i	$-0.0778989\pi$
$828$	9.64116e60	−	4.27106e61i	0.507566	−	2.24853i
$829$	−3.71513e61			−1.90690			−0.953452	−	0.301546i	$-0.902497\pi$
$829$	−3.71513e61			−1.90690			−0.953452	+	0.301546i	$0.902497\pi$
$830$	4.11180e60	+	4.58317e59i	0.205775	+	0.0229364i
$831$			3.01784e61i			1.47257i
$832$	7.62540e60	+	5.99218e60i	0.362805	+	0.285099i
$833$	1.34215e61			0.622666
$834$	−1.18366e60	+	1.06193e61i	−0.0535478	+	0.480405i
$835$		−	3.51093e61i		−	1.54884i
$836$	4.53262e60	+	1.02316e60i	0.194992	+	0.0440160i
$837$	1.31232e62			5.50559
$838$	−5.96411e60	−	6.64783e59i	−0.244018	−	0.0271992i
$839$			1.59908e61i			0.638072i	0.947743	+	0.319036i	$0.103359\pi$
$839$			1.59908e61i			0.638072i	−0.947743	+	0.319036i	$0.896641\pi$
$840$	−2.75039e60	+	7.95141e60i	−0.107036	+	0.309442i
$841$	1.89439e60			0.0719041
$842$	5.12890e60	−	4.60140e61i	0.189876	−	1.70348i
$843$			8.14165e61i			2.93990i
$844$	−8.13464e60	+	3.60367e61i	−0.286515	+	1.26927i
$845$	2.40759e61			0.827164
$846$	−1.40475e61	−	1.56579e60i	−0.470785	−	0.0524755i
$847$			5.36121e60i			0.175271i
$848$	2.92620e60	+	1.39200e60i	0.0933234	+	0.0443943i
$849$	−8.49351e61			−2.64256
$850$	2.43727e59	−	2.18660e60i	0.00739785	−	0.0663699i
$851$			3.30223e61i			0.977882i
$852$	−4.63316e61	−	1.04585e61i	−1.33858	−	0.302161i
$853$	−1.96123e61			−0.552838			−0.276419	−	0.961037i	$-0.589148\pi$
$853$	−1.96123e61			−0.552838			−0.276419	+	0.961037i	$0.589148\pi$
$854$	−4.49335e60	−	5.00846e59i	−0.123582	−	0.0137749i
$855$		−	1.45192e61i		−	0.389632i
$856$	6.04462e60	+	2.09083e60i	0.158278	+	0.0547482i
$857$	3.35638e61			0.857577			0.428789	−	0.903405i	$-0.358940\pi$
$857$	3.35638e61			0.857577			0.428789	+	0.903405i	$0.358940\pi$
$858$	5.66483e60	−	5.08221e61i	0.141239	−	1.26713i
$859$		−	6.73112e61i		−	1.63769i	−0.574017	−	0.818843i	$-0.694616\pi$
$859$		−	6.73112e61i		−	1.63769i	0.574017	−	0.818843i	$-0.305384\pi$
$860$	9.46270e60	−	4.19200e61i	0.224671	−	0.995300i
$861$	−1.08655e61			−0.251759
$862$	−4.65262e61	−	5.18598e60i	−1.05207	−	0.117268i
$863$		−	4.00076e61i		−	0.882908i	−0.897284	−	0.441454i	$-0.854463\pi$
$863$		−	4.00076e61i		−	0.882908i	0.897284	−	0.441454i	$-0.145537\pi$
$864$	1.26592e62	+	7.84927e61i	2.72658	+	1.69060i
$865$	−5.05138e61			−1.06187
$866$	2.71382e59	−	2.43471e60i	0.00556807	−	0.0499541i
$867$			5.65605e61i			1.13269i
$868$	1.39208e61	+	3.14238e60i	0.272114	+	0.0614248i
$869$	2.03498e61			0.388279
$870$	−1.11282e62	−	1.24039e61i	−2.07262	−	0.231022i
$871$		−	5.00888e60i		−	0.0910666i
$872$	2.48054e60	−	7.17128e60i	0.0440251	−	0.127277i
$873$	−2.35499e62			−4.08027
$874$	−7.82922e59	+	7.02400e60i	−0.0132428	+	0.118808i
$875$		−	9.26484e60i		−	0.152992i
$876$	2.85212e61	−	1.26350e62i	0.459813	−	2.03698i
$877$	6.73875e61			1.06069			0.530344	−	0.847782i	$-0.322063\pi$
$877$	6.73875e61			1.06069			0.530344	+	0.847782i	$0.322063\pi$
$878$	1.17181e62	+	1.30614e61i	1.80082	+	0.200726i
$879$			2.13132e62i			3.19803i
$880$	−4.44211e61	+	9.33798e61i	−0.650809	+	1.36810i
$881$	5.22171e61			0.746997			0.373498	−	0.927631i	$-0.378158\pi$
$881$	5.22171e61			0.746997			0.373498	+	0.927631i	$0.378158\pi$
$882$	−2.06438e61	+	1.85206e62i	−0.288370	+	2.58711i
$883$		−	1.34300e62i		−	1.83190i	−0.401290	−	0.915951i	$-0.631438\pi$
$883$		−	1.34300e62i		−	1.83190i	0.401290	−	0.915951i	$-0.368562\pi$
$884$	2.16116e61	+	4.87843e60i	0.287865	+	0.0649805i
$885$	2.07410e62			2.69786
$886$	−6.88798e61	−	7.67760e60i	−0.874951	−	0.0975254i
$887$		−	2.43070e60i		−	0.0301533i	−0.999886	−	0.0150766i	$-0.995201\pi$
$887$		−	2.43070e60i		−	0.0301533i	0.999886	−	0.0150766i	$-0.00479923\pi$
$888$	−1.69594e62	−	5.86625e61i	−2.05465	−	0.710703i
$889$	6.73293e60			0.0796649
$890$	−5.44794e60	+	4.88763e61i	−0.0629568	+	0.564818i
$891$		−	4.43893e62i		−	5.01010i
$892$	−5.07386e60	+	2.24774e61i	−0.0559341	+	0.247790i
$893$	2.28149e60			0.0245662
$894$	2.82199e62	+	3.14550e61i	2.96803	+	0.330828i
$895$		−	3.54373e61i		−	0.364064i
$896$	1.15491e61	+	1.13577e61i	0.115899	+	0.113978i
$897$	7.77784e61			0.762461
$898$	−1.03672e61	+	9.30091e61i	−0.0992788	+	0.890682i
$899$			1.89923e62i			1.77674i
$900$	2.97985e61	+	6.72649e60i	0.272334	+	0.0614746i
$901$	7.40276e60			0.0660957
$902$	−1.32720e62	−	1.47934e61i	−1.15770	−	0.129042i
$903$			3.54957e61i			0.302505i
$904$	1.95087e61	−	5.63999e61i	0.162439	−	0.469614i
$905$	1.35783e62			1.10465
$906$	2.62118e61	−	2.35160e62i	0.208356	−	1.86927i
$907$		−	3.52578e61i		−	0.273843i	−0.990582	−	0.136922i	$-0.956279\pi$
$907$		−	3.52578e61i		−	0.273843i	0.990582	−	0.136922i	$-0.0437208\pi$
$908$	−3.15483e61	+	1.39760e62i	−0.239427	+	1.06067i
$909$	−3.42105e62			−2.53698
$910$	−1.08105e61	−	1.20498e60i	−0.0783389	−	0.00873196i
$911$			8.28978e61i			0.587026i	0.955955	+	0.293513i	$0.0948244\pi$
$911$			8.28978e61i			0.587026i	−0.955955	+	0.293513i	$0.905176\pi$
$912$	−3.46827e61	−	1.64987e61i	−0.240006	−	0.114172i
$913$	−4.19992e61			−0.284024
$914$	1.08013e61	−	9.69043e61i	0.0713850	−	0.640432i
$915$			2.38565e62i			1.54086i
$916$	1.20447e62	+	2.71887e61i	0.760310	+	0.171626i
$917$	1.56447e61			0.0965188
$918$	3.38187e62	+	3.76957e61i	2.03921	+	0.227298i
$919$		−	2.59016e62i		−	1.52652i	−0.646094	−	0.763258i	$-0.723599\pi$
$919$		−	2.59016e62i		−	1.52652i	0.646094	−	0.763258i	$-0.276401\pi$
$920$	−1.48640e62	−	5.14143e61i	−0.856229	−	0.296169i
$921$	−1.95724e62			−1.10202
$922$	−2.99054e61	+	2.68297e62i	−0.164589	+	1.47661i
$923$		−	6.14062e61i		−	0.330352i
$924$	1.88067e61	−	8.33144e61i	0.0989014	−	0.438136i
$925$	−2.30391e61			−0.118438
$926$	−1.12861e62	−	1.25799e61i	−0.567168	−	0.0632187i
$927$			1.68748e62i			0.829021i
$928$	−1.13598e62	+	1.83209e62i	−0.545584	+	0.879910i
$929$	−1.65713e62			−0.778083			−0.389042	−	0.921220i	$-0.627194\pi$
$929$	−1.65713e62			−0.778083			−0.389042	+	0.921220i	$0.627194\pi$
$930$	8.34189e61	−	7.48394e62i	0.382933	−	3.43549i
$931$		−	3.00798e61i		−	0.134999i
$932$	−3.13652e62	−	7.08014e61i	−1.37630	−	0.310676i
$933$	−4.87842e60			−0.0209298
$934$	4.80234e61	+	5.35287e60i	0.201450	+	0.0224544i
$935$			2.36234e62i			0.968945i
$936$	−1.00560e62	+	2.90720e62i	−0.403304	+	1.16596i
$937$	4.29406e62			1.68398			0.841989	−	0.539494i	$-0.181385\pi$
$937$	4.29406e62			1.68398			0.841989	+	0.539494i	$0.181385\pi$
$938$	9.26768e59	−	8.31452e60i	0.00355395	−	0.0318844i
$939$			6.15350e62i			2.30752i
$940$	−1.11797e61	+	4.95263e61i	−0.0409963	+	0.181615i
$941$	3.52900e62			1.26552			0.632761	−	0.774348i	$-0.281922\pi$
$941$	3.52900e62			1.26552			0.632761	+	0.774348i	$0.281922\pi$
$942$	−3.51487e62	−	3.91781e61i	−1.23265	−	0.137396i
$943$		−	2.03115e62i		−	0.696619i
$944$	1.71533e62	−	3.60588e62i	0.575355	−	1.20948i
$945$	−1.67066e62			−0.548050
$946$	−4.83275e61	+	4.33571e62i	−0.155053	+	1.39106i
$947$			1.61719e62i			0.507470i	0.967274	+	0.253735i	$0.0816591\pi$
$947$			1.61719e62i			0.507470i	−0.967274	+	0.253735i	$0.918341\pi$
$948$	−1.64073e62	−	3.70365e61i	−0.503572	−	0.113672i
$949$	1.67459e62			0.502711
$950$	−4.90054e60	−	5.46233e59i	−0.0143896	−	0.00160392i
$951$		−	2.05539e62i		−	0.590342i
$952$	3.49717e61	+	1.20967e61i	0.0982519	+	0.0339852i
$953$	−2.29979e62			−0.632029			−0.316014	−	0.948754i	$-0.602345\pi$
$953$	−2.29979e62			−0.632029			−0.316014	+	0.948754i	$0.602345\pi$
$954$	−1.13863e61	+	1.02153e62i	−0.0306103	+	0.274621i
$955$		−	2.55010e62i		−	0.670634i
$956$	1.16432e62	−	5.15797e62i	0.299541	−	1.32697i
$957$	1.13667e63			2.86077
$958$	6.78539e62	+	7.56326e61i	1.67070	+	0.186223i
$959$		−	7.53774e61i		−	0.181573i
$960$	5.28102e62	−	6.72041e62i	1.24458	−	1.58380i
$961$	−8.43572e62			−1.94505
$962$	2.57009e61	−	2.30576e62i	0.0579791	−	0.520160i
$963$			2.02880e62i			0.447803i
$964$	−1.89463e62	−	4.27678e61i	−0.409172	−	0.0923633i
$965$	−5.35472e62			−1.13152
$966$	1.29109e62	+	1.43910e61i	0.266954	+	0.0297557i
$967$		−	8.52208e62i		−	1.72421i	−0.506731	−	0.862104i	$-0.669146\pi$
$967$		−	8.52208e62i		−	1.72421i	0.506731	−	0.862104i	$-0.330854\pi$
$968$	1.78035e62	−	5.14703e62i	0.352471	−	1.01900i
$969$	−8.77411e61			−0.169982
$970$	−9.37104e61	+	8.40725e62i	−0.177657	+	1.59385i
$971$			1.89088e62i			0.350801i	0.984497	+	0.175400i	$0.0561220\pi$
$971$			1.89088e62i			0.350801i	−0.984497	+	0.175400i	$0.943878\pi$
$972$	−4.18793e62	+	1.85527e63i	−0.760341	+	3.36833i
$973$	−2.30727e61			−0.0409947
$974$	−1.88293e62	−	2.09878e61i	−0.327413	−	0.0364947i
$975$			5.42648e61i			0.0923466i
$976$	4.14752e62	+	1.97299e62i	0.690785	+	0.328609i
$977$	−7.00263e62			−1.14150			−0.570750	−	0.821124i	$-0.693347\pi$
$977$	−7.00263e62			−1.14150			−0.570750	+	0.821124i	$0.693347\pi$
$978$	−1.72149e61	+	1.54444e62i	−0.0274655	+	0.246408i
$979$		−	4.99238e62i		−	0.779599i
$980$	6.52968e62	+	1.47396e62i	0.998032	+	0.225288i
$981$	2.40695e62			0.360096
$982$	−5.10971e59	−	5.69547e58i	−0.000748264	−	8.34043e-5i
$983$			2.81918e61i			0.0404110i	0.999796	+	0.0202055i	$0.00643204\pi$
$983$			2.81918e61i			0.0404110i	−0.999796	+	0.0202055i	$0.993568\pi$
$984$	1.04315e63	+	3.60823e62i	1.46369	+	0.506288i
$985$	9.21608e62			1.26586
$986$	−5.45545e61	+	4.89437e62i	−0.0733526	+	0.658085i
$987$		−	4.19363e61i		−	0.0551989i
$988$	1.09334e61	−	4.84353e61i	0.0140883	−	0.0624117i
$989$	−6.63538e62			−0.837036
$990$	−3.25986e63	−	3.63356e62i	−4.02587	−	0.448739i
$991$			4.32880e62i			0.523384i	0.965151	+	0.261692i	$0.0842805\pi$
$991$			4.32880e62i			0.523384i	−0.965151	+	0.261692i	$0.915720\pi$
$992$	−1.23212e63	−	7.63968e62i	−1.45850	−	0.904336i
$993$	1.68543e63			1.95334
$994$	1.13617e61	−	1.01932e62i	0.0128923	−	0.115663i
$995$			1.49835e63i			1.66467i
$996$	3.38624e62	+	7.64383e61i	0.368359	+	0.0831505i
$997$	−1.51374e63			−1.61232			−0.806162	−	0.591695i	$-0.798459\pi$
$997$	−1.51374e63			−1.61232			−0.806162	+	0.591695i	$0.798459\pi$
$998$	−9.39502e62	−	1.04720e62i	−0.979842	−	0.109217i
$999$		−	3.56332e63i		−	3.63898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.43.b.a.3.11	✓	20
4.3	odd	2	inner	4.43.b.a.3.12	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.43.b.a.3.11	✓	20	1.1	even	1	trivial
4.43.b.a.3.12	yes	20	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(232318. - 2.08424e6i) q^{2} -2.00495e10i q^{3} +(-4.29010e12 - 9.68414e11i) q^{4} -5.01114e14 q^{5} +(-4.17880e16 - 4.65785e15i) q^{6} -9.07936e16i q^{7} +(-3.01508e18 + 8.71664e18i) q^{8} -2.92563e20 q^{9} +O(q^{10})\)	\(q+(232318. - 2.08424e6i) q^{2} -2.00495e10i q^{3} +(-4.29010e12 - 9.68414e11i) q^{4} -5.01114e14 q^{5} +(-4.17880e16 - 4.65785e15i) q^{6} -9.07936e16i q^{7} +(-3.01508e18 + 8.71664e18i) q^{8} -2.92563e20 q^{9} +(-1.16418e20 + 1.04444e21i) q^{10} -1.06683e22i q^{11} +(-1.94162e22 + 8.60144e22i) q^{12} -1.14000e23 q^{13} +(-1.89236e23 - 2.10930e22i) q^{14} +1.00471e25i q^{15} +(1.74672e25 + 8.30920e24i) q^{16} +4.41888e25 q^{17} +(-6.79676e25 + 6.09773e26i) q^{18} -9.90347e25i q^{19} +(2.14983e27 + 4.85286e26i) q^{20} -1.82036e27 q^{21} +(-2.22353e28 - 2.47843e27i) q^{22} -3.40290e28i q^{23} +(1.74764e29 + 6.04508e28i) q^{24} +2.37415e28 q^{25} +(-2.64843e28 + 2.37605e29i) q^{26} +3.67195e30i q^{27} +(-8.79258e28 + 3.89514e29i) q^{28} -5.31418e30 q^{29} +(2.09406e31 + 2.33412e30i) q^{30} -3.57390e31i q^{31} +(2.13763e31 - 3.44755e31i) q^{32} -2.13893e32 q^{33} +(1.02659e31 - 9.21003e31i) q^{34} +4.54979e31i q^{35} +(1.25513e33 + 2.83322e32i) q^{36} -9.70417e32 q^{37} +(-2.06412e32 - 2.30075e31i) q^{38} +2.28565e33i q^{39} +(1.51090e33 - 4.36803e33i) q^{40} +5.96887e33 q^{41} +(-4.22903e32 + 3.79409e33i) q^{42} -1.94992e34i q^{43} +(-1.03313e34 + 4.57680e34i) q^{44} +1.46607e35 q^{45} +(-7.09247e34 - 7.90554e33i) q^{46} +2.30373e34i q^{47} +(1.66595e35 - 3.50208e35i) q^{48} +3.03730e35 q^{49} +(5.51557e33 - 4.94830e34i) q^{50} -8.85963e35i q^{51} +(4.89074e35 + 1.10400e35i) q^{52} +1.67526e35 q^{53} +(7.65323e36 + 8.53059e35i) q^{54} +5.34602e36i q^{55} +(7.91415e35 + 2.73750e35i) q^{56} -1.98559e36 q^{57} +(-1.23458e36 + 1.10760e37i) q^{58} -2.06438e37i q^{59} +(9.72974e36 - 4.31030e37i) q^{60} +2.37447e37 q^{61} +(-7.44887e37 - 8.30280e36i) q^{62} +2.65628e37i q^{63} +(-6.68892e37 - 5.25628e37i) q^{64} +5.71272e37 q^{65} +(-4.96913e37 + 4.45806e38i) q^{66} +4.39373e37i q^{67} +(-1.89575e38 - 4.27931e37i) q^{68} -6.82263e38 q^{69} +(9.48288e37 + 1.05700e37i) q^{70} +5.38649e38i q^{71} +(8.82101e38 - 2.55017e39i) q^{72} -1.46894e39 q^{73} +(-2.25445e38 + 2.02259e39i) q^{74} -4.76005e38i q^{75} +(-9.59066e37 + 4.24869e38i) q^{76} -9.68610e38 q^{77} +(4.76386e39 + 5.30998e38i) q^{78} +1.90750e39i q^{79} +(-8.75304e39 - 4.16385e39i) q^{80} +4.16087e40 q^{81} +(1.38668e39 - 1.24406e40i) q^{82} -3.93683e39i q^{83} +(7.80955e39 + 1.76287e39i) q^{84} -2.21436e40 q^{85} +(-4.06411e40 - 4.53002e39i) q^{86} +1.06547e41i q^{87} +(9.29915e40 + 3.21657e40i) q^{88} +4.67965e40 q^{89} +(3.40595e40 - 3.05566e41i) q^{90} +1.03505e40i q^{91} +(-3.29541e40 + 1.45988e41i) q^{92} -7.16548e41 q^{93} +(4.80154e40 + 5.35198e39i) q^{94} +4.96276e40i q^{95} +(-6.91215e41 - 4.28584e41i) q^{96} +8.04950e41 q^{97} +(7.05619e40 - 6.33048e41i) q^{98} +3.12114e42i 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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