LMFDB - Embedded newform 4.43.b.a.3.14

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			3.14
Root			$0.500000 + 3.38044e8i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.43.b.a.3.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12655e6 + 1.76888e6i) q^{2} -5.40870e9i q^{3} +(-1.85982e12 + 3.98546e12i) q^{4} -7.68266e14 q^{5} +(9.56734e15 - 6.09318e15i) q^{6} -1.45472e17i q^{7} +(-9.14497e18 + 1.20003e18i) q^{8} +8.01649e19 q^{9} +O(q^{10})$	\(q+(1.12655e6 + 1.76888e6i) q^{2} -5.40870e9i q^{3} +(-1.85982e12 + 3.98546e12i) q^{4} -7.68266e14 q^{5} +(9.56734e15 - 6.09318e15i) q^{6} -1.45472e17i q^{7} +(-9.14497e18 + 1.20003e18i) q^{8} +8.01649e19 q^{9} +(-8.65491e20 - 1.35897e21i) q^{10} -1.11705e22i q^{11} +(2.15562e22 + 1.00592e22i) q^{12} +1.25284e23 q^{13} +(2.57323e23 - 1.63882e23i) q^{14} +4.15533e24i q^{15} +(-1.24250e25 - 1.48245e25i) q^{16} -8.19966e25 q^{17} +(9.03098e25 + 1.41802e26i) q^{18} +1.04305e27i q^{19} +(1.42883e27 - 3.06190e27i) q^{20} -7.86817e26 q^{21} +(1.97593e28 - 1.25841e28i) q^{22} +3.19441e28i q^{23} +(6.49061e27 + 4.94625e28i) q^{24} +3.62860e29 q^{25} +(1.41138e29 + 2.21612e29i) q^{26} -1.02540e30i q^{27} +(5.79774e29 + 2.70552e29i) q^{28} +5.02026e30 q^{29} +(-7.35027e30 + 4.68118e30i) q^{30} +1.95472e31i q^{31} +(1.22253e31 - 3.86788e31i) q^{32} -6.04180e31 q^{33} +(-9.23732e31 - 1.45042e32i) q^{34} +1.11762e32i q^{35} +(-1.49092e32 + 3.19494e32i) q^{36} +5.56306e32 q^{37} +(-1.84503e33 + 1.17505e33i) q^{38} -6.77623e32i q^{39} +(7.02578e33 - 9.21942e32i) q^{40} +8.05453e33 q^{41} +(-8.86388e32 - 1.39178e33i) q^{42} +2.47053e34i q^{43} +(4.45196e34 + 2.07751e34i) q^{44} -6.15880e34 q^{45} +(-5.65052e34 + 3.59866e34i) q^{46} +4.59023e34i q^{47} +(-8.01811e34 + 6.72030e34i) q^{48} +2.90811e35 q^{49} +(4.08780e35 + 6.41855e35i) q^{50} +4.43495e35i q^{51} +(-2.33005e35 + 4.99313e35i) q^{52} +1.07910e36 q^{53} +(1.81381e36 - 1.15517e36i) q^{54} +8.58193e36i q^{55} +(1.74571e35 + 1.33034e36i) q^{56} +5.64156e36 q^{57} +(5.65557e36 + 8.88022e36i) q^{58} -1.77225e37i q^{59} +(-1.65609e37 - 7.72815e36i) q^{60} -1.86275e37 q^{61} +(-3.45766e37 + 2.20209e37i) q^{62} -1.16618e37i q^{63} +(8.21904e37 - 2.19485e37i) q^{64} -9.62513e37 q^{65} +(-6.80639e37 - 1.06872e38i) q^{66} -1.62877e38i q^{67} +(1.52499e38 - 3.26794e38i) q^{68} +1.72776e38 q^{69} +(-1.97693e38 + 1.25905e38i) q^{70} -3.83149e38i q^{71} +(-7.33106e38 + 9.62002e37i) q^{72} +4.14185e38 q^{73} +(6.26707e38 + 9.84038e38i) q^{74} -1.96260e39i q^{75} +(-4.15704e39 - 1.93989e39i) q^{76} -1.62500e39 q^{77} +(1.19863e39 - 7.63376e38i) q^{78} +1.20394e40i q^{79} +(9.54569e39 + 1.13891e40i) q^{80} +3.22546e39 q^{81} +(9.07383e39 + 1.42475e40i) q^{82} -1.87810e40i q^{83} +(1.46334e39 - 3.13583e39i) q^{84} +6.29952e40 q^{85} +(-4.37007e40 + 2.78318e40i) q^{86} -2.71531e40i q^{87} +(1.34049e40 + 1.02154e41i) q^{88} -8.49550e40 q^{89} +(-6.93820e40 - 1.08942e41i) q^{90} -1.82253e40i q^{91} +(-1.27312e41 - 5.94102e40i) q^{92} +1.05725e41 q^{93} +(-8.11956e40 + 5.17112e40i) q^{94} -8.01342e41i q^{95} +(-2.09202e41 - 6.61231e40i) q^{96} +5.03735e41 q^{97} +(3.27613e41 + 5.14410e41i) q^{98} -8.95483e41i 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 $

$2$	1.12655e6	+	1.76888e6i	0.537181	+	0.843467i
$2$	1.12655e6	+	1.76888e6i	0.537181	+	0.843467i
$3$		−	5.40870e9i		−	0.517067i	−0.966002	−	0.258534i	$-0.916761\pi$
$3$		−	5.40870e9i		−	0.517067i	0.966002	−	0.258534i	$-0.0832393\pi$
$4$	−1.85982e12	+	3.98546e12i	−0.422873	+	0.906189i
$5$	−7.68266e14			−1.61117			−0.805586	−	0.592479i	$-0.798149\pi$
$5$	−7.68266e14			−1.61117			−0.805586	+	0.592479i	$0.798149\pi$
$6$	9.56734e15	−	6.09318e15i	0.436129	−	0.277759i
$7$		−	1.45472e17i		−	0.260448i	−0.991485	−	0.130224i	$-0.958430\pi$
$7$		−	1.45472e17i		−	0.260448i	0.991485	−	0.130224i	$-0.0415697\pi$
$8$	−9.14497e18	+	1.20003e18i	−0.991500	+	0.130107i
$9$	8.01649e19			0.732642
$10$	−8.65491e20	−	1.35897e21i	−0.865491	−	1.35897i
$11$		−	1.11705e22i		−	1.50948i	−0.656025	−	0.754739i	$-0.727764\pi$
$11$		−	1.11705e22i		−	1.50948i	0.656025	−	0.754739i	$-0.272236\pi$
$12$	2.15562e22	+	1.00592e22i	0.468560	+	0.218654i
$13$	1.25284e23			0.507089			0.253545	−	0.967324i	$-0.418404\pi$
$13$	1.25284e23			0.507089			0.253545	+	0.967324i	$0.418404\pi$
$14$	2.57323e23	−	1.63882e23i	0.219680	−	0.139908i
$15$			4.15533e24i			0.833084i
$16$	−1.24250e25	−	1.48245e25i	−0.642356	−	0.766406i
$17$	−8.19966e25			−1.18678			−0.593388	−	0.804917i	$-0.702210\pi$
$17$	−8.19966e25			−1.18678			−0.593388	+	0.804917i	$0.702210\pi$
$18$	9.03098e25	+	1.41802e26i	0.393561	+	0.617959i
$19$			1.04305e27i			1.46043i	0.683218	+	0.730215i	$0.260580\pi$
$19$			1.04305e27i			1.46043i	−0.683218	+	0.730215i	$0.739420\pi$
$20$	1.42883e27	−	3.06190e27i	0.681322	−	1.46003i
$21$	−7.86817e26			−0.134669
$22$	1.97593e28	−	1.25841e28i	1.27319	−	0.810863i
$23$			3.19441e28i			0.809294i	0.914473	+	0.404647i	$0.132606\pi$
$23$			3.19441e28i			0.809294i	−0.914473	+	0.404647i	$0.867394\pi$
$24$	6.49061e27	+	4.94625e28i	0.0672743	+	0.512672i
$25$	3.62860e29			1.59587
$26$	1.41138e29	+	2.21612e29i	0.272399	+	0.427713i
$27$		−	1.02540e30i		−	0.895892i
$28$	5.79774e29	+	2.70552e29i	0.236015	+	0.110137i
$29$	5.02026e30			0.978066			0.489033	−	0.872265i	$-0.337350\pi$
$29$	5.02026e30			0.978066			0.489033	+	0.872265i	$0.337350\pi$
$30$	−7.35027e30	+	4.68118e30i	−0.702679	+	0.447517i
$31$			1.95472e31i			0.938617i	0.883034	+	0.469308i	$0.155497\pi$
$31$			1.95472e31i			0.938617i	−0.883034	+	0.469308i	$0.844503\pi$
$32$	1.22253e31	−	3.86788e31i	0.301377	−	0.953505i
$33$	−6.04180e31			−0.780501
$34$	−9.23732e31	−	1.45042e32i	−0.637513	−	1.00101i
$35$			1.11762e32i			0.419627i
$36$	−1.49092e32	+	3.19494e32i	−0.309815	+	0.663912i
$37$	5.56306e32			0.650246			0.325123	−	0.945672i	$-0.394594\pi$
$37$	5.56306e32			0.650246			0.325123	+	0.945672i	$0.394594\pi$
$38$	−1.84503e33	+	1.17505e33i	−1.23182	+	0.784515i
$39$		−	6.77623e32i		−	0.262199i
$40$	7.02578e33	−	9.21942e32i	1.59748	−	0.209625i
$41$	8.05453e33			1.09038			0.545192	−	0.838311i	$-0.316457\pi$
$41$	8.05453e33			1.09038			0.545192	+	0.838311i	$0.316457\pi$
$42$	−8.86388e32	−	1.39178e33i	−0.0723418	−	0.113589i
$43$			2.47053e34i			1.23014i	0.788474	+	0.615068i	$0.210871\pi$
$43$			2.47053e34i			1.23014i	−0.788474	+	0.615068i	$0.789129\pi$
$44$	4.45196e34	+	2.07751e34i	1.36787	+	0.638318i
$45$	−6.15880e34			−1.18041
$46$	−5.65052e34	+	3.59866e34i	−0.682612	+	0.434737i
$47$			4.59023e34i			0.353004i	0.984300	+	0.176502i	$0.0564782\pi$
$47$			4.59023e34i			0.353004i	−0.984300	+	0.176502i	$0.943522\pi$
$48$	−8.01811e34	+	6.72030e34i	−0.396284	+	0.332141i
$49$	2.90811e35			0.932167
$50$	4.08780e35	+	6.41855e35i	0.857273	+	1.34607i
$51$			4.43495e35i			0.613642i
$52$	−2.33005e35	+	4.99313e35i	−0.214434	+	0.459518i
$53$	1.07910e36			0.665686			0.332843	−	0.942982i	$-0.391992\pi$
$53$	1.07910e36			0.665686			0.332843	+	0.942982i	$0.391992\pi$
$54$	1.81381e36	−	1.15517e36i	0.755655	−	0.481256i
$55$			8.58193e36i			2.43203i
$56$	1.74571e35	+	1.33034e36i	0.0338863	+	0.258234i
$57$	5.64156e36			0.755140
$58$	5.65557e36	+	8.88022e36i	0.525398	+	0.824966i
$59$		−	1.77225e37i		−	1.14983i	−0.818213	−	0.574915i	$-0.805035\pi$
$59$		−	1.77225e37i		−	1.14983i	0.818213	−	0.574915i	$-0.194965\pi$
$60$	−1.65609e37	−	7.72815e36i	−0.754931	−	0.352289i
$61$	−1.86275e37			−0.600107			−0.300053	−	0.953922i	$-0.597005\pi$
$61$	−1.86275e37			−0.600107			−0.300053	+	0.953922i	$0.597005\pi$
$62$	−3.45766e37	+	2.20209e37i	−0.791692	+	0.504207i
$63$		−	1.16618e37i		−	0.190815i
$64$	8.21904e37	−	2.19485e37i	0.966144	−	0.258003i
$65$	−9.62513e37			−0.817007
$66$	−6.80639e37	−	1.06872e38i	−0.419270	−	0.658327i
$67$		−	1.62877e38i		−	0.731624i	−0.930689	−	0.365812i	$-0.880791\pi$
$67$		−	1.62877e38i		−	0.731624i	0.930689	−	0.365812i	$-0.119209\pi$
$68$	1.52499e38	−	3.26794e38i	0.501856	−	1.07544i
$69$	1.72776e38			0.418459
$70$	−1.97693e38	+	1.25905e38i	−0.353941	+	0.225416i
$71$		−	3.83149e38i		−	0.509264i	−0.967038	−	0.254632i	$-0.918046\pi$
$71$		−	3.83149e38i		−	0.509264i	0.967038	−	0.254632i	$-0.0819543\pi$
$72$	−7.33106e38	+	9.62002e37i	−0.726414	+	0.0953221i
$73$	4.14185e38			0.307195			0.153597	−	0.988133i	$-0.450914\pi$
$73$	4.14185e38			0.307195			0.153597	+	0.988133i	$0.450914\pi$
$74$	6.26707e38	+	9.84038e38i	0.349300	+	0.548461i
$75$		−	1.96260e39i		−	0.825174i
$76$	−4.15704e39	−	1.93989e39i	−1.32342	−	0.617577i
$77$	−1.62500e39			−0.393141
$78$	1.19863e39	−	7.63376e38i	0.221156	−	0.140848i
$79$			1.20394e40i			1.69994i	0.526829	+	0.849971i	$0.323381\pi$
$79$			1.20394e40i			1.69994i	−0.526829	+	0.849971i	$0.676619\pi$
$80$	9.54569e39	+	1.13891e40i	1.03495	+	1.23481i
$81$	3.22546e39			0.269405
$82$	9.07383e39	+	1.42475e40i	0.585733	+	0.919702i
$83$		−	1.87810e40i		−	0.939894i	−0.882695	−	0.469947i	$-0.844273\pi$
$83$		−	1.87810e40i		−	0.939894i	0.882695	−	0.469947i	$-0.155727\pi$
$84$	1.46334e39	−	3.13583e39i	0.0569481	−	0.122036i
$85$	6.29952e40			1.91210
$86$	−4.37007e40	+	2.78318e40i	−1.03758	+	0.660805i
$87$		−	2.71531e40i		−	0.505726i
$88$	1.34049e40	+	1.02154e41i	0.196394	+	1.49665i
$89$	−8.49550e40			−0.981745			−0.490873	−	0.871231i	$-0.663322\pi$
$89$	−8.49550e40			−0.981745			−0.490873	+	0.871231i	$0.663322\pi$
$90$	−6.93820e40	−	1.08942e41i	−0.634094	−	0.995638i
$91$		−	1.82253e40i		−	0.132070i
$92$	−1.27312e41	−	5.94102e40i	−0.733373	−	0.342229i
$93$	1.05725e41			0.485328
$94$	−8.11956e40	+	5.17112e40i	−0.297747	+	0.189627i
$95$		−	8.01342e41i		−	2.35300i
$96$	−2.09202e41	−	6.61231e40i	−0.493026	−	0.155832i
$97$	5.03735e41			0.954983			0.477491	−	0.878636i	$-0.341546\pi$
$97$	5.03735e41			0.954983			0.477491	+	0.878636i	$0.341546\pi$
$98$	3.27613e41	+	5.14410e41i	0.500742	+	0.786252i
$99$		−	8.95483e41i		−	1.10591i
$100$	−6.74853e41	+	1.44616e42i	−0.674853	+	1.44616i
$101$	5.48167e41			0.444799			0.222400	−	0.974956i	$-0.428611\pi$
$101$	5.48167e41			0.444799			0.222400	+	0.974956i	$0.428611\pi$
$102$	−7.84489e41	+	4.99620e41i	−0.517587	+	0.329637i
$103$		−	2.38055e42i		−	1.27966i	−0.768516	−	0.639830i	$-0.779005\pi$
$103$		−	2.38055e42i		−	1.27966i	0.768516	−	0.639830i	$-0.220995\pi$
$104$	−1.14572e42	+	1.50344e41i	−0.502779	+	0.0659761i
$105$	6.04485e41			0.216975
$106$	1.21566e42	+	1.90880e42i	0.357594	+	0.561484i
$107$			2.03844e42i			0.492309i	0.969231	+	0.246155i	$0.0791671\pi$
$107$			2.03844e42i			0.492309i	−0.969231	+	0.246155i	$0.920833\pi$
$108$	4.08670e42	+	1.90706e42i	0.811847	+	0.378849i
$109$	5.71474e42			0.935491			0.467746	−	0.883863i	$-0.345066\pi$
$109$	5.71474e42			0.935491			0.467746	+	0.883863i	$0.345066\pi$
$110$	−1.51804e43	+	9.66797e42i	−2.05133	+	1.30644i
$111$		−	3.00890e42i		−	0.336221i
$112$	−2.15655e42	+	1.80749e42i	−0.199609	+	0.167301i
$113$	1.50413e43			1.15515			0.577576	−	0.816337i	$-0.303999\pi$
$113$	1.50413e43			1.15515			0.577576	+	0.816337i	$0.303999\pi$
$114$	6.35550e42	+	9.97924e42i	0.405647	+	0.636936i
$115$		−	2.45416e43i		−	1.30391i
$116$	−9.33676e42	+	2.00080e43i	−0.413598	+	0.886312i
$117$	1.00434e43			0.371515
$118$	3.13490e43	−	1.99653e43i	0.969843	−	0.617666i
$119$			1.19282e43i			0.309094i
$120$	−4.98651e42	−	3.80003e43i	−0.108390	−	0.826003i
$121$	−7.00166e43			−1.27852
$122$	−2.09848e43	−	3.29498e43i	−0.322366	−	0.506170i
$123$		−	4.35646e43i		−	0.563801i
$124$	−7.79045e43	−	3.63541e43i	−0.850564	−	0.396916i
$125$	−1.04089e44			−0.960054
$126$	2.06283e43	−	1.31376e43i	0.160946	−	0.102502i
$127$		−	5.23918e43i		−	0.346246i	−0.984900	−	0.173123i	$-0.944614\pi$
$127$		−	5.23918e43i		−	0.346246i	0.984900	−	0.173123i	$-0.0553859\pi$
$128$	1.31416e44	+	1.20659e44i	0.736611	+	0.676316i
$129$	1.33624e44			0.636063
$130$	−1.08432e44	−	1.70257e44i	−0.438881	−	0.689119i
$131$			4.38267e44i			1.51023i	0.655595	+	0.755113i	$0.272418\pi$
$131$			4.38267e44i			1.51023i	−0.655595	+	0.755113i	$0.727582\pi$
$132$	1.12366e44	−	2.40794e44i	0.330053	−	0.707281i
$133$	1.51735e44			0.380366
$134$	2.88109e44	−	1.83489e44i	0.617101	−	0.393014i
$135$			7.87783e44i			1.44344i
$136$	7.49856e44	−	9.83983e43i	1.17669	−	0.154408i
$137$	−9.84880e44			−1.32511			−0.662554	−	0.749014i	$-0.730527\pi$
$137$	−9.84880e44			−1.32511			−0.662554	+	0.749014i	$0.730527\pi$
$138$	1.94641e44	+	3.05620e44i	0.224788	+	0.352956i
$139$			1.67856e45i			1.66581i	0.553414	+	0.832906i	$0.313325\pi$
$139$			1.67856e45i			1.66581i	−0.553414	+	0.832906i	$0.686675\pi$
$140$	−4.45421e44	−	2.07856e44i	−0.380261	−	0.177449i
$141$	2.48272e44			0.182527
$142$	6.77744e44	−	4.31637e44i	0.429547	−	0.273567i
$143$		−	1.39948e45i		−	0.765440i
$144$	−9.96047e44	−	1.18840e45i	−0.470617	−	0.561501i
$145$	−3.85689e45			−1.57583
$146$	4.66600e44	+	7.32643e44i	0.165019	+	0.259109i
$147$		−	1.57291e45i		−	0.481993i
$148$	−1.03463e45	+	2.21714e45i	−0.274972	+	0.589245i
$149$	7.39653e45			1.70654			0.853269	−	0.521471i	$-0.174616\pi$
$149$	7.39653e45			1.70654			0.853269	+	0.521471i	$0.174616\pi$
$150$	3.47160e45	−	2.21097e45i	0.696007	−	0.443268i
$151$			4.37128e45i			0.762243i	0.924525	+	0.381121i	$0.124462\pi$
$151$			4.37128e45i			0.762243i	−0.924525	+	0.381121i	$0.875538\pi$
$152$	−1.25169e45	−	9.53869e45i	−0.190013	−	1.44802i
$153$	−6.57325e45			−0.869481
$154$	−1.83064e45	−	2.87443e45i	−0.211188	−	0.331601i
$155$		−	1.50174e46i		−	1.51227i
$156$	2.70064e45	+	1.26025e45i	0.237602	+	0.110877i
$157$	6.56566e45			0.505109			0.252555	−	0.967583i	$-0.418729\pi$
$157$	6.56566e45			0.505109			0.252555	+	0.967583i	$0.418729\pi$
$158$	−2.12962e46	+	1.35629e46i	−1.43385	+	0.913177i
$159$		−	5.83655e45i		−	0.344204i
$160$	−9.39229e45	+	2.97156e46i	−0.485570	+	1.53626i
$161$	4.64698e45			0.210779
$162$	3.63364e45	+	5.70544e45i	0.144719	+	0.227234i
$163$		−	1.58013e46i		−	0.553037i	−0.961009	−	0.276518i	$-0.910819\pi$
$163$		−	1.58013e46i		−	0.553037i	0.961009	−	0.276518i	$-0.0891807\pi$
$164$	−1.49799e46	+	3.21010e46i	−0.461094	+	0.988093i
$165$	4.64171e46			1.25752
$166$	3.32213e46	−	2.11577e46i	0.792769	−	0.504893i
$167$		−	2.30783e46i		−	0.485465i	−0.970093	−	0.242733i	$-0.921956\pi$
$167$		−	2.30783e46i		−	0.485465i	0.970093	−	0.242733i	$-0.0780438\pi$
$168$	7.19542e45	−	9.44203e44i	0.133525	−	0.0175215i
$169$	−4.53449e46			−0.742861
$170$	7.09673e46	+	1.11431e47i	1.02714	+	1.61279i
$171$			8.36162e46i			1.06997i
$172$	−9.84621e46	−	4.59474e46i	−1.11474	−	0.520192i
$173$	1.47674e47			1.48025			0.740125	−	0.672469i	$-0.234766\pi$
$173$	1.47674e47			1.48025			0.740125	+	0.672469i	$0.234766\pi$
$174$	4.80305e46	−	3.05893e46i	0.426563	−	0.271666i
$175$		−	5.27860e46i		−	0.415643i
$176$	−1.65597e47	+	1.38793e47i	−1.15687	+	0.969622i
$177$	−9.58559e46			−0.594539
$178$	−9.57061e46	−	1.50275e47i	−0.527375	−	0.828070i
$179$		−	2.94153e47i		−	1.44098i	−0.693463	−	0.720492i	$-0.743916\pi$
$179$		−	2.94153e47i		−	1.44098i	0.693463	−	0.720492i	$-0.256084\pi$
$180$	1.14542e47	−	2.45457e47i	0.499165	−	1.06968i
$181$	−1.12921e47			−0.438052			−0.219026	−	0.975719i	$-0.570288\pi$
$181$	−1.12921e47			−0.438052			−0.219026	+	0.975719i	$0.570288\pi$
$182$	3.22384e46	−	2.05317e46i	0.111397	−	0.0709457i
$183$			1.00751e47i			0.310296i
$184$	−3.83339e46	−	2.92128e47i	−0.105295	−	0.802414i
$185$	−4.27391e47			−1.04766
$186$	1.19104e47	+	1.87014e47i	0.260709	+	0.409358i
$187$			9.15944e47i			1.79141i
$188$	−1.82942e47	−	8.53698e46i	−0.319888	−	0.149276i
$189$	−1.49168e47			−0.233334
$190$	1.41748e48	−	9.02752e47i	1.98468	−	1.26399i
$191$			5.60283e46i			0.0702598i	0.999383	+	0.0351299i	$0.0111845\pi$
$191$			5.60283e46i			0.0702598i	−0.999383	+	0.0351299i	$0.988816\pi$
$192$	−1.18713e47	−	4.44544e47i	−0.133405	−	0.499561i
$193$	−3.02096e47			−0.304398			−0.152199	−	0.988350i	$-0.548636\pi$
$193$	−3.02096e47			−0.304398			−0.152199	+	0.988350i	$0.548636\pi$
$194$	5.67482e47	+	8.91046e47i	0.512998	+	0.805496i
$195$			5.20595e47i			0.422448i
$196$	−5.40856e47	+	1.15902e48i	−0.394189	+	0.844719i
$197$	1.77145e48			1.16021			0.580107	−	0.814540i	$-0.303011\pi$
$197$	1.77145e48			1.16021			0.580107	+	0.814540i	$0.303011\pi$
$198$	1.58400e48	−	1.00881e48i	0.932795	−	0.594072i
$199$			2.23573e48i			1.18442i	0.805785	+	0.592208i	$0.201743\pi$
$199$			2.23573e48i			1.18442i	−0.805785	+	0.592208i	$0.798257\pi$
$200$	−3.31834e48	+	4.35442e47i	−1.58231	+	0.207635i
$201$	−8.80952e47			−0.378299
$202$	6.17537e47	+	9.69641e47i	0.238938	+	0.375173i
$203$		−	7.30308e47i		−	0.254736i
$204$	−1.76753e48	−	8.24820e47i	−0.556076	−	0.259493i
$205$	−6.18802e48			−1.75679
$206$	4.21090e48	−	2.68180e48i	1.07935	−	0.687409i
$207$			2.56080e48i			0.592922i
$208$	−1.55665e48	−	1.85726e48i	−0.325732	−	0.388636i
$209$	1.16514e49			2.20449
$210$	6.80983e47	+	1.06926e48i	0.116555	+	0.183011i
$211$		−	1.07225e49i		−	1.66098i	−0.557037	−	0.830488i	$-0.688062\pi$
$211$		−	1.07225e49i		−	1.66098i	0.557037	−	0.830488i	$-0.311938\pi$
$212$	−2.00693e48	+	4.30072e48i	−0.281501	+	0.603237i
$213$	−2.07234e48			−0.263323
$214$	−3.60575e48	+	2.29640e48i	−0.415247	+	0.264459i
$215$		−	1.89803e49i		−	1.98196i
$216$	1.23051e48	+	9.37728e48i	0.116562	+	0.888277i
$217$	2.84357e48			0.244461
$218$	6.43794e48	+	1.01087e49i	0.502528	+	0.789056i
$219$		−	2.24020e48i		−	0.158840i
$220$	−3.42029e49	−	1.59608e49i	−2.20388	−	1.02844i
$221$	−1.02728e49			−0.601801
$222$	5.32237e48	−	3.38967e48i	0.283591	−	0.180611i
$223$		−	3.08715e47i		−	0.0149677i	−0.999972	−	0.00748387i	$-0.997618\pi$
$223$		−	3.08715e47i		−	0.0149677i	0.999972	−	0.00748387i	$-0.00238221\pi$
$224$	−5.62669e48	−	1.77844e48i	−0.248339	−	0.0784931i
$225$	2.90886e49			1.16920
$226$	1.69448e49	+	2.66063e49i	0.620526	+	0.974333i
$227$			3.08165e49i			1.02858i	0.857615	+	0.514292i	$0.171945\pi$
$227$			3.08165e49i			1.02858i	−0.857615	+	0.514292i	$0.828055\pi$
$228$	−1.04923e49	+	2.24842e49i	−0.319329	+	0.684299i
$229$	−1.47807e49			−0.410346			−0.205173	−	0.978726i	$-0.565776\pi$
$229$	−1.47807e49			−0.410346			−0.205173	+	0.978726i	$0.565776\pi$
$230$	4.34111e49	−	2.76473e49i	1.09981	−	0.700436i
$231$			8.78915e48i			0.203280i
$232$	−4.59101e49	+	6.02446e48i	−0.969752	+	0.127254i
$233$	3.29359e49			0.635617			0.317809	−	0.948155i	$-0.397053\pi$
$233$	3.29359e49			0.635617			0.317809	+	0.948155i	$0.397053\pi$
$234$	1.13143e49	+	1.77655e49i	0.199570	+	0.313360i
$235$		−	3.52652e49i		−	0.568749i
$236$	7.06324e49	+	3.29607e49i	1.04196	+	0.486232i
$237$	6.51173e49			0.878984
$238$	−2.10996e49	+	1.34378e49i	−0.260710	+	0.166039i
$239$			1.46177e50i			1.65395i	0.562240	+	0.826974i	$0.309940\pi$
$239$			1.46177e50i			1.65395i	−0.562240	+	0.826974i	$0.690060\pi$
$240$	6.16004e49	−	5.16298e49i	0.638481	−	0.535137i
$241$	−1.84222e50			−1.74978			−0.874888	−	0.484325i	$-0.839065\pi$
$241$	−1.84222e50			−1.74978			−0.874888	+	0.484325i	$0.839065\pi$
$242$	−7.88772e49	−	1.23851e50i	−0.686798	−	1.07839i
$243$		−	1.29644e50i		−	1.03519i
$244$	3.46438e49	−	7.42393e49i	0.253769	−	0.543810i
$245$	−2.23421e50			−1.50188
$246$	7.70604e49	−	4.90777e49i	0.475548	−	0.302863i
$247$			1.30678e50i			0.740568i
$248$	−2.34572e49	−	1.78758e50i	−0.122121	−	0.930638i
$249$	−1.01581e50			−0.485988
$250$	−1.17262e50	−	1.84121e50i	−0.515723	−	0.809774i
$251$			2.27450e50i			0.919896i	0.887946	+	0.459948i	$0.152132\pi$
$251$			2.27450e50i			0.919896i	−0.887946	+	0.459948i	$0.847868\pi$
$252$	4.64775e49	+	2.16888e49i	0.172915	+	0.0806907i
$253$	3.56832e50			1.22161
$254$	9.26747e49	−	5.90220e49i	0.292047	−	0.185997i
$255$		−	3.40723e50i		−	0.988683i
$256$	−6.53844e49	+	3.68387e50i	−0.174757	+	0.984612i
$257$	6.22275e49			0.153245			0.0766225	−	0.997060i	$-0.475586\pi$
$257$	6.22275e49			0.153245			0.0766225	+	0.997060i	$0.475586\pi$
$258$	1.50534e50	+	2.36364e50i	0.341681	+	0.536498i
$259$		−	8.09271e49i		−	0.169355i
$260$	1.79010e50	−	3.83606e50i	0.345491	−	0.740363i
$261$	4.02448e50			0.716571
$262$	−7.75242e50	+	4.93730e50i	−1.27383	+	0.811264i
$263$			6.55665e50i			0.994514i	0.867603	+	0.497257i	$0.165659\pi$
$263$			6.55665e50i			0.994514i	−0.867603	+	0.497257i	$0.834341\pi$
$264$	5.52521e50	−	7.25034e49i	0.773867	−	0.101549i
$265$	−8.29038e50			−1.07253
$266$	1.70937e50	+	2.68401e50i	0.204326	+	0.320827i
$267$			4.59497e50i			0.507628i
$268$	6.49139e50	+	3.02921e50i	0.662990	+	0.309384i
$269$	7.50215e50			0.708578			0.354289	−	0.935136i	$-0.384723\pi$
$269$	7.50215e50			0.708578			0.354289	+	0.935136i	$0.384723\pi$
$270$	−1.39349e51	+	8.87477e50i	−1.21749	+	0.775386i
$271$		−	1.08717e51i		−	0.878903i	−0.898266	−	0.439451i	$-0.855173\pi$
$271$		−	1.08717e51i		−	0.878903i	0.898266	−	0.439451i	$-0.144827\pi$
$272$	1.01881e51	+	1.21555e51i	0.762332	+	0.909552i
$273$	−9.85753e49			−0.0682893
$274$	−1.10952e51	−	1.74213e51i	−0.711823	−	1.11768i
$275$		−	4.05333e51i		−	2.40894i
$276$	−3.21332e50	+	6.88593e50i	−0.176955	+	0.379203i
$277$	1.51482e51			0.773187			0.386594	−	0.922250i	$-0.373652\pi$
$277$	1.51482e51			0.773187			0.386594	+	0.922250i	$0.373652\pi$
$278$	−2.96917e51	+	1.89098e51i	−1.40506	+	0.894843i
$279$			1.56700e51i			0.687670i
$280$	−1.34117e50	−	1.02206e51i	−0.0545966	−	0.416060i
$281$	2.58446e51			0.976195			0.488097	−	0.872789i	$-0.337691\pi$
$281$	2.58446e51			0.976195			0.488097	+	0.872789i	$0.337691\pi$
$282$	2.79691e50	+	4.39163e50i	0.0980498	+	0.153955i
$283$		−	8.06900e50i		−	0.262606i	−0.991342	−	0.131303i	$-0.958084\pi$
$283$		−	8.06900e50i		−	0.262606i	0.991342	−	0.131303i	$-0.0419161\pi$
$284$	1.52703e51	+	7.12587e50i	0.461489	+	0.215354i
$285$	−4.33422e51			−1.21666
$286$	2.47552e51	−	1.57659e51i	0.645623	−	0.411179i
$287$		−	1.17171e51i		−	0.283988i
$288$	9.80040e50	−	3.10068e51i	0.220801	−	0.698577i
$289$	1.94974e51			0.408435
$290$	−4.34498e51	−	6.82238e51i	−0.846506	−	1.32916i
$291$		−	2.72455e51i		−	0.493790i
$292$	−7.70308e50	+	1.65072e51i	−0.129905	+	0.278377i
$293$	−2.54947e51			−0.400156			−0.200078	−	0.979780i	$-0.564120\pi$
$293$	−2.54947e51			−0.400156			−0.200078	+	0.979780i	$0.564120\pi$
$294$	2.78229e51	−	1.77196e51i	0.406545	−	0.258917i
$295$			1.36156e52i			1.85257i
$296$	−5.08740e51	+	6.67584e50i	−0.644719	+	0.0846018i
$297$	−1.14543e52			−1.35233
$298$	8.33256e51	+	1.30836e52i	0.916720	+	1.43941i
$299$			4.00208e51i			0.410384i
$300$	7.82187e51	+	3.65008e51i	0.747763	+	0.348944i
$301$	3.59394e51			0.320387
$302$	−7.73227e51	+	4.92447e51i	−0.642927	+	0.409462i
$303$		−	2.96487e51i		−	0.229991i
$304$	1.54627e52	−	1.29599e52i	1.11928	−	0.938116i
$305$	1.43109e52			0.966875
$306$	−7.40509e51	−	1.16273e52i	−0.467068	−	0.733378i
$307$			2.28530e52i			1.34598i	0.739653	+	0.672989i	$0.234990\pi$
$307$			2.28530e52i			1.34598i	−0.739653	+	0.672989i	$0.765010\pi$
$308$	3.02220e51	−	6.47637e51i	0.166249	−	0.356260i
$309$	−1.28757e52			−0.661670
$310$	2.65640e52	−	1.69179e52i	1.27555	−	0.812364i
$311$			1.65825e52i			0.744185i	0.928196	+	0.372093i	$0.121360\pi$
$311$			1.65825e52i			0.744185i	−0.928196	+	0.372093i	$0.878640\pi$
$312$	8.13167e50	+	6.19684e51i	0.0341141	+	0.259970i
$313$	1.96717e52			0.771633			0.385817	−	0.922575i	$-0.373920\pi$
$313$	1.96717e52			0.771633			0.385817	+	0.922575i	$0.373920\pi$
$314$	7.39654e51	+	1.16138e52i	0.271335	+	0.426043i
$315$			8.95935e51i			0.307436i
$316$	−4.79824e52	−	2.23910e52i	−1.54047	−	0.718860i
$317$	−6.06995e52			−1.82365			−0.911823	−	0.410584i	$-0.865325\pi$
$317$	−6.06995e52			−1.82365			−0.911823	+	0.410584i	$0.865325\pi$
$318$	1.03241e52	−	6.57516e51i	0.290325	−	0.184900i
$319$		−	5.60788e52i		−	1.47637i
$320$	−6.31442e52	+	1.68623e52i	−1.55662	+	0.415687i
$321$	1.10253e52			0.254557
$322$	5.23506e51	+	8.21995e51i	0.113227	+	0.177785i
$323$		−	8.55267e52i		−	1.73320i
$324$	−5.99876e51	+	1.28549e52i	−0.113924	+	0.244132i
$325$	4.54604e52			0.809250
$326$	2.79506e52	−	1.78010e52i	0.466468	−	0.297081i
$327$		−	3.09093e52i		−	0.483712i
$328$	−7.36584e52	+	9.66567e51i	−1.08111	+	0.141867i
$329$	6.67751e51			0.0919392
$330$	5.22912e52	+	8.21063e52i	0.675516	+	1.06068i
$331$			5.45281e51i			0.0661047i	0.999454	+	0.0330524i	$0.0105228\pi$
$331$			5.45281e51i			0.0661047i	−0.999454	+	0.0330524i	$0.989477\pi$
$332$	7.48509e52	+	3.49292e52i	0.851721	+	0.397456i
$333$	4.45962e52			0.476397
$334$	4.08227e52	−	2.59989e52i	0.409474	−	0.260783i
$335$			1.25133e53i			1.17877i
$336$	9.77618e51	+	1.16641e52i	0.0865056	+	0.103211i
$337$	−9.33192e51			−0.0775788			−0.0387894	−	0.999247i	$-0.512350\pi$
$337$	−9.33192e51			−0.0775788			−0.0387894	+	0.999247i	$0.512350\pi$
$338$	−5.10833e52	−	8.02096e52i	−0.399051	−	0.626579i
$339$		−	8.13542e52i		−	0.597291i
$340$	−1.17160e53	+	2.51065e53i	−0.808575	+	1.73272i
$341$	2.18352e53			1.41682
$342$	−1.47907e53	+	9.41978e52i	−0.902486	+	0.574768i
$343$		−	8.76885e52i		−	0.503230i
$344$	−2.96471e52	−	2.25930e53i	−0.160050	−	1.21968i
$345$	−1.32738e53			−0.674209
$346$	1.66362e53	+	2.61217e53i	0.795162	+	1.24854i
$347$			1.70608e53i			0.767506i	0.923436	+	0.383753i	$0.125369\pi$
$347$			1.70608e53i			0.767506i	−0.923436	+	0.383753i	$0.874631\pi$
$348$	1.08218e53	+	5.04998e52i	0.458283	+	0.213858i
$349$	8.44953e52			0.336898			0.168449	−	0.985710i	$-0.446124\pi$
$349$	8.44953e52			0.336898			0.168449	+	0.985710i	$0.446124\pi$
$350$	9.33721e52	−	5.94661e52i	0.350581	−	0.223275i
$351$		−	1.28466e53i		−	0.454297i
$352$	−4.32062e53	−	1.36563e53i	−1.43929	−	0.454922i
$353$	−3.26190e53			−1.02377			−0.511885	−	0.859054i	$-0.671052\pi$
$353$	−3.26190e53			−1.02377			−0.511885	+	0.859054i	$0.671052\pi$
$354$	−1.07987e53	−	1.69558e53i	−0.319375	−	0.501474i
$355$			2.94361e53i			0.820511i
$356$	1.58001e53	−	3.38585e53i	0.415154	−	0.889647i
$357$	6.45163e52			0.159822
$358$	5.20320e53	−	3.31378e53i	1.21542	−	0.774069i
$359$		−	1.65029e53i		−	0.363560i	−0.983339	−	0.181780i	$-0.941814\pi$
$359$		−	1.65029e53i		−	0.363560i	0.983339	−	0.181780i	$-0.0581859\pi$
$360$	5.63221e53	−	7.39074e52i	1.17038	−	0.153580i
$361$	−5.77864e53			−1.13285
$362$	−1.27211e53	−	1.99744e53i	−0.235313	−	0.369482i
$363$			3.78699e53i			0.661082i
$364$	7.26363e52	+	3.38957e52i	0.119681	+	0.0558491i
$365$	−3.18204e53			−0.494944
$366$	−1.78216e53	+	1.13501e53i	−0.261724	+	0.166685i
$367$			2.04571e52i			0.0283698i	0.999899	+	0.0141849i	$0.00451534\pi$
$367$			2.04571e52i			0.0283698i	−0.999899	+	0.0141849i	$0.995485\pi$
$368$	4.73554e53	−	3.96905e53i	0.620248	−	0.519855i
$369$	6.45690e53			0.798860
$370$	−4.81478e53	−	7.56003e53i	−0.562782	−	0.883665i
$371$		−	1.56980e53i		−	0.173377i
$372$	−1.96629e53	+	4.21362e53i	−0.205232	+	0.439799i
$373$	−5.80928e53			−0.573109			−0.286554	−	0.958064i	$-0.592510\pi$
$373$	−5.80928e53			−0.573109			−0.286554	+	0.958064i	$0.592510\pi$
$374$	−1.62019e54	+	1.03186e54i	−1.51100	+	0.962311i
$375$			5.62988e53i			0.496413i
$376$	−5.50841e52	−	4.19775e53i	−0.0459284	−	0.350003i
$377$	6.28956e53			0.495966
$378$	−1.68045e53	−	2.63860e53i	−0.125342	−	0.196809i
$379$			7.04731e53i			0.497278i	0.968596	+	0.248639i	$0.0799834\pi$
$379$			7.04731e53i			0.497278i	−0.968596	+	0.248639i	$0.920017\pi$
$380$	3.19372e54	+	1.49035e54i	2.13226	+	0.995022i
$381$	−2.83372e53			−0.179033
$382$	−9.91073e52	+	6.31187e52i	−0.0592618	+	0.0377422i
$383$			7.54108e52i			0.0426834i	0.999772	+	0.0213417i	$0.00679380\pi$
$383$			7.54108e52i			0.0426834i	−0.999772	+	0.0213417i	$0.993206\pi$
$384$	6.52608e53	−	7.10789e53i	0.349701	−	0.380877i
$385$	1.24843e54			0.633417
$386$	−3.40327e53	−	5.34372e53i	−0.163517	−	0.256750i
$387$			1.98050e54i			0.901248i
$388$	−9.36854e53	+	2.00761e54i	−0.403837	+	0.865394i
$389$	3.48563e53			0.142344			0.0711720	−	0.997464i	$-0.477326\pi$
$389$	3.48563e53			0.142344			0.0711720	+	0.997464i	$0.477326\pi$
$390$	−9.20869e53	+	5.86476e53i	−0.356321	+	0.226931i
$391$		−	2.61931e54i		−	0.960449i
$392$	−2.65946e54	+	3.48982e53i	−0.924243	+	0.121282i
$393$	2.37046e54			0.780888
$394$	1.99563e54	+	3.13348e54i	0.623245	+	0.978602i
$395$		−	9.24943e54i		−	2.73890i
$396$	3.56891e54	+	1.66543e54i	1.00216	+	0.467658i
$397$	−1.72045e54			−0.458185			−0.229092	−	0.973405i	$-0.573576\pi$
$397$	−1.72045e54			−0.458185			−0.229092	+	0.973405i	$0.573576\pi$
$398$	−3.95473e54	+	2.51866e54i	−0.999015	+	0.636245i
$399$		−	8.20691e53i		−	0.196675i
$400$	−4.50852e54	−	5.37920e54i	−1.02512	−	1.22309i
$401$	2.38591e54			0.514782			0.257391	−	0.966307i	$-0.417137\pi$
$401$	2.38591e54			0.514782			0.257391	+	0.966307i	$0.417137\pi$
$402$	−9.92436e53	−	1.55830e54i	−0.203215	−	0.319083i
$403$			2.44894e54i			0.475962i
$404$	−1.01949e54	+	2.18470e54i	−0.188094	+	0.403072i
$405$	−2.47801e54			−0.434058
$406$	1.29183e54	−	8.22729e53i	0.214861	−	0.136839i
$407$		−	6.21422e54i		−	0.981531i
$408$	−5.32207e53	−	4.05575e54i	−0.0798394	−	0.608426i
$409$	−4.88003e54			−0.695398			−0.347699	−	0.937606i	$-0.613037\pi$
$409$	−4.88003e54			−0.695398			−0.347699	+	0.937606i	$0.613037\pi$
$410$	−6.97112e54	−	1.09459e55i	−0.943716	−	1.48180i
$411$			5.32692e54i			0.685170i
$412$	9.48757e54	+	4.42738e54i	1.15961	+	0.541134i
$413$	−2.57814e54			−0.299471
$414$	−4.52974e54	+	2.88486e54i	−0.500110	+	0.318506i
$415$			1.44288e55i			1.51433i
$416$	1.53163e54	−	4.84582e54i	0.152825	−	0.483512i
$417$	9.07884e54			0.861337
$418$	1.31259e55	+	2.06100e55i	1.18421	+	1.85941i
$419$		−	1.28346e54i		−	0.110125i	−0.998483	−	0.0550627i	$-0.982464\pi$
$419$		−	1.28346e54i		−	0.110125i	0.998483	−	0.0550627i	$-0.0175359\pi$
$420$	−1.12423e54	+	2.40915e54i	−0.0917531	+	0.196621i
$421$	2.17048e55			1.68512			0.842561	−	0.538600i	$-0.181047\pi$
$421$	2.17048e55			1.68512			0.842561	+	0.538600i	$0.181047\pi$
$422$	1.89667e55	−	1.20794e55i	1.40098	−	0.892244i
$423$			3.67975e54i			0.258625i
$424$	−9.86836e54	+	1.29495e54i	−0.660028	+	0.0866107i
$425$	−2.97532e55			−1.89394
$426$	−2.33460e54	−	3.66572e54i	−0.141452	−	0.222105i
$427$			2.70979e54i			0.156297i
$428$	−8.12411e54	−	3.79112e54i	−0.446125	−	0.208184i
$429$	−7.56939e54			−0.395784
$430$	3.35738e55	−	2.13822e55i	1.67172	−	1.06467i
$431$			1.95456e55i			0.926885i	0.886127	+	0.463442i	$0.153386\pi$
$431$			1.95456e55i			0.926885i	−0.886127	+	0.463442i	$0.846614\pi$
$432$	−1.52010e55	+	1.27406e55i	−0.686617	+	0.575482i
$433$	−1.32998e55			−0.572269			−0.286135	−	0.958189i	$-0.592370\pi$
$433$	−1.32998e55			−0.572269			−0.286135	+	0.958189i	$0.592370\pi$
$434$	3.20343e54	+	5.02993e54i	0.131320	+	0.206195i
$435$			2.08608e55i			0.814811i
$436$	−1.06284e55	+	2.27759e55i	−0.395594	+	0.847732i
$437$	−3.33194e55			−1.18192
$438$	3.96265e54	−	2.52370e54i	0.133977	−	0.0853260i
$439$			1.37491e55i			0.443119i	0.975147	+	0.221559i	$0.0711147\pi$
$439$			1.37491e55i			0.443119i	−0.975147	+	0.221559i	$0.928885\pi$
$440$	−1.02986e55	−	7.84815e55i	−0.316425	−	2.41135i
$441$	2.33129e55			0.682944
$442$	−1.15729e55	−	1.81714e55i	−0.323276	−	0.507599i
$443$		−	4.39903e55i		−	1.17187i	−0.810359	−	0.585934i	$-0.800728\pi$
$443$		−	4.39903e55i		−	1.17187i	0.810359	−	0.585934i	$-0.199272\pi$
$444$	1.19918e55	+	5.59599e54i	0.304679	+	0.142179i
$445$	6.52681e55			1.58176
$446$	5.46080e53	−	3.47783e53i	0.0126248	−	0.00804038i
$447$		−	4.00056e55i		−	0.882395i
$448$	−3.19290e54	−	1.19564e55i	−0.0671965	−	0.251631i
$449$	−2.46071e55			−0.494181			−0.247091	−	0.968992i	$-0.579475\pi$
$449$	−2.46071e55			−0.494181			−0.247091	+	0.968992i	$0.579475\pi$
$450$	3.27698e55	+	5.14542e55i	0.628074	+	0.986185i
$451$		−	8.99732e55i		−	1.64591i
$452$	−2.79741e55	+	5.99467e55i	−0.488483	+	1.04679i
$453$	2.36430e55			0.394131
$454$	−5.45106e55	+	3.47163e55i	−0.867577	+	0.552536i
$455$			1.40019e55i			0.212788i
$456$	−5.15919e55	+	6.77004e54i	−0.748721	+	0.0982494i
$457$	1.29822e55			0.179931			0.0899657	−	0.995945i	$-0.471324\pi$
$457$	1.29822e55			0.179931			0.0899657	+	0.995945i	$0.471324\pi$
$458$	−1.66512e55	−	2.61453e55i	−0.220430	−	0.346113i
$459$			8.40796e55i			1.06322i
$460$	9.78095e55	+	4.56428e55i	1.18159	+	0.551389i
$461$	6.71140e52			0.000774629			0.000387315	−	1.00000i	$-0.499877\pi$
$461$	6.71140e52			0.000774629			0.000387315		1.00000i	$0.499877\pi$
$462$	−1.55469e55	+	9.90141e54i	−0.171460	+	0.109198i
$463$		−	1.08060e55i		−	0.113884i	−0.998377	−	0.0569421i	$-0.981865\pi$
$463$		−	1.08060e55i		−	0.113884i	0.998377	−	0.0569421i	$-0.0181350\pi$
$464$	−6.23766e55	−	7.44226e55i	−0.628266	−	0.749596i
$465$	−8.12249e55			−0.781946
$466$	3.71040e55	+	5.82597e55i	0.341441	+	0.536122i
$467$		−	1.39609e56i		−	1.22817i	−0.789238	−	0.614087i	$-0.789524\pi$
$467$		−	1.39609e56i		−	1.22817i	0.789238	−	0.614087i	$-0.210476\pi$
$468$	−1.86788e55	+	4.00274e55i	−0.157104	+	0.336662i
$469$	−2.36940e55			−0.190550
$470$	6.23798e55	−	3.97280e55i	0.479721	−	0.305521i
$471$		−	3.55117e55i		−	0.261175i
$472$	2.12676e55	+	1.62072e56i	0.149601	+	1.14006i
$473$	2.75971e56			1.85686
$474$	7.33579e55	+	1.15185e56i	0.472174	+	0.741394i
$475$			3.78482e56i			2.33066i
$476$	−4.75395e55	−	2.21843e55i	−0.280097	−	0.130707i
$477$	8.65061e55			0.487709
$478$	−2.58569e56	+	1.64675e56i	−1.39505	+	0.888469i
$479$		−	3.03320e56i		−	1.56623i	−0.621878	−	0.783114i	$-0.713630\pi$
$479$		−	3.03320e56i		−	1.56623i	0.621878	−	0.783114i	$-0.286370\pi$
$480$	1.60723e56	+	5.08001e55i	0.794350	+	0.251072i
$481$	6.96961e55			0.329733
$482$	−2.07535e56	−	3.25866e56i	−0.939946	−	1.47588i
$483$		−	2.51342e55i		−	0.108987i
$484$	1.30218e56	−	2.79049e56i	0.540653	−	1.15858i
$485$	−3.87002e56			−1.53864
$486$	2.29325e56	−	1.46051e56i	0.873151	−	0.556086i
$487$			3.41951e56i			1.24697i	0.781836	+	0.623484i	$0.214283\pi$
$487$			3.41951e56i			1.24697i	−0.781836	+	0.623484i	$0.785717\pi$
$488$	1.70348e56	−	2.23536e55i	0.595006	−	0.0780784i
$489$	−8.54648e55			−0.285957
$490$	−2.51694e56	−	3.95204e56i	−0.806781	−	1.26679i
$491$		−	3.45591e56i		−	1.06133i	−0.847581	−	0.530666i	$-0.821942\pi$
$491$		−	3.45591e56i		−	1.06133i	0.847581	−	0.530666i	$-0.178058\pi$
$492$	1.73625e56	+	8.10221e55i	0.510910	+	0.238417i
$493$	−4.11644e56			−1.16074
$494$	−2.31153e56	+	1.47215e56i	−0.624645	+	0.397819i
$495$			6.87970e56i			1.78180i
$496$	2.89776e56	−	2.42873e56i	0.719362	−	0.602926i
$497$	−5.57376e55			−0.132637
$498$	−1.14436e56	−	1.79684e56i	−0.261064	−	0.409915i
$499$		−	1.36133e56i		−	0.297750i	−0.988856	−	0.148875i	$-0.952435\pi$
$499$		−	1.36133e56i		−	0.297750i	0.988856	−	0.148875i	$-0.0475653\pi$
$500$	1.93587e56	−	4.14844e56i	0.405982	−	0.869991i
$501$	−1.24824e56			−0.251018
$502$	−4.02332e56	+	2.56234e56i	−0.775902	+	0.494150i
$503$		−	4.53974e56i		−	0.839659i	−0.907603	−	0.419830i	$-0.862090\pi$
$503$		−	4.53974e56i		−	0.839659i	0.907603	−	0.419830i	$-0.137910\pi$
$504$	1.39945e55	+	1.06647e56i	0.0248265	+	0.189193i
$505$	−4.21138e56			−0.716648
$506$	4.01989e56	+	6.31192e56i	0.656226	+	1.03039i
$507$			2.45257e56i			0.384109i
$508$	2.08805e56	+	9.74391e55i	0.313765	+	0.146418i
$509$	7.94135e56			1.14504			0.572520	−	0.819891i	$-0.305966\pi$
$509$	7.94135e56			1.14504			0.572520	+	0.819891i	$0.305966\pi$
$510$	6.02697e56	−	3.83841e56i	0.833922	−	0.531102i
$511$		−	6.02524e55i		−	0.0800084i
$512$	−7.25291e56	+	2.99349e56i	−0.924364	+	0.381513i
$513$	1.06955e57			1.30839
$514$	7.01023e55	+	1.10073e56i	0.0823203	+	0.129257i
$515$			1.82889e57i			2.06175i
$516$	−2.48516e56	+	5.32552e56i	−0.268974	+	0.576393i
$517$	5.12752e56			0.532851
$518$	1.43150e56	−	9.11685e55i	0.142846	−	0.0909745i
$519$		−	7.98724e56i		−	0.765389i
$520$	8.80215e56	−	1.15504e56i	0.810063	−	0.106299i
$521$	−1.08052e57			−0.955082			−0.477541	−	0.878610i	$-0.658472\pi$
$521$	−1.08052e57			−0.955082			−0.477541	+	0.878610i	$0.658472\pi$
$522$	4.53378e56	+	7.11882e56i	0.384928	+	0.604404i
$523$			1.72269e56i			0.140499i	0.997529	+	0.0702493i	$0.0223795\pi$
$523$			1.72269e56i			0.140499i	−0.997529	+	0.0702493i	$0.977621\pi$
$524$	−1.74670e57	−	8.15097e56i	−1.36855	−	0.638634i
$525$	−2.85504e56			−0.214915
$526$	−1.15979e57	+	7.38639e56i	−0.838840	+	0.534234i
$527$		−	1.60280e57i		−	1.11393i
$528$	7.50692e56	+	8.95664e56i	0.501360	+	0.598181i
$529$	5.37581e56			0.345044
$530$	−9.33953e56	−	1.46647e57i	−0.576145	−	0.904647i
$531$		−	1.42072e57i		−	0.842413i
$532$	−2.82200e56	+	6.04735e56i	−0.160847	+	0.344684i
$533$	1.00910e57			0.552921
$534$	−8.12794e56	+	5.17646e56i	−0.428168	+	0.272688i
$535$		−	1.56606e57i		−	0.793194i
$536$	1.95457e56	+	1.48950e57i	0.0951898	+	0.725405i
$537$	−1.59099e57			−0.745086
$538$	8.45154e56	+	1.32704e57i	0.380635	+	0.597662i
$539$		−	3.24851e57i		−	1.40708i
$540$	−3.13968e57	−	1.46513e57i	−1.30803	−	0.610391i
$541$	4.34223e57			1.74008			0.870042	−	0.492977i	$-0.164091\pi$
$541$	4.34223e57			1.74008			0.870042	+	0.492977i	$0.164091\pi$
$542$	1.92307e57	−	1.22475e57i	0.741326	−	0.472130i
$543$			6.10757e56i			0.226502i
$544$	−1.00243e57	+	3.17153e57i	−0.357667	+	1.13160i
$545$	−4.39044e57			−1.50724
$546$	−1.11050e56	−	1.74368e56i	−0.0366837	−	0.0575998i
$547$			1.08471e56i			0.0344810i	0.999851	+	0.0172405i	$0.00548810\pi$
$547$			1.08471e56i			0.0344810i	−0.999851	+	0.0172405i	$0.994512\pi$
$548$	1.83170e57	−	3.92520e57i	0.560353	−	1.20080i
$549$	−1.49327e57			−0.439663
$550$	7.16985e57	−	4.56628e57i	2.03186	−	1.29403i
$551$			5.23639e57i			1.42840i
$552$	−1.58003e57	+	2.07337e56i	−0.414902	+	0.0544446i
$553$	1.75139e57			0.442747
$554$	1.70652e57	+	2.67952e57i	0.415341	+	0.652158i
$555$			2.31163e57i			0.541709i
$556$	−6.68984e57	−	3.12181e57i	−1.50954	−	0.704428i
$557$	1.57463e57			0.342152			0.171076	−	0.985258i	$-0.445276\pi$
$557$	1.57463e57			0.342152			0.171076	+	0.985258i	$0.445276\pi$
$558$	−2.77183e57	+	1.76530e57i	−0.580027	+	0.369403i
$559$			3.09517e57i			0.623788i
$560$	1.65680e57	−	1.38863e57i	0.321605	−	0.269550i
$561$	4.95407e57			0.926279
$562$	2.91152e57	+	4.57159e57i	0.524393	+	0.823388i
$563$			1.92791e57i			0.334510i	0.985914	+	0.167255i	$0.0534904\pi$
$563$			1.92791e57i			0.334510i	−0.985914	+	0.167255i	$0.946510\pi$
$564$	−4.61740e56	+	9.89478e56i	−0.0771857	+	0.165404i
$565$	−1.15558e58			−1.86115
$566$	1.42731e57	−	9.09013e56i	0.221499	−	0.141067i
$567$		−	4.69215e56i		−	0.0701661i
$568$	4.59790e56	+	3.50389e57i	0.0662590	+	0.504935i
$569$	−4.80336e57			−0.667095			−0.333547	−	0.942733i	$-0.608246\pi$
$569$	−4.80336e57			−0.667095			−0.333547	+	0.942733i	$0.608246\pi$
$570$	−4.88272e57	−	7.66672e57i	−0.653567	−	1.02621i
$571$			2.11639e57i			0.273047i	0.990637	+	0.136523i	$0.0435929\pi$
$571$			2.11639e57i			0.273047i	−0.990637	+	0.136523i	$0.956407\pi$
$572$	5.57758e57	+	2.60278e57i	0.693633	+	0.323684i
$573$	3.03041e56			0.0363290
$574$	2.07261e57	−	1.31999e57i	0.239535	−	0.152553i
$575$			1.15912e58i			1.29153i
$576$	6.58879e57	−	1.75950e57i	0.707837	−	0.189024i
$577$	1.27929e58			1.32519			0.662595	−	0.748978i	$-0.269455\pi$
$577$	1.27929e58			1.32519			0.662595	+	0.748978i	$0.269455\pi$
$578$	2.19648e57	+	3.44886e57i	0.219403	+	0.344501i
$579$			1.63395e57i			0.157394i
$580$	7.17312e57	−	1.53715e58i	0.666377	−	1.42800i
$581$	−2.73212e57			−0.244794
$582$	4.81940e57	−	3.06934e57i	0.416496	−	0.265255i
$583$		−	1.20541e58i		−	1.00484i
$584$	−3.78771e57	+	4.97034e56i	−0.304584	+	0.0399684i
$585$	−7.71597e57			−0.598574
$586$	−2.87210e57	−	4.50970e57i	−0.214956	−	0.337519i
$587$		−	1.02920e58i		−	0.743193i	−0.928394	−	0.371596i	$-0.878811\pi$
$587$		−	1.02920e58i		−	0.743193i	0.928394	−	0.371596i	$-0.121189\pi$
$588$	6.26878e57	+	2.92533e57i	0.436776	+	0.203822i
$589$	−2.03887e58			−1.37078
$590$	−2.40844e58	+	1.53387e58i	−1.56258	+	0.995167i
$591$		−	9.58125e57i		−	0.599908i
$592$	−6.91209e57	−	8.24693e57i	−0.417689	−	0.498352i
$593$	2.42470e58			1.41420			0.707099	−	0.707115i	$-0.250004\pi$
$593$	2.42470e58			1.41420			0.707099	+	0.707115i	$0.250004\pi$
$594$	−1.29038e58	−	2.02612e58i	−0.726445	−	1.14064i
$595$		−	9.16406e57i		−	0.498003i
$596$	−1.37562e58	+	2.94786e58i	−0.721650	+	1.54645i
$597$	1.20924e58			0.612422
$598$	−7.07919e57	+	4.50854e57i	−0.346145	+	0.220450i
$599$		−	1.36010e57i		−	0.0642109i	−0.999484	−	0.0321055i	$-0.989779\pi$
$599$		−	1.36010e57i		−	0.0642109i	0.999484	−	0.0321055i	$-0.0102212\pi$
$600$	2.35518e57	+	1.79479e58i	0.107361	+	0.818160i
$601$	−2.40822e58			−1.06007			−0.530033	−	0.847977i	$-0.677820\pi$
$601$	−2.40822e58			−1.06007			−0.530033	+	0.847977i	$0.677820\pi$
$602$	4.04875e57	+	6.35725e57i	0.172106	+	0.270236i
$603$		−	1.30570e58i		−	0.536018i
$604$	−1.74216e58	−	8.12979e57i	−0.690736	−	0.322332i
$605$	5.37914e58			2.05992
$606$	5.24450e57	−	3.34008e57i	0.193990	−	0.123547i
$607$		−	8.69114e57i		−	0.310538i	−0.987872	−	0.155269i	$-0.950376\pi$
$607$		−	8.69114e57i		−	0.310538i	0.987872	−	0.155269i	$-0.0496244\pi$
$608$	4.03440e58	+	1.27516e58i	1.39253	+	0.440140i
$609$	−3.95002e57			−0.131715
$610$	1.61219e58	+	2.53142e58i	0.519387	+	0.815527i
$611$			5.75081e57i			0.179004i
$612$	1.22250e58	−	2.61974e58i	0.367680	−	0.787914i
$613$	7.87890e57			0.228979			0.114490	−	0.993424i	$-0.463477\pi$
$613$	7.87890e57			0.228979			0.114490	+	0.993424i	$0.463477\pi$
$614$	−4.04242e58	+	2.57451e58i	−1.13529	+	0.723033i
$615$			3.34692e58i			0.908381i
$616$	1.48606e58	−	1.95005e57i	0.389799	−	0.0511506i
$617$	−2.59777e58			−0.658584			−0.329292	−	0.944228i	$-0.606810\pi$
$617$	−2.59777e58			−0.658584			−0.329292	+	0.944228i	$0.606810\pi$
$618$	−1.45051e58	−	2.27755e58i	−0.355437	−	0.558097i
$619$			2.52789e58i			0.598761i	0.954134	+	0.299381i	$0.0967800\pi$
$619$			2.52789e58i			0.598761i	−0.954134	+	0.299381i	$0.903220\pi$
$620$	5.98514e58	+	2.79297e58i	1.37040	+	0.639500i
$621$	3.27556e58			0.725040
$622$	−2.93324e58	+	1.86810e58i	−0.627696	+	0.399762i
$623$			1.23586e58i			0.255694i
$624$	−1.00454e58	+	8.41944e57i	−0.200951	+	0.168425i
$625$	−2.53640e57			−0.0490612
$626$	2.21612e58	+	3.47969e58i	0.414507	+	0.650847i
$627$		−	6.30192e58i		−	1.13987i
$628$	−1.22109e58	+	2.61672e58i	−0.213597	+	0.457724i
$629$	−4.56152e58			−0.771695
$630$	−1.58480e58	+	1.00932e58i	−0.259312	+	0.165149i
$631$		−	3.89377e58i		−	0.616246i	−0.951347	−	0.308123i	$-0.900299\pi$
$631$		−	3.89377e58i		−	0.616246i	0.951347	−	0.308123i	$-0.0997008\pi$
$632$	−1.44476e58	−	1.10100e59i	−0.221175	−	1.68549i
$633$	−5.79947e58			−0.858836
$634$	−6.83810e58	−	1.07370e59i	−0.979628	−	1.53819i
$635$			4.02509e58i			0.557862i
$636$	2.32613e58	+	1.08549e58i	0.311914	+	0.145555i
$637$	3.64339e58			0.472692
$638$	9.91967e58	−	6.31756e58i	1.24527	−	0.793077i
$639$		−	3.07151e58i		−	0.373108i
$640$	−1.00962e59	−	9.26982e58i	−1.18681	−	1.08966i
$641$	1.90172e58			0.216336			0.108168	−	0.994133i	$-0.465502\pi$
$641$	1.90172e58			0.216336			0.108168	+	0.994133i	$0.465502\pi$
$642$	1.24206e58	+	1.95024e58i	0.136743	+	0.214710i
$643$			1.47695e59i			1.57375i	0.617111	+	0.786876i	$0.288303\pi$
$643$			1.47695e59i			1.57375i	−0.617111	+	0.786876i	$0.711697\pi$
$644$	−8.64254e57	+	1.85204e58i	−0.0891329	+	0.191006i
$645$	−1.02659e59			−1.02481
$646$	1.51286e59	−	9.63502e58i	1.46190	−	0.931043i
$647$			1.88098e59i			1.75952i	0.475415	+	0.879762i	$0.342298\pi$
$647$			1.88098e59i			1.75952i	−0.475415	+	0.879762i	$0.657702\pi$
$648$	−2.94967e58	+	3.87065e57i	−0.267115	+	0.0350516i
$649$	−1.97970e59			−1.73564
$650$	5.12134e58	+	8.04139e58i	0.434714	+	0.682576i
$651$		−	1.53800e58i		−	0.126403i
$652$	6.29756e58	+	2.93876e58i	0.501156	+	0.233865i
$653$	2.51313e59			1.93659			0.968295	−	0.249810i	$-0.0803683\pi$
$653$	2.51313e59			1.93659			0.968295	+	0.249810i	$0.0803683\pi$
$654$	5.46748e58	−	3.48209e58i	0.407995	−	0.259841i
$655$		−	3.36706e59i		−	2.43323i
$656$	−1.00077e59	−	1.19404e59i	−0.700414	−	0.835676i
$657$	3.32031e58			0.225064
$658$	7.52255e57	+	1.18117e58i	0.0493880	+	0.0775477i
$659$			4.29121e58i			0.272889i	0.990648	+	0.136444i	$0.0435675\pi$
$659$			4.29121e58i			0.272889i	−0.990648	+	0.136444i	$0.956432\pi$
$660$	−8.63274e58	+	1.84994e59i	−0.531772	+	1.13955i
$661$	6.55777e58			0.391314			0.195657	−	0.980672i	$-0.437316\pi$
$661$	6.55777e58			0.391314			0.195657	+	0.980672i	$0.437316\pi$
$662$	−9.64536e57	+	6.14286e57i	−0.0557572	+	0.0355102i
$663$			5.55627e58i			0.311171i
$664$	2.25378e58	+	1.71752e59i	0.122287	+	0.931904i
$665$	−1.16573e59			−0.612835
$666$	5.02399e58	+	7.88853e58i	0.255911	+	0.401825i
$667$			1.60368e59i			0.791542i
$668$	9.19777e58	+	4.29215e58i	0.439923	+	0.205290i
$669$	−1.66975e57			−0.00773933
$670$	−2.21345e59	+	1.40968e59i	−0.994255	+	0.633214i
$671$			2.08079e59i			0.905848i
$672$	−9.61908e57	+	3.04331e58i	−0.0405862	+	0.128408i
$673$	3.13427e59			1.28180			0.640899	−	0.767625i	$-0.278562\pi$
$673$	3.13427e59			1.28180			0.640899	+	0.767625i	$0.278562\pi$
$674$	−1.05129e58	−	1.65070e58i	−0.0416739	−	0.0654352i
$675$		−	3.72077e59i		−	1.42973i
$676$	8.43332e58	−	1.80720e59i	0.314136	−	0.673172i
$677$	−5.06848e59			−1.83027			−0.915137	−	0.403144i	$-0.867917\pi$
$677$	−5.06848e59			−1.83027			−0.915137	+	0.403144i	$0.867917\pi$
$678$	1.43906e59	−	9.16495e58i	0.503795	−	0.320853i
$679$		−	7.32795e58i		−	0.248724i
$680$	−5.76090e59	+	7.55961e58i	−1.89585	+	0.248778i
$681$	1.66677e59			0.531847
$682$	2.45984e59	+	3.86238e59i	0.761089	+	1.19504i
$683$		−	3.22236e59i		−	0.966805i	−0.875398	−	0.483402i	$-0.839401\pi$
$683$		−	3.22236e59i		−	0.966805i	0.875398	−	0.483402i	$-0.160599\pi$
$684$	−3.33249e59	−	1.55511e59i	−0.969596	−	0.452462i
$685$	7.56650e59			2.13498
$686$	1.55110e59	−	9.87855e58i	0.424458	−	0.270325i
$687$			7.99445e58i			0.212176i
$688$	3.66243e59	−	3.06963e59i	0.942784	−	0.790185i
$689$	1.35194e59			0.337562
$690$	−1.49536e59	−	2.34798e59i	−0.362172	−	0.568673i
$691$			2.53615e59i			0.595850i	0.954589	+	0.297925i	$0.0962945\pi$
$691$			2.53615e59i			0.595850i	−0.954589	+	0.297925i	$0.903706\pi$
$692$	−2.74646e59	+	5.88548e59i	−0.625959	+	1.34139i
$693$	−1.30268e59			−0.288031
$694$	−3.01786e59	+	1.92199e59i	−0.647366	+	0.412289i
$695$		−	1.28958e60i		−	2.68391i
$696$	3.25845e58	+	2.48314e59i	0.0657987	+	0.501427i
$697$	−6.60444e59			−1.29404
$698$	9.51881e58	+	1.49462e59i	0.180975	+	0.284162i
$699$		−	1.78141e59i		−	0.328657i
$700$	2.10377e59	+	9.81724e58i	0.376651	+	0.175764i
$701$	3.57809e59			0.621689			0.310845	−	0.950461i	$-0.399388\pi$
$701$	3.57809e59			0.621689			0.310845	+	0.950461i	$0.399388\pi$
$702$	2.27241e59	−	1.44724e59i	0.383185	−	0.244040i
$703$			5.80256e59i			0.949638i
$704$	−2.45176e59	−	9.18109e59i	−0.389450	−	1.45837i
$705$	−1.90739e59			−0.294082
$706$	−3.67470e59	−	5.76991e59i	−0.549949	−	0.863516i
$707$		−	7.97431e58i		−	0.115847i
$708$	1.78275e59	−	3.82030e59i	0.251415	−	0.538765i
$709$	−9.99610e59			−1.36855			−0.684274	−	0.729225i	$-0.739881\pi$
$709$	−9.99610e59			−1.36855			−0.684274	+	0.729225i	$0.739881\pi$
$710$	−5.20688e59	+	3.31612e59i	−0.692074	+	0.440763i
$711$			9.65134e59i			1.24545i
$712$	7.76911e59	−	1.01949e59i	0.973400	−	0.127732i
$713$	−6.24417e59			−0.759616
$714$	7.26808e58	+	1.14121e59i	0.0858534	+	0.134805i
$715$			1.07518e60i			1.23325i
$716$	1.17233e60	+	5.47070e59i	1.30580	+	0.609354i
$717$	7.90626e59			0.855202
$718$	2.91916e59	−	1.85913e59i	0.306651	−	0.195298i
$719$			7.25161e59i			0.739823i	0.929067	+	0.369911i	$0.120612\pi$
$719$			7.25161e59i			0.739823i	−0.929067	+	0.369911i	$0.879388\pi$
$720$	7.65229e59	+	9.13008e59i	0.758244	+	0.904675i
$721$	−3.46303e59			−0.333285
$722$	−6.50992e59	−	1.02217e60i	−0.608548	−	0.955525i
$723$			9.96400e59i			0.904752i
$724$	2.10013e59	−	4.50043e59i	0.185240	−	0.396958i
$725$	1.82165e60			1.56087
$726$	−6.69873e59	+	4.26624e59i	−0.557601	+	0.355121i
$727$		−	2.60561e57i		−	0.00210711i	−0.999999	−	0.00105355i	$-0.999665\pi$
$727$		−	2.60561e57i		−	0.00210711i	0.999999	−	0.00105355i	$-0.000335357\pi$
$728$	2.18709e58	+	1.66670e59i	0.0171834	+	0.130948i
$729$	−3.48281e59			−0.265859
$730$	−3.58473e59	−	5.62865e59i	−0.265874	−	0.417469i
$731$		−	2.02575e60i		−	1.45989i
$732$	−4.01538e59	−	1.87378e59i	−0.281186	−	0.131216i
$733$	1.27617e60			0.868412			0.434206	−	0.900814i	$-0.357029\pi$
$733$	1.27617e60			0.868412			0.434206	+	0.900814i	$0.357029\pi$
$734$	−3.61861e58	+	2.30459e58i	−0.0239290	+	0.0152397i
$735$			1.20842e60i			0.776573i
$736$	1.23556e60	+	3.90526e59i	0.771665	+	0.243902i
$737$	−1.81942e60			−1.10437
$738$	7.27403e59	+	1.14215e60i	0.429132	+	0.673812i
$739$			7.24474e59i			0.415422i	0.978190	+	0.207711i	$0.0666014\pi$
$739$			7.24474e59i			0.415422i	−0.978190	+	0.207711i	$0.933399\pi$
$740$	7.94869e59	−	1.70335e60i	0.443026	−	0.949375i
$741$	7.06796e59			0.382923
$742$	2.77678e59	−	1.76845e59i	0.146238	−	0.0931347i
$743$		−	5.70036e59i		−	0.291835i	−0.989297	−	0.145918i	$-0.953387\pi$
$743$		−	5.70036e59i		−	0.291835i	0.989297	−	0.145918i	$-0.0466134\pi$
$744$	−9.66851e59	+	1.26873e59i	−0.481202	+	0.0631448i
$745$	−5.68250e60			−2.74953
$746$	−6.54445e59	−	1.02759e60i	−0.307863	−	0.483399i
$747$		−	1.50558e60i		−	0.688605i
$748$	−3.65046e60	−	1.70349e60i	−1.62336	−	0.757540i
$749$	2.96536e59			0.128221
$750$	−9.95858e59	+	6.34235e59i	−0.418708	+	0.266663i
$751$		−	7.92389e59i		−	0.323966i	−0.986794	−	0.161983i	$-0.948211\pi$
$751$		−	7.92389e59i		−	0.323966i	0.986794	−	0.161983i	$-0.0517890\pi$
$752$	6.80476e59	−	5.70335e59i	0.270544	−	0.226754i
$753$	1.23021e60			0.475648
$754$	7.08551e59	+	1.11255e60i	0.266424	+	0.418331i
$755$		−	3.35831e60i		−	1.22810i
$756$	2.77425e59	−	5.94502e59i	0.0986706	−	0.211444i
$757$	4.92230e60			1.70276			0.851382	−	0.524546i	$-0.175765\pi$
$757$	4.92230e60			1.70276			0.851382	+	0.524546i	$0.175765\pi$
$758$	−1.24658e60	+	7.93914e59i	−0.419438	+	0.267128i
$759$		−	1.93000e60i		−	0.631655i
$760$	9.61634e59	+	7.32825e60i	0.306143	+	2.33300i
$761$	−1.22157e60			−0.378303			−0.189152	−	0.981948i	$-0.560574\pi$
$761$	−1.22157e60			−0.378303			−0.189152	+	0.981948i	$0.560574\pi$
$762$	−3.19232e59	−	5.01250e59i	−0.0961729	−	0.151008i
$763$		−	8.31336e59i		−	0.243647i
$764$	−2.23299e59	−	1.04202e59i	−0.0636686	−	0.0297110i
$765$	5.05001e60			1.40088
$766$	−1.33393e59	+	8.49541e58i	−0.0360021	+	0.0229287i
$767$		−	2.22034e60i		−	0.583066i
$768$	1.99250e60	+	3.53645e59i	0.509110	+	0.0903612i
$769$	2.29634e60			0.570931			0.285465	−	0.958389i	$-0.407852\pi$
$769$	2.29634e60			0.570931			0.285465	+	0.958389i	$0.407852\pi$
$770$	1.40642e60	+	2.20833e60i	0.340260	+	0.534267i
$771$		−	3.36570e59i		−	0.0792380i
$772$	5.61844e59	−	1.20399e60i	0.128722	−	0.275842i
$773$	2.24944e59			0.0501539			0.0250769	−	0.999686i	$-0.492017\pi$
$773$	2.24944e59			0.0501539			0.0250769	+	0.999686i	$0.492017\pi$
$774$	−3.50326e60	+	2.23113e60i	−0.760173	+	0.484133i
$775$			7.09288e60i			1.49791i
$776$	−4.60664e60	+	6.04497e59i	−0.946865	+	0.124250i
$777$	−4.37711e59			−0.0875681
$778$	3.92673e59	+	6.16565e59i	0.0764645	+	0.120063i
$779$			8.40130e60i			1.59243i
$780$	−2.07481e60	−	9.68211e59i	−0.382817	−	0.178642i
$781$	−4.27997e60			−0.768722
$782$	4.63324e60	−	2.95078e60i	0.810107	−	0.515935i
$783$		−	5.14779e60i		−	0.876241i
$784$	−3.61332e60	−	4.31112e60i	−0.598783	−	0.714418i
$785$	−5.04417e60			−0.813818
$786$	2.67044e60	+	4.19305e60i	0.419478	+	0.658653i
$787$			1.10859e60i			0.169552i	0.996400	+	0.0847761i	$0.0270175\pi$
$787$			1.10859e60i			0.169552i	−0.996400	+	0.0847761i	$0.972982\pi$
$788$	−3.29457e60	+	7.06004e60i	−0.490624	+	1.05137i
$789$	3.54630e60			0.514231
$790$	1.63611e61	−	1.04199e61i	2.31017	−	1.47128i
$791$		−	2.18810e60i		−	0.300857i
$792$	1.07461e60	+	8.18917e60i	0.143887	+	1.09651i
$793$	−2.33373e60			−0.304308
$794$	−1.93817e60	−	3.04326e60i	−0.246128	−	0.386464i
$795$			4.48402e60i			0.554572i
$796$	−8.91040e60	−	4.15804e60i	−1.07330	−	0.500858i
$797$	1.17673e60			0.138055			0.0690276	−	0.997615i	$-0.478010\pi$
$797$	1.17673e60			0.138055			0.0690276	+	0.997615i	$0.478010\pi$
$798$	1.45170e60	−	9.24550e59i	0.165889	−	0.105650i
$799$		−	3.76383e60i		−	0.418936i
$800$	4.43607e60	−	1.40350e61i	0.480960	−	1.52167i
$801$	−6.81041e60			−0.719267
$802$	2.68785e60	+	4.22039e60i	0.276531	+	0.434201i
$803$		−	4.62666e60i		−	0.463704i
$804$	1.63841e60	−	3.51100e60i	0.159973	−	0.342810i
$805$	−3.57012e60			−0.339601
$806$	−4.33188e60	+	2.75885e60i	−0.401458	+	0.255678i
$807$		−	4.05769e60i		−	0.366382i
$808$	−5.01297e60	+	6.57817e59i	−0.441018	+	0.0578717i
$809$	8.52929e60			0.731129			0.365564	−	0.930786i	$-0.380876\pi$
$809$	8.52929e60			0.731129			0.365564	+	0.930786i	$0.380876\pi$
$810$	−2.79160e60	−	4.38330e60i	−0.233168	−	0.366114i
$811$			1.45940e61i			1.18778i	0.804547	+	0.593889i	$0.202408\pi$
$811$			1.45940e61i			1.18778i	−0.804547	+	0.593889i	$0.797592\pi$
$812$	2.91062e60	+	1.35824e60i	0.230838	+	0.107721i
$813$	−5.88016e60			−0.454452
$814$	1.09922e61	−	7.00063e60i	0.827889	−	0.527260i
$815$			1.21396e61i			0.891037i
$816$	6.57458e60	−	5.51042e60i	0.470299	−	0.394177i
$817$	−2.57690e61			−1.79653
$818$	−5.49760e60	−	8.63218e60i	−0.373554	−	0.586545i
$819$		−	1.46103e60i		−	0.0967603i
$820$	1.15086e61	−	2.46621e61i	0.742902	−	1.59199i
$821$	2.83226e61			1.78208			0.891038	−	0.453928i	$-0.149978\pi$
$821$	2.83226e61			1.78208			0.891038	+	0.453928i	$0.149978\pi$
$822$	−9.42268e60	+	6.00105e60i	−0.577918	+	0.368060i
$823$			1.96023e61i			1.17195i	0.810329	+	0.585975i	$0.199288\pi$
$823$			1.96023e61i			1.17195i	−0.810329	+	0.585975i	$0.800712\pi$
$824$	2.85672e60	+	2.17700e61i	0.166493	+	1.26878i
$825$	−2.19233e61			−1.24558
$826$	−2.90440e60	−	4.56041e60i	−0.160870	−	0.252594i
$827$		−	3.11045e61i		−	1.67961i	−0.542890	−	0.839804i	$-0.682670\pi$
$827$		−	3.11045e61i		−	1.67961i	0.542890	−	0.839804i	$-0.317330\pi$
$828$	−1.02059e61	−	4.76261e60i	−0.537299	−	0.250731i
$829$	3.66607e61			1.88172			0.940862	−	0.338791i	$-0.110018\pi$
$829$	3.66607e61			1.88172			0.940862	+	0.338791i	$0.110018\pi$
$830$	−2.55228e61	+	1.62548e61i	−1.27729	+	0.813469i
$831$		−	8.19319e60i		−	0.399790i
$832$	1.02971e61	−	2.74979e60i	0.489921	−	0.130831i
$833$	−2.38455e61			−1.10627
$834$	1.02278e61	+	1.60594e61i	0.462694	+	0.726509i
$835$			1.77303e61i			0.782168i
$836$	−2.16695e61	+	4.64363e61i	−0.932218	+	1.99768i
$837$	2.00437e61			0.840899
$838$	2.27028e60	−	1.44588e60i	0.0928872	−	0.0591573i
$839$		−	1.67764e61i		−	0.669418i	−0.942322	−	0.334709i	$-0.891362\pi$
$839$		−	1.67764e61i		−	0.669418i	0.942322	−	0.334709i	$-0.108638\pi$
$840$	−5.52800e60	+	7.25400e59i	−0.215131	+	0.0282301i
$841$	−1.14310e60			−0.0433879
$842$	2.44515e61	+	3.83931e61i	0.905216	+	1.42135i
$843$		−	1.39786e61i		−	0.504758i
$844$	4.27340e61	+	1.99418e61i	1.50516	+	0.702382i
$845$	3.48369e61			1.19688
$846$	−6.50903e60	+	4.14542e60i	−0.218142	+	0.138929i
$847$			1.01855e61i			0.332989i
$848$	−1.34078e61	−	1.59971e61i	−0.427607	−	0.510186i
$849$	−4.36428e60			−0.135785
$850$	−3.35185e61	−	5.26299e61i	−1.01739	−	1.59748i
$851$			1.77707e61i			0.526240i
$852$	3.85417e60	−	8.25923e60i	0.111352	−	0.238621i
$853$	2.61426e61			0.736917			0.368458	−	0.929644i	$-0.379886\pi$
$853$	2.61426e61			0.736917			0.368458	+	0.929644i	$0.379886\pi$
$854$	−4.79329e60	+	3.05271e60i	−0.131831	+	0.0839597i
$855$		−	6.42395e61i		−	1.72391i
$856$	−2.44618e60	−	1.86414e61i	−0.0640531	−	0.488124i
$857$	−2.79253e61			−0.713510			−0.356755	−	0.934198i	$-0.616117\pi$
$857$	−2.79253e61			−0.713510			−0.356755	+	0.934198i	$0.616117\pi$
$858$	−8.52730e60	−	1.33893e61i	−0.212607	−	0.333830i
$859$		−	9.40013e60i		−	0.228706i	−0.993440	−	0.114353i	$-0.963521\pi$
$859$		−	9.40013e60i		−	0.228706i	0.993440	−	0.114353i	$-0.0364795\pi$
$860$	7.56451e61	+	3.52998e61i	1.79603	+	0.838118i
$861$	−6.33744e60			−0.146841
$862$	−3.45737e61	+	2.20191e61i	−0.781797	+	0.497905i
$863$			1.72518e60i			0.0380723i	0.999819	+	0.0190361i	$0.00605976\pi$
$863$			1.72518e60i			0.0380723i	−0.999819	+	0.0190361i	$0.993940\pi$
$864$	−3.96613e61	−	1.25359e61i	−0.854238	−	0.270001i
$865$	−1.13453e62			−2.38494
$866$	−1.49829e61	−	2.35258e61i	−0.307412	−	0.482690i
$867$		−	1.05456e61i		−	0.211188i
$868$	−5.28852e60	+	1.13329e61i	−0.103376	+	0.221528i
$869$	1.34486e62			2.56603
$870$	−3.69002e61	+	2.35007e61i	−0.687266	+	0.437701i
$871$		−	2.04058e61i		−	0.370999i
$872$	−5.22611e61	+	6.85785e60i	−0.927540	+	0.121714i
$873$	4.03818e61			0.699660
$874$	−3.75359e61	−	5.89379e61i	−0.634903	−	0.996907i
$875$			1.51421e61i			0.250045i
$876$	8.92824e60	+	4.16637e60i	0.143939	+	0.0671694i
$877$	−1.03468e62			−1.62860			−0.814302	−	0.580441i	$-0.802880\pi$
$877$	−1.03468e62			−1.62860			−0.814302	+	0.580441i	$0.802880\pi$
$878$	−2.43205e61	+	1.54891e61i	−0.373756	+	0.238035i
$879$			1.37893e61i			0.206908i
$880$	1.27222e62	−	1.06630e62i	1.86392	−	1.56223i
$881$	−6.16695e61			−0.882219			−0.441110	−	0.897453i	$-0.645415\pi$
$881$	−6.16695e61			−0.882219			−0.441110	+	0.897453i	$0.645415\pi$
$882$	2.62631e61	+	4.12376e61i	0.366864	+	0.576041i
$883$		−	2.15019e61i		−	0.293294i	−0.989189	−	0.146647i	$-0.953152\pi$
$883$		−	2.15019e61i		−	0.293294i	0.989189	−	0.146647i	$-0.0468481\pi$
$884$	1.91056e61	−	4.09420e61i	0.254485	−	0.545345i
$885$	7.36429e61			0.957904
$886$	7.78135e61	−	4.95573e61i	0.988433	−	0.629505i
$887$			1.43523e62i			1.78043i	0.455542	+	0.890214i	$0.349445\pi$
$887$			1.43523e62i			1.78043i	−0.455542	+	0.890214i	$0.650555\pi$
$888$	3.61076e60	+	2.75163e61i	0.0437448	+	0.333363i
$889$	−7.62156e60			−0.0901793
$890$	7.35278e61	+	1.15451e62i	0.849691	+	1.33416i
$891$		−	3.60300e61i		−	0.406661i
$892$	1.23037e60	+	5.74154e59i	0.0135636	+	0.00632946i
$893$	−4.78785e61			−0.515537
$894$	7.07651e61	−	4.50683e61i	0.744271	−	0.474006i
$895$			2.25988e62i			2.32167i
$896$	1.75525e61	−	1.91174e61i	0.176145	−	0.191849i
$897$	2.16460e61			0.212196
$898$	−2.77211e61	−	4.35269e61i	−0.265465	−	0.416826i
$899$			9.81318e61i			0.918028i
$900$	−5.40995e61	+	1.15931e62i	−0.494425	+	1.05952i
$901$	−8.84827e61			−0.790019
$902$	1.59152e62	−	1.01359e62i	1.38827	−	0.884151i
$903$		−	1.94386e61i		−	0.165661i
$904$	−1.37553e62	+	1.80501e61i	−1.14533	+	0.150294i
$905$	8.67536e61			0.705776
$906$	2.66350e61	+	4.18216e61i	0.211719	+	0.332436i
$907$		−	5.91833e61i		−	0.459670i	−0.973230	−	0.229835i	$-0.926181\pi$
$907$		−	5.91833e61i		−	0.459670i	0.973230	−	0.229835i	$-0.0738187\pi$
$908$	−1.22818e62	−	5.73130e61i	−0.932091	−	0.434961i
$909$	4.39437e61			0.325878
$910$	−2.47677e61	+	1.57738e61i	−0.179480	+	0.114306i
$911$		−	2.43935e62i		−	1.72738i	−0.504022	−	0.863691i	$-0.668147\pi$
$911$		−	2.43935e62i		−	1.72738i	0.504022	−	0.863691i	$-0.331853\pi$
$912$	−7.00963e61	−	8.36331e61i	−0.485069	−	0.578744i
$913$	−2.09793e62			−1.41875
$914$	1.46251e61	+	2.29639e61i	0.0966557	+	0.151766i
$915$		−	7.74034e61i		−	0.499939i
$916$	2.74894e61	−	5.89079e61i	0.173524	−	0.371851i
$917$	6.37558e61			0.393336
$918$	−1.48727e62	+	9.47198e61i	−0.896793	+	0.571143i
$919$			1.66174e62i			0.979351i	0.871905	+	0.489675i	$0.162885\pi$
$919$			1.66174e62i			0.979351i	−0.871905	+	0.489675i	$0.837115\pi$
$920$	2.94506e61	+	2.24432e62i	0.169649	+	1.29283i
$921$	1.23605e62			0.695961
$922$	7.56073e58	+	1.18717e59i	0.000416116	+	0.000653374i
$923$		−	4.80024e61i		−	0.258242i
$924$	−3.50288e61	−	1.63462e61i	−0.184210	−	0.0859618i
$925$	2.01861e62			1.03771
$926$	1.91145e61	−	1.21735e61i	0.0960575	−	0.0611764i
$927$		−	1.90836e62i		−	0.937532i
$928$	6.13742e61	−	1.94177e62i	0.294766	−	0.932590i
$929$	−1.84746e62			−0.867450			−0.433725	−	0.901045i	$-0.642801\pi$
$929$	−1.84746e62			−0.867450			−0.433725	+	0.901045i	$0.642801\pi$
$930$	−9.15039e61	−	1.43677e62i	−0.420047	−	0.659546i
$931$			3.03331e62i			1.36136i
$932$	−6.12548e61	+	1.31265e62i	−0.268786	+	0.575989i
$933$	8.96897e61			0.384794
$934$	2.46952e62	−	1.57277e62i	1.03592	−	0.659752i
$935$		−	7.03689e62i		−	2.88627i
$936$	−9.18462e61	+	1.20523e61i	−0.368357	+	0.0483368i
$937$	−1.40453e62			−0.550808			−0.275404	−	0.961329i	$-0.588812\pi$
$937$	−1.40453e62			−0.550808			−0.275404	+	0.961329i	$0.588812\pi$
$938$	−2.66925e61	−	4.19119e61i	−0.102360	−	0.160723i
$939$		−	1.06398e62i		−	0.398986i
$940$	1.40548e62	+	6.55868e61i	0.515394	+	0.240509i
$941$	1.71801e62			0.616090			0.308045	−	0.951372i	$-0.400325\pi$
$941$	1.71801e62			0.616090			0.308045	+	0.951372i	$0.400325\pi$
$942$	6.28159e61	−	4.00057e61i	0.220293	−	0.140298i
$943$			2.57295e62i			0.882440i
$944$	−2.62727e62	+	2.20202e62i	−0.881237	+	0.738600i
$945$	1.14601e62			0.375940
$946$	3.10895e62	+	4.88159e62i	0.997471	+	1.56620i
$947$		−	4.14807e62i		−	1.30166i	−0.759225	−	0.650828i	$-0.774422\pi$
$947$		−	4.14807e62i		−	1.30166i	0.759225	−	0.650828i	$-0.225578\pi$
$948$	−1.21106e62	+	2.59522e62i	−0.371699	+	0.796526i
$949$	5.18906e61			0.155775
$950$	−6.69488e62	+	4.26379e62i	−1.96584	+	1.25199i
$951$			3.28306e62i			0.942947i
$952$	−1.43142e61	−	1.09083e62i	−0.0402154	−	0.306466i
$953$	8.77435e61			0.241137			0.120569	−	0.992705i	$-0.461528\pi$
$953$	8.77435e61			0.241137			0.120569	+	0.992705i	$0.461528\pi$
$954$	9.74535e61	+	1.53019e62i	0.261988	+	0.411367i
$955$		−	4.30447e61i		−	0.113201i
$956$	−5.82581e62	−	2.71862e62i	−1.49879	−	0.699411i
$957$	−3.03314e62			−0.763381
$958$	5.36536e62	−	3.41705e62i	1.32106	−	0.841348i
$959$			1.43273e62i			0.345122i
$960$	9.12031e61	+	3.41528e62i	0.214938	+	0.804879i
$961$	5.16101e61			0.118999
$962$	7.85161e61	+	1.23284e62i	0.177126	+	0.278119i
$963$			1.63411e62i			0.360686i
$964$	3.42618e62	−	7.34208e62i	0.739934	−	1.58563i
$965$	2.32091e62			0.490438
$966$	4.44593e61	−	2.83149e61i	0.0919269	−	0.0585457i
$967$			5.20855e62i			1.05381i	0.849925	+	0.526903i	$0.176647\pi$
$967$			5.20855e62i			1.05381i	−0.849925	+	0.526903i	$0.823353\pi$
$968$	6.40300e62	−	8.40220e61i	1.26766	−	0.166345i
$969$	−4.62589e62			−0.896181
$970$	−4.35978e62	−	6.84560e62i	−0.826528	−	1.29779i
$971$			5.74776e62i			1.06634i	0.846009	+	0.533169i	$0.178999\pi$
$971$			5.74776e62i			1.06634i	−0.846009	+	0.533169i	$0.821001\pi$
$972$	5.16692e62	+	2.41114e62i	0.938080	+	0.437755i
$973$	2.44184e62			0.433858
$974$	−6.04869e62	+	3.85225e62i	−1.05178	+	0.669847i
$975$		−	2.45882e62i		−	0.418437i
$976$	2.31447e62	+	2.76143e62i	0.385482	+	0.459926i
$977$	3.38589e62			0.551933			0.275967	−	0.961167i	$-0.411002\pi$
$977$	3.38589e62			0.551933			0.275967	+	0.961167i	$0.411002\pi$
$978$	−9.62803e61	−	1.51177e62i	−0.153611	−	0.241196i
$979$			9.48991e62i			1.48192i
$980$	4.15521e62	−	8.90434e62i	0.635105	−	1.36099i
$981$	4.58121e62			0.685380
$982$	6.11309e62	−	3.89326e62i	0.895199	−	0.570128i
$983$		−	9.61676e62i		−	1.37849i	−0.724526	−	0.689247i	$-0.757941\pi$
$983$		−	9.61676e62i		−	1.37849i	0.724526	−	0.689247i	$-0.242059\pi$
$984$	5.22788e61	+	3.98397e62i	0.0733548	+	0.559009i
$985$	−1.36095e63			−1.86930
$986$	−4.63737e62	−	7.28148e62i	−0.623529	−	0.979049i
$987$		−	3.61167e61i		−	0.0475387i
$988$	−5.20810e62	−	2.43036e62i	−0.671094	−	0.313166i
$989$	−7.89189e62			−0.995541
$990$	−1.21693e63	+	7.75032e62i	−1.50289	+	0.957151i
$991$			2.98560e62i			0.360982i	0.983577	+	0.180491i	$0.0577687\pi$
$991$			2.98560e62i			0.360982i	−0.983577	+	0.180491i	$0.942231\pi$
$992$	7.56060e62	+	2.38970e62i	0.894976	+	0.282877i
$993$	2.94926e61			0.0341806
$994$	−6.27912e61	−	9.85931e61i	−0.0712500	−	0.111875i
$995$		−	1.71763e63i		−	1.90830i
$996$	1.88922e62	−	4.04847e62i	0.205511	−	0.440397i
$997$	−6.74559e62			−0.718491			−0.359246	−	0.933243i	$-0.616966\pi$
$997$	−6.74559e62			−0.718491			−0.359246	+	0.933243i	$0.616966\pi$
$998$	2.40803e62	−	1.53361e62i	0.251143	−	0.159946i
$999$		−	5.70438e62i		−	0.582550i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.43.b.a.3.14	yes	20
4.3	odd	2	inner	4.43.b.a.3.13	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.43.b.a.3.13	✓	20	4.3	odd	2	inner
4.43.b.a.3.14	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)

\(f(q)\)	\(=\)	\(q+(1.12655e6 + 1.76888e6i) q^{2} -5.40870e9i q^{3} +(-1.85982e12 + 3.98546e12i) q^{4} -7.68266e14 q^{5} +(9.56734e15 - 6.09318e15i) q^{6} -1.45472e17i q^{7} +(-9.14497e18 + 1.20003e18i) q^{8} +8.01649e19 q^{9} +O(q^{10})\)	\(q+(1.12655e6 + 1.76888e6i) q^{2} -5.40870e9i q^{3} +(-1.85982e12 + 3.98546e12i) q^{4} -7.68266e14 q^{5} +(9.56734e15 - 6.09318e15i) q^{6} -1.45472e17i q^{7} +(-9.14497e18 + 1.20003e18i) q^{8} +8.01649e19 q^{9} +(-8.65491e20 - 1.35897e21i) q^{10} -1.11705e22i q^{11} +(2.15562e22 + 1.00592e22i) q^{12} +1.25284e23 q^{13} +(2.57323e23 - 1.63882e23i) q^{14} +4.15533e24i q^{15} +(-1.24250e25 - 1.48245e25i) q^{16} -8.19966e25 q^{17} +(9.03098e25 + 1.41802e26i) q^{18} +1.04305e27i q^{19} +(1.42883e27 - 3.06190e27i) q^{20} -7.86817e26 q^{21} +(1.97593e28 - 1.25841e28i) q^{22} +3.19441e28i q^{23} +(6.49061e27 + 4.94625e28i) q^{24} +3.62860e29 q^{25} +(1.41138e29 + 2.21612e29i) q^{26} -1.02540e30i q^{27} +(5.79774e29 + 2.70552e29i) q^{28} +5.02026e30 q^{29} +(-7.35027e30 + 4.68118e30i) q^{30} +1.95472e31i q^{31} +(1.22253e31 - 3.86788e31i) q^{32} -6.04180e31 q^{33} +(-9.23732e31 - 1.45042e32i) q^{34} +1.11762e32i q^{35} +(-1.49092e32 + 3.19494e32i) q^{36} +5.56306e32 q^{37} +(-1.84503e33 + 1.17505e33i) q^{38} -6.77623e32i q^{39} +(7.02578e33 - 9.21942e32i) q^{40} +8.05453e33 q^{41} +(-8.86388e32 - 1.39178e33i) q^{42} +2.47053e34i q^{43} +(4.45196e34 + 2.07751e34i) q^{44} -6.15880e34 q^{45} +(-5.65052e34 + 3.59866e34i) q^{46} +4.59023e34i q^{47} +(-8.01811e34 + 6.72030e34i) q^{48} +2.90811e35 q^{49} +(4.08780e35 + 6.41855e35i) q^{50} +4.43495e35i q^{51} +(-2.33005e35 + 4.99313e35i) q^{52} +1.07910e36 q^{53} +(1.81381e36 - 1.15517e36i) q^{54} +8.58193e36i q^{55} +(1.74571e35 + 1.33034e36i) q^{56} +5.64156e36 q^{57} +(5.65557e36 + 8.88022e36i) q^{58} -1.77225e37i q^{59} +(-1.65609e37 - 7.72815e36i) q^{60} -1.86275e37 q^{61} +(-3.45766e37 + 2.20209e37i) q^{62} -1.16618e37i q^{63} +(8.21904e37 - 2.19485e37i) q^{64} -9.62513e37 q^{65} +(-6.80639e37 - 1.06872e38i) q^{66} -1.62877e38i q^{67} +(1.52499e38 - 3.26794e38i) q^{68} +1.72776e38 q^{69} +(-1.97693e38 + 1.25905e38i) q^{70} -3.83149e38i q^{71} +(-7.33106e38 + 9.62002e37i) q^{72} +4.14185e38 q^{73} +(6.26707e38 + 9.84038e38i) q^{74} -1.96260e39i q^{75} +(-4.15704e39 - 1.93989e39i) q^{76} -1.62500e39 q^{77} +(1.19863e39 - 7.63376e38i) q^{78} +1.20394e40i q^{79} +(9.54569e39 + 1.13891e40i) q^{80} +3.22546e39 q^{81} +(9.07383e39 + 1.42475e40i) q^{82} -1.87810e40i q^{83} +(1.46334e39 - 3.13583e39i) q^{84} +6.29952e40 q^{85} +(-4.37007e40 + 2.78318e40i) q^{86} -2.71531e40i q^{87} +(1.34049e40 + 1.02154e41i) q^{88} -8.49550e40 q^{89} +(-6.93820e40 - 1.08942e41i) q^{90} -1.82253e40i q^{91} +(-1.27312e41 - 5.94102e40i) q^{92} +1.05725e41 q^{93} +(-8.11956e40 + 5.17112e40i) q^{94} -8.01342e41i q^{95} +(-2.09202e41 - 6.61231e40i) q^{96} +5.03735e41 q^{97} +(3.27613e41 + 5.14410e41i) q^{98} -8.95483e41i 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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