LMFDB - Embedded newform 4.37.b.b.3.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,37,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, 37, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 37);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 37 $
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:	$32.8365034637$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + \cdots + 51\!\cdots\!00 $ x^16 + 6516989503065492x^14 + 17034486537407810917043361888198x^12 + 23072686962604400610679579162976738904788666844x^10 + 17414437736843557770548667414205720006669176493316634162548145x^8 + 7290100998556943999917076003638299976059510807819390063090897454035549344520x^6 + 1580065913442518903241377790659954072974637079040446265806555551201513339370568669874480400x^4 + 153535410141602761164144701301723551659810917407928334524859080419500779864196136193775339243188420422400*x^2 + 5156239739885100544994334306227490882529912274563409421561999152540966086224689966448180302613961864037075159771136000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{240}\cdot 3^{24}\cdot 5^{6}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.6
Root			$3.83971e7i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.37.b.b.3.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-167207. + 201894. i) q^{2} +6.14354e8i q^{3} +(-1.28029e10 - 6.75163e10i) q^{4} -3.33360e12 q^{5} +(-1.24034e14 - 1.02724e14i) q^{6} -2.74304e15i q^{7} +(1.57719e16 + 8.70438e15i) q^{8} -2.27336e17 q^{9} +O(q^{10})$	\(q+(-167207. + 201894. i) q^{2} +6.14354e8i q^{3} +(-1.28029e10 - 6.75163e10i) q^{4} -3.33360e12 q^{5} +(-1.24034e14 - 1.02724e14i) q^{6} -2.74304e15i q^{7} +(1.57719e16 + 8.70438e15i) q^{8} -2.27336e17 q^{9} +(5.57402e17 - 6.73034e17i) q^{10} +5.16595e18i q^{11} +(4.14789e19 - 7.86554e18i) q^{12} +1.38994e20 q^{13} +(5.53804e20 + 4.58656e20i) q^{14} -2.04801e21i q^{15} +(-4.39454e21 + 1.72882e21i) q^{16} -2.51975e21 q^{17} +(3.80122e22 - 4.58978e22i) q^{18} -5.92452e22i q^{19} +(4.26799e22 + 2.25072e23i) q^{20} +1.68520e24 q^{21} +(-1.04297e24 - 8.63784e23i) q^{22} -3.10457e24i q^{23} +(-5.34757e24 + 9.68952e24i) q^{24} -3.43902e24 q^{25} +(-2.32408e25 + 2.80620e25i) q^{26} -4.74535e25i q^{27} +(-1.85200e26 + 3.51190e25i) q^{28} +3.37207e26 q^{29} +(4.13481e26 + 3.42442e26i) q^{30} +6.60623e26i q^{31} +(3.85761e26 - 1.17630e27i) q^{32} -3.17372e27 q^{33} +(4.21320e26 - 5.08722e26i) q^{34} +9.14420e27i q^{35} +(2.91057e27 + 1.53489e28i) q^{36} -1.26292e28 q^{37} +(1.19613e28 + 9.90623e27i) q^{38} +8.53913e28i q^{39} +(-5.25772e28 - 2.90169e28i) q^{40} +3.78073e28 q^{41} +(-2.81777e29 + 3.40231e29i) q^{42} -2.97798e29i q^{43} +(3.48786e29 - 6.61394e28i) q^{44} +7.57847e29 q^{45} +(6.26794e29 + 5.19106e29i) q^{46} +8.86953e29i q^{47} +(-1.06210e30 - 2.69980e30i) q^{48} -4.87254e30 q^{49} +(5.75029e29 - 6.94318e29i) q^{50} -1.54802e30i q^{51} +(-1.77953e30 - 9.38434e30i) q^{52} +8.62173e30 q^{53} +(9.58058e30 + 7.93457e30i) q^{54} -1.72212e31i q^{55} +(2.38765e31 - 4.32629e31i) q^{56} +3.63975e31 q^{57} +(-5.63834e31 + 6.80801e31i) q^{58} -1.68733e31i q^{59} +(-1.38274e32 + 2.62206e31i) q^{60} +7.55382e31 q^{61} +(-1.33376e32 - 1.10461e32i) q^{62} +6.23592e32i q^{63} +(1.72986e32 + 2.74569e32i) q^{64} -4.63350e32 q^{65} +(5.30669e32 - 6.40755e32i) q^{66} +5.97442e32i q^{67} +(3.22602e31 + 1.70124e32i) q^{68} +1.90730e33 q^{69} +(-1.84616e33 - 1.52898e33i) q^{70} +1.32742e33i q^{71} +(-3.58552e33 - 1.97882e33i) q^{72} +2.88532e33 q^{73} +(2.11170e33 - 2.54977e33i) q^{74} -2.11278e33i q^{75} +(-4.00002e33 + 7.58513e32i) q^{76} +1.41704e34 q^{77} +(-1.72400e34 - 1.42780e34i) q^{78} +1.29702e34i q^{79} +(1.46496e34 - 5.76318e33i) q^{80} -4.96866e33 q^{81} +(-6.32166e33 + 7.63308e33i) q^{82} +3.72688e34i q^{83} +(-2.15755e34 - 1.13778e35i) q^{84} +8.39984e33 q^{85} +(6.01236e34 + 4.97940e34i) q^{86} +2.07164e35i q^{87} +(-4.49664e34 + 8.14768e34i) q^{88} +1.48586e35 q^{89} +(-1.26718e35 + 1.53005e35i) q^{90} -3.81265e35i q^{91} +(-2.09609e35 + 3.97476e34i) q^{92} -4.05856e35 q^{93} +(-1.79071e35 - 1.48305e35i) q^{94} +1.97500e35i q^{95} +(7.22665e35 + 2.36993e35i) q^{96} +8.33681e35 q^{97} +(8.14724e35 - 9.83737e35i) q^{98} -1.17441e36i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 177228 q^{2} - 5610707696 q^{4} + 5816089539360 q^{5} - 217628996575488 q^{6} + 11\!\cdots\!28 q^{8}+ \cdots - 93\!\cdots\!68 q^{9}+O(q^{10}) $ 16 * q + 177228 * q^2 - 5610707696 * q^4 + 5816089539360 * q^5 - 217628996575488 * q^6 + 11897560228206528 * q^8 - 935184460817545968 * q^9	$ 16 q + 177228 q^{2} - 5610707696 q^{4} + 5816089539360 q^{5} - 217628996575488 q^{6} + 11\!\cdots\!28 q^{8}+ \cdots + 10\!\cdots\!28 q^{98}+O(q^{100}) $ 16 * q + 177228 * q^2 - 5610707696 * q^4 + 5816089539360 * q^5 - 217628996575488 * q^6 + 11897560228206528 * q^8 - 935184460817545968 * q^9 - 2378142919315561000 * q^10 - 42882825786868930560 * q^12 + 194612014165659174176 * q^13 + 360192888461659120128 * q^14 - 22854023522524990832384 * q^16 + 41803218917907805318176 * q^17 + 138204474036544564333068 * q^18 + 104592026972614096023840 * q^20 - 175281296641396774711296 * q^21 - 4320007363229839528400640 * q^22 + 5118364442017682383085568 * q^24 + 61061610541832160307690800 * q^25 - 70158486911796111631798440 * q^26 - 303534200373547502486016000 * q^28 - 95320519344473743554877152 * q^29 + 361206724962468787334008320 * q^30 + 4662427702586163916855016448 * q^32 - 877278707167997370072668160 * q^33 - 9018225886246079564307746920 * q^34 - 927455191590908629268766192 * q^36 - 30841755082751179145922114784 * q^37 + 78752216997100984306444174080 * q^38 - 138122339194153338361474460800 * q^40 + 99165040763128472781035553312 * q^41 - 193406458925326074258433843200 * q^42 + 303084904999663560614745692160 * q^44 + 1511424637230487714612565241120 * q^45 - 919681205391808405630032112128 * q^46 - 1511312501851283767715389931520 * q^48 - 11342315683204385026834539108848 * q^49 + 11057816114707215621338245966500 * q^50 + 16094442403868561017575461524256 * q^52 + 20911545776251998404629518049056 * q^53 - 42689634574575573966970327785984 * q^54 - 18346492780981997297263940026368 * q^56 - 17591710635767034592583231047680 * q^57 + 33019206317228013320629044602456 * q^58 - 69704584574466315130190074982400 * q^60 + 216576725773383276684585233875232 * q^61 + 406820870675021165265665434183680 * q^62 - 266111502464782094817164314013696 * q^64 - 2065823886943449026422930314993600 * q^65 - 816784109200805225218136599695360 * q^66 + 3502994508232801473127246422490656 * q^68 + 3923547517779842564469076002041856 * q^69 + 312094823977274793710809307489280 * q^70 - 1875458138040165128132392402132032 * q^72 - 13529699358917711874787838251408864 * q^73 + 7683713356825244783786618034273240 * q^74 - 15736875982808342938482824299100160 * q^76 + 22639774155764461736245527294259200 * q^77 - 18389491597233550087389536189698560 * q^78 + 67235988583903584940074904608207360 * q^80 - 40716877106976112078739817594850800 * q^81 + 43227843112149006015980010857549336 * q^82 - 37119022564017857733030089777086464 * q^84 - 206886985961236391219562146270052800 * q^85 + 102108696026625816655543232864792832 * q^86 + 39749581676781586144951142033940480 * q^88 + 461506837768868190077604450557625888 * q^89 - 361659211507857840778210819426233000 * q^90 - 17511543929609412714530045318983680 * q^92 - 231978818535002459544922699145134080 * q^93 - 696830931593880576023589572144120832 * q^94 + 1050073689946737522972596709346639872 * q^96 + 451372245708940284684446048339288096 * q^97 + 1035415270688230597220229005750452428 * 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 $

$2$	−167207.	+	201894.i	−0.637845	+	0.770165i
$2$	−167207.	+	201894.i	−0.637845	+	0.770165i
$3$			6.14354e8i			1.58575i	0.609381	+	0.792877i	$0.291418\pi$
$3$			6.14354e8i			1.58575i	−0.609381	+	0.792877i	$0.708582\pi$
$4$	−1.28029e10	−	6.75163e10i	−0.186307	−	0.982491i
$5$	−3.33360e12			−0.873883			−0.436942	−	0.899490i	$-0.643938\pi$
$5$	−3.33360e12			−0.873883			−0.436942	+	0.899490i	$0.643938\pi$
$6$	−1.24034e14	−	1.02724e14i	−1.22129	−	1.01147i
$7$		−	2.74304e15i		−	1.68449i	−0.539098	−	0.842243i	$-0.681235\pi$
$7$		−	2.74304e15i		−	1.68449i	0.539098	−	0.842243i	$-0.318765\pi$
$8$	1.57719e16	+	8.70438e15i	0.875516	+	0.483190i
$9$	−2.27336e17			−1.51462
$10$	5.57402e17	−	6.73034e17i	0.557402	−	0.673034i
$11$			5.16595e18i			0.929141i	0.885536	+	0.464571i	$0.153791\pi$
$11$			5.16595e18i			0.929141i	−0.885536	+	0.464571i	$0.846209\pi$
$12$	4.14789e19	−	7.86554e18i	1.55799	−	0.295438i
$13$	1.38994e20			1.23599			0.617995	−	0.786182i	$-0.287945\pi$
$13$	1.38994e20			1.23599			0.617995	+	0.786182i	$0.287945\pi$
$14$	5.53804e20	+	4.58656e20i	1.29733	+	1.07444i
$15$		−	2.04801e21i		−	1.38576i
$16$	−4.39454e21	+	1.72882e21i	−0.930579	+	0.366091i
$17$	−2.51975e21			−0.179175			−0.0895873	−	0.995979i	$-0.528555\pi$
$17$	−2.51975e21			−0.179175			−0.0895873	+	0.995979i	$0.528555\pi$
$18$	3.80122e22	−	4.58978e22i	0.966091	−	1.16651i
$19$		−	5.92452e22i		−	0.568969i	−0.958681	−	0.284484i	$-0.908178\pi$
$19$		−	5.92452e22i		−	0.568969i	0.958681	−	0.284484i	$-0.0918224\pi$
$20$	4.26799e22	+	2.25072e23i	0.162811	+	0.858583i
$21$	1.68520e24			2.67118
$22$	−1.04297e24	−	8.63784e23i	−0.715592	−	0.592648i
$23$		−	3.10457e24i		−	0.956974i	−0.878095	−	0.478487i	$-0.841185\pi$
$23$		−	3.10457e24i		−	0.956974i	0.878095	−	0.478487i	$-0.158815\pi$
$24$	−5.34757e24	+	9.68952e24i	−0.766221	+	1.38835i
$25$	−3.43902e24			−0.236328
$26$	−2.32408e25	+	2.80620e25i	−0.788370	+	0.951916i
$27$		−	4.74535e25i		−	0.816057i
$28$	−1.85200e26	+	3.51190e25i	−1.65499	+	0.313832i
$29$	3.37207e26			1.60226			0.801129	−	0.598492i	$-0.204233\pi$
$29$	3.37207e26			1.60226			0.801129	+	0.598492i	$0.204233\pi$
$30$	4.13481e26	+	3.42442e26i	1.06727	+	0.883903i
$31$			6.60623e26i			0.945025i	0.881324	+	0.472512i	$0.156653\pi$
$31$			6.60623e26i			0.945025i	−0.881324	+	0.472512i	$0.843347\pi$
$32$	3.85761e26	−	1.17630e27i	0.311615	−	0.950208i
$33$	−3.17372e27			−1.47339
$34$	4.21320e26	−	5.08722e26i	0.114286	−	0.137994i
$35$			9.14420e27i			1.47204i
$36$	2.91057e27	+	1.53489e28i	0.282185	+	1.48810i
$37$	−1.26292e28			−0.747732			−0.373866	−	0.927483i	$-0.621968\pi$
$37$	−1.26292e28			−0.747732			−0.373866	+	0.927483i	$0.621968\pi$
$38$	1.19613e28	+	9.90623e27i	0.438200	+	0.362914i
$39$			8.53913e28i			1.95998i
$40$	−5.25772e28	−	2.90169e28i	−0.765099	−	0.422252i
$41$	3.78073e28			0.352750			0.176375	−	0.984323i	$-0.443563\pi$
$41$	3.78073e28			0.352750			0.176375	+	0.984323i	$0.443563\pi$
$42$	−2.81777e29	+	3.40231e29i	−1.70380	+	2.05725i
$43$		−	2.97798e29i		−	1.17893i	−0.807792	−	0.589467i	$-0.799338\pi$
$43$		−	2.97798e29i		−	1.17893i	0.807792	−	0.589467i	$-0.200662\pi$
$44$	3.48786e29	−	6.61394e28i	0.912874	−	0.173106i
$45$	7.57847e29			1.32360
$46$	6.26794e29	+	5.19106e29i	0.737028	+	0.610401i
$47$			8.86953e29i			0.708173i	0.935213	+	0.354086i	$0.115208\pi$
$47$			8.86953e29i			0.708173i	−0.935213	+	0.354086i	$0.884792\pi$
$48$	−1.06210e30	−	2.69980e30i	−0.580530	−	1.47567i
$49$	−4.87254e30			−1.83749
$50$	5.75029e29	−	6.94318e29i	0.150741	−	0.182011i
$51$		−	1.54802e30i		−	0.284127i
$52$	−1.77953e30	−	9.38434e30i	−0.230274	−	1.21435i
$53$	8.62173e30			0.791824			0.395912	−	0.918288i	$-0.370428\pi$
$53$	8.62173e30			0.791824			0.395912	+	0.918288i	$0.370428\pi$
$54$	9.58058e30	+	7.93457e30i	0.628499	+	0.520518i
$55$		−	1.72212e31i		−	0.811961i
$56$	2.38765e31	−	4.32629e31i	0.813927	−	1.47479i
$57$	3.63975e31			0.902245
$58$	−5.63834e31	+	6.80801e31i	−1.02199	+	1.23400i
$59$		−	1.68733e31i		−	0.224835i	−0.993661	−	0.112418i	$-0.964141\pi$
$59$		−	1.68733e31i		−	0.224835i	0.993661	−	0.112418i	$-0.0358595\pi$
$60$	−1.38274e32	+	2.62206e31i	−1.36150	+	0.258178i
$61$	7.55382e31			0.552369			0.276185	−	0.961105i	$-0.410930\pi$
$61$	7.55382e31			0.552369			0.276185	+	0.961105i	$0.410930\pi$
$62$	−1.33376e32	−	1.10461e32i	−0.727825	−	0.602779i
$63$			6.23592e32i			2.55135i
$64$	1.72986e32	+	2.74569e32i	0.533055	+	0.846081i
$65$	−4.63350e32			−1.08011
$66$	5.30669e32	−	6.40755e32i	0.939795	−	1.13475i
$67$			5.97442e32i			0.807141i	0.914949	+	0.403571i	$0.132231\pi$
$67$			5.97442e32i			0.807141i	−0.914949	+	0.403571i	$0.867769\pi$
$68$	3.22602e31	+	1.70124e32i	0.0333816	+	0.176038i
$69$	1.90730e33			1.51753
$70$	−1.84616e33	−	1.52898e33i	−1.13372	−	0.938936i
$71$			1.32742e33i			0.631477i	0.948846	+	0.315739i	$0.102252\pi$
$71$			1.32742e33i			0.631477i	−0.948846	+	0.315739i	$0.897748\pi$
$72$	−3.58552e33	−	1.97882e33i	−1.32607	−	0.731848i
$73$	2.88532e33			0.832497			0.416249	−	0.909251i	$-0.363345\pi$
$73$	2.88532e33			0.832497			0.416249	+	0.909251i	$0.363345\pi$
$74$	2.11170e33	−	2.54977e33i	0.476937	−	0.575877i
$75$		−	2.11278e33i		−	0.374758i
$76$	−4.00002e33	+	7.58513e32i	−0.559007	+	0.106003i
$77$	1.41704e34			1.56513
$78$	−1.72400e34	−	1.42780e34i	−1.50950	−	1.25016i
$79$			1.29702e34i			0.902938i	0.892287	+	0.451469i	$0.149100\pi$
$79$			1.29702e34i			0.902938i	−0.892287	+	0.451469i	$0.850900\pi$
$80$	1.46496e34	−	5.76318e33i	0.813218	−	0.319921i
$81$	−4.96866e33			−0.220551
$82$	−6.32166e33	+	7.63308e33i	−0.225000	+	0.271675i
$83$			3.72688e34i			1.06645i	0.845974	+	0.533224i	$0.179020\pi$
$83$			3.72688e34i			1.06645i	−0.845974	+	0.533224i	$0.820980\pi$
$84$	−2.15755e34	−	1.13778e35i	−0.497661	−	2.62441i
$85$	8.39984e33			0.156578
$86$	6.01236e34	+	4.97940e34i	0.907973	+	0.751977i
$87$			2.07164e35i			2.54079i
$88$	−4.49664e34	+	8.14768e34i	−0.448952	+	0.813478i
$89$	1.48586e35			1.21048			0.605238	−	0.796044i	$-0.293078\pi$
$89$	1.48586e35			1.21048			0.605238	+	0.796044i	$0.293078\pi$
$90$	−1.26718e35	+	1.53005e35i	−0.844251	+	1.01939i
$91$		−	3.81265e35i		−	2.08201i
$92$	−2.09609e35	+	3.97476e34i	−0.940219	+	0.178291i
$93$	−4.05856e35			−1.49858
$94$	−1.79071e35	−	1.48305e35i	−0.545410	−	0.451704i
$95$			1.97500e35i			0.497212i
$96$	7.22665e35	+	2.36993e35i	1.50680	+	0.494145i
$97$	8.33681e35			1.44248			0.721238	−	0.692687i	$-0.243573\pi$
$97$	8.33681e35			1.44248			0.721238	+	0.692687i	$0.243573\pi$
$98$	8.14724e35	−	9.83737e35i	1.17204	−	1.41517i
$99$		−	1.17441e36i		−	1.40729i
$100$	4.40296e34	+	2.32190e35i	0.0440296	+	0.232190i
$101$	−1.53819e36			−1.28595			−0.642976	−	0.765886i	$-0.722301\pi$
$101$	−1.53819e36			−1.28595			−0.642976	+	0.765886i	$0.722301\pi$
$102$	3.12535e35	+	2.58840e35i	0.218825	+	0.181229i
$103$		−	1.77261e36i		−	1.04122i	−0.853794	−	0.520611i	$-0.825704\pi$
$103$		−	1.77261e36i		−	1.04122i	0.853794	−	0.520611i	$-0.174296\pi$
$104$	2.19219e36	+	1.20985e36i	1.08213	+	0.597218i
$105$	−5.61778e36			−2.33430
$106$	−1.44162e36	+	1.74068e36i	−0.505061	+	0.609835i
$107$			1.57039e36i			0.464622i	0.972642	+	0.232311i	$0.0746287\pi$
$107$			1.57039e36i			0.464622i	−0.972642	+	0.232311i	$0.925371\pi$
$108$	−3.20389e36	+	6.07545e35i	−0.801769	+	0.152038i
$109$	5.61746e36			1.19087			0.595433	−	0.803405i	$-0.296980\pi$
$109$	5.61746e36			1.19087			0.595433	+	0.803405i	$0.296980\pi$
$110$	3.47686e36	+	2.87951e36i	0.625344	+	0.517905i
$111$		−	7.75882e36i		−	1.18572i
$112$	4.74221e36	+	1.20544e37i	0.616675	+	1.56755i
$113$	9.90271e36			1.09734			0.548671	−	0.836038i	$-0.315134\pi$
$113$	9.90271e36			1.09734			0.548671	+	0.836038i	$0.315134\pi$
$114$	−6.08593e36	+	7.34844e36i	−0.575492	+	0.694877i
$115$			1.03494e37i			0.836284i
$116$	−4.31724e36	−	2.27670e37i	−0.298513	−	1.57420i
$117$	−3.15983e37			−1.87205
$118$	3.40662e36	+	2.82134e36i	0.173160	+	0.143410i
$119$			6.91177e36i			0.301817i
$120$	1.78267e37	−	3.23010e37i	0.669587	−	1.21326i
$121$	4.22565e36			0.136696
$122$	−1.26305e37	+	1.52507e37i	−0.352326	+	0.425415i
$123$			2.32271e37i			0.559374i
$124$	4.46028e37	−	8.45792e36i	0.928479	−	0.176065i
$125$	5.99746e37			1.08041
$126$	−1.25900e38	−	1.04269e38i	−1.96496	−	1.62737i
$127$		−	1.51207e37i		−	0.204694i	−0.994749	−	0.102347i	$-0.967365\pi$
$127$		−	1.51207e37i		−	0.204694i	0.994749	−	0.102347i	$-0.0326352\pi$
$128$	−8.43584e37	−	1.09850e37i	−0.991628	−	0.129128i
$129$	1.82953e38			1.86950
$130$	7.74754e37	−	9.35475e37i	0.688943	−	0.831863i
$131$		−	1.98999e36i		−	0.0154158i	−0.999970	−	0.00770791i	$-0.997546\pi$
$131$		−	1.98999e36i		−	0.0154158i	0.999970	−	0.00770791i	$-0.00245353\pi$
$132$	4.06330e37	+	2.14278e38i	0.274504	+	1.44759i
$133$	−1.62512e38			−0.958420
$134$	−1.20620e38	−	9.98967e37i	−0.621632	−	0.514831i
$135$			1.58191e38i			0.713139i
$136$	−3.97412e37	−	2.19328e37i	−0.156870	−	0.0865754i
$137$	2.35330e38			0.814154			0.407077	−	0.913394i	$-0.366548\pi$
$137$	2.35330e38			0.814154			0.407077	+	0.913394i	$0.366548\pi$
$138$	−3.18915e38	+	3.85073e38i	−0.967947	+	1.16875i
$139$			3.85441e38i			1.02729i	0.858004	+	0.513643i	$0.171704\pi$
$139$			3.85441e38i			1.02729i	−0.858004	+	0.513643i	$0.828296\pi$
$140$	6.17383e38	−	1.17073e38i	1.44627	−	0.274253i
$141$	−5.44903e38			−1.12299
$142$	−2.67998e38	−	2.21954e38i	−0.486341	−	0.402785i
$143$			7.18035e38i			1.14841i
$144$	9.99036e38	−	3.93022e38i	1.40947	−	0.554488i
$145$	−1.12411e39			−1.40019
$146$	−4.82447e38	+	5.82529e38i	−0.531004	+	0.641160i
$147$		−	2.99346e39i		−	2.91382i
$148$	1.61691e38	+	8.52679e38i	0.139308	+	0.734640i
$149$	1.77368e39			1.35370			0.676850	−	0.736121i	$-0.263345\pi$
$149$	1.77368e39			1.35370			0.676850	+	0.736121i	$0.263345\pi$
$150$	4.26557e38	+	3.53272e38i	0.288625	+	0.239037i
$151$		−	2.04452e39i		−	1.22746i	−0.789517	−	0.613729i	$-0.789669\pi$
$151$		−	2.04452e39i		−	1.22746i	0.789517	−	0.613729i	$-0.210331\pi$
$152$	5.15693e38	−	9.34409e38i	0.274920	−	0.498141i
$153$	5.72829e38			0.271381
$154$	−2.36940e39	+	2.86092e39i	−0.998308	+	1.20541i
$155$		−	2.20225e39i		−	0.825842i
$156$	5.76531e39	−	1.09326e39i	1.92566	−	0.365158i
$157$	−3.45070e39			−1.02734			−0.513669	−	0.857988i	$-0.671714\pi$
$157$	−3.45070e39			−1.02734			−0.513669	+	0.857988i	$0.671714\pi$
$158$	−2.61860e39	−	2.16871e39i	−0.695411	−	0.575934i
$159$			5.29679e39i			1.25564i
$160$	−1.28597e39	+	3.92132e39i	−0.272315	+	0.830371i
$161$	−8.51596e39			−1.61201
$162$	8.30796e38	−	1.00314e39i	0.140677	−	0.169861i
$163$			3.27030e39i			0.495691i	0.968800	+	0.247846i	$0.0797226\pi$
$163$			3.27030e39i			0.495691i	−0.968800	+	0.247846i	$0.920277\pi$
$164$	−4.84045e38	−	2.55261e39i	−0.0657199	−	0.346574i
$165$	1.05799e40			1.28757
$166$	−7.52434e39	−	6.23161e39i	−0.821340	−	0.680228i
$167$			2.45888e39i			0.240903i	0.992719	+	0.120451i	$0.0384342\pi$
$167$			2.45888e39i			0.240903i	−0.992719	+	0.120451i	$0.961566\pi$
$168$	2.65787e40	+	1.46686e40i	2.33866	+	1.29069i
$169$	6.67304e39			0.527671
$170$	−1.40451e39	+	1.69588e39i	−0.0998723	+	0.120591i
$171$			1.34686e40i			0.861770i
$172$	−2.01062e40	+	3.81269e39i	−1.15829	+	0.219644i
$173$	1.45782e40			0.756611			0.378305	−	0.925681i	$-0.376507\pi$
$173$	1.45782e40			0.756611			0.378305	+	0.925681i	$0.376507\pi$
$174$	−4.18253e40	−	3.46394e40i	−1.95683	−	1.62063i
$175$			9.43338e39i			0.398091i
$176$	−8.93097e39	−	2.27019e40i	−0.340150	−	0.864640i
$177$	1.03662e40			0.356534
$178$	−2.48446e40	+	2.99985e40i	−0.772096	+	0.932266i
$179$		−	4.38644e40i		−	1.23242i	−0.787583	−	0.616209i	$-0.788668\pi$
$179$		−	4.38644e40i		−	1.23242i	0.787583	−	0.616209i	$-0.211332\pi$
$180$	−9.70268e39	−	5.11671e40i	−0.246596	−	1.30042i
$181$	−6.61493e39			−0.152164			−0.0760818	−	0.997102i	$-0.524241\pi$
$181$	−6.61493e39			−0.152164			−0.0760818	+	0.997102i	$0.524241\pi$
$182$	7.69752e40	+	6.37504e40i	1.60349	+	1.32800i
$183$			4.64072e40i			0.875922i
$184$	2.70233e40	−	4.89649e40i	0.462400	−	0.837846i
$185$	4.21008e40			0.653430
$186$	6.78621e40	−	8.19400e40i	0.955860	−	1.15415i
$187$		−	1.30169e40i		−	0.166479i
$188$	5.98838e40	−	1.13556e40i	0.695774	−	0.131938i
$189$	−1.30167e41			−1.37464
$190$	−3.98741e40	−	3.30234e40i	−0.382935	−	0.317144i
$191$			6.76496e40i			0.591105i	0.955326	+	0.295553i	$0.0955037\pi$
$191$			6.76496e40i			0.591105i	−0.955326	+	0.295553i	$0.904496\pi$
$192$	−1.68682e41	+	1.06275e41i	−1.34168	+	0.845295i
$193$	−5.40480e40			−0.391515			−0.195757	−	0.980652i	$-0.562716\pi$
$193$	−5.40480e40			−0.391515			−0.195757	+	0.980652i	$0.562716\pi$
$194$	−1.39398e41	+	1.68315e41i	−0.920077	+	1.11094i
$195$		−	2.84661e41i		−	1.71279i
$196$	6.23829e40	+	3.28976e41i	0.342339	+	1.80532i
$197$	2.02102e41			1.01200			0.505998	−	0.862535i	$-0.331124\pi$
$197$	2.02102e41			1.01200			0.505998	+	0.862535i	$0.331124\pi$
$198$	2.37106e41	+	1.96369e41i	1.08385	+	0.897635i
$199$			3.80168e41i			1.58716i	0.608466	+	0.793580i	$0.291785\pi$
$199$			3.80168e41i			1.58716i	−0.608466	+	0.793580i	$0.708215\pi$
$200$	−5.42399e40	−	2.99345e40i	−0.206909	−	0.114191i
$201$	−3.67041e41			−1.27993
$202$	2.57196e41	−	3.10551e41i	0.820238	−	0.990395i
$203$		−	9.24972e41i		−	2.69898i
$204$	−1.04516e41	+	1.98192e40i	−0.279152	+	0.0529350i
$205$	−1.26035e41			−0.308262
$206$	3.57880e41	+	2.96393e41i	0.801913	+	0.664138i
$207$			7.05780e41i			1.44945i
$208$	−6.10813e41	+	2.40295e41i	−1.15019	+	0.452485i
$209$	3.06058e41			0.528652
$210$	9.39333e41	−	1.13420e42i	1.48892	−	1.79780i
$211$		−	1.04017e42i		−	1.51364i	−0.653624	−	0.756819i	$-0.726752\pi$
$211$		−	1.04017e42i		−	1.51364i	0.653624	−	0.756819i	$-0.273248\pi$
$212$	−1.10384e41	−	5.82107e41i	−0.147523	−	0.777961i
$213$	−8.15505e41			−1.00137
$214$	−3.17053e41	−	2.62581e41i	−0.357836	−	0.296357i
$215$			9.92739e41i			1.03025i
$216$	4.13053e41	−	7.48431e41i	0.394311	−	0.714471i
$217$	1.81212e42			1.59188
$218$	−9.39280e41	+	1.13413e42i	−0.759588	+	0.917164i
$219$			1.77261e42i			1.32014i
$220$	−1.16271e42	+	2.20482e41i	−0.797745	+	0.151274i
$221$	−3.50229e41			−0.221458
$222$	1.56646e42	+	1.29733e42i	0.913199	+	0.756305i
$223$		−	2.32832e42i		−	1.25186i	−0.779879	−	0.625930i	$-0.784719\pi$
$223$		−	2.32832e42i		−	1.25186i	0.779879	−	0.625930i	$-0.215281\pi$
$224$	−3.22664e42	−	1.05816e42i	−1.60061	−	0.524911i
$225$	7.81813e41			0.357946
$226$	−1.65580e42	+	1.99930e42i	−0.699934	+	0.845134i
$227$			1.68132e42i			0.656426i	0.944604	+	0.328213i	$0.106446\pi$
$227$			1.68132e42i			0.656426i	−0.944604	+	0.328213i	$0.893554\pi$
$228$	−4.65996e41	−	2.45743e42i	−0.168095	−	0.886448i
$229$	5.03000e42			1.67698			0.838492	−	0.544914i	$-0.183438\pi$
$229$	5.03000e42			1.67698			0.838492	+	0.544914i	$0.183438\pi$
$230$	−2.08948e42	−	1.73049e42i	−0.644076	−	0.533420i
$231$			8.70565e42i			2.48191i
$232$	5.31839e42	+	2.93518e42i	1.40280	+	0.774195i
$233$	−3.15400e42			−0.769937			−0.384968	−	0.922930i	$-0.625788\pi$
$233$	−3.15400e42			−0.769937			−0.384968	+	0.922930i	$0.625788\pi$
$234$	5.28346e42	−	6.37950e42i	1.19408	−	1.44179i
$235$		−	2.95675e42i		−	0.618860i
$236$	−1.13922e42	+	2.16028e41i	−0.220899	+	0.0418885i
$237$	−7.96827e42			−1.43184
$238$	−1.39545e42	−	1.15570e42i	−0.232449	−	0.192513i
$239$		−	4.63973e42i		−	0.716688i	−0.933590	−	0.358344i	$-0.883341\pi$
$239$		−	4.63973e42i		−	0.716688i	0.933590	−	0.358344i	$-0.116659\pi$
$240$	3.54063e42	+	9.00005e42i	0.507316	+	1.28956i
$241$	−4.00732e42			−0.532780			−0.266390	−	0.963865i	$-0.585831\pi$
$241$	−4.00732e42			−0.532780			−0.266390	+	0.963865i	$0.585831\pi$
$242$	−7.06559e41	+	8.53133e41i	−0.0871910	+	0.105279i
$243$		−	1.01750e43i		−	1.16580i
$244$	−9.67112e41	−	5.10006e42i	−0.102911	−	0.542698i
$245$	1.62431e43			1.60576
$246$	−4.68941e42	−	3.88374e42i	−0.430810	−	0.356794i
$247$		−	8.23471e42i		−	0.703240i
$248$	−5.75031e42	+	1.04193e43i	−0.456626	+	0.827384i
$249$	−2.28962e43			−1.69112
$250$	−1.00282e43	+	1.21085e43i	−0.689132	+	0.832091i
$251$		−	1.88297e43i		−	1.20425i	−0.798403	−	0.602124i	$-0.794321\pi$
$251$		−	1.88297e43i		−	1.20425i	0.798403	−	0.602124i	$-0.205679\pi$
$252$	4.21026e43	−	7.98382e42i	2.50668	−	0.475336i
$253$	1.60380e43			0.889165
$254$	3.05278e42	+	2.52829e42i	0.157648	+	0.130563i
$255$			5.16047e42i			0.248294i
$256$	1.63231e43	−	1.51947e43i	0.731955	−	0.681353i
$257$	2.39158e43			0.999744			0.499872	−	0.866099i	$-0.333380\pi$
$257$	2.39158e43			0.999744			0.499872	+	0.866099i	$0.333380\pi$
$258$	−3.05911e43	+	3.69372e43i	−1.19245	+	1.43982i
$259$			3.46425e43i			1.25954i
$260$	5.93224e42	+	3.12837e43i	0.201233	+	1.06120i
$261$	−7.66593e43			−2.42681
$262$	4.01766e41	+	3.32740e41i	0.0118727	+	0.00983290i
$263$		−	9.96673e42i		−	0.275011i	−0.990501	−	0.137505i	$-0.956092\pi$
$263$		−	9.96673e42i		−	0.275011i	0.990501	−	0.137505i	$-0.0439084\pi$
$264$	−5.00556e43	−	2.76253e43i	−1.28998	−	0.711927i
$265$	−2.87414e43			−0.691962
$266$	2.71732e43	−	3.28102e43i	0.611324	−	0.738141i
$267$			9.12841e43i			1.91952i
$268$	4.03371e43	−	7.64902e42i	0.793009	−	0.150376i
$269$	−7.17904e42			−0.131985			−0.0659926	−	0.997820i	$-0.521021\pi$
$269$	−7.17904e42			−0.131985			−0.0659926	+	0.997820i	$0.521021\pi$
$270$	−3.19378e43	−	2.64507e43i	−0.549234	−	0.454872i
$271$		−	2.81551e43i		−	0.453012i	−0.974010	−	0.226506i	$-0.927270\pi$
$271$		−	2.81551e43i		−	0.453012i	0.974010	−	0.226506i	$-0.0727303\pi$
$272$	1.10731e43	−	4.35618e42i	0.166736	−	0.0655942i
$273$	2.34232e44			3.30155
$274$	−3.93488e43	+	4.75117e43i	−0.519304	+	0.627032i
$275$		−	1.77658e43i		−	0.219582i
$276$	−2.44191e43	−	1.28774e44i	−0.282726	−	1.49096i
$277$	1.33140e44			1.44436			0.722178	−	0.691708i	$-0.243141\pi$
$277$	1.33140e44			1.44436			0.722178	+	0.691708i	$0.243141\pi$
$278$	−7.78183e43	−	6.44485e43i	−0.791180	−	0.655249i
$279$		−	1.50183e44i		−	1.43135i
$280$	−7.95946e43	+	1.44221e44i	−0.711277	+	1.28880i
$281$	−1.44307e44			−1.20941			−0.604705	−	0.796450i	$-0.706709\pi$
$281$	−1.44307e44			−1.20941			−0.604705	+	0.796450i	$0.706709\pi$
$282$	9.11117e43	−	1.10013e44i	0.716292	−	0.864886i
$283$			1.35543e44i			0.999815i	0.866079	+	0.499908i	$0.166633\pi$
$283$			1.35543e44i			0.999815i	−0.866079	+	0.499908i	$0.833367\pi$
$284$	8.96224e43	−	1.69949e43i	0.620421	−	0.117649i
$285$	−1.21335e44			−0.788457
$286$	−1.44967e44	−	1.20061e44i	−0.884464	−	0.732507i
$287$		−	1.03707e44i		−	0.594202i
$288$	−8.76973e43	+	2.67416e44i	−0.471977	+	1.43920i
$289$	−1.91421e44			−0.967896
$290$	1.87960e44	−	2.26952e44i	0.893102	−	1.07837i
$291$			5.12175e44i			2.28741i
$292$	−3.69406e43	−	1.94806e44i	−0.155100	−	0.817922i
$293$	1.90590e44			0.752458			0.376229	−	0.926527i	$-0.377221\pi$
$293$	1.90590e44			0.752458			0.376229	+	0.926527i	$0.377221\pi$
$294$	6.04363e44	+	5.00529e44i	2.24412	+	1.85856i
$295$			5.62489e43i			0.196480i
$296$	−1.99187e44	−	1.09930e44i	−0.654651	−	0.361296i
$297$	2.45142e44			0.758233
$298$	−2.96572e44	+	3.58095e44i	−0.863450	+	1.04257i
$299$		−	4.31516e44i		−	1.18281i
$300$	−1.42647e44	+	2.70498e43i	−0.368196	+	0.0698202i
$301$	−8.16872e44			−1.98590
$302$	4.12777e44	+	3.41859e44i	0.945345	+	0.782928i
$303$		−	9.44992e44i		−	2.03920i
$304$	1.02424e44	+	2.60355e44i	0.208294	+	0.529470i
$305$	−2.51814e44			−0.482706
$306$	−9.57812e43	+	1.15651e44i	−0.173099	+	0.209008i
$307$			2.25478e44i			0.384250i	0.981371	+	0.192125i	$0.0615378\pi$
$307$			2.25478e44i			0.384250i	−0.981371	+	0.192125i	$0.938462\pi$
$308$	−1.81423e44	−	9.56734e44i	−0.291595	−	1.53772i
$309$	1.08901e45			1.65112
$310$	4.44622e44	+	3.68233e44i	0.636034	+	0.526759i
$311$			4.40395e44i			0.594505i	0.954799	+	0.297253i	$0.0960704\pi$
$311$			4.40395e44i			0.594505i	−0.954799	+	0.297253i	$0.903930\pi$
$312$	−7.43278e44	+	1.34678e45i	−0.947041	+	1.71599i
$313$	−3.57493e44			−0.430001			−0.215001	−	0.976614i	$-0.568975\pi$
$313$	−3.57493e44			−0.430001			−0.215001	+	0.976614i	$0.568975\pi$
$314$	5.76982e44	−	6.96676e44i	0.655282	−	0.791219i
$315$		−	2.07881e45i		−	2.22959i
$316$	8.75698e44	−	1.66056e44i	0.887129	−	0.168224i
$317$	−1.47137e44			−0.140817			−0.0704084	−	0.997518i	$-0.522430\pi$
$317$	−1.47137e44			−0.140817			−0.0704084	+	0.997518i	$0.522430\pi$
$318$	−1.06939e45	−	8.85662e44i	−0.967049	−	0.800903i
$319$			1.74199e45i			1.48872i
$320$	−5.76667e44	−	9.15303e44i	−0.465828	−	0.739376i
$321$	−9.64776e44			−0.736777
$322$	1.42393e45	−	1.71932e45i	1.02821	−	1.24151i
$323$			1.49283e44i			0.101945i
$324$	6.36135e43	+	3.35466e44i	0.0410903	+	0.216690i
$325$	−4.78002e44			−0.292099
$326$	−6.60255e44	−	5.46819e44i	−0.381764	−	0.316174i
$327$			3.45111e45i			1.88842i
$328$	5.96293e44	+	3.29089e44i	0.308838	+	0.170445i
$329$	2.43295e45			1.19291
$330$	−1.76904e45	+	2.13602e45i	−0.821271	+	0.991642i
$331$		−	1.32037e45i		−	0.580486i	−0.956953	−	0.290243i	$-0.906264\pi$
$331$		−	1.32037e45i		−	0.580486i	0.956953	−	0.290243i	$-0.0937361\pi$
$332$	2.51625e45	−	4.77150e44i	1.04778	−	0.198687i
$333$	2.87108e45			1.13253
$334$	−4.96434e44	−	4.11143e44i	−0.185535	−	0.153658i
$335$		−	1.99163e45i		−	0.705347i
$336$	−7.40566e45	+	2.91340e45i	−2.48575	+	0.977896i
$337$	3.36424e45			1.07041			0.535203	−	0.844724i	$-0.320235\pi$
$337$	3.36424e45			1.07041			0.535203	+	0.844724i	$0.320235\pi$
$338$	−1.11578e45	+	1.34725e45i	−0.336572	+	0.406393i
$339$			6.08377e45i			1.74011i
$340$	−1.07543e44	−	5.67126e44i	−0.0291716	−	0.153836i
$341$	−3.41275e45			−0.878062
$342$	−2.71922e45	−	2.25204e45i	−0.663705	−	0.549676i
$343$			6.09178e45i			1.41075i
$344$	2.59214e45	−	4.69683e45i	0.569649	−	1.03217i
$345$	−6.35819e45			−1.32614
$346$	−2.43757e45	+	2.94324e45i	−0.482601	+	0.582715i
$347$		−	1.00518e46i		−	1.88935i	−0.328011	−	0.944674i	$-0.606378\pi$
$347$		−	1.00518e46i		−	1.88935i	0.328011	−	0.944674i	$-0.393622\pi$
$348$	1.39870e46	−	2.65231e45i	2.49630	−	0.473368i
$349$	3.56047e45			0.603462			0.301731	−	0.953393i	$-0.402436\pi$
$349$	3.56047e45			0.603462			0.301731	+	0.953393i	$0.402436\pi$
$350$	−1.90454e45	−	1.57733e45i	−0.306596	−	0.253920i
$351$		−	6.59574e45i		−	1.00864i
$352$	6.07671e45	+	1.99282e45i	0.882878	+	0.289534i
$353$	−2.76793e45			−0.382130			−0.191065	−	0.981577i	$-0.561194\pi$
$353$	−2.76793e45			−0.382130			−0.191065	+	0.981577i	$0.561194\pi$
$354$	−1.73330e45	+	2.09287e45i	−0.227413	+	0.274590i
$355$		−	4.42508e45i		−	0.551837i
$356$	−1.90233e45	−	1.00319e46i	−0.225521	−	1.18928i
$357$	−4.24627e45			−0.478608
$358$	8.85597e45	+	7.33445e45i	0.949165	+	0.786092i
$359$		−	2.31432e45i		−	0.235897i	−0.993020	−	0.117949i	$-0.962368\pi$
$359$		−	2.31432e45i		−	0.235897i	0.993020	−	0.117949i	$-0.0376318\pi$
$360$	1.19527e46	+	6.59659e45i	1.15883	+	0.639550i
$361$	7.33251e45			0.676275
$362$	1.10606e45	−	1.33551e45i	0.0970568	−	0.117191i
$363$			2.59604e45i			0.216767i
$364$	−2.57416e46	+	4.88132e45i	−2.04556	+	0.387894i
$365$	−9.61851e45			−0.727506
$366$	−9.36934e45	−	7.75962e45i	−0.674605	−	0.558703i
$367$		−	3.24876e45i		−	0.222704i	−0.993781	−	0.111352i	$-0.964482\pi$
$367$		−	3.24876e45i		−	0.222704i	0.993781	−	0.111352i	$-0.0355181\pi$
$368$	5.36723e45	+	1.36431e46i	0.350340	+	0.890540i
$369$	−8.59497e45			−0.534281
$370$	−7.03956e45	+	8.49990e45i	−0.416787	+	0.503249i
$371$		−	2.36498e46i		−	1.33382i
$372$	5.19616e45	+	2.74019e46i	0.279196	+	1.47234i
$373$	−1.44373e46			−0.739141			−0.369571	−	0.929203i	$-0.620495\pi$
$373$	−1.44373e46			−0.739141			−0.369571	+	0.929203i	$0.620495\pi$
$374$	2.62803e45	+	2.17652e45i	0.128216	+	0.106188i
$375$			3.68456e46i			1.71326i
$376$	−7.72037e45	+	1.39889e46i	−0.342182	+	0.620016i
$377$	4.68696e46			1.98037
$378$	2.17649e46	−	2.62799e46i	0.876806	−	1.05870i
$379$			1.15828e46i			0.444947i	0.974939	+	0.222473i	$0.0714130\pi$
$379$			1.15828e46i			0.444947i	−0.974939	+	0.222473i	$0.928587\pi$
$380$	1.33345e46	−	2.52858e45i	0.488507	−	0.0926344i
$381$	9.28947e45			0.324595
$382$	−1.36581e46	−	1.13115e46i	−0.455248	−	0.377033i
$383$		−	1.46515e46i		−	0.465913i	−0.972487	−	0.232956i	$-0.925160\pi$
$383$		−	1.46515e46i		−	0.465913i	0.972487	−	0.232956i	$-0.0748400\pi$
$384$	6.74868e45	−	5.18259e46i	0.204765	−	1.57248i
$385$	−4.72385e46			−1.36774
$386$	9.03722e45	−	1.09120e46i	0.249726	−	0.301531i
$387$			6.77002e46i			1.78563i
$388$	−1.06736e46	−	5.62871e46i	−0.268744	−	1.41722i
$389$	1.39471e46			0.335267			0.167633	−	0.985849i	$-0.446388\pi$
$389$	1.39471e46			0.335267			0.167633	+	0.985849i	$0.446388\pi$
$390$	5.74713e46	+	4.75973e46i	1.31913	+	1.09250i
$391$			7.82273e45i			0.171466i
$392$	−7.68492e46	−	4.24124e46i	−1.60876	−	0.887859i
$393$	1.22256e45			0.0244457
$394$	−3.37929e46	+	4.08032e46i	−0.645497	+	0.779404i
$395$		−	4.32374e46i		−	0.789062i
$396$	−7.92916e46	+	1.50359e46i	−1.38265	+	0.262189i
$397$	6.95252e46			1.15855			0.579273	−	0.815134i	$-0.303337\pi$
$397$	6.95252e46			1.15855			0.579273	+	0.815134i	$0.303337\pi$
$398$	−7.67537e46	−	6.35669e46i	−1.22237	−	1.01236i
$399$		−	9.98399e46i		−	1.51982i
$400$	1.51129e46	−	5.94543e45i	0.219922	−	0.0865175i
$401$	7.27154e46			1.01164			0.505822	−	0.862638i	$-0.331189\pi$
$401$	7.27154e46			1.01164			0.505822	+	0.862638i	$0.331189\pi$
$402$	6.13719e46	−	7.41034e46i	0.816396	−	0.985755i
$403$			9.18225e46i			1.16804i
$404$	1.96933e46	+	1.03853e47i	0.239582	+	1.26344i
$405$	1.65635e46			0.192736
$406$	1.86746e47	+	1.54662e47i	2.07866	+	1.72153i
$407$		−	6.52420e46i		−	0.694749i
$408$	1.34745e46	−	2.44151e46i	0.137287	−	0.248758i
$409$	−9.48296e46			−0.924538			−0.462269	−	0.886740i	$-0.652964\pi$
$409$	−9.48296e46			−0.924538			−0.462269	+	0.886740i	$0.652964\pi$
$410$	2.10739e46	−	2.54456e46i	0.196623	−	0.237413i
$411$			1.44576e47i			1.29105i
$412$	−1.19680e47	+	2.26947e46i	−1.02299	+	0.193987i
$413$	−4.62842e46			−0.378732
$414$	−1.42493e47	−	1.18012e47i	−1.11632	−	0.924525i
$415$		−	1.24239e47i		−	0.931951i
$416$	5.36183e46	−	1.63498e47i	0.385153	−	1.17445i
$417$	−2.36797e47			−1.62902
$418$	−5.11751e46	+	6.17912e46i	−0.337198	+	0.407149i
$419$			2.48487e47i			1.56838i	0.620521	+	0.784190i	$0.286921\pi$
$419$			2.48487e47i			1.56838i	−0.620521	+	0.784190i	$0.713079\pi$
$420$	7.19241e46	+	3.79291e47i	0.434898	+	2.29343i
$421$	6.81753e46			0.394957			0.197478	−	0.980307i	$-0.436725\pi$
$421$	6.81753e46			0.394957			0.197478	+	0.980307i	$0.436725\pi$
$422$	2.10005e47	+	1.73925e47i	1.16575	+	0.965467i
$423$		−	2.01636e47i		−	1.07261i
$424$	1.35981e47	+	7.50468e46i	0.693255	+	0.382602i
$425$	8.66547e45			0.0423440
$426$	1.36358e47	−	1.64646e47i	0.638717	−	0.771218i
$427$		−	2.07204e47i		−	0.930459i
$428$	1.06027e47	−	2.01056e46i	0.456487	−	0.0865626i
$429$	−4.41127e47			−1.82110
$430$	−2.00428e47	−	1.65993e47i	−0.793463	−	0.657140i
$431$			1.42738e47i			0.541937i	0.962588	+	0.270969i	$0.0873440\pi$
$431$			1.42738e47i			0.541937i	−0.962588	+	0.270969i	$0.912656\pi$
$432$	8.20384e46	+	2.08536e47i	0.298751	+	0.759406i
$433$	5.27128e47			1.84134			0.920670	−	0.390341i	$-0.127643\pi$
$433$	5.27128e47			1.84134			0.920670	+	0.390341i	$0.127643\pi$
$434$	−3.02999e47	+	3.65855e47i	−1.01537	+	1.22601i
$435$		−	6.90603e47i		−	2.22035i
$436$	−7.19201e46	−	3.79270e47i	−0.221867	−	1.17002i
$437$	−1.83931e47			−0.544489
$438$	−3.57879e47	−	2.96393e47i	−1.01672	−	0.842042i
$439$		−	7.52444e46i		−	0.205169i	−0.994724	−	0.102585i	$-0.967289\pi$
$439$		−	7.52444e46i		−	0.205169i	0.994724	−	0.102585i	$-0.0327113\pi$
$440$	1.49900e47	−	2.71611e47i	0.392331	−	0.710885i
$441$	1.10770e48			2.78310
$442$	5.85609e46	−	7.07092e46i	0.141256	−	0.170559i
$443$		−	1.06255e47i		−	0.246083i	−0.992402	−	0.123041i	$-0.960735\pi$
$443$		−	1.06255e47i		−	0.246083i	0.992402	−	0.123041i	$-0.0392648\pi$
$444$	−5.23847e47	+	9.93357e46i	−1.16496	+	0.220908i
$445$	−4.95325e47			−1.05782
$446$	4.70075e47	+	3.89313e47i	0.964139	+	0.798493i
$447$			1.08967e48i			2.14663i
$448$	7.53154e47	−	4.74508e47i	1.42521	−	0.897924i
$449$	−8.30129e47			−1.50908			−0.754538	−	0.656256i	$-0.772139\pi$
$449$	−8.30129e47			−1.50908			−0.754538	+	0.656256i	$0.772139\pi$
$450$	−1.30725e47	+	1.57843e47i	−0.228314	+	0.275678i
$451$			1.95311e47i			0.327754i
$452$	−1.26784e47	−	6.68594e47i	−0.204443	−	1.07813i
$453$	1.25606e48			1.94645
$454$	−3.39449e47	−	2.81129e47i	−0.505556	−	0.418698i
$455$			1.27099e48i			1.81943i
$456$	5.74058e47	+	3.16818e47i	0.789929	+	0.435956i
$457$	−1.27875e48			−1.69159			−0.845795	−	0.533508i	$-0.820873\pi$
$457$	−1.27875e48			−1.69159			−0.845795	+	0.533508i	$0.820873\pi$
$458$	−8.41052e47	+	1.01553e48i	−1.06966	+	1.29155i
$459$			1.19571e47i			0.146217i
$460$	6.98753e47	−	1.32503e47i	0.821642	−	0.155806i
$461$	−4.72856e47			−0.534703			−0.267351	−	0.963599i	$-0.586148\pi$
$461$	−4.72856e47			−0.534703			−0.267351	+	0.963599i	$0.586148\pi$
$462$	−1.75762e48	−	1.45565e48i	−1.91148	−	1.58307i
$463$			2.03247e47i			0.212601i	0.994334	+	0.106301i	$0.0339006\pi$
$463$			2.03247e47i			0.212601i	−0.994334	+	0.106301i	$0.966099\pi$
$464$	−1.48187e48	+	5.82969e47i	−1.49103	+	0.586572i
$465$	1.35296e48			1.30958
$466$	5.27372e47	−	6.36774e47i	0.491100	−	0.592978i
$467$		−	3.67532e47i		−	0.329299i	−0.986352	−	0.164650i	$-0.947351\pi$
$467$		−	3.67532e47i		−	0.329299i	0.986352	−	0.164650i	$-0.0526494\pi$
$468$	4.04551e47	+	2.13340e48i	0.348777	+	1.83928i
$469$	1.63881e48			1.35962
$470$	5.96950e47	+	4.94390e47i	0.476624	+	0.394737i
$471$		−	2.11995e48i		−	1.62911i
$472$	1.46872e47	−	2.66124e47i	0.108638	−	0.196847i
$473$	1.53841e48			1.09540
$474$	1.33235e48	−	1.60875e48i	0.913291	−	1.10275i
$475$			2.03746e47i			0.134463i
$476$	4.66657e47	−	8.84911e46i	0.296533	−	0.0562308i
$477$	−1.96003e48			−1.19931
$478$	9.36733e47	+	7.75796e47i	0.551968	+	0.457136i
$479$			1.68095e48i			0.953925i	0.878924	+	0.476963i	$0.158262\pi$
$479$			1.68095e48i			0.953925i	−0.878924	+	0.476963i	$0.841738\pi$
$480$	−2.40908e48	−	7.90042e47i	−1.31677	−	0.431825i
$481$	−1.75538e48			−0.924189
$482$	6.70054e47	−	8.09055e47i	0.339831	−	0.410328i
$483$		−	5.23181e48i		−	2.55625i
$484$	−5.41008e46	−	2.85300e47i	−0.0254675	−	0.134303i
$485$	−2.77916e48			−1.26056
$486$	2.05428e48	+	1.70134e48i	0.897856	+	0.743598i
$487$		−	2.46020e48i		−	1.03621i	−0.855316	−	0.518107i	$-0.826637\pi$
$487$		−	2.46020e48i		−	1.03621i	0.855316	−	0.518107i	$-0.173363\pi$
$488$	1.19138e48	+	6.57513e47i	0.483608	+	0.266899i
$489$	−2.00912e48			−0.786045
$490$	−2.71597e48	+	3.27939e48i	−1.02422	+	1.23670i
$491$			3.35992e48i			1.22141i	0.791858	+	0.610706i	$0.209114\pi$
$491$			3.35992e48i			1.22141i	−0.791858	+	0.610706i	$0.790886\pi$
$492$	1.56821e48	−	2.97375e47i	0.549581	−	0.104216i
$493$	−8.49677e47			−0.287084
$494$	1.66254e48	+	1.37690e48i	0.541610	+	0.448558i
$495$			3.91500e48i			1.22981i
$496$	−1.14210e48	−	2.90313e48i	−0.345965	−	0.879420i
$497$	3.64116e48			1.06371
$498$	3.82841e48	−	4.62261e48i	1.07867	−	1.30244i
$499$		−	1.40771e48i		−	0.382564i	−0.981535	−	0.191282i	$-0.938735\pi$
$499$		−	1.40771e48i		−	0.382564i	0.981535	−	0.191282i	$-0.0612645\pi$
$500$	−7.67852e47	−	4.04926e48i	−0.201288	−	1.06149i
$501$	−1.51062e48			−0.382012
$502$	3.80160e48	+	3.14846e48i	0.927469	+	0.768123i
$503$		−	2.31603e48i		−	0.545155i	−0.962134	−	0.272578i	$-0.912124\pi$
$503$		−	2.31603e48i		−	0.545155i	0.962134	−	0.272578i	$-0.0878761\pi$
$504$	−5.42798e48	+	9.83522e48i	−1.23279	+	2.23375i
$505$	5.12771e48			1.12377
$506$	−2.68168e48	+	3.23799e48i	−0.567149	+	0.684803i
$507$			4.09961e48i			0.836756i
$508$	−1.02089e48	+	1.93590e47i	−0.201110	+	0.0381360i
$509$	3.39060e48			0.644698			0.322349	−	0.946621i	$-0.395528\pi$
$509$	3.39060e48			0.644698			0.322349	+	0.946621i	$0.395528\pi$
$510$	−1.04187e48	−	8.62868e47i	−0.191227	−	0.158373i
$511$		−	7.91456e48i		−	1.40233i
$512$	3.38369e47	+	5.83621e48i	0.0578804	+	0.998324i
$513$	−2.81139e48			−0.464311
$514$	−3.99890e48	+	4.82846e48i	−0.637682	+	0.769968i
$515$			5.90918e48i			0.909907i
$516$	−2.34234e48	−	1.23523e49i	−0.348302	−	1.83677i
$517$	−4.58195e48			−0.657993
$518$	−6.99411e48	−	5.79248e48i	−0.970057	−	0.803394i
$519$			8.95614e48i			1.19980i
$520$	−7.30790e48	−	4.03317e48i	−0.945654	−	0.521899i
$521$	8.79379e48			1.09925			0.549626	−	0.835411i	$-0.314770\pi$
$521$	8.79379e48			1.09925			0.549626	+	0.835411i	$0.314770\pi$
$522$	1.28180e49	−	1.54770e49i	1.54793	−	1.86904i
$523$			4.98961e48i			0.582152i	0.956700	+	0.291076i	$0.0940132\pi$
$523$			4.98961e48i			0.582152i	−0.956700	+	0.291076i	$0.905987\pi$
$524$	−1.34356e47	+	2.54777e46i	−0.0151459	+	0.00287208i
$525$	−5.79543e48			−0.631275
$526$	2.01222e48	+	1.66651e48i	0.211803	+	0.175414i
$527$		−	1.66460e48i		−	0.169325i
$528$	1.39470e49	−	5.48678e48i	1.37111	−	0.539395i
$529$	8.86165e47			0.0842000
$530$	4.80577e48	−	5.80272e48i	0.441365	−	0.532925i
$531$			3.83591e48i			0.340540i
$532$	2.08063e48	+	1.09722e49i	0.178561	+	0.941640i
$533$	5.25498e48			0.435995
$534$	−1.84297e49	−	1.52634e49i	−1.47835	−	1.22436i
$535$		−	5.23506e48i		−	0.406026i
$536$	−5.20036e48	+	9.42279e48i	−0.390002	+	0.706665i
$537$	2.69483e49			1.95431
$538$	1.20039e48	−	1.44941e48i	0.0841862	−	0.101650i
$539$		−	2.51713e49i		−	1.70729i
$540$	1.06805e49	−	2.02531e48i	0.700653	−	0.132863i
$541$	−2.06395e49			−1.30963			−0.654814	−	0.755790i	$-0.727253\pi$
$541$	−2.06395e49			−1.30963			−0.654814	+	0.755790i	$0.727253\pi$
$542$	5.68435e48	+	4.70774e48i	0.348894	+	0.288952i
$543$		−	4.06390e48i		−	0.241294i
$544$	−9.72020e47	+	2.96398e48i	−0.0558335	+	0.170253i
$545$	−1.87264e49			−1.04068
$546$	−3.91653e49	+	4.72900e49i	−2.10588	+	2.54274i
$547$			3.24152e49i			1.68646i	0.537551	+	0.843231i	$0.319350\pi$
$547$			3.24152e49i			1.68646i	−0.537551	+	0.843231i	$0.680650\pi$
$548$	−3.01291e48	−	1.58886e49i	−0.151683	−	0.799899i
$549$	−1.71726e49			−0.836628
$550$	3.58681e48	+	2.97057e48i	0.169114	+	0.140059i
$551$		−	1.99779e49i		−	0.911635i
$552$	3.00818e49	+	1.66019e49i	1.32862	+	0.733253i
$553$	3.55777e49			1.52099
$554$	−2.22620e49	+	2.68803e49i	−0.921275	+	1.11239i
$555$			2.58648e49i			1.03618i
$556$	2.60236e49	−	4.93478e48i	1.00930	−	0.191391i
$557$	−2.89906e49			−1.08859			−0.544295	−	0.838894i	$-0.683203\pi$
$557$	−2.89906e49			−1.08859			−0.544295	+	0.838894i	$0.683203\pi$
$558$	3.03211e49	+	2.51118e49i	1.10238	+	0.912980i
$559$		−	4.13920e49i		−	1.45715i
$560$	−1.58086e49	−	4.01845e49i	−0.538902	−	1.36985i
$561$	7.99698e48			0.263994
$562$	2.41292e49	−	2.91347e49i	0.771416	−	0.931445i
$563$			1.35622e49i			0.419932i	0.977709	+	0.209966i	$0.0673354\pi$
$563$			1.35622e49i			0.419932i	−0.977709	+	0.209966i	$0.932665\pi$
$564$	6.97637e48	+	3.67898e49i	0.209221	+	1.10333i
$565$	−3.30117e49			−0.958949
$566$	−2.73652e49	−	2.26637e49i	−0.770022	−	0.637727i
$567$			1.36292e49i			0.371515i
$568$	−1.15543e49	+	2.09359e49i	−0.305123	+	0.552868i
$569$	−2.26003e48			−0.0578220			−0.0289110	−	0.999582i	$-0.509204\pi$
$569$	−2.26003e48			−0.0578220			−0.0289110	+	0.999582i	$0.509204\pi$
$570$	2.02881e49	−	2.44968e49i	0.502913	−	0.607242i
$571$		−	6.44223e49i		−	1.54734i	−0.633588	−	0.773671i	$-0.718418\pi$
$571$		−	6.44223e49i		−	1.54734i	0.633588	−	0.773671i	$-0.281582\pi$
$572$	4.84790e49	−	9.19296e48i	1.12830	−	0.213957i
$573$	−4.15608e49			−0.937348
$574$	2.09378e49	+	1.73406e49i	0.457634	+	0.379009i
$575$			1.06767e49i			0.226160i
$576$	−3.93260e49	−	6.24194e49i	−0.807375	−	1.28149i
$577$	−1.18626e49			−0.236056			−0.118028	−	0.993010i	$-0.537657\pi$
$577$	−1.18626e49			−0.236056			−0.118028	+	0.993010i	$0.537657\pi$
$578$	3.20070e49	−	3.86468e49i	0.617368	−	0.745440i
$579$		−	3.32046e49i		−	0.620846i
$580$	1.43920e49	+	7.58960e49i	0.260865	+	1.37567i
$581$	1.02230e50			1.79642
$582$	−1.03405e50	−	8.56394e49i	−1.76169	−	1.45902i
$583$			4.45394e49i			0.735717i
$584$	4.55070e49	+	2.51149e49i	0.728864	+	0.402254i
$585$	1.05336e50			1.63596
$586$	−3.18680e49	+	3.84789e49i	−0.479952	+	0.579517i
$587$		−	1.66634e49i		−	0.243377i	−0.992568	−	0.121688i	$-0.961169\pi$
$587$		−	1.66634e49i		−	0.243377i	0.992568	−	0.121688i	$-0.0388308\pi$
$588$	−2.02108e50	+	3.83252e49i	−2.86280	+	0.542866i
$589$	3.91387e49			0.537690
$590$	−1.13563e49	−	9.40523e48i	−0.151322	−	0.125324i
$591$			1.24162e50i			1.60478i
$592$	5.54996e49	−	2.18336e49i	0.695824	−	0.273738i
$593$	7.80412e49			0.949161			0.474580	−	0.880212i	$-0.342600\pi$
$593$	7.80412e49			0.949161			0.474580	+	0.880212i	$0.342600\pi$
$594$	−4.09896e49	+	4.94928e49i	−0.483635	+	0.583964i
$595$		−	2.30411e49i		−	0.263753i
$596$	−2.27083e49	−	1.19752e50i	−0.252204	−	1.33000i
$597$	−2.33558e50			−2.51685
$598$	8.71205e49	+	7.21525e49i	0.910959	+	0.754450i
$599$			1.23378e50i			1.25185i	0.779882	+	0.625926i	$0.215279\pi$
$599$			1.23378e50i			1.25185i	−0.779882	+	0.625926i	$0.784721\pi$
$600$	1.83904e49	−	3.33225e49i	0.181079	−	0.328106i
$601$	−1.56049e50			−1.49115			−0.745575	−	0.666421i	$-0.767825\pi$
$601$	−1.56049e50			−1.49115			−0.745575	+	0.666421i	$0.767825\pi$
$602$	1.36587e50	−	1.64922e50i	1.26670	−	1.52947i
$603$		−	1.35820e50i		−	1.22251i
$604$	−1.38039e50	+	2.61759e49i	−1.20597	+	0.228685i
$605$	−1.40866e49			−0.119457
$606$	1.90788e50	+	1.58009e50i	1.57052	+	1.30070i
$607$			2.47790e50i			1.98010i	0.140701	+	0.990052i	$0.455064\pi$
$607$			2.47790e50i			1.98010i	−0.140701	+	0.990052i	$0.544936\pi$
$608$	−6.96902e49	−	2.28545e49i	−0.540639	−	0.177299i
$609$	5.68260e50			4.27992
$610$	4.21052e49	−	5.08398e49i	0.307892	−	0.371764i
$611$			1.23281e50i			0.875294i
$612$	−7.33391e48	−	3.86753e49i	−0.0505603	−	0.266630i
$613$	−1.69578e50			−1.13522			−0.567610	−	0.823298i	$-0.692132\pi$
$613$	−1.69578e50			−1.13522			−0.567610	+	0.823298i	$0.692132\pi$
$614$	−4.55227e49	−	3.77015e49i	−0.295935	−	0.245092i
$615$		−	7.74298e49i		−	0.488828i
$616$	2.23494e50	+	1.23345e50i	1.37029	+	0.756253i
$617$	−2.27776e50			−1.35636			−0.678180	−	0.734896i	$-0.737231\pi$
$617$	−2.27776e50			−1.35636			−0.678180	+	0.734896i	$0.737231\pi$
$618$	−1.82090e50	+	2.19865e50i	−1.05316	+	1.27164i
$619$		−	3.14061e50i		−	1.76434i	−0.470932	−	0.882169i	$-0.656082\pi$
$619$		−	3.14061e50i		−	1.76434i	0.470932	−	0.882169i	$-0.343918\pi$
$620$	−1.48688e50	+	2.81953e49i	−0.811382	+	0.153860i
$621$	−1.47323e50			−0.780946
$622$	−8.89132e49	−	7.36373e49i	−0.457867	−	0.379202i
$623$		−	4.07576e50i		−	2.03903i
$624$	−1.47626e50	−	3.75255e50i	−0.717530	−	1.82391i
$625$	−1.49887e50			−0.707821
$626$	5.97755e49	−	7.21758e49i	0.274274	−	0.331172i
$627$			1.88028e50i			0.838313i
$628$	4.41791e49	+	2.32978e50i	0.191401	+	1.00935i
$629$	3.18225e49			0.133975
$630$	4.19699e50	+	3.47591e50i	1.71715	+	1.42213i
$631$		−	3.34685e50i		−	1.33079i	−0.746493	−	0.665393i	$-0.768264\pi$
$631$		−	3.34685e50i		−	1.33079i	0.746493	−	0.665393i	$-0.231736\pi$
$632$	−1.12897e50	+	2.04564e50i	−0.436290	+	0.790536i
$633$	6.39035e50			2.40026
$634$	2.46023e49	−	2.97061e49i	0.0898193	−	0.108452i
$635$			5.04064e49i			0.178879i
$636$	3.57620e50	−	6.78146e49i	1.23365	−	0.233935i
$637$	−6.77253e50			−2.27112
$638$	−3.51698e50	−	2.91274e50i	−1.14656	−	0.949575i
$639$		−	3.01770e50i		−	0.956446i
$640$	2.81217e50	+	3.66196e49i	0.866567	+	0.112843i
$641$	5.81399e50			1.74193			0.870963	−	0.491348i	$-0.163496\pi$
$641$	5.81399e50			1.74193			0.870963	+	0.491348i	$0.163496\pi$
$642$	1.61318e50	−	1.94783e50i	0.469949	−	0.567439i
$643$		−	4.72135e49i		−	0.133742i	−0.997762	−	0.0668711i	$-0.978698\pi$
$643$		−	4.72135e49i		−	0.133742i	0.997762	−	0.0668711i	$-0.0213016\pi$
$644$	1.09029e50	+	5.74966e50i	0.300330	+	1.58379i
$645$	−6.09893e50			−1.63372
$646$	−3.01394e49	−	2.49612e49i	−0.0785143	−	0.0650250i
$647$			4.55310e50i			1.15353i	0.816909	+	0.576767i	$0.195686\pi$
$647$			4.55310e50i			1.15353i	−0.816909	+	0.576767i	$0.804314\pi$
$648$	−7.83652e49	−	4.32491e49i	−0.193096	−	0.106568i
$649$	8.71668e49			0.208904
$650$	7.99255e49	−	9.65059e49i	0.186314	−	0.224964i
$651$			1.11328e51i			2.52433i
$652$	2.20799e50	−	4.18695e49i	0.487012	−	0.0923510i
$653$	−3.29954e50			−0.707972			−0.353986	−	0.935251i	$-0.615174\pi$
$653$	−3.29954e50			−0.707972			−0.353986	+	0.935251i	$0.615174\pi$
$654$	−6.96759e50	−	5.77051e50i	−1.45440	−	1.20452i
$655$			6.63382e48i			0.0134716i
$656$	−1.66146e50	+	6.53619e49i	−0.328261	+	0.129138i
$657$	−6.55938e50			−1.26092
$658$	−4.06807e50	+	4.91198e50i	−0.760890	+	0.918735i
$659$			4.14820e50i			0.754957i	0.926018	+	0.377479i	$0.123209\pi$
$659$			4.14820e50i			0.754957i	−0.926018	+	0.377479i	$0.876791\pi$
$660$	−1.35454e50	−	7.14317e50i	−0.239884	−	1.26503i
$661$	7.07141e50			1.21865			0.609326	−	0.792920i	$-0.291440\pi$
$661$	7.07141e50			1.21865			0.609326	+	0.792920i	$0.291440\pi$
$662$	2.66575e50	+	2.20775e50i	0.447070	+	0.370260i
$663$		−	2.15165e50i		−	0.351178i
$664$	−3.24401e50	+	5.87799e50i	−0.515297	+	0.933691i
$665$	5.41750e50			0.837548
$666$	−4.80065e50	+	5.79654e50i	−0.722377	+	0.872233i
$667$		−	1.04688e51i		−	1.53332i
$668$	1.66015e50	−	3.14810e49i	0.236685	−	0.0448819i
$669$	1.43041e51			1.98514
$670$	4.02099e50	+	3.33016e50i	0.543234	+	0.449902i
$671$			3.90227e50i			0.513229i
$672$	6.50083e50	−	1.98230e51i	0.832380	−	2.53818i
$673$	9.28631e50			1.15764			0.578818	−	0.815457i	$-0.303514\pi$
$673$	9.28631e50			1.15764			0.578818	+	0.815457i	$0.303514\pi$
$674$	−5.62525e50	+	6.79220e50i	−0.682753	+	0.824389i
$675$			1.63194e50i			0.192857i
$676$	−8.54346e49	−	4.50539e50i	−0.0983090	−	0.518432i
$677$	−3.08900e50			−0.346117			−0.173058	−	0.984912i	$-0.555365\pi$
$677$	−3.08900e50			−0.346117			−0.173058	+	0.984912i	$0.555365\pi$
$678$	−1.22828e51	−	1.01725e51i	−1.34018	−	1.10992i
$679$		−	2.28682e51i		−	2.42983i
$680$	1.32481e50	+	7.31153e49i	0.137086	+	0.0756568i
$681$	−1.03293e51			−1.04093
$682$	5.70636e50	−	6.89013e50i	0.560067	−	0.676252i
$683$			1.95997e51i			1.87360i	0.349864	+	0.936801i	$0.386228\pi$
$683$			1.95997e51i			1.87360i	−0.349864	+	0.936801i	$0.613772\pi$
$684$	9.09348e50	−	1.72437e50i	0.846682	−	0.160554i
$685$	−7.84495e50			−0.711475
$686$	−1.22989e51	−	1.01859e51i	−1.08651	−	0.899839i
$687$			3.09020e51i			2.65929i
$688$	5.14838e50	+	1.30868e51i	0.431597	+	1.09709i
$689$	1.19837e51			0.978687
$690$	1.06314e51	−	1.28368e51i	0.845873	−	1.02135i
$691$		−	2.05067e51i		−	1.58961i	−0.606866	−	0.794804i	$-0.707574\pi$
$691$		−	2.05067e51i		−	1.58961i	0.606866	−	0.794804i	$-0.292426\pi$
$692$	−1.86643e50	−	9.84263e50i	−0.140962	−	0.743364i
$693$	−3.22144e51			−2.37057
$694$	2.02939e51	+	1.68073e51i	1.45511	+	1.20511i
$695$		−	1.28491e51i		−	0.897728i
$696$	−1.80324e51	+	3.26737e51i	−1.22768	+	2.22450i
$697$	−9.52650e49			−0.0632038
$698$	−5.95337e50	+	7.18838e50i	−0.384915	+	0.464765i
$699$		−	1.93767e51i		−	1.22093i
$700$	6.36907e50	−	1.20775e50i	0.391121	−	0.0741673i
$701$	7.95968e48			0.00476400			0.00238200	−	0.999997i	$-0.499242\pi$
$701$	7.95968e48			0.00476400			0.00238200	+	0.999997i	$0.499242\pi$
$702$	1.33164e51	+	1.10286e51i	0.776818	+	0.643355i
$703$			7.48221e50i			0.425436i
$704$	−1.41841e51	+	8.93638e50i	−0.786128	+	0.495284i
$705$	1.81649e51			0.981361
$706$	4.62819e50	−	5.58829e50i	0.243740	−	0.294303i
$707$			4.21931e51i			2.16617i
$708$	−1.32718e50	−	6.99887e50i	−0.0664249	−	0.350291i
$709$	−2.55500e51			−1.24669			−0.623346	−	0.781946i	$-0.714227\pi$
$709$	−2.55500e51			−1.24669			−0.623346	+	0.781946i	$0.714227\pi$
$710$	8.93398e50	+	7.39906e50i	0.425006	+	0.351987i
$711$		−	2.94859e51i		−	1.36761i
$712$	2.34347e51	+	1.29334e51i	1.05979	+	0.584890i
$713$	2.05095e51			0.904365
$714$	7.10008e50	−	8.57298e50i	0.305278	−	0.368607i
$715$		−	2.39364e51i		−	1.00358i
$716$	−2.96156e51	+	5.61594e50i	−1.21084	+	0.229609i
$717$	2.85043e51			1.13649
$718$	4.67247e50	+	3.86971e50i	0.181680	+	0.150466i
$719$		−	4.33731e50i		−	0.164475i	−0.996613	−	0.0822375i	$-0.973793\pi$
$719$		−	4.33731e50i		−	0.164475i	0.996613	−	0.0822375i	$-0.0262066\pi$
$720$	−3.33039e51	+	1.31018e51i	−1.23171	+	0.484558i
$721$	−4.86234e51			−1.75392
$722$	−1.22605e51	+	1.48039e51i	−0.431358	+	0.520843i
$723$		−	2.46191e51i		−	0.844858i
$724$	8.46906e49	+	4.46615e50i	0.0283492	+	0.149499i
$725$	−1.15966e51			−0.378658
$726$	−5.24126e50	−	4.34077e50i	−0.166946	−	0.138264i
$727$		−	5.09920e50i		−	0.158447i	−0.996857	−	0.0792233i	$-0.974756\pi$
$727$		−	5.09920e50i		−	0.158447i	0.996857	−	0.0792233i	$-0.0252440\pi$
$728$	3.31868e51	−	6.01328e51i	1.00601	−	1.82283i
$729$	5.50530e51			1.62812
$730$	1.60828e51	−	1.94192e51i	0.464036	−	0.560299i
$731$			7.50376e50i			0.211235i
$732$	3.13324e51	−	5.94149e50i	0.860586	−	0.163191i
$733$	−3.32731e51			−0.891705			−0.445853	−	0.895106i	$-0.647099\pi$
$733$	−3.32731e51			−0.891705			−0.445853	+	0.895106i	$0.647099\pi$
$734$	6.55905e50	+	5.43216e50i	0.171519	+	0.142051i
$735$			9.97902e51i			2.54634i
$736$	−3.65191e51	−	1.19762e51i	−0.909325	−	0.298207i
$737$	−3.08636e51			−0.749948
$738$	1.43714e51	−	1.73527e51i	0.340788	−	0.411484i
$739$			3.62282e50i			0.0838391i	0.999121	+	0.0419195i	$0.0133473\pi$
$739$			3.62282e50i			0.0838391i	−0.999121	+	0.0419195i	$0.986653\pi$
$740$	−5.39015e50	−	2.84249e51i	−0.121739	−	0.641990i
$741$	5.05903e51			1.11517
$742$	4.77475e51	+	3.95441e51i	1.02726	+	0.850769i
$743$		−	3.12893e51i		−	0.657048i	−0.944496	−	0.328524i	$-0.893449\pi$
$743$		−	3.12893e51i		−	0.657048i	0.944496	−	0.328524i	$-0.106551\pi$
$744$	−6.40112e51	−	3.53273e51i	−1.31203	−	0.724097i
$745$	−5.91274e51			−1.18298
$746$	2.41402e51	−	2.91481e51i	0.471458	−	0.569261i
$747$		−	8.47253e51i		−	1.61526i
$748$	−8.78852e50	+	1.66655e50i	−0.163564	+	0.0310162i
$749$	4.30765e51			0.782650
$750$	−7.43891e51	−	6.16086e51i	−1.31949	−	1.09279i
$751$			7.90348e51i			1.36867i	0.729167	+	0.684336i	$0.239908\pi$
$751$			7.90348e51i			1.36867i	−0.729167	+	0.684336i	$0.760092\pi$
$752$	−1.53338e51	−	3.89775e51i	−0.259256	−	0.659011i
$753$	1.15681e52			1.90964
$754$	−7.83694e51	+	9.46270e51i	−1.26317	+	1.52521i
$755$			6.81562e51i			1.07266i
$756$	1.66652e51	+	8.78839e51i	0.256105	+	1.35057i
$757$	6.88744e51			1.03355			0.516776	−	0.856121i	$-0.327132\pi$
$757$	6.88744e51			1.03355			0.516776	+	0.856121i	$0.327132\pi$
$758$	−2.33850e51	−	1.93673e51i	−0.342682	−	0.283807i
$759$			9.85304e51i			1.41000i
$760$	−1.71911e51	+	3.11495e51i	−0.240248	+	0.435317i
$761$	5.29343e50			0.0722460			0.0361230	−	0.999347i	$-0.488499\pi$
$761$	5.29343e50			0.0722460			0.0361230	+	0.999347i	$0.488499\pi$
$762$	−1.55327e51	+	1.87549e51i	−0.207041	+	0.249991i
$763$		−	1.54089e52i		−	2.00600i
$764$	4.56745e51	−	8.66115e50i	0.580756	−	0.110127i
$765$	−1.90958e51			−0.237155
$766$	2.95805e51	+	2.44984e51i	0.358830	+	0.297180i
$767$		−	2.34529e51i		−	0.277894i
$768$	9.33491e51	+	1.00282e52i	1.08046	+	1.16070i
$769$	−1.09434e52			−1.23731			−0.618654	−	0.785663i	$-0.712322\pi$
$769$	−1.09434e52			−1.23731			−0.618654	+	0.785663i	$0.712322\pi$
$770$	7.89862e51	−	9.53717e51i	0.872405	−	1.05338i
$771$			1.46928e52i			1.58535i
$772$	6.91974e50	+	3.64912e51i	0.0729421	+	0.384660i
$773$	−3.74896e51			−0.386082			−0.193041	−	0.981191i	$-0.561835\pi$
$773$	−3.74896e51			−0.386082			−0.193041	+	0.981191i	$0.561835\pi$
$774$	−1.36683e52	−	1.13200e52i	−1.37523	−	1.13896i
$775$		−	2.27190e51i		−	0.223336i
$776$	1.31487e52	+	7.25667e51i	1.26291	+	0.696990i
$777$	−2.12828e52			−1.99733
$778$	−2.33205e51	+	2.81583e51i	−0.213848	+	0.258211i
$779$		−	2.23990e51i		−	0.200704i
$780$	−1.92192e52	+	3.64450e51i	−1.68280	+	0.319106i
$781$	−6.85738e51			−0.586731
$782$	−1.57936e51	−	1.30802e51i	−0.132057	−	0.109368i
$783$		−	1.60017e52i		−	1.30753i
$784$	2.14126e52	−	8.42373e51i	1.70993	−	0.672690i
$785$	1.15033e52			0.897774
$786$	−2.04420e50	+	2.46827e50i	−0.0155926	+	0.0188272i
$787$			8.94781e51i			0.667070i	0.942738	+	0.333535i	$0.108242\pi$
$787$			8.94781e51i			0.667070i	−0.942738	+	0.333535i	$0.891758\pi$
$788$	−2.58750e51	−	1.36452e52i	−0.188542	−	0.994277i
$789$	6.12310e51			0.436099
$790$	8.72936e51	+	7.22960e51i	0.607708	+	0.503300i
$791$		−	2.71635e52i		−	1.84846i
$792$	1.02225e52	−	1.85226e52i	0.679990	−	1.23211i
$793$	1.04993e52			0.682723
$794$	−1.16251e52	+	1.40367e52i	−0.738973	+	0.892271i
$795$		−	1.76574e52i		−	1.09728i
$796$	2.56676e52	−	4.86728e51i	1.55937	−	0.295700i
$797$	1.26138e52			0.749197			0.374598	−	0.927187i	$-0.377781\pi$
$797$	1.26138e52			0.749197			0.374598	+	0.927187i	$0.377781\pi$
$798$	2.01571e52	+	1.66940e52i	1.17051	+	0.969409i
$799$		−	2.23490e51i		−	0.126887i
$800$	−1.32664e51	+	4.04533e51i	−0.0736433	+	0.224561i
$801$	−3.37788e52			−1.83341
$802$	−1.21585e52	+	1.46808e52i	−0.645272	+	0.779133i
$803$			1.49054e52i			0.773508i
$804$	4.69921e51	+	2.47812e52i	0.238460	+	1.25752i
$805$	2.83888e52			1.40871
$806$	−1.85384e52	−	1.53534e52i	−0.899584	−	0.745029i
$807$		−	4.41047e51i		−	0.209296i
$808$	−2.42601e52	−	1.33890e52i	−1.12587	−	0.621359i
$809$	−3.67925e52			−1.66988			−0.834941	−	0.550339i	$-0.814498\pi$
$809$	−3.67925e52			−1.66988			−0.834941	+	0.550339i	$0.814498\pi$
$810$	−2.76954e51	+	3.34408e51i	−0.122936	+	0.148438i
$811$		−	6.28854e50i		−	0.0273007i	−0.999907	−	0.0136504i	$-0.995655\pi$
$811$		−	6.28854e50i		−	0.0273007i	0.999907	−	0.0136504i	$-0.00434518\pi$
$812$	−6.24507e52	+	1.18424e52i	−2.65173	+	0.502840i
$813$	1.72972e52			0.718366
$814$	1.31720e52	+	1.09089e52i	0.535071	+	0.443142i
$815$		−	1.09019e52i		−	0.433176i
$816$	2.67624e51	+	6.80282e51i	0.104016	+	0.264403i
$817$	−1.76431e52			−0.670777
$818$	1.58562e52	−	1.91455e52i	0.589712	−	0.712046i
$819$			8.66754e52i			3.15345i
$820$	1.61361e51	+	8.50939e51i	0.0574315	+	0.302865i
$821$	5.00881e52			1.74404			0.872022	−	0.489466i	$-0.162808\pi$
$821$	5.00881e52			1.74404			0.872022	+	0.489466i	$0.162808\pi$
$822$	−2.91890e52	−	2.41741e52i	−0.994320	−	0.823488i
$823$		−	1.32020e52i		−	0.439989i	−0.975501	−	0.219995i	$-0.929396\pi$
$823$		−	1.32020e52i		−	0.439989i	0.975501	−	0.219995i	$-0.0706040\pi$
$824$	1.54295e52	−	2.79574e52i	0.503108	−	0.911606i
$825$	1.09145e52			0.348203
$826$	7.73906e51	−	9.34451e51i	0.241572	−	0.291686i
$827$			2.14975e52i			0.656580i	0.944577	+	0.328290i	$0.106472\pi$
$827$			2.14975e52i			0.656580i	−0.944577	+	0.328290i	$0.893528\pi$
$828$	4.76517e52	−	9.03607e51i	1.42407	−	0.270043i
$829$	−5.41400e52			−1.58320			−0.791602	−	0.611038i	$-0.790752\pi$
$829$	−5.41400e52			−1.58320			−0.791602	+	0.611038i	$0.790752\pi$
$830$	2.50832e52	+	2.07737e52i	0.717756	+	0.594440i
$831$			8.17953e52i			2.29039i
$832$	2.40440e52	+	3.81633e52i	0.658851	+	1.04575i
$833$	1.22776e52			0.329233
$834$	3.95942e52	−	4.78079e52i	1.03906	−	1.25462i
$835$		−	8.19693e51i		−	0.210521i
$836$	−3.91844e51	−	2.06639e52i	−0.0984919	−	0.519397i
$837$	3.13489e52			0.771194
$838$	−5.01680e52	−	4.15488e52i	−1.20791	−	1.00038i
$839$		−	6.20096e52i		−	1.46131i	−0.682744	−	0.730657i	$-0.739214\pi$
$839$		−	6.20096e52i		−	1.46131i	0.682744	−	0.730657i	$-0.260786\pi$
$840$	−8.86029e52	−	4.88992e52i	−2.04372	−	1.12791i
$841$	6.94162e52			1.56723
$842$	−1.13994e52	+	1.37642e52i	−0.251921	+	0.304182i
$843$		−	8.86555e52i		−	1.91783i
$844$	−7.02287e52	+	1.33173e52i	−1.48714	+	0.282002i
$845$	−2.22452e52			−0.461123
$846$	4.07092e52	+	3.37151e52i	0.826087	+	0.684160i
$847$		−	1.15911e52i		−	0.230263i
$848$	−3.78885e52	+	1.49054e52i	−0.736855	+	0.289880i
$849$	−8.32711e52			−1.58546
$850$	−1.44893e51	+	1.74951e51i	−0.0270089	+	0.0326118i
$851$			3.92083e52i			0.715560i
$852$	1.04409e52	+	5.50599e52i	0.186562	+	0.983835i
$853$	3.49825e52			0.612023			0.306012	−	0.952028i	$-0.401005\pi$
$853$	3.49825e52			0.612023			0.306012	+	0.952028i	$0.401005\pi$
$854$	4.18333e52	+	3.46461e52i	0.716607	+	0.593489i
$855$		−	4.48988e52i		−	0.753087i
$856$	−1.36693e52	+	2.47680e52i	−0.224501	+	0.406784i
$857$	3.05787e52			0.491772			0.245886	−	0.969299i	$-0.420921\pi$
$857$	3.05787e52			0.491772			0.245886	+	0.969299i	$0.420921\pi$
$858$	7.37597e52	−	8.90610e52i	1.16158	−	1.40254i
$859$		−	3.64312e52i		−	0.561819i	−0.959734	−	0.280910i	$-0.909364\pi$
$859$		−	3.64312e52i		−	0.561819i	0.959734	−	0.280910i	$-0.0906361\pi$
$860$	6.70261e52	−	1.27100e52i	1.01221	−	0.191943i
$861$	6.37128e52			0.942259
$862$	−2.88180e52	−	2.38668e52i	−0.417381	−	0.345672i
$863$			1.31039e53i			1.85868i	0.369222	+	0.929341i	$0.379624\pi$
$863$			1.31039e53i			1.85868i	−0.369222	+	0.929341i	$0.620376\pi$
$864$	−5.58196e52	−	1.83057e52i	−0.775425	−	0.254296i
$865$	−4.85977e52			−0.661190
$866$	−8.81397e52	+	1.06424e53i	−1.17449	+	1.41814i
$867$		−	1.17600e53i		−	1.53485i
$868$	−2.32004e52	−	1.22347e53i	−0.296579	−	1.56401i
$869$	−6.70032e52			−0.838957
$870$	1.39429e53	+	1.15474e53i	1.71004	+	1.41624i
$871$			8.30407e52i			0.997618i
$872$	8.85980e52	+	4.88965e52i	1.04262	+	0.575415i
$873$	−1.89526e53			−2.18480
$874$	3.07546e52	−	3.71345e52i	0.347299	−	0.419346i
$875$		−	1.64513e53i		−	1.81993i
$876$	1.19680e53	−	2.26946e52i	1.29702	−	0.245951i
$877$	1.61691e53			1.71669			0.858347	−	0.513070i	$-0.171492\pi$
$877$	1.61691e53			1.71669			0.858347	+	0.513070i	$0.171492\pi$
$878$	1.51914e52	+	1.25814e52i	0.158014	+	0.130866i
$879$			1.17090e53i			1.19321i
$880$	2.97723e52	+	7.56792e52i	0.297252	+	0.755594i
$881$	−1.63460e53			−1.59899			−0.799494	−	0.600674i	$-0.794899\pi$
$881$	−1.63460e53			−1.59899			−0.799494	+	0.600674i	$0.794899\pi$
$882$	−1.85216e53	+	2.23639e53i	−1.77519	+	2.14345i
$883$			5.44273e52i			0.511122i	0.966793	+	0.255561i	$0.0822601\pi$
$883$			5.44273e52i			0.511122i	−0.966793	+	0.255561i	$0.917740\pi$
$884$	4.48397e51	+	2.36462e52i	0.0412593	+	0.217581i
$885$	−3.45567e52			−0.311569
$886$	2.14522e52	+	1.77666e52i	0.189524	+	0.156963i
$887$		−	9.24934e52i		−	0.800729i	−0.916356	−	0.400365i	$-0.868883\pi$
$887$		−	9.24934e52i		−	0.800729i	0.916356	−	0.400365i	$-0.131117\pi$
$888$	6.75357e52	−	1.22371e53i	0.572928	−	1.03812i
$889$	−4.14767e52			−0.344804
$890$	8.28219e52	−	1.00003e53i	0.674722	−	0.814692i
$891$		−	2.56679e52i		−	0.204923i
$892$	−1.57200e53	+	2.98094e52i	−1.22994	+	0.233231i
$893$	5.25477e52			0.402928
$894$	−2.19997e53	−	1.82200e53i	−1.65326	−	1.36922i
$895$			1.46227e53i			1.07699i
$896$	−3.01323e52	+	2.31398e53i	−0.217514	+	1.67038i
$897$	2.65103e53			1.87565
$898$	1.38804e53	−	1.67598e53i	0.962557	−	1.16224i
$899$			2.22767e53i			1.51417i
$900$	−1.00095e52	−	5.27852e52i	−0.0666880	−	0.351679i
$901$	−2.17246e52			−0.141875
$902$	−3.94321e52	−	3.26574e52i	−0.252425	−	0.209056i
$903$		−	5.01848e53i		−	3.14915i
$904$	1.56184e53	+	8.61969e52i	0.960740	+	0.530225i
$905$	2.20515e52			0.132973
$906$	−2.10022e53	+	2.53591e53i	−1.24153	+	1.49909i
$907$			1.37123e52i			0.0794658i	0.999210	+	0.0397329i	$0.0126507\pi$
$907$			1.37123e52i			0.0794658i	−0.999210	+	0.0397329i	$0.987349\pi$
$908$	1.13517e53	−	2.15259e52i	0.644933	−	0.122297i
$909$	3.49686e53			1.94773
$910$	−2.56605e53	−	2.12518e53i	−1.40126	−	1.16052i
$911$			4.24237e52i			0.227132i	0.993530	+	0.113566i	$0.0362273\pi$
$911$			4.24237e52i			0.227132i	−0.993530	+	0.113566i	$0.963773\pi$
$912$	−1.59950e53	+	6.29246e52i	−0.839610	+	0.330304i
$913$	−1.92529e53			−0.990880
$914$	2.13817e53	−	2.58173e53i	1.07897	−	1.30280i
$915$		−	1.54703e53i		−	0.765454i
$916$	−6.43988e52	−	3.39607e53i	−0.312435	−	1.64762i
$917$	−5.45861e51			−0.0259677
$918$	−2.41407e52	−	1.99931e52i	−0.112611	−	0.0932637i
$919$			1.89470e53i			0.866684i	0.901230	+	0.433342i	$0.142666\pi$
$919$			1.89470e53i			0.866684i	−0.901230	+	0.433342i	$0.857334\pi$
$920$	−9.00850e52	+	1.63229e53i	−0.404084	+	0.732180i
$921$	−1.38523e53			−0.609325
$922$	7.90650e52	−	9.54668e52i	0.341057	−	0.411809i
$923$			1.84503e53i			0.780499i
$924$	5.87773e53	−	1.11458e53i	2.43845	−	0.462398i
$925$	4.34322e52			0.176710
$926$	−4.10343e52	−	3.39843e52i	−0.163738	−	0.135607i
$927$			4.02978e53i			1.57705i
$928$	1.30081e53	−	3.96657e53i	0.499287	−	1.52248i
$929$	9.19181e52			0.346034			0.173017	−	0.984919i	$-0.444648\pi$
$929$	9.19181e52			0.346034			0.173017	+	0.984919i	$0.444648\pi$
$930$	−2.26225e53	+	2.73155e53i	−0.835310	+	1.00859i
$931$			2.88675e53i			1.04548i
$932$	4.03805e52	+	2.12946e53i	0.143445	+	0.756456i
$933$	−2.70559e53			−0.942739
$934$	7.42025e52	+	6.14540e52i	0.253615	+	0.210042i
$935$			4.33931e52i			0.145483i
$936$	−4.98364e53	−	2.75043e53i	−1.63901	−	0.904557i
$937$	4.07988e53			1.31624			0.658119	−	0.752914i	$-0.271352\pi$
$937$	4.07988e53			1.31624			0.658119	+	0.752914i	$0.271352\pi$
$938$	−2.74021e53	+	3.30866e53i	−0.867226	+	1.04713i
$939$		−	2.19627e53i		−	0.681877i
$940$	−1.99629e53	+	3.78551e52i	−0.608025	+	0.115298i
$941$	−6.19370e53			−1.85070			−0.925352	−	0.379109i	$-0.876231\pi$
$941$	−6.19370e53			−1.85070			−0.925352	+	0.379109i	$0.876231\pi$
$942$	4.28005e53	+	3.54471e53i	1.25468	+	1.03912i
$943$		−	1.17375e53i		−	0.337572i
$944$	2.91709e52	+	7.41504e52i	0.0823102	+	0.209227i
$945$	4.33925e53			1.20127
$946$	−2.57233e53	+	3.10596e53i	−0.698693	+	0.843636i
$947$		−	1.10892e53i		−	0.295529i	−0.989023	−	0.147765i	$-0.952792\pi$
$947$		−	1.10892e53i		−	0.295529i	0.989023	−	0.147765i	$-0.0472078\pi$
$948$	1.02017e53	+	5.37988e53i	0.266762	+	1.40677i
$949$	4.01042e53			1.02896
$950$	−4.11350e52	−	3.40677e52i	−0.103559	−	0.0857666i
$951$		−	9.03941e52i		−	0.223301i
$952$	−6.01627e52	+	1.09012e53i	−0.145835	+	0.264246i
$953$	−1.03424e53			−0.246008			−0.123004	−	0.992406i	$-0.539253\pi$
$953$	−1.03424e53			−0.246008			−0.123004	+	0.992406i	$0.539253\pi$
$954$	3.27731e53	−	3.95718e53i	0.764975	−	0.923667i
$955$		−	2.25517e53i		−	0.516557i
$956$	−3.13257e53	+	5.94022e52i	−0.704140	+	0.133524i
$957$	−1.07020e54			−2.36075
$958$	−3.39373e53	−	2.81066e53i	−0.734679	−	0.608456i
$959$		−	6.45519e53i		−	1.37143i
$960$	5.62320e53	−	3.54278e53i	1.17247	−	0.738689i
$961$	5.22532e52			0.106928
$962$	2.93513e53	−	3.54402e53i	0.589489	−	0.711778i
$963$		−	3.57006e53i		−	0.703725i
$964$	5.13056e52	+	2.70560e53i	0.0992608	+	0.523451i
$965$	1.80174e53			0.342138
$966$	1.05627e54	+	8.74797e53i	1.96874	+	1.63049i
$967$		−	3.72630e53i		−	0.681713i	−0.940115	−	0.340857i	$-0.889283\pi$
$967$		−	3.72630e53i		−	0.681713i	0.940115	−	0.340857i	$-0.110717\pi$
$968$	6.66464e52	+	3.67816e52i	0.119680	+	0.0660503i
$969$	−9.17126e52			−0.161659
$970$	4.64696e53	−	5.61096e53i	0.804040	−	0.970836i
$971$			5.81972e53i			0.988453i	0.869333	+	0.494227i	$0.164549\pi$
$971$			5.81972e53i			0.988453i	−0.869333	+	0.494227i	$0.835451\pi$
$972$	−6.86981e53	+	1.30270e53i	−1.14539	+	0.217197i
$973$	1.05728e54			1.73045
$974$	4.96700e53	+	4.11363e53i	0.798055	+	0.660944i
$975$		−	2.93663e53i		−	0.463197i
$976$	−3.31955e53	+	1.30592e53i	−0.514023	+	0.202217i
$977$	−1.44555e53			−0.219752			−0.109876	−	0.993945i	$-0.535045\pi$
$977$	−1.44555e53			−0.219752			−0.109876	+	0.993945i	$0.535045\pi$
$978$	3.35940e53	−	4.05630e53i	0.501375	−	0.605384i
$979$			7.67585e53i			1.12470i
$980$	−2.07960e53	−	1.09667e54i	−0.299164	−	1.57764i
$981$	−1.27705e54			−1.80371
$982$	−6.78348e53	−	5.61803e53i	−0.940688	−	0.779071i
$983$		−	1.26010e54i		−	1.71571i	−0.513894	−	0.857854i	$-0.671798\pi$
$983$		−	1.26010e54i		−	1.71571i	0.513894	−	0.857854i	$-0.328202\pi$
$984$	−2.02177e53	+	3.66335e53i	−0.270284	+	0.489741i
$985$	−6.73728e53			−0.884366
$986$	1.42072e53	−	1.71545e53i	0.183115	−	0.221102i
$987$			1.49469e54i			1.89166i
$988$	−5.55977e53	+	1.05429e53i	−0.690927	+	0.131019i
$989$	−9.24534e53			−1.12821
$990$	−7.90415e53	−	6.54617e53i	−0.947157	−	0.784429i
$991$			7.56311e53i			0.889968i	0.895538	+	0.444984i	$0.146791\pi$
$991$			7.56311e53i			0.889968i	−0.895538	+	0.444984i	$0.853209\pi$
$992$	7.77092e53	+	2.54842e53i	0.897971	+	0.294484i
$993$	8.11174e53			0.920508
$994$	−6.08829e53	+	7.35129e53i	−0.678485	+	0.819236i
$995$		−	1.26733e54i		−	1.38699i
$996$	2.93139e53	+	1.54587e54i	0.315069	+	1.66151i
$997$	4.75844e53			0.502287			0.251143	−	0.967950i	$-0.419193\pi$
$997$	4.75844e53			0.502287			0.251143	+	0.967950i	$0.419193\pi$
$998$	2.84209e53	+	2.35380e53i	0.294638	+	0.244017i
$999$			5.99301e53i			0.610192i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.37.b.b.3.6	yes	16
4.3	odd	2	inner	4.37.b.b.3.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.37.b.b.3.5	✓	16	4.3	odd	2	inner
4.37.b.b.3.6	yes	16	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:	\( k \)	\(=\)	\( 37 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-167207. + 201894. i) q^{2} +6.14354e8i q^{3} +(-1.28029e10 - 6.75163e10i) q^{4} -3.33360e12 q^{5} +(-1.24034e14 - 1.02724e14i) q^{6} -2.74304e15i q^{7} +(1.57719e16 + 8.70438e15i) q^{8} -2.27336e17 q^{9} +O(q^{10})\)	\(q+(-167207. + 201894. i) q^{2} +6.14354e8i q^{3} +(-1.28029e10 - 6.75163e10i) q^{4} -3.33360e12 q^{5} +(-1.24034e14 - 1.02724e14i) q^{6} -2.74304e15i q^{7} +(1.57719e16 + 8.70438e15i) q^{8} -2.27336e17 q^{9} +(5.57402e17 - 6.73034e17i) q^{10} +5.16595e18i q^{11} +(4.14789e19 - 7.86554e18i) q^{12} +1.38994e20 q^{13} +(5.53804e20 + 4.58656e20i) q^{14} -2.04801e21i q^{15} +(-4.39454e21 + 1.72882e21i) q^{16} -2.51975e21 q^{17} +(3.80122e22 - 4.58978e22i) q^{18} -5.92452e22i q^{19} +(4.26799e22 + 2.25072e23i) q^{20} +1.68520e24 q^{21} +(-1.04297e24 - 8.63784e23i) q^{22} -3.10457e24i q^{23} +(-5.34757e24 + 9.68952e24i) q^{24} -3.43902e24 q^{25} +(-2.32408e25 + 2.80620e25i) q^{26} -4.74535e25i q^{27} +(-1.85200e26 + 3.51190e25i) q^{28} +3.37207e26 q^{29} +(4.13481e26 + 3.42442e26i) q^{30} +6.60623e26i q^{31} +(3.85761e26 - 1.17630e27i) q^{32} -3.17372e27 q^{33} +(4.21320e26 - 5.08722e26i) q^{34} +9.14420e27i q^{35} +(2.91057e27 + 1.53489e28i) q^{36} -1.26292e28 q^{37} +(1.19613e28 + 9.90623e27i) q^{38} +8.53913e28i q^{39} +(-5.25772e28 - 2.90169e28i) q^{40} +3.78073e28 q^{41} +(-2.81777e29 + 3.40231e29i) q^{42} -2.97798e29i q^{43} +(3.48786e29 - 6.61394e28i) q^{44} +7.57847e29 q^{45} +(6.26794e29 + 5.19106e29i) q^{46} +8.86953e29i q^{47} +(-1.06210e30 - 2.69980e30i) q^{48} -4.87254e30 q^{49} +(5.75029e29 - 6.94318e29i) q^{50} -1.54802e30i q^{51} +(-1.77953e30 - 9.38434e30i) q^{52} +8.62173e30 q^{53} +(9.58058e30 + 7.93457e30i) q^{54} -1.72212e31i q^{55} +(2.38765e31 - 4.32629e31i) q^{56} +3.63975e31 q^{57} +(-5.63834e31 + 6.80801e31i) q^{58} -1.68733e31i q^{59} +(-1.38274e32 + 2.62206e31i) q^{60} +7.55382e31 q^{61} +(-1.33376e32 - 1.10461e32i) q^{62} +6.23592e32i q^{63} +(1.72986e32 + 2.74569e32i) q^{64} -4.63350e32 q^{65} +(5.30669e32 - 6.40755e32i) q^{66} +5.97442e32i q^{67} +(3.22602e31 + 1.70124e32i) q^{68} +1.90730e33 q^{69} +(-1.84616e33 - 1.52898e33i) q^{70} +1.32742e33i q^{71} +(-3.58552e33 - 1.97882e33i) q^{72} +2.88532e33 q^{73} +(2.11170e33 - 2.54977e33i) q^{74} -2.11278e33i q^{75} +(-4.00002e33 + 7.58513e32i) q^{76} +1.41704e34 q^{77} +(-1.72400e34 - 1.42780e34i) q^{78} +1.29702e34i q^{79} +(1.46496e34 - 5.76318e33i) q^{80} -4.96866e33 q^{81} +(-6.32166e33 + 7.63308e33i) q^{82} +3.72688e34i q^{83} +(-2.15755e34 - 1.13778e35i) q^{84} +8.39984e33 q^{85} +(6.01236e34 + 4.97940e34i) q^{86} +2.07164e35i q^{87} +(-4.49664e34 + 8.14768e34i) q^{88} +1.48586e35 q^{89} +(-1.26718e35 + 1.53005e35i) q^{90} -3.81265e35i q^{91} +(-2.09609e35 + 3.97476e34i) q^{92} -4.05856e35 q^{93} +(-1.79071e35 - 1.48305e35i) q^{94} +1.97500e35i q^{95} +(7.22665e35 + 2.36993e35i) q^{96} +8.33681e35 q^{97} +(8.14724e35 - 9.83737e35i) q^{98} -1.17441e36i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 177228 q^{2} - 5610707696 q^{4} + 5816089539360 q^{5} - 217628996575488 q^{6} + 11\!\cdots\!28 q^{8}+ \cdots - 93\!\cdots\!68 q^{9}+O(q^{10}) \) 16 * q + 177228 * q^2 - 5610707696 * q^4 + 5816089539360 * q^5 - 217628996575488 * q^6 + 11897560228206528 * q^8 - 935184460817545968 * q^9	\( 16 q + 177228 q^{2} - 5610707696 q^{4} + 5816089539360 q^{5} - 217628996575488 q^{6} + 11\!\cdots\!28 q^{8}+ \cdots + 10\!\cdots\!28 q^{98}+O(q^{100}) \) 16 * q + 177228 * q^2 - 5610707696 * q^4 + 5816089539360 * q^5 - 217628996575488 * q^6 + 11897560228206528 * q^8 - 935184460817545968 * q^9 - 2378142919315561000 * q^10 - 42882825786868930560 * q^12 + 194612014165659174176 * q^13 + 360192888461659120128 * q^14 - 22854023522524990832384 * q^16 + 41803218917907805318176 * q^17 + 138204474036544564333068 * q^18 + 104592026972614096023840 * q^20 - 175281296641396774711296 * q^21 - 4320007363229839528400640 * q^22 + 5118364442017682383085568 * q^24 + 61061610541832160307690800 * q^25 - 70158486911796111631798440 * q^26 - 303534200373547502486016000 * q^28 - 95320519344473743554877152 * q^29 + 361206724962468787334008320 * q^30 + 4662427702586163916855016448 * q^32 - 877278707167997370072668160 * q^33 - 9018225886246079564307746920 * q^34 - 927455191590908629268766192 * q^36 - 30841755082751179145922114784 * q^37 + 78752216997100984306444174080 * q^38 - 138122339194153338361474460800 * q^40 + 99165040763128472781035553312 * q^41 - 193406458925326074258433843200 * q^42 + 303084904999663560614745692160 * q^44 + 1511424637230487714612565241120 * q^45 - 919681205391808405630032112128 * q^46 - 1511312501851283767715389931520 * q^48 - 11342315683204385026834539108848 * q^49 + 11057816114707215621338245966500 * q^50 + 16094442403868561017575461524256 * q^52 + 20911545776251998404629518049056 * q^53 - 42689634574575573966970327785984 * q^54 - 18346492780981997297263940026368 * q^56 - 17591710635767034592583231047680 * q^57 + 33019206317228013320629044602456 * q^58 - 69704584574466315130190074982400 * q^60 + 216576725773383276684585233875232 * q^61 + 406820870675021165265665434183680 * q^62 - 266111502464782094817164314013696 * q^64 - 2065823886943449026422930314993600 * q^65 - 816784109200805225218136599695360 * q^66 + 3502994508232801473127246422490656 * q^68 + 3923547517779842564469076002041856 * q^69 + 312094823977274793710809307489280 * q^70 - 1875458138040165128132392402132032 * q^72 - 13529699358917711874787838251408864 * q^73 + 7683713356825244783786618034273240 * q^74 - 15736875982808342938482824299100160 * q^76 + 22639774155764461736245527294259200 * q^77 - 18389491597233550087389536189698560 * q^78 + 67235988583903584940074904608207360 * q^80 - 40716877106976112078739817594850800 * q^81 + 43227843112149006015980010857549336 * q^82 - 37119022564017857733030089777086464 * q^84 - 206886985961236391219562146270052800 * q^85 + 102108696026625816655543232864792832 * q^86 + 39749581676781586144951142033940480 * q^88 + 461506837768868190077604450557625888 * q^89 - 361659211507857840778210819426233000 * q^90 - 17511543929609412714530045318983680 * q^92 - 231978818535002459544922699145134080 * q^93 - 696830931593880576023589572144120832 * q^94 + 1050073689946737522972596709346639872 * q^96 + 451372245708940284684446048339288096 * q^97 + 1035415270688230597220229005750452428 * q^98

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