LMFDB - Embedded newform 4.37.b.b.3.12

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			3.12
Root			$-2.95956e7i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.37.b.b.3.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(178949. + 191564. i) q^{2} -4.73530e8i q^{3} +(-4.67423e9 + 6.85603e10i) q^{4} +4.97998e11 q^{5} +(9.07113e13 - 8.47375e13i) q^{6} -9.39063e14i q^{7} +(-1.39702e16 + 1.13734e16i) q^{8} -7.41357e16 q^{9} +O(q^{10})$	\(q+(178949. + 191564. i) q^{2} -4.73530e8i q^{3} +(-4.67423e9 + 6.85603e10i) q^{4} +4.97998e11 q^{5} +(9.07113e13 - 8.47375e13i) q^{6} -9.39063e14i q^{7} +(-1.39702e16 + 1.13734e16i) q^{8} -7.41357e16 q^{9} +(8.91161e16 + 9.53986e16i) q^{10} -1.64809e18i q^{11} +(3.24653e19 + 2.21338e18i) q^{12} +1.14530e20 q^{13} +(1.79891e20 - 1.68044e20i) q^{14} -2.35817e20i q^{15} +(-4.67867e21 - 6.40933e20i) q^{16} -2.29593e22 q^{17} +(-1.32665e22 - 1.42017e22i) q^{18} -1.20463e23i q^{19} +(-2.32776e21 + 3.41429e22i) q^{20} -4.44674e23 q^{21} +(3.15714e23 - 2.94923e23i) q^{22} -2.81335e24i q^{23} +(5.38563e24 + 6.61528e24i) q^{24} -1.43039e25 q^{25} +(2.04950e25 + 2.19398e25i) q^{26} -3.59688e25i q^{27} +(6.43825e25 + 4.38939e24i) q^{28} -1.31366e25 q^{29} +(4.51741e25 - 4.21991e25i) q^{30} -7.15362e26i q^{31} +(-7.14462e26 - 1.01096e27i) q^{32} -7.80418e26 q^{33} +(-4.10853e27 - 4.39817e27i) q^{34} -4.67651e26i q^{35} +(3.46527e26 - 5.08277e27i) q^{36} +2.59863e28 q^{37} +(2.30764e28 - 2.15567e28i) q^{38} -5.42333e28i q^{39} +(-6.95711e27 + 5.66391e27i) q^{40} -1.71112e29 q^{41} +(-7.95738e28 - 8.51837e28i) q^{42} -4.11718e29i q^{43} +(1.12993e29 + 7.70353e27i) q^{44} -3.69194e28 q^{45} +(5.38937e29 - 5.03445e29i) q^{46} +8.93346e29i q^{47} +(-3.03501e29 + 2.21549e30i) q^{48} +1.76989e30 q^{49} +(-2.55967e30 - 2.74012e30i) q^{50} +1.08719e31i q^{51} +(-5.35338e29 + 7.85220e30i) q^{52} +3.45056e30 q^{53} +(6.89034e30 - 6.43657e30i) q^{54} -8.20743e29i q^{55} +(1.06803e31 + 1.31189e31i) q^{56} -5.70428e31 q^{57} +(-2.35078e30 - 2.51651e30i) q^{58} -2.87222e31i q^{59} +(1.61677e31 + 1.10226e30i) q^{60} -1.57408e31 q^{61} +(1.37038e32 - 1.28013e32i) q^{62} +6.96181e31i q^{63} +(6.58117e31 - 3.17775e32i) q^{64} +5.70356e31 q^{65} +(-1.39655e32 - 1.49500e32i) q^{66} +2.63364e32i q^{67} +(1.07317e32 - 1.57409e33i) q^{68} -1.33220e33 q^{69} +(8.95853e31 - 8.36856e31i) q^{70} +2.24092e33i q^{71} +(1.03569e33 - 8.43172e32i) q^{72} -4.63793e33 q^{73} +(4.65022e33 + 4.97805e33i) q^{74} +6.77333e33i q^{75} +(8.25898e33 + 5.63071e32i) q^{76} -1.54766e33 q^{77} +(1.03892e34 - 9.70497e33i) q^{78} +2.60170e34i q^{79} +(-2.32997e33 - 3.19183e32i) q^{80} -2.81597e34 q^{81} +(-3.06203e34 - 3.27790e34i) q^{82} -9.58149e32i q^{83} +(2.07851e33 - 3.04870e34i) q^{84} -1.14337e34 q^{85} +(7.88705e34 - 7.36765e34i) q^{86} +6.22058e33i q^{87} +(1.87443e34 + 2.30240e34i) q^{88} +3.91670e34 q^{89} +(-6.60668e33 - 7.07244e33i) q^{90} -1.07551e35i q^{91} +(1.92884e35 + 1.31502e34i) q^{92} -3.38745e35 q^{93} +(-1.71133e35 + 1.59863e35i) q^{94} -5.99903e34i q^{95} +(-4.78719e35 + 3.38319e35i) q^{96} +5.91294e35 q^{97} +(3.16720e35 + 3.39048e35i) q^{98} +1.22182e35i 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 $

$2$	178949.	+	191564.i	0.682635	+	0.730760i
$2$	178949.	+	191564.i	0.682635	+	0.730760i
$3$		−	4.73530e8i		−	1.22226i	−0.791529	−	0.611131i	$-0.790715\pi$
$3$		−	4.73530e8i		−	1.22226i	0.791529	−	0.611131i	$-0.209285\pi$
$4$	−4.67423e9	+	6.85603e10i	−0.0680190	+	0.997684i
$5$	4.97998e11			0.130547			0.0652736	−	0.997867i	$-0.479208\pi$
$5$	4.97998e11			0.130547			0.0652736	+	0.997867i	$0.479208\pi$
$6$	9.07113e13	−	8.47375e13i	0.893180	−	0.834359i
$7$		−	9.39063e14i		−	0.576673i	−0.957529	−	0.288337i	$-0.906898\pi$
$7$		−	9.39063e14i		−	0.576673i	0.957529	−	0.288337i	$-0.0931022\pi$
$8$	−1.39702e16	+	1.13734e16i	−0.775499	+	0.631349i
$9$	−7.41357e16			−0.493926
$10$	8.91161e16	+	9.53986e16i	0.0891161	+	0.0953986i
$11$		−	1.64809e18i		−	0.296423i	−0.988956	−	0.148211i	$-0.952648\pi$
$11$		−	1.64809e18i		−	0.296423i	0.988956	−	0.148211i	$-0.0473516\pi$
$12$	3.24653e19	+	2.21338e18i	1.21943	+	0.0831370i
$13$	1.14530e20			1.01845			0.509223	−	0.860634i	$-0.329933\pi$
$13$	1.14530e20			1.01845			0.509223	+	0.860634i	$0.329933\pi$
$14$	1.79891e20	−	1.68044e20i	0.421410	−	0.393657i
$15$		−	2.35817e20i		−	0.159563i
$16$	−4.67867e21	−	6.40933e20i	−0.990747	−	0.135723i
$17$	−2.29593e22			−1.63259			−0.816295	−	0.577635i	$-0.803976\pi$
$17$	−2.29593e22			−1.63259			−0.816295	+	0.577635i	$0.803976\pi$
$18$	−1.32665e22	−	1.42017e22i	−0.337171	−	0.360941i
$19$		−	1.20463e23i		−	1.15688i	−0.815725	−	0.578440i	$-0.803662\pi$
$19$		−	1.20463e23i		−	1.15688i	0.815725	−	0.578440i	$-0.196338\pi$
$20$	−2.32776e21	+	3.41429e22i	−0.00887968	+	0.130245i
$21$	−4.44674e23			−0.704847
$22$	3.15714e23	−	2.94923e23i	0.216614	−	0.202349i
$23$		−	2.81335e24i		−	0.867206i	−0.901104	−	0.433603i	$-0.857242\pi$
$23$		−	2.81335e24i		−	0.867206i	0.901104	−	0.433603i	$-0.142758\pi$
$24$	5.38563e24	+	6.61528e24i	0.771674	+	0.947864i
$25$	−1.43039e25			−0.982957
$26$	2.04950e25	+	2.19398e25i	0.695227	+	0.744240i
$27$		−	3.59688e25i		−	0.618555i
$28$	6.43825e25	+	4.38939e24i	0.575338	+	0.0392247i
$29$	−1.31366e25			−0.0624194			−0.0312097	−	0.999513i	$-0.509936\pi$
$29$	−1.31366e25			−0.0624194			−0.0312097	+	0.999513i	$0.509936\pi$
$30$	4.51741e25	−	4.21991e25i	0.116602	−	0.108923i
$31$		−	7.15362e26i		−	1.02333i	−0.859185	−	0.511664i	$-0.829029\pi$
$31$		−	7.15362e26i		−	1.02333i	0.859185	−	0.511664i	$-0.170971\pi$
$32$	−7.14462e26	−	1.01096e27i	−0.577138	−	0.816647i
$33$	−7.80418e26			−0.362306
$34$	−4.10853e27	−	4.39817e27i	−1.11446	−	1.19303i
$35$		−	4.67651e26i		−	0.0752831i
$36$	3.46527e26	−	5.08277e27i	0.0335964	−	0.492782i
$37$	2.59863e28			1.53856			0.769279	−	0.638913i	$-0.220616\pi$
$37$	2.59863e28			1.53856			0.769279	+	0.638913i	$0.220616\pi$
$38$	2.30764e28	−	2.15567e28i	0.845402	−	0.789727i
$39$		−	5.42333e28i		−	1.24481i
$40$	−6.95711e27	+	5.66391e27i	−0.101239	+	0.0824208i
$41$	−1.71112e29			−1.59651			−0.798256	−	0.602318i	$-0.794244\pi$
$41$	−1.71112e29			−1.59651			−0.798256	+	0.602318i	$0.794244\pi$
$42$	−7.95738e28	−	8.51837e28i	−0.481153	−	0.515073i
$43$		−	4.11718e29i		−	1.62993i	−0.579513	−	0.814963i	$-0.696757\pi$
$43$		−	4.11718e29i		−	1.62993i	0.579513	−	0.814963i	$-0.303243\pi$
$44$	1.12993e29	+	7.70353e27i	0.295736	+	0.0201624i
$45$	−3.69194e28			−0.0644807
$46$	5.38937e29	−	5.03445e29i	0.633719	−	0.591985i
$47$			8.93346e29i			0.713277i	0.934242	+	0.356639i	$0.116077\pi$
$47$			8.93346e29i			0.713277i	−0.934242	+	0.356639i	$0.883923\pi$
$48$	−3.03501e29	+	2.21549e30i	−0.165889	+	1.21095i
$49$	1.76989e30			0.667448
$50$	−2.55967e30	−	2.74012e30i	−0.671001	−	0.718306i
$51$			1.08719e31i			1.99546i
$52$	−5.35338e29	+	7.85220e30i	−0.0692737	+	1.01609i
$53$	3.45056e30			0.316902			0.158451	−	0.987367i	$-0.449350\pi$
$53$	3.45056e30			0.316902			0.158451	+	0.987367i	$0.449350\pi$
$54$	6.89034e30	−	6.43657e30i	0.452015	−	0.422247i
$55$		−	8.20743e29i		−	0.0386972i
$56$	1.06803e31	+	1.31189e31i	0.364082	+	0.447210i
$57$	−5.70428e31			−1.41401
$58$	−2.35078e30	−	2.51651e30i	−0.0426097	−	0.0456136i
$59$		−	2.87222e31i		−	0.382720i	−0.981520	−	0.191360i	$-0.938710\pi$
$59$		−	2.87222e31i		−	0.382720i	0.981520	−	0.191360i	$-0.0612899\pi$
$60$	1.61677e31	+	1.10226e30i	0.159193	+	0.0108533i
$61$	−1.57408e31			−0.115104			−0.0575519	−	0.998343i	$-0.518329\pi$
$61$	−1.57408e31			−0.115104			−0.0575519	+	0.998343i	$0.518329\pi$
$62$	1.37038e32	−	1.28013e32i	0.747807	−	0.698560i
$63$			6.96181e31i			0.284834i
$64$	6.58117e31	−	3.17775e32i	0.202798	−	0.979221i
$65$	5.70356e31			0.132955
$66$	−1.39655e32	−	1.49500e32i	−0.247323	−	0.264759i
$67$			2.63364e32i			0.355804i	0.984048	+	0.177902i	$0.0569310\pi$
$67$			2.63364e32i			0.355804i	−0.984048	+	0.177902i	$0.943069\pi$
$68$	1.07317e32	−	1.57409e33i	0.111047	−	1.62881i
$69$	−1.33220e33			−1.05995
$70$	8.95853e31	−	8.36856e31i	0.0550138	−	0.0513909i
$71$			2.24092e33i			1.06604i	0.846101	+	0.533022i	$0.178944\pi$
$71$			2.24092e33i			1.06604i	−0.846101	+	0.533022i	$0.821056\pi$
$72$	1.03569e33	−	8.43172e32i	0.383040	−	0.311840i
$73$	−4.63793e33			−1.33817			−0.669087	−	0.743184i	$-0.733315\pi$
$73$	−4.63793e33			−1.33817			−0.669087	+	0.743184i	$0.733315\pi$
$74$	4.65022e33	+	4.97805e33i	1.05027	+	1.12432i
$75$			6.77333e33i			1.20143i
$76$	8.25898e33	+	5.63071e32i	1.15420	+	0.0786898i
$77$	−1.54766e33			−0.170939
$78$	1.03892e34	−	9.70497e33i	0.909656	−	0.849751i
$79$			2.60170e34i			1.81121i	0.424119	+	0.905607i	$0.360584\pi$
$79$			2.60170e34i			1.81121i	−0.424119	+	0.905607i	$0.639416\pi$
$80$	−2.32997e33	−	3.19183e32i	−0.129339	−	0.0177182i
$81$	−2.81597e34			−1.24996
$82$	−3.06203e34	−	3.27790e34i	−1.08984	−	1.16667i
$83$		−	9.58149e32i		−	0.0274175i	−0.999906	−	0.0137087i	$-0.995636\pi$
$83$		−	9.58149e32i		−	0.0274175i	0.999906	−	0.0137087i	$-0.00436376\pi$
$84$	2.07851e33	−	3.04870e34i	0.0479429	−	0.703214i
$85$	−1.14337e34			−0.213130
$86$	7.88705e34	−	7.36765e34i	1.19108	−	1.11264i
$87$			6.22058e33i			0.0762930i
$88$	1.87443e34	+	2.30240e34i	0.187146	+	0.229876i
$89$	3.91670e34			0.319080			0.159540	−	0.987191i	$-0.448999\pi$
$89$	3.91670e34			0.319080			0.159540	+	0.987191i	$0.448999\pi$
$90$	−6.60668e33	−	7.07244e33i	−0.0440168	−	0.0471199i
$91$		−	1.07551e35i		−	0.587311i
$92$	1.92884e35	+	1.31502e34i	0.865198	+	0.0589864i
$93$	−3.38745e35			−1.25078
$94$	−1.71133e35	+	1.59863e35i	−0.521234	+	0.486908i
$95$		−	5.99903e34i		−	0.151027i
$96$	−4.78719e35	+	3.38319e35i	−0.998157	+	0.705414i
$97$	5.91294e35			1.02309			0.511543	−	0.859258i	$-0.329074\pi$
$97$	5.91294e35			1.02309			0.511543	+	0.859258i	$0.329074\pi$
$98$	3.16720e35	+	3.39048e35i	0.455623	+	0.487744i
$99$			1.22182e35i			0.146411i
$100$	6.68597e34	−	9.80681e35i	0.0668597	−	0.980681i
$101$	1.79261e36			1.49865			0.749325	−	0.662202i	$-0.230378\pi$
$101$	1.79261e36			1.49865			0.749325	+	0.662202i	$0.230378\pi$
$102$	−2.08267e36	+	1.94551e36i	−1.45820	+	1.36217i
$103$			5.54915e35i			0.325954i	0.986630	+	0.162977i	$0.0521096\pi$
$103$			5.54915e35i			0.325954i	−0.986630	+	0.162977i	$0.947890\pi$
$104$	−1.60000e36	+	1.30259e36i	−0.789805	+	0.642995i
$105$	−2.21447e35			−0.0920157
$106$	6.17474e35	+	6.61005e35i	0.216328	+	0.231579i
$107$		−	4.04653e36i		−	1.19722i	−0.801040	−	0.598611i	$-0.795720\pi$
$107$		−	4.04653e36i		−	1.19722i	0.801040	−	0.598611i	$-0.204280\pi$
$108$	2.46603e36	+	1.68126e35i	0.617122	+	0.0420735i
$109$	3.91818e36			0.830631			0.415315	−	0.909678i	$-0.363671\pi$
$109$	3.91818e36			0.830631			0.415315	+	0.909678i	$0.363671\pi$
$110$	1.57225e35	−	1.46871e35i	0.0282783	−	0.0264160i
$111$		−	1.23053e37i		−	1.88052i
$112$	−6.01876e35	+	4.39357e36i	−0.0782678	+	0.571337i
$113$	−4.45970e36			−0.494189			−0.247095	−	0.968991i	$-0.579476\pi$
$113$	−4.45970e36			−0.494189			−0.247095	+	0.968991i	$0.579476\pi$
$114$	−1.02077e37	−	1.09274e37i	−0.965254	−	1.03330i
$115$		−	1.40104e36i		−	0.113211i
$116$	6.14036e34	−	9.00651e35i	0.00424570	−	0.0622749i
$117$	−8.49075e36			−0.503038
$118$	5.50215e36	−	5.13980e36i	0.279677	−	0.261258i
$119$			2.15602e37i			0.941472i
$120$	2.68203e36	+	3.29440e36i	0.100740	+	0.123741i
$121$	2.81965e37			0.912134
$122$	−2.81679e36	−	3.01537e36i	−0.0785739	−	0.0841132i
$123$			8.10268e37i			1.95136i
$124$	4.90454e37	+	3.34376e36i	1.02096	+	0.0696057i
$125$	−1.43701e37			−0.258869
$126$	−1.33363e37	+	1.24581e37i	−0.208145	+	0.194438i
$127$			2.51694e37i			0.340726i	0.985381	+	0.170363i	$0.0544940\pi$
$127$			2.51694e37i			0.340726i	−0.985381	+	0.170363i	$0.945506\pi$
$128$	7.26513e37	−	4.42583e37i	0.854012	−	0.520254i
$129$	−1.94961e38			−1.99220
$130$	1.02064e37	+	1.09260e37i	0.0907600	+	0.0971584i
$131$		−	4.39588e37i		−	0.340535i	−0.985398	−	0.170268i	$-0.945537\pi$
$131$		−	4.39588e37i		−	0.340535i	0.985398	−	0.170268i	$-0.0544632\pi$
$132$	3.64785e36	−	5.35057e37i	0.0246437	−	0.361467i
$133$	−1.13122e38			−0.667142
$134$	−5.04512e37	+	4.71287e37i	−0.260007	+	0.242884i
$135$		−	1.79124e37i		−	0.0807506i
$136$	3.20744e38	−	2.61124e38i	1.26607	−	1.03073i
$137$	2.45741e38			0.850173			0.425086	−	0.905153i	$-0.360244\pi$
$137$	2.45741e38			0.850173			0.425086	+	0.905153i	$0.360244\pi$
$138$	−2.38396e38	−	2.55203e38i	−0.723562	−	0.774571i
$139$			7.52934e37i			0.200674i	0.994954	+	0.100337i	$0.0319920\pi$
$139$			7.52934e37i			0.200674i	−0.994954	+	0.100337i	$0.968008\pi$
$140$	3.20623e37	+	2.18591e36i	0.0751087	+	0.00512068i
$141$	4.23026e38			0.871812
$142$	−4.29279e38	+	4.01009e38i	−0.779022	+	0.727719i
$143$		−	1.88755e38i		−	0.301891i
$144$	3.46856e38	+	4.75160e37i	0.489356	+	0.0670371i
$145$	−6.54201e36			−0.00814868
$146$	−8.29951e38	−	8.88461e38i	−0.913484	−	0.977883i
$147$		−	8.38096e38i		−	0.815797i
$148$	−1.21466e38	+	1.78163e39i	−0.104651	+	1.53499i
$149$	−5.62189e38			−0.429071			−0.214536	−	0.976716i	$-0.568824\pi$
$149$	−5.62189e38			−0.429071			−0.214536	+	0.976716i	$0.568824\pi$
$150$	−1.29753e39	+	1.21208e39i	−0.877958	+	0.820140i
$151$		−	1.13127e38i		−	0.0679175i	−0.999423	−	0.0339587i	$-0.989189\pi$
$151$		−	1.13127e38i		−	0.0679175i	0.999423	−	0.0339587i	$-0.0108115\pi$
$152$	1.37007e39	+	1.68289e39i	0.730395	+	0.897160i
$153$	1.70210e39			0.806380
$154$	−2.76951e38	−	2.96476e38i	−0.116689	−	0.124915i
$155$		−	3.56249e38i		−	0.133593i
$156$	3.71825e39	+	2.53499e38i	1.24193	+	0.0846706i
$157$	3.45361e39			1.02820			0.514102	−	0.857729i	$-0.328125\pi$
$157$	3.45361e39			1.02820			0.514102	+	0.857729i	$0.328125\pi$
$158$	−4.98393e39	+	4.65571e39i	−1.32356	+	1.23640i
$159$		−	1.63394e39i		−	0.387337i
$160$	−3.55801e38	−	5.03456e38i	−0.0753437	−	0.106611i
$161$	−2.64191e39			−0.500095
$162$	−5.03914e39	−	5.39439e39i	−0.853269	−	0.913422i
$163$			5.94810e39i			0.901574i	0.892632	+	0.450787i	$0.148857\pi$
$163$			5.94810e39i			0.901574i	−0.892632	+	0.450787i	$0.851143\pi$
$164$	7.99818e38	−	1.17315e40i	0.108593	−	1.59281i
$165$	−3.88646e38			−0.0472981
$166$	1.83547e38	−	1.71459e38i	0.0200356	−	0.0187161i
$167$		−	1.39112e40i		−	1.36291i	−0.731861	−	0.681454i	$-0.761348\pi$
$167$		−	1.39112e40i		−	1.36291i	0.731861	−	0.681454i	$-0.238652\pi$
$168$	6.21217e39	−	5.05744e39i	0.546608	−	0.445004i
$169$	4.70867e38			0.0372338
$170$	−2.04604e39	−	2.19028e39i	−0.145490	−	0.155747i
$171$			8.93060e39i			0.571414i
$172$	2.82275e40	+	1.92446e39i	1.62615	+	0.110866i
$173$	−3.29833e40			−1.71185			−0.855923	−	0.517104i	$-0.827010\pi$
$173$	−3.29833e40			−1.71185			−0.855923	+	0.517104i	$0.827010\pi$
$174$	−1.19164e39	+	1.11316e39i	−0.0557518	+	0.0520802i
$175$			1.34323e40i			0.566845i
$176$	−1.05631e39	+	7.71085e39i	−0.0402313	+	0.293680i
$177$	−1.36008e40			−0.467785
$178$	7.00888e39	+	7.50299e39i	0.217815	+	0.233171i
$179$			5.49966e40i			1.54519i	0.634900	+	0.772594i	$0.281041\pi$
$179$			5.49966e40i			1.54519i	−0.634900	+	0.772594i	$0.718959\pi$
$180$	1.72570e38	−	2.53121e39i	0.00438591	−	0.0643314i
$181$	3.46531e40			0.797128			0.398564	−	0.917141i	$-0.369509\pi$
$181$	3.46531e40			0.797128			0.398564	+	0.917141i	$0.369509\pi$
$182$	2.06029e40	−	1.92461e40i	0.429183	−	0.400919i
$183$			7.45373e39i			0.140687i
$184$	3.19972e40	+	3.93029e40i	0.547509	+	0.672518i
$185$	1.29411e40			0.200854
$186$	−6.06180e40	−	6.48914e40i	−0.853824	−	0.914017i
$187$			3.78388e40i			0.483937i
$188$	−6.12481e40	−	4.17570e39i	−0.711625	−	0.0485164i
$189$	−3.37770e40			−0.356704
$190$	1.14920e40	−	1.07352e40i	0.110365	−	0.103097i
$191$		−	1.96526e41i		−	1.71719i	−0.512654	−	0.858595i	$-0.671338\pi$
$191$		−	1.96526e41i		−	1.71719i	0.512654	−	0.858595i	$-0.328662\pi$
$192$	−1.50476e41	−	3.11638e40i	−1.19686	−	0.247873i
$193$	2.74837e40			0.199087			0.0995437	−	0.995033i	$-0.468262\pi$
$193$	2.74837e40			0.199087			0.0995437	+	0.995033i	$0.468262\pi$
$194$	1.05811e41	+	1.13271e41i	0.698395	+	0.747630i
$195$		−	2.70081e40i		−	0.162506i
$196$	−8.27288e39	+	1.21344e41i	−0.0453991	+	0.665902i
$197$	1.69096e41			0.846725			0.423363	−	0.905960i	$-0.360850\pi$
$197$	1.69096e41			0.846725			0.423363	+	0.905960i	$0.360850\pi$
$198$	−2.34057e40	+	2.18643e40i	−0.106991	+	0.0999453i
$199$		−	4.25960e41i		−	1.77834i	−0.457581	−	0.889168i	$-0.651284\pi$
$199$		−	4.25960e41i		−	1.77834i	0.457581	−	0.889168i	$-0.348716\pi$
$200$	1.99828e41	−	1.62684e41i	0.762283	−	0.620589i
$201$	1.24711e41			0.434886
$202$	3.20785e41	+	3.43399e41i	1.02303	+	1.09515i
$203$			1.23361e40i			0.0359956i
$204$	−7.45380e41	−	5.08177e40i	−1.99083	−	0.135729i
$205$	−8.52137e40			−0.208420
$206$	−1.06302e41	+	9.93012e40i	−0.238194	+	0.222508i
$207$			2.08569e41i			0.428336i
$208$	−5.35847e41	−	7.34060e40i	−1.00902	−	0.138226i
$209$	−1.98533e41			−0.342926
$210$	−3.96276e40	−	4.24213e40i	−0.0628132	−	0.0672414i
$211$			8.66535e41i			1.26096i	0.776205	+	0.630481i	$0.217142\pi$
$211$			8.66535e41i			1.26096i	−0.776205	+	0.630481i	$0.782858\pi$
$212$	−1.61287e40	+	2.36572e41i	−0.0215553	+	0.316168i
$213$	1.06114e42			1.30299
$214$	7.75170e41	−	7.24120e41i	0.874881	−	0.817265i
$215$		−	2.05035e41i		−	0.212782i
$216$	4.09086e41	+	5.02490e41i	0.390524	+	0.479689i
$217$	−6.71770e41			−0.590127
$218$	7.01154e41	+	7.50584e41i	0.567017	+	0.606991i
$219$			2.19620e42i			1.63560i
$220$	5.62704e40	+	3.83634e39i	0.0386075	+	0.00263214i
$221$	−2.62952e42			−1.66271
$222$	2.35725e42	−	2.20202e42i	1.37421	−	1.28371i
$223$		−	3.01760e42i		−	1.62246i	−0.584725	−	0.811231i	$-0.698798\pi$
$223$		−	3.01760e42i		−	1.62246i	0.584725	−	0.811231i	$-0.301202\pi$
$224$	−9.49355e41	+	6.70925e41i	−0.470939	+	0.332820i
$225$	1.06043e42			0.485509
$226$	−7.98057e41	−	8.54318e41i	−0.337351	−	0.361133i
$227$			2.89079e41i			0.112863i	0.998406	+	0.0564315i	$0.0179723\pi$
$227$			2.89079e41i			0.112863i	−0.998406	+	0.0564315i	$0.982028\pi$
$228$	2.66631e41	−	3.91087e42i	0.0961796	−	1.41074i
$229$	−4.60426e42			−1.53505			−0.767523	−	0.641021i	$-0.778511\pi$
$229$	−4.60426e42			−1.53505			−0.767523	+	0.641021i	$0.778511\pi$
$230$	2.68389e41	−	2.50714e41i	0.0827302	−	0.0772820i
$231$			7.32861e41i			0.208933i
$232$	1.83521e41	−	1.49408e41i	0.0484062	−	0.0394084i
$233$	2.20539e41			0.0538368			0.0269184	−	0.999638i	$-0.491431\pi$
$233$	2.20539e41			0.0538368			0.0269184	+	0.999638i	$0.491431\pi$
$234$	−1.51941e42	−	1.62652e42i	−0.343391	−	0.367600i
$235$			4.44885e41i			0.0931163i
$236$	1.96920e42	+	1.34254e41i	0.381834	+	0.0260322i
$237$	1.23198e43			2.21378
$238$	−4.13016e42	+	3.85817e42i	−0.687990	+	0.642682i
$239$			2.95916e42i			0.457094i	0.973533	+	0.228547i	$0.0733975\pi$
$239$			2.95916e42i			0.457094i	−0.973533	+	0.228547i	$0.926603\pi$
$240$	−1.51143e41	+	1.10331e42i	−0.0216563	+	0.158086i
$241$	−3.45312e42			−0.459097			−0.229549	−	0.973297i	$-0.573725\pi$
$241$	−3.45312e42			−0.459097			−0.229549	+	0.973297i	$0.573725\pi$
$242$	5.04572e42	+	5.40144e42i	0.622654	+	0.666550i
$243$			7.93571e42i			0.909228i
$244$	7.35760e40	−	1.07919e42i	0.00782924	−	0.114837i
$245$	8.81402e41			0.0871334
$246$	−1.55218e43	+	1.44996e43i	−1.42597	+	1.33206i
$247$		−	1.37966e43i		−	1.17822i
$248$	8.13607e42	+	9.99371e42i	0.646077	+	0.793591i
$249$	−4.53712e41			−0.0335113
$250$	−2.57152e42	−	2.75281e42i	−0.176713	−	0.189171i
$251$		−	2.44151e43i		−	1.56146i	−0.624867	−	0.780731i	$-0.714847\pi$
$251$		−	2.44151e43i		−	1.56146i	0.624867	−	0.780731i	$-0.285153\pi$
$252$	−4.77304e42	−	3.25411e41i	−0.284175	−	0.0193741i
$253$	−4.63664e42			−0.257060
$254$	−4.82155e42	+	4.50402e42i	−0.248989	+	0.232591i
$255$			5.41418e42i			0.260501i
$256$	2.14792e43	+	5.99743e42i	0.963159	+	0.268934i
$257$	2.82654e43			1.18157			0.590785	−	0.806829i	$-0.298818\pi$
$257$	2.82654e43			1.18157			0.590785	+	0.806829i	$0.298818\pi$
$258$	−3.48880e43	−	3.73475e43i	−1.35994	−	1.45582i
$259$		−	2.44028e43i		−	0.887246i
$260$	−2.66597e41	+	3.91038e42i	−0.00904348	+	0.132647i
$261$	9.73893e41			0.0308306
$262$	8.42093e42	−	7.86636e42i	0.248849	−	0.232461i
$263$			4.72307e43i			1.30323i	0.758551	+	0.651614i	$0.225908\pi$
$263$			4.72307e43i			1.30323i	−0.758551	+	0.651614i	$0.774092\pi$
$264$	1.09026e43	−	8.87597e42i	0.280968	−	0.228742i
$265$	1.71837e42			0.0413706
$266$	−2.02431e43	−	2.16702e43i	−0.455415	−	0.487521i
$267$		−	1.85467e43i		−	0.390000i
$268$	−1.80563e43	−	1.23102e42i	−0.354980	−	0.0242014i
$269$	−3.43092e43			−0.630769			−0.315384	−	0.948964i	$-0.602133\pi$
$269$	−3.43092e43			−0.630769			−0.315384	+	0.948964i	$0.602133\pi$
$270$	3.43137e42	−	3.20540e42i	0.0590093	−	0.0551232i
$271$			3.96971e43i			0.638722i	0.947633	+	0.319361i	$0.103468\pi$
$271$			3.96971e43i			0.638722i	−0.947633	+	0.319361i	$0.896532\pi$
$272$	1.07419e44	+	1.47154e43i	1.61748	+	0.221580i
$273$	−5.09285e43			−0.717849
$274$	4.39750e43	+	4.70752e43i	0.580358	+	0.621272i
$275$			2.35741e43i			0.291371i
$276$	6.22702e42	−	9.13363e43i	0.0720969	−	1.05750i
$277$	8.05966e42			0.0874341			0.0437170	−	0.999044i	$-0.486080\pi$
$277$	8.05966e42			0.0874341			0.0437170	+	0.999044i	$0.486080\pi$
$278$	−1.44235e43	+	1.34737e43i	−0.146644	+	0.136987i
$279$			5.30338e43i			0.505449i
$280$	5.31877e42	+	6.53316e42i	0.0475299	+	0.0583820i
$281$	−1.90752e44			−1.59866			−0.799329	−	0.600894i	$-0.794812\pi$
$281$	−1.90752e44			−1.59866			−0.799329	+	0.600894i	$0.794812\pi$
$282$	7.56999e43	+	8.10366e43i	0.595130	+	0.637085i
$283$			7.67667e43i			0.566261i	0.959081	+	0.283131i	$0.0913730\pi$
$283$			7.67667e43i			0.566261i	−0.959081	+	0.283131i	$0.908627\pi$
$284$	−1.53638e44	−	1.04745e43i	−1.06358	−	0.0725112i
$285$	−2.84072e43			−0.184595
$286$	3.61587e43	−	3.37775e43i	0.220610	−	0.206081i
$287$			1.60685e44i			0.920666i
$288$	5.29671e43	+	7.49482e43i	0.285064	+	0.403363i
$289$	3.29357e44			1.66535
$290$	−1.17068e42	−	1.25322e42i	−0.00556257	−	0.00595473i
$291$		−	2.79995e44i		−	1.25048i
$292$	2.16787e43	−	3.17978e44i	0.0910212	−	1.33507i
$293$	2.66147e44			1.05076			0.525380	−	0.850868i	$-0.323923\pi$
$293$	2.66147e44			1.05076			0.525380	+	0.850868i	$0.323923\pi$
$294$	1.60549e44	−	1.49976e44i	0.596151	−	0.556891i
$295$		−	1.43036e43i		−	0.0499631i
$296$	−3.63033e44	+	2.95552e44i	−1.19315	+	0.971366i
$297$	−5.92797e43			−0.183354
$298$	−1.00603e44	−	1.07695e44i	−0.292899	−	0.313548i
$299$		−	3.22212e44i		−	0.883203i
$300$	−4.64382e44	−	3.16601e43i	−1.19865	−	0.0817202i
$301$	−3.86629e44			−0.939935
$302$	2.16711e43	−	2.02439e43i	0.0496313	−	0.0463628i
$303$		−	8.48852e44i		−	1.83174i
$304$	−7.72087e43	+	5.63606e44i	−0.157015	+	1.14618i
$305$	−7.83888e42			−0.0150265
$306$	3.04589e44	+	3.26062e44i	0.550463	+	0.589270i
$307$		−	2.07386e44i		−	0.353418i	−0.984263	−	0.176709i	$-0.943455\pi$
$307$		−	2.07386e44i		−	0.353418i	0.984263	−	0.176709i	$-0.0565451\pi$
$308$	7.23410e42	−	1.06108e44i	0.0116271	−	0.170543i
$309$	2.62769e44			0.398401
$310$	6.82445e43	−	6.37502e43i	0.0976241	−	0.0911950i
$311$			1.30713e45i			1.76454i	0.470744	+	0.882270i	$0.343986\pi$
$311$			1.30713e45i			1.76454i	−0.470744	+	0.882270i	$0.656014\pi$
$312$	6.16815e44	+	7.57647e44i	0.785909	+	0.965349i
$313$	9.40367e44			1.13110			0.565548	−	0.824716i	$-0.308665\pi$
$313$	9.40367e44			1.13110			0.565548	+	0.824716i	$0.308665\pi$
$314$	6.18018e44	+	6.61587e44i	0.701887	+	0.751369i
$315$			3.46697e43i			0.0371843i
$316$	−1.78373e45	−	1.21609e44i	−1.80702	−	0.123197i
$317$	1.00608e45			0.962864			0.481432	−	0.876483i	$-0.340117\pi$
$317$	1.00608e45			0.962864			0.481432	+	0.876483i	$0.340117\pi$
$318$	3.13005e44	−	2.92392e44i	0.283050	−	0.264410i
$319$			2.16503e43i			0.0185025i
$320$	3.27741e43	−	1.58251e44i	0.0264747	−	0.127834i
$321$	−1.91615e45			−1.46332
$322$	−4.72766e44	−	5.06095e44i	−0.341382	−	0.365449i
$323$			2.76574e45i			1.88871i
$324$	1.31625e44	−	1.93064e45i	0.0850212	−	1.24707i
$325$	−1.63822e45			−1.00109
$326$	−1.13944e45	+	1.06440e45i	−0.658834	+	0.615446i
$327$		−	1.85538e45i		−	1.01525i
$328$	2.39047e45	−	1.94612e45i	1.23809	−	1.00796i
$329$	8.38908e44			0.411328
$330$	−6.95477e43	−	7.44507e43i	−0.0322873	−	0.0345635i
$331$		−	1.31519e45i		−	0.578210i	−0.957297	−	0.289105i	$-0.906642\pi$
$331$		−	1.31519e45i		−	0.578210i	0.957297	−	0.289105i	$-0.0933577\pi$
$332$	6.56910e43	+	4.47861e42i	0.0273540	+	0.00186491i
$333$	−1.92651e45			−0.759934
$334$	2.66488e45	−	2.48938e45i	0.995958	−	0.930369i
$335$			1.31155e44i			0.0464492i
$336$	2.08048e45	+	2.85006e44i	0.698324	+	0.0956638i
$337$	−4.63066e44			−0.147334			−0.0736672	−	0.997283i	$-0.523470\pi$
$337$	−4.63066e44			−0.147334			−0.0736672	+	0.997283i	$0.523470\pi$
$338$	8.42610e43	+	9.02013e43i	0.0254171	+	0.0272090i
$339$			2.11180e45i			0.604029i
$340$	5.34436e43	−	7.83896e44i	0.0144969	−	0.212637i
$341$	−1.17898e45			−0.303338
$342$	−1.71078e45	+	1.59812e45i	−0.417566	+	0.390067i
$343$		−	4.15218e45i		−	0.961573i
$344$	4.68262e45	+	5.75177e45i	1.02905	+	1.26401i
$345$	−6.63435e44			−0.138374
$346$	−5.90232e45	−	6.31842e45i	−1.16857	−	1.25095i
$347$			8.69234e45i			1.63383i	0.576760	+	0.816913i	$0.304317\pi$
$347$			8.69234e45i			1.63383i	−0.576760	+	0.816913i	$0.695683\pi$
$348$	−4.26485e44	−	2.90764e43i	−0.0761163	−	0.00518937i
$349$	4.23539e45			0.717854			0.358927	−	0.933366i	$-0.383143\pi$
$349$	4.23539e45			0.717854			0.358927	+	0.933366i	$0.383143\pi$
$350$	−2.57314e45	+	2.40369e45i	−0.414228	+	0.386949i
$351$		−	4.11950e45i		−	0.629965i
$352$	−1.66615e45	+	1.17749e45i	−0.242073	+	0.171077i
$353$	2.46125e45			0.339790			0.169895	−	0.985462i	$-0.445657\pi$
$353$	2.46125e45			0.339790			0.169895	+	0.985462i	$0.445657\pi$
$354$	−2.43385e45	−	2.60543e45i	−0.319326	−	0.341838i
$355$			1.11597e45i			0.139169i
$356$	−1.83075e44	+	2.68530e45i	−0.0217035	+	0.318341i
$357$	1.02094e46			1.15073
$358$	−1.05354e46	+	9.84157e45i	−1.12916	+	1.05480i
$359$			4.62645e45i			0.471572i	0.971805	+	0.235786i	$0.0757664\pi$
$359$			4.62645e45i			0.471572i	−0.971805	+	0.235786i	$0.924234\pi$
$360$	5.15770e44	−	4.19898e44i	0.0500047	−	0.0407098i
$361$	−3.66881e45			−0.338373
$362$	6.20113e45	+	6.63830e45i	0.544147	+	0.582509i
$363$		−	1.33519e46i		−	1.11487i
$364$	7.37371e45	+	5.02717e44i	0.585951	+	0.0399483i
$365$	−2.30968e45			−0.174695
$366$	−1.42787e45	+	1.33384e45i	−0.102808	+	0.0960379i
$367$		−	1.95361e46i		−	1.33921i	−0.742718	−	0.669604i	$-0.766464\pi$
$367$		−	1.95361e46i		−	1.33921i	0.742718	−	0.669604i	$-0.233536\pi$
$368$	−1.80317e45	+	1.31627e46i	−0.117700	+	0.859182i
$369$	1.26855e46			0.788559
$370$	2.31580e45	+	2.47906e45i	0.137110	+	0.146776i
$371$		−	3.24030e45i		−	0.182749i
$372$	1.58337e45	−	2.32245e46i	0.0850765	−	1.24788i
$373$	−1.78396e46			−0.913325			−0.456662	−	0.889640i	$-0.650955\pi$
$373$	−1.78396e46			−0.913325			−0.456662	+	0.889640i	$0.650955\pi$
$374$	−7.24857e45	+	6.77121e45i	−0.353642	+	0.330352i
$375$			6.80469e45i			0.316407i
$376$	−1.01604e46	−	1.24802e46i	−0.450327	−	0.553146i
$377$	−1.50454e45			−0.0635709
$378$	−6.04434e45	−	6.47046e45i	−0.243499	−	0.260665i
$379$		−	1.59965e46i		−	0.614496i	−0.951629	−	0.307248i	$-0.900592\pi$
$379$		−	1.59965e46i		−	0.614496i	0.951629	−	0.307248i	$-0.0994081\pi$
$380$	4.11295e45	+	2.80408e44i	0.150678	+	0.0102727i
$381$	1.19184e46			0.416456
$382$	3.76473e46	−	3.51680e46i	1.25485	−	1.17221i
$383$			2.43670e46i			0.774862i	0.921899	+	0.387431i	$0.126638\pi$
$383$			2.43670e46i			0.774862i	−0.921899	+	0.387431i	$0.873362\pi$
$384$	−2.09576e46	−	3.44025e46i	−0.635887	−	1.04383i
$385$	−7.70730e44			−0.0223156
$386$	4.91817e45	+	5.26490e45i	0.135904	+	0.145485i
$387$			3.05230e46i			0.805064i
$388$	−2.76384e45	+	4.05393e46i	−0.0695893	+	1.02072i
$389$	−3.51428e46			−0.844780			−0.422390	−	0.906414i	$-0.638809\pi$
$389$	−3.51428e46			−0.844780			−0.422390	+	0.906414i	$0.638809\pi$
$390$	5.17378e45	−	4.83306e45i	0.118753	−	0.110933i
$391$			6.45924e46i			1.41579i
$392$	−2.47257e46	+	2.01296e46i	−0.517605	+	0.421392i
$393$	−2.08158e46			−0.416224
$394$	3.02596e46	+	3.23928e46i	0.578004	+	0.618753i
$395$			1.29564e46i			0.236449i
$396$	−8.37684e45	−	5.71106e44i	−0.146072	−	0.00995872i
$397$	9.09787e45			0.151604			0.0758020	−	0.997123i	$-0.475848\pi$
$397$	9.09787e45			0.151604			0.0758020	+	0.997123i	$0.475848\pi$
$398$	8.15987e46	−	7.62250e46i	1.29954	−	1.21395i
$399$			5.35667e46i			0.815423i
$400$	6.69233e46	+	9.16785e45i	0.973862	+	0.133410i
$401$	−2.80512e46			−0.390259			−0.195129	−	0.980778i	$-0.562513\pi$
$401$	−2.80512e46			−0.390259			−0.195129	+	0.980778i	$0.562513\pi$
$402$	2.23168e46	+	2.38901e46i	0.296868	+	0.317797i
$403$		−	8.19303e46i		−	1.04221i
$404$	−8.37905e45	+	1.22902e47i	−0.101937	+	1.49518i
$405$	−1.40235e46			−0.163179
$406$	−2.36316e45	+	2.20753e45i	−0.0263042	+	0.0245719i
$407$		−	4.28277e46i		−	0.456064i
$408$	−1.23650e47	−	1.51882e47i	−1.25983	−	1.54747i
$409$	2.66506e46			0.259829			0.129914	−	0.991525i	$-0.458530\pi$
$409$	2.66506e46			0.259829			0.129914	+	0.991525i	$0.458530\pi$
$410$	−1.52489e46	−	1.63239e46i	−0.142275	−	0.152305i
$411$		−	1.16366e47i		−	1.03913i
$412$	−3.80451e46	−	2.59380e45i	−0.325199	−	0.0221710i
$413$	−2.69720e46			−0.220705
$414$	−3.99544e46	+	3.73232e46i	−0.313011	+	0.292397i
$415$		−	4.77156e44i		−	0.00357927i
$416$	−8.18272e46	−	1.15785e47i	−0.587784	−	0.831711i
$417$	3.56537e46			0.245276
$418$	−3.55273e46	−	3.80319e46i	−0.234093	−	0.250596i
$419$		−	2.01039e46i		−	0.126890i	−0.997985	−	0.0634450i	$-0.979791\pi$
$419$		−	2.01039e46i		−	0.126890i	0.997985	−	0.0634450i	$-0.0202087\pi$
$420$	1.03509e45	−	1.51825e46i	0.00625881	−	0.0918026i
$421$	2.31091e47			1.33877			0.669384	−	0.742916i	$-0.266558\pi$
$421$	2.31091e47			1.33877			0.669384	+	0.742916i	$0.266558\pi$
$422$	−1.65997e47	+	1.55065e47i	−0.921460	+	0.860777i
$423$		−	6.62288e46i		−	0.352306i
$424$	−4.82049e46	+	3.92445e46i	−0.245757	+	0.200075i
$425$	3.28407e47			1.60477
$426$	1.89890e47	+	2.03276e47i	0.889464	+	0.952170i
$427$			1.47816e46i			0.0663773i
$428$	2.77431e47	+	1.89144e46i	1.19445	+	0.0814337i
$429$	−8.93811e46			−0.368990
$430$	3.92774e46	−	3.66907e46i	0.155493	−	0.145253i
$431$		−	1.16679e47i		−	0.443000i	−0.975160	−	0.221500i	$-0.928905\pi$
$431$		−	1.16679e47i		−	0.443000i	0.975160	−	0.221500i	$-0.0710952\pi$
$432$	−2.30536e46	+	1.68286e47i	−0.0839520	+	0.612831i
$433$	−2.80462e47			−0.979697			−0.489848	−	0.871808i	$-0.662948\pi$
$433$	−2.80462e47			−0.979697			−0.489848	+	0.871808i	$0.662948\pi$
$434$	−1.20212e47	−	1.28687e47i	−0.402841	−	0.431241i
$435$			3.09784e45i			0.00995983i
$436$	−1.83145e46	+	2.68632e47i	−0.0564986	+	0.828707i
$437$	−3.38904e47			−1.00325
$438$	−4.20713e47	+	3.93006e47i	−1.19523	+	1.11652i
$439$			1.85002e47i			0.504447i	0.967669	+	0.252224i	$0.0811618\pi$
$439$			1.85002e47i			0.504447i	−0.967669	+	0.252224i	$0.918838\pi$
$440$	9.33461e45	+	1.14659e46i	0.0244314	+	0.0300096i
$441$	−1.31212e47			−0.329670
$442$	−4.70549e47	−	5.03722e47i	−1.13502	−	1.21504i
$443$			1.13148e47i			0.262048i	0.991379	+	0.131024i	$0.0418265\pi$
$443$			1.13148e47i			0.262048i	−0.991379	+	0.131024i	$0.958173\pi$
$444$	8.43655e47	+	5.75178e46i	1.87617	+	0.127911i
$445$	1.95051e46			0.0416550
$446$	5.78065e47	−	5.39996e47i	1.18563	−	1.10755i
$447$			2.66213e47i			0.524438i
$448$	−2.98411e47	−	6.18014e46i	−0.564691	−	0.116948i
$449$	7.27545e47			1.32259			0.661295	−	0.750126i	$-0.270007\pi$
$449$	7.27545e47			1.32259			0.661295	+	0.750126i	$0.270007\pi$
$450$	1.89763e47	+	2.03141e47i	0.331425	+	0.354790i
$451$			2.82008e47i			0.473242i
$452$	2.08456e46	−	3.05758e47i	0.0336142	−	0.493045i
$453$	−5.35690e46			−0.0830130
$454$	−5.53773e46	+	5.17304e46i	−0.0824758	+	0.0770443i
$455$		−	5.35600e46i		−	0.0766718i
$456$	7.96896e47	−	6.48768e47i	1.09657	−	0.892734i
$457$	−7.18820e47			−0.950886			−0.475443	−	0.879747i	$-0.657712\pi$
$457$	−7.18820e47			−0.950886			−0.475443	+	0.879747i	$0.657712\pi$
$458$	−8.23927e47	−	8.82012e47i	−1.04788	−	1.12175i
$459$			8.25817e47i			1.00985i
$460$	9.60558e46	+	6.54878e45i	0.112949	+	0.00770051i
$461$	−6.51911e47			−0.737176			−0.368588	−	0.929593i	$-0.620159\pi$
$461$	−6.51911e47			−0.737176			−0.368588	+	0.929593i	$0.620159\pi$
$462$	−1.40390e47	+	1.31145e47i	−0.152679	+	0.142625i
$463$		−	7.31141e47i		−	0.764792i	−0.923999	−	0.382396i	$-0.875099\pi$
$463$		−	7.31141e47i		−	0.764792i	0.923999	−	0.382396i	$-0.124901\pi$
$464$	6.14619e46	+	8.41970e45i	0.0618419	+	0.00847174i
$465$	−1.68694e47			−0.163285
$466$	3.94652e46	+	4.22474e46i	0.0367509	+	0.0393417i
$467$		−	6.00670e47i		−	0.538185i	−0.963114	−	0.269093i	$-0.913276\pi$
$467$		−	6.00670e47i		−	0.538185i	0.963114	−	0.269093i	$-0.0867238\pi$
$468$	3.96877e46	−	5.82129e47i	0.0342161	−	0.501873i
$469$	2.47316e47			0.205183
$470$	−8.52240e46	+	7.96115e46i	−0.0680456	+	0.0635645i
$471$		−	1.63538e48i		−	1.25673i
$472$	3.26668e47	+	4.01254e47i	0.241630	+	0.296799i
$473$	−6.78547e47			−0.483147
$474$	2.20462e48	+	2.36004e48i	1.51120	+	1.61774i
$475$			1.72309e48i			1.13716i
$476$	−1.47817e48	−	1.00777e47i	−0.939291	−	0.0640379i
$477$	−2.55810e47			−0.156526
$478$	−5.66868e47	+	5.29537e47i	−0.334026	+	0.312028i
$479$		−	3.96347e47i		−	0.224924i	−0.993656	−	0.112462i	$-0.964126\pi$
$479$		−	3.96347e47i		−	0.224924i	0.993656	−	0.112462i	$-0.0358737\pi$
$480$	−2.38401e47	+	1.68482e47i	−0.130307	+	0.0920898i
$481$	2.97621e48			1.56694
$482$	−6.17931e47	−	6.61494e47i	−0.313396	−	0.335490i
$483$			1.25102e48i			0.611247i
$484$	−1.31797e47	+	1.93316e48i	−0.0620424	+	0.910021i
$485$	2.94463e47			0.133561
$486$	−1.52020e48	+	1.42009e48i	−0.664427	+	0.620671i
$487$			1.04806e48i			0.441434i	0.975338	+	0.220717i	$0.0708397\pi$
$487$			1.04806e48i			0.441434i	−0.975338	+	0.220717i	$0.929160\pi$
$488$	2.19901e47	−	1.79026e47i	0.0892629	−	0.0726706i
$489$	2.81660e48			1.10196
$490$	1.57726e47	+	1.68845e47i	0.0594803	+	0.0636736i
$491$		−	1.85047e48i		−	0.672691i	−0.941739	−	0.336346i	$-0.890809\pi$
$491$		−	1.85047e48i		−	0.672691i	0.941739	−	0.336346i	$-0.109191\pi$
$492$	−5.55523e48	−	3.78738e47i	−1.94684	−	0.132729i
$493$	3.01607e47			0.101905
$494$	2.64293e48	−	2.46888e48i	0.860996	−	0.804295i
$495$			6.08464e46i			0.0191135i
$496$	−4.58499e47	+	3.34694e48i	−0.138889	+	1.01386i
$497$	2.10436e48			0.614760
$498$	−8.11911e46	−	8.69150e46i	−0.0228760	−	0.0244887i
$499$		−	2.93720e48i		−	0.798223i	−0.916902	−	0.399112i	$-0.869319\pi$
$499$		−	2.93720e48i		−	0.798223i	0.916902	−	0.399112i	$-0.130681\pi$
$500$	6.71693e46	−	9.85222e47i	0.0176080	−	0.258270i
$501$	−6.58734e48			−1.66583
$502$	4.67706e48	−	4.36905e48i	1.14105	−	1.06591i
$503$		−	7.23105e48i		−	1.70207i	−0.525108	−	0.851036i	$-0.675975\pi$
$503$		−	7.23105e48i		−	1.70207i	0.525108	−	0.851036i	$-0.324025\pi$
$504$	−7.91792e47	−	9.72575e47i	−0.179830	−	0.220889i
$505$	8.92714e47			0.195645
$506$	−8.29720e47	−	8.88214e47i	−0.175478	−	0.187849i
$507$		−	2.22970e47i		−	0.0455095i
$508$	−1.72562e48	−	1.17647e47i	−0.339937	−	0.0231758i
$509$	−1.96709e48			−0.374028			−0.187014	−	0.982357i	$-0.559881\pi$
$509$	−1.96709e48			−0.374028			−0.187014	+	0.982357i	$0.559881\pi$
$510$	−1.03716e48	+	9.68860e47i	−0.190364	+	0.177827i
$511$			4.35531e48i			0.771689i
$512$	2.69477e48	+	5.18787e48i	0.460960	+	0.887421i
$513$	−4.33291e48			−0.715594
$514$	5.05806e48	+	5.41465e48i	0.806581	+	0.863444i
$515$			2.76346e47i			0.0425524i
$516$	9.11291e47	−	1.33666e49i	0.135507	−	1.98758i
$517$	1.47231e48			0.211432
$518$	4.67470e48	−	4.36685e48i	0.648363	−	0.605665i
$519$			1.56186e49i			2.09232i
$520$	−7.96796e47	+	6.48687e47i	−0.103107	+	0.0839412i
$521$	−3.03075e48			−0.378854			−0.189427	−	0.981895i	$-0.560663\pi$
$521$	−3.03075e48			−0.378854			−0.189427	+	0.981895i	$0.560663\pi$
$522$	1.74277e47	+	1.86563e47i	0.0210460	+	0.0225298i
$523$		−	3.63953e48i		−	0.424634i	−0.977201	−	0.212317i	$-0.931899\pi$
$523$		−	3.63953e48i		−	0.424634i	0.977201	−	0.212317i	$-0.0681010\pi$
$524$	3.01383e48	+	2.05473e47i	0.339747	+	0.0231629i
$525$	6.36058e48			0.692834
$526$	−9.04770e48	+	8.45186e48i	−0.952347	+	0.889629i
$527$			1.64242e49i			1.67068i
$528$	3.65132e48	+	5.00195e47i	0.358954	+	0.0491733i
$529$	2.60959e48			0.247954
$530$	3.07501e47	+	3.29179e47i	0.0282410	+	0.0302320i
$531$			2.12934e48i			0.189036i
$532$	5.28759e47	−	7.75570e48i	0.0453783	−	0.665597i
$533$	−1.95975e49			−1.62596
$534$	3.55289e48	−	3.31891e48i	0.284996	−	0.266228i
$535$		−	2.01516e48i		−	0.156294i
$536$	−2.99534e48	−	3.67924e48i	−0.224636	−	0.275925i
$537$	2.60425e49			1.88863
$538$	−6.13959e48	−	6.57242e48i	−0.430585	−	0.460940i
$539$		−	2.91693e48i		−	0.197847i
$540$	1.22808e48	+	8.37266e46i	0.0805636	+	0.00549257i
$541$	−2.94812e49			−1.87066			−0.935330	−	0.353777i	$-0.884897\pi$
$541$	−2.94812e49			−1.87066			−0.935330	+	0.353777i	$0.884897\pi$
$542$	−7.60455e48	+	7.10375e48i	−0.466752	+	0.436014i
$543$		−	1.64093e49i		−	0.974300i
$544$	1.64035e49	+	2.32109e49i	0.942230	+	1.33325i
$545$	1.95125e48			0.108436
$546$	−9.11358e48	−	9.75607e48i	−0.490029	−	0.524575i
$547$		−	2.55941e49i		−	1.33158i	−0.746138	−	0.665791i	$-0.768094\pi$
$547$		−	2.55941e49i		−	1.33158i	0.746138	−	0.665791i	$-0.231906\pi$
$548$	−1.14865e48	+	1.68481e49i	−0.0578279	+	0.848204i
$549$	1.16695e48			0.0568528
$550$	−4.51595e48	+	4.21855e48i	−0.212922	+	0.198900i
$551$			1.58248e48i			0.0722118i
$552$	1.86111e49	−	1.51516e49i	0.821993	−	0.669200i
$553$	2.44316e49			1.04448
$554$	1.44226e48	+	1.54394e48i	0.0596855	+	0.0638933i
$555$		−	6.12801e48i		−	0.245497i
$556$	−5.16214e48	−	3.51938e47i	−0.200209	−	0.0136496i
$557$	3.13988e49			1.17901			0.589507	−	0.807763i	$-0.299322\pi$
$557$	3.13988e49			1.17901			0.589507	+	0.807763i	$0.299322\pi$
$558$	−1.01594e49	+	9.49033e48i	−0.369362	+	0.345037i
$559$		−	4.71540e49i		−	1.65999i
$560$	−2.99733e47	+	2.18799e48i	−0.0102176	+	0.0745865i
$561$	1.79178e49			0.591498
$562$	−3.41348e49	−	3.65413e49i	−1.09130	−	1.16823i
$563$			3.22007e49i			0.997043i	0.866877	+	0.498521i	$0.166123\pi$
$563$			3.22007e49i			0.997043i	−0.866877	+	0.498521i	$0.833877\pi$
$564$	−1.97732e48	+	2.90028e49i	−0.0592998	+	0.869793i
$565$	−2.22092e48			−0.0645150
$566$	−1.47057e49	+	1.37373e49i	−0.413801	+	0.386550i
$567$			2.64437e49i			0.720821i
$568$	−2.54868e49	−	3.13059e49i	−0.673046	−	0.826717i
$569$	−1.36109e49			−0.348230			−0.174115	−	0.984725i	$-0.555706\pi$
$569$	−1.36109e49			−0.348230			−0.174115	+	0.984725i	$0.555706\pi$
$570$	−5.08343e48	−	5.44180e48i	−0.126011	−	0.134895i
$571$		−	1.02069e49i		−	0.245157i	−0.992459	−	0.122579i	$-0.960884\pi$
$571$		−	1.02069e49i		−	0.245157i	0.992459	−	0.122579i	$-0.0391164\pi$
$572$	1.29411e49	+	8.82284e47i	0.301192	+	0.0205343i
$573$	−9.30607e49			−2.09886
$574$	−3.07816e49	+	2.87544e49i	−0.672786	+	0.628479i
$575$			4.02419e49i			0.852427i
$576$	−4.87900e48	+	2.35585e49i	−0.100167	+	0.483663i
$577$	9.74285e49			1.93875			0.969374	−	0.245589i	$-0.0789813\pi$
$577$	9.74285e49			1.93875			0.969374	+	0.245589i	$0.0789813\pi$
$578$	5.89381e49	+	6.30931e49i	1.13683	+	1.21697i
$579$		−	1.30144e49i		−	0.243337i
$580$	3.05788e46	−	4.48522e47i	0.000554265	−	0.00812981i
$581$	−8.99762e47			−0.0158109
$582$	5.36371e49	−	5.01048e49i	0.913801	−	0.853622i
$583$		−	5.68683e48i		−	0.0939369i
$584$	6.47926e49	−	5.27488e49i	1.03775	−	0.844854i
$585$	−4.22838e48			−0.0656702
$586$	4.76266e49	+	5.09841e49i	0.717286	+	0.767853i
$587$			1.32820e50i			1.93989i	0.243333	+	0.969943i	$0.421759\pi$
$587$			1.32820e50i			1.93989i	−0.243333	+	0.969943i	$0.578241\pi$
$588$	5.74601e49	+	3.91745e48i	0.813907	+	0.0554896i
$589$	−8.61745e49			−1.18387
$590$	2.74006e48	−	2.55961e48i	0.0365110	−	0.0341065i
$591$		−	8.00722e49i		−	1.03492i
$592$	−1.21581e50	−	1.66555e49i	−1.52432	−	0.208817i
$593$	1.05208e49			0.127957			0.0639785	−	0.997951i	$-0.479621\pi$
$593$	1.05208e49			0.127957			0.0639785	+	0.997951i	$0.479621\pi$
$594$	−1.06080e49	−	1.13559e49i	−0.125164	−	0.133988i
$595$			1.07369e49i			0.122906i
$596$	2.62780e48	−	3.85438e49i	0.0291850	−	0.428077i
$597$	−2.01705e50			−2.17359
$598$	6.17243e49	−	5.76595e49i	0.645409	−	0.602905i
$599$		−	3.72920e49i		−	0.378384i	−0.981940	−	0.189192i	$-0.939413\pi$
$599$		−	3.72920e49i		−	0.378384i	0.981940	−	0.189192i	$-0.0605869\pi$
$600$	−7.70355e49	−	9.46244e49i	−0.758523	−	0.931710i
$601$	1.08974e50			1.04131			0.520656	−	0.853766i	$-0.325687\pi$
$601$	1.08974e50			1.04131			0.520656	+	0.853766i	$0.325687\pi$
$602$	−6.91868e49	−	7.40644e49i	−0.641633	−	0.686867i
$603$		−	1.95247e49i		−	0.175741i
$604$	7.75603e48	+	5.28782e47i	0.0677602	+	0.00461967i
$605$	1.40418e49			0.119076
$606$	1.62610e50	−	1.51901e50i	1.33856	−	1.25041i
$607$		−	3.62232e48i		−	0.0289461i	−0.999895	−	0.0144730i	$-0.995393\pi$
$607$		−	3.62232e48i		−	0.0289461i	0.999895	−	0.0144730i	$-0.00460707\pi$
$608$	−1.21783e50	+	8.60662e49i	−0.944763	+	0.667679i
$609$	5.84152e48			0.0439961
$610$	−1.40276e48	−	1.50165e48i	−0.0102576	−	0.0109807i
$611$			1.02315e50i			0.726435i
$612$	−7.95601e48	+	1.16697e50i	−0.0548491	+	0.804512i
$613$	1.74376e50			1.16734			0.583672	−	0.811990i	$-0.301616\pi$
$613$	1.74376e50			1.16734			0.583672	+	0.811990i	$0.301616\pi$
$614$	3.97277e49	−	3.71114e49i	0.258263	−	0.241255i
$615$			4.03512e49i			0.254744i
$616$	2.16210e49	−	1.76021e49i	0.132563	−	0.107922i
$617$	7.05688e49			0.420223			0.210111	−	0.977677i	$-0.432617\pi$
$617$	7.05688e49			0.420223			0.210111	+	0.977677i	$0.432617\pi$
$618$	4.70221e49	+	5.03370e49i	0.271963	+	0.291136i
$619$		−	1.56606e50i		−	0.879786i	−0.898050	−	0.439893i	$-0.855016\pi$
$619$		−	1.56606e50i		−	0.879786i	0.898050	−	0.439893i	$-0.144984\pi$
$620$	2.44245e49	+	1.66519e48i	0.133283	+	0.00908683i
$621$	−1.01193e50			−0.536415
$622$	−2.50399e50	+	2.33909e50i	−1.28945	+	1.20454i
$623$		−	3.67803e49i		−	0.184005i
$624$	−3.47599e49	+	2.53740e50i	−0.168949	+	1.23329i
$625$	2.00993e50			0.949163
$626$	1.68277e50	+	1.80141e50i	0.772125	+	0.826559i
$627$			9.40114e49i			0.419145i
$628$	−1.61429e49	+	2.36780e50i	−0.0699373	+	1.02582i
$629$	−5.96627e50			−2.51184
$630$	−6.64147e48	+	6.20409e48i	−0.0271728	+	0.0253833i
$631$		−	1.59388e50i		−	0.633763i	−0.948465	−	0.316881i	$-0.897364\pi$
$631$		−	1.59388e50i		−	0.633763i	0.948465	−	0.316881i	$-0.102636\pi$
$632$	−2.95901e50	−	3.63461e50i	−1.14351	−	1.40459i
$633$	4.10330e50			1.54123
$634$	1.80036e50	+	1.92729e50i	0.657285	+	0.703622i
$635$			1.25343e49i			0.0444808i
$636$	1.12024e50	+	7.63743e48i	0.386440	+	0.0263463i
$637$	2.02705e50			0.679760
$638$	−4.14742e48	+	3.87429e48i	−0.0135209	+	0.0126305i
$639$		−	1.66132e50i		−	0.526547i
$640$	3.61802e49	−	2.20405e49i	0.111489	−	0.0679176i
$641$	3.35970e50			1.00660			0.503299	−	0.864112i	$-0.332119\pi$
$641$	3.35970e50			1.00660			0.503299	+	0.864112i	$0.332119\pi$
$642$	−3.42893e50	−	3.67066e50i	−0.998913	−	1.06933i
$643$		−	3.38009e50i		−	0.957481i	−0.877956	−	0.478741i	$-0.841093\pi$
$643$		−	3.38009e50i		−	0.957481i	0.877956	−	0.478741i	$-0.158907\pi$
$644$	1.23489e49	−	1.81130e50i	0.0340159	−	0.498937i
$645$	−9.70901e49			−0.260076
$646$	−5.29817e50	+	4.94925e50i	−1.38019	+	1.28930i
$647$			3.22802e50i			0.817823i	0.912574	+	0.408912i	$0.134092\pi$
$647$			3.22802e50i			0.817823i	−0.912574	+	0.408912i	$0.865908\pi$
$648$	3.93395e50	−	3.20270e50i	0.969345	−	0.789162i
$649$	−4.73367e49			−0.113447
$650$	−2.93158e50	−	3.13825e50i	−0.683379	−	0.731556i
$651$			3.18103e50i			0.721290i
$652$	−4.07804e50	−	2.78028e49i	−0.899486	−	0.0613241i
$653$	−6.22917e50			−1.33657			−0.668287	−	0.743904i	$-0.732972\pi$
$653$	−6.22917e50			−1.33657			−0.668287	+	0.743904i	$0.732972\pi$
$654$	3.55424e50	−	3.32017e50i	0.741903	−	0.693044i
$655$		−	2.18914e49i		−	0.0444559i
$656$	8.00579e50	+	1.09672e50i	1.58174	+	0.216683i
$657$	3.43836e50			0.660959
$658$	1.50122e50	+	1.60705e50i	0.280787	+	0.300582i
$659$		−	9.66238e50i		−	1.75852i	−0.476345	−	0.879259i	$-0.658039\pi$
$659$		−	9.66238e50i		−	1.75852i	0.476345	−	0.879259i	$-0.341961\pi$
$660$	1.81662e48	−	2.66457e49i	0.00321717	−	0.0471885i
$661$	1.46714e50			0.252839			0.126420	−	0.991977i	$-0.459651\pi$
$661$	1.46714e50			0.252839			0.126420	+	0.991977i	$0.459651\pi$
$662$	2.51944e50	−	2.35352e50i	0.422532	−	0.394706i
$663$			1.24516e51i			2.03226i
$664$	1.08974e49	+	1.33855e49i	0.0173100	+	0.0212622i
$665$	−5.63347e49			−0.0870935
$666$	−3.44747e50	−	3.69051e50i	−0.518758	−	0.555329i
$667$			3.69579e49i			0.0541305i
$668$	9.53753e50	+	6.50239e49i	1.35975	+	0.0927036i
$669$	−1.42893e51			−1.98308
$670$	−2.51246e49	+	2.34700e49i	−0.0339432	+	0.0317078i
$671$			2.59422e49i			0.0341194i
$672$	3.17703e50	+	4.49548e50i	0.406794	+	0.575611i
$673$	−2.83286e50			−0.353146			−0.176573	−	0.984288i	$-0.556501\pi$
$673$	−2.83286e50			−0.353146			−0.176573	+	0.984288i	$0.556501\pi$
$674$	−8.28650e49	−	8.87068e49i	−0.100576	−	0.107666i
$675$			5.14495e50i			0.608013i
$676$	−2.20094e48	+	3.22828e49i	−0.00253261	+	0.0371476i
$677$	4.96112e49			0.0555883			0.0277941	−	0.999614i	$-0.491152\pi$
$677$	4.96112e49			0.0555883			0.0277941	+	0.999614i	$0.491152\pi$
$678$	−4.04545e50	+	3.77903e50i	−0.441400	+	0.412331i
$679$		−	5.55262e50i		−	0.589987i
$680$	1.59730e50	−	1.30039e50i	0.165282	−	0.134559i
$681$	1.36888e50			0.137948
$682$	−2.10976e50	−	2.25850e50i	−0.207069	−	0.221667i
$683$			6.67091e50i			0.637694i	0.947806	+	0.318847i	$0.103296\pi$
$683$			6.67091e50i			0.637694i	−0.947806	+	0.318847i	$0.896704\pi$
$684$	−6.12285e50	−	4.17437e49i	−0.570090	−	0.0388670i
$685$	1.22378e50			0.110988
$686$	7.95409e50	−	7.43027e50i	0.702679	−	0.656403i
$687$			2.18025e51i			1.87623i
$688$	−2.63884e50	+	1.92629e51i	−0.221218	+	1.61484i
$689$	3.95193e50			0.322747
$690$	−1.18721e50	−	1.27090e50i	−0.0944589	−	0.101118i
$691$		−	1.46173e51i		−	1.13308i	−0.824034	−	0.566541i	$-0.808281\pi$
$691$		−	1.46173e51i		−	1.13308i	0.824034	−	0.566541i	$-0.191719\pi$
$692$	1.54172e50	−	2.26135e51i	0.116438	−	1.70788i
$693$	1.14737e50			0.0844313
$694$	−1.66514e51	+	1.55548e51i	−1.19393	+	1.11531i
$695$			3.74960e49i			0.0261974i
$696$	−7.07489e49	−	8.69025e49i	−0.0481674	−	0.0591651i
$697$	3.92862e51			2.60645
$698$	7.57918e50	+	8.11350e50i	0.490032	+	0.524579i
$699$		−	1.04432e50i		−	0.0658027i
$700$	−9.20921e50	−	6.27855e49i	−0.565533	−	0.0385562i
$701$	−1.22498e51			−0.733172			−0.366586	−	0.930384i	$-0.619473\pi$
$701$	−1.22498e51			−0.733172			−0.366586	+	0.930384i	$0.619473\pi$
$702$	7.89149e50	−	7.37179e50i	0.460353	−	0.430036i
$703$		−	3.13039e51i		−	1.77993i
$704$	−5.23721e50	−	1.08463e50i	−0.290263	−	0.0601140i
$705$	2.10666e50			0.113813
$706$	4.40437e50	+	4.71487e50i	0.231953	+	0.248305i
$707$		−	1.68337e51i		−	0.864232i
$708$	6.35733e49	−	9.32476e50i	0.0318182	−	0.466702i
$709$	−1.49159e51			−0.727811			−0.363905	−	0.931436i	$-0.618557\pi$
$709$	−1.49159e51			−0.727811			−0.363905	+	0.931436i	$0.618557\pi$
$710$	−2.13780e50	+	1.99702e50i	−0.101699	+	0.0950017i
$711$		−	1.92879e51i		−	0.894606i
$712$	−5.47169e50	+	4.45460e50i	−0.247447	+	0.201451i
$713$	−2.01256e51			−0.887437
$714$	1.82696e51	+	1.95575e51i	0.785526	+	0.840904i
$715$		−	9.39996e49i		−	0.0394110i
$716$	−3.77059e51	−	2.57067e50i	−1.54161	−	0.105102i
$717$	1.40125e51			0.558689
$718$	−8.86262e50	+	8.27897e50i	−0.344605	+	0.321911i
$719$		−	2.75711e51i		−	1.04553i	−0.852478	−	0.522763i	$-0.824901\pi$
$719$		−	2.75711e51i		−	1.04553i	0.852478	−	0.522763i	$-0.175099\pi$
$720$	1.72734e50	+	2.36629e49i	0.0638840	+	0.00875150i
$721$	5.21100e50			0.187969
$722$	−6.56528e50	−	7.02812e50i	−0.230985	−	0.247269i
$723$			1.63515e51i			0.561138i
$724$	−1.61977e50	+	2.37583e51i	−0.0542198	+	0.795282i
$725$	1.87905e50			0.0613556
$726$	2.55774e51	−	2.38930e51i	0.814700	−	0.761047i
$727$			2.75423e51i			0.855817i	0.903822	+	0.427908i	$0.140749\pi$
$727$			2.75423e51i			0.855817i	−0.903822	+	0.427908i	$0.859251\pi$
$728$	1.22321e51	+	1.50250e51i	0.370798	+	0.455459i
$729$	−4.68820e50			−0.138647
$730$	−4.13314e50	−	4.42452e50i	−0.119253	−	0.127660i
$731$			9.45275e51i			2.66100i
$732$	−5.11030e50	−	3.48404e49i	−0.140361	−	0.00956939i
$733$	6.09851e51			1.63438			0.817188	−	0.576371i	$-0.195532\pi$
$733$	6.09851e51			1.63438			0.817188	+	0.576371i	$0.195532\pi$
$734$	3.74241e51	−	3.49595e51i	0.978639	−	0.914190i
$735$		−	4.17370e50i		−	0.106500i
$736$	−2.84418e51	+	2.01003e51i	−0.708201	+	0.500497i
$737$	4.34047e50			0.105468
$738$	2.27006e51	+	2.43010e51i	0.538298	+	0.576247i
$739$			5.69250e50i			0.131736i	0.997828	+	0.0658678i	$0.0209816\pi$
$739$			5.69250e50i			0.131736i	−0.997828	+	0.0658678i	$0.979018\pi$
$740$	−6.04898e49	+	8.87249e50i	−0.0136619	+	0.200389i
$741$	−6.53310e51			−1.44010
$742$	6.20725e50	−	5.79847e50i	0.133545	−	0.124751i
$743$			3.72054e51i			0.781282i	0.920543	+	0.390641i	$0.127747\pi$
$743$			3.72054e51i			0.781282i	−0.920543	+	0.390641i	$0.872253\pi$
$744$	4.73232e51	−	3.85267e51i	0.969976	−	0.789676i
$745$	−2.79969e50			−0.0560140
$746$	−3.19237e51	−	3.41742e51i	−0.623468	−	0.667421i
$747$			7.10330e49i			0.0135422i
$748$	−2.59424e51	−	1.76867e50i	−0.482816	−	0.0329169i
$749$	−3.79994e51			−0.690406
$750$	−1.30354e51	+	1.21769e51i	−0.231217	+	0.215990i
$751$		−	7.88181e51i		−	1.36492i	−0.730923	−	0.682460i	$-0.760910\pi$
$751$		−	7.88181e51i		−	1.36492i	0.730923	−	0.682460i	$-0.239090\pi$
$752$	5.72575e50	−	4.17967e51i	0.0968080	−	0.706677i
$753$	−1.15613e52			−1.90852
$754$	−2.69235e50	−	2.88215e50i	−0.0433957	−	0.0464550i
$755$		−	5.63370e49i		−	0.00886643i
$756$	1.57881e50	−	2.31576e51i	0.0242626	−	0.355878i
$757$	2.97017e51			0.445713			0.222857	−	0.974851i	$-0.428462\pi$
$757$	2.97017e51			0.445713			0.222857	+	0.974851i	$0.428462\pi$
$758$	3.06436e51	−	2.86255e51i	0.449049	−	0.419476i
$759$			2.19559e51i			0.314194i
$760$	6.82291e50	+	8.38073e50i	0.0953510	+	0.117122i
$761$	−1.54790e51			−0.211261			−0.105630	−	0.994405i	$-0.533686\pi$
$761$	−1.54790e51			−0.211261			−0.105630	+	0.994405i	$0.533686\pi$
$762$	2.13279e51	+	2.28315e51i	0.284288	+	0.304330i
$763$		−	3.67942e51i		−	0.479003i
$764$	1.34739e52	+	9.18605e50i	1.71321	+	0.116801i
$765$	8.47643e50			0.105271
$766$	−4.66785e51	+	4.36045e51i	−0.566238	+	0.528948i
$767$		−	3.28955e51i		−	0.389780i
$768$	2.83996e51	−	1.01710e52i	0.328708	−	1.17723i
$769$	1.52640e52			1.72582			0.862909	−	0.505359i	$-0.168640\pi$
$769$	1.52640e52			1.72582			0.862909	+	0.505359i	$0.168640\pi$
$770$	−1.37921e50	−	1.47644e50i	−0.0152334	−	0.0163074i
$771$		−	1.33845e52i		−	1.44419i
$772$	−1.28465e50	+	1.88429e51i	−0.0135417	+	0.198626i
$773$	6.53927e51			0.673439			0.336720	−	0.941605i	$-0.390683\pi$
$773$	6.53927e51			0.673439			0.336720	+	0.941605i	$0.390683\pi$
$774$	−5.84712e51	+	5.46206e51i	−0.588308	+	0.549565i
$775$			1.02325e52i			1.00589i
$776$	−8.26047e51	+	6.72500e51i	−0.793403	+	0.645924i
$777$	−1.15554e52			−1.08445
$778$	−6.28876e51	−	6.73211e51i	−0.576677	−	0.617331i
$779$			2.06127e52i			1.84697i
$780$	1.85168e51	+	1.26242e50i	0.162130	+	0.0110535i
$781$	3.69322e51			0.316000
$782$	−1.23736e52	+	1.15587e52i	−1.03460	+	0.966470i
$783$			4.72509e50i			0.0386099i
$784$	−8.28074e51	−	1.13438e51i	−0.661272	−	0.0905879i
$785$	1.71989e51			0.134229
$786$	−3.72496e51	−	3.98756e51i	−0.284129	−	0.304159i
$787$		−	2.21117e52i		−	1.64845i	−0.566260	−	0.824227i	$-0.691610\pi$
$787$		−	2.21117e52i		−	1.64845i	0.566260	−	0.824227i	$-0.308390\pi$
$788$	−7.90395e50	+	1.15933e52i	−0.0575934	+	0.844764i
$789$	2.23651e52			1.59289
$790$	−2.48198e51	+	2.31853e51i	−0.172787	+	0.161408i
$791$			4.18793e51i			0.284986i
$792$	−1.38962e51	−	1.70690e51i	−0.0924364	−	0.113542i
$793$	−1.80279e51			−0.117227
$794$	1.62805e51	+	1.74283e51i	0.103490	+	0.110786i
$795$		−	8.13701e50i		−	0.0505658i
$796$	2.92040e52	+	1.99103e51i	1.77422	+	0.120961i
$797$	−5.54069e51			−0.329090			−0.164545	−	0.986370i	$-0.552616\pi$
$797$	−5.54069e51			−0.329090			−0.164545	+	0.986370i	$0.552616\pi$
$798$	−1.02615e52	+	9.58570e51i	−0.595878	+	0.556636i
$799$		−	2.05106e52i		−	1.16449i
$800$	1.02196e52	+	1.44607e52i	0.567302	+	0.802729i
$801$	−2.90367e51			−0.157602
$802$	−5.01972e51	−	5.37361e51i	−0.266404	−	0.285185i
$803$			7.64370e51i			0.396665i
$804$	−5.82927e50	+	8.55021e51i	−0.0295805	+	0.433878i
$805$	−1.31567e51			−0.0652860
$806$	1.56949e52	−	1.46613e52i	0.761602	−	0.711446i
$807$			1.62464e52i			0.770965i
$808$	−2.50430e52	+	2.03880e52i	−1.16220	+	0.946171i
$809$	−1.84103e52			−0.835579			−0.417790	−	0.908544i	$-0.637195\pi$
$809$	−1.84103e52			−0.835579			−0.417790	+	0.908544i	$0.637195\pi$
$810$	−2.50948e51	−	2.68639e51i	−0.111392	−	0.119245i
$811$		−	2.91057e52i		−	1.26358i	−0.775140	−	0.631790i	$-0.782321\pi$
$811$		−	2.91057e52i		−	1.26358i	0.775140	−	0.631790i	$-0.217679\pi$
$812$	−8.45768e50	−	5.76618e49i	−0.0359123	−	0.00244839i
$813$	1.87978e52			0.780686
$814$	8.20426e51	−	7.66396e51i	0.333273	−	0.311325i
$815$			2.96214e51i			0.117698i
$816$	6.96815e51	−	5.08660e52i	0.270829	−	1.97699i
$817$	−4.95968e52			−1.88563
$818$	4.76909e51	+	5.10530e51i	0.177368	+	0.189872i
$819$			7.97335e51i			0.290089i
$820$	3.98308e50	−	5.84228e51i	0.0141765	−	0.207937i
$821$	3.87555e52			1.34945			0.674725	−	0.738069i	$-0.264262\pi$
$821$	3.87555e52			1.34945			0.674725	+	0.738069i	$0.264262\pi$
$822$	2.22915e52	−	2.08235e52i	0.759358	−	0.709350i
$823$			3.56451e52i			1.18796i	0.804479	+	0.593982i	$0.202445\pi$
$823$			3.56451e52i			1.18796i	−0.804479	+	0.593982i	$0.797555\pi$
$824$	−6.31125e51	−	7.75224e51i	−0.205790	−	0.252777i
$825$	1.11630e52			0.356132
$826$	−4.82660e51	−	5.16686e51i	−0.150661	−	0.161282i
$827$		−	1.29307e52i		−	0.394933i	−0.980310	−	0.197467i	$-0.936729\pi$
$827$		−	1.29307e52i		−	0.394933i	0.980310	−	0.197467i	$-0.0632714\pi$
$828$	−1.42996e52	−	9.74901e50i	−0.427344	−	0.0291350i
$829$	1.20493e52			0.352354			0.176177	−	0.984359i	$-0.443627\pi$
$829$	1.20493e52			0.352354			0.176177	+	0.984359i	$0.443627\pi$
$830$	9.14061e49	−	8.53865e49i	0.00261559	−	0.00244334i
$831$		−	3.81649e51i		−	0.106867i
$832$	7.53741e51	−	3.63948e52i	0.206539	−	0.997284i
$833$	−4.06354e52			−1.08967
$834$	6.38017e51	+	6.82996e51i	0.167434	+	0.179238i
$835$		−	6.92772e51i		−	0.177924i
$836$	9.27989e50	−	1.36115e52i	0.0233254	−	0.342131i
$837$	−2.57307e52			−0.632985
$838$	3.85118e51	−	3.59756e51i	0.0927261	−	0.0866195i
$839$			4.11789e52i			0.970419i	0.874398	+	0.485209i	$0.161257\pi$
$839$			4.11789e52i			0.970419i	−0.874398	+	0.485209i	$0.838743\pi$
$840$	3.09365e51	−	2.51860e51i	0.0713581	−	0.0580940i
$841$	−4.41197e52			−0.996104
$842$	4.13534e52	+	4.42688e52i	0.913890	+	0.978318i
$843$			9.03268e52i			1.95398i
$844$	−5.94099e52	−	4.05038e51i	−1.25804	−	0.0857693i
$845$	2.34491e50			0.00486077
$846$	1.26871e52	−	1.18516e52i	0.257451	−	0.240497i
$847$		−	2.64783e52i		−	0.526003i
$848$	−1.61441e52	−	2.21158e51i	−0.313969	−	0.0430108i
$849$	3.63513e52			0.692120
$850$	5.87681e52	+	6.29111e52i	1.09547	+	1.17270i
$851$		−	7.31086e52i		−	1.33425i
$852$	−4.96001e51	+	7.27521e52i	−0.0886278	+	1.29997i
$853$	1.79738e52			0.314455			0.157227	−	0.987562i	$-0.449744\pi$
$853$	1.79738e52			0.314455			0.157227	+	0.987562i	$0.449744\pi$
$854$	−2.83162e51	+	2.64515e51i	−0.0485058	+	0.0453115i
$855$			4.44742e51i			0.0745965i
$856$	4.60226e52	+	5.65306e52i	0.755864	+	0.928444i
$857$	−1.62628e52			−0.261541			−0.130770	−	0.991413i	$-0.541745\pi$
$857$	−1.62628e52			−0.261541			−0.130770	+	0.991413i	$0.541745\pi$
$858$	−1.59946e52	−	1.71222e52i	−0.251885	−	0.269643i
$859$			9.56110e52i			1.47445i	0.675646	+	0.737226i	$0.263865\pi$
$859$			9.56110e52i			1.47445i	−0.675646	+	0.737226i	$0.736135\pi$
$860$	1.40573e52	+	9.58380e50i	0.212290	+	0.0144732i
$861$	7.60893e52			1.12530
$862$	2.23516e52	−	2.08796e52i	0.323726	−	0.302407i
$863$		−	7.16740e52i		−	1.01664i	−0.861168	−	0.508320i	$-0.830267\pi$
$863$		−	7.16740e52i		−	1.01664i	0.861168	−	0.508320i	$-0.169733\pi$
$864$	−3.63630e52	+	2.56983e52i	−0.505141	+	0.356991i
$865$	−1.64256e52			−0.223477
$866$	−5.01883e52	−	5.37265e52i	−0.668775	−	0.715923i
$867$		−	1.55961e53i		−	2.03550i
$868$	3.14000e51	−	4.60567e52i	0.0401398	−	0.588760i
$869$	4.28782e52			0.536885
$870$	−5.93435e50	+	5.54354e50i	−0.00727824	+	0.00679893i
$871$			3.01631e52i			0.362367i
$872$	−5.47376e52	+	4.45629e52i	−0.644153	+	0.524417i
$873$	−4.38360e52			−0.505329
$874$	−6.06464e52	−	6.49219e52i	−0.684856	−	0.733137i
$875$			1.34945e52i			0.149283i
$876$	−1.50572e53	−	1.02655e52i	−1.63181	−	0.111252i
$877$	1.13472e53			1.20475			0.602373	−	0.798215i	$-0.294222\pi$
$877$	1.13472e53			1.20475			0.602373	+	0.798215i	$0.294222\pi$
$878$	−3.54398e52	+	3.31059e52i	−0.368629	+	0.344353i
$879$		−	1.26028e53i		−	1.28431i
$880$	−5.26042e50	+	3.83999e51i	−0.00525209	+	0.0383391i
$881$	−1.90245e52			−0.186101			−0.0930503	−	0.995661i	$-0.529662\pi$
$881$	−1.90245e52			−0.186101			−0.0930503	+	0.995661i	$0.529662\pi$
$882$	−2.34802e52	−	2.51356e52i	−0.225044	−	0.240910i
$883$			1.12738e53i			1.05871i	0.848401	+	0.529354i	$0.177566\pi$
$883$			1.12738e53i			1.05871i	−0.848401	+	0.529354i	$0.822434\pi$
$884$	1.22910e52	−	1.80281e53i	0.113096	−	1.65886i
$885$	−6.77318e51			−0.0610680
$886$	−2.16752e52	+	2.02477e52i	−0.191494	+	0.178883i
$887$		−	1.84545e53i		−	1.59763i	−0.601574	−	0.798817i	$-0.705459\pi$
$887$		−	1.84545e53i		−	1.59763i	0.601574	−	0.798817i	$-0.294541\pi$
$888$	1.39953e53	+	1.71907e53i	1.18727	+	1.45834i
$889$	2.36356e52			0.196488
$890$	3.49041e51	+	3.73648e51i	0.0284352	+	0.0304398i
$891$			4.64096e52i			0.370517i
$892$	2.06888e53	+	1.41050e52i	1.61871	+	0.110358i
$893$	1.07615e53			0.825177
$894$	−5.09969e52	+	4.76385e52i	−0.383238	+	0.358000i
$895$			2.73882e52i			0.201720i
$896$	−4.15613e52	−	6.82241e52i	−0.300016	−	0.492486i
$897$	−1.52577e53			−1.07951
$898$	1.30193e53	+	1.39372e53i	0.902847	+	0.966496i
$899$			9.39744e51i			0.0638756i
$900$	−4.95669e51	+	7.27035e52i	−0.0330238	+	0.484384i
$901$	−7.92224e52			−0.517371
$902$	−5.40226e52	+	5.04650e52i	−0.345826	+	0.323052i
$903$			1.83081e53i			1.14885i
$904$	6.23026e52	−	5.07217e52i	0.383243	−	0.312006i
$905$	1.72572e52			0.104063
$906$	−9.58610e51	−	1.02619e52i	−0.0566676	−	0.0606625i
$907$			2.03936e53i			1.18185i	0.806727	+	0.590924i	$0.201237\pi$
$907$			2.03936e53i			1.18185i	−0.806727	+	0.590924i	$0.798763\pi$
$908$	−1.98194e52	−	1.35122e51i	−0.112602	−	0.00767683i
$909$	−1.32896e53			−0.740223
$910$	1.02602e52	−	9.58450e51i	0.0560287	−	0.0523389i
$911$		−	1.63761e53i		−	0.876759i	−0.898790	−	0.438380i	$-0.855553\pi$
$911$		−	1.63761e53i		−	0.876759i	0.898790	−	0.438380i	$-0.144447\pi$
$912$	2.66884e53	+	3.65606e52i	1.40093	+	0.191914i
$913$	−1.57911e51			−0.00812716
$914$	−1.28632e53	−	1.37700e53i	−0.649108	−	0.694869i
$915$			3.71194e51i			0.0183663i
$916$	2.15214e52	−	3.15670e53i	0.104412	−	1.53149i
$917$	−4.12801e52			−0.196378
$918$	−1.58197e53	+	1.47779e53i	−0.737955	+	0.689357i
$919$			2.92565e53i			1.33827i	0.743142	+	0.669134i	$0.233335\pi$
$919$			2.92565e53i			1.33827i	−0.743142	+	0.669134i	$0.766665\pi$
$920$	1.59346e52	+	1.95728e52i	0.0714758	+	0.0877953i
$921$	−9.82033e52			−0.431969
$922$	−1.16659e53	−	1.24883e53i	−0.503222	−	0.538699i
$923$			2.56652e53i			1.08571i
$924$	−5.02452e52	−	3.42556e51i	−0.208449	−	0.0142114i
$925$	−3.71706e53			−1.51234
$926$	1.40060e53	−	1.30837e53i	0.558879	−	0.522074i
$927$		−	4.11390e52i		−	0.160997i
$928$	9.38562e51	+	1.32806e52i	0.0360246	+	0.0509746i
$929$	2.46140e53			0.926617			0.463308	−	0.886197i	$-0.346662\pi$
$929$	2.46140e53			0.926617			0.463308	+	0.886197i	$0.346662\pi$
$930$	−3.01876e52	−	3.23158e52i	−0.111464	−	0.119322i
$931$		−	2.13206e53i		−	0.772157i
$932$	−1.03085e51	+	1.51202e52i	−0.00366192	+	0.0537121i
$933$	6.18964e53			2.15673
$934$	1.15067e53	−	1.07489e53i	0.393284	−	0.367384i
$935$			1.88437e52i			0.0631766i
$936$	1.18617e53	−	9.65684e52i	0.390105	−	0.317592i
$937$	−2.02829e53			−0.654360			−0.327180	−	0.944962i	$-0.606098\pi$
$937$	−2.02829e53			−0.654360			−0.327180	+	0.944962i	$0.606098\pi$
$938$	4.42568e52	+	4.73768e52i	0.140065	+	0.149939i
$939$		−	4.45292e53i		−	1.38250i
$940$	−3.05014e52	−	2.07949e51i	−0.0929007	−	0.00633368i
$941$	1.67872e53			0.501610			0.250805	−	0.968038i	$-0.419305\pi$
$941$	1.67872e53			0.501610			0.250805	+	0.968038i	$0.419305\pi$
$942$	3.13281e53	−	2.92650e53i	0.918371	−	0.857891i
$943$			4.81399e53i			1.38451i
$944$	−1.84090e52	+	1.34382e53i	−0.0519439	+	0.379179i
$945$	−1.68209e52			−0.0465667
$946$	−1.21425e53	−	1.29985e53i	−0.329813	−	0.353064i
$947$		−	5.17119e53i		−	1.37813i	−0.724699	−	0.689065i	$-0.758021\pi$
$947$		−	5.17119e53i		−	1.37813i	0.724699	−	0.689065i	$-0.241979\pi$
$948$	−5.75856e52	+	8.44651e53i	−0.150579	+	2.20865i
$949$	−5.31181e53			−1.36286
$950$	−3.30083e53	+	3.08345e53i	−0.830994	+	0.776268i
$951$		−	4.76408e53i		−	1.17687i
$952$	−2.45212e53	−	3.01199e53i	−0.594397	−	0.730111i
$953$	4.48165e50			0.00106602			0.000533011	−	1.00000i	$-0.499830\pi$
$953$	4.48165e50			0.00106602			0.000533011		1.00000i	$0.499830\pi$
$954$	−4.57769e52	−	4.90040e52i	−0.106850	−	0.114383i
$955$		−	9.78693e52i		−	0.224174i
$956$	−2.02881e53	−	1.38318e52i	−0.456036	−	0.0310911i
$957$	1.02521e52			0.0226150
$958$	7.59259e52	−	7.09258e52i	0.164366	−	0.153541i
$959$		−	2.30766e53i		−	0.490272i
$960$	−7.49367e52	−	1.55195e52i	−0.156247	−	0.0323591i
$961$	−2.30663e52			−0.0472016
$962$	5.32589e53	+	5.70135e53i	1.06965	+	1.14506i
$963$			2.99992e53i			0.591339i
$964$	1.61407e52	−	2.36747e53i	0.0312273	−	0.458034i
$965$	1.36868e52			0.0259903
$966$	−2.39651e53	+	2.23869e53i	−0.446675	+	0.417259i
$967$			4.64961e52i			0.0850628i	0.999095	+	0.0425314i	$0.0135423\pi$
$967$			4.64961e52i			0.0850628i	−0.999095	+	0.0425314i	$0.986458\pi$
$968$	−3.93909e53	+	3.20689e53i	−0.707359	+	0.575874i
$969$	1.30966e54			2.30850
$970$	5.26938e52	+	5.64086e52i	0.0911734	+	0.0976010i
$971$		−	1.65013e53i		−	0.280268i	−0.990133	−	0.140134i	$-0.955247\pi$
$971$		−	1.65013e53i		−	0.280268i	0.990133	−	0.140134i	$-0.0447533\pi$
$972$	−5.44075e53	−	3.70933e52i	−0.907123	−	0.0618448i
$973$	7.07052e52			0.115723
$974$	−2.00771e53	+	1.87549e53i	−0.322582	+	0.301338i
$975$			7.75748e53i			1.22359i
$976$	7.36460e52	+	1.00888e52i	0.114039	+	0.0156222i
$977$	6.81679e53			1.03628			0.518140	−	0.855296i	$-0.326624\pi$
$977$	6.81679e53			1.03628			0.518140	+	0.855296i	$0.326624\pi$
$978$	5.04027e53	+	5.39560e53i	0.752236	+	0.805268i
$979$		−	6.45506e52i		−	0.0945827i
$980$	−4.11987e51	+	6.04292e52i	−0.00592672	+	0.0869316i
$981$	−2.90477e53			−0.410270
$982$	3.54484e53	−	3.31139e53i	0.491575	−	0.459202i
$983$			1.38213e54i			1.88185i	0.338615	+	0.940925i	$0.390041\pi$
$983$			1.38213e54i			1.88185i	−0.338615	+	0.940925i	$0.609959\pi$
$984$	−9.21548e53	−	1.13196e54i	−1.23199	−	1.51328i
$985$	8.42097e52			0.110538
$986$	5.39722e52	+	5.77772e52i	0.0695642	+	0.0744683i
$987$		−	3.97248e53i		−	0.502751i
$988$	9.45899e53	+	6.44884e52i	1.17549	+	0.0801414i
$989$	−1.15831e54			−1.41348
$990$	−1.16560e52	+	1.08884e52i	−0.0139674	+	0.0130476i
$991$		−	9.07771e53i		−	1.06819i	−0.845423	−	0.534097i	$-0.820652\pi$
$991$		−	9.07771e53i		−	1.06819i	0.845423	−	0.534097i	$-0.179348\pi$
$992$	−7.23202e53	+	5.11099e53i	−0.835698	+	0.590602i
$993$	−6.22783e53			−0.706724
$994$	3.76573e53	+	4.03120e53i	0.419656	+	0.449241i
$995$		−	2.12127e53i		−	0.232157i
$996$	2.12075e51	−	3.11066e52i	0.00227941	−	0.0334337i
$997$	−3.01638e53			−0.318400			−0.159200	−	0.987246i	$-0.550891\pi$
$997$	−3.01638e53			−0.318400			−0.159200	+	0.987246i	$0.550891\pi$
$998$	5.62663e53	−	5.25609e53i	0.583309	−	0.544895i
$999$		−	9.34697e53i		−	0.951683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.37.b.b.3.12	yes	16
4.3	odd	2	inner	4.37.b.b.3.11	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.37.b.b.3.11	✓	16	4.3	odd	2	inner
4.37.b.b.3.12	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)

\(f(q)\)	\(=\)	\(q+(178949. + 191564. i) q^{2} -4.73530e8i q^{3} +(-4.67423e9 + 6.85603e10i) q^{4} +4.97998e11 q^{5} +(9.07113e13 - 8.47375e13i) q^{6} -9.39063e14i q^{7} +(-1.39702e16 + 1.13734e16i) q^{8} -7.41357e16 q^{9} +O(q^{10})\)	\(q+(178949. + 191564. i) q^{2} -4.73530e8i q^{3} +(-4.67423e9 + 6.85603e10i) q^{4} +4.97998e11 q^{5} +(9.07113e13 - 8.47375e13i) q^{6} -9.39063e14i q^{7} +(-1.39702e16 + 1.13734e16i) q^{8} -7.41357e16 q^{9} +(8.91161e16 + 9.53986e16i) q^{10} -1.64809e18i q^{11} +(3.24653e19 + 2.21338e18i) q^{12} +1.14530e20 q^{13} +(1.79891e20 - 1.68044e20i) q^{14} -2.35817e20i q^{15} +(-4.67867e21 - 6.40933e20i) q^{16} -2.29593e22 q^{17} +(-1.32665e22 - 1.42017e22i) q^{18} -1.20463e23i q^{19} +(-2.32776e21 + 3.41429e22i) q^{20} -4.44674e23 q^{21} +(3.15714e23 - 2.94923e23i) q^{22} -2.81335e24i q^{23} +(5.38563e24 + 6.61528e24i) q^{24} -1.43039e25 q^{25} +(2.04950e25 + 2.19398e25i) q^{26} -3.59688e25i q^{27} +(6.43825e25 + 4.38939e24i) q^{28} -1.31366e25 q^{29} +(4.51741e25 - 4.21991e25i) q^{30} -7.15362e26i q^{31} +(-7.14462e26 - 1.01096e27i) q^{32} -7.80418e26 q^{33} +(-4.10853e27 - 4.39817e27i) q^{34} -4.67651e26i q^{35} +(3.46527e26 - 5.08277e27i) q^{36} +2.59863e28 q^{37} +(2.30764e28 - 2.15567e28i) q^{38} -5.42333e28i q^{39} +(-6.95711e27 + 5.66391e27i) q^{40} -1.71112e29 q^{41} +(-7.95738e28 - 8.51837e28i) q^{42} -4.11718e29i q^{43} +(1.12993e29 + 7.70353e27i) q^{44} -3.69194e28 q^{45} +(5.38937e29 - 5.03445e29i) q^{46} +8.93346e29i q^{47} +(-3.03501e29 + 2.21549e30i) q^{48} +1.76989e30 q^{49} +(-2.55967e30 - 2.74012e30i) q^{50} +1.08719e31i q^{51} +(-5.35338e29 + 7.85220e30i) q^{52} +3.45056e30 q^{53} +(6.89034e30 - 6.43657e30i) q^{54} -8.20743e29i q^{55} +(1.06803e31 + 1.31189e31i) q^{56} -5.70428e31 q^{57} +(-2.35078e30 - 2.51651e30i) q^{58} -2.87222e31i q^{59} +(1.61677e31 + 1.10226e30i) q^{60} -1.57408e31 q^{61} +(1.37038e32 - 1.28013e32i) q^{62} +6.96181e31i q^{63} +(6.58117e31 - 3.17775e32i) q^{64} +5.70356e31 q^{65} +(-1.39655e32 - 1.49500e32i) q^{66} +2.63364e32i q^{67} +(1.07317e32 - 1.57409e33i) q^{68} -1.33220e33 q^{69} +(8.95853e31 - 8.36856e31i) q^{70} +2.24092e33i q^{71} +(1.03569e33 - 8.43172e32i) q^{72} -4.63793e33 q^{73} +(4.65022e33 + 4.97805e33i) q^{74} +6.77333e33i q^{75} +(8.25898e33 + 5.63071e32i) q^{76} -1.54766e33 q^{77} +(1.03892e34 - 9.70497e33i) q^{78} +2.60170e34i q^{79} +(-2.32997e33 - 3.19183e32i) q^{80} -2.81597e34 q^{81} +(-3.06203e34 - 3.27790e34i) q^{82} -9.58149e32i q^{83} +(2.07851e33 - 3.04870e34i) q^{84} -1.14337e34 q^{85} +(7.88705e34 - 7.36765e34i) q^{86} +6.22058e33i q^{87} +(1.87443e34 + 2.30240e34i) q^{88} +3.91670e34 q^{89} +(-6.60668e33 - 7.07244e33i) q^{90} -1.07551e35i q^{91} +(1.92884e35 + 1.31502e34i) q^{92} -3.38745e35 q^{93} +(-1.71133e35 + 1.59863e35i) q^{94} -5.99903e34i q^{95} +(-4.78719e35 + 3.38319e35i) q^{96} +5.91294e35 q^{97} +(3.16720e35 + 3.39048e35i) q^{98} +1.22182e35i 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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