LMFDB - Embedded newform 4.37.b.b.3.1

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			3.1
Root			$-1.10776e7i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.37.b.b.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-227674. - 129939. i) q^{2} -1.77242e8i q^{3} +(3.49511e10 + 5.91675e10i) q^{4} +5.55508e12 q^{5} +(-2.30307e13 + 4.03533e13i) q^{6} -2.49971e15i q^{7} +(-2.69262e14 - 1.80124e16i) q^{8} +1.18680e17 q^{9} +O(q^{10})$	\(q+(-227674. - 129939. i) q^{2} -1.77242e8i q^{3} +(3.49511e10 + 5.91675e10i) q^{4} +5.55508e12 q^{5} +(-2.30307e13 + 4.03533e13i) q^{6} -2.49971e15i q^{7} +(-2.69262e14 - 1.80124e16i) q^{8} +1.18680e17 q^{9} +(-1.26475e18 - 7.21823e17i) q^{10} +5.40459e18i q^{11} +(1.04869e19 - 6.19479e18i) q^{12} +1.72435e20 q^{13} +(-3.24810e20 + 5.69117e20i) q^{14} -9.84593e20i q^{15} +(-2.27921e21 + 4.13593e21i) q^{16} +8.60485e21 q^{17} +(-2.70203e22 - 1.54212e22i) q^{18} +1.88804e23i q^{19} +(1.94156e23 + 3.28680e23i) q^{20} -4.43052e23 q^{21} +(7.02268e23 - 1.23048e24i) q^{22} +9.41760e23i q^{23} +(-3.19255e24 + 4.77245e22i) q^{24} +1.63070e25 q^{25} +(-3.92589e25 - 2.24060e25i) q^{26} -4.76381e25i q^{27} +(1.47901e26 - 8.73674e25i) q^{28} -4.55607e25 q^{29} +(-1.27937e26 + 2.24166e26i) q^{30} +5.01332e26i q^{31} +(1.05634e27 - 6.45484e26i) q^{32} +9.57919e26 q^{33} +(-1.95910e27 - 1.11811e27i) q^{34} -1.38861e28i q^{35} +(4.14799e27 + 7.02199e27i) q^{36} +1.31828e28 q^{37} +(2.45330e28 - 4.29857e28i) q^{38} -3.05627e28i q^{39} +(-1.49578e27 - 1.00060e29i) q^{40} +2.91126e27 q^{41} +(1.00871e29 + 5.75699e28i) q^{42} -6.20563e28i q^{43} +(-3.19776e29 + 1.88896e29i) q^{44} +6.59277e29 q^{45} +(1.22372e29 - 2.14414e29i) q^{46} +4.91358e29i q^{47} +(7.33060e29 + 4.03971e29i) q^{48} -3.59680e30 q^{49} +(-3.71268e30 - 2.11893e30i) q^{50} -1.52514e30i q^{51} +(6.02678e30 + 1.02025e31i) q^{52} +4.35112e29 q^{53} +(-6.19006e30 + 1.08459e31i) q^{54} +3.00230e31i q^{55} +(-4.50257e31 + 6.73077e29i) q^{56} +3.34639e31 q^{57} +(1.03730e31 + 5.92012e30i) q^{58} -5.43569e31i q^{59} +(5.82559e31 - 3.44126e31i) q^{60} -3.68830e31 q^{61} +(6.51427e31 - 1.14140e32i) q^{62} -2.96665e32i q^{63} +(-3.24374e32 + 9.70012e30i) q^{64} +9.57890e32 q^{65} +(-2.18093e32 - 1.24471e32i) q^{66} -9.33023e32i q^{67} +(3.00749e32 + 5.09127e32i) q^{68} +1.66919e32 q^{69} +(-1.80435e33 + 3.16149e33i) q^{70} +1.44228e33i q^{71} +(-3.19561e31 - 2.13771e33i) q^{72} +2.43678e33 q^{73} +(-3.00137e33 - 1.71296e33i) q^{74} -2.89029e33i q^{75} +(-1.11711e34 + 6.59890e33i) q^{76} +1.35099e34 q^{77} +(-3.97129e33 + 6.95831e33i) q^{78} -4.92391e33i q^{79} +(-1.26612e34 + 2.29755e34i) q^{80} +9.36977e33 q^{81} +(-6.62818e32 - 3.78287e32i) q^{82} -3.24535e34i q^{83} +(-1.54852e34 - 2.62143e34i) q^{84} +4.78007e34 q^{85} +(-8.06354e33 + 1.41286e34i) q^{86} +8.07526e33i q^{87} +(9.73496e34 - 1.45525e33i) q^{88} +9.08737e34 q^{89} +(-1.50100e35 - 8.56660e34i) q^{90} -4.31037e35i q^{91} +(-5.57215e34 + 3.29155e34i) q^{92} +8.88570e34 q^{93} +(6.38466e34 - 1.11869e35i) q^{94} +1.04882e36i q^{95} +(-1.14407e35 - 1.87227e35i) q^{96} -1.10168e36 q^{97} +(8.18897e35 + 4.67366e35i) q^{98} +6.41417e35i 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 $

$2$	−227674.	−	129939.i	−0.868506	−	0.495679i
$2$	−227674.	−	129939.i	−0.868506	−	0.495679i
$3$		−	1.77242e8i		−	0.457492i	−0.973486	−	0.228746i	$-0.926537\pi$
$3$		−	1.77242e8i		−	0.457492i	0.973486	−	0.228746i	$-0.0734625\pi$
$4$	3.49511e10	+	5.91675e10i	0.508605	+	0.861000i
$5$	5.55508e12			1.45623			0.728116	−	0.685454i	$-0.240396\pi$
$5$	5.55508e12			1.45623			0.728116	+	0.685454i	$0.240396\pi$
$6$	−2.30307e13	+	4.03533e13i	−0.226769	+	0.397334i
$7$		−	2.49971e15i		−	1.53506i	−0.641015	−	0.767528i	$-0.721486\pi$
$7$		−	2.49971e15i		−	1.53506i	0.641015	−	0.767528i	$-0.278514\pi$
$8$	−2.69262e14	−	1.80124e16i	−0.0149471	−	0.999888i
$9$	1.18680e17			0.790701
$10$	−1.26475e18	−	7.21823e17i	−1.26475	−	0.721823i
$11$			5.40459e18i			0.972063i	0.873941	+	0.486032i	$0.161556\pi$
$11$			5.40459e18i			0.972063i	−0.873941	+	0.486032i	$0.838444\pi$
$12$	1.04869e19	−	6.19479e18i	0.393901	−	0.232683i
$13$	1.72435e20			1.53336			0.766681	−	0.642028i	$-0.221907\pi$
$13$	1.72435e20			1.53336			0.766681	+	0.642028i	$0.221907\pi$
$14$	−3.24810e20	+	5.69117e20i	−0.760895	+	1.33321i
$15$		−	9.84593e20i		−	0.666214i
$16$	−2.27921e21	+	4.13593e21i	−0.482642	+	0.875818i
$17$	8.60485e21			0.611875			0.305937	−	0.952052i	$-0.401030\pi$
$17$	8.60485e21			0.611875			0.305937	+	0.952052i	$0.401030\pi$
$18$	−2.70203e22	−	1.54212e22i	−0.686729	−	0.391934i
$19$			1.88804e23i			1.81320i	0.421989	+	0.906601i	$0.361332\pi$
$19$			1.88804e23i			1.81320i	−0.421989	+	0.906601i	$0.638668\pi$
$20$	1.94156e23	+	3.28680e23i	0.740647	+	1.25382i
$21$	−4.43052e23			−0.702276
$22$	7.02268e23	−	1.23048e24i	0.481831	−	0.844243i
$23$			9.41760e23i			0.290295i	0.989410	+	0.145147i	$0.0463656\pi$
$23$			9.41760e23i			0.290295i	−0.989410	+	0.145147i	$0.953634\pi$
$24$	−3.19255e24	+	4.77245e22i	−0.457441	+	0.00683816i
$25$	1.63070e25			1.12061
$26$	−3.92589e25	−	2.24060e25i	−1.33173	−	0.760055i
$27$		−	4.76381e25i		−	0.819231i
$28$	1.47901e26	−	8.73674e25i	1.32168	−	0.780738i
$29$	−4.55607e25			−0.216484			−0.108242	−	0.994125i	$-0.534522\pi$
$29$	−4.55607e25			−0.216484			−0.108242	+	0.994125i	$0.534522\pi$
$30$	−1.27937e26	+	2.24166e26i	−0.330228	+	0.578611i
$31$			5.01332e26i			0.717158i	0.933499	+	0.358579i	$0.116739\pi$
$31$			5.01332e26i			0.717158i	−0.933499	+	0.358579i	$0.883261\pi$
$32$	1.05634e27	−	6.45484e26i	0.853302	−	0.521418i
$33$	9.57919e26			0.444711
$34$	−1.95910e27	−	1.11811e27i	−0.531417	−	0.303293i
$35$		−	1.38861e28i		−	2.23540i
$36$	4.14799e27	+	7.02199e27i	0.402155	+	0.680794i
$37$	1.31828e28			0.780504			0.390252	−	0.920708i	$-0.372388\pi$
$37$	1.31828e28			0.780504			0.390252	+	0.920708i	$0.372388\pi$
$38$	2.45330e28	−	4.29857e28i	0.898766	−	1.57478i
$39$		−	3.05627e28i		−	0.701501i
$40$	−1.49578e27	−	1.00060e29i	−0.0217664	−	1.45607i
$41$	2.91126e27			0.0271626			0.0135813	−	0.999908i	$-0.495677\pi$
$41$	2.91126e27			0.0271626			0.0135813	+	0.999908i	$0.495677\pi$
$42$	1.00871e29	+	5.75699e28i	0.609931	+	0.348103i
$43$		−	6.20563e28i		−	0.245671i	−0.992427	−	0.122835i	$-0.960801\pi$
$43$		−	6.20563e28i		−	0.245671i	0.992427	−	0.122835i	$-0.0391987\pi$
$44$	−3.19776e29	+	1.88896e29i	−0.836946	+	0.494396i
$45$	6.59277e29			1.15144
$46$	1.22372e29	−	2.14414e29i	0.143893	−	0.252123i
$47$			4.91358e29i			0.392316i	0.980572	+	0.196158i	$0.0628466\pi$
$47$			4.91358e29i			0.392316i	−0.980572	+	0.196158i	$0.937153\pi$
$48$	7.33060e29	+	4.03971e29i	0.400680	+	0.220805i
$49$	−3.59680e30			−1.35640
$50$	−3.71268e30	−	2.11893e30i	−0.973258	−	0.555464i
$51$		−	1.52514e30i		−	0.279928i
$52$	6.02678e30	+	1.02025e31i	0.779876	+	1.32022i
$53$	4.35112e29			0.0399609			0.0199805	−	0.999800i	$-0.493640\pi$
$53$	4.35112e29			0.0399609			0.0199805	+	0.999800i	$0.493640\pi$
$54$	−6.19006e30	+	1.08459e31i	−0.406076	+	0.711507i
$55$			3.00230e31i			1.41555i
$56$	−4.50257e31	+	6.73077e29i	−1.53489	+	0.0229446i
$57$	3.34639e31			0.829525
$58$	1.03730e31	+	5.92012e30i	0.188018	+	0.107307i
$59$		−	5.43569e31i		−	0.724300i	−0.932120	−	0.362150i	$-0.882043\pi$
$59$		−	5.43569e31i		−	0.724300i	0.932120	−	0.362150i	$-0.117957\pi$
$60$	5.82559e31	−	3.44126e31i	0.573611	−	0.338840i
$61$	−3.68830e31			−0.269705			−0.134853	−	0.990866i	$-0.543056\pi$
$61$	−3.68830e31			−0.269705			−0.134853	+	0.990866i	$0.543056\pi$
$62$	6.51427e31	−	1.14140e32i	0.355480	−	0.622856i
$63$		−	2.96665e32i		−	1.21377i
$64$	−3.24374e32	+	9.70012e30i	−0.999553	+	0.0298908i
$65$	9.57890e32			2.23293
$66$	−2.18093e32	−	1.24471e32i	−0.386234	−	0.220434i
$67$		−	9.33023e32i		−	1.26051i	−0.776389	−	0.630254i	$-0.782951\pi$
$67$		−	9.33023e32i		−	1.26051i	0.776389	−	0.630254i	$-0.217049\pi$
$68$	3.00749e32	+	5.09127e32i	0.311203	+	0.526824i
$69$	1.66919e32			0.132807
$70$	−1.80435e33	+	3.16149e33i	−1.10804	+	1.94146i
$71$			1.44228e33i			0.686118i	0.939314	+	0.343059i	$0.111463\pi$
$71$			1.44228e33i			0.686118i	−0.939314	+	0.343059i	$0.888537\pi$
$72$	−3.19561e31	−	2.13771e33i	−0.0118187	−	0.790613i
$73$	2.43678e33			0.703079			0.351540	−	0.936173i	$-0.385658\pi$
$73$	2.43678e33			0.703079			0.351540	+	0.936173i	$0.385658\pi$
$74$	−3.00137e33	−	1.71296e33i	−0.677873	−	0.386879i
$75$		−	2.89029e33i		−	0.512671i
$76$	−1.11711e34	+	6.59890e33i	−1.56117	+	0.922204i
$77$	1.35099e34			1.49217
$78$	−3.97129e33	+	6.95831e33i	−0.347719	+	0.609258i
$79$		−	4.92391e33i		−	0.342786i	−0.985203	−	0.171393i	$-0.945173\pi$
$79$		−	4.92391e33i		−	0.342786i	0.985203	−	0.171393i	$-0.0548267\pi$
$80$	−1.26612e34	+	2.29755e34i	−0.702838	+	1.27539i
$81$	9.36977e33			0.415909
$82$	−6.62818e32	−	3.78287e32i	−0.0235909	−	0.0134639i
$83$		−	3.24535e34i		−	0.928659i	−0.885663	−	0.464329i	$-0.846295\pi$
$83$		−	3.24535e34i		−	0.928659i	0.885663	−	0.464329i	$-0.153705\pi$
$84$	−1.54852e34	−	2.62143e34i	−0.357181	−	0.604660i
$85$	4.78007e34			0.891032
$86$	−8.06354e33	+	1.41286e34i	−0.121774	+	0.213367i
$87$			8.07526e33i			0.0990398i
$88$	9.73496e34	−	1.45525e33i	0.971955	−	0.0145295i
$89$	9.08737e34			0.740317			0.370159	−	0.928969i	$-0.379303\pi$
$89$	9.08737e34			0.740317			0.370159	+	0.928969i	$0.379303\pi$
$90$	−1.50100e35	−	8.56660e34i	−1.00004	−	0.570747i
$91$		−	4.31037e35i		−	2.35380i
$92$	−5.57215e34	+	3.29155e34i	−0.249944	+	0.147645i
$93$	8.88570e34			0.328094
$94$	6.38466e34	−	1.11869e35i	0.194463	−	0.340729i
$95$			1.04882e36i			2.64044i
$96$	−1.14407e35	−	1.87227e35i	−0.238544	−	0.390379i
$97$	−1.10168e36			−1.90618			−0.953089	−	0.302692i	$-0.902115\pi$
$97$	−1.10168e36			−1.90618			−0.953089	+	0.302692i	$0.902115\pi$
$98$	8.18897e35	+	4.67366e35i	1.17804	+	0.672338i
$99$			6.41417e35i			0.768612i
$100$	5.69949e35	+	9.64847e35i	0.569949	+	0.964847i
$101$	−6.22174e35			−0.520148			−0.260074	−	0.965589i	$-0.583747\pi$
$101$	−6.22174e35			−0.520148			−0.260074	+	0.965589i	$0.583747\pi$
$102$	−1.98175e35	+	3.47234e35i	−0.138754	+	0.243119i
$103$		−	9.69079e35i		−	0.569232i	−0.958642	−	0.284616i	$-0.908134\pi$
$103$		−	9.69079e35i		−	0.569232i	0.958642	−	0.284616i	$-0.0918661\pi$
$104$	−4.64302e34	−	3.10596e36i	−0.0229193	−	1.53319i
$105$	−2.46119e36			−1.02268
$106$	−9.90636e34	−	5.65382e34i	−0.0347063	−	0.0198078i
$107$			2.89529e36i			0.856612i	0.903634	+	0.428306i	$0.140890\pi$
$107$			2.89529e36i			0.856612i	−0.903634	+	0.428306i	$0.859110\pi$
$108$	2.81862e36	−	1.66500e36i	0.705358	−	0.416665i
$109$	1.76879e36			0.374972			0.187486	−	0.982267i	$-0.439966\pi$
$109$	1.76879e36			0.374972			0.187486	+	0.982267i	$0.439966\pi$
$110$	3.90116e36	−	6.83544e36i	0.701658	−	1.22941i
$111$		−	2.33654e36i		−	0.357074i
$112$	1.03386e37	+	5.69736e36i	1.34443	+	0.740883i
$113$	−9.72750e36			−1.07793			−0.538963	−	0.842329i	$-0.681184\pi$
$113$	−9.72750e36			−1.07793			−0.538963	+	0.842329i	$0.681184\pi$
$114$	−7.61886e36	−	4.34828e36i	−0.720448	−	0.411178i
$115$			5.23155e36i			0.422736i
$116$	−1.59240e36	−	2.69571e36i	−0.110105	−	0.186393i
$117$	2.04646e37			1.21243
$118$	−7.06309e36	+	1.23756e37i	−0.359020	+	0.629059i
$119$		−	2.15096e37i		−	0.939262i
$120$	−1.77349e37	+	2.65114e35i	−0.666140	+	0.00995795i
$121$	1.70307e36			0.0550930
$122$	8.39728e36	+	4.79255e36i	0.234240	+	0.133687i
$123$		−	5.15997e35i		−	0.0124267i
$124$	−2.96625e37	+	1.75221e37i	−0.617473	+	0.364750i
$125$	9.74991e36			0.175639
$126$	−3.85484e37	+	6.75428e37i	−0.601641	+	1.05417i
$127$			1.66370e37i			0.225220i	0.993639	+	0.112610i	$0.0359211\pi$
$127$			1.66370e37i			0.225220i	−0.993639	+	0.112610i	$0.964079\pi$
$128$	7.51117e37	+	3.99404e37i	0.882934	+	0.469497i
$129$	−1.09990e37			−0.112392
$130$	−2.18086e38	−	1.24467e38i	−1.93931	−	1.10682i
$131$			6.71691e37i			0.520339i	0.965563	+	0.260169i	$0.0837784\pi$
$131$			6.71691e37i			0.520339i	−0.965563	+	0.260169i	$0.916222\pi$
$132$	3.34803e37	+	5.66777e37i	0.226182	+	0.382896i
$133$	4.71955e38			2.78337
$134$	−1.21236e38	+	2.12425e38i	−0.624807	+	1.09476i
$135$		−	2.64634e38i		−	1.19299i
$136$	−2.31696e36	−	1.54994e38i	−0.00914573	−	0.611806i
$137$	−3.97555e38			−1.37539			−0.687696	−	0.725998i	$-0.741378\pi$
$137$	−3.97555e38			−1.37539			−0.687696	+	0.725998i	$0.741378\pi$
$138$	−3.80031e37	−	2.16893e37i	−0.115344	−	0.0658298i
$139$		−	6.21549e38i		−	1.65657i	−0.560310	−	0.828283i	$-0.689318\pi$
$139$		−	6.21549e38i		−	1.65657i	0.560310	−	0.828283i	$-0.310682\pi$
$140$	8.21604e38	−	4.85334e38i	1.92468	−	1.13694i
$141$	8.70891e37			0.179482
$142$	1.87409e38	−	3.28369e38i	0.340094	−	0.595898i
$143$			9.31940e38i			1.49052i
$144$	−2.70497e38	+	4.90852e38i	−0.381625	+	0.692510i
$145$	−2.53094e38			−0.315251
$146$	−5.54790e38	−	3.16633e38i	−0.610629	−	0.348502i
$147$			6.37504e38i			0.620542i
$148$	4.60752e38	+	7.79990e38i	0.396968	+	0.672014i
$149$	−2.03376e39			−1.55220			−0.776099	−	0.630612i	$-0.782804\pi$
$149$	−2.03376e39			−1.55220			−0.776099	+	0.630612i	$0.782804\pi$
$150$	−3.75562e38	+	6.58043e38i	−0.254120	+	0.445258i
$151$			8.29777e38i			0.498169i	0.968482	+	0.249084i	$0.0801297\pi$
$151$			8.29777e38i			0.498169i	−0.968482	+	0.249084i	$0.919870\pi$
$152$	3.40081e39	−	5.08378e37i	1.81300	−	0.0271021i
$153$	1.02122e39			0.483810
$154$	−3.07585e39	−	1.75547e39i	−1.29596	−	0.739638i
$155$			2.78494e39i			1.04435i
$156$	1.80831e39	−	1.06820e39i	0.603992	−	0.356787i
$157$	−5.73764e39			−1.70820			−0.854102	−	0.520106i	$-0.825893\pi$
$157$	−5.73764e39			−1.70820			−0.854102	+	0.520106i	$0.825893\pi$
$158$	−6.39809e38	+	1.12105e39i	−0.169912	+	0.297711i
$159$		−	7.71201e37i		−	0.0182818i
$160$	5.86804e39	−	3.58572e39i	1.24261	−	0.759305i
$161$	2.35412e39			0.445619
$162$	−2.13325e39	−	1.21750e39i	−0.361220	−	0.206157i
$163$		−	1.05702e40i		−	1.60217i	−0.598553	−	0.801083i	$-0.704257\pi$
$163$		−	1.05702e40i		−	1.60217i	0.598553	−	0.801083i	$-0.295743\pi$
$164$	1.01752e38	+	1.72252e38i	0.0138151	+	0.0233870i
$165$	5.32132e39			0.647603
$166$	−4.21699e39	+	7.38881e39i	−0.460317	+	0.806546i
$167$		−	5.72510e39i		−	0.560902i	−0.959868	−	0.280451i	$-0.909516\pi$
$167$		−	5.72510e39i		−	0.560902i	0.959868	−	0.280451i	$-0.0904839\pi$
$168$	1.19297e38	+	7.98043e39i	0.0104970	+	0.702198i
$169$	1.70876e40			1.35120
$170$	−1.08829e40	−	6.21118e39i	−0.773866	−	0.441666i
$171$			2.24073e40i			1.43370i
$172$	3.67171e39	−	2.16893e39i	0.211523	−	0.124949i
$173$	3.94413e39			0.204701			0.102351	−	0.994748i	$-0.467364\pi$
$173$	3.94413e39			0.204701			0.102351	+	0.994748i	$0.467364\pi$
$174$	1.04929e39	−	1.83852e39i	0.0490919	−	0.0860167i
$175$		−	4.07628e40i		−	1.72020i
$176$	−2.23530e40	−	1.23182e40i	−0.851350	−	0.469158i
$177$	−9.63431e39			−0.331361
$178$	−2.06895e40	−	1.18081e40i	−0.642970	−	0.366960i
$179$			1.65711e40i			0.465584i	0.972527	+	0.232792i	$0.0747861\pi$
$179$			1.65711e40i			0.465584i	−0.972527	+	0.232792i	$0.925214\pi$
$180$	2.30425e40	+	3.90078e40i	0.585630	+	0.991394i
$181$	1.17619e40			0.270560			0.135280	−	0.990807i	$-0.456807\pi$
$181$	1.17619e40			0.270560			0.135280	+	0.990807i	$0.456807\pi$
$182$	−5.60086e40	+	9.81357e40i	−1.16673	+	2.04429i
$183$			6.53721e39i			0.123388i
$184$	1.69633e40	−	2.53581e38i	0.290262	−	0.00433905i
$185$	7.32313e40			1.13660
$186$	−2.02304e40	−	1.15460e40i	−0.284952	−	0.162629i
$187$			4.65057e40i			0.594781i
$188$	−2.90724e40	+	1.71735e40i	−0.337784	+	0.199534i
$189$	−1.19081e41			−1.25757
$190$	1.36283e41	−	2.38789e41i	1.30881	−	2.29324i
$191$		−	3.43456e39i		−	0.0300103i	−0.999887	−	0.0150052i	$-0.995224\pi$
$191$		−	3.43456e39i		−	0.0300103i	0.999887	−	0.0150052i	$-0.00477647\pi$
$192$	1.71927e39	+	5.74925e40i	0.0136748	+	0.457288i
$193$	−1.70230e41			−1.23312			−0.616560	−	0.787308i	$-0.711474\pi$
$193$	−1.70230e41			−1.23312			−0.616560	+	0.787308i	$0.711474\pi$
$194$	2.50823e41	+	1.43151e41i	1.65553	+	0.944852i
$195$		−	1.69778e41i		−	1.02155i
$196$	−1.25712e41	−	2.12814e41i	−0.689871	−	1.16786i
$197$	2.06546e41			1.03425			0.517124	−	0.855911i	$-0.327003\pi$
$197$	2.06546e41			1.03425			0.517124	+	0.855911i	$0.327003\pi$
$198$	8.33452e40	−	1.46034e41i	0.380984	−	0.667544i
$199$			1.76694e41i			0.737677i	0.929493	+	0.368839i	$0.120245\pi$
$199$			1.76694e41i			0.737677i	−0.929493	+	0.368839i	$0.879755\pi$
$200$	−4.39088e39	−	2.93729e41i	−0.0167499	−	1.12049i
$201$	−1.65371e41			−0.576672
$202$	1.41653e41	+	8.08448e40i	0.451752	+	0.257826i
$203$			1.13888e41i			0.332316i
$204$	9.02386e40	−	5.33052e40i	0.241018	−	0.142373i
$205$	1.61723e40			0.0395551
$206$	−1.25921e41	+	2.20634e41i	−0.282156	+	0.494381i
$207$			1.11768e41i			0.229536i
$208$	−3.93015e41	+	7.13179e41i	−0.740065	+	1.34295i
$209$	−1.02041e42			−1.76255
$210$	5.60349e41	+	3.19806e41i	0.888201	+	0.506919i
$211$			5.79120e41i			0.842721i	0.906893	+	0.421361i	$0.138447\pi$
$211$			5.79120e41i			0.842721i	−0.906893	+	0.421361i	$0.861553\pi$
$212$	1.52076e40	+	2.57445e40i	0.0203243	+	0.0344064i
$213$	2.55632e41			0.313893
$214$	3.76212e41	−	6.59181e41i	0.424605	−	0.743973i
$215$		−	3.44728e41i		−	0.357754i
$216$	−8.58076e41	+	1.28271e40i	−0.819140	+	0.0122451i
$217$	1.25318e42			1.10088
$218$	−4.02706e41	−	2.29835e41i	−0.325665	−	0.185866i
$219$		−	4.31899e41i		−	0.321653i
$220$	−1.77638e42	+	1.04933e42i	−1.21879	+	0.719956i
$221$	1.48378e42			0.938226
$222$	−3.03608e41	+	5.31967e41i	−0.176994	+	0.310121i
$223$		−	3.33880e42i		−	1.79516i	−0.440854	−	0.897579i	$-0.645324\pi$
$223$		−	3.33880e42i		−	1.79516i	0.440854	−	0.897579i	$-0.354676\pi$
$224$	−1.61352e42	−	2.64053e42i	−0.800406	−	1.30987i
$225$	1.93532e42			0.886069
$226$	2.21470e42	+	1.26398e42i	0.936186	+	0.534306i
$227$			2.18249e42i			0.852094i	0.904701	+	0.426047i	$0.140094\pi$
$227$			2.18249e42i			0.852094i	−0.904701	+	0.426047i	$0.859906\pi$
$228$	1.16960e42	+	1.97998e42i	0.421901	+	0.714221i
$229$	−4.96346e41			−0.165480			−0.0827401	−	0.996571i	$-0.526367\pi$
$229$	−4.96346e41			−0.165480			−0.0827401	+	0.996571i	$0.526367\pi$
$230$	6.79784e41	−	1.19109e42i	0.209541	−	0.367149i
$231$		−	2.39452e42i		−	0.682657i
$232$	1.22678e40	+	8.20657e41i	0.00323581	+	0.216460i
$233$	9.17240e40			0.0223912			0.0111956	−	0.999937i	$-0.496436\pi$
$233$	9.17240e40			0.0223912			0.0111956	+	0.999937i	$0.496436\pi$
$234$	−4.65924e42	−	2.65915e42i	−1.05300	−	0.600976i
$235$			2.72953e42i			0.571304i
$236$	3.21616e42	−	1.89983e42i	0.623622	−	0.368383i
$237$	−8.72723e41			−0.156822
$238$	−2.79494e42	+	4.89717e42i	−0.465572	+	0.815755i
$239$		−	1.35213e42i		−	0.208861i	−0.994532	−	0.104431i	$-0.966698\pi$
$239$		−	1.35213e42i		−	0.208861i	0.994532	−	0.104431i	$-0.0333020\pi$
$240$	4.07221e42	+	2.24410e42i	0.583482	+	0.321543i
$241$	2.74106e42			0.364428			0.182214	−	0.983259i	$-0.441674\pi$
$241$	2.74106e42			0.364428			0.182214	+	0.983259i	$0.441674\pi$
$242$	−3.87744e41	−	2.21296e41i	−0.0478486	−	0.0273084i
$243$		−	8.81094e42i		−	1.00951i
$244$	−1.28910e42	−	2.18227e42i	−0.137173	−	0.232216i
$245$	−1.99806e43			−1.97523
$246$	−6.70483e40	+	1.17479e41i	−0.00615965	+	0.0107927i
$247$			3.25564e43i			2.78030i
$248$	9.03019e42	−	1.34990e41i	0.717078	−	0.0107194i
$249$	−5.75212e42			−0.424854
$250$	−2.21980e42	−	1.26690e42i	−0.152543	−	0.0870604i
$251$			1.24102e43i			0.793690i	0.917886	+	0.396845i	$0.129895\pi$
$251$			1.24102e43i			0.793690i	−0.917886	+	0.396845i	$0.870105\pi$
$252$	1.75529e43	−	1.03688e43i	1.04506	−	0.617330i
$253$	−5.08983e42			−0.282185
$254$	2.16179e42	−	3.78780e42i	0.111637	−	0.195605i
$255$		−	8.47227e42i		−	0.407640i
$256$	−1.19111e43	−	1.88533e43i	−0.534114	−	0.845413i
$257$	1.46390e43			0.611950			0.305975	−	0.952039i	$-0.401018\pi$
$257$	1.46390e43			0.611950			0.305975	+	0.952039i	$0.401018\pi$
$258$	2.50417e42	+	1.42920e42i	0.0976135	+	0.0557105i
$259$		−	3.29530e43i		−	1.19812i
$260$	3.34793e43	+	5.66759e43i	1.13568	+	1.92255i
$261$	−5.40714e42			−0.171174
$262$	8.72790e42	−	1.52926e43i	0.257921	−	0.451917i
$263$		−	3.20359e43i		−	0.883961i	−0.897025	−	0.441981i	$-0.854276\pi$
$263$		−	3.20359e43i		−	0.883961i	0.897025	−	0.441981i	$-0.145724\pi$
$264$	−2.57932e41	−	1.72544e43i	−0.00664713	−	0.444661i
$265$	2.41709e42			0.0581924
$266$	−1.07452e44	−	6.13254e43i	−2.41737	−	1.37966i
$267$		−	1.61066e43i		−	0.338689i
$268$	5.52046e43	−	3.26101e43i	1.08530	−	0.641101i
$269$	8.67222e43			1.59437			0.797186	−	0.603734i	$-0.206321\pi$
$269$	8.67222e43			1.59437			0.797186	+	0.603734i	$0.206321\pi$
$270$	−3.43863e43	+	6.02501e43i	−0.591340	+	1.03612i
$271$			2.10087e43i			0.338028i	0.985614	+	0.169014i	$0.0540582\pi$
$271$			2.10087e43i			0.338028i	−0.985614	+	0.169014i	$0.945942\pi$
$272$	−1.96123e43	+	3.55891e43i	−0.295316	+	0.535891i
$273$	−7.63977e43			−1.07684
$274$	9.05127e43	+	5.16580e43i	1.19454	+	0.681753i
$275$			8.81329e43i			1.08931i
$276$	5.83400e42	+	9.87618e42i	0.0675465	+	0.114347i
$277$	6.95926e43			0.754965			0.377483	−	0.926017i	$-0.376790\pi$
$277$	6.95926e43			0.754965			0.377483	+	0.926017i	$0.376790\pi$
$278$	−8.07636e43	+	1.41510e44i	−0.821125	+	1.43874i
$279$			5.94981e43i			0.567058i
$280$	−2.50122e44	+	3.73900e42i	−2.23515	+	0.0334127i
$281$	1.66599e43			0.139623			0.0698116	−	0.997560i	$-0.477760\pi$
$281$	1.66599e43			0.139623			0.0698116	+	0.997560i	$0.477760\pi$
$282$	−1.98279e43	−	1.13163e43i	−0.155881	−	0.0889652i
$283$		−	2.44437e44i		−	1.80306i	−0.432716	−	0.901530i	$-0.642445\pi$
$283$		−	2.44437e44i		−	1.80306i	0.432716	−	0.901530i	$-0.357555\pi$
$284$	−8.53360e43	+	5.04092e43i	−0.590748	+	0.348963i
$285$	1.85895e44			1.20798
$286$	1.21096e44	−	2.12178e44i	0.738822	−	1.29453i
$287$		−	7.27731e42i		−	0.0416962i
$288$	1.25366e44	−	7.66060e43i	0.674707	−	0.412286i
$289$	−1.23727e44			−0.625609
$290$	5.76227e43	+	3.28868e43i	0.273798	+	0.156263i
$291$			1.95263e44i			0.872061i
$292$	8.51680e43	+	1.44178e44i	0.357590	+	0.605351i
$293$	−3.79928e44			−1.49998			−0.749989	−	0.661451i	$-0.769941\pi$
$293$	−3.79928e44			−1.49998			−0.749989	+	0.661451i	$0.769941\pi$
$294$	8.28368e43	−	1.45143e44i	0.307589	−	0.538944i
$295$		−	3.01957e44i		−	1.05475i
$296$	−3.54962e42	−	2.37453e44i	−0.0116663	−	0.780417i
$297$	2.57464e44			0.796345
$298$	4.63033e44	+	2.64265e44i	1.34809	+	0.769391i
$299$			1.62392e44i			0.445127i
$300$	1.71011e44	−	1.01019e44i	0.441410	−	0.260747i
$301$	−1.55123e44			−0.377119
$302$	1.07821e44	−	1.88918e44i	0.246932	−	0.432663i
$303$			1.10275e44i			0.237964i
$304$	−7.80880e44	−	4.30324e44i	−1.58803	−	0.875127i
$305$	−2.04888e44			−0.392753
$306$	−2.32506e44	−	1.32697e44i	−0.420192	−	0.239814i
$307$			2.56547e44i			0.437196i	0.975815	+	0.218598i	$0.0701483\pi$
$307$			2.56547e44i			0.437196i	−0.975815	+	0.218598i	$0.929852\pi$
$308$	4.72185e44	+	7.99346e44i	0.758926	+	1.28476i
$309$	−1.71761e44			−0.260419
$310$	3.61873e44	−	6.34058e44i	0.517662	−	0.907023i
$311$			1.36571e45i			1.84363i	0.387634	+	0.921813i	$0.373292\pi$
$311$			1.36571e45i			1.84363i	−0.387634	+	0.921813i	$0.626708\pi$
$312$	−5.50506e44	+	8.22937e42i	−0.701422	+	0.0104854i
$313$	1.27288e43			0.0153105			0.00765526	−	0.999971i	$-0.497563\pi$
$313$	1.27288e43			0.0153105			0.00765526	+	0.999971i	$0.497563\pi$
$314$	1.30631e45	+	7.45545e44i	1.48359	+	0.846720i
$315$		−	1.64800e45i		−	1.76753i
$316$	2.91335e44	−	1.72096e44i	0.295139	−	0.174343i
$317$	−1.70217e45			−1.62906			−0.814530	−	0.580122i	$-0.803005\pi$
$317$	−1.70217e45			−1.62906			−0.814530	+	0.580122i	$0.803005\pi$
$318$	−1.00209e43	+	1.75582e43i	−0.00906191	+	0.0158779i
$319$		−	2.46237e44i		−	0.210436i
$320$	−1.80192e45	+	5.38850e43i	−1.45558	+	0.0435279i
$321$	5.13167e44			0.391893
$322$	−5.35972e44	−	3.05893e44i	−0.387023	−	0.220884i
$323$			1.62463e45i			1.10945i
$324$	3.27484e44	+	5.54386e44i	0.211534	+	0.358098i
$325$	2.81190e45			1.71830
$326$	−1.37349e45	+	2.40656e45i	−0.794160	+	1.39149i
$327$		−	3.13503e44i		−	0.171547i
$328$	−7.83894e41	−	5.24388e43i	−0.000406002	−	0.0271596i
$329$	1.22825e45			0.602228
$330$	−1.21152e45	−	6.91448e44i	−0.562447	−	0.321003i
$331$		−	2.28914e45i		−	1.00640i	−0.864171	−	0.503198i	$-0.832157\pi$
$331$		−	2.28914e45i		−	1.00640i	0.864171	−	0.503198i	$-0.167843\pi$
$332$	1.92019e45	−	1.13429e45i	0.799575	−	0.472321i
$333$	1.56453e45			0.617146
$334$	−7.43915e44	+	1.30345e45i	−0.278027	+	0.487146i
$335$		−	5.18302e45i		−	1.83559i
$336$	1.00981e45	−	1.83244e45i	0.338948	−	0.615066i
$337$	1.62264e45			0.516277			0.258139	−	0.966108i	$-0.416891\pi$
$337$	1.62264e45			0.516277			0.258139	+	0.966108i	$0.416891\pi$
$338$	−3.89039e45	−	2.22034e45i	−1.17352	−	0.669761i
$339$			1.72412e45i			0.493143i
$340$	1.67068e45	+	2.82824e45i	0.453183	+	0.767178i
$341$	−2.70949e45			−0.697123
$342$	2.91158e45	−	5.10154e45i	0.710655	−	1.24518i
$343$			2.36241e45i			0.547092i
$344$	−1.11778e45	+	1.67094e43i	−0.245643	+	0.00367206i
$345$	9.27250e44			0.193398
$346$	−8.97973e44	−	5.12497e44i	−0.177784	−	0.101466i
$347$			4.94592e45i			0.929643i	0.885404	+	0.464821i	$0.153881\pi$
$347$			4.94592e45i			0.929643i	−0.885404	+	0.464821i	$0.846119\pi$
$348$	−4.77793e44	+	2.82239e44i	−0.0852733	+	0.0503722i
$349$	−1.07278e45			−0.181824			−0.0909120	−	0.995859i	$-0.528978\pi$
$349$	−1.07278e45			−0.181824			−0.0909120	+	0.995859i	$0.528978\pi$
$350$	−5.29669e45	+	9.28062e45i	−0.852668	+	1.49401i
$351$		−	8.21447e45i		−	1.25618i
$352$	3.48858e45	+	5.70907e45i	0.506851	+	0.829463i
$353$	−2.96408e45			−0.409209			−0.204605	−	0.978845i	$-0.565591\pi$
$353$	−2.96408e45			−0.409209			−0.204605	+	0.978845i	$0.565591\pi$
$354$	2.19348e45	+	1.25188e45i	0.287789	+	0.164249i
$355$			8.01198e45i			0.999147i
$356$	3.17613e45	+	5.37677e45i	0.376529	+	0.637413i
$357$	−3.81240e45			−0.429705
$358$	2.15324e45	−	3.77281e45i	0.230780	−	0.404362i
$359$			1.60495e46i			1.63592i	0.575277	+	0.817959i	$0.304894\pi$
$359$			1.60495e46i			1.63592i	−0.575277	+	0.817959i	$0.695106\pi$
$360$	−1.77519e44	−	1.18752e46i	−0.0172107	−	1.15132i
$361$	−2.48044e46			−2.28770
$362$	−2.67788e45	−	1.52833e45i	−0.234983	−	0.134111i
$363$		−	3.01855e44i		−	0.0252046i
$364$	2.55033e46	−	1.50652e46i	2.02662	−	1.19715i
$365$	1.35365e46			1.02385
$366$	8.49440e44	−	1.48835e45i	0.0611608	−	0.107163i
$367$		−	1.32063e46i		−	0.905296i	−0.891689	−	0.452648i	$-0.850479\pi$
$367$		−	1.32063e46i		−	0.905296i	0.891689	−	0.452648i	$-0.149521\pi$
$368$	−3.89505e45	−	2.14647e45i	−0.254245	−	0.140108i
$369$	3.45509e44			0.0214775
$370$	−1.66728e46	−	9.51562e45i	−0.987140	−	0.563386i
$371$		−	1.08765e45i		−	0.0613423i
$372$	3.10565e45	+	5.25744e45i	0.166870	+	0.282489i
$373$	1.36447e46			0.698561			0.349281	−	0.937018i	$-0.386426\pi$
$373$	1.36447e46			0.698561			0.349281	+	0.937018i	$0.386426\pi$
$374$	6.04291e45	−	1.05881e46i	0.294820	−	0.516571i
$375$		−	1.72809e45i		−	0.0803533i
$376$	8.85053e45	−	1.32304e44i	0.392272	−	0.00586398i
$377$	−7.85625e45			−0.331949
$378$	2.71117e46	+	1.54733e46i	1.09220	+	0.623349i
$379$		−	4.54211e46i		−	1.74483i	−0.488769	−	0.872413i	$-0.662554\pi$
$379$		−	4.54211e46i		−	1.74483i	0.488769	−	0.872413i	$-0.337446\pi$
$380$	−6.20561e46	+	3.66574e46i	−2.27342	+	1.34294i
$381$	2.94876e45			0.103036
$382$	−4.46284e44	+	7.81959e44i	−0.0148755	+	0.0260642i
$383$			5.17389e46i			1.64528i	0.568564	+	0.822639i	$0.307499\pi$
$383$			5.17389e46i			1.64528i	−0.568564	+	0.822639i	$0.692501\pi$
$384$	7.07910e45	−	1.33129e46i	0.214791	−	0.403935i
$385$	7.50486e46			2.17295
$386$	3.87569e46	+	2.21196e46i	1.07097	+	0.611231i
$387$		−	7.36484e45i		−	0.194252i
$388$	−3.85048e46	−	6.51835e46i	−0.969491	−	1.64122i
$389$	−7.75327e46			−1.86377			−0.931884	−	0.362755i	$-0.881836\pi$
$389$	−7.75327e46			−1.86377			−0.931884	+	0.362755i	$0.881836\pi$
$390$	−2.20608e46	+	3.86540e46i	−0.506360	+	0.887220i
$391$			8.10370e45i			0.177624i
$392$	9.68484e44	+	6.47870e46i	0.0202742	+	1.35625i
$393$	1.19052e46			0.238051
$394$	−4.70251e46	−	2.68384e46i	−0.898250	−	0.512655i
$395$		−	2.73528e46i		−	0.499176i
$396$	−3.79510e46	+	2.24182e46i	−0.661774	+	0.390920i
$397$	1.56490e46			0.260770			0.130385	−	0.991463i	$-0.458379\pi$
$397$	1.56490e46			0.260770			0.130385	+	0.991463i	$0.458379\pi$
$398$	2.29595e46	−	4.02286e46i	0.365651	−	0.640677i
$399$		−	8.36500e46i		−	1.27337i
$400$	−3.71672e46	+	6.74449e46i	−0.540854	+	0.981452i
$401$	7.79235e46			1.08410			0.542051	−	0.840346i	$-0.317648\pi$
$401$	7.79235e46			1.08410			0.542051	+	0.840346i	$0.317648\pi$
$402$	3.76505e46	+	2.14881e46i	0.500843	+	0.285844i
$403$			8.64471e46i			1.09966i
$404$	−2.17456e46	−	3.68124e46i	−0.264550	−	0.447847i
$405$	5.20499e46			0.605661
$406$	1.47986e46	−	2.59294e46i	0.164722	−	0.288618i
$407$			7.12474e46i			0.758700i
$408$	−2.74714e46	+	4.10662e44i	−0.279897	+	0.00418410i
$409$	−4.70283e46			−0.458501			−0.229250	−	0.973367i	$-0.573627\pi$
$409$	−4.70283e46			−0.458501			−0.229250	+	0.973367i	$0.573627\pi$
$410$	−3.68201e45	−	2.10142e45i	−0.0343539	−	0.0196066i
$411$			7.04633e46i			0.629231i
$412$	5.73380e46	−	3.38704e46i	0.490109	−	0.289514i
$413$	−1.35876e47			−1.11184
$414$	1.45231e46	−	2.54466e46i	0.113776	−	0.199354i
$415$		−	1.80282e47i		−	1.35234i
$416$	1.82149e47	−	1.11304e47i	1.30842	−	0.799522i
$417$	−1.10164e47			−0.757866
$418$	2.32320e47	+	1.32591e47i	1.53078	+	0.873657i
$419$		−	1.28693e47i		−	0.812271i	−0.913813	−	0.406136i	$-0.866876\pi$
$419$		−	1.28693e47i		−	0.812271i	0.913813	−	0.406136i	$-0.133124\pi$
$420$	−8.60214e46	−	1.45623e47i	−0.520139	−	0.880525i
$421$	−9.75674e46			−0.565232			−0.282616	−	0.959233i	$-0.591202\pi$
$421$	−9.75674e46			−0.565232			−0.282616	+	0.959233i	$0.591202\pi$
$422$	7.52503e46	−	1.31850e47i	0.417719	−	0.731908i
$423$			5.83143e46i			0.310205i
$424$	−1.17159e44	−	7.83741e45i	−0.000597299	−	0.0399565i
$425$	1.40320e47			0.685674
$426$	−5.82007e46	−	3.32166e46i	−0.272618	−	0.155590i
$427$			9.21967e46i			0.414013i
$428$	−1.71307e47	+	1.01194e47i	−0.737543	+	0.435677i
$429$	1.65179e47			0.681903
$430$	−4.47937e46	+	7.84854e46i	−0.177331	+	0.310711i
$431$			3.43872e47i			1.30559i	0.757535	+	0.652794i	$0.226403\pi$
$431$			3.43872e47i			1.30559i	−0.757535	+	0.652794i	$0.773597\pi$
$432$	1.97028e47	+	1.08577e47i	0.717497	+	0.395395i
$433$	−3.22358e47			−1.12605			−0.563023	−	0.826441i	$-0.690362\pi$
$433$	−3.22358e47			−1.12605			−0.563023	+	0.826441i	$0.690362\pi$
$434$	−2.85317e47	−	1.62838e47i	−0.956119	−	0.545682i
$435$			4.48587e46i			0.144225i
$436$	6.18210e46	+	1.04655e47i	0.190713	+	0.322851i
$437$	−1.77808e47			−0.526363
$438$	−5.61206e46	+	9.83319e46i	−0.159437	+	0.279358i
$439$			1.85153e47i			0.504857i	0.967616	+	0.252428i	$0.0812292\pi$
$439$			1.85153e47i			0.504857i	−0.967616	+	0.252428i	$0.918771\pi$
$440$	5.40785e47	−	8.08406e45i	1.41539	−	0.0211583i
$441$	−4.26869e47			−1.07251
$442$	−3.37817e47	−	1.92801e47i	−0.814854	−	0.465058i
$443$		−	3.20119e47i		−	0.741386i	−0.928756	−	0.370693i	$-0.879120\pi$
$443$		−	3.20119e47i		−	0.741386i	0.928756	−	0.370693i	$-0.120880\pi$
$444$	1.38247e47	−	8.16644e46i	0.307441	−	0.181610i
$445$	5.04811e47			1.07807
$446$	−4.33841e47	+	7.60156e47i	−0.889822	+	1.55911i
$447$			3.60467e47i			0.710118i
$448$	2.42475e46	+	8.10839e47i	0.0458841	+	1.53437i
$449$	1.01672e48			1.84827			0.924136	−	0.382065i	$-0.124787\pi$
$449$	1.01672e48			1.84827			0.924136	+	0.382065i	$0.124787\pi$
$450$	−4.40621e47	−	2.51474e47i	−0.769556	−	0.439206i
$451$			1.57342e46i			0.0264038i
$452$	−3.39987e47	−	5.75552e47i	−0.548239	−	0.928095i
$453$	1.47071e47			0.227908
$454$	2.83591e47	−	4.96896e47i	0.422365	−	0.740048i
$455$		−	2.39444e48i		−	3.42768i
$456$	−9.01058e45	−	6.02765e47i	−0.0123990	−	0.829433i
$457$	−1.12133e47			−0.148335			−0.0741675	−	0.997246i	$-0.523630\pi$
$457$	−1.12133e47			−0.148335			−0.0741675	+	0.997246i	$0.523630\pi$
$458$	1.13005e47	+	6.44948e46i	0.143720	+	0.0820250i
$459$		−	4.09918e47i		−	0.501267i
$460$	−3.09538e47	+	1.82848e47i	−0.363976	+	0.215006i
$461$	1.02919e48			1.16380			0.581900	−	0.813260i	$-0.302309\pi$
$461$	1.02919e48			1.16380			0.581900	+	0.813260i	$0.302309\pi$
$462$	−3.11142e47	+	5.45168e47i	−0.338378	+	0.592891i
$463$			1.07221e48i			1.12156i	0.827966	+	0.560778i	$0.189498\pi$
$463$			1.07221e48i			1.12156i	−0.827966	+	0.560778i	$0.810502\pi$
$464$	1.03842e47	−	1.88436e47i	0.104484	−	0.189601i
$465$	4.93608e47			0.477781
$466$	−2.08831e46	−	1.19185e46i	−0.0194469	−	0.0110988i
$467$		−	2.64750e47i		−	0.237210i	−0.992942	−	0.118605i	$-0.962158\pi$
$467$		−	2.64750e47i		−	0.237210i	0.992942	−	0.118605i	$-0.0378422\pi$
$468$	7.15259e47	+	1.21084e48i	0.616649	+	1.04390i
$469$	−2.33228e48			−1.93495
$470$	3.54673e47	−	6.21443e47i	0.283183	−	0.496181i
$471$			1.01695e48i			0.781489i
$472$	−9.79098e47	+	1.46363e46i	−0.724219	+	0.0108262i
$473$	3.35389e47			0.238808
$474$	1.98696e47	+	1.13401e47i	0.136201	+	0.0777332i
$475$			3.07883e48i			2.03190i
$476$	1.27267e48	−	7.51783e47i	0.808705	−	0.477714i
$477$	5.16391e46			0.0315972
$478$	−1.75695e47	+	3.07845e47i	−0.103528	+	0.181397i
$479$		−	1.15049e48i		−	0.652897i	−0.945215	−	0.326449i	$-0.894148\pi$
$479$		−	1.15049e48i		−	0.652897i	0.945215	−	0.326449i	$-0.105852\pi$
$480$	−6.35539e47	−	1.04006e48i	−0.347376	−	0.568482i
$481$	2.27317e48			1.19680
$482$	−6.24067e47	−	3.56171e47i	−0.316508	−	0.180639i
$483$		−	4.17249e47i		−	0.203867i
$484$	5.95242e46	+	1.00766e47i	0.0280206	+	0.0474351i
$485$	−6.11991e48			−2.77584
$486$	−1.14489e48	+	2.00602e48i	−0.500391	+	0.876762i
$487$		−	2.97014e48i		−	1.25099i	−0.780226	−	0.625497i	$-0.784896\pi$
$487$		−	2.97014e48i		−	1.25099i	0.780226	−	0.625497i	$-0.215104\pi$
$488$	9.93121e45	+	6.64351e47i	0.00403130	+	0.269675i
$489$	−1.87349e48			−0.732978
$490$	4.54904e48	+	2.59626e48i	1.71550	+	0.979080i
$491$			3.36774e48i			1.22425i	0.790759	+	0.612127i	$0.209686\pi$
$491$			3.36774e48i			1.22425i	−0.790759	+	0.612127i	$0.790314\pi$
$492$	3.05303e46	−	1.80347e46i	0.0106994	−	0.00632028i
$493$	−3.92043e47			−0.132461
$494$	4.23035e48	−	7.41223e48i	1.37813	−	2.41470i
$495$			3.56313e48i			1.11928i
$496$	−2.07348e48	−	1.14264e48i	−0.628100	−	0.346131i
$497$	3.60527e48			1.05323
$498$	1.30961e48	+	7.47426e47i	0.368988	+	0.210591i
$499$		−	4.09580e48i		−	1.11309i	−0.830818	−	0.556544i	$-0.812127\pi$
$499$		−	4.09580e48i		−	1.11309i	0.830818	−	0.556544i	$-0.187873\pi$
$500$	3.40770e47	+	5.76877e47i	0.0893308	+	0.151225i
$501$	−1.01473e48			−0.256608
$502$	1.61257e48	−	2.82547e48i	0.393415	−	0.689325i
$503$			4.07583e48i			0.959383i	0.877437	+	0.479692i	$0.159251\pi$
$503$			4.07583e48i			0.959383i	−0.877437	+	0.479692i	$0.840749\pi$
$504$	−5.34365e48	+	7.98808e46i	−1.21364	+	0.0181423i
$505$	−3.45623e48			−0.757456
$506$	1.15882e48	+	6.61368e47i	0.245079	+	0.139873i
$507$		−	3.02863e48i		−	0.618163i
$508$	−9.84367e47	+	5.81480e47i	−0.193914	+	0.114548i
$509$	8.39304e48			1.59588			0.797938	−	0.602740i	$-0.205924\pi$
$509$	8.39304e48			1.59588			0.797938	+	0.602740i	$0.205924\pi$
$510$	−1.10088e48	+	1.92891e48i	−0.202058	+	0.354038i
$511$		−	6.09123e48i		−	1.07927i
$512$	2.62064e47	+	5.84013e48i	0.0448278	+	0.998995i
$513$	8.99426e48			1.48543
$514$	−3.33292e48	−	1.90218e48i	−0.531483	−	0.303331i
$515$		−	5.38332e48i		−	0.828934i
$516$	−3.84426e47	−	6.50781e47i	−0.0571633	−	0.0967699i
$517$	−2.65559e48			−0.381356
$518$	−4.28189e48	+	7.50254e48i	−0.593882	+	1.04057i
$519$		−	6.99064e47i		−	0.0936493i
$520$	−2.57924e47	−	1.72539e49i	−0.0333758	−	2.23268i
$521$	−2.34160e48			−0.292708			−0.146354	−	0.989232i	$-0.546754\pi$
$521$	−2.34160e48			−0.292708			−0.146354	+	0.989232i	$0.546754\pi$
$522$	1.23106e48	+	7.02600e47i	0.148666	+	0.0848475i
$523$			8.19584e48i			0.956232i	0.878297	+	0.478116i	$0.158680\pi$
$523$			8.19584e48i			0.956232i	−0.878297	+	0.478116i	$0.841320\pi$
$524$	−3.97423e48	+	2.34763e48i	−0.448012	+	0.264647i
$525$	−7.22488e48			−0.786979
$526$	−4.16272e48	+	7.29372e48i	−0.438161	+	0.767725i
$527$			4.31389e48i			0.438811i
$528$	−2.18330e48	+	3.96189e48i	−0.214636	+	0.389486i
$529$	9.63760e48			0.915729
$530$	−5.50307e47	−	3.14074e47i	−0.0505405	−	0.0288447i
$531$		−	6.45108e48i		−	0.572705i
$532$	1.64953e49	+	2.79244e49i	1.41564	+	2.39648i
$533$	5.02003e47			0.0416502
$534$	−2.09288e48	+	3.66705e48i	−0.167881	+	0.294154i
$535$			1.60836e49i			1.24743i
$536$	−1.68060e49	+	2.51228e47i	−1.26037	+	0.0188409i
$537$	2.93710e48			0.213001
$538$	−1.97444e49	−	1.12686e49i	−1.38472	−	0.790296i
$539$		−	1.94393e49i		−	1.31851i
$540$	1.56577e49	−	9.24923e48i	1.02717	−	0.606761i
$541$	−8.30545e48			−0.527002			−0.263501	−	0.964659i	$-0.584877\pi$
$541$	−8.30545e48			−0.527002			−0.263501	+	0.964659i	$0.584877\pi$
$542$	2.72986e48	−	4.78313e48i	0.167553	−	0.293579i
$543$		−	2.08470e48i		−	0.123779i
$544$	9.08961e48	−	5.55429e48i	0.522114	−	0.319042i
$545$	9.82576e48			0.546046
$546$	1.73937e49	+	9.92705e48i	0.935245	+	0.533768i
$547$			1.87034e49i			0.973080i	0.873658	+	0.486540i	$0.161741\pi$
$547$			1.87034e49i			0.973080i	−0.873658	+	0.486540i	$0.838259\pi$
$548$	−1.38950e49	−	2.35223e49i	−0.699532	−	1.18421i
$549$	−4.37727e48			−0.213256
$550$	1.14519e49	−	2.00655e49i	0.539946	−	0.946068i
$551$		−	8.60204e48i		−	0.392530i
$552$	−4.49451e46	−	3.00661e48i	−0.00198508	−	0.132793i
$553$	−1.23083e49			−0.526196
$554$	−1.58444e49	−	9.04280e48i	−0.655692	−	0.374220i
$555$		−	1.29797e49i		−	0.519983i
$556$	3.67755e49	−	2.17238e49i	1.42630	−	0.842538i
$557$	−2.22627e49			−0.835957			−0.417979	−	0.908457i	$-0.637261\pi$
$557$	−2.22627e49			−0.835957			−0.417979	+	0.908457i	$0.637261\pi$
$558$	7.73113e48	−	1.35461e49i	0.281079	−	0.492493i
$559$		−	1.07007e49i		−	0.376702i
$560$	5.74319e49	+	3.16493e49i	1.95780	+	1.07890i
$561$	8.24275e48			0.272108
$562$	−3.79301e48	−	2.16477e48i	−0.121264	−	0.0692082i
$563$			5.58851e49i			1.73039i	0.501433	+	0.865197i	$0.332806\pi$
$563$			5.58851e49i			1.73039i	−0.501433	+	0.865197i	$0.667194\pi$
$564$	3.04386e48	+	5.15284e48i	0.0912852	+	0.154534i
$565$	−5.40371e49			−1.56971
$566$	−3.17619e49	+	5.56518e49i	−0.893739	+	1.56597i
$567$		−	2.34217e49i		−	0.638444i
$568$	2.59789e49	−	3.88351e47i	0.686041	−	0.0102555i
$569$	2.83847e49			0.726213			0.363106	−	0.931748i	$-0.381716\pi$
$569$	2.83847e49			0.726213			0.363106	+	0.931748i	$0.381716\pi$
$570$	−4.23234e49	−	2.41551e49i	−1.04914	−	0.598771i
$571$			1.22959e49i			0.295333i	0.989037	+	0.147666i	$0.0471762\pi$
$571$			1.22959e49i			0.295333i	−0.989037	+	0.147666i	$0.952824\pi$
$572$	−5.51405e49	+	3.25723e49i	−1.28334	+	0.758088i
$573$	−6.08748e47			−0.0137295
$574$	−9.45608e47	+	1.65685e48i	−0.0206679	+	0.0362134i
$575$			1.53573e49i			0.325308i
$576$	−3.84967e49	+	1.15121e48i	−0.790348	+	0.0236347i
$577$	5.25738e49			1.04618			0.523088	−	0.852279i	$-0.324780\pi$
$577$	5.25738e49			1.04618			0.523088	+	0.852279i	$0.324780\pi$
$578$	2.81694e49	+	1.60770e49i	0.543345	+	0.310101i
$579$			3.01719e49i			0.564142i
$580$	−8.84589e48	−	1.49749e49i	−0.160338	−	0.271431i
$581$	−8.11243e49			−1.42554
$582$	2.53724e49	−	4.44563e49i	0.432262	−	0.757390i
$583$			2.35160e48i			0.0388446i
$584$	−6.56133e47	−	4.38922e49i	−0.0105090	−	0.703001i
$585$	1.13682e50			1.76558
$586$	8.64997e49	+	4.93676e49i	1.30274	+	0.743507i
$587$		−	5.78785e49i		−	0.845340i	−0.906284	−	0.422670i	$-0.861093\pi$
$587$		−	5.78785e49i		−	0.845340i	0.906284	−	0.422670i	$-0.138907\pi$
$588$	−3.77195e49	+	2.22814e49i	−0.534286	+	0.315611i
$589$	−9.46535e49			−1.30035
$590$	−3.92361e49	+	6.87477e49i	−0.522817	+	0.916056i
$591$		−	3.66086e49i		−	0.473160i
$592$	−3.00463e49	+	5.45230e49i	−0.376704	+	0.683580i
$593$	1.05326e50			1.28100			0.640502	−	0.767956i	$-0.278726\pi$
$593$	1.05326e50			1.28100			0.640502	+	0.767956i	$0.278726\pi$
$594$	−5.86178e49	−	3.34547e49i	−0.691630	−	0.394731i
$595$		−	1.19488e50i		−	1.36778i
$596$	−7.10821e49	−	1.20332e50i	−0.789455	−	1.33644i
$597$	3.13176e49			0.337481
$598$	2.11011e49	−	3.69724e49i	0.220640	−	0.386595i
$599$			1.30983e50i			1.32902i	0.747278	+	0.664511i	$0.231360\pi$
$599$			1.30983e50i			1.32902i	−0.747278	+	0.664511i	$0.768640\pi$
$600$	−5.20610e49	+	7.78246e47i	−0.512614	+	0.00766293i
$601$	1.73160e50			1.65466			0.827329	−	0.561718i	$-0.189859\pi$
$601$	1.73160e50			1.65466			0.827329	+	0.561718i	$0.189859\pi$
$602$	3.53173e49	+	2.01565e49i	0.327530	+	0.186930i
$603$		−	1.10731e50i		−	0.996685i
$604$	−4.90958e49	+	2.90016e49i	−0.428923	+	0.253371i
$605$	9.46071e48			0.0802282
$606$	1.43291e49	−	2.51067e49i	0.117953	−	0.206673i
$607$		−	9.98769e49i		−	0.798121i	−0.916925	−	0.399060i	$-0.869336\pi$
$607$		−	9.98769e49i		−	0.798121i	0.916925	−	0.399060i	$-0.130664\pi$
$608$	1.21870e50	+	1.99440e50i	0.945436	+	1.54721i
$609$	2.01858e49			0.152032
$610$	4.66476e49	+	2.66230e49i	0.341108	+	0.194679i
$611$			8.47272e49i			0.601563i
$612$	3.56928e49	+	6.04232e49i	0.246068	+	0.416560i
$613$	−2.26002e50			−1.51294			−0.756472	−	0.654026i	$-0.773079\pi$
$613$	−2.26002e50			−1.51294			−0.756472	+	0.654026i	$0.773079\pi$
$614$	3.33355e49	−	5.84089e49i	0.216709	−	0.379707i
$615$		−	2.86641e48i		−	0.0180961i
$616$	−3.63771e48	−	2.43345e50i	−0.0223036	−	1.49201i
$617$	−1.84910e50			−1.10110			−0.550552	−	0.834801i	$-0.685583\pi$
$617$	−1.84910e50			−1.10110			−0.550552	+	0.834801i	$0.685583\pi$
$618$	3.91055e49	+	2.23185e49i	0.226175	+	0.129084i
$619$			2.69650e50i			1.51485i	0.652924	+	0.757424i	$0.273542\pi$
$619$			2.69650e50i			1.51485i	−0.652924	+	0.757424i	$0.726458\pi$
$620$	−1.64778e50	+	9.73367e49i	−0.899184	+	0.531161i
$621$	4.48636e49			0.237818
$622$	1.77460e50	−	3.10937e50i	0.913847	−	1.60120i
$623$		−	2.27158e50i		−	1.13643i
$624$	1.26405e50	+	6.96587e49i	0.614387	+	0.338574i
$625$	−1.83137e50			−0.864841
$626$	−2.89801e48	−	1.65397e48i	−0.0132973	−	0.00758910i
$627$			1.80859e50i			0.806351i
$628$	−2.00537e50	−	3.39482e50i	−0.868801	−	1.47076i
$629$	1.13436e50			0.477571
$630$	−2.14140e50	+	3.75206e50i	−0.876128	+	1.53511i
$631$			3.25280e50i			1.29339i	0.762749	+	0.646694i	$0.223849\pi$
$631$			3.25280e50i			1.29339i	−0.762749	+	0.646694i	$0.776151\pi$
$632$	−8.86914e49	+	1.32583e48i	−0.342747	+	0.00512364i
$633$	1.02644e50			0.385538
$634$	3.87540e50	+	2.21179e50i	1.41485	+	0.807490i
$635$			9.24197e49i			0.327973i
$636$	4.56300e48	−	2.69543e48i	0.0157406	−	0.00929822i
$637$	−6.20214e50			−2.07985
$638$	−3.19958e49	+	5.60617e49i	−0.104309	+	0.182765i
$639$			1.71170e50i			0.542514i
$640$	4.17252e50	+	2.21872e50i	1.28576	+	0.683697i
$641$	2.58731e50			0.775183			0.387591	−	0.921831i	$-0.373307\pi$
$641$	2.58731e50			0.775183			0.387591	+	0.921831i	$0.373307\pi$
$642$	−1.16834e50	−	6.66805e49i	−0.340362	−	0.194253i
$643$		−	1.55303e50i		−	0.439928i	−0.975508	−	0.219964i	$-0.929406\pi$
$643$		−	1.55303e50i		−	0.439928i	0.975508	−	0.219964i	$-0.0705940\pi$
$644$	8.22791e49	+	1.39288e50i	0.226644	+	0.383678i
$645$	−6.11002e49			−0.163669
$646$	2.11103e50	−	3.69885e50i	0.549932	−	0.963566i
$647$		−	6.88086e50i		−	1.74327i	−0.490152	−	0.871637i	$-0.663059\pi$
$647$		−	6.88086e50i		−	1.74327i	0.490152	−	0.871637i	$-0.336941\pi$
$648$	−2.52293e48	−	1.68772e50i	−0.00621663	−	0.415863i
$649$	2.93777e50			0.704066
$650$	−6.40196e50	−	3.65377e50i	−1.49236	−	0.851727i
$651$		−	2.22116e50i		−	0.503643i
$652$	6.25414e50	−	3.69441e50i	1.37947	−	0.814870i
$653$	−1.99284e50			−0.427596			−0.213798	−	0.976878i	$-0.568584\pi$
$653$	−1.99284e50			−0.427596			−0.213798	+	0.976878i	$0.568584\pi$
$654$	−4.07363e49	+	7.13763e49i	−0.0850320	+	0.148989i
$655$			3.73130e50i			0.757734i
$656$	−6.63539e48	+	1.20408e49i	−0.0131098	+	0.0237895i
$657$	2.89197e50			0.555926
$658$	−2.79640e50	−	1.59598e50i	−0.523038	−	0.298512i
$659$		−	3.60744e50i		−	0.656541i	−0.944584	−	0.328270i	$-0.893534\pi$
$659$		−	3.60744e50i		−	0.656541i	0.944584	−	0.328270i	$-0.106466\pi$
$660$	1.85986e50	+	3.14849e50i	0.329374	+	0.557586i
$661$	−4.59971e50			−0.792691			−0.396346	−	0.918101i	$-0.629722\pi$
$661$	−4.59971e50			−0.792691			−0.396346	+	0.918101i	$0.629722\pi$
$662$	−2.97449e50	+	5.21177e50i	−0.498849	+	0.874060i
$663$		−	2.62987e50i		−	0.429231i
$664$	−5.84565e50	+	8.73852e48i	−0.928555	+	0.0138807i
$665$	2.62175e51			4.05323
$666$	−3.56202e50	−	2.03294e50i	−0.535995	−	0.305906i
$667$		−	4.29072e49i		−	0.0628442i
$668$	3.38740e50	−	2.00098e50i	0.482936	−	0.285277i
$669$	−5.91774e50			−0.821270
$670$	−6.73478e50	+	1.18004e51i	−0.909864	+	1.59422i
$671$		−	1.99338e50i		−	0.262170i
$672$	−4.68012e50	+	2.85983e50i	−0.599253	+	0.366179i
$673$	−8.21833e50			−1.02450			−0.512251	−	0.858836i	$-0.671188\pi$
$673$	−8.21833e50			−1.02450			−0.512251	+	0.858836i	$0.671188\pi$
$674$	−3.69432e50	−	2.10844e50i	−0.448390	−	0.255908i
$675$		−	7.76837e50i		−	0.918040i
$676$	5.97228e50	+	1.01103e51i	0.687227	+	1.16338i
$677$	3.47381e50			0.389234			0.194617	−	0.980879i	$-0.437654\pi$
$677$	3.47381e50			0.389234			0.194617	+	0.980879i	$0.437654\pi$
$678$	2.24031e50	−	3.92536e50i	0.244440	−	0.428297i
$679$			2.75387e51i			2.92609i
$680$	−1.28709e49	−	8.61004e50i	−0.0133183	−	0.890932i
$681$	3.86829e50			0.389826
$682$	6.16880e50	+	3.52070e50i	0.605456	+	0.345549i
$683$			8.87361e50i			0.848257i	0.905602	+	0.424129i	$0.139420\pi$
$683$			8.87361e50i			0.848257i	−0.905602	+	0.424129i	$0.860580\pi$
$684$	−1.32578e51	+	7.83157e50i	−1.23442	+	0.729188i
$685$	−2.20845e51			−2.00289
$686$	3.06969e50	−	5.37858e50i	0.271182	−	0.475153i
$687$			8.79732e49i			0.0757058i
$688$	2.56661e50	+	1.41439e50i	0.215163	+	0.118571i
$689$	7.50285e49			0.0612746
$690$	−2.11110e50	−	1.20486e50i	−0.167968	−	0.0958635i
$691$		−	1.71672e51i		−	1.33074i	−0.746512	−	0.665372i	$-0.768273\pi$
$691$		−	1.71672e51i		−	1.33074i	0.746512	−	0.665372i	$-0.231727\pi$
$692$	1.37851e50	+	2.33364e50i	0.104112	+	0.176248i
$693$	1.60335e51			1.17986
$694$	6.42668e50	−	1.12605e51i	0.460804	−	0.807400i
$695$		−	3.45276e51i		−	2.41234i
$696$	1.45455e50	−	2.17436e48i	0.0990288	−	0.00148035i
$697$	2.50510e49			0.0166201
$698$	2.44243e50	+	1.39396e50i	0.157915	+	0.0901263i
$699$		−	1.62573e49i		−	0.0102438i
$700$	2.41183e51	−	1.42471e51i	1.48109	−	0.874904i
$701$	−2.04153e51			−1.22189			−0.610944	−	0.791674i	$-0.709210\pi$
$701$	−2.04153e51			−1.22189			−0.610944	+	0.791674i	$0.709210\pi$
$702$	−1.06738e51	+	1.87022e51i	−0.622661	+	1.09100i
$703$			2.48896e51i			1.41521i
$704$	−5.24252e49	−	1.75311e51i	−0.0290557	−	0.971629i
$705$	4.83787e50			0.261367
$706$	6.74843e50	+	3.85151e50i	0.355401	+	0.202836i
$707$			1.55525e51i			0.798457i
$708$	−3.36730e50	−	5.70038e50i	−0.168532	−	0.285302i
$709$	−1.72817e50			−0.0843245			−0.0421622	−	0.999111i	$-0.513425\pi$
$709$	−1.72817e50			−0.0843245			−0.0421622	+	0.999111i	$0.513425\pi$
$710$	1.04107e51	−	1.82412e51i	0.495256	−	0.867765i
$711$		−	5.84370e50i		−	0.271041i
$712$	−2.44689e49	−	1.63685e51i	−0.0110656	−	0.740235i
$713$	−4.72134e50			−0.208187
$714$	8.67983e50	+	4.95380e50i	0.373201	+	0.212996i
$715$			5.17700e51i			2.17055i
$716$	−9.80472e50	+	5.79179e50i	−0.400867	+	0.236798i
$717$	−2.39655e50			−0.0955523
$718$	2.08546e51	−	3.65405e51i	0.810889	−	1.42080i
$719$		−	3.23849e51i		−	1.22807i	−0.789279	−	0.614034i	$-0.789546\pi$
$719$		−	3.23849e51i		−	1.22807i	0.789279	−	0.614034i	$-0.210454\pi$
$720$	−1.50263e51	+	2.72673e51i	−0.555735	+	1.00846i
$721$	−2.42241e51			−0.873803
$722$	5.64731e51	+	3.22307e51i	1.98688	+	1.13397i
$723$		−	4.85830e50i		−	0.166723i
$724$	4.11091e50	+	6.95922e50i	0.137608	+	0.232952i
$725$	−7.42960e50			−0.242595
$726$	−3.92229e49	+	6.87245e49i	−0.0124934	+	0.0218903i
$727$		−	2.42075e51i		−	0.752196i	−0.926580	−	0.376098i	$-0.877266\pi$
$727$		−	2.42075e51i		−	0.752196i	0.926580	−	0.376098i	$-0.122734\pi$
$728$	−7.76400e51	+	1.16062e50i	−2.35353	+	0.0351824i
$729$	−1.55313e50			−0.0459317
$730$	−3.08190e51	−	1.75892e51i	−0.889217	−	0.507499i
$731$		−	5.33985e50i		−	0.150320i
$732$	−3.86790e50	+	2.28482e50i	−0.106237	+	0.0627557i
$733$	2.02046e51			0.541475			0.270738	−	0.962653i	$-0.412732\pi$
$733$	2.02046e51			0.541475			0.270738	+	0.962653i	$0.412732\pi$
$734$	−1.71601e51	+	3.00672e51i	−0.448736	+	0.786255i
$735$			3.54139e51i			0.903652i
$736$	6.07891e50	+	9.94815e50i	0.151365	+	0.247709i
$737$	5.04261e51			1.22529
$738$	−7.86632e49	−	4.48951e49i	−0.0186534	−	0.0106460i
$739$		−	2.96849e51i		−	0.686966i	−0.939159	−	0.343483i	$-0.888393\pi$
$739$		−	2.96849e51i		−	0.686966i	0.939159	−	0.343483i	$-0.111607\pi$
$740$	2.55951e51	+	4.33291e51i	0.578078	+	0.978608i
$741$	5.77035e51			1.27196
$742$	−1.41329e50	+	2.47630e50i	−0.0304061	+	0.0532762i
$743$			3.73279e51i			0.783854i	0.919996	+	0.391927i	$0.128191\pi$
$743$			3.73279e51i			0.783854i	−0.919996	+	0.391927i	$0.871809\pi$
$744$	−2.39258e49	−	1.60053e51i	−0.00490404	−	0.328057i
$745$	−1.12977e52			−2.26036
$746$	−3.10653e51	−	1.77298e51i	−0.606704	−	0.346262i
$747$		−	3.85158e51i		−	0.734292i
$748$	−2.75162e51	+	1.62542e51i	−0.512106	+	0.302509i
$749$	7.23738e51			1.31495
$750$	−2.24547e50	+	3.93441e50i	−0.0398294	+	0.0697873i
$751$		−	4.60658e51i		−	0.797737i	−0.917008	−	0.398868i	$-0.869403\pi$
$751$		−	4.60658e51i		−	0.797737i	0.917008	−	0.398868i	$-0.130597\pi$
$752$	−2.03222e51	−	1.11991e51i	−0.343598	−	0.189348i
$753$	2.19960e51			0.363107
$754$	1.78866e51	+	1.02084e51i	0.288299	+	0.164540i
$755$			4.60948e51i			0.725449i
$756$	−4.16202e51	−	7.04574e51i	−0.639605	−	1.08276i
$757$	−7.44791e51			−1.11766			−0.558829	−	0.829283i	$-0.688749\pi$
$757$	−7.44791e51			−1.11766			−0.558829	+	0.829283i	$0.688749\pi$
$758$	−5.90199e51	+	1.03412e52i	−0.864873	+	1.51539i
$759$			9.02130e50i			0.129097i
$760$	1.88918e52	−	2.82408e50i	2.64015	−	0.0394669i
$761$	1.23442e52			1.68476			0.842380	−	0.538884i	$-0.181154\pi$
$761$	1.23442e52			1.68476			0.842380	+	0.538884i	$0.181154\pi$
$762$	−6.71356e50	−	3.83160e50i	−0.0894877	−	0.0510729i
$763$		−	4.42145e51i		−	0.575603i
$764$	2.03214e50	−	1.20042e50i	0.0258389	−	0.0152634i
$765$	5.67298e51			0.704540
$766$	6.72291e51	−	1.17796e52i	0.815529	−	1.42893i
$767$		−	9.37302e51i		−	1.11061i
$768$	−3.34160e51	+	2.11115e51i	−0.386769	+	0.244353i
$769$	6.04399e51			0.683360			0.341680	−	0.939816i	$-0.389004\pi$
$769$	6.04399e51			0.683360			0.341680	+	0.939816i	$0.389004\pi$
$770$	−1.70866e52	−	9.75176e51i	−1.88722	−	1.07708i
$771$		−	2.59465e51i		−	0.279962i
$772$	−5.94973e51	−	1.00721e52i	−0.627171	−	1.06172i
$773$	−8.79086e51			−0.905316			−0.452658	−	0.891684i	$-0.649524\pi$
$773$	−8.79086e51			−0.905316			−0.452658	+	0.891684i	$0.649524\pi$
$774$	−9.56981e50	+	1.67678e51i	−0.0962867	+	0.168709i
$775$			8.17525e51i			0.803656i
$776$	2.96640e50	+	1.98438e52i	0.0284918	+	1.90596i
$777$	−5.84065e51			−0.548129
$778$	1.76521e52	+	1.00745e52i	1.61869	+	0.923831i
$779$			5.49658e50i			0.0492514i
$780$	1.00453e52	−	5.93393e51i	0.879553	−	0.519564i
$781$	−7.79493e51			−0.666950
$782$	1.05299e51	−	1.84500e51i	0.0880444	−	0.154267i
$783$			2.17042e51i			0.177351i
$784$	8.19788e51	−	1.48761e52i	0.654655	−	1.18796i
$785$	−3.18731e52			−2.48754
$786$	−2.71049e51	−	1.54695e51i	−0.206749	−	0.117997i
$787$			1.01676e52i			0.758005i	0.925396	+	0.379003i	$0.123733\pi$
$787$			1.01676e52i			0.758005i	−0.925396	+	0.379003i	$0.876267\pi$
$788$	7.21900e51	+	1.22208e52i	0.526024	+	0.890487i
$789$	−5.67809e51			−0.404405
$790$	−3.55420e51	+	6.22750e51i	−0.247431	+	0.433537i
$791$			2.43159e52i			1.65468i
$792$	1.15534e52	−	1.72709e50i	0.768526	−	0.0114885i
$793$	−6.35991e51			−0.413556
$794$	−3.56286e51	−	2.03342e51i	−0.226480	−	0.129258i
$795$		−	4.28409e50i		−	0.0266226i
$796$	−1.04545e52	+	6.17564e51i	−0.635140	+	0.375186i
$797$	2.59769e52			1.54290			0.771450	−	0.636290i	$-0.219532\pi$
$797$	2.59769e52			1.54290			0.771450	+	0.636290i	$0.219532\pi$
$798$	−1.08694e52	+	1.90449e52i	−0.631182	+	1.10593i
$799$			4.22806e51i			0.240048i
$800$	1.72257e52	−	1.05259e52i	0.956220	−	0.584307i
$801$	1.07849e52			0.585370
$802$	−1.77411e52	−	1.01253e52i	−0.941549	−	0.537366i
$803$			1.31698e52i			0.683438i
$804$	−5.77988e51	−	9.78456e51i	−0.293299	−	0.496515i
$805$	1.30774e52			0.648924
$806$	1.12329e52	−	1.96817e52i	0.545080	−	0.955064i
$807$		−	1.53708e52i		−	0.729412i
$808$	1.67528e50	+	1.12068e52i	0.00777469	+	0.520090i
$809$	−3.56777e52			−1.61929			−0.809643	−	0.586923i	$-0.800339\pi$
$809$	−3.56777e52			−1.61929			−0.809643	+	0.586923i	$0.800339\pi$
$810$	−1.18504e52	−	6.76332e51i	−0.526020	−	0.300213i
$811$		−	1.06999e52i		−	0.464518i	−0.972654	−	0.232259i	$-0.925388\pi$
$811$		−	1.06999e52i		−	0.464518i	0.972654	−	0.232259i	$-0.0746117\pi$
$812$	−6.73849e51	+	3.98052e51i	−0.286124	+	0.169017i
$813$	3.72362e51			0.154645
$814$	9.25784e51	−	1.62212e52i	0.376071	−	0.658935i
$815$		−	5.87185e52i		−	2.33313i
$816$	6.30787e51	+	3.47611e51i	0.245166	+	0.135105i
$817$	1.17165e52			0.445451
$818$	1.07071e52	+	6.11083e51i	0.398211	+	0.227269i
$819$		−	5.11554e52i		−	1.86115i
$820$	5.65240e50	+	9.56875e50i	0.0201179	+	0.0340570i
$821$	2.44699e52			0.852032			0.426016	−	0.904716i	$-0.359917\pi$
$821$	2.44699e52			0.852032			0.426016	+	0.904716i	$0.359917\pi$
$822$	9.15595e51	−	1.60426e52i	0.311897	−	0.546491i
$823$			5.26840e52i			1.75583i	0.478819	+	0.877914i	$0.341065\pi$
$823$			5.26840e52i			1.75583i	−0.478819	+	0.877914i	$0.658935\pi$
$824$	−1.74554e52	+	2.60937e50i	−0.569168	+	0.00850835i
$825$	1.56208e52			0.498349
$826$	3.09355e52	+	1.76557e52i	0.965641	+	0.551116i
$827$			5.95412e52i			1.81852i	0.416227	+	0.909261i	$0.363352\pi$
$827$			5.95412e52i			1.81852i	−0.416227	+	0.909261i	$0.636648\pi$
$828$	−6.61303e51	+	3.90641e51i	−0.197631	+	0.116743i
$829$	3.96449e52			1.15933			0.579663	−	0.814856i	$-0.303184\pi$
$829$	3.96449e52			1.15933			0.579663	+	0.814856i	$0.303184\pi$
$830$	−2.34257e52	+	4.10455e52i	−0.670328	+	1.17452i
$831$		−	1.23347e52i		−	0.345390i
$832$	−5.59333e52	+	1.67264e51i	−1.53268	+	0.0458334i
$833$	−3.09500e52			−0.829946
$834$	2.50815e52	+	1.43147e52i	0.658211	+	0.375658i
$835$		−	3.18034e52i		−	0.816803i
$836$	−3.56644e52	−	6.03750e52i	−0.896440	−	1.51755i
$837$	2.38825e52			0.587518
$838$	−1.67222e52	+	2.92999e52i	−0.402626	+	0.705462i
$839$		−	3.09117e52i		−	0.728464i	−0.931308	−	0.364232i	$-0.881332\pi$
$839$		−	3.09117e52i		−	0.728464i	0.931308	−	0.364232i	$-0.118668\pi$
$840$	6.62707e50	+	4.43320e52i	0.0152860	+	1.02256i
$841$	−4.22165e52			−0.953135
$842$	2.22135e52	+	1.26778e52i	0.490907	+	0.280174i
$843$		−	2.95282e51i		−	0.0638765i
$844$	−3.42650e52	+	2.02408e52i	−0.725583	+	0.428612i
$845$	9.49228e52			1.96766
$846$	7.57732e51	−	1.32766e52i	0.153762	−	0.269415i
$847$		−	4.25718e51i		−	0.0845708i
$848$	−9.91713e50	+	1.79960e51i	−0.0192868	+	0.0349985i
$849$	−4.33244e52			−0.824886
$850$	−3.19471e52	−	1.82330e52i	−0.595512	−	0.339874i
$851$			1.24150e52i			0.226576i
$852$	8.93461e51	+	1.51251e52i	0.159648	+	0.270262i
$853$	−2.17155e52			−0.379916			−0.189958	−	0.981792i	$-0.560835\pi$
$853$	−2.17155e52			−0.379916			−0.189958	+	0.981792i	$0.560835\pi$
$854$	1.19800e52	−	2.09908e52i	0.205217	−	0.359572i
$855$			1.24474e53i			2.08780i
$856$	5.21511e52	−	7.79593e50i	0.856517	−	0.0128038i
$857$	−9.70662e52			−1.56104			−0.780518	−	0.625133i	$-0.785045\pi$
$857$	−9.70662e52			−1.56104			−0.780518	+	0.625133i	$0.785045\pi$
$858$	−3.76068e52	−	2.14632e52i	−0.592237	−	0.338005i
$859$		−	3.82443e52i		−	0.589780i	−0.955531	−	0.294890i	$-0.904717\pi$
$859$		−	3.82443e52i		−	0.589780i	0.955531	−	0.294890i	$-0.0952831\pi$
$860$	2.03967e52	−	1.20486e52i	0.308026	−	0.181955i
$861$	−1.28984e51			−0.0190757
$862$	4.46825e52	−	7.82906e52i	0.647152	−	1.13391i
$863$			6.79896e52i			0.964380i	0.876067	+	0.482190i	$0.160159\pi$
$863$			6.79896e52i			0.964380i	−0.876067	+	0.482190i	$0.839841\pi$
$864$	−3.07496e52	−	5.03218e52i	−0.427162	−	0.699051i
$865$	2.19100e52			0.298093
$866$	7.33924e52	+	4.18870e52i	0.977978	+	0.558158i
$867$			2.19296e52i			0.286211i
$868$	4.38001e52	+	7.41477e52i	0.559912	+	0.947856i
$869$	2.66117e52			0.333209
$870$	5.82891e51	−	1.02132e52i	0.0714893	−	0.125260i
$871$		−	1.60886e53i		−	1.93282i
$872$	−4.76268e50	−	3.18601e52i	−0.00560473	−	0.374930i
$873$	−1.30747e53			−1.50722
$874$	4.04822e52	+	2.31042e52i	0.457149	+	0.260907i
$875$		−	2.43719e52i		−	0.269615i
$876$	2.55543e52	−	1.50953e52i	0.276943	−	0.163594i
$877$	1.62144e52			0.172151			0.0860753	−	0.996289i	$-0.472567\pi$
$877$	1.62144e52			0.172151			0.0860753	+	0.996289i	$0.472567\pi$
$878$	2.40586e52	−	4.21543e52i	0.250247	−	0.438471i
$879$			6.73392e52i			0.686227i
$880$	−1.24173e53	−	6.84287e52i	−1.23976	−	0.683203i
$881$	8.46178e52			0.827743			0.413871	−	0.910335i	$-0.364176\pi$
$881$	8.46178e52			0.827743			0.413871	+	0.910335i	$0.364176\pi$
$882$	9.71868e52	+	5.54670e52i	0.931478	+	0.531619i
$883$			7.26326e52i			0.682086i	0.940048	+	0.341043i	$0.110780\pi$
$883$			7.26326e52i			0.682086i	−0.940048	+	0.341043i	$0.889220\pi$
$884$	5.18595e52	+	8.77912e52i	0.477186	+	0.807812i
$885$	−5.35194e52			−0.482539
$886$	−4.15960e52	+	7.28826e52i	−0.367489	+	0.643898i
$887$		−	1.74737e53i		−	1.51272i	−0.654154	−	0.756361i	$-0.726975\pi$
$887$		−	1.74737e53i		−	1.51272i	0.654154	−	0.756361i	$-0.273025\pi$
$888$	−4.20866e52	+	6.29141e50i	−0.357035	+	0.00533722i
$889$	4.15875e52			0.345725
$890$	−1.14932e53	−	6.55947e52i	−0.936314	−	0.534378i
$891$			5.06398e52i			0.404290i
$892$	1.97548e53	−	1.16695e53i	1.54563	−	0.913026i
$893$	−9.27703e52			−0.711349
$894$	4.68388e52	−	8.20689e52i	0.351990	−	0.616741i
$895$			9.20540e52i			0.677998i
$896$	9.98393e52	−	1.87757e53i	0.720704	−	1.35535i
$897$	2.87827e52			0.203642
$898$	−2.31479e53	−	1.32111e53i	−1.60523	−	0.916149i
$899$		−	2.28410e52i		−	0.155253i
$900$	6.76415e52	+	1.14508e53i	0.450659	+	0.762905i
$901$	3.74408e51			0.0244511
$902$	2.04449e51	−	3.58226e51i	0.0130878	−	0.0229319i
$903$			2.74942e52i			0.172529i
$904$	2.61925e51	+	1.75216e53i	0.0161118	+	1.07781i
$905$	6.53384e52			0.393998
$906$	−3.34842e52	−	1.91103e52i	−0.197940	−	0.112969i
$907$			1.65404e53i			0.958548i	0.877665	+	0.479274i	$0.159100\pi$
$907$			1.65404e53i			0.958548i	−0.877665	+	0.479274i	$0.840900\pi$
$908$	−1.29133e53	+	7.62805e52i	−0.733653	+	0.433379i
$909$	−7.38396e52			−0.411282
$910$	−3.11132e53	+	5.45152e53i	−1.69903	+	2.97696i
$911$		−	2.53956e53i		−	1.35965i	−0.733373	−	0.679826i	$-0.762055\pi$
$911$		−	2.53956e53i		−	1.35965i	0.733373	−	0.679826i	$-0.237945\pi$
$912$	−7.62714e52	+	1.38405e53i	−0.400364	+	0.726513i
$913$	1.75398e53			0.902715
$914$	2.55298e52	+	1.45705e52i	0.128830	+	0.0735265i
$915$			3.63147e52i			0.179681i
$916$	−1.73478e52	−	2.93675e52i	−0.0841640	−	0.142478i
$917$	1.67903e53			0.798750
$918$	−5.32645e52	+	9.33276e52i	−0.248467	+	0.435353i
$919$		−	2.43607e52i		−	0.111432i	−0.998447	−	0.0557160i	$-0.982256\pi$
$919$		−	2.43607e52i		−	0.111432i	0.998447	−	0.0557160i	$-0.0177442\pi$
$920$	9.42328e52	−	1.40866e51i	0.422689	−	0.00631867i
$921$	4.54708e52			0.200013
$922$	−2.34319e53	−	1.33732e53i	−1.01077	−	0.576871i
$923$			2.48699e53i			1.05207i
$924$	1.41678e53	−	8.36910e52i	0.587767	−	0.347203i
$925$	2.14972e53			0.874642
$926$	1.39322e53	−	2.44113e53i	0.555931	−	0.974078i
$927$		−	1.15010e53i		−	0.450092i
$928$	−4.81274e52	+	2.94087e52i	−0.184726	+	0.112879i
$929$	−4.58586e53			−1.72639			−0.863194	−	0.504873i	$-0.831539\pi$
$929$	−4.58586e53			−1.72639			−0.863194	+	0.504873i	$0.831539\pi$
$930$	−1.12382e53	−	6.41390e52i	−0.414956	−	0.236826i
$931$		−	6.79091e53i		−	2.45943i
$932$	3.20585e51	+	5.42708e51i	0.0113883	+	0.0192788i
$933$	2.42062e53			0.843444
$934$	−3.44015e52	+	6.02767e52i	−0.117580	+	0.206018i
$935$			2.58343e53i			0.866139i
$936$	−5.51034e51	−	3.68616e53i	−0.0181223	−	1.21230i
$937$	2.90053e53			0.935759			0.467880	−	0.883792i	$-0.345018\pi$
$937$	2.90053e53			0.935759			0.467880	+	0.883792i	$0.345018\pi$
$938$	5.30999e53	+	3.03055e53i	1.68052	+	0.959115i
$939$		−	2.25608e51i		−	0.00700444i
$940$	−1.61500e53	+	9.54001e52i	−0.491892	+	0.290568i
$941$	−1.25452e53			−0.374855			−0.187427	−	0.982278i	$-0.560015\pi$
$941$	−1.25452e53			−0.374855			−0.187427	+	0.982278i	$0.560015\pi$
$942$	1.32142e53	−	2.31533e53i	0.387368	−	0.678728i
$943$			2.74171e51i			0.00788517i
$944$	2.24817e53	+	1.23891e53i	0.634355	+	0.349578i
$945$	−6.61506e53			−1.83131
$946$	−7.63592e52	−	4.35802e52i	−0.207406	−	0.118372i
$947$		−	4.45622e53i		−	1.18759i	−0.804616	−	0.593796i	$-0.797629\pi$
$947$		−	4.45622e53i		−	1.18759i	0.804616	−	0.593796i	$-0.202371\pi$
$948$	−3.05026e52	−	5.16368e52i	−0.0797603	−	0.135023i
$949$	4.20185e53			1.07808
$950$	4.00061e53	−	7.00969e53i	1.00717	−	1.76471i
$951$			3.01696e53i			0.745281i
$952$	−3.87439e53	+	5.79173e51i	−0.939158	+	0.0140392i
$953$	−2.89388e52			−0.0688348			−0.0344174	−	0.999408i	$-0.510958\pi$
$953$	−2.89388e52			−0.0688348			−0.0344174	+	0.999408i	$0.510958\pi$
$954$	−1.17569e52	−	6.70995e51i	−0.0274423	−	0.0156620i
$955$		−	1.90793e52i		−	0.0437020i
$956$	8.00024e52	−	4.72585e52i	0.179829	−	0.106228i
$957$	−4.36435e52			−0.0962730
$958$	−1.49494e53	+	2.61937e53i	−0.323627	+	0.567045i
$959$			9.93770e53i			2.11131i
$960$	9.55067e51	+	3.19376e53i	0.0199137	+	0.665917i
$961$	2.37342e53			0.485684
$962$	−5.17540e53	−	2.95374e53i	−1.03942	−	0.593226i
$963$			3.43613e53i			0.677324i
$964$	9.58029e52	+	1.62181e53i	0.185350	+	0.313772i
$965$	−9.45643e53			−1.79571
$966$	−5.42170e52	+	9.49966e52i	−0.101053	+	0.177060i
$967$			1.29472e53i			0.236864i	0.992962	+	0.118432i	$0.0377868\pi$
$967$			1.29472e53i			0.236864i	−0.992962	+	0.118432i	$0.962213\pi$
$968$	−4.58573e50	−	3.06764e52i	−0.000823479	−	0.0550868i
$969$	2.87952e53			0.507566
$970$	1.39334e54	+	7.95217e53i	2.41083	+	1.37592i
$971$			2.93305e52i			0.0498165i	0.999690	+	0.0249083i	$0.00792937\pi$
$971$			2.93305e52i			0.0498165i	−0.999690	+	0.0249083i	$0.992071\pi$
$972$	5.21321e53	−	3.07952e53i	0.869185	−	0.513440i
$973$	−1.55369e54			−2.54292
$974$	−3.85938e53	+	6.76222e53i	−0.620092	+	1.08650i
$975$		−	4.98387e53i		−	0.786110i
$976$	8.40641e52	−	1.52546e53i	0.130171	−	0.236213i
$977$	−1.42303e53			−0.216328			−0.108164	−	0.994133i	$-0.534497\pi$
$977$	−1.42303e53			−0.216328			−0.108164	+	0.994133i	$0.534497\pi$
$978$	4.26543e53	+	2.43439e53i	0.636596	+	0.363322i
$979$			4.91135e53i			0.719635i
$980$	−6.98342e53	−	1.18220e54i	−1.00461	−	1.70067i
$981$	2.09920e53			0.296491
$982$	4.37602e53	−	7.66746e53i	0.606837	−	1.06327i
$983$		−	3.48459e53i		−	0.474447i	−0.971455	−	0.237224i	$-0.923763\pi$
$983$		−	3.48459e53i		−	0.474447i	0.971455	−	0.237224i	$-0.0762374\pi$
$984$	−9.29435e51	+	1.38939e50i	−0.0124253	+	0.000185743i
$985$	1.14738e54			1.50610
$986$	8.92578e52	+	5.09417e52i	0.115043	+	0.0656583i
$987$		−	2.17697e53i		−	0.275514i
$988$	−1.92628e54	+	1.13788e54i	−2.39383	+	1.41407i
$989$	5.84421e52			0.0713169
$990$	4.62990e53	−	8.11230e53i	0.554802	−	0.972098i
$991$		−	1.15645e54i		−	1.36082i	−0.732831	−	0.680411i	$-0.761801\pi$
$991$		−	1.15645e54i		−	1.36082i	0.732831	−	0.680411i	$-0.238199\pi$
$992$	3.23602e53	+	5.29575e53i	0.373939	+	0.611952i
$993$	−4.05731e53			−0.460418
$994$	−8.20826e53	−	4.68467e53i	−0.914737	−	0.522064i
$995$			9.81550e53i			1.07423i
$996$	−2.01043e53	−	3.40338e53i	−0.216083	−	0.365799i
$997$	8.94257e53			0.943951			0.471976	−	0.881612i	$-0.343541\pi$
$997$	8.94257e53			0.943951			0.471976	+	0.881612i	$0.343541\pi$
$998$	−5.32205e53	+	9.32506e53i	−0.551734	+	0.966723i
$999$		−	6.28001e53i		−	0.639414i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.37.b.b.3.1	✓	16
4.3	odd	2	inner	4.37.b.b.3.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.37.b.b.3.1	✓	16	1.1	even	1	trivial
4.37.b.b.3.2	yes	16	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 37 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-227674. - 129939. i) q^{2} -1.77242e8i q^{3} +(3.49511e10 + 5.91675e10i) q^{4} +5.55508e12 q^{5} +(-2.30307e13 + 4.03533e13i) q^{6} -2.49971e15i q^{7} +(-2.69262e14 - 1.80124e16i) q^{8} +1.18680e17 q^{9} +O(q^{10})\)	\(q+(-227674. - 129939. i) q^{2} -1.77242e8i q^{3} +(3.49511e10 + 5.91675e10i) q^{4} +5.55508e12 q^{5} +(-2.30307e13 + 4.03533e13i) q^{6} -2.49971e15i q^{7} +(-2.69262e14 - 1.80124e16i) q^{8} +1.18680e17 q^{9} +(-1.26475e18 - 7.21823e17i) q^{10} +5.40459e18i q^{11} +(1.04869e19 - 6.19479e18i) q^{12} +1.72435e20 q^{13} +(-3.24810e20 + 5.69117e20i) q^{14} -9.84593e20i q^{15} +(-2.27921e21 + 4.13593e21i) q^{16} +8.60485e21 q^{17} +(-2.70203e22 - 1.54212e22i) q^{18} +1.88804e23i q^{19} +(1.94156e23 + 3.28680e23i) q^{20} -4.43052e23 q^{21} +(7.02268e23 - 1.23048e24i) q^{22} +9.41760e23i q^{23} +(-3.19255e24 + 4.77245e22i) q^{24} +1.63070e25 q^{25} +(-3.92589e25 - 2.24060e25i) q^{26} -4.76381e25i q^{27} +(1.47901e26 - 8.73674e25i) q^{28} -4.55607e25 q^{29} +(-1.27937e26 + 2.24166e26i) q^{30} +5.01332e26i q^{31} +(1.05634e27 - 6.45484e26i) q^{32} +9.57919e26 q^{33} +(-1.95910e27 - 1.11811e27i) q^{34} -1.38861e28i q^{35} +(4.14799e27 + 7.02199e27i) q^{36} +1.31828e28 q^{37} +(2.45330e28 - 4.29857e28i) q^{38} -3.05627e28i q^{39} +(-1.49578e27 - 1.00060e29i) q^{40} +2.91126e27 q^{41} +(1.00871e29 + 5.75699e28i) q^{42} -6.20563e28i q^{43} +(-3.19776e29 + 1.88896e29i) q^{44} +6.59277e29 q^{45} +(1.22372e29 - 2.14414e29i) q^{46} +4.91358e29i q^{47} +(7.33060e29 + 4.03971e29i) q^{48} -3.59680e30 q^{49} +(-3.71268e30 - 2.11893e30i) q^{50} -1.52514e30i q^{51} +(6.02678e30 + 1.02025e31i) q^{52} +4.35112e29 q^{53} +(-6.19006e30 + 1.08459e31i) q^{54} +3.00230e31i q^{55} +(-4.50257e31 + 6.73077e29i) q^{56} +3.34639e31 q^{57} +(1.03730e31 + 5.92012e30i) q^{58} -5.43569e31i q^{59} +(5.82559e31 - 3.44126e31i) q^{60} -3.68830e31 q^{61} +(6.51427e31 - 1.14140e32i) q^{62} -2.96665e32i q^{63} +(-3.24374e32 + 9.70012e30i) q^{64} +9.57890e32 q^{65} +(-2.18093e32 - 1.24471e32i) q^{66} -9.33023e32i q^{67} +(3.00749e32 + 5.09127e32i) q^{68} +1.66919e32 q^{69} +(-1.80435e33 + 3.16149e33i) q^{70} +1.44228e33i q^{71} +(-3.19561e31 - 2.13771e33i) q^{72} +2.43678e33 q^{73} +(-3.00137e33 - 1.71296e33i) q^{74} -2.89029e33i q^{75} +(-1.11711e34 + 6.59890e33i) q^{76} +1.35099e34 q^{77} +(-3.97129e33 + 6.95831e33i) q^{78} -4.92391e33i q^{79} +(-1.26612e34 + 2.29755e34i) q^{80} +9.36977e33 q^{81} +(-6.62818e32 - 3.78287e32i) q^{82} -3.24535e34i q^{83} +(-1.54852e34 - 2.62143e34i) q^{84} +4.78007e34 q^{85} +(-8.06354e33 + 1.41286e34i) q^{86} +8.07526e33i q^{87} +(9.73496e34 - 1.45525e33i) q^{88} +9.08737e34 q^{89} +(-1.50100e35 - 8.56660e34i) q^{90} -4.31037e35i q^{91} +(-5.57215e34 + 3.29155e34i) q^{92} +8.88570e34 q^{93} +(6.38466e34 - 1.11869e35i) q^{94} +1.04882e36i q^{95} +(-1.14407e35 - 1.87227e35i) q^{96} -1.10168e36 q^{97} +(8.18897e35 + 4.67366e35i) q^{98} +6.41417e35i 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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