LMFDB - Embedded newform 4.37.b.b.3.9

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			3.9
Root			$-2.99676e7i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.37.b.b.3.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(98385.8 - 242981. i) q^{2} -4.79482e8i q^{3} +(-4.93600e10 - 4.78117e10i) q^{4} +6.60636e12 q^{5} +(-1.16505e14 - 4.71742e13i) q^{6} +2.27014e14i q^{7} +(-1.64737e16 + 7.28954e15i) q^{8} -7.98083e16 q^{9} +O(q^{10})$	\(q+(98385.8 - 242981. i) q^{2} -4.79482e8i q^{3} +(-4.93600e10 - 4.78117e10i) q^{4} +6.60636e12 q^{5} +(-1.16505e14 - 4.71742e13i) q^{6} +2.27014e14i q^{7} +(-1.64737e16 + 7.28954e15i) q^{8} -7.98083e16 q^{9} +(6.49972e17 - 1.60522e18i) q^{10} -8.91010e18i q^{11} +(-2.29249e19 + 2.36672e19i) q^{12} -1.69290e20 q^{13} +(5.51601e19 + 2.23350e19i) q^{14} -3.16763e21i q^{15} +(1.50445e20 + 4.71997e21i) q^{16} -1.04222e22 q^{17} +(-7.85200e21 + 1.93919e22i) q^{18} +7.97251e21i q^{19} +(-3.26090e23 - 3.15861e23i) q^{20} +1.08849e23 q^{21} +(-2.16498e24 - 8.76627e23i) q^{22} -1.29261e24i q^{23} +(3.49520e24 + 7.89882e24i) q^{24} +2.90921e25 q^{25} +(-1.66557e25 + 4.11341e25i) q^{26} -3.37010e25i q^{27} +(1.08539e25 - 1.12054e25i) q^{28} +6.13174e25 q^{29} +(-7.69674e26 - 3.11650e26i) q^{30} +7.63022e26i q^{31} +(1.16166e27 + 4.27823e26i) q^{32} -4.27223e27 q^{33} +(-1.02539e27 + 2.53239e27i) q^{34} +1.49974e27i q^{35} +(3.93934e27 + 3.81577e27i) q^{36} -1.94121e28 q^{37} +(1.93717e27 + 7.84381e26i) q^{38} +8.11713e28i q^{39} +(-1.08831e29 + 4.81573e28i) q^{40} +5.45164e28 q^{41} +(1.07092e28 - 2.64483e28i) q^{42} -1.65794e29i q^{43} +(-4.26007e29 + 4.39802e29i) q^{44} -5.27243e29 q^{45} +(-3.14080e29 - 1.27174e29i) q^{46} -5.00094e29i q^{47} +(2.26314e30 - 7.21357e28i) q^{48} +2.60020e30 q^{49} +(2.86225e30 - 7.06882e30i) q^{50} +4.99724e30i q^{51} +(8.35613e30 + 8.09403e30i) q^{52} -2.38312e30 q^{53} +(-8.18870e30 - 3.31570e30i) q^{54} -5.88633e31i q^{55} +(-1.65483e30 - 3.73975e30i) q^{56} +3.82267e30 q^{57} +(6.03276e30 - 1.48990e31i) q^{58} +7.57344e31i q^{59} +(-1.51450e32 + 1.56354e32i) q^{60} +1.15248e32 q^{61} +(1.85400e32 + 7.50705e31i) q^{62} -1.81176e31i q^{63} +(2.18244e32 - 2.40171e32i) q^{64} -1.11839e33 q^{65} +(-4.20327e32 + 1.03807e33i) q^{66} -9.05989e32i q^{67} +(5.14438e32 + 4.98302e32i) q^{68} -6.19784e32 q^{69} +(3.64408e32 + 1.47553e32i) q^{70} -7.34519e32i q^{71} +(1.31473e33 - 5.81766e32i) q^{72} +3.68724e33 q^{73} +(-1.90988e33 + 4.71677e33i) q^{74} -1.39491e34i q^{75} +(3.81179e32 - 3.93523e32i) q^{76} +2.02272e33 q^{77} +(1.97231e34 + 7.98610e33i) q^{78} -2.27270e34i q^{79} +(9.93894e32 + 3.11818e34i) q^{80} -2.81378e34 q^{81} +(5.36364e33 - 1.32465e34i) q^{82} +1.22370e34i q^{83} +(-5.37279e33 - 5.20427e33i) q^{84} -6.88526e34 q^{85} +(-4.02848e34 - 1.63118e34i) q^{86} -2.94006e34i q^{87} +(6.49505e34 + 1.46782e35i) q^{88} +8.48753e32 q^{89} +(-5.18732e34 + 1.28110e35i) q^{90} -3.84311e34i q^{91} +(-6.18019e34 + 6.38032e34i) q^{92} +3.65855e35 q^{93} +(-1.21513e35 - 4.92021e34i) q^{94} +5.26692e34i q^{95} +(2.05133e35 - 5.56997e35i) q^{96} -2.86871e35 q^{97} +(2.55822e35 - 6.31798e35i) q^{98} +7.11100e35i 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 $

$2$	98385.8	−	242981.i	0.375312	−	0.926899i
$2$	98385.8	−	242981.i	0.375312	−	0.926899i
$3$		−	4.79482e8i		−	1.23763i	−0.785538	−	0.618813i	$-0.787614\pi$
$3$		−	4.79482e8i		−	1.23763i	0.785538	−	0.618813i	$-0.212386\pi$
$4$	−4.93600e10	−	4.78117e10i	−0.718282	−	0.695752i
$5$	6.60636e12			1.73182			0.865909	−	0.500202i	$-0.166741\pi$
$5$	6.60636e12			1.73182			0.865909	+	0.500202i	$0.166741\pi$
$6$	−1.16505e14	−	4.71742e13i	−1.14715	−	0.464496i
$7$			2.27014e14i			0.139408i	0.997568	+	0.0697041i	$0.0222055\pi$
$7$			2.27014e14i			0.139408i	−0.997568	+	0.0697041i	$0.977794\pi$
$8$	−1.64737e16	+	7.28954e15i	−0.914471	+	0.404650i
$9$	−7.98083e16			−0.531720
$10$	6.49972e17	−	1.60522e18i	0.649972	−	1.60522i
$11$		−	8.91010e18i		−	1.60256i	−0.598289	−	0.801280i	$-0.704153\pi$
$11$		−	8.91010e18i		−	1.60256i	0.598289	−	0.801280i	$-0.295847\pi$
$12$	−2.29249e19	+	2.36672e19i	−0.861081	+	0.888965i
$13$	−1.69290e20			−1.50539			−0.752696	−	0.658368i	$-0.771247\pi$
$13$	−1.69290e20			−1.50539			−0.752696	+	0.658368i	$0.771247\pi$
$14$	5.51601e19	+	2.23350e19i	0.129217	+	0.0523216i
$15$		−	3.16763e21i		−	2.14334i
$16$	1.50445e20	+	4.71997e21i	0.0318580	+	0.999492i
$17$	−1.04222e22			−0.741101			−0.370551	−	0.928812i	$-0.620831\pi$
$17$	−1.04222e22			−0.741101			−0.370551	+	0.928812i	$0.620831\pi$
$18$	−7.85200e21	+	1.93919e22i	−0.199561	+	0.492851i
$19$			7.97251e21i			0.0765649i	0.999267	+	0.0382825i	$0.0121887\pi$
$19$			7.97251e21i			0.0765649i	−0.999267	+	0.0382825i	$0.987811\pi$
$20$	−3.26090e23	−	3.15861e23i	−1.24393	−	1.20492i
$21$	1.08849e23			0.172535
$22$	−2.16498e24	−	8.76627e23i	−1.48541	−	0.601460i
$23$		−	1.29261e24i		−	0.398443i	−0.979954	−	0.199222i	$-0.936159\pi$
$23$		−	1.29261e24i		−	0.398443i	0.979954	−	0.199222i	$-0.0638414\pi$
$24$	3.49520e24	+	7.89882e24i	0.500806	+	1.13177i
$25$	2.90921e25			1.99919
$26$	−1.66557e25	+	4.11341e25i	−0.564992	+	1.39535i
$27$		−	3.37010e25i		−	0.579556i
$28$	1.08539e25	−	1.12054e25i	0.0969936	−	0.100134i
$29$	6.13174e25			0.291353			0.145677	−	0.989332i	$-0.453464\pi$
$29$	6.13174e25			0.291353			0.145677	+	0.989332i	$0.453464\pi$
$30$	−7.69674e26	−	3.11650e26i	−1.98666	−	0.804423i
$31$			7.63022e26i			1.09151i	0.837946	+	0.545754i	$0.183757\pi$
$31$			7.63022e26i			1.09151i	−0.837946	+	0.545754i	$0.816243\pi$
$32$	1.16166e27	+	4.27823e26i	0.938385	+	0.345592i
$33$	−4.27223e27			−1.98337
$34$	−1.02539e27	+	2.53239e27i	−0.278144	+	0.686926i
$35$			1.49974e27i			0.241430i
$36$	3.93934e27	+	3.81577e27i	0.381925	+	0.369945i
$37$	−1.94121e28			−1.14932			−0.574661	−	0.818392i	$-0.694866\pi$
$37$	−1.94121e28			−1.14932			−0.574661	+	0.818392i	$0.694866\pi$
$38$	1.93717e27	+	7.84381e26i	0.0709679	+	0.0287357i
$39$			8.11713e28i			1.86311i
$40$	−1.08831e29	+	4.81573e28i	−1.58370	+	0.700781i
$41$	5.45164e28			0.508649			0.254324	−	0.967119i	$-0.418147\pi$
$41$	5.45164e28			0.508649			0.254324	+	0.967119i	$0.418147\pi$
$42$	1.07092e28	−	2.64483e28i	0.0647546	−	0.159923i
$43$		−	1.65794e29i		−	0.656353i	−0.944616	−	0.328176i	$-0.893566\pi$
$43$		−	1.65794e29i		−	0.656353i	0.944616	−	0.328176i	$-0.106434\pi$
$44$	−4.26007e29	+	4.39802e29i	−1.11498	+	1.15109i
$45$	−5.27243e29			−0.920842
$46$	−3.14080e29	−	1.27174e29i	−0.369317	−	0.149541i
$47$		−	5.00094e29i		−	0.399292i	−0.979868	−	0.199646i	$-0.936021\pi$
$47$		−	5.00094e29i		−	0.399292i	0.979868	−	0.199646i	$-0.0639791\pi$
$48$	2.26314e30	−	7.21357e28i	1.23700	−	0.0394283i
$49$	2.60020e30			0.980565
$50$	2.86225e30	−	7.06882e30i	0.750321	−	1.85305i
$51$			4.99724e30i			0.917207i
$52$	8.35613e30	+	8.09403e30i	1.08130	+	1.04738i
$53$	−2.38312e30			−0.218867			−0.109433	−	0.993994i	$-0.534904\pi$
$53$	−2.38312e30			−0.218867			−0.109433	+	0.993994i	$0.534904\pi$
$54$	−8.18870e30	−	3.31570e30i	−0.537189	−	0.217514i
$55$		−	5.88633e31i		−	2.77534i
$56$	−1.65483e30	−	3.73975e30i	−0.0564116	−	0.127485i
$57$	3.82267e30			0.0947588
$58$	6.03276e30	−	1.48990e31i	0.109348	−	0.270055i
$59$			7.57344e31i			1.00915i	0.863367	+	0.504576i	$0.168351\pi$
$59$			7.57344e31i			1.00915i	−0.863367	+	0.504576i	$0.831649\pi$
$60$	−1.51450e32	+	1.56354e32i	−1.49124	+	1.53953i
$61$	1.15248e32			0.842748			0.421374	−	0.906887i	$-0.361548\pi$
$61$	1.15248e32			0.842748			0.421374	+	0.906887i	$0.361548\pi$
$62$	1.85400e32	+	7.50705e31i	1.01172	+	0.409656i
$63$		−	1.81176e31i		−	0.0741261i
$64$	2.18244e32	−	2.40171e32i	0.672516	−	0.740083i
$65$	−1.11839e33			−2.60707
$66$	−4.20327e32	+	1.03807e33i	−0.744383	+	1.83838i
$67$		−	9.05989e32i		−	1.22399i	−0.790863	−	0.611993i	$-0.790368\pi$
$67$		−	9.05989e32i		−	1.22399i	0.790863	−	0.611993i	$-0.209632\pi$
$68$	5.14438e32	+	4.98302e32i	0.532320	+	0.515623i
$69$	−6.19784e32			−0.493124
$70$	3.64408e32	+	1.47553e32i	0.223781	+	0.0906114i
$71$		−	7.34519e32i		−	0.349424i	−0.984620	−	0.174712i	$-0.944101\pi$
$71$		−	7.34519e32i		−	0.349424i	0.984620	−	0.174712i	$-0.0558995\pi$
$72$	1.31473e33	−	5.81766e32i	0.486243	−	0.215161i
$73$	3.68724e33			1.06387			0.531937	−	0.846784i	$-0.321464\pi$
$73$	3.68724e33			1.06387			0.531937	+	0.846784i	$0.321464\pi$
$74$	−1.90988e33	+	4.71677e33i	−0.431354	+	1.06531i
$75$		−	1.39491e34i		−	2.47426i
$76$	3.81179e32	−	3.93523e32i	0.0532702	−	0.0549952i
$77$	2.02272e33			0.223410
$78$	1.97231e34	+	7.98610e33i	1.72692	+	0.699249i
$79$		−	2.27270e34i		−	1.58217i	−0.611705	−	0.791086i	$-0.709516\pi$
$79$		−	2.27270e34i		−	1.58217i	0.611705	−	0.791086i	$-0.290484\pi$
$80$	9.93894e32	+	3.11818e34i	0.0551722	+	1.73094i
$81$	−2.81378e34			−1.24899
$82$	5.36364e33	−	1.32465e34i	0.190902	−	0.471466i
$83$			1.22370e34i			0.350163i	0.984554	+	0.175082i	$0.0560189\pi$
$83$			1.22370e34i			0.350163i	−0.984554	+	0.175082i	$0.943981\pi$
$84$	−5.37279e33	−	5.20427e33i	−0.123929	−	0.120042i
$85$	−6.88526e34			−1.28345
$86$	−4.02848e34	−	1.63118e34i	−0.608372	−	0.246337i
$87$		−	2.94006e34i		−	0.360586i
$88$	6.49505e34	+	1.46782e35i	0.648477	+	1.46550i
$89$	8.48753e32			0.00691451			0.00345725	−	0.999994i	$-0.498900\pi$
$89$	8.48753e32			0.00691451			0.00345725	+	0.999994i	$0.498900\pi$
$90$	−5.18732e34	+	1.28110e35i	−0.345603	+	0.853527i
$91$		−	3.84311e34i		−	0.209864i
$92$	−6.18019e34	+	6.38032e34i	−0.277218	+	0.286195i
$93$	3.65855e35			1.35088
$94$	−1.21513e35	−	4.92021e34i	−0.370103	−	0.149859i
$95$			5.26692e34i			0.132597i
$96$	2.05133e35	−	5.56997e35i	0.427714	−	1.16137i
$97$	−2.86871e35			−0.496358			−0.248179	−	0.968714i	$-0.579832\pi$
$97$	−2.86871e35			−0.496358			−0.248179	+	0.968714i	$0.579832\pi$
$98$	2.55822e35	−	6.31798e35i	0.368018	−	0.908885i
$99$			7.11100e35i			0.852113i
$100$	−1.43598e36	−	1.39094e36i	−1.43598	−	1.39094i
$101$	5.18410e35			0.433400			0.216700	−	0.976238i	$-0.430471\pi$
$101$	5.18410e35			0.433400			0.216700	+	0.976238i	$0.430471\pi$
$102$	1.21423e36	+	4.91657e35i	0.850158	+	0.344239i
$103$			5.22189e35i			0.306731i	0.988170	+	0.153366i	$0.0490112\pi$
$103$			5.22189e35i			0.306731i	−0.988170	+	0.153366i	$0.950989\pi$
$104$	2.78882e36	−	1.23404e36i	1.37664	−	0.609158i
$105$	7.19097e35			0.298800
$106$	−2.34465e35	+	5.79052e35i	−0.0821433	+	0.202867i
$107$			3.32310e36i			0.983184i	0.870826	+	0.491592i	$0.163585\pi$
$107$			3.32310e36i			0.983184i	−0.870826	+	0.491592i	$0.836415\pi$
$108$	−1.61130e36	+	1.66348e36i	−0.403227	+	0.416285i
$109$	5.60436e36			1.18809			0.594044	−	0.804432i	$-0.297530\pi$
$109$	5.60436e36			1.18809			0.594044	+	0.804432i	$0.297530\pi$
$110$	−1.43027e37	−	5.79132e36i	−2.57246	−	1.04162i
$111$			9.30776e36i			1.42243i
$112$	−1.07150e36	+	3.41532e34i	−0.139337	+	0.00444126i
$113$	−1.35908e37			−1.50603			−0.753016	−	0.658003i	$-0.771402\pi$
$113$	−1.35908e37			−1.50603			−0.753016	+	0.658003i	$0.771402\pi$
$114$	3.76097e35	−	9.28836e35i	0.0355641	−	0.0878318i
$115$		−	8.53945e36i		−	0.690032i
$116$	−3.02662e36	−	2.93169e36i	−0.209274	−	0.202710i
$117$	1.35107e37			0.800448
$118$	1.84020e37	+	7.45119e36i	0.935382	+	0.378747i
$119$		−	2.36598e36i		−	0.103316i
$120$	2.30906e37	+	5.21825e37i	0.867305	+	1.96003i
$121$	−4.84772e37			−1.56820
$122$	1.13388e37	−	2.80031e37i	0.316293	−	0.781142i
$123$		−	2.61397e37i		−	0.629517i
$124$	3.64814e37	−	3.76627e37i	0.759418	−	0.784010i
$125$	9.60576e37			1.73042
$126$	−4.40224e36	−	1.78252e36i	−0.0687074	−	0.0278204i
$127$		−	1.31905e38i		−	1.78564i	−0.450411	−	0.892822i	$-0.648722\pi$
$127$		−	1.31905e38i		−	1.78564i	0.450411	−	0.892822i	$-0.351278\pi$
$128$	−3.68848e37	−	7.66585e37i	−0.433578	−	0.901116i
$129$	−7.94953e37			−0.812320
$130$	−1.10033e38	+	2.71747e38i	−0.978463	+	2.41649i
$131$			2.23577e36i			0.0173198i	0.999963	+	0.00865992i	$0.00275657\pi$
$131$			2.23577e36i			0.0173198i	−0.999963	+	0.00865992i	$0.997243\pi$
$132$	2.10877e38	+	2.04263e38i	1.42462	+	1.37993i
$133$	−1.80987e36			−0.0106738
$134$	−2.20138e38	−	8.91365e37i	−1.13451	−	0.459377i
$135$		−	2.22641e38i		−	1.00369i
$136$	1.71691e38	−	7.59728e37i	0.677716	−	0.299887i
$137$	−2.11161e38			−0.730539			−0.365270	−	0.930902i	$-0.619023\pi$
$137$	−2.11161e38			−0.730539			−0.365270	+	0.930902i	$0.619023\pi$
$138$	−6.09779e37	+	1.50596e38i	−0.185075	+	0.457076i
$139$			3.04795e38i			0.812347i	0.913796	+	0.406173i	$0.133137\pi$
$139$			3.04795e38i			0.812347i	−0.913796	+	0.406173i	$0.866863\pi$
$140$	7.17050e37	−	7.40270e37i	0.167975	−	0.173415i
$141$	−2.39786e38			−0.494174
$142$	−1.78474e38	−	7.22662e37i	−0.323881	−	0.131143i
$143$			1.50839e39i			2.41248i
$144$	−1.20068e37	−	3.76693e38i	−0.0169395	−	0.531450i
$145$	4.05085e38			0.504570
$146$	3.62772e38	−	8.95930e38i	0.399285	−	0.986103i
$147$		−	1.24675e39i		−	1.21357i
$148$	9.58181e38	+	9.28127e38i	0.825537	+	0.799643i
$149$	1.09009e39			0.831976			0.415988	−	0.909370i	$-0.363436\pi$
$149$	1.09009e39			0.831976			0.415988	+	0.909370i	$0.363436\pi$
$150$	−3.38937e39	−	1.37240e39i	−2.29338	−	0.928617i
$151$		−	1.45223e39i		−	0.871869i	−0.899978	−	0.435934i	$-0.856418\pi$
$151$		−	1.45223e39i		−	0.871869i	0.899978	−	0.435934i	$-0.143582\pi$
$152$	−5.81159e37	−	1.31336e38i	−0.0309820	−	0.0700165i
$153$	8.31776e38			0.394058
$154$	1.99007e38	−	4.91482e38i	0.0838484	−	0.207078i
$155$			5.04080e39i			1.89029i
$156$	3.88094e39	−	4.00661e39i	1.29627	−	1.33824i
$157$	3.77925e39			1.12515			0.562576	−	0.826745i	$-0.309810\pi$
$157$	3.77925e39			1.12515			0.562576	+	0.826745i	$0.309810\pi$
$158$	−5.52222e39	−	2.23601e39i	−1.46651	−	0.593808i
$159$			1.14266e39i			0.270876i
$160$	7.67437e39	+	2.82635e39i	1.62511	+	0.598503i
$161$	2.93441e38			0.0555463
$162$	−2.76836e39	+	6.83696e39i	−0.468762	+	1.15769i
$163$			5.70992e39i			0.865472i	0.901521	+	0.432736i	$0.142452\pi$
$163$			5.70992e39i			0.865472i	−0.901521	+	0.432736i	$0.857548\pi$
$164$	−2.69093e39	−	2.60653e39i	−0.365353	−	0.353894i
$165$	−2.82239e40			−3.43484
$166$	2.97337e39	+	1.20395e39i	0.324566	+	0.131420i
$167$		−	2.00063e40i		−	1.96006i	−0.198841	−	0.980032i	$-0.563718\pi$
$167$		−	2.00063e40i		−	1.96006i	0.198841	−	0.980032i	$-0.436282\pi$
$168$	−1.79314e39	+	7.93460e38i	−0.157779	+	0.0698165i
$169$	1.60127e40			1.26621
$170$	−6.77412e39	+	1.67299e40i	−0.481695	+	1.18963i
$171$		−	6.36272e38i		−	0.0407111i
$172$	−7.92691e39	+	8.18360e39i	−0.456659	+	0.471446i
$173$	−1.52851e39			−0.0793301			−0.0396651	−	0.999213i	$-0.512629\pi$
$173$	−1.52851e39			−0.0793301			−0.0396651	+	0.999213i	$0.512629\pi$
$174$	−7.14378e39	−	2.89260e39i	−0.334227	−	0.135332i
$175$			6.60432e39i			0.278704i
$176$	4.20554e40	−	1.34048e39i	1.60175	−	0.0510543i
$177$	3.63133e40			1.24895
$178$	8.35052e37	−	2.06231e38i	0.00259510	−	0.00640905i
$179$		−	5.96587e40i		−	1.67617i	−0.545536	−	0.838087i	$-0.683674\pi$
$179$		−	5.96587e40i		−	1.67617i	0.545536	−	0.838087i	$-0.316326\pi$
$180$	2.60247e40	+	2.52084e40i	0.661424	+	0.640678i
$181$	2.49321e39			0.0573515			0.0286758	−	0.999589i	$-0.490871\pi$
$181$	2.49321e39			0.0573515			0.0286758	+	0.999589i	$0.490871\pi$
$182$	−9.33803e39	−	3.78108e39i	−0.194523	−	0.0787645i
$183$		−	5.52595e40i		−	1.04301i
$184$	9.42253e39	+	2.12940e40i	0.161230	+	0.364365i
$185$	−1.28243e41			−1.99042
$186$	3.59949e40	−	8.88958e40i	0.507001	−	1.25213i
$187$			9.28626e40i			1.18766i
$188$	−2.39103e40	+	2.46846e40i	−0.277808	+	0.286804i
$189$	7.65061e39			0.0807948
$190$	1.27976e40	+	5.18190e39i	0.122904	+	0.0497651i
$191$		−	2.34835e40i		−	0.205193i	−0.994723	−	0.102596i	$-0.967285\pi$
$191$		−	2.34835e40i		−	0.205193i	0.994723	−	0.102596i	$-0.0327150\pi$
$192$	−1.15157e41	−	1.04644e41i	−0.915946	−	0.832324i
$193$	1.49860e41			1.08556			0.542781	−	0.839874i	$-0.317371\pi$
$193$	1.49860e41			1.08556			0.542781	+	0.839874i	$0.317371\pi$
$194$	−2.82240e40	+	6.97041e40i	−0.186289	+	0.460073i
$195$			5.36247e41i			3.22658i
$196$	−1.28346e41	−	1.24320e41i	−0.704322	−	0.682230i
$197$	2.26156e41			1.13244			0.566222	−	0.824253i	$-0.308404\pi$
$197$	2.26156e41			1.13244			0.566222	+	0.824253i	$0.308404\pi$
$198$	1.72784e41	+	6.99621e40i	0.789823	+	0.319808i
$199$		−	2.93782e41i		−	1.22650i	−0.789887	−	0.613252i	$-0.789861\pi$
$199$		−	2.93782e41i		−	1.22650i	0.789887	−	0.613252i	$-0.210139\pi$
$200$	−4.79253e41	+	2.12068e41i	−1.82821	+	0.808975i
$201$	−4.34406e41			−1.51484
$202$	5.10041e40	−	1.25964e41i	0.162660	−	0.401717i
$203$			1.39199e40i			0.0406170i
$204$	2.38927e41	−	2.46664e41i	0.638149	−	0.658813i
$205$	3.60155e41			0.880887
$206$	1.26882e41	+	5.13760e40i	0.284309	+	0.115120i
$207$			1.03161e41i			0.211860i
$208$	−2.54688e40	−	7.99042e41i	−0.0479588	−	1.50463i
$209$	7.10358e40			0.122700
$210$	7.07489e40	−	1.74727e41i	0.112143	−	0.276957i
$211$			6.82410e41i			0.993027i	0.868029	+	0.496513i	$0.165387\pi$
$211$			6.82410e41i			0.993027i	−0.868029	+	0.496513i	$0.834613\pi$
$212$	1.17631e41	+	1.13941e41i	0.157208	+	0.152277i
$213$	−3.52189e41			−0.432457
$214$	8.07449e41	+	3.26945e41i	0.911312	+	0.369001i
$215$		−	1.09530e42i		−	1.13668i
$216$	2.45665e41	+	5.55179e41i	0.234518	+	0.529987i
$217$	−1.73217e41			−0.152165
$218$	5.51389e41	−	1.36175e42i	0.445904	−	1.10124i
$219$		−	1.76797e42i		−	1.31668i
$220$	−2.81436e42	+	2.90549e42i	−1.93095	+	1.99348i
$221$	1.76436e42			1.11565
$222$	2.26161e42	+	9.15751e41i	1.31845	+	0.533856i
$223$		−	2.30581e42i		−	1.23976i	−0.784698	−	0.619878i	$-0.787182\pi$
$223$		−	2.30581e42i		−	1.23976i	0.784698	−	0.619878i	$-0.212818\pi$
$224$	−9.71218e40	+	2.63714e41i	−0.0481784	+	0.130819i
$225$	−2.32179e42			−1.06301
$226$	−1.33714e42	+	3.30231e42i	−0.565231	+	1.39594i
$227$			4.50702e42i			1.75964i	0.475304	+	0.879821i	$0.342338\pi$
$227$			4.50702e42i			1.75964i	−0.475304	+	0.879821i	$0.657662\pi$
$228$	−1.88687e41	−	1.82769e41i	−0.0680636	−	0.0659287i
$229$	−3.67329e42			−1.22466			−0.612331	−	0.790602i	$-0.709768\pi$
$229$	−3.67329e42			−1.22466			−0.612331	+	0.790602i	$0.709768\pi$
$230$	−2.07492e42	−	8.40161e41i	−0.639589	−	0.258977i
$231$		−	9.69858e41i		−	0.276498i
$232$	−1.01012e42	+	4.46975e41i	−0.266434	+	0.117896i
$233$	4.12814e42			1.00774			0.503869	−	0.863780i	$-0.331910\pi$
$233$	4.12814e42			1.00774			0.503869	+	0.863780i	$0.331910\pi$
$234$	1.32926e42	−	3.28285e42i	0.300417	−	0.741934i
$235$		−	3.30380e42i		−	0.691500i
$236$	3.62099e42	−	3.73825e42i	0.702120	−	0.724856i
$237$	−1.08972e43			−1.95814
$238$	−5.74888e41	−	2.32779e41i	−0.0957631	−	0.0387756i
$239$			2.53834e41i			0.0392092i	0.999808	+	0.0196046i	$0.00624074\pi$
$239$			2.53834e41i			0.0392092i	−0.999808	+	0.0196046i	$0.993759\pi$
$240$	1.49511e43	−	4.76554e41i	2.14226	−	0.0682826i
$241$	1.11078e43			1.47680			0.738402	−	0.674360i	$-0.235581\pi$
$241$	1.11078e43			1.47680			0.738402	+	0.674360i	$0.235581\pi$
$242$	−4.76947e42	+	1.17790e43i	−0.588564	+	1.45356i
$243$			8.43324e42i			0.966232i
$244$	−5.68865e42	−	5.51022e42i	−0.605331	−	0.586344i
$245$	1.71778e43			1.69816
$246$	−6.35144e42	−	2.57177e42i	−0.583499	−	0.236265i
$247$		−	1.34966e42i		−	0.115260i
$248$	−5.56208e42	−	1.25698e43i	−0.441679	−	0.998152i
$249$	5.86744e42			0.433371
$250$	9.45070e42	−	2.33402e43i	0.649447	−	1.60392i
$251$		−	7.49923e41i		−	0.0479611i	−0.999712	−	0.0239806i	$-0.992366\pi$
$251$		−	7.49923e41i		−	0.0479611i	0.999712	−	0.0239806i	$-0.00763398\pi$
$252$	−8.66235e41	+	8.94285e41i	−0.0515734	+	0.0532435i
$253$	−1.15173e43			−0.638530
$254$	−3.20504e43	−	1.29776e43i	−1.65511	−	0.670173i
$255$			3.30136e43i			1.58844i
$256$	−2.22555e43	+	1.42019e42i	−0.997970	+	0.0636836i
$257$	−1.46734e43			−0.613385			−0.306692	−	0.951809i	$-0.599222\pi$
$257$	−1.46734e43			−0.613385			−0.306692	+	0.951809i	$0.599222\pi$
$258$	−7.82121e42	+	1.93158e43i	−0.304873	+	0.752938i
$259$		−	4.40683e42i		−	0.160225i
$260$	5.52036e43	+	5.34721e43i	1.87261	+	1.81387i
$261$	−4.89364e42			−0.154918
$262$	5.43249e41	+	2.19968e41i	0.0160537	+	0.00650034i
$263$		−	5.72464e42i		−	0.157959i	−0.996876	−	0.0789796i	$-0.974834\pi$
$263$		−	5.72464e42i		−	0.157959i	0.996876	−	0.0789796i	$-0.0251662\pi$
$264$	7.03793e43	−	3.11426e43i	1.81374	−	0.802572i
$265$	−1.57437e43			−0.379038
$266$	−1.78066e41	+	4.39764e41i	−0.00400600	+	0.00989351i
$267$		−	4.06962e41i		−	0.00855758i
$268$	−4.33169e43	+	4.47196e43i	−0.851591	+	0.879167i
$269$	−4.65647e42			−0.0856083			−0.0428041	−	0.999083i	$-0.513629\pi$
$269$	−4.65647e42			−0.0856083			−0.0428041	+	0.999083i	$0.513629\pi$
$270$	−5.40975e43	−	2.19047e43i	−0.930314	−	0.376695i
$271$			5.26399e43i			0.846970i	0.905903	+	0.423485i	$0.139193\pi$
$271$			5.26399e43i			0.846970i	−0.905903	+	0.423485i	$0.860807\pi$
$272$	−1.56796e42	−	4.91923e43i	−0.0236100	−	0.740725i
$273$	−1.84270e43			−0.259733
$274$	−2.07752e43	+	5.13081e43i	−0.274180	+	0.677136i
$275$		−	2.59213e44i		−	3.20383i
$276$	3.05925e43	+	2.96329e43i	0.354202	+	0.343092i
$277$	1.07450e44			1.16565			0.582827	−	0.812597i	$-0.301947\pi$
$277$	1.07450e44			1.16565			0.582827	+	0.812597i	$0.301947\pi$
$278$	7.40594e43	+	2.99875e43i	0.752963	+	0.304883i
$279$		−	6.08955e43i		−	0.580376i
$280$	−1.09324e43	−	2.47062e43i	−0.0976946	−	0.220780i
$281$	−4.65870e43			−0.390437			−0.195219	−	0.980760i	$-0.562542\pi$
$281$	−4.65870e43			−0.390437			−0.195219	+	0.980760i	$0.562542\pi$
$282$	−2.35915e43	+	5.82634e43i	−0.185469	+	0.458049i
$283$			2.53833e42i			0.0187237i	0.999956	+	0.00936186i	$0.00298002\pi$
$283$			2.53833e42i			0.0187237i	−0.999956	+	0.00936186i	$0.997020\pi$
$284$	−3.51186e43	+	3.62558e43i	−0.243113	+	0.250985i
$285$	2.52540e43			0.164105
$286$	3.66509e44	+	1.48404e44i	2.23613	+	0.905433i
$287$			1.23760e43i			0.0709098i
$288$	−9.27105e43	−	3.41438e43i	−0.498958	−	0.183758i
$289$	−8.91487e43			−0.450769
$290$	3.98546e43	−	9.84278e43i	0.189371	−	0.467686i
$291$			1.37549e44i			0.614306i
$292$	−1.82002e44	−	1.76293e44i	−0.764162	−	0.740193i
$293$	−1.58940e43			−0.0627504			−0.0313752	−	0.999508i	$-0.509989\pi$
$293$	−1.58940e43			−0.0627504			−0.0313752	+	0.999508i	$0.509989\pi$
$294$	−3.02936e44	−	1.22662e44i	−1.12486	−	0.455469i
$295$			5.00329e44i			1.74767i
$296$	3.19788e44	−	1.41505e44i	1.05102	−	0.465074i
$297$	−3.00280e44			−0.928773
$298$	1.07250e44	−	2.64872e44i	0.312251	−	0.771157i
$299$			2.18826e44i			0.599814i
$300$	−6.66932e44	+	6.88529e44i	−1.72147	+	1.77721i
$301$	3.76376e43			0.0915009
$302$	−3.52865e44	−	1.42879e44i	−0.808134	−	0.327223i
$303$		−	2.48568e44i		−	0.536387i
$304$	−3.76300e43	+	1.19942e42i	−0.0765261	+	0.00243920i
$305$	7.61372e44			1.45949
$306$	8.18349e43	−	2.02106e44i	0.147895	−	0.365252i
$307$		−	3.63013e44i		−	0.618630i	−0.950960	−	0.309315i	$-0.899900\pi$
$307$		−	3.63013e44i		−	0.618630i	0.950960	−	0.309315i	$-0.100100\pi$
$308$	−9.98414e43	−	9.67097e43i	−0.160471	−	0.155438i
$309$	2.50380e44			0.379619
$310$	1.22482e45	+	4.95943e44i	1.75211	+	0.709449i
$311$			9.78683e44i			1.32116i	0.750756	+	0.660580i	$0.229689\pi$
$311$			9.78683e44i			1.32116i	−0.750756	+	0.660580i	$0.770311\pi$
$312$	−5.91701e44	−	1.33719e45i	−0.753910	−	1.70377i
$313$	2.69011e44			0.323573			0.161786	−	0.986826i	$-0.448274\pi$
$313$	2.69011e44			0.323573			0.161786	+	0.986826i	$0.448274\pi$
$314$	3.71824e44	−	9.18284e44i	0.422283	−	1.04290i
$315$		−	1.19692e44i		−	0.128373i
$316$	−1.08661e45	+	1.12180e45i	−1.10080	+	1.13645i
$317$	−3.60812e44			−0.345314			−0.172657	−	0.984982i	$-0.555235\pi$
$317$	−3.60812e44			−0.345314			−0.172657	+	0.984982i	$0.555235\pi$
$318$	2.77645e44	+	1.12422e44i	0.251074	+	0.101663i
$319$		−	5.46344e44i		−	0.466911i
$320$	1.44180e45	−	1.58665e45i	1.16468	−	1.28169i
$321$	1.59336e45			1.21681
$322$	2.88704e43	−	7.13006e43i	0.0208472	−	0.0514858i
$323$		−	8.30908e43i		−	0.0567424i
$324$	1.38888e45	+	1.34532e45i	0.897130	+	0.868990i
$325$	−4.92499e45			−3.00957
$326$	1.38740e45	+	5.61775e44i	0.802205	+	0.324822i
$327$		−	2.68719e45i		−	1.47041i
$328$	−8.98085e44	+	3.97400e44i	−0.465145	+	0.205825i
$329$	1.13528e44			0.0556645
$330$	−2.77683e45	+	6.85787e45i	−1.28914	+	3.18375i
$331$			1.74226e45i			0.765963i	0.923756	+	0.382982i	$0.125103\pi$
$331$			1.74226e45i			0.765963i	−0.923756	+	0.382982i	$0.874897\pi$
$332$	5.85074e44	−	6.04020e44i	0.243627	−	0.251516i
$333$	1.54925e45			0.611118
$334$	−4.86115e45	−	1.96833e45i	−1.81678	−	0.735635i
$335$		−	5.98529e45i		−	2.11972i
$336$	1.63758e43	+	5.13765e44i	0.00549662	+	0.172448i
$337$	−2.28010e45			−0.725464			−0.362732	−	0.931894i	$-0.618156\pi$
$337$	−2.28010e45			−0.725464			−0.362732	+	0.931894i	$0.618156\pi$
$338$	1.57543e45	−	3.89079e45i	0.475223	−	1.17365i
$339$			6.51656e45i			1.86390i
$340$	3.39856e45	+	3.29196e45i	0.921881	+	0.892965i
$341$	6.79860e45			1.74921
$342$	−1.54602e44	−	6.26001e43i	−0.0377351	−	0.0152794i
$343$			1.19226e45i			0.276107i
$344$	1.20856e45	+	2.73124e45i	0.265593	+	0.600216i
$345$	−4.09451e45			−0.854001
$346$	−1.50384e44	+	3.71399e44i	−0.0297735	+	0.0735310i
$347$		−	6.07436e45i		−	1.14175i	−0.821038	−	0.570873i	$-0.806605\pi$
$347$		−	6.07436e45i		−	1.14175i	0.821038	−	0.570873i	$-0.193395\pi$
$348$	−1.40569e45	+	1.45121e45i	−0.250879	+	0.259003i
$349$	1.91350e44			0.0324317			0.0162159	−	0.999869i	$-0.494838\pi$
$349$	1.91350e44			0.0324317			0.0162159	+	0.999869i	$0.494838\pi$
$350$	1.60472e45	+	6.49771e44i	0.258330	+	0.104601i
$351$			5.70523e45i			0.872459i
$352$	3.81194e45	−	1.03505e46i	0.553832	−	1.50382i
$353$	−4.83055e45			−0.666887			−0.333443	−	0.942770i	$-0.608211\pi$
$353$	−4.83055e45			−0.666887			−0.333443	+	0.942770i	$0.608211\pi$
$354$	3.57271e45	−	8.82343e45i	0.468748	−	1.15765i
$355$		−	4.85250e45i		−	0.605139i
$356$	−4.18944e43	−	4.05804e43i	−0.00496657	−	0.00481078i
$357$	−1.13445e45			−0.127866
$358$	−1.44959e46	−	5.86957e45i	−1.55364	−	0.629088i
$359$		−	4.78046e45i		−	0.487270i	−0.969867	−	0.243635i	$-0.921660\pi$
$359$		−	4.78046e45i		−	0.487270i	0.969867	−	0.243635i	$-0.0783400\pi$
$360$	8.68561e45	−	3.84335e45i	0.842084	−	0.372619i
$361$	1.07789e46			0.994138
$362$	2.45297e44	−	6.05803e44i	0.0215247	−	0.0531591i
$363$			2.32440e46i			1.94085i
$364$	−1.83746e45	+	1.89696e45i	−0.146013	+	0.150742i
$365$	2.43593e46			1.84244
$366$	−1.34270e46	−	5.43675e45i	−0.966762	−	0.391453i
$367$			2.65158e46i			1.81767i	0.417153	+	0.908836i	$0.363028\pi$
$367$			2.65158e46i			1.81767i	−0.417153	+	0.908836i	$0.636972\pi$
$368$	6.10108e45	−	1.94467e44i	0.398241	−	0.0126936i
$369$	−4.35087e45			−0.270459
$370$	−1.26173e46	+	3.11607e46i	−0.747027	+	1.84491i
$371$		−	5.41002e44i		−	0.0305118i
$372$	−1.80586e46	−	1.74922e46i	−0.970312	−	0.939876i
$373$	−1.20802e46			−0.618466			−0.309233	−	0.950986i	$-0.600072\pi$
$373$	−1.20802e46			−0.618466			−0.309233	+	0.950986i	$0.600072\pi$
$374$	2.25638e46	+	9.13636e45i	1.10084	+	0.445743i
$375$		−	4.60579e46i		−	2.14161i
$376$	3.64545e45	+	8.23837e45i	0.161574	+	0.365141i
$377$	−1.03804e46			−0.438601
$378$	7.52711e44	−	1.85895e45i	0.0303233	−	0.0748886i
$379$		−	1.04283e45i		−	0.0400596i	−0.999799	−	0.0200298i	$-0.993624\pi$
$379$		−	1.04283e45i		−	0.0400596i	0.999799	−	0.0200298i	$-0.00637611\pi$
$380$	2.51821e45	−	2.59975e45i	0.0922543	−	0.0952417i
$381$	−6.32461e46			−2.20996
$382$	−5.70604e45	−	2.31044e45i	−0.190193	−	0.0770113i
$383$			7.05484e45i			0.224341i	0.993689	+	0.112171i	$0.0357804\pi$
$383$			7.05484e45i			0.224341i	−0.993689	+	0.112171i	$0.964220\pi$
$384$	−3.67564e46	+	1.76856e46i	−1.11525	+	0.536608i
$385$	1.33628e46			0.386905
$386$	1.47441e46	−	3.64132e46i	0.407424	−	1.00621i
$387$			1.32318e46i			0.348996i
$388$	1.41599e46	+	1.37158e46i	0.356525	+	0.345342i
$389$	4.05550e46			0.974881			0.487440	−	0.873156i	$-0.337931\pi$
$389$	4.05550e46			0.974881			0.487440	+	0.873156i	$0.337931\pi$
$390$	1.30298e47	+	5.27591e46i	2.99071	+	1.21097i
$391$			1.34718e46i			0.295287i
$392$	−4.28347e46	+	1.89542e46i	−0.896699	+	0.396786i
$393$	1.07201e45			0.0214355
$394$	2.22506e46	−	5.49517e46i	0.425020	−	1.04966i
$395$		−	1.50142e47i		−	2.74003i
$396$	3.39989e46	−	3.50999e46i	0.592860	−	0.612058i
$397$	5.04352e46			0.840436			0.420218	−	0.907423i	$-0.361954\pi$
$397$	5.04352e46			0.840436			0.420218	+	0.907423i	$0.361954\pi$
$398$	−7.13833e46	−	2.89039e46i	−1.13685	−	0.460322i
$399$			8.67801e44i			0.0132102i
$400$	4.37676e45	+	1.37314e47i	0.0636902	+	1.99818i
$401$	6.66873e46			0.927779			0.463889	−	0.885893i	$-0.346453\pi$
$401$	6.66873e46			0.927779			0.463889	+	0.885893i	$0.346453\pi$
$402$	−4.27393e46	+	1.05552e47i	−0.568537	+	1.40410i
$403$		−	1.29172e47i		−	1.64315i
$404$	−2.55887e46	−	2.47861e46i	−0.311303	−	0.301539i
$405$	−1.85889e47			−2.16303
$406$	3.38227e45	+	1.36952e45i	0.0376478	+	0.0152440i
$407$			1.72964e47i			1.84186i
$408$	−3.64276e46	−	8.23228e46i	−0.371148	−	0.838759i
$409$	2.73256e46			0.266410			0.133205	−	0.991089i	$-0.457473\pi$
$409$	2.73256e46			0.266410			0.133205	+	0.991089i	$0.457473\pi$
$410$	3.54342e46	−	8.75109e46i	0.330607	−	0.816493i
$411$			1.01248e47i			0.904135i
$412$	2.49668e46	−	2.57752e46i	0.213409	−	0.220319i
$413$	−1.71928e46			−0.140684
$414$	2.50662e46	+	1.01496e46i	0.196373	+	0.0795137i
$415$			8.08423e46i			0.606419i
$416$	−1.96658e47	−	7.24259e46i	−1.41264	−	0.520252i
$417$	1.46144e47			1.00538
$418$	6.98891e45	−	1.72604e46i	0.0460507	−	0.113730i
$419$			2.27184e47i			1.43392i	0.697113	+	0.716961i	$0.254468\pi$
$419$			2.27184e47i			1.43392i	−0.697113	+	0.716961i	$0.745532\pi$
$420$	−3.54946e46	−	3.43813e46i	−0.214622	−	0.207891i
$421$	−1.97959e47			−1.14683			−0.573414	−	0.819266i	$-0.694381\pi$
$421$	−1.97959e47			−1.14683			−0.573414	+	0.819266i	$0.694381\pi$
$422$	1.65813e47	+	6.71394e46i	0.920435	+	0.372695i
$423$			3.99117e46i			0.212311i
$424$	3.92587e46	−	1.73718e46i	0.200148	−	0.0885646i
$425$	−3.03203e47			−1.48160
$426$	−3.46504e46	+	8.55752e46i	−0.162306	+	0.400844i
$427$			2.61630e46i			0.117486i
$428$	1.58883e47	−	1.64028e47i	0.684052	−	0.706203i
$429$	7.23245e47			2.98575
$430$	−2.66136e47	−	1.07762e47i	−1.05359	−	0.426611i
$431$		−	3.25686e47i		−	1.23654i	−0.785965	−	0.618270i	$-0.787834\pi$
$431$		−	3.25686e47i		−	1.23654i	0.785965	−	0.618270i	$-0.212166\pi$
$432$	1.59068e47	−	5.07015e45i	0.579262	−	0.0184635i
$433$	1.63248e47			0.570251			0.285126	−	0.958490i	$-0.407965\pi$
$433$	1.63248e47			0.570251			0.285126	+	0.958490i	$0.407965\pi$
$434$	−1.70421e46	+	4.20884e46i	−0.0571093	+	0.141042i
$435$		−	1.94231e47i		−	0.624470i
$436$	−2.76631e47	−	2.67954e47i	−0.853382	−	0.826615i
$437$	1.03053e46			0.0305068
$438$	−4.29582e47	−	1.73943e47i	−1.22043	−	0.494165i
$439$			2.84803e47i			0.776574i	0.921539	+	0.388287i	$0.126933\pi$
$439$			2.84803e47i			0.776574i	−0.921539	+	0.388287i	$0.873067\pi$
$440$	4.29086e47	+	9.69694e47i	1.12304	+	2.53797i
$441$	−2.07517e47			−0.521386
$442$	1.73588e47	−	4.28707e47i	0.418716	−	1.03409i
$443$			1.55992e47i			0.361272i	0.983550	+	0.180636i	$0.0578157\pi$
$443$			1.55992e47i			0.361272i	−0.983550	+	0.180636i	$0.942184\pi$
$444$	4.45020e47	−	4.59431e47i	0.989660	−	1.02171i
$445$	5.60717e45			0.0119747
$446$	−5.60268e47	−	2.26859e47i	−1.14913	−	0.465295i
$447$		−	5.22680e47i		−	1.02968i
$448$	5.45221e46	+	4.95445e46i	0.103174	+	0.0937542i
$449$	−6.78002e46			−0.123253			−0.0616264	−	0.998099i	$-0.519629\pi$
$449$	−6.78002e46			−0.123253			−0.0616264	+	0.998099i	$0.519629\pi$
$450$	−2.28431e47	+	5.64151e47i	−0.398961	+	0.985303i
$451$		−	4.85747e47i		−	0.815140i
$452$	6.70843e47	+	6.49801e47i	1.08176	+	1.04782i
$453$	−6.96319e47			−1.07905
$454$	1.09512e48	+	4.43427e47i	1.63101	+	0.660415i
$455$		−	2.53890e47i		−	0.363446i
$456$	−6.29734e46	+	2.78655e46i	−0.0866542	+	0.0383442i
$457$	−1.03943e48			−1.37500			−0.687498	−	0.726186i	$-0.741291\pi$
$457$	−1.03943e48			−1.37500			−0.687498	+	0.726186i	$0.741291\pi$
$458$	−3.61399e47	+	8.92538e47i	−0.459630	+	1.13514i
$459$			3.51238e47i			0.429510i
$460$	−4.08286e47	+	4.21507e47i	−0.480091	+	0.495637i
$461$	−5.48232e47			−0.619937			−0.309968	−	0.950747i	$-0.600318\pi$
$461$	−5.48232e47			−0.619937			−0.309968	+	0.950747i	$0.600318\pi$
$462$	−2.35657e47	−	9.54202e46i	−0.256286	−	0.103773i
$463$		−	6.58825e46i		−	0.0689148i	−0.999406	−	0.0344574i	$-0.989030\pi$
$463$		−	6.58825e46i		−	0.0689148i	0.999406	−	0.0344574i	$-0.0109703\pi$
$464$	9.22489e45	+	2.89416e47i	0.00928192	+	0.291205i
$465$	2.41697e48			2.33948
$466$	4.06150e47	−	1.00306e48i	0.378216	−	0.934070i
$467$			1.28722e48i			1.15332i	0.816984	+	0.576660i	$0.195644\pi$
$467$			1.28722e48i			1.15332i	−0.816984	+	0.576660i	$0.804356\pi$
$468$	−6.66888e47	−	6.45971e47i	−0.574947	−	0.556913i
$469$	2.05672e47			0.170634
$470$	−8.02760e47	−	3.25047e47i	−0.640951	−	0.259528i
$471$		−	1.81208e48i		−	1.39252i
$472$	−5.52069e47	−	1.24762e48i	−0.408354	−	0.922842i
$473$	−1.47724e48			−1.05184
$474$	−1.07213e48	+	2.64780e48i	−0.734912	+	1.81500i
$475$			2.31937e47i			0.153068i
$476$	−1.13122e47	+	1.16785e47i	−0.0718820	+	0.0742097i
$477$	1.90193e47			0.116376
$478$	6.16769e46	+	2.49737e46i	0.0363430	+	0.0147157i
$479$		−	1.18212e47i		−	0.0670847i	−0.999437	−	0.0335423i	$-0.989321\pi$
$479$		−	1.18212e47i		−	0.0670847i	0.999437	−	0.0335423i	$-0.0106789\pi$
$480$	1.35518e48	−	3.67972e48i	0.740723	−	2.01128i
$481$	3.28627e48			1.73018
$482$	1.09285e48	−	2.69899e48i	0.554262	−	1.36885i
$483$		−	1.40700e47i		−	0.0687456i
$484$	2.39283e48	+	2.31778e48i	1.12641	+	1.09108i
$485$	−1.89517e48			−0.859601
$486$	2.04912e48	+	8.29711e47i	0.895599	+	0.362639i
$487$			6.47797e47i			0.272846i	0.990651	+	0.136423i	$0.0435606\pi$
$487$			6.47797e47i			0.272846i	−0.990651	+	0.136423i	$0.956439\pi$
$488$	−1.89856e48	+	8.40107e47i	−0.770669	+	0.341018i
$489$	2.73780e48			1.07113
$490$	1.69005e48	−	4.17388e48i	0.637340	−	1.57402i
$491$			4.44317e48i			1.61520i	0.589731	+	0.807600i	$0.299234\pi$
$491$			4.44317e48i			1.61520i	−0.589731	+	0.807600i	$0.700766\pi$
$492$	−1.24978e48	+	1.29025e48i	−0.437988	+	0.452171i
$493$	−6.39060e47			−0.215922
$494$	−3.27942e47	−	1.32788e47i	−0.106835	−	0.0432586i
$495$			4.69779e48i			1.47571i
$496$	−3.60144e48	+	1.14793e47i	−1.09095	+	0.0347732i
$497$	1.66746e47			0.0487126
$498$	5.77272e47	−	1.42568e48i	0.162649	−	0.401691i
$499$		−	9.00710e47i		−	0.244779i	−0.992482	−	0.122390i	$-0.960944\pi$
$499$		−	9.00710e47i		−	0.244779i	0.992482	−	0.122390i	$-0.0390558\pi$
$500$	−4.74140e48	−	4.59268e48i	−1.24293	−	1.20394i
$501$	−9.59266e48			−2.42583
$502$	−1.82217e47	−	7.37817e46i	−0.0444551	−	0.0180004i
$503$		−	2.54884e48i		−	0.599954i	−0.953946	−	0.299977i	$-0.903021\pi$
$503$		−	2.54884e48i		−	0.599954i	0.953946	−	0.299977i	$-0.0969791\pi$
$504$	1.32069e47	+	2.98463e47i	0.0299952	+	0.0677862i
$505$	3.42480e48			0.750569
$506$	−1.13314e48	+	2.79848e48i	−0.239648	+	0.591852i
$507$		−	7.67782e48i		−	1.56709i
$508$	−6.30661e48	+	6.51083e48i	−1.24236	+	1.28260i
$509$	6.81591e48			1.29600			0.647998	−	0.761642i	$-0.275606\pi$
$509$	6.81591e48			1.29600			0.647998	+	0.761642i	$0.275606\pi$
$510$	8.02167e48	+	3.24807e48i	1.47232	+	0.596159i
$511$			8.37057e47i			0.148313i
$512$	−1.84454e48	+	5.54738e48i	−0.315522	+	0.948918i
$513$	2.68682e47			0.0443737
$514$	−1.44365e48	+	3.56534e48i	−0.230211	+	0.568546i
$515$			3.44977e48i			0.531203i
$516$	3.92389e48	+	3.80081e48i	0.583474	+	0.565173i
$517$	−4.45589e48			−0.639889
$518$	−1.07077e48	−	4.33569e47i	−0.148512	−	0.0601343i
$519$			7.32893e47i			0.0981811i
$520$	1.84239e49	−	8.15253e48i	2.38409	−	1.05495i
$521$	−5.58419e48			−0.698041			−0.349020	−	0.937115i	$-0.613486\pi$
$521$	−5.58419e48			−0.698041			−0.349020	+	0.937115i	$0.613486\pi$
$522$	−4.81464e47	+	1.18906e48i	−0.0581427	+	0.143594i
$523$		−	1.22870e49i		−	1.43356i	−0.697298	−	0.716781i	$-0.745615\pi$
$523$		−	1.22870e49i		−	1.43356i	0.697298	−	0.716781i	$-0.254385\pi$
$524$	1.06896e47	−	1.10357e47i	0.0120503	−	0.0124405i
$525$	3.16665e48			0.344931
$526$	−1.39098e48	−	5.63223e47i	−0.146412	−	0.0592839i
$527$		−	7.95234e48i		−	0.808917i
$528$	−6.42736e47	−	2.01648e49i	−0.0631862	−	1.98236i
$529$	8.85367e48			0.841243
$530$	−1.54896e48	+	3.82543e48i	−0.142257	+	0.351329i
$531$		−	6.04424e48i		−	0.536587i
$532$	8.93352e46	+	8.65331e46i	0.00766679	+	0.00742631i
$533$	−9.22907e48			−0.765716
$534$	−9.88840e46	−	4.00393e46i	−0.00793201	−	0.00321176i
$535$			2.19536e49i			1.70270i
$536$	6.60424e48	+	1.49250e49i	0.495287	+	1.11930i
$537$	−2.86053e49			−2.07448
$538$	−4.58130e47	+	1.13143e48i	−0.0321298	+	0.0793502i
$539$		−	2.31680e49i		−	1.57141i
$540$	−1.06449e49	+	1.09896e49i	−0.698316	+	0.720929i
$541$	2.08018e49			1.31993			0.659964	−	0.751297i	$-0.270572\pi$
$541$	2.08018e49			1.31993			0.659964	+	0.751297i	$0.270572\pi$
$542$	1.27905e49	+	5.17902e48i	0.785055	+	0.317878i
$543$		−	1.19545e48i		−	0.0709798i
$544$	−1.21071e49	−	4.45884e48i	−0.695438	−	0.256119i
$545$	3.70244e49			2.05755
$546$	−1.81296e48	+	4.47742e48i	−0.0974811	+	0.240747i
$547$			2.21627e49i			1.15305i	0.817078	+	0.576527i	$0.195593\pi$
$547$			2.21627e49i			1.15305i	−0.817078	+	0.576527i	$0.804407\pi$
$548$	1.04229e49	+	1.00960e49i	0.524733	+	0.508274i
$549$	−9.19778e48			−0.448106
$550$	−6.29839e49	−	2.55029e49i	−2.96962	−	1.20243i
$551$			4.88853e47i			0.0223074i
$552$	1.02101e49	−	4.51793e48i	0.450948	−	0.199543i
$553$	5.15934e48			0.220568
$554$	1.05715e49	−	2.61082e49i	0.437484	−	1.08044i
$555$			6.14904e49i			2.46339i
$556$	1.45728e49	−	1.50447e49i	0.565192	−	0.583494i
$557$	−3.43445e49			−1.28962			−0.644812	−	0.764341i	$-0.723065\pi$
$557$	−3.43445e49			−1.28962			−0.644812	+	0.764341i	$0.723065\pi$
$558$	−1.47964e49	−	5.99125e48i	−0.537950	−	0.217822i
$559$			2.80672e49i			0.988069i
$560$	−7.07872e48	+	2.25628e47i	−0.241307	+	0.00769146i
$561$	4.45259e49			1.46988
$562$	−4.58350e48	+	1.13198e49i	−0.146536	+	0.361896i
$563$		−	3.38206e49i		−	1.04720i	−0.851964	−	0.523601i	$-0.824588\pi$
$563$		−	3.38206e49i		−	1.04720i	0.851964	−	0.523601i	$-0.175412\pi$
$564$	1.18358e49	+	1.14646e49i	0.354956	+	0.343823i
$565$	−8.97859e49			−2.60817
$566$	6.16766e47	+	2.49735e47i	0.0173550	+	0.00702724i
$567$		−	6.38769e48i		−	0.174120i
$568$	5.35431e48	+	1.21002e49i	0.141395	+	0.319538i
$569$	6.96348e49			1.78158			0.890791	−	0.454414i	$-0.150151\pi$
$569$	6.96348e49			1.78158			0.890791	+	0.454414i	$0.150151\pi$
$570$	2.48463e48	−	6.13623e48i	0.0615906	−	0.152109i
$571$			1.13276e48i			0.0272076i	0.999907	+	0.0136038i	$0.00433035\pi$
$571$			1.13276e48i			0.0272076i	−0.999907	+	0.0136038i	$0.995670\pi$
$572$	7.21186e49	−	7.44539e49i	1.67849	−	1.73284i
$573$	−1.12599e49			−0.253952
$574$	3.00713e48	+	1.21762e48i	0.0657262	+	0.0266133i
$575$		−	3.76047e49i		−	0.796565i
$576$	−1.74177e49	+	1.91676e49i	−0.357590	+	0.393517i
$577$	3.94515e48			0.0785052			0.0392526	−	0.999229i	$-0.487502\pi$
$577$	3.94515e48			0.0785052			0.0392526	+	0.999229i	$0.487502\pi$
$578$	−8.77097e48	+	2.16614e49i	−0.169179	+	0.417817i
$579$		−	7.18553e49i		−	1.34352i
$580$	−1.99950e49	−	1.93678e49i	−0.362424	−	0.351056i
$581$	−2.77798e48			−0.0488156
$582$	3.34219e49	+	1.35329e49i	0.569399	+	0.230556i
$583$			2.12338e49i			0.350747i
$584$	−6.07424e49	+	2.68783e49i	−0.972882	+	0.430497i
$585$	8.92567e49			1.38623
$586$	−1.56374e48	+	3.86194e48i	−0.0235510	+	0.0581633i
$587$			7.75747e49i			1.13301i	0.824058	+	0.566506i	$0.191705\pi$
$587$			7.75747e49i			1.13301i	−0.824058	+	0.566506i	$0.808295\pi$
$588$	−5.96091e49	+	6.15394e49i	−0.844347	+	0.871688i
$589$	−6.08320e48			−0.0835712
$590$	1.21570e50	+	4.92252e49i	1.61991	+	0.655921i
$591$		−	1.08438e50i		−	1.40154i
$592$	−2.92046e48	−	9.16246e49i	−0.0366151	−	1.14874i
$593$	3.70508e49			0.450623			0.225311	−	0.974287i	$-0.427660\pi$
$593$	3.70508e49			0.450623			0.225311	+	0.974287i	$0.427660\pi$
$594$	−2.95432e49	+	7.29622e49i	−0.348580	+	0.860878i
$595$		−	1.56305e49i		−	0.178924i
$596$	−5.38070e49	−	5.21192e49i	−0.597593	−	0.578849i
$597$	−1.40863e50			−1.51796
$598$	5.31704e49	+	2.15293e49i	0.555967	+	0.225117i
$599$		−	1.01866e50i		−	1.03359i	−0.856109	−	0.516795i	$-0.827125\pi$
$599$		−	1.01866e50i		−	1.03359i	0.856109	−	0.516795i	$-0.172875\pi$
$600$	1.01683e50	+	2.29793e50i	1.00121	+	2.26264i
$601$	−6.84375e49			−0.653963			−0.326982	−	0.945031i	$-0.606032\pi$
$601$	−6.84375e49			−0.653963			−0.326982	+	0.945031i	$0.606032\pi$
$602$	3.70301e48	−	9.14523e48i	0.0343414	−	0.0848121i
$603$			7.23055e49i			0.650818i
$604$	−6.94337e49	+	7.16821e49i	−0.606605	+	0.626248i
$605$	−3.20258e50			−2.71584
$606$	−6.03973e49	−	2.44556e49i	−0.497176	−	0.201312i
$607$			4.26011e49i			0.340428i	0.985407	+	0.170214i	$0.0544458\pi$
$607$			4.26011e49i			0.340428i	−0.985407	+	0.170214i	$0.945554\pi$
$608$	−3.41082e48	+	9.26137e48i	−0.0264603	+	0.0718474i
$609$	6.67435e48			0.0502687
$610$	7.49082e49	−	1.84999e50i	0.547762	−	1.35280i
$611$			8.46607e49i			0.601091i
$612$	−4.10564e49	−	3.97686e49i	−0.283045	−	0.274167i
$613$	2.84023e50			1.90137			0.950683	−	0.310165i	$-0.100384\pi$
$613$	2.84023e50			1.90137			0.950683	+	0.310165i	$0.100384\pi$
$614$	−8.82051e49	−	3.57153e49i	−0.573407	−	0.232179i
$615$		−	1.72688e50i		−	1.09021i
$616$	−3.33216e49	+	1.47447e49i	−0.204302	+	0.0904030i
$617$	1.94103e50			1.15584			0.577921	−	0.816093i	$-0.303864\pi$
$617$	1.94103e50			1.15584			0.577921	+	0.816093i	$0.303864\pi$
$618$	2.46339e49	−	6.08376e49i	0.142475	−	0.351868i
$619$			2.91886e50i			1.63976i	0.572533	+	0.819882i	$0.305961\pi$
$619$			2.91886e50i			1.63976i	−0.572533	+	0.819882i	$0.694039\pi$
$620$	2.41009e50	−	2.48814e50i	1.31517	−	1.35776i
$621$	−4.35623e49			−0.230920
$622$	2.37801e50	+	9.62885e49i	1.22458	+	0.495847i
$623$			1.92679e47i			0.000963939i
$624$	−3.83126e50	+	1.22118e49i	−1.86217	+	0.0593550i
$625$	2.11246e50			0.997580
$626$	2.64668e49	−	6.53645e49i	0.121441	−	0.299919i
$627$		−	3.40604e49i		−	0.151857i
$628$	−1.86543e50	−	1.80692e50i	−0.808177	−	0.782827i
$629$	2.02316e50			0.851764
$630$	−2.90828e49	−	1.17759e49i	−0.118989	−	0.0481799i
$631$			4.24994e50i			1.68988i	0.534864	+	0.844938i	$0.320363\pi$
$631$			4.24994e50i			1.68988i	−0.534864	+	0.844938i	$0.679637\pi$
$632$	1.65669e50	+	3.74396e50i	0.640226	+	1.44685i
$633$	3.27203e50			1.22900
$634$	−3.54988e49	+	8.76704e49i	−0.129600	+	0.320071i
$635$		−	8.71413e50i		−	3.09241i
$636$	5.46327e49	−	5.64018e49i	0.188462	−	0.194565i
$637$	−4.40186e50			−1.47614
$638$	−1.32751e50	−	5.37525e49i	−0.432779	−	0.175237i
$639$			5.86208e49i			0.185796i
$640$	−2.43674e50	−	5.06433e50i	−0.750879	−	1.56057i
$641$	−4.30618e50			−1.29017			−0.645085	−	0.764111i	$-0.723178\pi$
$641$	−4.30618e50			−1.29017			−0.645085	+	0.764111i	$0.723178\pi$
$642$	1.56764e50	−	3.87157e50i	0.456685	−	1.12786i
$643$			4.66172e50i			1.32053i	0.751032	+	0.660266i	$0.229556\pi$
$643$			4.66172e50i			1.32053i	−0.751032	+	0.660266i	$0.770444\pi$
$644$	−1.44842e49	−	1.40299e49i	−0.0398979	−	0.0386464i
$645$	−5.25175e50			−1.40679
$646$	−2.01895e49	−	8.17495e48i	−0.0525944	−	0.0212961i
$647$			7.15036e50i			1.81155i	0.423758	+	0.905776i	$0.360711\pi$
$647$			7.15036e50i			1.81155i	−0.423758	+	0.905776i	$0.639289\pi$
$648$	4.63533e50	−	2.05112e50i	1.14217	−	0.505406i
$649$	6.74801e50			1.61723
$650$	−4.84549e50	+	1.19668e51i	−1.12953	+	2.78957i
$651$			8.30543e49i			0.188324i
$652$	2.73001e50	−	2.81841e50i	0.602154	−	0.621653i
$653$	−9.56236e49			−0.205177			−0.102588	−	0.994724i	$-0.532712\pi$
$653$	−9.56236e49			−0.205177			−0.102588	+	0.994724i	$0.532712\pi$
$654$	−6.52935e50	−	2.64381e50i	−1.36292	−	0.551862i
$655$			1.47703e49i			0.0299948i
$656$	8.20173e48	+	2.57316e50i	0.0162045	+	0.508391i
$657$	−2.94273e50			−0.565683
$658$	1.11696e49	−	2.75852e49i	0.0208916	−	0.0515954i
$659$		−	4.92362e50i		−	0.896080i	−0.894014	−	0.448040i	$-0.852122\pi$
$659$		−	4.92362e50i		−	0.896080i	0.894014	−	0.448040i	$-0.147878\pi$
$660$	1.39313e51	+	1.34943e51i	2.46718	+	2.38980i
$661$	3.31963e50			0.572088			0.286044	−	0.958216i	$-0.407660\pi$
$661$	3.31963e50			0.572088			0.286044	+	0.958216i	$0.407660\pi$
$662$	4.23335e50	+	1.71413e50i	0.709970	+	0.287475i
$663$		−	8.45981e50i		−	1.38076i
$664$	−8.92023e49	−	2.01589e50i	−0.141694	−	0.320214i
$665$	−1.19567e49			−0.0184850
$666$	1.52424e50	−	3.76438e50i	0.229360	−	0.566444i
$667$		−	7.92595e49i		−	0.116088i
$668$	−9.56535e50	+	9.87510e50i	−1.36372	+	1.40788i
$669$	−1.10559e51			−1.53436
$670$	−1.45431e51	−	5.88868e50i	−1.96477	−	0.795557i
$671$		−	1.02687e51i		−	1.35055i
$672$	1.26446e50	+	4.65681e49i	0.161905	+	0.0596269i
$673$	1.51276e51			1.88582			0.942908	−	0.333054i	$-0.108079\pi$
$673$	1.51276e51			1.88582			0.942908	+	0.333054i	$0.108079\pi$
$674$	−2.24329e50	+	5.54021e50i	−0.272275	+	0.672431i
$675$		−	9.80433e50i		−	1.15864i
$676$	−7.90388e50	−	7.65597e50i	−0.909494	−	0.880967i
$677$	−1.31869e51			−1.47757			−0.738785	−	0.673942i	$-0.764600\pi$
$677$	−1.31869e51			−1.47757			−0.738785	+	0.673942i	$0.764600\pi$
$678$	1.58340e51	+	6.41137e50i	1.72765	+	0.699546i
$679$		−	6.51237e49i		−	0.0691964i
$680$	1.13425e51	−	5.01904e50i	1.17368	−	0.519350i
$681$	2.16104e51			2.17778
$682$	6.68886e50	−	1.65193e51i	0.656498	−	1.62134i
$683$			7.41047e50i			0.708391i	0.935171	+	0.354196i	$0.115245\pi$
$683$			7.41047e50i			0.708391i	−0.935171	+	0.354196i	$0.884755\pi$
$684$	−3.04213e49	+	3.14064e49i	−0.0283248	+	0.0292421i
$685$	−1.39501e51			−1.26516
$686$	2.89697e50	+	1.17302e50i	0.255923	+	0.103626i
$687$			1.76127e51i			1.51567i
$688$	7.82544e50	−	2.49429e49i	0.656019	−	0.0209101i
$689$	4.03437e50			0.329481
$690$	−4.02842e50	+	9.94889e50i	−0.320517	+	0.791573i
$691$		−	3.66751e50i		−	0.284293i	−0.989846	−	0.142147i	$-0.954600\pi$
$691$		−	3.66751e50i		−	0.284293i	0.989846	−	0.142147i	$-0.0454004\pi$
$692$	7.54472e49	+	7.30807e49i	0.0569814	+	0.0551941i
$693$	−1.61430e50			−0.118792
$694$	−1.47595e51	−	5.97630e50i	−1.05828	−	0.428511i
$695$			2.01359e51i			1.40684i
$696$	2.14317e50	+	4.84335e50i	0.145911	+	0.329746i
$697$	−5.68180e50			−0.376960
$698$	1.88261e49	−	4.64943e49i	0.0121720	−	0.0300609i
$699$		−	1.97937e51i		−	1.24720i
$700$	3.15764e50	−	3.25989e50i	0.193909	−	0.200188i
$701$	1.61915e49			0.00969085			0.00484542	−	0.999988i	$-0.498458\pi$
$701$	1.61915e49			0.00969085			0.00484542	+	0.999988i	$0.498458\pi$
$702$	1.38626e51	+	5.61314e50i	0.808681	+	0.327444i
$703$		−	1.54763e50i		−	0.0879978i
$704$	−2.13994e51	−	1.94458e51i	−1.18603	−	1.07775i
$705$	−1.58411e51			−0.855819
$706$	−4.75258e50	+	1.17373e51i	−0.250291	+	0.618136i
$707$			1.17686e50i			0.0604194i
$708$	−1.79242e51	−	1.73620e51i	−0.897102	−	0.868963i
$709$	2.41201e51			1.17692			0.588460	−	0.808527i	$-0.299735\pi$
$709$	2.41201e51			1.17692			0.588460	+	0.808527i	$0.299735\pi$
$710$	−1.17906e51	−	4.77417e50i	−0.560903	−	0.227116i
$711$			1.81380e51i			0.841272i
$712$	−1.39821e49	+	6.18702e48i	−0.00632312	+	0.00279796i
$713$	9.86290e50			0.434904
$714$	−1.11613e50	+	2.75648e50i	−0.0479897	+	0.118519i
$715$			9.96495e51i			4.17798i
$716$	−2.85239e51	+	2.94475e51i	−1.16620	+	1.20397i
$717$	1.21709e50			0.0485264
$718$	−1.16156e51	−	4.70330e50i	−0.451650	−	0.182878i
$719$		−	3.96171e51i		−	1.50232i	−0.660120	−	0.751160i	$-0.729495\pi$
$719$		−	3.96171e51i		−	1.50232i	0.660120	−	0.751160i	$-0.270505\pi$
$720$	−7.93210e49	−	2.48857e51i	−0.0293362	−	0.920375i
$721$	−1.18544e50			−0.0427608
$722$	1.06049e51	−	2.61908e51i	0.373112	−	0.921465i
$723$		−	5.32601e51i		−	1.82773i
$724$	−1.23065e50	−	1.19205e50i	−0.0411946	−	0.0399025i
$725$	1.78385e51			0.582471
$726$	5.64784e51	+	2.28687e51i	1.79897	+	0.728422i
$727$		−	1.85957e51i		−	0.577821i	−0.957356	−	0.288910i	$-0.906707\pi$
$727$		−	1.85957e51i		−	0.577821i	0.957356	−	0.288910i	$-0.0932929\pi$
$728$	2.80145e50	+	6.33101e50i	0.0849216	+	0.191915i
$729$	−1.79751e50			−0.0531588
$730$	2.39660e51	−	5.91883e51i	0.691488	−	1.70775i
$731$			1.72794e51i			0.486424i
$732$	−2.64205e51	+	2.72761e51i	−0.725675	+	0.749173i
$733$	5.64939e50			0.151401			0.0757007	−	0.997131i	$-0.475881\pi$
$733$	5.64939e50			0.151401			0.0757007	+	0.997131i	$0.475881\pi$
$734$	6.44283e51	+	2.60878e51i	1.68480	+	0.682194i
$735$		−	8.23646e51i		−	2.10169i
$736$	5.53008e50	−	1.50158e51i	0.137699	−	0.373893i
$737$	−8.07246e51			−1.96151
$738$	−4.28063e50	+	1.05718e51i	−0.101506	+	0.250688i
$739$			3.16982e51i			0.733558i	0.930308	+	0.366779i	$0.119539\pi$
$739$			3.16982e51i			0.733558i	−0.930308	+	0.366779i	$0.880461\pi$
$740$	6.33009e51	+	6.13154e51i	1.42968	+	1.38484i
$741$	−6.47139e50			−0.142649
$742$	−1.31453e50	−	5.32269e49i	−0.0282814	−	0.0114515i
$743$		−	3.80186e50i		−	0.0798358i	−0.999203	−	0.0399179i	$-0.987290\pi$
$743$		−	3.80186e50i		−	0.0798358i	0.999203	−	0.0399179i	$-0.0127096\pi$
$744$	−6.02697e51	+	2.66691e51i	−1.23534	+	0.546634i
$745$	7.20155e51			1.44083
$746$	−1.18852e51	+	2.93526e51i	−0.232118	+	0.573255i
$747$		−	9.76617e50i		−	0.186189i
$748$	4.43992e51	−	4.58369e51i	0.826316	−	0.853074i
$749$	−7.54390e50			−0.137064
$750$	−1.11912e52	−	4.53144e51i	−1.98506	−	0.803774i
$751$			2.08756e51i			0.361510i	0.983528	+	0.180755i	$0.0578540\pi$
$751$			2.08756e51i			0.361510i	−0.983528	+	0.180755i	$0.942146\pi$
$752$	2.36043e51	−	7.52366e49i	0.399089	−	0.0127206i
$753$	−3.59574e50			−0.0593580
$754$	−1.02128e51	+	2.52224e51i	−0.164612	+	0.406539i
$755$		−	9.59397e51i		−	1.50992i
$756$	−3.77634e50	−	3.65789e50i	−0.0580335	−	0.0562132i
$757$	−1.95547e51			−0.293444			−0.146722	−	0.989178i	$-0.546872\pi$
$757$	−1.95547e51			−0.293444			−0.146722	+	0.989178i	$0.546872\pi$
$758$	−2.53387e50	−	1.02599e50i	−0.0371312	−	0.0150349i
$759$			5.52233e51i			0.790261i
$760$	−3.83934e50	−	8.67655e50i	−0.0536553	−	0.121256i
$761$	−1.08898e52			−1.48627			−0.743135	−	0.669142i	$-0.766662\pi$
$761$	−1.08898e52			−1.48627			−0.743135	+	0.669142i	$0.766662\pi$
$762$	−6.22252e51	+	1.53676e52i	−0.829424	+	2.04841i
$763$			1.27227e51i			0.165629i
$764$	−1.12279e51	+	1.15914e51i	−0.142763	+	0.147386i
$765$	5.49501e51			0.682437
$766$	1.71419e51	+	6.94096e50i	0.207942	+	0.0841980i
$767$		−	1.28210e52i		−	1.51917i
$768$	6.80956e50	+	1.06711e52i	0.0788165	+	1.23511i
$769$	3.33302e51			0.376846			0.188423	−	0.982088i	$-0.439662\pi$
$769$	3.33302e51			0.376846			0.188423	+	0.982088i	$0.439662\pi$
$770$	1.31471e51	−	3.24691e51i	0.145210	−	0.358622i
$771$			7.03561e51i			0.759142i
$772$	−7.39709e51	−	7.16507e51i	−0.779740	−	0.755282i
$773$	1.13759e51			0.117153			0.0585766	−	0.998283i	$-0.481344\pi$
$773$	1.13759e51			0.117153			0.0585766	+	0.998283i	$0.481344\pi$
$774$	3.21506e51	+	1.30182e51i	0.323484	+	0.130982i
$775$			2.21979e52i			2.18213i
$776$	4.72581e51	−	2.09115e51i	0.453905	−	0.200851i
$777$	−2.11299e51			−0.198299
$778$	3.99003e51	−	9.85409e51i	0.365884	−	0.903615i
$779$			4.34633e50i			0.0389447i
$780$	2.56389e52	−	2.64691e52i	2.24490	−	2.31759i
$781$	−6.54464e51			−0.559973
$782$	3.27339e51	+	1.32543e51i	0.273701	+	0.110825i
$783$		−	2.06646e51i		−	0.168855i
$784$	3.91186e50	+	1.22728e52i	0.0312388	+	0.980068i
$785$	2.49671e52			1.94856
$786$	1.05471e50	−	2.60478e50i	0.00804499	−	0.0198685i
$787$			6.69833e51i			0.499369i	0.968327	+	0.249684i	$0.0803268\pi$
$787$			6.69833e51i			0.499369i	−0.968327	+	0.249684i	$0.919673\pi$
$788$	−1.11631e52	−	1.08129e52i	−0.813414	−	0.787900i
$789$	−2.74486e51			−0.195494
$790$	−3.64817e52	−	1.47719e52i	−2.53973	−	1.02837i
$791$		−	3.08531e51i		−	0.209953i
$792$	−5.18359e51	−	1.17144e52i	−0.344808	−	0.779233i
$793$	−1.95103e52			−1.26867
$794$	4.96210e51	−	1.22548e52i	0.315426	−	0.778999i
$795$			7.54884e51i			0.469107i
$796$	−1.40462e52	+	1.45011e52i	−0.853343	+	0.880976i
$797$	2.43626e52			1.44702			0.723508	−	0.690316i	$-0.242529\pi$
$797$	2.43626e52			1.44702			0.723508	+	0.690316i	$0.242529\pi$
$798$	2.10859e50	+	8.53793e49i	0.0122445	+	0.00495793i
$799$			5.21206e51i			0.295915i
$800$	3.37952e52	+	1.24463e52i	1.87601	+	0.690906i
$801$	−6.77376e49			−0.00367658
$802$	6.56108e51	−	1.62037e52i	0.348206	−	0.859957i
$803$		−	3.28537e52i		−	1.70492i
$804$	2.14422e52	+	2.07697e52i	1.08808	+	1.05395i
$805$	1.93858e51			0.0961961
$806$	−3.13862e52	−	1.27087e52i	−1.52303	−	0.616693i
$807$			2.23269e51i			0.105951i
$808$	−8.54010e51	+	3.77897e51i	−0.396331	+	0.175375i
$809$	−3.66483e51			−0.166334			−0.0831668	−	0.996536i	$-0.526503\pi$
$809$	−3.66483e51			−0.166334			−0.0831668	+	0.996536i	$0.526503\pi$
$810$	−1.82888e52	+	4.51674e52i	−0.811811	+	2.00491i
$811$		−	1.26501e52i		−	0.549186i	−0.961561	−	0.274593i	$-0.911457\pi$
$811$		−	1.26501e52i		−	0.549186i	0.961561	−	0.274593i	$-0.0885431\pi$
$812$	6.65535e50	−	6.87086e50i	0.0282594	−	0.0291745i
$813$	2.52399e52			1.04823
$814$	4.20269e52	+	1.70172e52i	1.70722	+	0.691271i
$815$			3.77218e52i			1.49884i
$816$	−2.35868e52	+	7.51810e50i	−0.916741	+	0.0292203i
$817$	1.32180e51			0.0502536
$818$	2.68845e51	−	6.63959e51i	0.0999867	−	0.246935i
$819$			3.06712e51i			0.111589i
$820$	−1.77773e52	−	1.72196e52i	−0.632725	−	0.612879i
$821$	−1.21528e52			−0.423155			−0.211578	−	0.977361i	$-0.567860\pi$
$821$	−1.21528e52			−0.423155			−0.211578	+	0.977361i	$0.567860\pi$
$822$	2.46013e52	+	9.96135e51i	0.838042	+	0.339333i
$823$			1.18381e52i			0.394535i	0.980350	+	0.197268i	$0.0632068\pi$
$823$			1.18381e52i			0.394535i	−0.980350	+	0.197268i	$0.936793\pi$
$824$	−3.80652e51	−	8.60237e51i	−0.124119	−	0.280497i
$825$	−1.24288e53			−3.96514
$826$	−1.69153e51	+	4.17752e51i	−0.0528005	+	0.130400i
$827$			3.34744e52i			1.02238i	0.859467	+	0.511192i	$0.170796\pi$
$827$			3.34744e52i			1.02238i	−0.859467	+	0.511192i	$0.829204\pi$
$828$	4.93231e51	−	5.09203e51i	0.147402	−	0.152175i
$829$	4.02173e52			1.17607			0.588033	−	0.808837i	$-0.299902\pi$
$829$	4.02173e52			1.17607			0.588033	+	0.808837i	$0.299902\pi$
$830$	1.96431e52	+	7.95373e51i	0.562089	+	0.227596i
$831$		−	5.15202e52i		−	1.44264i
$832$	−3.69464e52	+	4.06584e52i	−1.01240	+	1.11412i
$833$	−2.70997e52			−0.726698
$834$	1.43785e52	−	3.55101e52i	0.377332	−	0.931887i
$835$		−	1.32169e53i		−	3.39447i
$836$	−3.50633e51	−	3.39635e51i	−0.0881332	−	0.0853687i
$837$	2.57146e52			0.632589
$838$	5.52014e52	+	2.23517e52i	1.32910	+	0.538168i
$839$			8.09034e51i			0.190657i	0.995446	+	0.0953283i	$0.0303901\pi$
$839$			8.09034e51i			0.190657i	−0.995446	+	0.0953283i	$0.969610\pi$
$840$	−1.18462e52	+	5.24188e51i	−0.273244	+	0.120909i
$841$	−4.05324e52			−0.915113
$842$	−1.94764e52	+	4.81003e52i	−0.430418	+	1.06299i
$843$			2.23376e52i			0.483216i
$844$	3.26272e52	−	3.36837e52i	0.690901	−	0.713273i
$845$	1.05786e53			2.19284
$846$	9.69777e51	+	3.92674e51i	0.196791	+	0.0796830i
$847$		−	1.10050e52i		−	0.218620i
$848$	−3.58528e50	−	1.12482e52i	−0.00697265	−	0.218756i
$849$	1.21708e51			0.0231730
$850$	−2.98308e52	+	7.36725e52i	−0.556064	+	1.37330i
$851$			2.50923e52i			0.457940i
$852$	1.73840e52	+	1.68388e52i	0.310626	+	0.300883i
$853$	4.99450e52			0.873794			0.436897	−	0.899511i	$-0.356077\pi$
$853$	4.99450e52			0.873794			0.436897	+	0.899511i	$0.356077\pi$
$854$	6.35711e51	+	2.57407e51i	0.108898	+	0.0440939i
$855$		−	4.20344e51i		−	0.0705042i
$856$	−2.42238e52	−	5.47435e52i	−0.397846	−	0.899094i
$857$	7.48536e52			1.20381			0.601905	−	0.798568i	$-0.294409\pi$
$857$	7.48536e52			1.20381			0.601905	+	0.798568i	$0.294409\pi$
$858$	7.11570e52	−	1.75735e53i	1.12059	−	2.76749i
$859$			1.11454e53i			1.71877i	0.511331	+	0.859384i	$0.329153\pi$
$859$			1.11454e53i			1.71877i	−0.511331	+	0.859384i	$0.670847\pi$
$860$	−5.23680e52	+	5.40638e52i	−0.790850	+	0.816459i
$861$	5.93407e51			0.0877599
$862$	−7.91355e52	−	3.20429e52i	−1.14615	−	0.464089i
$863$		−	1.10358e53i		−	1.56534i	−0.622439	−	0.782669i	$-0.713858\pi$
$863$		−	1.10358e53i		−	1.56534i	0.622439	−	0.782669i	$-0.286142\pi$
$864$	1.44181e52	−	3.91493e52i	0.200290	−	0.543846i
$865$	−1.00979e52			−0.137385
$866$	1.60613e52	−	3.96662e52i	0.214022	−	0.528565i
$867$			4.27452e52i			0.557884i
$868$	8.54998e51	+	8.28179e51i	0.109297	+	0.105869i
$869$	−2.02499e53			−2.53553
$870$	−4.71944e52	−	1.91095e52i	−0.578820	−	0.234371i
$871$			1.53375e53i			1.84258i
$872$	−9.23242e52	+	4.08531e52i	−1.08647	+	0.480761i
$873$	2.28947e52			0.263923
$874$	1.01390e51	−	2.50400e51i	0.0114496	−	0.0282767i
$875$			2.18065e52i			0.241235i
$876$	−8.45295e52	+	8.72668e52i	−0.916082	+	0.945747i
$877$	−1.92716e52			−0.204610			−0.102305	−	0.994753i	$-0.532622\pi$
$877$	−1.92716e52			−0.204610			−0.102305	+	0.994753i	$0.532622\pi$
$878$	6.92016e52	+	2.80205e52i	0.719805	+	0.291457i
$879$			7.62089e51i			0.0776616i
$880$	2.77833e53	−	8.85570e51i	2.77393	−	0.0884168i
$881$	−1.86439e53			−1.82377			−0.911886	−	0.410444i	$-0.865374\pi$
$881$	−1.86439e53			−1.82377			−0.911886	+	0.410444i	$0.865374\pi$
$882$	−2.04167e52	+	5.04227e52i	−0.195682	+	0.483272i
$883$		−	2.64090e52i		−	0.248004i	−0.992282	−	0.124002i	$-0.960427\pi$
$883$		−	2.64090e52i		−	0.248004i	0.992282	−	0.124002i	$-0.0395730\pi$
$884$	−8.70890e52	−	8.43573e52i	−0.801350	−	0.776215i
$885$	2.39899e53			2.16296
$886$	3.79030e52	+	1.53474e52i	0.334863	+	0.135590i
$887$			9.02798e52i			0.781565i	0.920483	+	0.390783i	$0.127796\pi$
$887$			9.02798e52i			0.781565i	−0.920483	+	0.390783i	$0.872204\pi$
$888$	−6.78492e52	−	1.53333e53i	−0.575588	−	1.30077i
$889$	2.99443e52			0.248933
$890$	5.51666e50	−	1.36244e51i	0.00449424	−	0.0110993i
$891$			2.50711e53i			2.00159i
$892$	−1.10245e53	+	1.13815e53i	−0.862563	+	0.890494i
$893$	3.98700e51			0.0305717
$894$	−1.27001e53	−	5.14243e52i	−0.954405	−	0.386450i
$895$		−	3.94127e53i		−	2.90283i
$896$	1.74026e52	−	8.37337e51i	0.125623	−	0.0604444i
$897$	1.04923e53			0.742346
$898$	−6.67058e51	+	1.64742e52i	−0.0462583	+	0.114243i
$899$			4.67865e52i			0.318014i
$900$	1.14604e53	+	1.11009e53i	0.763542	+	0.739592i
$901$	2.48373e52			0.162203
$902$	−1.18027e53	−	4.77906e52i	−0.755553	−	0.305932i
$903$		−	1.80466e52i		−	0.113244i
$904$	2.23891e53	−	9.90708e52i	1.37722	−	0.609416i
$905$	1.64711e52			0.0993224
$906$	−6.85079e52	+	1.69192e53i	−0.404980	+	1.00017i
$907$		−	2.46300e53i		−	1.42736i	−0.700471	−	0.713681i	$-0.747027\pi$
$907$		−	2.46300e53i		−	1.42736i	0.700471	−	0.713681i	$-0.252973\pi$
$908$	2.15489e53	−	2.22467e53i	1.22428	−	1.26392i
$909$	−4.13734e52			−0.230447
$910$	−6.16904e52	−	2.49792e52i	−0.336878	−	0.136406i
$911$			7.65690e52i			0.409942i	0.978768	+	0.204971i	$0.0657099\pi$
$911$			7.65690e52i			0.409942i	−0.978768	+	0.204971i	$0.934290\pi$
$912$	5.75102e50	+	1.80429e52i	0.00301882	+	0.0947107i
$913$	1.09033e53			0.561158
$914$	−1.02265e53	+	2.52560e53i	−0.516053	+	1.27448i
$915$		−	3.65064e53i		−	1.80630i
$916$	1.81313e53	+	1.75626e53i	0.879652	+	0.852061i
$917$	−5.07551e50			−0.00241453
$918$	8.53441e52	+	3.45568e52i	0.398112	+	0.161200i
$919$		−	1.66167e53i		−	0.760092i	−0.924968	−	0.380046i	$-0.875908\pi$
$919$		−	1.66167e53i		−	0.760092i	0.924968	−	0.380046i	$-0.124092\pi$
$920$	6.22486e52	+	1.40676e53i	0.279222	+	0.631014i
$921$	−1.74058e53			−0.765633
$922$	−5.39382e52	+	1.33210e53i	−0.232670	+	0.574619i
$923$			1.24346e53i			0.526021i
$924$	−4.63706e52	+	4.78721e52i	−0.192374	+	0.198604i
$925$	−5.64739e53			−2.29772
$926$	−1.60082e52	−	6.48190e51i	−0.0638770	−	0.0258645i
$927$		−	4.16751e52i		−	0.163095i
$928$	7.12302e52	+	2.62330e52i	0.273401	+	0.100689i
$929$	−3.79141e53			−1.42731			−0.713654	−	0.700498i	$-0.752961\pi$
$929$	−3.79141e53			−1.42731			−0.713654	+	0.700498i	$0.752961\pi$
$930$	2.37796e53	−	5.87278e53i	0.878033	−	2.16846i
$931$			2.07301e52i			0.0750769i
$932$	−2.03765e53	−	1.97373e53i	−0.723840	−	0.701135i
$933$	4.69261e53			1.63510
$934$	3.12770e53	+	1.26644e53i	1.06901	+	0.432855i
$935$			6.13484e53i			2.05681i
$936$	−2.22571e53	+	9.84869e52i	−0.731986	+	0.323902i
$937$	1.11283e53			0.359018			0.179509	−	0.983756i	$-0.442549\pi$
$937$	1.11283e53			0.359018			0.179509	+	0.983756i	$0.442549\pi$
$938$	2.02352e52	−	4.99745e52i	0.0640409	−	0.158160i
$939$		−	1.28986e53i		−	0.400462i
$940$	−1.57960e53	+	1.63075e53i	−0.481113	+	0.496692i
$941$	5.75058e53			1.71830			0.859149	−	0.511725i	$-0.170993\pi$
$941$	5.75058e53			1.71830			0.859149	+	0.511725i	$0.170993\pi$
$942$	−4.40301e53	−	1.78283e53i	−1.29072	−	0.522629i
$943$		−	7.04685e52i		−	0.202668i
$944$	−3.57464e53	+	1.13939e52i	−1.00864	+	0.0321496i
$945$	5.05427e52			0.139922
$946$	−1.45340e53	+	3.58942e53i	−0.394770	+	0.974953i
$947$			3.74447e53i			0.997909i	0.866628	+	0.498955i	$0.166283\pi$
$947$			3.74447e53i			0.997909i	−0.866628	+	0.498955i	$0.833717\pi$
$948$	5.37884e53	+	5.21012e53i	1.40650	+	1.36238i
$949$	−6.24212e53			−1.60155
$950$	5.63562e52	+	2.28193e52i	0.141879	+	0.0574483i
$951$			1.73003e53i			0.427370i
$952$	1.72469e52	+	3.89763e52i	0.0418067	+	0.0944792i
$953$	4.13944e53			0.984622			0.492311	−	0.870419i	$-0.336152\pi$
$953$	4.13944e53			0.984622			0.492311	+	0.870419i	$0.336152\pi$
$954$	1.87123e52	−	4.62132e52i	0.0436773	−	0.107869i
$955$		−	1.55140e53i		−	0.355356i
$956$	1.21363e52	−	1.25293e52i	0.0272799	−	0.0281633i
$957$	−2.61962e53			−0.577861
$958$	−2.87233e52	−	1.16304e52i	−0.0621807	−	0.0251777i
$959$		−	4.79366e52i		−	0.101843i
$960$	−7.60772e53	−	6.91316e53i	−1.58625	−	1.44143i
$961$	−9.35266e52			−0.191388
$962$	3.23322e53	−	7.98500e53i	0.649358	−	1.60370i
$963$		−	2.65211e53i		−	0.522779i
$964$	−5.48283e53	−	5.31085e53i	−1.06076	−	1.02749i
$965$	9.90031e53			1.88000
$966$	−3.41873e52	−	1.38428e52i	−0.0637202	−	0.0258010i
$967$		−	6.95431e53i		−	1.27226i	−0.771580	−	0.636132i	$-0.780533\pi$
$967$		−	6.95431e53i		−	1.27226i	0.771580	−	0.636132i	$-0.219467\pi$
$968$	7.98597e53	−	3.53377e53i	1.43407	−	0.634573i
$969$	−3.98405e52			−0.0702259
$970$	−1.86458e53	+	4.60490e53i	−0.322619	+	0.796763i
$971$			3.68158e53i			0.625299i	0.949869	+	0.312650i	$0.101217\pi$
$971$			3.68158e53i			0.625299i	−0.949869	+	0.312650i	$0.898783\pi$
$972$	4.03208e53	−	4.16264e53i	0.672258	−	0.694027i
$973$	−6.91928e52			−0.113248
$974$	1.57402e53	+	6.37340e52i	0.252901	+	0.102402i
$975$			2.36144e54i			3.72473i
$976$	1.73385e52	+	5.43969e53i	0.0268482	+	0.842320i
$977$	−6.57791e53			−0.999968			−0.499984	−	0.866035i	$-0.666661\pi$
$977$	−6.57791e53			−0.999968			−0.499984	+	0.866035i	$0.666661\pi$
$978$	2.69361e53	−	6.65234e53i	0.402008	−	0.992830i
$979$		−	7.56248e51i		−	0.0110809i
$980$	−8.47897e53	−	8.21302e53i	−1.21976	−	1.18150i
$981$	−4.47274e53			−0.631730
$982$	1.07961e54	+	4.37145e53i	1.49713	+	0.606203i
$983$		−	9.93199e53i		−	1.35230i	−0.736764	−	0.676150i	$-0.763647\pi$
$983$		−	9.93199e53i		−	1.35230i	0.736764	−	0.676150i	$-0.236353\pi$
$984$	1.90546e53	+	4.30616e53i	0.254735	+	0.575676i
$985$	1.49407e54			1.96119
$986$	−6.28744e52	+	1.55279e53i	−0.0810381	+	0.200138i
$987$		−	5.44348e52i		−	0.0688919i
$988$	−6.45297e52	+	6.66193e52i	−0.0801926	+	0.0827894i
$989$	−2.14307e53			−0.261519
$990$	1.14147e54	+	4.62195e53i	1.36783	+	0.553850i
$991$		−	2.96029e53i		−	0.348344i	−0.984715	−	0.174172i	$-0.944275\pi$
$991$		−	2.96029e53i		−	0.348344i	0.984715	−	0.174172i	$-0.0557248\pi$
$992$	−3.26438e53	+	8.86375e53i	−0.377216	+	1.02425i
$993$	8.35380e53			0.947977
$994$	1.64055e52	−	4.05162e52i	0.0182824	−	0.0451516i
$995$		−	1.94083e54i		−	2.12408i
$996$	−2.89617e53	−	2.80532e53i	−0.311283	−	0.301519i
$997$	−1.49692e54			−1.58011			−0.790053	−	0.613039i	$-0.789947\pi$
$997$	−1.49692e54			−1.58011			−0.790053	+	0.613039i	$0.789947\pi$
$998$	−2.18855e53	−	8.86170e52i	−0.226886	−	0.0918687i
$999$			6.54208e53i			0.666096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.37.b.b.3.9	✓	16
4.3	odd	2	inner	4.37.b.b.3.10	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.37.b.b.3.9	✓	16	1.1	even	1	trivial
4.37.b.b.3.10	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)

\(f(q)\)	\(=\)	\(q+(98385.8 - 242981. i) q^{2} -4.79482e8i q^{3} +(-4.93600e10 - 4.78117e10i) q^{4} +6.60636e12 q^{5} +(-1.16505e14 - 4.71742e13i) q^{6} +2.27014e14i q^{7} +(-1.64737e16 + 7.28954e15i) q^{8} -7.98083e16 q^{9} +O(q^{10})\)	\(q+(98385.8 - 242981. i) q^{2} -4.79482e8i q^{3} +(-4.93600e10 - 4.78117e10i) q^{4} +6.60636e12 q^{5} +(-1.16505e14 - 4.71742e13i) q^{6} +2.27014e14i q^{7} +(-1.64737e16 + 7.28954e15i) q^{8} -7.98083e16 q^{9} +(6.49972e17 - 1.60522e18i) q^{10} -8.91010e18i q^{11} +(-2.29249e19 + 2.36672e19i) q^{12} -1.69290e20 q^{13} +(5.51601e19 + 2.23350e19i) q^{14} -3.16763e21i q^{15} +(1.50445e20 + 4.71997e21i) q^{16} -1.04222e22 q^{17} +(-7.85200e21 + 1.93919e22i) q^{18} +7.97251e21i q^{19} +(-3.26090e23 - 3.15861e23i) q^{20} +1.08849e23 q^{21} +(-2.16498e24 - 8.76627e23i) q^{22} -1.29261e24i q^{23} +(3.49520e24 + 7.89882e24i) q^{24} +2.90921e25 q^{25} +(-1.66557e25 + 4.11341e25i) q^{26} -3.37010e25i q^{27} +(1.08539e25 - 1.12054e25i) q^{28} +6.13174e25 q^{29} +(-7.69674e26 - 3.11650e26i) q^{30} +7.63022e26i q^{31} +(1.16166e27 + 4.27823e26i) q^{32} -4.27223e27 q^{33} +(-1.02539e27 + 2.53239e27i) q^{34} +1.49974e27i q^{35} +(3.93934e27 + 3.81577e27i) q^{36} -1.94121e28 q^{37} +(1.93717e27 + 7.84381e26i) q^{38} +8.11713e28i q^{39} +(-1.08831e29 + 4.81573e28i) q^{40} +5.45164e28 q^{41} +(1.07092e28 - 2.64483e28i) q^{42} -1.65794e29i q^{43} +(-4.26007e29 + 4.39802e29i) q^{44} -5.27243e29 q^{45} +(-3.14080e29 - 1.27174e29i) q^{46} -5.00094e29i q^{47} +(2.26314e30 - 7.21357e28i) q^{48} +2.60020e30 q^{49} +(2.86225e30 - 7.06882e30i) q^{50} +4.99724e30i q^{51} +(8.35613e30 + 8.09403e30i) q^{52} -2.38312e30 q^{53} +(-8.18870e30 - 3.31570e30i) q^{54} -5.88633e31i q^{55} +(-1.65483e30 - 3.73975e30i) q^{56} +3.82267e30 q^{57} +(6.03276e30 - 1.48990e31i) q^{58} +7.57344e31i q^{59} +(-1.51450e32 + 1.56354e32i) q^{60} +1.15248e32 q^{61} +(1.85400e32 + 7.50705e31i) q^{62} -1.81176e31i q^{63} +(2.18244e32 - 2.40171e32i) q^{64} -1.11839e33 q^{65} +(-4.20327e32 + 1.03807e33i) q^{66} -9.05989e32i q^{67} +(5.14438e32 + 4.98302e32i) q^{68} -6.19784e32 q^{69} +(3.64408e32 + 1.47553e32i) q^{70} -7.34519e32i q^{71} +(1.31473e33 - 5.81766e32i) q^{72} +3.68724e33 q^{73} +(-1.90988e33 + 4.71677e33i) q^{74} -1.39491e34i q^{75} +(3.81179e32 - 3.93523e32i) q^{76} +2.02272e33 q^{77} +(1.97231e34 + 7.98610e33i) q^{78} -2.27270e34i q^{79} +(9.93894e32 + 3.11818e34i) q^{80} -2.81378e34 q^{81} +(5.36364e33 - 1.32465e34i) q^{82} +1.22370e34i q^{83} +(-5.37279e33 - 5.20427e33i) q^{84} -6.88526e34 q^{85} +(-4.02848e34 - 1.63118e34i) q^{86} -2.94006e34i q^{87} +(6.49505e34 + 1.46782e35i) q^{88} +8.48753e32 q^{89} +(-5.18732e34 + 1.28110e35i) q^{90} -3.84311e34i q^{91} +(-6.18019e34 + 6.38032e34i) q^{92} +3.65855e35 q^{93} +(-1.21513e35 - 4.92021e34i) q^{94} +5.26692e34i q^{95} +(2.05133e35 - 5.56997e35i) q^{96} -2.86871e35 q^{97} +(2.55822e35 - 6.31798e35i) q^{98} +7.11100e35i 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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