LMFDB - Embedded newform 4.37.b.b.3.8

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			3.8
Root			$-8.47589e6i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.37.b.b.3.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-39525.7 + 259147. i) q^{2} -1.35614e8i q^{3} +(-6.55949e10 - 2.04859e10i) q^{4} -1.24080e12 q^{5} +(3.51440e13 + 5.36025e12i) q^{6} +4.20496e14i q^{7} +(7.90156e15 - 1.61890e16i) q^{8} +1.31703e17 q^{9} +O(q^{10})$	\(q+(-39525.7 + 259147. i) q^{2} -1.35614e8i q^{3} +(-6.55949e10 - 2.04859e10i) q^{4} -1.24080e12 q^{5} +(3.51440e13 + 5.36025e12i) q^{6} +4.20496e14i q^{7} +(7.90156e15 - 1.61890e16i) q^{8} +1.31703e17 q^{9} +(4.90435e16 - 3.21549e17i) q^{10} -3.22138e18i q^{11} +(-2.77819e18 + 8.89561e18i) q^{12} -2.28918e19 q^{13} +(-1.08970e20 - 1.66204e19i) q^{14} +1.68270e20i q^{15} +(3.88302e21 + 2.68755e21i) q^{16} +6.53319e21 q^{17} +(-5.20567e21 + 3.41305e22i) q^{18} +1.34943e23i q^{19} +(8.13901e22 + 2.54189e22i) q^{20} +5.70253e22 q^{21} +(8.34811e23 + 1.27327e23i) q^{22} -4.96373e22i q^{23} +(-2.19546e24 - 1.07156e24i) q^{24} -1.30123e25 q^{25} +(9.04813e23 - 5.93233e24i) q^{26} -3.82158e25i q^{27} +(8.61427e24 - 2.75824e25i) q^{28} -1.19240e26 q^{29} +(-4.36067e25 - 6.65100e24i) q^{30} +7.37399e26i q^{31} +(-8.49949e26 + 9.00045e26i) q^{32} -4.36865e26 q^{33} +(-2.58229e26 + 1.69306e27i) q^{34} -5.21751e26i q^{35} +(-8.63907e27 - 2.69807e27i) q^{36} -2.48980e28 q^{37} +(-3.49701e28 - 5.33372e27i) q^{38} +3.10445e27i q^{39} +(-9.80425e27 + 2.00873e28i) q^{40} -1.04174e29 q^{41} +(-2.25397e27 + 1.47779e28i) q^{42} +2.34072e29i q^{43} +(-6.59930e28 + 2.11306e29i) q^{44} -1.63417e29 q^{45} +(1.28634e28 + 1.96195e27i) q^{46} -6.54567e29i q^{47} +(3.64470e29 - 5.26593e29i) q^{48} +2.47491e30 q^{49} +(5.14322e29 - 3.37211e30i) q^{50} -8.85993e29i q^{51} +(1.50158e30 + 4.68959e29i) q^{52} +8.42648e30 q^{53} +(9.90352e30 + 1.51051e30i) q^{54} +3.99708e30i q^{55} +(6.80742e30 + 3.32258e30i) q^{56} +1.83002e31 q^{57} +(4.71306e30 - 3.09007e31i) q^{58} +6.65287e31i q^{59} +(3.44717e30 - 1.10377e31i) q^{60} -1.74158e32 q^{61} +(-1.91095e32 - 2.91462e31i) q^{62} +5.53808e31i q^{63} +(-1.99649e32 - 2.55837e32i) q^{64} +2.84041e31 q^{65} +(1.72674e31 - 1.13212e32i) q^{66} +1.02480e33i q^{67} +(-4.28544e32 - 1.33839e32i) q^{68} -6.73153e30 q^{69} +(1.35210e32 + 2.06226e31i) q^{70} +3.10980e33i q^{71} +(1.04066e33 - 2.13215e33i) q^{72} +3.37473e33 q^{73} +(9.84112e32 - 6.45225e33i) q^{74} +1.76466e33i q^{75} +(2.76443e33 - 8.85157e33i) q^{76} +1.35458e33 q^{77} +(-8.04509e32 - 1.22706e32i) q^{78} +1.58850e34i q^{79} +(-4.81804e33 - 3.33471e33i) q^{80} +1.45854e34 q^{81} +(4.11757e33 - 2.69965e34i) q^{82} +6.39239e34i q^{83} +(-3.74057e33 - 1.16822e33i) q^{84} -8.10637e33 q^{85} +(-6.06590e34 - 9.25185e33i) q^{86} +1.61707e34i q^{87} +(-5.21509e34 - 2.54539e34i) q^{88} -1.63956e35 q^{89} +(6.45919e33 - 4.23491e34i) q^{90} -9.62590e33i q^{91} +(-1.01687e33 + 3.25596e33i) q^{92} +1.00002e35 q^{93} +(1.69629e35 + 2.58722e34i) q^{94} -1.67437e35i q^{95} +(1.22059e35 + 1.15265e35i) q^{96} +3.39752e35 q^{97} +(-9.78227e34 + 6.41367e35i) q^{98} -4.24267e35i 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 $

$2$	−39525.7	+	259147.i	−0.150779	+	0.988568i
$2$	−39525.7	+	259147.i	−0.150779	+	0.988568i
$3$		−	1.35614e8i		−	0.350044i	−0.984565	−	0.175022i	$-0.944000\pi$
$3$		−	1.35614e8i		−	0.350044i	0.984565	−	0.175022i	$-0.0559997\pi$
$4$	−6.55949e10	−	2.04859e10i	−0.954532	−	0.298110i
$5$	−1.24080e12			−0.325268			−0.162634	−	0.986686i	$-0.551999\pi$
$5$	−1.24080e12			−0.325268			−0.162634	+	0.986686i	$0.551999\pi$
$6$	3.51440e13	+	5.36025e12i	0.346042	+	0.0527792i
$7$			4.20496e14i			0.258225i	0.991630	+	0.129112i	$0.0412128\pi$
$7$			4.20496e14i			0.258225i	−0.991630	+	0.129112i	$0.958787\pi$
$8$	7.90156e15	−	1.61890e16i	0.438625	−	0.898670i
$9$	1.31703e17			0.877469
$10$	4.90435e16	−	3.21549e17i	0.0490435	−	0.321549i
$11$		−	3.22138e18i		−	0.579394i	−0.957118	−	0.289697i	$-0.906446\pi$
$11$		−	3.22138e18i		−	0.579394i	0.957118	−	0.289697i	$-0.0935545\pi$
$12$	−2.77819e18	+	8.89561e18i	−0.104352	+	0.334128i
$13$	−2.28918e19			−0.203563			−0.101781	−	0.994807i	$-0.532454\pi$
$13$	−2.28918e19			−0.203563			−0.101781	+	0.994807i	$0.532454\pi$
$14$	−1.08970e20	−	1.66204e19i	−0.255272	−	0.0389348i
$15$			1.68270e20i			0.113858i
$16$	3.88302e21	+	2.68755e21i	0.822261	+	0.569110i
$17$	6.53319e21			0.464563			0.232281	−	0.972649i	$-0.425381\pi$
$17$	6.53319e21			0.464563			0.232281	+	0.972649i	$0.425381\pi$
$18$	−5.20567e21	+	3.41305e22i	−0.132304	+	0.867437i
$19$			1.34943e23i			1.29594i	0.761665	+	0.647971i	$0.224382\pi$
$19$			1.34943e23i			1.29594i	−0.761665	+	0.647971i	$0.775618\pi$
$20$	8.13901e22	+	2.54189e22i	0.310479	+	0.0969656i
$21$	5.70253e22			0.0903900
$22$	8.34811e23	+	1.27327e23i	0.572770	+	0.0873602i
$23$		−	4.96373e22i		−	0.0153006i	−0.999971	−	0.00765028i	$-0.997565\pi$
$23$		−	4.96373e22i		−	0.0153006i	0.999971	−	0.00765028i	$-0.00243518\pi$
$24$	−2.19546e24	−	1.07156e24i	−0.314574	−	0.153538i
$25$	−1.30123e25			−0.894201
$26$	9.04813e23	−	5.93233e24i	0.0306930	−	0.201236i
$27$		−	3.82158e25i		−	0.657197i
$28$	8.61427e24	−	2.75824e25i	0.0769793	−	0.246484i
$29$	−1.19240e26			−0.566577			−0.283288	−	0.959035i	$-0.591425\pi$
$29$	−1.19240e26			−0.566577			−0.283288	+	0.959035i	$0.591425\pi$
$30$	−4.36067e25	−	6.65100e24i	−0.112556	−	0.0171674i
$31$			7.37399e26i			1.05485i	0.849601	+	0.527427i	$0.176843\pi$
$31$			7.37399e26i			1.05485i	−0.849601	+	0.527427i	$0.823157\pi$
$32$	−8.49949e26	+	9.00045e26i	−0.686584	+	0.727051i
$33$	−4.36865e26			−0.202813
$34$	−2.58229e26	+	1.69306e27i	−0.0700462	+	0.459252i
$35$		−	5.21751e26i		−	0.0839922i
$36$	−8.63907e27	−	2.69807e27i	−0.837572	−	0.261582i
$37$	−2.48980e28			−1.47412			−0.737061	−	0.675826i	$-0.763787\pi$
$37$	−2.48980e28			−1.47412			−0.737061	+	0.675826i	$0.763787\pi$
$38$	−3.49701e28	−	5.33372e27i	−1.28113	−	0.195400i
$39$			3.10445e27i			0.0712560i
$40$	−9.80425e27	+	2.00873e28i	−0.142671	+	0.292309i
$41$	−1.04174e29			−0.971968			−0.485984	−	0.873968i	$-0.661539\pi$
$41$	−1.04174e29			−0.971968			−0.485984	+	0.873968i	$0.661539\pi$
$42$	−2.25397e27	+	1.47779e28i	−0.0136289	+	0.0893566i
$43$			2.34072e29i			0.926651i	0.886188	+	0.463326i	$0.153344\pi$
$43$			2.34072e29i			0.926651i	−0.886188	+	0.463326i	$0.846656\pi$
$44$	−6.59930e28	+	2.11306e29i	−0.172723	+	0.553049i
$45$	−1.63417e29			−0.285413
$46$	1.28634e28	+	1.96195e27i	0.0151256	+	0.00230700i
$47$		−	6.54567e29i		−	0.522628i	−0.965254	−	0.261314i	$-0.915844\pi$
$47$		−	6.54567e29i		−	0.522628i	0.965254	−	0.261314i	$-0.0841557\pi$
$48$	3.64470e29	−	5.26593e29i	0.199214	−	0.287828i
$49$	2.47491e30			0.933320
$50$	5.14322e29	−	3.37211e30i	0.134826	−	0.883978i
$51$		−	8.85993e29i		−	0.162618i
$52$	1.50158e30	+	4.68959e29i	0.194307	+	0.0606841i
$53$	8.42648e30			0.773893			0.386946	−	0.922102i	$-0.373530\pi$
$53$	8.42648e30			0.773893			0.386946	+	0.922102i	$0.373530\pi$
$54$	9.90352e30	+	1.51051e30i	0.649684	+	0.0990913i
$55$			3.99708e30i			0.188458i
$56$	6.80742e30	+	3.32258e30i	0.232059	+	0.113264i
$57$	1.83002e31			0.453637
$58$	4.71306e30	−	3.09007e31i	0.0854277	−	0.560099i
$59$			6.65287e31i			0.886488i	0.896401	+	0.443244i	$0.146172\pi$
$59$			6.65287e31i			0.886488i	−0.896401	+	0.443244i	$0.853828\pi$
$60$	3.44717e30	−	1.10377e31i	0.0339422	−	0.108681i
$61$	−1.74158e32			−1.27352			−0.636761	−	0.771062i	$-0.719726\pi$
$61$	−1.74158e32			−1.27352			−0.636761	+	0.771062i	$0.719726\pi$
$62$	−1.91095e32	−	2.91462e31i	−1.04279	−	0.159049i
$63$			5.53808e31i			0.226584i
$64$	−1.99649e32	−	2.55837e32i	−0.615217	−	0.788358i
$65$	2.84041e31			0.0662125
$66$	1.72674e31	−	1.13212e32i	0.0305799	−	0.200495i
$67$			1.02480e33i			1.38450i	0.721656	+	0.692252i	$0.243381\pi$
$67$			1.02480e33i			1.38450i	−0.721656	+	0.692252i	$0.756619\pi$
$68$	−4.28544e32	−	1.33839e32i	−0.443440	−	0.138491i
$69$	−6.73153e30			−0.00535587
$70$	1.35210e32	+	2.06226e31i	0.0830319	+	0.0126642i
$71$			3.10980e33i			1.47939i	0.672942	+	0.739695i	$0.265030\pi$
$71$			3.10980e33i			1.47939i	−0.672942	+	0.739695i	$0.734970\pi$
$72$	1.04066e33	−	2.13215e33i	0.384880	−	0.788555i
$73$	3.37473e33			0.973704			0.486852	−	0.873484i	$-0.338145\pi$
$73$	3.37473e33			0.973704			0.486852	+	0.873484i	$0.338145\pi$
$74$	9.84112e32	−	6.45225e33i	0.222266	−	1.45727i
$75$			1.76466e33i			0.313010i
$76$	2.76443e33	−	8.85157e33i	0.386333	−	1.23702i
$77$	1.35458e33			0.149614
$78$	−8.04509e32	−	1.22706e32i	−0.0704414	−	0.0107439i
$79$			1.58850e34i			1.10586i	0.833228	+	0.552929i	$0.186490\pi$
$79$			1.58850e34i			1.10586i	−0.833228	+	0.552929i	$0.813510\pi$
$80$	−4.81804e33	−	3.33471e33i	−0.267455	−	0.185113i
$81$	1.45854e34			0.647421
$82$	4.11757e33	−	2.69965e34i	0.146552	−	0.960856i
$83$			6.39239e34i			1.82918i	0.404377	+	0.914592i	$0.367488\pi$
$83$			6.39239e34i			1.82918i	−0.404377	+	0.914592i	$0.632512\pi$
$84$	−3.74057e33	−	1.16822e33i	−0.0862801	−	0.0269461i
$85$	−8.10637e33			−0.151107
$86$	−6.06590e34	−	9.25185e33i	−0.916058	−	0.139719i
$87$			1.61707e34i			0.198327i
$88$	−5.21509e34	−	2.54539e34i	−0.520684	−	0.254136i
$89$	−1.63956e35			−1.33570			−0.667849	−	0.744296i	$-0.732785\pi$
$89$	−1.63956e35			−1.33570			−0.667849	+	0.744296i	$0.732785\pi$
$90$	6.45919e33	−	4.23491e34i	0.0430341	−	0.282150i
$91$		−	9.62590e33i		−	0.0525650i
$92$	−1.01687e33	+	3.25596e33i	−0.00456125	+	0.0146049i
$93$	1.00002e35			0.369245
$94$	1.69629e35	+	2.58722e34i	0.516653	+	0.0788011i
$95$		−	1.67437e35i		−	0.421528i
$96$	1.22059e35	+	1.15265e35i	0.254500	+	0.240335i
$97$	3.39752e35			0.587855			0.293928	−	0.955828i	$-0.405038\pi$
$97$	3.39752e35			0.587855			0.293928	+	0.955828i	$0.405038\pi$
$98$	−9.78227e34	+	6.41367e35i	−0.140725	+	0.922650i
$99$		−	4.24267e35i		−	0.508400i
$100$	8.53543e35	+	2.66570e35i	0.853543	+	0.266570i
$101$	5.85528e35			0.489512			0.244756	−	0.969585i	$-0.421292\pi$
$101$	5.85528e35			0.489512			0.244756	+	0.969585i	$0.421292\pi$
$102$	2.29603e35	+	3.50195e34i	0.160758	+	0.0245193i
$103$		−	2.61949e36i		−	1.53868i	−0.638842	−	0.769338i	$-0.720586\pi$
$103$		−	2.61949e36i		−	1.53868i	0.638842	−	0.769338i	$-0.279414\pi$
$104$	−1.80881e35	+	3.70595e35i	−0.0892877	+	0.182936i
$105$	−7.07570e34			−0.0294010
$106$	−3.33063e35	+	2.18370e36i	−0.116687	+	0.765045i
$107$		−	3.83523e36i		−	1.13471i	−0.823474	−	0.567354i	$-0.807967\pi$
$107$		−	3.83523e36i		−	1.13471i	0.823474	−	0.567354i	$-0.192033\pi$
$108$	−7.82888e35	+	2.50676e36i	−0.195917	+	0.627315i
$109$	−7.01177e36			−1.48645			−0.743226	−	0.669041i	$-0.766705\pi$
$109$	−7.01177e36			−1.48645			−0.743226	+	0.669041i	$0.766705\pi$
$110$	−1.03583e36	−	1.57988e35i	−0.186304	−	0.0284155i
$111$			3.37653e36i			0.516008i
$112$	−1.13010e36	+	1.63280e36i	−0.146958	+	0.212328i
$113$	1.16771e36			0.129396			0.0646981	−	0.997905i	$-0.479392\pi$
$113$	1.16771e36			0.129396			0.0646981	+	0.997905i	$0.479392\pi$
$114$	−7.23328e35	+	4.74244e36i	−0.0683987	+	0.448450i
$115$			6.15900e34i			0.00497678i
$116$	7.82155e36	+	2.44275e36i	0.540815	+	0.168902i
$117$	−3.01492e36			−0.178620
$118$	−1.72407e37	−	2.62959e36i	−0.876353	−	0.133663i
$119$			2.74718e36i			0.119962i
$120$	2.72412e36	+	1.32960e36i	0.102321	+	0.0499410i
$121$	2.05354e37			0.664303
$122$	6.88372e36	−	4.51325e37i	0.192020	−	1.25896i
$123$			1.41275e37i			0.340232i
$124$	1.51063e37	−	4.83696e37i	0.314462	−	1.00689i
$125$	3.42017e37			0.616123
$126$	−1.43518e37	−	2.18897e36i	−0.223994	−	0.0341640i
$127$			5.02086e37i			0.679690i	0.940481	+	0.339845i	$0.110375\pi$
$127$			5.02086e37i			0.679690i	−0.940481	+	0.339845i	$0.889625\pi$
$128$	7.41906e37	−	4.16264e37i	0.872107	−	0.489316i
$129$	3.17434e37			0.324369
$130$	−1.12269e36	+	7.36083e36i	−0.00998343	+	0.0654555i
$131$			1.96393e38i			1.52140i	0.649106	+	0.760698i	$0.275143\pi$
$131$			1.96393e38i			1.52140i	−0.649106	+	0.760698i	$0.724857\pi$
$132$	2.86561e37	+	8.94960e36i	0.193592	+	0.0604606i
$133$	−5.67430e37			−0.334644
$134$	−2.65575e38	−	4.05061e37i	−1.36867	−	0.208754i
$135$			4.74182e37i			0.213765i
$136$	5.16224e37	−	1.05766e38i	0.203769	−	0.417489i
$137$	−2.08851e38			−0.722547			−0.361273	−	0.932460i	$-0.617658\pi$
$137$	−2.08851e38			−0.722547			−0.361273	+	0.932460i	$0.617658\pi$
$138$	2.66069e35	−	1.74446e36i	0.000807551	−	0.00529464i
$139$		−	3.11254e38i		−	0.829563i	−0.909921	−	0.414781i	$-0.863858\pi$
$139$		−	3.11254e38i		−	0.829563i	0.909921	−	0.414781i	$-0.136142\pi$
$140$	−1.06886e37	+	3.42242e37i	−0.0250389	+	0.0801732i
$141$	−8.87686e37			−0.182943
$142$	−8.05897e38	−	1.22917e38i	−1.46248	−	0.223060i
$143$			7.37431e37i			0.117943i
$144$	5.11407e38	+	3.53959e38i	0.721509	+	0.499377i
$145$	1.47953e38			0.184289
$146$	−1.33389e38	+	8.74550e38i	−0.146814	+	0.962573i
$147$		−	3.35634e38i		−	0.326703i
$148$	1.63318e39	+	5.10059e38i	1.40710	+	0.439450i
$149$	4.95139e38			0.377897			0.188949	−	0.981987i	$-0.439492\pi$
$149$	4.95139e38			0.377897			0.188949	+	0.981987i	$0.439492\pi$
$150$	−4.57306e38	−	6.97494e37i	−0.309431	−	0.0471952i
$151$		−	2.72979e39i		−	1.63887i	−0.573171	−	0.819436i	$-0.694287\pi$
$151$		−	2.72979e39i		−	1.63887i	0.573171	−	0.819436i	$-0.305713\pi$
$152$	2.18459e39	+	1.06626e39i	1.16462	+	0.568432i
$153$	8.60443e38			0.407640
$154$	−5.35407e37	+	3.51035e38i	−0.0225585	+	0.147903i
$155$		−	9.14964e38i		−	0.343110i
$156$	6.35976e37	−	2.03636e38i	0.0212421	−	0.0680161i
$157$	−1.89635e39			−0.564579			−0.282290	−	0.959329i	$-0.591094\pi$
$157$	−1.89635e39			−0.564579			−0.282290	+	0.959329i	$0.591094\pi$
$158$	−4.11655e39	−	6.27866e38i	−1.09322	−	0.166740i
$159$		−	1.14275e39i		−	0.270897i
$160$	1.05462e39	−	1.11678e39i	0.223324	−	0.236486i
$161$	2.08723e37			0.00395098
$162$	−5.76497e38	+	3.77975e39i	−0.0976173	+	0.640019i
$163$			1.43646e38i			0.0217730i	0.999941	+	0.0108865i	$0.00346534\pi$
$163$			1.43646e38i			0.0217730i	−0.999941	+	0.0108865i	$0.996535\pi$
$164$	6.83332e39	+	2.13411e39i	0.927774	+	0.289753i
$165$	5.42062e38			0.0659687
$166$	−1.65657e40	−	2.52664e39i	−1.80827	−	0.275802i
$167$			1.17608e40i			1.15223i	0.817368	+	0.576115i	$0.195432\pi$
$167$			1.17608e40i			1.15223i	−0.817368	+	0.576115i	$0.804568\pi$
$168$	4.50589e38	−	9.23183e38i	0.0396473	−	0.0812308i
$169$	−1.21222e40			−0.958562
$170$	3.20410e38	−	2.10074e39i	0.0227838	−	0.149380i
$171$			1.77724e40i			1.13715i
$172$	4.79518e39	−	1.53539e40i	0.276244	−	0.884518i
$173$	1.17976e40			0.612297			0.306149	−	0.951984i	$-0.400960\pi$
$173$	1.17976e40			0.612297			0.306149	+	0.951984i	$0.400960\pi$
$174$	−4.19058e39	−	6.39158e38i	−0.196060	−	0.0299035i
$175$		−	5.47164e39i		−	0.230905i
$176$	8.65761e39	−	1.25087e40i	0.329739	−	0.476413i
$177$	9.02224e39			0.310310
$178$	6.48050e39	−	4.24888e40i	0.201395	−	1.32043i
$179$			1.15903e40i			0.325643i	0.986656	+	0.162821i	$0.0520595\pi$
$179$			1.15903e40i			0.325643i	−0.986656	+	0.162821i	$0.947941\pi$
$180$	1.07194e40	+	3.34776e39i	0.272435	+	0.0850843i
$181$	1.73830e40			0.399862			0.199931	−	0.979810i	$-0.435928\pi$
$181$	1.73830e40			0.399862			0.199931	+	0.979810i	$0.435928\pi$
$182$	2.49452e39	+	3.80471e38i	0.0519640	+	0.00792568i
$183$			2.36183e40i			0.445789i
$184$	−8.03579e38	−	3.92212e38i	−0.0137502	−	0.00671120i
$185$	3.08934e40			0.479485
$186$	−3.95265e39	+	2.59152e40i	−0.0556743	+	0.365024i
$187$		−	2.10459e40i		−	0.269165i
$188$	−1.34094e40	+	4.29362e40i	−0.155800	+	0.498865i
$189$	1.60696e40			0.169704
$190$	4.33908e40	+	6.61807e39i	0.416709	+	0.0635574i
$191$		−	4.26867e40i		−	0.372986i	−0.982456	−	0.186493i	$-0.940288\pi$
$191$		−	4.26867e40i		−	0.372986i	0.982456	−	0.186493i	$-0.0597121\pi$
$192$	−3.46951e40	+	2.70753e40i	−0.275960	+	0.215353i
$193$	−1.11984e41			−0.811197			−0.405599	−	0.914051i	$-0.632937\pi$
$193$	−1.11984e41			−0.811197			−0.405599	+	0.914051i	$0.632937\pi$
$194$	−1.34289e40	+	8.80456e40i	−0.0886360	+	0.581135i
$195$		−	3.85200e39i		−	0.0231773i
$196$	−1.62342e41	−	5.07010e40i	−0.890883	−	0.278232i
$197$	−3.14173e41			−1.57317			−0.786586	−	0.617480i	$-0.788153\pi$
$197$	−3.14173e41			−1.57317			−0.786586	+	0.617480i	$0.788153\pi$
$198$	1.09947e41	+	1.67694e40i	0.502588	+	0.0766559i
$199$		−	4.13949e41i		−	1.72819i	−0.503330	−	0.864094i	$-0.667892\pi$
$199$		−	4.13949e41i		−	1.72819i	0.503330	−	0.864094i	$-0.332108\pi$
$200$	−1.02818e41	+	2.10657e41i	−0.392219	+	0.803592i
$201$	1.38978e41			0.484637
$202$	−2.31434e40	+	1.51738e41i	−0.0738080	+	0.483916i
$203$		−	5.01401e40i		−	0.146304i
$204$	−1.81504e40	+	5.81167e40i	−0.0484779	+	0.155224i
$205$	1.29260e41			0.316150
$206$	6.78834e41	+	1.03537e41i	1.52108	+	0.231999i
$207$		−	6.53741e39i		−	0.0134258i
$208$	−8.88891e40	−	6.15227e40i	−0.167382	−	0.115850i
$209$	4.34702e41			0.750860
$210$	2.79672e39	−	1.83365e40i	0.00443304	−	0.0290649i
$211$			5.11268e41i			0.743985i	0.928236	+	0.371992i	$0.121325\pi$
$211$			5.11268e41i			0.743985i	−0.928236	+	0.371992i	$0.878675\pi$
$212$	−5.52735e41	−	1.72625e41i	−0.738705	−	0.230705i
$213$	4.21734e41			0.517852
$214$	9.93889e41	+	1.51590e41i	1.12173	+	0.171090i
$215$		−	2.90436e41i		−	0.301410i
$216$	−6.18676e41	−	3.01965e41i	−0.590604	−	0.288263i
$217$	−3.10074e41			−0.272389
$218$	2.77145e41	−	1.81708e42i	0.224125	−	1.46946i
$219$		−	4.57661e41i		−	0.340840i
$220$	8.18841e40	−	2.62188e41i	0.0561812	−	0.179889i
$221$	−1.49556e41			−0.0945678
$222$	−8.75017e41	−	1.33460e41i	−0.510109	−	0.0778030i
$223$			2.98870e42i			1.60692i	0.595356	+	0.803462i	$0.297011\pi$
$223$			2.98870e42i			1.60692i	−0.595356	+	0.803462i	$0.702989\pi$
$224$	−3.78466e41	−	3.57401e41i	−0.187742	−	0.177293i
$225$	−1.71377e42			−0.784633
$226$	−4.61544e40	+	3.02607e41i	−0.0195102	+	0.127917i
$227$			3.18256e42i			1.24254i	0.783595	+	0.621272i	$0.213384\pi$
$227$			3.18256e42i			1.24254i	−0.783595	+	0.621272i	$0.786616\pi$
$228$	−1.20040e42	−	3.74897e41i	−0.433011	−	0.135234i
$229$	−1.23648e41			−0.0412238			−0.0206119	−	0.999788i	$-0.506561\pi$
$229$	−1.23648e41			−0.0412238			−0.0206119	+	0.999788i	$0.506561\pi$
$230$	−1.59609e40	−	2.43439e39i	−0.00491989	−	0.000750393i
$231$		−	1.83700e41i		−	0.0523714i
$232$	−9.42184e41	+	1.93038e42i	−0.248515	+	0.509166i
$233$	8.58420e41			0.209553			0.104776	−	0.994496i	$-0.466587\pi$
$233$	8.58420e41			0.209553			0.104776	+	0.994496i	$0.466587\pi$
$234$	1.19167e41	−	7.81308e41i	0.0269321	−	0.176578i
$235$			8.12185e41i			0.169994i
$236$	1.36290e42	−	4.36394e42i	0.264271	−	0.846181i
$237$	2.15423e42			0.387099
$238$	−7.11924e41	−	1.08584e41i	−0.118590	−	0.0180876i
$239$		−	7.66299e42i		−	1.18368i	−0.806054	−	0.591842i	$-0.798401\pi$
$239$		−	7.66299e42i		−	1.18368i	0.806054	−	0.591842i	$-0.201599\pi$
$240$	−4.52234e41	+	6.53396e41i	−0.0647979	+	0.0936211i
$241$	1.20673e42			0.160437			0.0802183	−	0.996777i	$-0.474438\pi$
$241$	1.20673e42			0.160437			0.0802183	+	0.996777i	$0.474438\pi$
$242$	−8.11676e41	+	5.32169e42i	−0.100163	+	0.656708i
$243$		−	7.71398e42i		−	0.883823i
$244$	1.14239e43	+	3.56779e42i	1.21562	+	0.379649i
$245$	−3.07087e42			−0.303579
$246$	−3.66111e42	−	5.58402e41i	−0.336342	−	0.0512997i
$247$		−	3.08908e42i		−	0.263806i
$248$	1.19378e43	+	5.82660e42i	0.947966	+	0.462685i
$249$	8.66899e42			0.640296
$250$	−1.35185e42	+	8.86327e42i	−0.0928982	+	0.609079i
$251$		−	5.34548e42i		−	0.341869i	−0.985282	−	0.170934i	$-0.945321\pi$
$251$		−	5.34548e42i		−	0.341869i	0.985282	−	0.170934i	$-0.0546786\pi$
$252$	1.13453e42	−	3.63270e42i	0.0675469	−	0.216282i
$253$	−1.59901e41			−0.00886505
$254$	−1.30114e43	−	1.98453e42i	−0.671920	−	0.102483i
$255$			1.09934e42i			0.0528943i
$256$	7.85492e42	+	2.08716e43i	0.352227	+	0.935915i
$257$	−2.19858e43			−0.919064			−0.459532	−	0.888161i	$-0.651983\pi$
$257$	−2.19858e43			−0.919064			−0.459532	+	0.888161i	$0.651983\pi$
$258$	−1.25468e42	+	8.22622e42i	−0.0489079	+	0.320661i
$259$		−	1.04695e43i		−	0.380655i
$260$	−1.86316e42	−	5.81884e41i	−0.0632019	−	0.0197386i
$261$	−1.57043e43			−0.497154
$262$	−5.08946e43	−	7.76257e42i	−1.50400	−	0.229394i
$263$		−	2.34032e42i		−	0.0645762i	−0.999479	−	0.0322881i	$-0.989721\pi$
$263$		−	2.34032e42i		−	0.0645762i	0.999479	−	0.0322881i	$-0.0102794\pi$
$264$	−3.45192e42	+	7.07241e42i	−0.0889589	+	0.182262i
$265$	−1.04556e43			−0.251723
$266$	2.24281e42	−	1.47048e43i	0.0504572	−	0.330818i
$267$			2.22348e43i			0.467554i
$268$	2.09941e43	−	6.72219e43i	0.412734	−	1.32155i
$269$	5.58028e43			1.02592			0.512961	−	0.858412i	$-0.328548\pi$
$269$	5.58028e43			1.02592			0.512961	+	0.858412i	$0.328548\pi$
$270$	−1.22883e43	−	1.87424e42i	−0.211321	−	0.0322312i
$271$			5.41976e43i			0.872033i	0.899939	+	0.436017i	$0.143611\pi$
$271$			5.41976e43i			0.872033i	−0.899939	+	0.436017i	$0.856389\pi$
$272$	2.53685e43	+	1.75583e43i	0.381992	+	0.264388i
$273$	−1.30541e42			−0.0184001
$274$	8.25498e42	−	5.41231e43i	0.108945	−	0.714286i
$275$			4.19177e43i			0.518094i
$276$	4.41554e41	+	1.37902e41i	0.00511235	+	0.00159664i
$277$	−2.91199e43			−0.315903			−0.157952	−	0.987447i	$-0.550489\pi$
$277$	−2.91199e43			−0.315903			−0.157952	+	0.987447i	$0.550489\pi$
$278$	8.06607e43	+	1.23026e43i	0.820079	+	0.125080i
$279$			9.71180e43i			0.925601i
$280$	−8.44664e42	−	4.12265e42i	−0.0754813	−	0.0368410i
$281$	1.85422e44			1.55399			0.776995	−	0.629507i	$-0.216743\pi$
$281$	1.85422e44			1.55399			0.776995	+	0.629507i	$0.216743\pi$
$282$	3.50864e42	−	2.30041e43i	0.0275839	−	0.180851i
$283$		−	5.61975e43i		−	0.414535i	−0.978284	−	0.207268i	$-0.933543\pi$
$283$		−	5.61975e43i		−	0.414535i	0.978284	−	0.207268i	$-0.0664571\pi$
$284$	6.37073e43	−	2.03987e44i	0.441021	−	1.41212i
$285$	−2.27069e43			−0.147553
$286$	−1.91103e43	−	2.91475e42i	−0.116595	−	0.0177833i
$287$		−	4.38050e43i		−	0.250986i
$288$	−1.11941e44	+	1.18539e44i	−0.602456	+	0.637965i
$289$	−1.55088e44			−0.784181
$290$	−5.84795e42	+	3.83416e43i	−0.0277869	+	0.182182i
$291$		−	4.60752e43i		−	0.205775i
$292$	−2.21365e44	−	6.91345e43i	−0.929432	−	0.290271i
$293$	−6.61412e43			−0.261129			−0.130564	−	0.991440i	$-0.541679\pi$
$293$	−6.61412e43			−0.261129			−0.130564	+	0.991440i	$0.541679\pi$
$294$	8.69785e43	+	1.32662e43i	0.322968	+	0.0492599i
$295$		−	8.25487e43i		−	0.288346i
$296$	−1.96733e44	+	4.03074e44i	−0.646586	+	1.32475i
$297$	−1.23108e44			−0.380776
$298$	−1.95707e43	+	1.28314e44i	−0.0569789	+	0.373577i
$299$			1.13629e42i			0.00311463i
$300$	3.61507e43	−	1.15753e44i	0.0933113	−	0.298778i
$301$	−9.84262e43			−0.239284
$302$	7.07418e44	+	1.07897e44i	1.62014	+	0.247107i
$303$		−	7.94060e43i		−	0.171351i
$304$	−3.62666e44	+	5.23986e44i	−0.737534	+	1.06560i
$305$	2.16095e44			0.414236
$306$	−3.40096e43	+	2.22981e44i	−0.0614633	+	0.402979i
$307$		−	6.49386e44i		−	1.10666i	−0.832964	−	0.553328i	$-0.813358\pi$
$307$		−	6.49386e44i		−	1.10666i	0.832964	−	0.553328i	$-0.186642\pi$
$308$	−8.88535e43	−	2.77498e43i	−0.142811	−	0.0446013i
$309$	−3.55241e44			−0.538604
$310$	2.37110e44	+	3.61646e43i	0.339187	+	0.0517337i
$311$		−	4.95093e44i		−	0.668344i	−0.942512	−	0.334172i	$-0.891543\pi$
$311$		−	4.95093e44i		−	0.668344i	0.942512	−	0.334172i	$-0.108457\pi$
$312$	5.02580e43	+	2.45300e43i	0.0640357	+	0.0312547i
$313$	−5.21360e43			−0.0627104			−0.0313552	−	0.999508i	$-0.509982\pi$
$313$	−5.21360e43			−0.0627104			−0.0313552	+	0.999508i	$0.509982\pi$
$314$	7.49546e43	−	4.91434e44i	0.0851265	−	0.558125i
$315$		−	6.87164e43i		−	0.0737005i
$316$	3.25419e44	−	1.04197e45i	0.329667	−	1.05558i
$317$	1.74925e45			1.67411			0.837056	−	0.547117i	$-0.184275\pi$
$317$	1.74925e45			1.67411			0.837056	+	0.547117i	$0.184275\pi$
$318$	2.96141e44	+	4.51681e43i	0.267800	+	0.0408454i
$319$			3.84118e44i			0.328271i
$320$	2.47725e44	+	3.17442e44i	0.200110	+	0.256428i
$321$	−5.20112e44			−0.397198
$322$	−8.24994e41	+	5.40900e42i	−0.000595724	+	0.00390581i
$323$			8.81607e44i			0.602046i
$324$	−9.56725e44	−	2.98795e44i	−0.617984	−	0.193003i
$325$	2.97875e44			0.182026
$326$	−3.72255e43	−	5.67772e42i	−0.0215240	−	0.00328290i
$327$			9.50897e44i			0.520324i
$328$	−8.23141e44	+	1.68648e45i	−0.426329	+	0.873479i
$329$	2.75243e44			0.134955
$330$	−2.14254e43	+	1.40474e44i	−0.00994667	+	0.0652145i
$331$			3.93879e45i			1.73164i	0.500352	+	0.865822i	$0.333204\pi$
$331$			3.93879e45i			1.73164i	−0.500352	+	0.865822i	$0.666796\pi$
$332$	1.30954e45	−	4.19308e45i	0.545298	−	1.74601i
$333$	−3.27915e45			−1.29350
$334$	−3.04777e45	−	4.64853e44i	−1.13906	−	0.173732i
$335$		−	1.27157e45i		−	0.450335i
$336$	2.21430e44	+	1.53258e44i	0.0743242	+	0.0514419i
$337$	−1.37207e45			−0.436553			−0.218277	−	0.975887i	$-0.570044\pi$
$337$	−1.37207e45			−0.436553			−0.218277	+	0.975887i	$0.570044\pi$
$338$	4.79138e44	−	3.14143e45i	0.144531	−	0.947603i
$339$		−	1.58358e44i		−	0.0452944i
$340$	5.31737e44	+	1.66067e44i	0.144237	+	0.0450466i
$341$	2.37544e45			0.611175
$342$	−4.60568e45	−	7.02469e44i	−1.12415	−	0.171458i
$343$			2.15574e45i			0.499231i
$344$	3.78939e45	+	1.84953e45i	0.832754	+	0.406452i
$345$	8.35248e42			0.00174209
$346$	−4.66307e44	+	3.05730e45i	−0.0923214	+	0.605297i
$347$		−	3.78358e45i		−	0.711169i	−0.934644	−	0.355585i	$-0.884282\pi$
$347$		−	3.78358e45i		−	0.711169i	0.934644	−	0.355585i	$-0.115718\pi$
$348$	3.31272e44	−	1.06071e45i	0.0591232	−	0.189309i
$349$	−1.87966e45			−0.318581			−0.159291	−	0.987232i	$-0.550921\pi$
$349$	−1.87966e45			−0.318581			−0.159291	+	0.987232i	$0.550921\pi$
$350$	1.41796e45	+	2.16271e44i	0.228265	+	0.0348155i
$351$			8.74828e44i			0.133781i
$352$	2.89939e45	+	2.73801e45i	0.421249	+	0.397802i
$353$	1.31475e46			1.81509			0.907545	−	0.419954i	$-0.137954\pi$
$353$	1.31475e46			1.81509			0.907545	+	0.419954i	$0.137954\pi$
$354$	−3.56611e44	+	2.33809e45i	−0.0467881	+	0.306762i
$355$		−	3.85864e45i		−	0.481198i
$356$	1.07547e46	+	3.35880e45i	1.27497	+	0.398185i
$357$	3.72557e44			0.0419918
$358$	−3.00360e45	−	4.58117e44i	−0.321920	−	0.0491000i
$359$		−	1.37878e46i		−	1.40539i	−0.711493	−	0.702693i	$-0.751981\pi$
$359$		−	1.37878e46i		−	1.40539i	0.711493	−	0.702693i	$-0.248019\pi$
$360$	−1.29125e45	+	2.64557e45i	−0.125189	+	0.256492i
$361$	−7.36708e45			−0.679463
$362$	−6.87076e44	+	4.50475e45i	−0.0602907	+	0.395291i
$363$		−	2.78489e45i		−	0.232535i
$364$	−1.97196e44	+	6.31410e44i	−0.0156701	+	0.0501749i
$365$	−4.18736e45			−0.316715
$366$	−6.12061e45	−	9.33531e44i	−0.440692	−	0.0672154i
$367$		−	2.09789e45i		−	0.143811i	−0.997411	−	0.0719057i	$-0.977092\pi$
$367$		−	2.09789e45i		−	0.143811i	0.997411	−	0.0719057i	$-0.0229081\pi$
$368$	1.33403e44	−	1.92743e44i	0.00870771	−	0.0125811i
$369$	−1.37201e46			−0.852872
$370$	−1.22108e45	+	8.00594e45i	−0.0722961	+	0.474003i
$371$			3.54331e45i			0.199838i
$372$	−6.55961e45	−	2.04863e45i	−0.352456	−	0.110076i
$373$	−5.35973e45			−0.274400			−0.137200	−	0.990543i	$-0.543810\pi$
$373$	−5.35973e45			−0.274400			−0.137200	+	0.990543i	$0.543810\pi$
$374$	5.45398e45	+	8.31854e44i	0.266088	+	0.0405843i
$375$		−	4.63824e45i		−	0.215670i
$376$	−1.05968e46	−	5.17210e45i	−0.469670	−	0.229237i
$377$	2.72962e45			0.115334
$378$	−6.35164e44	+	4.16440e45i	−0.0255878	+	0.167764i
$379$			3.69366e45i			0.141890i	0.997480	+	0.0709449i	$0.0226014\pi$
$379$			3.69366e45i			0.141890i	−0.997480	+	0.0709449i	$0.977399\pi$
$380$	−3.43011e45	+	1.09830e46i	−0.125662	+	0.402362i
$381$	6.80900e45			0.237922
$382$	1.10621e46	+	1.68722e45i	0.368722	+	0.0562383i
$383$			4.03454e46i			1.28297i	0.767136	+	0.641485i	$0.221681\pi$
$383$			4.03454e46i			1.28297i	−0.767136	+	0.641485i	$0.778319\pi$
$384$	−5.64513e45	−	1.00613e46i	−0.171282	−	0.305276i
$385$	−1.68076e45			−0.0486645
$386$	4.42627e45	−	2.90205e46i	0.122311	−	0.801923i
$387$			3.08280e46i			0.813108i
$388$	−2.22860e46	−	6.96013e45i	−0.561126	−	0.175245i
$389$	4.29638e46			1.03278			0.516392	−	0.856352i	$-0.327275\pi$
$389$	4.29638e46			1.03278			0.516392	+	0.856352i	$0.327275\pi$
$390$	9.98234e44	+	1.52253e44i	0.0229123	+	0.00349464i
$391$		−	3.24290e44i		−	0.00710807i
$392$	1.95557e46	−	4.00664e46i	0.409377	−	0.838747i
$393$	2.66337e46			0.532556
$394$	1.24179e46	−	8.14169e46i	0.237201	−	1.55519i
$395$		−	1.97101e46i		−	0.359700i
$396$	−8.69151e45	+	2.78297e46i	−0.151559	+	0.485284i
$397$	−4.06613e46			−0.677567			−0.338784	−	0.940864i	$-0.610015\pi$
$397$	−4.06613e46			−0.677567			−0.338784	+	0.940864i	$0.610015\pi$
$398$	1.07274e47	+	1.63616e46i	1.70843	+	0.260574i
$399$			7.69516e45i			0.117140i
$400$	−5.05271e46	−	3.49713e46i	−0.735267	−	0.508899i
$401$	3.03189e46			0.421808			0.210904	−	0.977507i	$-0.432359\pi$
$401$	3.03189e46			0.421808			0.210904	+	0.977507i	$0.432359\pi$
$402$	−5.49320e45	+	3.60157e46i	−0.0730730	+	0.479097i
$403$		−	1.68804e46i		−	0.214729i
$404$	−3.84077e46	−	1.19951e46i	−0.467255	−	0.145928i
$405$	−1.80975e46			−0.210585
$406$	1.29937e46	+	1.98182e45i	0.144631	+	0.0220595i
$407$			8.02060e46i			0.854097i
$408$	−1.43434e46	−	7.00073e45i	−0.146140	−	0.0713281i
$409$	−2.61966e46			−0.255403			−0.127701	−	0.991813i	$-0.540760\pi$
$409$	−2.61966e46			−0.255403			−0.127701	+	0.991813i	$0.540760\pi$
$410$	−5.10908e45	+	3.34972e46i	−0.0476687	+	0.312536i
$411$			2.83232e46i			0.252923i
$412$	−5.36628e46	+	1.71825e47i	−0.458694	+	1.46871i
$413$	−2.79751e46			−0.228913
$414$	1.69415e45	+	2.58396e44i	0.0132723	+	0.00202432i
$415$		−	7.93167e46i		−	0.594975i
$416$	1.94568e46	−	2.06036e46i	0.139763	−	0.148001i
$417$	−4.22106e46			−0.290384
$418$	−1.71819e46	+	1.12652e47i	−0.113214	+	0.742276i
$419$		−	2.06412e47i		−	1.30281i	−0.758730	−	0.651406i	$-0.774180\pi$
$419$		−	2.06412e47i		−	1.30281i	0.758730	−	0.651406i	$-0.225820\pi$
$420$	4.64130e45	+	1.44952e45i	0.0280642	+	0.00876472i
$421$	−3.68409e46			−0.213429			−0.106714	−	0.994290i	$-0.534033\pi$
$421$	−3.68409e46			−0.213429			−0.106714	+	0.994290i	$0.534033\pi$
$422$	−1.32493e47	−	2.02082e46i	−0.735479	−	0.112177i
$423$		−	8.62086e46i		−	0.458590i
$424$	6.65824e46	−	1.36416e47i	0.339448	−	0.695474i
$425$	−8.50120e46			−0.415412
$426$	−1.66693e46	+	1.09291e47i	−0.0780810	+	0.511932i
$427$		−	7.32328e46i		−	0.328855i
$428$	−7.85684e46	+	2.51572e47i	−0.338267	+	1.08311i
$429$	1.00006e46			0.0412853
$430$	7.52656e46	+	1.14797e46i	0.297964	+	0.0454462i
$431$		−	1.33320e47i		−	0.506181i	−0.967443	−	0.253091i	$-0.918553\pi$
$431$		−	1.33320e47i		−	0.506181i	0.967443	−	0.253091i	$-0.0814470\pi$
$432$	1.02707e47	−	1.48393e47i	0.374018	−	0.540388i
$433$	2.32639e47			0.812646			0.406323	−	0.913730i	$-0.366811\pi$
$433$	2.32639e47			0.812646			0.406323	+	0.913730i	$0.366811\pi$
$434$	1.22559e46	−	8.03547e46i	0.0410705	−	0.269275i
$435$		−	2.00646e46i		−	0.0645094i
$436$	4.59937e47	+	1.43643e47i	1.41887	+	0.443126i
$437$	6.69821e45			0.0198286
$438$	1.18602e47	+	1.80894e46i	0.336943	+	0.0513913i
$439$			1.54201e47i			0.420462i	0.977652	+	0.210231i	$0.0674216\pi$
$439$			1.54201e47i			0.420462i	−0.977652	+	0.210231i	$0.932578\pi$
$440$	6.47088e46	+	3.15832e46i	0.169362	+	0.0826624i
$441$	3.25955e47			0.818959
$442$	5.91131e45	−	3.87570e46i	0.0142588	−	0.0934867i
$443$			5.24128e47i			1.21386i	0.794754	+	0.606932i	$0.207600\pi$
$443$			5.24128e47i			1.21386i	−0.794754	+	0.606932i	$0.792400\pi$
$444$	6.91713e46	−	2.21483e47i	0.153827	−	0.492546i
$445$	2.03437e47			0.434460
$446$	−7.74514e47	−	1.18131e47i	−1.58855	−	0.242290i
$447$		−	6.71479e46i		−	0.132281i
$448$	1.07578e47	−	8.39518e46i	0.203573	−	0.158864i
$449$	−6.42975e47			−1.16885			−0.584427	−	0.811447i	$-0.698681\pi$
$449$	−6.42975e47			−1.16885			−0.584427	+	0.811447i	$0.698681\pi$
$450$	6.77379e46	−	4.44118e47i	0.118306	−	0.775663i
$451$			3.35586e47i			0.563152i
$452$	−7.65955e46	−	2.39215e46i	−0.123513	−	0.0385742i
$453$	−3.70199e47			−0.573678
$454$	−8.24752e47	−	1.25793e47i	−1.22834	−	0.187349i
$455$			1.19438e46i			0.0170977i
$456$	1.44600e47	−	2.96262e47i	0.198976	−	0.407670i
$457$	9.18113e47			1.21452			0.607260	−	0.794503i	$-0.292269\pi$
$457$	9.18113e47			1.21452			0.607260	+	0.794503i	$0.292269\pi$
$458$	4.88727e45	−	3.20430e46i	0.00621567	−	0.0407525i
$459$		−	2.49671e47i		−	0.305309i
$460$	1.26173e45	−	4.03999e45i	0.00148363	−	0.00475050i
$461$	−9.35047e47			−1.05735			−0.528673	−	0.848826i	$-0.677310\pi$
$461$	−9.35047e47			−1.05735			−0.528673	+	0.848826i	$0.677310\pi$
$462$	4.76054e46	+	7.26089e45i	0.0517727	+	0.00789649i
$463$			1.13538e48i			1.18764i	0.804599	+	0.593818i	$0.202380\pi$
$463$			1.13538e48i			1.18764i	−0.804599	+	0.593818i	$0.797620\pi$
$464$	−4.63012e47	−	3.20464e47i	−0.465874	−	0.322445i
$465$	−1.24082e47			−0.120104
$466$	−3.39297e46	+	2.22457e47i	−0.0315961	+	0.207157i
$467$			1.04572e48i			0.936940i	0.883479	+	0.468470i	$0.155195\pi$
$467$			1.04572e48i			0.936940i	−0.883479	+	0.468470i	$0.844805\pi$
$468$	1.97764e47	+	6.17635e46i	0.170499	+	0.0532484i
$469$	−4.30926e47			−0.357513
$470$	−2.10475e47	−	3.21022e46i	−0.168051	−	0.0256315i
$471$			2.57172e47i			0.197628i
$472$	1.07703e48	+	5.25680e47i	0.796660	+	0.388835i
$473$	7.54033e47			0.536896
$474$	−8.51476e46	+	5.58263e47i	−0.0583663	+	0.382674i
$475$		−	1.75592e48i		−	1.15883i
$476$	5.62786e46	−	1.80201e47i	0.0357617	−	0.114507i
$477$	1.10980e48			0.679067
$478$	1.98584e48	+	3.02885e47i	1.17015	+	0.178474i
$479$		−	2.65599e48i		−	1.50726i	−0.657300	−	0.753629i	$-0.728302\pi$
$479$		−	2.65599e48i		−	1.50726i	0.657300	−	0.753629i	$-0.271698\pi$
$480$	−1.51451e47	−	1.43021e47i	−0.0827807	−	0.0781731i
$481$	5.69959e47			0.300077
$482$	−4.76969e46	+	3.12721e47i	−0.0241904	+	0.158602i
$483$		−	2.83059e45i		−	0.00138302i
$484$	−1.34702e48	−	4.20687e47i	−0.634098	−	0.198035i
$485$	−4.21563e47			−0.191210
$486$	1.99905e48	+	3.04900e47i	0.873719	+	0.133262i
$487$		−	3.04604e48i		−	1.28296i	−0.767139	−	0.641481i	$-0.778320\pi$
$487$		−	3.04604e48i		−	1.28296i	0.767139	−	0.641481i	$-0.221680\pi$
$488$	−1.37612e48	+	2.81944e48i	−0.558598	+	1.14448i
$489$	1.94805e46			0.00762150
$490$	1.21378e47	−	7.95807e47i	0.0457733	−	0.300108i
$491$			1.05583e48i			0.383821i	0.981412	+	0.191911i	$0.0614683\pi$
$491$			1.05583e48i			0.383821i	−0.981412	+	0.191911i	$0.938532\pi$
$492$	2.89416e47	−	9.26695e47i	0.101426	−	0.324762i
$493$	−7.79019e47			−0.263211
$494$	8.00526e47	+	1.22098e47i	0.260790	+	0.0397763i
$495$			5.26430e47i			0.165366i
$496$	−1.98180e48	+	2.86333e48i	−0.600328	+	0.867365i
$497$	−1.30766e48			−0.382015
$498$	−3.42648e47	+	2.24654e48i	−0.0965429	+	0.632975i
$499$		−	4.01580e48i		−	1.09135i	−0.837998	−	0.545673i	$-0.816274\pi$
$499$		−	4.01580e48i		−	1.09135i	0.837998	−	0.545673i	$-0.183726\pi$
$500$	−2.24346e48	−	7.00654e47i	−0.588109	−	0.183672i
$501$	1.59493e48			0.403332
$502$	1.38527e48	+	2.11284e47i	0.337961	+	0.0515465i
$503$			5.68934e48i			1.33918i	0.742732	+	0.669589i	$0.233530\pi$
$503$			5.68934e48i			1.33918i	−0.742732	+	0.669589i	$0.766470\pi$
$504$	8.96560e47	+	4.37595e47i	0.203624	+	0.0993854i
$505$	−7.26523e47			−0.159223
$506$	6.32019e45	−	4.14378e46i	0.00133666	−	0.00876370i
$507$			1.64394e48i			0.335539i
$508$	1.02857e48	−	3.29343e48i	0.202622	−	0.648786i
$509$	−9.32459e48			−1.77300			−0.886501	−	0.462726i	$-0.846871\pi$
$509$	−9.32459e48			−1.77300			−0.886501	+	0.462726i	$0.846871\pi$
$510$	−2.84891e47	−	4.34522e46i	−0.0522896	−	0.00797533i
$511$			1.41906e48i			0.251434i
$512$	−5.71928e48	+	1.21061e48i	−0.978323	+	0.207084i
$513$	5.15696e48			0.851689
$514$	8.69004e47	−	5.69755e48i	0.138575	−	0.908556i
$515$			3.25026e48i			0.500482i
$516$	−2.08221e48	−	6.50295e47i	−0.309620	−	0.0966976i
$517$	−2.10861e48			−0.302807
$518$	2.71315e48	+	4.13815e47i	0.376303	+	0.0573946i
$519$		−	1.59992e48i		−	0.214331i
$520$	2.24436e47	−	4.59834e47i	0.0290424	−	0.0595032i
$521$	1.06132e49			1.32669			0.663344	−	0.748314i	$-0.269137\pi$
$521$	1.06132e49			1.32669			0.663344	+	0.748314i	$0.269137\pi$
$522$	6.20725e47	−	4.06973e48i	0.0749602	−	0.491470i
$523$			3.03586e47i			0.0354202i	0.999843	+	0.0177101i	$0.00563759\pi$
$523$			3.03586e47i			0.0354202i	−0.999843	+	0.0177101i	$0.994362\pi$
$524$	4.02329e48	−	1.28824e49i	0.453543	−	1.45222i
$525$	−7.42033e47			−0.0808268
$526$	6.06488e47	+	9.25030e46i	0.0638379	+	0.00973672i
$527$			4.81757e48i			0.490046i
$528$	−1.69636e48	−	1.17410e48i	−0.166766	−	0.115423i
$529$	1.05221e49			0.999766
$530$	4.13264e47	−	2.70953e48i	0.0379544	−	0.248845i
$531$			8.76205e48i			0.777866i
$532$	3.72205e48	+	1.16243e48i	0.319428	+	0.0997606i
$533$	2.38474e48			0.197857
$534$	−5.76209e48	−	8.78848e47i	−0.462208	−	0.0704971i
$535$			4.75875e48i			0.369084i
$536$	1.65905e49	+	8.09754e48i	1.24421	+	0.607277i
$537$	1.57182e48			0.113989
$538$	−2.20564e48	+	1.44611e49i	−0.154687	+	1.01419i
$539$		−	7.97264e48i		−	0.540760i
$540$	9.71406e47	−	3.11039e48i	0.0637255	−	0.204046i
$541$	−2.03164e49			−1.28913			−0.644564	−	0.764550i	$-0.722961\pi$
$541$	−2.03164e49			−1.28913			−0.644564	+	0.764550i	$0.722961\pi$
$542$	−1.40452e49	−	2.14220e48i	−0.862064	−	0.131484i
$543$		−	2.35738e48i		−	0.139969i
$544$	−5.55288e48	+	5.88016e48i	−0.318961	+	0.337761i
$545$	8.70020e48			0.483495
$546$	5.15973e46	−	3.38293e47i	0.00277434	−	0.0181897i
$547$		−	1.38426e49i		−	0.720187i	−0.932916	−	0.360093i	$-0.882745\pi$
$547$		−	1.38426e49i		−	0.720187i	0.932916	−	0.360093i	$-0.117255\pi$
$548$	1.36996e49	+	4.27851e48i	0.689694	+	0.215398i
$549$	−2.29372e49			−1.11748
$550$	−1.08628e49	−	1.65683e48i	−0.512171	−	0.0781175i
$551$		−	1.60906e49i		−	0.734250i
$552$	−5.31896e46	+	1.08977e47i	−0.00234922	+	0.00481316i
$553$	−6.67958e48			−0.285560
$554$	1.15098e48	−	7.54633e48i	0.0476315	−	0.312292i
$555$		−	4.18959e48i		−	0.167841i
$556$	−6.37634e48	+	2.04167e49i	−0.247301	+	0.791844i
$557$	−6.90930e48			−0.259442			−0.129721	−	0.991551i	$-0.541408\pi$
$557$	−6.90930e48			−0.259442			−0.129721	+	0.991551i	$0.541408\pi$
$558$	−2.51678e49	−	3.83866e48i	−0.915019	−	0.139561i
$559$		−	5.35831e48i		−	0.188632i
$560$	1.40223e48	−	2.02597e48i	0.0478008	−	0.0690635i
$561$	−2.85412e48			−0.0942196
$562$	−7.32895e48	+	4.80517e49i	−0.234309	+	1.53622i
$563$		−	1.68532e49i		−	0.521834i	−0.965361	−	0.260917i	$-0.915975\pi$
$563$		−	1.68532e49i		−	0.521834i	0.965361	−	0.260917i	$-0.0840249\pi$
$564$	5.82277e48	+	1.81851e48i	0.174625	+	0.0545370i
$565$	−1.44889e48			−0.0420884
$566$	1.45634e49	+	2.22125e48i	0.409796	+	0.0625030i
$567$			6.13309e48i			0.167180i
$568$	5.03446e49	+	2.45723e49i	1.32948	+	0.648897i
$569$	6.09249e49			1.55874			0.779370	−	0.626564i	$-0.215539\pi$
$569$	6.09249e49			1.55874			0.779370	+	0.626564i	$0.215539\pi$
$570$	8.97505e47	−	5.88441e48i	0.0222479	−	0.145867i
$571$		−	1.00419e48i		−	0.0241194i	−0.999927	−	0.0120597i	$-0.996161\pi$
$571$		−	1.00419e48i		−	0.0241194i	0.999927	−	0.0120597i	$-0.00383882\pi$
$572$	1.51070e48	−	4.83717e48i	0.0351600	−	0.112580i
$573$	−5.78893e48			−0.130561
$574$	1.13519e49	+	1.73142e48i	0.248117	+	0.0378433i
$575$			6.45898e47i			0.0136818i
$576$	−2.62945e49	−	3.36946e49i	−0.539834	−	0.691760i
$577$	4.23848e49			0.843423			0.421711	−	0.906730i	$-0.361430\pi$
$577$	4.23848e49			0.843423			0.421711	+	0.906730i	$0.361430\pi$
$578$	6.12996e48	−	4.01906e49i	0.118238	−	0.775216i
$579$			1.51867e49i			0.283955i
$580$	−9.70497e48	−	3.03096e48i	−0.175910	−	0.0549384i
$581$	−2.68798e49			−0.472341
$582$	1.19402e49	+	1.82115e48i	0.203423	+	0.0310265i
$583$		−	2.71449e49i		−	0.448388i
$584$	2.66656e49	−	5.46335e49i	0.427091	−	0.875039i
$585$	3.74091e48			0.0580994
$586$	2.61428e48	−	1.71403e49i	0.0393727	−	0.258144i
$587$			6.40630e49i			0.935667i	0.883817	+	0.467833i	$0.154965\pi$
$587$			6.40630e49i			0.935667i	−0.883817	+	0.467833i	$0.845035\pi$
$588$	−6.87577e48	+	2.20159e49i	−0.0973934	+	0.311849i
$589$	−9.95068e49			−1.36703
$590$	2.13923e49	+	3.26280e48i	0.285050	+	0.0434764i
$591$			4.26063e49i			0.550680i
$592$	−9.66794e49	−	6.69146e49i	−1.21211	−	0.838938i
$593$	8.41910e49			1.02396			0.511978	−	0.858999i	$-0.328913\pi$
$593$	8.41910e49			1.02396			0.511978	+	0.858999i	$0.328913\pi$
$594$	4.86592e48	−	3.19030e49i	0.0574129	−	0.376423i
$595$		−	3.40870e48i		−	0.0390196i
$596$	−3.24786e49	−	1.01434e49i	−0.360715	−	0.112655i
$597$	−5.61373e49			−0.604942
$598$	−2.94465e47	−	4.49125e46i	−0.00307902	−	0.000469620i
$599$			1.23174e50i			1.24978i	0.780711	+	0.624892i	$0.214857\pi$
$599$			1.23174e50i			1.24978i	−0.780711	+	0.624892i	$0.785143\pi$
$600$	2.85681e49	+	1.39436e49i	0.281293	+	0.137294i
$601$	6.16907e49			0.589494			0.294747	−	0.955575i	$-0.404765\pi$
$601$	6.16907e49			0.589494			0.294747	+	0.955575i	$0.404765\pi$
$602$	3.89037e48	−	2.55069e49i	0.0360790	−	0.236549i
$603$			1.34970e50i			1.21486i
$604$	−5.59224e49	+	1.79061e50i	−0.488564	+	1.56435i
$605$	−2.54803e49			−0.216077
$606$	2.05778e49	+	3.13858e48i	0.169392	+	0.0258360i
$607$		−	1.56513e50i		−	1.25071i	−0.780342	−	0.625353i	$-0.784955\pi$
$607$		−	1.56513e50i		−	1.25071i	0.780342	−	0.625353i	$-0.215045\pi$
$608$	−1.21455e50	−	1.14695e50i	−0.942215	−	0.889772i
$609$	−6.79971e48			−0.0512129
$610$	−8.54131e48	+	5.60004e49i	−0.0624579	+	0.409500i
$611$			1.49842e49i			0.106388i
$612$	−5.64407e49	−	1.76270e49i	−0.389105	−	0.121521i
$613$	−2.39697e50			−1.60462			−0.802312	−	0.596905i	$-0.796397\pi$
$613$	−2.39697e50			−1.60462			−0.802312	+	0.596905i	$0.796397\pi$
$614$	1.68287e50	+	2.56675e49i	1.09400	+	0.166860i
$615$		−	1.75294e49i		−	0.110666i
$616$	1.07033e49	−	2.19293e49i	0.0656242	−	0.134453i
$617$	2.72430e50			1.62227			0.811134	−	0.584861i	$-0.198851\pi$
$617$	2.72430e50			1.62227			0.811134	+	0.584861i	$0.198851\pi$
$618$	1.40411e49	−	9.20596e49i	0.0812101	−	0.532447i
$619$		−	2.09904e50i		−	1.17920i	−0.807695	−	0.589601i	$-0.799285\pi$
$619$		−	2.09904e50i		−	1.17920i	0.807695	−	0.589601i	$-0.200715\pi$
$620$	−1.87439e49	+	6.00170e49i	−0.102284	+	0.327509i
$621$	−1.89693e48			−0.0100555
$622$	1.28302e50	+	1.95689e49i	0.660703	+	0.100772i
$623$		−	6.89431e49i		−	0.344910i
$624$	−8.34336e48	+	1.20546e49i	−0.0405526	+	0.0585911i
$625$	1.46917e50			0.693796
$626$	2.06071e48	−	1.35109e49i	0.00945538	−	0.0619934i
$627$		−	5.89519e49i		−	0.262834i
$628$	1.24391e50	+	3.88485e49i	0.538909	+	0.168307i
$629$	−1.62663e50			−0.684823
$630$	1.78077e49	+	2.71607e48i	0.0728580	+	0.0111125i
$631$		−	3.26117e50i		−	1.29672i	−0.761336	−	0.648358i	$-0.775456\pi$
$631$		−	3.26117e50i		−	1.29672i	0.761336	−	0.648358i	$-0.224544\pi$
$632$	2.57162e50	+	1.25516e50i	0.993802	+	0.485057i
$633$	6.93352e49			0.260428
$634$	−6.91403e49	+	4.53312e50i	−0.252420	+	1.65497i
$635$		−	6.22987e49i		−	0.221081i
$636$	−2.34104e49	+	7.49587e49i	−0.0807569	+	0.258579i
$637$	−5.66551e49			−0.189989
$638$	−9.95431e49	−	1.51825e49i	−0.324518	−	0.0494963i
$639$			4.09572e50i			1.29812i
$640$	−9.20556e49	+	5.16500e49i	−0.283668	+	0.159159i
$641$	4.77352e49			0.143019			0.0715095	−	0.997440i	$-0.477218\pi$
$641$	4.77352e49			0.143019			0.0715095	+	0.997440i	$0.477218\pi$
$642$	2.05578e49	−	1.34786e50i	0.0598889	−	0.392657i
$643$		−	3.60916e50i		−	1.02237i	−0.859470	−	0.511186i	$-0.829206\pi$
$643$		−	3.60916e50i		−	1.02237i	0.859470	−	0.511186i	$-0.170794\pi$
$644$	−1.36912e48	−	4.27589e47i	−0.00377134	−	0.00117783i
$645$	−3.93872e49			−0.105507
$646$	−2.28466e50	−	3.48462e49i	−0.595163	−	0.0907757i
$647$			2.90885e50i			0.736962i	0.929635	+	0.368481i	$0.120122\pi$
$647$			2.90885e50i			0.736962i	−0.929635	+	0.368481i	$0.879878\pi$
$648$	1.15247e50	−	2.36122e50i	0.283975	−	0.581818i
$649$	2.14314e50			0.513625
$650$	−1.17737e49	+	7.71935e49i	−0.0274457	+	0.179945i
$651$			4.20504e49i			0.0953482i
$652$	2.94273e48	−	9.42246e48i	0.00649073	−	0.0207830i
$653$	−7.81253e50			−1.67631			−0.838155	−	0.545432i	$-0.816365\pi$
$653$	−7.81253e50			−1.67631			−0.838155	+	0.545432i	$0.816365\pi$
$654$	−2.46422e50	−	3.75849e49i	−0.514375	−	0.0784537i
$655$		−	2.43684e50i		−	0.494861i
$656$	−4.04511e50	−	2.79974e50i	−0.799211	−	0.553157i
$657$	4.44463e50			0.854395
$658$	−1.08792e49	+	7.13284e49i	−0.0203484	+	0.133412i
$659$			7.80856e50i			1.42113i	0.703632	+	0.710565i	$0.251561\pi$
$659$			7.80856e50i			1.42113i	−0.703632	+	0.710565i	$0.748439\pi$
$660$	−3.55565e49	−	1.11047e49i	−0.0629692	−	0.0196659i
$661$	−7.08006e50			−1.22014			−0.610072	−	0.792346i	$-0.708859\pi$
$661$	−7.08006e50			−1.22014			−0.610072	+	0.792346i	$0.708859\pi$
$662$	−1.02073e51	−	1.55683e50i	−1.71185	−	0.261095i
$663$			2.02819e49i			0.0331029i
$664$	1.03486e51	+	5.05099e50i	1.64383	+	0.802326i
$665$	7.04067e49			0.108849
$666$	1.29611e50	−	8.49783e50i	0.195032	−	1.27871i
$667$			5.91877e48i			0.00866894i
$668$	2.40931e50	−	7.71447e50i	0.343491	−	1.09984i
$669$	4.05311e50			0.562494
$670$	3.29525e50	+	5.02599e49i	0.445186	+	0.0679008i
$671$			5.61029e50i			0.737870i
$672$	−4.84686e49	+	5.13254e49i	−0.0620603	+	0.0657181i
$673$	1.17951e51			1.47038			0.735190	−	0.677861i	$-0.237093\pi$
$673$	1.17951e51			1.47038			0.735190	+	0.677861i	$0.237093\pi$
$674$	5.42320e49	−	3.55567e50i	0.0658229	−	0.431562i
$675$			4.97277e50i			0.587666i
$676$	7.95154e50	+	2.48334e50i	0.914978	+	0.285757i
$677$	−3.48039e50			−0.389971			−0.194986	−	0.980806i	$-0.562466\pi$
$677$	−3.48039e50			−0.389971			−0.194986	+	0.980806i	$0.562466\pi$
$678$	4.10379e49	+	6.25919e48i	0.0447765	+	0.00682942i
$679$			1.42864e50i			0.151799i
$680$	−6.40530e49	+	1.31234e50i	−0.0662794	+	0.135796i
$681$	4.31601e50			0.434945
$682$	−9.38911e49	+	6.15589e50i	−0.0921522	+	0.604188i
$683$			1.02243e49i			0.00977376i	0.999988	+	0.00488688i	$0.00155555\pi$
$683$			1.02243e49i			0.00977376i	−0.999988	+	0.00488688i	$0.998444\pi$
$684$	3.64085e50	−	1.16578e51i	0.338995	−	1.08544i
$685$	2.59142e50			0.235021
$686$	−5.58653e50	−	8.52070e49i	−0.493523	−	0.0752733i
$687$			1.67684e49i			0.0144301i
$688$	−6.29079e50	+	9.08904e50i	−0.527367	+	0.761949i
$689$	−1.92897e50			−0.157536
$690$	−3.30138e47	+	2.16452e48i	−0.000262671	+	0.00172218i
$691$		−	1.93134e51i		−	1.49711i	−0.663072	−	0.748556i	$-0.730748\pi$
$691$		−	1.93134e51i		−	1.49711i	0.663072	−	0.748556i	$-0.269252\pi$
$692$	−7.73860e50	−	2.41684e50i	−0.584457	−	0.182532i
$693$	1.78403e50			0.131281
$694$	9.80505e50	+	1.49549e50i	0.703039	+	0.107229i
$695$			3.86204e50i			0.269830i
$696$	2.61787e50	+	1.27774e50i	0.178231	+	0.0869911i
$697$	−6.80591e50			−0.451540
$698$	7.42947e49	−	4.87107e50i	0.0480353	−	0.314939i
$699$		−	1.16414e50i		−	0.0733527i
$700$	−1.12092e50	+	3.58912e50i	−0.0688349	+	0.220406i
$701$	−1.77887e51			−1.06468			−0.532342	−	0.846530i	$-0.678688\pi$
$701$	−1.77887e51			−1.06468			−0.532342	+	0.846530i	$0.678688\pi$
$702$	−2.26709e50	−	3.45782e49i	−0.132252	−	0.0201713i
$703$		−	3.35981e51i		−	1.91038i
$704$	−8.24148e50	+	6.43146e50i	−0.456770	+	0.356453i
$705$	1.10144e50			0.0595054
$706$	−5.19664e50	+	3.40713e51i	−0.273677	+	1.79434i
$707$			2.46213e50i			0.126404i
$708$	−5.91813e50	−	1.84829e50i	−0.296201	−	0.0925064i
$709$	−8.79132e50			−0.428965			−0.214483	−	0.976728i	$-0.568807\pi$
$709$	−8.79132e50			−0.428965			−0.214483	+	0.976728i	$0.568807\pi$
$710$	9.99955e50	+	1.52516e50i	0.475697	+	0.0725544i
$711$			2.09211e51i			0.970356i
$712$	−1.29551e51	+	2.65429e51i	−0.585870	+	1.20035i
$713$	3.66025e49			0.0161399
$714$	−1.47256e49	+	9.65471e49i	−0.00633147	+	0.0415118i
$715$		−	9.15003e49i		−	0.0383631i
$716$	2.37439e50	−	7.60267e50i	0.0970773	−	0.310836i
$717$	−1.03921e51			−0.414342
$718$	3.57307e51	+	5.44974e50i	1.38932	+	0.211902i
$719$			4.94759e50i			0.187618i	0.995590	+	0.0938088i	$0.0299042\pi$
$719$			4.94759e50i			0.187618i	−0.995590	+	0.0938088i	$0.970096\pi$
$720$	−6.34553e50	−	4.39192e50i	−0.234684	−	0.162431i
$721$	1.10149e51			0.397324
$722$	2.91189e50	−	1.90916e51i	0.102449	−	0.671695i
$723$		−	1.63650e50i		−	0.0561599i
$724$	−1.14024e51	−	3.56107e50i	−0.381681	−	0.119203i
$725$	1.55159e51			0.506633
$726$	7.21697e50	+	1.10075e50i	0.229877	+	0.0350614i
$727$		−	4.79107e51i		−	1.48872i	−0.667779	−	0.744359i	$-0.732755\pi$
$727$		−	4.79107e51i		−	1.48872i	0.667779	−	0.744359i	$-0.267245\pi$
$728$	−1.55834e50	−	7.60596e49i	−0.0472386	−	0.0230563i
$729$	1.14306e51			0.338044
$730$	1.65508e50	−	1.08514e51i	0.0477538	−	0.313094i
$731$			1.52923e51i			0.430488i
$732$	4.83843e50	−	1.54924e51i	0.132894	−	0.425519i
$733$	1.73318e50			0.0464486			0.0232243	−	0.999730i	$-0.492607\pi$
$733$	1.73318e50			0.0464486			0.0232243	+	0.999730i	$0.492607\pi$
$734$	5.43661e50	+	8.29205e49i	0.142167	+	0.0216837i
$735$			4.16454e50i			0.106266i
$736$	4.46759e49	+	4.21892e49i	0.0111243	+	0.0105051i
$737$	3.30128e51			0.802172
$738$	5.42298e50	−	3.55553e51i	0.128595	−	0.843121i
$739$		−	2.48623e51i		−	0.575363i	−0.957726	−	0.287682i	$-0.907115\pi$
$739$		−	2.48623e51i		−	0.575363i	0.957726	−	0.287682i	$-0.0928845\pi$
$740$	−2.02645e51	−	6.32881e50i	−0.457683	−	0.142939i
$741$	−4.18923e50			−0.0923436
$742$	−9.18237e50	−	1.40052e50i	−0.197553	−	0.0301313i
$743$			8.27336e51i			1.73733i	0.495396	+	0.868667i	$0.335023\pi$
$743$			8.27336e51i			1.73733i	−0.495396	+	0.868667i	$0.664977\pi$
$744$	7.90171e50	−	1.61893e51i	0.161960	−	0.331830i
$745$	−6.14367e50			−0.122918
$746$	2.11847e50	−	1.38896e51i	0.0413737	−	0.271263i
$747$			8.41900e51i			1.60505i
$748$	−4.31145e50	+	1.38050e51i	−0.0802406	+	0.256926i
$749$	1.61270e51			0.293009
$750$	1.20199e51	+	1.83330e50i	0.213205	+	0.0325185i
$751$		−	9.42693e50i		−	0.163249i	−0.996663	−	0.0816247i	$-0.973989\pi$
$751$		−	9.42693e50i		−	0.163249i	0.996663	−	0.0816247i	$-0.0260109\pi$
$752$	1.75918e51	−	2.54169e51i	0.297433	−	0.429736i
$753$	−7.24923e50			−0.119669
$754$	−1.07890e50	+	7.07373e50i	−0.0173899	+	0.114016i
$755$			3.38713e51i			0.533072i
$756$	−1.05409e51	−	3.29202e50i	−0.161988	−	0.0505906i
$757$	−2.71850e51			−0.407947			−0.203974	−	0.978976i	$-0.565386\pi$
$757$	−2.71850e51			−0.407947			−0.203974	+	0.978976i	$0.565386\pi$
$758$	−9.57201e50	−	1.45995e50i	−0.140268	−	0.0213939i
$759$			2.16848e49i			0.00310316i
$760$	−2.71064e51	−	1.32301e51i	−0.378815	−	0.184893i
$761$	−4.38319e51			−0.598227			−0.299114	−	0.954218i	$-0.596691\pi$
$761$	−4.38319e51			−0.598227			−0.299114	+	0.954218i	$0.596691\pi$
$762$	−2.69131e50	+	1.76453e51i	−0.0358735	+	0.235202i
$763$		−	2.94843e51i		−	0.383838i
$764$	−8.74478e50	+	2.80003e51i	−0.111191	+	0.356027i
$765$	−1.06764e51			−0.132592
$766$	−1.04554e52	−	1.59468e51i	−1.26830	−	0.193444i
$767$		−	1.52296e51i		−	0.180456i
$768$	2.83049e51	−	1.06524e51i	0.327612	−	0.123295i
$769$	−1.54036e52			−1.74160			−0.870802	−	0.491634i	$-0.836400\pi$
$769$	−1.54036e52			−1.74160			−0.870802	+	0.491634i	$0.836400\pi$
$770$	6.64333e49	−	4.35564e50i	0.00733757	−	0.0481082i
$771$			2.98159e51i			0.321713i
$772$	7.34561e51	+	2.29411e51i	0.774313	+	0.241826i
$773$	1.47512e52			1.51914			0.759568	−	0.650428i	$-0.225410\pi$
$773$	1.47512e52			1.51914			0.759568	+	0.650428i	$0.225410\pi$
$774$	−7.98899e51	−	1.21850e51i	−0.803812	−	0.122599i
$775$		−	9.59528e51i		−	0.943251i
$776$	2.68457e51	−	5.50024e51i	0.257848	−	0.528288i
$777$	−1.41982e51			−0.133246
$778$	−1.69817e51	+	1.11339e52i	−0.155722	+	1.02098i
$779$		−	1.40576e52i		−	1.25961i
$780$	−7.89118e49	+	2.52671e50i	−0.00690938	+	0.0221235i
$781$	1.00179e52			0.857149
$782$	8.40388e49	+	1.28178e49i	0.00702681	+	0.00107175i
$783$			4.55687e51i			0.372353i
$784$	9.61013e51	+	6.65145e51i	0.767433	+	0.531162i
$785$	2.35299e51			0.183640
$786$	−1.05272e51	+	6.90204e51i	−0.0802981	+	0.526468i
$787$		−	9.48013e51i		−	0.706755i	−0.935481	−	0.353378i	$-0.885033\pi$
$787$		−	9.48013e51i		−	0.706755i	0.935481	−	0.353378i	$-0.114967\pi$
$788$	2.06081e52	+	6.43613e51i	1.50164	+	0.468978i
$789$	−3.17381e50			−0.0226045
$790$	5.10781e51	+	7.79055e50i	0.355588	+	0.0542351i
$791$			4.91016e50i			0.0334133i
$792$	−6.86846e51	−	3.35237e51i	−0.456884	−	0.222997i
$793$	3.98678e51			0.259242
$794$	1.60717e51	−	1.05373e52i	0.102163	−	0.669821i
$795$			1.41793e51i			0.0881140i
$796$	−8.48013e51	+	2.71529e52i	−0.515190	+	1.64961i
$797$	1.29143e52			0.767045			0.383522	−	0.923532i	$-0.374711\pi$
$797$	1.29143e52			0.767045			0.383522	+	0.923532i	$0.374711\pi$
$798$	−1.99418e51	−	3.04157e50i	−0.115801	−	0.0176622i
$799$		−	4.27641e51i		−	0.242793i
$800$	1.10598e52	−	1.17117e52i	0.613944	−	0.650129i
$801$	−2.15936e52			−1.17203
$802$	−1.19838e51	+	7.85705e51i	−0.0635996	+	0.416985i
$803$		−	1.08713e52i		−	0.564158i
$804$	−9.11625e51	−	2.84709e51i	−0.462602	−	0.144475i
$805$	−2.58984e49			−0.00128513
$806$	4.37450e51	+	6.67209e50i	0.212274	+	0.0323766i
$807$		−	7.56765e51i		−	0.359118i
$808$	4.62659e51	−	9.47912e51i	0.214712	−	0.439910i
$809$	−5.78633e51			−0.262621			−0.131310	−	0.991341i	$-0.541918\pi$
$809$	−5.78633e51			−0.262621			−0.131310	+	0.991341i	$0.541918\pi$
$810$	7.15317e50	−	4.68991e51i	0.0317518	−	0.208178i
$811$			1.48645e52i			0.645320i	0.946515	+	0.322660i	$0.104577\pi$
$811$			1.48645e52i			0.645320i	−0.946515	+	0.322660i	$0.895423\pi$
$812$	−1.02717e51	+	3.28893e51i	−0.0436147	+	0.139652i
$813$	7.34997e51			0.305250
$814$	−2.07851e52	−	3.17020e51i	−0.844333	−	0.128780i
$815$		−	1.78236e50i		−	0.00708205i
$816$	2.38115e51	−	3.44033e51i	0.0925473	−	0.133714i
$817$	−3.15863e52			−1.20089
$818$	1.03544e51	−	6.78877e51i	0.0385093	−	0.252483i
$819$		−	1.26776e51i		−	0.0461241i
$820$	−8.47877e51	−	2.64800e51i	−0.301775	−	0.0942474i
$821$	−8.33480e51			−0.290214			−0.145107	−	0.989416i	$-0.546353\pi$
$821$	−8.33480e51			−0.290214			−0.145107	+	0.989416i	$0.546353\pi$
$822$	−7.33986e51	−	1.11949e51i	−0.250032	−	0.0381354i
$823$			4.87866e52i			1.62594i	0.582307	+	0.812969i	$0.302150\pi$
$823$			4.87866e52i			1.62594i	−0.582307	+	0.812969i	$0.697850\pi$
$824$	−4.24070e52	−	2.06981e52i	−1.38276	−	0.674901i
$825$	5.68464e51			0.181356
$826$	1.10574e51	−	7.24966e51i	0.0345152	−	0.226296i
$827$			4.32795e52i			1.32185i	0.750451	+	0.660926i	$0.229836\pi$
$827$			4.32795e52i			1.32185i	−0.750451	+	0.660926i	$0.770164\pi$
$828$	−1.33925e50	+	4.28821e50i	−0.00400235	+	0.0128153i
$829$	2.32097e52			0.678715			0.339358	−	0.940657i	$-0.389790\pi$
$829$	2.32097e52			0.678715			0.339358	+	0.940657i	$0.389790\pi$
$830$	2.05547e52	+	3.13505e51i	0.588173	+	0.0897096i
$831$			3.94907e51i			0.110580i
$832$	4.57032e51	+	5.85655e51i	0.125235	+	0.160481i
$833$	1.61691e52			0.433586
$834$	1.66840e51	−	1.09387e52i	0.0437836	−	0.287064i
$835$		−	1.45928e52i		−	0.374784i
$836$	−2.85143e52	−	8.90529e51i	−0.716720	−	0.223839i
$837$	2.81803e52			0.693247
$838$	5.34909e52	+	8.15857e51i	1.28792	+	0.196436i
$839$			1.45030e52i			0.341778i	0.985290	+	0.170889i	$0.0546639\pi$
$839$			1.45030e52i			0.341778i	−0.985290	+	0.170889i	$0.945336\pi$
$840$	−5.59090e50	+	1.14548e51i	−0.0128960	+	0.0264218i
$841$	−3.00740e52			−0.678991
$842$	1.45616e51	−	9.54722e51i	0.0321805	−	0.210989i
$843$		−	2.51459e52i		−	0.543965i
$844$	1.04738e52	−	3.35366e52i	0.221789	−	0.710157i
$845$	1.50412e52			0.311790
$846$	2.23407e52	+	3.40746e51i	0.453347	+	0.0691455i
$847$			8.63506e51i			0.171539i
$848$	3.27202e52	+	2.26466e52i	0.636342	+	0.440430i
$849$	−7.62119e51			−0.145106
$850$	3.36016e51	−	2.20306e52i	0.0626353	−	0.410663i
$851$			1.23587e51i			0.0225549i
$852$	−2.76636e52	−	8.63962e51i	−0.494306	−	0.154377i
$853$	9.95728e52			1.74204			0.871020	−	0.491247i	$-0.163459\pi$
$853$	9.95728e52			1.74204			0.871020	+	0.491247i	$0.163459\pi$
$854$	1.89781e52	+	2.89458e51i	0.325095	+	0.0495842i
$855$		−	2.20520e52i		−	0.369878i
$856$	−6.20886e52	−	3.03043e52i	−1.01973	−	0.497711i
$857$	−1.15586e53			−1.85887			−0.929436	−	0.368983i	$-0.879706\pi$
$857$	−1.15586e53			−1.85887			−0.929436	+	0.368983i	$0.879706\pi$
$858$	−3.95281e50	+	2.59163e51i	−0.00622494	+	0.0408133i
$859$		−	1.27482e52i		−	0.196595i	−0.995157	−	0.0982977i	$-0.968660\pi$
$859$		−	1.27482e52i		−	0.196595i	0.995157	−	0.0982977i	$-0.0313397\pi$
$860$	−5.94985e51	+	1.90511e52i	−0.0898533	+	0.287705i
$861$	−5.94058e51			−0.0878562
$862$	3.45496e52	+	5.26959e51i	0.500394	+	0.0763213i
$863$		−	1.07169e53i		−	1.52011i	−0.649860	−	0.760054i	$-0.725173\pi$
$863$		−	1.07169e53i		−	1.52011i	0.649860	−	0.760054i	$-0.274827\pi$
$864$	3.43960e52	+	3.24815e52i	0.477816	+	0.451221i
$865$	−1.46384e52			−0.199161
$866$	−9.19524e51	+	6.02878e52i	−0.122530	+	0.803355i
$867$			2.10321e52i			0.274498i
$868$	2.03393e52	+	6.35215e51i	0.260004	+	0.0812019i
$869$	5.11716e52			0.640727
$870$	5.19967e51	+	7.93066e50i	0.0637719	+	0.00972664i
$871$		−	2.34595e52i		−	0.281834i
$872$	−5.54039e52	+	1.13514e53i	−0.651994	+	1.33583i
$873$	4.47464e52			0.515825
$874$	−2.64751e50	+	1.73582e51i	−0.00298973	+	0.0196019i
$875$			1.43817e52i			0.159098i
$876$	−9.37562e51	+	3.00202e52i	−0.101608	+	0.325342i
$877$	−7.34833e52			−0.780182			−0.390091	−	0.920776i	$-0.627557\pi$
$877$	−7.34833e52			−0.780182			−0.390091	+	0.920776i	$0.627557\pi$
$878$	−3.99608e52	−	6.09492e51i	−0.415655	−	0.0633967i
$879$			8.96969e51i			0.0914066i
$880$	−1.07424e52	+	1.55208e52i	−0.107254	+	0.154962i
$881$	−1.24738e53			−1.22020			−0.610100	−	0.792325i	$-0.708871\pi$
$881$	−1.24738e53			−1.22020			−0.610100	+	0.792325i	$0.708871\pi$
$882$	−1.28836e52	+	8.44702e52i	−0.123482	+	0.809597i
$883$		−	7.42343e51i		−	0.0697128i	−0.999392	−	0.0348564i	$-0.988903\pi$
$883$		−	7.42343e51i		−	0.0697128i	0.999392	−	0.0348564i	$-0.0110974\pi$
$884$	9.81012e51	+	3.06380e51i	0.0902680	+	0.0281916i
$885$	−1.11948e52			−0.100934
$886$	−1.35826e53	−	2.07165e52i	−1.19999	−	0.183025i
$887$		−	2.59315e52i		−	0.224493i	−0.993680	−	0.112247i	$-0.964195\pi$
$887$		−	2.59315e52i		−	0.224493i	0.993680	−	0.112247i	$-0.0358046\pi$
$888$	5.46626e52	+	2.66798e52i	0.463721	+	0.226334i
$889$	−2.11125e52			−0.175513
$890$	−8.04100e51	+	5.27201e52i	−0.0655073	+	0.429493i
$891$		−	4.69850e52i		−	0.375112i
$892$	6.12264e52	−	1.96044e53i	0.479040	−	1.53386i
$893$	8.83291e52			0.677295
$894$	1.74012e52	+	2.65407e51i	0.130769	+	0.0199451i
$895$		−	1.43813e52i		−	0.105921i
$896$	1.75037e52	+	3.11969e52i	0.126353	+	0.225199i
$897$	1.54097e50			0.00109026
$898$	2.54141e52	−	1.66625e53i	0.176238	−	1.15549i
$899$		−	8.79276e52i		−	0.597655i
$900$	1.12414e53	+	3.51082e52i	0.748957	+	0.233907i
$901$	5.50518e52			0.359522
$902$	−8.69660e52	−	1.32643e52i	−0.556714	−	0.0849113i
$903$			1.33480e52i			0.0837600i
$904$	9.22669e51	−	1.89040e52i	0.0567563	−	0.116284i
$905$	−2.15688e52			−0.130062
$906$	1.46324e52	−	9.59360e52i	0.0864983	−	0.567119i
$907$			2.36432e53i			1.37017i	0.728463	+	0.685085i	$0.240235\pi$
$907$			2.36432e53i			1.37017i	−0.728463	+	0.685085i	$0.759765\pi$
$908$	6.51978e52	−	2.08760e53i	0.370414	−	1.18605i
$909$	7.71161e52			0.429532
$910$	−3.09520e51	−	4.72088e50i	−0.0169022	−	0.00257797i
$911$			1.98515e53i			1.06282i	0.847113	+	0.531412i	$0.178338\pi$
$911$			1.98515e53i			1.06282i	−0.847113	+	0.531412i	$0.821662\pi$
$912$	7.10600e52	+	4.91826e52i	0.373008	+	0.258169i
$913$	2.05923e53			1.05982
$914$	−3.62891e52	+	2.37926e53i	−0.183124	+	1.20063i
$915$		−	2.93056e52i		−	0.145001i
$916$	8.11067e51	+	2.53304e51i	0.0393494	+	0.0122892i
$917$	−8.25825e52			−0.392862
$918$	6.47016e52	+	9.86844e51i	0.301819	+	0.0460341i
$919$			3.05673e53i			1.39823i	0.715010	+	0.699114i	$0.246422\pi$
$919$			3.05673e53i			1.39823i	−0.715010	+	0.699114i	$0.753578\pi$
$920$	9.97080e50	+	4.86657e50i	0.00447249	+	0.00218294i
$921$	−8.80661e52			−0.387378
$922$	3.69584e52	−	2.42315e53i	0.159425	−	1.04526i
$923$		−	7.11889e52i		−	0.301149i
$924$	−3.76327e51	+	1.20498e52i	−0.0156124	+	0.0499902i
$925$	3.23981e53			1.31816
$926$	−2.94231e53	−	4.48767e52i	−1.17406	−	0.179070i
$927$		−	3.44996e53i		−	1.35014i
$928$	1.01348e53	−	1.07322e53i	0.389002	−	0.411930i
$929$	−6.70608e52			−0.252456			−0.126228	−	0.992001i	$-0.540287\pi$
$929$	−6.70608e52			−0.252456			−0.126228	+	0.992001i	$0.540287\pi$
$930$	4.90444e51	−	3.21555e52i	0.0181091	−	0.118731i
$931$			3.33972e53i			1.20953i
$932$	−5.63080e52	−	1.75855e52i	−0.200025	−	0.0624697i
$933$	−6.71417e52			−0.233950
$934$	−2.70995e53	−	4.13329e52i	−0.926228	−	0.141271i
$935$			2.61137e52i			0.0875507i
$936$	−2.38226e52	+	4.88086e52i	−0.0783472	+	0.160521i
$937$	−1.81223e53			−0.584657			−0.292328	−	0.956318i	$-0.594430\pi$
$937$	−1.81223e53			−0.584657			−0.292328	+	0.956318i	$0.594430\pi$
$938$	1.70327e52	−	1.11673e53i	0.0539053	−	0.353426i
$939$			7.07038e51i			0.0219514i
$940$	1.66384e52	−	5.32752e52i	0.0506769	−	0.162265i
$941$	−6.50888e53			−1.94488			−0.972441	−	0.233149i	$-0.925097\pi$
$941$	−6.50888e53			−1.94488			−0.972441	+	0.233149i	$0.925097\pi$
$942$	−6.66454e52	−	1.01649e52i	−0.195368	−	0.0297980i
$943$			5.17094e51i			0.0148717i
$944$	−1.78799e53	+	2.58332e53i	−0.504509	+	0.728924i
$945$	−1.99392e52			−0.0551994
$946$	−2.98037e52	+	1.95406e53i	−0.0809524	+	0.530758i
$947$		−	3.30949e53i		−	0.881986i	−0.897511	−	0.440993i	$-0.854626\pi$
$947$		−	3.30949e53i		−	0.881986i	0.897511	−	0.440993i	$-0.145374\pi$
$948$	−1.41307e53	−	4.41315e52i	−0.369498	−	0.115398i
$949$	−7.72534e52			−0.198210
$950$	4.55042e53	+	6.94041e52i	1.14558	+	0.174727i
$951$		−	2.37223e53i		−	0.586013i
$952$	4.44741e52	+	2.17070e52i	0.107806	+	0.0526181i
$953$	5.37052e53			1.27745			0.638726	−	0.769434i	$-0.279462\pi$
$953$	5.37052e53			1.27745			0.638726	+	0.769434i	$0.279462\pi$
$954$	−4.38655e52	+	2.87601e53i	−0.102389	+	0.671304i
$955$			5.29656e52i			0.121320i
$956$	−1.56984e53	+	5.02653e53i	−0.352868	+	1.12986i
$957$	5.20919e52			0.114909
$958$	6.88293e53	+	1.04980e53i	1.49003	+	0.227262i
$959$		−	8.78210e52i		−	0.186579i
$960$	4.30497e52	−	3.35950e52i	0.0897610	−	0.0700475i
$961$	−5.50815e52			−0.112716
$962$	−2.25280e52	+	1.47703e53i	−0.0452452	+	0.296646i
$963$		−	5.05113e53i		−	0.995670i
$964$	−7.91554e52	−	2.47210e52i	−0.153142	−	0.0478277i
$965$	1.38950e53			0.263856
$966$	7.33538e50	+	1.11881e50i	0.00136721	+	0.000208530i
$967$			3.34104e53i			0.611230i	0.952155	+	0.305615i	$0.0988621\pi$
$967$			3.34104e53i			0.611230i	−0.952155	+	0.305615i	$0.901138\pi$
$968$	1.62262e53	−	3.32448e53i	0.291380	−	0.596989i
$969$	1.19559e53			0.210743
$970$	1.66626e52	−	1.09247e53i	0.0288305	−	0.189024i
$971$		−	6.83065e53i		−	1.16016i	−0.814561	−	0.580078i	$-0.803022\pi$
$971$		−	6.83065e53i		−	1.16016i	0.814561	−	0.580078i	$-0.196978\pi$
$972$	−1.58028e53	+	5.05998e53i	−0.263476	+	0.843637i
$973$	1.30881e53			0.214213
$974$	7.89372e53	+	1.20397e53i	1.26829	+	0.193443i
$975$		−	4.03961e52i		−	0.0637172i
$976$	−6.76258e53	−	4.68058e53i	−1.04717	−	0.724774i
$977$	6.41085e53			0.974571			0.487285	−	0.873243i	$-0.337987\pi$
$977$	6.41085e53			0.974571			0.487285	+	0.873243i	$0.337987\pi$
$978$	−7.69980e50	+	5.04831e51i	−0.00114916	+	0.00753437i
$979$			5.28166e53i			0.773895i
$980$	2.01433e53	+	6.29097e52i	0.289776	+	0.0904999i
$981$	−9.23474e53			−1.30432
$982$	−2.73616e53	−	4.17326e52i	−0.379433	−	0.0578720i
$983$		−	1.20736e54i		−	1.64390i	−0.569561	−	0.821949i	$-0.692887\pi$
$983$		−	1.20736e54i		−	1.64390i	0.569561	−	0.821949i	$-0.307113\pi$
$984$	2.28711e53	+	1.11630e53i	0.305756	+	0.149234i
$985$	3.89825e53			0.511703
$986$	3.07913e52	−	2.01880e53i	0.0396865	−	0.260201i
$987$		−	3.73269e52i		−	0.0472403i
$988$	−6.32827e52	+	2.02628e53i	−0.0786430	+	0.251811i
$989$	1.16187e52			0.0141783
$990$	−1.36423e53	−	2.08075e52i	−0.163476	−	0.0249337i
$991$			9.10869e53i			1.07184i	0.844269	+	0.535920i	$0.180035\pi$
$991$			9.10869e53i			1.07184i	−0.844269	+	0.535920i	$0.819965\pi$
$992$	−6.63693e53	−	6.26752e53i	−0.766932	−	0.724245i
$993$	5.34156e53			0.606152
$994$	5.16863e52	−	3.38877e53i	0.0575997	−	0.377648i
$995$			5.13627e53i			0.562124i
$996$	−5.68642e53	−	1.77593e53i	−0.611182	−	0.190878i
$997$	−1.52141e54			−1.60596			−0.802979	−	0.596008i	$-0.796753\pi$
$997$	−1.52141e54			−1.60596			−0.802979	+	0.596008i	$0.796753\pi$
$998$	1.04068e54	+	1.58727e53i	1.07887	+	0.164552i
$999$			9.51498e53i			0.968789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.37.b.b.3.8	yes	16
4.3	odd	2	inner	4.37.b.b.3.7	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.37.b.b.3.7	✓	16	4.3	odd	2	inner
4.37.b.b.3.8	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-39525.7 + 259147. i) q^{2} -1.35614e8i q^{3} +(-6.55949e10 - 2.04859e10i) q^{4} -1.24080e12 q^{5} +(3.51440e13 + 5.36025e12i) q^{6} +4.20496e14i q^{7} +(7.90156e15 - 1.61890e16i) q^{8} +1.31703e17 q^{9} +O(q^{10})\)	\(q+(-39525.7 + 259147. i) q^{2} -1.35614e8i q^{3} +(-6.55949e10 - 2.04859e10i) q^{4} -1.24080e12 q^{5} +(3.51440e13 + 5.36025e12i) q^{6} +4.20496e14i q^{7} +(7.90156e15 - 1.61890e16i) q^{8} +1.31703e17 q^{9} +(4.90435e16 - 3.21549e17i) q^{10} -3.22138e18i q^{11} +(-2.77819e18 + 8.89561e18i) q^{12} -2.28918e19 q^{13} +(-1.08970e20 - 1.66204e19i) q^{14} +1.68270e20i q^{15} +(3.88302e21 + 2.68755e21i) q^{16} +6.53319e21 q^{17} +(-5.20567e21 + 3.41305e22i) q^{18} +1.34943e23i q^{19} +(8.13901e22 + 2.54189e22i) q^{20} +5.70253e22 q^{21} +(8.34811e23 + 1.27327e23i) q^{22} -4.96373e22i q^{23} +(-2.19546e24 - 1.07156e24i) q^{24} -1.30123e25 q^{25} +(9.04813e23 - 5.93233e24i) q^{26} -3.82158e25i q^{27} +(8.61427e24 - 2.75824e25i) q^{28} -1.19240e26 q^{29} +(-4.36067e25 - 6.65100e24i) q^{30} +7.37399e26i q^{31} +(-8.49949e26 + 9.00045e26i) q^{32} -4.36865e26 q^{33} +(-2.58229e26 + 1.69306e27i) q^{34} -5.21751e26i q^{35} +(-8.63907e27 - 2.69807e27i) q^{36} -2.48980e28 q^{37} +(-3.49701e28 - 5.33372e27i) q^{38} +3.10445e27i q^{39} +(-9.80425e27 + 2.00873e28i) q^{40} -1.04174e29 q^{41} +(-2.25397e27 + 1.47779e28i) q^{42} +2.34072e29i q^{43} +(-6.59930e28 + 2.11306e29i) q^{44} -1.63417e29 q^{45} +(1.28634e28 + 1.96195e27i) q^{46} -6.54567e29i q^{47} +(3.64470e29 - 5.26593e29i) q^{48} +2.47491e30 q^{49} +(5.14322e29 - 3.37211e30i) q^{50} -8.85993e29i q^{51} +(1.50158e30 + 4.68959e29i) q^{52} +8.42648e30 q^{53} +(9.90352e30 + 1.51051e30i) q^{54} +3.99708e30i q^{55} +(6.80742e30 + 3.32258e30i) q^{56} +1.83002e31 q^{57} +(4.71306e30 - 3.09007e31i) q^{58} +6.65287e31i q^{59} +(3.44717e30 - 1.10377e31i) q^{60} -1.74158e32 q^{61} +(-1.91095e32 - 2.91462e31i) q^{62} +5.53808e31i q^{63} +(-1.99649e32 - 2.55837e32i) q^{64} +2.84041e31 q^{65} +(1.72674e31 - 1.13212e32i) q^{66} +1.02480e33i q^{67} +(-4.28544e32 - 1.33839e32i) q^{68} -6.73153e30 q^{69} +(1.35210e32 + 2.06226e31i) q^{70} +3.10980e33i q^{71} +(1.04066e33 - 2.13215e33i) q^{72} +3.37473e33 q^{73} +(9.84112e32 - 6.45225e33i) q^{74} +1.76466e33i q^{75} +(2.76443e33 - 8.85157e33i) q^{76} +1.35458e33 q^{77} +(-8.04509e32 - 1.22706e32i) q^{78} +1.58850e34i q^{79} +(-4.81804e33 - 3.33471e33i) q^{80} +1.45854e34 q^{81} +(4.11757e33 - 2.69965e34i) q^{82} +6.39239e34i q^{83} +(-3.74057e33 - 1.16822e33i) q^{84} -8.10637e33 q^{85} +(-6.06590e34 - 9.25185e33i) q^{86} +1.61707e34i q^{87} +(-5.21509e34 - 2.54539e34i) q^{88} -1.63956e35 q^{89} +(6.45919e33 - 4.23491e34i) q^{90} -9.62590e33i q^{91} +(-1.01687e33 + 3.25596e33i) q^{92} +1.00002e35 q^{93} +(1.69629e35 + 2.58722e34i) q^{94} -1.67437e35i q^{95} +(1.22059e35 + 1.15265e35i) q^{96} +3.39752e35 q^{97} +(-9.78227e34 + 6.41367e35i) q^{98} -4.24267e35i 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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