LMFDB - Embedded newform 4.23.b.a.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,23,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, 23, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 23);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 23 $
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:	$12.2682973937$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5 x^{9} - 63342 x^{8} - 45742928 x^{7} + 34835133568 x^{6} + 12622768560288 x^{5} + \cdots + 11\!\cdots\!40 $ x^10 - 5x^9 - 63342x^8 - 45742928x^7 + 34835133568x^6 + 12622768560288x^5 + 13335465927292608x^4 - 404504858109047040x^3 - 95573988251584922880x^2 - 1820809561188275535801600*x + 1168838172864011361183920640
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{90}\cdot 3^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.8
Root			$407.912 - 251.607i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.23.b.a.3.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1783.65 + 1006.43i) q^{2} +267899. i q^{3} +(2.16851e6 + 3.59023e6i) q^{4} +8.57934e7 q^{5} +(-2.69621e8 + 4.77838e8i) q^{6} -2.80689e8i q^{7} +(2.54549e8 + 8.58616e9i) q^{8} -4.03887e10 q^{9} +O(q^{10})$	\(q+(1783.65 + 1006.43i) q^{2} +267899. i q^{3} +(2.16851e6 + 3.59023e6i) q^{4} +8.57934e7 q^{5} +(-2.69621e8 + 4.77838e8i) q^{6} -2.80689e8i q^{7} +(2.54549e8 + 8.58616e9i) q^{8} -4.03887e10 q^{9} +(1.53025e11 + 8.63449e10i) q^{10} -3.14573e11i q^{11} +(-9.61819e11 + 5.80941e11i) q^{12} -8.66330e11 q^{13} +(2.82493e11 - 5.00651e11i) q^{14} +2.29840e13i q^{15} +(-8.18733e12 + 1.55709e13i) q^{16} -3.75137e12 q^{17} +(-7.20393e13 - 4.06483e13i) q^{18} -1.33634e14i q^{19} +(1.86044e14 + 3.08018e14i) q^{20} +7.51962e13 q^{21} +(3.16595e14 - 5.61088e14i) q^{22} -6.25471e14i q^{23} +(-2.30022e15 + 6.81933e13i) q^{24} +4.97633e15 q^{25} +(-1.54523e15 - 8.71899e14i) q^{26} -2.41314e15i q^{27} +(1.00774e15 - 6.08676e14i) q^{28} -8.54642e14 q^{29} +(-2.31317e16 + 4.09953e16i) q^{30} -1.29693e16i q^{31} +(-3.02743e16 + 1.95331e16i) q^{32} +8.42737e16 q^{33} +(-6.69114e15 - 3.77549e15i) q^{34} -2.40813e16i q^{35} +(-8.75833e16 - 1.45005e17i) q^{36} +7.84749e16 q^{37} +(1.34493e17 - 2.38356e17i) q^{38} -2.32089e17i q^{39} +(2.18386e16 + 7.36636e17i) q^{40} -1.08475e17 q^{41} +(1.34124e17 + 7.56796e16i) q^{42} +5.77743e17i q^{43} +(1.12939e18 - 6.82154e17i) q^{44} -3.46509e18 q^{45} +(6.29492e17 - 1.11562e18i) q^{46} +3.78620e18i q^{47} +(-4.17142e18 - 2.19338e18i) q^{48} +3.83103e18 q^{49} +(8.87602e18 + 5.00831e18i) q^{50} -1.00499e18i q^{51} +(-1.87864e18 - 3.11033e18i) q^{52} -1.21175e19 q^{53} +(2.42865e18 - 4.30420e18i) q^{54} -2.69883e19i q^{55} +(2.41004e18 - 7.14490e16i) q^{56} +3.58004e19 q^{57} +(-1.52438e18 - 8.60136e17i) q^{58} +3.48973e19i q^{59} +(-8.25177e19 + 4.98409e19i) q^{60} +3.03732e19 q^{61} +(1.30527e19 - 2.31328e19i) q^{62} +1.13367e19i q^{63} +(-7.36574e19 + 4.37119e18i) q^{64} -7.43254e19 q^{65} +(1.50315e20 + 8.48155e19i) q^{66} -9.42821e19i q^{67} +(-8.13488e18 - 1.34683e19i) q^{68} +1.67563e20 q^{69} +(2.42361e19 - 4.29525e19i) q^{70} -2.75278e20i q^{71} +(-1.02809e19 - 3.46784e20i) q^{72} -4.18518e20 q^{73} +(1.39972e20 + 7.89793e19i) q^{74} +1.33315e21i q^{75} +(4.79777e20 - 2.89786e20i) q^{76} -8.82972e19 q^{77} +(2.33581e20 - 4.13965e20i) q^{78} -9.99374e20i q^{79} +(-7.02419e20 + 1.33588e21i) q^{80} -6.20963e20 q^{81} +(-1.93481e20 - 1.09172e20i) q^{82} +1.27883e20i q^{83} +(1.63064e20 + 2.69972e20i) q^{84} -3.21843e20 q^{85} +(-5.81457e20 + 1.03049e21i) q^{86} -2.28957e20i q^{87} +(2.70098e21 - 8.00741e19i) q^{88} +5.20354e21 q^{89} +(-6.18050e21 - 3.48736e21i) q^{90} +2.43169e20i q^{91} +(2.24559e21 - 1.35634e21i) q^{92} +3.47447e21 q^{93} +(-3.81054e21 + 6.75326e21i) q^{94} -1.14649e22i q^{95} +(-5.23288e21 - 8.11045e21i) q^{96} -2.44391e21 q^{97} +(6.83322e21 + 3.85566e21i) q^{98} +1.27052e22i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 1540 q^{2} + 2264464 q^{4} - 17091100 q^{5} - 791935776 q^{6} + 9804431680 q^{8} - 104309613702 q^{9}+O(q^{10}) $ 10 * q + 1540 * q^2 + 2264464 * q^4 - 17091100 * q^5 - 791935776 * q^6 + 9804431680 * q^8 - 104309613702 * q^9	$ 10 q + 1540 q^{2} + 2264464 q^{4} - 17091100 q^{5} - 791935776 q^{6} + 9804431680 q^{8} - 104309613702 q^{9} + 159414035240 q^{10} + 519021175680 q^{12} - 531230356540 q^{13} - 5894008940736 q^{14} - 27717620084480 q^{16} + 14058178115540 q^{17} + 16283956279140 q^{18} + 233643631625120 q^{20} - 313135665760512 q^{21} + 120589650366240 q^{22} - 20\!\cdots\!36 q^{24}+ \cdots - 23\!\cdots\!20 q^{98}+O(q^{100}) $ 10 * q + 1540 * q^2 + 2264464 * q^4 - 17091100 * q^5 - 791935776 * q^6 + 9804431680 * q^8 - 104309613702 * q^9 + 159414035240 * q^10 + 519021175680 * q^12 - 531230356540 * q^13 - 5894008940736 * q^14 - 27717620084480 * q^16 + 14058178115540 * q^17 + 16283956279140 * q^18 + 233643631625120 * q^20 - 313135665760512 * q^21 + 120589650366240 * q^22 - 2007619616180736 * q^24 + 7710175817606670 * q^25 - 3953973318046744 * q^26 + 1177952265288960 * q^28 - 14464474185570172 * q^29 + 10252783730669760 * q^30 - 73831192092953600 * q^32 + 72906957628179840 * q^33 - 26625976920357496 * q^34 - 36609276067793136 * q^36 + 324587767823538020 * q^37 + 369140808808591200 * q^38 - 1158049295468479360 * q^40 - 1355457345814233100 * q^41 + 2644455724909770240 * q^42 - 1919761520625210240 * q^44 + 9367295763131460 * q^45 + 6132624002565203904 * q^46 - 18374169355003791360 * q^48 + 183553700661552298 * q^49 + 29084394113996178540 * q^50 - 38492433127521128800 * q^52 - 11424344766226018780 * q^53 + 79182840955393027008 * q^54 - 102844865827678657536 * q^56 + 30188516183231506560 * q^57 + 173059696836432320360 * q^58 - 377769459746631548160 * q^60 + 58241718146183220740 * q^61 + 317897221476923285760 * q^62 - 412080172429987966976 * q^64 - 121531695066047433560 * q^65 + 700585278654050000640 * q^66 - 667890522330713878240 * q^68 + 54497497397908094208 * q^69 + 1014396282552321513600 * q^70 - 1244773253376491901120 * q^72 + 83030422224875883380 * q^73 + 801906083011176262184 * q^74 + 286747421140990627200 * q^76 - 704201825495570814720 * q^77 - 964412732782594923840 * q^78 + 1509611955050789726720 * q^80 + 251577744224553978858 * q^81 - 2389572513290905036600 * q^82 + 6185640644326191863808 * q^84 - 1796890366112110859960 * q^85 - 8221838255181360278496 * q^86 + 11178210842814940531200 * q^88 + 3420669206528505615668 * q^89 - 24782809563337507735320 * q^90 + 21476264197983864733440 * q^92 + 15493754050318100597760 * q^93 - 20874543047091388369536 * q^94 + 29250284502468708163584 * q^96 - 20429910746446196146540 * q^97 - 23110416876469762175420 * 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 $

$2$	1783.65	+	1006.43i	0.870923	+	0.491420i
$2$	1783.65	+	1006.43i	0.870923	+	0.491420i
$3$			267899.i			1.51230i	0.654400	+	0.756148i	$0.272921\pi$
$3$			267899.i			1.51230i	−0.654400	+	0.756148i	$0.727079\pi$
$4$	2.16851e6	+	3.59023e6i	0.517013	+	0.855978i
$5$	8.57934e7			1.75705			0.878525	−	0.477697i	$-0.158528\pi$
$5$	8.57934e7			1.75705			0.878525	+	0.477697i	$0.158528\pi$
$6$	−2.69621e8	+	4.77838e8i	−0.743173	+	1.31709i
$7$		−	2.80689e8i		−	0.141954i	−0.997478	−	0.0709769i	$-0.977388\pi$
$7$		−	2.80689e8i		−	0.141954i	0.997478	−	0.0709769i	$-0.0226117\pi$
$8$	2.54549e8	+	8.58616e9i	0.0296334	+	0.999561i
$9$	−4.03887e10			−1.28704
$10$	1.53025e11	+	8.63449e10i	1.53025	+	0.863449i
$11$		−	3.14573e11i		−	1.10256i	−0.834321	−	0.551280i	$-0.814140\pi$
$11$		−	3.14573e11i		−	1.10256i	0.834321	−	0.551280i	$-0.185860\pi$
$12$	−9.61819e11	+	5.80941e11i	−1.29449	+	0.781876i
$13$	−8.66330e11			−0.483400			−0.241700	−	0.970351i	$-0.577705\pi$
$13$	−8.66330e11			−0.483400			−0.241700	+	0.970351i	$0.577705\pi$
$14$	2.82493e11	−	5.00651e11i	0.0697589	−	0.123631i
$15$			2.29840e13i			2.65718i
$16$	−8.18733e12	+	1.55709e13i	−0.465396	+	0.885103i
$17$	−3.75137e12			−0.109459			−0.0547296	−	0.998501i	$-0.517430\pi$
$17$	−3.75137e12			−0.109459			−0.0547296	+	0.998501i	$0.517430\pi$
$18$	−7.20393e13	−	4.06483e13i	−1.12091	−	0.632478i
$19$		−	1.33634e14i		−	1.14717i	−0.819147	−	0.573584i	$-0.805553\pi$
$19$		−	1.33634e14i		−	1.14717i	0.819147	−	0.573584i	$-0.194447\pi$
$20$	1.86044e14	+	3.08018e14i	0.908417	+	1.50400i
$21$	7.51962e13			0.214676
$22$	3.16595e14	−	5.61088e14i	0.541820	−	0.960244i
$23$		−	6.25471e14i		−	0.656449i	−0.944600	−	0.328225i	$-0.893550\pi$
$23$		−	6.25471e14i		−	0.656449i	0.944600	−	0.328225i	$-0.106450\pi$
$24$	−2.30022e15	+	6.81933e13i	−1.51163	+	0.0448144i
$25$	4.97633e15			2.08722
$26$	−1.54523e15	−	8.71899e14i	−0.421004	−	0.237552i
$27$		−	2.41314e15i		−	0.434091i
$28$	1.00774e15	−	6.08676e14i	0.121509	−	0.0733919i
$29$	−8.54642e14			−0.0700497			−0.0350248	−	0.999386i	$-0.511151\pi$
$29$	−8.54642e14			−0.0700497			−0.0350248	+	0.999386i	$0.511151\pi$
$30$	−2.31317e16	+	4.09953e16i	−1.30579	+	2.31420i
$31$		−	1.29693e16i		−	0.510433i	−0.966884	−	0.255217i	$-0.917853\pi$
$31$		−	1.29693e16i		−	0.510433i	0.966884	−	0.255217i	$-0.0821468\pi$
$32$	−3.02743e16	+	1.95331e16i	−0.840281	+	0.542151i
$33$	8.42737e16			1.66740
$34$	−6.69114e15	−	3.77549e15i	−0.0953305	−	0.0537904i
$35$		−	2.40813e16i		−	0.249420i
$36$	−8.75833e16	−	1.45005e17i	−0.665417	−	1.10168i
$37$	7.84749e16			0.441074			0.220537	−	0.975379i	$-0.429219\pi$
$37$	7.84749e16			0.441074			0.220537	+	0.975379i	$0.429219\pi$
$38$	1.34493e17	−	2.38356e17i	0.563742	−	0.999095i
$39$		−	2.32089e17i		−	0.731044i
$40$	2.18386e16	+	7.36636e17i	0.0520673	+	1.75628i
$41$	−1.08475e17			−0.197109			−0.0985545	−	0.995132i	$-0.531422\pi$
$41$	−1.08475e17			−0.197109			−0.0985545	+	0.995132i	$0.531422\pi$
$42$	1.34124e17	+	7.56796e16i	0.186966	+	0.105496i
$43$			5.77743e17i			0.621701i	0.950459	+	0.310851i	$0.100614\pi$
$43$			5.77743e17i			0.621701i	−0.950459	+	0.310851i	$0.899386\pi$
$44$	1.12939e18	−	6.82154e17i	0.943766	−	0.570037i
$45$	−3.46509e18			−2.26139
$46$	6.29492e17	−	1.11562e18i	0.322592	−	0.571716i
$47$			3.78620e18i			1.53154i	0.643116	+	0.765769i	$0.277641\pi$
$47$			3.78620e18i			1.53154i	−0.643116	+	0.765769i	$0.722359\pi$
$48$	−4.17142e18	−	2.19338e18i	−1.33854	−	0.703817i
$49$	3.83103e18			0.979849
$50$	8.87602e18	+	5.00831e18i	1.81781	+	1.02570i
$51$		−	1.00499e18i		−	0.165535i
$52$	−1.87864e18	−	3.11033e18i	−0.249924	−	0.413780i
$53$	−1.21175e19			−1.30731			−0.653653	−	0.756795i	$-0.726764\pi$
$53$	−1.21175e19			−1.30731			−0.653653	+	0.756795i	$0.726764\pi$
$54$	2.42865e18	−	4.30420e18i	0.213321	−	0.378060i
$55$		−	2.69883e19i		−	1.93725i
$56$	2.41004e18	−	7.14490e16i	0.141891	−	0.00420657i
$57$	3.58004e19			1.73486
$58$	−1.52438e18	−	8.60136e17i	−0.0610078	−	0.0344238i
$59$			3.48973e19i			1.15723i	0.815600	+	0.578615i	$0.196407\pi$
$59$			3.48973e19i			1.15723i	−0.815600	+	0.578615i	$0.803593\pi$
$60$	−8.25177e19	+	4.98409e19i	−2.27449	+	1.37380i
$61$	3.03732e19			0.698010			0.349005	−	0.937121i	$-0.386520\pi$
$61$	3.03732e19			0.698010			0.349005	+	0.937121i	$0.386520\pi$
$62$	1.30527e19	−	2.31328e19i	0.250837	−	0.444548i
$63$			1.13367e19i			0.182700i
$64$	−7.36574e19	+	4.37119e18i	−0.998244	+	0.0592407i
$65$	−7.43254e19			−0.849357
$66$	1.50315e20	+	8.48155e19i	1.45217	+	0.819392i
$67$		−	9.42821e19i		−	0.771980i	−0.922503	−	0.385990i	$-0.873860\pi$
$67$		−	9.42821e19i		−	0.771980i	0.922503	−	0.385990i	$-0.126140\pi$
$68$	−8.13488e18	−	1.34683e19i	−0.0565918	−	0.0936946i
$69$	1.67563e20			0.992746
$70$	2.42361e19	−	4.29525e19i	0.122570	−	0.217225i
$71$		−	2.75278e20i		−	1.19105i	−0.803337	−	0.595525i	$-0.796944\pi$
$71$		−	2.75278e20i		−	1.19105i	0.803337	−	0.595525i	$-0.203056\pi$
$72$	−1.02809e19	−	3.46784e20i	−0.0381393	−	1.28648i
$73$	−4.18518e20			−1.33402			−0.667011	−	0.745048i	$-0.732427\pi$
$73$	−4.18518e20			−1.33402			−0.667011	+	0.745048i	$0.732427\pi$
$74$	1.39972e20	+	7.89793e19i	0.384141	+	0.216753i
$75$			1.33315e21i			3.15650i
$76$	4.79777e20	−	2.89786e20i	0.981951	−	0.593101i
$77$	−8.82972e19			−0.156512
$78$	2.33581e20	−	4.13965e20i	0.359250	−	0.636683i
$79$		−	9.99374e20i		−	1.33607i	−0.744129	−	0.668036i	$-0.767135\pi$
$79$		−	9.99374e20i		−	1.33607i	0.744129	−	0.668036i	$-0.232865\pi$
$80$	−7.02419e20	+	1.33588e21i	−0.817724	+	1.55517i
$81$	−6.20963e20			−0.630566
$82$	−1.93481e20	−	1.09172e20i	−0.171667	−	0.0968633i
$83$			1.27883e20i			0.0993010i	0.998767	+	0.0496505i	$0.0158108\pi$
$83$			1.27883e20i			0.0993010i	−0.998767	+	0.0496505i	$0.984189\pi$
$84$	1.63064e20	+	2.69972e20i	0.110990	+	0.183758i
$85$	−3.21843e20			−0.192325
$86$	−5.81457e20	+	1.03049e21i	−0.305517	+	0.541454i
$87$		−	2.28957e20i		−	0.105936i
$88$	2.70098e21	−	8.00741e19i	1.10208	−	0.0326725i
$89$	5.20354e21			1.87503			0.937517	−	0.347939i	$-0.113118\pi$
$89$	5.20354e21			1.87503			0.937517	+	0.347939i	$0.113118\pi$
$90$	−6.18050e21	−	3.48736e21i	−1.96950	−	1.11129i
$91$			2.43169e20i			0.0686204i
$92$	2.24559e21	−	1.35634e21i	0.561906	−	0.339393i
$93$	3.47447e21			0.771927
$94$	−3.81054e21	+	6.75326e21i	−0.752628	+	1.33385i
$95$		−	1.14649e22i		−	2.01563i
$96$	−5.23288e21	−	8.11045e21i	−0.819893	−	1.27075i
$97$	−2.44391e21			−0.341661			−0.170831	−	0.985300i	$-0.554645\pi$
$97$	−2.44391e21			−0.341661			−0.170831	+	0.985300i	$0.554645\pi$
$98$	6.83322e21	+	3.85566e21i	0.853373	+	0.481518i
$99$			1.27052e22i			1.41904i
$100$	1.07912e22	+	1.78662e22i	1.07912	+	1.78662i
$101$	−1.82886e22			−1.63925			−0.819625	−	0.572900i	$-0.805818\pi$
$101$	−1.82886e22			−1.63925			−0.819625	+	0.572900i	$0.805818\pi$
$102$	1.01145e21	−	1.79255e21i	0.0813471	−	0.144168i
$103$			1.47608e22i			1.06635i	0.846005	+	0.533175i	$0.179001\pi$
$103$			1.47608e22i			1.06635i	−0.846005	+	0.533175i	$0.820999\pi$
$104$	−2.20523e20	−	7.43845e21i	−0.0143248	−	0.483188i
$105$	6.45134e21			0.377197
$106$	−2.16133e22	−	1.21954e22i	−1.13856	−	0.642436i
$107$		−	1.08643e22i		−	0.516154i	−0.966124	−	0.258077i	$-0.916911\pi$
$107$		−	1.08643e22i		−	0.516154i	0.966124	−	0.258077i	$-0.0830888\pi$
$108$	8.66373e21	−	5.23292e21i	0.371573	−	0.224431i
$109$	−3.84349e21			−0.148948			−0.0744740	−	0.997223i	$-0.523728\pi$
$109$	−3.84349e21			−0.148948			−0.0744740	+	0.997223i	$0.523728\pi$
$110$	2.71618e22	−	4.81377e22i	0.952004	−	1.68720i
$111$			2.10233e22i			0.667035i
$112$	4.37058e21	+	2.29809e21i	0.125644	+	0.0660647i
$113$	−2.39468e22			−0.624288			−0.312144	−	0.950035i	$-0.601047\pi$
$113$	−2.39468e22			−0.624288			−0.312144	+	0.950035i	$0.601047\pi$
$114$	6.38553e22	+	3.60305e22i	1.51093	+	0.852544i
$115$		−	5.36613e22i		−	1.15341i
$116$	−1.85330e21	−	3.06836e21i	−0.0362166	−	0.0599610i
$117$	3.49900e22			0.622156
$118$	−3.51217e22	+	6.22446e22i	−0.568687	+	1.00786i
$119$			1.05297e21i			0.0155381i
$120$	−1.97344e23	+	5.85053e21i	−2.65601	+	0.0787411i
$121$	−1.75534e22			−0.215637
$122$	5.41751e22	+	3.05684e22i	0.607913	+	0.343016i
$123$		−	2.90603e22i		−	0.298087i
$124$	4.65629e22	−	2.81241e22i	0.436920	−	0.263901i
$125$	2.22389e23			1.91030
$126$	−1.14095e22	+	2.02206e22i	−0.0897826	+	0.159118i
$127$			2.31209e23i			1.66787i	0.551859	+	0.833937i	$0.313919\pi$
$127$			2.31209e23i			1.66787i	−0.551859	+	0.833937i	$0.686081\pi$
$128$	−1.35778e23	−	6.63342e22i	−0.898505	−	0.438963i
$129$	−1.54777e23			−0.940197
$130$	−1.32571e23	−	7.48032e22i	−0.739725	−	0.417391i
$131$		−	2.78891e23i		−	1.43038i	−0.698931	−	0.715189i	$-0.746341\pi$
$131$		−	2.78891e23i		−	1.43038i	0.698931	−	0.715189i	$-0.253659\pi$
$132$	1.82748e23	+	3.02562e23i	0.862065	+	1.42725i
$133$	−3.75096e22			−0.162845
$134$	9.48881e22	−	1.68166e23i	0.379367	−	0.672335i
$135$		−	2.07032e23i		−	0.762720i
$136$	−9.54907e20	−	3.22099e22i	−0.00324364	−	0.109411i
$137$	3.76004e23			1.17833			0.589164	−	0.808014i	$-0.299457\pi$
$137$	3.76004e23			1.17833			0.589164	+	0.808014i	$0.299457\pi$
$138$	2.98874e23	+	1.68640e23i	0.864605	+	0.487855i
$139$			1.58212e23i			0.422742i	0.977406	+	0.211371i	$0.0677929\pi$
$139$			1.58212e23i			0.422742i	−0.977406	+	0.211371i	$0.932207\pi$
$140$	8.64573e22	−	5.22204e22i	0.213498	−	0.128953i
$141$	−1.01432e24			−2.31614
$142$	2.77048e23	−	4.91000e23i	0.585306	−	1.03731i
$143$			2.72524e23i			0.532977i
$144$	3.30676e23	−	6.28888e23i	0.598984	−	1.13916i
$145$	−7.33226e22			−0.123081
$146$	−7.46490e23	−	4.21209e23i	−1.16183	−	0.655565i
$147$			1.02633e24i			1.48182i
$148$	1.70173e23	+	2.81743e23i	0.228041	+	0.377550i
$149$	2.83081e23			0.352259			0.176129	−	0.984367i	$-0.443642\pi$
$149$	2.83081e23			0.352259			0.176129	+	0.984367i	$0.443642\pi$
$150$	−1.34172e24	+	2.37788e24i	−1.55117	+	2.74907i
$151$			4.36848e22i			0.0469444i	0.999724	+	0.0234722i	$0.00747213\pi$
$151$			4.36848e22i			0.0469444i	−0.999724	+	0.0234722i	$0.992528\pi$
$152$	1.14740e24	−	3.40163e22i	1.14666	−	0.0339944i
$153$	1.51513e23			0.140878
$154$	−1.57491e23	−	8.88648e22i	−0.136310	−	0.0769134i
$155$		−	1.11268e24i		−	0.896857i
$156$	8.33253e23	−	5.03287e23i	0.625757	−	0.377959i
$157$	4.00138e22			0.0280100			0.0140050	−	0.999902i	$-0.495542\pi$
$157$	4.00138e22			0.0280100			0.0140050	+	0.999902i	$0.495542\pi$
$158$	1.00580e24	−	1.78253e24i	0.656573	−	1.16362i
$159$		−	3.24625e24i		−	1.97703i
$160$	−2.59734e24	+	1.67581e24i	−1.47642	+	0.952586i
$161$	−1.75563e23			−0.0931854
$162$	−1.10758e24	−	6.24955e23i	−0.549174	−	0.309873i
$163$			1.75209e24i			0.811883i	0.913899	+	0.405941i	$0.133056\pi$
$163$			1.75209e24i			0.811883i	−0.913899	+	0.405941i	$0.866944\pi$
$164$	−2.35228e23	−	3.89449e23i	−0.101908	−	0.168721i
$165$	7.23013e24			2.92970
$166$	−1.28705e23	+	2.28098e23i	−0.0487985	+	0.0864835i
$167$		−	6.61040e23i		−	0.234610i	−0.993096	−	0.117305i	$-0.962574\pi$
$167$		−	6.61040e23i		−	0.234610i	0.993096	−	0.117305i	$-0.0374255\pi$
$168$	1.91411e22	+	6.45647e23i	0.00636158	+	0.214582i
$169$	−2.46131e24			−0.766325
$170$	−5.74056e23	−	3.23912e23i	−0.167500	−	0.0945125i
$171$			5.39730e24i			1.47645i
$172$	−2.07423e24	+	1.25284e24i	−0.532163	+	0.321427i
$173$	−4.58679e24			−1.10408			−0.552041	−	0.833817i	$-0.686151\pi$
$173$	−4.58679e24			−1.10408			−0.552041	+	0.833817i	$0.686151\pi$
$174$	2.30429e23	−	4.08380e23i	0.0520590	−	0.0922620i
$175$		−	1.39680e24i		−	0.296289i
$176$	4.89818e24	+	2.57551e24i	0.975878	+	0.513127i
$177$	−9.34895e24			−1.75008
$178$	9.28130e24	+	5.23699e24i	1.63301	+	0.921430i
$179$		−	5.77013e24i		−	0.954557i	−0.878752	−	0.477279i	$-0.841623\pi$
$179$		−	5.77013e24i		−	0.954557i	0.878752	−	0.477279i	$-0.158377\pi$
$180$	−7.51407e24	−	1.24405e25i	−1.16917	−	1.93570i
$181$	2.20708e24			0.323112			0.161556	−	0.986864i	$-0.448349\pi$
$181$	2.20708e24			0.323112			0.161556	+	0.986864i	$0.448349\pi$
$182$	−2.44733e23	+	4.33729e23i	−0.0337215	+	0.0597631i
$183$			8.13693e24i			1.05560i
$184$	5.37040e24	−	1.59213e23i	0.656161	−	0.0194528i
$185$	6.73263e24			0.774989
$186$	6.19724e24	+	3.49680e24i	0.672289	+	0.379340i
$187$			1.18008e24i			0.120685i
$188$	−1.35933e25	+	8.21041e24i	−1.31096	+	0.791824i
$189$	−6.77342e23			−0.0616209
$190$	1.15386e25	−	2.04494e25i	0.990522	−	1.75546i
$191$			8.70625e24i			0.705446i	0.935728	+	0.352723i	$0.114744\pi$
$191$			8.70625e24i			0.705446i	−0.935728	+	0.352723i	$0.885256\pi$
$192$	−1.17104e24	−	1.97327e25i	−0.0895895	−	1.50964i
$193$	−1.26103e25			−0.911162			−0.455581	−	0.890194i	$-0.650568\pi$
$193$	−1.26103e25			−0.911162			−0.455581	+	0.890194i	$0.650568\pi$
$194$	−4.35908e24	−	2.45962e24i	−0.297561	−	0.167899i
$195$		−	1.99117e25i		−	1.28448i
$196$	8.30763e24	+	1.37543e25i	0.506594	+	0.838729i
$197$	1.67517e25			0.965897			0.482949	−	0.875649i	$-0.339566\pi$
$197$	1.67517e25			0.965897			0.482949	+	0.875649i	$0.339566\pi$
$198$	−1.27869e25	+	2.26616e25i	−0.697344	+	1.23587i
$199$		−	1.44695e25i		−	0.746570i	−0.927717	−	0.373285i	$-0.878231\pi$
$199$		−	1.44695e25i		−	0.746570i	0.927717	−	0.373285i	$-0.121769\pi$
$200$	1.26672e24	+	4.27275e25i	0.0618514	+	2.08631i
$201$	2.52580e25			1.16746
$202$	−3.26205e25	−	1.84062e25i	−1.42766	−	0.805561i
$203$			2.39888e23i			0.00994381i
$204$	3.60814e24	−	2.17933e24i	0.141694	−	0.0855836i
$205$	−9.30642e24			−0.346330
$206$	−1.48557e25	+	2.63280e25i	−0.524026	+	0.928708i
$207$			2.52620e25i			0.844877i
$208$	7.09293e24	−	1.34895e25i	0.224972	−	0.427859i
$209$	−4.20376e25			−1.26482
$210$	1.15069e25	+	6.49281e24i	0.328509	+	0.185362i
$211$		−	7.78670e23i		−	0.0210983i	−0.999944	−	0.0105491i	$-0.996642\pi$
$211$		−	7.78670e23i		−	0.0210983i	0.999944	−	0.0105491i	$-0.00335795\pi$
$212$	−2.62768e25	−	4.35045e25i	−0.675893	−	1.11902i
$213$	7.37467e25			1.80122
$214$	1.09341e25	−	1.93781e25i	0.253648	−	0.449530i
$215$			4.95666e25i			1.09236i
$216$	2.07196e25	−	6.14262e23i	0.433901	−	0.0128636i
$217$	−3.64035e24			−0.0724579
$218$	−6.85545e24	−	3.86820e24i	−0.129722	−	0.0731961i
$219$		−	1.12121e26i		−	2.01744i
$220$	9.68942e25	−	5.85243e25i	1.65824	−	1.00158i
$221$	3.24993e24			0.0529126
$222$	−2.11585e25	+	3.74982e25i	−0.327794	+	0.580936i
$223$		−	4.07489e25i		−	0.600845i	−0.953806	−	0.300422i	$-0.902872\pi$
$223$		−	4.07489e25i		−	0.600845i	0.953806	−	0.300422i	$-0.0971276\pi$
$224$	5.48271e24	+	8.49767e24i	0.0769604	+	0.119281i
$225$	−2.00987e26			−2.68634
$226$	−4.27127e25	−	2.41007e25i	−0.543706	−	0.306787i
$227$			1.44325e26i			1.75008i	0.484055	+	0.875038i	$0.339164\pi$
$227$			1.44325e26i			1.75008i	−0.484055	+	0.875038i	$0.660836\pi$
$228$	7.76334e25	+	1.28532e26i	0.896944	+	1.48500i
$229$	2.44064e25			0.268729			0.134364	−	0.990932i	$-0.457101\pi$
$229$	2.44064e25			0.268729			0.134364	+	0.990932i	$0.457101\pi$
$230$	5.40063e25	−	9.57130e25i	0.566811	−	1.00453i
$231$		−	2.36547e25i		−	0.236693i
$232$	−2.17548e23	−	7.33809e24i	−0.00207581	−	0.0700189i
$233$	−5.11004e25			−0.465060			−0.232530	−	0.972589i	$-0.574700\pi$
$233$	−5.11004e25			−0.465060			−0.232530	+	0.972589i	$0.574700\pi$
$234$	6.24098e25	+	3.52149e25i	0.541849	+	0.305740i
$235$			3.24831e26i			2.69099i
$236$	−1.25289e26	+	7.56751e25i	−0.990564	+	0.598303i
$237$	2.67731e26			2.02054
$238$	−1.05974e24	+	1.87813e24i	−0.00763576	+	0.0135325i
$239$		−	2.84734e26i		−	1.95912i	−0.201141	−	0.979562i	$-0.564465\pi$
$239$		−	2.84734e26i		−	1.95912i	0.201141	−	0.979562i	$-0.435535\pi$
$240$	−3.57881e26	−	1.88177e26i	−2.35188	−	1.23664i
$241$	−1.87072e26			−1.17441			−0.587206	−	0.809438i	$-0.699772\pi$
$241$	−1.87072e26			−1.17441			−0.587206	+	0.809438i	$0.699772\pi$
$242$	−3.13092e25	−	1.76663e25i	−0.187803	−	0.105968i
$243$		−	2.42082e26i		−	1.38769i
$244$	6.58644e25	+	1.09047e26i	0.360880	+	0.597481i
$245$	3.28678e26			1.72164
$246$	2.92471e25	−	5.18333e25i	0.146486	−	0.259611i
$247$			1.15771e26i			0.554541i
$248$	1.11357e26	−	3.30133e24i	0.510209	−	0.0151259i
$249$	−3.42597e25			−0.150173
$250$	3.96663e26	+	2.23818e26i	1.66373	+	0.938761i
$251$		−	1.85043e26i		−	0.742782i	−0.928477	−	0.371391i	$-0.878881\pi$
$251$		−	1.85043e26i		−	0.742782i	0.928477	−	0.371391i	$-0.121119\pi$
$252$	−4.07013e25	+	2.45837e25i	−0.156387	+	0.0944584i
$253$	−1.96756e26			−0.723774
$254$	−2.32695e26	+	4.12396e26i	−0.819627	+	1.45259i
$255$		−	8.62214e25i		−	0.290853i
$256$	−1.75420e26	−	2.54968e26i	−0.566813	−	0.823846i
$257$	5.48207e26			1.69699			0.848497	−	0.529201i	$-0.177508\pi$
$257$	5.48207e26			1.69699			0.848497	+	0.529201i	$0.177508\pi$
$258$	−2.76067e26	−	1.55772e26i	−0.818839	−	0.462032i
$259$		−	2.20270e25i		−	0.0626121i
$260$	−1.61175e26	−	2.66845e26i	−0.439129	−	0.727031i
$261$	3.45179e25			0.0901568
$262$	2.80684e26	−	4.97444e26i	0.702916	−	1.24575i
$263$			8.51401e24i			0.0204466i	0.999948	+	0.0102233i	$0.00325423\pi$
$263$			8.51401e24i			0.0204466i	−0.999948	+	0.0102233i	$0.996746\pi$
$264$	2.14518e25	+	7.23588e26i	0.0494106	+	1.66666i
$265$	−1.03960e27			−2.29700
$266$	−6.69039e25	−	3.77507e25i	−0.141825	−	0.0800252i
$267$			1.39402e27i			2.83561i
$268$	3.38494e26	−	2.04451e26i	0.660798	−	0.399124i
$269$	7.78681e24			0.0145910			0.00729549	−	0.999973i	$-0.497678\pi$
$269$	7.78681e24			0.0145910			0.00729549	+	0.999973i	$0.497678\pi$
$270$	2.08362e26	−	3.69272e26i	0.374816	−	0.664270i
$271$			2.88467e26i			0.498234i	0.968473	+	0.249117i	$0.0801404\pi$
$271$			2.88467e26i			0.498234i	−0.968473	+	0.249117i	$0.919860\pi$
$272$	3.07137e25	−	5.84122e25i	0.0509419	−	0.0968826i
$273$	−6.51448e25			−0.103774
$274$	6.70659e26	+	3.78421e26i	1.02623	+	0.579054i
$275$		−	1.56542e27i		−	2.30129i
$276$	3.63362e26	+	6.01590e26i	0.513262	+	0.849768i
$277$	−3.96390e26			−0.538078			−0.269039	−	0.963129i	$-0.586706\pi$
$277$	−3.96390e26			−0.538078			−0.269039	+	0.963129i	$0.586706\pi$
$278$	−1.59229e26	+	2.82194e26i	−0.207744	+	0.368176i
$279$			5.23815e26i			0.656949i
$280$	2.06766e26	−	6.12985e24i	0.249310	−	0.00739114i
$281$	−1.00095e27			−1.16049			−0.580247	−	0.814440i	$-0.697044\pi$
$281$	−1.00095e27			−1.16049			−0.580247	+	0.814440i	$0.697044\pi$
$282$	−1.80919e27	−	1.02084e27i	−2.01718	−	1.13820i
$283$		−	9.65777e26i		−	1.03568i	−0.855477	−	0.517840i	$-0.826736\pi$
$283$		−	9.65777e26i		−	1.03568i	0.855477	−	0.517840i	$-0.173264\pi$
$284$	9.88313e26	−	5.96943e26i	1.01951	−	0.615788i
$285$	3.07144e27			3.04823
$286$	−2.74276e26	+	4.86088e26i	−0.261916	+	0.464182i
$287$			3.04477e25i			0.0279804i
$288$	1.22274e27	−	7.88915e26i	1.08148	−	0.697771i
$289$	−1.16049e27			−0.988019
$290$	−1.30782e26	−	7.37940e25i	−0.107194	−	0.0604843i
$291$		−	6.54720e26i		−	0.516693i
$292$	−9.07561e26	−	1.50258e27i	−0.689706	−	1.14189i
$293$	1.47998e27			1.08321			0.541605	−	0.840633i	$-0.317817\pi$
$293$	1.47998e27			1.08321			0.541605	+	0.840633i	$0.317817\pi$
$294$	−1.03293e27	+	1.83061e27i	−0.728197	+	1.29055i
$295$			2.99396e27i			2.03331i
$296$	1.99757e25	+	6.73798e26i	0.0130705	+	0.440880i
$297$	−7.59109e26			−0.478612
$298$	5.04918e26	+	2.84901e26i	0.306790	+	0.173107i
$299$			5.41865e26i			0.317327i
$300$	−4.78632e27	+	2.89095e27i	−2.70189	+	1.63195i
$301$	1.62166e26			0.0882528
$302$	−4.39656e25	+	7.79184e25i	−0.0230694	+	0.0408850i
$303$		−	4.89949e27i		−	2.47903i
$304$	2.08080e27	+	1.09411e27i	1.01536	+	0.533887i
$305$	2.60582e27			1.22644
$306$	2.70246e26	+	1.52487e26i	0.122694	+	0.0692305i
$307$			6.27649e24i			0.00274913i	0.999999	+	0.00137456i	$0.000437537\pi$
$307$			6.27649e24i			0.00274913i	−0.999999	+	0.00137456i	$0.999562\pi$
$308$	−1.91473e26	−	3.17007e26i	−0.0809189	−	0.133971i
$309$	−3.95439e27			−1.61264
$310$	1.11984e27	−	1.98464e27i	0.440733	−	0.781093i
$311$			1.91039e27i			0.725703i	0.931847	+	0.362851i	$0.118197\pi$
$311$			1.91039e27i			0.725703i	−0.931847	+	0.362851i	$0.881803\pi$
$312$	1.99275e27	−	5.90779e25i	0.730723	−	0.0216633i
$313$	−3.82065e26			−0.135254			−0.0676268	−	0.997711i	$-0.521543\pi$
$313$	−3.82065e26			−0.135254			−0.0676268	+	0.997711i	$0.521543\pi$
$314$	7.13706e25	+	4.02710e25i	0.0243946	+	0.0137647i
$315$			9.72612e26i			0.321014i
$316$	3.58798e27	−	2.16715e27i	1.14365	−	0.690767i
$317$	−3.27599e26			−0.100854			−0.0504268	−	0.998728i	$-0.516058\pi$
$317$	−3.27599e26			−0.100854			−0.0504268	+	0.998728i	$0.516058\pi$
$318$	3.26712e27	−	5.79018e27i	0.971554	−	1.72184i
$319$			2.68847e26i			0.0772339i
$320$	−6.31932e27	+	3.75019e26i	−1.75396	+	0.104089i
$321$	2.91053e27			0.780577
$322$	−3.13143e26	−	1.76691e26i	−0.0811573	−	0.0457932i
$323$			5.01311e26i			0.125568i
$324$	−1.34656e27	−	2.22940e27i	−0.326011	−	0.539751i
$325$	−4.31114e27			−1.00896
$326$	−1.76336e27	+	3.12512e27i	−0.398976	+	0.707087i
$327$		−	1.02967e27i		−	0.225254i
$328$	−2.76121e25	−	9.31382e26i	−0.00584100	−	0.197022i
$329$	1.06275e27			0.217407
$330$	1.28960e28	+	7.27661e27i	2.55154	+	1.43971i
$331$			1.01525e28i			1.94296i	0.237113	+	0.971482i	$0.423799\pi$
$331$			1.01525e28i			1.94296i	−0.237113	+	0.971482i	$0.576201\pi$
$332$	−4.59129e26	+	2.77315e26i	−0.0849995	+	0.0513399i
$333$	−3.16950e27			−0.567681
$334$	6.65290e26	−	1.17906e27i	0.115292	−	0.204327i
$335$		−	8.08878e27i		−	1.35641i
$336$	−6.15657e26	+	1.17087e27i	−0.0999094	+	0.190010i
$337$	−4.94241e27			−0.776265			−0.388132	−	0.921604i	$-0.626880\pi$
$337$	−4.94241e27			−0.776265			−0.388132	+	0.921604i	$0.626880\pi$
$338$	−4.39012e27	−	2.47713e27i	−0.667409	−	0.376587i
$339$		−	6.41532e27i		−	0.944108i
$340$	−6.97920e26	−	1.15549e27i	−0.0994345	−	0.164626i
$341$	−4.07980e27			−0.562783
$342$	−5.43200e27	+	9.62690e27i	−0.725559	+	1.28588i
$343$		−	2.17277e27i		−	0.281047i
$344$	−4.96060e27	+	1.47064e26i	−0.621428	+	0.0184231i
$345$	1.43758e28			1.74430
$346$	−8.18122e27	−	4.61627e27i	−0.961571	−	0.542568i
$347$			1.36988e28i			1.55977i	0.625926	+	0.779883i	$0.284721\pi$
$347$			1.36988e28i			1.55977i	−0.625926	+	0.779883i	$0.715279\pi$
$348$	8.22010e26	−	4.96496e26i	0.0906788	−	0.0547702i
$349$	1.40195e28			1.49849			0.749244	−	0.662295i	$-0.230417\pi$
$349$	1.40195e28			1.49849			0.749244	+	0.662295i	$0.230417\pi$
$350$	1.40578e27	−	2.49140e27i	0.145602	−	0.258045i
$351$			2.09058e27i			0.209840i
$352$	6.14457e27	+	9.52348e27i	0.597754	+	0.926460i
$353$	8.46104e27			0.797814			0.398907	−	0.916991i	$-0.369390\pi$
$353$	8.46104e27			0.797814			0.398907	+	0.916991i	$0.369390\pi$
$354$	−1.66753e28	−	9.40905e27i	−1.52418	−	0.860023i
$355$		−	2.36171e28i		−	2.09273i
$356$	1.12839e28	+	1.86819e28i	0.969416	+	1.60499i
$357$	−2.82089e26			−0.0234983
$358$	5.80722e27	−	1.02919e28i	0.469089	−	0.831346i
$359$			1.04685e28i			0.820057i	0.912073	+	0.410028i	$0.134481\pi$
$359$			1.04685e28i			0.820057i	−0.912073	+	0.410028i	$0.865519\pi$
$360$	−8.82033e26	−	2.97518e28i	−0.0670127	−	2.26040i
$361$	−4.28805e27			−0.315995
$362$	3.93666e27	+	2.22127e27i	0.281406	+	0.158784i
$363$		−	4.70255e27i		−	0.326107i
$364$	−8.73034e26	+	5.27315e26i	−0.0587376	+	0.0354776i
$365$	−3.59061e28			−2.34394
$366$	−8.18924e27	+	1.45134e28i	−0.518742	+	0.919345i
$367$		−	2.54112e28i		−	1.56206i	−0.624492	−	0.781031i	$-0.714694\pi$
$367$		−	2.54112e28i		−	1.56206i	0.624492	−	0.781031i	$-0.285306\pi$
$368$	9.73914e27	+	5.12094e27i	0.581025	+	0.305509i
$369$	4.38116e27			0.253687
$370$	1.20086e28	+	6.77591e27i	0.674955	+	0.380845i
$371$			3.40124e27i			0.185577i
$372$	7.53442e27	+	1.24741e28i	0.399096	+	0.660752i
$373$	2.29802e28			1.18183			0.590917	−	0.806733i	$-0.298766\pi$
$373$	2.29802e28			1.18183			0.590917	+	0.806733i	$0.298766\pi$
$374$	−1.18767e27	+	2.10485e27i	−0.0593071	+	0.105108i
$375$			5.95776e28i			2.88894i
$376$	−3.25090e28	+	9.63773e26i	−1.53086	+	0.0453846i
$377$	7.40402e26			0.0338620
$378$	−1.20814e27	−	6.81696e26i	−0.0536671	−	0.0302818i
$379$			2.30104e28i			0.992872i	0.868073	+	0.496436i	$0.165358\pi$
$379$			2.30104e28i			0.992872i	−0.868073	+	0.496436i	$0.834642\pi$
$380$	4.11617e28	−	2.48618e28i	1.72534	−	1.04211i
$381$	−6.19406e28			−2.52232
$382$	−8.76222e27	+	1.55289e28i	−0.346671	+	0.614389i
$383$			2.48176e27i			0.0954053i	0.998862	+	0.0477027i	$0.0151900\pi$
$383$			2.48176e27i			0.0954053i	−0.998862	+	0.0477027i	$0.984810\pi$
$384$	1.77709e28	−	3.63748e28i	0.663842	−	1.35881i
$385$	−7.57532e27			−0.275000
$386$	−2.24924e28	−	1.26914e28i	−0.793552	−	0.447763i
$387$		−	2.33343e28i		−	0.800155i
$388$	−5.29963e27	−	8.77419e27i	−0.176643	−	0.292454i
$389$	8.25579e27			0.267493			0.133747	−	0.991016i	$-0.457299\pi$
$389$	8.25579e27			0.267493			0.133747	+	0.991016i	$0.457299\pi$
$390$	2.00397e28	−	3.55155e28i	0.631220	−	1.11868i
$391$			2.34638e27i			0.0718544i
$392$	9.75184e26	+	3.28939e28i	0.0290362	+	0.979419i
$393$	7.47146e28			2.16315
$394$	2.98792e28	+	1.68594e28i	0.841222	+	0.474661i
$395$		−	8.57397e28i		−	2.34755i
$396$	−4.56146e28	+	2.75513e28i	−1.21467	+	0.733661i
$397$	−1.00296e28			−0.259771			−0.129885	−	0.991529i	$-0.541461\pi$
$397$	−1.00296e28			−0.259771			−0.129885	+	0.991529i	$0.541461\pi$
$398$	1.45625e28	−	2.58086e28i	0.366879	−	0.650204i
$399$		−	1.00488e28i		−	0.246270i
$400$	−4.07428e28	+	7.74858e28i	−0.971385	+	1.84741i
$401$	3.46650e28			0.804088			0.402044	−	0.915620i	$-0.368300\pi$
$401$	3.46650e28			0.804088			0.402044	+	0.915620i	$0.368300\pi$
$402$	4.50515e28	+	2.54204e28i	1.01677	+	0.573715i
$403$			1.12357e28i			0.246743i
$404$	−3.96590e28	−	6.56603e28i	−0.847513	−	1.40316i
$405$	−5.32746e28			−1.10794
$406$	−2.41431e26	+	4.27877e26i	−0.00488659	+	0.00866029i
$407$		−	2.46861e28i		−	0.486310i
$408$	8.62900e27	−	2.55818e26i	0.165462	−	0.00490535i
$409$	4.91690e28			0.917773			0.458887	−	0.888495i	$-0.348248\pi$
$409$	4.91690e28			0.917773			0.458887	+	0.888495i	$0.348248\pi$
$410$	−1.65994e28	−	9.36625e27i	−0.301627	−	0.170194i
$411$			1.00731e29i			1.78198i
$412$	−5.29946e28	+	3.20089e28i	−0.912772	+	0.551316i
$413$	9.79530e27			0.164273
$414$	−2.54244e28	+	4.50585e28i	−0.415190	+	0.735823i
$415$			1.09715e28i			0.174477i
$416$	2.62276e28	−	1.69221e28i	0.406192	−	0.262076i
$417$	−4.23847e28			−0.639312
$418$	−7.49804e28	−	4.23079e28i	−1.10156	−	0.621558i
$419$			6.76307e28i			0.967810i	0.875121	+	0.483905i	$0.160782\pi$
$419$			6.76307e28i			0.967810i	−0.875121	+	0.483905i	$0.839218\pi$
$420$	1.39898e28	+	2.31618e28i	0.195015	+	0.322872i
$421$	9.52059e28			1.29289			0.646444	−	0.762961i	$-0.276255\pi$
$421$	9.52059e28			1.29289			0.646444	+	0.762961i	$0.276255\pi$
$422$	7.83676e26	−	1.38887e27i	0.0103681	−	0.0183749i
$423$		−	1.52920e29i		−	1.97115i
$424$	−3.08448e27	−	1.04042e29i	−0.0387398	−	1.30673i
$425$	−1.86681e28			−0.228466
$426$	1.31538e29	+	7.42208e28i	1.56873	+	0.885157i
$427$		−	8.52541e27i		−	0.0990852i
$428$	3.90052e28	−	2.35593e28i	0.441816	−	0.266858i
$429$	−7.30089e28			−0.806019
$430$	−4.98852e28	+	8.84094e28i	−0.536808	+	0.951361i
$431$			8.12075e28i			0.851817i	0.904766	+	0.425909i	$0.140045\pi$
$431$			8.12075e28i			0.851817i	−0.904766	+	0.425909i	$0.859955\pi$
$432$	3.75747e28	+	1.97572e28i	0.384216	+	0.202024i
$433$	−1.24571e29			−1.24180			−0.620900	−	0.783890i	$-0.713233\pi$
$433$	−1.24571e29			−1.24180			−0.620900	+	0.783890i	$0.713233\pi$
$434$	−6.49311e27	−	3.66375e27i	−0.0631053	−	0.0356073i
$435$		−	1.96430e28i		−	0.186135i
$436$	−8.33465e27	−	1.37990e28i	−0.0770080	−	0.127496i
$437$	−8.35842e28			−0.753058
$438$	1.12841e29	−	1.99984e29i	0.991409	−	1.75703i
$439$		−	4.66769e28i		−	0.399937i	−0.979802	−	0.199969i	$-0.935916\pi$
$439$		−	4.66769e28i		−	0.399937i	0.979802	−	0.199969i	$-0.0640840\pi$
$440$	2.31726e29	−	6.86983e27i	1.93640	−	0.0574072i
$441$	−1.54731e29			−1.26111
$442$	5.79673e27	+	3.27082e27i	0.0460827	+	0.0260023i
$443$			3.78978e28i			0.293882i	0.989145	+	0.146941i	$0.0469427\pi$
$443$			3.78978e28i			0.293882i	−0.989145	+	0.146941i	$0.953057\pi$
$444$	−7.54786e28	+	4.55892e28i	−0.570967	+	0.344865i
$445$	4.46430e29			3.29453
$446$	4.10108e28	−	7.26817e28i	0.295267	−	0.523289i
$447$			7.58371e28i			0.532720i
$448$	1.22694e27	+	2.06748e28i	0.00840944	+	0.141704i
$449$	−3.23098e28			−0.216085			−0.108042	−	0.994146i	$-0.534458\pi$
$449$	−3.23098e28			−0.216085			−0.108042	+	0.994146i	$0.534458\pi$
$450$	−3.58491e29	−	2.02279e29i	−2.33960	−	1.32012i
$451$			3.41232e28i			0.217324i
$452$	−5.19288e28	−	8.59746e28i	−0.322765	−	0.534376i
$453$	−1.17031e28			−0.0709939
$454$	−1.45253e29	+	2.57425e29i	−0.860022	+	1.52418i
$455$			2.08623e28i			0.120569i
$456$	9.11293e27	+	3.07388e29i	0.0514097	+	1.73410i
$457$	−1.33674e29			−0.736153			−0.368077	−	0.929796i	$-0.619984\pi$
$457$	−1.33674e29			−0.736153			−0.368077	+	0.929796i	$0.619984\pi$
$458$	4.35325e28	+	2.45633e28i	0.234042	+	0.132059i
$459$			9.05259e27i			0.0475153i
$460$	1.92657e29	−	1.16365e29i	0.987296	−	0.596329i
$461$	−1.95249e29			−0.976966			−0.488483	−	0.872574i	$-0.662449\pi$
$461$	−1.95249e29			−0.976966			−0.488483	+	0.872574i	$0.662449\pi$
$462$	2.38068e28	−	4.21917e28i	0.116316	−	0.206142i
$463$		−	1.90763e29i		−	0.910129i	−0.890458	−	0.455064i	$-0.849616\pi$
$463$		−	1.90763e29i		−	0.910129i	0.890458	−	0.455064i	$-0.150384\pi$
$464$	6.99723e27	−	1.33075e28i	0.0326008	−	0.0620011i
$465$	2.98087e29			1.35631
$466$	−9.11452e28	−	5.14289e28i	−0.405031	−	0.228540i
$467$			1.72854e29i			0.750229i	0.926978	+	0.375114i	$0.122397\pi$
$467$			1.72854e29i			0.750229i	−0.926978	+	0.375114i	$0.877603\pi$
$468$	7.58760e28	+	1.25622e29i	0.321662	+	0.532551i
$469$	−2.64639e28			−0.109586
$470$	−3.26920e29	+	5.79385e29i	−1.32240	+	2.34364i
$471$			1.07197e28i			0.0423595i
$472$	−2.99634e29	+	8.88306e27i	−1.15672	+	0.0342926i
$473$	1.81742e29			0.685463
$474$	4.77539e29	+	2.69452e29i	1.75973	+	0.992933i
$475$		−	6.65006e29i		−	2.39440i
$476$	−3.78040e27	+	2.28337e27i	−0.0133003	+	0.00803342i
$477$	4.89409e29			1.68256
$478$	2.86564e29	−	5.07865e29i	0.962753	−	1.70625i
$479$			3.61418e28i			0.118664i	0.998238	+	0.0593320i	$0.0188971\pi$
$479$			3.61418e28i			0.118664i	−0.998238	+	0.0593320i	$0.981103\pi$
$480$	−4.48947e29	−	6.95824e29i	−1.44059	−	2.23278i
$481$	−6.79851e28			−0.213215
$482$	−3.33670e29	−	1.88274e29i	−1.02282	−	0.577129i
$483$		−	4.70331e28i		−	0.140924i
$484$	−3.80648e28	−	6.30209e28i	−0.111487	−	0.184580i
$485$	−2.09671e29			−0.600316
$486$	2.43638e29	−	4.31790e29i	0.681941	−	1.20857i
$487$			4.99770e29i			1.36758i	0.729680	+	0.683788i	$0.239669\pi$
$487$			4.99770e29i			1.36758i	−0.729680	+	0.683788i	$0.760331\pi$
$488$	7.73144e27	+	2.60789e29i	0.0206844	+	0.697704i
$489$	−4.69383e29			−1.22781
$490$	5.86246e29	+	3.30790e29i	1.49942	+	0.846050i
$491$		−	2.47728e29i		−	0.619552i	−0.950810	−	0.309776i	$-0.899746\pi$
$491$		−	2.47728e29i		−	0.619552i	0.950810	−	0.309776i	$-0.100254\pi$
$492$	1.04333e29	−	6.30174e28i	0.255156	−	0.154115i
$493$	3.20608e27			0.00766758
$494$	−1.16515e29	+	2.06495e29i	−0.272513	+	0.482962i
$495$			1.09002e30i			2.49332i
$496$	2.01944e29	+	1.06184e29i	0.451786	+	0.237554i
$497$	−7.72676e28			−0.169074
$498$	−6.11073e28	−	3.44799e28i	−0.130789	−	0.0737978i
$499$			3.25496e29i			0.681459i	0.940161	+	0.340729i	$0.110674\pi$
$499$			3.25496e29i			0.681459i	−0.940161	+	0.340729i	$0.889326\pi$
$500$	4.82251e29	+	7.98426e29i	0.987651	+	1.63518i
$501$	1.77092e29			0.354800
$502$	1.86232e29	−	3.30052e29i	0.365018	−	0.646906i
$503$		−	8.60359e29i		−	1.64980i	−0.565277	−	0.824901i	$-0.691231\pi$
$503$		−	8.60359e29i		−	1.64980i	0.565277	−	0.824901i	$-0.308769\pi$
$504$	−9.73385e28	+	2.88573e27i	−0.182620	+	0.00541402i
$505$	−1.56904e30			−2.88024
$506$	−3.50944e29	−	1.98021e29i	−0.630351	−	0.355677i
$507$		−	6.59382e29i		−	1.15891i
$508$	−8.30093e29	+	5.01378e29i	−1.42766	+	0.862312i
$509$	5.03542e29			0.847500			0.423750	−	0.905779i	$-0.360713\pi$
$509$	5.03542e29			0.847500			0.423750	+	0.905779i	$0.360713\pi$
$510$	8.67757e28	−	1.53789e29i	0.142931	−	0.253310i
$511$			1.17473e29i			0.189369i
$512$	−5.62811e28	−	6.31322e29i	−0.0887960	−	0.996050i
$513$	−3.22478e29			−0.497976
$514$	9.77809e29	+	5.51731e29i	1.47795	+	0.833937i
$515$			1.26638e30i			1.87363i
$516$	−3.35635e29	−	5.55684e29i	−0.486094	−	0.804788i
$517$	1.19104e30			1.68861
$518$	2.21686e28	−	3.92885e28i	0.0307689	−	0.0545303i
$519$		−	1.22880e30i		−	1.66970i
$520$	−1.89194e28	−	6.38170e29i	−0.0251693	−	0.848984i
$521$	2.77421e29			0.361348			0.180674	−	0.983543i	$-0.442172\pi$
$521$	2.77421e29			0.361348			0.180674	+	0.983543i	$0.442172\pi$
$522$	6.15678e28	+	3.47398e28i	0.0785196	+	0.0443049i
$523$			1.12615e30i			1.40630i	0.711041	+	0.703151i	$0.248224\pi$
$523$			1.12615e30i			1.40630i	−0.711041	+	0.703151i	$0.751776\pi$
$524$	1.00128e30	−	6.04778e29i	1.22437	−	0.739523i
$525$	3.74201e29			0.448077
$526$	−8.56874e27	+	1.51860e28i	−0.0100479	+	0.0178074i
$527$			4.86528e28i			0.0558716i
$528$	−6.89977e29	+	1.31222e30i	−0.776000	+	1.47582i
$529$	5.16632e29			0.569074
$530$	−1.85428e30	−	1.04628e30i	−2.00051	−	1.12879i
$531$		−	1.40946e30i		−	1.48940i
$532$	−8.13398e28	−	1.34668e29i	−0.0841929	−	0.139392i
$533$	9.39750e28			0.0952824
$534$	−1.40298e30	+	2.48645e30i	−1.39347	+	2.46960i
$535$		−	9.32083e29i		−	0.906907i
$536$	8.09521e29	−	2.39994e28i	0.771641	−	0.0228764i
$537$	1.54581e30			1.44357
$538$	1.38889e28	+	7.83687e27i	0.0127076	+	0.00717030i
$539$		−	1.20514e30i		−	1.08034i
$540$	7.43291e29	−	4.48950e29i	0.652871	−	0.394336i
$541$	−1.55221e30			−1.33592			−0.667961	−	0.744196i	$-0.732833\pi$
$541$	−1.55221e30			−1.33592			−0.667961	+	0.744196i	$0.732833\pi$
$542$	−2.90321e29	+	5.14523e29i	−0.244842	+	0.433923i
$543$			5.91274e29i			0.488642i
$544$	1.13570e29	−	7.32758e28i	0.0919765	−	0.0593434i
$545$	−3.29747e29			−0.261709
$546$	−1.16195e29	−	6.55635e28i	−0.0903795	−	0.0509969i
$547$			1.63115e30i			1.24346i	0.783231	+	0.621730i	$0.213570\pi$
$547$			1.63115e30i			1.24346i	−0.783231	+	0.621730i	$0.786430\pi$
$548$	8.15367e29	+	1.34994e30i	0.609210	+	1.00862i
$549$	−1.22673e30			−0.898368
$550$	1.57548e30	−	2.79216e30i	1.13090	−	2.00424i
$551$			1.14209e29i			0.0803588i
$552$	4.26529e28	+	1.43872e30i	0.0294184	+	0.992310i
$553$	−2.80513e29			−0.189661
$554$	−7.07020e29	−	3.98938e29i	−0.468624	−	0.264422i
$555$			1.80366e30i			1.17201i
$556$	−5.68016e29	+	3.43083e29i	−0.361858	+	0.218563i
$557$	8.52258e29			0.532309			0.266155	−	0.963930i	$-0.414247\pi$
$557$	8.52258e29			0.532309			0.266155	+	0.963930i	$0.414247\pi$
$558$	−5.27182e29	+	9.34302e29i	−0.322838	+	0.572152i
$559$		−	5.00516e29i		−	0.300530i
$560$	3.74967e29	+	1.97161e29i	0.220762	+	0.116079i
$561$	−3.16142e29			−0.182512
$562$	−1.78535e30	−	1.00739e30i	−1.01070	−	0.570290i
$563$			1.42628e30i			0.791795i	0.918295	+	0.395898i	$0.129566\pi$
$563$			1.42628e30i			0.791795i	−0.918295	+	0.395898i	$0.870434\pi$
$564$	−2.19956e30	−	3.64164e30i	−1.19747	−	1.98256i
$565$	−2.05448e30			−1.09690
$566$	9.71985e29	−	1.72261e30i	0.508954	−	0.901998i
$567$			1.74298e29i			0.0895112i
$568$	2.36358e30	−	7.00717e28i	1.19053	−	0.0352948i
$569$	3.71992e30			1.83780			0.918900	−	0.394491i	$-0.129079\pi$
$569$	3.71992e30			1.83780			0.918900	+	0.394491i	$0.129079\pi$
$570$	5.47837e30	+	3.09118e30i	2.65477	+	1.49796i
$571$			2.41058e29i			0.114584i	0.998357	+	0.0572920i	$0.0182466\pi$
$571$			2.41058e29i			0.114584i	−0.998357	+	0.0572920i	$0.981753\pi$
$572$	−9.78425e29	+	5.90971e29i	−0.456217	+	0.275556i
$573$	−2.33239e30			−1.06684
$574$	−3.06434e28	+	5.43080e28i	−0.0137501	+	0.0243687i
$575$		−	3.11255e30i		−	1.37016i
$576$	2.97493e30	−	1.76547e29i	1.28478	−	0.0762452i
$577$	−3.06040e30			−1.29671			−0.648356	−	0.761337i	$-0.724543\pi$
$577$	−3.06040e30			−1.29671			−0.648356	+	0.761337i	$0.724543\pi$
$578$	−2.06991e30	−	1.16795e30i	−0.860488	−	0.485532i
$579$		−	3.37829e30i		−	1.37795i
$580$	−1.59001e29	−	2.63245e29i	−0.0636343	−	0.105354i
$581$	3.58953e28			0.0140962
$582$	6.58929e29	−	1.16779e30i	0.253913	−	0.450000i
$583$			3.81183e30i			1.44138i
$584$	−1.06533e29	−	3.59347e30i	−0.0395316	−	1.33344i
$585$	3.00191e30			1.09316
$586$	2.63977e30	+	1.48950e30i	0.943392	+	0.532311i
$587$		−	5.23600e30i		−	1.83646i	−0.396053	−	0.918228i	$-0.629620\pi$
$587$		−	5.23600e30i		−	1.83646i	0.396053	−	0.918228i	$-0.370380\pi$
$588$	−3.68476e30	+	2.22560e30i	−1.26841	+	0.766121i
$589$	−1.73314e30			−0.585553
$590$	−3.01321e30	+	5.34018e30i	−0.999210	+	1.77086i
$591$			4.48777e30i			1.46072i
$592$	−6.42500e29	+	1.22192e30i	−0.205274	+	0.390396i
$593$	5.59907e29			0.175596			0.0877980	−	0.996138i	$-0.472017\pi$
$593$	5.59907e29			0.175596			0.0877980	+	0.996138i	$0.472017\pi$
$594$	−1.35398e30	−	7.63989e29i	−0.416834	−	0.235199i
$595$			9.03378e28i			0.0273013i
$596$	6.13864e29	+	1.01633e30i	0.182122	+	0.301526i
$597$	3.87637e30			1.12903
$598$	−5.45348e29	+	9.66497e29i	−0.155941	+	0.276368i
$599$			4.68629e30i			1.31563i	0.753179	+	0.657816i	$0.228519\pi$
$599$			4.68629e30i			1.31563i	−0.753179	+	0.657816i	$0.771481\pi$
$600$	−1.14467e31	+	3.39352e29i	−3.15511	+	0.0935377i
$601$	5.27119e30			1.42656			0.713279	−	0.700880i	$-0.247209\pi$
$601$	5.27119e30			1.42656			0.713279	+	0.700880i	$0.247209\pi$
$602$	2.89248e29	+	1.63209e29i	0.0768614	+	0.0433692i
$603$			3.80793e30i			0.993570i
$604$	−1.56839e29	+	9.47309e28i	−0.0401834	+	0.0242709i
$605$	−1.50597e30			−0.378885
$606$	4.93099e30	−	8.73898e30i	1.21825	−	2.15905i
$607$		−	6.32056e30i		−	1.53349i	−0.641954	−	0.766743i	$-0.721876\pi$
$607$		−	6.32056e30i		−	1.53349i	0.641954	−	0.766743i	$-0.278124\pi$
$608$	2.61028e30	+	4.04568e30i	0.621939	+	0.963944i
$609$	−6.42658e28			−0.0150380
$610$	4.64786e30	+	2.62257e30i	1.06813	+	0.602696i
$611$		−	3.28010e30i		−	0.740345i
$612$	3.28558e29	+	5.43967e29i	0.0728360	+	0.120589i
$613$	−1.22641e30			−0.267036			−0.133518	−	0.991046i	$-0.542627\pi$
$613$	−1.22641e30			−0.267036			−0.133518	+	0.991046i	$0.542627\pi$
$614$	−6.31684e27	+	1.11951e28i	−0.00135098	+	0.00239428i
$615$		−	2.49318e30i		−	0.523754i
$616$	−2.24759e28	−	7.58134e29i	−0.00463799	−	0.156444i
$617$	−5.14844e30			−1.04361			−0.521806	−	0.853064i	$-0.674741\pi$
$617$	−5.14844e30			−1.04361			−0.521806	+	0.853064i	$0.674741\pi$
$618$	−7.05325e30	−	3.97981e30i	−1.40448	−	0.792482i
$619$		−	5.64491e29i		−	0.110423i	−0.998475	−	0.0552115i	$-0.982417\pi$
$619$		−	5.64491e29i		−	0.110423i	0.998475	−	0.0552115i	$-0.0175833\pi$
$620$	3.99479e30	−	2.41286e30i	0.767689	−	0.463686i
$621$	−1.50935e30			−0.284959
$622$	−1.92268e30	+	3.40747e30i	−0.356625	+	0.632031i
$623$		−	1.46058e30i		−	0.266168i
$624$	3.61383e30	+	1.90019e30i	0.647049	+	0.340225i
$625$	7.21499e30			1.26927
$626$	−6.81469e29	−	3.84521e29i	−0.117795	−	0.0664664i
$627$		−	1.12618e31i		−	1.91278i
$628$	8.67703e28	+	1.43659e29i	0.0144815	+	0.0239760i
$629$	−2.94389e29			−0.0482796
$630$	−9.78864e29	+	1.73480e30i	−0.157752	+	0.279578i
$631$			3.98760e30i			0.631522i	0.948839	+	0.315761i	$0.102260\pi$
$631$			3.98760e30i			0.631522i	−0.948839	+	0.315761i	$0.897740\pi$
$632$	8.58079e30	−	2.54389e29i	1.33549	−	0.0395923i
$633$	2.08605e29			0.0319068
$634$	−5.84323e29	−	3.29705e29i	−0.0878357	−	0.0495615i
$635$			1.98362e31i			2.93054i
$636$	1.16548e31	−	7.03953e30i	1.69230	−	1.02215i
$637$	−3.31894e30			−0.473659
$638$	−2.70575e29	+	4.79529e29i	−0.0379543	+	0.0672648i
$639$			1.11181e31i			1.53293i
$640$	−1.16489e31	−	5.69104e30i	−1.57872	−	0.771280i
$641$	−1.15604e31			−1.54005			−0.770025	−	0.638014i	$-0.779756\pi$
$641$	−1.15604e31			−1.54005			−0.770025	+	0.638014i	$0.779756\pi$
$642$	5.19136e30	+	2.92923e30i	0.679823	+	0.383591i
$643$			6.53408e29i			0.0841131i	0.999115	+	0.0420566i	$0.0133910\pi$
$643$			6.53408e29i			0.0841131i	−0.999115	+	0.0420566i	$0.986609\pi$
$644$	−3.80709e29	−	6.30311e29i	−0.0481780	−	0.0797647i
$645$	−1.32788e31			−1.65197
$646$	−5.04533e29	+	8.94163e29i	−0.0617067	+	0.109360i
$647$		−	3.52258e30i		−	0.423558i	−0.977318	−	0.211779i	$-0.932074\pi$
$647$		−	3.52258e30i		−	0.423558i	0.977318	−	0.211779i	$-0.0679258\pi$
$648$	−1.58065e29	−	5.33169e30i	−0.0186858	−	0.630289i
$649$	1.09778e31			1.27592
$650$	−7.68957e30	−	4.33885e30i	−0.878729	−	0.495825i
$651$		−	9.75245e29i		−	0.109578i
$652$	−6.29042e30	+	3.79943e30i	−0.694954	+	0.419754i
$653$	−8.05431e29			−0.0874950			−0.0437475	−	0.999043i	$-0.513930\pi$
$653$	−8.05431e29			−0.0874950			−0.0437475	+	0.999043i	$0.513930\pi$
$654$	1.03629e30	−	1.83657e30i	0.110694	−	0.196179i
$655$		−	2.39270e31i		−	2.51324i
$656$	8.88119e29	−	1.68905e30i	0.0917337	−	0.174462i
$657$	1.69034e31			1.71694
$658$	1.89557e30	+	1.06958e30i	0.189345	+	0.106838i
$659$			1.21812e31i			1.19660i	0.801272	+	0.598300i	$0.204157\pi$
$659$			1.21812e31i			1.19660i	−0.801272	+	0.598300i	$0.795843\pi$
$660$	1.56786e31	+	2.59578e31i	1.51469	+	2.50776i
$661$	−1.00500e31			−0.954878			−0.477439	−	0.878665i	$-0.658435\pi$
$661$	−1.00500e31			−0.954878			−0.477439	+	0.878665i	$0.658435\pi$
$662$	−1.02178e31	+	1.81085e31i	−0.954811	+	1.69217i
$663$			8.70652e29i			0.0800195i
$664$	−1.09802e30	+	3.25524e28i	−0.0992574	+	0.00294262i
$665$	−3.21807e30			−0.286126
$666$	−5.65328e30	−	3.18987e30i	−0.494406	−	0.278970i
$667$			5.34554e29i			0.0459840i
$668$	2.37329e30	−	1.43347e30i	0.200821	−	0.121296i
$669$	1.09166e31			0.908656
$670$	8.14078e30	−	1.44275e31i	0.666566	−	1.18133i
$671$		−	9.55458e30i		−	0.769598i
$672$	−2.27651e30	+	1.46881e30i	−0.180388	+	0.116387i
$673$	1.49663e31			1.16667			0.583337	−	0.812230i	$-0.301747\pi$
$673$	1.49663e31			1.16667			0.583337	+	0.812230i	$0.301747\pi$
$674$	−8.81553e30	−	4.97418e30i	−0.676066	−	0.381472i
$675$		−	1.20086e31i		−	0.906045i
$676$	−5.33737e30	−	8.83667e30i	−0.396199	−	0.655957i
$677$	1.33892e31			0.977868			0.488934	−	0.872321i	$-0.337386\pi$
$677$	1.33892e31			0.977868			0.488934	+	0.872321i	$0.337386\pi$
$678$	6.45656e30	−	1.14427e31i	0.463954	−	0.822245i
$679$			6.85978e29i			0.0485001i
$680$	−8.19247e28	−	2.76340e30i	−0.00569924	−	0.192241i
$681$	−3.86645e31			−2.64663
$682$	−7.27694e30	−	4.10603e30i	−0.490141	−	0.276563i
$683$		−	4.01559e30i		−	0.266147i	−0.991106	−	0.133074i	$-0.957515\pi$
$683$		−	4.01559e30i		−	0.266147i	0.991106	−	0.133074i	$-0.0424847\pi$
$684$	−1.93776e31	+	1.17041e31i	−1.26381	+	0.763345i
$685$	3.22587e31			2.07038
$686$	2.18674e30	−	3.87547e30i	0.138112	−	0.244770i
$687$			6.53845e30i			0.406397i
$688$	−8.99597e30	−	4.73017e30i	−0.550269	−	0.289337i
$689$	1.04977e31			0.631951
$690$	2.56414e31	+	1.44682e31i	1.51915	+	0.857186i
$691$			1.43806e31i			0.838530i	0.907864	+	0.419265i	$0.137712\pi$
$691$			1.43806e31i			0.838530i	−0.907864	+	0.419265i	$0.862288\pi$
$692$	−9.94649e30	−	1.64676e31i	−0.570825	−	0.945070i
$693$	3.56621e30			0.201438
$694$	−1.37869e31	+	2.44339e31i	−0.766500	+	1.35843i
$695$			1.35735e31i			0.742779i
$696$	1.96587e30	−	5.82808e28i	0.105889	−	0.00313924i
$697$	4.06929e29			0.0215754
$698$	2.50059e31	+	1.41096e31i	1.30507	+	0.736387i
$699$		−	1.36897e31i		−	0.703309i
$700$	5.01483e30	−	3.02897e30i	0.253617	−	0.153185i
$701$	−4.96499e30			−0.247184			−0.123592	−	0.992333i	$-0.539441\pi$
$701$	−4.96499e30			−0.247184			−0.123592	+	0.992333i	$0.539441\pi$
$702$	−2.10402e30	+	3.72886e30i	−0.103119	+	0.182754i
$703$		−	1.04869e31i		−	0.505986i
$704$	1.37506e30	+	2.31706e31i	0.0653164	+	1.10062i
$705$	−8.70219e31			−4.06957
$706$	1.50915e31	+	8.51543e30i	0.694835	+	0.392062i
$707$			5.13341e30i			0.232698i
$708$	−2.02733e31	−	3.35649e31i	−0.904812	−	1.49803i
$709$	−2.61604e31			−1.14957			−0.574786	−	0.818304i	$-0.694915\pi$
$709$	−2.61604e31			−1.14957			−0.574786	+	0.818304i	$0.694915\pi$
$710$	2.37689e31	−	4.21246e31i	1.02841	−	1.82261i
$711$			4.03634e31i			1.71958i
$712$	1.32455e30	+	4.46785e31i	0.0555636	+	1.87421i
$713$	−8.11195e30			−0.335074
$714$	−5.03148e29	−	2.83903e29i	−0.0204652	−	0.0115475i
$715$			2.33808e31i			0.936467i
$716$	2.07161e31	−	1.25126e31i	0.817080	−	0.493518i
$717$	7.62798e31			2.96278
$718$	−1.05358e31	+	1.86721e31i	−0.402992	+	0.714206i
$719$		−	2.86784e31i		−	1.08028i	−0.841575	−	0.540141i	$-0.818371\pi$
$719$		−	2.86784e31i		−	1.08028i	0.841575	−	0.540141i	$-0.181629\pi$
$720$	2.83698e31	−	5.39545e31i	1.05244	−	2.00157i
$721$	4.14319e30			0.151372
$722$	−7.64838e30	−	4.31561e30i	−0.275207	−	0.155286i
$723$		−	5.01163e31i		−	1.77606i
$724$	4.78607e30	+	7.92393e30i	0.167053	+	0.276577i
$725$	−4.25298e30			−0.146209
$726$	4.73278e30	−	8.38770e30i	0.160256	−	0.284014i
$727$			1.94554e30i			0.0648875i	0.999474	+	0.0324438i	$0.0103290\pi$
$727$			1.94554e30i			0.0648875i	−0.999474	+	0.0324438i	$0.989671\pi$
$728$	−2.08789e30	+	6.18984e28i	−0.0685903	+	0.00203345i
$729$	4.53671e31			1.46804
$730$	−6.40439e31	−	3.61369e31i	−2.04139	−	1.15186i
$731$		−	2.16733e30i		−	0.0680509i
$732$	−2.92135e31	+	1.76450e31i	−0.903569	+	0.545758i
$733$	−9.29673e30			−0.283261			−0.141630	−	0.989920i	$-0.545234\pi$
$733$	−9.29673e30			−0.283261			−0.141630	+	0.989920i	$0.545234\pi$
$734$	2.55745e31	−	4.53247e31i	0.767629	−	1.36044i
$735$			8.80523e31i			2.60364i
$736$	1.22174e31	+	1.89357e31i	0.355895	+	0.551602i
$737$	−2.96586e31			−0.851154
$738$	7.81445e30	+	4.40932e30i	0.220942	+	0.124667i
$739$		−	4.98883e31i		−	1.38966i	−0.719172	−	0.694832i	$-0.755479\pi$
$739$		−	4.98883e31i		−	1.38966i	0.719172	−	0.694832i	$-0.244521\pi$
$740$	1.45998e31	+	2.41717e31i	0.400679	+	0.663373i
$741$	−3.10149e31			−0.838631
$742$	−3.42310e30	+	6.06662e30i	−0.0911962	+	0.161623i
$743$		−	4.92849e31i		−	1.29371i	−0.762613	−	0.646856i	$-0.776084\pi$
$743$		−	4.92849e31i		−	1.29371i	0.762613	−	0.646856i	$-0.223916\pi$
$744$	8.84421e29	+	2.98324e31i	0.0228748	+	0.771588i
$745$	2.42865e31			0.618936
$746$	4.09886e31	+	2.31279e31i	1.02929	+	0.580777i
$747$		−	5.16503e30i		−	0.127805i
$748$	−4.23676e30	+	2.55902e30i	−0.103304	+	0.0623958i
$749$	−3.04948e30			−0.0732700
$750$	−5.99606e31	+	1.06266e32i	−1.41969	+	2.51605i
$751$			3.56833e31i			0.832579i	0.909232	+	0.416289i	$0.136670\pi$
$751$			3.56833e31i			0.832579i	−0.909232	+	0.416289i	$0.863330\pi$
$752$	−5.89546e31	−	3.09989e31i	−1.35557	−	0.712771i
$753$	4.95728e31			1.12331
$754$	1.32062e30	+	7.45161e29i	0.0294912	+	0.0166405i
$755$			3.74787e30i			0.0824837i
$756$	−1.46882e30	−	2.43181e30i	−0.0318588	−	0.0527461i
$757$	3.74576e31			0.800729			0.400365	−	0.916356i	$-0.368883\pi$
$757$	3.74576e31			0.800729			0.400365	+	0.916356i	$0.368883\pi$
$758$	−2.31583e31	+	4.10425e31i	−0.487917	+	0.864715i
$759$		−	5.27108e31i		−	1.09456i
$760$	9.84396e31	−	2.91838e30i	2.01475	−	0.0597299i
$761$	−5.65983e30			−0.114175			−0.0570876	−	0.998369i	$-0.518181\pi$
$761$	−5.65983e30			−0.114175			−0.0570876	+	0.998369i	$0.518181\pi$
$762$	−1.10480e32	−	6.23387e31i	−2.19675	−	1.23952i
$763$			1.07883e30i			0.0211437i
$764$	−3.12574e31	+	1.88796e31i	−0.603846	+	0.364725i
$765$	1.29988e31			0.247530
$766$	−2.49771e30	+	4.42658e30i	−0.0468841	+	0.0830907i
$767$		−	3.02326e31i		−	0.559405i
$768$	6.83056e31	−	4.69949e31i	1.24590	−	0.857190i
$769$	−9.56001e31			−1.71897			−0.859486	−	0.511160i	$-0.829216\pi$
$769$	−9.56001e31			−1.71897			−0.859486	+	0.511160i	$0.829216\pi$
$770$	−1.35117e31	−	7.62401e30i	−0.239504	−	0.135141i
$771$			1.46864e32i			2.56636i
$772$	−2.73456e31	−	4.52740e31i	−0.471082	−	0.779935i
$773$	7.72862e31			1.31258			0.656292	−	0.754507i	$-0.272124\pi$
$773$	7.72862e31			1.31258			0.656292	+	0.754507i	$0.272124\pi$
$774$	2.34843e31	−	4.16202e31i	0.393212	−	0.696873i
$775$		−	6.45396e31i		−	1.06539i
$776$	−6.22093e29	−	2.09838e31i	−0.0101246	−	0.341511i
$777$	5.90101e30			0.0946881
$778$	1.47254e31	+	8.30886e30i	0.232966	+	0.131452i
$779$			1.44959e31i			0.226117i
$780$	7.14876e31	−	4.31787e31i	1.09949	−	0.664093i
$781$	−8.65952e31			−1.31320
$782$	−2.36146e30	+	4.18511e30i	−0.0353107	+	0.0625796i
$783$			2.06237e30i			0.0304080i
$784$	−3.13660e31	+	5.96526e31i	−0.456018	+	0.867267i
$785$	3.43292e30			0.0492150
$786$	1.33265e32	+	7.51949e31i	1.88394	+	1.06302i
$787$			9.08921e31i			1.26708i	0.773710	+	0.633540i	$0.218399\pi$
$787$			9.08921e31i			1.26708i	−0.773710	+	0.633540i	$0.781601\pi$
$788$	3.63262e31	+	6.01425e31i	0.499381	+	0.826787i
$789$	−2.28089e30			−0.0309213
$790$	8.62909e31	−	1.52930e32i	1.15363	−	2.04453i
$791$			6.72160e30i			0.0886200i
$792$	−1.09089e32	+	3.23409e30i	−1.41842	+	0.0420509i
$793$	−2.63132e31			−0.337418
$794$	−1.78894e31	−	1.00941e31i	−0.226240	−	0.127656i
$795$		−	2.78507e32i		−	3.47374i
$796$	5.19489e31	−	3.13773e31i	0.639047	−	0.385986i
$797$	8.44018e31			1.02402			0.512012	−	0.858978i	$-0.328900\pi$
$797$	8.44018e31			1.02402			0.512012	+	0.858978i	$0.328900\pi$
$798$	1.01134e31	−	1.79235e31i	0.121022	−	0.214482i
$799$		−	1.42035e31i		−	0.167641i
$800$	−1.50655e32	+	9.72028e31i	−1.75385	+	1.13159i
$801$	−2.10164e32			−2.41325
$802$	6.18303e31	+	3.48879e31i	0.700299	+	0.395145i
$803$			1.31655e32i			1.47084i
$804$	5.47723e31	+	9.06822e31i	0.603593	+	0.999323i
$805$	−1.50621e31			−0.163731
$806$	−1.13080e31	+	2.00406e31i	−0.121255	+	0.214895i
$807$			2.08608e30i			0.0220659i
$808$	−4.65534e30	−	1.57029e32i	−0.0485765	−	1.63853i
$809$	8.31537e31			0.855949			0.427975	−	0.903791i	$-0.359227\pi$
$809$	8.31537e31			0.855949			0.427975	+	0.903791i	$0.359227\pi$
$810$	−9.50231e31	−	5.36170e31i	−0.964926	−	0.544462i
$811$			1.42183e32i			1.42435i	0.702000	+	0.712177i	$0.252291\pi$
$811$			1.42183e32i			1.42435i	−0.702000	+	0.712177i	$0.747709\pi$
$812$	−8.61255e29	+	5.20200e29i	−0.00851168	+	0.00514108i
$813$	−7.72799e31			−0.753478
$814$	2.48448e31	−	4.40313e31i	0.238983	−	0.423539i
$815$			1.50318e32i			1.42652i
$816$	1.56486e31	+	8.22817e30i	0.146515	+	0.0770392i
$817$	7.72061e31			0.713196
$818$	8.77003e31	+	4.94851e31i	0.799309	+	0.451012i
$819$		−	9.82130e30i		−	0.0883173i
$820$	−2.01811e31	−	3.34122e31i	−0.179057	−	0.296451i
$821$	−1.47220e32			−1.28882			−0.644408	−	0.764682i	$-0.722896\pi$
$821$	−1.47220e32			−1.28882			−0.644408	+	0.764682i	$0.722896\pi$
$822$	−1.01379e32	+	1.79669e32i	−0.875701	+	1.55197i
$823$		−	7.24701e31i		−	0.617676i	−0.951115	−	0.308838i	$-0.900060\pi$
$823$		−	7.24701e31i		−	0.617676i	0.951115	−	0.308838i	$-0.0999400\pi$
$824$	−1.26738e32	+	3.75733e30i	−1.06588	+	0.0315995i
$825$	4.19374e32			3.48023
$826$	1.74714e31	+	9.85826e30i	0.143069	+	0.0807272i
$827$		−	2.03312e31i		−	0.164287i	−0.996621	−	0.0821435i	$-0.973823\pi$
$827$		−	2.03312e31i		−	0.164287i	0.996621	−	0.0821435i	$-0.0261766\pi$
$828$	−9.06963e31	+	5.47808e31i	−0.723196	+	0.436812i
$829$	1.34305e32			1.05680			0.528400	−	0.848995i	$-0.322792\pi$
$829$	1.34305e32			1.05680			0.528400	+	0.848995i	$0.322792\pi$
$830$	−1.10420e31	+	1.95693e31i	−0.0857414	+	0.151956i
$831$		−	1.06192e32i		−	0.813733i
$832$	6.38116e31	−	3.78689e30i	0.482551	−	0.0286369i
$833$	−1.43716e31			−0.107253
$834$	−7.55995e31	−	4.26572e31i	−0.556791	−	0.314171i
$835$		−	5.67129e31i		−	0.412222i
$836$	−9.11589e31	−	1.50925e32i	−0.653928	−	1.08266i
$837$	−3.12968e31			−0.221575
$838$	−6.80655e31	+	1.20630e32i	−0.475601	+	0.842887i
$839$		−	2.32877e32i		−	1.60600i	−0.595979	−	0.803000i	$-0.703236\pi$
$839$		−	2.32877e32i		−	1.60600i	0.595979	−	0.803000i	$-0.296764\pi$
$840$	1.64218e30	+	5.53923e31i	0.0111776	+	0.377031i
$841$	−1.48122e32			−0.995093
$842$	1.69814e32	+	9.58179e31i	1.12601	+	0.635351i
$843$		−	2.68153e32i		−	1.75501i
$844$	2.79561e30	−	1.68855e30i	0.0180596	−	0.0109081i
$845$	−2.11164e32			−1.34647
$846$	1.53903e32	−	2.72756e32i	0.968663	−	1.71672i
$847$			4.92706e30i			0.0306105i
$848$	9.92096e31	−	1.88680e32i	0.608414	−	1.15710i
$849$	2.58730e32			1.56626
$850$	−3.32973e31	−	1.87881e31i	−0.198976	−	0.112273i
$851$		−	4.90838e31i		−	0.289543i
$852$	1.59920e32	+	2.64768e32i	0.931255	+	1.54181i
$853$	−8.66959e31			−0.498379			−0.249189	−	0.968455i	$-0.580164\pi$
$853$	−8.66959e31			−0.498379			−0.249189	+	0.968455i	$0.580164\pi$
$854$	8.58021e30	−	1.52063e31i	0.0486924	−	0.0862955i
$855$			4.63053e32i			2.59420i
$856$	9.32824e31	−	2.76548e30i	0.515927	−	0.0152954i
$857$	2.83995e32			1.55068			0.775338	−	0.631547i	$-0.217580\pi$
$857$	2.83995e32			1.55068			0.775338	+	0.631547i	$0.217580\pi$
$858$	−1.30222e32	−	7.34782e31i	−0.701981	−	0.396094i
$859$			2.85305e32i			1.51839i	0.650862	+	0.759196i	$0.274408\pi$
$859$			2.85305e32i			1.51839i	−0.650862	+	0.759196i	$0.725592\pi$
$860$	−1.77955e32	+	1.07485e32i	−0.935036	+	0.564764i
$861$	−8.15690e30			−0.0423146
$862$	−8.17296e31	+	1.44846e32i	−0.418600	+	0.741867i
$863$			2.61684e32i			1.32330i	0.749813	+	0.661650i	$0.230144\pi$
$863$			2.61684e32i			1.32330i	−0.749813	+	0.661650i	$0.769856\pi$
$864$	4.71360e31	+	7.30562e31i	0.235343	+	0.364759i
$865$	−3.93516e32			−1.93993
$866$	−2.22192e32	−	1.25372e32i	−1.08151	−	0.610245i
$867$		−	3.10894e32i		−	1.49418i
$868$	−7.89413e30	−	1.30697e31i	−0.0374617	−	0.0620224i
$869$	−3.14376e32			−1.47310
$870$	1.97693e31	−	3.50363e31i	0.0914703	−	0.162109i
$871$			8.16794e31i			0.373175i
$872$	−9.78356e29	−	3.30009e31i	−0.00441383	−	0.148883i
$873$	9.87063e31			0.439732
$874$	−1.49085e32	−	8.41215e31i	−0.655855	−	0.370068i
$875$		−	6.24220e31i		−	0.271175i
$876$	4.02539e32	−	2.43134e32i	1.72688	−	1.04304i
$877$	1.57667e32			0.667950			0.333975	−	0.942582i	$-0.391610\pi$
$877$	1.57667e32			0.667950			0.333975	+	0.942582i	$0.391610\pi$
$878$	4.69769e31	−	8.32552e31i	0.196537	−	0.348314i
$879$			3.96485e32i			1.63813i
$880$	4.20232e32	+	2.20962e32i	1.71467	+	0.901589i
$881$	1.25411e32			0.505360			0.252680	−	0.967550i	$-0.418688\pi$
$881$	1.25411e32			0.505360			0.252680	+	0.967550i	$0.418688\pi$
$882$	−2.75985e32	−	1.55725e32i	−1.09833	−	0.619733i
$883$		−	1.75586e31i		−	0.0690115i	−0.999404	−	0.0345057i	$-0.989014\pi$
$883$		−	1.75586e31i		−	0.0690115i	0.999404	−	0.0345057i	$-0.0109857\pi$
$884$	7.04750e30	+	1.16680e31i	0.0273565	+	0.0452920i
$885$	−8.02079e32			−3.07497
$886$	−3.81414e31	+	6.75963e31i	−0.144419	+	0.255948i
$887$		−	5.04667e32i		−	1.88732i	−0.330920	−	0.943659i	$-0.607359\pi$
$887$		−	5.04667e32i		−	1.88732i	0.330920	−	0.943659i	$-0.392641\pi$
$888$	−1.80510e32	+	5.35146e30i	−0.666742	+	0.0197665i
$889$	6.48978e31			0.236761
$890$	7.96275e32	+	4.49300e32i	2.86928	+	1.61900i
$891$			1.95338e32i			0.695237i
$892$	1.46298e32	−	8.83643e31i	0.514310	−	0.310644i
$893$	5.05965e32			1.75693
$894$	−7.63246e31	+	1.35267e32i	−0.261789	+	0.463958i
$895$		−	4.95039e32i		−	1.67720i
$896$	−1.86193e31	+	3.81115e31i	−0.0623124	+	0.127546i
$897$	−1.45165e32			−0.479893
$898$	−5.76294e31	−	3.25175e31i	−0.188193	−	0.106188i
$899$			1.10841e31i			0.0357557i
$900$	−4.35843e32	−	7.21591e32i	−1.38887	−	2.29945i
$901$	4.54571e31			0.143097
$902$	−3.43426e31	+	6.08639e31i	−0.106798	+	0.189273i
$903$			4.34441e31i			0.133464i
$904$	−6.09563e30	−	2.05611e32i	−0.0184997	−	0.624013i
$905$	1.89353e32			0.567725
$906$	−2.08743e31	−	1.17783e31i	−0.0618302	−	0.0348878i
$907$		−	2.36351e32i		−	0.691635i	−0.938302	−	0.345818i	$-0.887602\pi$
$907$		−	2.36351e32i		−	0.691635i	0.938302	−	0.345818i	$-0.112398\pi$
$908$	−5.18160e32	+	3.12970e32i	−1.49803	+	0.904811i
$909$	7.38653e32			2.10978
$910$	−2.09964e31	+	3.72111e31i	−0.0592503	+	0.105007i
$911$		−	2.67714e32i		−	0.746395i	−0.927752	−	0.373198i	$-0.878261\pi$
$911$		−	2.67714e32i		−	0.746395i	0.927752	−	0.373198i	$-0.121739\pi$
$912$	−2.93110e32	+	5.57444e32i	−0.807396	+	1.53553i
$913$	4.02285e31			0.109485
$914$	−2.38427e32	−	1.34533e32i	−0.641132	−	0.361760i
$915$			6.98095e32i			1.85474i
$916$	5.29255e31	+	8.76247e31i	0.138936	+	0.230026i
$917$	−7.82817e31			−0.203047
$918$	−9.11079e30	+	1.61467e31i	−0.0233500	+	0.0413822i
$919$			4.48284e32i			1.13523i	0.823296	+	0.567613i	$0.192133\pi$
$919$			4.48284e32i			1.13523i	−0.823296	+	0.567613i	$0.807867\pi$
$920$	4.60745e32	−	1.36594e31i	1.15291	−	0.0341795i
$921$	−1.68146e30			−0.00415749
$922$	−3.48256e32	−	1.96504e32i	−0.850861	−	0.480100i
$923$			2.38482e32i			0.575754i
$924$	8.49259e31	−	5.12954e31i	0.202604	−	0.122373i
$925$	3.90516e32			0.920620
$926$	1.91989e32	−	3.40254e32i	0.447256	−	0.792652i
$927$		−	5.96169e32i		−	1.37244i
$928$	2.58737e31	−	1.66938e31i	0.0588614	−	0.0379775i
$929$	−4.41033e32			−0.991513			−0.495756	−	0.868462i	$-0.665109\pi$
$929$	−4.41033e32			−0.991513			−0.495756	+	0.868462i	$0.665109\pi$
$930$	5.31682e32	+	3.00003e32i	1.18124	+	0.666520i
$931$		−	5.11956e32i		−	1.12405i
$932$	−1.10812e32	−	1.83462e32i	−0.240442	−	0.398081i
$933$	−5.11792e32			−1.09748
$934$	−1.73965e32	+	3.08311e32i	−0.368678	+	0.653391i
$935$			1.01243e32i			0.212050i
$936$	8.90665e30	+	3.00430e32i	0.0184366	+	0.621882i
$937$	−1.84224e32			−0.376887			−0.188443	−	0.982084i	$-0.560344\pi$
$937$	−1.84224e32			−0.376887			−0.188443	+	0.982084i	$0.560344\pi$
$938$	−4.72024e31	−	2.66341e31i	−0.0954405	−	0.0538525i
$939$		−	1.02355e32i		−	0.204544i
$940$	−1.16622e33	+	7.04400e32i	−2.30342	+	1.39127i
$941$	4.95672e31			0.0967628			0.0483814	−	0.998829i	$-0.484594\pi$
$941$	4.95672e31			0.0967628			0.0483814	+	0.998829i	$0.484594\pi$
$942$	−1.07886e31	+	1.91201e31i	−0.0208163	+	0.0368918i
$943$			6.78478e31i			0.129392i
$944$	−5.43382e32	−	2.85716e32i	−1.02427	−	0.538571i
$945$	−5.81115e31			−0.108271
$946$	3.24165e32	+	1.82911e32i	0.596985	+	0.336850i
$947$			9.42481e31i			0.171563i	0.996314	+	0.0857814i	$0.0273387\pi$
$947$			9.42481e31i			0.171563i	−0.996314	+	0.0857814i	$0.972661\pi$
$948$	5.80577e32	+	9.61217e32i	1.04464	+	1.72954i
$949$	3.62575e32			0.644866
$950$	6.69281e32	−	1.18614e33i	1.17665	−	2.08533i
$951$		−	8.77635e31i		−	0.152521i
$952$	−9.04096e30	+	2.68032e29i	−0.0155313	+	0.000460447i
$953$	−2.65478e32			−0.450823			−0.225412	−	0.974264i	$-0.572373\pi$
$953$	−2.65478e32			−0.450823			−0.225412	+	0.974264i	$0.572373\pi$
$954$	8.72934e32	+	4.92555e32i	1.46538	+	0.826842i
$955$			7.46939e32i			1.23950i
$956$	1.02226e33	−	6.17447e32i	1.67697	−	1.01289i
$957$	−7.20239e31			−0.116801
$958$	−3.63741e31	+	6.44643e31i	−0.0583139	+	0.103347i
$959$		−	1.05540e32i		−	0.167268i
$960$	−1.00467e32	−	1.69294e33i	−0.157413	−	2.65251i
$961$	4.77387e32			0.739458
$962$	−1.21262e32	−	6.84222e31i	−0.185694	−	0.104778i
$963$			4.38794e32i			0.664311i
$964$	−4.05666e32	−	6.71630e32i	−0.607186	−	1.00527i
$965$	−1.08188e33			−1.60096
$966$	4.73354e31	−	8.38905e31i	0.0692529	−	0.122734i
$967$		−	3.97701e31i		−	0.0575261i	−0.999586	−	0.0287631i	$-0.990843\pi$
$967$		−	3.97701e31i		−	0.0575261i	0.999586	−	0.0287631i	$-0.00915683\pi$
$968$	−4.46820e30	−	1.50717e32i	−0.00639005	−	0.215542i
$969$	−1.34301e32			−0.189896
$970$	−3.73980e32	−	2.11019e32i	−0.522829	−	0.295007i
$971$			6.20494e32i			0.857682i	0.903380	+	0.428841i	$0.141078\pi$
$971$			6.20494e32i			0.857682i	−0.903380	+	0.428841i	$0.858922\pi$
$972$	8.69131e32	−	5.24957e32i	1.18784	−	0.717456i
$973$	4.44083e31			0.0600099
$974$	−5.02983e32	+	8.91415e32i	−0.672055	+	1.19105i
$975$		−	1.15495e33i		−	1.52585i
$976$	−2.48675e32	+	4.72937e32i	−0.324851	+	0.617811i
$977$	−2.10265e32			−0.271598			−0.135799	−	0.990736i	$-0.543360\pi$
$977$	−2.10265e32			−0.271598			−0.135799	+	0.990736i	$0.543360\pi$
$978$	−8.37216e32	−	4.72401e32i	−1.06933	−	0.603369i
$979$		−	1.63689e33i		−	2.06734i
$980$	7.12740e32	+	1.18003e33i	0.890111	+	1.47369i
$981$	1.55234e32			0.191702
$982$	2.49320e32	−	4.41859e32i	0.304460	−	0.539582i
$983$			1.57482e33i			1.90171i	0.309644	+	0.950853i	$0.399790\pi$
$983$			1.57482e33i			1.90171i	−0.309644	+	0.950853i	$0.600210\pi$
$984$	2.49516e32	−	7.39725e30i	0.297956	−	0.00883332i
$985$	1.43719e33			1.69713
$986$	5.71852e30	+	3.22669e30i	0.00667787	+	0.00376800i
$987$			2.84708e32i			0.328785i
$988$	−4.15645e32	+	2.51051e32i	−0.474675	+	0.286705i
$989$	3.61362e32			0.408115
$990$	−1.09703e33	+	1.94422e33i	−1.22527	+	2.17149i
$991$			8.27884e32i			0.914448i	0.889351	+	0.457224i	$0.151156\pi$
$991$			8.27884e32i			0.914448i	−0.889351	+	0.457224i	$0.848844\pi$
$992$	2.53331e32	+	3.92638e32i	0.276732	+	0.428908i
$993$	−2.71984e33			−2.93834
$994$	−1.37818e32	−	7.77643e31i	−0.147250	−	0.0830864i
$995$		−	1.24139e33i		−	1.31176i
$996$	−7.42924e31	−	1.23000e32i	−0.0776411	−	0.128544i
$997$	9.51422e32			0.983392			0.491696	−	0.870767i	$-0.336377\pi$
$997$	9.51422e32			0.983392			0.491696	+	0.870767i	$0.336377\pi$
$998$	−3.27588e32	+	5.80571e32i	−0.334883	+	0.593498i
$999$		−	1.89371e32i		−	0.191467i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.23.b.a.3.8	yes	10
3.2	odd	2		36.23.d.c.19.3		10
4.3	odd	2	inner	4.23.b.a.3.7	✓	10
8.3	odd	2		64.23.c.e.63.9		10
8.5	even	2		64.23.c.e.63.2		10
12.11	even	2		36.23.d.c.19.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.23.b.a.3.7	✓	10	4.3	odd	2	inner
4.23.b.a.3.8	yes	10	1.1	even	1	trivial
36.23.d.c.19.3		10	3.2	odd	2
36.23.d.c.19.4		10	12.11	even	2
64.23.c.e.63.2		10	8.5	even	2
64.23.c.e.63.9		10	8.3	odd	2

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:	\( k \)	\(=\)	\( 23 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1783.65 + 1006.43i) q^{2} +267899. i q^{3} +(2.16851e6 + 3.59023e6i) q^{4} +8.57934e7 q^{5} +(-2.69621e8 + 4.77838e8i) q^{6} -2.80689e8i q^{7} +(2.54549e8 + 8.58616e9i) q^{8} -4.03887e10 q^{9} +O(q^{10})\)	\(q+(1783.65 + 1006.43i) q^{2} +267899. i q^{3} +(2.16851e6 + 3.59023e6i) q^{4} +8.57934e7 q^{5} +(-2.69621e8 + 4.77838e8i) q^{6} -2.80689e8i q^{7} +(2.54549e8 + 8.58616e9i) q^{8} -4.03887e10 q^{9} +(1.53025e11 + 8.63449e10i) q^{10} -3.14573e11i q^{11} +(-9.61819e11 + 5.80941e11i) q^{12} -8.66330e11 q^{13} +(2.82493e11 - 5.00651e11i) q^{14} +2.29840e13i q^{15} +(-8.18733e12 + 1.55709e13i) q^{16} -3.75137e12 q^{17} +(-7.20393e13 - 4.06483e13i) q^{18} -1.33634e14i q^{19} +(1.86044e14 + 3.08018e14i) q^{20} +7.51962e13 q^{21} +(3.16595e14 - 5.61088e14i) q^{22} -6.25471e14i q^{23} +(-2.30022e15 + 6.81933e13i) q^{24} +4.97633e15 q^{25} +(-1.54523e15 - 8.71899e14i) q^{26} -2.41314e15i q^{27} +(1.00774e15 - 6.08676e14i) q^{28} -8.54642e14 q^{29} +(-2.31317e16 + 4.09953e16i) q^{30} -1.29693e16i q^{31} +(-3.02743e16 + 1.95331e16i) q^{32} +8.42737e16 q^{33} +(-6.69114e15 - 3.77549e15i) q^{34} -2.40813e16i q^{35} +(-8.75833e16 - 1.45005e17i) q^{36} +7.84749e16 q^{37} +(1.34493e17 - 2.38356e17i) q^{38} -2.32089e17i q^{39} +(2.18386e16 + 7.36636e17i) q^{40} -1.08475e17 q^{41} +(1.34124e17 + 7.56796e16i) q^{42} +5.77743e17i q^{43} +(1.12939e18 - 6.82154e17i) q^{44} -3.46509e18 q^{45} +(6.29492e17 - 1.11562e18i) q^{46} +3.78620e18i q^{47} +(-4.17142e18 - 2.19338e18i) q^{48} +3.83103e18 q^{49} +(8.87602e18 + 5.00831e18i) q^{50} -1.00499e18i q^{51} +(-1.87864e18 - 3.11033e18i) q^{52} -1.21175e19 q^{53} +(2.42865e18 - 4.30420e18i) q^{54} -2.69883e19i q^{55} +(2.41004e18 - 7.14490e16i) q^{56} +3.58004e19 q^{57} +(-1.52438e18 - 8.60136e17i) q^{58} +3.48973e19i q^{59} +(-8.25177e19 + 4.98409e19i) q^{60} +3.03732e19 q^{61} +(1.30527e19 - 2.31328e19i) q^{62} +1.13367e19i q^{63} +(-7.36574e19 + 4.37119e18i) q^{64} -7.43254e19 q^{65} +(1.50315e20 + 8.48155e19i) q^{66} -9.42821e19i q^{67} +(-8.13488e18 - 1.34683e19i) q^{68} +1.67563e20 q^{69} +(2.42361e19 - 4.29525e19i) q^{70} -2.75278e20i q^{71} +(-1.02809e19 - 3.46784e20i) q^{72} -4.18518e20 q^{73} +(1.39972e20 + 7.89793e19i) q^{74} +1.33315e21i q^{75} +(4.79777e20 - 2.89786e20i) q^{76} -8.82972e19 q^{77} +(2.33581e20 - 4.13965e20i) q^{78} -9.99374e20i q^{79} +(-7.02419e20 + 1.33588e21i) q^{80} -6.20963e20 q^{81} +(-1.93481e20 - 1.09172e20i) q^{82} +1.27883e20i q^{83} +(1.63064e20 + 2.69972e20i) q^{84} -3.21843e20 q^{85} +(-5.81457e20 + 1.03049e21i) q^{86} -2.28957e20i q^{87} +(2.70098e21 - 8.00741e19i) q^{88} +5.20354e21 q^{89} +(-6.18050e21 - 3.48736e21i) q^{90} +2.43169e20i q^{91} +(2.24559e21 - 1.35634e21i) q^{92} +3.47447e21 q^{93} +(-3.81054e21 + 6.75326e21i) q^{94} -1.14649e22i q^{95} +(-5.23288e21 - 8.11045e21i) q^{96} -2.44391e21 q^{97} +(6.83322e21 + 3.85566e21i) q^{98} +1.27052e22i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 1540 q^{2} + 2264464 q^{4} - 17091100 q^{5} - 791935776 q^{6} + 9804431680 q^{8} - 104309613702 q^{9}+O(q^{10}) \) 10 * q + 1540 * q^2 + 2264464 * q^4 - 17091100 * q^5 - 791935776 * q^6 + 9804431680 * q^8 - 104309613702 * q^9	\( 10 q + 1540 q^{2} + 2264464 q^{4} - 17091100 q^{5} - 791935776 q^{6} + 9804431680 q^{8} - 104309613702 q^{9} + 159414035240 q^{10} + 519021175680 q^{12} - 531230356540 q^{13} - 5894008940736 q^{14} - 27717620084480 q^{16} + 14058178115540 q^{17} + 16283956279140 q^{18} + 233643631625120 q^{20} - 313135665760512 q^{21} + 120589650366240 q^{22} - 20\!\cdots\!36 q^{24}+ \cdots - 23\!\cdots\!20 q^{98}+O(q^{100}) \) 10 * q + 1540 * q^2 + 2264464 * q^4 - 17091100 * q^5 - 791935776 * q^6 + 9804431680 * q^8 - 104309613702 * q^9 + 159414035240 * q^10 + 519021175680 * q^12 - 531230356540 * q^13 - 5894008940736 * q^14 - 27717620084480 * q^16 + 14058178115540 * q^17 + 16283956279140 * q^18 + 233643631625120 * q^20 - 313135665760512 * q^21 + 120589650366240 * q^22 - 2007619616180736 * q^24 + 7710175817606670 * q^25 - 3953973318046744 * q^26 + 1177952265288960 * q^28 - 14464474185570172 * q^29 + 10252783730669760 * q^30 - 73831192092953600 * q^32 + 72906957628179840 * q^33 - 26625976920357496 * q^34 - 36609276067793136 * q^36 + 324587767823538020 * q^37 + 369140808808591200 * q^38 - 1158049295468479360 * q^40 - 1355457345814233100 * q^41 + 2644455724909770240 * q^42 - 1919761520625210240 * q^44 + 9367295763131460 * q^45 + 6132624002565203904 * q^46 - 18374169355003791360 * q^48 + 183553700661552298 * q^49 + 29084394113996178540 * q^50 - 38492433127521128800 * q^52 - 11424344766226018780 * q^53 + 79182840955393027008 * q^54 - 102844865827678657536 * q^56 + 30188516183231506560 * q^57 + 173059696836432320360 * q^58 - 377769459746631548160 * q^60 + 58241718146183220740 * q^61 + 317897221476923285760 * q^62 - 412080172429987966976 * q^64 - 121531695066047433560 * q^65 + 700585278654050000640 * q^66 - 667890522330713878240 * q^68 + 54497497397908094208 * q^69 + 1014396282552321513600 * q^70 - 1244773253376491901120 * q^72 + 83030422224875883380 * q^73 + 801906083011176262184 * q^74 + 286747421140990627200 * q^76 - 704201825495570814720 * q^77 - 964412732782594923840 * q^78 + 1509611955050789726720 * q^80 + 251577744224553978858 * q^81 - 2389572513290905036600 * q^82 + 6185640644326191863808 * q^84 - 1796890366112110859960 * q^85 - 8221838255181360278496 * q^86 + 11178210842814940531200 * q^88 + 3420669206528505615668 * q^89 - 24782809563337507735320 * q^90 + 21476264197983864733440 * q^92 + 15493754050318100597760 * q^93 - 20874543047091388369536 * q^94 + 29250284502468708163584 * q^96 - 20429910746446196146540 * q^97 - 23110416876469762175420 * q^98

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