LMFDB - Embedded newform 4.23.b.a.3.9

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			3.9
Root			$408.476 + 250.605i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.23.b.a.3.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1785.90 - 1002.42i) q^{2} +127855. i q^{3} +(2.18461e6 - 3.58046e6i) q^{4} -6.52379e7 q^{5} +(1.28165e8 + 2.28337e8i) q^{6} -3.27904e9i q^{7} +(3.12381e8 - 8.58425e9i) q^{8} +1.50341e10 q^{9} +O(q^{10})$	\(q+(1785.90 - 1002.42i) q^{2} +127855. i q^{3} +(2.18461e6 - 3.58046e6i) q^{4} -6.52379e7 q^{5} +(1.28165e8 + 2.28337e8i) q^{6} -3.27904e9i q^{7} +(3.12381e8 - 8.58425e9i) q^{8} +1.50341e10 q^{9} +(-1.16509e11 + 6.53958e10i) q^{10} -2.30540e11i q^{11} +(4.57780e11 + 2.79314e11i) q^{12} -1.19775e12 q^{13} +(-3.28698e12 - 5.85606e12i) q^{14} -8.34100e12i q^{15} +(-8.04715e12 - 1.56438e13i) q^{16} -2.07597e13 q^{17} +(2.68495e13 - 1.50705e13i) q^{18} -6.48196e12i q^{19} +(-1.42519e14 + 2.33581e14i) q^{20} +4.19243e14 q^{21} +(-2.31098e14 - 4.11722e14i) q^{22} +1.02386e15i q^{23} +(1.09754e15 + 3.99395e13i) q^{24} +1.87179e15 q^{25} +(-2.13907e15 + 1.20065e15i) q^{26} +5.93442e15i q^{27} +(-1.17405e16 - 7.16343e15i) q^{28} +1.56390e16 q^{29} +(-8.36119e15 - 1.48962e16i) q^{30} -2.85873e16i q^{31} +(-3.00531e16 - 1.98717e16i) q^{32} +2.94757e16 q^{33} +(-3.70748e16 + 2.08100e16i) q^{34} +2.13918e17i q^{35} +(3.28436e16 - 5.38289e16i) q^{36} +2.10744e17 q^{37} +(-6.49765e15 - 1.15762e16i) q^{38} -1.53139e17i q^{39} +(-2.03791e16 + 5.60018e17i) q^{40} -5.57168e17 q^{41} +(7.48728e17 - 4.20258e17i) q^{42} -8.07417e17i q^{43} +(-8.25438e17 - 5.03639e17i) q^{44} -9.80792e17 q^{45} +(1.02634e18 + 1.82852e18i) q^{46} -8.59587e17i q^{47} +(2.00014e18 - 1.02887e18i) q^{48} -6.84231e18 q^{49} +(3.34285e18 - 1.87632e18i) q^{50} -2.65424e18i q^{51} +(-2.61662e18 + 4.28850e18i) q^{52} +1.56480e19 q^{53} +(5.94879e18 + 1.05983e19i) q^{54} +1.50399e19i q^{55} +(-2.81481e19 - 1.02431e18i) q^{56} +8.28753e17 q^{57} +(2.79297e19 - 1.56768e19i) q^{58} +7.82838e18i q^{59} +(-2.98646e19 - 1.82218e19i) q^{60} +1.24317e19 q^{61} +(-2.86565e19 - 5.10542e19i) q^{62} -4.92975e19i q^{63} +(-7.35918e19 - 5.36311e18i) q^{64} +7.81387e19 q^{65} +(5.26408e19 - 2.95471e19i) q^{66} +1.36610e20i q^{67} +(-4.53518e19 + 7.43292e19i) q^{68} -1.30906e20 q^{69} +(2.14436e20 + 3.82037e20i) q^{70} -2.01190e20i q^{71} +(4.69636e18 - 1.29056e20i) q^{72} +2.57734e19 q^{73} +(3.76369e20 - 2.11254e20i) q^{74} +2.39319e20i q^{75} +(-2.32084e19 - 1.41606e19i) q^{76} -7.55950e20 q^{77} +(-1.53509e20 - 2.73491e20i) q^{78} -8.27585e20i q^{79} +(5.24979e20 + 1.02057e21i) q^{80} -2.86961e20 q^{81} +(-9.95050e20 + 5.58517e20i) q^{82} -6.46586e20i q^{83} +(9.15882e20 - 1.50108e21i) q^{84} +1.35432e21 q^{85} +(-8.09371e20 - 1.44197e21i) q^{86} +1.99952e21i q^{87} +(-1.97901e21 - 7.20162e19i) q^{88} +1.96738e21 q^{89} +(-1.75160e21 + 9.83167e20i) q^{90} +3.92748e21i q^{91} +(3.66590e21 + 2.23674e21i) q^{92} +3.65504e21 q^{93} +(-8.61668e20 - 1.53514e21i) q^{94} +4.22869e20i q^{95} +(2.54070e21 - 3.84245e21i) q^{96} -3.08304e21 q^{97} +(-1.22197e22 + 6.85887e21i) q^{98} -3.46596e21i 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 $

$2$	1785.90	−	1002.42i	0.872024	−	0.489463i
$2$	1785.90	−	1002.42i	0.872024	−	0.489463i
$3$			127855.i			0.721747i	0.932615	+	0.360873i	$0.117521\pi$
$3$			127855.i			0.721747i	−0.932615	+	0.360873i	$0.882479\pi$
$4$	2.18461e6	−	3.58046e6i	0.520851	−	0.853647i
$5$	−6.52379e7			−1.33607			−0.668036	−	0.744129i	$-0.732865\pi$
$5$	−6.52379e7			−1.33607			−0.668036	+	0.744129i	$0.732865\pi$
$6$	1.28165e8	+	2.28337e8i	0.353268	+	0.629380i
$7$		−	3.27904e9i		−	1.65832i	−0.559010	−	0.829161i	$-0.688819\pi$
$7$		−	3.27904e9i		−	1.65832i	0.559010	−	0.829161i	$-0.311181\pi$
$8$	3.12381e8	−	8.58425e9i	0.0363659	−	0.999339i
$9$	1.50341e10			0.479082
$10$	−1.16509e11	+	6.53958e10i	−1.16509	+	0.653958i
$11$		−	2.30540e11i		−	0.808028i	−0.914753	−	0.404014i	$-0.867615\pi$
$11$		−	2.30540e11i		−	0.808028i	0.914753	−	0.404014i	$-0.132385\pi$
$12$	4.57780e11	+	2.79314e11i	0.616117	+	0.375923i
$13$	−1.19775e12			−0.668328			−0.334164	−	0.942515i	$-0.608454\pi$
$13$	−1.19775e12			−0.668328			−0.334164	+	0.942515i	$0.608454\pi$
$14$	−3.28698e12	−	5.85606e12i	−0.811688	−	1.44610i
$15$		−	8.34100e12i		−	0.964305i
$16$	−8.04715e12	−	1.56438e13i	−0.457428	−	0.889247i
$17$	−2.07597e13			−0.605735			−0.302868	−	0.953033i	$-0.597944\pi$
$17$	−2.07597e13			−0.605735			−0.302868	+	0.953033i	$0.597944\pi$
$18$	2.68495e13	−	1.50705e13i	0.417771	−	0.234493i
$19$		−	6.48196e12i		−	0.0556438i	−0.999613	−	0.0278219i	$-0.991143\pi$
$19$		−	6.48196e12i		−	0.0556438i	0.999613	−	0.0278219i	$-0.00885713\pi$
$20$	−1.42519e14	+	2.33581e14i	−0.695895	+	1.14053i
$21$	4.19243e14			1.19689
$22$	−2.31098e14	−	4.11722e14i	−0.395500	−	0.704620i
$23$			1.02386e15i			1.07457i	0.843400	+	0.537286i	$0.180550\pi$
$23$			1.02386e15i			1.07457i	−0.843400	+	0.537286i	$0.819450\pi$
$24$	1.09754e15	+	3.99395e13i	0.721269	+	0.0262470i
$25$	1.87179e15			0.785087
$26$	−2.13907e15	+	1.20065e15i	−0.582798	+	0.327122i
$27$			5.93442e15i			1.06752i
$28$	−1.17405e16	−	7.16343e15i	−1.41562	−	0.863739i
$29$	1.56390e16			1.28183			0.640914	−	0.767613i	$-0.278556\pi$
$29$	1.56390e16			1.28183			0.640914	+	0.767613i	$0.278556\pi$
$30$	−8.36119e15	−	1.48962e16i	−0.471992	−	0.840897i
$31$		−	2.85873e16i		−	1.12511i	−0.826760	−	0.562554i	$-0.809819\pi$
$31$		−	2.85873e16i		−	1.12511i	0.826760	−	0.562554i	$-0.190181\pi$
$32$	−3.00531e16	−	1.98717e16i	−0.834141	−	0.551551i
$33$	2.94757e16			0.583191
$34$	−3.70748e16	+	2.08100e16i	−0.528216	+	0.296485i
$35$			2.13918e17i			2.21564i
$36$	3.28436e16	−	5.38289e16i	0.249530	−	0.408967i
$37$	2.10744e17			1.18450			0.592252	−	0.805753i	$-0.298239\pi$
$37$	2.10744e17			1.18450			0.592252	+	0.805753i	$0.298239\pi$
$38$	−6.49765e15	−	1.15762e16i	−0.0272356	−	0.0485227i
$39$		−	1.53139e17i		−	0.482364i
$40$	−2.03791e16	+	5.60018e17i	−0.0485874	+	1.33519i
$41$	−5.57168e17			−1.01243			−0.506214	−	0.862408i	$-0.668955\pi$
$41$	−5.57168e17			−1.01243			−0.506214	+	0.862408i	$0.668955\pi$
$42$	7.48728e17	−	4.20258e17i	1.04372	−	0.585833i
$43$		−	8.07417e17i		−	0.868850i	−0.900708	−	0.434425i	$-0.856952\pi$
$43$		−	8.07417e17i		−	0.868850i	0.900708	−	0.434425i	$-0.143048\pi$
$44$	−8.25438e17	−	5.03639e17i	−0.689771	−	0.420862i
$45$	−9.80792e17			−0.640088
$46$	1.02634e18	+	1.82852e18i	0.525964	+	0.937053i
$47$		−	8.59587e17i		−	0.347707i	−0.984772	−	0.173854i	$-0.944378\pi$
$47$		−	8.59587e17i		−	0.347707i	0.984772	−	0.173854i	$-0.0556219\pi$
$48$	2.00014e18	−	1.02887e18i	0.641811	−	0.330147i
$49$	−6.84231e18			−1.75003
$50$	3.34285e18	−	1.87632e18i	0.684615	−	0.384271i
$51$		−	2.65424e18i		−	0.437187i
$52$	−2.61662e18	+	4.28850e18i	−0.348100	+	0.570517i
$53$	1.56480e19			1.68821			0.844103	−	0.536181i	$-0.180133\pi$
$53$	1.56480e19			1.68821			0.844103	+	0.536181i	$0.180133\pi$
$54$	5.94879e18	+	1.05983e19i	0.522513	+	0.930905i
$55$			1.50399e19i			1.07958i
$56$	−2.81481e19	−	1.02431e18i	−1.65722	−	0.0603064i
$57$	8.28753e17			0.0401607
$58$	2.79297e19	−	1.56768e19i	1.11778	−	0.627408i
$59$			7.82838e18i			0.259597i	0.991540	+	0.129799i	$0.0414331\pi$
$59$			7.82838e18i			0.259597i	−0.991540	+	0.129799i	$0.958567\pi$
$60$	−2.98646e19	−	1.82218e19i	−0.823176	−	0.502260i
$61$	1.24317e19			0.285694			0.142847	−	0.989745i	$-0.454374\pi$
$61$	1.24317e19			0.285694			0.142847	+	0.989745i	$0.454374\pi$
$62$	−2.86565e19	−	5.10542e19i	−0.550699	−	0.981121i
$63$		−	4.92975e19i		−	0.794472i
$64$	−7.35918e19	−	5.36311e18i	−0.997355	−	0.0726837i
$65$	7.81387e19			0.892934
$66$	5.26408e19	−	2.95471e19i	0.508557	−	0.285451i
$67$			1.36610e20i			1.11856i	0.828979	+	0.559279i	$0.188922\pi$
$67$			1.36610e20i			1.11856i	−0.828979	+	0.559279i	$0.811078\pi$
$68$	−4.53518e19	+	7.43292e19i	−0.315498	+	0.517084i
$69$	−1.30906e20			−0.775569
$70$	2.14436e20	+	3.82037e20i	1.08447	+	1.93209i
$71$		−	2.01190e20i		−	0.870492i	−0.900312	−	0.435246i	$-0.856661\pi$
$71$		−	2.01190e20i		−	0.870492i	0.900312	−	0.435246i	$-0.143339\pi$
$72$	4.69636e18	−	1.29056e20i	0.0174222	−	0.478765i
$73$	2.57734e19			0.0821524			0.0410762	−	0.999156i	$-0.486921\pi$
$73$	2.57734e19			0.0821524			0.0410762	+	0.999156i	$0.486921\pi$
$74$	3.76369e20	−	2.11254e20i	1.03292	−	0.579771i
$75$			2.39319e20i			0.566634i
$76$	−2.32084e19	−	1.41606e19i	−0.0475002	−	0.0289822i
$77$	−7.55950e20			−1.33997
$78$	−1.53509e20	−	2.73491e20i	−0.236099	−	0.420633i
$79$		−	8.27585e20i		−	1.10641i	−0.833046	−	0.553203i	$-0.813405\pi$
$79$		−	8.27585e20i		−	1.10641i	0.833046	−	0.553203i	$-0.186595\pi$
$80$	5.24979e20	+	1.02057e21i	0.611156	+	1.18810i
$81$	−2.86961e20			−0.291399
$82$	−9.95050e20	+	5.58517e20i	−0.882861	+	0.495546i
$83$		−	6.46586e20i		−	0.502074i	−0.967978	−	0.251037i	$-0.919228\pi$
$83$		−	6.46586e20i		−	0.502074i	0.967978	−	0.251037i	$-0.0807715\pi$
$84$	9.15882e20	−	1.50108e21i	0.623401	−	1.02172i
$85$	1.35432e21			0.809306
$86$	−8.09371e20	−	1.44197e21i	−0.425270	−	0.757658i
$87$			1.99952e21i			0.925155i
$88$	−1.97901e21	−	7.20162e19i	−0.807493	−	0.0293847i
$89$	1.96738e21			0.708923			0.354461	−	0.935071i	$-0.384664\pi$
$89$	1.96738e21			0.708923			0.354461	+	0.935071i	$0.384664\pi$
$90$	−1.75160e21	+	9.83167e20i	−0.558172	+	0.313299i
$91$			3.92748e21i			1.10830i
$92$	3.66590e21	+	2.23674e21i	0.917306	+	0.559693i
$93$	3.65504e21			0.812043
$94$	−8.61668e20	−	1.53514e21i	−0.170190	−	0.303209i
$95$			4.22869e20i			0.0743441i
$96$	2.54070e21	−	3.84245e21i	0.398080	−	0.602039i
$97$	−3.08304e21			−0.431013			−0.215506	−	0.976502i	$-0.569140\pi$
$97$	−3.08304e21			−0.431013			−0.215506	+	0.976502i	$0.569140\pi$
$98$	−1.22197e22	+	6.85887e21i	−1.52607	+	0.856576i
$99$		−	3.46596e21i		−	0.387111i
$100$	4.08914e21	−	6.70187e21i	0.408914	−	0.670187i
$101$	1.90013e21			0.170313			0.0851565	−	0.996368i	$-0.472861\pi$
$101$	1.90013e21			0.170313			0.0851565	+	0.996368i	$0.472861\pi$
$102$	−2.66066e21	−	4.74021e21i	−0.213987	−	0.381238i
$103$		−	2.69990e22i		−	1.95046i	−0.221184	−	0.975232i	$-0.570992\pi$
$103$		−	2.69990e22i		−	1.95046i	0.221184	−	0.975232i	$-0.429008\pi$
$104$	−3.74154e20	+	1.02818e22i	−0.0243044	+	0.667886i
$105$	−2.73505e22			−1.59913
$106$	2.79459e22	−	1.56859e22i	1.47216	−	0.826315i
$107$			2.37790e22i			1.12973i	0.825185	+	0.564863i	$0.191071\pi$
$107$			2.37790e22i			1.12973i	−0.825185	+	0.564863i	$0.808929\pi$
$108$	2.12479e22	+	1.29644e22i	0.911288	+	0.556021i
$109$	−1.54276e22			−0.597872			−0.298936	−	0.954273i	$-0.596632\pi$
$109$	−1.54276e22			−0.597872			−0.298936	+	0.954273i	$0.596632\pi$
$110$	1.50763e22	+	2.68599e22i	0.528416	+	0.941422i
$111$			2.69447e22i			0.854911i
$112$	−5.12967e22	+	2.63870e22i	−1.47466	+	0.758562i
$113$	4.91614e22			1.28162			0.640812	−	0.767697i	$-0.278598\pi$
$113$	4.91614e22			1.28162			0.640812	+	0.767697i	$0.278598\pi$
$114$	1.48007e21	−	8.30759e20i	0.0350211	−	0.0196572i
$115$		−	6.67946e22i		−	1.43571i
$116$	3.41650e22	−	5.59946e22i	0.667642	−	1.09423i
$117$	−1.80071e22			−0.320184
$118$	7.84733e21	+	1.39807e22i	0.127063	+	0.226375i
$119$			6.80720e22i			1.00450i
$120$	−7.16013e22	−	2.60557e21i	−0.963667	−	0.0350678i
$121$	2.82542e22			0.347091
$122$	2.22018e22	−	1.24618e22i	0.249132	−	0.139837i
$123$		−	7.12369e22i		−	0.730716i
$124$	−1.02356e23	−	6.24521e22i	−0.960446	−	0.586014i
$125$	3.34274e22			0.287139
$126$	−4.94168e22	−	8.80406e22i	−0.388865	−	0.692798i
$127$			1.68835e23i			1.21793i	0.793198	+	0.608964i	$0.208414\pi$
$127$			1.68835e23i			1.21793i	−0.793198	+	0.608964i	$0.791586\pi$
$128$	−1.36804e23	+	6.41920e22i	−0.905293	+	0.424787i
$129$	1.03232e23			0.627089
$130$	1.39548e23	−	7.83279e22i	0.778660	−	0.437058i
$131$			3.80646e22i			0.195226i	0.995224	+	0.0976129i	$0.0311207\pi$
$131$			3.80646e22i			0.195226i	−0.995224	+	0.0976129i	$0.968879\pi$
$132$	6.43929e22	−	1.05537e23i	0.303756	−	0.497840i
$133$	−2.12546e22			−0.0922754
$134$	1.36940e23	+	2.43972e23i	0.547493	+	0.975410i
$135$		−	3.87149e23i		−	1.42629i
$136$	−6.48493e21	+	1.78206e23i	−0.0220281	+	0.605335i
$137$	−1.78768e23			−0.560226			−0.280113	−	0.959967i	$-0.590372\pi$
$137$	−1.78768e23			−0.560226			−0.280113	+	0.959967i	$0.590372\pi$
$138$	−2.33786e23	+	1.31223e23i	−0.676315	+	0.379613i
$139$			3.00886e23i			0.803970i	0.915646	+	0.401985i	$0.131680\pi$
$139$			3.00886e23i			0.803970i	−0.915646	+	0.401985i	$0.868320\pi$
$140$	7.65924e23	+	4.67327e23i	1.89137	+	1.15402i
$141$	1.09903e23			0.250956
$142$	−2.01677e23	−	3.59306e23i	−0.426074	−	0.759090i
$143$			2.76129e23i			0.540028i
$144$	−1.20982e23	−	2.35190e23i	−0.219145	−	0.426022i
$145$	−1.02025e24			−1.71261
$146$	4.60288e22	−	2.58358e22i	0.0716389	−	0.0402106i
$147$		−	8.74825e23i		−	1.26308i
$148$	4.60393e23	−	7.54560e23i	0.616950	−	1.01115i
$149$	1.60515e23			0.199740			0.0998701	−	0.995000i	$-0.468157\pi$
$149$	1.60515e23			0.199740			0.0998701	+	0.995000i	$0.468157\pi$
$150$	2.39898e23	+	4.27400e23i	0.277346	+	0.494118i
$151$		−	1.36960e24i		−	1.47180i	−0.677091	−	0.735900i	$-0.736759\pi$
$151$		−	1.36960e24i		−	1.47180i	0.677091	−	0.735900i	$-0.263241\pi$
$152$	−5.56428e22	−	2.02484e21i	−0.0556070	−	0.00202354i
$153$	−3.12103e23			−0.290197
$154$	−1.35005e24	+	7.57780e23i	−1.16849	+	0.655866i
$155$			1.86497e24i			1.50323i
$156$	−5.48307e23	−	3.34548e23i	−0.411768	−	0.251240i
$157$	1.70659e24			1.19463			0.597315	−	0.802007i	$-0.296234\pi$
$157$	1.70659e24			1.19463			0.597315	+	0.802007i	$0.296234\pi$
$158$	−8.29589e23	−	1.47799e24i	−0.541545	−	0.964813i
$159$			2.00068e24i			1.21846i
$160$	1.96060e24	+	1.29639e24i	1.11447	+	0.736911i
$161$	3.35729e24			1.78199
$162$	−5.12485e23	+	2.87656e23i	−0.254107	+	0.142629i
$163$		−	2.89527e23i		−	0.134161i	−0.997748	−	0.0670805i	$-0.978632\pi$
$163$		−	2.89527e23i		−	0.134161i	0.997748	−	0.0670805i	$-0.0213684\pi$
$164$	−1.21720e24	+	1.99492e24i	−0.527324	+	0.864256i
$165$	−1.92293e24			−0.779185
$166$	−6.48151e23	−	1.15474e24i	−0.245747	−	0.437820i
$167$			6.70501e23i			0.237968i	0.992896	+	0.118984i	$0.0379637\pi$
$167$			6.70501e23i			0.237968i	−0.992896	+	0.118984i	$0.962036\pi$
$168$	1.30963e23	−	3.59889e24i	0.0435259	−	1.19610i
$169$	−1.77723e24			−0.553338
$170$	2.41868e24	−	1.35760e24i	0.705734	−	0.396125i
$171$		−	9.74504e22i		−	0.0266579i
$172$	−2.89092e24	−	1.76389e24i	−0.741691	−	0.452542i
$173$	1.20344e24			0.289680			0.144840	−	0.989455i	$-0.453733\pi$
$173$	1.20344e24			0.289680			0.144840	+	0.989455i	$0.453733\pi$
$174$	2.00436e24	+	3.57096e24i	0.452829	+	0.806757i
$175$		−	6.13769e24i		−	1.30193i
$176$	−3.60652e24	+	1.85519e24i	−0.718536	+	0.369614i
$177$	−1.00090e24			−0.187363
$178$	3.51356e24	−	1.97215e24i	0.618198	−	0.346992i
$179$		−	2.09363e24i		−	0.346351i	−0.984891	−	0.173175i	$-0.944597\pi$
$179$		−	2.09363e24i		−	0.346351i	0.984891	−	0.173175i	$-0.0554027\pi$
$180$	−2.14265e24	+	3.51168e24i	−0.333391	+	0.546409i
$181$	−6.07098e24			−0.888780			−0.444390	−	0.895833i	$-0.646580\pi$
$181$	−6.07098e24			−0.888780			−0.444390	+	0.895833i	$0.646580\pi$
$182$	3.93699e24	+	7.01410e24i	0.542474	+	0.966467i
$183$			1.58946e24i			0.206199i
$184$	8.78910e24	+	3.19835e23i	1.07386	+	0.0390778i
$185$	−1.37485e25			−1.58258
$186$	6.52755e24	−	3.66388e24i	0.708121	−	0.397465i
$187$			4.78594e24i			0.489451i
$188$	−3.07772e24	−	1.87786e24i	−0.296819	−	0.181104i
$189$	1.94592e25			1.77030
$190$	4.23893e23	+	7.55205e23i	0.0363887	+	0.0648298i
$191$		−	3.81076e24i		−	0.308777i	−0.988010	−	0.154388i	$-0.950659\pi$
$191$		−	3.81076e24i		−	0.308777i	0.988010	−	0.154388i	$-0.0493407\pi$
$192$	6.85702e23	−	9.40910e24i	0.0524592	−	0.719838i
$193$	1.79870e24			0.129965			0.0649827	−	0.997886i	$-0.479301\pi$
$193$	1.79870e24			0.129965			0.0649827	+	0.997886i	$0.479301\pi$
$194$	−5.50601e24	+	3.09050e24i	−0.375853	+	0.210965i
$195$			9.99045e24i			0.644472i
$196$	−1.49478e25	+	2.44986e25i	−0.911506	+	1.49391i
$197$	7.75126e24			0.446934			0.223467	−	0.974711i	$-0.428262\pi$
$197$	7.75126e24			0.446934			0.223467	+	0.974711i	$0.428262\pi$
$198$	−3.47435e24	−	6.18987e24i	−0.189477	−	0.337570i
$199$			1.90298e25i			0.981860i	0.871199	+	0.490930i	$0.163343\pi$
$199$			1.90298e25i			0.981860i	−0.871199	+	0.490930i	$0.836657\pi$
$200$	5.84712e23	−	1.60679e25i	0.0285504	−	0.784568i
$201$	−1.74663e25			−0.807316
$202$	3.39345e24	−	1.90473e24i	0.148517	−	0.0833620i
$203$		−	5.12808e25i		−	2.12568i
$204$	−9.50338e24	−	5.79847e24i	−0.373204	−	0.227710i
$205$	3.63485e25			1.35268
$206$	−2.70643e25	−	4.82176e25i	−0.954681	−	1.70085i
$207$			1.53929e25i			0.514808i
$208$	9.63848e24	+	1.87374e25i	0.305712	+	0.594309i
$209$	−1.49435e24			−0.0449617
$210$	−4.88454e25	+	2.74167e25i	−1.39448	+	0.782714i
$211$			1.37490e25i			0.372532i	0.982499	+	0.186266i	$0.0596386\pi$
$211$			1.37490e25i			0.372532i	−0.982499	+	0.186266i	$0.940361\pi$
$212$	3.41849e25	−	5.60272e25i	0.879305	−	1.44113i
$213$	2.57232e25			0.628275
$214$	2.38366e25	+	4.24671e25i	0.552959	+	0.985147i
$215$			5.26741e25i			1.16085i
$216$	5.09426e25	+	1.85380e24i	1.06682	+	0.0388214i
$217$	−9.37390e25			−1.86579
$218$	−2.75523e25	+	1.54650e25i	−0.521358	+	0.292636i
$219$			3.29526e24i			0.0592932i
$220$	5.38498e25	+	3.28563e25i	0.921583	+	0.562302i
$221$	2.48650e25			0.404830
$222$	2.70100e25	+	4.81207e25i	0.418448	+	0.745503i
$223$		−	1.07103e26i		−	1.57923i	−0.613600	−	0.789617i	$-0.710279\pi$
$223$		−	1.07103e26i		−	1.57923i	0.613600	−	0.789617i	$-0.289721\pi$
$224$	−6.51602e25	+	9.85455e25i	−0.914648	+	1.38328i
$225$	2.81407e25			0.376121
$226$	8.77975e25	−	4.92804e25i	1.11761	−	0.627308i
$227$			1.17534e25i			0.142521i	0.997458	+	0.0712607i	$0.0227022\pi$
$227$			1.17534e25i			0.142521i	−0.997458	+	0.0712607i	$0.977298\pi$
$228$	1.81050e24	−	2.96731e24i	0.0209178	−	0.0342831i
$229$	−9.48445e25			−1.04429			−0.522146	−	0.852856i	$-0.674868\pi$
$229$	−9.48445e25			−1.04429			−0.522146	+	0.852856i	$0.674868\pi$
$230$	−6.69563e25	−	1.19289e26i	−0.702725	−	1.25197i
$231$		−	9.66522e25i		−	0.967119i
$232$	4.88531e24	−	1.34249e26i	0.0466148	−	1.28098i
$233$	−8.11776e25			−0.738790			−0.369395	−	0.929273i	$-0.620435\pi$
$233$	−8.11776e25			−0.738790			−0.369395	+	0.929273i	$0.620435\pi$
$234$	−3.21590e25	+	1.80507e25i	−0.279208	+	0.156718i
$235$			5.60776e25i			0.464562i
$236$	2.80292e25	+	1.71020e25i	0.221604	+	0.135212i
$237$	1.05811e26			0.798545
$238$	6.82367e25	+	1.21570e26i	0.491668	+	0.875952i
$239$			1.56047e25i			0.107369i	0.998558	+	0.0536845i	$0.0170965\pi$
$239$			1.56047e25i			0.107369i	−0.998558	+	0.0536845i	$0.982903\pi$
$240$	−1.30485e26	+	6.71213e25i	−0.857505	+	0.441100i
$241$	−1.58806e26			−0.996964			−0.498482	−	0.866900i	$-0.666109\pi$
$241$	−1.58806e26			−0.996964			−0.498482	+	0.866900i	$0.666109\pi$
$242$	5.04593e25	−	2.83226e25i	0.302672	−	0.169888i
$243$			1.49539e26i			0.857206i
$244$	2.71584e25	−	4.45111e25i	0.148804	−	0.243882i
$245$	4.46378e26			2.33817
$246$	−7.14093e25	−	1.27222e26i	−0.357659	−	0.637202i
$247$			7.76378e24i			0.0371883i
$248$	−2.45401e26	−	8.93012e24i	−1.12436	−	0.0409156i
$249$	8.26694e25			0.362370
$250$	5.96981e25	−	3.35083e25i	0.250392	−	0.140544i
$251$			1.35006e26i			0.541929i	0.962589	+	0.270965i	$0.0873426\pi$
$251$			1.35006e26i			0.541929i	−0.962589	+	0.270965i	$0.912657\pi$
$252$	−1.76507e26	−	1.07696e26i	−0.678199	−	0.413802i
$253$	2.36041e26			0.868284
$254$	1.69244e26	+	3.01523e26i	0.596131	+	1.06206i
$255$			1.73157e26i			0.584114i
$256$	−1.79972e26	+	2.51776e26i	−0.581520	+	0.813532i
$257$	−4.06306e26			−1.25773			−0.628867	−	0.777513i	$-0.716481\pi$
$257$	−4.06306e26			−1.25773			−0.628867	+	0.777513i	$0.716481\pi$
$258$	1.84363e26	−	1.03482e26i	0.546837	−	0.306937i
$259$		−	6.91039e26i		−	1.96429i
$260$	1.70703e26	−	2.79772e26i	0.465086	−	0.762251i
$261$	2.35117e26			0.614100
$262$	3.81568e25	+	6.79798e25i	0.0955559	+	0.170242i
$263$			4.30318e26i			1.03342i	0.856161	+	0.516709i	$0.172843\pi$
$263$			4.30318e26i			1.03342i	−0.856161	+	0.516709i	$0.827157\pi$
$264$	9.20765e24	−	2.53027e26i	0.0212083	−	0.582806i
$265$	−1.02085e27			−2.25556
$266$	−3.79588e25	+	2.13061e25i	−0.0804663	+	0.0451654i
$267$			2.51540e26i			0.511663i
$268$	4.89125e26	+	2.98439e26i	0.954854	+	0.582603i
$269$	4.75629e26			0.891237			0.445619	−	0.895223i	$-0.352984\pi$
$269$	4.75629e26			0.891237			0.445619	+	0.895223i	$0.352984\pi$
$270$	−3.88086e26	−	6.91411e26i	−0.698115	−	1.24376i
$271$		−	9.39071e26i		−	1.62194i	−0.585085	−	0.810972i	$-0.698939\pi$
$271$		−	9.39071e26i		−	1.62194i	0.585085	−	0.810972i	$-0.301061\pi$
$272$	1.67056e26	+	3.24760e26i	0.277080	+	0.538648i
$273$	−5.02149e26			−0.799914
$274$	−3.19262e26	+	1.79201e26i	−0.488530	+	0.274210i
$275$		−	4.31523e26i		−	0.634372i
$276$	−2.85979e26	+	4.68704e26i	−0.403956	+	0.662062i
$277$	−5.11627e26			−0.694505			−0.347253	−	0.937772i	$-0.612885\pi$
$277$	−5.11627e26			−0.694505			−0.347253	+	0.937772i	$0.612885\pi$
$278$	3.01615e26	+	5.37354e26i	0.393514	+	0.701081i
$279$		−	4.29784e26i		−	0.539019i
$280$	1.83632e27	+	6.68238e25i	2.21417	+	0.0805736i
$281$	1.13838e27			1.31983			0.659917	−	0.751339i	$-0.270592\pi$
$281$	1.13838e27			1.31983			0.659917	+	0.751339i	$0.270592\pi$
$282$	1.96276e26	−	1.10169e26i	0.218840	−	0.122834i
$283$			1.28612e27i			1.37922i	0.724183	+	0.689608i	$0.242217\pi$
$283$			1.28612e27i			1.37922i	−0.724183	+	0.689608i	$0.757783\pi$
$284$	−7.20352e26	−	4.39522e26i	−0.743093	−	0.453397i
$285$	−5.40661e25			−0.0536576
$286$	2.76798e26	+	4.93141e26i	0.264324	+	0.470917i
$287$			1.82698e27i			1.67893i
$288$	−4.51821e26	−	2.98753e26i	−0.399622	−	0.264238i
$289$	−7.43598e26			−0.633085
$290$	−1.82207e27	+	1.02272e27i	−1.49344	+	0.838261i
$291$		−	3.94183e26i		−	0.311082i
$292$	5.63048e25	−	9.22805e25i	0.0427892	−	0.0701292i
$293$	2.23679e27			1.63712			0.818560	−	0.574421i	$-0.194773\pi$
$293$	2.23679e27			1.63712			0.818560	+	0.574421i	$0.194773\pi$
$294$	−8.76943e26	−	1.56235e27i	−0.618231	−	1.10144i
$295$		−	5.10707e26i		−	0.346840i
$296$	6.58324e25	−	1.80908e27i	0.0430755	−	1.18372i
$297$	1.36812e27			0.862588
$298$	2.86664e26	−	1.60903e26i	0.174178	−	0.0977655i
$299$		−	1.22633e27i		−	0.718167i
$300$	8.56870e26	+	5.22818e26i	0.483706	+	0.295132i
$301$	−2.64756e27			−1.44083
$302$	−1.37292e27	−	2.44598e27i	−0.720392	−	1.28344i
$303$			2.42941e26i			0.122923i
$304$	−1.01403e26	+	5.21613e25i	−0.0494811	+	0.0254530i
$305$	−8.11016e26			−0.381708
$306$	−5.57387e26	+	3.12859e26i	−0.253059	+	0.142041i
$307$		−	2.10997e27i		−	0.924175i	−0.886834	−	0.462088i	$-0.847101\pi$
$307$		−	2.10997e27i		−	0.924175i	0.886834	−	0.462088i	$-0.152899\pi$
$308$	−1.65146e27	+	2.70665e27i	−0.697925	+	1.14386i
$309$	3.45196e27			1.40774
$310$	1.86949e27	+	3.33067e27i	0.735774	+	1.31085i
$311$			2.95432e27i			1.12226i	0.827727	+	0.561130i	$0.189633\pi$
$311$			2.95432e27i			1.12226i	−0.827727	+	0.561130i	$0.810367\pi$
$312$	−1.31458e27	−	4.78376e25i	−0.482044	−	0.0175416i
$313$	−2.10744e26			−0.0746050			−0.0373025	−	0.999304i	$-0.511877\pi$
$313$	−2.10744e26			−0.0746050			−0.0373025	+	0.999304i	$0.511877\pi$
$314$	3.04781e27	−	1.71072e27i	1.04175	−	0.584727i
$315$			3.21606e27i			1.06147i
$316$	−2.96313e27	−	1.80795e27i	−0.944481	−	0.576274i
$317$	−2.00178e27			−0.616260			−0.308130	−	0.951344i	$-0.599703\pi$
$317$	−2.00178e27			−0.616260			−0.308130	+	0.951344i	$0.599703\pi$
$318$	2.00553e27	+	3.57303e27i	0.596390	+	1.06252i
$319$		−	3.60540e27i		−	1.03575i
$320$	4.80097e27	+	3.49878e26i	1.33254	+	0.0971106i
$321$	−3.04028e27			−0.815375
$322$	5.99580e27	−	3.36542e27i	1.55394	−	0.872217i
$323$			1.34564e26i			0.0337054i
$324$	−6.26898e26	+	1.02745e27i	−0.151775	+	0.248752i
$325$	−2.24194e27			−0.524696
$326$	−2.90228e26	−	5.17069e26i	−0.0656669	−	0.116992i
$327$		−	1.97250e27i		−	0.431512i
$328$	−1.74049e26	+	4.78287e27i	−0.0368178	+	1.01176i
$329$	−2.81862e27			−0.576610
$330$	−3.43418e27	+	1.92759e27i	−0.679468	+	0.381383i
$331$		−	9.42339e25i		−	0.0180343i	−0.999959	−	0.00901715i	$-0.997130\pi$
$331$		−	9.42339e25i		−	0.0180343i	0.999959	−	0.00901715i	$-0.00287029\pi$
$332$	−2.31507e27	−	1.41254e27i	−0.428594	−	0.261506i
$333$	3.16835e27			0.567474
$334$	6.72124e26	+	1.19745e27i	0.116476	+	0.207513i
$335$		−	8.91212e27i		−	1.49447i
$336$	−3.37371e27	−	6.55855e27i	−0.547490	−	1.06433i
$337$	5.66099e27			0.889126			0.444563	−	0.895748i	$-0.353359\pi$
$337$	5.66099e27			0.889126			0.444563	+	0.895748i	$0.353359\pi$
$338$	−3.17397e27	+	1.78153e27i	−0.482524	+	0.270838i
$339$			6.28554e27i			0.925008i
$340$	2.95866e27	−	4.84908e27i	0.421528	−	0.690862i
$341$	−6.59051e27			−0.909119
$342$	−9.76864e25	−	1.74037e26i	−0.0130481	−	0.0232464i
$343$			9.61576e27i			1.24379i
$344$	−6.93107e27	−	2.52221e26i	−0.868275	−	0.0315965i
$345$	8.54005e27			1.03622
$346$	2.14924e27	−	1.20636e27i	0.252608	−	0.141788i
$347$		−	4.71029e27i		−	0.536319i	−0.963375	−	0.268159i	$-0.913585\pi$
$347$		−	4.71029e27i		−	0.536319i	0.963375	−	0.268159i	$-0.0864154\pi$
$348$	7.15920e27	+	4.36817e27i	0.789756	+	0.481868i
$349$	−5.26090e27			−0.562315			−0.281158	−	0.959662i	$-0.590718\pi$
$349$	−5.26090e27			−0.562315			−0.281158	+	0.959662i	$0.590718\pi$
$350$	−6.15255e27	−	1.09613e28i	−0.637245	−	1.13531i
$351$		−	7.10796e27i		−	0.713455i
$352$	−4.58122e27	+	6.92844e27i	−0.445668	+	0.674009i
$353$	1.91623e28			1.80686			0.903431	−	0.428733i	$-0.141040\pi$
$353$	1.91623e28			1.80686			0.903431	+	0.428733i	$0.141040\pi$
$354$	−1.78751e27	+	1.00332e27i	−0.163385	+	0.0917075i
$355$			1.31252e28i			1.16304i
$356$	4.29797e27	−	7.04413e27i	0.369244	−	0.605170i
$357$	−8.70336e27			−0.724997
$358$	−2.09870e27	−	3.73902e27i	−0.169526	−	0.302026i
$359$			1.89213e28i			1.48222i	0.671384	+	0.741109i	$0.265700\pi$
$359$			1.89213e28i			1.48222i	−0.671384	+	0.741109i	$0.734300\pi$
$360$	−3.06381e26	+	8.41937e27i	−0.0232774	+	0.639664i
$361$	1.35280e28			0.996904
$362$	−1.08422e28	+	6.08567e27i	−0.775037	+	0.435025i
$363$			3.61244e27i			0.250512i
$364$	1.40622e28	+	8.58001e27i	0.946100	+	0.577261i
$365$	−1.68140e27			−0.109761
$366$	1.59330e27	+	2.83862e27i	0.100927	+	0.179810i
$367$		−	1.27013e28i		−	0.780766i	−0.920653	−	0.390383i	$-0.872343\pi$
$367$		−	1.27013e28i		−	0.780766i	0.920653	−	0.390383i	$-0.127657\pi$
$368$	1.60171e28	−	8.23918e27i	0.955560	−	0.491539i
$369$	−8.37652e27			−0.485036
$370$	−2.45535e28	+	1.37818e28i	−1.38005	+	0.774615i
$371$		−	5.13106e28i		−	2.79959i
$372$	7.98482e27	−	1.30867e28i	0.422954	−	0.693199i
$373$	−2.94227e28			−1.51316			−0.756582	−	0.653899i	$-0.773132\pi$
$373$	−2.94227e28			−1.51316			−0.756582	+	0.653899i	$0.773132\pi$
$374$	4.79752e27	+	8.54723e27i	0.239568	+	0.426813i
$375$			4.27387e27i			0.207242i
$376$	−7.37892e27	−	2.68519e26i	−0.347477	−	0.0126447i
$377$	−1.87316e28			−0.856682
$378$	3.47523e28	−	1.95063e28i	1.54374	−	0.866495i
$379$			8.36564e25i			0.00360967i	0.999998	+	0.00180484i	$0.000574498\pi$
$379$			8.36564e25i			0.00360967i	−0.999998	+	0.00180484i	$0.999426\pi$
$380$	1.51407e27	+	9.23804e26i	0.0634637	+	0.0387222i
$381$	−2.15864e28			−0.879035
$382$	−3.81998e27	−	6.80565e27i	−0.151135	−	0.269261i
$383$			3.20966e28i			1.23388i	0.787011	+	0.616939i	$0.211627\pi$
$383$			3.20966e28i			1.23388i	−0.787011	+	0.616939i	$0.788373\pi$
$384$	−8.20728e27	−	1.74911e28i	−0.306588	−	0.653392i
$385$	4.93166e28			1.79030
$386$	3.21230e27	−	1.80305e27i	0.113333	−	0.0636133i
$387$		−	1.21388e28i		−	0.416250i
$388$	−6.73523e27	+	1.10387e28i	−0.224493	+	0.367933i
$389$	−1.31115e28			−0.424820			−0.212410	−	0.977181i	$-0.568131\pi$
$389$	−1.31115e28			−0.424820			−0.212410	+	0.977181i	$0.568131\pi$
$390$	1.00146e28	+	1.78420e28i	0.315445	+	0.561995i
$391$		−	2.12551e28i		−	0.650906i
$392$	−2.13741e27	+	5.87361e28i	−0.0636415	+	1.74887i
$393$	−4.86676e27			−0.140904
$394$	1.38430e28	−	7.77002e27i	0.389737	−	0.218758i
$395$			5.39899e28i			1.47824i
$396$	−1.24097e28	−	7.57176e27i	−0.330457	−	0.201628i
$397$	4.02852e28			1.04340			0.521699	−	0.853130i	$-0.325298\pi$
$397$	4.02852e28			1.04340			0.521699	+	0.853130i	$0.325298\pi$
$398$	1.90758e28	+	3.39853e28i	0.480584	+	0.856205i
$399$		−	2.71752e27i		−	0.0665994i
$400$	−1.50626e28	−	2.92820e28i	−0.359120	−	0.698136i
$401$	−1.55924e27			−0.0361679			−0.0180840	−	0.999836i	$-0.505757\pi$
$401$	−1.55924e27			−0.0361679			−0.0180840	+	0.999836i	$0.505757\pi$
$402$	−3.11931e28	+	1.75085e28i	−0.703999	+	0.395151i
$403$			3.42405e28i			0.751942i
$404$	4.15104e27	−	6.80333e27i	0.0887078	−	0.145387i
$405$	1.87207e28			0.389330
$406$	−5.14050e28	−	9.15827e28i	−1.04044	−	1.85365i
$407$		−	4.85849e28i		−	0.957112i
$408$	−2.27846e28	−	8.29132e26i	−0.436898	−	0.0158987i
$409$	4.83341e28			0.902189			0.451095	−	0.892476i	$-0.351034\pi$
$409$	4.83341e28			0.902189			0.451095	+	0.892476i	$0.351034\pi$
$410$	6.49149e28	−	3.64365e28i	1.17957	−	0.662085i
$411$		−	2.28564e28i		−	0.404341i
$412$	−9.66687e28	−	5.89822e28i	−1.66501	−	1.01590i
$413$	2.56696e28			0.430496
$414$	1.54301e28	+	2.74902e28i	0.251980	+	0.448925i
$415$			4.21819e28i			0.670806i
$416$	3.59962e28	+	2.38014e28i	0.557480	+	0.368617i
$417$	−3.84699e28			−0.580262
$418$	−2.66877e27	+	1.49797e27i	−0.0392077	+	0.0220071i
$419$			2.67025e28i			0.382119i	0.981578	+	0.191059i	$0.0611923\pi$
$419$			2.67025e28i			0.382119i	−0.981578	+	0.191059i	$0.938808\pi$
$420$	−5.97502e28	+	9.79273e28i	−0.832908	+	1.36509i
$421$	−9.08309e28			−1.23348			−0.616738	−	0.787168i	$-0.711546\pi$
$421$	−9.08309e28			−1.23348			−0.616738	+	0.787168i	$0.711546\pi$
$422$	1.37823e28	+	2.45544e28i	0.182341	+	0.324857i
$423$		−	1.29231e28i		−	0.166580i
$424$	4.88815e27	−	1.34327e29i	0.0613932	−	1.68709i
$425$	−3.88579e28			−0.475555
$426$	4.59392e28	−	2.57855e28i	0.547870	−	0.307517i
$427$		−	4.07640e28i		−	0.473773i
$428$	8.51398e28	+	5.19479e28i	0.964387	+	0.588419i
$429$	−3.53046e28			−0.389763
$430$	5.28017e28	+	9.40710e28i	0.568191	+	1.01229i
$431$		−	1.37308e28i		−	0.144028i	−0.997404	−	0.0720138i	$-0.977057\pi$
$431$		−	1.37308e28i		−	0.144028i	0.997404	−	0.0720138i	$-0.0229426\pi$
$432$	9.28369e28	−	4.77552e28i	0.949291	−	0.488314i
$433$	1.64110e29			1.63595			0.817973	−	0.575256i	$-0.195098\pi$
$433$	1.64110e29			1.63595			0.817973	+	0.575256i	$0.195098\pi$
$434$	−1.67409e29	+	9.39659e28i	−1.62702	+	0.913237i
$435$		−	1.30445e29i		−	1.23607i
$436$	−3.37034e28	+	5.52380e28i	−0.311402	+	0.510372i
$437$	6.63664e27			0.0597933
$438$	3.30324e27	+	5.88503e27i	0.0290218	+	0.0517051i
$439$			4.23898e28i			0.363205i	0.983372	+	0.181602i	$0.0581284\pi$
$439$			4.23898e28i			0.363205i	−0.983372	+	0.181602i	$0.941872\pi$
$440$	1.29106e29	+	4.69818e27i	1.07887	+	0.0392600i
$441$	−1.02868e29			−0.838408
$442$	4.44064e28	−	2.49251e28i	0.353021	−	0.198149i
$443$			1.30441e29i			1.01152i	0.862675	+	0.505758i	$0.168787\pi$
$443$			1.30441e29i			1.01152i	−0.862675	+	0.505758i	$0.831213\pi$
$444$	9.64744e28	+	5.88637e28i	0.729793	+	0.445282i
$445$	−1.28348e29			−0.947172
$446$	−1.07362e29	−	1.91275e29i	−0.772977	−	1.37713i
$447$			2.05226e28i			0.144162i
$448$	−1.75859e28	+	2.41311e29i	−0.120533	+	1.65394i
$449$	−1.82786e29			−1.22246			−0.611229	−	0.791454i	$-0.709325\pi$
$449$	−1.82786e29			−1.22246			−0.611229	+	0.791454i	$0.709325\pi$
$450$	5.02567e28	−	2.82088e28i	0.327986	−	0.184097i
$451$			1.28449e29i			0.818070i
$452$	1.07398e29	−	1.76020e29i	0.667536	−	1.09406i
$453$	1.75111e29			1.06227
$454$	1.17819e28	+	2.09905e28i	0.0697590	+	0.124282i
$455$		−	2.56220e29i		−	1.48077i
$456$	2.58886e26	−	7.11422e27i	0.00146048	−	0.0401342i
$457$	1.35905e29			0.748441			0.374220	−	0.927340i	$-0.377910\pi$
$457$	1.35905e29			0.748441			0.374220	+	0.927340i	$0.377910\pi$
$458$	−1.69383e29	+	9.50741e28i	−0.910648	+	0.511143i
$459$		−	1.23197e29i		−	0.646636i
$460$	−2.39155e29	−	1.45920e29i	−1.22559	−	0.747789i
$461$	1.93686e29			0.969145			0.484572	−	0.874751i	$-0.338975\pi$
$461$	1.93686e29			0.969145			0.484572	+	0.874751i	$0.338975\pi$
$462$	−9.68861e28	−	1.72612e29i	−0.473369	−	0.843351i
$463$			4.24549e28i			0.202552i	0.994858	+	0.101276i	$0.0322926\pi$
$463$			4.24549e28i			0.202552i	−0.994858	+	0.101276i	$0.967707\pi$
$464$	−1.25849e29	−	2.44653e29i	−0.586343	−	1.13986i
$465$	−2.38447e29			−1.08495
$466$	−1.44975e29	+	8.13741e28i	−0.644242	+	0.361610i
$467$			9.50103e28i			0.412368i	0.978513	+	0.206184i	$0.0661045\pi$
$467$			9.50103e28i			0.412368i	−0.978513	+	0.206184i	$0.933895\pi$
$468$	−3.93385e28	+	6.44737e28i	−0.166768	+	0.273324i
$469$	4.47949e29			1.85493
$470$	5.62134e28	+	1.00149e29i	0.227386	+	0.405109i
$471$			2.18197e29i			0.862220i
$472$	6.72008e28	+	2.44544e27i	0.259425	+	0.00944048i
$473$	−1.86142e29			−0.702055
$474$	1.88969e29	−	1.06067e29i	0.696351	−	0.390859i
$475$		−	1.21329e28i		−	0.0436852i
$476$	2.43729e29	+	1.48711e29i	0.857492	+	0.523197i
$477$	2.35254e29			0.808789
$478$	1.56425e28	+	2.78685e28i	0.0525532	+	0.0936283i
$479$		−	1.57564e29i		−	0.517329i	−0.965967	−	0.258664i	$-0.916718\pi$
$479$		−	1.57564e29i		−	0.517329i	0.965967	−	0.258664i	$-0.0832824\pi$
$480$	−1.65750e29	+	2.50673e29i	−0.531863	+	0.804367i
$481$	−2.52419e29			−0.791637
$482$	−2.83612e29	+	1.59190e29i	−0.869376	+	0.487977i
$483$			4.29247e29i			1.28614i
$484$	6.17243e28	−	1.01163e29i	0.180783	−	0.296293i
$485$	2.01131e29			0.575864
$486$	1.49901e29	+	2.67062e29i	0.419571	+	0.747504i
$487$			5.04059e29i			1.37931i	0.724137	+	0.689656i	$0.242238\pi$
$487$			5.04059e29i			1.37931i	−0.724137	+	0.689656i	$0.757762\pi$
$488$	3.88342e27	−	1.06717e29i	0.0103895	−	0.285505i
$489$	3.70176e28			0.0968302
$490$	7.97188e29	−	4.47458e29i	2.03894	−	1.14445i
$491$		−	7.75458e29i		−	1.93938i	−0.244348	−	0.969688i	$-0.578574\pi$
$491$		−	7.75458e29i		−	1.93938i	0.244348	−	0.969688i	$-0.421426\pi$
$492$	−2.55061e29	−	1.55625e29i	−0.623774	−	0.380595i
$493$	−3.24660e29			−0.776448
$494$	7.78257e27	+	1.38654e28i	0.0182023	+	0.0324291i
$495$			2.26112e29i			0.517209i
$496$	−4.47214e29	+	2.30046e29i	−1.00050	+	0.514656i
$497$	−6.59711e29			−1.44356
$498$	1.47640e29	−	8.28696e28i	0.315995	−	0.177367i
$499$		−	9.28584e29i		−	1.94408i	−0.234805	−	0.972042i	$-0.575445\pi$
$499$		−	9.28584e29i		−	1.94408i	0.234805	−	0.972042i	$-0.424555\pi$
$500$	7.30258e28	−	1.19685e29i	0.149557	−	0.245116i
$501$	−8.57270e28			−0.171752
$502$	1.35333e29	+	2.41108e29i	0.265254	+	0.472575i
$503$		−	5.16238e29i		−	0.989925i	−0.868914	−	0.494963i	$-0.835182\pi$
$503$		−	5.16238e29i		−	0.989925i	0.868914	−	0.494963i	$-0.164818\pi$
$504$	−4.23182e29	−	1.53996e28i	−0.793946	−	0.0288917i
$505$	−1.23960e29			−0.227550
$506$	4.21547e29	−	2.36613e29i	0.757165	−	0.424993i
$507$		−	2.27228e29i		−	0.399369i
$508$	6.04506e29	+	3.68838e29i	1.03968	+	0.634359i
$509$	4.57096e28			0.0769328			0.0384664	−	0.999260i	$-0.487753\pi$
$509$	4.57096e28			0.0769328			0.0384664	+	0.999260i	$0.487753\pi$
$510$	1.73576e29	+	3.09241e29i	0.285902	+	0.509361i
$511$		−	8.45121e28i		−	0.136235i
$512$	−6.90270e28	+	6.30055e29i	−0.108905	+	0.994052i
$513$	3.84667e28			0.0594010
$514$	−7.25624e29	+	4.07290e29i	−1.09677	+	0.615615i
$515$			1.76136e30i			2.60596i
$516$	2.25523e29	−	3.69619e29i	0.326620	−	0.535313i
$517$	−1.98169e29			−0.280957
$518$	−6.92712e29	−	1.23413e30i	−0.961447	−	1.71291i
$519$			1.53867e29i			0.209076i
$520$	2.44090e28	−	6.70763e29i	0.0324724	−	0.892344i
$521$	8.14119e29			1.06041			0.530204	−	0.847870i	$-0.322115\pi$
$521$	8.14119e29			1.06041			0.530204	+	0.847870i	$0.322115\pi$
$522$	4.19898e29	−	2.35687e29i	0.535510	−	0.300580i
$523$		−	1.37304e29i		−	0.171461i	−0.996318	−	0.0857303i	$-0.972678\pi$
$523$		−	1.37304e29i		−	0.171461i	0.996318	−	0.0857303i	$-0.0273224\pi$
$524$	1.36289e29	+	8.31563e28i	0.166654	+	0.101684i
$525$	7.84736e29			0.939661
$526$	4.31360e29	+	7.68507e29i	0.505820	+	0.901166i
$527$			5.93463e29i			0.681518i
$528$	−2.37196e29	−	4.61112e29i	−0.266768	−	0.518601i
$529$	−1.40449e29			−0.154706
$530$	−1.82313e30	+	1.02332e30i	−1.96691	+	1.10402i
$531$			1.17693e29i			0.124368i
$532$	−4.64331e28	+	7.61013e28i	−0.0480618	+	0.0787706i
$533$	6.67349e29			0.676634
$534$	2.52149e29	+	4.49227e29i	0.250440	+	0.446182i
$535$		−	1.55129e30i		−	1.50939i
$536$	1.17269e30	+	4.26742e28i	1.11782	+	0.0406774i
$537$	2.67681e29			0.249977
$538$	8.49428e29	−	4.76780e29i	0.777180	−	0.436228i
$539$			1.57742e30i			1.41407i
$540$	−1.38617e30	−	8.45769e29i	−1.21755	−	0.742883i
$541$	−7.37739e29			−0.634940			−0.317470	−	0.948268i	$-0.602833\pi$
$541$	−7.37739e29			−0.634940			−0.317470	+	0.948268i	$0.602833\pi$
$542$	−9.41344e29	−	1.67709e30i	−0.793882	−	1.41437i
$543$		−	7.76206e29i		−	0.641474i
$544$	6.23894e29	+	4.12531e29i	0.505269	+	0.334094i
$545$	1.00647e30			0.798799
$546$	−8.96790e29	+	5.03364e29i	−0.697544	+	0.391529i
$547$			5.34377e29i			0.407368i	0.979037	+	0.203684i	$0.0652915\pi$
$547$			5.34377e29i			0.407368i	−0.979037	+	0.203684i	$0.934708\pi$
$548$	−3.90538e29	+	6.40070e29i	−0.291794	+	0.478235i
$549$	1.86899e29			0.136871
$550$	−4.32567e29	−	7.70659e29i	−0.310502	−	0.553188i
$551$		−	1.01371e29i		−	0.0713258i
$552$	−4.08926e28	+	1.12373e30i	−0.0282043	+	0.775056i
$553$	−2.71369e30			−1.83478
$554$	−9.13717e29	+	5.12865e29i	−0.605625	+	0.339935i
$555$		−	1.75782e30i		−	1.14222i
$556$	1.07731e30	+	6.57319e29i	0.686306	+	0.418749i
$557$	1.04477e30			0.652552			0.326276	−	0.945275i	$-0.394206\pi$
$557$	1.04477e30			0.652552			0.326276	+	0.945275i	$0.394206\pi$
$558$	−4.30824e29	−	7.67554e29i	−0.263830	−	0.470037i
$559$			9.67084e29i			0.580677i
$560$	3.34649e30	−	1.72143e30i	1.97025	−	1.01349i
$561$	−6.11907e29			−0.353260
$562$	2.03304e30	−	1.14114e30i	1.15093	−	0.646010i
$563$		−	3.25171e30i		−	1.80518i	−0.430506	−	0.902588i	$-0.641665\pi$
$563$		−	3.25171e30i		−	1.80518i	0.430506	−	0.902588i	$-0.358335\pi$
$564$	2.40095e29	−	3.93502e29i	0.130711	−	0.214228i
$565$	−3.20718e30			−1.71234
$566$	1.28924e30	+	2.29690e30i	0.675075	+	1.20271i
$567$			9.40958e29i			0.483233i
$568$	−1.72707e30	−	6.28479e28i	−0.869916	−	0.0316562i
$569$	−4.71831e28			−0.0233105			−0.0116552	−	0.999932i	$-0.503710\pi$
$569$	−4.71831e28			−0.0233105			−0.0116552	+	0.999932i	$0.503710\pi$
$570$	−9.65569e28	+	5.41970e28i	−0.0467907	+	0.0262634i
$571$			2.23338e30i			1.06161i	0.847494	+	0.530805i	$0.178110\pi$
$571$			2.23338e30i			1.06161i	−0.847494	+	0.530805i	$0.821890\pi$
$572$	9.88669e29	+	6.03235e29i	0.460993	+	0.281274i
$573$	4.87225e29			0.222858
$574$	1.83140e30	+	3.26281e30i	0.821775	+	1.46407i
$575$			1.91646e30i			0.843633i
$576$	−1.10639e30	−	8.06295e28i	−0.477815	−	0.0348214i
$577$	4.12783e30			1.74899			0.874496	−	0.485033i	$-0.161192\pi$
$577$	4.12783e30			1.74899			0.874496	+	0.485033i	$0.161192\pi$
$578$	−1.32800e30	+	7.45398e29i	−0.552065	+	0.309872i
$579$			2.29973e29i			0.0938021i
$580$	−2.22885e30	+	3.65297e30i	−0.892017	+	1.46197i
$581$	−2.12018e30			−0.832600
$582$	−3.95137e29	−	7.03973e29i	−0.152263	−	0.271271i
$583$		−	3.60750e30i		−	1.36412i
$584$	8.05111e27	−	2.21245e29i	0.00298755	−	0.0820981i
$585$	1.17475e30			0.427789
$586$	3.99469e30	−	2.24220e30i	1.42761	−	0.801310i
$587$			9.89293e29i			0.346981i	0.984836	+	0.173491i	$0.0555046\pi$
$587$			9.89293e29i			0.346981i	−0.984836	+	0.173491i	$0.944495\pi$
$588$	−3.13227e30	−	1.91115e30i	−1.07822	−	0.657877i
$589$	−1.85302e29			−0.0626053
$590$	−5.11943e29	−	9.12074e29i	−0.169766	−	0.302453i
$591$			9.91039e29i			0.322573i
$592$	−1.69589e30	−	3.29684e30i	−0.541824	−	1.05332i
$593$	9.95491e29			0.312202			0.156101	−	0.987741i	$-0.450107\pi$
$593$	9.95491e29			0.312202			0.156101	+	0.987741i	$0.450107\pi$
$594$	2.44333e30	−	1.37143e30i	0.752197	−	0.422205i
$595$		−	4.44087e30i		−	1.34209i
$596$	3.50662e29	−	5.74716e29i	0.104035	−	0.170508i
$597$	−2.43305e30			−0.708654
$598$	−1.22930e30	−	2.19011e30i	−0.351516	−	0.626259i
$599$			3.75250e30i			1.05348i	0.850027	+	0.526739i	$0.176586\pi$
$599$			3.75250e30i			1.05348i	−0.850027	+	0.526739i	$0.823414\pi$
$600$	2.05437e30	+	7.47585e28i	0.566259	+	0.0206062i
$601$	1.84318e30			0.498825			0.249413	−	0.968397i	$-0.419762\pi$
$601$	1.84318e30			0.498825			0.249413	+	0.968397i	$0.419762\pi$
$602$	−4.72828e30	+	2.65396e30i	−1.25644	+	0.705235i
$603$			2.05380e30i			0.535881i
$604$	−4.90381e30	−	2.99205e30i	−1.25640	−	0.766589i
$605$	−1.84324e30			−0.463739
$606$	2.43529e29	+	4.33870e29i	0.0601662	+	0.107192i
$607$		−	2.22364e30i		−	0.539497i	−0.962931	−	0.269748i	$-0.913059\pi$
$607$		−	2.22364e30i		−	0.539497i	0.962931	−	0.269748i	$-0.0869405\pi$
$608$	−1.28808e29	+	1.94803e29i	−0.0306904	+	0.0464148i
$609$	6.55652e30			1.53420
$610$	−1.44840e30	+	8.12980e29i	−0.332859	+	0.186832i
$611$			1.02957e30i			0.232382i
$612$	−6.81824e29	+	1.11747e30i	−0.151149	+	0.247726i
$613$	1.39971e29			0.0304771			0.0152386	−	0.999884i	$-0.495149\pi$
$613$	1.39971e29			0.0304771			0.0152386	+	0.999884i	$0.495149\pi$
$614$	−2.11508e30	−	3.76821e30i	−0.452350	−	0.805903i
$615$			4.64734e30i			0.976289i
$616$	−2.36144e29	+	6.48927e30i	−0.0487292	+	1.33908i
$617$	8.02739e30			1.62719			0.813593	−	0.581434i	$-0.197508\pi$
$617$	8.02739e30			1.62719			0.813593	+	0.581434i	$0.197508\pi$
$618$	6.16488e30	−	3.46032e30i	1.22758	−	0.689037i
$619$			3.49783e30i			0.684229i	0.939658	+	0.342114i	$0.111143\pi$
$619$			3.49783e30i			0.684229i	−0.939658	+	0.342114i	$0.888857\pi$
$620$	6.67746e30	+	4.07424e30i	1.28322	+	0.782957i
$621$	−6.07603e30			−1.14713
$622$	2.96148e30	+	5.27614e30i	0.549305	+	0.978638i
$623$		−	6.45114e30i		−	1.17562i
$624$	−2.39567e30	+	1.23233e30i	−0.428940	+	0.220646i
$625$	−6.64343e30			−1.16873
$626$	−3.76369e29	+	2.11254e29i	−0.0650573	+	0.0365164i
$627$		−	1.91060e29i		−	0.0324510i
$628$	3.72823e30	−	6.11037e30i	0.622225	−	1.01979i
$629$	−4.37498e30			−0.717495
$630$	3.22385e30	+	5.74358e30i	0.519551	+	0.925628i
$631$			9.52513e28i			0.0150851i	0.999972	+	0.00754254i	$0.00240089\pi$
$631$			9.52513e28i			0.0150851i	−0.999972	+	0.00754254i	$0.997599\pi$
$632$	−7.10420e30	−	2.58522e29i	−1.10567	−	0.0402355i
$633$	−1.75788e30			−0.268874
$634$	−3.57498e30	+	2.00662e30i	−0.537393	+	0.301636i
$635$		−	1.10144e31i		−	1.62724i
$636$	7.16337e30	+	4.37071e30i	1.04013	+	0.634635i
$637$	8.19538e30			1.16960
$638$	−3.61413e30	−	6.43890e30i	−0.506963	−	0.903201i
$639$		−	3.02471e30i		−	0.417037i
$640$	8.92481e30	−	4.18775e30i	1.20954	−	0.567545i
$641$	−8.21339e30			−1.09417			−0.547084	−	0.837077i	$-0.684262\pi$
$641$	−8.21339e30			−1.09417			−0.547084	+	0.837077i	$0.684262\pi$
$642$	−5.42964e30	+	3.04764e30i	−0.711027	+	0.399096i
$643$			1.43951e31i			1.85308i	0.376201	+	0.926538i	$0.377230\pi$
$643$			1.43951e31i			1.85308i	−0.376201	+	0.926538i	$0.622770\pi$
$644$	7.33437e30	−	1.20206e31i	0.928150	−	1.52119i
$645$	−6.73467e30			−0.837836
$646$	1.34889e29	+	2.40318e29i	0.0164976	+	0.0293919i
$647$			4.12645e30i			0.496169i	0.968738	+	0.248084i	$0.0798010\pi$
$647$			4.12645e30i			0.496169i	−0.968738	+	0.248084i	$0.920199\pi$
$648$	−8.96411e28	+	2.46335e30i	−0.0105970	+	0.291206i
$649$	1.80475e30			0.209762
$650$	−4.00390e30	+	2.24737e30i	−0.457547	+	0.256819i
$651$		−	1.19850e31i		−	1.34663i
$652$	−1.03664e30	−	6.32504e29i	−0.114526	−	0.0698779i
$653$	−7.02751e30			−0.763408			−0.381704	−	0.924285i	$-0.624663\pi$
$653$	−7.02751e30			−0.763408			−0.381704	+	0.924285i	$0.624663\pi$
$654$	−1.97728e30	−	3.52271e30i	−0.211209	−	0.376289i
$655$		−	2.48325e30i		−	0.260836i
$656$	4.48362e30	+	8.71623e30i	0.463112	+	0.900298i
$657$	3.87480e29			0.0393577
$658$	−5.03380e30	+	2.82545e30i	−0.502818	+	0.282230i
$659$		−	1.07907e31i		−	1.06001i	−0.847994	−	0.530006i	$-0.822190\pi$
$659$		−	1.07907e31i		−	1.06001i	0.847994	−	0.530006i	$-0.177810\pi$
$660$	−4.20086e30	+	6.88498e30i	−0.405840	+	0.665149i
$661$	1.30479e31			1.23973			0.619863	−	0.784710i	$-0.287188\pi$
$661$	1.30479e31			1.23973			0.619863	+	0.784710i	$0.287188\pi$
$662$	−9.44620e28	−	1.68293e29i	−0.00882713	−	0.0157263i
$663$			3.17911e30i			0.292185i
$664$	−5.55046e30	−	2.01981e29i	−0.501742	−	0.0182584i
$665$	1.38661e30			0.123286
$666$	5.65836e30	−	3.17602e30i	0.494851	−	0.277758i
$667$			1.60121e31i			1.37742i
$668$	2.40070e30	+	1.46478e30i	0.203140	+	0.123946i
$669$	1.36936e31			1.13981
$670$	−8.93370e30	−	1.59162e31i	−0.731490	−	1.30322i
$671$		−	2.86600e30i		−	0.230849i
$672$	−1.25996e31	−	8.33107e30i	−0.998374	−	0.660144i
$673$	6.04617e30			0.471319			0.235659	−	0.971836i	$-0.424275\pi$
$673$	6.04617e30			0.471319			0.235659	+	0.971836i	$0.424275\pi$
$674$	1.01100e31	−	5.67469e30i	0.775339	−	0.435195i
$675$			1.11080e31i			0.838098i
$676$	−3.88256e30	+	6.36330e30i	−0.288207	+	0.472355i
$677$	6.59036e30			0.481320			0.240660	−	0.970609i	$-0.422636\pi$
$677$	6.59036e30			0.481320			0.240660	+	0.970609i	$0.422636\pi$
$678$	6.30075e30	+	1.12254e31i	0.452758	+	0.806629i
$679$			1.01094e31i			0.714758i
$680$	4.23063e29	−	1.16258e31i	0.0294311	−	0.808770i
$681$	−1.50274e30			−0.102864
$682$	−1.17700e31	+	6.60646e30i	−0.792773	+	0.444980i
$683$			2.51024e31i			1.66375i	0.554965	+	0.831874i	$0.312732\pi$
$683$			2.51024e31i			1.66375i	−0.554965	+	0.831874i	$0.687268\pi$
$684$	−3.48917e29	−	2.12891e29i	−0.0227565	−	0.0138848i
$685$	1.16624e31			0.748501
$686$	9.63904e30	+	1.71728e31i	0.608791	+	1.08462i
$687$		−	1.21264e31i		−	0.753714i
$688$	−1.26311e31	+	6.49740e30i	−0.772622	+	0.397436i
$689$	−1.87425e31			−1.12828
$690$	1.52517e31	−	8.56072e30i	0.903605	−	0.507189i
$691$		−	1.46330e31i		−	0.853250i	−0.904429	−	0.426625i	$-0.859702\pi$
$691$		−	1.46330e31i		−	0.853250i	0.904429	−	0.426625i	$-0.140298\pi$
$692$	2.62905e30	−	4.30888e30i	0.150880	−	0.247285i
$693$	−1.13650e31			−0.641955
$694$	−4.72169e30	−	8.41213e30i	−0.262508	−	0.467683i
$695$		−	1.96292e31i		−	1.07416i
$696$	1.71644e31	+	6.24612e29i	0.924543	+	0.0336441i
$697$	1.15666e31			0.613263
$698$	−9.39546e30	+	5.27363e30i	−0.490353	+	0.275233i
$699$		−	1.03790e31i		−	0.533219i
$700$	−2.19757e31	−	1.34085e31i	−1.11139	−	0.678111i
$701$	−3.75758e31			−1.87073			−0.935363	−	0.353689i	$-0.884927\pi$
$701$	−3.75758e31			−1.87073			−0.935363	+	0.353689i	$0.884927\pi$
$702$	−7.12517e30	−	1.26941e31i	−0.349210	−	0.622150i
$703$		−	1.36603e30i		−	0.0659103i
$704$	−1.23641e30	+	1.69658e31i	−0.0587304	+	0.805891i
$705$	−7.16982e30			−0.335296
$706$	3.42220e31	−	1.92087e31i	1.57563	−	0.884393i
$707$		−	6.23060e30i		−	0.282434i
$708$	−2.18657e30	+	3.58368e30i	−0.0975885	+	0.159942i
$709$	1.52222e31			0.668914			0.334457	−	0.942411i	$-0.391447\pi$
$709$	1.52222e31			0.668914			0.334457	+	0.942411i	$0.391447\pi$
$710$	1.31570e31	+	2.34404e31i	0.569265	+	1.01420i
$711$		−	1.24420e31i		−	0.530059i
$712$	6.14573e29	−	1.68885e31i	0.0257806	−	0.708454i
$713$	2.92695e31			1.20901
$714$	−1.55434e31	+	8.72443e30i	−0.632215	+	0.354860i
$715$		−	1.80141e31i		−	0.721516i
$716$	−7.49614e30	−	4.57376e30i	−0.295661	−	0.180397i
$717$	−1.99514e30			−0.0774932
$718$	1.89671e31	+	3.37917e31i	0.725492	+	1.29253i
$719$			3.45942e31i			1.30312i	0.758595	+	0.651562i	$0.225886\pi$
$719$			3.45942e31i			1.30312i	−0.758595	+	0.651562i	$0.774114\pi$
$720$	7.89258e30	+	1.53433e31i	0.292794	+	0.569196i
$721$	−8.85309e31			−3.23450
$722$	2.41597e31	−	1.35607e31i	0.869324	−	0.487948i
$723$		−	2.03042e31i		−	0.719555i
$724$	−1.32627e31	+	2.17369e31i	−0.462922	+	0.758705i
$725$	2.92729e31			1.00635
$726$	3.62119e30	+	6.45148e30i	0.122616	+	0.218452i
$727$			4.78687e31i			1.59652i	0.602316	+	0.798258i	$0.294245\pi$
$727$			4.78687e31i			1.59652i	−0.602316	+	0.798258i	$0.705755\pi$
$728$	3.37145e31	+	1.22687e30i	1.10757	+	0.0403044i
$729$	−2.81245e31			−0.910084
$730$	−3.00282e30	+	1.68547e30i	−0.0957146	+	0.0537242i
$731$			1.67617e31i			0.526293i
$732$	5.69098e30	+	3.47234e30i	0.176021	+	0.107399i
$733$	6.29217e31			1.91715			0.958577	−	0.284835i	$-0.0919387\pi$
$733$	6.29217e31			1.91715			0.958577	+	0.284835i	$0.0919387\pi$
$734$	−1.27320e31	−	2.26833e31i	−0.382156	−	0.680846i
$735$			5.70717e31i			1.68756i
$736$	2.03459e31	−	3.07703e31i	0.592681	−	0.896345i
$737$	3.14940e31			0.903826
$738$	−1.49597e31	+	8.39680e30i	−0.422963	+	0.237407i
$739$		−	4.80915e31i		−	1.33961i	−0.742535	−	0.669807i	$-0.766377\pi$
$739$		−	4.80915e31i		−	1.33961i	0.742535	−	0.669807i	$-0.233623\pi$
$740$	−3.00351e31	+	4.92259e31i	−0.824290	+	1.35097i
$741$	−9.92640e29			−0.0268405
$742$	−5.14348e31	−	9.16359e31i	−1.37030	−	2.44131i
$743$		−	4.82491e31i		−	1.26652i	−0.773939	−	0.633260i	$-0.781716\pi$
$743$		−	4.82491e31i		−	1.26652i	0.773939	−	0.633260i	$-0.218284\pi$
$744$	1.14176e30	−	3.13757e31i	0.0295307	−	0.811506i
$745$	−1.04716e31			−0.266867
$746$	−5.25462e31	+	2.94940e31i	−1.31951	+	0.740638i
$747$		−	9.72084e30i		−	0.240534i
$748$	1.71358e31	+	1.04554e31i	0.417818	+	0.254931i
$749$	7.79725e31			1.87345
$750$	4.28421e30	+	7.63272e30i	0.101437	+	0.180720i
$751$		−	7.60469e31i		−	1.77436i	−0.461422	−	0.887181i	$-0.652661\pi$
$751$		−	7.60469e31i		−	1.77436i	0.461422	−	0.887181i	$-0.347339\pi$
$752$	−1.34472e31	+	6.91723e30i	−0.309197	+	0.159051i
$753$	−1.72612e31			−0.391136
$754$	−3.34528e31	+	1.87769e31i	−0.747047	+	0.419314i
$755$			8.93500e31i			1.96643i
$756$	4.25108e31	−	6.96729e31i	0.922061	−	1.51121i
$757$	−2.48369e31			−0.530936			−0.265468	−	0.964120i	$-0.585527\pi$
$757$	−2.48369e31			−0.530936			−0.265468	+	0.964120i	$0.585527\pi$
$758$	8.38589e28	+	1.49402e29i	0.00176680	+	0.00314772i
$759$			3.01791e31i			0.626681i
$760$	3.63002e30	+	1.32096e29i	0.0742949	+	0.00270359i
$761$	−8.17239e31			−1.64861			−0.824305	−	0.566146i	$-0.808434\pi$
$761$	−8.17239e31			−1.64861			−0.824305	+	0.566146i	$0.808434\pi$
$762$	−3.85513e31	+	2.16387e31i	−0.766539	+	0.430255i
$763$			5.05879e31i			0.991464i
$764$	−1.36443e31	−	8.32502e30i	−0.263586	−	0.160827i
$765$	2.03610e31			0.387724
$766$	3.21743e31	+	5.73214e31i	0.603938	+	1.07597i
$767$		−	9.37645e30i		−	0.173496i
$768$	−3.21909e31	−	2.30103e31i	−0.587164	−	0.419710i
$769$	7.16587e31			1.28848			0.644242	−	0.764821i	$-0.277173\pi$
$769$	7.16587e31			1.28848			0.644242	+	0.764821i	$0.277173\pi$
$770$	8.80747e31	−	4.94359e31i	1.56118	−	0.876284i
$771$		−	5.19484e31i		−	0.907766i
$772$	3.92945e30	−	6.44016e30i	0.0676927	−	0.110945i
$773$	−2.38900e31			−0.405734			−0.202867	−	0.979206i	$-0.565026\pi$
$773$	−2.38900e31			−0.405734			−0.202867	+	0.979206i	$0.565026\pi$
$774$	−1.21682e31	−	2.16787e31i	−0.203739	−	0.362980i
$775$		−	5.35095e31i		−	0.883308i
$776$	−9.63082e29	+	2.64656e31i	−0.0156742	+	0.430727i
$777$	8.83530e31			1.41772
$778$	−2.34158e31	+	1.31432e31i	−0.370454	+	0.207934i
$779$			3.61154e30i			0.0563353i
$780$	3.57704e31	+	2.18252e31i	0.550152	+	0.335674i
$781$	−4.63823e31			−0.703382
$782$	−2.13065e31	−	3.79596e31i	−0.318595	−	0.567606i
$783$			9.28081e31i			1.36838i
$784$	5.50611e31	+	1.07040e32i	0.800513	+	1.55621i
$785$	−1.11334e32			−1.59611
$786$	−8.69157e30	+	4.87854e30i	−0.122871	+	0.0689671i
$787$			1.19967e32i			1.67240i	0.548426	+	0.836199i	$0.315227\pi$
$787$			1.19967e32i			1.67240i	−0.548426	+	0.836199i	$0.684773\pi$
$788$	1.69335e31	−	2.77530e31i	0.232786	−	0.381524i
$789$	−5.50184e31			−0.745866
$790$	5.41206e31	+	9.64208e31i	0.723543	+	1.28906i
$791$		−	1.61202e32i		−	2.12535i
$792$	−2.97526e31	−	1.08270e30i	−0.386855	−	0.0140777i
$793$	−1.48901e31			−0.190938
$794$	7.19456e31	−	4.03827e31i	0.909868	−	0.510705i
$795$		−	1.30520e32i		−	1.62795i
$796$	6.81352e31	+	4.15726e31i	0.838162	+	0.511403i
$797$	6.78264e31			0.822919			0.411460	−	0.911428i	$-0.365019\pi$
$797$	6.78264e31			0.822919			0.411460	+	0.911428i	$0.365019\pi$
$798$	−2.72410e30	−	4.85323e30i	−0.0325980	−	0.0580763i
$799$			1.78448e31i			0.210618i
$800$	−5.62532e31	−	3.71957e31i	−0.654874	−	0.433015i
$801$	2.95778e31			0.339632
$802$	−2.78465e30	+	1.56301e30i	−0.0315393	+	0.0177029i
$803$		−	5.94179e30i		−	0.0663814i
$804$	−3.81570e31	+	6.25372e31i	−0.420492	+	0.689163i
$805$	−2.19023e32			−2.38086
$806$	3.43233e31	+	6.11502e31i	0.368048	+	0.655711i
$807$			6.08117e31i			0.643247i
$808$	5.93563e29	−	1.63112e31i	0.00619359	−	0.170200i
$809$	1.23186e32			1.26803			0.634013	−	0.773322i	$-0.281406\pi$
$809$	1.23186e32			1.26803			0.634013	+	0.773322i	$0.281406\pi$
$810$	3.34334e31	−	1.87660e31i	0.339505	−	0.190563i
$811$		−	5.06028e31i		−	0.506927i	−0.967345	−	0.253463i	$-0.918430\pi$
$811$		−	5.06028e31i		−	0.506927i	0.967345	−	0.253463i	$-0.0815697\pi$
$812$	−1.83609e32	−	1.12029e32i	−1.81458	−	1.10717i
$813$	1.20065e32			1.17063
$814$	−4.87025e31	−	8.67680e31i	−0.468471	−	0.834624i
$815$			1.88882e31i			0.179249i
$816$	−4.15223e31	+	2.13590e31i	−0.388768	+	0.199982i
$817$	−5.23365e30			−0.0483461
$818$	8.63202e31	−	4.84511e31i	0.786731	−	0.441588i
$819$			5.90461e31i			0.530968i
$820$	7.94072e31	−	1.30144e32i	0.704543	−	1.15471i
$821$	−1.58714e32			−1.38944			−0.694721	−	0.719279i	$-0.744472\pi$
$821$	−1.58714e32			−1.38944			−0.694721	+	0.719279i	$0.744472\pi$
$822$	−2.29117e31	−	4.08194e31i	−0.197910	−	0.352595i
$823$			6.75406e31i			0.575661i	0.957681	+	0.287830i	$0.0929339\pi$
$823$			6.75406e31i			0.575661i	−0.957681	+	0.287830i	$0.907066\pi$
$824$	−2.31766e32	−	8.43396e30i	−1.94917	−	0.0709304i
$825$	5.51724e31			0.457856
$826$	4.58435e31	−	2.57317e31i	0.375402	−	0.210712i
$827$		−	4.05763e31i		−	0.327878i	−0.986471	−	0.163939i	$-0.947580\pi$
$827$		−	4.05763e31i		−	0.327878i	0.986471	−	0.163939i	$-0.0524200\pi$
$828$	5.51134e31	+	3.36274e31i	0.439465	+	0.268139i
$829$	2.34323e31			0.184381			0.0921905	−	0.995741i	$-0.470613\pi$
$829$	2.34323e31			0.184381			0.0921905	+	0.995741i	$0.470613\pi$
$830$	4.22840e31	+	7.53329e31i	0.328335	+	0.584959i
$831$		−	6.54141e31i		−	0.501257i
$832$	8.81447e31	+	6.42367e30i	0.666560	+	0.0485766i
$833$	1.42044e32			1.06006
$834$	−6.87036e31	+	3.85630e31i	−0.506003	+	0.284017i
$835$		−	4.37420e31i		−	0.317942i
$836$	−3.26457e30	+	5.35046e30i	−0.0234184	+	0.0383815i
$837$	1.69649e32			1.20108
$838$	2.67672e31	+	4.76882e31i	0.187033	+	0.333217i
$839$			2.15473e32i			1.48597i	0.669305	+	0.742987i	$0.266592\pi$
$839$			2.15473e32i			1.48597i	−0.669305	+	0.742987i	$0.733408\pi$
$840$	−8.54377e30	+	2.34784e32i	−0.0581537	+	1.59807i
$841$	9.57244e31			0.643082
$842$	−1.62215e32	+	9.10508e31i	−1.07562	+	0.603741i
$843$			1.45548e32i			0.952585i
$844$	4.92276e31	+	3.00361e31i	0.318011	+	0.194034i
$845$	1.15943e32			0.739298
$846$	−1.29544e31	−	2.30795e31i	−0.0815349	−	0.145262i
$847$		−	9.26467e31i		−	0.575589i
$848$	−1.25922e32	−	2.44795e32i	−0.772232	−	1.50123i
$849$	−1.64438e32			−0.995444
$850$	−6.93964e31	+	3.89519e31i	−0.414695	+	0.232767i
$851$			2.15773e32i			1.27283i
$852$	5.61952e31	−	9.21008e31i	0.327238	−	0.536325i
$853$	−1.86518e32			−1.07221			−0.536107	−	0.844150i	$-0.680106\pi$
$853$	−1.86518e32			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$854$	−4.08627e31	−	7.28007e31i	−0.231895	−	0.413142i
$855$			6.35746e30i			0.0356169i
$856$	2.04125e32	+	7.42811e30i	1.12898	+	0.0410835i
$857$	1.54711e32			0.844757			0.422378	−	0.906420i	$-0.361195\pi$
$857$	1.54711e32			0.844757			0.422378	+	0.906420i	$0.361195\pi$
$858$	−6.30506e31	+	3.53900e31i	−0.339883	+	0.190775i
$859$		−	2.79101e32i		−	1.48538i	−0.669636	−	0.742689i	$-0.733550\pi$
$859$		−	2.79101e32i		−	1.48538i	0.669636	−	0.742689i	$-0.266450\pi$
$860$	1.88597e32	+	1.15072e32i	0.990953	+	0.604628i
$861$	−2.33589e32			−1.21176
$862$	−1.37640e31	−	2.45219e31i	−0.0704962	−	0.125595i
$863$		−	2.40407e32i		−	1.21570i	−0.794050	−	0.607852i	$-0.792031\pi$
$863$		−	2.40407e32i		−	1.21570i	0.794050	−	0.607852i	$-0.207969\pi$
$864$	1.17927e32	−	1.78348e32i	0.588793	−	0.890465i
$865$	−7.85101e31			−0.387033
$866$	2.93085e32	−	1.64508e32i	1.42658	−	0.800736i
$867$		−	9.50729e31i		−	0.456927i
$868$	−2.04783e32	+	3.35628e32i	−0.971800	+	1.59273i
$869$	−1.90791e32			−0.894007
$870$	−1.30760e32	−	2.32962e32i	−0.605012	−	1.07789i
$871$		−	1.63624e32i		−	0.747564i
$872$	−4.81930e30	+	1.32435e32i	−0.0217421	+	0.597476i
$873$	−4.63507e31			−0.206490
$874$	1.18524e31	−	6.65271e30i	0.0521412	−	0.0292666i
$875$		−	1.09610e32i		−	0.476169i
$876$	1.17985e31	+	7.19886e30i	0.0506155	+	0.0308830i
$877$	−9.86957e31			−0.418122			−0.209061	−	0.977903i	$-0.567041\pi$
$877$	−9.86957e31			−0.418122			−0.209061	+	0.977903i	$0.567041\pi$
$878$	4.24924e31	+	7.57041e31i	0.177775	+	0.316723i
$879$			2.85985e32i			1.18159i
$880$	2.35281e32	−	1.21029e32i	0.960016	−	0.493831i
$881$	−2.75102e32			−1.10856			−0.554279	−	0.832331i	$-0.687006\pi$
$881$	−2.75102e32			−1.10856			−0.554279	+	0.832331i	$0.687006\pi$
$882$	−1.83712e32	+	1.03117e32i	−0.731112	+	0.410370i
$883$			1.84640e31i			0.0725703i	0.999341	+	0.0362851i	$0.0115525\pi$
$883$			1.84640e31i			0.0725703i	−0.999341	+	0.0362851i	$0.988448\pi$
$884$	5.43202e31	−	8.90279e31i	0.210856	−	0.345582i
$885$	6.52966e31			0.250331
$886$	1.30757e32	+	2.32955e32i	0.495100	+	0.882066i
$887$			1.64137e32i			0.613830i	0.951737	+	0.306915i	$0.0992967\pi$
$887$			1.64137e32i			0.613830i	−0.951737	+	0.306915i	$0.900703\pi$
$888$	2.31300e32	+	8.41701e30i	0.854346	+	0.0310896i
$889$	5.53617e32			2.01972
$890$	−2.29217e32	+	1.28659e32i	−0.825956	+	0.463606i
$891$			6.61559e31i			0.235458i
$892$	−3.83476e32	−	2.33977e32i	−1.34811	−	0.822546i
$893$	−5.57181e30			−0.0193478
$894$	2.05723e31	+	3.66515e31i	0.0705619	+	0.125713i
$895$			1.36584e32i			0.462749i
$896$	2.10488e32	+	4.48587e32i	0.704433	+	1.50127i
$897$	1.56793e32			0.518335
$898$	−3.26439e32	+	1.83229e32i	−1.06601	+	0.598349i
$899$		−	4.47075e32i		−	1.44220i
$900$	6.14765e31	−	1.00757e32i	0.195903	−	0.321075i
$901$	−3.24849e32			−1.02261
$902$	1.28760e32	+	2.29398e32i	0.400415	+	0.713376i
$903$		−	3.38504e32i		−	1.03992i
$904$	1.53571e31	−	4.22013e32i	0.0466074	−	1.28078i
$905$	3.96058e32			1.18747
$906$	3.12732e32	−	1.75535e32i	0.926322	−	0.519940i
$907$			6.26471e32i			1.83324i	0.399754	+	0.916622i	$0.369096\pi$
$907$			6.26471e32i			1.83324i	−0.399754	+	0.916622i	$0.630904\pi$
$908$	4.20826e31	+	2.56766e31i	0.121663	+	0.0742325i
$909$	2.85667e31			0.0815939
$910$	−2.56841e32	−	4.57585e32i	−0.724784	−	1.29127i
$911$			4.63208e32i			1.29144i	0.763575	+	0.645719i	$0.223442\pi$
$911$			4.63208e32i			1.29144i	−0.763575	+	0.645719i	$0.776558\pi$
$912$	−6.66910e30	−	1.29648e31i	−0.0183706	−	0.0357128i
$913$	−1.49064e32			−0.405689
$914$	2.42714e32	−	1.36234e32i	0.652658	−	0.366334i
$915$		−	1.03693e32i		−	0.275497i
$916$	−2.07198e32	+	3.39587e32i	−0.543921	+	0.891457i
$917$	1.24816e32			0.323747
$918$	−1.23495e32	−	2.20018e32i	−0.316505	−	0.563882i
$919$			1.22010e32i			0.308977i	0.987995	+	0.154489i	$0.0493730\pi$
$919$			1.22010e32i			0.308977i	−0.987995	+	0.154489i	$0.950627\pi$
$920$	−5.73382e32	−	2.08654e31i	−1.43476	−	0.0522107i
$921$	2.69771e32			0.667020
$922$	3.45905e32	−	1.94155e32i	0.845117	−	0.474361i
$923$			2.40976e32i			0.581774i
$924$	−3.46059e32	−	2.11147e32i	−0.825578	−	0.503725i
$925$	3.94469e32			0.929938
$926$	4.25577e31	+	7.58204e31i	0.0991419	+	0.176630i
$927$		−	4.05905e32i		−	0.934432i
$928$	−4.69999e32	−	3.10773e32i	−1.06923	−	0.706993i
$929$	−3.74937e32			−0.842918			−0.421459	−	0.906847i	$-0.638482\pi$
$929$	−3.74937e32			−0.842918			−0.421459	+	0.906847i	$0.638482\pi$
$930$	−4.25843e32	+	2.39024e32i	−0.946100	+	0.531042i
$931$			4.43516e31i			0.0973784i
$932$	−1.77341e32	+	2.90653e32i	−0.384800	+	0.630666i
$933$	−3.77726e32			−0.809988
$934$	9.52402e31	+	1.69679e32i	0.201839	+	0.359595i
$935$		−	3.12224e32i		−	0.653941i
$936$	−5.62507e30	+	1.54578e32i	−0.0116438	+	0.319972i
$937$	5.17088e32			1.05786			0.528931	−	0.848665i	$-0.322593\pi$
$937$	5.17088e32			1.05786			0.528931	+	0.848665i	$0.322593\pi$
$938$	7.99995e32	−	4.49034e32i	1.61754	−	0.907920i
$939$		−	2.69447e31i		−	0.0538459i
$940$	2.00784e32	+	1.22508e32i	0.396572	+	0.241968i
$941$	3.96797e32			0.774610			0.387305	−	0.921952i	$-0.373406\pi$
$941$	3.96797e32			0.774610			0.387305	+	0.921952i	$0.373406\pi$
$942$	2.18725e32	+	3.89678e32i	0.422025	+	0.751876i
$943$		−	5.70464e32i		−	1.08793i
$944$	1.22466e32	−	6.29962e31i	0.230846	−	0.118747i
$945$	−1.26948e33			−2.36524
$946$	−3.32431e32	+	1.86592e32i	−0.612209	+	0.343630i
$947$		−	7.69103e31i		−	0.140002i	−0.997547	−	0.0700011i	$-0.977700\pi$
$947$		−	7.69103e31i		−	0.140002i	0.997547	−	0.0700011i	$-0.0223003\pi$
$948$	2.31156e32	−	3.78852e32i	0.415923	−	0.681676i
$949$	−3.08701e31			−0.0549048
$950$	−1.21623e31	−	2.16682e31i	−0.0213823	−	0.0380946i
$951$		−	2.55938e32i		−	0.444783i
$952$	5.84347e32	+	2.12644e31i	1.00384	+	0.0365297i
$953$	−3.98077e32			−0.675997			−0.337999	−	0.941147i	$-0.609750\pi$
$953$	−3.98077e32			−0.675997			−0.337999	+	0.941147i	$0.609750\pi$
$954$	4.20142e32	−	2.35824e32i	0.705283	−	0.395873i
$955$			2.48606e32i			0.412548i
$956$	5.58720e31	+	3.40902e31i	0.0916552	+	0.0559233i
$957$	4.60969e32			0.747551
$958$	−1.57946e32	−	2.81395e32i	−0.253213	−	0.451123i
$959$			5.86187e32i			0.929034i
$960$	−4.47337e31	+	6.13830e32i	−0.0700893	+	0.961755i
$961$	−1.71643e32			−0.265869
$962$	−4.50796e32	+	2.53030e32i	−0.690326	+	0.387477i
$963$			3.57496e32i			0.541231i
$964$	−3.46929e32	+	5.68598e32i	−0.519270	+	0.851056i
$965$	−1.17343e32			−0.173643
$966$	4.30287e32	+	7.66595e32i	0.629520	+	1.12155i
$967$			3.16875e32i			0.458349i	0.973385	+	0.229175i	$0.0736027\pi$
$967$			3.16875e32i			0.458349i	−0.973385	+	0.229175i	$0.926397\pi$
$968$	8.82606e30	−	2.42541e32i	0.0126223	−	0.346862i
$969$	−1.72047e31			−0.0243268
$970$	3.59201e32	−	2.01618e32i	0.502167	−	0.281864i
$971$			1.32804e32i			0.183569i	0.995779	+	0.0917846i	$0.0292571\pi$
$971$			1.32804e32i			0.183569i	−0.995779	+	0.0917846i	$0.970743\pi$
$972$	5.35418e32	+	3.26684e32i	0.731752	+	0.446477i
$973$	9.86619e32			1.33324
$974$	5.05279e32	+	9.00201e32i	0.675122	+	1.20279i
$975$		−	2.86644e32i		−	0.378697i
$976$	−1.00040e32	−	1.94479e32i	−0.130684	−	0.254053i
$977$	−1.31201e33			−1.69472			−0.847361	−	0.531018i	$-0.821810\pi$
$977$	−1.31201e33			−1.69472			−0.847361	+	0.531018i	$0.821810\pi$
$978$	6.61099e31	−	3.71072e31i	0.0844383	−	0.0473948i
$979$		−	4.53560e32i		−	0.572829i
$980$	9.75161e32	−	1.59824e33i	1.21784	−	1.99597i
$981$	−2.31941e32			−0.286429
$982$	−7.77335e32	−	1.38489e33i	−0.949253	−	1.69118i
$983$		−	3.40017e32i		−	0.410593i	−0.978700	−	0.205296i	$-0.934184\pi$
$983$		−	3.40017e32i		−	0.410593i	0.978700	−	0.205296i	$-0.0658159\pi$
$984$	−6.11515e32	−	2.22530e31i	−0.730233	−	0.0265732i
$985$	−5.05675e32			−0.597136
$986$	−5.79812e32	+	3.25446e32i	−0.677081	+	0.380043i
$987$		−	3.60376e32i		−	0.416167i
$988$	2.77979e31	+	1.69608e31i	0.0317457	+	0.0193696i
$989$	8.26684e32			0.933642
$990$	2.26659e32	+	4.03814e32i	0.253155	+	0.451018i
$991$		−	1.23788e32i		−	0.136731i	−0.997660	−	0.0683657i	$-0.978222\pi$
$991$		−	1.23788e32i		−	0.136731i	0.997660	−	0.0683657i	$-0.0217785\pi$
$992$	−5.68078e32	+	8.59137e32i	−0.620554	+	0.938500i
$993$	1.20483e31			0.0130162
$994$	−1.17818e33	+	6.61308e32i	−1.25882	+	0.706567i
$995$		−	1.24146e33i		−	1.31183i
$996$	1.80600e32	−	2.95994e32i	0.188741	−	0.309336i
$997$	4.21179e32			0.435331			0.217665	−	0.976023i	$-0.430156\pi$
$997$	4.21179e32			0.435331			0.217665	+	0.976023i	$0.430156\pi$
$998$	−9.30832e32	−	1.65836e33i	−0.951558	−	1.69529i
$999$			1.25064e33i			1.26448i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.23.b.a.3.9	✓	10
3.2	odd	2		36.23.d.c.19.2		10
4.3	odd	2	inner	4.23.b.a.3.10	yes	10
8.3	odd	2		64.23.c.e.63.7		10
8.5	even	2		64.23.c.e.63.4		10
12.11	even	2		36.23.d.c.19.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.23.b.a.3.9	✓	10	1.1	even	1	trivial
4.23.b.a.3.10	yes	10	4.3	odd	2	inner
36.23.d.c.19.1		10	12.11	even	2
36.23.d.c.19.2		10	3.2	odd	2
64.23.c.e.63.4		10	8.5	even	2
64.23.c.e.63.7		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)

\(f(q)\)	\(=\)	\(q+(1785.90 - 1002.42i) q^{2} +127855. i q^{3} +(2.18461e6 - 3.58046e6i) q^{4} -6.52379e7 q^{5} +(1.28165e8 + 2.28337e8i) q^{6} -3.27904e9i q^{7} +(3.12381e8 - 8.58425e9i) q^{8} +1.50341e10 q^{9} +O(q^{10})\)	\(q+(1785.90 - 1002.42i) q^{2} +127855. i q^{3} +(2.18461e6 - 3.58046e6i) q^{4} -6.52379e7 q^{5} +(1.28165e8 + 2.28337e8i) q^{6} -3.27904e9i q^{7} +(3.12381e8 - 8.58425e9i) q^{8} +1.50341e10 q^{9} +(-1.16509e11 + 6.53958e10i) q^{10} -2.30540e11i q^{11} +(4.57780e11 + 2.79314e11i) q^{12} -1.19775e12 q^{13} +(-3.28698e12 - 5.85606e12i) q^{14} -8.34100e12i q^{15} +(-8.04715e12 - 1.56438e13i) q^{16} -2.07597e13 q^{17} +(2.68495e13 - 1.50705e13i) q^{18} -6.48196e12i q^{19} +(-1.42519e14 + 2.33581e14i) q^{20} +4.19243e14 q^{21} +(-2.31098e14 - 4.11722e14i) q^{22} +1.02386e15i q^{23} +(1.09754e15 + 3.99395e13i) q^{24} +1.87179e15 q^{25} +(-2.13907e15 + 1.20065e15i) q^{26} +5.93442e15i q^{27} +(-1.17405e16 - 7.16343e15i) q^{28} +1.56390e16 q^{29} +(-8.36119e15 - 1.48962e16i) q^{30} -2.85873e16i q^{31} +(-3.00531e16 - 1.98717e16i) q^{32} +2.94757e16 q^{33} +(-3.70748e16 + 2.08100e16i) q^{34} +2.13918e17i q^{35} +(3.28436e16 - 5.38289e16i) q^{36} +2.10744e17 q^{37} +(-6.49765e15 - 1.15762e16i) q^{38} -1.53139e17i q^{39} +(-2.03791e16 + 5.60018e17i) q^{40} -5.57168e17 q^{41} +(7.48728e17 - 4.20258e17i) q^{42} -8.07417e17i q^{43} +(-8.25438e17 - 5.03639e17i) q^{44} -9.80792e17 q^{45} +(1.02634e18 + 1.82852e18i) q^{46} -8.59587e17i q^{47} +(2.00014e18 - 1.02887e18i) q^{48} -6.84231e18 q^{49} +(3.34285e18 - 1.87632e18i) q^{50} -2.65424e18i q^{51} +(-2.61662e18 + 4.28850e18i) q^{52} +1.56480e19 q^{53} +(5.94879e18 + 1.05983e19i) q^{54} +1.50399e19i q^{55} +(-2.81481e19 - 1.02431e18i) q^{56} +8.28753e17 q^{57} +(2.79297e19 - 1.56768e19i) q^{58} +7.82838e18i q^{59} +(-2.98646e19 - 1.82218e19i) q^{60} +1.24317e19 q^{61} +(-2.86565e19 - 5.10542e19i) q^{62} -4.92975e19i q^{63} +(-7.35918e19 - 5.36311e18i) q^{64} +7.81387e19 q^{65} +(5.26408e19 - 2.95471e19i) q^{66} +1.36610e20i q^{67} +(-4.53518e19 + 7.43292e19i) q^{68} -1.30906e20 q^{69} +(2.14436e20 + 3.82037e20i) q^{70} -2.01190e20i q^{71} +(4.69636e18 - 1.29056e20i) q^{72} +2.57734e19 q^{73} +(3.76369e20 - 2.11254e20i) q^{74} +2.39319e20i q^{75} +(-2.32084e19 - 1.41606e19i) q^{76} -7.55950e20 q^{77} +(-1.53509e20 - 2.73491e20i) q^{78} -8.27585e20i q^{79} +(5.24979e20 + 1.02057e21i) q^{80} -2.86961e20 q^{81} +(-9.95050e20 + 5.58517e20i) q^{82} -6.46586e20i q^{83} +(9.15882e20 - 1.50108e21i) q^{84} +1.35432e21 q^{85} +(-8.09371e20 - 1.44197e21i) q^{86} +1.99952e21i q^{87} +(-1.97901e21 - 7.20162e19i) q^{88} +1.96738e21 q^{89} +(-1.75160e21 + 9.83167e20i) q^{90} +3.92748e21i q^{91} +(3.66590e21 + 2.23674e21i) q^{92} +3.65504e21 q^{93} +(-8.61668e20 - 1.53514e21i) q^{94} +4.22869e20i q^{95} +(2.54070e21 - 3.84245e21i) q^{96} -3.08304e21 q^{97} +(-1.22197e22 + 6.85887e21i) q^{98} -3.46596e21i 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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