LMFDB - Embedded newform 83.13.b.c.82.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [83,13,Mod(82,83)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(83, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("83.82");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 83 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	83.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:	$75.8614868339$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			82.12
Character	$\chi$	$=$	83.82
Dual form			83.13.b.c.82.69

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-97.6509i q^{2} +955.647 q^{3} -5439.71 q^{4} +28739.5i q^{5} -93319.9i q^{6} +19697.5 q^{7} +131214. i q^{8} +381821. q^{9} +O(q^{10})$	\(q-97.6509i q^{2} +955.647 q^{3} -5439.71 q^{4} +28739.5i q^{5} -93319.9i q^{6} +19697.5 q^{7} +131214. i q^{8} +381821. q^{9} +2.80644e6 q^{10} -631949. q^{11} -5.19844e6 q^{12} +6.20388e6i q^{13} -1.92348e6i q^{14} +2.74648e7i q^{15} -9.46784e6 q^{16} +1.25627e7 q^{17} -3.72852e7i q^{18} -6.20809e7i q^{19} -1.56334e8i q^{20} +1.88238e7 q^{21} +6.17105e7i q^{22} -3.04058e7 q^{23} +1.25395e8i q^{24} -5.81818e8 q^{25} +6.05814e8 q^{26} -1.42984e8 q^{27} -1.07148e8 q^{28} -8.74309e8 q^{29} +2.68197e9 q^{30} +1.37178e9 q^{31} +1.46200e9i q^{32} -6.03921e8 q^{33} -1.22676e9i q^{34} +5.66095e8i q^{35} -2.07699e9 q^{36} -8.02787e8 q^{37} -6.06226e9 q^{38} +5.92872e9i q^{39} -3.77103e9 q^{40} -2.56240e9 q^{41} -1.83817e9i q^{42} +8.75501e9i q^{43} +3.43762e9 q^{44} +1.09733e10i q^{45} +2.96916e9i q^{46} +1.61133e10i q^{47} -9.04792e9 q^{48} -1.34533e10 q^{49} +5.68151e10i q^{50} +1.20055e10 q^{51} -3.37473e10i q^{52} +4.49539e9i q^{53} +1.39625e10i q^{54} -1.81619e10i q^{55} +2.58459e9i q^{56} -5.93275e10i q^{57} +8.53771e10i q^{58} -3.54589e10 q^{59} -1.49401e11i q^{60} -1.41218e10 q^{61} -1.33955e11i q^{62} +7.52091e9 q^{63} +1.03985e11 q^{64} -1.78296e11 q^{65} +5.89734e10i q^{66} +1.10454e11i q^{67} -6.83375e10 q^{68} -2.90573e10 q^{69} +5.52797e10 q^{70} +1.17141e11i q^{71} +5.01004e10i q^{72} -7.98278e10i q^{73} +7.83929e10i q^{74} -5.56013e11 q^{75} +3.37702e11i q^{76} -1.24478e10 q^{77} +5.78945e11 q^{78} +1.93125e11i q^{79} -2.72101e11i q^{80} -3.39558e11 q^{81} +2.50221e11i q^{82} +(1.62988e11 - 2.83417e11i) q^{83} -1.02396e11 q^{84} +3.61046e11i q^{85} +8.54935e11 q^{86} -8.35531e11 q^{87} -8.29208e10i q^{88} -3.82512e11i q^{89} +1.07156e12 q^{90} +1.22201e11i q^{91} +1.65399e11 q^{92} +1.31094e12 q^{93} +1.57348e12 q^{94} +1.78417e12 q^{95} +1.39715e12i q^{96} +1.04243e12i q^{97} +1.31373e12i q^{98} -2.41292e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 918 q^{3} - 181150 q^{4} + 103918 q^{7} + 14902142 q^{9}+O(q^{10}) $ 80 * q + 918 * q^3 - 181150 * q^4 + 103918 * q^7 + 14902142 * q^9	\( 80 q + 918 q^{3} - 181150 q^{4} + 103918 q^{7} + 14902142 q^{9} + 1177482 q^{10} + 510406 q^{11} - 9260402 q^{12} + 203791850 q^{16} + 5571718 q^{17} + 46565862 q^{21} + 804389464 q^{23} - 4263713272 q^{25} + 18061794 q^{26} - 2326165338 q^{27} - 204811652 q^{28} + 1486960270 q^{29} - 2621683648 q^{30} - 665743010 q^{31} + 135224502 q^{33} - 54936709824 q^{36} - 280627202 q^{37} + 6646145310 q^{38} - 7119722058 q^{40} + 51318109072 q^{41} - 11512674650 q^{44} + 85368259738 q^{48} + 148785395094 q^{49} - 100143389562 q^{51} - 63584241050 q^{59} - 29216180978 q^{61} - 332932206620 q^{63} - 323596534090 q^{64} + 362112989184 q^{65} - 86115426752 q^{68} + 272383417100 q^{69} + 105630718656 q^{70} + 785418808326 q^{75} - 663355117738 q^{77} + 1483841884620 q^{78} + 2430778545148 q^{81} + 837315119192 q^{83} - 3013574788354 q^{84} + 452180651958 q^{86} - 682263689498 q^{87} - 499714512022 q^{90} + 997428187414 q^{92} - 1487992716298 q^{93} + 3169817690580 q^{94} + 1542762610848 q^{95} + 2021347267420 q^{99}+O(q^{100}) \) 80 * q + 918 * q^3 - 181150 * q^4 + 103918 * q^7 + 14902142 * q^9 + 1177482 * q^10 + 510406 * q^11 - 9260402 * q^12 + 203791850 * q^16 + 5571718 * q^17 + 46565862 * q^21 + 804389464 * q^23 - 4263713272 * q^25 + 18061794 * q^26 - 2326165338 * q^27 - 204811652 * q^28 + 1486960270 * q^29 - 2621683648 * q^30 - 665743010 * q^31 + 135224502 * q^33 - 54936709824 * q^36 - 280627202 * q^37 + 6646145310 * q^38 - 7119722058 * q^40 + 51318109072 * q^41 - 11512674650 * q^44 + 85368259738 * q^48 + 148785395094 * q^49 - 100143389562 * q^51 - 63584241050 * q^59 - 29216180978 * q^61 - 332932206620 * q^63 - 323596534090 * q^64 + 362112989184 * q^65 - 86115426752 * q^68 + 272383417100 * q^69 + 105630718656 * q^70 + 785418808326 * q^75 - 663355117738 * q^77 + 1483841884620 * q^78 + 2430778545148 * q^81 + 837315119192 * q^83 - 3013574788354 * q^84 + 452180651958 * q^86 - 682263689498 * q^87 - 499714512022 * q^90 + 997428187414 * q^92 - 1487992716298 * q^93 + 3169817690580 * q^94 + 1542762610848 * q^95 + 2021347267420 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/83\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	97.6509i		−	1.52580i	−0.646519	−	0.762898i	$-0.723776\pi$
$2$		−	97.6509i		−	1.52580i	0.646519	−	0.762898i	$-0.276224\pi$
$3$	955.647			1.31090			0.655451	−	0.755238i	$-0.272479\pi$
$3$	955.647			1.31090			0.655451	+	0.755238i	$0.272479\pi$
$4$	−5439.71			−1.32805
$5$			28739.5i			1.83933i	0.392706	+	0.919664i	$0.371539\pi$
$5$			28739.5i			1.83933i	−0.392706	+	0.919664i	$0.628461\pi$
$6$		−	93319.9i		−	2.00017i
$7$	19697.5			0.167426			0.0837129	−	0.996490i	$-0.473322\pi$
$7$	19697.5			0.167426			0.0837129	+	0.996490i	$0.473322\pi$
$8$			131214.i			0.500543i
$9$	381821.			0.718464
$10$	2.80644e6			2.80644
$11$	−631949.			−0.356719			−0.178360	−	0.983965i	$-0.557079\pi$
$11$	−631949.			−0.356719			−0.178360	+	0.983965i	$0.557079\pi$
$12$	−5.19844e6			−1.74095
$13$			6.20388e6i			1.28530i	0.766162	+	0.642648i	$0.222164\pi$
$13$			6.20388e6i			1.28530i	−0.766162	+	0.642648i	$0.777836\pi$
$14$		−	1.92348e6i		−	0.255457i
$15$			2.74648e7i			2.41118i
$16$	−9.46784e6			−0.564327
$17$	1.25627e7			0.520463			0.260232	−	0.965546i	$-0.416201\pi$
$17$	1.25627e7			0.520463			0.260232	+	0.965546i	$0.416201\pi$
$18$		−	3.72852e7i		−	1.09623i
$19$		−	6.20809e7i		−	1.31958i	−0.751449	−	0.659791i	$-0.770645\pi$
$19$		−	6.20809e7i		−	1.31958i	0.751449	−	0.659791i	$-0.229355\pi$
$20$		−	1.56334e8i		−	2.44273i
$21$	1.88238e7			0.219479
$22$			6.17105e7i			0.544280i
$23$	−3.04058e7			−0.205395			−0.102698	−	0.994713i	$-0.532747\pi$
$23$	−3.04058e7			−0.205395			−0.102698	+	0.994713i	$0.532747\pi$
$24$			1.25395e8i			0.656162i
$25$	−5.81818e8			−2.38313
$26$	6.05814e8			1.96110
$27$	−1.42984e8			−0.369067
$28$	−1.07148e8			−0.222350
$29$	−8.74309e8			−1.46986			−0.734932	−	0.678141i	$-0.762786\pi$
$29$	−8.74309e8			−1.46986			−0.734932	+	0.678141i	$0.762786\pi$
$30$	2.68197e9			3.67897
$31$	1.37178e9			1.54566			0.772829	−	0.634614i	$-0.218841\pi$
$31$	1.37178e9			1.54566			0.772829	+	0.634614i	$0.218841\pi$
$32$			1.46200e9i			1.36159i
$33$	−6.03921e8			−0.467624
$34$		−	1.22676e9i		−	0.794121i
$35$			5.66095e8i			0.307951i
$36$	−2.07699e9			−0.954158
$37$	−8.02787e8			−0.312889			−0.156444	−	0.987687i	$-0.550003\pi$
$37$	−8.02787e8			−0.312889			−0.156444	+	0.987687i	$0.550003\pi$
$38$	−6.06226e9			−2.01341
$39$			5.92872e9i			1.68490i
$40$	−3.77103e9			−0.920662
$41$	−2.56240e9			−0.539440			−0.269720	−	0.962939i	$-0.586931\pi$
$41$	−2.56240e9			−0.539440			−0.269720	+	0.962939i	$0.586931\pi$
$42$		−	1.83817e9i		−	0.334880i
$43$			8.75501e9i			1.38499i	0.721424	+	0.692494i	$0.243488\pi$
$43$			8.75501e9i			1.38499i	−0.721424	+	0.692494i	$0.756512\pi$
$44$	3.43762e9			0.473742
$45$			1.09733e10i			1.32149i
$46$			2.96916e9i			0.313391i
$47$			1.61133e10i			1.49485i	0.664344	+	0.747427i	$0.268711\pi$
$47$			1.61133e10i			1.49485i	−0.664344	+	0.747427i	$0.731289\pi$
$48$	−9.04792e9			−0.739778
$49$	−1.34533e10			−0.971969
$50$			5.68151e10i			3.63617i
$51$	1.20055e10			0.682276
$52$		−	3.37473e10i		−	1.70694i
$53$			4.49539e9i			0.202820i	0.994845	+	0.101410i	$0.0323355\pi$
$53$			4.49539e9i			0.202820i	−0.994845	+	0.101410i	$0.967665\pi$
$54$			1.39625e10i			0.563120i
$55$		−	1.81619e10i		−	0.656123i
$56$			2.58459e9i			0.0838037i
$57$		−	5.93275e10i		−	1.72984i
$58$			8.53771e10i			2.24271i
$59$	−3.54589e10			−0.840647			−0.420324	−	0.907374i	$-0.638083\pi$
$59$	−3.54589e10			−0.840647			−0.420324	+	0.907374i	$0.638083\pi$
$60$		−	1.49401e11i		−	3.20217i
$61$	−1.41218e10			−0.274100			−0.137050	−	0.990564i	$-0.543762\pi$
$61$	−1.41218e10			−0.274100			−0.137050	+	0.990564i	$0.543762\pi$
$62$		−	1.33955e11i		−	2.35836i
$63$	7.52091e9			0.120289
$64$	1.03985e11			1.51318
$65$	−1.78296e11			−2.36408
$66$			5.89734e10i			0.713498i
$67$			1.10454e11i			1.22105i	0.791997	+	0.610525i	$0.209042\pi$
$67$			1.10454e11i			1.22105i	−0.791997	+	0.610525i	$0.790958\pi$
$68$	−6.83375e10			−0.691203
$69$	−2.90573e10			−0.269253
$70$	5.52797e10			0.469870
$71$			1.17141e11i			0.914445i	0.889352	+	0.457222i	$0.151156\pi$
$71$			1.17141e11i			0.914445i	−0.889352	+	0.457222i	$0.848844\pi$
$72$			5.01004e10i			0.359622i
$73$		−	7.98278e10i		−	0.527494i	−0.964592	−	0.263747i	$-0.915042\pi$
$73$		−	7.98278e10i		−	0.527494i	0.964592	−	0.263747i	$-0.0849583\pi$
$74$			7.83929e10i			0.477404i
$75$	−5.56013e11			−3.12405
$76$			3.37702e11i			1.75248i
$77$	−1.24478e10			−0.0597239
$78$	5.78945e11			2.57081
$79$			1.93125e11i			0.794467i	0.917718	+	0.397234i	$0.130030\pi$
$79$			1.93125e11i			0.794467i	−0.917718	+	0.397234i	$0.869970\pi$
$80$		−	2.72101e11i		−	1.03798i
$81$	−3.39558e11			−1.20227
$82$			2.50221e11i			0.823076i
$83$	1.62988e11	−	2.83417e11i	0.498525	−	0.866876i
$83$	1.62988e11	−	2.83417e11i	0.498525	−	0.866876i
$84$	−1.02396e11			−0.291479
$85$			3.61046e11i			0.957303i
$86$	8.54935e11			2.11321
$87$	−8.35531e11			−1.92685
$88$		−	8.29208e10i		−	0.178553i
$89$		−	3.82512e11i		−	0.769671i	−0.922985	−	0.384835i	$-0.874258\pi$
$89$		−	3.82512e11i		−	0.769671i	0.922985	−	0.384835i	$-0.125742\pi$
$90$	1.07156e12			2.01632
$91$			1.22201e11i			0.215192i
$92$	1.65399e11			0.272776
$93$	1.31094e12			2.02621
$94$	1.57348e12			2.28084
$95$	1.78417e12			2.42715
$96$			1.39715e12i			1.78491i
$97$			1.04243e12i			1.25146i	0.780041	+	0.625728i	$0.215198\pi$
$97$			1.04243e12i			1.25146i	−0.780041	+	0.625728i	$0.784802\pi$
$98$			1.31373e12i			1.48303i
$99$	−2.41292e11			−0.256290
$100$	3.16492e12			3.16492
$101$			1.22614e12i			1.15508i	0.816361	+	0.577541i	$0.195988\pi$
$101$			1.22614e12i			1.15508i	−0.816361	+	0.577541i	$0.804012\pi$
$102$		−	1.17235e12i		−	1.04101i
$103$		−	4.67481e11i		−	0.391508i	−0.980653	−	0.195754i	$-0.937285\pi$
$103$		−	4.67481e11i		−	0.391508i	0.980653	−	0.195754i	$-0.0627154\pi$
$104$	−8.14037e11			−0.643345
$105$			5.40988e11i			0.403693i
$106$	4.38979e11			0.309463
$107$		−	2.18453e12i		−	1.45565i	−0.685765	−	0.727823i	$-0.740532\pi$
$107$		−	2.18453e12i		−	1.45565i	0.685765	−	0.727823i	$-0.259468\pi$
$108$	7.77791e11			0.490140
$109$	1.72055e12			1.02591			0.512955	−	0.858416i	$-0.328551\pi$
$109$	1.72055e12			1.02591			0.512955	+	0.858416i	$0.328551\pi$
$110$	−1.77353e12			−1.00111
$111$	−7.67181e11			−0.410166
$112$	−1.86493e11			−0.0944829
$113$	−2.16437e12			−1.03959			−0.519793	−	0.854293i	$-0.673991\pi$
$113$	−2.16437e12			−1.03959			−0.519793	+	0.854293i	$0.673991\pi$
$114$	−5.79338e12			−2.63939
$115$		−	8.73849e11i		−	0.377789i
$116$	4.75598e12			1.95206
$117$			2.36877e12i			0.923438i
$118$			3.46260e12i			1.28266i
$119$	2.47454e11			0.0871389
$120$	−3.60378e12			−1.20690
$121$	−2.73907e12			−0.872752
$122$			1.37900e12i			0.418221i
$123$	−2.44875e12			−0.707153
$124$	−7.46207e12			−2.05272
$125$		−	9.70469e12i		−	2.54403i
$126$		−	7.34424e11i		−	0.183537i
$127$	−2.71185e12			−0.646315			−0.323157	−	0.946345i	$-0.604744\pi$
$127$	−2.71185e12			−0.646315			−0.323157	+	0.946345i	$0.604744\pi$
$128$		−	4.16591e12i		−	0.947217i
$129$			8.36671e12i			1.81558i
$130$			1.74108e13i			3.60710i
$131$	5.21270e12			1.03142			0.515709	−	0.856764i	$-0.327529\pi$
$131$	5.21270e12			1.03142			0.515709	+	0.856764i	$0.327529\pi$
$132$	3.28515e12			0.621029
$133$		−	1.22284e12i		−	0.220932i
$134$	1.07860e13			1.86307
$135$		−	4.10929e12i		−	0.678835i
$136$			1.64841e12i			0.260514i
$137$			3.34279e11i			0.0505575i	0.999680	+	0.0252788i	$0.00804734\pi$
$137$			3.34279e11i			0.0505575i	−0.999680	+	0.0252788i	$0.991953\pi$
$138$			2.83747e12i			0.410825i
$139$		−	8.48899e12i		−	1.17697i	−0.808506	−	0.588487i	$-0.799724\pi$
$139$		−	8.48899e12i		−	1.17697i	0.808506	−	0.588487i	$-0.200276\pi$
$140$		−	3.07939e12i		−	0.408975i
$141$			1.53987e13i			1.95961i
$142$	1.14389e13			1.39526
$143$		−	3.92054e12i		−	0.458489i
$144$	−3.61502e12			−0.405449
$145$		−	2.51272e13i		−	2.70356i
$146$	−7.79526e12			−0.804848
$147$	−1.28566e13			−1.27416
$148$	4.36693e12			0.415533
$149$		−	1.02172e13i		−	0.933718i	−0.884332	−	0.466859i	$-0.845386\pi$
$149$		−	1.02172e13i		−	0.933718i	0.884332	−	0.466859i	$-0.154614\pi$
$150$			5.42952e13i			4.76666i
$151$	−9.37350e11			−0.0790751			−0.0395376	−	0.999218i	$-0.512588\pi$
$151$	−9.37350e11			−0.0790751			−0.0395376	+	0.999218i	$0.512588\pi$
$152$	8.14590e12			0.660507
$153$	4.79671e12			0.373934
$154$			1.21554e12i			0.0911265i
$155$			3.94242e13i			2.84297i
$156$		−	3.22505e13i		−	2.23763i
$157$			1.10551e13i			0.738183i	0.929393	+	0.369092i	$0.120331\pi$
$157$			1.10551e13i			0.738183i	−0.929393	+	0.369092i	$0.879669\pi$
$158$	1.88588e13			1.21220
$159$			4.29600e12i			0.265878i
$160$	−4.20171e13			−2.50441
$161$	−5.98918e11			−0.0343884
$162$			3.31581e13i			1.83442i
$163$		−	2.81920e13i		−	1.50314i	−0.659652	−	0.751571i	$-0.729296\pi$
$163$		−	2.81920e13i		−	1.50314i	0.659652	−	0.751571i	$-0.270704\pi$
$164$	1.39387e13			0.716405
$165$		−	1.73564e13i		−	0.860113i
$166$	−2.76759e13	−	1.59159e13i	−1.32268	−	0.760647i
$167$	1.09695e13			0.505693			0.252846	−	0.967506i	$-0.418633\pi$
$167$	1.09695e13			0.505693			0.252846	+	0.967506i	$0.418633\pi$
$168$			2.46996e12i			0.109858i
$169$	−1.51900e13			−0.651985
$170$	3.52565e13			1.46065
$171$		−	2.37038e13i		−	0.948072i
$172$		−	4.76247e13i		−	1.83934i
$173$	−6.98275e12			−0.260465			−0.130233	−	0.991483i	$-0.541572\pi$
$173$	−6.98275e12			−0.260465			−0.130233	+	0.991483i	$0.541572\pi$
$174$			8.15904e13i			2.93997i
$175$	−1.14603e13			−0.398997
$176$	5.98320e12			0.201306
$177$	−3.38862e13			−1.10201
$178$	−3.73526e13			−1.17436
$179$			2.72368e13i			0.828016i	0.910273	+	0.414008i	$0.135871\pi$
$179$			2.72368e13i			0.828016i	−0.910273	+	0.414008i	$0.864129\pi$
$180$		−	5.96918e13i		−	1.75501i
$181$			5.40831e12i			0.153812i	0.997038	+	0.0769059i	$0.0245041\pi$
$181$			5.40831e12i			0.153812i	−0.997038	+	0.0769059i	$0.975496\pi$
$182$	1.19330e13			0.328338
$183$	−1.34954e13			−0.359319
$184$		−	3.98968e12i		−	0.102809i
$185$		−	2.30717e13i		−	0.575505i
$186$		−	1.28014e14i		−	3.09158i
$187$	−7.93900e12			−0.185659
$188$		−	8.76519e13i		−	1.98524i
$189$	−2.81642e12			−0.0617912
$190$		−	1.74226e14i		−	3.70333i
$191$	5.91942e12			0.121921			0.0609605	−	0.998140i	$-0.480584\pi$
$191$	5.91942e12			0.121921			0.0609605	+	0.998140i	$0.480584\pi$
$192$	9.93731e13			1.98363
$193$	3.97976e13			0.770039			0.385020	−	0.922908i	$-0.374195\pi$
$193$	3.97976e13			0.770039			0.385020	+	0.922908i	$0.374195\pi$
$194$	1.01794e14			1.90947
$195$	−1.70388e14			−3.09908
$196$	7.31820e13			1.29083
$197$	7.08581e13			1.21225			0.606125	−	0.795369i	$-0.292723\pi$
$197$	7.08581e13			1.21225			0.606125	+	0.795369i	$0.292723\pi$
$198$			2.35624e13i			0.391046i
$199$	6.42943e13			1.03527			0.517636	−	0.855601i	$-0.326812\pi$
$199$	6.42943e13			1.03527			0.517636	+	0.855601i	$0.326812\pi$
$200$		−	7.63428e13i		−	1.19286i
$201$			1.05555e14i			1.60068i
$202$	1.19734e14			1.76242
$203$	−1.72217e13			−0.246093
$204$	−6.53066e13			−0.906099
$205$		−	7.36420e13i		−	0.992208i
$206$	−4.56499e13			−0.597361
$207$	−1.16096e13			−0.147569
$208$		−	5.87373e13i		−	0.725328i
$209$			3.92320e13i			0.470720i
$210$	5.28279e13			0.615954
$211$			7.77453e13i			0.881007i	0.897751	+	0.440503i	$0.145200\pi$
$211$			7.77453e13i			0.881007i	−0.897751	+	0.440503i	$0.854800\pi$
$212$		−	2.44536e13i		−	0.269356i
$213$			1.11945e14i			1.19875i
$214$	−2.13322e14			−2.22102
$215$	−2.51615e14			−2.54745
$216$		−	1.87615e13i		−	0.184734i
$217$	2.70205e13			0.258783
$218$		−	1.68014e14i		−	1.56533i
$219$		−	7.62873e13i		−	0.691492i
$220$			9.87955e13i			0.871367i
$221$			7.79375e13i			0.668949i
$222$			7.49160e13i			0.625830i
$223$			7.73318e13i			0.628824i	0.949287	+	0.314412i	$0.101807\pi$
$223$			7.73318e13i			0.628824i	−0.949287	+	0.314412i	$0.898193\pi$
$224$			2.87976e13i			0.227965i
$225$	−2.22150e14			−1.71219
$226$			2.11352e14i			1.58619i
$227$	9.92447e13			0.725358			0.362679	−	0.931914i	$-0.381862\pi$
$227$	9.92447e13			0.725358			0.362679	+	0.931914i	$0.381862\pi$
$228$			3.22724e14i			2.29732i
$229$	−1.56025e14			−1.08189			−0.540943	−	0.841059i	$-0.681933\pi$
$229$	−1.56025e14			−1.08189			−0.540943	+	0.841059i	$0.681933\pi$
$230$	−8.53321e13			−0.576429
$231$	−1.18957e13			−0.0782922
$232$		−	1.14722e14i		−	0.735729i
$233$		−	2.00896e14i		−	1.25556i	−0.778392	−	0.627778i	$-0.783965\pi$
$233$		−	2.00896e14i		−	1.25556i	0.778392	−	0.627778i	$-0.216035\pi$
$234$	2.31313e14			1.40898
$235$	−4.63089e14			−2.74953
$236$	1.92886e14			1.11642
$237$			1.84559e14i			1.04147i
$238$		−	2.41641e13i		−	0.132956i
$239$			1.44962e14i			0.777797i	0.921281	+	0.388899i	$0.127144\pi$
$239$			1.44962e14i			0.777797i	−0.921281	+	0.388899i	$0.872856\pi$
$240$		−	2.60033e14i		−	1.36069i
$241$	3.71198e14			1.89454			0.947269	−	0.320440i	$-0.103831\pi$
$241$	3.71198e14			1.89454			0.947269	+	0.320440i	$0.103831\pi$
$242$			2.67473e14i			1.33164i
$243$	−2.48510e14			−1.20700
$244$	7.68182e13			0.364020
$245$		−	3.86641e14i		−	1.78777i
$246$			2.39123e14i			1.07897i
$247$	3.85142e14			1.69605
$248$			1.79997e14i			0.773668i
$249$	1.55759e14	−	2.70846e14i	0.653517	−	1.13639i
$250$	−9.47672e14			−3.88166
$251$			2.10538e14i			0.841955i	0.907071	+	0.420978i	$0.138313\pi$
$251$			2.10538e14i			0.841955i	−0.907071	+	0.420978i	$0.861687\pi$
$252$	−4.09115e13			−0.159751
$253$	1.92150e13			0.0732683
$254$			2.64815e14i			0.986145i
$255$			3.45033e14i			1.25493i
$256$	1.91185e13			0.0679225
$257$			1.27420e14i			0.442219i	0.975249	+	0.221110i	$0.0709679\pi$
$257$			1.27420e14i			0.442219i	−0.975249	+	0.221110i	$0.929032\pi$
$258$	8.17017e14			2.77021
$259$	−1.58129e13			−0.0523856
$260$	9.69880e14			3.13962
$261$	−3.33829e14			−1.05604
$262$		−	5.09025e14i		−	1.57373i
$263$		−	4.94740e14i		−	1.49500i	−0.664259	−	0.747502i	$-0.731253\pi$
$263$		−	4.94740e14i		−	1.49500i	0.664259	−	0.747502i	$-0.268747\pi$
$264$		−	7.92430e13i		−	0.234066i
$265$	−1.29195e14			−0.373053
$266$	−1.19411e14			−0.337097
$267$		−	3.65546e14i		−	1.00896i
$268$		−	6.00839e14i		−	1.62162i
$269$			6.83810e14i			1.80477i	0.430931	+	0.902385i	$0.358185\pi$
$269$			6.83810e14i			1.80477i	−0.430931	+	0.902385i	$0.641815\pi$
$270$	−4.01276e14			−1.03576
$271$			7.68866e14i			1.94104i	0.241016	+	0.970521i	$0.422519\pi$
$271$			7.68866e14i			1.94104i	−0.241016	+	0.970521i	$0.577481\pi$
$272$	−1.18942e14			−0.293712
$273$			1.16781e14i			0.282095i
$274$	3.26427e13			0.0771405
$275$	3.67680e14			0.850107
$276$	1.58063e14			0.357582
$277$	1.07222e14			0.237360			0.118680	−	0.992933i	$-0.462134\pi$
$277$	1.07222e14			0.237360			0.118680	+	0.992933i	$0.462134\pi$
$278$	−8.28958e14			−1.79582
$279$	5.23773e14			1.11050
$280$	−7.42798e13			−0.154143
$281$		−	1.18509e13i		−	0.0240721i	−0.999928	−	0.0120360i	$-0.996169\pi$
$281$		−	1.18509e13i		−	0.0240721i	0.999928	−	0.0120360i	$-0.00383128\pi$
$282$	1.50370e15			2.98996
$283$			8.28790e12i			0.0161334i	0.999967	+	0.00806670i	$0.00256774\pi$
$283$			8.28790e12i			0.0161334i	−0.999967	+	0.00806670i	$0.997432\pi$
$284$		−	6.37211e14i		−	1.21443i
$285$	1.70504e15			3.18175
$286$	−3.82844e14			−0.699561
$287$	−5.04727e13			−0.0903162
$288$			5.58221e14i			0.978254i
$289$	−4.24800e14			−0.729118
$290$	−2.45369e15			−4.12508
$291$			9.96193e14i			1.64054i
$292$			4.34240e14i			0.700540i
$293$	−1.13692e15			−1.79691			−0.898454	−	0.439067i	$-0.855309\pi$
$293$	−1.13692e15			−1.79691			−0.898454	+	0.439067i	$0.855309\pi$
$294$			1.25546e15i			1.94410i
$295$		−	1.01907e15i		−	1.54623i
$296$		−	1.05337e14i		−	0.156614i
$297$	9.03587e13			0.131653
$298$	−9.97722e14			−1.42466
$299$		−	1.88634e14i		−	0.263993i
$300$	3.02455e15			4.14890
$301$			1.72452e14i			0.231883i
$302$			9.15331e13i			0.120653i
$303$			1.17176e15i			1.51420i
$304$			5.87772e14i			0.744677i
$305$		−	4.05852e14i		−	0.504160i
$306$		−	4.68403e14i		−	0.570547i
$307$		−	1.02332e15i		−	1.22231i	−0.791510	−	0.611157i	$-0.790705\pi$
$307$		−	1.02332e15i		−	1.22231i	0.791510	−	0.611157i	$-0.209295\pi$
$308$	6.77124e13			0.0793166
$309$		−	4.46747e14i		−	0.513228i
$310$	3.84981e15			4.33780
$311$		−	4.06992e14i		−	0.449804i	−0.974381	−	0.224902i	$-0.927794\pi$
$311$		−	4.06992e14i		−	0.449804i	0.974381	−	0.224902i	$-0.0722063\pi$
$312$	−7.77932e14			−0.843362
$313$	−1.04033e15			−1.10638			−0.553192	−	0.833054i	$-0.686590\pi$
$313$	−1.04033e15			−1.10638			−0.553192	+	0.833054i	$0.686590\pi$
$314$	1.07954e15			1.12632
$315$			2.16147e14i			0.221251i
$316$		−	1.05054e15i		−	1.05510i
$317$	1.32115e15			1.30196			0.650980	−	0.759095i	$-0.274358\pi$
$317$	1.32115e15			1.30196			0.650980	+	0.759095i	$0.274358\pi$
$318$	4.19509e14			0.405675
$319$	5.52519e14			0.524328
$320$			2.98848e15i			2.78324i
$321$		−	2.08764e15i		−	1.90821i
$322$			5.84849e13i			0.0524697i
$323$		−	7.79905e14i		−	0.686794i
$324$	1.84709e15			1.59668
$325$		−	3.60953e15i		−	3.06302i
$326$	−2.75297e15			−2.29349
$327$	1.64424e15			1.34487
$328$		−	3.36223e14i		−	0.270013i
$329$			3.17392e14i			0.250277i
$330$	−1.69487e15			−1.31236
$331$			2.26710e15i			1.72386i	0.507025	+	0.861932i	$0.330745\pi$
$331$			2.26710e15i			1.72386i	−0.507025	+	0.861932i	$0.669255\pi$
$332$	−8.86606e14	+	1.54170e15i	−0.662067	+	1.15126i
$333$	−3.06521e14			−0.224799
$334$		−	1.07118e15i		−	0.771584i
$335$	−3.17440e15			−2.24591
$336$	−1.78221e14			−0.123858
$337$		−	2.12898e14i		−	0.145342i	−0.997356	−	0.0726710i	$-0.976848\pi$
$337$		−	2.12898e14i		−	0.145342i	0.997356	−	0.0726710i	$-0.0231523\pi$
$338$			1.48332e15i			0.994795i
$339$	−2.06837e15			−1.36279
$340$		−	1.96399e15i		−	1.27135i
$341$	−8.66894e14			−0.551366
$342$	−2.31470e15			−1.44656
$343$	−5.37634e14			−0.330158
$344$	−1.14878e15			−0.693246
$345$		−	8.35091e14i		−	0.495244i
$346$			6.81872e14i			0.397417i
$347$			1.96746e15i			1.12701i	0.826112	+	0.563506i	$0.190548\pi$
$347$			1.96746e15i			1.12701i	−0.826112	+	0.563506i	$0.809452\pi$
$348$	4.54504e15			2.55896
$349$	−3.14211e13			−0.0173888			−0.00869439	−	0.999962i	$-0.502768\pi$
$349$	−3.14211e13			−0.0173888			−0.00869439	+	0.999962i	$0.502768\pi$
$350$			1.11911e15i			0.608788i
$351$		−	8.87055e14i		−	0.474360i
$352$		−	9.23909e14i		−	0.485705i
$353$	1.96886e15			1.01758			0.508788	−	0.860892i	$-0.330094\pi$
$353$	1.96886e15			1.01758			0.508788	+	0.860892i	$0.330094\pi$
$354$			3.30902e15i			1.68144i
$355$	−3.36656e15			−1.68196
$356$			2.08075e15i			1.02216i
$357$	2.36479e14			0.114231
$358$	2.65970e15			1.26338
$359$	2.17538e14			0.101618			0.0508088	−	0.998708i	$-0.483820\pi$
$359$	2.17538e14			0.101618			0.0508088	+	0.998708i	$0.483820\pi$
$360$	−1.43986e15			−0.661462
$361$	−1.64073e15			−0.741298
$362$	5.28126e14			0.234686
$363$	−2.61758e15			−1.14409
$364$		−	6.64736e14i		−	0.285786i
$365$	2.29421e15			0.970234
$366$			1.31784e15i			0.548247i
$367$		−	6.76638e14i		−	0.276924i	−0.990368	−	0.138462i	$-0.955784\pi$
$367$		−	6.76638e14i		−	0.276924i	0.990368	−	0.138462i	$-0.0442158\pi$
$368$	2.87878e14			0.115910
$369$	−9.78377e14			−0.387568
$370$	−2.25297e15			−0.878103
$371$			8.85477e13i			0.0339574i
$372$	−7.13110e15			−2.69091
$373$	5.24840e15			1.94883			0.974415	−	0.224756i	$-0.0721586\pi$
$373$	5.24840e15			1.94883			0.974415	+	0.224756i	$0.0721586\pi$
$374$			7.75251e14i			0.283278i
$375$		−	9.27426e15i		−	3.33497i
$376$	−2.11430e15			−0.748238
$377$		−	5.42410e15i		−	1.88921i
$378$			2.75026e14i			0.0942808i
$379$			4.07765e15i			1.37586i	0.725776	+	0.687931i	$0.241481\pi$
$379$			4.07765e15i			1.37586i	−0.725776	+	0.687931i	$0.758519\pi$
$380$	−9.70539e15			−3.22338
$381$	−2.59158e15			−0.847255
$382$		−	5.78037e14i		−	0.186027i
$383$	1.31358e15			0.416164			0.208082	−	0.978111i	$-0.433278\pi$
$383$	1.31358e15			0.416164			0.208082	+	0.978111i	$0.433278\pi$
$384$		−	3.98114e15i		−	1.24171i
$385$		−	3.57744e14i		−	0.109852i
$386$		−	3.88627e15i		−	1.17492i
$387$			3.34285e15i			0.995063i
$388$		−	5.67050e15i		−	1.66200i
$389$		−	2.41474e15i		−	0.696905i	−0.937326	−	0.348452i	$-0.886707\pi$
$389$		−	2.41474e15i		−	0.696905i	0.937326	−	0.348452i	$-0.113293\pi$
$390$			1.66386e16i			4.72856i
$391$	−3.81980e14			−0.106901
$392$		−	1.76526e15i		−	0.486512i
$393$	4.98150e15			1.35209
$394$		−	6.91936e15i		−	1.84965i
$395$	−5.55032e15			−1.46129
$396$	1.31256e15			0.340366
$397$	4.57644e15			1.16892			0.584460	−	0.811423i	$-0.301306\pi$
$397$	4.57644e15			1.16892			0.584460	+	0.811423i	$0.301306\pi$
$398$		−	6.27840e15i		−	1.57961i
$399$		−	1.16860e15i		−	0.289620i
$400$	5.50856e15			1.34486
$401$	−1.95393e15			−0.469940			−0.234970	−	0.972003i	$-0.575499\pi$
$401$	−1.95393e15			−0.469940			−0.234970	+	0.972003i	$0.575499\pi$
$402$	1.03076e16			2.44231
$403$			8.51034e15i			1.98663i
$404$		−	6.66986e15i		−	1.53401i
$405$		−	9.75872e15i		−	2.21138i
$406$			1.68171e15i			0.375488i
$407$	5.07321e14			0.111613
$408$			1.57530e15i			0.341508i
$409$	8.28001e15			1.76885			0.884425	−	0.466682i	$-0.154551\pi$
$409$	8.28001e15			1.76885			0.884425	+	0.466682i	$0.154551\pi$
$410$	−7.19121e15			−1.51391
$411$			3.19453e14i			0.0662759i
$412$			2.54296e15i			0.519943i
$413$	−6.98451e14			−0.140746
$414$			1.13369e15i			0.225160i
$415$	8.14525e15	+	4.68419e15i	1.59447	+	0.916950i
$416$	−9.07005e15			−1.75005
$417$		−	8.11248e15i		−	1.54290i
$418$	3.83104e15			0.718223
$419$	−6.58479e15			−1.21691			−0.608454	−	0.793589i	$-0.708210\pi$
$419$	−6.58479e15			−1.21691			−0.608454	+	0.793589i	$0.708210\pi$
$420$		−	2.94281e15i		−	0.536126i
$421$		−	6.03653e15i		−	1.08416i	−0.840325	−	0.542082i	$-0.817636\pi$
$421$		−	6.03653e15i		−	1.08416i	0.840325	−	0.542082i	$-0.182364\pi$
$422$	7.59190e15			1.34424
$423$			6.15241e15i			1.07400i
$424$	−5.89859e14			−0.101520
$425$	−7.30922e15			−1.24033
$426$	1.09315e16			1.82904
$427$	−2.78163e14			−0.0458914
$428$			1.18832e16i			1.93318i
$429$		−	3.74665e15i		−	0.601035i
$430$			2.45704e16i			3.88689i
$431$	6.28774e15			0.980914			0.490457	−	0.871465i	$-0.336830\pi$
$431$	6.28774e15			0.980914			0.490457	+	0.871465i	$0.336830\pi$
$432$	1.35375e15			0.208274
$433$		−	3.18882e14i		−	0.0483841i	−0.999707	−	0.0241920i	$-0.992299\pi$
$433$		−	3.18882e14i		−	0.0483841i	0.999707	−	0.0241920i	$-0.00770131\pi$
$434$		−	2.63858e15i		−	0.394850i
$435$		−	2.40127e16i		−	3.54410i
$436$	−9.35930e15			−1.36246
$437$			1.88762e15i			0.271036i
$438$	−7.44952e15			−1.05508
$439$		−	8.36953e15i		−	1.16927i	−0.811298	−	0.584633i	$-0.801238\pi$
$439$		−	8.36953e15i		−	1.16927i	0.811298	−	0.584633i	$-0.198762\pi$
$440$	2.38310e15			0.328418
$441$	−5.13675e15			−0.698324
$442$	7.61067e15			1.02068
$443$	−1.06764e16			−1.41254			−0.706270	−	0.707942i	$-0.749624\pi$
$443$	−1.06764e16			−1.41254			−0.706270	+	0.707942i	$0.749624\pi$
$444$	4.17324e15			0.544723
$445$	1.09932e16			1.41568
$446$	7.55153e15			0.959457
$447$		−	9.76407e15i		−	1.22401i
$448$	2.04824e15			0.253346
$449$			3.87654e15i			0.473114i	0.971618	+	0.236557i	$0.0760190\pi$
$449$			3.87654e15i			0.473114i	−0.971618	+	0.236557i	$0.923981\pi$
$450$			2.16932e16i			2.61245i
$451$	1.61931e15			0.192429
$452$	1.17735e16			1.38062
$453$	−8.95776e14			−0.103660
$454$		−	9.69134e15i		−	1.10675i
$455$	−3.51199e15			−0.395808
$456$	7.78461e15			0.865860
$457$			1.23650e15i			0.135736i	0.997694	+	0.0678681i	$0.0216197\pi$
$457$			1.23650e15i			0.135736i	−0.997694	+	0.0678681i	$0.978380\pi$
$458$			1.52360e16i			1.65074i
$459$	−1.79627e15			−0.192086
$460$			4.75348e15i			0.501724i
$461$		−	7.62040e15i		−	0.793911i	−0.917838	−	0.396956i	$-0.870067\pi$
$461$		−	7.62040e15i		−	0.793911i	0.917838	−	0.396956i	$-0.129933\pi$
$462$			1.16163e15i			0.119458i
$463$	1.80836e16			1.83569			0.917845	−	0.396939i	$-0.129927\pi$
$463$	1.80836e16			1.83569			0.917845	+	0.396939i	$0.129927\pi$
$464$	8.27782e15			0.829484
$465$			3.76756e16i			3.72686i
$466$	−1.96177e16			−1.91572
$467$		−	8.77908e15i		−	0.846345i	−0.906049	−	0.423173i	$-0.860916\pi$
$467$		−	8.77908e15i		−	0.846345i	0.906049	−	0.423173i	$-0.139084\pi$
$468$		−	1.28854e16i		−	1.22637i
$469$			2.17567e15i			0.204435i
$470$			4.52211e16i			4.19521i
$471$			1.05648e16i			0.967686i
$472$		−	4.65272e15i		−	0.420780i
$473$		−	5.53273e15i		−	0.494052i
$474$	1.80224e16			1.58907
$475$			3.61198e16i			3.14473i
$476$	−1.34608e15			−0.115725
$477$			1.71643e15i			0.145719i
$478$	1.41557e16			1.18676
$479$	3.46216e14			0.0286638			0.0143319	−	0.999897i	$-0.495438\pi$
$479$	3.46216e14			0.0286638			0.0143319	+	0.999897i	$0.495438\pi$
$480$	−4.01535e16			−3.28304
$481$		−	4.98039e15i		−	0.402155i
$482$		−	3.62478e16i		−	2.89068i
$483$	−5.72354e14			−0.0450798
$484$	1.48997e16			1.15906
$485$	−2.99588e16			−2.30184
$486$			2.42672e16i			1.84163i
$487$		−	9.45014e14i		−	0.0708377i	−0.999373	−	0.0354189i	$-0.988723\pi$
$487$		−	9.45014e14i		−	0.0708377i	0.999373	−	0.0354189i	$-0.0112765\pi$
$488$		−	1.85298e15i		−	0.137199i
$489$		−	2.69416e16i		−	1.97047i
$490$	−3.77559e16			−2.72777
$491$			1.36624e16i			0.975075i	0.873102	+	0.487538i	$0.162105\pi$
$491$			1.36624e16i			0.975075i	−0.873102	+	0.487538i	$0.837895\pi$
$492$	1.33205e16			0.939137
$493$	−1.09837e16			−0.765010
$494$		−	3.76095e16i		−	2.58783i
$495$		−	6.93460e15i		−	0.471401i
$496$	−1.29878e16			−0.872257
$497$			2.30737e15i			0.153102i
$498$	−2.64484e16	−	1.52100e16i	−1.73390	−	0.997133i
$499$	2.57809e16			1.66991			0.834957	−	0.550315i	$-0.185492\pi$
$499$	2.57809e16			1.66991			0.834957	+	0.550315i	$0.185492\pi$
$500$			5.27906e16i			3.37860i
$501$	1.04829e16			0.662913
$502$	2.05593e16			1.28465
$503$		−	7.49799e15i		−	0.462953i	−0.972840	−	0.231476i	$-0.925644\pi$
$503$		−	7.49799e15i		−	0.462953i	0.972840	−	0.231476i	$-0.0743556\pi$
$504$			9.86850e14i			0.0602099i
$505$	−3.52388e16			−2.12458
$506$		−	1.87636e15i		−	0.111793i
$507$	−1.45163e16			−0.854688
$508$	1.47517e16			0.858341
$509$	−2.95268e16			−1.69789			−0.848946	−	0.528480i	$-0.822762\pi$
$509$	−2.95268e16			−1.69789			−0.848946	+	0.528480i	$0.822762\pi$
$510$	3.36928e16			1.91477
$511$		−	1.57241e15i		−	0.0883160i
$512$		−	1.89305e16i		−	1.05085i
$513$			8.87658e15i			0.487014i
$514$	1.24427e16			0.674737
$515$	1.34352e16			0.720111
$516$		−	4.55124e16i		−	2.41119i
$517$		−	1.01828e16i		−	0.533243i
$518$			1.54414e15i			0.0799298i
$519$	−6.67304e15			−0.341444
$520$		−	2.33950e16i		−	1.18332i
$521$	2.02513e16			1.01257			0.506286	−	0.862366i	$-0.331018\pi$
$521$	2.02513e16			1.01257			0.506286	+	0.862366i	$0.331018\pi$
$522$			3.25988e16i			1.61131i
$523$	2.62731e14			0.0128381			0.00641905	−	0.999979i	$-0.497957\pi$
$523$	2.62731e14			0.0128381			0.00641905	+	0.999979i	$0.497957\pi$
$524$	−2.83555e16			−1.36978
$525$	−1.09520e16			−0.523046
$526$	−4.83118e16			−2.28107
$527$	1.72333e16			0.804458
$528$	5.71783e15			0.263893
$529$	−2.09901e16			−0.957813
$530$			1.26160e16i			0.569203i
$531$	−1.35390e16			−0.603974
$532$			6.65187e15i			0.293410i
$533$		−	1.58968e16i		−	0.693340i
$534$	−3.56960e16			−1.53947
$535$	6.27824e16			2.67741
$536$	−1.44932e16			−0.611188
$537$			2.60288e16i			1.08545i
$538$	6.67747e16			2.75371
$539$	8.50180e15			0.346720
$540$			2.23533e16i			0.901529i
$541$			6.02660e15i			0.240375i	0.992751	+	0.120187i	$0.0383496\pi$
$541$			6.02660e15i			0.240375i	−0.992751	+	0.120187i	$0.961650\pi$
$542$	7.50805e16			2.96163
$543$			5.16843e15i			0.201632i
$544$			1.83667e16i			0.708658i
$545$			4.94478e16i			1.88698i
$546$	1.14037e16			0.430419
$547$	−6.25171e15			−0.233386			−0.116693	−	0.993168i	$-0.537229\pi$
$547$	−6.25171e15			−0.233386			−0.116693	+	0.993168i	$0.537229\pi$
$548$		−	1.81838e15i		−	0.0671431i
$549$	−5.39198e15			−0.196931
$550$		−	3.59043e16i		−	1.29709i
$551$			5.42779e16i			1.93961i
$552$		−	3.81273e15i		−	0.134772i
$553$			3.80407e15i			0.133014i
$554$		−	1.04704e16i		−	0.362163i
$555$		−	2.20484e16i		−	0.754431i
$556$			4.61776e16i			1.56309i
$557$	7.20609e15			0.241306			0.120653	−	0.992695i	$-0.461501\pi$
$557$	7.20609e15			0.241306			0.120653	+	0.992695i	$0.461501\pi$
$558$		−	5.11470e16i		−	1.69439i
$559$	−5.43150e16			−1.78012
$560$		−	5.35970e15i		−	0.173785i
$561$	−7.58689e15			−0.243381
$562$	−1.15725e15			−0.0367291
$563$	−4.92574e16			−1.54675			−0.773377	−	0.633946i	$-0.781434\pi$
$563$	−4.92574e16			−1.54675			−0.773377	+	0.633946i	$0.781434\pi$
$564$		−	8.37643e16i		−	2.60246i
$565$		−	6.22028e16i		−	1.91214i
$566$	8.09321e14			0.0246163
$567$	−6.68842e15			−0.201292
$568$	−1.53705e16			−0.457719
$569$			4.58644e16i			1.35146i	0.737151	+	0.675728i	$0.236171\pi$
$569$			4.58644e16i			1.35146i	−0.737151	+	0.675728i	$0.763829\pi$
$570$		−	1.66499e17i		−	4.85470i
$571$		−	4.63268e16i		−	1.33664i	−0.743872	−	0.668322i	$-0.767013\pi$
$571$		−	4.63268e16i		−	1.33664i	0.743872	−	0.668322i	$-0.232987\pi$
$572$			2.13266e16i			0.608898i
$573$	5.65688e15			0.159827
$574$			4.92871e15i			0.137804i
$575$	1.76907e16			0.489483
$576$	3.97037e16			1.08717
$577$		−	2.97087e16i		−	0.805062i	−0.915406	−	0.402531i	$-0.868131\pi$
$577$		−	2.97087e16i		−	0.805062i	0.915406	−	0.402531i	$-0.131869\pi$
$578$			4.14822e16i			1.11249i
$579$	3.80325e16			1.00945
$580$			1.36685e17i			3.59047i
$581$	3.21045e15	−	5.58259e15i	0.0834658	−	0.145137i
$582$	9.72792e16			2.50312
$583$		−	2.84086e15i		−	0.0723499i
$584$	1.04746e16			0.264033
$585$	−6.80773e16			−1.69851
$586$			1.11022e17i			2.74172i
$587$			4.12110e16i			1.00736i	0.863890	+	0.503680i	$0.168021\pi$
$587$			4.12110e16i			1.00736i	−0.863890	+	0.503680i	$0.831979\pi$
$588$	6.99362e16			1.69215
$589$		−	8.51612e16i		−	2.03962i
$590$	−9.95134e16			−2.35923
$591$	6.77154e16			1.58914
$592$	7.60066e15			0.176572
$593$	−6.82688e16			−1.56998			−0.784990	−	0.619508i	$-0.787332\pi$
$593$	−6.82688e16			−1.56998			−0.784990	+	0.619508i	$0.787332\pi$
$594$		−	8.82361e15i		−	0.200876i
$595$			7.11170e15i			0.160277i
$596$			5.55787e16i			1.24003i
$597$	6.14427e16			1.35714
$598$	−1.84203e16			−0.402800
$599$		−	6.91739e15i		−	0.149755i	−0.997193	−	0.0748775i	$-0.976143\pi$
$599$		−	6.91739e15i		−	0.149755i	0.997193	−	0.0748775i	$-0.0238566\pi$
$600$		−	7.29568e16i		−	1.56372i
$601$		−	6.67844e16i		−	1.41719i	−0.705616	−	0.708595i	$-0.749329\pi$
$601$		−	6.67844e16i		−	1.41719i	0.705616	−	0.708595i	$-0.250671\pi$
$602$	1.68401e16			0.353806
$603$			4.21738e16i			0.877281i
$604$	5.09891e15			0.105016
$605$		−	7.87195e16i		−	1.60528i
$606$	1.14424e17			2.31036
$607$	−4.30775e16			−0.861229			−0.430614	−	0.902536i	$-0.641703\pi$
$607$	−4.30775e16			−0.861229			−0.430614	+	0.902536i	$0.641703\pi$
$608$	9.07622e16			1.79673
$609$	−1.64578e16			−0.322604
$610$	−3.96318e16			−0.769246
$611$	−9.99652e16			−1.92133
$612$	−2.60927e16			−0.496604
$613$			3.90683e16i			0.736311i	0.929764	+	0.368156i	$0.120011\pi$
$613$			3.90683e16i			0.736311i	−0.929764	+	0.368156i	$0.879989\pi$
$614$	−9.99285e16			−1.86500
$615$		−	7.03758e16i		−	1.30069i
$616$		−	1.63333e15i		−	0.0298944i
$617$	−4.39724e16			−0.797019			−0.398510	−	0.917164i	$-0.630472\pi$
$617$	−4.39724e16			−0.797019			−0.398510	+	0.917164i	$0.630472\pi$
$618$	−4.36252e16			−0.783082
$619$	6.71230e15			0.119324			0.0596619	−	0.998219i	$-0.480998\pi$
$619$	6.71230e15			0.119324			0.0596619	+	0.998219i	$0.480998\pi$
$620$		−	2.14456e17i		−	3.77562i
$621$	4.34755e15			0.0758045
$622$	−3.97432e16			−0.686310
$623$		−	7.53452e15i		−	0.128863i
$624$		−	5.61322e16i		−	0.950833i
$625$	1.36862e17			2.29617
$626$			1.01589e17i			1.68812i
$627$			3.74920e16i			0.617068i
$628$		−	6.01364e16i		−	0.980347i
$629$	−1.00852e16			−0.162847
$630$	2.11070e16			0.337585
$631$			3.68304e16i			0.583485i	0.956497	+	0.291743i	$0.0942351\pi$
$631$			3.68304e16i			0.583485i	−0.956497	+	0.291743i	$0.905765\pi$
$632$	−2.53408e16			−0.397665
$633$			7.42971e16i			1.15491i
$634$		−	1.29012e17i		−	1.98652i
$635$		−	7.79373e16i		−	1.18878i
$636$		−	2.33690e16i		−	0.353100i
$637$		−	8.34626e16i		−	1.24927i
$638$		−	5.39540e16i		−	0.800018i
$639$			4.47267e16i			0.656995i
$640$	1.19726e17			1.74224
$641$		−	1.07539e17i		−	1.55031i	−0.631771	−	0.775155i	$-0.717672\pi$
$641$		−	1.07539e17i		−	1.55031i	0.631771	−	0.775155i	$-0.282328\pi$
$642$	−2.03860e17			−2.91154
$643$		−	3.31628e16i		−	0.469230i	−0.972088	−	0.234615i	$-0.924617\pi$
$643$		−	3.31628e16i		−	0.469230i	0.972088	−	0.234615i	$-0.0753829\pi$
$644$	3.25794e15			0.0456696
$645$	−2.40455e17			−3.33945
$646$	−7.61585e16			−1.04791
$647$			1.23802e17i			1.68773i	0.536557	+	0.843864i	$0.319725\pi$
$647$			1.23802e17i			1.68773i	−0.536557	+	0.843864i	$0.680275\pi$
$648$		−	4.45548e16i		−	0.601789i
$649$	2.24083e16			0.299875
$650$	−3.52474e17			−4.67355
$651$	2.58221e16			0.339239
$652$			1.53356e17i			1.99625i
$653$			7.72401e16i			0.996239i	0.867108	+	0.498120i	$0.165976\pi$
$653$			7.72401e16i			0.996239i	−0.867108	+	0.498120i	$0.834024\pi$
$654$		−	1.60562e17i		−	2.05199i
$655$			1.49810e17i			1.89712i
$656$	2.42604e16			0.304421
$657$		−	3.04799e16i		−	0.378985i
$658$	3.09936e16			0.381871
$659$	2.83383e16			0.345988			0.172994	−	0.984923i	$-0.444656\pi$
$659$	2.83383e16			0.345988			0.172994	+	0.984923i	$0.444656\pi$
$660$			9.44136e16i			1.14228i
$661$		−	2.28913e16i		−	0.274449i	−0.990540	−	0.137225i	$-0.956182\pi$
$661$		−	2.28913e16i		−	0.274449i	0.990540	−	0.137225i	$-0.0438182\pi$
$662$	2.21384e17			2.63026
$663$			7.44808e16i			0.876927i
$664$	3.71883e16	+	2.13863e16i	0.433908	+	0.249533i
$665$	3.51437e16			0.406367
$666$			2.99321e16i			0.342998i
$667$	2.65841e16			0.301903
$668$	−5.96707e16			−0.671587
$669$			7.39020e16i			0.824327i
$670$			3.09983e17i			3.42681i
$671$	8.92423e15			0.0977768
$672$			2.75204e16i			0.298840i
$673$	−6.87186e16			−0.739577			−0.369789	−	0.929116i	$-0.620570\pi$
$673$	−6.87186e16			−0.739577			−0.369789	+	0.929116i	$0.620570\pi$
$674$	−2.07897e16			−0.221762
$675$	8.31907e16			0.879533
$676$	8.26291e16			0.865870
$677$			1.57269e17i			1.63347i	0.577010	+	0.816737i	$0.304219\pi$
$677$			1.57269e17i			1.63347i	−0.577010	+	0.816737i	$0.695781\pi$
$678$			2.01978e17i			2.07935i
$679$			2.05332e16i			0.209526i
$680$	−4.73744e16			−0.479171
$681$	9.48429e16			0.950873
$682$			8.46530e16i			0.841272i
$683$			3.81235e16i			0.375550i	0.982212	+	0.187775i	$0.0601276\pi$
$683$			3.81235e16i			0.375550i	−0.982212	+	0.187775i	$0.939872\pi$
$684$			1.28942e17i			1.25909i
$685$	−9.60701e15			−0.0929919
$686$			5.25005e16i			0.503754i
$687$	−1.49105e17			−1.41825
$688$		−	8.28911e16i		−	0.781587i
$689$	−2.78888e16			−0.260684
$690$	−8.15474e16			−0.755641
$691$	2.12770e17			1.95453			0.977265	−	0.212021i	$-0.0680045\pi$
$691$	2.12770e17			1.95453			0.977265	+	0.212021i	$0.0680045\pi$
$692$	3.79841e16			0.345912
$693$	−4.75283e15			−0.0429095
$694$	1.92124e17			1.71959
$695$	2.43969e17			2.16484
$696$		−	1.09634e17i		−	0.964469i
$697$	−3.21907e16			−0.280759
$698$			3.06830e15i			0.0265317i
$699$		−	1.91986e17i		−	1.64591i
$700$	6.23409e16			0.529889
$701$	1.65539e16			0.139506			0.0697529	−	0.997564i	$-0.477779\pi$
$701$	1.65539e16			0.139506			0.0697529	+	0.997564i	$0.477779\pi$
$702$	−8.66218e16			−0.723776
$703$			4.98378e16i			0.412883i
$704$	−6.57134e16			−0.539781
$705$	−4.42550e17			−3.60436
$706$		−	1.92261e17i		−	1.55261i
$707$			2.41519e16i			0.193391i
$708$	1.84331e17			1.46352
$709$		−	1.28444e17i		−	1.01120i	−0.862768	−	0.505600i	$-0.831271\pi$
$709$		−	1.28444e17i		−	1.01120i	0.862768	−	0.505600i	$-0.168729\pi$
$710$			3.28748e17i			2.56633i
$711$			7.37392e16i			0.570796i
$712$	5.01910e16			0.385253
$713$	−4.17100e16			−0.317471
$714$		−	2.30924e16i		−	0.174293i
$715$	1.12674e17			0.843312
$716$		−	1.48160e17i		−	1.09965i
$717$			1.38532e17i			1.01962i
$718$		−	2.12428e16i		−	0.155048i
$719$		−	1.23505e17i		−	0.893947i	−0.894547	−	0.446973i	$-0.852502\pi$
$719$		−	1.23505e17i		−	0.893947i	0.894547	−	0.446973i	$-0.147498\pi$
$720$		−	1.03894e17i		−	0.745753i
$721$		−	9.20819e15i		−	0.0655485i
$722$			1.60218e17i			1.13107i
$723$	3.54734e17			2.48355
$724$		−	2.94196e16i		−	0.204270i
$725$	5.08689e17			3.50287
$726$			2.55609e17i			1.74565i
$727$	1.25476e17			0.849873			0.424936	−	0.905223i	$-0.360296\pi$
$727$	1.25476e17			0.849873			0.424936	+	0.905223i	$0.360296\pi$
$728$	−1.60345e16			−0.107713
$729$	−5.70329e16			−0.379980
$730$		−	2.24032e17i		−	1.48038i
$731$			1.09987e17i			0.720835i
$732$	7.34111e16			0.477194
$733$	−8.19737e16			−0.528507			−0.264253	−	0.964453i	$-0.585126\pi$
$733$	−8.19737e16			−0.528507			−0.264253	+	0.964453i	$0.585126\pi$
$734$	−6.60744e16			−0.422529
$735$		−	3.69492e17i		−	2.34359i
$736$		−	4.44533e16i		−	0.279664i
$737$		−	6.98015e16i		−	0.435572i
$738$			9.55394e16i			0.591350i
$739$	1.25313e17			0.769358			0.384679	−	0.923050i	$-0.374312\pi$
$739$	1.25313e17			0.769358			0.384679	+	0.923050i	$0.374312\pi$
$740$			1.25503e17i			0.764302i
$741$	3.68060e17			2.22336
$742$	8.64677e15			0.0518120
$743$		−	1.67091e17i		−	0.993163i	−0.867990	−	0.496582i	$-0.834588\pi$
$743$		−	1.67091e17i		−	0.993163i	0.867990	−	0.496582i	$-0.165412\pi$
$744$			1.72013e17i			1.01420i
$745$	2.93638e17			1.71741
$746$		−	5.12511e17i		−	2.97352i
$747$	6.22322e16	−	1.08214e17i	0.358172	−	0.622818i
$748$	4.31859e16			0.246565
$749$		−	4.30298e16i		−	0.243713i
$750$	−9.05640e17			−5.08848
$751$	2.05326e16			0.114447			0.0572236	−	0.998361i	$-0.481775\pi$
$751$	2.05326e16			0.114447			0.0572236	+	0.998361i	$0.481775\pi$
$752$		−	1.52559e17i		−	0.843587i
$753$			2.01201e17i			1.10372i
$754$	−5.29669e17			−2.88255
$755$		−	2.69390e16i		−	0.145445i
$756$	1.53205e16			0.0820621
$757$	8.50887e16			0.452165			0.226082	−	0.974108i	$-0.427408\pi$
$757$	8.50887e16			0.452165			0.226082	+	0.974108i	$0.427408\pi$
$758$	3.98186e17			2.09928
$759$	1.83627e16			0.0960476
$760$			2.34109e17i			1.21489i
$761$			1.88570e17i			0.970877i	0.874271	+	0.485438i	$0.161340\pi$
$761$			1.88570e17i			0.970877i	−0.874271	+	0.485438i	$0.838660\pi$
$762$			2.53070e17i			1.29274i
$763$	3.38905e16			0.171764
$764$	−3.21999e16			−0.161918
$765$			1.37855e17i			0.687787i
$766$		−	1.28272e17i		−	0.634981i
$767$		−	2.19983e17i		−	1.08048i
$768$	1.82705e16			0.0890397
$769$		−	1.10450e17i		−	0.534081i	−0.963685	−	0.267040i	$-0.913954\pi$
$769$		−	1.10450e17i		−	0.534081i	0.963685	−	0.267040i	$-0.0860457\pi$
$770$	−3.49340e16			−0.167612
$771$			1.21768e17i			0.579706i
$772$	−2.16487e17			−1.02265
$773$	−2.62004e17			−1.22809			−0.614046	−	0.789270i	$-0.710459\pi$
$773$	−2.62004e17			−1.22809			−0.614046	+	0.789270i	$0.710459\pi$
$774$	3.26432e17			1.51826
$775$	−7.98125e17			−3.68350
$776$	−1.36781e17			−0.626407
$777$	−1.51115e16			−0.0686724
$778$	−2.35802e17			−1.06333
$779$			1.59076e17i			0.711836i
$780$	9.26863e17			4.11574
$781$		−	7.40270e16i		−	0.326200i
$782$			3.73007e16i			0.163108i
$783$	1.25012e17			0.542478
$784$	1.27374e17			0.548509
$785$	−3.17718e17			−1.35776
$786$		−	4.86448e17i		−	2.06301i
$787$	2.09712e16			0.0882623			0.0441312	−	0.999026i	$-0.485948\pi$
$787$	2.09712e16			0.0882623			0.0441312	+	0.999026i	$0.485948\pi$
$788$	−3.85447e17			−1.60993
$789$		−	4.72797e17i		−	1.95980i
$790$			5.41994e17i			2.22962i
$791$	−4.26325e16			−0.174053
$792$		−	3.16609e16i		−	0.128284i
$793$		−	8.76096e16i		−	0.352300i
$794$		−	4.46894e17i		−	1.78353i
$795$	−1.23465e17			−0.489036
$796$	−3.49742e17			−1.37490
$797$			3.63154e17i			1.41691i	0.705758	+	0.708453i	$0.250606\pi$
$797$			3.63154e17i			1.41691i	−0.705758	+	0.708453i	$0.749394\pi$
$798$	−1.14115e17			−0.441901
$799$			2.02427e17i			0.778016i
$800$		−	8.50617e17i		−	3.24485i
$801$		−	1.46051e17i		−	0.552980i
$802$			1.90803e17i			0.717033i
$803$			5.04472e16i			0.188167i
$804$		−	5.74190e17i		−	2.12579i
$805$		−	1.72126e16i		−	0.0632516i
$806$	8.31042e17			3.03119
$807$			6.53481e17i			2.36588i
$808$	−1.60888e17			−0.578168
$809$			4.76768e17i			1.70066i	0.526254	+	0.850328i	$0.323596\pi$
$809$			4.76768e17i			1.70066i	−0.526254	+	0.850328i	$0.676404\pi$
$810$	−9.52948e17			−3.37411
$811$	−2.43827e17			−0.856952			−0.428476	−	0.903553i	$-0.640949\pi$
$811$	−2.43827e17			−0.856952			−0.428476	+	0.903553i	$0.640949\pi$
$812$	9.36808e16			0.326825
$813$			7.34765e17i			2.54452i
$814$		−	4.95404e16i		−	0.170299i
$815$	8.10224e17			2.76477
$816$	−1.13666e17			−0.385027
$817$	5.43519e17			1.82761
$818$		−	8.08551e17i		−	2.69890i
$819$			4.66588e16i			0.154607i
$820$			4.00591e17i			1.31770i
$821$		−	1.09326e17i		−	0.356996i	−0.983940	−	0.178498i	$-0.942876\pi$
$821$		−	1.09326e17i		−	0.356996i	0.983940	−	0.178498i	$-0.0571238\pi$
$822$	3.11949e16			0.101124
$823$			5.93190e17i			1.90895i	0.298291	+	0.954475i	$0.403583\pi$
$823$			5.93190e17i			1.90895i	−0.298291	+	0.954475i	$0.596417\pi$
$824$	6.13401e16			0.195966
$825$	3.51372e17			1.11441
$826$			6.82044e16i			0.214750i
$827$		−	2.32256e17i		−	0.725994i	−0.931790	−	0.362997i	$-0.881753\pi$
$827$		−	2.32256e17i		−	0.725994i	0.931790	−	0.362997i	$-0.118247\pi$
$828$	6.31527e16			0.195979
$829$			2.49554e17i			0.768842i	0.923158	+	0.384421i	$0.125599\pi$
$829$			2.49554e17i			0.768842i	−0.923158	+	0.384421i	$0.874401\pi$
$830$	4.57415e17	−	7.95392e17i	1.39908	−	2.43283i
$831$	1.02467e17			0.311155
$832$			6.45111e17i			1.94489i
$833$	−1.69010e17			−0.505874
$834$	−7.92191e17			−2.35415
$835$			3.15257e17i			0.930134i
$836$		−	2.13411e17i		−	0.625142i
$837$	−1.96142e17			−0.570451
$838$			6.43011e17i			1.85675i
$839$	−3.94621e17			−1.13138			−0.565690	−	0.824618i	$-0.691390\pi$
$839$	−3.94621e17			−1.13138			−0.565690	+	0.824618i	$0.691390\pi$
$840$	−7.09853e16			−0.202066
$841$	4.10601e17			1.16050
$842$	−5.89473e17			−1.65421
$843$		−	1.13253e16i		−	0.0315561i
$844$		−	4.22912e17i		−	1.17002i
$845$		−	4.36553e17i		−	1.19921i
$846$	6.00789e17			1.63870
$847$	−5.39527e16			−0.146121
$848$		−	4.25616e16i		−	0.114457i
$849$			7.92031e15i			0.0211493i
$850$			7.13752e17i			1.89249i
$851$	2.44094e16			0.0642658
$852$		−	6.08949e17i		−	1.59200i
$853$	−1.32333e17			−0.343538			−0.171769	−	0.985137i	$-0.554948\pi$
$853$	−1.32333e17			−0.343538			−0.171769	+	0.985137i	$0.554948\pi$
$854$			2.71629e16i			0.0700210i
$855$	6.81235e17			1.74382
$856$	2.86642e17			0.728613
$857$	3.37575e17			0.852089			0.426045	−	0.904702i	$-0.359907\pi$
$857$	3.37575e17			0.852089			0.426045	+	0.904702i	$0.359907\pi$
$858$	−3.65864e17			−0.917056
$859$	−7.73248e16			−0.192469			−0.0962343	−	0.995359i	$-0.530680\pi$
$859$	−7.73248e16			−0.192469			−0.0962343	+	0.995359i	$0.530680\pi$
$860$	1.36871e18			3.38315
$861$	−4.82341e16			−0.118396
$862$		−	6.14004e17i		−	1.49668i
$863$	−4.36044e17			−1.05552			−0.527759	−	0.849394i	$-0.676967\pi$
$863$	−4.36044e17			−1.05552			−0.527759	+	0.849394i	$0.676967\pi$
$864$		−	2.09042e17i		−	0.502518i
$865$		−	2.00681e17i		−	0.479081i
$866$	−3.11391e16			−0.0738242
$867$	−4.05959e17			−0.955802
$868$	−1.46984e17			−0.343678
$869$		−	1.22045e17i		−	0.283402i
$870$	−2.34487e18			−5.40758
$871$	−6.85245e17			−1.56941
$872$			2.25761e17i			0.513511i
$873$			3.98021e17i			0.899125i
$874$	1.84328e17			0.413545
$875$		−	1.91158e17i		−	0.425935i
$876$			4.14980e17i			0.918339i
$877$		−	2.93086e17i		−	0.644166i	−0.946712	−	0.322083i	$-0.895617\pi$
$877$		−	2.93086e17i		−	0.644166i	0.946712	−	0.322083i	$-0.104383\pi$
$878$	−8.17292e17			−1.78406
$879$	−1.08650e18			−2.35557
$880$			1.71954e17i			0.370268i
$881$	3.52923e17			0.754787			0.377393	−	0.926053i	$-0.376820\pi$
$881$	3.52923e17			0.754787			0.377393	+	0.926053i	$0.376820\pi$
$882$			5.01609e17i			1.06550i
$883$		−	3.03617e17i		−	0.640563i	−0.947322	−	0.320281i	$-0.896223\pi$
$883$		−	3.03617e17i		−	0.640563i	0.947322	−	0.320281i	$-0.103777\pi$
$884$		−	4.23957e17i		−	0.888400i
$885$		−	9.73874e17i		−	2.02695i
$886$			1.04256e18i			2.15525i
$887$			1.15035e17i			0.236204i	0.993001	+	0.118102i	$0.0376810\pi$
$887$			1.15035e17i			0.236204i	−0.993001	+	0.118102i	$0.962319\pi$
$888$		−	1.00665e17i		−	0.205306i
$889$	−5.34167e16			−0.108210
$890$		−	1.07350e18i		−	2.16003i
$891$	2.14583e17			0.428874
$892$		−	4.20662e17i		−	0.835112i
$893$	1.00033e18			1.97258
$894$	−9.53471e17			−1.86759
$895$	−7.82773e17			−1.52299
$896$		−	8.20578e16i		−	0.158589i
$897$		−	1.80268e17i		−	0.346069i
$898$	3.78547e17			0.721875
$899$	−1.19936e18			−2.27191
$900$	1.20843e18			2.27388
$901$			5.64743e16i			0.105561i
$902$		−	1.58127e17i		−	0.293607i
$903$			1.64803e17i			0.303975i
$904$		−	2.83996e17i		−	0.520357i
$905$	−1.55432e17			−0.282910
$906$			8.74734e16i			0.158164i
$907$	8.50152e17			1.52705			0.763524	−	0.645779i	$-0.223467\pi$
$907$	8.50152e17			1.52705			0.763524	+	0.645779i	$0.223467\pi$
$908$	−5.39862e17			−0.963314
$909$			4.68167e17i			0.829885i
$910$			3.42949e17i			0.603922i
$911$	−8.63068e17			−1.50985			−0.754927	−	0.655809i	$-0.772328\pi$
$911$	−8.63068e17			−1.50985			−0.754927	+	0.655809i	$0.772328\pi$
$912$			5.61703e17i			0.976198i
$913$	−1.03000e17	+	1.79105e17i	−0.177833	+	0.309231i
$914$	1.20745e17			0.207106
$915$		−	3.87852e17i		−	0.660905i
$916$	8.48731e17			1.43680
$917$	1.02677e17			0.172686
$918$			1.75407e17i			0.293083i
$919$			2.02852e17i			0.336733i	0.985724	+	0.168367i	$0.0538492\pi$
$919$			2.02852e17i			0.336733i	−0.985724	+	0.168367i	$0.946151\pi$
$920$	1.14661e17			0.189099
$921$		−	9.77936e17i		−	1.60233i
$922$	−7.44139e17			−1.21135
$923$	−7.26726e17			−1.17533
$924$	6.47092e16			0.103976
$925$	4.67076e17			0.745654
$926$		−	1.76588e18i		−	2.80089i
$927$		−	1.78494e17i		−	0.281284i
$928$		−	1.27824e18i		−	2.00135i
$929$	9.72053e17			1.51215			0.756076	−	0.654484i	$-0.227114\pi$
$929$	9.72053e17			1.51215			0.756076	+	0.654484i	$0.227114\pi$
$930$	3.67906e18			5.68642
$931$			8.35193e17i			1.28259i
$932$			1.09282e18i			1.66745i
$933$		−	3.88941e17i		−	0.589649i
$934$	−8.57285e17			−1.29135
$935$		−	2.28163e17i		−	0.341488i
$936$	−3.10816e17			−0.462220
$937$			1.16650e18i			1.72364i	0.507212	+	0.861822i	$0.330676\pi$
$937$			1.16650e18i			1.72364i	−0.507212	+	0.861822i	$0.669324\pi$
$938$	2.12456e17			0.311927
$939$	−9.94190e17			−1.45036
$940$	2.51907e18			3.65152
$941$	−4.33278e17			−0.624064			−0.312032	−	0.950072i	$-0.601010\pi$
$941$	−4.33278e17			−0.624064			−0.312032	+	0.950072i	$0.601010\pi$
$942$	1.03166e18			1.47649
$943$	7.79118e16			0.110798
$944$	3.35720e17			0.474400
$945$		−	8.09426e16i		−	0.113654i
$946$	−5.40276e17			−0.753822
$947$		−	4.53340e17i		−	0.628528i	−0.949336	−	0.314264i	$-0.898242\pi$
$947$		−	4.53340e17i		−	0.628528i	0.949336	−	0.314264i	$-0.101758\pi$
$948$		−	1.00395e18i		−	1.38313i
$949$	4.95242e17			0.677985
$950$	3.52713e18			4.79822
$951$	1.26256e18			1.70674
$952$			3.24695e16i			0.0436168i
$953$	−5.82554e17			−0.777640			−0.388820	−	0.921314i	$-0.627117\pi$
$953$	−5.82554e17			−0.777640			−0.388820	+	0.921314i	$0.627117\pi$
$954$	1.67611e17			0.222338
$955$			1.70121e17i			0.224253i
$956$		−	7.88550e17i		−	1.03296i
$957$	5.28013e17			0.687343
$958$		−	3.38083e16i		−	0.0437352i
$959$			6.58445e15i			0.00846463i
$960$			2.85593e18i			3.64855i
$961$	1.09411e18			1.38906
$962$	−4.86340e17			−0.613606
$963$		−	8.34100e17i		−	1.04583i
$964$	−2.01921e18			−2.51605
$965$			1.14376e18i			1.41636i
$966$			5.58910e16i			0.0687826i
$967$		−	5.99152e17i		−	0.732787i	−0.930460	−	0.366394i	$-0.880592\pi$
$967$		−	5.99152e17i		−	0.732787i	0.930460	−	0.366394i	$-0.119408\pi$
$968$		−	3.59405e17i		−	0.436849i
$969$		−	7.45314e17i		−	0.900320i
$970$			2.92551e18i			3.51213i
$971$		−	1.52609e18i		−	1.82082i	−0.413712	−	0.910408i	$-0.635768\pi$
$971$		−	1.52609e18i		−	1.82082i	0.413712	−	0.910408i	$-0.364232\pi$
$972$	1.35182e18			1.60296
$973$		−	1.67212e17i		−	0.197056i
$974$	−9.22815e16			−0.108084
$975$		−	3.44944e18i		−	4.01532i
$976$	1.33703e17			0.154682
$977$	−1.29241e18			−1.48605			−0.743023	−	0.669266i	$-0.766609\pi$
$977$	−1.29241e18			−1.48605			−0.743023	+	0.669266i	$0.766609\pi$
$978$	−2.63087e18			−3.00654
$979$			2.41728e17i			0.274556i
$980$			2.10321e18i			2.37425i
$981$	6.56943e17			0.737078
$982$	1.33415e18			1.48777
$983$	−1.74812e17			−0.193753			−0.0968767	−	0.995296i	$-0.530885\pi$
$983$	−1.74812e17			−0.193753			−0.0968767	+	0.995296i	$0.530885\pi$
$984$		−	3.21311e17i		−	0.353960i
$985$			2.03643e18i			2.22973i
$986$			1.07257e18i			1.16725i
$987$			3.03315e17i			0.328088i
$988$	−2.09506e18			−2.25245
$989$		−	2.66203e17i		−	0.284470i
$990$	−6.77170e17			−0.719261
$991$	3.74945e16			0.0395845			0.0197923	−	0.999804i	$-0.493700\pi$
$991$	3.74945e16			0.0395845			0.0197923	+	0.999804i	$0.493700\pi$
$992$			2.00553e18i			2.10455i
$993$			2.16655e18i			2.25982i
$994$	2.25317e17			0.233602
$995$			1.84779e18i			1.90420i
$996$	−8.47283e17	+	1.47332e18i	−0.867905	+	1.50918i
$997$	1.14852e18			1.16941			0.584705	−	0.811246i	$-0.301210\pi$
$997$	1.14852e18			1.16941			0.584705	+	0.811246i	$0.301210\pi$
$998$		−	2.51752e18i		−	2.54795i
$999$	1.14786e17			0.115477

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	83.13.b.c.82.12	✓	80
83.82	odd	2	inner	83.13.b.c.82.69	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
83.13.b.c.82.12	✓	80	1.1	even	1	trivial
83.13.b.c.82.69	yes	80	83.82	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 83 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	83.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-97.6509i q^{2} +955.647 q^{3} -5439.71 q^{4} +28739.5i q^{5} -93319.9i q^{6} +19697.5 q^{7} +131214. i q^{8} +381821. q^{9} +O(q^{10})\)	\(q-97.6509i q^{2} +955.647 q^{3} -5439.71 q^{4} +28739.5i q^{5} -93319.9i q^{6} +19697.5 q^{7} +131214. i q^{8} +381821. q^{9} +2.80644e6 q^{10} -631949. q^{11} -5.19844e6 q^{12} +6.20388e6i q^{13} -1.92348e6i q^{14} +2.74648e7i q^{15} -9.46784e6 q^{16} +1.25627e7 q^{17} -3.72852e7i q^{18} -6.20809e7i q^{19} -1.56334e8i q^{20} +1.88238e7 q^{21} +6.17105e7i q^{22} -3.04058e7 q^{23} +1.25395e8i q^{24} -5.81818e8 q^{25} +6.05814e8 q^{26} -1.42984e8 q^{27} -1.07148e8 q^{28} -8.74309e8 q^{29} +2.68197e9 q^{30} +1.37178e9 q^{31} +1.46200e9i q^{32} -6.03921e8 q^{33} -1.22676e9i q^{34} +5.66095e8i q^{35} -2.07699e9 q^{36} -8.02787e8 q^{37} -6.06226e9 q^{38} +5.92872e9i q^{39} -3.77103e9 q^{40} -2.56240e9 q^{41} -1.83817e9i q^{42} +8.75501e9i q^{43} +3.43762e9 q^{44} +1.09733e10i q^{45} +2.96916e9i q^{46} +1.61133e10i q^{47} -9.04792e9 q^{48} -1.34533e10 q^{49} +5.68151e10i q^{50} +1.20055e10 q^{51} -3.37473e10i q^{52} +4.49539e9i q^{53} +1.39625e10i q^{54} -1.81619e10i q^{55} +2.58459e9i q^{56} -5.93275e10i q^{57} +8.53771e10i q^{58} -3.54589e10 q^{59} -1.49401e11i q^{60} -1.41218e10 q^{61} -1.33955e11i q^{62} +7.52091e9 q^{63} +1.03985e11 q^{64} -1.78296e11 q^{65} +5.89734e10i q^{66} +1.10454e11i q^{67} -6.83375e10 q^{68} -2.90573e10 q^{69} +5.52797e10 q^{70} +1.17141e11i q^{71} +5.01004e10i q^{72} -7.98278e10i q^{73} +7.83929e10i q^{74} -5.56013e11 q^{75} +3.37702e11i q^{76} -1.24478e10 q^{77} +5.78945e11 q^{78} +1.93125e11i q^{79} -2.72101e11i q^{80} -3.39558e11 q^{81} +2.50221e11i q^{82} +(1.62988e11 - 2.83417e11i) q^{83} -1.02396e11 q^{84} +3.61046e11i q^{85} +8.54935e11 q^{86} -8.35531e11 q^{87} -8.29208e10i q^{88} -3.82512e11i q^{89} +1.07156e12 q^{90} +1.22201e11i q^{91} +1.65399e11 q^{92} +1.31094e12 q^{93} +1.57348e12 q^{94} +1.78417e12 q^{95} +1.39715e12i q^{96} +1.04243e12i q^{97} +1.31373e12i q^{98} -2.41292e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 918 q^{3} - 181150 q^{4} + 103918 q^{7} + 14902142 q^{9}+O(q^{10}) \) 80 * q + 918 * q^3 - 181150 * q^4 + 103918 * q^7 + 14902142 * q^9	\( 80 q + 918 q^{3} - 181150 q^{4} + 103918 q^{7} + 14902142 q^{9} + 1177482 q^{10} + 510406 q^{11} - 9260402 q^{12} + 203791850 q^{16} + 5571718 q^{17} + 46565862 q^{21} + 804389464 q^{23} - 4263713272 q^{25} + 18061794 q^{26} - 2326165338 q^{27} - 204811652 q^{28} + 1486960270 q^{29} - 2621683648 q^{30} - 665743010 q^{31} + 135224502 q^{33} - 54936709824 q^{36} - 280627202 q^{37} + 6646145310 q^{38} - 7119722058 q^{40} + 51318109072 q^{41} - 11512674650 q^{44} + 85368259738 q^{48} + 148785395094 q^{49} - 100143389562 q^{51} - 63584241050 q^{59} - 29216180978 q^{61} - 332932206620 q^{63} - 323596534090 q^{64} + 362112989184 q^{65} - 86115426752 q^{68} + 272383417100 q^{69} + 105630718656 q^{70} + 785418808326 q^{75} - 663355117738 q^{77} + 1483841884620 q^{78} + 2430778545148 q^{81} + 837315119192 q^{83} - 3013574788354 q^{84} + 452180651958 q^{86} - 682263689498 q^{87} - 499714512022 q^{90} + 997428187414 q^{92} - 1487992716298 q^{93} + 3169817690580 q^{94} + 1542762610848 q^{95} + 2021347267420 q^{99}+O(q^{100}) \) 80 * q + 918 * q^3 - 181150 * q^4 + 103918 * q^7 + 14902142 * q^9 + 1177482 * q^10 + 510406 * q^11 - 9260402 * q^12 + 203791850 * q^16 + 5571718 * q^17 + 46565862 * q^21 + 804389464 * q^23 - 4263713272 * q^25 + 18061794 * q^26 - 2326165338 * q^27 - 204811652 * q^28 + 1486960270 * q^29 - 2621683648 * q^30 - 665743010 * q^31 + 135224502 * q^33 - 54936709824 * q^36 - 280627202 * q^37 + 6646145310 * q^38 - 7119722058 * q^40 + 51318109072 * q^41 - 11512674650 * q^44 + 85368259738 * q^48 + 148785395094 * q^49 - 100143389562 * q^51 - 63584241050 * q^59 - 29216180978 * q^61 - 332932206620 * q^63 - 323596534090 * q^64 + 362112989184 * q^65 - 86115426752 * q^68 + 272383417100 * q^69 + 105630718656 * q^70 + 785418808326 * q^75 - 663355117738 * q^77 + 1483841884620 * q^78 + 2430778545148 * q^81 + 837315119192 * q^83 - 3013574788354 * q^84 + 452180651958 * q^86 - 682263689498 * q^87 - 499714512022 * q^90 + 997428187414 * q^92 - 1487992716298 * q^93 + 3169817690580 * q^94 + 1542762610848 * q^95 + 2021347267420 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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