LMFDB - Embedded newform 83.13.b.c.82.14

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			82.14
Character	$\chi$	$=$	83.82
Dual form			83.13.b.c.82.67

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-91.3709i q^{2} -1031.91 q^{3} -4252.64 q^{4} +26144.5i q^{5} +94286.4i q^{6} +118004. q^{7} +14312.3i q^{8} +533393. q^{9} +O(q^{10})$	\(q-91.3709i q^{2} -1031.91 q^{3} -4252.64 q^{4} +26144.5i q^{5} +94286.4i q^{6} +118004. q^{7} +14312.3i q^{8} +533393. q^{9} +2.38885e6 q^{10} +3.09977e6 q^{11} +4.38833e6 q^{12} +8.03334e6i q^{13} -1.07822e7i q^{14} -2.69788e7i q^{15} -1.61111e7 q^{16} -2.54166e6 q^{17} -4.87366e7i q^{18} +3.16944e7i q^{19} -1.11183e8i q^{20} -1.21770e8 q^{21} -2.83229e8i q^{22} +1.46122e8 q^{23} -1.47689e7i q^{24} -4.39396e8 q^{25} +7.34013e8 q^{26} -2.01445e6 q^{27} -5.01830e8 q^{28} +9.31145e8 q^{29} -2.46507e9 q^{30} -9.08130e8 q^{31} +1.53071e9i q^{32} -3.19868e9 q^{33} +2.32234e8i q^{34} +3.08517e9i q^{35} -2.26833e9 q^{36} -3.76095e9 q^{37} +2.89594e9 q^{38} -8.28967e9i q^{39} -3.74188e8 q^{40} +7.25063e9 q^{41} +1.11262e10i q^{42} +3.78924e9i q^{43} -1.31822e10 q^{44} +1.39453e10i q^{45} -1.33513e10i q^{46} +3.02248e9i q^{47} +1.66252e10 q^{48} +8.37370e7 q^{49} +4.01480e10i q^{50} +2.62276e9 q^{51} -3.41629e10i q^{52} -3.03161e10i q^{53} +1.84062e8i q^{54} +8.10420e10i q^{55} +1.68891e9i q^{56} -3.27057e10i q^{57} -8.50795e10i q^{58} -1.39910e10 q^{59} +1.14731e11i q^{60} +2.94505e10 q^{61} +8.29767e10i q^{62} +6.29427e10 q^{63} +7.38711e10 q^{64} -2.10028e11 q^{65} +2.92266e11i q^{66} +1.57706e10i q^{67} +1.08088e10 q^{68} -1.50784e11 q^{69} +2.81895e11 q^{70} -9.81989e10i q^{71} +7.63407e9i q^{72} -2.92091e10i q^{73} +3.43641e11i q^{74} +4.53416e11 q^{75} -1.34785e11i q^{76} +3.65786e11 q^{77} -7.57434e11 q^{78} +2.75757e10i q^{79} -4.21217e11i q^{80} -2.81388e11 q^{81} -6.62497e11i q^{82} +(2.92090e11 - 1.46878e11i) q^{83} +5.17842e11 q^{84} -6.64504e10i q^{85} +3.46226e11 q^{86} -9.60856e11 q^{87} +4.43647e10i q^{88} +3.66610e11i q^{89} +1.27420e12 q^{90} +9.47969e11i q^{91} -6.21404e11 q^{92} +9.37107e11 q^{93} +2.76167e11 q^{94} -8.28635e11 q^{95} -1.57955e12i q^{96} -4.25118e11i q^{97} -7.65112e9i q^{98} +1.65340e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	91.3709i		−	1.42767i	−0.700314	−	0.713835i	$-0.746957\pi$
$2$		−	91.3709i		−	1.42767i	0.700314	−	0.713835i	$-0.253043\pi$
$3$	−1031.91			−1.41551			−0.707756	−	0.706457i	$-0.750292\pi$
$3$	−1031.91			−1.41551			−0.707756	+	0.706457i	$0.750292\pi$
$4$	−4252.64			−1.03824
$5$			26144.5i			1.67325i	0.547776	+	0.836625i	$0.315475\pi$
$5$			26144.5i			1.67325i	−0.547776	+	0.836625i	$0.684525\pi$
$6$			94286.4i			2.02088i
$7$	118004.			1.00302			0.501510	−	0.865152i	$-0.332778\pi$
$7$	118004.			1.00302			0.501510	+	0.865152i	$0.332778\pi$
$8$			14312.3i			0.0545970i
$9$	533393.			1.00367
$10$	2.38885e6			2.38885
$11$	3.09977e6			1.74974			0.874869	−	0.484359i	$-0.160947\pi$
$11$	3.09977e6			1.74974			0.874869	+	0.484359i	$0.160947\pi$
$12$	4.38833e6			1.46964
$13$			8.03334e6i			1.66432i	0.554538	+	0.832159i	$0.312895\pi$
$13$			8.03334e6i			1.66432i	−0.554538	+	0.832159i	$0.687105\pi$
$14$		−	1.07822e7i		−	1.43198i
$15$		−	2.69788e7i		−	2.36851i
$16$	−1.61111e7			−0.960296
$17$	−2.54166e6			−0.105299			−0.0526494	−	0.998613i	$-0.516767\pi$
$17$	−2.54166e6			−0.105299			−0.0526494	+	0.998613i	$0.516767\pi$
$18$		−	4.87366e7i		−	1.43291i
$19$			3.16944e7i			0.673691i	0.941560	+	0.336845i	$0.109360\pi$
$19$			3.16944e7i			0.673691i	−0.941560	+	0.336845i	$0.890640\pi$
$20$		−	1.11183e8i		−	1.73724i
$21$	−1.21770e8			−1.41979
$22$		−	2.83229e8i		−	2.49805i
$23$	1.46122e8			0.987071			0.493536	−	0.869726i	$-0.335704\pi$
$23$	1.46122e8			0.987071			0.493536	+	0.869726i	$0.335704\pi$
$24$		−	1.47689e7i		−	0.0772827i
$25$	−4.39396e8			−1.79977
$26$	7.34013e8			2.37610
$27$	−2.01445e6			−0.00519965
$28$	−5.01830e8			−1.04138
$29$	9.31145e8			1.56541			0.782707	−	0.622390i	$-0.213838\pi$
$29$	9.31145e8			1.56541			0.782707	+	0.622390i	$0.213838\pi$
$30$	−2.46507e9			−3.38144
$31$	−9.08130e8			−1.02324			−0.511620	−	0.859212i	$-0.670955\pi$
$31$	−9.08130e8			−1.02324			−0.511620	+	0.859212i	$0.670955\pi$
$32$			1.53071e9i			1.42558i
$33$	−3.19868e9			−2.47678
$34$			2.32234e8i			0.150332i
$35$			3.08517e9i			1.67830i
$36$	−2.26833e9			−1.04206
$37$	−3.76095e9			−1.46584			−0.732921	−	0.680314i	$-0.761843\pi$
$37$	−3.76095e9			−1.46584			−0.732921	+	0.680314i	$0.761843\pi$
$38$	2.89594e9			0.961808
$39$		−	8.28967e9i		−	2.35586i
$40$	−3.74188e8			−0.0913544
$41$	7.25063e9			1.52642			0.763208	−	0.646153i	$-0.223623\pi$
$41$	7.25063e9			1.52642			0.763208	+	0.646153i	$0.223623\pi$
$42$			1.11262e10i			2.02699i
$43$			3.78924e9i			0.599434i	0.954028	+	0.299717i	$0.0968922\pi$
$43$			3.78924e9i			0.599434i	−0.954028	+	0.299717i	$0.903108\pi$
$44$	−1.31822e10			−1.81665
$45$			1.39453e10i			1.67940i
$46$		−	1.33513e10i		−	1.40921i
$47$			3.02248e9i			0.280399i	0.990123	+	0.140200i	$0.0447744\pi$
$47$			3.02248e9i			0.280399i	−0.990123	+	0.140200i	$0.955226\pi$
$48$	1.66252e10			1.35931
$49$	8.37370e7			0.00604980
$50$			4.01480e10i			2.56947i
$51$	2.62276e9			0.149052
$52$		−	3.41629e10i		−	1.72796i
$53$		−	3.03161e10i		−	1.36779i	−0.729582	−	0.683893i	$-0.760286\pi$
$53$		−	3.03161e10i		−	1.36779i	0.729582	−	0.683893i	$-0.239714\pi$
$54$			1.84062e8i			0.00742339i
$55$			8.10420e10i			2.92775i
$56$			1.68891e9i			0.0547619i
$57$		−	3.27057e10i		−	0.953617i
$58$		−	8.50795e10i		−	2.23490i
$59$	−1.39910e10			−0.331694			−0.165847	−	0.986151i	$-0.553036\pi$
$59$	−1.39910e10			−0.331694			−0.165847	+	0.986151i	$0.553036\pi$
$60$			1.14731e11i			2.45908i
$61$	2.94505e10			0.571628			0.285814	−	0.958285i	$-0.407736\pi$
$61$	2.94505e10			0.571628			0.285814	+	0.958285i	$0.407736\pi$
$62$			8.29767e10i			1.46085i
$63$	6.29427e10			1.00670
$64$	7.38711e10			1.07497
$65$	−2.10028e11			−2.78482
$66$			2.92266e11i			3.53602i
$67$			1.57706e10i			0.174341i	0.996193	+	0.0871704i	$0.0277825\pi$
$67$			1.57706e10i			0.174341i	−0.996193	+	0.0871704i	$0.972218\pi$
$68$	1.08088e10			0.109326
$69$	−1.50784e11			−1.39721
$70$	2.81895e11			2.39606
$71$		−	9.81989e10i		−	0.766578i	−0.923628	−	0.383289i	$-0.874791\pi$
$71$		−	9.81989e10i		−	0.766578i	0.923628	−	0.383289i	$-0.125209\pi$
$72$			7.63407e9i			0.0547975i
$73$		−	2.92091e10i		−	0.193010i	−0.995332	−	0.0965052i	$-0.969234\pi$
$73$		−	2.92091e10i		−	0.193010i	0.995332	−	0.0965052i	$-0.0307664\pi$
$74$			3.43641e11i			2.09274i
$75$	4.53416e11			2.54759
$76$		−	1.34785e11i		−	0.699454i
$77$	3.65786e11			1.75502
$78$	−7.57434e11			−3.36339
$79$			2.75757e10i			0.113440i	0.998390	+	0.0567198i	$0.0180642\pi$
$79$			2.75757e10i			0.113440i	−0.998390	+	0.0567198i	$0.981936\pi$
$80$		−	4.21217e11i		−	1.60681i
$81$	−2.81388e11			−0.996313
$82$		−	6.62497e11i		−	2.17922i
$83$	2.92090e11	−	1.46878e11i	0.893406	−	0.449251i
$83$	2.92090e11	−	1.46878e11i	0.893406	−	0.449251i
$84$	5.17842e11			1.47408
$85$		−	6.64504e10i		−	0.176191i
$86$	3.46226e11			0.855793
$87$	−9.60856e11			−2.21586
$88$			4.43647e10i			0.0955304i
$89$			3.66610e11i			0.737674i	0.929494	+	0.368837i	$0.120244\pi$
$89$			3.66610e11i			0.737674i	−0.929494	+	0.368837i	$0.879756\pi$
$90$	1.27420e12			2.39762
$91$			9.47969e11i			1.66934i
$92$	−6.21404e11			−1.02482
$93$	9.37107e11			1.44841
$94$	2.76167e11			0.400317
$95$	−8.28635e11			−1.12725
$96$		−	1.57955e12i		−	2.01793i
$97$		−	4.25118e11i		−	0.510363i	−0.966893	−	0.255182i	$-0.917865\pi$
$97$		−	4.25118e11i		−	0.510363i	0.966893	−	0.255182i	$-0.0821353\pi$
$98$		−	7.65112e9i		−	0.00863711i
$99$	1.65340e12			1.75617
$100$	1.86859e12			1.86859
$101$		−	1.04225e12i		−	0.981849i	−0.871202	−	0.490925i	$-0.836659\pi$
$101$		−	1.04225e12i		−	0.981849i	0.871202	−	0.490925i	$-0.163341\pi$
$102$		−	2.39644e11i		−	0.212797i
$103$			1.96498e12i			1.64564i	0.568302	+	0.822820i	$0.307601\pi$
$103$			1.96498e12i			1.64564i	−0.568302	+	0.822820i	$0.692399\pi$
$104$	−1.14975e11			−0.0908667
$105$		−	3.18361e12i		−	2.37566i
$106$	−2.77001e12			−1.95275
$107$			2.78010e12i			1.85250i	0.376913	+	0.926249i	$0.376986\pi$
$107$			2.78010e12i			1.85250i	−0.376913	+	0.926249i	$0.623014\pi$
$108$	8.56673e9			0.00539850
$109$	1.49128e12			0.889201			0.444600	−	0.895729i	$-0.353346\pi$
$109$	1.49128e12			0.889201			0.444600	+	0.895729i	$0.353346\pi$
$110$	7.40488e12			4.17986
$111$	3.88095e12			2.07492
$112$	−1.90118e12			−0.963196
$113$	−1.64722e12			−0.791190			−0.395595	−	0.918425i	$-0.629462\pi$
$113$	−1.64722e12			−0.791190			−0.395595	+	0.918425i	$0.629462\pi$
$114$	−2.98835e12			−1.36145
$115$			3.82029e12i			1.65162i
$116$	−3.95982e12			−1.62528
$117$			4.28493e12i			1.67043i
$118$			1.27837e12i			0.473550i
$119$	−2.99927e11			−0.105617
$120$	3.86127e11			0.129313
$121$	6.47014e12			2.06159
$122$		−	2.69092e12i		−	0.816097i
$123$	−7.48199e12			−2.16066
$124$	3.86195e12			1.06237
$125$		−	5.10486e12i		−	1.33821i
$126$		−	5.75113e12i		−	1.43724i
$127$	4.46406e12			1.06392			0.531958	−	0.846771i	$-0.321456\pi$
$127$	4.46406e12			1.06392			0.531958	+	0.846771i	$0.321456\pi$
$128$		−	4.79889e11i		−	0.109114i
$129$		−	3.91014e12i		−	0.848505i
$130$			1.91904e13i			3.97580i
$131$	−2.39347e12			−0.473587			−0.236794	−	0.971560i	$-0.576096\pi$
$131$	−2.39347e12			−0.473587			−0.236794	+	0.971560i	$0.576096\pi$
$132$	1.36028e13			2.57149
$133$			3.74008e12i			0.675726i
$134$	1.44097e12			0.248901
$135$		−	5.26669e10i		−	0.00870032i
$136$		−	3.63769e10i		−	0.00574900i
$137$			3.77685e12i			0.571224i	0.958345	+	0.285612i	$0.0921969\pi$
$137$			3.77685e12i			0.571224i	−0.958345	+	0.285612i	$0.907803\pi$
$138$			1.37773e13i			1.99476i
$139$			2.38035e12i			0.330029i	0.986291	+	0.165014i	$0.0527670\pi$
$139$			2.38035e12i			0.330029i	−0.986291	+	0.165014i	$0.947233\pi$
$140$		−	1.31201e13i		−	1.74249i
$141$		−	3.11892e12i		−	0.396908i
$142$	−8.97252e12			−1.09442
$143$			2.49015e13i			2.91212i
$144$	−8.59354e12			−0.963823
$145$			2.43444e13i			2.61933i
$146$	−2.66886e12			−0.275555
$147$	−8.64088e10			−0.00856356
$148$	1.59940e13			1.52190
$149$			7.56888e12i			0.691694i	0.938291	+	0.345847i	$0.112408\pi$
$149$			7.56888e12i			0.691694i	−0.938291	+	0.345847i	$0.887592\pi$
$150$		−	4.14290e13i		−	3.63712i
$151$	−3.79579e12			−0.320214			−0.160107	−	0.987100i	$-0.551184\pi$
$151$	−3.79579e12			−0.320214			−0.160107	+	0.987100i	$0.551184\pi$
$152$	−4.53619e11			−0.0367815
$153$	−1.35570e12			−0.105686
$154$		−	3.34222e13i		−	2.50559i
$155$		−	2.37426e13i		−	1.71214i
$156$			3.52530e13i			2.44595i
$157$		−	6.24955e12i		−	0.417303i	−0.977990	−	0.208651i	$-0.933093\pi$
$157$		−	6.24955e12i		−	0.417303i	0.977990	−	0.208651i	$-0.0669074\pi$
$158$	2.51962e12			0.161954
$159$			3.12834e13i			1.93612i
$160$	−4.00196e13			−2.38536
$161$	1.72430e13			0.990053
$162$			2.57107e13i			1.42241i
$163$		−	2.19068e13i		−	1.16803i	−0.811743	−	0.584015i	$-0.801481\pi$
$163$		−	2.19068e13i		−	1.16803i	0.811743	−	0.584015i	$-0.198519\pi$
$164$	−3.08343e13			−1.58479
$165$		−	8.36279e13i		−	4.14427i
$166$	−1.34204e13	−	2.66886e13i	−0.641382	−	1.27549i
$167$	2.04056e13			0.940698			0.470349	−	0.882481i	$-0.344128\pi$
$167$	2.04056e13			0.940698			0.470349	+	0.882481i	$0.344128\pi$
$168$		−	1.74280e12i		−	0.0775161i
$169$	−4.12365e13			−1.76995
$170$	−6.07164e12			−0.251543
$171$			1.69056e13i			0.676166i
$172$		−	1.61143e13i		−	0.622357i
$173$	3.52156e13			1.31359			0.656794	−	0.754070i	$-0.271912\pi$
$173$	3.52156e13			1.31359			0.656794	+	0.754070i	$0.271912\pi$
$174$			8.77943e13i			3.16352i
$175$	−5.18506e13			−1.80520
$176$	−4.99406e13			−1.68027
$177$	1.44375e13			0.469517
$178$	3.34975e13			1.05316
$179$			6.15953e12i			0.187253i	0.995607	+	0.0936266i	$0.0298460\pi$
$179$			6.15953e12i			0.187253i	−0.995607	+	0.0936266i	$0.970154\pi$
$180$		−	5.93044e13i		−	1.74362i
$181$			4.30397e13i			1.22405i	0.790840	+	0.612023i	$0.209644\pi$
$181$			4.30397e13i			1.22405i	−0.790840	+	0.612023i	$0.790356\pi$
$182$	8.66168e13			2.38327
$183$	−3.03902e13			−0.809147
$184$			2.09134e12i			0.0538911i
$185$		−	9.83282e13i		−	2.45272i
$186$		−	8.56243e13i		−	2.06785i
$187$	−7.87855e12			−0.184245
$188$		−	1.28535e13i		−	0.291122i
$189$	−2.37714e11			−0.00521536
$190$			7.57131e13i			1.60935i
$191$	−4.24185e13			−0.873686			−0.436843	−	0.899538i	$-0.643904\pi$
$191$	−4.24185e13			−0.873686			−0.436843	+	0.899538i	$0.643904\pi$
$192$	−7.62282e13			−1.52163
$193$	−3.19719e13			−0.618621			−0.309311	−	0.950961i	$-0.600098\pi$
$193$	−3.19719e13			−0.618621			−0.309311	+	0.950961i	$0.600098\pi$
$194$	−3.88434e13			−0.728630
$195$	2.16730e14			3.94194
$196$	−3.56103e11			−0.00628115
$197$	−7.74444e13			−1.32493			−0.662465	−	0.749093i	$-0.730489\pi$
$197$	−7.74444e13			−1.32493			−0.662465	+	0.749093i	$0.730489\pi$
$198$		−	1.51072e14i		−	2.50723i
$199$	6.48260e13			1.04383			0.521916	−	0.852997i	$-0.325217\pi$
$199$	6.48260e13			1.04383			0.521916	+	0.852997i	$0.325217\pi$
$200$		−	6.28875e12i		−	0.0982618i
$201$		−	1.62738e13i		−	0.246781i
$202$	−9.52316e13			−1.40176
$203$	1.09879e14			1.57014
$204$	−1.11536e13			−0.154752
$205$			1.89564e14i			2.55407i
$206$	1.79542e14			2.34943
$207$	7.79405e13			0.990697
$208$		−	1.29426e14i		−	1.59824i
$209$			9.82453e13i			1.17878i
$210$	−2.90889e14			−3.39166
$211$		−	1.08830e14i		−	1.23325i	−0.787255	−	0.616627i	$-0.788499\pi$
$211$		−	1.08830e14i		−	1.23325i	0.787255	−	0.616627i	$-0.211501\pi$
$212$			1.28923e14i			1.42009i
$213$			1.01332e14i			1.08510i
$214$	2.54020e14			2.64476
$215$	−9.90678e13			−1.00300
$216$		−	2.88314e10i		−	0.000283885i
$217$	−1.07163e14			−1.02633
$218$		−	1.36259e14i		−	1.26949i
$219$			3.01411e13i			0.273209i
$220$		−	3.44642e14i		−	3.03971i
$221$		−	2.04180e13i		−	0.175251i
$222$		−	3.54606e14i		−	2.96229i
$223$			1.97750e14i			1.60800i	0.594627	+	0.804001i	$0.297300\pi$
$223$			1.97750e14i			1.60800i	−0.594627	+	0.804001i	$0.702700\pi$
$224$			1.80630e14i			1.42989i
$225$	−2.34371e14			−1.80638
$226$			1.50508e14i			1.12956i
$227$	−2.00468e14			−1.46517			−0.732587	−	0.680674i	$-0.761687\pi$
$227$	−2.00468e14			−1.46517			−0.732587	+	0.680674i	$0.761687\pi$
$228$			1.39086e14i			0.990086i
$229$	−1.90756e14			−1.32272			−0.661358	−	0.750071i	$-0.730019\pi$
$229$	−1.90756e14			−1.32272			−0.661358	+	0.750071i	$0.730019\pi$
$230$	3.49063e14			2.35796
$231$	−3.77458e14			−2.48426
$232$			1.33268e13i			0.0854669i
$233$			2.65991e14i			1.66239i	0.555983	+	0.831193i	$0.312342\pi$
$233$			2.65991e14i			1.66239i	−0.555983	+	0.831193i	$0.687658\pi$
$234$	3.91518e14			2.38482
$235$	−7.90214e13			−0.469178
$236$	5.94988e13			0.344379
$237$		−	2.84556e13i		−	0.160575i
$238$			2.74046e13i			0.150786i
$239$			2.89537e14i			1.55352i	0.629796	+	0.776760i	$0.283138\pi$
$239$			2.89537e14i			1.55352i	−0.629796	+	0.776760i	$0.716862\pi$
$240$			4.34657e14i			2.27446i
$241$	−3.32563e14			−1.69735			−0.848675	−	0.528915i	$-0.822599\pi$
$241$	−3.32563e14			−1.69735			−0.848675	+	0.528915i	$0.822599\pi$
$242$		−	5.91182e14i		−	2.94326i
$243$	2.91437e14			1.41549
$244$	−1.25242e14			−0.593489
$245$			2.18926e12i			0.0101228i
$246$			6.83636e14i			3.08471i
$247$	−2.54612e14			−1.12124
$248$		−	1.29974e13i		−	0.0558659i
$249$	−3.01410e14	+	1.51565e14i	−1.26463	+	0.635920i
$250$	−4.66435e14			−1.91052
$251$		−	3.09536e14i		−	1.23785i	−0.785449	−	0.618926i	$-0.787568\pi$
$251$		−	3.09536e14i		−	1.23785i	0.785449	−	0.618926i	$-0.212432\pi$
$252$	−2.67673e14			−1.04520
$253$	4.52944e14			1.72712
$254$		−	4.07885e14i		−	1.51892i
$255$			6.85707e13i			0.249401i
$256$	2.58728e14			0.919187
$257$		−	9.26173e13i		−	0.321435i	−0.987000	−	0.160718i	$-0.948619\pi$
$257$		−	9.26173e13i		−	0.321435i	0.987000	−	0.160718i	$-0.0513808\pi$
$258$	−3.57273e14			−1.21139
$259$	−4.43808e14			−1.47027
$260$	8.93173e14			2.89132
$261$	4.96666e14			1.57116
$262$			2.18693e14i			0.676126i
$263$			2.19905e14i			0.664507i	0.943190	+	0.332254i	$0.107809\pi$
$263$			2.19905e14i			0.664507i	−0.943190	+	0.332254i	$0.892191\pi$
$264$		−	4.57803e13i		−	0.135224i
$265$	7.92600e14			2.28865
$266$	3.41734e14			0.964713
$267$		−	3.78308e14i		−	1.04419i
$268$		−	6.70666e13i		−	0.181008i
$269$			4.29883e14i			1.13458i	0.823517	+	0.567292i	$0.192009\pi$
$269$			4.29883e14i			1.13458i	−0.823517	+	0.567292i	$0.807991\pi$
$270$	−4.81222e12			−0.0124212
$271$			8.12448e13i			0.205107i	0.994728	+	0.102553i	$0.0327012\pi$
$271$			8.12448e13i			0.205107i	−0.994728	+	0.102553i	$0.967299\pi$
$272$	4.09489e13			0.101118
$273$		−	9.78217e14i		−	2.36298i
$274$	3.45094e14			0.815520
$275$	−1.36203e15			−3.14912
$276$	6.41232e14			1.45064
$277$	2.80882e14			0.621792			0.310896	−	0.950444i	$-0.399371\pi$
$277$	2.80882e14			0.621792			0.310896	+	0.950444i	$0.399371\pi$
$278$	2.17494e14			0.471172
$279$	−4.84390e14			−1.02700
$280$	−4.41558e13			−0.0916303
$281$		−	7.21853e14i		−	1.46626i	−0.680089	−	0.733130i	$-0.738059\pi$
$281$		−	7.21853e14i		−	1.46626i	0.680089	−	0.733130i	$-0.261941\pi$
$282$	−2.84979e14			−0.566654
$283$		−	4.00256e14i		−	0.779147i	−0.920995	−	0.389574i	$-0.872622\pi$
$283$		−	4.00256e14i		−	0.779147i	0.920995	−	0.389574i	$-0.127378\pi$
$284$			4.17605e14i			0.795894i
$285$	8.55075e14			1.59564
$286$	2.27527e15			4.15755
$287$	8.55606e14			1.53103
$288$			8.16469e14i			1.43082i
$289$	−5.76162e14			−0.988912
$290$	2.22437e15			3.73954
$291$			4.38683e14i			0.722425i
$292$			1.24216e14i			0.200392i
$293$	1.93786e14			0.306279			0.153140	−	0.988205i	$-0.451062\pi$
$293$	1.93786e14			0.306279			0.153140	+	0.988205i	$0.451062\pi$
$294$			7.89525e12i			0.0122259i
$295$		−	3.65789e14i		−	0.555007i
$296$		−	5.38277e13i		−	0.0800305i
$297$	−6.24433e12			−0.00909803
$298$	6.91575e14			0.987510
$299$			1.17385e15i			1.64280i
$300$	−1.92822e15			−2.64501
$301$			4.47146e14i			0.601244i
$302$			3.46825e14i			0.457160i
$303$			1.07551e15i			1.38982i
$304$		−	5.10631e14i		−	0.646942i
$305$			7.69970e14i			0.956477i
$306$			1.23872e14i			0.150884i
$307$			6.66731e14i			0.796381i	0.917303	+	0.398190i	$0.130362\pi$
$307$			6.66731e14i			0.796381i	−0.917303	+	0.398190i	$0.869638\pi$
$308$	−1.55556e15			−1.82214
$309$		−	2.02768e15i		−	2.32942i
$310$	−2.16939e15			−2.44437
$311$		−	1.45066e15i		−	1.60325i	−0.597825	−	0.801626i	$-0.703968\pi$
$311$		−	1.45066e15i		−	1.60325i	0.597825	−	0.801626i	$-0.296032\pi$
$312$	1.18644e14			0.128623
$313$	−4.08282e14			−0.434204			−0.217102	−	0.976149i	$-0.569660\pi$
$313$	−4.08282e14			−0.434204			−0.217102	+	0.976149i	$0.569660\pi$
$314$	−5.71027e14			−0.595771
$315$			1.64561e15i			1.68447i
$316$		−	1.17270e14i		−	0.117778i
$317$	5.89404e14			0.580842			0.290421	−	0.956899i	$-0.406205\pi$
$317$	5.89404e14			0.580842			0.290421	+	0.956899i	$0.406205\pi$
$318$	2.85839e15			2.76414
$319$	2.88633e15			2.73907
$320$			1.93132e15i			1.79869i
$321$		−	2.86881e15i		−	2.62223i
$322$		−	1.57551e15i		−	1.41347i
$323$		−	8.05563e13i		−	0.0709389i
$324$	1.19664e15			1.03441
$325$		−	3.52982e15i		−	2.99538i
$326$	−2.00165e15			−1.66756
$327$	−1.53886e15			−1.25867
$328$			1.03773e14i			0.0833377i
$329$			3.56666e14i			0.281246i
$330$	−7.64116e15			−5.91664
$331$		−	2.14761e14i		−	0.163300i	−0.996661	−	0.0816501i	$-0.973981\pi$
$331$		−	2.14761e14i		−	0.163300i	0.996661	−	0.0816501i	$-0.0260190\pi$
$332$	−1.24216e15	+	6.24620e14i	−0.927571	+	0.466431i
$333$	−2.00606e15			−1.47123
$334$		−	1.86448e15i		−	1.34301i
$335$	−4.12315e14			−0.291716
$336$	1.96184e15			1.36342
$337$		−	3.38716e14i		−	0.231237i	−0.993294	−	0.115618i	$-0.963115\pi$
$337$		−	3.38716e14i		−	0.231237i	0.993294	−	0.115618i	$-0.0368850\pi$
$338$			3.76781e15i			2.52691i
$339$	1.69978e15			1.11994
$340$			2.82590e14i			0.182929i
$341$	−2.81499e15			−1.79040
$342$	1.54468e15			0.965342
$343$	−1.62345e15			−0.996952
$344$	−5.42326e13			−0.0327273
$345$		−	3.94219e15i		−	2.33788i
$346$		−	3.21768e15i		−	1.87537i
$347$			6.60472e14i			0.378336i	0.981945	+	0.189168i	$0.0605791\pi$
$347$			6.60472e14i			0.378336i	−0.981945	+	0.189168i	$0.939421\pi$
$348$	4.08617e15			2.30060
$349$	1.32685e15			0.734290			0.367145	−	0.930164i	$-0.380335\pi$
$349$	1.32685e15			0.734290			0.367145	+	0.930164i	$0.380335\pi$
$350$			4.73764e15i			2.57723i
$351$		−	1.61828e13i		−	0.00865387i
$352$			4.74484e15i			2.49440i
$353$	−9.31626e14			−0.481497			−0.240748	−	0.970588i	$-0.577393\pi$
$353$	−9.31626e14			−0.481497			−0.240748	+	0.970588i	$0.577393\pi$
$354$		−	1.31916e15i		−	0.670315i
$355$	2.56736e15			1.28268
$356$		−	1.55906e15i		−	0.765884i
$357$	3.09497e14			0.149502
$358$	5.62802e14			0.267336
$359$	−2.57011e15			−1.20056			−0.600282	−	0.799788i	$-0.704945\pi$
$359$	−2.57011e15			−1.20056			−0.600282	+	0.799788i	$0.704945\pi$
$360$	−1.99589e14			−0.0916900
$361$	1.20878e15			0.546140
$362$	3.93257e15			1.74753
$363$	−6.67659e15			−2.91820
$364$		−	4.03137e15i		−	1.73318i
$365$	7.63658e14			0.322955
$366$			2.77678e15i			1.15519i
$367$			1.95177e15i			0.798789i	0.916779	+	0.399395i	$0.130780\pi$
$367$			1.95177e15i			0.798789i	−0.916779	+	0.399395i	$0.869220\pi$
$368$	−2.35418e15			−0.947880
$369$	3.86744e15			1.53202
$370$	−8.98434e15			−3.50167
$371$		−	3.57743e15i		−	1.37192i
$372$	−3.98518e15			−1.50380
$373$	3.25054e15			1.20699			0.603493	−	0.797368i	$-0.293775\pi$
$373$	3.25054e15			1.20699			0.603493	+	0.797368i	$0.293775\pi$
$374$			7.19870e14i			0.263042i
$375$			5.26774e15i			1.89425i
$376$	−4.32586e13			−0.0153089
$377$			7.48021e15i			2.60535i
$378$			2.17201e13i			0.00744581i
$379$			1.11774e15i			0.377141i	0.982060	+	0.188571i	$0.0603854\pi$
$379$			1.11774e15i			0.377141i	−0.982060	+	0.188571i	$0.939615\pi$
$380$	3.52389e15			1.17036
$381$	−4.60650e15			−1.50599
$382$			3.87582e15i			1.24734i
$383$	2.75028e15			0.871332			0.435666	−	0.900108i	$-0.356513\pi$
$383$	2.75028e15			0.871332			0.435666	+	0.900108i	$0.356513\pi$
$384$			4.95201e14i			0.154452i
$385$			9.56331e15i			2.93659i
$386$			2.92130e15i			0.883187i
$387$			2.02115e15i			0.601636i
$388$			1.80787e15i			0.529881i
$389$			6.78499e14i			0.195817i	0.995195	+	0.0979087i	$0.0312153\pi$
$389$			6.78499e14i			0.195817i	−0.995195	+	0.0979087i	$0.968785\pi$
$390$		−	1.98028e16i		−	5.62779i
$391$	−3.71392e14			−0.103937
$392$			1.19847e12i			0.000330301i
$393$	2.46984e15			0.670368
$394$			7.07616e15i			1.89156i
$395$	−7.20954e14			−0.189813
$396$	−7.03130e15			−1.82333
$397$	−3.75198e15			−0.958337			−0.479168	−	0.877723i	$-0.659062\pi$
$397$	−3.75198e15			−0.958337			−0.479168	+	0.877723i	$0.659062\pi$
$398$		−	5.92321e15i		−	1.49025i
$399$		−	3.85941e15i		−	0.956498i
$400$	7.07915e15			1.72831
$401$	3.44218e15			0.827880			0.413940	−	0.910304i	$-0.364152\pi$
$401$	3.44218e15			0.827880			0.413940	+	0.910304i	$0.364152\pi$
$402$	−1.48695e15			−0.352322
$403$		−	7.29532e15i		−	1.70300i
$404$			4.43233e15i			1.01940i
$405$		−	7.35676e15i		−	1.66708i
$406$		−	1.00398e16i		−	2.24165i
$407$	−1.16581e16			−2.56484
$408$			3.75376e13i			0.00813777i
$409$	5.62196e15			1.20101			0.600507	−	0.799620i	$-0.294966\pi$
$409$	5.62196e15			1.20101			0.600507	+	0.799620i	$0.294966\pi$
$410$	1.73207e16			3.64638
$411$		−	3.89736e15i		−	0.808574i
$412$		−	8.35635e15i		−	1.70857i
$413$	−1.65100e15			−0.332696
$414$		−	7.12149e15i		−	1.41439i
$415$	3.84006e15	+	7.63657e15i	0.751709	+	1.49489i
$416$	−1.22967e16			−2.37262
$417$		−	2.45630e15i		−	0.467159i
$418$	8.97676e15			1.68291
$419$	1.24653e15			0.230366			0.115183	−	0.993344i	$-0.463255\pi$
$419$	1.24653e15			0.230366			0.115183	+	0.993344i	$0.463255\pi$
$420$			1.35387e16i			2.46651i
$421$		−	7.53963e14i		−	0.135412i	−0.997705	−	0.0677060i	$-0.978432\pi$
$421$		−	7.53963e14i		−	0.135412i	0.997705	−	0.0677060i	$-0.0215680\pi$
$422$	−9.94386e15			−1.76068
$423$			1.61217e15i			0.281429i
$424$	4.33892e14			0.0746770
$425$	1.11679e15			0.189513
$426$	9.25882e15			1.54917
$427$	3.47529e15			0.573355
$428$		−	1.18228e16i		−	1.92334i
$429$		−	2.56961e16i		−	4.12214i
$430$			9.05192e15i			1.43196i
$431$	−8.69555e15			−1.35654			−0.678271	−	0.734812i	$-0.737271\pi$
$431$	−8.69555e15			−1.35654			−0.678271	+	0.734812i	$0.737271\pi$
$432$	3.24550e13			0.00499320
$433$		−	1.29783e15i		−	0.196920i	−0.995141	−	0.0984600i	$-0.968608\pi$
$433$		−	1.29783e15i		−	0.196920i	0.995141	−	0.0984600i	$-0.0313917\pi$
$434$			9.79161e15i			1.46526i
$435$		−	2.51211e16i		−	3.70769i
$436$	−6.34187e15			−0.923206
$437$			4.63125e15i			0.664981i
$438$	2.75402e15			0.390052
$439$			2.37896e15i			0.332354i	0.986096	+	0.166177i	$0.0531423\pi$
$439$			2.37896e15i			0.332354i	−0.986096	+	0.166177i	$0.946858\pi$
$440$	−1.15990e15			−0.159846
$441$	4.46647e13			0.00607202
$442$	−1.86561e15			−0.250200
$443$	−3.65845e15			−0.484033			−0.242017	−	0.970272i	$-0.577809\pi$
$443$	−3.65845e15			−0.484033			−0.242017	+	0.970272i	$0.577809\pi$
$444$	−1.65043e16			−2.15426
$445$	−9.58485e15			−1.23431
$446$	1.80686e16			2.29570
$447$		−	7.81038e15i		−	0.979100i
$448$	8.71711e15			1.07821
$449$			3.36690e15i			0.410916i	0.978666	+	0.205458i	$0.0658684\pi$
$449$			3.36690e15i			0.410916i	−0.978666	+	0.205458i	$0.934132\pi$
$450$			2.14147e16i			2.57891i
$451$	2.24753e16			2.67083
$452$	7.00503e15			0.821447
$453$	3.91691e15			0.453267
$454$			1.83169e16i			2.09178i
$455$	−2.47842e16			−2.79323
$456$	4.68093e14			0.0520646
$457$			2.96159e15i			0.325108i	0.986700	+	0.162554i	$0.0519732\pi$
$457$			2.96159e15i			0.325108i	−0.986700	+	0.162554i	$0.948027\pi$
$458$			1.74296e16i			1.88840i
$459$	5.12005e12			0.000547517
$460$		−	1.62463e16i		−	1.71478i
$461$			3.39294e15i			0.353485i	0.984257	+	0.176743i	$0.0565560\pi$
$461$			3.39294e15i			0.353485i	−0.984257	+	0.176743i	$0.943444\pi$
$462$			3.44886e16i			3.54670i
$463$	−9.98756e15			−1.01385			−0.506925	−	0.861990i	$-0.669218\pi$
$463$	−9.98756e15			−1.01385			−0.506925	+	0.861990i	$0.669218\pi$
$464$	−1.50018e16			−1.50326
$465$			2.45002e16i			2.42355i
$466$	2.43039e16			2.37334
$467$		−	8.36333e15i		−	0.806265i	−0.915142	−	0.403133i	$-0.867921\pi$
$467$		−	8.36333e15i		−	0.806265i	0.915142	−	0.403133i	$-0.132079\pi$
$468$		−	1.82223e16i		−	1.73431i
$469$			1.86100e15i			0.174867i
$470$			7.22026e15i			0.669831i
$471$			6.44897e15i			0.590697i
$472$		−	2.00243e14i		−	0.0181095i
$473$			1.17458e16i			1.04885i
$474$	−2.60001e15			−0.229248
$475$		−	1.39264e16i		−	1.21249i
$476$	1.27548e15			0.109656
$477$		−	1.61704e16i		−	1.37281i
$478$	2.64553e16			2.21791
$479$	1.33219e15			0.110295			0.0551473	−	0.998478i	$-0.482437\pi$
$479$	1.33219e15			0.110295			0.0551473	+	0.998478i	$0.482437\pi$
$480$	4.12966e16			3.37650
$481$		−	3.02130e16i		−	2.43962i
$482$			3.03865e16i			2.42326i
$483$	−1.77932e16			−1.40143
$484$	−2.75152e16			−2.14043
$485$	1.11145e16			0.853965
$486$		−	2.66289e16i		−	2.02086i
$487$			1.01781e16i			0.762947i	0.924380	+	0.381473i	$0.124583\pi$
$487$			1.01781e16i			0.762947i	−0.924380	+	0.381473i	$0.875417\pi$
$488$			4.21504e14i			0.0312092i
$489$			2.26058e16i			1.65336i
$490$	2.00035e14			0.0144520
$491$		−	1.97557e16i		−	1.40995i	−0.709232	−	0.704975i	$-0.750958\pi$
$491$		−	1.97557e16i		−	1.40995i	0.709232	−	0.704975i	$-0.249042\pi$
$492$	3.18182e16			2.24329
$493$	−2.36665e15			−0.164836
$494$			2.32641e16i			1.60075i
$495$			4.32273e16i			2.93851i
$496$	1.46310e16			0.982614
$497$		−	1.15879e16i		−	0.768894i
$498$	1.38486e16	+	2.75401e16i	0.907883	+	1.80547i
$499$	8.71824e15			0.564710			0.282355	−	0.959310i	$-0.408884\pi$
$499$	8.71824e15			0.564710			0.282355	+	0.959310i	$0.408884\pi$
$500$			2.17091e16i			1.38938i
$501$	−2.10567e16			−1.33157
$502$	−2.82826e16			−1.76724
$503$		−	2.39619e16i		−	1.47950i	−0.672884	−	0.739748i	$-0.734945\pi$
$503$		−	2.39619e16i		−	1.47950i	0.672884	−	0.739748i	$-0.265055\pi$
$504$			9.00853e14i			0.0549630i
$505$	2.72492e16			1.64288
$506$		−	4.13859e16i		−	2.46575i
$507$	4.25522e16			2.50539
$508$	−1.89840e16			−1.10460
$509$	5.12947e15			0.294962			0.147481	−	0.989065i	$-0.452883\pi$
$509$	5.12947e15			0.294962			0.147481	+	0.989065i	$0.452883\pi$
$510$	6.26537e15			0.356062
$511$		−	3.44680e15i		−	0.193593i
$512$		−	2.56058e16i		−	1.42141i
$513$		−	6.38468e13i		−	0.00350296i
$514$	−8.46252e15			−0.458903
$515$	−5.13735e16			−2.75357
$516$			1.66284e16i			0.880954i
$517$			9.36900e15i			0.490625i
$518$			4.05511e16i			2.09906i
$519$	−3.63393e16			−1.85940
$520$		−	3.00598e15i		−	0.152043i
$521$	1.35691e15			0.0678462			0.0339231	−	0.999424i	$-0.489200\pi$
$521$	1.35691e15			0.0678462			0.0339231	+	0.999424i	$0.489200\pi$
$522$		−	4.53809e16i		−	2.24311i
$523$	−2.87853e16			−1.40657			−0.703283	−	0.710910i	$-0.748283\pi$
$523$	−2.87853e16			−1.40657			−0.703283	+	0.710910i	$0.748283\pi$
$524$	1.01786e16			0.491698
$525$	5.35051e16			2.55528
$526$	2.00929e16			0.948697
$527$	2.30816e15			0.107746
$528$	5.15342e16			2.37844
$529$	−5.62993e14			−0.0256903
$530$		−	7.24206e16i		−	3.26743i
$531$	−7.46272e15			−0.332912
$532$		−	1.59052e16i		−	0.701567i
$533$			5.82468e16i			2.54044i
$534$	−3.45663e16			−1.49075
$535$	−7.26844e16			−3.09969
$536$	−2.25713e14			−0.00951848
$537$		−	6.35607e15i		−	0.265059i
$538$	3.92788e16			1.61981
$539$	2.59565e14			0.0105856
$540$			2.23973e14i			0.00903303i
$541$			9.29095e14i			0.0370575i	0.999828	+	0.0185288i	$0.00589823\pi$
$541$			9.29095e14i			0.0370575i	−0.999828	+	0.0185288i	$0.994102\pi$
$542$	7.42341e15			0.292825
$543$		−	4.44130e16i		−	1.73265i
$544$		−	3.89053e15i		−	0.150112i
$545$			3.89888e16i			1.48786i
$546$	−8.93805e16			−3.37355
$547$	−4.29076e16			−1.60181			−0.800903	−	0.598794i	$-0.795647\pi$
$547$	−4.29076e16			−1.60181			−0.800903	+	0.598794i	$0.795647\pi$
$548$		−	1.60616e16i		−	0.593069i
$549$	1.57087e16			0.573728
$550$			1.24450e17i			4.49590i
$551$			2.95121e16i			1.05461i
$552$		−	2.15807e15i		−	0.0762835i
$553$			3.25406e15i			0.113782i
$554$		−	2.56644e16i		−	0.887713i
$555$			1.01466e17i			3.47185i
$556$		−	1.01228e16i		−	0.342650i
$557$	1.46946e16			0.492070			0.246035	−	0.969261i	$-0.420872\pi$
$557$	1.46946e16			0.492070			0.246035	+	0.969261i	$0.420872\pi$
$558$			4.42592e16i			1.46622i
$559$	−3.04402e16			−0.997648
$560$		−	4.97054e16i		−	1.61167i
$561$	8.12994e15			0.260802
$562$	−6.59563e16			−2.09333
$563$	5.83929e16			1.83362			0.916811	−	0.399322i	$-0.130754\pi$
$563$	5.83929e16			1.83362			0.916811	+	0.399322i	$0.130754\pi$
$564$			1.32637e16i			0.412087i
$565$		−	4.30658e16i		−	1.32386i
$566$	−3.65718e16			−1.11237
$567$	−3.32050e16			−0.999322
$568$	1.40545e15			0.0418529
$569$		−	1.38584e16i		−	0.408357i	−0.978934	−	0.204179i	$-0.934548\pi$
$569$		−	1.38584e16i		−	0.408357i	0.978934	−	0.204179i	$-0.0654524\pi$
$570$		−	7.81290e16i		−	2.27805i
$571$		−	5.90331e16i		−	1.70325i	−0.524149	−	0.851627i	$-0.675617\pi$
$571$		−	5.90331e16i		−	1.70325i	0.524149	−	0.851627i	$-0.324383\pi$
$572$		−	1.05897e17i		−	3.02349i
$573$	4.37720e16			1.23671
$574$		−	7.81775e16i		−	2.18580i
$575$	−6.42054e16			−1.77650
$576$	3.94023e16			1.07891
$577$			3.77732e16i			1.02360i	0.859106	+	0.511798i	$0.171020\pi$
$577$			3.77732e16i			1.02360i	−0.859106	+	0.511798i	$0.828980\pi$
$578$			5.26445e16i			1.41184i
$579$	3.29921e16			0.875665
$580$		−	1.03528e17i		−	2.71950i
$581$	3.44679e16	−	1.73323e16i	0.896104	−	0.450608i
$582$	4.00829e16			1.03138
$583$		−	9.39729e16i		−	2.39327i
$584$	4.18048e14			0.0105378
$585$	−1.12027e17			−2.79505
$586$		−	1.77064e16i		−	0.437266i
$587$			2.89014e16i			0.706463i	0.935536	+	0.353232i	$0.114917\pi$
$587$			2.89014e16i			0.706463i	−0.935536	+	0.353232i	$0.885083\pi$
$588$	3.67466e14			0.00889104
$589$		−	2.87826e16i		−	0.689348i
$590$	−3.34225e16			−0.792367
$591$	7.99155e16			1.87545
$592$	6.05929e16			1.40764
$593$	1.32370e16			0.304412			0.152206	−	0.988349i	$-0.451362\pi$
$593$	1.32370e16			0.304412			0.152206	+	0.988349i	$0.451362\pi$
$594$			5.70550e14i			0.0129890i
$595$		−	7.84144e15i		−	0.176723i
$596$		−	3.21877e16i		−	0.718145i
$597$	−6.68945e16			−1.47756
$598$	1.07255e17			2.34538
$599$		−	1.98923e16i		−	0.430649i	−0.976543	−	0.215324i	$-0.930919\pi$
$599$		−	1.98923e16i		−	0.430649i	0.976543	−	0.215324i	$-0.0690809\pi$
$600$			6.48941e15i			0.139091i
$601$			4.93896e16i			1.04807i	0.851698	+	0.524033i	$0.175573\pi$
$601$			4.93896e16i			1.04807i	−0.851698	+	0.524033i	$0.824427\pi$
$602$	4.08562e16			0.858378
$603$			8.41192e15i			0.174981i
$604$	1.61421e16			0.332460
$605$			1.69159e17i			3.44955i
$606$	9.82702e16			1.98420
$607$	2.70349e16			0.540497			0.270248	−	0.962791i	$-0.412894\pi$
$607$	2.70349e16			0.540497			0.270248	+	0.962791i	$0.412894\pi$
$608$	−4.85148e16			−0.960402
$609$	−1.13385e17			−2.22256
$610$	7.03528e16			1.36553
$611$	−2.42806e16			−0.466673
$612$	5.76531e15			0.109727
$613$			2.30592e16i			0.434592i	0.976106	+	0.217296i	$0.0697236\pi$
$613$			2.30592e16i			0.434592i	−0.976106	+	0.217296i	$0.930276\pi$
$614$	6.09198e16			1.13697
$615$		−	1.95613e17i		−	3.61532i
$616$			5.23523e15i			0.0958190i
$617$	−5.81498e16			−1.05399			−0.526996	−	0.849868i	$-0.676682\pi$
$617$	−5.81498e16			−1.05399			−0.526996	+	0.849868i	$0.676682\pi$
$618$	−1.85271e17			−3.32565
$619$	2.06848e16			0.367712			0.183856	−	0.982953i	$-0.441142\pi$
$619$	2.06848e16			0.367712			0.183856	+	0.982953i	$0.441142\pi$
$620$			1.00969e17i			1.77761i
$621$	−2.94356e14			−0.00513243
$622$	−1.32548e17			−2.28892
$623$			4.32616e16i			0.739902i
$624$			1.33556e17i			2.26232i
$625$	2.61897e16			0.439391
$626$			3.73051e16i			0.619900i
$627$		−	1.01380e17i		−	1.66858i
$628$			2.65771e16i			0.433261i
$629$	9.55904e15			0.154351
$630$	1.50361e17			2.40487
$631$			7.59582e16i			1.20337i	0.798734	+	0.601684i	$0.205503\pi$
$631$			7.59582e16i			1.20337i	−0.798734	+	0.601684i	$0.794497\pi$
$632$	−3.94671e14			−0.00619345
$633$			1.12302e17i			1.74569i
$634$		−	5.38544e16i		−	0.829250i
$635$			1.16711e17i			1.78020i
$636$		−	1.33037e17i		−	2.01016i
$637$			6.72687e14i			0.0100688i
$638$		−	2.63727e17i		−	3.91048i
$639$		−	5.23786e16i		−	0.769394i
$640$	1.25465e16			0.182575
$641$		−	2.26437e15i		−	0.0326437i	−0.999867	−	0.0163219i	$-0.994804\pi$
$641$		−	2.26437e15i		−	0.0326437i	0.999867	−	0.0163219i	$-0.00519564\pi$
$642$	−2.62125e17			−3.74368
$643$			5.18967e16i			0.734301i	0.930162	+	0.367151i	$0.119667\pi$
$643$			5.18967e16i			0.734301i	−0.930162	+	0.367151i	$0.880333\pi$
$644$	−7.33284e16			−1.02791
$645$	1.02229e17			1.41976
$646$	−7.36050e15			−0.101277
$647$			7.24219e16i			0.987289i	0.869664	+	0.493645i	$0.164336\pi$
$647$			7.24219e16i			0.987289i	−0.869664	+	0.493645i	$0.835664\pi$
$648$		−	4.02730e15i		−	0.0543957i
$649$	−4.33690e16			−0.580378
$650$	−3.22523e17			−4.27642
$651$	1.10583e17			1.45278
$652$			9.31619e16i			1.21270i
$653$			4.44574e16i			0.573410i	0.958019	+	0.286705i	$0.0925599\pi$
$653$			4.44574e16i			0.573410i	−0.958019	+	0.286705i	$0.907440\pi$
$654$			1.40607e17i			1.79697i
$655$		−	6.25761e16i		−	0.792430i
$656$	−1.16816e17			−1.46581
$657$		−	1.55799e16i		−	0.193719i
$658$	3.25889e16			0.401527
$659$	1.25967e17			1.53796			0.768982	−	0.639271i	$-0.220764\pi$
$659$	1.25967e17			1.53796			0.768982	+	0.639271i	$0.220764\pi$
$660$			3.55639e17i			4.30275i
$661$			4.29662e15i			0.0515132i	0.999668	+	0.0257566i	$0.00819949\pi$
$661$			4.29662e15i			0.0515132i	−0.999668	+	0.0257566i	$0.991801\pi$
$662$	−1.96229e16			−0.233139
$663$			2.10695e16i			0.248069i
$664$	2.10216e15	+	4.18048e15i	0.0245277	+	0.0487773i
$665$	−9.77825e16			−1.13066
$666$			1.83296e17i			2.10043i
$667$	1.36061e17			1.54518
$668$	−8.67776e16			−0.976672
$669$		−	2.04060e17i		−	2.27615i
$670$			3.76735e16i			0.416474i
$671$	9.12898e16			1.00020
$672$		−	1.86394e17i		−	2.02402i
$673$	1.56079e17			1.67978			0.839892	−	0.542753i	$-0.182618\pi$
$673$	1.56079e17			1.67978			0.839892	+	0.542753i	$0.182618\pi$
$674$	−3.09488e16			−0.330130
$675$	8.85142e14			0.00935815
$676$	1.75364e17			1.83764
$677$			4.62547e16i			0.480423i	0.970721	+	0.240212i	$0.0772168\pi$
$677$			4.62547e16i			0.480423i	−0.970721	+	0.240212i	$0.922783\pi$
$678$		−	1.55310e17i		−	1.59890i
$679$		−	5.01658e16i		−	0.511905i
$680$	9.51057e14			0.00961951
$681$	2.06864e17			2.07397
$682$			2.57208e17i			2.55611i
$683$			1.96004e17i			1.93081i	0.260747	+	0.965407i	$0.416031\pi$
$683$			1.96004e17i			1.93081i	−0.260747	+	0.965407i	$0.583969\pi$
$684$		−	7.18933e16i		−	0.702024i
$685$	−9.87440e16			−0.955801
$686$			1.48336e17i			1.42332i
$687$	1.96843e17			1.87232
$688$		−	6.10487e16i		−	0.575633i
$689$	2.43540e17			2.27643
$690$	−3.60201e17			−3.33773
$691$	1.67986e16			0.154314			0.0771570	−	0.997019i	$-0.475416\pi$
$691$	1.67986e16			0.154314			0.0771570	+	0.997019i	$0.475416\pi$
$692$	−1.49759e17			−1.36382
$693$	1.95108e17			1.76147
$694$	6.03479e16			0.540139
$695$	−6.22331e16			−0.552220
$696$		−	1.37520e16i		−	0.120979i
$697$	−1.84286e16			−0.160730
$698$		−	1.21235e17i		−	1.04832i
$699$		−	2.74479e17i		−	2.35313i
$700$	2.20502e17			1.87424
$701$	1.02374e17			0.862744			0.431372	−	0.902174i	$-0.358030\pi$
$701$	1.02374e17			0.862744			0.431372	+	0.902174i	$0.358030\pi$
$702$	−1.47863e15			−0.0123549
$703$		−	1.19201e17i		−	0.987524i
$704$	2.28983e17			1.88091
$705$	8.15428e16			0.664127
$706$			8.51235e16i			0.687419i
$707$		−	1.22990e17i		−	0.984815i
$708$	−6.13973e16			−0.487472
$709$		−	1.33895e17i		−	1.05411i	−0.849831	−	0.527055i	$-0.823296\pi$
$709$		−	1.33895e17i		−	1.05411i	0.849831	−	0.527055i	$-0.176704\pi$
$710$		−	2.34582e17i		−	1.83124i
$711$			1.47087e16i			0.113856i
$712$	−5.24702e15			−0.0402748
$713$	−1.32698e17			−1.01001
$714$		−	2.82790e16i		−	0.213439i
$715$	−6.51038e17			−4.87271
$716$		−	2.61943e16i		−	0.194414i
$717$		−	2.98776e17i		−	2.19903i
$718$			2.34834e17i			1.71401i
$719$		−	4.55563e15i		−	0.0329743i	−0.999864	−	0.0164871i	$-0.994752\pi$
$719$		−	4.55563e15i		−	0.0329743i	0.999864	−	0.0164871i	$-0.00524826\pi$
$720$		−	2.24674e17i		−	1.61272i
$721$			2.31876e17i			1.65061i
$722$		−	1.10447e17i		−	0.779708i
$723$	3.43174e17			2.40262
$724$		−	1.83032e17i		−	1.27086i
$725$	−4.09141e17			−2.81738
$726$			6.10046e17i			4.16623i
$727$	1.67233e17			1.13270			0.566349	−	0.824165i	$-0.308355\pi$
$727$	1.67233e17			1.13270			0.566349	+	0.824165i	$0.308355\pi$
$728$	−1.35676e16			−0.0911411
$729$	−1.51195e17			−1.00733
$730$		−	6.97761e16i		−	0.461073i
$731$		−	9.63094e15i		−	0.0631197i
$732$	1.29239e17			0.840090
$733$	−3.23515e16			−0.208579			−0.104290	−	0.994547i	$-0.533257\pi$
$733$	−3.23515e16			−0.208579			−0.104290	+	0.994547i	$0.533257\pi$
$734$	1.78335e17			1.14041
$735$		−	2.25912e15i		−	0.0143290i
$736$			2.23670e17i			1.40715i
$737$			4.88852e16i			0.305051i
$738$		−	3.53371e17i		−	2.18722i
$739$	−2.09698e17			−1.28744			−0.643720	−	0.765261i	$-0.722610\pi$
$739$	−2.09698e17			−1.28744			−0.643720	+	0.765261i	$0.722610\pi$
$740$			4.18154e17i			2.54652i
$741$	2.62736e17			1.58712
$742$	−3.26873e17			−1.95864
$743$			2.48799e17i			1.47882i	0.673255	+	0.739410i	$0.264896\pi$
$743$			2.48799e17i			1.47882i	−0.673255	+	0.739410i	$0.735104\pi$
$744$			1.34121e16i			0.0790788i
$745$	−1.97885e17			−1.15738
$746$		−	2.97005e17i		−	1.72318i
$747$	1.55799e17	−	7.83438e16i	0.896688	−	0.450901i
$748$	3.35046e16			0.191291
$749$			3.28064e17i			1.85809i
$750$	4.81319e17			2.70436
$751$	8.99654e16			0.501459			0.250730	−	0.968057i	$-0.419329\pi$
$751$	8.99654e16			0.501459			0.250730	+	0.968057i	$0.419329\pi$
$752$		−	4.86955e16i		−	0.269266i
$753$			3.19413e17i			1.75219i
$754$	6.83473e17			3.71957
$755$		−	9.92392e16i		−	0.535798i
$756$	1.01091e15			0.00541480
$757$	−1.62727e17			−0.864740			−0.432370	−	0.901696i	$-0.642323\pi$
$757$	−1.62727e17			−0.864740			−0.432370	+	0.901696i	$0.642323\pi$
$758$	1.02129e17			0.538433
$759$	−4.67397e17			−2.44475
$760$		−	1.18596e16i		−	0.0615446i
$761$		−	3.25356e17i		−	1.67514i	−0.546332	−	0.837569i	$-0.683976\pi$
$761$		−	3.25356e17i		−	1.67514i	0.546332	−	0.837569i	$-0.316024\pi$
$762$			4.20900e17i			2.15005i
$763$	1.75977e17			0.891886
$764$	1.80391e17			0.907098
$765$		−	3.54442e16i		−	0.176838i
$766$		−	2.51295e17i		−	1.24398i
$767$		−	1.12395e17i		−	0.552044i
$768$	−2.66984e17			−1.30112
$769$		−	1.44184e17i		−	0.697201i	−0.937271	−	0.348601i	$-0.886657\pi$
$769$		−	1.44184e17i		−	0.697201i	0.937271	−	0.348601i	$-0.113343\pi$
$770$	8.73808e17			4.19249
$771$			9.55725e16i			0.454995i
$772$	1.35965e17			0.642278
$773$	−7.65031e16			−0.358593			−0.179297	−	0.983795i	$-0.557382\pi$
$773$	−7.65031e16			−0.358593			−0.179297	+	0.983795i	$0.557382\pi$
$774$	1.84675e17			0.858937
$775$	3.99029e17			1.84159
$776$	6.08441e15			0.0278643
$777$	4.57969e17			2.08118
$778$	6.19950e16			0.279563
$779$			2.29804e17i			1.02833i
$780$	−9.21672e17			−4.09269
$781$		−	3.04394e17i		−	1.34131i
$782$			3.39344e16i			0.148388i
$783$	−1.87575e15			−0.00813961
$784$	−1.34909e15			−0.00580959
$785$	1.63392e17			0.698252
$786$		−	2.25671e17i		−	0.957064i
$787$	−6.46436e16			−0.272068			−0.136034	−	0.990704i	$-0.543436\pi$
$787$	−6.46436e16			−0.272068			−0.136034	+	0.990704i	$0.543436\pi$
$788$	3.29343e17			1.37560
$789$		−	2.26921e17i		−	0.940618i
$790$			6.58742e16i			0.270990i
$791$	−1.94379e17			−0.793580
$792$			2.36638e16i			0.0958814i
$793$			2.36586e17i			0.951371i
$794$			3.42822e17i			1.36819i
$795$	−8.17891e17			−3.23961
$796$	−2.75682e17			−1.08375
$797$		−	2.10780e17i		−	0.822395i	−0.911546	−	0.411197i	$-0.865111\pi$
$797$		−	2.10780e17i		−	0.822395i	0.911546	−	0.411197i	$-0.134889\pi$
$798$	−3.52638e17			−1.36556
$799$		−	7.68212e15i		−	0.0295257i
$800$		−	6.72587e17i		−	2.56571i
$801$			1.95547e17i			0.740384i
$802$		−	3.14515e17i		−	1.18194i
$803$		−	9.05414e16i		−	0.337718i
$804$			6.92066e16i			0.256219i
$805$			4.50811e17i			1.65661i
$806$	−6.66580e17			−2.43132
$807$		−	4.43600e17i		−	1.60602i
$808$	1.49170e16			0.0536060
$809$		−	4.13036e17i		−	1.47332i	−0.676264	−	0.736659i	$-0.736402\pi$
$809$		−	4.13036e17i		−	1.47332i	0.676264	−	0.736659i	$-0.263598\pi$
$810$	−6.72194e17			−2.38004
$811$	−2.31270e17			−0.812818			−0.406409	−	0.913691i	$-0.633219\pi$
$811$	−2.31270e17			−0.812818			−0.406409	+	0.913691i	$0.633219\pi$
$812$	−4.67276e17			−1.63019
$813$		−	8.38371e16i		−	0.290331i
$814$			1.06521e18i			3.66174i
$815$	5.72744e17			1.95441
$816$	−4.22555e16			−0.143134
$817$	−1.20098e17			−0.403833
$818$		−	5.13683e17i		−	1.71465i
$819$			5.05640e17i			1.67548i
$820$		−	8.06149e17i		−	2.65175i
$821$			5.18554e17i			1.69330i	0.532147	+	0.846652i	$0.321386\pi$
$821$			5.18554e17i			1.69330i	−0.532147	+	0.846652i	$0.678614\pi$
$822$	−3.56106e17			−1.15438
$823$			3.01693e17i			0.970882i	0.874269	+	0.485441i	$0.161341\pi$
$823$			3.01693e17i			0.970882i	−0.874269	+	0.485441i	$0.838659\pi$
$824$	−2.81233e16			−0.0898470
$825$	1.40549e18			4.45762
$826$			1.50854e17i			0.474980i
$827$		−	4.46790e17i		−	1.39659i	−0.715808	−	0.698297i	$-0.753942\pi$
$827$		−	4.46790e17i		−	1.39659i	0.715808	−	0.698297i	$-0.246058\pi$
$828$	−3.31453e17			−1.02858
$829$			1.64608e17i			0.507137i	0.967317	+	0.253568i	$0.0816043\pi$
$829$			1.64608e17i			0.507137i	−0.967317	+	0.253568i	$0.918396\pi$
$830$	6.97760e17	−	3.50870e17i	2.13421	−	1.07319i
$831$	−2.89844e17			−0.880153
$832$			5.93432e17i			1.78908i
$833$	−2.12831e14			−0.000637036
$834$	−2.24434e17			−0.666950
$835$			5.33494e17i			1.57402i
$836$		−	4.17802e17i		−	1.22386i
$837$	1.82938e15			0.00532050
$838$		−	1.13896e17i		−	0.328886i
$839$	−3.32989e17			−0.954681			−0.477340	−	0.878719i	$-0.658399\pi$
$839$	−3.32989e17			−0.954681			−0.477340	+	0.878719i	$0.658399\pi$
$840$	4.55647e16			0.129704
$841$	5.13216e17			1.45052
$842$	−6.88902e16			−0.193324
$843$			7.44886e17i			2.07551i
$844$			4.62813e17i			1.28042i
$845$		−	1.07811e18i		−	2.96157i
$846$	1.47306e17			0.401788
$847$	7.63505e17			2.06781
$848$			4.88425e17i			1.31348i
$849$			4.13028e17i			1.10289i
$850$		−	1.02042e17i		−	0.270562i
$851$	−5.49557e17			−1.44689
$852$		−	4.30929e17i		−	1.12660i
$853$	−7.05937e16			−0.183262			−0.0916309	−	0.995793i	$-0.529208\pi$
$853$	−7.05937e16			−0.183262			−0.0916309	+	0.995793i	$0.529208\pi$
$854$		−	3.17540e17i		−	0.818562i
$855$	−4.41988e17			−1.13139
$856$	−3.97895e16			−0.101141
$857$	1.66087e17			0.419228			0.209614	−	0.977784i	$-0.432779\pi$
$857$	1.66087e17			0.419228			0.209614	+	0.977784i	$0.432779\pi$
$858$	−2.34787e18			−5.88506
$859$	4.45575e17			1.10908			0.554539	−	0.832158i	$-0.312895\pi$
$859$	4.45575e17			1.10908			0.554539	+	0.832158i	$0.312895\pi$
$860$	4.21300e17			1.04136
$861$	−8.82907e17			−2.16718
$862$			7.94520e17i			1.93670i
$863$	−1.54887e17			−0.374930			−0.187465	−	0.982271i	$-0.560027\pi$
$863$	−1.54887e17			−0.374930			−0.187465	+	0.982271i	$0.560027\pi$
$864$		−	3.08354e15i		−	0.00741253i
$865$			9.20696e17i			2.19796i
$866$	−1.18584e17			−0.281137
$867$	5.94546e17			1.39982
$868$	4.55727e17			1.06558
$869$			8.54784e16i			0.198490i
$870$	−2.29534e18			−5.29336
$871$	−1.26690e17			−0.290158
$872$			2.13436e16i			0.0485477i
$873$		−	2.26755e17i		−	0.512238i
$874$	4.23161e17			0.949374
$875$		−	6.02395e17i		−	1.34225i
$876$		−	1.28179e17i		−	0.283657i
$877$		−	4.64346e17i		−	1.02057i	−0.860005	−	0.510286i	$-0.829539\pi$
$877$		−	4.64346e17i		−	1.02057i	0.860005	−	0.510286i	$-0.170461\pi$
$878$	2.17368e17			0.474491
$879$	−1.99970e17			−0.433542
$880$		−	1.30567e18i		−	2.81151i
$881$	2.90462e17			0.621203			0.310602	−	0.950540i	$-0.399469\pi$
$881$	2.90462e17			0.621203			0.310602	+	0.950540i	$0.399469\pi$
$882$		−	4.08106e15i		−	0.00866884i
$883$			4.04985e17i			0.854426i	0.904151	+	0.427213i	$0.140504\pi$
$883$			4.04985e17i			0.854426i	−0.904151	+	0.427213i	$0.859496\pi$
$884$			8.68304e16i			0.181953i
$885$			3.77461e17i			0.785619i
$886$			3.34276e17i			0.691040i
$887$			3.18158e17i			0.653283i	0.945148	+	0.326641i	$0.105917\pi$
$887$			3.18158e17i			0.653283i	−0.945148	+	0.326641i	$0.894083\pi$
$888$			5.55452e16i			0.113284i
$889$	5.26778e17			1.06713
$890$			8.75776e17i			1.76219i
$891$	−8.72239e17			−1.74329
$892$		−	8.40958e17i		−	1.66950i
$893$	−9.57957e16			−0.188902
$894$	−7.13642e17			−1.39783
$895$	−1.61038e17			−0.313321
$896$		−	5.66290e16i		−	0.109444i
$897$		−	1.21130e18i		−	2.32540i
$898$	3.07637e17			0.586652
$899$	−8.45601e17			−1.60180
$900$	9.96694e17			1.87546
$901$			7.70531e16i			0.144026i
$902$		−	2.05359e18i		−	3.81306i
$903$		−	4.61414e17i		−	0.851068i
$904$		−	2.35754e16i		−	0.0431966i
$905$	−1.12525e18			−2.04813
$906$		−	3.57891e17i		−	0.647116i
$907$	−4.49714e17			−0.807779			−0.403889	−	0.914808i	$-0.632342\pi$
$907$	−4.49714e17			−0.807779			−0.403889	+	0.914808i	$0.632342\pi$
$908$	8.52516e17			1.52120
$909$		−	5.55931e17i		−	0.985456i
$910$			2.26455e18i			3.98781i
$911$	1.49404e17			0.261367			0.130683	−	0.991424i	$-0.458283\pi$
$911$	1.49404e17			0.261367			0.130683	+	0.991424i	$0.458283\pi$
$912$			5.26924e17i			0.915755i
$913$	9.05413e17	−	4.55288e17i	1.56323	−	0.786071i
$914$	2.70603e17			0.464147
$915$		−	7.94538e17i		−	1.35390i
$916$	8.11218e17			1.37330
$917$	−2.82440e17			−0.475017
$918$		−	4.67823e14i		−	0.000781674i
$919$		−	8.58057e17i		−	1.42437i	−0.701992	−	0.712185i	$-0.747706\pi$
$919$		−	8.58057e17i		−	1.42437i	0.701992	−	0.712185i	$-0.252294\pi$
$920$	−5.46770e16			−0.0901733
$921$		−	6.88005e17i		−	1.12729i
$922$	3.10016e17			0.504660
$923$	7.88865e17			1.27583
$924$	1.60519e18			2.57926
$925$	1.65255e18			2.63817
$926$			9.12573e17i			1.44744i
$927$			1.04811e18i			1.65168i
$928$			1.42531e18i			2.23163i
$929$	4.97090e17			0.773288			0.386644	−	0.922229i	$-0.373634\pi$
$929$	4.97090e17			0.773288			0.386644	+	0.922229i	$0.373634\pi$
$930$	2.23861e18			3.46003
$931$			2.65399e15i			0.00407569i
$932$		−	1.13117e18i		−	1.72596i
$933$			1.49694e18i			2.26942i
$934$	−7.64165e17			−1.15108
$935$		−	2.05981e17i		−	0.308289i
$936$	−6.13271e16			−0.0912005
$937$			1.25002e18i			1.84705i	0.383543	+	0.923523i	$0.374704\pi$
$937$			1.25002e18i			1.84705i	−0.383543	+	0.923523i	$0.625296\pi$
$938$	1.70041e17			0.249653
$939$	4.21309e17			0.614621
$940$	3.36050e17			0.487120
$941$	1.21068e18			1.74378			0.871890	−	0.489702i	$-0.162895\pi$
$941$	1.21068e18			1.74378			0.871890	+	0.489702i	$0.162895\pi$
$942$	5.89248e17			0.843320
$943$	1.05948e18			1.50668
$944$	2.25411e17			0.318524
$945$		−	6.21492e15i		−	0.00872659i
$946$	1.07322e18			1.49742
$947$		−	7.17880e17i		−	0.995296i	−0.867379	−	0.497648i	$-0.834197\pi$
$947$		−	7.17880e17i		−	0.995296i	0.867379	−	0.497648i	$-0.165803\pi$
$948$			1.21011e17i			0.166716i
$949$	2.34647e17			0.321231
$950$	−1.27247e18			−1.73103
$951$	−6.08211e17			−0.822188
$952$		−	4.29263e15i		−	0.00576636i
$953$	−1.44977e18			−1.93527			−0.967634	−	0.252358i	$-0.918794\pi$
$953$	−1.44977e18			−1.93527			−0.967634	+	0.252358i	$0.918794\pi$
$954$	−1.47750e18			−1.95992
$955$		−	1.10901e18i		−	1.46190i
$956$		−	1.23130e18i		−	1.61293i
$957$	−2.97843e18			−3.87718
$958$		−	1.21724e17i		−	0.157464i
$959$			4.45685e17i			0.572949i
$960$		−	1.99295e18i		−	2.54606i
$961$	3.70375e16			0.0470221
$962$	−2.76059e18			−3.48298
$963$			1.48289e18i			1.85930i
$964$	1.41427e18			1.76226
$965$		−	8.35891e17i		−	1.03511i
$966$			1.62578e18i			2.00078i
$967$		−	1.22525e18i		−	1.49853i	−0.662268	−	0.749267i	$-0.730406\pi$
$967$		−	1.22525e18i		−	1.49853i	0.662268	−	0.749267i	$-0.269594\pi$
$968$			9.26024e16i			0.112556i
$969$			8.31267e16i			0.100415i
$970$		−	1.01554e18i		−	1.21918i
$971$		−	1.31270e18i		−	1.56621i	−0.621887	−	0.783107i	$-0.713634\pi$
$971$		−	1.31270e18i		−	1.56621i	0.621887	−	0.783107i	$-0.286366\pi$
$972$	−1.23938e18			−1.46962
$973$			2.80891e17i			0.331025i
$974$	9.29985e17			1.08924
$975$			3.64245e18i			4.24000i
$976$	−4.74480e17			−0.548932
$977$	−1.85118e17			−0.212853			−0.106427	−	0.994321i	$-0.533941\pi$
$977$	−1.85118e17			−0.212853			−0.106427	+	0.994321i	$0.533941\pi$
$978$	2.06552e18			2.36045
$979$			1.13641e18i			1.29074i
$980$		−	9.31015e15i		−	0.0105099i
$981$	7.95438e17			0.892467
$982$	−1.80510e18			−2.01294
$983$	1.22152e18			1.35387			0.676936	−	0.736042i	$-0.263307\pi$
$983$	1.22152e18			1.35387			0.676936	+	0.736042i	$0.263307\pi$
$984$		−	1.07084e17i		−	0.117965i
$985$		−	2.02475e18i		−	2.21694i
$986$			2.16243e17i			0.235332i
$987$		−	3.68047e17i		−	0.398107i
$988$	1.08277e18			1.16411
$989$			5.53691e17i			0.591684i
$990$	3.94971e18			4.19522
$991$	2.43413e17			0.256982			0.128491	−	0.991711i	$-0.458987\pi$
$991$	2.43413e17			0.256982			0.128491	+	0.991711i	$0.458987\pi$
$992$		−	1.39008e18i		−	1.45871i
$993$			2.21613e17i			0.231153i
$994$	−1.05880e18			−1.09773
$995$			1.69485e18i			1.74659i
$996$	1.28179e18	−	6.44550e17i	1.31299	−	0.660238i
$997$	5.06517e17			0.515730			0.257865	−	0.966181i	$-0.416981\pi$
$997$	5.06517e17			0.515730			0.257865	+	0.966181i	$0.416981\pi$
$998$		−	7.96593e17i		−	0.806219i
$999$	7.57625e15			0.00762186

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	83.13.b.c.82.14	✓	80
83.82	odd	2	inner	83.13.b.c.82.67	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
83.13.b.c.82.14	✓	80	1.1	even	1	trivial
83.13.b.c.82.67	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)

\(f(q)\)	\(=\)	\(q-91.3709i q^{2} -1031.91 q^{3} -4252.64 q^{4} +26144.5i q^{5} +94286.4i q^{6} +118004. q^{7} +14312.3i q^{8} +533393. q^{9} +O(q^{10})\)	\(q-91.3709i q^{2} -1031.91 q^{3} -4252.64 q^{4} +26144.5i q^{5} +94286.4i q^{6} +118004. q^{7} +14312.3i q^{8} +533393. q^{9} +2.38885e6 q^{10} +3.09977e6 q^{11} +4.38833e6 q^{12} +8.03334e6i q^{13} -1.07822e7i q^{14} -2.69788e7i q^{15} -1.61111e7 q^{16} -2.54166e6 q^{17} -4.87366e7i q^{18} +3.16944e7i q^{19} -1.11183e8i q^{20} -1.21770e8 q^{21} -2.83229e8i q^{22} +1.46122e8 q^{23} -1.47689e7i q^{24} -4.39396e8 q^{25} +7.34013e8 q^{26} -2.01445e6 q^{27} -5.01830e8 q^{28} +9.31145e8 q^{29} -2.46507e9 q^{30} -9.08130e8 q^{31} +1.53071e9i q^{32} -3.19868e9 q^{33} +2.32234e8i q^{34} +3.08517e9i q^{35} -2.26833e9 q^{36} -3.76095e9 q^{37} +2.89594e9 q^{38} -8.28967e9i q^{39} -3.74188e8 q^{40} +7.25063e9 q^{41} +1.11262e10i q^{42} +3.78924e9i q^{43} -1.31822e10 q^{44} +1.39453e10i q^{45} -1.33513e10i q^{46} +3.02248e9i q^{47} +1.66252e10 q^{48} +8.37370e7 q^{49} +4.01480e10i q^{50} +2.62276e9 q^{51} -3.41629e10i q^{52} -3.03161e10i q^{53} +1.84062e8i q^{54} +8.10420e10i q^{55} +1.68891e9i q^{56} -3.27057e10i q^{57} -8.50795e10i q^{58} -1.39910e10 q^{59} +1.14731e11i q^{60} +2.94505e10 q^{61} +8.29767e10i q^{62} +6.29427e10 q^{63} +7.38711e10 q^{64} -2.10028e11 q^{65} +2.92266e11i q^{66} +1.57706e10i q^{67} +1.08088e10 q^{68} -1.50784e11 q^{69} +2.81895e11 q^{70} -9.81989e10i q^{71} +7.63407e9i q^{72} -2.92091e10i q^{73} +3.43641e11i q^{74} +4.53416e11 q^{75} -1.34785e11i q^{76} +3.65786e11 q^{77} -7.57434e11 q^{78} +2.75757e10i q^{79} -4.21217e11i q^{80} -2.81388e11 q^{81} -6.62497e11i q^{82} +(2.92090e11 - 1.46878e11i) q^{83} +5.17842e11 q^{84} -6.64504e10i q^{85} +3.46226e11 q^{86} -9.60856e11 q^{87} +4.43647e10i q^{88} +3.66610e11i q^{89} +1.27420e12 q^{90} +9.47969e11i q^{91} -6.21404e11 q^{92} +9.37107e11 q^{93} +2.76167e11 q^{94} -8.28635e11 q^{95} -1.57955e12i q^{96} -4.25118e11i q^{97} -7.65112e9i q^{98} +1.65340e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 918 q^{3} - 181150 q^{4} + 103918 q^{7} + 14902142 q^{9}+O(q^{10}) \) 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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