LMFDB - Embedded newform 83.13.b.c.82.16

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			82.16
Character	$\chi$	$=$	83.82
Dual form			83.13.b.c.82.65

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-87.7892i q^{2} -807.149 q^{3} -3610.94 q^{4} -1433.36i q^{5} +70858.9i q^{6} +30455.0 q^{7} -42583.4i q^{8} +120049. q^{9} +O(q^{10})$	\(q-87.7892i q^{2} -807.149 q^{3} -3610.94 q^{4} -1433.36i q^{5} +70858.9i q^{6} +30455.0 q^{7} -42583.4i q^{8} +120049. q^{9} -125833. q^{10} -2.57404e6 q^{11} +2.91456e6 q^{12} +5.91008e6i q^{13} -2.67362e6i q^{14} +1.15693e6i q^{15} -1.85288e7 q^{16} +1.24540e7 q^{17} -1.05390e7i q^{18} +2.75162e7i q^{19} +5.17576e6i q^{20} -2.45818e7 q^{21} +2.25973e8i q^{22} -1.47966e8 q^{23} +3.43712e7i q^{24} +2.42086e8 q^{25} +5.18841e8 q^{26} +3.32055e8 q^{27} -1.09971e8 q^{28} -5.75041e7 q^{29} +1.01566e8 q^{30} +1.14446e9 q^{31} +1.45220e9i q^{32} +2.07763e9 q^{33} -1.09333e9i q^{34} -4.36530e7i q^{35} -4.33487e8 q^{36} -1.38932e9 q^{37} +2.41562e9 q^{38} -4.77031e9i q^{39} -6.10373e7 q^{40} +1.93871e8 q^{41} +2.15801e9i q^{42} +4.07004e9i q^{43} +9.29469e9 q^{44} -1.72072e8i q^{45} +1.29898e10i q^{46} -9.55285e9i q^{47} +1.49555e10 q^{48} -1.29138e10 q^{49} -2.12525e10i q^{50} -1.00522e10 q^{51} -2.13409e10i q^{52} -6.19935e9i q^{53} -2.91508e10i q^{54} +3.68952e9i q^{55} -1.29688e9i q^{56} -2.22097e10i q^{57} +5.04824e9i q^{58} +6.84411e10 q^{59} -4.17761e9i q^{60} -1.69530e10 q^{61} -1.00471e11i q^{62} +3.65608e9 q^{63} +5.15938e10 q^{64} +8.47125e9 q^{65} -1.82394e11i q^{66} +8.30868e10i q^{67} -4.49705e10 q^{68} +1.19431e11 q^{69} -3.83226e9 q^{70} +5.76125e10i q^{71} -5.11208e9i q^{72} -2.90102e10i q^{73} +1.21968e11i q^{74} -1.95400e11 q^{75} -9.93592e10i q^{76} -7.83925e10 q^{77} -4.18782e11 q^{78} -1.86600e11i q^{79} +2.65583e10i q^{80} -3.31817e11 q^{81} -1.70198e10i q^{82} +(-2.09136e11 + 2.51301e11i) q^{83} +8.87631e10 q^{84} -1.78510e10i q^{85} +3.57305e11 q^{86} +4.64144e10 q^{87} +1.09611e11i q^{88} -3.89346e9i q^{89} -1.51061e10 q^{90} +1.79992e11i q^{91} +5.34297e11 q^{92} -9.23749e11 q^{93} -8.38637e11 q^{94} +3.94405e10 q^{95} -1.17214e12i q^{96} +3.48984e10i q^{97} +1.13369e12i q^{98} -3.09010e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	87.7892i		−	1.37171i	−0.727740	−	0.685853i	$-0.759429\pi$
$2$		−	87.7892i		−	1.37171i	0.727740	−	0.685853i	$-0.240571\pi$
$3$	−807.149			−1.10720			−0.553600	−	0.832783i	$-0.686746\pi$
$3$	−807.149			−1.10720			−0.553600	+	0.832783i	$0.686746\pi$
$4$	−3610.94			−0.881576
$5$		−	1433.36i		−	0.0917349i	−0.998948	−	0.0458674i	$-0.985395\pi$
$5$		−	1433.36i		−	0.0917349i	0.998948	−	0.0458674i	$-0.0146052\pi$
$6$			70858.9i			1.51875i
$7$	30455.0			0.258864			0.129432	−	0.991588i	$-0.458685\pi$
$7$	30455.0			0.258864			0.129432	+	0.991588i	$0.458685\pi$
$8$		−	42583.4i		−	0.162443i
$9$	120049.			0.225893
$10$	−125833.			−0.125833
$11$	−2.57404e6			−1.45298			−0.726489	−	0.687178i	$-0.758849\pi$
$11$	−2.57404e6			−1.45298			−0.726489	+	0.687178i	$0.758849\pi$
$12$	2.91456e6			0.976081
$13$			5.91008e6i			1.22443i	0.790692	+	0.612214i	$0.209721\pi$
$13$			5.91008e6i			1.22443i	−0.790692	+	0.612214i	$0.790279\pi$
$14$		−	2.67362e6i		−	0.355085i
$15$			1.15693e6i			0.101569i
$16$	−1.85288e7			−1.10440
$17$	1.24540e7			0.515959			0.257979	−	0.966150i	$-0.416943\pi$
$17$	1.24540e7			0.515959			0.257979	+	0.966150i	$0.416943\pi$
$18$		−	1.05390e7i		−	0.309858i
$19$			2.75162e7i			0.584880i	0.956284	+	0.292440i	$0.0944672\pi$
$19$			2.75162e7i			0.584880i	−0.956284	+	0.292440i	$0.905533\pi$
$20$			5.17576e6i			0.0808713i
$21$	−2.45818e7			−0.286614
$22$			2.25973e8i			1.99306i
$23$	−1.47966e8			−0.999530			−0.499765	−	0.866161i	$-0.666580\pi$
$23$	−1.47966e8			−0.999530			−0.499765	+	0.866161i	$0.666580\pi$
$24$			3.43712e7i			0.179857i
$25$	2.42086e8			0.991585
$26$	5.18841e8			1.67955
$27$	3.32055e8			0.857092
$28$	−1.09971e8			−0.228208
$29$	−5.75041e7			−0.0966743			−0.0483371	−	0.998831i	$-0.515392\pi$
$29$	−5.75041e7			−0.0966743			−0.0483371	+	0.998831i	$0.515392\pi$
$30$	1.01566e8			0.139323
$31$	1.14446e9			1.28953			0.644763	−	0.764382i	$-0.276956\pi$
$31$	1.14446e9			1.28953			0.644763	+	0.764382i	$0.276956\pi$
$32$			1.45220e9i			1.35247i
$33$	2.07763e9			1.60874
$34$		−	1.09333e9i		−	0.707743i
$35$		−	4.36530e7i		−	0.0237468i
$36$	−4.33487e8			−0.199141
$37$	−1.38932e9			−0.541494			−0.270747	−	0.962651i	$-0.587271\pi$
$37$	−1.38932e9			−0.541494			−0.270747	+	0.962651i	$0.587271\pi$
$38$	2.41562e9			0.802283
$39$		−	4.77031e9i		−	1.35569i
$40$	−6.10373e7			−0.0149017
$41$	1.93871e8			0.0408141			0.0204071	−	0.999792i	$-0.493504\pi$
$41$	1.93871e8			0.0408141			0.0204071	+	0.999792i	$0.493504\pi$
$42$			2.15801e9i			0.393150i
$43$			4.07004e9i			0.643854i	0.946764	+	0.321927i	$0.104331\pi$
$43$			4.07004e9i			0.643854i	−0.946764	+	0.321927i	$0.895669\pi$
$44$	9.29469e9			1.28091
$45$		−	1.72072e8i		−	0.0207222i
$46$			1.29898e10i			1.37106i
$47$		−	9.55285e9i		−	0.886229i	−0.896465	−	0.443115i	$-0.853873\pi$
$47$		−	9.55285e9i		−	0.886229i	0.896465	−	0.443115i	$-0.146127\pi$
$48$	1.49555e10			1.22279
$49$	−1.29138e10			−0.932990
$50$		−	2.12525e10i		−	1.36016i
$51$	−1.00522e10			−0.571270
$52$		−	2.13409e10i		−	1.07943i
$53$		−	6.19935e9i		−	0.279699i	−0.990173	−	0.139849i	$-0.955338\pi$
$53$		−	6.19935e9i		−	0.279699i	0.990173	−	0.139849i	$-0.0446619\pi$
$54$		−	2.91508e10i		−	1.17568i
$55$			3.68952e9i			0.133289i
$56$		−	1.29688e9i		−	0.0420506i
$57$		−	2.22097e10i		−	0.647579i
$58$			5.04824e9i			0.132609i
$59$	6.84411e10			1.62258			0.811288	−	0.584647i	$-0.198767\pi$
$59$	6.84411e10			1.62258			0.811288	+	0.584647i	$0.198767\pi$
$60$		−	4.17761e9i		−	0.0895407i
$61$	−1.69530e10			−0.329054			−0.164527	−	0.986373i	$-0.552610\pi$
$61$	−1.69530e10			−0.329054			−0.164527	+	0.986373i	$0.552610\pi$
$62$		−	1.00471e11i		−	1.76885i
$63$	3.65608e9			0.0584754
$64$	5.15938e10			0.750788
$65$	8.47125e9			0.112323
$66$		−	1.82394e11i		−	2.20671i
$67$			8.30868e10i			0.918508i	0.888305	+	0.459254i	$0.151883\pi$
$67$			8.30868e10i			0.918508i	−0.888305	+	0.459254i	$0.848117\pi$
$68$	−4.49705e10			−0.454857
$69$	1.19431e11			1.10668
$70$	−3.83226e9			−0.0325736
$71$			5.76125e10i			0.449745i	0.974388	+	0.224873i	$0.0721966\pi$
$71$			5.76125e10i			0.449745i	−0.974388	+	0.224873i	$0.927803\pi$
$72$		−	5.11208e9i		−	0.0366946i
$73$		−	2.90102e10i		−	0.191696i	−0.995396	−	0.0958480i	$-0.969444\pi$
$73$		−	2.90102e10i		−	0.191696i	0.995396	−	0.0958480i	$-0.0305563\pi$
$74$			1.21968e11i			0.742770i
$75$	−1.95400e11			−1.09788
$76$		−	9.93592e10i		−	0.515616i
$77$	−7.83925e10			−0.376123
$78$	−4.18782e11			−1.85960
$79$		−	1.86600e11i		−	0.767623i	−0.923411	−	0.383812i	$-0.874611\pi$
$79$		−	1.86600e11i		−	0.767623i	0.923411	−	0.383812i	$-0.125389\pi$
$80$			2.65583e10i			0.101312i
$81$	−3.31817e11			−1.17487
$82$		−	1.70198e10i		−	0.0559850i
$83$	−2.09136e11	+	2.51301e11i	−0.639677	+	0.768644i
$83$	−2.09136e11	+	2.51301e11i	−0.639677	+	0.768644i
$84$	8.87631e10			0.252672
$85$		−	1.78510e10i		−	0.0473314i
$86$	3.57305e11			0.883178
$87$	4.64144e10			0.107038
$88$			1.09611e11i			0.236026i
$89$		−	3.89346e9i		−	0.00783421i	−0.999992	−	0.00391710i	$-0.998753\pi$
$89$		−	3.89346e9i		−	0.00783421i	0.999992	−	0.00391710i	$-0.00124686\pi$
$90$	−1.51061e10			−0.0284248
$91$			1.79992e11i			0.316960i
$92$	5.34297e11			0.881162
$93$	−9.23749e11			−1.42776
$94$	−8.38637e11			−1.21565
$95$	3.94405e10			0.0536539
$96$		−	1.17214e12i		−	1.49745i
$97$			3.48984e10i			0.0418963i	0.999781	+	0.0209481i	$0.00666849\pi$
$97$			3.48984e10i			0.0418963i	−0.999781	+	0.0209481i	$0.993332\pi$
$98$			1.13369e12i			1.27979i
$99$	−3.09010e11			−0.328217
$100$	−8.74157e11			−0.874157
$101$		−	1.95281e12i		−	1.83964i	−0.392341	−	0.919820i	$-0.628335\pi$
$101$		−	1.95281e12i		−	1.83964i	0.392341	−	0.919820i	$-0.371665\pi$
$102$			8.82476e11i			0.783614i
$103$		−	7.71641e11i		−	0.646237i	−0.946359	−	0.323119i	$-0.895269\pi$
$103$		−	7.71641e11i		−	0.646237i	0.946359	−	0.323119i	$-0.104731\pi$
$104$	2.51671e11			0.198900
$105$			3.52344e10i			0.0262925i
$106$	−5.44235e11			−0.383664
$107$		−	3.43996e11i		−	0.229219i	−0.993411	−	0.114610i	$-0.963438\pi$
$107$		−	3.43996e11i		−	0.229219i	0.993411	−	0.114610i	$-0.0365617\pi$
$108$	−1.19903e12			−0.755592
$109$	−1.70354e12			−1.01576			−0.507881	−	0.861427i	$-0.669571\pi$
$109$	−1.70354e12			−1.01576			−0.507881	+	0.861427i	$0.669571\pi$
$110$	3.23900e11			0.182833
$111$	1.12139e12			0.599542
$112$	−5.64294e11			−0.285889
$113$	−2.78149e12			−1.33600			−0.668001	−	0.744160i	$-0.732850\pi$
$113$	−2.78149e12			−1.33600			−0.668001	+	0.744160i	$0.732850\pi$
$114$	−1.94977e12			−0.888288
$115$			2.12089e11i			0.0916918i
$116$	2.07644e11			0.0852257
$117$			7.09496e11i			0.276589i
$118$		−	6.00839e12i		−	2.22570i
$119$	3.79287e11			0.133563
$120$	4.92662e10			0.0164991
$121$	3.48725e12			1.11115
$122$			1.48829e12i			0.451365i
$123$	−1.56483e11			−0.0451894
$124$	−4.13257e12			−1.13682
$125$		−	6.96937e11i		−	0.182698i
$126$		−	3.20964e11i		−	0.0802110i
$127$	3.96754e12			0.945582			0.472791	−	0.881175i	$-0.343247\pi$
$127$	3.96754e12			0.945582			0.472791	+	0.881175i	$0.343247\pi$
$128$			1.41884e12i			0.322608i
$129$		−	3.28513e12i		−	0.712875i
$130$		−	7.43684e11i		−	0.154074i
$131$	−2.51904e12			−0.498434			−0.249217	−	0.968448i	$-0.580173\pi$
$131$	−2.51904e12			−0.498434			−0.249217	+	0.968448i	$0.580173\pi$
$132$	−7.50220e12			−1.41822
$133$			8.38007e11i			0.151404i
$134$	7.29412e12			1.25992
$135$		−	4.75954e11i		−	0.0786252i
$136$		−	5.30334e11i		−	0.0838138i
$137$		−	1.23464e13i		−	1.86731i	−0.358168	−	0.933657i	$-0.616598\pi$
$137$		−	1.23464e13i		−	1.86731i	0.358168	−	0.933657i	$-0.383402\pi$
$138$		−	1.04847e13i		−	1.51804i
$139$		−	1.21044e13i		−	1.67825i	−0.543941	−	0.839124i	$-0.683068\pi$
$139$		−	1.21044e13i		−	1.67825i	0.543941	−	0.839124i	$-0.316932\pi$
$140$			1.57628e11i			0.0209346i
$141$			7.71058e12i			0.981233i
$142$	5.05775e12			0.616918
$143$		−	1.52128e13i		−	1.77907i
$144$	−2.22435e12			−0.249476
$145$			8.24239e10i			0.00886840i
$146$	−2.54678e12			−0.262950
$147$	1.04233e13			1.03301
$148$	5.01676e12			0.477368
$149$		−	5.77817e12i		−	0.528047i	−0.964516	−	0.264024i	$-0.914950\pi$
$149$		−	5.77817e12i		−	0.528047i	0.964516	−	0.264024i	$-0.0850497\pi$
$150$			1.71540e13i			1.50597i
$151$	2.12380e13			1.79165			0.895823	−	0.444411i	$-0.146587\pi$
$151$	2.12380e13			1.79165			0.895823	+	0.444411i	$0.146587\pi$
$152$	1.17173e12			0.0950096
$153$	1.49508e12			0.116551
$154$			6.88201e12i			0.515930i
$155$		−	1.64042e12i		−	0.118295i
$156$			1.72253e13i			1.19514i
$157$		−	1.51537e13i		−	1.01186i	−0.862574	−	0.505931i	$-0.831149\pi$
$157$		−	1.51537e13i		−	1.01186i	0.862574	−	0.505931i	$-0.168851\pi$
$158$	−1.63814e13			−1.05295
$159$			5.00380e12i			0.309683i
$160$	2.08152e12			0.124069
$161$	−4.50632e12			−0.258742
$162$			2.91299e13i			1.61157i
$163$			3.50948e13i			1.87118i	0.353082	+	0.935592i	$0.385134\pi$
$163$			3.50948e13i			1.87118i	−0.353082	+	0.935592i	$0.614866\pi$
$164$	−7.00057e11			−0.0359808
$165$		−	2.97799e12i		−	0.147577i
$166$	2.20615e13	+	1.83599e13i	1.05435	+	0.877448i
$167$	−2.19908e13			−1.01378			−0.506889	−	0.862012i	$-0.669204\pi$
$167$	−2.19908e13			−1.01378			−0.506889	+	0.862012i	$0.669204\pi$
$168$			1.04678e12i			0.0465584i
$169$	−1.16309e13			−0.499222
$170$	−1.56713e12			−0.0649247
$171$			3.30328e12i			0.132120i
$172$		−	1.46966e13i		−	0.567606i
$173$	1.35896e13			0.506909			0.253455	−	0.967347i	$-0.418433\pi$
$173$	1.35896e13			0.506909			0.253455	+	0.967347i	$0.418433\pi$
$174$		−	4.07468e12i		−	0.146824i
$175$	7.37274e12			0.256685
$176$	4.76937e13			1.60467
$177$	−5.52422e13			−1.79652
$178$	−3.41803e11			−0.0107462
$179$		−	1.14414e13i		−	0.347824i	−0.984761	−	0.173912i	$-0.944359\pi$
$179$		−	1.14414e13i		−	0.347824i	0.984761	−	0.173912i	$-0.0556408\pi$
$180$			6.21343e11i			0.0182682i
$181$			5.32503e13i			1.51444i	0.653162	+	0.757218i	$0.273442\pi$
$181$			5.32503e13i			1.51444i	−0.653162	+	0.757218i	$0.726558\pi$
$182$	1.58013e13			0.434775
$183$	1.36836e13			0.364329
$184$			6.30092e12i			0.162367i
$185$			1.99140e12i			0.0496738i
$186$			8.10952e13i			1.95847i
$187$	−3.20571e13			−0.749677
$188$			3.44947e13i			0.781278i
$189$	1.01128e13			0.221870
$190$		−	3.46245e12i		−	0.0735973i
$191$	2.68768e13			0.553576			0.276788	−	0.960931i	$-0.410730\pi$
$191$	2.68768e13			0.553576			0.276788	+	0.960931i	$0.410730\pi$
$192$	−4.16439e13			−0.831273
$193$	−2.12945e13			−0.412024			−0.206012	−	0.978549i	$-0.566049\pi$
$193$	−2.12945e13			−0.412024			−0.206012	+	0.978549i	$0.566049\pi$
$194$	3.06370e12			0.0574694
$195$	−6.83756e12			−0.124364
$196$	4.66308e13			0.822501
$197$	6.34400e13			1.08534			0.542670	−	0.839946i	$-0.317413\pi$
$197$	6.34400e13			1.08534			0.542670	+	0.839946i	$0.317413\pi$
$198$			2.71277e13i			0.450217i
$199$	6.79660e13			1.09439			0.547196	−	0.837004i	$-0.315695\pi$
$199$	6.79660e13			1.09439			0.547196	+	0.837004i	$0.315695\pi$
$200$		−	1.03089e13i		−	0.161076i
$201$		−	6.70634e13i		−	1.01697i
$202$	−1.71436e14			−2.52344
$203$	−1.75129e12			−0.0250254
$204$	3.62979e13			0.503618
$205$		−	2.77887e11i		−	0.00374408i
$206$	−6.77417e13			−0.886447
$207$	−1.77631e13			−0.225786
$208$		−	1.09506e14i		−	1.35226i
$209$		−	7.08278e13i		−	0.849818i
$210$	3.09320e12			0.0360655
$211$			1.44236e14i			1.63448i	0.576300	+	0.817238i	$0.304496\pi$
$211$			1.44236e14i			1.63448i	−0.576300	+	0.817238i	$0.695504\pi$
$212$			2.23854e13i			0.246576i
$213$		−	4.65018e13i		−	0.497958i
$214$	−3.01991e13			−0.314421
$215$	5.83382e12			0.0590639
$216$		−	1.41400e13i		−	0.139229i
$217$	3.48546e13			0.333811
$218$			1.49552e14i			1.39333i
$219$			2.34155e13i			0.212246i
$220$		−	1.33226e13i		−	0.117504i
$221$			7.36040e13i			0.631754i
$222$		−	9.84460e13i		−	0.822395i
$223$		−	1.66718e14i		−	1.35567i	−0.735216	−	0.677833i	$-0.762919\pi$
$223$		−	1.66718e14i		−	1.35567i	0.735216	−	0.677833i	$-0.237081\pi$
$224$			4.42269e13i			0.350105i
$225$	2.90621e13			0.223992
$226$			2.44185e14i			1.83260i
$227$	1.98724e14			1.45243			0.726214	−	0.687468i	$-0.241278\pi$
$227$	1.98724e14			1.45243			0.726214	+	0.687468i	$0.241278\pi$
$228$			8.01977e13i			0.570890i
$229$	1.95449e14			1.35525			0.677627	−	0.735406i	$-0.263009\pi$
$229$	1.95449e14			1.35525			0.677627	+	0.735406i	$0.263009\pi$
$230$	1.86191e13			0.125774
$231$	6.32744e13			0.416444
$232$			2.44872e12i			0.0157041i
$233$		−	2.31915e14i		−	1.44941i	−0.689057	−	0.724707i	$-0.741975\pi$
$233$		−	2.31915e14i		−	1.44941i	0.689057	−	0.724707i	$-0.258025\pi$
$234$	6.22860e13			0.379399
$235$	−1.36927e13			−0.0812981
$236$	−2.47136e14			−1.43042
$237$			1.50614e14i			0.849913i
$238$		−	3.32973e13i		−	0.183209i
$239$			1.48756e14i			0.798157i	0.916917	+	0.399078i	$0.130670\pi$
$239$			1.48756e14i			0.798157i	−0.916917	+	0.399078i	$0.869330\pi$
$240$		−	2.14365e13i		−	0.112173i
$241$	2.70385e14			1.38000			0.690001	−	0.723808i	$-0.257610\pi$
$241$	2.70385e14			1.38000			0.690001	+	0.723808i	$0.257610\pi$
$242$		−	3.06143e14i		−	1.52416i
$243$	9.13578e13			0.443719
$244$	6.12162e13			0.290086
$245$			1.85101e13i			0.0855877i
$246$			1.37375e13i			0.0619866i
$247$	−1.62623e14			−0.716143
$248$		−	4.87350e13i		−	0.209474i
$249$	1.68804e14	−	2.02837e14i	0.708250	−	0.851043i
$250$	−6.11835e13			−0.250608
$251$		−	3.69438e14i		−	1.47740i	−0.674032	−	0.738702i	$-0.735439\pi$
$251$		−	3.69438e14i		−	1.47740i	0.674032	−	0.738702i	$-0.264561\pi$
$252$	−1.32019e13			−0.0515505
$253$	3.80871e14			1.45230
$254$		−	3.48307e14i		−	1.29706i
$255$			1.44084e13i			0.0524053i
$256$	3.35887e14			1.19331
$257$			2.69276e14i			0.934544i	0.884114	+	0.467272i	$0.154763\pi$
$257$			2.69276e14i			0.934544i	−0.884114	+	0.467272i	$0.845237\pi$
$258$	−2.88398e14			−0.977855
$259$	−4.23119e13			−0.140173
$260$	−3.05891e13			−0.0990210
$261$	−6.90328e12			−0.0218380
$262$			2.21145e14i			0.683705i
$263$		−	1.19501e14i		−	0.361108i	−0.983565	−	0.180554i	$-0.942211\pi$
$263$		−	1.19501e14i		−	0.361108i	0.983565	−	0.180554i	$-0.0577891\pi$
$264$		−	8.84728e13i		−	0.261328i
$265$	−8.88588e12			−0.0256581
$266$	7.35679e13			0.207682
$267$			3.14260e12i			0.00867404i
$268$		−	3.00021e14i		−	0.809735i
$269$			2.73894e14i			0.722884i	0.932395	+	0.361442i	$0.117715\pi$
$269$			2.73894e14i			0.722884i	−0.932395	+	0.361442i	$0.882285\pi$
$270$	−4.17836e13			−0.107851
$271$			1.36663e14i			0.345012i	0.985008	+	0.172506i	$0.0551865\pi$
$271$			1.36663e14i			0.345012i	−0.985008	+	0.172506i	$0.944814\pi$
$272$	−2.30757e14			−0.569825
$273$		−	1.45280e14i		−	0.350938i
$274$	−1.08388e15			−2.56141
$275$	−6.23139e14			−1.44075
$276$	−4.31257e14			−0.975623
$277$	2.41760e14			0.535186			0.267593	−	0.963532i	$-0.413772\pi$
$277$	2.41760e14			0.535186			0.267593	+	0.963532i	$0.413772\pi$
$278$	−1.06264e15			−2.30206
$279$	1.37391e14			0.291294
$280$	−1.85889e12			−0.00385750
$281$			1.35527e14i			0.275288i	0.990482	+	0.137644i	$0.0439529\pi$
$281$			1.35527e14i			0.275288i	−0.990482	+	0.137644i	$0.956047\pi$
$282$	6.76905e14			1.34596
$283$		−	6.29190e14i		−	1.22479i	−0.790550	−	0.612397i	$-0.790205\pi$
$283$		−	6.29190e14i		−	1.22479i	0.790550	−	0.612397i	$-0.209795\pi$
$284$		−	2.08035e14i		−	0.396484i
$285$	−3.18344e13			−0.0594056
$286$	−1.33552e15			−2.44035
$287$	5.90436e12			0.0105653
$288$			1.74335e14i			0.305512i
$289$	−4.27520e14			−0.733787
$290$	7.23593e12			0.0121648
$291$		−	2.81682e13i		−	0.0463876i
$292$			1.04754e14i			0.168995i
$293$	1.83899e14			0.290652			0.145326	−	0.989384i	$-0.453577\pi$
$293$	1.83899e14			0.290652			0.145326	+	0.989384i	$0.453577\pi$
$294$		−	9.15056e14i		−	1.41698i
$295$		−	9.81006e13i		−	0.148847i
$296$			5.91622e13i			0.0879618i
$297$	−8.54723e14			−1.24534
$298$	−5.07261e14			−0.724325
$299$		−	8.74492e14i		−	1.22385i
$300$	7.05575e14			0.967867
$301$			1.23953e14i			0.166670i
$302$		−	1.86447e15i		−	2.45761i
$303$			1.57621e15i			2.03685i
$304$		−	5.09841e14i		−	0.645941i
$305$			2.42997e13i			0.0301857i
$306$		−	1.31252e14i		−	0.159874i
$307$			1.27326e15i			1.52085i	0.649426	+	0.760425i	$0.275009\pi$
$307$			1.27326e15i			1.52085i	−0.649426	+	0.760425i	$0.724991\pi$
$308$	2.83070e14			0.331581
$309$			6.22829e14i			0.715514i
$310$	−1.44011e14			−0.162265
$311$			2.28550e14i			0.252592i	0.991993	+	0.126296i	$0.0403088\pi$
$311$			2.28550e14i			0.252592i	−0.991993	+	0.126296i	$0.959691\pi$
$312$	−2.03136e14			−0.220222
$313$	7.19234e13			0.0764899			0.0382450	−	0.999268i	$-0.487823\pi$
$313$	7.19234e13			0.0764899			0.0382450	+	0.999268i	$0.487823\pi$
$314$	−1.33033e15			−1.38798
$315$		−	5.24047e12i		−	0.00536423i
$316$			6.73799e14i			0.676718i
$317$	2.29458e14			0.226125			0.113062	−	0.993588i	$-0.463934\pi$
$317$	2.29458e14			0.226125			0.113062	+	0.993588i	$0.463934\pi$
$318$	4.39279e14			0.424793
$319$	1.48018e14			0.140466
$320$		−	7.39523e13i		−	0.0688735i
$321$			2.77656e14i			0.253792i
$322$			3.95606e14i			0.354918i
$323$			3.42686e14i			0.301774i
$324$	1.19817e15			1.03573
$325$			1.43075e15i			1.21412i
$326$	3.08094e15			2.56671
$327$	1.37501e15			1.12465
$328$		−	8.25571e12i		−	0.00662997i
$329$		−	2.90933e14i		−	0.229412i
$330$	−2.61435e14			−0.202433
$331$		−	3.61739e14i		−	0.275060i	−0.990498	−	0.137530i	$-0.956084\pi$
$331$		−	3.61739e14i		−	0.275060i	0.990498	−	0.137530i	$-0.0439163\pi$
$332$	7.55177e14	−	9.07431e14i	0.563923	−	0.677618i
$333$	−1.66786e14			−0.122319
$334$			1.93055e15i			1.39060i
$335$	1.19093e14			0.0842592
$336$	4.55469e14			0.316536
$337$		−	1.32965e14i		−	0.0907730i	−0.998970	−	0.0453865i	$-0.985548\pi$
$337$		−	1.32965e14i		−	0.0907730i	0.998970	−	0.0453865i	$-0.0144519\pi$
$338$			1.02107e15i			0.684785i
$339$	2.24508e15			1.47922
$340$			6.44589e13i			0.0417262i
$341$	−2.94588e15			−1.87365
$342$	2.89992e14			0.181230
$343$	−8.14827e14			−0.500381
$344$	1.73316e14			0.104590
$345$		−	1.71187e14i		−	0.101521i
$346$		−	1.19302e15i		−	0.695330i
$347$		−	5.79274e14i		−	0.331824i	−0.986141	−	0.165912i	$-0.946943\pi$
$347$		−	5.79274e14i		−	0.331824i	0.986141	−	0.165912i	$-0.0530567\pi$
$348$	−1.67599e14			−0.0943619
$349$	3.06814e14			0.169794			0.0848970	−	0.996390i	$-0.472944\pi$
$349$	3.06814e14			0.169794			0.0848970	+	0.996390i	$0.472944\pi$
$350$		−	6.47247e14i		−	0.352096i
$351$			1.96247e15i			1.04945i
$352$		−	3.73802e15i		−	1.96511i
$353$	9.55390e14			0.493779			0.246889	−	0.969044i	$-0.420592\pi$
$353$	9.55390e14			0.493779			0.246889	+	0.969044i	$0.420592\pi$
$354$			4.84966e15i			2.46429i
$355$	8.25793e13			0.0412573
$356$			1.40590e13i			0.00690645i
$357$	−3.06141e14			−0.147881
$358$	−1.00443e15			−0.477112
$359$	−8.14520e14			−0.380483			−0.190241	−	0.981737i	$-0.560927\pi$
$359$	−8.14520e14			−0.380483			−0.190241	+	0.981737i	$0.560927\pi$
$360$	−7.32744e12			−0.00336618
$361$	1.45617e15			0.657916
$362$	4.67480e15			2.07736
$363$	−2.81473e15			−1.23026
$364$		−	6.49938e14i		−	0.279424i
$365$	−4.15819e13			−0.0175852
$366$		−	1.20127e15i		−	0.499752i
$367$		−	2.81373e15i		−	1.15156i	−0.817605	−	0.575780i	$-0.804699\pi$
$367$		−	2.81373e15i		−	1.15156i	0.817605	−	0.575780i	$-0.195301\pi$
$368$	2.74163e15			1.10388
$369$	2.32740e13			0.00921961
$370$	1.74823e14			0.0681379
$371$		−	1.88801e14i		−	0.0724039i
$372$	3.33560e15			1.25868
$373$	1.32451e15			0.491815			0.245907	−	0.969293i	$-0.420914\pi$
$373$	1.32451e15			0.491815			0.245907	+	0.969293i	$0.420914\pi$
$374$			2.81426e15i			1.02834i
$375$			5.62532e14i			0.202283i
$376$	−4.06793e14			−0.143962
$377$		−	3.39854e14i		−	0.118371i
$378$		−	8.87790e14i		−	0.304340i
$379$			2.09333e15i			0.706323i	0.935562	+	0.353161i	$0.114893\pi$
$379$			2.09333e15i			0.706323i	−0.935562	+	0.353161i	$0.885107\pi$
$380$	−1.42417e14			−0.0473000
$381$	−3.20240e15			−1.04695
$382$		−	2.35949e15i		−	0.759343i
$383$	5.03669e15			1.59570			0.797852	−	0.602853i	$-0.205969\pi$
$383$	5.03669e15			1.59570			0.797852	+	0.602853i	$0.205969\pi$
$384$		−	1.14522e15i		−	0.357191i
$385$			1.12364e14i			0.0345036i
$386$			1.86942e15i			0.565176i
$387$			4.88602e14i			0.145442i
$388$		−	1.26016e14i		−	0.0369348i
$389$		−	5.09832e15i		−	1.47140i	−0.677309	−	0.735698i	$-0.736854\pi$
$389$		−	5.09832e15i		−	1.47140i	0.677309	−	0.735698i	$-0.263146\pi$
$390$			6.00264e14i			0.170590i
$391$	−1.84277e15			−0.515716
$392$			5.49913e14i			0.151558i
$393$	2.03324e15			0.551866
$394$		−	5.56934e15i		−	1.48877i
$395$	−2.67464e14			−0.0704178
$396$	1.11581e15			0.289348
$397$	−2.50078e14			−0.0638753			−0.0319377	−	0.999490i	$-0.510168\pi$
$397$	−2.50078e14			−0.0638753			−0.0319377	+	0.999490i	$0.510168\pi$
$398$		−	5.96668e15i		−	1.50118i
$399$		−	6.76396e14i		−	0.167635i
$400$	−4.48555e15			−1.09511
$401$	−8.80455e14			−0.211758			−0.105879	−	0.994379i	$-0.533766\pi$
$401$	−8.80455e14			−0.211758			−0.105879	+	0.994379i	$0.533766\pi$
$402$	−5.88744e15			−1.39499
$403$			6.76384e15i			1.57893i
$404$			7.05149e15i			1.62178i
$405$			4.75612e14i			0.107776i
$406$			1.53744e14i			0.0343275i
$407$	3.57618e15			0.786778
$408$			4.28058e14i			0.0927987i
$409$	−3.30464e15			−0.705967			−0.352983	−	0.935630i	$-0.614833\pi$
$409$	−3.30464e15			−0.705967			−0.352983	+	0.935630i	$0.614833\pi$
$410$	−2.43955e13			−0.00513578
$411$			9.96540e15i			2.06749i
$412$			2.78634e15i			0.569707i
$413$	2.08438e15			0.420026
$414$			1.55941e15i			0.309712i
$415$	3.60204e14	+	2.99767e14i	0.0705115	+	0.0586806i
$416$	−8.58262e15			−1.65600
$417$			9.77009e15i			1.85816i
$418$	−6.21791e15			−1.16570
$419$	2.13951e15			0.395394			0.197697	−	0.980263i	$-0.436654\pi$
$419$	2.13951e15			0.395394			0.197697	+	0.980263i	$0.436654\pi$
$420$		−	1.27229e14i		−	0.0231788i
$421$			1.32904e15i			0.238695i	0.992853	+	0.119348i	$0.0380803\pi$
$421$			1.32904e15i			0.238695i	−0.992853	+	0.119348i	$0.961920\pi$
$422$	1.26624e16			2.24202
$423$		−	1.14681e15i		−	0.200193i
$424$	−2.63989e14			−0.0454351
$425$	3.01494e15			0.511617
$426$	−4.08236e15			−0.683051
$427$	−5.16304e14			−0.0851801
$428$			1.24215e15i			0.202074i
$429$			1.22790e16i			1.96978i
$430$		−	5.12146e14i		−	0.0810182i
$431$	−3.35332e15			−0.523133			−0.261566	−	0.965185i	$-0.584239\pi$
$431$	−3.35332e15			−0.523133			−0.261566	+	0.965185i	$0.584239\pi$
$432$	−6.15257e15			−0.946572
$433$		−	1.25567e15i		−	0.190524i	−0.995452	−	0.0952618i	$-0.969631\pi$
$433$		−	1.25567e15i		−	0.190524i	0.995452	−	0.0952618i	$-0.0303688\pi$
$434$		−	3.05985e15i		−	0.457891i
$435$		−	6.65284e13i		−	0.00981910i
$436$	6.15136e15			0.895472
$437$		−	4.07147e15i		−	0.584605i
$438$	2.05563e15			0.291139
$439$			4.16491e15i			0.581861i	0.956744	+	0.290930i	$0.0939648\pi$
$439$			4.16491e15i			0.581861i	−0.956744	+	0.290930i	$0.906035\pi$
$440$	1.57112e14			0.0216518
$441$	−1.55028e15			−0.210755
$442$	6.46163e15			0.866580
$443$	5.33353e15			0.705654			0.352827	−	0.935689i	$-0.385220\pi$
$443$	5.33353e15			0.705654			0.352827	+	0.935689i	$0.385220\pi$
$444$	−4.04927e15			−0.528542
$445$	−5.58071e12			−0.000718670
$446$	−1.46360e16			−1.85957
$447$			4.66385e15i			0.584654i
$448$	1.57129e15			0.194352
$449$		−	8.57848e15i		−	1.04697i	−0.852036	−	0.523483i	$-0.824632\pi$
$449$		−	8.57848e15i		−	1.04697i	0.852036	−	0.523483i	$-0.175368\pi$
$450$		−	2.55134e15i		−	0.307250i
$451$	−4.99033e14			−0.0593021
$452$	1.00438e16			1.17779
$453$	−1.71422e16			−1.98371
$454$		−	1.74458e16i		−	1.99230i
$455$	2.57992e14			0.0290762
$456$	−9.45764e14			−0.105195
$457$		−	3.79441e15i		−	0.416531i	−0.978072	−	0.208265i	$-0.933218\pi$
$457$		−	3.79441e15i		−	0.416531i	0.978072	−	0.208265i	$-0.0667818\pi$
$458$		−	1.71583e16i		−	1.85901i
$459$	4.13541e15			0.442224
$460$		−	7.65838e14i		−	0.0808333i
$461$		−	1.04570e16i		−	1.08943i	−0.838620	−	0.544717i	$-0.816637\pi$
$461$		−	1.04570e16i		−	1.08943i	0.838620	−	0.544717i	$-0.183363\pi$
$462$		−	5.55481e15i		−	0.571238i
$463$	−9.08660e15			−0.922392			−0.461196	−	0.887298i	$-0.652579\pi$
$463$	−9.08660e15			−0.922392			−0.461196	+	0.887298i	$0.652579\pi$
$464$	1.06548e15			0.106767
$465$			1.32406e15i			0.130976i
$466$	−2.03596e16			−1.98817
$467$			1.84917e16i			1.78269i	0.453322	+	0.891347i	$0.350239\pi$
$467$			1.84917e16i			1.78269i	−0.453322	+	0.891347i	$0.649761\pi$
$468$		−	2.56194e15i		−	0.243834i
$469$			2.53041e15i			0.237768i
$470$			1.20207e15i			0.111517i
$471$			1.22313e16i			1.12033i
$472$		−	2.91446e15i		−	0.263576i
$473$		−	1.04764e16i		−	0.935506i
$474$	1.32223e16			1.16583
$475$			6.66129e15i			0.579958i
$476$	−1.36958e15			−0.117746
$477$		−	7.44222e14i		−	0.0631819i
$478$	1.30592e16			1.09484
$479$	2.26939e16			1.87887			0.939435	−	0.342728i	$-0.111351\pi$
$479$	2.26939e16			1.87887			0.939435	+	0.342728i	$0.111351\pi$
$480$	−1.68010e15			−0.137369
$481$		−	8.21101e15i		−	0.663019i
$482$		−	2.37369e16i		−	1.89296i
$483$	3.63727e15			0.286479
$484$	−1.25922e16			−0.979559
$485$	5.00219e13			0.00384335
$486$		−	8.02022e15i		−	0.608652i
$487$		−	7.49112e15i		−	0.561530i	−0.959777	−	0.280765i	$-0.909412\pi$
$487$		−	7.49112e15i		−	0.561530i	0.959777	−	0.280765i	$-0.0905881\pi$
$488$			7.21917e14i			0.0534525i
$489$		−	2.83267e16i		−	2.07178i
$490$	1.62498e15			0.117401
$491$			7.26021e15i			0.518156i	0.965856	+	0.259078i	$0.0834187\pi$
$491$			7.26021e15i			0.518156i	−0.965856	+	0.259078i	$0.916581\pi$
$492$	5.65050e14			0.0398379
$493$	−7.16155e14			−0.0498799
$494$			1.42765e16i			0.982337i
$495$			4.42921e14i			0.0301089i
$496$	−2.12054e16			−1.42415
$497$			1.75459e15i			0.116423i
$498$	−1.78069e16	−	1.48192e16i	−1.16738	−	0.971510i
$499$	−3.74015e15			−0.242262			−0.121131	−	0.992637i	$-0.538652\pi$
$499$	−3.74015e15			−0.242262			−0.121131	+	0.992637i	$0.538652\pi$
$500$			2.51659e15i			0.161062i
$501$	1.77499e16			1.12245
$502$	−3.24327e16			−2.02656
$503$		−	2.36789e15i		−	0.146202i	−0.997325	−	0.0731011i	$-0.976710\pi$
$503$		−	2.36789e15i		−	0.146202i	0.997325	−	0.0731011i	$-0.0232896\pi$
$504$		−	1.55689e14i		−	0.00949891i
$505$	−2.79908e15			−0.168759
$506$		−	3.34364e16i		−	1.99212i
$507$	9.38788e15			0.552738
$508$	−1.43265e16			−0.833602
$509$	7.97530e15			0.458607			0.229303	−	0.973355i	$-0.426355\pi$
$509$	7.97530e15			0.458607			0.229303	+	0.973355i	$0.426355\pi$
$510$	1.26490e15			0.0718847
$511$		−	8.83506e14i		−	0.0496231i
$512$		−	2.36757e16i		−	1.31426i
$513$			9.13689e15i			0.501296i
$514$	2.36396e16			1.28192
$515$	−1.10604e15			−0.0592825
$516$			1.18624e16i			0.628454i
$517$			2.45894e16i			1.28767i
$518$			3.71453e15i			0.192276i
$519$	−1.09688e16			−0.561250
$520$		−	3.60735e14i		−	0.0182460i
$521$	1.59095e16			0.795482			0.397741	−	0.917498i	$-0.369794\pi$
$521$	1.59095e16			0.795482			0.397741	+	0.917498i	$0.369794\pi$
$522$			6.06033e14i			0.0299553i
$523$	2.83134e16			1.38351			0.691754	−	0.722133i	$-0.256838\pi$
$523$	2.83134e16			1.38351			0.691754	+	0.722133i	$0.256838\pi$
$524$	9.09610e15			0.439408
$525$	−5.95090e15			−0.284202
$526$	−1.04909e16			−0.495334
$527$	1.42531e16			0.665342
$528$	−3.84960e16			−1.77669
$529$	−2.05784e13			−0.000939028
$530$			7.80084e14i			0.0351954i
$531$	8.21626e15			0.366528
$532$		−	3.02599e15i		−	0.133474i
$533$			1.14579e15i			0.0499739i
$534$	2.75886e14			0.0118982
$535$	−4.93070e14			−0.0210274
$536$	3.53812e15			0.149205
$537$			9.23489e15i			0.385111i
$538$	2.40449e16			0.991584
$539$	3.32406e16			1.35561
$540$			1.71864e15i			0.0693141i
$541$			2.39204e16i			0.954080i	0.878882	+	0.477040i	$0.158290\pi$
$541$			2.39204e16i			0.954080i	−0.878882	+	0.477040i	$0.841710\pi$
$542$	1.19975e16			0.473255
$543$		−	4.29810e16i		−	1.67678i
$544$			1.80857e16i			0.697818i
$545$			2.44178e15i			0.0931809i
$546$	−1.27540e16			−0.481383
$547$	1.90933e15			0.0712782			0.0356391	−	0.999365i	$-0.488653\pi$
$547$	1.90933e15			0.0712782			0.0356391	+	0.999365i	$0.488653\pi$
$548$			4.45821e16i			1.64618i
$549$	−2.03518e15			−0.0743309
$550$			5.47049e16i			1.97629i
$551$		−	1.58229e15i		−	0.0565428i
$552$		−	5.08578e15i		−	0.179772i
$553$		−	5.68290e15i		−	0.198710i
$554$		−	2.12239e16i		−	0.734118i
$555$		−	1.60736e15i		−	0.0549989i
$556$			4.37083e16i			1.47950i
$557$	2.76801e16			0.926909			0.463455	−	0.886121i	$-0.346610\pi$
$557$	2.76801e16			0.926909			0.463455	+	0.886121i	$0.346610\pi$
$558$		−	1.20614e16i		−	0.399570i
$559$	−2.40542e16			−0.788352
$560$			8.08835e14i			0.0262260i
$561$	2.58748e16			0.830042
$562$	1.18978e16			0.377614
$563$	2.02067e16			0.634518			0.317259	−	0.948339i	$-0.397237\pi$
$563$	2.02067e16			0.634518			0.317259	+	0.948339i	$0.397237\pi$
$564$		−	2.78424e16i		−	0.865032i
$565$			3.98687e15i			0.122558i
$566$	−5.52360e16			−1.68006
$567$	−1.01055e16			−0.304130
$568$	2.45334e15			0.0730579
$569$			1.96819e16i			0.579955i	0.957033	+	0.289978i	$0.0936479\pi$
$569$			1.96819e16i			0.579955i	−0.957033	+	0.289978i	$0.906352\pi$
$570$			2.79471e15i			0.0814870i
$571$			9.26888e14i			0.0267430i	0.999911	+	0.0133715i	$0.00425641\pi$
$571$			9.26888e14i			0.0267430i	−0.999911	+	0.0133715i	$0.995744\pi$
$572$			5.49323e16i			1.56838i
$573$	−2.16936e16			−0.612920
$574$		−	5.18339e14i		−	0.0144925i
$575$	−3.58206e16			−0.991119
$576$	6.19376e15			0.169597
$577$		−	1.34981e16i		−	0.365777i	−0.983134	−	0.182889i	$-0.941455\pi$
$577$		−	1.34981e16i		−	0.365777i	0.983134	−	0.182889i	$-0.0585448\pi$
$578$			3.75317e16i			1.00654i
$579$	1.71878e16			0.456194
$580$		−	2.97627e14i		−	0.00781817i
$581$	−6.36925e15	+	7.65338e15i	−0.165589	+	0.198974i
$582$	−2.47287e15			−0.0636301
$583$			1.59574e16i			0.406396i
$584$	−1.23535e15			−0.0311397
$585$	1.01696e15			0.0253728
$586$		−	1.61443e16i		−	0.398689i
$587$			4.24883e16i			1.03858i	0.854598	+	0.519291i	$0.173804\pi$
$587$			4.24883e16i			1.03858i	−0.854598	+	0.519291i	$0.826196\pi$
$588$	−3.76380e16			−0.910674
$589$			3.14912e16i			0.754218i
$590$	−8.61217e15			−0.204174
$591$	−5.12055e16			−1.20169
$592$	2.57424e16			0.598025
$593$	3.25604e16			0.748792			0.374396	−	0.927269i	$-0.377850\pi$
$593$	3.25604e16			0.748792			0.374396	+	0.927269i	$0.377850\pi$
$594$			7.50354e16i			1.70823i
$595$		−	5.43654e14i		−	0.0122524i
$596$			2.08646e16i			0.465514i
$597$	−5.48587e16			−1.21171
$598$	−7.67709e16			−1.67876
$599$		−	8.01350e16i		−	1.73485i	−0.497571	−	0.867423i	$-0.665774\pi$
$599$		−	8.01350e16i		−	1.73485i	0.497571	−	0.867423i	$-0.334226\pi$
$600$			8.32079e15i			0.178343i
$601$		−	5.31134e15i		−	0.112709i	−0.998411	−	0.0563543i	$-0.982052\pi$
$601$		−	5.31134e15i		−	0.112709i	0.998411	−	0.0563543i	$-0.0179476\pi$
$602$	1.08817e16			0.228623
$603$			9.97445e15i			0.207484i
$604$	−7.66891e16			−1.57947
$605$		−	4.99848e15i		−	0.101931i
$606$	1.38374e17			2.79396
$607$	4.22789e16			0.845263			0.422631	−	0.906302i	$-0.361106\pi$
$607$	4.22789e16			0.845263			0.422631	+	0.906302i	$0.361106\pi$
$608$	−3.99591e16			−0.791032
$609$	1.41355e15			0.0277082
$610$	2.13325e15			0.0414059
$611$	5.64581e16			1.08512
$612$	−5.39865e15			−0.102749
$613$		−	9.75014e16i		−	1.83759i	−0.394738	−	0.918794i	$-0.629165\pi$
$613$		−	9.75014e16i		−	1.83759i	0.394738	−	0.918794i	$-0.370835\pi$
$614$	1.11778e17			2.08616
$615$			2.24296e14i			0.00414545i
$616$			3.33822e15i			0.0610986i
$617$	−2.70420e16			−0.490149			−0.245075	−	0.969504i	$-0.578812\pi$
$617$	−2.70420e16			−0.490149			−0.245075	+	0.969504i	$0.578812\pi$
$618$	5.46776e16			0.981474
$619$	5.99702e16			1.06609			0.533043	−	0.846088i	$-0.321049\pi$
$619$	5.99702e16			1.06609			0.533043	+	0.846088i	$0.321049\pi$
$620$			5.92345e15i			0.104286i
$621$	−4.91330e16			−0.856690
$622$	2.00642e16			0.346481
$623$		−	1.18575e14i		−	0.00202799i
$624$			8.83879e16i			1.49722i
$625$	5.81041e16			0.974825
$626$		−	6.31409e15i		−	0.104922i
$627$			5.71686e16i			0.940918i
$628$			5.47191e16i			0.892033i
$629$	−1.73026e16			−0.279388
$630$	−4.60057e14			−0.00735814
$631$			3.54591e15i			0.0561762i	0.999605	+	0.0280881i	$0.00894189\pi$
$631$			3.54591e15i			0.0561762i	−0.999605	+	0.0280881i	$0.991058\pi$
$632$	−7.94605e15			−0.124695
$633$		−	1.16420e17i		−	1.80969i
$634$		−	2.01439e16i		−	0.310177i
$635$		−	5.68691e15i		−	0.0867429i
$636$		−	1.80684e16i		−	0.273009i
$637$		−	7.63214e16i		−	1.14238i
$638$		−	1.29944e16i		−	0.192677i
$639$			6.91629e15i			0.101594i
$640$	2.03371e15			0.0295944
$641$		−	1.67406e16i		−	0.241337i	−0.992693	−	0.120668i	$-0.961496\pi$
$641$		−	1.67406e16i		−	0.241337i	0.992693	−	0.120668i	$-0.0385037\pi$
$642$	2.43752e16			0.348127
$643$			3.40563e16i			0.481871i	0.970541	+	0.240936i	$0.0774543\pi$
$643$			3.40563e16i			0.481871i	−0.970541	+	0.240936i	$0.922546\pi$
$644$	1.62720e16			0.228101
$645$	−4.70876e15			−0.0653955
$646$	3.00841e16			0.413945
$647$			9.90228e16i			1.34992i	0.737852	+	0.674962i	$0.235840\pi$
$647$			9.90228e16i			1.34992i	−0.737852	+	0.674962i	$0.764160\pi$
$648$			1.41299e16i			0.190849i
$649$	−1.76170e17			−2.35757
$650$	1.25604e17			1.66542
$651$	−2.81328e16			−0.369596
$652$		−	1.26725e17i		−	1.64959i
$653$		−	1.29001e17i		−	1.66384i	−0.554893	−	0.831922i	$-0.687241\pi$
$653$		−	1.29001e17i		−	1.66384i	0.554893	−	0.831922i	$-0.312759\pi$
$654$		−	1.20711e17i		−	1.54269i
$655$			3.61069e15i			0.0457238i
$656$	−3.59220e15			−0.0450751
$657$		−	3.48263e15i		−	0.0433027i
$658$	−2.55407e16			−0.314686
$659$	5.83965e16			0.712975			0.356488	−	0.934300i	$-0.383974\pi$
$659$	5.83965e16			0.712975			0.356488	+	0.934300i	$0.383974\pi$
$660$			1.07533e16i			0.130101i
$661$			2.59444e16i			0.311054i	0.987832	+	0.155527i	$0.0497076\pi$
$661$			2.59444e16i			0.311054i	−0.987832	+	0.155527i	$0.950292\pi$
$662$	−3.17567e16			−0.377301
$663$		−	5.94094e16i		−	0.699478i
$664$	1.07013e16	+	8.90573e15i	0.124861	+	0.103911i
$665$	1.20116e15			0.0138890
$666$			1.46420e16i			0.167786i
$667$	8.50867e15			0.0966289
$668$	7.94074e16			0.893721
$669$			1.34566e17i			1.50099i
$670$		−	1.04551e16i		−	0.115579i
$671$	4.36377e16			0.478109
$672$		−	3.56977e16i		−	0.387636i
$673$	9.44987e16			1.01703			0.508517	−	0.861052i	$-0.330194\pi$
$673$	9.44987e16			1.01703			0.508517	+	0.861052i	$0.330194\pi$
$674$	−1.16729e16			−0.124514
$675$	8.03859e16			0.849879
$676$	4.19984e16			0.440102
$677$		−	5.57572e16i		−	0.579121i	−0.957160	−	0.289560i	$-0.906491\pi$
$677$		−	5.57572e16i		−	0.579121i	0.957160	−	0.289560i	$-0.0935091\pi$
$678$		−	1.97094e17i		−	2.02906i
$679$			1.06283e15i			0.0108454i
$680$	−7.60158e14			−0.00768865
$681$	−1.60400e17			−1.60813
$682$			2.58617e17i			2.57010i
$683$		−	5.61282e16i		−	0.552913i	−0.961026	−	0.276456i	$-0.910840\pi$
$683$		−	5.61282e16i		−	0.552913i	0.961026	−	0.276456i	$-0.0891601\pi$
$684$		−	1.19279e16i		−	0.116474i
$685$	−1.76968e16			−0.171298
$686$			7.15329e16i			0.686375i
$687$	−1.57756e17			−1.50054
$688$		−	7.54127e16i		−	0.711072i
$689$	3.66386e16			0.342471
$690$	−1.50284e16			−0.139257
$691$	−6.31977e16			−0.580541			−0.290271	−	0.956945i	$-0.593745\pi$
$691$	−6.31977e16			−0.580541			−0.290271	+	0.956945i	$0.593745\pi$
$692$	−4.90712e16			−0.446879
$693$	−9.41090e15			−0.0849634
$694$	−5.08540e16			−0.455164
$695$	−1.73500e16			−0.153954
$696$		−	1.97648e15i		−	0.0173875i
$697$	2.41447e15			0.0210584
$698$		−	2.69349e16i		−	0.232907i
$699$			1.87190e17i			1.60479i
$700$	−2.66225e16			−0.226287
$701$	−1.65722e17			−1.39660			−0.698301	−	0.715804i	$-0.746060\pi$
$701$	−1.65722e17			−1.39660			−0.698301	+	0.715804i	$0.746060\pi$
$702$	1.72284e17			1.43953
$703$		−	3.82289e16i		−	0.316709i
$704$	−1.32804e17			−1.09088
$705$	1.10520e16			0.0900133
$706$		−	8.38729e16i		−	0.677319i
$707$		−	5.94730e16i		−	0.476216i
$708$	1.99476e17			1.58377
$709$			6.58602e16i			0.518496i	0.965811	+	0.259248i	$0.0834748\pi$
$709$			6.58602e16i			0.518496i	−0.965811	+	0.259248i	$0.916525\pi$
$710$		−	7.24956e15i		−	0.0565929i
$711$		−	2.24010e16i		−	0.173400i
$712$	−1.65797e14			−0.00127261
$713$	−1.69341e17			−1.28892
$714$			2.68759e16i			0.202849i
$715$	−2.18053e16			−0.163202
$716$			4.13140e16i			0.306633i
$717$		−	1.20069e17i		−	0.883720i
$718$			7.15060e16i			0.521910i
$719$		−	8.23704e16i		−	0.596208i	−0.954533	−	0.298104i	$-0.903646\pi$
$719$		−	8.23704e16i		−	0.596208i	0.954533	−	0.298104i	$-0.0963542\pi$
$720$			3.18829e15i			0.0228856i
$721$		−	2.35004e16i		−	0.167287i
$722$		−	1.27836e17i		−	0.902466i
$723$	−2.18241e17			−1.52794
$724$		−	1.92283e17i		−	1.33509i
$725$	−1.39209e16			−0.0958607
$726$			2.47103e17i			1.68756i
$727$	2.00563e17			1.35846			0.679228	−	0.733928i	$-0.262315\pi$
$727$	2.00563e17			1.35846			0.679228	+	0.733928i	$0.262315\pi$
$728$	7.66466e15			0.0514878
$729$	1.02602e17			0.683579
$730$			3.65044e15i			0.0241217i
$731$			5.06882e16i			0.332202i
$732$	−4.94106e16			−0.321184
$733$	−5.59730e16			−0.360873			−0.180437	−	0.983587i	$-0.557751\pi$
$733$	−5.59730e16			−0.360873			−0.180437	+	0.983587i	$0.557751\pi$
$734$	−2.47015e17			−1.57960
$735$		−	1.49404e16i		−	0.0947627i
$736$		−	2.14877e17i		−	1.35183i
$737$		−	2.13869e17i		−	1.33457i
$738$		−	2.04320e15i		−	0.0126466i
$739$	−1.04021e17			−0.638638			−0.319319	−	0.947647i	$-0.603454\pi$
$739$	−1.04021e17			−0.638638			−0.319319	+	0.947647i	$0.603454\pi$
$740$		−	7.19081e15i		−	0.0437913i
$741$	1.31261e17			0.792913
$742$	−1.65747e16			−0.0993168
$743$			2.09693e17i			1.24638i	0.782070	+	0.623190i	$0.214164\pi$
$743$			2.09693e17i			1.24638i	−0.782070	+	0.623190i	$0.785836\pi$
$744$			3.93364e16i			0.231930i
$745$	−8.28218e15			−0.0484403
$746$		−	1.16277e17i		−	0.674625i
$747$	−2.51065e16	+	3.01683e16i	−0.144498	+	0.173631i
$748$	1.15756e17			0.660897
$749$		−	1.04764e16i		−	0.0593365i
$750$	4.93842e16			0.277473
$751$	5.99191e16			0.333984			0.166992	−	0.985958i	$-0.446595\pi$
$751$	5.99191e16			0.333984			0.166992	+	0.985958i	$0.446595\pi$
$752$			1.77002e17i			0.978751i
$753$			2.98192e17i			1.63578i
$754$	−2.98355e16			−0.162370
$755$		−	3.04417e16i		−	0.164356i
$756$	−3.65165e16			−0.195595
$757$	−2.84521e17			−1.51195			−0.755977	−	0.654598i	$-0.772838\pi$
$757$	−2.84521e17			−1.51195			−0.755977	+	0.654598i	$0.772838\pi$
$758$	1.83772e17			0.968867
$759$	−3.07420e17			−1.60798
$760$		−	1.67951e15i		−	0.00871569i
$761$			1.05870e17i			0.545088i	0.962143	+	0.272544i	$0.0878651\pi$
$761$			1.05870e17i			0.545088i	−0.962143	+	0.272544i	$0.912135\pi$
$762$			2.81136e17i			1.43611i
$763$	−5.18813e16			−0.262944
$764$	−9.70504e16			−0.488019
$765$		−	2.14299e15i		−	0.0106918i
$766$		−	4.42167e17i		−	2.18884i
$767$			4.04492e17i			1.98673i
$768$	−2.71111e17			−1.32123
$769$		−	3.45026e17i		−	1.66837i	−0.551481	−	0.834187i	$-0.685937\pi$
$769$		−	3.45026e17i		−	1.66837i	0.551481	−	0.834187i	$-0.314063\pi$
$770$	9.86438e15			0.0473288
$771$		−	2.17346e17i		−	1.03473i
$772$	7.68929e16			0.363231
$773$	1.82502e17			0.855440			0.427720	−	0.903911i	$-0.359317\pi$
$773$	1.82502e17			0.855440			0.427720	+	0.903911i	$0.359317\pi$
$774$	4.28939e16			0.199503
$775$	2.77058e17			1.27867
$776$	1.48610e15			0.00680576
$777$	3.41520e16			0.155200
$778$	−4.47577e17			−2.01832
$779$			5.33460e15i			0.0238714i
$780$	2.46900e16			0.109636
$781$		−	1.48297e17i		−	0.653470i
$782$			1.61775e17i			0.707411i
$783$	−1.90945e16			−0.0828587
$784$	2.39276e17			1.03039
$785$	−2.17207e16			−0.0928230
$786$		−	1.78497e17i		−	0.756998i
$787$	−3.50584e17			−1.47552			−0.737758	−	0.675066i	$-0.764115\pi$
$787$	−3.50584e17			−1.47552			−0.737758	+	0.675066i	$0.764115\pi$
$788$	−2.29078e17			−0.956810
$789$			9.64553e16i			0.399819i
$790$			2.34804e16i			0.0965925i
$791$	−8.47105e16			−0.345842
$792$			1.31587e16i			0.0533165i
$793$		−	1.00193e17i		−	0.402903i
$794$			2.19542e16i			0.0876182i
$795$	7.17223e15			0.0284087
$796$	−2.45421e17			−0.964790
$797$			2.26865e17i			0.885153i	0.896731	+	0.442576i	$0.145935\pi$
$797$			2.26865e17i			0.885153i	−0.896731	+	0.442576i	$0.854065\pi$
$798$	−5.93803e16			−0.229945
$799$		−	1.18971e17i		−	0.457258i
$800$			3.51558e17i			1.34109i
$801$		−	4.67404e14i		−	0.00176969i
$802$			7.72944e16i			0.290470i
$803$			7.46733e16i			0.278530i
$804$			2.42162e17i			0.896539i
$805$			6.45917e15i			0.0237357i
$806$	5.93792e17			2.16583
$807$		−	2.21073e17i		−	0.800377i
$808$	−8.31575e16			−0.298836
$809$			8.13875e15i			0.0290313i	0.999895	+	0.0145157i	$0.00462064\pi$
$809$			8.13875e15i			0.0290313i	−0.999895	+	0.0145157i	$0.995379\pi$
$810$	4.17536e16			0.147837
$811$	4.32077e17			1.51857			0.759287	−	0.650756i	$-0.225548\pi$
$811$	4.32077e17			1.51857			0.759287	+	0.650756i	$0.225548\pi$
$812$	6.32379e15			0.0220618
$813$		−	1.10307e17i		−	0.381998i
$814$		−	3.13949e17i		−	1.07923i
$815$	5.03033e16			0.171653
$816$	1.86255e17			0.630910
$817$	−1.11992e17			−0.376577
$818$			2.90111e17i			0.968378i
$819$			2.16077e16i			0.0715988i
$820$			1.00343e15i			0.00330069i
$821$		−	2.20592e17i		−	0.720328i	−0.932889	−	0.360164i	$-0.882721\pi$
$821$		−	2.20592e17i		−	0.720328i	0.932889	−	0.360164i	$-0.117279\pi$
$822$	8.74854e17			2.83599
$823$		−	4.07021e17i		−	1.30984i	−0.755699	−	0.654919i	$-0.772703\pi$
$823$		−	4.07021e17i		−	1.30984i	0.755699	−	0.654919i	$-0.227297\pi$
$824$	−3.28591e16			−0.104977
$825$	5.02966e17			1.59520
$826$		−	1.82986e17i		−	0.576152i
$827$			1.71673e17i			0.536621i	0.963332	+	0.268311i	$0.0864653\pi$
$827$			1.71673e17i			0.536621i	−0.963332	+	0.268311i	$0.913535\pi$
$828$	6.41416e16			0.199048
$829$			1.80282e17i			0.555424i	0.960664	+	0.277712i	$0.0895762\pi$
$829$			1.80282e17i			0.555424i	−0.960664	+	0.277712i	$0.910424\pi$
$830$	2.63163e16	−	3.16220e16i	0.0804926	−	0.0967210i
$831$	−1.95136e17			−0.592558
$832$			3.04923e17i			0.919286i
$833$	−1.60828e17			−0.481384
$834$	8.57708e17			2.54884
$835$			3.15207e16i			0.0929987i
$836$			2.55754e17i			0.749179i
$837$	3.80023e17			1.10524
$838$		−	1.87826e17i		−	0.542365i
$839$	−6.21220e16			−0.178104			−0.0890520	−	0.996027i	$-0.528384\pi$
$839$	−6.21220e16			−0.178104			−0.0890520	+	0.996027i	$0.528384\pi$
$840$	1.50040e15			0.00427103
$841$	−3.50508e17			−0.990654
$842$	1.16675e17			0.327420
$843$		−	1.09390e17i		−	0.304799i
$844$		−	5.20827e17i		−	1.44092i
$845$			1.66712e16i			0.0457960i
$846$	−1.00677e17			−0.274605
$847$	1.06204e17			0.287635
$848$			1.14866e17i			0.308899i
$849$			5.07850e17i			1.35609i
$850$		−	2.64679e17i		−	0.701787i
$851$	2.05573e17			0.541239
$852$			1.67915e17i			0.438988i
$853$	4.05122e17			1.05170			0.525850	−	0.850577i	$-0.323747\pi$
$853$	4.05122e17			1.05170			0.525850	+	0.850577i	$0.323747\pi$
$854$			4.53259e16i			0.116842i
$855$	4.73478e15			0.0121200
$856$	−1.46485e16			−0.0372350
$857$	−5.90157e17			−1.48964			−0.744822	−	0.667264i	$-0.767465\pi$
$857$	−5.90157e17			−1.48964			−0.744822	+	0.667264i	$0.767465\pi$
$858$	1.07796e18			2.70196
$859$	−1.70190e17			−0.423618			−0.211809	−	0.977311i	$-0.567936\pi$
$859$	−1.70190e17			−0.423618			−0.211809	+	0.977311i	$0.567936\pi$
$860$	−2.10655e16			−0.0520693
$861$	−4.76570e15			−0.0116979
$862$			2.94386e17i			0.717584i
$863$	5.02423e17			1.21620			0.608100	−	0.793860i	$-0.291932\pi$
$863$	5.02423e17			1.21620			0.608100	+	0.793860i	$0.291932\pi$
$864$			4.82211e17i			1.15919i
$865$		−	1.94788e16i		−	0.0465013i
$866$	−1.10234e17			−0.261342
$867$	3.45073e17			0.812449
$868$	−1.25858e17			−0.294280
$869$			4.80315e17i			1.11534i
$870$	−5.84047e15			−0.0134689
$871$	−4.91049e17			−1.12465
$872$			7.25424e16i			0.165004i
$873$			4.18951e15i			0.00946406i
$874$	−3.57431e17			−0.801906
$875$		−	2.12252e16i		−	0.0472938i
$876$		−	8.45519e16i		−	0.187111i
$877$		−	3.41376e17i		−	0.750302i	−0.926964	−	0.375151i	$-0.877591\pi$
$877$		−	3.41376e17i		−	0.750302i	0.926964	−	0.375151i	$-0.122409\pi$
$878$	3.65634e17			0.798141
$879$	−1.48434e17			−0.321810
$880$		−	6.83622e16i		−	0.147204i
$881$	−4.70596e17			−1.00645			−0.503225	−	0.864155i	$-0.667853\pi$
$881$	−4.70596e17			−1.00645			−0.503225	+	0.864155i	$0.667853\pi$
$882$			1.36098e17i			0.289094i
$883$			2.20653e17i			0.465528i	0.972533	+	0.232764i	$0.0747770\pi$
$883$			2.20653e17i			0.465528i	−0.972533	+	0.232764i	$0.925223\pi$
$884$		−	2.65779e17i		−	0.556939i
$885$			7.91818e16i			0.164803i
$886$		−	4.68226e17i		−	0.967950i
$887$			1.66529e17i			0.341938i	0.985276	+	0.170969i	$0.0546898\pi$
$887$			1.66529e17i			0.341938i	−0.985276	+	0.170969i	$0.945310\pi$
$888$		−	4.77527e16i		−	0.0973913i
$889$	1.20832e17			0.244777
$890$			4.89926e14i			0.000985804i
$891$	8.54109e17			1.70705
$892$			6.02007e17i			1.19512i
$893$	2.62858e17			0.518338
$894$	4.09435e17			0.801973
$895$	−1.63996e16			−0.0319076
$896$			4.32110e16i			0.0835114i
$897$			7.05846e17i			1.35505i
$898$	−7.53098e17			−1.43613
$899$	−6.58111e16			−0.124664
$900$	−1.04941e17			−0.197466
$901$		−	7.72066e16i		−	0.144313i
$902$			4.38097e16i			0.0813450i
$903$		−	1.00049e17i		−	0.184538i
$904$			1.18446e17i			0.217024i
$905$	7.63268e16			0.138927
$906$			1.50490e18i			2.72107i
$907$	−4.85441e17			−0.871952			−0.435976	−	0.899958i	$-0.643597\pi$
$907$	−4.85441e17			−0.871952			−0.435976	+	0.899958i	$0.643597\pi$
$908$	−7.17579e17			−1.28043
$909$		−	2.34433e17i		−	0.415561i
$910$		−	2.26489e16i		−	0.0398841i
$911$	−6.97064e17			−1.21945			−0.609723	−	0.792615i	$-0.708719\pi$
$911$	−6.97064e17			−1.21945			−0.609723	+	0.792615i	$0.708719\pi$
$912$			4.11517e17i			0.715186i
$913$	5.38325e17	−	6.46858e17i	0.929436	−	1.11682i
$914$	−3.33108e17			−0.571358
$915$		−	1.96135e16i		−	0.0334217i
$916$	−7.05753e17			−1.19476
$917$	−7.67176e16			−0.129026
$918$		−	3.63044e17i		−	0.606601i
$919$		−	1.18874e18i		−	1.97330i	−0.162852	−	0.986650i	$-0.552069\pi$
$919$		−	1.18874e18i		−	1.97330i	0.162852	−	0.986650i	$-0.447931\pi$
$920$	9.03147e15			0.0148947
$921$		−	1.02771e18i		−	1.68388i
$922$	−9.18010e17			−1.49438
$923$	−3.40494e17			−0.550680
$924$	−2.28480e17			−0.367127
$925$	−3.36336e17			−0.536937
$926$			7.97705e17i			1.26525i
$927$		−	9.26344e16i		−	0.145980i
$928$		−	8.35076e16i		−	0.130749i
$929$	−8.32553e17			−1.29514			−0.647571	−	0.762005i	$-0.724215\pi$
$929$	−8.32553e17			−1.29514			−0.647571	+	0.762005i	$0.724215\pi$
$930$	1.16238e17			0.179660
$931$		−	3.55338e17i		−	0.545687i
$932$			8.37428e17i			1.27777i
$933$		−	1.84474e17i		−	0.279669i
$934$	1.62337e18			2.44533
$935$			4.59492e16i			0.0687715i
$936$	3.02128e16			0.0449299
$937$			8.17381e17i			1.20778i	0.797068	+	0.603889i	$0.206383\pi$
$937$			8.17381e17i			1.20778i	−0.797068	+	0.603889i	$0.793617\pi$
$938$	2.22143e17			0.326148
$939$	−5.80529e16			−0.0846896
$940$	4.94433e16			0.0716705
$941$	−9.12576e16			−0.131441			−0.0657205	−	0.997838i	$-0.520935\pi$
$941$	−9.12576e16			−0.131441			−0.0657205	+	0.997838i	$0.520935\pi$
$942$	1.07378e18			1.53677
$943$	−2.86865e16			−0.0407950
$944$	−1.26813e18			−1.79197
$945$		−	1.44952e16i		−	0.0203532i
$946$	−9.19717e17			−1.28324
$947$		−	5.86578e17i		−	0.813253i	−0.913594	−	0.406627i	$-0.866705\pi$
$947$		−	5.86578e17i		−	0.813253i	0.913594	−	0.406627i	$-0.133295\pi$
$948$		−	5.43856e17i		−	0.749263i
$949$	1.71452e17			0.234718
$950$	5.84789e17			0.795532
$951$	−1.85207e17			−0.250365
$952$		−	1.61513e16i		−	0.0216964i
$953$	1.36981e16			0.0182854			0.00914268	−	0.999958i	$-0.497090\pi$
$953$	1.36981e16			0.0182854			0.00914268	+	0.999958i	$0.497090\pi$
$954$	−6.53347e16			−0.0866669
$955$		−	3.85241e16i		−	0.0507822i
$956$		−	5.37150e17i		−	0.703636i
$957$	−1.19472e17			−0.155524
$958$		−	1.99228e18i		−	2.57725i
$959$		−	3.76011e17i		−	0.483380i
$960$			5.96906e16i			0.0762567i
$961$	5.22124e17			0.662878
$962$	−7.20838e17			−0.909467
$963$		−	4.12962e16i		−	0.0517789i
$964$	−9.76342e17			−1.21658
$965$			3.05226e16i			0.0377970i
$966$		−	3.19313e17i		−	0.392965i
$967$			8.98244e17i			1.09859i	0.835629	+	0.549295i	$0.185104\pi$
$967$			8.98244e17i			1.09859i	−0.835629	+	0.549295i	$0.814896\pi$
$968$		−	1.48499e17i		−	0.180498i
$969$		−	2.76599e17i		−	0.334124i
$970$		−	4.39138e15i		−	0.00527194i
$971$			1.01340e18i			1.20911i	0.796562	+	0.604556i	$0.206650\pi$
$971$			1.01340e18i			1.20911i	−0.796562	+	0.604556i	$0.793350\pi$
$972$	−3.29887e17			−0.391172
$973$		−	3.68641e17i		−	0.434437i
$974$	−6.57639e17			−0.770254
$975$		−	1.15483e18i		−	1.34428i
$976$	3.14118e17			0.363407
$977$	1.11005e18			1.27637			0.638185	−	0.769883i	$-0.279686\pi$
$977$	1.11005e18			1.27637			0.638185	+	0.769883i	$0.279686\pi$
$978$	−2.48678e18			−2.84187
$979$			1.00219e16i			0.0113829i
$980$		−	6.68386e16i		−	0.0754520i
$981$	−2.04507e17			−0.229453
$982$	6.37368e17			0.710757
$983$	1.21754e18			1.34946			0.674731	−	0.738063i	$-0.264260\pi$
$983$	1.21754e18			1.34946			0.674731	+	0.738063i	$0.264260\pi$
$984$			6.66359e15i			0.00734070i
$985$		−	9.09322e16i		−	0.0995635i
$986$			6.28707e16i			0.0684206i
$987$			2.34826e17i			0.254006i
$988$	5.87220e17			0.631334
$989$		−	6.02228e17i		−	0.643552i
$990$	3.88837e16			0.0413006
$991$	−8.08816e17			−0.853901			−0.426951	−	0.904275i	$-0.640412\pi$
$991$	−8.08816e17			−0.853901			−0.426951	+	0.904275i	$0.640412\pi$
$992$			1.66199e18i			1.74404i
$993$			2.91977e17i			0.304546i
$994$	1.54034e17			0.159698
$995$		−	9.74196e16i		−	0.100394i
$996$	−6.09540e17	+	7.32432e17i	−0.624376	+	0.750259i
$997$	7.63630e17			0.777520			0.388760	−	0.921339i	$-0.372903\pi$
$997$	7.63630e17			0.777520			0.388760	+	0.921339i	$0.372903\pi$
$998$			3.28345e17i			0.332312i
$999$	−4.61332e17			−0.464110

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	83.13.b.c.82.16	✓	80
83.82	odd	2	inner	83.13.b.c.82.65	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
83.13.b.c.82.16	✓	80	1.1	even	1	trivial
83.13.b.c.82.65	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)

\(f(q)\)	\(=\)	\(q-87.7892i q^{2} -807.149 q^{3} -3610.94 q^{4} -1433.36i q^{5} +70858.9i q^{6} +30455.0 q^{7} -42583.4i q^{8} +120049. q^{9} +O(q^{10})\)	\(q-87.7892i q^{2} -807.149 q^{3} -3610.94 q^{4} -1433.36i q^{5} +70858.9i q^{6} +30455.0 q^{7} -42583.4i q^{8} +120049. q^{9} -125833. q^{10} -2.57404e6 q^{11} +2.91456e6 q^{12} +5.91008e6i q^{13} -2.67362e6i q^{14} +1.15693e6i q^{15} -1.85288e7 q^{16} +1.24540e7 q^{17} -1.05390e7i q^{18} +2.75162e7i q^{19} +5.17576e6i q^{20} -2.45818e7 q^{21} +2.25973e8i q^{22} -1.47966e8 q^{23} +3.43712e7i q^{24} +2.42086e8 q^{25} +5.18841e8 q^{26} +3.32055e8 q^{27} -1.09971e8 q^{28} -5.75041e7 q^{29} +1.01566e8 q^{30} +1.14446e9 q^{31} +1.45220e9i q^{32} +2.07763e9 q^{33} -1.09333e9i q^{34} -4.36530e7i q^{35} -4.33487e8 q^{36} -1.38932e9 q^{37} +2.41562e9 q^{38} -4.77031e9i q^{39} -6.10373e7 q^{40} +1.93871e8 q^{41} +2.15801e9i q^{42} +4.07004e9i q^{43} +9.29469e9 q^{44} -1.72072e8i q^{45} +1.29898e10i q^{46} -9.55285e9i q^{47} +1.49555e10 q^{48} -1.29138e10 q^{49} -2.12525e10i q^{50} -1.00522e10 q^{51} -2.13409e10i q^{52} -6.19935e9i q^{53} -2.91508e10i q^{54} +3.68952e9i q^{55} -1.29688e9i q^{56} -2.22097e10i q^{57} +5.04824e9i q^{58} +6.84411e10 q^{59} -4.17761e9i q^{60} -1.69530e10 q^{61} -1.00471e11i q^{62} +3.65608e9 q^{63} +5.15938e10 q^{64} +8.47125e9 q^{65} -1.82394e11i q^{66} +8.30868e10i q^{67} -4.49705e10 q^{68} +1.19431e11 q^{69} -3.83226e9 q^{70} +5.76125e10i q^{71} -5.11208e9i q^{72} -2.90102e10i q^{73} +1.21968e11i q^{74} -1.95400e11 q^{75} -9.93592e10i q^{76} -7.83925e10 q^{77} -4.18782e11 q^{78} -1.86600e11i q^{79} +2.65583e10i q^{80} -3.31817e11 q^{81} -1.70198e10i q^{82} +(-2.09136e11 + 2.51301e11i) q^{83} +8.87631e10 q^{84} -1.78510e10i q^{85} +3.57305e11 q^{86} +4.64144e10 q^{87} +1.09611e11i q^{88} -3.89346e9i q^{89} -1.51061e10 q^{90} +1.79992e11i q^{91} +5.34297e11 q^{92} -9.23749e11 q^{93} -8.38637e11 q^{94} +3.94405e10 q^{95} -1.17214e12i q^{96} +3.48984e10i q^{97} +1.13369e12i q^{98} -3.09010e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 918 q^{3} - 181150 q^{4} + 103918 q^{7} + 14902142 q^{9}+O(q^{10}) \) 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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