LMFDB - Embedded newform 83.13.b.c.82.17

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			82.17
Character	$\chi$	$=$	83.82
Dual form			83.13.b.c.82.64

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-87.6467i q^{2} +305.164 q^{3} -3585.94 q^{4} -19977.0i q^{5} -26746.6i q^{6} +69148.7 q^{7} -44704.8i q^{8} -438316. q^{9} +O(q^{10})$	\(q-87.6467i q^{2} +305.164 q^{3} -3585.94 q^{4} -19977.0i q^{5} -26746.6i q^{6} +69148.7 q^{7} -44704.8i q^{8} -438316. q^{9} -1.75092e6 q^{10} +1.49896e6 q^{11} -1.09430e6 q^{12} +8.07846e6i q^{13} -6.06066e6i q^{14} -6.09627e6i q^{15} -1.86063e7 q^{16} +1.25776e7 q^{17} +3.84169e7i q^{18} +8.82966e7i q^{19} +7.16365e7i q^{20} +2.11017e7 q^{21} -1.31379e8i q^{22} -2.03689e8 q^{23} -1.36423e7i q^{24} -1.54941e8 q^{25} +7.08050e8 q^{26} -2.95935e8 q^{27} -2.47963e8 q^{28} -4.03081e8 q^{29} -5.34318e8 q^{30} -1.61516e9 q^{31} +1.44767e9i q^{32} +4.57428e8 q^{33} -1.10238e9i q^{34} -1.38139e9i q^{35} +1.57178e9 q^{36} +2.03291e9 q^{37} +7.73891e9 q^{38} +2.46525e9i q^{39} -8.93070e8 q^{40} -1.17241e9 q^{41} -1.84949e9i q^{42} +2.18456e9i q^{43} -5.37518e9 q^{44} +8.75625e9i q^{45} +1.78527e10i q^{46} +9.97929e9i q^{47} -5.67796e9 q^{48} -9.05974e9 q^{49} +1.35801e10i q^{50} +3.83823e9 q^{51} -2.89689e10i q^{52} +1.56114e10i q^{53} +2.59377e10i q^{54} -2.99448e10i q^{55} -3.09128e9i q^{56} +2.69449e10i q^{57} +3.53287e10i q^{58} -7.09776e10 q^{59} +2.18609e10i q^{60} -1.99790e9 q^{61} +1.41563e11i q^{62} -3.03090e10 q^{63} +5.06719e10 q^{64} +1.61384e11 q^{65} -4.00921e10i q^{66} -1.14770e11i q^{67} -4.51025e10 q^{68} -6.21586e10 q^{69} -1.21074e11 q^{70} +1.31719e11i q^{71} +1.95948e10i q^{72} +2.41235e10i q^{73} -1.78177e11i q^{74} -4.72824e10 q^{75} -3.16627e11i q^{76} +1.03651e11 q^{77} +2.16071e11 q^{78} -6.48375e10i q^{79} +3.71698e11i q^{80} +1.42630e11 q^{81} +1.02758e11i q^{82} +(2.97113e11 - 1.36432e11i) q^{83} -7.56695e10 q^{84} -2.51263e11i q^{85} +1.91469e11 q^{86} -1.23006e11 q^{87} -6.70107e10i q^{88} +3.77195e11i q^{89} +7.67456e11 q^{90} +5.58615e11i q^{91} +7.30418e11 q^{92} -4.92888e11 q^{93} +8.74652e11 q^{94} +1.76390e12 q^{95} +4.41775e11i q^{96} -6.75552e11i q^{97} +7.94057e11i q^{98} -6.57018e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	87.6467i		−	1.36948i	−0.728788	−	0.684740i	$-0.759916\pi$
$2$		−	87.6467i		−	1.36948i	0.728788	−	0.684740i	$-0.240084\pi$
$3$	305.164			0.418606			0.209303	−	0.977851i	$-0.432880\pi$
$3$	305.164			0.418606			0.209303	+	0.977851i	$0.432880\pi$
$4$	−3585.94			−0.875474
$5$		−	19977.0i		−	1.27853i	−0.768987	−	0.639265i	$-0.779239\pi$
$5$		−	19977.0i		−	1.27853i	0.768987	−	0.639265i	$-0.220761\pi$
$6$		−	26746.6i		−	0.573273i
$7$	69148.7			0.587754			0.293877	−	0.955843i	$-0.405054\pi$
$7$	69148.7			0.587754			0.293877	+	0.955843i	$0.405054\pi$
$8$		−	44704.8i		−	0.170535i
$9$	−438316.			−0.824769
$10$	−1.75092e6			−1.75092
$11$	1.49896e6			0.846124			0.423062	−	0.906101i	$-0.360955\pi$
$11$	1.49896e6			0.846124			0.423062	+	0.906101i	$0.360955\pi$
$12$	−1.09430e6			−0.366479
$13$			8.07846e6i			1.67366i	0.547460	+	0.836832i	$0.315595\pi$
$13$			8.07846e6i			1.67366i	−0.547460	+	0.836832i	$0.684405\pi$
$14$		−	6.06066e6i		−	0.804918i
$15$		−	6.09627e6i		−	0.535201i
$16$	−1.86063e7			−1.10902
$17$	1.25776e7			0.521079			0.260540	−	0.965463i	$-0.416100\pi$
$17$	1.25776e7			0.521079			0.260540	+	0.965463i	$0.416100\pi$
$18$			3.84169e7i			1.12950i
$19$			8.82966e7i			1.87682i	0.345525	+	0.938410i	$0.387701\pi$
$19$			8.82966e7i			1.87682i	−0.345525	+	0.938410i	$0.612299\pi$
$20$			7.16365e7i			1.11932i
$21$	2.11017e7			0.246038
$22$		−	1.31379e8i		−	1.15875i
$23$	−2.03689e8			−1.37594			−0.687972	−	0.725737i	$-0.741499\pi$
$23$	−2.03689e8			−1.37594			−0.687972	+	0.725737i	$0.741499\pi$
$24$		−	1.36423e7i		−	0.0713872i
$25$	−1.54941e8			−0.634639
$26$	7.08050e8			2.29205
$27$	−2.95935e8			−0.763860
$28$	−2.47963e8			−0.514564
$29$	−4.03081e8			−0.677648			−0.338824	−	0.940850i	$-0.610029\pi$
$29$	−4.03081e8			−0.677648			−0.338824	+	0.940850i	$0.610029\pi$
$30$	−5.34318e8			−0.732946
$31$	−1.61516e9			−1.81989			−0.909944	−	0.414732i	$-0.863875\pi$
$31$	−1.61516e9			−1.81989			−0.909944	+	0.414732i	$0.863875\pi$
$32$			1.44767e9i			1.34824i
$33$	4.57428e8			0.354193
$34$		−	1.10238e9i		−	0.713607i
$35$		−	1.38139e9i		−	0.751461i
$36$	1.57178e9			0.722064
$37$	2.03291e9			0.792332			0.396166	−	0.918179i	$-0.370341\pi$
$37$	2.03291e9			0.792332			0.396166	+	0.918179i	$0.370341\pi$
$38$	7.73891e9			2.57027
$39$			2.46525e9i			0.700606i
$40$	−8.93070e8			−0.218035
$41$	−1.17241e9			−0.246819			−0.123409	−	0.992356i	$-0.539383\pi$
$41$	−1.17241e9			−0.246819			−0.123409	+	0.992356i	$0.539383\pi$
$42$		−	1.84949e9i		−	0.336944i
$43$			2.18456e9i			0.345583i	0.984958	+	0.172792i	$0.0552787\pi$
$43$			2.18456e9i			0.345583i	−0.984958	+	0.172792i	$0.944721\pi$
$44$	−5.37518e9			−0.740759
$45$			8.75625e9i			1.05449i
$46$			1.78527e10i			1.88433i
$47$			9.97929e9i			0.925790i	0.886413	+	0.462895i	$0.153189\pi$
$47$			9.97929e9i			0.925790i	−0.886413	+	0.462895i	$0.846811\pi$
$48$	−5.67796e9			−0.464242
$49$	−9.05974e9			−0.654545
$50$			1.35801e10i			0.869125i
$51$	3.83823e9			0.218127
$52$		−	2.89689e10i		−	1.46525i
$53$			1.56114e10i			0.704348i	0.935934	+	0.352174i	$0.114558\pi$
$53$			1.56114e10i			0.704348i	−0.935934	+	0.352174i	$0.885442\pi$
$54$			2.59377e10i			1.04609i
$55$		−	2.99448e10i		−	1.08179i
$56$		−	3.09128e9i		−	0.100233i
$57$			2.69449e10i			0.785648i
$58$			3.53287e10i			0.928025i
$59$	−7.09776e10			−1.68271			−0.841355	−	0.540484i	$-0.818241\pi$
$59$	−7.09776e10			−1.68271			−0.841355	+	0.540484i	$0.818241\pi$
$60$			2.18609e10i			0.468554i
$61$	−1.99790e9			−0.0387788			−0.0193894	−	0.999812i	$-0.506172\pi$
$61$	−1.99790e9			−0.0387788			−0.0193894	+	0.999812i	$0.506172\pi$
$62$			1.41563e11i			2.49230i
$63$	−3.03090e10			−0.484761
$64$	5.06719e10			0.737373
$65$	1.61384e11			2.13983
$66$		−	4.00921e10i		−	0.485060i
$67$		−	1.14770e11i		−	1.26876i	−0.773020	−	0.634382i	$-0.781255\pi$
$67$		−	1.14770e11i		−	1.26876i	0.773020	−	0.634382i	$-0.218745\pi$
$68$	−4.51025e10			−0.456192
$69$	−6.21586e10			−0.575979
$70$	−1.21074e11			−1.02911
$71$			1.31719e11i			1.02825i	0.857716	+	0.514123i	$0.171883\pi$
$71$			1.31719e11i			1.02825i	−0.857716	+	0.514123i	$0.828117\pi$
$72$			1.95948e10i			0.140652i
$73$			2.41235e10i			0.159405i	0.996819	+	0.0797026i	$0.0253971\pi$
$73$			2.41235e10i			0.159405i	−0.996819	+	0.0797026i	$0.974603\pi$
$74$		−	1.78177e11i		−	1.08508i
$75$	−4.72824e10			−0.265664
$76$		−	3.16627e11i		−	1.64311i
$77$	1.03651e11			0.497313
$78$	2.16071e11			0.959466
$79$		−	6.48375e10i		−	0.266725i	−0.991067	−	0.133362i	$-0.957423\pi$
$79$		−	6.48375e10i		−	0.266725i	0.991067	−	0.133362i	$-0.0425774\pi$
$80$			3.71698e11i			1.41791i
$81$	1.42630e11			0.505012
$82$			1.02758e11i			0.338013i
$83$	2.97113e11	−	1.36432e11i	0.908769	−	0.417300i
$83$	2.97113e11	−	1.36432e11i	0.908769	−	0.417300i
$84$	−7.56695e10			−0.215400
$85$		−	2.51263e11i		−	0.666215i
$86$	1.91469e11			0.473269
$87$	−1.23006e11			−0.283668
$88$		−	6.70107e10i		−	0.144294i
$89$			3.77195e11i			0.758972i	0.925198	+	0.379486i	$0.123899\pi$
$89$			3.77195e11i			0.758972i	−0.925198	+	0.379486i	$0.876101\pi$
$90$	7.67456e11			1.44410
$91$			5.58615e11i			0.983703i
$92$	7.30418e11			1.20460
$93$	−4.92888e11			−0.761816
$94$	8.74652e11			1.26785
$95$	1.76390e12			2.39957
$96$			4.41775e11i			0.564383i
$97$		−	6.75552e11i		−	0.811014i	−0.914092	−	0.405507i	$-0.867095\pi$
$97$		−	6.75552e11i		−	0.811014i	0.914092	−	0.405507i	$-0.132905\pi$
$98$			7.94057e11i			0.896386i
$99$	−6.57018e11			−0.697856
$100$	5.55610e11			0.555610
$101$			2.13950e11i			0.201551i	0.994909	+	0.100775i	$0.0321323\pi$
$101$			2.13950e11i			0.201551i	−0.994909	+	0.100775i	$0.967868\pi$
$102$		−	3.36408e11i		−	0.298721i
$103$		−	2.05656e12i		−	1.72234i	−0.508317	−	0.861170i	$-0.669732\pi$
$103$		−	2.05656e12i		−	1.72234i	0.508317	−	0.861170i	$-0.330268\pi$
$104$	3.61146e11			0.285419
$105$		−	4.21549e11i		−	0.314566i
$106$	1.36829e12			0.964591
$107$		−	1.33849e12i		−	0.891892i	−0.895060	−	0.445946i	$-0.852867\pi$
$107$		−	1.33849e12i		−	0.891892i	0.895060	−	0.445946i	$-0.147133\pi$
$108$	1.06121e12			0.668740
$109$	5.03378e11			0.300148			0.150074	−	0.988675i	$-0.452049\pi$
$109$	5.03378e11			0.300148			0.150074	+	0.988675i	$0.452049\pi$
$110$	−2.62456e12			−1.48150
$111$	6.20370e11			0.331675
$112$	−1.28660e12			−0.651831
$113$	9.42616e11			0.452756			0.226378	−	0.974040i	$-0.427312\pi$
$113$	9.42616e11			0.452756			0.226378	+	0.974040i	$0.427312\pi$
$114$	2.36164e12			1.07593
$115$			4.06910e12i			1.75919i
$116$	1.44543e12			0.593264
$117$		−	3.54092e12i		−	1.38039i
$118$			6.22095e12i			2.30444i
$119$	8.69724e11			0.306267
$120$	−2.72533e11			−0.0912707
$121$	−8.91549e11			−0.284075
$122$			1.75109e11i			0.0531068i
$123$	−3.57779e11			−0.103320
$124$	5.79186e12			1.59326
$125$		−	1.78194e12i		−	0.467125i
$126$			2.65648e12i			0.663871i
$127$	−7.57681e12			−1.80578			−0.902888	−	0.429876i	$-0.858557\pi$
$127$	−7.57681e12			−1.80578			−0.902888	+	0.429876i	$0.858557\pi$
$128$			1.48841e12i			0.338426i
$129$			6.66648e11i			0.144663i
$130$		−	1.41447e13i		−	2.93045i
$131$	4.67918e12			0.925852			0.462926	−	0.886397i	$-0.346800\pi$
$131$	4.67918e12			0.925852			0.462926	+	0.886397i	$0.346800\pi$
$132$	−1.64031e12			−0.310087
$133$			6.10560e12i			1.10311i
$134$	−1.00592e13			−1.73755
$135$			5.91190e12i			0.976617i
$136$		−	5.62279e11i		−	0.0888625i
$137$		−	4.50369e12i		−	0.681153i	−0.940217	−	0.340577i	$-0.889378\pi$
$137$		−	4.50369e12i		−	0.681153i	0.940217	−	0.340577i	$-0.110622\pi$
$138$			5.44800e12i			0.788792i
$139$			1.20147e13i			1.66580i	0.553424	+	0.832900i	$0.313321\pi$
$139$			1.20147e13i			1.66580i	−0.553424	+	0.832900i	$0.686679\pi$
$140$			4.95357e12i			0.657885i
$141$			3.04532e12i			0.387541i
$142$	1.15447e13			1.40816
$143$			1.21093e13i			1.41613i
$144$	8.15542e12			0.914684
$145$			8.05236e12i			0.866393i
$146$	2.11434e12			0.218302
$147$	−2.76471e12			−0.273997
$148$	−7.28988e12			−0.693666
$149$		−	5.89190e12i		−	0.538440i	−0.963079	−	0.269220i	$-0.913234\pi$
$149$		−	5.89190e12i		−	0.538440i	0.963079	−	0.269220i	$-0.0867659\pi$
$150$			4.14415e12i			0.363821i
$151$	5.58809e12			0.471413			0.235706	−	0.971824i	$-0.424260\pi$
$151$	5.58809e12			0.471413			0.235706	+	0.971824i	$0.424260\pi$
$152$	3.94729e12			0.320064
$153$	−5.51296e12			−0.429770
$154$		−	9.08468e12i		−	0.681060i
$155$			3.22660e13i			2.32678i
$156$		−	8.84026e12i		−	0.613363i
$157$		−	1.82752e13i		−	1.22029i	−0.792289	−	0.610147i	$-0.791111\pi$
$157$		−	1.82752e13i		−	1.22029i	0.792289	−	0.610147i	$-0.208889\pi$
$158$	−5.68279e12			−0.365274
$159$			4.76405e12i			0.294845i
$160$	2.89201e13			1.72377
$161$	−1.40848e13			−0.808717
$162$		−	1.25011e13i		−	0.691604i
$163$			1.84197e12i			0.0982100i	0.998794	+	0.0491050i	$0.0156369\pi$
$163$			1.84197e12i			0.0982100i	−0.998794	+	0.0491050i	$0.984363\pi$
$164$	4.20421e12			0.216083
$165$		−	9.13806e12i		−	0.452846i
$166$	−1.19578e13	−	2.60410e13i	−0.571483	−	1.24454i
$167$	1.34151e13			0.618437			0.309219	−	0.950991i	$-0.399933\pi$
$167$	1.34151e13			0.618437			0.309219	+	0.950991i	$0.399933\pi$
$168$		−	9.43348e11i		−	0.0419581i
$169$	−4.19634e13			−1.80115
$170$	−2.20224e13			−0.912368
$171$		−	3.87018e13i		−	1.54794i
$172$		−	7.83370e12i		−	0.302549i
$173$	−9.76195e12			−0.364133			−0.182066	−	0.983286i	$-0.558279\pi$
$173$	−9.76195e12			−0.364133			−0.182066	+	0.983286i	$0.558279\pi$
$174$			1.07811e13i			0.388477i
$175$	−1.07140e13			−0.373012
$176$	−2.78900e13			−0.938367
$177$	−2.16598e13			−0.704393
$178$	3.30599e13			1.03940
$179$		−	1.14334e13i		−	0.347582i	−0.984783	−	0.173791i	$-0.944398\pi$
$179$		−	1.14334e13i		−	0.347582i	0.984783	−	0.173791i	$-0.0556018\pi$
$180$		−	3.13994e13i		−	0.923180i
$181$			1.78396e13i			0.507358i	0.967289	+	0.253679i	$0.0816406\pi$
$181$			1.78396e13i			0.507358i	−0.967289	+	0.253679i	$0.918359\pi$
$182$	4.89607e13			1.34716
$183$	−6.09686e11			−0.0162330
$184$			9.10589e12i			0.234647i
$185$		−	4.06114e13i		−	1.01302i
$186$			4.32000e13i			1.04329i
$187$	1.88533e13			0.440897
$188$		−	3.57852e13i		−	0.810505i
$189$	−2.04635e13			−0.448962
$190$		−	1.54600e14i		−	3.28616i
$191$	−9.18356e13			−1.89152			−0.945760	−	0.324867i	$-0.894681\pi$
$191$	−9.18356e13			−1.89152			−0.945760	+	0.324867i	$0.894681\pi$
$192$	1.54632e13			0.308669
$193$	−1.68375e13			−0.325787			−0.162893	−	0.986644i	$-0.552083\pi$
$193$	−1.68375e13			−0.325787			−0.162893	+	0.986644i	$0.552083\pi$
$194$	−5.92099e13			−1.11067
$195$	4.92485e13			0.895746
$196$	3.24877e13			0.573037
$197$	2.18849e12			0.0374410			0.0187205	−	0.999825i	$-0.494041\pi$
$197$	2.18849e12			0.0374410			0.0187205	+	0.999825i	$0.494041\pi$
$198$			5.75854e13i			0.955700i
$199$	8.42837e12			0.135714			0.0678571	−	0.997695i	$-0.478384\pi$
$199$	8.42837e12			0.135714			0.0678571	+	0.997695i	$0.478384\pi$
$200$			6.92662e12i			0.108228i
$201$		−	3.50238e13i		−	0.531112i
$202$	1.87520e13			0.276019
$203$	−2.78725e13			−0.398291
$204$	−1.37637e13			−0.190965
$205$			2.34214e13i			0.315565i
$206$	−1.80251e14			−2.35871
$207$	8.92802e13			1.13484
$208$		−	1.50310e14i		−	1.85613i
$209$			1.32353e14i			1.58802i
$210$	−3.69474e13			−0.430792
$211$			1.11800e14i			1.26691i	0.773778	+	0.633456i	$0.218364\pi$
$211$			1.11800e14i			1.26691i	−0.773778	+	0.633456i	$0.781636\pi$
$212$		−	5.59817e13i		−	0.616639i
$213$			4.01958e13i			0.430431i
$214$	−1.17314e14			−1.22143
$215$	4.36410e13			0.441838
$216$			1.32297e13i			0.130265i
$217$	−1.11686e14			−1.06965
$218$		−	4.41194e13i		−	0.411046i
$219$			7.36161e12i			0.0667280i
$220$			1.07380e14i			0.947083i
$221$			1.01608e14i			0.872112i
$222$		−	5.43734e13i		−	0.454222i
$223$		−	1.45911e14i		−	1.18647i	−0.805028	−	0.593236i	$-0.797850\pi$
$223$		−	1.45911e14i		−	1.18647i	0.805028	−	0.593236i	$-0.202150\pi$
$224$			1.00104e14i			0.792436i
$225$	6.79131e13			0.523430
$226$		−	8.26172e13i		−	0.620040i
$227$	1.36268e14			0.995952			0.497976	−	0.867191i	$-0.334077\pi$
$227$	1.36268e14			0.995952			0.497976	+	0.867191i	$0.334077\pi$
$228$		−	9.66230e13i		−	0.687815i
$229$	−1.62055e14			−1.12370			−0.561850	−	0.827239i	$-0.689910\pi$
$229$	−1.62055e14			−1.12370			−0.561850	+	0.827239i	$0.689910\pi$
$230$	3.56644e14			2.40917
$231$	3.16306e13			0.208178
$232$			1.80197e13i			0.115563i
$233$			2.76441e14i			1.72770i	0.503751	+	0.863849i	$0.331953\pi$
$233$			2.76441e14i			1.72770i	−0.503751	+	0.863849i	$0.668047\pi$
$234$	−3.10350e14			−1.89041
$235$	1.99357e14			1.18365
$236$	2.54521e14			1.47317
$237$		−	1.97861e13i		−	0.111653i
$238$		−	7.62284e13i		−	0.419426i
$239$		−	1.36387e14i		−	0.731791i	−0.930656	−	0.365895i	$-0.880763\pi$
$239$		−	1.36387e14i		−	0.731791i	0.930656	−	0.365895i	$-0.119237\pi$
$240$			1.13429e14i			0.593548i
$241$	−1.57101e14			−0.801820			−0.400910	−	0.916118i	$-0.631306\pi$
$241$	−1.57101e14			−0.801820			−0.400910	+	0.916118i	$0.631306\pi$
$242$			7.81413e13i			0.389035i
$243$	2.00798e14			0.975261
$244$	7.16435e12			0.0339498
$245$			1.80987e14i			0.836855i
$246$			3.13581e13i			0.141494i
$247$	−7.13300e14			−3.14117
$248$			7.22053e13i			0.310355i
$249$	9.06683e13	−	4.16342e13i	0.380416	−	0.174684i
$250$	−1.56181e14			−0.639719
$251$		−	8.16916e12i		−	0.0326690i	−0.999867	−	0.0163345i	$-0.994800\pi$
$251$		−	8.16916e12i		−	0.0326690i	0.999867	−	0.0163345i	$-0.00519966\pi$
$252$	1.08686e14			0.424396
$253$	−3.05322e14			−1.16422
$254$			6.64082e14i			2.47297i
$255$		−	7.66764e13i		−	0.278882i
$256$	3.38007e14			1.20084
$257$			1.19694e14i			0.415405i	0.978192	+	0.207703i	$0.0665986\pi$
$257$			1.19694e14i			0.415405i	−0.978192	+	0.207703i	$0.933401\pi$
$258$	5.84295e13			0.198113
$259$	1.40573e14			0.465696
$260$	−5.78712e14			−1.87337
$261$	1.76677e14			0.558903
$262$		−	4.10114e14i		−	1.26794i
$263$		−	4.52709e14i		−	1.36800i	−0.729484	−	0.683998i	$-0.760240\pi$
$263$		−	4.52709e14i		−	1.36800i	0.729484	−	0.683998i	$-0.239760\pi$
$264$		−	2.04493e13i		−	0.0604024i
$265$	3.11870e14			0.900530
$266$	5.35135e14			1.51068
$267$			1.15106e14i			0.317710i
$268$			4.11560e14i			1.11077i
$269$			2.39933e14i			0.633253i	0.948550	+	0.316626i	$0.102550\pi$
$269$			2.39933e14i			0.633253i	−0.948550	+	0.316626i	$0.897450\pi$
$270$	5.18158e14			1.33746
$271$			2.49517e14i			0.629919i	0.949105	+	0.314959i	$0.101991\pi$
$271$			2.49517e14i			0.629919i	−0.949105	+	0.314959i	$0.898009\pi$
$272$	−2.34022e14			−0.577887
$273$			1.70469e14i			0.411784i
$274$	−3.94733e14			−0.932825
$275$	−2.32250e14			−0.536983
$276$	2.22897e14			0.504255
$277$	−7.22584e14			−1.59959			−0.799796	−	0.600271i	$-0.795059\pi$
$277$	−7.22584e14			−1.59959			−0.799796	+	0.600271i	$0.795059\pi$
$278$	1.05305e15			2.28128
$279$	7.07949e14			1.50099
$280$	−6.17546e13			−0.128151
$281$		−	2.11172e14i		−	0.428942i	−0.976730	−	0.214471i	$-0.931197\pi$
$281$		−	2.11172e14i		−	0.428942i	0.976730	−	0.214471i	$-0.0688028\pi$
$282$	2.66912e14			0.530730
$283$		−	2.64791e12i		−	0.00515447i	−0.999997	−	0.00257723i	$-0.999180\pi$
$283$		−	2.64791e12i		−	0.00515447i	0.999997	−	0.00257723i	$-0.000820360\pi$
$284$		−	4.72336e14i		−	0.900204i
$285$	5.38280e14			1.00447
$286$	1.06134e15			1.93936
$287$	−8.10709e13			−0.145069
$288$		−	6.34535e14i		−	1.11199i
$289$	−4.24427e14			−0.728476
$290$	7.05763e14			1.18651
$291$		−	2.06154e14i		−	0.339496i
$292$		−	8.65054e13i		−	0.139555i
$293$	−6.00420e14			−0.948963			−0.474481	−	0.880266i	$-0.657364\pi$
$293$	−6.00420e14			−0.948963			−0.474481	+	0.880266i	$0.657364\pi$
$294$			2.42317e14i			0.375233i
$295$			1.41792e15i			2.15139i
$296$		−	9.08807e13i		−	0.135121i
$297$	−4.43594e14			−0.646320
$298$	−5.16405e14			−0.737383
$299$		−	1.64549e15i		−	2.30287i
$300$	1.69552e14			0.232582
$301$			1.51059e14i			0.203118i
$302$		−	4.89777e14i		−	0.645590i
$303$			6.52898e13i			0.0843704i
$304$		−	1.64287e15i		−	2.08143i
$305$			3.99121e13i			0.0495798i
$306$			4.83192e14i			0.588561i
$307$		−	1.37655e15i		−	1.64423i	−0.569322	−	0.822115i	$-0.692794\pi$
$307$		−	1.37655e15i		−	1.64423i	0.569322	−	0.822115i	$-0.307206\pi$
$308$	−3.71687e14			−0.435385
$309$		−	6.27589e14i		−	0.720982i
$310$	2.82801e15			3.18648
$311$			1.78532e15i			1.97312i	0.163395	+	0.986561i	$0.447755\pi$
$311$			1.78532e15i			1.97312i	−0.163395	+	0.986561i	$0.552245\pi$
$312$	1.10209e14			0.119478
$313$	1.48074e15			1.57475			0.787375	−	0.616474i	$-0.211440\pi$
$313$	1.48074e15			1.57475			0.787375	+	0.616474i	$0.211440\pi$
$314$	−1.60176e15			−1.67117
$315$			6.05483e14i			0.619782i
$316$			2.32503e14i			0.233511i
$317$	1.46003e15			1.43882			0.719412	−	0.694584i	$-0.244411\pi$
$317$	1.46003e15			1.43882			0.719412	+	0.694584i	$0.244411\pi$
$318$	4.17553e14			0.403784
$319$	−6.04202e14			−0.573374
$320$		−	1.01227e15i		−	0.942753i
$321$		−	4.08459e14i		−	0.373352i
$322$			1.23449e15i			1.10752i
$323$			1.11056e15i			0.977972i
$324$	−5.11464e14			−0.442125
$325$		−	1.25168e15i		−	1.06217i
$326$	1.61442e14			0.134497
$327$	1.53613e14			0.125644
$328$			5.24126e13i			0.0420913i
$329$			6.90055e14i			0.544137i
$330$	−8.00921e14			−0.620163
$331$		−	8.95019e14i		−	0.680557i	−0.940325	−	0.340278i	$-0.889479\pi$
$331$		−	8.95019e14i		−	0.680557i	0.940325	−	0.340278i	$-0.110521\pi$
$332$	−1.06543e15	+	4.89238e14i	−0.795604	+	0.365335i
$333$	−8.91055e14			−0.653490
$334$		−	1.17579e15i		−	0.846937i
$335$	−2.29277e15			−1.62215
$336$	−3.92623e14			−0.272860
$337$			6.46870e14i			0.441609i	0.975318	+	0.220804i	$0.0708683\pi$
$337$			6.46870e14i			0.441609i	−0.975318	+	0.220804i	$0.929132\pi$
$338$			3.67795e15i			2.46664i
$339$	2.87653e14			0.189527
$340$			9.01014e14i			0.583255i
$341$	−2.42105e15			−1.53985
$342$	−3.39209e15			−2.11987
$343$	−1.58358e15			−0.972466
$344$	9.76603e13			0.0589342
$345$			1.24174e15i			0.736406i
$346$			8.55603e14i			0.498673i
$347$		−	2.10751e15i		−	1.20724i	−0.797272	−	0.603620i	$-0.793725\pi$
$347$		−	2.10751e15i		−	1.20724i	0.797272	−	0.603620i	$-0.206275\pi$
$348$	4.41092e14			0.248344
$349$	3.37720e15			1.86898			0.934490	−	0.355988i	$-0.115856\pi$
$349$	3.37720e15			1.86898			0.934490	+	0.355988i	$0.115856\pi$
$350$			9.39045e14i			0.510832i
$351$		−	2.39070e15i		−	1.27844i
$352$			2.16999e15i			1.14078i
$353$	−5.25865e14			−0.271785			−0.135893	−	0.990724i	$-0.543390\pi$
$353$	−5.25865e14			−0.271785			−0.135893	+	0.990724i	$0.543390\pi$
$354$			1.89841e15i			0.964651i
$355$	2.63135e15			1.31464
$356$		−	1.35260e15i		−	0.664460i
$357$	2.65408e14			0.128205
$358$	−1.00210e15			−0.476007
$359$	−1.52192e15			−0.710927			−0.355464	−	0.934690i	$-0.615677\pi$
$359$	−1.52192e15			−0.710927			−0.355464	+	0.934690i	$0.615677\pi$
$360$	3.91447e14			0.179828
$361$	−5.58298e15			−2.52245
$362$	1.56358e15			0.694816
$363$	−2.72069e14			−0.118916
$364$		−	2.00316e15i		−	0.861207i
$365$	4.81915e14			0.203804
$366$			5.34370e13i			0.0222308i
$367$			3.72278e14i			0.152360i	0.997094	+	0.0761801i	$0.0242724\pi$
$367$			3.72278e14i			0.152360i	−0.997094	+	0.0761801i	$0.975728\pi$
$368$	3.78989e15			1.52595
$369$	5.13888e14			0.203568
$370$	−3.55946e15			−1.38731
$371$			1.07951e15i			0.413984i
$372$	1.76747e15			0.666950
$373$	3.45293e15			1.28214			0.641070	−	0.767483i	$-0.278491\pi$
$373$	3.45293e15			1.28214			0.641070	+	0.767483i	$0.278491\pi$
$374$		−	1.65243e15i		−	0.603800i
$375$		−	5.43784e14i		−	0.195542i
$376$	4.46122e14			0.157880
$377$		−	3.25627e15i		−	1.13416i
$378$			1.79356e15i			0.614844i
$379$		−	4.72330e15i		−	1.59371i	−0.604168	−	0.796857i	$-0.706494\pi$
$379$		−	4.72330e15i		−	1.59371i	0.604168	−	0.796857i	$-0.293506\pi$
$380$	−6.32526e15			−2.10076
$381$	−2.31217e15			−0.755909
$382$			8.04909e15i			2.59040i
$383$	8.05813e14			0.255295			0.127647	−	0.991820i	$-0.459257\pi$
$383$	8.05813e14			0.255295			0.127647	+	0.991820i	$0.459257\pi$
$384$			4.54211e14i			0.141667i
$385$		−	2.07064e15i		−	0.635829i
$386$			1.47575e15i			0.446158i
$387$		−	9.57526e14i		−	0.285026i
$388$			2.42249e15i			0.710022i
$389$		−	1.46705e14i		−	0.0423397i	−0.999776	−	0.0211699i	$-0.993261\pi$
$389$		−	1.46705e14i		−	0.0423397i	0.999776	−	0.0211699i	$-0.00673908\pi$
$390$		−	4.31646e15i		−	1.22671i
$391$	−2.56192e15			−0.716976
$392$			4.05014e14i			0.111623i
$393$	1.42792e15			0.387567
$394$		−	1.91814e14i		−	0.0512746i
$395$	−1.29526e15			−0.341016
$396$	2.35603e15			0.610955
$397$	−4.15403e15			−1.06103			−0.530513	−	0.847676i	$-0.678001\pi$
$397$	−4.15403e15			−1.06103			−0.530513	+	0.847676i	$0.678001\pi$
$398$		−	7.38719e14i		−	0.185858i
$399$			1.86321e15i			0.461768i
$400$	2.88287e15			0.703826
$401$	−4.35574e15			−1.04760			−0.523800	−	0.851841i	$-0.675486\pi$
$401$	−4.35574e15			−1.04760			−0.523800	+	0.851841i	$0.675486\pi$
$402$	−3.06972e15			−0.727347
$403$		−	1.30480e16i		−	3.04588i
$404$		−	7.67213e14i		−	0.176452i
$405$		−	2.84933e15i		−	0.645673i
$406$			2.44293e15i			0.545451i
$407$	3.04724e15			0.670410
$408$		−	1.71587e14i		−	0.0371984i
$409$	−8.01301e15			−1.71181			−0.855905	−	0.517133i	$-0.826999\pi$
$409$	−8.01301e15			−1.71181			−0.855905	+	0.517133i	$0.826999\pi$
$410$	2.05280e15			0.432160
$411$		−	1.37436e15i		−	0.285135i
$412$			7.37472e15i			1.50786i
$413$	−4.90801e15			−0.989020
$414$		−	7.82512e15i		−	1.55413i
$415$	−2.72551e15	−	5.93544e15i	−0.533530	−	1.16189i
$416$	−1.16949e16			−2.25651
$417$			3.66644e15i			0.697314i
$418$	1.16003e16			2.17476
$419$	5.67000e15			1.04785			0.523924	−	0.851765i	$-0.324467\pi$
$419$	5.67000e15			1.04785			0.523924	+	0.851765i	$0.324467\pi$
$420$			1.51165e15i			0.275395i
$421$			4.42809e15i			0.795287i	0.917540	+	0.397644i	$0.130172\pi$
$421$			4.42809e15i			0.795287i	−0.917540	+	0.397644i	$0.869828\pi$
$422$	9.79889e15			1.73501
$423$		−	4.37408e15i		−	0.763563i
$424$	6.97906e14			0.120116
$425$	−1.94879e15			−0.330697
$426$	3.52303e15			0.589466
$427$	−1.38152e14			−0.0227924
$428$			4.79975e15i			0.780829i
$429$			3.69532e15i			0.592800i
$430$		−	3.82499e15i		−	0.605089i
$431$	5.00652e15			0.781038			0.390519	−	0.920595i	$-0.372296\pi$
$431$	5.00652e15			0.781038			0.390519	+	0.920595i	$0.372296\pi$
$432$	5.50624e15			0.847135
$433$			8.47472e15i			1.28587i	0.765920	+	0.642936i	$0.222284\pi$
$433$			8.47472e15i			1.28587i	−0.765920	+	0.642936i	$0.777716\pi$
$434$			9.78891e15i			1.46486i
$435$			2.45729e15i			0.362678i
$436$	−1.80508e15			−0.262772
$437$		−	1.79851e16i		−	2.58240i
$438$	6.45221e14			0.0913827
$439$		−	5.93685e14i		−	0.0829410i	−0.999140	−	0.0414705i	$-0.986796\pi$
$439$		−	5.93685e14i		−	0.0829410i	0.999140	−	0.0414705i	$-0.0132042\pi$
$440$	−1.33868e15			−0.184484
$441$	3.97103e15			0.539848
$442$	8.90556e15			1.19434
$443$	6.20750e15			0.821286			0.410643	−	0.911796i	$-0.365304\pi$
$443$	6.20750e15			0.821286			0.410643	+	0.911796i	$0.365304\pi$
$444$	−2.22461e15			−0.290373
$445$	7.53523e15			0.970368
$446$	−1.27886e16			−1.62485
$447$		−	1.79799e15i		−	0.225394i
$448$	3.50390e15			0.433394
$449$			1.19350e16i			1.45661i	0.685252	+	0.728306i	$0.259692\pi$
$449$			1.19350e16i			1.45661i	−0.685252	+	0.728306i	$0.740308\pi$
$450$		−	5.95236e15i		−	0.716827i
$451$	−1.75740e15			−0.208839
$452$	−3.38017e15			−0.396376
$453$	1.70528e15			0.197336
$454$		−	1.19434e16i		−	1.36394i
$455$	1.11595e16			1.25769
$456$	1.20457e15			0.133981
$457$		−	1.57140e16i		−	1.72501i	−0.506052	−	0.862503i	$-0.668896\pi$
$457$		−	1.57140e16i		−	1.72501i	0.506052	−	0.862503i	$-0.331104\pi$
$458$			1.42036e16i			1.53889i
$459$	−3.72215e15			−0.398031
$460$		−	1.45916e16i		−	1.54012i
$461$			4.04459e15i			0.421376i	0.977553	+	0.210688i	$0.0675703\pi$
$461$			4.04459e15i			0.421376i	−0.977553	+	0.210688i	$0.932430\pi$
$462$		−	2.77232e15i		−	0.285096i
$463$	−4.39860e15			−0.446507			−0.223253	−	0.974760i	$-0.571668\pi$
$463$	−4.39860e15			−0.446507			−0.223253	+	0.974760i	$0.571668\pi$
$464$	7.49983e15			0.751525
$465$			9.84643e15i			0.974005i
$466$	2.42292e16			2.36605
$467$			1.86141e16i			1.79449i	0.441537	+	0.897243i	$0.354433\pi$
$467$			1.86141e16i			1.79449i	−0.441537	+	0.897243i	$0.645567\pi$
$468$			1.26975e16i			1.20849i
$469$		−	7.93622e15i		−	0.745721i
$470$		−	1.74729e16i		−	1.62098i
$471$		−	5.57693e15i		−	0.510822i
$472$			3.17304e15i			0.286961i
$473$			3.27456e15i			0.292406i
$474$	−1.73418e15			−0.152906
$475$		−	1.36808e16i		−	1.19110i
$476$	−3.11878e15			−0.268129
$477$		−	6.84274e15i		−	0.580925i
$478$	−1.19539e16			−1.00217
$479$	−7.49761e15			−0.620740			−0.310370	−	0.950616i	$-0.600453\pi$
$479$	−7.49761e15			−0.620740			−0.310370	+	0.950616i	$0.600453\pi$
$480$	8.82536e15			0.721581
$481$			1.64227e16i			1.32610i
$482$			1.37694e16i			1.09808i
$483$	−4.29819e15			−0.338534
$484$	3.19704e15			0.248700
$485$	−1.34955e16			−1.03691
$486$		−	1.75992e16i		−	1.33560i
$487$			1.70835e16i			1.28057i	0.768137	+	0.640286i	$0.221184\pi$
$487$			1.70835e16i			1.28057i	−0.768137	+	0.640286i	$0.778816\pi$
$488$			8.93157e13i			0.00661316i
$489$			5.62101e14i			0.0411113i
$490$	1.58629e16			1.14606
$491$			1.22578e16i			0.874827i	0.899261	+	0.437413i	$0.144105\pi$
$491$			1.22578e16i			0.874827i	−0.899261	+	0.437413i	$0.855895\pi$
$492$	1.28297e15			0.0904539
$493$	−5.06979e15			−0.353108
$494$			6.25184e16i			4.30176i
$495$			1.31253e16i			0.892230i
$496$	3.00520e16			2.01829
$497$			9.10818e15i			0.604357i
$498$	−3.64910e15	−	7.94677e15i	−0.239226	−	0.520973i
$499$	−3.89577e15			−0.252342			−0.126171	−	0.992008i	$-0.540269\pi$
$499$	−3.89577e15			−0.252342			−0.126171	+	0.992008i	$0.540269\pi$
$500$			6.38994e15i			0.408956i
$501$	4.09381e15			0.258882
$502$	−7.16000e14			−0.0447395
$503$			2.08593e16i			1.28793i	0.765055	+	0.643965i	$0.222712\pi$
$503$			2.08593e16i			1.28793i	−0.765055	+	0.643965i	$0.777288\pi$
$504$			1.35496e15i			0.0826690i
$505$	4.27409e15			0.257689
$506$			2.67604e16i			1.59437i
$507$	−1.28057e16			−0.753973
$508$	2.71700e16			1.58091
$509$	−5.28005e15			−0.303621			−0.151810	−	0.988410i	$-0.548510\pi$
$509$	−5.28005e15			−0.303621			−0.151810	+	0.988410i	$0.548510\pi$
$510$	−6.72043e15			−0.381923
$511$			1.66811e15i			0.0936911i
$512$		−	2.35286e16i		−	1.30610i
$513$		−	2.61301e16i		−	1.43363i
$514$	1.04907e16			0.568889
$515$	−4.10840e16			−2.20206
$516$		−	2.39056e15i		−	0.126649i
$517$			1.49585e16i			0.783333i
$518$		−	1.23207e16i		−	0.637762i
$519$	−2.97900e15			−0.152428
$520$		−	7.21463e15i		−	0.364917i
$521$	−3.18265e16			−1.59134			−0.795668	−	0.605733i	$-0.792880\pi$
$521$	−3.18265e16			−1.59134			−0.795668	+	0.605733i	$0.792880\pi$
$522$		−	1.54851e16i		−	0.765406i
$523$	1.20550e16			0.589055			0.294527	−	0.955643i	$-0.404838\pi$
$523$	1.20550e16			0.589055			0.294527	+	0.955643i	$0.404838\pi$
$524$	−1.67793e16			−0.810560
$525$	−3.26952e15			−0.156145
$526$	−3.96785e16			−1.87344
$527$	−2.03148e16			−0.948305
$528$	−8.51103e15			−0.392806
$529$	1.95747e16			0.893223
$530$		−	2.73344e16i		−	1.23326i
$531$	3.11106e16			1.38785
$532$		−	2.18943e16i		−	0.965743i
$533$		−	9.47130e15i		−	0.413092i
$534$	1.00887e16			0.435098
$535$	−2.67391e16			−1.14031
$536$	−5.13079e15			−0.216369
$537$		−	3.48907e15i		−	0.145500i
$538$	2.10294e16			0.867227
$539$	−1.35802e16			−0.553826
$540$		−	2.11997e16i		−	0.855003i
$541$			1.95634e16i			0.780297i	0.920752	+	0.390148i	$0.127576\pi$
$541$			1.95634e16i			0.780297i	−0.920752	+	0.390148i	$0.872424\pi$
$542$	2.18693e16			0.862661
$543$			5.44401e15i			0.212383i
$544$			1.82081e16i			0.702542i
$545$		−	1.00560e16i		−	0.383748i
$546$	1.49411e16			0.563930
$547$	4.11481e16			1.53612			0.768061	−	0.640376i	$-0.221222\pi$
$547$	4.11481e16			1.53612			0.768061	+	0.640376i	$0.221222\pi$
$548$			1.61500e16i			0.596332i
$549$	8.75710e14			0.0319835
$550$			2.03560e16i			0.735387i
$551$		−	3.55907e16i		−	1.27182i
$552$			2.77879e15i			0.0982248i
$553$		−	4.48343e15i		−	0.156769i
$554$			6.33321e16i			2.19061i
$555$		−	1.23931e16i		−	0.424056i
$556$		−	4.30839e16i		−	1.45836i
$557$	1.64895e16			0.552175			0.276087	−	0.961133i	$-0.410962\pi$
$557$	1.64895e16			0.552175			0.276087	+	0.961133i	$0.410962\pi$
$558$		−	6.20494e16i		−	2.05557i
$559$	−1.76479e16			−0.578390
$560$			2.57024e16i			0.833385i
$561$	5.75335e15			0.184562
$562$	−1.85085e16			−0.587428
$563$	3.51450e16			1.10360			0.551801	−	0.833976i	$-0.313941\pi$
$563$	3.51450e16			1.10360			0.551801	+	0.833976i	$0.313941\pi$
$564$		−	1.09203e16i		−	0.339283i
$565$		−	1.88307e16i		−	0.578862i
$566$	−2.32080e14			−0.00705894
$567$	9.86271e15			0.296823
$568$	5.88846e15			0.175353
$569$		−	3.11129e16i		−	0.916783i	−0.888750	−	0.458392i	$-0.848426\pi$
$569$		−	3.11129e16i		−	0.916783i	0.888750	−	0.458392i	$-0.151574\pi$
$570$		−	4.71785e16i		−	1.37561i
$571$			1.45443e16i			0.419640i	0.977740	+	0.209820i	$0.0672878\pi$
$571$			1.45443e16i			0.419640i	−0.977740	+	0.209820i	$0.932712\pi$
$572$		−	4.34232e16i		−	1.23978i
$573$	−2.80249e16			−0.791802
$574$			7.10560e15i			0.198669i
$575$	3.15598e16			0.873228
$576$	−2.22103e16			−0.608162
$577$			6.41136e15i			0.173738i	0.996220	+	0.0868691i	$0.0276862\pi$
$577$			6.41136e15i			0.173738i	−0.996220	+	0.0868691i	$0.972314\pi$
$578$			3.71996e16i			0.997634i
$579$	−5.13820e15			−0.136376
$580$		−	2.88753e16i		−	0.758505i
$581$	2.05450e16	−	9.43410e15i	0.534133	−	0.245270i
$582$	−1.80687e16			−0.464932
$583$			2.34009e16i			0.595966i
$584$	1.07844e15			0.0271842
$585$	−7.07370e16			−1.76486
$586$			5.26248e16i			1.29959i
$587$			1.21434e16i			0.296834i	0.988925	+	0.148417i	$0.0474177\pi$
$587$			1.21434e16i			0.296834i	−0.988925	+	0.148417i	$0.952582\pi$
$588$	9.91408e15			0.239877
$589$		−	1.42613e17i		−	3.41560i
$590$	1.24276e17			2.94629
$591$	6.67848e14			0.0156730
$592$	−3.78248e16			−0.878711
$593$	5.44384e16			1.25192			0.625961	−	0.779854i	$-0.284707\pi$
$593$	5.44384e16			1.25192			0.625961	+	0.779854i	$0.284707\pi$
$594$			3.88796e16i			0.885122i
$595$		−	1.73745e16i		−	0.391571i
$596$			2.11280e16i			0.471391i
$597$	2.57203e15			0.0568108
$598$	−1.44222e17			−3.15373
$599$			1.08175e16i			0.234190i	0.993121	+	0.117095i	$0.0373582\pi$
$599$			1.08175e16i			0.234190i	−0.993121	+	0.117095i	$0.962642\pi$
$600$			2.11375e15i			0.0453051i
$601$			2.26917e16i			0.481526i	0.970584	+	0.240763i	$0.0773977\pi$
$601$			2.26917e16i			0.481526i	−0.970584	+	0.240763i	$0.922602\pi$
$602$	1.32398e16			0.278166
$603$			5.03056e16i			1.04644i
$604$	−2.00386e16			−0.412710
$605$			1.78105e16i			0.363198i
$606$	5.72244e15			0.115543
$607$	−1.91880e16			−0.383617			−0.191808	−	0.981432i	$-0.561435\pi$
$607$	−1.91880e16			−0.383617			−0.191808	+	0.981432i	$0.561435\pi$
$608$	−1.27824e17			−2.53041
$609$	−8.50569e15			−0.166727
$610$	3.49816e15			0.0678986
$611$	−8.06172e16			−1.54946
$612$	1.97691e16			0.376253
$613$			1.51219e16i			0.284999i	0.989795	+	0.142500i	$0.0455140\pi$
$613$			1.51219e16i			0.284999i	−0.989795	+	0.142500i	$0.954486\pi$
$614$	−1.20650e17			−2.25174
$615$			7.14735e15i			0.132098i
$616$		−	4.63371e15i		−	0.0848094i
$617$	−5.95046e16			−1.07855			−0.539274	−	0.842130i	$-0.681301\pi$
$617$	−5.95046e16			−1.07855			−0.539274	+	0.842130i	$0.681301\pi$
$618$	−5.50061e16			−0.987371
$619$	2.31261e16			0.411110			0.205555	−	0.978646i	$-0.434100\pi$
$619$	2.31261e16			0.411110			0.205555	+	0.978646i	$0.434100\pi$
$620$		−	1.15704e17i		−	2.03704i
$621$	6.02787e16			1.05103
$622$	1.56477e17			2.70215
$623$			2.60825e16i			0.446089i
$624$		−	4.58691e16i		−	0.776986i
$625$	−7.34253e16			−1.23187
$626$		−	1.29782e17i		−	2.15659i
$627$			4.03894e16i			0.664756i
$628$			6.55338e16i			1.06834i
$629$	2.55691e16			0.412868
$630$	5.30686e16			0.848779
$631$			4.18340e16i			0.662755i	0.943498	+	0.331378i	$0.107513\pi$
$631$			4.18340e16i			0.662755i	−0.943498	+	0.331378i	$0.892487\pi$
$632$	−2.89855e15			−0.0454860
$633$			3.41173e16i			0.530338i
$634$		−	1.27967e17i		−	1.97044i
$635$			1.51362e17i			2.30874i
$636$		−	1.70836e16i		−	0.258129i
$637$		−	7.31888e16i		−	1.09549i
$638$			5.29563e16i			0.785224i
$639$		−	5.77344e16i		−	0.848066i
$640$	2.97341e16			0.432688
$641$			9.36397e16i			1.34993i	0.737849	+	0.674966i	$0.235842\pi$
$641$			9.36397e16i			1.34993i	−0.737849	+	0.674966i	$0.764158\pi$
$642$	−3.58001e16			−0.511298
$643$			2.87727e16i			0.407113i	0.979063	+	0.203557i	$0.0652501\pi$
$643$			2.87727e16i			0.407113i	−0.979063	+	0.203557i	$0.934750\pi$
$644$	5.05074e16			0.708011
$645$	1.33176e16			0.184956
$646$	9.73368e16			1.33931
$647$		−	7.01409e16i		−	0.956193i	−0.878307	−	0.478096i	$-0.841327\pi$
$647$		−	7.01409e16i		−	0.956193i	0.878307	−	0.478096i	$-0.158673\pi$
$648$		−	6.37627e15i		−	0.0861225i
$649$	−1.06392e17			−1.42378
$650$	−1.09706e17			−1.45462
$651$	−3.40825e16			−0.447761
$652$		−	6.60518e15i		−	0.0859804i
$653$			5.90437e15i			0.0761543i	0.999275	+	0.0380771i	$0.0121233\pi$
$653$			5.90437e15i			0.0761543i	−0.999275	+	0.0380771i	$0.987877\pi$
$654$		−	1.34637e16i		−	0.172067i
$655$		−	9.34760e16i		−	1.18373i
$656$	2.18142e16			0.273727
$657$		−	1.05737e16i		−	0.131472i
$658$	6.04810e16			0.745184
$659$	−9.68029e16			−1.18189			−0.590944	−	0.806713i	$-0.701244\pi$
$659$	−9.68029e16			−1.18189			−0.590944	+	0.806713i	$0.701244\pi$
$660$			3.27686e16i			0.396455i
$661$			9.33831e16i			1.11959i	0.828631	+	0.559796i	$0.189120\pi$
$661$			9.33831e16i			1.11959i	−0.828631	+	0.559796i	$0.810880\pi$
$662$	−7.84454e16			−0.932008
$663$			3.10069e16i			0.365071i
$664$	−6.09917e15	−	1.32824e16i	−0.0711643	−	0.154977i
$665$	1.21972e17			1.41036
$666$			7.80980e16i			0.894942i
$667$	8.21032e16			0.932406
$668$	−4.81058e16			−0.541426
$669$		−	4.45267e16i		−	0.496665i
$670$			2.00954e17i			2.22150i
$671$	−2.99477e15			−0.0328116
$672$			3.05482e16i			0.331719i
$673$	2.43897e16			0.262492			0.131246	−	0.991350i	$-0.458102\pi$
$673$	2.43897e16			0.262492			0.131246	+	0.991350i	$0.458102\pi$
$674$	5.66961e16			0.604774
$675$	4.58525e16			0.484775
$676$	1.50478e17			1.57686
$677$			4.09037e16i			0.424845i	0.977178	+	0.212423i	$0.0681353\pi$
$677$			4.09037e16i			0.424845i	−0.977178	+	0.212423i	$0.931865\pi$
$678$		−	2.52118e16i		−	0.259553i
$679$		−	4.67135e16i		−	0.476677i
$680$	−1.12327e16			−0.113613
$681$	4.15841e16			0.416912
$682$			2.12197e17i			2.10879i
$683$		−	9.91072e16i		−	0.976295i	−0.872761	−	0.488148i	$-0.837673\pi$
$683$		−	9.91072e16i		−	0.976295i	0.872761	−	0.488148i	$-0.162327\pi$
$684$			1.38782e17i			1.35518i
$685$	−8.99703e16			−0.870875
$686$			1.38795e17i			1.33177i
$687$	−4.94535e16			−0.470388
$688$		−	4.06464e16i		−	0.383258i
$689$	−1.26116e17			−1.17884
$690$	1.08835e17			1.00849
$691$	1.39046e16			0.127729			0.0638646	−	0.997959i	$-0.479657\pi$
$691$	1.39046e16			0.127729			0.0638646	+	0.997959i	$0.479657\pi$
$692$	3.50058e16			0.318789
$693$	−4.54319e16			−0.410168
$694$	−1.84717e17			−1.65329
$695$	2.40017e17			2.12977
$696$			5.49895e15i			0.0483754i
$697$	−1.47461e16			−0.128612
$698$		−	2.96001e17i		−	2.55953i
$699$			8.43600e16i			0.723225i
$700$	3.84197e16			0.326562
$701$	1.51707e17			1.27849			0.639246	−	0.769002i	$-0.279247\pi$
$701$	1.51707e17			1.27849			0.639246	+	0.769002i	$0.279247\pi$
$702$	−2.09537e17			−1.75080
$703$			1.79499e17i			1.48706i
$704$	7.59551e16			0.623909
$705$	6.08364e16			0.495483
$706$			4.60903e16i			0.372205i
$707$			1.47944e16i			0.118462i
$708$	7.76708e16			0.616678
$709$			9.37293e16i			0.737901i	0.929449	+	0.368950i	$0.120283\pi$
$709$			9.37293e16i			0.737901i	−0.929449	+	0.368950i	$0.879717\pi$
$710$		−	2.30629e17i		−	1.80038i
$711$			2.84193e16i			0.219986i
$712$	1.68624e16			0.129432
$713$	3.28990e17			2.50406
$714$		−	2.32622e16i		−	0.175574i
$715$	2.41907e17			1.81056
$716$			4.09996e16i			0.304299i
$717$		−	4.16205e16i		−	0.306332i
$718$			1.33391e17i			0.973600i
$719$		−	1.53434e17i		−	1.11058i	−0.831657	−	0.555289i	$-0.812607\pi$
$719$		−	1.53434e17i		−	1.11058i	0.831657	−	0.555289i	$-0.187393\pi$
$720$		−	1.62921e17i		−	1.16945i
$721$		−	1.42209e17i		−	1.01231i
$722$			4.89330e17i			3.45445i
$723$	−4.79416e16			−0.335647
$724$		−	6.39719e16i		−	0.444179i
$725$	6.24538e16			0.430062
$726$			2.38459e16i			0.162852i
$727$	−9.31523e16			−0.630939			−0.315469	−	0.948936i	$-0.602162\pi$
$727$	−9.31523e16			−0.630939			−0.315469	+	0.948936i	$0.602162\pi$
$728$	2.49728e16			0.167756
$729$	−1.45234e16			−0.0967619
$730$		−	4.22383e16i		−	0.279106i
$731$			2.74765e16i			0.180076i
$732$	2.18630e15			0.0142116
$733$	2.91203e17			1.87747			0.938733	−	0.344645i	$-0.112001\pi$
$733$	2.91203e17			1.87747			0.938733	+	0.344645i	$0.112001\pi$
$734$	3.26290e16			0.208654
$735$			5.52306e16i			0.350313i
$736$		−	2.94874e17i		−	1.85511i
$737$		−	1.72036e17i		−	1.07353i
$738$		−	4.50406e16i		−	0.278783i
$739$	−1.47404e17			−0.904989			−0.452495	−	0.891767i	$-0.649466\pi$
$739$	−1.47404e17			−0.904989			−0.452495	+	0.891767i	$0.649466\pi$
$740$			1.45630e17i			0.886873i
$741$	−2.17674e17			−1.31491
$742$	9.46155e16			0.566942
$743$			8.52312e16i			0.506601i	0.967388	+	0.253300i	$0.0815161\pi$
$743$			8.52312e16i			0.506601i	−0.967388	+	0.253300i	$0.918484\pi$
$744$			2.20345e16i			0.129917i
$745$	−1.17703e17			−0.688412
$746$		−	3.02638e17i		−	1.75586i
$747$	−1.30229e17	+	5.98004e16i	−0.749524	+	0.344176i
$748$	−6.76068e16			−0.385994
$749$		−	9.25549e16i		−	0.524214i
$750$	−4.76609e16			−0.267790
$751$	2.12355e17			1.18365			0.591824	−	0.806067i	$-0.298408\pi$
$751$	2.12355e17			1.18365			0.591824	+	0.806067i	$0.298408\pi$
$752$		−	1.85677e17i		−	1.02672i
$753$		−	2.49293e15i		−	0.0136754i
$754$	−2.85401e17			−1.55320
$755$		−	1.11633e17i		−	0.602716i
$756$	7.33810e16			0.393055
$757$	2.94830e17			1.56674			0.783369	−	0.621557i	$-0.213500\pi$
$757$	2.94830e17			1.56674			0.783369	+	0.621557i	$0.213500\pi$
$758$	−4.13982e17			−2.18256
$759$	−9.31732e16			−0.487349
$760$		−	7.88550e16i		−	0.409212i
$761$		−	2.96476e17i		−	1.52645i	−0.646134	−	0.763224i	$-0.723615\pi$
$761$		−	2.96476e17i		−	1.52645i	0.646134	−	0.763224i	$-0.276385\pi$
$762$			2.02654e17i			1.03520i
$763$	3.48079e16			0.176413
$764$	3.29317e17			1.65598
$765$			1.10133e17i			0.549474i
$766$		−	7.06268e16i		−	0.349621i
$767$		−	5.73389e17i		−	2.81629i
$768$	1.03147e17			0.502680
$769$			1.26079e17i			0.609655i	0.952408	+	0.304828i	$0.0985989\pi$
$769$			1.26079e17i			0.609655i	−0.952408	+	0.304828i	$0.901401\pi$
$770$	−1.81485e17			−0.870755
$771$			3.65261e16i			0.173891i
$772$	6.03783e16			0.285218
$773$	9.95712e16			0.466720			0.233360	−	0.972390i	$-0.425028\pi$
$773$	9.95712e16			0.466720			0.233360	+	0.972390i	$0.425028\pi$
$774$	−8.39240e16			−0.390338
$775$	2.50254e17			1.15497
$776$	−3.02004e16			−0.138307
$777$	4.28978e16			0.194943
$778$	−1.28582e16			−0.0579834
$779$		−	1.03520e17i		−	0.463234i
$780$	−1.76602e17			−0.784203
$781$			1.97441e17i			0.870024i
$782$			2.24544e17i			0.981884i
$783$	1.19286e17			0.517628
$784$	1.68568e17			0.725903
$785$	−3.65084e17			−1.56018
$786$		−	1.25152e17i		−	0.530766i
$787$	3.23758e17			1.36261			0.681306	−	0.731999i	$-0.261412\pi$
$787$	3.23758e17			1.36261			0.681306	+	0.731999i	$0.261412\pi$
$788$	−7.84780e15			−0.0327786
$789$		−	1.38150e17i		−	0.572652i
$790$			1.13525e17i			0.467014i
$791$	6.51807e16			0.266109
$792$			2.93719e16i			0.119009i
$793$		−	1.61399e16i		−	0.0649027i
$794$			3.64087e17i			1.45305i
$795$	9.51715e16			0.376968
$796$	−3.02236e16			−0.118814
$797$			6.71293e16i			0.261916i	0.991388	+	0.130958i	$0.0418053\pi$
$797$			6.71293e16i			0.261916i	−0.991388	+	0.130958i	$0.958195\pi$
$798$	1.63304e17			0.632382
$799$			1.25515e17i			0.482410i
$800$		−	2.24303e17i		−	0.855648i
$801$		−	1.65330e17i		−	0.625976i
$802$			3.81766e17i			1.43467i
$803$			3.61601e16i			0.134877i
$804$			1.25593e17i			0.464975i
$805$			2.81373e17i			1.03397i
$806$	−1.14361e18			−4.17127
$807$			7.32191e16i			0.265084i
$808$	9.56460e15			0.0343715
$809$		−	1.06998e17i		−	0.381667i	−0.981622	−	0.190834i	$-0.938881\pi$
$809$		−	1.06998e17i		−	0.381667i	0.981622	−	0.190834i	$-0.0611191\pi$
$810$	−2.49734e17			−0.884236
$811$	4.57793e17			1.60896			0.804478	−	0.593983i	$-0.202445\pi$
$811$	4.57793e17			1.60896			0.804478	+	0.593983i	$0.202445\pi$
$812$	9.99493e16			0.348693
$813$			7.61436e16i			0.263688i
$814$		−	2.67081e17i		−	0.918113i
$815$	3.67970e16			0.125564
$816$	−7.14150e16			−0.241907
$817$	−1.92889e17			−0.648597
$818$			7.02313e17i			2.34429i
$819$		−	2.44850e17i		−	0.811328i
$820$		−	8.39876e16i		−	0.276269i
$821$		−	5.10544e17i		−	1.66715i	−0.552408	−	0.833574i	$-0.686291\pi$
$821$		−	5.10544e17i		−	1.66715i	0.552408	−	0.833574i	$-0.313709\pi$
$822$	−1.20458e17			−0.390486
$823$			1.86767e17i			0.601036i	0.953776	+	0.300518i	$0.0971595\pi$
$823$			1.86767e17i			0.601036i	−0.953776	+	0.300518i	$0.902841\pi$
$824$	−9.19383e16			−0.293720
$825$	−7.08745e16			−0.224784
$826$			4.30171e17i			1.35444i
$827$		−	1.45193e16i		−	0.0453851i	−0.999742	−	0.0226926i	$-0.992776\pi$
$827$		−	1.45193e16i		−	0.0453851i	0.999742	−	0.0226926i	$-0.00722388\pi$
$828$	−3.20154e17			−0.993520
$829$			6.36489e17i			1.96094i	0.196672	+	0.980469i	$0.436986\pi$
$829$			6.36489e17i			1.96094i	−0.196672	+	0.980469i	$0.563014\pi$
$830$	−5.20222e17	+	2.38882e17i	−1.59118	+	0.730658i
$831$	−2.20506e17			−0.669600
$832$			4.09351e17i			1.23411i
$833$	−1.13950e17			−0.341070
$834$	3.21351e17			0.954957
$835$		−	2.67994e17i		−	0.790691i
$836$		−	4.74610e17i		−	1.39027i
$837$	4.77981e17			1.39014
$838$		−	4.96956e17i		−	1.43501i
$839$	1.48380e17			0.425405			0.212703	−	0.977117i	$-0.431773\pi$
$839$	1.48380e17			0.425405			0.212703	+	0.977117i	$0.431773\pi$
$840$	−1.88453e16			−0.0536447
$841$	−1.91341e17			−0.540793
$842$	3.88108e17			1.08913
$843$		−	6.44421e16i		−	0.179558i
$844$		−	4.00908e17i		−	1.10915i
$845$			8.38304e17i			2.30283i
$846$	−3.83374e17			−1.04568
$847$	−6.16495e16			−0.166966
$848$		−	2.90470e17i		−	0.781136i
$849$		−	8.08045e14i		−	0.00215769i
$850$			1.70805e17i			0.452883i
$851$	−4.14081e17			−1.09020
$852$		−	1.44140e17i		−	0.376831i
$853$	1.97839e17			0.513592			0.256796	−	0.966466i	$-0.417333\pi$
$853$	1.97839e17			0.513592			0.256796	+	0.966466i	$0.417333\pi$
$854$			1.21086e16i			0.0312137i
$855$	−7.73147e17			−1.97909
$856$	−5.98370e16			−0.152099
$857$	1.52650e17			0.385311			0.192655	−	0.981266i	$-0.438290\pi$
$857$	1.52650e17			0.385311			0.192655	+	0.981266i	$0.438290\pi$
$858$	3.23882e17			0.811827
$859$	−5.81541e17			−1.44751			−0.723754	−	0.690058i	$-0.757585\pi$
$859$	−5.81541e17			−1.44751			−0.723754	+	0.690058i	$0.757585\pi$
$860$	−1.56494e17			−0.386818
$861$	−2.47399e16			−0.0607267
$862$		−	4.38805e17i		−	1.06962i
$863$	−3.56252e17			−0.862368			−0.431184	−	0.902264i	$-0.641904\pi$
$863$	−3.56252e17			−0.862368			−0.431184	+	0.902264i	$0.641904\pi$
$864$		−	4.28415e17i		−	1.02987i
$865$			1.95015e17i			0.465555i
$866$	7.42781e17			1.76098
$867$	−1.29520e17			−0.304945
$868$	4.00500e17			0.936448
$869$		−	9.71887e16i		−	0.225682i
$870$	2.15373e17			0.496680
$871$	9.27167e17			2.12348
$872$		−	2.25034e16i		−	0.0511858i
$873$			2.96105e17i			0.668899i
$874$	−1.57633e18			−3.53654
$875$		−	1.23219e17i		−	0.274555i
$876$		−	2.63983e16i		−	0.0584187i
$877$			3.24330e17i			0.712837i	0.934327	+	0.356418i	$0.116002\pi$
$877$			3.24330e17i			0.712837i	−0.934327	+	0.356418i	$0.883998\pi$
$878$	−5.20345e16			−0.113586
$879$	−1.83226e17			−0.397242
$880$			5.57160e17i			1.19973i
$881$	7.98958e17			1.70871			0.854356	−	0.519689i	$-0.173952\pi$
$881$	7.98958e17			1.70871			0.854356	+	0.519689i	$0.173952\pi$
$882$		−	3.48048e17i		−	0.739311i
$883$			3.31390e17i			0.699157i	0.936907	+	0.349579i	$0.113675\pi$
$883$			3.31390e17i			0.699157i	−0.936907	+	0.349579i	$0.886325\pi$
$884$		−	3.64359e17i		−	0.763511i
$885$			4.32698e17i			0.900587i
$886$		−	5.44067e17i		−	1.12473i
$887$		−	1.92043e17i		−	0.394326i	−0.980371	−	0.197163i	$-0.936827\pi$
$887$		−	1.92043e17i		−	0.394326i	0.980371	−	0.197163i	$-0.0631729\pi$
$888$		−	2.77335e16i		−	0.0565623i
$889$	−5.23926e17			−1.06135
$890$		−	6.60438e17i		−	1.32890i
$891$	2.13797e17			0.427303
$892$			5.23227e17i			1.03873i
$893$	−8.81137e17			−1.73754
$894$	−1.57588e17			−0.308673
$895$	−2.28406e17			−0.444394
$896$			1.02922e17i			0.198912i
$897$		−	5.02146e17i		−	0.963995i
$898$	1.04606e18			1.99480
$899$	6.51039e17			1.23324
$900$	−2.43533e17			−0.458250
$901$			1.96354e17i			0.367021i
$902$			1.54030e17i			0.286001i
$903$			4.60979e16i			0.0850265i
$904$		−	4.21395e16i		−	0.0772109i
$905$	3.56383e17			0.648672
$906$		−	1.49462e17i		−	0.270248i
$907$	−5.21120e17			−0.936039			−0.468019	−	0.883718i	$-0.655032\pi$
$907$	−5.21120e17			−0.936039			−0.468019	+	0.883718i	$0.655032\pi$
$908$	−4.88649e17			−0.871930
$909$		−	9.37777e16i		−	0.166233i
$910$		−	9.78090e17i		−	1.72239i
$911$	−1.21855e17			−0.213173			−0.106587	−	0.994303i	$-0.533992\pi$
$911$	−1.21855e17			−0.213173			−0.106587	+	0.994303i	$0.533992\pi$
$912$		−	5.01345e17i		−	0.871299i
$913$	4.45361e17	−	2.04506e17i	0.768931	−	0.353087i
$914$	−1.37728e18			−2.36236
$915$			1.21797e16i			0.0207544i
$916$	5.81121e17			0.983771
$917$	3.23559e17			0.544173
$918$			3.26234e17i			0.545096i
$919$			1.72448e17i			0.286262i	0.989704	+	0.143131i	$0.0457171\pi$
$919$			1.72448e17i			0.286262i	−0.989704	+	0.143131i	$0.954283\pi$
$920$	1.81909e17			0.300004
$921$		−	4.20074e17i		−	0.688285i
$922$	3.54495e17			0.577065
$923$	−1.06408e18			−1.72094
$924$	−1.13425e17			−0.182255
$925$	−3.14981e17			−0.502844
$926$			3.85522e17i			0.611482i
$927$			9.01425e17i			1.42053i
$928$		−	5.83526e17i		−	0.913635i
$929$	−1.36427e17			−0.212230			−0.106115	−	0.994354i	$-0.533841\pi$
$929$	−1.36427e17			−0.212230			−0.106115	+	0.994354i	$0.533841\pi$
$930$	8.63007e17			1.33388
$931$		−	7.99945e17i		−	1.22846i
$932$		−	9.91303e17i		−	1.51255i
$933$			5.44815e17i			0.825961i
$934$	1.63146e18			2.45751
$935$		−	3.76633e17i		−	0.563701i
$936$	−1.58296e17			−0.235405
$937$		−	3.27749e17i		−	0.484288i	−0.970240	−	0.242144i	$-0.922149\pi$
$937$		−	3.27749e17i		−	0.484288i	0.970240	−	0.242144i	$-0.0778507\pi$
$938$	−6.95583e17			−1.02125
$939$	4.51867e17			0.659200
$940$	−7.14881e17			−1.03626
$941$	7.43010e17			1.07018			0.535090	−	0.844795i	$-0.320278\pi$
$941$	7.43010e17			1.07018			0.535090	+	0.844795i	$0.320278\pi$
$942$	−4.88800e17			−0.699561
$943$	2.38808e17			0.339609
$944$	1.32063e18			1.86616
$945$			4.08800e17i			0.574011i
$946$	2.87005e17			0.400444
$947$		−	9.53123e17i		−	1.32145i	−0.750630	−	0.660723i	$-0.770250\pi$
$947$		−	9.53123e17i		−	1.32145i	0.750630	−	0.660723i	$-0.229750\pi$
$948$			7.09517e16i			0.0977491i
$949$	−1.94880e17			−0.266791
$950$	−1.19907e18			−1.63119
$951$	4.45550e17			0.602301
$952$		−	3.88809e16i		−	0.0522293i
$953$	−7.89388e17			−1.05374			−0.526870	−	0.849946i	$-0.676634\pi$
$953$	−7.89388e17			−1.05374			−0.526870	+	0.849946i	$0.676634\pi$
$954$	−5.99743e17			−0.795564
$955$			1.83460e18i			2.41836i
$956$			4.89078e17i			0.640664i
$957$	−1.84381e17			−0.240018
$958$			6.57141e17i			0.850091i
$959$		−	3.11424e17i		−	0.400351i
$960$		−	3.08909e17i		−	0.394642i
$961$	1.82107e18			2.31199
$962$	1.43940e18			1.81606
$963$			5.86682e17i			0.735605i
$964$	5.63355e17			0.701972
$965$			3.36363e17i			0.416528i
$966$			3.76722e17i			0.463616i
$967$		−	4.07817e17i		−	0.498776i	−0.968404	−	0.249388i	$-0.919770\pi$
$967$		−	4.07817e17i		−	0.498776i	0.968404	−	0.249388i	$-0.0802295\pi$
$968$			3.98565e16i			0.0484448i
$969$			3.38902e17i			0.409385i
$970$			1.18284e18i			1.42002i
$971$		−	8.02418e17i		−	0.957382i	−0.877983	−	0.478691i	$-0.841111\pi$
$971$		−	8.02418e17i		−	0.957382i	0.877983	−	0.478691i	$-0.158889\pi$
$972$	−7.20049e17			−0.853816
$973$			8.30798e17i			0.979081i
$974$	1.49732e18			1.75372
$975$		−	3.81969e17i		−	0.444632i
$976$	3.71734e16			0.0430064
$977$	1.35883e18			1.56242			0.781211	−	0.624267i	$-0.214602\pi$
$977$	1.35883e18			1.56242			0.781211	+	0.624267i	$0.214602\pi$
$978$	4.92663e16			0.0563011
$979$			5.65400e17i			0.642184i
$980$		−	6.49008e17i		−	0.732645i
$981$	−2.20639e17			−0.247553
$982$	1.07435e18			1.19806
$983$	1.18297e16			0.0131115			0.00655576	−	0.999979i	$-0.497913\pi$
$983$	1.18297e16			0.0131115			0.00655576	+	0.999979i	$0.497913\pi$
$984$			1.59944e16i			0.0176197i
$985$		−	4.37195e16i		−	0.0478694i
$986$			4.44350e17i			0.483575i
$987$			2.10580e17i			0.227779i
$988$	2.55785e18			2.75001
$989$		−	4.44971e17i		−	0.475503i
$990$	1.15039e18			1.22189
$991$	−1.16129e18			−1.22603			−0.613014	−	0.790072i	$-0.710043\pi$
$991$	−1.16129e18			−1.22603			−0.613014	+	0.790072i	$0.710043\pi$
$992$		−	2.33821e18i		−	2.45365i
$993$		−	2.73128e17i		−	0.284885i
$994$	7.98302e17			0.827654
$995$		−	1.68374e17i		−	0.173515i
$996$	−3.25131e17	+	1.49298e17i	−0.333045	+	0.152932i
$997$	−1.17945e18			−1.20091			−0.600454	−	0.799659i	$-0.705014\pi$
$997$	−1.17945e18			−1.20091			−0.600454	+	0.799659i	$0.705014\pi$
$998$			3.41451e17i			0.345578i
$999$	−6.01608e17			−0.605230

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	83.13.b.c.82.17	✓	80
83.82	odd	2	inner	83.13.b.c.82.64	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
83.13.b.c.82.17	✓	80	1.1	even	1	trivial
83.13.b.c.82.64	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)

\(f(q)\)	\(=\)	\(q-87.6467i q^{2} +305.164 q^{3} -3585.94 q^{4} -19977.0i q^{5} -26746.6i q^{6} +69148.7 q^{7} -44704.8i q^{8} -438316. q^{9} +O(q^{10})\)	\(q-87.6467i q^{2} +305.164 q^{3} -3585.94 q^{4} -19977.0i q^{5} -26746.6i q^{6} +69148.7 q^{7} -44704.8i q^{8} -438316. q^{9} -1.75092e6 q^{10} +1.49896e6 q^{11} -1.09430e6 q^{12} +8.07846e6i q^{13} -6.06066e6i q^{14} -6.09627e6i q^{15} -1.86063e7 q^{16} +1.25776e7 q^{17} +3.84169e7i q^{18} +8.82966e7i q^{19} +7.16365e7i q^{20} +2.11017e7 q^{21} -1.31379e8i q^{22} -2.03689e8 q^{23} -1.36423e7i q^{24} -1.54941e8 q^{25} +7.08050e8 q^{26} -2.95935e8 q^{27} -2.47963e8 q^{28} -4.03081e8 q^{29} -5.34318e8 q^{30} -1.61516e9 q^{31} +1.44767e9i q^{32} +4.57428e8 q^{33} -1.10238e9i q^{34} -1.38139e9i q^{35} +1.57178e9 q^{36} +2.03291e9 q^{37} +7.73891e9 q^{38} +2.46525e9i q^{39} -8.93070e8 q^{40} -1.17241e9 q^{41} -1.84949e9i q^{42} +2.18456e9i q^{43} -5.37518e9 q^{44} +8.75625e9i q^{45} +1.78527e10i q^{46} +9.97929e9i q^{47} -5.67796e9 q^{48} -9.05974e9 q^{49} +1.35801e10i q^{50} +3.83823e9 q^{51} -2.89689e10i q^{52} +1.56114e10i q^{53} +2.59377e10i q^{54} -2.99448e10i q^{55} -3.09128e9i q^{56} +2.69449e10i q^{57} +3.53287e10i q^{58} -7.09776e10 q^{59} +2.18609e10i q^{60} -1.99790e9 q^{61} +1.41563e11i q^{62} -3.03090e10 q^{63} +5.06719e10 q^{64} +1.61384e11 q^{65} -4.00921e10i q^{66} -1.14770e11i q^{67} -4.51025e10 q^{68} -6.21586e10 q^{69} -1.21074e11 q^{70} +1.31719e11i q^{71} +1.95948e10i q^{72} +2.41235e10i q^{73} -1.78177e11i q^{74} -4.72824e10 q^{75} -3.16627e11i q^{76} +1.03651e11 q^{77} +2.16071e11 q^{78} -6.48375e10i q^{79} +3.71698e11i q^{80} +1.42630e11 q^{81} +1.02758e11i q^{82} +(2.97113e11 - 1.36432e11i) q^{83} -7.56695e10 q^{84} -2.51263e11i q^{85} +1.91469e11 q^{86} -1.23006e11 q^{87} -6.70107e10i q^{88} +3.77195e11i q^{89} +7.67456e11 q^{90} +5.58615e11i q^{91} +7.30418e11 q^{92} -4.92888e11 q^{93} +8.74652e11 q^{94} +1.76390e12 q^{95} +4.41775e11i q^{96} -6.75552e11i q^{97} +7.94057e11i q^{98} -6.57018e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 918 q^{3} - 181150 q^{4} + 103918 q^{7} + 14902142 q^{9}+O(q^{10}) \) 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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