LMFDB - Embedded newform 21.22.c.b.20.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,22,Mod(20,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("21.20");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	21.c (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:	$58.6902423003$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			20.9
Character	$\chi$	$=$	21.20
Dual form			21.22.c.b.20.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1925.57i q^{2} +(78349.6 - 65739.6i) q^{3} -1.61068e6 q^{4} +2.77549e7 q^{5} +(-1.26586e8 - 1.50868e8i) q^{6} +(7.43581e8 + 7.50540e7i) q^{7} -9.36744e8i q^{8} +(1.81697e9 - 1.03013e10i) q^{9} +O(q^{10})$	\(q-1925.57i q^{2} +(78349.6 - 65739.6i) q^{3} -1.61068e6 q^{4} +2.77549e7 q^{5} +(-1.26586e8 - 1.50868e8i) q^{6} +(7.43581e8 + 7.50540e7i) q^{7} -9.36744e8i q^{8} +(1.81697e9 - 1.03013e10i) q^{9} -5.34441e10i q^{10} +5.61106e10i q^{11} +(-1.26196e11 + 1.05885e11i) q^{12} +3.86369e11i q^{13} +(1.44522e11 - 1.43182e12i) q^{14} +(2.17459e12 - 1.82460e12i) q^{15} -5.18160e12 q^{16} +1.33419e13 q^{17} +(-1.98360e13 - 3.49870e12i) q^{18} +3.04856e13i q^{19} -4.47042e13 q^{20} +(6.31933e13 - 4.30023e13i) q^{21} +1.08045e14 q^{22} -2.80800e14i q^{23} +(-6.15811e13 - 7.33935e13i) q^{24} +2.93499e14 q^{25} +7.43981e14 q^{26} +(-5.34847e14 - 9.26553e14i) q^{27} +(-1.19767e15 - 1.20888e14i) q^{28} -2.28112e15i q^{29} +(-3.51340e15 - 4.18733e15i) q^{30} -3.90771e15i q^{31} +8.01305e15i q^{32} +(3.68869e15 + 4.39624e15i) q^{33} -2.56909e16i q^{34} +(2.06380e16 + 2.08312e15i) q^{35} +(-2.92655e15 + 1.65921e16i) q^{36} +3.61922e16 q^{37} +5.87023e16 q^{38} +(2.53997e16 + 3.02718e16i) q^{39} -2.59993e16i q^{40} +7.43654e16 q^{41} +(-8.28040e16 - 1.21683e17i) q^{42} -1.37569e17 q^{43} -9.03760e16i q^{44} +(5.04298e16 - 2.85913e17i) q^{45} -5.40700e17 q^{46} -1.27732e17 q^{47} +(-4.05976e17 + 3.40636e17i) q^{48} +(5.47280e17 + 1.11617e17i) q^{49} -5.65154e17i q^{50} +(1.04534e18 - 8.77094e17i) q^{51} -6.22315e17i q^{52} +1.55747e18i q^{53} +(-1.78414e18 + 1.02989e18i) q^{54} +1.55734e18i q^{55} +(7.03063e16 - 6.96545e17i) q^{56} +(2.00411e18 + 2.38854e18i) q^{57} -4.39246e18 q^{58} -6.38773e18 q^{59} +(-3.50256e18 + 2.93884e18i) q^{60} -1.92216e18i q^{61} -7.52457e18 q^{62} +(2.12422e18 - 7.52351e18i) q^{63} +4.56311e18 q^{64} +1.07236e19i q^{65} +(8.46528e18 - 7.10283e18i) q^{66} +2.86226e18 q^{67} -2.14896e19 q^{68} +(-1.84597e19 - 2.20006e19i) q^{69} +(4.01120e18 - 3.97400e19i) q^{70} +2.30678e19i q^{71} +(-9.64971e18 - 1.70203e18i) q^{72} -1.86483e19i q^{73} -6.96907e19i q^{74} +(2.29955e19 - 1.92945e19i) q^{75} -4.91025e19i q^{76} +(-4.21132e18 + 4.17227e19i) q^{77} +(5.82906e19 - 4.89090e19i) q^{78} -1.57015e20 q^{79} -1.43815e20 q^{80} +(-1.02816e20 - 3.74344e19i) q^{81} -1.43196e20i q^{82} +1.76885e20 q^{83} +(-1.01784e20 + 6.92627e19i) q^{84} +3.70305e20 q^{85} +2.64898e20i q^{86} +(-1.49960e20 - 1.78725e20i) q^{87} +5.25612e19 q^{88} -3.24298e20 q^{89} +(-5.50546e20 - 9.71062e19i) q^{90} +(-2.89985e19 + 2.87296e20i) q^{91} +4.52278e20i q^{92} +(-2.56891e20 - 3.06167e20i) q^{93} +2.45958e20i q^{94} +8.46127e20i q^{95} +(5.26775e20 + 6.27820e20i) q^{96} +2.37119e20i q^{97} +(2.14927e20 - 1.05383e21i) q^{98} +(5.78014e20 + 1.01951e20i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 58720260 q^{4} + 1422287188 q^{7} + 10150644696 q^{9}+O(q^{10}) $ 52 * q - 58720260 * q^4 + 1422287188 * q^7 + 10150644696 * q^9	$ 52 q - 58720260 q^{4} + 1422287188 q^{7} + 10150644696 q^{9} - 687153165468 q^{15} + 36241782390404 q^{16} + 36759093002772 q^{18} + 79412641656180 q^{21} + 228880341648112 q^{22} + 45\!\cdots\!12 q^{25}+ \cdots + 15\!\cdots\!28 q^{99}+O(q^{100}) $ 52 * q - 58720260 * q^4 + 1422287188 * q^7 + 10150644696 * q^9 - 687153165468 * q^15 + 36241782390404 * q^16 + 36759093002772 * q^18 + 79412641656180 * q^21 + 228880341648112 * q^22 + 4502168959229812 * q^25 - 328465100861772 * q^28 - 2422487119598196 * q^30 + 94669723666911312 * q^36 - 111253244635261912 * q^37 - 198389110134084780 * q^39 - 125754675449474820 * q^42 + 808208758088766656 * q^43 - 1124214920076830456 * q^46 + 760563680048831596 * q^49 + 4341973540932052200 * q^51 - 13080454499124088812 * q^57 - 10814528487339424568 * q^58 + 13643758017961015644 * q^60 - 38182310822257441896 * q^63 - 30480555033993680900 * q^64 - 25547251957658589040 * q^67 + 73727169165159410040 * q^70 + 39846964674222889428 * q^72 + 45848199464273536260 * q^78 + 199210197493083963080 * q^79 + 235499606962845306588 * q^81 - 373919224753720758924 * q^84 - 570842672309470848672 * q^85 - 1060053674241923431168 * q^88 - 923077800435233893128 * q^91 - 2832166256981601869904 * q^93 + 1525182290356701596928 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	1925.57i		−	1.32967i	−0.746989	−	0.664837i	$-0.768501\pi$
$2$		−	1925.57i		−	1.32967i	0.746989	−	0.664837i	$-0.231499\pi$
$3$	78349.6	−	65739.6i	0.766061	−	0.642767i
$3$	78349.6	−	65739.6i	0.766061	−	0.642767i
$4$	−1.61068e6			−0.768030
$5$	2.77549e7			1.27103			0.635514	−	0.772089i	$-0.280788\pi$
$5$	2.77549e7			1.27103			0.635514	+	0.772089i	$0.280788\pi$
$6$	−1.26586e8	−	1.50868e8i	−0.854670	−	1.01861i
$7$	7.43581e8	+	7.50540e7i	0.994945	+	0.100426i
$7$	7.43581e8	+	7.50540e7i	0.994945	+	0.100426i
$8$		−	9.36744e8i		−	0.308444i
$9$	1.81697e9	−	1.03013e10i	0.173700	−	0.984799i
$10$		−	5.34441e10i		−	1.69005i
$11$			5.61106e10i			0.652261i	0.945325	+	0.326131i	$0.105745\pi$
$11$			5.61106e10i			0.652261i	−0.945325	+	0.326131i	$0.894255\pi$
$12$	−1.26196e11	+	1.05885e11i	−0.588359	+	0.493665i
$13$			3.86369e11i			0.777314i	0.921382	+	0.388657i	$0.127061\pi$
$13$			3.86369e11i			0.777314i	−0.921382	+	0.388657i	$0.872939\pi$
$14$	1.44522e11	−	1.43182e12i	0.133533	−	1.32295i
$15$	2.17459e12	−	1.82460e12i	0.973686	−	0.816975i
$16$	−5.18160e12			−1.17816
$17$	1.33419e13			1.60511			0.802556	−	0.596576i	$-0.203473\pi$
$17$	1.33419e13			1.60511			0.802556	+	0.596576i	$0.203473\pi$
$18$	−1.98360e13	−	3.49870e12i	−1.30946	−	0.230965i
$19$			3.04856e13i			1.14073i	0.821392	+	0.570365i	$0.193198\pi$
$19$			3.04856e13i			1.14073i	−0.821392	+	0.570365i	$0.806802\pi$
$20$	−4.47042e13			−0.976188
$21$	6.31933e13	−	4.30023e13i	0.826739	−	0.562586i
$22$	1.08045e14			0.867294
$23$		−	2.80800e14i		−	1.41337i	−0.707530	−	0.706683i	$-0.750191\pi$
$23$		−	2.80800e14i		−	1.41337i	0.707530	−	0.706683i	$-0.249809\pi$
$24$	−6.15811e13	−	7.33935e13i	−0.198258	−	0.236287i
$25$	2.93499e14			0.615513
$26$	7.43981e14			1.03357
$27$	−5.34847e14	−	9.26553e14i	−0.499931	−	0.866065i
$28$	−1.19767e15	−	1.20888e14i	−0.764148	−	0.0771299i
$29$		−	2.28112e15i		−	1.00686i	−0.864036	−	0.503430i	$-0.832071\pi$
$29$		−	2.28112e15i		−	1.00686i	0.864036	−	0.503430i	$-0.167929\pi$
$30$	−3.51340e15	−	4.18733e15i	−1.08631	−	1.29468i
$31$		−	3.90771e15i		−	0.856297i	−0.903708	−	0.428148i	$-0.859166\pi$
$31$		−	3.90771e15i		−	0.856297i	0.903708	−	0.428148i	$-0.140834\pi$
$32$			8.01305e15i			1.25812i
$33$	3.68869e15	+	4.39624e15i	0.419252	+	0.499672i
$34$		−	2.56909e16i		−	2.13428i
$35$	2.06380e16	+	2.08312e15i	1.26460	+	0.127644i
$36$	−2.92655e15	+	1.65921e16i	−0.133407	+	0.756355i
$37$	3.61922e16			1.23736			0.618681	−	0.785642i	$-0.287667\pi$
$37$	3.61922e16			1.23736			0.618681	+	0.785642i	$0.287667\pi$
$38$	5.87023e16			1.51680
$39$	2.53997e16	+	3.02718e16i	0.499632	+	0.595471i
$40$		−	2.59993e16i		−	0.392041i
$41$	7.43654e16			0.865248			0.432624	−	0.901574i	$-0.357588\pi$
$41$	7.43654e16			0.865248			0.432624	+	0.901574i	$0.357588\pi$
$42$	−8.28040e16	−	1.21683e17i	−0.748055	−	1.09929i
$43$	−1.37569e17			−0.970735			−0.485367	−	0.874310i	$-0.661314\pi$
$43$	−1.37569e17			−0.970735			−0.485367	+	0.874310i	$0.661314\pi$
$44$		−	9.03760e16i		−	0.500956i
$45$	5.04298e16	−	2.85913e17i	0.220778	−	1.25171i
$46$	−5.40700e17			−1.87931
$47$	−1.27732e17			−0.354220			−0.177110	−	0.984191i	$-0.556675\pi$
$47$	−1.27732e17			−0.354220			−0.177110	+	0.984191i	$0.556675\pi$
$48$	−4.05976e17	+	3.40636e17i	−0.902543	+	0.757283i
$49$	5.47280e17	+	1.11617e17i	0.979829	+	0.199836i
$50$		−	5.65154e17i		−	0.818430i
$51$	1.04534e18	−	8.77094e17i	1.22961	−	1.03171i
$52$		−	6.22315e17i		−	0.597001i
$53$			1.55747e18i			1.22327i	0.791139	+	0.611636i	$0.209488\pi$
$53$			1.55747e18i			1.22327i	−0.791139	+	0.611636i	$0.790512\pi$
$54$	−1.78414e18	+	1.02989e18i	−1.15158	+	0.664745i
$55$			1.55734e18i			0.829042i
$56$	7.03063e16	−	6.96545e17i	0.0309756	−	0.306884i
$57$	2.00411e18	+	2.38854e18i	0.733224	+	0.873869i
$58$	−4.39246e18			−1.33879
$59$	−6.38773e18			−1.62705			−0.813524	−	0.581531i	$-0.802454\pi$
$59$	−6.38773e18			−1.62705			−0.813524	+	0.581531i	$0.802454\pi$
$60$	−3.50256e18	+	2.93884e18i	−0.747820	+	0.627462i
$61$		−	1.92216e18i		−	0.345006i	−0.985009	−	0.172503i	$-0.944815\pi$
$61$		−	1.92216e18i		−	0.345006i	0.985009	−	0.172503i	$-0.0551854\pi$
$62$	−7.52457e18			−1.13859
$63$	2.12422e18	−	7.52351e18i	0.271721	−	0.962376i
$64$	4.56311e18			0.494733
$65$			1.07236e19i			0.987988i
$66$	8.46528e18	−	7.10283e18i	0.664400	−	0.557468i
$67$	2.86226e18			0.191833			0.0959165	−	0.995389i	$-0.469422\pi$
$67$	2.86226e18			0.191833			0.0959165	+	0.995389i	$0.469422\pi$
$68$	−2.14896e19			−1.23278
$69$	−1.84597e19	−	2.20006e19i	−0.908465	−	1.08273i
$70$	4.01120e18	−	3.97400e19i	0.169724	−	1.68151i
$71$			2.30678e19i			0.840995i	0.907294	+	0.420498i	$0.138145\pi$
$71$			2.30678e19i			0.840995i	−0.907294	+	0.420498i	$0.861855\pi$
$72$	−9.64971e18	−	1.70203e18i	−0.303755	−	0.0535767i
$73$		−	1.86483e19i		−	0.507866i	−0.967222	−	0.253933i	$-0.918276\pi$
$73$		−	1.86483e19i		−	0.507866i	0.967222	−	0.253933i	$-0.0817243\pi$
$74$		−	6.96907e19i		−	1.64529i
$75$	2.29955e19	−	1.92945e19i	0.471520	−	0.395631i
$76$		−	4.91025e19i		−	0.876115i
$77$	−4.21132e18	+	4.17227e19i	−0.0655037	+	0.648964i
$78$	5.82906e19	−	4.89090e19i	0.791781	−	0.664348i
$79$	−1.57015e20			−1.86576			−0.932879	−	0.360190i	$-0.882712\pi$
$79$	−1.57015e20			−1.86576			−0.932879	+	0.360190i	$0.882712\pi$
$80$	−1.43815e20			−1.49747
$81$	−1.02816e20	−	3.74344e19i	−0.939656	−	0.342120i
$82$		−	1.43196e20i		−	1.15050i
$83$	1.76885e20			1.25133			0.625665	−	0.780092i	$-0.284828\pi$
$83$	1.76885e20			1.25133			0.625665	+	0.780092i	$0.284828\pi$
$84$	−1.01784e20	+	6.92627e19i	−0.634961	+	0.432083i
$85$	3.70305e20			2.04014
$86$			2.64898e20i			1.29076i
$87$	−1.49960e20	−	1.78725e20i	−0.647177	−	0.771317i
$88$	5.25612e19			0.201186
$89$	−3.24298e20			−1.10242			−0.551212	−	0.834365i	$-0.685835\pi$
$89$	−3.24298e20			−1.10242			−0.551212	+	0.834365i	$0.685835\pi$
$90$	−5.50546e20	−	9.71062e19i	−1.66436	−	0.293562i
$91$	−2.89985e19	+	2.87296e20i	−0.0780622	+	0.773385i
$92$			4.52278e20i			1.08551i
$93$	−2.56891e20	−	3.06167e20i	−0.550399	−	0.655976i
$94$			2.45958e20i			0.470997i
$95$			8.46127e20i			1.44990i
$96$	5.26775e20	+	6.27820e20i	0.808681	+	0.963800i
$97$			2.37119e20i			0.326485i	0.986586	+	0.163243i	$0.0521954\pi$
$97$			2.37119e20i			0.326485i	−0.986586	+	0.163243i	$0.947805\pi$
$98$	2.14927e20	−	1.05383e21i	0.265716	−	1.30285i
$99$	5.78014e20	+	1.01951e20i	0.642346	+	0.113298i
$100$	−4.72732e20			−0.472732
$101$	4.39518e20			0.395916			0.197958	−	0.980211i	$-0.436569\pi$
$101$	4.39518e20			0.395916			0.197958	+	0.980211i	$0.436569\pi$
$102$	−1.68891e21	−	2.01287e21i	−1.37184	−	1.63499i
$103$			4.97085e20i			0.364452i	0.983257	+	0.182226i	$0.0583302\pi$
$103$			4.97085e20i			0.364452i	−0.983257	+	0.182226i	$0.941670\pi$
$104$	3.61928e20			0.239758
$105$	1.75393e21	−	1.19352e21i	1.05081	−	0.715062i
$106$	2.99902e21			1.62655
$107$			9.87407e20i			0.485251i	0.970120	+	0.242626i	$0.0780087\pi$
$107$			9.87407e20i			0.485251i	−0.970120	+	0.242626i	$0.921991\pi$
$108$	8.61466e20	+	1.49238e21i	0.383962	+	0.665164i
$109$	−3.08434e21			−1.24791			−0.623956	−	0.781459i	$-0.714476\pi$
$109$	−3.08434e21			−1.24791			−0.623956	+	0.781459i	$0.714476\pi$
$110$	2.99878e21			1.10235
$111$	2.83564e21	−	2.37926e21i	0.947895	−	0.795336i
$112$	−3.85294e21	−	3.88900e20i	−1.17220	−	0.118317i
$113$			6.50283e21i			1.80210i	0.433715	+	0.901050i	$0.357203\pi$
$113$			6.50283e21i			1.80210i	−0.433715	+	0.901050i	$0.642797\pi$
$114$	4.59930e21	−	3.85907e21i	1.16196	−	0.974948i
$115$		−	7.79358e21i		−	1.79643i
$116$			3.67415e21i			0.773299i
$117$	3.98012e21	+	7.02019e20i	0.765498	+	0.135020i
$118$			1.23000e22i			2.16344i
$119$	9.92082e21	+	1.00137e21i	1.59700	+	0.161194i
$120$	−1.70918e21	−	2.03703e21i	−0.251991	−	0.300327i
$121$	4.25185e21			0.574556
$122$	−3.70126e21			−0.458745
$123$	5.82650e21	−	4.88875e21i	0.662833	−	0.556153i
$124$			6.29405e21i			0.657662i
$125$	−5.08853e21			−0.488694
$126$	−1.44871e22	−	4.09034e21i	−1.27965	−	0.361300i
$127$	−5.07003e21			−0.412165			−0.206083	−	0.978535i	$-0.566072\pi$
$127$	−5.07003e21			−0.412165			−0.206083	+	0.978535i	$0.566072\pi$
$128$			8.01800e21i			0.600290i
$129$	−1.07784e22	+	9.04370e21i	−0.743642	+	0.623956i
$130$	2.06491e22			1.31370
$131$	1.15331e22			0.677013			0.338507	−	0.940964i	$-0.390078\pi$
$131$	1.15331e22			0.677013			0.338507	+	0.940964i	$0.390078\pi$
$132$	−5.94128e21	−	7.08092e21i	−0.321998	−	0.383763i
$133$	−2.28807e21	+	2.26685e22i	−0.114558	+	1.13496i
$134$		−	5.51148e21i		−	0.255075i
$135$	−1.48447e22	−	2.57164e22i	−0.635427	−	1.10079i
$136$		−	1.24980e22i		−	0.495087i
$137$			5.50329e21i			0.201863i	0.994893	+	0.100932i	$0.0321823\pi$
$137$			5.50329e21i			0.201863i	−0.994893	+	0.100932i	$0.967818\pi$
$138$	−4.23637e22	+	3.55454e22i	−1.43967	+	1.20796i
$139$		−	3.09790e22i		−	0.975915i	−0.872867	−	0.487958i	$-0.837742\pi$
$139$		−	3.09790e22i		−	0.975915i	0.872867	−	0.487958i	$-0.162258\pi$
$140$	−3.32412e22	−	3.35523e21i	−0.971253	−	0.0980343i
$141$	−1.00078e22	+	8.39707e21i	−0.271354	+	0.227681i
$142$	4.44187e22			1.11825
$143$	−2.16794e22			−0.507012
$144$	−9.41479e21	+	5.33774e22i	−0.204647	+	1.16025i
$145$		−	6.33123e22i		−	1.27975i
$146$	−3.59086e22			−0.675296
$147$	5.02168e22	−	2.72328e22i	0.879057	−	0.476716i
$148$	−5.82939e22			−0.950332
$149$		−	2.26280e22i		−	0.343709i	−0.985122	−	0.171854i	$-0.945024\pi$
$149$		−	2.26280e22i		−	0.343709i	0.985122	−	0.171854i	$-0.0549759\pi$
$150$	−3.71530e22	−	4.42796e22i	−0.526060	−	0.626968i
$151$	−9.09150e21			−0.120054			−0.0600271	−	0.998197i	$-0.519119\pi$
$151$	−9.09150e21			−0.120054			−0.0600271	+	0.998197i	$0.519119\pi$
$152$	2.85572e22			0.351851
$153$	2.42419e22	−	1.37440e23i	0.278809	−	1.58071i
$154$	8.03402e22	+	8.10920e21i	0.862909	+	0.0870985i
$155$		−	1.08458e23i		−	1.08838i
$156$	−4.09107e22	−	4.87581e22i	−0.383733	−	0.457340i
$157$		−	1.65613e23i		−	1.45261i	−0.687373	−	0.726304i	$-0.741236\pi$
$157$		−	1.65613e23i		−	1.45261i	0.687373	−	0.726304i	$-0.258764\pi$
$158$			3.02343e23i			2.48085i
$159$	1.02387e23	+	1.22027e23i	0.786280	+	0.937102i
$160$			2.22402e23i			1.59911i
$161$	2.10751e22	−	2.08797e23i	0.141938	−	1.40622i
$162$	−7.20826e22	+	1.97980e23i	−0.454907	+	1.24944i
$163$	−1.13381e23			−0.670763			−0.335381	−	0.942082i	$-0.608865\pi$
$163$	−1.13381e23			−0.670763			−0.335381	+	0.942082i	$0.608865\pi$
$164$	−1.19779e23			−0.664537
$165$	1.02379e23	+	1.22017e23i	0.532881	+	0.635097i
$166$		−	3.40606e23i		−	1.66386i
$167$	−5.03836e22			−0.231082			−0.115541	−	0.993303i	$-0.536860\pi$
$167$	−5.03836e22			−0.231082			−0.115541	+	0.993303i	$0.536860\pi$
$168$	−4.02821e22	−	5.91959e22i	−0.173526	−	0.255002i
$169$	9.77838e22			0.395782
$170$		−	7.13049e23i		−	2.71272i
$171$	3.14043e23	+	5.53914e22i	1.12339	+	0.198145i
$172$	2.21579e23			0.745554
$173$	−2.90415e23			−0.919465			−0.459732	−	0.888057i	$-0.652055\pi$
$173$	−2.90415e23			−0.919465			−0.459732	+	0.888057i	$0.652055\pi$
$174$	−3.44147e23	+	2.88759e23i	−1.02560	+	0.860533i
$175$	2.18240e23	+	2.20283e22i	0.612401	+	0.0618132i
$176$		−	2.90743e23i		−	0.768468i
$177$	−5.00476e23	+	4.19927e23i	−1.24642	+	1.04581i
$178$			6.24459e23i			1.46586i
$179$			1.65216e23i			0.365676i	0.983143	+	0.182838i	$0.0585283\pi$
$179$			1.65216e23i			0.365676i	−0.983143	+	0.182838i	$0.941472\pi$
$180$	−8.12261e22	+	4.60513e23i	−0.169564	+	0.961349i
$181$			5.22379e23i			1.02887i	0.857529	+	0.514436i	$0.171999\pi$
$181$			5.22379e23i			1.02887i	−0.857529	+	0.514436i	$0.828001\pi$
$182$	5.53210e23	+	5.58387e22i	1.02835	+	0.103797i
$183$	−1.26362e23	−	1.50600e23i	−0.221758	−	0.264296i
$184$	−2.63037e23			−0.435944
$185$	1.00451e24			1.57272
$186$	−5.89547e23	+	4.94662e23i	−0.872233	+	0.731851i
$187$			7.48624e23i			1.04695i
$188$	2.05736e23			0.272052
$189$	−3.28161e23	−	7.29109e23i	−0.410429	−	0.911893i
$190$	1.62928e24			1.92789
$191$			7.34429e23i			0.822431i	0.911538	+	0.411215i	$0.134896\pi$
$191$			7.34429e23i			0.822431i	−0.911538	+	0.411215i	$0.865104\pi$
$192$	3.57518e23	−	2.99977e23i	0.378996	−	0.317998i
$193$	1.04432e24			1.04829			0.524147	−	0.851628i	$-0.324384\pi$
$193$	1.04432e24			1.04829			0.524147	+	0.851628i	$0.324384\pi$
$194$	4.56591e23			0.434119
$195$	7.04967e23	+	8.40193e23i	0.635047	+	0.756860i
$196$	−8.81491e23	−	1.79780e23i	−0.752539	−	0.153480i
$197$			8.01223e23i			0.648423i	0.945985	+	0.324211i	$0.105099\pi$
$197$			8.01223e23i			0.648423i	−0.945985	+	0.324211i	$0.894901\pi$
$198$	1.96314e23	−	1.11301e24i	0.150649	−	0.854110i
$199$		−	1.31900e24i		−	0.960039i	−0.877258	−	0.480019i	$-0.840630\pi$
$199$		−	1.31900e24i		−	0.960039i	0.877258	−	0.480019i	$-0.159370\pi$
$200$		−	2.74934e23i		−	0.189851i
$201$	2.24257e23	−	1.88164e23i	0.146956	−	0.123304i
$202$		−	8.46325e23i		−	0.526438i
$203$	1.71207e23	−	1.69620e24i	0.101114	−	1.00177i
$204$	−1.68370e24	+	1.41271e24i	−0.944382	+	0.792388i
$205$	2.06401e24			1.09975
$206$	9.57174e23			0.484602
$207$	−2.89262e24	−	5.10204e23i	−1.39188	−	0.245502i
$208$		−	2.00201e24i		−	0.915800i
$209$	−1.71057e24			−0.744053
$210$	−2.29822e24	−	3.37731e24i	−0.950799	−	1.39723i
$211$	6.91056e23			0.271987			0.135993	−	0.990710i	$-0.456577\pi$
$211$	6.91056e23			0.271987			0.135993	+	0.990710i	$0.456577\pi$
$212$		−	2.50858e24i		−	0.939511i
$213$	1.51647e24	+	1.80735e24i	0.540564	+	0.644254i
$214$	1.90132e24			0.645226
$215$	−3.81821e24			−1.23383
$216$	−8.67942e23	+	5.01015e23i	−0.267132	+	0.154201i
$217$	2.93289e23	−	2.90570e24i	0.0859941	−	0.851968i
$218$			5.93912e24i			1.65932i
$219$	−1.22593e24	−	1.46109e24i	−0.326440	−	0.389057i
$220$		−	2.50838e24i		−	0.636730i
$221$			5.15491e24i			1.24768i
$222$	−4.58144e24	−	5.46024e24i	−1.05754	−	1.26039i
$223$			6.92689e24i			1.52524i	0.646849	+	0.762618i	$0.276086\pi$
$223$			6.92689e24i			1.52524i	−0.646849	+	0.762618i	$0.723914\pi$
$224$	−6.01412e23	+	5.95835e24i	−0.126348	+	1.25176i
$225$	5.33278e23	−	3.02344e24i	0.106915	−	0.606156i
$226$	1.25217e25			2.39620
$227$	−1.03328e24			−0.188776			−0.0943882	−	0.995535i	$-0.530089\pi$
$227$	−1.03328e24			−0.188776			−0.0943882	+	0.995535i	$0.530089\pi$
$228$	−3.22798e24	−	3.84716e24i	−0.563138	−	0.671158i
$229$			9.83603e24i			1.63888i	0.573164	+	0.819441i	$0.305716\pi$
$229$			9.83603e24i			1.63888i	−0.573164	+	0.819441i	$0.694284\pi$
$230$	−1.50071e25			−2.38866
$231$	2.41288e24	+	3.54581e24i	0.366953	+	0.539250i
$232$	−2.13682e24			−0.310560
$233$			5.26607e24i			0.731559i	0.930702	+	0.365779i	$0.119198\pi$
$233$			5.26607e24i			0.731559i	−0.930702	+	0.365779i	$0.880802\pi$
$234$	1.35179e24	−	7.66400e24i	0.179532	−	1.01786i
$235$	−3.54520e24			−0.450224
$236$	1.02886e25			1.24962
$237$	−1.23020e25	+	1.03221e25i	−1.42929	+	1.19925i
$238$	1.92820e24	−	1.91033e25i	0.214336	−	2.12349i
$239$		−	7.97115e24i		−	0.847897i	−0.905686	−	0.423948i	$-0.860644\pi$
$239$		−	7.97115e24i		−	0.847897i	0.905686	−	0.423948i	$-0.139356\pi$
$240$	−1.12678e25	+	9.45434e24i	−1.14716	+	0.962527i
$241$		−	1.14952e25i		−	1.12031i	−0.828388	−	0.560154i	$-0.810742\pi$
$241$		−	1.14952e25i		−	1.12031i	0.828388	−	0.560154i	$-0.189258\pi$
$242$		−	8.18725e24i		−	0.763971i
$243$	−1.05165e25	+	3.82613e24i	−0.939738	+	0.341896i
$244$			3.09598e24i			0.264975i
$245$	1.51897e25	+	3.09793e24i	1.24539	+	0.253997i
$246$	−9.41365e24	−	1.12194e25i	−0.739502	−	0.881351i
$247$	−1.17787e25			−0.886705
$248$	−3.66052e24			−0.264119
$249$	1.38589e25	−	1.16284e25i	0.958596	−	0.804315i
$250$			9.79834e24i			0.649804i
$251$	1.98280e24			0.126097			0.0630485	−	0.998010i	$-0.479918\pi$
$251$	1.98280e24			0.126097			0.0630485	+	0.998010i	$0.479918\pi$
$252$	−3.42143e24	+	1.21179e25i	−0.208690	+	0.739134i
$253$	1.57558e25			0.921884
$254$			9.76271e24i			0.548045i
$255$	2.90132e25	−	2.43437e25i	1.56288	−	1.31134i
$256$	2.50088e25			1.29292
$257$	2.28306e25			1.13297			0.566487	−	0.824070i	$-0.308302\pi$
$257$	2.28306e25			1.13297			0.566487	+	0.824070i	$0.308302\pi$
$258$	1.74143e25	+	2.07547e25i	0.829658	+	0.988801i
$259$	2.69118e25	+	2.71637e24i	1.23111	+	0.124263i
$260$		−	1.72723e25i		−	0.758805i
$261$	−2.34986e25	−	4.14472e24i	−0.991554	−	0.174892i
$262$		−	2.22078e25i		−	0.900207i
$263$		−	2.78372e25i		−	1.08415i	−0.840329	−	0.542076i	$-0.817638\pi$
$263$		−	2.78372e25i		−	1.08415i	0.840329	−	0.542076i	$-0.182362\pi$
$264$	4.11815e24	−	3.45535e24i	0.154121	−	0.129316i
$265$			4.32275e25i			1.55481i
$266$	4.36499e25	+	4.40584e24i	1.50913	+	0.152325i
$267$	−2.54086e25	+	2.13192e25i	−0.844525	+	0.708602i
$268$	−4.61017e24			−0.147334
$269$	2.33332e25			0.717091			0.358546	−	0.933512i	$-0.383273\pi$
$269$	2.33332e25			0.717091			0.358546	+	0.933512i	$0.383273\pi$
$270$	−4.95188e25	+	2.85845e25i	−1.46369	+	0.844910i
$271$			2.60440e25i			0.740508i	0.928931	+	0.370254i	$0.120729\pi$
$271$			2.60440e25i			0.740508i	−0.928931	+	0.370254i	$0.879271\pi$
$272$	−6.91326e25			−1.89108
$273$	1.66147e25	+	2.44159e25i	0.437306	+	0.642636i
$274$	1.05970e25			0.268412
$275$			1.64684e25i			0.401475i
$276$	2.97326e25	+	3.54358e25i	0.697729	+	0.831566i
$277$	−1.05713e25			−0.238830			−0.119415	−	0.992844i	$-0.538102\pi$
$277$	−1.05713e25			−0.238830			−0.119415	+	0.992844i	$0.538102\pi$
$278$	−5.96523e25			−1.29765
$279$	−4.02546e25	−	7.10017e24i	−0.843280	−	0.148739i
$280$	1.95135e24	−	1.93326e25i	0.0393709	−	0.390059i
$281$		−	4.52746e25i		−	0.879909i	−0.898020	−	0.439955i	$-0.854995\pi$
$281$		−	4.52746e25i		−	0.879909i	0.898020	−	0.439955i	$-0.145005\pi$
$282$	1.61692e25	+	1.92707e25i	0.302742	+	0.360813i
$283$		−	8.01307e24i		−	0.144558i	−0.997384	−	0.0722789i	$-0.976973\pi$
$283$		−	8.01307e24i		−	0.144558i	0.997384	−	0.0722789i	$-0.0230272\pi$
$284$		−	3.71548e25i		−	0.645910i
$285$	5.56240e25	+	6.62937e25i	0.931948	+	1.11071i
$286$			4.17452e25i			0.674160i
$287$	5.52967e25	+	5.58142e24i	0.860874	+	0.0868930i
$288$	8.25452e25	+	1.45594e25i	1.23900	+	0.218536i
$289$	1.08916e26			1.57639
$290$	−1.21912e26			−1.70165
$291$	1.55881e25	+	1.85782e25i	0.209854	+	0.250108i
$292$			3.00364e25i			0.390057i
$293$	6.16639e24			0.0772540			0.0386270	−	0.999254i	$-0.487702\pi$
$293$	6.16639e24			0.0772540			0.0386270	+	0.999254i	$0.487702\pi$
$294$	−5.24386e25	−	9.66961e25i	−0.633876	−	1.16886i
$295$	−1.77291e26			−2.06802
$296$		−	3.39028e25i		−	0.381656i
$297$	5.19894e25	−	3.00106e25i	0.564900	−	0.326086i
$298$	−4.35719e25			−0.457020
$299$	1.08492e26			1.09863
$300$	−3.70384e25	+	3.10772e25i	−0.362142	+	0.303857i
$301$	−1.02293e26	−	1.03251e25i	−0.965827	−	0.0974866i
$302$			1.75063e25i			0.159633i
$303$	3.44361e25	−	2.88938e25i	0.303296	−	0.254482i
$304$		−	1.57964e26i		−	1.34396i
$305$		−	5.33494e25i		−	0.438512i
$306$	−2.64651e26	−	4.66795e25i	−2.10183	−	0.370724i
$307$			7.64771e25i			0.586919i	0.955971	+	0.293460i	$0.0948066\pi$
$307$			7.64771e25i			0.586919i	−0.955971	+	0.293460i	$0.905193\pi$
$308$	6.78308e24	−	6.72019e25i	0.0503088	−	0.498424i
$309$	3.26782e25	+	3.89464e25i	0.234258	+	0.279192i
$310$	−2.08844e26			−1.44719
$311$	1.67333e26			1.12098			0.560488	−	0.828162i	$-0.310613\pi$
$311$	1.67333e26			1.12098			0.560488	+	0.828162i	$0.310613\pi$
$312$	2.83569e25	−	2.37930e25i	0.183669	−	0.154108i
$313$		−	3.15921e26i		−	1.97862i	−0.145814	−	0.989312i	$-0.546580\pi$
$313$		−	3.15921e26i		−	1.97862i	0.145814	−	0.989312i	$-0.453420\pi$
$314$	−3.18900e26			−1.93150
$315$	5.89575e25	−	2.08815e26i	0.345365	−	1.22321i
$316$	2.52900e26			1.43296
$317$			1.06857e26i			0.585706i	0.956157	+	0.292853i	$0.0946047\pi$
$317$			1.06857e26i			0.585706i	−0.956157	+	0.292853i	$0.905395\pi$
$318$	2.34972e26	−	1.97154e26i	1.24604	−	1.04549i
$319$	1.27995e26			0.656735
$320$	1.26649e26			0.628820
$321$	6.49118e25	+	7.73630e25i	0.311904	+	0.371732i
$322$	−4.02055e26	−	4.05817e25i	−1.86981	−	0.188731i
$323$			4.06738e26i			1.83100i
$324$	1.65604e26	+	6.02947e25i	0.721685	+	0.262758i
$325$			1.13399e26i			0.478447i
$326$			2.18323e26i			0.891895i
$327$	−2.41657e26	+	2.02763e26i	−0.955977	+	0.802117i
$328$		−	6.96613e25i		−	0.266880i
$329$	−9.49794e25	−	9.58682e24i	−0.352430	−	0.0355728i
$330$	2.34953e26	−	1.97139e26i	0.844472	−	0.708558i
$331$	4.53313e26			1.57835			0.789177	−	0.614166i	$-0.210507\pi$
$331$	4.53313e26			1.57835			0.789177	+	0.614166i	$0.210507\pi$
$332$	−2.84905e26			−0.961060
$333$	6.57600e25	−	3.72828e26i	0.214930	−	1.21855i
$334$			9.70173e25i			0.307264i
$335$	7.94417e25			0.243825
$336$	−3.27442e26	+	2.22821e26i	−0.974031	+	0.662816i
$337$	−6.68212e26			−1.92664			−0.963320	−	0.268357i	$-0.913519\pi$
$337$	−6.68212e26			−1.92664			−0.963320	+	0.268357i	$0.913519\pi$
$338$		−	1.88290e26i		−	0.526261i
$339$	4.27494e26	+	5.09494e26i	1.15833	+	1.38052i
$340$	−5.96441e26			−1.56689
$341$	2.19264e26			0.558529
$342$	1.06660e26	−	6.04713e26i	0.263468	−	1.49374i
$343$	3.98569e26	+	1.24072e26i	0.954807	+	0.297225i
$344$			1.28866e26i			0.299417i
$345$	−5.12347e26	−	6.10624e26i	−1.15469	−	1.37617i
$346$			5.59215e26i			1.22259i
$347$			4.27377e26i			0.906466i	0.891392	+	0.453233i	$0.149729\pi$
$347$			4.27377e26i			0.906466i	−0.891392	+	0.453233i	$0.850271\pi$
$348$	2.41537e26	+	2.87868e26i	0.497051	+	0.592395i
$349$			4.85429e26i			0.969301i	0.874708	+	0.484650i	$0.161053\pi$
$349$			4.85429e26i			0.969301i	−0.874708	+	0.484650i	$0.838947\pi$
$350$	4.24171e25	−	4.20238e26i	0.0821913	−	0.814293i
$351$	3.57991e26	−	2.06648e26i	0.673205	−	0.388604i
$352$	−4.49617e26			−0.820625
$353$	−7.81307e26			−1.38416			−0.692082	−	0.721819i	$-0.743306\pi$
$353$	−7.81307e26			−1.38416			−0.692082	+	0.721819i	$0.743306\pi$
$354$	8.08599e26	+	9.63703e26i	1.39059	+	1.65733i
$355$			6.40245e26i			1.06893i
$356$	5.22339e26			0.846696
$357$	8.43122e26	−	5.73734e26i	1.32701	−	0.903013i
$358$	3.18136e26			0.486229
$359$		−	2.80022e26i		−	0.415624i	−0.978169	−	0.207812i	$-0.933366\pi$
$359$		−	2.80022e26i		−	0.415624i	0.978169	−	0.207812i	$-0.0666343\pi$
$360$	−2.67827e26	−	4.72398e25i	−0.386081	−	0.0680976i
$361$	−2.15165e26			−0.301263
$362$	1.00588e27			1.36806
$363$	3.33131e26	−	2.79515e26i	0.440145	−	0.369306i
$364$	4.67072e25	−	4.62742e26i	0.0599542	−	0.593983i
$365$		−	5.17582e26i		−	0.645512i
$366$	−2.89992e26	+	2.43319e26i	−0.351427	+	0.294866i
$367$			6.09104e26i			0.717295i	0.933473	+	0.358647i	$0.116762\pi$
$367$			6.09104e26i			0.717295i	−0.933473	+	0.358647i	$0.883238\pi$
$368$			1.45499e27i			1.66517i
$369$	1.35119e26	−	7.66064e26i	0.150294	−	0.852095i
$370$		−	1.93426e27i		−	2.09121i
$371$	−1.16894e26	+	1.15811e27i	−0.122848	+	1.21709i
$372$	4.13768e26	+	4.93136e26i	0.422724	+	0.503809i
$373$	−7.50786e26			−0.745716			−0.372858	−	0.927888i	$-0.621622\pi$
$373$	−7.50786e26			−0.745716			−0.372858	+	0.927888i	$0.621622\pi$
$374$	1.44153e27			1.39210
$375$	−3.98684e26	+	3.34518e26i	−0.374370	+	0.314117i
$376$			1.19652e26i			0.109257i
$377$	8.81353e26			0.782647
$378$	−1.40395e27	+	6.31897e26i	−1.21252	+	0.545736i
$379$	−1.75903e27			−1.47761			−0.738806	−	0.673918i	$-0.764610\pi$
$379$	−1.75903e27			−1.47761			−0.738806	+	0.673918i	$0.764610\pi$
$380$		−	1.36284e27i		−	1.11357i
$381$	−3.97235e26	+	3.33302e26i	−0.315744	+	0.264926i
$382$	1.41420e27			1.09356
$383$	7.73461e26			0.581904			0.290952	−	0.956738i	$-0.406028\pi$
$383$	7.73461e26			0.581904			0.290952	+	0.956738i	$0.406028\pi$
$384$	5.27100e26	+	6.28207e26i	0.385847	+	0.459859i
$385$	−1.16885e26	+	1.15801e27i	−0.0832570	+	0.824851i
$386$		−	2.01092e27i		−	1.39389i
$387$	−2.49957e26	+	1.41714e27i	−0.168617	+	0.955978i
$388$		−	3.81923e26i		−	0.250751i
$389$		−	2.54238e27i		−	1.62469i	−0.583179	−	0.812344i	$-0.698191\pi$
$389$		−	2.54238e27i		−	1.62469i	0.583179	−	0.812344i	$-0.301809\pi$
$390$	1.61785e27	−	1.35747e27i	1.00638	−	0.844404i
$391$		−	3.74642e27i		−	2.26861i
$392$	1.04557e26	−	5.12661e26i	0.0616381	−	0.302222i
$393$	9.03613e26	−	7.58181e26i	0.518634	−	0.435162i
$394$	1.54281e27			0.862190
$395$	−4.35793e27			−2.37143
$396$	−9.30994e26	−	1.64210e26i	−0.493341	−	0.0870163i
$397$			2.81779e27i			1.45415i	0.686560	+	0.727073i	$0.259120\pi$
$397$			2.81779e27i			1.45415i	−0.686560	+	0.727073i	$0.740880\pi$
$398$	−2.53984e27			−1.27654
$399$	1.31095e27	+	1.92649e27i	0.641758	+	0.943085i
$400$	−1.52080e27			−0.725172
$401$			2.77530e27i			1.28912i	0.764553	+	0.644560i	$0.222960\pi$
$401$			2.77530e27i			1.28912i	−0.764553	+	0.644560i	$0.777040\pi$
$402$	−3.62323e26	−	4.31822e26i	−0.163954	−	0.195403i
$403$	1.50982e27			0.665612
$404$	−7.07922e26			−0.304075
$405$	−2.85366e27	−	1.03899e27i	−1.19433	−	0.434844i
$406$	−3.26615e27	−	3.29672e26i	−1.33203	−	0.134449i
$407$			2.03076e27i			0.807083i
$408$	−8.21612e26	−	9.79212e26i	−0.318226	−	0.379267i
$409$		−	5.91345e26i		−	0.223227i	−0.993752	−	0.111613i	$-0.964398\pi$
$409$		−	5.91345e26i		−	0.223227i	0.993752	−	0.111613i	$-0.0356018\pi$
$410$		−	3.97440e27i		−	1.46231i
$411$	3.61784e26	+	4.31181e26i	0.129751	+	0.154639i
$412$		−	8.00644e26i		−	0.279910i
$413$	−4.74979e27	−	4.79425e26i	−1.61882	−	0.163397i
$414$	−9.82434e26	+	5.56994e27i	−0.326437	+	1.85075i
$415$	4.90944e27			1.59048
$416$	−3.09599e27			−0.977957
$417$	−2.03655e27	−	2.42719e27i	−0.627287	−	0.747611i
$418$			3.29382e27i			0.989348i
$419$	2.24733e27			0.658294			0.329147	−	0.944279i	$-0.393239\pi$
$419$	2.24733e27			0.658294			0.329147	+	0.944279i	$0.393239\pi$
$420$	−2.82501e27	+	1.92238e27i	−0.807053	+	0.549190i
$421$	2.26692e27			0.631647			0.315823	−	0.948818i	$-0.397719\pi$
$421$	2.26692e27			0.631647			0.315823	+	0.948818i	$0.397719\pi$
$422$		−	1.33068e27i		−	0.361653i
$423$	−2.32085e26	+	1.31581e27i	−0.0615282	+	0.348836i
$424$	1.45895e27			0.377311
$425$	3.91585e27			0.987967
$426$	3.48019e27	−	2.92007e27i	0.856647	−	0.718774i
$427$	1.44266e26	−	1.42928e27i	0.0346474	−	0.343262i
$428$		−	1.59039e27i		−	0.372688i
$429$	−1.69857e27	+	1.42519e27i	−0.388402	+	0.325891i
$430$			7.35223e27i			1.64059i
$431$			5.14323e27i			1.12002i	0.828487	+	0.560008i	$0.189202\pi$
$431$			5.14323e27i			1.12002i	−0.828487	+	0.560008i	$0.810798\pi$
$432$	2.77137e27	+	4.80103e27i	0.588999	+	1.02036i
$433$		−	9.09697e27i		−	1.88701i	−0.331361	−	0.943504i	$-0.607508\pi$
$433$		−	9.09697e27i		−	1.88701i	0.331361	−	0.943504i	$-0.392492\pi$
$434$	−5.59513e27	−	5.64749e26i	−1.13284	−	0.114344i
$435$	−4.16213e27	−	4.96049e27i	−0.822580	−	0.980365i
$436$	4.96787e27			0.958435
$437$	8.56037e27			1.61227
$438$	−2.81343e27	+	2.36062e27i	−0.517318	+	0.434058i
$439$		−	9.97832e27i		−	1.79135i	−0.444712	−	0.895674i	$-0.646694\pi$
$439$		−	9.97832e27i		−	1.79135i	0.444712	−	0.895674i	$-0.353306\pi$
$440$	1.45883e27			0.255713
$441$	2.14420e27	−	5.43491e27i	0.366995	−	0.930223i
$442$	9.92615e27			1.65900
$443$			4.96044e27i			0.809619i	0.914401	+	0.404809i	$0.132662\pi$
$443$			4.96044e27i			0.809619i	−0.914401	+	0.404809i	$0.867338\pi$
$444$	−4.56731e27	+	3.83222e27i	−0.728013	+	0.610842i
$445$	−9.00086e27			−1.40121
$446$	1.33382e28			2.02807
$447$	−1.48756e27	−	1.77290e27i	−0.220925	−	0.263302i
$448$	3.39304e27	+	3.42480e26i	0.492232	+	0.0496839i
$449$			2.45297e26i			0.0347621i	0.999849	+	0.0173811i	$0.00553284\pi$
$449$			2.45297e26i			0.0347621i	−0.999849	+	0.0173811i	$0.994467\pi$
$450$	−5.82184e27	−	1.02687e27i	−0.805989	−	0.142162i
$451$			4.17269e27i			0.564368i
$452$		−	1.04740e28i		−	1.38407i
$453$	−7.12316e26	+	5.97672e26i	−0.0919690	+	0.0771670i
$454$			1.98966e27i			0.251011i
$455$	−8.04852e26	+	7.97389e27i	−0.0992193	+	0.982994i
$456$	2.23745e27	−	1.87734e27i	0.269539	−	0.226158i
$457$	6.64451e27			0.782245			0.391122	−	0.920339i	$-0.372087\pi$
$457$	6.64451e27			0.782245			0.391122	+	0.920339i	$0.372087\pi$
$458$	1.89400e28			2.17918
$459$	−7.13590e27	−	1.23620e28i	−0.802446	−	1.39013i
$460$			1.25529e28i			1.37971i
$461$	−3.34150e27			−0.358989			−0.179495	−	0.983759i	$-0.557446\pi$
$461$	−3.34150e27			−0.358989			−0.179495	+	0.983759i	$0.557446\pi$
$462$	6.82772e27	−	4.64618e27i	0.717026	−	0.487927i
$463$	−6.64484e27			−0.682157			−0.341079	−	0.940035i	$-0.610792\pi$
$463$	−6.64484e27			−0.682157			−0.341079	+	0.940035i	$0.610792\pi$
$464$			1.18199e28i			1.18624i
$465$	−7.12999e27	−	8.49765e27i	−0.699573	−	0.833764i
$466$	1.01402e28			0.972734
$467$	−8.33818e27			−0.782067			−0.391034	−	0.920376i	$-0.627882\pi$
$467$	−8.33818e27			−0.782067			−0.391034	+	0.920376i	$0.627882\pi$
$468$	−6.41068e27	−	1.13073e27i	−0.587926	−	0.103699i
$469$	2.12832e27	+	2.14824e26i	0.190863	+	0.0192649i
$470$			6.82654e27i			0.598651i
$471$	−1.08873e28	−	1.29757e28i	−0.933690	−	1.11279i
$472$			5.98366e27i			0.501853i
$473$		−	7.71905e27i		−	0.633172i
$474$	1.98759e28	+	2.36884e28i	1.59461	+	1.90048i
$475$			8.94751e27i			0.702133i
$476$	−1.59792e28	−	1.61288e27i	−1.22654	−	0.123802i
$477$	1.60440e28	+	2.82987e27i	1.20468	+	0.212483i
$478$	−1.53490e28			−1.12743
$479$	1.41307e28			1.01541			0.507705	−	0.861531i	$-0.330494\pi$
$479$	1.41307e28			1.01541			0.507705	+	0.861531i	$0.330494\pi$
$480$	1.46206e28	+	1.74251e28i	1.02786	+	1.22502i
$481$			1.39835e28i			0.961819i
$482$	−2.21348e28			−1.48964
$483$	−1.20750e28	−	1.77447e28i	−0.795140	−	1.16848i
$484$	−6.84836e27			−0.441276
$485$			6.58123e27i			0.414972i
$486$	7.36749e27	+	2.02503e28i	0.454610	+	1.24954i
$487$	1.06815e28			0.645030			0.322515	−	0.946564i	$-0.395472\pi$
$487$	1.06815e28			0.645030			0.322515	+	0.946564i	$0.395472\pi$
$488$	−1.80057e27			−0.106415
$489$	−8.88333e27	+	7.45360e27i	−0.513846	+	0.431144i
$490$	5.96530e27	−	2.92489e28i	0.337733	−	1.65596i
$491$			2.41648e27i			0.133914i	0.997756	+	0.0669571i	$0.0213291\pi$
$491$			2.41648e27i			0.133914i	−0.997756	+	0.0669571i	$0.978671\pi$
$492$	−9.38461e27	+	7.87420e27i	−0.509076	+	0.427143i
$493$		−	3.04346e28i		−	1.61612i
$494$			2.26807e28i			1.17903i
$495$	1.60427e28	+	2.82964e27i	0.816439	+	0.144005i
$496$			2.02482e28i			1.00885i
$497$	−1.73133e27	+	1.71528e28i	−0.0844574	+	0.836744i
$498$	−2.23913e28	−	2.66863e28i	−1.06948	−	1.27462i
$499$	−1.64695e27			−0.0770237			−0.0385119	−	0.999258i	$-0.512262\pi$
$499$	−1.64695e27			−0.0770237			−0.0385119	+	0.999258i	$0.512262\pi$
$500$	8.19598e27			0.375332
$501$	−3.94754e27	+	3.31220e27i	−0.177023	+	0.148532i
$502$		−	3.81802e27i		−	0.167668i
$503$	−3.37523e28			−1.45158			−0.725788	−	0.687919i	$-0.758525\pi$
$503$	−3.37523e28			−1.45158			−0.725788	+	0.687919i	$0.758525\pi$
$504$	−7.04760e27	−	1.98985e27i	−0.296839	−	0.0838107i
$505$	1.21988e28			0.503220
$506$		−	3.03390e28i		−	1.22580i
$507$	7.66132e27	−	6.42827e27i	0.303194	−	0.254396i
$508$	8.16618e27			0.316555
$509$	−8.01174e27			−0.304222			−0.152111	−	0.988363i	$-0.548607\pi$
$509$	−8.01174e27			−0.304222			−0.152111	+	0.988363i	$0.548607\pi$
$510$	−4.68755e28	−	5.58671e28i	−1.74365	−	2.07811i
$511$	1.39963e27	−	1.38665e28i	0.0510027	−	0.505298i
$512$		−	3.13412e28i		−	1.11887i
$513$	2.82466e28	−	1.63052e28i	0.987946	−	0.570286i
$514$		−	4.39620e28i		−	1.50649i
$515$			1.37966e28i			0.463228i
$516$	1.73606e28	−	1.45665e28i	0.571140	−	0.479218i
$517$		−	7.16713e27i		−	0.231044i
$518$	5.23056e27	−	5.18207e28i	0.165229	−	1.63697i
$519$	−2.27539e28	+	1.90918e28i	−0.704367	+	0.591002i
$520$	1.00453e28			0.304739
$521$	−9.08908e26			−0.0270224			−0.0135112	−	0.999909i	$-0.504301\pi$
$521$	−9.08908e26			−0.0270224			−0.0135112	+	0.999909i	$0.504301\pi$
$522$	−7.98095e27	+	4.52482e28i	−0.232549	+	1.31844i
$523$			3.59245e28i			1.02594i	0.858406	+	0.512972i	$0.171455\pi$
$523$			3.59245e28i			1.02594i	−0.858406	+	0.512972i	$0.828545\pi$
$524$	−1.85761e28			−0.519967
$525$	1.85472e28	−	1.26211e28i	0.508868	−	0.346279i
$526$	−5.36026e28			−1.44157
$527$		−	5.21364e28i		−	1.37445i
$528$	−1.91133e28	−	2.27796e28i	−0.493946	−	0.588693i
$529$	−3.93770e28			−0.997603
$530$	8.32377e28			2.06739
$531$	−1.16063e28	+	6.58022e28i	−0.282619	+	1.60231i
$532$	3.68534e27	−	3.65117e28i	0.0879843	−	0.871686i
$533$			2.87325e28i			0.672570i
$534$	4.10517e28	+	4.89261e28i	0.942210	+	1.12294i
$535$			2.74054e28i			0.616768i
$536$		−	2.68120e27i		−	0.0591696i
$537$	1.08612e28	+	1.29446e28i	0.235044	+	0.280130i
$538$		−	4.49297e28i		−	0.953497i
$539$	−6.26292e27	+	3.07082e28i	−0.130345	+	0.639105i
$540$	2.39099e28	+	4.14208e28i	0.488027	+	0.845443i
$541$	−1.75217e28			−0.350756			−0.175378	−	0.984501i	$-0.556115\pi$
$541$	−1.75217e28			−0.350756			−0.175378	+	0.984501i	$0.556115\pi$
$542$	5.01496e28			0.984634
$543$	3.43410e28	+	4.09282e28i	0.661325	+	0.788179i
$544$			1.06910e29i			2.01943i
$545$	−8.56057e28			−1.58613
$546$	4.70146e28	−	3.19929e28i	0.854496	−	0.581474i
$547$	3.46969e28			0.618620			0.309310	−	0.950961i	$-0.399902\pi$
$547$	3.46969e28			0.618620			0.309310	+	0.950961i	$0.399902\pi$
$548$		−	8.86403e27i		−	0.155037i
$549$	−1.98008e28	−	3.49250e27i	−0.339761	−	0.0599276i
$550$	3.17111e28			0.533830
$551$	6.95414e28			1.14855
$552$	−2.06089e28	+	1.72920e28i	−0.333960	+	0.280210i
$553$	−1.16753e29	−	1.17846e28i	−1.85633	−	0.187370i
$554$			2.03557e28i			0.317566i
$555$	7.87031e28	−	6.60362e28i	1.20480	−	1.01089i
$556$			4.98972e28i			0.749533i
$557$		−	4.15528e28i		−	0.612520i	−0.951948	−	0.306260i	$-0.900922\pi$
$557$		−	4.15528e28i		−	0.612520i	0.951948	−	0.306260i	$-0.0990777\pi$
$558$	−1.36719e28	+	7.75132e28i	−0.197774	+	1.12129i
$559$		−	5.31522e28i		−	0.754566i
$560$	−1.06938e29	−	1.07939e28i	−1.48990	−	0.150385i
$561$	4.92142e28	+	5.86544e28i	0.672947	+	0.802030i
$562$	−8.71794e28			−1.16999
$563$	−5.10572e27			−0.0672542			−0.0336271	−	0.999434i	$-0.510706\pi$
$563$	−5.10572e27			−0.0672542			−0.0336271	+	0.999434i	$0.510706\pi$
$564$	1.61193e28	−	1.35250e28i	0.208409	−	0.174866i
$565$			1.80486e29i			2.29052i
$566$	−1.54298e28			−0.192215
$567$	−7.36426e28	−	3.55523e28i	−0.900549	−	0.434756i
$568$	2.16086e28			0.259400
$569$			7.65351e28i			0.901949i	0.892537	+	0.450974i	$0.148923\pi$
$569$			7.65351e28i			0.901949i	−0.892537	+	0.450974i	$0.851077\pi$
$570$	1.27653e29	−	1.07108e29i	1.47688	−	1.23919i
$571$	−8.22289e28			−0.933997			−0.466999	−	0.884258i	$-0.654665\pi$
$571$	−8.22289e28			−0.933997			−0.466999	+	0.884258i	$0.654665\pi$
$572$	3.49184e28			0.389401
$573$	4.82810e28	+	5.75422e28i	0.528632	+	0.630033i
$574$	1.07474e28	−	1.06478e29i	0.115539	−	1.14468i
$575$		−	8.24145e28i		−	0.869944i
$576$	8.29102e27	−	4.70061e28i	0.0859353	−	0.487213i
$577$			8.74909e28i			0.890465i	0.895415	+	0.445233i	$0.146879\pi$
$577$			8.74909e28i			0.890465i	−0.895415	+	0.445233i	$0.853121\pi$
$578$		−	2.09725e29i		−	2.09608i
$579$	8.18223e28	−	6.86534e28i	0.803058	−	0.673809i
$580$			1.01976e29i			0.982885i
$581$	1.31529e29	+	1.32760e28i	1.24500	+	0.125666i
$582$	3.57737e28	−	3.00161e28i	0.332562	−	0.279037i
$583$	−8.73905e28			−0.797893
$584$	−1.74687e28			−0.156648
$585$	1.10468e29	+	1.94845e28i	0.972970	+	0.171614i
$586$		−	1.18738e28i		−	0.102723i
$587$	−5.04337e28			−0.428569			−0.214285	−	0.976771i	$-0.568742\pi$
$587$	−5.04337e28			−0.428569			−0.214285	+	0.976771i	$0.568742\pi$
$588$	−8.08831e28	+	4.38632e28i	−0.675143	+	0.366132i
$589$	1.19129e29			0.976803
$590$			3.41387e29i			2.74980i
$591$	5.26721e28	+	6.27755e28i	0.416785	+	0.496732i
$592$	−1.87534e29			−1.45781
$593$	1.97856e29			1.51104			0.755518	−	0.655128i	$-0.227385\pi$
$593$	1.97856e29			1.51104			0.755518	+	0.655128i	$0.227385\pi$
$594$	−5.77875e28	−	1.00109e29i	−0.433587	−	0.751133i
$595$	2.75352e29	+	2.77929e28i	2.02983	+	0.204883i
$596$			3.64464e28i			0.263979i
$597$	−8.67108e28	−	1.03343e29i	−0.617082	−	0.735449i
$598$		−	2.08910e29i		−	1.46082i
$599$			1.49836e28i			0.102952i	0.998674	+	0.0514761i	$0.0163926\pi$
$599$			1.49836e28i			0.102952i	−0.998674	+	0.0514761i	$0.983607\pi$
$600$	−1.80740e28	−	2.15409e28i	−0.122030	−	0.145437i
$601$		−	1.76300e29i		−	1.16969i	−0.811147	−	0.584843i	$-0.801156\pi$
$601$		−	1.76300e29i		−	1.16969i	0.811147	−	0.584843i	$-0.198844\pi$
$602$	−1.98817e28	+	1.96973e29i	−0.129625	+	1.28423i
$603$	5.20062e27	−	2.94851e28i	0.0333214	−	0.188917i
$604$	1.46435e28			0.0922054
$605$	1.18010e29			0.730276
$606$	−5.56370e28	−	6.63092e28i	−0.338377	−	0.403284i
$607$		−	2.80398e29i		−	1.67607i	−0.545613	−	0.838037i	$-0.683703\pi$
$607$		−	2.80398e29i		−	1.67607i	0.545613	−	0.838037i	$-0.316297\pi$
$608$	−2.44283e29			−1.43518
$609$	−9.80933e28	−	1.44151e29i	−0.566445	−	0.832410i
$610$	−1.02728e29			−0.583078
$611$		−	4.93518e28i		−	0.275341i
$612$	−3.90458e28	+	2.21371e29i	−0.214133	+	1.21404i
$613$	5.20652e28			0.280680			0.140340	−	0.990103i	$-0.455180\pi$
$613$	5.20652e28			0.280680			0.140340	+	0.990103i	$0.455180\pi$
$614$	1.47262e29			0.780411
$615$	1.61714e29	−	1.35687e29i	0.842480	−	0.706886i
$616$	3.90835e28	+	3.94493e27i	0.200169	+	0.0202042i
$617$		−	1.37863e28i		−	0.0694150i	−0.999398	−	0.0347075i	$-0.988950\pi$
$617$		−	1.37863e28i		−	0.0694150i	0.999398	−	0.0347075i	$-0.0110500\pi$
$618$	7.49942e28	−	6.29242e28i	0.371235	−	0.311486i
$619$			3.20993e29i			1.56223i	0.624390	+	0.781113i	$0.285348\pi$
$619$			3.20993e29i			1.56223i	−0.624390	+	0.781113i	$0.714652\pi$
$620$			1.74691e29i			0.835907i
$621$	−2.60176e29	+	1.50185e29i	−1.22407	+	0.706586i
$622$		−	3.22211e29i		−	1.49053i
$623$	−2.41142e29	−	2.43398e28i	−1.09685	−	0.110712i
$624$	−1.31611e29	−	1.56857e29i	−0.588647	−	0.701559i
$625$	−2.81183e29			−1.23666
$626$	−6.08329e29			−2.63092
$627$	−1.34022e29	+	1.12452e29i	−0.569990	+	0.478253i
$628$			2.66749e29i			1.11565i
$629$	4.82874e29			1.98611
$630$	−4.02088e29	−	1.13527e29i	−1.62647	−	0.459223i
$631$	−7.58492e28			−0.301747			−0.150873	−	0.988553i	$-0.548209\pi$
$631$	−7.58492e28			−0.301747			−0.150873	+	0.988553i	$0.548209\pi$
$632$			1.47082e29i			0.575481i
$633$	5.41440e28	−	4.54297e28i	0.208358	−	0.174824i
$634$	2.05760e29			0.778798
$635$	−1.40718e29			−0.523874
$636$	−1.64913e29	−	1.96546e29i	−0.603887	−	0.719723i
$637$	−4.31255e28	+	2.11452e29i	−0.155335	+	0.761635i
$638$		−	2.46463e29i		−	0.873243i
$639$	2.37629e29	+	4.19134e28i	0.828211	+	0.146081i
$640$			2.22539e29i			0.762985i
$641$		−	2.72204e29i		−	0.918089i	−0.888413	−	0.459045i	$-0.848192\pi$
$641$		−	2.72204e29i		−	0.918089i	0.888413	−	0.459045i	$-0.151808\pi$
$642$	1.48968e29	−	1.24992e29i	0.494282	−	0.414730i
$643$		−	3.19978e28i		−	0.104449i	−0.998635	−	0.0522246i	$-0.983369\pi$
$643$		−	3.19978e28i		−	0.104449i	0.998635	−	0.0522246i	$-0.0166312\pi$
$644$	−3.39452e28	+	3.36305e29i	−0.109013	+	1.08002i
$645$	−2.99155e29	+	2.51007e29i	−0.945190	+	0.793066i
$646$	7.83203e29			2.43463
$647$	−1.36569e29			−0.417693			−0.208846	−	0.977948i	$-0.566971\pi$
$647$	−1.36569e29			−0.417693			−0.208846	+	0.977948i	$0.566971\pi$
$648$	−3.50664e28	+	9.63125e28i	−0.105525	+	0.289831i
$649$		−	3.58419e29i		−	1.06126i
$650$	2.18358e29			0.636178
$651$	−1.68040e29	−	2.46941e29i	−0.481740	−	0.707934i
$652$	1.82620e29			0.515166
$653$		−	3.54552e29i		−	0.984220i	−0.870533	−	0.492110i	$-0.836226\pi$
$653$		−	3.54552e29i		−	0.984220i	0.870533	−	0.492110i	$-0.163774\pi$
$654$	3.90435e29	+	4.65328e29i	1.06655	+	1.27114i
$655$	3.20100e29			0.860503
$656$	−3.85332e29			−1.01940
$657$	−1.92102e29	−	3.38833e28i	−0.500146	−	0.0882165i
$658$	−1.84601e28	+	1.82890e29i	−0.0473002	+	0.468616i
$659$			1.19685e28i			0.0301816i	0.999886	+	0.0150908i	$0.00480374\pi$
$659$			1.19685e28i			0.0301816i	−0.999886	+	0.0150908i	$0.995196\pi$
$660$	−1.64900e29	−	1.96530e29i	−0.409269	−	0.487774i
$661$		−	9.19128e28i		−	0.224523i	−0.993679	−	0.112261i	$-0.964191\pi$
$661$		−	9.19128e28i		−	0.224523i	0.993679	−	0.112261i	$-0.0358094\pi$
$662$		−	8.72887e29i		−	2.09869i
$663$	3.38882e29	+	4.03885e29i	0.801966	+	0.955797i
$664$		−	1.65696e29i		−	0.385965i
$665$	−6.35052e28	+	6.29164e29i	−0.145607	+	1.44257i
$666$	−7.17907e29	−	1.26626e29i	−1.62028	−	0.285787i
$667$	−6.40538e29			−1.42306
$668$	8.11517e28			0.177478
$669$	4.55371e29	+	5.42719e29i	0.980372	+	1.16842i
$670$		−	1.52971e29i		−	0.324208i
$671$	1.07853e29			0.225034
$672$	3.44579e29	+	5.06371e29i	0.707802	+	1.04014i
$673$	−1.38103e29			−0.279282			−0.139641	−	0.990202i	$-0.544595\pi$
$673$	−1.38103e29			−0.279282			−0.139641	+	0.990202i	$0.544595\pi$
$674$			1.28669e30i			2.56180i
$675$	−1.56977e29	−	2.71942e29i	−0.307714	−	0.533074i
$676$	−1.57498e29			−0.303973
$677$	8.51714e29			1.61850			0.809250	−	0.587464i	$-0.199874\pi$
$677$	8.51714e29			1.61850			0.809250	+	0.587464i	$0.199874\pi$
$678$	9.81068e29	−	8.23170e29i	1.83564	−	1.54020i
$679$	−1.77968e28	+	1.76317e29i	−0.0327875	+	0.324835i
$680$		−	3.46881e29i		−	0.629269i
$681$	−8.09573e28	+	6.79276e28i	−0.144614	+	0.121339i
$682$		−	4.22208e29i		−	0.742661i
$683$		−	9.04924e29i		−	1.56745i	−0.621106	−	0.783727i	$-0.713316\pi$
$683$		−	9.04924e29i		−	1.56745i	0.621106	−	0.783727i	$-0.286684\pi$
$684$	−5.05822e29	−	8.92176e28i	−0.862797	−	0.152181i
$685$			1.52744e29i			0.256574i
$686$	2.38910e29	−	7.67474e29i	0.395213	−	1.26958i
$687$	6.46617e29	+	7.70649e29i	1.05342	+	1.25548i
$688$	7.12826e29			1.14368
$689$	−6.01758e29			−0.950867
$690$	−1.17580e30	+	9.86561e29i	−1.82986	+	1.53535i
$691$		−	4.48765e29i		−	0.687859i	−0.938995	−	0.343930i	$-0.888242\pi$
$691$		−	4.48765e29i		−	0.687859i	0.938995	−	0.343930i	$-0.111758\pi$
$692$	4.67765e29			0.706177
$693$	4.22148e29	+	1.19191e29i	0.627720	+	0.177233i
$694$	8.22945e29			1.20530
$695$		−	8.59820e29i		−	1.24042i
$696$	−1.67419e29	+	1.40474e29i	−0.237908	+	0.199618i
$697$	9.92180e29			1.38882
$698$	9.34728e29			1.28885
$699$	3.46189e29	+	4.12594e29i	0.470222	+	0.560419i
$700$	−3.51515e29	−	3.54804e28i	−0.470342	−	0.0474744i
$701$			1.27363e29i			0.167882i	0.996471	+	0.0839411i	$0.0267507\pi$
$701$			1.27363e29i			0.167882i	−0.996471	+	0.0839411i	$0.973249\pi$
$702$	−3.97916e29	−	6.89337e29i	−0.516716	−	0.895142i
$703$			1.10334e30i			1.41150i
$704$			2.56039e29i			0.322695i
$705$	−2.77765e29	+	2.33060e29i	−0.344899	+	0.289389i
$706$			1.50446e30i			1.84048i
$707$	3.26818e29	+	3.29876e28i	0.393914	+	0.0397601i
$708$	8.06105e29	−	6.76366e29i	0.957288	−	0.803217i
$709$	4.06778e29			0.475962			0.237981	−	0.971270i	$-0.423514\pi$
$709$	4.06778e29			0.475962			0.237981	+	0.971270i	$0.423514\pi$
$710$	1.23284e30			1.42133
$711$	−2.85290e29	+	1.61746e30i	−0.324083	+	1.83740i
$712$			3.03784e29i			0.340036i
$713$	−1.09728e30			−1.21026
$714$	−1.10477e30	−	1.62349e30i	−1.20071	−	1.76449i
$715$	−6.01709e29			−0.644426
$716$		−	2.66110e29i		−	0.280850i
$717$	−5.24020e29	−	6.24536e29i	−0.545000	−	0.649541i
$718$	−5.39203e29			−0.552645
$719$	−1.44590e30			−1.46044			−0.730221	−	0.683211i	$-0.760583\pi$
$719$	−1.44590e30			−1.46044			−0.730221	+	0.683211i	$0.760583\pi$
$720$	−2.61307e29	+	1.48149e30i	−0.260112	+	1.47471i
$721$	−3.73082e28	+	3.69623e29i	−0.0366003	+	0.362609i
$722$			4.14316e29i			0.400582i
$723$	−7.55690e29	−	9.00644e29i	−0.720098	−	0.858225i
$724$		−	8.41384e29i		−	0.790205i
$725$		−	6.69507e29i		−	0.619735i
$726$	−5.38227e29	−	6.41468e29i	−0.491056	−	0.585249i
$727$		−	1.70184e30i		−	1.53040i	−0.643790	−	0.765202i	$-0.722639\pi$
$727$		−	1.70184e30i		−	1.53040i	0.643790	−	0.765202i	$-0.277361\pi$
$728$	2.69123e29	+	2.71642e28i	0.238546	+	0.0240778i
$729$	−5.72438e29	+	9.91128e29i	−0.500137	+	0.865946i
$730$	−9.96642e29			−0.858320
$731$	−1.83543e30			−1.55814
$732$	2.03528e29	+	2.42569e29i	0.170317	+	0.202987i
$733$			7.82447e29i			0.645451i	0.946493	+	0.322726i	$0.104599\pi$
$733$			7.82447e29i			0.645451i	−0.946493	+	0.322726i	$0.895401\pi$
$734$	1.17287e30			0.953767
$735$	1.39376e30	−	7.55843e29i	1.11731	−	0.605919i
$736$	2.25006e30			1.77819
$737$			1.60603e29i			0.125125i
$738$	−1.47511e30	−	2.60182e29i	−1.13301	−	0.199842i
$739$	−1.72597e30			−1.30697			−0.653486	−	0.756939i	$-0.726694\pi$
$739$	−1.72597e30			−1.30697			−0.653486	+	0.756939i	$0.726694\pi$
$740$	−1.61794e30			−1.20790
$741$	−9.22856e29	+	7.74327e29i	−0.679271	+	0.569945i
$742$	2.23002e30	+	2.25089e29i	1.61833	+	0.163347i
$743$			1.66446e30i			1.19094i	0.803377	+	0.595470i	$0.203034\pi$
$743$			1.66446e30i			1.19094i	−0.803377	+	0.595470i	$0.796966\pi$
$744$	−2.86800e29	+	2.40641e29i	−0.202332	+	0.169767i
$745$		−	6.28039e29i		−	0.436864i
$746$			1.44569e30i			0.991559i
$747$	3.21395e29	−	1.82216e30i	0.217357	−	1.23231i
$748$		−	1.20579e30i		−	0.804091i
$749$	−7.41089e28	+	7.34217e29i	−0.0487316	+	0.482798i
$750$	6.44139e29	+	7.67696e29i	0.417673	+	0.497790i
$751$	1.15511e30			0.738590			0.369295	−	0.929312i	$-0.379599\pi$
$751$	1.15511e30			0.738590			0.369295	+	0.929312i	$0.379599\pi$
$752$	6.61858e29			0.417328
$753$	1.55352e29	−	1.30348e29i	0.0965980	−	0.0810510i
$754$		−	1.69711e30i		−	1.04066i
$755$	−2.52334e29			−0.152592
$756$	5.28561e29	+	1.17436e30i	0.315222	+	0.700361i
$757$	−1.75730e30			−1.03357			−0.516783	−	0.856116i	$-0.672871\pi$
$757$	−1.75730e30			−1.03357			−0.516783	+	0.856116i	$0.672871\pi$
$758$			3.38713e30i			1.96474i
$759$	1.23446e30	−	1.03578e30i	0.706219	−	0.592557i
$760$	7.92604e29			0.447212
$761$	−2.62418e30			−1.46034			−0.730170	−	0.683265i	$-0.760559\pi$
$761$	−2.62418e30			−1.46034			−0.730170	+	0.683265i	$0.760559\pi$
$762$	6.41796e29	+	7.64904e29i	0.352265	+	0.419836i
$763$	−2.29346e30	−	2.31492e29i	−1.24160	−	0.125322i
$764$		−	1.18293e30i		−	0.631652i
$765$	6.72831e29	−	3.81464e30i	0.354373	−	2.00913i
$766$		−	1.48935e30i		−	0.773742i
$767$		−	2.46802e30i		−	1.26473i
$768$	1.95943e30	−	1.64407e30i	0.990458	−	0.831049i
$769$			1.48357e30i			0.739745i	0.929083	+	0.369872i	$0.120599\pi$
$769$			1.48357e30i			0.739745i	−0.929083	+	0.369872i	$0.879401\pi$
$770$	2.22984e30	+	2.25070e29i	1.09678	+	0.110705i
$771$	1.78877e30	−	1.50088e30i	0.867928	−	0.728239i
$772$	−1.68207e30			−0.805122
$773$	2.94864e30			1.39231			0.696156	−	0.717890i	$-0.254892\pi$
$773$	2.94864e30			1.39231			0.696156	+	0.717890i	$0.254892\pi$
$774$	2.72881e30	+	4.81311e29i	1.27114	+	0.224205i
$775$		−	1.14691e30i		−	0.527061i
$776$	2.22120e29			0.100702
$777$	2.28710e30	−	1.55635e30i	1.02298	−	0.696122i
$778$	−4.89554e30			−2.16030
$779$			2.26708e30i			0.987014i
$780$	−1.13547e30	−	1.35328e30i	−0.487735	−	0.581291i
$781$	−1.29435e30			−0.548548
$782$	−7.21400e30			−3.01651
$783$	−2.11358e30	+	1.22005e30i	−0.872006	+	0.503361i
$784$	−2.83578e30	−	5.78357e29i	−1.15440	−	0.235438i
$785$		−	4.59658e30i		−	1.84631i
$786$	−1.45993e30	−	1.73997e30i	−0.578623	−	0.689614i
$787$		−	2.02175e30i		−	0.790665i	−0.918538	−	0.395333i	$-0.870629\pi$
$787$		−	2.02175e30i		−	0.790665i	0.918538	−	0.395333i	$-0.129371\pi$
$788$		−	1.29051e30i		−	0.498008i
$789$	−1.83001e30	−	2.18104e30i	−0.696858	−	0.830528i
$790$			8.39150e30i			3.15323i
$791$	−4.88064e29	+	4.83538e30i	−0.180977	+	1.79299i
$792$	9.55019e28	−	5.41451e29i	0.0349460	−	0.198127i
$793$	7.42662e29			0.268178
$794$	5.42585e30			1.93354
$795$	2.84176e30	+	3.38686e30i	0.999384	+	1.19108i
$796$			2.12449e30i			0.737339i
$797$	4.02250e30			1.37779			0.688897	−	0.724860i	$-0.258095\pi$
$797$	4.02250e30			1.37779			0.688897	+	0.724860i	$0.258095\pi$
$798$	3.70959e30	−	2.52433e30i	1.25400	−	0.853328i
$799$	−1.70420e30			−0.568563
$800$			2.35183e30i			0.774391i
$801$	−5.89238e29	+	3.34070e30i	−0.191491	+	1.08567i
$802$	5.34404e30			1.71411
$803$	1.04637e30			0.331261
$804$	−3.61205e29	+	3.03071e29i	−0.112867	+	0.0947012i
$805$	5.84939e29	−	5.79516e30i	0.180407	−	1.78735i
$806$		−	2.90726e30i		−	0.885046i
$807$	1.82814e30	−	1.53391e30i	0.549336	−	0.460923i
$808$		−	4.11716e29i		−	0.122118i
$809$		−	3.38212e30i		−	0.990215i	−0.868832	−	0.495108i	$-0.835129\pi$
$809$		−	3.38212e30i		−	0.990215i	0.868832	−	0.495108i	$-0.164871\pi$
$810$	−2.00065e30	+	5.49493e30i	−0.578200	+	1.58807i
$811$			5.13434e30i			1.46476i	0.680898	+	0.732378i	$0.261590\pi$
$811$			5.13434e30i			1.46476i	−0.680898	+	0.732378i	$0.738410\pi$
$812$	−2.75759e29	+	2.73202e30i	−0.0776590	+	0.769390i
$813$	1.71212e30	+	2.04054e30i	0.475974	+	0.567275i
$814$	3.91038e30			1.07316
$815$	−3.14687e30			−0.852558
$816$	−5.41651e30	+	4.54475e30i	−1.44868	+	1.21552i
$817$		−	4.19387e30i		−	1.10735i
$818$	−1.13868e30			−0.296819
$819$	2.90685e30	+	8.20731e29i	0.748069	+	0.211213i
$820$	−3.32445e30			−0.844645
$821$			1.64038e30i			0.411474i	0.978607	+	0.205737i	$0.0659591\pi$
$821$			1.64038e30i			0.411474i	−0.978607	+	0.205737i	$0.934041\pi$
$822$	8.30270e29	−	6.96642e29i	0.205620	−	0.172526i
$823$	−2.65209e30			−0.648471			−0.324235	−	0.945976i	$-0.605107\pi$
$823$	−2.65209e30			−0.648471			−0.324235	+	0.945976i	$0.605107\pi$
$824$	4.65641e29			0.112413
$825$	1.08263e30	+	1.29029e30i	0.258055	+	0.307554i
$826$	−9.23167e29	+	9.14607e30i	−0.217265	+	2.15250i
$827$			7.64665e30i			1.77690i	0.458972	+	0.888451i	$0.348218\pi$
$827$			7.64665e30i			1.77690i	−0.458972	+	0.888451i	$0.651782\pi$
$828$	4.65907e30	+	8.21773e29i	1.06901	+	0.188553i
$829$			5.91672e30i			1.34047i	0.742147	+	0.670237i	$0.233808\pi$
$829$			5.91672e30i			1.34047i	−0.742147	+	0.670237i	$0.766192\pi$
$830$		−	9.45349e30i		−	2.11481i
$831$	−8.28254e29	+	6.94950e29i	−0.182959	+	0.153512i
$832$			1.76304e30i			0.384563i
$833$	7.30178e30	+	1.48919e30i	1.57274	+	0.320759i
$834$	−4.67374e30	+	3.92152e30i	−0.994078	+	0.834086i
$835$	−1.39839e30			−0.293712
$836$	2.75517e30			0.571456
$837$	−3.62070e30	+	2.09003e30i	−0.741609	+	0.428089i
$838$		−	4.32740e30i		−	0.875315i
$839$	−3.72323e30			−0.743736			−0.371868	−	0.928286i	$-0.621283\pi$
$839$	−3.72323e30			−0.743736			−0.371868	+	0.928286i	$0.621283\pi$
$840$	−1.11803e30	−	1.64298e30i	−0.220556	−	0.324115i
$841$	−7.06627e28			−0.0137668
$842$		−	4.36512e30i		−	0.839884i
$843$	−2.97633e30	−	3.54724e30i	−0.565577	−	0.674065i
$844$	−1.11307e30			−0.208894
$845$	2.71398e30			0.503051
$846$	2.53370e30	+	4.46897e29i	0.463837	+	0.0818123i
$847$	3.16160e30	+	3.19119e29i	0.571651	+	0.0577001i
$848$		−	8.07019e30i		−	1.44121i
$849$	−5.26776e29	−	6.27821e29i	−0.0929170	−	0.110740i
$850$		−	7.54025e30i		−	1.31367i
$851$		−	1.01628e31i		−	1.74885i
$852$	−2.44254e30	−	2.91106e30i	−0.415170	−	0.494807i
$853$			4.89017e30i			0.821030i	0.911854	+	0.410515i	$0.134651\pi$
$853$			4.89017e30i			0.821030i	−0.911854	+	0.410515i	$0.865349\pi$
$854$	−2.75219e30	−	2.77794e29i	−0.456426	−	0.0460697i
$855$	8.71624e30	+	1.53738e30i	1.42786	+	0.251848i
$856$	9.24947e29			0.149673
$857$	4.94780e30			0.790885			0.395443	−	0.918491i	$-0.370591\pi$
$857$	4.94780e30			0.790885			0.395443	+	0.918491i	$0.370591\pi$
$858$	2.74431e30	+	3.27072e30i	0.433328	+	0.516448i
$859$		−	8.08698e30i		−	1.26142i	−0.776020	−	0.630708i	$-0.782765\pi$
$859$		−	8.08698e30i		−	1.26142i	0.776020	−	0.630708i	$-0.217235\pi$
$860$	6.14990e30			0.947620
$861$	4.69940e30	−	3.19788e30i	0.715334	−	0.486776i
$862$	9.90365e30			1.48926
$863$			1.18236e31i			1.75645i	0.478250	+	0.878224i	$0.341271\pi$
$863$			1.18236e31i			1.75645i	−0.478250	+	0.878224i	$0.658729\pi$
$864$	7.42452e30	−	4.28576e30i	1.08962	−	0.628975i
$865$	−8.06045e30			−1.16867
$866$	−1.75169e31			−2.50910
$867$	8.53349e30	−	7.16007e30i	1.20761	−	1.01325i
$868$	−4.72394e29	+	4.68014e30i	−0.0660461	+	0.654337i
$869$		−	8.81017e30i		−	1.21696i
$870$	−9.55179e30	+	8.01447e30i	−1.30356	+	1.09376i
$871$			1.10589e30i			0.149114i
$872$			2.88924e30i			0.384911i
$873$	2.44265e30	+	4.30838e29i	0.321522	+	0.0567106i
$874$		−	1.64836e31i		−	2.14379i
$875$	−3.78374e30	−	3.81915e29i	−0.486224	−	0.0490774i
$876$	1.97458e30	+	2.35334e30i	0.250716	+	0.298807i
$877$	−1.13182e31			−1.41998			−0.709992	−	0.704210i	$-0.751301\pi$
$877$	−1.13182e31			−1.41998			−0.709992	+	0.704210i	$0.751301\pi$
$878$	−1.92140e31			−2.38191
$879$	4.83134e29	−	4.05376e29i	0.0591813	−	0.0496563i
$880$		−	8.06954e30i		−	0.976744i
$881$	−3.39245e30			−0.405758			−0.202879	−	0.979204i	$-0.565030\pi$
$881$	−3.39245e30			−0.405758			−0.202879	+	0.979204i	$0.565030\pi$
$882$	−1.04653e31	−	4.12881e30i	−1.23689	−	0.487983i
$883$	−1.57655e29			−0.0184128			−0.00920638	−	0.999958i	$-0.502931\pi$
$883$	−1.57655e29			−0.0184128			−0.00920638	+	0.999958i	$0.502931\pi$
$884$		−	8.30289e30i		−	0.958254i
$885$	−1.38907e31	+	1.16550e31i	−1.58423	+	1.32926i
$886$	9.55168e30			1.07653
$887$	1.54056e31			1.71586			0.857930	−	0.513767i	$-0.171750\pi$
$887$	1.54056e31			1.71586			0.857930	+	0.513767i	$0.171750\pi$
$888$	−2.22876e30	−	2.65627e30i	−0.245316	−	0.292372i
$889$	−3.76998e30	−	3.80526e29i	−0.410082	−	0.0413919i
$890$			1.73318e31i			1.86315i
$891$	2.10046e30	−	5.76908e30i	0.223151	−	0.612901i
$892$		−	1.11570e31i		−	1.17143i
$893$		−	3.89400e30i		−	0.404069i
$894$	−3.41384e30	+	2.86440e30i	−0.350106	+	0.293758i
$895$			4.58557e30i			0.464784i
$896$	−6.01782e29	+	5.96203e30i	−0.0602845	+	0.597255i
$897$	8.50033e30	−	7.13224e30i	0.841618	−	0.706163i
$898$	4.72338e29			0.0462223
$899$	−8.91395e30			−0.862171
$900$	−8.58939e29	+	4.86978e30i	−0.0821137	+	0.465546i
$901$			2.07797e31i			1.96349i
$902$	8.03481e30			0.750424
$903$	−8.69341e30	+	5.91576e30i	−0.802544	+	0.546121i
$904$	6.09149e30			0.555846
$905$			1.44986e31i			1.30772i
$906$	1.15086e30	+	1.37162e30i	0.102607	+	0.122289i
$907$	−9.96862e30			−0.878533			−0.439267	−	0.898357i	$-0.644762\pi$
$907$	−9.96862e30			−0.878533			−0.439267	+	0.898357i	$0.644762\pi$
$908$	1.66428e30			0.144986
$909$	7.98590e29	−	4.52763e30i	0.0687707	−	0.389897i
$910$	1.53543e31	+	1.54980e30i	1.30706	+	0.131929i
$911$			1.02408e29i			0.00861769i	0.999991	+	0.00430884i	$0.00137155\pi$
$911$			1.02408e29i			0.00861769i	−0.999991	+	0.00430884i	$0.998628\pi$
$912$	−1.03845e31	−	1.23765e31i	−0.863854	−	1.02956i
$913$			9.92514e30i			0.816194i
$914$		−	1.27945e31i		−	1.04013i
$915$	−3.50717e30	−	4.17991e30i	−0.281861	−	0.335927i
$916$		−	1.58427e31i		−	1.25871i
$917$	8.57579e30	+	8.65605e29i	0.673591	+	0.0679895i
$918$	−2.38040e31	+	1.37407e31i	−1.84842	+	1.06699i
$919$	1.42310e31			1.09250			0.546251	−	0.837621i	$-0.316054\pi$
$919$	1.42310e31			1.09250			0.546251	+	0.837621i	$0.316054\pi$
$920$	−7.30059e30			−0.554097
$921$	5.02757e30	+	5.99195e30i	0.377253	+	0.449616i
$922$			6.43429e30i			0.477338i
$923$	−8.91268e30			−0.653718
$924$	−3.88637e30	−	5.71116e30i	−0.281831	−	0.414160i
$925$	1.06224e31			0.761612
$926$			1.27951e31i			0.907046i
$927$	5.12064e30	+	9.03187e29i	0.358912	+	0.0633054i
$928$	1.82787e31			1.26675
$929$	3.24960e30			0.222672			0.111336	−	0.993783i	$-0.464487\pi$
$929$	3.24960e30			0.222672			0.111336	+	0.993783i	$0.464487\pi$
$930$	−1.63628e31	+	1.37293e31i	−1.10863	+	0.930204i
$931$	−3.40273e30	+	1.66842e31i	−0.227959	+	1.11772i
$932$		−	8.48193e30i		−	0.561859i
$933$	1.31104e31	−	1.10004e31i	0.858737	−	0.720527i
$934$			1.60558e31i			1.03989i
$935$			2.07780e31i			1.33071i
$936$	6.57612e29	−	3.72835e30i	0.0416460	−	0.236113i
$937$		−	8.80853e30i		−	0.551617i	−0.961213	−	0.275808i	$-0.911054\pi$
$937$		−	8.80853e30i		−	0.551617i	0.961213	−	0.275808i	$-0.0889456\pi$
$938$	4.13659e29	−	4.09823e30i	0.0256161	−	0.253786i
$939$	−2.07685e31	−	2.47523e31i	−1.27179	−	1.51575i
$940$	5.71018e30			0.345786
$941$	−2.04489e31			−1.22455			−0.612277	−	0.790643i	$-0.709746\pi$
$941$	−2.04489e31			−1.22455			−0.612277	+	0.790643i	$0.709746\pi$
$942$	−2.49857e31	+	2.09644e31i	−1.47964	+	1.24150i
$943$		−	2.08818e31i		−	1.22291i
$944$	3.30987e31			1.91692
$945$	−9.10808e30	−	2.02364e31i	−0.521667	−	1.15904i
$946$	−1.48636e31			−0.841912
$947$		−	3.16162e31i		−	1.77107i	−0.464574	−	0.885534i	$-0.653793\pi$
$947$		−	3.16162e31i		−	1.77107i	0.464574	−	0.885534i	$-0.346207\pi$
$948$	1.98146e31	−	1.66255e31i	1.09773	−	0.921059i
$949$	7.20512e30			0.394771
$950$	1.72291e31			0.933608
$951$	7.02472e30	+	8.37219e30i	0.376473	+	0.448687i
$952$	9.38023e29	−	9.29326e30i	0.0497194	−	0.492584i
$953$			2.91883e31i			1.53015i	0.643943	+	0.765074i	$0.277297\pi$
$953$			2.91883e31i			1.53015i	−0.643943	+	0.765074i	$0.722703\pi$
$954$	5.44912e30	−	3.08939e31i	0.282533	−	1.60183i
$955$			2.03840e31i			1.04533i
$956$			1.28389e31i			0.651211i
$957$	1.00283e31	−	8.41433e30i	0.503100	−	0.422128i
$958$		−	2.72097e31i		−	1.35016i
$959$	−4.13044e29	+	4.09215e30i	−0.0202722	+	0.200843i
$960$	9.92288e30	−	8.32584e30i	0.481715	−	0.404185i
$961$	5.55533e30			0.266756
$962$	2.69263e31			1.27891
$963$	1.01716e31	+	1.79409e30i	0.477875	+	0.0842883i
$964$			1.85150e31i			0.860431i
$965$	2.89851e31			1.33241
$966$	−3.41686e31	+	2.32513e31i	−1.55370	+	1.05728i
$967$	−2.31648e31			−1.04196			−0.520980	−	0.853569i	$-0.674433\pi$
$967$	−2.31648e31			−1.04196			−0.520980	+	0.853569i	$0.674433\pi$
$968$		−	3.98290e30i		−	0.177218i
$969$	2.67388e31	+	3.18677e31i	1.17691	+	1.40266i
$970$	1.26726e31			0.551777
$971$	2.02820e31			0.873593			0.436797	−	0.899560i	$-0.356113\pi$
$971$	2.02820e31			0.873593			0.436797	+	0.899560i	$0.356113\pi$
$972$	1.69387e31	−	6.16266e30i	0.721747	−	0.262586i
$973$	2.32510e30	−	2.30354e31i	0.0980069	−	0.970982i
$974$		−	2.05681e31i		−	0.857678i
$975$	7.45480e30	+	8.88476e30i	0.307530	+	0.366520i
$976$			9.95987e30i			0.406472i
$977$			2.24319e31i			0.905678i	0.891592	+	0.452839i	$0.149589\pi$
$977$			2.24319e31i			0.905678i	−0.891592	+	0.452839i	$0.850411\pi$
$978$	1.43524e31	+	1.71055e31i	0.573281	+	0.683247i
$979$		−	1.81965e31i		−	0.719068i
$980$	−2.44657e31	−	4.98977e30i	−0.956498	−	0.195077i
$981$	−5.60414e30	+	3.17728e31i	−0.216763	+	1.22894i
$982$	4.65310e30			0.178062
$983$	−1.30765e31			−0.495084			−0.247542	−	0.968877i	$-0.579623\pi$
$983$	−1.30765e31			−0.495084			−0.247542	+	0.968877i	$0.579623\pi$
$984$	−4.57951e30	−	5.45794e30i	−0.171542	−	0.204447i
$985$			2.22379e31i			0.824163i
$986$	−5.86040e31			−2.14892
$987$	−8.07183e30	+	5.49278e30i	−0.292848	+	0.199279i
$988$	1.89717e31			0.681017
$989$			3.86292e31i			1.37200i
$990$	5.44868e30	−	3.08915e31i	0.191479	−	1.08560i
$991$	3.34927e31			1.16460			0.582300	−	0.812974i	$-0.302153\pi$
$991$	3.34927e31			1.16460			0.582300	+	0.812974i	$0.302153\pi$
$992$	3.13127e31			1.07733
$993$	3.55169e31	−	2.98006e31i	1.20912	−	1.01451i
$994$	3.30289e31	+	3.33380e30i	1.11260	+	0.112301i
$995$		−	3.66089e31i		−	1.22024i
$996$	−2.23222e31	+	1.87296e31i	−0.736231	+	0.617738i
$997$			8.79905e30i			0.287168i	0.989638	+	0.143584i	$0.0458628\pi$
$997$			8.79905e30i			0.287168i	−0.989638	+	0.143584i	$0.954137\pi$
$998$			3.17132e30i			0.102416i
$999$	−1.93573e31	−	3.35340e31i	−0.618596	−	1.07164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.22.c.b.20.9	✓	52
3.2	odd	2	inner	21.22.c.b.20.44	yes	52
7.6	odd	2	inner	21.22.c.b.20.43	yes	52
21.20	even	2	inner	21.22.c.b.20.10	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.22.c.b.20.9	✓	52	1.1	even	1	trivial
21.22.c.b.20.10	yes	52	21.20	even	2	inner
21.22.c.b.20.43	yes	52	7.6	odd	2	inner
21.22.c.b.20.44	yes	52	3.2	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	21.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1925.57i q^{2} +(78349.6 - 65739.6i) q^{3} -1.61068e6 q^{4} +2.77549e7 q^{5} +(-1.26586e8 - 1.50868e8i) q^{6} +(7.43581e8 + 7.50540e7i) q^{7} -9.36744e8i q^{8} +(1.81697e9 - 1.03013e10i) q^{9} +O(q^{10})\)	\(q-1925.57i q^{2} +(78349.6 - 65739.6i) q^{3} -1.61068e6 q^{4} +2.77549e7 q^{5} +(-1.26586e8 - 1.50868e8i) q^{6} +(7.43581e8 + 7.50540e7i) q^{7} -9.36744e8i q^{8} +(1.81697e9 - 1.03013e10i) q^{9} -5.34441e10i q^{10} +5.61106e10i q^{11} +(-1.26196e11 + 1.05885e11i) q^{12} +3.86369e11i q^{13} +(1.44522e11 - 1.43182e12i) q^{14} +(2.17459e12 - 1.82460e12i) q^{15} -5.18160e12 q^{16} +1.33419e13 q^{17} +(-1.98360e13 - 3.49870e12i) q^{18} +3.04856e13i q^{19} -4.47042e13 q^{20} +(6.31933e13 - 4.30023e13i) q^{21} +1.08045e14 q^{22} -2.80800e14i q^{23} +(-6.15811e13 - 7.33935e13i) q^{24} +2.93499e14 q^{25} +7.43981e14 q^{26} +(-5.34847e14 - 9.26553e14i) q^{27} +(-1.19767e15 - 1.20888e14i) q^{28} -2.28112e15i q^{29} +(-3.51340e15 - 4.18733e15i) q^{30} -3.90771e15i q^{31} +8.01305e15i q^{32} +(3.68869e15 + 4.39624e15i) q^{33} -2.56909e16i q^{34} +(2.06380e16 + 2.08312e15i) q^{35} +(-2.92655e15 + 1.65921e16i) q^{36} +3.61922e16 q^{37} +5.87023e16 q^{38} +(2.53997e16 + 3.02718e16i) q^{39} -2.59993e16i q^{40} +7.43654e16 q^{41} +(-8.28040e16 - 1.21683e17i) q^{42} -1.37569e17 q^{43} -9.03760e16i q^{44} +(5.04298e16 - 2.85913e17i) q^{45} -5.40700e17 q^{46} -1.27732e17 q^{47} +(-4.05976e17 + 3.40636e17i) q^{48} +(5.47280e17 + 1.11617e17i) q^{49} -5.65154e17i q^{50} +(1.04534e18 - 8.77094e17i) q^{51} -6.22315e17i q^{52} +1.55747e18i q^{53} +(-1.78414e18 + 1.02989e18i) q^{54} +1.55734e18i q^{55} +(7.03063e16 - 6.96545e17i) q^{56} +(2.00411e18 + 2.38854e18i) q^{57} -4.39246e18 q^{58} -6.38773e18 q^{59} +(-3.50256e18 + 2.93884e18i) q^{60} -1.92216e18i q^{61} -7.52457e18 q^{62} +(2.12422e18 - 7.52351e18i) q^{63} +4.56311e18 q^{64} +1.07236e19i q^{65} +(8.46528e18 - 7.10283e18i) q^{66} +2.86226e18 q^{67} -2.14896e19 q^{68} +(-1.84597e19 - 2.20006e19i) q^{69} +(4.01120e18 - 3.97400e19i) q^{70} +2.30678e19i q^{71} +(-9.64971e18 - 1.70203e18i) q^{72} -1.86483e19i q^{73} -6.96907e19i q^{74} +(2.29955e19 - 1.92945e19i) q^{75} -4.91025e19i q^{76} +(-4.21132e18 + 4.17227e19i) q^{77} +(5.82906e19 - 4.89090e19i) q^{78} -1.57015e20 q^{79} -1.43815e20 q^{80} +(-1.02816e20 - 3.74344e19i) q^{81} -1.43196e20i q^{82} +1.76885e20 q^{83} +(-1.01784e20 + 6.92627e19i) q^{84} +3.70305e20 q^{85} +2.64898e20i q^{86} +(-1.49960e20 - 1.78725e20i) q^{87} +5.25612e19 q^{88} -3.24298e20 q^{89} +(-5.50546e20 - 9.71062e19i) q^{90} +(-2.89985e19 + 2.87296e20i) q^{91} +4.52278e20i q^{92} +(-2.56891e20 - 3.06167e20i) q^{93} +2.45958e20i q^{94} +8.46127e20i q^{95} +(5.26775e20 + 6.27820e20i) q^{96} +2.37119e20i q^{97} +(2.14927e20 - 1.05383e21i) q^{98} +(5.78014e20 + 1.01951e20i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 58720260 q^{4} + 1422287188 q^{7} + 10150644696 q^{9}+O(q^{10}) \) 52 * q - 58720260 * q^4 + 1422287188 * q^7 + 10150644696 * q^9	\( 52 q - 58720260 q^{4} + 1422287188 q^{7} + 10150644696 q^{9} - 687153165468 q^{15} + 36241782390404 q^{16} + 36759093002772 q^{18} + 79412641656180 q^{21} + 228880341648112 q^{22} + 45\!\cdots\!12 q^{25}+ \cdots + 15\!\cdots\!28 q^{99}+O(q^{100}) \) 52 * q - 58720260 * q^4 + 1422287188 * q^7 + 10150644696 * q^9 - 687153165468 * q^15 + 36241782390404 * q^16 + 36759093002772 * q^18 + 79412641656180 * q^21 + 228880341648112 * q^22 + 4502168959229812 * q^25 - 328465100861772 * q^28 - 2422487119598196 * q^30 + 94669723666911312 * q^36 - 111253244635261912 * q^37 - 198389110134084780 * q^39 - 125754675449474820 * q^42 + 808208758088766656 * q^43 - 1124214920076830456 * q^46 + 760563680048831596 * q^49 + 4341973540932052200 * q^51 - 13080454499124088812 * q^57 - 10814528487339424568 * q^58 + 13643758017961015644 * q^60 - 38182310822257441896 * q^63 - 30480555033993680900 * q^64 - 25547251957658589040 * q^67 + 73727169165159410040 * q^70 + 39846964674222889428 * q^72 + 45848199464273536260 * q^78 + 199210197493083963080 * q^79 + 235499606962845306588 * q^81 - 373919224753720758924 * q^84 - 570842672309470848672 * q^85 - 1060053674241923431168 * q^88 - 923077800435233893128 * q^91 - 2832166256981601869904 * q^93 + 1525182290356701596928 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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