LMFDB - Embedded newform 21.22.c.b.20.2

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			20.2
Character	$\chi$	$=$	21.20
Dual form			21.22.c.b.20.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1223.76i q^{2} +(-94027.5 + 40239.2i) q^{3} +599559. q^{4} +3.45471e7 q^{5} +(-4.92432e7 - 1.15067e8i) q^{6} +(-6.99978e8 - 2.61872e8i) q^{7} +3.30013e9i q^{8} +(7.22197e9 - 7.56717e9i) q^{9} +O(q^{10})$	\(q+1223.76i q^{2} +(-94027.5 + 40239.2i) q^{3} +599559. q^{4} +3.45471e7 q^{5} +(-4.92432e7 - 1.15067e8i) q^{6} +(-6.99978e8 - 2.61872e8i) q^{7} +3.30013e9i q^{8} +(7.22197e9 - 7.56717e9i) q^{9} +4.22775e10i q^{10} -1.38407e11i q^{11} +(-5.63750e10 + 2.41257e10i) q^{12} -1.98416e11i q^{13} +(3.20469e11 - 8.56606e11i) q^{14} +(-3.24838e12 + 1.39015e12i) q^{15} -2.78121e12 q^{16} -1.12113e13 q^{17} +(9.26042e12 + 8.83798e12i) q^{18} +1.31763e13i q^{19} +2.07130e13 q^{20} +(7.63546e13 - 3.54339e12i) q^{21} +1.69378e14 q^{22} +2.41160e14i q^{23} +(-1.32795e14 - 3.10303e14i) q^{24} +7.16668e14 q^{25} +2.42815e14 q^{26} +(-3.74567e14 + 1.00213e15i) q^{27} +(-4.19678e14 - 1.57008e14i) q^{28} +2.94084e15i q^{29} +(-1.70121e15 - 3.97524e15i) q^{30} +5.22972e15i q^{31} +3.51734e15i q^{32} +(5.56940e15 + 1.30141e16i) q^{33} -1.37200e16i q^{34} +(-2.41822e16 - 9.04692e15i) q^{35} +(4.33000e15 - 4.53696e15i) q^{36} +1.95264e16 q^{37} -1.61247e16 q^{38} +(7.98411e15 + 1.86566e16i) q^{39} +1.14010e17i q^{40} -8.86426e16 q^{41} +(4.33626e15 + 9.34399e16i) q^{42} -2.83588e16 q^{43} -8.29834e16i q^{44} +(2.49499e17 - 2.61424e17i) q^{45} -2.95123e17 q^{46} -5.37703e17 q^{47} +(2.61510e17 - 1.11914e17i) q^{48} +(4.21392e17 + 3.66609e17i) q^{49} +8.77031e17i q^{50} +(1.05417e18 - 4.51135e17i) q^{51} -1.18962e17i q^{52} +1.93110e18i q^{53} +(-1.22637e18 - 4.58381e17i) q^{54} -4.78158e18i q^{55} +(8.64211e17 - 2.31002e18i) q^{56} +(-5.30204e17 - 1.23894e18i) q^{57} -3.59888e18 q^{58} -1.38432e18 q^{59} +(-1.94759e18 + 8.33475e17i) q^{60} +2.80127e18i q^{61} -6.39993e18 q^{62} +(-7.03685e18 + 3.40562e18i) q^{63} -1.01370e19 q^{64} -6.85472e18i q^{65} +(-1.59262e19 + 6.81562e18i) q^{66} +1.55480e19 q^{67} -6.72185e18 q^{68} +(-9.70408e18 - 2.26757e19i) q^{69} +(1.10713e19 - 2.95933e19i) q^{70} +1.31437e19i q^{71} +(2.49727e19 + 2.38335e19i) q^{72} +3.15045e19i q^{73} +2.38956e19i q^{74} +(-6.73865e19 + 2.88381e19i) q^{75} +7.89997e18i q^{76} +(-3.62450e19 + 9.68821e19i) q^{77} +(-2.28312e19 + 9.77065e18i) q^{78} -6.56128e18 q^{79} -9.60829e19 q^{80} +(-5.10520e18 - 1.09300e20i) q^{81} -1.08477e20i q^{82} -1.99817e20 q^{83} +(4.57791e19 - 2.12447e18i) q^{84} -3.87320e20 q^{85} -3.47045e19i q^{86} +(-1.18337e20 - 2.76519e20i) q^{87} +4.56763e20 q^{88} +7.23185e19 q^{89} +(3.19921e20 + 3.05327e20i) q^{90} +(-5.19597e19 + 1.38887e20i) q^{91} +1.44590e20i q^{92} +(-2.10440e20 - 4.91737e20i) q^{93} -6.58020e20i q^{94} +4.55204e20i q^{95} +(-1.41535e20 - 3.30726e20i) q^{96} -6.71547e19i q^{97} +(-4.48642e20 + 5.15684e20i) q^{98} +(-1.04735e21 - 9.99575e20i) 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 $

$2$			1223.76i			0.845049i	0.906351	+	0.422525i	$0.138856\pi$
$2$			1223.76i			0.845049i	−0.906351	+	0.422525i	$0.861144\pi$
$3$	−94027.5	+	40239.2i	−0.919351	+	0.393437i
$3$	−94027.5	+	40239.2i	−0.919351	+	0.393437i
$4$	599559.			0.285892
$5$	3.45471e7			1.58208			0.791038	−	0.611768i	$-0.209541\pi$
$5$	3.45471e7			1.58208			0.791038	+	0.611768i	$0.209541\pi$
$6$	−4.92432e7	−	1.15067e8i	−0.332474	−	0.776897i
$7$	−6.99978e8	−	2.61872e8i	−0.936602	−	0.350396i
$7$	−6.99978e8	−	2.61872e8i	−0.936602	−	0.350396i
$8$			3.30013e9i			1.08664i
$9$	7.22197e9	−	7.56717e9i	0.690414	−	0.723415i
$10$			4.22775e10i			1.33693i
$11$		−	1.38407e11i		−	1.60893i	−0.594002	−	0.804463i	$-0.702453\pi$
$11$		−	1.38407e11i		−	1.60893i	0.594002	−	0.804463i	$-0.297547\pi$
$12$	−5.63750e10	+	2.41257e10i	−0.262835	+	0.112481i
$13$		−	1.98416e11i		−	0.399183i	−0.979879	−	0.199592i	$-0.936038\pi$
$13$		−	1.98416e11i		−	0.399183i	0.979879	−	0.199592i	$-0.0639616\pi$
$14$	3.20469e11	−	8.56606e11i	0.296102	−	0.791474i
$15$	−3.24838e12	+	1.39015e12i	−1.45448	+	0.622448i
$16$	−2.78121e12			−0.632374
$17$	−1.12113e13			−1.34879			−0.674394	−	0.738372i	$-0.735595\pi$
$17$	−1.12113e13			−1.34879			−0.674394	+	0.738372i	$0.735595\pi$
$18$	9.26042e12	+	8.83798e12i	0.611321	+	0.583434i
$19$			1.31763e13i			0.493039i	0.969138	+	0.246519i	$0.0792869\pi$
$19$			1.31763e13i			0.493039i	−0.969138	+	0.246519i	$0.920713\pi$
$20$	2.07130e13			0.452302
$21$	7.63546e13	−	3.54339e12i	0.998925	−	0.0463571i
$22$	1.69378e14			1.35962
$23$			2.41160e14i			1.21384i	0.794761	+	0.606922i	$0.207596\pi$
$23$			2.41160e14i			1.21384i	−0.794761	+	0.606922i	$0.792404\pi$
$24$	−1.32795e14	−	3.10303e14i	−0.427526	−	0.999006i
$25$	7.16668e14			1.50296
$26$	2.42815e14			0.337330
$27$	−3.74567e14	+	1.00213e15i	−0.350115	+	0.936707i
$28$	−4.19678e14	−	1.57008e14i	−0.267767	−	0.100175i
$29$			2.94084e15i			1.29805i	0.760767	+	0.649026i	$0.224823\pi$
$29$			2.94084e15i			1.29805i	−0.760767	+	0.649026i	$0.775177\pi$
$30$	−1.70121e15	−	3.97524e15i	−0.525999	−	1.22911i
$31$			5.22972e15i			1.14599i	0.819559	+	0.572995i	$0.194218\pi$
$31$			5.22972e15i			1.14599i	−0.819559	+	0.572995i	$0.805782\pi$
$32$			3.51734e15i			0.552255i
$33$	5.56940e15	+	1.30141e16i	0.633012	+	1.47917i
$34$		−	1.37200e16i		−	1.13979i
$35$	−2.41822e16	−	9.04692e15i	−1.48177	−	0.554353i
$36$	4.33000e15	−	4.53696e15i	0.197384	−	0.206818i
$37$	1.95264e16			0.667580			0.333790	−	0.942648i	$-0.391672\pi$
$37$	1.95264e16			0.667580			0.333790	+	0.942648i	$0.391672\pi$
$38$	−1.61247e16			−0.416642
$39$	7.98411e15	+	1.86566e16i	0.157054	+	0.366990i
$40$			1.14010e17i			1.71915i
$41$	−8.86426e16			−1.03136			−0.515682	−	0.856780i	$-0.672461\pi$
$41$	−8.86426e16			−1.03136			−0.515682	+	0.856780i	$0.672461\pi$
$42$	4.33626e15	+	9.34399e16i	0.0391740	+	0.844141i
$43$	−2.83588e16			−0.200110			−0.100055	−	0.994982i	$-0.531902\pi$
$43$	−2.83588e16			−0.200110			−0.100055	+	0.994982i	$0.531902\pi$
$44$		−	8.29834e16i		−	0.459979i
$45$	2.49499e17	−	2.61424e17i	1.09229	−	1.14450i
$46$	−2.95123e17			−1.02576
$47$	−5.37703e17			−1.49113			−0.745564	−	0.666434i	$-0.767820\pi$
$47$	−5.37703e17			−1.49113			−0.745564	+	0.666434i	$0.767820\pi$
$48$	2.61510e17	−	1.11914e17i	0.581374	−	0.248800i
$49$	4.21392e17	+	3.66609e17i	0.754445	+	0.656363i
$50$			8.77031e17i			1.27008i
$51$	1.05417e18	−	4.51135e17i	1.24001	−	0.530664i
$52$		−	1.18962e17i		−	0.114123i
$53$			1.93110e18i			1.51673i	0.651831	+	0.758364i	$0.274001\pi$
$53$			1.93110e18i			1.51673i	−0.651831	+	0.758364i	$0.725999\pi$
$54$	−1.22637e18	−	4.58381e17i	−0.791563	−	0.295864i
$55$		−	4.78158e18i		−	2.54544i
$56$	8.64211e17	−	2.31002e18i	0.380755	−	1.01775i
$57$	−5.30204e17	−	1.23894e18i	−0.193980	−	0.453276i
$58$	−3.59888e18			−1.09692
$59$	−1.38432e18			−0.352606			−0.176303	−	0.984336i	$-0.556414\pi$
$59$	−1.38432e18			−0.352606			−0.176303	+	0.984336i	$0.556414\pi$
$60$	−1.94759e18	+	8.33475e17i	−0.415825	+	0.177953i
$61$			2.80127e18i			0.502796i	0.967884	+	0.251398i	$0.0808903\pi$
$61$			2.80127e18i			0.502796i	−0.967884	+	0.251398i	$0.919110\pi$
$62$	−6.39993e18			−0.968417
$63$	−7.03685e18	+	3.40562e18i	−0.900124	+	0.435633i
$64$	−1.01370e19			−1.09906
$65$		−	6.85472e18i		−	0.631538i
$66$	−1.59262e19	+	6.81562e18i	−1.24997	+	0.534926i
$67$	1.55480e19			1.04205			0.521026	−	0.853541i	$-0.325549\pi$
$67$	1.55480e19			1.04205			0.521026	+	0.853541i	$0.325549\pi$
$68$	−6.72185e18			−0.385608
$69$	−9.70408e18	−	2.26757e19i	−0.477572	−	1.11595i
$70$	1.10713e19	−	2.95933e19i	0.468456	−	1.25217i
$71$			1.31437e19i			0.479188i	0.970873	+	0.239594i	$0.0770143\pi$
$71$			1.31437e19i			0.479188i	−0.970873	+	0.239594i	$0.922986\pi$
$72$	2.49727e19	+	2.38335e19i	0.786093	+	0.750233i
$73$			3.15045e19i			0.857991i	0.903307	+	0.428996i	$0.141132\pi$
$73$			3.15045e19i			0.857991i	−0.903307	+	0.428996i	$0.858868\pi$
$74$			2.38956e19i			0.564138i
$75$	−6.73865e19	+	2.88381e19i	−1.38175	+	0.591322i
$76$			7.89997e18i			0.140956i
$77$	−3.62450e19	+	9.68821e19i	−0.563762	+	1.50692i
$78$	−2.28312e19	+	9.77065e18i	−0.310124	+	0.132718i
$79$	−6.56128e18			−0.0779658			−0.0389829	−	0.999240i	$-0.512412\pi$
$79$	−6.56128e18			−0.0779658			−0.0389829	+	0.999240i	$0.512412\pi$
$80$	−9.60829e19			−1.00046
$81$	−5.10520e18	−	1.09300e20i	−0.0466573	−	0.998911i
$82$		−	1.08477e20i		−	0.871553i
$83$	−1.99817e20			−1.41355			−0.706776	−	0.707438i	$-0.749851\pi$
$83$	−1.99817e20			−1.41355			−0.706776	+	0.707438i	$0.749851\pi$
$84$	4.57791e19	−	2.12447e18i	0.285585	−	0.0132531i
$85$	−3.87320e20			−2.13388
$86$		−	3.47045e19i		−	0.169103i
$87$	−1.18337e20	−	2.76519e20i	−0.510702	−	1.19337i
$88$	4.56763e20			1.74833
$89$	7.23185e19			0.245841			0.122921	−	0.992417i	$-0.460774\pi$
$89$	7.23185e19			0.245841			0.122921	+	0.992417i	$0.460774\pi$
$90$	3.19921e20	+	3.05327e20i	0.967156	+	0.923036i
$91$	−5.19597e19	+	1.38887e20i	−0.139872	+	0.373876i
$92$			1.44590e20i			0.347028i
$93$	−2.10440e20	−	4.91737e20i	−0.450875	−	1.05357i
$94$		−	6.58020e20i		−	1.26008i
$95$			4.55204e20i			0.780024i
$96$	−1.41535e20	−	3.30726e20i	−0.217278	−	0.507716i
$97$		−	6.71547e19i		−	0.0924641i	−0.998931	−	0.0462320i	$-0.985279\pi$
$97$		−	6.71547e19i		−	0.0924641i	0.998931	−	0.0462320i	$-0.0147214\pi$
$98$	−4.48642e20	+	5.15684e20i	−0.554659	+	0.637543i
$99$	−1.04735e21	−	9.99575e20i	−1.16392	−	1.11083i
$100$	4.29685e20			0.429685
$101$	1.32040e21			1.18941			0.594704	−	0.803945i	$-0.297269\pi$
$101$	1.32040e21			1.18941			0.594704	+	0.803945i	$0.297269\pi$
$102$	5.52082e20	+	1.29006e21i	0.448437	+	1.04787i
$103$			9.37344e20i			0.687240i	0.939109	+	0.343620i	$0.111653\pi$
$103$			9.37344e20i			0.687240i	−0.939109	+	0.343620i	$0.888347\pi$
$104$	6.54801e20			0.433769
$105$	2.63783e21	−	1.22414e20i	1.58037	−	0.0733403i
$106$	−2.36320e21			−1.28171
$107$		−	1.56246e21i		−	0.767857i	−0.923363	−	0.383928i	$-0.874571\pi$
$107$		−	1.56246e21i		−	0.767857i	0.923363	−	0.383928i	$-0.125429\pi$
$108$	−2.24575e20	+	6.00835e20i	−0.100095	+	0.267797i
$109$	2.46852e21			0.998754			0.499377	−	0.866385i	$-0.333562\pi$
$109$	2.46852e21			0.998754			0.499377	+	0.866385i	$0.333562\pi$
$110$	5.85152e21			2.15102
$111$	−1.83601e21	+	7.85724e20i	−0.613740	+	0.262651i
$112$	1.94679e21	+	7.28320e20i	0.592282	+	0.221581i
$113$			1.13111e21i			0.313461i	0.987641	+	0.156730i	$0.0500954\pi$
$113$			1.13111e21i			0.313461i	−0.987641	+	0.156730i	$0.949905\pi$
$114$	1.51616e21	−	6.48843e20i	0.383040	−	0.163923i
$115$			8.33139e21i			1.92039i
$116$			1.76320e21i			0.371102i
$117$	−1.50145e21	−	1.43296e21i	−0.288775	−	0.275602i
$118$		−	1.69407e21i		−	0.297969i
$119$	7.84769e21	+	2.93593e21i	1.26328	+	0.472610i
$120$	−4.58767e21	−	1.07201e22i	−0.676378	−	1.58050i
$121$	−1.17564e22			−1.58864
$122$	−3.42809e21			−0.424887
$123$	8.33484e21	−	3.56690e21i	0.948186	−	0.405777i
$124$			3.13552e21i			0.327629i
$125$	8.28547e21			0.795724
$126$	−4.16767e21	−	8.61143e21i	−0.368131	−	0.760649i
$127$	5.14526e21			0.418281			0.209140	−	0.977886i	$-0.432933\pi$
$127$	5.14526e21			0.418281			0.209140	+	0.977886i	$0.432933\pi$
$128$		−	5.02889e21i		−	0.376502i
$129$	2.66651e21	−	1.14114e21i	0.183972	−	0.0787309i
$130$	8.38855e21			0.533681
$131$	−1.92037e22			−1.12729			−0.563647	−	0.826016i	$-0.690602\pi$
$131$	−1.92037e22			−1.12729			−0.563647	+	0.826016i	$0.690602\pi$
$132$	3.33918e21	+	7.80272e21i	0.180973	+	0.422882i
$133$	3.45050e21	−	9.22313e21i	0.172759	−	0.461781i
$134$			1.90271e22i			0.880585i
$135$	−1.29402e22	+	3.46207e22i	−0.553908	+	1.48194i
$136$		−	3.69989e22i		−	1.46565i
$137$			1.79781e22i			0.659446i	0.944078	+	0.329723i	$0.106955\pi$
$137$			1.79781e22i			0.659446i	−0.944078	+	0.329723i	$0.893045\pi$
$138$	2.77496e22	−	1.18755e22i	0.943033	−	0.403572i
$139$		−	4.29132e22i		−	1.35187i	−0.736961	−	0.675935i	$-0.763740\pi$
$139$		−	4.29132e22i		−	1.35187i	0.736961	−	0.675935i	$-0.236260\pi$
$140$	−1.44987e22	−	5.42416e21i	−0.423627	−	0.158485i
$141$	5.05588e22	−	2.16367e22i	1.37087	−	0.586666i
$142$	−1.60848e22			−0.404937
$143$	−2.74623e22			−0.642257
$144$	−2.00858e22	+	2.10459e22i	−0.436600	+	0.457469i
$145$			1.01597e23i			2.05361i
$146$	−3.85540e22			−0.725045
$147$	−5.43745e22	−	1.75148e22i	−0.951838	−	0.306601i
$148$	1.17072e22			0.190856
$149$		−	7.26126e22i		−	1.10295i	−0.834191	−	0.551475i	$-0.814065\pi$
$149$		−	7.26126e22i		−	1.10295i	0.834191	−	0.551475i	$-0.185935\pi$
$150$	−3.52910e22	−	8.24650e22i	−0.499696	−	1.16765i
$151$	−4.63871e22			−0.612546			−0.306273	−	0.951944i	$-0.599082\pi$
$151$	−4.63871e22			−0.612546			−0.306273	+	0.951944i	$0.599082\pi$
$152$	−4.34836e22			−0.535757
$153$	−8.09680e22	+	8.48381e22i	−0.931222	+	0.975733i
$154$	−1.18561e23	−	4.43552e22i	−1.27342	−	0.476406i
$155$			1.80672e23i			1.81304i
$156$	4.78694e21	+	1.11857e22i	0.0449004	+	0.104919i
$157$			9.02342e22i			0.791453i	0.918368	+	0.395726i	$0.129507\pi$
$157$			9.02342e22i			0.791453i	−0.918368	+	0.395726i	$0.870493\pi$
$158$		−	8.02945e21i		−	0.0658850i
$159$	−7.77058e22	−	1.81576e23i	−0.596738	−	1.39441i
$160$			1.21514e23i			0.873709i
$161$	6.31530e22	−	1.68807e23i	0.425327	−	1.13689i
$162$	1.33757e23	−	6.24755e21i	0.844129	−	0.0394277i
$163$	4.02213e22			0.237950			0.118975	−	0.992897i	$-0.462039\pi$
$163$	4.02213e22			0.237950			0.118975	+	0.992897i	$0.462039\pi$
$164$	−5.31464e22			−0.294859
$165$	1.92407e23	+	4.49600e23i	1.00147	+	2.34016i
$166$		−	2.44528e23i		−	1.19452i
$167$	−5.26157e22			−0.241320			−0.120660	−	0.992694i	$-0.538501\pi$
$167$	−5.26157e22			−0.241320			−0.120660	+	0.992694i	$0.538501\pi$
$168$	1.16936e22	+	2.51980e23i	0.0503735	+	1.08547i
$169$	2.07695e23			0.840653
$170$		−	4.73987e23i		−	1.80324i
$171$	9.97074e22	+	9.51590e22i	0.356671	+	0.340401i
$172$	−1.70028e22			−0.0572099
$173$	3.02093e23			0.956436			0.478218	−	0.878241i	$-0.341283\pi$
$173$	3.02093e23			0.956436			0.478218	+	0.878241i	$0.341283\pi$
$174$	3.38394e23	−	1.44816e23i	1.00845	−	0.431568i
$175$	−5.01652e23	−	1.87675e23i	−1.40768	−	0.526632i
$176$			3.84940e23i			1.01744i
$177$	1.30164e23	−	5.57037e22i	0.324168	−	0.138728i
$178$			8.85006e22i			0.207748i
$179$		−	5.35659e23i		−	1.18558i	−0.805356	−	0.592791i	$-0.798026\pi$
$179$		−	5.35659e23i		−	1.18558i	0.805356	−	0.592791i	$-0.201974\pi$
$180$	1.49589e23	−	1.56739e23i	0.312276	−	0.327202i
$181$		−	8.67409e22i		−	0.170844i	−0.996345	−	0.0854218i	$-0.972776\pi$
$181$		−	8.67409e22i		−	0.170844i	0.996345	−	0.0854218i	$-0.0272238\pi$
$182$	−1.69965e23	−	6.35863e22i	−0.315943	−	0.118199i
$183$	−1.12721e23	−	2.63396e23i	−0.197819	−	0.462246i
$184$	−7.95860e23			−1.31901
$185$	6.74580e23			1.05616
$186$	6.01769e23	−	2.57528e23i	0.890316	−	0.381012i
$187$			1.55173e24i			2.17010i
$188$	−3.22384e23			−0.426301
$189$	5.24618e23	−	6.03379e23i	0.656136	−	0.754642i
$190$	−5.57061e23			−0.659159
$191$			4.88545e23i			0.547084i	0.961860	+	0.273542i	$0.0881953\pi$
$191$			4.88545e23i			0.547084i	−0.961860	+	0.273542i	$0.911805\pi$
$192$	9.53157e23	−	4.07905e23i	1.01042	−	0.432410i
$193$	8.38721e23			0.841910			0.420955	−	0.907082i	$-0.361695\pi$
$193$	8.38721e23			0.841910			0.420955	+	0.907082i	$0.361695\pi$
$194$	8.21813e22			0.0781367
$195$	2.75828e23	+	6.44532e23i	0.248471	+	0.580606i
$196$	2.52649e23	+	2.19804e23i	0.215690	+	0.187649i
$197$		−	1.14045e24i		−	0.922955i	−0.887152	−	0.461478i	$-0.847319\pi$
$197$		−	1.14045e24i		−	0.922955i	0.887152	−	0.461478i	$-0.152681\pi$
$198$	1.22324e24	−	1.28171e24i	0.938702	−	0.983570i
$199$		−	5.50546e23i		−	0.400716i	−0.979723	−	0.200358i	$-0.935790\pi$
$199$		−	5.50546e23i		−	0.400716i	0.979723	−	0.200358i	$-0.0642105\pi$
$200$			2.36510e24i			1.63318i
$201$	−1.46194e24	+	6.25639e23i	−0.958012	+	0.409982i
$202$			1.61585e24i			1.00511i
$203$	7.70122e23	−	2.05852e24i	0.454832	−	1.21576i
$204$	6.32039e23	−	2.70482e23i	0.354509	−	0.151712i
$205$	−3.06235e24			−1.63169
$206$	−1.14709e24			−0.580751
$207$	1.82490e24	+	1.74165e24i	0.878113	+	0.838055i
$208$			5.51838e23i			0.252433i
$209$	1.82370e24			0.793263
$210$	1.49805e23	+	3.22808e24i	0.0619762	+	1.33549i
$211$	−4.11913e24			−1.62121			−0.810605	−	0.585593i	$-0.800862\pi$
$211$	−4.11913e24			−1.62121			−0.810605	+	0.585593i	$0.800862\pi$
$212$			1.15781e24i			0.433620i
$213$	−5.28892e23	−	1.23587e24i	−0.188530	−	0.440542i
$214$	1.91208e24			0.648877
$215$	−9.79717e23			−0.316590
$216$	−3.30715e24	−	1.23612e24i	−1.01786	−	0.380449i
$217$	1.36952e24	−	3.66069e24i	0.401550	−	1.07334i
$218$			3.02088e24i			0.843996i
$219$	−1.26772e24	−	2.96229e24i	−0.337566	−	0.788795i
$220$		−	2.86684e24i		−	0.727721i
$221$			2.22451e24i			0.538414i
$222$	−9.61539e23	−	2.24684e24i	−0.221953	−	0.518641i
$223$			8.67661e24i			1.91051i	0.295787	+	0.955254i	$0.404418\pi$
$223$			8.67661e24i			1.91051i	−0.295787	+	0.955254i	$0.595582\pi$
$224$	9.21092e23	−	2.46206e24i	0.193508	−	0.517243i
$225$	5.17576e24	−	5.42315e24i	1.03767	−	1.08726i
$226$	−1.38422e24			−0.264890
$227$	1.73350e23			0.0316702			0.0158351	−	0.999875i	$-0.494959\pi$
$227$	1.73350e23			0.0316702			0.0158351	+	0.999875i	$0.494959\pi$
$228$	−3.17888e23	−	7.42814e23i	−0.0554573	−	0.129588i
$229$		−	1.02017e25i		−	1.69981i	−0.526936	−	0.849905i	$-0.676659\pi$
$229$		−	1.02017e25i		−	1.69981i	0.526936	−	0.849905i	$-0.323341\pi$
$230$	−1.01956e25			−1.62283
$231$	−4.90431e23	−	1.05680e25i	−0.0745851	−	1.60720i
$232$	−9.70515e24			−1.41052
$233$			1.18566e25i			1.64711i	0.567234	+	0.823557i	$0.308014\pi$
$233$			1.18566e25i			1.64711i	−0.567234	+	0.823557i	$0.691986\pi$
$234$	1.75360e24	−	1.83742e24i	0.232897	−	0.244029i
$235$	−1.85761e25			−2.35908
$236$	−8.29979e23			−0.100807
$237$	6.16941e23	−	2.64021e23i	0.0716780	−	0.0306747i
$238$	−3.59288e24	+	9.60370e24i	−0.399379	+	1.06753i
$239$		−	6.52754e23i		−	0.0694339i	−0.999397	−	0.0347170i	$-0.988947\pi$
$239$		−	6.52754e23i		−	0.0694339i	0.999397	−	0.0347170i	$-0.0110530\pi$
$240$	9.03443e24	−	3.86629e24i	0.919777	−	0.393620i
$241$			1.09066e24i			0.106295i	0.998587	+	0.0531474i	$0.0169253\pi$
$241$			1.09066e24i			0.106295i	−0.998587	+	0.0531474i	$0.983075\pi$
$242$		−	1.43870e25i		−	1.34248i
$243$	4.87816e24	+	1.00718e25i	0.435903	+	0.899993i
$244$			1.67953e24i			0.143745i
$245$	1.45579e25	+	1.26653e25i	1.19359	+	1.03842i
$246$	4.36504e24	+	1.01999e25i	0.342902	+	0.801263i
$247$	2.61440e24			0.196813
$248$	−1.72588e25			−1.24528
$249$	1.87882e25	−	8.04045e24i	1.29955	−	0.556144i
$250$			1.01394e25i			0.672426i
$251$	−7.60023e24			−0.483340			−0.241670	−	0.970359i	$-0.577695\pi$
$251$	−7.60023e24			−0.483340			−0.241670	+	0.970359i	$0.577695\pi$
$252$	−4.21901e24	+	2.04187e24i	−0.257338	+	0.124544i
$253$	3.33783e25			1.95299
$254$			6.29657e24i			0.353468i
$255$	3.64187e25	−	1.55854e25i	1.96179	−	0.839550i
$256$	−1.51047e25			−0.780894
$257$	1.51964e25			0.754126			0.377063	−	0.926188i	$-0.376934\pi$
$257$	1.51964e25			0.754126			0.377063	+	0.926188i	$0.376934\pi$
$258$	1.39648e24	+	3.26317e24i	0.0665315	+	0.155465i
$259$	−1.36680e25	−	5.11340e24i	−0.625256	−	0.233917i
$260$		−	4.10981e24i		−	0.180552i
$261$	2.22538e25	+	2.12386e25i	0.939029	+	0.896193i
$262$		−	2.35008e25i		−	0.952619i
$263$		−	2.96038e25i		−	1.15296i	−0.817113	−	0.576478i	$-0.804427\pi$
$263$		−	2.96038e25i		−	1.15296i	0.817113	−	0.576478i	$-0.195573\pi$
$264$	−4.29482e25	+	1.83797e25i	−1.60733	+	0.687857i
$265$			6.67139e25i			2.39958i
$266$	1.12869e25	+	4.22260e24i	0.390228	+	0.145990i
$267$	−6.79992e24	+	2.91004e24i	−0.226014	+	0.0967231i
$268$	9.32194e24			0.297914
$269$	2.14097e25			0.657979			0.328989	−	0.944334i	$-0.393292\pi$
$269$	2.14097e25			0.657979			0.328989	+	0.944334i	$0.393292\pi$
$270$	−4.23675e25	−	1.58358e25i	−1.25231	−	0.468079i
$271$			3.15046e25i			0.895770i	0.894091	+	0.447885i	$0.147823\pi$
$271$			3.15046e25i			0.895770i	−0.894091	+	0.447885i	$0.852177\pi$
$272$	3.11811e25			0.852938
$273$	−7.03066e23	−	1.51500e25i	−0.0185050	−	0.398754i
$274$	−2.20010e25			−0.557264
$275$		−	9.91922e25i		−	2.41816i
$276$	−5.81817e24	−	1.35954e25i	−0.136534	−	0.319041i
$277$	−5.47081e25			−1.23599			−0.617994	−	0.786183i	$-0.712054\pi$
$277$	−5.47081e25			−1.23599			−0.617994	+	0.786183i	$0.712054\pi$
$278$	5.25155e25			1.14240
$279$	3.95742e25	+	3.77689e25i	0.829026	+	0.791207i
$280$	2.98560e25	−	7.98046e25i	0.602383	−	1.61016i
$281$			1.52007e24i			0.0295425i	0.999891	+	0.0147712i	$0.00470201\pi$
$281$			1.52007e24i			0.0295425i	−0.999891	+	0.0147712i	$0.995298\pi$
$282$	2.64782e25	+	6.18720e25i	0.495761	+	1.15845i
$283$		−	2.48723e25i		−	0.448703i	−0.974508	−	0.224351i	$-0.927974\pi$
$283$		−	2.48723e25i		−	0.448703i	0.974508	−	0.224351i	$-0.0720263\pi$
$284$			7.88043e24i			0.136996i
$285$	−1.83170e25	−	4.28017e25i	−0.306891	−	0.717117i
$286$		−	3.36073e25i		−	0.542739i
$287$	6.20478e25	+	2.32130e25i	0.965977	+	0.361386i
$288$	2.66163e25	+	2.54021e25i	0.399509	+	0.381284i
$289$	5.66021e25			0.819229
$290$	−1.24331e26			−1.73541
$291$	2.70225e24	+	6.31438e24i	0.0363788	+	0.0850070i
$292$			1.88888e25i			0.245293i
$293$	−1.45882e26			−1.82764			−0.913821	−	0.406116i	$-0.866883\pi$
$293$	−1.45882e26			−1.82764			−0.913821	+	0.406116i	$0.866883\pi$
$294$	2.14340e25	−	6.65414e25i	0.259093	−	0.804350i
$295$	−4.78242e25			−0.557849
$296$			6.44396e25i			0.725420i
$297$	1.38702e26	+	5.18429e25i	1.50709	+	0.563309i
$298$	8.88605e25			0.932047
$299$	4.78501e25			0.484547
$300$	−4.04022e25	+	1.72901e25i	−0.395031	+	0.169054i
$301$	1.98506e25	+	7.42638e24i	0.187424	+	0.0701179i
$302$		−	5.67667e25i		−	0.517632i
$303$	−1.24154e26	+	5.31318e25i	−1.09348	+	0.467958i
$304$		−	3.66461e25i		−	0.311785i
$305$			9.67759e25i			0.795461i
$306$	−1.03822e26	−	9.90855e25i	−0.824542	−	0.786928i
$307$			1.28667e26i			0.987445i	0.869619	+	0.493723i	$0.164364\pi$
$307$			1.28667e26i			0.987445i	−0.869619	+	0.493723i	$0.835636\pi$
$308$	−2.17310e25	+	5.80865e25i	−0.161175	+	0.430817i
$309$	−3.77180e25	−	8.81361e25i	−0.270386	−	0.631815i
$310$	−2.21099e26			−1.53211
$311$	−1.53383e26			−1.02752			−0.513762	−	0.857933i	$-0.671749\pi$
$311$	−1.53383e26			−1.02752			−0.513762	+	0.857933i	$0.671749\pi$
$312$	−6.15692e25	+	2.63486e25i	−0.398787	+	0.170661i
$313$		−	6.75251e25i		−	0.422912i	−0.977388	−	0.211456i	$-0.932180\pi$
$313$		−	6.75251e25i		−	0.422912i	0.977388	−	0.211456i	$-0.0678205\pi$
$314$	−1.10425e26			−0.668816
$315$	−2.43103e26	+	1.17655e26i	−1.42406	+	0.689204i
$316$	−3.93388e24			−0.0222898
$317$			2.10670e24i			0.0115473i	0.999983	+	0.00577365i	$0.00183782\pi$
$317$			2.10670e24i			0.0115473i	−0.999983	+	0.00577365i	$0.998162\pi$
$318$	2.22206e26	−	9.50933e25i	1.17834	−	0.504273i
$319$	4.07034e26			2.08847
$320$	−3.50205e26			−1.73879
$321$	6.28722e25	+	1.46914e26i	0.302104	+	0.705930i
$322$	2.06579e26	+	7.72843e25i	0.960727	+	0.359422i
$323$		−	1.47724e26i		−	0.665005i
$324$	−3.06087e24	−	6.55317e25i	−0.0133389	−	0.285581i
$325$		−	1.42199e26i		−	0.599958i
$326$			4.92213e25i			0.201080i
$327$	−2.32109e26	+	9.93312e25i	−0.918206	+	0.392947i
$328$		−	2.92532e26i		−	1.12072i
$329$	3.76380e26	+	1.40809e26i	1.39659	+	0.522485i
$330$	−5.50203e26	+	2.35460e26i	−1.97755	+	0.846294i
$331$	6.10254e25			0.212479			0.106240	−	0.994341i	$-0.466119\pi$
$331$	6.10254e25			0.212479			0.106240	+	0.994341i	$0.466119\pi$
$332$	−1.19802e26			−0.404123
$333$	1.41019e26	−	1.47759e26i	0.460906	−	0.482937i
$334$		−	6.43891e25i		−	0.203927i
$335$	5.37139e26			1.64860
$336$	−2.12358e26	+	9.85490e24i	−0.631694	+	0.0293150i
$337$	3.60725e26			1.04007			0.520034	−	0.854146i	$-0.325919\pi$
$337$	3.60725e26			1.04007			0.520034	+	0.854146i	$0.325919\pi$
$338$			2.54170e26i			0.710393i
$339$	−4.55151e25	−	1.06356e26i	−0.123327	−	0.288180i
$340$	−2.32221e26			−0.610060
$341$	7.23832e26			1.84381
$342$	−1.16452e26	+	1.22018e26i	−0.287655	+	0.301405i
$343$	−1.98961e26	−	3.66969e26i	−0.476627	−	0.879105i
$344$		−	9.35879e25i		−	0.217448i
$345$	−3.35248e26	−	7.83380e26i	−0.755555	−	1.76552i
$346$			3.69689e26i			0.808236i
$347$			7.67821e26i			1.62855i	0.580481	+	0.814274i	$0.302865\pi$
$347$			7.67821e26i			1.62855i	−0.580481	+	0.814274i	$0.697135\pi$
$348$	−7.09498e25	−	1.65790e26i	−0.146006	−	0.341173i
$349$		−	2.40328e26i		−	0.479884i	−0.970787	−	0.239942i	$-0.922872\pi$
$349$		−	2.40328e26i		−	0.479884i	0.970787	−	0.239942i	$-0.0771285\pi$
$350$	2.29670e26	−	6.13902e26i	0.445030	−	1.18956i
$351$	1.98839e26	+	7.43203e25i	0.373918	+	0.139760i
$352$	4.86826e26			0.888537
$353$	1.97397e25			0.0349708			0.0174854	−	0.999847i	$-0.494434\pi$
$353$	1.97397e25			0.0349708			0.0174854	+	0.999847i	$0.494434\pi$
$354$	6.81681e25	+	1.59289e26i	0.117232	+	0.273938i
$355$			4.54078e26i			0.758111i
$356$	4.33592e25			0.0702840
$357$	−8.56038e26	+	3.97261e25i	−1.34734	+	0.0625258i
$358$	6.55520e26			1.00188
$359$		−	7.21127e26i		−	1.07034i	−0.844746	−	0.535168i	$-0.820248\pi$
$359$		−	7.21127e26i		−	1.07034i	0.844746	−	0.535168i	$-0.179752\pi$
$360$	8.62734e26	+	8.23378e26i	1.24366	+	1.18692i
$361$	5.40594e26			0.756913
$362$	1.06150e26			0.144371
$363$	1.10542e27	−	4.73066e26i	1.46052	−	0.625032i
$364$	−3.11529e25	+	8.32710e25i	−0.0399884	+	0.106888i
$365$			1.08839e27i			1.35741i
$366$	3.22335e26	−	1.37943e26i	0.390621	−	0.167167i
$367$			2.53576e26i			0.298616i	0.988791	+	0.149308i	$0.0477047\pi$
$367$			2.53576e26i			0.298616i	−0.988791	+	0.149308i	$0.952295\pi$
$368$		−	6.70717e26i		−	0.767604i
$369$	−6.40174e26	+	6.70774e26i	−0.712068	+	0.746104i
$370$			8.25525e26i			0.892508i
$371$	5.05700e26	−	1.35173e27i	0.531456	−	1.42057i
$372$	−1.26171e26	−	2.94825e26i	−0.128902	−	0.301206i
$373$	−4.36853e26			−0.433903			−0.216952	−	0.976182i	$-0.569611\pi$
$373$	−4.36853e26			−0.433903			−0.216952	+	0.976182i	$0.569611\pi$
$374$	−1.89895e27			−1.83384
$375$	−7.79062e26	+	3.33400e26i	−0.731550	+	0.313067i
$376$		−	1.77449e27i		−	1.62032i
$377$	5.83510e26			0.518161
$378$	7.38392e26	+	6.42007e26i	0.637710	+	0.554467i
$379$	9.77018e26			0.820712			0.410356	−	0.911925i	$-0.365404\pi$
$379$	9.77018e26			0.820712			0.410356	+	0.911925i	$0.365404\pi$
$380$			2.72922e26i			0.223003i
$381$	−4.83795e26	+	2.07041e26i	−0.384547	+	0.164567i
$382$	−5.97863e26			−0.462313
$383$	−1.58081e27			−1.18930			−0.594652	−	0.803984i	$-0.702710\pi$
$383$	−1.58081e27			−1.18930			−0.594652	+	0.803984i	$0.702710\pi$
$384$	2.02358e26	+	4.72853e26i	0.148130	+	0.346138i
$385$	−1.25216e27	+	3.34700e27i	−0.891913	+	2.38407i
$386$			1.02639e27i			0.711455i
$387$	−2.04807e26	+	2.14596e26i	−0.138159	+	0.144763i
$388$		−	4.02632e25i		−	0.0264347i
$389$		−	4.76046e26i		−	0.304213i	−0.988364	−	0.152107i	$-0.951394\pi$
$389$		−	4.76046e26i		−	0.304213i	0.988364	−	0.152107i	$-0.0486057\pi$
$390$	−7.88754e26	+	3.37548e26i	−0.490640	+	0.209970i
$391$		−	2.70373e27i		−	1.63722i
$392$	−1.20986e27	+	1.39065e27i	−0.713232	+	0.819812i
$393$	1.80568e27	−	7.72742e26i	1.03638	−	0.443520i
$394$	1.39564e27			0.779943
$395$	−2.26674e26			−0.123348
$396$	−6.27950e26	−	5.99304e26i	−0.332756	−	0.317576i
$397$		−	3.21025e27i		−	1.65668i	−0.560225	−	0.828340i	$-0.689285\pi$
$397$		−	3.21025e27i		−	1.65668i	0.560225	−	0.828340i	$-0.310715\pi$
$398$	6.73737e26			0.338624
$399$	4.66888e25	+	1.00607e27i	0.0228558	+	0.492509i
$400$	−1.99320e27			−0.950434
$401$			2.46908e27i			1.14688i	0.819247	+	0.573441i	$0.194392\pi$
$401$			2.46908e27i			1.14688i	−0.819247	+	0.573441i	$0.805608\pi$
$402$	−7.65633e26	−	1.78907e27i	−0.346455	−	0.809567i
$403$	1.03766e27			0.457460
$404$	7.91657e26			0.340042
$405$	−1.76370e26	−	3.77600e27i	−0.0738154	−	1.58035i
$406$	2.51914e27	+	9.42446e26i	1.02737	+	0.384355i
$407$		−	2.70259e27i		−	1.07409i
$408$	1.48880e27	+	3.47891e27i	0.576642	+	1.34745i
$409$			1.42944e26i			0.0539597i	0.999636	+	0.0269799i	$0.00858900\pi$
$409$			1.42944e26i			0.0539597i	−0.999636	+	0.0269799i	$0.991411\pi$
$410$		−	3.74758e27i		−	1.37886i
$411$	−7.23426e26	−	1.69044e27i	−0.259451	−	0.606262i
$412$			5.61993e26i			0.196476i
$413$	9.68991e26	+	3.62513e26i	0.330251	+	0.123552i
$414$	−2.13137e27	+	2.23324e27i	−0.708198	+	0.742049i
$415$	−6.90309e27			−2.23634
$416$	6.97898e26			0.220451
$417$	1.72679e27	+	4.03502e27i	0.531877	+	1.24284i
$418$			2.23177e27i			0.670346i
$419$	−1.51781e27			−0.444601			−0.222301	−	0.974978i	$-0.571357\pi$
$419$	−1.51781e27			−0.444601			−0.222301	+	0.974978i	$0.571357\pi$
$420$	1.58154e27	−	7.33943e25i	0.451816	−	0.0209674i
$421$	−5.17334e26			−0.144148			−0.0720741	−	0.997399i	$-0.522962\pi$
$421$	−5.17334e26			−0.144148			−0.0720741	+	0.997399i	$0.522962\pi$
$422$		−	5.04083e27i		−	1.37000i
$423$	−3.88328e27	+	4.06889e27i	−1.02950	+	1.07870i
$424$	−6.37288e27			−1.64814
$425$	−8.03481e27			−2.02718
$426$	1.51241e27	−	6.47238e26i	0.372279	−	0.159317i
$427$	7.33574e26	−	1.96083e27i	0.176178	−	0.470920i
$428$		−	9.36788e26i		−	0.219524i
$429$	2.58221e27	−	1.10506e27i	0.590460	−	0.252688i
$430$		−	1.19894e27i		−	0.267534i
$431$			1.93756e27i			0.421933i	0.977493	+	0.210966i	$0.0676611\pi$
$431$			1.93756e27i			0.421933i	−0.977493	+	0.210966i	$0.932339\pi$
$432$	1.04175e27	−	2.78713e27i	0.221403	−	0.592349i
$433$			3.70466e27i			0.768468i	0.923236	+	0.384234i	$0.125534\pi$
$433$			3.70466e27i			0.768468i	−0.923236	+	0.384234i	$0.874466\pi$
$434$	4.47981e27	+	1.67596e27i	0.907021	+	0.339330i
$435$	−4.08820e27	−	9.55295e27i	−0.807969	−	1.88799i
$436$	1.48002e27			0.285536
$437$	−3.17760e27			−0.598473
$438$	3.62514e27	−	1.55138e27i	0.666571	−	0.285260i
$439$		−	2.42257e27i		−	0.434910i	−0.976070	−	0.217455i	$-0.930224\pi$
$439$		−	2.42257e27i		−	0.434910i	0.976070	−	0.217455i	$-0.0697756\pi$
$440$	1.57798e28			2.76598
$441$	5.81748e27	−	5.41108e26i	0.995702	−	0.0926144i
$442$	−2.72228e27			−0.454986
$443$			4.87788e27i			0.796145i	0.917354	+	0.398073i	$0.130321\pi$
$443$			4.87788e27i			0.796145i	−0.917354	+	0.398073i	$0.869679\pi$
$444$	−1.10080e27	+	4.71088e26i	−0.175463	+	0.0750898i
$445$	2.49840e27			0.388939
$446$	−1.06181e28			−1.61447
$447$	2.92187e27	+	6.82758e27i	0.433942	+	1.01400i
$448$	7.09568e27	+	2.65460e27i	1.02938	+	0.385105i
$449$			1.25132e28i			1.77330i	0.462440	+	0.886650i	$0.346974\pi$
$449$			1.25132e28i			1.77330i	−0.462440	+	0.886650i	$0.653026\pi$
$450$	6.63665e27	+	6.33390e27i	0.918792	+	0.876879i
$451$			1.22688e28i			1.65939i
$452$			6.78170e26i			0.0896159i
$453$	4.36166e27	−	1.86658e27i	0.563145	−	0.240999i
$454$			2.12139e26i			0.0267629i
$455$	−1.79506e27	+	4.79815e27i	−0.221289	+	0.591500i
$456$	4.08865e27	−	1.74974e27i	0.492549	−	0.210787i
$457$	3.85988e27			0.454416			0.227208	−	0.973846i	$-0.427040\pi$
$457$	3.85988e27			0.454416			0.227208	+	0.973846i	$0.427040\pi$
$458$	1.24845e28			1.43642
$459$	4.19940e27	−	1.12352e28i	0.472230	−	1.26342i
$460$			4.99516e27i			0.549025i
$461$	1.14925e28			1.23468			0.617338	−	0.786698i	$-0.288211\pi$
$461$	1.14925e28			1.23468			0.617338	+	0.786698i	$0.288211\pi$
$462$	1.29328e28	−	6.00171e26i	1.35816	−	0.0630281i
$463$	−9.73227e27			−0.999111			−0.499556	−	0.866282i	$-0.666503\pi$
$463$	−9.73227e27			−0.999111			−0.499556	+	0.866282i	$0.666503\pi$
$464$		−	8.17908e27i		−	0.820854i
$465$	−7.27009e27	−	1.69881e28i	−0.713319	−	1.66682i
$466$	−1.45097e28			−1.39189
$467$	−1.54696e28			−1.45094			−0.725472	−	0.688252i	$-0.758378\pi$
$467$	−1.54696e28			−1.45094			−0.725472	+	0.688252i	$0.758378\pi$
$468$	−9.00208e26	−	8.59143e26i	−0.0825585	−	0.0787923i
$469$	−1.08833e28	−	4.07158e27i	−0.975987	−	0.365131i
$470$		−	2.27327e28i		−	1.99354i
$471$	−3.63095e27	−	8.48450e27i	−0.311387	−	0.727623i
$472$		−	4.56843e27i		−	0.383156i
$473$			3.92507e27i			0.321963i
$474$	3.23098e26	+	7.54989e26i	0.0259216	+	0.0605714i
$475$			9.44304e27i			0.741018i
$476$	4.70515e27	+	1.76026e27i	0.361161	+	0.135115i
$477$	1.46129e28	+	1.39463e28i	1.09722	+	1.04717i
$478$	7.98815e26			0.0586751
$479$	1.75617e28			1.26196			0.630978	−	0.775801i	$-0.282654\pi$
$479$	1.75617e28			1.26196			0.630978	+	0.775801i	$0.282654\pi$
$480$	−4.88962e27	−	1.14257e28i	−0.343750	−	0.803245i
$481$		−	3.87435e27i		−	0.266487i
$482$	−1.33471e27			−0.0898243
$483$	8.54523e26	+	1.84137e28i	0.0562703	+	1.21254i
$484$	−7.04863e27			−0.454181
$485$		−	2.32000e27i		−	0.146285i
$486$	−1.23254e28	+	5.96971e27i	−0.760539	+	0.368360i
$487$	1.24697e28			0.753013			0.376506	−	0.926414i	$-0.377125\pi$
$487$	1.24697e28			0.753013			0.376506	+	0.926414i	$0.377125\pi$
$488$	−9.24457e27			−0.546359
$489$	−3.78190e27	+	1.61847e27i	−0.218760	+	0.0936185i
$490$	−1.54993e28	+	1.78154e28i	−0.877512	+	1.00864i
$491$			1.80793e28i			1.00190i	0.865475	+	0.500952i	$0.167017\pi$
$491$			1.80793e28i			1.00190i	−0.865475	+	0.500952i	$0.832983\pi$
$492$	4.99722e27	−	2.13857e27i	0.271079	−	0.116008i
$493$		−	3.29707e28i		−	1.75080i
$494$			3.19940e27i			0.166317i
$495$	−3.61830e28	−	3.45325e28i	−1.84141	−	1.75741i
$496$		−	1.45449e28i		−	0.724694i
$497$	3.44197e27	−	9.20031e27i	0.167905	−	0.448808i
$498$	9.83960e27	+	2.29923e28i	0.469969	+	1.09818i
$499$	−1.50235e28			−0.702611			−0.351305	−	0.936261i	$-0.614262\pi$
$499$	−1.50235e28			−0.702611			−0.351305	+	0.936261i	$0.614262\pi$
$500$	4.96763e27			0.227491
$501$	4.94732e27	−	2.11721e27i	0.221857	−	0.0949442i
$502$		−	9.30087e27i		−	0.408446i
$503$	8.00712e27			0.344360			0.172180	−	0.985066i	$-0.444919\pi$
$503$	8.00712e27			0.344360			0.172180	+	0.985066i	$0.444919\pi$
$504$	−1.12390e28	−	2.32225e28i	−0.473377	−	0.978113i
$505$	4.56160e28			1.88173
$506$			4.08472e28i			1.65037i
$507$	−1.95291e28	+	8.35749e27i	−0.772855	+	0.330744i
$508$	3.08488e27			0.119583
$509$	−4.61539e28			−1.75255			−0.876277	−	0.481807i	$-0.839981\pi$
$509$	−4.61539e28			−1.75255			−0.876277	+	0.481807i	$0.839981\pi$
$510$	1.90728e28	+	4.45678e28i	0.709461	+	1.65781i
$511$	8.25014e27	−	2.20525e28i	0.300637	−	0.803596i
$512$		−	2.90309e28i		−	1.03640i
$513$	−1.32044e28	−	4.93541e27i	−0.461833	−	0.172620i
$514$			1.85968e28i			0.637273i
$515$			3.23826e28i			1.08727i
$516$	1.59873e27	−	6.84178e26i	0.0525960	−	0.0225085i
$517$			7.44221e28i			2.39911i
$518$	6.25759e27	−	1.67264e28i	0.197672	−	0.528372i
$519$	−2.84050e28	+	1.21560e28i	−0.879301	+	0.376298i
$520$	2.26215e28			0.686256
$521$	−3.96504e28			−1.17883			−0.589416	−	0.807830i	$-0.700642\pi$
$521$	−3.96504e28			−1.17883			−0.589416	+	0.807830i	$0.700642\pi$
$522$	−2.59910e28	+	2.72334e28i	−0.757327	+	0.793526i
$523$		−	3.10901e28i		−	0.887881i	−0.896056	−	0.443940i	$-0.853580\pi$
$523$		−	3.10901e28i		−	0.887881i	0.896056	−	0.443940i	$-0.146420\pi$
$524$	−1.15138e28			−0.322284
$525$	5.47209e28	−	2.53943e27i	1.50135	−	0.0696729i
$526$	3.62280e28			0.974304
$527$		−	5.86321e28i		−	1.54570i
$528$	−1.54897e28	−	3.61949e28i	−0.400300	−	0.935388i
$529$	−1.86866e28			−0.473419
$530$	−8.16420e28			−2.02776
$531$	−9.99749e27	+	1.04754e28i	−0.243444	+	0.255080i
$532$	2.06878e27	−	5.52981e27i	0.0493904	−	0.132019i
$533$			1.75881e28i			0.411703i
$534$	−3.56119e27	−	8.32149e27i	−0.0817358	−	0.190993i
$535$		−	5.39786e28i		−	1.21481i
$536$			5.13105e28i			1.13234i
$537$	2.15545e28	+	5.03667e28i	0.466453	+	1.08997i
$538$			2.62004e28i			0.556025i
$539$	5.07414e28	−	5.83238e28i	1.05604	−	1.21385i
$540$	−7.75843e27	+	2.07571e28i	−0.158358	+	0.423675i
$541$	−5.02334e28			−1.00559			−0.502795	−	0.864406i	$-0.667695\pi$
$541$	−5.02334e28			−1.00559			−0.502795	+	0.864406i	$0.667695\pi$
$542$	−3.85541e28			−0.756970
$543$	3.49038e27	+	8.15603e27i	0.0672163	+	0.157065i
$544$		−	3.94341e28i		−	0.744875i
$545$	8.52803e28			1.58010
$546$	1.85400e28	−	8.60386e26i	0.336967	−	0.0156376i
$547$	−3.14126e28			−0.560062			−0.280031	−	0.959991i	$-0.590345\pi$
$547$	−3.14126e28			−0.560062			−0.280031	+	0.959991i	$0.590345\pi$
$548$			1.07790e28i			0.188530i
$549$	2.11977e28	+	2.02307e28i	0.363730	+	0.347137i
$550$	1.21388e29			2.04346
$551$	−3.87494e28			−0.639990
$552$	7.48327e28	−	3.20247e28i	1.21264	−	0.518950i
$553$	4.59275e27	+	1.71822e27i	0.0730229	+	0.0273189i
$554$		−	6.69497e28i		−	1.04447i
$555$	−6.34290e28	+	2.71445e28i	−0.970983	+	0.415533i
$556$		−	2.57290e28i		−	0.386489i
$557$		−	8.26677e28i		−	1.21859i	−0.792945	−	0.609293i	$-0.791453\pi$
$557$		−	8.26677e28i		−	1.21859i	0.792945	−	0.609293i	$-0.208547\pi$
$558$	−4.62201e28	+	4.84294e28i	−0.668609	+	0.700567i
$559$			5.62686e27i			0.0798808i
$560$	6.72559e28	+	2.51614e28i	0.937035	+	0.350558i
$561$	−6.24404e28	−	1.45905e29i	−0.853799	−	1.99509i
$562$	−1.86020e27			−0.0249649
$563$	1.30474e29			1.71865			0.859323	−	0.511433i	$-0.170885\pi$
$563$	1.30474e29			1.71865			0.859323	+	0.511433i	$0.170885\pi$
$564$	3.03130e28	−	1.29725e28i	0.391921	−	0.167723i
$565$			3.90768e28i			0.495918i
$566$	3.04378e28			0.379176
$567$	−2.50490e28	+	7.78444e28i	−0.306315	+	0.951930i
$568$	−4.33760e28			−0.520705
$569$		−	9.08661e28i		−	1.07084i	−0.844587	−	0.535418i	$-0.820154\pi$
$569$		−	9.08661e28i		−	1.07084i	0.844587	−	0.535418i	$-0.179846\pi$
$570$	5.23791e28	−	2.24157e28i	0.605999	−	0.259338i
$571$	9.49646e28			1.07865			0.539327	−	0.842096i	$-0.318679\pi$
$571$	9.49646e28			1.07865			0.539327	+	0.842096i	$0.318679\pi$
$572$	−1.64653e28			−0.183616
$573$	−1.96586e28	−	4.59366e28i	−0.215243	−	0.502962i
$574$	−2.84072e28	+	7.59318e28i	−0.305389	+	0.816298i
$575$			1.72832e29i			1.82436i
$576$	−7.32092e28	+	7.67085e28i	−0.758804	+	0.795073i
$577$		−	5.39460e28i		−	0.549052i	−0.961580	−	0.274526i	$-0.911479\pi$
$577$		−	5.39460e28i		−	0.549052i	0.961580	−	0.274526i	$-0.0885209\pi$
$578$			6.92675e28i			0.692289i
$579$	−7.88628e28	+	3.37494e28i	−0.774011	+	0.331239i
$580$			6.09137e28i			0.587112i
$581$	1.39867e29	+	5.23263e28i	1.32393	+	0.495303i
$582$	−7.72730e27	+	3.30691e27i	−0.0718351	+	0.0307419i
$583$	2.67278e29			2.44030
$584$	−1.03969e29			−0.932329
$585$	−5.18709e28	−	4.95046e28i	−0.456864	−	0.436023i
$586$		−	1.78525e29i		−	1.54445i
$587$	1.58353e29			1.34563			0.672817	−	0.739809i	$-0.265084\pi$
$587$	1.58353e29			1.34563			0.672817	+	0.739809i	$0.265084\pi$
$588$	−3.26007e28	−	1.05012e28i	−0.272123	−	0.0876548i
$589$	−6.89084e28			−0.565017
$590$		−	5.85254e28i		−	0.471409i
$591$	4.58907e28	+	1.07234e29i	0.363125	+	0.848520i
$592$	−5.43069e28			−0.422160
$593$	1.48490e28			0.113402			0.0567012	−	0.998391i	$-0.481942\pi$
$593$	1.48490e28			0.113402			0.0567012	+	0.998391i	$0.481942\pi$
$594$	−6.34433e28	+	1.69738e29i	−0.476023	+	1.27357i
$595$	2.71115e29	+	1.01428e29i	1.99860	+	0.747705i
$596$		−	4.35355e28i		−	0.315325i
$597$	2.21535e28	+	5.17664e28i	0.157657	+	0.368399i
$598$			5.85572e28i			0.409466i
$599$		−	7.20867e28i		−	0.495306i	−0.968849	−	0.247653i	$-0.920341\pi$
$599$		−	7.20867e28i		−	0.495306i	0.968849	−	0.247653i	$-0.0796593\pi$
$600$	−9.51696e28	−	2.22384e29i	−0.642555	−	1.50147i
$601$			5.80781e28i			0.385328i	0.981265	+	0.192664i	$0.0617128\pi$
$601$			5.80781e28i			0.385328i	−0.981265	+	0.192664i	$0.938287\pi$
$602$	−9.08812e27	+	2.42924e28i	−0.0592531	+	0.158382i
$603$	1.12287e29	−	1.17654e29i	0.719447	−	0.753835i
$604$	−2.78118e28			−0.175122
$605$	−4.06149e29			−2.51335
$606$	−6.50206e28	−	1.51935e29i	−0.395447	−	0.924048i
$607$		−	1.15339e29i		−	0.689438i	−0.938706	−	0.344719i	$-0.887974\pi$
$607$		−	1.15339e29i		−	0.689438i	0.938706	−	0.344719i	$-0.112026\pi$
$608$	−4.63456e28			−0.272283
$609$	1.04205e28	+	2.24546e29i	0.0601738	+	1.29666i
$610$	−1.18431e29			−0.672204
$611$			1.06689e29i			0.595233i
$612$	−4.85451e28	+	5.08654e28i	−0.266229	+	0.278954i
$613$	−2.77828e29			−1.49776			−0.748878	−	0.662708i	$-0.769407\pi$
$613$	−2.77828e29			−1.49776			−0.748878	+	0.662708i	$0.769407\pi$
$614$	−1.57457e29			−0.834440
$615$	2.87945e29	−	1.23226e29i	1.50010	−	0.641970i
$616$	−3.19724e29	−	1.19613e29i	−1.63749	−	0.612607i
$617$			1.84076e29i			0.926836i	0.886140	+	0.463418i	$0.153377\pi$
$617$			1.84076e29i			0.926836i	−0.886140	+	0.463418i	$0.846623\pi$
$618$	1.07858e29	−	4.61578e28i	0.533915	−	0.228489i
$619$			2.28968e29i			1.11435i	0.830394	+	0.557177i	$0.188115\pi$
$619$			2.28968e29i			1.11435i	−0.830394	+	0.557177i	$0.811885\pi$
$620$			1.08323e29i			0.518334i
$621$	−2.41673e29	−	9.03307e28i	−1.13702	−	0.424985i
$622$		−	1.87704e29i		−	0.868309i
$623$	−5.06214e28	−	1.89382e28i	−0.230255	−	0.0861417i
$624$	−2.22055e28	−	5.18879e28i	−0.0993167	−	0.232075i
$625$	−5.54945e28			−0.244067
$626$	8.26347e28			0.357381
$627$	−1.71478e29	+	7.33841e28i	−0.729288	+	0.312099i
$628$			5.41007e28i			0.226270i
$629$	−2.18917e29			−0.900424
$630$	−1.43981e29	−	2.97500e29i	−0.582411	−	1.20340i
$631$	3.78698e29			1.50656			0.753278	−	0.657703i	$-0.228472\pi$
$631$	3.78698e29			1.50656			0.753278	+	0.657703i	$0.228472\pi$
$632$		−	2.16531e28i		−	0.0847210i
$633$	3.87311e29	−	1.65750e29i	1.49046	−	0.637845i
$634$	−2.57810e27			−0.00975803
$635$	1.77754e29			0.661752
$636$	−4.65892e28	−	1.08866e29i	−0.170602	−	0.398649i
$637$	7.27412e28	−	8.36112e28i	0.262009	−	0.301162i
$638$			4.98112e29i			1.76486i
$639$	9.94608e28	+	9.49236e28i	0.346651	+	0.330838i
$640$		−	1.73734e29i		−	0.595654i
$641$		−	1.64616e29i		−	0.555218i	−0.960694	−	0.277609i	$-0.910458\pi$
$641$		−	1.64616e29i		−	0.555218i	0.960694	−	0.277609i	$-0.0895420\pi$
$642$	−1.79788e29	+	7.69406e28i	−0.596546	+	0.255292i
$643$		−	2.84507e29i		−	0.928705i	−0.885650	−	0.464353i	$-0.846287\pi$
$643$		−	2.84507e29i		−	0.928705i	0.885650	−	0.464353i	$-0.153713\pi$
$644$	3.78639e28	−	1.01210e29i	0.121597	−	0.325027i
$645$	9.21203e28	−	3.94230e28i	0.291057	−	0.124558i
$646$	1.80779e29			0.561962
$647$	−3.09210e29			−0.945713			−0.472856	−	0.881140i	$-0.656777\pi$
$647$	−3.09210e29			−0.945713			−0.472856	+	0.881140i	$0.656777\pi$
$648$	3.60704e29	−	1.68478e28i	1.08546	−	0.0506998i
$649$			1.91600e29i			0.567316i
$650$	1.74017e29			0.506994
$651$	1.85309e28	+	3.99313e29i	0.0531247	+	1.14476i
$652$	2.41150e28			0.0680280
$653$			1.03787e29i			0.288108i	0.989570	+	0.144054i	$0.0460139\pi$
$653$			1.03787e29i			0.288108i	−0.989570	+	0.144054i	$0.953986\pi$
$654$	−1.21558e29	−	2.84046e29i	−0.332060	−	0.775929i
$655$	−6.63434e29			−1.78346
$656$	2.46534e29			0.652208
$657$	2.38400e29	+	2.27525e29i	0.620683	+	0.592369i
$658$	−1.72317e29	+	4.60600e29i	−0.441526	+	1.18019i
$659$		−	6.06577e29i		−	1.52964i	−0.644244	−	0.764820i	$-0.722828\pi$
$659$		−	6.06577e29i		−	1.52964i	0.644244	−	0.764820i	$-0.277172\pi$
$660$	1.15359e29	+	2.69562e29i	0.286313	+	0.669032i
$661$			1.05277e29i			0.257170i	0.991699	+	0.128585i	$0.0410434\pi$
$661$			1.05277e29i			0.257170i	−0.991699	+	0.128585i	$0.958957\pi$
$662$			7.46806e28i			0.179556i
$663$	−8.95126e28	−	2.09165e29i	−0.211832	−	0.494992i
$664$		−	6.59421e29i		−	1.53602i
$665$	1.19205e29	−	3.18633e29i	0.273318	−	0.730572i
$666$	1.80822e29	+	1.72573e29i	0.408105	+	0.389488i
$667$	−7.09212e29			−1.57563
$668$	−3.15462e28			−0.0689913
$669$	−3.49139e29	−	8.15839e29i	−0.751665	−	1.75643i
$670$			6.57331e29i			1.39315i
$671$	3.87717e29			0.808962
$672$	1.24633e28	+	2.68565e29i	0.0256009	+	0.551661i
$673$	5.79956e28			0.117284			0.0586418	−	0.998279i	$-0.481323\pi$
$673$	5.79956e28			0.117284			0.0586418	+	0.998279i	$0.481323\pi$
$674$			4.41441e29i			0.878909i
$675$	−2.68440e29	+	7.18193e29i	−0.526209	+	1.40783i
$676$	1.24526e29			0.240336
$677$	−1.55680e29			−0.295837			−0.147919	−	0.989000i	$-0.547257\pi$
$677$	−1.55680e29			−0.295837			−0.147919	+	0.989000i	$0.547257\pi$
$678$	1.30154e29	−	5.56997e28i	0.243527	−	0.104218i
$679$	−1.75859e28	+	4.70068e28i	−0.0323991	+	0.0866020i
$680$		−	1.27821e30i		−	2.31877i
$681$	−1.62996e28	+	6.97544e27i	−0.0291161	+	0.0124603i
$682$			8.85798e29i			1.55811i
$683$			4.88251e29i			0.845718i	0.906196	+	0.422859i	$0.138973\pi$
$683$			4.88251e29i			0.845718i	−0.906196	+	0.422859i	$0.861027\pi$
$684$	5.97805e28	+	5.70534e28i	0.101969	+	0.0973178i
$685$			6.21094e29i			1.04329i
$686$	4.49082e29	−	2.43481e29i	0.742887	−	0.402774i
$687$	4.10508e29	+	9.59241e29i	0.668769	+	1.56272i
$688$	7.88719e28			0.126545
$689$	3.83162e29			0.605453
$690$	9.58670e29	−	4.10264e29i	1.49195	−	0.638481i
$691$		−	4.46432e29i		−	0.684283i	−0.939649	−	0.342141i	$-0.888848\pi$
$691$		−	4.46432e29i		−	0.684283i	0.939649	−	0.342141i	$-0.111152\pi$
$692$	1.81122e29			0.273437
$693$	4.71363e29	+	9.73952e29i	0.700901	+	1.44823i
$694$	−9.39630e29			−1.37620
$695$		−	1.48253e30i		−	2.13876i
$696$	9.12550e29	−	3.90527e29i	1.29676	−	0.554950i
$697$	9.93802e29			1.39109
$698$	2.94104e29			0.405526
$699$	−4.77100e29	−	1.11485e30i	−0.648036	−	1.51428i
$700$	−3.00770e29	−	1.12522e29i	−0.402443	−	0.150560i
$701$			1.85634e29i			0.244692i	0.992488	+	0.122346i	$0.0390417\pi$
$701$			1.85634e29i			0.244692i	−0.992488	+	0.122346i	$0.960958\pi$
$702$	−9.09503e28	+	2.43331e29i	−0.118104	+	0.315979i
$703$			2.57285e29i			0.329143i
$704$			1.40304e30i			1.76830i
$705$	1.74666e30	−	7.47487e29i	2.16882	−	0.928149i
$706$			2.41567e28i			0.0295521i
$707$	−9.24251e29	−	3.45775e29i	−1.11400	−	0.416764i
$708$	7.80408e28	−	3.33977e28i	0.0926771	−	0.0396613i
$709$	2.39282e28			0.0279978			0.0139989	−	0.999902i	$-0.495544\pi$
$709$	2.39282e28			0.0279978			0.0139989	+	0.999902i	$0.495544\pi$
$710$	−5.55683e29			−0.640641
$711$	−4.73854e28	+	4.96504e28i	−0.0538287	+	0.0564016i
$712$			2.38661e29i			0.267141i
$713$	−1.26120e30			−1.39105
$714$	−4.86153e28	−	1.04759e30i	−0.0528374	−	1.13857i
$715$	−9.48745e29			−1.01610
$716$		−	3.21159e29i		−	0.338949i
$717$	2.62663e28	+	6.13768e28i	0.0273179	+	0.0638342i
$718$	8.82487e29			0.904486
$719$	1.27733e30			1.29018			0.645091	−	0.764106i	$-0.276820\pi$
$719$	1.27733e30			1.29018			0.645091	+	0.764106i	$0.276820\pi$
$720$	−6.93908e29	+	7.27076e29i	−0.690734	+	0.723750i
$721$	2.45464e29	−	6.56120e29i	0.240806	−	0.643670i
$722$			6.61559e29i			0.639629i
$723$	−4.38874e28	−	1.02552e29i	−0.0418203	−	0.0977222i
$724$		−	5.20063e28i		−	0.0488428i
$725$			2.10760e30i			1.95092i
$726$	5.78920e29	+	1.35277e30i	0.528183	+	1.23421i
$727$		−	4.55339e29i		−	0.409472i	−0.978817	−	0.204736i	$-0.934366\pi$
$727$		−	4.55339e29i		−	0.409472i	0.978817	−	0.204736i	$-0.0656335\pi$
$728$	−4.58346e29	−	1.71474e29i	−0.406269	−	0.151991i
$729$	−8.63960e29	−	7.50729e29i	−0.754840	−	0.655909i
$730$	−1.33193e30			−1.14708
$731$	3.17940e29			0.269907
$732$	−6.75827e28	−	1.57922e29i	−0.0565548	−	0.132152i
$733$		−	1.30029e30i		−	1.07262i	−0.844020	−	0.536312i	$-0.819817\pi$
$733$		−	1.30029e30i		−	1.07262i	0.844020	−	0.536312i	$-0.180183\pi$
$734$	−3.10316e29			−0.252346
$735$	−1.87848e30	−	6.05087e29i	−1.50588	−	0.485066i
$736$	−8.48242e29			−0.670352
$737$		−	2.15196e30i		−	1.67658i
$738$	−8.20867e29	−	7.83421e29i	−0.630494	−	0.601732i
$739$	7.52338e27			0.00569700			0.00284850	−	0.999996i	$-0.499093\pi$
$739$	7.52338e27			0.00569700			0.00284850	+	0.999996i	$0.499093\pi$
$740$	4.04450e29			0.301948
$741$	−2.45825e29	+	1.05201e29i	−0.180940	+	0.0774336i
$742$	1.65419e30	+	6.18856e29i	1.20045	+	0.449106i
$743$			1.12099e30i			0.802086i	0.916059	+	0.401043i	$0.131352\pi$
$743$			1.12099e30i			0.802086i	−0.916059	+	0.401043i	$0.868648\pi$
$744$	1.62280e30	−	6.94478e29i	1.14485	−	0.489940i
$745$		−	2.50856e30i		−	1.74495i
$746$		−	5.34604e29i		−	0.366669i
$747$	−1.44307e30	+	1.51205e30i	−0.975936	+	1.02258i
$748$			9.30355e29i			0.620414i
$749$	−4.09165e29	+	1.09369e30i	−0.269054	+	0.719176i
$750$	−4.08003e29	−	9.53386e29i	−0.264557	−	0.618195i
$751$	6.89593e29			0.440934			0.220467	−	0.975394i	$-0.429242\pi$
$751$	6.89593e29			0.440934			0.220467	+	0.975394i	$0.429242\pi$
$752$	1.49546e30			0.942950
$753$	7.14630e29	−	3.05827e29i	0.444359	−	0.190164i
$754$			7.14078e29i			0.437871i
$755$	−1.60254e30			−0.969094
$756$	3.14539e29	−	3.61761e29i	0.187584	−	0.215746i
$757$	3.24718e30			1.90985			0.954926	−	0.296844i	$-0.0959343\pi$
$757$	3.24718e30			1.90985			0.954926	+	0.296844i	$0.0959343\pi$
$758$			1.19564e30i			0.693542i
$759$	−3.13848e30	+	1.34312e30i	−1.79548	+	0.768378i
$760$	−1.50223e30			−0.847607
$761$	−2.08186e30			−1.15855			−0.579273	−	0.815133i	$-0.696664\pi$
$761$	−2.08186e30			−1.15855			−0.579273	+	0.815133i	$0.696664\pi$
$762$	−2.53369e29	−	5.92050e29i	−0.139068	−	0.324961i
$763$	−1.72791e30	−	6.46436e29i	−0.935435	−	0.349959i
$764$			2.92911e29i			0.156407i
$765$	−2.79721e30	+	2.93091e30i	−1.47326	+	1.54368i
$766$		−	1.93454e30i		−	1.00502i
$767$			2.74671e29i			0.140754i
$768$	1.42025e30	−	6.07800e29i	0.717916	−	0.307233i
$769$			2.15347e30i			1.07377i	0.843654	+	0.536887i	$0.180400\pi$
$769$			2.15347e30i			1.07377i	−0.843654	+	0.536887i	$0.819600\pi$
$770$	−4.09593e30	−	1.53235e30i	−2.01465	−	0.753710i
$771$	−1.42888e30	+	6.11492e29i	−0.693306	+	0.296701i
$772$	5.02862e29			0.240695
$773$	3.12807e30			1.47704			0.738519	−	0.674232i	$-0.235525\pi$
$773$	3.12807e30			1.47704			0.738519	+	0.674232i	$0.235525\pi$
$774$	−2.62615e29	−	2.50635e29i	−0.122332	−	0.116751i
$775$			3.74797e30i			1.72238i
$776$	2.21619e29			0.100475
$777$	1.49093e30	−	6.91894e28i	0.666862	−	0.0309470i
$778$	5.82567e29			0.257075
$779$		−	1.16798e30i		−	0.508502i
$780$	1.65375e29	+	3.86435e29i	0.0710358	+	0.165990i
$781$	1.81919e30			0.770977
$782$	3.30872e30			1.38353
$783$	−2.94709e30	−	1.10154e30i	−1.21589	−	0.454467i
$784$	−1.17198e30	−	1.01962e30i	−0.477091	−	0.415067i
$785$			3.11734e30i			1.25214i
$786$	9.45653e29	+	2.20972e30i	0.374796	+	0.875792i
$787$			5.46046e29i			0.213548i	0.994283	+	0.106774i	$0.0340521\pi$
$787$			5.46046e29i			0.213548i	−0.994283	+	0.106774i	$0.965948\pi$
$788$		−	6.83766e29i		−	0.263865i
$789$	1.19123e30	+	2.78357e30i	0.453616	+	1.05997i
$790$		−	2.77395e29i		−	0.104235i
$791$	2.96207e29	−	7.91755e29i	0.109835	−	0.293588i
$792$	3.29873e30	−	3.45640e30i	1.20707	−	1.26477i
$793$	5.55818e29			0.200708
$794$	3.92858e30			1.39998
$795$	−2.68451e30	−	6.27294e30i	−0.944084	−	2.20605i
$796$		−	3.30085e29i		−	0.114561i
$797$	−4.55179e30			−1.55909			−0.779543	−	0.626349i	$-0.784548\pi$
$797$	−4.55179e30			−1.55909			−0.779543	+	0.626349i	$0.784548\pi$
$798$	−1.23119e30	+	5.71359e28i	−0.416194	+	0.0193143i
$799$	6.02837e30			2.01122
$800$			2.52076e30i			0.830018i
$801$	5.22282e29	−	5.47247e29i	0.169732	−	0.177845i
$802$	−3.02156e30			−0.969172
$803$	4.36046e30			1.38044
$804$	−8.76519e29	+	3.75107e29i	−0.273888	+	0.117211i
$805$	2.18176e30	−	5.83179e30i	0.672899	−	1.79864i
$806$			1.26985e30i			0.386576i
$807$	−2.01310e30	+	8.61509e29i	−0.604914	+	0.258874i
$808$			4.35749e30i			1.29246i
$809$			4.76054e30i			1.39379i	0.717174	+	0.696894i	$0.245435\pi$
$809$			4.76054e30i			1.39379i	−0.717174	+	0.696894i	$0.754565\pi$
$810$	4.62092e30	−	2.15835e29i	1.33548	−	0.0623776i
$811$		−	6.56149e30i		−	1.87191i	−0.352126	−	0.935953i	$-0.614541\pi$
$811$		−	6.56149e30i		−	1.87191i	0.352126	−	0.935953i	$-0.385459\pi$
$812$	4.61733e29	−	1.23420e30i	0.130033	−	0.347575i
$813$	−1.26772e30	−	2.96230e30i	−0.352429	−	0.823527i
$814$	3.30733e30			0.907656
$815$	1.38953e30			0.376455
$816$	−2.93188e30	+	1.25470e30i	−0.784150	+	0.335578i
$817$		−	3.73665e29i		−	0.0986622i
$818$	−1.74929e29			−0.0455986
$819$	6.75732e29	+	1.39623e30i	0.173897	+	0.359315i
$820$	−1.83606e30			−0.466488
$821$		−	6.17237e30i		−	1.54828i	−0.633016	−	0.774139i	$-0.718183\pi$
$821$		−	6.17237e30i		−	1.54828i	0.633016	−	0.774139i	$-0.281817\pi$
$822$	2.06870e30	−	8.85301e29i	0.512321	−	0.219249i
$823$	1.36233e30			0.333107			0.166553	−	0.986032i	$-0.446736\pi$
$823$	1.36233e30			0.333107			0.166553	+	0.986032i	$0.446736\pi$
$824$	−3.09336e30			−0.746784
$825$	3.99141e30	+	9.32679e30i	0.951393	+	2.22313i
$826$	−4.43630e29	+	1.18581e30i	−0.104407	+	0.279078i
$827$		−	7.42719e29i		−	0.172590i	−0.996270	−	0.0862952i	$-0.972497\pi$
$827$		−	7.42719e29i		−	0.172590i	0.996270	−	0.0862952i	$-0.0275028\pi$
$828$	1.09413e30	+	1.04422e30i	0.251045	+	0.239593i
$829$			3.07527e30i			0.696725i	0.937360	+	0.348362i	$0.113262\pi$
$829$			3.07527e30i			0.696725i	−0.937360	+	0.348362i	$0.886738\pi$
$830$		−	8.44774e30i		−	1.88982i
$831$	5.14407e30	−	2.20141e30i	1.13631	−	0.486284i
$832$			2.01135e30i			0.438725i
$833$	−4.72437e30	−	4.11018e30i	−1.01759	−	0.885295i
$834$	−4.93790e30	+	2.11318e30i	−1.05026	+	0.449462i
$835$	−1.81772e30			−0.381786
$836$	1.09341e30			0.226787
$837$	−5.24085e30	−	1.95888e30i	−1.07346	−	0.401228i
$838$		−	1.85744e30i		−	0.375710i
$839$	−7.06842e29			−0.141196			−0.0705979	−	0.997505i	$-0.522491\pi$
$839$	−7.06842e29			−0.141196			−0.0705979	+	0.997505i	$0.522491\pi$
$840$	4.03982e29	+	8.70520e30i	0.0796947	+	1.71730i
$841$	−3.51567e30			−0.684937
$842$		−	6.33094e29i		−	0.121812i
$843$	−6.11663e28	−	1.42928e29i	−0.0116231	−	0.0271599i
$844$	−2.46966e30			−0.463491
$845$	7.17528e30			1.32998
$846$	−4.97935e30	−	4.75220e30i	−0.911558	−	0.869974i
$847$	8.22920e30	+	3.07866e30i	1.48793	+	0.556655i
$848$		−	5.37079e30i		−	0.959139i
$849$	1.00084e30	+	2.33868e30i	0.176536	+	0.412515i
$850$		−	9.83269e30i		−	1.71306i
$851$			4.70898e30i			0.810338i
$852$	−3.17102e29	−	7.40977e29i	−0.0538993	−	0.125947i
$853$			6.72774e30i			1.12955i	0.825246	+	0.564774i	$0.191037\pi$
$853$			6.72774e30i			1.12955i	−0.825246	+	0.564774i	$0.808963\pi$
$854$	2.39959e30	+	8.97720e29i	0.397950	+	0.148879i
$855$	3.44461e30	+	3.28747e30i	0.564281	+	0.538540i
$856$	5.15633e30			0.834385
$857$	−3.33984e30			−0.533860			−0.266930	−	0.963716i	$-0.586009\pi$
$857$	−3.33984e30			−0.533860			−0.266930	+	0.963716i	$0.586009\pi$
$858$	1.35233e30	+	3.16001e30i	0.213534	+	0.498967i
$859$			8.26887e30i			1.28979i	0.764273	+	0.644893i	$0.223098\pi$
$859$			8.26887e30i			1.28979i	−0.764273	+	0.644893i	$0.776902\pi$
$860$	−5.87398e29			−0.0905104
$861$	−6.76827e30	+	3.14095e29i	−1.03025	+	0.0478110i
$862$	−2.37111e30			−0.356554
$863$			5.44686e30i			0.809157i	0.914503	+	0.404578i	$0.132582\pi$
$863$			5.44686e30i			0.809157i	−0.914503	+	0.404578i	$0.867418\pi$
$864$	−3.52482e30	−	1.31748e30i	−0.517301	−	0.193352i
$865$	1.04364e31			1.51315
$866$	−4.53363e30			−0.649393
$867$	−5.32216e30	+	2.27762e30i	−0.753160	+	0.322316i
$868$	8.21105e29	−	2.19480e30i	0.114800	−	0.306858i
$869$			9.08130e29i			0.125441i
$870$	1.16905e31	−	5.00298e30i	1.59545	−	0.682773i
$871$		−	3.08498e30i		−	0.415970i
$872$			8.14644e30i			1.08529i
$873$	−5.08171e29	−	4.84989e29i	−0.0668899	−	0.0638385i
$874$		−	3.88863e30i		−	0.505739i
$875$	−5.79965e30	−	2.16973e30i	−0.745276	−	0.278818i
$876$	−7.60070e29	−	1.77607e30i	−0.0965073	−	0.225510i
$877$	−5.45253e30			−0.684073			−0.342036	−	0.939687i	$-0.611117\pi$
$877$	−5.45253e30			−0.684073			−0.342036	+	0.939687i	$0.611117\pi$
$878$	2.96466e30			0.367521
$879$	1.37169e31	−	5.87016e30i	1.68025	−	0.719063i
$880$			1.32986e31i			1.60967i
$881$	4.32410e30			0.517189			0.258594	−	0.965986i	$-0.416741\pi$
$881$	4.32410e30			0.517189			0.258594	+	0.965986i	$0.416741\pi$
$882$	6.62187e29	+	7.11921e30i	0.0782638	+	0.841417i
$883$	−1.51091e31			−1.76463			−0.882313	−	0.470663i	$-0.844015\pi$
$883$	−1.51091e31			−1.76463			−0.882313	+	0.470663i	$0.844015\pi$
$884$			1.33373e30i			0.153928i
$885$	4.49679e30	−	1.92440e30i	0.512859	−	0.219479i
$886$	−5.96937e30			−0.672782
$887$	4.54938e30			0.506704			0.253352	−	0.967374i	$-0.418467\pi$
$887$	4.54938e30			0.506704			0.253352	+	0.967374i	$0.418467\pi$
$888$	−2.59299e30	−	6.05909e30i	−0.285407	−	0.666916i
$889$	−3.60157e30	−	1.34740e30i	−0.391763	−	0.146564i
$890$			3.05744e30i			0.328673i
$891$	−1.51279e31	+	7.06597e29i	−1.60717	+	0.0750682i
$892$			5.20214e30i			0.546199i
$893$		−	7.08494e30i		−	0.735184i
$894$	−8.35533e30	+	3.57567e30i	−0.856879	+	0.366702i
$895$		−	1.85055e31i		−	1.87568i
$896$	−1.31692e30	+	3.52011e30i	−0.131925	+	0.352632i
$897$	−4.49923e30	+	1.92545e30i	−0.445469	+	0.190639i
$898$	−1.53132e31			−1.49853
$899$	−1.53797e31			−1.48755
$900$	3.10317e30	−	3.25150e30i	0.296660	−	0.310840i
$901$		−	2.16502e31i		−	2.04574i
$902$	−1.50141e31			−1.40226
$903$	−2.16533e30	+	1.00486e29i	−0.199895	+	0.00927653i
$904$	−3.73283e30			−0.340619
$905$		−	2.99665e30i		−	0.270288i
$906$	2.28424e30	+	5.33763e30i	0.203656	+	0.475885i
$907$	8.51973e29			0.0750844			0.0375422	−	0.999295i	$-0.488047\pi$
$907$	8.51973e29			0.0750844			0.0375422	+	0.999295i	$0.488047\pi$
$908$	1.03933e29			0.00905427
$909$	9.53589e30	−	9.99169e30i	0.821184	−	0.860435i
$910$	−5.87180e30	−	2.19672e30i	−0.499846	−	0.187000i
$911$		−	1.49202e31i		−	1.25554i	−0.778397	−	0.627772i	$-0.783967\pi$
$911$		−	1.49202e31i		−	1.25554i	0.778397	−	0.627772i	$-0.216033\pi$
$912$	1.47461e30	+	3.44574e30i	0.122668	+	0.286640i
$913$			2.76561e31i			2.27430i
$914$			4.72358e30i			0.384004i
$915$	−3.89418e30	−	9.09959e30i	−0.312964	−	0.731308i
$916$		−	6.11652e30i		−	0.485962i
$917$	1.34422e31	+	5.02892e30i	1.05583	+	0.394999i
$918$	1.37492e31	+	5.13906e30i	1.06765	+	0.399058i
$919$	1.75641e31			1.34838			0.674191	−	0.738557i	$-0.264492\pi$
$919$	1.75641e31			1.34838			0.674191	+	0.738557i	$0.264492\pi$
$920$	−2.74947e31			−2.08678
$921$	−5.17744e30	−	1.20982e31i	−0.388498	−	0.907809i
$922$			1.40640e31i			1.04336i
$923$	2.60793e30			0.191284
$924$	−2.94042e29	−	6.33617e30i	−0.0213233	−	0.459485i
$925$	1.39939e31			1.00335
$926$		−	1.19100e31i		−	0.844298i
$927$	7.09305e30	+	6.76948e30i	0.497159	+	0.474480i
$928$	−1.03439e31			−0.716855
$929$	2.32430e31			1.59267			0.796337	−	0.604854i	$-0.206768\pi$
$929$	2.32430e31			1.59267			0.796337	+	0.604854i	$0.206768\pi$
$930$	2.07894e31	−	8.89685e30i	1.40855	−	0.602789i
$931$	−4.83055e30	+	5.55240e30i	−0.323612	+	0.371971i
$932$			7.10874e30i			0.470896i
$933$	1.44222e31	−	6.17199e30i	0.944656	−	0.404267i
$934$		−	1.89310e31i		−	1.22612i
$935$			5.36079e31i			3.43326i
$936$	4.72895e30	−	4.95499e30i	0.299480	−	0.313795i
$937$			9.60967e30i			0.601787i	0.953658	+	0.300894i	$0.0972849\pi$
$937$			9.60967e30i			0.601787i	−0.953658	+	0.300894i	$0.902715\pi$
$938$	4.98265e30	−	1.33185e31i	0.308554	−	0.824757i
$939$	2.71715e30	+	6.34922e30i	0.166389	+	0.388805i
$940$	−1.11375e31			−0.674441
$941$	2.22360e31			1.33157			0.665787	−	0.746142i	$-0.268096\pi$
$941$	2.22360e31			1.33157			0.665787	+	0.746142i	$0.268096\pi$
$942$	1.03830e31	−	4.44342e30i	0.614877	−	0.263137i
$943$		−	2.13771e31i		−	1.25192i
$944$	3.85007e30			0.222979
$945$	1.81240e31	−	2.08450e31i	1.03806	−	1.19390i
$946$	−4.80336e30			−0.272074
$947$			1.97635e30i			0.110710i	0.998467	+	0.0553552i	$0.0176291\pi$
$947$			1.97635e30i			0.110710i	−0.998467	+	0.0553552i	$0.982371\pi$
$948$	3.69892e29	−	1.58296e29i	0.0204922	−	0.00876964i
$949$	6.25102e30			0.342496
$950$	−1.15560e31			−0.626197
$951$	−8.47718e28	−	1.98088e29i	−0.00454314	−	0.0106160i
$952$	−9.68896e30	+	2.58984e31i	−0.513558	+	1.37273i
$953$			1.62170e31i			0.850148i	0.905159	+	0.425074i	$0.139752\pi$
$953$			1.62170e31i			0.850148i	−0.905159	+	0.425074i	$0.860248\pi$
$954$	−1.70670e31	+	1.78828e31i	−0.884910	+	0.927207i
$955$			1.68778e31i			0.865528i
$956$		−	3.91364e29i		−	0.0198506i
$957$	−3.82723e31	+	1.63787e31i	−1.92004	+	0.821682i
$958$			2.14914e31i			1.06641i
$959$	4.70797e30	−	1.25843e31i	0.231067	−	0.617638i
$960$	3.29289e31	−	1.40919e31i	1.59856	−	0.684105i
$961$	−6.52446e30			−0.313292
$962$	4.74128e30			0.225194
$963$	−1.18234e31	−	1.12841e31i	−0.555479	−	0.530139i
$964$			6.53917e29i			0.0303888i
$965$	2.89754e31			1.33196
$966$	−2.25340e31	+	1.04573e30i	−1.02466	+	0.0475511i
$967$	8.22436e30			0.369934			0.184967	−	0.982745i	$-0.440782\pi$
$967$	8.22436e30			0.369934			0.184967	+	0.982745i	$0.440782\pi$
$968$		−	3.87976e31i		−	1.72629i
$969$	5.94429e30	+	1.38901e31i	0.261638	+	0.611373i
$970$	2.83913e30			0.123618
$971$	5.95372e30			0.256440			0.128220	−	0.991746i	$-0.459074\pi$
$971$	5.95372e30			0.256440			0.128220	+	0.991746i	$0.459074\pi$
$972$	2.92474e30	+	6.03861e30i	0.124621	+	0.257301i
$973$	−1.12377e31	+	3.00383e31i	−0.473690	+	1.26616i
$974$			1.52600e31i			0.636333i
$975$	5.72196e30	+	1.33706e31i	0.236046	+	0.551572i
$976$		−	7.79092e30i		−	0.317955i
$977$		−	2.19800e31i		−	0.887430i	−0.896168	−	0.443715i	$-0.853660\pi$
$977$		−	2.19800e31i		−	0.887430i	0.896168	−	0.443715i	$-0.146340\pi$
$978$	−1.98062e30	−	4.62815e30i	−0.0791122	−	0.184863i
$979$		−	1.00094e31i		−	0.395540i
$980$	8.72832e30	+	7.59359e30i	0.341237	+	0.296875i
$981$	1.78276e31	−	1.86797e31i	0.689554	−	0.722513i
$982$	−2.21248e31			−0.846658
$983$	−2.71245e31			−1.02695			−0.513476	−	0.858104i	$-0.671642\pi$
$983$	−2.71245e31			−1.02695			−0.513476	+	0.858104i	$0.671642\pi$
$984$	1.17712e31	+	2.75061e31i	0.440934	+	1.03034i
$985$		−	3.93993e31i		−	1.46018i
$986$	4.03483e31			1.47951
$987$	−4.10561e31	+	1.90529e30i	−1.48952	+	0.0691243i
$988$	1.56748e30			0.0562672
$989$		−	6.83902e30i		−	0.242903i
$990$	4.22595e31	−	4.42794e31i	1.48510	−	1.55608i
$991$	3.07076e30			0.106776			0.0533879	−	0.998574i	$-0.482998\pi$
$991$	3.07076e30			0.106776			0.0533879	+	0.998574i	$0.482998\pi$
$992$	−1.83947e31			−0.632878
$993$	−5.73806e30	+	2.45561e30i	−0.195343	+	0.0835973i
$994$	1.12590e31	+	4.21215e30i	0.379265	+	0.141888i
$995$		−	1.90198e31i		−	0.633962i
$996$	1.12647e31	−	4.82072e30i	0.371531	−	0.158997i
$997$			8.82897e30i			0.288145i	0.989567	+	0.144073i	$0.0460199\pi$
$997$			8.82897e30i			0.288145i	−0.989567	+	0.144073i	$0.953980\pi$
$998$		−	1.83852e31i		−	0.593741i
$999$	−7.31393e30	+	1.95679e31i	−0.233729	+	0.625327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.22.c.b.20.2	yes	52
3.2	odd	2	inner	21.22.c.b.20.51	yes	52
7.6	odd	2	inner	21.22.c.b.20.52	yes	52
21.20	even	2	inner	21.22.c.b.20.1	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.22.c.b.20.1	✓	52	21.20	even	2	inner
21.22.c.b.20.2	yes	52	1.1	even	1	trivial
21.22.c.b.20.51	yes	52	3.2	odd	2	inner
21.22.c.b.20.52	yes	52	7.6	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)

\(f(q)\)	\(=\)	\(q+1223.76i q^{2} +(-94027.5 + 40239.2i) q^{3} +599559. q^{4} +3.45471e7 q^{5} +(-4.92432e7 - 1.15067e8i) q^{6} +(-6.99978e8 - 2.61872e8i) q^{7} +3.30013e9i q^{8} +(7.22197e9 - 7.56717e9i) q^{9} +O(q^{10})\)	\(q+1223.76i q^{2} +(-94027.5 + 40239.2i) q^{3} +599559. q^{4} +3.45471e7 q^{5} +(-4.92432e7 - 1.15067e8i) q^{6} +(-6.99978e8 - 2.61872e8i) q^{7} +3.30013e9i q^{8} +(7.22197e9 - 7.56717e9i) q^{9} +4.22775e10i q^{10} -1.38407e11i q^{11} +(-5.63750e10 + 2.41257e10i) q^{12} -1.98416e11i q^{13} +(3.20469e11 - 8.56606e11i) q^{14} +(-3.24838e12 + 1.39015e12i) q^{15} -2.78121e12 q^{16} -1.12113e13 q^{17} +(9.26042e12 + 8.83798e12i) q^{18} +1.31763e13i q^{19} +2.07130e13 q^{20} +(7.63546e13 - 3.54339e12i) q^{21} +1.69378e14 q^{22} +2.41160e14i q^{23} +(-1.32795e14 - 3.10303e14i) q^{24} +7.16668e14 q^{25} +2.42815e14 q^{26} +(-3.74567e14 + 1.00213e15i) q^{27} +(-4.19678e14 - 1.57008e14i) q^{28} +2.94084e15i q^{29} +(-1.70121e15 - 3.97524e15i) q^{30} +5.22972e15i q^{31} +3.51734e15i q^{32} +(5.56940e15 + 1.30141e16i) q^{33} -1.37200e16i q^{34} +(-2.41822e16 - 9.04692e15i) q^{35} +(4.33000e15 - 4.53696e15i) q^{36} +1.95264e16 q^{37} -1.61247e16 q^{38} +(7.98411e15 + 1.86566e16i) q^{39} +1.14010e17i q^{40} -8.86426e16 q^{41} +(4.33626e15 + 9.34399e16i) q^{42} -2.83588e16 q^{43} -8.29834e16i q^{44} +(2.49499e17 - 2.61424e17i) q^{45} -2.95123e17 q^{46} -5.37703e17 q^{47} +(2.61510e17 - 1.11914e17i) q^{48} +(4.21392e17 + 3.66609e17i) q^{49} +8.77031e17i q^{50} +(1.05417e18 - 4.51135e17i) q^{51} -1.18962e17i q^{52} +1.93110e18i q^{53} +(-1.22637e18 - 4.58381e17i) q^{54} -4.78158e18i q^{55} +(8.64211e17 - 2.31002e18i) q^{56} +(-5.30204e17 - 1.23894e18i) q^{57} -3.59888e18 q^{58} -1.38432e18 q^{59} +(-1.94759e18 + 8.33475e17i) q^{60} +2.80127e18i q^{61} -6.39993e18 q^{62} +(-7.03685e18 + 3.40562e18i) q^{63} -1.01370e19 q^{64} -6.85472e18i q^{65} +(-1.59262e19 + 6.81562e18i) q^{66} +1.55480e19 q^{67} -6.72185e18 q^{68} +(-9.70408e18 - 2.26757e19i) q^{69} +(1.10713e19 - 2.95933e19i) q^{70} +1.31437e19i q^{71} +(2.49727e19 + 2.38335e19i) q^{72} +3.15045e19i q^{73} +2.38956e19i q^{74} +(-6.73865e19 + 2.88381e19i) q^{75} +7.89997e18i q^{76} +(-3.62450e19 + 9.68821e19i) q^{77} +(-2.28312e19 + 9.77065e18i) q^{78} -6.56128e18 q^{79} -9.60829e19 q^{80} +(-5.10520e18 - 1.09300e20i) q^{81} -1.08477e20i q^{82} -1.99817e20 q^{83} +(4.57791e19 - 2.12447e18i) q^{84} -3.87320e20 q^{85} -3.47045e19i q^{86} +(-1.18337e20 - 2.76519e20i) q^{87} +4.56763e20 q^{88} +7.23185e19 q^{89} +(3.19921e20 + 3.05327e20i) q^{90} +(-5.19597e19 + 1.38887e20i) q^{91} +1.44590e20i q^{92} +(-2.10440e20 - 4.91737e20i) q^{93} -6.58020e20i q^{94} +4.55204e20i q^{95} +(-1.41535e20 - 3.30726e20i) q^{96} -6.71547e19i q^{97} +(-4.48642e20 + 5.15684e20i) q^{98} +(-1.04735e21 - 9.99575e20i) 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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