LMFDB - Embedded newform 21.22.c.b.20.12

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			20.12
Character	$\chi$	$=$	21.20
Dual form			21.22.c.b.20.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1704.62i q^{2} +(-65800.8 + 78298.2i) q^{3} -808569. q^{4} -2.49846e7 q^{5} +(-1.33469e8 - 1.12165e8i) q^{6} +(7.21028e7 - 7.43873e8i) q^{7} +2.19654e9i q^{8} +(-1.80087e9 - 1.03042e10i) q^{9} +O(q^{10})$	\(q+1704.62i q^{2} +(-65800.8 + 78298.2i) q^{3} -808569. q^{4} -2.49846e7 q^{5} +(-1.33469e8 - 1.12165e8i) q^{6} +(7.21028e7 - 7.43873e8i) q^{7} +2.19654e9i q^{8} +(-1.80087e9 - 1.03042e10i) q^{9} -4.25893e10i q^{10} +5.38334e10i q^{11} +(5.32045e10 - 6.33095e10i) q^{12} -8.15234e11i q^{13} +(1.26802e12 + 1.22908e11i) q^{14} +(1.64401e12 - 1.95625e12i) q^{15} -5.43995e12 q^{16} +7.14032e12 q^{17} +(1.75647e13 - 3.06979e12i) q^{18} +2.64515e13i q^{19} +2.02018e13 q^{20} +(5.34995e13 + 5.45929e13i) q^{21} -9.17654e13 q^{22} -9.27517e13i q^{23} +(-1.71985e14 - 1.44534e14i) q^{24} +1.47395e14 q^{25} +1.38966e15 q^{26} +(9.25296e14 + 5.37017e14i) q^{27} +(-5.83001e13 + 6.01473e14i) q^{28} +2.96948e15i q^{29} +(3.33466e15 + 2.80241e15i) q^{30} -4.95268e15i q^{31} -4.66656e15i q^{32} +(-4.21506e15 - 3.54228e15i) q^{33} +1.21715e16i q^{34} +(-1.80146e15 + 1.85854e16i) q^{35} +(1.45613e15 + 8.33163e15i) q^{36} +3.48905e16 q^{37} -4.50897e16 q^{38} +(6.38314e16 + 5.36430e16i) q^{39} -5.48798e16i q^{40} +8.41304e15 q^{41} +(-9.30601e16 + 9.11962e16i) q^{42} -7.53851e15 q^{43} -4.35281e16i q^{44} +(4.49940e16 + 2.57446e17i) q^{45} +1.58106e17 q^{46} +2.39922e17 q^{47} +(3.57953e17 - 4.25939e17i) q^{48} +(-5.48148e17 - 1.07271e17i) q^{49} +2.51253e17i q^{50} +(-4.69838e17 + 5.59074e17i) q^{51} +6.59173e17i q^{52} -1.77085e18i q^{53} +(-9.15409e17 + 1.57728e18i) q^{54} -1.34501e18i q^{55} +(1.63395e18 + 1.58377e17i) q^{56} +(-2.07111e18 - 1.74053e18i) q^{57} -5.06183e18 q^{58} -6.53938e18 q^{59} +(-1.32929e18 + 1.58177e18i) q^{60} -4.21755e17i q^{61} +8.44243e18 q^{62} +(-7.79484e18 + 5.96658e17i) q^{63} -3.45371e18 q^{64} +2.03683e19i q^{65} +(6.03824e18 - 7.18507e18i) q^{66} -1.30627e19 q^{67} -5.77344e18 q^{68} +(7.26229e18 + 6.10313e18i) q^{69} +(-3.16810e19 - 3.07081e18i) q^{70} +3.56914e19i q^{71} +(2.26335e19 - 3.95568e18i) q^{72} +3.10669e19i q^{73} +5.94750e19i q^{74} +(-9.69872e18 + 1.15408e19i) q^{75} -2.13879e19i q^{76} +(4.00452e19 + 3.88154e18i) q^{77} +(-9.14408e19 + 1.08808e20i) q^{78} +1.16544e20 q^{79} +1.35915e20 q^{80} +(-1.02933e20 + 3.71129e19i) q^{81} +1.43410e19i q^{82} -1.17516e19 q^{83} +(-4.32580e19 - 4.41422e19i) q^{84} -1.78398e20 q^{85} -1.28503e19i q^{86} +(-2.32505e20 - 1.95394e20i) q^{87} -1.18247e20 q^{88} -8.40556e19 q^{89} +(-4.38847e20 + 7.66976e19i) q^{90} +(-6.06430e20 - 5.87807e19i) q^{91} +7.49961e19i q^{92} +(3.87786e20 + 3.25890e20i) q^{93} +4.08975e20i q^{94} -6.60882e20i q^{95} +(3.65383e20 + 3.07063e20i) q^{96} +4.28920e20i q^{97} +(1.82856e20 - 9.34383e20i) q^{98} +(5.54709e20 - 9.69469e19i) 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 $

$2$			1704.62i			1.17710i	0.808462	+	0.588548i	$0.200300\pi$
$2$			1704.62i			1.17710i	−0.808462	+	0.588548i	$0.799700\pi$
$3$	−65800.8	+	78298.2i	−0.643366	+	0.765559i
$3$	−65800.8	+	78298.2i	−0.643366	+	0.765559i
$4$	−808569.			−0.385556
$5$	−2.49846e7			−1.14416			−0.572082	−	0.820197i	$-0.693864\pi$
$5$	−2.49846e7			−1.14416			−0.572082	+	0.820197i	$0.693864\pi$
$6$	−1.33469e8	−	1.12165e8i	−0.901137	−	0.757303i
$7$	7.21028e7	−	7.43873e8i	0.0964768	−	0.995335i
$7$	7.21028e7	−	7.43873e8i	0.0964768	−	0.995335i
$8$			2.19654e9i			0.723260i
$9$	−1.80087e9	−	1.03042e10i	−0.172161	−	0.985069i
$10$		−	4.25893e10i		−	1.34679i
$11$			5.38334e10i			0.625790i	0.949788	+	0.312895i	$0.101299\pi$
$11$			5.38334e10i			0.625790i	−0.949788	+	0.312895i	$0.898701\pi$
$12$	5.32045e10	−	6.33095e10i	0.248053	−	0.295166i
$13$		−	8.15234e11i		−	1.64013i	−0.572274	−	0.820063i	$-0.693939\pi$
$13$		−	8.15234e11i		−	1.64013i	0.572274	−	0.820063i	$-0.306061\pi$
$14$	1.26802e12	+	1.22908e11i	1.17161	+	0.113562i
$15$	1.64401e12	−	1.95625e12i	0.736116	−	0.875925i
$16$	−5.43995e12			−1.23690
$17$	7.14032e12			0.859021			0.429510	−	0.903062i	$-0.358686\pi$
$17$	7.14032e12			0.859021			0.429510	+	0.903062i	$0.358686\pi$
$18$	1.75647e13	−	3.06979e12i	1.15952	−	0.202650i
$19$			2.64515e13i			0.989778i	0.868956	+	0.494889i	$0.164791\pi$
$19$			2.64515e13i			0.989778i	−0.868956	+	0.494889i	$0.835209\pi$
$20$	2.02018e13			0.441139
$21$	5.34995e13	+	5.45929e13i	0.699918	+	0.714223i
$22$	−9.17654e13			−0.736616
$23$		−	9.27517e13i		−	0.466852i	−0.972375	−	0.233426i	$-0.925006\pi$
$23$		−	9.27517e13i		−	0.466852i	0.972375	−	0.233426i	$-0.0749937\pi$
$24$	−1.71985e14	−	1.44534e14i	−0.553698	−	0.465321i
$25$	1.47395e14			0.309110
$26$	1.38966e15			1.93059
$27$	9.25296e14	+	5.37017e14i	0.864891	+	0.501960i
$28$	−5.83001e13	+	6.01473e14i	−0.0371972	+	0.383757i
$29$			2.96948e15i			1.31069i	0.755328	+	0.655347i	$0.227478\pi$
$29$			2.96948e15i			1.31069i	−0.755328	+	0.655347i	$0.772522\pi$
$30$	3.33466e15	+	2.80241e15i	1.03105	+	0.866479i
$31$		−	4.95268e15i		−	1.08528i	−0.839965	−	0.542641i	$-0.817424\pi$
$31$		−	4.95268e15i		−	1.08528i	0.839965	−	0.542641i	$-0.182576\pi$
$32$		−	4.66656e15i		−	0.732693i
$33$	−4.21506e15	−	3.54228e15i	−0.479080	−	0.402612i
$34$			1.21715e16i			1.01115i
$35$	−1.80146e15	+	1.85854e16i	−0.110385	+	1.13883i
$36$	1.45613e15	+	8.33163e15i	0.0663778	+	0.379799i
$37$	3.48905e16			1.19286			0.596430	−	0.802665i	$-0.296585\pi$
$37$	3.48905e16			1.19286			0.596430	+	0.802665i	$0.296585\pi$
$38$	−4.50897e16			−1.16506
$39$	6.38314e16	+	5.36430e16i	1.25561	+	1.05520i
$40$		−	5.48798e16i		−	0.827528i
$41$	8.41304e15			0.0978864			0.0489432	−	0.998802i	$-0.484415\pi$
$41$	8.41304e15			0.0978864			0.0489432	+	0.998802i	$0.484415\pi$
$42$	−9.30601e16	+	9.11962e16i	−0.840709	+	0.823871i
$43$	−7.53851e15			−0.0531945			−0.0265973	−	0.999646i	$-0.508467\pi$
$43$	−7.53851e15			−0.0531945			−0.0265973	+	0.999646i	$0.508467\pi$
$44$		−	4.35281e16i		−	0.241277i
$45$	4.49940e16	+	2.57446e17i	0.196981	+	1.12708i
$46$	1.58106e17			0.549530
$47$	2.39922e17			0.665337			0.332669	−	0.943044i	$-0.392051\pi$
$47$	2.39922e17			0.665337			0.332669	+	0.943044i	$0.392051\pi$
$48$	3.57953e17	−	4.25939e17i	0.795781	−	0.946922i
$49$	−5.48148e17	−	1.07271e17i	−0.981384	−	0.192054i
$50$			2.51253e17i			0.363853i
$51$	−4.69838e17	+	5.59074e17i	−0.552665	+	0.657631i
$52$			6.59173e17i			0.632360i
$53$		−	1.77085e18i		−	1.39086i	−0.718592	−	0.695432i	$-0.755213\pi$
$53$		−	1.77085e18i		−	1.39086i	0.718592	−	0.695432i	$-0.244787\pi$
$54$	−9.15409e17	+	1.57728e18i	−0.590855	+	1.01806i
$55$		−	1.34501e18i		−	0.716007i
$56$	1.63395e18	+	1.58377e17i	0.719886	+	0.0697778i
$57$	−2.07111e18	−	1.74053e18i	−0.757733	−	0.636789i
$58$	−5.06183e18			−1.54281
$59$	−6.53938e18			−1.66567			−0.832837	−	0.553518i	$-0.813285\pi$
$59$	−6.53938e18			−1.66567			−0.832837	+	0.553518i	$0.813285\pi$
$60$	−1.32929e18	+	1.58177e18i	−0.283814	+	0.337718i
$61$		−	4.21755e17i		−	0.0757003i	−0.999283	−	0.0378501i	$-0.987949\pi$
$61$		−	4.21755e17i		−	0.0757003i	0.999283	−	0.0378501i	$-0.0120510\pi$
$62$	8.44243e18			1.27748
$63$	−7.79484e18	+	5.96658e17i	−0.997083	+	0.0763219i
$64$	−3.45371e18			−0.374452
$65$			2.03683e19i			1.87657i
$66$	6.03824e18	−	7.18507e18i	0.473913	−	0.563923i
$67$	−1.30627e19			−0.875479			−0.437740	−	0.899102i	$-0.644221\pi$
$67$	−1.30627e19			−0.875479			−0.437740	+	0.899102i	$0.644221\pi$
$68$	−5.77344e18			−0.331200
$69$	7.26229e18	+	6.10313e18i	0.357403	+	0.300357i
$70$	−3.16810e19	−	3.07081e18i	−1.34051	−	0.129934i
$71$			3.56914e19i			1.30122i	0.759411	+	0.650611i	$0.225487\pi$
$71$			3.56914e19i			1.30122i	−0.759411	+	0.650611i	$0.774513\pi$
$72$	2.26335e19	−	3.95568e18i	0.712461	−	0.124517i
$73$			3.10669e19i			0.846074i	0.906112	+	0.423037i	$0.139036\pi$
$73$			3.10669e19i			0.846074i	−0.906112	+	0.423037i	$0.860964\pi$
$74$			5.94750e19i			1.40411i
$75$	−9.69872e18	+	1.15408e19i	−0.198871	+	0.236642i
$76$		−	2.13879e19i		−	0.381615i
$77$	4.00452e19	+	3.88154e18i	0.622871	+	0.0603743i
$78$	−9.14408e19	+	1.08808e20i	−1.24207	+	1.47798i
$79$	1.16544e20			1.38486			0.692429	−	0.721486i	$-0.256541\pi$
$79$	1.16544e20			1.38486			0.692429	+	0.721486i	$0.256541\pi$
$80$	1.35915e20			1.41522
$81$	−1.02933e20	+	3.71129e19i	−0.940721	+	0.339181i
$82$			1.43410e19i			0.115222i
$83$	−1.17516e19			−0.0831339			−0.0415670	−	0.999136i	$-0.513235\pi$
$83$	−1.17516e19			−0.0831339			−0.0415670	+	0.999136i	$0.513235\pi$
$84$	−4.32580e19	−	4.41422e19i	−0.269857	−	0.275373i
$85$	−1.78398e20			−0.982860
$86$		−	1.28503e19i		−	0.0626151i
$87$	−2.32505e20	−	1.95394e20i	−1.00341	−	0.843256i
$88$	−1.18247e20			−0.452609
$89$	−8.40556e19			−0.285740			−0.142870	−	0.989741i	$-0.545633\pi$
$89$	−8.40556e19			−0.285740			−0.142870	+	0.989741i	$0.545633\pi$
$90$	−4.38847e20	+	7.66976e19i	−1.32668	+	0.231865i
$91$	−6.06430e20	−	5.87807e19i	−1.63247	−	0.158234i
$92$			7.49961e19i			0.179998i
$93$	3.87786e20	+	3.25890e20i	0.830848	+	0.698234i
$94$			4.08975e20i			0.783166i
$95$		−	6.60882e20i		−	1.13247i
$96$	3.65383e20	+	3.07063e20i	0.560920	+	0.471390i
$97$			4.28920e20i			0.590573i	0.955409	+	0.295286i	$0.0954150\pi$
$97$			4.28920e20i			0.590573i	−0.955409	+	0.295286i	$0.904585\pi$
$98$	1.82856e20	−	9.34383e20i	0.226065	−	1.15518i
$99$	5.54709e20	−	9.69469e19i	0.616447	−	0.107737i
$100$	−1.19179e20			−0.119179
$101$	9.89833e20			0.891636			0.445818	−	0.895124i	$-0.352913\pi$
$101$	9.89833e20			0.891636			0.445818	+	0.895124i	$0.352913\pi$
$102$	−9.53007e20	−	8.00895e20i	−0.774095	−	0.650539i
$103$		−	2.36391e21i		−	1.73316i	−0.499035	−	0.866582i	$-0.666312\pi$
$103$		−	2.36391e21i		−	1.73316i	0.499035	−	0.866582i	$-0.333688\pi$
$104$	1.79069e21			1.18624
$105$	−1.33667e21	−	1.36399e21i	−0.800821	−	0.817188i
$106$	3.01862e21			1.63718
$107$			1.14232e21i			0.561381i	0.959798	+	0.280690i	$0.0905634\pi$
$107$			1.14232e21i			0.561381i	−0.959798	+	0.280690i	$0.909437\pi$
$108$	−7.48166e20	−	4.34216e20i	−0.333464	−	0.193533i
$109$	4.60801e21			1.86438			0.932192	−	0.361964i	$-0.117894\pi$
$109$	4.60801e21			1.86438			0.932192	+	0.361964i	$0.117894\pi$
$110$	2.29273e21			0.842809
$111$	−2.29582e21	+	2.73187e21i	−0.767445	+	0.913204i
$112$	−3.92236e20	+	4.04664e21i	−0.119332	+	1.23113i
$113$			4.28982e21i			1.18882i	0.804162	+	0.594410i	$0.202614\pi$
$113$			4.28982e21i			1.18882i	−0.804162	+	0.594410i	$0.797386\pi$
$114$	2.96694e21	−	3.53044e21i	0.749562	−	0.891925i
$115$			2.31737e21i			0.534155i
$116$		−	2.40103e21i		−	0.505346i
$117$	−8.40031e21	+	1.46813e21i	−1.61564	+	0.282366i
$118$		−	1.11471e22i		−	1.96066i
$119$	5.14837e20	−	5.31149e21i	0.0828756	−	0.855014i
$120$	4.29699e21	+	3.61113e21i	0.633521	+	0.532403i
$121$	4.50221e21			0.608386
$122$	7.18932e20			0.0891065
$123$	−5.53585e20	+	6.58726e20i	−0.0629768	+	0.0749378i
$124$			4.00459e21i			0.418437i
$125$	8.23099e21			0.790491
$126$	−1.01707e21	−	1.32872e22i	−0.0898383	−	1.17366i
$127$	5.81932e21			0.473079			0.236539	−	0.971622i	$-0.423987\pi$
$127$	5.81932e21			0.473079			0.236539	+	0.971622i	$0.423987\pi$
$128$		−	1.56737e22i		−	1.17346i
$129$	4.96040e20	−	5.90252e20i	0.0342235	−	0.0407235i
$130$	−3.47202e22			−2.20891
$131$	4.60586e21			0.270372			0.135186	−	0.990820i	$-0.456837\pi$
$131$	4.60586e21			0.270372			0.135186	+	0.990820i	$0.456837\pi$
$132$	3.40817e21	+	2.86418e21i	0.184712	+	0.155229i
$133$	1.96766e22	+	1.90723e21i	0.985161	+	0.0954906i
$134$		−	2.22668e22i		−	1.03052i
$135$	−2.31182e22	−	1.34172e22i	−0.989577	−	0.574324i
$136$			1.56840e22i			0.621296i
$137$			3.64031e22i			1.33528i	0.744485	+	0.667640i	$0.232695\pi$
$137$			3.64031e22i			1.33528i	−0.744485	+	0.667640i	$0.767305\pi$
$138$	−1.04035e22	+	1.23794e22i	−0.353549	+	0.420698i
$139$			4.77330e22i			1.50371i	0.659329	+	0.751854i	$0.270840\pi$
$139$			4.77330e22i			1.50371i	−0.659329	+	0.751854i	$0.729160\pi$
$140$	1.45661e21	−	1.50276e22i	0.0425597	−	0.439081i
$141$	−1.57870e22	+	1.87854e22i	−0.428055	+	0.509355i
$142$	−6.08402e22			−1.53166
$143$	4.38868e22			1.02637
$144$	9.79664e21	+	5.60542e22i	0.212947	+	1.21843i
$145$		−	7.41914e22i		−	1.49965i
$146$	−5.29572e22			−0.995910
$147$	4.44677e22	−	3.58605e22i	0.778417	−	0.627747i
$148$	−2.82114e22			−0.459914
$149$			5.73702e22i			0.871426i	0.900086	+	0.435713i	$0.143504\pi$
$149$			5.73702e22i			0.871426i	−0.900086	+	0.435713i	$0.856496\pi$
$150$	−1.96726e22	−	1.65326e22i	−0.278551	−	0.234090i
$151$	3.45094e22			0.455701			0.227850	−	0.973696i	$-0.426830\pi$
$151$	3.45094e22			0.455701			0.227850	+	0.973696i	$0.426830\pi$
$152$	−5.81018e22			−0.715867
$153$	−1.28588e22	−	7.35750e22i	−0.147890	−	0.846195i
$154$	−6.61655e21	+	6.82618e22i	−0.0710663	+	0.733180i
$155$			1.23741e23i			1.24174i
$156$	−5.16121e22	−	4.33741e22i	−0.484109	−	0.406838i
$157$			3.31549e21i			0.0290805i	0.999894	+	0.0145402i	$0.00462847\pi$
$157$			3.31549e21i			0.0290805i	−0.999894	+	0.0145402i	$0.995372\pi$
$158$			1.98663e23i			1.63011i
$159$	1.38654e23	+	1.16523e23i	1.06479	+	0.894834i
$160$			1.16592e23i			0.838321i
$161$	−6.89955e22	−	6.68766e21i	−0.464675	−	0.0450404i
$162$	−6.32633e22	−	1.75461e23i	−0.399249	−	1.10732i
$163$	2.61004e23			1.54411			0.772055	−	0.635556i	$-0.219229\pi$
$163$	2.61004e23			1.54411			0.772055	+	0.635556i	$0.219229\pi$
$164$	−6.80252e21			−0.0377407
$165$	1.05312e23	+	8.85027e22i	0.548145	+	0.460654i
$166$		−	2.00320e22i		−	0.0978566i
$167$	−1.31835e23			−0.604653			−0.302327	−	0.953204i	$-0.597763\pi$
$167$	−1.31835e23			−0.604653			−0.302327	+	0.953204i	$0.597763\pi$
$168$	−1.19916e23	+	1.17514e23i	−0.516569	+	0.506223i
$169$	−4.17542e23			−1.69001
$170$		−	3.04101e23i		−	1.15692i
$171$	2.72561e23	−	4.76357e22i	0.974999	−	0.170401i
$172$	6.09541e21			0.0205094
$173$	−5.55338e22			−0.175822			−0.0879110	−	0.996128i	$-0.528019\pi$
$173$	−5.55338e22			−0.175822			−0.0879110	+	0.996128i	$0.528019\pi$
$174$	3.33072e23	−	3.96332e23i	0.992593	−	1.18111i
$175$	1.06276e22	−	1.09643e23i	0.0298220	−	0.307668i
$176$		−	2.92851e23i		−	0.774042i
$177$	4.30296e23	−	5.12021e23i	1.07164	−	1.27517i
$178$		−	1.43283e23i		−	0.336344i
$179$			2.31473e23i			0.512323i	0.966634	+	0.256162i	$0.0824579\pi$
$179$			2.31473e23i			0.512323i	−0.966634	+	0.256162i	$0.917542\pi$
$180$	−3.63808e22	−	2.08163e23i	−0.0759470	−	0.434552i
$181$			1.00558e24i			1.98057i	0.139053	+	0.990285i	$0.455594\pi$
$181$			1.00558e24i			1.98057i	−0.139053	+	0.990285i	$0.544406\pi$
$182$	1.00199e23	−	1.03373e24i	0.186257	−	1.92158i
$183$	3.30227e22	+	2.77518e22i	0.0579530	+	0.0487030i
$184$	2.03733e23			0.337656
$185$	−8.71727e23			−1.36483
$186$	−5.55519e23	+	6.61027e23i	−0.821888	+	0.977988i
$187$			3.84388e23i			0.537567i
$188$	−1.93993e23			−0.256525
$189$	4.66189e23	−	6.49583e23i	0.583060	−	0.812429i
$190$	1.12655e24			1.33302
$191$		−	9.60897e23i		−	1.07604i	−0.842933	−	0.538018i	$-0.819173\pi$
$191$		−	9.60897e23i		−	1.07604i	0.842933	−	0.538018i	$-0.180827\pi$
$192$	2.27257e23	−	2.70419e23i	0.240909	−	0.286665i
$193$	6.33104e23			0.635512			0.317756	−	0.948173i	$-0.397071\pi$
$193$	6.33104e23			0.635512			0.317756	+	0.948173i	$0.397071\pi$
$194$	−7.31145e23			−0.695161
$195$	−1.59480e24	−	1.34025e24i	−1.43663	−	1.20732i
$196$	4.43216e23	+	8.67358e22i	0.378378	+	0.0740473i
$197$			1.44208e24i			1.16706i	0.812091	+	0.583531i	$0.198330\pi$
$197$			1.44208e24i			1.16706i	−0.812091	+	0.583531i	$0.801670\pi$
$198$	1.65257e23	+	9.45566e23i	0.126817	+	0.725617i
$199$		−	7.52755e23i		−	0.547894i	−0.961745	−	0.273947i	$-0.911671\pi$
$199$		−	7.52755e23i		−	0.547894i	0.961745	−	0.273947i	$-0.0883292\pi$
$200$			3.23760e23i			0.223567i
$201$	8.59533e23	−	1.02278e24i	0.563253	−	0.670231i
$202$			1.68729e24i			1.04954i
$203$	2.20892e24	+	2.14108e23i	1.30458	+	0.126452i
$204$	3.79897e23	−	4.52050e23i	0.213083	−	0.253554i
$205$	−2.10197e23			−0.111998
$206$	4.02956e24			2.04010
$207$	−9.55729e23	+	1.67034e23i	−0.459882	+	0.0803739i
$208$			4.43484e24i			2.02867i
$209$	−1.42398e24			−0.619394
$210$	2.32507e24	−	2.27850e24i	0.961909	−	0.942643i
$211$	2.43940e24			0.960100			0.480050	−	0.877241i	$-0.340619\pi$
$211$	2.43940e24			0.960100			0.480050	+	0.877241i	$0.340619\pi$
$212$			1.43185e24i			0.536256i
$213$	−2.79458e24	−	2.34852e24i	−0.996162	−	0.837161i
$214$	−1.94722e24			−0.660799
$215$	1.88347e23			0.0608632
$216$	−1.17958e24	+	2.03245e24i	−0.363047	+	0.625541i
$217$	−3.68417e24	−	3.57103e23i	−1.08022	−	0.104705i
$218$			7.85490e24i			2.19456i
$219$	−2.43249e24	−	2.04423e24i	−0.647719	−	0.544335i
$220$			1.08753e24i			0.276060i
$221$		−	5.82103e24i		−	1.40890i
$222$	−4.65679e24	−	3.91350e24i	−1.07493	−	0.903356i
$223$			4.17894e24i			0.920164i	0.887876	+	0.460082i	$0.152180\pi$
$223$			4.17894e24i			0.920164i	−0.887876	+	0.460082i	$0.847820\pi$
$224$	−3.47133e24	−	3.36472e23i	−0.729275	−	0.0706879i
$225$	−2.65439e23	−	1.51879e24i	−0.0532168	−	0.304495i
$226$	−7.31251e24			−1.39935
$227$	8.20116e24			1.49832			0.749159	−	0.662391i	$-0.230458\pi$
$227$	8.20116e24			1.49832			0.749159	+	0.662391i	$0.230458\pi$
$228$	1.67463e24	+	1.40734e24i	0.292148	+	0.245518i
$229$			2.44570e24i			0.407504i	0.979023	+	0.203752i	$0.0653136\pi$
$229$			2.44570e24i			0.407504i	−0.979023	+	0.203752i	$0.934686\pi$
$230$	−3.95023e24			−0.628752
$231$	−2.93893e24	+	2.88006e24i	−0.446954	+	0.438002i
$232$	−6.52259e24			−0.947973
$233$		−	6.61945e23i		−	0.0919570i	−0.998942	−	0.0459785i	$-0.985359\pi$
$233$		−	6.61945e23i		−	0.0919570i	0.998942	−	0.0459785i	$-0.0146406\pi$
$234$	−2.50260e24	−	1.43193e25i	−0.332372	−	1.90176i
$235$	−5.99436e24			−0.761255
$236$	5.28754e24			0.642210
$237$	−7.66868e24	+	9.12519e24i	−0.890970	+	1.06019i
$238$	9.05406e24	+	8.77600e23i	1.00643	+	0.0975526i
$239$		−	1.32177e25i		−	1.40597i	−0.711204	−	0.702986i	$-0.751850\pi$
$239$		−	1.32177e25i		−	1.40597i	0.711204	−	0.702986i	$-0.248150\pi$
$240$	−8.94333e24	+	1.06419e25i	−0.910503	+	1.08343i
$241$			1.06254e25i			1.03554i	0.855519	+	0.517772i	$0.173238\pi$
$241$			1.06254e25i			1.03554i	−0.855519	+	0.517772i	$0.826762\pi$
$242$			7.67455e24i			0.716129i
$243$	3.86718e24	−	1.05015e25i	0.345564	−	0.938395i
$244$			3.41018e23i			0.0291867i
$245$	1.36953e25	+	2.68012e24i	1.12286	+	0.219741i
$246$	−1.12288e24	−	9.43650e23i	−0.0882091	−	0.0741297i
$247$	2.15642e25			1.62336
$248$	1.08788e25			0.784942
$249$	7.73266e23	−	9.20132e23i	0.0534855	−	0.0636439i
$250$			1.40307e25i			0.930484i
$251$	−1.49038e25			−0.947815			−0.473907	−	0.880575i	$-0.657157\pi$
$251$	−1.49038e25			−0.947815			−0.473907	+	0.880575i	$0.657157\pi$
$252$	6.30267e24	−	4.82439e23i	0.384431	−	0.0294264i
$253$	4.99314e24			0.292152
$254$			9.91972e24i			0.556859i
$255$	1.17387e25	−	1.39683e25i	0.632339	−	0.752438i
$256$	1.94748e25			1.00682
$257$	−3.02992e25			−1.50360			−0.751801	−	0.659390i	$-0.770814\pi$
$257$	−3.02992e25			−1.50360			−0.751801	+	0.659390i	$0.770814\pi$
$258$	1.00615e24	+	8.45558e23i	0.0479355	+	0.0402844i
$259$	2.51570e24	−	2.59541e25i	0.115083	−	1.18730i
$260$		−	1.64692e25i		−	0.723523i
$261$	3.05980e25	−	5.34764e24i	1.29112	−	0.225651i
$262$			7.85123e24i			0.318254i
$263$		−	2.50284e25i		−	0.974760i	−0.873190	−	0.487380i	$-0.837953\pi$
$263$		−	2.50284e25i		−	0.974760i	0.873190	−	0.487380i	$-0.162047\pi$
$264$	7.78077e24	−	9.25856e24i	0.291193	−	0.346499i
$265$			4.42440e25i			1.59138i
$266$	−3.25110e24	+	3.35410e25i	−0.112402	+	1.15963i
$267$	5.53093e24	−	6.58141e24i	0.183836	−	0.218751i
$268$	1.05621e25			0.337546
$269$	2.63526e25			0.809886			0.404943	−	0.914342i	$-0.367291\pi$
$269$	2.63526e25			0.809886			0.404943	+	0.914342i	$0.367291\pi$
$270$	2.28712e25	−	3.94077e25i	0.676035	−	1.16483i
$271$			1.18404e25i			0.336658i	0.985731	+	0.168329i	$0.0538371\pi$
$271$			1.18404e25i			0.336658i	−0.985731	+	0.168329i	$0.946163\pi$
$272$	−3.88430e25			−1.06253
$273$	4.45060e25	−	4.36146e25i	1.17142	−	1.14795i
$274$	−6.20533e25			−1.57175
$275$			7.93479e24i			0.193438i
$276$	−5.87206e24	−	4.93480e24i	−0.137799	−	0.115804i
$277$	5.94698e25			1.34356			0.671782	−	0.740749i	$-0.265529\pi$
$277$	5.94698e25			1.34356			0.671782	+	0.740749i	$0.265529\pi$
$278$	−8.13666e25			−1.77001
$279$	−5.10333e25	+	8.91913e24i	−1.06908	+	0.186844i
$280$	−4.08236e25	−	3.95699e24i	−0.823668	−	0.0798372i
$281$		−	5.39388e25i		−	1.04830i	−0.851626	−	0.524149i	$-0.824383\pi$
$281$		−	5.39388e25i		−	1.04830i	0.851626	−	0.524149i	$-0.175617\pi$
$282$	−3.20220e25	−	2.69108e25i	−0.599560	−	0.503862i
$283$		−	8.93895e25i		−	1.61261i	−0.591501	−	0.806304i	$-0.701465\pi$
$283$		−	8.93895e25i		−	1.61261i	0.591501	−	0.806304i	$-0.298535\pi$
$284$		−	2.88590e25i		−	0.501694i
$285$	5.17459e25	+	4.34865e25i	0.866971	+	0.728591i
$286$			7.48103e25i			1.20814i
$287$	6.06604e23	−	6.25823e24i	0.00944377	−	0.0974298i
$288$	−4.80850e25	+	8.40386e24i	−0.721753	+	0.126141i
$289$	−1.81078e25			−0.262083
$290$	1.26468e26			1.76523
$291$	−3.35837e25	−	2.82233e25i	−0.452118	−	0.379954i
$292$		−	2.51198e25i		−	0.326209i
$293$	−4.40075e25			−0.551336			−0.275668	−	0.961253i	$-0.588899\pi$
$293$	−4.40075e25			−0.551336			−0.275668	+	0.961253i	$0.588899\pi$
$294$	6.11285e25	+	7.58004e25i	0.738919	+	0.916272i
$295$	1.63384e26			1.90580
$296$			7.66385e25i			0.862748i
$297$	−2.89095e25	+	4.98119e25i	−0.314122	+	0.541241i
$298$	−9.77942e25			−1.02575
$299$	−7.56143e25			−0.765696
$300$	7.84209e24	−	9.33152e24i	0.0766758	−	0.0912387i
$301$	−5.43548e23	+	5.60769e24i	−0.00513203	+	0.0529464i
$302$			5.88254e25i			0.536404i
$303$	−6.51318e25	+	7.75022e25i	−0.573648	+	0.682600i
$304$		−	1.43895e26i		−	1.22426i
$305$			1.05374e25i			0.0866135i
$306$	1.25417e26	−	2.19193e25i	0.996053	−	0.174081i
$307$			8.79033e25i			0.674609i	0.941396	+	0.337305i	$0.109515\pi$
$307$			8.79033e25i			0.674609i	−0.941396	+	0.337305i	$0.890485\pi$
$308$	−3.23793e25	−	3.13850e24i	−0.240152	−	0.0232776i
$309$	1.85090e26	+	1.55547e26i	1.32684	+	1.11506i
$310$	−2.10931e26			−1.46165
$311$	5.79802e25			0.388414			0.194207	−	0.980961i	$-0.437787\pi$
$311$	5.79802e25			0.388414			0.194207	+	0.980961i	$0.437787\pi$
$312$	−1.17829e26	+	1.40208e26i	−0.763184	+	0.908134i
$313$		−	1.53921e26i		−	0.964013i	−0.876168	−	0.482006i	$-0.839908\pi$
$313$		−	1.53921e26i		−	0.964013i	0.876168	−	0.482006i	$-0.160092\pi$
$314$	−5.65165e24			−0.0342305
$315$	1.94751e26	−	1.49073e25i	1.14083	−	0.0873248i
$316$	−9.42338e25			−0.533940
$317$		−	2.62029e24i		−	0.0143624i	−0.999974	−	0.00718121i	$-0.997714\pi$
$317$		−	2.62029e24i		−	0.0143624i	0.999974	−	0.00718121i	$-0.00228587\pi$
$318$	−1.98628e26	+	2.36353e26i	−1.05331	+	1.25336i
$319$	−1.59857e26			−0.820220
$320$	8.62897e25			0.428434
$321$	−8.94415e25	−	7.51654e25i	−0.429770	−	0.361173i
$322$	1.13999e25	−	1.17611e26i	0.0530169	−	0.546967i
$323$			1.88872e26i			0.850240i
$324$	8.32282e25	−	3.00083e25i	0.362700	−	0.130773i
$325$		−	1.20162e26i		−	0.506979i
$326$			4.44913e26i			1.81757i
$327$	−3.03211e26	+	3.60799e26i	−1.19948	+	1.42730i
$328$			1.84796e25i			0.0707973i
$329$	1.72990e25	−	1.78471e26i	0.0641896	−	0.662234i
$330$	−1.50863e26	+	1.79516e26i	−0.542234	+	0.645220i
$331$	4.00443e26			1.39427			0.697135	−	0.716940i	$-0.254458\pi$
$331$	4.00443e26			1.39427			0.697135	+	0.716940i	$0.254458\pi$
$332$	9.50200e24			0.0320528
$333$	−6.28332e25	−	3.59518e26i	−0.205364	−	1.17505i
$334$		−	2.24727e26i		−	0.711735i
$335$	3.26366e26			1.00169
$336$	−2.91035e26	−	2.96983e26i	−0.865730	−	0.883424i
$337$	−8.65529e25			−0.249556			−0.124778	−	0.992185i	$-0.539822\pi$
$337$	−8.65529e25			−0.249556			−0.124778	+	0.992185i	$0.539822\pi$
$338$		−	7.11749e26i		−	1.98931i
$339$	−3.35886e26	−	2.82274e26i	−0.910111	−	0.764845i
$340$	1.44247e26			0.378947
$341$	2.66620e26			0.679160
$342$	8.12006e25	+	4.64612e26i	0.200579	+	1.14767i
$343$	−1.19319e26	+	4.00018e26i	−0.285838	+	0.958278i
$344$		−	1.65586e25i		−	0.0384735i
$345$	−1.81446e26	−	1.52485e26i	−0.408928	−	0.343657i
$346$		−	9.46638e25i		−	0.206959i
$347$		−	3.69203e26i		−	0.783078i	−0.920161	−	0.391539i	$-0.871943\pi$
$347$		−	3.69203e26i		−	0.783078i	0.920161	−	0.391539i	$-0.128057\pi$
$348$	1.87996e26	+	1.57990e26i	0.386872	+	0.325122i
$349$		−	5.13323e26i		−	1.02500i	−0.858687	−	0.512500i	$-0.828720\pi$
$349$		−	5.13323e26i		−	1.02500i	0.858687	−	0.512500i	$-0.171280\pi$
$350$	1.86900e26	+	1.81160e25i	0.362155	+	0.0351033i
$351$	4.37795e26	−	7.54333e26i	0.823277	−	1.41853i
$352$	2.51217e26			0.458513
$353$	7.67815e26			1.36026			0.680130	−	0.733091i	$-0.261923\pi$
$353$	7.67815e26			1.36026			0.680130	+	0.733091i	$0.261923\pi$
$354$	8.72801e26	+	7.33490e26i	1.50100	+	1.26142i
$355$		−	8.91738e26i		−	1.48881i
$356$	6.79648e25			0.110169
$357$	3.82003e26	+	3.89811e26i	0.601244	+	0.613533i
$358$	−3.94573e26			−0.603054
$359$			4.03983e25i			0.0599614i	0.999550	+	0.0299807i	$0.00954458\pi$
$359$			4.03983e25i			0.0599614i	−0.999550	+	0.0299807i	$0.990455\pi$
$360$	−5.65491e26	+	9.88313e25i	−0.815172	+	0.142468i
$361$	1.45267e25			0.0203395
$362$	−1.71412e27			−2.33132
$363$	−2.96249e26	+	3.52515e26i	−0.391415	+	0.465756i
$364$	4.90341e26	+	4.75282e25i	0.629410	+	0.0610080i
$365$		−	7.76196e26i		−	0.968047i
$366$	−4.73063e25	+	5.62911e25i	−0.0573281	+	0.0682163i
$367$			9.04216e26i			1.06483i	0.846485	+	0.532413i	$0.178715\pi$
$367$			9.04216e26i			1.06483i	−0.846485	+	0.532413i	$0.821285\pi$
$368$			5.04565e26i			0.577451i
$369$	−1.51508e25	−	8.66894e25i	−0.0168523	−	0.0964249i
$370$		−	1.48596e27i		−	1.60653i
$371$	−1.31729e27	−	1.27683e26i	−1.38438	−	0.134186i
$372$	−3.13552e26	−	2.63505e26i	−0.320338	−	0.269208i
$373$	1.38478e27			1.37542			0.687712	−	0.725984i	$-0.258615\pi$
$373$	1.38478e27			1.37542			0.687712	+	0.725984i	$0.258615\pi$
$374$	−6.55234e26			−0.632768
$375$	−5.41605e26	+	6.44472e26i	−0.508575	+	0.605167i
$376$			5.26998e26i			0.481212i
$377$	2.42082e27			2.14970
$378$	1.10729e27	+	7.94674e26i	0.956307	+	0.686318i
$379$	−3.97744e26			−0.334112			−0.167056	−	0.985947i	$-0.553426\pi$
$379$	−3.97744e26			−0.334112			−0.167056	+	0.985947i	$0.553426\pi$
$380$			5.34368e26i			0.436629i
$381$	−3.82916e26	+	4.55643e26i	−0.304363	+	0.362170i
$382$	1.63796e27			1.26660
$383$	4.37995e25			0.0329520			0.0164760	−	0.999864i	$-0.494755\pi$
$383$	4.37995e25			0.0329520			0.0164760	+	0.999864i	$0.494755\pi$
$384$	1.22723e27	+	1.03134e27i	0.898352	+	0.754963i
$385$	−1.00052e27	−	9.69790e25i	−0.712667	−	0.0690780i
$386$			1.07920e27i			0.748058i
$387$	1.35759e25	+	7.76781e25i	0.00915803	+	0.0524002i
$388$		−	3.46812e26i		−	0.227699i
$389$			6.30559e26i			0.402954i	0.979493	+	0.201477i	$0.0645741\pi$
$389$			6.30559e26i			0.402954i	−0.979493	+	0.201477i	$0.935426\pi$
$390$	2.28462e27	−	2.71853e27i	1.42113	−	1.69105i
$391$		−	6.62276e26i		−	0.401036i
$392$	2.35624e26	−	1.20403e27i	0.138905	−	0.709796i
$393$	−3.03069e26	+	3.60631e26i	−0.173948	+	0.206986i
$394$	−2.45820e27			−1.37375
$395$	−2.91181e27			−1.58450
$396$	−4.48520e26	+	7.83883e25i	−0.237675	+	0.0415386i
$397$		−	9.29130e26i		−	0.479486i	−0.970836	−	0.239743i	$-0.922937\pi$
$397$		−	9.29130e26i		−	0.479486i	0.970836	−	0.239743i	$-0.0770633\pi$
$398$	1.28316e27			0.644924
$399$	−1.44407e27	+	1.41514e27i	−0.706922	+	0.692763i
$400$	−8.01823e26			−0.382339
$401$		−	1.41731e27i		−	0.658337i	−0.944271	−	0.329168i	$-0.893232\pi$
$401$		−	1.41731e27i		−	0.658337i	0.944271	−	0.329168i	$-0.106768\pi$
$402$	1.74345e27	+	1.46517e27i	0.788927	+	0.663003i
$403$	−4.03760e27			−1.78000
$404$	−8.00348e26			−0.343775
$405$	2.57174e27	−	9.27252e26i	1.07634	−	0.388079i
$406$	−3.64972e26	+	3.76536e27i	−0.148846	+	1.53562i
$407$			1.87828e27i			0.746480i
$408$	−1.22803e27	−	1.03202e27i	−0.475638	−	0.399720i
$409$			2.56372e27i			0.967780i	0.875129	+	0.483890i	$0.160776\pi$
$409$			2.56372e27i			0.967780i	−0.875129	+	0.483890i	$0.839224\pi$
$410$		−	3.58305e26i		−	0.131833i
$411$	−2.85030e27	−	2.39535e27i	−1.02224	−	0.859073i
$412$			1.91138e27i			0.668231i
$413$	−4.71507e26	+	4.86447e27i	−0.160699	+	1.65790i
$414$	−2.84728e26	−	1.62915e27i	−0.0946078	−	0.541325i
$415$	2.93610e26			0.0951188
$416$	−3.80434e27			−1.20171
$417$	−3.73741e27	−	3.14087e27i	−1.15118	−	0.967435i
$418$		−	2.42733e27i		−	0.729086i
$419$	−2.76286e26			−0.0809303			−0.0404651	−	0.999181i	$-0.512884\pi$
$419$	−2.76286e26			−0.0809303			−0.0404651	+	0.999181i	$0.512884\pi$
$420$	1.08079e27	+	1.10288e27i	0.308761	+	0.315072i
$421$	7.66524e26			0.213581			0.106791	−	0.994282i	$-0.465943\pi$
$421$	7.66524e26			0.213581			0.106791	+	0.994282i	$0.465943\pi$
$422$			4.15824e27i			1.13013i
$423$	−4.32067e26	−	2.47219e27i	−0.114545	−	0.655403i
$424$	3.88974e27			1.00596
$425$	1.05245e27			0.265532
$426$	4.00334e27	−	4.76368e27i	0.985420	−	1.17258i
$427$	−3.13733e26	−	3.04098e25i	−0.0753472	−	0.00730332i
$428$		−	9.23643e26i		−	0.216444i
$429$	−2.88779e27	+	3.43626e27i	−0.660334	+	0.785750i
$430$			3.21060e26i			0.0716419i
$431$		−	7.46042e27i		−	1.62462i	−0.583225	−	0.812311i	$-0.698209\pi$
$431$		−	7.46042e27i		−	1.62462i	0.583225	−	0.812311i	$-0.301791\pi$
$432$	−5.03357e27	−	2.92135e27i	−1.06979	−	0.620875i
$433$			5.21226e27i			1.08119i	0.841282	+	0.540596i	$0.181801\pi$
$433$			5.21226e27i			1.08119i	−0.841282	+	0.540596i	$0.818199\pi$
$434$	6.08723e26	−	6.28010e27i	0.123247	−	1.27152i
$435$	5.80905e27	+	4.88185e27i	1.14807	+	0.964823i
$436$	−3.72590e27			−0.718824
$437$	2.45342e27			0.462080
$438$	3.48463e27	−	4.14646e27i	0.640735	−	0.762428i
$439$		−	4.85066e26i		−	0.0870809i	−0.999052	−	0.0435405i	$-0.986136\pi$
$439$		−	4.85066e26i		−	0.0870809i	0.999052	−	0.0435405i	$-0.0138637\pi$
$440$	2.95437e27			0.517859
$441$	−1.18193e26	+	5.84139e27i	−0.0202295	+	0.999795i
$442$	9.92262e27			1.65841
$443$			1.00313e28i			1.63726i	0.574324	+	0.818628i	$0.305265\pi$
$443$			1.00313e28i			1.63726i	−0.574324	+	0.818628i	$0.694735\pi$
$444$	1.85633e27	−	2.20890e27i	0.295893	−	0.352091i
$445$	2.10010e27			0.326934
$446$	−7.12350e27			−1.08312
$447$	−4.49198e27	−	3.77500e27i	−0.667128	−	0.560645i
$448$	−2.49022e26	+	2.56912e27i	−0.0361259	+	0.372705i
$449$		−	1.26558e27i		−	0.179350i	−0.995971	−	0.0896752i	$-0.971417\pi$
$449$		−	1.26558e27i		−	0.179350i	0.995971	−	0.0896752i	$-0.0285829\pi$
$450$	2.58895e27	−	4.52473e26i	0.358420	−	0.0626413i
$451$			4.52903e26i			0.0612564i
$452$		−	3.46862e27i		−	0.458356i
$453$	−2.27075e27	+	2.70203e27i	−0.293182	+	0.348866i
$454$			1.39798e28i			1.76366i
$455$	1.51514e28	+	1.46861e27i	1.86782	+	0.181046i
$456$	3.82315e27	−	4.54927e27i	0.460564	−	0.548038i
$457$	1.22284e28			1.43963			0.719813	−	0.694168i	$-0.244227\pi$
$457$	1.22284e28			1.43963			0.719813	+	0.694168i	$0.244227\pi$
$458$	−4.16899e27			−0.479671
$459$	6.60691e27	+	3.83447e27i	0.742959	+	0.431194i
$460$		−	1.87375e27i		−	0.205947i
$461$	1.60244e28			1.72156			0.860782	−	0.508973i	$-0.169975\pi$
$461$	1.60244e28			1.72156			0.860782	+	0.508973i	$0.169975\pi$
$462$	−4.90941e27	−	5.00975e27i	−0.515571	−	0.526108i
$463$	−1.36001e28			−1.39618			−0.698092	−	0.716008i	$-0.745968\pi$
$463$	−1.36001e28			−1.39618			−0.698092	+	0.716008i	$0.745968\pi$
$464$		−	1.61538e28i		−	1.62120i
$465$	−9.68870e27	−	8.14226e27i	−0.950626	−	0.798893i
$466$	1.12836e27			0.108242
$467$	3.65637e27			0.342944			0.171472	−	0.985189i	$-0.445148\pi$
$467$	3.65637e27			0.342944			0.171472	+	0.985189i	$0.445148\pi$
$468$	6.79223e27	−	1.18708e27i	0.622918	−	0.108868i
$469$	−9.41854e26	+	9.71695e27i	−0.0844634	+	0.871395i
$470$		−	1.02181e28i		−	0.896070i
$471$	−2.59597e26	−	2.18162e26i	−0.0222628	−	0.0187094i
$472$		−	1.43640e28i		−	1.20472i
$473$		−	4.05824e26i		−	0.0332886i
$474$	−1.55550e28	−	1.30722e28i	−1.24795	−	1.04876i
$475$			3.89883e27i			0.305951i
$476$	−4.16281e26	+	4.29470e27i	−0.0319532	+	0.329655i
$477$	−1.82471e28	+	3.18906e27i	−1.37010	+	0.239453i
$478$	2.25310e28			1.65496
$479$	−1.10483e28			−0.793912			−0.396956	−	0.917838i	$-0.629933\pi$
$479$	−1.10483e28			−0.793912			−0.396956	+	0.917838i	$0.629933\pi$
$480$	−9.12898e27	−	7.67187e27i	−0.641784	−	0.539347i
$481$		−	2.84439e28i		−	1.95644i
$482$	−1.81123e28			−1.21893
$483$	5.06359e27	−	4.96217e27i	0.333437	−	0.326758i
$484$	−3.64035e27			−0.234567
$485$		−	1.07164e28i		−	0.675712i
$486$	1.79011e28	+	6.59207e27i	1.10458	+	0.406762i
$487$	−1.02733e28			−0.620375			−0.310187	−	0.950675i	$-0.600392\pi$
$487$	−1.02733e28			−0.620375			−0.310187	+	0.950675i	$0.600392\pi$
$488$	9.26403e26			0.0547510
$489$	−1.71743e28	+	2.04362e28i	−0.993427	+	1.18211i
$490$	−4.56858e27	+	2.33452e28i	−0.258656	+	1.32172i
$491$			4.32085e27i			0.239450i	0.992807	+	0.119725i	$0.0382012\pi$
$491$			4.32085e27i			0.239450i	−0.992807	+	0.119725i	$0.961799\pi$
$492$	4.47611e26	−	5.32625e26i	0.0242811	−	0.0288927i
$493$			2.12030e28i			1.12591i
$494$			3.67587e28i			1.91085i
$495$	−1.38592e28	+	2.42218e27i	−0.705316	+	0.123269i
$496$			2.69424e28i			1.34239i
$497$	2.65499e28	+	2.57345e27i	1.29515	+	0.125538i
$498$	1.56847e27	+	1.31812e27i	0.0749150	+	0.0629576i
$499$	−2.48378e28			−1.16160			−0.580802	−	0.814045i	$-0.697261\pi$
$499$	−2.48378e28			−1.16160			−0.580802	+	0.814045i	$0.697261\pi$
$500$	−6.65532e27			−0.304778
$501$	8.67481e27	−	1.03224e28i	0.389013	−	0.462898i
$502$		−	2.54053e28i		−	1.11567i
$503$	1.16976e28			0.503074			0.251537	−	0.967848i	$-0.419064\pi$
$503$	1.16976e28			0.503074			0.251537	+	0.967848i	$0.419064\pi$
$504$	−1.31058e27	−	1.71217e28i	−0.0552006	−	0.721150i
$505$	−2.47306e28			−1.02018
$506$			8.51140e27i			0.343891i
$507$	2.74746e28	−	3.26928e28i	1.08729	−	1.29380i
$508$	−4.70532e27			−0.182398
$509$	−2.68759e28			−1.02053			−0.510266	−	0.860016i	$-0.670453\pi$
$509$	−2.68759e28			−1.02053			−0.510266	+	0.860016i	$0.670453\pi$
$510$	2.38105e28	+	2.00101e28i	0.885692	+	0.744324i
$511$	2.31098e28	+	2.24001e27i	0.842127	+	0.0816265i
$512$			3.26836e26i			0.0116680i
$513$	−1.42049e28	+	2.44755e28i	−0.496829	+	0.856050i
$514$		−	5.16485e28i		−	1.76988i
$515$			5.90614e28i			1.98302i
$516$	−4.01082e26	+	4.77259e26i	−0.0131951	+	0.0157012i
$517$			1.29158e28i			0.416362i
$518$	4.42418e28	+	4.28831e27i	1.39756	+	0.135464i
$519$	3.65416e27	−	4.34819e27i	0.113118	−	0.134602i
$520$	−4.47399e28			−1.35725
$521$	9.47556e27			0.281714			0.140857	−	0.990030i	$-0.455014\pi$
$521$	9.47556e27			0.281714			0.140857	+	0.990030i	$0.455014\pi$
$522$	9.11568e27	+	5.21579e28i	0.265613	+	1.51978i
$523$		−	7.28173e27i		−	0.207954i	−0.994580	−	0.103977i	$-0.966843\pi$
$523$		−	7.28173e27i		−	0.207954i	0.994580	−	0.103977i	$-0.0331568\pi$
$524$	−3.72416e27			−0.104244
$525$	7.88557e27	+	8.04674e27i	0.216352	+	0.220774i
$526$	4.26639e28			1.14739
$527$		−	3.53637e28i		−	0.932281i
$528$	2.29297e28	+	1.92699e28i	0.592575	+	0.497992i
$529$	3.08687e28			0.782049
$530$	−7.54191e28			−1.87320
$531$	1.17766e28	+	6.73828e28i	0.286765	+	1.64080i
$532$	−1.59099e28	−	1.54213e27i	−0.379834	−	0.0368170i
$533$		−	6.85859e27i		−	0.160546i
$534$	1.12188e28	+	9.42811e27i	0.257491	+	0.216392i
$535$		−	2.85404e28i		−	0.642311i
$536$		−	2.86927e28i		−	0.633199i
$537$	−1.81239e28	−	1.52311e28i	−0.392214	−	0.329611i
$538$			4.49210e28i			0.953313i
$539$	5.77475e27	−	2.95087e28i	0.120185	−	0.614141i
$540$	1.86927e28	+	1.08487e28i	0.381537	+	0.221434i
$541$	−4.20480e28			−0.841733			−0.420867	−	0.907123i	$-0.638274\pi$
$541$	−4.20480e28			−0.841733			−0.420867	+	0.907123i	$0.638274\pi$
$542$	−2.01833e28			−0.396279
$543$	−7.87349e28	−	6.61677e28i	−1.51624	−	1.27423i
$544$		−	3.33207e28i		−	0.629399i
$545$	−1.15130e29			−2.13316
$546$	7.43462e28	+	7.58657e28i	1.35125	+	1.37887i
$547$	4.84337e28			0.863537			0.431768	−	0.901984i	$-0.357890\pi$
$547$	4.84337e28			0.863537			0.431768	+	0.901984i	$0.357890\pi$
$548$		−	2.94344e28i		−	0.514825i
$549$	−4.34584e27	+	7.59526e26i	−0.0745700	+	0.0130327i
$550$	−1.35258e28			−0.227695
$551$	−7.85473e28			−1.29730
$552$	−1.34058e28	+	1.59519e28i	−0.217236	+	0.258495i
$553$	8.40315e27	−	8.66939e28i	0.133607	−	1.37840i
$554$			1.01373e29i			1.58151i
$555$	5.73603e28	−	6.82547e28i	0.878082	−	1.04486i
$556$		−	3.85955e28i		−	0.579764i
$557$		−	1.13096e28i		−	0.166712i	−0.996520	−	0.0833560i	$-0.973436\pi$
$557$		−	1.13096e28i		−	0.166712i	0.996520	−	0.0833560i	$-0.0265639\pi$
$558$	−1.52037e28	−	8.69922e28i	−0.219933	−	1.25841i
$559$			6.14565e27i			0.0872456i
$560$	9.79988e27	−	1.01104e29i	0.136536	−	1.40862i
$561$	−3.00969e28	−	2.52930e28i	−0.411539	−	0.345852i
$562$	9.19451e28			1.23395
$563$	1.20262e29			1.58412			0.792062	−	0.610441i	$-0.209008\pi$
$563$	1.20262e29			1.58412			0.792062	+	0.610441i	$0.209008\pi$
$564$	1.27649e28	−	1.51893e28i	0.165039	−	0.196385i
$565$		−	1.07180e29i		−	1.36020i
$566$	1.52375e29			1.89819
$567$	2.01855e28	+	7.92448e28i	0.246841	+	0.969056i
$568$	−7.83977e28			−0.941122
$569$		−	9.26804e28i		−	1.09222i	−0.837714	−	0.546109i	$-0.816109\pi$
$569$		−	9.26804e28i		−	1.09222i	0.837714	−	0.546109i	$-0.183891\pi$
$570$	−7.41279e28	+	8.82069e28i	−0.857622	+	1.02051i
$571$	−9.42718e27			−0.107079			−0.0535393	−	0.998566i	$-0.517050\pi$
$571$	−9.42718e27			−0.107079			−0.0535393	+	0.998566i	$0.517050\pi$
$572$	−3.54855e28			−0.395725
$573$	7.52365e28	+	6.32278e28i	0.823769	+	0.692284i
$574$	1.06679e28	+	1.03403e27i	0.114684	+	0.0111162i
$575$		−	1.36712e28i		−	0.144309i
$576$	6.21967e27	+	3.55876e28i	0.0644661	+	0.368861i
$577$			1.82632e28i			0.185879i	0.995672	+	0.0929395i	$0.0296263\pi$
$577$			1.82632e28i			0.185879i	−0.995672	+	0.0929395i	$0.970374\pi$
$578$		−	3.08669e28i		−	0.308497i
$579$	−4.16588e28	+	4.95709e28i	−0.408866	+	0.486522i
$580$			5.99889e28i			0.578198i
$581$	−8.47326e26	+	8.74172e27i	−0.00802049	+	0.0827461i
$582$	4.81099e28	−	5.72473e28i	0.447243	−	0.532187i
$583$	9.53309e28			0.870390
$584$	−6.82398e28			−0.611931
$585$	2.09879e29	−	3.66807e28i	1.84855	−	0.323073i
$586$		−	7.50160e28i		−	0.648976i
$587$	1.02461e29			0.870684			0.435342	−	0.900265i	$-0.356628\pi$
$587$	1.02461e29			0.870684			0.435342	+	0.900265i	$0.356628\pi$
$588$	−3.59552e28	+	2.89957e28i	−0.300123	+	0.242032i
$589$	1.31006e29			1.07419
$590$			2.78507e29i			2.24332i
$591$	−1.12912e29	−	9.48901e28i	−0.893456	−	0.750848i
$592$	−1.89803e29			−1.47545
$593$	9.65141e28			0.737084			0.368542	−	0.929611i	$-0.379857\pi$
$593$	9.65141e28			0.737084			0.368542	+	0.929611i	$0.379857\pi$
$594$	−8.49102e28	−	4.92796e28i	−0.637092	−	0.369751i
$595$	−1.28630e28	+	1.32706e29i	−0.0948232	+	0.978276i
$596$		−	4.63877e28i		−	0.335983i
$597$	5.89394e28	+	4.95319e28i	0.419445	+	0.352496i
$598$		−	1.28893e29i		−	0.901298i
$599$			1.55669e29i			1.06960i	0.844979	+	0.534799i	$0.179613\pi$
$599$			1.55669e29i			1.06960i	−0.844979	+	0.534799i	$0.820387\pi$
$600$	−2.53498e28	−	2.13036e28i	−0.171154	−	0.143835i
$601$		−	4.35706e28i		−	0.289076i	−0.989499	−	0.144538i	$-0.953830\pi$
$601$		−	4.35706e28i		−	0.289076i	0.989499	−	0.144538i	$-0.0461695\pi$
$602$	−9.55897e27	−	9.26541e26i	−0.0623230	−	0.00604090i
$603$	2.35241e28	+	1.34600e29i	0.150724	+	0.862407i
$604$	−2.79033e28			−0.175698
$605$	−1.12486e29			−0.696093
$606$	−1.32112e29	−	1.11025e29i	−0.803486	−	0.675239i
$607$		−	4.72217e28i		−	0.282267i	−0.989991	−	0.141134i	$-0.954925\pi$
$607$		−	4.72217e28i		−	0.282267i	0.989991	−	0.141134i	$-0.0450747\pi$
$608$	1.23438e29			0.725204
$609$	−1.62113e29	+	1.58866e29i	−0.936128	+	0.917379i
$610$	−1.79623e28			−0.101952
$611$		−	1.95592e29i		−	1.09124i
$612$	1.03972e28	+	5.94905e28i	0.0570199	+	0.326255i
$613$	2.58348e29			1.39274			0.696370	−	0.717682i	$-0.254797\pi$
$613$	2.58348e29			1.39274			0.696370	+	0.717682i	$0.254797\pi$
$614$	−1.49842e29			−0.794080
$615$	1.38311e28	−	1.64580e28i	0.0720557	−	0.0857411i
$616$	−8.52597e27	+	8.79610e28i	−0.0436663	+	0.450498i
$617$			4.81699e28i			0.242539i	0.992620	+	0.121269i	$0.0386965\pi$
$617$			4.81699e28i			0.242539i	−0.992620	+	0.121269i	$0.961304\pi$
$618$	−2.65148e29	+	3.15507e29i	−1.31253	+	1.56182i
$619$		−	6.83865e28i		−	0.332827i	−0.986056	−	0.166414i	$-0.946781\pi$
$619$		−	6.83865e28i		−	0.332827i	0.986056	−	0.166414i	$-0.0532187\pi$
$620$		−	1.00053e29i		−	0.478760i
$621$	4.98093e28	−	8.58228e28i	0.234341	−	0.403776i
$622$			9.88340e28i			0.457201i
$623$	−6.06065e27	+	6.25267e28i	−0.0275673	+	0.284408i
$624$	−3.47240e29	−	2.91816e29i	−1.55307	−	1.30518i
$625$	−2.75932e29			−1.21356
$626$	2.62377e29			1.13474
$627$	9.36987e28	−	1.11495e29i	0.398497	−	0.474182i
$628$		−	2.68080e27i		−	0.0112121i
$629$	2.49129e29			1.02469
$630$	2.54112e28	+	3.31976e29i	0.102790	+	1.34286i
$631$	−2.90971e29			−1.15755			−0.578777	−	0.815486i	$-0.696470\pi$
$631$	−2.90971e29			−1.15755			−0.578777	+	0.815486i	$0.696470\pi$
$632$			2.55994e29i			1.00161i
$633$	−1.60514e29	+	1.91000e29i	−0.617695	+	0.735013i
$634$	4.46660e27			0.0169059
$635$	−1.45394e29			−0.541279
$636$	−1.12112e29	−	9.42170e28i	−0.410535	−	0.345008i
$637$	−8.74507e28	+	4.46869e29i	−0.314992	+	1.60959i
$638$		−	2.72496e29i		−	0.965478i
$639$	3.67770e29	−	6.42756e28i	1.28179	−	0.224020i
$640$			3.91603e29i			1.34263i
$641$		−	1.64057e29i		−	0.553332i	−0.960966	−	0.276666i	$-0.910770\pi$
$641$		−	1.64057e29i		−	0.553332i	0.960966	−	0.276666i	$-0.0892296\pi$
$642$	1.28128e29	−	1.52463e29i	0.425135	−	0.505881i
$643$		−	1.74137e29i		−	0.568427i	−0.958761	−	0.284214i	$-0.908267\pi$
$643$		−	1.74137e29i		−	0.568427i	0.958761	−	0.284214i	$-0.0917325\pi$
$644$	5.57876e28	+	5.40743e27i	0.179158	+	0.0173656i
$645$	−1.23934e28	+	1.47472e28i	−0.0391573	+	0.0465944i
$646$	−3.21955e29			−1.00081
$647$	−8.97286e28			−0.274433			−0.137216	−	0.990541i	$-0.543816\pi$
$647$	−8.97286e28			−0.274433			−0.137216	+	0.990541i	$0.543816\pi$
$648$	−8.15200e28	−	2.26096e29i	−0.245316	−	0.680386i
$649$		−	3.52037e29i		−	1.04236i
$650$	2.04830e29			0.596764
$651$	2.70382e29	−	2.64966e29i	0.775134	−	0.759609i
$652$	−2.11040e29			−0.595340
$653$		−	5.20171e29i		−	1.44397i	−0.691910	−	0.721984i	$-0.743230\pi$
$653$		−	5.20171e29i		−	1.44397i	0.691910	−	0.721984i	$-0.256770\pi$
$654$	−6.15025e29	−	5.16858e29i	−1.68007	−	1.41190i
$655$	−1.15076e29			−0.309350
$656$	−4.57666e28			−0.121076
$657$	3.20119e29	−	5.59474e28i	0.833441	−	0.145661i
$658$	3.04225e29	+	2.94882e28i	0.779513	+	0.0755573i
$659$			6.00874e29i			1.51526i	0.652685	+	0.757629i	$0.273642\pi$
$659$			6.00874e29i			1.51526i	−0.652685	+	0.757629i	$0.726358\pi$
$660$	−8.51519e28	−	7.15605e28i	−0.211341	−	0.177608i
$661$			2.78191e29i			0.679559i	0.940505	+	0.339779i	$0.110352\pi$
$661$			2.78191e29i			0.679559i	−0.940505	+	0.339779i	$0.889648\pi$
$662$			6.82602e29i			1.64119i
$663$	4.55776e29	+	3.83028e29i	1.07860	+	0.906439i
$664$		−	2.58129e28i		−	0.0601274i
$665$	−4.91612e29	−	4.76514e28i	−1.12719	−	0.109257i
$666$	6.12840e29	−	1.07107e29i	1.38315	−	0.241733i
$667$	2.75424e29			0.611901
$668$	1.06597e29			0.233127
$669$	−3.27204e29	−	2.74978e29i	−0.704440	−	0.592002i
$670$			5.56329e29i			1.17909i
$671$	2.27046e28			0.0473725
$672$	2.54761e29	−	2.49659e29i	0.523307	−	0.512825i
$673$	8.91219e29			1.80230			0.901149	−	0.433510i	$-0.142725\pi$
$673$	8.91219e29			1.80230			0.901149	+	0.433510i	$0.142725\pi$
$674$		−	1.47540e29i		−	0.293751i
$675$	1.36384e29	+	7.91538e28i	0.267347	+	0.155161i
$676$	3.37611e29			0.651593
$677$	−4.37738e29			−0.831827			−0.415914	−	0.909404i	$-0.636538\pi$
$677$	−4.37738e29			−0.831827			−0.415914	+	0.909404i	$0.636538\pi$
$678$	4.81169e29	−	5.72556e29i	0.900297	−	1.07129i
$679$	3.19062e29	+	3.09264e28i	0.587818	+	0.0569765i
$680$		−	3.91859e29i		−	0.710864i
$681$	−5.39643e29	+	6.42136e29i	−0.963966	+	1.14705i
$682$			4.54485e29i			0.799436i
$683$			1.06104e30i			1.83787i	0.394414	+	0.918933i	$0.370948\pi$
$683$			1.06104e30i			1.83787i	−0.394414	+	0.918933i	$0.629052\pi$
$684$	−2.20384e29	+	3.85167e28i	−0.375917	+	0.0656993i
$685$		−	9.09518e29i		−	1.52778i
$686$	−6.81878e29	−	2.03393e29i	−1.12799	−	0.336459i
$687$	−1.91494e29	−	1.60929e29i	−0.311968	−	0.262174i
$688$	4.10092e28			0.0657964
$689$	−1.44366e30			−2.28119
$690$	2.59928e29	−	3.09296e29i	0.404518	−	0.481347i
$691$		−	1.29496e29i		−	0.198490i	−0.995063	−	0.0992448i	$-0.968357\pi$
$691$		−	1.29496e29i		−	0.198490i	0.995063	−	0.0992448i	$-0.0316427\pi$
$692$	4.49029e28			0.0677891
$693$	−3.21201e28	−	4.19623e29i	−0.0477615	−	0.623965i
$694$	6.29349e29			0.921759
$695$		−	1.19259e30i		−	1.72049i
$696$	4.29191e29	−	5.10707e29i	0.609893	−	0.725729i
$697$	6.00718e28			0.0840865
$698$	8.75019e29			1.20652
$699$	5.18291e28	+	4.35565e28i	0.0703985	+	0.0591620i
$700$	−8.59316e27	+	8.86542e28i	−0.0114980	+	0.118623i
$701$			5.98641e28i			0.0789091i	0.999221	+	0.0394545i	$0.0125620\pi$
$701$			5.98641e28i			0.0789091i	−0.999221	+	0.0394545i	$0.987438\pi$
$702$	1.28585e30	+	7.46273e29i	1.66975	+	0.969076i
$703$			9.22907e29i			1.18067i
$704$		−	1.85925e29i		−	0.234328i
$705$	3.94433e29	−	4.69347e29i	0.489765	−	0.582785i
$706$			1.30883e30i			1.60116i
$707$	7.13698e28	−	7.36310e29i	0.0860222	−	0.887476i
$708$	−3.47924e29	+	4.14005e29i	−0.413176	+	0.491650i
$709$	3.11942e29			0.364996			0.182498	−	0.983206i	$-0.441582\pi$
$709$	3.11942e29			0.364996			0.182498	+	0.983206i	$0.441582\pi$
$710$	1.52007e30			1.75247
$711$	−2.09880e29	−	1.20089e30i	−0.238419	−	1.36418i
$712$		−	1.84632e29i		−	0.206665i
$713$	−4.59370e29			−0.506667
$714$	−6.64478e29	+	6.51170e29i	−0.722187	+	0.707722i
$715$	−1.09650e30			−1.17434
$716$		−	1.87162e29i		−	0.197529i
$717$	1.03492e30	+	8.69732e29i	1.07635	+	0.904554i
$718$	−6.88637e28			−0.0705803
$719$	6.52660e29			0.659225			0.329613	−	0.944116i	$-0.393082\pi$
$719$	6.52660e29			0.659225			0.329613	+	0.944116i	$0.393082\pi$
$720$	−2.44766e29	−	1.40049e30i	−0.243646	−	1.39409i
$721$	−1.75845e30	−	1.70444e29i	−1.72508	−	0.167210i
$722$			2.47624e28i			0.0239416i
$723$	−8.31953e29	−	6.99163e29i	−0.792769	−	0.666233i
$724$		−	8.13078e29i		−	0.763620i
$725$			4.37687e29i			0.405149i
$726$	−6.00903e29	−	5.04991e29i	−0.548239	−	0.460733i
$727$		−	2.41749e29i		−	0.217397i	−0.994075	−	0.108698i	$-0.965332\pi$
$727$		−	2.41749e29i		−	0.217397i	0.994075	−	0.108698i	$-0.0346682\pi$
$728$	1.29114e29	−	1.33205e30i	0.114444	−	1.18070i
$729$	5.67786e29	+	9.93801e29i	0.496073	+	0.868281i
$730$	1.32312e30			1.13948
$731$	−5.38273e28			−0.0456952
$732$	−2.67011e28	−	2.24393e28i	−0.0223441	−	0.0187777i
$733$			1.91838e30i			1.58250i	0.611493	+	0.791250i	$0.290569\pi$
$733$			1.91838e30i			1.58250i	−0.611493	+	0.791250i	$0.709431\pi$
$734$	−1.54134e30			−1.25340
$735$	−1.11101e30	+	8.95963e29i	−0.890637	+	0.718245i
$736$	−4.32832e29			−0.342060
$737$		−	7.03208e29i		−	0.547867i
$738$	1.47772e29	−	2.58263e28i	0.113501	−	0.0198367i
$739$	−1.83945e30			−1.39290			−0.696452	−	0.717604i	$-0.745239\pi$
$739$	−1.83945e30			−1.39290			−0.696452	+	0.717604i	$0.745239\pi$
$740$	7.04851e29			0.526217
$741$	−1.41894e30	+	1.68844e30i	−1.04441	+	1.24278i
$742$	2.17651e29	−	2.24547e30i	0.157950	−	1.62954i
$743$			1.87045e30i			1.33833i	0.743115	+	0.669164i	$0.233348\pi$
$743$			1.87045e30i			1.33833i	−0.743115	+	0.669164i	$0.766652\pi$
$744$	−7.15832e29	+	8.51789e29i	−0.505004	+	0.600919i
$745$		−	1.43337e30i		−	0.997053i
$746$			2.36051e30i			1.61901i
$747$	2.11631e28	+	1.21091e29i	0.0143124	+	0.0818926i
$748$		−	3.10804e29i		−	0.207262i
$749$	8.49740e29	+	8.23644e28i	0.558762	+	0.0541602i
$750$	−1.09858e30	−	9.23230e29i	−0.712340	−	0.598641i
$751$	−2.87327e29			−0.183721			−0.0918603	−	0.995772i	$-0.529281\pi$
$751$	−2.87327e29			−0.183721			−0.0918603	+	0.995772i	$0.529281\pi$
$752$	−1.30516e30			−0.822957
$753$	9.80683e29	−	1.16694e30i	0.609791	−	0.725608i
$754$			4.12657e30i			2.53041i
$755$	−8.62206e29			−0.521396
$756$	−3.76946e29	+	5.25232e29i	−0.224802	+	0.313237i
$757$	−9.46707e29			−0.556812			−0.278406	−	0.960463i	$-0.589806\pi$
$757$	−9.46707e29			−0.556812			−0.278406	+	0.960463i	$0.589806\pi$
$758$		−	6.78001e29i		−	0.393282i
$759$	−3.28553e29	+	3.90954e29i	−0.187960	+	0.223659i
$760$	1.45165e30			0.819069
$761$	2.30806e30			1.28442			0.642212	−	0.766527i	$-0.278017\pi$
$761$	2.30806e30			1.28442			0.642212	+	0.766527i	$0.278017\pi$
$762$	−7.76697e29	−	6.52725e29i	−0.426309	−	0.358264i
$763$	3.32251e29	−	3.42778e30i	0.179870	−	1.85569i
$764$			7.76952e29i			0.414872i
$765$	3.21272e29	+	1.83825e30i	0.169211	+	0.968185i
$766$			7.46613e28i			0.0387877i
$767$			5.33112e30i			2.73191i
$768$	−1.28146e30	+	1.52484e30i	−0.647755	+	0.770782i
$769$		−	2.99233e29i		−	0.149205i	−0.997213	−	0.0746024i	$-0.976231\pi$
$769$		−	2.99233e29i		−	0.149205i	0.997213	−	0.0746024i	$-0.0237688\pi$
$770$	1.65312e29	−	1.70550e30i	0.0813115	−	0.838877i
$771$	1.99371e30	−	2.37237e30i	0.967365	−	1.15110i
$772$	−5.11909e29			−0.245025
$773$	3.76572e30			1.77813			0.889065	−	0.457780i	$-0.151355\pi$
$773$	3.76572e30			1.77813			0.889065	+	0.457780i	$0.151355\pi$
$774$	−1.32411e29	+	2.31417e28i	−0.0616801	+	0.0107799i
$775$		−	7.30002e29i		−	0.335472i
$776$	−9.42141e29			−0.427138
$777$	1.86663e30	+	1.90478e30i	0.834904	+	0.851968i
$778$	−1.07486e30			−0.474315
$779$			2.22538e29i			0.0968858i
$780$	1.28951e30	+	1.08369e30i	0.553899	+	0.465490i
$781$	−1.92139e30			−0.814292
$782$	1.12893e30			0.472058
$783$	−1.59466e30	+	2.74765e30i	−0.657916	+	1.13361i
$784$	2.98190e30	+	5.83548e29i	1.21388	+	0.237551i
$785$		−	8.28364e28i		−	0.0332728i
$786$	−6.14738e29	−	5.16617e29i	−0.243642	−	0.204754i
$787$		−	2.53125e30i		−	0.989921i	−0.868915	−	0.494961i	$-0.835183\pi$
$787$		−	2.53125e30i		−	0.989921i	0.868915	−	0.494961i	$-0.164817\pi$
$788$		−	1.16602e30i		−	0.449968i
$789$	1.95968e30	+	1.64689e30i	0.746236	+	0.627127i
$790$		−	4.96352e30i		−	1.86511i
$791$	3.19108e30	+	3.09308e29i	1.18327	+	0.114693i
$792$	2.12948e29	+	1.21844e30i	0.0779218	+	0.445851i
$793$	−3.43829e29			−0.124158
$794$	1.58381e30			0.564402
$795$	−3.46423e30	−	2.91129e30i	−1.21829	−	1.02384i
$796$			6.08654e29i			0.211244i
$797$	−1.37850e30			−0.472164			−0.236082	−	0.971733i	$-0.575863\pi$
$797$	−1.37850e30			−0.472164			−0.236082	+	0.971733i	$0.575863\pi$
$798$	−2.41228e30	−	2.46158e30i	−0.815449	−	0.832116i
$799$	1.71312e30			0.571539
$800$		−	6.87829e29i		−	0.226483i
$801$	1.51373e29	+	8.66123e29i	0.0491934	+	0.281474i
$802$	2.41597e30			0.774926
$803$	−1.67244e30			−0.529465
$804$	−6.94991e29	+	8.26990e29i	−0.217166	+	0.258411i
$805$	1.72383e30	+	1.67089e29i	0.531664	+	0.0515336i
$806$		−	6.88256e30i		−	2.09523i
$807$	−1.73402e30	+	2.06336e30i	−0.521053	+	0.620015i
$808$			2.17421e30i			0.644885i
$809$		−	3.23821e30i		−	0.948082i	−0.880503	−	0.474041i	$-0.842795\pi$
$809$		−	3.23821e30i		−	0.948082i	0.880503	−	0.474041i	$-0.157205\pi$
$810$	1.58061e30	+	4.38383e30i	0.456806	+	1.26695i
$811$		−	9.38781e29i		−	0.267822i	−0.990993	−	0.133911i	$-0.957246\pi$
$811$		−	9.38781e29i		−	0.267822i	0.990993	−	0.133911i	$-0.0427536\pi$
$812$	−1.78606e30	−	1.73121e29i	−0.502988	−	0.0487541i
$813$	−9.27082e29	−	7.79107e29i	−0.257731	−	0.216594i
$814$	−3.20174e30			−0.878679
$815$	−6.52110e30			−1.76671
$816$	2.55590e30	−	3.04134e30i	0.683592	−	0.813426i
$817$		−	1.99405e29i		−	0.0526507i
$818$	−4.37017e30			−1.13917
$819$	4.86415e29	+	6.35462e30i	0.125178	+	1.63534i
$820$	1.69959e29			0.0431815
$821$		−	6.38629e30i		−	1.60194i	−0.598706	−	0.800969i	$-0.704318\pi$
$821$		−	6.38629e30i		−	1.60194i	0.598706	−	0.800969i	$-0.295682\pi$
$822$	4.08316e30	−	4.85866e30i	1.01121	−	1.20327i
$823$	7.01330e30			1.71484			0.857421	−	0.514616i	$-0.172066\pi$
$823$	7.01330e30			1.71484			0.857421	+	0.514616i	$0.172066\pi$
$824$	5.19242e30			1.25353
$825$	−6.21280e29	−	5.22116e29i	−0.148088	−	0.124452i
$826$	−8.29205e30	−	8.03740e29i	−1.95151	−	0.189158i
$827$			1.77840e30i			0.413259i	0.978419	+	0.206630i	$0.0662495\pi$
$827$			1.77840e30i			0.413259i	−0.978419	+	0.206630i	$0.933750\pi$
$828$	7.72773e29	−	1.35058e29i	0.177310	−	0.0309886i
$829$		−	4.26678e30i		−	0.966668i	−0.875436	−	0.483334i	$-0.839426\pi$
$829$		−	4.26678e30i		−	0.966668i	0.875436	−	0.483334i	$-0.160574\pi$
$830$			5.00493e29i			0.111964i
$831$	−3.91316e30	+	4.65638e30i	−0.864403	+	1.02858i
$832$			2.81558e30i			0.614148i
$833$	−3.91395e30	−	7.65947e29i	−0.843030	−	0.164978i
$834$	5.35398e30	−	6.37086e30i	1.13876	−	1.35505i
$835$	3.29384e30			0.691822
$836$	1.15138e30			0.238811
$837$	2.65968e30	−	4.58270e30i	0.544768	−	0.938651i
$838$		−	4.70961e29i		−	0.0952628i
$839$	−8.99381e30			−1.79657			−0.898283	−	0.439417i	$-0.855185\pi$
$839$	−8.99381e30			−1.79657			−0.898283	+	0.439417i	$0.855185\pi$
$840$	2.99605e30	−	2.93604e30i	0.591040	−	0.579202i
$841$	−3.68497e30			−0.717920
$842$			1.30663e30i			0.251406i
$843$	4.22331e30	+	3.54922e30i	0.802535	+	0.674439i
$844$	−1.97242e30			−0.370172
$845$	1.04321e31			1.93365
$846$	4.21414e30	−	7.36509e29i	0.771472	−	0.134831i
$847$	3.24622e29	−	3.34907e30i	0.0586952	−	0.605548i
$848$			9.63334e30i			1.72036i
$849$	6.99904e30	+	5.88190e30i	1.23455	+	1.03750i
$850$			1.79402e30i			0.312557i
$851$		−	3.23615e30i		−	0.556889i
$852$	2.25961e30	+	1.89894e30i	0.384076	+	0.322772i
$853$		−	4.18128e30i		−	0.702011i	−0.936373	−	0.351006i	$-0.885840\pi$
$853$		−	4.18128e30i		−	0.702011i	0.936373	−	0.351006i	$-0.114160\pi$
$854$	5.18370e28	−	5.34794e29i	0.00859671	−	0.0886909i
$855$	−6.80984e30	+	1.19016e30i	−1.11556	+	0.194967i
$856$	−2.50915e30			−0.406024
$857$	−1.09174e30			−0.174510			−0.0872548	−	0.996186i	$-0.527809\pi$
$857$	−1.09174e30			−0.174510			−0.0872548	+	0.996186i	$0.527809\pi$
$858$	−5.85751e30	−	4.92257e30i	−0.924904	−	0.777277i
$859$		−	2.29470e29i		−	0.0357929i	−0.999840	−	0.0178964i	$-0.994303\pi$
$859$		−	2.29470e29i		−	0.0357929i	0.999840	−	0.0178964i	$-0.00569692\pi$
$860$	−1.52292e29			−0.0234662
$861$	4.50094e29	+	4.59293e29i	0.0685125	+	0.0699128i
$862$	1.27172e31			1.91234
$863$			6.94201e30i			1.03127i	0.856809	+	0.515635i	$0.172444\pi$
$863$			6.94201e30i			1.03127i	−0.856809	+	0.515635i	$0.827556\pi$
$864$	2.50603e30	−	4.31795e30i	0.367783	−	0.633700i
$865$	1.38749e30			0.201169
$866$	−8.88491e30			−1.27267
$867$	1.19151e30	−	1.41781e30i	0.168615	−	0.200640i
$868$	2.97890e30	+	2.88742e29i	0.416485	+	0.0403695i
$869$			6.27396e30i			0.866631i
$870$	−8.32169e30	+	9.90222e30i	−1.13569	+	1.35139i
$871$			1.06491e31i			1.43590i
$872$			1.01217e31i			1.34843i
$873$	4.41966e30	−	7.72429e29i	0.581755	−	0.101674i
$874$			4.18215e30i			0.543913i
$875$	5.93478e29	−	6.12281e30i	0.0762640	−	0.786803i
$876$	1.96683e30	+	1.65290e30i	0.249732	+	0.209871i
$877$	9.85421e30			1.23631			0.618153	−	0.786058i	$-0.287881\pi$
$877$	9.85421e30			1.23631			0.618153	+	0.786058i	$0.287881\pi$
$878$	8.26851e29			0.102503
$879$	2.89573e30	−	3.44571e30i	0.354711	−	0.422081i
$880$			7.31679e30i			0.885630i
$881$	8.91446e30			1.06622			0.533111	−	0.846045i	$-0.321023\pi$
$881$	8.91446e30			1.06622			0.533111	+	0.846045i	$0.321023\pi$
$882$	−9.95734e30	−	2.01473e29i	−1.17686	−	0.0238121i
$883$	−1.33427e31			−1.55832			−0.779158	−	0.626827i	$-0.784353\pi$
$883$	−1.33427e31			−1.55832			−0.779158	+	0.626827i	$0.784353\pi$
$884$			4.70670e30i			0.543210i
$885$	−1.07508e31	+	1.27927e31i	−1.22613	+	1.45901i
$886$	−1.70995e31			−1.92721
$887$	−3.55260e30			−0.395683			−0.197842	−	0.980234i	$-0.563393\pi$
$887$	−3.55260e30			−0.395683			−0.197842	+	0.980234i	$0.563393\pi$
$888$	−6.00065e30	−	5.04287e30i	−0.660484	−	0.555062i
$889$	4.19590e29	−	4.32884e30i	0.0456411	−	0.470872i
$890$			3.57987e30i			0.384833i
$891$	−1.99791e30	−	5.54122e30i	−0.212257	−	0.588694i
$892$		−	3.37896e30i		−	0.354774i
$893$			6.34629e30i			0.658536i
$894$	6.43493e30	−	7.65711e30i	0.659933	−	0.785274i
$895$		−	5.78328e30i		−	0.586181i
$896$	−1.16593e31	−	1.13012e30i	−1.16799	−	0.113212i
$897$	4.97548e30	−	5.92047e30i	0.492623	−	0.586186i
$898$	2.15733e30			0.211113
$899$	1.47069e31			1.42247
$900$	2.14626e29	+	1.22804e30i	0.0205181	+	0.117400i
$901$		−	1.26444e31i		−	1.19478i
$902$	−7.72026e29			−0.0721047
$903$	−4.03307e29	−	4.11549e29i	−0.0372318	−	0.0379927i
$904$	−9.42277e30			−0.859825
$905$		−	2.51240e31i		−	2.26610i
$906$	−4.60592e30	−	3.87076e30i	−0.410649	−	0.345104i
$907$	−6.95111e30			−0.612601			−0.306300	−	0.951935i	$-0.599091\pi$
$907$	−6.95111e30			−0.612601			−0.306300	+	0.951935i	$0.599091\pi$
$908$	−6.63120e30			−0.577685
$909$	−1.78256e30	−	1.01994e31i	−0.153505	−	0.878323i
$910$	−2.50342e30	+	2.58274e31i	−0.213108	+	2.19860i
$911$		−	1.18167e31i		−	0.994381i	−0.867641	−	0.497191i	$-0.834365\pi$
$911$		−	1.18167e31i		−	0.994381i	0.867641	−	0.497191i	$-0.165635\pi$
$912$	1.12667e31	+	9.46841e30i	0.937242	+	0.787646i
$913$		−	6.32631e29i		−	0.0520244i
$914$			2.08448e31i			1.69458i
$915$	−8.25060e29	−	6.93370e29i	−0.0663077	−	0.0557242i
$916$		−	1.97752e30i		−	0.157115i
$917$	3.32096e29	−	3.42618e30i	0.0260847	−	0.269111i
$918$	−6.53631e30	+	1.12623e31i	−0.507557	+	0.874535i
$919$	−1.62113e31			−1.24453			−0.622263	−	0.782808i	$-0.713786\pi$
$919$	−1.62113e31			−1.24453			−0.622263	+	0.782808i	$0.713786\pi$
$920$	−5.09019e30			−0.386333
$921$	−6.88267e30	−	5.78411e30i	−0.516453	−	0.434021i
$922$			2.73156e31i			2.02645i
$923$	2.90969e31			2.13417
$924$	2.37632e30	−	2.32873e30i	0.172326	−	0.168874i
$925$	5.14270e30			0.368725
$926$		−	2.31830e31i		−	1.64344i
$927$	−2.43581e31	+	4.25709e30i	−1.70729	+	0.298384i
$928$	1.38573e31			0.960337
$929$	3.12710e30			0.214277			0.107139	−	0.994244i	$-0.465831\pi$
$929$	3.12710e30			0.214277			0.107139	+	0.994244i	$0.465831\pi$
$930$	1.38794e31	−	1.65155e31i	0.940374	−	1.11898i
$931$	2.83747e30	−	1.44994e31i	0.190090	−	0.971353i
$932$			5.35228e29i			0.0354545i
$933$	−3.81514e30	+	4.53974e30i	−0.249893	+	0.297354i
$934$			6.23271e30i			0.403678i
$935$		−	9.60379e30i		−	0.615065i
$936$	−3.22480e30	−	1.84516e31i	−0.204224	−	1.16853i
$937$			1.97842e31i			1.23895i	0.785018	+	0.619473i	$0.212654\pi$
$937$			1.97842e31i			1.23895i	−0.785018	+	0.619473i	$0.787346\pi$
$938$	−1.65637e31	−	1.60550e30i	−1.02572	−	0.0994216i
$939$	1.20518e31	+	1.01281e31i	0.738009	+	0.620213i
$940$	4.84685e30			0.293506
$941$	−2.40995e31			−1.44317			−0.721585	−	0.692326i	$-0.756586\pi$
$941$	−2.40995e31			−1.44317			−0.721585	+	0.692326i	$0.756586\pi$
$942$	3.71883e29	−	4.42514e29i	0.0220227	−	0.0262055i
$943$		−	7.80324e29i		−	0.0456985i
$944$	3.55739e31			2.06028
$945$	−1.16476e31	+	1.62296e31i	−0.667116	+	0.929552i
$946$	6.91775e29			0.0391839
$947$			1.27295e31i			0.713078i	0.934281	+	0.356539i	$0.116043\pi$
$947$			1.27295e31i			0.713078i	−0.934281	+	0.356539i	$0.883957\pi$
$948$	6.20066e30	−	7.37834e30i	0.343519	−	0.408763i
$949$	2.53268e31			1.38767
$950$	−6.64601e30			−0.360133
$951$	2.05164e29	+	1.72417e29i	0.0109953	+	0.00924028i
$952$	1.16669e31	+	1.13086e30i	0.618397	+	0.0599406i
$953$		−	1.29646e31i		−	0.679645i	−0.940490	−	0.339822i	$-0.889633\pi$
$953$		−	1.29646e31i		−	0.679645i	0.940490	−	0.339822i	$-0.110367\pi$
$954$	−5.43613e30	−	3.11044e31i	−0.281859	−	1.61274i
$955$			2.40077e31i			1.23116i
$956$			1.06874e31i			0.542080i
$957$	1.05187e31	−	1.25165e31i	0.527701	−	0.627927i
$958$		−	1.88331e31i		−	0.934511i
$959$	2.70793e31	+	2.62476e30i	1.32905	+	0.128823i
$960$	−5.67793e30	+	6.75633e30i	−0.275640	+	0.327992i
$961$	−3.70357e30			−0.177838
$962$	4.84860e31			2.30292
$963$	1.17706e31	−	2.05716e30i	0.552998	−	0.0966480i
$964$		−	8.59141e30i		−	0.399260i
$965$	−1.58179e31			−0.727129
$966$	8.45860e30	+	8.63148e30i	0.384626	+	0.392487i
$967$	2.95203e31			1.32783			0.663916	−	0.747808i	$-0.268893\pi$
$967$	2.95203e31			1.32783			0.663916	+	0.747808i	$0.268893\pi$
$968$			9.88929e30i			0.440021i
$969$	−1.47884e31	−	1.24279e31i	−0.650909	−	0.547015i
$970$	1.82674e31			0.795378
$971$	1.92379e31			0.828619			0.414309	−	0.910136i	$-0.364023\pi$
$971$	1.92379e31			0.828619			0.414309	+	0.910136i	$0.364023\pi$
$972$	−3.12688e30	+	8.49119e30i	−0.133234	+	0.361804i
$973$	3.55073e31	+	3.44169e30i	1.49669	+	0.145073i
$974$		−	1.75120e31i		−	0.730241i
$975$	9.40844e30	+	7.90673e30i	0.388123	+	0.326173i
$976$			2.29433e30i			0.0936339i
$977$			4.39902e31i			1.77608i	0.459764	+	0.888041i	$0.347934\pi$
$977$			4.39902e31i			1.77608i	−0.459764	+	0.888041i	$0.652066\pi$
$978$	−3.48359e31	−	2.92756e31i	−1.39145	−	1.16936i
$979$		−	4.52500e30i		−	0.178814i
$980$	−1.10736e31	−	2.16706e30i	−0.432927	−	0.0847223i
$981$	−8.29842e30	−	4.74817e31i	−0.320975	−	1.83655i
$982$	−7.36540e30			−0.281855
$983$	−5.07704e31			−1.92220			−0.961100	−	0.276200i	$-0.910925\pi$
$983$	−5.07704e31			−1.92220			−0.961100	+	0.276200i	$0.910925\pi$
$984$	−1.44692e30	−	1.21597e30i	−0.0541995	−	0.0455486i
$985$		−	3.60299e31i		−	1.33531i
$986$	−3.61431e31			−1.32531
$987$	1.28357e31	+	1.30980e31i	0.465682	+	0.475199i
$988$	−1.74361e31			−0.625896
$989$			6.99210e29i			0.0248340i
$990$	−4.12890e30	−	2.36246e31i	−0.145099	−	0.830225i
$991$	−3.70813e31			−1.28938			−0.644692	−	0.764443i	$-0.723014\pi$
$991$	−3.70813e31			−1.28938			−0.644692	+	0.764443i	$0.723014\pi$
$992$	−2.31120e31			−0.795179
$993$	−2.63495e31	+	3.13540e31i	−0.897025	+	1.06740i
$994$	−4.38675e30	+	4.52574e31i	−0.147770	+	1.52452i
$995$			1.88073e31i			0.626880i
$996$	−6.25239e29	+	7.43990e29i	−0.0206216	+	0.0245383i
$997$			5.97176e30i			0.194896i	0.995241	+	0.0974480i	$0.0310680\pi$
$997$			5.97176e30i			0.194896i	−0.995241	+	0.0974480i	$0.968932\pi$
$998$		−	4.23390e31i		−	1.36732i
$999$	3.22841e31	+	1.87368e31i	1.03169	+	0.598767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.22.c.b.20.12	yes	52
3.2	odd	2	inner	21.22.c.b.20.41	yes	52
7.6	odd	2	inner	21.22.c.b.20.42	yes	52
21.20	even	2	inner	21.22.c.b.20.11	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.22.c.b.20.11	✓	52	21.20	even	2	inner
21.22.c.b.20.12	yes	52	1.1	even	1	trivial
21.22.c.b.20.41	yes	52	3.2	odd	2	inner
21.22.c.b.20.42	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)

\(f(q)\)	\(=\)	\(q+1704.62i q^{2} +(-65800.8 + 78298.2i) q^{3} -808569. q^{4} -2.49846e7 q^{5} +(-1.33469e8 - 1.12165e8i) q^{6} +(7.21028e7 - 7.43873e8i) q^{7} +2.19654e9i q^{8} +(-1.80087e9 - 1.03042e10i) q^{9} +O(q^{10})\)	\(q+1704.62i q^{2} +(-65800.8 + 78298.2i) q^{3} -808569. q^{4} -2.49846e7 q^{5} +(-1.33469e8 - 1.12165e8i) q^{6} +(7.21028e7 - 7.43873e8i) q^{7} +2.19654e9i q^{8} +(-1.80087e9 - 1.03042e10i) q^{9} -4.25893e10i q^{10} +5.38334e10i q^{11} +(5.32045e10 - 6.33095e10i) q^{12} -8.15234e11i q^{13} +(1.26802e12 + 1.22908e11i) q^{14} +(1.64401e12 - 1.95625e12i) q^{15} -5.43995e12 q^{16} +7.14032e12 q^{17} +(1.75647e13 - 3.06979e12i) q^{18} +2.64515e13i q^{19} +2.02018e13 q^{20} +(5.34995e13 + 5.45929e13i) q^{21} -9.17654e13 q^{22} -9.27517e13i q^{23} +(-1.71985e14 - 1.44534e14i) q^{24} +1.47395e14 q^{25} +1.38966e15 q^{26} +(9.25296e14 + 5.37017e14i) q^{27} +(-5.83001e13 + 6.01473e14i) q^{28} +2.96948e15i q^{29} +(3.33466e15 + 2.80241e15i) q^{30} -4.95268e15i q^{31} -4.66656e15i q^{32} +(-4.21506e15 - 3.54228e15i) q^{33} +1.21715e16i q^{34} +(-1.80146e15 + 1.85854e16i) q^{35} +(1.45613e15 + 8.33163e15i) q^{36} +3.48905e16 q^{37} -4.50897e16 q^{38} +(6.38314e16 + 5.36430e16i) q^{39} -5.48798e16i q^{40} +8.41304e15 q^{41} +(-9.30601e16 + 9.11962e16i) q^{42} -7.53851e15 q^{43} -4.35281e16i q^{44} +(4.49940e16 + 2.57446e17i) q^{45} +1.58106e17 q^{46} +2.39922e17 q^{47} +(3.57953e17 - 4.25939e17i) q^{48} +(-5.48148e17 - 1.07271e17i) q^{49} +2.51253e17i q^{50} +(-4.69838e17 + 5.59074e17i) q^{51} +6.59173e17i q^{52} -1.77085e18i q^{53} +(-9.15409e17 + 1.57728e18i) q^{54} -1.34501e18i q^{55} +(1.63395e18 + 1.58377e17i) q^{56} +(-2.07111e18 - 1.74053e18i) q^{57} -5.06183e18 q^{58} -6.53938e18 q^{59} +(-1.32929e18 + 1.58177e18i) q^{60} -4.21755e17i q^{61} +8.44243e18 q^{62} +(-7.79484e18 + 5.96658e17i) q^{63} -3.45371e18 q^{64} +2.03683e19i q^{65} +(6.03824e18 - 7.18507e18i) q^{66} -1.30627e19 q^{67} -5.77344e18 q^{68} +(7.26229e18 + 6.10313e18i) q^{69} +(-3.16810e19 - 3.07081e18i) q^{70} +3.56914e19i q^{71} +(2.26335e19 - 3.95568e18i) q^{72} +3.10669e19i q^{73} +5.94750e19i q^{74} +(-9.69872e18 + 1.15408e19i) q^{75} -2.13879e19i q^{76} +(4.00452e19 + 3.88154e18i) q^{77} +(-9.14408e19 + 1.08808e20i) q^{78} +1.16544e20 q^{79} +1.35915e20 q^{80} +(-1.02933e20 + 3.71129e19i) q^{81} +1.43410e19i q^{82} -1.17516e19 q^{83} +(-4.32580e19 - 4.41422e19i) q^{84} -1.78398e20 q^{85} -1.28503e19i q^{86} +(-2.32505e20 - 1.95394e20i) q^{87} -1.18247e20 q^{88} -8.40556e19 q^{89} +(-4.38847e20 + 7.66976e19i) q^{90} +(-6.06430e20 - 5.87807e19i) q^{91} +7.49961e19i q^{92} +(3.87786e20 + 3.25890e20i) q^{93} +4.08975e20i q^{94} -6.60882e20i q^{95} +(3.65383e20 + 3.07063e20i) q^{96} +4.28920e20i q^{97} +(1.82856e20 - 9.34383e20i) q^{98} +(5.54709e20 - 9.69469e19i) 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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