LMFDB - Embedded newform 63.6.p.b.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(17,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("63.17");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.p (of order $6$, degree $2$, 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:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	63.17
Dual form			63.6.p.b.26.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30242 + 0.751952i) q^{2} +(-14.8691 + 25.7541i) q^{4} +(-8.15150 - 14.1188i) q^{5} +(-67.6518 - 110.590i) q^{7} -92.8484i q^{8} +O(q^{10})$	\(q+(-1.30242 + 0.751952i) q^{2} +(-14.8691 + 25.7541i) q^{4} +(-8.15150 - 14.1188i) q^{5} +(-67.6518 - 110.590i) q^{7} -92.8484i q^{8} +(21.2333 + 12.2591i) q^{10} +(558.327 + 322.350i) q^{11} -524.737i q^{13} +(171.270 + 93.1641i) q^{14} +(-405.995 - 703.204i) q^{16} +(1004.44 - 1739.74i) q^{17} +(-421.992 + 243.637i) q^{19} +484.823 q^{20} -969.568 q^{22} +(1456.23 - 840.752i) q^{23} +(1429.61 - 2476.15i) q^{25} +(394.577 + 683.428i) q^{26} +(3854.08 - 97.9271i) q^{28} -1652.07i q^{29} +(-6396.37 - 3692.95i) q^{31} +(3630.64 + 2096.15i) q^{32} +3021.16i q^{34} +(-1009.94 + 1856.64i) q^{35} +(4484.96 + 7768.18i) q^{37} +(366.407 - 634.636i) q^{38} +(-1310.91 + 756.854i) q^{40} -14382.5 q^{41} +1615.95 q^{43} +(-16603.7 + 9586.15i) q^{44} +(-1264.41 + 2190.02i) q^{46} +(-2309.84 - 4000.77i) q^{47} +(-7653.47 + 14963.3i) q^{49} +4299.98i q^{50} +(13514.1 + 7802.39i) q^{52} +(332.149 + 191.766i) q^{53} -10510.6i q^{55} +(-10268.1 + 6281.36i) q^{56} +(1242.28 + 2151.69i) q^{58} +(6032.47 - 10448.5i) q^{59} +(10068.3 - 5812.91i) q^{61} +11107.7 q^{62} +19678.8 q^{64} +(-7408.67 + 4277.40i) q^{65} +(-7390.10 + 12800.0i) q^{67} +(29870.3 + 51736.9i) q^{68} +(-80.7374 - 3177.55i) q^{70} -56016.9i q^{71} +(-53690.2 - 30998.0i) q^{73} +(-11682.6 - 6744.95i) q^{74} -14490.7i q^{76} +(-2122.98 - 83553.2i) q^{77} +(-7045.58 - 12203.3i) q^{79} +(-6618.93 + 11464.3i) q^{80} +(18732.1 - 10815.0i) q^{82} +120269. q^{83} -32750.8 q^{85} +(-2104.64 + 1215.12i) q^{86} +(29929.7 - 51839.8i) q^{88} +(42263.8 + 73203.0i) q^{89} +(-58030.9 + 35499.4i) q^{91} +50005.0i q^{92} +(6016.77 + 3473.78i) q^{94} +(6879.74 + 3972.02i) q^{95} -128230. i q^{97} +(-1283.64 - 25243.5i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 304 q^{4} - 436 q^{7}+O(q^{10}) $ 24 * q + 304 * q^4 - 436 * q^7	$ 24 q + 304 q^{4} - 436 q^{7} + 1992 q^{10} - 3644 q^{16} + 3804 q^{19} - 5648 q^{22} - 18852 q^{25} - 39172 q^{28} + 38652 q^{31} + 20548 q^{37} + 132060 q^{40} + 2200 q^{43} - 25712 q^{46} - 125676 q^{49} - 2940 q^{52} + 154300 q^{58} + 48504 q^{61} - 327880 q^{64} + 156324 q^{67} - 9468 q^{70} - 703236 q^{73} + 165756 q^{79} + 1081020 q^{82} - 284448 q^{85} + 582308 q^{88} - 19812 q^{91} - 1481724 q^{94}+O(q^{100}) $ 24 * q + 304 * q^4 - 436 * q^7 + 1992 * q^10 - 3644 * q^16 + 3804 * q^19 - 5648 * q^22 - 18852 * q^25 - 39172 * q^28 + 38652 * q^31 + 20548 * q^37 + 132060 * q^40 + 2200 * q^43 - 25712 * q^46 - 125676 * q^49 - 2940 * q^52 + 154300 * q^58 + 48504 * q^61 - 327880 * q^64 + 156324 * q^67 - 9468 * q^70 - 703236 * q^73 + 165756 * q^79 + 1081020 * q^82 - 284448 * q^85 + 582308 * q^88 - 19812 * q^91 - 1481724 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.30242	+	0.751952i	−0.230237	+	0.132928i	−0.610682	−	0.791876i	$-0.709104\pi$
$2$	−1.30242	+	0.751952i	−0.230237	+	0.132928i	0.380444	+	0.924804i	$0.375771\pi$
$3$		0			0
$3$		0			0
$4$	−14.8691	+	25.7541i	−0.464661	+	0.804816i
$5$	−8.15150	−	14.1188i	−0.145818	−	0.252565i	0.783860	−	0.620938i	$-0.213248\pi$
$5$	−8.15150	−	14.1188i	−0.145818	−	0.252565i	−0.929678	+	0.368373i	$0.879915\pi$
$6$		0			0
$7$	−67.6518	−	110.590i	−0.521836	−	0.853046i
$7$	−67.6518	−	110.590i	−0.521836	−	0.853046i
$8$		−	92.8484i		−	0.512920i
$9$		0			0
$10$	21.2333	+	12.2591i	0.0671457	+	0.0387666i
$11$	558.327	+	322.350i	1.39126	+	0.803242i	0.993454	−	0.114229i	$-0.0364398\pi$
$11$	558.327	+	322.350i	1.39126	+	0.803242i	0.397802	+	0.917471i	$0.369773\pi$
$12$		0			0
$13$		−	524.737i		−	0.861160i	−0.902553	−	0.430580i	$-0.858309\pi$
$13$		−	524.737i		−	0.861160i	0.902553	−	0.430580i	$-0.141691\pi$
$14$	171.270	+	93.1641i	0.233539	+	0.127037i
$15$		0			0
$16$	−405.995	−	703.204i	−0.396479	−	0.686722i
$17$	1004.44	−	1739.74i	0.842950	−	1.46003i	−0.0444401	−	0.999012i	$-0.514150\pi$
$17$	1004.44	−	1739.74i	0.842950	−	1.46003i	0.887390	−	0.461020i	$-0.152516\pi$
$18$		0			0
$19$	−421.992	+	243.637i	−0.268176	+	0.154832i	−0.628059	−	0.778166i	$-0.716150\pi$
$19$	−421.992	+	243.637i	−0.268176	+	0.154832i	0.359882	+	0.932998i	$0.382817\pi$
$20$	484.823			0.271024
$21$		0			0
$22$	−969.568			−0.427092
$23$	1456.23	−	840.752i	0.573996	−	0.331397i	−0.184748	−	0.982786i	$-0.559147\pi$
$23$	1456.23	−	840.752i	0.573996	−	0.331397i	0.758744	+	0.651389i	$0.225813\pi$
$24$		0			0
$25$	1429.61	−	2476.15i	0.457474	−	0.792368i
$26$	394.577	+	683.428i	0.114472	+	0.198271i
$27$		0			0
$28$	3854.08	−	97.9271i	0.929021	−	0.0236052i
$29$		−	1652.07i		−	0.364782i	−0.983226	−	0.182391i	$-0.941616\pi$
$29$		−	1652.07i		−	0.364782i	0.983226	−	0.182391i	$-0.0583837\pi$
$30$		0			0
$31$	−6396.37	−	3692.95i	−1.19544	−	0.690190i	−0.235908	−	0.971775i	$-0.575807\pi$
$31$	−6396.37	−	3692.95i	−1.19544	−	0.690190i	−0.959536	+	0.281585i	$0.909140\pi$
$32$	3630.64	+	2096.15i	0.626770	+	0.361866i
$33$		0			0
$34$			3021.16i			0.448205i
$35$	−1009.94	+	1856.64i	−0.139356	+	0.256187i
$36$		0			0
$37$	4484.96	+	7768.18i	0.538585	+	0.932856i	0.998981	+	0.0451426i	$0.0143742\pi$
$37$	4484.96	+	7768.18i	0.538585	+	0.932856i	−0.460396	+	0.887714i	$0.652292\pi$
$38$	366.407	−	634.636i	0.0411628	−	0.0712961i
$39$		0			0
$40$	−1310.91	+	756.854i	−0.129546	+	0.0747932i
$41$	−14382.5			−1.33621			−0.668106	−	0.744066i	$-0.732895\pi$
$41$	−14382.5			−1.33621			−0.668106	+	0.744066i	$0.732895\pi$
$42$		0			0
$43$	1615.95			0.133277			0.0666387	−	0.997777i	$-0.478773\pi$
$43$	1615.95			0.133277			0.0666387	+	0.997777i	$0.478773\pi$
$44$	−16603.7	+	9586.15i	−1.29292	+	0.746470i
$45$		0			0
$46$	−1264.41	+	2190.02i	−0.0881036	+	0.152600i
$47$	−2309.84	−	4000.77i	−0.152524	−	0.264179i	0.779631	−	0.626240i	$-0.215407\pi$
$47$	−2309.84	−	4000.77i	−0.152524	−	0.264179i	−0.932155	+	0.362060i	$0.882073\pi$
$48$		0			0
$49$	−7653.47	+	14963.3i	−0.455374	+	0.890300i
$50$			4299.98i			0.243244i
$51$		0			0
$52$	13514.1	+	7802.39i	0.693075	+	0.400147i
$53$	332.149	+	191.766i	0.0162421	+	0.00937741i	0.508099	−	0.861299i	$-0.330348\pi$
$53$	332.149	+	191.766i	0.0162421	+	0.00937741i	−0.491857	+	0.870676i	$0.663682\pi$
$54$		0			0
$55$		−	10510.6i		−	0.468510i
$56$	−10268.1	+	6281.36i	−0.437544	+	0.267660i
$57$		0			0
$58$	1242.28	+	2151.69i	0.0484896	+	0.0839865i
$59$	6032.47	−	10448.5i	0.225614	−	0.390774i	−0.730890	−	0.682495i	$-0.760895\pi$
$59$	6032.47	−	10448.5i	0.225614	−	0.390774i	0.956503	+	0.291721i	$0.0942280\pi$
$60$		0			0
$61$	10068.3	−	5812.91i	0.346441	−	0.200018i	−0.316676	−	0.948534i	$-0.602567\pi$
$61$	10068.3	−	5812.91i	0.346441	−	0.200018i	0.663117	+	0.748516i	$0.269233\pi$
$62$	11107.7			0.366981
$63$		0			0
$64$	19678.8			0.600551
$65$	−7408.67	+	4277.40i	−0.217499	+	0.125573i
$66$		0			0
$67$	−7390.10	+	12800.0i	−0.201124	+	0.348357i	−0.948891	−	0.315605i	$-0.897793\pi$
$67$	−7390.10	+	12800.0i	−0.201124	+	0.348357i	0.747767	+	0.663961i	$0.231126\pi$
$68$	29870.3	+	51736.9i	0.783371	+	1.35684i
$69$		0			0
$70$	−80.7374	−	3177.55i	−0.00196938	−	0.0775082i
$71$		−	56016.9i		−	1.31878i	−0.751800	−	0.659391i	$-0.770814\pi$
$71$		−	56016.9i		−	1.31878i	0.751800	−	0.659391i	$-0.229186\pi$
$72$		0			0
$73$	−53690.2	−	30998.0i	−1.17920	−	0.680812i	−0.223371	−	0.974733i	$-0.571706\pi$
$73$	−53690.2	−	30998.0i	−1.17920	−	0.680812i	−0.955829	+	0.293922i	$0.905039\pi$
$74$	−11682.6	−	6744.95i	−0.248005	−	0.143186i
$75$		0			0
$76$		−	14490.7i		−	0.287777i
$77$	−2122.98	−	83553.2i	−0.0408055	−	1.60597i
$78$		0			0
$79$	−7045.58	−	12203.3i	−0.127013	−	0.219993i	0.795505	−	0.605947i	$-0.207206\pi$
$79$	−7045.58	−	12203.3i	−0.127013	−	0.219993i	−0.922518	+	0.385954i	$0.873872\pi$
$80$	−6618.93	+	11464.3i	−0.115628	+	0.200274i
$81$		0			0
$82$	18732.1	−	10815.0i	0.307646	−	0.177619i
$83$	120269.			1.91627			0.958135	−	0.286316i	$-0.0924307\pi$
$83$	120269.			1.91627			0.958135	+	0.286316i	$0.0924307\pi$
$84$		0			0
$85$	−32750.8			−0.491671
$86$	−2104.64	+	1215.12i	−0.0306854	+	0.0177162i
$87$		0			0
$88$	29929.7	−	51839.8i	0.411999	−	0.713603i
$89$	42263.8	+	73203.0i	0.565579	+	0.979612i	0.996996	+	0.0774591i	$0.0246807\pi$
$89$	42263.8	+	73203.0i	0.565579	+	0.979612i	−0.431416	+	0.902153i	$0.641986\pi$
$90$		0			0
$91$	−58030.9	+	35499.4i	−0.734609	+	0.449384i
$92$			50005.0i			0.615948i
$93$		0			0
$94$	6016.77	+	3473.78i	0.0702334	+	0.0405493i
$95$	6879.74	+	3972.02i	0.0782101	+	0.0451546i
$96$		0			0
$97$		−	128230.i		−	1.38376i	−0.722015	−	0.691878i	$-0.756784\pi$
$97$		−	128230.i		−	1.38376i	0.722015	−	0.691878i	$-0.243216\pi$
$98$	−1283.64	−	25243.5i	−0.0135013	−	0.265512i
$99$		0			0
$100$	42514.0	+	73636.4i	0.425140	+	0.736364i
$101$	72024.0	−	124749.i	0.702545	−	1.21684i	−0.265026	−	0.964241i	$-0.585380\pi$
$101$	72024.0	−	124749.i	0.702545	−	1.21684i	0.967570	−	0.252602i	$-0.0812862\pi$
$102$		0			0
$103$	59571.5	−	34393.6i	0.553281	−	0.319437i	−0.197163	−	0.980371i	$-0.563173\pi$
$103$	59571.5	−	34393.6i	0.553281	−	0.319437i	0.750444	+	0.660934i	$0.229840\pi$
$104$	−48721.0			−0.441706
$105$		0			0
$106$	−576.796			−0.00498606
$107$	−162377.	+	93748.5i	−1.37109	+	0.791599i	−0.991065	−	0.133378i	$-0.957418\pi$
$107$	−162377.	+	93748.5i	−1.37109	+	0.791599i	−0.380024	+	0.924977i	$0.624084\pi$
$108$		0			0
$109$	−60480.1	+	104755.i	−0.487581	+	0.844514i	−0.999898	−	0.0142818i	$-0.995454\pi$
$109$	−60480.1	+	104755.i	−0.487581	+	0.844514i	0.512317	+	0.858796i	$0.328787\pi$
$110$	7903.43	+	13689.1i	0.0622779	+	0.107869i
$111$		0			0
$112$	−50301.3	+	92472.1i	−0.378908	+	0.696572i
$113$		−	99229.1i		−	0.731043i	−0.930803	−	0.365522i	$-0.880891\pi$
$113$		−	99229.1i		−	0.731043i	0.930803	−	0.365522i	$-0.119109\pi$
$114$		0			0
$115$	−23740.8	−	13706.8i	−0.167398	−	0.0966476i
$116$	42547.6	+	24564.9i	0.293583	+	0.169500i
$117$		0			0
$118$			18144.5i			0.119961i
$119$	−260351.	+	6615.17i	−1.68536	+	0.0428226i
$120$		0			0
$121$	127294.	+	220480.i	0.790396	+	1.36901i
$122$	−8742.06	+	15141.7i	−0.0531758	+	0.0921032i
$123$		0			0
$124$	190217.	−	109822.i	1.11095	−	0.641408i
$125$	−97560.6			−0.558469
$126$		0			0
$127$	−28421.2			−0.156363			−0.0781814	−	0.996939i	$-0.524911\pi$
$127$	−28421.2			−0.156363			−0.0781814	+	0.996939i	$0.524911\pi$
$128$	−141811.	+	81874.4i	−0.765040	+	0.441696i
$129$		0			0
$130$	6432.79	−	11141.9i	0.0333842	−	0.0578232i
$131$	137923.	+	238890.i	0.702197	+	1.21624i	0.967694	+	0.252129i	$0.0811309\pi$
$131$	137923.	+	238890.i	0.702197	+	1.21624i	−0.265496	+	0.964112i	$0.585536\pi$
$132$		0			0
$133$	55492.5	+	30185.8i	0.272023	+	0.147970i
$134$		−	22228.0i		−	0.106940i
$135$		0			0
$136$	−161532.	−	93260.7i	−0.748879	−	0.432366i
$137$	61554.5	+	35538.5i	0.280194	+	0.161770i	0.633511	−	0.773734i	$-0.281613\pi$
$137$	61554.5	+	35538.5i	0.280194	+	0.161770i	−0.353317	+	0.935504i	$0.614946\pi$
$138$		0			0
$139$			229120.i			1.00583i	0.864335	+	0.502917i	$0.167740\pi$
$139$			229120.i			1.00583i	−0.864335	+	0.502917i	$0.832260\pi$
$140$	−32799.1	−	53616.8i	−0.141430	−	0.231196i
$141$		0			0
$142$	42122.0	+	72957.4i	0.175302	+	0.303633i
$143$	169149.	−	292975.i	0.691720	−	1.19809i
$144$		0			0
$145$	−23325.3	+	13466.9i	−0.0921312	+	0.0531920i
$146$	93236.1			0.361995
$147$		0			0
$148$	−266750.			−1.00104
$149$	−366534.	+	211619.i	−1.35254	+	0.780887i	−0.988604	−	0.150538i	$-0.951899\pi$
$149$	−366534.	+	211619.i	−1.35254	+	0.780887i	−0.363932	+	0.931425i	$0.618566\pi$
$150$		0			0
$151$	265507.	−	459872.i	0.947620	−	1.64133i	0.197203	−	0.980363i	$-0.436814\pi$
$151$	265507.	−	459872.i	0.947620	−	1.64133i	0.750418	−	0.660964i	$-0.229852\pi$
$152$	22621.3	+	39181.3i	0.0794163	+	0.137553i
$153$		0			0
$154$	65593.0	+	107225.i	0.222872	+	0.364329i
$155$			120412.i			0.402570i
$156$		0			0
$157$	−225789.	−	130360.i	−0.731062	−	0.422079i	0.0877484	−	0.996143i	$-0.472033\pi$
$157$	−225789.	−	130360.i	−0.731062	−	0.422079i	−0.818811	+	0.574064i	$0.805366\pi$
$158$	18352.6	+	10595.9i	0.0584863	+	0.0337671i
$159$		0			0
$160$		−	68347.1i		−	0.211067i
$161$	−191495.	−	104166.i	−0.582229	−	0.316710i
$162$		0			0
$163$	55954.0	+	96915.1i	0.164954	+	0.285708i	0.936639	−	0.350297i	$-0.113919\pi$
$163$	55954.0	+	96915.1i	0.164954	+	0.285708i	−0.771685	+	0.636005i	$0.780586\pi$
$164$	213856.	−	370409.i	0.620885	−	1.07540i
$165$		0			0
$166$	−156640.	+	90436.2i	−0.441197	+	0.254725i
$167$	536626.			1.48895			0.744476	−	0.667649i	$-0.232699\pi$
$167$	536626.			1.48895			0.744476	+	0.667649i	$0.232699\pi$
$168$		0			0
$169$	95943.6			0.258404
$170$	42655.2	−	24627.0i	0.113201	−	0.0653566i
$171$		0			0
$172$	−24027.8	+	41617.3i	−0.0619287	+	0.107264i
$173$	103171.	+	178698.i	0.262086	+	0.453947i	0.966796	−	0.255549i	$-0.0822562\pi$
$173$	103171.	+	178698.i	0.262086	+	0.453947i	−0.704710	+	0.709496i	$0.748923\pi$
$174$		0			0
$175$	−370554.	+	9415.28i	−0.914653	+	0.0232401i
$176$		−	523490.i		−	1.27388i
$177$		0			0
$178$	−110090.	−	63560.7i	−0.260435	−	0.150362i
$179$	430278.	+	248421.i	1.00373	+	0.579504i	0.909350	−	0.416033i	$-0.136580\pi$
$179$	430278.	+	248421.i	1.00373	+	0.579504i	0.0943799	+	0.995536i	$0.469913\pi$
$180$		0			0
$181$		−	436840.i		−	0.991119i	−0.868574	−	0.495560i	$-0.834963\pi$
$181$		−	436840.i		−	0.991119i	0.868574	−	0.495560i	$-0.165037\pi$
$182$	48886.7	−	89871.6i	0.109399	−	0.201115i
$183$		0			0
$184$	−78062.5	−	135208.i	−0.169980	−	0.294414i
$185$	73118.3	−	126645.i	0.157071	−	0.272055i
$186$		0			0
$187$	1.12161e6	−	647563.i	2.34552	−	1.35419i
$188$	137382.			0.283487
$189$		0			0
$190$	−11947.1			−0.0240092
$191$	97090.4	−	56055.1i	0.192572	−	0.111181i	−0.400614	−	0.916247i	$-0.631203\pi$
$191$	97090.4	−	56055.1i	0.192572	−	0.111181i	0.593186	+	0.805065i	$0.297870\pi$
$192$		0			0
$193$	−308549.	+	534423.i	−0.596254	+	1.03274i	0.397115	+	0.917769i	$0.370011\pi$
$193$	−308549.	+	534423.i	−0.596254	+	1.03274i	−0.993369	+	0.114973i	$0.963322\pi$
$194$	96422.6	+	167009.i	0.183939	+	0.318592i
$195$		0			0
$196$	−271565.	−	419599.i	−0.504933	−	0.780180i
$197$			285216.i			0.523610i	0.965121	+	0.261805i	$0.0843178\pi$
$197$			285216.i			0.523610i	−0.965121	+	0.261805i	$0.915682\pi$
$198$		0			0
$199$	194496.	+	112292.i	0.348159	+	0.201010i	0.663874	−	0.747844i	$-0.268911\pi$
$199$	194496.	+	112292.i	0.348159	+	0.201010i	−0.315715	+	0.948854i	$0.602244\pi$
$200$	−229907.	−	132737.i	−0.406421	−	0.234648i
$201$		0			0
$202$			216634.i			0.373550i
$203$	−182703.	+	111766.i	−0.311176	+	0.190357i
$204$		0			0
$205$	117239.	+	203064.i	0.194844	+	0.337480i
$206$	−51724.7	+	89589.8i	−0.0849239	+	0.147093i
$207$		0			0
$208$	−368997.	+	213041.i	−0.591378	+	0.341432i
$209$	−314146.			−0.497470
$210$		0			0
$211$	−198368.			−0.306736			−0.153368	−	0.988169i	$-0.549012\pi$
$211$	−198368.			−0.306736			−0.153368	+	0.988169i	$0.549012\pi$
$212$	−9877.54	+	5702.80i	−0.0150942	+	0.00871462i
$213$		0			0
$214$	140989.	−	244200.i	0.210451	−	0.364511i
$215$	−13172.4	−	22815.3i	−0.0194343	−	0.0336612i
$216$		0			0
$217$	24321.5	+	957212.i	0.0350623	+	1.37994i
$218$		−	181913.i		−	0.259252i
$219$		0			0
$220$	270690.	+	156283.i	0.377064	+	0.217698i
$221$	−912907.	−	527067.i	−1.25732	−	0.725914i
$222$		0			0
$223$		−	197877.i		−	0.266461i	−0.991085	−	0.133231i	$-0.957465\pi$
$223$		−	197877.i		−	0.266461i	0.991085	−	0.133231i	$-0.0425351\pi$
$224$	−13805.1	−	543323.i	−0.0183831	−	0.723499i
$225$		0			0
$226$	74615.5	+	129238.i	0.0971758	+	0.168313i
$227$	−587866.	+	1.01821e6i	−0.757205	+	1.31152i	0.187066	+	0.982347i	$0.440102\pi$
$227$	−587866.	+	1.01821e6i	−0.757205	+	1.31152i	−0.944271	+	0.329170i	$0.893231\pi$
$228$		0			0
$229$	−505690.	+	291960.i	−0.637229	+	0.367904i	−0.783546	−	0.621333i	$-0.786591\pi$
$229$	−505690.	+	291960.i	−0.637229	+	0.367904i	0.146317	+	0.989238i	$0.453258\pi$
$230$	41227.4			0.0513885
$231$		0			0
$232$	−153392.			−0.187104
$233$	−444083.	+	256392.i	−0.535889	+	0.309396i	−0.743411	−	0.668835i	$-0.766793\pi$
$233$	−444083.	+	256392.i	−0.535889	+	0.309396i	0.207522	+	0.978230i	$0.433460\pi$
$234$		0			0
$235$	−37657.4	+	65224.5i	−0.0444816	+	0.0770444i
$236$	179395.	+	310722.i	0.209667	+	0.363155i
$237$		0			0
$238$	334112.	−	204387.i	0.382339	−	0.233890i
$239$			1.24958e6i			1.41504i	0.706691	+	0.707522i	$0.250187\pi$
$239$			1.24958e6i			1.41504i	−0.706691	+	0.707522i	$0.749813\pi$
$240$		0			0
$241$	293064.	+	169200.i	0.325027	+	0.187654i	0.653631	−	0.756813i	$-0.273245\pi$
$241$	293064.	+	169200.i	0.325027	+	0.187654i	−0.328604	+	0.944468i	$0.606578\pi$
$242$	−331581.	−	191438.i	−0.363957	−	0.210131i
$243$		0			0
$244$			345732.i			0.371762i
$245$	273651.	−	13915.2i	0.291261	−	0.0148107i
$246$		0			0
$247$	127846.	+	221435.i	0.133335	+	0.230943i
$248$	−342884.	+	593893.i	−0.354012	+	0.613167i
$249$		0			0
$250$	127065.	−	73360.9i	0.128581	−	0.0742360i
$251$	363580.			0.364264			0.182132	−	0.983274i	$-0.441700\pi$
$251$	363580.			0.364264			0.182132	+	0.983274i	$0.441700\pi$
$252$		0			0
$253$	1.08407e6			1.06477
$254$	37016.3	−	21371.4i	0.0360005	−	0.0207849i
$255$		0			0
$256$	−191730.	+	332087.i	−0.182848	+	0.316702i
$257$	−562347.	−	974014.i	−0.531095	−	0.919883i	−0.999341	−	0.0362852i	$-0.988448\pi$
$257$	−562347.	−	974014.i	−0.531095	−	0.919883i	0.468247	−	0.883598i	$-0.344886\pi$
$258$		0			0
$259$	555670.	−	1.02152e6i	0.514716	−	0.946236i
$260$		−	254405.i		−	0.233395i
$261$		0			0
$262$	−359268.	−	207423.i	−0.323344	−	0.186683i
$263$	478729.	+	276394.i	0.426777	+	0.246400i	0.697972	−	0.716125i	$-0.254086\pi$
$263$	478729.	+	276394.i	0.426777	+	0.246400i	−0.271196	+	0.962524i	$0.587419\pi$
$264$		0			0
$265$		−	6252.73i		−	0.00546960i
$266$	−94972.7	+	2413.13i	−0.0822991	+	0.00209111i
$267$		0			0
$268$	−219769.	−	380651.i	−0.186909	−	0.323735i
$269$	297808.	−	515819.i	0.250932	−	0.434627i	−0.712851	−	0.701316i	$-0.752596\pi$
$269$	297808.	−	515819.i	0.250932	−	0.434627i	0.963783	+	0.266689i	$0.0859296\pi$
$270$		0			0
$271$	−1.67977e6	+	969817.i	−1.38940	+	0.802171i	−0.993248	−	0.116014i	$-0.962988\pi$
$271$	−1.67977e6	+	969817.i	−1.38940	+	0.802171i	−0.396153	+	0.918185i	$0.629655\pi$
$272$	−1.63119e6			−1.33685
$273$		0			0
$274$	−106893.			−0.0860148
$275$	1.59638e6	−	921668.i	1.27293	−	0.734925i
$276$		0			0
$277$	−242395.	+	419840.i	−0.189812	+	0.328764i	−0.945187	−	0.326528i	$-0.894121\pi$
$277$	−242395.	+	419840.i	−0.189812	+	0.328764i	0.755375	+	0.655292i	$0.227455\pi$
$278$	−172287.	−	298411.i	−0.133703	−	0.231581i
$279$		0			0
$280$	172386.	+	93771.5i	0.131404	+	0.0714785i
$281$		−	1.74771e6i		−	1.32039i	−0.751093	−	0.660196i	$-0.770473\pi$
$281$		−	1.74771e6i		−	1.32039i	0.751093	−	0.660196i	$-0.229527\pi$
$282$		0			0
$283$	757991.	+	437626.i	0.562598	+	0.324816i	0.754188	−	0.656659i	$-0.228031\pi$
$283$	757991.	+	437626.i	0.562598	+	0.324816i	−0.191590	+	0.981475i	$0.561364\pi$
$284$	1.44266e6	+	832922.i	1.06138	+	0.612786i
$285$		0			0
$286$			508769.i			0.367795i
$287$	973003.	+	1.59057e6i	0.697284	+	1.13985i
$288$		0			0
$289$	−1.30787e6	−	2.26530e6i	−0.921129	−	1.59544i
$290$	20252.9	−	35079.0i	0.0141414	−	0.0244936i
$291$		0			0
$292$	1.59665e6	−	921828.i	1.09586	−	0.632693i
$293$	−685929.			−0.466778			−0.233389	−	0.972383i	$-0.574982\pi$
$293$	−685929.			−0.466778			−0.233389	+	0.972383i	$0.574982\pi$
$294$		0			0
$295$	−196695.			−0.131594
$296$	721263.	−	416421.i	0.478481	−	0.276251i
$297$		0			0
$298$	318254.	−	551232.i	0.207603	−	0.359579i
$299$	−441174.	−	764136.i	−0.285386	−	0.494302i
$300$		0			0
$301$	−109322.	−	178708.i	−0.0695490	−	0.113692i
$302$			798595.i			0.503860i
$303$		0			0
$304$	342653.	+	197831.i	0.212653	+	0.122775i
$305$	−164143.	−	94767.8i	−0.101035	−	0.0583326i
$306$		0			0
$307$		−	2.11927e6i		−	1.28333i	−0.766983	−	0.641667i	$-0.778243\pi$
$307$		−	2.11927e6i		−	1.28333i	0.766983	−	0.641667i	$-0.221757\pi$
$308$	2.18340e6	+	1.18769e6i	1.31147	+	0.713388i
$309$		0			0
$310$	−90544.2	−	156827.i	−0.0535126	−	0.0926866i
$311$	1.03198e6	−	1.78744e6i	0.605021	−	1.04793i	−0.387028	−	0.922068i	$-0.626498\pi$
$311$	1.03198e6	−	1.78744e6i	0.605021	−	1.04793i	0.992048	−	0.125858i	$-0.0401685\pi$
$312$		0			0
$313$	−2.56108e6	+	1.47864e6i	−1.47762	+	0.853102i	−0.999680	−	0.0252930i	$-0.991948\pi$
$313$	−2.56108e6	+	1.47864e6i	−1.47762	+	0.853102i	−0.477936	+	0.878395i	$0.658615\pi$
$314$	392096.			0.224424
$315$		0			0
$316$	419047.			0.236072
$317$	1.83915e6	−	1.06183e6i	1.02794	−	0.593483i	0.111549	−	0.993759i	$-0.464419\pi$
$317$	1.83915e6	−	1.06183e6i	1.02794	−	0.593483i	0.916395	+	0.400275i	$0.131086\pi$
$318$		0			0
$319$	532546.	−	922397.i	0.293009	−	0.507506i
$320$	−160412.	−	277842.i	−0.0875714	−	0.151678i
$321$		0			0
$322$	327735.	−	8327.32i	0.176150	−	0.00447575i
$323$			978877.i			0.522061i
$324$		0			0
$325$	−1.29933e6	−	750168.i	−0.682355	−	0.393958i
$326$	−145751.	−	84149.4i	−0.0759570	−	0.0438538i
$327$		0			0
$328$			1.33539e6i			0.685370i
$329$	−286181.	+	526106.i	−0.145764	+	0.267968i
$330$		0			0
$331$	−750158.	−	1.29931e6i	−0.376342	−	0.651843i	0.614185	−	0.789162i	$-0.289485\pi$
$331$	−750158.	−	1.29931e6i	−0.376342	−	0.651843i	−0.990527	+	0.137319i	$0.956152\pi$
$332$	−1.78829e6	+	3.09741e6i	−0.890415	+	1.54224i
$333$		0			0
$334$	−698912.	+	403517.i	−0.342812	+	0.197923i
$335$	240962.			0.117310
$336$		0			0
$337$	813881.			0.390379			0.195189	−	0.980766i	$-0.437468\pi$
$337$	813881.			0.390379			0.195189	+	0.980766i	$0.437468\pi$
$338$	−124959.	+	72145.0i	−0.0594943	+	0.0343490i
$339$		0			0
$340$	486976.	−	843467.i	0.228460	−	0.395704i
$341$	−2.38085e6	−	4.12375e6i	−1.10878	−	1.92046i
$342$		0			0
$343$	2.17257e6	−	165892.i	0.997097	−	0.0761359i
$344$		−	150038.i		−	0.0683606i
$345$		0			0
$346$	−268745.	−	155160.i	−0.120684	−	0.0696770i
$347$	−135948.	−	78489.6i	−0.0606107	−	0.0349936i	0.469388	−	0.882992i	$-0.344474\pi$
$347$	−135948.	−	78489.6i	−0.0606107	−	0.0349936i	−0.529999	+	0.847998i	$0.677808\pi$
$348$		0			0
$349$			4.23214e6i			1.85993i	0.367648	+	0.929965i	$0.380163\pi$
$349$			4.23214e6i			1.85993i	−0.367648	+	0.929965i	$0.619837\pi$
$350$	475537.	−	290901.i	0.207498	−	0.126933i
$351$		0			0
$352$	1.35139e6	+	2.34068e6i	0.581332	+	1.00690i
$353$	−1.47153e6	+	2.54877e6i	−0.628540	+	1.08866i	0.359305	+	0.933220i	$0.383014\pi$
$353$	−1.47153e6	+	2.54877e6i	−0.628540	+	1.08866i	−0.987845	+	0.155443i	$0.950320\pi$
$354$		0			0
$355$	−790892.	+	456621.i	−0.333078	+	0.192303i
$356$	−2.51370e6			−1.05121
$357$		0			0
$358$	−747203.			−0.308128
$359$	839875.	−	484902.i	0.343937	−	0.198572i	−0.318075	−	0.948066i	$-0.603036\pi$
$359$	839875.	−	484902.i	0.343937	−	0.198572i	0.662011	+	0.749494i	$0.269703\pi$
$360$		0			0
$361$	−1.11933e6	+	1.93874e6i	−0.452054	+	0.782981i
$362$	328483.	+	568949.i	0.131747	+	0.228193i
$363$		0			0
$364$	−51386.0	−	2.02238e6i	−0.0203278	−	0.800036i
$365$			1.01072e6i			0.397100i
$366$		0			0
$367$	1.64339e6	+	948809.i	0.636905	+	0.367717i	0.783421	−	0.621491i	$-0.213473\pi$
$367$	1.64339e6	+	948809.i	0.636905	+	0.367717i	−0.146517	+	0.989208i	$0.546806\pi$
$368$	−1.18244e6	−	682682.i	−0.455155	−	0.262784i
$369$		0			0
$370$			219926.i			0.0835164i
$371$	−1262.96	−	49705.8i	−0.000476381	−	0.0187488i
$372$		0			0
$373$	−1.06754e6	−	1.84904e6i	−0.397296	−	0.688136i	0.596096	−	0.802913i	$-0.296718\pi$
$373$	−1.06754e6	−	1.84904e6i	−0.397296	−	0.688136i	−0.993391	+	0.114777i	$0.963385\pi$
$374$	−973873.	+	1.68680e6i	−0.360017	+	0.623568i
$375$		0			0
$376$	−371465.	+	214465.i	−0.135503	+	0.0782326i
$377$	−866904.			−0.314136
$378$		0			0
$379$	4.01801e6			1.43685			0.718427	−	0.695602i	$-0.244862\pi$
$379$	4.01801e6			1.43685			0.718427	+	0.695602i	$0.244862\pi$
$380$	−204592.	+	118121.i	−0.0726823	+	0.0419632i
$381$		0			0
$382$	−84301.6	+	146015.i	−0.0295581	+	0.0511962i
$383$	−343222.	−	594478.i	−0.119558	−	0.207080i	0.800035	−	0.599954i	$-0.204814\pi$
$383$	−343222.	−	594478.i	−0.119558	−	0.207080i	−0.919593	+	0.392874i	$0.871481\pi$
$384$		0			0
$385$	−1.16237e6	+	711058.i	−0.399661	+	0.244486i
$386$		−	928056.i		−	0.317034i
$387$		0			0
$388$	3.30244e6	+	1.90666e6i	1.11367	+	0.642976i
$389$	−3.03173e6	−	1.75037e6i	−1.01582	−	0.586485i	−0.102930	−	0.994689i	$-0.532822\pi$
$389$	−3.03173e6	−	1.75037e6i	−1.01582	−	0.586485i	−0.912891	+	0.408204i	$0.866155\pi$
$390$		0			0
$391$		−	3.37794e6i		−	1.11740i
$392$	1.38932e6	+	710613.i	0.456653	+	0.233570i
$393$		0			0
$394$	−214469.	−	371471.i	−0.0696023	−	0.120555i
$395$	−114864.	+	198950.i	−0.0370417	+	0.0641582i
$396$		0			0
$397$	728015.	−	420320.i	0.231827	−	0.133845i	−0.379588	−	0.925156i	$-0.623934\pi$
$397$	728015.	−	420320.i	0.231827	−	0.133845i	0.611415	+	0.791310i	$0.290601\pi$
$398$	−337754.			−0.106879
$399$		0			0
$400$	−2.32165e6			−0.725516
$401$	630296.	−	363902.i	0.195742	−	0.113012i	−0.398926	−	0.916983i	$-0.630617\pi$
$401$	630296.	−	363902.i	0.195742	−	0.113012i	0.594668	+	0.803972i	$0.297284\pi$
$402$		0			0
$403$	−1.93783e6	+	3.35642e6i	−0.594364	+	1.02947i
$404$	2.14187e6	+	3.70983e6i	0.652889	+	1.13084i
$405$		0			0
$406$	153914.	−	282950.i	0.0463407	−	0.0851911i
$407$			5.78291e6i			1.73046i
$408$		0			0
$409$	4.37664e6	+	2.52685e6i	1.29370	+	0.746916i	0.979307	−	0.202378i	$-0.0648671\pi$
$409$	4.37664e6	+	2.52685e6i	1.29370	+	0.746916i	0.314389	+	0.949294i	$0.398200\pi$
$410$	−305389.	−	176316.i	−0.0897209	−	0.0518004i
$411$		0			0
$412$			2.04561e6i			0.593719i
$413$	−1.56362e6	+	39729.4i	−0.451081	+	0.0114614i
$414$		0			0
$415$	−980369.	−	1.69805e6i	−0.279428	−	0.483983i
$416$	1.09993e6	−	1.90513e6i	0.311624	−	0.539749i
$417$		0			0
$418$	409150.	−	236223.i	0.114536	−	0.0661274i
$419$	3.01228e6			0.838226			0.419113	−	0.907934i	$-0.362341\pi$
$419$	3.01228e6			0.838226			0.419113	+	0.907934i	$0.362341\pi$
$420$		0			0
$421$	−4.91319e6			−1.35101			−0.675504	−	0.737356i	$-0.736074\pi$
$421$	−4.91319e6			−1.35101			−0.675504	+	0.737356i	$0.736074\pi$
$422$	258358.	−	149163.i	0.0706222	−	0.0407737i
$423$		0			0
$424$	17805.2	−	30839.5i	0.00480986	−	0.00833092i
$425$	−2.87191e6	−	4.97429e6i	−0.771255	−	1.33585i
$426$		0			0
$427$	−1.32399e6	−	720198.i	−0.351410	−	0.191154i
$428$		−	5.57584e6i		−	1.47130i
$429$		0			0
$430$	34312.0	+	19810.0i	0.00894900	+	0.00516671i
$431$	915677.	+	528667.i	0.237437	+	0.137085i	0.613998	−	0.789307i	$-0.289560\pi$
$431$	915677.	+	528667.i	0.237437	+	0.137085i	−0.376561	+	0.926392i	$0.622893\pi$
$432$		0			0
$433$		−	3.11733e6i		−	0.799029i	−0.916727	−	0.399514i	$-0.869179\pi$
$433$		−	3.11733e6i		−	0.799029i	0.916727	−	0.399514i	$-0.130821\pi$
$434$	−751454.	−	1.22840e6i	−0.191504	−	0.313052i
$435$		0			0
$436$	−1.79857e6	−	3.11522e6i	−0.453119	−	0.784825i
$437$	−409677.	+	709582.i	−0.102622	+	0.177746i
$438$		0			0
$439$	−306124.	+	176741.i	−0.0758117	+	0.0437699i	−0.537427	−	0.843310i	$-0.680604\pi$
$439$	−306124.	+	176741.i	−0.0758117	+	0.0437699i	0.461615	+	0.887080i	$0.347270\pi$
$440$	−975889.			−0.240308
$441$		0			0
$442$	1.58532e6			0.385976
$443$	4.29060e6	−	2.47718e6i	1.03874	−	0.599719i	0.119267	−	0.992862i	$-0.461946\pi$
$443$	4.29060e6	−	2.47718e6i	1.03874	−	0.599719i	0.919477	+	0.393143i	$0.128612\pi$
$444$		0			0
$445$	689027.	−	1.19343e6i	0.164944	−	0.285691i
$446$	148794.	+	257719.i	0.0354200	+	0.0613493i
$447$		0			0
$448$	−1.33131e6	−	2.17629e6i	−0.313389	−	0.512297i
$449$			3.49011e6i			0.817002i	0.912758	+	0.408501i	$0.133948\pi$
$449$			3.49011e6i			0.817002i	−0.912758	+	0.408501i	$0.866052\pi$
$450$		0			0
$451$	−8.03015e6	−	4.63621e6i	−1.85901	−	1.07330i
$452$	2.55556e6	+	1.47545e6i	0.588355	+	0.339687i
$453$		0			0
$454$		−	1.76819e6i		−	0.402614i
$455$	974249.	+	529954.i	0.220618	+	0.120008i
$456$		0			0
$457$	3.70912e6	+	6.42438e6i	0.830768	+	1.43893i	0.897430	+	0.441157i	$0.145432\pi$
$457$	3.70912e6	+	6.42438e6i	0.830768	+	1.43893i	−0.0666616	+	0.997776i	$0.521235\pi$
$458$	439080.	−	760509.i	0.0978093	−	0.169411i
$459$		0			0
$460$	706012.	−	407616.i	0.155567	−	0.0898166i
$461$	8.24924e6			1.80785			0.903923	−	0.427695i	$-0.140674\pi$
$461$	8.24924e6			1.80785			0.903923	+	0.427695i	$0.140674\pi$
$462$		0			0
$463$	5.32457e6			1.15434			0.577168	−	0.816626i	$-0.304158\pi$
$463$	5.32457e6			1.15434			0.577168	+	0.816626i	$0.304158\pi$
$464$	−1.16174e6	+	670732.i	−0.250504	+	0.144629i
$465$		0			0
$466$	385588.	−	667859.i	0.0822544	−	0.142469i
$467$	2.40428e6	+	4.16434e6i	0.510145	+	0.883597i	0.999931	+	0.0117541i	$0.00374152\pi$
$467$	2.40428e6	+	4.16434e6i	0.510145	+	0.883597i	−0.489786	+	0.871843i	$0.662925\pi$
$468$		0			0
$469$	1.91551e6	−	48670.7i	0.402118	−	0.0102173i
$470$		−	113266.i		−	0.0236513i
$471$		0			0
$472$	−970131.	−	560105.i	−0.200436	−	0.115722i
$473$	902228.	+	520902.i	0.185423	+	0.107054i
$474$		0			0
$475$			1.39322e6i			0.283326i
$476$	3.70082e6	−	6.80346e6i	0.748654	−	1.37630i
$477$		0			0
$478$	−939626.	−	1.62748e6i	−0.188098	−	0.325796i
$479$	69733.0	−	120781.i	0.0138867	−	0.0240525i	−0.858999	−	0.511978i	$-0.828913\pi$
$479$	69733.0	−	120781.i	0.0138867	−	0.0240525i	0.872885	+	0.487926i	$0.162246\pi$
$480$		0			0
$481$	4.07625e6	−	2.35343e6i	0.803338	−	0.463808i
$482$	−508922.			−0.0997777
$483$		0			0
$484$	−7.57101e6			−1.46906
$485$	−1.81045e6	+	1.04526e6i	−0.349488	+	0.201777i
$486$		0			0
$487$	4.34156e6	−	7.51980e6i	0.829513	−	1.43676i	−0.0689079	−	0.997623i	$-0.521951\pi$
$487$	4.34156e6	−	7.51980e6i	0.829513	−	1.43676i	0.898421	−	0.439136i	$-0.144715\pi$
$488$	−539719.	−	934821.i	−0.102593	−	0.177697i
$489$		0			0
$490$	−345945.	+	223896.i	−0.0650903	+	0.0421265i
$491$		−	3.71569e6i		−	0.695562i	−0.937576	−	0.347781i	$-0.886935\pi$
$491$		−	3.71569e6i		−	0.695562i	0.937576	−	0.347781i	$-0.113065\pi$
$492$		0			0
$493$	−2.87418e6	−	1.65941e6i	−0.532594	−	0.307493i
$494$	−333017.	−	192268.i	−0.0613973	−	0.0354478i
$495$		0			0
$496$			5.99727e6i			1.09458i
$497$	−6.19493e6	+	3.78964e6i	−1.12498	+	0.688188i
$498$		0			0
$499$	2.68841e6	+	4.65647e6i	0.483331	+	0.837154i	0.999817	−	0.0191419i	$-0.00609343\pi$
$499$	2.68841e6	+	4.65647e6i	0.483331	+	0.837154i	−0.516486	+	0.856296i	$0.672760\pi$
$500$	1.45064e6	−	2.51259e6i	0.259499	−	0.449465i
$501$		0			0
$502$	−473534.	+	273395.i	−0.0838672	+	0.0484207i
$503$	−1.54773e6			−0.272757			−0.136378	−	0.990657i	$-0.543546\pi$
$503$	−1.54773e6			−0.272757			−0.136378	+	0.990657i	$0.543546\pi$
$504$		0			0
$505$	−2.34841e6			−0.409776
$506$	−1.41191e6	+	815167.i	−0.245149	+	0.141537i
$507$		0			0
$508$	422599.	−	731963.i	0.0726556	−	0.125843i
$509$	2.28252e6	+	3.95344e6i	0.390499	+	0.676364i	0.992515	−	0.122120i	$-0.0389692\pi$
$509$	2.28252e6	+	3.95344e6i	0.390499	+	0.676364i	−0.602016	+	0.798484i	$0.705636\pi$
$510$		0			0
$511$	204151.	+	8.03469e6i	0.0345859	+	1.36118i
$512$		−	5.81665e6i		−	0.980614i
$513$		0			0
$514$	1.46482e6	+	845716.i	0.244556	+	0.141194i
$515$	−971194.	−	560719.i	−0.161357	−	0.0931595i
$516$		0			0
$517$		−	2.97832e6i		−	0.490055i
$518$	44421.7	+	1.74829e6i	0.00727396	+	0.286279i
$519$		0			0
$520$	397150.	+	687883.i	0.0644089	+	0.111559i
$521$	4.88420e6	−	8.45969e6i	0.788314	−	1.36540i	−0.138685	−	0.990337i	$-0.544288\pi$
$521$	4.88420e6	−	8.45969e6i	0.788314	−	1.36540i	0.926999	−	0.375064i	$-0.122379\pi$
$522$		0			0
$523$	−1.46853e6	+	847854.i	−0.234762	+	0.135540i	−0.612767	−	0.790264i	$-0.709944\pi$
$523$	−1.46853e6	+	847854.i	−0.234762	+	0.135540i	0.378005	+	0.925804i	$0.376610\pi$
$524$	−8.20320e6			−1.30513
$525$		0			0
$526$	−831341.			−0.131013
$527$	−1.28495e7	+	7.41869e6i	−2.01540	+	1.16359i
$528$		0			0
$529$	−1.80444e6	+	3.12539e6i	−0.280352	+	0.485584i
$530$	4701.75	+	8143.68i	0.000727060	+	0.00125930i
$531$		0			0
$532$	−1.60253e6	+	980322.i	−0.245487	+	0.150172i
$533$			7.54705e6i			1.15069i
$534$		0			0
$535$	2.64724e6	+	1.52838e6i	0.399860	+	0.230859i
$536$	1.18846e6	+	686159.i	0.178679	+	0.103160i
$537$		0			0
$538$			895751.i			0.133423i
$539$	−9.09656e6	+	5.88731e6i	−1.34867	+	0.872860i
$540$		0			0
$541$	977067.	+	1.69233e6i	0.143526	+	0.248595i	0.928822	−	0.370526i	$-0.120823\pi$
$541$	977067.	+	1.69233e6i	0.143526	+	0.248595i	−0.785296	+	0.619121i	$0.787489\pi$
$542$	1.45851e6	−	2.52622e6i	0.213261	−	0.369379i
$543$		0			0
$544$	7.29352e6	−	4.21092e6i	1.05667	−	0.610070i
$545$	1.97201e6			0.284393
$546$		0			0
$547$	1.10047e7			1.57257			0.786285	−	0.617864i	$-0.212002\pi$
$547$	1.10047e7			1.57257			0.786285	+	0.617864i	$0.212002\pi$
$548$	−1.83053e6	+	1.05685e6i	−0.260390	+	0.150336i
$549$		0			0
$550$	−1.38610e6	+	2.40080e6i	−0.195384	+	0.338414i
$551$	402506.	+	697162.i	0.0564799	+	0.0978260i
$552$		0			0
$553$	−872921.	+	1.60475e6i	−0.121384	+	0.223148i
$554$		−	729077.i		−	0.100925i
$555$		0			0
$556$	−5.90079e6	−	3.40682e6i	−0.809511	−	0.467371i
$557$	4.90482e6	+	2.83180e6i	0.669861	+	0.386744i	0.796024	−	0.605265i	$-0.206933\pi$
$557$	4.90482e6	+	2.83180e6i	0.669861	+	0.386744i	−0.126163	+	0.992010i	$0.540266\pi$
$558$		0			0
$559$		−	847949.i		−	0.114773i
$560$	1.71563e6	−	43591.8i	0.231181	−	0.00587401i
$561$		0			0
$562$	1.31419e6	+	2.27625e6i	0.175517	+	0.304004i
$563$	998718.	−	1.72983e6i	0.132792	−	0.230002i	−0.791960	−	0.610573i	$-0.790939\pi$
$563$	998718.	−	1.72983e6i	0.132792	−	0.230002i	0.924752	+	0.380571i	$0.124272\pi$
$564$		0			0
$565$	−1.40100e6	+	808866.i	−0.184636	+	0.106600i
$566$	−1.31630e6			−0.172708
$567$		0			0
$568$	−5.20108e6			−0.676429
$569$	−8.93377e6	+	5.15791e6i	−1.15679	+	0.667872i	−0.950532	−	0.310626i	$-0.899461\pi$
$569$	−8.93377e6	+	5.15791e6i	−1.15679	+	0.667872i	−0.206256	+	0.978498i	$0.566128\pi$
$570$		0			0
$571$	−4.70677e6	+	8.15237e6i	−0.604134	+	1.04639i	0.388054	+	0.921637i	$0.373147\pi$
$571$	−4.70677e6	+	8.15237e6i	−0.604134	+	1.04639i	−0.992188	+	0.124753i	$0.960186\pi$
$572$	5.03021e6	+	8.71258e6i	0.642830	+	1.11341i
$573$		0			0
$574$	−2.46329e6	−	1.33993e6i	−0.312058	−	0.169748i
$575$		−	4.80778e6i		−	0.606422i
$576$		0			0
$577$	−1.82532e6	−	1.05385e6i	−0.228244	−	0.131777i	0.381518	−	0.924361i	$-0.375401\pi$
$577$	−1.82532e6	−	1.05385e6i	−0.228244	−	0.131777i	−0.609762	+	0.792585i	$0.708735\pi$
$578$	3.40679e6	+	1.96691e6i	0.424156	+	0.244887i
$579$		0			0
$580$		−	800962.i		−	0.0988649i
$581$	−8.13638e6	−	1.33005e7i	−0.999979	−	1.63467i
$582$		0			0
$583$	123632.	+	214137.i	0.0150647	+	0.0260928i
$584$	−2.87812e6	+	4.98505e6i	−0.349202	+	0.604835i
$585$		0			0
$586$	893367.	−	515786.i	0.107470	−	0.0620476i
$587$	4.33237e6			0.518955			0.259478	−	0.965749i	$-0.416450\pi$
$587$	4.33237e6			0.518955			0.259478	+	0.965749i	$0.416450\pi$
$588$		0			0
$589$	3.59896e6			0.427453
$590$	256179.	−	147905.i	0.0302980	−	0.0174925i
$591$		0			0
$592$	3.64174e6	−	6.30768e6i	0.427076	−	0.739717i
$593$	2.40917e6	+	4.17280e6i	0.281339	+	0.487294i	0.971715	−	0.236157i	$-0.0758881\pi$
$593$	2.40917e6	+	4.17280e6i	0.281339	+	0.487294i	−0.690376	+	0.723451i	$0.742555\pi$
$594$		0			0
$595$	2.21565e6	+	3.62192e6i	0.256571	+	0.419417i
$596$		−	1.25863e7i		−	1.45139i
$597$		0			0
$598$	1.14919e6	+	663484.i	0.131413	+	0.0758712i
$599$	−1.49206e6	−	861444.i	−0.169911	−	0.0980980i	0.412633	−	0.910897i	$-0.364609\pi$
$599$	−1.49206e6	−	861444.i	−0.169911	−	0.0980980i	−0.582544	+	0.812799i	$0.697943\pi$
$600$		0			0
$601$		−	8.38741e6i		−	0.947200i	−0.880740	−	0.473600i	$-0.842954\pi$
$601$		−	8.38741e6i		−	0.947200i	0.880740	−	0.473600i	$-0.157046\pi$
$602$	276763.	+	150548.i	0.0311255	+	0.0169311i
$603$		0			0
$604$	7.89573e6	+	1.36758e7i	0.880644	+	1.52532i
$605$	2.07528e6	−	3.59448e6i	0.230509	−	0.399253i
$606$		0			0
$607$	−2.98294e6	+	1.72220e6i	−0.328604	+	0.189719i	−0.655221	−	0.755437i	$-0.727425\pi$
$607$	−2.98294e6	+	1.72220e6i	−0.328604	+	0.189719i	0.326617	+	0.945157i	$0.394091\pi$
$608$	−2.04280e6			−0.224113
$609$		0			0
$610$	285043.			0.0310160
$611$	−2.09935e6	+	1.21206e6i	−0.227501	+	0.131347i
$612$		0			0
$613$	5.91715e6	−	1.02488e7i	0.636006	−	1.10159i	−0.350295	−	0.936639i	$-0.613919\pi$
$613$	5.91715e6	−	1.02488e7i	0.636006	−	1.10159i	0.986301	−	0.164955i	$-0.0527479\pi$
$614$	1.59359e6	+	2.76017e6i	0.170590	+	0.295471i
$615$		0			0
$616$	−7.75779e6	+	197115.i	−0.823732	+	0.0209299i
$617$			9.61290e6i			1.01658i	0.861186	+	0.508290i	$0.169722\pi$
$617$			9.61290e6i			1.01658i	−0.861186	+	0.508290i	$0.830278\pi$
$618$		0			0
$619$	−8.89250e6	−	5.13409e6i	−0.932819	−	0.538563i	−0.0451169	−	0.998982i	$-0.514366\pi$
$619$	−8.89250e6	−	5.13409e6i	−0.932819	−	0.538563i	−0.887702	+	0.460418i	$0.847699\pi$
$620$	−3.10111e6	−	1.79043e6i	−0.323995	−	0.187058i
$621$		0			0
$622$			3.10400e6i			0.321696i
$623$	5.23633e6	−	9.62629e6i	0.540514	−	0.993662i
$624$		0			0
$625$	−3.67225e6	−	6.36053e6i	−0.376039	−	0.651318i
$626$	2.22373e6	−	3.85161e6i	0.226802	−	0.392832i
$627$		0			0
$628$	6.71459e6	−	3.87667e6i	0.679392	−	0.392247i
$629$	1.80195e7			1.81600
$630$		0			0
$631$	−1.53687e7			−1.53661			−0.768304	−	0.640085i	$-0.778899\pi$
$631$	−1.53687e7			−1.53661			−0.768304	+	0.640085i	$0.778899\pi$
$632$	−1.13306e6	+	654171.i	−0.112839	+	0.0651476i
$633$		0			0
$634$	−1.59690e6	+	2.76591e6i	−0.157781	+	0.273284i
$635$	231675.	+	401274.i	0.0228006	+	0.0394917i
$636$		0			0
$637$	7.85179e6	+	4.01606e6i	0.766691	+	0.392150i
$638$			1.60180e6i			0.155796i
$639$		0			0
$640$	2.31194e6	+	1.33480e6i	0.223114	+	0.128815i
$641$	−4.93288e6	−	2.84800e6i	−0.474193	−	0.273776i	0.243800	−	0.969825i	$-0.421606\pi$
$641$	−4.93288e6	−	2.84800e6i	−0.474193	−	0.273776i	−0.717993	+	0.696050i	$0.754939\pi$
$642$		0			0
$643$		−	9.28940e6i		−	0.886054i	−0.896508	−	0.443027i	$-0.853905\pi$
$643$		−	9.28940e6i		−	0.886054i	0.896508	−	0.443027i	$-0.146095\pi$
$644$	5.53008e6	−	3.38293e6i	0.525432	−	0.321424i
$645$		0			0
$646$	−736068.	−	1.27491e6i	−0.0693964	−	0.120198i
$647$	5.38119e6	−	9.32049e6i	0.505379	−	0.875342i	−0.494601	−	0.869120i	$-0.664686\pi$
$647$	5.38119e6	−	9.32049e6i	0.505379	−	0.875342i	0.999981	−	0.00622252i	$-0.00198070\pi$
$648$		0			0
$649$	6.73619e6	−	3.88914e6i	0.627773	−	0.362445i
$650$	2.25636e6			0.209472
$651$		0			0
$652$	−3.32795e6			−0.306590
$653$	1.46989e7	−	8.48641e6i	1.34897	−	0.778827i	0.360865	−	0.932618i	$-0.382482\pi$
$653$	1.46989e7	−	8.48641e6i	1.34897	−	0.778827i	0.988103	+	0.153791i	$0.0491483\pi$
$654$		0			0
$655$	2.24856e6	−	3.89462e6i	0.204787	−	0.354701i
$656$	5.83923e6	+	1.01138e7i	0.529780	+	0.917606i
$657$		0			0
$658$	−22878.1	−	900405.i	−0.00205994	−	0.0810724i
$659$		−	6.26238e6i		−	0.561728i	−0.959748	−	0.280864i	$-0.909379\pi$
$659$		−	6.26238e6i		−	0.561728i	0.959748	−	0.280864i	$-0.0906210\pi$
$660$		0			0
$661$	−5.83705e6	−	3.37002e6i	−0.519625	−	0.300006i	0.217156	−	0.976137i	$-0.430322\pi$
$661$	−5.83705e6	−	3.37002e6i	−0.519625	−	0.300006i	−0.736781	+	0.676131i	$0.763655\pi$
$662$	1.95404e6	+	1.12817e6i	0.173296	+	0.100052i
$663$		0			0
$664$		−	1.11667e7i		−	0.982893i
$665$	−26159.4	−	1.02955e6i	−0.00229390	−	0.0902801i
$666$		0			0
$667$	−1.38898e6	−	2.40579e6i	−0.120888	−	0.209384i
$668$	−7.97917e6	+	1.38203e7i	−0.691857	+	1.19833i
$669$		0			0
$670$	−313833.	+	181192.i	−0.0270092	+	0.0155938i
$671$	7.49517e6			0.642651
$672$		0			0
$673$	1.69087e7			1.43904			0.719522	−	0.694470i	$-0.244361\pi$
$673$	1.69087e7			1.43904			0.719522	+	0.694470i	$0.244361\pi$
$674$	−1.06001e6	+	612000.i	−0.0898798	+	0.0518921i
$675$		0			0
$676$	−1.42660e6	+	2.47094e6i	−0.120070	+	0.207968i
$677$	4.82631e6	+	8.35941e6i	0.404709	+	0.700977i	0.994288	−	0.106734i	$-0.0340394\pi$
$677$	4.82631e6	+	8.35941e6i	0.404709	+	0.700977i	−0.589578	+	0.807711i	$0.700706\pi$
$678$		0			0
$679$	−1.41810e7	+	8.67497e6i	−1.18041	+	0.722094i
$680$			3.04086e6i			0.252188i
$681$		0			0
$682$	6.20172e6	+	3.58056e6i	0.510565	+	0.294775i
$683$	−5.63739e6	−	3.25475e6i	−0.462409	−	0.266972i	0.250647	−	0.968078i	$-0.419357\pi$
$683$	−5.63739e6	−	3.25475e6i	−0.462409	−	0.266972i	−0.713057	+	0.701106i	$0.752690\pi$
$684$		0			0
$685$		−	1.15877e6i		−	0.0943562i
$686$	−2.70485e6	+	1.84973e6i	−0.219448	+	0.150071i
$687$		0			0
$688$	−656067.	−	1.13634e6i	−0.0528417	−	0.0915246i
$689$	100627.	−	174291.i	0.00807544	−	0.0139871i
$690$		0			0
$691$	−2.10422e6	+	1.21487e6i	−0.167647	+	0.0967909i	−0.581476	−	0.813564i	$-0.697524\pi$
$691$	−2.10422e6	+	1.21487e6i	−0.167647	+	0.0967909i	0.413829	+	0.910355i	$0.364191\pi$
$692$	−6.13628e6			−0.487124
$693$		0			0
$694$	236082.			0.0186065
$695$	3.23491e6	−	1.86767e6i	0.254038	−	0.146669i
$696$		0			0
$697$	−1.44464e7	+	2.50219e7i	−1.12636	+	1.95091i
$698$	−3.18237e6	−	5.51202e6i	−0.247236	−	0.428225i
$699$		0			0
$700$	5.26733e6	−	9.68328e6i	0.406299	−	0.746926i
$701$		−	1.79918e6i		−	0.138287i	−0.997607	−	0.0691434i	$-0.977973\pi$
$701$		−	1.79918e6i		−	0.138287i	0.997607	−	0.0691434i	$-0.0220266\pi$
$702$		0			0
$703$	−3.78524e6	−	2.18541e6i	−0.288872	−	0.166780i
$704$	1.09872e7	+	6.34348e6i	0.835520	+	0.482388i
$705$		0			0
$706$		−	4.42608e6i		−	0.334201i
$707$	−1.86686e7	+	474345.i	−1.40464	+	0.0356899i
$708$		0			0
$709$	1.09852e6	+	1.90269e6i	0.0820715	+	0.142152i	0.904140	−	0.427237i	$-0.140513\pi$
$709$	1.09852e6	+	1.90269e6i	0.0820715	+	0.142152i	−0.822068	+	0.569389i	$0.807180\pi$
$710$	686715.	−	1.18942e6i	0.0511247	−	0.0885505i
$711$		0			0
$712$	6.79679e6	−	3.92413e6i	0.502463	−	0.290097i
$713$	−1.24194e7			−0.914908
$714$		0			0
$715$	−5.51528e6			−0.403462
$716$	−1.27957e7	+	7.38762e6i	−0.932787	+	0.538545i
$717$		0			0
$718$	−729246.	+	1.26309e6i	−0.0527914	+	0.0914373i
$719$	−1.12942e7	−	1.95621e7i	−0.814766	−	1.41122i	−0.909496	−	0.415714i	$-0.863532\pi$
$719$	−1.12942e7	−	1.95621e7i	−0.814766	−	1.41122i	0.0947293	−	0.995503i	$-0.469801\pi$
$720$		0			0
$721$	−7.83372e6	−	4.26125e6i	−0.561216	−	0.305280i
$722$		−	3.36673e6i		−	0.240362i
$723$		0			0
$724$	1.12504e7	+	6.49543e6i	0.797668	+	0.460534i
$725$	−4.09078e6	−	2.36181e6i	−0.289042	−	0.166878i
$726$		0			0
$727$			5.05297e6i			0.354577i	0.984159	+	0.177289i	$0.0567326\pi$
$727$			5.05297e6i			0.354577i	−0.984159	+	0.177289i	$0.943267\pi$
$728$	3.29607e6	+	5.38808e6i	0.230498	+	0.376795i
$729$		0			0
$730$	−760014.	−	1.31638e6i	−0.0527855	−	0.0914272i
$731$	1.62312e6	−	2.81133e6i	0.112346	−	0.194589i
$732$		0			0
$733$	−9.09011e6	+	5.24818e6i	−0.624898	+	0.360785i	−0.778774	−	0.627305i	$-0.784158\pi$
$733$	−9.09011e6	+	5.24818e6i	−0.624898	+	0.360785i	0.153875	+	0.988090i	$0.450825\pi$
$734$	−2.85384e6			−0.195519
$735$		0			0
$736$	7.04938e6			0.479685
$737$	−8.25219e6	+	4.76440e6i	−0.559629	+	0.323102i
$738$		0			0
$739$	5.95321e6	−	1.03113e7i	0.400996	−	0.694545i	−0.592850	−	0.805313i	$-0.701997\pi$
$739$	5.95321e6	−	1.03113e7i	0.400996	−	0.694545i	0.993846	+	0.110767i	$0.0353308\pi$
$740$	2.17441e6	+	3.76619e6i	0.145970	+	0.252827i
$741$		0			0
$742$	39021.3	+	63788.1i	0.00260191	+	0.00425334i
$743$			9.06937e6i			0.602706i	0.953513	+	0.301353i	$0.0974382\pi$
$743$			9.06937e6i			0.602706i	−0.953513	+	0.301353i	$0.902562\pi$
$744$		0			0
$745$	5.97561e6	+	3.45002e6i	0.394449	+	0.227736i
$746$	2.78078e6	+	1.60548e6i	0.182944	+	0.105623i
$747$		0			0
$748$			3.85148e7i			2.51695i
$749$	2.13528e7	+	1.16151e7i	1.39075	+	0.756517i
$750$		0			0
$751$	8.32542e6	+	1.44201e7i	0.538650	+	0.932968i	0.998977	+	0.0452192i	$0.0143986\pi$
$751$	8.32542e6	+	1.44201e7i	0.538650	+	0.932968i	−0.460328	+	0.887749i	$0.652268\pi$
$752$	−1.87557e6	+	3.24858e6i	−0.120945	+	0.209483i
$753$		0			0
$754$	1.12907e6	−	651870.i	0.0723258	−	0.0417573i
$755$	−8.65714e6			−0.552722
$756$		0			0
$757$	−2.32625e6			−0.147542			−0.0737711	−	0.997275i	$-0.523503\pi$
$757$	−2.32625e6			−0.147542			−0.0737711	+	0.997275i	$0.523503\pi$
$758$	−5.23313e6	+	3.02135e6i	−0.330817	+	0.190998i
$759$		0			0
$760$	368796.	−	638773.i	0.0231607	−	0.0401155i
$761$	−1.57069e6	−	2.72051e6i	−0.0983169	−	0.170290i	0.812671	−	0.582723i	$-0.198013\pi$
$761$	−1.57069e6	−	2.72051e6i	−0.0983169	−	0.170290i	−0.910988	+	0.412433i	$0.864679\pi$
$762$		0			0
$763$	1.56764e7	−	398318.i	0.974847	−	0.0247696i
$764$			3.33397e6i			0.206646i
$765$		0			0
$766$	894037.	+	516173.i	0.0550533	+	0.0317851i
$767$	−5.48274e6	−	3.16546e6i	−0.336519	−	0.194289i
$768$		0			0
$769$		−	4.64877e6i		−	0.283480i	−0.989904	−	0.141740i	$-0.954730\pi$
$769$		−	4.64877e6i		−	0.283480i	0.989904	−	0.141740i	$-0.0452697\pi$
$770$	979207.	−	1.80014e6i	0.0595179	−	0.109416i
$771$		0			0
$772$	−9.17572e6	−	1.58928e7i	−0.554111	−	0.959748i
$773$	−7.95216e6	+	1.37736e7i	−0.478670	+	0.829081i	−0.999701	−	0.0244566i	$-0.992214\pi$
$773$	−7.95216e6	+	1.37736e7i	−0.478670	+	0.829081i	0.521030	+	0.853538i	$0.325548\pi$
$774$		0			0
$775$	−1.82886e7	+	1.05589e7i	−1.09377	+	0.631488i
$776$	−1.19059e7			−0.709756
$777$		0			0
$778$	5.26478e6			0.311840
$779$	6.06931e6	−	3.50412e6i	0.358340	−	0.206888i
$780$		0			0
$781$	1.80571e7	−	3.12757e7i	1.05930	−	1.83476i
$782$	2.54005e6	+	4.39949e6i	0.148534	+	0.257268i
$783$		0			0
$784$	1.36295e7	−	693062.i	0.791935	−	0.0402701i
$785$			4.25050e6i			0.246188i
$786$		0			0
$787$	1.39494e7	+	8.05371e6i	0.802823	+	0.463510i	0.844457	−	0.535623i	$-0.179923\pi$
$787$	1.39494e7	+	8.05371e6i	0.802823	+	0.463510i	−0.0416344	+	0.999133i	$0.513256\pi$
$788$	−7.34548e6	−	4.24092e6i	−0.421410	−	0.243301i
$789$		0			0
$790$		−	345489.i		−	0.0196955i
$791$	−1.09738e7	+	6.71303e6i	−0.623613	+	0.381485i
$792$		0			0
$793$	−3.05025e6	−	5.28319e6i	−0.172247	−	0.298341i
$794$	−632120.	+	1.09486e6i	−0.0355835	+	0.0616324i
$795$		0			0
$796$	−5.78398e6	+	3.33938e6i	−0.323552	+	0.186803i
$797$	1.98565e7			1.10728			0.553640	−	0.832756i	$-0.313238\pi$
$797$	1.98565e7			1.10728			0.553640	+	0.832756i	$0.313238\pi$
$798$		0			0
$799$	−9.28040e6			−0.514280
$800$	1.03808e7	−	5.99334e6i	0.573462	−	0.331089i
$801$		0			0
$802$	−547273.	+	947905.i	−0.0300447	+	0.0520390i
$803$	−1.99845e7	−	3.46141e7i	−1.09371	−	1.89437i
$804$		0			0
$805$	90271.9	+	3.55280e6i	0.00490979	+	0.193233i
$806$		−	5.82861e6i		−	0.316029i
$807$		0			0
$808$	−1.15828e7	−	6.68732e6i	−0.624143	−	0.360349i
$809$	1.56463e6	+	903339.i	0.0840505	+	0.0485266i	0.541436	−	0.840742i	$-0.317881\pi$
$809$	1.56463e6	+	903339.i	0.0840505	+	0.0485266i	−0.457386	+	0.889268i	$0.651214\pi$
$810$		0			0
$811$			3.03388e7i			1.61974i	0.586607	+	0.809872i	$0.300463\pi$
$811$			3.03388e7i			1.61974i	−0.586607	+	0.809872i	$0.699537\pi$
$812$	−161782.	−	6.36722e6i	−0.00861076	−	0.338891i
$813$		0			0
$814$	−4.34847e6	−	7.53178e6i	−0.230025	−	0.398416i
$815$	912217.	−	1.58001e6i	0.0481066	−	0.0833230i
$816$		0			0
$817$	−681918.	+	393706.i	−0.0357419	+	0.0206356i
$818$	−7.60029e6			−0.397143
$819$		0			0
$820$	−6.97298e6			−0.362146
$821$	2.53489e7	−	1.46352e7i	1.31251	−	0.757776i	0.329996	−	0.943982i	$-0.392953\pi$
$821$	2.53489e7	−	1.46352e7i	1.31251	−	0.757776i	0.982511	+	0.186207i	$0.0596194\pi$
$822$		0			0
$823$	−1.25215e7	+	2.16879e7i	−0.644402	+	1.11614i	0.340037	+	0.940412i	$0.389560\pi$
$823$	−1.25215e7	+	2.16879e7i	−0.644402	+	1.11614i	−0.984439	+	0.175725i	$0.943773\pi$
$824$	−3.19339e6	−	5.53112e6i	−0.163845	−	0.283789i
$825$		0			0
$826$	2.00661e6	−	1.22751e6i	0.102332	−	0.0626000i
$827$			1.33339e7i			0.677941i	0.940797	+	0.338971i	$0.110079\pi$
$827$			1.33339e7i			0.677941i	−0.940797	+	0.338971i	$0.889921\pi$
$828$		0			0
$829$	−2.67007e7	−	1.54157e7i	−1.34939	−	0.779068i	−0.361224	−	0.932479i	$-0.617641\pi$
$829$	−2.67007e7	−	1.54157e7i	−1.34939	−	0.779068i	−0.988163	+	0.153411i	$0.950974\pi$
$830$	2.55370e6	+	1.47438e6i	0.128669	+	0.0742873i
$831$		0			0
$832$		−	1.03262e7i		−	0.517170i
$833$	1.83448e7	+	2.83448e7i	0.916009	+	1.41534i
$834$		0			0
$835$	−4.37431e6	−	7.57652e6i	−0.217117	−	0.376057i
$836$	4.67109e6	−	8.09056e6i	0.231154	−	0.400371i
$837$		0			0
$838$	−3.92326e6	+	2.26509e6i	−0.192991	+	0.111423i
$839$	−1.16409e7			−0.570930			−0.285465	−	0.958389i	$-0.592148\pi$
$839$	−1.16409e7			−0.570930			−0.285465	+	0.958389i	$0.592148\pi$
$840$		0			0
$841$	1.77818e7			0.866934
$842$	6.39903e6	−	3.69448e6i	0.311053	−	0.179586i
$843$		0			0
$844$	2.94956e6	−	5.10879e6i	0.142528	−	0.246866i
$845$	−782084.	−	1.35461e6i	−0.0376801	−	0.0652638i
$846$		0			0
$847$	1.57713e7	−	2.89934e7i	0.755368	−	1.38864i
$848$		−	311425.i		−	0.0148718i
$849$		0			0
$850$	7.48085e6	+	4.31907e6i	0.355143	+	0.205042i
$851$	1.30622e7	+	7.54148e6i	0.618291	+	0.356971i
$852$		0			0
$853$		−	1.20975e7i		−	0.569274i	−0.958635	−	0.284637i	$-0.908127\pi$
$853$		−	1.20975e7i		−	0.569274i	0.958635	−	0.284637i	$-0.0918731\pi$
$854$	2.26594e6	−	57574.5i	0.106317	−	0.00270138i
$855$		0			0
$856$	8.70440e6	+	1.50765e7i	0.406027	+	0.703259i
$857$	−4.49145e6	+	7.77942e6i	−0.208898	+	0.361822i	−0.951368	−	0.308058i	$-0.900321\pi$
$857$	−4.49145e6	+	7.77942e6i	−0.208898	+	0.361822i	0.742470	+	0.669880i	$0.233654\pi$
$858$		0			0
$859$	1.21521e7	−	7.01600e6i	0.561911	−	0.324419i	−0.192001	−	0.981395i	$-0.561498\pi$
$859$	1.21521e7	−	7.01600e6i	0.561911	−	0.324419i	0.753912	+	0.656975i	$0.228164\pi$
$860$	783449.			0.0361214
$861$		0			0
$862$	−1.59013e6			−0.0728893
$863$	2.52851e7	−	1.45983e7i	1.15568	−	0.667231i	0.205414	−	0.978675i	$-0.434146\pi$
$863$	2.52851e7	−	1.45983e7i	1.15568	−	0.667231i	0.950264	+	0.311444i	$0.100813\pi$
$864$		0			0
$865$	1.68200e6	−	2.91332e6i	0.0764340	−	0.132388i
$866$	2.34408e6	+	4.06006e6i	0.106213	+	0.183966i
$867$		0			0
$868$	−2.50138e7	−	1.36065e7i	−1.12689	−	0.612983i
$869$		−	9.08458e6i		−	0.408089i
$870$		0			0
$871$	6.71665e6	+	3.87786e6i	0.299991	+	0.173200i
$872$	9.72630e6	+	5.61548e6i	0.433168	+	0.250090i
$873$		0			0
$874$		−	1.23223e6i		−	0.0545649i
$875$	6.60015e6	+	1.07893e7i	0.291430	+	0.476400i
$876$		0			0
$877$	−2.08667e7	−	3.61421e7i	−0.916123	−	1.58677i	−0.805248	−	0.592938i	$-0.797968\pi$
$877$	−2.08667e7	−	3.61421e7i	−0.916123	−	1.58677i	−0.110875	−	0.993834i	$-0.535365\pi$
$878$	265801.	−	460381.i	0.0116365	−	0.0201549i
$879$		0			0
$880$	−7.39106e6	+	4.26723e6i	−0.321736	+	0.185755i
$881$	5.30257e6			0.230169			0.115085	−	0.993356i	$-0.463286\pi$
$881$	5.30257e6			0.230169			0.115085	+	0.993356i	$0.463286\pi$
$882$		0			0
$883$	−2.09992e7			−0.906359			−0.453179	−	0.891419i	$-0.649710\pi$
$883$	−2.09992e7			−0.906359			−0.453179	+	0.891419i	$0.649710\pi$
$884$	2.71483e7	−	1.56741e7i	1.16845	−	0.674607i
$885$		0			0
$886$	−3.72544e6	+	6.45265e6i	−0.159438	+	0.276155i
$887$	−9.77969e6	−	1.69389e7i	−0.417365	−	0.722897i	0.578308	−	0.815818i	$-0.303713\pi$
$887$	−9.77969e6	−	1.69389e7i	−0.417365	−	0.722897i	−0.995674	+	0.0929207i	$0.970380\pi$
$888$		0			0
$889$	1.92275e6	+	3.14311e6i	0.0815957	+	0.133385i
$890$			2.07246e6i			0.0877023i
$891$		0			0
$892$	5.09615e6	+	2.94227e6i	0.214452	+	0.123814i
$893$	1.94947e6	+	1.12553e6i	0.0818067	+	0.0472311i
$894$		0			0
$895$		−	8.10002e6i		−	0.338009i
$896$	1.86483e7	+	1.01439e7i	0.776012	+	0.422121i
$897$		0			0
$898$	−2.62439e6	−	4.54558e6i	−0.108602	−	0.188104i
$899$	−6.10101e6	+	1.05673e7i	−0.251769	+	0.436077i
$900$		0			0
$901$	667248.	−	385236.i	0.0273826	−	0.0158094i
$902$	1.39448e7			0.570686
$903$		0			0
$904$	−9.21327e6			−0.374967
$905$	−6.16766e6	+	3.56090e6i	−0.250322	+	0.144523i
$906$		0			0
$907$	−4.78288e6	+	8.28420e6i	−0.193051	+	0.334374i	−0.946260	−	0.323408i	$-0.895172\pi$
$907$	−4.78288e6	+	8.28420e6i	−0.193051	+	0.334374i	0.753209	+	0.657781i	$0.228505\pi$
$908$	−1.74821e7	−	3.02799e7i	−0.703686	−	1.21882i
$909$		0			0
$910$	−1.66738e6	+	42365.9i	−0.0667469	+	0.00169595i
$911$			2.89995e7i			1.15769i	0.815436	+	0.578847i	$0.196497\pi$
$911$			2.89995e7i			1.15769i	−0.815436	+	0.578847i	$0.803503\pi$
$912$		0			0
$913$	6.71492e7	+	3.87686e7i	2.66602	+	1.53923i
$914$	−9.66164e6	−	5.57815e6i	−0.382548	−	0.220864i
$915$		0			0
$916$		−	1.73648e7i		−	0.683802i
$917$	1.70882e7	−	3.14143e7i	0.671078	−	1.23369i
$918$		0			0
$919$	−5.65927e6	−	9.80214e6i	−0.221040	−	0.382853i	0.734084	−	0.679059i	$-0.237612\pi$
$919$	−5.65927e6	−	9.80214e6i	−0.221040	−	0.382853i	−0.955124	+	0.296206i	$0.904279\pi$
$920$	−1.27265e6	+	2.20430e6i	−0.0495725	+	0.0858620i
$921$		0			0
$922$	−1.07440e7	+	6.20303e6i	−0.416234	+	0.240313i
$923$	−2.93941e7			−1.13568
$924$		0			0
$925$	2.56469e7			0.985554
$926$	−6.93482e6	+	4.00382e6i	−0.265771	+	0.153443i
$927$		0			0
$928$	3.46299e6	−	5.99808e6i	0.132002	−	0.228635i
$929$	3.73202e6	+	6.46405e6i	0.141875	+	0.245734i	0.928203	−	0.372075i	$-0.121354\pi$
$929$	3.73202e6	+	6.46405e6i	0.141875	+	0.245734i	−0.786328	+	0.617809i	$0.788020\pi$
$930$		0			0
$931$	−415907.	−	8.17906e6i	−0.0157261	−	0.309264i
$932$		−	1.52493e7i		−	0.575056i
$933$		0			0
$934$	−6.26277e6	−	3.61581e6i	−0.234909	−	0.135625i
$935$	−1.82856e7	−	1.05572e7i	−0.684040	−	0.394931i
$936$		0			0
$937$			4.70992e6i			0.175253i	0.996153	+	0.0876264i	$0.0279282\pi$
$937$			4.70992e6i			0.175253i	−0.996153	+	0.0876264i	$0.972072\pi$
$938$	−2.45820e6	+	1.50376e6i	−0.0912243	+	0.0558049i
$939$		0			0
$940$	−1.11987e6	−	1.93966e6i	−0.0413377	−	0.0715990i
$941$	−1.86886e7	+	3.23697e7i	−0.688024	+	1.19169i	0.284452	+	0.958690i	$0.408188\pi$
$941$	−1.86886e7	+	3.23697e7i	−0.688024	+	1.19169i	−0.972476	+	0.233002i	$0.925145\pi$
$942$		0			0
$943$	−2.09442e7	+	1.20921e7i	−0.766981	+	0.442816i
$944$	−9.79661e6			−0.357804
$945$		0			0
$946$	−1.56677e6			−0.0569217
$947$	−1.40420e7	+	8.10714e6i	−0.508807	+	0.293760i	−0.732343	−	0.680936i	$-0.761573\pi$
$947$	−1.40420e7	+	8.10714e6i	−0.508807	+	0.293760i	0.223536	+	0.974696i	$0.428240\pi$
$948$		0			0
$949$	−1.62658e7	+	2.81732e7i	−0.586288	+	1.01548i
$950$	−1.04764e6	−	1.81456e6i	−0.0376618	−	0.0652322i
$951$		0			0
$952$	614208.	+	2.41732e7i	0.0219646	+	0.864452i
$953$			1.37737e7i			0.491268i	0.969363	+	0.245634i	$0.0789961\pi$
$953$			1.37737e7i			0.491268i	−0.969363	+	0.245634i	$0.921004\pi$
$954$		0			0
$955$	−1.58286e6	−	913867.i	−0.0561610	−	0.0324246i
$956$	−3.21819e7	−	1.85802e7i	−1.13885	−	0.657515i
$957$		0			0
$958$			209744.i			0.00738371i
$959$	−234054.	−	9.21159e6i	−0.00821807	−	0.323436i
$960$		0			0
$961$	1.29611e7	+	2.24494e7i	0.452725	+	0.784143i
$962$	−3.53933e6	+	6.13029e6i	−0.123306	+	0.213572i
$963$		0			0
$964$	−8.71520e6	+	5.03172e6i	−0.302054	+	0.174391i
$965$	1.00605e7			0.347779
$966$		0			0
$967$	2.43451e7			0.837233			0.418616	−	0.908163i	$-0.362515\pi$
$967$	2.43451e7			0.837233			0.418616	+	0.908163i	$0.362515\pi$
$968$	2.04712e7	−	1.18191e7i	0.702191	−	0.405410i
$969$		0			0
$970$	1.57198e6	−	2.72274e6i	0.0536435	−	0.0929132i
$971$	1.63398e7	+	2.83013e7i	0.556157	+	0.963292i	0.997813	+	0.0661075i	$0.0210580\pi$
$971$	1.63398e7	+	2.83013e7i	0.556157	+	0.963292i	−0.441655	+	0.897185i	$0.645609\pi$
$972$		0			0
$973$	2.53385e7	−	1.55004e7i	0.858023	−	0.524881i
$974$			1.30586e7i			0.441061i
$975$		0			0
$976$	−8.17532e6	−	4.72002e6i	−0.274714	−	0.158606i
$977$	−6.95119e6	−	4.01327e6i	−0.232982	−	0.134512i	0.378965	−	0.925411i	$-0.376280\pi$
$977$	−6.95119e6	−	4.01327e6i	−0.232982	−	0.134512i	−0.611947	+	0.790899i	$0.709613\pi$
$978$		0			0
$979$			5.44950e7i			1.81719i
$980$	−3.71058e6	+	7.25454e6i	−0.123417	+	0.241293i
$981$		0			0
$982$	2.79402e6	+	4.83939e6i	0.0924594	+	0.160144i
$983$	−1.20696e7	+	2.09051e7i	−0.398389	+	0.690030i	−0.993527	−	0.113593i	$-0.963764\pi$
$983$	−1.20696e7	+	2.09051e7i	−0.398389	+	0.690030i	0.595138	+	0.803623i	$0.297097\pi$
$984$		0			0
$985$	4.02691e6	−	2.32494e6i	0.132246	−	0.0763521i
$986$	4.99118e6			0.163497
$987$		0			0
$988$	−7.60382e6			−0.247822
$989$	2.35319e6	−	1.35861e6i	0.0765007	−	0.0441677i
$990$		0			0
$991$	1.55178e7	−	2.68777e7i	0.501935	−	0.869377i	−0.498063	−	0.867141i	$-0.665955\pi$
$991$	1.55178e7	−	2.68777e7i	0.501935	−	0.869377i	0.999998	−	0.00223552i	$-0.000711589\pi$
$992$	−1.54820e7	−	2.68155e7i	−0.499513	−	0.865182i
$993$		0			0
$994$	5.21876e6	−	9.59399e6i	0.167533	−	0.307988i
$995$		−	3.66140e6i		−	0.117244i
$996$		0			0
$997$	−1.34308e7	−	7.75426e6i	−0.427921	−	0.247060i	0.270540	−	0.962709i	$-0.412798\pi$
$997$	−1.34308e7	−	7.75426e6i	−0.427921	−	0.247060i	−0.698460	+	0.715649i	$0.746131\pi$
$998$	−7.00288e6	−	4.04311e6i	−0.222562	−	0.128496i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.p.b.17.6	✓	24
3.2	odd	2	inner	63.6.p.b.17.7	yes	24
7.3	odd	6		441.6.c.b.440.11		24
7.4	even	3		441.6.c.b.440.13		24
7.5	odd	6	inner	63.6.p.b.26.7	yes	24
21.5	even	6	inner	63.6.p.b.26.6	yes	24
21.11	odd	6		441.6.c.b.440.12		24
21.17	even	6		441.6.c.b.440.14		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.p.b.17.6	✓	24	1.1	even	1	trivial
63.6.p.b.17.7	yes	24	3.2	odd	2	inner
63.6.p.b.26.6	yes	24	21.5	even	6	inner
63.6.p.b.26.7	yes	24	7.5	odd	6	inner
441.6.c.b.440.11		24	7.3	odd	6
441.6.c.b.440.12		24	21.11	odd	6
441.6.c.b.440.13		24	7.4	even	3
441.6.c.b.440.14		24	21.17	even	6

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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30242 + 0.751952i) q^{2} +(-14.8691 + 25.7541i) q^{4} +(-8.15150 - 14.1188i) q^{5} +(-67.6518 - 110.590i) q^{7} -92.8484i q^{8} +O(q^{10})\)	\(q+(-1.30242 + 0.751952i) q^{2} +(-14.8691 + 25.7541i) q^{4} +(-8.15150 - 14.1188i) q^{5} +(-67.6518 - 110.590i) q^{7} -92.8484i q^{8} +(21.2333 + 12.2591i) q^{10} +(558.327 + 322.350i) q^{11} -524.737i q^{13} +(171.270 + 93.1641i) q^{14} +(-405.995 - 703.204i) q^{16} +(1004.44 - 1739.74i) q^{17} +(-421.992 + 243.637i) q^{19} +484.823 q^{20} -969.568 q^{22} +(1456.23 - 840.752i) q^{23} +(1429.61 - 2476.15i) q^{25} +(394.577 + 683.428i) q^{26} +(3854.08 - 97.9271i) q^{28} -1652.07i q^{29} +(-6396.37 - 3692.95i) q^{31} +(3630.64 + 2096.15i) q^{32} +3021.16i q^{34} +(-1009.94 + 1856.64i) q^{35} +(4484.96 + 7768.18i) q^{37} +(366.407 - 634.636i) q^{38} +(-1310.91 + 756.854i) q^{40} -14382.5 q^{41} +1615.95 q^{43} +(-16603.7 + 9586.15i) q^{44} +(-1264.41 + 2190.02i) q^{46} +(-2309.84 - 4000.77i) q^{47} +(-7653.47 + 14963.3i) q^{49} +4299.98i q^{50} +(13514.1 + 7802.39i) q^{52} +(332.149 + 191.766i) q^{53} -10510.6i q^{55} +(-10268.1 + 6281.36i) q^{56} +(1242.28 + 2151.69i) q^{58} +(6032.47 - 10448.5i) q^{59} +(10068.3 - 5812.91i) q^{61} +11107.7 q^{62} +19678.8 q^{64} +(-7408.67 + 4277.40i) q^{65} +(-7390.10 + 12800.0i) q^{67} +(29870.3 + 51736.9i) q^{68} +(-80.7374 - 3177.55i) q^{70} -56016.9i q^{71} +(-53690.2 - 30998.0i) q^{73} +(-11682.6 - 6744.95i) q^{74} -14490.7i q^{76} +(-2122.98 - 83553.2i) q^{77} +(-7045.58 - 12203.3i) q^{79} +(-6618.93 + 11464.3i) q^{80} +(18732.1 - 10815.0i) q^{82} +120269. q^{83} -32750.8 q^{85} +(-2104.64 + 1215.12i) q^{86} +(29929.7 - 51839.8i) q^{88} +(42263.8 + 73203.0i) q^{89} +(-58030.9 + 35499.4i) q^{91} +50005.0i q^{92} +(6016.77 + 3473.78i) q^{94} +(6879.74 + 3972.02i) q^{95} -128230. i q^{97} +(-1283.64 - 25243.5i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 304 q^{4} - 436 q^{7}+O(q^{10}) \) 24 * q + 304 * q^4 - 436 * q^7	\( 24 q + 304 q^{4} - 436 q^{7} + 1992 q^{10} - 3644 q^{16} + 3804 q^{19} - 5648 q^{22} - 18852 q^{25} - 39172 q^{28} + 38652 q^{31} + 20548 q^{37} + 132060 q^{40} + 2200 q^{43} - 25712 q^{46} - 125676 q^{49} - 2940 q^{52} + 154300 q^{58} + 48504 q^{61} - 327880 q^{64} + 156324 q^{67} - 9468 q^{70} - 703236 q^{73} + 165756 q^{79} + 1081020 q^{82} - 284448 q^{85} + 582308 q^{88} - 19812 q^{91} - 1481724 q^{94}+O(q^{100}) \) 24 * q + 304 * q^4 - 436 * q^7 + 1992 * q^10 - 3644 * q^16 + 3804 * q^19 - 5648 * q^22 - 18852 * q^25 - 39172 * q^28 + 38652 * q^31 + 20548 * q^37 + 132060 * q^40 + 2200 * q^43 - 25712 * q^46 - 125676 * q^49 - 2940 * q^52 + 154300 * q^58 + 48504 * q^61 - 327880 * q^64 + 156324 * q^67 - 9468 * q^70 - 703236 * q^73 + 165756 * q^79 + 1081020 * q^82 - 284448 * q^85 + 582308 * q^88 - 19812 * q^91 - 1481724 * q^94

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