LMFDB - Embedded newform 117.5.j.b.73.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,5,Mod(73,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("117.73");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	117.j (of order $4$, 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:	$12.0942856808$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 5446 x^{16} - 1452 x^{15} + 106320 x^{13} + 8376897 x^{12} - 1643220 x^{11} + 1054152 x^{10} + \cdots + 2103506496 $ x^20 + 5446x^16 - 1452x^15 + 106320x^13 + 8376897x^12 - 1643220x^11 + 1054152x^10 + 232107192x^9 + 3337033804x^8 + 3105930144x^7 + 2297014848x^6 + 21034904256x^5 + 158658808624x^4 + 235144077504x^3 + 177846480000x^2 + 27353289600*x + 2103506496
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{10} $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			73.3
Root			$-2.89776 - 2.89776i$ of defining polynomial
Character	$\chi$	$=$	117.73
Dual form			117.5.j.b.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.89776 - 2.89776i) q^{2} +0.794047i q^{4} +(-18.6373 - 18.6373i) q^{5} +(-15.2549 + 15.2549i) q^{7} +(-44.0632 + 44.0632i) q^{8} +108.013i q^{10} +(59.2741 - 59.2741i) q^{11} +(-157.156 - 62.1541i) q^{13} +88.4101 q^{14} +268.074 q^{16} +272.906i q^{17} +(-54.5892 - 54.5892i) q^{19} +(14.7989 - 14.7989i) q^{20} -343.524 q^{22} +596.223i q^{23} +69.6962i q^{25} +(275.292 + 635.507i) q^{26} +(-12.1131 - 12.1131i) q^{28} +1314.18 q^{29} +(874.924 + 874.924i) q^{31} +(-71.8036 - 71.8036i) q^{32} +(790.817 - 790.817i) q^{34} +568.619 q^{35} +(-403.847 + 403.847i) q^{37} +316.373i q^{38} +1642.44 q^{40} +(-983.966 - 983.966i) q^{41} +2237.13i q^{43} +(47.0664 + 47.0664i) q^{44} +(1727.71 - 1727.71i) q^{46} +(369.867 - 369.867i) q^{47} +1935.58i q^{49} +(201.963 - 201.963i) q^{50} +(49.3532 - 124.789i) q^{52} -4399.13 q^{53} -2209.42 q^{55} -1344.36i q^{56} +(-3808.17 - 3808.17i) q^{58} +(-976.401 + 976.401i) q^{59} -6163.60 q^{61} -5070.64i q^{62} -3873.05i q^{64} +(1770.57 + 4087.33i) q^{65} +(-1708.57 - 1708.57i) q^{67} -216.700 q^{68} +(-1647.72 - 1647.72i) q^{70} +(-672.586 - 672.586i) q^{71} +(-1169.63 + 1169.63i) q^{73} +2340.51 q^{74} +(43.3464 - 43.3464i) q^{76} +1808.44i q^{77} +8345.50 q^{79} +(-4996.17 - 4996.17i) q^{80} +5702.60i q^{82} +(-6513.68 - 6513.68i) q^{83} +(5086.23 - 5086.23i) q^{85} +(6482.67 - 6482.67i) q^{86} +5223.62i q^{88} +(-8366.65 + 8366.65i) q^{89} +(3345.55 - 1449.24i) q^{91} -473.429 q^{92} -2143.57 q^{94} +2034.79i q^{95} +(2271.58 + 2271.58i) q^{97} +(5608.84 - 5608.84i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 24 q^{5} - 24 q^{7} - 372 q^{11} - 224 q^{13} - 480 q^{14} - 2328 q^{16} - 840 q^{19} - 228 q^{20} + 3536 q^{22} + 828 q^{26} - 1984 q^{28} + 5064 q^{29} + 1712 q^{31} + 7260 q^{32} + 8040 q^{34}+ \cdots - 11544 q^{98}+O(q^{100}) $ 20 * q - 24 * q^5 - 24 * q^7 - 372 * q^11 - 224 * q^13 - 480 * q^14 - 2328 * q^16 - 840 * q^19 - 228 * q^20 + 3536 * q^22 + 828 * q^26 - 1984 * q^28 + 5064 * q^29 + 1712 * q^31 + 7260 * q^32 + 8040 * q^34 - 5976 * q^35 - 868 * q^37 + 6336 * q^40 + 6000 * q^41 - 20868 * q^44 - 1992 * q^46 - 1692 * q^47 - 8952 * q^50 - 12416 * q^52 + 18816 * q^53 - 3280 * q^55 + 1256 * q^58 + 6588 * q^59 - 5512 * q^61 - 33048 * q^65 - 4704 * q^67 + 28296 * q^68 - 31096 * q^70 - 9756 * q^71 + 13692 * q^73 + 28296 * q^74 - 17072 * q^76 - 5056 * q^79 - 42228 * q^80 - 24708 * q^83 - 4752 * q^85 + 77424 * q^86 - 36000 * q^89 + 19104 * q^91 - 12912 * q^92 + 112832 * q^94 + 50012 * q^97 - 11544 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−2.89776	−	2.89776i	−0.724440	−	0.724440i	0.245066	−	0.969506i	$-0.421190\pi$
$2$	−2.89776	−	2.89776i	−0.724440	−	0.724440i	−0.969506	+	0.245066i	$0.921190\pi$
$3$		0			0
$3$		0			0
$4$			0.794047i			0.0496279i
$5$	−18.6373	−	18.6373i	−0.745491	−	0.745491i	0.228138	−	0.973629i	$-0.426736\pi$
$5$	−18.6373	−	18.6373i	−0.745491	−	0.745491i	−0.973629	+	0.228138i	$0.926736\pi$
$6$		0			0
$7$	−15.2549	+	15.2549i	−0.311324	+	0.311324i	−0.845422	−	0.534098i	$-0.820651\pi$
$7$	−15.2549	+	15.2549i	−0.311324	+	0.311324i	0.534098	+	0.845422i	$0.320651\pi$
$8$	−44.0632	+	44.0632i	−0.688488	+	0.688488i
$9$		0			0
$10$			108.013i			1.08013i
$11$	59.2741	−	59.2741i	0.489869	−	0.489869i	−0.418396	−	0.908265i	$-0.637408\pi$
$11$	59.2741	−	59.2741i	0.489869	−	0.489869i	0.908265	+	0.418396i	$0.137408\pi$
$12$		0			0
$13$	−157.156	−	62.1541i	−0.929915	−	0.367776i
$13$	−157.156	−	62.1541i	−0.929915	−	0.367776i
$14$	88.4101			0.451072
$15$		0			0
$16$	268.074			1.04717
$17$			272.906i			0.944312i	0.881515	+	0.472156i	$0.156524\pi$
$17$			272.906i			0.944312i	−0.881515	+	0.472156i	$0.843476\pi$
$18$		0			0
$19$	−54.5892	−	54.5892i	−0.151217	−	0.151217i	0.627445	−	0.778661i	$-0.284101\pi$
$19$	−54.5892	−	54.5892i	−0.151217	−	0.151217i	−0.778661	+	0.627445i	$0.784101\pi$
$20$	14.7989	−	14.7989i	0.0369972	−	0.0369972i
$21$		0			0
$22$	−343.524			−0.709761
$23$			596.223i			1.12708i	0.826090	+	0.563538i	$0.190560\pi$
$23$			596.223i			1.12708i	−0.826090	+	0.563538i	$0.809440\pi$
$24$		0			0
$25$			69.6962i			0.111514i
$26$	275.292	+	635.507i	0.407236	+	0.940099i
$27$		0			0
$28$	−12.1131	−	12.1131i	−0.0154504	−	0.0154504i
$29$	1314.18			1.56263			0.781317	−	0.624135i	$-0.214548\pi$
$29$	1314.18			1.56263			0.781317	+	0.624135i	$0.214548\pi$
$30$		0			0
$31$	874.924	+	874.924i	0.910431	+	0.910431i	0.996306	−	0.0858748i	$-0.0273685\pi$
$31$	874.924	+	874.924i	0.910431	+	0.910431i	−0.0858748	+	0.996306i	$0.527368\pi$
$32$	−71.8036	−	71.8036i	−0.0701207	−	0.0701207i
$33$		0			0
$34$	790.817	−	790.817i	0.684098	−	0.684098i
$35$	568.619			0.464179
$36$		0			0
$37$	−403.847	+	403.847i	−0.294994	+	0.294994i	−0.839049	−	0.544055i	$-0.816888\pi$
$37$	−403.847	+	403.847i	−0.294994	+	0.294994i	0.544055	+	0.839049i	$0.316888\pi$
$38$			316.373i			0.219095i
$39$		0			0
$40$	1642.44			1.02652
$41$	−983.966	−	983.966i	−0.585346	−	0.585346i	0.351022	−	0.936367i	$-0.385834\pi$
$41$	−983.966	−	983.966i	−0.585346	−	0.585346i	−0.936367	+	0.351022i	$0.885834\pi$
$42$		0			0
$43$			2237.13i			1.20991i	0.796258	+	0.604957i	$0.206810\pi$
$43$			2237.13i			1.20991i	−0.796258	+	0.604957i	$0.793190\pi$
$44$	47.0664	+	47.0664i	0.0243112	+	0.0243112i
$45$		0			0
$46$	1727.71	−	1727.71i	0.816500	−	0.816500i
$47$	369.867	−	369.867i	0.167437	−	0.167437i	−0.618415	−	0.785852i	$-0.712225\pi$
$47$	369.867	−	369.867i	0.167437	−	0.167437i	0.785852	+	0.618415i	$0.212225\pi$
$48$		0			0
$49$			1935.58i			0.806154i
$50$	201.963	−	201.963i	0.0807852	−	0.0807852i
$51$		0			0
$52$	49.3532	−	124.789i	0.0182519	−	0.0461497i
$53$	−4399.13			−1.56608			−0.783041	−	0.621970i	$-0.786333\pi$
$53$	−4399.13			−1.56608			−0.783041	+	0.621970i	$0.786333\pi$
$54$		0			0
$55$	−2209.42			−0.730385
$56$		−	1344.36i		−	0.428686i
$57$		0			0
$58$	−3808.17	−	3808.17i	−1.13204	−	1.13204i
$59$	−976.401	+	976.401i	−0.280495	+	0.280495i	−0.833306	−	0.552812i	$-0.813555\pi$
$59$	−976.401	+	976.401i	−0.280495	+	0.280495i	0.552812	+	0.833306i	$0.313555\pi$
$60$		0			0
$61$	−6163.60			−1.65644			−0.828219	−	0.560405i	$-0.810646\pi$
$61$	−6163.60			−1.65644			−0.828219	+	0.560405i	$0.810646\pi$
$62$		−	5070.64i		−	1.31911i
$63$		0			0
$64$		−	3873.05i		−	0.945568i
$65$	1770.57	+	4087.33i	0.419070	+	0.967416i
$66$		0			0
$67$	−1708.57	−	1708.57i	−0.380612	−	0.380612i	0.490711	−	0.871322i	$-0.336737\pi$
$67$	−1708.57	−	1708.57i	−0.380612	−	0.380612i	−0.871322	+	0.490711i	$0.836737\pi$
$68$	−216.700			−0.0468642
$69$		0			0
$70$	−1647.72	−	1647.72i	−0.336270	−	0.336270i
$71$	−672.586	−	672.586i	−0.133423	−	0.133423i	0.637241	−	0.770664i	$-0.280075\pi$
$71$	−672.586	−	672.586i	−0.133423	−	0.133423i	−0.770664	+	0.637241i	$0.780075\pi$
$72$		0			0
$73$	−1169.63	+	1169.63i	−0.219485	+	0.219485i	−0.808281	−	0.588797i	$-0.799602\pi$
$73$	−1169.63	+	1169.63i	−0.219485	+	0.219485i	0.588797	+	0.808281i	$0.299602\pi$
$74$	2340.51			0.427412
$75$		0			0
$76$	43.3464	−	43.3464i	0.00750457	−	0.00750457i
$77$			1808.44i			0.305016i
$78$		0			0
$79$	8345.50			1.33720			0.668602	−	0.743620i	$-0.266893\pi$
$79$	8345.50			1.33720			0.668602	+	0.743620i	$0.266893\pi$
$80$	−4996.17	−	4996.17i	−0.780652	−	0.780652i
$81$		0			0
$82$			5702.60i			0.848096i
$83$	−6513.68	−	6513.68i	−0.945519	−	0.945519i	0.0530714	−	0.998591i	$-0.483099\pi$
$83$	−6513.68	−	6513.68i	−0.945519	−	0.945519i	−0.998591	+	0.0530714i	$0.983099\pi$
$84$		0			0
$85$	5086.23	−	5086.23i	0.703976	−	0.703976i
$86$	6482.67	−	6482.67i	0.876510	−	0.876510i
$87$		0			0
$88$			5223.62i			0.674537i
$89$	−8366.65	+	8366.65i	−1.05626	+	1.05626i	−0.0579425	+	0.998320i	$0.518454\pi$
$89$	−8366.65	+	8366.65i	−1.05626	+	1.05626i	−0.998320	+	0.0579425i	$0.981546\pi$
$90$		0			0
$91$	3345.55	−	1449.24i	0.404003	−	0.175008i
$92$	−473.429			−0.0559345
$93$		0			0
$94$	−2143.57			−0.242596
$95$			2034.79i			0.225461i
$96$		0			0
$97$	2271.58	+	2271.58i	0.241426	+	0.241426i	0.817440	−	0.576014i	$-0.195393\pi$
$97$	2271.58	+	2271.58i	0.241426	+	0.241426i	−0.576014	+	0.817440i	$0.695393\pi$
$98$	5608.84	−	5608.84i	0.584011	−	0.584011i
$99$		0			0
$100$	−55.3421			−0.00553421
$101$			6490.97i			0.636308i	0.948039	+	0.318154i	$0.103063\pi$
$101$			6490.97i			0.636308i	−0.948039	+	0.318154i	$0.896937\pi$
$102$		0			0
$103$			5614.96i			0.529264i	0.964350	+	0.264632i	$0.0852504\pi$
$103$			5614.96i			0.529264i	−0.964350	+	0.264632i	$0.914750\pi$
$104$	9663.49	−	4186.07i	0.893444	−	0.387026i
$105$		0			0
$106$	12747.6	+	12747.6i	1.13453	+	1.13453i
$107$	−9686.14			−0.846025			−0.423012	−	0.906124i	$-0.639027\pi$
$107$	−9686.14			−0.846025			−0.423012	+	0.906124i	$0.639027\pi$
$108$		0			0
$109$	−16372.1	−	16372.1i	−1.37801	−	1.37801i	−0.847980	−	0.530029i	$-0.822181\pi$
$109$	−16372.1	−	16372.1i	−1.37801	−	1.37801i	−0.530029	−	0.847980i	$-0.677819\pi$
$110$	6402.36	+	6402.36i	0.529121	+	0.529121i
$111$		0			0
$112$	−4089.44	+	4089.44i	−0.326008	+	0.326008i
$113$	19245.1			1.50717			0.753585	−	0.657350i	$-0.228323\pi$
$113$	19245.1			1.50717			0.753585	+	0.657350i	$0.228323\pi$
$114$		0			0
$115$	11112.0	−	11112.0i	0.840225	−	0.840225i
$116$			1043.52i			0.0775503i
$117$		0			0
$118$	5658.76			0.406403
$119$	−4163.15	−	4163.15i	−0.293987	−	0.293987i
$120$		0			0
$121$			7614.16i			0.520057i
$122$	17860.7	+	17860.7i	1.19999	+	1.19999i
$123$		0			0
$124$	−694.731	+	694.731i	−0.0451828	+	0.0451828i
$125$	−10349.4	+	10349.4i	−0.662358	+	0.662358i
$126$		0			0
$127$			26337.0i			1.63290i	0.577417	+	0.816449i	$0.304061\pi$
$127$			26337.0i			1.63290i	−0.577417	+	0.816449i	$0.695939\pi$
$128$	−12372.0	+	12372.0i	−0.755129	+	0.755129i
$129$		0			0
$130$	6713.43	−	16974.8i	0.397245	−	1.00443i
$131$	3094.41			0.180316			0.0901581	−	0.995927i	$-0.471263\pi$
$131$	3094.41			0.180316			0.0901581	+	0.995927i	$0.471263\pi$
$132$		0			0
$133$	1665.51			0.0941549
$134$			9902.03i			0.551461i
$135$		0			0
$136$	−12025.1	−	12025.1i	−0.650147	−	0.650147i
$137$	10453.9	−	10453.9i	0.556978	−	0.556978i	−0.371467	−	0.928446i	$-0.621145\pi$
$137$	10453.9	−	10453.9i	0.556978	−	0.556978i	0.928446	+	0.371467i	$0.121145\pi$
$138$		0			0
$139$	5922.48			0.306531			0.153265	−	0.988185i	$-0.451021\pi$
$139$	5922.48			0.306531			0.153265	+	0.988185i	$0.451021\pi$
$140$			451.511i			0.0230363i
$141$		0			0
$142$			3897.99i			0.193314i
$143$	−12999.4	+	5631.13i	−0.635698	+	0.275374i
$144$		0			0
$145$	−24492.6	−	24492.6i	−1.16493	−	1.16493i
$146$	6778.64			0.318007
$147$		0			0
$148$	−320.674	−	320.674i	−0.0146400	−	0.0146400i
$149$	22740.7	+	22740.7i	1.02431	+	1.02431i	0.999697	+	0.0246105i	$0.00783457\pi$
$149$	22740.7	+	22740.7i	1.02431	+	1.02431i	0.0246105	+	0.999697i	$0.492165\pi$
$150$		0			0
$151$	−30969.3	+	30969.3i	−1.35824	+	1.35824i	−0.482161	+	0.876082i	$0.660148\pi$
$151$	−30969.3	+	30969.3i	−1.35824	+	1.35824i	−0.876082	+	0.482161i	$0.839852\pi$
$152$	4810.76			0.208222
$153$		0			0
$154$	5240.43	−	5240.43i	0.220966	−	0.220966i
$155$		−	32612.4i		−	1.35744i
$156$		0			0
$157$	−16868.7			−0.684358			−0.342179	−	0.939635i	$-0.611165\pi$
$157$	−16868.7			−0.684358			−0.342179	+	0.939635i	$0.611165\pi$
$158$	−24183.3	−	24183.3i	−0.968725	−	0.968725i
$159$		0			0
$160$			2676.45i			0.104549i
$161$	−9095.32	−	9095.32i	−0.350886	−	0.350886i
$162$		0			0
$163$	23110.4	−	23110.4i	0.869826	−	0.869826i	−0.122626	−	0.992453i	$-0.539132\pi$
$163$	23110.4	−	23110.4i	0.869826	−	0.869826i	0.992453	+	0.122626i	$0.0391317\pi$
$164$	781.315	−	781.315i	0.0290495	−	0.0290495i
$165$		0			0
$166$			37750.2i			1.36994i
$167$	−16613.8	+	16613.8i	−0.595710	+	0.595710i	−0.939168	−	0.343458i	$-0.888402\pi$
$167$	−16613.8	+	16613.8i	−0.595710	+	0.595710i	0.343458	+	0.939168i	$0.388402\pi$
$168$		0			0
$169$	20834.7	+	19535.7i	0.729482	+	0.684000i
$170$	−29477.3			−1.01998
$171$		0			0
$172$	−1776.39			−0.0600455
$173$			9230.43i			0.308411i	0.988039	+	0.154206i	$0.0492818\pi$
$173$			9230.43i			0.308411i	−0.988039	+	0.154206i	$0.950718\pi$
$174$		0			0
$175$	−1063.21	−	1063.21i	−0.0347170	−	0.0347170i
$176$	15889.9	−	15889.9i	0.512973	−	0.512973i
$177$		0			0
$178$	48489.1			1.53040
$179$		−	28771.7i		−	0.897965i	−0.893541	−	0.448982i	$-0.851787\pi$
$179$		−	28771.7i		−	0.897965i	0.893541	−	0.448982i	$-0.148213\pi$
$180$		0			0
$181$			2334.88i			0.0712700i	0.999365	+	0.0356350i	$0.0113454\pi$
$181$			2334.88i			0.0712700i	−0.999365	+	0.0356350i	$0.988655\pi$
$182$	−13894.1	−	5495.05i	−0.419458	−	0.165893i
$183$		0			0
$184$	−26271.5	−	26271.5i	−0.775978	−	0.775978i
$185$	15053.2			0.439831
$186$		0			0
$187$	16176.3	+	16176.3i	0.462589	+	0.462589i
$188$	293.692	+	293.692i	0.00830953	+	0.00830953i
$189$		0			0
$190$	5896.34	−	5896.34i	0.163333	−	0.163333i
$191$	11500.7			0.315251			0.157625	−	0.987499i	$-0.449616\pi$
$191$	11500.7			0.315251			0.157625	+	0.987499i	$0.449616\pi$
$192$		0			0
$193$	36690.3	−	36690.3i	0.985002	−	0.985002i	−0.0148869	−	0.999889i	$-0.504739\pi$
$193$	36690.3	−	36690.3i	0.985002	−	0.985002i	0.999889	+	0.0148869i	$0.00473884\pi$
$194$		−	13165.0i		−	0.349797i
$195$		0			0
$196$	−1536.94			−0.0400078
$197$	−3775.20	−	3775.20i	−0.0972763	−	0.0972763i	0.656794	−	0.754070i	$-0.271912\pi$
$197$	−3775.20	−	3775.20i	−0.0972763	−	0.0972763i	−0.754070	+	0.656794i	$0.771912\pi$
$198$		0			0
$199$		−	47612.3i		−	1.20230i	−0.799136	−	0.601151i	$-0.794709\pi$
$199$		−	47612.3i		−	1.20230i	0.799136	−	0.601151i	$-0.205291\pi$
$200$	−3071.04	−	3071.04i	−0.0767760	−	0.0767760i
$201$		0			0
$202$	18809.3	−	18809.3i	0.460967	−	0.460967i
$203$	−20047.6	+	20047.6i	−0.486486	+	0.486486i
$204$		0			0
$205$			36676.9i			0.872740i
$206$	16270.8	−	16270.8i	0.383420	−	0.383420i
$207$		0			0
$208$	−42129.4	−	16661.9i	−0.973774	−	0.385122i
$209$	−6471.46			−0.148153
$210$		0			0
$211$	−75668.4			−1.69961			−0.849806	−	0.527096i	$-0.823281\pi$
$211$	−75668.4			−1.69961			−0.849806	+	0.527096i	$0.823281\pi$
$212$		−	3493.11i		−	0.0777215i
$213$		0			0
$214$	28068.1	+	28068.1i	0.612894	+	0.612894i
$215$	41694.0	−	41694.0i	0.901980	−	0.901980i
$216$		0			0
$217$	−26693.8			−0.566879
$218$			94885.0i			1.99657i
$219$		0			0
$220$		−	1754.38i		−	0.0362475i
$221$	16962.2	−	42888.7i	0.347295	−	0.878129i
$222$		0			0
$223$	−953.201	−	953.201i	−0.0191679	−	0.0191679i	0.697458	−	0.716626i	$-0.254314\pi$
$223$	−953.201	−	953.201i	−0.0191679	−	0.0191679i	−0.716626	+	0.697458i	$0.754314\pi$
$224$	2190.71			0.0436606
$225$		0			0
$226$	−55767.6	−	55767.6i	−1.09186	−	1.09186i
$227$	−6110.06	−	6110.06i	−0.118575	−	0.118575i	0.645329	−	0.763905i	$-0.276720\pi$
$227$	−6110.06	−	6110.06i	−0.118575	−	0.118575i	−0.763905	+	0.645329i	$0.776720\pi$
$228$		0			0
$229$	9576.99	−	9576.99i	0.182624	−	0.182624i	−0.609874	−	0.792498i	$-0.708780\pi$
$229$	9576.99	−	9576.99i	0.182624	−	0.182624i	0.792498	+	0.609874i	$0.208780\pi$
$230$	−64399.7			−1.21739
$231$		0			0
$232$	−57906.8	+	57906.8i	−1.07585	+	1.07585i
$233$			72801.5i			1.34100i	0.741910	+	0.670500i	$0.233920\pi$
$233$			72801.5i			1.34100i	−0.741910	+	0.670500i	$0.766080\pi$
$234$		0			0
$235$	−13786.6			−0.249645
$236$	−775.309	−	775.309i	−0.0139204	−	0.0139204i
$237$		0			0
$238$			24127.7i			0.425952i
$239$	−72643.5	−	72643.5i	−1.27175	−	1.27175i	−0.945170	−	0.326578i	$-0.894105\pi$
$239$	−72643.5	−	72643.5i	−1.27175	−	1.27175i	−0.326578	−	0.945170i	$-0.605895\pi$
$240$		0			0
$241$	64322.5	−	64322.5i	1.10746	−	1.10746i	0.113978	−	0.993483i	$-0.463641\pi$
$241$	64322.5	−	64322.5i	1.10746	−	1.10746i	0.993483	−	0.113978i	$-0.0363593\pi$
$242$	22064.0	−	22064.0i	0.376751	−	0.376751i
$243$		0			0
$244$		−	4894.19i		−	0.0822056i
$245$	36073.9	−	36073.9i	0.600981	−	0.600981i
$246$		0			0
$247$	5186.06	+	11971.9i	0.0850048	+	0.196232i
$248$	−77104.0			−1.25364
$249$		0			0
$250$	59979.9			0.959678
$251$			49293.7i			0.782427i	0.920300	+	0.391213i	$0.127945\pi$
$251$			49293.7i			0.782427i	−0.920300	+	0.391213i	$0.872055\pi$
$252$		0			0
$253$	35340.6	+	35340.6i	0.552119	+	0.552119i
$254$	76318.4	−	76318.4i	1.18294	−	1.18294i
$255$		0			0
$256$	9733.62			0.148523
$257$			82424.4i			1.24793i	0.781453	+	0.623964i	$0.214479\pi$
$257$			82424.4i			1.24793i	−0.781453	+	0.623964i	$0.785521\pi$
$258$		0			0
$259$		−	12321.3i		−	0.183678i
$260$	−3245.54	+	1405.92i	−0.0480109	+	0.0207976i
$261$		0			0
$262$	−8966.85	−	8966.85i	−0.130628	−	0.130628i
$263$	−41367.3			−0.598062			−0.299031	−	0.954243i	$-0.596663\pi$
$263$	−41367.3			−0.598062			−0.299031	+	0.954243i	$0.596663\pi$
$264$		0			0
$265$	81987.7	+	81987.7i	1.16750	+	1.16750i
$266$	−4826.24	−	4826.24i	−0.0682096	−	0.0682096i
$267$		0			0
$268$	1356.68	−	1356.68i	0.0188890	−	0.0188890i
$269$	59626.2			0.824011			0.412005	−	0.911181i	$-0.364828\pi$
$269$	59626.2			0.824011			0.412005	+	0.911181i	$0.364828\pi$
$270$		0			0
$271$	−75798.8	+	75798.8i	−1.03210	+	1.03210i	−0.0326374	+	0.999467i	$0.510391\pi$
$271$	−75798.8	+	75798.8i	−1.03210	+	1.03210i	−0.999467	+	0.0326374i	$0.989609\pi$
$272$			73159.1i			0.988850i
$273$		0			0
$274$	−60586.0			−0.806996
$275$	4131.18	+	4131.18i	0.0546272	+	0.0546272i
$276$		0			0
$277$			134127.i			1.74806i	0.485876	+	0.874028i	$0.338501\pi$
$277$			134127.i			1.74806i	−0.485876	+	0.874028i	$0.661499\pi$
$278$	−17161.9	−	17161.9i	−0.222063	−	0.222063i
$279$		0			0
$280$	−25055.2	+	25055.2i	−0.319582	+	0.319582i
$281$	19968.0	−	19968.0i	0.252885	−	0.252885i	−0.569268	−	0.822152i	$-0.692773\pi$
$281$	19968.0	−	19968.0i	0.252885	−	0.252885i	0.822152	+	0.569268i	$0.192773\pi$
$282$		0			0
$283$		−	151960.i		−	1.89739i	−0.316186	−	0.948697i	$-0.602402\pi$
$283$		−	151960.i		−	1.89739i	0.316186	−	0.948697i	$-0.397598\pi$
$284$	534.065	−	534.065i	0.00662151	−	0.00662151i
$285$		0			0
$286$	53986.8	+	21351.4i	0.660017	+	0.261033i
$287$	30020.6			0.364465
$288$		0			0
$289$	9043.27			0.108275
$290$			141948.i			1.68784i
$291$		0			0
$292$	−928.744	−	928.744i	−0.0108926	−	0.0108926i
$293$	−22398.8	+	22398.8i	−0.260909	+	0.260909i	−0.825423	−	0.564514i	$-0.809063\pi$
$293$	−22398.8	+	22398.8i	−0.260909	+	0.260909i	0.564514	+	0.825423i	$0.309063\pi$
$294$		0			0
$295$	36394.9			0.418212
$296$		−	35589.6i		−	0.406200i
$297$		0			0
$298$		−	131794.i		−	1.48410i
$299$	37057.7	−	93699.8i	0.414511	−	1.04808i
$300$		0			0
$301$	−34127.2	−	34127.2i	−0.376676	−	0.376676i
$302$	179483.			1.96793
$303$		0			0
$304$	−14634.0	−	14634.0i	−0.158349	−	0.158349i
$305$	114873.	+	114873.i	1.23486	+	1.23486i
$306$		0			0
$307$	36789.1	−	36789.1i	0.390339	−	0.390339i	−0.484469	−	0.874808i	$-0.660987\pi$
$307$	36789.1	−	36789.1i	0.390339	−	0.390339i	0.874808	+	0.484469i	$0.160987\pi$
$308$	−1435.99			−0.0151373
$309$		0			0
$310$	−94503.0	+	94503.0i	−0.983382	+	0.983382i
$311$			78846.4i			0.815194i	0.913162	+	0.407597i	$0.133633\pi$
$311$			78846.4i			0.815194i	−0.913162	+	0.407597i	$0.866367\pi$
$312$		0			0
$313$	20618.6			0.210460			0.105230	−	0.994448i	$-0.466442\pi$
$313$	20618.6			0.210460			0.105230	+	0.994448i	$0.466442\pi$
$314$	48881.6	+	48881.6i	0.495777	+	0.495777i
$315$		0			0
$316$			6626.72i			0.0663627i
$317$	−42129.4	−	42129.4i	−0.419244	−	0.419244i	0.465699	−	0.884943i	$-0.345803\pi$
$317$	−42129.4	−	42129.4i	−0.419244	−	0.419244i	−0.884943	+	0.465699i	$0.845803\pi$
$318$		0			0
$319$	77896.6	−	77896.6i	0.765485	−	0.765485i
$320$	−72183.1	+	72183.1i	−0.704913	+	0.704913i
$321$		0			0
$322$			52712.2i			0.508392i
$323$	14897.7	−	14897.7i	0.142796	−	0.142796i
$324$		0			0
$325$	4331.90	−	10953.2i	0.0410121	−	0.103698i
$326$	−133937.			−1.26027
$327$		0			0
$328$	86713.5			0.806007
$329$			11284.6i			0.104254i
$330$		0			0
$331$	68308.6	+	68308.6i	0.623476	+	0.623476i	0.946418	−	0.322943i	$-0.104672\pi$
$331$	68308.6	+	68308.6i	0.623476	+	0.623476i	−0.322943	+	0.946418i	$0.604672\pi$
$332$	5172.17	−	5172.17i	0.0469242	−	0.0469242i
$333$		0			0
$334$	96285.5			0.863113
$335$			63686.0i			0.567485i
$336$		0			0
$337$			87835.7i			0.773412i	0.922203	+	0.386706i	$0.126387\pi$
$337$			87835.7i			0.773412i	−0.922203	+	0.386706i	$0.873613\pi$
$338$	−3764.29	−	116984.i	−0.0329495	−	1.02398i
$339$		0			0
$340$	4038.70	+	4038.70i	0.0349369	+	0.0349369i
$341$	103721.			0.891983
$342$		0			0
$343$	−66154.0	−	66154.0i	−0.562300	−	0.562300i
$344$	−98575.2	−	98575.2i	−0.833011	−	0.833011i
$345$		0			0
$346$	26747.6	−	26747.6i	0.223425	−	0.223425i
$347$	−98270.4			−0.816138			−0.408069	−	0.912951i	$-0.633798\pi$
$347$	−98270.4			−0.816138			−0.408069	+	0.912951i	$0.633798\pi$
$348$		0			0
$349$	−17440.9	+	17440.9i	−0.143192	+	0.143192i	−0.775069	−	0.631877i	$-0.782285\pi$
$349$	−17440.9	+	17440.9i	−0.143192	+	0.143192i	0.631877	+	0.775069i	$0.282285\pi$
$350$			6161.85i			0.0503008i
$351$		0			0
$352$	−8512.19			−0.0686999
$353$	−63740.5	−	63740.5i	−0.511524	−	0.511524i	0.403469	−	0.914993i	$-0.367804\pi$
$353$	−63740.5	−	63740.5i	−0.511524	−	0.511524i	−0.914993	+	0.403469i	$0.867804\pi$
$354$		0			0
$355$			25070.3i			0.198931i
$356$	−6643.52	−	6643.52i	−0.0524201	−	0.0524201i
$357$		0			0
$358$	−83373.5	+	83373.5i	−0.650522	+	0.650522i
$359$	168217.	−	168217.i	1.30521	−	1.30521i	0.380377	−	0.924831i	$-0.375794\pi$
$359$	168217.	−	168217.i	1.30521	−	1.30521i	0.924831	−	0.380377i	$-0.124206\pi$
$360$		0			0
$361$		−	124361.i		−	0.954267i
$362$	6765.91	−	6765.91i	0.0516308	−	0.0516308i
$363$		0			0
$364$	1150.76	+	2656.52i	0.00868527	+	0.0200498i
$365$	43597.6			0.327248
$366$		0			0
$367$	4967.29			0.0368797			0.0184399	−	0.999830i	$-0.494130\pi$
$367$	4967.29			0.0368797			0.0184399	+	0.999830i	$0.494130\pi$
$368$			159832.i			1.18023i
$369$		0			0
$370$	−43620.7	−	43620.7i	−0.318632	−	0.318632i
$371$	67108.2	−	67108.2i	0.487560	−	0.487560i
$372$		0			0
$373$	−115465.			−0.829914			−0.414957	−	0.909841i	$-0.636203\pi$
$373$	−115465.			−0.829914			−0.414957	+	0.909841i	$0.636203\pi$
$374$		−	93749.9i		−	0.670236i
$375$		0			0
$376$			32595.1i			0.230556i
$377$	−206530.	−	81681.3i	−1.45312	−	0.574698i
$378$		0			0
$379$	−79418.8	−	79418.8i	−0.552898	−	0.552898i	0.374378	−	0.927276i	$-0.377856\pi$
$379$	−79418.8	−	79418.8i	−0.552898	−	0.552898i	−0.927276	+	0.374378i	$0.877856\pi$
$380$	−1615.72			−0.0111892
$381$		0			0
$382$	−33326.2	−	33326.2i	−0.228380	−	0.228380i
$383$	−30297.2	−	30297.2i	−0.206540	−	0.206540i	0.596255	−	0.802795i	$-0.296655\pi$
$383$	−30297.2	−	30297.2i	−0.206540	−	0.206540i	−0.802795	+	0.596255i	$0.796655\pi$
$384$		0			0
$385$	33704.4	−	33704.4i	0.227387	−	0.227387i
$386$	−212640.			−1.42715
$387$		0			0
$388$	−1803.74	+	1803.74i	−0.0119815	+	0.0119815i
$389$		−	135764.i		−	0.897193i	−0.893734	−	0.448597i	$-0.851924\pi$
$389$		−	135764.i		−	0.897193i	0.893734	−	0.448597i	$-0.148076\pi$
$390$		0			0
$391$	−162713.			−1.06431
$392$	−85287.7	−	85287.7i	−0.555028	−	0.555028i
$393$		0			0
$394$			21879.2i			0.140942i
$395$	−155537.	−	155537.i	−0.996874	−	0.996874i
$396$		0			0
$397$	−122596.	+	122596.i	−0.777851	+	0.777851i	−0.979465	−	0.201614i	$-0.935381\pi$
$397$	−122596.	+	122596.i	−0.777851	+	0.777851i	0.201614	+	0.979465i	$0.435381\pi$
$398$	−137969.	+	137969.i	−0.870996	+	0.870996i
$399$		0			0
$400$			18683.8i			0.116774i
$401$	−132123.	+	132123.i	−0.821653	+	0.821653i	−0.986345	−	0.164692i	$-0.947337\pi$
$401$	−132123.	+	132123.i	−0.821653	+	0.821653i	0.164692	+	0.986345i	$0.447337\pi$
$402$		0			0
$403$	−83119.1	−	191879.i	−0.511789	−	1.18146i
$404$	−5154.14			−0.0315786
$405$		0			0
$406$	116186.			0.704860
$407$			47875.4i			0.289017i
$408$		0			0
$409$	2700.68	+	2700.68i	0.0161445	+	0.0161445i	0.715133	−	0.698988i	$-0.246366\pi$
$409$	2700.68	+	2700.68i	0.0161445	+	0.0161445i	−0.698988	+	0.715133i	$0.746366\pi$
$410$	106281.	−	106281.i	0.632248	−	0.632248i
$411$		0			0
$412$	−4458.54			−0.0262663
$413$		−	29789.8i		−	0.174650i
$414$		0			0
$415$			242795.i			1.40975i
$416$	6821.45	+	15747.2i	0.0394176	+	0.0909950i
$417$		0			0
$418$	18752.7	+	18752.7i	0.107328	+	0.107328i
$419$	94447.5			0.537975			0.268988	−	0.963144i	$-0.413311\pi$
$419$	94447.5			0.537975			0.268988	+	0.963144i	$0.413311\pi$
$420$		0			0
$421$	15371.4	+	15371.4i	0.0867262	+	0.0867262i	0.749139	−	0.662413i	$-0.230468\pi$
$421$	15371.4	+	15371.4i	0.0867262	+	0.0867262i	−0.662413	+	0.749139i	$0.730468\pi$
$422$	219269.	+	219269.i	1.23127	+	1.23127i
$423$		0			0
$424$	193840.	−	193840.i	1.07823	−	1.07823i
$425$	−19020.5			−0.105304
$426$		0			0
$427$	94025.1	−	94025.1i	0.515689	−	0.515689i
$428$		−	7691.25i		−	0.0419865i
$429$		0			0
$430$	−241639.			−1.30686
$431$	42041.0	+	42041.0i	0.226317	+	0.226317i	0.811152	−	0.584835i	$-0.198841\pi$
$431$	42041.0	+	42041.0i	0.226317	+	0.226317i	−0.584835	+	0.811152i	$0.698841\pi$
$432$		0			0
$433$		−	29381.2i		−	0.156709i	−0.996926	−	0.0783545i	$-0.975033\pi$
$433$		−	29381.2i		−	0.156709i	0.996926	−	0.0783545i	$-0.0249666\pi$
$434$	77352.1	+	77352.1i	0.410670	+	0.410670i
$435$		0			0
$436$	13000.2	−	13000.2i	0.0683877	−	0.0683877i
$437$	32547.4	−	32547.4i	0.170433	−	0.170433i
$438$		0			0
$439$		−	354668.i		−	1.84032i	−0.391542	−	0.920160i	$-0.628058\pi$
$439$		−	354668.i		−	1.84032i	0.391542	−	0.920160i	$-0.371942\pi$
$440$	97354.0	−	97354.0i	0.502862	−	0.502862i
$441$		0			0
$442$	−173434.	+	75128.8i	−0.887747	+	0.384558i
$443$	22527.8			0.114792			0.0573960	−	0.998351i	$-0.481720\pi$
$443$	22527.8			0.114792			0.0573960	+	0.998351i	$0.481720\pi$
$444$		0			0
$445$	311863.			1.57487
$446$			5524.30i			0.0277720i
$447$		0			0
$448$	59082.9	+	59082.9i	0.294378	+	0.294378i
$449$	53263.7	−	53263.7i	0.264204	−	0.264204i	−0.562556	−	0.826759i	$-0.690182\pi$
$449$	53263.7	−	53263.7i	0.264204	−	0.264204i	0.826759	+	0.562556i	$0.190182\pi$
$450$		0			0
$451$	−116647.			−0.573485
$452$			15281.5i			0.0747978i
$453$		0			0
$454$			35411.0i			0.171801i
$455$	−89361.7	−	35342.0i	−0.431647	−	0.170714i
$456$		0			0
$457$	94033.6	+	94033.6i	0.450247	+	0.450247i	0.895436	−	0.445189i	$-0.146864\pi$
$457$	94033.6	+	94033.6i	0.450247	+	0.450247i	−0.445189	+	0.895436i	$0.646864\pi$
$458$	−55503.7			−0.264601
$459$		0			0
$460$	8823.43	+	8823.43i	0.0416986	+	0.0416986i
$461$	220771.	+	220771.i	1.03882	+	1.03882i	0.999215	+	0.0396051i	$0.0126100\pi$
$461$	220771.	+	220771.i	1.03882	+	1.03882i	0.0396051	+	0.999215i	$0.487390\pi$
$462$		0			0
$463$	−148393.	+	148393.i	−0.692231	+	0.692231i	−0.962722	−	0.270491i	$-0.912814\pi$
$463$	−148393.	+	148393.i	−0.692231	+	0.692231i	0.270491	+	0.962722i	$0.412814\pi$
$464$	352296.			1.63634
$465$		0			0
$466$	210962.	−	210962.i	0.971474	−	0.971474i
$467$			89596.5i			0.410826i	0.978675	+	0.205413i	$0.0658537\pi$
$467$			89596.5i			0.410826i	−0.978675	+	0.205413i	$0.934146\pi$
$468$		0			0
$469$	52128.0			0.236987
$470$	39950.4	+	39950.4i	0.180853	+	0.180853i
$471$		0			0
$472$		−	86046.8i		−	0.386234i
$473$	132604.	+	132604.i	0.592699	+	0.592699i
$474$		0			0
$475$	3804.66	−	3804.66i	0.0168628	−	0.0168628i
$476$	3305.74	−	3305.74i	0.0145900	−	0.0145900i
$477$		0			0
$478$			421007.i			1.84261i
$479$	−290497.	+	290497.i	−1.26611	+	1.26611i	−0.318023	+	0.948083i	$0.603019\pi$
$479$	−290497.	+	290497.i	−1.26611	+	1.26611i	−0.948083	+	0.318023i	$0.896981\pi$
$480$		0			0
$481$	88567.6	−	38366.1i	0.382811	−	0.165828i
$482$	−372782.			−1.60458
$483$		0			0
$484$	−6046.00			−0.0258094
$485$		−	84672.0i		−	0.359962i
$486$		0			0
$487$	186744.	+	186744.i	0.787388	+	0.787388i	0.981065	−	0.193677i	$-0.0620414\pi$
$487$	186744.	+	186744.i	0.787388	+	0.787388i	−0.193677	+	0.981065i	$0.562041\pi$
$488$	271588.	−	271588.i	1.14044	−	1.14044i
$489$		0			0
$490$	−209067.			−0.870750
$491$			26475.0i			0.109818i	0.998491	+	0.0549088i	$0.0174868\pi$
$491$			26475.0i			0.109818i	−0.998491	+	0.0549088i	$0.982513\pi$
$492$		0			0
$493$			358646.i			1.47561i
$494$	19663.9	−	49719.8i	0.0805778	−	0.203740i
$495$		0			0
$496$	234545.	+	234545.i	0.953372	+	0.953372i
$497$	20520.4			0.0830757
$498$		0			0
$499$	72703.0	+	72703.0i	0.291979	+	0.291979i	0.837862	−	0.545883i	$-0.183806\pi$
$499$	72703.0	+	72703.0i	0.291979	+	0.291979i	−0.545883	+	0.837862i	$0.683806\pi$
$500$	−8217.87	−	8217.87i	−0.0328715	−	0.0328715i
$501$		0			0
$502$	142841.	−	142841.i	0.566822	−	0.566822i
$503$	−245797.			−0.971496			−0.485748	−	0.874099i	$-0.661453\pi$
$503$	−245797.			−0.971496			−0.485748	+	0.874099i	$0.661453\pi$
$504$		0			0
$505$	120974.	−	120974.i	0.474362	−	0.474362i
$506$		−	204817.i		−	0.799955i
$507$		0			0
$508$	−20912.8			−0.0810374
$509$	105992.	+	105992.i	0.409109	+	0.409109i	0.881428	−	0.472319i	$-0.156583\pi$
$509$	105992.	+	105992.i	0.409109	+	0.409109i	−0.472319	+	0.881428i	$0.656583\pi$
$510$		0			0
$511$		−	35685.3i		−	0.136662i
$512$	169747.	+	169747.i	0.647533	+	0.647533i
$513$		0			0
$514$	238846.	−	238846.i	0.904049	−	0.904049i
$515$	104648.	−	104648.i	0.394561	−	0.394561i
$516$		0			0
$517$		−	43847.1i		−	0.164044i
$518$	−35704.2	+	35704.2i	−0.133064	+	0.133064i
$519$		0			0
$520$	−258118.	−	102084.i	−0.954579	−	0.377530i
$521$	−408225.			−1.50392			−0.751959	−	0.659209i	$-0.770891\pi$
$521$	−408225.			−1.50392			−0.751959	+	0.659209i	$0.770891\pi$
$522$		0			0
$523$	−145126.			−0.530567			−0.265284	−	0.964170i	$-0.585466\pi$
$523$	−145126.			−0.530567			−0.265284	+	0.964170i	$0.585466\pi$
$524$			2457.10i			0.00894872i
$525$		0			0
$526$	119873.	+	119873.i	0.433260	+	0.433260i
$527$	−238772.	+	238772.i	−0.859731	+	0.859731i
$528$		0			0
$529$	−75641.2			−0.270300
$530$		−	475162.i		−	1.69157i
$531$		0			0
$532$			1322.49i			0.00467271i
$533$	93478.3	+	215793.i	0.329046	+	0.759597i
$534$		0			0
$535$	180523.	+	180523.i	0.630704	+	0.630704i
$536$	150570.			0.524093
$537$		0			0
$538$	−172783.	−	172783.i	−0.596947	−	0.596947i
$539$	114730.	+	114730.i	0.394910	+	0.394910i
$540$		0			0
$541$	−376207.	+	376207.i	−1.28538	+	1.28538i	−0.347823	+	0.937560i	$0.613079\pi$
$541$	−376207.	+	376207.i	−1.28538	+	1.28538i	−0.937560	+	0.347823i	$0.886921\pi$
$542$	439294.			1.49540
$543$		0			0
$544$	19595.6	−	19595.6i	0.0662158	−	0.0662158i
$545$			610263.i			2.05459i
$546$		0			0
$547$	−110782.			−0.370249			−0.185124	−	0.982715i	$-0.559269\pi$
$547$	−110782.			−0.370249			−0.185124	+	0.982715i	$0.559269\pi$
$548$	8300.91	+	8300.91i	0.0276417	+	0.0276417i
$549$		0			0
$550$		−	23942.4i		−	0.0791483i
$551$	−71739.8	−	71739.8i	−0.236296	−	0.236296i
$552$		0			0
$553$	−127310.	+	127310.i	−0.416304	+	0.416304i
$554$	388667.	−	388667.i	1.26636	−	1.26636i
$555$		0			0
$556$			4702.73i			0.0152125i
$557$	−141690.	+	141690.i	−0.456696	+	0.456696i	−0.897569	−	0.440873i	$-0.854669\pi$
$557$	−141690.	+	141690.i	−0.456696	+	0.456696i	0.440873	+	0.897569i	$0.354669\pi$
$558$		0			0
$559$	139047.	−	351577.i	0.444977	−	1.12512i
$560$	152432.			0.486072
$561$		0			0
$562$	−115725.			−0.366400
$563$		−	301845.i		−	0.952287i	−0.879368	−	0.476143i	$-0.842034\pi$
$563$		−	301845.i		−	0.952287i	0.879368	−	0.476143i	$-0.157966\pi$
$564$		0			0
$565$	−358675.	−	358675.i	−1.12358	−	1.12358i
$566$	−440345.	+	440345.i	−1.37455	+	1.37455i
$567$		0			0
$568$	59272.6			0.183720
$569$			149750.i			0.462532i	0.972891	+	0.231266i	$0.0742867\pi$
$569$			149750.i			0.462532i	−0.972891	+	0.231266i	$0.925713\pi$
$570$		0			0
$571$		−	477531.i		−	1.46463i	−0.680964	−	0.732317i	$-0.738439\pi$
$571$		−	477531.i		−	1.46463i	0.680964	−	0.732317i	$-0.261561\pi$
$572$	−4471.38	−	10322.1i	−0.0136663	−	0.0315484i
$573$		0			0
$574$	−86992.5	−	86992.5i	−0.264033	−	0.264033i
$575$	−41554.5			−0.125685
$576$		0			0
$577$	108891.	+	108891.i	0.327069	+	0.327069i	0.851471	−	0.524402i	$-0.175711\pi$
$577$	108891.	+	108891.i	0.327069	+	0.327069i	−0.524402	+	0.851471i	$0.675711\pi$
$578$	−26205.2	−	26205.2i	−0.0784391	−	0.0784391i
$579$		0			0
$580$	19448.3	−	19448.3i	0.0578131	−	0.0578131i
$581$	198731.			0.588726
$582$		0			0
$583$	−260754.	+	260754.i	−0.767175	+	0.767175i
$584$		−	103076.i		−	0.302225i
$585$		0			0
$586$	129813.			0.378026
$587$	−379654.	−	379654.i	−1.10182	−	1.10182i	−0.994191	−	0.107632i	$-0.965673\pi$
$587$	−379654.	−	379654.i	−1.10182	−	1.10182i	−0.107632	−	0.994191i	$-0.534327\pi$
$588$		0			0
$589$		−	95522.9i		−	0.275345i
$590$	−105464.	−	105464.i	−0.302970	−	0.302970i
$591$		0			0
$592$	−108261.	+	108261.i	−0.308908	+	0.308908i
$593$	−20445.7	+	20445.7i	−0.0581423	+	0.0581423i	−0.735580	−	0.677438i	$-0.763090\pi$
$593$	−20445.7	+	20445.7i	−0.0581423	+	0.0581423i	0.677438	+	0.735580i	$0.263090\pi$
$594$		0			0
$595$			155180.i			0.438330i
$596$	−18057.1	+	18057.1i	−0.0508343	+	0.0508343i
$597$		0			0
$598$	−378904.	+	164135.i	−1.05956	+	0.458986i
$599$	−45314.1			−0.126293			−0.0631466	−	0.998004i	$-0.520114\pi$
$599$	−45314.1			−0.126293			−0.0631466	+	0.998004i	$0.520114\pi$
$600$		0			0
$601$	−71319.6			−0.197451			−0.0987256	−	0.995115i	$-0.531477\pi$
$601$	−71319.6			−0.197451			−0.0987256	+	0.995115i	$0.531477\pi$
$602$			197785.i			0.545758i
$603$		0			0
$604$	−24591.1	−	24591.1i	−0.0674068	−	0.0674068i
$605$	141907.	−	141907.i	0.387698	−	0.387698i
$606$		0			0
$607$	37835.4			0.102688			0.0513441	−	0.998681i	$-0.483649\pi$
$607$	37835.4			0.102688			0.0513441	+	0.998681i	$0.483649\pi$
$608$			7839.41i			0.0212069i
$609$		0			0
$610$		−	665748.i		−	1.78916i
$611$	−81115.5	+	35138.0i	−0.217281	+	0.0941226i
$612$		0			0
$613$	269915.	+	269915.i	0.718301	+	0.718301i	0.968257	−	0.249956i	$-0.0804162\pi$
$613$	269915.	+	269915.i	0.718301	+	0.718301i	−0.249956	+	0.968257i	$0.580416\pi$
$614$	−213212.			−0.565555
$615$		0			0
$616$	−79685.7	−	79685.7i	−0.210000	−	0.210000i
$617$	−128460.	−	128460.i	−0.337440	−	0.337440i	0.517963	−	0.855403i	$-0.326690\pi$
$617$	−128460.	−	128460.i	−0.337440	−	0.337440i	−0.855403	+	0.517963i	$0.826690\pi$
$618$		0			0
$619$	−78942.1	+	78942.1i	−0.206029	+	0.206029i	−0.802577	−	0.596548i	$-0.796538\pi$
$619$	−78942.1	+	78942.1i	−0.206029	+	0.206029i	0.596548	+	0.802577i	$0.296538\pi$
$620$	25895.8			0.0673668
$621$		0			0
$622$	228478.	−	228478.i	0.590560	−	0.590560i
$623$		−	255265.i		−	0.657680i
$624$		0			0
$625$	429328.			1.09908
$626$	−59747.7	−	59747.7i	−0.152466	−	0.152466i
$627$		0			0
$628$		−	13394.6i		−	0.0339633i
$629$	−110212.	−	110212.i	−0.278567	−	0.278567i
$630$		0			0
$631$	−138220.	+	138220.i	−0.347146	+	0.347146i	−0.859045	−	0.511899i	$-0.828942\pi$
$631$	−138220.	+	138220.i	−0.347146	+	0.347146i	0.511899	+	0.859045i	$0.328942\pi$
$632$	−367729.	+	367729.i	−0.920649	+	0.920649i
$633$		0			0
$634$			244162.i			0.607435i
$635$	490850.	−	490850.i	1.21731	−	1.21731i
$636$		0			0
$637$	120304.	−	304187.i	0.296484	−	0.749655i
$638$	−451451.			−1.10910
$639$		0			0
$640$	461162.			1.12588
$641$		−	369011.i		−	0.898098i	−0.893507	−	0.449049i	$-0.851763\pi$
$641$		−	369011.i		−	0.898098i	0.893507	−	0.449049i	$-0.148237\pi$
$642$		0			0
$643$	111450.	+	111450.i	0.269561	+	0.269561i	0.828923	−	0.559362i	$-0.188954\pi$
$643$	111450.	+	111450.i	0.269561	+	0.269561i	−0.559362	+	0.828923i	$0.688954\pi$
$644$	7222.11	−	7222.11i	0.0174138	−	0.0174138i
$645$		0			0
$646$	−86340.2			−0.206894
$647$		−	401104.i		−	0.958184i	−0.877765	−	0.479092i	$-0.840966\pi$
$647$		−	401104.i		−	0.958184i	0.877765	−	0.479092i	$-0.159034\pi$
$648$		0			0
$649$			115751.i			0.274811i
$650$	−44292.5	+	19186.8i	−0.104834	+	0.0454125i
$651$		0			0
$652$	18350.8	+	18350.8i	0.0431677	+	0.0431677i
$653$	341135.			0.800018			0.400009	−	0.916511i	$-0.369007\pi$
$653$	341135.			0.800018			0.400009	+	0.916511i	$0.369007\pi$
$654$		0			0
$655$	−57671.3	−	57671.3i	−0.134424	−	0.134424i
$656$	−263776.	−	263776.i	−0.612954	−	0.612954i
$657$		0			0
$658$	32700.0	−	32700.0i	0.0755259	−	0.0755259i
$659$	−32739.6			−0.0753881			−0.0376941	−	0.999289i	$-0.512001\pi$
$659$	−32739.6			−0.0753881			−0.0376941	+	0.999289i	$0.512001\pi$
$660$		0			0
$661$	20237.5	−	20237.5i	0.0463184	−	0.0463184i	−0.683568	−	0.729887i	$-0.739573\pi$
$661$	20237.5	−	20237.5i	0.0463184	−	0.0463184i	0.729887	+	0.683568i	$0.239573\pi$
$662$		−	395884.i		−	0.903342i
$663$		0			0
$664$	574028.			1.30196
$665$	−31040.5	−	31040.5i	−0.0701916	−	0.0701916i
$666$		0			0
$667$			783542.i			1.76121i
$668$	−13192.1	−	13192.1i	−0.0295639	−	0.0295639i
$669$		0			0
$670$	184547.	−	184547.i	0.411109	−	0.411109i
$671$	−365342.	+	365342.i	−0.811437	+	0.811437i
$672$		0			0
$673$		−	151692.i		−	0.334914i	−0.985879	−	0.167457i	$-0.946444\pi$
$673$		−	151692.i		−	0.334914i	0.985879	−	0.167457i	$-0.0535556\pi$
$674$	254527.	−	254527.i	0.560291	−	0.560291i
$675$		0			0
$676$	−15512.3	+	16543.8i	−0.0339455	+	0.0362027i
$677$	753102.			1.64315			0.821574	−	0.570102i	$-0.193096\pi$
$677$	753102.			1.64315			0.821574	+	0.570102i	$0.193096\pi$
$678$		0			0
$679$	−69305.3			−0.150323
$680$			448231.i			0.969358i
$681$		0			0
$682$	−300558.	−	300558.i	−0.646189	−	0.646189i
$683$	−50909.1	+	50909.1i	−0.109132	+	0.109132i	−0.759564	−	0.650432i	$-0.774588\pi$
$683$	−50909.1	+	50909.1i	−0.109132	+	0.109132i	0.650432	+	0.759564i	$0.274588\pi$
$684$		0			0
$685$	−389666.			−0.830445
$686$			383397.i			0.814705i
$687$		0			0
$688$			599717.i			1.26698i
$689$	691347.	+	273424.i	1.45632	+	0.575967i
$690$		0			0
$691$	−281346.	−	281346.i	−0.589230	−	0.589230i	0.348193	−	0.937423i	$-0.386795\pi$
$691$	−281346.	−	281346.i	−0.589230	−	0.589230i	−0.937423	+	0.348193i	$0.886795\pi$
$692$	−7329.40			−0.0153058
$693$		0			0
$694$	284764.	+	284764.i	0.591243	+	0.591243i
$695$	−110379.	−	110379.i	−0.228516	−	0.228516i
$696$		0			0
$697$	268530.	−	268530.i	0.552749	−	0.552749i
$698$	101079.			0.207468
$699$		0			0
$700$	844.238	−	844.238i	0.00172293	−	0.00172293i
$701$			212436.i			0.432307i	0.976359	+	0.216154i	$0.0693512\pi$
$701$			212436.i			0.432307i	−0.976359	+	0.216154i	$0.930649\pi$
$702$		0			0
$703$	44091.4			0.0892161
$704$	−229571.	−	229571.i	−0.463204	−	0.463204i
$705$		0			0
$706$			369410.i			0.741138i
$707$	−99019.1	−	99019.1i	−0.198098	−	0.198098i
$708$		0			0
$709$	27433.3	−	27433.3i	0.0545741	−	0.0545741i	−0.679293	−	0.733867i	$-0.737713\pi$
$709$	27433.3	−	27433.3i	0.0545741	−	0.0545741i	0.733867	+	0.679293i	$0.237713\pi$
$710$	72647.8	−	72647.8i	0.144114	−	0.144114i
$711$		0			0
$712$		−	737324.i		−	1.45445i
$713$	−521650.	+	521650.i	−1.02613	+	1.02613i
$714$		0			0
$715$	347222.	+	137324.i	0.679196	+	0.268618i
$716$	22846.1			0.0445641
$717$		0			0
$718$	−974903.			−1.89109
$719$		−	537471.i		−	1.03967i	−0.854265	−	0.519837i	$-0.825993\pi$
$719$		−	537471.i		−	1.03967i	0.854265	−	0.519837i	$-0.174007\pi$
$720$		0			0
$721$	−85655.6	−	85655.6i	−0.164773	−	0.164773i
$722$	−360369.	+	360369.i	−0.691310	+	0.691310i
$723$		0			0
$724$	−1854.00			−0.00353698
$725$			91593.1i			0.174256i
$726$		0			0
$727$		−	330967.i		−	0.626204i	−0.949720	−	0.313102i	$-0.898632\pi$
$727$		−	330967.i		−	0.626204i	0.949720	−	0.313102i	$-0.101368\pi$
$728$	−83557.4	+	211274.i	−0.157660	+	0.398642i
$729$		0			0
$730$	−126335.	−	126335.i	−0.237071	−	0.237071i
$731$	−610526.			−1.14254
$732$		0			0
$733$	−164154.	−	164154.i	−0.305522	−	0.305522i	0.537648	−	0.843170i	$-0.319313\pi$
$733$	−164154.	−	164154.i	−0.305522	−	0.305522i	−0.843170	+	0.537648i	$0.819313\pi$
$734$	−14394.0	−	14394.0i	−0.0267171	−	0.0267171i
$735$		0			0
$736$	42811.0	−	42811.0i	0.0790314	−	0.0790314i
$737$	−202547.			−0.372899
$738$		0			0
$739$	−268903.	+	268903.i	−0.492387	+	0.492387i	−0.909058	−	0.416670i	$-0.863197\pi$
$739$	−268903.	+	268903.i	−0.492387	+	0.492387i	0.416670	+	0.909058i	$0.363197\pi$
$740$			11953.0i			0.0218279i
$741$		0			0
$742$	−388927.			−0.706416
$743$	397022.	+	397022.i	0.719180	+	0.719180i	0.968437	−	0.249258i	$-0.0801866\pi$
$743$	397022.	+	397022.i	0.719180	+	0.719180i	−0.249258	+	0.968437i	$0.580187\pi$
$744$		0			0
$745$		−	847648.i		−	1.52722i
$746$	334590.	+	334590.i	0.601223	+	0.601223i
$747$		0			0
$748$	−12844.7	+	12844.7i	−0.0229573	+	0.0229573i
$749$	147761.	−	147761.i	0.263388	−	0.263388i
$750$		0			0
$751$			100943.i			0.178976i	0.995988	+	0.0894882i	$0.0285231\pi$
$751$			100943.i			0.178976i	−0.995988	+	0.0894882i	$0.971477\pi$
$752$	99151.9	−	99151.9i	0.175334	−	0.175334i
$753$		0			0
$754$	361782.	+	835168.i	0.636361	+	1.46903i
$755$	1.15437e6			2.02512
$756$		0			0
$757$	−418346.			−0.730035			−0.365018	−	0.931001i	$-0.618937\pi$
$757$	−418346.			−0.730035			−0.365018	+	0.931001i	$0.618937\pi$
$758$			460273.i			0.801083i
$759$		0			0
$760$	−89659.4	−	89659.4i	−0.155227	−	0.155227i
$761$	70616.1	−	70616.1i	0.121937	−	0.121937i	−0.643505	−	0.765442i	$-0.722520\pi$
$761$	70616.1	−	70616.1i	0.121937	−	0.121937i	0.765442	+	0.643505i	$0.222520\pi$
$762$		0			0
$763$	499510.			0.858015
$764$			9132.06i			0.0156452i
$765$		0			0
$766$			175588.i			0.299253i
$767$	214134.	−	92759.6i	0.363995	−	0.157677i
$768$		0			0
$769$	−642589.	−	642589.i	−1.08663	−	1.08663i	−0.995873	−	0.0907545i	$-0.971072\pi$
$769$	−642589.	−	642589.i	−1.08663	−	1.08663i	−0.0907545	−	0.995873i	$-0.528928\pi$
$770$	−195335.			−0.329456
$771$		0			0
$772$	29133.9	+	29133.9i	0.0488836	+	0.0488836i
$773$	−152962.	−	152962.i	−0.255990	−	0.255990i	0.567431	−	0.823421i	$-0.307937\pi$
$773$	−152962.	−	152962.i	−0.255990	−	0.255990i	−0.823421	+	0.567431i	$0.807937\pi$
$774$		0			0
$775$	−60978.9	+	60978.9i	−0.101526	+	0.101526i
$776$	−200186.			−0.332438
$777$		0			0
$778$	−393412.	+	393412.i	−0.649963	+	0.649963i
$779$			107428.i			0.177028i
$780$		0			0
$781$	−79733.8			−0.130720
$782$	471503.	+	471503.i	0.771030	+	0.771030i
$783$		0			0
$784$			518878.i			0.844177i
$785$	314387.	+	314387.i	0.510183	+	0.510183i
$786$		0			0
$787$	210034.	−	210034.i	0.339110	−	0.339110i	−0.516922	−	0.856032i	$-0.672922\pi$
$787$	210034.	−	210034.i	0.339110	−	0.339110i	0.856032	+	0.516922i	$0.172922\pi$
$788$	2997.68	−	2997.68i	0.00482762	−	0.00482762i
$789$		0			0
$790$			901420.i			1.44435i
$791$	−293581.	+	293581.i	−0.469219	+	0.469219i
$792$		0			0
$793$	968645.	+	383093.i	1.54035	+	0.609197i
$794$	710510.			1.12701
$795$		0			0
$796$	37806.4			0.0596677
$797$		−	508211.i		−	0.800069i	−0.916500	−	0.400035i	$-0.868998\pi$
$797$		−	508211.i		−	0.800069i	0.916500	−	0.400035i	$-0.131002\pi$
$798$		0			0
$799$	100939.	+	100939.i	0.158112	+	0.158112i
$800$	5004.44	−	5004.44i	0.00781944	−	0.00781944i
$801$		0			0
$802$	765719.			1.19048
$803$			138658.i			0.215037i
$804$		0			0
$805$			339024.i			0.523165i
$806$	−315161.	+	796880.i	−0.485135	+	1.22666i
$807$		0			0
$808$	−286013.	−	286013.i	−0.438090	−	0.438090i
$809$	302513.			0.462218			0.231109	−	0.972928i	$-0.425765\pi$
$809$	302513.			0.462218			0.231109	+	0.972928i	$0.425765\pi$
$810$		0			0
$811$	261828.	+	261828.i	0.398083	+	0.398083i	0.877557	−	0.479473i	$-0.159172\pi$
$811$	261828.	+	261828.i	0.398083	+	0.398083i	−0.479473	+	0.877557i	$0.659172\pi$
$812$	−15918.7	−	15918.7i	−0.0241433	−	0.0241433i
$813$		0			0
$814$	138731.	−	138731.i	0.209376	−	0.209376i
$815$	−861431.			−1.29690
$816$		0			0
$817$	122123.	−	122123.i	0.182959	−	0.182959i
$818$		−	15651.8i		−	0.0233915i
$819$		0			0
$820$	−29123.2			−0.0433123
$821$	141594.	+	141594.i	0.210068	+	0.210068i	0.804296	−	0.594228i	$-0.202542\pi$
$821$	141594.	+	141594.i	0.210068	+	0.210068i	−0.594228	+	0.804296i	$0.702542\pi$
$822$		0			0
$823$		−	1.05798e6i		−	1.56199i	−0.624540	−	0.780993i	$-0.714713\pi$
$823$		−	1.05798e6i		−	1.56199i	0.624540	−	0.780993i	$-0.285287\pi$
$824$	−247413.	−	247413.i	−0.364392	−	0.364392i
$825$		0			0
$826$	−86323.7	+	86323.7i	−0.126523	+	0.126523i
$827$	−95483.6	+	95483.6i	−0.139610	+	0.139610i	−0.773458	−	0.633848i	$-0.781475\pi$
$827$	−95483.6	+	95483.6i	−0.139610	+	0.139610i	0.633848	+	0.773458i	$0.281475\pi$
$828$		0			0
$829$			623513.i			0.907270i	0.891188	+	0.453635i	$0.149873\pi$
$829$			623513.i			0.907270i	−0.891188	+	0.453635i	$0.850127\pi$
$830$	703561.	−	703561.i	1.02128	−	1.02128i
$831$		0			0
$832$	−240726.	+	608671.i	−0.347757	+	0.879298i
$833$	−528231.			−0.761261
$834$		0			0
$835$	619271.			0.888193
$836$		−	5138.64i		−	0.00735251i
$837$		0			0
$838$	−273686.	−	273686.i	−0.389731	−	0.389731i
$839$	666830.	−	666830.i	0.947308	−	0.947308i	−0.0513717	−	0.998680i	$-0.516359\pi$
$839$	666830.	−	666830.i	0.947308	−	0.947308i	0.998680	+	0.0513717i	$0.0163593\pi$
$840$		0			0
$841$	1.01978e6			1.44182
$842$		−	89085.5i		−	0.125656i
$843$		0			0
$844$		−	60084.3i		−	0.0843482i
$845$	−24210.4	−	752395.i	−0.0339070	−	1.05374i
$846$		0			0
$847$	−116153.	−	116153.i	−0.161907	−	0.161907i
$848$	−1.17929e6			−1.63995
$849$		0			0
$850$	55117.0	+	55117.0i	0.0762864	+	0.0762864i
$851$	−240783.	−	240783.i	−0.332481	−	0.332481i
$852$		0			0
$853$	−515777.	+	515777.i	−0.708866	+	0.708866i	−0.966297	−	0.257431i	$-0.917124\pi$
$853$	−515777.	+	515777.i	−0.708866	+	0.708866i	0.257431	+	0.966297i	$0.417124\pi$
$854$	−544925.			−0.747172
$855$		0			0
$856$	426802.	−	426802.i	0.582478	−	0.582478i
$857$		−	489846.i		−	0.666957i	−0.942758	−	0.333479i	$-0.891778\pi$
$857$		−	489846.i		−	0.666957i	0.942758	−	0.333479i	$-0.108222\pi$
$858$		0			0
$859$	1.37694e6			1.86607			0.933037	−	0.359780i	$-0.117148\pi$
$859$	1.37694e6			1.86607			0.933037	+	0.359780i	$0.117148\pi$
$860$	33107.0	+	33107.0i	0.0447634	+	0.0447634i
$861$		0			0
$862$		−	243649.i		−	0.327907i
$863$	715898.	+	715898.i	0.961235	+	0.961235i	0.999276	−	0.0380415i	$-0.0121119\pi$
$863$	715898.	+	715898.i	0.961235	+	0.961235i	−0.0380415	+	0.999276i	$0.512112\pi$
$864$		0			0
$865$	172030.	−	172030.i	0.229918	−	0.229918i
$866$	−85139.8	+	85139.8i	−0.113526	+	0.113526i
$867$		0			0
$868$		−	21196.1i		−	0.0281330i
$869$	494672.	−	494672.i	0.655055	−	0.655055i
$870$		0			0
$871$	162316.	+	374705.i	0.213957	+	0.493916i
$872$	1.44282e6			1.89748
$873$		0			0
$874$	−188629.			−0.246937
$875$		−	315756.i		−	0.412417i
$876$		0			0
$877$	−123217.	−	123217.i	−0.160203	−	0.160203i	0.622454	−	0.782657i	$-0.286136\pi$
$877$	−123217.	−	123217.i	−0.160203	−	0.160203i	−0.782657	+	0.622454i	$0.786136\pi$
$878$	−1.02774e6	+	1.02774e6i	−1.33320	+	1.33320i
$879$		0			0
$880$	−592288.			−0.764834
$881$			863892.i			1.11303i	0.830837	+	0.556516i	$0.187862\pi$
$881$			863892.i			1.11303i	−0.830837	+	0.556516i	$0.812138\pi$
$882$		0			0
$883$		−	268829.i		−	0.344790i	−0.985028	−	0.172395i	$-0.944850\pi$
$883$		−	268829.i		−	0.344790i	0.985028	−	0.172395i	$-0.0551505\pi$
$884$	34055.7	+	13468.8i	0.0435797	+	0.0172355i
$885$		0			0
$886$	−65280.2	−	65280.2i	−0.0831599	−	0.0831599i
$887$	−1.04691e6			−1.33065			−0.665323	−	0.746556i	$-0.731706\pi$
$887$	−1.04691e6			−1.33065			−0.665323	+	0.746556i	$0.731706\pi$
$888$		0			0
$889$	−401768.	−	401768.i	−0.508361	−	0.508361i
$890$	−903706.	−	903706.i	−1.14090	−	1.14090i
$891$		0			0
$892$	756.886	−	756.886i	0.000951263	−	0.000951263i
$893$	−40381.5			−0.0506384
$894$		0			0
$895$	−536226.	+	536226.i	−0.669425	+	0.669425i
$896$		−	377468.i		−	0.470180i
$897$		0			0
$898$	−308691.			−0.382800
$899$	1.14980e6	+	1.14980e6i	1.42267	+	1.42267i
$900$		0			0
$901$		−	1.20055e6i		−	1.47887i
$902$	338016.	+	338016.i	0.415456	+	0.415456i
$903$		0			0
$904$	−847999.	+	847999.i	−1.03767	+	1.03767i
$905$	43515.7	−	43515.7i	0.0531311	−	0.0531311i
$906$		0			0
$907$		−	293077.i		−	0.356260i	−0.984007	−	0.178130i	$-0.942995\pi$
$907$		−	293077.i		−	0.356260i	0.984007	−	0.178130i	$-0.0570047\pi$
$908$	4851.68	−	4851.68i	0.00588464	−	0.00588464i
$909$		0			0
$910$	156536.	+	361362.i	0.189031	+	0.436374i
$911$	1.22775e6			1.47936			0.739681	−	0.672958i	$-0.234976\pi$
$911$	1.22775e6			1.47936			0.739681	+	0.672958i	$0.234976\pi$
$912$		0			0
$913$	−772185.			−0.926361
$914$		−	544974.i		−	0.652354i
$915$		0			0
$916$	7604.58	+	7604.58i	0.00906326	+	0.00906326i
$917$	−47204.8	+	47204.8i	−0.0561368	+	0.0561368i
$918$		0			0
$919$	−952406.			−1.12769			−0.563847	−	0.825879i	$-0.690679\pi$
$919$	−952406.			−1.12769			−0.563847	+	0.825879i	$0.690679\pi$
$920$			979259.i			1.15697i
$921$		0			0
$922$		−	1.27948e6i		−	1.50513i
$923$	63896.6	+	147504.i	0.0750023	+	0.173142i
$924$		0			0
$925$	−28146.6	−	28146.6i	−0.0328960	−	0.0328960i
$926$	860015.			1.00296
$927$		0			0
$928$	−94362.5	−	94362.5i	−0.109573	−	0.109573i
$929$	−865268.	−	865268.i	−1.00258	−	1.00258i	−0.999997	−	0.00258353i	$-0.999178\pi$
$929$	−865268.	−	865268.i	−1.00258	−	1.00258i	−0.00258353	−	0.999997i	$-0.500822\pi$
$930$		0			0
$931$	105662.	−	105662.i	0.121904	−	0.121904i
$932$	−57807.8			−0.0665511
$933$		0			0
$934$	259629.	−	259629.i	0.297619	−	0.297619i
$935$		−	602963.i		−	0.689712i
$936$		0			0
$937$	−829106.			−0.944345			−0.472173	−	0.881506i	$-0.656530\pi$
$937$	−829106.			−0.944345			−0.472173	+	0.881506i	$0.656530\pi$
$938$	−151054.	−	151054.i	−0.171683	−	0.171683i
$939$		0			0
$940$		−	10947.2i		−	0.0123894i
$941$	−1.18512e6	−	1.18512e6i	−1.33839	−	1.33839i	−0.897618	−	0.440774i	$-0.854704\pi$
$941$	−1.18512e6	−	1.18512e6i	−1.33839	−	1.33839i	−0.440774	−	0.897618i	$-0.645296\pi$
$942$		0			0
$943$	586664.	−	586664.i	0.659729	−	0.659729i
$944$	−261748.	+	261748.i	−0.293724	+	0.293724i
$945$		0			0
$946$		−	768509.i		−	0.858750i
$947$	−94860.4	+	94860.4i	−0.105775	+	0.105775i	−0.758014	−	0.652238i	$-0.773830\pi$
$947$	−94860.4	+	94860.4i	−0.105775	+	0.105775i	0.652238	+	0.758014i	$0.273830\pi$
$948$		0			0
$949$	256512.	−	111117.i	0.284823	−	0.123381i
$950$	−22050.0			−0.0244322
$951$		0			0
$952$	366884.			0.404813
$953$		−	313080.i		−	0.344723i	−0.985034	−	0.172361i	$-0.944860\pi$
$953$		−	313080.i		−	0.344723i	0.985034	−	0.172361i	$-0.0551397\pi$
$954$		0			0
$955$	−214341.	−	214341.i	−0.235016	−	0.235016i
$956$	57682.4	−	57682.4i	0.0631142	−	0.0631142i
$957$		0			0
$958$	1.68358e6			1.83444
$959$			318947.i			0.346802i
$960$		0			0
$961$			607464.i			0.657770i
$962$	−367824.	−	145472.i	−0.397456	−	0.157192i
$963$		0			0
$964$	51075.1	+	51075.1i	0.0549610	+	0.0549610i
$965$	−1.36762e6			−1.46862
$966$		0			0
$967$	359201.	+	359201.i	0.384136	+	0.384136i	0.872590	−	0.488454i	$-0.162439\pi$
$967$	359201.	+	359201.i	0.384136	+	0.384136i	−0.488454	+	0.872590i	$0.662439\pi$
$968$	−335504.	−	335504.i	−0.358053	−	0.358053i
$969$		0			0
$970$	−245359.	+	245359.i	−0.260771	+	0.260771i
$971$	1.68455e6			1.78668			0.893338	−	0.449385i	$-0.148357\pi$
$971$	1.68455e6			1.78668			0.893338	+	0.449385i	$0.148357\pi$
$972$		0			0
$973$	−90346.8	+	90346.8i	−0.0954305	+	0.0954305i
$974$		−	1.08228e6i		−	1.14083i
$975$		0			0
$976$	−1.65230e6			−1.73456
$977$	−857213.	−	857213.i	−0.898048	−	0.898048i	0.0972150	−	0.995263i	$-0.469007\pi$
$977$	−857213.	−	857213.i	−0.898048	−	0.898048i	−0.995263	+	0.0972150i	$0.969007\pi$
$978$		0			0
$979$			991852.i			1.03486i
$980$	28644.4	+	28644.4i	0.0298254	+	0.0298254i
$981$		0			0
$982$	76718.1	−	76718.1i	0.0795564	−	0.0795564i
$983$	−821373.	+	821373.i	−0.850029	+	0.850029i	−0.990136	−	0.140107i	$-0.955255\pi$
$983$	−821373.	+	821373.i	−0.850029	+	0.850029i	0.140107	+	0.990136i	$0.455255\pi$
$984$		0			0
$985$			140719.i			0.145037i
$986$	1.03927e6	−	1.03927e6i	1.06899	−	1.06899i
$987$		0			0
$988$	−9506.29	+	4117.98i	−0.00973861	+	0.00421861i
$989$	−1.33383e6			−1.36366
$990$		0			0
$991$	−1.01521e6			−1.03374			−0.516868	−	0.856065i	$-0.672902\pi$
$991$	−1.01521e6			−1.03374			−0.516868	+	0.856065i	$0.672902\pi$
$992$		−	125645.i		−	0.127680i
$993$		0			0
$994$	−59463.3	−	59463.3i	−0.0601834	−	0.0601834i
$995$	−887364.	+	887364.i	−0.896305	+	0.896305i
$996$		0			0
$997$	590999.			0.594561			0.297280	−	0.954790i	$-0.403920\pi$
$997$	590999.			0.594561			0.297280	+	0.954790i	$0.403920\pi$
$998$		−	421352.i		−	0.423043i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.5.j.b.73.3		20
3.2	odd	2		39.5.g.a.34.8	yes	20
13.5	odd	4	inner	117.5.j.b.109.3		20
39.5	even	4		39.5.g.a.31.8	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.5.g.a.31.8	✓	20	39.5	even	4
39.5.g.a.34.8	yes	20	3.2	odd	2
117.5.j.b.73.3		20	1.1	even	1	trivial
117.5.j.b.109.3		20	13.5	odd	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	117.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.89776 - 2.89776i) q^{2} +0.794047i q^{4} +(-18.6373 - 18.6373i) q^{5} +(-15.2549 + 15.2549i) q^{7} +(-44.0632 + 44.0632i) q^{8} +108.013i q^{10} +(59.2741 - 59.2741i) q^{11} +(-157.156 - 62.1541i) q^{13} +88.4101 q^{14} +268.074 q^{16} +272.906i q^{17} +(-54.5892 - 54.5892i) q^{19} +(14.7989 - 14.7989i) q^{20} -343.524 q^{22} +596.223i q^{23} +69.6962i q^{25} +(275.292 + 635.507i) q^{26} +(-12.1131 - 12.1131i) q^{28} +1314.18 q^{29} +(874.924 + 874.924i) q^{31} +(-71.8036 - 71.8036i) q^{32} +(790.817 - 790.817i) q^{34} +568.619 q^{35} +(-403.847 + 403.847i) q^{37} +316.373i q^{38} +1642.44 q^{40} +(-983.966 - 983.966i) q^{41} +2237.13i q^{43} +(47.0664 + 47.0664i) q^{44} +(1727.71 - 1727.71i) q^{46} +(369.867 - 369.867i) q^{47} +1935.58i q^{49} +(201.963 - 201.963i) q^{50} +(49.3532 - 124.789i) q^{52} -4399.13 q^{53} -2209.42 q^{55} -1344.36i q^{56} +(-3808.17 - 3808.17i) q^{58} +(-976.401 + 976.401i) q^{59} -6163.60 q^{61} -5070.64i q^{62} -3873.05i q^{64} +(1770.57 + 4087.33i) q^{65} +(-1708.57 - 1708.57i) q^{67} -216.700 q^{68} +(-1647.72 - 1647.72i) q^{70} +(-672.586 - 672.586i) q^{71} +(-1169.63 + 1169.63i) q^{73} +2340.51 q^{74} +(43.3464 - 43.3464i) q^{76} +1808.44i q^{77} +8345.50 q^{79} +(-4996.17 - 4996.17i) q^{80} +5702.60i q^{82} +(-6513.68 - 6513.68i) q^{83} +(5086.23 - 5086.23i) q^{85} +(6482.67 - 6482.67i) q^{86} +5223.62i q^{88} +(-8366.65 + 8366.65i) q^{89} +(3345.55 - 1449.24i) q^{91} -473.429 q^{92} -2143.57 q^{94} +2034.79i q^{95} +(2271.58 + 2271.58i) q^{97} +(5608.84 - 5608.84i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 24 q^{5} - 24 q^{7} - 372 q^{11} - 224 q^{13} - 480 q^{14} - 2328 q^{16} - 840 q^{19} - 228 q^{20} + 3536 q^{22} + 828 q^{26} - 1984 q^{28} + 5064 q^{29} + 1712 q^{31} + 7260 q^{32} + 8040 q^{34}+ \cdots - 11544 q^{98}+O(q^{100}) \) 20 * q - 24 * q^5 - 24 * q^7 - 372 * q^11 - 224 * q^13 - 480 * q^14 - 2328 * q^16 - 840 * q^19 - 228 * q^20 + 3536 * q^22 + 828 * q^26 - 1984 * q^28 + 5064 * q^29 + 1712 * q^31 + 7260 * q^32 + 8040 * q^34 - 5976 * q^35 - 868 * q^37 + 6336 * q^40 + 6000 * q^41 - 20868 * q^44 - 1992 * q^46 - 1692 * q^47 - 8952 * q^50 - 12416 * q^52 + 18816 * q^53 - 3280 * q^55 + 1256 * q^58 + 6588 * q^59 - 5512 * q^61 - 33048 * q^65 - 4704 * q^67 + 28296 * q^68 - 31096 * q^70 - 9756 * q^71 + 13692 * q^73 + 28296 * q^74 - 17072 * q^76 - 5056 * q^79 - 42228 * q^80 - 24708 * q^83 - 4752 * q^85 + 77424 * q^86 - 36000 * q^89 + 19104 * q^91 - 12912 * q^92 + 112832 * q^94 + 50012 * q^97 - 11544 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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