LMFDB - Embedded newform 245.4.j.f.214.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(79,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("245.79");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.j (of order $6$, degree $2$, not 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:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
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} - 55 x^{18} + 2042 x^{16} - 41247 x^{14} + 600234 x^{12} - 4812047 x^{10} + 27547801 x^{8} + \cdots + 12960000 $ x^20 - 55x^18 + 2042x^16 - 41247x^14 + 600234x^12 - 4812047x^10 + 27547801x^8 - 79828440x^6 + 160801200x^4 - 48816000*x^2 + 12960000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2}\cdot 7^{8} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			214.1
Root			$-3.73574 - 2.15683i$ of defining polynomial
Character	$\chi$	$=$	245.214
Dual form			245.4.j.f.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.60176 + 2.65683i) q^{2} +(1.67956 + 0.969693i) q^{3} +(10.1175 - 17.5240i) q^{4} +(8.30643 - 7.48353i) q^{5} -10.3052 q^{6} +65.0123i q^{8} +(-11.6194 - 20.1254i) q^{9} +(-18.3418 + 56.5062i) q^{10} +(-12.7710 + 22.1200i) q^{11} +(33.9858 - 19.6217i) q^{12} +64.1014i q^{13} +(21.2079 - 4.51433i) q^{15} +(-91.7868 - 158.979i) q^{16} +(23.9847 + 13.8476i) q^{17} +(106.939 + 61.7415i) q^{18} +(-0.396218 - 0.686270i) q^{19} +(-47.1011 - 221.276i) q^{20} -135.721i q^{22} +(94.0560 - 54.3032i) q^{23} +(-63.0420 + 109.192i) q^{24} +(12.9936 - 124.323i) q^{25} +(-170.307 - 294.980i) q^{26} -97.4324i q^{27} +234.000 q^{29} +(-85.5997 + 77.1195i) q^{30} +(64.6019 - 111.894i) q^{31} +(394.343 + 227.674i) q^{32} +(-42.8992 + 24.7679i) q^{33} -147.163 q^{34} -470.236 q^{36} +(-33.1781 + 19.1554i) q^{37} +(3.64660 + 2.10537i) q^{38} +(-62.1587 + 107.662i) q^{39} +(486.522 + 540.021i) q^{40} +403.216 q^{41} +172.895i q^{43} +(258.420 + 447.597i) q^{44} +(-247.124 - 80.2160i) q^{45} +(-288.549 + 499.781i) q^{46} +(179.218 - 103.471i) q^{47} -356.020i q^{48} +(270.511 + 606.626i) q^{50} +(26.8558 + 46.5157i) q^{51} +(1123.31 + 648.545i) q^{52} +(-124.735 - 72.0155i) q^{53} +(258.861 + 448.361i) q^{54} +(59.4542 + 279.310i) q^{55} -1.53684i q^{57} +(-1076.81 + 621.699i) q^{58} +(339.543 - 588.105i) q^{59} +(135.461 - 417.320i) q^{60} +(-287.358 - 497.719i) q^{61} +686.544i q^{62} -950.977 q^{64} +(479.705 + 532.454i) q^{65} +(131.608 - 227.952i) q^{66} +(446.557 + 257.820i) q^{67} +(485.330 - 280.205i) q^{68} +210.630 q^{69} +556.612 q^{71} +(1308.40 - 755.404i) q^{72} +(-150.033 - 86.6217i) q^{73} +(101.785 - 176.297i) q^{74} +(142.379 - 196.207i) q^{75} -16.0349 q^{76} -660.580i q^{78} +(39.6645 + 68.7010i) q^{79} +(-1952.15 - 633.663i) q^{80} +(-219.244 + 379.742i) q^{81} +(-1855.50 + 1071.28i) q^{82} -1043.56i q^{83} +(302.856 - 64.4663i) q^{85} +(-459.352 - 795.620i) q^{86} +(393.017 + 226.909i) q^{87} +(-1438.07 - 830.271i) q^{88} +(-326.030 - 564.700i) q^{89} +(1350.33 - 287.432i) q^{90} -2197.65i q^{92} +(217.005 - 125.288i) q^{93} +(-549.812 + 952.302i) q^{94} +(-8.42688 - 2.73534i) q^{95} +(441.548 + 764.784i) q^{96} +515.714i q^{97} +593.564 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 36 q^{4} + 6 q^{5} - 24 q^{6} + 46 q^{9} - 16 q^{10} - 84 q^{11} + 16 q^{15} - 148 q^{16} + 72 q^{19} + 136 q^{20} + 72 q^{24} + 362 q^{25} - 620 q^{26} + 176 q^{29} - 52 q^{30} + 120 q^{31} - 1928 q^{34}+ \cdots - 10608 q^{99}+O(q^{100}) $ 20 * q + 36 * q^4 + 6 * q^5 - 24 * q^6 + 46 * q^9 - 16 * q^10 - 84 * q^11 + 16 * q^15 - 148 * q^16 + 72 * q^19 + 136 * q^20 + 72 * q^24 + 362 * q^25 - 620 * q^26 + 176 * q^29 - 52 * q^30 + 120 * q^31 - 1928 * q^34 - 840 * q^36 - 212 * q^39 + 1396 * q^40 + 1704 * q^41 + 1424 * q^44 - 510 * q^45 - 176 * q^46 + 3288 * q^50 - 1276 * q^51 - 996 * q^54 + 2272 * q^55 + 864 * q^59 + 1692 * q^60 - 884 * q^61 - 5448 * q^64 - 520 * q^65 + 1148 * q^66 - 9616 * q^69 + 1760 * q^71 - 3024 * q^74 + 720 * q^75 + 5344 * q^76 + 3580 * q^79 - 2316 * q^80 + 302 * q^81 + 3144 * q^85 - 2432 * q^86 - 1492 * q^89 + 15496 * q^90 + 1652 * q^94 + 1628 * q^95 + 4080 * q^96 - 10608 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−4.60176	+	2.65683i	−1.62697	+	0.939331i	−0.641978	+	0.766723i	$0.721886\pi$
$2$	−4.60176	+	2.65683i	−1.62697	+	0.939331i	−0.984991	+	0.172608i	$0.944781\pi$
$3$	1.67956	+	0.969693i	0.323231	+	0.186617i	0.652832	−	0.757503i	$-0.273581\pi$
$3$	1.67956	+	0.969693i	0.323231	+	0.186617i	−0.329601	+	0.944120i	$0.606914\pi$
$4$	10.1175	−	17.5240i	1.26468	−	2.19050i
$5$	8.30643	−	7.48353i	0.742950	−	0.669347i
$5$	8.30643	−	7.48353i	0.742950	−	0.669347i
$6$	−10.3052			−0.701182
$7$		0			0
$7$		0			0
$8$			65.0123i			2.87317i
$9$	−11.6194	−	20.1254i	−0.430348	−	0.745384i
$10$	−18.3418	+	56.5062i	−0.580018	+	1.78688i
$11$	−12.7710	+	22.1200i	−0.350054	+	0.606311i	−0.986259	−	0.165209i	$-0.947170\pi$
$11$	−12.7710	+	22.1200i	−0.350054	+	0.606311i	0.636205	+	0.771520i	$0.280503\pi$
$12$	33.9858	−	19.6217i	0.817570	−	0.472024i
$13$			64.1014i			1.36758i	0.729679	+	0.683790i	$0.239670\pi$
$13$			64.1014i			1.36758i	−0.729679	+	0.683790i	$0.760330\pi$
$14$		0			0
$15$	21.2079	−	4.51433i	0.365056	−	0.0777063i
$16$	−91.7868	−	158.979i	−1.43417	−	2.48405i
$17$	23.9847	+	13.8476i	0.342185	+	0.197561i	0.661238	−	0.750176i	$-0.270031\pi$
$17$	23.9847	+	13.8476i	0.342185	+	0.197561i	−0.319053	+	0.947737i	$0.603365\pi$
$18$	106.939	+	61.7415i	1.40032	+	0.808478i
$19$	−0.396218	−	0.686270i	−0.00478414	−	0.00828637i	0.863623	−	0.504137i	$-0.168190\pi$
$19$	−0.396218	−	0.686270i	−0.00478414	−	0.00828637i	−0.868408	+	0.495851i	$0.834856\pi$
$20$	−47.1011	−	221.276i	−0.526606	−	2.47394i
$21$		0			0
$22$		−	135.721i		−	1.31527i
$23$	94.0560	−	54.3032i	0.852697	−	0.492305i	−0.00886320	−	0.999961i	$-0.502821\pi$
$23$	94.0560	−	54.3032i	0.852697	−	0.492305i	0.861560	+	0.507656i	$0.169488\pi$
$24$	−63.0420	+	109.192i	−0.536183	+	0.928696i
$25$	12.9936	−	124.323i	0.103949	−	0.994583i
$26$	−170.307	−	294.980i	−1.28461	−	2.22501i
$27$		−	97.4324i		−	0.694477i
$28$		0			0
$29$	234.000			1.49837			0.749186	−	0.662360i	$-0.230445\pi$
$29$	234.000			1.49837			0.749186	+	0.662360i	$0.230445\pi$
$30$	−85.5997	+	77.1195i	−0.520943	+	0.469334i
$31$	64.6019	−	111.894i	0.374285	−	0.648281i	−0.615935	−	0.787797i	$-0.711221\pi$
$31$	64.6019	−	111.894i	0.374285	−	0.648281i	0.990220	+	0.139516i	$0.0445548\pi$
$32$	394.343	+	227.674i	2.17846	+	1.25773i
$33$	−42.8992	+	24.7679i	−0.226297	+	0.130652i
$34$	−147.163			−0.742300
$35$		0			0
$36$	−470.236			−2.17702
$37$	−33.1781	+	19.1554i	−0.147418	+	0.0851116i	−0.571895	−	0.820327i	$-0.693791\pi$
$37$	−33.1781	+	19.1554i	−0.147418	+	0.0851116i	0.424477	+	0.905439i	$0.360458\pi$
$38$	3.64660	+	2.10537i	0.0155673	+	0.00898778i
$39$	−62.1587	+	107.662i	−0.255214	+	0.442044i
$40$	486.522	+	540.021i	1.92315	+	2.13462i
$41$	403.216			1.53590			0.767949	−	0.640511i	$-0.221278\pi$
$41$	403.216			1.53590			0.767949	+	0.640511i	$0.221278\pi$
$42$		0			0
$43$			172.895i			0.613167i	0.951844	+	0.306584i	$0.0991859\pi$
$43$			172.895i			0.613167i	−0.951844	+	0.306584i	$0.900814\pi$
$44$	258.420	+	447.597i	0.885416	+	1.53359i
$45$	−247.124	−	80.2160i	−0.818648	−	0.265731i
$46$	−288.549	+	499.781i	−0.924874	+	1.60193i
$47$	179.218	−	103.471i	0.556205	−	0.321125i	−0.195416	−	0.980720i	$-0.562606\pi$
$47$	179.218	−	103.471i	0.556205	−	0.321125i	0.751621	+	0.659596i	$0.229272\pi$
$48$		−	356.020i		−	1.07056i
$49$		0			0
$50$	270.511	+	606.626i	0.765120	+	1.71580i
$51$	26.8558	+	46.5157i	0.0737366	+	0.127716i
$52$	1123.31	+	648.545i	2.99568	+	1.72956i
$53$	−124.735	−	72.0155i	−0.323276	−	0.186643i	0.329576	−	0.944129i	$-0.393094\pi$
$53$	−124.735	−	72.0155i	−0.323276	−	0.186643i	−0.652852	+	0.757486i	$0.726428\pi$
$54$	258.861	+	448.361i	0.652343	+	1.12989i
$55$	59.4542	+	279.310i	0.145760	+	0.684767i
$56$		0			0
$57$		−	1.53684i		−	0.00357122i
$58$	−1076.81	+	621.699i	−2.43780	+	1.40747i
$59$	339.543	−	588.105i	0.749232	−	1.29771i	−0.198959	−	0.980008i	$-0.563756\pi$
$59$	339.543	−	588.105i	0.749232	−	1.29771i	0.948191	−	0.317701i	$-0.102911\pi$
$60$	135.461	−	417.320i	0.291466	−	0.897929i
$61$	−287.358	−	497.719i	−0.603155	−	1.04470i	−0.992340	−	0.123536i	$-0.960577\pi$
$61$	−287.358	−	497.719i	−0.603155	−	1.04470i	0.389185	−	0.921160i	$-0.372757\pi$
$62$			686.544i			1.40631i
$63$		0			0
$64$	−950.977			−1.85738
$65$	479.705	+	532.454i	0.915386	+	1.01604i
$66$	131.608	−	227.952i	0.245452	−	0.425135i
$67$	446.557	+	257.820i	0.814263	+	0.470115i	0.848434	−	0.529301i	$-0.177546\pi$
$67$	446.557	+	257.820i	0.814263	+	0.470115i	−0.0341709	+	0.999416i	$0.510879\pi$
$68$	485.330	−	280.205i	0.865513	−	0.499704i
$69$	210.630			0.367491
$70$		0			0
$71$	556.612			0.930391			0.465195	−	0.885208i	$-0.345984\pi$
$71$	556.612			0.930391			0.465195	+	0.885208i	$0.345984\pi$
$72$	1308.40	−	755.404i	2.14161	−	1.23646i
$73$	−150.033	−	86.6217i	−0.240549	−	0.138881i	0.374880	−	0.927073i	$-0.377684\pi$
$73$	−150.033	−	86.6217i	−0.240549	−	0.138881i	−0.615429	+	0.788192i	$0.711017\pi$
$74$	101.785	−	176.297i	0.159896	−	0.276948i
$75$	142.379	−	196.207i	0.219206	−	0.302081i
$76$	−16.0349			−0.0242017
$77$		0			0
$78$		−	660.580i		−	0.958923i
$79$	39.6645	+	68.7010i	0.0564887	+	0.0978413i	0.892887	−	0.450281i	$-0.148676\pi$
$79$	39.6645	+	68.7010i	0.0564887	+	0.0978413i	−0.836398	+	0.548122i	$0.815343\pi$
$80$	−1952.15	−	633.663i	−2.72821	−	0.885570i
$81$	−219.244	+	379.742i	−0.300746	+	0.520908i
$82$	−1855.50	+	1071.28i	−2.49886	+	1.44272i
$83$		−	1043.56i		−	1.38007i	−0.723777	−	0.690034i	$-0.757596\pi$
$83$		−	1043.56i		−	1.38007i	0.723777	−	0.690034i	$-0.242404\pi$
$84$		0			0
$85$	302.856	−	64.4663i	0.386463	−	0.0822630i
$86$	−459.352	−	795.620i	−0.575967	−	0.997604i
$87$	393.017	+	226.909i	0.484320	+	0.279622i
$88$	−1438.07	−	830.271i	−1.74203	−	1.00576i
$89$	−326.030	−	564.700i	−0.388304	−	0.672563i	0.603917	−	0.797047i	$-0.293606\pi$
$89$	−326.030	−	564.700i	−0.388304	−	0.672563i	−0.992222	+	0.124484i	$0.960272\pi$
$90$	1350.33	−	287.432i	1.58152	−	0.336645i
$91$		0			0
$92$		−	2197.65i		−	2.49044i
$93$	217.005	−	125.288i	0.241961	−	0.139696i
$94$	−549.812	+	952.302i	−0.603285	+	1.04492i
$95$	−8.42688	−	2.73534i	−0.00910083	−	0.00295411i
$96$	441.548	+	764.784i	0.469431	+	0.813078i
$97$			515.714i			0.539823i	0.962885	+	0.269912i	$0.0869945\pi$
$97$			515.714i			0.539823i	−0.962885	+	0.269912i	$0.913005\pi$
$98$		0			0
$99$	593.564			0.602580
$100$	−2047.17	−	1485.53i	−2.04717	−	1.48553i
$101$	−268.170	+	464.484i	−0.264197	+	0.457602i	−0.967353	−	0.253433i	$-0.918440\pi$
$101$	−268.170	+	464.484i	−0.264197	+	0.457602i	0.703156	+	0.711036i	$0.251774\pi$
$102$	−247.168	−	142.703i	−0.239934	−	0.138526i
$103$	−330.556	+	190.846i	−0.316220	+	0.182570i	−0.649706	−	0.760185i	$-0.725108\pi$
$103$	−330.556	+	190.846i	−0.316220	+	0.182570i	0.333487	+	0.942755i	$0.391775\pi$
$104$	−4167.38			−3.92928
$105$		0			0
$106$	765.332			0.701279
$107$	1196.08	−	690.560i	1.08065	−	0.623915i	0.149580	−	0.988750i	$-0.452208\pi$
$107$	1196.08	−	690.560i	1.08065	−	0.623915i	0.931072	+	0.364835i	$0.118874\pi$
$108$	−1707.40	−	985.770i	−1.52125	−	0.878294i
$109$	−195.291	+	338.254i	−0.171610	+	0.297237i	−0.938983	−	0.343964i	$-0.888230\pi$
$109$	−195.291	+	338.254i	−0.171610	+	0.297237i	0.767373	+	0.641201i	$0.221564\pi$
$110$	−1015.67	−	1127.36i	−0.880369	−	0.977177i
$111$	−74.2995			−0.0635333
$112$		0			0
$113$			1643.15i			1.36792i	0.729521	+	0.683958i	$0.239743\pi$
$113$			1643.15i			1.36792i	−0.729521	+	0.683958i	$0.760257\pi$
$114$	4.08312	+	7.07217i	0.00335455	+	0.00581026i
$115$	374.890	−	1154.94i	0.303988	−	0.936508i
$116$	2367.49	−	4100.62i	1.89497	−	3.28218i
$117$	1290.07	−	744.820i	1.01937	−	0.588535i
$118$			3608.43i			2.81511i
$119$		0			0
$120$	293.487	+	1378.77i	0.223263	+	1.04887i
$121$	339.304	+	587.692i	0.254924	+	0.441542i
$122$	2644.71	+	1526.92i	1.96263	+	1.13312i
$123$	677.225	+	390.996i	0.496450	+	0.286625i
$124$	−1307.22	−	2264.16i	−0.946705	−	1.63974i
$125$	−822.443	−	1129.92i	−0.588492	−	0.808503i
$126$		0			0
$127$			192.032i			0.134174i	0.997747	+	0.0670869i	$0.0213705\pi$
$127$			192.032i			0.134174i	−0.997747	+	0.0670869i	$0.978630\pi$
$128$	1221.42	−	705.189i	0.843434	−	0.486957i
$129$	−167.655	+	290.387i	−0.114428	+	0.198195i
$130$	−3622.13	−	1175.73i	−2.44370	−	0.793221i
$131$	1041.45	+	1803.84i	0.694594	+	1.20307i	0.970317	+	0.241835i	$0.0777493\pi$
$131$	1041.45	+	1803.84i	0.694594	+	1.20307i	−0.275723	+	0.961237i	$0.588917\pi$
$132$			1002.35i			0.660936i
$133$		0			0
$134$	−2739.93			−1.76637
$135$	−729.138	−	809.316i	−0.464846	−	0.515961i
$136$	−900.264	+	1559.30i	−0.567625	+	0.983156i
$137$	−67.6980	−	39.0855i	−0.0422177	−	0.0243744i	0.478743	−	0.877955i	$-0.341093\pi$
$137$	−67.6980	−	39.0855i	−0.0422177	−	0.0243744i	−0.520960	+	0.853581i	$0.674426\pi$
$138$	−969.268	+	559.607i	−0.597896	+	0.345195i
$139$	1393.67			0.850426			0.425213	−	0.905093i	$-0.360199\pi$
$139$	1393.67			0.850426			0.425213	+	0.905093i	$0.360199\pi$
$140$		0			0
$141$	401.342			0.239710
$142$	−2561.40	+	1478.82i	−1.51372	+	0.873945i
$143$	−1417.92	−	818.638i	−0.829179	−	0.478727i
$144$	−2133.01	+	3694.49i	−1.23438	+	2.13801i
$145$	1943.71	−	1751.15i	1.11322	−	1.00293i
$146$	920.556			0.521820
$147$		0			0
$148$			775.217i			0.430557i
$149$	16.2501	+	28.1460i	0.00893463	+	0.0154752i	0.870458	−	0.492242i	$-0.163823\pi$
$149$	16.2501	+	28.1460i	0.00893463	+	0.0154752i	−0.861524	+	0.507718i	$0.830489\pi$
$150$	−133.902	+	1281.18i	−0.0728872	+	0.697384i
$151$	−233.381	+	404.228i	−0.125777	+	0.217852i	−0.922036	−	0.387103i	$-0.873476\pi$
$151$	−233.381	+	404.228i	−0.125777	+	0.217852i	0.796260	+	0.604955i	$0.206809\pi$
$152$	44.6160	−	25.7591i	0.0238081	−	0.0137456i
$153$		−	643.602i		−	0.340080i
$154$		0			0
$155$	−300.749	−	1412.89i	−0.155850	−	0.732167i
$156$	1257.78	+	2178.54i	0.645531	+	1.11809i
$157$	−1449.30	−	836.751i	−0.736729	−	0.425351i	0.0841500	−	0.996453i	$-0.473183\pi$
$157$	−1449.30	−	836.751i	−0.736729	−	0.425351i	−0.820879	+	0.571103i	$0.806516\pi$
$158$	−365.053	−	210.764i	−0.183811	−	0.106123i
$159$	−139.666	−	241.908i	−0.0696618	−	0.120658i
$160$	4979.39	−	1059.92i	2.46035	−	0.523712i
$161$		0			0
$162$		−	2329.98i		−	1.13000i
$163$	1618.91	−	934.679i	0.777932	−	0.449139i	−0.0577648	−	0.998330i	$-0.518397\pi$
$163$	1618.91	−	934.679i	0.777932	−	0.449139i	0.835697	+	0.549191i	$0.185064\pi$
$164$	4079.53	−	7065.95i	1.94243	−	3.36438i
$165$	−170.988	+	526.770i	−0.0806752	+	0.248539i
$166$	2772.56	+	4802.22i	1.29634	+	2.24533i
$167$			46.5250i			0.0215581i	0.999942	+	0.0107791i	$0.00343115\pi$
$167$			46.5250i			0.0215581i	−0.999942	+	0.0107791i	$0.996569\pi$
$168$		0			0
$169$	−1911.99			−0.870275
$170$	−1222.40	+	1101.30i	−0.551492	+	0.496856i
$171$	−9.20762	+	15.9481i	−0.00411769	+	0.00713204i
$172$	3029.80	+	1749.26i	1.34314	+	0.775463i
$173$	−2161.84	+	1248.14i	−0.950066	+	0.548521i	−0.893102	−	0.449855i	$-0.851476\pi$
$173$	−2161.84	+	1248.14i	−0.950066	+	0.548521i	−0.0569648	+	0.998376i	$0.518142\pi$
$174$	−2411.43			−1.05063
$175$		0			0
$176$	4688.83			2.00815
$177$	1140.56	−	658.504i	0.484350	−	0.279640i
$178$	3000.62	+	1732.41i	1.26352	+	0.729492i
$179$	1487.85	−	2577.03i	0.621269	−	1.07607i	−0.367981	−	0.929833i	$-0.619951\pi$
$179$	1487.85	−	2577.03i	0.621269	−	1.07607i	0.989250	−	0.146236i	$-0.0467158\pi$
$180$	−3905.98	+	3519.02i	−1.61741	+	1.45718i
$181$	−966.273			−0.396809			−0.198405	−	0.980120i	$-0.563576\pi$
$181$	−966.273			−0.396809			−0.198405	+	0.980120i	$0.563576\pi$
$182$		0			0
$183$		−	1114.60i		−	0.450237i
$184$	3530.38	+	6114.80i	1.41447	+	2.44994i
$185$	−132.242	+	407.403i	−0.0525547	+	0.161907i
$186$	−665.737	+	1153.09i	−0.262442	+	0.454563i
$187$	−612.617	+	353.695i	−0.239567	+	0.138314i
$188$		−	4187.48i		−	1.62449i
$189$		0			0
$190$	46.0458	−	9.80136i	0.0175817	−	0.00374245i
$191$	772.749	+	1338.44i	0.292744	+	0.507048i	0.974458	−	0.224571i	$-0.0720982\pi$
$191$	772.749	+	1338.44i	0.292744	+	0.507048i	−0.681713	+	0.731619i	$0.738765\pi$
$192$	−1597.22	−	922.156i	−0.600362	−	0.346619i
$193$	1995.37	+	1152.03i	0.744195	+	0.429661i	0.823593	−	0.567182i	$-0.191966\pi$
$193$	1995.37	+	1152.03i	0.744195	+	0.429661i	−0.0793975	+	0.996843i	$0.525300\pi$
$194$	−1370.16	−	2373.20i	−0.507073	−	0.878276i
$195$	289.375	+	1359.45i	0.106270	+	0.499244i
$196$		0			0
$197$			222.021i			0.0802960i	0.999194	+	0.0401480i	$0.0127829\pi$
$197$			222.021i			0.0802960i	−0.999194	+	0.0401480i	$0.987217\pi$
$198$	−2731.44	+	1577.00i	−0.980379	+	0.566022i
$199$	−1790.28	+	3100.85i	−0.637736	+	1.10459i	0.348193	+	0.937423i	$0.386795\pi$
$199$	−1790.28	+	3100.85i	−0.637736	+	1.10459i	−0.985928	+	0.167168i	$0.946538\pi$
$200$	8082.52	+	844.747i	2.85760	+	0.298663i
$201$	500.012	+	866.047i	0.175463	+	0.303912i
$202$		−	2849.92i		−	0.992673i
$203$		0			0
$204$	1086.85			0.373014
$205$	3349.29	−	3017.48i	1.14109	−	1.02805i
$206$	1014.09	−	1756.46i	0.342986	−	0.594070i
$207$	−2185.75	−	1261.94i	−0.733912	−	0.423724i
$208$	10190.8	−	5883.67i	3.39714	−	1.96134i
$209$	20.2404			0.00669883
$210$		0			0
$211$	−4181.04			−1.36415			−0.682073	−	0.731284i	$-0.738921\pi$
$211$	−4181.04			−1.36415			−0.682073	+	0.731284i	$0.738921\pi$
$212$	−2524.00	+	1457.23i	−0.817683	+	0.472090i
$213$	934.863	+	539.743i	0.300731	+	0.173627i
$214$	−3669.40	+	6355.58i	−1.17213	+	2.03018i
$215$	1293.86	+	1436.14i	0.410422	+	0.455553i
$216$	6334.31			1.99535
$217$		0			0
$218$		−	2075.42i		−	0.644794i
$219$	−167.993	−	290.972i	−0.0518352	−	0.0897812i
$220$	5496.15	+	1784.04i	1.68432	+	0.546726i
$221$	−887.651	+	1537.46i	−0.270180	+	0.467966i
$222$	341.908	−	197.401i	0.103367	−	0.0596787i
$223$		−	2361.52i		−	0.709145i	−0.935028	−	0.354573i	$-0.884626\pi$
$223$		−	2361.52i		−	0.709145i	0.935028	−	0.354573i	$-0.115374\pi$
$224$		0			0
$225$	−2653.02	+	1183.05i	−0.786081	+	0.350534i
$226$	−4365.57	−	7561.39i	−1.28493	−	2.22556i
$227$	−508.250	−	293.438i	−0.148607	−	0.0857982i	0.423853	−	0.905731i	$-0.360677\pi$
$227$	−508.250	−	293.438i	−0.148607	−	0.0857982i	−0.572460	+	0.819933i	$0.694011\pi$
$228$	−26.9315	−	15.5489i	−0.00782274	−	0.00451646i
$229$	2309.78	+	4000.65i	0.666526	+	1.15446i	0.978869	+	0.204487i	$0.0655527\pi$
$229$	2309.78	+	4000.65i	0.666526	+	1.15446i	−0.312344	+	0.949969i	$0.601114\pi$
$230$	1343.31	+	6310.76i	0.385111	+	1.80921i
$231$		0			0
$232$			15212.9i			4.30507i
$233$	−4434.43	+	2560.22i	−1.24682	+	0.719853i	−0.970474	−	0.241205i	$-0.922457\pi$
$233$	−4434.43	+	2560.22i	−1.24682	+	0.719853i	−0.276347	+	0.961058i	$0.589124\pi$
$234$	−3957.72	+	6854.97i	−1.10566	+	1.91506i
$235$	714.329	−	2200.66i	0.198288	−	0.610874i
$236$	−6870.63	−	11900.3i	−1.89508	−	3.28238i
$237$			153.850i			0.0421671i
$238$		0			0
$239$	−1127.51			−0.305158			−0.152579	−	0.988291i	$-0.548758\pi$
$239$	−1127.51			−0.305158			−0.152579	+	0.988291i	$0.548758\pi$
$240$	−2664.29	−	2957.26i	−0.716579	−	0.795375i
$241$	−1774.77	+	3073.98i	−0.474368	+	0.821630i	−0.999569	−	0.0293484i	$-0.990657\pi$
$241$	−1774.77	+	3073.98i	−0.474368	+	0.821630i	0.525201	+	0.850978i	$0.323990\pi$
$242$	−3122.80	−	1802.95i	−0.829508	−	0.478917i
$243$	−3014.70	+	1740.54i	−0.795856	+	0.459487i
$244$	−11629.4			−3.05120
$245$		0			0
$246$	−4155.24			−1.07694
$247$	43.9909	−	25.3981i	0.0113323	−	0.00654269i
$248$	7274.47	+	4199.92i	1.86262	+	1.07538i
$249$	1011.93	−	1752.72i	0.257545	−	0.446081i
$250$	6786.68	+	3014.52i	1.71691	+	0.762620i
$251$	−4717.19			−1.18624			−0.593120	−	0.805114i	$-0.702104\pi$
$251$	−4717.19			−1.18624			−0.593120	+	0.805114i	$0.702104\pi$
$252$		0			0
$253$			2774.02i			0.689333i
$254$	−510.196	−	883.685i	−0.126034	−	0.218297i
$255$	571.177	+	185.403i	0.140269	+	0.0455309i
$256$	56.7760	−	98.3390i	0.0138613	−	0.0240085i
$257$	5421.59	−	3130.16i	1.31591	−	0.759742i	0.332844	−	0.942982i	$-0.391992\pi$
$257$	5421.59	−	3130.16i	1.31591	−	0.759742i	0.983068	+	0.183239i	$0.0586584\pi$
$258$		−	1781.72i		−	0.429942i
$259$		0			0
$260$	14184.1	−	3019.25i	3.38331	−	0.720176i
$261$	−2718.94	−	4709.35i	−0.644821	−	1.11686i
$262$	−9585.00	−	5533.90i	−2.26017	−	1.30491i
$263$	4982.28	+	2876.52i	1.16814	+	0.674425i	0.953241	−	0.302212i	$-0.0977251\pi$
$263$	4982.28	+	2876.52i	1.16814	+	0.674425i	0.214897	+	0.976637i	$0.431058\pi$
$264$	−1610.22	−	2788.98i	−0.375386	−	0.650188i
$265$	−1575.03	+	335.262i	−0.365107	+	0.0777170i
$266$		0			0
$267$		−	1264.60i		−	0.289858i
$268$	9036.06	−	5216.97i	2.05957	−	1.18909i
$269$	3529.60	−	6113.45i	0.800014	−	1.38566i	−0.119593	−	0.992823i	$-0.538159\pi$
$269$	3529.60	−	6113.45i	0.800014	−	1.38566i	0.919606	−	0.392841i	$-0.128508\pi$
$270$	5505.53	+	1787.08i	1.24095	+	0.402809i
$271$	−4267.26	−	7391.11i	−0.956523	−	1.65675i	−0.730844	−	0.682544i	$-0.760874\pi$
$271$	−4267.26	−	7391.11i	−0.956523	−	1.65675i	−0.225678	−	0.974202i	$-0.572460\pi$
$272$		−	5084.11i		−	1.13334i
$273$		0			0
$274$	415.373			0.0915826
$275$	2584.08	+	1875.14i	0.566639	+	0.411183i
$276$	2131.04	−	3691.07i	0.464760	−	0.804987i
$277$	−1137.91	−	656.972i	−0.246824	−	0.142504i	0.371485	−	0.928439i	$-0.378849\pi$
$277$	−1137.91	−	656.972i	−0.246824	−	0.142504i	−0.618309	+	0.785935i	$0.712182\pi$
$278$	−6413.32	+	3702.73i	−1.38362	+	0.798832i
$279$	−3002.54			−0.644291
$280$		0			0
$281$	−247.229			−0.0524856			−0.0262428	−	0.999656i	$-0.508354\pi$
$281$	−247.229			−0.0524856			−0.0262428	+	0.999656i	$0.508354\pi$
$282$	−1846.88	+	1066.30i	−0.390001	+	0.225167i
$283$	−7859.10	−	4537.45i	−1.65079	−	0.953087i	−0.976746	−	0.214400i	$-0.931221\pi$
$283$	−7859.10	−	4537.45i	−1.65079	−	0.953087i	−0.674049	−	0.738687i	$-0.735446\pi$
$284$	5631.51	−	9754.07i	1.17665	−	2.03802i
$285$	−11.5010	−	12.7657i	−0.00239038	−	0.00265323i
$286$	8699.92			1.79873
$287$		0			0
$288$		−	10581.7i		−	2.16505i
$289$	−2072.99	−	3590.52i	−0.421939	−	0.730820i
$290$	−4291.98	+	13222.5i	−0.869083	+	2.67741i
$291$	−500.085	+	866.172i	−0.100740	+	0.174488i
$292$	−3035.91	+	1752.79i	−0.608436	+	0.351281i
$293$			2740.72i			0.546466i	0.961948	+	0.273233i	$0.0880930\pi$
$293$			2740.72i			0.546466i	−0.961948	+	0.273233i	$0.911907\pi$
$294$		0			0
$295$	−1580.71	−	7426.04i	−0.311975	−	1.46563i
$296$	−1245.34	−	2156.99i	−0.244540	−	0.423555i
$297$	2155.20	+	1244.31i	0.421069	+	0.243104i
$298$	−149.558	−	86.3475i	−0.0290727	−	0.0167851i
$299$	3480.91	+	6029.12i	0.673266	+	1.16613i
$300$	−1997.83	−	4480.16i	−0.384482	−	0.862208i
$301$		0			0
$302$		−	2480.21i		−	0.472584i
$303$	−900.813	+	520.085i	−0.170793	+	0.0986075i
$304$	−72.7352	+	125.981i	−0.0137225	+	0.0237681i
$305$	−6111.62	−	1983.82i	−1.14738	−	0.372436i
$306$	1709.94	+	2961.71i	0.319447	+	0.553299i
$307$		−	6985.46i		−	1.29864i	−0.760517	−	0.649318i	$-0.775054\pi$
$307$		−	6985.46i		−	1.29864i	0.760517	−	0.649318i	$-0.224946\pi$
$308$		0			0
$309$	−740.250			−0.136283
$310$	5137.77	+	5702.73i	0.941309	+	1.04482i
$311$	−178.421	+	309.033i	−0.0325315	+	0.0563462i	−0.881833	−	0.471562i	$-0.843690\pi$
$311$	−178.421	+	309.033i	−0.0325315	+	0.0563462i	0.849301	+	0.527908i	$0.177024\pi$
$312$	−6999.36	−	4041.08i	−1.27007	−	0.733273i
$313$	−5741.85	+	3315.06i	−1.03690	+	0.598653i	−0.918953	−	0.394368i	$-0.870964\pi$
$313$	−5741.85	+	3315.06i	−1.03690	+	0.598653i	−0.117944	+	0.993020i	$0.537630\pi$
$314$	8892.42			1.59818
$315$		0			0
$316$	1605.22			0.285762
$317$	−2159.91	+	1247.02i	−0.382689	+	0.220946i	−0.678988	−	0.734150i	$-0.737581\pi$
$317$	−2159.91	+	1247.02i	−0.382689	+	0.220946i	0.296298	+	0.955095i	$0.404248\pi$
$318$	1285.42	+	742.137i	0.226675	+	0.130871i
$319$	−2988.41	+	5176.08i	−0.524511	+	0.908480i
$320$	−7899.23	+	7116.66i	−1.37994	+	1.24323i
$321$	2678.52			0.465734
$322$		0			0
$323$		−	21.9467i		−	0.00378063i
$324$	4436.39	+	7684.06i	0.760698	+	1.31757i
$325$	7969.27	+	832.911i	1.36017	+	0.142159i
$326$	−4966.56	+	8602.34i	−0.843781	+	1.46147i
$327$	−656.005	+	378.744i	−0.110939	+	0.0640508i
$328$			26214.0i			4.41289i
$329$		0			0
$330$	−612.690	−	2878.35i	−0.102204	−	0.480146i
$331$	2341.23	+	4055.14i	0.388779	+	0.673385i	0.992286	−	0.123973i	$-0.0395636\pi$
$331$	2341.23	+	4055.14i	0.388779	+	0.673385i	−0.603506	+	0.797358i	$0.706230\pi$
$332$	−18287.3	−	10558.2i	−3.02304	−	1.74535i
$333$	771.020	+	445.148i	0.126882	+	0.0732552i
$334$	−123.609	−	214.097i	−0.0202502	−	0.0350744i
$335$	5638.70	−	1200.26i	0.919627	−	0.195753i
$336$		0			0
$337$			3596.60i			0.581363i	0.956820	+	0.290681i	$0.0938820\pi$
$337$			3596.60i			0.581363i	−0.956820	+	0.290681i	$0.906118\pi$
$338$	8798.54	−	5079.84i	1.41591	−	0.817476i
$339$	−1593.35	+	2759.77i	−0.255277	+	0.442153i
$340$	1934.44	−	5959.49i	0.308557	−	0.950584i
$341$	1650.06	+	2857.98i	0.262040	+	0.453867i
$342$		−	97.8523i		−	0.0154715i
$343$		0			0
$344$	−11240.3			−1.76173
$345$	1749.58	−	1576.25i	0.273027	−	0.245979i
$346$	6632.18	−	11487.3i	1.03049	−	1.78485i
$347$	−1645.03	−	949.756i	−0.254495	−	0.146932i	0.367326	−	0.930092i	$-0.380273\pi$
$347$	−1645.03	−	949.756i	−0.254495	−	0.146932i	−0.621821	+	0.783160i	$0.713607\pi$
$348$	7952.68	−	4591.48i	1.22502	−	0.707268i
$349$	−1037.55			−0.159137			−0.0795683	−	0.996829i	$-0.525354\pi$
$349$	−1037.55			−0.159137			−0.0795683	+	0.996829i	$0.525354\pi$
$350$		0			0
$351$	6245.56			0.949752
$352$	−10072.3	+	5815.25i	−1.52516	+	0.880550i
$353$	3539.51	+	2043.54i	0.533681	+	0.308121i	0.742514	−	0.669830i	$-0.233633\pi$
$353$	3539.51	+	2043.54i	0.533681	+	0.308121i	−0.208833	+	0.977951i	$0.566967\pi$
$354$	−3499.07	+	6060.56i	−0.525348	+	0.909930i
$355$	4623.46	−	4165.42i	0.691234	−	0.622754i
$356$	−13194.4			−1.96433
$357$		0			0
$358$			15811.8i			2.33431i
$359$	1736.33	+	3007.42i	0.255265	+	0.442132i	0.964967	−	0.262369i	$-0.0845039\pi$
$359$	1736.33	+	3007.42i	0.255265	+	0.442132i	−0.709702	+	0.704502i	$0.751171\pi$
$360$	5215.03	−	16066.1i	0.763490	−	2.35211i
$361$	3429.19	−	5939.52i	0.499954	−	0.865946i
$362$	4446.56	−	2567.22i	0.645596	−	0.372735i
$363$			1316.08i			0.190293i
$364$		0			0
$365$	−1894.48	+	403.260i	−0.271675	+	0.0578290i
$366$	2961.30	+	5129.11i	0.422922	+	0.732522i
$367$	7594.29	+	4384.57i	1.08016	+	0.623631i	0.930940	−	0.365173i	$-0.118990\pi$
$367$	7594.29	+	4384.57i	1.08016	+	0.623631i	0.149221	+	0.988804i	$0.452323\pi$
$368$	−17266.2	−	9968.64i	−2.44582	−	1.41210i
$369$	−4685.13	−	8114.88i	−0.660970	−	1.14483i
$370$	−473.853	−	2226.11i	−0.0665796	−	0.312784i
$371$		0			0
$372$		−	5070.39i		−	0.706687i
$373$	−9845.73	+	5684.43i	−1.36674	+	0.789085i	−0.990510	−	0.137443i	$-0.956112\pi$
$373$	−9845.73	+	5684.43i	−1.36674	+	0.789085i	−0.376226	+	0.926528i	$0.622778\pi$
$374$	1879.41	−	3255.24i	0.259845	−	0.450065i
$375$	−285.667	−	2695.28i	−0.0393380	−	0.371156i
$376$	6726.92	+	11651.4i	0.922645	+	1.59807i
$377$			14999.8i			2.04914i
$378$		0			0
$379$	12137.4			1.64500			0.822501	−	0.568764i	$-0.192578\pi$
$379$	12137.4			1.64500			0.822501	+	0.568764i	$0.192578\pi$
$380$	−133.193	+	119.998i	−0.0179807	+	0.0161993i
$381$	−186.212	+	322.529i	−0.0250392	+	0.0433692i
$382$	−7112.01	−	4106.12i	−0.952571	−	0.549967i
$383$	−8547.33	+	4934.80i	−1.14033	+	0.658373i	−0.946514	−	0.322664i	$-0.895422\pi$
$383$	−8547.33	+	4934.80i	−1.14033	+	0.658373i	−0.193821	+	0.981037i	$0.562088\pi$
$384$	2735.27			0.363499
$385$		0			0
$386$	−12242.9			−1.61438
$387$	3479.57	−	2008.93i	0.457045	−	0.263875i
$388$	9037.37	+	5217.73i	1.18248	+	0.682706i
$389$	28.5583	−	49.4644i	0.00372227	−	0.00644716i	−0.864158	−	0.503220i	$-0.832148\pi$
$389$	28.5583	−	49.4644i	0.00372227	−	0.00644716i	0.867881	+	0.496773i	$0.165482\pi$
$390$	−4943.47	−	5487.06i	−0.641852	−	0.712431i
$391$	3007.88			0.389041
$392$		0			0
$393$			4039.54i			0.518494i
$394$	−589.871	−	1021.69i	−0.0754245	−	0.130639i
$395$	843.596	+	273.829i	0.107458	+	0.0348806i
$396$	6005.37	−	10401.6i	0.762073	−	1.31995i
$397$	6439.91	−	3718.09i	0.814131	−	0.470039i	−0.0342574	−	0.999413i	$-0.510907\pi$
$397$	6439.91	−	3718.09i	0.814131	−	0.470039i	0.848388	+	0.529374i	$0.177573\pi$
$398$		−	19025.8i		−	2.39618i
$399$		0			0
$400$	−20957.4	+	9345.47i	−2.61968	+	1.16818i
$401$	6232.49	+	10795.0i	0.776149	+	1.34433i	0.934147	+	0.356890i	$0.116163\pi$
$401$	6232.49	+	10795.0i	0.776149	+	1.34433i	−0.157998	+	0.987439i	$0.550504\pi$
$402$	−4601.87	−	2656.89i	−0.570947	−	0.329636i
$403$	7172.55	+	4141.07i	0.886576	+	0.511865i
$404$	5426.40	+	9398.80i	0.668251	+	1.15745i
$405$	1020.67	+	4795.02i	0.125229	+	0.588312i
$406$		0			0
$407$		−	978.533i		−	0.119175i
$408$	−3024.09	+	1745.96i	−0.366948	+	0.211858i
$409$	854.358	−	1479.79i	0.103289	−	0.178902i	−0.809749	−	0.586777i	$-0.800397\pi$
$409$	854.358	−	1479.79i	0.103289	−	0.178902i	0.913038	+	0.407875i	$0.133730\pi$
$410$	−7395.70	+	22784.2i	−0.890848	+	2.74447i
$411$	−75.8018	−	131.293i	−0.00909739	−	0.0157571i
$412$			7723.54i			0.923571i
$413$		0			0
$414$	13411.0			1.59207
$415$	−7809.51	−	8668.26i	−0.923744	−	1.02532i
$416$	−14594.2	+	25278.0i	−1.72005	+	2.97922i
$417$	2340.74	+	1351.43i	0.274884	+	0.158704i
$418$	−93.1413	+	53.7752i	−0.0108988	+	0.00629242i
$419$	10618.8			1.23810			0.619050	−	0.785352i	$-0.287518\pi$
$419$	10618.8			1.23810			0.619050	+	0.785352i	$0.287518\pi$
$420$		0			0
$421$	13273.5			1.53661			0.768304	−	0.640085i	$-0.221101\pi$
$421$	13273.5			1.53661			0.768304	+	0.640085i	$0.221101\pi$
$422$	19240.2	−	11108.3i	2.21942	−	1.28138i
$423$	−4164.81	−	2404.55i	−0.478723	−	0.276391i
$424$	4681.90	−	8109.29i	0.536257	−	0.928825i
$425$	2033.22	−	2801.92i	0.232060	−	0.319795i
$426$	−5736.02			−0.652373
$427$		0			0
$428$		−	27946.9i		−	3.15622i
$429$	−1587.65	−	2749.90i	−0.178678	−	0.309479i
$430$	−9769.62	−	3171.20i	−1.09566	−	0.355648i
$431$	−3959.10	+	6857.37i	−0.442467	+	0.766375i	−0.997872	−	0.0652048i	$-0.979230\pi$
$431$	−3959.10	+	6857.37i	−0.442467	+	0.766375i	0.555405	+	0.831580i	$0.312563\pi$
$432$	−15489.7	+	8943.01i	−1.72512	+	0.995997i
$433$		−	4433.34i		−	0.492038i	−0.969265	−	0.246019i	$-0.920877\pi$
$433$		−	4433.34i		−	0.492038i	0.969265	−	0.246019i	$-0.0791226\pi$
$434$		0			0
$435$	4962.65	−	1056.35i	0.546990	−	0.116433i
$436$	3951.70	+	6844.55i	0.434065	+	0.751822i
$437$	−74.5333	−	43.0318i	−0.00815884	−	0.00471051i
$438$	1546.13	+	892.656i	0.168668	+	0.0973807i
$439$	−6479.19	−	11222.3i	−0.704408	−	1.22007i	−0.966905	−	0.255137i	$-0.917879\pi$
$439$	−6479.19	−	11222.3i	−0.704408	−	1.22007i	0.262497	−	0.964933i	$-0.415454\pi$
$440$	−18158.6	+	3865.26i	−1.96745	+	0.418793i
$441$		0			0
$442$		−	9433.34i		−	1.01515i
$443$	−10427.3	+	6020.22i	−1.11832	+	0.645664i	−0.940972	−	0.338483i	$-0.890086\pi$
$443$	−10427.3	+	6020.22i	−1.11832	+	0.645664i	−0.177351	+	0.984148i	$0.556753\pi$
$444$	−751.723	+	1302.02i	−0.0803495	+	0.139169i
$445$	−6934.09	−	2250.79i	−0.738669	−	0.239770i
$446$	6274.17	+	10867.2i	0.666122	+	1.15376i
$447$			63.0304i			0.00666943i
$448$		0			0
$449$	−11586.3			−1.21780			−0.608899	−	0.793247i	$-0.708389\pi$
$449$	−11586.3			−1.21780			−0.608899	+	0.793247i	$0.708389\pi$
$450$	9065.40	−	12492.8i	0.949661	−	1.30870i
$451$	−5149.46	+	8919.13i	−0.537647	+	0.931232i
$452$	28794.5	+	16624.5i	2.99642	+	1.72998i
$453$	−783.954	+	452.616i	−0.0813099	+	0.0469443i
$454$	3118.46			0.322371
$455$		0			0
$456$	99.9135			0.0102607
$457$	−8430.18	+	4867.17i	−0.862904	+	0.498198i	−0.864984	−	0.501800i	$-0.832671\pi$
$457$	−8430.18	+	4867.17i	−0.862904	+	0.498198i	0.00207942	+	0.999998i	$0.499338\pi$
$458$	−21258.1	−	12273.4i	−2.16883	−	1.25218i
$459$	1349.20	−	2336.89i	0.137201	−	0.237640i
$460$	−16446.1	−	18254.6i	−1.66697	−	1.85027i
$461$	1343.41			0.135724			0.0678621	−	0.997695i	$-0.478382\pi$
$461$	1343.41			0.135724			0.0678621	+	0.997695i	$0.478382\pi$
$462$		0			0
$463$		−	6613.72i		−	0.663857i	−0.943305	−	0.331929i	$-0.892301\pi$
$463$		−	6613.72i		−	0.663857i	0.943305	−	0.331929i	$-0.107699\pi$
$464$	−21478.2	−	37201.2i	−2.14892	−	3.72204i
$465$	864.942	−	2664.66i	0.0862597	−	0.265743i
$466$	13604.1	−	23563.1i	1.35236	−	2.34236i
$467$	−12721.0	+	7344.47i	−1.26051	+	0.727755i	−0.973173	−	0.230076i	$-0.926103\pi$
$467$	−12721.0	+	7344.47i	−1.26051	+	0.727755i	−0.287335	+	0.957830i	$0.592769\pi$
$468$		−	30142.8i		−	2.97724i
$469$		0			0
$470$	2559.60	+	12024.8i	0.251204	+	1.18013i
$471$	−1622.78	−	2810.74i	−0.158756	−	0.274973i
$472$	38234.1	+	22074.5i	3.72853	+	2.15267i
$473$	−3824.43	−	2208.03i	−0.371770	−	0.214642i
$474$	−408.752	−	707.979i	−0.0396089	−	0.0686046i
$475$	−90.4673	+	40.3418i	−0.00873879	+	0.00389686i
$476$		0			0
$477$			3347.11i			0.321286i
$478$	5188.55	−	2995.61i	0.496482	−	0.286644i
$479$	7649.31	−	13249.0i	0.729657	−	1.26380i	−0.227371	−	0.973808i	$-0.573013\pi$
$479$	7649.31	−	13249.0i	0.729657	−	1.26380i	0.957028	−	0.289995i	$-0.0936538\pi$
$480$	9390.97	+	3048.29i	0.892994	+	0.289864i
$481$	−1227.89	−	2126.77i	−0.116397	−	0.201605i
$482$		−	18861.0i		−	1.78235i
$483$		0			0
$484$	13731.6			1.28960
$485$	3859.36	+	4283.75i	0.361329	+	0.401062i
$486$	9248.61	−	16019.1i	0.863221	−	1.49514i
$487$	−8360.44	−	4826.90i	−0.777921	−	0.449133i	0.0577719	−	0.998330i	$-0.481600\pi$
$487$	−8360.44	−	4826.90i	−0.777921	−	0.449133i	−0.835693	+	0.549197i	$0.814934\pi$
$488$	32357.9	−	18681.8i	3.00158	−	1.73297i
$489$	3625.41			0.335269
$490$		0			0
$491$	20142.6			1.85137			0.925684	−	0.378297i	$-0.123490\pi$
$491$	20142.6			1.85137			0.925684	+	0.378297i	$0.123490\pi$
$492$	13703.6	−	7911.78i	1.25570	−	0.724981i
$493$	5612.44	+	3240.34i	0.512721	+	0.296020i
$494$	−134.957	+	233.752i	−0.0122915	+	0.0212895i
$495$	4930.40	−	4441.95i	0.447687	−	0.403335i
$496$	−23718.4			−2.14715
$497$		0			0
$498$			10754.1i			0.967679i
$499$	−654.645	−	1133.88i	−0.0587293	−	0.101722i	0.835166	−	0.549998i	$-0.185372\pi$
$499$	−654.645	−	1133.88i	−0.0587293	−	0.101722i	−0.893895	+	0.448276i	$0.852038\pi$
$500$	−28121.7	+	2980.56i	−2.51528	+	0.266589i
$501$	−45.1149	+	78.1413i	−0.00402313	+	0.00696826i
$502$	21707.4	−	12532.8i	1.92998	−	1.11427i
$503$		−	2186.17i		−	0.193791i	−0.995295	−	0.0968953i	$-0.969109\pi$
$503$		−	2186.17i		−	0.193791i	0.995295	−	0.0968953i	$-0.0308912\pi$
$504$		0			0
$505$	1248.44	+	5865.06i	0.110010	+	0.516815i
$506$	−7370.10	−	12765.4i	−0.647512	−	1.12152i
$507$	−3211.30	−	1854.05i	−0.281300	−	0.162409i
$508$	3365.16	+	1942.88i	0.293908	+	0.169688i
$509$	−1795.56	−	3110.00i	−0.156359	−	0.270822i	0.777194	−	0.629261i	$-0.216642\pi$
$509$	−1795.56	−	3110.00i	−0.156359	−	0.270822i	−0.933553	+	0.358439i	$0.883309\pi$
$510$	−3121.01	+	664.340i	−0.270981	+	0.0576813i
$511$		0			0
$512$			11886.4i			1.02600i
$513$	−66.8649	+	38.6045i	−0.00575469	+	0.00332247i
$514$	−16632.6	+	28808.5i	−1.42730	+	2.47215i
$515$	−1317.53	+	4058.98i	−0.112733	+	0.347301i
$516$	3392.49	+	5875.96i	0.289430	+	0.501307i
$517$			5285.73i			0.449644i
$518$		0			0
$519$	−4841.24			−0.409455
$520$	−34616.1	+	31186.7i	−2.91926	+	2.63005i
$521$	−4302.67	+	7452.44i	−0.361811	+	0.626674i	−0.988259	−	0.152789i	$-0.951175\pi$
$521$	−4302.67	+	7452.44i	−0.361811	+	0.626674i	0.626448	+	0.779463i	$0.284508\pi$
$522$	25023.9	+	14447.5i	2.09821	+	1.21140i
$523$	−19517.1	+	11268.2i	−1.63179	+	0.942113i	−0.648245	+	0.761432i	$0.724497\pi$
$523$	−19517.1	+	11268.2i	−1.63179	+	0.942113i	−0.983542	+	0.180681i	$0.942170\pi$
$524$	42147.3			3.51377
$525$		0			0
$526$	−30569.7			−2.53403
$527$	3098.92	−	1789.16i	0.256150	−	0.147888i
$528$	7875.16	+	4546.72i	0.649095	+	0.374755i
$529$	−185.819	+	321.847i	−0.0152723	+	0.0264525i
$530$	6357.18	−	5727.38i	0.521015	−	0.469399i
$531$	−15781.1			−1.28972
$532$		0			0
$533$			25846.7i			2.10046i
$534$	3359.81	+	5819.37i	0.272272	+	0.471589i
$535$	4767.37	−	14687.0i	0.385255	−	1.18687i
$536$	−16761.5	+	29031.7i	−1.35072	+	2.33951i
$537$	4997.86	−	2885.51i	0.401627	−	0.231879i
$538$			37510.2i			3.00591i
$539$		0			0
$540$	−21559.5	+	4589.17i	−1.71810	+	0.365716i
$541$	−4391.22	−	7605.81i	−0.348971	−	0.604435i	0.637096	−	0.770784i	$-0.280135\pi$
$541$	−4391.22	−	7605.81i	−0.348971	−	0.604435i	−0.986067	+	0.166349i	$0.946802\pi$
$542$	39273.8	+	22674.8i	3.11246	+	1.79698i
$543$	−1622.91	−	936.988i	−0.128261	−	0.0740516i
$544$	6305.48	+	10921.4i	0.496958	+	0.860757i
$545$	909.161	+	4271.15i	0.0714572	+	0.335699i
$546$		0			0
$547$		−	22593.0i		−	1.76601i	−0.469366	−	0.883004i	$-0.655518\pi$
$547$		−	22593.0i		−	1.76601i	0.469366	−	0.883004i	$-0.344482\pi$
$548$	−1369.87	+	790.892i	−0.106784	+	0.0616519i
$549$	−6677.86	+	11566.4i	−0.519133	+	0.899165i
$550$	−16873.2	−	1763.51i	−1.30814	−	0.136721i
$551$	−92.7152	−	160.587i	−0.00716842	−	0.0124161i
$552$			13693.5i			1.05586i
$553$		0			0
$554$	6981.84			0.535433
$555$	−617.163	+	556.022i	−0.0472020	+	0.0425258i
$556$	14100.4	−	24422.6i	1.07552	−	1.86286i
$557$	−6290.92	−	3632.06i	−0.478554	−	0.276294i	0.241259	−	0.970461i	$-0.422440\pi$
$557$	−6290.92	−	3632.06i	−0.478554	−	0.276294i	−0.719814	+	0.694167i	$0.755773\pi$
$558$	13817.0	−	7977.23i	1.04824	−	0.605202i
$559$	−11082.8			−0.838555
$560$		0			0
$561$	−1371.90			−0.103247
$562$	1137.69	−	656.846i	0.0853924	−	0.0493013i
$563$	3335.43	+	1925.71i	0.249683	+	0.144154i	0.619619	−	0.784903i	$-0.287287\pi$
$563$	3335.43	+	1925.71i	0.249683	+	0.144154i	−0.369936	+	0.929057i	$0.620620\pi$
$564$	4060.57	−	7033.11i	0.303158	−	0.525084i
$565$	12296.6	+	13648.7i	0.915611	+	1.01629i
$566$	48220.9			3.58105
$567$		0			0
$568$			36186.7i			2.67317i
$569$	8290.14	+	14358.9i	0.610792	+	1.05792i	0.991107	+	0.133066i	$0.0424822\pi$
$569$	8290.14	+	14358.9i	0.610792	+	1.05792i	−0.380315	+	0.924857i	$0.624184\pi$
$570$	86.8409	+	28.1884i	0.00638134	+	0.00207137i
$571$	−3192.93	+	5530.32i	−0.234010	+	0.405318i	−0.958985	−	0.283458i	$-0.908518\pi$
$571$	−3192.93	+	5530.32i	−0.234010	+	0.405318i	0.724974	+	0.688776i	$0.241852\pi$
$572$	−28691.6	+	16565.1i	−2.09730	+	1.21088i
$573$			2997.32i			0.218525i
$574$		0			0
$575$	−5529.00	−	12398.9i	−0.401001	−	0.899252i
$576$	11049.8	+	19138.8i	0.799318	+	1.38446i
$577$	9577.44	+	5529.54i	0.691012	+	0.398956i	0.803991	−	0.594641i	$-0.202706\pi$
$577$	9577.44	+	5529.54i	0.691012	+	0.398956i	−0.112979	+	0.993597i	$0.536039\pi$
$578$	19078.8	+	11015.1i	1.37296	+	0.792681i
$579$	2234.22	+	3869.79i	0.160365	+	0.277760i
$580$	−11021.7	−	51778.7i	−0.789052	−	3.70689i
$581$		0			0
$582$		−	5314.56i		−	0.378515i
$583$	3185.96	−	1839.42i	0.226328	−	0.130670i
$584$	5631.48	−	9754.00i	0.399028	−	0.691136i
$585$	5141.96	−	15841.0i	0.363409	−	1.11957i
$586$	−7281.62	−	12612.1i	−0.513312	−	0.889083i
$587$		−	7871.25i		−	0.553461i	−0.960948	−	0.276730i	$-0.910749\pi$
$587$		−	7871.25i		−	0.553461i	0.960948	−	0.276730i	$-0.0892509\pi$
$588$		0			0
$589$	−102.386			−0.00716253
$590$	27003.8	+	29973.2i	1.88428	+	2.09148i
$591$	−215.292	+	372.896i	−0.0149846	+	0.0259542i
$592$	6090.63	+	3516.43i	0.422844	+	0.244129i
$593$	1747.69	−	1009.03i	0.121027	−	0.0698750i	−0.438264	−	0.898846i	$-0.644407\pi$
$593$	1747.69	−	1009.03i	0.121027	−	0.0698750i	0.559291	+	0.828971i	$0.311073\pi$
$594$	−13223.6			−0.913422
$595$		0			0
$596$	657.640			0.0451980
$597$	−6013.75	+	3472.04i	−0.412272	+	0.238025i
$598$	−32036.7	−	18496.4i	−2.19076	−	1.26484i
$599$	−678.335	+	1174.91i	−0.0462705	+	0.0801428i	−0.888233	−	0.459393i	$-0.848067\pi$
$599$	−678.335	+	1174.91i	−0.0462705	+	0.0801428i	0.841963	+	0.539536i	$0.181400\pi$
$600$	12755.9	+	9256.36i	0.867929	+	0.629815i
$601$	−11178.7			−0.758715			−0.379358	−	0.925250i	$-0.623855\pi$
$601$	−11178.7			−0.758715			−0.379358	+	0.925250i	$0.623855\pi$
$602$		0			0
$603$		−	11982.8i		−	0.809252i
$604$	4722.46	+	8179.53i	0.318136	+	0.551027i
$605$	7216.42	+	2342.43i	0.484941	+	0.157411i
$606$	2763.55	−	4786.61i	0.185250	−	0.320863i
$607$	8144.69	−	4702.34i	0.544617	−	0.314435i	−0.202331	−	0.979317i	$-0.564852\pi$
$607$	8144.69	−	4702.34i	0.544617	−	0.314435i	0.746948	+	0.664882i	$0.231518\pi$
$608$		−	360.835i		−	0.0240687i
$609$		0			0
$610$	33394.9	−	7108.47i	2.21659	−	0.471825i
$611$	6632.67	+	11488.1i	0.439164	+	0.760654i
$612$	−11278.5	−	6511.63i	−0.744943	−	0.430093i
$613$	16400.8	+	9468.99i	1.08062	+	0.623897i	0.931064	−	0.364856i	$-0.118882\pi$
$613$	16400.8	+	9468.99i	1.08062	+	0.623897i	0.149557	+	0.988753i	$0.452215\pi$
$614$	18559.2	+	32145.4i	1.21985	+	2.11284i
$615$	8551.35	−	1820.25i	0.560689	−	0.119349i
$616$		0			0
$617$		−	17716.9i		−	1.15600i	−0.816036	−	0.578001i	$-0.803833\pi$
$617$		−	17716.9i		−	1.15600i	0.816036	−	0.578001i	$-0.196167\pi$
$618$	3406.45	−	1966.72i	0.221728	−	0.128015i
$619$	3120.16	−	5404.28i	0.202601	−	0.350915i	−0.746765	−	0.665088i	$-0.768394\pi$
$619$	3120.16	−	5404.28i	0.202601	−	0.350915i	0.949366	+	0.314173i	$0.101727\pi$
$620$	−27802.2	−	9024.54i	−1.80091	−	0.584571i
$621$	−5290.89	−	9164.10i	−0.341894	−	0.592178i
$622$		−	1896.13i		−	0.122231i
$623$		0			0
$624$	22821.4			1.46408
$625$	−15287.3	−	3230.81i	−0.978389	−	0.206772i
$626$	17615.1	−	30510.2i	1.12467	−	1.94798i
$627$	33.9949	+	19.6269i	0.00216527	+	0.00125012i
$628$	−29326.4	+	16931.6i	−1.86346	+	1.07587i
$629$	−1061.03			−0.0672589
$630$		0			0
$631$	−25887.7			−1.63323			−0.816617	−	0.577179i	$-0.804153\pi$
$631$	−25887.7			−1.63323			−0.816617	+	0.577179i	$0.804153\pi$
$632$	−4466.41	+	2578.68i	−0.281114	+	0.162301i
$633$	−7022.30	−	4054.33i	−0.440934	−	0.254573i
$634$	6626.25	−	11477.0i	0.415082	−	0.718944i
$635$	1437.08	+	1595.10i	0.0898089	+	0.0996845i
$636$	−5652.27			−0.352401
$637$		0			0
$638$		−	31758.8i		−	1.97076i
$639$	−6467.50	−	11202.0i	−0.400392	−	0.693499i
$640$	4868.37	−	14998.2i	0.300686	−	0.926335i
$641$	−9399.22	+	16279.9i	−0.579168	+	1.00315i	0.416407	+	0.909178i	$0.363289\pi$
$641$	−9399.22	+	16279.9i	−0.579168	+	1.00315i	−0.995575	+	0.0939701i	$0.970044\pi$
$642$	−12325.9	+	7116.38i	−0.757734	+	0.437478i
$643$			2287.70i			0.140308i	0.997536	+	0.0701541i	$0.0223491\pi$
$643$			2287.70i			0.140308i	−0.997536	+	0.0701541i	$0.977651\pi$
$644$		0			0
$645$	780.503	+	3666.73i	0.0476469	+	0.223841i
$646$	58.3085	+	100.993i	0.00355127	+	0.00615097i
$647$	−1532.27	−	884.654i	−0.0931060	−	0.0537548i	0.452724	−	0.891651i	$-0.350452\pi$
$647$	−1532.27	−	884.654i	−0.0931060	−	0.0537548i	−0.545830	+	0.837896i	$0.683786\pi$
$648$	−24687.9	−	14253.6i	−1.49666	−	0.864094i
$649$	8672.59	+	15021.4i	0.524544	+	0.908536i
$650$	−38885.6	+	17340.1i	−2.34649	+	1.04636i
$651$		0			0
$652$		−	37826.4i		−	2.27208i
$653$	3370.12	−	1945.74i	0.201965	−	0.116604i	−0.395607	−	0.918420i	$-0.629466\pi$
$653$	3370.12	−	1945.74i	0.201965	−	0.116604i	0.597572	+	0.801816i	$0.296132\pi$
$654$	2012.52	−	3485.78i	0.120330	−	0.208417i
$655$	22149.8	+	7189.78i	1.32132	+	0.428898i
$656$	−37009.9	−	64103.1i	−2.20274	−	3.81525i
$657$			4025.96i			0.239068i
$658$		0			0
$659$	−20097.6			−1.18800			−0.594001	−	0.804465i	$-0.702452\pi$
$659$	−20097.6			−1.18800			−0.594001	+	0.804465i	$0.702452\pi$
$660$	7501.13	+	8325.97i	0.442396	+	0.491043i
$661$	−13584.0	+	23528.1i	−0.799326	+	1.38447i	0.120730	+	0.992685i	$0.461477\pi$
$661$	−13584.0	+	23528.1i	−0.799326	+	1.38447i	−0.920056	+	0.391788i	$0.871857\pi$
$662$	−21547.6	−	12440.5i	−1.26506	−	0.730384i
$663$	−2981.72	+	1721.50i	−0.174661	+	0.100841i
$664$	67844.3			3.96516
$665$		0			0
$666$	−4730.73			−0.275243
$667$	22009.1	−	12707.0i	1.27766	−	0.737655i
$668$	815.303	+	470.715i	0.0472231	+	0.0272642i
$669$	2289.95	−	3966.32i	0.132339	−	0.229218i
$670$	−22759.1	+	20504.4i	−1.31233	+	1.18232i
$671$	14679.4			0.844548
$672$		0			0
$673$			25909.7i			1.48402i	0.670389	+	0.742010i	$0.266127\pi$
$673$			25909.7i			1.48402i	−0.670389	+	0.742010i	$0.733873\pi$
$674$	−9555.55	−	16550.7i	−0.546092	−	0.945859i
$675$	−12113.1	−	1266.00i	−0.690714	−	0.0721902i
$676$	−19344.6	+	33505.7i	−1.10062	+	1.90634i
$677$	3775.19	−	2179.61i	0.214317	−	0.123736i	−0.388999	−	0.921238i	$-0.627179\pi$
$677$	3775.19	−	2179.61i	0.214317	−	0.123736i	0.603316	+	0.797502i	$0.293846\pi$
$678$		−	16933.0i		−	0.959159i
$679$		0			0
$680$	4191.11	+	19689.4i	0.236355	+	1.11037i
$681$	−569.090	−	985.693i	−0.0320229	−	0.0554653i
$682$	−15186.3	−	8767.84i	−0.852662	−	0.492284i
$683$	−25739.9	−	14860.9i	−1.44203	−	0.832559i	−0.444049	−	0.896003i	$-0.646458\pi$
$683$	−25739.9	−	14860.9i	−1.44203	−	0.832559i	−0.997985	+	0.0634439i	$0.979792\pi$
$684$	186.316	+	322.708i	0.0104152	+	0.0180396i
$685$	−854.826	+	181.959i	−0.0476806	+	0.0101493i
$686$		0			0
$687$			8959.10i			0.497541i
$688$	27486.7	−	15869.5i	1.52314	−	0.879386i
$689$	4616.30	−	7995.67i	0.255250	−	0.442105i
$690$	−3863.32	+	11901.9i	−0.213151	+	0.656662i
$691$	−2464.57	−	4268.75i	−0.135682	−	0.235009i	0.790176	−	0.612881i	$-0.209989\pi$
$691$	−2464.57	−	4268.75i	−0.135682	−	0.235009i	−0.925858	+	0.377872i	$0.876656\pi$
$692$			50512.0i			2.77482i
$693$		0			0
$694$	10093.4			0.552073
$695$	11576.4	−	10429.5i	0.631824	−	0.569230i
$696$	−14751.9	+	25551.0i	−0.803402	+	1.39153i
$697$	9671.03	+	5583.57i	0.525562	+	0.303433i
$698$	4774.55	−	2756.59i	0.258910	−	0.149482i
$699$	−9930.51			−0.537348
$700$		0			0
$701$	−19358.8			−1.04304			−0.521520	−	0.853239i	$-0.674635\pi$
$701$	−19358.8			−1.04304			−0.521520	+	0.853239i	$0.674635\pi$
$702$	−28740.6	+	16593.4i	−1.54522	+	0.892132i
$703$	26.2916	+	15.1794i	0.00141053	+	0.000814372i
$704$	12144.9	−	21035.6i	0.650182	−	1.12615i
$705$	3333.72	−	3003.46i	0.178093	−	0.160449i
$706$	−21717.3			−1.15771
$707$		0			0
$708$		−	26649.6i		−	1.41462i
$709$	−8593.15	−	14883.8i	−0.455180	−	0.788394i	0.543519	−	0.839397i	$-0.317092\pi$
$709$	−8593.15	−	14883.8i	−0.455180	−	0.788394i	−0.998699	+	0.0510026i	$0.983758\pi$
$710$	−10209.3	+	31452.0i	−0.539643	+	1.66250i
$711$	921.755	−	1596.53i	0.0486196	−	0.0842116i
$712$	36712.5	−	21196.0i	1.93239	−	1.11566i
$713$		−	14032.4i		−	0.737049i
$714$		0			0
$715$	−17904.2	+	3811.10i	−0.936473	+	0.199339i
$716$	−30106.6	−	52146.1i	−1.57142	−	2.72178i
$717$	−1893.72	−	1093.34i	−0.0986365	−	0.0569478i
$718$	−15980.4	−	9226.28i	−0.830617	−	0.479557i
$719$	7553.65	+	13083.3i	0.391799	+	0.678616i	0.992687	−	0.120717i	$-0.0385195\pi$
$719$	7553.65	+	13083.3i	0.391799	+	0.678616i	−0.600888	+	0.799333i	$0.705186\pi$
$720$	9930.07	+	46650.5i	0.513989	+	2.41467i
$721$		0			0
$722$			36443.0i			1.87849i
$723$	−5961.64	+	3441.96i	−0.306661	+	0.177051i
$724$	−9776.24	+	16932.9i	−0.501839	+	0.869210i
$725$	3040.52	−	29091.6i	0.155754	−	1.49025i
$726$	−3496.61	−	6056.31i	−0.178748	−	0.309601i
$727$		−	15840.9i		−	0.808124i	−0.914732	−	0.404062i	$-0.867598\pi$
$727$		−	15840.9i		−	0.808124i	0.914732	−	0.404062i	$-0.132402\pi$
$728$		0			0
$729$	5088.04			0.258499
$730$	7646.53	−	6889.00i	0.387686	−	0.349279i
$731$	−2394.18	+	4146.83i	−0.121138	+	0.209817i
$732$	−19532.2	−	11276.9i	−0.986244	−	0.569408i
$733$	23936.7	−	13819.9i	1.20617	−	0.696382i	0.244249	−	0.969713i	$-0.421459\pi$
$733$	23936.7	−	13819.9i	1.20617	−	0.696382i	0.961920	+	0.273331i	$0.0881253\pi$
$734$	−46596.2			−2.34318
$735$		0			0
$736$	49453.8			2.47675
$737$	−11405.9	+	6585.22i	−0.570072	+	0.329131i
$738$	43119.7	+	24895.2i	2.15075	+	1.24174i
$739$	17437.2	−	30202.1i	0.867982	−	1.50339i	0.00392555	−	0.999992i	$-0.498750\pi$
$739$	17437.2	−	30202.1i	0.867982	−	1.50339i	0.864056	−	0.503396i	$-0.167916\pi$
$740$	5801.36	+	6439.29i	0.288192	+	0.319883i
$741$	98.5136			0.00488392
$742$		0			0
$743$		−	27686.7i		−	1.36706i	−0.729922	−	0.683530i	$-0.760444\pi$
$743$		−	27686.7i		−	1.36706i	0.729922	−	0.683530i	$-0.239556\pi$
$744$	8145.26	+	14108.0i	0.401371	+	0.695194i
$745$	345.612	+	112.185i	0.0169963	+	0.00551696i
$746$	30205.1	−	52316.8i	1.48242	−	2.56763i
$747$	−21002.0	+	12125.5i	−1.02868	+	0.593909i
$748$			14314.0i			0.699694i
$749$		0			0
$750$	8475.46	+	11644.1i	0.412640	+	0.566908i
$751$	−2403.42	−	4162.85i	−0.116781	−	0.202270i	0.801710	−	0.597714i	$-0.203924\pi$
$751$	−2403.42	−	4162.85i	−0.116781	−	0.202270i	−0.918490	+	0.395444i	$0.870591\pi$
$752$	−32899.7	−	18994.6i	−1.59538	−	0.921094i
$753$	−7922.79	−	4574.23i	−0.383430	−	0.221373i
$754$	−39851.8	−	69025.3i	−1.92482	−	3.33389i
$755$	1086.49	+	5104.21i	0.0523726	+	0.246041i
$756$		0			0
$757$			40166.6i			1.92851i	0.264983	+	0.964253i	$0.414634\pi$
$757$			40166.6i			1.92851i	−0.264983	+	0.964253i	$0.585366\pi$
$758$	−55853.4	+	32247.0i	−2.67637	+	1.54520i
$759$	−2689.95	+	4659.13i	−0.128642	+	0.222814i
$760$	177.831	−	547.851i	0.00848765	−	0.0261482i
$761$	12956.2	+	22440.7i	0.617162	+	1.06896i	0.990001	+	0.141060i	$0.0450512\pi$
$761$	12956.2	+	22440.7i	0.617162	+	1.06896i	−0.372839	+	0.927896i	$0.621616\pi$
$762$		−	1978.93i		−	0.0940803i
$763$		0			0
$764$	31273.1			1.48092
$765$	−4816.42	−	5346.04i	−0.227631	−	0.252662i
$766$	26221.9	−	45417.6i	1.23686	−	2.14230i
$767$	37698.4	+	21765.2i	1.77472	+	1.02464i
$768$	190.717	−	110.111i	0.00896082	−	0.00517353i
$769$	−23231.3			−1.08939			−0.544697	−	0.838633i	$-0.683355\pi$
$769$	−23231.3			−1.08939			−0.544697	+	0.838633i	$0.683355\pi$
$770$		0			0
$771$	12141.2			0.567125
$772$	40376.2	−	23311.2i	1.88234	−	1.08677i
$773$	724.262	+	418.153i

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.60176 + 2.65683i) q^{2} +(1.67956 + 0.969693i) q^{3} +(10.1175 - 17.5240i) q^{4} +(8.30643 - 7.48353i) q^{5} -10.3052 q^{6} +65.0123i q^{8} +(-11.6194 - 20.1254i) q^{9} +(-18.3418 + 56.5062i) q^{10} +(-12.7710 + 22.1200i) q^{11} +(33.9858 - 19.6217i) q^{12} +64.1014i q^{13} +(21.2079 - 4.51433i) q^{15} +(-91.7868 - 158.979i) q^{16} +(23.9847 + 13.8476i) q^{17} +(106.939 + 61.7415i) q^{18} +(-0.396218 - 0.686270i) q^{19} +(-47.1011 - 221.276i) q^{20} -135.721i q^{22} +(94.0560 - 54.3032i) q^{23} +(-63.0420 + 109.192i) q^{24} +(12.9936 - 124.323i) q^{25} +(-170.307 - 294.980i) q^{26} -97.4324i q^{27} +234.000 q^{29} +(-85.5997 + 77.1195i) q^{30} +(64.6019 - 111.894i) q^{31} +(394.343 + 227.674i) q^{32} +(-42.8992 + 24.7679i) q^{33} -147.163 q^{34} -470.236 q^{36} +(-33.1781 + 19.1554i) q^{37} +(3.64660 + 2.10537i) q^{38} +(-62.1587 + 107.662i) q^{39} +(486.522 + 540.021i) q^{40} +403.216 q^{41} +172.895i q^{43} +(258.420 + 447.597i) q^{44} +(-247.124 - 80.2160i) q^{45} +(-288.549 + 499.781i) q^{46} +(179.218 - 103.471i) q^{47} -356.020i q^{48} +(270.511 + 606.626i) q^{50} +(26.8558 + 46.5157i) q^{51} +(1123.31 + 648.545i) q^{52} +(-124.735 - 72.0155i) q^{53} +(258.861 + 448.361i) q^{54} +(59.4542 + 279.310i) q^{55} -1.53684i q^{57} +(-1076.81 + 621.699i) q^{58} +(339.543 - 588.105i) q^{59} +(135.461 - 417.320i) q^{60} +(-287.358 - 497.719i) q^{61} +686.544i q^{62} -950.977 q^{64} +(479.705 + 532.454i) q^{65} +(131.608 - 227.952i) q^{66} +(446.557 + 257.820i) q^{67} +(485.330 - 280.205i) q^{68} +210.630 q^{69} +556.612 q^{71} +(1308.40 - 755.404i) q^{72} +(-150.033 - 86.6217i) q^{73} +(101.785 - 176.297i) q^{74} +(142.379 - 196.207i) q^{75} -16.0349 q^{76} -660.580i q^{78} +(39.6645 + 68.7010i) q^{79} +(-1952.15 - 633.663i) q^{80} +(-219.244 + 379.742i) q^{81} +(-1855.50 + 1071.28i) q^{82} -1043.56i q^{83} +(302.856 - 64.4663i) q^{85} +(-459.352 - 795.620i) q^{86} +(393.017 + 226.909i) q^{87} +(-1438.07 - 830.271i) q^{88} +(-326.030 - 564.700i) q^{89} +(1350.33 - 287.432i) q^{90} -2197.65i q^{92} +(217.005 - 125.288i) q^{93} +(-549.812 + 952.302i) q^{94} +(-8.42688 - 2.73534i) q^{95} +(441.548 + 764.784i) q^{96} +515.714i q^{97} +593.564 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 36 q^{4} + 6 q^{5} - 24 q^{6} + 46 q^{9} - 16 q^{10} - 84 q^{11} + 16 q^{15} - 148 q^{16} + 72 q^{19} + 136 q^{20} + 72 q^{24} + 362 q^{25} - 620 q^{26} + 176 q^{29} - 52 q^{30} + 120 q^{31} - 1928 q^{34}+ \cdots - 10608 q^{99}+O(q^{100}) \) 20 * q + 36 * q^4 + 6 * q^5 - 24 * q^6 + 46 * q^9 - 16 * q^10 - 84 * q^11 + 16 * q^15 - 148 * q^16 + 72 * q^19 + 136 * q^20 + 72 * q^24 + 362 * q^25 - 620 * q^26 + 176 * q^29 - 52 * q^30 + 120 * q^31 - 1928 * q^34 - 840 * q^36 - 212 * q^39 + 1396 * q^40 + 1704 * q^41 + 1424 * q^44 - 510 * q^45 - 176 * q^46 + 3288 * q^50 - 1276 * q^51 - 996 * q^54 + 2272 * q^55 + 864 * q^59 + 1692 * q^60 - 884 * q^61 - 5448 * q^64 - 520 * q^65 + 1148 * q^66 - 9616 * q^69 + 1760 * q^71 - 3024 * q^74 + 720 * q^75 + 5344 * q^76 + 3580 * q^79 - 2316 * q^80 + 302 * q^81 + 3144 * q^85 - 2432 * q^86 - 1492 * q^89 + 15496 * q^90 + 1652 * q^94 + 1628 * q^95 + 4080 * q^96 - 10608 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more