LMFDB - Embedded newform 245.4.j.e.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.e.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	0.329601	−	0.944120i	$-0.393086\pi$
$3$	−1.67956	−	0.969693i	−0.323231	−	0.186617i	−0.652832	+	0.757503i	$0.726419\pi$
$4$	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	$-0.760330\pi$
$13$		−	64.1014i		−	1.36758i	0.729679	−	0.683790i	$-0.239670\pi$
$14$		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	0.319053	−	0.947737i	$-0.396635\pi$
$17$	−23.9847	−	13.8476i	−0.342185	−	0.197561i	−0.661238	+	0.750176i	$0.729969\pi$
$18$	106.939	+	61.7415i	1.40032	+	0.808478i
$19$	0.396218	+	0.686270i	0.00478414	+	0.00828637i	0.868408	−	0.495851i	$-0.165144\pi$
$19$	0.396218	+	0.686270i	0.00478414	+	0.00828637i	−0.863623	+	0.504137i	$0.831810\pi$
$20$	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	−0.990220	−	0.139516i	$-0.955445\pi$
$31$	−64.6019	+	111.894i	−0.374285	+	0.648281i	0.615935	+	0.787797i	$0.288779\pi$
$32$	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	$-0.778722\pi$
$41$	−403.216			−1.53590			−0.767949	+	0.640511i	$0.778722\pi$
$42$		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	−0.751621	−	0.659596i	$-0.770728\pi$
$47$	−179.218	+	103.471i	−0.556205	+	0.321125i	0.195416	+	0.980720i	$0.437394\pi$
$48$			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	$0.436244\pi$
$59$	−339.543	+	588.105i	−0.749232	+	1.29771i	−0.948191	+	0.317701i	$0.897089\pi$
$60$	135.461	−	417.320i	0.291466	−	0.897929i
$61$	287.358	+	497.719i	0.603155	+	1.04470i	0.992340	+	0.123536i	$0.0394234\pi$
$61$	287.358	+	497.719i	0.603155	+	1.04470i	−0.389185	+	0.921160i	$0.627243\pi$
$62$		−	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	0.615429	−	0.788192i	$-0.288983\pi$
$73$	150.033	+	86.6217i	0.240549	+	0.138881i	−0.374880	+	0.927073i	$0.622316\pi$
$74$	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	$0.242404\pi$
$83$			1043.56i			1.38007i	−0.723777	+	0.690034i	$0.757596\pi$
$84$		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	0.992222	−	0.124484i	$-0.0397276\pi$
$89$	326.030	+	564.700i	0.388304	+	0.672563i	−0.603917	+	0.797047i	$0.706394\pi$
$90$	−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	$-0.913005\pi$
$97$		−	515.714i		−	0.539823i	0.962885	−	0.269912i	$-0.0869945\pi$
$98$		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	−0.703156	−	0.711036i	$-0.748226\pi$
$101$	268.170	−	464.484i	0.264197	−	0.457602i	0.967353	+	0.253433i	$0.0815598\pi$
$102$	−247.168	−	142.703i	−0.239934	−	0.138526i
$103$	330.556	−	190.846i	0.316220	−	0.182570i	−0.333487	−	0.942755i	$-0.608225\pi$
$103$	330.556	−	190.846i	0.316220	−	0.182570i	0.649706	+	0.760185i	$0.274892\pi$
$104$	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	$-0.922251\pi$
$131$	−1041.45	−	1803.84i	−0.694594	−	1.20307i	0.275723	−	0.961237i	$-0.411083\pi$
$132$		−	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	$-0.639801\pi$
$139$	−1393.67			−0.850426			−0.425213	+	0.905093i	$0.639801\pi$
$140$		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	0.820879	−	0.571103i	$-0.193484\pi$
$157$	1449.30	+	836.751i	0.736729	+	0.425351i	−0.0841500	+	0.996453i	$0.526817\pi$
$158$	−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	$-0.996569\pi$
$167$		−	46.5250i		−	0.0215581i	0.999942	−	0.0107791i	$-0.00343115\pi$
$168$		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	0.0569648	−	0.998376i	$-0.481858\pi$
$173$	2161.84	−	1248.14i	0.950066	−	0.548521i	0.893102	+	0.449855i	$0.148524\pi$
$174$	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	$-0.436424\pi$
$181$	966.273			0.396809			0.198405	+	0.980120i	$0.436424\pi$
$182$		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	$-0.613205\pi$
$199$	1790.28	−	3100.85i	0.637736	−	1.10459i	0.985928	−	0.167168i	$-0.0534622\pi$
$200$	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	$0.115374\pi$
$223$			2361.52i			0.709145i	−0.935028	+	0.354573i	$0.884626\pi$
$224$		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	0.572460	−	0.819933i	$-0.305989\pi$
$227$	508.250	+	293.438i	0.148607	+	0.0857982i	−0.423853	+	0.905731i	$0.639323\pi$
$228$	−26.9315	−	15.5489i	−0.00782274	−	0.00451646i
$229$	−2309.78	−	4000.65i	−0.666526	−	1.15446i	−0.978869	−	0.204487i	$-0.934447\pi$
$229$	−2309.78	−	4000.65i	−0.666526	−	1.15446i	0.312344	−	0.949969i	$-0.398886\pi$
$230$	−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	−0.525201	−	0.850978i	$-0.676010\pi$
$241$	1774.77	−	3073.98i	0.474368	−	0.821630i	0.999569	+	0.0293484i	$0.00934323\pi$
$242$	−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	$-0.297896\pi$
$251$	4717.19			1.18624			0.593120	+	0.805114i	$0.297896\pi$
$252$		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	−0.983068	−	0.183239i	$-0.941342\pi$
$257$	−5421.59	+	3130.16i	−1.31591	+	0.759742i	−0.332844	+	0.942982i	$0.608008\pi$
$258$			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	$0.461841\pi$
$269$	−3529.60	+	6113.45i	−0.800014	+	1.38566i	−0.919606	+	0.392841i	$0.871492\pi$
$270$	5505.53	+	1787.08i	1.24095	+	0.402809i
$271$	4267.26	+	7391.11i	0.956523	+	1.65675i	0.730844	+	0.682544i	$0.239126\pi$
$271$	4267.26	+	7391.11i	0.956523	+	1.65675i	0.225678	+	0.974202i	$0.427540\pi$
$272$			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	$0.0687795\pi$
$283$	7859.10	+	4537.45i	1.65079	+	0.953087i	0.674049	+	0.738687i	$0.264554\pi$
$284$	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	$-0.911907\pi$
$293$		−	2740.72i		−	0.546466i	0.961948	−	0.273233i	$-0.0880930\pi$
$294$		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	$0.224946\pi$
$307$			6985.46i			1.29864i	−0.760517	+	0.649318i	$0.775054\pi$
$308$		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	−0.849301	−	0.527908i	$-0.822976\pi$
$311$	178.421	−	309.033i	0.0325315	−	0.0563462i	0.881833	+	0.471562i	$0.156310\pi$
$312$	−6999.36	−	4041.08i	−1.27007	−	0.733273i
$313$	5741.85	−	3315.06i	1.03690	−	0.598653i	0.117944	−	0.993020i	$-0.462370\pi$
$313$	5741.85	−	3315.06i	1.03690	−	0.598653i	0.918953	+	0.394368i	$0.129036\pi$
$314$	−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	$-0.474646\pi$
$349$	1037.55			0.159137			0.0795683	+	0.996829i	$0.474646\pi$
$350$		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	0.208833	−	0.977951i	$-0.433033\pi$
$353$	−3539.51	−	2043.54i	−0.533681	−	0.308121i	−0.742514	+	0.669830i	$0.766367\pi$
$354$	−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	−0.149221	−	0.988804i	$-0.547677\pi$
$367$	−7594.29	−	4384.57i	−1.08016	−	0.623631i	−0.930940	+	0.365173i	$0.881010\pi$
$368$	−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	0.193821	−	0.981037i	$-0.437912\pi$
$383$	8547.33	−	4934.80i	1.14033	−	0.658373i	0.946514	+	0.322664i	$0.104578\pi$
$384$	−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	−0.848388	−	0.529374i	$-0.822427\pi$
$397$	−6439.91	+	3718.09i	−0.814131	+	0.470039i	0.0342574	+	0.999413i	$0.489093\pi$
$398$			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	−0.913038	−	0.407875i	$-0.866270\pi$
$409$	−854.358	+	1479.79i	−0.103289	+	0.178902i	0.809749	+	0.586777i	$0.199603\pi$
$410$	−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	$-0.712482\pi$
$419$	−10618.8			−1.23810			−0.619050	+	0.785352i	$0.712482\pi$
$420$		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	$0.0791226\pi$
$433$			4433.34i			0.492038i	−0.969265	+	0.246019i	$0.920877\pi$
$434$		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	$0.0821206\pi$
$439$	6479.19	+	11222.3i	0.704408	+	1.22007i	−0.262497	+	0.964933i	$0.584546\pi$
$440$	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	$-0.521618\pi$
$461$	−1343.41			−0.135724			−0.0678621	+	0.997695i	$0.521618\pi$
$462$		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	0.287335	−	0.957830i	$-0.407231\pi$
$467$	12721.0	−	7344.47i	1.26051	−	0.727755i	0.973173	+	0.230076i	$0.0738974\pi$
$468$			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	$0.426987\pi$
$479$	−7649.31	+	13249.0i	−0.729657	+	1.26380i	−0.957028	+	0.289995i	$0.906346\pi$
$480$	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	$0.0308912\pi$
$503$			2186.17i			0.193791i	−0.995295	+	0.0968953i	$0.969109\pi$
$504$		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	0.933553	−	0.358439i	$-0.116691\pi$
$509$	1795.56	+	3110.00i	0.156359	+	0.270822i	−0.777194	+	0.629261i	$0.783358\pi$
$510$	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	−0.626448	−	0.779463i	$-0.715492\pi$
$521$	4302.67	−	7452.44i	0.361811	−	0.626674i	0.988259	+	0.152789i	$0.0488254\pi$
$522$	25023.9	+	14447.5i	2.09821	+	1.21140i
$523$	19517.1	−	11268.2i	1.63179	−	0.942113i	0.648245	−	0.761432i	$-0.275503\pi$
$523$	19517.1	−	11268.2i	1.63179	−	0.942113i	0.983542	−	0.180681i	$-0.0578301\pi$
$524$	−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	0.369936	−	0.929057i	$-0.379380\pi$
$563$	−3335.43	−	1925.71i	−0.249683	−	0.144154i	−0.619619	+	0.784903i	$0.712713\pi$
$564$	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	0.112979	−	0.993597i	$-0.463961\pi$
$577$	−9577.44	−	5529.54i	−0.691012	−	0.398956i	−0.803991	+	0.594641i	$0.797294\pi$
$578$	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	$0.0892509\pi$
$587$			7871.25i			0.553461i	−0.960948	+	0.276730i	$0.910749\pi$
$588$		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	−0.559291	−	0.828971i	$-0.688927\pi$
$593$	−1747.69	+	1009.03i	−0.121027	+	0.0698750i	0.438264	+	0.898846i	$0.355593\pi$
$594$	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	$-0.376145\pi$
$601$	11178.7			0.758715			0.379358	+	0.925250i	$0.376145\pi$
$602$		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	−0.746948	−	0.664882i	$-0.768482\pi$
$607$	−8144.69	+	4702.34i	−0.544617	+	0.314435i	0.202331	+	0.979317i	$0.435148\pi$
$608$			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	−0.949366	−	0.314173i	$-0.898273\pi$
$619$	−3120.16	+	5404.28i	−0.202601	+	0.350915i	0.746765	+	0.665088i	$0.231606\pi$
$620$	−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	$-0.977651\pi$
$643$		−	2287.70i		−	0.140308i	0.997536	−	0.0701541i	$-0.0223491\pi$
$644$		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	0.545830	−	0.837896i	$-0.316214\pi$
$647$	1532.27	+	884.654i	0.0931060	+	0.0537548i	−0.452724	+	0.891651i	$0.649548\pi$
$648$	−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	$-0.538523\pi$
$661$	13584.0	−	23528.1i	0.799326	−	1.38447i	0.920056	−	0.391788i	$-0.128143\pi$
$662$	−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	−0.603316	−	0.797502i	$-0.706154\pi$
$677$	−3775.19	+	2179.61i	−0.214317	+	0.123736i	0.388999	+	0.921238i	$0.372821\pi$
$678$			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	0.925858	−	0.377872i	$-0.123344\pi$
$691$	2464.57	+	4268.75i	0.135682	+	0.235009i	−0.790176	+	0.612881i	$0.790011\pi$
$692$		−	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	0.600888	−	0.799333i	$-0.294814\pi$
$719$	−7553.65	−	13083.3i	−0.391799	−	0.678616i	−0.992687	+	0.120717i	$0.961481\pi$
$720$	−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	$0.132402\pi$
$727$			15840.9i			0.808124i	−0.914732	+	0.404062i	$0.867598\pi$
$728$		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	−0.961920	−	0.273331i	$-0.911875\pi$
$733$	−23936.7	+	13819.9i	−1.20617	+	0.696382i	−0.244249	+	0.969713i	$0.578541\pi$
$734$	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	$-0.954949\pi$
$761$	−12956.2	−	22440.7i	−0.617162	−	1.06896i	0.372839	−	0.927896i	$-0.378384\pi$
$762$			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	$-0.316645\pi$
$769$	23231.3			1.08939			0.544697	+	0.838633i	$0.316645\pi$
$770$		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