LMFDB - Embedded newform 245.4.j.e.79.10

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			79.10
Root			$3.73574 - 2.15683i$ of defining polynomial
Character	$\chi$	$=$	245.79
Dual form			245.4.j.e.214.10

$q$-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} +(10.6341 + 3.45182i) q^{5} +10.3052 q^{6} +65.0123i q^{8} +(-11.6194 + 20.1254i) q^{9} +(39.7649 + 44.1375i) 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} +(101.170 + 73.4142i) q^{25} +(170.307 - 294.980i) q^{26} +97.4324i q^{27} +234.000 q^{29} +(109.587 + 35.5718i) 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} +(-224.411 + 691.350i) q^{40} -403.216 q^{41} +172.895i q^{43} +(258.420 - 447.597i) q^{44} +(-193.031 + 173.908i) 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} +(293.679 + 325.972i) q^{60} +(287.358 - 497.719i) q^{61} -686.544i q^{62} -950.977 q^{64} +(221.266 - 681.664i) 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} +(241.110 + 25.1997i) q^{75} +16.0349 q^{76} -660.580i q^{78} +(39.6645 - 68.7010i) q^{79} +(-1524.84 + 1373.78i) 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} +(6.58232 - 5.93022i) 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 $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

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

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	0.984991	+	0.172608i	$0.0552192\pi$
$2$	4.60176	+	2.65683i	1.62697	+	0.939331i	0.641978	+	0.766723i	$0.278114\pi$
$3$	1.67956	−	0.969693i	0.323231	−	0.186617i	−0.329601	−	0.944120i	$-0.606914\pi$
$3$	1.67956	−	0.969693i	0.323231	−	0.186617i	0.652832	+	0.757503i	$0.273581\pi$
$4$	10.1175	+	17.5240i	1.26468	+	2.19050i
$5$	10.6341	+	3.45182i	0.951146	+	0.308740i
$5$	10.6341	+	3.45182i	0.951146	+	0.308740i
$6$	10.3052			0.701182
$7$		0			0
$7$		0			0
$8$			65.0123i			2.87317i
$9$	−11.6194	+	20.1254i	−0.430348	+	0.745384i
$10$	39.7649	+	44.1375i	1.25748	+	1.39575i
$11$	−12.7710	−	22.1200i	−0.350054	−	0.606311i	0.636205	−	0.771520i	$-0.280503\pi$
$11$	−12.7710	−	22.1200i	−0.350054	−	0.606311i	−0.986259	+	0.165209i	$0.947170\pi$
$12$	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	$-0.603365\pi$
$17$	23.9847	−	13.8476i	0.342185	−	0.197561i	0.661238	+	0.750176i	$0.270031\pi$
$18$	−106.939	+	61.7415i	−1.40032	+	0.808478i
$19$	0.396218	−	0.686270i	0.00478414	−	0.00828637i	−0.863623	−	0.504137i	$-0.831810\pi$
$19$	0.396218	−	0.686270i	0.00478414	−	0.00828637i	0.868408	+	0.495851i	$0.165144\pi$
$20$	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	$-0.497179\pi$
$23$	−94.0560	−	54.3032i	−0.852697	−	0.492305i	−0.861560	+	0.507656i	$0.830512\pi$
$24$	63.0420	+	109.192i	0.536183	+	0.928696i
$25$	101.170	+	73.4142i	0.809359	+	0.587314i
$26$	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	$0.230445\pi$
$30$	109.587	+	35.5718i	0.666927	+	0.216483i
$31$	−64.6019	−	111.894i	−0.374285	−	0.648281i	0.615935	−	0.787797i	$-0.288779\pi$
$31$	−64.6019	−	111.894i	−0.374285	−	0.648281i	−0.990220	+	0.139516i	$0.955445\pi$
$32$	−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	$-0.306209\pi$
$37$	33.1781	+	19.1554i	0.147418	+	0.0851116i	−0.424477	+	0.905439i	$0.639542\pi$
$38$	3.64660	−	2.10537i	0.0155673	−	0.00898778i
$39$	−62.1587	−	107.662i	−0.255214	−	0.442044i
$40$	−224.411	+	691.350i	−0.887061	+	2.73280i
$41$	−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
$45$	−193.031	+	173.908i	−0.639454	+	0.576104i
$46$	−288.549	−	499.781i	−0.924874	−	1.60193i
$47$	179.218	+	103.471i	0.556205	+	0.321125i	0.751621	−	0.659596i	$-0.229272\pi$
$47$	179.218	+	103.471i	0.556205	+	0.321125i	−0.195416	+	0.980720i	$0.562606\pi$
$48$			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	$-0.606906\pi$
$53$	124.735	−	72.0155i	0.323276	−	0.186643i	0.652852	+	0.757486i	$0.273572\pi$
$54$	−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	−0.948191	−	0.317701i	$-0.897089\pi$
$59$	−339.543	−	588.105i	−0.749232	−	1.29771i	0.198959	−	0.980008i	$-0.436244\pi$
$60$	293.679	+	325.972i	0.631896	+	0.701381i
$61$	287.358	−	497.719i	0.603155	−	1.04470i	−0.389185	−	0.921160i	$-0.627243\pi$
$61$	287.358	−	497.719i	0.603155	−	1.04470i	0.992340	−	0.123536i	$-0.0394234\pi$
$62$		−	686.544i		−	1.40631i
$63$		0			0
$64$	−950.977			−1.85738
$65$	221.266	−	681.664i	0.422227	−	1.30077i
$66$	−131.608	−	227.952i	−0.245452	−	0.425135i
$67$	−446.557	+	257.820i	−0.814263	+	0.470115i	−0.848434	−	0.529301i	$-0.822454\pi$
$67$	−446.557	+	257.820i	−0.814263	+	0.470115i	0.0341709	+	0.999416i	$0.489121\pi$
$68$	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	$-0.711017\pi$
$73$	−150.033	+	86.6217i	−0.240549	+	0.138881i	0.374880	+	0.927073i	$0.377684\pi$
$74$	101.785	+	176.297i	0.159896	+	0.276948i
$75$	241.110	+	25.1997i	0.371213	+	0.0387974i
$76$	16.0349			0.0242017
$77$		0			0
$78$		−	660.580i		−	0.958923i
$79$	39.6645	−	68.7010i	0.0564887	−	0.0978413i	−0.836398	−	0.548122i	$-0.815343\pi$
$79$	39.6645	−	68.7010i	0.0564887	−	0.0978413i	0.892887	+	0.450281i	$0.148676\pi$
$80$	−1524.84	+	1373.78i	−2.13103	+	1.91991i
$81$	−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	−0.603917	−	0.797047i	$-0.706394\pi$
$89$	326.030	−	564.700i	0.388304	−	0.672563i	0.992222	+	0.124484i	$0.0397276\pi$
$90$	−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
$95$	6.58232	−	5.93022i	0.00710875	−	0.00640450i
$96$	−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
$100$	−262.926	+	2515.67i	−0.262926	+	2.51567i
$101$	268.170	+	464.484i	0.264197	+	0.457602i	0.967353	−	0.253433i	$-0.0815598\pi$
$101$	268.170	+	464.484i	0.264197	+	0.457602i	−0.703156	+	0.711036i	$0.748226\pi$
$102$	247.168	−	142.703i	0.239934	−	0.138526i
$103$	−330.556	−	190.846i	−0.316220	−	0.182570i	0.333487	−	0.942755i	$-0.391775\pi$
$103$	−330.556	−	190.846i	−0.316220	−	0.182570i	−0.649706	+	0.760185i	$0.725108\pi$
$104$	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	$-0.547792\pi$
$107$	−1196.08	−	690.560i	−1.08065	−	0.623915i	−0.931072	+	0.364835i	$0.881126\pi$
$108$	−1707.40	+	985.770i	−1.52125	+	0.878294i
$109$	−195.291	−	338.254i	−0.171610	−	0.297237i	0.767373	−	0.641201i	$-0.221564\pi$
$109$	−195.291	−	338.254i	−0.171610	−	0.297237i	−0.938983	+	0.343964i	$0.888230\pi$
$110$	468.485	−	1443.28i	0.406075	−	1.25101i
$111$	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
$115$	−812.759	−	902.132i	−0.659045	−	0.731515i
$116$	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
$130$	2829.28	−	2548.99i	1.90880	−	1.71970i
$131$	−1041.45	+	1803.84i	−0.694594	+	1.20307i	0.275723	+	0.961237i	$0.411083\pi$
$131$	−1041.45	+	1803.84i	−0.694594	+	1.20307i	−0.970317	+	0.241835i	$0.922251\pi$
$132$		−	1002.35i		−	0.660936i
$133$		0			0
$134$	−2739.93			−1.76637
$135$	−336.319	+	1036.11i	−0.214413	+	0.660549i
$136$	900.264	+	1559.30i	0.567625	+	0.983156i
$137$	67.6980	−	39.0855i	0.0422177	−	0.0243744i	−0.478743	−	0.877955i	$-0.658907\pi$
$137$	67.6980	−	39.0855i	0.0422177	−	0.0243744i	0.520960	+	0.853581i	$0.325574\pi$
$138$	−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
$145$	2488.39	+	807.727i	1.42517	+	0.462607i
$146$	−920.556			−0.521820
$147$		0			0
$148$			775.217i			0.430557i
$149$	16.2501	−	28.1460i	0.00893463	−	0.0154752i	−0.861524	−	0.507718i	$-0.830489\pi$
$149$	16.2501	−	28.1460i	0.00893463	−	0.0154752i	0.870458	+	0.492242i	$0.163823\pi$
$150$	1042.58	+	756.551i	0.567508	+	0.411814i
$151$	−233.381	−	404.228i	−0.125777	−	0.217852i	0.796260	−	0.604955i	$-0.206809\pi$
$151$	−233.381	−	404.228i	−0.125777	−	0.217852i	−0.922036	+	0.387103i	$0.873476\pi$
$152$	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	$-0.806516\pi$
$157$	−1449.30	+	836.751i	−0.736729	+	0.425351i	0.0841500	+	0.996453i	$0.473183\pi$
$158$	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	$-0.481603\pi$
$163$	−1618.91	−	934.679i	−0.777932	−	0.449139i	−0.835697	+	0.549191i	$0.814936\pi$
$164$	−4079.53	−	7065.95i	−1.94243	−	3.36438i
$165$	−370.702	−	411.465i	−0.174904	−	0.194136i
$166$	−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
$170$	1564.95	+	507.979i	0.706036	+	0.229178i
$171$	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	$-0.518142\pi$
$173$	−2161.84	−	1248.14i	−0.950066	−	0.548521i	−0.893102	+	0.449855i	$0.851476\pi$
$174$	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	0.989250	+	0.146236i	$0.0467158\pi$
$179$	1487.85	+	2577.03i	0.621269	+	1.07607i	−0.367981	+	0.929833i	$0.619951\pi$
$180$	−5000.55	−	1623.17i	−2.07066	−	0.672132i
$181$	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
$185$	286.700	+	318.226i	0.113938	+	0.126467i
$186$	−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	−0.681713	−	0.731619i	$-0.738765\pi$
$191$	772.749	−	1338.44i	0.292744	−	0.507048i	0.974458	+	0.224571i	$0.0720982\pi$
$192$	−1597.22	+	922.156i	−0.600362	+	0.346619i
$193$	−1995.37	+	1152.03i	−0.744195	+	0.429661i	−0.823593	−	0.567182i	$-0.808034\pi$
$193$	−1995.37	+	1152.03i	−0.744195	+	0.429661i	0.0793975	+	0.996843i	$0.474700\pi$
$194$	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	0.985928	+	0.167168i	$0.0534622\pi$
$199$	1790.28	+	3100.85i	0.637736	+	1.10459i	−0.348193	+	0.937423i	$0.613205\pi$
$200$	−4772.83	+	6577.29i	−1.68745	+	2.32542i
$201$	−500.012	+	866.047i	−0.175463	+	0.303912i
$202$			2849.92i			0.992673i
$203$		0			0
$204$	1086.85			0.373014
$205$	−4287.86	−	1391.83i	−1.46086	−	0.474193i
$206$	−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
$215$	−596.801	+	1838.59i	−0.189309	+	0.583212i
$216$	−6334.31			−1.99535
$217$		0			0
$218$		−	2075.42i		−	0.644794i
$219$	−167.993	+	290.972i	−0.0518352	+	0.0897812i
$220$	4293.10	−	3867.79i	1.31564	−	1.18530i
$221$	−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	$-0.694011\pi$
$227$	−508.250	+	293.438i	−0.148607	+	0.0857982i	0.423853	+	0.905731i	$0.360677\pi$
$228$	26.9315	−	15.5489i	0.00782274	−	0.00451646i
$229$	−2309.78	+	4000.65i	−0.666526	+	1.15446i	0.312344	+	0.949969i	$0.398886\pi$
$229$	−2309.78	+	4000.65i	−0.666526	+	1.15446i	−0.978869	+	0.204487i	$0.934447\pi$
$230$	−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	$-0.0775426\pi$
$233$	4434.43	+	2560.22i	1.24682	+	0.719853i	0.276347	+	0.961058i	$0.410876\pi$
$234$	3957.72	+	6854.97i	1.10566	+	1.91506i
$235$	1548.66	+	1718.96i	0.429888	+	0.477159i
$236$	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	$0.548758\pi$
$240$	−1228.92	+	3785.97i	−0.330526	+	1.01826i
$241$	1774.77	+	3073.98i	0.474368	+	0.821630i	0.999569	−	0.0293484i	$-0.00934323\pi$
$241$	1774.77	+	3073.98i	0.474368	+	0.821630i	−0.525201	+	0.850978i	$0.676010\pi$
$242$	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
$250$	782.688	+	7384.70i	0.198006	+	1.86820i
$251$	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
$255$	446.152	−	401.953i	0.109565	−	0.0987108i
$256$	56.7760	+	98.3390i	0.0138613	+	0.0240085i
$257$	5421.59	+	3130.16i	1.31591	+	0.759742i	0.983068	−	0.183239i	$-0.0586584\pi$
$257$	5421.59	+	3130.16i	1.31591	+	0.759742i	0.332844	+	0.942982i	$0.391992\pi$
$258$			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	$-0.902275\pi$
$263$	−4982.28	+	2876.52i	−1.16814	+	0.674425i	−0.214897	+	0.976637i	$0.568942\pi$
$264$	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	−0.919606	−	0.392841i	$-0.871492\pi$
$269$	−3529.60	−	6113.45i	−0.800014	−	1.38566i	0.119593	−	0.992823i	$-0.461841\pi$
$270$	−4300.42	+	3874.39i	−0.969317	+	0.873288i
$271$	4267.26	−	7391.11i	0.956523	−	1.65675i	0.225678	−	0.974202i	$-0.427540\pi$
$271$	4267.26	−	7391.11i	0.956523	−	1.65675i	0.730844	−	0.682544i	$-0.239126\pi$
$272$			5084.11i			1.13334i
$273$		0			0
$274$	415.373			0.0915826
$275$	331.883	−	3175.45i	0.0727756	−	0.696315i
$276$	−2131.04	−	3691.07i	−0.464760	−	0.804987i
$277$	1137.91	−	656.972i	0.246824	−	0.142504i	−0.371485	−	0.928439i	$-0.621151\pi$
$277$	1137.91	−	656.972i	0.246824	−	0.142504i	0.618309	+	0.785935i	$0.287818\pi$
$278$	−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	−0.674049	+	0.738687i	$0.735446\pi$
$283$	−7859.10	+	4537.45i	−1.65079	+	0.953087i	−0.976746	+	0.214400i	$0.931221\pi$
$284$	5631.51	+	9754.07i	1.17665	+	2.03802i
$285$	5.30489	−	16.3430i	0.00110258	−	0.00339675i
$286$	−8699.92			−1.79873
$287$		0			0
$288$		−	10581.7i		−	2.16505i
$289$	−2072.99	+	3590.52i	−0.421939	+	0.730820i
$290$	9305.00	+	10328.2i	1.88417	+	2.09135i
$291$	−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
$305$	4773.85	−	4300.91i	0.896228	−	0.807441i
$306$	−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
$310$	2369.83	−	7300.81i	0.434184	−	1.33761i
$311$	178.421	+	309.033i	0.0325315	+	0.0563462i	0.881833	−	0.471562i	$-0.156310\pi$
$311$	178.421	+	309.033i	0.0325315	+	0.0563462i	−0.849301	+	0.527908i	$0.822976\pi$
$312$	6999.36	−	4041.08i	1.27007	−	0.733273i
$313$	−5741.85	−	3315.06i	−1.03690	−	0.598653i	−0.117944	−	0.993020i	$-0.537630\pi$
$313$	−5741.85	−	3315.06i	−1.03690	−	0.598653i	−0.918953	+	0.394368i	$0.870964\pi$
$314$	−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	$-0.262419\pi$
$317$	2159.91	+	1247.02i	0.382689	+	0.220946i	−0.296298	+	0.955095i	$0.595752\pi$
$318$	1285.42	−	742.137i	0.226675	−	0.130871i
$319$	−2988.41	−	5176.08i	−0.524511	−	0.908480i
$320$	−10112.8	−	3282.60i	−1.76664	−	0.573447i
$321$	−2678.52			−0.465734
$322$		0			0
$323$		−	21.9467i		−	0.00378063i
$324$	4436.39	−	7684.06i	0.760698	−	1.31757i
$325$	4705.96	−	6485.14i	0.803199	−	1.10686i
$326$	−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	−0.603506	−	0.797358i	$-0.706230\pi$
$331$	2341.23	−	4055.14i	0.388779	−	0.673385i	0.992286	+	0.123973i	$0.0395636\pi$
$332$	−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
$340$	4193.85	+	4655.01i	0.668951	+	0.742511i
$341$	−1650.06	+	2857.98i	−0.262040	+	0.453867i
$342$			97.8523i			0.0154715i
$343$		0			0
$344$	−11240.3			−1.76173
$345$	−2239.87	−	727.056i	−0.349537	−	0.113459i
$346$	−6632.18	−	11487.3i	−1.03049	−	1.78485i
$347$	1645.03	−	949.756i	0.254495	−	0.146932i	−0.367326	−	0.930092i	$-0.619727\pi$
$347$	1645.03	−	949.756i	0.254495	−	0.146932i	0.621821	+	0.783160i	$0.286393\pi$
$348$	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	$-0.566967\pi$
$353$	3539.51	−	2043.54i	0.533681	−	0.308121i	0.742514	+	0.669830i	$0.233633\pi$
$354$	−3499.07	−	6060.56i	−0.525348	−	0.909930i
$355$	5919.10	+	1921.32i	0.884938	+	0.287249i
$356$	13194.4			1.96433
$357$		0			0
$358$			15811.8i			2.33431i
$359$	1736.33	−	3007.42i	0.255265	−	0.442132i	−0.709702	−	0.704502i	$-0.751171\pi$
$359$	1736.33	−	3007.42i	0.255265	−	0.442132i	0.964967	+	0.262369i	$0.0845039\pi$
$360$	−11306.2	−	12549.4i	−1.65524	−	1.83726i
$361$	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	$-0.452323\pi$
$367$	7594.29	−	4384.57i	1.08016	−	0.623631i	0.930940	+	0.365173i	$0.118990\pi$
$368$	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	$-0.0438883\pi$
$373$	9845.73	+	5684.43i	1.36674	+	0.789085i	0.376226	+	0.926528i	$0.377222\pi$
$374$	−1879.41	−	3255.24i	−0.259845	−	0.450065i
$375$	2477.01	+	1100.24i	0.341100	+	0.151510i
$376$	−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	$0.192578\pi$
$380$	170.517	+	55.3496i	0.0230194	+	0.00747203i
$381$	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	$-0.562088\pi$
$383$	−8547.33	−	4934.80i	−1.14033	−	0.658373i	−0.946514	+	0.322664i	$0.895422\pi$
$384$	−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	0.867881	−	0.496773i	$-0.165482\pi$
$389$	28.5583	+	49.4644i	0.00372227	+	0.00644716i	−0.864158	+	0.503220i	$0.832148\pi$
$390$	2280.20	−	7024.70i	0.296058	−	0.912076i
$391$	−3007.88			−0.389041
$392$		0			0
$393$			4039.54i			0.518494i
$394$	−589.871	+	1021.69i	−0.0754245	+	0.130639i
$395$	658.941	−	593.661i	0.0839365	−	0.0756211i
$396$	6005.37	+	10401.6i	0.762073	+	1.31995i
$397$	6439.91	+	3718.09i	0.814131	+	0.470039i	0.848388	−	0.529374i	$-0.177573\pi$
$397$	6439.91	+	3718.09i	0.814131	+	0.470039i	−0.0342574	+	0.999413i	$0.510907\pi$
$398$			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	−0.157998	−	0.987439i	$-0.550504\pi$
$401$	6232.49	−	10795.0i	0.776149	−	1.34433i	0.934147	−	0.356890i	$-0.116163\pi$
$402$	−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	$-0.199603\pi$
$409$	−854.358	−	1479.79i	−0.103289	−	0.178902i	−0.913038	+	0.407875i	$0.866270\pi$
$410$	−16033.8	−	17797.0i	−1.93135	−	2.14373i
$411$	75.8018	−	131.293i	0.00909739	−	0.0157571i
$412$		−	7723.54i		−	0.923571i
$413$		0			0
$414$	13411.0			1.59207
$415$	−3602.18	+	11097.4i	−0.426082	+	1.31265i
$416$	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
$425$	3443.14	+	359.861i	0.392981	+	0.0410725i
$426$	5736.02			0.652373
$427$		0			0
$428$		−	27946.9i		−	3.15622i
$429$	−1587.65	+	2749.90i	−0.178678	+	0.309479i
$430$	−7631.15	+	6875.14i	−0.855829	+	0.771044i
$431$	−3959.10	−	6857.37i	−0.442467	−	0.766375i	0.555405	−	0.831580i	$-0.312563\pi$
$431$	−3959.10	−	6857.37i	−0.442467	−	0.766375i	−0.997872	+	0.0652048i	$0.979230\pi$
$432$	−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	−0.262497	−	0.964933i	$-0.584546\pi$
$439$	6479.19	−	11222.3i	0.704408	−	1.22007i	0.966905	−	0.255137i	$-0.0821206\pi$
$440$	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	$-0.109914\pi$
$443$	10427.3	+	6020.22i	1.11832	+	0.645664i	0.177351	+	0.984148i	$0.443247\pi$
$444$	751.723	+	1302.02i	0.0803495	+	0.139169i
$445$	5416.29	−	4879.71i	0.576981	−	0.519821i
$446$	−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	$0.708389\pi$
$450$	−15351.7	−	1604.49i	−1.60820	−	0.168081i
$451$	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	$-0.167329\pi$
$457$	8430.18	+	4867.17i	0.862904	+	0.498198i	−0.00207942	+	0.999998i	$0.500662\pi$
$458$	−21258.1	+	12273.4i	−2.16883	+	1.25218i
$459$	1349.20	+	2336.89i	0.137201	+	0.237640i
$460$	7585.87	−	23370.1i	0.768898	−	2.36877i
$461$	−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
$465$	−1875.19	−	2081.39i	−0.187011	−	0.207575i
$466$	13604.1	+	23563.1i	1.35236	+	2.34236i
$467$	−12721.0	−	7344.47i	−1.26051	−	0.727755i	−0.287335	−	0.957830i	$-0.592769\pi$
$467$	−12721.0	−	7344.47i	−1.26051	−	0.727755i	−0.973173	+	0.230076i	$0.926103\pi$
$468$			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	−0.957028	−	0.289995i	$-0.906346\pi$
$479$	−7649.31	−	13249.0i	−0.729657	−	1.26380i	0.227371	−	0.973808i	$-0.426987\pi$
$480$	−7335.38	+	6608.68i	−0.697527	+	0.628424i
$481$	1227.89	−	2126.77i	0.116397	−	0.201605i
$482$			18861.0i			1.78235i
$483$		0			0
$484$	13731.6			1.28960
$485$	1780.15	−	5484.18i	0.166665	−	0.513451i
$486$	−9248.61	−	16019.1i	−0.863221	−	1.49514i
$487$	8360.44	−	4826.90i	0.777921	−	0.449133i	−0.0577719	−	0.998330i	$-0.518400\pi$
$487$	8360.44	−	4826.90i	0.777921	−	0.449133i	0.835693	+	0.549197i	$0.185066\pi$
$488$	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
$495$	6312.04	+	2048.87i	0.573142	+	0.186041i
$496$	23718.4			2.14715
$497$		0			0
$498$			10754.1i			0.967679i
$499$	−654.645	+	1133.88i	−0.0587293	+	0.101722i	−0.893895	−	0.448276i	$-0.852038\pi$
$499$	−654.645	+	1133.88i	−0.0587293	+	0.101722i	0.835166	+	0.549998i	$0.185372\pi$
$500$	−11479.6	+	25844.4i	−1.02677	+	2.31159i
$501$	−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	−0.777194	−	0.629261i	$-0.783358\pi$
$509$	1795.56	−	3110.00i	0.156359	−	0.270822i	0.933553	+	0.358439i	$0.116691\pi$
$510$	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
$515$	−2856.41	−	3170.51i	−0.244405	−	0.271280i
$516$	−3392.49	+	5875.96i	−0.289430	+	0.501307i
$517$		−	5285.73i		−	0.449644i
$518$		0			0
$519$	−4841.24			−0.409455
$520$	44316.5	+	14385.0i	3.73733	+	1.21313i
$521$	4302.67	+	7452.44i	0.361811	+	0.626674i	0.988259	−	0.152789i	$-0.0488254\pi$
$521$	4302.67	+	7452.44i	0.361811	+	0.626674i	−0.626448	+	0.779463i	$0.715492\pi$
$522$	−25023.9	+	14447.5i	−2.09821	+	1.21140i
$523$	−19517.1	−	11268.2i	−1.63179	−	0.942113i	−0.983542	−	0.180681i	$-0.942170\pi$
$523$	−19517.1	−	11268.2i	−1.63179	−	0.942113i	−0.648245	−	0.761432i	$-0.724497\pi$
$524$	−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
$530$	8138.65	+	2641.79i	0.667019	+	0.216513i
$531$	15781.1			1.28972
$532$		0			0
$533$			25846.7i			2.10046i
$534$	3359.81	−	5819.37i	0.272272	−	0.471589i
$535$	−10335.6	−	11472.2i	−0.835231	−	0.927075i
$536$	−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	−0.986067	−	0.166349i	$-0.946802\pi$
$541$	−4391.22	+	7605.81i	−0.348971	+	0.604435i	0.637096	+	0.770784i	$0.280135\pi$
$542$	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
$550$	9963.87	−	13730.9i	0.772474	−	1.06452i
$551$	92.7152	−	160.587i	0.00716842	−	0.0124161i
$552$		−	13693.5i		−	1.05586i
$553$		0			0
$554$	6981.84			0.535433
$555$	790.111	+	256.468i	0.0604294	+	0.0196153i
$556$	−14100.4	−	24422.6i	−1.07552	−	1.86286i
$557$	6290.92	−	3632.06i	0.478554	−	0.276294i	−0.241259	−	0.970461i	$-0.577560\pi$
$557$	6290.92	−	3632.06i	0.478554	−	0.276294i	0.719814	+	0.694167i	$0.244227\pi$
$558$	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	$-0.620620\pi$
$563$	3335.43	−	1925.71i	0.249683	−	0.144154i	0.619619	+	0.784903i	$0.287287\pi$
$564$	4060.57	+	7033.11i	0.303158	+	0.525084i
$565$	−5671.86	+	17473.5i	−0.422331	+	1.30109i
$566$	−48220.9			−3.58105
$567$		0			0
$568$			36186.7i			2.67317i
$569$	8290.14	−	14358.9i	0.610792	−	1.05792i	−0.380315	−	0.924857i	$-0.624184\pi$
$569$	8290.14	−	14358.9i	0.610792	−	1.05792i	0.991107	−	0.133066i	$-0.0424822\pi$
$570$	67.8323	−	61.1123i	0.00498453	−	0.00449072i
$571$	−3192.93	−	5530.32i	−0.234010	−	0.405318i	0.724974	−	0.688776i	$-0.241852\pi$
$571$	−3192.93	−	5530.32i	−0.234010	−	0.405318i	−0.958985	+	0.283458i	$0.908518\pi$
$572$	−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	$-0.536039\pi$
$577$	9577.44	−	5529.54i	0.691012	−	0.398956i	0.803991	+	0.594641i	$0.202706\pi$
$578$	−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
$585$	11147.8	+	12373.6i	0.787868	+	0.874504i
$586$	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
$590$	12455.6	−	38372.5i	0.869136	−	2.67758i
$591$	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	$-0.311073\pi$
$593$	1747.69	+	1009.03i	0.121027	+	0.0698750i	−0.438264	+	0.898846i	$0.644407\pi$
$594$	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	0.841963	−	0.539536i	$-0.181400\pi$
$599$	−678.335	−	1174.91i	−0.0462705	−	0.0801428i	−0.888233	+	0.459393i	$0.848067\pi$
$600$	−1638.29	+	15675.1i	−0.111471	+	1.06656i
$601$	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
$605$	5636.82	−	5078.39i	0.378792	−	0.341266i
$606$	2763.55	+	4786.61i	0.185250	+	0.320863i
$607$	8144.69	+	4702.34i	0.544617	+	0.314435i	0.746948	−	0.664882i	$-0.231518\pi$
$607$	8144.69	+	4702.34i	0.544617	+	0.314435i	−0.202331	+	0.979317i	$0.564852\pi$
$608$			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	$-0.881118\pi$
$613$	−16400.8	+	9468.99i	−1.08062	+	0.623897i	−0.149557	+	0.988753i	$0.547785\pi$
$614$	−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	$-0.231606\pi$
$619$	−3120.16	−	5404.28i	−0.202601	−	0.350915i	−0.949366	+	0.314173i	$0.898273\pi$
$620$	21716.6	−	19565.2i	1.40671	−	1.26735i
$621$	5290.89	−	9164.10i	0.341894	−	0.592178i
$622$			1896.13i			0.122231i
$623$		0			0
$624$	22821.4			1.46408
$625$	4845.70	+	14854.6i	0.310125	+	0.950696i
$626$	−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
$635$	−662.859	+	2042.10i	−0.0414248	+	0.127619i
$636$	5652.27			0.352401
$637$		0			0
$638$		−	31758.8i		−	1.97076i
$639$	−6467.50	+	11202.0i	−0.400392	+	0.693499i
$640$	−10554.6	−	11715.2i	−0.651886	−	0.723569i
$641$	−9399.22	−	16279.9i	−0.579168	−	1.00315i	−0.995575	−	0.0939701i	$-0.970044\pi$
$641$	−9399.22	−	16279.9i	−0.579168	−	1.00315i	0.416407	−	0.909178i	$-0.363289\pi$
$642$	−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	$-0.683786\pi$
$647$	−1532.27	+	884.654i	−0.0931060	+	0.0537548i	0.452724	+	0.891651i	$0.350452\pi$
$648$	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	$-0.370534\pi$
$653$	−3370.12	−	1945.74i	−0.201965	−	0.116604i	−0.597572	+	0.801816i	$0.703868\pi$
$654$	−2012.52	−	3485.78i	−0.120330	−	0.208417i
$655$	−17301.5	+	15587.4i	−1.03210	+	0.929849i
$656$	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	$0.702452\pi$
$660$	3459.94	−	10659.2i	0.204057	−	0.628647i
$661$	13584.0	+	23528.1i	0.799326	+	1.38447i	0.920056	+	0.391788i	$0.128143\pi$
$661$	13584.0	+	23528.1i	0.799326	+	1.38447i	−0.120730	+	0.992685i	$0.538523\pi$
$662$	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
$670$	−29136.8	−	9457.75i	−1.68008	−	0.545350i
$671$	−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
$675$	−7152.92	+	9857.23i	−0.407876	+	0.562081i
$676$	−19344.6	−	33505.7i	−1.10062	−	1.90634i
$677$	3775.19	+	2179.61i	0.214317	+	0.123736i	0.603316	−	0.797502i	$-0.293846\pi$
$677$	3775.19	+	2179.61i	0.214317	+	0.123736i	−0.388999	+	0.921238i	$0.627179\pi$
$678$			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	$-0.353542\pi$
$683$	25739.9	−	14860.9i	1.44203	−	0.832559i	0.997985	+	0.0634439i	$0.0202084\pi$
$684$	−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
$690$	−8375.67	−	9296.68i	−0.462111	−	0.512925i
$691$	2464.57	−	4268.75i	0.135682	−	0.235009i	−0.790176	−	0.612881i	$-0.790011\pi$
$691$	2464.57	−	4268.75i	0.135682	−	0.235009i	0.925858	+	0.377872i	$0.123344\pi$
$692$		−	50512.0i		−	2.77482i
$693$		0			0
$694$	10093.4			0.552073
$695$	−14820.4	−	4810.68i	−0.808880	−	0.262561i
$696$	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
$705$	4267.93	+	1385.36i	0.227999	+	0.0740081i
$706$	21717.3			1.15771
$707$		0			0
$708$		−	26649.6i		−	1.41462i
$709$	−8593.15	+	14883.8i	−0.455180	+	0.788394i	−0.998699	−	0.0510026i	$-0.983758\pi$
$709$	−8593.15	+	14883.8i	−0.455180	+	0.788394i	0.543519	+	0.839397i	$0.317092\pi$
$710$	22133.6	+	24567.5i	1.16994	+	1.29859i
$711$	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	$-0.961481\pi$
$719$	−7553.65	+	13083.3i	−0.391799	+	0.678616i	0.600888	+	0.799333i	$0.294814\pi$
$720$	−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
$725$	23673.8	+	17179.0i	1.21272	+	0.880015i
$726$	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
$730$	−9789.32	−	3177.59i	−0.496327	−	0.161107i
$731$	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	$-0.0881253\pi$
$733$	23936.7	+	13819.9i	1.20617	+	0.696382i	0.244249	+	0.969713i	$0.421459\pi$
$734$	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	0.864056	+	0.503396i	$0.167916\pi$
$739$	17437.2	+	30202.1i	0.867982	+	1.50339i	0.00392555	+	0.999992i	$0.498750\pi$
$740$	−2675.91	+	8243.77i	−0.132930	+	0.409523i
$741$	−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
$745$	269.961	−	243.216i	0.0132760	−	0.0119607i
$746$	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	−0.918490	−	0.395444i	$-0.870591\pi$
$751$	−2403.42	+	4162.85i	−0.116781	+	0.202270i	0.801710	+	0.597714i	$0.203924\pi$
$752$	−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
$760$	385.537	+	427.932i	0.0184012	+	0.0204246i
$761$	−12956.2	+	22440.7i	−0.617162	+	1.06896i	0.372839	+	0.927896i	$0.378384\pi$
$761$	−12956.2	+	22440.7i	−0.617162	+	1.06896i	−0.990001	+	0.141060i	$0.954949\pi$
$762$			1978.93i			0.0940803i
$763$		0			0
$764$	31273.1			1.48092
$765$	−2221.60	+	6844.16i	−0.104996	+	0.323465i
$766$	−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	0.0336997	−	0.0194566i

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} +(10.6341 + 3.45182i) q^{5} +10.3052 q^{6} +65.0123i q^{8} +(-11.6194 + 20.1254i) q^{9} +(39.7649 + 44.1375i) 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} +(101.170 + 73.4142i) q^{25} +(170.307 - 294.980i) q^{26} +97.4324i q^{27} +234.000 q^{29} +(109.587 + 35.5718i) 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} +(-224.411 + 691.350i) q^{40} -403.216 q^{41} +172.895i q^{43} +(258.420 - 447.597i) q^{44} +(-193.031 + 173.908i) 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} +(293.679 + 325.972i) q^{60} +(287.358 - 497.719i) q^{61} -686.544i q^{62} -950.977 q^{64} +(221.266 - 681.664i) 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} +(241.110 + 25.1997i) q^{75} +16.0349 q^{76} -660.580i q^{78} +(39.6645 - 68.7010i) q^{79} +(-1524.84 + 1373.78i) 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} +(6.58232 - 5.93022i) 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

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