LMFDB - Embedded newform 245.4.b.d.99.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(99,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("245.99");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.b (of order $2$, degree $1$, 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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 55x^{8} + 983x^{6} + 6409x^{4} + 13560x^{2} + 3600 $ x^10 + 55x^8 + 983x^6 + 6409x^4 + 13560x^2 + 3600
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.8
Root			$1.85474i$ of defining polynomial
Character	$\chi$	$=$	245.99
Dual form			245.4.b.d.99.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.85474i q^{2} +8.98858i q^{3} -0.149548 q^{4} +(-3.91321 + 10.4731i) q^{5} -25.6601 q^{6} +22.4110i q^{8} -53.7945 q^{9} +(-29.8981 - 11.1712i) q^{10} +37.4408 q^{11} -1.34423i q^{12} +3.96370i q^{13} +(-94.1387 - 35.1742i) q^{15} -65.1740 q^{16} -51.6780i q^{17} -153.569i q^{18} +25.9323 q^{19} +(0.585214 - 1.56624i) q^{20} +106.884i q^{22} +173.454i q^{23} -201.443 q^{24} +(-94.3736 - 81.9673i) q^{25} -11.3154 q^{26} -240.845i q^{27} +245.676 q^{29} +(100.413 - 268.742i) q^{30} +172.074 q^{31} -6.76690i q^{32} +336.539i q^{33} +147.527 q^{34} +8.04488 q^{36} -250.699i q^{37} +74.0300i q^{38} -35.6281 q^{39} +(-234.714 - 87.6990i) q^{40} +48.8649 q^{41} +143.612i q^{43} -5.59920 q^{44} +(210.509 - 563.398i) q^{45} -495.167 q^{46} +36.6415i q^{47} -585.822i q^{48} +(233.995 - 269.412i) q^{50} +464.511 q^{51} -0.592765i q^{52} -645.286i q^{53} +687.549 q^{54} +(-146.514 + 392.123i) q^{55} +233.094i q^{57} +701.343i q^{58} +395.495 q^{59} +(14.0783 + 5.26024i) q^{60} -47.5130 q^{61} +491.228i q^{62} -502.074 q^{64} +(-41.5125 - 15.5108i) q^{65} -960.733 q^{66} +263.189i q^{67} +7.72835i q^{68} -1559.11 q^{69} -268.177 q^{71} -1205.59i q^{72} +199.757i q^{73} +715.680 q^{74} +(736.769 - 848.284i) q^{75} -3.87813 q^{76} -101.709i q^{78} -473.640 q^{79} +(255.040 - 682.577i) q^{80} +712.399 q^{81} +139.497i q^{82} -72.7028i q^{83} +(541.231 + 202.227i) q^{85} -409.975 q^{86} +2208.28i q^{87} +839.086i q^{88} -1552.25 q^{89} +(1608.36 + 600.950i) q^{90} -25.9398i q^{92} +1546.70i q^{93} -104.602 q^{94} +(-101.478 + 271.593i) q^{95} +60.8248 q^{96} -243.338i q^{97} -2014.11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 36 q^{4} - 6 q^{5} - 12 q^{6} - 46 q^{9} + 16 q^{10} + 84 q^{11} + 8 q^{15} + 148 q^{16} - 72 q^{19} + 68 q^{20} - 72 q^{24} - 362 q^{25} + 620 q^{26} + 88 q^{29} + 52 q^{30} - 120 q^{31} - 964 q^{34}+ \cdots - 5304 q^{99}+O(q^{100}) $ 10 * q - 36 * q^4 - 6 * q^5 - 12 * q^6 - 46 * q^9 + 16 * q^10 + 84 * q^11 + 8 * q^15 + 148 * q^16 - 72 * q^19 + 68 * q^20 - 72 * q^24 - 362 * q^25 + 620 * q^26 + 88 * q^29 + 52 * q^30 - 120 * q^31 - 964 * q^34 - 420 * q^36 + 212 * q^39 - 1396 * q^40 + 852 * q^41 - 1424 * q^44 + 510 * q^45 + 176 * q^46 + 1644 * q^50 + 1276 * q^51 + 996 * q^54 + 1136 * q^55 - 864 * q^59 - 1692 * q^60 + 884 * q^61 - 2724 * q^64 + 520 * q^65 - 1148 * q^66 - 4808 * q^69 + 880 * q^71 + 3024 * q^74 - 720 * q^75 + 2672 * q^76 - 3580 * q^79 + 2316 * q^80 - 302 * q^81 + 1572 * q^85 + 2432 * q^86 + 1492 * q^89 + 7748 * q^90 - 1652 * q^94 - 1628 * q^95 - 4080 * q^96 - 5304 * q^99

Character values

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

$n$	$101$	$197$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			2.85474i			1.00930i	0.863323	+	0.504652i	$0.168379\pi$
$2$			2.85474i			1.00930i	−0.863323	+	0.504652i	$0.831621\pi$
$3$			8.98858i			1.72985i	0.501899	+	0.864926i	$0.332635\pi$
$3$			8.98858i			1.72985i	−0.501899	+	0.864926i	$0.667365\pi$
$4$	−0.149548			−0.0186935
$5$	−3.91321	+	10.4731i	−0.350008	+	0.936747i
$5$	−3.91321	+	10.4731i	−0.350008	+	0.936747i
$6$	−25.6601			−1.74595
$7$		0			0
$7$		0			0
$8$			22.4110i			0.990436i
$9$	−53.7945			−1.99239
$10$	−29.8981	−	11.1712i	−0.945462	−	0.353265i
$11$	37.4408			1.02626			0.513128	−	0.858312i	$-0.328487\pi$
$11$	37.4408			1.02626			0.513128	+	0.858312i	$0.328487\pi$
$12$		−	1.34423i		−	0.0323371i
$13$			3.96370i			0.0845641i	0.999106	+	0.0422821i	$0.0134628\pi$
$13$			3.96370i			0.0845641i	−0.999106	+	0.0422821i	$0.986537\pi$
$14$		0			0
$15$	−94.1387	−	35.1742i	−1.62043	−	0.605463i
$16$	−65.1740			−1.01834
$17$		−	51.6780i		−	0.737279i	−0.929572	−	0.368640i	$-0.879824\pi$
$17$		−	51.6780i		−	0.737279i	0.929572	−	0.368640i	$-0.120176\pi$
$18$		−	153.569i		−	2.01093i
$19$	25.9323			0.313120			0.156560	−	0.987668i	$-0.449960\pi$
$19$	25.9323			0.313120			0.156560	+	0.987668i	$0.449960\pi$
$20$	0.585214	−	1.56624i	0.00654289	−	0.0175111i
$21$		0			0
$22$			106.884i			1.03580i
$23$			173.454i			1.57251i	0.617902	+	0.786255i	$0.287983\pi$
$23$			173.454i			1.57251i	−0.617902	+	0.786255i	$0.712017\pi$
$24$	−201.443			−1.71331
$25$	−94.3736	−	81.9673i	−0.754988	−	0.655738i
$26$	−11.3154			−0.0853509
$27$		−	240.845i		−	1.71669i
$28$		0			0
$29$	245.676			1.57314			0.786568	−	0.617503i	$-0.211856\pi$
$29$	245.676			1.57314			0.786568	+	0.617503i	$0.211856\pi$
$30$	100.413	−	268.742i	0.611096	−	1.63551i
$31$	172.074			0.996951			0.498475	−	0.866904i	$-0.333893\pi$
$31$	172.074			0.996951			0.498475	+	0.866904i	$0.333893\pi$
$32$		−	6.76690i		−	0.0373822i
$33$			336.539i			1.77527i
$34$	147.527			0.744139
$35$		0			0
$36$	8.04488			0.0372448
$37$		−	250.699i		−	1.11391i	−0.830543	−	0.556954i	$-0.811970\pi$
$37$		−	250.699i		−	1.11391i	0.830543	−	0.556954i	$-0.188030\pi$
$38$			74.0300i			0.316033i
$39$	−35.6281			−0.146283
$40$	−234.714	−	87.6990i	−0.927788	−	0.346661i
$41$	48.8649			0.186132			0.0930661	−	0.995660i	$-0.470333\pi$
$41$	48.8649			0.186132			0.0930661	+	0.995660i	$0.470333\pi$
$42$		0			0
$43$			143.612i			0.509317i	0.967031	+	0.254658i	$0.0819630\pi$
$43$			143.612i			0.509317i	−0.967031	+	0.254658i	$0.918037\pi$
$44$	−5.59920			−0.0191844
$45$	210.509	−	563.398i	0.697353	−	1.86636i
$46$	−495.167			−1.58714
$47$			36.6415i			0.113717i	0.998382	+	0.0568587i	$0.0181085\pi$
$47$			36.6415i			0.113717i	−0.998382	+	0.0568587i	$0.981892\pi$
$48$		−	585.822i		−	1.76159i
$49$		0			0
$50$	233.995	−	269.412i	0.661839	−	0.762012i
$51$	464.511			1.27538
$52$		−	0.592765i		−	0.00158080i
$53$		−	645.286i		−	1.67239i	−0.548430	−	0.836196i	$-0.684774\pi$
$53$		−	645.286i		−	1.67239i	0.548430	−	0.836196i	$-0.315226\pi$
$54$	687.549			1.73266
$55$	−146.514	+	392.123i	−0.359198	+	0.961342i
$56$		0			0
$57$			233.094i			0.541651i
$58$			701.343i			1.58777i
$59$	395.495			0.872696			0.436348	−	0.899778i	$-0.356272\pi$
$59$	395.495			0.872696			0.436348	+	0.899778i	$0.356272\pi$
$60$	14.0783	+	5.26024i	0.0302916	+	0.0113182i
$61$	−47.5130			−0.0997282			−0.0498641	−	0.998756i	$-0.515879\pi$
$61$	−47.5130			−0.0997282			−0.0498641	+	0.998756i	$0.515879\pi$
$62$			491.228i			1.00623i
$63$		0			0
$64$	−502.074			−0.980614
$65$	−41.5125	−	15.5108i	−0.0792152	−	0.0295981i
$66$	−960.733			−1.79179
$67$			263.189i			0.479906i	0.970785	+	0.239953i	$0.0771320\pi$
$67$			263.189i			0.479906i	−0.970785	+	0.239953i	$0.922868\pi$
$68$			7.72835i			0.0137824i
$69$	−1559.11			−2.72021
$70$		0			0
$71$	−268.177			−0.448264			−0.224132	−	0.974559i	$-0.571955\pi$
$71$	−268.177			−0.448264			−0.224132	+	0.974559i	$0.571955\pi$
$72$		−	1205.59i		−	1.97333i
$73$			199.757i			0.320271i	0.987095	+	0.160136i	$0.0511931\pi$
$73$			199.757i			0.320271i	−0.987095	+	0.160136i	$0.948807\pi$
$74$	715.680			1.12427
$75$	736.769	−	848.284i	1.13433	−	1.30602i
$76$	−3.87813			−0.00585331
$77$		0			0
$78$		−	101.709i		−	0.147644i
$79$	−473.640			−0.674540			−0.337270	−	0.941408i	$-0.609503\pi$
$79$	−473.640			−0.674540			−0.337270	+	0.941408i	$0.609503\pi$
$80$	255.040	−	682.577i	0.356429	−	0.953930i
$81$	712.399			0.977227
$82$			139.497i			0.187864i
$83$		−	72.7028i		−	0.0961466i	−0.998844	−	0.0480733i	$-0.984692\pi$
$83$		−	72.7028i		−	0.0961466i	0.998844	−	0.0480733i	$-0.0153081\pi$
$84$		0			0
$85$	541.231	+	202.227i	0.690644	+	0.258054i
$86$	−409.975			−0.514055
$87$			2208.28i			2.72129i
$88$			839.086i			1.01644i
$89$	−1552.25			−1.84874			−0.924369	−	0.381500i	$-0.875408\pi$
$89$	−1552.25			−1.84874			−0.924369	+	0.381500i	$0.875408\pi$
$90$	1608.36	+	600.950i	1.88373	+	0.703841i
$91$		0			0
$92$		−	25.9398i		−	0.0293958i
$93$			1546.70i			1.72458i
$94$	−104.602			−0.114775
$95$	−101.478	+	271.593i	−0.109594	+	0.293314i
$96$	60.8248			0.0646657
$97$		−	243.338i		−	0.254714i	−0.991857	−	0.127357i	$-0.959351\pi$
$97$		−	243.338i		−	0.254714i	0.991857	−	0.127357i	$-0.0406494\pi$
$98$		0			0
$99$	−2014.11			−2.04470
$100$	14.1134	+	12.2581i	0.0141134	+	0.0122581i
$101$	1539.34			1.51653			0.758265	−	0.651946i	$-0.226047\pi$
$101$	1539.34			1.51653			0.758265	+	0.651946i	$0.226047\pi$
$102$			1326.06i			1.28725i
$103$			948.628i			0.907486i	0.891133	+	0.453743i	$0.149912\pi$
$103$			948.628i			0.907486i	−0.891133	+	0.453743i	$0.850088\pi$
$104$	−88.8306			−0.0837554
$105$		0			0
$106$	1842.12			1.68795
$107$			863.983i			0.780602i	0.920687	+	0.390301i	$0.127629\pi$
$107$			863.983i			0.780602i	−0.920687	+	0.390301i	$0.872371\pi$
$108$			36.0179i			0.0320910i
$109$	−886.319			−0.778844			−0.389422	−	0.921060i	$-0.627325\pi$
$109$	−886.319			−0.778844			−0.389422	+	0.921060i	$0.627325\pi$
$110$	−1119.41	−	418.259i	−0.970286	−	0.362540i
$111$	2253.42			1.92690
$112$		0			0
$113$		−	765.957i		−	0.637657i	−0.947812	−	0.318828i	$-0.896711\pi$
$113$		−	765.957i		−	0.637657i	0.947812	−	0.318828i	$-0.103289\pi$
$114$	−665.424			−0.546690
$115$	−1816.61	−	678.763i	−1.47304	−	0.550391i
$116$	−36.7405			−0.0294075
$117$		−	213.226i		−	0.168485i
$118$			1129.04i			0.880816i
$119$		0			0
$120$	788.289	−	2109.74i	0.599672	−	1.60494i
$121$	70.8116			0.0532018
$122$		−	135.637i		−	0.100656i
$123$			439.226i			0.321981i
$124$	−25.7334			−0.0186365
$125$	1227.76	−	667.633i	0.878513	−	0.477719i
$126$		0			0
$127$			505.042i			0.352876i	0.984312	+	0.176438i	$0.0564575\pi$
$127$			505.042i			0.352876i	−0.984312	+	0.176438i	$0.943543\pi$
$128$		−	1487.43i		−	1.02712i
$129$	−1290.87			−0.881043
$130$	44.2794	−	118.507i	0.0298735	−	0.0799521i
$131$	−672.930			−0.448811			−0.224405	−	0.974496i	$-0.572044\pi$
$131$	−672.930			−0.448811			−0.224405	+	0.974496i	$0.572044\pi$
$132$		−	50.3289i		−	0.0331861i
$133$		0			0
$134$	−751.337			−0.484371
$135$	2522.40	+	942.476i	1.60810	+	0.600855i
$136$	1158.16			0.730228
$137$			1552.28i			0.968032i	0.875059	+	0.484016i	$0.160822\pi$
$137$			1552.28i			0.968032i	−0.875059	+	0.484016i	$0.839178\pi$
$138$		−	4450.85i		−	2.74552i
$139$	−1072.02			−0.654154			−0.327077	−	0.944998i	$-0.606064\pi$
$139$	−1072.02			−0.654154			−0.327077	+	0.944998i	$0.606064\pi$
$140$		0			0
$141$	−329.355			−0.196714
$142$		−	765.575i		−	0.452434i
$143$			148.404i			0.0867845i
$144$	3506.01			2.02894
$145$	−961.384	+	2573.00i	−0.550611	+	1.47363i
$146$	−570.255			−0.323251
$147$		0			0
$148$			37.4915i			0.0208229i
$149$	−645.936			−0.355149			−0.177574	−	0.984107i	$-0.556825\pi$
$149$	−645.936			−0.355149			−0.177574	+	0.984107i	$0.556825\pi$
$150$	2421.63	+	2103.29i	1.31817	+	1.14488i
$151$	243.194			0.131065			0.0655326	−	0.997850i	$-0.479125\pi$
$151$	243.194			0.131065			0.0655326	+	0.997850i	$0.479125\pi$
$152$			581.169i			0.310125i
$153$			2779.99i			1.46895i
$154$		0			0
$155$	−673.363	+	1802.16i	−0.348941	+	0.933890i
$156$	5.32811			0.00273455
$157$			1552.56i			0.789223i	0.918848	+	0.394611i	$0.129121\pi$
$157$			1552.56i			0.789223i	−0.918848	+	0.394611i	$0.870879\pi$
$158$		−	1352.12i		−	0.680815i
$159$	5800.20			2.89299
$160$	70.8707	+	26.4803i	0.0350176	+	0.0130841i
$161$		0			0
$162$			2033.71i			0.986319i
$163$		−	2553.65i		−	1.22710i	−0.789656	−	0.613550i	$-0.789741\pi$
$163$		−	2553.65i		−	1.22710i	0.789656	−	0.613550i	$-0.210259\pi$
$164$	−7.30766			−0.00347947
$165$	−3524.63	−	1316.95i	−1.66298	−	0.621360i
$166$	207.548			0.0970411
$167$		−	3573.14i		−	1.65568i	−0.560966	−	0.827839i	$-0.689570\pi$
$167$		−	3573.14i		−	1.65568i	0.560966	−	0.827839i	$-0.310430\pi$
$168$		0			0
$169$	2181.29			0.992849
$170$	−577.305	+	1545.07i	−0.260455	+	0.697069i
$171$	−1395.01			−0.623856
$172$		−	21.4769i		−	0.00952093i
$173$			2234.71i			0.982090i	0.871134	+	0.491045i	$0.163385\pi$
$173$			2234.71i			0.982090i	−0.871134	+	0.491045i	$0.836615\pi$
$174$	−6304.07			−2.74661
$175$		0			0
$176$	−2440.17			−1.04508
$177$			3554.94i			1.50964i
$178$		−	4431.26i		−	1.86594i
$179$	1830.53			0.764361			0.382180	−	0.924088i	$-0.375173\pi$
$179$	1830.53			0.764361			0.382180	+	0.924088i	$0.375173\pi$
$180$	−31.4813	+	84.2552i	−0.0130360	+	0.0348889i
$181$	−2437.22			−1.00087			−0.500433	−	0.865775i	$-0.666826\pi$
$181$	−2437.22			−1.00087			−0.500433	+	0.865775i	$0.666826\pi$
$182$		0			0
$183$		−	427.075i		−	0.172515i
$184$	−3887.29			−1.55747
$185$	2625.60	+	981.037i	1.04345	+	0.389877i
$186$	−4415.44			−1.74062
$187$		−	1934.86i		−	0.756638i
$188$		−	5.47968i		−	0.00212578i
$189$		0			0
$190$	−775.327	−	289.695i	−0.296043	−	0.110614i
$191$	5079.50			1.92429			0.962145	−	0.272538i	$-0.0878632\pi$
$191$	5079.50			1.92429			0.962145	+	0.272538i	$0.0878632\pi$
$192$		−	4512.93i		−	1.69632i
$193$			2805.09i			1.04619i	0.852274	+	0.523095i	$0.175223\pi$
$193$			2805.09i			1.04619i	−0.852274	+	0.523095i	$0.824777\pi$
$194$	694.667			0.257084
$195$	139.420	−	373.138i	0.0512004	−	0.137031i
$196$		0			0
$197$		−	3107.79i		−	1.12396i	−0.827149	−	0.561982i	$-0.810039\pi$
$197$		−	3107.79i		−	1.12396i	0.827149	−	0.561982i	$-0.189961\pi$
$198$		−	5749.76i		−	2.06373i
$199$	−2145.63			−0.764321			−0.382161	−	0.924096i	$-0.624820\pi$
$199$	−2145.63			−0.764321			−0.382161	+	0.924096i	$0.624820\pi$
$200$	1836.97	−	2115.01i	0.649467	−	0.747768i
$201$	−2365.70			−0.830166
$202$			4394.41i			1.53064i
$203$		0			0
$204$	−69.4669			−0.0238414
$205$	−191.219	+	511.769i	−0.0651478	+	0.174359i
$206$	−2708.09			−0.915929
$207$		−	9330.89i		−	3.13305i
$208$		−	258.331i		−	0.0861154i
$209$	970.925			0.321341
$210$		0			0
$211$	2837.45			0.925772			0.462886	−	0.886418i	$-0.346814\pi$
$211$	2837.45			0.925772			0.462886	+	0.886418i	$0.346814\pi$
$212$			96.5013i			0.0312629i
$213$		−	2410.53i		−	0.775430i
$214$	−2466.45			−0.787864
$215$	−1504.07	−	561.984i	−0.477101	−	0.178265i
$216$	5397.57			1.70027
$217$		0			0
$218$		−	2530.21i		−	0.786089i
$219$	−1795.53			−0.554022
$220$	21.9109	−	58.6413i	0.00671468	−	0.0179709i
$221$	204.836			0.0623474
$222$			6432.94i			1.94482i
$223$		−	4741.40i		−	1.42380i	−0.702280	−	0.711901i	$-0.747834\pi$
$223$		−	4741.40i		−	1.42380i	0.702280	−	0.711901i	$-0.252166\pi$
$224$		0			0
$225$	5076.78	+	4409.39i	1.50423	+	1.30649i
$226$	2186.61			0.643589
$227$			960.790i			0.280925i	0.990086	+	0.140462i	$0.0448589\pi$
$227$			960.790i			0.280925i	−0.990086	+	0.140462i	$0.955141\pi$
$228$		−	34.8589i		−	0.0101254i
$229$	744.006			0.214696			0.107348	−	0.994222i	$-0.465764\pi$
$229$	744.006			0.214696			0.107348	+	0.994222i	$0.465764\pi$
$230$	1937.69	−	5185.96i	0.555512	−	1.48675i
$231$		0			0
$232$			5505.86i			1.55809i
$233$		−	1550.56i		−	0.435968i	−0.975952	−	0.217984i	$-0.930052\pi$
$233$		−	1550.56i		−	0.435968i	0.975952	−	0.217984i	$-0.0699480\pi$
$234$	608.704			0.170052
$235$	−383.752	−	143.386i	−0.106524	−	0.0398020i
$236$	−59.1456			−0.0163138
$237$		−	4257.35i		−	1.16685i
$238$		0			0
$239$	−2775.00			−0.751045			−0.375523	−	0.926813i	$-0.622537\pi$
$239$	−2775.00			−0.751045			−0.375523	+	0.926813i	$0.622537\pi$
$240$	6135.40	+	2292.44i	1.65016	+	0.616569i
$241$	2550.20			0.681630			0.340815	−	0.940130i	$-0.389297\pi$
$241$	2550.20			0.681630			0.340815	+	0.940130i	$0.389297\pi$
$242$			202.149i			0.0536968i
$243$		−	99.3558i		−	0.0262291i
$244$	7.10549			0.00186427
$245$		0			0
$246$	−1253.88			−0.324977
$247$			102.788i			0.0264787i
$248$			3856.36i			0.987416i
$249$	653.494			0.166319
$250$	1905.92	+	3504.93i	0.482164	+	0.886686i
$251$	2933.00			0.737568			0.368784	−	0.929515i	$-0.379774\pi$
$251$	2933.00			0.737568			0.368784	+	0.929515i	$0.379774\pi$
$252$		0			0
$253$			6494.26i			1.61380i
$254$	−1441.76			−0.356159
$255$	−1817.73	+	4864.90i	−0.446395	+	1.19471i
$256$	229.626			0.0560611
$257$		−	2725.22i		−	0.661459i	−0.943726	−	0.330729i	$-0.892705\pi$
$257$		−	2725.22i		−	0.661459i	0.943726	−	0.330729i	$-0.107295\pi$
$258$		−	3685.09i		−	0.889240i
$259$		0			0
$260$	6.20811	+	2.31961i	0.00148081	+	0.000553294i
$261$	−13216.0			−3.13430
$262$		−	1921.04i		−	0.452986i
$263$		−	3027.26i		−	0.709767i	−0.934910	−	0.354884i	$-0.884520\pi$
$263$		−	3027.26i		−	0.709767i	0.934910	−	0.354884i	$-0.115480\pi$
$264$	−7542.19			−1.75829
$265$	6758.17	+	2525.14i	1.56661	+	0.585351i
$266$		0			0
$267$		−	13952.5i		−	3.19804i
$268$		−	39.3595i		−	0.00897114i
$269$	−1442.46			−0.326946			−0.163473	−	0.986548i	$-0.552270\pi$
$269$	−1442.46			−0.326946			−0.163473	+	0.986548i	$0.552270\pi$
$270$	−2690.52	+	7200.80i	−0.606445	+	1.62306i
$271$	6464.45			1.44903			0.724516	−	0.689258i	$-0.242063\pi$
$271$	6464.45			1.44903			0.724516	+	0.689258i	$0.242063\pi$
$272$			3368.06i			0.750804i
$273$		0			0
$274$	−4431.36			−0.977038
$275$	−3533.42	−	3068.92i	−0.774812	−	0.672955i
$276$	233.162			0.0508503
$277$		−	876.614i		−	0.190147i	−0.995470	−	0.0950733i	$-0.969691\pi$
$277$		−	876.614i		−	0.190147i	0.995470	−	0.0950733i	$-0.0303086\pi$
$278$		−	3060.33i		−	0.660240i
$279$	−9256.66			−1.98631
$280$		0			0
$281$	6252.19			1.32731			0.663655	−	0.748038i	$-0.269004\pi$
$281$	6252.19			1.32731			0.663655	+	0.748038i	$0.269004\pi$
$282$		−	940.224i		−	0.198544i
$283$		−	2250.07i		−	0.472625i	−0.971677	−	0.236312i	$-0.924061\pi$
$283$		−	2250.07i		−	0.472625i	0.971677	−	0.236312i	$-0.0759389\pi$
$284$	40.1054			0.00837963
$285$	−2441.23	−	912.147i	−0.507390	−	0.189582i
$286$	−423.655			−0.0875919
$287$		0			0
$288$			364.022i			0.0744799i
$289$	2242.39			0.456419
$290$	−7345.26	−	2744.50i	−1.48734	−	0.555733i
$291$	2187.26			0.440617
$292$		−	29.8733i		−	0.00598700i
$293$			5917.86i			1.17995i	0.807422	+	0.589975i	$0.200862\pi$
$293$			5917.86i			1.17995i	−0.807422	+	0.589975i	$0.799138\pi$
$294$		0			0
$295$	−1547.66	+	4142.08i	−0.305451	+	0.817495i
$296$	5618.41			1.10325
$297$		−	9017.41i		−	1.76176i
$298$		−	1843.98i		−	0.358453i
$299$	−687.522			−0.132978
$300$	−110.183	+	126.859i	−0.0212046	+	0.0244141i
$301$		0			0
$302$			694.256i			0.132284i
$303$			13836.4i			2.62337i
$304$	−1690.11			−0.318864
$305$	185.929	−	497.611i	0.0349057	−	0.0934200i
$306$	−7936.16			−1.48261
$307$			9458.47i			1.75838i	0.476469	+	0.879191i	$0.341916\pi$
$307$			9458.47i			1.75838i	−0.476469	+	0.879191i	$0.658084\pi$
$308$		0			0
$309$	−8526.81			−1.56982
$310$	−5144.70	−	1922.28i	−0.942579	−	0.352187i
$311$	7576.78			1.38148			0.690739	−	0.723104i	$-0.257285\pi$
$311$	7576.78			1.38148			0.690739	+	0.723104i	$0.257285\pi$
$312$		−	798.461i		−	0.144884i
$313$			9172.41i			1.65641i	0.560427	+	0.828204i	$0.310637\pi$
$313$			9172.41i			1.65641i	−0.560427	+	0.828204i	$0.689363\pi$
$314$	−4432.16			−0.796565
$315$		0			0
$316$	70.8320			0.0126095
$317$			3077.94i			0.545345i	0.962107	+	0.272672i	$0.0879075\pi$
$317$			3077.94i			0.545345i	−0.962107	+	0.272672i	$0.912092\pi$
$318$			16558.1i			2.91991i
$319$	9198.31			1.61444
$320$	1964.72	−	5258.30i	0.343223	−	0.918587i
$321$	−7765.98			−1.35033
$322$		0			0
$323$		−	1340.13i		−	0.230857i
$324$	−106.538			−0.0182678
$325$	324.894	−	374.069i	0.0554519	−	0.0638449i
$326$	7290.01			1.23852
$327$		−	7966.75i		−	1.34728i
$328$			1095.11i			0.184352i
$329$		0			0
$330$	3759.55	−	10061.9i	0.627141	−	1.67845i
$331$	3234.50			0.537113			0.268557	−	0.963264i	$-0.413453\pi$
$331$	3234.50			0.537113			0.268557	+	0.963264i	$0.413453\pi$
$332$			10.8726i			0.00179732i
$333$			13486.2i			2.21934i
$334$	10200.4			1.67108
$335$	−2756.42	−	1029.92i	−0.449550	−	0.167971i
$336$		0			0
$337$			3777.84i			0.610658i	0.952247	+	0.305329i	$0.0987665\pi$
$337$			3777.84i			0.610658i	−0.952247	+	0.305329i	$0.901234\pi$
$338$			6227.02i			1.00209i
$339$	6884.87			1.10305
$340$	−80.9401	−	30.2427i	−0.0129106	−	0.00482394i
$341$	6442.60			1.02313
$342$		−	3982.41i		−	0.629660i
$343$		0			0
$344$	−3218.49			−0.504446
$345$	6101.12	−	16328.8i	0.952096	−	2.54815i
$346$	−6379.51			−0.991227
$347$			8244.08i			1.27540i	0.770283	+	0.637702i	$0.220115\pi$
$347$			8244.08i			1.27540i	−0.770283	+	0.637702i	$0.779885\pi$
$348$		−	330.245i		−	0.0508706i
$349$	7173.78			1.10030			0.550148	−	0.835067i	$-0.314571\pi$
$349$	7173.78			1.10030			0.550148	+	0.835067i	$0.314571\pi$
$350$		0			0
$351$	954.637			0.145170
$352$		−	253.358i		−	0.0383637i
$353$			4191.51i			0.631987i	0.948761	+	0.315994i	$0.102338\pi$
$353$			4191.51i			0.631987i	−0.948761	+	0.315994i	$0.897662\pi$
$354$	−10148.4			−1.52368
$355$	1049.43	−	2808.65i	0.156896	−	0.419910i
$356$	232.136			0.0345594
$357$		0			0
$358$			5225.70i			0.771472i
$359$	3136.29			0.461078			0.230539	−	0.973063i	$-0.425951\pi$
$359$	3136.29			0.461078			0.230539	+	0.973063i	$0.425951\pi$
$360$	12626.3	+	4717.73i	1.84851	+	0.690683i
$361$	−6186.52			−0.901956
$362$		−	6957.62i		−	1.01018i
$363$			636.496i			0.0920313i
$364$		0			0
$365$	−2092.08	−	781.691i	−0.300013	−	0.112098i
$366$	1219.19			0.174120
$367$			1723.30i			0.245110i	0.992462	+	0.122555i	$0.0391088\pi$
$367$			1723.30i			0.245110i	−0.992462	+	0.122555i	$0.960891\pi$
$368$		−	11304.7i		−	1.60136i
$369$	−2628.67			−0.370848
$370$	−2800.61	+	7495.42i	−0.393504	+	1.05316i
$371$		0			0
$372$		−	231.307i		−	0.0322384i
$373$		−	2818.55i		−	0.391258i	−0.980678	−	0.195629i	$-0.937325\pi$
$373$		−	2818.55i		−	0.391258i	0.980678	−	0.195629i	$-0.0626748\pi$
$374$	5523.53			0.763677
$375$	6001.07	+	11035.8i	0.826384	+	1.51970i
$376$	−821.174			−0.112630
$377$			973.788i			0.133031i
$378$		0			0
$379$	10466.1			1.41849			0.709246	−	0.704961i	$-0.249036\pi$
$379$	10466.1			1.41849			0.709246	+	0.704961i	$0.249036\pi$
$380$	15.1759	−	40.6162i	0.00204871	−	0.00548307i
$381$	−4539.61			−0.610423
$382$			14500.6i			1.94219i
$383$		−	258.055i		−	0.0344282i	−0.999852	−	0.0172141i	$-0.994520\pi$
$383$		−	258.055i		−	0.0344282i	0.999852	−	0.0172141i	$-0.00547969\pi$
$384$	13369.9			1.77677
$385$		0			0
$386$	−8007.81			−1.05592
$387$		−	7725.54i		−	1.01476i
$388$			36.3908i			0.00476150i
$389$	−4573.87			−0.596156			−0.298078	−	0.954542i	$-0.596346\pi$
$389$	−4573.87			−0.596156			−0.298078	+	0.954542i	$0.596346\pi$
$390$	1065.21	+	398.008i	0.138305	+	0.0516768i
$391$	8963.77			1.15938
$392$		0			0
$393$		−	6048.69i		−	0.776376i
$394$	8871.94			1.13442
$395$	1853.45	−	4960.50i	0.236094	−	0.631873i
$396$	301.206			0.0382227
$397$		−	3624.55i		−	0.458215i	−0.973401	−	0.229107i	$-0.926419\pi$
$397$		−	3624.55i		−	0.458215i	0.973401	−	0.229107i	$-0.0735807\pi$
$398$		−	6125.23i		−	0.771432i
$399$		0			0
$400$	6150.70	+	5342.14i	0.768838	+	0.667767i
$401$	6358.32			0.791819			0.395910	−	0.918289i	$-0.370429\pi$
$401$	6358.32			0.791819			0.395910	+	0.918289i	$0.370429\pi$
$402$		−	6753.45i		−	0.837890i
$403$			682.052i			0.0843063i
$404$	−230.205			−0.0283493
$405$	−2787.77	+	7461.05i	−0.342038	+	0.915414i
$406$		0			0
$407$		−	9386.35i		−	1.14316i
$408$			10410.2i			1.26319i
$409$	−6536.39			−0.790228			−0.395114	−	0.918632i	$-0.629295\pi$
$409$	−6536.39			−0.790228			−0.395114	+	0.918632i	$0.629295\pi$
$410$	−1460.97	−	545.880i	−0.175981	−	0.0657539i
$411$	−13952.8			−1.67455
$412$		−	141.866i		−	0.0169641i
$413$		0			0
$414$	26637.3			3.16220
$415$	761.427	+	284.501i	0.0900650	+	0.0336521i
$416$	26.8220			0.00316119
$417$		−	9635.91i		−	1.13159i
$418$			2771.74i			0.324331i
$419$	6333.56			0.738460			0.369230	−	0.929338i	$-0.379621\pi$
$419$	6333.56			0.738460			0.369230	+	0.929338i	$0.379621\pi$
$420$		0			0
$421$	−8139.62			−0.942282			−0.471141	−	0.882058i	$-0.656158\pi$
$421$	−8139.62			−0.942282			−0.471141	+	0.882058i	$0.656158\pi$
$422$			8100.18i			0.934385i
$423$		−	1971.11i		−	0.226569i
$424$	14461.5			1.65640
$425$	−4235.90	+	4877.03i	−0.483462	+	0.556637i
$426$	6881.43			0.782645
$427$		0			0
$428$		−	129.207i		−	0.0145922i
$429$	−1333.94			−0.150124
$430$	1604.32	−	4293.73i	0.179924	−	0.481539i
$431$	−14367.6			−1.60571			−0.802856	−	0.596173i	$-0.796687\pi$
$431$	−14367.6			−1.60571			−0.802856	+	0.596173i	$0.796687\pi$
$432$			15696.8i			1.74818i
$433$		−	8399.05i		−	0.932176i	−0.884738	−	0.466088i	$-0.845663\pi$
$433$		−	8399.05i		−	0.932176i	0.884738	−	0.466088i	$-0.154337\pi$
$434$		0			0
$435$	−23127.6	−	8641.47i	−2.54916	−	0.952475i
$436$	132.547			0.0145593
$437$			4498.07i			0.492384i
$438$		−	5125.78i		−	0.559176i
$439$	−17860.8			−1.94180			−0.970901	−	0.239482i	$-0.923022\pi$
$439$	−17860.8			−1.94180			−0.970901	+	0.239482i	$0.923022\pi$
$440$	−8787.87	−	3283.52i	−0.952148	−	0.355763i
$441$		0			0
$442$			584.754i			0.0629274i
$443$		−	1901.57i		−	0.203942i	−0.994787	−	0.101971i	$-0.967485\pi$
$443$		−	1901.57i		−	0.203942i	0.994787	−	0.101971i	$-0.0325148\pi$
$444$	−336.996			−0.0360205
$445$	6074.26	−	16256.9i	0.647074	−	1.73180i
$446$	13535.5			1.43705
$447$		−	5806.05i		−	0.614355i
$448$		0			0
$449$	5185.68			0.545050			0.272525	−	0.962149i	$-0.412141\pi$
$449$	5185.68			0.545050			0.272525	+	0.962149i	$0.412141\pi$
$450$	−12587.7	+	14492.9i	−1.31864	+	1.51823i
$451$	1829.54			0.191019
$452$			114.548i			0.0119201i
$453$			2185.97i			0.226723i
$454$	−2742.81			−0.283538
$455$		0			0
$456$	−5223.88			−0.536471
$457$		−	11198.8i		−	1.14630i	−0.819451	−	0.573149i	$-0.805722\pi$
$457$		−	11198.8i		−	1.14630i	0.819451	−	0.573149i	$-0.194278\pi$
$458$			2123.94i			0.216693i
$459$	−12446.4			−1.26568
$460$	271.671	+	101.508i	0.0275364	+	0.0102888i
$461$	−17270.7			−1.74485			−0.872427	−	0.488744i	$-0.837455\pi$
$461$	−17270.7			−1.74485			−0.872427	+	0.488744i	$0.837455\pi$
$462$		0			0
$463$		−	385.660i		−	0.0387109i	−0.999813	−	0.0193554i	$-0.993839\pi$
$463$		−	385.660i		−	0.0387109i	0.999813	−	0.0193554i	$-0.00616141\pi$
$464$	−16011.7			−1.60199
$465$	−16198.9	−	6052.58i	−1.61549	−	0.603616i
$466$	4426.44			0.440024
$467$		−	5035.36i		−	0.498947i	−0.968382	−	0.249474i	$-0.919742\pi$
$467$		−	5035.36i		−	0.498947i	0.968382	−	0.249474i	$-0.0802576\pi$
$468$			31.8875i			0.00314957i
$469$		0			0
$470$	409.330	−	1095.51i	0.0401723	−	0.107515i
$471$	−13955.3			−1.36524
$472$			8863.45i			0.864350i
$473$			5376.94i			0.522689i
$474$	12153.6			1.17771
$475$	−2447.32	−	2125.60i	−0.236402	−	0.205324i
$476$		0			0
$477$			34712.8i			3.33206i
$478$		−	7921.91i		−	0.758033i
$479$	−8681.99			−0.828163			−0.414082	−	0.910240i	$-0.635897\pi$
$479$	−8681.99			−0.828163			−0.414082	+	0.910240i	$0.635897\pi$
$480$	−238.020	+	637.027i	−0.0226335	+	0.0605754i
$481$	993.695			0.0941967
$482$			7280.16i			0.687972i
$483$		0			0
$484$	−10.5898			−0.000994530
$485$	2548.51	+	952.233i	0.238602	+	0.0891519i
$486$	283.635			0.0264731
$487$			890.476i			0.0828569i	0.999141	+	0.0414284i	$0.0131909\pi$
$487$			890.476i			0.0828569i	−0.999141	+	0.0414284i	$0.986809\pi$
$488$		−	1064.81i		−	0.0987744i
$489$	22953.7			2.12270
$490$		0			0
$491$	1562.48			0.143613			0.0718063	−	0.997419i	$-0.477124\pi$
$491$	1562.48			0.143613			0.0718063	+	0.997419i	$0.477124\pi$
$492$		−	65.6855i		−	0.00601897i
$493$		−	12696.1i		−	1.15984i
$494$	−293.433			−0.0267250
$495$	7881.63	−	21094.1i	0.715663	−	1.91537i
$496$	−11214.8			−1.01524
$497$		0			0
$498$			1865.56i			0.167867i
$499$	−8234.33			−0.738716			−0.369358	−	0.929287i	$-0.620422\pi$
$499$	−8234.33			−0.738716			−0.369358	+	0.929287i	$0.620422\pi$
$500$	−183.609	+	99.8433i	−0.0164225	+	0.00893026i
$501$	32117.5			2.86408
$502$			8372.97i			0.744430i
$503$			72.5340i			0.00642969i	0.999995	+	0.00321484i	$0.00102332\pi$
$503$			72.5340i			0.00642969i	−0.999995	+	0.00321484i	$0.998977\pi$
$504$		0			0
$505$	−6023.75	+	16121.7i	−0.530798	+	1.42061i
$506$	−18539.4			−1.62881
$507$			19606.7i			1.71748i
$508$		−	75.5281i		−	0.00659649i
$509$	7793.44			0.678660			0.339330	−	0.940667i	$-0.389800\pi$
$509$	7793.44			0.678660			0.339330	+	0.940667i	$0.389800\pi$
$510$	−13888.0	−	5189.15i	−1.20583	−	0.450548i
$511$		0			0
$512$		−	11243.9i		−	0.970537i
$513$		−	6245.65i		−	0.537529i
$514$	7779.81			0.667612
$515$	−9935.12	−	3712.18i	−0.850084	−	0.317628i
$516$	193.047			0.0164698
$517$			1371.89i			0.116703i
$518$		0			0
$519$	−20086.8			−1.69887
$520$	347.613	−	930.336i	0.0293151	−	0.0784576i
$521$	−4645.42			−0.390633			−0.195316	−	0.980740i	$-0.562573\pi$
$521$	−4645.42			−0.390633			−0.195316	+	0.980740i	$0.562573\pi$
$522$		−	37728.4i		−	3.16346i
$523$			8783.88i			0.734402i	0.930142	+	0.367201i	$0.119684\pi$
$523$			8783.88i			0.734402i	−0.930142	+	0.367201i	$0.880316\pi$
$524$	100.636			0.00838986
$525$		0			0
$526$	8642.04			0.716371
$527$		−	8892.46i		−	0.735031i
$528$		−	21933.6i		−	1.80784i
$529$	−17919.4			−1.47279
$530$	−7208.62	+	19292.8i	−0.590797	+	1.58118i
$531$	−21275.5			−1.73875
$532$		0			0
$533$			193.686i			0.0157401i
$534$	39830.7			3.22780
$535$	−9048.62	−	3380.95i	−0.731226	−	0.273217i
$536$	−5898.34			−0.475316
$537$			16453.9i			1.32223i
$538$		−	4117.86i		−	0.329988i
$539$		0			0
$540$	−377.221	−	140.946i	−0.0300611	−	0.0112321i
$541$	−7054.13			−0.560593			−0.280296	−	0.959913i	$-0.590433\pi$
$541$	−7054.13			−0.560593			−0.280296	+	0.959913i	$0.590433\pi$
$542$			18454.3i			1.46251i
$543$		−	21907.1i		−	1.73135i
$544$	−349.700			−0.0275611
$545$	3468.35	−	9282.55i	0.272602	−	0.729579i
$546$		0			0
$547$		−	5776.83i		−	0.451553i	−0.974179	−	0.225776i	$-0.927508\pi$
$547$		−	5776.83i		−	0.451553i	0.974179	−	0.225776i	$-0.0724919\pi$
$548$		−	232.141i		−	0.0180959i
$549$	2555.94			0.198697
$550$	8760.97	−	10087.0i	0.679216	−	0.782020i
$551$	6370.95			0.492580
$552$		−	34941.2i		−	2.69419i
$553$		0			0
$554$	2502.51			0.191916
$555$	−8818.12	+	23600.4i	−0.674430	+	1.80501i
$556$	160.318			0.0122284
$557$			20562.6i			1.56421i	0.623145	+	0.782106i	$0.285854\pi$
$557$			20562.6i			1.56421i	−0.623145	+	0.782106i	$0.714146\pi$
$558$		−	26425.4i		−	2.00479i
$559$	−569.235			−0.0430699
$560$		0			0
$561$	17391.7			1.30887
$562$			17848.4i			1.33966i
$563$		−	24009.5i		−	1.79730i	−0.438666	−	0.898650i	$-0.644549\pi$
$563$		−	24009.5i		−	1.79730i	0.438666	−	0.898650i	$-0.355451\pi$
$564$	49.2545			0.00367729
$565$	8021.98	+	2997.35i	0.597323	+	0.223185i
$566$	6423.37			0.477022
$567$		0			0
$568$		−	6010.11i		−	0.443977i
$569$	24157.5			1.77985			0.889925	−	0.456107i	$-0.150757\pi$
$569$	24157.5			1.77985			0.889925	+	0.456107i	$0.150757\pi$
$570$	2603.94	−	6969.08i	0.191346	−	0.512110i
$571$	−706.993			−0.0518157			−0.0259078	−	0.999664i	$-0.508248\pi$
$571$	−706.993			−0.0518157			−0.0259078	+	0.999664i	$0.508248\pi$
$572$		−	22.1936i		−	0.00162231i
$573$			45657.4i			3.32874i
$574$		0			0
$575$	14217.6	−	16369.5i	1.03115	−	1.18723i
$576$	27008.9			1.95377
$577$		−	16057.2i		−	1.15853i	−0.815139	−	0.579265i	$-0.803340\pi$
$577$		−	16057.2i		−	1.15853i	0.815139	−	0.579265i	$-0.196660\pi$
$578$			6401.44i			0.460665i
$579$	−25213.8			−1.80976
$580$	143.773	−	384.788i	0.0102929	−	0.0275474i
$581$		0			0
$582$			6244.07i			0.444717i
$583$		−	24160.0i		−	1.71630i
$584$	−4476.76			−0.317208
$585$	2233.14	+	834.397i	0.157827	+	0.0589710i
$586$	−16894.0			−1.19093
$587$		−	8605.63i		−	0.605098i	−0.953134	−	0.302549i	$-0.902162\pi$
$587$		−	8605.63i		−	0.605098i	0.953134	−	0.302549i	$-0.0978376\pi$
$588$		0			0
$589$	4462.28			0.312165
$590$	−11824.6	−	4418.16i	−0.825101	−	0.308293i
$591$	27934.6			1.94429
$592$			16339.0i			1.13434i
$593$		−	20355.6i		−	1.40962i	−0.709397	−	0.704809i	$-0.751033\pi$
$593$		−	20355.6i		−	1.40962i	0.709397	−	0.704809i	$-0.248967\pi$
$594$	25742.4			1.77815
$595$		0			0
$596$	96.5986			0.00663898
$597$		−	19286.2i		−	1.32216i
$598$		−	1962.70i		−	0.134215i
$599$	−22635.7			−1.54402			−0.772010	−	0.635610i	$-0.780749\pi$
$599$	−22635.7			−1.54402			−0.772010	+	0.635610i	$0.780749\pi$
$600$	19010.9	+	16511.7i	1.29353	+	1.12348i
$601$	22553.8			1.53077			0.765383	−	0.643575i	$-0.222550\pi$
$601$	22553.8			1.53077			0.765383	+	0.643575i	$0.222550\pi$
$602$		0			0
$603$		−	14158.1i		−	0.956159i
$604$	−36.3692			−0.00245007
$605$	−277.101	+	741.620i	−0.0186211	+	0.0498366i
$606$	−39499.4			−2.64778
$607$			17534.2i			1.17248i	0.810139	+	0.586238i	$0.199392\pi$
$607$			17534.2i			1.17248i	−0.810139	+	0.586238i	$0.800608\pi$
$608$		−	175.481i		−	0.0117051i
$609$		0			0
$610$	1420.55	+	530.778i	0.0942892	+	0.0352304i
$611$	−145.236			−0.00961641
$612$		−	415.743i		−	0.0274598i
$613$			10445.5i			0.688238i	0.938926	+	0.344119i	$0.111822\pi$
$613$			10445.5i			0.688238i	−0.938926	+	0.344119i	$0.888178\pi$
$614$	−27001.5			−1.77474
$615$	−4600.08	−	1718.78i	−0.301615	−	0.112696i
$616$		0			0
$617$			13218.9i			0.862516i	0.902229	+	0.431258i	$0.141930\pi$
$617$			13218.9i			0.862516i	−0.902229	+	0.431258i	$0.858070\pi$
$618$		−	24341.8i		−	1.58442i
$619$	23438.9			1.52195			0.760976	−	0.648780i	$-0.224720\pi$
$619$	23438.9			1.52195			0.760976	+	0.648780i	$0.224720\pi$
$620$	100.700	−	269.510i	0.00652294	−	0.0174577i
$621$	41775.5			2.69951
$622$			21629.8i			1.39433i
$623$		0			0
$624$	2322.02			0.148967
$625$	2187.74	+	15471.1i	0.140015	+	0.990149i
$626$	−26184.9			−1.67182
$627$			8727.23i			0.555873i
$628$		−	232.183i		−	0.0147534i
$629$	−12955.6			−0.821262
$630$		0			0
$631$	−874.004			−0.0551403			−0.0275702	−	0.999620i	$-0.508777\pi$
$631$	−874.004			−0.0551403			−0.0275702	+	0.999620i	$0.508777\pi$
$632$		−	10614.7i		−	0.668089i
$633$			25504.6i			1.60145i
$634$	−8786.72			−0.550419
$635$	−5289.38	−	1976.34i	−0.330555	−	0.123509i
$636$	−867.410			−0.0540802
$637$		0			0
$638$			26258.8i			1.62946i
$639$	14426.4			0.893116
$640$	15578.0	+	5820.62i	0.962151	+	0.359500i
$641$	23977.0			1.47743			0.738715	−	0.674017i	$-0.235433\pi$
$641$	23977.0			1.47743			0.738715	+	0.674017i	$0.235433\pi$
$642$		−	22169.9i		−	1.36289i
$643$		−	27698.0i		−	1.69876i	−0.527782	−	0.849380i	$-0.676976\pi$
$643$		−	27698.0i		−	1.69876i	0.527782	−	0.849380i	$-0.323024\pi$
$644$		0			0
$645$	5051.44	−	13519.4i	0.308372	−	0.825314i
$646$	3825.72			0.233004
$647$			10965.1i			0.666282i	0.942877	+	0.333141i	$0.108109\pi$
$647$			10965.1i			0.666282i	−0.942877	+	0.333141i	$0.891891\pi$
$648$			15965.6i			0.967881i
$649$	14807.6			0.895610
$650$	1067.87	+	927.488i	0.0644389	+	0.0559678i
$651$		0			0
$652$			381.894i			0.0229388i
$653$			12336.2i			0.739285i	0.929174	+	0.369642i	$0.120520\pi$
$653$			12336.2i			0.739285i	−0.929174	+	0.369642i	$0.879480\pi$
$654$	22743.0			1.35982
$655$	2633.32	−	7047.70i	0.157087	−	0.420422i
$656$	−3184.72			−0.189547
$657$		−	10745.8i		−	0.638105i
$658$		0			0
$659$	25275.6			1.49408			0.747040	−	0.664779i	$-0.231474\pi$
$659$	25275.6			1.49408			0.747040	+	0.664779i	$0.231474\pi$
$660$	527.102	+	196.947i	0.0310870	+	0.0116154i
$661$	4447.92			0.261731			0.130865	−	0.991400i	$-0.458224\pi$
$661$	4447.92			0.261731			0.130865	+	0.991400i	$0.458224\pi$
$662$			9233.67i			0.542110i
$663$			1841.19i			0.107852i
$664$	1629.34			0.0952270
$665$		0			0
$666$	−38499.7			−2.23999
$667$			42613.6i			2.47377i
$668$			534.357i			0.0309505i
$669$	42618.5			2.46297
$670$	2940.14	−	7868.87i	0.169534	−	0.453733i
$671$	−1778.92			−0.102347
$672$		0			0
$673$		−	30358.9i		−	1.73885i	−0.494061	−	0.869427i	$-0.664488\pi$
$673$		−	30358.9i		−	1.73885i	0.494061	−	0.869427i	$-0.335512\pi$
$674$	−10784.7			−0.616340
$675$	−19741.4	+	22729.4i	−1.12570	+	1.29608i
$676$	−326.208			−0.0185599
$677$		−	6916.48i		−	0.392647i	−0.980539	−	0.196324i	$-0.937100\pi$
$677$		−	6916.48i		−	0.392647i	0.980539	−	0.196324i	$-0.0629003\pi$
$678$			19654.5i			1.11331i
$679$		0			0
$680$	−4532.11	+	12129.5i	−0.255586	+	0.684039i
$681$	−8636.14			−0.485958
$682$			18392.0i			1.03265i
$683$		−	4532.72i		−	0.253938i	−0.991907	−	0.126969i	$-0.959475\pi$
$683$		−	4532.72i		−	0.253938i	0.991907	−	0.126969i	$-0.0405249\pi$
$684$	208.622			0.0116621
$685$	−16257.3	−	6074.40i	−0.906800	−	0.338819i
$686$		0			0
$687$			6687.56i			0.371392i
$688$		−	9359.77i		−	0.518660i
$689$	2557.72			0.141424
$690$	46614.4	+	17417.1i	2.57185	+	0.960954i
$691$	−27235.2			−1.49939			−0.749694	−	0.661785i	$-0.769799\pi$
$691$	−27235.2			−1.49939			−0.749694	+	0.661785i	$0.769799\pi$
$692$		−	334.197i		−	0.0183587i
$693$		0			0
$694$	−23534.7			−1.28727
$695$	4195.03	−	11227.4i	0.228959	−	0.612776i
$696$	−49489.8			−2.69527
$697$		−	2525.24i		−	0.137231i
$698$			20479.3i			1.11053i
$699$	13937.3			0.754160
$700$		0			0
$701$	−17144.3			−0.923726			−0.461863	−	0.886951i	$-0.652819\pi$
$701$	−17144.3			−0.923726			−0.461863	+	0.886951i	$0.652819\pi$
$702$			2725.24i			0.146521i
$703$		−	6501.19i		−	0.348787i
$704$	−18798.1			−1.00636
$705$	1288.84	−	3449.39i	0.0688516	−	0.184271i
$706$	−11965.7			−0.637867
$707$		0			0
$708$		−	531.635i		−	0.0282204i
$709$	−16724.1			−0.885877			−0.442939	−	0.896552i	$-0.646064\pi$
$709$	−16724.1			−0.885877			−0.442939	+	0.896552i	$0.646064\pi$
$710$	8017.98	+	2995.86i	0.423816	+	0.158356i
$711$	25479.2			1.34395
$712$		−	34787.4i		−	1.83106i
$713$			29847.0i			1.56771i
$714$		0			0
$715$	−1554.26	−	580.737i	−0.0812951	−	0.0303753i
$716$	−273.753			−0.0142886
$717$		−	24943.3i		−	1.29920i
$718$			8953.30i			0.465368i
$719$	4308.66			0.223485			0.111743	−	0.993737i	$-0.464357\pi$
$719$	4308.66			0.223485			0.111743	+	0.993737i	$0.464357\pi$
$720$	−13719.7	+	36718.9i	−0.710145	+	1.90060i
$721$		0			0
$722$		−	17660.9i		−	0.910347i
$723$			22922.7i			1.17912i
$724$	364.481			0.0187097
$725$	−23185.4	−	20137.4i	−1.18770	−	1.03157i
$726$	−1817.03			−0.0928875
$727$			29435.6i			1.50166i	0.660496	+	0.750830i	$0.270346\pi$
$727$			29435.6i			1.50166i	−0.660496	+	0.750830i	$0.729654\pi$
$728$		0			0
$729$	20127.8			1.02260
$730$	2231.53	−	5972.36i	0.113140	−	0.302804i
$731$	7421.58			0.375509
$732$			63.8683i			0.00322492i
$733$		−	6587.69i		−	0.331954i	−0.986130	−	0.165977i	$-0.946922\pi$
$733$		−	6587.69i		−	0.331954i	0.986130	−	0.165977i	$-0.0530777\pi$
$734$	−4919.57			−0.247390
$735$		0			0
$736$	1173.75			0.0587839
$737$			9854.01i			0.492506i
$738$		−	7504.16i		−	0.374298i
$739$	−3684.46			−0.183404			−0.0917018	−	0.995787i	$-0.529231\pi$
$739$	−3684.46			−0.183404			−0.0917018	+	0.995787i	$0.529231\pi$
$740$	−392.654	−	146.712i	−0.0195058	−	0.00728818i
$741$	−923.917			−0.0458042
$742$		0			0
$743$		−	12271.9i		−	0.605940i	−0.953000	−	0.302970i	$-0.902022\pi$
$743$		−	12271.9i		−	0.605940i	0.953000	−	0.302970i	$-0.0979783\pi$
$744$	−34663.2			−1.70808
$745$	2527.68	−	6764.98i	0.124305	−	0.332684i
$746$	8046.24			0.394898
$747$			3911.01i			0.191561i
$748$			289.355i			0.0141442i
$749$		0			0
$750$	−31504.4	+	17131.5i	−1.53384	+	0.834072i
$751$	−30871.0			−1.50000			−0.749999	−	0.661439i	$-0.769946\pi$
$751$	−30871.0			−1.50000			−0.749999	+	0.661439i	$0.769946\pi$
$752$		−	2388.08i		−	0.115803i
$753$			26363.5i			1.27588i
$754$	−2779.91			−0.134269
$755$	−951.669	+	2547.00i	−0.0458739	+	0.122775i
$756$		0			0
$757$			11442.1i			0.549368i	0.961535	+	0.274684i	$0.0885732\pi$
$757$			11442.1i			0.549368i	−0.961535	+	0.274684i	$0.911427\pi$
$758$			29878.1i			1.43169i
$759$	−58374.2			−2.79163
$760$	−6086.66	−	2274.24i	−0.290509	−	0.108546i
$761$	−14423.3			−0.687048			−0.343524	−	0.939144i	$-0.611621\pi$
$761$	−14423.3			−0.687048			−0.343524	+	0.939144i	$0.611621\pi$
$762$		−	12959.4i		−	0.616102i
$763$		0			0
$764$	−759.630			−0.0359718
$765$	−29115.3	−	10878.7i	−1.37603	−	0.514144i
$766$	736.681			0.0347485
$767$			1567.63i			0.0737988i
$768$			2064.01i			0.0969775i
$769$	26772.8			1.25546			0.627731	−	0.778430i	$-0.283984\pi$
$769$	26772.8			1.25546			0.627731	+	0.778430i	$0.283984\pi$
$770$		0			0
$771$	24495.9			1.14423
$772$		−	419.496i		−	0.0195570i
$773$			27669.3i			1.28745i	0.765258	+	0.643724i	$0.222611\pi$
$773$			27669.3i			1.28745i	−0.765258	+	0.643724i	$0.777389\pi$
$774$	22054.4			1.02420
$775$	−16239.3	−	14104.5i	−0.752686	−	0.653739i
$776$	5453.45			0.252278
$777$		0			0
$778$		−	13057.2i		−	0.601702i
$779$	1267.18			0.0582816
$780$	−20.8500	+	55.8021i	−0.000957117	+	0.00256159i
$781$	−10040.7			−0.460034
$782$			25589.2i			1.17017i
$783$		−	59169.8i		−	2.70058i
$784$		0			0
$785$	−16260.2	−	6075.51i	−0.739302	−	0.276235i
$786$	17267.4			0.783599
$787$			10934.5i			0.495263i	0.968854	+	0.247632i	$0.0796523\pi$
$787$			10934.5i			0.495263i	−0.968854	+	0.247632i	$0.920348\pi$
$788$			464.765i			0.0210109i
$789$	27210.8			1.22779
$790$	14160.9	+	5291.13i	0.637752	+	0.238291i
$791$		0			0
$792$		−	45138.2i		−	2.02515i
$793$		−	188.328i		−	0.00843343i
$794$	10347.2			0.462478
$795$	−22697.4	+	60746.3i	−1.01257	+	2.71000i
$796$	320.876			0.0142879
$797$			31967.3i			1.42075i	0.703823	+	0.710376i	$0.251475\pi$
$797$			31967.3i			1.42075i	−0.703823	+	0.710376i	$0.748525\pi$
$798$		0			0
$799$	1893.56			0.0838415
$800$	−554.664	+	638.616i	−0.0245129	+	0.0282231i
$801$	83502.3			3.68341
$802$			18151.4i			0.799186i
$803$			7479.06i			0.328680i
$804$	353.786			0.0155187
$805$		0			0
$806$	−1947.08			−0.0850906
$807$		−	12965.7i		−	0.565568i
$808$			34498.1i			1.50203i
$809$	17924.8			0.778989			0.389495	−	0.921029i	$-0.372650\pi$
$809$	17924.8			0.778989			0.389495	+	0.921029i	$0.372650\pi$
$810$	−21299.4	−	7958.35i	−0.923931	−	0.345220i
$811$	−28541.4			−1.23579			−0.617895	−	0.786261i	$-0.712014\pi$
$811$	−28541.4			−1.23579			−0.617895	+	0.786261i	$0.712014\pi$
$812$		0			0
$813$			58106.2i			2.50661i
$814$	26795.6			1.15379
$815$	26744.7	+	9992.97i	1.14948	+	0.429495i
$816$	−30274.1			−1.29878
$817$			3724.19i			0.159477i
$818$		−	18659.7i		−	0.797580i
$819$		0			0
$820$	28.5964	−	76.5342i	0.00121784	−	0.00325938i
$821$	18878.6			0.802517			0.401259	−	0.915965i	$-0.368573\pi$
$821$	18878.6			0.802517			0.401259	+	0.915965i	$0.368573\pi$
$822$		−	39831.6i		−	1.69013i
$823$		−	46589.1i		−	1.97326i	−0.162971	−	0.986631i	$-0.552108\pi$
$823$		−	46589.1i		−	1.97326i	0.162971	−	0.986631i	$-0.447892\pi$
$824$	−21259.7			−0.898807
$825$	27585.2	−	31760.4i	1.16411	−	1.34031i
$826$		0			0
$827$			14649.8i			0.615989i	0.951388	+	0.307994i	$0.0996578\pi$
$827$			14649.8i			0.615989i	−0.951388	+	0.307994i	$0.900342\pi$
$828$			1395.42i			0.0585678i
$829$	−34408.0			−1.44154			−0.720771	−	0.693173i	$-0.756212\pi$
$829$	−34408.0			−1.44154			−0.720771	+	0.693173i	$0.756212\pi$
$830$	−812.178	+	2173.68i	−0.0339652	+	0.0909029i
$831$	7879.51			0.328926
$832$		−	1990.07i		−	0.0829248i
$833$		0			0
$834$	27508.0			1.14212
$835$	37422.0	+	13982.5i	1.55095	+	0.579501i
$836$	−145.200			−0.00600700
$837$		−	41443.2i		−	1.71145i
$838$			18080.7i			0.745331i
$839$	25934.2			1.06716			0.533580	−	0.845749i	$-0.320846\pi$
$839$	25934.2			1.06716			0.533580	+	0.845749i	$0.320846\pi$
$840$		0			0
$841$	35967.9			1.47476
$842$		−	23236.5i		−	0.951048i
$843$			56198.3i			2.29605i
$844$	−424.335			−0.0173060
$845$	−8535.84	+	22845.0i	−0.347505	+	0.930048i
$846$	5627.02			0.228677
$847$		0			0
$848$			42055.9i			1.70307i
$849$	20224.9			0.817571
$850$	−13922.7	−	12092.4i	−0.561816	−	0.487960i
$851$	43484.8			1.75163
$852$			360.490i			0.0144955i
$853$		−	48456.3i		−	1.94503i	−0.232836	−	0.972516i	$-0.574801\pi$
$853$		−	48456.3i		−	1.94503i	0.232836	−	0.972516i	$-0.425199\pi$
$854$		0			0
$855$	5458.99	−	14610.2i	0.218355	−	0.584395i
$856$	−19362.7			−0.773136
$857$		−	36273.9i		−	1.44585i	−0.690928	−	0.722924i	$-0.742798\pi$
$857$		−	36273.9i		−	1.44585i	0.690928	−	0.722924i	$-0.257202\pi$
$858$		−	3808.06i		−	0.151521i
$859$	28067.2			1.11483			0.557415	−	0.830234i	$-0.311793\pi$
$859$	28067.2			1.11483			0.557415	+	0.830234i	$0.311793\pi$
$860$	224.931	+	84.0437i	0.00891870	+	0.00333240i
$861$		0			0
$862$		−	41015.7i		−	1.62065i
$863$			8330.92i			0.328607i	0.986410	+	0.164303i	$0.0525376\pi$
$863$			8330.92i			0.328607i	−0.986410	+	0.164303i	$0.947462\pi$
$864$	−1629.77			−0.0641736
$865$	−23404.4	−	8744.88i	−0.919970	−	0.343740i
$866$	23977.1			0.940849
$867$			20155.9i			0.789538i
$868$		0			0
$869$	−17733.4			−0.692251
$870$	24669.2	−	66023.5i	0.961337	−	2.57288i
$871$	−1043.20			−0.0405828
$872$		−	19863.3i		−	0.771395i
$873$			13090.3i			0.507489i
$874$	−12840.8			−0.496965
$875$		0			0
$876$	268.519			0.0103566
$877$		−	16469.6i		−	0.634137i	−0.948403	−	0.317068i	$-0.897302\pi$
$877$		−	16469.6i		−	0.634137i	0.948403	−	0.317068i	$-0.102698\pi$
$878$		−	50988.0i		−	1.95987i
$879$	−53193.1			−2.04114
$880$	9548.88	−	25556.2i	0.365787	−	0.978977i
$881$	46635.9			1.78343			0.891715	−	0.452597i	$-0.149502\pi$
$881$	46635.9			1.78343			0.891715	+	0.452597i	$0.149502\pi$
$882$		0			0
$883$		−	14075.8i		−	0.536453i	−0.963356	−	0.268227i	$-0.913562\pi$
$883$		−	14075.8i		−	0.536453i	0.963356	−	0.268227i	$-0.0864376\pi$
$884$	−30.6329			−0.00116549
$885$	−37231.4	−	13911.2i	−1.41415	−	0.528385i
$886$	5428.48			0.205839
$887$		−	26222.9i		−	0.992649i	−0.868137	−	0.496324i	$-0.834683\pi$
$887$		−	26222.9i		−	0.992649i	0.868137	−	0.496324i	$-0.165317\pi$
$888$			50501.5i			1.90847i
$889$		0			0
$890$	46409.2	+	17340.5i	1.74791	+	0.653094i
$891$	26672.8			1.00289
$892$			709.069i			0.0266159i
$893$			950.199i			0.0356072i
$894$	16574.8			0.620070
$895$	−7163.27	+	19171.5i	−0.267533	+	0.716012i
$896$		0			0
$897$		−	6179.84i		−	0.230032i
$898$			14803.8i			0.550121i
$899$	42274.6			1.56834
$900$	−759.224	−	659.417i	−0.0281194	−	0.0244228i
$901$	−33347.1			−1.23302
$902$			5222.87i			0.192796i
$903$		0			0
$904$	17165.9			0.631558
$905$	9537.34	−	25525.3i	0.350312	−	0.937558i
$906$	−6240.37			−0.228833
$907$		−	15373.0i		−	0.562793i	−0.959592	−	0.281396i	$-0.909202\pi$
$907$		−	15373.0i		−	0.562793i	0.959592	−	0.281396i	$-0.0907975\pi$
$908$		−	143.685i		−	0.00525147i
$909$	−82807.8			−3.02152
$910$		0			0
$911$	−21189.3			−0.770619			−0.385310	−	0.922787i	$-0.625905\pi$
$911$	−21189.3			−0.770619			−0.385310	+	0.922787i	$0.625905\pi$
$912$		−	15191.7i		−	0.551587i
$913$		−	2722.05i		−	0.0986710i
$914$	31969.7			1.15696
$915$	4472.81	+	1671.23i	0.161603	+	0.0603817i
$916$	−111.265			−0.00401342
$917$		0			0
$918$		−	35531.1i		−	1.27745i
$919$	18364.2			0.659172			0.329586	−	0.944126i	$-0.393091\pi$
$919$	18364.2			0.659172			0.329586	+	0.944126i	$0.393091\pi$
$920$	15211.8	−	40712.1i	0.545128	−	1.45896i
$921$	−85018.2			−3.04174
$922$		−	49303.4i		−	1.76109i
$923$		−	1062.97i		−	0.0379070i
$924$		0			0
$925$	−20549.1	+	23659.3i	−0.730432	+	0.840988i
$926$	1100.96			0.0390710
$927$		−	51031.0i		−	1.80807i
$928$		−	1662.47i		−	0.0588073i
$929$	15460.6			0.546011			0.273006	−	0.962012i	$-0.411982\pi$
$929$	15460.6			0.546011			0.273006	+	0.962012i	$0.411982\pi$
$930$	17278.5	−	46243.5i	0.609232	−	1.63052i
$931$		0			0
$932$			231.883i			0.00814978i
$933$			68104.5i			2.38975i
$934$	14374.6			0.503589
$935$	20264.1	+	7571.53i	0.708778	+	0.264829i
$936$	4778.60			0.166873
$937$		−	28824.7i		−	1.00498i	−0.864584	−	0.502488i	$-0.832418\pi$
$937$		−	28824.7i		−	1.00498i	0.864584	−	0.502488i	$-0.167582\pi$
$938$		0			0
$939$	−82446.9			−2.86534
$940$	57.3895	+	21.4431i	0.00199132	+	0.000744040i
$941$	−42172.5			−1.46098			−0.730492	−	0.682922i	$-0.760709\pi$
$941$	−42172.5			−1.46098			−0.730492	+	0.682922i	$0.760709\pi$
$942$		−	39838.9i		−	1.37794i
$943$			8475.83i			0.292695i
$944$	−25776.0			−0.888705
$945$		0			0
$946$	−15349.8			−0.527552
$947$			8926.33i			0.306301i	0.988203	+	0.153150i	$0.0489419\pi$
$947$			8926.33i			0.306301i	−0.988203	+	0.153150i	$0.951058\pi$
$948$			636.679i			0.0218126i
$949$	−791.778			−0.0270835
$950$	6068.03	−	6986.47i	0.207235	−	0.238601i
$951$	−27666.3			−0.943366
$952$		0			0
$953$			40420.6i			1.37392i	0.726693	+	0.686962i	$0.241056\pi$
$953$			40420.6i			1.37392i	−0.726693	+	0.686962i	$0.758944\pi$
$954$	−99096.2			−3.36306
$955$	−19877.1	+	53198.3i	−0.673517	+	1.80257i
$956$	414.996			0.0140397
$957$			82679.8i			2.79274i
$958$		−	24784.8i		−	0.835868i
$959$		0			0
$960$	47264.6	+	17660.1i	1.58902	+	0.593725i
$961$	−181.408			−0.00608935
$962$			2836.74i			0.0950730i
$963$		−	46477.6i		−	1.55526i
$964$	−381.378			−0.0127421
$965$	−29378.1	−	10976.9i	−0.980016	−	0.366175i
$966$		0			0
$967$		−	33914.1i		−	1.12782i	−0.825836	−	0.563910i	$-0.809296\pi$
$967$		−	33914.1i		−	1.12782i	0.825836	−	0.563910i	$-0.190704\pi$
$968$			1586.96i			0.0526930i
$969$	12045.8			0.399348
$970$	−2718.38	+	7275.35i	−0.0899813	+	0.240822i
$971$	59339.0			1.96115			0.980577	−	0.196136i	$-0.0628393\pi$
$971$	59339.0			1.96115			0.980577	+	0.196136i	$0.0628393\pi$
$972$			14.8585i			0.000490315i
$973$		0			0
$974$	−2542.08			−0.0836277
$975$	3362.35	+	2920.33i	0.110442	+	0.0959236i
$976$	3096.62			0.101558
$977$			7032.14i			0.230274i	0.993350	+	0.115137i	$0.0367308\pi$
$977$			7032.14i			0.230274i	−0.993350	+	0.115137i	$0.963269\pi$
$978$			65526.8i			2.14245i
$979$	−58117.3			−1.89728
$980$		0			0
$981$	47679.1			1.55176
$982$			4460.48i			0.144949i
$983$		−	1703.63i		−	0.0552772i	−0.999618	−	0.0276386i	$-0.991201\pi$
$983$		−	1703.63i		−	0.0552772i	0.999618	−	0.0276386i	$-0.00879876\pi$
$984$	−9843.50			−0.318902
$985$	32548.4	+	12161.4i	1.05287	+	0.393397i
$986$	36244.0			1.17063
$987$		0			0
$988$		−	15.3718i		−	0.000494980i
$989$	−24910.1			−0.800906
$990$	60218.1	+	22500.0i	1.93319	+	0.722321i
$991$	12740.3			0.408383			0.204192	−	0.978931i	$-0.434543\pi$
$991$	12740.3			0.408383			0.204192	+	0.978931i	$0.434543\pi$
$992$		−	1164.41i		−	0.0372682i
$993$			29073.6i			0.929126i
$994$		0			0
$995$	8396.32	−	22471.5i	0.267519	−	0.715975i
$996$	−97.7290			−0.00310910
$997$			16609.6i			0.527615i	0.964575	+	0.263808i	$0.0849784\pi$
$997$			16609.6i			0.527615i	−0.964575	+	0.263808i	$0.915022\pi$
$998$		−	23506.9i		−	0.745589i
$999$	−60379.4			−1.91223

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.b.d.99.8		10
5.2	odd	4		1225.4.a.be.1.2		5
5.3	odd	4		1225.4.a.bh.1.4		5
5.4	even	2	inner	245.4.b.d.99.3		10
7.2	even	3		245.4.j.f.214.8		20
7.3	odd	6		245.4.j.e.79.3		20
7.4	even	3		245.4.j.f.79.3		20
7.5	odd	6		245.4.j.e.214.8		20
7.6	odd	2		35.4.b.a.29.8	yes	10
21.20	even	2		315.4.d.c.64.3		10
28.27	even	2		560.4.g.f.449.10		10
35.4	even	6		245.4.j.f.79.8		20
35.9	even	6		245.4.j.f.214.3		20
35.13	even	4		175.4.a.j.1.4		5
35.19	odd	6		245.4.j.e.214.3		20
35.24	odd	6		245.4.j.e.79.8		20
35.27	even	4		175.4.a.i.1.2		5
35.34	odd	2		35.4.b.a.29.3	✓	10
105.62	odd	4		1575.4.a.bq.1.4		5
105.83	odd	4		1575.4.a.bn.1.2		5
105.104	even	2		315.4.d.c.64.8		10
140.139	even	2		560.4.g.f.449.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.b.a.29.3	✓	10	35.34	odd	2
35.4.b.a.29.8	yes	10	7.6	odd	2
175.4.a.i.1.2		5	35.27	even	4
175.4.a.j.1.4		5	35.13	even	4
245.4.b.d.99.3		10	5.4	even	2	inner
245.4.b.d.99.8		10	1.1	even	1	trivial
245.4.j.e.79.3		20	7.3	odd	6
245.4.j.e.79.8		20	35.24	odd	6
245.4.j.e.214.3		20	35.19	odd	6
245.4.j.e.214.8		20	7.5	odd	6
245.4.j.f.79.3		20	7.4	even	3
245.4.j.f.79.8		20	35.4	even	6
245.4.j.f.214.3		20	35.9	even	6
245.4.j.f.214.8		20	7.2	even	3
315.4.d.c.64.3		10	21.20	even	2
315.4.d.c.64.8		10	105.104	even	2
560.4.g.f.449.1		10	140.139	even	2
560.4.g.f.449.10		10	28.27	even	2
1225.4.a.be.1.2		5	5.2	odd	4
1225.4.a.bh.1.4		5	5.3	odd	4
1575.4.a.bn.1.2		5	105.83	odd	4
1575.4.a.bq.1.4		5	105.62	odd	4

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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.85474i q^{2} +8.98858i q^{3} -0.149548 q^{4} +(-3.91321 + 10.4731i) q^{5} -25.6601 q^{6} +22.4110i q^{8} -53.7945 q^{9} +(-29.8981 - 11.1712i) q^{10} +37.4408 q^{11} -1.34423i q^{12} +3.96370i q^{13} +(-94.1387 - 35.1742i) q^{15} -65.1740 q^{16} -51.6780i q^{17} -153.569i q^{18} +25.9323 q^{19} +(0.585214 - 1.56624i) q^{20} +106.884i q^{22} +173.454i q^{23} -201.443 q^{24} +(-94.3736 - 81.9673i) q^{25} -11.3154 q^{26} -240.845i q^{27} +245.676 q^{29} +(100.413 - 268.742i) q^{30} +172.074 q^{31} -6.76690i q^{32} +336.539i q^{33} +147.527 q^{34} +8.04488 q^{36} -250.699i q^{37} +74.0300i q^{38} -35.6281 q^{39} +(-234.714 - 87.6990i) q^{40} +48.8649 q^{41} +143.612i q^{43} -5.59920 q^{44} +(210.509 - 563.398i) q^{45} -495.167 q^{46} +36.6415i q^{47} -585.822i q^{48} +(233.995 - 269.412i) q^{50} +464.511 q^{51} -0.592765i q^{52} -645.286i q^{53} +687.549 q^{54} +(-146.514 + 392.123i) q^{55} +233.094i q^{57} +701.343i q^{58} +395.495 q^{59} +(14.0783 + 5.26024i) q^{60} -47.5130 q^{61} +491.228i q^{62} -502.074 q^{64} +(-41.5125 - 15.5108i) q^{65} -960.733 q^{66} +263.189i q^{67} +7.72835i q^{68} -1559.11 q^{69} -268.177 q^{71} -1205.59i q^{72} +199.757i q^{73} +715.680 q^{74} +(736.769 - 848.284i) q^{75} -3.87813 q^{76} -101.709i q^{78} -473.640 q^{79} +(255.040 - 682.577i) q^{80} +712.399 q^{81} +139.497i q^{82} -72.7028i q^{83} +(541.231 + 202.227i) q^{85} -409.975 q^{86} +2208.28i q^{87} +839.086i q^{88} -1552.25 q^{89} +(1608.36 + 600.950i) q^{90} -25.9398i q^{92} +1546.70i q^{93} -104.602 q^{94} +(-101.478 + 271.593i) q^{95} +60.8248 q^{96} -243.338i q^{97} -2014.11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 36 q^{4} - 6 q^{5} - 12 q^{6} - 46 q^{9} + 16 q^{10} + 84 q^{11} + 8 q^{15} + 148 q^{16} - 72 q^{19} + 68 q^{20} - 72 q^{24} - 362 q^{25} + 620 q^{26} + 88 q^{29} + 52 q^{30} - 120 q^{31} - 964 q^{34}+ \cdots - 5304 q^{99}+O(q^{100}) \) 10 * q - 36 * q^4 - 6 * q^5 - 12 * q^6 - 46 * q^9 + 16 * q^10 + 84 * q^11 + 8 * q^15 + 148 * q^16 - 72 * q^19 + 68 * q^20 - 72 * q^24 - 362 * q^25 + 620 * q^26 + 88 * q^29 + 52 * q^30 - 120 * q^31 - 964 * q^34 - 420 * q^36 + 212 * q^39 - 1396 * q^40 + 852 * q^41 - 1424 * q^44 + 510 * q^45 + 176 * q^46 + 1644 * q^50 + 1276 * q^51 + 996 * q^54 + 1136 * q^55 - 864 * q^59 - 1692 * q^60 + 884 * q^61 - 2724 * q^64 + 520 * q^65 - 1148 * q^66 - 4808 * q^69 + 880 * q^71 + 3024 * q^74 - 720 * q^75 + 2672 * q^76 - 3580 * q^79 + 2316 * q^80 - 302 * q^81 + 1572 * q^85 + 2432 * q^86 + 1492 * q^89 + 7748 * q^90 - 1652 * q^94 - 1628 * q^95 - 4080 * q^96 - 5304 * q^99

Introduction

L-functions

Modular forms

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Database

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