LMFDB - Embedded newform 60.4.i.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,4,Mod(17,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("60.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	60.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.54011460034$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.2
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	60.17
Dual form			60.4.i.a.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.53553 + 4.53553i) q^{3} +(3.53553 - 10.6066i) q^{5} +(23.0000 + 23.0000i) q^{7} +(-14.1421 + 23.0000i) q^{9} +O(q^{10})$	\(q+(2.53553 + 4.53553i) q^{3} +(3.53553 - 10.6066i) q^{5} +(23.0000 + 23.0000i) q^{7} +(-14.1421 + 23.0000i) q^{9} +7.07107i q^{11} +(-24.0000 + 24.0000i) q^{13} +(57.0711 - 10.8579i) q^{15} +(77.7817 - 77.7817i) q^{17} -68.0000i q^{19} +(-46.0000 + 162.635i) q^{21} +(-98.9949 - 98.9949i) q^{23} +(-100.000 - 75.0000i) q^{25} +(-140.175 - 5.82486i) q^{27} -134.350 q^{29} +94.0000 q^{31} +(-32.0711 + 17.9289i) q^{33} +(325.269 - 162.635i) q^{35} +(-66.0000 - 66.0000i) q^{37} +(-169.706 - 48.0000i) q^{39} +197.990i q^{41} +(126.000 - 126.000i) q^{43} +(193.952 + 231.317i) q^{45} +(84.8528 - 84.8528i) q^{47} +715.000i q^{49} +(550.000 + 155.563i) q^{51} +(-325.269 - 325.269i) q^{53} +(75.0000 + 25.0000i) q^{55} +(308.416 - 172.416i) q^{57} -49.4975 q^{59} -126.000 q^{61} +(-854.269 + 203.731i) q^{63} +(169.706 + 339.411i) q^{65} +(68.0000 + 68.0000i) q^{67} +(197.990 - 700.000i) q^{69} +947.523i q^{71} +(403.000 - 403.000i) q^{73} +(86.6117 - 643.718i) q^{75} +(-162.635 + 162.635i) q^{77} -234.000i q^{79} +(-329.000 - 650.538i) q^{81} +(721.249 + 721.249i) q^{83} +(-550.000 - 1100.00i) q^{85} +(-340.650 - 609.350i) q^{87} -1032.38 q^{89} -1104.00 q^{91} +(238.340 + 426.340i) q^{93} +(-721.249 - 240.416i) q^{95} +(723.000 + 723.000i) q^{97} +(-162.635 - 100.000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 92 q^{7}+O(q^{10}) $ 4 * q - 4 * q^3 + 92 * q^7	$ 4 q - 4 q^{3} + 92 q^{7} - 96 q^{13} + 200 q^{15} - 184 q^{21} - 400 q^{25} - 292 q^{27} + 376 q^{31} - 100 q^{33} - 264 q^{37} + 504 q^{43} - 200 q^{45} + 2200 q^{51} + 300 q^{55} + 272 q^{57} - 504 q^{61} - 2116 q^{63} + 272 q^{67} + 1612 q^{73} + 700 q^{75} - 1316 q^{81} - 2200 q^{85} - 1900 q^{87} - 4416 q^{91} - 376 q^{93} + 2892 q^{97}+O(q^{100}) $ 4 * q - 4 * q^3 + 92 * q^7 - 96 * q^13 + 200 * q^15 - 184 * q^21 - 400 * q^25 - 292 * q^27 + 376 * q^31 - 100 * q^33 - 264 * q^37 + 504 * q^43 - 200 * q^45 + 2200 * q^51 + 300 * q^55 + 272 * q^57 - 504 * q^61 - 2116 * q^63 + 272 * q^67 + 1612 * q^73 + 700 * q^75 - 1316 * q^81 - 2200 * q^85 - 1900 * q^87 - 4416 * q^91 - 376 * q^93 + 2892 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.53553	+	4.53553i	0.487964	+	0.872864i
$3$	2.53553	+	4.53553i	0.487964	+	0.872864i
$4$		0			0
$5$	3.53553	−	10.6066i	0.316228	−	0.948683i
$5$	3.53553	−	10.6066i	0.316228	−	0.948683i
$6$		0			0
$7$	23.0000	+	23.0000i	1.24188	+	1.24188i	0.959219	+	0.282664i	$0.0912183\pi$
$7$	23.0000	+	23.0000i	1.24188	+	1.24188i	0.282664	+	0.959219i	$0.408782\pi$
$8$		0			0
$9$	−14.1421	+	23.0000i	−0.523783	+	0.851852i
$10$		0			0
$11$			7.07107i			0.193819i	0.995293	+	0.0969094i	$0.0308957\pi$
$11$			7.07107i			0.193819i	−0.995293	+	0.0969094i	$0.969104\pi$
$12$		0			0
$13$	−24.0000	+	24.0000i	−0.512031	+	0.512031i	−0.915148	−	0.403117i	$-0.867927\pi$
$13$	−24.0000	+	24.0000i	−0.512031	+	0.512031i	0.403117	+	0.915148i	$0.367927\pi$
$14$		0			0
$15$	57.0711	−	10.8579i	0.982379	−	0.186899i
$16$		0			0
$17$	77.7817	−	77.7817i	1.10970	−	1.10970i	0.116507	−	0.993190i	$-0.462830\pi$
$17$	77.7817	−	77.7817i	1.10970	−	1.10970i	0.993190	−	0.116507i	$-0.0371697\pi$
$18$		0			0
$19$		−	68.0000i		−	0.821067i	−0.911846	−	0.410533i	$-0.865343\pi$
$19$		−	68.0000i		−	0.821067i	0.911846	−	0.410533i	$-0.134657\pi$
$20$		0			0
$21$	−46.0000	+	162.635i	−0.478001	+	1.68999i
$22$		0			0
$23$	−98.9949	−	98.9949i	−0.897473	−	0.897473i	0.0977393	−	0.995212i	$-0.468839\pi$
$23$	−98.9949	−	98.9949i	−0.897473	−	0.897473i	−0.995212	+	0.0977393i	$0.968839\pi$
$24$		0			0
$25$	−100.000	−	75.0000i	−0.800000	−	0.600000i
$26$		0			0
$27$	−140.175	−	5.82486i	−0.999138	−	0.0415183i
$28$		0			0
$29$	−134.350			−0.860284			−0.430142	−	0.902761i	$-0.641536\pi$
$29$	−134.350			−0.860284			−0.430142	+	0.902761i	$0.641536\pi$
$30$		0			0
$31$	94.0000			0.544610			0.272305	−	0.962211i	$-0.412214\pi$
$31$	94.0000			0.544610			0.272305	+	0.962211i	$0.412214\pi$
$32$		0			0
$33$	−32.0711	+	17.9289i	−0.169177	+	0.0945766i
$34$		0			0
$35$	325.269	−	162.635i	1.57087	−	0.785436i
$36$		0			0
$37$	−66.0000	−	66.0000i	−0.293252	−	0.293252i	0.545111	−	0.838364i	$-0.316487\pi$
$37$	−66.0000	−	66.0000i	−0.293252	−	0.293252i	−0.838364	+	0.545111i	$0.816487\pi$
$38$		0			0
$39$	−169.706	−	48.0000i	−0.696786	−	0.197081i
$40$		0			0
$41$			197.990i			0.754167i	0.926179	+	0.377083i	$0.123073\pi$
$41$			197.990i			0.754167i	−0.926179	+	0.377083i	$0.876927\pi$
$42$		0			0
$43$	126.000	−	126.000i	0.446856	−	0.446856i	−0.447452	−	0.894308i	$-0.647668\pi$
$43$	126.000	−	126.000i	0.446856	−	0.446856i	0.894308	+	0.447452i	$0.147668\pi$
$44$		0			0
$45$	193.952	+	231.317i	0.642503	+	0.766283i
$46$		0			0
$47$	84.8528	−	84.8528i	0.263342	−	0.263342i	−0.563069	−	0.826410i	$-0.690379\pi$
$47$	84.8528	−	84.8528i	0.263342	−	0.263342i	0.826410	+	0.563069i	$0.190379\pi$
$48$		0			0
$49$			715.000i			2.08455i
$50$		0			0
$51$	550.000	+	155.563i	1.51011	+	0.427122i
$52$		0			0
$53$	−325.269	−	325.269i	−0.843003	−	0.843003i	0.146246	−	0.989248i	$-0.453281\pi$
$53$	−325.269	−	325.269i	−0.843003	−	0.843003i	−0.989248	+	0.146246i	$0.953281\pi$
$54$		0			0
$55$	75.0000	+	25.0000i	0.183873	+	0.0612909i
$56$		0			0
$57$	308.416	−	172.416i	0.716680	−	0.400651i
$58$		0			0
$59$	−49.4975			−0.109221			−0.0546104	−	0.998508i	$-0.517392\pi$
$59$	−49.4975			−0.109221			−0.0546104	+	0.998508i	$0.517392\pi$
$60$		0			0
$61$	−126.000			−0.264470			−0.132235	−	0.991218i	$-0.542215\pi$
$61$	−126.000			−0.264470			−0.132235	+	0.991218i	$0.542215\pi$
$62$		0			0
$63$	−854.269	+	203.731i	−1.70838	+	0.407423i
$64$		0			0
$65$	169.706	+	339.411i	0.323837	+	0.647674i
$66$		0			0
$67$	68.0000	+	68.0000i	0.123993	+	0.123993i	0.766380	−	0.642387i	$-0.222056\pi$
$67$	68.0000	+	68.0000i	0.123993	+	0.123993i	−0.642387	+	0.766380i	$0.722056\pi$
$68$		0			0
$69$	197.990	−	700.000i	0.345437	−	1.22131i
$70$		0			0
$71$			947.523i			1.58381i	0.610646	+	0.791904i	$0.290910\pi$
$71$			947.523i			1.58381i	−0.610646	+	0.791904i	$0.709090\pi$
$72$		0			0
$73$	403.000	−	403.000i	0.646131	−	0.646131i	−0.305925	−	0.952056i	$-0.598966\pi$
$73$	403.000	−	403.000i	0.646131	−	0.646131i	0.952056	+	0.305925i	$0.0989655\pi$
$74$		0			0
$75$	86.6117	−	643.718i	0.133347	−	0.991069i
$76$		0			0
$77$	−162.635	+	162.635i	−0.240700	+	0.240700i
$78$		0			0
$79$		−	234.000i		−	0.333254i	−0.986020	−	0.166627i	$-0.946712\pi$
$79$		−	234.000i		−	0.333254i	0.986020	−	0.166627i	$-0.0532876\pi$
$80$		0			0
$81$	−329.000	−	650.538i	−0.451303	−	0.892371i
$82$		0			0
$83$	721.249	+	721.249i	0.953824	+	0.953824i	0.998980	−	0.0451564i	$-0.0143786\pi$
$83$	721.249	+	721.249i	0.953824	+	0.953824i	−0.0451564	+	0.998980i	$0.514379\pi$
$84$		0			0
$85$	−550.000	−	1100.00i	−0.701834	−	1.40367i
$86$		0			0
$87$	−340.650	−	609.350i	−0.419787	−	0.750910i
$88$		0			0
$89$	−1032.38			−1.22957			−0.614784	−	0.788695i	$-0.710757\pi$
$89$	−1032.38			−1.22957			−0.614784	+	0.788695i	$0.710757\pi$
$90$		0			0
$91$	−1104.00			−1.27177
$92$		0			0
$93$	238.340	+	426.340i	0.265750	+	0.475370i
$94$		0			0
$95$	−721.249	−	240.416i	−0.778932	−	0.259644i
$96$		0			0
$97$	723.000	+	723.000i	0.756799	+	0.756799i	0.975738	−	0.218939i	$-0.0702597\pi$
$97$	723.000	+	723.000i	0.756799	+	0.756799i	−0.218939	+	0.975738i	$0.570260\pi$
$98$		0			0
$99$	−162.635	−	100.000i	−0.165105	−	0.101519i
$100$		0			0
$101$		−	728.320i		−	0.717530i	−0.933428	−	0.358765i	$-0.883198\pi$
$101$		−	728.320i		−	0.717530i	0.933428	−	0.358765i	$-0.116802\pi$
$102$		0			0
$103$	73.0000	−	73.0000i	0.0698340	−	0.0698340i	−0.671327	−	0.741161i	$-0.734275\pi$
$103$	73.0000	−	73.0000i	0.0698340	−	0.0698340i	0.741161	+	0.671327i	$0.234275\pi$
$104$		0			0
$105$	1562.37	+	1062.90i	1.45211	+	0.987893i
$106$		0			0
$107$	−664.680	+	664.680i	−0.600533	+	0.600533i	−0.940454	−	0.339921i	$-0.889600\pi$
$107$	−664.680	+	664.680i	−0.600533	+	0.600533i	0.339921	+	0.940454i	$0.389600\pi$
$108$		0			0
$109$			62.0000i			0.0544819i	0.999629	+	0.0272409i	$0.00867213\pi$
$109$			62.0000i			0.0544819i	−0.999629	+	0.0272409i	$0.991328\pi$
$110$		0			0
$111$	132.000	−	466.690i	0.112873	−	0.399066i
$112$		0			0
$113$	205.061	+	205.061i	0.170713	+	0.170713i	0.787292	−	0.616580i	$-0.211482\pi$
$113$	205.061	+	205.061i	0.170713	+	0.170713i	−0.616580	+	0.787292i	$0.711482\pi$
$114$		0			0
$115$	−1400.00	+	700.000i	−1.13522	+	0.567612i
$116$		0			0
$117$	−212.589	−	891.411i	−0.167982	−	0.704368i
$118$		0			0
$119$	3577.96			2.75623
$120$		0			0
$121$	1281.00			0.962434
$122$		0			0
$123$	−897.990	+	502.010i	−0.658285	+	0.368006i
$124$		0			0
$125$	−1149.05	+	795.495i	−0.822192	+	0.569210i
$126$		0			0
$127$	1529.00	+	1529.00i	1.06832	+	1.06832i	0.997488	+	0.0708332i	$0.0225658\pi$
$127$	1529.00	+	1529.00i	1.06832	+	1.06832i	0.0708332	+	0.997488i	$0.477434\pi$
$128$		0			0
$129$	890.955	+	252.000i	0.608094	+	0.171995i
$130$		0			0
$131$		−	2114.25i		−	1.41010i	−0.709159	−	0.705049i	$-0.750925\pi$
$131$		−	2114.25i		−	1.41010i	0.709159	−	0.705049i	$-0.249075\pi$
$132$		0			0
$133$	1564.00	−	1564.00i	1.01967	−	1.01967i
$134$		0			0
$135$	−557.376	+	1466.19i	−0.355343	+	0.934736i
$136$		0			0
$137$	615.183	−	615.183i	0.383640	−	0.383640i	−0.488772	−	0.872412i	$-0.662555\pi$
$137$	615.183	−	615.183i	0.383640	−	0.383640i	0.872412	+	0.488772i	$0.162555\pi$
$138$		0			0
$139$			1376.00i			0.839646i	0.907606	+	0.419823i	$0.137908\pi$
$139$			1376.00i			0.839646i	−0.907606	+	0.419823i	$0.862092\pi$
$140$		0			0
$141$	600.000	+	169.706i	0.358363	+	0.101360i
$142$		0			0
$143$	−169.706	−	169.706i	−0.0992412	−	0.0992412i
$144$		0			0
$145$	−475.000	+	1425.00i	−0.272046	+	0.816137i
$146$		0			0
$147$	−3242.91	+	1812.91i	−1.81953	+	1.01718i
$148$		0			0
$149$	−2100.11			−1.15468			−0.577341	−	0.816503i	$-0.695909\pi$
$149$	−2100.11			−1.15468			−0.577341	+	0.816503i	$0.695909\pi$
$150$		0			0
$151$	−1616.00			−0.870915			−0.435458	−	0.900209i	$-0.643413\pi$
$151$	−1616.00			−0.870915			−0.435458	+	0.900209i	$0.643413\pi$
$152$		0			0
$153$	688.980	+	2888.98i	0.364057	+	1.52654i
$154$		0			0
$155$	332.340	−	997.021i	0.172221	−	0.516662i
$156$		0			0
$157$	−1872.00	−	1872.00i	−0.951604	−	0.951604i	0.0472776	−	0.998882i	$-0.484945\pi$
$157$	−1872.00	−	1872.00i	−0.951604	−	0.951604i	−0.998882	+	0.0472776i	$0.984945\pi$
$158$		0			0
$159$	650.538	−	2300.00i	0.324472	−	1.14718i
$160$		0			0
$161$		−	4553.77i		−	2.22911i
$162$		0			0
$163$	2156.00	−	2156.00i	1.03602	−	1.03602i	0.0366915	−	0.999327i	$-0.488318\pi$
$163$	2156.00	−	2156.00i	1.03602	−	1.03602i	0.999327	−	0.0366915i	$-0.0116819\pi$
$164$		0			0
$165$	76.7767	+	403.553i	0.0362246	+	0.190404i
$166$		0			0
$167$	−565.685	+	565.685i	−0.262120	+	0.262120i	−0.825915	−	0.563795i	$-0.809341\pi$
$167$	−565.685	+	565.685i	−0.262120	+	0.262120i	0.563795	+	0.825915i	$0.309341\pi$
$168$		0			0
$169$			1045.00i			0.475649i
$170$		0			0
$171$	1564.00	+	961.665i	0.699427	+	0.430061i
$172$		0			0
$173$	1534.42	+	1534.42i	0.674335	+	0.674335i	0.958712	−	0.284378i	$-0.0917869\pi$
$173$	1534.42	+	1534.42i	0.674335	+	0.674335i	−0.284378	+	0.958712i	$0.591787\pi$
$174$		0			0
$175$	−575.000	−	4025.00i	−0.248377	−	1.73864i
$176$		0			0
$177$	−125.503	−	224.497i	−0.0532957	−	0.0953348i
$178$		0			0
$179$	1958.69			0.817872			0.408936	−	0.912563i	$-0.365900\pi$
$179$	1958.69			0.817872			0.408936	+	0.912563i	$0.365900\pi$
$180$		0			0
$181$	−4366.00			−1.79294			−0.896470	−	0.443104i	$-0.853877\pi$
$181$	−4366.00			−1.79294			−0.896470	+	0.443104i	$0.853877\pi$
$182$		0			0
$183$	−319.477	−	571.477i	−0.129052	−	0.230846i
$184$		0			0
$185$	−933.381	+	466.690i	−0.370938	+	0.185469i
$186$		0			0
$187$	550.000	+	550.000i	0.215080	+	0.215080i
$188$		0			0
$189$	−3090.06	−	3358.00i	−1.18925	−	1.29237i
$190$		0			0
$191$			3917.37i			1.48404i	0.670379	+	0.742018i	$0.266131\pi$
$191$			3917.37i			1.48404i	−0.670379	+	0.742018i	$0.733869\pi$
$192$		0			0
$193$	−879.000	+	879.000i	−0.327833	+	0.327833i	−0.851762	−	0.523929i	$-0.824466\pi$
$193$	−879.000	+	879.000i	−0.327833	+	0.327833i	0.523929	+	0.851762i	$0.324466\pi$
$194$		0			0
$195$	−1109.12	+	1630.29i	−0.407310	+	0.598707i
$196$		0			0
$197$	933.381	−	933.381i	0.337567	−	0.337567i	−0.517884	−	0.855451i	$-0.673280\pi$
$197$	933.381	−	933.381i	0.337567	−	0.337567i	0.855451	+	0.517884i	$0.173280\pi$
$198$		0			0
$199$			312.000i			0.111141i	0.998455	+	0.0555706i	$0.0176978\pi$
$199$			312.000i			0.111141i	−0.998455	+	0.0555706i	$0.982302\pi$
$200$		0			0
$201$	−136.000	+	480.833i	−0.0477249	+	0.168733i
$202$		0			0
$203$	−3090.06	−	3090.06i	−1.06837	−	1.06837i
$204$		0			0
$205$	2100.00	+	700.000i	0.715465	+	0.238488i
$206$		0			0
$207$	3676.88	−	876.884i	1.23459	−	0.294433i
$208$		0			0
$209$	480.833			0.159138
$210$		0			0
$211$	4064.00			1.32596			0.662979	−	0.748638i	$-0.269292\pi$
$211$	4064.00			1.32596			0.662979	+	0.748638i	$0.269292\pi$
$212$		0			0
$213$	−4297.52	+	2402.48i	−1.38245	+	0.772840i
$214$		0			0
$215$	−890.955	−	1781.91i	−0.282617	−	0.565233i
$216$		0			0
$217$	2162.00	+	2162.00i	0.676342	+	0.676342i
$218$		0			0
$219$	2849.64	+	806.000i	0.879273	+	0.248696i
$220$		0			0
$221$			3733.52i			1.13640i
$222$		0			0
$223$	−969.000	+	969.000i	−0.290982	+	0.290982i	−0.837468	−	0.546486i	$-0.815965\pi$
$223$	−969.000	+	969.000i	−0.290982	+	0.290982i	0.546486	+	0.837468i	$0.315965\pi$
$224$		0			0
$225$	3139.21	−	1239.34i	0.930137	−	0.367212i
$226$		0			0
$227$	1449.57	−	1449.57i	0.423838	−	0.423838i	−0.462685	−	0.886523i	$-0.653114\pi$
$227$	1449.57	−	1449.57i	0.423838	−	0.423838i	0.886523	+	0.462685i	$0.153114\pi$
$228$		0			0
$229$			3282.00i			0.947077i	0.880773	+	0.473539i	$0.157024\pi$
$229$			3282.00i			0.947077i	−0.880773	+	0.473539i	$0.842976\pi$
$230$		0			0
$231$	−1150.00	−	325.269i	−0.327552	−	0.0926456i
$232$		0			0
$233$	997.021	+	997.021i	0.280330	+	0.280330i	0.833241	−	0.552910i	$-0.186483\pi$
$233$	997.021	+	997.021i	0.280330	+	0.280330i	−0.552910	+	0.833241i	$0.686483\pi$
$234$		0			0
$235$	−600.000	−	1200.00i	−0.166552	−	0.333104i
$236$		0			0
$237$	1061.31	−	593.315i	0.290885	−	0.162616i
$238$		0			0
$239$	−5727.56			−1.55015			−0.775074	−	0.631870i	$-0.782287\pi$
$239$	−5727.56			−1.55015			−0.775074	+	0.631870i	$0.782287\pi$
$240$		0			0
$241$	484.000			0.129366			0.0646829	−	0.997906i	$-0.479396\pi$
$241$	484.000			0.129366			0.0646829	+	0.997906i	$0.479396\pi$
$242$		0			0
$243$	2116.35	−	3141.65i	0.558699	−	0.829371i
$244$		0			0
$245$	7583.72	+	2527.91i	1.97758	+	0.659192i
$246$		0			0
$247$	1632.00	+	1632.00i	0.420412	+	0.420412i
$248$		0			0
$249$	−1442.50	+	5100.00i	−0.367127	+	1.29799i
$250$		0			0
$251$			4009.30i			1.00823i	0.863638	+	0.504113i	$0.168180\pi$
$251$			4009.30i			1.00823i	−0.863638	+	0.504113i	$0.831820\pi$
$252$		0			0
$253$	700.000	−	700.000i	0.173947	−	0.173947i
$254$		0			0
$255$	3594.54	−	5283.63i	0.882741	−	1.29754i
$256$		0			0
$257$	−1393.00	+	1393.00i	−0.338105	+	0.338105i	−0.855654	−	0.517549i	$-0.826845\pi$
$257$	−1393.00	+	1393.00i	−0.338105	+	0.338105i	0.517549	+	0.855654i	$0.326845\pi$
$258$		0			0
$259$		−	3036.00i		−	0.728370i
$260$		0			0
$261$	1900.00	−	3090.06i	0.450602	−	0.732834i
$262$		0			0
$263$	1753.62	+	1753.62i	0.411153	+	0.411153i	0.882140	−	0.470987i	$-0.156102\pi$
$263$	1753.62	+	1753.62i	0.411153	+	0.411153i	−0.470987	+	0.882140i	$0.656102\pi$
$264$		0			0
$265$	−4600.00	+	2300.00i	−1.06632	+	0.533162i
$266$		0			0
$267$	−2617.62	−	4682.38i	−0.599985	−	1.07325i
$268$		0			0
$269$	−4843.68			−1.09786			−0.548930	−	0.835868i	$-0.684965\pi$
$269$	−4843.68			−1.09786			−0.548930	+	0.835868i	$0.684965\pi$
$270$		0			0
$271$	912.000			0.204428			0.102214	−	0.994762i	$-0.467407\pi$
$271$	912.000			0.204428			0.102214	+	0.994762i	$0.467407\pi$
$272$		0			0
$273$	−2799.23	−	5007.23i	−0.620575	−	1.11008i
$274$		0			0
$275$	530.330	−	707.107i	0.116291	−	0.155055i
$276$		0			0
$277$	−4782.00	−	4782.00i	−1.03727	−	1.03727i	−0.999278	−	0.0379872i	$-0.987905\pi$
$277$	−4782.00	−	4782.00i	−1.03727	−	1.03727i	−0.0379872	−	0.999278i	$-0.512095\pi$
$278$		0			0
$279$	−1329.36	+	2162.00i	−0.285257	+	0.463927i
$280$		0			0
$281$			4200.21i			0.891686i	0.895111	+	0.445843i	$0.147096\pi$
$281$			4200.21i			0.891686i	−0.895111	+	0.445843i	$0.852904\pi$
$282$		0			0
$283$	−4084.00	+	4084.00i	−0.857840	+	0.857840i	−0.991083	−	0.133244i	$-0.957461\pi$
$283$	−4084.00	+	4084.00i	−0.857840	+	0.857840i	0.133244	+	0.991083i	$0.457461\pi$
$284$		0			0
$285$	−738.335	−	3880.83i	−0.153457	−	0.806599i
$286$		0			0
$287$	−4553.77	+	4553.77i	−0.936587	+	0.936587i
$288$		0			0
$289$		−	7187.00i		−	1.46285i
$290$		0			0
$291$	−1446.00	+	5112.38i	−0.291292	+	1.02987i
$292$		0			0
$293$	−4751.76	−	4751.76i	−0.947442	−	0.947442i	0.0512437	−	0.998686i	$-0.483681\pi$
$293$	−4751.76	−	4751.76i	−0.947442	−	0.947442i	−0.998686	+	0.0512437i	$0.983681\pi$
$294$		0			0
$295$	−175.000	+	525.000i	−0.0345386	+	0.103616i
$296$		0			0
$297$	41.1880	−	991.188i	0.00804703	−	0.193652i
$298$		0			0
$299$	4751.76			0.919068
$300$		0			0
$301$	5796.00			1.10989
$302$		0			0
$303$	3303.32	−	1846.68i	0.626306	−	0.350129i
$304$		0			0
$305$	−445.477	+	1336.43i	−0.0836326	+	0.250898i
$306$		0			0
$307$	−2262.00	−	2262.00i	−0.420518	−	0.420518i	0.464864	−	0.885382i	$-0.346103\pi$
$307$	−2262.00	−	2262.00i	−0.420518	−	0.420518i	−0.885382	+	0.464864i	$0.846103\pi$
$308$		0			0
$309$	516.188	+	146.000i	0.0950321	+	0.0268791i
$310$		0			0
$311$			98.9949i			0.0180498i	0.999959	+	0.00902490i	$0.00287275\pi$
$311$			98.9949i			0.0180498i	−0.999959	+	0.00902490i	$0.997127\pi$
$312$		0			0
$313$	3441.00	−	3441.00i	0.621396	−	0.621396i	−0.324493	−	0.945888i	$-0.605194\pi$
$313$	3441.00	−	3441.00i	0.621396	−	0.621396i	0.945888	+	0.324493i	$0.105194\pi$
$314$		0			0
$315$	−859.405	+	9781.19i	−0.153721	+	1.74955i
$316$		0			0
$317$	6003.34	−	6003.34i	1.06366	−	1.06366i	0.0658316	−	0.997831i	$-0.479030\pi$
$317$	6003.34	−	6003.34i	1.06366	−	1.06366i	0.997831	−	0.0658316i	$-0.0209700\pi$
$318$		0			0
$319$		−	950.000i		−	0.166739i
$320$		0			0
$321$	−4700.00	−	1329.36i	−0.817222	−	0.231145i
$322$		0			0
$323$	−5289.16	−	5289.16i	−0.911135	−	0.911135i
$324$		0			0
$325$	4200.00	−	600.000i	0.716843	−	0.102406i
$326$		0			0
$327$	−281.203	+	157.203i	−0.0475553	+	0.0265852i
$328$		0			0
$329$	3903.23			0.654079
$330$		0			0
$331$	−608.000			−0.100963			−0.0504814	−	0.998725i	$-0.516076\pi$
$331$	−608.000			−0.100963			−0.0504814	+	0.998725i	$0.516076\pi$
$332$		0			0
$333$	2451.38	−	584.619i	0.403408	−	0.0962070i
$334$		0			0
$335$	961.665	−	480.833i	0.156840	−	0.0784200i
$336$		0			0
$337$	−1497.00	−	1497.00i	−0.241979	−	0.241979i	0.575690	−	0.817668i	$-0.304734\pi$
$337$	−1497.00	−	1497.00i	−0.241979	−	0.241979i	−0.817668	+	0.575690i	$0.804734\pi$
$338$		0			0
$339$	−410.122	+	1450.00i	−0.0657073	+	0.232310i
$340$		0			0
$341$			664.680i			0.105556i
$342$		0			0
$343$	−8556.00	+	8556.00i	−1.34688	+	1.34688i
$344$		0			0
$345$	−6724.62	−	4574.87i	−1.04940	−	0.713922i
$346$		0			0
$347$	−219.203	+	219.203i	−0.0339119	+	0.0339119i	−0.723859	−	0.689947i	$-0.757634\pi$
$347$	−219.203	+	219.203i	−0.0339119	+	0.0339119i	0.689947	+	0.723859i	$0.257634\pi$
$348$		0			0
$349$			10486.0i			1.60832i	0.594415	+	0.804159i	$0.297384\pi$
$349$			10486.0i			1.60832i	−0.594415	+	0.804159i	$0.702616\pi$
$350$		0			0
$351$	3504.00	−	3224.41i	0.532848	−	0.490331i
$352$		0			0
$353$	6809.44	+	6809.44i	1.02671	+	1.02671i	0.999633	+	0.0270801i	$0.00862093\pi$
$353$	6809.44	+	6809.44i	1.02671	+	1.02671i	0.0270801	+	0.999633i	$0.491379\pi$
$354$		0			0
$355$	10050.0	+	3350.00i	1.50253	+	0.500844i
$356$		0			0
$357$	9072.04	+	16228.0i	1.34494	+	2.40581i
$358$		0			0
$359$	−7014.50			−1.03123			−0.515614	−	0.856821i	$-0.672436\pi$
$359$	−7014.50			−1.03123			−0.515614	+	0.856821i	$0.672436\pi$
$360$		0			0
$361$	2235.00			0.325849
$362$		0			0
$363$	3248.02	+	5810.02i	0.469633	+	0.840074i
$364$		0			0
$365$	−2849.64	−	5699.28i	−0.408649	−	0.817299i
$366$		0			0
$367$	1853.00	+	1853.00i	0.263558	+	0.263558i	0.826498	−	0.562940i	$-0.190330\pi$
$367$	1853.00	+	1853.00i	0.263558	+	0.263558i	−0.562940	+	0.826498i	$0.690330\pi$
$368$		0			0
$369$	−4553.77	−	2800.00i	−0.642438	−	0.395019i
$370$		0			0
$371$		−	14962.4i		−	2.09382i
$372$		0			0
$373$	1636.00	−	1636.00i	0.227102	−	0.227102i	−0.584379	−	0.811481i	$-0.698662\pi$
$373$	1636.00	−	1636.00i	0.227102	−	0.227102i	0.811481	+	0.584379i	$0.198662\pi$
$374$		0			0
$375$	−6521.45	−	3194.54i	−0.898043	−	0.439908i
$376$		0			0
$377$	3224.41	−	3224.41i	0.440492	−	0.440492i
$378$		0			0
$379$		−	1928.00i		−	0.261305i	−0.991428	−	0.130653i	$-0.958293\pi$
$379$		−	1928.00i		−	0.261305i	0.991428	−	0.130653i	$-0.0417073\pi$
$380$		0			0
$381$	−3058.00	+	10811.7i	−0.411197	+	1.45380i
$382$		0			0
$383$	5600.29	+	5600.29i	0.747157	+	0.747157i	0.973944	−	0.226787i	$-0.0728222\pi$
$383$	5600.29	+	5600.29i	0.747157	+	0.747157i	−0.226787	+	0.973944i	$0.572822\pi$
$384$		0			0
$385$	1150.00	+	2300.00i	0.152232	+	0.304465i
$386$		0			0
$387$	1116.09	+	4679.91i	0.146600	+	0.614711i
$388$		0			0
$389$	9142.89			1.19168			0.595839	−	0.803104i	$-0.296820\pi$
$389$	9142.89			1.19168			0.595839	+	0.803104i	$0.296820\pi$
$390$		0			0
$391$	−15400.0			−1.99185
$392$		0			0
$393$	9589.25	−	5360.75i	1.23082	−	0.688077i
$394$		0			0
$395$	−2481.94	−	827.315i	−0.316152	−	0.105384i
$396$		0			0
$397$	1558.00	+	1558.00i	0.196962	+	0.196962i	0.798696	−	0.601735i	$-0.205523\pi$
$397$	1558.00	+	1558.00i	0.196962	+	0.196962i	−0.601735	+	0.798696i	$0.705523\pi$
$398$		0			0
$399$	11059.2	+	3128.00i	1.38759	+	0.392471i
$400$		0			0
$401$		−	12515.8i		−	1.55863i	−0.626635	−	0.779313i	$-0.715568\pi$
$401$		−	12515.8i		−	1.55863i	0.626635	−	0.779313i	$-0.284432\pi$
$402$		0			0
$403$	−2256.00	+	2256.00i	−0.278857	+	0.278857i
$404$		0			0
$405$	−8063.19	+	1189.57i	−0.989292	+	0.145951i
$406$		0			0
$407$	466.690	−	466.690i	0.0568378	−	0.0568378i
$408$		0			0
$409$		−	12768.0i		−	1.54361i	−0.635859	−	0.771806i	$-0.719354\pi$
$409$		−	12768.0i		−	1.54361i	0.635859	−	0.771806i	$-0.280646\pi$
$410$		0			0
$411$	4350.00	+	1230.37i	0.522067	+	0.147663i
$412$		0			0
$413$	−1138.44	−	1138.44i	−0.135639	−	0.135639i
$414$		0			0
$415$	10200.0	−	5100.00i	1.20650	−	0.603251i
$416$		0			0
$417$	−6240.89	+	3488.89i	−0.732897	+	0.409717i
$418$		0			0
$419$	−1972.83			−0.230021			−0.115011	−	0.993364i	$-0.536690\pi$
$419$	−1972.83			−0.230021			−0.115011	+	0.993364i	$0.536690\pi$
$420$		0			0
$421$	9062.00			1.04906			0.524531	−	0.851392i	$-0.324241\pi$
$421$	9062.00			1.04906			0.524531	+	0.851392i	$0.324241\pi$
$422$		0			0
$423$	751.615	+	3151.61i	0.0863942	+	0.362262i
$424$		0			0
$425$	−13611.8	+	1944.54i	−1.55358	+	0.221939i
$426$		0			0
$427$	−2898.00	−	2898.00i	−0.328440	−	0.328440i
$428$		0			0
$429$	339.411	−	1200.00i	0.0381980	−	0.135050i
$430$		0			0
$431$			791.960i			0.0885089i	0.999020	+	0.0442545i	$0.0140912\pi$
$431$			791.960i			0.0885089i	−0.999020	+	0.0442545i	$0.985909\pi$
$432$		0			0
$433$	−7969.00	+	7969.00i	−0.884447	+	0.884447i	−0.993983	−	0.109536i	$-0.965064\pi$
$433$	−7969.00	+	7969.00i	−0.884447	+	0.884447i	0.109536	+	0.993983i	$0.465064\pi$
$434$		0			0
$435$	−7667.51	+	1458.76i	−0.845125	+	0.160786i
$436$		0			0
$437$	−6731.66	+	6731.66i	−0.736885	+	0.736885i
$438$		0			0
$439$		−	12928.0i		−	1.40551i	−0.711431	−	0.702756i	$-0.751953\pi$
$439$		−	12928.0i		−	1.40551i	0.711431	−	0.702756i	$-0.248047\pi$
$440$		0			0
$441$	−16445.0	−	10111.6i	−1.77573	−	1.09185i
$442$		0			0
$443$	−997.021	−	997.021i	−0.106930	−	0.106930i	0.651618	−	0.758547i	$-0.274091\pi$
$443$	−997.021	−	997.021i	−0.106930	−	0.106930i	−0.758547	+	0.651618i	$0.774091\pi$
$444$		0			0
$445$	−3650.00	+	10950.0i	−0.388824	+	1.16647i
$446$		0			0
$447$	−5324.89	−	9525.11i	−0.563442	−	1.00788i
$448$		0			0
$449$	15033.1			1.58008			0.790039	−	0.613056i	$-0.210060\pi$
$449$	15033.1			1.58008			0.790039	+	0.613056i	$0.210060\pi$
$450$		0			0
$451$	−1400.00			−0.146172
$452$		0			0
$453$	−4097.42	−	7329.42i	−0.424975	−	0.760191i
$454$		0			0
$455$	−3903.23	+	11709.7i	−0.402168	+	1.20650i
$456$		0			0
$457$	−13431.0	−	13431.0i	−1.37478	−	1.37478i	−0.853202	−	0.521581i	$-0.825343\pi$
$457$	−13431.0	−	13431.0i	−1.37478	−	1.37478i	−0.521581	−	0.853202i	$-0.674657\pi$
$458$		0			0
$459$	−11356.1	+	10450.0i	−1.15481	+	1.06267i
$460$		0			0
$461$			6243.75i			0.630804i	0.948958	+	0.315402i	$0.102139\pi$
$461$			6243.75i			0.630804i	−0.948958	+	0.315402i	$0.897861\pi$
$462$		0			0
$463$	11813.0	−	11813.0i	1.18574	−	1.18574i	0.207504	−	0.978234i	$-0.433466\pi$
$463$	11813.0	−	11813.0i	1.18574	−	1.18574i	0.978234	−	0.207504i	$-0.0665339\pi$
$464$		0			0
$465$	5364.68	−	1020.64i	0.535013	−	0.101787i
$466$		0			0
$467$	4002.22	−	4002.22i	0.396576	−	0.396576i	−0.480448	−	0.877023i	$-0.659526\pi$
$467$	4002.22	−	4002.22i	0.396576	−	0.396576i	0.877023	+	0.480448i	$0.159526\pi$
$468$		0			0
$469$			3128.00i			0.307969i
$470$		0			0
$471$	3744.00	−	13237.0i	0.366273	−	1.29497i
$472$		0			0
$473$	890.955	+	890.955i	0.0866092	+	0.0866092i
$474$		0			0
$475$	−5100.00	+	6800.00i	−0.492640	+	0.656853i
$476$		0			0
$477$	12081.2	−	2881.19i	1.15966	−	0.276563i
$478$		0			0
$479$	−4228.50			−0.403351			−0.201675	−	0.979452i	$-0.564639\pi$
$479$	−4228.50			−0.403351			−0.201675	+	0.979452i	$0.564639\pi$
$480$		0			0
$481$	3168.00			0.300308
$482$		0			0
$483$	20653.8	−	11546.2i	1.94571	−	1.08773i
$484$		0			0
$485$	10224.8	−	5112.38i	0.957284	−	0.478642i
$486$		0			0
$487$	7233.00	+	7233.00i	0.673015	+	0.673015i	0.958410	−	0.285395i	$-0.0921247\pi$
$487$	7233.00	+	7233.00i	0.673015	+	0.673015i	−0.285395	+	0.958410i	$0.592125\pi$
$488$		0			0
$489$	15245.2	+	4312.00i	1.40984	+	0.398764i
$490$		0			0
$491$		−	4207.29i		−	0.386705i	−0.981129	−	0.193352i	$-0.938064\pi$
$491$		−	4207.29i		−	0.386705i	0.981129	−	0.193352i	$-0.0619361\pi$
$492$		0			0
$493$	−10450.0	+	10450.0i	−0.954654	+	0.954654i
$494$		0			0
$495$	−1635.66	+	1371.45i	−0.148520	+	0.124529i
$496$		0			0
$497$	−21793.0	+	21793.0i	−1.96690	+	1.96690i
$498$		0			0
$499$		−	5668.00i		−	0.508486i	−0.967140	−	0.254243i	$-0.918174\pi$
$499$		−	5668.00i		−	0.508486i	0.967140	−	0.254243i	$-0.0818263\pi$
$500$		0			0
$501$	−4000.00	−	1131.37i	−0.356700	−	0.100890i
$502$		0			0
$503$	9206.53	+	9206.53i	0.816101	+	0.816101i	0.985541	−	0.169439i	$-0.0541957\pi$
$503$	9206.53	+	9206.53i	0.816101	+	0.816101i	−0.169439	+	0.985541i	$0.554196\pi$
$504$		0			0
$505$	−7725.00	−	2575.00i	−0.680709	−	0.226903i
$506$		0			0
$507$	−4739.63	+	2649.63i	−0.415177	+	0.232099i
$508$		0			0
$509$	−1407.14			−0.122535			−0.0612677	−	0.998121i	$-0.519514\pi$
$509$	−1407.14			−0.122535			−0.0612677	+	0.998121i	$0.519514\pi$
$510$		0			0
$511$	18538.0			1.60484
$512$		0			0
$513$	−396.090	+	9531.91i	−0.0340893	+	0.820359i
$514$		0			0
$515$	−516.188	−	1032.38i	−0.0441669	−	0.0883338i
$516$		0			0
$517$	600.000	+	600.000i	0.0510406	+	0.0510406i
$518$		0			0
$519$	−3068.84	+	10850.0i	−0.259552	+	0.917653i
$520$		0			0
$521$		−	2757.72i		−	0.231896i	−0.993255	−	0.115948i	$-0.963009\pi$
$521$		−	2757.72i		−	0.231896i	0.993255	−	0.115948i	$-0.0369906\pi$
$522$		0			0
$523$	−7704.00	+	7704.00i	−0.644115	+	0.644115i	−0.951565	−	0.307449i	$-0.900525\pi$
$523$	−7704.00	+	7704.00i	−0.644115	+	0.644115i	0.307449	+	0.951565i	$0.400525\pi$
$524$		0			0
$525$	16797.6	−	12813.5i	1.39639	−	1.06519i
$526$		0			0
$527$	7311.48	−	7311.48i	0.604352	−	0.604352i
$528$		0			0
$529$			7433.00i			0.610915i
$530$		0			0
$531$	700.000	−	1138.44i	0.0572079	−	0.0930399i
$532$		0			0
$533$	−4751.76	−	4751.76i	−0.386157	−	0.386157i
$534$		0			0
$535$	4700.00	+	9400.00i	0.379811	+	0.759621i
$536$		0			0
$537$	4966.31	+	8883.69i	0.399092	+	0.713891i
$538$		0			0
$539$	−5055.81			−0.404025
$540$		0			0
$541$	9814.00			0.779920			0.389960	−	0.920832i	$-0.372489\pi$
$541$	9814.00			0.779920			0.389960	+	0.920832i	$0.372489\pi$
$542$		0			0
$543$	−11070.1	−	19802.1i	−0.874890	−	1.56499i
$544$		0			0
$545$	657.609	+	219.203i	0.0516860	+	0.0172287i
$546$		0			0
$547$	10014.0	+	10014.0i	0.782756	+	0.782756i	0.980295	−	0.197539i	$-0.0632948\pi$
$547$	10014.0	+	10014.0i	0.782756	+	0.782756i	−0.197539	+	0.980295i	$0.563295\pi$
$548$		0			0
$549$	1781.91	−	2898.00i	0.138525	−	0.225289i
$550$		0			0
$551$			9135.82i			0.706350i
$552$		0			0
$553$	5382.00	−	5382.00i	0.413862	−	0.413862i
$554$		0			0
$555$	−4483.31	−	3050.07i	−0.342893	−	0.233276i
$556$		0			0
$557$	3054.70	−	3054.70i	0.232373	−	0.232373i	−0.581309	−	0.813683i	$-0.697459\pi$
$557$	3054.70	−	3054.70i	0.232373	−	0.232373i	0.813683	+	0.581309i	$0.197459\pi$
$558$		0			0
$559$			6048.00i			0.457608i
$560$		0			0
$561$	−1100.00	+	3889.09i	−0.0827844	+	0.292687i
$562$		0			0
$563$	6342.75	+	6342.75i	0.474805	+	0.474805i	0.903465	−	0.428661i	$-0.141014\pi$
$563$	6342.75	+	6342.75i	0.474805	+	0.474805i	−0.428661	+	0.903465i	$0.641014\pi$
$564$		0			0
$565$	2900.00	−	1450.00i	0.215936	−	0.107968i
$566$		0			0
$567$	7395.38	−	22529.4i	0.547754	−	1.66869i
$568$		0			0
$569$	−15202.8			−1.12010			−0.560048	−	0.828460i	$-0.689217\pi$
$569$	−15202.8			−1.12010			−0.560048	+	0.828460i	$0.689217\pi$
$570$		0			0
$571$	−21616.0			−1.58424			−0.792120	−	0.610365i	$-0.791023\pi$
$571$	−21616.0			−1.58424			−0.792120	+	0.610365i	$0.791023\pi$
$572$		0			0
$573$	−17767.4	+	9932.63i	−1.29536	+	0.724156i
$574$		0			0
$575$	2474.87	+	17324.1i	0.179495	+	1.25646i
$576$		0			0
$577$	−1667.00	−	1667.00i	−0.120274	−	0.120274i	0.644408	−	0.764682i	$-0.277104\pi$
$577$	−1667.00	−	1667.00i	−0.120274	−	0.120274i	−0.764682	+	0.644408i	$0.777104\pi$
$578$		0			0
$579$	−6215.47	−	1758.00i	−0.446124	−	0.126183i
$580$		0			0
$581$			33177.5i			2.36907i
$582$		0			0
$583$	2300.00	−	2300.00i	0.163390	−	0.163390i
$584$		0			0
$585$	−10206.5	−	896.771i	−0.721342	−	0.0633793i
$586$		0			0
$587$	9630.79	−	9630.79i	0.677181	−	0.677181i	−0.282180	−	0.959361i	$-0.591058\pi$
$587$	9630.79	−	9630.79i	0.677181	−	0.677181i	0.959361	+	0.282180i	$0.0910576\pi$
$588$		0			0
$589$		−	6392.00i		−	0.447161i
$590$		0			0
$591$	6600.00	+	1866.76i	0.459370	+	0.129929i
$592$		0			0
$593$	−7459.98	−	7459.98i	−0.516601	−	0.516601i	0.399940	−	0.916541i	$-0.369031\pi$
$593$	−7459.98	−	7459.98i	−0.516601	−	0.516601i	−0.916541	+	0.399940i	$0.869031\pi$
$594$		0			0
$595$	12650.0	−	37950.0i	0.871596	−	2.61479i
$596$		0			0
$597$	−1415.09	+	791.087i	−0.0970111	+	0.0542329i
$598$		0			0
$599$	9560.08			0.652111			0.326055	−	0.945351i	$-0.394280\pi$
$599$	9560.08			0.652111			0.326055	+	0.945351i	$0.394280\pi$
$600$		0			0
$601$	−5626.00			−0.381846			−0.190923	−	0.981605i	$-0.561148\pi$
$601$	−5626.00			−0.381846			−0.190923	+	0.981605i	$0.561148\pi$
$602$		0			0
$603$	−2525.67	+	602.335i	−0.170569	+	0.0406782i
$604$		0			0
$605$	4529.02	−	13587.1i	0.304348	−	0.913045i
$606$		0			0
$607$	−6381.00	−	6381.00i	−0.426683	−	0.426683i	0.460814	−	0.887497i	$-0.347558\pi$
$607$	−6381.00	−	6381.00i	−0.426683	−	0.426683i	−0.887497	+	0.460814i	$0.847558\pi$
$608$		0			0
$609$	6180.11	−	21850.0i	0.411216	−	1.45387i
$610$		0			0
$611$			4072.94i			0.269678i
$612$		0			0
$613$	738.000	−	738.000i	0.0486257	−	0.0486257i	−0.682376	−	0.731002i	$-0.739053\pi$
$613$	738.000	−	738.000i	0.0486257	−	0.0486257i	0.731002	+	0.682376i	$0.239053\pi$
$614$		0			0
$615$	2149.75	+	11299.5i	0.140953	+	0.740877i
$616$		0			0
$617$	10670.2	−	10670.2i	0.696220	−	0.696220i	−0.267373	−	0.963593i	$-0.586156\pi$
$617$	10670.2	−	10670.2i	0.696220	−	0.696220i	0.963593	+	0.267373i	$0.0861556\pi$
$618$		0			0
$619$			4512.00i			0.292977i	0.989212	+	0.146488i	$0.0467971\pi$
$619$			4512.00i			0.292977i	−0.989212	+	0.146488i	$0.953203\pi$
$620$		0			0
$621$	13300.0	+	14453.3i	0.859437	+	0.933960i
$622$		0			0
$623$	−23744.6	−	23744.6i	−1.52698	−	1.52698i
$624$		0			0
$625$	4375.00	+	15000.0i	0.280000	+	0.960000i
$626$		0			0
$627$	1219.17	+	2180.83i	0.0776537	+	0.138906i
$628$		0			0
$629$	−10267.2			−0.650842
$630$		0			0
$631$	−23726.0			−1.49686			−0.748429	−	0.663215i	$-0.769191\pi$
$631$	−23726.0			−1.49686			−0.748429	+	0.663215i	$0.769191\pi$
$632$		0			0
$633$	10304.4	+	18432.4i	0.647020	+	1.15738i
$634$		0			0
$635$	21623.3	−	10811.7i	1.35133	−	0.675666i
$636$		0			0
$637$	−17160.0	−	17160.0i	−1.06735	−	1.06735i
$638$		0			0
$639$	−21793.0	−	13400.0i	−1.34917	−	0.829571i
$640$		0			0
$641$		−	2743.57i		−	0.169056i	−0.996421	−	0.0845278i	$-0.973062\pi$
$641$		−	2743.57i		−	0.169056i	0.996421	−	0.0845278i	$-0.0269382\pi$
$642$		0			0
$643$	−4392.00	+	4392.00i	−0.269368	+	0.269368i	−0.828845	−	0.559478i	$-0.811002\pi$
$643$	−4392.00	+	4392.00i	−0.269368	+	0.269368i	0.559478	+	0.828845i	$0.311002\pi$
$644$		0			0
$645$	5822.86	−	8559.05i	0.355465	−	0.522499i
$646$		0			0
$647$	−11045.0	+	11045.0i	−0.671135	+	0.671135i	−0.957978	−	0.286843i	$-0.907394\pi$
$647$	−11045.0	+	11045.0i	−0.671135	+	0.671135i	0.286843	+	0.957978i	$0.407394\pi$
$648$		0			0
$649$		−	350.000i		−	0.0211690i
$650$		0			0
$651$	−4324.00	+	15287.6i	−0.260324	+	0.920384i
$652$		0			0
$653$	−4942.68	−	4942.68i	−0.296205	−	0.296205i	0.543320	−	0.839525i	$-0.317167\pi$
$653$	−4942.68	−	4942.68i	−0.296205	−	0.296205i	−0.839525	+	0.543320i	$0.817167\pi$
$654$		0			0
$655$	−22425.0	−	7475.00i	−1.33774	−	0.445912i
$656$		0			0
$657$	3569.72	+	14968.3i	0.211976	+	0.888841i
$658$		0			0
$659$	−21375.8			−1.26356			−0.631779	−	0.775149i	$-0.717675\pi$
$659$	−21375.8			−1.26356			−0.631779	+	0.775149i	$0.717675\pi$
$660$		0			0
$661$	7082.00			0.416729			0.208365	−	0.978051i	$-0.433186\pi$
$661$	7082.00			0.416729			0.208365	+	0.978051i	$0.433186\pi$
$662$		0			0
$663$	−16933.5	+	9466.48i	−0.991921	+	0.554521i
$664$		0			0
$665$	−11059.2	−	22118.3i	−0.644895	−	1.28979i
$666$		0			0
$667$	13300.0	+	13300.0i	0.772081	+	0.772081i
$668$		0			0
$669$	−6851.86	−	1938.00i	−0.395977	−	0.111999i
$670$		0			0
$671$		−	890.955i		−	0.0512592i
$672$		0			0
$673$	21853.0	−	21853.0i	1.25167	−	1.25167i	0.296693	−	0.954973i	$-0.404116\pi$
$673$	21853.0	−	21853.0i	1.25167	−	1.25167i	0.954973	−	0.296693i	$-0.0958839\pi$
$674$		0			0
$675$	13580.7	+	11095.6i	0.774399	+	0.632697i
$676$		0			0
$677$	6356.89	−	6356.89i	0.360879	−	0.360879i	−0.503257	−	0.864137i	$-0.667865\pi$
$677$	6356.89	−	6356.89i	0.360879	−	0.360879i	0.864137	+	0.503257i	$0.167865\pi$
$678$		0			0
$679$			33258.0i			1.87971i
$680$		0			0
$681$	10250.0	+	2899.14i	0.576771	+	0.163135i
$682$		0			0
$683$	20322.2	+	20322.2i	1.13852	+	1.13852i	0.988716	+	0.149804i	$0.0478644\pi$
$683$	20322.2	+	20322.2i	1.13852	+	1.13852i	0.149804	+	0.988716i	$0.452136\pi$
$684$		0			0
$685$	−4350.00	−	8700.00i	−0.242635	−	0.485270i
$686$		0			0
$687$	−14885.6	+	8321.62i	−0.826669	+	0.462139i
$688$		0			0
$689$	15612.9			0.863287
$690$		0			0
$691$	21972.0			1.20963			0.604815	−	0.796366i	$-0.293247\pi$
$691$	21972.0			1.20963			0.604815	+	0.796366i	$0.293247\pi$
$692$		0			0
$693$	−1440.59	−	6040.59i	−0.0789663	−	0.331116i
$694$		0			0
$695$	14594.7	+	4864.89i	0.796558	+	0.265519i
$696$		0			0
$697$	15400.0	+	15400.0i	0.836896	+	0.836896i
$698$		0			0
$699$	−1994.04	+	7050.00i	−0.107899	+	0.381481i
$700$		0			0
$701$		−	7162.99i		−	0.385938i	−0.981205	−	0.192969i	$-0.938188\pi$
$701$		−	7162.99i		−	0.385938i	0.981205	−	0.192969i	$-0.0618117\pi$
$702$		0			0
$703$	−4488.00	+	4488.00i	−0.240780	+	0.240780i
$704$		0			0
$705$	3921.32	−	5763.96i	0.209483	−	0.307920i
$706$		0			0
$707$	16751.4	−	16751.4i	0.891089	−	0.891089i
$708$		0			0
$709$			14002.0i			0.741687i	0.928695	+	0.370844i	$0.120931\pi$
$709$			14002.0i			0.741687i	−0.928695	+	0.370844i	$0.879069\pi$
$710$		0			0
$711$	5382.00	+	3309.26i	0.283883	+	0.174553i
$712$		0			0
$713$	−9305.53	−	9305.53i	−0.488772	−	0.488772i
$714$		0			0
$715$	−2400.00	+	1200.00i	−0.125531	+	0.0627657i
$716$		0			0
$717$	−14522.4	−	25977.6i	−0.756416	−	1.35307i
$718$		0			0
$719$	22288.0			1.15605			0.578027	−	0.816018i	$-0.303823\pi$
$719$	22288.0			1.15605			0.578027	+	0.816018i	$0.303823\pi$
$720$		0			0
$721$	3358.00			0.173451
$722$		0			0
$723$	1227.20	+	2195.20i	0.0631259	+	0.112919i
$724$		0			0
$725$	13435.0	+	10076.3i	0.688227	+	0.516170i
$726$		0			0
$727$	−6747.00	−	6747.00i	−0.344199	−	0.344199i	0.513745	−	0.857943i	$-0.328258\pi$
$727$	−6747.00	−	6747.00i	−0.344199	−	0.344199i	−0.857943	+	0.513745i	$0.828258\pi$
$728$		0			0
$729$	19615.1	+	1633.00i	0.996552	+	0.0829650i
$730$		0			0
$731$		−	19601.0i		−	0.991750i
$732$		0			0
$733$	12718.0	−	12718.0i	0.640860	−	0.640860i	−0.309907	−	0.950767i	$-0.600298\pi$
$733$	12718.0	−	12718.0i	0.640860	−	0.640860i	0.950767	+	0.309907i	$0.100298\pi$
$734$		0			0
$735$	7763.37	+	40805.8i	0.389600	+	2.04782i
$736$		0			0
$737$	−480.833	+	480.833i	−0.0240322	+	0.0240322i
$738$		0			0
$739$		−	5824.00i		−	0.289904i	−0.989439	−	0.144952i	$-0.953697\pi$
$739$		−	5824.00i		−	0.289904i	0.989439	−	0.144952i	$-0.0463028\pi$
$740$		0			0
$741$	−3264.00	+	11540.0i	−0.161817	+	0.572108i
$742$		0			0
$743$	−6010.41	−	6010.41i	−0.296770	−	0.296770i	0.542977	−	0.839748i	$-0.317297\pi$
$743$	−6010.41	−	6010.41i	−0.296770	−	0.296770i	−0.839748	+	0.542977i	$0.817297\pi$
$744$		0			0
$745$	−7425.00	+	22275.0i	−0.365142	+	1.09543i
$746$		0			0
$747$	−26788.7	+	6388.73i	−1.31211	+	0.312920i
$748$		0			0
$749$	−30575.3			−1.49158
$750$		0			0
$751$	13602.0			0.660911			0.330455	−	0.943822i	$-0.392798\pi$
$751$	13602.0			0.660911			0.330455	+	0.943822i	$0.392798\pi$
$752$		0			0
$753$	−18184.3	+	10165.7i	−0.880043	+	0.491977i
$754$		0			0
$755$	−5713.42	+	17140.3i	−0.275408	+	0.826223i
$756$		0			0
$757$	21258.0	+	21258.0i	1.02065	+	1.02065i	0.999782	+	0.0208719i	$0.00664423\pi$
$757$	21258.0	+	21258.0i	1.02065	+	1.02065i	0.0208719	+	0.999782i	$0.493356\pi$
$758$		0			0
$759$	4949.75	+	1400.00i	0.236712	+	0.0669523i
$760$		0			0
$761$		−	18002.9i		−	0.857564i	−0.903408	−	0.428782i	$-0.858943\pi$
$761$		−	18002.9i		−	0.857564i	0.903408	−	0.428782i	$-0.141057\pi$
$762$		0			0
$763$	−1426.00	+	1426.00i	−0.0676601	+	0.0676601i
$764$		0			0
$765$	33078.2	+	2906.35i	1.56333	+	0.137359i
$766$		0			0
$767$	1187.94	−	1187.94i	0.0559244	−	0.0559244i
$768$		0			0
$769$			6602.00i			0.309589i	0.987947	+	0.154795i	$0.0494716\pi$
$769$			6602.00i			0.309589i	−0.987947	+	0.154795i	$0.950528\pi$
$770$		0			0
$771$	−9850.00	−	2786.00i	−0.460103	−	0.130137i
$772$		0			0
$773$	−21192.0	−	21192.0i	−0.986058	−	0.986058i	0.0138460	−	0.999904i	$-0.495593\pi$
$773$	−21192.0	−	21192.0i	−0.986058	−	0.986058i	−0.999904	+	0.0138460i	$0.995593\pi$
$774$		0			0
$775$	−9400.00	−	7050.00i	−0.435688	−	0.326766i
$776$		0			0
$777$	13769.9	−	7697.88i	0.635768	−	0.355418i
$778$		0			0
$779$	13463.3			0.619221
$780$		0			0
$781$	−6700.00			−0.306972
$782$		0			0
$783$	18832.6	+	782.571i	0.859542	+	0.0357175i
$784$		0			0
$785$	−26474.1	+	13237.0i	−1.20369	+	0.601847i
$786$		0			0
$787$	−6092.00	−	6092.00i	−0.275929	−	0.275929i	0.555552	−	0.831482i	$-0.312507\pi$
$787$	−6092.00	−	6092.00i	−0.275929	−	0.275929i	−0.831482	+	0.555552i	$0.812507\pi$
$788$		0			0
$789$	−3507.25	+	12400.0i	−0.158253	+	0.559508i
$790$		0			0
$791$			9432.80i			0.424010i
$792$		0			0
$793$	3024.00	−	3024.00i	0.135417	−	0.135417i
$794$		0			0
$795$	−22095.2	−	15031.7i	−0.985705	−	0.670592i
$796$		0			0
$797$	−19240.4	+	19240.4i	−0.855118	+	0.855118i	−0.990758	−	0.135640i	$-0.956691\pi$
$797$	−19240.4	+	19240.4i	−0.855118	+	0.855118i	0.135640	+	0.990758i	$0.456691\pi$
$798$		0			0
$799$		−	13200.0i		−	0.584459i
$800$		0			0
$801$	14600.0	−	23744.6i	0.644027	−	1.04741i
$802$		0			0
$803$	2849.64	+	2849.64i	0.125232	+	0.125232i
$804$		0			0
$805$	−48300.0	−	16100.0i	−2.11472	−	0.704907i
$806$		0			0
$807$	−12281.3	−	21968.7i	−0.535716	−	0.958283i
$808$		0			0
$809$	41181.9			1.78971			0.894857	−	0.446353i	$-0.147277\pi$
$809$	41181.9			1.78971			0.894857	+	0.446353i	$0.147277\pi$
$810$		0			0
$811$	−39916.0			−1.72829			−0.864143	−	0.503246i	$-0.832139\pi$
$811$	−39916.0			−1.72829			−0.864143	+	0.503246i	$0.832139\pi$
$812$		0			0
$813$	2312.41	+	4136.41i	0.0997536	+	0.178438i
$814$		0			0
$815$	−15245.2	−	30490.4i	−0.655235	−	1.31047i
$816$		0			0
$817$	−8568.00	−	8568.00i	−0.366899	−	0.366899i
$818$		0			0
$819$	15612.9	−	25392.0i	0.666129	−	1.08336i
$820$		0			0
$821$			14135.1i			0.600874i	0.953802	+	0.300437i	$0.0971324\pi$
$821$			14135.1i			0.600874i	−0.953802	+	0.300437i	$0.902868\pi$
$822$		0			0
$823$	8591.00	−	8591.00i	0.363868	−	0.363868i	−0.501367	−	0.865235i	$-0.667169\pi$
$823$	8591.00	−	8591.00i	0.363868	−	0.363868i	0.865235	+	0.501367i	$0.167169\pi$
$824$		0			0
$825$	4551.78	+	612.437i	0.192088	+	0.0258452i
$826$		0			0
$827$	−5876.06	+	5876.06i	−0.247074	+	0.247074i	−0.819769	−	0.572694i	$-0.805898\pi$
$827$	−5876.06	+	5876.06i	−0.247074	+	0.247074i	0.572694	+	0.819769i	$0.305898\pi$
$828$		0			0
$829$		−	42634.0i		−	1.78618i	−0.449882	−	0.893088i	$-0.648534\pi$
$829$		−	42634.0i		−	1.78618i	0.449882	−	0.893088i	$-0.351466\pi$
$830$		0			0
$831$	9564.00	−	33813.8i	0.399244	−	1.41154i
$832$		0			0
$833$	55613.9	+	55613.9i	2.31322	+	2.31322i
$834$		0			0
$835$	4000.00	+	8000.00i	0.165779	+	0.331559i
$836$		0			0
$837$	−13176.5	−	547.536i	−0.544140	−	0.0226113i
$838$		0			0
$839$	−21863.7			−0.899666			−0.449833	−	0.893113i	$-0.648517\pi$
$839$	−21863.7			−0.899666			−0.449833	+	0.893113i	$0.648517\pi$
$840$		0			0
$841$	−6339.00			−0.259912
$842$		0			0
$843$	−19050.2	+	10649.8i	−0.778321	+	0.435110i
$844$		0			0
$845$	11083.9	+	3694.63i	0.451240	+	0.150413i
$846$		0			0
$847$	29463.0	+	29463.0i	1.19523	+	1.19523i
$848$		0			0
$849$	−28878.2	−	8168.00i	−1.16737	−	0.330183i
$850$		0			0
$851$			13067.3i			0.526372i
$852$		0			0
$853$	25966.0	−	25966.0i	1.04227	−	1.04227i	0.0432069	−	0.999066i	$-0.486243\pi$
$853$	25966.0	−	25966.0i	1.04227	−	1.04227i	0.999066	−	0.0432069i	$-0.0137575\pi$
$854$		0			0
$855$	15729.6	−	13188.7i	0.629170	−	0.527538i
$856$		0			0
$857$	−29931.8	+	29931.8i	−1.19306	+	1.19306i	−0.216856	+	0.976204i	$0.569580\pi$
$857$	−29931.8	+	29931.8i	−1.19306	+	1.19306i	−0.976204	+	0.216856i	$0.930420\pi$
$858$		0			0
$859$		−	8104.00i		−	0.321892i	−0.986963	−	0.160946i	$-0.948546\pi$
$859$		−	8104.00i		−	0.321892i	0.986963	−	0.160946i	$-0.0514544\pi$
$860$		0			0
$861$	−32200.0	−	9107.54i	−1.27453	−	0.360492i
$862$		0			0
$863$	31636.0	+	31636.0i	1.24786	+	1.24786i	0.956665	+	0.291192i	$0.0940520\pi$
$863$	31636.0	+	31636.0i	1.24786	+	1.24786i	0.291192	+	0.956665i	$0.405948\pi$
$864$		0			0
$865$	21700.0	−	10850.0i	0.852974	−	0.426487i
$866$		0			0
$867$	32596.9	−	18222.9i	1.27687	−	0.713820i
$868$		0			0
$869$	1654.63			0.0645909
$870$		0			0
$871$	−3264.00			−0.126976
$872$		0			0
$873$	−26853.8	+	6404.24i	−1.04108	+	0.248282i
$874$		0			0
$875$	−44724.5	−	8131.73i	−1.72796	−	0.314174i
$876$		0			0
$877$	−8052.00	−	8052.00i	−0.310030	−	0.310030i	0.534891	−	0.844921i	$-0.320353\pi$
$877$	−8052.00	−	8052.00i	−0.310030	−	0.310030i	−0.844921	+	0.534891i	$0.820353\pi$
$878$		0			0
$879$	9503.52	−	33600.0i	0.364671	−	1.28931i
$880$		0			0
$881$		−	39810.1i		−	1.52240i	−0.648516	−	0.761201i	$-0.724610\pi$
$881$		−	39810.1i		−	1.52240i	0.648516	−	0.761201i	$-0.275390\pi$
$882$		0			0
$883$	−1964.00	+	1964.00i	−0.0748515	+	0.0748515i	−0.743541	−	0.668690i	$-0.766855\pi$
$883$	−1964.00	+	1964.00i	−0.0748515	+	0.0748515i	0.668690	+	0.743541i	$0.266855\pi$
$884$		0			0
$885$	−2824.87	+	537.437i	−0.107296	+	0.0204133i
$886$		0			0
$887$	−20831.4	+	20831.4i	−0.788556	+	0.788556i	−0.981257	−	0.192702i	$-0.938275\pi$
$887$	−20831.4	+	20831.4i	−0.788556	+	0.788556i	0.192702	+	0.981257i	$0.438275\pi$
$888$		0			0
$889$			70334.0i			2.65346i
$890$		0			0
$891$	4600.00	−	2326.38i	0.172958	−	0.0874711i
$892$		0			0
$893$	−5769.99	−	5769.99i	−0.216221	−	0.216221i
$894$		0			0
$895$	6925.00	−	20775.0i	0.258634	−	0.775901i
$896$		0			0
$897$	12048.2	+	21551.8i	0.448472	+	0.802221i
$898$		0			0
$899$	−12628.9			−0.468519
$900$		0			0
$901$	−50600.0			−1.87095
$902$		0			0
$903$	14696.0	+	26288.0i	0.541584	+	0.968780i
$904$		0			0
$905$	−15436.1	+	46308.4i	−0.566978	+	1.70093i
$906$		0			0
$907$	9094.00	+	9094.00i	0.332923	+	0.332923i	0.853696	−	0.520772i	$-0.174356\pi$
$907$	9094.00	+	9094.00i	0.332923	+	0.332923i	−0.520772	+	0.853696i	$0.674356\pi$
$908$		0			0
$909$	16751.4	+	10300.0i	0.611229	+	0.375830i
$910$		0			0
$911$		−	22090.0i		−	0.803375i	−0.915777	−	0.401688i	$-0.868424\pi$
$911$		−	22090.0i		−	0.803375i	0.915777	−	0.401688i	$-0.131576\pi$
$912$		0			0
$913$	−5100.00	+	5100.00i	−0.184869	+	0.184869i
$914$		0			0
$915$	−7190.95	+	1368.09i	−0.259809	+	0.0494292i
$916$		0			0
$917$	48627.7	−	48627.7i	1.75118	−	1.75118i
$918$		0			0
$919$			7502.00i			0.269280i	0.990895	+	0.134640i	$0.0429878\pi$
$919$			7502.00i			0.269280i	−0.990895	+	0.134640i	$0.957012\pi$
$920$		0			0
$921$	4524.00	−	15994.8i	0.161858	−	0.572253i
$922$		0			0
$923$	−22740.6	−	22740.6i	−0.810958	−	0.810958i
$924$		0			0
$925$	1650.00	+	11550.0i	0.0586504	+	0.410553i
$926$		0			0
$927$	646.624	+	2711.38i	0.0229104	+	0.0960661i
$928$		0			0
$929$	15457.4			0.545898			0.272949	−	0.962028i	$-0.412001\pi$
$929$	15457.4			0.545898			0.272949	+	0.962028i	$0.412001\pi$
$930$		0			0
$931$	48620.0			1.71155
$932$		0			0
$933$	−448.995	+	251.005i	−0.0157550	+	0.00880765i
$934$		0			0
$935$	7778.17	−	3889.09i	0.272057	−	0.136029i
$936$		0			0
$937$	31123.0	+	31123.0i	1.08511	+	1.08511i	0.996024	+	0.0890814i	$0.0283931\pi$
$937$	31123.0	+	31123.0i	1.08511	+	1.08511i	0.0890814	+	0.996024i	$0.471607\pi$
$938$		0			0
$939$	24331.5	+	6882.00i	0.845612	+	0.239175i
$940$		0			0
$941$			7700.39i			0.266765i	0.991065	+	0.133382i	$0.0425838\pi$
$941$			7700.39i			0.266765i	−0.991065	+	0.133382i	$0.957416\pi$
$942$		0			0
$943$	19600.0	−	19600.0i	0.676844	−	0.676844i
$944$		0			0
$945$	−46542.0	+	20902.7i	−1.60213	+	0.719539i
$946$		0			0
$947$	−23157.7	+	23157.7i	−0.794642	+	0.794642i	−0.982245	−	0.187603i	$-0.939928\pi$
$947$	−23157.7	+	23157.7i	−0.794642	+	0.794642i	0.187603	+	0.982245i	$0.439928\pi$
$948$		0			0
$949$			19344.0i			0.661678i
$950$		0			0
$951$	42450.0	+	12006.7i	1.44746	+	0.409404i
$952$		0			0
$953$	8591.35	+	8591.35i	0.292026	+	0.292026i	0.837880	−	0.545854i	$-0.183795\pi$
$953$	8591.35	+	8591.35i	0.292026	+	0.292026i	−0.545854	+	0.837880i	$0.683795\pi$
$954$		0			0
$955$	41550.0	+	13850.0i	1.40788	+	0.469294i
$956$		0			0
$957$	4308.76	−	2408.76i	0.145541	−	0.0813627i
$958$		0			0
$959$	28298.4			0.952871
$960$		0			0
$961$	−20955.0			−0.703400
$962$		0			0
$963$	−5887.65	−	24687.6i	−0.197016	−	0.826115i
$964$		0			0
$965$	6215.47	+	12430.9i	0.207340	+	0.414680i
$966$		0			0
$967$	−24101.0	−	24101.0i	−0.801485	−	0.801485i	0.181843	−	0.983328i	$-0.441794\pi$
$967$	−24101.0	−	24101.0i	−0.801485	−	0.801485i	−0.983328	+	0.181843i	$0.941794\pi$
$968$		0			0
$969$	10578.3	−	37400.0i	0.350696	−	1.23990i
$970$		0			0
$971$			43310.3i			1.43140i	0.698406	+	0.715702i	$0.253893\pi$
$971$			43310.3i			1.43140i	−0.698406	+	0.715702i	$0.746107\pi$
$972$		0			0
$973$	−31648.0	+	31648.0i	−1.04274	+	1.04274i
$974$		0			0
$975$	13370.6	+	17527.9i	0.439180	+	0.575736i
$976$		0			0
$977$	32647.1	−	32647.1i	1.06906	−	1.06906i	0.0716312	−	0.997431i	$-0.477180\pi$
$977$	32647.1	−	32647.1i	1.06906	−	1.06906i	0.997431	−	0.0716312i	$-0.0228204\pi$
$978$		0			0
$979$		−	7300.00i		−	0.238314i
$980$		0			0
$981$	−1426.00	−	876.812i	−0.0464105	−	0.0285367i
$982$		0			0
$983$	−2192.03	−	2192.03i	−0.0711240	−	0.0711240i	0.670650	−	0.741774i	$-0.266015\pi$
$983$	−2192.03	−	2192.03i	−0.0711240	−	0.0711240i	−0.741774	+	0.670650i	$0.766015\pi$
$984$		0			0
$985$	−6600.00	−	13200.0i	−0.213496	−	0.426992i
$986$		0			0
$987$	9896.77	+	17703.2i	0.319167	+	0.570922i
$988$		0			0
$989$	−24946.7			−0.802083
$990$		0			0
$991$	−15656.0			−0.501846			−0.250923	−	0.968007i	$-0.580734\pi$
$991$	−15656.0			−0.501846			−0.250923	+	0.968007i	$0.580734\pi$
$992$		0			0
$993$	−1541.60	−	2757.60i	−0.0492662	−	0.0881268i
$994$		0			0
$995$	3309.26	+	1103.09i	0.105438	+	0.0351459i
$996$		0			0
$997$	−31136.0	−	31136.0i	−0.989054	−	0.989054i	0.0108866	−	0.999941i	$-0.496535\pi$
$997$	−31136.0	−	31136.0i	−0.989054	−	0.989054i	−0.999941	+	0.0108866i	$0.996535\pi$
$998$		0			0
$999$	8867.12	+	9636.00i	0.280824	+	0.305175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.4.i.a.17.2	yes	4
3.2	odd	2	inner	60.4.i.a.17.1	✓	4
4.3	odd	2		240.4.v.a.17.1		4
5.2	odd	4		300.4.i.c.293.2		4
5.3	odd	4	inner	60.4.i.a.53.1	yes	4
5.4	even	2		300.4.i.c.257.1		4
12.11	even	2		240.4.v.a.17.2		4
15.2	even	4		300.4.i.c.293.1		4
15.8	even	4	inner	60.4.i.a.53.2	yes	4
15.14	odd	2		300.4.i.c.257.2		4
20.3	even	4		240.4.v.a.113.2		4
60.23	odd	4		240.4.v.a.113.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.4.i.a.17.1	✓	4	3.2	odd	2	inner
60.4.i.a.17.2	yes	4	1.1	even	1	trivial
60.4.i.a.53.1	yes	4	5.3	odd	4	inner
60.4.i.a.53.2	yes	4	15.8	even	4	inner
240.4.v.a.17.1		4	4.3	odd	2
240.4.v.a.17.2		4	12.11	even	2
240.4.v.a.113.1		4	60.23	odd	4
240.4.v.a.113.2		4	20.3	even	4
300.4.i.c.257.1		4	5.4	even	2
300.4.i.c.257.2		4	15.14	odd	2
300.4.i.c.293.1		4	15.2	even	4
300.4.i.c.293.2		4	5.2	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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	60.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.53553 + 4.53553i) q^{3} +(3.53553 - 10.6066i) q^{5} +(23.0000 + 23.0000i) q^{7} +(-14.1421 + 23.0000i) q^{9} +O(q^{10})\)	\(q+(2.53553 + 4.53553i) q^{3} +(3.53553 - 10.6066i) q^{5} +(23.0000 + 23.0000i) q^{7} +(-14.1421 + 23.0000i) q^{9} +7.07107i q^{11} +(-24.0000 + 24.0000i) q^{13} +(57.0711 - 10.8579i) q^{15} +(77.7817 - 77.7817i) q^{17} -68.0000i q^{19} +(-46.0000 + 162.635i) q^{21} +(-98.9949 - 98.9949i) q^{23} +(-100.000 - 75.0000i) q^{25} +(-140.175 - 5.82486i) q^{27} -134.350 q^{29} +94.0000 q^{31} +(-32.0711 + 17.9289i) q^{33} +(325.269 - 162.635i) q^{35} +(-66.0000 - 66.0000i) q^{37} +(-169.706 - 48.0000i) q^{39} +197.990i q^{41} +(126.000 - 126.000i) q^{43} +(193.952 + 231.317i) q^{45} +(84.8528 - 84.8528i) q^{47} +715.000i q^{49} +(550.000 + 155.563i) q^{51} +(-325.269 - 325.269i) q^{53} +(75.0000 + 25.0000i) q^{55} +(308.416 - 172.416i) q^{57} -49.4975 q^{59} -126.000 q^{61} +(-854.269 + 203.731i) q^{63} +(169.706 + 339.411i) q^{65} +(68.0000 + 68.0000i) q^{67} +(197.990 - 700.000i) q^{69} +947.523i q^{71} +(403.000 - 403.000i) q^{73} +(86.6117 - 643.718i) q^{75} +(-162.635 + 162.635i) q^{77} -234.000i q^{79} +(-329.000 - 650.538i) q^{81} +(721.249 + 721.249i) q^{83} +(-550.000 - 1100.00i) q^{85} +(-340.650 - 609.350i) q^{87} -1032.38 q^{89} -1104.00 q^{91} +(238.340 + 426.340i) q^{93} +(-721.249 - 240.416i) q^{95} +(723.000 + 723.000i) q^{97} +(-162.635 - 100.000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 92 q^{7}+O(q^{10}) \) 4 * q - 4 * q^3 + 92 * q^7	\( 4 q - 4 q^{3} + 92 q^{7} - 96 q^{13} + 200 q^{15} - 184 q^{21} - 400 q^{25} - 292 q^{27} + 376 q^{31} - 100 q^{33} - 264 q^{37} + 504 q^{43} - 200 q^{45} + 2200 q^{51} + 300 q^{55} + 272 q^{57} - 504 q^{61} - 2116 q^{63} + 272 q^{67} + 1612 q^{73} + 700 q^{75} - 1316 q^{81} - 2200 q^{85} - 1900 q^{87} - 4416 q^{91} - 376 q^{93} + 2892 q^{97}+O(q^{100}) \) 4 * q - 4 * q^3 + 92 * q^7 - 96 * q^13 + 200 * q^15 - 184 * q^21 - 400 * q^25 - 292 * q^27 + 376 * q^31 - 100 * q^33 - 264 * q^37 + 504 * q^43 - 200 * q^45 + 2200 * q^51 + 300 * q^55 + 272 * q^57 - 504 * q^61 - 2116 * q^63 + 272 * q^67 + 1612 * q^73 + 700 * q^75 - 1316 * q^81 - 2200 * q^85 - 1900 * q^87 - 4416 * q^91 - 376 * q^93 + 2892 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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