LMFDB - Embedded newform 60.4.i.b.17.1

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:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.370150560000.7
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 131x^{4} + 705x^{2} + 1600 $ x^8 + 3x^6 + 131x^4 + 705*x^2 + 1600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.1
Root			$2.52950 - 2.26556i$ of defining polynomial
Character	$\chi$	$=$	60.17
Dual form			60.4.i.b.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.05899 + 1.18601i) q^{3} +(8.06226 - 7.74597i) q^{5} +(-16.2450 - 16.2450i) q^{7} +(24.1868 - 12.0000i) q^{9} +O(q^{10})$	\(q+(-5.05899 + 1.18601i) q^{3} +(8.06226 - 7.74597i) q^{5} +(-16.2450 - 16.2450i) q^{7} +(24.1868 - 12.0000i) q^{9} -70.9789i q^{11} +(2.51000 - 2.51000i) q^{13} +(-31.6001 + 48.7487i) q^{15} +(-24.8194 + 24.8194i) q^{17} +114.450i q^{19} +(101.450 + 62.9166i) q^{21} +(-45.7657 - 45.7657i) q^{23} +(5.00000 - 124.900i) q^{25} +(-108.129 + 89.3936i) q^{27} +42.0477 q^{29} +193.800 q^{31} +(84.1815 + 359.081i) q^{33} +(-256.805 - 5.13815i) q^{35} +(-37.4100 - 37.4100i) q^{37} +(-9.72120 + 15.6750i) q^{39} -245.341i q^{41} +(-171.065 + 171.065i) q^{43} +(102.048 - 284.097i) q^{45} +(253.487 - 253.487i) q^{47} +184.800i q^{49} +(96.1249 - 154.997i) q^{51} +(224.794 + 224.794i) q^{53} +(-549.800 - 572.250i) q^{55} +(-135.739 - 579.001i) q^{57} +225.743 q^{59} +183.800 q^{61} +(-587.854 - 197.974i) q^{63} +(0.793892 - 39.6787i) q^{65} +(316.205 + 316.205i) q^{67} +(285.807 + 177.250i) q^{69} +225.898i q^{71} +(349.980 - 349.980i) q^{73} +(122.837 + 637.798i) q^{75} +(-1153.05 + 1153.05i) q^{77} +323.750i q^{79} +(441.000 - 580.483i) q^{81} +(553.837 + 553.837i) q^{83} +(-7.85014 + 392.350i) q^{85} +(-212.719 + 49.8689i) q^{87} -351.886 q^{89} -81.5500 q^{91} +(-980.432 + 229.848i) q^{93} +(886.526 + 922.725i) q^{95} +(-114.920 - 114.920i) q^{97} +(-851.746 - 1716.75i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 80 q^{7}+O(q^{10}) $ 8 * q - 80 * q^7	$ 8 q - 80 q^{7} + 120 q^{13} - 120 q^{15} + 312 q^{21} + 40 q^{25} - 448 q^{31} - 600 q^{33} + 600 q^{37} + 480 q^{43} + 1560 q^{45} - 480 q^{51} - 2400 q^{55} - 1560 q^{57} - 528 q^{61} - 960 q^{63} + 2080 q^{67} + 2600 q^{73} + 3120 q^{75} + 3528 q^{81} - 3560 q^{85} - 2400 q^{87} - 1152 q^{91} - 6240 q^{93} - 120 q^{97}+O(q^{100}) $ 8 * q - 80 * q^7 + 120 * q^13 - 120 * q^15 + 312 * q^21 + 40 * q^25 - 448 * q^31 - 600 * q^33 + 600 * q^37 + 480 * q^43 + 1560 * q^45 - 480 * q^51 - 2400 * q^55 - 1560 * q^57 - 528 * q^61 - 960 * q^63 + 2080 * q^67 + 2600 * q^73 + 3120 * q^75 + 3528 * q^81 - 3560 * q^85 - 2400 * q^87 - 1152 * q^91 - 6240 * q^93 - 120 * 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
$3$	−5.05899	+	1.18601i	−0.973603	+	0.228247i
$3$	−5.05899	+	1.18601i	−0.973603	+	0.228247i
$4$		0			0
$5$	8.06226	−	7.74597i	0.721110	−	0.692820i
$5$	8.06226	−	7.74597i	0.721110	−	0.692820i
$6$		0			0
$7$	−16.2450	−	16.2450i	−0.877147	−	0.877147i	0.116091	−	0.993239i	$-0.462964\pi$
$7$	−16.2450	−	16.2450i	−0.877147	−	0.877147i	−0.993239	+	0.116091i	$0.962964\pi$
$8$		0			0
$9$	24.1868	−	12.0000i	0.895806	−	0.444444i
$10$		0			0
$11$		−	70.9789i		−	1.94554i	−0.231774	−	0.972770i	$-0.574453\pi$
$11$		−	70.9789i		−	1.94554i	0.231774	−	0.972770i	$-0.425547\pi$
$12$		0			0
$13$	2.51000	−	2.51000i	0.0535500	−	0.0535500i	−0.679825	−	0.733375i	$-0.737944\pi$
$13$	2.51000	−	2.51000i	0.0535500	−	0.0535500i	0.733375	+	0.679825i	$0.237944\pi$
$14$		0			0
$15$	−31.6001	+	48.7487i	−0.543941	+	0.839123i
$16$		0			0
$17$	−24.8194	+	24.8194i	−0.354093	+	0.354093i	−0.861630	−	0.507537i	$-0.830556\pi$
$17$	−24.8194	+	24.8194i	−0.354093	+	0.354093i	0.507537	+	0.861630i	$0.330556\pi$
$18$		0			0
$19$			114.450i			1.38193i	0.722889	+	0.690964i	$0.242814\pi$
$19$			114.450i			1.38193i	−0.722889	+	0.690964i	$0.757186\pi$
$20$		0			0
$21$	101.450	+	62.9166i	1.05420	+	0.653787i
$22$		0			0
$23$	−45.7657	−	45.7657i	−0.414905	−	0.414905i	0.468538	−	0.883443i	$-0.344781\pi$
$23$	−45.7657	−	45.7657i	−0.414905	−	0.414905i	−0.883443	+	0.468538i	$0.844781\pi$
$24$		0			0
$25$	5.00000	−	124.900i	0.0400000	−	0.999200i
$26$		0			0
$27$	−108.129	+	89.3936i	−0.770717	+	0.637178i
$28$		0			0
$29$	42.0477			0.269244			0.134622	−	0.990897i	$-0.457018\pi$
$29$	42.0477			0.269244			0.134622	+	0.990897i	$0.457018\pi$
$30$		0			0
$31$	193.800			1.12282			0.561411	−	0.827537i	$-0.310259\pi$
$31$	193.800			1.12282			0.561411	+	0.827537i	$0.310259\pi$
$32$		0			0
$33$	84.1815	+	359.081i	0.444064	+	1.89418i
$34$		0			0
$35$	−256.805	−	5.13815i	−1.24023	−	0.0248144i
$36$		0			0
$37$	−37.4100	−	37.4100i	−0.166221	−	0.166221i	0.619095	−	0.785316i	$-0.287499\pi$
$37$	−37.4100	−	37.4100i	−0.166221	−	0.166221i	−0.785316	+	0.619095i	$0.787499\pi$
$38$		0			0
$39$	−9.72120	+	15.6750i	−0.0399138	+	0.0643591i
$40$		0			0
$41$		−	245.341i		−	0.934531i	−0.884117	−	0.467265i	$-0.845239\pi$
$41$		−	245.341i		−	0.934531i	0.884117	−	0.467265i	$-0.154761\pi$
$42$		0			0
$43$	−171.065	+	171.065i	−0.606678	+	0.606678i	−0.942076	−	0.335398i	$-0.891129\pi$
$43$	−171.065	+	171.065i	−0.606678	+	0.606678i	0.335398	+	0.942076i	$0.391129\pi$
$44$		0			0
$45$	102.048	−	284.097i	0.338055	−	0.941126i
$46$		0			0
$47$	253.487	−	253.487i	0.786699	−	0.786699i	−0.194253	−	0.980951i	$-0.562228\pi$
$47$	253.487	−	253.487i	0.786699	−	0.786699i	0.980951	+	0.194253i	$0.0622282\pi$
$48$		0			0
$49$			184.800i			0.538775i
$50$		0			0
$51$	96.1249	−	154.997i	0.263925	−	0.425567i
$52$		0			0
$53$	224.794	+	224.794i	0.582601	+	0.582601i	0.935617	−	0.353016i	$-0.114844\pi$
$53$	224.794	+	224.794i	0.582601	+	0.582601i	−0.353016	+	0.935617i	$0.614844\pi$
$54$		0			0
$55$	−549.800	−	572.250i	−1.34791	−	1.40295i
$56$		0			0
$57$	−135.739	−	579.001i	−0.315421	−	1.34545i
$58$		0			0
$59$	225.743			0.498123			0.249062	−	0.968488i	$-0.419878\pi$
$59$	225.743			0.498123			0.249062	+	0.968488i	$0.419878\pi$
$60$		0			0
$61$	183.800			0.385790			0.192895	−	0.981219i	$-0.438212\pi$
$61$	183.800			0.385790			0.192895	+	0.981219i	$0.438212\pi$
$62$		0			0
$63$	−587.854	−	197.974i	−1.17560	−	0.395911i
$64$		0			0
$65$	0.793892	−	39.6787i	0.00151493	−	0.0757160i
$66$		0			0
$67$	316.205	+	316.205i	0.576576	+	0.576576i	0.933958	−	0.357382i	$-0.116331\pi$
$67$	316.205	+	316.205i	0.576576	+	0.576576i	−0.357382	+	0.933958i	$0.616331\pi$
$68$		0			0
$69$	285.807	+	177.250i	0.498654	+	0.309252i
$70$		0			0
$71$			225.898i			0.377594i	0.982016	+	0.188797i	$0.0604588\pi$
$71$			225.898i			0.377594i	−0.982016	+	0.188797i	$0.939541\pi$
$72$		0			0
$73$	349.980	−	349.980i	0.561124	−	0.561124i	−0.368503	−	0.929627i	$-0.620129\pi$
$73$	349.980	−	349.980i	0.561124	−	0.561124i	0.929627	+	0.368503i	$0.120129\pi$
$74$		0			0
$75$	122.837	+	637.798i	0.189120	+	0.981954i
$76$		0			0
$77$	−1153.05	+	1153.05i	−1.70652	+	1.70652i
$78$		0			0
$79$			323.750i			0.461073i	0.973064	+	0.230536i	$0.0740480\pi$
$79$			323.750i			0.461073i	−0.973064	+	0.230536i	$0.925952\pi$
$80$		0			0
$81$	441.000	−	580.483i	0.604938	−	0.796272i
$82$		0			0
$83$	553.837	+	553.837i	0.732427	+	0.732427i	0.971100	−	0.238673i	$-0.0767123\pi$
$83$	553.837	+	553.837i	0.732427	+	0.732427i	−0.238673	+	0.971100i	$0.576712\pi$
$84$		0			0
$85$	−7.85014	+	392.350i	−0.0100173	+	0.500663i
$86$		0			0
$87$	−212.719	+	49.8689i	−0.262137	+	0.0614541i
$88$		0			0
$89$	−351.886			−0.419100			−0.209550	−	0.977798i	$-0.567200\pi$
$89$	−351.886			−0.419100			−0.209550	+	0.977798i	$0.567200\pi$
$90$		0			0
$91$	−81.5500			−0.0939425
$92$		0			0
$93$	−980.432	+	229.848i	−1.09318	+	0.256281i
$94$		0			0
$95$	886.526	+	922.725i	0.957428	+	0.996522i
$96$		0			0
$97$	−114.920	−	114.920i	−0.120292	−	0.120292i	0.644398	−	0.764690i	$-0.277108\pi$
$97$	−114.920	−	114.920i	−0.120292	−	0.120292i	−0.764690	+	0.644398i	$0.777108\pi$
$98$		0			0
$99$	−851.746	−	1716.75i	−0.864684	−	1.74283i
$100$		0			0
$101$			942.478i			0.928515i	0.885700	+	0.464258i	$0.153679\pi$
$101$			942.478i			0.928515i	−0.885700	+	0.464258i	$0.846321\pi$
$102$		0			0
$103$	1156.00	−	1156.00i	1.10587	−	1.10587i	0.112182	−	0.993688i	$-0.464216\pi$
$103$	1156.00	−	1156.00i	1.10587	−	1.10587i	0.993688	−	0.112182i	$-0.0357839\pi$
$104$		0			0
$105$	1305.27	−	278.578i	1.21315	−	0.258919i
$106$		0			0
$107$	899.565	−	899.565i	0.812750	−	0.812750i	−0.172296	−	0.985045i	$-0.555118\pi$
$107$	899.565	−	899.565i	0.812750	−	0.812750i	0.985045	+	0.172296i	$0.0551184\pi$
$108$		0			0
$109$			1366.70i			1.20097i	0.799635	+	0.600487i	$0.205026\pi$
$109$			1366.70i			1.20097i	−0.799635	+	0.600487i	$0.794974\pi$
$110$		0			0
$111$	233.625	+	144.888i	0.199772	+	0.123893i
$112$		0			0
$113$	−1450.08	−	1450.08i	−1.20718	−	1.20718i	−0.971935	−	0.235249i	$-0.924410\pi$
$113$	−1450.08	−	1450.08i	−1.20718	−	1.20718i	−0.235249	−	0.971935i	$-0.575590\pi$
$114$		0			0
$115$	−723.475	−	14.4753i	−0.586647	−	0.0117376i
$116$		0			0
$117$	30.5888	−	90.8289i	0.0241704	−	0.0717704i
$118$		0			0
$119$	806.381			0.621183
$120$		0			0
$121$	−3707.00			−2.78512
$122$		0			0
$123$	290.976	+	1241.18i	0.213304	+	0.909862i
$124$		0			0
$125$	−927.160	−	1045.71i	−0.663421	−	0.748246i
$126$		0			0
$127$	1318.21	+	1318.21i	0.921044	+	0.921044i	0.997103	−	0.0760589i	$-0.0242337\pi$
$127$	1318.21	+	1318.21i	0.921044	+	0.921044i	−0.0760589	+	0.997103i	$0.524234\pi$
$128$		0			0
$129$	662.532	−	1068.30i	0.452191	−	0.729136i
$130$		0			0
$131$		−	535.737i		−	0.357310i	−0.983912	−	0.178655i	$-0.942825\pi$
$131$		−	535.737i		−	0.357310i	0.983912	−	0.178655i	$-0.0571745\pi$
$132$		0			0
$133$	1859.24	−	1859.24i	1.21215	−	1.21215i
$134$		0			0
$135$	−179.321	+	1558.27i	−0.114322	+	0.993444i
$136$		0			0
$137$	1893.99	−	1893.99i	1.18112	−	1.18112i	0.201672	−	0.979453i	$-0.435363\pi$
$137$	1893.99	−	1893.99i	1.18112	−	1.18112i	0.979453	−	0.201672i	$-0.0646373\pi$
$138$		0			0
$139$		−	2069.75i		−	1.26298i	−0.775385	−	0.631489i	$-0.782444\pi$
$139$		−	2069.75i		−	1.26298i	0.775385	−	0.631489i	$-0.217556\pi$
$140$		0			0
$141$	−981.750	+	1583.02i	−0.586370	+	0.945494i
$142$		0			0
$143$	−178.157	−	178.157i	−0.104184	−	0.104184i
$144$		0			0
$145$	339.000	−	325.700i	0.194154	−	0.186537i
$146$		0			0
$147$	−219.174	−	934.901i	−0.122974	−	0.524553i
$148$		0			0
$149$	−2099.66			−1.15444			−0.577218	−	0.816590i	$-0.695862\pi$
$149$	−2099.66			−1.15444			−0.577218	+	0.816590i	$0.695862\pi$
$150$		0			0
$151$	−665.800			−0.358821			−0.179411	−	0.983774i	$-0.557419\pi$
$151$	−665.800			−0.358821			−0.179411	+	0.983774i	$0.557419\pi$
$152$		0			0
$153$	−302.468	+	898.132i	−0.159824	+	0.474573i
$154$		0			0
$155$	1562.46	−	1501.17i	0.809679	−	0.777914i
$156$		0			0
$157$	937.530	+	937.530i	0.476580	+	0.476580i	0.904036	−	0.427456i	$-0.140590\pi$
$157$	937.530	+	937.530i	0.476580	+	0.476580i	−0.427456	+	0.904036i	$0.640590\pi$
$158$		0			0
$159$	−1403.84	−	870.625i	−0.700200	−	0.434245i
$160$		0			0
$161$			1486.93i			0.727866i
$162$		0			0
$163$	−506.165	+	506.165i	−0.243226	+	0.243226i	−0.818184	−	0.574957i	$-0.805019\pi$
$163$	−506.165	+	506.165i	−0.243226	+	0.243226i	0.574957	+	0.818184i	$0.305019\pi$
$164$		0			0
$165$	3460.13	+	2242.94i	1.63255	+	1.05826i
$166$		0			0
$167$	−1318.81	+	1318.81i	−0.611096	+	0.611096i	−0.943232	−	0.332136i	$-0.892231\pi$
$167$	−1318.81	+	1318.81i	−0.611096	+	0.611096i	0.332136	+	0.943232i	$0.392231\pi$
$168$		0			0
$169$			2184.40i			0.994265i
$170$		0			0
$171$	1373.40	+	2768.18i	0.614190	+	1.23794i
$172$		0			0
$173$	381.909	+	381.909i	0.167838	+	0.167838i	0.786028	−	0.618190i	$-0.212134\pi$
$173$	381.909	+	381.909i	0.167838	+	0.167838i	−0.618190	+	0.786028i	$0.712134\pi$
$174$		0			0
$175$	−2110.22	+	1947.77i	−0.911531	+	0.841360i
$176$		0			0
$177$	−1142.03	+	267.733i	−0.484974	+	0.113695i
$178$		0			0
$179$	−3400.04			−1.41973			−0.709863	−	0.704340i	$-0.751243\pi$
$179$	−3400.04			−1.41973			−0.709863	+	0.704340i	$0.751243\pi$
$180$		0			0
$181$	1713.60			0.703706			0.351853	−	0.936055i	$-0.385552\pi$
$181$	1713.60			0.703706			0.351853	+	0.936055i	$0.385552\pi$
$182$		0			0
$183$	−929.842	+	217.988i	−0.375606	+	0.0880554i
$184$		0			0
$185$	−591.385	−	11.8324i	−0.235024	−	0.00470237i
$186$		0			0
$187$	1761.65	+	1761.65i	0.688902	+	0.688902i
$188$		0			0
$189$	3208.75	+	304.350i	1.23493	+	0.117133i
$190$		0			0
$191$		−	3489.07i		−	1.32178i	−0.750483	−	0.660890i	$-0.770179\pi$
$191$		−	3489.07i		−	1.32178i	0.750483	−	0.660890i	$-0.229821\pi$
$192$		0			0
$193$	2574.56	−	2574.56i	0.960212	−	0.960212i	−0.0390264	−	0.999238i	$-0.512426\pi$
$193$	2574.56	−	2574.56i	0.960212	−	0.960212i	0.999238	+	0.0390264i	$0.0124256\pi$
$194$		0			0
$195$	43.0429	+	201.676i	0.0158070	+	0.0740631i
$196$		0			0
$197$	−1793.29	+	1793.29i	−0.648561	+	0.648561i	−0.952645	−	0.304084i	$-0.901650\pi$
$197$	−1793.29	+	1793.29i	−0.648561	+	0.648561i	0.304084	+	0.952645i	$0.401650\pi$
$198$		0			0
$199$		−	1529.65i		−	0.544894i	−0.962171	−	0.272447i	$-0.912167\pi$
$199$		−	1529.65i		−	0.544894i	0.962171	−	0.272447i	$-0.0878330\pi$
$200$		0			0
$201$	−1974.70	−	1224.66i	−0.692958	−	0.429754i
$202$		0			0
$203$	−683.065	−	683.065i	−0.236166	−	0.236166i
$204$		0			0
$205$	−1900.40	−	1978.00i	−0.647462	−	0.673900i
$206$		0			0
$207$	−1656.11	−	557.737i	−0.556077	−	0.187272i
$208$		0			0
$209$	8123.53			2.68859
$210$		0			0
$211$	−487.401			−0.159024			−0.0795119	−	0.996834i	$-0.525336\pi$
$211$	−487.401			−0.159024			−0.0795119	+	0.996834i	$0.525336\pi$
$212$		0			0
$213$	−267.917	−	1142.82i	−0.0861848	−	0.367627i
$214$		0			0
$215$	−54.1063	+	2704.23i	−0.0171629	+	0.857801i
$216$		0			0
$217$	−3148.28	−	3148.28i	−0.984881	−	0.984881i
$218$		0			0
$219$	−1355.47	+	2185.62i	−0.418237	+	0.674387i
$220$		0			0
$221$			124.593i			0.0379233i
$222$		0			0
$223$	−1777.01	+	1777.01i	−0.533622	+	0.533622i	−0.921648	−	0.388026i	$-0.873157\pi$
$223$	−1777.01	+	1777.01i	−0.533622	+	0.533622i	0.388026	+	0.921648i	$0.373157\pi$
$224$		0			0
$225$	−1377.87	−	3080.93i	−0.408256	−	0.912867i
$226$		0			0
$227$	2347.93	−	2347.93i	0.686509	−	0.686509i	−0.274949	−	0.961459i	$-0.588661\pi$
$227$	2347.93	−	2347.93i	0.686509	−	0.686509i	0.961459	+	0.274949i	$0.0886611\pi$
$228$		0			0
$229$			3684.30i			1.06317i	0.847006	+	0.531584i	$0.178403\pi$
$229$			3684.30i			1.06317i	−0.847006	+	0.531584i	$0.821597\pi$
$230$		0			0
$231$	4465.75	−	7200.80i	1.27197	−	2.05099i
$232$		0			0
$233$	−870.550	−	870.550i	−0.244771	−	0.244771i	0.574050	−	0.818821i	$-0.305372\pi$
$233$	−870.550	−	870.550i	−0.244771	−	0.244771i	−0.818821	+	0.574050i	$0.805372\pi$
$234$		0			0
$235$	80.1756	−	4007.17i	0.0222556	−	1.11234i
$236$		0			0
$237$	−383.970	−	1637.85i	−0.105239	−	0.448902i
$238$		0			0
$239$	−1783.12			−0.482597			−0.241298	−	0.970451i	$-0.577573\pi$
$239$	−1783.12			−0.482597			−0.241298	+	0.970451i	$0.577573\pi$
$240$		0			0
$241$	3303.40			0.882949			0.441474	−	0.897274i	$-0.354456\pi$
$241$	3303.40			0.882949			0.441474	+	0.897274i	$0.354456\pi$
$242$		0			0
$243$	−1542.56	+	3459.69i	−0.407223	+	0.913329i
$244$		0			0
$245$	1431.45	+	1489.90i	0.373274	+	0.388516i
$246$		0			0
$247$	287.270	+	287.270i	0.0740022	+	0.0740022i
$248$		0			0
$249$	−3458.71	−	2145.00i	−0.880268	−	0.545919i
$250$		0			0
$251$			1449.19i			0.364431i	0.983259	+	0.182215i	$0.0583268\pi$
$251$			1449.19i			0.364431i	−0.983259	+	0.182215i	$0.941673\pi$
$252$		0			0
$253$	−3248.40	+	3248.40i	−0.807214	+	0.807214i
$254$		0			0
$255$	−425.616	−	1994.21i	−0.104522	−	0.489733i
$256$		0			0
$257$	−1530.38	+	1530.38i	−0.371449	+	0.371449i	−0.868005	−	0.496556i	$-0.834598\pi$
$257$	−1530.38	+	1530.38i	−0.371449	+	0.371449i	0.496556	+	0.868005i	$0.334598\pi$
$258$		0			0
$259$			1215.45i			0.291600i
$260$		0			0
$261$	1017.00	−	504.573i	0.241190	−	0.119664i
$262$		0			0
$263$	5005.90	+	5005.90i	1.17368	+	1.17368i	0.981327	+	0.192349i	$0.0616106\pi$
$263$	5005.90	+	5005.90i	1.17368	+	1.17368i	0.192349	+	0.981327i	$0.438389\pi$
$264$		0			0
$265$	3553.60	+	71.1004i	0.823758	+	0.0164818i
$266$		0			0
$267$	1780.19	−	417.340i	0.408037	−	0.0956584i
$268$		0			0
$269$	1939.65			0.439639			0.219819	−	0.975541i	$-0.429453\pi$
$269$	1939.65			0.439639			0.219819	+	0.975541i	$0.429453\pi$
$270$		0			0
$271$	938.999			0.210480			0.105240	−	0.994447i	$-0.466439\pi$
$271$	938.999			0.210480			0.105240	+	0.994447i	$0.466439\pi$
$272$		0			0
$273$	412.561	−	96.7189i	0.0914627	−	0.0214421i
$274$		0			0
$275$	−8865.26	−	354.894i	−1.94398	−	0.0778216i
$276$		0			0
$277$	−4495.57	−	4495.57i	−0.975136	−	0.975136i	0.0245626	−	0.999698i	$-0.492181\pi$
$277$	−4495.57	−	4495.57i	−0.975136	−	0.975136i	−0.999698	+	0.0245626i	$0.992181\pi$
$278$		0			0
$279$	4687.39	−	2325.60i	1.00583	−	0.499032i
$280$		0			0
$281$			351.513i			0.0746246i	0.999304	+	0.0373123i	$0.0118796\pi$
$281$			351.513i			0.0746246i	−0.999304	+	0.0373123i	$0.988120\pi$
$282$		0			0
$283$	−1031.47	+	1031.47i	−0.216658	+	0.216658i	−0.807089	−	0.590430i	$-0.798958\pi$
$283$	−1031.47	+	1031.47i	−0.216658	+	0.216658i	0.590430	+	0.807089i	$0.298958\pi$
$284$		0			0
$285$	−5579.28	−	3616.63i	−1.15961	−	0.751687i
$286$		0			0
$287$	−3985.56	+	3985.56i	−0.819721	+	0.819721i
$288$		0			0
$289$			3681.00i			0.749237i
$290$		0			0
$291$	717.675	+	445.083i	0.144573	+	0.0896606i
$292$		0			0
$293$	5035.56	+	5035.56i	1.00403	+	1.00403i	0.999992	+	0.00403640i	$0.00128483\pi$
$293$	5035.56	+	5035.56i	1.00403	+	1.00403i	0.00403640	+	0.999992i	$0.498715\pi$
$294$		0			0
$295$	1820.00	−	1748.60i	0.359202	−	0.345110i
$296$		0			0
$297$	6345.05	+	7674.84i	1.23965	+	1.49946i
$298$		0			0
$299$	−229.744			−0.0444363
$300$		0			0
$301$	5557.90			1.06429
$302$		0			0
$303$	−1117.79	−	4767.99i	−0.211931	−	0.904005i
$304$		0			0
$305$	1481.84	−	1423.71i	0.278197	−	0.267283i
$306$		0			0
$307$	4076.20	+	4076.20i	0.757789	+	0.757789i	0.975920	−	0.218130i	$-0.0699958\pi$
$307$	4076.20	+	4076.20i	0.757789	+	0.757789i	−0.218130	+	0.975920i	$0.569996\pi$
$308$		0			0
$309$	−4477.19	+	7219.25i	−0.824266	+	1.32909i
$310$		0			0
$311$			7036.15i			1.28290i	0.767163	+	0.641452i	$0.221668\pi$
$311$			7036.15i			1.28290i	−0.767163	+	0.641452i	$0.778332\pi$
$312$		0			0
$313$	−830.740	+	830.740i	−0.150020	+	0.150020i	−0.778127	−	0.628107i	$-0.783830\pi$
$313$	−830.740	+	830.740i	−0.150020	+	0.150020i	0.628107	+	0.778127i	$0.283830\pi$
$314$		0			0
$315$	−6272.93	+	2957.38i	−1.12203	+	0.528982i
$316$		0			0
$317$	2049.10	−	2049.10i	0.363056	−	0.363056i	−0.501881	−	0.864937i	$-0.667358\pi$
$317$	2049.10	−	2049.10i	0.363056	−	0.363056i	0.864937	+	0.501881i	$0.167358\pi$
$318$		0			0
$319$		−	2984.50i		−	0.523824i
$320$		0			0
$321$	−3484.00	+	5617.78i	−0.605788	+	0.976804i
$322$		0			0
$323$	−2840.57	−	2840.57i	−0.489331	−	0.489331i
$324$		0			0
$325$	−300.949	−	326.049i	−0.0513651	−	0.0556491i
$326$		0			0
$327$	−1620.92	−	6914.12i	−0.274119	−	1.16927i
$328$		0			0
$329$	−8235.78			−1.38010
$330$		0			0
$331$	363.000			0.0602789			0.0301394	−	0.999546i	$-0.490405\pi$
$331$	363.000			0.0602789			0.0301394	+	0.999546i	$0.490405\pi$
$332$		0			0
$333$	−1353.75	−	455.907i	−0.222777	−	0.0750256i
$334$		0			0
$335$	4998.64	+	100.013i	0.815238	+	0.0163113i
$336$		0			0
$337$	−2287.12	−	2287.12i	−0.369696	−	0.369696i	0.497671	−	0.867366i	$-0.334189\pi$
$337$	−2287.12	−	2287.12i	−0.369696	−	0.369696i	−0.867366	+	0.497671i	$0.834189\pi$
$338$		0			0
$339$	9055.73	+	5616.12i	1.45085	+	0.899782i
$340$		0			0
$341$		−	13755.7i		−	2.18450i
$342$		0			0
$343$	−2569.96	+	2569.96i	−0.404562	+	0.404562i
$344$		0			0
$345$	3677.22	−	784.816i	0.573840	−	0.122473i
$346$		0			0
$347$	4355.82	−	4355.82i	0.673869	−	0.673869i	−0.284737	−	0.958606i	$-0.591906\pi$
$347$	4355.82	−	4355.82i	0.673869	−	0.673869i	0.958606	+	0.284737i	$0.0919063\pi$
$348$		0			0
$349$		−	8217.50i		−	1.26038i	−0.776441	−	0.630190i	$-0.782977\pi$
$349$		−	8217.50i		−	1.26038i	0.776441	−	0.630190i	$-0.217023\pi$
$350$		0			0
$351$	−47.0249	+	495.781i	−0.00715101	+	0.0753927i
$352$		0			0
$353$	−3373.66	−	3373.66i	−0.508673	−	0.508673i	0.405446	−	0.914119i	$-0.367116\pi$
$353$	−3373.66	−	3373.66i	−0.508673	−	0.508673i	−0.914119	+	0.405446i	$0.867116\pi$
$354$		0			0
$355$	1749.80	+	1821.25i	0.261605	+	0.272287i
$356$		0			0
$357$	−4079.47	+	956.373i	−0.604786	+	0.141783i
$358$		0			0
$359$	4939.81			0.726220			0.363110	−	0.931746i	$-0.381715\pi$
$359$	4939.81			0.726220			0.363110	+	0.931746i	$0.381715\pi$
$360$		0			0
$361$	−6239.80			−0.909724
$362$		0			0
$363$	18753.7	−	4396.53i	2.71161	−	0.635697i
$364$		0			0
$365$	110.696	−	5532.56i	0.0158742	−	0.793391i
$366$		0			0
$367$	−4599.54	−	4599.54i	−0.654208	−	0.654208i	0.299796	−	0.954003i	$-0.403082\pi$
$367$	−4599.54	−	4599.54i	−0.654208	−	0.654208i	−0.954003	+	0.299796i	$0.903082\pi$
$368$		0			0
$369$	−2944.09	−	5934.00i	−0.415347	−	0.837159i
$370$		0			0
$371$		−	7303.57i		−	1.02205i
$372$		0			0
$373$	−5559.59	+	5559.59i	−0.771755	+	0.771755i	−0.978413	−	0.206658i	$-0.933741\pi$
$373$	−5559.59	+	5559.59i	−0.771755	+	0.771755i	0.206658	+	0.978413i	$0.433741\pi$
$374$		0			0
$375$	5930.71	+	4190.60i	0.816694	+	0.577071i
$376$		0			0
$377$	105.540	−	105.540i	0.0144180	−	0.0144180i
$378$		0			0
$379$		−	9794.15i		−	1.32742i	−0.747991	−	0.663709i	$-0.768981\pi$
$379$		−	9794.15i		−	1.32742i	0.747991	−	0.663709i	$-0.231019\pi$
$380$		0			0
$381$	−8232.25	−	5105.42i	−1.10696	−	0.686506i
$382$		0			0
$383$	−9135.79	−	9135.79i	−1.21884	−	1.21884i	−0.968038	−	0.250805i	$-0.919305\pi$
$383$	−9135.79	−	9135.79i	−1.21884	−	1.21884i	−0.250805	−	0.968038i	$-0.580695\pi$
$384$		0			0
$385$	−364.700	+	18227.7i	−0.0482775	+	2.41291i
$386$		0			0
$387$	−2084.73	+	6190.29i	−0.273831	+	0.813101i
$388$		0			0
$389$	6803.55			0.886771			0.443385	−	0.896331i	$-0.353777\pi$
$389$	6803.55			0.886771			0.443385	+	0.896331i	$0.353777\pi$
$390$		0			0
$391$	2271.75			0.293830
$392$		0			0
$393$	635.388	+	2710.29i	0.0815549	+	0.347878i
$394$		0			0
$395$	2507.76	+	2610.16i	0.319440	+	0.332484i
$396$		0			0
$397$	3213.53	+	3213.53i	0.406253	+	0.406253i	0.880430	−	0.474177i	$-0.157254\pi$
$397$	3213.53	+	3213.53i	0.406253	+	0.406253i	−0.474177	+	0.880430i	$0.657254\pi$
$398$		0			0
$399$	−7200.80	+	11610.9i	−0.903487	+	1.45683i
$400$		0			0
$401$			7126.29i			0.887456i	0.896161	+	0.443728i	$0.146344\pi$
$401$			7126.29i			0.887456i	−0.896161	+	0.443728i	$0.853656\pi$
$402$		0			0
$403$	486.439	−	486.439i	0.0601271	−	0.0601271i
$404$		0			0
$405$	−940.943	−	8095.97i	−0.115446	−	0.993314i
$406$		0			0
$407$	−2655.32	+	2655.32i	−0.323389	+	0.323389i
$408$		0			0
$409$		−	6060.40i		−	0.732683i	−0.930480	−	0.366341i	$-0.880610\pi$
$409$		−	6060.40i		−	0.732683i	0.930480	−	0.366341i	$-0.119390\pi$
$410$		0			0
$411$	−7335.37	+	11827.9i	−0.880358	+	1.41954i
$412$		0			0
$413$	−3667.20	−	3667.20i	−0.436927	−	0.436927i
$414$		0			0
$415$	8755.17	+	175.174i	1.03560	+	0.0207203i
$416$		0			0
$417$	2454.74	+	10470.8i	0.288271	+	1.22964i
$418$		0			0
$419$	−3345.71			−0.390093			−0.195046	−	0.980794i	$-0.562486\pi$
$419$	−3345.71			−0.390093			−0.195046	+	0.980794i	$0.562486\pi$
$420$		0			0
$421$	7671.00			0.888032			0.444016	−	0.896019i	$-0.353553\pi$
$421$	7671.00			0.888032			0.444016	+	0.896019i	$0.353553\pi$
$422$		0			0
$423$	3089.18	−	9172.87i	0.355086	−	1.05437i
$424$		0			0
$425$	2975.84	+	3224.03i	0.339646	+	0.367973i
$426$		0			0
$427$	−2985.83	−	2985.83i	−0.338394	−	0.338394i
$428$		0			0
$429$	1112.59	+	690.000i	0.125213	+	0.0776539i
$430$		0			0
$431$			10347.5i			1.15643i	0.815884	+	0.578215i	$0.196251\pi$
$431$			10347.5i			1.15643i	−0.815884	+	0.578215i	$0.803749\pi$
$432$		0			0
$433$	9546.16	−	9546.16i	1.05949	−	1.05949i	0.0613748	−	0.998115i	$-0.480452\pi$
$433$	9546.16	−	9546.16i	1.05949	−	1.05949i	0.998115	−	0.0613748i	$-0.0195485\pi$
$434$		0			0
$435$	−1328.71	+	2049.77i	−0.146453	+	0.225929i
$436$		0			0
$437$	5237.89	−	5237.89i	0.573369	−	0.573369i
$438$		0			0
$439$			4907.95i			0.533585i	0.963754	+	0.266792i	$0.0859638\pi$
$439$			4907.95i			0.533585i	−0.963754	+	0.266792i	$0.914036\pi$
$440$		0			0
$441$	2217.60	+	4469.71i	0.239456	+	0.482638i
$442$		0			0
$443$	−2995.75	−	2995.75i	−0.321292	−	0.321292i	0.527970	−	0.849263i	$-0.322953\pi$
$443$	−2995.75	−	2995.75i	−0.321292	−	0.321292i	−0.849263	+	0.527970i	$0.822953\pi$
$444$		0			0
$445$	−2837.00	+	2725.70i	−0.302217	+	0.290361i
$446$		0			0
$447$	10622.2	−	2490.21i	1.12396	−	0.263497i
$448$		0			0
$449$	−13875.5			−1.45841			−0.729205	−	0.684295i	$-0.760110\pi$
$449$	−13875.5			−1.45841			−0.729205	+	0.684295i	$0.760110\pi$
$450$		0			0
$451$	−17414.0			−1.81817
$452$		0			0
$453$	3368.28	−	789.644i	0.349350	−	0.0819000i
$454$		0			0
$455$	−657.477	+	631.684i	−0.0677429	+	0.0650853i
$456$		0			0
$457$	2544.54	+	2544.54i	0.260456	+	0.260456i	0.825239	−	0.564783i	$-0.191040\pi$
$457$	2544.54	+	2544.54i	0.260456	+	0.260456i	−0.564783	+	0.825239i	$0.691040\pi$
$458$		0			0
$459$	464.990	−	4902.37i	0.0472852	−	0.498525i
$460$		0			0
$461$			10977.0i			1.10900i	0.832183	+	0.554502i	$0.187091\pi$
$461$			10977.0i			1.10900i	−0.832183	+	0.554502i	$0.812909\pi$
$462$		0			0
$463$	−5370.90	+	5370.90i	−0.539107	+	0.539107i	−0.923267	−	0.384159i	$-0.874491\pi$
$463$	−5370.90	+	5370.90i	−0.539107	+	0.539107i	0.384159	+	0.923267i	$0.374491\pi$
$464$		0			0
$465$	−6124.10	+	9447.49i	−0.610749	+	0.942187i
$466$		0			0
$467$	−3265.83	+	3265.83i	−0.323607	+	0.323607i	−0.850149	−	0.526542i	$-0.823488\pi$
$467$	−3265.83	+	3265.83i	−0.323607	+	0.323607i	0.526542	+	0.850149i	$0.323488\pi$
$468$		0			0
$469$		−	10273.5i		−	1.01148i
$470$		0			0
$471$	−5854.87	−	3631.04i	−0.572778	−	0.355222i
$472$		0			0
$473$	12142.0	+	12142.0i	1.18032	+	1.18032i
$474$		0			0
$475$	14294.8	+	572.250i	1.38082	+	0.0552771i
$476$		0			0
$477$	8134.58	+	2739.52i	0.780832	+	0.262964i
$478$		0			0
$479$	−6609.07			−0.630430			−0.315215	−	0.949020i	$-0.602077\pi$
$479$	−6609.07			−0.630430			−0.315215	+	0.949020i	$0.602077\pi$
$480$		0			0
$481$	−187.798			−0.0178022
$482$		0			0
$483$	−1763.51	−	7522.36i	−0.166133	−	0.708652i
$484$		0			0
$485$	−1816.68	−	36.3482i	−0.170085	−	0.00340306i
$486$		0			0
$487$	9393.55	+	9393.55i	0.874051	+	0.874051i	0.992911	−	0.118860i	$-0.0379241\pi$
$487$	9393.55	+	9393.55i	0.874051	+	0.874051i	−0.118860	+	0.992911i	$0.537924\pi$
$488$		0			0
$489$	1960.37	−	3161.00i	0.181290	−	0.292322i
$490$		0			0
$491$		−	7629.90i		−	0.701289i	−0.936509	−	0.350644i	$-0.885963\pi$
$491$		−	7629.90i		−	0.701289i	0.936509	−	0.350644i	$-0.114037\pi$
$492$		0			0
$493$	−1043.60	+	1043.60i	−0.0953373	+	0.0953373i
$494$		0			0
$495$	−20164.9	−	7243.28i	−1.83100	−	0.657699i
$496$		0			0
$497$	3669.72	−	3669.72i	0.331206	−	0.331206i
$498$		0			0
$499$			6245.25i			0.560272i	0.959960	+	0.280136i	$0.0903795\pi$
$499$			6245.25i			0.560272i	−0.959960	+	0.280136i	$0.909620\pi$
$500$		0			0
$501$	5107.75	−	8236.00i	0.455484	−	0.734445i
$502$		0			0
$503$	12908.8	+	12908.8i	1.14429	+	1.14429i	0.987657	+	0.156631i	$0.0500633\pi$
$503$	12908.8	+	12908.8i	1.14429	+	1.14429i	0.156631	+	0.987657i	$0.449937\pi$
$504$		0			0
$505$	7300.40	+	7598.50i	0.643294	+	0.669562i
$506$		0			0
$507$	−2590.71	−	11050.9i	−0.226938	−	0.968019i
$508$		0			0
$509$	9172.99			0.798793			0.399396	−	0.916778i	$-0.369220\pi$
$509$	9172.99			0.798793			0.399396	+	0.916778i	$0.369220\pi$
$510$		0			0
$511$	−11370.8			−0.984377
$512$		0			0
$513$	−10231.1	−	12375.3i	−0.880534	−	1.06507i
$514$		0			0
$515$	365.634	−	18274.4i	0.0312850	−	1.56362i
$516$		0			0
$517$	−17992.2	−	17992.2i	−1.53055	−	1.53055i
$518$		0			0
$519$	−2385.02	−	1479.13i	−0.201716	−	0.125099i
$520$		0			0
$521$			7584.85i			0.637809i	0.947787	+	0.318904i	$0.103315\pi$
$521$			7584.85i			0.637809i	−0.947787	+	0.318904i	$0.896685\pi$
$522$		0			0
$523$	−14806.3	+	14806.3i	−1.23792	+	1.23792i	−0.277072	+	0.960849i	$0.589364\pi$
$523$	−14806.3	+	14806.3i	−1.23792	+	1.23792i	−0.960849	+	0.277072i	$0.910636\pi$
$524$		0			0
$525$	8365.53	−	12356.5i	0.695432	−	1.02720i
$526$		0			0
$527$	−4809.99	+	4809.99i	−0.397583	+	0.397583i
$528$		0			0
$529$		−	7978.00i		−	0.655708i
$530$		0			0
$531$	5460.00	−	2708.92i	0.446222	−	0.221388i
$532$		0			0
$533$	−615.806	−	615.806i	−0.0500441	−	0.0500441i
$534$		0			0
$535$	284.524	−	14220.5i	0.0229926	−	1.14917i
$536$		0			0
$537$	17200.8	−	4032.47i	1.38225	−	0.324048i
$538$		0			0
$539$	13116.9			1.04821
$540$		0			0
$541$	9344.00			0.742569			0.371284	−	0.928519i	$-0.378917\pi$
$541$	9344.00			0.742569			0.371284	+	0.928519i	$0.378917\pi$
$542$		0			0
$543$	−8669.09	+	2032.34i	−0.685131	+	0.160619i
$544$		0			0
$545$	10586.4	+	11018.7i	0.832059	+	0.866034i
$546$		0			0
$547$	−7494.24	−	7494.24i	−0.585796	−	0.585796i	0.350694	−	0.936490i	$-0.385946\pi$
$547$	−7494.24	−	7494.24i	−0.585796	−	0.585796i	−0.936490	+	0.350694i	$0.885946\pi$
$548$		0			0
$549$	4445.53	−	2205.60i	0.345593	−	0.171462i
$550$		0			0
$551$			4812.36i			0.372075i
$552$		0			0
$553$	5259.32	−	5259.32i	0.404429	−	0.404429i
$554$		0			0
$555$	3005.85	−	641.527i	0.229894	−	0.0490654i
$556$		0			0
$557$	5195.51	−	5195.51i	0.395226	−	0.395226i	−0.481319	−	0.876545i	$-0.659842\pi$
$557$	5195.51	−	5195.51i	0.395226	−	0.395226i	0.876545	+	0.481319i	$0.159842\pi$
$558$		0			0
$559$			858.747i			0.0649752i
$560$		0			0
$561$	−11001.5	−	6822.84i	−0.827957	−	0.513477i
$562$		0			0
$563$	−6566.25	−	6566.25i	−0.491536	−	0.491536i	0.417254	−	0.908790i	$-0.362992\pi$
$563$	−6566.25	−	6566.25i	−0.491536	−	0.491536i	−0.908790	+	0.417254i	$0.862992\pi$
$564$		0			0
$565$	−22923.1	−	458.646i	−1.70687	−	0.0341512i
$566$		0			0
$567$	−16594.0	+	2265.89i	−1.22907	+	0.167828i
$568$		0			0
$569$	−11468.7			−0.844982			−0.422491	−	0.906367i	$-0.638844\pi$
$569$	−11468.7			−0.844982			−0.422491	+	0.906367i	$0.638844\pi$
$570$		0			0
$571$	21325.8			1.56297			0.781486	−	0.623923i	$-0.214462\pi$
$571$	21325.8			1.56297			0.781486	+	0.623923i	$0.214462\pi$
$572$		0			0
$573$	4138.06	+	17651.2i	0.301693	+	1.28689i
$574$		0			0
$575$	−5944.97	+	5487.31i	−0.431169	+	0.397977i
$576$		0			0
$577$	8094.88	+	8094.88i	0.584046	+	0.584046i	0.936012	−	0.351967i	$-0.114487\pi$
$577$	8094.88	+	8094.88i	0.584046	+	0.584046i	−0.351967	+	0.936012i	$0.614487\pi$
$578$		0			0
$579$	−9971.23	+	16078.1i	−0.715700	+	1.15403i
$580$		0			0
$581$		−	17994.1i		−	1.28489i
$582$		0			0
$583$	15955.6	−	15955.6i	1.13347	−	1.13347i
$584$		0			0
$585$	−456.943	−	969.227i	−0.0322945	−	0.0685001i
$586$		0			0
$587$	−9466.34	+	9466.34i	−0.665618	+	0.665618i	−0.956699	−	0.291081i	$-0.905985\pi$
$587$	−9466.34	+	9466.34i	−0.665618	+	0.665618i	0.291081	+	0.956699i	$0.405985\pi$
$588$		0			0
$589$			22180.4i			1.55166i
$590$		0			0
$591$	6945.37	−	11199.1i	0.483409	−	0.779473i
$592$		0			0
$593$	−5827.84	−	5827.84i	−0.403576	−	0.403576i	0.475915	−	0.879491i	$-0.342117\pi$
$593$	−5827.84	−	5827.84i	−0.403576	−	0.403576i	−0.879491	+	0.475915i	$0.842117\pi$
$594$		0			0
$595$	6501.25	−	6246.20i	0.447942	−	0.430368i
$596$		0			0
$597$	1814.18	+	7738.48i	0.124371	+	0.530511i
$598$		0			0
$599$	23869.0			1.62815			0.814074	−	0.580761i	$-0.197245\pi$
$599$	23869.0			1.62815			0.814074	+	0.580761i	$0.197245\pi$
$600$		0			0
$601$	13301.0			0.902760			0.451380	−	0.892332i	$-0.350932\pi$
$601$	13301.0			0.902760			0.451380	+	0.892332i	$0.350932\pi$
$602$		0			0
$603$	11442.4	+	3853.52i	0.772756	+	0.260244i
$604$		0			0
$605$	−29886.8	+	28714.3i	−2.00838	+	1.92959i
$606$		0			0
$607$	6018.61	+	6018.61i	0.402451	+	0.402451i	0.879096	−	0.476645i	$-0.158147\pi$
$607$	6018.61	+	6018.61i	0.402451	+	0.402451i	−0.476645	+	0.879096i	$0.658147\pi$
$608$		0			0
$609$	4265.74	+	2645.50i	0.283837	+	0.176028i
$610$		0			0
$611$		−	1272.51i		−	0.0842554i
$612$		0			0
$613$	−13054.9	+	13054.9i	−0.860165	+	0.860165i	−0.991357	−	0.131192i	$-0.958120\pi$
$613$	−13054.9	+	13054.9i	−0.860165	+	0.860165i	0.131192	+	0.991357i	$0.458120\pi$
$614$		0			0
$615$	11960.0	+	7752.79i	0.784187	+	0.508330i
$616$		0			0
$617$	−15767.6	+	15767.6i	−1.02882	+	1.02882i	−0.0292434	+	0.999572i	$0.509310\pi$
$617$	−15767.6	+	15767.6i	−1.02882	+	1.02882i	−0.999572	+	0.0292434i	$0.990690\pi$
$618$		0			0
$619$			11641.0i			0.755886i	0.925829	+	0.377943i	$0.123368\pi$
$619$			11641.0i			0.755886i	−0.925829	+	0.377943i	$0.876632\pi$
$620$		0			0
$621$	9039.74	+	857.421i	0.584142	+	0.0554060i
$622$		0			0
$623$	5716.39	+	5716.39i	0.367612	+	0.367612i
$624$		0			0
$625$	−15575.0	−	1249.00i	−0.996800	−	0.0799360i
$626$		0			0
$627$	−41096.9	+	9634.57i	−2.61762	+	0.613664i
$628$		0			0
$629$	1856.98			0.117715
$630$		0			0
$631$	−10510.6			−0.663107			−0.331553	−	0.943436i	$-0.607573\pi$
$631$	−10510.6			−0.663107			−0.331553	+	0.943436i	$0.607573\pi$
$632$		0			0
$633$	2465.75	−	578.061i	0.154826	−	0.0362968i
$634$		0			0
$635$	20838.6	+	416.940i	1.30229	+	0.0260563i
$636$		0			0
$637$	463.849	+	463.849i	0.0288514	+	0.0288514i
$638$		0			0
$639$	2710.78	+	5463.75i	0.167820	+	0.338251i
$640$		0			0
$641$		−	2236.47i		−	0.137808i	−0.997623	−	0.0689042i	$-0.978050\pi$
$641$		−	2236.47i		−	0.137808i	0.997623	−	0.0689042i	$-0.0219503\pi$
$642$		0			0
$643$	−8648.84	+	8648.84i	−0.530446	+	0.530446i	−0.920705	−	0.390259i	$-0.872386\pi$
$643$	−8648.84	+	8648.84i	−0.530446	+	0.530446i	0.390259	+	0.920705i	$0.372386\pi$
$644$		0			0
$645$	−2933.52	−	13744.9i	−0.179081	−	0.839075i
$646$		0			0
$647$	18663.5	−	18663.5i	1.13406	−	1.13406i	0.144563	−	0.989496i	$-0.453822\pi$
$647$	18663.5	−	18663.5i	1.13406	−	1.13406i	0.989496	−	0.144563i	$-0.0461777\pi$
$648$		0			0
$649$		−	16023.0i		−	0.969118i
$650$		0			0
$651$	19661.0	+	12193.2i	1.18368	+	0.734087i
$652$		0			0
$653$	−8326.62	−	8326.62i	−0.498998	−	0.498998i	0.412128	−	0.911126i	$-0.364786\pi$
$653$	−8326.62	−	8326.62i	−0.498998	−	0.498998i	−0.911126	+	0.412128i	$0.864786\pi$
$654$		0			0
$655$	−4149.80	−	4319.25i	−0.247551	−	0.257660i
$656$		0			0
$657$	4265.13	−	12664.6i	0.253270	−	0.752047i
$658$		0			0
$659$	−15781.2			−0.932849			−0.466425	−	0.884561i	$-0.654458\pi$
$659$	−15781.2			−0.932849			−0.466425	+	0.884561i	$0.654458\pi$
$660$		0			0
$661$	32891.0			1.93542			0.967709	−	0.252070i	$-0.0811113\pi$
$661$	32891.0			1.93542			0.967709	+	0.252070i	$0.0811113\pi$
$662$		0			0
$663$	−147.769	−	630.317i	−0.00865590	−	0.0369223i
$664$		0			0
$665$	588.061	−	29391.3i	0.0342918	−	1.71390i
$666$		0			0
$667$	−1924.34	−	1924.34i	−0.111711	−	0.111711i
$668$		0			0
$669$	6882.35	−	11097.5i	0.397738	−	0.641334i
$670$		0			0
$671$		−	13045.9i		−	0.750569i
$672$		0			0
$673$	−3966.52	+	3966.52i	−0.227189	+	0.227189i	−0.811517	−	0.584329i	$-0.801358\pi$
$673$	−3966.52	+	3966.52i	−0.227189	+	0.227189i	0.584329	+	0.811517i	$0.301358\pi$
$674$		0			0
$675$	10624.6	+	13952.2i	0.605839	+	0.795587i
$676$		0			0
$677$	−16422.8	+	16422.8i	−0.932320	+	0.932320i	−0.997851	−	0.0655303i	$-0.979126\pi$
$677$	−16422.8	+	16422.8i	−0.932320	+	0.932320i	0.0655303	+	0.997851i	$0.479126\pi$
$678$		0			0
$679$			3733.75i			0.211028i
$680$		0			0
$681$	−9093.50	+	14662.8i	−0.511694	+	0.825082i
$682$		0			0
$683$	8812.97	+	8812.97i	0.493732	+	0.493732i	0.909480	−	0.415748i	$-0.136480\pi$
$683$	8812.97	+	8812.97i	0.493732	+	0.493732i	−0.415748	+	0.909480i	$0.636480\pi$
$684$		0			0
$685$	599.051	−	29940.5i	0.0334139	−	1.67003i
$686$		0			0
$687$	−4369.61	−	18638.8i	−0.242665	−	1.03510i
$688$		0			0
$689$	1128.47			0.0623966
$690$		0			0
$691$	−157.000			−0.00864334			−0.00432167	−	0.999991i	$-0.501376\pi$
$691$	−157.000			−0.00864334			−0.00432167	+	0.999991i	$0.501376\pi$
$692$		0			0
$693$	−14052.0	+	41725.2i	−0.770260	+	2.28717i
$694$		0			0
$695$	−16032.2	−	16686.9i	−0.875016	−	0.910746i
$696$		0			0
$697$	6089.20	+	6089.20i	0.330911	+	0.330911i
$698$		0			0
$699$	5436.58	+	3371.63i	0.294178	+	0.182441i
$700$		0			0
$701$		−	26772.3i		−	1.44248i	−0.692686	−	0.721239i	$-0.743573\pi$
$701$		−	26772.3i		−	1.44248i	0.692686	−	0.721239i	$-0.256427\pi$
$702$		0			0
$703$	4281.57	−	4281.57i	0.229705	−	0.229705i
$704$		0			0
$705$	4346.93	+	20367.3i	0.232220	+	1.08805i
$706$		0			0
$707$	15310.5	−	15310.5i	0.814445	−	0.814445i
$708$		0			0
$709$			28613.5i			1.51566i	0.652453	+	0.757830i	$0.273740\pi$
$709$			28613.5i			1.51566i	−0.652453	+	0.757830i	$0.726260\pi$
$710$		0			0
$711$	3885.00	+	7830.47i	0.204921	+	0.413032i
$712$		0			0
$713$	−8869.39	−	8869.39i	−0.465865	−	0.465865i
$714$		0			0
$715$	−2816.35	−	56.3495i	−0.147308	−	0.00294735i
$716$		0			0
$717$	9020.80	−	2114.80i	0.469858	−	0.110151i
$718$		0			0
$719$	4772.86			0.247563			0.123781	−	0.992310i	$-0.460498\pi$
$719$	4772.86			0.247563			0.123781	+	0.992310i	$0.460498\pi$
$720$		0			0
$721$	−37558.6			−1.94002
$722$		0			0
$723$	−16711.9	+	3917.86i	−0.859642	+	0.201531i
$724$		0			0
$725$	210.239	−	5251.76i	0.0107697	−	0.269028i
$726$		0			0
$727$	−8584.64	−	8584.64i	−0.437946	−	0.437946i	0.453374	−	0.891320i	$-0.350220\pi$
$727$	−8584.64	−	8584.64i	−0.437946	−	0.437946i	−0.891320	+	0.453374i	$0.850220\pi$
$728$		0			0
$729$	3700.58	−	19332.0i	0.188009	−	0.982167i
$730$		0			0
$731$		−	8491.44i		−	0.429641i
$732$		0			0
$733$	22656.0	−	22656.0i	1.14164	−	1.14164i	0.153485	−	0.988151i	$-0.450950\pi$
$733$	22656.0	−	22656.0i	1.14164	−	1.14164i	0.988151	−	0.153485i	$-0.0490498\pi$
$734$		0			0
$735$	−9008.75	−	5839.70i	−0.452099	−	0.293062i
$736$		0			0
$737$	22443.9	−	22443.9i	1.12175	−	1.12175i
$738$		0			0
$739$		−	12918.7i		−	0.643063i	−0.946899	−	0.321532i	$-0.895802\pi$
$739$		−	12918.7i		−	0.643063i	0.946899	−	0.321532i	$-0.104198\pi$
$740$		0			0
$741$	−1794.00	−	1112.59i	−0.0889396	−	0.0551580i
$742$		0			0
$743$	14755.7	+	14755.7i	0.728581	+	0.728581i	0.970337	−	0.241756i	$-0.0777234\pi$
$743$	14755.7	+	14755.7i	0.728581	+	0.728581i	−0.241756	+	0.970337i	$0.577723\pi$
$744$		0			0
$745$	−16928.0	+	16263.9i	−0.832475	+	0.799816i
$746$		0			0
$747$	20041.6	+	6749.48i	0.981636	+	0.330590i
$748$		0			0
$749$	−29226.9			−1.42580
$750$		0			0
$751$	−30369.0			−1.47561			−0.737803	−	0.675016i	$-0.764137\pi$
$751$	−30369.0			−1.47561			−0.737803	+	0.675016i	$0.764137\pi$
$752$		0			0
$753$	−1718.75	−	7331.45i	−0.0831803	−	0.354811i
$754$		0			0
$755$	−5367.85	+	5157.26i	−0.258750	+	0.248599i
$756$		0			0
$757$	8724.03	+	8724.03i	0.418864	+	0.418864i	0.884812	−	0.465948i	$-0.154287\pi$
$757$	8724.03	+	8724.03i	0.418864	+	0.418864i	−0.465948	+	0.884812i	$0.654287\pi$
$758$		0			0
$759$	12581.0	−	20286.2i	0.601662	−	0.970150i
$760$		0			0
$761$		−	739.375i		−	0.0352199i	−0.999845	−	0.0176099i	$-0.994394\pi$
$761$		−	739.375i		−	0.0352199i	0.999845	−	0.0176099i	$-0.00560570\pi$
$762$		0			0
$763$	22202.0	−	22202.0i	1.05343	−	1.05343i
$764$		0			0
$765$	4518.33	+	9583.88i	0.213543	+	0.452949i
$766$		0			0
$767$	566.616	−	566.616i	0.0266745	−	0.0266745i
$768$		0			0
$769$			15935.6i			0.747272i	0.927575	+	0.373636i	$0.121889\pi$
$769$			15935.6i			0.747272i	−0.927575	+	0.373636i	$0.878111\pi$
$770$		0			0
$771$	5927.13	−	9557.20i	0.276861	−	0.446426i
$772$		0			0
$773$	7830.30	+	7830.30i	0.364342	+	0.364342i	0.865409	−	0.501067i	$-0.167059\pi$
$773$	7830.30	+	7830.30i	0.364342	+	0.364342i	−0.501067	+	0.865409i	$0.667059\pi$
$774$		0			0
$775$	969.000	−	24205.6i	0.0449129	−	1.12192i
$776$		0			0
$777$	−1441.53	−	6148.95i	−0.0665569	−	0.283903i
$778$		0			0
$779$	28079.2			1.29145
$780$		0			0
$781$	16034.0			0.734624
$782$		0			0
$783$	−4546.56	+	3758.80i	−0.207511	+	0.171556i
$784$		0			0
$785$	14820.7	+	296.532i	0.673851	+	0.0134824i
$786$		0			0
$787$	17343.4	+	17343.4i	0.785547	+	0.785547i	0.980761	−	0.195214i	$-0.0625401\pi$
$787$	17343.4	+	17343.4i	0.785547	+	0.785547i	−0.195214	+	0.980761i	$0.562540\pi$
$788$		0			0
$789$	−31261.8	−	19387.7i	−1.41058	−	0.874806i
$790$		0			0
$791$			47113.0i			2.11776i
$792$		0			0
$793$	461.339	−	461.339i	0.0206590	−	0.0206590i
$794$		0			0
$795$	−18062.0	+	3854.90i	−0.805775	+	0.171974i
$796$		0			0
$797$	−4065.57	+	4065.57i	−0.180690	+	0.180690i	−0.791656	−	0.610967i	$-0.790781\pi$
$797$	−4065.57	+	4065.57i	−0.180690	+	0.180690i	0.610967	+	0.791656i	$0.290781\pi$
$798$		0			0
$799$			12582.8i			0.557129i
$800$		0			0
$801$	−8511.00	+	4222.64i	−0.375432	+	0.186267i
$802$		0			0
$803$	−24841.2	−	24841.2i	−1.09169	−	1.09169i
$804$		0			0
$805$	11517.7	+	11988.0i	0.504280	+	0.524871i
$806$		0			0
$807$	−9812.69	+	2300.44i	−0.428034	+	0.100346i
$808$		0			0
$809$	−7547.89			−0.328022			−0.164011	−	0.986459i	$-0.552443\pi$
$809$	−7547.89			−0.328022			−0.164011	+	0.986459i	$0.552443\pi$
$810$		0			0
$811$	−17579.0			−0.761137			−0.380568	−	0.924753i	$-0.624272\pi$
$811$	−17579.0			−0.761137			−0.380568	+	0.924753i	$0.624272\pi$
$812$		0			0
$813$	−4750.39	+	1113.66i	−0.204924	+	0.0480415i
$814$		0			0
$815$	−160.095	+	8001.57i	−0.00688086	+	0.343905i
$816$		0			0
$817$	−19578.4	−	19578.4i	−0.838385	−	0.838385i
$818$		0			0
$819$	−1972.43	+	978.600i	−0.0841543	+	0.0417522i
$820$		0			0
$821$			42229.0i			1.79513i	0.440880	+	0.897566i	$0.354667\pi$
$821$			42229.0i			1.79513i	−0.440880	+	0.897566i	$0.645333\pi$
$822$		0			0
$823$	1972.69	−	1972.69i	0.0835523	−	0.0835523i	−0.664095	−	0.747648i	$-0.731183\pi$
$823$	1972.69	−	1972.69i	0.0835523	−	0.0835523i	0.747648	+	0.664095i	$0.231183\pi$
$824$		0			0
$825$	45270.2	−	8718.85i	1.91043	−	0.367941i
$826$		0			0
$827$	−24544.6	+	24544.6i	−1.03204	+	1.03204i	−0.0325753	+	0.999469i	$0.510371\pi$
$827$	−24544.6	+	24544.6i	−1.03204	+	1.03204i	−0.999469	+	0.0325753i	$0.989629\pi$
$828$		0			0
$829$			26627.5i			1.11557i	0.829984	+	0.557787i	$0.188349\pi$
$829$			26627.5i			1.11557i	−0.829984	+	0.557787i	$0.811651\pi$
$830$		0			0
$831$	28074.8	+	17411.3i	1.17197	+	0.726823i
$832$		0			0
$833$	−4586.61	−	4586.61i	−0.190776	−	0.190776i
$834$		0			0
$835$	−417.129	+	20848.1i	−0.0172879	+	0.864047i
$836$		0			0
$837$	−20955.3	+	17324.5i	−0.865378	+	0.715438i
$838$		0			0
$839$	−27271.0			−1.12217			−0.561085	−	0.827758i	$-0.689616\pi$
$839$	−27271.0			−1.12217			−0.561085	+	0.827758i	$0.689616\pi$
$840$		0			0
$841$	−22621.0			−0.927508
$842$		0			0
$843$	−416.897	−	1778.30i	−0.0170329	−	0.0726548i
$844$		0			0
$845$	16920.3	+	17611.2i	0.688847	+	0.716975i
$846$		0			0
$847$	60220.2	+	60220.2i	2.44296	+	2.44296i
$848$		0			0
$849$	3994.85	−	6441.50i	0.161487	−	0.260391i
$850$		0			0
$851$			3424.19i			0.137931i
$852$		0			0
$853$	13559.8	−	13559.8i	0.544290	−	0.544290i	−0.380494	−	0.924783i	$-0.624246\pi$
$853$	13559.8	−	13559.8i	0.544290	−	0.544290i	0.924783	+	0.380494i	$0.124246\pi$
$854$		0			0
$855$	32514.9	+	11679.4i	1.30057	+	0.467168i
$856$		0			0
$857$	−14012.4	+	14012.4i	−0.558521	+	0.558521i	−0.928886	−	0.370365i	$-0.879233\pi$
$857$	−14012.4	+	14012.4i	−0.558521	+	0.558521i	0.370365	+	0.928886i	$0.379233\pi$
$858$		0			0
$859$		−	30507.7i		−	1.21177i	−0.795552	−	0.605885i	$-0.792819\pi$
$859$		−	30507.7i		−	1.21177i	0.795552	−	0.605885i	$-0.207181\pi$
$860$		0			0
$861$	15436.0	−	24889.8i	0.610984	−	0.985182i
$862$		0			0
$863$	−12023.0	−	12023.0i	−0.474237	−	0.474237i	0.429046	−	0.903283i	$-0.358850\pi$
$863$	−12023.0	−	12023.0i	−0.474237	−	0.474237i	−0.903283	+	0.429046i	$0.858850\pi$
$864$		0			0
$865$	6037.30	+	120.794i	0.237311	+	0.00474813i
$866$		0			0
$867$	−4365.69	−	18622.1i	−0.171011	−	0.729459i
$868$		0			0
$869$	22979.4			0.897035
$870$		0			0
$871$	1587.35			0.0617513
$872$		0			0
$873$	−4158.58	−	1400.50i	−0.161222	−	0.0542954i
$874$		0			0
$875$	−1925.78	+	32049.2i	−0.0744036	+	1.23824i
$876$		0			0
$877$	−31093.1	−	31093.1i	−1.19719	−	1.19719i	−0.975004	−	0.222189i	$-0.928680\pi$
$877$	−31093.1	−	31093.1i	−1.19719	−	1.19719i	−0.222189	−	0.975004i	$-0.571320\pi$
$878$		0			0
$879$	−31447.0	−	19502.6i	−1.20669	−	0.748358i
$880$		0			0
$881$		−	2943.72i		−	0.112573i	−0.998415	−	0.0562863i	$-0.982074\pi$
$881$		−	2943.72i		−	0.112573i	0.998415	−	0.0562863i	$-0.0179260\pi$
$882$		0			0
$883$	13065.6	−	13065.6i	0.497954	−	0.497954i	−0.412847	−	0.910801i	$-0.635465\pi$
$883$	13065.6	−	13065.6i	0.497954	−	0.497954i	0.910801	+	0.412847i	$0.135465\pi$
$884$		0			0
$885$	−7133.51	+	11004.7i	−0.270950	+	0.417987i
$886$		0			0
$887$	17997.6	−	17997.6i	0.681284	−	0.681284i	−0.279006	−	0.960289i	$-0.590005\pi$
$887$	17997.6	−	17997.6i	0.681284	−	0.681284i	0.960289	+	0.279006i	$0.0900048\pi$
$888$		0			0
$889$		−	42828.8i		−	1.61578i
$890$		0			0
$891$	−41202.0	−	31301.7i	−1.54918	−	1.17693i
$892$		0			0
$893$	29011.5	+	29011.5i	1.08716	+	1.08716i
$894$		0			0
$895$	−27412.0	+	26336.6i	−1.02378	+	0.983615i
$896$		0			0
$897$	1162.27	−	272.478i	0.0432633	−	0.0101425i
$898$		0			0
$899$	8148.85			0.302313
$900$		0			0
$901$	−11158.5			−0.412590
$902$		0			0
$903$	−28117.4	+	6591.71i	−1.03620	+	0.242922i
$904$		0			0
$905$	13815.5	−	13273.5i	0.507450	−	0.487542i
$906$		0			0
$907$	−7878.94	−	7878.94i	−0.288441	−	0.288441i	0.548023	−	0.836464i	$-0.315381\pi$
$907$	−7878.94	−	7878.94i	−0.288441	−	0.288441i	−0.836464	+	0.548023i	$0.815381\pi$
$908$		0			0
$909$	11309.7	+	22795.5i	0.412673	+	0.831770i
$910$		0			0
$911$		−	29902.5i		−	1.08750i	−0.839247	−	0.543751i	$-0.817004\pi$
$911$		−	29902.5i		−	1.08750i	0.839247	−	0.543751i	$-0.182996\pi$
$912$		0			0
$913$	39310.7	−	39310.7i	1.42497	−	1.42497i
$914$		0			0
$915$	−5808.10	+	8960.00i	−0.209847	+	0.323725i
$916$		0			0
$917$	−8703.04	+	8703.04i	−0.313413	+	0.313413i
$918$		0			0
$919$			11226.3i			0.402963i	0.979492	+	0.201482i	$0.0645756\pi$
$919$			11226.3i			0.402963i	−0.979492	+	0.201482i	$0.935424\pi$
$920$		0			0
$921$	−25455.9	−	15787.1i	−0.910749	−	0.564823i
$922$		0			0
$923$	567.005	+	567.005i	0.0202202	+	0.0202202i
$924$		0			0
$925$	−4859.55	+	4485.45i	−0.172736	+	0.159439i
$926$		0			0
$927$	14088.0	−	41832.1i	0.499147	−	1.48214i
$928$		0			0
$929$	34890.0			1.23219			0.616094	−	0.787672i	$-0.288714\pi$
$929$	34890.0			1.23219			0.616094	+	0.787672i	$0.288714\pi$
$930$		0			0
$931$	−21150.3			−0.744548
$932$		0			0
$933$	−8344.93	−	35595.8i	−0.292819	−	1.24904i
$934$		0			0
$935$	27848.6	+	557.194i	0.974059	+	0.0194890i
$936$		0			0
$937$	26125.6	+	26125.6i	0.910870	+	0.910870i	0.996341	−	0.0854704i	$-0.0272393\pi$
$937$	26125.6	+	26125.6i	0.910870	+	0.910870i	−0.0854704	+	0.996341i	$0.527239\pi$
$938$		0			0
$939$	3217.44	−	5187.97i	0.111818	−	0.180301i
$940$		0			0
$941$			38049.6i			1.31815i	0.752077	+	0.659076i	$0.229052\pi$
$941$			38049.6i			1.31815i	−0.752077	+	0.659076i	$0.770948\pi$
$942$		0			0
$943$	−11228.2	+	11228.2i	−0.387741	+	0.387741i
$944$		0			0
$945$	28227.2	−	22401.1i	0.971674	−	0.771119i
$946$		0			0
$947$	1231.74	−	1231.74i	0.0422663	−	0.0422663i	−0.685658	−	0.727924i	$-0.740485\pi$
$947$	1231.74	−	1231.74i	0.0422663	−	0.0422663i	0.727924	+	0.685658i	$0.240485\pi$
$948$		0			0
$949$		−	1756.90i		−	0.0600964i
$950$		0			0
$951$	−7936.12	+	12796.6i	−0.270606	+	0.436339i
$952$		0			0
$953$	−5889.16	−	5889.16i	−0.200177	−	0.200177i	0.599899	−	0.800076i	$-0.295207\pi$
$953$	−5889.16	−	5889.16i	−0.200177	−	0.200177i	−0.800076	+	0.599899i	$0.795207\pi$
$954$		0			0
$955$	−27026.2	−	28129.8i	−0.915756	−	0.953149i
$956$		0			0
$957$	3539.64	+	15098.6i	0.119561	+	0.509997i
$958$		0			0
$959$	−61535.6			−2.07204
$960$		0			0
$961$	7767.41			0.260730
$962$		0			0
$963$	10962.8	−	32552.3i	0.366844	−	1.08929i
$964$		0			0
$965$	814.310	−	40699.2i	0.0271643	−	1.35767i
$966$		0			0
$967$	−15844.1	−	15844.1i	−0.526899	−	0.526899i	0.392747	−	0.919646i	$-0.371525\pi$
$967$	−15844.1	−	15844.1i	−0.526899	−	0.526899i	−0.919646	+	0.392747i	$0.871525\pi$
$968$		0			0
$969$	17739.4	+	11001.5i	0.588102	+	0.364726i
$970$		0			0
$971$		−	6706.59i		−	0.221653i	−0.993840	−	0.110826i	$-0.964650\pi$
$971$		−	6706.59i		−	0.221653i	0.993840	−	0.110826i	$-0.0353497\pi$
$972$		0			0
$973$	−33623.1	+	33623.1i	−1.10782	+	1.10782i
$974$		0			0
$975$	1909.20	+	1292.55i	0.0627110	+	0.0424562i
$976$		0			0
$977$	40695.5	−	40695.5i	1.33261	−	1.33261i	0.429588	−	0.903025i	$-0.358659\pi$
$977$	40695.5	−	40695.5i	1.33261	−	1.33261i	0.903025	−	0.429588i	$-0.141341\pi$
$978$		0			0
$979$			24976.5i			0.815375i
$980$		0			0
$981$	16400.4	+	33056.1i	0.533766	+	1.07584i
$982$		0			0
$983$	−35928.4	−	35928.4i	−1.16576	−	1.16576i	−0.983194	−	0.182563i	$-0.941561\pi$
$983$	−35928.4	−	35928.4i	−1.16576	−	1.16576i	−0.182563	−	0.983194i	$-0.558439\pi$
$984$		0			0
$985$	−567.201	+	28348.7i	−0.0183477	+	0.917020i
$986$		0			0
$987$	41664.7	−	9767.70i	1.34367	−	0.315004i
$988$		0			0
$989$	15657.8			0.503427
$990$		0			0
$991$	14290.6			0.458078			0.229039	−	0.973417i	$-0.426442\pi$
$991$	14290.6			0.458078			0.229039	+	0.973417i	$0.426442\pi$
$992$		0			0
$993$	−1836.42	+	430.521i	−0.0586877	+	0.0137585i
$994$		0			0
$995$	−11848.6	−	12332.4i	−0.377514	−	0.392929i
$996$		0			0
$997$	16298.4	+	16298.4i	0.517728	+	0.517728i	0.916883	−	0.399155i	$-0.130697\pi$
$997$	16298.4	+	16298.4i	0.517728	+	0.517728i	−0.399155	+	0.916883i	$0.630697\pi$
$998$		0			0
$999$	7389.30	+	700.875i	0.234021	+	0.0221969i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.4.i.b.17.1	✓	8
3.2	odd	2	inner	60.4.i.b.17.2	yes	8
4.3	odd	2		240.4.v.b.17.4		8
5.2	odd	4		300.4.i.f.293.3		8
5.3	odd	4	inner	60.4.i.b.53.2	yes	8
5.4	even	2		300.4.i.f.257.4		8
12.11	even	2		240.4.v.b.17.3		8
15.2	even	4		300.4.i.f.293.4		8
15.8	even	4	inner	60.4.i.b.53.1	yes	8
15.14	odd	2		300.4.i.f.257.3		8
20.3	even	4		240.4.v.b.113.3		8
60.23	odd	4		240.4.v.b.113.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.4.i.b.17.1	✓	8	1.1	even	1	trivial
60.4.i.b.17.2	yes	8	3.2	odd	2	inner
60.4.i.b.53.1	yes	8	15.8	even	4	inner
60.4.i.b.53.2	yes	8	5.3	odd	4	inner
240.4.v.b.17.3		8	12.11	even	2
240.4.v.b.17.4		8	4.3	odd	2
240.4.v.b.113.3		8	20.3	even	4
240.4.v.b.113.4		8	60.23	odd	4
300.4.i.f.257.3		8	15.14	odd	2
300.4.i.f.257.4		8	5.4	even	2
300.4.i.f.293.3		8	5.2	odd	4
300.4.i.f.293.4		8	15.2	even	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)

\(f(q)\)	\(=\)	\(q+(-5.05899 + 1.18601i) q^{3} +(8.06226 - 7.74597i) q^{5} +(-16.2450 - 16.2450i) q^{7} +(24.1868 - 12.0000i) q^{9} +O(q^{10})\)	\(q+(-5.05899 + 1.18601i) q^{3} +(8.06226 - 7.74597i) q^{5} +(-16.2450 - 16.2450i) q^{7} +(24.1868 - 12.0000i) q^{9} -70.9789i q^{11} +(2.51000 - 2.51000i) q^{13} +(-31.6001 + 48.7487i) q^{15} +(-24.8194 + 24.8194i) q^{17} +114.450i q^{19} +(101.450 + 62.9166i) q^{21} +(-45.7657 - 45.7657i) q^{23} +(5.00000 - 124.900i) q^{25} +(-108.129 + 89.3936i) q^{27} +42.0477 q^{29} +193.800 q^{31} +(84.1815 + 359.081i) q^{33} +(-256.805 - 5.13815i) q^{35} +(-37.4100 - 37.4100i) q^{37} +(-9.72120 + 15.6750i) q^{39} -245.341i q^{41} +(-171.065 + 171.065i) q^{43} +(102.048 - 284.097i) q^{45} +(253.487 - 253.487i) q^{47} +184.800i q^{49} +(96.1249 - 154.997i) q^{51} +(224.794 + 224.794i) q^{53} +(-549.800 - 572.250i) q^{55} +(-135.739 - 579.001i) q^{57} +225.743 q^{59} +183.800 q^{61} +(-587.854 - 197.974i) q^{63} +(0.793892 - 39.6787i) q^{65} +(316.205 + 316.205i) q^{67} +(285.807 + 177.250i) q^{69} +225.898i q^{71} +(349.980 - 349.980i) q^{73} +(122.837 + 637.798i) q^{75} +(-1153.05 + 1153.05i) q^{77} +323.750i q^{79} +(441.000 - 580.483i) q^{81} +(553.837 + 553.837i) q^{83} +(-7.85014 + 392.350i) q^{85} +(-212.719 + 49.8689i) q^{87} -351.886 q^{89} -81.5500 q^{91} +(-980.432 + 229.848i) q^{93} +(886.526 + 922.725i) q^{95} +(-114.920 - 114.920i) q^{97} +(-851.746 - 1716.75i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 80 q^{7}+O(q^{10}) \) 8 * q - 80 * q^7	\( 8 q - 80 q^{7} + 120 q^{13} - 120 q^{15} + 312 q^{21} + 40 q^{25} - 448 q^{31} - 600 q^{33} + 600 q^{37} + 480 q^{43} + 1560 q^{45} - 480 q^{51} - 2400 q^{55} - 1560 q^{57} - 528 q^{61} - 960 q^{63} + 2080 q^{67} + 2600 q^{73} + 3120 q^{75} + 3528 q^{81} - 3560 q^{85} - 2400 q^{87} - 1152 q^{91} - 6240 q^{93} - 120 q^{97}+O(q^{100}) \) 8 * q - 80 * q^7 + 120 * q^13 - 120 * q^15 + 312 * q^21 + 40 * q^25 - 448 * q^31 - 600 * q^33 + 600 * q^37 + 480 * q^43 + 1560 * q^45 - 480 * q^51 - 2400 * q^55 - 1560 * q^57 - 528 * q^61 - 960 * q^63 + 2080 * q^67 + 2600 * q^73 + 3120 * q^75 + 3528 * q^81 - 3560 * q^85 - 2400 * q^87 - 1152 * q^91 - 6240 * q^93 - 120 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more