LMFDB - Embedded newform 180.4.i.c.61.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,4,Mod(61,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("180.61");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	180.i (of order $3$, 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:	$10.6203438010$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 7 x^{13} + 180 x^{12} - 989 x^{11} + 11627 x^{10} - 49236 x^{9} + 328637 x^{8} - 1029725 x^{7} + \cdots + 1484973 $ x^14 - 7x^13 + 180x^12 - 989x^11 + 11627x^10 - 49236x^9 + 328637x^8 - 1029725x^7 + 3973395x^6 - 8512360x^5 + 18130585x^4 - 23182065x^3 + 18357462x^2 - 8027505*x + 1484973
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			61.5
Root			$0.500000 - 0.166136i$ of defining polynomial
Character	$\chi$	$=$	180.61
Dual form			180.4.i.c.121.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.39211 - 4.61279i) q^{3} +(-2.50000 - 4.33013i) q^{5} +(-12.3017 + 21.3072i) q^{7} +(-15.5556 - 22.0686i) q^{9} +(31.3139 - 54.2372i) q^{11} +(-29.8261 - 51.6603i) q^{13} +(-25.9542 + 1.17384i) q^{15} -85.2021 q^{17} -75.1746 q^{19} +(68.8587 + 107.715i) q^{21} +(48.7776 + 84.4852i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(-139.008 + 18.9645i) q^{27} +(-79.6256 + 137.915i) q^{29} +(-159.255 - 275.838i) q^{31} +(-175.279 - 274.185i) q^{33} +123.017 q^{35} +393.612 q^{37} +(-309.646 + 14.0045i) q^{39} +(-42.5407 - 73.6826i) q^{41} +(20.3818 - 35.3023i) q^{43} +(-56.6706 + 122.529i) q^{45} +(45.1454 - 78.1941i) q^{47} +(-131.166 - 227.185i) q^{49} +(-203.812 + 393.019i) q^{51} +691.499 q^{53} -313.139 q^{55} +(-179.826 + 346.765i) q^{57} +(-141.759 - 245.534i) q^{59} +(216.078 - 374.258i) q^{61} +(661.582 - 59.9660i) q^{63} +(-149.131 + 258.302i) q^{65} +(-154.180 - 267.048i) q^{67} +(506.394 - 22.9029i) q^{69} +302.675 q^{71} -457.563 q^{73} +(69.9685 + 109.451i) q^{75} +(770.430 + 1334.42i) q^{77} +(420.848 - 728.929i) q^{79} +(-245.044 + 686.582i) q^{81} +(394.090 - 682.584i) q^{83} +(213.005 + 368.936i) q^{85} +(445.702 + 697.205i) q^{87} +1119.35 q^{89} +1467.65 q^{91} +(-1653.34 + 74.7763i) q^{93} +(187.937 + 325.516i) q^{95} +(-598.850 + 1037.24i) q^{97} +(-1684.04 + 152.642i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 5 q^{3} - 35 q^{5} - 8 q^{7} + 5 q^{9} - 27 q^{11} - 32 q^{13} - 20 q^{15} + 246 q^{17} - 134 q^{19} + 28 q^{21} - 42 q^{23} - 175 q^{25} - 484 q^{27} - 324 q^{29} - 98 q^{31} + 657 q^{33} + 80 q^{35}+ \cdots + 270 q^{99}+O(q^{100}) $ 14 * q + 5 * q^3 - 35 * q^5 - 8 * q^7 + 5 * q^9 - 27 * q^11 - 32 * q^13 - 20 * q^15 + 246 * q^17 - 134 * q^19 + 28 * q^21 - 42 * q^23 - 175 * q^25 - 484 * q^27 - 324 * q^29 - 98 * q^31 + 657 * q^33 + 80 * q^35 + 712 * q^37 - 848 * q^39 - 339 * q^41 - 119 * q^43 - 125 * q^45 + 96 * q^47 - 813 * q^49 + 1383 * q^51 + 1716 * q^53 + 270 * q^55 - 599 * q^57 - 549 * q^59 - 260 * q^61 - 632 * q^63 - 160 * q^65 - 881 * q^67 + 666 * q^69 + 684 * q^71 + 1474 * q^73 - 25 * q^75 + 456 * q^77 - 1886 * q^79 + 353 * q^81 + 132 * q^83 - 615 * q^85 + 4302 * q^87 + 792 * q^89 + 2528 * q^91 - 4904 * q^93 + 335 * q^95 - 1991 * q^97 + 270 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	2.39211	−	4.61279i	0.460361	−	0.887732i
$3$	2.39211	−	4.61279i	0.460361	−	0.887732i
$4$		0			0
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$		0			0
$7$	−12.3017	+	21.3072i	−0.664232	+	1.15048i	0.315262	+	0.949005i	$0.397908\pi$
$7$	−12.3017	+	21.3072i	−0.664232	+	1.15048i	−0.979493	+	0.201478i	$0.935426\pi$
$8$		0			0
$9$	−15.5556	−	22.0686i	−0.576135	−	0.817355i
$10$		0			0
$11$	31.3139	−	54.2372i	0.858316	−	1.48665i	−0.0152173	−	0.999884i	$-0.504844\pi$
$11$	31.3139	−	54.2372i	0.858316	−	1.48665i	0.873534	−	0.486764i	$-0.161823\pi$
$12$		0			0
$13$	−29.8261	−	51.6603i	−0.636329	−	1.10215i	−0.986232	−	0.165368i	$-0.947119\pi$
$13$	−29.8261	−	51.6603i	−0.636329	−	1.10215i	0.349903	−	0.936786i	$-0.386215\pi$
$14$		0			0
$15$	−25.9542	+	1.17384i	−0.446757	+	0.0202057i
$16$		0			0
$17$	−85.2021			−1.21556			−0.607780	−	0.794105i	$-0.707940\pi$
$17$	−85.2021			−1.21556			−0.607780	+	0.794105i	$0.707940\pi$
$18$		0			0
$19$	−75.1746			−0.907697			−0.453849	−	0.891079i	$-0.649949\pi$
$19$	−75.1746			−0.907697			−0.453849	+	0.891079i	$0.649949\pi$
$20$		0			0
$21$	68.8587	+	107.715i	0.715533	+	1.11930i
$22$		0			0
$23$	48.7776	+	84.4852i	0.442210	+	0.765930i	0.997853	−	0.0654909i	$-0.0208613\pi$
$23$	48.7776	+	84.4852i	0.442210	+	0.765930i	−0.555643	+	0.831421i	$0.687528\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$		0			0
$27$	−139.008	+	18.9645i	−0.990822	+	0.135175i
$28$		0			0
$29$	−79.6256	+	137.915i	−0.509865	+	0.883113i	0.490069	+	0.871683i	$0.336971\pi$
$29$	−79.6256	+	137.915i	−0.509865	+	0.883113i	−0.999935	+	0.0114292i	$0.996362\pi$
$30$		0			0
$31$	−159.255	−	275.838i	−0.922680	−	1.59813i	−0.795251	−	0.606280i	$-0.792661\pi$
$31$	−159.255	−	275.838i	−0.922680	−	1.59813i	−0.127428	−	0.991848i	$-0.540672\pi$
$32$		0			0
$33$	−175.279	−	274.185i	−0.924609	−	1.44635i
$34$		0			0
$35$	123.017			0.594107
$36$		0			0
$37$	393.612			1.74890			0.874451	−	0.485114i	$-0.161222\pi$
$37$	393.612			1.74890			0.874451	+	0.485114i	$0.161222\pi$
$38$		0			0
$39$	−309.646	+	14.0045i	−1.27136	+	0.0575003i
$40$		0			0
$41$	−42.5407	−	73.6826i	−0.162042	−	0.280666i	0.773559	−	0.633725i	$-0.218475\pi$
$41$	−42.5407	−	73.6826i	−0.162042	−	0.280666i	−0.935601	+	0.353059i	$0.885141\pi$
$42$		0			0
$43$	20.3818	−	35.3023i	0.0722835	−	0.125199i	−0.827618	−	0.561291i	$-0.810305\pi$
$43$	20.3818	−	35.3023i	0.0722835	−	0.125199i	0.899902	+	0.436093i	$0.143638\pi$
$44$		0			0
$45$	−56.6706	+	122.529i	−0.187732	+	0.405902i
$46$		0			0
$47$	45.1454	−	78.1941i	0.140109	−	0.242676i	−0.787428	−	0.616406i	$-0.788588\pi$
$47$	45.1454	−	78.1941i	0.140109	−	0.242676i	0.927538	+	0.373730i	$0.121921\pi$
$48$		0			0
$49$	−131.166	−	227.185i	−0.382407	−	0.662348i
$50$		0			0
$51$	−203.812	+	393.019i	−0.559597	+	1.07909i
$52$		0			0
$53$	691.499			1.79216			0.896081	−	0.443890i	$-0.146402\pi$
$53$	691.499			1.79216			0.896081	+	0.443890i	$0.146402\pi$
$54$		0			0
$55$	−313.139			−0.767702
$56$		0			0
$57$	−179.826	+	346.765i	−0.417869	+	0.805791i
$58$		0			0
$59$	−141.759	−	245.534i	−0.312805	−	0.541794i	0.666164	−	0.745806i	$-0.267935\pi$
$59$	−141.759	−	245.534i	−0.312805	−	0.541794i	−0.978968	+	0.204012i	$0.934602\pi$
$60$		0			0
$61$	216.078	−	374.258i	0.453540	−	0.785555i	−0.545063	−	0.838395i	$-0.683494\pi$
$61$	216.078	−	374.258i	0.453540	−	0.785555i	0.998603	+	0.0528404i	$0.0168275\pi$
$62$		0			0
$63$	661.582	−	59.9660i	1.32304	−	0.119921i
$64$		0			0
$65$	−149.131	+	258.302i	−0.284575	+	0.492898i
$66$		0			0
$67$	−154.180	−	267.048i	−0.281136	−	0.486942i	0.690529	−	0.723305i	$-0.257378\pi$
$67$	−154.180	−	267.048i	−0.281136	−	0.486942i	−0.971665	+	0.236363i	$0.924045\pi$
$68$		0			0
$69$	506.394	−	22.9029i	0.883517	−	0.0399592i
$70$		0			0
$71$	302.675			0.505928			0.252964	−	0.967476i	$-0.418595\pi$
$71$	302.675			0.505928			0.252964	+	0.967476i	$0.418595\pi$
$72$		0			0
$73$	−457.563			−0.733613			−0.366806	−	0.930297i	$-0.619549\pi$
$73$	−457.563			−0.733613			−0.366806	+	0.930297i	$0.619549\pi$
$74$		0			0
$75$	69.9685	+	109.451i	0.107724	+	0.168510i
$76$		0			0
$77$	770.430	+	1334.42i	1.14024	+	1.97496i
$78$		0			0
$79$	420.848	−	728.929i	0.599355	−	1.03811i	−0.393561	−	0.919298i	$-0.628757\pi$
$79$	420.848	−	728.929i	0.599355	−	1.03811i	0.992916	−	0.118815i	$-0.0379096\pi$
$80$		0			0
$81$	−245.044	+	686.582i	−0.336137	+	0.941813i
$82$		0			0
$83$	394.090	−	682.584i	0.521169	−	0.902691i	−0.478528	−	0.878072i	$-0.658830\pi$
$83$	394.090	−	682.584i	0.521169	−	0.902691i	0.999697	−	0.0246184i	$-0.00783707\pi$
$84$		0			0
$85$	213.005	+	368.936i	0.271808	+	0.470785i
$86$		0			0
$87$	445.702	+	697.205i	0.549245	+	0.859174i
$88$		0			0
$89$	1119.35			1.33316			0.666578	−	0.745436i	$-0.267759\pi$
$89$	1119.35			1.33316			0.666578	+	0.745436i	$0.267759\pi$
$90$		0			0
$91$	1467.65			1.69068
$92$		0			0
$93$	−1653.34	+	74.7763i	−1.84347	+	0.0833757i
$94$		0			0
$95$	187.937	+	325.516i	0.202967	+	0.351550i
$96$		0			0
$97$	−598.850	+	1037.24i	−0.626846	+	1.08573i	0.361335	+	0.932436i	$0.382321\pi$
$97$	−598.850	+	1037.24i	−0.626846	+	1.08573i	−0.988181	+	0.153292i	$0.951012\pi$
$98$		0			0
$99$	−1684.04	+	152.642i	−1.70962	+	0.154961i
$100$		0			0
$101$	−708.679	+	1227.47i	−0.698180	+	1.20928i	0.270917	+	0.962603i	$0.412673\pi$
$101$	−708.679	+	1227.47i	−0.698180	+	1.20928i	−0.969097	+	0.246680i	$0.920660\pi$
$102$		0			0
$103$	−207.647	−	359.655i	−0.198641	−	0.344057i	0.749447	−	0.662065i	$-0.230320\pi$
$103$	−207.647	−	359.655i	−0.198641	−	0.344057i	−0.948088	+	0.318008i	$0.896986\pi$
$104$		0			0
$105$	294.271	−	567.453i	0.273504	−	0.527407i
$106$		0			0
$107$	766.240			0.692292			0.346146	−	0.938181i	$-0.387490\pi$
$107$	766.240			0.692292			0.346146	+	0.938181i	$0.387490\pi$
$108$		0			0
$109$	349.214			0.306868			0.153434	−	0.988159i	$-0.450967\pi$
$109$	349.214			0.306868			0.153434	+	0.988159i	$0.450967\pi$
$110$		0			0
$111$	941.562	−	1815.65i	0.805127	−	1.55256i
$112$		0			0
$113$	559.969	+	969.896i	0.466173	+	0.807435i	0.999254	−	0.0386296i	$-0.0122993\pi$
$113$	559.969	+	969.896i	0.466173	+	0.807435i	−0.533081	+	0.846064i	$0.678966\pi$
$114$		0			0
$115$	243.888	−	422.426i	0.197762	−	0.342534i
$116$		0			0
$117$	−676.106	+	1461.83i	−0.534239	+	1.15510i
$118$		0			0
$119$	1048.13	−	1815.42i	0.807414	−	1.39848i
$120$		0			0
$121$	−1295.61	−	2244.07i	−0.973414	−	1.68600i
$122$		0			0
$123$	−441.644	+	19.9744i	−0.323754	+	0.0146426i
$124$		0			0
$125$	125.000			0.0894427
$126$		0			0
$127$	−871.649			−0.609027			−0.304513	−	0.952508i	$-0.598494\pi$
$127$	−871.649			−0.609027			−0.304513	+	0.952508i	$0.598494\pi$
$128$		0			0
$129$	−114.086	−	178.464i	−0.0778663	−	0.121805i
$130$		0			0
$131$	60.4825	+	104.759i	0.0403388	+	0.0698688i	0.885490	−	0.464659i	$-0.153823\pi$
$131$	60.4825	+	104.759i	0.0403388	+	0.0698688i	−0.845151	+	0.534527i	$0.820490\pi$
$132$		0			0
$133$	924.779	−	1601.76i	0.602921	−	1.04429i
$134$		0			0
$135$	429.640	+	554.513i	0.273908	+	0.353518i
$136$		0			0
$137$	227.352	−	393.785i	0.141781	−	0.245572i	−0.786386	−	0.617735i	$-0.788050\pi$
$137$	227.352	−	393.785i	0.141781	−	0.245572i	0.928167	+	0.372163i	$0.121384\pi$
$138$		0			0
$139$	−1170.31	−	2027.03i	−0.714130	−	1.23691i	−0.963294	−	0.268448i	$-0.913489\pi$
$139$	−1170.31	−	2027.03i	−0.714130	−	1.23691i	0.249164	−	0.968461i	$-0.419844\pi$
$140$		0			0
$141$	−252.700	−	395.295i	−0.150931	−	0.236098i
$142$		0			0
$143$	−3735.88			−2.18469
$144$		0			0
$145$	796.256			0.456037
$146$		0			0
$147$	−1361.72	+	61.5872i	−0.764033	+	0.0345553i
$148$		0			0
$149$	−1084.18	−	1877.86i	−0.596106	−	1.03249i	−0.993390	−	0.114790i	$-0.963380\pi$
$149$	−1084.18	−	1877.86i	−0.596106	−	1.03249i	0.397283	−	0.917696i	$-0.369953\pi$
$150$		0			0
$151$	−1344.51	+	2328.76i	−0.724601	+	1.25504i	0.234538	+	0.972107i	$0.424642\pi$
$151$	−1344.51	+	2328.76i	−0.724601	+	1.25504i	−0.959138	+	0.282938i	$0.908691\pi$
$152$		0			0
$153$	1325.37	+	1880.29i	0.700327	+	0.993544i
$154$		0			0
$155$	−796.276	+	1379.19i	−0.412635	+	0.714704i
$156$		0			0
$157$	1358.22	+	2352.50i	0.690430	+	1.19586i	0.971697	+	0.236230i	$0.0759120\pi$
$157$	1358.22	+	2352.50i	0.690430	+	1.19586i	−0.281267	+	0.959630i	$0.590755\pi$
$158$		0			0
$159$	1654.14	−	3189.74i	0.825042	−	1.59096i
$160$		0			0
$161$	−2400.20			−1.17492
$162$		0			0
$163$	289.025			0.138885			0.0694423	−	0.997586i	$-0.477878\pi$
$163$	289.025			0.138885			0.0694423	+	0.997586i	$0.477878\pi$
$164$		0			0
$165$	−749.061	+	1444.44i	−0.353420	+	0.681513i
$166$		0			0
$167$	179.279	+	310.521i	0.0830721	+	0.143885i	0.904568	−	0.426329i	$-0.140193\pi$
$167$	179.279	+	310.521i	0.0830721	+	0.143885i	−0.821496	+	0.570214i	$0.806860\pi$
$168$		0			0
$169$	−680.694	+	1179.00i	−0.309829	+	0.536639i
$170$		0			0
$171$	1169.39	+	1659.00i	0.522956	+	0.741910i
$172$		0			0
$173$	675.169	−	1169.43i	0.296718	−	0.513930i	−0.678665	−	0.734448i	$-0.737441\pi$
$173$	675.169	−	1169.43i	0.296718	−	0.513930i	0.975383	+	0.220518i	$0.0707746\pi$
$174$		0			0
$175$	−307.543	−	532.681i	−0.132846	−	0.230097i
$176$		0			0
$177$	−1471.70	+	66.5613i	−0.624971	+	0.0282659i
$178$		0			0
$179$	1192.29			0.497854			0.248927	−	0.968522i	$-0.419922\pi$
$179$	1192.29			0.497854			0.248927	+	0.968522i	$0.419922\pi$
$180$		0			0
$181$	−1785.62			−0.733283			−0.366641	−	0.930362i	$-0.619492\pi$
$181$	−1785.62			−0.733283			−0.366641	+	0.930362i	$0.619492\pi$
$182$		0			0
$183$	−1209.49	−	1891.99i	−0.488570	−	0.764261i
$184$		0			0
$185$	−984.029	−	1704.39i	−0.391066	−	0.677347i
$186$		0			0
$187$	−2668.00	+	4621.12i	−1.04334	+	1.80711i
$188$		0			0
$189$	1305.96	−	3195.18i	0.502619	−	1.22971i
$190$		0			0
$191$	786.425	−	1362.13i	0.297925	−	0.516022i	−0.677736	−	0.735305i	$-0.737039\pi$
$191$	786.425	−	1362.13i	0.297925	−	0.516022i	0.975661	+	0.219284i	$0.0703720\pi$
$192$		0			0
$193$	−149.039	−	258.144i	−0.0555860	−	0.0962777i	0.836893	−	0.547366i	$-0.184369\pi$
$193$	−149.039	−	258.144i	−0.0555860	−	0.0962777i	−0.892479	+	0.451088i	$0.851036\pi$
$194$		0			0
$195$	834.755	+	1305.79i	0.306554	+	0.479537i
$196$		0			0
$197$	881.991			0.318981			0.159490	−	0.987199i	$-0.449015\pi$
$197$	881.991			0.318981			0.159490	+	0.987199i	$0.449015\pi$
$198$		0			0
$199$	2647.66			0.943155			0.471578	−	0.881825i	$-0.343685\pi$
$199$	2647.66			0.943155			0.471578	+	0.881825i	$0.343685\pi$
$200$		0			0
$201$	−1600.65	+	72.3934i	−0.561698	+	0.0254042i
$202$		0			0
$203$	−1959.07	−	3393.20i	−0.677337	−	1.17318i
$204$		0			0
$205$	−212.703	+	368.413i	−0.0724675	+	0.125517i
$206$		0			0
$207$	1105.70	−	2390.67i	0.371264	−	0.802721i
$208$		0			0
$209$	−2354.01	+	4077.26i	−0.779091	+	1.34943i
$210$		0			0
$211$	−1832.29	−	3173.61i	−0.597819	−	1.03545i	−0.993142	−	0.116911i	$-0.962701\pi$
$211$	−1832.29	−	3173.61i	−0.597819	−	1.03545i	0.395324	−	0.918542i	$-0.370632\pi$
$212$		0			0
$213$	724.030	−	1396.17i	0.232910	−	0.449128i
$214$		0			0
$215$	−203.818			−0.0646523
$216$		0			0
$217$	7836.46			2.45149
$218$		0			0
$219$	−1094.54	+	2110.64i	−0.337727	+	0.651251i
$220$		0			0
$221$	2541.25	+	4401.57i	0.773497	+	1.33974i
$222$		0			0
$223$	−1988.20	+	3443.66i	−0.597039	+	1.03410i	0.396217	+	0.918157i	$0.370323\pi$
$223$	−1988.20	+	3443.66i	−0.597039	+	1.03410i	−0.993256	+	0.115945i	$0.963010\pi$
$224$		0			0
$225$	672.244	−	60.9325i	0.199183	−	0.0180541i
$226$		0			0
$227$	−221.774	+	384.123i	−0.0648442	+	0.112313i	−0.896625	−	0.442791i	$-0.853988\pi$
$227$	−221.774	+	384.123i	−0.0648442	+	0.112313i	0.831781	+	0.555104i	$0.187322\pi$
$228$		0			0
$229$	347.983	+	602.724i	0.100416	+	0.173926i	0.911856	−	0.410510i	$-0.134649\pi$
$229$	347.983	+	602.724i	0.100416	+	0.173926i	−0.811440	+	0.584436i	$0.801316\pi$
$230$		0			0
$231$	7998.36	−	361.746i	2.27815	−	0.103035i
$232$		0			0
$233$	1469.06			0.413052			0.206526	−	0.978441i	$-0.433784\pi$
$233$	1469.06			0.413052			0.206526	+	0.978441i	$0.433784\pi$
$234$		0			0
$235$	−451.454			−0.125317
$236$		0			0
$237$	−2355.69	−	3684.96i	−0.645646	−	1.00997i
$238$		0			0
$239$	−1794.90	−	3108.86i	−0.485784	−	0.841403i	0.514082	−	0.857741i	$-0.328133\pi$
$239$	−1794.90	−	3108.86i	−0.485784	−	0.841403i	−0.999867	+	0.0163378i	$0.994799\pi$
$240$		0			0
$241$	1950.32	−	3378.05i	0.521290	−	0.902900i	−0.478404	−	0.878140i	$-0.658784\pi$
$241$	1950.32	−	3378.05i	0.521290	−	0.902900i	0.999693	−	0.0247604i	$-0.00788228\pi$
$242$		0			0
$243$	2580.89	+	2772.71i	0.681333	+	0.731974i
$244$		0			0
$245$	−655.828	+	1135.93i	−0.171018	+	0.296211i
$246$		0			0
$247$	2242.17	+	3883.55i	0.577594	+	1.00042i
$248$		0			0
$249$	−2205.91	−	3450.67i	−0.561421	−	0.878222i
$250$		0			0
$251$	−5079.37			−1.27732			−0.638659	−	0.769490i	$-0.720511\pi$
$251$	−5079.37			−1.27732			−0.638659	+	0.769490i	$0.720511\pi$
$252$		0			0
$253$	6109.65			1.51822
$254$		0			0
$255$	2211.35	−	100.014i	0.543060	−	0.0245612i
$256$		0			0
$257$	−1573.68	−	2725.69i	−0.381959	−	0.661572i	0.609383	−	0.792876i	$-0.291417\pi$
$257$	−1573.68	−	2725.69i	−0.381959	−	0.661572i	−0.991342	+	0.131304i	$0.958084\pi$
$258$		0			0
$259$	−4842.11	+	8386.78i	−1.16168	+	2.01208i
$260$		0			0
$261$	4282.23	−	388.142i	1.01557	−	0.0920514i
$262$		0			0
$263$	−148.631	+	257.437i	−0.0348479	+	0.0603583i	−0.882923	−	0.469517i	$-0.844428\pi$
$263$	−148.631	+	257.437i	−0.0348479	+	0.0603583i	0.848075	+	0.529875i	$0.177761\pi$
$264$		0			0
$265$	−1728.75	−	2994.28i	−0.400740	−	0.694102i
$266$		0			0
$267$	2677.60	−	5163.32i	0.613733	−	1.18348i
$268$		0			0
$269$	−98.5534			−0.0223379			−0.0111690	−	0.999938i	$-0.503555\pi$
$269$	−98.5534			−0.0223379			−0.0111690	+	0.999938i	$0.503555\pi$
$270$		0			0
$271$	2602.14			0.583280			0.291640	−	0.956528i	$-0.405799\pi$
$271$	2602.14			0.583280			0.291640	+	0.956528i	$0.405799\pi$
$272$		0			0
$273$	3510.78	−	6769.97i	0.778323	−	1.50087i
$274$		0			0
$275$	782.846	+	1355.93i	0.171663	+	0.297330i
$276$		0			0
$277$	−3184.32	+	5515.40i	−0.690712	+	1.19635i	0.280893	+	0.959739i	$0.409369\pi$
$277$	−3184.32	+	5515.40i	−0.690712	+	1.19635i	−0.971605	+	0.236609i	$0.923964\pi$
$278$		0			0
$279$	−3610.03	+	7805.37i	−0.774649	+	1.67489i
$280$		0			0
$281$	−937.780	+	1624.28i	−0.199086	+	0.344828i	−0.948232	−	0.317577i	$-0.897131\pi$
$281$	−937.780	+	1624.28i	−0.199086	+	0.344828i	0.749146	+	0.662405i	$0.230464\pi$
$282$		0			0
$283$	1034.85	+	1792.41i	0.217369	+	0.376494i	0.954003	−	0.299798i	$-0.0969192\pi$
$283$	1034.85	+	1792.41i	0.217369	+	0.376494i	−0.736634	+	0.676292i	$0.763586\pi$
$284$		0			0
$285$	1951.10	−	88.2433i	0.405520	−	0.0183406i
$286$		0			0
$287$	2093.30			0.430534
$288$		0			0
$289$	2346.39			0.477588
$290$		0			0
$291$	3352.05	+	5243.56i	0.675260	+	1.05630i
$292$		0			0
$293$	1144.25	+	1981.90i	0.228149	+	0.395166i	0.957260	−	0.289230i	$-0.0933993\pi$
$293$	1144.25	+	1981.90i	0.228149	+	0.395166i	−0.729111	+	0.684396i	$0.760066\pi$
$294$		0			0
$295$	−708.796	+	1227.67i	−0.139891	+	0.242298i
$296$		0			0
$297$	−3324.31	+	8133.28i	−0.649481	+	1.58903i
$298$		0			0
$299$	2909.69	−	5039.73i	0.562782	−	0.974767i
$300$		0			0
$301$	501.462	+	868.558i	0.0960259	+	0.166322i
$302$		0			0
$303$	3966.81	+	6205.22i	0.752104	+	1.17650i
$304$		0			0
$305$	−2160.78			−0.405659
$306$		0			0
$307$	−8234.22			−1.53079			−0.765394	−	0.643563i	$-0.777456\pi$
$307$	−8234.22			−1.53079			−0.765394	+	0.643563i	$0.777456\pi$
$308$		0			0
$309$	−2155.73	+	97.4980i	−0.396877	+	0.0179497i
$310$		0			0
$311$	−2978.83	−	5159.49i	−0.543132	−	0.940732i	−0.998722	−	0.0505426i	$-0.983905\pi$
$311$	−2978.83	−	5159.49i	−0.543132	−	0.940732i	0.455590	−	0.890190i	$-0.349428\pi$
$312$		0			0
$313$	−2566.33	+	4445.01i	−0.463442	+	0.802705i	−0.999130	−	0.0417112i	$-0.986719\pi$
$313$	−2566.33	+	4445.01i	−0.463442	+	0.802705i	0.535688	+	0.844416i	$0.320052\pi$
$314$		0			0
$315$	−1913.62	−	2714.82i	−0.342286	−	0.485596i
$316$		0			0
$317$	3842.89	−	6656.08i	0.680878	−	1.17931i	−0.293836	−	0.955856i	$-0.594932\pi$
$317$	3842.89	−	6656.08i	0.680878	−	1.17931i	0.974713	−	0.223459i	$-0.0717348\pi$
$318$		0			0
$319$	4986.77	+	8637.33i	0.875252	+	1.51598i
$320$		0			0
$321$	1832.93	−	3534.50i	0.318704	−	0.614569i
$322$		0			0
$323$	6405.03			1.10336
$324$		0			0
$325$	1491.31			0.254532
$326$		0			0
$327$	835.356	−	1610.85i	0.141270	−	0.272416i
$328$		0			0
$329$	1110.73	+	1923.85i	0.186130	+	0.322386i
$330$		0			0
$331$	5790.60	−	10029.6i	0.961571	−	1.66549i	0.243013	−	0.970023i	$-0.421864\pi$
$331$	5790.60	−	10029.6i	0.961571	−	1.66549i	0.718558	−	0.695467i	$-0.244803\pi$
$332$		0			0
$333$	−6122.89	−	8686.45i	−1.00760	−	1.42947i
$334$		0			0
$335$	−770.901	+	1335.24i	−0.125728	+	0.217767i
$336$		0			0
$337$	−3339.65	−	5784.44i	−0.539828	−	0.935010i	−0.998913	−	0.0466176i	$-0.985156\pi$
$337$	−3339.65	−	5784.44i	−0.539828	−	0.935010i	0.459084	−	0.888393i	$-0.348178\pi$
$338$		0			0
$339$	5813.43	−	262.927i	0.931393	−	0.0421246i
$340$		0			0
$341$	−19947.6			−3.16780
$342$		0			0
$343$	−1984.73			−0.312436
$344$		0			0
$345$	−1365.16	−	2135.49i	−0.213036	−	0.333249i
$346$		0			0
$347$	−2550.12	−	4416.94i	−0.394518	−	0.683325i	0.598522	−	0.801107i	$-0.295755\pi$
$347$	−2550.12	−	4416.94i	−0.394518	−	0.683325i	−0.993039	+	0.117782i	$0.962422\pi$
$348$		0			0
$349$	1196.19	−	2071.86i	0.183469	−	0.317778i	−0.759591	−	0.650402i	$-0.774601\pi$
$349$	1196.19	−	2071.86i	0.183469	−	0.317778i	0.943060	+	0.332624i	$0.107934\pi$
$350$		0			0
$351$	5125.80	+	6615.59i	0.779472	+	1.00602i
$352$		0			0
$353$	−1879.20	+	3254.86i	−0.283341	+	0.490762i	−0.972206	−	0.234129i	$-0.924776\pi$
$353$	−1879.20	+	3254.86i	−0.283341	+	0.490762i	0.688864	+	0.724890i	$0.258110\pi$
$354$		0			0
$355$	−756.687	−	1310.62i	−0.113129	−	0.195945i
$356$		0			0
$357$	−5866.90	−	9177.50i	−0.869775	−	1.36057i
$358$		0			0
$359$	796.747			0.117133			0.0585664	−	0.998284i	$-0.481347\pi$
$359$	796.747			0.117133			0.0585664	+	0.998284i	$0.481347\pi$
$360$		0			0
$361$	−1207.77			−0.176086
$362$		0			0
$363$	−13450.7	+	608.340i	−1.94484	+	0.0879602i
$364$		0			0
$365$	1143.91	+	1981.31i	0.164041	+	0.284127i
$366$		0			0
$367$	5648.53	−	9783.54i	0.803408	−	1.39154i	−0.113952	−	0.993486i	$-0.536351\pi$
$367$	5648.53	−	9783.54i	0.803408	−	1.39154i	0.917360	−	0.398058i	$-0.130316\pi$
$368$		0			0
$369$	−964.322	+	2084.99i	−0.136045	+	0.294147i
$370$		0			0
$371$	−8506.63	+	14733.9i	−1.19041	+	2.06185i
$372$		0			0
$373$	−4976.58	−	8619.69i	−0.690825	−	1.19654i	−0.971568	−	0.236761i	$-0.923914\pi$
$373$	−4976.58	−	8619.69i	−0.690825	−	1.19654i	0.280743	−	0.959783i	$-0.409419\pi$
$374$		0			0
$375$	299.013	−	576.599i	0.0411760	−	0.0794011i
$376$		0			0
$377$	9499.68			1.29777
$378$		0			0
$379$	−5649.80			−0.765727			−0.382864	−	0.923805i	$-0.625062\pi$
$379$	−5649.80			−0.765727			−0.382864	+	0.923805i	$0.625062\pi$
$380$		0			0
$381$	−2085.08	+	4020.73i	−0.280372	+	0.540652i
$382$		0			0
$383$	259.482	+	449.436i	0.0346186	+	0.0599611i	0.882816	−	0.469720i	$-0.155645\pi$
$383$	259.482	+	449.436i	0.0346186	+	0.0599611i	−0.848197	+	0.529681i	$0.822312\pi$
$384$		0			0
$385$	3852.15	−	6672.12i	0.509932	−	0.883227i
$386$		0			0
$387$	−1096.12	+	99.3529i	−0.143977	+	0.0130501i
$388$		0			0
$389$	−1161.52	+	2011.81i	−0.151391	+	0.262218i	−0.931739	−	0.363128i	$-0.881709\pi$
$389$	−1161.52	+	2011.81i	−0.151391	+	0.262218i	0.780348	+	0.625346i	$0.215042\pi$
$390$		0			0
$391$	−4155.95	−	7198.32i	−0.537533	−	0.931035i
$392$		0			0
$393$	627.911	−	28.3988i	0.0805952	−	0.00364512i
$394$		0			0
$395$	−4208.48			−0.536080
$396$		0			0
$397$	4598.47			0.581336			0.290668	−	0.956824i	$-0.406122\pi$
$397$	4598.47			0.581336			0.290668	+	0.956824i	$0.406122\pi$
$398$		0			0
$399$	−5176.43	−	8097.40i	−0.649488	−	1.01598i
$400$		0			0
$401$	4714.52	+	8165.78i	0.587112	+	1.01691i	0.994609	+	0.103701i	$0.0330684\pi$
$401$	4714.52	+	8165.78i	0.587112	+	1.01691i	−0.407497	+	0.913207i	$0.633598\pi$
$402$		0			0
$403$	−9499.92	+	16454.3i	−1.17426	+	2.03387i
$404$		0			0
$405$	3585.60	−	655.384i	0.439925	−	0.0804106i
$406$		0			0
$407$	12325.5	−	21348.4i	1.50111	−	2.60000i
$408$		0			0
$409$	−2982.30	−	5165.49i	−0.360551	−	0.624492i	0.627501	−	0.778616i	$-0.284078\pi$
$409$	−2982.30	−	5165.49i	−0.360551	−	0.624492i	−0.988052	+	0.154124i	$0.950745\pi$
$410$		0			0
$411$	−1272.60	−	1990.70i	−0.152731	−	0.238915i
$412$		0			0
$413$	6975.54			0.831099
$414$		0			0
$415$	−3940.90			−0.466147
$416$		0			0
$417$	−12149.8	+	549.503i	−1.42680	+	0.0645306i
$418$		0			0
$419$	4974.57	+	8616.21i	0.580009	+	1.00460i	0.995478	+	0.0949970i	$0.0302842\pi$
$419$	4974.57	+	8616.21i	0.580009	+	1.00460i	−0.415469	+	0.909607i	$0.636383\pi$
$420$		0			0
$421$	1596.08	−	2764.50i	0.184771	−	0.320032i	−0.758729	−	0.651407i	$-0.774179\pi$
$421$	1596.08	−	2764.50i	0.184771	−	0.320032i	0.943499	+	0.331375i	$0.107512\pi$
$422$		0			0
$423$	−2427.90	+	220.066i	−0.279074	+	0.0252954i
$424$		0			0
$425$	1065.03	−	1844.68i	0.121556	−	0.210541i
$426$		0			0
$427$	5316.27	+	9208.05i	0.602512	+	1.04358i
$428$		0			0
$429$	−8936.63	+	17232.8i	−1.00574	+	1.93942i
$430$		0			0
$431$	8301.53			0.927774			0.463887	−	0.885894i	$-0.346454\pi$
$431$	8301.53			0.927774			0.463887	+	0.885894i	$0.346454\pi$
$432$		0			0
$433$	4712.24			0.522993			0.261496	−	0.965204i	$-0.415784\pi$
$433$	4712.24			0.522993			0.261496	+	0.965204i	$0.415784\pi$
$434$		0			0
$435$	1904.73	−	3672.96i	0.209942	−	0.404839i
$436$		0			0
$437$	−3666.84	−	6351.15i	−0.401393	−	0.695232i
$438$		0			0
$439$	−1316.94	+	2281.02i	−0.143176	+	0.247988i	−0.928691	−	0.370854i	$-0.879065\pi$
$439$	−1316.94	+	2281.02i	−0.143176	+	0.247988i	0.785515	+	0.618843i	$0.212398\pi$
$440$		0			0
$441$	−2973.29	+	6428.65i	−0.321055	+	0.694164i
$442$		0			0
$443$	−4670.68	+	8089.86i	−0.500928	+	0.867632i	0.499072	+	0.866561i	$0.333674\pi$
$443$	−4670.68	+	8089.86i	−0.500928	+	0.867632i	−0.999999	+	0.00107135i	$0.999659\pi$
$444$		0			0
$445$	−2798.37	−	4846.93i	−0.298103	−	0.516329i
$446$		0			0
$447$	−11255.7	+	509.065i	−1.19100	+	0.0538657i
$448$		0			0
$449$	16365.3			1.72010			0.860051	−	0.510208i	$-0.170432\pi$
$449$	16365.3			1.72010			0.860051	+	0.510208i	$0.170432\pi$
$450$		0			0
$451$	−5328.45			−0.556334
$452$		0			0
$453$	7525.87	+	11772.6i	0.780565	+	1.22102i
$454$		0			0
$455$	−3669.13	−	6355.12i	−0.378047	−	0.654797i
$456$		0			0
$457$	−5330.73	+	9233.10i	−0.545648	+	0.945090i	0.452918	+	0.891552i	$0.350383\pi$
$457$	−5330.73	+	9233.10i	−0.545648	+	0.945090i	−0.998566	+	0.0535381i	$0.982950\pi$
$458$		0			0
$459$	11843.8	−	1615.82i	1.20440	−	0.164313i
$460$		0			0
$461$	−1172.45	+	2030.74i	−0.118452	+	0.205164i	−0.919154	−	0.393898i	$-0.871126\pi$
$461$	−1172.45	+	2030.74i	−0.118452	+	0.205164i	0.800703	+	0.599062i	$0.204460\pi$
$462$		0			0
$463$	−1864.86	−	3230.04i	−0.187187	−	0.324217i	0.757124	−	0.653271i	$-0.226604\pi$
$463$	−1864.86	−	3230.04i	−0.187187	−	0.324217i	−0.944311	+	0.329054i	$0.893270\pi$
$464$		0			0
$465$	4457.14	+	6972.22i	0.444505	+	0.695331i
$466$		0			0
$467$	−4100.10			−0.406274			−0.203137	−	0.979150i	$-0.565114\pi$
$467$	−4100.10			−0.406274			−0.203137	+	0.979150i	$0.565114\pi$
$468$		0			0
$469$	7586.74			0.746957
$470$		0			0
$471$	14100.6	−	637.734i	1.37945	−	0.0623890i
$472$		0			0
$473$	−1276.46	−	2210.90i	−0.124084	−	0.214920i
$474$		0			0
$475$	939.683	−	1627.58i	0.0907697	−	0.157218i
$476$		0			0
$477$	−10756.7	−	15260.4i	−1.03253	−	1.46483i
$478$		0			0
$479$	2658.24	−	4604.21i	0.253566	−	0.439190i	−0.710939	−	0.703254i	$-0.751730\pi$
$479$	2658.24	−	4604.21i	0.253566	−	0.439190i	0.964505	+	0.264064i	$0.0850631\pi$
$480$		0			0
$481$	−11739.9	−	20334.1i	−1.11288	−	1.92756i
$482$		0			0
$483$	−5741.53	+	11071.6i	−0.540887	+	1.04301i
$484$		0			0
$485$	5988.50			0.560668
$486$		0			0
$487$	3958.43			0.368324			0.184162	−	0.982896i	$-0.441043\pi$
$487$	3958.43			0.368324			0.184162	+	0.982896i	$0.441043\pi$
$488$		0			0
$489$	691.378	−	1333.21i	0.0639370	−	0.123292i
$490$		0			0
$491$	2025.85	+	3508.88i	0.186203	+	0.322512i	0.943981	−	0.329999i	$-0.107049\pi$
$491$	2025.85	+	3508.88i	0.186203	+	0.322512i	−0.757778	+	0.652512i	$0.773715\pi$
$492$		0			0
$493$	6784.26	−	11750.7i	0.619772	−	1.07348i
$494$		0			0
$495$	4871.07	+	6910.52i	0.442300	+	0.627484i
$496$		0			0
$497$	−3723.42	+	6449.16i	−0.336053	+	0.582061i
$498$		0			0
$499$	4551.45	+	7883.35i	0.408319	+	0.707229i	0.994702	−	0.102805i	$-0.0327818\pi$
$499$	4551.45	+	7883.35i	0.408319	+	0.707229i	−0.586383	+	0.810034i	$0.699449\pi$
$500$		0			0
$501$	1861.22	−	84.1784i	0.165975	−	0.00750661i
$502$		0			0
$503$	4980.47			0.441487			0.220744	−	0.975332i	$-0.429152\pi$
$503$	4980.47			0.441487			0.220744	+	0.975332i	$0.429152\pi$
$504$		0			0
$505$	7086.79			0.624471
$506$		0			0
$507$	3810.17	+	5960.18i	0.333759	+	0.522093i
$508$		0			0
$509$	8192.39	+	14189.6i	0.713402	+	1.23565i	0.963573	+	0.267446i	$0.0861798\pi$
$509$	8192.39	+	14189.6i	0.713402	+	1.23565i	−0.250171	+	0.968202i	$0.580487\pi$
$510$		0			0
$511$	5628.83	−	9749.41i	0.487289	−	0.844009i
$512$		0			0
$513$	10449.9	−	1425.65i	0.899366	−	0.122698i
$514$		0			0
$515$	−1038.23	+	1798.27i	−0.0888351	+	0.153867i
$516$		0			0
$517$	−2827.35	−	4897.12i	−0.240516	−	0.416586i
$518$		0			0
$519$	−3779.24	−	5911.81i	−0.319635	−	0.499999i
$520$		0			0
$521$	4814.03			0.404811			0.202406	−	0.979302i	$-0.435124\pi$
$521$	4814.03			0.404811			0.202406	+	0.979302i	$0.435124\pi$
$522$		0			0
$523$	−815.794			−0.0682069			−0.0341034	−	0.999418i	$-0.510858\pi$
$523$	−815.794			−0.0682069			−0.0341034	+	0.999418i	$0.510858\pi$
$524$		0			0
$525$	−3192.82	+	144.403i	−0.265421	+	0.0120043i
$526$		0			0
$527$	13568.9	+	23502.0i	1.12157	+	1.94262i
$528$		0			0
$529$	1325.00	−	2294.96i	0.108901	−	0.188622i
$530$		0			0
$531$	−3213.43	+	6947.87i	−0.262620	+	0.567819i
$532$		0			0
$533$	−2537.64	+	4395.33i	−0.206224	+	0.357191i
$534$		0			0
$535$	−1915.60	−	3317.92i	−0.154801	−	0.268123i
$536$		0			0
$537$	2852.08	−	5499.77i	0.229192	−	0.441960i
$538$		0			0
$539$	−16429.2			−1.31290
$540$		0			0
$541$	3305.78			0.262711			0.131355	−	0.991335i	$-0.458067\pi$
$541$	3305.78			0.262711			0.131355	+	0.991335i	$0.458067\pi$
$542$		0			0
$543$	−4271.40	+	8236.69i	−0.337575	+	0.650958i
$544$		0			0
$545$	−873.034	−	1512.14i	−0.0686177	−	0.118849i
$546$		0			0
$547$	3392.16	−	5875.39i	0.265152	−	0.459257i	−0.702451	−	0.711732i	$-0.747911\pi$
$547$	3392.16	−	5875.39i	0.265152	−	0.459257i	0.967603	+	0.252475i	$0.0812445\pi$
$548$		0			0
$549$	−11620.6	+	1053.29i	−0.903377	+	0.0818825i
$550$		0			0
$551$	5985.82	−	10367.7i	0.462803	−	0.801599i
$552$		0			0
$553$	10354.3	+	17934.2i	0.796221	+	1.37910i
$554$		0			0
$555$	−10215.9	+	462.039i	−0.781334	+	0.0353378i
$556$		0			0
$557$	5708.87			0.434278			0.217139	−	0.976141i	$-0.430328\pi$
$557$	5708.87			0.434278			0.217139	+	0.976141i	$0.430328\pi$
$558$		0			0
$559$	−2431.64			−0.183984
$560$		0			0
$561$	14934.1	+	23361.2i	1.12392	+	1.75813i
$562$		0			0
$563$	−11002.5	−	19056.9i	−0.823625	−	1.42656i	−0.902965	−	0.429713i	$-0.858615\pi$
$563$	−11002.5	−	19056.9i	−0.823625	−	1.42656i	0.0793400	−	0.996848i	$-0.474719\pi$
$564$		0			0
$565$	2799.85	−	4849.48i	0.208479	−	0.361096i
$566$		0			0
$567$	−11614.7	−	13667.4i	−0.860267	−	1.01230i
$568$		0			0
$569$	10965.5	−	18992.8i	0.807906	−	1.39933i	−0.106406	−	0.994323i	$-0.533934\pi$
$569$	10965.5	−	18992.8i	0.807906	−	1.39933i	0.914312	−	0.405011i	$-0.132732\pi$
$570$		0			0
$571$	−4986.51	−	8636.89i	−0.365462	−	0.632999i	0.623388	−	0.781913i	$-0.285756\pi$
$571$	−4986.51	−	8636.89i	−0.365462	−	0.632999i	−0.988850	+	0.148913i	$0.952422\pi$
$572$		0			0
$573$	−4402.00	−	6885.97i	−0.320936	−	0.502034i
$574$		0			0
$575$	−2438.88			−0.176884
$576$		0			0
$577$	−2721.94			−0.196388			−0.0981941	−	0.995167i	$-0.531307\pi$
$577$	−2721.94			−0.196388			−0.0981941	+	0.995167i	$0.531307\pi$
$578$		0			0
$579$	−1547.28	+	69.9797i	−0.111058	+	0.00502289i
$580$		0			0
$581$	9695.98	+	16793.9i	0.692353	+	1.19919i
$582$		0			0
$583$	21653.5	−	37504.9i	1.53824	−	2.66431i
$584$		0			0
$585$	8020.17	−	726.951i	0.566826	−	0.0513773i
$586$		0			0
$587$	13084.5	−	22663.0i	0.920027	−	1.59353i	0.120656	−	0.992694i	$-0.461500\pi$
$587$	13084.5	−	22663.0i	0.920027	−	1.59353i	0.799371	−	0.600838i	$-0.205166\pi$
$588$		0			0
$589$	11971.9	+	20736.0i	0.837513	+	1.45062i
$590$		0			0
$591$	2109.82	−	4068.44i	0.146846	−	0.283169i
$592$		0			0
$593$	19409.1			1.34408			0.672038	−	0.740516i	$-0.265419\pi$
$593$	19409.1			1.34408			0.672038	+	0.740516i	$0.265419\pi$
$594$		0			0
$595$	−10481.3			−0.722173
$596$		0			0
$597$	6333.49	−	12213.1i	0.434192	−	0.837269i
$598$		0			0
$599$	7756.16	+	13434.1i	0.529062	+	0.916363i	0.999426	+	0.0338898i	$0.0107895\pi$
$599$	7756.16	+	13434.1i	0.529062	+	0.916363i	−0.470363	+	0.882473i	$0.655877\pi$
$600$		0			0
$601$	−11723.2	+	20305.2i	−0.795675	+	1.37815i	0.126735	+	0.991937i	$0.459550\pi$
$601$	−11723.2	+	20305.2i	−0.795675	+	1.37815i	−0.922410	+	0.386212i	$0.873783\pi$
$602$		0			0
$603$	−3494.99	+	7556.64i	−0.236032	+	0.510332i
$604$		0			0
$605$	−6478.07	+	11220.4i	−0.435324	+	0.754003i
$606$		0			0
$607$	8365.68	+	14489.8i	0.559394	+	0.968899i	0.997547	+	0.0699988i	$0.0222995\pi$
$607$	8365.68	+	14489.8i	0.559394	+	0.968899i	−0.438153	+	0.898901i	$0.644367\pi$
$608$		0			0
$609$	−20338.4	+	919.855i	−1.35329	+	0.0612059i
$610$		0			0
$611$	−5386.05			−0.356622
$612$		0			0
$613$	−5457.03			−0.359555			−0.179777	−	0.983707i	$-0.557538\pi$
$613$	−5457.03			−0.359555			−0.179777	+	0.983707i	$0.557538\pi$
$614$		0			0
$615$	1190.60	+	1862.44i	0.0780646	+	0.122115i
$616$		0			0
$617$	2475.48	+	4287.66i	0.161522	+	0.279764i	0.935415	−	0.353552i	$-0.115026\pi$
$617$	2475.48	+	4287.66i	0.161522	+	0.279764i	−0.773893	+	0.633317i	$0.781693\pi$
$618$		0			0
$619$	−3244.81	+	5620.17i	−0.210694	+	0.364933i	−0.951932	−	0.306309i	$-0.900906\pi$
$619$	−3244.81	+	5620.17i	−0.210694	+	0.364933i	0.741238	+	0.671243i	$0.234239\pi$
$620$		0			0
$621$	−8382.72	−	10819.1i	−0.541686	−	0.699124i
$622$		0			0
$623$	−13769.9	+	23850.2i	−0.885524	+	1.53377i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	13176.5	+	20611.8i	0.839265	+	1.31285i
$628$		0			0
$629$	−33536.5			−2.12590
$630$		0			0
$631$	−16613.1			−1.04811			−0.524054	−	0.851685i	$-0.675581\pi$
$631$	−16613.1			−1.04811			−0.524054	+	0.851685i	$0.675581\pi$
$632$		0			0
$633$	−19022.2	+	860.328i	−1.19442	+	0.0540205i
$634$		0			0
$635$	2179.12	+	3774.35i	0.136182	+	0.235875i
$636$		0			0
$637$	−7824.32	+	13552.1i	−0.486673	+	0.842943i
$638$		0			0
$639$	−4708.30	−	6679.60i	−0.291483	−	0.413522i
$640$		0			0
$641$	−9390.29	+	16264.5i	−0.578618	+	1.00220i	0.417020	+	0.908897i	$0.363074\pi$
$641$	−9390.29	+	16264.5i	−0.578618	+	1.00220i	−0.995638	+	0.0932982i	$0.970259\pi$
$642$		0			0
$643$	5040.38	+	8730.20i	0.309134	+	0.535436i	0.978173	−	0.207791i	$-0.0666275\pi$
$643$	5040.38	+	8730.20i	0.309134	+	0.535436i	−0.669039	+	0.743227i	$0.733294\pi$
$644$		0			0
$645$	−487.554	+	940.168i	−0.0297634	+	0.0573939i
$646$		0			0
$647$	14010.0			0.851296			0.425648	−	0.904889i	$-0.360046\pi$
$647$	14010.0			0.851296			0.425648	+	0.904889i	$0.360046\pi$
$648$		0			0
$649$	−17756.1			−1.07394
$650$		0			0
$651$	18745.7	−	36147.9i	1.12857	−	2.17627i
$652$		0			0
$653$	−10833.4	−	18764.0i	−0.649226	−	1.12449i	−0.983308	−	0.181948i	$-0.941760\pi$
$653$	−10833.4	−	18764.0i	−0.649226	−	1.12449i	0.334082	−	0.942544i	$-0.391574\pi$
$654$		0			0
$655$	302.412	−	523.794i	0.0180401	−	0.0312463i
$656$		0			0
$657$	7117.69	+	10097.8i	0.422660	+	0.599622i
$658$		0			0
$659$	7697.74	−	13332.9i	0.455025	−	0.788126i	−0.543665	−	0.839302i	$-0.682964\pi$
$659$	7697.74	−	13332.9i	0.455025	−	0.788126i	0.998690	+	0.0511765i	$0.0162971\pi$
$660$		0			0
$661$	9831.93	+	17029.4i	0.578544	+	1.00207i	0.995647	+	0.0932085i	$0.0297123\pi$
$661$	9831.93	+	17029.4i	0.578544	+	1.00207i	−0.417102	+	0.908860i	$0.636954\pi$
$662$		0			0
$663$	26382.4	−	1193.21i	1.54541	−	0.0698951i
$664$		0			0
$665$	−9247.79			−0.539269
$666$		0			0
$667$	−15535.8			−0.901870
$668$		0			0
$669$	11128.9	+	17408.8i	0.643151	+	1.00607i
$670$		0			0
$671$	−13532.5	−	23438.9i	−0.778562	−	1.34851i
$672$		0			0
$673$	−571.113	+	989.197i	−0.0327114	+	0.0566579i	−0.881918	−	0.471403i	$-0.843748\pi$
$673$	−571.113	+	989.197i	−0.0327114	+	0.0566579i	0.849206	+	0.528061i	$0.177081\pi$
$674$		0			0
$675$	1327.01	−	3246.68i	0.0756692	−	0.185133i
$676$		0			0
$677$	−10714.7	+	18558.3i	−0.608269	+	1.05355i	0.383257	+	0.923642i	$0.374802\pi$
$677$	−10714.7	+	18558.3i	−0.608269	+	1.05355i	−0.991526	+	0.129911i	$0.958531\pi$
$678$		0			0
$679$	−14733.8	−	25519.7i	−0.832741	−	1.44235i
$680$		0			0
$681$	1241.37	+	1941.86i	0.0698525	+	0.109269i
$682$		0			0
$683$	−246.980			−0.0138366			−0.00691832	−	0.999976i	$-0.502202\pi$
$683$	−246.980			−0.0138366			−0.00691832	+	0.999976i	$0.502202\pi$
$684$		0			0
$685$	−2273.52			−0.126813
$686$		0			0
$687$	3612.65	−	163.391i	0.200628	−	0.00907388i
$688$		0			0
$689$	−20624.7	−	35723.0i	−1.14040	−	1.97524i
$690$		0			0
$691$	15118.0	−	26185.2i	0.832297	−	1.44158i	−0.0639146	−	0.997955i	$-0.520359\pi$
$691$	15118.0	−	26185.2i	0.832297	−	1.44158i	0.896212	−	0.443626i	$-0.146308\pi$
$692$		0			0
$693$	17464.3	−	37760.1i	0.957306	−	2.06982i
$694$		0			0
$695$	−5851.53	+	10135.1i	−0.319369	+	0.553163i
$696$		0			0
$697$	3624.55	+	6277.91i	0.196972	+	0.341166i
$698$		0			0
$699$	3514.14	−	6776.45i	0.190153	−	0.366679i
$700$		0			0
$701$	−30606.5			−1.64906			−0.824530	−	0.565818i	$-0.808560\pi$
$701$	−30606.5			−1.64906			−0.824530	+	0.565818i	$0.808560\pi$
$702$		0			0
$703$	−29589.6			−1.58747
$704$		0			0
$705$	−1079.93	+	2082.46i	−0.0576913	+	0.111248i
$706$		0			0
$707$	−17436.0	−	30200.0i	−0.927506	−	1.60649i
$708$		0			0
$709$	6148.17	−	10648.9i	0.325669	−	0.564075i	−0.655978	−	0.754780i	$-0.727744\pi$
$709$	6148.17	−	10648.9i	0.325669	−	0.564075i	0.981648	+	0.190704i	$0.0610771\pi$
$710$		0			0
$711$	−22633.0	+	2051.46i	−1.19382	+	0.108208i
$712$		0			0
$713$	15536.2	−	26909.4i	0.816036	−	1.41342i
$714$		0			0
$715$	9339.70	+	16176.8i	0.488511	+	0.846125i
$716$		0			0
$717$	−18634.1	+	842.774i	−0.970577	+	0.0438967i
$718$		0			0
$719$	32946.1			1.70888			0.854438	−	0.519553i	$-0.173902\pi$
$719$	32946.1			1.70888			0.854438	+	0.519553i	$0.173902\pi$
$720$		0			0
$721$	10217.7			0.527775
$722$		0			0
$723$	−10916.8	−	17077.0i	−0.561552	−	0.878426i
$724$		0			0
$725$	−1990.64	−	3447.89i	−0.101973	−	0.176623i
$726$		0			0
$727$	−5714.65	+	9898.06i	−0.291533	+	0.504950i	−0.974172	−	0.225805i	$-0.927499\pi$
$727$	−5714.65	+	9898.06i	−0.291533	+	0.504950i	0.682639	+	0.730755i	$0.260832\pi$
$728$		0			0
$729$	18963.7	−	5272.46i	0.963455	−	0.267869i
$730$		0			0
$731$	−1736.57	+	3007.82i	−0.0878650	+	0.152187i
$732$		0			0
$733$	11461.8	+	19852.4i	0.577560	+	1.00036i	0.995758	+	0.0920074i	$0.0293284\pi$
$733$	11461.8	+	19852.4i	0.577560	+	1.00036i	−0.418198	+	0.908356i	$0.637338\pi$
$734$		0			0
$735$	3670.98	+	5742.46i	0.184226	+	0.288182i
$736$		0			0
$737$	−19311.9			−0.965215
$738$		0			0
$739$	−4769.73			−0.237426			−0.118713	−	0.992929i	$-0.537877\pi$
$739$	−4769.73			−0.237426			−0.118713	+	0.992929i	$0.537877\pi$
$740$		0			0
$741$	23277.5	−	1052.78i	1.15401	−	0.0521929i
$742$		0			0
$743$	−7013.95	−	12148.5i	−0.346322	−	0.599847i	0.639271	−	0.768981i	$-0.279236\pi$
$743$	−7013.95	−	12148.5i	−0.346322	−	0.599847i	−0.985593	+	0.169135i	$0.945903\pi$
$744$		0			0
$745$	−5420.92	+	9389.31i	−0.266587	+	0.461742i
$746$		0			0
$747$	−21194.0	+	1921.03i	−1.03808	+	0.0940921i
$748$		0			0
$749$	−9426.08	+	16326.5i	−0.459842	+	0.796470i
$750$		0			0
$751$	14096.6	+	24415.9i	0.684941	+	1.18635i	0.973455	+	0.228877i	$0.0735052\pi$
$751$	14096.6	+	24415.9i	0.684941	+	1.18635i	−0.288515	+	0.957475i	$0.593161\pi$
$752$		0			0
$753$	−12150.4	+	23430.1i	−0.588028	+	1.13392i
$754$		0			0
$755$	13445.1			0.648102
$756$		0			0
$757$	−13350.5			−0.640992			−0.320496	−	0.947250i	$-0.603850\pi$
$757$	−13350.5			−0.640992			−0.320496	+	0.947250i	$0.603850\pi$
$758$		0			0
$759$	14614.9	−	28182.5i	0.698931	−	1.34778i
$760$		0			0
$761$	−242.926	−	420.759i	−0.0115717	−	0.0200427i	0.860182	−	0.509988i	$-0.170350\pi$
$761$	−242.926	−	420.759i	−0.0115717	−	0.0200427i	−0.871753	+	0.489945i	$0.837017\pi$
$762$		0			0
$763$	−4295.93	+	7440.78i	−0.203831	+	0.353046i
$764$		0			0
$765$	4828.45	−	10439.8i	0.228200	−	0.493399i
$766$		0			0
$767$	−8456.26	+	14646.7i	−0.398094	+	0.689518i
$768$		0			0
$769$	−7067.93	−	12242.0i	−0.331438	−	0.574068i	0.651356	−	0.758773i	$-0.274201\pi$
$769$	−7067.93	−	12242.0i	−0.331438	−	0.574068i	−0.982794	+	0.184704i	$0.940867\pi$
$770$		0			0
$771$	−16337.4	+	738.902i	−0.763137	+	0.0345148i
$772$		0			0
$773$	25340.8			1.17910			0.589552	−	0.807731i	$-0.299304\pi$
$773$	25340.8			1.17910			0.589552	+	0.807731i	$0.299304\pi$
$774$		0			0
$775$	7962.76			0.369072
$776$		0			0
$777$	27103.6	+	42397.7i	1.25140	+	1.95754i
$778$		0			0
$779$	3197.98	+	5539.06i	0.147085	+	0.254759i
$780$		0			0
$781$	9477.91	−	16416.2i	0.434246	−	0.752136i
$782$		0			0
$783$	8453.12	−	20681.5i	0.385811	−	0.943928i
$784$		0			0
$785$	6791.08	−	11762.5i	0.308770	−	0.534805i
$786$		0			0
$787$	11100.4	+	19226.5i	0.502780	+	0.870840i	0.999995	+	0.00321296i	$0.00102272\pi$
$787$	11100.4	+	19226.5i	0.502780	+	0.870840i	−0.497215	+	0.867627i	$0.665644\pi$
$788$		0			0
$789$	831.959	+	1301.42i	0.0375393	+	0.0587222i
$790$		0			0
$791$	−27554.4			−1.23859
$792$		0			0
$793$	−25779.1			−1.15440
$794$		0			0
$795$	−17947.3	+	811.712i	−0.800661	+	0.0362119i
$796$		0			0
$797$	15935.9	+	27601.8i	0.708255	+	1.22673i	0.965504	+	0.260389i	$0.0838507\pi$
$797$	15935.9	+	27601.8i	0.708255	+	1.22673i	−0.257249	+	0.966345i	$0.582816\pi$
$798$		0			0
$799$	−3846.48	+	6662.30i	−0.170311	+	0.294988i
$800$		0			0
$801$	−17412.2	−	24702.4i	−0.768077	−	1.08966i
$802$		0			0
$803$	−14328.1	+	24816.9i	−0.629672	+	1.09062i
$804$		0			0
$805$	6000.49	+	10393.2i	0.262720	+	0.455044i
$806$		0			0
$807$	−235.750	+	454.606i	−0.0102835	+	0.0198301i
$808$		0			0
$809$	−29707.7			−1.29106			−0.645529	−	0.763736i	$-0.723363\pi$
$809$	−29707.7			−1.29106			−0.645529	+	0.763736i	$0.723363\pi$
$810$		0			0
$811$	34903.2			1.51124			0.755621	−	0.655009i	$-0.227335\pi$
$811$	34903.2			1.51124			0.755621	+	0.655009i	$0.227335\pi$
$812$		0			0
$813$	6224.60	−	12003.1i	0.268520	−	0.517796i
$814$		0			0
$815$	−722.562	−	1251.51i	−0.0310555	−	0.0537897i
$816$		0			0
$817$	−1532.19	+	2653.83i	−0.0656115	+	0.113642i
$818$		0			0
$819$	−22830.3	−	32389.0i	−0.974059	−	1.38188i
$820$		0			0
$821$	21082.2	−	36515.4i	0.896191	−	1.55225i	0.0638668	−	0.997958i	$-0.479657\pi$
$821$	21082.2	−	36515.4i	0.896191	−	1.55225i	0.832324	−	0.554289i	$-0.187010\pi$
$822$		0			0
$823$	2126.50	+	3683.21i	0.0900671	+	0.156001i	0.907539	−	0.419967i	$-0.137959\pi$
$823$	2126.50	+	3683.21i	0.0900671	+	0.156001i	−0.817472	+	0.575968i	$0.804625\pi$
$824$		0			0
$825$	8127.27	−	367.576i	0.342976	−	0.0155119i
$826$		0			0
$827$	−31806.5			−1.33739			−0.668694	−	0.743538i	$-0.733146\pi$
$827$	−31806.5			−1.33739			−0.668694	+	0.743538i	$0.733146\pi$
$828$		0			0
$829$	32483.0			1.36089			0.680447	−	0.732797i	$-0.261785\pi$
$829$	32483.0			1.36089			0.680447	+	0.732797i	$0.261785\pi$
$830$		0			0
$831$	17824.2	+	27882.0i	0.744059	+	1.16392i
$832$		0			0
$833$	11175.6	+	19356.7i	0.464839	+	0.805125i
$834$		0			0
$835$	896.396	−	1552.60i	0.0371510	−	0.0643474i
$836$		0			0
$837$	27368.9	+	35323.6i	1.13024	+	1.45874i
$838$		0			0
$839$	−9372.04	+	16232.8i	−0.385648	+	0.667962i	−0.991859	−	0.127342i	$-0.959355\pi$
$839$	−9372.04	+	16232.8i	−0.385648	+	0.667962i	0.606211	+	0.795304i	$0.292689\pi$
$840$		0			0
$841$	−485.957	−	841.701i	−0.0199252	−	0.0345115i
$842$		0			0
$843$	5249.20	+	8211.24i	0.214463	+	0.335480i
$844$		0			0
$845$	6806.94			0.277119
$846$		0			0
$847$	63753.2			2.58629
$848$		0			0
$849$	10743.5	−	485.901i	0.434294	−	0.0196420i
$850$		0			0
$851$	19199.4	+	33254.4i	0.773382	+	1.33954i
$852$		0			0
$853$	−15064.1	+	26091.7i	−0.604670	+	1.04732i	0.387434	+	0.921898i	$0.373362\pi$
$853$	−15064.1	+	26091.7i	−0.604670	+	1.04732i	−0.992104	+	0.125421i	$0.959972\pi$
$854$		0			0
$855$	4260.19	−	9211.10i	0.170404	−	0.368436i
$856$		0			0
$857$	9199.23	−	15933.5i	0.366674	−	0.635098i	−0.622369	−	0.782724i	$-0.713830\pi$
$857$	9199.23	−	15933.5i	0.366674	−	0.635098i	0.989043	+	0.147626i	$0.0471631\pi$
$858$		0			0
$859$	9130.70	+	15814.8i	0.362672	+	0.628166i	0.988400	−	0.151875i	$-0.0485312\pi$
$859$	9130.70	+	15814.8i	0.362672	+	0.628166i	−0.625728	+	0.780042i	$0.715198\pi$
$860$		0			0
$861$	5007.39	−	9655.93i	0.198201	−	0.382199i
$862$		0			0
$863$	−44247.0			−1.74529			−0.872645	−	0.488355i	$-0.837597\pi$
$863$	−44247.0			−1.74529			−0.872645	+	0.488355i	$0.837597\pi$
$864$		0			0
$865$	−6751.69			−0.265392
$866$		0			0
$867$	5612.82	−	10823.4i	0.219863	−	0.423970i
$868$		0			0
$869$	−26356.7	−	45651.2i	−1.02887	−	1.78206i
$870$		0			0
$871$	−9197.19	+	15930.0i	−0.357790	+	0.619710i
$872$		0			0
$873$	32205.9	−	2919.15i	1.24857	−	0.113171i
$874$		0			0
$875$	−1537.72	+	2663.40i	−0.0594107	+	0.102902i
$876$		0			0
$877$	10906.9	+	18891.3i	0.419954	+	0.727381i	0.995934	−	0.0900820i	$-0.0287129\pi$
$877$	10906.9	+	18891.3i	0.419954	+	0.727381i	−0.575980	+	0.817463i	$0.695380\pi$
$878$		0			0
$879$	11879.2	−	537.268i	0.455832	−	0.0206161i
$880$		0			0
$881$	−10425.7			−0.398694			−0.199347	−	0.979929i	$-0.563882\pi$
$881$	−10425.7			−0.398694			−0.199347	+	0.979929i	$0.563882\pi$
$882$		0			0
$883$	3527.13			0.134425			0.0672125	−	0.997739i	$-0.478589\pi$
$883$	3527.13			0.134425			0.0672125	+	0.997739i	$0.478589\pi$
$884$		0			0
$885$	3967.47	+	6206.25i	0.150695	+	0.235730i
$886$		0			0
$887$	14373.4	+	24895.4i	0.544093	+	0.942397i	0.998663	+	0.0516861i	$0.0164595\pi$
$887$	14373.4	+	24895.4i	0.544093	+	0.942397i	−0.454570	+	0.890711i	$0.650207\pi$
$888$		0			0
$889$	10722.8	−	18572.4i	0.404535	−	0.700675i
$890$		0			0
$891$	29565.0	+	34790.0i	1.11163	+	1.30809i
$892$		0			0
$893$	−3393.79	+	5878.21i	−0.127177	+	0.220277i
$894$		0			0
$895$	−2980.72	−	5162.76i	−0.111323	−	0.192818i
$896$		0			0
$897$	−16286.9	−	25477.4i	−0.606248	−	0.948344i
$898$		0			0
$899$	50723.1			1.88177
$900$		0			0
$901$	−58917.1			−2.17848
$902$		0			0
$903$	5206.03	−	235.455i	0.191856	−	0.00867715i
$904$		0			0
$905$	4464.05	+	7731.97i	0.163967	+	0.283999i
$906$		0			0
$907$	16153.3	−	27978.3i	0.591357	−	1.02426i	−0.402693	−	0.915335i	$-0.631926\pi$
$907$	16153.3	−	27978.3i	0.591357	−	1.02426i	0.994050	−	0.108925i	$-0.0347409\pi$
$908$		0			0
$909$	38112.4	−	3454.52i	1.39066	−	0.126050i
$910$		0			0
$911$	23693.5	−	41038.3i	0.861691	−	1.49249i	−0.00860466	−	0.999963i	$-0.502739\pi$
$911$	23693.5	−	41038.3i	0.861691	−	1.49249i	0.870296	−	0.492530i	$-0.163928\pi$
$912$		0			0
$913$	−24680.9	−	42748.7i	−0.894655	−	1.54959i
$914$		0			0
$915$	−5168.82	+	9967.23i	−0.186750	+	0.360116i
$916$		0			0
$917$	−2976.16			−0.107177
$918$		0			0
$919$	−25628.3			−0.919914			−0.459957	−	0.887941i	$-0.652135\pi$
$919$	−25628.3			−0.919914			−0.459957	+	0.887941i	$0.652135\pi$
$920$		0			0
$921$	−19697.1	+	37982.7i	−0.704715	+	1.35893i
$922$		0			0
$923$	−9027.61	−	15636.3i	−0.321936	−	0.557610i
$924$		0			0
$925$	−4920.15	+	8521.95i	−0.174890	+	0.302919i
$926$		0			0
$927$	−4706.99	+	10177.1i	−0.166772	+	0.360583i
$928$		0			0
$929$	18272.3	−	31648.6i	0.645312	−	1.11771i	−0.338917	−	0.940816i	$-0.610061\pi$
$929$	18272.3	−	31648.6i	0.645312	−	1.11771i	0.984229	−	0.176897i	$-0.0566060\pi$
$930$		0			0
$931$	9860.33	+	17078.6i	0.347110	+	0.601212i
$932$		0			0
$933$	−30925.3	+	1398.67i	−1.08516	+	0.0490788i
$934$		0			0
$935$	26680.0			0.933188
$936$		0			0
$937$	−46590.4			−1.62438			−0.812189	−	0.583394i	$-0.801724\pi$
$937$	−46590.4			−1.62438			−0.812189	+	0.583394i	$0.801724\pi$
$938$		0			0
$939$	14365.0	+	22470.9i	0.499236	+	0.780946i
$940$		0			0
$941$	6750.15	+	11691.6i	0.233846	+	0.405032i	0.958937	−	0.283621i	$-0.0915356\pi$
$941$	6750.15	+	11691.6i	0.233846	+	0.405032i	−0.725091	+	0.688653i	$0.758202\pi$
$942$		0			0
$943$	4150.06	−	7188.11i	0.143313	−	0.248226i
$944$		0			0
$945$	−17100.5	+	2332.97i	−0.588654	+	0.0803084i
$946$		0			0
$947$	−17927.8	+	31051.8i	−0.615179	+	1.06552i	0.375174	+	0.926955i	$0.377583\pi$
$947$	−17927.8	+	31051.8i	−0.615179	+	1.06552i	−0.990353	+	0.138567i	$0.955750\pi$
$948$		0			0
$949$	13647.3	+	23637.9i	0.466819	+	0.808554i
$950$		0			0
$951$	−21510.5	−	33648.5i	−0.733465	−	1.14735i
$952$		0			0
$953$	44408.4			1.50948			0.754738	−	0.656027i	$-0.227764\pi$
$953$	44408.4			1.50948			0.754738	+	0.656027i	$0.227764\pi$
$954$		0			0
$955$	−7864.25			−0.266473
$956$		0			0
$957$	51771.1	−	2341.47i	1.74872	−	0.0790900i
$958$		0			0
$959$	5593.65	+	9688.48i	0.188351	+	0.326233i
$960$		0			0
$961$	−35828.9	+	62057.5i	−1.20268	+	2.08309i
$962$		0			0
$963$	−11919.4	−	16909.8i	−0.398853	−	0.565848i
$964$		0			0
$965$	−745.197	+	1290.72i	−0.0248588	+	0.0430567i
$966$		0			0
$967$	1812.84	+	3139.93i	0.0602865	+	0.104419i	0.894593	−	0.446881i	$-0.147465\pi$
$967$	1812.84	+	3139.93i	0.0602865	+	0.104419i	−0.834307	+	0.551300i	$0.814132\pi$
$968$		0			0
$969$	15321.5	−	29545.1i	0.507945	−	0.979489i
$970$		0			0
$971$	−7066.70			−0.233554			−0.116777	−	0.993158i	$-0.537256\pi$
$971$	−7066.70			−0.233554			−0.116777	+	0.993158i	$0.537256\pi$
$972$		0			0
$973$	57587.2			1.89739
$974$		0			0
$975$	3567.36	−	6879.08i	0.117176	−	0.225956i
$976$		0			0
$977$	−6297.24	−	10907.1i	−0.206209	−	0.357165i	0.744308	−	0.667836i	$-0.232779\pi$
$977$	−6297.24	−	10907.1i	−0.206209	−	0.357165i	−0.950517	+	0.310671i	$0.899446\pi$
$978$		0			0
$979$	35051.1	−	60710.4i	1.14427	−	1.98193i
$980$		0			0
$981$	−5432.24	−	7706.65i	−0.176797	−	0.250820i
$982$		0			0
$983$	−8645.35	+	14974.2i	−0.280513	+	0.485862i	−0.971511	−	0.236994i	$-0.923838\pi$
$983$	−8645.35	+	14974.2i	−0.280513	+	0.485862i	0.690998	+	0.722856i	$0.257171\pi$
$984$		0			0
$985$	−2204.98	−	3819.13i	−0.0713263	−	0.123541i
$986$		0			0
$987$	11531.3	−	521.531i	0.371880	−	0.0168192i
$988$		0			0
$989$	3976.69			0.127858
$990$		0			0
$991$	−355.437			−0.0113934			−0.00569669	−	0.999984i	$-0.501813\pi$
$991$	−355.437			−0.0113934			−0.00569669	+	0.999984i	$0.501813\pi$
$992$		0			0
$993$	−32412.7	−	50702.7i	−1.03584	−	1.62034i
$994$		0			0
$995$	−6619.16	−	11464.7i	−0.210896	−	0.365282i
$996$		0			0
$997$	9008.94	−	15603.9i	0.286175	−	0.495669i	−0.686719	−	0.726923i	$-0.740950\pi$
$997$	9008.94	−	15603.9i	0.286175	−	0.495669i	0.972893	+	0.231254i	$0.0742829\pi$
$998$		0			0
$999$	−54715.4	+	7464.66i	−1.73285	+	0.236408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.4.i.c.61.5	✓	14
3.2	odd	2		540.4.i.c.181.2		14
9.2	odd	6		1620.4.a.k.1.6		7
9.4	even	3	inner	180.4.i.c.121.5	yes	14
9.5	odd	6		540.4.i.c.361.2		14
9.7	even	3		1620.4.a.l.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.4.i.c.61.5	✓	14	1.1	even	1	trivial
180.4.i.c.121.5	yes	14	9.4	even	3	inner
540.4.i.c.181.2		14	3.2	odd	2
540.4.i.c.361.2		14	9.5	odd	6
1620.4.a.k.1.6		7	9.2	odd	6
1620.4.a.l.1.6		7	9.7	even	3

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	180.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.39211 - 4.61279i) q^{3} +(-2.50000 - 4.33013i) q^{5} +(-12.3017 + 21.3072i) q^{7} +(-15.5556 - 22.0686i) q^{9} +(31.3139 - 54.2372i) q^{11} +(-29.8261 - 51.6603i) q^{13} +(-25.9542 + 1.17384i) q^{15} -85.2021 q^{17} -75.1746 q^{19} +(68.8587 + 107.715i) q^{21} +(48.7776 + 84.4852i) q^{23} +(-12.5000 + 21.6506i) q^{25} +(-139.008 + 18.9645i) q^{27} +(-79.6256 + 137.915i) q^{29} +(-159.255 - 275.838i) q^{31} +(-175.279 - 274.185i) q^{33} +123.017 q^{35} +393.612 q^{37} +(-309.646 + 14.0045i) q^{39} +(-42.5407 - 73.6826i) q^{41} +(20.3818 - 35.3023i) q^{43} +(-56.6706 + 122.529i) q^{45} +(45.1454 - 78.1941i) q^{47} +(-131.166 - 227.185i) q^{49} +(-203.812 + 393.019i) q^{51} +691.499 q^{53} -313.139 q^{55} +(-179.826 + 346.765i) q^{57} +(-141.759 - 245.534i) q^{59} +(216.078 - 374.258i) q^{61} +(661.582 - 59.9660i) q^{63} +(-149.131 + 258.302i) q^{65} +(-154.180 - 267.048i) q^{67} +(506.394 - 22.9029i) q^{69} +302.675 q^{71} -457.563 q^{73} +(69.9685 + 109.451i) q^{75} +(770.430 + 1334.42i) q^{77} +(420.848 - 728.929i) q^{79} +(-245.044 + 686.582i) q^{81} +(394.090 - 682.584i) q^{83} +(213.005 + 368.936i) q^{85} +(445.702 + 697.205i) q^{87} +1119.35 q^{89} +1467.65 q^{91} +(-1653.34 + 74.7763i) q^{93} +(187.937 + 325.516i) q^{95} +(-598.850 + 1037.24i) q^{97} +(-1684.04 + 152.642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 5 q^{3} - 35 q^{5} - 8 q^{7} + 5 q^{9} - 27 q^{11} - 32 q^{13} - 20 q^{15} + 246 q^{17} - 134 q^{19} + 28 q^{21} - 42 q^{23} - 175 q^{25} - 484 q^{27} - 324 q^{29} - 98 q^{31} + 657 q^{33} + 80 q^{35}+ \cdots + 270 q^{99}+O(q^{100}) \) 14 * q + 5 * q^3 - 35 * q^5 - 8 * q^7 + 5 * q^9 - 27 * q^11 - 32 * q^13 - 20 * q^15 + 246 * q^17 - 134 * q^19 + 28 * q^21 - 42 * q^23 - 175 * q^25 - 484 * q^27 - 324 * q^29 - 98 * q^31 + 657 * q^33 + 80 * q^35 + 712 * q^37 - 848 * q^39 - 339 * q^41 - 119 * q^43 - 125 * q^45 + 96 * q^47 - 813 * q^49 + 1383 * q^51 + 1716 * q^53 + 270 * q^55 - 599 * q^57 - 549 * q^59 - 260 * q^61 - 632 * q^63 - 160 * q^65 - 881 * q^67 + 666 * q^69 + 684 * q^71 + 1474 * q^73 - 25 * q^75 + 456 * q^77 - 1886 * q^79 + 353 * q^81 + 132 * q^83 - 615 * q^85 + 4302 * q^87 + 792 * q^89 + 2528 * q^91 - 4904 * q^93 + 335 * q^95 - 1991 * q^97 + 270 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more