LMFDB - Embedded newform 189.4.g.a.100.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(100,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("189.100");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.14
Character	$\chi$	$=$	189.100
Dual form			189.4.g.a.172.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.667800 + 1.15666i) q^{2} +(3.10809 - 5.38337i) q^{4} -9.00469 q^{5} +(-14.2234 + 11.8615i) q^{7} +18.9871 q^{8} +O(q^{10})$	\(q+(0.667800 + 1.15666i) q^{2} +(3.10809 - 5.38337i) q^{4} -9.00469 q^{5} +(-14.2234 + 11.8615i) q^{7} +18.9871 q^{8} +(-6.01333 - 10.4154i) q^{10} -29.3524 q^{11} +(-21.1758 - 36.6776i) q^{13} +(-23.2181 - 8.53053i) q^{14} +(-12.1851 - 21.1052i) q^{16} +(2.56927 + 4.45010i) q^{17} +(-71.2462 + 123.402i) q^{19} +(-27.9874 + 48.4756i) q^{20} +(-19.6015 - 33.9509i) q^{22} -178.083 q^{23} -43.9155 q^{25} +(28.2824 - 48.9866i) q^{26} +(19.6474 + 113.436i) q^{28} +(109.202 - 189.143i) q^{29} +(-73.9272 + 128.046i) q^{31} +(92.2229 - 159.735i) q^{32} +(-3.43151 + 5.94356i) q^{34} +(128.077 - 106.809i) q^{35} +(-21.2781 + 36.8547i) q^{37} -190.313 q^{38} -170.973 q^{40} +(-83.7600 - 145.077i) q^{41} +(121.454 - 210.365i) q^{43} +(-91.2299 + 158.015i) q^{44} +(-118.924 - 205.982i) q^{46} +(-38.2567 - 66.2626i) q^{47} +(61.6086 - 337.422i) q^{49} +(-29.3267 - 50.7954i) q^{50} -263.265 q^{52} +(181.368 + 314.138i) q^{53} +264.310 q^{55} +(-270.061 + 225.216i) q^{56} +291.699 q^{58} +(-60.7676 + 105.253i) q^{59} +(321.236 + 556.396i) q^{61} -197.474 q^{62} +51.3838 q^{64} +(190.682 + 330.271i) q^{65} +(81.4788 - 141.125i) q^{67} +31.9420 q^{68} +(209.072 + 76.8148i) q^{70} +833.862 q^{71} +(-62.4792 - 108.217i) q^{73} -56.8380 q^{74} +(442.879 + 767.089i) q^{76} +(417.490 - 348.164i) q^{77} +(-421.425 - 729.929i) q^{79} +(109.723 + 190.046i) q^{80} +(111.870 - 193.764i) q^{82} +(-566.958 + 982.000i) q^{83} +(-23.1355 - 40.0718i) q^{85} +324.428 q^{86} -557.318 q^{88} +(248.052 - 429.639i) q^{89} +(736.244 + 270.502i) q^{91} +(-553.497 + 958.685i) q^{92} +(51.0957 - 88.5003i) q^{94} +(641.550 - 1111.20i) q^{95} +(-128.912 + 223.282i) q^{97} +(431.425 - 154.070i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) $ 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8	$ 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} + 10 q^{11} - 14 q^{13} + 79 q^{14} - 247 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} - 186 q^{23} + 698 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} + 61 q^{31} + 163 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} - 1522 q^{38} + 36 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} + 1005 q^{47} - 277 q^{49} - 239 q^{50} + 670 q^{52} - 258 q^{53} - 870 q^{55} - 714 q^{56} - 474 q^{58} + 1665 q^{59} + 439 q^{61} - 1812 q^{62} + 872 q^{64} + 613 q^{65} + 295 q^{67} - 2748 q^{68} - 1044 q^{70} - 636 q^{71} - 338 q^{73} + 2238 q^{74} + 1006 q^{76} + 2909 q^{77} + 133 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} - 6686 q^{86} - 738 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} - 1191 q^{94} - 3083 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) $ 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 + 10 * q^11 - 14 * q^13 + 79 * q^14 - 247 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 - 186 * q^23 + 698 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 + 61 * q^31 + 163 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 - 1522 * q^38 + 36 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 + 1005 * q^47 - 277 * q^49 - 239 * q^50 + 670 * q^52 - 258 * q^53 - 870 * q^55 - 714 * q^56 - 474 * q^58 + 1665 * q^59 + 439 * q^61 - 1812 * q^62 + 872 * q^64 + 613 * q^65 + 295 * q^67 - 2748 * q^68 - 1044 * q^70 - 636 * q^71 - 338 * q^73 + 2238 * q^74 + 1006 * q^76 + 2909 * q^77 + 133 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 - 6686 * q^86 - 738 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 - 1191 * q^94 - 3083 * q^95 - 266 * q^97 - 3601 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.667800	+	1.15666i	0.236103	+	0.408942i	0.959593	−	0.281393i	$-0.0907965\pi$
$2$	0.667800	+	1.15666i	0.236103	+	0.408942i	−0.723490	+	0.690335i	$0.757463\pi$
$3$		0			0
$3$		0			0
$4$	3.10809	−	5.38337i	0.388511	−	0.672921i
$5$	−9.00469			−0.805404			−0.402702	−	0.915331i	$-0.631929\pi$
$5$	−9.00469			−0.805404			−0.402702	+	0.915331i	$0.631929\pi$
$6$		0			0
$7$	−14.2234	+	11.8615i	−0.767990	+	0.640462i
$7$	−14.2234	+	11.8615i	−0.767990	+	0.640462i
$8$	18.9871			0.839120
$9$		0			0
$10$	−6.01333	−	10.4154i	−0.190158	−	0.329364i
$11$	−29.3524			−0.804554			−0.402277	−	0.915518i	$-0.631781\pi$
$11$	−29.3524			−0.804554			−0.402277	+	0.915518i	$0.631781\pi$
$12$		0			0
$13$	−21.1758	−	36.6776i	−0.451779	−	0.782504i	0.546718	−	0.837317i	$-0.315877\pi$
$13$	−21.1758	−	36.6776i	−0.451779	−	0.782504i	−0.998497	+	0.0548133i	$0.982544\pi$
$14$	−23.2181	−	8.53053i	−0.443236	−	0.162849i
$15$		0			0
$16$	−12.1851	−	21.1052i	−0.190392	−	0.329769i
$17$	2.56927	+	4.45010i	0.0366552	+	0.0634888i	0.883771	−	0.467920i	$-0.154996\pi$
$17$	2.56927	+	4.45010i	0.0366552	+	0.0634888i	−0.847116	+	0.531408i	$0.821663\pi$
$18$		0			0
$19$	−71.2462	+	123.402i	−0.860263	+	1.49002i	0.0114121	+	0.999935i	$0.496367\pi$
$19$	−71.2462	+	123.402i	−0.860263	+	1.49002i	−0.871675	+	0.490084i	$0.836966\pi$
$20$	−27.9874	+	48.4756i	−0.312908	+	0.541973i
$21$		0			0
$22$	−19.6015	−	33.9509i	−0.189957	−	0.329016i
$23$	−178.083			−1.61447			−0.807235	−	0.590230i	$-0.799037\pi$
$23$	−178.083			−1.61447			−0.807235	+	0.590230i	$0.799037\pi$
$24$		0			0
$25$	−43.9155			−0.351324
$26$	28.2824	−	48.9866i	0.213332	−	0.369503i
$27$		0			0
$28$	19.6474	+	113.436i	0.132608	+	0.765623i
$29$	109.202	−	189.143i	0.699249	−	1.21114i	−0.269478	−	0.963007i	$-0.586851\pi$
$29$	109.202	−	189.143i	0.699249	−	1.21114i	0.968727	−	0.248129i	$-0.0798156\pi$
$30$		0			0
$31$	−73.9272	+	128.046i	−0.428314	+	0.741861i	−0.996723	−	0.0808847i	$-0.974225\pi$
$31$	−73.9272	+	128.046i	−0.428314	+	0.741861i	0.568410	+	0.822745i	$0.307559\pi$
$32$	92.2229	−	159.735i	0.509464	−	0.882418i
$33$		0			0
$34$	−3.43151	+	5.94356i	−0.0173088	+	0.0299797i
$35$	128.077	−	106.809i	0.618542	−	0.515831i
$36$		0			0
$37$	−21.2781	+	36.8547i	−0.0945431	+	0.163753i	−0.909418	−	0.415884i	$-0.863472\pi$
$37$	−21.2781	+	36.8547i	−0.0945431	+	0.163753i	0.814875	+	0.579637i	$0.196806\pi$
$38$	−190.313			−0.812442
$39$		0			0
$40$	−170.973			−0.675831
$41$	−83.7600	−	145.077i	−0.319051	−	0.552613i	0.661239	−	0.750175i	$-0.270031\pi$
$41$	−83.7600	−	145.077i	−0.319051	−	0.552613i	−0.980290	+	0.197562i	$0.936698\pi$
$42$		0			0
$43$	121.454	−	210.365i	0.430734	−	0.746054i	−0.566202	−	0.824266i	$-0.691588\pi$
$43$	121.454	−	210.365i	0.430734	−	0.746054i	0.996937	+	0.0782125i	$0.0249213\pi$
$44$	−91.2299	+	158.015i	−0.312578	+	0.541401i
$45$		0			0
$46$	−118.924	−	205.982i	−0.381181	−	0.660225i
$47$	−38.2567	−	66.2626i	−0.118730	−	0.205647i	0.800535	−	0.599287i	$-0.204549\pi$
$47$	−38.2567	−	66.2626i	−0.118730	−	0.205647i	−0.919265	+	0.393640i	$0.871216\pi$
$48$		0			0
$49$	61.6086	−	337.422i	0.179617	−	0.983737i
$50$	−29.3267	−	50.7954i	−0.0829485	−	0.143671i
$51$		0			0
$52$	−263.265			−0.702084
$53$	181.368	+	314.138i	0.470053	+	0.814155i	0.999414	−	0.0342417i	$-0.0109016\pi$
$53$	181.368	+	314.138i	0.470053	+	0.814155i	−0.529361	+	0.848397i	$0.677568\pi$
$54$		0			0
$55$	264.310			0.647991
$56$	−270.061	+	225.216i	−0.644435	+	0.537424i
$57$		0			0
$58$	291.699			0.660379
$59$	−60.7676	+	105.253i	−0.134089	+	0.232249i	−0.925249	−	0.379360i	$-0.876144\pi$
$59$	−60.7676	+	105.253i	−0.134089	+	0.232249i	0.791160	+	0.611609i	$0.209478\pi$
$60$		0			0
$61$	321.236	+	556.396i	0.674262	+	1.16786i	0.976684	+	0.214683i	$0.0688717\pi$
$61$	321.236	+	556.396i	0.674262	+	1.16786i	−0.302421	+	0.953174i	$0.597795\pi$
$62$	−197.474			−0.404504
$63$		0			0
$64$	51.3838			0.100359
$65$	190.682	+	330.271i	0.363864	+	0.630232i
$66$		0			0
$67$	81.4788	−	141.125i	0.148570	−	0.257332i	−0.782129	−	0.623117i	$-0.785866\pi$
$67$	81.4788	−	141.125i	0.148570	−	0.257332i	0.930699	+	0.365785i	$0.119199\pi$
$68$	31.9420			0.0569639
$69$		0			0
$70$	209.072	+	76.8148i	0.356985	+	0.131159i
$71$	833.862			1.39382			0.696910	−	0.717159i	$-0.254558\pi$
$71$	833.862			1.39382			0.696910	+	0.717159i	$0.254558\pi$
$72$		0			0
$73$	−62.4792	−	108.217i	−0.100173	−	0.173505i	0.811583	−	0.584238i	$-0.198606\pi$
$73$	−62.4792	−	108.217i	−0.100173	−	0.173505i	−0.911756	+	0.410733i	$0.865273\pi$
$74$	−56.8380			−0.0892876
$75$		0			0
$76$	442.879	+	767.089i	0.668443	+	1.15778i
$77$	417.490	−	348.164i	0.617889	−	0.515286i
$78$		0			0
$79$	−421.425	−	729.929i	−0.600177	−	1.03954i	−0.992794	−	0.119835i	$-0.961763\pi$
$79$	−421.425	−	729.929i	−0.600177	−	1.03954i	0.392616	−	0.919702i	$-0.371570\pi$
$80$	109.723	+	190.046i	0.153343	+	0.265598i
$81$		0			0
$82$	111.870	−	193.764i	0.150658	−	0.260947i
$83$	−566.958	+	982.000i	−0.749780	+	1.29866i	0.198148	+	0.980172i	$0.436507\pi$
$83$	−566.958	+	982.000i	−0.749780	+	1.29866i	−0.947928	+	0.318485i	$0.896826\pi$
$84$		0			0
$85$	−23.1355	−	40.0718i	−0.0295223	−	0.0511341i
$86$	324.428			0.406790
$87$		0			0
$88$	−557.318			−0.675117
$89$	248.052	−	429.639i	0.295432	−	0.511704i	−0.679653	−	0.733534i	$-0.737870\pi$
$89$	248.052	−	429.639i	0.295432	−	0.511704i	0.975085	+	0.221830i	$0.0712029\pi$
$90$		0			0
$91$	736.244	+	270.502i	0.848125	+	0.311608i
$92$	−553.497	+	958.685i	−0.627240	+	1.08641i
$93$		0			0
$94$	51.0957	−	88.5003i	0.0560651	−	0.0971075i
$95$	641.550	−	1111.20i	0.692860	−	1.20007i
$96$		0			0
$97$	−128.912	+	223.282i	−0.134938	+	0.233720i	−0.925574	−	0.378567i	$-0.876417\pi$
$97$	−128.912	+	223.282i	−0.134938	+	0.233720i	0.790636	+	0.612287i	$0.209750\pi$
$98$	431.425	−	154.070i	0.444699	−	0.158810i
$99$		0			0
$100$	−136.493	+	236.413i	−0.136493	+	0.236413i
$101$	808.041			0.796070			0.398035	−	0.917370i	$-0.369692\pi$
$101$	808.041			0.796070			0.398035	+	0.917370i	$0.369692\pi$
$102$		0			0
$103$	301.776			0.288688			0.144344	−	0.989528i	$-0.453893\pi$
$103$	301.776			0.288688			0.144344	+	0.989528i	$0.453893\pi$
$104$	−402.068	−	696.402i	−0.379096	−	0.656614i
$105$		0			0
$106$	−242.235	+	419.563i	−0.221961	+	0.384449i
$107$	−575.282	+	996.417i	−0.519762	+	0.900255i	0.479974	+	0.877283i	$0.340646\pi$
$107$	−575.282	+	996.417i	−0.519762	+	0.900255i	−0.999736	+	0.0229719i	$0.992687\pi$
$108$		0			0
$109$	−901.841	−	1562.04i	−0.792484	−	1.37262i	−0.924425	−	0.381365i	$-0.875454\pi$
$109$	−901.841	−	1562.04i	−0.792484	−	1.37262i	0.131941	−	0.991258i	$-0.457879\pi$
$110$	176.506	+	305.717i	0.152992	+	0.264991i
$111$		0			0
$112$	423.654	+	155.654i	0.357424	+	0.131320i
$113$	610.273	+	1057.02i	0.508050	+	0.879968i	0.999957	+	0.00932039i	$0.00296681\pi$
$113$	610.273	+	1057.02i	0.508050	+	0.879968i	−0.491907	+	0.870648i	$0.663700\pi$
$114$		0			0
$115$	1603.58			1.30030
$116$	−678.816	−	1175.74i	−0.543332	−	0.941079i
$117$		0			0
$118$	−162.322			−0.126635
$119$	−89.3287	−	32.8201i	−0.0688130	−	0.0252824i
$120$		0			0
$121$	−469.435			−0.352694
$122$	−429.042	+	743.123i	−0.318391	+	0.551469i
$123$		0			0
$124$	459.544	+	795.954i	0.332809	+	0.576442i
$125$	1521.03			1.08836
$126$		0			0
$127$	1090.19			0.761724			0.380862	−	0.924632i	$-0.375627\pi$
$127$	1090.19			0.761724			0.380862	+	0.924632i	$0.375627\pi$
$128$	−703.469	−	1218.44i	−0.485769	−	0.841377i
$129$		0			0
$130$	−254.675	+	441.110i	−0.171819	+	0.297599i
$131$	−2603.46			−1.73638			−0.868189	−	0.496234i	$-0.834716\pi$
$131$	−2603.46			−1.73638			−0.868189	+	0.496234i	$0.834716\pi$
$132$		0			0
$133$	−450.375	−	2600.28i	−0.293627	−	1.69529i
$134$	217.646			0.140312
$135$		0			0
$136$	48.7830	+	84.4946i	0.0307581	+	0.0532747i
$137$	−12.1486			−0.00757613			−0.00378806	−	0.999993i	$-0.501206\pi$
$137$	−12.1486			−0.00757613			−0.00378806	+	0.999993i	$0.501206\pi$
$138$		0			0
$139$	−938.072	−	1624.79i	−0.572419	−	0.991458i	−0.996317	−	0.0857483i	$-0.972672\pi$
$139$	−938.072	−	1624.79i	−0.572419	−	0.991458i	0.423898	−	0.905710i	$-0.360661\pi$
$140$	−176.919	−	1021.46i	−0.106803	−	0.616636i
$141$		0			0
$142$	556.853	+	964.497i	0.329085	+	0.569992i
$143$	621.562	+	1076.58i	0.363480	+	0.629566i
$144$		0			0
$145$	−983.327	+	1703.17i	−0.563178	+	0.975454i
$146$	83.4472	−	144.535i	0.0473023	−	0.0819300i
$147$		0			0
$148$	132.268	+	229.095i	0.0734620	+	0.127240i
$149$	−906.270			−0.498285			−0.249143	−	0.968467i	$-0.580149\pi$
$149$	−906.270			−0.498285			−0.249143	+	0.968467i	$0.580149\pi$
$150$		0			0
$151$	333.990			0.179998			0.0899989	−	0.995942i	$-0.471314\pi$
$151$	333.990			0.179998			0.0899989	+	0.995942i	$0.471314\pi$
$152$	−1352.76	+	2343.05i	−0.721864	+	1.25030i
$153$		0			0
$154$	681.509	+	250.392i	0.356607	+	0.131020i
$155$	665.692	−	1153.01i	0.344966	−	0.597498i
$156$		0			0
$157$	−686.495	+	1189.04i	−0.348970	+	0.604434i	−0.986067	−	0.166350i	$-0.946802\pi$
$157$	−686.495	+	1189.04i	−0.348970	+	0.604434i	0.637097	+	0.770784i	$0.280135\pi$
$158$	562.855	−	974.893i	0.283407	−	0.490876i
$159$		0			0
$160$	−830.439	+	1438.36i	−0.410325	+	0.710703i
$161$	2532.94	−	2112.33i	1.23990	−	1.03401i
$162$		0			0
$163$	−77.5751	+	134.364i	−0.0372770	+	0.0645657i	−0.884062	−	0.467370i	$-0.845202\pi$
$163$	−77.5751	+	134.364i	−0.0372770	+	0.0645657i	0.846785	+	0.531935i	$0.178535\pi$
$164$	−1041.33			−0.495820
$165$		0			0
$166$	−1514.46			−0.708101
$167$	−656.542	−	1137.16i	−0.304220	−	0.526924i	0.672867	−	0.739763i	$-0.265062\pi$
$167$	−656.542	−	1137.16i	−0.304220	−	0.526924i	−0.977087	+	0.212839i	$0.931729\pi$
$168$		0			0
$169$	201.667	−	349.298i	0.0917922	−	0.158989i
$170$	30.8997	−	53.5199i	0.0139406	−	0.0241458i
$171$		0			0
$172$	−754.980	−	1307.66i	−0.334690	−	0.579700i
$173$	96.5500	+	167.230i	0.0424310	+	0.0734926i	0.886461	−	0.462803i	$-0.153156\pi$
$173$	96.5500	+	167.230i	0.0424310	+	0.0734926i	−0.844030	+	0.536296i	$0.819823\pi$
$174$		0			0
$175$	624.626	−	520.904i	0.269813	−	0.225009i
$176$	357.663	+	619.490i	0.153181	+	0.265317i
$177$		0			0
$178$	662.597			0.279010
$179$	−1997.68	−	3460.08i	−0.834152	−	1.44479i	−0.894719	−	0.446630i	$-0.852624\pi$
$179$	−1997.68	−	3460.08i	−0.834152	−	1.44479i	0.0605663	−	0.998164i	$-0.480709\pi$
$180$		0			0
$181$	−4626.29			−1.89983			−0.949916	−	0.312506i	$-0.898831\pi$
$181$	−4626.29			−1.89983			−0.949916	+	0.312506i	$0.898831\pi$
$182$	178.784	+	1032.23i	0.0728152	+	0.420406i
$183$		0			0
$184$	−3381.28			−1.35473
$185$	191.603	−	331.865i	0.0761454	−	0.131888i
$186$		0			0
$187$	−75.4143	−	130.621i	−0.0294911	−	0.0510801i
$188$	−475.621			−0.184512
$189$		0			0
$190$	1713.71			0.654344
$191$	−1204.08	−	2085.52i	−0.456146	−	0.790069i	0.542607	−	0.839987i	$-0.317437\pi$
$191$	−1204.08	−	2085.52i	−0.456146	−	0.790069i	−0.998753	+	0.0499181i	$0.984104\pi$
$192$		0			0
$193$	−452.017	+	782.917i	−0.168585	+	0.291998i	−0.937923	−	0.346845i	$-0.887253\pi$
$193$	−452.017	+	782.917i	−0.168585	+	0.291998i	0.769338	+	0.638843i	$0.220586\pi$
$194$	−344.349			−0.127437
$195$		0			0
$196$	−1624.98	−	1380.40i	−0.592194	−	0.503060i
$197$	−3416.80			−1.23572			−0.617860	−	0.786288i	$-0.712000\pi$
$197$	−3416.80			−1.23572			−0.617860	+	0.786288i	$0.712000\pi$
$198$		0			0
$199$	1312.92	+	2274.04i	0.467691	+	0.810064i	0.999318	−	0.0369141i	$-0.0117528\pi$
$199$	1312.92	+	2274.04i	0.467691	+	0.810064i	−0.531628	+	0.846978i	$0.678419\pi$
$200$	−833.828			−0.294803
$201$		0			0
$202$	539.609	+	934.631i	0.187954	+	0.325546i
$203$	690.305	+	3985.54i	0.238670	+	1.37798i
$204$		0			0
$205$	754.233	+	1306.37i	0.256965	+	0.445077i
$206$	201.526	+	349.053i	0.0681601	+	0.118057i
$207$		0			0
$208$	−516.060	+	893.842i	−0.172030	+	0.297965i
$209$	2091.25	−	3622.15i	0.692128	−	1.19880i
$210$		0			0
$211$	−417.588	−	723.284i	−0.136246	−	0.235985i	0.789827	−	0.613330i	$-0.210170\pi$
$211$	−417.588	−	723.284i	−0.136246	−	0.235985i	−0.926073	+	0.377345i	$0.876837\pi$
$212$	2254.83			0.730482
$213$		0			0
$214$	−1536.69			−0.490869
$215$	−1093.66	+	1894.27i	−0.346915	+	0.600875i
$216$		0			0
$217$	−467.322	−	2698.13i	−0.146193	−	0.844060i
$218$	1204.50	−	2086.25i	0.374215	−	0.648160i
$219$		0			0
$220$	821.497	−	1422.88i	0.251752	−	0.436047i
$221$	108.813	−	188.469i	0.0331201	−	0.0573657i
$222$		0			0
$223$	−1077.64	+	1866.53i	−0.323606	+	0.560501i	−0.981229	−	0.192845i	$-0.938228\pi$
$223$	−1077.64	+	1866.53i	−0.323606	+	0.560501i	0.657624	+	0.753347i	$0.271562\pi$
$224$	582.976	+	3365.87i	0.173892	+	1.00398i
$225$		0			0
$226$	−815.080	+	1411.76i	−0.239904	+	0.415526i
$227$	1404.59			0.410687			0.205344	−	0.978690i	$-0.434169\pi$
$227$	1404.59			0.410687			0.205344	+	0.978690i	$0.434169\pi$
$228$		0			0
$229$	5749.00			1.65897			0.829487	−	0.558527i	$-0.188633\pi$
$229$	5749.00			1.65897			0.829487	+	0.558527i	$0.188633\pi$
$230$	1070.87	+	1854.80i	0.307005	+	0.531748i
$231$		0			0
$232$	2073.42	−	3591.27i	0.586754	−	1.01629i
$233$	−245.476	+	425.178i	−0.0690202	+	0.119546i	−0.898470	−	0.439034i	$-0.855321\pi$
$233$	−245.476	+	425.178i	−0.0690202	+	0.119546i	0.829450	+	0.558581i	$0.188654\pi$
$234$		0			0
$235$	344.490	+	596.675i	0.0956258	+	0.165629i
$236$	377.742	+	654.268i	0.104190	+	0.180463i
$237$		0			0
$238$	−21.6919	−	125.240i	−0.00590789	−	0.0341098i
$239$	3286.81	+	5692.92i	0.889565	+	1.54077i	0.840391	+	0.541981i	$0.182325\pi$
$239$	3286.81	+	5692.92i	0.889565	+	1.54077i	0.0491738	+	0.998790i	$0.484341\pi$
$240$		0			0
$241$	−949.494			−0.253785			−0.126893	−	0.991916i	$-0.540500\pi$
$241$	−949.494			−0.253785			−0.126893	+	0.991916i	$0.540500\pi$
$242$	−313.489	−	542.978i	−0.0832719	−	0.144231i
$243$		0			0
$244$	3993.71			1.04783
$245$	−554.767	+	3038.38i	−0.144664	+	0.792306i
$246$		0			0
$247$	6034.79			1.55459
$248$	−1403.66	+	2431.22i	−0.359406	+	0.622510i
$249$		0			0
$250$	1015.74	+	1759.32i	0.256965	+	0.445077i
$251$	−5293.14			−1.33107			−0.665537	−	0.746365i	$-0.731798\pi$
$251$	−5293.14			−1.33107			−0.665537	+	0.746365i	$0.731798\pi$
$252$		0			0
$253$	5227.16			1.29893
$254$	728.030	+	1260.99i	0.179845	+	0.311501i
$255$		0			0
$256$	1145.09	−	1983.35i	0.279562	−	0.484216i
$257$	−3723.53			−0.903764			−0.451882	−	0.892078i	$-0.649247\pi$
$257$	−3723.53			−0.903764			−0.451882	+	0.892078i	$0.649247\pi$
$258$		0			0
$259$	−134.507	−	776.589i	−0.0322697	−	0.186312i
$260$	2370.63			0.565461
$261$		0			0
$262$	−1738.59	−	3011.33i	−0.409964	−	0.710078i
$263$	4578.03			1.07336			0.536680	−	0.843786i	$-0.319678\pi$
$263$	4578.03			1.07336			0.536680	+	0.843786i	$0.319678\pi$
$264$		0			0
$265$	−1633.16	−	2828.72i	−0.378582	−	0.655724i
$266$	2706.89	−	2257.40i	0.623947	−	0.520338i
$267$		0			0
$268$	−506.487	−	877.260i	−0.115443	−	0.199952i
$269$	−2948.50	−	5106.95i	−0.668302	−	1.15753i	−0.978379	−	0.206821i	$-0.933688\pi$
$269$	−2948.50	−	5106.95i	−0.668302	−	1.15753i	0.310077	−	0.950711i	$-0.399645\pi$
$270$		0			0
$271$	−2578.14	+	4465.47i	−0.577899	+	1.00095i	0.417821	+	0.908530i	$0.362794\pi$
$271$	−2578.14	+	4465.47i	−0.577899	+	1.00095i	−0.995720	+	0.0924215i	$0.970539\pi$
$272$	62.6137	−	108.450i	0.0139578	−	0.0241756i
$273$		0			0
$274$	−8.11286	−	14.0519i	−0.00178874	−	0.00309820i
$275$	1289.03			0.282659
$276$		0			0
$277$	−5054.18			−1.09630			−0.548152	−	0.836379i	$-0.684668\pi$
$277$	−5054.18			−1.09630			−0.548152	+	0.836379i	$0.684668\pi$
$278$	1252.89	−	2170.07i	0.270299	−	0.468172i
$279$		0			0
$280$	2431.81	−	2028.00i	0.519031	−	0.432844i
$281$	909.511	−	1575.32i	0.193085	−	0.334433i	−0.753186	−	0.657807i	$-0.771484\pi$
$281$	909.511	−	1575.32i	0.193085	−	0.334433i	0.946271	+	0.323375i	$0.104817\pi$
$282$		0			0
$283$	−677.482	+	1173.43i	−0.142304	+	0.246478i	−0.928364	−	0.371672i	$-0.878784\pi$
$283$	−677.482	+	1173.43i	−0.142304	+	0.246478i	0.786060	+	0.618151i	$0.212118\pi$
$284$	2591.72	−	4488.98i	0.541514	−	0.937930i
$285$		0			0
$286$	−830.158	+	1437.88i	−0.171637	+	0.297285i
$287$	2912.18	+	1069.96i	0.598956	+	0.220061i
$288$		0			0
$289$	2443.30	−	4231.92i	0.497313	−	0.861371i
$290$	−2626.66			−0.531872
$291$		0			0
$292$	−776.764			−0.155673
$293$	598.046	+	1035.85i	0.119243	+	0.206535i	0.919468	−	0.393165i	$-0.128620\pi$
$293$	598.046	+	1035.85i	0.119243	+	0.206535i	−0.800225	+	0.599700i	$0.795287\pi$
$294$		0			0
$295$	547.194	−	947.767i	0.107996	−	0.187055i
$296$	−404.009	+	699.765i	−0.0793330	+	0.137409i
$297$		0			0
$298$	−605.206	−	1048.25i	−0.117647	−	0.203770i
$299$	3771.05	+	6531.66i	0.729383	+	1.26333i
$300$		0			0
$301$	767.758	+	4432.73i	0.147019	+	0.848831i
$302$	223.038	+	386.313i	0.0424980	+	0.0736087i
$303$		0			0
$304$	3472.57			0.655150
$305$	−2892.63	−	5010.18i	−0.543054	−	0.940597i
$306$		0			0
$307$	3157.09			0.586921			0.293460	−	0.955971i	$-0.405193\pi$
$307$	3157.09			0.586921			0.293460	+	0.955971i	$0.405193\pi$
$308$	−576.699	−	3329.63i	−0.106690	−	0.615984i
$309$		0			0
$310$	1778.20			0.325789
$311$	720.189	−	1247.40i	0.131313	−	0.227440i	−0.792870	−	0.609390i	$-0.791414\pi$
$311$	720.189	−	1247.40i	0.131313	−	0.227440i	0.924183	+	0.381951i	$0.124748\pi$
$312$		0			0
$313$	−2707.65	−	4689.79i	−0.488963	−	0.846909i	0.510956	−	0.859607i	$-0.329291\pi$
$313$	−2707.65	−	4689.79i	−0.488963	−	0.846909i	−0.999919	+	0.0126978i	$0.995958\pi$
$314$	−1833.77			−0.329571
$315$		0			0
$316$	−5239.30			−0.932702
$317$	2246.86	+	3891.67i	0.398095	+	0.689521i	0.993491	−	0.113911i	$-0.0363380\pi$
$317$	2246.86	+	3891.67i	0.398095	+	0.689521i	−0.595396	+	0.803433i	$0.703005\pi$
$318$		0			0
$319$	−3205.33	+	5551.80i	−0.562583	+	0.974423i
$320$	−462.695			−0.0808295
$321$		0			0
$322$	4134.75	+	1519.14i	0.715592	+	0.262914i
$323$	−732.202			−0.126133
$324$		0			0
$325$	929.947	+	1610.72i	0.158721	+	0.274912i
$326$	−207.219			−0.0352048
$327$		0			0
$328$	−1590.36	−	2754.58i	−0.267722	−	0.463709i
$329$	1330.12	+	488.695i	0.222892	+	0.0818924i
$330$		0			0
$331$	4933.61	+	8545.26i	0.819262	+	1.41900i	0.906227	+	0.422792i	$0.138950\pi$
$331$	4933.61	+	8545.26i	0.819262	+	1.41900i	−0.0869648	+	0.996211i	$0.527717\pi$
$332$	3524.31	+	6104.29i	0.582596	+	1.00909i
$333$		0			0
$334$	876.876	−	1518.79i	0.143654	−	0.248817i
$335$	−733.692	+	1270.79i	−0.119659	+	0.207256i
$336$		0			0
$337$	1310.64	+	2270.10i	0.211855	+	0.366944i	0.952295	−	0.305178i	$-0.0987161\pi$
$337$	1310.64	+	2270.10i	0.211855	+	0.366944i	−0.740440	+	0.672123i	$0.765383\pi$
$338$	538.694			0.0866895
$339$		0			0
$340$	−287.628			−0.0458789
$341$	2169.94	−	3758.45i	0.344601	−	0.596867i
$342$		0			0
$343$	3126.05	+	5530.05i	0.492102	+	0.870538i
$344$	2306.06	−	3994.22i	0.361438	−	0.626028i
$345$		0			0
$346$	−128.952	+	223.352i	−0.0200362	+	0.0347036i
$347$	−6045.62	+	10471.3i	−0.935290	+	1.61997i	−0.161175	+	0.986926i	$0.551528\pi$
$347$	−6045.62	+	10471.3i	−0.935290	+	1.61997i	−0.774115	+	0.633045i	$0.781805\pi$
$348$		0			0
$349$	2.47828	−	4.29251i	0.000380113	−	0.000658375i	−0.865835	−	0.500329i	$-0.833212\pi$
$349$	2.47828	−	4.29251i	0.000380113	−	0.000658375i	0.866215	+	0.499671i	$0.166546\pi$
$350$	1019.64	+	374.622i	0.155719	+	0.0572125i
$351$		0			0
$352$	−2706.96	+	4688.60i	−0.409891	+	0.709952i
$353$	523.540			0.0789383			0.0394691	−	0.999221i	$-0.487433\pi$
$353$	523.540			0.0789383			0.0394691	+	0.999221i	$0.487433\pi$
$354$		0			0
$355$	−7508.67			−1.12259
$356$	−1541.94	−	2670.71i	−0.229557	−	0.397605i
$357$		0			0
$358$	2668.09	−	4621.27i	0.393891	−	0.682240i
$359$	−596.823	+	1033.73i	−0.0877412	+	0.151972i	−0.906556	−	0.422086i	$-0.861298\pi$
$359$	−596.823	+	1033.73i	−0.0877412	+	0.151972i	0.818815	+	0.574058i	$0.194632\pi$
$360$		0			0
$361$	−6722.54	−	11643.8i	−0.980105	−	1.69759i
$362$	−3089.43	−	5351.06i	−0.448556	−	0.776921i
$363$		0			0
$364$	3744.52	−	3122.73i	0.539193	−	0.449658i
$365$	562.606	+	974.463i	0.0806799	+	0.139742i
$366$		0			0
$367$	−2795.58			−0.397624			−0.198812	−	0.980038i	$-0.563708\pi$
$367$	−2795.58			−0.397624			−0.198812	+	0.980038i	$0.563708\pi$
$368$	2169.96	+	3758.48i	0.307383	+	0.532403i
$369$		0			0
$370$	511.809			0.0719126
$371$	−6305.82	−	2316.81i	−0.882431	−	0.324212i
$372$		0			0
$373$	−6274.19			−0.870952			−0.435476	−	0.900200i	$-0.643420\pi$
$373$	−6274.19			−0.870952			−0.435476	+	0.900200i	$0.643420\pi$
$374$	100.723	−	174.458i	0.0139259	−	0.0241203i
$375$		0			0
$376$	−726.385	−	1258.14i	−0.0996288	−	0.172562i
$377$	−9249.74			−1.26362
$378$		0			0
$379$	−12176.6			−1.65031			−0.825157	−	0.564903i	$-0.808913\pi$
$379$	−12176.6			−1.65031			−0.825157	+	0.564903i	$0.808913\pi$
$380$	−3987.99	−	6907.40i	−0.538367	−	0.932479i
$381$		0			0
$382$	1608.16	−	2785.42i	0.215395	−	0.373075i
$383$	−11877.2			−1.58459			−0.792295	−	0.610138i	$-0.791114\pi$
$383$	−11877.2			−1.58459			−0.792295	+	0.610138i	$0.791114\pi$
$384$		0			0
$385$	−3759.37	+	3135.11i	−0.497651	+	0.415014i
$386$	−1207.43			−0.159214
$387$		0			0
$388$	801.338	+	1387.96i	0.104850	+	0.181605i
$389$	573.950			0.0748082			0.0374041	−	0.999300i	$-0.488091\pi$
$389$	573.950			0.0748082			0.0374041	+	0.999300i	$0.488091\pi$
$390$		0			0
$391$	−457.543	−	792.487i	−0.0591788	−	0.102501i
$392$	1169.77	−	6406.66i	0.150720	−	0.825473i
$393$		0			0
$394$	−2281.74	−	3952.09i	−0.291757	−	0.505338i
$395$	3794.80	+	6572.79i	0.483386	+	0.837248i
$396$		0			0
$397$	−3496.01	+	6055.26i	−0.441964	+	0.765503i	−0.997835	−	0.0657648i	$-0.979051\pi$
$397$	−3496.01	+	6055.26i	−0.441964	+	0.765503i	0.555872	+	0.831268i	$0.312385\pi$
$398$	−1753.54	+	3037.21i	−0.220846	+	0.382517i
$399$		0			0
$400$	535.115	+	926.846i	0.0668894	+	0.115856i
$401$	1591.12			0.198147			0.0990735	−	0.995080i	$-0.468412\pi$
$401$	1591.12			0.198147			0.0990735	+	0.995080i	$0.468412\pi$
$402$		0			0
$403$	6261.88			0.774012
$404$	2511.46	−	4349.98i	0.309282	−	0.535692i
$405$		0			0
$406$	−4148.95	+	3460.00i	−0.507164	+	0.422948i
$407$	624.563	−	1081.78i	0.0760650	−	0.131748i
$408$		0			0
$409$	2558.02	−	4430.61i	0.309256	−	0.535647i	−0.668944	−	0.743313i	$-0.733253\pi$
$409$	2558.02	−	4430.61i	0.309256	−	0.535647i	0.978200	+	0.207666i	$0.0665866\pi$
$410$	−1007.35	+	1744.79i	−0.121341	+	0.210168i
$411$		0			0
$412$	937.946	−	1624.57i	0.112158	−	0.194264i
$413$	−384.135	−	2217.84i	−0.0457677	−	0.264244i
$414$		0			0
$415$	5105.29	−	8842.61i	0.603876	−	1.04594i
$416$	−7811.59			−0.920660
$417$		0			0
$418$	5586.14			0.653653
$419$	−690.084	−	1195.26i	−0.0804602	−	0.139361i	0.822988	−	0.568059i	$-0.192306\pi$
$419$	−690.084	−	1195.26i	−0.0804602	−	0.139361i	−0.903448	+	0.428698i	$0.858972\pi$
$420$		0			0
$421$	−2454.61	+	4251.52i	−0.284158	+	0.492176i	−0.972405	−	0.233301i	$-0.925047\pi$
$421$	−2454.61	+	4251.52i	−0.284158	+	0.492176i	0.688247	+	0.725477i	$0.258381\pi$
$422$	557.730	−	966.017i	0.0643362	−	0.111434i
$423$		0			0
$424$	3443.65	+	5964.58i	0.394430	+	0.683173i
$425$	−112.831	−	195.428i	−0.0128779	−	0.0223051i
$426$		0			0
$427$	−11168.8	−	4103.49i	−1.26579	−	0.465063i
$428$	3576.05	+	6193.90i	0.403867	+	0.699518i
$429$		0			0
$430$	−2921.37			−0.327631
$431$	2673.64	+	4630.87i	0.298804	+	0.517544i	0.975863	−	0.218385i	$-0.0700790\pi$
$431$	2673.64	+	4630.87i	0.298804	+	0.517544i	−0.677059	+	0.735929i	$0.736746\pi$
$432$		0			0
$433$	6346.11			0.704329			0.352165	−	0.935938i	$-0.385446\pi$
$433$	6346.11			0.704329			0.352165	+	0.935938i	$0.385446\pi$
$434$	2808.75	−	2342.35i	0.310655	−	0.259069i
$435$		0			0
$436$	−11212.0			−1.23155
$437$	12687.7	−	21975.8i	1.38887	−	2.40559i
$438$		0			0
$439$	4810.92	+	8332.76i	0.523036	+	0.905925i	0.999641	+	0.0268073i	$0.00853406\pi$
$439$	4810.92	+	8332.76i	0.523036	+	0.905925i	−0.476604	+	0.879118i	$0.658133\pi$
$440$	5018.48			0.543742
$441$		0			0
$442$	290.661			0.0312790
$443$	1042.81	+	1806.21i	0.111841	+	0.193714i	0.916513	−	0.400006i	$-0.130992\pi$
$443$	1042.81	+	1806.21i	0.111841	+	0.193714i	−0.804672	+	0.593720i	$0.797659\pi$
$444$		0			0
$445$	−2233.63	+	3868.77i	−0.237943	+	0.412129i
$446$	−2878.59			−0.305617
$447$		0			0
$448$	−730.850	+	609.490i	−0.0770746	+	0.0642761i
$449$	−10279.2			−1.08042			−0.540208	−	0.841532i	$-0.681654\pi$
$449$	−10279.2			−1.08042			−0.540208	+	0.841532i	$0.681654\pi$
$450$		0			0
$451$	2458.56	+	4258.35i	0.256694	+	0.444607i
$452$	7587.13			0.789532
$453$		0			0
$454$	937.985	+	1624.64i	0.0969644	+	0.167947i
$455$	−6629.66	−	2435.79i	−0.683084	−	0.250970i
$456$		0			0
$457$	−4873.37	−	8440.93i	−0.498833	−	0.864005i	0.501166	−	0.865351i	$-0.332905\pi$
$457$	−4873.37	−	8440.93i	−0.498833	−	0.864005i	−0.999999	+	0.00134654i	$0.999571\pi$
$458$	3839.18	+	6649.66i	0.391688	+	0.678424i
$459$		0			0
$460$	4984.07	−	8632.66i	0.505181	−	0.875000i
$461$	3900.98	−	6756.70i	0.394115	−	0.682627i	−0.598873	−	0.800844i	$-0.704385\pi$
$461$	3900.98	−	6756.70i	0.394115	−	0.682627i	0.992988	+	0.118217i	$0.0377179\pi$
$462$		0			0
$463$	3544.24	+	6138.81i	0.355756	+	0.616187i	0.987247	−	0.159196i	$-0.0508901\pi$
$463$	3544.24	+	6138.81i	0.355756	+	0.616187i	−0.631491	+	0.775383i	$0.717557\pi$
$464$	−5322.54			−0.532527
$465$		0			0
$466$	−655.716			−0.0651834
$467$	8800.70	−	15243.3i	0.872051	−	1.51044i	0.0121791	−	0.999926i	$-0.496123\pi$
$467$	8800.70	−	15243.3i	0.872051	−	1.51044i	0.859872	−	0.510510i	$-0.170543\pi$
$468$		0			0
$469$	515.059	+	2973.74i	0.0507105	+	0.292782i
$470$	−460.101	+	796.918i	−0.0451550	+	0.0782108i
$471$		0			0
$472$	−1153.80	+	1998.44i	−0.112517	+	0.194885i
$473$	−3564.97	+	6174.71i	−0.346549	+	0.600240i
$474$		0			0
$475$	3128.81	−	5419.26i	0.302231	−	0.523479i
$476$	−454.324	+	378.881i	−0.0437477	+	0.0364832i
$477$		0			0
$478$	−4389.86	+	7603.46i	−0.420057	+	0.727561i
$479$	−10984.8			−1.04782			−0.523911	−	0.851773i	$-0.675528\pi$
$479$	−10984.8			−1.04782			−0.523911	+	0.851773i	$0.675528\pi$
$480$		0			0
$481$	1802.32			0.170850
$482$	−634.072	−	1098.24i	−0.0599195	−	0.103784i
$483$		0			0
$484$	−1459.05	+	2527.14i	−0.137025	+	0.237335i
$485$	1160.81	−	2010.58i	0.108680	−	0.188239i
$486$		0			0
$487$	5700.22	+	9873.07i	0.530394	+	0.918669i	0.999371	+	0.0354587i	$0.0112892\pi$
$487$	5700.22	+	9873.07i	0.530394	+	0.918669i	−0.468977	+	0.883210i	$0.655377\pi$
$488$	6099.34	+	10564.4i	0.565787	+	0.979972i
$489$		0			0
$490$	−3884.85	+	1387.35i	−0.358163	+	0.127906i
$491$	−7398.90	−	12815.3i	−0.680056	−	1.17789i	−0.974963	−	0.222366i	$-0.928622\pi$
$491$	−7398.90	−	12815.3i	−0.680056	−	1.17789i	0.294907	−	0.955526i	$-0.404711\pi$
$492$		0			0
$493$	1122.27			0.102525
$494$	4030.03	+	6980.22i	0.367044	+	0.635739i
$495$		0			0
$496$	3603.25			0.326191
$497$	−11860.3	+	9890.87i	−1.07044	+	0.892689i
$498$		0			0
$499$	13476.4			1.20900			0.604498	−	0.796607i	$-0.293374\pi$
$499$	13476.4			1.20900			0.604498	+	0.796607i	$0.293374\pi$
$500$	4727.50	−	8188.27i	0.422841	−	0.732381i
$501$		0			0
$502$	−3534.75	−	6122.37i	−0.314270	−	0.544332i
$503$	21056.6			1.86653			0.933267	−	0.359182i	$-0.116944\pi$
$503$	21056.6			1.86653			0.933267	+	0.359182i	$0.116944\pi$
$504$		0			0
$505$	−7276.16			−0.641158
$506$	3490.70	+	6046.06i	0.306681	+	0.531186i
$507$		0			0
$508$	3388.41	−	5868.91i	0.295938	−	0.512580i
$509$	9659.36			0.841146			0.420573	−	0.907259i	$-0.361829\pi$
$509$	9659.36			0.841146			0.420573	+	0.907259i	$0.361829\pi$
$510$		0			0
$511$	2172.29	+	798.115i	0.188055	+	0.0690930i
$512$	−8196.75			−0.707517
$513$		0			0
$514$	−2486.57	−	4306.87i	−0.213381	−	0.369587i
$515$	−2717.40			−0.232511
$516$		0			0
$517$	1122.93	+	1944.97i	0.0955248	+	0.165454i
$518$	808.428	−	674.185i	0.0685719	−	0.0571853i
$519$		0			0
$520$	3620.50	+	6270.89i	0.305326	+	0.528840i
$521$	4153.71	+	7194.44i	0.349285	+	0.604979i	0.986123	−	0.166019i	$-0.0530912\pi$
$521$	4153.71	+	7194.44i	0.349285	+	0.604979i	−0.636838	+	0.770998i	$0.719758\pi$
$522$		0			0
$523$	7905.79	−	13693.2i	0.660987	−	1.14486i	−0.319370	−	0.947630i	$-0.603471\pi$
$523$	7905.79	−	13693.2i	0.660987	−	1.14486i	0.980357	−	0.197233i	$-0.0631955\pi$
$524$	−8091.78	+	14015.4i	−0.674602	+	1.16844i
$525$		0			0
$526$	3057.21	+	5295.24i	0.253423	+	0.438942i
$527$	−759.756			−0.0627998
$528$		0			0
$529$	19546.5			1.60652
$530$	2181.25	−	3778.04i	0.178769	−	0.309637i
$531$		0			0
$532$	−15398.1	−	5657.37i	−1.25487	−	0.461049i
$533$	−3547.38	+	6144.23i	−0.288281	+	0.499318i
$534$		0			0
$535$	5180.23	−	8972.43i	0.418619	−	0.725069i
$536$	1547.05	−	2679.56i	0.124668	−	0.215932i
$537$		0			0
$538$	3938.01	−	6820.84i	0.315576	−	0.546593i
$539$	−1808.36	+	9904.14i	−0.144511	+	0.791469i
$540$		0			0
$541$	8990.23	−	15571.5i	0.714455	−	1.23747i	−0.248715	−	0.968577i	$-0.580008\pi$
$541$	8990.23	−	15571.5i	0.714455	−	1.23747i	0.963169	−	0.268895i	$-0.0866585\pi$
$542$	−6886.72			−0.545775
$543$		0			0
$544$	947.781			0.0746982
$545$	8120.81	+	14065.7i	0.638270	+	1.10552i
$546$		0			0
$547$	−9366.21	+	16222.7i	−0.732121	+	1.26807i	0.223854	+	0.974623i	$0.428136\pi$
$547$	−9366.21	+	16222.7i	−0.732121	+	1.26807i	−0.955975	+	0.293448i	$0.905197\pi$
$548$	−37.7591	+	65.4006i	−0.00294341	+	0.00509813i
$549$		0			0
$550$	860.811	+	1490.97i	0.0667365	+	0.115591i
$551$	15560.4	+	26951.4i	1.20308	+	2.08379i
$552$		0			0
$553$	14652.2	+	5383.32i	1.12671	+	0.413964i
$554$	−3375.18	−	5845.98i	−0.258840	−	0.448325i
$555$		0			0
$556$	−11662.4			−0.889564
$557$	−3032.30	−	5252.10i	−0.230669	−	0.399531i	0.727336	−	0.686282i	$-0.240758\pi$
$557$	−3032.30	−	5252.10i	−0.230669	−	0.399531i	−0.958005	+	0.286751i	$0.907425\pi$
$558$		0			0
$559$	−10287.6			−0.778386
$560$	−3814.87	−	1401.61i	−0.287871	−	0.105766i
$561$		0			0
$562$	2429.48			0.182352
$563$	−8513.55	+	14745.9i	−0.637306	+	1.10385i	0.348715	+	0.937229i	$0.386618\pi$
$563$	−8513.55	+	14745.9i	−0.637306	+	1.10385i	−0.986021	+	0.166618i	$0.946715\pi$
$564$		0			0
$565$	−5495.32	−	9518.18i	−0.409186	−	0.708730i
$566$	−1809.69			−0.134394
$567$		0			0
$568$	15832.6			1.16958
$569$	−3154.28	−	5463.38i	−0.232398	−	0.402525i	0.726115	−	0.687573i	$-0.241324\pi$
$569$	−3154.28	−	5463.38i	−0.232398	−	0.402525i	−0.958513	+	0.285048i	$0.907990\pi$
$570$		0			0
$571$	−195.044	+	337.826i	−0.0142948	+	0.0247593i	−0.873084	−	0.487569i	$-0.837884\pi$
$571$	−195.044	+	337.826i	−0.0142948	+	0.0247593i	0.858790	+	0.512329i	$0.171217\pi$
$572$	7727.48			0.564864
$573$		0			0
$574$	707.172	+	4082.92i	0.0514230	+	0.296895i
$575$	7820.59			0.567202
$576$		0			0
$577$	−8361.29	−	14482.2i	−0.603267	−	1.04489i	−0.992323	−	0.123674i	$-0.960532\pi$
$577$	−8361.29	−	14482.2i	−0.603267	−	1.04489i	0.389056	−	0.921214i	$-0.372801\pi$
$578$	6526.53			0.469668
$579$		0			0
$580$	6112.53	+	10587.2i	0.437602	+	0.757949i
$581$	−3583.96	−	20692.3i	−0.255917	−	1.47756i
$582$		0			0
$583$	−5323.59	−	9220.72i	−0.378182	−	0.655031i
$584$	−1186.30	−	2054.73i	−0.0840573	−	0.145591i
$585$		0			0
$586$	−798.750	+	1383.48i	−0.0563073	+	0.0975270i
$587$	9740.55	−	16871.1i	0.684899	−	1.18628i	−0.288570	−	0.957459i	$-0.593180\pi$
$587$	9740.55	−	16871.1i	0.684899	−	1.18628i	0.973469	−	0.228821i	$-0.0734869\pi$
$588$		0			0
$589$	−10534.1	−	18245.5i	−0.736925	−	1.27639i
$590$	1461.66			0.101993
$591$		0			0
$592$	1037.10			0.0720011
$593$	7105.59	−	12307.2i	0.492060	−	0.852273i	−0.507898	−	0.861417i	$-0.669577\pi$
$593$	7105.59	−	12307.2i	0.492060	−	0.852273i	0.999958	+	0.00914421i	$0.00291073\pi$
$594$		0			0
$595$	804.377	+	295.535i	0.0554223	+	0.0203626i
$596$	−2816.76	+	4878.78i	−0.193589	+	0.335306i
$597$		0			0
$598$	−5036.62	+	8723.67i	−0.344419	+	0.596551i
$599$	−4430.99	+	7674.69i	−0.302246	+	0.523505i	−0.976644	−	0.214863i	$-0.931070\pi$
$599$	−4430.99	+	7674.69i	−0.302246	+	0.523505i	0.674399	+	0.738367i	$0.264403\pi$
$600$		0			0
$601$	−6052.58	+	10483.4i	−0.410798	+	0.711524i	−0.994977	−	0.100101i	$-0.968083\pi$
$601$	−6052.58	+	10483.4i	−0.410798	+	0.711524i	0.584179	+	0.811625i	$0.301417\pi$
$602$	−4614.46	+	3848.21i	−0.312411	+	0.260534i
$603$		0			0
$604$	1038.07	−	1797.99i	0.0699311	−	0.121124i
$605$	4227.12			0.284061
$606$		0			0
$607$	2920.51			0.195288			0.0976439	−	0.995221i	$-0.468869\pi$
$607$	2920.51			0.195288			0.0976439	+	0.995221i	$0.468869\pi$
$608$	13141.1	+	22761.0i	0.876546	+	1.51822i
$609$		0			0
$610$	3863.39	−	6691.59i	0.256433	−	0.444155i
$611$	−1620.24	+	2806.33i	−0.107280	+	0.185814i
$612$		0			0
$613$	13246.6	+	22943.8i	0.872799	+	1.51173i	0.859089	+	0.511827i	$0.171031\pi$
$613$	13246.6	+	22943.8i	0.872799	+	1.51173i	0.0137106	+	0.999906i	$0.495636\pi$
$614$	2108.30	+	3651.69i	0.138574	+	0.240017i
$615$		0			0
$616$	7926.94	−	6610.64i	0.518483	−	0.432387i
$617$	2694.79	+	4667.52i	0.175832	+	0.304550i	0.940449	−	0.339935i	$-0.110405\pi$
$617$	2694.79	+	4667.52i	0.175832	+	0.304550i	−0.764617	+	0.644485i	$0.777072\pi$
$618$		0			0
$619$	−3600.96			−0.233821			−0.116910	−	0.993142i	$-0.537299\pi$
$619$	−3600.96			−0.233821			−0.116910	+	0.993142i	$0.537299\pi$
$620$	−4138.06	−	7167.33i	−0.268046	−	0.464269i
$621$		0			0
$622$	1923.77			0.124013
$623$	1568.03	+	9053.19i	0.100838	+	0.582197i
$624$		0			0
$625$	−8207.00			−0.525248
$626$	3616.34	−	6263.68i	0.230891	−	0.399915i
$627$		0			0
$628$	4267.37	+	7391.31i	0.271157	+	0.469658i
$629$	−218.676			−0.0138620
$630$		0			0
$631$	7891.32			0.497858			0.248929	−	0.968522i	$-0.419921\pi$
$631$	7891.32			0.497858			0.248929	+	0.968522i	$0.419921\pi$
$632$	−8001.64	−	13859.3i	−0.503621	−	0.872297i
$633$		0			0
$634$	−3000.90	+	5197.72i	−0.187983	+	0.325596i
$635$	−9816.85			−0.613496
$636$		0			0
$637$	−13680.4	+	4885.53i	−0.850924	+	0.303880i
$638$	−8562.08			−0.531310
$639$		0			0
$640$	6334.52	+	10971.7i	0.391241	+	0.677649i
$641$	−10822.0			−0.666841			−0.333420	−	0.942778i	$-0.608203\pi$
$641$	−10822.0			−0.666841			−0.333420	+	0.942778i	$0.608203\pi$
$642$		0			0
$643$	−5256.94	−	9105.29i	−0.322416	−	0.558441i	0.658570	−	0.752520i	$-0.271162\pi$
$643$	−5256.94	−	9105.29i	−0.322416	−	0.558441i	−0.980986	+	0.194079i	$0.937828\pi$
$644$	−3498.87	−	20201.0i	−0.214091	−	1.23608i
$645$		0			0
$646$	−488.965	−	846.911i	−0.0297803	−	0.0515809i
$647$	−1267.12	−	2194.72i	−0.0769948	−	0.133359i	0.824957	−	0.565195i	$-0.191199\pi$
$647$	−1267.12	−	2194.72i	−0.0769948	−	0.133359i	−0.901952	+	0.431836i	$0.857866\pi$
$648$		0			0
$649$	1783.68	−	3089.42i	0.107882	−	0.186857i
$650$	−1242.04	+	2151.27i	−0.0749487	+	0.129815i
$651$		0			0
$652$	482.220	+	835.230i	0.0289650	+	0.0501689i
$653$	22809.9			1.36695			0.683477	−	0.729972i	$-0.260467\pi$
$653$	22809.9			1.36695			0.683477	+	0.729972i	$0.260467\pi$
$654$		0			0
$655$	23443.4			1.39849
$656$	−2041.25	+	3535.55i	−0.121490	+	0.210427i
$657$		0			0
$658$	322.995	+	1864.85i	0.0191363	+	0.110485i
$659$	15066.4	−	26095.7i	0.890595	−	1.54256i	0.0514322	−	0.998676i	$-0.483621\pi$
$659$	15066.4	−	26095.7i	0.890595	−	1.54256i	0.839163	−	0.543880i	$-0.183045\pi$
$660$		0			0
$661$	1104.44	−	1912.94i	0.0649888	−	0.112564i	−0.831700	−	0.555225i	$-0.812632\pi$
$661$	1104.44	−	1912.94i	0.0649888	−	0.112564i	0.896689	+	0.442661i	$0.145966\pi$
$662$	−6589.33	+	11413.0i	−0.386860	+	0.670061i
$663$		0			0
$664$	−10764.9	+	18645.4i	−0.629155	+	1.08973i
$665$	4055.49	+	23414.7i	0.236489	+	1.36539i
$666$		0			0
$667$	−19446.9	+	33683.1i	−1.12892	+	1.95534i
$668$	−8162.35			−0.472771
$669$		0			0
$670$	−1959.84			−0.113008
$671$	−9429.05	−	16331.6i	−0.542480	−	0.939603i
$672$		0			0
$673$	4400.74	−	7622.31i	0.252060	−	0.436580i	−0.712033	−	0.702146i	$-0.752225\pi$
$673$	4400.74	−	7622.31i	0.252060	−	0.436580i	0.964093	+	0.265566i	$0.0855588\pi$
$674$	−1750.49	+	3031.94i	−0.100039	+	0.173273i
$675$		0			0
$676$	−1253.60	−	2171.30i	−0.0713245	−	0.123538i
$677$	−8843.34	−	15317.1i	−0.502034	−	0.869549i	−0.999997	−	0.00235053i	$-0.999252\pi$
$677$	−8843.34	−	15317.1i	−0.502034	−	0.869549i	0.497963	−	0.867198i	$-0.334082\pi$
$678$		0			0
$679$	−814.901	−	4704.91i	−0.0460575	−	0.265917i
$680$	−439.276	−	760.848i	−0.0247727	−	0.0429077i
$681$		0			0
$682$	5796.35			0.325445
$683$	147.258	+	255.059i	0.00824990	+	0.0142892i	0.870121	−	0.492838i	$-0.164041\pi$
$683$	147.258	+	255.059i	0.00824990	+	0.0142892i	−0.861871	+	0.507128i	$0.830707\pi$
$684$		0			0
$685$	109.395			0.00610184
$686$	−4308.82	+	7308.75i	−0.239813	+	0.406778i
$687$		0			0
$688$	−5919.73			−0.328034
$689$	7681.23	−	13304.3i	0.424719	−	0.735636i
$690$		0			0
$691$	−15716.8	−	27222.4i	−0.865263	−	1.49868i	−0.866785	−	0.498681i	$-0.833818\pi$
$691$	−15716.8	−	27222.4i	−0.865263	−	1.49868i	0.00152204	−	0.999999i	$-0.499516\pi$
$692$	1200.34			0.0659396
$693$		0			0
$694$	−16149.0			−0.883299
$695$	8447.05	+	14630.7i	0.461029	+	0.798525i
$696$		0			0
$697$	430.404	−	745.481i	0.0233898	−	0.0405124i
$698$	6.61998			0.000358983
$699$		0			0
$700$	−862.826	−	4981.61i	−0.0465882	−	0.268981i
$701$	−23597.8			−1.27144			−0.635719	−	0.771921i	$-0.719296\pi$
$701$	−23597.8			−1.27144			−0.635719	+	0.771921i	$0.719296\pi$
$702$		0			0
$703$	−3031.96	−	5251.52i	−0.162664	−	0.281742i
$704$	−1508.24			−0.0807441
$705$		0			0
$706$	349.620	+	605.559i	0.0186376	+	0.0322812i
$707$	−11493.1	+	9584.59i	−0.611374	+	0.509852i
$708$		0			0
$709$	−3759.23	−	6511.18i	−0.199127	−	0.344898i	0.749119	−	0.662436i	$-0.230477\pi$
$709$	−3759.23	−	6511.18i	−0.199127	−	0.344898i	−0.948246	+	0.317538i	$0.897144\pi$
$710$	−5014.29	−	8685.00i	−0.265046	−	0.459074i
$711$		0			0
$712$	4709.80	−	8157.61i	0.247903	−	0.429381i
$713$	13165.2	−	22802.7i	0.691500	−	1.19771i
$714$		0			0
$715$	−5596.98	−	9694.25i	−0.292748	−	0.507055i
$716$	−24835.8			−1.29631
$717$		0			0
$718$	−1594.23			−0.0828638
$719$	12749.8	−	22083.2i	0.661315	−	1.14543i	−0.318955	−	0.947770i	$-0.603332\pi$
$719$	12749.8	−	22083.2i	0.661315	−	1.14543i	0.980270	−	0.197662i	$-0.0633349\pi$
$720$		0			0
$721$	−4292.27	+	3579.52i	−0.221710	+	0.184894i
$722$	8978.62	−	15551.4i	0.462811	−	0.801612i
$723$		0			0
$724$	−14378.9	+	24905.0i	−0.738105	+	1.27844i
$725$	−4795.64	+	8306.29i	−0.245663	+	0.425501i
$726$		0			0
$727$	16313.3	−	28255.5i	0.832224	−	1.44145i	−0.0640474	−	0.997947i	$-0.520401\pi$
$727$	16313.3	−	28255.5i	0.832224	−	1.44145i	0.896271	−	0.443507i	$-0.146266\pi$
$728$	13979.2	+	5136.05i	0.711679	+	0.261476i
$729$		0			0
$730$	−751.417	+	1301.49i	−0.0380975	+	0.0659868i
$731$	1248.19			0.0631547
$732$		0			0
$733$	−10794.6			−0.543938			−0.271969	−	0.962306i	$-0.587675\pi$
$733$	−10794.6			−0.543938			−0.271969	+	0.962306i	$0.587675\pi$
$734$	−1866.89	−	3233.54i	−0.0938802	−	0.162605i
$735$		0			0
$736$	−16423.3	+	28446.0i	−0.822515	+	1.42464i
$737$	−2391.60	+	4142.37i	−0.119533	+	0.207037i
$738$		0			0
$739$	7733.72	+	13395.2i	0.384965	+	0.666779i	0.991764	−	0.128076i	$-0.0408801\pi$
$739$	7733.72	+	13395.2i	0.384965	+	0.666779i	−0.606799	+	0.794855i	$0.707547\pi$
$740$	−1191.04	−	2062.93i	−0.0591667	−	0.102480i
$741$		0			0
$742$	−1531.26	−	8840.87i	−0.0757605	−	0.437410i
$743$	14278.8	+	24731.7i	0.705033	+	1.22115i	0.966680	+	0.255990i	$0.0824013\pi$
$743$	14278.8	+	24731.7i	0.705033	+	1.22115i	−0.261646	+	0.965164i	$0.584265\pi$
$744$		0			0
$745$	8160.68			0.401321
$746$	−4189.90	−	7257.12i	−0.205634	−	0.356169i
$747$		0			0
$748$	−937.577			−0.0458305
$749$	−3636.58	−	20996.1i	−0.177407	−	1.02427i
$750$		0			0
$751$	7659.12			0.372151			0.186075	−	0.982535i	$-0.440423\pi$
$751$	7659.12			0.372151			0.186075	+	0.982535i	$0.440423\pi$
$752$	−932.325	+	1614.84i	−0.0452107	+	0.0783071i
$753$		0			0
$754$	−6176.98	−	10698.8i	−0.298345	−	0.516749i
$755$	−3007.47			−0.144971
$756$		0			0
$757$	−14615.5			−0.701728			−0.350864	−	0.936426i	$-0.614112\pi$
$757$	−14615.5			−0.701728			−0.350864	+	0.936426i	$0.614112\pi$
$758$	−8131.52	−	14084.2i	−0.389644	−	0.674883i
$759$		0			0
$760$	12181.2	−	21098.4i	0.581392	−	1.00700i
$761$	−21419.0			−1.02029			−0.510144	−	0.860089i	$-0.670408\pi$
$761$	−21419.0			−1.02029			−0.510144	+	0.860089i	$0.670408\pi$
$762$		0			0
$763$	31355.3	+	11520.2i	1.48773	+	0.546604i
$764$	−14969.5			−0.708871
$765$		0			0
$766$	−7931.61	−	13738.0i	−0.374126	−	0.648006i
$767$	5147.22			0.242315
$768$		0			0
$769$	2461.01	+	4262.59i	0.115405	+	0.199887i	0.917941	−	0.396716i	$-0.129850\pi$
$769$	2461.01	+	4262.59i	0.115405	+	0.199887i	−0.802537	+	0.596603i	$0.796517\pi$
$770$	−6136.78	−	2254.70i	−0.287213	−	0.105524i
$771$		0			0
$772$	2809.82	+	4866.75i	0.130994	+	0.226889i
$773$	400.334	+	693.399i	0.0186275	+	0.0322637i	0.875189	−	0.483781i	$-0.160737\pi$
$773$	400.334	+	693.399i	0.0186275	+	0.0322637i	−0.856561	+	0.516045i	$0.827404\pi$
$774$		0			0
$775$	3246.55	−	5623.19i	0.150477	−	0.260633i
$776$	−2447.66	+	4239.47i	−0.113229	+	0.196119i
$777$		0			0
$778$	383.283	+	663.866i	0.0176624	+	0.0305922i
$779$	23870.3			1.09787
$780$		0			0
$781$	−24475.9			−1.12140
$782$	611.094	−	1058.44i	0.0279446	−	0.0484014i
$783$		0			0
$784$	−7872.07	+	2811.26i	−0.358604	+	0.128064i
$785$	6181.68	−	10707.0i	0.281062	−	0.486814i
$786$		0			0
$787$	−3599.49	+	6234.50i	−0.163034	+	0.282384i	−0.935955	−	0.352118i	$-0.885461\pi$
$787$	−3599.49	+	6234.50i	−0.163034	+	0.282384i	0.772921	+	0.634502i	$0.218795\pi$
$788$	−10619.7	+	18393.9i	−0.480091	+	0.831542i
$789$		0			0
$790$	−5068.34	+	8778.62i	−0.228257	+	0.395353i
$791$	−21218.0	−	7795.68i	−0.953764	−	0.350420i
$792$		0			0
$793$	13604.9	−	23564.3i	0.609235	−	1.05523i
$794$	−9338.53			−0.417395
$795$		0			0
$796$	16322.7			0.726812
$797$	6877.32	+	11911.9i	0.305655	+	0.529410i	0.977407	−	0.211366i	$-0.0677912\pi$
$797$	6877.32	+	11911.9i	0.305655	+	0.529410i	−0.671752	+	0.740776i	$0.734458\pi$
$798$		0			0
$799$	196.584	−	340.493i	0.00870417	−	0.0150761i
$800$	−4050.01	+	7014.82i	−0.178987	+	0.310014i
$801$		0			0
$802$	1062.55	+	1840.39i	0.0467830	+	0.0810306i
$803$	1833.92	+	3176.44i	0.0805947	+	0.139594i
$804$		0			0
$805$	−22808.3	+	19020.9i	−0.998619	+	0.832794i
$806$	4181.68	+	7242.89i	0.182746	+	0.316526i
$807$		0			0
$808$	15342.4			0.667998
$809$	20138.6	+	34881.0i	0.875196	+	1.51588i	0.856553	+	0.516058i	$0.172601\pi$
$809$	20138.6	+	34881.0i	0.875196	+	1.51588i	0.0186429	+	0.999826i	$0.494065\pi$
$810$		0			0
$811$	−22470.6			−0.972936			−0.486468	−	0.873698i	$-0.661715\pi$
$811$	−22470.6			−0.972936			−0.486468	+	0.873698i	$0.661715\pi$
$812$	23601.2	+	8671.25i	1.02000	+	0.374755i
$813$		0			0
$814$	1668.33			0.0718366
$815$	698.540	−	1209.91i	0.0300231	−	0.0520015i
$816$		0			0
$817$	17306.3	+	29975.4i	0.741090	+	1.28360i
$818$	6832.97			0.292065
$819$		0			0
$820$	9376.89			0.399335
$821$	−2074.13	−	3592.50i	−0.0881701	−	0.152715i	0.818568	−	0.574410i	$-0.194769\pi$
$821$	−2074.13	−	3592.50i	−0.0881701	−	0.152715i	−0.906738	+	0.421695i	$0.861435\pi$
$822$		0			0
$823$	−8373.94	+	14504.1i	−0.354675	+	0.614315i	−0.987062	−	0.160338i	$-0.948742\pi$
$823$	−8373.94	+	14504.1i	−0.354675	+	0.614315i	0.632388	+	0.774652i	$0.282075\pi$
$824$	5729.85			0.242244
$825$		0			0
$826$	2308.77	−	1925.39i	0.0972547	−	0.0811052i
$827$	−20050.5			−0.843076			−0.421538	−	0.906811i	$-0.638510\pi$
$827$	−20050.5			−0.843076			−0.421538	+	0.906811i	$0.638510\pi$
$828$		0			0
$829$	−6444.75	−	11162.6i	−0.270007	−	0.467665i	0.698857	−	0.715262i	$-0.253693\pi$
$829$	−6444.75	−	11162.6i	−0.270007	−	0.467665i	−0.968863	+	0.247597i	$0.920359\pi$
$830$	13637.2			0.570307
$831$		0			0
$832$	−1088.09	−	1884.64i	−0.0453400	−	0.0785312i
$833$	1659.85	−	592.762i	0.0690401	−	0.0246555i
$834$		0			0
$835$	5911.96	+	10239.8i	0.245020	+	0.424387i
$836$	−12999.6	−	22515.9i	−0.537798	−	0.931494i
$837$		0			0
$838$	921.676	−	1596.39i	0.0379938	−	0.0658071i
$839$	−15106.5	+	26165.3i	−0.621615	+	1.07667i	0.367570	+	0.929996i	$0.380190\pi$
$839$	−15106.5	+	26165.3i	−0.621615	+	1.07667i	−0.989185	+	0.146673i	$0.953143\pi$
$840$		0			0
$841$	−11655.5	−	20187.9i	−0.477899	−	0.827746i
$842$	−6556.76			−0.268362
$843$		0			0
$844$	−5191.60			−0.211733
$845$	−1815.95	+	3145.32i	−0.0739298	+	0.128050i
$846$		0			0
$847$	6676.95	−	5568.22i	0.270865	−	0.225887i
$848$	4419.98	−	7655.62i	0.178989	−	0.310018i
$849$		0			0
$850$	150.697	−	261.014i	0.00608100	−	0.0105326i
$851$	3789.26	−	6563.19i	0.152637	−	0.264375i
$852$		0			0
$853$	12389.8	−	21459.7i	0.497324	−	0.861391i	−0.502671	−	0.864478i	$-0.667649\pi$
$853$	12389.8	−	21459.7i	0.497324	−	0.861391i	0.999995	+	0.00308694i	$0.000982605\pi$
$854$	−2712.14	−	15658.8i	−0.108674	−	0.627439i
$855$		0			0
$856$	−10922.9	+	18919.1i	−0.436143	+	0.755421i
$857$	21752.6			0.867043			0.433521	−	0.901143i	$-0.357271\pi$
$857$	21752.6			0.867043			0.433521	+	0.901143i	$0.357271\pi$
$858$		0			0
$859$	−33967.3			−1.34918			−0.674591	−	0.738191i	$-0.735680\pi$
$859$	−33967.3			−1.34918			−0.674591	+	0.738191i	$0.735680\pi$
$860$	6798.36	+	11775.1i	0.269561	+	0.466893i
$861$		0			0
$862$	−3570.91	+	6184.99i	−0.141097	+	0.244387i
$863$	2327.47	−	4031.29i	0.0918052	−	0.159011i	−0.816466	−	0.577394i	$-0.804070\pi$
$863$	2327.47	−	4031.29i	0.0918052	−	0.159011i	0.908271	+	0.418383i	$0.137403\pi$
$864$		0			0
$865$	−869.404	−	1505.85i	−0.0341741	−	0.0591913i
$866$	4237.93	+	7340.31i	0.166294	+	0.288030i
$867$		0			0
$868$	−15977.5	−	5870.26i	−0.624783	−	0.229550i
$869$	12369.8	+	21425.2i	0.482875	+	0.836364i
$870$		0			0
$871$	−6901.53			−0.268484
$872$	−17123.4	−	29658.5i	−0.664989	−	1.15179i
$873$		0			0
$874$	33891.4			1.31166
$875$	−21634.2	+	18041.8i	−0.835851	+	0.697055i
$876$		0			0
$877$	33734.5			1.29890			0.649449	−	0.760405i	$-0.275000\pi$
$877$	33734.5			1.29890			0.649449	+	0.760405i	$0.275000\pi$
$878$	−6425.47	+	11129.2i	−0.246981	+	0.427783i
$879$		0			0
$880$	−3220.64	−	5578.32i	−0.123373	−	0.213688i
$881$	−26328.0			−1.00683			−0.503413	−	0.864046i	$-0.667922\pi$
$881$	−26328.0			−1.00683			−0.503413	+	0.864046i	$0.667922\pi$
$882$		0			0
$883$	24806.9			0.945436			0.472718	−	0.881214i	$-0.343273\pi$
$883$	24806.9			0.945436			0.472718	+	0.881214i	$0.343273\pi$
$884$	−676.400	−	1171.56i	−0.0257351	−	0.0445744i
$885$		0			0
$886$	−1392.78	+	2412.37i	−0.0528119	+	0.0914730i
$887$	−7109.64			−0.269130			−0.134565	−	0.990905i	$-0.542964\pi$
$887$	−7109.64			−0.269130			−0.134565	+	0.990905i	$0.542964\pi$
$888$		0			0
$889$	−15506.2	+	12931.3i	−0.584996	+	0.487855i
$890$	−5966.48			−0.224716
$891$		0			0
$892$	6698.79	+	11602.6i	0.251449	+	0.435522i
$893$	10902.6			0.408557
$894$		0			0
$895$	17988.5	+	31156.9i	0.671830	+	1.16364i
$896$	24458.3	+	8986.17i	0.911936	+	0.335052i
$897$		0			0
$898$	−6864.46	−	11889.6i	−0.255089	−	0.441827i
$899$	16145.9	+	27965.6i	0.598996	+	1.03749i
$900$		0			0
$901$	−931.965	+	1614.21i	−0.0344598	+	0.0596861i
$902$	−3283.65	+	5687.45i	−0.121212	+	0.209946i
$903$		0			0
$904$	11587.3	+	20069.8i	0.426315	+	0.738399i
$905$	41658.3			1.53013
$906$		0			0
$907$	−30787.5			−1.12710			−0.563552	−	0.826081i	$-0.690566\pi$
$907$	−30787.5			−1.12710			−0.563552	+	0.826081i	$0.690566\pi$
$908$	4365.59	−	7561.42i	0.159556	−	0.276360i
$909$		0			0
$910$	−1609.90	−	9294.90i	−0.0586457	−	0.338596i
$911$	−2335.16	+	4044.61i	−0.0849256	+	0.147095i	−0.905360	−	0.424646i	$-0.860399\pi$
$911$	−2335.16	+	4044.61i	−0.0849256	+	0.147095i	0.820434	+	0.571741i	$0.193732\pi$
$912$		0			0
$913$	16641.6	−	28824.1i	0.603238	−	1.04484i
$914$	6508.88	−	11273.7i	0.235552	−	0.407988i
$915$		0			0
$916$	17868.4	−	30949.0i	0.644529	−	1.11636i
$917$	37030.0	−	30881.0i	1.33352	−	1.11208i
$918$		0			0
$919$	14646.3	−	25368.1i	0.525720	−	0.910573i	−0.473832	−	0.880616i	$-0.657129\pi$
$919$	14646.3	−	25368.1i	0.525720	−	0.910573i	0.999551	−	0.0299576i	$-0.00953723\pi$
$920$	30447.4			1.09111
$921$		0			0
$922$	10420.3			0.372206
$923$	−17657.7	−	30584.1i	−0.629698	−	1.09067i
$924$		0			0
$925$	934.437	−	1618.49i	0.0332152	−	0.0575305i
$926$	−4733.69	+	8198.99i	−0.167990	+	0.290967i
$927$		0			0
$928$	−20141.8	−	34886.6i	−0.712485	−	1.23406i
$929$	1561.66	+	2704.87i	0.0551521	+	0.0955263i	0.892283	−	0.451476i	$-0.149102\pi$
$929$	1561.66	+	2704.87i	0.0551521	+	0.0955263i	−0.837131	+	0.547002i	$0.815769\pi$
$930$		0			0
$931$	37249.1	+	31642.6i	1.31127	+	1.11390i
$932$	1525.92	+	2642.98i	0.0536302	+	0.0928902i
$933$		0			0
$934$	23508.4			0.823574
$935$	679.083	+	1176.21i	0.0237523	+	0.0411401i
$936$		0			0
$937$	−27500.6			−0.958810			−0.479405	−	0.877594i	$-0.659147\pi$
$937$	−27500.6			−0.958810			−0.479405	+	0.877594i	$0.659147\pi$
$938$	−3095.66	+	2581.61i	−0.107758	+	0.0898643i
$939$		0			0
$940$	4282.82			0.148607
$941$	2427.68	−	4204.87i	0.0841022	−	0.145669i	−0.820906	−	0.571063i	$-0.806531\pi$
$941$	2427.68	−	4204.87i	0.0841022	−	0.145669i	0.905008	+	0.425394i	$0.139864\pi$
$942$		0			0
$943$	14916.2	+	25835.6i	0.515099	+	0.892178i
$944$	2961.84			0.102118
$945$		0			0
$946$	−9522.75			−0.327285
$947$	−5910.11	−	10236.6i	−0.202801	−	0.351262i	0.746629	−	0.665241i	$-0.231671\pi$
$947$	−5910.11	−	10236.6i	−0.202801	−	0.351262i	−0.949430	+	0.313979i	$0.898338\pi$
$948$		0			0
$949$	−2646.10	+	4583.18i	−0.0905122	+	0.156772i
$950$	8357.67			0.285430
$951$		0			0
$952$	−1696.09	−	623.158i	−0.0577423	−	0.0212150i
$953$	7208.84			0.245034			0.122517	−	0.992466i	$-0.460903\pi$
$953$	7208.84			0.245034			0.122517	+	0.992466i	$0.460903\pi$
$954$		0			0
$955$	10842.3	+	18779.5i	0.367382	+	0.636325i
$956$	40862.7			1.38242
$957$		0			0
$958$	−7335.63	−	12705.7i	−0.247394	−	0.428499i
$959$	172.795	−	144.101i	0.00581839	−	0.00485222i
$960$		0			0
$961$	3965.03	+	6867.64i	0.133095	+	0.230527i
$962$	1203.59	+	2084.68i	0.0403382	+	0.0698678i
$963$		0			0
$964$	−2951.11	+	5111.47i	−0.0985984	+	0.170777i
$965$	4070.28	−	7049.93i	0.135779	−	0.235176i
$966$		0			0
$967$	9875.62	+	17105.1i	0.328416	+	0.568834i	0.982198	−	0.187850i	$-0.0601518\pi$
$967$	9875.62	+	17105.1i	0.328416	+	0.568834i	−0.653781	+	0.756683i	$0.726818\pi$
$968$	−8913.22			−0.295952
$969$		0			0
$970$	3100.76			0.102638
$971$	−2214.80	+	3836.14i	−0.0731990	+	0.126784i	−0.900302	−	0.435267i	$-0.856654\pi$
$971$	−2214.80	+	3836.14i	−0.0731990	+	0.126784i	0.827103	+	0.562051i	$0.189987\pi$
$972$		0			0
$973$	32615.0	+	11983.0i	1.07460	+	0.394818i
$974$	−7613.21	+	13186.5i	−0.250455	+	0.433801i
$975$		0			0
$976$	7828.59	−	13559.5i	0.256749	−	0.444702i
$977$	−1311.76	+	2272.04i	−0.0429549	+	0.0744001i	−0.886704	−	0.462338i	$-0.847011\pi$
$977$	−1311.76	+	2272.04i	−0.0429549	+	0.0744001i	0.843749	+	0.536739i	$0.180344\pi$
$978$		0			0
$979$	−7280.93	+	12610.9i	−0.237691	+	0.411693i
$980$	14632.4	+	12430.1i	0.476955	+	0.405167i
$981$		0			0
$982$	9881.96	−	17116.1i	0.321126	−	0.556207i
$983$	−20812.8			−0.675306			−0.337653	−	0.941271i	$-0.609633\pi$
$983$	−20812.8			−0.675306			−0.337653	+	0.941271i	$0.609633\pi$
$984$		0			0
$985$	30767.2			0.995255
$986$	749.454	+	1298.09i	0.0242064	+	0.0419266i
$987$		0			0
$988$	18756.7	−	32487.5i	0.603977	−	1.04612i
$989$	−21628.9	+	37462.3i	−0.695408	+	1.20448i
$990$		0			0
$991$	−15076.8	−	26113.7i	−0.483279	−	0.837063i	0.516537	−	0.856265i	$-0.327221\pi$
$991$	−15076.8	−	26113.7i	−0.483279	−	0.837063i	−0.999816	+	0.0192017i	$0.993888\pi$
$992$	13635.6	+	23617.5i	0.436421	+	0.755903i
$993$		0			0
$994$	−19360.7	−	7113.28i	−0.617792	−	0.226981i
$995$	−11822.4	−	20477.1i	−0.376680	−	0.652429i
$996$		0			0
$997$	−43996.6			−1.39758			−0.698790	−	0.715327i	$-0.746278\pi$
$997$	−43996.6			−1.39758			−0.698790	+	0.715327i	$0.746278\pi$
$998$	8999.57	+	15587.7i	0.285447	+	0.494409i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.g.a.100.14		44
3.2	odd	2		63.4.g.a.16.9	yes	44
7.4	even	3		189.4.h.a.46.9		44
9.4	even	3		189.4.h.a.37.9		44
9.5	odd	6		63.4.h.a.58.14	yes	44
21.11	odd	6		63.4.h.a.25.14	yes	44
63.4	even	3	inner	189.4.g.a.172.14		44
63.32	odd	6		63.4.g.a.4.9	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.9	✓	44	63.32	odd	6
63.4.g.a.16.9	yes	44	3.2	odd	2
63.4.h.a.25.14	yes	44	21.11	odd	6
63.4.h.a.58.14	yes	44	9.5	odd	6
189.4.g.a.100.14		44	1.1	even	1	trivial
189.4.g.a.172.14		44	63.4	even	3	inner
189.4.h.a.37.9		44	9.4	even	3
189.4.h.a.46.9		44	7.4	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.667800 + 1.15666i) q^{2} +(3.10809 - 5.38337i) q^{4} -9.00469 q^{5} +(-14.2234 + 11.8615i) q^{7} +18.9871 q^{8} +O(q^{10})\)	\(q+(0.667800 + 1.15666i) q^{2} +(3.10809 - 5.38337i) q^{4} -9.00469 q^{5} +(-14.2234 + 11.8615i) q^{7} +18.9871 q^{8} +(-6.01333 - 10.4154i) q^{10} -29.3524 q^{11} +(-21.1758 - 36.6776i) q^{13} +(-23.2181 - 8.53053i) q^{14} +(-12.1851 - 21.1052i) q^{16} +(2.56927 + 4.45010i) q^{17} +(-71.2462 + 123.402i) q^{19} +(-27.9874 + 48.4756i) q^{20} +(-19.6015 - 33.9509i) q^{22} -178.083 q^{23} -43.9155 q^{25} +(28.2824 - 48.9866i) q^{26} +(19.6474 + 113.436i) q^{28} +(109.202 - 189.143i) q^{29} +(-73.9272 + 128.046i) q^{31} +(92.2229 - 159.735i) q^{32} +(-3.43151 + 5.94356i) q^{34} +(128.077 - 106.809i) q^{35} +(-21.2781 + 36.8547i) q^{37} -190.313 q^{38} -170.973 q^{40} +(-83.7600 - 145.077i) q^{41} +(121.454 - 210.365i) q^{43} +(-91.2299 + 158.015i) q^{44} +(-118.924 - 205.982i) q^{46} +(-38.2567 - 66.2626i) q^{47} +(61.6086 - 337.422i) q^{49} +(-29.3267 - 50.7954i) q^{50} -263.265 q^{52} +(181.368 + 314.138i) q^{53} +264.310 q^{55} +(-270.061 + 225.216i) q^{56} +291.699 q^{58} +(-60.7676 + 105.253i) q^{59} +(321.236 + 556.396i) q^{61} -197.474 q^{62} +51.3838 q^{64} +(190.682 + 330.271i) q^{65} +(81.4788 - 141.125i) q^{67} +31.9420 q^{68} +(209.072 + 76.8148i) q^{70} +833.862 q^{71} +(-62.4792 - 108.217i) q^{73} -56.8380 q^{74} +(442.879 + 767.089i) q^{76} +(417.490 - 348.164i) q^{77} +(-421.425 - 729.929i) q^{79} +(109.723 + 190.046i) q^{80} +(111.870 - 193.764i) q^{82} +(-566.958 + 982.000i) q^{83} +(-23.1355 - 40.0718i) q^{85} +324.428 q^{86} -557.318 q^{88} +(248.052 - 429.639i) q^{89} +(736.244 + 270.502i) q^{91} +(-553.497 + 958.685i) q^{92} +(51.0957 - 88.5003i) q^{94} +(641.550 - 1111.20i) q^{95} +(-128.912 + 223.282i) q^{97} +(431.425 - 154.070i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8	\( 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} + 10 q^{11} - 14 q^{13} + 79 q^{14} - 247 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} - 186 q^{23} + 698 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} + 61 q^{31} + 163 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} - 1522 q^{38} + 36 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} + 1005 q^{47} - 277 q^{49} - 239 q^{50} + 670 q^{52} - 258 q^{53} - 870 q^{55} - 714 q^{56} - 474 q^{58} + 1665 q^{59} + 439 q^{61} - 1812 q^{62} + 872 q^{64} + 613 q^{65} + 295 q^{67} - 2748 q^{68} - 1044 q^{70} - 636 q^{71} - 338 q^{73} + 2238 q^{74} + 1006 q^{76} + 2909 q^{77} + 133 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} - 6686 q^{86} - 738 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} - 1191 q^{94} - 3083 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) \) 44 * q - q^2 - 79 * q^4 - 38 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 + 10 * q^11 - 14 * q^13 + 79 * q^14 - 247 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 - 186 * q^23 + 698 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 + 61 * q^31 + 163 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 - 1522 * q^38 + 36 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 + 1005 * q^47 - 277 * q^49 - 239 * q^50 + 670 * q^52 - 258 * q^53 - 870 * q^55 - 714 * q^56 - 474 * q^58 + 1665 * q^59 + 439 * q^61 - 1812 * q^62 + 872 * q^64 + 613 * q^65 + 295 * q^67 - 2748 * q^68 - 1044 * q^70 - 636 * q^71 - 338 * q^73 + 2238 * q^74 + 1006 * q^76 + 2909 * q^77 + 133 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 - 6686 * q^86 - 738 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 - 1191 * q^94 - 3083 * q^95 - 266 * q^97 - 3601 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more