LMFDB - Embedded newform 189.4.h.a.37.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(37,189)]

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([2, 2]))

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

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

chi := DirichletCharacter("189.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.h (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			37.9
Character	$\chi$	$=$	189.37
Dual form			189.4.h.a.46.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.33560 q^{2} -6.21617 q^{4} +(4.50235 + 7.79829i) q^{5} +(-3.16069 - 18.2486i) q^{7} +18.9871 q^{8} +O(q^{10})$	\(q-1.33560 q^{2} -6.21617 q^{4} +(4.50235 + 7.79829i) q^{5} +(-3.16069 - 18.2486i) q^{7} +18.9871 q^{8} +(-6.01333 - 10.4154i) q^{10} +(14.6762 - 25.4199i) q^{11} +(-21.1758 + 36.6776i) q^{13} +(4.22142 + 24.3728i) q^{14} +24.3702 q^{16} +(2.56927 + 4.45010i) q^{17} +(-71.2462 + 123.402i) q^{19} +(-27.9874 - 48.4756i) q^{20} +(-19.6015 + 33.9509i) q^{22} +(89.0414 + 154.224i) q^{23} +(21.9577 - 38.0319i) q^{25} +(28.2824 - 48.9866i) q^{26} +(19.6474 + 113.436i) q^{28} +(109.202 + 189.143i) q^{29} +147.854 q^{31} -184.446 q^{32} +(-3.43151 - 5.94356i) q^{34} +(128.077 - 106.809i) q^{35} +(-21.2781 + 36.8547i) q^{37} +(95.1564 - 164.816i) q^{38} +(85.4866 + 148.067i) q^{40} +(-83.7600 + 145.077i) q^{41} +(121.454 + 210.365i) q^{43} +(-91.2299 + 158.015i) q^{44} +(-118.924 - 205.982i) q^{46} +76.5135 q^{47} +(-323.020 + 115.356i) q^{49} +(-29.3267 + 50.7954i) q^{50} +(131.633 - 227.995i) q^{52} +(181.368 + 314.138i) q^{53} +264.310 q^{55} +(-60.0124 - 346.487i) q^{56} +(-145.850 - 252.619i) q^{58} +121.535 q^{59} -642.471 q^{61} -197.474 q^{62} +51.3838 q^{64} -381.364 q^{65} -162.958 q^{67} +(-15.9710 - 27.6626i) q^{68} +(-171.060 + 142.655i) q^{70} +833.862 q^{71} +(-62.4792 - 108.217i) q^{73} +(28.4190 - 49.2231i) q^{74} +(442.879 - 767.089i) q^{76} +(-510.264 - 187.475i) q^{77} +842.850 q^{79} +(109.723 + 190.046i) q^{80} +(111.870 - 193.764i) q^{82} +(-566.958 - 982.000i) q^{83} +(-23.1355 + 40.0718i) q^{85} +(-162.214 - 280.963i) q^{86} +(278.659 - 482.651i) q^{88} +(248.052 - 429.639i) q^{89} +(736.244 + 270.502i) q^{91} +(-553.497 - 958.685i) q^{92} -102.191 q^{94} -1283.10 q^{95} +(-128.912 - 223.282i) q^{97} +(431.425 - 154.070i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) $ 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8	$ 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} - 5 q^{11} - 14 q^{13} + 52 q^{14} + 494 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} + 93 q^{23} - 349 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} - 122 q^{31} - 326 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} + 761 q^{38} - 18 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} - 2010 q^{47} + 317 q^{49} - 239 q^{50} - 335 q^{52} - 258 q^{53} - 870 q^{55} + 1752 q^{56} + 237 q^{58} - 3330 q^{59} - 878 q^{61} - 1812 q^{62} + 872 q^{64} - 1226 q^{65} - 590 q^{67} + 1374 q^{68} + 1251 q^{70} - 636 q^{71} - 338 q^{73} - 1119 q^{74} + 1006 q^{76} - 2269 q^{77} - 266 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} + 3343 q^{86} + 369 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} + 2382 q^{94} + 6166 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) $ 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 - 5 * q^11 - 14 * q^13 + 52 * q^14 + 494 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 + 93 * q^23 - 349 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 - 122 * q^31 - 326 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 + 761 * q^38 - 18 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 - 2010 * q^47 + 317 * q^49 - 239 * q^50 - 335 * q^52 - 258 * q^53 - 870 * q^55 + 1752 * q^56 + 237 * q^58 - 3330 * q^59 - 878 * q^61 - 1812 * q^62 + 872 * q^64 - 1226 * q^65 - 590 * q^67 + 1374 * q^68 + 1251 * q^70 - 636 * q^71 - 338 * q^73 - 1119 * q^74 + 1006 * q^76 - 2269 * q^77 - 266 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 + 3343 * q^86 + 369 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 + 2382 * q^94 + 6166 * q^95 - 266 * q^97 - 3601 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.33560			−0.472206			−0.236103	−	0.971728i	$-0.575870\pi$
$2$	−1.33560			−0.472206			−0.236103	+	0.971728i	$0.575870\pi$
$3$		0			0
$3$		0			0
$4$	−6.21617			−0.777022
$5$	4.50235	+	7.79829i	0.402702	+	0.697501i	0.994051	−	0.108915i	$-0.0347377\pi$
$5$	4.50235	+	7.79829i	0.402702	+	0.697501i	−0.591349	+	0.806416i	$0.701404\pi$
$6$		0			0
$7$	−3.16069	−	18.2486i	−0.170661	−	0.985330i
$7$	−3.16069	−	18.2486i	−0.170661	−	0.985330i
$8$	18.9871			0.839120
$9$		0			0
$10$	−6.01333	−	10.4154i	−0.190158	−	0.329364i
$11$	14.6762	−	25.4199i	0.402277	−	0.696764i	−0.591724	−	0.806141i	$-0.701552\pi$
$11$	14.6762	−	25.4199i	0.402277	−	0.696764i	0.994000	+	0.109377i	$0.0348856\pi$
$12$		0			0
$13$	−21.1758	+	36.6776i	−0.451779	+	0.782504i	−0.998497	−	0.0548133i	$-0.982544\pi$
$13$	−21.1758	+	36.6776i	−0.451779	+	0.782504i	0.546718	+	0.837317i	$0.315877\pi$
$14$	4.22142	+	24.3728i	0.0805873	+	0.465278i
$15$		0			0
$16$	24.3702			0.380785
$17$	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
$23$	89.0414	+	154.224i	0.807235	+	1.39817i	0.914772	+	0.403972i	$0.132371\pi$
$23$	89.0414	+	154.224i	0.807235	+	1.39817i	−0.107536	+	0.994201i	$0.534296\pi$
$24$		0			0
$25$	21.9577	−	38.0319i	0.175662	−	0.304255i
$26$	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	0.968727	+	0.248129i	$0.0798156\pi$
$29$	109.202	+	189.143i	0.699249	+	1.21114i	−0.269478	+	0.963007i	$0.586851\pi$
$30$		0			0
$31$	147.854			0.856627			0.428314	−	0.903630i	$-0.359108\pi$
$31$	147.854			0.856627			0.428314	+	0.903630i	$0.359108\pi$
$32$	−184.446			−1.01893
$33$		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	$0.196806\pi$
$38$	95.1564	−	164.816i	0.406221	−	0.703595i
$39$		0			0
$40$	85.4866	+	148.067i	0.337915	+	0.585287i
$41$	−83.7600	+	145.077i	−0.319051	+	0.552613i	−0.980290	−	0.197562i	$-0.936698\pi$
$41$	−83.7600	+	145.077i	−0.319051	+	0.552613i	0.661239	+	0.750175i	$0.270031\pi$
$42$		0			0
$43$	121.454	+	210.365i	0.430734	+	0.746054i	0.996937	−	0.0782125i	$-0.0249213\pi$
$43$	121.454	+	210.365i	0.430734	+	0.746054i	−0.566202	+	0.824266i	$0.691588\pi$
$44$	−91.2299	+	158.015i	−0.312578	+	0.541401i
$45$		0			0
$46$	−118.924	−	205.982i	−0.381181	−	0.660225i
$47$	76.5135			0.237460			0.118730	−	0.992927i	$-0.462118\pi$
$47$	76.5135			0.237460			0.118730	+	0.992927i	$0.462118\pi$
$48$		0			0
$49$	−323.020	+	115.356i	−0.941749	+	0.336315i
$50$	−29.3267	+	50.7954i	−0.0829485	+	0.143671i
$51$		0			0
$52$	131.633	−	227.995i	0.351042	−	0.608022i
$53$	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
$56$	−60.0124	−	346.487i	−0.143205	−	0.826810i
$57$		0			0
$58$	−145.850	−	252.619i	−0.330189	−	0.571905i
$59$	121.535			0.268179			0.134089	−	0.990969i	$-0.457189\pi$
$59$	121.535			0.268179			0.134089	+	0.990969i	$0.457189\pi$
$60$		0			0
$61$	−642.471			−1.34852			−0.674262	−	0.738492i	$-0.735538\pi$
$61$	−642.471			−1.34852			−0.674262	+	0.738492i	$0.735538\pi$
$62$	−197.474			−0.404504
$63$		0			0
$64$	51.3838			0.100359
$65$	−381.364			−0.727729
$66$		0			0
$67$	−162.958			−0.297141			−0.148570	−	0.988902i	$-0.547467\pi$
$67$	−162.958			−0.297141			−0.148570	+	0.988902i	$0.547467\pi$
$68$	−15.9710	−	27.6626i	−0.0284819	−	0.0493321i
$69$		0			0
$70$	−171.060	+	142.655i	−0.292079	+	0.243578i
$71$	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	$0.865273\pi$
$74$	28.4190	−	49.2231i	0.0446438	−	0.0773253i
$75$		0			0
$76$	442.879	−	767.089i	0.668443	−	1.15778i
$77$	−510.264	−	187.475i	−0.755195	−	0.277465i
$78$		0			0
$79$	842.850			1.20035			0.600177	−	0.799867i	$-0.295097\pi$
$79$	842.850			1.20035			0.600177	+	0.799867i	$0.295097\pi$
$80$	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	−0.947928	−	0.318485i	$-0.896826\pi$
$83$	−566.958	−	982.000i	−0.749780	−	1.29866i	0.198148	−	0.980172i	$-0.436507\pi$
$84$		0			0
$85$	−23.1355	+	40.0718i	−0.0295223	+	0.0511341i
$86$	−162.214	−	280.963i	−0.203395	−	0.352291i
$87$		0			0
$88$	278.659	−	482.651i	0.337558	−	0.584668i
$89$	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
$94$	−102.191			−0.112130
$95$	−1283.10			−1.38572
$96$		0			0
$97$	−128.912	−	223.282i	−0.134938	−	0.233720i	0.790636	−	0.612287i	$-0.209750\pi$
$97$	−128.912	−	223.282i	−0.134938	−	0.233720i	−0.925574	+	0.378567i	$0.876417\pi$
$98$	431.425	−	154.070i	0.444699	−	0.158810i
$99$		0			0
$100$	−136.493	+	236.413i	−0.136493	+	0.236413i
$101$	−404.020	+	699.784i	−0.398035	+	0.689417i	−0.993483	−	0.113977i	$-0.963641\pi$
$101$	−404.020	+	699.784i	−0.398035	+	0.689417i	0.595449	+	0.803393i	$0.296974\pi$
$102$		0			0
$103$	−150.888	−	261.346i	−0.144344	−	0.250011i	0.784784	−	0.619769i	$-0.212774\pi$
$103$	−150.888	−	261.346i	−0.144344	−	0.250011i	−0.929128	+	0.369758i	$0.879441\pi$
$104$	−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	$-0.457879\pi$
$110$	−353.012			−0.305985
$111$		0			0
$112$	−77.0268	−	444.722i	−0.0649853	−	0.375199i
$113$	610.273	−	1057.02i	0.508050	−	0.879968i	−0.491907	−	0.870648i	$-0.663700\pi$
$113$	610.273	−	1057.02i	0.508050	−	0.879968i	0.999957	−	0.00932039i	$-0.00296681\pi$
$114$		0			0
$115$	−801.791	+	1388.74i	−0.650151	+	1.12609i
$116$	−678.816	−	1175.74i	−0.543332	−	0.941079i
$117$		0			0
$118$	−162.322			−0.126635
$119$	73.0873	−	60.9509i	0.0563017	−	0.0469526i
$120$		0			0
$121$	234.718	+	406.543i	0.176347	+	0.305442i
$122$	858.084			0.636781
$123$		0			0
$124$	−919.089			−0.665618
$125$	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	$0.375627\pi$
$128$	1406.94			0.971538
$129$		0			0
$130$	509.349			0.343638
$131$	1301.73	+	2254.66i	0.868189	+	1.50375i	0.863846	+	0.503756i	$0.168049\pi$
$131$	1301.73	+	2254.66i	0.868189	+	1.50375i	0.00434280	+	0.999991i	$0.498618\pi$
$132$		0			0
$133$	2477.10	+	910.105i	1.61497	+	0.593354i
$134$	217.646			0.140312
$135$		0			0
$136$	48.7830	+	84.4946i	0.0307581	+	0.0532747i
$137$	6.07432	−	10.5210i	0.00378806	−	0.00656112i	−0.864125	−	0.503277i	$-0.832128\pi$
$137$	6.07432	−	10.5210i	0.00378806	−	0.00656112i	0.867913	+	0.496716i	$0.165461\pi$
$138$		0			0
$139$	−938.072	+	1624.79i	−0.572419	+	0.991458i	0.423898	+	0.905710i	$0.360661\pi$
$139$	−938.072	+	1624.79i	−0.572419	+	0.991458i	−0.996317	+	0.0857483i	$0.972672\pi$
$140$	−796.150	+	663.946i	−0.480621	+	0.400812i
$141$		0			0
$142$	−1113.71			−0.658170
$143$	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
$149$	453.135	+	784.852i	0.249143	+	0.431528i	0.963288	−	0.268470i	$-0.0865179\pi$
$149$	453.135	+	784.852i	0.249143	+	0.431528i	−0.714146	+	0.699997i	$0.753185\pi$
$150$		0			0
$151$	−166.995	+	289.243i	−0.0899989	+	0.155883i	−0.907510	−	0.420030i	$-0.862020\pi$
$151$	−166.995	+	289.243i	−0.0899989	+	0.155883i	0.817511	+	0.575912i	$0.195353\pi$
$152$	−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
$157$	1372.99			0.697940			0.348970	−	0.937134i	$-0.386532\pi$
$157$	1372.99			0.697940			0.348970	+	0.937134i	$0.386532\pi$
$158$	−1125.71			−0.566814
$159$		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	$0.178535\pi$
$164$	520.667	−	901.821i	0.247910	−	0.429393i
$165$		0			0
$166$	757.229	+	1311.56i	0.354050	+	0.613233i
$167$	−656.542	+	1137.16i	−0.304220	+	0.526924i	−0.977087	−	0.212839i	$-0.931729\pi$
$167$	−656.542	+	1137.16i	−0.304220	+	0.526924i	0.672867	+	0.739763i	$0.265062\pi$
$168$		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
$173$	−193.100			−0.0848620			−0.0424310	−	0.999099i	$-0.513510\pi$
$173$	−193.100			−0.0848620			−0.0424310	+	0.999099i	$0.513510\pi$
$174$		0			0
$175$	−763.429	−	280.490i	−0.329770	−	0.121160i
$176$	357.663	−	619.490i	0.153181	−	0.265317i
$177$		0			0
$178$	−331.298	+	573.826i	−0.139505	+	0.241629i
$179$	−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	$0.898831\pi$
$182$	−983.327	−	361.282i	−0.400489	−	0.147143i
$183$		0			0
$184$	1690.64	+	2928.27i	0.677367	+	1.17323i
$185$	−383.205			−0.152291
$186$		0			0
$187$	150.829			0.0589822
$188$	−475.621			−0.184512
$189$		0			0
$190$	1713.71			0.654344
$191$	2408.15			0.912293			0.456146	−	0.889905i	$-0.349229\pi$
$191$	2408.15			0.912293			0.456146	+	0.889905i	$0.349229\pi$
$192$		0			0
$193$	904.035			0.337170			0.168585	−	0.985687i	$-0.446080\pi$
$193$	904.035			0.337170			0.168585	+	0.985687i	$0.446080\pi$
$194$	172.174	+	298.215i	0.0637185	+	0.110364i
$195$		0			0
$196$	2007.95	−	717.074i	0.731760	−	0.261324i
$197$	−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	$0.678419\pi$
$200$	416.914	−	722.116i	0.147401	−	0.255307i
$201$		0			0
$202$	539.609	−	934.631i	0.187954	−	0.325546i
$203$	3106.43	−	2590.59i	1.07403	−	0.895685i
$204$		0			0
$205$	−1508.47			−0.513931
$206$	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	−0.926073	−	0.377345i	$-0.876837\pi$
$211$	−417.588	+	723.284i	−0.136246	+	0.235985i	0.789827	+	0.613330i	$0.210170\pi$
$212$	−1127.41	−	1952.74i	−0.365241	−	0.632616i
$213$		0			0
$214$	768.346	−	1330.81i	0.245435	−	0.425105i
$215$	−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
$220$	−1642.99			−0.503503
$221$	−217.626			−0.0662402
$222$		0			0
$223$	−1077.64	−	1866.53i	−0.323606	−	0.560501i	0.657624	−	0.753347i	$-0.271562\pi$
$223$	−1077.64	−	1866.53i	−0.323606	−	0.560501i	−0.981229	+	0.192845i	$0.938228\pi$
$224$	582.976	+	3365.87i	0.173892	+	1.00398i
$225$		0			0
$226$	−815.080	+	1411.76i	−0.239904	+	0.415526i
$227$	−702.295	+	1216.41i	−0.205344	+	0.355665i	−0.950242	−	0.311512i	$-0.899164\pi$
$227$	−702.295	+	1216.41i	−0.205344	+	0.355665i	0.744899	+	0.667178i	$0.232498\pi$
$228$		0			0
$229$	−2874.50	−	4978.78i	−0.829487	−	1.43671i	−0.898442	−	0.439093i	$-0.855300\pi$
$229$	−2874.50	−	4978.78i	−0.829487	−	1.43671i	0.0689549	−	0.997620i	$-0.478034\pi$
$230$	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
$236$	−755.484			−0.208381
$237$		0			0
$238$	−97.6154	+	81.4059i	−0.0265860	+	0.0221713i
$239$	3286.81	−	5692.92i	0.889565	−	1.54077i	0.0491738	−	0.998790i	$-0.484341\pi$
$239$	3286.81	−	5692.92i	0.889565	−	1.54077i	0.840391	−	0.541981i	$-0.182325\pi$
$240$		0			0
$241$	474.747	−	822.286i	0.126893	−	0.219785i	−0.795578	−	0.605851i	$-0.792833\pi$
$241$	474.747	−	822.286i	0.126893	−	0.219785i	0.922471	+	0.386066i	$0.126166\pi$
$242$	−313.489	−	542.978i	−0.0832719	−	0.144231i
$243$		0			0
$244$	3993.71			1.04783
$245$	−2353.93	−	1999.63i	−0.613825	−	0.521436i
$246$		0			0
$247$	−3017.40	−	5226.28i	−0.777297	−	1.34632i
$248$	2807.33			0.718813
$249$		0			0
$250$	−2031.49			−0.513931
$251$	−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
$254$	−1456.06			−0.359690
$255$		0			0
$256$	−2290.18			−0.559125
$257$	1861.76	+	3224.67i	0.451882	+	0.782683i	0.998503	−	0.0546976i	$-0.0174195\pi$
$257$	1861.76	+	3224.67i	0.451882	+	0.782683i	−0.546621	+	0.837380i	$0.684086\pi$
$258$		0			0
$259$	739.799	+	271.808i	0.177486	+	0.0652097i
$260$	2370.63			0.565461
$261$		0			0
$262$	−1738.59	−	3011.33i	−0.409964	−	0.710078i
$263$	−2289.02	+	3964.69i	−0.536680	+	0.929557i	0.462400	+	0.886671i	$0.346988\pi$
$263$	−2289.02	+	3964.69i	−0.536680	+	0.929557i	−0.999080	+	0.0428853i	$0.986345\pi$
$264$		0			0
$265$	−1633.16	+	2828.72i	−0.378582	+	0.655724i
$266$	−3308.41	−	1215.54i	−0.762600	−	0.280185i
$267$		0			0
$268$	1012.97			0.230885
$269$	−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
$275$	−644.513	−	1116.33i	−0.141329	−	0.244790i
$276$		0			0
$277$	2527.09	−	4377.05i	0.548152	−	0.949427i	−0.450249	−	0.892903i	$-0.648665\pi$
$277$	2527.09	−	4377.05i	0.548152	−	0.949427i	0.998401	−	0.0565242i	$-0.0180018\pi$
$278$	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	0.946271	−	0.323375i	$-0.104817\pi$
$281$	909.511	+	1575.32i	0.193085	+	0.334433i	−0.753186	+	0.657807i	$0.771484\pi$
$282$		0			0
$283$	1354.96			0.284609			0.142304	−	0.989823i	$-0.454549\pi$
$283$	1354.96			0.284609			0.142304	+	0.989823i	$0.454549\pi$
$284$	−5183.43			−1.08303
$285$		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
$290$	1313.33	−	2274.76i	0.265936	−	0.460615i
$291$		0			0
$292$	388.382	+	672.697i	0.0778367	+	0.134817i
$293$	598.046	−	1035.85i	0.119243	−	0.206535i	−0.800225	−	0.599700i	$-0.795287\pi$
$293$	598.046	−	1035.85i	0.119243	−	0.206535i	0.919468	+	0.393165i	$0.128620\pi$
$294$		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
$299$	−7542.11			−1.45877
$300$		0			0
$301$	3454.97	−	2881.26i	0.661599	−	0.551738i
$302$	223.038	−	386.313i	0.0424980	−	0.0736087i
$303$		0			0
$304$	−1736.29	+	3007.34i	−0.327575	+	0.567377i
$305$	−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	$0.405193\pi$
$308$	3171.89	+	1165.38i	0.586803	+	0.215596i
$309$		0			0
$310$	−889.098	−	1539.96i	−0.162895	−	0.282142i
$311$	−1440.38			−0.262625			−0.131313	−	0.991341i	$-0.541919\pi$
$311$	−1440.38			−0.262625			−0.131313	+	0.991341i	$0.541919\pi$
$312$		0			0
$313$	5415.30			0.977926			0.488963	−	0.872305i	$-0.337375\pi$
$313$	5415.30			0.977926			0.488963	+	0.872305i	$0.337375\pi$
$314$	−1833.77			−0.329571
$315$		0			0
$316$	−5239.30			−0.932702
$317$	−4493.72			−0.796191			−0.398095	−	0.917344i	$-0.630329\pi$
$317$	−4493.72			−0.796191			−0.398095	+	0.917344i	$0.630329\pi$
$318$		0			0
$319$	6410.66			1.12517
$320$	231.348	+	400.706i	0.0404148	+	0.0700004i
$321$		0			0
$322$	−3382.99	+	2821.23i	−0.585486	+	0.488264i
$323$	−732.202			−0.126133
$324$		0			0
$325$	929.947	+	1610.72i	0.158721	+	0.274912i
$326$	103.609	−	179.456i	0.0176024	−	0.0304883i
$327$		0			0
$328$	−1590.36	+	2754.58i	−0.267722	+	0.463709i
$329$	−241.836	−	1396.26i	−0.0405253	−	0.233977i
$330$		0			0
$331$	−9867.22			−1.63852			−0.819262	−	0.573419i	$-0.805617\pi$
$331$	−9867.22			−1.63852			−0.819262	+	0.573419i	$0.805617\pi$
$332$	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	−0.740440	−	0.672123i	$-0.765383\pi$
$337$	1310.64	−	2270.10i	0.211855	−	0.366944i	0.952295	+	0.305178i	$0.0987161\pi$
$338$	−269.347	−	466.522i	−0.0433448	−	0.0750753i
$339$		0			0
$340$	143.814	−	249.094i	0.0229395	−	0.0397323i
$341$	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
$346$	257.904			0.0400723
$347$	12091.2			1.87058			0.935290	−	0.353881i	$-0.115138\pi$
$347$	12091.2			1.87058			0.935290	+	0.353881i	$0.115138\pi$
$348$		0			0
$349$	2.47828	+	4.29251i	0.000380113	+	0.000658375i	0.866215	−	0.499671i	$-0.166546\pi$
$349$	2.47828	+	4.29251i	0.000380113	+	0.000658375i	−0.865835	+	0.500329i	$0.833212\pi$
$350$	1019.64	+	374.622i	0.155719	+	0.0572125i
$351$		0			0
$352$	−2706.96	+	4688.60i	−0.409891	+	0.709952i
$353$	−261.770	+	453.399i	−0.0394691	+	0.0683626i	−0.885085	−	0.465429i	$-0.845900\pi$
$353$	−261.770	+	453.399i	−0.0394691	+	0.0683626i	0.845616	+	0.533792i	$0.179233\pi$
$354$		0			0
$355$	3754.34	+	6502.70i	0.561294	+	0.972190i
$356$	−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
$362$	6178.87			0.897111
$363$		0			0
$364$	−4576.62	−	1681.49i	−0.659012	−	0.242126i
$365$	562.606	−	974.463i	0.0806799	−	0.139742i
$366$		0			0
$367$	1397.79	−	2421.04i	0.198812	−	0.344353i	−0.749331	−	0.662195i	$-0.769625\pi$
$367$	1397.79	−	2421.04i	0.198812	−	0.344353i	0.948144	+	0.317842i	$0.102958\pi$
$368$	2169.96	+	3758.48i	0.307383	+	0.532403i
$369$		0			0
$370$	511.809			0.0719126
$371$	5159.32	−	4302.60i	0.721991	−	0.602102i
$372$		0			0
$373$	3137.09	+	5433.60i	0.435476	+	0.754266i	0.997334	−	0.0729670i	$-0.0232468\pi$
$373$	3137.09	+	5433.60i	0.435476	+	0.754266i	−0.561858	+	0.827233i	$0.689913\pi$
$374$	−201.446			−0.0278517
$375$		0			0
$376$	1452.77			0.199258
$377$	−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	$0.808913\pi$
$380$	7975.98			1.07673
$381$		0			0
$382$	−3216.33			−0.430790
$383$	5938.62	+	10286.0i	0.792295	+	1.37230i	0.924542	+	0.381079i	$0.124447\pi$
$383$	5938.62	+	10286.0i	0.792295	+	1.37230i	−0.132247	+	0.991217i	$0.542219\pi$
$384$		0			0
$385$	−835.402	−	4823.27i	−0.110587	−	0.638485i
$386$	−1207.43			−0.159214
$387$		0			0
$388$	801.338	+	1387.96i	0.104850	+	0.181605i
$389$	−286.975	+	497.055i	−0.0374041	+	0.0647858i	−0.884121	−	0.467257i	$-0.845242\pi$
$389$	−286.975	+	497.055i	−0.0374041	+	0.0647858i	0.846717	+	0.532043i	$0.178576\pi$
$390$		0			0
$391$	−457.543	+	792.487i	−0.0591788	+	0.102501i
$392$	−6133.22	+	2190.28i	−0.790240	+	0.282209i
$393$		0			0
$394$	4563.48			0.583514
$395$	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
$401$	−795.562	−	1377.95i	−0.0990735	−	0.171600i	0.812228	−	0.583340i	$-0.198255\pi$
$401$	−795.562	−	1377.95i	−0.0990735	−	0.171600i	−0.911301	+	0.411740i	$0.864921\pi$
$402$		0			0
$403$	−3130.94	+	5422.95i	−0.387006	+	0.670314i
$404$	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
$409$	−5116.03			−0.618512			−0.309256	−	0.950979i	$-0.600080\pi$
$409$	−5116.03			−0.618512			−0.309256	+	0.950979i	$0.600080\pi$
$410$	2014.71			0.242681
$411$		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
$416$	3905.79	−	6765.03i	0.460330	−	0.797315i
$417$		0			0
$418$	−2793.07	−	4837.74i	−0.326827	−	0.566080i
$419$	−690.084	+	1195.26i	−0.0804602	+	0.139361i	−0.903448	−	0.428698i	$-0.858972\pi$
$419$	−690.084	+	1195.26i	−0.0804602	+	0.139361i	0.822988	+	0.568059i	$0.192306\pi$
$420$		0			0
$421$	−2454.61	−	4251.52i	−0.284158	−	0.492176i	0.688247	−	0.725477i	$-0.258381\pi$
$421$	−2454.61	−	4251.52i	−0.284158	−	0.492176i	−0.972405	+	0.233301i	$0.925047\pi$
$422$	557.730	−	966.017i	0.0643362	−	0.111434i
$423$		0			0
$424$	3443.65	+	5964.58i	0.394430	+	0.683173i
$425$	225.661			0.0257557
$426$		0			0
$427$	2030.65	+	11724.2i	0.230141	+	1.32874i
$428$	3576.05	−	6193.90i	0.403867	−	0.699518i
$429$		0			0
$430$	1460.69	−	2529.98i	0.163815	−	0.283737i
$431$	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	$0.385446\pi$
$434$	624.155	+	3603.62i	0.0690332	+	0.398570i
$435$		0			0
$436$	5606.00	+	9709.88i	0.615777	+	1.06656i
$437$	−25375.4			−2.77774
$438$		0			0
$439$	−9621.85			−1.04607			−0.523036	−	0.852311i	$-0.675201\pi$
$439$	−9621.85			−1.04607			−0.523036	+	0.852311i	$0.675201\pi$
$440$	5018.48			0.543742
$441$		0			0
$442$	290.661			0.0312790
$443$	−2085.63			−0.223682			−0.111841	−	0.993726i	$-0.535675\pi$
$443$	−2085.63			−0.223682			−0.111841	+	0.993726i	$0.535675\pi$
$444$		0			0
$445$	4467.27			0.475885
$446$	1439.29	+	2492.93i	0.152808	+	0.264672i
$447$		0			0
$448$	−162.408	−	937.680i	−0.0171274	−	0.0988866i
$449$	−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
$452$	−3793.56	+	6570.64i	−0.394766	+	0.683755i
$453$		0			0
$454$	937.985	−	1624.64i	0.0969644	−	0.167947i
$455$	1205.37	+	6959.34i	0.124195	+	0.717053i
$456$		0			0
$457$	9746.75			0.997667			0.498833	−	0.866698i	$-0.333762\pi$
$457$	9746.75			0.997667			0.498833	+	0.866698i	$0.333762\pi$
$458$	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	0.992988	−	0.118217i	$-0.0377179\pi$
$461$	3900.98	+	6756.70i	0.394115	+	0.682627i	−0.598873	+	0.800844i	$0.704385\pi$
$462$		0			0
$463$	3544.24	−	6138.81i	0.355756	−	0.616187i	−0.631491	−	0.775383i	$-0.717557\pi$
$463$	3544.24	−	6138.81i	0.355756	−	0.616187i	0.987247	+	0.159196i	$0.0508901\pi$
$464$	2661.27	+	4609.45i	0.266264	+	0.461182i
$465$		0			0
$466$	327.858	−	567.867i	0.0325917	−	0.0564505i
$467$	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
$472$	2307.60			0.225034
$473$	7129.94			0.693098
$474$		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
$479$	5492.39	−	9513.09i	0.523911	−	0.907441i	−0.475701	−	0.879607i	$-0.657806\pi$
$479$	5492.39	−	9513.09i	0.523911	−	0.907441i	0.999613	−	0.0278342i	$-0.00886105\pi$
$480$		0			0
$481$	−901.162	−	1560.86i	−0.0854251	−	0.147961i
$482$	−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	$0.655377\pi$
$488$	−12198.7			−1.13157
$489$		0			0
$490$	3143.91	+	2670.71i	0.289852	+	0.246225i
$491$	−7398.90	+	12815.3i	−0.680056	+	1.17789i	0.294907	+	0.955526i	$0.404711\pi$
$491$	−7398.90	+	12815.3i	−0.680056	+	1.17789i	−0.974963	+	0.222366i	$0.928622\pi$
$492$		0			0
$493$	−561.137	+	971.917i	−0.0512623	+	0.0887889i
$494$	4030.03	+	6980.22i	0.367044	+	0.635739i
$495$		0			0
$496$	3603.25			0.326191
$497$	−2635.58	−	15216.8i	−0.237871	−	1.37337i
$498$		0			0
$499$	−6738.22	−	11670.9i	−0.604498	−	1.04702i	−0.992131	−	0.125207i	$-0.960041\pi$
$499$	−6738.22	−	11670.9i	−0.604498	−	1.04702i	0.387633	−	0.921814i	$-0.373293\pi$
$500$	−9455.00			−0.845681
$501$		0			0
$502$	7069.51			0.628541
$503$	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
$506$	−6981.39			−0.613361
$507$		0			0
$508$	−6776.83			−0.591876
$509$	−4829.68	−	8365.25i	−0.420573	−	0.728454i	0.575422	−	0.817856i	$-0.304838\pi$
$509$	−4829.68	−	8365.25i	−0.420573	−	0.728454i	−0.995996	+	0.0894023i	$0.971504\pi$
$510$		0			0
$511$	−1777.33	+	1482.20i	−0.153864	+	0.128314i
$512$	−8196.75			−0.707517
$513$		0			0
$514$	−2486.57	−	4306.87i	−0.213381	−	0.369587i
$515$	1358.70	−	2353.34i	0.116255	−	0.201360i
$516$		0			0
$517$	1122.93	−	1944.97i	0.0955248	−	0.165454i
$518$	−988.075	−	363.026i	−0.0838099	−	0.0307924i
$519$		0			0
$520$	−7241.00			−0.610652
$521$	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
$527$	379.878	+	657.968i	0.0313999	+	0.0543862i
$528$		0			0
$529$	−9773.24	+	16927.7i	−0.803258	+	1.39128i
$530$	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
$535$	−10360.5			−0.837238
$536$	−3094.09			−0.249337
$537$		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	$-0.0866585\pi$
$542$	3443.36	−	5964.07i	0.272887	−	0.472655i
$543$		0			0
$544$	−473.891	−	820.803i	−0.0373491	−	0.0646905i
$545$	8120.81	−	14065.7i	0.638270	−	1.10552i
$546$		0			0
$547$	−9366.21	−	16222.7i	−0.732121	−	1.26807i	−0.955975	−	0.293448i	$-0.905197\pi$
$547$	−9366.21	−	16222.7i	−0.732121	−	1.26807i	0.223854	−	0.974623i	$-0.428136\pi$
$548$	−37.7591	+	65.4006i	−0.00294341	+	0.00509813i
$549$		0			0
$550$	860.811	+	1490.97i	0.0667365	+	0.115591i
$551$	−31120.8			−2.40615
$552$		0			0
$553$	−2663.99	−	15380.8i	−0.204854	−	1.18275i
$554$	−3375.18	+	5845.98i	−0.258840	+	0.448325i
$555$		0			0
$556$	5831.22	−	10100.0i	0.444782	−	0.770385i
$557$	−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
$560$	3121.27	−	2602.97i	0.235532	−	0.196421i
$561$		0			0
$562$	−1214.74	−	2103.99i	−0.0911758	−	0.157921i
$563$	17027.1			1.27461			0.637306	−	0.770611i	$-0.280049\pi$
$563$	17027.1			1.27461			0.637306	+	0.770611i	$0.280049\pi$
$564$		0			0
$565$	10990.6			0.818371
$566$	−1809.69			−0.134394
$567$		0			0
$568$	15832.6			1.16958
$569$	6308.56			0.464796			0.232398	−	0.972621i	$-0.425343\pi$
$569$	6308.56			0.464796			0.232398	+	0.972621i	$0.425343\pi$
$570$		0			0
$571$	390.088			0.0285896			0.0142948	−	0.999898i	$-0.495450\pi$
$571$	390.088			0.0285896			0.0142948	+	0.999898i	$0.495450\pi$
$572$	−3863.74	−	6692.19i	−0.282432	−	0.489187i
$573$		0			0
$574$	−3889.50	−	1429.03i	−0.282830	−	0.103914i
$575$	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	$-0.372801\pi$
$578$	−3263.27	+	5652.14i	−0.234834	+	0.406744i
$579$		0			0
$580$	6112.53	−	10587.2i	0.437602	−	0.757949i
$581$	−16128.1	+	13450.0i	−1.15165	+	0.960411i
$582$		0			0
$583$	10647.2			0.756365
$584$	−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	0.973469	+	0.228821i	$0.0734869\pi$
$587$	9740.55	+	16871.1i	0.684899	+	1.18628i	−0.288570	+	0.957459i	$0.593180\pi$
$588$		0			0
$589$	−10534.1	+	18245.5i	−0.736925	+	1.27639i
$590$	−730.832	−	1265.84i	−0.0509964	−	0.0883283i
$591$		0			0
$592$	−518.552	+	898.158i	−0.0360006	+	0.0623548i
$593$	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
$598$	10073.2			0.688838
$599$	8861.97			0.604491			0.302246	−	0.953230i	$-0.402264\pi$
$599$	8861.97			0.604491			0.302246	+	0.953230i	$0.402264\pi$
$600$		0			0
$601$	−6052.58	−	10483.4i	−0.410798	−	0.711524i	0.584179	−	0.811625i	$-0.301417\pi$
$601$	−6052.58	−	10483.4i	−0.410798	−	0.711524i	−0.994977	+	0.100101i	$0.968083\pi$
$602$	−4614.46	+	3848.21i	−0.312411	+	0.260534i
$603$		0			0
$604$	1038.07	−	1797.99i	0.0699311	−	0.121124i
$605$	−2113.56	+	3660.79i	−0.142030	+	0.246004i
$606$		0			0
$607$	−1460.25	−	2529.23i	−0.0976439	−	0.169124i	0.813065	−	0.582173i	$-0.197797\pi$
$607$	−1460.25	−	2529.23i	−0.0976439	−	0.169124i	−0.910709	+	0.413049i	$0.864464\pi$
$608$	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	$0.495636\pi$
$614$	−4216.61			−0.277147
$615$		0			0
$616$	−9688.45	−	3559.61i	−0.633699	−	0.232826i
$617$	2694.79	−	4667.52i	0.175832	−	0.304550i	−0.764617	−	0.644485i	$-0.777072\pi$
$617$	2694.79	−	4667.52i	0.175832	−	0.304550i	0.940449	+	0.339935i	$0.110405\pi$
$618$		0			0
$619$	1800.48	−	3118.53i	0.116910	−	0.202495i	−0.801631	−	0.597819i	$-0.796034\pi$
$619$	1800.48	−	3118.53i	0.116910	−	0.202495i	0.918542	+	0.395324i	$0.129368\pi$
$620$	−4138.06	−	7167.33i	−0.268046	−	0.464269i
$621$		0			0
$622$	1923.77			0.124013
$623$	−8624.31	−	3168.64i	−0.554616	−	0.203770i
$624$		0			0
$625$	4103.50	+	7107.47i	0.262624	+	0.454878i
$626$	−7232.67			−0.461782
$627$		0			0
$628$	−8534.75			−0.542315
$629$	−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	$0.419921\pi$
$632$	16003.3			1.00724
$633$		0			0
$634$	6001.81			0.375966
$635$	4908.43	+	8501.64i	0.306748	+	0.531303i
$636$		0			0
$637$	2609.23	−	14290.4i	0.162294	−	0.888862i
$638$	−8562.08			−0.531310
$639$		0			0
$640$	6334.52	+	10971.7i	0.391241	+	0.677649i
$641$	5411.02	−	9372.16i	0.333420	−	0.577501i	−0.649760	−	0.760140i	$-0.725131\pi$
$641$	5411.02	−	9372.16i	0.333420	−	0.577501i	0.983180	+	0.182639i	$0.0584639\pi$
$642$		0			0
$643$	−5256.94	+	9105.29i	−0.322416	+	0.558441i	−0.980986	−	0.194079i	$-0.937828\pi$
$643$	−5256.94	+	9105.29i	−0.322416	+	0.558441i	0.658570	+	0.752520i	$0.271162\pi$
$644$	−15745.2	+	13130.6i	−0.963427	+	0.803446i
$645$		0			0
$646$	977.929			0.0595605
$647$	−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
$653$	−11405.0	−	19754.0i	−0.683477	−	1.18382i	−0.973913	−	0.226922i	$-0.927134\pi$
$653$	−11405.0	−	19754.0i	−0.683477	−	1.18382i	0.290436	−	0.956894i	$-0.406200\pi$
$654$		0			0
$655$	−11721.7	+	20302.6i	−0.699243	+	1.21112i
$656$	−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	0.839163	+	0.543880i	$0.183045\pi$
$659$	15066.4	+	26095.7i	0.890595	+	1.54256i	0.0514322	+	0.998676i	$0.483621\pi$
$660$		0			0
$661$	−2208.87			−0.129978			−0.0649888	−	0.997886i	$-0.520701\pi$
$661$	−2208.87			−0.129978			−0.0649888	+	0.997886i	$0.520701\pi$
$662$	13178.7			0.773720
$663$		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
$668$	4081.18	−	7068.81i	0.236385	−	0.409432i
$669$		0			0
$670$	979.918	+	1697.27i	0.0565038	+	0.0978674i
$671$	−9429.05	+	16331.6i	−0.542480	+	0.939603i
$672$		0			0
$673$	4400.74	+	7622.31i	0.252060	+	0.436580i	0.964093	−	0.265566i	$-0.0855588\pi$
$673$	4400.74	+	7622.31i	0.252060	+	0.436580i	−0.712033	+	0.702146i	$0.752225\pi$
$674$	−1750.49	+	3031.94i	−0.100039	+	0.173273i
$675$		0			0
$676$	−1253.60	−	2171.30i	−0.0713245	−	0.123538i
$677$	17686.7			1.00407			0.502034	−	0.864848i	$-0.332585\pi$
$677$	17686.7			1.00407			0.502034	+	0.864848i	$0.332585\pi$
$678$		0			0
$679$	−3667.12	+	3058.18i	−0.207262	+	0.172845i
$680$	−439.276	+	760.848i	−0.0247727	+	0.0429077i
$681$		0			0
$682$	−2898.17	+	5019.78i	−0.162723	+	0.281844i
$683$	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
$686$	−4175.15	−	7385.92i	−0.232373	−	0.411073i
$687$		0			0
$688$	2959.86	+	5126.63i	0.164017	+	0.284086i
$689$	−15362.5			−0.849439
$690$		0			0
$691$	31433.7			1.73053			0.865263	−	0.501318i	$-0.167151\pi$
$691$	31433.7			1.73053			0.865263	+	0.501318i	$0.167151\pi$
$692$	1200.34			0.0659396
$693$		0			0
$694$	−16149.0			−0.883299
$695$	−16894.1			−0.922057
$696$		0			0
$697$	−860.807			−0.0467796
$698$	−3.30999	−	5.73307i	−0.000179491	−	0.000310888i
$699$		0			0
$700$	4745.61	+	1743.57i	0.256239	+	0.0941442i
$701$	−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
$704$	754.119	−	1306.17i	0.0403721	−	0.0699265i
$705$		0			0
$706$	349.620	−	605.559i	0.0186376	−	0.0322812i
$707$	14047.0	+	5160.99i	0.747232	+	0.274539i
$708$		0			0
$709$	7518.46			0.398254			0.199127	−	0.979974i	$-0.436189\pi$
$709$	7518.46			0.398254			0.199127	+	0.979974i	$0.436189\pi$
$710$	−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
$716$	12417.9	+	21508.4i	0.648155	+	1.12264i
$717$		0			0
$718$	797.116	−	1380.65i	0.0414319	−	0.0717621i
$719$	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
$724$	28757.8			1.47621
$725$	9591.28			0.491326
$726$		0			0
$727$	16313.3	+	28255.5i	0.832224	+	1.44145i	0.896271	+	0.443507i	$0.146266\pi$
$727$	16313.3	+	28255.5i	0.832224	+	1.44145i	−0.0640474	+	0.997947i	$0.520401\pi$
$728$	13979.2	+	5136.05i	0.711679	+	0.261476i
$729$		0			0
$730$	−751.417	+	1301.49i	−0.0380975	+	0.0659868i
$731$	−624.096	+	1080.97i	−0.0315773	+	0.0546936i
$732$		0			0
$733$	5397.29	+	9348.37i	0.271969	+	0.471064i	0.969366	−	0.245621i	$-0.0789918\pi$
$733$	5397.29	+	9348.37i	0.271969	+	0.471064i	−0.697397	+	0.716685i	$0.745659\pi$
$734$	−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	$0.707547\pi$
$740$	2382.07			0.118333
$741$		0			0
$742$	−6890.79	+	5746.54i	−0.340928	+	0.284316i
$743$	14278.8	−	24731.7i	0.705033	−	1.22115i	−0.261646	−	0.965164i	$-0.584265\pi$
$743$	14278.8	−	24731.7i	0.705033	−	1.22115i	0.966680	−	0.255990i	$-0.0824013\pi$
$744$		0			0
$745$	−4080.34	+	7067.36i	−0.200661	+	0.347554i
$746$	−4189.90	−	7257.12i	−0.205634	−	0.356169i
$747$		0			0
$748$	−937.577			−0.0458305
$749$	20001.5	+	7348.69i	0.975751	+	0.358499i
$750$		0			0
$751$	−3829.56	−	6633.00i	−0.186075	−	0.322292i	0.757863	−	0.652414i	$-0.226244\pi$
$751$	−3829.56	−	6633.00i	−0.186075	−	0.322292i	−0.943938	+	0.330122i	$0.892910\pi$
$752$	1864.65			0.0904213
$753$		0			0
$754$	12354.0			0.596690
$755$	−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	$0.614112\pi$
$758$	16263.0			0.779288
$759$		0			0
$760$	−24362.4			−1.16278
$761$	10709.5	+	18549.4i	0.510144	+	0.883595i	0.999931	+	0.0117529i	$0.00374115\pi$
$761$	10709.5	+	18549.4i	0.510144	+	0.883595i	−0.489787	+	0.871842i	$0.662926\pi$
$762$		0			0
$763$	−25654.5	+	21394.4i	−1.21724	+	1.01511i
$764$	−14969.5			−0.708871
$765$		0			0
$766$	−7931.61	−	13738.0i	−0.374126	−	0.648006i
$767$	−2573.61	+	4457.62i	−0.121157	+	0.209851i
$768$		0			0
$769$	2461.01	−	4262.59i	0.115405	−	0.199887i	−0.802537	−	0.596603i	$-0.796517\pi$
$769$	2461.01	−	4262.59i	0.115405	−	0.199887i	0.917941	+	0.396716i	$0.129850\pi$
$770$	1115.76	+	6441.96i	0.0522198	+	0.301496i
$771$		0			0
$772$	−5619.64			−0.261989
$773$	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
$779$	−11935.2	−	20672.3i	−0.548936	−	0.950785i
$780$		0			0
$781$	12237.9	−	21196.7i	0.560701	−	0.971163i
$782$	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
$787$	7198.98			0.326068			0.163034	−	0.986620i	$-0.447872\pi$
$787$	7198.98			0.326068			0.163034	+	0.986620i	$0.447872\pi$
$788$	21239.4			0.960182
$789$		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
$794$	4669.26	−	8087.40i	0.208698	−	0.361475i
$795$		0			0
$796$	−8161.34	−	14135.9i	−0.363406	−	0.629437i
$797$	6877.32	−	11911.9i	0.305655	−	0.529410i	−0.671752	−	0.740776i	$-0.734458\pi$
$797$	6877.32	−	11911.9i	0.305655	−	0.529410i	0.977407	+	0.211366i	$0.0677912\pi$
$798$		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
$803$	−3667.83			−0.161189
$804$		0			0
$805$	27876.8	+	10242.1i	1.22053	+	0.448432i
$806$	4181.68	−	7242.89i	0.182746	−	0.316526i
$807$		0			0
$808$	−7671.18	+	13286.9i	−0.333999	+	0.578503i
$809$	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	$0.661715\pi$
$812$	−19310.1	+	16103.6i	−0.834547	+	0.695967i
$813$		0			0
$814$	−834.166	−	1444.82i	−0.0359183	−	0.0622123i
$815$	−1397.08			−0.0600461
$816$		0			0
$817$	−34612.6			−1.48218
$818$	6832.97			0.292065
$819$		0			0
$820$	9376.89			0.399335
$821$	4148.26			0.176340			0.0881701	−	0.996105i	$-0.471898\pi$
$821$	4148.26			0.176340			0.0881701	+	0.996105i	$0.471898\pi$
$822$		0			0
$823$	16747.9			0.709349			0.354675	−	0.934990i	$-0.384592\pi$
$823$	16747.9			0.709349			0.354675	+	0.934990i	$0.384592\pi$
$824$	−2864.93	−	4962.20i	−0.121122	−	0.209789i
$825$		0			0
$826$	513.051	+	2962.15i	0.0216118	+	0.124778i
$827$	−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	$0.920359\pi$
$830$	−6818.62	+	11810.2i	−0.285154	+	0.493901i
$831$		0			0
$832$	−1088.09	+	1884.64i	−0.0453400	+	0.0785312i
$833$	−1343.27	−	1141.09i	−0.0558723	−	0.0474628i
$834$		0			0
$835$	−11823.9			−0.490040
$836$	−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	−0.989185	−	0.146673i	$-0.953143\pi$
$839$	−15106.5	−	26165.3i	−0.621615	−	1.07667i	0.367570	−	0.929996i	$-0.380190\pi$
$840$		0			0
$841$	−11655.5	+	20187.9i	−0.477899	+	0.827746i
$842$	3278.38	+	5678.32i	0.134181	+	0.232408i
$843$		0			0
$844$	2595.80	−	4496.06i	0.105866	−	0.183366i
$845$	−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
$850$	−301.393			−0.0121620
$851$	−7578.52			−0.305274
$852$		0			0
$853$	12389.8	+	21459.7i	0.497324	+	0.861391i	0.999995	−	0.00308694i	$-0.000982605\pi$
$853$	12389.8	+	21459.7i	0.497324	+	0.861391i	−0.502671	+	0.864478i	$0.667649\pi$
$854$	−2712.14	−	15658.8i	−0.108674	−	0.627439i
$855$		0			0
$856$	−10922.9	+	18919.1i	−0.436143	+	0.755421i
$857$	−10876.3	+	18838.3i	−0.433521	+	0.750881i	−0.997174	−	0.0751313i	$-0.976062\pi$
$857$	−10876.3	+	18838.3i	−0.433521	+	0.750881i	0.563652	+	0.826012i	$0.309396\pi$
$858$		0			0
$859$	16983.6	+	29416.5i	0.674591	+	1.16843i	0.976588	+	0.215118i	$0.0690135\pi$
$859$	16983.6	+	29416.5i	0.674591	+	1.16843i	−0.301997	+	0.953309i	$0.597653\pi$
$860$	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
$866$	−8475.86			−0.332588
$867$		0			0
$868$	2904.96	+	16772.1i	0.113595	+	0.655853i
$869$	12369.8	−	21425.2i	0.482875	−	0.836364i
$870$		0			0
$871$	3450.77	−	5976.90i	0.134242	−	0.232514i
$872$	−17123.4	−	29658.5i	−0.664989	−	1.15179i
$873$		0			0
$874$	33891.4			1.31166
$875$	−4807.52	−	27756.7i	−0.185741	−	1.07240i
$876$		0			0
$877$	−16867.2	−	29214.9i	−0.649449	−	1.12488i	−0.983255	−	0.182236i	$-0.941666\pi$
$877$	−16867.2	−	29214.9i	−0.649449	−	1.12488i	0.333806	−	0.942642i	$-0.391667\pi$
$878$	12850.9			0.493961
$879$		0			0
$880$	6441.29			0.246745
$881$	−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	$0.343273\pi$
$884$	1352.80			0.0514701
$885$		0			0
$886$	2785.56			0.105624
$887$	3554.82	+	6157.13i	0.134565	+	0.233073i	0.925431	−	0.378916i	$-0.123703\pi$
$887$	3554.82	+	6157.13i	0.134565	+	0.233073i	−0.790866	+	0.611989i	$0.790370\pi$
$888$		0			0
$889$	−3445.76	−	19894.5i	−0.129997	−	0.750549i
$890$	−5966.48			−0.224716
$891$		0			0
$892$	6698.79	+	11602.6i	0.251449	+	0.435522i
$893$	−5451.29	+	9441.92i	−0.204278	+	0.353821i
$894$		0			0
$895$	17988.5	−	31156.9i	0.671830	−	1.16364i
$896$	−4446.90	−	25674.6i	−0.165804	−	0.957286i
$897$		0			0
$898$	13728.9			0.510178
$899$	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
$905$	−20829.2	−	36077.2i	−0.765066	−	1.32513i
$906$		0			0
$907$	15393.8	−	26662.8i	0.563552	−	0.976101i	−0.433631	−	0.901091i	$-0.642768\pi$
$907$	15393.8	−	26662.8i	0.563552	−	0.976101i	0.997183	−	0.0750100i	$-0.0238989\pi$
$908$	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	0.820434	−	0.571741i	$-0.193732\pi$
$911$	−2335.16	−	4044.61i	−0.0849256	−	0.147095i	−0.905360	+	0.424646i	$0.860399\pi$
$912$		0			0
$913$	−33283.2			−1.20648
$914$	−13017.8			−0.471104
$915$		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	$-0.00953723\pi$
$920$	−15223.7	+	26368.2i	−0.545554	+	0.944928i
$921$		0			0
$922$	−5210.15	−	9024.24i	−0.186103	−	0.322340i
$923$	−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
$929$	−3123.32			−0.110304			−0.0551521	−	0.998478i	$-0.517564\pi$
$929$	−3123.32			−0.110304			−0.0551521	+	0.998478i	$0.517564\pi$
$930$		0			0
$931$	8778.76	−	48080.0i	0.309036	−	1.69254i
$932$	1525.92	−	2642.98i	0.0536302	−	0.0928902i
$933$		0			0
$934$	−11754.2	+	20358.9i	−0.411787	+	0.713236i
$935$	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	$0.659147\pi$
$938$	−687.912	−	3971.73i	−0.0239458	−	0.138253i
$939$		0			0
$940$	−2141.41	−	3709.03i	−0.0743034	−	0.128697i
$941$	−4855.36			−0.168204			−0.0841022	−	0.996457i	$-0.526802\pi$
$941$	−4855.36			−0.168204			−0.0841022	+	0.996457i	$0.526802\pi$
$942$		0			0
$943$	−29832.4			−1.03020
$944$	2961.84			0.102118
$945$		0			0
$946$	−9522.75			−0.327285
$947$	11820.2			0.405602			0.202801	−	0.979220i	$-0.434996\pi$
$947$	11820.2			0.405602			0.202801	+	0.979220i	$0.434996\pi$
$948$		0			0
$949$	5292.20			0.181024
$950$	−4178.84	−	7237.96i	−0.142715	−	0.247190i
$951$		0			0
$952$	1387.72	−	1157.28i	0.0472439	−	0.0393988i
$953$	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
$956$	−20431.4	+	35388.2i	−0.691211	+	1.19721i
$957$		0			0
$958$	−7335.63	+	12705.7i	−0.247394	+	0.428499i
$959$	−211.193	−	77.5939i	−0.00711134	−	0.00261276i
$960$		0			0
$961$	−7930.07			−0.266190
$962$	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	−0.653781	−	0.756683i	$-0.726818\pi$
$967$	9875.62	−	17105.1i	0.328416	−	0.568834i	0.982198	+	0.187850i	$0.0601518\pi$
$968$	4456.61	+	7719.07i	0.147976	+	0.256302i
$969$		0			0
$970$	−1550.38	+	2685.33i	−0.0513192	+	0.0888875i
$971$	−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
$976$	−15657.2			−0.513498
$977$	2623.52			0.0859099			0.0429549	−	0.999077i	$-0.486323\pi$
$977$	2623.52			0.0859099			0.0429549	+	0.999077i	$0.486323\pi$
$978$		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
$983$	10406.4	−	18024.4i	0.337653	−	0.584832i	−0.646338	−	0.763051i	$-0.723700\pi$
$983$	10406.4	−	18024.4i	0.337653	−	0.584832i	0.983991	+	0.178219i	$0.0570337\pi$
$984$		0			0
$985$	−15383.6	−	26645.2i	−0.497627	−	0.861916i
$986$	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	$0.993888\pi$
$992$	−27271.1			−0.872842
$993$		0			0
$994$	3520.08	+	20323.5i	0.112324	+	0.648514i
$995$	−11822.4	+	20477.1i	−0.376680	+	0.652429i
$996$		0			0
$997$	21998.3	−	38102.2i	0.698790	−	1.21034i	−0.270096	−	0.962833i	$-0.587056\pi$
$997$	21998.3	−	38102.2i	0.698790	−	1.21034i	0.968886	−	0.247506i	$-0.0796111\pi$
$998$	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.h.a.37.9		44
3.2	odd	2		63.4.h.a.58.14	yes	44
7.4	even	3		189.4.g.a.172.14		44
9.2	odd	6		63.4.g.a.16.9	yes	44
9.7	even	3		189.4.g.a.100.14		44
21.11	odd	6		63.4.g.a.4.9	✓	44
63.11	odd	6		63.4.h.a.25.14	yes	44
63.25	even	3	inner	189.4.h.a.46.9		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.9	✓	44	21.11	odd	6
63.4.g.a.16.9	yes	44	9.2	odd	6
63.4.h.a.25.14	yes	44	63.11	odd	6
63.4.h.a.58.14	yes	44	3.2	odd	2
189.4.g.a.100.14		44	9.7	even	3
189.4.g.a.172.14		44	7.4	even	3
189.4.h.a.37.9		44	1.1	even	1	trivial
189.4.h.a.46.9		44	63.25	even	3	inner

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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.33560 q^{2} -6.21617 q^{4} +(4.50235 + 7.79829i) q^{5} +(-3.16069 - 18.2486i) q^{7} +18.9871 q^{8} +O(q^{10})\)	\(q-1.33560 q^{2} -6.21617 q^{4} +(4.50235 + 7.79829i) q^{5} +(-3.16069 - 18.2486i) q^{7} +18.9871 q^{8} +(-6.01333 - 10.4154i) q^{10} +(14.6762 - 25.4199i) q^{11} +(-21.1758 + 36.6776i) q^{13} +(4.22142 + 24.3728i) q^{14} +24.3702 q^{16} +(2.56927 + 4.45010i) q^{17} +(-71.2462 + 123.402i) q^{19} +(-27.9874 - 48.4756i) q^{20} +(-19.6015 + 33.9509i) q^{22} +(89.0414 + 154.224i) q^{23} +(21.9577 - 38.0319i) q^{25} +(28.2824 - 48.9866i) q^{26} +(19.6474 + 113.436i) q^{28} +(109.202 + 189.143i) q^{29} +147.854 q^{31} -184.446 q^{32} +(-3.43151 - 5.94356i) q^{34} +(128.077 - 106.809i) q^{35} +(-21.2781 + 36.8547i) q^{37} +(95.1564 - 164.816i) q^{38} +(85.4866 + 148.067i) q^{40} +(-83.7600 + 145.077i) q^{41} +(121.454 + 210.365i) q^{43} +(-91.2299 + 158.015i) q^{44} +(-118.924 - 205.982i) q^{46} +76.5135 q^{47} +(-323.020 + 115.356i) q^{49} +(-29.3267 + 50.7954i) q^{50} +(131.633 - 227.995i) q^{52} +(181.368 + 314.138i) q^{53} +264.310 q^{55} +(-60.0124 - 346.487i) q^{56} +(-145.850 - 252.619i) q^{58} +121.535 q^{59} -642.471 q^{61} -197.474 q^{62} +51.3838 q^{64} -381.364 q^{65} -162.958 q^{67} +(-15.9710 - 27.6626i) q^{68} +(-171.060 + 142.655i) q^{70} +833.862 q^{71} +(-62.4792 - 108.217i) q^{73} +(28.4190 - 49.2231i) q^{74} +(442.879 - 767.089i) q^{76} +(-510.264 - 187.475i) q^{77} +842.850 q^{79} +(109.723 + 190.046i) q^{80} +(111.870 - 193.764i) q^{82} +(-566.958 - 982.000i) q^{83} +(-23.1355 + 40.0718i) q^{85} +(-162.214 - 280.963i) q^{86} +(278.659 - 482.651i) q^{88} +(248.052 - 429.639i) q^{89} +(736.244 + 270.502i) q^{91} +(-553.497 - 958.685i) q^{92} -102.191 q^{94} -1283.10 q^{95} +(-128.912 - 223.282i) q^{97} +(431.425 - 154.070i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8	\( 44 q + 2 q^{2} + 158 q^{4} + 19 q^{5} - 7 q^{7} + 24 q^{8} - 18 q^{10} - 5 q^{11} - 14 q^{13} + 52 q^{14} + 494 q^{16} + 162 q^{17} + 58 q^{19} + 362 q^{20} - 18 q^{22} + 93 q^{23} - 349 q^{25} + 266 q^{26} - 172 q^{28} - 248 q^{29} - 122 q^{31} - 326 q^{32} + 6 q^{34} - 289 q^{35} - 86 q^{37} + 761 q^{38} - 18 q^{40} + 692 q^{41} - 86 q^{43} + 443 q^{44} - 270 q^{46} - 2010 q^{47} + 317 q^{49} - 239 q^{50} - 335 q^{52} - 258 q^{53} - 870 q^{55} + 1752 q^{56} + 237 q^{58} - 3330 q^{59} - 878 q^{61} - 1812 q^{62} + 872 q^{64} - 1226 q^{65} - 590 q^{67} + 1374 q^{68} + 1251 q^{70} - 636 q^{71} - 338 q^{73} - 1119 q^{74} + 1006 q^{76} - 2269 q^{77} - 266 q^{79} + 4817 q^{80} + 6 q^{82} + 1356 q^{83} + 483 q^{85} + 3343 q^{86} + 369 q^{88} + 2200 q^{89} + 1552 q^{91} + 396 q^{92} + 2382 q^{94} + 6166 q^{95} - 266 q^{97} - 3601 q^{98}+O(q^{100}) \) 44 * q + 2 * q^2 + 158 * q^4 + 19 * q^5 - 7 * q^7 + 24 * q^8 - 18 * q^10 - 5 * q^11 - 14 * q^13 + 52 * q^14 + 494 * q^16 + 162 * q^17 + 58 * q^19 + 362 * q^20 - 18 * q^22 + 93 * q^23 - 349 * q^25 + 266 * q^26 - 172 * q^28 - 248 * q^29 - 122 * q^31 - 326 * q^32 + 6 * q^34 - 289 * q^35 - 86 * q^37 + 761 * q^38 - 18 * q^40 + 692 * q^41 - 86 * q^43 + 443 * q^44 - 270 * q^46 - 2010 * q^47 + 317 * q^49 - 239 * q^50 - 335 * q^52 - 258 * q^53 - 870 * q^55 + 1752 * q^56 + 237 * q^58 - 3330 * q^59 - 878 * q^61 - 1812 * q^62 + 872 * q^64 - 1226 * q^65 - 590 * q^67 + 1374 * q^68 + 1251 * q^70 - 636 * q^71 - 338 * q^73 - 1119 * q^74 + 1006 * q^76 - 2269 * q^77 - 266 * q^79 + 4817 * q^80 + 6 * q^82 + 1356 * q^83 + 483 * q^85 + 3343 * q^86 + 369 * q^88 + 2200 * q^89 + 1552 * q^91 + 396 * q^92 + 2382 * q^94 + 6166 * q^95 - 266 * q^97 - 3601 * q^98

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