LMFDB - Embedded newform 189.4.g.a.100.7

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			100.7
Character	$\chi$	$=$	189.100
Dual form			189.4.g.a.172.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32738 - 2.29909i) q^{2} +(0.476130 - 0.824682i) q^{4} -7.35561 q^{5} +(16.6607 - 8.08840i) q^{7} -23.7661 q^{8} +O(q^{10})$	\(q+(-1.32738 - 2.29909i) q^{2} +(0.476130 - 0.824682i) q^{4} -7.35561 q^{5} +(16.6607 - 8.08840i) q^{7} -23.7661 q^{8} +(9.76368 + 16.9112i) q^{10} -11.3432 q^{11} +(-30.2941 - 52.4710i) q^{13} +(-40.7110 - 27.5680i) q^{14} +(27.7376 + 48.0429i) q^{16} +(5.29282 + 9.16743i) q^{17} +(-41.6545 + 72.1477i) q^{19} +(-3.50223 + 6.06604i) q^{20} +(15.0568 + 26.0791i) q^{22} -87.6234 q^{23} -70.8950 q^{25} +(-80.4236 + 139.298i) q^{26} +(1.26229 - 17.5909i) q^{28} +(67.6917 - 117.246i) q^{29} +(-26.7514 + 46.3349i) q^{31} +(-21.4278 + 37.1141i) q^{32} +(14.0511 - 24.3373i) q^{34} +(-122.549 + 59.4952i) q^{35} +(-149.868 + 259.578i) q^{37} +221.165 q^{38} +174.814 q^{40} +(194.038 + 336.083i) q^{41} +(-215.569 + 373.377i) q^{43} +(-5.40086 + 9.35456i) q^{44} +(116.309 + 201.454i) q^{46} +(-255.582 - 442.681i) q^{47} +(212.155 - 269.516i) q^{49} +(94.1045 + 162.994i) q^{50} -57.6958 q^{52} +(-116.232 - 201.320i) q^{53} +83.4364 q^{55} +(-395.959 + 192.230i) q^{56} -359.410 q^{58} +(31.1816 - 54.0081i) q^{59} +(-170.015 - 294.474i) q^{61} +142.037 q^{62} +557.572 q^{64} +(222.832 + 385.956i) q^{65} +(274.599 - 475.620i) q^{67} +10.0803 q^{68} +(299.454 + 202.779i) q^{70} -505.089 q^{71} +(-99.1981 - 171.816i) q^{73} +795.724 q^{74} +(39.6659 + 68.7034i) q^{76} +(-188.986 + 91.7487i) q^{77} +(-588.922 - 1020.04i) q^{79} +(-204.027 - 353.385i) q^{80} +(515.123 - 892.219i) q^{82} +(722.688 - 1251.73i) q^{83} +(-38.9319 - 67.4320i) q^{85} +1144.57 q^{86} +269.584 q^{88} +(507.365 - 878.783i) q^{89} +(-929.126 - 629.170i) q^{91} +(-41.7201 + 72.2614i) q^{92} +(-678.509 + 1175.21i) q^{94} +(306.394 - 530.690i) q^{95} +(551.029 - 954.410i) q^{97} +(-901.252 - 130.014i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.32738	−	2.29909i	−0.469299	−	0.812850i	0.530085	−	0.847945i	$-0.322160\pi$
$2$	−1.32738	−	2.29909i	−0.469299	−	0.812850i	−0.999384	+	0.0350944i	$0.988827\pi$
$3$		0			0
$3$		0			0
$4$	0.476130	−	0.824682i	0.0595163	−	0.103085i
$5$	−7.35561			−0.657906			−0.328953	−	0.944346i	$-0.606696\pi$
$5$	−7.35561			−0.657906			−0.328953	+	0.944346i	$0.606696\pi$
$6$		0			0
$7$	16.6607	−	8.08840i	0.899591	−	0.436733i
$7$	16.6607	−	8.08840i	0.899591	−	0.436733i
$8$	−23.7661			−1.05032
$9$		0			0
$10$	9.76368	+	16.9112i	0.308755	+	0.534779i
$11$	−11.3432			−0.310919			−0.155460	−	0.987842i	$-0.549686\pi$
$11$	−11.3432			−0.310919			−0.155460	+	0.987842i	$0.549686\pi$
$12$		0			0
$13$	−30.2941	−	52.4710i	−0.646314	−	1.11945i	−0.983996	−	0.178188i	$-0.942976\pi$
$13$	−30.2941	−	52.4710i	−0.646314	−	1.11945i	0.337683	−	0.941260i	$-0.390357\pi$
$14$	−40.7110	−	27.5680i	−0.777176	−	0.526275i
$15$		0			0
$16$	27.7376	+	48.0429i	0.433399	+	0.750670i
$17$	5.29282	+	9.16743i	0.0755116	+	0.130790i	0.901309	−	0.433178i	$-0.142608\pi$
$17$	5.29282	+	9.16743i	0.0755116	+	0.130790i	−0.825797	+	0.563967i	$0.809274\pi$
$18$		0			0
$19$	−41.6545	+	72.1477i	−0.502958	+	0.871148i	0.497037	+	0.867730i	$0.334421\pi$
$19$	−41.6545	+	72.1477i	−0.502958	+	0.871148i	−0.999994	+	0.00341841i	$0.998912\pi$
$20$	−3.50223	+	6.06604i	−0.0391561	+	0.0678204i
$21$		0			0
$22$	15.0568	+	26.0791i	0.145914	+	0.252731i
$23$	−87.6234			−0.794380			−0.397190	−	0.917736i	$-0.630015\pi$
$23$	−87.6234			−0.794380			−0.397190	+	0.917736i	$0.630015\pi$
$24$		0			0
$25$	−70.8950			−0.567160
$26$	−80.4236	+	139.298i	−0.606629	+	1.05071i
$27$		0			0
$28$	1.26229	−	17.5909i	0.00851964	−	0.118727i
$29$	67.6917	−	117.246i	0.433450	−	0.750757i	−0.563718	−	0.825967i	$-0.690630\pi$
$29$	67.6917	−	117.246i	0.433450	−	0.750757i	0.997168	+	0.0752104i	$0.0239629\pi$
$30$		0			0
$31$	−26.7514	+	46.3349i	−0.154990	+	0.268451i	−0.933056	−	0.359732i	$-0.882868\pi$
$31$	−26.7514	+	46.3349i	−0.154990	+	0.268451i	0.778065	+	0.628184i	$0.216201\pi$
$32$	−21.4278	+	37.1141i	−0.118373	+	0.205028i
$33$		0			0
$34$	14.0511	−	24.3373i	0.0708751	−	0.122759i
$35$	−122.549	+	59.4952i	−0.591846	+	0.287329i
$36$		0			0
$37$	−149.868	+	259.578i	−0.665894	+	1.15336i	0.313148	+	0.949704i	$0.398616\pi$
$37$	−149.868	+	259.578i	−0.665894	+	1.15336i	−0.979042	+	0.203658i	$0.934717\pi$
$38$	221.165			0.944150
$39$		0			0
$40$	174.814			0.691013
$41$	194.038	+	336.083i	0.739112	+	1.28018i	0.952896	+	0.303298i	$0.0980879\pi$
$41$	194.038	+	336.083i	0.739112	+	1.28018i	−0.213784	+	0.976881i	$0.568579\pi$
$42$		0			0
$43$	−215.569	+	373.377i	−0.764511	+	1.32417i	0.175993	+	0.984391i	$0.443686\pi$
$43$	−215.569	+	373.377i	−0.764511	+	1.32417i	−0.940505	+	0.339781i	$0.889647\pi$
$44$	−5.40086	+	9.35456i	−0.0185048	+	0.0320512i
$45$		0			0
$46$	116.309	+	201.454i	0.372802	+	0.645712i
$47$	−255.582	−	442.681i	−0.793202	−	1.37387i	−0.923975	−	0.382454i	$-0.875079\pi$
$47$	−255.582	−	442.681i	−0.793202	−	1.37387i	0.130773	−	0.991412i	$-0.458254\pi$
$48$		0			0
$49$	212.155	−	269.516i	0.618529	−	0.785762i
$50$	94.1045	+	162.994i	0.266168	+	0.461016i
$51$		0			0
$52$	−57.6958			−0.153865
$53$	−116.232	−	201.320i	−0.301240	−	0.521762i	0.675177	−	0.737655i	$-0.264067\pi$
$53$	−116.232	−	201.320i	−0.301240	−	0.521762i	−0.976417	+	0.215893i	$0.930734\pi$
$54$		0			0
$55$	83.4364			0.204556
$56$	−395.959	+	192.230i	−0.944861	+	0.458710i
$57$		0			0
$58$	−359.410			−0.813671
$59$	31.1816	−	54.0081i	0.0688050	−	0.119174i	−0.829571	−	0.558402i	$-0.811415\pi$
$59$	31.1816	−	54.0081i	0.0688050	−	0.119174i	0.898376	+	0.439228i	$0.144748\pi$
$60$		0			0
$61$	−170.015	−	294.474i	−0.356855	−	0.618091i	0.630579	−	0.776125i	$-0.282818\pi$
$61$	−170.015	−	294.474i	−0.356855	−	0.618091i	−0.987434	+	0.158035i	$0.949484\pi$
$62$	142.037			0.290948
$63$		0			0
$64$	557.572			1.08901
$65$	222.832	+	385.956i	0.425214	+	0.736492i
$66$		0			0
$67$	274.599	−	475.620i	0.500711	−	0.867258i	−0.499288	−	0.866436i	$-0.666405\pi$
$67$	274.599	−	475.620i	0.500711	−	0.867258i	1.00000		0.000821626i	$-0.000261532\pi$
$68$	10.0803			0.0179767
$69$		0			0
$70$	299.454	+	202.779i	0.511309	+	0.346239i
$71$	−505.089			−0.844269			−0.422134	−	0.906533i	$-0.638719\pi$
$71$	−505.089			−0.844269			−0.422134	+	0.906533i	$0.638719\pi$
$72$		0			0
$73$	−99.1981	−	171.816i	−0.159045	−	0.275473i	0.775480	−	0.631372i	$-0.217508\pi$
$73$	−99.1981	−	171.816i	−0.159045	−	0.275473i	−0.934524	+	0.355899i	$0.884175\pi$
$74$	795.724			1.25001
$75$		0			0
$76$	39.6659	+	68.7034i	0.0598683	+	0.103695i
$77$	−188.986	+	91.7487i	−0.279700	+	0.135789i
$78$		0			0
$79$	−588.922	−	1020.04i	−0.838720	−	1.45271i	−0.890965	−	0.454072i	$-0.849971\pi$
$79$	−588.922	−	1020.04i	−0.838720	−	1.45271i	0.0522448	−	0.998634i	$-0.483362\pi$
$80$	−204.027	−	353.385i	−0.285136	−	0.493870i
$81$		0			0
$82$	515.123	−	892.219i	0.693730	−	1.20157i
$83$	722.688	−	1251.73i	0.955726	−	1.65537i	0.223028	−	0.974812i	$-0.428406\pi$
$83$	722.688	−	1251.73i	0.955726	−	1.65537i	0.732698	−	0.680554i	$-0.238261\pi$
$84$		0			0
$85$	−38.9319	−	67.4320i	−0.0496795	−	0.0860474i
$86$	1144.57			1.43514
$87$		0			0
$88$	269.584			0.326566
$89$	507.365	−	878.783i	0.604277	−	1.04664i	−0.387889	−	0.921706i	$-0.626796\pi$
$89$	507.365	−	878.783i	0.604277	−	1.04664i	0.992165	−	0.124932i	$-0.0398712\pi$
$90$		0			0
$91$	−929.126	−	629.170i	−1.07032	−	0.724779i
$92$	−41.7201	+	72.2614i	−0.0472785	+	0.0818888i
$93$		0			0
$94$	−678.509	+	1175.21i	−0.744498	+	1.28951i
$95$	306.394	−	530.690i	0.330899	−	0.573133i
$96$		0			0
$97$	551.029	−	954.410i	0.576789	−	0.999028i	−0.419056	−	0.907960i	$-0.637639\pi$
$97$	551.029	−	954.410i	0.576789	−	0.999028i	0.995845	−	0.0910671i	$-0.0290278\pi$
$98$	−901.252	−	130.014i	−0.928982	−	0.134014i
$99$		0			0
$100$	−33.7552	+	58.4658i	−0.0337552	+	0.0584658i
$101$	−401.873			−0.395919			−0.197960	−	0.980210i	$-0.563431\pi$
$101$	−401.873			−0.395919			−0.197960	+	0.980210i	$0.563431\pi$
$102$		0			0
$103$	28.2453			0.0270203			0.0135102	−	0.999909i	$-0.495699\pi$
$103$	28.2453			0.0270203			0.0135102	+	0.999909i	$0.495699\pi$
$104$	719.973	+	1247.03i	0.678838	+	1.17578i
$105$		0			0
$106$	−308.568	+	534.455i	−0.282743	+	0.489725i
$107$	−837.694	+	1450.93i	−0.756850	+	1.31090i	0.187600	+	0.982246i	$0.439929\pi$
$107$	−837.694	+	1450.93i	−0.756850	+	1.31090i	−0.944449	+	0.328657i	$0.893404\pi$
$108$		0			0
$109$	−197.497	−	342.074i	−0.173548	−	0.300594i	0.766110	−	0.642710i	$-0.222190\pi$
$109$	−197.497	−	342.074i	−0.173548	−	0.300594i	−0.939658	+	0.342116i	$0.888857\pi$
$110$	−110.752	−	191.828i	−0.0959979	−	0.166273i
$111$		0			0
$112$	850.716	+	576.073i	0.717724	+	0.486016i
$113$	94.3578	+	163.433i	0.0785525	+	0.136057i	0.902626	−	0.430426i	$-0.141637\pi$
$113$	94.3578	+	163.433i	0.0785525	+	0.136057i	−0.824073	+	0.566483i	$0.808303\pi$
$114$		0			0
$115$	644.523			0.522627
$116$	−64.4602	−	111.648i	−0.0515946	−	0.0893645i
$117$		0			0
$118$	−165.559			−0.129161
$119$	162.332	+	109.925i	0.125050	+	0.0846791i
$120$		0			0
$121$	−1202.33			−0.903329
$122$	−451.348	+	781.757i	−0.334943	+	0.580139i
$123$		0			0
$124$	25.4743	+	44.1229i	0.0184489	+	0.0319544i
$125$	1440.93			1.03104
$126$		0			0
$127$	340.864			0.238164			0.119082	−	0.992884i	$-0.462005\pi$
$127$	340.864			0.238164			0.119082	+	0.992884i	$0.462005\pi$
$128$	−568.687	−	984.995i	−0.392698	−	0.680172i
$129$		0			0
$130$	591.564	−	1024.62i	0.399105	−	0.691270i
$131$	899.917			0.600199			0.300100	−	0.953908i	$-0.402980\pi$
$131$	899.917			0.600199			0.300100	+	0.953908i	$0.402980\pi$
$132$		0			0
$133$	−110.432	+	1538.95i	−0.0719973	+	1.00334i
$134$	−1457.99			−0.939934
$135$		0			0
$136$	−125.790	−	217.874i	−0.0793115	−	0.137372i
$137$	73.3173			0.0457220			0.0228610	−	0.999739i	$-0.492722\pi$
$137$	73.3173			0.0457220			0.0228610	+	0.999739i	$0.492722\pi$
$138$		0			0
$139$	744.772	+	1289.98i	0.454466	+	0.787158i	0.998657	−	0.0518033i	$-0.0164969\pi$
$139$	744.772	+	1289.98i	0.454466	+	0.787158i	−0.544192	+	0.838961i	$0.683164\pi$
$140$	−9.28489	+	129.392i	−0.00560512	+	0.0781114i
$141$		0			0
$142$	670.445	+	1161.24i	0.396215	+	0.686264i
$143$	343.633	+	595.190i	0.200951	+	0.348058i
$144$		0			0
$145$	−497.914	+	862.413i	−0.285169	+	0.493927i
$146$	−263.347	+	456.130i	−0.149279	+	0.258559i
$147$		0			0
$148$	142.713	+	247.186i	0.0792631	+	0.137288i
$149$	−1453.55			−0.799190			−0.399595	−	0.916692i	$-0.630849\pi$
$149$	−1453.55			−0.799190			−0.399595	+	0.916692i	$0.630849\pi$
$150$		0			0
$151$	2041.92			1.10046			0.550230	−	0.835013i	$-0.314540\pi$
$151$	2041.92			1.10046			0.550230	+	0.835013i	$0.314540\pi$
$152$	989.964	−	1714.67i	0.528268	−	0.914986i
$153$		0			0
$154$	461.794	+	312.710i	0.241639	+	0.163629i
$155$	196.773	−	340.821i	0.101969	−	0.176616i
$156$		0			0
$157$	48.5694	−	84.1247i	0.0246896	−	0.0427636i	−0.853417	−	0.521229i	$-0.825474\pi$
$157$	48.5694	−	84.1247i	0.0246896	−	0.0427636i	0.878106	+	0.478466i	$0.158807\pi$
$158$	−1563.45	+	2707.97i	−0.787222	+	1.36351i
$159$		0			0
$160$	157.615	−	272.997i	0.0778784	−	0.134889i
$161$	−1459.86	+	708.733i	−0.714617	+	0.346932i
$162$		0			0
$163$	−972.103	+	1683.73i	−0.467122	+	0.809080i	−0.999295	−	0.0375565i	$-0.988043\pi$
$163$	−972.103	+	1683.73i	−0.467122	+	0.809080i	0.532172	+	0.846636i	$0.321376\pi$
$164$	369.549			0.175957
$165$		0			0
$166$	−3837.12			−1.79409
$167$	−1790.86	−	3101.86i	−0.829825	−	1.43730i	−0.898175	−	0.439638i	$-0.855107\pi$
$167$	−1790.86	−	3101.86i	−0.829825	−	1.43730i	0.0683496	−	0.997661i	$-0.478227\pi$
$168$		0			0
$169$	−736.967	+	1276.46i	−0.335443	+	0.581004i
$170$	−103.355	+	179.016i	−0.0466291	+	0.0807640i
$171$		0			0
$172$	205.278	+	355.552i	0.0910018	+	0.157620i
$173$	−199.217	−	345.053i	−0.0875501	−	0.151641i	0.818925	−	0.573901i	$-0.194570\pi$
$173$	−199.217	−	345.053i	−0.0875501	−	0.151641i	−0.906475	+	0.422259i	$0.861237\pi$
$174$		0			0
$175$	−1181.16	+	573.427i	−0.510212	+	0.247697i
$176$	−314.634	−	544.961i	−0.134752	−	0.233398i
$177$		0			0
$178$	−2693.86			−1.13435
$179$	2119.43	+	3670.96i	0.884993	+	1.53285i	0.845722	+	0.533624i	$0.179170\pi$
$179$	2119.43	+	3670.96i	0.884993	+	1.53285i	0.0392708	+	0.999229i	$0.487497\pi$
$180$		0			0
$181$	−1047.33			−0.430096			−0.215048	−	0.976603i	$-0.568991\pi$
$181$	−1047.33			−0.430096			−0.215048	+	0.976603i	$0.568991\pi$
$182$	−213.214	+	2971.29i	−0.0868377	+	1.21015i
$183$		0			0
$184$	2082.46			0.834355
$185$	1102.37	−	1909.36i	0.438096	−	0.758804i
$186$		0			0
$187$	−60.0377	−	103.988i	−0.0234780	−	0.0406651i
$188$	−486.762			−0.188834
$189$		0			0
$190$	−1626.80			−0.621162
$191$	28.3215	+	49.0543i	0.0107292	+	0.0185835i	0.871340	−	0.490679i	$-0.163251\pi$
$191$	28.3215	+	49.0543i	0.0107292	+	0.0185835i	−0.860611	+	0.509263i	$0.829918\pi$
$192$		0			0
$193$	2465.98	−	4271.21i	0.919716	−	1.59300i	0.119871	−	0.992790i	$-0.461752\pi$
$193$	2465.98	−	4271.21i	0.919716	−	1.59300i	0.799846	−	0.600206i	$-0.204915\pi$
$194$	−2925.70			−1.08275
$195$		0			0
$196$	−121.252	−	303.286i	−0.0441879	−	0.110527i
$197$	−1854.91			−0.670846			−0.335423	−	0.942068i	$-0.608879\pi$
$197$	−1854.91			−0.670846			−0.335423	+	0.942068i	$0.608879\pi$
$198$		0			0
$199$	785.414	+	1360.38i	0.279782	+	0.484596i	0.971330	−	0.237734i	$-0.0764046\pi$
$199$	785.414	+	1360.38i	0.279782	+	0.484596i	−0.691549	+	0.722330i	$0.743071\pi$
$200$	1684.90			0.595701
$201$		0			0
$202$	533.438	+	923.941i	0.185805	+	0.321823i
$203$	179.460	−	2500.91i	0.0620474	−	0.864676i
$204$		0			0
$205$	−1427.27	−	2472.10i	−0.486266	−	0.842238i
$206$	−37.4922	−	64.9385i	−0.0126806	−	0.0219635i
$207$		0			0
$208$	1680.57	−	2910.83i	0.560224	−	0.970336i
$209$	472.497	−	818.388i	0.156379	−	0.270857i
$210$		0			0
$211$	542.645	+	939.888i	0.177048	+	0.306657i	0.940868	−	0.338773i	$-0.110012\pi$
$211$	542.645	+	939.888i	0.177048	+	0.306657i	−0.763820	+	0.645429i	$0.776678\pi$
$212$	−221.366			−0.0717146
$213$		0			0
$214$	4447.75			1.42076
$215$	1585.64	−	2746.41i	0.502977	−	0.871181i
$216$		0			0
$217$	−70.9218	+	988.346i	−0.0221866	+	0.309186i
$218$	−524.306	+	908.124i	−0.162892	+	0.282137i
$219$		0			0
$220$	39.7266	−	68.8085i	0.0121744	−	0.0210867i
$221$	320.682	−	555.438i	0.0976083	−	0.169063i
$222$		0			0
$223$	2030.15	−	3516.32i	0.609636	−	1.05592i	−0.381664	−	0.924301i	$-0.624649\pi$
$223$	2030.15	−	3516.32i	0.609636	−	1.05592i	0.991300	−	0.131620i	$-0.0420178\pi$
$224$	−56.8081	+	791.663i	−0.0169449	+	0.236139i
$225$		0			0
$226$	250.497	−	433.874i	0.0737293	−	0.127703i
$227$	−5129.17			−1.49971			−0.749857	−	0.661600i	$-0.769878\pi$
$227$	−5129.17			−1.49971			−0.749857	+	0.661600i	$0.769878\pi$
$228$		0			0
$229$	−5498.50			−1.58669			−0.793343	−	0.608775i	$-0.791661\pi$
$229$	−5498.50			−1.58669			−0.793343	+	0.608775i	$0.791661\pi$
$230$	−855.527	−	1481.82i	−0.245269	−	0.424818i
$231$		0			0
$232$	−1608.77	+	2786.47i	−0.455262	+	0.788537i
$233$	2344.75	−	4061.23i	0.659270	−	1.14189i	−0.321536	−	0.946898i	$-0.604199\pi$
$233$	2344.75	−	4061.23i	0.659270	−	1.14189i	0.980805	−	0.194991i	$-0.0624677\pi$
$234$		0			0
$235$	1879.96	+	3256.19i	0.521852	+	0.903875i
$236$	−29.6930	−	51.4298i	−0.00819004	−	0.0141856i
$237$		0			0
$238$	37.2515	−	519.127i	0.0101456	−	0.141387i
$239$	2236.53	+	3873.78i	0.605309	+	1.04843i	0.992003	+	0.126218i	$0.0402839\pi$
$239$	2236.53	+	3873.78i	0.605309	+	1.04843i	−0.386693	+	0.922208i	$0.626383\pi$
$240$		0			0
$241$	−859.590			−0.229756			−0.114878	−	0.993380i	$-0.536648\pi$
$241$	−859.590			−0.229756			−0.114878	+	0.993380i	$0.536648\pi$
$242$	1595.95	+	2764.26i	0.423932	+	0.734271i
$243$		0			0
$244$	−323.797			−0.0849547
$245$	−1560.53	+	1982.46i	−0.406934	+	0.516957i
$246$		0			0
$247$	5047.54			1.30027
$248$	635.777	−	1101.20i	0.162790	−	0.281960i
$249$		0			0
$250$	−1912.66	−	3312.82i	−0.483868	−	0.838084i
$251$	1788.58			0.449778			0.224889	−	0.974384i	$-0.427798\pi$
$251$	1788.58			0.449778			0.224889	+	0.974384i	$0.427798\pi$
$252$		0			0
$253$	993.932			0.246988
$254$	−452.456	−	783.676i	−0.111770	−	0.193591i
$255$		0			0
$256$	720.563	−	1248.05i	0.175919	−	0.304700i
$257$	1739.96			0.422318			0.211159	−	0.977452i	$-0.432276\pi$
$257$	1739.96			0.422318			0.211159	+	0.977452i	$0.432276\pi$
$258$		0			0
$259$	−397.319	+	5536.93i	−0.0953213	+	1.32837i
$260$	424.388			0.101229
$261$		0			0
$262$	−1194.53	−	2068.99i	−0.281673	−	0.487872i
$263$	2515.54			0.589791			0.294896	−	0.955529i	$-0.404715\pi$
$263$	2515.54			0.589791			0.294896	+	0.955529i	$0.404715\pi$
$264$		0			0
$265$	854.958	+	1480.83i	0.198187	+	0.343270i
$266$	3684.76	−	1788.87i	0.849350	−	0.412341i
$267$		0			0
$268$	−261.490	−	452.914i	−0.0596010	−	0.103232i
$269$	−993.225	−	1720.32i	−0.225123	−	0.389924i	0.731234	−	0.682127i	$-0.238945\pi$
$269$	−993.225	−	1720.32i	−0.225123	−	0.389924i	−0.956356	+	0.292203i	$0.905612\pi$
$270$		0			0
$271$	2220.71	−	3846.38i	0.497780	−	0.862180i	−0.502217	−	0.864742i	$-0.667482\pi$
$271$	2220.71	−	3846.38i	0.497780	−	0.862180i	0.999997	+	0.00256147i	$0.000815341\pi$
$272$	−293.620	+	508.564i	−0.0654533	+	0.113368i
$273$		0			0
$274$	−97.3199	−	168.563i	−0.0214573	−	0.0371652i
$275$	804.178			0.176341
$276$		0			0
$277$	−8445.38			−1.83189			−0.915946	−	0.401302i	$-0.868558\pi$
$277$	−8445.38			−1.83189			−0.915946	+	0.401302i	$0.868558\pi$
$278$	1977.19	−	3424.59i	0.426561	−	0.738825i
$279$		0			0
$280$	2912.52	−	1413.97i	0.621630	−	0.301788i
$281$	−3944.00	+	6831.21i	−0.837293	+	1.45023i	0.0548575	+	0.998494i	$0.482530\pi$
$281$	−3944.00	+	6831.21i	−0.837293	+	1.45023i	−0.892150	+	0.451739i	$0.850804\pi$
$282$		0			0
$283$	3567.92	−	6179.83i	0.749438	−	1.29807i	−0.198654	−	0.980070i	$-0.563657\pi$
$283$	3567.92	−	6179.83i	0.749438	−	1.29807i	0.948092	−	0.317996i	$-0.103010\pi$
$284$	−240.488	+	416.538i	−0.0502477	+	0.0870316i
$285$		0			0
$286$	912.263	−	1580.09i	0.188613	−	0.326687i
$287$	5951.17	+	4029.91i	1.22400	+	0.828844i
$288$		0			0
$289$	2400.47	−	4157.74i	0.488596	−	0.846273i
$290$	2643.68			0.535319
$291$		0			0
$292$	−188.925			−0.0378630
$293$	2502.16	+	4333.86i	0.498900	+	0.864119i	0.999999	−	0.00127016i	$-0.000404304\pi$
$293$	2502.16	+	4333.86i	0.498900	+	0.864119i	−0.501100	+	0.865390i	$0.667071\pi$
$294$		0			0
$295$	−229.360	+	397.263i	−0.0452672	+	0.0784052i
$296$	3561.76	−	6169.16i	0.699403	−	1.21140i
$297$		0			0
$298$	1929.41	+	3341.83i	0.375059	+	0.649622i
$299$	2654.47	+	4597.68i	0.513418	+	0.889267i
$300$		0			0
$301$	−571.503	+	7964.31i	−0.109438	+	1.52510i
$302$	−2710.41	−	4694.56i	−0.516445	−	0.894509i
$303$		0			0
$304$	−4621.57			−0.871926
$305$	1250.56	+	2166.04i	0.234777	+	0.406646i
$306$		0			0
$307$	−5233.06			−0.972855			−0.486428	−	0.873721i	$-0.661700\pi$
$307$	−5233.06			−0.972855			−0.486428	+	0.873721i	$0.661700\pi$
$308$	−14.3184	+	199.538i	−0.00264892	+	0.0369146i
$309$		0			0
$310$	−1044.77			−0.191416
$311$	1205.51	−	2088.01i	0.219802	−	0.380709i	−0.734945	−	0.678127i	$-0.762792\pi$
$311$	1205.51	−	2088.01i	0.219802	−	0.380709i	0.954747	+	0.297418i	$0.0961255\pi$
$312$		0			0
$313$	−794.607	−	1376.30i	−0.143495	−	0.248540i	0.785316	−	0.619096i	$-0.212501\pi$
$313$	−794.607	−	1376.30i	−0.143495	−	0.248540i	−0.928810	+	0.370556i	$0.879167\pi$
$314$	−257.880			−0.0463472
$315$		0			0
$316$	−1121.61			−0.199670
$317$	−1758.75	−	3046.25i	−0.311614	−	0.539730i	0.667098	−	0.744970i	$-0.267536\pi$
$317$	−1758.75	−	3046.25i	−0.311614	−	0.539730i	−0.978712	+	0.205239i	$0.934203\pi$
$318$		0			0
$319$	−767.843	+	1329.94i	−0.134768	+	0.233425i
$320$	−4101.29			−0.716465
$321$		0			0
$322$	3567.23	+	2415.60i	0.617373	+	0.418062i
$323$	−881.878			−0.151916
$324$		0			0
$325$	2147.70	+	3719.93i	0.366563	+	0.634906i
$326$	5161.39			0.876881
$327$		0			0
$328$	−4611.52	−	7987.38i	−0.776306	−	1.34460i
$329$	−7838.75	−	5308.11i	−1.31357	−	0.889501i
$330$		0			0
$331$	−1382.48	−	2394.52i	−0.229571	−	0.397628i	0.728110	−	0.685460i	$-0.240399\pi$
$331$	−1382.48	−	2394.52i	−0.229571	−	0.397628i	−0.957681	+	0.287832i	$0.907066\pi$
$332$	−688.187	−	1191.97i	−0.113763	−	0.197042i
$333$		0			0
$334$	−4754.30	+	8234.68i	−0.778873	+	1.34905i
$335$	−2019.85	+	3498.48i	−0.329421	+	0.570574i
$336$		0			0
$337$	1746.39	+	3024.83i	0.282290	+	0.488941i	0.971948	−	0.235194i	$-0.0755726\pi$
$337$	1746.39	+	3024.83i	0.282290	+	0.488941i	−0.689658	+	0.724135i	$0.742239\pi$
$338$	3912.94			0.629692
$339$		0			0
$340$	−74.1467			−0.0118270
$341$	303.448	−	525.587i	0.0481895	−	0.0834667i
$342$		0			0
$343$	1354.69	−	6206.32i	0.213255	−	0.976997i
$344$	5123.23	−	8873.70i	0.802983	−	1.39081i
$345$		0			0
$346$	−528.872	+	916.033i	−0.0821744	+	0.142330i
$347$	1028.57	−	1781.54i	0.159126	−	0.275614i	−0.775428	−	0.631436i	$-0.782466\pi$
$347$	1028.57	−	1781.54i	0.159126	−	0.275614i	0.934554	+	0.355822i	$0.115799\pi$
$348$		0			0
$349$	992.838	−	1719.65i	0.152279	−	0.263755i	−0.779786	−	0.626046i	$-0.784672\pi$
$349$	992.838	−	1719.65i	0.152279	−	0.263755i	0.932065	+	0.362291i	$0.118005\pi$
$350$	2886.20	+	1954.43i	0.440783	+	0.298482i
$351$		0			0
$352$	243.061	−	420.994i	0.0368045	−	0.0637473i
$353$	−12320.8			−1.85771			−0.928854	−	0.370446i	$-0.879205\pi$
$353$	−12320.8			−1.85771			−0.928854	+	0.370446i	$0.879205\pi$
$354$		0			0
$355$	3715.24			0.555449
$356$	−483.144	−	836.830i	−0.0719286	−	0.124584i
$357$		0			0
$358$	5626.58	−	9745.52i	0.830653	−	1.43873i
$359$	−6436.37	+	11148.1i	−0.946236	+	1.63893i	−0.192979	+	0.981203i	$0.561815\pi$
$359$	−6436.37	+	11148.1i	−0.946236	+	1.63893i	−0.753257	+	0.657726i	$0.771518\pi$
$360$		0			0
$361$	−40.6911	−	70.4791i	−0.00593252	−	0.0102754i
$362$	1390.20	+	2407.90i	0.201844	+	0.349604i
$363$		0			0
$364$	−961.250	+	466.667i	−0.138415	+	0.0671978i
$365$	729.662	+	1263.81i	0.104636	+	0.181236i
$366$		0			0
$367$	10802.7			1.53650			0.768250	−	0.640151i	$-0.221128\pi$
$367$	10802.7			1.53650			0.768250	+	0.640151i	$0.221128\pi$
$368$	−2430.46	−	4209.68i	−0.344284	−	0.596317i
$369$		0			0
$370$	−5853.04			−0.822392
$371$	−3564.86	−	2413.99i	−0.498863	−	0.337812i
$372$		0			0
$373$	−1283.29			−0.178140			−0.0890700	−	0.996025i	$-0.528389\pi$
$373$	−1283.29			−0.178140			−0.0890700	+	0.996025i	$0.528389\pi$
$374$	−159.385	+	276.064i	−0.0220364	+	0.0381682i
$375$		0			0
$376$	6074.19	+	10520.8i	0.833118	+	1.44300i
$377$	−8202.65			−1.12058
$378$		0			0
$379$	1490.02			0.201945			0.100973	−	0.994889i	$-0.467805\pi$
$379$	1490.02			0.201945			0.100973	+	0.994889i	$0.467805\pi$
$380$	−291.767	−	505.355i	−0.0393877	−	0.0682215i
$381$		0			0
$382$	75.1867	−	130.227i	0.0100704	−	0.0174424i
$383$	−5514.21			−0.735674			−0.367837	−	0.929890i	$-0.619902\pi$
$383$	−5514.21			−0.735674			−0.367837	+	0.929890i	$0.619902\pi$
$384$		0			0
$385$	1390.11	−	674.868i	0.184017	−	0.0893362i
$386$	−13093.2			−1.72649
$387$		0			0
$388$	−524.723	−	908.847i	−0.0686567	−	0.118917i
$389$	1364.95			0.177906			0.0889531	−	0.996036i	$-0.471648\pi$
$389$	1364.95			0.177906			0.0889531	+	0.996036i	$0.471648\pi$
$390$		0			0
$391$	−463.774	−	803.281i	−0.0599849	−	0.103897i
$392$	−5042.10	+	6405.35i	−0.649655	+	0.825303i
$393$		0			0
$394$	2462.16	+	4264.59i	0.314827	+	0.545297i
$395$	4331.88	+	7503.04i	0.551799	+	0.955744i
$396$		0			0
$397$	3119.14	−	5402.51i	0.394321	−	0.682984i	−0.598694	−	0.800978i	$-0.704313\pi$
$397$	3119.14	−	5402.51i	0.394321	−	0.682984i	0.993014	+	0.117995i	$0.0376466\pi$
$398$	2085.09	−	3611.47i	0.262603	−	0.454841i
$399$		0			0
$400$	−1966.45	−	3406.00i	−0.245807	−	0.425750i
$401$	−383.040			−0.0477010			−0.0238505	−	0.999716i	$-0.507593\pi$
$401$	−383.040			−0.0477010			−0.0238505	+	0.999716i	$0.507593\pi$
$402$		0			0
$403$	3241.65			0.400690
$404$	−191.344	+	331.417i	−0.0235636	+	0.0408134i
$405$		0			0
$406$	−5988.02	+	2907.06i	−0.731971	+	0.355357i
$407$	1699.98	−	2944.46i	0.207039	−	0.358603i
$408$		0			0
$409$	−4917.59	+	8517.51i	−0.594521	+	1.02974i	0.399093	+	0.916910i	$0.369325\pi$
$409$	−4917.59	+	8517.51i	−0.594521	+	1.02974i	−0.993614	+	0.112830i	$0.964008\pi$
$410$	−3789.05	+	6562.82i	−0.456409	+	0.790523i
$411$		0			0
$412$	13.4485	−	23.2934i	0.00160815	−	0.00278540i
$413$	82.6667	−	1152.02i	0.00984930	−	0.137257i
$414$		0			0
$415$	−5315.81	+	9207.25i	−0.628778	+	1.08908i
$416$	2596.55			0.306025
$417$		0			0
$418$	−2508.73			−0.293555
$419$	3138.73	+	5436.44i	0.365959	+	0.633860i	0.988930	−	0.148386i	$-0.0474077\pi$
$419$	3138.73	+	5436.44i	0.365959	+	0.633860i	−0.622970	+	0.782245i	$0.714074\pi$
$420$		0			0
$421$	−6522.30	+	11297.0i	−0.755054	+	1.30779i	0.190294	+	0.981727i	$0.439056\pi$
$421$	−6522.30	+	11297.0i	−0.755054	+	1.30779i	−0.945348	+	0.326064i	$0.894277\pi$
$422$	1440.59	−	2495.18i	0.166177	−	0.287828i
$423$		0			0
$424$	2762.38	+	4784.58i	0.316399	+	0.548019i
$425$	−375.234	−	649.925i	−0.0428271	−	0.0741788i
$426$		0			0
$427$	−5214.38	−	3530.99i	−0.590964	−	0.400179i
$428$	797.703	+	1381.66i	0.0900898	+	0.156040i
$429$		0			0
$430$	−8419.00			−0.944186
$431$	−4874.53	−	8442.93i	−0.544774	−	0.943577i	−0.998621	−	0.0524973i	$-0.983282\pi$
$431$	−4874.53	−	8442.93i	−0.544774	−	0.943577i	0.453847	−	0.891080i	$-0.350051\pi$
$432$		0			0
$433$	−322.352			−0.0357765			−0.0178883	−	0.999840i	$-0.505694\pi$
$433$	−322.352			−0.0357765			−0.0178883	+	0.999840i	$0.505694\pi$
$434$	2366.43	−	1148.85i	0.261734	−	0.127066i
$435$		0			0
$436$	−376.136			−0.0413158
$437$	3649.90	−	6321.82i	0.399539	−	0.692022i
$438$		0			0
$439$	1552.49	+	2689.00i	0.168785	+	0.292344i	0.937993	−	0.346655i	$-0.112682\pi$
$439$	1552.49	+	2689.00i	0.168785	+	0.292344i	−0.769208	+	0.638998i	$0.779349\pi$
$440$	−1982.96			−0.214850
$441$		0			0
$442$	−1702.67			−0.183230
$443$	−1199.65	−	2077.86i	−0.128662	−	0.222849i	0.794497	−	0.607269i	$-0.207735\pi$
$443$	−1199.65	−	2077.86i	−0.128662	−	0.222849i	−0.923158	+	0.384420i	$0.874402\pi$
$444$		0			0
$445$	−3731.98	+	6463.98i	−0.397557	+	0.688589i
$446$	−10779.1			−1.14441
$447$		0			0
$448$	9289.53	−	4509.87i	0.979663	−	0.475606i
$449$	9003.79			0.946358			0.473179	−	0.880966i	$-0.343106\pi$
$449$	9003.79			0.946358			0.473179	+	0.880966i	$0.343106\pi$
$450$		0			0
$451$	−2201.01	−	3812.27i	−0.229804	−	0.398033i
$452$	179.706			0.0187006
$453$		0			0
$454$	6808.36	+	11792.4i	0.703815	+	1.21904i
$455$	6834.29	+	4627.93i	0.704168	+	0.476837i
$456$		0			0
$457$	3367.49	+	5832.66i	0.344692	+	0.597024i	0.985298	−	0.170846i	$-0.0546499\pi$
$457$	3367.49	+	5832.66i	0.344692	+	0.597024i	−0.640606	+	0.767870i	$0.721317\pi$
$458$	7298.60	+	12641.5i	0.744631	+	1.28974i
$459$		0			0
$460$	306.877	−	531.527i	0.0311048	−	0.0538751i
$461$	−1082.44	+	1874.84i	−0.109358	+	0.189414i	−0.915510	−	0.402294i	$-0.868213\pi$
$461$	−1082.44	+	1874.84i	−0.109358	+	0.189414i	0.806152	+	0.591708i	$0.201546\pi$
$462$		0			0
$463$	−1458.61	−	2526.39i	−0.146409	−	0.253589i	0.783488	−	0.621406i	$-0.213438\pi$
$463$	−1458.61	−	2526.39i	−0.146409	−	0.253589i	−0.929898	+	0.367818i	$0.880105\pi$
$464$	7510.41			0.751427
$465$		0			0
$466$	−12449.5			−1.23758
$467$	−870.004	+	1506.89i	−0.0862077	+	0.149316i	−0.905905	−	0.423481i	$-0.860808\pi$
$467$	−870.004	+	1506.89i	−0.0862077	+	0.149316i	0.819698	+	0.572797i	$0.194142\pi$
$468$		0			0
$469$	728.001	−	10145.2i	0.0716758	−	0.998854i
$470$	4990.85	−	8644.40i	0.489810	−	0.848376i
$471$		0			0
$472$	−741.064	+	1283.56i	−0.0722675	+	0.125171i
$473$	2445.25	−	4235.30i	0.237701	−	0.411711i
$474$		0			0
$475$	2953.09	−	5114.91i	0.285257	−	0.494080i
$476$	167.944	−	81.5334i	0.0161717	−	0.00785100i
$477$		0			0
$478$	5937.44	−	10283.9i	0.568142	−	0.984052i
$479$	11232.7			1.07148			0.535738	−	0.844384i	$-0.320034\pi$
$479$	11232.7			1.07148			0.535738	+	0.844384i	$0.320034\pi$
$480$		0			0
$481$	18160.4			1.72150
$482$	1141.00	+	1976.27i	0.107824	+	0.186757i
$483$		0			0
$484$	−572.466	+	991.541i	−0.0537628	+	0.0931199i
$485$	−4053.16	+	7020.27i	−0.379473	+	0.657266i
$486$		0			0
$487$	−825.982	−	1430.64i	−0.0768558	−	0.133118i	0.825036	−	0.565080i	$-0.191155\pi$
$487$	−825.982	−	1430.64i	−0.0768558	−	0.133118i	−0.901892	+	0.431962i	$0.857821\pi$
$488$	4040.58	+	6998.49i	0.374813	+	0.649195i
$489$		0			0
$490$	6629.26	+	956.330i	0.611183	+	0.0881685i
$491$	7910.90	+	13702.1i	0.727116	+	1.25940i	0.958097	+	0.286443i	$0.0924730\pi$
$491$	7910.90	+	13702.1i	0.727116	+	1.25940i	−0.230982	+	0.972958i	$0.574194\pi$
$492$		0			0
$493$	1433.12			0.130922
$494$	−6700.00	−	11604.7i	−0.610217	−	1.05693i
$495$		0			0
$496$	−2968.08			−0.268691
$497$	−8415.12	+	4085.37i	−0.759497	+	0.368720i
$498$		0			0
$499$	−14109.6			−1.26580			−0.632900	−	0.774233i	$-0.718136\pi$
$499$	−14109.6			−1.26580			−0.632900	+	0.774233i	$0.718136\pi$
$500$	686.069	−	1188.31i	0.0613639	−	0.106285i
$501$		0			0
$502$	−2374.13	−	4112.11i	−0.211081	−	0.365602i
$503$	12196.8			1.08117			0.540585	−	0.841289i	$-0.318203\pi$
$503$	12196.8			1.08117			0.540585	+	0.841289i	$0.318203\pi$
$504$		0			0
$505$	2956.02			0.260478
$506$	−1319.32	−	2285.14i	−0.115911	−	0.200764i
$507$		0			0
$508$	162.296	−	281.104i	0.0141746	−	0.0245512i
$509$	−558.453			−0.0486306			−0.0243153	−	0.999704i	$-0.507741\pi$
$509$	−558.453			−0.0486306			−0.0243153	+	0.999704i	$0.507741\pi$
$510$		0			0
$511$	−3042.42	−	2060.22i	−0.263383	−	0.178353i
$512$	−12924.8			−1.11563
$513$		0			0
$514$	−2309.58	−	4000.32i	−0.198193	−	0.343281i
$515$	−207.762			−0.0177768
$516$		0			0
$517$	2899.13	+	5021.44i	0.246622	+	0.427162i
$518$	13257.3	−	6436.14i	1.12450	−	0.545922i
$519$		0			0
$520$	−5295.84	−	9172.66i	−0.446611	−	0.773554i
$521$	−5208.33	−	9021.10i	−0.437968	−	0.758583i	0.559565	−	0.828787i	$-0.310968\pi$
$521$	−5208.33	−	9021.10i	−0.437968	−	0.758583i	−0.997533	+	0.0702040i	$0.977635\pi$
$522$		0			0
$523$	−4310.74	+	7466.43i	−0.360412	+	0.624252i	−0.988029	−	0.154270i	$-0.950697\pi$
$523$	−4310.74	+	7466.43i	−0.360412	+	0.624252i	0.627616	+	0.778523i	$0.284031\pi$
$524$	428.478	−	742.145i	0.0357216	−	0.0618717i
$525$		0			0
$526$	−3339.08	−	5783.46i	−0.276789	−	0.479412i
$527$	−566.362			−0.0468143
$528$		0			0
$529$	−4489.15			−0.368961
$530$	2269.71	−	3931.25i	0.186018	−	0.322193i
$531$		0			0
$532$	1216.56	+	823.810i	0.0991440	+	0.0671366i
$533$	11756.4	−	20362.7i	0.955396	−	1.65479i
$534$		0			0
$535$	6161.75	−	10672.5i	0.497936	−	0.862450i
$536$	−6526.15	+	11303.6i	−0.525908	+	0.910900i
$537$		0			0
$538$	−2636.77	+	4567.02i	−0.211300	+	0.365982i
$539$	−2406.53	+	3057.19i	−0.192313	+	0.244309i
$540$		0			0
$541$	−5922.96	+	10258.9i	−0.470699	+	0.815274i	−0.999438	−	0.0335100i	$-0.989331\pi$
$541$	−5922.96	+	10258.9i	−0.470699	+	0.815274i	0.528740	+	0.848784i	$0.322665\pi$
$542$	−11790.9			−0.934431
$543$		0			0
$544$	−453.655			−0.0357542
$545$	1452.71	+	2516.16i	0.114178	+	0.197763i
$546$		0			0
$547$	6313.20	−	10934.8i	0.493479	−	0.854730i	−0.506493	−	0.862244i	$-0.669058\pi$
$547$	6313.20	−	10934.8i	0.493479	−	0.854730i	0.999972	+	0.00751393i	$0.00239178\pi$
$548$	34.9086	−	60.4635i	0.00272121	−	0.00471327i
$549$		0			0
$550$	−1067.45	−	1848.88i	−0.0827567	−	0.143339i
$551$	5639.33	+	9767.60i	0.436014	+	0.755198i
$552$		0			0
$553$	−18062.4	−	12231.2i	−1.38895	−	0.940545i
$554$	11210.2	+	19416.7i	0.859705	+	1.48905i
$555$		0			0
$556$	1418.43			0.108192
$557$	−10649.8	−	18446.0i	−0.810136	−	1.40320i	−0.912769	−	0.408477i	$-0.866060\pi$
$557$	−10649.8	−	18446.0i	−0.810136	−	1.40320i	0.102633	−	0.994719i	$-0.467273\pi$
$558$		0			0
$559$	26121.9			1.97646
$560$	−6257.54	−	4237.37i	−0.472195	−	0.319753i
$561$		0			0
$562$	20940.7			1.57176
$563$	1263.11	−	2187.77i	0.0945536	−	0.163772i	−0.814869	−	0.579646i	$-0.803191\pi$
$563$	1263.11	−	2187.77i	0.0945536	−	0.163772i	0.909422	+	0.415874i	$0.136524\pi$
$564$		0			0
$565$	−694.059	−	1202.15i	−0.0516802	−	0.0895127i
$566$	−18944.0			−1.40684
$567$		0			0
$568$	12004.0			0.886754
$569$	−235.493	−	407.886i	−0.0173504	−	0.0300518i	0.857220	−	0.514951i	$-0.172190\pi$
$569$	−235.493	−	407.886i	−0.0173504	−	0.0300518i	−0.874570	+	0.484899i	$0.838856\pi$
$570$		0			0
$571$	5308.08	−	9193.86i	0.389030	−	0.673820i	−0.603289	−	0.797523i	$-0.706144\pi$
$571$	5308.08	−	9193.86i	0.389030	−	0.673820i	0.992319	+	0.123702i	$0.0394768\pi$
$572$	654.457			0.0478395
$573$		0			0
$574$	1365.66	−	19031.5i	0.0993060	−	1.38390i
$575$	6212.05			0.450540
$576$		0			0
$577$	10567.4	+	18303.2i	0.762434	+	1.32057i	0.941592	+	0.336755i	$0.109329\pi$
$577$	10567.4	+	18303.2i	0.762434	+	1.32057i	−0.179158	+	0.983820i	$0.557337\pi$
$578$	−12745.3			−0.917191
$579$		0			0
$580$	474.144	+	821.242i	0.0339444	+	0.0587935i
$581$	1915.94	−	26700.1i	0.136810	−	1.90655i
$582$		0			0
$583$	1318.45	+	2283.62i	0.0936612	+	0.162226i
$584$	2357.55	+	4083.40i	0.167048	+	0.289336i
$585$		0			0
$586$	6642.62	−	11505.4i	0.468266	−	0.811061i
$587$	6558.36	−	11359.4i	0.461146	−	0.798727i	−0.537873	−	0.843026i	$-0.680772\pi$
$587$	6558.36	−	11359.4i	0.461146	−	0.798727i	0.999018	+	0.0442985i	$0.0141053\pi$
$588$		0			0
$589$	−2228.64	−	3860.11i	−0.155907	−	0.270039i
$590$	1217.79			0.0849756
$591$		0			0
$592$	−16627.8			−1.15439
$593$	6711.80	−	11625.2i	0.464790	−	0.805040i	−0.534402	−	0.845231i	$-0.679463\pi$
$593$	6711.80	−	11625.2i	0.464790	−	0.805040i	0.999192	+	0.0401902i	$0.0127964\pi$
$594$		0			0
$595$	−1194.05	−	808.566i	−0.0822710	−	0.0557109i
$596$	−692.078	+	1198.71i	−0.0475648	+	0.0823847i
$597$		0			0
$598$	7046.98	−	12205.7i	0.481894	−	0.834665i
$599$	5017.02	−	8689.74i	0.342220	−	0.592743i	−0.642624	−	0.766181i	$-0.722154\pi$
$599$	5017.02	−	8689.74i	0.342220	−	0.592743i	0.984845	+	0.173438i	$0.0554877\pi$
$600$		0			0
$601$	−6335.96	+	10974.2i	−0.430032	+	0.744837i	−0.996876	−	0.0789886i	$-0.974831\pi$
$601$	−6335.96	+	10974.2i	−0.430032	+	0.744837i	0.566844	+	0.823825i	$0.308164\pi$
$602$	19069.3	−	9257.73i	1.29104	−	0.626772i
$603$		0			0
$604$	972.222	−	1683.94i	0.0654953	−	0.113441i
$605$	8843.88			0.594306
$606$		0			0
$607$	−9972.50			−0.666839			−0.333420	−	0.942779i	$-0.608203\pi$
$607$	−9972.50			−0.666839			−0.333420	+	0.942779i	$0.608203\pi$
$608$	−1785.13	−	3091.94i	−0.119073	−	0.206241i
$609$		0			0
$610$	3319.94	−	5750.30i	0.220361	−	0.381677i
$611$	−15485.3	+	26821.3i	−1.02531	+	1.77590i
$612$		0			0
$613$	−14113.2	−	24444.7i	−0.929895	−	1.61063i	−0.783493	−	0.621401i	$-0.786564\pi$
$613$	−14113.2	−	24444.7i	−0.929895	−	1.61063i	−0.146403	−	0.989225i	$-0.546770\pi$
$614$	6946.25	+	12031.3i	0.456560	+	0.790786i
$615$		0			0
$616$	4491.45	−	2180.51i	0.293776	−	0.142622i
$617$	−98.5457	−	170.686i	−0.00642999	−	0.0111371i	0.862793	−	0.505558i	$-0.168713\pi$
$617$	−98.5457	−	170.686i	−0.00642999	−	0.0111371i	−0.869222	+	0.494421i	$0.835380\pi$
$618$		0			0
$619$	13151.6			0.853967			0.426983	−	0.904259i	$-0.359576\pi$
$619$	13151.6			0.853967			0.426983	+	0.904259i	$0.359576\pi$
$620$	−187.379	−	324.551i	−0.0121376	−	0.0210230i
$621$		0			0
$622$	−6400.70			−0.412612
$623$	1345.10	−	18744.9i	0.0865010	−	1.20545i
$624$		0			0
$625$	−1737.03			−0.111170
$626$	−2109.49	+	3653.74i	−0.134684	+	0.233279i
$627$		0			0
$628$	−46.2507	−	80.1086i	−0.00293886	−	0.00509026i
$629$	−3172.89			−0.201131
$630$		0			0
$631$	−342.571			−0.0216126			−0.0108063	−	0.999942i	$-0.503440\pi$
$631$	−342.571			−0.0216126			−0.0108063	+	0.999942i	$0.503440\pi$
$632$	13996.4	+	24242.4i	0.880927	+	1.52581i
$633$		0			0
$634$	−4669.07	+	8087.06i	−0.292480	+	0.506590i
$635$	−2507.26			−0.156689
$636$		0			0
$637$	−20568.8	−	2967.24i	−1.27938	−	0.184562i
$638$	4076.88			0.252986
$639$		0			0
$640$	4183.04	+	7245.24i	0.258358	+	0.447490i
$641$	−19194.0			−1.18271			−0.591355	−	0.806411i	$-0.701407\pi$
$641$	−19194.0			−1.18271			−0.591355	+	0.806411i	$0.701407\pi$
$642$		0			0
$643$	4980.89	+	8627.15i	0.305485	+	0.529116i	0.977369	−	0.211540i	$-0.0678480\pi$
$643$	4980.89	+	8627.15i	0.305485	+	0.529116i	−0.671884	+	0.740656i	$0.734515\pi$
$644$	−110.606	+	1541.37i	−0.00676782	+	0.0943145i
$645$		0			0
$646$	1170.59	+	2027.52i	0.0712943	+	0.123485i
$647$	10665.4	+	18472.9i	0.648065	+	1.12248i	0.983584	+	0.180449i	$0.0577550\pi$
$647$	10665.4	+	18472.9i	0.648065	+	1.12248i	−0.335519	+	0.942033i	$0.608912\pi$
$648$		0			0
$649$	−353.700	+	612.627i	−0.0213928	+	0.0370535i
$650$	5701.63	−	9875.50i	0.344056	−	0.595922i
$651$		0			0
$652$	925.695	+	1603.35i	0.0556028	+	0.0963068i
$653$	−6821.02			−0.408770			−0.204385	−	0.978891i	$-0.565519\pi$
$653$	−6821.02			−0.408770			−0.204385	+	0.978891i	$0.565519\pi$
$654$		0			0
$655$	−6619.44			−0.394875
$656$	−10764.3	+	18644.2i	−0.640661	+	1.10966i
$657$		0			0
$658$	−1798.82	+	25067.9i	−0.106573	+	1.48518i
$659$	3066.00	−	5310.47i	0.181236	−	0.313910i	−0.761066	−	0.648675i	$-0.775324\pi$
$659$	3066.00	−	5310.47i	0.181236	−	0.313910i	0.942302	+	0.334765i	$0.108657\pi$
$660$		0			0
$661$	−8576.92	+	14855.7i	−0.504695	+	0.874158i	0.495290	+	0.868728i	$0.335062\pi$
$661$	−8576.92	+	14855.7i	−0.504695	+	0.874158i	−0.999985	+	0.00543034i	$0.998271\pi$
$662$	−3670.15	+	6356.88i	−0.215475	+	0.373213i
$663$		0			0
$664$	−17175.5	+	29748.8i	−1.00382	+	1.73867i
$665$	812.293	−	11319.9i	0.0473675	−	0.660100i
$666$		0			0
$667$	−5931.38	+	10273.4i	−0.344324	+	0.596386i
$668$	−3410.73			−0.197552
$669$		0			0
$670$	10724.4			0.618388
$671$	1928.52	+	3340.29i	0.110953	+	0.192176i
$672$		0			0
$673$	4616.02	−	7995.19i	0.264390	−	0.457937i	−0.703013	−	0.711177i	$-0.748163\pi$
$673$	4616.02	−	7995.19i	0.264390	−	0.457937i	0.967404	+	0.253239i	$0.0814960\pi$
$674$	4636.24	−	8030.20i	0.264957	−	0.458919i
$675$		0			0
$676$	701.785	+	1215.53i	0.0399286	+	0.0691583i
$677$	12538.3	+	21717.0i	0.711797	+	1.23287i	0.964182	+	0.265242i	$0.0854517\pi$
$677$	12538.3	+	21717.0i	0.711797	+	1.23287i	−0.252385	+	0.967627i	$0.581215\pi$
$678$		0			0
$679$	1460.85	−	20358.1i	0.0825661	−	1.15062i
$680$	925.259	+	1602.60i	0.0521795	+	0.0903776i
$681$		0			0
$682$	−1611.16			−0.0904613
$683$	1958.77	+	3392.69i	0.109737	+	0.190070i	0.915664	−	0.401945i	$-0.131666\pi$
$683$	1958.77	+	3392.69i	0.109737	+	0.190070i	−0.805927	+	0.592015i	$0.798332\pi$
$684$		0			0
$685$	−539.294			−0.0300808
$686$	−16067.1	+	5123.58i	−0.894232	+	0.285159i
$687$		0			0
$688$	−23917.4			−1.32535
$689$	−7042.29	+	12197.6i	−0.389390	+	0.674444i
$690$		0			0
$691$	15962.4	+	27647.7i	0.878784	+	1.52210i	0.852677	+	0.522439i	$0.174978\pi$
$691$	15962.4	+	27647.7i	0.878784	+	1.52210i	0.0261068	+	0.999659i	$0.491689\pi$
$692$	−379.412			−0.0208426
$693$		0			0
$694$	−5461.22			−0.298711
$695$	−5478.25	−	9488.61i	−0.298996	−	0.517876i
$696$		0			0
$697$	−2054.01	+	3557.65i	−0.111623	+	0.193337i
$698$	−5271.49			−0.285858
$699$		0			0
$700$	−89.4898	+	1247.10i	−0.00483199	+	0.0673373i
$701$	8392.31			0.452173			0.226087	−	0.974107i	$-0.427407\pi$
$701$	8392.31			0.452173			0.226087	+	0.974107i	$0.427407\pi$
$702$		0			0
$703$	−12485.3	−	21625.2i	−0.669833	−	1.16018i
$704$	−6324.67			−0.338594
$705$		0			0
$706$	16354.4	+	28326.6i	0.871821	+	1.51004i
$707$	−6695.47	+	3250.51i	−0.356166	+	0.172911i
$708$		0			0
$709$	−770.986	−	1335.39i	−0.0408392	−	0.0707355i	0.844883	−	0.534951i	$-0.179670\pi$
$709$	−770.986	−	1335.39i	−0.0408392	−	0.0707355i	−0.885722	+	0.464215i	$0.846336\pi$
$710$	−4931.53	−	8541.67i	−0.260672	−	0.451497i
$711$		0			0
$712$	−12058.1	+	20885.2i	−0.634685	+	1.09931i
$713$	2344.05	−	4060.02i	0.123121	−	0.213252i
$714$		0			0
$715$	−2527.63	−	4377.99i	−0.132207	−	0.228990i
$716$	4036.50			0.210686
$717$		0			0
$718$	34174.0			1.77627
$719$	12510.3	−	21668.5i	0.648896	−	1.12392i	−0.334492	−	0.942399i	$-0.608565\pi$
$719$	12510.3	−	21668.5i	0.648896	−	1.12392i	0.983387	−	0.181521i	$-0.0581021\pi$
$720$		0			0
$721$	470.586	−	228.460i	0.0243073	−	0.0118007i
$722$	−108.025	+	187.105i	−0.00556825	+	0.00964450i
$723$		0			0
$724$	−498.666	+	863.714i	−0.0255977	+	0.0443366i
$725$	−4799.00	+	8312.12i	−0.245835	+	0.425799i
$726$		0			0
$727$	−712.918	+	1234.81i	−0.0363695	+	0.0629939i	−0.883637	−	0.468172i	$-0.844913\pi$
$727$	−712.918	+	1234.81i	−0.0363695	+	0.0629939i	0.847268	+	0.531166i	$0.178246\pi$
$728$	22081.7	+	14952.9i	1.12418	+	0.761252i
$729$		0			0
$730$	1937.08	−	3355.12i	0.0982116	−	0.170107i
$731$	−4563.87			−0.230918
$732$		0			0
$733$	2588.08			0.130413			0.0652067	−	0.997872i	$-0.479229\pi$
$733$	2588.08			0.130413			0.0652067	+	0.997872i	$0.479229\pi$
$734$	−14339.2	−	24836.3i	−0.721078	−	1.24894i
$735$		0			0
$736$	1877.58	−	3252.06i	0.0940333	−	0.162870i
$737$	−3114.85	+	5395.07i	−0.155681	+	0.269647i
$738$		0			0
$739$	−2281.47	−	3951.62i	−0.113566	−	0.196702i	0.803640	−	0.595116i	$-0.202894\pi$
$739$	−2281.47	−	3951.62i	−0.113566	−	0.196702i	−0.917206	+	0.398414i	$0.869561\pi$
$740$	−1049.74	−	1818.20i	−0.0521476	−	0.0903224i
$741$		0			0
$742$	−818.056	+	11400.2i	−0.0404741	+	0.564036i
$743$	−5519.60	−	9560.23i	−0.272536	−	0.472047i	0.696974	−	0.717096i	$-0.254529\pi$
$743$	−5519.60	−	9560.23i	−0.272536	−	0.472047i	−0.969511	+	0.245049i	$0.921196\pi$
$744$		0			0
$745$	10691.7			0.525792
$746$	1703.41	+	2950.40i	0.0836010	+	0.144801i
$747$		0			0
$748$	−114.343			−0.00558930
$749$	−2220.84	+	30949.0i	−0.108342	+	1.50982i
$750$		0			0
$751$	19178.1			0.931850			0.465925	−	0.884824i	$-0.345722\pi$
$751$	19178.1			0.931850			0.465925	+	0.884824i	$0.345722\pi$
$752$	14178.5	−	24557.8i	0.687546	−	1.19087i
$753$		0			0
$754$	10888.0	+	18858.6i	0.525886	+	0.910862i
$755$	−15019.6			−0.723999
$756$		0			0
$757$	−17087.1			−0.820399			−0.410199	−	0.911996i	$-0.634541\pi$
$757$	−17087.1			−0.820399			−0.410199	+	0.911996i	$0.634541\pi$
$758$	−1977.82	−	3425.69i	−0.0947727	−	0.164151i
$759$		0			0
$760$	−7281.79	+	12612.4i	−0.347550	+	0.601975i
$761$	−35823.8			−1.70646			−0.853228	−	0.521538i	$-0.825358\pi$
$761$	−35823.8			−1.70646			−0.853228	+	0.521538i	$0.825358\pi$
$762$		0			0
$763$	−6057.26	−	4101.75i	−0.287402	−	0.194618i
$764$	53.9389			0.00255424
$765$		0			0
$766$	7319.45	+	12677.7i	0.345251	+	0.597993i
$767$	−3778.48			−0.177879
$768$		0			0
$769$	−15798.1	−	27363.1i	−0.740823	−	1.28314i	−0.952121	−	0.305722i	$-0.901102\pi$
$769$	−15798.1	−	27363.1i	−0.740823	−	1.28314i	0.211297	−	0.977422i	$-0.432231\pi$
$770$	−3396.78	−	2300.17i	−0.158976	−	0.107653i
$771$		0			0
$772$	−2348.26	−	4067.30i	−0.109476	−	0.189618i
$773$	18673.5	+	32343.5i	0.868875	+	1.50493i	0.863148	+	0.504951i	$0.168490\pi$
$773$	18673.5	+	32343.5i	0.868875	+	1.50493i	0.00572679	+	0.999984i	$0.498177\pi$
$774$		0			0
$775$	1896.54	−	3284.91i	0.0879043	−	0.152255i
$776$	−13095.8	+	22682.6i	−0.605814	+	1.04930i
$777$		0			0
$778$	−1811.80	−	3138.13i	−0.0834913	−	0.144611i
$779$	−32330.1			−1.48697
$780$		0			0
$781$	5729.35			0.262500
$782$	−1231.21	+	2132.52i	−0.0563017	+	0.0975174i
$783$		0			0
$784$	18833.0	+	2716.83i	0.857918	+	0.123762i
$785$	−357.258	+	618.789i	−0.0162434	+	0.0281344i
$786$		0			0
$787$	−2403.09	+	4162.27i	−0.108845	+	0.188524i	−0.915302	−	0.402767i	$-0.868048\pi$
$787$	−2403.09	+	4162.27i	−0.108845	+	0.188524i	0.806458	+	0.591292i	$0.201382\pi$
$788$	−883.177	+	1529.71i	−0.0399262	+	0.0691543i
$789$		0			0
$790$	11500.1	−	19918.8i	0.517918	−	0.897060i
$791$	2893.97	+	1959.69i	0.130086	+	0.0880892i
$792$		0			0
$793$	−10300.9	+	17841.7i	−0.461280	+	0.798961i
$794$	−16561.1			−0.740218
$795$		0			0
$796$	1495.84			0.0666063
$797$	3158.63	+	5470.91i	0.140382	+	0.243149i	0.927640	−	0.373474i	$-0.121834\pi$
$797$	3158.63	+	5470.91i	0.140382	+	0.243149i	−0.787259	+	0.616623i	$0.788500\pi$
$798$		0			0
$799$	2705.50	−	4686.06i	0.119792	−	0.207486i
$800$	1519.13	−	2631.20i	0.0671365	−	0.116284i
$801$		0			0
$802$	508.439	+	880.642i	0.0223860	+	0.0387737i
$803$	1125.23	+	1948.95i	0.0494501	+	0.0856500i
$804$		0			0
$805$	10738.2	−	5213.17i	0.470151	−	0.228248i
$806$	−4302.89	−	7452.83i	−0.188043	−	0.325701i
$807$		0			0
$808$	9550.94			0.415843
$809$	−14191.1	−	24579.7i	−0.616727	−	1.06820i	−0.990079	−	0.140513i	$-0.955125\pi$
$809$	−14191.1	−	24579.7i	−0.616727	−	1.06820i	0.373352	−	0.927690i	$-0.378208\pi$
$810$		0			0
$811$	14857.2			0.643290			0.321645	−	0.946860i	$-0.395764\pi$
$811$	14857.2			0.643290			0.321645	+	0.946860i	$0.395764\pi$
$812$	−1977.01	−	1338.75i	−0.0854425	−	0.0578585i
$813$		0			0
$814$	−9026.09			−0.388654
$815$	7150.41	−	12384.9i	0.307323	−	0.532298i
$816$		0			0
$817$	−17958.8	−	31105.6i	−0.769033	−	1.33201i
$818$	26110.0			1.11603
$819$		0			0
$820$	−2718.26			−0.115763
$821$	−10905.9	−	18889.6i	−0.463605	−	0.802988i	0.535532	−	0.844515i	$-0.320111\pi$
$821$	−10905.9	−	18889.6i	−0.463605	−	0.802988i	−0.999137	+	0.0415269i	$0.986778\pi$
$822$		0			0
$823$	−14374.2	+	24896.9i	−0.608814	+	1.05450i	0.382622	+	0.923905i	$0.375021\pi$
$823$	−14374.2	+	24896.9i	−0.608814	+	1.05450i	−0.991436	+	0.130592i	$0.958312\pi$
$824$	−671.281			−0.0283801
$825$		0			0
$826$	−2758.33	+	1339.11i	−0.116192	+	0.0564087i
$827$	−41358.3			−1.73902			−0.869509	−	0.493917i	$-0.835565\pi$
$827$	−41358.3			−1.73902			−0.869509	+	0.493917i	$0.835565\pi$
$828$		0			0
$829$	−16989.4	−	29426.5i	−0.711781	−	1.23284i	−0.964188	−	0.265220i	$-0.914555\pi$
$829$	−16989.4	−	29426.5i	−0.711781	−	1.23284i	0.252407	−	0.967621i	$-0.418778\pi$
$830$	28224.4			1.18034
$831$		0			0
$832$	−16891.2	−	29256.4i	−0.703841	−	1.21909i
$833$	3593.67	+	518.419i	0.149476	+	0.0215632i
$834$		0			0
$835$	13172.9	+	22816.1i	0.545947	+	0.945608i
$836$	−449.940	−	779.319i	−0.0186142	−	0.0322408i
$837$		0			0
$838$	8332.56	−	14432.4i	0.343489	−	0.594940i
$839$	−9203.77	+	15941.4i	−0.378724	+	0.655969i	−0.990877	−	0.134770i	$-0.956970\pi$
$839$	−9203.77	+	15941.4i	−0.378724	+	0.655969i	0.612153	+	0.790739i	$0.290304\pi$
$840$		0			0
$841$	3030.16	+	5248.38i	0.124243	+	0.215195i
$842$	34630.3			1.41738
$843$		0			0
$844$	1033.48			0.0421490
$845$	5420.85	−	9389.18i	0.220690	−	0.382246i
$846$		0			0
$847$	−20031.6	+	9724.94i	−0.812627	+	0.394513i
$848$	6447.98	−	11168.2i	0.261114	−	0.452263i
$849$		0			0
$850$	−996.156	+	1725.39i	−0.0401975	+	0.0696241i
$851$	13131.9	−	22745.1i	0.528972	−	0.916207i
$852$		0			0
$853$	9015.26	−	15614.9i	0.361872	−	0.626780i	−0.626397	−	0.779504i	$-0.715471\pi$
$853$	9015.26	−	15614.9i	0.361872	−	0.626780i	0.988269	+	0.152724i	$0.0488045\pi$
$854$	−1196.58	+	16675.3i	−0.0479465	+	0.668169i
$855$		0			0
$856$	19908.7	−	34482.9i	0.794936	−	1.37687i
$857$	−7725.62			−0.307937			−0.153969	−	0.988076i	$-0.549205\pi$
$857$	−7725.62			−0.307937			−0.153969	+	0.988076i	$0.549205\pi$
$858$		0			0
$859$	4827.45			0.191747			0.0958734	−	0.995394i	$-0.469436\pi$
$859$	4827.45			0.191747			0.0958734	+	0.995394i	$0.469436\pi$
$860$	−1509.95	−	2615.30i	−0.0598706	−	0.103699i
$861$		0			0
$862$	−12940.7	+	22413.9i	−0.511325	+	0.885640i
$863$	14645.0	−	25365.8i	0.577660	−	1.00054i	−0.418087	−	0.908407i	$-0.637299\pi$
$863$	14645.0	−	25365.8i	0.577660	−	1.00054i	0.995747	−	0.0921291i	$-0.0293672\pi$
$864$		0			0
$865$	1465.36	+	2538.08i	0.0575997	+	0.0997656i
$866$	427.883	+	741.114i	0.0167899	+	0.0290809i
$867$		0			0
$868$	781.303	+	529.069i	0.0305520	+	0.0206887i
$869$	6680.28	+	11570.6i	0.260774	+	0.451675i
$870$		0			0
$871$	−33275.0			−1.29447
$872$	4693.72	+	8129.76i	0.182281	+	0.315721i
$873$		0			0
$874$	−19379.2			−0.750014
$875$	24006.8	−	11654.8i	0.927518	−	0.450291i
$876$		0			0
$877$	21537.7			0.829279			0.414640	−	0.909986i	$-0.363908\pi$
$877$	21537.7			0.829279			0.414640	+	0.909986i	$0.363908\pi$
$878$	4121.49	−	7138.64i	0.158421	−	0.274393i
$879$		0			0
$880$	2314.32	+	4008.53i	0.0886543	+	0.153554i
$881$	1711.46			0.0654489			0.0327245	−	0.999464i	$-0.489582\pi$
$881$	1711.46			0.0654489			0.0327245	+	0.999464i	$0.489582\pi$
$882$		0			0
$883$	27707.9			1.05600			0.527999	−	0.849245i	$-0.322943\pi$
$883$	27707.9			1.05600			0.527999	+	0.849245i	$0.322943\pi$
$884$	−305.373	−	528.922i	−0.0116186	−	0.0201240i
$885$		0			0
$886$	−3184.79	+	5516.21i	−0.120762	+	0.209166i
$887$	18214.3			0.689490			0.344745	−	0.938696i	$-0.387965\pi$
$887$	18214.3			0.689490			0.344745	+	0.938696i	$0.387965\pi$
$888$		0			0
$889$	5679.02	−	2757.04i	0.214250	−	0.104014i
$890$	19815.0			0.746293
$891$		0			0
$892$	−1933.23	−	3348.46i	−0.0725666	−	0.125689i
$893$	42584.6			1.59579
$894$		0			0
$895$	−15589.7	−	27002.2i	−0.582242	−	1.00847i
$896$	−17441.7	−	11810.9i	−0.650321	−	0.440373i
$897$		0			0
$898$	−11951.4	−	20700.5i	−0.444125	−	0.769248i
$899$	3621.70	+	6272.98i	0.134361	+	0.232720i
$900$		0			0
$901$	1230.39	−	2131.10i	0.0454941	−	0.0787982i
$902$	−5843.16	+	10120.7i	−0.215694	+	0.373593i
$903$		0			0
$904$	−2242.52	−	3884.15i	−0.0825055	−	0.142904i
$905$	7703.76			0.282963
$906$		0			0
$907$	−13875.7			−0.507976			−0.253988	−	0.967207i	$-0.581742\pi$
$907$	−13875.7			−0.507976			−0.253988	+	0.967207i	$0.581742\pi$
$908$	−2442.15	+	4229.94i	−0.0892574	+	0.154598i
$909$		0			0
$910$	1568.32	−	21855.7i	0.0571311	−	0.796163i
$911$	−12028.7	+	20834.4i	−0.437464	+	0.757709i	−0.997493	−	0.0707633i	$-0.977456\pi$
$911$	−12028.7	+	20834.4i	−0.437464	+	0.757709i	0.560029	+	0.828473i	$0.310790\pi$
$912$		0			0
$913$	−8197.62	+	14198.7i	−0.297154	+	0.514686i
$914$	8939.86	−	15484.3i	0.323528	−	0.560366i
$915$		0			0
$916$	−2618.00	+	4534.51i	−0.0944337	+	0.163564i
$917$	14993.2	−	7278.89i	0.539934	−	0.262127i
$918$		0			0
$919$	6717.74	−	11635.5i	0.241129	−	0.417648i	−0.719907	−	0.694071i	$-0.755816\pi$
$919$	6717.74	−	11635.5i	0.241129	−	0.417648i	0.961036	+	0.276422i	$0.0891489\pi$
$920$	−15317.8			−0.548927
$921$		0			0
$922$	5747.21			0.205287
$923$	15301.2	+	26502.5i	0.545662	+	0.945115i
$924$		0			0
$925$	10624.9	−	18402.8i	0.377668	−	0.654140i
$926$	−3872.27	+	6706.97i	−0.137420	+	0.238018i
$927$		0			0
$928$	2900.98	+	5024.64i	0.102618	+	0.177739i
$929$	4303.84	+	7454.47i	0.151996	+	0.263265i	0.931961	−	0.362558i	$-0.118097\pi$
$929$	4303.84	+	7454.47i	0.151996	+	0.263265i	−0.779965	+	0.625823i	$0.784763\pi$
$930$		0			0
$931$	10607.8	+	26533.1i	0.373421	+	0.934035i
$932$	−2232.81	−	3867.35i	−0.0784745	−	0.135922i
$933$		0			0
$934$	4619.30			0.161829
$935$	441.614	+	764.898i	0.0154463	+	0.0267538i
$936$		0			0
$937$	26751.4			0.932688			0.466344	−	0.884603i	$-0.345571\pi$
$937$	26751.4			0.932688			0.466344	+	0.884603i	$0.345571\pi$
$938$	−24291.1	+	11792.8i	−0.845556	+	0.410500i
$939$		0			0
$940$	3580.43			0.124235
$941$	2254.78	−	3905.40i	0.0781125	−	0.135295i	−0.824323	−	0.566120i	$-0.808444\pi$
$941$	2254.78	−	3905.40i	0.0781125	−	0.135295i	0.902436	+	0.430825i	$0.141777\pi$
$942$		0			0
$943$	−17002.2	−	29448.7i	−0.587136	−	1.01695i
$944$	3459.60			0.119280
$945$		0			0
$946$	−12983.1			−0.446213
$947$	−11507.9	−	19932.3i	−0.394887	−	0.683964i	0.598200	−	0.801347i	$-0.295883\pi$
$947$	−11507.9	−	19932.3i	−0.394887	−	0.683964i	−0.993087	+	0.117383i	$0.962549\pi$
$948$		0			0
$949$	−6010.24	+	10410.0i	−0.205585	+	0.356084i
$950$	−15679.5			−0.535484
$951$		0			0
$952$	−3857.99	−	2612.49i	−0.131343	−	0.0889403i
$953$	30615.2			1.04063			0.520317	−	0.853973i	$-0.325814\pi$
$953$	30615.2			1.04063			0.520317	+	0.853973i	$0.325814\pi$
$954$		0			0
$955$	−208.322	−	360.824i	−0.00705878	−	0.0122262i
$956$	4259.51			0.144103
$957$		0			0
$958$	−14910.1	−	25825.0i	−0.502843	−	0.870949i
$959$	1221.52	−	593.020i	0.0411312	−	0.0199683i
$960$		0			0
$961$	13464.2	+	23320.7i	0.451956	+	0.782811i
$962$	−24105.8	−	41752.4i	−0.807901	−	1.39933i
$963$		0			0
$964$	−409.277	+	708.889i	−0.0136742	+	0.0236844i
$965$	−18138.8	+	31417.3i	−0.605087	+	1.04804i
$966$		0			0
$967$	29059.4	+	50332.3i	0.966377	+	1.67381i	0.705869	+	0.708343i	$0.250557\pi$
$967$	29059.4	+	50332.3i	0.966377	+	1.67381i	0.260509	+	0.965472i	$0.416110\pi$
$968$	28574.7			0.948787
$969$		0			0
$970$	21520.3			0.712345
$971$	11506.1	−	19929.2i	0.380277	−	0.658660i	−0.610824	−	0.791766i	$-0.709162\pi$
$971$	11506.1	−	19929.2i	0.380277	−	0.658660i	0.991102	+	0.133106i	$0.0424952\pi$
$972$		0			0
$973$	22842.3	+	15468.0i	0.752611	+	0.509640i
$974$	−2192.78	+	3798.01i	−0.0721368	+	0.124945i
$975$		0			0
$976$	9431.58	−	16336.0i	0.309321	−	0.535760i
$977$	−23253.7	+	40276.6i	−0.761466	+	1.31890i	0.180630	+	0.983551i	$0.442186\pi$
$977$	−23253.7	+	40276.6i	−0.761466	+	1.31890i	−0.942095	+	0.335346i	$0.891147\pi$
$978$		0			0
$979$	−5755.17	+	9968.24i	−0.187881	+	0.325420i
$980$	891.880	+	2230.85i	0.0290715	+	0.0727163i
$981$		0			0
$982$	21001.5	−	36375.7i	0.682470	−	1.18207i
$983$	−121.906			−0.00395543			−0.00197772	−	0.999998i	$-0.500630\pi$
$983$	−121.906			−0.00395543			−0.00197772	+	0.999998i	$0.500630\pi$
$984$		0			0
$985$	13644.0			0.441353
$986$	−1902.29	−	3294.87i	−0.0614415	−	0.106420i
$987$		0			0
$988$	2403.29	−	4162.62i	0.0773874	−	0.134039i
$989$	18888.9	−	32716.5i	0.607312	−	1.05190i
$990$		0			0
$991$	−4981.68	−	8628.52i	−0.159685	−	0.276583i	0.775070	−	0.631876i	$-0.217715\pi$
$991$	−4981.68	−	8628.52i	−0.159685	−	0.276583i	−0.934755	+	0.355292i	$0.884381\pi$
$992$	−1146.45	−	1985.71i	−0.0366934	−	0.0635549i
$993$		0			0
$994$	20562.7	+	13924.3i	0.656145	+	0.444317i
$995$	−5777.20	−	10006.4i	−0.184070	−	0.318819i
$996$		0			0
$997$	16249.6			0.516179			0.258090	−	0.966121i	$-0.416907\pi$
$997$	16249.6			0.516179			0.258090	+	0.966121i	$0.416907\pi$
$998$	18728.8	+	32439.3i	0.594039	+	1.02891i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.g.a.100.7		44
3.2	odd	2		63.4.g.a.16.16	yes	44
7.4	even	3		189.4.h.a.46.16		44
9.4	even	3		189.4.h.a.37.16		44
9.5	odd	6		63.4.h.a.58.7	yes	44
21.11	odd	6		63.4.h.a.25.7	yes	44
63.4	even	3	inner	189.4.g.a.172.7		44
63.32	odd	6		63.4.g.a.4.16	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.g.a.4.16	✓	44	63.32	odd	6
63.4.g.a.16.16	yes	44	3.2	odd	2
63.4.h.a.25.7	yes	44	21.11	odd	6
63.4.h.a.58.7	yes	44	9.5	odd	6
189.4.g.a.100.7		44	1.1	even	1	trivial
189.4.g.a.172.7		44	63.4	even	3	inner
189.4.h.a.37.16		44	9.4	even	3
189.4.h.a.46.16		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)

\(f(q)\)	\(=\)	\(q+(-1.32738 - 2.29909i) q^{2} +(0.476130 - 0.824682i) q^{4} -7.35561 q^{5} +(16.6607 - 8.08840i) q^{7} -23.7661 q^{8} +O(q^{10})\)	\(q+(-1.32738 - 2.29909i) q^{2} +(0.476130 - 0.824682i) q^{4} -7.35561 q^{5} +(16.6607 - 8.08840i) q^{7} -23.7661 q^{8} +(9.76368 + 16.9112i) q^{10} -11.3432 q^{11} +(-30.2941 - 52.4710i) q^{13} +(-40.7110 - 27.5680i) q^{14} +(27.7376 + 48.0429i) q^{16} +(5.29282 + 9.16743i) q^{17} +(-41.6545 + 72.1477i) q^{19} +(-3.50223 + 6.06604i) q^{20} +(15.0568 + 26.0791i) q^{22} -87.6234 q^{23} -70.8950 q^{25} +(-80.4236 + 139.298i) q^{26} +(1.26229 - 17.5909i) q^{28} +(67.6917 - 117.246i) q^{29} +(-26.7514 + 46.3349i) q^{31} +(-21.4278 + 37.1141i) q^{32} +(14.0511 - 24.3373i) q^{34} +(-122.549 + 59.4952i) q^{35} +(-149.868 + 259.578i) q^{37} +221.165 q^{38} +174.814 q^{40} +(194.038 + 336.083i) q^{41} +(-215.569 + 373.377i) q^{43} +(-5.40086 + 9.35456i) q^{44} +(116.309 + 201.454i) q^{46} +(-255.582 - 442.681i) q^{47} +(212.155 - 269.516i) q^{49} +(94.1045 + 162.994i) q^{50} -57.6958 q^{52} +(-116.232 - 201.320i) q^{53} +83.4364 q^{55} +(-395.959 + 192.230i) q^{56} -359.410 q^{58} +(31.1816 - 54.0081i) q^{59} +(-170.015 - 294.474i) q^{61} +142.037 q^{62} +557.572 q^{64} +(222.832 + 385.956i) q^{65} +(274.599 - 475.620i) q^{67} +10.0803 q^{68} +(299.454 + 202.779i) q^{70} -505.089 q^{71} +(-99.1981 - 171.816i) q^{73} +795.724 q^{74} +(39.6659 + 68.7034i) q^{76} +(-188.986 + 91.7487i) q^{77} +(-588.922 - 1020.04i) q^{79} +(-204.027 - 353.385i) q^{80} +(515.123 - 892.219i) q^{82} +(722.688 - 1251.73i) q^{83} +(-38.9319 - 67.4320i) q^{85} +1144.57 q^{86} +269.584 q^{88} +(507.365 - 878.783i) q^{89} +(-929.126 - 629.170i) q^{91} +(-41.7201 + 72.2614i) q^{92} +(-678.509 + 1175.21i) q^{94} +(306.394 - 530.690i) q^{95} +(551.029 - 954.410i) q^{97} +(-901.252 - 130.014i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - q^{2} - 79 q^{4} - 38 q^{5} - 7 q^{7} + 24 q^{8}+O(q^{10}) \) 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