LMFDB - Embedded newform 189.3.j.b.44.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,3,Mod(44,189)]

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([5, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("189.44");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	189.j (of order $6$, 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:	$5.14987699641$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			44.2
Character	$\chi$	$=$	189.44
Dual form			189.3.j.b.116.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.22356i q^{2} -6.39137 q^{4} +(4.79167 - 2.76647i) q^{5} +(-6.99696 - 0.206413i) q^{7} +7.70873i q^{8} +O(q^{10})$	\(q-3.22356i q^{2} -6.39137 q^{4} +(4.79167 - 2.76647i) q^{5} +(-6.99696 - 0.206413i) q^{7} +7.70873i q^{8} +(-8.91790 - 15.4463i) q^{10} +(-15.3189 - 8.84435i) q^{11} +(2.03775 - 3.52949i) q^{13} +(-0.665386 + 22.5551i) q^{14} -0.715882 q^{16} +(14.3348 - 8.27617i) q^{17} +(-3.92096 + 6.79130i) q^{19} +(-30.6253 + 17.6815i) q^{20} +(-28.5103 + 49.3813i) q^{22} +(-8.71877 + 5.03378i) q^{23} +(2.80674 - 4.86141i) q^{25} +(-11.3775 - 6.56882i) q^{26} +(44.7201 + 1.31926i) q^{28} +(39.9040 - 23.0386i) q^{29} +29.6235 q^{31} +33.1426i q^{32} +(-26.6788 - 46.2090i) q^{34} +(-34.0981 + 18.3678i) q^{35} +(15.5948 - 27.0110i) q^{37} +(21.8922 + 12.6395i) q^{38} +(21.3260 + 36.9377i) q^{40} +(-27.8184 - 16.0609i) q^{41} +(3.35243 + 5.80658i) q^{43} +(97.9085 + 56.5275i) q^{44} +(16.2267 + 28.1055i) q^{46} -16.4402i q^{47} +(48.9148 + 2.88853i) q^{49} +(-15.6711 - 9.04769i) q^{50} +(-13.0240 + 22.5583i) q^{52} +(32.5897 - 18.8157i) q^{53} -97.8706 q^{55} +(1.59118 - 53.9377i) q^{56} +(-74.2663 - 128.633i) q^{58} -95.0557i q^{59} -73.7679 q^{61} -95.4932i q^{62} +103.974 q^{64} -22.5495i q^{65} -12.1909 q^{67} +(-91.6187 + 52.8961i) q^{68} +(59.2099 + 109.918i) q^{70} -20.0140i q^{71} +(-11.4932 - 19.9068i) q^{73} +(-87.0715 - 50.2708i) q^{74} +(25.0603 - 43.4057i) q^{76} +(105.360 + 65.0455i) q^{77} +138.880 q^{79} +(-3.43027 + 1.98047i) q^{80} +(-51.7735 + 89.6743i) q^{82} +(-13.6928 + 7.90552i) q^{83} +(45.7916 - 79.3134i) q^{85} +(18.7179 - 10.8068i) q^{86} +(68.1787 - 118.089i) q^{88} +(46.9444 + 27.1034i) q^{89} +(-14.9866 + 24.2750i) q^{91} +(55.7249 - 32.1728i) q^{92} -52.9962 q^{94} +43.3889i q^{95} +(86.1189 + 149.162i) q^{97} +(9.31136 - 157.680i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 24 q^{4} - 12 q^{5}+O(q^{10}) $ 22 * q - 24 * q^4 - 12 * q^5	$ 22 q - 24 q^{4} - 12 q^{5} + 25 q^{10} - 24 q^{11} - 18 q^{13} + 60 q^{14} - 24 q^{16} + 6 q^{17} + 3 q^{19} + 39 q^{20} - 59 q^{22} - 81 q^{23} + 57 q^{25} - 3 q^{26} + 34 q^{28} + 63 q^{29} + 58 q^{31} - 99 q^{34} - 27 q^{35} - 20 q^{37} + 48 q^{38} - 105 q^{40} + 51 q^{41} + 65 q^{43} + 54 q^{44} + 75 q^{46} + 4 q^{49} - 63 q^{50} - 46 q^{52} - 63 q^{53} - 100 q^{55} - 192 q^{56} + 40 q^{58} - 156 q^{61} + 106 q^{64} + 264 q^{67} - 27 q^{68} + 236 q^{70} + q^{73} - 342 q^{74} + 233 q^{76} + 531 q^{77} - 280 q^{79} + 96 q^{80} - 157 q^{82} - 255 q^{83} + 102 q^{85} - 504 q^{86} + 408 q^{88} - 720 q^{89} - 70 q^{91} + 1239 q^{92} - 522 q^{94} + 178 q^{97} + 483 q^{98}+O(q^{100}) $ 22 * q - 24 * q^4 - 12 * q^5 + 25 * q^10 - 24 * q^11 - 18 * q^13 + 60 * q^14 - 24 * q^16 + 6 * q^17 + 3 * q^19 + 39 * q^20 - 59 * q^22 - 81 * q^23 + 57 * q^25 - 3 * q^26 + 34 * q^28 + 63 * q^29 + 58 * q^31 - 99 * q^34 - 27 * q^35 - 20 * q^37 + 48 * q^38 - 105 * q^40 + 51 * q^41 + 65 * q^43 + 54 * q^44 + 75 * q^46 + 4 * q^49 - 63 * q^50 - 46 * q^52 - 63 * q^53 - 100 * q^55 - 192 * q^56 + 40 * q^58 - 156 * q^61 + 106 * q^64 + 264 * q^67 - 27 * q^68 + 236 * q^70 + q^73 - 342 * q^74 + 233 * q^76 + 531 * q^77 - 280 * q^79 + 96 * q^80 - 157 * q^82 - 255 * q^83 + 102 * q^85 - 504 * q^86 + 408 * q^88 - 720 * q^89 - 70 * q^91 + 1239 * q^92 - 522 * q^94 + 178 * q^97 + 483 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	3.22356i		−	1.61178i	−0.592064	−	0.805891i	$-0.701687\pi$
$2$		−	3.22356i		−	1.61178i	0.592064	−	0.805891i	$-0.298313\pi$
$3$		0			0
$3$		0			0
$4$	−6.39137			−1.59784
$5$	4.79167	−	2.76647i	0.958334	−	0.553294i	0.0626741	−	0.998034i	$-0.480037\pi$
$5$	4.79167	−	2.76647i	0.958334	−	0.553294i	0.895660	+	0.444740i	$0.146704\pi$
$6$		0			0
$7$	−6.99696	−	0.206413i	−0.999565	−	0.0294876i
$7$	−6.99696	−	0.206413i	−0.999565	−	0.0294876i
$8$			7.70873i			0.963591i
$9$		0			0
$10$	−8.91790	−	15.4463i	−0.891790	−	1.54463i
$11$	−15.3189	−	8.84435i	−1.39262	−	0.804032i	−0.399018	−	0.916943i	$-0.630649\pi$
$11$	−15.3189	−	8.84435i	−1.39262	−	0.804032i	−0.993605	+	0.112911i	$0.963982\pi$
$12$		0			0
$13$	2.03775	−	3.52949i	0.156750	−	0.271499i	−0.776945	−	0.629569i	$-0.783232\pi$
$13$	2.03775	−	3.52949i	0.156750	−	0.271499i	0.933695	+	0.358070i	$0.116565\pi$
$14$	−0.665386	+	22.5551i	−0.0475276	+	1.61108i
$15$		0			0
$16$	−0.715882			−0.0447426
$17$	14.3348	−	8.27617i	0.843221	−	0.486834i	−0.0151370	−	0.999885i	$-0.504818\pi$
$17$	14.3348	−	8.27617i	0.843221	−	0.486834i	0.858358	+	0.513052i	$0.171485\pi$
$18$		0			0
$19$	−3.92096	+	6.79130i	−0.206366	+	0.357437i	−0.950567	−	0.310519i	$-0.899497\pi$
$19$	−3.92096	+	6.79130i	−0.206366	+	0.357437i	0.744201	+	0.667956i	$0.232830\pi$
$20$	−30.6253	+	17.6815i	−1.53127	+	0.884077i
$21$		0			0
$22$	−28.5103	+	49.3813i	−1.29592	+	2.24461i
$23$	−8.71877	+	5.03378i	−0.379077	+	0.218860i	−0.677417	−	0.735600i	$-0.736901\pi$
$23$	−8.71877	+	5.03378i	−0.379077	+	0.218860i	0.298340	+	0.954460i	$0.403567\pi$
$24$		0			0
$25$	2.80674	−	4.86141i	0.112269	−	0.194456i
$26$	−11.3775	−	6.56882i	−0.437597	−	0.252647i
$27$		0			0
$28$	44.7201	+	1.31926i	1.59715	+	0.0471165i
$29$	39.9040	−	23.0386i	1.37600	−	0.794434i	0.384324	−	0.923198i	$-0.374434\pi$
$29$	39.9040	−	23.0386i	1.37600	−	0.794434i	0.991675	+	0.128764i	$0.0411011\pi$
$30$		0			0
$31$	29.6235			0.955596			0.477798	−	0.878470i	$-0.341435\pi$
$31$	29.6235			0.955596			0.477798	+	0.878470i	$0.341435\pi$
$32$			33.1426i			1.03571i
$33$		0			0
$34$	−26.6788	−	46.2090i	−0.784670	−	1.35909i
$35$	−34.0981	+	18.3678i	−0.974233	+	0.524795i
$36$		0			0
$37$	15.5948	−	27.0110i	0.421481	−	0.730026i	−0.574604	−	0.818432i	$-0.694844\pi$
$37$	15.5948	−	27.0110i	0.421481	−	0.730026i	0.996085	+	0.0884059i	$0.0281772\pi$
$38$	21.8922	+	12.6395i	0.576110	+	0.332617i
$39$		0			0
$40$	21.3260	+	36.9377i	0.533150	+	0.923442i
$41$	−27.8184	−	16.0609i	−0.678497	−	0.391730i	0.120792	−	0.992678i	$-0.461457\pi$
$41$	−27.8184	−	16.0609i	−0.678497	−	0.391730i	−0.799288	+	0.600948i	$0.794790\pi$
$42$		0			0
$43$	3.35243	+	5.80658i	0.0779635	+	0.135037i	0.902371	−	0.430960i	$-0.141825\pi$
$43$	3.35243	+	5.80658i	0.0779635	+	0.135037i	−0.824408	+	0.565997i	$0.808492\pi$
$44$	97.9085	+	56.5275i	2.22519	+	1.28472i
$45$		0			0
$46$	16.2267	+	28.1055i	0.352755	+	0.610990i
$47$		−	16.4402i		−	0.349792i	−0.984587	−	0.174896i	$-0.944041\pi$
$47$		−	16.4402i		−	0.349792i	0.984587	−	0.174896i	$-0.0559590\pi$
$48$		0			0
$49$	48.9148	+	2.88853i	0.998261	+	0.0589496i
$50$	−15.6711	−	9.04769i	−0.313421	−	0.180954i
$51$		0			0
$52$	−13.0240	+	22.5583i	−0.250462	+	0.433813i
$53$	32.5897	−	18.8157i	0.614900	−	0.355013i	−0.159981	−	0.987120i	$-0.551143\pi$
$53$	32.5897	−	18.8157i	0.614900	−	0.355013i	0.774881	+	0.632108i	$0.217810\pi$
$54$		0			0
$55$	−97.8706			−1.77946
$56$	1.59118	−	53.9377i	0.0284140	−	0.963172i
$57$		0			0
$58$	−74.2663	−	128.633i	−1.28045	−	2.21781i
$59$		−	95.0557i		−	1.61111i	−0.592519	−	0.805557i	$-0.701866\pi$
$59$		−	95.0557i		−	1.61111i	0.592519	−	0.805557i	$-0.298134\pi$
$60$		0			0
$61$	−73.7679			−1.20931			−0.604655	−	0.796488i	$-0.706689\pi$
$61$	−73.7679			−1.20931			−0.604655	+	0.796488i	$0.706689\pi$
$62$		−	95.4932i		−	1.54021i
$63$		0			0
$64$	103.974			1.62459
$65$		−	22.5495i		−	0.346916i
$66$		0			0
$67$	−12.1909			−0.181954			−0.0909769	−	0.995853i	$-0.528999\pi$
$67$	−12.1909			−0.181954			−0.0909769	+	0.995853i	$0.528999\pi$
$68$	−91.6187	+	52.8961i	−1.34733	+	0.777883i
$69$		0			0
$70$	59.2099	+	109.918i	0.845855	+	1.57025i
$71$		−	20.0140i		−	0.281887i	−0.990018	−	0.140944i	$-0.954986\pi$
$71$		−	20.0140i		−	0.281887i	0.990018	−	0.140944i	$-0.0450136\pi$
$72$		0			0
$73$	−11.4932	−	19.9068i	−0.157441	−	0.272696i	0.776504	−	0.630112i	$-0.216991\pi$
$73$	−11.4932	−	19.9068i	−0.157441	−	0.272696i	−0.933945	+	0.357416i	$0.883658\pi$
$74$	−87.0715	−	50.2708i	−1.17664	−	0.679335i
$75$		0			0
$76$	25.0603	−	43.4057i	0.329741	−	0.571128i
$77$	105.360	+	65.0455i	1.36831	+	0.844747i
$78$		0			0
$79$	138.880			1.75798			0.878988	−	0.476844i	$-0.158219\pi$
$79$	138.880			1.75798			0.878988	+	0.476844i	$0.158219\pi$
$80$	−3.43027	+	1.98047i	−0.0428784	+	0.0247559i
$81$		0			0
$82$	−51.7735	+	89.6743i	−0.631384	+	1.09359i
$83$	−13.6928	+	7.90552i	−0.164973	+	0.0952472i	−0.580213	−	0.814465i	$-0.697031\pi$
$83$	−13.6928	+	7.90552i	−0.164973	+	0.0952472i	0.415240	+	0.909712i	$0.363697\pi$
$84$		0			0
$85$	45.7916	−	79.3134i	0.538725	−	0.933099i
$86$	18.7179	−	10.8068i	0.217650	−	0.125660i
$87$		0			0
$88$	68.1787	−	118.089i	0.774758	−	1.34192i
$89$	46.9444	+	27.1034i	0.527466	+	0.304532i	0.739984	−	0.672625i	$-0.234833\pi$
$89$	46.9444	+	27.1034i	0.527466	+	0.304532i	−0.212518	+	0.977157i	$0.568166\pi$
$90$		0			0
$91$	−14.9866	+	24.2750i	−0.164688	+	0.266759i
$92$	55.7249	−	32.1728i	0.605705	−	0.349704i
$93$		0			0
$94$	−52.9962			−0.563789
$95$			43.3889i			0.456725i
$96$		0			0
$97$	86.1189	+	149.162i	0.887823	+	1.53776i	0.842443	+	0.538785i	$0.181117\pi$
$97$	86.1189	+	149.162i	0.887823	+	1.53776i	0.0453802	+	0.998970i	$0.485550\pi$
$98$	9.31136	−	157.680i	0.0950139	−	1.60898i
$99$		0			0
$100$	−17.9389	+	31.0710i	−0.179389	+	0.310710i
$101$	14.9975	+	8.65880i	0.148490	+	0.0857307i	0.572404	−	0.819972i	$-0.306011\pi$
$101$	14.9975	+	8.65880i	0.148490	+	0.0857307i	−0.423914	+	0.905702i	$0.639344\pi$
$102$		0			0
$103$	13.7999	+	23.9021i	0.133979	+	0.232059i	0.925207	−	0.379463i	$-0.123891\pi$
$103$	13.7999	+	23.9021i	0.133979	+	0.232059i	−0.791228	+	0.611521i	$0.790558\pi$
$104$	27.2079	+	15.7085i	0.261614	+	0.151043i
$105$		0			0
$106$	−60.6535	−	105.055i	−0.572203	−	0.991085i
$107$	106.089	+	61.2506i	0.991488	+	0.572436i	0.905719	−	0.423879i	$-0.139332\pi$
$107$	106.089	+	61.2506i	0.991488	+	0.572436i	0.0857691	+	0.996315i	$0.472665\pi$
$108$		0			0
$109$	−17.0725	−	29.5705i	−0.156629	−	0.271289i	0.777022	−	0.629473i	$-0.216729\pi$
$109$	−17.0725	−	29.5705i	−0.156629	−	0.271289i	−0.933651	+	0.358184i	$0.883396\pi$
$110$			315.492i			2.86811i
$111$		0			0
$112$	5.00900	+	0.147768i	0.0447232	+	0.00131935i
$113$	−67.4250	−	38.9278i	−0.596681	−	0.344494i	0.171054	−	0.985262i	$-0.445283\pi$
$113$	−67.4250	−	38.9278i	−0.596681	−	0.344494i	−0.767735	+	0.640768i	$0.778616\pi$
$114$		0			0
$115$	−27.8516	+	48.2405i	−0.242188	+	0.419482i
$116$	−255.041	+	147.248i	−2.19863	+	1.26938i
$117$		0			0
$118$	−306.418			−2.59676
$119$	−102.008	+	54.9491i	−0.857210	+	0.461757i
$120$		0			0
$121$	95.9449	+	166.182i	0.792933	+	1.37340i
$122$			237.795i			1.94914i
$123$		0			0
$124$	−189.335			−1.52689
$125$			107.265i			0.858117i
$126$		0			0
$127$	14.0742			0.110821			0.0554103	−	0.998464i	$-0.482353\pi$
$127$	14.0742			0.110821			0.0554103	+	0.998464i	$0.482353\pi$
$128$		−	202.596i		−	1.58278i
$129$		0			0
$130$	−72.6898			−0.559152
$131$	−19.2863	+	11.1349i	−0.147223	+	0.0849995i	−0.571802	−	0.820391i	$-0.693756\pi$
$131$	−19.2863	+	11.1349i	−0.147223	+	0.0849995i	0.424579	+	0.905391i	$0.360422\pi$
$132$		0			0
$133$	28.8366	−	46.7091i	0.216816	−	0.351196i
$134$			39.2982i			0.293270i
$135$		0			0
$136$	63.7988	+	110.503i	0.469109	+	0.812520i
$137$	−32.1175	−	18.5430i	−0.234434	−	0.135351i	0.378182	−	0.925731i	$-0.376549\pi$
$137$	−32.1175	−	18.5430i	−0.234434	−	0.135351i	−0.612616	+	0.790381i	$0.709883\pi$
$138$		0			0
$139$	70.5358	−	122.172i	0.507451	−	0.878932i	−0.492511	−	0.870306i	$-0.663921\pi$
$139$	70.5358	−	122.172i	0.507451	−	0.878932i	0.999963	−	0.00862568i	$-0.00274567\pi$
$140$	217.934	−	117.396i	1.55667	−	0.838539i
$141$		0			0
$142$	−64.5164			−0.454341
$143$	−62.4320	+	36.0451i	−0.436587	+	0.252064i
$144$		0			0
$145$	127.471	−	220.787i	0.879111	−	1.52267i
$146$	−64.1710	+	37.0491i	−0.439527	+	0.253761i
$147$		0			0
$148$	−99.6720	+	172.637i	−0.673459	+	1.16647i
$149$	−100.215	+	57.8590i	−0.672582	+	0.388315i	−0.797054	−	0.603908i	$-0.793610\pi$
$149$	−100.215	+	57.8590i	−0.672582	+	0.388315i	0.124472	+	0.992223i	$0.460276\pi$
$150$		0			0
$151$	75.1579	−	130.177i	0.497734	−	0.862101i	−0.502262	−	0.864715i	$-0.667499\pi$
$151$	75.1579	−	130.177i	0.497734	−	0.862101i	0.999997	+	0.00261420i	$0.000832125\pi$
$152$	−52.3523	−	30.2256i	−0.344423	−	0.198853i
$153$		0			0
$154$	209.678	−	339.634i	1.36155	−	2.20542i
$155$	141.946	−	81.9525i	0.915780	−	0.528726i
$156$		0			0
$157$	−274.056			−1.74558			−0.872788	−	0.488099i	$-0.837691\pi$
$157$	−274.056			−1.74558			−0.872788	+	0.488099i	$0.837691\pi$
$158$		−	447.689i		−	2.83347i
$159$		0			0
$160$	91.6881	+	158.808i	0.573051	+	0.992553i
$161$	62.0439	−	33.4215i	0.385366	−	0.207587i
$162$		0			0
$163$	−111.326	+	192.822i	−0.682981	+	1.18296i	0.291085	+	0.956697i	$0.405984\pi$
$163$	−111.326	+	192.822i	−0.682981	+	1.18296i	−0.974067	+	0.226261i	$0.927350\pi$
$164$	177.797	+	102.651i	1.08413	+	0.625923i
$165$		0			0
$166$	25.4839	+	44.1395i	0.153518	+	0.265900i
$167$	−62.7878	−	36.2506i	−0.375975	−	0.217069i	0.300091	−	0.953911i	$-0.402983\pi$
$167$	−62.7878	−	36.2506i	−0.375975	−	0.217069i	−0.676066	+	0.736841i	$0.736316\pi$
$168$		0			0
$169$	76.1951	+	131.974i	0.450859	+	0.780910i
$170$	−255.672	−	147.612i	−1.50395	−	0.868307i
$171$		0			0
$172$	−21.4266	−	37.1120i	−0.124573	−	0.215768i
$173$		−	211.173i		−	1.22066i	−0.792149	−	0.610328i	$-0.791038\pi$
$173$		−	211.173i		−	1.22066i	0.792149	−	0.610328i	$-0.208962\pi$
$174$		0			0
$175$	−20.6421	+	33.4357i	−0.117955	+	0.191061i
$176$	10.9665	+	6.33151i	0.0623096	+	0.0359745i
$177$		0			0
$178$	87.3695	−	151.328i	0.490840	−	0.850160i
$179$	−69.5967	+	40.1817i	−0.388809	+	0.224479i	−0.681644	−	0.731684i	$-0.738735\pi$
$179$	−69.5967	+	40.1817i	−0.388809	+	0.224479i	0.292835	+	0.956163i	$0.405401\pi$
$180$		0			0
$181$	122.944			0.679250			0.339625	−	0.940561i	$-0.389700\pi$
$181$	122.944			0.679250			0.339625	+	0.940561i	$0.389700\pi$
$182$	78.2522	+	48.3102i	0.429957	+	0.265441i
$183$		0			0
$184$	−38.8041	−	67.2107i	−0.210892	−	0.365275i
$185$		−	172.570i		−	0.932811i
$186$		0			0
$187$	−292.789			−1.56572
$188$			105.076i			0.558913i
$189$		0			0
$190$	139.867			0.736141
$191$			355.490i			1.86120i	0.366032	+	0.930602i	$0.380716\pi$
$191$			355.490i			1.86120i	−0.366032	+	0.930602i	$0.619284\pi$
$192$		0			0
$193$	−39.6593			−0.205488			−0.102744	−	0.994708i	$-0.532762\pi$
$193$	−39.6593			−0.205488			−0.102744	+	0.994708i	$0.532762\pi$
$194$	480.834	−	277.610i	2.47853	−	1.43098i
$195$		0			0
$196$	−312.632	−	18.4617i	−1.59506	−	0.0941921i
$197$			130.634i			0.663119i	0.943434	+	0.331559i	$0.107575\pi$
$197$			130.634i			0.663119i	−0.943434	+	0.331559i	$0.892425\pi$
$198$		0			0
$199$	108.521	+	187.964i	0.545331	+	0.944540i	0.998586	+	0.0531596i	$0.0169292\pi$
$199$	108.521	+	187.964i	0.545331	+	0.944540i	−0.453255	+	0.891381i	$0.649737\pi$
$200$	37.4753	+	21.6364i	0.187376	+	0.108182i
$201$		0			0
$202$	27.9122	−	48.3454i	0.138179	−	0.239333i
$203$	−283.962	+	152.963i	−1.39883	+	0.753513i
$204$		0			0
$205$	−177.729			−0.866969
$206$	77.0498	−	44.4847i	0.374028	−	0.215945i
$207$		0			0
$208$	−1.45879	+	2.52670i	−0.00701341	+	0.0121476i
$209$	120.129	−	69.3566i	0.574781	−	0.331850i
$210$		0			0
$211$	54.6113	−	94.5895i	0.258821	−	0.448292i	−0.707105	−	0.707108i	$-0.749999\pi$
$211$	54.6113	−	94.5895i	0.258821	−	0.448292i	0.965926	+	0.258817i	$0.0833326\pi$
$212$	−208.293	+	120.258i	−0.982513	+	0.567254i
$213$		0			0
$214$	197.445	−	341.985i	0.922642	−	1.59806i
$215$	32.1275	+	18.5488i	0.149430	+	0.0862736i
$216$		0			0
$217$	−207.274	−	6.11468i	−0.955180	−	0.0281782i
$218$	−95.3224	+	55.0344i	−0.437259	+	0.252451i
$219$		0			0
$220$	625.527			2.84330
$221$		−	67.4591i		−	0.305245i
$222$		0			0
$223$	−93.3685	−	161.719i	−0.418693	−	0.725197i	0.577115	−	0.816663i	$-0.304178\pi$
$223$	−93.3685	−	161.719i	−0.418693	−	0.725197i	−0.995808	+	0.0914653i	$0.970845\pi$
$224$	6.84107	−	231.897i	0.0305405	−	1.03526i
$225$		0			0
$226$	−125.486	+	217.349i	−0.555249	+	0.961720i
$227$	−175.411	−	101.274i	−0.772737	−	0.446140i	0.0611131	−	0.998131i	$-0.480535\pi$
$227$	−175.411	−	101.274i	−0.772737	−	0.446140i	−0.833850	+	0.551991i	$0.813868\pi$
$228$		0			0
$229$	39.6366	+	68.6525i	0.173085	+	0.299793i	0.939497	−	0.342557i	$-0.111293\pi$
$229$	39.6366	+	68.6525i	0.173085	+	0.299793i	−0.766412	+	0.642350i	$0.777960\pi$
$230$	155.506	+	89.7816i	0.676114	+	0.390355i
$231$		0			0
$232$	177.598	+	307.609i	0.765509	+	1.32590i
$233$	−282.430	−	163.061i	−1.21215	−	0.699833i	−0.248921	−	0.968524i	$-0.580076\pi$
$233$	−282.430	−	163.061i	−1.21215	−	0.699833i	−0.963227	+	0.268690i	$0.913409\pi$
$234$		0			0
$235$	−45.4814	−	78.7762i	−0.193538	−	0.335218i
$236$			607.536i			2.57430i
$237$		0			0
$238$	177.132	+	328.829i	0.744252	+	1.38164i
$239$	210.918	+	121.774i	0.882503	+	0.509514i	0.871483	−	0.490426i	$-0.163159\pi$
$239$	210.918	+	121.774i	0.882503	+	0.509514i	0.0110203	+	0.999939i	$0.496492\pi$
$240$		0			0
$241$	−14.1702	+	24.5436i	−0.0587976	+	0.101840i	−0.893926	−	0.448215i	$-0.852060\pi$
$241$	−14.1702	+	24.5436i	−0.0587976	+	0.101840i	0.835128	+	0.550055i	$0.185393\pi$
$242$	535.697	−	309.285i	2.21362	−	1.27804i
$243$		0			0
$244$	471.478			1.93229
$245$	242.375	−	121.481i	0.989284	−	0.495839i
$246$		0			0
$247$	15.9799	+	27.6779i	0.0646958	+	0.112056i
$248$			228.359i			0.920804i
$249$		0			0
$250$	345.774			1.38310
$251$		−	140.132i		−	0.558294i	−0.960248	−	0.279147i	$-0.909948\pi$
$251$		−	140.132i		−	0.558294i	0.960248	−	0.279147i	$-0.0900516\pi$
$252$		0			0
$253$	178.082			0.703882
$254$		−	45.3692i		−	0.178619i
$255$		0			0
$256$	−237.186			−0.926506
$257$	−95.8445	+	55.3359i	−0.372936	+	0.215315i	−0.674740	−	0.738055i	$-0.735744\pi$
$257$	−95.8445	+	55.3359i	−0.372936	+	0.215315i	0.301804	+	0.953370i	$0.402411\pi$
$258$		0			0
$259$	−114.691	+	185.775i	−0.442824	+	0.717280i
$260$			144.122i			0.554316i
$261$		0			0
$262$	35.8942	+	62.1705i	0.137001	+	0.237292i
$263$	42.7543	+	24.6842i	0.162564	+	0.0938563i	0.579075	−	0.815274i	$-0.303414\pi$
$263$	42.7543	+	24.6842i	0.162564	+	0.0938563i	−0.416511	+	0.909131i	$0.636747\pi$
$264$		0			0
$265$	104.106	−	180.317i	0.392853	−	0.680441i
$266$	−150.570	−	92.9566i	−0.566052	−	0.349461i
$267$		0			0
$268$	77.9166			0.290734
$269$	162.040	−	93.5538i	0.602379	−	0.347784i	−0.167598	−	0.985855i	$-0.553601\pi$
$269$	162.040	−	93.5538i	0.602379	−	0.347784i	0.769977	+	0.638072i	$0.220268\pi$
$270$		0			0
$271$	108.146	−	187.315i	0.399064	−	0.691199i	−0.594547	−	0.804061i	$-0.702668\pi$
$271$	108.146	−	187.315i	0.399064	−	0.691199i	0.993611	+	0.112862i	$0.0360018\pi$
$272$	−10.2620	+	5.92476i	−0.0377279	+	0.0217822i
$273$		0			0
$274$	−59.7747	+	103.533i	−0.218156	+	0.377857i
$275$	−85.9920	+	49.6475i	−0.312698	+	0.180536i
$276$		0			0
$277$	−39.0618	+	67.6570i	−0.141017	+	0.244249i	−0.927880	−	0.372879i	$-0.878371\pi$
$277$	−39.0618	+	67.6570i	−0.141017	+	0.244249i	0.786863	+	0.617128i	$0.211704\pi$
$278$	−393.828	−	227.377i	−1.41665	−	0.817901i
$279$		0			0
$280$	−141.593	−	262.853i	−0.505688	−	0.938762i
$281$	385.051	−	222.309i	1.37029	−	0.791135i	0.379323	−	0.925264i	$-0.376157\pi$
$281$	385.051	−	222.309i	1.37029	−	0.791135i	0.990964	+	0.134129i	$0.0428237\pi$
$282$		0			0
$283$	−128.424			−0.453796			−0.226898	−	0.973919i	$-0.572858\pi$
$283$	−128.424			−0.453796			−0.226898	+	0.973919i	$0.572858\pi$
$284$			127.917i			0.450411i
$285$		0			0
$286$	116.194	+	201.254i	0.406272	+	0.703684i
$287$	191.329	+	118.120i	0.666650	+	0.411567i
$288$		0			0
$289$	−7.50994	+	13.0076i	−0.0259859	+	0.0450090i
$290$	−711.720	−	410.912i	−2.45421	−	1.41694i
$291$		0			0
$292$	73.4574	+	127.232i	0.251566	+	0.435726i
$293$	42.6510	+	24.6246i	0.145567	+	0.0840429i	0.571014	−	0.820940i	$-0.306550\pi$
$293$	42.6510	+	24.6246i	0.145567	+	0.0840429i	−0.425448	+	0.904983i	$0.639883\pi$
$294$		0			0
$295$	−262.969	−	455.475i	−0.891420	−	1.54398i
$296$	208.220	+	120.216i	0.703446	+	0.406135i
$297$		0			0
$298$	186.512	+	323.049i	0.625880	+	1.08406i
$299$			41.0304i			0.137225i
$300$		0			0
$301$	−22.2583	−	41.3204i	−0.0739477	−	0.137277i
$302$	−419.635	−	242.276i	−1.38952	−	0.802239i
$303$		0			0
$304$	2.80694	−	4.86177i	0.00923337	−	0.0159927i
$305$	−353.471	+	204.077i	−1.15892	+	0.669104i
$306$		0			0
$307$	−387.296			−1.26155			−0.630776	−	0.775965i	$-0.717263\pi$
$307$	−387.296			−1.26155			−0.630776	+	0.775965i	$0.717263\pi$
$308$	−673.393	−	415.730i	−2.18634	−	1.34977i
$309$		0			0
$310$	−264.179	−	457.572i	−0.852191	−	1.47604i
$311$			101.097i			0.325070i	0.986703	+	0.162535i	$0.0519671\pi$
$311$			101.097i			0.325070i	−0.986703	+	0.162535i	$0.948033\pi$
$312$		0			0
$313$	364.791			1.16547			0.582733	−	0.812663i	$-0.301983\pi$
$313$	364.791			1.16547			0.582733	+	0.812663i	$0.301983\pi$
$314$			883.436i			2.81349i
$315$		0			0
$316$	−887.634			−2.80897
$317$			33.1510i			0.104577i	0.998632	+	0.0522886i	$0.0166516\pi$
$317$			33.1510i			0.104577i	−0.998632	+	0.0522886i	$0.983348\pi$
$318$		0			0
$319$	−815.045			−2.55500
$320$	498.208	−	287.641i	1.55690	−	0.898877i
$321$		0			0
$322$	−107.736	−	200.003i	−0.334585	−	0.621126i
$323$			129.802i			0.401864i
$324$		0			0
$325$	−11.4388	−	19.8127i	−0.0351965	−	0.0609621i
$326$	621.575	+	358.866i	1.90667	+	1.10082i
$327$		0			0
$328$	123.809	−	214.444i	0.377468	−	0.653794i
$329$	−3.39348	+	115.032i	−0.0103145	+	0.349640i
$330$		0			0
$331$	−90.5077			−0.273437			−0.136719	−	0.990610i	$-0.543656\pi$
$331$	−90.5077			−0.273437			−0.136719	+	0.990610i	$0.543656\pi$
$332$	87.5154	−	50.5271i	0.263601	−	0.152190i
$333$		0			0
$334$	−116.856	+	202.401i	−0.349869	+	0.605990i
$335$	−58.4148	+	33.7258i	−0.174373	+	0.100674i
$336$		0			0
$337$	216.839	−	375.576i	0.643438	−	1.11447i	−0.341221	−	0.939983i	$-0.610841\pi$
$337$	216.839	−	375.576i	0.643438	−	1.11447i	0.984660	−	0.174485i	$-0.0558261\pi$
$338$	425.426	−	245.620i	1.25866	−	0.726686i
$339$		0			0
$340$	−292.671	+	506.921i	−0.860797	+	1.49094i
$341$	−453.798	−	262.000i	−1.33079	−	0.768329i
$342$		0			0
$343$	−341.658	−	30.3076i	−0.996089	−	0.0883603i
$344$	−44.7614	+	25.8430i	−0.130120	+	0.0751250i
$345$		0			0
$346$	−680.731			−1.96743
$347$			11.6949i			0.0337029i	0.999858	+	0.0168514i	$0.00536423\pi$
$347$			11.6949i			0.0337029i	−0.999858	+	0.0168514i	$0.994636\pi$
$348$		0			0
$349$	91.7075	+	158.842i	0.262772	+	0.455135i	0.966978	−	0.254862i	$-0.0820299\pi$
$349$	91.7075	+	158.842i	0.262772	+	0.455135i	−0.704205	+	0.709996i	$0.748697\pi$
$350$	107.782	+	66.5410i	0.307949	+	0.190117i
$351$		0			0
$352$	293.125	−	507.707i	0.832741	−	1.44235i
$353$	58.9619	+	34.0417i	0.167031	+	0.0964353i	0.581185	−	0.813771i	$-0.302589\pi$
$353$	58.9619	+	34.0417i	0.167031	+	0.0964353i	−0.414154	+	0.910207i	$0.635923\pi$
$354$		0			0
$355$	−55.3681	−	95.9004i	−0.155967	−	0.270142i
$356$	−300.039	−	173.228i	−0.842807	−	0.486595i
$357$		0			0
$358$	129.528	+	224.350i	0.361811	+	0.626675i
$359$	386.169	+	222.955i	1.07568	+	0.621044i	0.929728	−	0.368247i	$-0.120042\pi$
$359$	386.169	+	222.955i	1.07568	+	0.621044i	0.145952	+	0.989292i	$0.453375\pi$
$360$		0			0
$361$	149.752	+	259.378i	0.414826	+	0.718500i
$362$		−	396.319i		−	1.09480i
$363$		0			0
$364$	95.7848	−	155.151i	0.263145	−	0.426238i
$365$	−110.143	−	63.5913i	−0.301763	−	0.174223i
$366$		0			0
$367$	−63.3424	+	109.712i	−0.172595	+	0.298943i	−0.939326	−	0.343025i	$-0.888549\pi$
$367$	−63.3424	+	109.712i	−0.172595	+	0.298943i	0.766731	+	0.641968i	$0.221882\pi$
$368$	6.24161	−	3.60360i	0.0169609	−	0.00979238i
$369$		0			0
$370$	−556.291			−1.50349
$371$	−231.912	+	124.925i	−0.625101	+	0.336726i
$372$		0			0
$373$	306.165	+	530.293i	0.820817	+	1.42170i	0.905075	+	0.425252i	$0.139815\pi$
$373$	306.165	+	530.293i	0.820817	+	1.42170i	−0.0842582	+	0.996444i	$0.526852\pi$
$374$			943.825i			2.52360i
$375$		0			0
$376$	126.733			0.337057
$377$		−	187.787i		−	0.498110i
$378$		0			0
$379$	410.847			1.08403			0.542015	−	0.840369i	$-0.317662\pi$
$379$	410.847			1.08403			0.542015	+	0.840369i	$0.317662\pi$
$380$		−	277.314i		−	0.729775i
$381$		0			0
$382$	1145.95			2.99986
$383$	−190.627	+	110.059i	−0.497722	+	0.287360i	−0.727772	−	0.685819i	$-0.759444\pi$
$383$	−190.627	+	110.059i	−0.497722	+	0.287360i	0.230051	+	0.973179i	$0.426111\pi$
$384$		0			0
$385$	684.796	+	20.2018i	1.77869	+	0.0524721i
$386$			127.844i			0.331203i
$387$		0			0
$388$	−550.417	−	953.351i	−1.41860	−	2.45709i
$389$	−149.180	−	86.1293i	−0.383497	−	0.221412i	0.295842	−	0.955237i	$-0.404400\pi$
$389$	−149.180	−	86.1293i	−0.383497	−	0.221412i	−0.679339	+	0.733825i	$0.737733\pi$
$390$		0			0
$391$	−83.3209	+	144.316i	−0.213097	+	0.369095i
$392$	−22.2669	+	377.071i	−0.0568033	+	0.961916i
$393$		0			0
$394$	421.109			1.06880
$395$	665.468	−	384.208i	1.68473	−	0.972678i
$396$		0			0
$397$	−185.521	+	321.332i	−0.467308	+	0.809401i	−0.999302	−	0.0373470i	$-0.988109\pi$
$397$	−185.521	+	321.332i	−0.467308	+	0.809401i	0.531995	+	0.846748i	$0.321443\pi$
$398$	605.912	−	349.824i	1.52239	−	0.878954i
$399$		0			0
$400$	−2.00929	+	3.48020i	−0.00502323	+	0.00870049i
$401$	259.303	−	149.708i	0.646640	−	0.373338i	−0.140528	−	0.990077i	$-0.544880\pi$
$401$	259.303	−	149.708i	0.646640	−	0.373338i	0.787168	+	0.616739i	$0.211547\pi$
$402$		0			0
$403$	60.3652	−	104.556i	0.149790	−	0.259443i
$404$	−95.8544	−	55.3416i	−0.237263	−	0.136984i
$405$		0			0
$406$	493.087	+	915.370i	1.21450	+	2.25460i
$407$	−477.788	+	275.851i	−1.17393	+	0.677767i
$408$		0			0
$409$	−374.401			−0.915407			−0.457703	−	0.889105i	$-0.651328\pi$
$409$	−374.401			−0.915407			−0.457703	+	0.889105i	$0.651328\pi$
$410$			572.919i			1.39736i
$411$		0			0
$412$	−88.2000	−	152.767i	−0.214078	−	0.370793i
$413$	−19.6208	+	665.100i	−0.0475079	+	1.61041i
$414$		0			0
$415$	−43.7408	+	75.7613i	−0.105399	+	0.182557i
$416$	116.976	+	67.5364i	0.281193	+	0.162347i
$417$		0			0
$418$	−223.576	−	387.244i	−0.534870	−	0.926422i
$419$	−350.317	−	202.256i	−0.836080	−	0.482711i	0.0198501	−	0.999803i	$-0.493681\pi$
$419$	−350.317	−	202.256i	−0.836080	−	0.482711i	−0.855930	+	0.517092i	$0.827014\pi$
$420$		0			0
$421$	−231.002	−	400.107i	−0.548698	−	0.950372i	−0.998364	−	0.0571757i	$-0.981790\pi$
$421$	−231.002	−	400.107i	−0.548698	−	0.950372i	0.449666	−	0.893197i	$-0.351543\pi$
$422$	−304.916	−	176.043i	−0.722549	−	0.417164i
$423$		0			0
$424$	145.045	+	251.225i	0.342087	+	0.592512i
$425$		−	92.9161i		−	0.218626i
$426$		0			0
$427$	516.150	+	15.2267i	1.20878	+	0.0356596i
$428$	−678.055	−	391.475i	−1.58424	−	0.914662i
$429$		0			0
$430$	59.7933	−	103.565i	0.139054	−	0.240849i
$431$	−197.559	+	114.061i	−0.458374	+	0.264643i	−0.711360	−	0.702827i	$-0.751921\pi$
$431$	−197.559	+	114.061i	−0.458374	+	0.264643i	0.252986	+	0.967470i	$0.418587\pi$
$432$		0			0
$433$	777.626			1.79590			0.897951	−	0.440095i	$-0.145055\pi$
$433$	777.626			1.79590			0.897951	+	0.440095i	$0.145055\pi$
$434$	−19.7111	+	668.161i	−0.0454172	+	1.53954i
$435$		0			0
$436$	109.117	+	188.996i	0.250268	+	0.433477i
$437$		−	78.9490i		−	0.180661i
$438$		0			0
$439$	68.8012			0.156722			0.0783612	−	0.996925i	$-0.475031\pi$
$439$	68.8012			0.156722			0.0783612	+	0.996925i	$0.475031\pi$
$440$		−	754.458i		−	1.71468i
$441$		0			0
$442$	−217.459			−0.491988
$443$		−	208.330i		−	0.470271i	−0.971963	−	0.235136i	$-0.924447\pi$
$443$		−	208.330i		−	0.470271i	0.971963	−	0.235136i	$-0.0755534\pi$
$444$		0			0
$445$	299.923			0.673984
$446$	−521.312	+	300.979i	−1.16886	+	0.674842i
$447$		0			0
$448$	−727.500	−	21.4616i	−1.62388	−	0.0479053i
$449$		−	259.045i		−	0.576937i	−0.957489	−	0.288469i	$-0.906854\pi$
$449$		−	259.045i		−	0.576937i	0.957489	−	0.288469i	$-0.0931461\pi$
$450$		0			0
$451$	284.097	+	492.071i	0.629927	+	1.09107i
$452$	430.938	+	248.802i	0.953402	+	0.550447i
$453$		0			0
$454$	−326.463	+	565.450i	−0.719081	+	1.24548i
$455$	−4.65452	+	157.778i	−0.0102297	+	0.346765i
$456$		0			0
$457$	159.437			0.348878			0.174439	−	0.984668i	$-0.444189\pi$
$457$	159.437			0.348878			0.174439	+	0.984668i	$0.444189\pi$
$458$	221.306	−	127.771i	0.483201	−	0.278976i
$459$		0			0
$460$	178.010	−	308.323i	0.386979	−	0.670267i
$461$	176.910	−	102.139i	0.383752	−	0.221559i	−0.295697	−	0.955282i	$-0.595552\pi$
$461$	176.910	−	102.139i	0.383752	−	0.221559i	0.679449	+	0.733722i	$0.262219\pi$
$462$		0			0
$463$	−381.105	+	660.092i	−0.823120	+	1.42569i	0.0802276	+	0.996777i	$0.474435\pi$
$463$	−381.105	+	660.092i	−0.823120	+	1.42569i	−0.903348	+	0.428909i	$0.858898\pi$
$464$	−28.5666	+	16.4929i	−0.0615659	+	0.0355451i
$465$		0			0
$466$	−525.638	+	910.432i	−1.12798	+	1.95372i
$467$	462.046	+	266.762i	0.989391	+	0.571225i	0.905092	−	0.425215i	$-0.139802\pi$
$467$	462.046	+	266.762i	0.989391	+	0.571225i	0.0842988	+	0.996441i	$0.473135\pi$
$468$		0			0
$469$	85.2993	+	2.51636i	0.181875	+	0.00536538i
$470$	−253.940	+	146.612i	−0.540298	+	0.311941i
$471$		0			0
$472$	732.759			1.55245
$473$		−	118.600i		−	0.250741i
$474$		0			0
$475$	22.0102	+	38.1228i	0.0463372	+	0.0802584i
$476$	651.970	−	351.200i	1.36969	−	0.737815i
$477$		0			0
$478$	392.545	−	679.909i	0.821225	−	1.42240i
$479$	−523.526	−	302.258i	−1.09296	−	0.631019i	−0.158595	−	0.987344i	$-0.550696\pi$
$479$	−523.526	−	302.258i	−1.09296	−	0.631019i	−0.934362	+	0.356325i	$0.884030\pi$
$480$		0			0
$481$	−63.5565	−	110.083i	−0.132134	−	0.228863i
$482$	79.1177	+	45.6787i	0.164145	+	0.0947690i
$483$		0			0
$484$	−613.220	−	1062.13i	−1.26698	−	2.19448i
$485$	825.306	+	476.491i	1.70166	+	0.982455i
$486$		0			0
$487$	−78.1017	−	135.276i	−0.160373	−	0.277774i	0.774629	−	0.632415i	$-0.217936\pi$
$487$	−78.1017	−	135.276i	−0.160373	−	0.277774i	−0.935002	+	0.354641i	$0.884603\pi$
$488$		−	568.657i		−	1.16528i
$489$		0			0
$490$	−391.600	−	781.310i	−0.799184	−	1.59451i
$491$	346.903	+	200.285i	0.706523	+	0.407911i	0.809772	−	0.586744i	$-0.199591\pi$
$491$	346.903	+	200.285i	0.706523	+	0.407911i	−0.103249	+	0.994656i	$0.532924\pi$
$492$		0			0
$493$	381.342	−	660.505i	0.773514	−	1.33977i
$494$	89.2216	−	51.5121i	0.180611	−	0.104276i
$495$		0			0
$496$	−21.2069			−0.0427559
$497$	−4.13115	+	140.037i	−0.00831218	+	0.281765i
$498$		0			0
$499$	61.1444	+	105.905i	0.122534	+	0.212235i	0.920766	−	0.390115i	$-0.127565\pi$
$499$	61.1444	+	105.905i	0.122534	+	0.212235i	−0.798232	+	0.602350i	$0.794231\pi$
$500$		−	685.567i		−	1.37113i
$501$		0			0
$502$	−451.724			−0.899848
$503$		−	786.814i		−	1.56424i	−0.623126	−	0.782121i	$-0.714138\pi$
$503$		−	786.814i		−	1.56424i	0.623126	−	0.782121i	$-0.285862\pi$
$504$		0			0
$505$	95.8173			0.189737
$506$		−	574.059i		−	1.13450i
$507$		0			0
$508$	−89.9536			−0.177074
$509$	781.867	−	451.411i	1.53609	−	0.886859i	0.537023	−	0.843568i	$-0.319549\pi$
$509$	781.867	−	451.411i	1.53609	−	0.886859i	0.999062	−	0.0432914i	$-0.0137844\pi$
$510$		0			0
$511$	76.3085	+	141.660i	0.149332	+	0.277220i
$512$		−	45.8004i		−	0.0894539i
$513$		0			0
$514$	178.379	+	308.961i	0.347040	+	0.601092i
$515$	132.249	+	76.3539i	0.256794	+	0.148260i
$516$		0			0
$517$	−145.403	+	251.846i	−0.281244	+	0.487129i
$518$	598.859	+	369.715i	1.15610	+	0.713736i
$519$		0			0
$520$	173.828			0.334285
$521$	−442.743	+	255.618i	−0.849795	+	0.490630i	−0.860582	−	0.509312i	$-0.829900\pi$
$521$	−442.743	+	255.618i	−0.849795	+	0.490630i	0.0107865	+	0.999942i	$0.496566\pi$
$522$		0			0
$523$	489.654	−	848.105i	0.936240	−	1.62162i	0.163833	−	0.986488i	$-0.447614\pi$
$523$	489.654	−	848.105i	0.936240	−	1.62162i	0.772407	−	0.635128i	$-0.219053\pi$
$524$	123.266	−	71.1675i	0.235240	−	0.135816i
$525$		0			0
$526$	79.5711	−	137.821i	0.151276	−	0.262018i
$527$	424.645	−	245.169i	0.805778	−	0.465216i
$528$		0			0
$529$	−213.822	+	370.351i	−0.404200	+	0.700096i
$530$	−581.263	−	335.592i	−1.09672	−	0.633193i
$531$		0			0
$532$	−184.305	+	298.535i	−0.346438	+	0.561156i
$533$	−113.374	+	65.4564i	−0.212709	+	0.122807i
$534$		0			0
$535$	677.793			1.26690
$536$		−	93.9764i		−	0.175329i
$537$		0			0
$538$	−301.577	−	522.346i	−0.560552	−	0.970904i
$539$	−723.772	−	476.868i	−1.34280	−	0.884728i
$540$		0			0
$541$	350.265	−	606.676i	0.647439	−	1.12140i	−0.336293	−	0.941757i	$-0.609173\pi$
$541$	350.265	−	606.676i	0.647439	−	1.12140i	0.983732	−	0.179640i	$-0.0574934\pi$
$542$	−603.822	−	348.617i	−1.11406	−	0.643204i
$543$		0			0
$544$	274.294	+	475.091i	0.504217	+	0.873329i
$545$	−163.612	−	94.4613i	−0.300205	−	0.173324i
$546$		0			0
$547$	294.015	+	509.248i	0.537504	+	0.930984i	0.999038	+	0.0438616i	$0.0139660\pi$
$547$	294.015	+	509.248i	0.537504	+	0.930984i	−0.461534	+	0.887123i	$0.652701\pi$
$548$	205.275	+	118.515i	0.374589	+	0.216269i
$549$		0			0
$550$	160.042	+	277.201i	0.290985	+	0.504001i
$551$			361.333i			0.655777i
$552$		0			0
$553$	−971.738	−	28.6667i	−1.75721	−	0.0518385i
$554$	218.097	+	125.918i	0.393676	+	0.227289i
$555$		0			0
$556$	−450.820	+	780.843i	−0.810827	+	1.40439i
$557$	−347.042	+	200.365i	−0.623055	+	0.359721i	−0.778057	−	0.628193i	$-0.783795\pi$
$557$	−347.042	+	200.365i	−0.623055	+	0.359721i	0.155002	+	0.987914i	$0.450461\pi$
$558$		0			0
$559$	27.3257			0.0488831
$560$	24.4103	−	13.1492i	0.0435897	−	0.0234807i
$561$		0			0
$562$	−716.628	−	1241.24i	−1.27514	−	2.20860i
$563$			91.1620i			0.161922i	0.996717	+	0.0809609i	$0.0257989\pi$
$563$			91.1620i			0.161922i	−0.996717	+	0.0809609i	$0.974201\pi$
$564$		0			0
$565$	−430.771			−0.762426
$566$			413.984i			0.731421i
$567$		0			0
$568$	154.282			0.271624
$569$			295.137i			0.518693i	0.965784	+	0.259347i	$0.0835072\pi$
$569$			295.137i			0.518693i	−0.965784	+	0.259347i	$0.916493\pi$
$570$		0			0
$571$	914.813			1.60212			0.801062	−	0.598581i	$-0.204268\pi$
$571$	914.813			1.60212			0.801062	+	0.598581i	$0.204268\pi$
$572$	399.026	−	230.378i	0.697598	−	0.402758i
$573$		0			0
$574$	380.767	−	616.760i	0.663357	−	1.07450i
$575$			56.5140i			0.0982852i
$576$		0			0
$577$	−267.301	−	462.978i	−0.463259	−	0.802389i	0.535862	−	0.844306i	$-0.319987\pi$
$577$	−267.301	−	462.978i	−0.463259	−	0.802389i	−0.999121	+	0.0419171i	$0.986653\pi$
$578$	41.9308	+	24.2088i	0.0725447	+	0.0418837i
$579$		0			0
$580$	−814.715	+	1411.13i	−1.40468	+	2.43298i
$581$	97.4394	−	52.4882i	0.167710	−	0.0903411i
$582$		0			0
$583$	−665.649			−1.14177
$584$	153.456	−	88.5981i	0.262768	−	0.151709i
$585$		0			0
$586$	79.3789	−	137.488i	0.135459	−	0.234622i
$587$	−299.889	+	173.141i	−0.510884	+	0.294959i	−0.733197	−	0.680016i	$-0.761973\pi$
$587$	−299.889	+	173.141i	−0.510884	+	0.294959i	0.222313	+	0.974975i	$0.428639\pi$
$588$		0			0
$589$	−116.152	+	201.182i	−0.197203	+	0.341565i
$590$	−1468.25	+	847.697i	−2.48857	+	1.43677i
$591$		0			0
$592$	−11.1640	+	19.3367i	−0.0188582	+	0.0326633i
$593$	−3.55214	−	2.05083i	−0.00599012	−	0.00345840i	0.497002	−	0.867749i	$-0.334434\pi$
$593$	−3.55214	−	2.05083i	−0.00599012	−	0.00345840i	−0.502992	+	0.864291i	$0.667768\pi$
$594$		0			0
$595$	−336.773	+	545.500i	−0.566005	+	0.916807i
$596$	640.509	−	369.798i	1.07468	−	0.620467i
$597$		0			0
$598$	132.264			0.221177
$599$		−	169.572i		−	0.283091i	−0.989932	−	0.141546i	$-0.954793\pi$
$599$		−	169.572i		−	0.283091i	0.989932	−	0.141546i	$-0.0452072\pi$
$600$		0			0
$601$	−312.975	−	542.089i	−0.520757	−	0.901978i	−0.999709	−	0.0241366i	$-0.992316\pi$
$601$	−312.975	−	542.089i	−0.520757	−	0.901978i	0.478951	−	0.877841i	$-0.341017\pi$
$602$	−133.199	+	71.7510i	−0.221261	+	0.119188i
$603$		0			0
$604$	−480.362	+	832.011i	−0.795301	+	1.37750i
$605$	919.473	+	530.858i	1.51979	+	0.877451i
$606$		0			0
$607$	18.8059	+	32.5727i	0.0309817	+	0.0536618i	0.881101	−	0.472929i	$-0.156803\pi$
$607$	18.8059	+	32.5727i	0.0309817	+	0.0536618i	−0.850119	+	0.526591i	$0.823470\pi$
$608$	−225.081	−	129.951i	−0.370200	−	0.213735i
$609$		0			0
$610$	657.855	+	1139.44i	1.07845	+	1.86793i
$611$	−58.0256	−	33.5011i	−0.0949682	−	0.0548299i
$612$		0			0
$613$	−149.019	−	258.108i	−0.243098	−	0.421057i	0.718497	−	0.695530i	$-0.244830\pi$
$613$	−149.019	−	258.108i	−0.243098	−	0.421057i	−0.961595	+	0.274472i	$0.911497\pi$
$614$			1248.48i			2.03335i
$615$		0			0
$616$	−501.418	+	812.190i	−0.813991	+	1.31849i
$617$	−818.560	−	472.596i	−1.32668	−	0.765957i	−0.341893	−	0.939739i	$-0.611068\pi$
$617$	−818.560	−	472.596i	−1.32668	−	0.765957i	−0.984784	+	0.173782i	$0.944401\pi$
$618$		0			0
$619$	596.799	−	1033.69i	0.964133	−	1.66993i	0.252208	−	0.967673i	$-0.418843\pi$
$619$	596.799	−	1033.69i	0.964133	−	1.66993i	0.711926	−	0.702255i	$-0.247823\pi$
$620$	−907.229	+	523.789i	−1.46327	+	0.844820i
$621$		0			0
$622$	325.892			0.523943
$623$	−322.874	−	199.331i	−0.518256	−	0.319954i
$624$		0			0
$625$	366.913	+	635.512i	0.587061	+	1.01682i
$626$		−	1175.93i		−	1.87848i
$627$		0			0
$628$	1751.59			2.78916
$629$		−	516.260i		−	0.820764i
$630$		0			0
$631$	−823.055			−1.30437			−0.652183	−	0.758062i	$-0.726147\pi$
$631$	−823.055			−1.30437			−0.652183	+	0.758062i	$0.726147\pi$
$632$			1070.59i			1.69397i
$633$		0			0
$634$	106.864			0.168556
$635$	67.4390	−	38.9359i	0.106203	−	0.0613165i
$636$		0			0
$637$	109.871	−	166.758i	0.172482	−	0.261786i
$638$			2627.35i			4.11810i
$639$		0			0
$640$	−560.476	−	970.773i	−0.875744	−	1.51683i
$641$	617.070	+	356.265i	0.962667	+	0.555796i	0.896993	−	0.442045i	$-0.145747\pi$
$641$	617.070	+	356.265i	0.962667	+	0.555796i	0.0656744	+	0.997841i	$0.479080\pi$
$642$		0			0
$643$	534.902	−	926.478i	0.831885	−	1.44087i	−0.0646564	−	0.997908i	$-0.520595\pi$
$643$	534.902	−	926.478i	0.831885	−	1.44087i	0.896542	−	0.442960i	$-0.146072\pi$
$644$	−396.545	+	213.609i	−0.615754	+	0.331691i
$645$		0			0
$646$	418.425			0.647717
$647$	−973.422	+	562.006i	−1.50452	+	0.868633i	−0.504531	+	0.863394i	$0.668334\pi$
$647$	−973.422	+	562.006i	−1.50452	+	0.868633i	−0.999986	+	0.00523936i	$0.998332\pi$
$648$		0			0
$649$	−840.705	+	1456.14i	−1.29539	+	2.24367i
$650$	−63.8674	+	36.8739i	−0.0982576	+	0.0567290i
$651$		0			0
$652$	711.525	−	1232.40i	1.09130	−	1.89018i
$653$	−41.9432	+	24.2159i	−0.0642315	+	0.0370841i	−0.531772	−	0.846888i	$-0.678474\pi$
$653$	−41.9432	+	24.2159i	−0.0642315	+	0.0370841i	0.467540	+	0.883972i	$0.345140\pi$
$654$		0			0
$655$	−61.6090	+	106.710i	−0.0940595	+	0.162916i
$656$	19.9147	+	11.4977i	0.0303577	+	0.0175270i
$657$		0			0
$658$	370.812	+	10.9391i	0.563544	+	0.0166248i
$659$	818.128	−	472.346i	1.24147	−	0.716762i	0.272076	−	0.962276i	$-0.412290\pi$
$659$	818.128	−	472.346i	1.24147	−	0.716762i	0.969393	+	0.245514i	$0.0789566\pi$
$660$		0			0
$661$	281.194			0.425407			0.212703	−	0.977117i	$-0.431773\pi$
$661$	281.194			0.425407			0.212703	+	0.977117i	$0.431773\pi$
$662$			291.757i			0.440721i
$663$		0			0
$664$	−60.9415	−	105.554i	−0.0917794	−	0.158967i
$665$	8.95604	−	303.590i	0.0134677	−	0.456526i
$666$		0			0
$667$	−231.942	+	401.736i	−0.347740	+	0.602303i
$668$	401.300	+	231.691i	0.600749	+	0.346843i
$669$		0			0
$670$	108.717	+	188.304i	0.162265	+	0.281051i
$671$	1130.04	+	652.429i	1.68411	+	0.972323i
$672$		0			0
$673$	246.892	+	427.630i	0.366854	+	0.635409i	0.989072	−	0.147435i	$-0.0471017\pi$
$673$	246.892	+	427.630i	0.366854	+	0.635409i	−0.622218	+	0.782844i	$0.713768\pi$
$674$	−1210.69	−	698.994i	−1.79628	−	1.03708i
$675$		0			0
$676$	−486.991	−	843.494i	−0.720401	−	1.24777i
$677$		−	705.620i		−	1.04227i	−0.853473	−	0.521137i	$-0.825508\pi$
$677$		−	705.620i		−	1.04227i	0.853473	−	0.521137i	$-0.174492\pi$
$678$		0			0
$679$	−571.781	−	1061.46i	−0.842093	−	1.56327i
$680$	611.405	+	352.995i	0.899126	+	0.519110i
$681$		0			0
$682$	−844.575	+	1462.85i	−1.23838	+	2.14494i
$683$	1010.24	−	583.260i	1.47912	−	0.853968i	0.479394	−	0.877600i	$-0.340856\pi$
$683$	1010.24	−	583.260i	1.47912	−	0.853968i	0.999721	+	0.0236320i	$0.00752300\pi$
$684$		0			0
$685$	−205.195			−0.299555
$686$	−97.6984	+	1101.36i	−0.142417	+	1.60548i
$687$		0			0
$688$	−2.39995	−	4.15683i	−0.00348829	−	0.00604190i
$689$		−	153.366i		−	0.222593i
$690$		0			0
$691$	365.668			0.529186			0.264593	−	0.964360i	$-0.414762\pi$
$691$	365.668			0.529186			0.264593	+	0.964360i	$0.414762\pi$
$692$			1349.69i			1.95041i
$693$		0			0
$694$	37.6993			0.0543217
$695$		−	780.541i		−	1.12308i
$696$		0			0
$697$	−531.692			−0.762830
$698$	512.038	−	295.625i	0.733578	−	0.423532i
$699$		0			0
$700$	131.931	−	213.700i	0.188473	−	0.305286i
$701$		−	254.519i		−	0.363080i	−0.983384	−	0.181540i	$-0.941892\pi$
$701$		−	254.519i		−	0.363080i	0.983384	−	0.181540i	$-0.0581083\pi$
$702$		0			0
$703$	122.293	+	211.818i	0.173959	+	0.301305i
$704$	−1592.76	−	919.581i	−2.26244	−	1.30622i
$705$		0			0
$706$	109.735	−	190.067i	0.155433	−	0.269217i
$707$	−103.149	−	63.6809i	−0.145897	−	0.0900720i
$708$		0			0
$709$	−1040.99			−1.46825			−0.734124	−	0.679015i	$-0.762407\pi$
$709$	−1040.99			−1.46825			−0.734124	+	0.679015i	$0.762407\pi$
$710$	−309.141	+	178.483i	−0.435410	+	0.251384i
$711$		0			0
$712$	−208.933	+	361.882i	−0.293445	+	0.508261i
$713$	−258.280	+	149.118i	−0.362244	+	0.209142i
$714$		0			0
$715$	−199.436	+	345.433i	−0.278931	+	0.483123i
$716$	444.818	−	256.816i	0.621255	−	0.358682i
$717$		0			0
$718$	718.710	−	1244.84i	1.00099	−	1.73376i
$719$	−653.543	−	377.323i	−0.908961	−	0.524789i	−0.0288642	−	0.999583i	$-0.509189\pi$
$719$	−653.543	−	377.323i	−0.908961	−	0.524789i	−0.880097	+	0.474795i	$0.842522\pi$
$720$		0			0
$721$	−91.6233	−	170.090i	−0.127078	−	0.235909i
$722$	836.123	−	482.736i	1.15807	−	0.668609i
$723$		0			0
$724$	−785.782			−1.08533
$725$		−	258.653i		−	0.356762i
$726$		0			0
$727$	698.773	+	1210.31i	0.961174	+	1.66480i	0.719561	+	0.694429i	$0.244343\pi$
$727$	698.773	+	1210.31i	0.961174	+	1.66480i	0.241612	+	0.970373i	$0.422324\pi$
$728$	−187.130	−	115.528i	−0.257046	−	0.158692i
$729$		0			0
$730$	−204.991	+	355.054i	−0.280809	+	0.486376i
$731$	96.1126	+	55.4906i	0.131481	+	0.0759106i
$732$		0			0
$733$	−626.744	−	1085.55i	−0.855039	−	1.48097i	−0.876609	−	0.481204i	$-0.840200\pi$
$733$	−626.744	−	1085.55i	−0.855039	−	1.48097i	0.0215697	−	0.999767i	$-0.493134\pi$
$734$	353.664	+	204.188i	0.481832	+	0.278186i
$735$		0			0
$736$	−166.833	−	288.963i	−0.226675	−	0.392613i
$737$	186.751	+	107.821i	0.253393	+	0.146297i
$738$		0			0
$739$	−534.999	−	926.646i	−0.723950	−	1.25392i	−0.959405	−	0.282033i	$-0.908991\pi$
$739$	−534.999	−	926.646i	−0.723950	−	1.25392i	0.235454	−	0.971885i	$-0.424342\pi$
$740$			1102.96i			1.49049i
$741$		0			0
$742$	402.705	+	747.585i	0.542729	+	1.00753i
$743$	620.266	+	358.111i	0.834813	+	0.481980i	0.855498	−	0.517806i	$-0.173251\pi$
$743$	620.266	+	358.111i	0.834813	+	0.481980i	−0.0206847	+	0.999786i	$0.506585\pi$
$744$		0			0
$745$	−320.131	+	554.483i	−0.429706	+	0.744272i
$746$	1709.43	−	986.941i	2.29146	−	1.32298i
$747$		0			0
$748$	1871.32			2.50177
$749$	−729.659	−	450.466i	−0.974177	−	0.601423i
$750$		0			0
$751$	60.3209	+	104.479i	0.0803208	+	0.139120i	0.903388	−	0.428825i	$-0.141072\pi$
$751$	60.3209	+	104.479i	0.0803208	+	0.139120i	−0.823067	+	0.567944i	$0.807739\pi$
$752$			11.7693i			0.0156506i
$753$		0			0
$754$	−605.345			−0.802845
$755$		−	831.689i		−	1.10157i
$756$		0			0
$757$	−369.403			−0.487983			−0.243992	−	0.969777i	$-0.578457\pi$
$757$	−369.403			−0.487983			−0.243992	+	0.969777i	$0.578457\pi$
$758$		−	1324.39i		−	1.74722i
$759$		0			0
$760$	−334.473			−0.440096
$761$	−992.067	+	572.770i	−1.30364	+	0.752655i	−0.981026	−	0.193877i	$-0.937894\pi$
$761$	−992.067	+	572.770i	−1.30364	+	0.752655i	−0.322610	+	0.946532i	$0.604560\pi$
$762$		0			0
$763$	113.352	+	210.427i	0.148561	+	0.275790i
$764$		−	2272.07i		−	2.97391i
$765$		0			0
$766$	354.782	+	614.500i	0.463161	+	0.802219i
$767$	−335.498	−	193.700i	−0.437416	−	0.252542i
$768$		0			0
$769$	319.295	−	553.035i	0.415208	−	0.719162i	−0.580242	−	0.814444i	$-0.697042\pi$
$769$	319.295	−	553.035i	0.415208	−	0.719162i	0.995450	+	0.0952822i	$0.0303754\pi$
$770$	65.1217	−	2207.48i	0.0845737	−	2.86686i
$771$		0			0
$772$	253.477			0.328338
$773$	−169.438	+	97.8250i	−0.219195	+	0.126552i	−0.605578	−	0.795786i	$-0.707058\pi$
$773$	−169.438	+	97.8250i	−0.219195	+	0.126552i	0.386382	+	0.922339i	$0.373725\pi$
$774$		0			0
$775$	83.1452	−	144.012i	0.107284	−	0.185822i
$776$	−1149.85	+	663.867i	−1.48177	+	0.855499i
$777$		0			0
$778$	−277.643	+	480.892i	−0.356868	+	0.618114i
$779$	218.149	−	125.949i	0.280038	−	0.161680i
$780$		0			0
$781$	−177.011	+	306.591i	−0.226646	+	0.392563i
$782$	465.212	+	268.590i	0.594901	+	0.343466i
$783$		0			0
$784$	−35.0172	−	2.06785i	−0.0446648	−	0.00263756i
$785$	−1313.18	+	758.167i	−1.67285	+	0.965818i
$786$		0			0
$787$	−17.3655			−0.0220654			−0.0110327	−	0.999939i	$-0.503512\pi$
$787$	−17.3655			−0.0220654			−0.0110327	+	0.999939i	$0.503512\pi$
$788$		−	834.933i		−	1.05956i
$789$		0			0
$790$	−1238.52	−	2145.18i	−1.56775	−	2.71542i
$791$	463.734	+	286.294i	0.586263	+	0.361939i
$792$		0			0
$793$	−150.320	+	260.363i	−0.189559	+	0.328326i
$794$	1035.83	+	598.040i	1.30458	+	0.753198i
$795$		0			0
$796$	−693.596	−	1201.34i	−0.871352	−	1.50923i
$797$	871.920	+	503.403i	1.09400	+	0.631622i	0.934639	−	0.355598i	$-0.115723\pi$
$797$	871.920	+	503.403i	1.09400	+	0.631622i	0.159363	+	0.987220i	$0.449056\pi$
$798$		0			0
$799$	−136.062	−	235.667i	−0.170291	−	0.294952i
$800$	161.120	+	93.0225i	0.201400	+	0.116278i
$801$		0			0
$802$	−482.595	−	835.879i	−0.601739	−	1.04224i
$803$			406.600i			0.506351i
$804$		0			0
$805$	204.834	−	331.788i	0.254452	−	0.412158i
$806$	−337.042	−	194.591i	−0.418166	−	0.241428i
$807$		0			0
$808$	−66.7484	+	115.612i	−0.0826094	+	0.143084i
$809$	−364.210	+	210.277i	−0.450198	+	0.259922i	−0.707914	−	0.706299i	$-0.750364\pi$
$809$	−364.210	+	210.277i	−0.450198	+	0.259922i	0.257716	+	0.966221i	$0.417030\pi$
$810$		0			0
$811$	1318.39			1.62564			0.812819	−	0.582517i	$-0.197932\pi$
$811$	1318.39			1.62564			0.812819	+	0.582517i	$0.197932\pi$
$812$	1814.91	−	977.644i	2.23510	−	1.20400i
$813$		0			0
$814$	889.224	+	1540.18i	1.09241	+	1.89212i
$815$			1231.92i			1.51156i
$816$		0			0
$817$	−52.5790			−0.0643562
$818$			1206.91i			1.47544i
$819$		0			0
$820$	1135.93			1.38528
$821$			771.778i			0.940047i	0.882654	+	0.470023i	$0.155755\pi$
$821$			771.778i			0.940047i	−0.882654	+	0.470023i	$0.844245\pi$
$822$		0			0
$823$	906.455			1.10140			0.550702	−	0.834702i	$-0.314360\pi$
$823$	906.455			1.10140			0.550702	+	0.834702i	$0.314360\pi$
$824$	−184.255	+	106.379i	−0.223610	+	0.129101i
$825$		0			0
$826$	2143.99	+	63.2488i	2.59563	+	0.0765723i
$827$		−	509.463i		−	0.616038i	−0.951380	−	0.308019i	$-0.900334\pi$
$827$		−	509.463i		−	0.616038i	0.951380	−	0.308019i	$-0.0996660\pi$
$828$		0			0
$829$	332.585	+	576.054i	0.401188	+	0.694878i	0.993870	−	0.110559i	$-0.0352641\pi$
$829$	332.585	+	576.054i	0.401188	+	0.694878i	−0.592682	+	0.805437i	$0.701931\pi$
$830$	244.221	+	141.001i	0.294243	+	0.169881i
$831$		0			0
$832$	211.873	−	366.974i	0.254655	−	0.441075i
$833$	725.087	−	363.421i	0.870453	−	0.436280i
$834$		0			0
$835$	−401.145			−0.480413
$836$	−767.790	+	443.284i	−0.918409	+	0.530244i
$837$		0			0
$838$	−651.985	+	1129.27i	−0.778025	+	1.34758i
$839$	−1237.78	+	714.635i	−1.47531	+	0.851770i	−0.999612	−	0.0278396i	$-0.991137\pi$
$839$	−1237.78	+	714.635i	−1.47531	+	0.851770i	−0.475696	+	0.879610i	$0.657804\pi$
$840$		0			0
$841$	641.052	−	1110.33i	0.762250	−	1.32026i
$842$	−1289.77	+	744.649i	−1.53179	+	0.884381i
$843$		0			0
$844$	−349.041	+	604.557i	−0.413556	+	0.716299i
$845$	730.204	+	421.583i	0.864147	+	0.498915i
$846$		0			0
$847$	−637.020	−	1182.57i	−0.752090	−	1.39619i
$848$	−23.3304	+	13.4698i	−0.0275122	+	0.0158842i
$849$		0			0
$850$	−299.521			−0.352378
$851$			314.003i			0.368981i
$852$		0			0
$853$	485.171	+	840.341i	0.568782	+	0.985159i	0.996687	+	0.0813353i	$0.0259185\pi$
$853$	485.171	+	840.341i	0.568782	+	0.985159i	−0.427905	+	0.903824i	$0.640748\pi$
$854$	49.0841	−	1663.84i	0.0574756	−	1.94830i
$855$		0			0
$856$	−472.165	+	817.813i	−0.551594	+	0.955389i
$857$	1308.06	+	755.208i	1.52632	+	0.881223i	0.999512	+	0.0312415i	$0.00994611\pi$
$857$	1308.06	+	755.208i	1.52632	+	0.881223i	0.526812	+	0.849982i	$0.323387\pi$
$858$		0			0
$859$	614.191	+	1063.81i	0.715007	+	1.23843i	0.962957	+	0.269655i	$0.0869097\pi$
$859$	614.191	+	1063.81i	0.715007	+	1.23843i	−0.247950	+	0.968773i	$0.579757\pi$
$860$	−205.339	−	118.552i	−0.238766	−	0.137852i
$861$		0			0
$862$	367.683	+	636.845i	0.426546	+	0.738800i
$863$	−1292.69	−	746.335i	−1.49790	−	0.864815i	−0.497906	−	0.867231i	$-0.665898\pi$
$863$	−1292.69	−	746.335i	−1.49790	−	0.864815i	−0.999997	+	0.00241587i	$0.999231\pi$
$864$		0			0
$865$	−584.205	−	1011.87i	−0.675382	−	1.16980i
$866$		−	2506.73i		−	2.89460i
$867$		0			0
$868$	1324.77	+	39.0811i	1.52623	+	0.0450244i
$869$	−2127.48	−	1228.30i	−2.44820	−	1.41347i
$870$		0			0
$871$	−24.8420	+	43.0277i	−0.0285213	+	0.0494003i
$872$	227.951	−	131.608i	0.261412	−	0.150926i
$873$		0			0
$874$	−254.497			−0.291187
$875$	22.1408	−	750.526i	0.0253038	−	0.857744i
$876$		0			0
$877$	173.474	+	300.466i	0.197804	+	0.342607i	0.947816	−	0.318817i	$-0.103286\pi$
$877$	173.474	+	300.466i	0.197804	+	0.342607i	−0.750012	+	0.661424i	$0.769952\pi$
$878$		−	221.785i		−	0.252602i
$879$		0			0
$880$	70.0638			0.0796179
$881$			738.403i			0.838142i	0.907953	+	0.419071i	$0.137644\pi$
$881$			738.403i			0.838142i	−0.907953	+	0.419071i	$0.862356\pi$
$882$		0			0
$883$	872.215			0.987786			0.493893	−	0.869523i	$-0.335573\pi$
$883$	872.215			0.987786			0.493893	+	0.869523i	$0.335573\pi$
$884$			431.156i			0.487733i
$885$		0			0
$886$	−671.566			−0.757975
$887$	−548.437	+	316.640i	−0.618306	+	0.356979i	−0.776209	−	0.630476i	$-0.782860\pi$
$887$	−548.437	+	316.640i	−0.618306	+	0.356979i	0.157903	+	0.987455i	$0.449527\pi$
$888$		0			0
$889$	−98.4767	−	2.90511i	−0.110772	−	0.00326784i
$890$		−	966.821i		−	1.08632i
$891$		0			0
$892$	596.753	+	1033.61i	0.669005	+	1.15875i
$893$	111.651	+	64.4615i	0.125029	+	0.0721853i
$894$		0			0
$895$	−222.323	+	385.075i	−0.248406	+	0.430251i
$896$	−41.8185	+	1417.55i	−0.0466724	+	1.58209i
$897$		0			0
$898$	−835.048			−0.929897
$899$	1182.09	−	682.483i	1.31490	−	0.759158i
$900$		0			0
$901$	311.443	−	539.436i	0.345664	−	0.598708i
$902$	1586.22	−	915.805i	1.75856	−	1.01531i
$903$		0			0
$904$	300.084	−	519.761i	0.331951	−	0.574957i
$905$	589.108	−	340.122i	0.650948	−	0.375825i
$906$		0			0
$907$	−560.854	+	971.427i	−0.618361	+	1.07103i	0.371424	+	0.928464i	$0.378870\pi$
$907$	−560.854	+	971.427i	−0.618361	+	1.07103i	−0.989785	+	0.142570i	$0.954464\pi$
$908$	1121.12	+	647.278i	1.23471	+	0.712861i
$909$		0			0
$910$	508.607	+	15.0041i	0.558909	+	0.0164881i
$911$	770.852	−	445.052i	0.846160	−	0.488531i	−0.0131931	−	0.999913i	$-0.504200\pi$
$911$	770.852	−	445.052i	0.846160	−	0.488531i	0.859353	+	0.511382i	$0.170866\pi$
$912$		0			0
$913$	279.677			0.306327
$914$		−	513.956i		−	0.562315i
$915$		0			0
$916$	−253.332	−	438.784i	−0.276563	−	0.479021i
$917$	137.244	−	73.9297i	0.149666	−	0.0806213i
$918$		0			0
$919$	567.953	−	983.724i	0.618012	−	1.07043i	−0.371836	−	0.928299i	$-0.621271\pi$
$919$	567.953	−	983.724i	0.618012	−	1.07043i	0.989848	−	0.142130i	$-0.0453952\pi$
$920$	−371.873	−	214.701i	−0.404210	−	0.233371i
$921$		0			0
$922$	−329.251	−	570.280i	−0.357105	−	0.618525i
$923$	−70.6391	−	40.7835i	−0.0765321	−	0.0441858i
$924$		0			0
$925$	−87.5408	−	151.625i	−0.0946387	−	0.163919i
$926$	2127.85	+	1228.52i	2.29790	+	1.32669i
$927$		0			0
$928$	763.559	+	1322.52i	0.822800	+	1.42513i
$929$			719.197i			0.774162i	0.922046	+	0.387081i	$0.126517\pi$
$929$			719.197i			0.774162i	−0.922046	+	0.387081i	$0.873483\pi$
$930$		0			0
$931$	−211.410	+	320.869i	−0.227078	+	0.344650i
$932$	1805.12	+	1042.18i	1.93682	+	1.11822i
$933$		0			0
$934$	859.925	−	1489.43i	0.920691	−	1.59468i
$935$	−1402.95	+	809.994i	−1.50048	+	0.866303i
$936$		0			0
$937$	−1522.34			−1.62470			−0.812348	−	0.583172i	$-0.801811\pi$
$937$	−1522.34			−1.62470			−0.812348	+	0.583172i	$0.801811\pi$
$938$	8.11166	−	274.968i	0.00864783	−	0.293142i
$939$		0			0
$940$	290.689	+	503.488i	0.309243	+	0.535625i
$941$			1023.51i			1.08768i	0.839188	+	0.543841i	$0.183030\pi$
$941$			1023.51i			1.08768i	−0.839188	+	0.543841i	$0.816970\pi$
$942$		0			0
$943$	323.389			0.342937
$944$			68.0487i			0.0720855i
$945$		0			0
$946$	−382.316			−0.404139
$947$			1572.43i			1.66043i	0.557441	+	0.830217i	$0.311783\pi$
$947$			1572.43i			1.66043i	−0.557441	+	0.830217i	$0.688217\pi$
$948$		0			0
$949$	−93.6812			−0.0987157
$950$	122.891	−	70.9512i	0.129359	−	0.0746855i
$951$		0			0
$952$	−423.588	−	786.352i	−0.444945	−	0.826000i
$953$			1342.92i			1.40915i	0.709629	+	0.704576i	$0.248863\pi$
$953$			1342.92i			1.40915i	−0.709629	+	0.704576i	$0.751137\pi$
$954$		0			0
$955$	983.453	+	1703.39i	1.02979	+	1.78366i
$956$	−1348.06	−	778.301i	−1.41010	−	0.814122i
$957$		0			0
$958$	−974.348	+	1687.62i	−1.01706	+	1.76161i
$959$	220.897	+	136.374i	0.230341	+	0.142205i
$960$		0			0
$961$	−83.4501			−0.0868367
$962$	−354.860	+	204.879i	−0.368877	+	0.212971i
$963$		0			0
$964$	90.5672	−	156.867i	0.0939493	−	0.162725i
$965$	−190.034	+	109.716i	−0.196927	+	0.113696i
$966$		0			0
$967$	−867.804	+	1503.08i	−0.897418	+	1.55437i	−0.0666355	+	0.997777i	$0.521226\pi$
$967$	−867.804	+	1503.08i	−0.897418	+	1.55437i	−0.830783	+	0.556597i	$0.812107\pi$
$968$	−1281.05	+	739.614i	−1.32340	+	0.764064i
$969$		0			0
$970$	1536.00	−	2660.43i	1.58350	−	2.74271i
$971$	43.8474	+	25.3153i	0.0451569	+	0.0260714i	0.522409	−	0.852695i	$-0.325034\pi$
$971$	43.8474	+	25.3153i	0.0451569	+	0.0260714i	−0.477252	+	0.878767i	$0.658367\pi$
$972$		0			0
$973$	−518.753	+	840.269i	−0.533148	+	0.863586i
$974$	−436.071	+	251.766i	−0.447712	+	0.258486i
$975$		0			0
$976$	52.8091			0.0541077
$977$		−	585.107i		−	0.598881i	−0.954115	−	0.299440i	$-0.903200\pi$
$977$		−	585.107i		−	0.598881i	0.954115	−	0.299440i	$-0.0968000\pi$
$978$		0			0
$979$	−479.423	−	830.386i	−0.489707	−	0.848198i
$980$	−1549.11	+	776.427i	−1.58072	+	0.792272i
$981$		0			0
$982$	645.630	−	1118.26i	0.657464	−	1.13876i
$983$	−839.089	−	484.448i	−0.853600	−	0.492826i	0.00826378	−	0.999966i	$-0.497370\pi$
$983$	−839.089	−	484.448i	−0.853600	−	0.492826i	−0.861864	+	0.507140i	$0.830703\pi$
$984$		0			0
$985$	361.397	+	625.957i	0.366900	+	0.635489i
$986$	−2129.18	−	1229.28i	−2.15941	−	1.24674i
$987$		0			0
$988$	−102.133	−	176.900i	−0.103374	−	0.179048i
$989$	−58.4582	−	33.7508i	−0.0591084	−	0.0341262i
$990$		0			0
$991$	−104.448	−	180.910i	−0.105397	−	0.182553i	0.808503	−	0.588492i	$-0.200278\pi$
$991$	−104.448	−	180.910i	−0.105397	−	0.182553i	−0.913900	+	0.405939i	$0.866945\pi$
$992$			981.799i			0.989717i
$993$		0			0
$994$	451.418	+	13.3170i	0.454143	+	0.0133974i
$995$	1039.99	+	600.439i	1.04522	+	0.603457i
$996$		0			0
$997$	−76.0851	+	131.783i	−0.0763140	+	0.132180i	−0.901657	−	0.432452i	$-0.857648\pi$
$997$	−76.0851	+	131.783i	−0.0763140	+	0.132180i	0.825343	+	0.564632i	$0.190982\pi$
$998$	341.392	−	197.103i	0.342077	−	0.197498i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.j.b.44.2		22
3.2	odd	2		63.3.j.b.23.10	yes	22
7.4	even	3		189.3.n.b.179.10		22
9.2	odd	6		189.3.n.b.170.10		22
9.7	even	3		63.3.n.b.2.2	yes	22
21.2	odd	6		441.3.r.g.50.10		22
21.5	even	6		441.3.r.f.50.10		22
21.11	odd	6		63.3.n.b.32.2	yes	22
21.17	even	6		441.3.n.f.410.2		22
21.20	even	2		441.3.j.f.275.10		22
63.11	odd	6	inner	189.3.j.b.116.10		22
63.16	even	3		441.3.r.g.344.10		22
63.25	even	3		63.3.j.b.11.2	✓	22
63.34	odd	6		441.3.n.f.128.2		22
63.52	odd	6		441.3.j.f.263.2		22
63.61	odd	6		441.3.r.f.344.10		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.2	✓	22	63.25	even	3
63.3.j.b.23.10	yes	22	3.2	odd	2
63.3.n.b.2.2	yes	22	9.7	even	3
63.3.n.b.32.2	yes	22	21.11	odd	6
189.3.j.b.44.2		22	1.1	even	1	trivial
189.3.j.b.116.10		22	63.11	odd	6	inner
189.3.n.b.170.10		22	9.2	odd	6
189.3.n.b.179.10		22	7.4	even	3
441.3.j.f.263.2		22	63.52	odd	6
441.3.j.f.275.10		22	21.20	even	2
441.3.n.f.128.2		22	63.34	odd	6
441.3.n.f.410.2		22	21.17	even	6
441.3.r.f.50.10		22	21.5	even	6
441.3.r.f.344.10		22	63.61	odd	6
441.3.r.g.50.10		22	21.2	odd	6
441.3.r.g.344.10		22	63.16	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	189.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-3.22356i q^{2} -6.39137 q^{4} +(4.79167 - 2.76647i) q^{5} +(-6.99696 - 0.206413i) q^{7} +7.70873i q^{8} +O(q^{10})\)	\(q-3.22356i q^{2} -6.39137 q^{4} +(4.79167 - 2.76647i) q^{5} +(-6.99696 - 0.206413i) q^{7} +7.70873i q^{8} +(-8.91790 - 15.4463i) q^{10} +(-15.3189 - 8.84435i) q^{11} +(2.03775 - 3.52949i) q^{13} +(-0.665386 + 22.5551i) q^{14} -0.715882 q^{16} +(14.3348 - 8.27617i) q^{17} +(-3.92096 + 6.79130i) q^{19} +(-30.6253 + 17.6815i) q^{20} +(-28.5103 + 49.3813i) q^{22} +(-8.71877 + 5.03378i) q^{23} +(2.80674 - 4.86141i) q^{25} +(-11.3775 - 6.56882i) q^{26} +(44.7201 + 1.31926i) q^{28} +(39.9040 - 23.0386i) q^{29} +29.6235 q^{31} +33.1426i q^{32} +(-26.6788 - 46.2090i) q^{34} +(-34.0981 + 18.3678i) q^{35} +(15.5948 - 27.0110i) q^{37} +(21.8922 + 12.6395i) q^{38} +(21.3260 + 36.9377i) q^{40} +(-27.8184 - 16.0609i) q^{41} +(3.35243 + 5.80658i) q^{43} +(97.9085 + 56.5275i) q^{44} +(16.2267 + 28.1055i) q^{46} -16.4402i q^{47} +(48.9148 + 2.88853i) q^{49} +(-15.6711 - 9.04769i) q^{50} +(-13.0240 + 22.5583i) q^{52} +(32.5897 - 18.8157i) q^{53} -97.8706 q^{55} +(1.59118 - 53.9377i) q^{56} +(-74.2663 - 128.633i) q^{58} -95.0557i q^{59} -73.7679 q^{61} -95.4932i q^{62} +103.974 q^{64} -22.5495i q^{65} -12.1909 q^{67} +(-91.6187 + 52.8961i) q^{68} +(59.2099 + 109.918i) q^{70} -20.0140i q^{71} +(-11.4932 - 19.9068i) q^{73} +(-87.0715 - 50.2708i) q^{74} +(25.0603 - 43.4057i) q^{76} +(105.360 + 65.0455i) q^{77} +138.880 q^{79} +(-3.43027 + 1.98047i) q^{80} +(-51.7735 + 89.6743i) q^{82} +(-13.6928 + 7.90552i) q^{83} +(45.7916 - 79.3134i) q^{85} +(18.7179 - 10.8068i) q^{86} +(68.1787 - 118.089i) q^{88} +(46.9444 + 27.1034i) q^{89} +(-14.9866 + 24.2750i) q^{91} +(55.7249 - 32.1728i) q^{92} -52.9962 q^{94} +43.3889i q^{95} +(86.1189 + 149.162i) q^{97} +(9.31136 - 157.680i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 24 q^{4} - 12 q^{5}+O(q^{10}) \) 22 * q - 24 * q^4 - 12 * q^5	\( 22 q - 24 q^{4} - 12 q^{5} + 25 q^{10} - 24 q^{11} - 18 q^{13} + 60 q^{14} - 24 q^{16} + 6 q^{17} + 3 q^{19} + 39 q^{20} - 59 q^{22} - 81 q^{23} + 57 q^{25} - 3 q^{26} + 34 q^{28} + 63 q^{29} + 58 q^{31} - 99 q^{34} - 27 q^{35} - 20 q^{37} + 48 q^{38} - 105 q^{40} + 51 q^{41} + 65 q^{43} + 54 q^{44} + 75 q^{46} + 4 q^{49} - 63 q^{50} - 46 q^{52} - 63 q^{53} - 100 q^{55} - 192 q^{56} + 40 q^{58} - 156 q^{61} + 106 q^{64} + 264 q^{67} - 27 q^{68} + 236 q^{70} + q^{73} - 342 q^{74} + 233 q^{76} + 531 q^{77} - 280 q^{79} + 96 q^{80} - 157 q^{82} - 255 q^{83} + 102 q^{85} - 504 q^{86} + 408 q^{88} - 720 q^{89} - 70 q^{91} + 1239 q^{92} - 522 q^{94} + 178 q^{97} + 483 q^{98}+O(q^{100}) \) 22 * q - 24 * q^4 - 12 * q^5 + 25 * q^10 - 24 * q^11 - 18 * q^13 + 60 * q^14 - 24 * q^16 + 6 * q^17 + 3 * q^19 + 39 * q^20 - 59 * q^22 - 81 * q^23 + 57 * q^25 - 3 * q^26 + 34 * q^28 + 63 * q^29 + 58 * q^31 - 99 * q^34 - 27 * q^35 - 20 * q^37 + 48 * q^38 - 105 * q^40 + 51 * q^41 + 65 * q^43 + 54 * q^44 + 75 * q^46 + 4 * q^49 - 63 * q^50 - 46 * q^52 - 63 * q^53 - 100 * q^55 - 192 * q^56 + 40 * q^58 - 156 * q^61 + 106 * q^64 + 264 * q^67 - 27 * q^68 + 236 * q^70 + q^73 - 342 * q^74 + 233 * q^76 + 531 * q^77 - 280 * q^79 + 96 * q^80 - 157 * q^82 - 255 * q^83 + 102 * q^85 - 504 * q^86 + 408 * q^88 - 720 * q^89 - 70 * q^91 + 1239 * q^92 - 522 * q^94 + 178 * q^97 + 483 * q^98

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