LMFDB - Embedded newform 189.4.e.f.163.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,4,Mod(109,189)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("189.109"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,-1,0,-31,1,0,20,168,0,-12,-98,0,-248] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 44 x^{12} + 23 x^{11} + 1346 x^{10} + 854 x^{9} + 20545 x^{8} + 27750 x^{7} + \cdots + 254016 $ x^14 - x^13 + 44x^12 + 23x^11 + 1346x^10 + 854x^9 + 20545x^8 + 27750x^7 + 221349x^6 + 172746x^5 + 551772x^4 + 275616x^3 + 1006128x^2 + 471744x + 254016
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.2
Root			$2.38108 - 4.12414i$ of defining polynomial
Character	$\chi$	$=$	189.163
Dual form			189.4.e.f.109.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.38108 + 4.12414i) q^{2} +(-7.33904 - 12.7116i) q^{4} +(-9.35067 + 16.1958i) q^{5} +(14.2072 - 11.8809i) q^{7} +31.8020 q^{8} +(-44.5293 - 77.1270i) q^{10} +(-29.7289 - 51.4920i) q^{11} -12.2112 q^{13} +(15.1702 + 86.8818i) q^{14} +(-17.0107 + 29.4633i) q^{16} +(-5.76073 - 9.97788i) q^{17} +(-24.9027 + 43.1328i) q^{19} +274.500 q^{20} +283.147 q^{22} +(62.8958 - 108.939i) q^{23} +(-112.370 - 194.631i) q^{25} +(29.0758 - 50.3607i) q^{26} +(-255.292 - 93.4013i) q^{28} +228.511 q^{29} +(94.7837 + 164.170i) q^{31} +(46.2007 + 80.0220i) q^{32} +54.8669 q^{34} +(59.5747 + 341.192i) q^{35} +(-16.5729 + 28.7051i) q^{37} +(-118.590 - 205.405i) q^{38} +(-297.370 + 515.060i) q^{40} -524.149 q^{41} +234.349 q^{43} +(-436.363 + 755.803i) q^{44} +(299.519 + 518.783i) q^{46} +(136.871 - 237.067i) q^{47} +(60.6878 - 337.588i) q^{49} +1070.25 q^{50} +(89.6185 + 155.224i) q^{52} +(-127.968 - 221.647i) q^{53} +1111.94 q^{55} +(451.817 - 377.837i) q^{56} +(-544.101 + 942.411i) q^{58} +(-84.4163 - 146.213i) q^{59} +(97.5707 - 168.997i) q^{61} -902.749 q^{62} -712.200 q^{64} +(114.183 - 197.771i) q^{65} +(-257.574 - 446.132i) q^{67} +(-84.5564 + 146.456i) q^{68} +(-1548.98 - 566.709i) q^{70} +319.048 q^{71} +(-317.759 - 550.375i) q^{73} +(-78.9227 - 136.698i) q^{74} +731.048 q^{76} +(-1034.14 - 378.349i) q^{77} +(426.001 - 737.855i) q^{79} +(-318.122 - 551.004i) q^{80} +(1248.04 - 2161.67i) q^{82} -264.419 q^{83} +215.467 q^{85} +(-558.004 + 966.491i) q^{86} +(-945.439 - 1637.55i) q^{88} +(457.099 - 791.718i) q^{89} +(-173.487 + 145.080i) q^{91} -1846.38 q^{92} +(651.800 + 1128.95i) q^{94} +(-465.714 - 806.640i) q^{95} -455.582 q^{97} +(1247.76 + 1054.11i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 31 q^{4} + q^{5} + 20 q^{7} + 168 q^{8} - 12 q^{10} - 98 q^{11} - 248 q^{13} - 134 q^{14} - 139 q^{16} - 30 q^{17} - 182 q^{19} - 220 q^{20} + 552 q^{22} + 6 q^{23} - 388 q^{25} + 245 q^{26}+ \cdots + 10160 q^{98}+O(q^{100}) $ 14 * q - q^2 - 31 * q^4 + q^5 + 20 * q^7 + 168 * q^8 - 12 * q^10 - 98 * q^11 - 248 * q^13 - 134 * q^14 - 139 * q^16 - 30 * q^17 - 182 * q^19 - 220 * q^20 + 552 * q^22 + 6 * q^23 - 388 * q^25 + 245 * q^26 + 425 * q^28 + 646 * q^29 - 26 * q^31 - 398 * q^32 + 228 * q^34 + 1025 * q^35 + 112 * q^37 - 1015 * q^38 + 147 * q^40 - 1048 * q^41 + 16 * q^43 - 937 * q^44 + 339 * q^46 - 288 * q^47 + 446 * q^49 + 5152 * q^50 + 1075 * q^52 - 1353 * q^53 + 312 * q^55 + 1980 * q^56 + 81 * q^58 - 165 * q^59 - 56 * q^61 - 2430 * q^62 - 3412 * q^64 - 1694 * q^65 + 988 * q^67 - 2625 * q^68 - 4941 * q^70 + 1584 * q^71 - 1487 * q^73 - 2736 * q^74 + 3904 * q^76 - 34 * q^77 + 1273 * q^79 + 2501 * q^80 + 2049 * q^82 - 2340 * q^83 + 432 * q^85 + 160 * q^86 - 9 * q^88 - 1058 * q^89 + 3538 * q^91 + 7668 * q^92 - 1653 * q^94 - 3260 * q^95 - 7460 * q^97 + 10160 * q^98

Character values

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

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

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 $

$2$	−2.38108	+	4.12414i	−0.841837	+	1.45810i	0.0465026	+	0.998918i	$0.485192\pi$
$2$	−2.38108	+	4.12414i	−0.841837	+	1.45810i	−0.888340	+	0.459187i	$0.848141\pi$
$3$		0			0
$3$		0			0
$4$	−7.33904	−	12.7116i	−0.917380	−	1.58895i
$5$	−9.35067	+	16.1958i	−0.836350	+	1.44860i	0.0565773	+	0.998398i	$0.481981\pi$
$5$	−9.35067	+	16.1958i	−0.836350	+	1.44860i	−0.892927	+	0.450202i	$0.851352\pi$
$6$		0			0
$7$	14.2072	−	11.8809i	0.767116	−	0.641509i
$7$	14.2072	−	11.8809i	0.767116	−	0.641509i
$8$	31.8020			1.40546
$9$		0			0
$10$	−44.5293	−	77.1270i	−1.40814	−	2.43897i
$11$	−29.7289	−	51.4920i	−0.814873	−	1.41140i	−0.909419	−	0.415881i	$-0.863473\pi$
$11$	−29.7289	−	51.4920i	−0.814873	−	1.41140i	0.0945458	−	0.995521i	$-0.469860\pi$
$12$		0			0
$13$	−12.2112			−0.260521			−0.130261	−	0.991480i	$-0.541581\pi$
$13$	−12.2112			−0.260521			−0.130261	+	0.991480i	$0.541581\pi$
$14$	15.1702	+	86.8818i	0.289601	+	1.65858i
$15$		0			0
$16$	−17.0107	+	29.4633i	−0.265791	+	0.460364i
$17$	−5.76073	−	9.97788i	−0.0821872	−	0.142352i	0.822002	−	0.569485i	$-0.192857\pi$
$17$	−5.76073	−	9.97788i	−0.0821872	−	0.142352i	−0.904189	+	0.427132i	$0.859524\pi$
$18$		0			0
$19$	−24.9027	+	43.1328i	−0.300688	+	0.520807i	−0.976292	−	0.216458i	$-0.930550\pi$
$19$	−24.9027	+	43.1328i	−0.300688	+	0.520807i	0.675604	+	0.737265i	$0.263883\pi$
$20$	274.500			3.06900
$21$		0			0
$22$	283.147			2.74396
$23$	62.8958	−	108.939i	0.570204	−	0.987622i	−0.426341	−	0.904562i	$-0.640198\pi$
$23$	62.8958	−	108.939i	0.570204	−	0.987622i	0.996545	−	0.0830591i	$-0.0264690\pi$
$24$		0			0
$25$	−112.370	−	194.631i	−0.898961	−	1.55705i
$26$	29.0758	−	50.3607i	0.219317	−	0.379867i
$27$		0			0
$28$	−255.292	−	93.4013i	−1.72306	−	0.630400i
$29$	228.511			1.46322			0.731610	−	0.681723i	$-0.238769\pi$
$29$	228.511			1.46322			0.731610	+	0.681723i	$0.238769\pi$
$30$		0			0
$31$	94.7837	+	164.170i	0.549150	+	0.951156i	0.998333	+	0.0577163i	$0.0183819\pi$
$31$	94.7837	+	164.170i	0.549150	+	0.951156i	−0.449183	+	0.893440i	$0.648285\pi$
$32$	46.2007	+	80.0220i	0.255225	+	0.442063i
$33$		0			0
$34$	54.8669			0.276753
$35$	59.5747	+	341.192i	0.287713	+	1.64777i
$36$		0			0
$37$	−16.5729	+	28.7051i	−0.0736370	+	0.127543i	−0.900493	−	0.434871i	$-0.856794\pi$
$37$	−16.5729	+	28.7051i	−0.0736370	+	0.127543i	0.826856	+	0.562414i	$0.190127\pi$
$38$	−118.590	−	205.405i	−0.506261	−	0.876869i
$39$		0			0
$40$	−297.370	+	515.060i	−1.17546	+	2.03595i
$41$	−524.149			−1.99654			−0.998272	−	0.0587584i	$-0.981286\pi$
$41$	−524.149			−1.99654			−0.998272	+	0.0587584i	$0.981286\pi$
$42$		0			0
$43$	234.349			0.831115			0.415558	−	0.909567i	$-0.363586\pi$
$43$	234.349			0.831115			0.415558	+	0.909567i	$0.363586\pi$
$44$	−436.363	+	755.803i	−1.49510	+	2.58958i
$45$		0			0
$46$	299.519	+	518.783i	0.960037	+	1.66283i
$47$	136.871	−	237.067i	0.424780	−	0.735741i	−0.571620	−	0.820519i	$-0.693685\pi$
$47$	136.871	−	237.067i	0.424780	−	0.735741i	0.996400	+	0.0847779i	$0.0270181\pi$
$48$		0			0
$49$	60.6878	−	337.588i	0.176932	−	0.984223i
$50$	1070.25			3.02712
$51$		0			0
$52$	89.6185	+	155.224i	0.238997	+	0.413955i
$53$	−127.968	−	221.647i	−0.331656	−	0.574445i	0.651181	−	0.758923i	$-0.274274\pi$
$53$	−127.968	−	221.647i	−0.331656	−	0.574445i	−0.982837	+	0.184478i	$0.940941\pi$
$54$		0			0
$55$	1111.94			2.72608
$56$	451.817	−	377.837i	1.07815	−	0.901617i
$57$		0			0
$58$	−544.101	+	942.411i	−1.23179	+	2.13353i
$59$	−84.4163	−	146.213i	−0.186272	−	0.322633i	0.757732	−	0.652566i	$-0.226307\pi$
$59$	−84.4163	−	146.213i	−0.186272	−	0.322633i	−0.944005	+	0.329933i	$0.892974\pi$
$60$		0			0
$61$	97.5707	−	168.997i	0.204797	−	0.354720i	−0.745271	−	0.666762i	$-0.767680\pi$
$61$	97.5707	−	168.997i	0.204797	−	0.354720i	0.950068	+	0.312042i	$0.101013\pi$
$62$	−902.749			−1.84918
$63$		0			0
$64$	−712.200			−1.39102
$65$	114.183	−	197.771i	0.217887	−	0.377391i
$66$		0			0
$67$	−257.574	−	446.132i	−0.469667	−	0.813487i	0.529732	−	0.848165i	$-0.322293\pi$
$67$	−257.574	−	446.132i	−0.469667	−	0.813487i	−0.999399	+	0.0346782i	$0.988959\pi$
$68$	−84.5564	+	146.456i	−0.150794	+	0.261182i
$69$		0			0
$70$	−1548.98	−	566.709i	−2.64483	−	0.967638i
$71$	319.048			0.533295			0.266648	−	0.963794i	$-0.414084\pi$
$71$	319.048			0.533295			0.266648	+	0.963794i	$0.414084\pi$
$72$		0			0
$73$	−317.759	−	550.375i	−0.509464	−	0.882418i	−0.999940	−	0.0109632i	$-0.996510\pi$
$73$	−317.759	−	550.375i	−0.509464	−	0.882418i	0.490476	−	0.871455i	$-0.336823\pi$
$74$	−78.9227	−	136.698i	−0.123981	−	0.214741i
$75$		0			0
$76$	731.048			1.10338
$77$	−1034.14	−	378.349i	−1.53053	−	0.559960i
$78$		0			0
$79$	426.001	−	737.855i	0.606694	−	1.05083i	−0.385087	−	0.922880i	$-0.625829\pi$
$79$	426.001	−	737.855i	0.606694	−	1.05083i	0.991781	−	0.127945i	$-0.0408380\pi$
$80$	−318.122	−	551.004i	−0.444589	−	0.770051i
$81$		0			0
$82$	1248.04	−	2161.67i	1.68077	−	2.91117i
$83$	−264.419			−0.349684			−0.174842	−	0.984597i	$-0.555941\pi$
$83$	−264.419			−0.349684			−0.174842	+	0.984597i	$0.555941\pi$
$84$		0			0
$85$	215.467			0.274949
$86$	−558.004	+	966.491i	−0.699664	+	1.21185i
$87$		0			0
$88$	−945.439	−	1637.55i	−1.14527	−	1.98367i
$89$	457.099	−	791.718i	0.544409	−	0.942943i	−0.454235	−	0.890882i	$-0.650087\pi$
$89$	457.099	−	791.718i	0.544409	−	0.942943i	0.998644	−	0.0520615i	$-0.0165792\pi$
$90$		0			0
$91$	−173.487	+	145.080i	−0.199850	+	0.167127i
$92$	−1846.38			−2.09237
$93$		0			0
$94$	651.800	+	1128.95i	0.715191	+	1.23875i
$95$	−465.714	−	806.640i	−0.502961	−	0.871153i
$96$		0			0
$97$	−455.582			−0.476880			−0.238440	−	0.971157i	$-0.576636\pi$
$97$	−455.582			−0.476880			−0.238440	+	0.971157i	$0.576636\pi$
$98$	1247.76	+	1054.11i	1.28615	+	1.08654i
$99$		0			0
$100$	−1649.38	+	2856.81i	−1.64938	+	2.85681i
$101$	450.092	+	779.583i	0.443424	+	0.768034i	0.997941	−	0.0641390i	$-0.0204301\pi$
$101$	450.092	+	779.583i	0.443424	+	0.768034i	−0.554517	+	0.832173i	$0.687097\pi$
$102$		0			0
$103$	57.1898	−	99.0557i	0.0547095	−	0.0947597i	−0.837374	−	0.546631i	$-0.815910\pi$
$103$	57.1898	−	99.0557i	0.0547095	−	0.0947597i	0.892083	+	0.451871i	$0.149243\pi$
$104$	−388.341			−0.366153
$105$		0			0
$106$	1218.81			1.11680
$107$	452.033	−	782.944i	0.408408	−	0.707384i	−0.586303	−	0.810092i	$-0.699417\pi$
$107$	452.033	−	782.944i	0.408408	−	0.707384i	0.994712	+	0.102708i	$0.0327507\pi$
$108$		0			0
$109$	−723.304	−	1252.80i	−0.635596	−	1.10088i	−0.986389	−	0.164431i	$-0.947421\pi$
$109$	−723.304	−	1252.80i	−0.635596	−	1.10088i	0.350793	−	0.936453i	$-0.385912\pi$
$110$	−2647.62	+	4585.81i	−2.29491	+	3.97490i
$111$		0			0
$112$	108.378	+	620.693i	0.0914351	+	0.523660i
$113$	10.2655			0.00854596			0.00427298	−	0.999991i	$-0.498640\pi$
$113$	10.2655			0.00854596			0.00427298	+	0.999991i	$0.498640\pi$
$114$		0			0
$115$	1176.24	+	2037.30i	0.953779	+	1.65199i
$116$	−1677.05	−	2904.74i	−1.34233	−	2.32498i
$117$		0			0
$118$	804.006			0.627244
$119$	−200.390	−	73.3148i	−0.154367	−	0.0564769i
$120$		0			0
$121$	−1102.12	+	1908.92i	−0.828037	+	1.43420i
$122$	464.646	+	804.791i	0.344812	+	0.597232i
$123$		0			0
$124$	1391.24	−	2409.70i	1.00756	−	1.74514i
$125$	1865.28			1.33468
$126$		0			0
$127$	−1590.09			−1.11101			−0.555503	−	0.831514i	$-0.687474\pi$
$127$	−1590.09			−1.11101			−0.555503	+	0.831514i	$0.687474\pi$
$128$	1326.20	−	2297.04i	0.915783	−	1.58618i
$129$		0			0
$130$	543.756	+	941.813i	0.366851	+	0.635404i
$131$	−112.441	+	194.753i	−0.0749924	+	0.129891i	−0.901083	−	0.433647i	$-0.857227\pi$
$131$	−112.441	+	194.753i	−0.0749924	+	0.129891i	0.826091	+	0.563537i	$0.190560\pi$
$132$		0			0
$133$	158.659	+	908.662i	0.103440	+	0.592413i
$134$	2453.21			1.58153
$135$		0			0
$136$	−183.203	−	317.317i	−0.115511	−	0.200071i
$137$	−1125.86	−	1950.04i	−0.702106	−	1.21608i	−0.967726	−	0.252006i	$-0.918910\pi$
$137$	−1125.86	−	1950.04i	−0.702106	−	1.21608i	0.265619	−	0.964078i	$-0.414424\pi$
$138$		0			0
$139$	3015.34			1.83998			0.919992	−	0.391937i	$-0.128195\pi$
$139$	3015.34			1.83998			0.919992	+	0.391937i	$0.128195\pi$
$140$	3899.87	−	3261.31i	2.35428	−	1.96879i
$141$		0			0
$142$	−759.676	+	1315.80i	−0.448948	+	0.777601i
$143$	363.026	+	628.779i	0.212292	+	0.367700i
$144$		0			0
$145$	−2136.73	+	3700.92i	−1.22376	+	2.11962i
$146$	3026.43			1.71554
$147$		0			0
$148$	486.517			0.270212
$149$	193.654	−	335.418i	0.106475	−	0.184420i	−0.807865	−	0.589368i	$-0.799377\pi$
$149$	193.654	−	335.418i	0.106475	−	0.184420i	0.914340	+	0.404948i	$0.132710\pi$
$150$		0			0
$151$	−821.513	−	1422.90i	−0.442740	−	0.766848i	0.555152	−	0.831749i	$-0.312660\pi$
$151$	−821.513	−	1422.90i	−0.442740	−	0.766848i	−0.997892	+	0.0649008i	$0.979327\pi$
$152$	−791.956	+	1371.71i	−0.422606	+	0.731975i
$153$		0			0
$154$	4022.72	−	3364.05i	2.10494	−	1.76028i
$155$	−3545.17			−1.83713
$156$		0			0
$157$	346.834	+	600.734i	0.176308	+	0.305374i	0.940613	−	0.339480i	$-0.110251\pi$
$157$	346.834	+	600.734i	0.176308	+	0.305374i	−0.764305	+	0.644855i	$0.776918\pi$
$158$	2028.68	+	3513.78i	1.02148	+	1.76925i
$159$		0			0
$160$	−1728.03			−0.853830
$161$	−400.720	−	2294.97i	−0.196156	−	1.12341i
$162$		0			0
$163$	−872.770	+	1511.68i	−0.419390	+	0.726406i	−0.995878	−	0.0907002i	$-0.971089\pi$
$163$	−872.770	+	1511.68i	−0.419390	+	0.726406i	0.576488	+	0.817106i	$0.304423\pi$
$164$	3846.75	+	6662.77i	1.83159	+	3.17241i
$165$		0			0
$166$	629.602	−	1090.50i	0.294377	−	0.509876i
$167$	−3320.55			−1.53863			−0.769316	−	0.638868i	$-0.779403\pi$
$167$	−3320.55			−1.53863			−0.769316	+	0.638868i	$0.779403\pi$
$168$		0			0
$169$	−2047.89			−0.932129
$170$	−513.043	+	888.616i	−0.231462	+	0.400904i
$171$		0			0
$172$	−1719.90	−	2978.95i	−0.762448	−	1.32060i
$173$	−27.0575	+	46.8650i	−0.0118910	+	0.0205958i	−0.871910	−	0.489667i	$-0.837118\pi$
$173$	−27.0575	+	46.8650i	−0.0118910	+	0.0205958i	0.860019	+	0.510263i	$0.170452\pi$
$174$		0			0
$175$	−3908.85	−	1430.09i	−1.68847	−	0.617743i
$176$	2022.83			0.866345
$177$		0			0
$178$	2176.77	+	3770.28i	0.916607	+	1.58761i
$179$	1860.27	+	3222.08i	0.776776	+	1.34542i	0.933791	+	0.357820i	$0.116480\pi$
$179$	1860.27	+	3222.08i	0.776776	+	1.34542i	−0.157014	+	0.987596i	$0.550187\pi$
$180$		0			0
$181$	1280.85			0.525992			0.262996	−	0.964797i	$-0.415289\pi$
$181$	1280.85			0.525992			0.262996	+	0.964797i	$0.415289\pi$
$182$	−185.247	−	1060.93i	−0.0754472	−	0.432096i
$183$		0			0
$184$	2000.21	−	3464.47i	0.801400	−	1.38807i
$185$	−309.936	−	536.824i	−0.123173	−	0.213341i
$186$		0			0
$187$	−342.521	+	593.263i	−0.133944	+	0.231998i
$188$	−4018.00			−1.55874
$189$		0			0
$190$	4435.60			1.69364
$191$	−470.005	+	814.072i	−0.178054	+	0.308399i	−0.941214	−	0.337811i	$-0.890314\pi$
$191$	−470.005	+	814.072i	−0.178054	+	0.308399i	0.763160	+	0.646210i	$0.223647\pi$
$192$		0			0
$193$	706.461	+	1223.63i	0.263483	+	0.456365i	0.967165	−	0.254149i	$-0.0817955\pi$
$193$	706.461	+	1223.63i	0.263483	+	0.456365i	−0.703682	+	0.710515i	$0.748462\pi$
$194$	1084.78	−	1878.89i	0.401455	−	0.695341i
$195$		0			0
$196$	−4736.68	+	1706.14i	−1.72619	+	0.621770i
$197$	3007.74			1.08778			0.543890	−	0.839156i	$-0.316951\pi$
$197$	3007.74			1.08778			0.543890	+	0.839156i	$0.316951\pi$
$198$		0			0
$199$	11.0224	+	19.0913i	0.00392640	+	0.00680073i	0.867982	−	0.496596i	$-0.165417\pi$
$199$	11.0224	+	19.0913i	0.00392640	+	0.00680073i	−0.864056	+	0.503397i	$0.832084\pi$
$200$	−3573.60	−	6189.65i	−1.26346	−	2.18837i
$201$		0			0
$202$	−4286.82			−1.49316
$203$	3246.49	−	2714.92i	1.12246	−	0.938669i
$204$		0			0
$205$	4901.15	−	8489.03i	1.66981	−	2.89219i
$206$	272.347	+	471.718i	0.0921130	+	0.159544i
$207$		0			0
$208$	207.720	−	359.782i	0.0692443	−	0.119935i
$209$	2961.32			0.980090
$210$		0			0
$211$	−4881.84			−1.59279			−0.796397	−	0.604774i	$-0.793264\pi$
$211$	−4881.84			−1.59279			−0.796397	+	0.604774i	$0.793264\pi$
$212$	−1878.32	+	3253.35i	−0.608509	+	1.05397i
$213$		0			0
$214$	2152.65	+	3728.50i	0.687626	+	1.19100i
$215$	−2191.33	+	3795.49i	−0.695103	+	1.20395i
$216$		0			0
$217$	3297.10	+	1206.28i	1.03144	+	0.377362i
$218$	6888.96			2.14027
$219$		0			0
$220$	−8160.58	−	14134.5i	−2.50085	−	4.33159i
$221$	70.3454	+	121.842i	0.0214115	+	0.0370858i
$222$		0			0
$223$	144.053			0.0432579			0.0216290	−	0.999766i	$-0.493115\pi$
$223$	144.053			0.0432579			0.0216290	+	0.999766i	$0.493115\pi$
$224$	1607.12	+	587.980i	0.479375	+	0.175384i
$225$		0			0
$226$	−24.4428	+	42.3362i	−0.00719431	+	0.0124609i
$227$	−2461.07	−	4262.69i	−0.719590	−	1.24637i	−0.961163	−	0.275983i	$-0.910997\pi$
$227$	−2461.07	−	4262.69i	−0.719590	−	1.24637i	0.241573	−	0.970383i	$-0.422337\pi$
$228$		0			0
$229$	7.89445	−	13.6736i	0.00227808	−	0.00394575i	−0.864884	−	0.501972i	$-0.832608\pi$
$229$	7.89445	−	13.6736i	0.00227808	−	0.00394575i	0.867162	+	0.498026i	$0.165942\pi$
$230$	−11202.8			−3.21171
$231$		0			0
$232$	7267.10			2.05650
$233$	363.752	−	630.037i	0.102276	−	0.177146i	−0.810346	−	0.585951i	$-0.800721\pi$
$233$	363.752	−	630.037i	0.102276	−	0.177146i	0.912622	+	0.408805i	$0.134054\pi$
$234$		0			0
$235$	2559.67	+	4433.48i	0.710529	+	1.23067i
$236$	−1239.07	+	2146.13i	−0.341765	+	0.591954i
$237$		0			0
$238$	779.504	−	651.869i	0.212301	−	0.177540i
$239$	63.6850			0.0172361			0.00861807	−	0.999963i	$-0.497257\pi$
$239$	63.6850			0.0172361			0.00861807	+	0.999963i	$0.497257\pi$
$240$		0			0
$241$	−1674.89	−	2900.99i	−0.447672	−	0.775391i	0.550562	−	0.834794i	$-0.314414\pi$
$241$	−1674.89	−	2900.99i	−0.447672	−	0.775391i	−0.998234	+	0.0594033i	$0.981080\pi$
$242$	−5248.45	−	9090.57i	−1.39414	−	2.41473i
$243$		0			0
$244$	−2864.30			−0.751508
$245$	4900.06	+	4139.57i	1.27777	+	1.07946i
$246$		0			0
$247$	304.092	−	526.703i	0.0783356	−	0.135681i
$248$	3014.31	+	5220.94i	0.771811	+	1.33682i
$249$		0			0
$250$	−4441.37	+	7692.67i	−1.12359	+	1.94611i
$251$	4922.71			1.23792			0.618961	−	0.785422i	$-0.287554\pi$
$251$	4922.71			1.23792			0.618961	+	0.785422i	$0.287554\pi$
$252$		0			0
$253$	−7479.30			−1.85857
$254$	3786.13	−	6557.77i	0.935287	−	1.61996i
$255$		0			0
$256$	3466.74	+	6004.58i	0.846373	+	1.46596i
$257$	1436.70	−	2488.43i	0.348711	−	0.603985i	−0.637310	−	0.770608i	$-0.719953\pi$
$257$	1436.70	−	2488.43i	0.348711	−	0.603985i	0.986021	+	0.166622i	$0.0532861\pi$
$258$		0			0
$259$	105.589	+	604.720i	0.0253319	+	0.145079i
$260$	−3351.97			−0.799540
$261$		0			0
$262$	−535.461	−	927.445i	−0.126263	−	0.218694i
$263$	−2183.85	−	3782.54i	−0.512023	−	0.886850i	−0.999903	−	0.0139391i	$-0.995563\pi$
$263$	−2183.85	−	3782.54i	−0.512023	−	0.886850i	0.487880	−	0.872911i	$-0.337770\pi$
$264$		0			0
$265$	4786.35			1.10952
$266$	−4125.23	−	1509.26i	−0.950880	−	0.347889i
$267$		0			0
$268$	−3780.69	+	6548.35i	−0.861726	+	1.49255i
$269$	−2677.45	−	4637.48i	−0.606866	−	1.05112i	−0.991754	−	0.128160i	$-0.959093\pi$
$269$	−2677.45	−	4637.48i	−0.606866	−	1.05112i	0.384887	−	0.922964i	$-0.374240\pi$
$270$		0			0
$271$	1521.12	−	2634.66i	0.340966	−	0.590570i	−0.643647	−	0.765323i	$-0.722579\pi$
$271$	1521.12	−	2634.66i	0.340966	−	0.590570i	0.984612	+	0.174753i	$0.0559127\pi$
$272$	391.975			0.0873786
$273$		0			0
$274$	10723.0			2.36424
$275$	−6681.29	+	11572.3i	−1.46508	+	2.53759i
$276$		0			0
$277$	4290.02	+	7430.53i	0.930549	+	1.61176i	0.782384	+	0.622796i	$0.214003\pi$
$277$	4290.02	+	7430.53i	0.930549	+	1.61176i	0.148165	+	0.988963i	$0.452663\pi$
$278$	−7179.75	+	12435.7i	−1.54897	+	2.68289i
$279$		0			0
$280$	1894.59	+	10850.6i	0.404370	+	2.31588i
$281$	−953.058			−0.202330			−0.101165	−	0.994870i	$-0.532257\pi$
$281$	−953.058			−0.202330			−0.101165	+	0.994870i	$0.532257\pi$
$282$		0			0
$283$	3765.80	+	6522.56i	0.791002	+	1.37006i	0.925347	+	0.379122i	$0.123774\pi$
$283$	3765.80	+	6522.56i	0.791002	+	1.37006i	−0.134345	+	0.990935i	$0.542893\pi$
$284$	−2341.50	−	4055.60i	−0.489234	−	0.847379i
$285$		0			0
$286$	−3457.57			−0.714861
$287$	−7446.68	+	6227.37i	−1.53158	+	1.28080i
$288$		0			0
$289$	2390.13	−	4139.82i	0.486491	−	0.842626i
$290$	−10175.4	−	17624.4i	−2.06042	−	3.56875i
$291$		0			0
$292$	−4664.09	+	8078.45i	−0.934745	+	1.61903i
$293$	−1325.09			−0.264207			−0.132104	−	0.991236i	$-0.542173\pi$
$293$	−1325.09			−0.264207			−0.132104	+	0.991236i	$0.542173\pi$
$294$		0			0
$295$	3157.40			0.623155
$296$	−527.052	+	912.880i	−0.103494	+	0.179257i
$297$		0			0
$298$	922.209	+	1597.31i	0.179269	+	0.310503i
$299$	−768.033	+	1330.27i	−0.148550	+	0.257296i
$300$		0			0
$301$	3329.44	−	2784.29i	0.637561	−	0.533168i
$302$	7824.33			1.49086
$303$		0			0
$304$	−847.223	−	1467.43i	−0.159841	−	0.276852i
$305$	1824.70	+	3160.48i	0.342564	+	0.593339i
$306$		0			0
$307$	−8871.73			−1.64930			−0.824652	−	0.565640i	$-0.808629\pi$
$307$	−8871.73			−1.64930			−0.824652	+	0.565640i	$0.808629\pi$
$308$	2780.14	+	15922.2i	0.514329	+	2.94563i
$309$		0			0
$310$	8441.31	−	14620.8i	1.54656	−	2.67872i
$311$	2265.54	+	3924.04i	0.413078	+	0.715472i	0.995225	−	0.0976120i	$-0.0311204\pi$
$311$	2265.54	+	3924.04i	0.413078	+	0.715472i	−0.582147	+	0.813084i	$0.697787\pi$
$312$		0			0
$313$	−2158.30	+	3738.29i	−0.389759	+	0.675082i	−0.992417	−	0.122917i	$-0.960775\pi$
$313$	−2158.30	+	3738.29i	−0.389759	+	0.675082i	0.602658	+	0.798000i	$0.294108\pi$
$314$	−3303.35			−0.593691
$315$		0			0
$316$	−12505.7			−2.22628
$317$	−3348.77	+	5800.24i	−0.593331	+	1.02768i	0.400449	+	0.916319i	$0.368854\pi$
$317$	−3348.77	+	5800.24i	−0.593331	+	1.02768i	−0.993780	+	0.111360i	$0.964479\pi$
$318$		0			0
$319$	−6793.38	−	11766.5i	−1.19234	−	2.06519i
$320$	6659.55	−	11534.7i	1.16338	−	2.01503i
$321$		0			0
$322$	10418.9	+	3811.87i	1.80318	+	0.659713i
$323$	573.831			0.0988508
$324$		0			0
$325$	1372.17	+	2376.68i	0.234199	+	0.405644i
$326$	−4156.26	−	7198.86i	−0.706117	−	1.22303i
$327$		0			0
$328$	−16669.0			−2.80607
$329$	−872.027	−	4994.21i	−0.146129	−	0.836898i
$330$		0			0
$331$	4032.83	−	6985.07i	0.669681	−	1.15992i	−0.308312	−	0.951285i	$-0.599764\pi$
$331$	4032.83	−	6985.07i	0.669681	−	1.15992i	0.977993	−	0.208636i	$-0.0669025\pi$
$332$	1940.58	+	3361.19i	0.320793	+	0.555630i
$333$		0			0
$334$	7906.47	−	13694.4i	1.29528	−	2.24349i
$335$	9633.97			1.57122
$336$		0			0
$337$	−480.216			−0.0776232			−0.0388116	−	0.999247i	$-0.512357\pi$
$337$	−480.216			−0.0776232			−0.0388116	+	0.999247i	$0.512357\pi$
$338$	4876.17	−	8445.78i	0.784701	−	1.35914i
$339$		0			0
$340$	−1581.32	−	2738.93i	−0.252233	−	0.436880i
$341$	5635.63	−	9761.20i	0.894976	−	1.55014i
$342$		0			0
$343$	−3148.66	−	5517.21i	−0.495660	−	0.868516i
$344$	7452.78			1.16810
$345$		0			0
$346$	−128.852	−	223.178i	−0.0200206	−	0.0346767i
$347$	1118.56	+	1937.40i	0.173047	+	0.299727i	0.939484	−	0.342593i	$-0.111305\pi$
$347$	1118.56	+	1937.40i	0.173047	+	0.299727i	−0.766437	+	0.642320i	$0.777972\pi$
$348$		0			0
$349$	2602.84			0.399217			0.199609	−	0.979876i	$-0.436033\pi$
$349$	2602.84			0.399217			0.199609	+	0.979876i	$0.436033\pi$
$350$	15205.2	−	12715.5i	2.32215	−	1.94192i
$351$		0			0
$352$	2746.99	−	4757.93i	0.415953	−	0.720451i
$353$	3469.23	+	6008.89i	0.523084	+	0.906008i	0.999639	+	0.0268634i	$0.00855192\pi$
$353$	3469.23	+	6008.89i	0.523084	+	0.906008i	−0.476555	+	0.879145i	$0.658115\pi$
$354$		0			0
$355$	−2983.31	+	5167.24i	−0.446021	+	0.772532i
$356$	−13418.7			−1.99772
$357$		0			0
$358$	−17717.8			−2.61568
$359$	−1076.56	+	1864.65i	−0.158269	+	0.274130i	−0.934244	−	0.356633i	$-0.883925\pi$
$359$	−1076.56	+	1864.65i	−0.158269	+	0.274130i	0.775976	+	0.630763i	$0.217258\pi$
$360$		0			0
$361$	2189.21	+	3791.82i	0.319173	+	0.552825i
$362$	−3049.79	+	5282.40i	−0.442800	+	0.766952i
$363$		0			0
$364$	3117.42	+	1140.54i	0.448894	+	0.164233i
$365$	11885.0			1.70436
$366$		0			0
$367$	−924.490	−	1601.26i	−0.131493	−	0.227753i	0.792759	−	0.609535i	$-0.208644\pi$
$367$	−924.490	−	1601.26i	−0.131493	−	0.227753i	−0.924252	+	0.381782i	$0.875310\pi$
$368$	2139.80	+	3706.24i	0.303111	+	0.525003i
$369$		0			0
$370$	2951.92			0.414765
$371$	−4451.43	−	1628.60i	−0.622930	−	0.227905i
$372$		0			0
$373$	22.1091	−	38.2941i	0.00306908	−	0.00531581i	−0.864487	−	0.502656i	$-0.832356\pi$
$373$	22.1091	−	38.2941i	0.00306908	−	0.00531581i	0.867556	+	0.497340i	$0.165690\pi$
$374$	−1631.13	−	2825.21i	−0.225519	−	0.390610i
$375$		0			0
$376$	4352.77	−	7539.21i	0.597013	−	1.03406i
$377$	−2790.39			−0.381200
$378$		0			0
$379$	3338.62			0.452489			0.226245	−	0.974071i	$-0.427355\pi$
$379$	3338.62			0.452489			0.226245	+	0.974071i	$0.427355\pi$
$380$	−6835.79	+	11839.9i	−0.922812	+	1.59836i
$381$		0			0
$382$	−2238.23	−	3876.73i	−0.299785	−	0.519243i
$383$	−4000.27	+	6928.67i	−0.533693	+	0.924383i	0.465533	+	0.885031i	$0.345863\pi$
$383$	−4000.27	+	6928.67i	−0.533693	+	0.924383i	−0.999225	+	0.0393522i	$0.987471\pi$
$384$		0			0
$385$	15797.5	−	13210.9i	2.09121	−	1.74880i
$386$	−6728.54			−0.887238
$387$		0			0
$388$	3343.53	+	5791.17i	0.437480	+	0.757738i
$389$	562.916	+	974.998i	0.0733701	+	0.127081i	0.900376	−	0.435112i	$-0.143291\pi$
$389$	562.916	+	974.998i	0.0733701	+	0.127081i	−0.827006	+	0.562193i	$0.809958\pi$
$390$		0			0
$391$	−1449.30			−0.187454
$392$	1929.99	−	10736.0i	0.248672	−	1.38329i
$393$		0			0
$394$	−7161.66	+	12404.4i	−0.915734	+	1.58610i
$395$	7966.79	+	13798.9i	1.01482	+	1.75771i
$396$		0			0
$397$	−91.3716	+	158.260i	−0.0115512	+	0.0200072i	−0.871743	−	0.489963i	$-0.837010\pi$
$397$	−91.3716	+	158.260i	−0.0115512	+	0.0200072i	0.860192	+	0.509970i	$0.170344\pi$
$398$	−104.980			−0.0132216
$399$		0			0
$400$	7645.96			0.955745
$401$	4698.90	−	8138.74i	0.585167	−	1.01354i	−0.409687	−	0.912226i	$-0.634362\pi$
$401$	4698.90	−	8138.74i	0.585167	−	1.01354i	0.994855	−	0.101313i	$-0.0323045\pi$
$402$		0			0
$403$	−1157.42	−	2004.72i	−0.143065	−	0.247796i
$404$	6606.49	−	11442.8i	0.813577	−	1.40916i
$405$		0			0
$406$	3466.56	+	19853.4i	0.423750	+	2.42687i
$407$	1970.78			0.240019
$408$		0			0
$409$	−1304.28	−	2259.07i	−0.157683	−	0.273115i	0.776350	−	0.630302i	$-0.217069\pi$
$409$	−1304.28	−	2259.07i	−0.157683	−	0.273115i	−0.934033	+	0.357187i	$0.883736\pi$
$410$	23340.0	+	40426.1i	2.81141	+	4.86951i
$411$		0			0
$412$	−1678.87			−0.200758
$413$	−2936.47	−	1074.34i	−0.349864	−	0.128002i
$414$		0			0
$415$	2472.50	−	4282.49i	0.292458	−	0.506552i
$416$	−564.166	−	977.164i	−0.0664916	−	0.115167i
$417$		0			0
$418$	−7051.13	+	12212.9i	−0.825077	+	1.42907i
$419$	−9533.73			−1.11158			−0.555792	−	0.831322i	$-0.687585\pi$
$419$	−9533.73			−1.11158			−0.555792	+	0.831322i	$0.687585\pi$
$420$		0			0
$421$	−11430.2			−1.32322			−0.661611	−	0.749848i	$-0.730127\pi$
$421$	−11430.2			−1.32322			−0.661611	+	0.749848i	$0.730127\pi$
$422$	11624.0	−	20133.4i	1.34087	−	2.32246i
$423$		0			0
$424$	−4069.64	−	7048.82i	−0.466130	−	0.807361i
$425$	−1294.67	+	2242.43i	−0.147766	+	0.255939i
$426$		0			0
$427$	−621.639	−	3560.20i	−0.0704525	−	0.403490i
$428$	−13269.9			−1.49866
$429$		0			0
$430$	−10435.4	−	18074.7i	−1.17033	−	2.02707i
$431$	−3496.39	−	6055.93i	−0.390755	−	0.676807i	0.601794	−	0.798651i	$-0.294453\pi$
$431$	−3496.39	−	6055.93i	−0.390755	−	0.676807i	−0.992549	+	0.121844i	$0.961119\pi$
$432$		0			0
$433$	−4730.76			−0.525048			−0.262524	−	0.964925i	$-0.584555\pi$
$433$	−4730.76			−0.525048			−0.262524	+	0.964925i	$0.584555\pi$
$434$	−12825.5	+	10725.5i	−1.41854	+	1.18627i
$435$		0			0
$436$	−10616.7	+	18388.7i	−1.16617	+	2.01986i
$437$	3132.55	+	5425.74i	0.342907	+	0.593932i
$438$		0			0
$439$	4304.64	−	7455.86i	0.467994	−	0.810590i	−0.531337	−	0.847161i	$-0.678310\pi$
$439$	4304.64	−	7455.86i	0.467994	−	0.810590i	0.999331	+	0.0365709i	$0.0116435\pi$
$440$	35362.0			3.83140
$441$		0			0
$442$	−669.991			−0.0721000
$443$	−2635.95	+	4565.61i	−0.282704	+	0.489658i	−0.972050	−	0.234775i	$-0.924565\pi$
$443$	−2635.95	+	4565.61i	−0.282704	+	0.489658i	0.689346	+	0.724433i	$0.257898\pi$
$444$		0			0
$445$	8548.36	+	14806.2i	0.910632	+	1.57726i
$446$	−343.002	+	594.096i	−0.0364162	+	0.0630746i
$447$		0			0
$448$	−10118.4	+	8461.59i	−1.06707	+	0.892349i
$449$	−13513.8			−1.42039			−0.710197	−	0.704003i	$-0.751394\pi$
$449$	−13513.8			−1.42039			−0.710197	+	0.704003i	$0.751394\pi$
$450$		0			0
$451$	15582.4	+	26989.5i	1.62693	+	2.81793i
$452$	−75.3386	−	130.490i	−0.00783989	−	0.0135791i
$453$		0			0
$454$	23440.0			2.42311
$455$	−727.478	−	4166.36i	−0.0749554	−	0.429279i
$456$		0			0
$457$	−3644.19	+	6311.93i	−0.373016	+	0.646082i	−0.990028	−	0.140871i	$-0.955010\pi$
$457$	−3644.19	+	6311.93i	−0.373016	+	0.646082i	0.617012	+	0.786954i	$0.288343\pi$
$458$	37.5945	+	65.1157i	0.00383554	+	0.00664335i
$459$		0			0
$460$	17264.9	−	29903.7i	1.74996	−	3.03101i
$461$	5654.21			0.571243			0.285621	−	0.958343i	$-0.407800\pi$
$461$	5654.21			0.571243			0.285621	+	0.958343i	$0.407800\pi$
$462$		0			0
$463$	4102.17			0.411758			0.205879	−	0.978577i	$-0.433995\pi$
$463$	4102.17			0.411758			0.205879	+	0.978577i	$0.433995\pi$
$464$	−3887.12	+	6732.69i	−0.388912	+	0.673615i
$465$		0			0
$466$	1732.24	+	3000.33i	0.172199	+	0.298257i
$467$	2552.06	−	4420.29i	0.252880	−	0.438001i	−0.711437	−	0.702750i	$-0.751955\pi$
$467$	2552.06	−	4420.29i	0.252880	−	0.438001i	0.964318	+	0.264748i	$0.0852888\pi$
$468$		0			0
$469$	−8959.85	−	3278.05i	−0.882148	−	0.322743i
$470$	−24379.1			−2.39260
$471$		0			0
$472$	−2684.61	−	4649.88i	−0.261799	−	0.453449i
$473$	−6966.96	−	12067.1i	−0.677254	−	1.17304i
$474$		0			0
$475$	11193.3			1.08123
$476$	538.723	+	3085.33i	0.0518747	+	0.297093i
$477$		0			0
$478$	−151.639	+	262.646i	−0.0145100	+	0.0251321i
$479$	2100.22	+	3637.69i	0.200337	+	0.346994i	0.948637	−	0.316366i	$-0.102463\pi$
$479$	2100.22	+	3637.69i	0.200337	+	0.346994i	−0.748300	+	0.663361i	$0.769130\pi$
$480$		0			0
$481$	202.375	−	350.524i	0.0191840	−	0.0332277i
$482$	15952.1			1.50747
$483$		0			0
$484$	32353.9			3.03850
$485$	4260.00	−	7378.53i	0.398838	−	0.690808i
$486$		0			0
$487$	−2150.49	−	3724.76i	−0.200099	−	0.346581i	0.748461	−	0.663179i	$-0.230793\pi$
$487$	−2150.49	−	3724.76i	−0.200099	−	0.346581i	−0.948560	+	0.316597i	$0.897460\pi$
$488$	3102.94	−	5374.45i	0.287835	−	0.498545i
$489$		0			0
$490$	−28739.6	+	10351.9i	−2.64964	+	0.954391i
$491$	1774.44			0.163095			0.0815474	−	0.996669i	$-0.474014\pi$
$491$	1774.44			0.163095			0.0815474	+	0.996669i	$0.474014\pi$
$492$		0			0
$493$	−1316.39	−	2280.05i	−0.120258	−	0.208293i
$494$	1448.13	+	2508.24i	0.131892	+	0.228443i
$495$		0			0
$496$	−6449.33			−0.583838
$497$	4532.77	−	3790.58i	0.409099	−	0.342114i
$498$		0			0
$499$	3427.39	−	5936.41i	0.307477	−	0.532566i	−0.670333	−	0.742061i	$-0.733849\pi$
$499$	3427.39	−	5936.41i	0.307477	−	0.532566i	0.977810	+	0.209495i	$0.0671820\pi$
$500$	−13689.3	−	23710.6i	−1.22441	−	2.12074i
$501$		0			0
$502$	−11721.3	+	20301.9i	−1.04213	+	1.80502i
$503$	−6584.76			−0.583698			−0.291849	−	0.956464i	$-0.594270\pi$
$503$	−6584.76			−0.583698			−0.291849	+	0.956464i	$0.594270\pi$
$504$		0			0
$505$	−16834.7			−1.48343
$506$	17808.8	−	30845.7i	1.56462	−	2.71000i
$507$		0			0
$508$	11669.7	+	20212.6i	1.01922	+	1.76533i
$509$	−2110.15	+	3654.88i	−0.183754	+	0.318271i	−0.943156	−	0.332351i	$-0.892158\pi$
$509$	−2110.15	+	3654.88i	−0.183754	+	0.318271i	0.759402	+	0.650621i	$0.225492\pi$
$510$		0			0
$511$	−11053.4	−	4044.01i	−0.956897	−	0.350091i
$512$	−11799.2			−1.01847
$513$		0			0
$514$	6841.77	+	11850.3i	0.587116	+	1.01691i
$515$	1069.53	+	1852.47i	0.0915126	+	0.158504i
$516$		0			0
$517$	−16276.1			−1.38457
$518$	−2745.37	−	1004.42i	−0.232866	−	0.0851963i
$519$		0			0
$520$	3631.25	−	6289.50i	0.306232	−	0.530409i
$521$	2555.50	+	4426.25i	0.214891	+	0.372203i	0.953239	−	0.302218i	$-0.0977269\pi$
$521$	2555.50	+	4426.25i	0.214891	+	0.372203i	−0.738348	+	0.674420i	$0.764394\pi$
$522$		0			0
$523$	−7073.84	+	12252.3i	−0.591429	+	1.02439i	0.402611	+	0.915371i	$0.368103\pi$
$523$	−7073.84	+	12252.3i	−0.591429	+	1.02439i	−0.994040	+	0.109014i	$0.965231\pi$
$524$	3300.83			0.275186
$525$		0			0
$526$	20799.7			1.72416
$527$	1092.05	−	1891.48i	0.0902662	−	0.156346i
$528$		0			0
$529$	−1828.27	−	3166.65i	−0.150264	−	0.260265i
$530$	−11396.7	+	19739.6i	−0.934036	+	1.61780i
$531$		0			0
$532$	10386.1	−	8685.51i	0.846420	−	0.707828i
$533$	6400.49			0.520142
$534$		0			0
$535$	8453.62	+	14642.1i	0.683144	+	1.18324i
$536$	−8191.37	−	14187.9i	−0.660100	−	1.14333i
$537$		0			0
$538$	25500.8			2.04353
$539$	−19187.3	+	6911.20i	−1.53331	+	0.552294i
$540$		0			0
$541$	−10813.7	+	18729.9i	−0.859368	+	1.48847i	0.0131641	+	0.999913i	$0.495810\pi$
$541$	−10813.7	+	18729.9i	−0.859368	+	1.48847i	−0.872532	+	0.488556i	$0.837524\pi$
$542$	7243.82	+	12546.7i	0.574075	+	0.994328i
$543$		0			0
$544$	532.300	−	921.970i	0.0419525	−	0.0726639i
$545$	27053.5			2.12632
$546$		0			0
$547$	−11453.9			−0.895305			−0.447652	−	0.894208i	$-0.647740\pi$
$547$	−11453.9			−0.895305			−0.447652	+	0.894208i	$0.647740\pi$
$548$	−16525.4	+	28622.9i	−1.28820	+	2.23122i
$549$		0			0
$550$	−31817.3	−	55109.2i	−2.46672	−	4.27248i
$551$	−5690.54	+	9856.30i	−0.439973	+	0.762055i
$552$		0			0
$553$	−2714.12	−	15544.1i	−0.208709	−	1.19530i
$554$	−40859.4			−3.13348
$555$		0			0
$556$	−22129.7	−	38329.8i	−1.68796	−	2.92364i
$557$	−520.712	−	901.900i	−0.0396109	−	0.0686081i	0.845540	−	0.533912i	$-0.179279\pi$
$557$	−520.712	−	901.900i	−0.0396109	−	0.0686081i	−0.885151	+	0.465304i	$0.845945\pi$
$558$		0			0
$559$	−2861.69			−0.216523
$560$	−11066.0	−	4048.63i	−0.835046	−	0.305510i
$561$		0			0
$562$	2269.30	−	3930.55i	0.170329	−	0.295018i
$563$	9969.46	+	17267.6i	0.746293	+	1.29262i	0.949588	+	0.313500i	$0.101501\pi$
$563$	9969.46	+	17267.6i	0.746293	+	1.29262i	−0.203296	+	0.979117i	$0.565165\pi$
$564$		0			0
$565$	−95.9890	+	166.258i	−0.00714741	+	0.0123797i
$566$	−35866.6			−2.66358
$567$		0			0
$568$	10146.4			0.749527
$569$	7025.60	−	12168.7i	0.517625	−	0.896553i	−0.482165	−	0.876080i	$-0.660150\pi$
$569$	7025.60	−	12168.7i	0.517625	−	0.896553i	0.999790	−	0.0204726i	$-0.00651707\pi$
$570$		0			0
$571$	10751.2	+	18621.6i	0.787956	+	1.36478i	0.927217	+	0.374524i	$0.122194\pi$
$571$	10751.2	+	18621.6i	0.787956	+	1.36478i	−0.139261	+	0.990256i	$0.544473\pi$
$572$	5328.52	−	9229.26i	0.389504	−	0.674642i
$573$		0			0
$574$	−7951.46	−	45539.0i	−0.578201	−	3.31143i
$575$	−28270.4			−2.05036
$576$		0			0
$577$	−8430.47	−	14602.0i	−0.608259	−	1.05353i	−0.991527	−	0.129898i	$-0.958535\pi$
$577$	−8430.47	−	14602.0i	−0.608259	−	1.05353i	0.383269	−	0.923637i	$-0.374798\pi$
$578$	11382.1	+	19714.5i	0.819092	+	1.41871i
$579$		0			0
$580$	62726.2			4.49063
$581$	−3756.65	+	3141.54i	−0.268248	+	0.224325i
$582$		0			0
$583$	−7608.70	+	13178.7i	−0.540515	+	0.936199i
$584$	−10105.4	−	17503.0i	−0.716033	−	1.24021i
$585$		0			0
$586$	3155.14	−	5464.87i	0.222419	−	0.385241i
$587$	−3952.45			−0.277913			−0.138957	−	0.990298i	$-0.544375\pi$
$587$	−3952.45			−0.277913			−0.138957	+	0.990298i	$0.544375\pi$
$588$		0			0
$589$	−9441.48			−0.660492
$590$	−7518.00	+	13021.6i	−0.524595	+	0.908626i
$591$		0			0
$592$	−563.832	−	976.585i	−0.0391442	−	0.0677997i
$593$	7580.86	−	13130.4i	0.524973	−	0.909279i	−0.474605	−	0.880199i	$-0.657409\pi$
$593$	7580.86	−	13130.4i	0.524973	−	0.909279i	0.999577	−	0.0290799i	$-0.00925774\pi$
$594$		0			0
$595$	3061.18	−	2559.94i	0.210918	−	0.176382i
$596$	−5684.93			−0.390711
$597$		0			0
$598$	−3657.49	−	6334.96i	−0.250110	−	0.433203i
$599$	3705.69	+	6418.44i	0.252772	+	0.437814i	0.964288	−	0.264856i	$-0.0853244\pi$
$599$	3705.69	+	6418.44i	0.252772	+	0.437814i	−0.711516	+	0.702670i	$0.751991\pi$
$600$		0			0
$601$	10776.0			0.731388			0.365694	−	0.930735i	$-0.380832\pi$
$601$	10776.0			0.731388			0.365694	+	0.930735i	$0.380832\pi$
$602$	3555.13	+	20360.7i	0.240692	+	1.37847i
$603$		0			0
$604$	−12058.2	+	20885.5i	−0.812322	+	1.40698i
$605$	−20611.1	−	35699.4i	−1.38506	−	2.39899i
$606$		0			0
$607$	−5.81913	+	10.0790i	−0.000389113	+	0.000673963i	−0.866220	−	0.499663i	$-0.833457\pi$
$607$	−5.81913	+	10.0790i	−0.000389113	+	0.000673963i	0.865831	+	0.500337i	$0.166791\pi$
$608$	−4602.09			−0.306973
$609$		0			0
$610$	−17379.0			−1.15353
$611$	−1671.36	+	2894.88i	−0.110664	+	0.191676i
$612$		0			0
$613$	−7810.70	−	13528.5i	−0.514635	−	0.891373i	−0.999856	−	0.0169819i	$-0.994594\pi$
$613$	−7810.70	−	13528.5i	−0.514635	−	0.891373i	0.485221	−	0.874391i	$-0.338739\pi$
$614$	21124.3	−	36588.3i	1.38845	−	2.40486i
$615$		0			0
$616$	−32887.6	−	12032.3i	−2.15110	−	0.787003i
$617$	26376.5			1.72103			0.860517	−	0.509422i	$-0.170141\pi$
$617$	26376.5			1.72103			0.860517	+	0.509422i	$0.170141\pi$
$618$		0			0
$619$	10578.3	+	18322.1i	0.686877	+	1.18971i	0.972843	+	0.231466i	$0.0743523\pi$
$619$	10578.3	+	18322.1i	0.686877	+	1.18971i	−0.285966	+	0.958240i	$0.592314\pi$
$620$	26018.1	+	45064.7i	1.68534	+	2.91910i
$621$		0			0
$622$	−21577.7			−1.39098
$623$	−2912.25	−	16678.8i	−0.187282	−	1.07259i
$624$		0			0
$625$	−3395.34	+	5880.90i	−0.217302	+	0.376377i
$626$	−10278.2	−	17802.3i	−0.656227	−	1.13662i
$627$		0			0
$628$	5090.85	−	8817.62i	0.323483	−	0.560289i
$629$	381.888			0.0242081
$630$		0			0
$631$	18757.1			1.18337			0.591686	−	0.806169i	$-0.298463\pi$
$631$	18757.1			1.18337			0.591686	+	0.806169i	$0.298463\pi$
$632$	13547.7	−	23465.3i	0.852686	−	1.47690i
$633$		0			0
$634$	−15947.4	−	27621.6i	−0.998976	−	1.73028i
$635$	14868.4	−	25752.9i	0.929190	−	1.60940i
$636$		0			0
$637$	−741.071	+	4122.36i	−0.0460947	+	0.256411i
$638$	64702.2			4.01502
$639$		0			0
$640$	24801.6	+	42957.7i	1.53183	+	2.65321i
$641$	−1998.41	−	3461.36i	−0.123140	−	0.213284i	0.797864	−	0.602837i	$-0.205963\pi$
$641$	−1998.41	−	3461.36i	−0.123140	−	0.213284i	−0.921004	+	0.389552i	$0.872630\pi$
$642$		0			0
$643$	−22237.8			−1.36388			−0.681940	−	0.731408i	$-0.738864\pi$
$643$	−22237.8			−1.36388			−0.681940	+	0.731408i	$0.738864\pi$
$644$	−26231.8	+	21936.7i	−1.60509	+	1.34228i
$645$		0			0
$646$	−1366.34	+	2366.56i	−0.0832163	+	0.144135i
$647$	−11496.1	−	19911.9i	−0.698545	−	1.20992i	−0.968971	−	0.247175i	$-0.920498\pi$
$647$	−11496.1	−	19911.9i	−0.698545	−	1.20992i	0.270425	−	0.962741i	$-0.412836\pi$
$648$		0			0
$649$	−5019.21	+	8693.53i	−0.303577	+	0.525810i
$650$	−13069.0			−0.788628
$651$		0			0
$652$	25621.2			1.53896
$653$	−14849.7	+	25720.4i	−0.889912	+	1.54137i	−0.0499339	+	0.998753i	$0.515901\pi$
$653$	−14849.7	+	25720.4i	−0.889912	+	1.54137i	−0.839978	+	0.542620i	$0.817432\pi$
$654$		0			0
$655$	−2102.80	−	3642.15i	−0.125440	−	0.217268i
$656$	8916.12	−	15443.2i	0.530665	−	0.919138i
$657$		0			0
$658$	22673.2	+	8295.22i	1.34330	+	0.491461i
$659$	388.786			0.0229817			0.0114909	−	0.999934i	$-0.496342\pi$
$659$	388.786			0.0229817			0.0114909	+	0.999934i	$0.496342\pi$
$660$		0			0
$661$	−4994.02	−	8649.89i	−0.293865	−	0.508989i	0.680855	−	0.732418i	$-0.261608\pi$
$661$	−4994.02	−	8649.89i	−0.293865	−	0.508989i	−0.974720	+	0.223429i	$0.928275\pi$
$662$	19204.9	+	33263.9i	1.12752	+	1.95293i
$663$		0			0
$664$	−8409.06			−0.491468
$665$	−16200.1	−	5926.98i	−0.944682	−	0.345621i
$666$		0			0
$667$	14372.4	−	24893.7i	0.834334	−	1.44511i
$668$	24369.6	+	42209.4i	1.41151	+	2.44481i
$669$		0			0
$670$	−22939.2	+	39731.9i	−1.32271	+	2.29101i
$671$	−11602.7			−0.667536
$672$		0			0
$673$	19996.8			1.14535			0.572674	−	0.819783i	$-0.305906\pi$
$673$	19996.8			1.14535			0.572674	+	0.819783i	$0.305906\pi$
$674$	1143.43	−	1980.48i	0.0653461	−	0.113183i
$675$		0			0
$676$	15029.5	+	26031.9i	0.855116	+	1.48110i
$677$	12561.9	−	21757.8i	0.713135	−	1.23519i	−0.250540	−	0.968106i	$-0.580608\pi$
$677$	12561.9	−	21757.8i	0.713135	−	1.23519i	0.963675	−	0.267079i	$-0.0860585\pi$
$678$		0			0
$679$	−6472.54	+	5412.73i	−0.365822	+	0.305923i
$680$	6852.28			0.386431
$681$		0			0
$682$	26837.7	+	46484.3i	1.50685	+	2.60994i
$683$	−11544.9	−	19996.3i	−0.646782	−	1.12026i	−0.983887	−	0.178792i	$-0.942781\pi$
$683$	−11544.9	−	19996.3i	−0.646782	−	1.12026i	0.337105	−	0.941467i	$-0.390552\pi$
$684$		0			0
$685$	42110.1			2.34883
$686$	30250.9	+	151.372i	1.68365	+	0.00842481i
$687$		0			0
$688$	−3986.44	+	6904.71i	−0.220903	+	0.382616i
$689$	1562.64	+	2706.58i	0.0864034	+	0.149655i
$690$		0			0
$691$	5377.95	−	9314.88i	0.296074	−	0.512814i	−0.679161	−	0.733990i	$-0.737656\pi$
$691$	5377.95	−	9314.88i	0.296074	−	0.512814i	0.975234	+	0.221175i	$0.0709893\pi$
$692$	794.304			0.0436343
$693$		0			0
$694$	−10653.5			−0.582710
$695$	−28195.5	+	48836.0i	−1.53887	+	2.66540i
$696$		0			0
$697$	3019.48	+	5229.89i	0.164090	+	0.284213i
$698$	−6197.55	+	10734.5i	−0.336076	+	0.582100i
$699$		0			0
$700$	10508.5	+	60183.3i	0.567404	+	3.24959i
$701$	31197.1			1.68088			0.840442	−	0.541901i	$-0.182295\pi$
$701$	31197.1			1.68088			0.840442	+	0.541901i	$0.182295\pi$
$702$		0			0
$703$	−825.420	−	1429.67i	−0.0442835	−	0.0767013i
$704$	21172.9	+	36672.6i	1.13350	+	1.96328i
$705$		0			0
$706$	−33042.0			−1.76141
$707$	15656.7	+	5728.16i	0.832858	+	0.304710i
$708$		0			0
$709$	−14447.7	+	25024.2i	−0.765296	+	1.32553i	0.174793	+	0.984605i	$0.444074\pi$
$709$	−14447.7	+	25024.2i	−0.765296	+	1.32553i	−0.940090	+	0.340927i	$0.889259\pi$
$710$	−14207.0	−	24607.2i	−0.750955	−	1.30069i
$711$		0			0
$712$	14536.7	−	25178.2i	0.765146	−	1.32527i
$713$	23846.0			1.25251
$714$		0			0
$715$	−13578.1			−0.710201
$716$	27305.2	−	47293.9i	1.42520	−	2.46852i
$717$		0			0
$718$	−5126.73	−	8879.75i	−0.266473	−	0.461545i
$719$	95.1583	−	164.819i	0.00493575	−	0.00854898i	−0.863547	−	0.504268i	$-0.831762\pi$
$719$	95.1583	−	164.819i	0.00493575	−	0.00854898i	0.868483	+	0.495719i	$0.165096\pi$
$720$		0			0
$721$	−364.366	−	2086.77i	−0.0188207	−	0.107788i
$722$	−20850.7			−1.07477
$723$		0			0
$724$	−9400.18	−	16281.6i	−0.482535	−	0.835775i
$725$	−25677.8	−	44475.3i	−1.31538	−	2.27830i
$726$		0			0
$727$	−5281.27			−0.269424			−0.134712	−	0.990885i	$-0.543011\pi$
$727$	−5281.27			−0.269424			−0.134712	+	0.990885i	$0.543011\pi$
$728$	−5517.22	+	4613.84i	−0.280882	+	0.234891i
$729$		0			0
$730$	−28299.2	+	49015.6i	−1.43479	+	2.48514i
$731$	−1350.02	−	2338.31i	−0.0683070	−	0.118311i
$732$		0			0
$733$	13908.6	−	24090.4i	0.700853	−	1.21391i	−0.267314	−	0.963609i	$-0.586136\pi$
$733$	13908.6	−	24090.4i	0.700853	−	1.21391i	0.968167	−	0.250304i	$-0.0805306\pi$
$734$	8805.12			0.442783
$735$		0			0
$736$	11623.3			0.582122
$737$	−15314.8	+	26526.0i	−0.765438	+	1.32578i
$738$		0			0
$739$	4276.71	+	7407.48i	0.212884	+	0.368726i	0.952616	−	0.304176i	$-0.0983810\pi$
$739$	4276.71	+	7407.48i	0.212884	+	0.368726i	−0.739732	+	0.672902i	$0.765048\pi$
$740$	−4549.26	+	7879.55i	−0.225992	+	0.391430i
$741$		0			0
$742$	17315.8	−	14480.5i	0.856715	−	0.716438i
$743$	−14150.4			−0.698693			−0.349346	−	0.936994i	$-0.613596\pi$
$743$	−14150.4			−0.698693			−0.349346	+	0.936994i	$0.613596\pi$
$744$		0			0
$745$	3621.59	+	6272.78i	0.178100	+	0.308479i
$746$	105.287	+	182.362i	0.00516733	+	0.00895009i
$747$		0			0
$748$	10055.1			0.491511
$749$	−2879.98	−	16494.0i	−0.140497	−	0.804642i
$750$		0			0
$751$	12121.6	−	20995.3i	0.588981	−	1.02014i	−0.405386	−	0.914146i	$-0.632863\pi$
$751$	12121.6	−	20995.3i	0.588981	−	1.02014i	0.994366	−	0.105999i	$-0.0338039\pi$
$752$	4656.53	+	8065.34i	0.225806	+	0.391107i
$753$		0			0
$754$	6644.13	−	11508.0i	0.320908	−	0.555830i
$755$	30726.8			1.48114
$756$		0			0
$757$	−13428.2			−0.644722			−0.322361	−	0.946617i	$-0.604476\pi$
$757$	−13428.2			−0.644722			−0.322361	+	0.946617i	$0.604476\pi$
$758$	−7949.50	+	13768.9i	−0.380922	+	0.659776i
$759$		0			0
$760$	−14810.6	−	25652.8i	−0.706893	−	1.22437i
$761$	−5262.95	+	9115.70i	−0.250699	+	0.434223i	−0.963718	−	0.266921i	$-0.913994\pi$
$761$	−5262.95	+	9115.70i	−0.250699	+	0.434223i	0.713020	+	0.701144i	$0.247327\pi$
$762$		0			0
$763$	−25160.5	−	9205.23i	−1.19380	−	0.436765i
$764$	13797.5			0.653373
$765$		0			0
$766$	−19049.9	−	32995.4i	−0.898565	−	1.55636i
$767$	1030.82	+	1785.44i	0.0485279	+	0.0840528i
$768$		0			0
$769$	31855.3			1.49380			0.746900	−	0.664936i	$-0.231541\pi$
$769$	31855.3			1.49380			0.746900	+	0.664936i	$0.231541\pi$
$770$	16868.4	+	96607.5i	0.789474	+	4.52142i
$771$		0			0
$772$	10369.5	−	17960.5i	0.483427	−	0.837321i
$773$	7406.35	+	12828.2i	0.344616	+	0.596892i	0.985284	−	0.170926i	$-0.0546759\pi$
$773$	7406.35	+	12828.2i	0.344616	+	0.596892i	−0.640668	+	0.767818i	$0.721343\pi$
$774$		0			0
$775$	21301.7	−	36895.7i	0.987330	−	1.71011i
$776$	−14488.4			−0.670237
$777$		0			0
$778$	−5361.38			−0.247063
$779$	13052.7	−	22608.0i	0.600337	−	1.03981i
$780$		0			0
$781$	−9484.94	−	16428.4i	−0.434568	−	0.752694i
$782$	3450.90	−	5977.13i	0.157806	−	0.273327i
$783$		0			0
$784$	8914.14	+	7530.67i	0.406074	+	0.343051i
$785$	−12972.5			−0.589821
$786$		0			0
$787$	−19179.7	−	33220.1i	−0.868718	−	1.50466i	−0.863308	−	0.504678i	$-0.831611\pi$
$787$	−19179.7	−	33220.1i	−0.868718	−	1.50466i	−0.00541041	−	0.999985i	$-0.501722\pi$
$788$	−22073.9	−	38233.2i	−0.997908	−	1.72843i
$789$		0			0
$790$	−75878.1			−3.41724
$791$	145.843	−	121.963i	0.00655574	−	0.00548231i
$792$		0			0
$793$	−1191.45	+	2063.66i	−0.0533541	+	0.0924120i
$794$	−435.125	−	753.659i	−0.0194484	−	0.0336856i
$795$		0			0
$796$	161.787	−	280.223i	0.00720400	−	0.0124777i
$797$	26078.1			1.15901			0.579506	−	0.814968i	$-0.303246\pi$
$797$	26078.1			1.15901			0.579506	+	0.814968i	$0.303246\pi$
$798$		0			0
$799$	−3153.90			−0.139646
$800$	10383.2	−	17984.2i	0.458875	−	0.794795i
$801$		0			0
$802$	22376.9	+	38757.9i	0.985231	+	1.70647i
$803$	−18893.3	+	32724.1i	−0.830298	+	1.43812i
$804$		0			0
$805$	40916.0	+	14969.5i	1.79143	+	0.655412i
$806$	11023.6			0.481751
$807$		0			0
$808$	14313.8	+	24792.3i	0.623217	+	1.07944i
$809$	16938.9	+	29339.0i	0.736142	+	1.27504i	0.954221	+	0.299104i	$0.0966877\pi$
$809$	16938.9	+	29339.0i	0.736142	+	1.27504i	−0.218079	+	0.975931i	$0.569979\pi$
$810$		0			0
$811$	15463.4			0.669537			0.334769	−	0.942300i	$-0.391342\pi$
$811$	15463.4			0.669537			0.334769	+	0.942300i	$0.391342\pi$
$812$	−58337.1	−	21343.2i	−2.52122	−	0.922414i
$813$		0			0
$814$	−4692.57	+	8127.77i	−0.202057	+	0.349973i
$815$	−16322.0	−	28270.5i	−0.701514	−	1.21506i
$816$		0			0
$817$	−5835.94	+	10108.1i	−0.249906	+	0.432851i
$818$	12422.3			0.530973
$819$		0			0
$820$	−143879.			−6.12740
$821$	−14573.3	+	25241.7i	−0.619503	+	1.07301i	0.370073	+	0.929003i	$0.379333\pi$
$821$	−14573.3	+	25241.7i	−0.619503	+	1.07301i	−0.989576	+	0.144008i	$0.954001\pi$
$822$		0			0
$823$	915.651	+	1585.95i	0.0387820	+	0.0671724i	0.884765	−	0.466038i	$-0.154319\pi$
$823$	915.651	+	1585.95i	0.0387820	+	0.0671724i	−0.845983	+	0.533210i	$0.820986\pi$
$824$	1818.75	−	3150.17i	0.0768922	−	0.133181i
$825$		0			0
$826$	11422.7	−	9552.33i	0.481169	−	0.402383i
$827$	19801.5			0.832609			0.416304	−	0.909225i	$-0.363325\pi$
$827$	19801.5			0.832609			0.416304	+	0.909225i	$0.363325\pi$
$828$		0			0
$829$	−10353.8	−	17933.3i	−0.433778	−	0.751326i	0.563417	−	0.826173i	$-0.309487\pi$
$829$	−10353.8	−	17933.3i	−0.433778	−	0.751326i	−0.997195	+	0.0748468i	$0.976153\pi$
$830$	11774.4	+	20393.9i	0.492404	+	0.852869i
$831$		0			0
$832$	8696.82			0.362389
$833$	−3718.02	+	1339.22i	−0.154648	+	0.0557038i
$834$		0			0
$835$	31049.4	−	53779.1i	1.28683	−	2.22886i
$836$	−21733.3	−	37643.1i	−0.899115	−	1.55731i
$837$		0			0
$838$	22700.5	−	39318.5i	0.935772	−	1.62080i
$839$	28880.2			1.18838			0.594192	−	0.804323i	$-0.297472\pi$
$839$	28880.2			1.18838			0.594192	+	0.804323i	$0.297472\pi$
$840$		0			0
$841$	27828.2			1.14101
$842$	27216.3	−	47140.0i	1.11394	−	1.92940i
$843$		0			0
$844$	35828.0	+	62055.9i	1.46120	+	2.53087i
$845$	19149.1	−	33167.2i	0.779585	−	1.35028i
$846$		0			0
$847$	7021.77	+	40214.5i	0.284853	+	1.63139i
$848$	8707.28			0.352605
$849$		0			0
$850$	−6165.41	−	10678.8i	−0.248790	−	0.430917i
$851$	2084.73	+	3610.86i	0.0839761	+	0.145451i
$852$		0			0
$853$	34006.5			1.36502			0.682509	−	0.730877i	$-0.260889\pi$
$853$	34006.5			1.36502			0.682509	+	0.730877i	$0.260889\pi$
$854$	16163.0	+	5913.38i	0.647641	+	0.236946i
$855$		0			0
$856$	14375.6	−	24899.2i	0.574003	−	0.994202i
$857$	−13905.0	−	24084.2i	−0.554243	−	0.959977i	−0.997962	−	0.0638114i	$-0.979674\pi$
$857$	−13905.0	−	24084.2i	−0.554243	−	0.959977i	0.443719	−	0.896166i	$-0.353659\pi$
$858$		0			0
$859$	−7769.19	+	13456.6i	−0.308593	+	0.534499i	−0.978055	−	0.208348i	$-0.933191\pi$
$859$	−7769.19	+	13456.6i	−0.308593	+	0.534499i	0.669462	+	0.742847i	$0.266525\pi$
$860$	64328.9			2.55069
$861$		0			0
$862$	33300.7			1.31581
$863$	17295.2	−	29956.2i	0.682196	−	1.18160i	−0.292113	−	0.956384i	$-0.594358\pi$
$863$	17295.2	−	29956.2i	0.682196	−	1.18160i	0.974309	−	0.225214i	$-0.0723083\pi$
$864$		0			0
$865$	−506.012	−	876.438i	−0.0198901	−	0.0344506i
$866$	11264.3	−	19510.3i	0.442005	−	0.765575i
$867$		0			0
$868$	−8863.84	−	50764.3i	−0.346611	−	1.98508i
$869$	−50658.2			−1.97752
$870$		0			0
$871$	3145.29	+	5447.80i	0.122358	+	0.211931i
$872$	−23002.5	−	39841.5i	−0.893307	−	1.54725i
$873$		0			0
$874$	−29835.4			−1.15469
$875$	26500.3	−	22161.2i	1.02386	−	0.856212i
$876$		0			0
$877$	6942.18	−	12024.2i	0.267298	−	0.462975i	−0.700865	−	0.713294i	$-0.747202\pi$
$877$	6942.18	−	12024.2i	0.267298	−	0.462975i	0.968163	+	0.250320i	$0.0805357\pi$
$878$	20499.4	+	35505.9i	0.787950	+	1.36477i
$879$		0			0
$880$	−18914.9	+	32761.5i	−0.724568	+	1.25499i
$881$	−50252.5			−1.92173			−0.960867	−	0.277009i	$-0.910657\pi$
$881$	−50252.5			−1.92173			−0.960867	+	0.277009i	$0.910657\pi$
$882$		0			0
$883$	−22551.2			−0.859466			−0.429733	−	0.902956i	$-0.641392\pi$
$883$	−22551.2			−0.859466			−0.429733	+	0.902956i	$0.641392\pi$
$884$	1032.54	−	1788.40i	0.0392850	−	0.0680436i
$885$		0			0
$886$	−12552.8	−	21742.1i	−0.475982	−	0.824425i
$887$	−14007.6	+	24261.9i	−0.530248	+	0.918417i	0.469129	+	0.883130i	$0.344568\pi$
$887$	−14007.6	+	24261.9i	−0.530248	+	0.918417i	−0.999377	+	0.0352873i	$0.988765\pi$
$888$		0			0
$889$	−22590.7	+	18891.7i	−0.852271	+	0.712721i
$890$	−81417.1			−3.06641
$891$		0			0
$892$	−1057.21	−	1831.15i	−0.0396840	−	0.0687346i
$893$	6816.91	+	11807.2i	0.255453	+	0.442457i
$894$		0			0
$895$	−69579.0			−2.59863
$896$	−8449.42	−	48390.9i	−0.315039	−	1.80427i
$897$		0			0
$898$	32177.4	−	55733.0i	1.19574	−	2.07108i
$899$	21659.1	+	37514.7i	0.803528	+	1.39175i
$900$		0			0
$901$	−1474.38	+	2553.70i	−0.0545157	+	0.0944240i
$902$	−148411.			−5.47844
$903$		0			0
$904$	326.462			0.0120110
$905$	−11976.8	+	20744.4i	−0.439913	+	0.761952i
$906$		0			0
$907$	−13412.9	−	23231.9i	−0.491035	−	0.850498i	0.508911	−	0.860819i	$-0.330048\pi$
$907$	−13412.9	−	23231.9i	−0.491035	−	0.850498i	−0.999947	+	0.0103208i	$0.996715\pi$
$908$	−36123.7	+	62568.2i	−1.32027	+	2.28678i
$909$		0			0
$910$	18914.8	+	6920.19i	0.689034	+	0.252090i
$911$	−9637.55			−0.350501			−0.175250	−	0.984524i	$-0.556074\pi$
$911$	−9637.55			−0.350501			−0.175250	+	0.984524i	$0.556074\pi$
$912$		0			0
$913$	7860.89	+	13615.5i	0.284948	+	0.493545i
$914$	−17354.2	−	30058.4i	−0.628037	−	1.08779i
$915$		0			0
$916$	−231.751			−0.00835945
$917$	716.380	+	4102.80i	0.0257982	+	0.147749i
$918$		0			0
$919$	−1879.62	+	3255.60i	−0.0674678	+	0.116858i	−0.897786	−	0.440432i	$-0.854825\pi$
$919$	−1879.62	+	3255.60i	−0.0674678	+	0.116858i	0.830318	+	0.557290i	$0.188159\pi$
$920$	37406.7	+	64790.2i	1.34050	+	2.32182i
$921$		0			0
$922$	−13463.1	+	23318.8i	−0.480893	+	0.832932i
$923$	−3895.95			−0.138935
$924$		0			0
$925$	7449.20			0.264787
$926$	−9767.58	+	16918.0i	−0.346634	+	0.600387i
$927$		0			0
$928$	10557.4	+	18285.9i	0.373451	+	0.646836i
$929$	2081.28	−	3604.88i	0.0735033	−	0.127312i	−0.826931	−	0.562303i	$-0.809915\pi$
$929$	2081.28	−	3604.88i	0.0735033	−	0.127312i	0.900434	+	0.434992i	$0.143249\pi$
$930$		0			0
$931$	13049.8	+	11024.5i	0.459389	+	0.388092i
$932$	−10678.4			−0.375302
$933$		0			0
$934$	12153.3	+	21050.1i	0.425768	+	0.737452i
$935$	−6405.59	−	11094.8i	−0.224049	−	0.388063i
$936$		0			0
$937$	−39048.7			−1.36144			−0.680718	−	0.732545i	$-0.738332\pi$
$937$	−39048.7			−1.36144			−0.680718	+	0.732545i	$0.738332\pi$
$938$	34853.2	−	29146.4i	1.21322	−	1.01457i
$939$		0			0
$940$	37571.0	−	65074.9i	1.30365	−	2.25799i
$941$	7507.70	+	13003.7i	0.260089	+	0.450488i	0.966265	−	0.257548i	$-0.0829147\pi$
$941$	7507.70	+	13003.7i	0.260089	+	0.450488i	−0.706176	+	0.708036i	$0.749581\pi$
$942$		0			0
$943$	−32966.8	+	57100.1i	−1.13844	+	1.97183i
$944$	5743.91			0.198038
$945$		0			0
$946$	66355.4			2.28055
$947$	−6233.93	+	10797.5i	−0.213913	+	0.370508i	−0.952936	−	0.303173i	$-0.901954\pi$
$947$	−6233.93	+	10797.5i	−0.213913	+	0.370508i	0.739023	+	0.673680i	$0.235287\pi$
$948$		0			0
$949$	3880.22	+	6720.74i	0.132726	+	0.229889i
$950$	−26652.1	+	46162.7i	−0.910218	+	1.57654i
$951$		0			0
$952$	−6372.80	−	2331.56i	−0.216958	−	0.0793762i
$953$	26584.1			0.903612			0.451806	−	0.892116i	$-0.350780\pi$
$953$	26584.1			0.903612			0.451806	+	0.892116i	$0.350780\pi$
$954$		0			0
$955$	−8789.72	−	15224.2i	−0.297831	−	0.515859i
$956$	−467.386	−	809.537i	−0.0158121	−	0.0273873i
$957$		0			0
$958$	−20003.1			−0.674605
$959$	−39163.6	−	14328.4i	−1.31873	−	0.482469i
$960$		0			0
$961$	−3072.41	+	5321.57i	−0.103132	+	0.178630i
$962$	963.740	+	1669.25i	0.0322996	+	0.0559446i
$963$		0			0
$964$	−24584.1	+	42581.0i	−0.821371	+	1.42266i
$965$	−26423.5			−0.881455
$966$		0			0
$967$	26613.6			0.885041			0.442521	−	0.896758i	$-0.354084\pi$
$967$	26613.6			0.885041			0.442521	+	0.896758i	$0.354084\pi$
$968$	−35049.5	+	60707.5i	−1.16377	+	2.01572i
$969$		0			0
$970$	20286.8	+	35137.7i	0.671514	+	1.16310i
$971$	5136.34	−	8896.40i	0.169756	−	0.294026i	−0.768578	−	0.639756i	$-0.779035\pi$
$971$	5136.34	−	8896.40i	0.169756	−	0.294026i	0.938334	+	0.345730i	$0.112369\pi$
$972$		0			0
$973$	42839.5	−	35825.0i	1.41148	−	1.18037i
$974$	20481.9			0.673803
$975$		0			0
$976$	3319.48	+	5749.51i	0.108867	+	0.188563i
$977$	−18448.9	−	31954.4i	−0.604127	−	1.04638i	−0.992189	−	0.124745i	$-0.960189\pi$
$977$	−18448.9	−	31954.4i	−0.604127	−	1.04638i	0.388062	−	0.921633i	$-0.373145\pi$
$978$		0			0
$979$	−54356.2			−1.77450
$980$	16658.8	−	92668.0i	0.543006	−	3.02058i
$981$		0			0
$982$	−4225.09	+	7318.06i	−0.137299	+	0.237809i
$983$	10721.7	+	18570.5i	0.347883	+	0.602551i	0.985873	−	0.167493i	$-0.0535673\pi$
$983$	10721.7	+	18570.5i	0.347883	+	0.602551i	−0.637990	+	0.770044i	$0.720234\pi$
$984$		0			0
$985$	−28124.4	+	48712.9i	−0.909765	+	1.57576i
$986$	12537.7			0.404951
$987$		0			0
$988$	−8926.97			−0.287454
$989$	14739.6	−	25529.7i	0.473905	−	0.820827i
$990$		0			0
$991$	8333.94	+	14434.8i	0.267141	+	0.462701i	0.968122	−	0.250478i	$-0.0805878\pi$
$991$	8333.94	+	14434.8i	0.267141	+	0.462701i	−0.700982	+	0.713179i	$0.747254\pi$
$992$	−8758.15	+	15169.6i	−0.280314	+	0.485518i
$993$		0			0
$994$	4840.02	+	27719.4i	0.154443	+	0.884514i
$995$	−412.266			−0.0131354
$996$		0			0
$997$	−10124.4	−	17535.9i	−0.321606	−	0.557039i	0.659213	−	0.751956i	$-0.270889\pi$
$997$	−10124.4	−	17535.9i	−0.321606	−	0.557039i	−0.980820	+	0.194917i	$0.937556\pi$
$998$	16321.7	+	28270.1i	0.517691	+	0.896667i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.e.f.163.2	yes	14
3.2	odd	2		189.4.e.g.163.6	yes	14
7.2	even	3		1323.4.a.bj.1.6		7
7.4	even	3	inner	189.4.e.f.109.2	✓	14
7.5	odd	6		1323.4.a.bk.1.6		7
21.2	odd	6		1323.4.a.bi.1.2		7
21.5	even	6		1323.4.a.bh.1.2		7
21.11	odd	6		189.4.e.g.109.6	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.4.e.f.109.2	✓	14	7.4	even	3	inner
189.4.e.f.163.2	yes	14	1.1	even	1	trivial
189.4.e.g.109.6	yes	14	21.11	odd	6
189.4.e.g.163.6	yes	14	3.2	odd	2
1323.4.a.bh.1.2		7	21.5	even	6
1323.4.a.bi.1.2		7	21.2	odd	6
1323.4.a.bj.1.6		7	7.2	even	3
1323.4.a.bk.1.6		7	7.5	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.38108 + 4.12414i) q^{2} +(-7.33904 - 12.7116i) q^{4} +(-9.35067 + 16.1958i) q^{5} +(14.2072 - 11.8809i) q^{7} +31.8020 q^{8} +(-44.5293 - 77.1270i) q^{10} +(-29.7289 - 51.4920i) q^{11} -12.2112 q^{13} +(15.1702 + 86.8818i) q^{14} +(-17.0107 + 29.4633i) q^{16} +(-5.76073 - 9.97788i) q^{17} +(-24.9027 + 43.1328i) q^{19} +274.500 q^{20} +283.147 q^{22} +(62.8958 - 108.939i) q^{23} +(-112.370 - 194.631i) q^{25} +(29.0758 - 50.3607i) q^{26} +(-255.292 - 93.4013i) q^{28} +228.511 q^{29} +(94.7837 + 164.170i) q^{31} +(46.2007 + 80.0220i) q^{32} +54.8669 q^{34} +(59.5747 + 341.192i) q^{35} +(-16.5729 + 28.7051i) q^{37} +(-118.590 - 205.405i) q^{38} +(-297.370 + 515.060i) q^{40} -524.149 q^{41} +234.349 q^{43} +(-436.363 + 755.803i) q^{44} +(299.519 + 518.783i) q^{46} +(136.871 - 237.067i) q^{47} +(60.6878 - 337.588i) q^{49} +1070.25 q^{50} +(89.6185 + 155.224i) q^{52} +(-127.968 - 221.647i) q^{53} +1111.94 q^{55} +(451.817 - 377.837i) q^{56} +(-544.101 + 942.411i) q^{58} +(-84.4163 - 146.213i) q^{59} +(97.5707 - 168.997i) q^{61} -902.749 q^{62} -712.200 q^{64} +(114.183 - 197.771i) q^{65} +(-257.574 - 446.132i) q^{67} +(-84.5564 + 146.456i) q^{68} +(-1548.98 - 566.709i) q^{70} +319.048 q^{71} +(-317.759 - 550.375i) q^{73} +(-78.9227 - 136.698i) q^{74} +731.048 q^{76} +(-1034.14 - 378.349i) q^{77} +(426.001 - 737.855i) q^{79} +(-318.122 - 551.004i) q^{80} +(1248.04 - 2161.67i) q^{82} -264.419 q^{83} +215.467 q^{85} +(-558.004 + 966.491i) q^{86} +(-945.439 - 1637.55i) q^{88} +(457.099 - 791.718i) q^{89} +(-173.487 + 145.080i) q^{91} -1846.38 q^{92} +(651.800 + 1128.95i) q^{94} +(-465.714 - 806.640i) q^{95} -455.582 q^{97} +(1247.76 + 1054.11i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 31 q^{4} + q^{5} + 20 q^{7} + 168 q^{8} - 12 q^{10} - 98 q^{11} - 248 q^{13} - 134 q^{14} - 139 q^{16} - 30 q^{17} - 182 q^{19} - 220 q^{20} + 552 q^{22} + 6 q^{23} - 388 q^{25} + 245 q^{26}+ \cdots + 10160 q^{98}+O(q^{100}) \) 14 * q - q^2 - 31 * q^4 + q^5 + 20 * q^7 + 168 * q^8 - 12 * q^10 - 98 * q^11 - 248 * q^13 - 134 * q^14 - 139 * q^16 - 30 * q^17 - 182 * q^19 - 220 * q^20 + 552 * q^22 + 6 * q^23 - 388 * q^25 + 245 * q^26 + 425 * q^28 + 646 * q^29 - 26 * q^31 - 398 * q^32 + 228 * q^34 + 1025 * q^35 + 112 * q^37 - 1015 * q^38 + 147 * q^40 - 1048 * q^41 + 16 * q^43 - 937 * q^44 + 339 * q^46 - 288 * q^47 + 446 * q^49 + 5152 * q^50 + 1075 * q^52 - 1353 * q^53 + 312 * q^55 + 1980 * q^56 + 81 * q^58 - 165 * q^59 - 56 * q^61 - 2430 * q^62 - 3412 * q^64 - 1694 * q^65 + 988 * q^67 - 2625 * q^68 - 4941 * q^70 + 1584 * q^71 - 1487 * q^73 - 2736 * q^74 + 3904 * q^76 - 34 * q^77 + 1273 * q^79 + 2501 * q^80 + 2049 * q^82 - 2340 * q^83 + 432 * q^85 + 160 * q^86 - 9 * q^88 - 1058 * q^89 + 3538 * q^91 + 7668 * q^92 - 1653 * q^94 - 3260 * q^95 - 7460 * q^97 + 10160 * q^98

Introduction

L-functions

Modular forms

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Database

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