LMFDB - Embedded newform 490.4.c.f.99.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [490,4,Mod(99,490)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(490, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("490.99"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	490.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,-48,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$28.9109359028$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 185x^{10} + 12748x^{8} + 405460x^{6} + 5908496x^{4} + 33016000x^{2} + 60840000 $ x^12 + 185x^10 + 12748x^8 + 405460x^6 + 5908496x^4 + 33016000*x^2 + 60840000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.9
Root			$-2.06759i$ of defining polynomial
Character	$\chi$	$=$	490.99
Dual form			490.4.c.f.99.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000i q^{2} -3.06759i q^{3} -4.00000 q^{4} +(-9.26709 + 6.25468i) q^{5} +6.13518 q^{6} -8.00000i q^{8} +17.5899 q^{9} +(-12.5094 - 18.5342i) q^{10} -49.5016 q^{11} +12.2704i q^{12} +44.6154i q^{13} +(19.1868 + 28.4276i) q^{15} +16.0000 q^{16} +39.2912i q^{17} +35.1798i q^{18} +56.3157 q^{19} +(37.0684 - 25.0187i) q^{20} -99.0033i q^{22} -91.6603i q^{23} -24.5407 q^{24} +(46.7580 - 115.925i) q^{25} -89.2307 q^{26} -136.783i q^{27} -281.845 q^{29} +(-56.8553 + 38.3736i) q^{30} +70.5654 q^{31} +32.0000i q^{32} +151.851i q^{33} -78.5824 q^{34} -70.3596 q^{36} -197.089i q^{37} +112.631i q^{38} +136.862 q^{39} +(50.0374 + 74.1367i) q^{40} +399.021 q^{41} -203.567i q^{43} +198.007 q^{44} +(-163.007 + 110.019i) q^{45} +183.321 q^{46} -68.4988i q^{47} -49.0814i q^{48} +(231.851 + 93.5161i) q^{50} +120.529 q^{51} -178.461i q^{52} -617.486i q^{53} +273.567 q^{54} +(458.736 - 309.617i) q^{55} -172.753i q^{57} -563.690i q^{58} -480.513 q^{59} +(-76.7471 - 113.711i) q^{60} -23.4974 q^{61} +141.131i q^{62} -64.0000 q^{64} +(-279.055 - 413.455i) q^{65} -303.701 q^{66} -252.124i q^{67} -157.165i q^{68} -281.176 q^{69} +835.640 q^{71} -140.719i q^{72} -257.786i q^{73} +394.179 q^{74} +(-355.611 - 143.434i) q^{75} -225.263 q^{76} +273.723i q^{78} +773.700 q^{79} +(-148.273 + 100.075i) q^{80} +55.3315 q^{81} +798.043i q^{82} -1341.21i q^{83} +(-245.754 - 364.115i) q^{85} +407.134 q^{86} +864.584i q^{87} +396.013i q^{88} -1301.12 q^{89} +(-220.038 - 326.014i) q^{90} +366.641i q^{92} -216.466i q^{93} +136.998 q^{94} +(-521.883 + 352.236i) q^{95} +98.1629 q^{96} +323.729i q^{97} -870.729 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 48 q^{4} + 8 q^{5} + 28 q^{6} - 62 q^{9} - 12 q^{10} + 62 q^{11} + 86 q^{15} + 192 q^{16} - 186 q^{19} - 32 q^{20} - 112 q^{24} - 126 q^{25} + 236 q^{26} - 338 q^{29} - 28 q^{30} + 652 q^{31} - 272 q^{34}+ \cdots - 8546 q^{99}+O(q^{100}) $ 12 * q - 48 * q^4 + 8 * q^5 + 28 * q^6 - 62 * q^9 - 12 * q^10 + 62 * q^11 + 86 * q^15 + 192 * q^16 - 186 * q^19 - 32 * q^20 - 112 * q^24 - 126 * q^25 + 236 * q^26 - 338 * q^29 - 28 * q^30 + 652 * q^31 - 272 * q^34 + 248 * q^36 + 868 * q^39 + 48 * q^40 + 396 * q^41 - 248 * q^44 - 664 * q^45 - 376 * q^46 + 160 * q^50 + 1448 * q^51 - 1540 * q^54 + 298 * q^55 - 1336 * q^59 - 344 * q^60 + 314 * q^61 - 768 * q^64 - 1862 * q^65 + 1600 * q^66 + 90 * q^69 + 2216 * q^71 + 1012 * q^74 + 4550 * q^75 + 744 * q^76 + 1772 * q^79 + 128 * q^80 - 1228 * q^81 + 2282 * q^85 - 396 * q^86 - 6094 * q^89 + 100 * q^90 - 3604 * q^94 - 1166 * q^95 + 448 * q^96 - 8546 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$1$	$-1$

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 $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$		−	3.06759i		−	0.590358i	−0.955442	−	0.295179i	$-0.904621\pi$
$3$		−	3.06759i		−	0.590358i	0.955442	−	0.295179i	$-0.0953793\pi$
$4$	−4.00000			−0.500000
$5$	−9.26709	+	6.25468i	−0.828874	+	0.559435i
$5$	−9.26709	+	6.25468i	−0.828874	+	0.559435i
$6$	6.13518			0.417446
$7$		0			0
$7$		0			0
$8$		−	8.00000i		−	0.353553i
$9$	17.5899			0.651478
$10$	−12.5094	−	18.5342i	−0.395581	−	0.586102i
$11$	−49.5016			−1.35685			−0.678423	−	0.734672i	$-0.737336\pi$
$11$	−49.5016			−1.35685			−0.678423	+	0.734672i	$0.737336\pi$
$12$			12.2704i			0.295179i
$13$			44.6154i			0.951852i	0.879485	+	0.475926i	$0.157887\pi$
$13$			44.6154i			0.951852i	−0.879485	+	0.475926i	$0.842113\pi$
$14$		0			0
$15$	19.1868	+	28.4276i	0.330267	+	0.489332i
$16$	16.0000			0.250000
$17$			39.2912i			0.560560i	0.959918	+	0.280280i	$0.0904273\pi$
$17$			39.2912i			0.560560i	−0.959918	+	0.280280i	$0.909573\pi$
$18$			35.1798i			0.460664i
$19$	56.3157			0.679984			0.339992	−	0.940428i	$-0.389576\pi$
$19$	56.3157			0.679984			0.339992	+	0.940428i	$0.389576\pi$
$20$	37.0684	−	25.0187i	0.414437	−	0.279718i
$21$		0			0
$22$		−	99.0033i		−	0.959435i
$23$		−	91.6603i		−	0.830978i	−0.909598	−	0.415489i	$-0.863610\pi$
$23$		−	91.6603i		−	0.830978i	0.909598	−	0.415489i	$-0.136390\pi$
$24$	−24.5407			−0.208723
$25$	46.7580	−	115.925i	0.374064	−	0.927403i
$26$	−89.2307			−0.673061
$27$		−	136.783i		−	0.974963i
$28$		0			0
$29$	−281.845			−1.80473			−0.902367	−	0.430969i	$-0.858172\pi$
$29$	−281.845			−1.80473			−0.902367	+	0.430969i	$0.858172\pi$
$30$	−56.8553	+	38.3736i	−0.346010	+	0.233534i
$31$	70.5654			0.408836			0.204418	−	0.978884i	$-0.434470\pi$
$31$	70.5654			0.408836			0.204418	+	0.978884i	$0.434470\pi$
$32$			32.0000i			0.176777i
$33$			151.851i			0.801025i
$34$	−78.5824			−0.396376
$35$		0			0
$36$	−70.3596			−0.325739
$37$		−	197.089i		−	0.875710i	−0.899046	−	0.437855i	$-0.855738\pi$
$37$		−	197.089i		−	0.875710i	0.899046	−	0.437855i	$-0.144262\pi$
$38$			112.631i			0.480822i
$39$	136.862			0.561933
$40$	50.0374	+	74.1367i	0.197790	+	0.293051i
$41$	399.021			1.51992			0.759959	−	0.649971i	$-0.225219\pi$
$41$	399.021			1.51992			0.759959	+	0.649971i	$0.225219\pi$
$42$		0			0
$43$		−	203.567i		−	0.721946i	−0.932576	−	0.360973i	$-0.882445\pi$
$43$		−	203.567i		−	0.721946i	0.932576	−	0.360973i	$-0.117555\pi$
$44$	198.007			0.678423
$45$	−163.007	+	110.019i	−0.539993	+	0.364460i
$46$	183.321			0.587590
$47$		−	68.4988i		−	0.212587i	−0.994335	−	0.106293i	$-0.966102\pi$
$47$		−	68.4988i		−	0.212587i	0.994335	−	0.106293i	$-0.0338983\pi$
$48$		−	49.0814i		−	0.147589i
$49$		0			0
$50$	231.851	+	93.5161i	0.655773	+	0.264503i
$51$	120.529			0.330931
$52$		−	178.461i		−	0.475926i
$53$		−	617.486i		−	1.60034i	−0.599771	−	0.800172i	$-0.704742\pi$
$53$		−	617.486i		−	1.60034i	0.599771	−	0.800172i	$-0.295258\pi$
$54$	273.567			0.689403
$55$	458.736	−	309.617i	1.12465	−	0.759068i
$56$		0			0
$57$		−	172.753i		−	0.401434i
$58$		−	563.690i		−	1.27614i
$59$	−480.513			−1.06029			−0.530147	−	0.847905i	$-0.677863\pi$
$59$	−480.513			−1.06029			−0.530147	+	0.847905i	$0.677863\pi$
$60$	−76.7471	−	113.711i	−0.165134	−	0.244666i
$61$	−23.4974			−0.0493202			−0.0246601	−	0.999696i	$-0.507850\pi$
$61$	−23.4974			−0.0493202			−0.0246601	+	0.999696i	$0.507850\pi$
$62$			141.131i			0.289091i
$63$		0			0
$64$	−64.0000			−0.125000
$65$	−279.055	−	413.455i	−0.532500	−	0.788965i
$66$	−303.701			−0.566410
$67$		−	252.124i		−	0.459729i	−0.973223	−	0.229865i	$-0.926172\pi$
$67$		−	252.124i		−	0.459729i	0.973223	−	0.229865i	$-0.0738283\pi$
$68$		−	157.165i		−	0.280280i
$69$	−281.176			−0.490574
$70$		0			0
$71$	835.640			1.39679			0.698396	−	0.715711i	$-0.253897\pi$
$71$	835.640			1.39679			0.698396	+	0.715711i	$0.253897\pi$
$72$		−	140.719i		−	0.230332i
$73$		−	257.786i		−	0.413309i	−0.978414	−	0.206654i	$-0.933742\pi$
$73$		−	257.786i		−	0.413309i	0.978414	−	0.206654i	$-0.0662576\pi$
$74$	394.179			0.619221
$75$	−355.611	−	143.434i	−0.547500	−	0.220832i
$76$	−225.263			−0.339992
$77$		0			0
$78$			273.723i			0.397347i
$79$	773.700			1.10187			0.550937	−	0.834547i	$-0.314270\pi$
$79$	773.700			1.10187			0.550937	+	0.834547i	$0.314270\pi$
$80$	−148.273	+	100.075i	−0.207218	+	0.139859i
$81$	55.3315			0.0759006
$82$			798.043i			1.07474i
$83$		−	1341.21i		−	1.77369i	−0.462065	−	0.886846i	$-0.652891\pi$
$83$		−	1341.21i		−	1.77369i	0.462065	−	0.886846i	$-0.347109\pi$
$84$		0			0
$85$	−245.754	−	364.115i	−0.313597	−	0.464633i
$86$	407.134			0.510493
$87$			864.584i			1.06544i
$88$			396.013i			0.479717i
$89$	−1301.12			−1.54964			−0.774821	−	0.632181i	$-0.782160\pi$
$89$	−1301.12			−1.54964			−0.774821	+	0.632181i	$0.782160\pi$
$90$	−220.038	−	326.014i	−0.257712	−	0.381833i
$91$		0			0
$92$			366.641i			0.415489i
$93$		−	216.466i		−	0.241360i
$94$	136.998			0.150322
$95$	−521.883	+	352.236i	−0.563621	+	0.380407i
$96$	98.1629			0.104362
$97$			323.729i			0.338862i	0.985542	+	0.169431i	$0.0541931\pi$
$97$			323.729i			0.338862i	−0.985542	+	0.169431i	$0.945807\pi$
$98$		0			0
$99$	−870.729			−0.883955
$100$	−187.032	+	463.701i	−0.187032	+	0.463701i
$101$	1181.02			1.16352			0.581761	−	0.813360i	$-0.302364\pi$
$101$	1181.02			1.16352			0.581761	+	0.813360i	$0.302364\pi$
$102$			241.059i			0.234003i
$103$		−	732.042i		−	0.700294i	−0.936695	−	0.350147i	$-0.886132\pi$
$103$		−	732.042i		−	0.700294i	0.936695	−	0.350147i	$-0.113868\pi$
$104$	356.923			0.336530
$105$		0			0
$106$	1234.97			1.13161
$107$		−	1338.04i		−	1.20891i	−0.796639	−	0.604455i	$-0.793391\pi$
$107$		−	1338.04i		−	1.20891i	0.796639	−	0.604455i	$-0.206609\pi$
$108$			547.134i			0.487481i
$109$	51.7571			0.0454810			0.0227405	−	0.999741i	$-0.492761\pi$
$109$	51.7571			0.0454810			0.0227405	+	0.999741i	$0.492761\pi$
$110$	619.233	+	917.473i	0.536742	+	0.795251i
$111$	−604.589			−0.516982
$112$		0			0
$113$			471.803i			0.392774i	0.980526	+	0.196387i	$0.0629209\pi$
$113$			471.803i			0.392774i	−0.980526	+	0.196387i	$0.937079\pi$
$114$	345.507			0.283857
$115$	573.306	+	849.424i	0.464878	+	0.688776i
$116$	1127.38			0.902367
$117$			784.780i			0.620110i
$118$		−	961.025i		−	0.749742i
$119$		0			0
$120$	227.421	−	153.494i	0.173005	−	0.116767i
$121$	1119.41			0.841031
$122$		−	46.9948i		−	0.0348746i
$123$		−	1224.03i		−	0.897296i
$124$	−282.262			−0.204418
$125$	291.765	+	1366.75i	0.208770	+	0.977965i
$126$		0			0
$127$		−	202.294i		−	0.141344i	−0.997500	−	0.0706721i	$-0.977486\pi$
$127$		−	202.294i		−	0.141344i	0.997500	−	0.0706721i	$-0.0225144\pi$
$128$		−	128.000i		−	0.0883883i
$129$	−624.460			−0.426206
$130$	826.909	−	558.109i	0.557883	−	0.376534i
$131$	−1168.96			−0.779635			−0.389817	−	0.920892i	$-0.627462\pi$
$131$	−1168.96			−0.779635			−0.389817	+	0.920892i	$0.627462\pi$
$132$		−	607.403i		−	0.400512i
$133$		0			0
$134$	504.248			0.325078
$135$	855.537	+	1267.59i	0.545429	+	0.808121i
$136$	314.330			0.198188
$137$		−	146.718i		−	0.0914958i	−0.998953	−	0.0457479i	$-0.985433\pi$
$137$		−	146.718i		−	0.0914958i	0.998953	−	0.0457479i	$-0.0145671\pi$
$138$		−	562.352i		−	0.346888i
$139$	2505.64			1.52896			0.764479	−	0.644648i	$-0.222996\pi$
$139$	2505.64			1.52896			0.764479	+	0.644648i	$0.222996\pi$
$140$		0			0
$141$	−210.126			−0.125502
$142$			1671.28i			0.987681i
$143$		−	2208.53i		−	1.29152i
$144$	281.438			0.162869
$145$	2611.88	−	1762.85i	1.49590	−	1.00963i
$146$	515.571			0.292253
$147$		0			0
$148$			788.357i			0.437855i
$149$	−2108.18			−1.15912			−0.579559	−	0.814930i	$-0.696775\pi$
$149$	−2108.18			−1.15912			−0.579559	+	0.814930i	$0.696775\pi$
$150$	286.869	−	711.223i	0.156152	−	0.387141i
$151$	−2215.51			−1.19401			−0.597004	−	0.802238i	$-0.703642\pi$
$151$	−2215.51			−1.19401			−0.597004	+	0.802238i	$0.703642\pi$
$152$		−	450.525i		−	0.240411i
$153$			691.128i			0.365192i
$154$		0			0
$155$	−653.936	+	441.364i	−0.338874	+	0.228717i
$156$	−547.446			−0.280967
$157$			2262.03i			1.14987i	0.818199	+	0.574935i	$0.194972\pi$
$157$			2262.03i			1.14987i	−0.818199	+	0.574935i	$0.805028\pi$
$158$			1547.40i			0.779143i
$159$	−1894.19			−0.944775
$160$	−200.150	−	296.547i	−0.0988951	−	0.146526i
$161$		0			0
$162$			110.663i			0.0536698i
$163$			87.7158i			0.0421499i	0.999778	+	0.0210750i	$0.00670886\pi$
$163$			87.7158i			0.0421499i	−0.999778	+	0.0210750i	$0.993291\pi$
$164$	−1596.09			−0.759959
$165$	−949.777	−	1407.21i	−0.448122	−	0.663949i
$166$	2682.41			1.25419
$167$			1851.38i			0.857868i	0.903336	+	0.428934i	$0.141111\pi$
$167$			1851.38i			0.857868i	−0.903336	+	0.428934i	$0.858889\pi$
$168$		0			0
$169$	206.469			0.0939779
$170$	728.230	−	491.508i	0.328545	−	0.221747i
$171$	990.587			0.442995
$172$			814.268i			0.360973i
$173$			1842.08i			0.809541i	0.914418	+	0.404771i	$0.132649\pi$
$173$			1842.08i			0.809541i	−0.914418	+	0.404771i	$0.867351\pi$
$174$	−1729.17			−0.753379
$175$		0			0
$176$	−792.026			−0.339211
$177$			1474.02i			0.625953i
$178$		−	2602.23i		−	1.09576i
$179$	−748.532			−0.312558			−0.156279	−	0.987713i	$-0.549950\pi$
$179$	−748.532			−0.312558			−0.156279	+	0.987713i	$0.549950\pi$
$180$	652.029	−	440.076i	0.269996	−	0.182230i
$181$	−1393.90			−0.572418			−0.286209	−	0.958167i	$-0.592395\pi$
$181$	−1393.90			−0.572418			−0.286209	+	0.958167i	$0.592395\pi$
$182$		0			0
$183$			72.0803i			0.0291166i
$184$	−733.282			−0.293795
$185$	1232.73	+	1826.44i	0.489903	+	0.725853i
$186$	432.931			0.170667
$187$		−	1944.98i		−	0.760593i
$188$			273.995i			0.106293i
$189$		0			0
$190$	−704.473	−	1043.77i	−0.268989	−	0.398541i
$191$	−958.174			−0.362990			−0.181495	−	0.983392i	$-0.558094\pi$
$191$	−958.174			−0.362990			−0.181495	+	0.983392i	$0.558094\pi$
$192$			196.326i			0.0737947i
$193$			4577.04i			1.70706i	0.521044	+	0.853530i	$0.325543\pi$
$193$			4577.04i			1.70706i	−0.521044	+	0.853530i	$0.674457\pi$
$194$	−647.457			−0.239612
$195$	−1268.31	+	856.025i	−0.465772	+	0.314365i
$196$		0			0
$197$		−	3429.27i		−	1.24023i	−0.784511	−	0.620115i	$-0.787086\pi$
$197$		−	3429.27i		−	1.24023i	0.784511	−	0.620115i	$-0.212914\pi$
$198$		−	1741.46i		−	0.625050i
$199$	146.016			0.0520140			0.0260070	−	0.999662i	$-0.491721\pi$
$199$	146.016			0.0520140			0.0260070	+	0.999662i	$0.491721\pi$
$200$	−927.403	−	374.064i	−0.327886	−	0.132252i
$201$	−773.413			−0.271405
$202$			2362.04i			0.822734i
$203$		0			0
$204$	−482.117			−0.165465
$205$	−3697.77	+	2495.75i	−1.25982	+	0.850296i
$206$	1464.08			0.495182
$207$		−	1612.29i		−	0.541363i
$208$			713.846i			0.237963i
$209$	−2787.72			−0.922634
$210$		0			0
$211$	−705.410			−0.230154			−0.115077	−	0.993357i	$-0.536711\pi$
$211$	−705.410			−0.230154			−0.115077	+	0.993357i	$0.536711\pi$
$212$			2469.94i			0.800172i
$213$		−	2563.40i		−	0.824607i
$214$	2676.08			0.854829
$215$	1273.25	+	1886.47i	0.403882	+	0.598402i
$216$	−1094.27			−0.344701
$217$		0			0
$218$			103.514i			0.0321600i
$219$	−790.781			−0.244000
$220$	−1834.95	+	1238.47i	−0.562327	+	0.379534i
$221$	−1752.99			−0.533570
$222$		−	1209.18i		−	0.365562i
$223$			2232.07i			0.670271i	0.942170	+	0.335135i	$0.108782\pi$
$223$			2232.07i			0.670271i	−0.942170	+	0.335135i	$0.891218\pi$
$224$		0			0
$225$	822.469	−	2039.11i	0.243694	−	0.604182i
$226$	−943.606			−0.277733
$227$		−	5464.96i		−	1.59789i	−0.601401	−	0.798947i	$-0.705391\pi$
$227$		−	5464.96i		−	1.59789i	0.601401	−	0.798947i	$-0.294609\pi$
$228$			691.014i			0.200717i
$229$	−1943.89			−0.560942			−0.280471	−	0.959862i	$-0.590491\pi$
$229$	−1943.89			−0.560942			−0.280471	+	0.959862i	$0.590491\pi$
$230$	−1698.85	+	1146.61i	−0.487038	+	0.328719i
$231$		0			0
$232$			2254.76i			0.638070i
$233$		−	3307.25i		−	0.929893i	−0.885339	−	0.464946i	$-0.846074\pi$
$233$		−	3307.25i		−	0.929893i	0.885339	−	0.464946i	$-0.153926\pi$
$234$	−1569.56			−0.438484
$235$	428.438	+	634.785i	0.118929	+	0.176208i
$236$	1922.05			0.530147
$237$		−	2373.39i		−	0.650500i
$238$		0			0
$239$	−6107.99			−1.65311			−0.826554	−	0.562857i	$-0.809702\pi$
$239$	−6107.99			−1.65311			−0.826554	+	0.562857i	$0.809702\pi$
$240$	306.989	+	454.842i	0.0825668	+	0.122333i
$241$	−3962.60			−1.05914			−0.529571	−	0.848265i	$-0.677647\pi$
$241$	−3962.60			−1.05914			−0.529571	+	0.848265i	$0.677647\pi$
$242$			2238.82i			0.594699i
$243$		−	3862.89i		−	1.01977i
$244$	93.9895			0.0246601
$245$		0			0
$246$	2448.07			0.634484
$247$			2512.54i			0.647244i
$248$		−	564.523i		−	0.144545i
$249$	−4114.27			−1.04711
$250$	−2733.49	+	583.529i	−0.691526	+	0.147623i
$251$	−3.92299			−0.000986522			−0.000493261	−	1.00000i	$-0.500157\pi$
$251$	−3.92299			−0.000986522			−0.000493261		1.00000i	$0.500157\pi$
$252$		0			0
$253$			4537.33i			1.12751i
$254$	404.589			0.0999455
$255$	−1116.96	+	753.872i	−0.274300	+	0.185134i
$256$	256.000			0.0625000
$257$		−	219.595i		−	0.0532994i	−0.999645	−	0.0266497i	$-0.991516\pi$
$257$		−	219.595i		−	0.0532994i	0.999645	−	0.0266497i	$-0.00848386\pi$
$258$		−	1248.92i		−	0.301373i
$259$		0			0
$260$	1116.22	+	1653.82i	0.266250	+	0.394483i
$261$	−4957.62			−1.17574
$262$		−	2337.91i		−	0.551285i
$263$			5467.72i			1.28195i	0.767560	+	0.640977i	$0.221471\pi$
$263$			5467.72i			1.28195i	−0.767560	+	0.640977i	$0.778529\pi$
$264$	1214.81			0.283205
$265$	3862.17	+	5722.30i	0.895289	+	1.32648i
$266$		0			0
$267$			3991.29i			0.914843i
$268$			1008.50i			0.229865i
$269$	291.731			0.0661233			0.0330616	−	0.999453i	$-0.489474\pi$
$269$	291.731			0.0661233			0.0330616	+	0.999453i	$0.489474\pi$
$270$	−2535.17	+	1711.07i	−0.571428	+	0.385676i
$271$	2661.02			0.596478			0.298239	−	0.954491i	$-0.403601\pi$
$271$	2661.02			0.596478			0.298239	+	0.954491i	$0.403601\pi$
$272$			628.659i			0.140140i
$273$		0			0
$274$	293.435			0.0646973
$275$	−2314.60	+	5738.49i	−0.507547	+	1.25834i
$276$	1124.70			0.245287
$277$		−	4502.66i		−	0.976673i	−0.872655	−	0.488336i	$-0.837604\pi$
$277$		−	4502.66i		−	0.976673i	0.872655	−	0.488336i	$-0.162396\pi$
$278$			5011.27i			1.08114i
$279$	1241.24			0.266348
$280$		0			0
$281$	−462.388			−0.0981628			−0.0490814	−	0.998795i	$-0.515629\pi$
$281$	−462.388			−0.0981628			−0.0490814	+	0.998795i	$0.515629\pi$
$282$		−	420.253i		−	0.0887435i
$283$		−	7145.71i		−	1.50095i	−0.660899	−	0.750474i	$-0.729825\pi$
$283$		−	7145.71i		−	1.50095i	0.660899	−	0.750474i	$-0.270175\pi$
$284$	−3342.56			−0.698396
$285$	1080.52	+	1600.92i	0.224576	+	0.332738i
$286$	4417.07			0.913240
$287$		0			0
$288$			562.877i			0.115166i
$289$	3369.20			0.685773
$290$	3525.70	+	5223.76i	0.713917	+	1.05776i
$291$	993.066			0.200050
$292$			1031.14i			0.206654i
$293$		−	8656.21i		−	1.72594i	−0.505254	−	0.862971i	$-0.668601\pi$
$293$		−	8656.21i		−	1.72594i	0.505254	−	0.862971i	$-0.331399\pi$
$294$		0			0
$295$	4452.95	−	3005.45i	0.878851	−	0.593166i
$296$	−1576.71			−0.309610
$297$			6771.01i			1.32287i
$298$		−	4216.36i		−	0.819621i
$299$	4089.46			0.790968
$300$	1422.45	+	573.738i	0.273750	+	0.110416i
$301$		0			0
$302$		−	4431.01i		−	0.844291i
$303$		−	3622.88i		−	0.686894i
$304$	901.051			0.169996
$305$	217.752	−	146.969i	0.0408802	−	0.0275915i
$306$	−1382.26			−0.258230
$307$			4296.26i			0.798699i	0.916799	+	0.399349i	$0.130764\pi$
$307$			4296.26i			0.798699i	−0.916799	+	0.399349i	$0.869236\pi$
$308$		0			0
$309$	−2245.60			−0.413424
$310$	−882.728	−	1307.87i	−0.161728	−	0.239620i
$311$	3935.13			0.717494			0.358747	−	0.933435i	$-0.383204\pi$
$311$	3935.13			0.717494			0.358747	+	0.933435i	$0.383204\pi$
$312$		−	1094.89i		−	0.198673i
$313$		−	10498.9i		−	1.89596i	−0.318334	−	0.947979i	$-0.603123\pi$
$313$		−	10498.9i		−	1.89596i	0.318334	−	0.947979i	$-0.396877\pi$
$314$	−4524.05			−0.813080
$315$		0			0
$316$	−3094.80			−0.550937
$317$			5747.17i			1.01828i	0.860685	+	0.509138i	$0.170036\pi$
$317$			5747.17i			1.01828i	−0.860685	+	0.509138i	$0.829964\pi$
$318$		−	3788.39i		−	0.668057i
$319$	13951.8			2.44874
$320$	593.094	−	400.299i	0.103609	−	0.0699294i
$321$	−4104.56			−0.713690
$322$		0			0
$323$			2212.71i			0.381172i
$324$	−221.326			−0.0379503
$325$	5172.05	+	2086.13i	0.882750	+	0.356054i
$326$	−175.432			−0.0298045
$327$		−	158.770i		−	0.0268501i
$328$		−	3192.17i		−	0.537372i
$329$		0			0
$330$	2814.43	−	1899.55i	0.469483	−	0.316870i
$331$	9408.09			1.56228			0.781141	−	0.624355i	$-0.214638\pi$
$331$	9408.09			1.56228			0.781141	+	0.624355i	$0.214638\pi$
$332$			5364.82i			0.886846i
$333$		−	3466.78i		−	0.570506i
$334$	−3702.76			−0.606605
$335$	1576.95	+	2336.46i	0.257189	+	0.381058i
$336$		0			0
$337$		−	4501.95i		−	0.727706i	−0.931456	−	0.363853i	$-0.881461\pi$
$337$		−	4501.95i		−	0.727706i	0.931456	−	0.363853i	$-0.118539\pi$
$338$			412.939i			0.0664524i
$339$	1447.30			0.231877
$340$	983.015	+	1456.46i	0.156798	+	0.232317i
$341$	−3493.10			−0.554728
$342$			1981.17i			0.313244i
$343$		0			0
$344$	−1628.54			−0.255246
$345$	2605.69	−	1758.67i	0.406624	−	0.274445i
$346$	−3684.16			−0.572432
$347$			4993.36i			0.772500i	0.922394	+	0.386250i	$0.126230\pi$
$347$			4993.36i			0.772500i	−0.922394	+	0.386250i	$0.873770\pi$
$348$		−	3458.34i		−	0.532719i
$349$	−6675.06			−1.02381			−0.511903	−	0.859044i	$-0.671059\pi$
$349$	−6675.06			−1.02381			−0.511903	+	0.859044i	$0.671059\pi$
$350$		0			0
$351$	6102.65			0.928020
$352$		−	1584.05i		−	0.239859i
$353$		−	2839.32i		−	0.428107i	−0.976822	−	0.214054i	$-0.931333\pi$
$353$		−	2839.32i		−	0.428107i	0.976822	−	0.214054i	$-0.0686667\pi$
$354$	−2948.03			−0.442616
$355$	−7743.96	+	5226.66i	−1.15776	+	0.781415i
$356$	5204.47			0.774821
$357$		0			0
$358$		−	1497.06i		−	0.221012i
$359$	8484.41			1.24733			0.623663	−	0.781693i	$-0.285644\pi$
$359$	8484.41			1.24733			0.623663	+	0.781693i	$0.285644\pi$
$360$	880.153	+	1304.06i	0.128856	+	0.190916i
$361$	−3687.54			−0.537621
$362$		−	2787.80i		−	0.404761i
$363$		−	3433.90i		−	0.496509i
$364$		0			0
$365$	1612.37	+	2388.92i	0.231220	+	0.342581i
$366$	−144.161			−0.0205885
$367$			11319.7i			1.61004i	0.593247	+	0.805020i	$0.297846\pi$
$367$			11319.7i			1.61004i	−0.593247	+	0.805020i	$0.702154\pi$
$368$		−	1466.56i		−	0.207744i
$369$	7018.74			0.990193
$370$	−3652.89	+	2465.46i	−0.513256	+	0.346414i
$371$		0			0
$372$			865.863i			0.120680i
$373$		−	11306.2i		−	1.56947i	−0.619832	−	0.784735i	$-0.712799\pi$
$373$		−	11306.2i		−	1.56947i	0.619832	−	0.784735i	$-0.287201\pi$
$374$	3889.96			0.537821
$375$	4192.62	−	895.014i	0.577349	−	0.123249i
$376$	−547.991			−0.0751608
$377$		−	12574.6i		−	1.71784i
$378$		0			0
$379$	10626.4			1.44022			0.720109	−	0.693861i	$-0.244092\pi$
$379$	10626.4			1.44022			0.720109	+	0.693861i	$0.244092\pi$
$380$	2087.53	−	1408.95i	0.281811	−	0.190204i
$381$	−620.556			−0.0834437
$382$		−	1916.35i		−	0.256672i
$383$			7582.88i			1.01166i	0.862632	+	0.505832i	$0.168814\pi$
$383$			7582.88i			1.01166i	−0.862632	+	0.505832i	$0.831186\pi$
$384$	−392.651			−0.0521808
$385$		0			0
$386$	−9154.08			−1.20707
$387$		−	3580.72i		−	0.470332i
$388$		−	1294.91i		−	0.169431i
$389$	−3212.83			−0.418758			−0.209379	−	0.977835i	$-0.567144\pi$
$389$	−3212.83			−0.418758			−0.209379	+	0.977835i	$0.567144\pi$
$390$	−1712.05	−	2536.62i	−0.222290	−	0.329350i
$391$	3601.44			0.465813
$392$		0			0
$393$			3585.88i			0.460264i
$394$	6858.54			0.876976
$395$	−7169.95	+	4839.24i	−0.913315	+	0.616427i
$396$	3482.91			0.441977
$397$			13180.8i			1.66631i	0.553039	+	0.833155i	$0.313468\pi$
$397$			13180.8i			1.66631i	−0.553039	+	0.833155i	$0.686532\pi$
$398$			292.031i			0.0367794i
$399$		0			0
$400$	748.128	−	1854.81i	0.0935161	−	0.231851i
$401$	−7194.23			−0.895917			−0.447959	−	0.894054i	$-0.647849\pi$
$401$	−7194.23			−0.895917			−0.447959	+	0.894054i	$0.647849\pi$
$402$		−	1546.83i		−	0.191912i
$403$			3148.30i			0.389152i
$404$	−4724.07			−0.581761
$405$	−512.762	+	346.081i	−0.0629120	+	0.0424615i
$406$		0			0
$407$			9756.24i			1.18820i
$408$		−	964.234i		−	0.117002i
$409$	1089.15			0.131675			0.0658376	−	0.997830i	$-0.479028\pi$
$409$	1089.15			0.131675			0.0658376	+	0.997830i	$0.479028\pi$
$410$	−4991.50	−	7395.53i	−0.601250	−	0.890828i
$411$	−450.069			−0.0540153
$412$			2928.17i			0.350147i
$413$		0			0
$414$	3224.59			0.382802
$415$	8388.81	+	12429.1i	0.992266	+	1.47017i
$416$	−1427.69			−0.168265
$417$		−	7686.26i		−	0.902633i
$418$		−	5575.44i		−	0.652401i
$419$	12514.5			1.45913			0.729563	−	0.683914i	$-0.239724\pi$
$419$	12514.5			1.45913			0.729563	+	0.683914i	$0.239724\pi$
$420$		0			0
$421$	−827.022			−0.0957401			−0.0478701	−	0.998854i	$-0.515243\pi$
$421$	−827.022			−0.0957401			−0.0478701	+	0.998854i	$0.515243\pi$
$422$		−	1410.82i		−	0.162743i
$423$		−	1204.89i		−	0.138496i
$424$	−4939.89			−0.565807
$425$	4554.85	+	1837.18i	0.519865	+	0.209685i
$426$	5126.80			0.583085
$427$		0			0
$428$			5352.17i			0.604455i
$429$	−6774.87			−0.762457
$430$	−3772.95	+	2546.49i	−0.423134	+	0.285588i
$431$	−1680.44			−0.187805			−0.0939025	−	0.995581i	$-0.529934\pi$
$431$	−1680.44			−0.187805			−0.0939025	+	0.995581i	$0.529934\pi$
$432$		−	2188.54i		−	0.243741i
$433$		−	7421.56i		−	0.823689i	−0.911254	−	0.411845i	$-0.864885\pi$
$433$		−	7421.56i		−	0.823689i	0.911254	−	0.411845i	$-0.135115\pi$
$434$		0			0
$435$	−5407.69	−	8012.18i	−0.596044	−	0.883114i
$436$	−207.028			−0.0227405
$437$		−	5161.91i		−	0.565052i
$438$		−	1581.56i		−	0.172534i
$439$	−4798.23			−0.521656			−0.260828	−	0.965385i	$-0.583996\pi$
$439$	−4798.23			−0.521656			−0.260828	+	0.965385i	$0.583996\pi$
$440$	−2476.93	−	3669.89i	−0.268371	−	0.397625i
$441$		0			0
$442$		−	3505.98i		−	0.377291i
$443$		−	15935.6i		−	1.70908i	−0.519384	−	0.854541i	$-0.673839\pi$
$443$		−	15935.6i		−	1.70908i	0.519384	−	0.854541i	$-0.326161\pi$
$444$	2418.36			0.258491
$445$	12057.6	−	8138.06i	1.28446	−	0.866924i
$446$	−4464.14			−0.473953
$447$			6467.03i			0.684295i
$448$		0			0
$449$	9352.06			0.982964			0.491482	−	0.870888i	$-0.336455\pi$
$449$	9352.06			0.982964			0.491482	+	0.870888i	$0.336455\pi$
$450$	4078.23	+	1644.94i	0.427221	+	0.172318i
$451$	−19752.2			−2.06230
$452$		−	1887.21i		−	0.196387i
$453$			6796.26i			0.704892i
$454$	10929.9			1.12988
$455$		0			0
$456$	−1382.03			−0.141928
$457$		−	8577.22i		−	0.877955i	−0.898498	−	0.438977i	$-0.855341\pi$
$457$		−	8577.22i		−	0.877955i	0.898498	−	0.438977i	$-0.144659\pi$
$458$		−	3887.78i		−	0.396646i
$459$	5374.39			0.546525
$460$	−2293.22	−	3397.70i	−0.232439	−	0.344388i
$461$	−8463.98			−0.855113			−0.427556	−	0.903989i	$-0.640625\pi$
$461$	−8463.98			−0.855113			−0.427556	+	0.903989i	$0.640625\pi$
$462$		0			0
$463$		−	4297.74i		−	0.431388i	−0.976461	−	0.215694i	$-0.930799\pi$
$463$		−	4297.74i		−	0.431388i	0.976461	−	0.215694i	$-0.0692014\pi$
$464$	−4509.52			−0.451183
$465$	1353.92	+	2006.01i	0.135025	+	0.200057i
$466$	6614.50			0.657533
$467$			1030.13i			0.102074i	0.998697	+	0.0510371i	$0.0162527\pi$
$467$			1030.13i			0.102074i	−0.998697	+	0.0510371i	$0.983747\pi$
$468$		−	3139.12i		−	0.310055i
$469$		0			0
$470$	−1269.57	+	856.876i	−0.124598	+	0.0840952i
$471$	6938.97			0.678834
$472$			3844.10i			0.374871i
$473$			10076.9i			0.979569i
$474$	4746.79			0.459973
$475$	2633.21	−	6528.42i	0.254358	−	0.630619i
$476$		0			0
$477$		−	10861.5i		−	1.04259i
$478$		−	12216.0i		−	1.16892i
$479$	−5137.48			−0.490058			−0.245029	−	0.969516i	$-0.578797\pi$
$479$	−5137.48			−0.490058			−0.245029	+	0.969516i	$0.578797\pi$
$480$	−909.684	+	613.977i	−0.0865025	+	0.0583835i
$481$	8793.21			0.833546
$482$		−	7925.20i		−	0.748927i
$483$		0			0
$484$	−4477.65			−0.420515
$485$	−2024.82	−	3000.02i	−0.189572	−	0.280874i
$486$	7725.78			0.721087
$487$		−	526.537i		−	0.0489932i	−0.999700	−	0.0244966i	$-0.992202\pi$
$487$		−	526.537i		−	0.0489932i	0.999700	−	0.0244966i	$-0.00779829\pi$
$488$			187.979i			0.0174373i
$489$	269.076			0.0248835
$490$		0			0
$491$	−1546.87			−0.142178			−0.0710889	−	0.997470i	$-0.522647\pi$
$491$	−1546.87			−0.142178			−0.0710889	+	0.997470i	$0.522647\pi$
$492$			4896.13i			0.448648i
$493$		−	11074.0i		−	1.01166i
$494$	−5025.09			−0.457671
$495$	8069.12	−	5446.13i	0.732687	−	0.494515i
$496$	1129.05			0.102209
$497$		0			0
$498$		−	8228.54i		−	0.740421i
$499$	−9492.84			−0.851619			−0.425809	−	0.904813i	$-0.640011\pi$
$499$	−9492.84			−0.851619			−0.425809	+	0.904813i	$0.640011\pi$
$500$	−1167.06	−	5466.99i	−0.104385	−	0.488982i
$501$	5679.27			0.506449
$502$		−	7.84599i		−	0.000697577i
$503$		−	9819.97i		−	0.870479i	−0.900315	−	0.435239i	$-0.856664\pi$
$503$		−	9819.97i		−	0.870479i	0.900315	−	0.435239i	$-0.143336\pi$
$504$		0			0
$505$	−10944.6	+	7386.89i	−0.964413	+	0.650915i
$506$	−9074.67			−0.797269
$507$		−	633.363i		−	0.0554806i
$508$			809.177i			0.0706721i
$509$	2638.05			0.229724			0.114862	−	0.993381i	$-0.463357\pi$
$509$	2638.05			0.229724			0.114862	+	0.993381i	$0.463357\pi$
$510$	−1507.74	−	2233.91i	−0.130910	−	0.193959i
$511$		0			0
$512$			512.000i			0.0441942i
$513$		−	7703.06i		−	0.662960i
$514$	439.189			0.0376884
$515$	4578.69	+	6783.90i	0.391769	+	0.580455i
$516$	2497.84			0.213103
$517$			3390.80i			0.288448i
$518$		0			0
$519$	5650.74			0.477919
$520$	−3307.64	+	2232.44i	−0.278941	+	0.188267i
$521$	4426.35			0.372211			0.186106	−	0.982530i	$-0.440413\pi$
$521$	4426.35			0.372211			0.186106	+	0.982530i	$0.440413\pi$
$522$		−	9915.24i		−	0.831376i
$523$			905.764i			0.0757291i	0.999283	+	0.0378645i	$0.0120555\pi$
$523$			905.764i			0.0757291i	−0.999283	+	0.0378645i	$0.987944\pi$
$524$	4675.82			0.389817
$525$		0			0
$526$	−10935.4			−0.906478
$527$			2772.60i			0.229177i
$528$			2429.61i			0.200256i
$529$	3765.39			0.309476
$530$	−11444.6	+	7724.35i	−0.937965	+	0.633065i
$531$	−8452.16			−0.690758
$532$		0			0
$533$			17802.5i			1.44674i
$534$	−7982.58			−0.646892
$535$	8369.02	+	12399.8i	0.676307	+	1.00203i
$536$	−2016.99			−0.162539
$537$			2296.19i			0.184521i
$538$			583.462i			0.0467562i
$539$		0			0
$540$	−3422.15	−	5070.34i	−0.272714	−	0.404061i
$541$	19620.6			1.55926			0.779628	−	0.626243i	$-0.215408\pi$
$541$	19620.6			1.55926			0.779628	+	0.626243i	$0.215408\pi$
$542$			5322.04i			0.421774i
$543$			4275.91i			0.337932i
$544$	−1257.32			−0.0990939
$545$	−479.638	+	323.724i	−0.0376980	+	0.0254437i
$546$		0			0
$547$		−	6717.26i		−	0.525062i	−0.964923	−	0.262531i	$-0.915443\pi$
$547$		−	6717.26i		−	0.525062i	0.964923	−	0.262531i	$-0.0845573\pi$
$548$			586.870i			0.0457479i
$549$	−413.316			−0.0321310
$550$	−11477.0	−	4629.20i	−0.889783	−	0.358890i
$551$	−15872.3			−1.22719
$552$			2249.41i			0.173444i
$553$		0			0
$554$	9005.31			0.690612
$555$	5602.78	−	3781.51i	0.428513	−	0.289218i
$556$	−10022.5			−0.764479
$557$			13104.0i			0.996827i	0.866940	+	0.498413i	$0.166084\pi$
$557$			13104.0i			0.996827i	−0.866940	+	0.498413i	$0.833916\pi$
$558$			2482.48i			0.188336i
$559$	9082.21			0.687186
$560$		0			0
$561$	−5966.40			−0.449022
$562$		−	924.776i		−	0.0694116i
$563$		−	16648.7i		−	1.24629i	−0.782108	−	0.623143i	$-0.785855\pi$
$563$		−	16648.7i		−	1.24629i	0.782108	−	0.623143i	$-0.214145\pi$
$564$	840.505			0.0627512
$565$	−2950.97	−	4372.24i	−0.219732	−	0.325560i
$566$	14291.4			1.06133
$567$		0			0
$568$		−	6685.12i		−	0.493841i
$569$	−14697.7			−1.08288			−0.541441	−	0.840739i	$-0.682121\pi$
$569$	−14697.7			−1.08288			−0.541441	+	0.840739i	$0.682121\pi$
$570$	−3201.84	+	2161.03i	−0.235282	+	0.158800i
$571$	2997.78			0.219708			0.109854	−	0.993948i	$-0.464962\pi$
$571$	2997.78			0.219708			0.109854	+	0.993948i	$0.464962\pi$
$572$			8834.13i			0.645758i
$573$			2939.28i			0.214294i
$574$		0			0
$575$	−10625.8	−	4285.85i	−0.770651	−	0.310839i
$576$	−1125.75			−0.0814347
$577$		−	4873.27i		−	0.351607i	−0.984425	−	0.175803i	$-0.943748\pi$
$577$		−	4873.27i		−	0.351607i	0.984425	−	0.175803i	$-0.0562523\pi$
$578$			6738.40i			0.484915i
$579$	14040.5			1.00778
$580$	−10447.5	+	7051.39i	−0.747948	+	0.504816i
$581$		0			0
$582$			1986.13i			0.141457i
$583$			30566.6i			2.17142i
$584$	−2062.29			−0.146127
$585$	−4908.54	−	7272.62i	−0.346912	−	0.513993i
$586$	17312.4			1.22043
$587$			23971.4i			1.68553i	0.538283	+	0.842764i	$0.319073\pi$
$587$			23971.4i			1.68553i	−0.538283	+	0.842764i	$0.680927\pi$
$588$		0			0
$589$	3973.94			0.278002
$590$	6010.90	+	8905.91i	0.419432	+	0.621441i
$591$	−10519.6			−0.732180
$592$		−	3153.43i		−	0.218928i
$593$		−	1561.67i		−	0.108145i	−0.998537	−	0.0540726i	$-0.982780\pi$
$593$		−	1561.67i		−	0.108145i	0.998537	−	0.0540726i	$-0.0172202\pi$
$594$	−13542.0			−0.935413
$595$		0			0
$596$	8432.71			0.579559
$597$		−	447.916i		−	0.0307069i
$598$			8178.91i			0.559299i
$599$	−17401.4			−1.18698			−0.593491	−	0.804841i	$-0.702251\pi$
$599$	−17401.4			−1.18698			−0.593491	+	0.804841i	$0.702251\pi$
$600$	−1147.48	+	2844.89i	−0.0780758	+	0.193570i
$601$	−26823.7			−1.82057			−0.910283	−	0.413987i	$-0.864136\pi$
$601$	−26823.7			−1.82057			−0.910283	+	0.413987i	$0.864136\pi$
$602$		0			0
$603$		−	4434.84i		−	0.299503i
$604$	8862.02			0.597004
$605$	−10373.7	+	7001.56i	−0.697109	+	0.470502i
$606$	7245.76			0.485707
$607$		−	22721.4i		−	1.51933i	−0.650315	−	0.759665i	$-0.725363\pi$
$607$		−	22721.4i		−	1.51933i	0.650315	−	0.759665i	$-0.274637\pi$
$608$			1802.10i			0.120205i
$609$		0			0
$610$	293.937	+	435.505i	0.0195101	+	0.0289067i
$611$	3056.10			0.202351
$612$		−	2764.51i		−	0.182596i
$613$		−	22931.6i		−	1.51092i	−0.655192	−	0.755462i	$-0.727412\pi$
$613$		−	22931.6i		−	1.51092i	0.655192	−	0.755462i	$-0.272588\pi$
$614$	−8592.52			−0.564765
$615$	7655.93	+	11343.2i	0.501979	+	0.743745i
$616$		0			0
$617$		−	4299.04i		−	0.280507i	−0.990116	−	0.140253i	$-0.955208\pi$
$617$		−	4299.04i		−	0.280507i	0.990116	−	0.140253i	$-0.0447918\pi$
$618$		−	4491.21i		−	0.292335i
$619$	5321.89			0.345565			0.172783	−	0.984960i	$-0.444724\pi$
$619$	5321.89			0.345565			0.172783	+	0.984960i	$0.444724\pi$
$620$	2615.75	−	1765.46i	0.169437	−	0.114359i
$621$	−12537.6			−0.810173
$622$			7870.25i			0.507345i
$623$		0			0
$624$	2189.79			0.140483
$625$	−11252.4	−	10840.9i	−0.720152	−	0.693816i
$626$	20997.9			1.34064
$627$			8551.58i			0.544684i
$628$		−	9048.11i		−	0.574935i
$629$	7743.87			0.490888
$630$		0			0
$631$	19486.3			1.22938			0.614688	−	0.788771i	$-0.289282\pi$
$631$	19486.3			1.22938			0.614688	+	0.788771i	$0.289282\pi$
$632$		−	6189.60i		−	0.389571i
$633$			2163.91i			0.135873i
$634$	−11494.3			−0.720030
$635$	1265.29	+	1874.68i	0.0790730	+	0.117157i
$636$	7576.77			0.472388
$637$		0			0
$638$			27903.6i			1.73152i
$639$	14698.8			0.909979
$640$	800.599	+	1186.19i	0.0494476	+	0.0732628i
$641$	−28574.7			−1.76074			−0.880368	−	0.474290i	$-0.842705\pi$
$641$	−28574.7			−1.76074			−0.880368	+	0.474290i	$0.842705\pi$
$642$		−	8209.13i		−	0.504655i
$643$		−	6347.10i		−	0.389277i	−0.980875	−	0.194639i	$-0.937647\pi$
$643$		−	6347.10i		−	0.389277i	0.980875	−	0.194639i	$-0.0623534\pi$
$644$		0			0
$645$	5786.93	−	3905.80i	0.353271	−	0.238435i
$646$	−4425.42			−0.269529
$647$			2649.69i			0.161005i	0.996754	+	0.0805024i	$0.0256525\pi$
$647$			2649.69i			0.161005i	−0.996754	+	0.0805024i	$0.974348\pi$
$648$		−	442.652i		−	0.0268349i
$649$	23786.2			1.43866
$650$	−4172.25	+	10344.1i	−0.251768	+	0.624199i
$651$		0			0
$652$		−	350.863i		−	0.0210750i
$653$			7061.62i			0.423189i	0.977358	+	0.211595i	$0.0678657\pi$
$653$			7061.62i			0.423189i	−0.977358	+	0.211595i	$0.932134\pi$
$654$	317.539			0.0189859
$655$	10832.8	−	7311.44i	0.646219	−	0.436155i
$656$	6384.34			0.379980
$657$		−	4534.42i		−	0.269261i
$658$		0			0
$659$	−11227.0			−0.663646			−0.331823	−	0.943342i	$-0.607664\pi$
$659$	−11227.0			−0.663646			−0.331823	+	0.943342i	$0.607664\pi$
$660$	3799.11	+	5628.86i	0.224061	+	0.331974i
$661$	28750.0			1.69175			0.845873	−	0.533385i	$-0.179080\pi$
$661$	28750.0			1.69175			0.845873	+	0.533385i	$0.179080\pi$
$662$			18816.2i			1.10470i
$663$			5377.46i			0.314997i
$664$	−10729.6			−0.627095
$665$		0			0
$666$	6933.56			0.403408
$667$			25834.0i			1.49969i
$668$		−	7405.52i		−	0.428934i
$669$	6847.07			0.395700
$670$	−4672.91	+	3153.91i	−0.269448	+	0.181860i
$671$	1163.16			0.0669199
$672$		0			0
$673$		−	4440.57i		−	0.254341i	−0.991881	−	0.127170i	$-0.959411\pi$
$673$		−	4440.57i		−	0.254341i	0.991881	−	0.127170i	$-0.0405895\pi$
$674$	9003.90			0.514566
$675$	−15856.7	−	6395.73i	−0.904183	−	0.364699i
$676$	−825.878			−0.0469889
$677$			16309.8i			0.925905i	0.886383	+	0.462953i	$0.153210\pi$
$677$			16309.8i			0.925905i	−0.886383	+	0.462953i	$0.846790\pi$
$678$			2894.59i			0.163962i
$679$		0			0
$680$	−2912.92	+	1966.03i	−0.164273	+	0.110873i
$681$	−16764.3			−0.943330
$682$		−	6986.21i		−	0.392252i
$683$			4866.44i			0.272634i	0.990665	+	0.136317i	$0.0435266\pi$
$683$			4866.44i			0.272634i	−0.990665	+	0.136317i	$0.956473\pi$
$684$	−3962.35			−0.221497
$685$	917.671	+	1359.65i	0.0511860	+	0.0758385i
$686$		0			0
$687$			5963.05i			0.331157i
$688$		−	3257.07i		−	0.180486i
$689$	27549.4			1.52329
$690$	3517.33	+	5211.37i	0.194062	+	0.287527i
$691$	−15027.1			−0.827291			−0.413646	−	0.910438i	$-0.635745\pi$
$691$	−15027.1			−0.827291			−0.413646	+	0.910438i	$0.635745\pi$
$692$		−	7368.31i		−	0.404771i
$693$		0			0
$694$	−9986.72			−0.546240
$695$	−23220.0	+	15671.9i	−1.26731	+	0.855353i
$696$	6916.67			0.376689
$697$			15678.0i			0.852005i
$698$		−	13350.1i		−	0.723939i
$699$	−10145.3			−0.548970
$700$		0			0
$701$	−10821.8			−0.583073			−0.291536	−	0.956560i	$-0.594166\pi$
$701$	−10821.8			−0.583073			−0.291536	+	0.956560i	$0.594166\pi$
$702$			12205.3i			0.656209i
$703$		−	11099.2i		−	0.595469i
$704$	3168.10			0.169606
$705$	1947.26	−	1314.27i	0.104026	−	0.0702104i
$706$	5678.64			0.302718
$707$		0			0
$708$		−	5896.06i		−	0.312977i
$709$	−20502.7			−1.08603			−0.543016	−	0.839722i	$-0.682718\pi$
$709$	−20502.7			−1.08603			−0.543016	+	0.839722i	$0.682718\pi$
$710$	−10453.3	−	15487.9i	−0.552544	−	0.818663i
$711$	13609.3			0.717846
$712$			10408.9i			0.547881i
$713$		−	6468.05i		−	0.339734i
$714$		0			0
$715$	13813.7	+	20466.7i	0.722520	+	1.07050i
$716$	2994.13			0.156279
$717$			18736.8i			0.975926i
$718$			16968.8i			0.881993i
$719$	−273.658			−0.0141943			−0.00709717	−	0.999975i	$-0.502259\pi$
$719$	−273.658			−0.0141943			−0.00709717	+	0.999975i	$0.502259\pi$
$720$	−2608.11	+	1760.31i	−0.134998	+	0.0911149i
$721$		0			0
$722$		−	7375.09i		−	0.380156i
$723$			12155.6i			0.625273i
$724$	5575.60			0.286209
$725$	−13178.5	+	32673.0i	−0.675086	+	1.67371i
$726$	6867.79			0.351085
$727$		−	1244.59i		−	0.0634931i	−0.999496	−	0.0317465i	$-0.989893\pi$
$727$		−	1244.59i		−	0.0634931i	0.999496	−	0.0317465i	$-0.0101069\pi$
$728$		0			0
$729$	−10355.8			−0.526129
$730$	−4777.85	+	3224.73i	−0.242241	+	0.163497i
$731$	7998.39			0.404694
$732$		−	288.321i		−	0.0145583i
$733$		−	15653.2i		−	0.788765i	−0.918946	−	0.394383i	$-0.870958\pi$
$733$		−	15653.2i		−	0.788765i	0.918946	−	0.394383i	$-0.129042\pi$
$734$	−22639.5			−1.13847
$735$		0			0
$736$	2933.13			0.146898
$737$			12480.6i			0.623782i
$738$			14037.5i			0.700172i
$739$	5366.29			0.267121			0.133560	−	0.991041i	$-0.457359\pi$
$739$	5366.29			0.267121			0.133560	+	0.991041i	$0.457359\pi$
$740$	−4930.92	−	7305.78i	−0.244952	−	0.362927i
$741$	7707.46			0.382106
$742$		0			0
$743$			7927.48i			0.391428i	0.980661	+	0.195714i	$0.0627024\pi$
$743$			7927.48i			0.391428i	−0.980661	+	0.195714i	$0.937298\pi$
$744$	−1731.73			−0.0853335
$745$	19536.7	−	13186.0i	0.960763	−	0.648452i
$746$	22612.4			1.10978
$747$		−	23591.7i		−	1.15552i
$748$			7779.91i			0.380297i
$749$		0			0
$750$	1790.03	+	8385.24i	0.0871501	+	0.408248i
$751$	7386.52			0.358906			0.179453	−	0.983767i	$-0.442567\pi$
$751$	7386.52			0.358906			0.179453	+	0.983767i	$0.442567\pi$
$752$		−	1095.98i		−	0.0531467i
$753$			12.0341i			0.000582401i
$754$	25149.2			1.21470
$755$	20531.3	−	13857.3i	0.989683	−	0.667970i
$756$		0			0
$757$			13406.0i			0.643659i	0.946798	+	0.321829i	$0.104298\pi$
$757$			13406.0i			0.643659i	−0.946798	+	0.321829i	$0.895702\pi$
$758$			21252.8i			1.01839i
$759$	13918.7			0.665634
$760$	2817.89	+	4175.06i	0.134494	+	0.199270i
$761$	−25885.0			−1.23302			−0.616510	−	0.787347i	$-0.711454\pi$
$761$	−25885.0			−1.23302			−0.616510	+	0.787347i	$0.711454\pi$
$762$		−	1241.11i		−	0.0590036i
$763$		0			0
$764$	3832.69			0.181495
$765$	−4322.78	−	6404.75i	−0.204301	−	0.302698i
$766$	−15165.8			−0.715354
$767$		−	21438.2i		−	1.00924i
$768$		−	785.303i		−	0.0368974i
$769$	−11600.6			−0.543991			−0.271996	−	0.962299i	$-0.587684\pi$
$769$	−11600.6			−0.543991			−0.271996	+	0.962299i	$0.587684\pi$
$770$		0			0
$771$	−673.626			−0.0314657
$772$		−	18308.2i		−	0.853530i
$773$			28247.3i			1.31434i	0.753742	+	0.657170i	$0.228247\pi$
$773$			28247.3i			1.31434i	−0.753742	+	0.657170i	$0.771753\pi$
$774$	7161.44			0.332575
$775$	3299.50	−	8180.32i	0.152931	−	0.379156i
$776$	2589.83			0.119806
$777$		0			0
$778$		−	6425.65i		−	0.296106i
$779$	22471.2			1.03352
$780$	5073.24	−	3424.10i	0.232886	−	0.157183i
$781$	−41365.6			−1.89523
$782$			7202.89i			0.329379i
$783$			38551.7i			1.75955i
$784$		0			0
$785$	−14148.3	−	20962.4i	−0.643277	−	0.953097i
$786$	−7171.75			−0.325456
$787$		−	10505.3i		−	0.475822i	−0.971287	−	0.237911i	$-0.923537\pi$
$787$		−	10505.3i		−	0.475822i	0.971287	−	0.237911i	$-0.0764627\pi$
$788$			13717.1i			0.620115i
$789$	16772.7			0.756812
$790$	−9678.49	−	14339.9i	−0.435880	−	0.645811i
$791$		0			0
$792$			6965.83i			0.312525i
$793$		−	1048.34i		−	0.0469455i
$794$	−26361.6			−1.17826
$795$	17553.7	−	11847.6i	0.783100	−	0.528541i
$796$	−584.063			−0.0260070
$797$			2165.99i			0.0962651i	0.998841	+	0.0481325i	$0.0153270\pi$
$797$			2165.99i			0.0962651i	−0.998841	+	0.0481325i	$0.984673\pi$
$798$		0			0
$799$	2691.40			0.119168
$800$	3709.61	+	1496.26i	0.163943	+	0.0661258i
$801$	−22886.5			−1.00956
$802$		−	14388.5i		−	0.633509i
$803$			12760.8i			0.560796i
$804$	3093.65			0.135702
$805$		0			0
$806$	−6296.60			−0.275172
$807$		−	894.911i		−	0.0390364i
$808$		−	9448.14i		−	0.411367i
$809$	−5348.67			−0.232446			−0.116223	−	0.993223i	$-0.537079\pi$
$809$	−5348.67			−0.232446			−0.116223	+	0.993223i	$0.537079\pi$
$810$	−692.162	−	1025.52i	−0.0300248	−	0.0444855i
$811$	−33841.2			−1.46526			−0.732629	−	0.680628i	$-0.761707\pi$
$811$	−33841.2			−1.46526			−0.732629	+	0.680628i	$0.761707\pi$
$812$		0			0
$813$		−	8162.92i		−	0.352135i
$814$	−19512.5			−0.840187
$815$	−548.634	−	812.871i	−0.0235801	−	0.0349370i
$816$	1928.47			0.0827327
$817$		−	11464.0i		−	0.490912i
$818$			2178.31i			0.0931084i
$819$		0			0
$820$	14791.1	−	9983.00i	0.629910	−	0.425148i
$821$	14581.5			0.619850			0.309925	−	0.950761i	$-0.399696\pi$
$821$	14581.5			0.619850			0.309925	+	0.950761i	$0.399696\pi$
$822$		−	900.138i		−	0.0381946i
$823$		−	3078.27i		−	0.130379i	−0.997873	−	0.0651894i	$-0.979235\pi$
$823$		−	3078.27i		−	0.130379i	0.997873	−	0.0651894i	$-0.0207651\pi$
$824$	−5856.34			−0.247591
$825$	17603.3	+	7100.24i	0.742873	+	0.299635i
$826$		0			0
$827$			40275.0i			1.69347i	0.532017	+	0.846734i	$0.321434\pi$
$827$			40275.0i			1.69347i	−0.532017	+	0.846734i	$0.678566\pi$
$828$			6449.18i			0.270682i
$829$	−29186.9			−1.22280			−0.611402	−	0.791320i	$-0.709394\pi$
$829$	−29186.9			−1.22280			−0.611402	+	0.791320i	$0.709394\pi$
$830$	−24858.2	+	16777.6i	−1.03957	+	0.701638i
$831$	−13812.3			−0.576587
$832$		−	2855.38i		−	0.118981i
$833$		0			0
$834$	15372.5			0.638258
$835$	−11579.8	−	17156.9i	−0.479922	−	0.711065i
$836$	11150.9			0.461317
$837$		−	9652.18i		−	0.398600i
$838$			25029.0i			1.03176i
$839$	−9396.07			−0.386637			−0.193318	−	0.981136i	$-0.561925\pi$
$839$	−9396.07			−0.386637			−0.193318	+	0.981136i	$0.561925\pi$
$840$		0			0
$841$	55047.5			2.25706
$842$		−	1654.04i		−	0.0676985i
$843$			1418.42i			0.0579512i
$844$	2821.64			0.115077
$845$	−1913.37	+	1291.40i	−0.0778958	+	0.0525745i
$846$	2409.77			0.0979312
$847$		0			0
$848$		−	9879.77i		−	0.400086i
$849$	−21920.1			−0.886097
$850$	−3674.36	+	9109.69i	−0.148270	+	0.367600i
$851$	−18065.3			−0.727696
$852$			10253.6i			0.412304i
$853$			20167.0i			0.809502i	0.914427	+	0.404751i	$0.132642\pi$
$853$			20167.0i			0.809502i	−0.914427	+	0.404751i	$0.867358\pi$
$854$		0			0
$855$	−9179.86	+	6195.80i	−0.367187	+	0.247827i
$856$	−10704.3			−0.427414
$857$		−	42479.4i		−	1.69320i	−0.532232	−	0.846599i	$-0.678647\pi$
$857$		−	42479.4i		−	1.69320i	0.532232	−	0.846599i	$-0.321353\pi$
$858$		−	13549.7i		−	0.539138i
$859$	−21043.7			−0.835857			−0.417929	−	0.908480i	$-0.637244\pi$
$859$	−21043.7			−0.835857			−0.417929	+	0.908480i	$0.637244\pi$
$860$	−5092.98	−	7545.90i	−0.201941	−	0.299201i
$861$		0			0
$862$		−	3360.88i		−	0.132798i
$863$		−	8451.15i		−	0.333349i	−0.986012	−	0.166675i	$-0.946697\pi$
$863$		−	8451.15i		−	0.333349i	0.986012	−	0.166675i	$-0.0533029\pi$
$864$	4377.07			0.172351
$865$	−11521.6	−	17070.7i	−0.452886	−	0.671008i
$866$	14843.1			0.582436
$867$		−	10335.3i		−	0.404851i
$868$		0			0
$869$	−38299.4			−1.49507
$870$	16024.4	−	10815.4i	0.624456	−	0.421467i
$871$	11248.6			0.437594
$872$		−	414.057i		−	0.0160800i
$873$			5694.35i			0.220761i
$874$	10323.8			0.399552
$875$		0			0
$876$	3163.12			0.122000
$877$		−	34430.9i		−	1.32571i	−0.748747	−	0.662856i	$-0.769344\pi$
$877$		−	34430.9i		−	1.32571i	0.748747	−	0.662856i	$-0.230656\pi$
$878$		−	9596.46i		−	0.368867i
$879$	−26553.7			−1.01892
$880$	7339.78	−	4953.87i	0.281164	−	0.189767i
$881$	−11602.4			−0.443695			−0.221848	−	0.975081i	$-0.571209\pi$
$881$	−11602.4			−0.443695			−0.221848	+	0.975081i	$0.571209\pi$
$882$		0			0
$883$		−	37934.8i		−	1.44576i	−0.690974	−	0.722880i	$-0.742818\pi$
$883$		−	37934.8i		−	1.44576i	0.690974	−	0.722880i	$-0.257182\pi$
$884$	7011.96			0.266785
$885$	−9219.49	−	13659.8i	−0.350181	−	0.518837i
$886$	31871.2			1.20850
$887$			25436.3i			0.962871i	0.876481	+	0.481436i	$0.159885\pi$
$887$			25436.3i			0.962871i	−0.876481	+	0.481436i	$0.840115\pi$
$888$			4836.71i			0.182781i
$889$		0			0
$890$	16276.1	+	24115.1i	0.613008	+	0.908249i
$891$	−2739.00			−0.102985
$892$		−	8928.28i		−	0.335135i
$893$		−	3857.56i		−	0.144556i
$894$	−12934.1			−0.483870
$895$	6936.72	−	4681.83i	0.259071	−	0.174856i
$896$		0			0
$897$		−	12544.8i		−	0.466954i
$898$			18704.1i			0.695061i
$899$	−19888.5			−0.737840
$900$	−3289.87	+	8156.46i	−0.121847	+	0.302091i
$901$	24261.8			0.897088
$902$		−	39504.4i		−	1.45826i
$903$		0			0
$904$	3774.42			0.138867
$905$	12917.4	−	8718.39i	0.474463	−	0.320231i
$906$	−13592.5			−0.498434
$907$			6031.85i			0.220821i	0.993886	+	0.110410i	$0.0352165\pi$
$907$			6031.85i			0.220821i	−0.993886	+	0.110410i	$0.964783\pi$
$908$			21859.8i			0.798947i
$909$	20774.0			0.758008
$910$		0			0
$911$	−21631.5			−0.786699			−0.393349	−	0.919389i	$-0.628684\pi$
$911$	−21631.5			−0.786699			−0.393349	+	0.919389i	$0.628684\pi$
$912$		−	2764.05i		−	0.100359i
$913$			66391.9i			2.40663i
$914$	17154.4			0.620808
$915$	−450.839	−	667.975i	−0.0162888	−	0.0241340i
$916$	7775.56			0.280471
$917$		0			0
$918$			10748.8i			0.386451i
$919$	28244.7			1.01383			0.506913	−	0.861997i	$-0.330786\pi$
$919$	28244.7			1.01383			0.506913	+	0.861997i	$0.330786\pi$
$920$	6795.40	−	4586.44i	0.243519	−	0.164359i
$921$	13179.2			0.471518
$922$		−	16928.0i		−	0.604656i
$923$			37282.4i			1.32954i
$924$		0			0
$925$	−22847.6	−	9215.50i	−0.812136	−	0.327572i
$926$	8595.47			0.305038
$927$		−	12876.5i		−	0.456226i
$928$		−	9019.03i		−	0.319035i
$929$	−44944.2			−1.58727			−0.793633	−	0.608396i	$-0.791813\pi$
$929$	−44944.2			−1.58727			−0.793633	+	0.608396i	$0.791813\pi$
$930$	−4012.02	+	2707.85i	−0.141462	+	0.0954772i
$931$		0			0
$932$			13229.0i			0.464946i
$933$		−	12071.4i		−	0.423578i
$934$	−2060.25			−0.0721773
$935$	12165.2	+	18024.3i	0.425503	+	0.630436i
$936$	6278.24			0.219242
$937$			3777.71i			0.131710i	0.997829	+	0.0658551i	$0.0209775\pi$
$937$			3777.71i			0.131710i	−0.997829	+	0.0658551i	$0.979022\pi$
$938$		0			0
$939$	−32206.4			−1.11929
$940$	−1713.75	−	2539.14i	−0.0594643	−	0.0881039i
$941$	−352.846			−0.0122236			−0.00611182	−	0.999981i	$-0.501945\pi$
$941$	−352.846			−0.0122236			−0.00611182	+	0.999981i	$0.501945\pi$
$942$			13877.9i			0.480008i
$943$		−	36574.4i		−	1.26302i
$944$	−7688.20			−0.265074
$945$		0			0
$946$	−20153.8			−0.692660
$947$			13534.8i			0.464438i	0.972664	+	0.232219i	$0.0745986\pi$
$947$			13534.8i			0.464438i	−0.972664	+	0.232219i	$0.925401\pi$
$948$			9493.58i			0.325250i
$949$	11501.2			0.393409
$950$	13056.8	+	5266.42i	0.445915	+	0.179858i
$951$	17630.0			0.601147
$952$		0			0
$953$		−	51886.1i		−	1.76365i	−0.471579	−	0.881824i	$-0.656316\pi$
$953$		−	51886.1i		−	1.76365i	0.471579	−	0.881824i	$-0.343684\pi$
$954$	21723.0			0.737221
$955$	8879.48	−	5993.07i	0.300873	−	0.203069i
$956$	24432.0			0.826554
$957$		−	42798.3i		−	1.44564i
$958$		−	10275.0i		−	0.346523i
$959$		0			0
$960$	−1227.95	−	1819.37i	−0.0412834	−	0.0611665i
$961$	−24811.5			−0.832853
$962$			17586.4i			0.589406i
$963$		−	23536.0i		−	0.787578i
$964$	15850.4			0.529571
$965$	−28627.9	−	42415.8i	−0.954989	−	1.41494i
$966$		0			0
$967$		−	45517.8i		−	1.51371i	−0.653585	−	0.756853i	$-0.726736\pi$
$967$		−	45517.8i		−	1.51371i	0.653585	−	0.756853i	$-0.273264\pi$
$968$		−	8955.30i		−	0.297349i
$969$	6787.69			0.225028
$970$	6000.05	−	4049.64i	0.198608	−	0.134047i
$971$	23398.3			0.773313			0.386656	−	0.922224i	$-0.373630\pi$
$971$	23398.3			0.773313			0.386656	+	0.922224i	$0.373630\pi$
$972$			15451.6i			0.509886i
$973$		0			0
$974$	1053.07			0.0346434
$975$	6399.38	−	15865.7i	0.210199	−	0.521139i
$976$	−375.958			−0.0123300
$977$		−	34323.9i		−	1.12397i	−0.827148	−	0.561985i	$-0.810038\pi$
$977$		−	34323.9i		−	1.12397i	0.827148	−	0.561985i	$-0.189962\pi$
$978$			538.152i			0.0175953i
$979$	64407.4			2.10262
$980$		0			0
$981$	910.402			0.0296299
$982$		−	3093.74i		−	0.100535i
$983$			37157.0i			1.20562i	0.797885	+	0.602809i	$0.205952\pi$
$983$			37157.0i			1.20562i	−0.797885	+	0.602809i	$0.794048\pi$
$984$	−9792.27			−0.317242
$985$	21449.0	+	31779.4i	0.693829	+	1.02800i
$986$	22148.0			0.715352
$987$		0			0
$988$		−	10050.2i		−	0.323622i
$989$	−18659.0			−0.599921
$990$	10892.3	+	16138.2i	0.349675	+	0.518088i
$991$	−10542.5			−0.337935			−0.168968	−	0.985622i	$-0.554043\pi$
$991$	−10542.5			−0.337935			−0.168968	+	0.985622i	$0.554043\pi$
$992$			2258.09i			0.0722727i
$993$		−	28860.2i		−	0.922306i
$994$		0			0
$995$	−1353.14	+	913.281i	−0.0431130	+	0.0290985i
$996$	16457.1			0.523556
$997$			36255.9i			1.15169i	0.817558	+	0.575846i	$0.195327\pi$
$997$			36255.9i			1.15169i	−0.817558	+	0.575846i	$0.804673\pi$
$998$		−	18985.7i		−	0.602185i
$999$	−26958.6			−0.853785

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.c.f.99.9		12
5.2	odd	4		2450.4.a.cv.1.3		6
5.3	odd	4		2450.4.a.cy.1.4		6
5.4	even	2	inner	490.4.c.f.99.4		12
7.2	even	3		70.4.i.a.39.10	yes	24
7.4	even	3		70.4.i.a.9.3	✓	24
7.6	odd	2		490.4.c.e.99.10		12
35.2	odd	12		350.4.e.o.151.4		12
35.4	even	6		70.4.i.a.9.10	yes	24
35.9	even	6		70.4.i.a.39.3	yes	24
35.13	even	4		2450.4.a.cx.1.3		6
35.18	odd	12		350.4.e.n.51.3		12
35.23	odd	12		350.4.e.n.151.3		12
35.27	even	4		2450.4.a.cw.1.4		6
35.32	odd	12		350.4.e.o.51.4		12
35.34	odd	2		490.4.c.e.99.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.i.a.9.3	✓	24	7.4	even	3
70.4.i.a.9.10	yes	24	35.4	even	6
70.4.i.a.39.3	yes	24	35.9	even	6
70.4.i.a.39.10	yes	24	7.2	even	3
350.4.e.n.51.3		12	35.18	odd	12
350.4.e.n.151.3		12	35.23	odd	12
350.4.e.o.51.4		12	35.32	odd	12
350.4.e.o.151.4		12	35.2	odd	12
490.4.c.e.99.3		12	35.34	odd	2
490.4.c.e.99.10		12	7.6	odd	2
490.4.c.f.99.4		12	5.4	even	2	inner
490.4.c.f.99.9		12	1.1	even	1	trivial
2450.4.a.cv.1.3		6	5.2	odd	4
2450.4.a.cw.1.4		6	35.27	even	4
2450.4.a.cx.1.3		6	35.13	even	4
2450.4.a.cy.1.4		6	5.3	odd	4

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	490.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -3.06759i q^{3} -4.00000 q^{4} +(-9.26709 + 6.25468i) q^{5} +6.13518 q^{6} -8.00000i q^{8} +17.5899 q^{9} +(-12.5094 - 18.5342i) q^{10} -49.5016 q^{11} +12.2704i q^{12} +44.6154i q^{13} +(19.1868 + 28.4276i) q^{15} +16.0000 q^{16} +39.2912i q^{17} +35.1798i q^{18} +56.3157 q^{19} +(37.0684 - 25.0187i) q^{20} -99.0033i q^{22} -91.6603i q^{23} -24.5407 q^{24} +(46.7580 - 115.925i) q^{25} -89.2307 q^{26} -136.783i q^{27} -281.845 q^{29} +(-56.8553 + 38.3736i) q^{30} +70.5654 q^{31} +32.0000i q^{32} +151.851i q^{33} -78.5824 q^{34} -70.3596 q^{36} -197.089i q^{37} +112.631i q^{38} +136.862 q^{39} +(50.0374 + 74.1367i) q^{40} +399.021 q^{41} -203.567i q^{43} +198.007 q^{44} +(-163.007 + 110.019i) q^{45} +183.321 q^{46} -68.4988i q^{47} -49.0814i q^{48} +(231.851 + 93.5161i) q^{50} +120.529 q^{51} -178.461i q^{52} -617.486i q^{53} +273.567 q^{54} +(458.736 - 309.617i) q^{55} -172.753i q^{57} -563.690i q^{58} -480.513 q^{59} +(-76.7471 - 113.711i) q^{60} -23.4974 q^{61} +141.131i q^{62} -64.0000 q^{64} +(-279.055 - 413.455i) q^{65} -303.701 q^{66} -252.124i q^{67} -157.165i q^{68} -281.176 q^{69} +835.640 q^{71} -140.719i q^{72} -257.786i q^{73} +394.179 q^{74} +(-355.611 - 143.434i) q^{75} -225.263 q^{76} +273.723i q^{78} +773.700 q^{79} +(-148.273 + 100.075i) q^{80} +55.3315 q^{81} +798.043i q^{82} -1341.21i q^{83} +(-245.754 - 364.115i) q^{85} +407.134 q^{86} +864.584i q^{87} +396.013i q^{88} -1301.12 q^{89} +(-220.038 - 326.014i) q^{90} +366.641i q^{92} -216.466i q^{93} +136.998 q^{94} +(-521.883 + 352.236i) q^{95} +98.1629 q^{96} +323.729i q^{97} -870.729 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 48 q^{4} + 8 q^{5} + 28 q^{6} - 62 q^{9} - 12 q^{10} + 62 q^{11} + 86 q^{15} + 192 q^{16} - 186 q^{19} - 32 q^{20} - 112 q^{24} - 126 q^{25} + 236 q^{26} - 338 q^{29} - 28 q^{30} + 652 q^{31} - 272 q^{34}+ \cdots - 8546 q^{99}+O(q^{100}) \) 12 * q - 48 * q^4 + 8 * q^5 + 28 * q^6 - 62 * q^9 - 12 * q^10 + 62 * q^11 + 86 * q^15 + 192 * q^16 - 186 * q^19 - 32 * q^20 - 112 * q^24 - 126 * q^25 + 236 * q^26 - 338 * q^29 - 28 * q^30 + 652 * q^31 - 272 * q^34 + 248 * q^36 + 868 * q^39 + 48 * q^40 + 396 * q^41 - 248 * q^44 - 664 * q^45 - 376 * q^46 + 160 * q^50 + 1448 * q^51 - 1540 * q^54 + 298 * q^55 - 1336 * q^59 - 344 * q^60 + 314 * q^61 - 768 * q^64 - 1862 * q^65 + 1600 * q^66 + 90 * q^69 + 2216 * q^71 + 1012 * q^74 + 4550 * q^75 + 744 * q^76 + 1772 * q^79 + 128 * q^80 - 1228 * q^81 + 2282 * q^85 - 396 * q^86 - 6094 * q^89 + 100 * q^90 - 3604 * q^94 - 1166 * q^95 + 448 * q^96 - 8546 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more