LMFDB - Embedded newform 200.6.f.c.149.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [200,6,Mod(149,200)] 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("200.149"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(200, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$32.0767639626$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 $ x^20 - 2x^19 - 17x^18 + 78x^17 + 253x^16 - 884x^15 + 2396x^14 + 19376x^13 - 109104x^12 - 96128x^11 + 3580672x^10 - 1538048x^9 - 27930624x^8 + 79364096x^7 + 157024256x^6 - 926941184x^5 + 4244635648x^4 + 20937965568x^3 - 73014444032x^2 - 137438953472*x + 1099511627776
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{45}\cdot 3^{4}\cdot 5^{8} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.19
Root			$3.18502 + 2.41984i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.6.f.c.149.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.60486 - 0.765181i) q^{2} -17.3148 q^{3} +(30.8290 - 8.57748i) q^{4} +(-97.0471 + 13.2490i) q^{6} +9.19080i q^{7} +(166.229 - 71.6654i) q^{8} +56.8021 q^{9} +160.480i q^{11} +(-533.798 + 148.517i) q^{12} +368.546 q^{13} +(7.03263 + 51.5132i) q^{14} +(876.854 - 528.870i) q^{16} +1261.09i q^{17} +(318.368 - 43.4639i) q^{18} -2486.75i q^{19} -159.137i q^{21} +(122.796 + 899.467i) q^{22} -422.882i q^{23} +(-2878.22 + 1240.87i) q^{24} +(2065.65 - 282.005i) q^{26} +3223.98 q^{27} +(78.8339 + 283.343i) q^{28} -5666.05i q^{29} +9387.13 q^{31} +(4509.96 - 3635.20i) q^{32} -2778.67i q^{33} +(964.961 + 7068.23i) q^{34} +(1751.15 - 487.219i) q^{36} +3566.43 q^{37} +(-1902.81 - 13937.9i) q^{38} -6381.30 q^{39} -5949.95 q^{41} +(-121.769 - 891.941i) q^{42} +10658.5 q^{43} +(1376.51 + 4947.43i) q^{44} +(-323.581 - 2370.20i) q^{46} -9243.94i q^{47} +(-15182.5 + 9157.27i) q^{48} +16722.5 q^{49} -21835.5i q^{51} +(11361.9 - 3161.20i) q^{52} +8976.82 q^{53} +(18070.0 - 2466.93i) q^{54} +(658.662 + 1527.78i) q^{56} +43057.5i q^{57} +(-4335.55 - 31757.4i) q^{58} -27435.6i q^{59} -50515.3i q^{61} +(52613.6 - 7182.86i) q^{62} +522.057i q^{63} +(22496.2 - 23825.7i) q^{64} +(-2126.19 - 15574.1i) q^{66} +5964.39 q^{67} +(10817.0 + 38878.1i) q^{68} +7322.11i q^{69} +67286.3 q^{71} +(9442.16 - 4070.75i) q^{72} +85768.5i q^{73} +(19989.3 - 2728.96i) q^{74} +(-21330.0 - 76663.9i) q^{76} -1474.94 q^{77} +(-35766.3 + 4882.86i) q^{78} -56567.2 q^{79} -69625.4 q^{81} +(-33348.6 + 4552.79i) q^{82} -30208.1 q^{83} +(-1364.99 - 4906.03i) q^{84} +(59739.7 - 8155.72i) q^{86} +98106.4i q^{87} +(11500.8 + 26676.4i) q^{88} -113965. q^{89} +3387.24i q^{91} +(-3627.26 - 13037.0i) q^{92} -162536. q^{93} +(-7073.29 - 51811.0i) q^{94} +(-78089.1 + 62942.7i) q^{96} +138806. i q^{97} +(93727.5 - 12795.8i) q^{98} +9115.59i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 36 q^{3} + 32 q^{4} + 204 q^{6} + 248 q^{8} + 1620 q^{9} + 1252 q^{12} - 2708 q^{14} + 3080 q^{16} + 2070 q^{18} + 8244 q^{22} - 1032 q^{24} - 8084 q^{26} + 11664 q^{27} + 22924 q^{28}+ \cdots + 663674 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 + 36 * q^3 + 32 * q^4 + 204 * q^6 + 248 * q^8 + 1620 * q^9 + 1252 * q^12 - 2708 * q^14 + 3080 * q^16 + 2070 * q^18 + 8244 * q^22 - 1032 * q^24 - 8084 * q^26 + 11664 * q^27 + 22924 * q^28 + 7160 * q^31 + 14792 * q^32 - 21132 * q^34 + 18344 * q^36 - 3608 * q^37 - 16884 * q^38 + 44904 * q^39 + 11608 * q^41 - 49444 * q^42 - 51772 * q^43 - 72296 * q^44 - 28516 * q^46 - 85048 * q^48 - 18756 * q^49 - 111624 * q^52 + 928 * q^53 + 100584 * q^54 - 53624 * q^56 + 152344 * q^58 + 228648 * q^62 + 11264 * q^64 - 56688 * q^66 - 161604 * q^67 + 359040 * q^68 - 200312 * q^71 + 563448 * q^72 - 78876 * q^74 - 153872 * q^76 + 26008 * q^77 - 624640 * q^78 - 282080 * q^79 + 65172 * q^81 - 410576 * q^82 - 99092 * q^83 + 297128 * q^84 + 27452 * q^86 - 464496 * q^88 + 3160 * q^89 - 519244 * q^92 + 293472 * q^93 - 148820 * q^94 + 395168 * q^96 + 663674 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	5.60486	−	0.765181i	0.990809	−	0.135266i
$2$	5.60486	−	0.765181i	0.990809	−	0.135266i
$3$	−17.3148			−1.11074			−0.555372	−	0.831602i	$-0.687424\pi$
$3$	−17.3148			−1.11074			−0.555372	+	0.831602i	$0.687424\pi$
$4$	30.8290	−	8.57748i	0.963406	−	0.268046i
$5$		0			0
$5$		0			0
$6$	−97.0471	+	13.2490i	−1.10054	+	0.150246i
$7$			9.19080i			0.0708938i	0.999372	+	0.0354469i	$0.0112855\pi$
$7$			9.19080i			0.0708938i	−0.999372	+	0.0354469i	$0.988715\pi$
$8$	166.229	−	71.6654i	0.918294	−	0.395899i
$9$	56.8021			0.233754
$10$		0			0
$11$			160.480i			0.399888i	0.979807	+	0.199944i	$0.0640760\pi$
$11$			160.480i			0.399888i	−0.979807	+	0.199944i	$0.935924\pi$
$12$	−533.798	+	148.517i	−1.07010	+	0.297731i
$13$	368.546			0.604831			0.302415	−	0.953176i	$-0.402207\pi$
$13$	368.546			0.604831			0.302415	+	0.953176i	$0.402207\pi$
$14$	7.03263	+	51.5132i	0.00958954	+	0.0702423i
$15$		0			0
$16$	876.854	−	528.870i	0.856303	−	0.516475i
$17$			1261.09i			1.05833i	0.848517	+	0.529167i	$0.177496\pi$
$17$			1261.09i			1.05833i	−0.848517	+	0.529167i	$0.822504\pi$
$18$	318.368	−	43.4639i	0.231605	−	0.0316190i
$19$		−	2486.75i		−	1.58033i	−0.612894	−	0.790165i	$-0.709995\pi$
$19$		−	2486.75i		−	1.58033i	0.612894	−	0.790165i	$-0.290005\pi$
$20$		0			0
$21$		−	159.137i		−	0.0787449i
$22$	122.796	+	899.467i	0.0540914	+	0.396213i
$23$		−	422.882i		−	0.166686i	−0.996521	−	0.0833431i	$-0.973440\pi$
$23$		−	422.882i		−	0.166686i	0.996521	−	0.0833431i	$-0.0265597\pi$
$24$	−2878.22	+	1240.87i	−1.01999	+	0.439743i
$25$		0			0
$26$	2065.65	−	282.005i	0.599272	−	0.0818132i
$27$	3223.98			0.851104
$28$	78.8339	+	283.343i	0.0190028	+	0.0682995i
$29$		−	5666.05i		−	1.25108i	−0.780192	−	0.625540i	$-0.784879\pi$
$29$		−	5666.05i		−	1.25108i	0.780192	−	0.625540i	$-0.215121\pi$
$30$		0			0
$31$	9387.13			1.75440			0.877200	−	0.480125i	$-0.159409\pi$
$31$	9387.13			1.75440			0.877200	+	0.480125i	$0.159409\pi$
$32$	4509.96	−	3635.20i	0.778571	−	0.627557i
$33$		−	2778.67i		−	0.444174i
$34$	964.961	+	7068.23i	0.143157	+	1.04861i
$35$		0			0
$36$	1751.15	−	487.219i	0.225200	−	0.0626568i
$37$	3566.43			0.428281			0.214141	−	0.976803i	$-0.431305\pi$
$37$	3566.43			0.428281			0.214141	+	0.976803i	$0.431305\pi$
$38$	−1902.81	−	13937.9i	−0.213765	−	1.56581i
$39$	−6381.30			−0.671812
$40$		0			0
$41$	−5949.95			−0.552782			−0.276391	−	0.961045i	$-0.589138\pi$
$41$	−5949.95			−0.552782			−0.276391	+	0.961045i	$0.589138\pi$
$42$	−121.769	−	891.941i	−0.0106515	−	0.0780212i
$43$	10658.5			0.879077			0.439538	−	0.898224i	$-0.355142\pi$
$43$	10658.5			0.879077			0.439538	+	0.898224i	$0.355142\pi$
$44$	1376.51	+	4947.43i	0.107188	+	0.385255i
$45$		0			0
$46$	−323.581	−	2370.20i	−0.0225470	−	0.165154i
$47$		−	9243.94i		−	0.610397i	−0.952289	−	0.305198i	$-0.901277\pi$
$47$		−	9243.94i		−	0.610397i	0.952289	−	0.305198i	$-0.0987228\pi$
$48$	−15182.5	+	9157.27i	−0.951133	+	0.573671i
$49$	16722.5			0.994974
$50$		0			0
$51$		−	21835.5i		−	1.17554i
$52$	11361.9	−	3161.20i	0.582697	−	0.162122i
$53$	8976.82			0.438968			0.219484	−	0.975616i	$-0.429563\pi$
$53$	8976.82			0.438968			0.219484	+	0.975616i	$0.429563\pi$
$54$	18070.0	−	2466.93i	0.843282	−	0.115126i
$55$		0			0
$56$	658.662	+	1527.78i	0.0280668	+	0.0651014i
$57$			43057.5i			1.75534i
$58$	−4335.55	−	31757.4i	−0.169229	−	1.23958i
$59$		−	27435.6i		−	1.02609i	−0.858363	−	0.513044i	$-0.828518\pi$
$59$		−	27435.6i		−	1.02609i	0.858363	−	0.513044i	$-0.171482\pi$
$60$		0			0
$61$		−	50515.3i		−	1.73819i	−0.494642	−	0.869097i	$-0.664701\pi$
$61$		−	50515.3i		−	1.73819i	0.494642	−	0.869097i	$-0.335299\pi$
$62$	52613.6	−	7182.86i	1.73828	−	0.237311i
$63$			522.057i			0.0165717i
$64$	22496.2	−	23825.7i	0.686528	−	0.727103i
$65$		0			0
$66$	−2126.19	−	15574.1i	−0.0600817	−	0.440091i
$67$	5964.39			0.162323			0.0811613	−	0.996701i	$-0.474137\pi$
$67$	5964.39			0.162323			0.0811613	+	0.996701i	$0.474137\pi$
$68$	10817.0	+	38878.1i	0.283683	+	1.01961i
$69$			7322.11i			0.185146i
$70$		0			0
$71$	67286.3			1.58409			0.792046	−	0.610461i	$-0.209016\pi$
$71$	67286.3			1.58409			0.792046	+	0.610461i	$0.209016\pi$
$72$	9442.16	−	4070.75i	0.214655	−	0.0925428i
$73$			85768.5i			1.88374i	0.335979	+	0.941869i	$0.390933\pi$
$73$			85768.5i			1.88374i	−0.335979	+	0.941869i	$0.609067\pi$
$74$	19989.3	−	2728.96i	0.424345	−	0.0579320i
$75$		0			0
$76$	−21330.0	−	76663.9i	−0.423601	−	1.52250i
$77$	−1474.94			−0.0283496
$78$	−35766.3	+	4882.86i	−0.665638	+	0.0908735i
$79$	−56567.2			−1.01976			−0.509879	−	0.860246i	$-0.670310\pi$
$79$	−56567.2			−1.01976			−0.509879	+	0.860246i	$0.670310\pi$
$80$		0			0
$81$	−69625.4			−1.17911
$82$	−33348.6	+	4552.79i	−0.547701	+	0.0747727i
$83$	−30208.1			−0.481314			−0.240657	−	0.970610i	$-0.577363\pi$
$83$	−30208.1			−0.481314			−0.240657	+	0.970610i	$0.577363\pi$
$84$	−1364.99	−	4906.03i	−0.0211073	−	0.0758633i
$85$		0			0
$86$	59739.7	−	8155.72i	0.870997	−	0.118909i
$87$			98106.4i			1.38963i
$88$	11500.8	+	26676.4i	0.158315	+	0.367215i
$89$	−113965.			−1.52509			−0.762544	−	0.646936i	$-0.776050\pi$
$89$	−113965.			−1.52509			−0.762544	+	0.646936i	$0.776050\pi$
$90$		0			0
$91$			3387.24i			0.0428787i
$92$	−3627.26	−	13037.0i	−0.0446796	−	0.160586i
$93$	−162536.			−1.94869
$94$	−7073.29	−	51811.0i	−0.0825661	−	0.604787i
$95$		0			0
$96$	−78089.1	+	62942.7i	−0.864794	+	0.697055i
$97$			138806.i			1.49788i	0.662635	+	0.748942i	$0.269438\pi$
$97$			138806.i			1.49788i	−0.662635	+	0.748942i	$0.730562\pi$
$98$	93727.5	−	12795.8i	0.985830	−	0.134586i
$99$			9115.59i			0.0934753i
$100$		0			0
$101$			128473.i			1.25317i	0.779354	+	0.626584i	$0.215547\pi$
$101$			128473.i			1.25317i	−0.779354	+	0.626584i	$0.784453\pi$
$102$	−16708.1	−	122385.i	−0.159011	−	1.16474i
$103$		−	117231.i		−	1.08880i	−0.838825	−	0.544401i	$-0.816757\pi$
$103$		−	117231.i		−	1.08880i	0.838825	−	0.544401i	$-0.183243\pi$
$104$	61263.1	−	26412.0i	0.555412	−	0.239452i
$105$		0			0
$106$	50313.9	−	6868.90i	0.434934	−	0.0593776i
$107$	−17654.6			−0.149073			−0.0745366	−	0.997218i	$-0.523748\pi$
$107$	−17654.6			−0.149073			−0.0745366	+	0.997218i	$0.523748\pi$
$108$	99392.0	−	27653.6i	0.819959	−	0.228135i
$109$			75398.4i			0.607849i	0.952696	+	0.303925i	$0.0982971\pi$
$109$			75398.4i			0.607849i	−0.952696	+	0.303925i	$0.901703\pi$
$110$		0			0
$111$	−61752.0			−0.475711
$112$	4860.74	+	8058.99i	0.0366149	+	0.0607066i
$113$			69211.7i			0.509898i	0.966954	+	0.254949i	$0.0820587\pi$
$113$			69211.7i			0.509898i	−0.966954	+	0.254949i	$0.917941\pi$
$114$	32946.8	+	241332.i	0.237439	+	1.73921i
$115$		0			0
$116$	−48600.4	−	174678.i	−0.335347	−	1.20530i
$117$	20934.2			0.141381
$118$	−20993.2	−	153773.i	−0.138795	−	1.01666i
$119$	−11590.4			−0.0750294
$120$		0			0
$121$	135297.			0.840089
$122$	−38653.4	−	283131.i	−0.235119	−	1.72222i
$123$	103022.			0.613999
$124$	289396.	−	80517.9i	1.69020	−	0.470260i
$125$		0			0
$126$	399.469	+	2926.06i	0.00224159	+	0.0164194i
$127$			118525.i			0.652078i	0.945356	+	0.326039i	$0.105714\pi$
$127$			118525.i			0.652078i	−0.945356	+	0.326039i	$0.894286\pi$
$128$	107857.	−	150754.i	0.581866	−	0.813285i
$129$	−184551.			−0.976430
$130$		0			0
$131$			83761.8i			0.426450i	0.977003	+	0.213225i	$0.0683967\pi$
$131$			83761.8i			0.426450i	−0.977003	+	0.213225i	$0.931603\pi$
$132$	−23834.0	−	85663.7i	−0.119059	−	0.427920i
$133$	22855.2			0.112036
$134$	33429.6	−	4563.84i	0.160831	−	0.0219568i
$135$		0			0
$136$	90376.3	+	209629.i	0.418994	+	0.971863i
$137$		−	174055.i		−	0.792291i	−0.918188	−	0.396145i	$-0.870348\pi$
$137$		−	174055.i		−	0.792291i	0.918188	−	0.396145i	$-0.129652\pi$
$138$	5602.75	+	41039.5i	0.0250440	+	0.183444i
$139$		−	310792.i		−	1.36437i	−0.731179	−	0.682186i	$-0.761029\pi$
$139$		−	310792.i		−	1.36437i	0.731179	−	0.682186i	$-0.238971\pi$
$140$		0			0
$141$			160057.i			0.677995i
$142$	377130.	−	51486.2i	1.56953	−	0.214274i
$143$			59144.2i			0.241865i
$144$	49807.2	−	30040.9i	0.200164	−	0.120728i
$145$		0			0
$146$	65628.5	+	480721.i	0.254806	+	1.86643i
$147$	−289547.			−1.10516
$148$	109949.	−	30590.9i	0.412609	−	0.114799i
$149$			293656.i			1.08361i	0.840504	+	0.541805i	$0.182259\pi$
$149$			293656.i			1.08361i	−0.840504	+	0.541805i	$0.817741\pi$
$150$		0			0
$151$	26058.5			0.0930052			0.0465026	−	0.998918i	$-0.485192\pi$
$151$	26058.5			0.0930052			0.0465026	+	0.998918i	$0.485192\pi$
$152$	−178214.	−	413370.i	−0.625651	−	1.45121i
$153$			71632.5i			0.247390i
$154$	−8266.82	+	1128.60i	−0.0280890	+	0.00383474i
$155$		0			0
$156$	−196729.	+	54735.5i	−0.647228	+	0.180077i
$157$	−427448.			−1.38399			−0.691997	−	0.721900i	$-0.743269\pi$
$157$	−427448.			−1.38399			−0.691997	+	0.721900i	$0.743269\pi$
$158$	−317051.	+	43284.2i	−1.01039	+	0.137939i
$159$	−155432.			−0.487581
$160$		0			0
$161$	3886.62			0.0118170
$162$	−390241.	+	53276.1i	−1.16828	+	0.159494i
$163$	547292.			1.61343			0.806715	−	0.590941i	$-0.201243\pi$
$163$	547292.			1.61343			0.806715	+	0.590941i	$0.201243\pi$
$164$	−183431.	+	51035.5i	−0.532553	+	0.148171i
$165$		0			0
$166$	−169312.	+	23114.7i	−0.476890	+	0.0651055i
$167$			203146.i			0.563659i	0.959465	+	0.281829i	$0.0909412\pi$
$167$			203146.i			0.563659i	−0.959465	+	0.281829i	$0.909059\pi$
$168$	−11404.6	−	26453.2i	−0.0311750	−	0.0723110i
$169$	−235467.			−0.634180
$170$		0			0
$171$		−	141253.i		−	0.369408i
$172$	328592.	−	91423.4i	0.846908	−	0.235633i
$173$	−94689.2			−0.240539			−0.120269	−	0.992741i	$-0.538376\pi$
$173$	−94689.2			−0.240539			−0.120269	+	0.992741i	$0.538376\pi$
$174$	75069.2	+	549873.i	0.187970	+	1.37686i
$175$		0			0
$176$	84872.9	+	140717.i	0.206532	+	0.342425i
$177$			475042.i			1.13972i
$178$	−638756.	+	87203.6i	−1.51107	+	0.206293i
$179$		−	290099.i		−	0.676727i	−0.941016	−	0.338363i	$-0.890127\pi$
$179$		−	290099.i		−	0.676727i	0.941016	−	0.338363i	$-0.109873\pi$
$180$		0			0
$181$			63999.0i			0.145203i	0.997361	+	0.0726017i	$0.0231302\pi$
$181$			63999.0i			0.145203i	−0.997361	+	0.0726017i	$0.976870\pi$
$182$	2591.85	+	18985.0i	0.00580005	+	0.0424847i
$183$			874662.i			1.93069i
$184$	−30306.0	−	70295.2i	−0.0659909	−	0.153067i
$185$		0			0
$186$	−910994.	+	124370.i	−1.93078	+	0.263592i
$187$	−202379.			−0.423216
$188$	−79289.6	−	284981.i	−0.163615	−	0.588060i
$189$			29630.9i			0.0603380i
$190$		0			0
$191$	−391768.			−0.777044			−0.388522	−	0.921439i	$-0.627014\pi$
$191$	−391768.			−0.777044			−0.388522	+	0.921439i	$0.627014\pi$
$192$	−389516.	+	412537.i	−0.762557	+	0.807626i
$193$		−	641122.i		−	1.23893i	−0.785024	−	0.619466i	$-0.787349\pi$
$193$		−	641122.i		−	1.23893i	0.785024	−	0.619466i	$-0.212651\pi$
$194$	106212.	+	777988.i	0.202613	+	1.48412i
$195$		0			0
$196$	515539.	−	143437.i	0.958564	−	0.266699i
$197$	312130.			0.573019			0.286510	−	0.958077i	$-0.407505\pi$
$197$	312130.			0.573019			0.286510	+	0.958077i	$0.407505\pi$
$198$	6975.08	+	51091.7i	0.0126441	+	0.0926162i
$199$	−171473.			−0.306946			−0.153473	−	0.988153i	$-0.549046\pi$
$199$	−171473.			−0.306946			−0.153473	+	0.988153i	$0.549046\pi$
$200$		0			0
$201$	−103272.			−0.180299
$202$	98305.3	+	720075.i	0.169511	+	1.24165i
$203$	52075.5			0.0886938
$204$	−187293.	−	673166.i	−0.315099	−	1.13252i
$205$		0			0
$206$	−89702.8	−	657063.i	−0.147278	−	1.07879i
$207$		−	24020.6i		−	0.0389635i
$208$	323161.	−	194913.i	0.517918	−	0.312380i
$209$	399073.			0.631955
$210$		0			0
$211$		−	679022.i		−	1.04997i	−0.851111	−	0.524986i	$-0.824070\pi$
$211$		−	679022.i		−	1.04997i	0.851111	−	0.524986i	$-0.175930\pi$
$212$	276746.	−	76998.5i	0.422905	−	0.117664i
$213$	−1.16505e6			−1.75952
$214$	−98951.8	+	13509.0i	−0.147703	+	0.0201646i
$215$		0			0
$216$	535919.	−	231048.i	0.781564	−	0.336951i
$217$			86275.3i			0.124376i
$218$	57693.5	+	422598.i	0.0822215	+	0.602263i
$219$		−	1.48506e6i		−	2.09235i
$220$		0			0
$221$			464769.i			0.640113i
$222$	−346111.	+	47251.5i	−0.471339	+	0.0643477i
$223$			976043.i			1.31434i	0.753743	+	0.657169i	$0.228246\pi$
$223$			976043.i			1.31434i	−0.753743	+	0.657169i	$0.771754\pi$
$224$	33410.4	+	41450.2i	0.0444899	+	0.0551959i
$225$		0			0
$226$	52959.5	+	387922.i	0.0689720	+	0.505212i
$227$	243426.			0.313547			0.156773	−	0.987635i	$-0.449891\pi$
$227$	243426.			0.313547			0.156773	+	0.987635i	$0.449891\pi$
$228$	369325.	+	1.32742e6i	0.470513	+	1.69111i
$229$			1.33345e6i			1.68030i	0.542354	+	0.840150i	$0.317533\pi$
$229$			1.33345e6i			1.68030i	−0.542354	+	0.840150i	$0.682467\pi$
$230$		0			0
$231$	25538.2			0.0314892
$232$	−406059.	−	941861.i	−0.495301	−	1.14886i
$233$		−	1.01947e6i		−	1.23023i	−0.788438	−	0.615114i	$-0.789110\pi$
$233$		−	1.01947e6i		−	1.23023i	0.788438	−	0.615114i	$-0.210890\pi$
$234$	117333.	−	16018.5i	0.140082	−	0.0191241i
$235$		0			0
$236$	−235328.	−	845812.i	−0.275039	−	0.988539i
$237$	979449.			1.13269
$238$	−64962.7	+	8868.77i	−0.0743398	+	0.0101489i
$239$	975796.			1.10501			0.552503	−	0.833511i	$-0.313673\pi$
$239$	975796.			1.10501			0.552503	+	0.833511i	$0.313673\pi$
$240$		0			0
$241$	359018.			0.398175			0.199087	−	0.979982i	$-0.436202\pi$
$241$	359018.			0.398175			0.199087	+	0.979982i	$0.436202\pi$
$242$	758323.	−	103527.i	0.832368	−	0.113636i
$243$	422124.			0.458589
$244$	−433294.	−	1.55734e6i	−0.465916	−	1.67459i
$245$		0			0
$246$	577425.	−	78830.6i	0.608356	−	0.0830534i
$247$		−	916482.i		−	0.955832i
$248$	1.56041e6	−	672732.i	1.61106	−	0.694565i
$249$	523047.			0.534616
$250$		0			0
$251$			208180.i			0.208572i	0.994547	+	0.104286i	$0.0332557\pi$
$251$			208180.i			0.208572i	−0.994547	+	0.104286i	$0.966744\pi$
$252$	4477.93	+	16094.5i	0.00444198	+	0.0159653i
$253$	67864.0			0.0666558
$254$	90692.8	+	664314.i	0.0882041	+	0.646084i
$255$		0			0
$256$	489169.	−	927483.i	0.466508	−	0.884517i
$257$		−	1.82101e6i		−	1.71981i	−0.510456	−	0.859904i	$-0.670523\pi$
$257$		−	1.82101e6i		−	1.71981i	0.510456	−	0.859904i	$-0.329477\pi$
$258$	−1.03438e6	+	141215.i	−0.967456	+	0.132078i
$259$			32778.3i			0.0303625i
$260$		0			0
$261$		−	321844.i		−	0.292445i
$262$	64093.0	+	469474.i	0.0576843	+	0.422531i
$263$		−	1.74901e6i		−	1.55921i	−0.626274	−	0.779603i	$-0.715421\pi$
$263$		−	1.74901e6i		−	1.55921i	0.626274	−	0.779603i	$-0.284579\pi$
$264$	−199135.	−	461896.i	−0.175848	−	0.407882i
$265$		0			0
$266$	128100.	−	17488.4i	0.111006	−	0.0151546i
$267$	1.97327e6			1.69398
$268$	183876.	−	51159.4i	0.156383	−	0.0435099i
$269$			1.48042e6i			1.24740i	0.781665	+	0.623699i	$0.214371\pi$
$269$			1.48042e6i			1.24740i	−0.781665	+	0.623699i	$0.785629\pi$
$270$		0			0
$271$	1.04418e6			0.863680			0.431840	−	0.901950i	$-0.357864\pi$
$271$	1.04418e6			0.863680			0.431840	+	0.901950i	$0.357864\pi$
$272$	666951.	+	1.10579e6i	0.546603	+	0.906255i
$273$		−	58649.3i		−	0.0476273i
$274$	−133183.	−	975553.i	−0.107170	−	0.785009i
$275$		0			0
$276$	62805.3	+	225733.i	0.0496276	+	0.178371i
$277$	−22792.5			−0.0178481			−0.00892407	−	0.999960i	$-0.502841\pi$
$277$	−22792.5			−0.0178481			−0.00892407	+	0.999960i	$0.502841\pi$
$278$	−237812.	−	1.74195e6i	−0.184553	−	1.35183i
$279$	533209.			0.410098
$280$		0			0
$281$	181092.			0.136815			0.0684074	−	0.997657i	$-0.478208\pi$
$281$	181092.			0.136815			0.0684074	+	0.997657i	$0.478208\pi$
$282$	122473.	+	897097.i	0.0917099	+	0.671764i
$283$	1.00940e6			0.749200			0.374600	−	0.927187i	$-0.377780\pi$
$283$	1.00940e6			0.749200			0.374600	+	0.927187i	$0.377780\pi$
$284$	2.07437e6	−	577146.i	1.52612	−	0.424610i
$285$		0			0
$286$	45256.1	+	331495.i	0.0327161	+	0.239642i
$287$		−	54684.8i		−	0.0391888i
$288$	256176.	−	206487.i	0.181994	−	0.146694i
$289$	−170486.			−0.120073
$290$		0			0
$291$		−	2.40339e6i		−	1.66377i
$292$	735677.	+	2.64416e6i	0.504929	+	1.81481i
$293$	−2.25558e6			−1.53493			−0.767465	−	0.641090i	$-0.778482\pi$
$293$	−2.25558e6			−1.53493			−0.767465	+	0.641090i	$0.778482\pi$
$294$	−1.62287e6	+	221556.i	−1.09500	+	0.149491i
$295$		0			0
$296$	592844.	−	255589.i	0.393288	−	0.169556i
$297$			517383.i			0.340346i
$298$	224700.	+	1.64590e6i	0.146576	+	1.07365i
$299$		−	155852.i		−	0.100817i
$300$		0			0
$301$			97960.6i			0.0623211i
$302$	146054.	−	19939.5i	0.0921504	−	0.0125805i
$303$		−	2.22449e6i		−	1.39195i
$304$	−1.31517e6	−	2.18051e6i	−0.816200	−	1.35324i
$305$		0			0
$306$	54811.9	+	401490.i	0.0334635	+	0.245116i
$307$	−2.42181e6			−1.46654			−0.733270	−	0.679938i	$-0.762007\pi$
$307$	−2.42181e6			−1.46654			−0.733270	+	0.679938i	$0.762007\pi$
$308$	−45470.8	+	12651.2i	−0.0273122	+	0.00759900i
$309$			2.02983e6i			1.20938i
$310$		0			0
$311$	−1.04918e6			−0.615107			−0.307554	−	0.951531i	$-0.599510\pi$
$311$	−1.04918e6			−0.615107			−0.307554	+	0.951531i	$0.599510\pi$
$312$	−1.06076e6	+	457318.i	−0.616921	+	0.265970i
$313$			919355.i			0.530423i	0.964190	+	0.265212i	$0.0854418\pi$
$313$			919355.i			0.530423i	−0.964190	+	0.265212i	$0.914558\pi$
$314$	−2.39579e6	+	327075.i	−1.37127	+	0.187208i
$315$		0			0
$316$	−1.74391e6	+	485204.i	−0.982441	+	0.273342i
$317$	761677.			0.425719			0.212859	−	0.977083i	$-0.431722\pi$
$317$	761677.			0.425719			0.212859	+	0.977083i	$0.431722\pi$
$318$	−871174.	+	118934.i	−0.483100	+	0.0659533i
$319$	909285.			0.500292
$320$		0			0
$321$	305686.			0.165582
$322$	21784.0	−	2973.97i	0.0117084	−	0.00159844i
$323$	3.13601e6			1.67252
$324$	−2.14648e6	+	597211.i	−1.13596	+	0.316057i
$325$		0			0
$326$	3.06750e6	−	418778.i	1.59860	−	0.218243i
$327$		−	1.30551e6i		−	0.675165i
$328$	−989054.	+	426405.i	−0.507616	+	0.218846i
$329$	84959.2			0.0432734
$330$		0			0
$331$			1.27292e6i			0.638605i	0.947653	+	0.319302i	$0.103449\pi$
$331$			1.27292e6i			0.638605i	−0.947653	+	0.319302i	$0.896551\pi$
$332$	−931285.	+	259109.i	−0.463700	+	0.129014i
$333$	202581.			0.100112
$334$	155443.	+	1.13860e6i	0.0762440	+	0.558478i
$335$		0			0
$336$	−84162.7	−	139540.i	−0.0406697	−	0.0674295i
$337$		−	1.61635e6i		−	0.775286i	−0.921810	−	0.387643i	$-0.873289\pi$
$337$		−	1.61635e6i		−	0.775286i	0.921810	−	0.387643i	$-0.126711\pi$
$338$	−1.31976e6	+	180175.i	−0.628351	+	0.0857832i
$339$		−	1.19839e6i		−	0.566367i
$340$		0			0
$341$			1.50644e6i			0.701564i
$342$	−108084.	−	791701.i	−0.0499684	−	0.366013i
$343$			308163.i			0.141431i
$344$	1.77176e6	−	763848.i	0.807251	−	0.348026i
$345$		0			0
$346$	−530720.	+	72454.4i	−0.238328	+	0.0325368i
$347$	349978.			0.156033			0.0780167	−	0.996952i	$-0.475141\pi$
$347$	349978.			0.156033			0.0780167	+	0.996952i	$0.475141\pi$
$348$	841505.	+	3.02452e6i	0.372485	+	1.33878i
$349$		−	2.38580e6i		−	1.04850i	−0.851563	−	0.524252i	$-0.824345\pi$
$349$		−	2.38580e6i		−	1.04850i	0.851563	−	0.524252i	$-0.175655\pi$
$350$		0			0
$351$	1.18819e6			0.514774
$352$	583375.	+	723758.i	0.250952	+	0.311341i
$353$			3.84764e6i			1.64345i	0.569882	+	0.821727i	$0.306989\pi$
$353$			3.84764e6i			1.64345i	−0.569882	+	0.821727i	$0.693011\pi$
$354$	363493.	+	2.66254e6i	0.154166	+	1.12925i
$355$		0			0
$356$	−3.51342e6	+	977529.i	−1.46928	+	0.408794i
$357$	200686.			0.0833385
$358$	−221978.	−	1.62596e6i	−0.0915383	−	0.670507i
$359$	2.69844e6			1.10503			0.552517	−	0.833501i	$-0.313667\pi$
$359$	2.69844e6			1.10503			0.552517	+	0.833501i	$0.313667\pi$
$360$		0			0
$361$	−3.70781e6			−1.49744
$362$	48970.9	+	358706.i	0.0196411	+	0.143869i
$363$	−2.34264e6			−0.933125
$364$	29053.9	+	104425.i	0.0114935	+	0.0413096i
$365$		0			0
$366$	669275.	+	4.90236e6i	0.261157	+	1.91295i
$367$		−	1.14096e6i		−	0.442186i	−0.975253	−	0.221093i	$-0.929038\pi$
$367$		−	1.14096e6i		−	0.442186i	0.975253	−	0.221093i	$-0.0709625\pi$
$368$	−223650.	−	370806.i	−0.0860892	−	0.142734i
$369$	−337970.			−0.129215
$370$		0			0
$371$			82504.2i			0.0311201i
$372$	−5.01083e6	+	1.39415e6i	−1.87738	+	0.522339i
$373$	461958.			0.171922			0.0859608	−	0.996299i	$-0.472604\pi$
$373$	461958.			0.171922			0.0859608	+	0.996299i	$0.472604\pi$
$374$	−1.13431e6	+	154857.i	−0.419326	+	0.0572468i
$375$		0			0
$376$	−662470.	−	1.53661e6i	−0.241655	−	0.560524i
$377$		−	2.08820e6i		−	0.756691i
$378$	22673.1	+	166077.i	0.00816170	+	0.0597835i
$379$		−	4.36174e6i		−	1.55977i	−0.625920	−	0.779887i	$-0.715277\pi$
$379$		−	4.36174e6i		−	1.55977i	0.625920	−	0.779887i	$-0.284723\pi$
$380$		0			0
$381$		−	2.05223e6i		−	0.724292i
$382$	−2.19581e6	+	299774.i	−0.769903	+	0.105108i
$383$		−	417638.i		−	0.145480i	−0.997351	−	0.0727400i	$-0.976826\pi$
$383$		−	417638.i		−	0.145480i	0.997351	−	0.0727400i	$-0.0231743\pi$
$384$	−1.86752e6	+	2.61027e6i	−0.646304	+	0.903352i
$385$		0			0
$386$	−490574.	−	3.59340e6i	−0.167586	−	1.22754i
$387$	605428.			0.205487
$388$	1.19060e6	+	4.27924e6i	0.401502	+	1.44307i
$389$			1.92396e6i			0.644647i	0.946630	+	0.322323i	$0.104464\pi$
$389$			1.92396e6i			0.644647i	−0.946630	+	0.322323i	$0.895536\pi$
$390$		0			0
$391$	533291.			0.176410
$392$	2.77977e6	−	1.19843e6i	0.913679	−	0.393909i
$393$		−	1.45032e6i		−	0.473677i
$394$	1.74944e6	−	238836.i	0.567753	−	0.0775102i
$395$		0			0
$396$	78188.8	+	281025.i	0.0250557	+	0.0900547i
$397$	−2.95436e6			−0.940778			−0.470389	−	0.882459i	$-0.655886\pi$
$397$	−2.95436e6			−0.940778			−0.470389	+	0.882459i	$0.655886\pi$
$398$	−961080.	+	131208.i	−0.304125	+	0.0415194i
$399$	−395733.			−0.124443
$400$		0			0
$401$	−1.57105e6			−0.487898			−0.243949	−	0.969788i	$-0.578443\pi$
$401$	−1.57105e6			−0.487898			−0.243949	+	0.969788i	$0.578443\pi$
$402$	−578826.	+	79021.9i	−0.178642	+	0.0243884i
$403$	3.45959e6			1.06112
$404$	1.10198e6	+	3.96070e6i	0.335907	+	1.20731i
$405$		0			0
$406$	291876.	−	39847.2i	0.0878787	−	0.0119973i
$407$			572339.i			0.171265i
$408$	−1.56485e6	−	3.62969e6i	−0.465395	−	1.07949i
$409$	5.18294e6			1.53203			0.766016	−	0.642821i	$-0.222236\pi$
$409$	5.18294e6			1.53203			0.766016	+	0.642821i	$0.222236\pi$
$410$		0			0
$411$			3.01372e6i			0.880033i
$412$	−1.00554e6	−	3.61411e6i	−0.291849	−	1.04896i
$413$	252155.			0.0727432
$414$	−18380.1	−	134632.i	−0.00527045	−	0.0386054i
$415$		0			0
$416$	1.66213e6	−	1.33974e6i	0.470903	−	0.379565i
$417$			5.38130e6i			1.51547i
$418$	2.23675e6	−	305363.i	0.626147	−	0.0854822i
$419$			4.81218e6i			1.33908i	0.742776	+	0.669540i	$0.233509\pi$
$419$			4.81218e6i			1.33908i	−0.742776	+	0.669540i	$0.766491\pi$
$420$		0			0
$421$			4.66983e6i			1.28409i	0.766667	+	0.642045i	$0.221914\pi$
$421$			4.66983e6i			1.28409i	−0.766667	+	0.642045i	$0.778086\pi$
$422$	−519575.	−	3.80583e6i	−0.142026	−	1.04032i
$423$		−	525075.i		−	0.142683i
$424$	1.49221e6	−	643327.i	0.403102	−	0.173787i
$425$		0			0
$426$	−6.52994e6	+	891473.i	−1.74335	+	0.238004i
$427$	464276.			0.123227
$428$	−544275.	+	151432.i	−0.143618	+	0.0399585i
$429$		−	1.02407e6i		−	0.268650i
$430$		0			0
$431$	−3.07756e6			−0.798020			−0.399010	−	0.916947i	$-0.630646\pi$
$431$	−3.07756e6			−0.798020			−0.399010	+	0.916947i	$0.630646\pi$
$432$	2.82696e6	−	1.70506e6i	0.728803	−	0.439574i
$433$		−	2.60694e6i		−	0.668206i	−0.942537	−	0.334103i	$-0.891567\pi$
$433$		−	2.60694e6i		−	0.668206i	0.942537	−	0.334103i	$-0.108433\pi$
$434$	66016.3	+	483561.i	0.0168239	+	0.123233i
$435$		0			0
$436$	646728.	+	2.32446e6i	0.162932	+	0.585606i
$437$	−1.05160e6			−0.263419
$438$	−1.13634e6	−	8.32358e6i	−0.283025	−	2.07312i
$439$	−7.17040e6			−1.77575			−0.887876	−	0.460083i	$-0.847820\pi$
$439$	−7.17040e6			−1.77575			−0.887876	+	0.460083i	$0.847820\pi$
$440$		0			0
$441$	949875.			0.232579
$442$	355633.	+	2.60497e6i	0.0865857	+	0.634230i
$443$	−5.08067e6			−1.23002			−0.615009	−	0.788520i	$-0.710848\pi$
$443$	−5.08067e6			−1.23002			−0.615009	+	0.788520i	$0.710848\pi$
$444$	−1.90375e6	+	529676.i	−0.458303	+	0.127513i
$445$		0			0
$446$	746850.	+	5.47059e6i	0.177786	+	1.30226i
$447$		−	5.08459e6i		−	1.20361i
$448$	218978.	+	206758.i	0.0515471	+	0.0486706i
$449$	−3.18246e6			−0.744984			−0.372492	−	0.928035i	$-0.621497\pi$
$449$	−3.18246e6			−0.744984			−0.372492	+	0.928035i	$0.621497\pi$
$450$		0			0
$451$		−	954846.i		−	0.221051i
$452$	593662.	+	2.13373e6i	0.136676	+	0.491239i
$453$	−451198.			−0.103305
$454$	1.36437e6	−	186265.i	0.310665	−	0.0424123i
$455$		0			0
$456$	3.08573e6	+	7.15741e6i	0.694938	+	1.61192i
$457$			1.54454e6i			0.345946i	0.984927	+	0.172973i	$0.0553373\pi$
$457$			1.54454e6i			0.345946i	−0.984927	+	0.172973i	$0.944663\pi$
$458$	1.02033e6	+	7.47378e6i	0.227288	+	1.66486i
$459$			4.06572e6i			0.900753i
$460$		0			0
$461$		−	888536.i		−	0.194725i	−0.995249	−	0.0973627i	$-0.968959\pi$
$461$		−	888536.i		−	0.194725i	0.995249	−	0.0973627i	$-0.0310407\pi$
$462$	143138.	−	19541.4i	0.0311998	−	0.00425942i
$463$			3.53164e6i			0.765640i	0.923823	+	0.382820i	$0.125047\pi$
$463$			3.53164e6i			0.765640i	−0.923823	+	0.382820i	$0.874953\pi$
$464$	−2.99660e6	−	4.96829e6i	−0.646151	−	1.07130i
$465$		0			0
$466$	−780081.	−	5.71400e6i	−0.166408	−	1.21892i
$467$	−7.13335e6			−1.51357			−0.756783	−	0.653666i	$-0.773230\pi$
$467$	−7.13335e6			−1.51357			−0.756783	+	0.653666i	$0.773230\pi$
$468$	645381.	−	179563.i	0.136208	−	0.0378967i
$469$			54817.5i			0.0115077i
$470$		0			0
$471$	7.40118e6			1.53726
$472$	−1.96618e6	−	4.56059e6i	−0.406227	−	0.942250i
$473$			1.71048e6i			0.351532i
$474$	5.48968e6	−	749457.i	1.12228	−	0.153215i
$475$		0			0
$476$	−357321.	+	99416.5i	−0.0722838	+	0.0201113i
$477$	509903.			0.102610
$478$	5.46920e6	−	746661.i	1.09485	−	0.149470i
$479$	−5.02213e6			−1.00011			−0.500057	−	0.865992i	$-0.666688\pi$
$479$	−5.02213e6			−1.00011			−0.500057	+	0.865992i	$0.666688\pi$
$480$		0			0
$481$	1.31439e6			0.259038
$482$	2.01225e6	−	274714.i	0.394515	−	0.0538596i
$483$	−67296.1			−0.0131257
$484$	4.17108e6	−	1.16051e6i	0.809347	−	0.225183i
$485$		0			0
$486$	2.36595e6	−	323001.i	0.454375	−	0.0620317i
$487$			9.04360e6i			1.72790i	0.503576	+	0.863951i	$0.332017\pi$
$487$			9.04360e6i			1.72790i	−0.503576	+	0.863951i	$0.667983\pi$
$488$	−3.62020e6	−	8.39710e6i	−0.688149	−	1.59617i
$489$	−9.47625e6			−1.79211
$490$		0			0
$491$			1.91922e6i			0.359270i	0.983733	+	0.179635i	$0.0574916\pi$
$491$			1.91922e6i			0.359270i	−0.983733	+	0.179635i	$0.942508\pi$
$492$	3.17607e6	−	883670.i	0.591531	−	0.164580i
$493$	7.14538e6			1.32406
$494$	−701275.	−	5.13675e6i	−0.129292	−	0.947047i
$495$		0			0
$496$	8.23114e6	−	4.96457e6i	1.50230	−	0.906103i
$497$			618415.i			0.112302i
$498$	2.93161e6	−	400226.i	0.529703	−	0.0723156i
$499$			1.22004e6i			0.219342i	0.993968	+	0.109671i	$0.0349797\pi$
$499$			1.22004e6i			0.219342i	−0.993968	+	0.109671i	$0.965020\pi$
$500$		0			0
$501$		−	3.51742e6i		−	0.626081i
$502$	159296.	+	1.16682e6i	0.0282127	+	0.206655i
$503$			7.08742e6i			1.24902i	0.781018	+	0.624508i	$0.214700\pi$
$503$			7.08742e6i			1.24902i	−0.781018	+	0.624508i	$0.785300\pi$
$504$	37413.4	+	86781.1i	0.00656071	+	0.0152177i
$505$		0			0
$506$	380368.	−	51928.3i	0.0660432	−	0.00901628i
$507$	4.07706e6			0.704412
$508$	1.01664e6	+	3.65399e6i	0.174787	+	0.628215i
$509$		−	5.58984e6i		−	0.956324i	−0.878272	−	0.478162i	$-0.841303\pi$
$509$		−	5.58984e6i		−	0.956324i	0.878272	−	0.478162i	$-0.158697\pi$
$510$		0			0
$511$	−788281.			−0.133545
$512$	2.03203e6	−	5.57272e6i	0.342575	−	0.939490i
$513$		−	8.01722e6i		−	1.34502i
$514$	−1.39340e6	−	1.02065e7i	−0.232632	−	1.70400i
$515$		0			0
$516$	−5.68951e6	+	1.58298e6i	−0.940698	+	0.261728i
$517$	1.48346e6			0.244090
$518$	25081.4	+	183718.i	0.00410702	+	0.0300834i
$519$	1.63952e6			0.267177
$520$		0			0
$521$	8.47810e6			1.36837			0.684186	−	0.729308i	$-0.260158\pi$
$521$	8.47810e6			1.36837			0.684186	+	0.729308i	$0.260158\pi$
$522$	−246269.	−	1.80389e6i	−0.0395579	−	0.289757i
$523$	−6.21299e6			−0.993223			−0.496611	−	0.867973i	$-0.665423\pi$
$523$	−6.21299e6			−0.993223			−0.496611	+	0.867973i	$0.665423\pi$
$524$	718465.	+	2.58229e6i	0.114308	+	0.410844i
$525$		0			0
$526$	−1.33831e6	−	9.80298e6i	−0.210908	−	1.54488i
$527$			1.18380e7i			1.85674i
$528$	−1.46956e6	−	2.43649e6i	−0.229404	−	0.380347i
$529$	6.25751e6			0.972216
$530$		0			0
$531$		−	1.55840e6i		−	0.239852i
$532$	704603.	−	196040.i	0.107936	−	0.0300307i
$533$	−2.19283e6			−0.334339
$534$	1.10599e7	−	1.50991e6i	1.67842	−	0.229139i
$535$		0			0
$536$	991454.	−	427440.i	0.149060	−	0.0642633i
$537$			5.02300e6i			0.751670i
$538$	1.13279e6	+	8.29757e6i	0.168731	+	1.23593i
$539$			2.68363e6i			0.397878i
$540$		0			0
$541$		−	7.13892e6i		−	1.04867i	−0.851512	−	0.524335i	$-0.824314\pi$
$541$		−	7.13892e6i		−	1.04867i	0.851512	−	0.524335i	$-0.175686\pi$
$542$	5.85250e6	−	798989.i	0.855742	−	0.116827i
$543$		−	1.10813e6i		−	0.161284i
$544$	4.58430e6	+	5.68746e6i	0.664165	+	0.823989i
$545$		0			0
$546$	−44877.4	−	328721.i	−0.00644237	−	0.0471896i
$547$	7.31142e6			1.04480			0.522400	−	0.852700i	$-0.325037\pi$
$547$	7.31142e6			1.04480			0.522400	+	0.852700i	$0.325037\pi$
$548$	−1.49295e6	−	5.36593e6i	−0.212370	−	0.763298i
$549$		−	2.86938e6i		−	0.406309i
$550$		0			0
$551$	−1.40900e7			−1.97712
$552$	524742.	+	1.21715e6i	0.0732990	+	0.170018i
$553$		−	519898.i		−	0.0722945i
$554$	−127749.	+	17440.4i	−0.0176841	+	0.00241425i
$555$		0			0
$556$	−2.66581e6	−	9.58140e6i	−0.365715	−	1.31444i
$557$	−1.92783e6			−0.263288			−0.131644	−	0.991297i	$-0.542026\pi$
$557$	−1.92783e6			−0.263288			−0.131644	+	0.991297i	$0.542026\pi$
$558$	2.98857e6	−	408002.i	0.406329	−	0.0554724i
$559$	3.92817e6			0.531692
$560$		0			0
$561$	3.50415e6			0.470084
$562$	1.01499e6	−	138568.i	0.135557	−	0.0185064i
$563$	−1.29516e7			−1.72208			−0.861039	−	0.508539i	$-0.830186\pi$
$563$	−1.29516e7			−1.72208			−0.861039	+	0.508539i	$0.830186\pi$
$564$	1.37288e6	+	4.93439e6i	0.181734	+	0.653185i
$565$		0			0
$566$	5.65756e6	−	772375.i	0.742314	−	0.101341i
$567$		−	639914.i		−	0.0835918i
$568$	1.11849e7	−	4.82210e6i	1.45466	−	0.627141i
$569$	−7.26039e6			−0.940112			−0.470056	−	0.882637i	$-0.655766\pi$
$569$	−7.26039e6			−0.940112			−0.470056	+	0.882637i	$0.655766\pi$
$570$		0			0
$571$			1.83619e6i			0.235682i	0.993032	+	0.117841i	$0.0375973\pi$
$571$			1.83619e6i			0.235682i	−0.993032	+	0.117841i	$0.962403\pi$
$572$	507308.	+	1.82336e6i	0.0648309	+	0.233014i
$573$	6.78339e6			0.863098
$574$	−41843.8	−	306501.i	−0.00530092	−	0.0388286i
$575$		0			0
$576$	1.27783e6	−	1.35335e6i	0.160478	−	0.169963i
$577$		−	2.04937e6i		−	0.256260i	−0.991757	−	0.128130i	$-0.959102\pi$
$577$		−	2.04937e6i		−	0.256260i	0.991757	−	0.128130i	$-0.0408975\pi$
$578$	−955550.	+	130453.i	−0.118969	+	0.0162418i
$579$			1.11009e7i			1.37614i
$580$		0			0
$581$		−	277637.i		−	0.0341222i
$582$	−1.83903e6	−	1.34707e7i	−0.225052	−	1.64848i
$583$			1.44060e6i			0.175538i
$584$	6.14663e6	+	1.42572e7i	0.745770	+	1.72983i
$585$		0			0
$586$	−1.26422e7	+	1.72593e6i	−1.52082	+	0.207624i
$587$	2.38716e6			0.285947			0.142974	−	0.989726i	$-0.454334\pi$
$587$	2.38716e6			0.285947			0.142974	+	0.989726i	$0.454334\pi$
$588$	−8.92645e6	+	2.48358e6i	−1.06472	+	0.296234i
$589$		−	2.33434e7i		−	2.77253i
$590$		0			0
$591$	−5.40446e6			−0.636478
$592$	3.12724e6	−	1.88618e6i	0.366738	−	0.221196i
$593$			1.01237e7i			1.18223i	0.806587	+	0.591116i	$0.201312\pi$
$593$			1.01237e7i			1.18223i	−0.806587	+	0.591116i	$0.798688\pi$
$594$	395892.	+	2.89986e6i	0.0460374	+	0.337218i
$595$		0			0
$596$	2.51883e6	+	9.05311e6i	0.290457	+	1.04396i
$597$	2.96901e6			0.340939
$598$	−119255.	−	873527.i	−0.0136371	−	0.0998903i
$599$	−3.96697e6			−0.451743			−0.225872	−	0.974157i	$-0.572523\pi$
$599$	−3.96697e6			−0.451743			−0.225872	+	0.974157i	$0.572523\pi$
$600$		0			0
$601$	5.94578e6			0.671464			0.335732	−	0.941958i	$-0.391016\pi$
$601$	5.94578e6			0.671464			0.335732	+	0.941958i	$0.391016\pi$
$602$	74957.6	+	549056.i	0.00842994	+	0.0617483i
$603$	338790.			0.0379435
$604$	803358.	−	223516.i	0.0896018	−	0.0249297i
$605$		0			0
$606$	−1.70214e6	−	1.24680e7i	−0.188284	−	1.37916i
$607$			900508.i			0.0992010i	0.998769	+	0.0496005i	$0.0157948\pi$
$607$			900508.i			0.0992010i	−0.998769	+	0.0496005i	$0.984205\pi$
$608$	−9.03981e6	−	1.12151e7i	−0.991746	−	1.23040i
$609$	−901677.			−0.0985162
$610$		0			0
$611$		−	3.40682e6i		−	0.369187i
$612$	614426.	+	2.20836e6i	0.0663118	+	0.238337i
$613$	−4.07379e6			−0.437872			−0.218936	−	0.975739i	$-0.570259\pi$
$613$	−4.07379e6			−0.437872			−0.218936	+	0.975739i	$0.570259\pi$
$614$	−1.35739e7	+	1.85312e6i	−1.45306	+	0.198373i
$615$		0			0
$616$	−245177.	+	105702.i	−0.0260333	+	0.0112236i
$617$		−	3.83021e6i		−	0.405051i	−0.979277	−	0.202525i	$-0.935085\pi$
$617$		−	3.83021e6i		−	0.405051i	0.979277	−	0.202525i	$-0.0649148\pi$
$618$	1.55319e6	+	1.13769e7i	0.163588	+	1.19826i
$619$		−	9.65601e6i		−	1.01291i	−0.862266	−	0.506455i	$-0.830955\pi$
$619$		−	9.65601e6i		−	1.01291i	0.862266	−	0.506455i	$-0.169045\pi$
$620$		0			0
$621$		−	1.36336e6i		−	0.141867i
$622$	−5.88053e6	+	802816.i	−0.609454	+	0.0832032i
$623$		−	1.04743e6i		−	0.108119i
$624$	−5.59547e6	+	3.37488e6i	−0.575275	+	0.346974i
$625$		0			0
$626$	703473.	+	5.15286e6i	0.0717483	+	0.525548i
$627$	−6.90986e6			−0.701941
$628$	−1.31778e7	+	3.66643e6i	−1.33335	+	0.370974i
$629$			4.49758e6i			0.453265i
$630$		0			0
$631$	8.80367e6			0.880218			0.440109	−	0.897944i	$-0.354940\pi$
$631$	8.80367e6			0.880218			0.440109	+	0.897944i	$0.354940\pi$
$632$	−9.40311e6	+	4.05391e6i	−0.936437	+	0.403721i
$633$			1.17571e7i			1.16625i
$634$	4.26910e6	−	582821.i	0.421806	−	0.0575854i
$635$		0			0
$636$	−4.79181e6	+	1.33321e6i	−0.469739	+	0.130694i
$637$	6.16303e6			0.601791
$638$	5.09642e6	−	695768.i	0.495694	−	0.0676726i
$639$	3.82201e6			0.370288
$640$		0			0
$641$	−8.42581e6			−0.809966			−0.404983	−	0.914324i	$-0.632722\pi$
$641$	−8.42581e6			−0.809966			−0.404983	+	0.914324i	$0.632722\pi$
$642$	1.71333e6	−	233906.i	0.164060	−	0.0223977i
$643$	559011.			0.0533204			0.0266602	−	0.999645i	$-0.491513\pi$
$643$	559011.			0.0533204			0.0266602	+	0.999645i	$0.491513\pi$
$644$	119821.	−	33337.4i	0.0113846	−	0.00316751i
$645$		0			0
$646$	1.75769e7	−	2.39961e6i	1.65715	−	0.226235i
$647$			1.60950e7i			1.51158i	0.654814	+	0.755790i	$0.272747\pi$
$647$			1.60950e7i			1.51158i	−0.654814	+	0.755790i	$0.727253\pi$
$648$	−1.15738e7	+	4.98973e6i	−1.08277	+	0.466810i
$649$	4.40286e6			0.410320
$650$		0			0
$651$		−	1.49384e6i		−	0.138150i
$652$	1.68725e7	−	4.69438e6i	1.55439	−	0.432473i
$653$	2.03856e7			1.87085			0.935427	−	0.353520i	$-0.115015\pi$
$653$	2.03856e7			1.87085			0.935427	+	0.353520i	$0.115015\pi$
$654$	−998951.	−	7.31720e6i	−0.0913271	−	0.668960i
$655$		0			0
$656$	−5.21723e6	+	3.14675e6i	−0.473348	+	0.285498i
$657$			4.87184e6i			0.440331i
$658$	476185.	−	65009.2i	0.0428757	−	0.00585343i
$659$			6.70475e6i			0.601408i	0.953718	+	0.300704i	$0.0972216\pi$
$659$			6.70475e6i			0.601408i	−0.953718	+	0.300704i	$0.902778\pi$
$660$		0			0
$661$		−	5.17558e6i		−	0.460739i	−0.973103	−	0.230370i	$-0.926006\pi$
$661$		−	5.17558e6i		−	0.460739i	0.973103	−	0.230370i	$-0.0739935\pi$
$662$	974017.	+	7.13456e6i	0.0863817	+	0.632736i
$663$		−	8.04739e6i		−	0.711002i
$664$	−5.02146e6	+	2.16487e6i	−0.441987	+	0.190552i
$665$		0			0
$666$	1.13544e6	−	155011.i	0.0991922	−	0.0135418i
$667$	−2.39607e6			−0.208538
$668$	1.74248e6	+	6.26278e6i	0.151087	+	0.543032i
$669$		−	1.69000e7i		−	1.45989i
$670$		0			0
$671$	8.10668e6			0.695083
$672$	−578494.	−	717702.i	−0.0494169	−	0.0613085i
$673$		−	2.31161e6i		−	0.196733i	−0.995150	−	0.0983664i	$-0.968638\pi$
$673$		−	2.31161e6i		−	0.196733i	0.995150	−	0.0983664i	$-0.0313617\pi$
$674$	−1.23680e6	−	9.05945e6i	−0.104870	−	0.768160i
$675$		0			0
$676$	−7.25920e6	+	2.01971e6i	−0.610973	+	0.169989i
$677$	−1.01425e7			−0.850496			−0.425248	−	0.905077i	$-0.639813\pi$
$677$	−1.01425e7			−0.850496			−0.425248	+	0.905077i	$0.639813\pi$
$678$	−916983.	−	6.71679e6i	−0.0766103	−	0.561161i
$679$	−1.27574e6			−0.106191
$680$		0			0
$681$	−4.21487e6			−0.348270
$682$	1.15270e6	+	8.44342e6i	0.0948979	+	0.695116i
$683$	5.34488e6			0.438416			0.219208	−	0.975678i	$-0.429653\pi$
$683$	5.34488e6			0.438416			0.219208	+	0.975678i	$0.429653\pi$
$684$	−1.21159e6	−	4.35468e6i	−0.0990183	−	0.355890i
$685$		0			0
$686$	235801.	+	1.72721e6i	0.0191309	+	0.140131i
$687$		−	2.30883e7i		−	1.86638i
$688$	9.34599e6	−	5.63698e6i	0.752756	−	0.454021i
$689$	3.30837e6			0.265501
$690$		0			0
$691$			5.80594e6i			0.462570i	0.972886	+	0.231285i	$0.0742930\pi$
$691$			5.80594e6i			0.462570i	−0.972886	+	0.231285i	$0.925707\pi$
$692$	−2.91917e6	+	812195.i	−0.231737	+	0.0644755i
$693$	−83779.6			−0.00662682
$694$	1.96158e6	−	267797.i	0.154599	−	0.0211060i
$695$		0			0
$696$	7.03083e6	+	1.63081e7i	0.550153	+	1.27609i
$697$		−	7.50341e6i		−	0.585028i
$698$	−1.82557e6	−	1.33721e7i	−0.141827	−	1.03887i
$699$			1.76520e7i			1.36647i
$700$		0			0
$701$		−	6.84282e6i		−	0.525945i	−0.964803	−	0.262972i	$-0.915297\pi$
$701$		−	6.84282e6i		−	0.525945i	0.964803	−	0.262972i	$-0.0847028\pi$
$702$	6.65962e6	−	909177.i	0.510043	−	0.0696315i
$703$		−	8.86881e6i		−	0.676826i
$704$	3.82355e6	+	3.61018e6i	0.290760	+	0.274534i
$705$		0			0
$706$	2.94414e6	+	2.15655e7i	0.222304	+	1.62835i
$707$	−1.18077e6			−0.0888418
$708$	4.07466e6	+	1.46451e7i	0.305498	+	1.09801i
$709$			1.09625e7i			0.819019i	0.912306	+	0.409509i	$0.134300\pi$
$709$			1.09625e7i			0.819019i	−0.912306	+	0.409509i	$0.865700\pi$
$710$		0			0
$711$	−3.21314e6			−0.238372
$712$	−1.89442e7	+	8.16732e6i	−1.40048	+	0.603781i
$713$		−	3.96965e6i		−	0.292434i
$714$	1.12482e6	−	153561.i	0.0825726	−	0.0112729i
$715$		0			0
$716$	−2.48831e6	−	8.94345e6i	−0.181394	−	0.651963i
$717$	−1.68957e7			−1.22738
$718$	1.51244e7	−	2.06479e6i	1.09488	−	0.149474i
$719$	−4.16072e6			−0.300156			−0.150078	−	0.988674i	$-0.547952\pi$
$719$	−4.16072e6			−0.300156			−0.150078	+	0.988674i	$0.547952\pi$
$720$		0			0
$721$	1.07744e6			0.0771893
$722$	−2.07818e7	+	2.83715e6i	−1.48368	+	0.202553i
$723$	−6.21633e6			−0.442271
$724$	548950.	+	1.97303e6i	0.0389212	+	0.139890i
$725$		0			0
$726$	−1.31302e7	+	1.79255e6i	−0.924549	+	0.126220i
$727$		−	2.27412e7i		−	1.59580i	−0.602791	−	0.797899i	$-0.705945\pi$
$727$		−	2.27412e7i		−	1.59580i	0.602791	−	0.797899i	$-0.294055\pi$
$728$	242748.	+	563057.i	0.0169756	+	0.0393753i
$729$	9.61000e6			0.669737
$730$		0			0
$731$			1.34414e7i			0.930358i
$732$	7.50239e6	+	2.69649e7i	0.517514	+	1.86004i
$733$	2.60697e7			1.79216			0.896078	−	0.443898i	$-0.146405\pi$
$733$	2.60697e7			1.79216			0.896078	+	0.443898i	$0.146405\pi$
$734$	−873041.	−	6.39492e6i	−0.0598129	−	0.438122i
$735$		0			0
$736$	−1.53726e6	−	1.90718e6i	−0.104605	−	0.129777i
$737$			957163.i			0.0649109i
$738$	−1.89427e6	+	258608.i	−0.128027	+	0.0174784i
$739$			467568.i			0.0314944i	0.999876	+	0.0157472i	$0.00501270\pi$
$739$			467568.i			0.0314944i	−0.999876	+	0.0157472i	$0.994987\pi$
$740$		0			0
$741$			1.58687e7i			1.06168i
$742$	63130.7	+	462425.i	0.00420950	+	0.0308341i
$743$			1.98379e6i			0.131833i	0.997825	+	0.0659165i	$0.0209971\pi$
$743$			1.98379e6i			0.131833i	−0.997825	+	0.0659165i	$0.979003\pi$
$744$	−2.70182e7	+	1.16482e7i	−1.78947	+	0.771485i
$745$		0			0
$746$	2.58921e6	−	353482.i	0.170341	−	0.0232552i
$747$	−1.71588e6			−0.112509
$748$	−6.23914e6	+	1.73590e6i	−0.407728	+	0.113441i
$749$		−	162260.i		−	0.0105684i
$750$		0			0
$751$	1.55338e7			1.00503			0.502515	−	0.864568i	$-0.332408\pi$
$751$	1.55338e7			1.00503			0.502515	+	0.864568i	$0.332408\pi$
$752$	−4.88884e6	−	8.10558e6i	−0.315254	−	0.522684i
$753$		−	3.60460e6i		−	0.231670i
$754$	−1.59785e6	−	1.17041e7i	−0.102355	−	0.749737i
$755$		0			0
$756$	254159.	+	913492.i	0.0161734	+	0.0581300i
$757$	−2.40224e6			−0.152362			−0.0761811	−	0.997094i	$-0.524273\pi$
$757$	−2.40224e6			−0.152362			−0.0761811	+	0.997094i	$0.524273\pi$
$758$	−3.33752e6	−	2.44470e7i	−0.210985	−	1.54544i
$759$	−1.17505e6			−0.0740376
$760$		0			0
$761$	−2.53929e7			−1.58946			−0.794732	−	0.606960i	$-0.792389\pi$
$761$	−2.53929e7			−1.58946			−0.794732	+	0.606960i	$0.792389\pi$
$762$	−1.57033e6	−	1.15025e7i	−0.0979722	−	0.717635i
$763$	−692972.			−0.0430928
$764$	−1.20778e7	+	3.36038e6i	−0.748609	+	0.208284i
$765$		0			0
$766$	−319569.	−	2.34081e6i	−0.0196785	−	0.144143i
$767$		−	1.01113e7i		−	0.620609i
$768$	−8.46987e6	+	1.60592e7i	−0.518171	+	0.982472i
$769$	1.96036e6			0.119542			0.0597709	−	0.998212i	$-0.480963\pi$
$769$	1.96036e6			0.119542			0.0597709	+	0.998212i	$0.480963\pi$
$770$		0			0
$771$			3.15305e7i			1.91027i
$772$	−5.49921e6	−	1.97651e7i	−0.332091	−	1.19359i
$773$	−3.14540e7			−1.89334			−0.946668	−	0.322211i	$-0.895574\pi$
$773$	−3.14540e7			−1.89334			−0.946668	+	0.322211i	$0.895574\pi$
$774$	3.39334e6	−	463262.i	0.203599	−	0.0277955i
$775$		0			0
$776$	9.94757e6	+	2.30736e7i	0.593011	+	1.37550i
$777$		−	567550.i		−	0.0337250i
$778$	1.47218e6	+	1.07835e7i	0.0871990	+	0.638722i
$779$			1.47960e7i			0.873577i
$780$		0			0
$781$			1.07981e7i			0.633460i
$782$	2.98902e6	−	408065.i	0.174788	−	0.0238623i
$783$		−	1.82672e7i		−	1.06480i
$784$	1.46632e7	−	8.84404e6i	0.851999	−	0.513879i
$785$		0			0
$786$	−1.10976e6	−	8.12884e6i	−0.0640725	−	0.469323i
$787$	2.21797e7			1.27650			0.638248	−	0.769831i	$-0.279660\pi$
$787$	2.21797e7			1.27650			0.638248	+	0.769831i	$0.279660\pi$
$788$	9.62264e6	−	2.67728e6i	0.552050	−	0.153596i
$789$			3.02838e7i			1.73188i
$790$		0			0
$791$	−636111.			−0.0361486
$792$	653272.	+	1.51528e6i	0.0370068	+	0.0858378i
$793$		−	1.86172e7i		−	1.05131i
$794$	−1.65588e7	+	2.26062e6i	−0.932131	+	0.127255i
$795$		0			0
$796$	−5.28633e6	+	1.47080e6i	−0.295714	+	0.0822757i
$797$	2.05722e7			1.14719			0.573595	−	0.819139i	$-0.305548\pi$
$797$	2.05722e7			1.14719			0.573595	+	0.819139i	$0.305548\pi$
$798$	−2.21803e6	+	302808.i	−0.123299	+	0.0168329i
$799$	1.16574e7			0.646004
$800$		0			0
$801$	−6.47344e6			−0.356495
$802$	−8.80553e6	+	1.20214e6i	−0.483414	+	0.0659962i
$803$	−1.37641e7			−0.753285
$804$	−3.18378e6	+	885814.i	−0.173701	+	0.0483284i
$805$		0			0
$806$	1.93906e7	−	2.64722e6i	1.05136	−	0.143533i
$807$		−	2.56332e7i		−	1.38554i
$808$	9.20708e6	+	2.13560e7i	0.496128	+	1.15078i
$809$	3.45753e7			1.85735			0.928676	−	0.370892i	$-0.120948\pi$
$809$	3.45753e7			1.85735			0.928676	+	0.370892i	$0.120948\pi$
$810$		0			0
$811$		−	2.43908e7i		−	1.30219i	−0.758997	−	0.651094i	$-0.774310\pi$
$811$		−	2.43908e7i		−	1.30219i	0.758997	−	0.651094i	$-0.225690\pi$
$812$	1.60544e6	−	446676.i	0.0854482	−	0.0237740i
$813$	−1.80798e7			−0.959328
$814$	437944.	+	3.20788e6i	0.0231663	+	0.169691i
$815$		0			0
$816$	−1.15481e7	−	1.91465e7i	−0.607136	−	1.00662i
$817$		−	2.65051e7i		−	1.38923i
$818$	2.90497e7	−	3.96589e6i	1.51795	−	0.207232i
$819$			192402.i			0.0100231i
$820$		0			0
$821$		−	5.77124e6i		−	0.298821i	−0.988775	−	0.149410i	$-0.952262\pi$
$821$		−	5.77124e6i		−	0.298821i	0.988775	−	0.149410i	$-0.0477376\pi$
$822$	2.30604e6	+	1.68915e7i	0.119039	+	0.871944i
$823$		−	9.22421e6i		−	0.474711i	−0.971423	−	0.237356i	$-0.923719\pi$
$823$		−	9.22421e6i		−	0.474711i	0.971423	−	0.237356i	$-0.0762807\pi$
$824$	−8.40139e6	−	1.94872e7i	−0.431055	−	0.999840i
$825$		0			0
$826$	1.41329e6	−	192944.i	0.0720747	−	0.00983970i
$827$	−1.36273e7			−0.692859			−0.346430	−	0.938076i	$-0.612606\pi$
$827$	−1.36273e7			−0.692859			−0.346430	+	0.938076i	$0.612606\pi$
$828$	−206036.	−	740531.i	−0.0104440	−	0.0375377i
$829$		−	5.64154e6i		−	0.285109i	−0.989787	−	0.142555i	$-0.954468\pi$
$829$		−	5.64154e6i		−	0.285109i	0.989787	−	0.142555i	$-0.0455317\pi$
$830$		0			0
$831$	394648.			0.0198247
$832$	8.29087e6	−	8.78088e6i	0.415233	−	0.439774i
$833$			2.10886e7i			1.05302i
$834$	4.11767e6	+	3.01614e7i	0.204992	+	1.50154i
$835$		0			0
$836$	1.23030e7	−	3.42304e6i	0.608829	−	0.169393i
$837$	3.02639e7			1.49318
$838$	3.68219e6	+	2.69716e7i	0.181132	+	1.32677i
$839$	−1.01209e7			−0.496379			−0.248189	−	0.968712i	$-0.579836\pi$
$839$	−1.01209e7			−0.496379			−0.248189	+	0.968712i	$0.579836\pi$
$840$		0			0
$841$	−1.15929e7			−0.565201
$842$	3.57327e6	+	2.61737e7i	0.173694	+	1.27229i
$843$	−3.13557e6			−0.151966
$844$	−5.82430e6	−	2.09336e7i	−0.281441	−	1.01155i
$845$		0			0
$846$	−401778.	−	2.94298e6i	−0.0193001	−	0.141371i
$847$			1.24349e6i			0.0595572i
$848$	7.87136e6	−	4.74757e6i	0.375890	−	0.226716i
$849$	−1.74776e7			−0.832170
$850$		0			0
$851$		−	1.50818e6i		−	0.0713886i
$852$	−3.59173e7	+	9.99317e6i	−1.69513	+	0.471633i
$853$	8.59170e6			0.404302			0.202151	−	0.979354i	$-0.435207\pi$
$853$	8.59170e6			0.404302			0.202151	+	0.979354i	$0.435207\pi$
$854$	2.60220e6	−	355255.i	0.122095	−	0.0166685i
$855$		0			0
$856$	−2.93471e6	+	1.26523e6i	−0.136893	+	0.0590179i
$857$			1.17834e7i			0.548049i	0.961723	+	0.274024i	$0.0883549\pi$
$857$			1.17834e7i			0.548049i	−0.961723	+	0.274024i	$0.911645\pi$
$858$	−783599.	−	5.73977e6i	−0.0363392	−	0.266181i
$859$			2.83473e6i			0.131078i	0.997850	+	0.0655389i	$0.0208767\pi$
$859$			2.83473e6i			0.131078i	−0.997850	+	0.0655389i	$0.979123\pi$
$860$		0			0
$861$			946856.i			0.0435287i
$862$	−1.72493e7	+	2.35489e6i	−0.790685	+	0.107945i
$863$			2.08041e7i			0.950870i	0.879751	+	0.475435i	$0.157709\pi$
$863$			2.08041e7i			0.950870i	−0.879751	+	0.475435i	$0.842291\pi$
$864$	1.45400e7	−	1.17198e7i	0.662645	−	0.534116i
$865$		0			0
$866$	−1.99478e6	−	1.46115e7i	−0.0903858	−	0.662065i
$867$	2.95193e6			0.133370
$868$	740024.	+	2.65978e6i	0.0333385	+	0.119825i
$869$		−	9.07789e6i		−	0.407789i
$870$		0			0
$871$	2.19815e6			0.0981776
$872$	5.40345e6	+	1.25334e7i	0.240647	+	0.558184i
$873$			7.88447e6i			0.350136i
$874$	−5.89408e6	+	804665.i	−0.260998	+	0.0356317i
$875$		0			0
$876$	−1.27381e7	−	4.57830e7i	−0.560847	−	2.01579i
$877$	−2.82780e7			−1.24151			−0.620754	−	0.784006i	$-0.713173\pi$
$877$	−2.82780e7			−1.24151			−0.620754	+	0.784006i	$0.713173\pi$
$878$	−4.01891e7	+	5.48666e6i	−1.75943	+	0.240199i
$879$	3.90549e7			1.70492
$880$		0			0
$881$	−1.63898e6			−0.0711432			−0.0355716	−	0.999367i	$-0.511325\pi$
$881$	−1.63898e6			−0.0711432			−0.0355716	+	0.999367i	$0.511325\pi$
$882$	5.32392e6	−	726827.i	0.230441	−	0.0314601i
$883$	2.72729e7			1.17714			0.588572	−	0.808445i	$-0.299690\pi$
$883$	2.72729e7			1.17714			0.588572	+	0.808445i	$0.299690\pi$
$884$	3.98655e6	+	1.43284e7i	0.171580	+	0.616689i
$885$		0			0
$886$	−2.84765e7	+	3.88763e6i	−1.21871	+	0.166380i
$887$			3.68277e7i			1.57168i	0.618427	+	0.785842i	$0.287770\pi$
$887$			3.68277e7i			1.57168i	−0.618427	+	0.785842i	$0.712230\pi$
$888$	−1.02650e7	+	4.42548e6i	−0.436843	+	0.188334i
$889$	−1.08934e6			−0.0462283
$890$		0			0
$891$		−	1.11735e7i		−	0.471513i
$892$	8.37199e6	+	3.00904e7i	0.352303	+	1.26624i
$893$	−2.29873e7			−0.964628
$894$	−3.89063e6	−	2.84984e7i	−0.162808	−	1.19255i
$895$		0			0
$896$	1.38555e6	+	991291.i	0.0576569	+	0.0412507i
$897$			2.69854e6i			0.111982i
$898$	−1.78373e7	+	2.43516e6i	−0.738137	+	0.100771i
$899$		−	5.31879e7i		−	2.19490i
$900$		0			0
$901$			1.13206e7i			0.464575i
$902$	−730631.	−	5.35178e6i	−0.0299007	−	0.219019i
$903$		−	1.69617e6i		−	0.0692228i
$904$	4.96008e6	+	1.15050e7i	0.201868	+	0.468236i
$905$		0			0
$906$	−2.52890e6	+	345248.i	−0.102356	+	0.0139737i
$907$	−1.18940e7			−0.480077			−0.240038	−	0.970763i	$-0.577160\pi$
$907$	−1.18940e7			−0.480077			−0.240038	+	0.970763i	$0.577160\pi$
$908$	7.50458e6	−	2.08798e6i	0.302073	−	0.0840450i
$909$			7.29756e6i			0.292933i
$910$		0			0
$911$	−3.24936e7			−1.29719			−0.648593	−	0.761135i	$-0.724642\pi$
$911$	−3.24936e7			−1.29719			−0.648593	+	0.761135i	$0.724642\pi$
$912$	2.27718e7	+	3.77552e7i	0.906590	+	1.50310i
$913$		−	4.84779e6i		−	0.192472i
$914$	1.18185e6	+	8.65692e6i	0.0467948	+	0.342766i
$915$		0			0
$916$	1.14376e7	+	4.11088e7i	0.450398	+	1.61881i
$917$	−769839.			−0.0302327
$918$	3.11101e6	+	2.27878e7i	0.121841	+	0.892474i
$919$	−6.30861e6			−0.246402			−0.123201	−	0.992382i	$-0.539316\pi$
$919$	−6.30861e6			−0.246402			−0.123201	+	0.992382i	$0.539316\pi$
$920$		0			0
$921$	4.19331e7			1.62895
$922$	−679891.	−	4.98012e6i	−0.0263398	−	0.192936i
$923$	2.47981e7			0.958108
$924$	787318.	−	219054.i	0.0303368	−	0.00844055i
$925$		0			0
$926$	2.70235e6	+	1.97944e7i	0.103565	+	0.758603i
$927$		−	6.65896e6i		−	0.254511i
$928$	−2.05972e7	−	2.55537e7i	−0.785123	−	0.974054i
$929$	9.87673e6			0.375469			0.187734	−	0.982220i	$-0.439886\pi$
$929$	9.87673e6			0.375469			0.187734	+	0.982220i	$0.439886\pi$
$930$		0			0
$931$		−	4.15847e7i		−	1.57239i
$932$	−8.74450e6	−	3.14293e7i	−0.329758	−	1.18521i
$933$	1.81664e7			0.683227
$934$	−3.99815e7	+	5.45831e6i	−1.49966	+	0.204734i
$935$		0			0
$936$	3.47987e6	−	1.50026e6i	0.129830	−	0.0559727i
$937$		−	1.06437e7i		−	0.396046i	−0.980197	−	0.198023i	$-0.936548\pi$
$937$		−	1.06437e7i		−	0.396046i	0.980197	−	0.198023i	$-0.0634520\pi$
$938$	41945.3	+	307245.i	0.00155660	+	0.0114019i
$939$		−	1.59184e7i		−	0.589165i
$940$		0			0
$941$		−	4.65943e7i		−	1.71537i	−0.514174	−	0.857686i	$-0.671901\pi$
$941$		−	4.65943e7i		−	1.71537i	0.514174	−	0.857686i	$-0.328099\pi$
$942$	4.14826e7	−	5.66324e6i	1.52314	−	0.207940i
$943$			2.51613e6i			0.0921410i
$944$	−1.45099e7	−	2.40570e7i	−0.529948	−	0.878641i
$945$		0			0
$946$	1.30883e6	+	9.58701e6i	0.0475505	+	0.348302i
$947$	2.99997e7			1.08703			0.543516	−	0.839399i	$-0.317093\pi$
$947$	2.99997e7			1.08703			0.543516	+	0.839399i	$0.317093\pi$
$948$	3.01954e7	−	8.40120e6i	1.09124	−	0.303613i
$949$			3.16097e7i			1.13934i
$950$		0			0
$951$	−1.31883e7			−0.472865
$952$	−1.92666e6	+	830631.i	−0.0688991	+	0.0297041i
$953$		−	1.52026e7i		−	0.542233i	−0.962547	−	0.271116i	$-0.912607\pi$
$953$		−	1.52026e7i		−	0.542233i	0.962547	−	0.271116i	$-0.0873928\pi$
$954$	2.85794e6	−	390168.i	0.101667	−	0.0138797i
$955$		0			0
$956$	3.00828e7	−	8.36987e6i	1.06457	−	0.296192i
$957$	−1.57441e7			−0.555697
$958$	−2.81484e7	+	3.84284e6i	−0.990922	+	0.135282i
$959$	1.59970e6			0.0561685
$960$		0			0
$961$	5.94891e7			2.07792
$962$	7.36700e6	−	1.00575e6i	0.256657	−	0.0350390i
$963$	−1.00282e6			−0.0348464
$964$	1.10682e7	−	3.07947e6i	0.383604	−	0.106729i
$965$		0			0
$966$	−377186.	+	51493.7i	−0.0130051	+	0.00177546i
$967$			4.59930e7i			1.58171i	0.612006	+	0.790853i	$0.290363\pi$
$967$			4.59930e7i			1.58171i	−0.612006	+	0.790853i	$0.709637\pi$
$968$	2.24903e7	−	9.69613e6i	0.771449	−	0.332591i
$969$	−5.42993e7			−1.85774
$970$		0			0
$971$		−	3.27040e7i		−	1.11315i	−0.830799	−	0.556573i	$-0.812116\pi$
$971$		−	3.27040e7i		−	1.11315i	0.830799	−	0.556573i	$-0.187884\pi$
$972$	1.30136e7	−	3.62076e6i	0.441808	−	0.122923i
$973$	2.85643e6			0.0967255
$974$	6.92000e6	+	5.06882e7i	0.233727	+	1.71202i
$975$		0			0
$976$	−2.67160e7	−	4.42945e7i	−0.897733	−	1.48842i
$977$		−	1.60025e7i		−	0.536353i	−0.963370	−	0.268177i	$-0.913579\pi$
$977$		−	1.60025e7i		−	0.536353i	0.963370	−	0.268177i	$-0.0864210\pi$
$978$	−5.31131e7	+	7.25105e6i	−1.77564	+	0.242412i
$979$		−	1.82890e7i		−	0.609865i
$980$		0			0
$981$			4.28279e6i			0.142087i
$982$	1.46855e6	+	1.07570e7i	0.0485971	+	0.355968i
$983$			5.81035e7i			1.91787i	0.283634	+	0.958933i	$0.408460\pi$
$983$			5.81035e7i			1.91787i	−0.283634	+	0.958933i	$0.591540\pi$
$984$	1.71253e7	−	7.38312e6i	0.563832	−	0.243082i
$985$		0			0
$986$	4.00489e7	−	5.46751e6i	1.31189	−	0.179101i
$987$	−1.47105e6			−0.0480657
$988$	−7.86110e6	−	2.82542e7i	−0.256207	−	0.920854i
$989$		−	4.50731e6i		−	0.146530i
$990$		0			0
$991$	−1.47014e7			−0.475527			−0.237764	−	0.971323i	$-0.576414\pi$
$991$	−1.47014e7			−0.475527			−0.237764	+	0.971323i	$0.576414\pi$
$992$	4.23356e7	−	3.41241e7i	1.36593	−	1.10099i
$993$		−	2.20404e7i		−	0.709327i
$994$	473200.	+	3.46613e6i	0.0151907	+	0.111270i
$995$		0			0
$996$	1.61250e7	−	4.48642e6i	0.515053	−	0.143302i
$997$	3.26322e7			1.03970			0.519850	−	0.854257i	$-0.325988\pi$
$997$	3.26322e7			1.03970			0.519850	+	0.854257i	$0.325988\pi$
$998$	933550.	+	6.83815e6i	0.0296696	+	0.217326i
$999$	1.14981e7			0.364512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.f.c.149.19		20
4.3	odd	2		800.6.f.b.49.15		20
5.2	odd	4		40.6.d.a.21.12	yes	20
5.3	odd	4		200.6.d.b.101.9		20
5.4	even	2		200.6.f.b.149.2		20
8.3	odd	2		800.6.f.c.49.5		20
8.5	even	2		200.6.f.b.149.1		20
15.2	even	4		360.6.k.b.181.9		20
20.3	even	4		800.6.d.c.401.16		20
20.7	even	4		160.6.d.a.81.5		20
20.19	odd	2		800.6.f.c.49.6		20
40.3	even	4		800.6.d.c.401.5		20
40.13	odd	4		200.6.d.b.101.10		20
40.19	odd	2		800.6.f.b.49.16		20
40.27	even	4		160.6.d.a.81.16		20
40.29	even	2	inner	200.6.f.c.149.20		20
40.37	odd	4		40.6.d.a.21.11	✓	20
120.77	even	4		360.6.k.b.181.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.11	✓	20	40.37	odd	4
40.6.d.a.21.12	yes	20	5.2	odd	4
160.6.d.a.81.5		20	20.7	even	4
160.6.d.a.81.16		20	40.27	even	4
200.6.d.b.101.9		20	5.3	odd	4
200.6.d.b.101.10		20	40.13	odd	4
200.6.f.b.149.1		20	8.5	even	2
200.6.f.b.149.2		20	5.4	even	2
200.6.f.c.149.19		20	1.1	even	1	trivial
200.6.f.c.149.20		20	40.29	even	2	inner
360.6.k.b.181.9		20	15.2	even	4
360.6.k.b.181.10		20	120.77	even	4
800.6.d.c.401.5		20	40.3	even	4
800.6.d.c.401.16		20	20.3	even	4
800.6.f.b.49.15		20	4.3	odd	2
800.6.f.b.49.16		20	40.19	odd	2
800.6.f.c.49.5		20	8.3	odd	2
800.6.f.c.49.6		20	20.19	odd	2

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.60486 - 0.765181i) q^{2} -17.3148 q^{3} +(30.8290 - 8.57748i) q^{4} +(-97.0471 + 13.2490i) q^{6} +9.19080i q^{7} +(166.229 - 71.6654i) q^{8} +56.8021 q^{9} +160.480i q^{11} +(-533.798 + 148.517i) q^{12} +368.546 q^{13} +(7.03263 + 51.5132i) q^{14} +(876.854 - 528.870i) q^{16} +1261.09i q^{17} +(318.368 - 43.4639i) q^{18} -2486.75i q^{19} -159.137i q^{21} +(122.796 + 899.467i) q^{22} -422.882i q^{23} +(-2878.22 + 1240.87i) q^{24} +(2065.65 - 282.005i) q^{26} +3223.98 q^{27} +(78.8339 + 283.343i) q^{28} -5666.05i q^{29} +9387.13 q^{31} +(4509.96 - 3635.20i) q^{32} -2778.67i q^{33} +(964.961 + 7068.23i) q^{34} +(1751.15 - 487.219i) q^{36} +3566.43 q^{37} +(-1902.81 - 13937.9i) q^{38} -6381.30 q^{39} -5949.95 q^{41} +(-121.769 - 891.941i) q^{42} +10658.5 q^{43} +(1376.51 + 4947.43i) q^{44} +(-323.581 - 2370.20i) q^{46} -9243.94i q^{47} +(-15182.5 + 9157.27i) q^{48} +16722.5 q^{49} -21835.5i q^{51} +(11361.9 - 3161.20i) q^{52} +8976.82 q^{53} +(18070.0 - 2466.93i) q^{54} +(658.662 + 1527.78i) q^{56} +43057.5i q^{57} +(-4335.55 - 31757.4i) q^{58} -27435.6i q^{59} -50515.3i q^{61} +(52613.6 - 7182.86i) q^{62} +522.057i q^{63} +(22496.2 - 23825.7i) q^{64} +(-2126.19 - 15574.1i) q^{66} +5964.39 q^{67} +(10817.0 + 38878.1i) q^{68} +7322.11i q^{69} +67286.3 q^{71} +(9442.16 - 4070.75i) q^{72} +85768.5i q^{73} +(19989.3 - 2728.96i) q^{74} +(-21330.0 - 76663.9i) q^{76} -1474.94 q^{77} +(-35766.3 + 4882.86i) q^{78} -56567.2 q^{79} -69625.4 q^{81} +(-33348.6 + 4552.79i) q^{82} -30208.1 q^{83} +(-1364.99 - 4906.03i) q^{84} +(59739.7 - 8155.72i) q^{86} +98106.4i q^{87} +(11500.8 + 26676.4i) q^{88} -113965. q^{89} +3387.24i q^{91} +(-3627.26 - 13037.0i) q^{92} -162536. q^{93} +(-7073.29 - 51811.0i) q^{94} +(-78089.1 + 62942.7i) q^{96} +138806. i q^{97} +(93727.5 - 12795.8i) q^{98} +9115.59i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 36 q^{3} + 32 q^{4} + 204 q^{6} + 248 q^{8} + 1620 q^{9} + 1252 q^{12} - 2708 q^{14} + 3080 q^{16} + 2070 q^{18} + 8244 q^{22} - 1032 q^{24} - 8084 q^{26} + 11664 q^{27} + 22924 q^{28}+ \cdots + 663674 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 + 36 * q^3 + 32 * q^4 + 204 * q^6 + 248 * q^8 + 1620 * q^9 + 1252 * q^12 - 2708 * q^14 + 3080 * q^16 + 2070 * q^18 + 8244 * q^22 - 1032 * q^24 - 8084 * q^26 + 11664 * q^27 + 22924 * q^28 + 7160 * q^31 + 14792 * q^32 - 21132 * q^34 + 18344 * q^36 - 3608 * q^37 - 16884 * q^38 + 44904 * q^39 + 11608 * q^41 - 49444 * q^42 - 51772 * q^43 - 72296 * q^44 - 28516 * q^46 - 85048 * q^48 - 18756 * q^49 - 111624 * q^52 + 928 * q^53 + 100584 * q^54 - 53624 * q^56 + 152344 * q^58 + 228648 * q^62 + 11264 * q^64 - 56688 * q^66 - 161604 * q^67 + 359040 * q^68 - 200312 * q^71 + 563448 * q^72 - 78876 * q^74 - 153872 * q^76 + 26008 * q^77 - 624640 * q^78 - 282080 * q^79 + 65172 * q^81 - 410576 * q^82 - 99092 * q^83 + 297128 * q^84 + 27452 * q^86 - 464496 * q^88 + 3160 * q^89 - 519244 * q^92 + 293472 * q^93 - 148820 * q^94 + 395168 * q^96 + 663674 * q^98

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