LMFDB - Embedded newform 200.6.f.b.149.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,6,Mod(149,200)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			149.1
Root			$3.18502 - 2.41984i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.6.f.b.149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.60486 - 0.765181i) q^{2} +17.3148 q^{3} +(30.8290 + 8.57748i) q^{4} +(-97.0471 - 13.2490i) q^{6} +9.19080i q^{7} +(-166.229 - 71.6654i) q^{8} +56.8021 q^{9} +O(q^{10})$	\(q+(-5.60486 - 0.765181i) q^{2} +17.3148 q^{3} +(30.8290 + 8.57748i) q^{4} +(-97.0471 - 13.2490i) q^{6} +9.19080i q^{7} +(-166.229 - 71.6654i) q^{8} +56.8021 q^{9} -160.480i q^{11} +(533.798 + 148.517i) q^{12} -368.546 q^{13} +(7.03263 - 51.5132i) q^{14} +(876.854 + 528.870i) q^{16} +1261.09i q^{17} +(-318.368 - 43.4639i) q^{18} +2486.75i q^{19} +159.137i q^{21} +(-122.796 + 899.467i) q^{22} -422.882i q^{23} +(-2878.22 - 1240.87i) q^{24} +(2065.65 + 282.005i) q^{26} -3223.98 q^{27} +(-78.8339 + 283.343i) q^{28} +5666.05i q^{29} +9387.13 q^{31} +(-4509.96 - 3635.20i) q^{32} -2778.67i q^{33} +(964.961 - 7068.23i) q^{34} +(1751.15 + 487.219i) q^{36} -3566.43 q^{37} +(1902.81 - 13937.9i) q^{38} -6381.30 q^{39} -5949.95 q^{41} +(121.769 - 891.941i) q^{42} -10658.5 q^{43} +(1376.51 - 4947.43i) q^{44} +(-323.581 + 2370.20i) q^{46} -9243.94i q^{47} +(15182.5 + 9157.27i) q^{48} +16722.5 q^{49} +21835.5i q^{51} +(-11361.9 - 3161.20i) q^{52} -8976.82 q^{53} +(18070.0 + 2466.93i) q^{54} +(658.662 - 1527.78i) q^{56} +43057.5i q^{57} +(4335.55 - 31757.4i) q^{58} +27435.6i q^{59} +50515.3i q^{61} +(-52613.6 - 7182.86i) q^{62} +522.057i q^{63} +(22496.2 + 23825.7i) q^{64} +(-2126.19 + 15574.1i) q^{66} -5964.39 q^{67} +(-10817.0 + 38878.1i) q^{68} -7322.11i q^{69} +67286.3 q^{71} +(-9442.16 - 4070.75i) q^{72} +85768.5i q^{73} +(19989.3 + 2728.96i) q^{74} +(-21330.0 + 76663.9i) q^{76} +1474.94 q^{77} +(35766.3 + 4882.86i) q^{78} -56567.2 q^{79} -69625.4 q^{81} +(33348.6 + 4552.79i) q^{82} +30208.1 q^{83} +(-1364.99 + 4906.03i) q^{84} +(59739.7 + 8155.72i) q^{86} +98106.4i q^{87} +(-11500.8 + 26676.4i) q^{88} -113965. q^{89} -3387.24i q^{91} +(3627.26 - 13037.0i) q^{92} +162536. q^{93} +(-7073.29 + 51811.0i) q^{94} +(-78089.1 - 62942.7i) q^{96} +138806. i q^{97} +(-93727.5 - 12795.8i) q^{98} -9115.59i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 36 q^{3} + 32 q^{4} + 204 q^{6} - 248 q^{8} + 1620 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 - 36 * q^3 + 32 * q^4 + 204 * q^6 - 248 * q^8 + 1620 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$-0.312576\pi$
$3$	17.3148			1.11074			0.555372	+	0.831602i	$0.312576\pi$
$4$	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	$-0.935924\pi$
$11$		−	160.480i		−	0.399888i	0.979807	−	0.199944i	$-0.0640760\pi$
$12$	533.798	+	148.517i	1.07010	+	0.297731i
$13$	−368.546			−0.604831			−0.302415	−	0.953176i	$-0.597793\pi$
$13$	−368.546			−0.604831			−0.302415	+	0.953176i	$0.597793\pi$
$14$	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	$0.290005\pi$
$19$			2486.75i			1.58033i	−0.612894	+	0.790165i	$0.709995\pi$
$20$		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	$0.215121\pi$
$29$			5666.05i			1.25108i	−0.780192	+	0.625540i	$0.784879\pi$
$30$		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	$-0.568695\pi$
$37$	−3566.43			−0.428281			−0.214141	+	0.976803i	$0.568695\pi$
$38$	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	$-0.644858\pi$
$43$	−10658.5			−0.879077			−0.439538	+	0.898224i	$0.644858\pi$
$44$	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	$-0.570437\pi$
$53$	−8976.82			−0.438968			−0.219484	+	0.975616i	$0.570437\pi$
$54$	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	$0.171482\pi$
$59$			27435.6i			1.02609i	−0.858363	+	0.513044i	$0.828518\pi$
$60$		0			0
$61$			50515.3i			1.73819i	0.494642	+	0.869097i	$0.335299\pi$
$61$			50515.3i			1.73819i	−0.494642	+	0.869097i	$0.664701\pi$
$62$	−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	$-0.525863\pi$
$67$	−5964.39			−0.162323			−0.0811613	+	0.996701i	$0.525863\pi$
$68$	−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	$-0.422637\pi$
$83$	30208.1			0.481314			0.240657	+	0.970610i	$0.422637\pi$
$84$	−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	$-0.784453\pi$
$101$		−	128473.i		−	1.25317i	0.779354	−	0.626584i	$-0.215547\pi$
$102$	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	$-0.476252\pi$
$107$	17654.6			0.149073			0.0745366	+	0.997218i	$0.476252\pi$
$108$	−99392.0	−	27653.6i	−0.819959	−	0.228135i
$109$		−	75398.4i		−	0.607849i	−0.952696	−	0.303925i	$-0.901703\pi$
$109$		−	75398.4i		−	0.607849i	0.952696	−	0.303925i	$-0.0982971\pi$
$110$		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	$-0.931603\pi$
$131$		−	83761.8i		−	0.426450i	0.977003	−	0.213225i	$-0.0683967\pi$
$132$	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	$0.238971\pi$
$139$			310792.i			1.36437i	−0.731179	+	0.682186i	$0.761029\pi$
$140$		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	$-0.817741\pi$
$149$		−	293656.i		−	1.08361i	0.840504	−	0.541805i	$-0.182259\pi$
$150$		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	$-0.256731\pi$
$157$	427448.			1.38399			0.691997	+	0.721900i	$0.256731\pi$
$158$	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	$-0.798757\pi$
$163$	−547292.			−1.61343			−0.806715	+	0.590941i	$0.798757\pi$
$164$	−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	$-0.461624\pi$
$173$	94689.2			0.240539			0.120269	+	0.992741i	$0.461624\pi$
$174$	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	$0.109873\pi$
$179$			290099.i			0.676727i	−0.941016	+	0.338363i	$0.890127\pi$
$180$		0			0
$181$		−	63999.0i		−	0.145203i	−0.997361	−	0.0726017i	$-0.976870\pi$
$181$		−	63999.0i		−	0.145203i	0.997361	−	0.0726017i	$-0.0231302\pi$
$182$	−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	$-0.592495\pi$
$197$	−312130.			−0.573019			−0.286510	+	0.958077i	$0.592495\pi$
$198$	−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	$0.175930\pi$
$211$			679022.i			1.04997i	−0.851111	+	0.524986i	$0.824070\pi$
$212$	−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	$-0.550109\pi$
$227$	−243426.			−0.313547			−0.156773	+	0.987635i	$0.550109\pi$
$228$	−369325.	+	1.32742e6i	−0.470513	+	1.69111i
$229$		−	1.33345e6i		−	1.68030i	−0.542354	−	0.840150i	$-0.682467\pi$
$229$		−	1.33345e6i		−	1.68030i	0.542354	−	0.840150i	$-0.317533\pi$
$230$		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	$-0.966744\pi$
$251$		−	208180.i		−	0.208572i	0.994547	−	0.104286i	$-0.0332557\pi$
$252$	−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	$-0.785629\pi$
$269$		−	1.48042e6i		−	1.24740i	0.781665	−	0.623699i	$-0.214371\pi$
$270$		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	$-0.497159\pi$
$277$	22792.5			0.0178481			0.00892407	+	0.999960i	$0.497159\pi$
$278$	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	$-0.622220\pi$
$283$	−1.00940e6			−0.749200			−0.374600	+	0.927187i	$0.622220\pi$
$284$	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	$-0.221518\pi$
$293$	2.25558e6			1.53493			0.767465	+	0.641090i	$0.221518\pi$
$294$	−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	$-0.237993\pi$
$307$	2.42181e6			1.46654			0.733270	+	0.679938i	$0.237993\pi$
$308$	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	$-0.568278\pi$
$317$	−761677.			−0.425719			−0.212859	+	0.977083i	$0.568278\pi$
$318$	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	$-0.896551\pi$
$331$		−	1.27292e6i		−	0.638605i	0.947653	−	0.319302i	$-0.103449\pi$
$332$	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	$-0.524859\pi$
$347$	−349978.			−0.156033			−0.0780167	+	0.996952i	$0.524859\pi$
$348$	−841505.	+	3.02452e6i	−0.372485	+	1.33878i
$349$			2.38580e6i			1.04850i	0.851563	+	0.524252i	$0.175655\pi$
$349$			2.38580e6i			1.04850i	−0.851563	+	0.524252i	$0.824345\pi$
$350$		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	$-0.527396\pi$
$373$	−461958.			−0.171922			−0.0859608	+	0.996299i	$0.527396\pi$
$374$	−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	$0.284723\pi$
$379$			4.36174e6i			1.55977i	−0.625920	+	0.779887i	$0.715277\pi$
$380$		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	$-0.895536\pi$
$389$		−	1.92396e6i		−	0.644647i	0.946630	−	0.322323i	$-0.104464\pi$
$390$		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	$-0.344114\pi$
$397$	2.95436e6			0.940778			0.470389	+	0.882459i	$0.344114\pi$
$398$	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	$-0.766491\pi$
$419$		−	4.81218e6i		−	1.33908i	0.742776	−	0.669540i	$-0.233509\pi$
$420$		0			0
$421$		−	4.66983e6i		−	1.28409i	−0.766667	−	0.642045i	$-0.778086\pi$
$421$		−	4.66983e6i		−	1.28409i	0.766667	−	0.642045i	$-0.221914\pi$
$422$	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	$-0.289152\pi$
$443$	5.08067e6			1.23002			0.615009	+	0.788520i	$0.289152\pi$
$444$	−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	$0.0310407\pi$
$461$			888536.i			0.194725i	−0.995249	+	0.0973627i	$0.968959\pi$
$462$	−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	$-0.226770\pi$
$467$	7.13335e6			1.51357			0.756783	+	0.653666i	$0.226770\pi$
$468$	−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	$-0.942508\pi$
$491$		−	1.91922e6i		−	0.359270i	0.983733	−	0.179635i	$-0.0574916\pi$
$492$	−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	$-0.965020\pi$
$499$		−	1.22004e6i		−	0.219342i	0.993968	−	0.109671i	$-0.0349797\pi$
$500$		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	$0.158697\pi$
$509$			5.58984e6i			0.956324i	−0.878272	+	0.478162i	$0.841303\pi$
$510$		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	$-0.334577\pi$
$523$	6.21299e6			0.993223			0.496611	+	0.867973i	$0.334577\pi$
$524$	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	$0.175686\pi$
$541$			7.13892e6i			1.04867i	−0.851512	+	0.524335i	$0.824314\pi$
$542$	−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	$-0.674963\pi$
$547$	−7.31142e6			−1.04480			−0.522400	+	0.852700i	$0.674963\pi$
$548$	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	$-0.457974\pi$
$557$	1.92783e6			0.263288			0.131644	+	0.991297i	$0.457974\pi$
$558$	−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	$-0.169814\pi$
$563$	1.29516e7			1.72208			0.861039	+	0.508539i	$0.169814\pi$
$564$	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	$-0.962403\pi$
$571$		−	1.83619e6i		−	0.235682i	0.993032	−	0.117841i	$-0.0375973\pi$
$572$	−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	$-0.545666\pi$
$587$	−2.38716e6			−0.285947			−0.142974	+	0.989726i	$0.545666\pi$
$588$	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	$-0.429741\pi$
$613$	4.07379e6			0.437872			0.218936	+	0.975739i	$0.429741\pi$
$614$	−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	$0.169045\pi$
$619$			9.65601e6i			1.01291i	−0.862266	+	0.506455i	$0.830955\pi$
$620$		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	$-0.508487\pi$
$643$	−559011.			−0.0533204			−0.0266602	+	0.999645i	$0.508487\pi$
$644$	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	$-0.884985\pi$
$653$	−2.03856e7			−1.87085			−0.935427	+	0.353520i	$0.884985\pi$
$654$	−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	$-0.902778\pi$
$659$		−	6.70475e6i		−	0.601408i	0.953718	−	0.300704i	$-0.0972216\pi$
$660$		0			0
$661$			5.17558e6i			0.460739i	0.973103	+	0.230370i	$0.0739935\pi$
$661$			5.17558e6i			0.460739i	−0.973103	+	0.230370i	$0.926006\pi$
$662$	−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	$-0.360187\pi$
$677$	1.01425e7			0.850496			0.425248	+	0.905077i	$0.360187\pi$
$678$	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	$-0.570347\pi$
$683$	−5.34488e6			−0.438416			−0.219208	+	0.975678i	$0.570347\pi$
$684$	−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	$-0.925707\pi$
$691$		−	5.80594e6i		−	0.462570i	0.972886	−	0.231285i	$-0.0742930\pi$
$692$	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	$0.0847028\pi$
$701$			6.84282e6i			0.525945i	−0.964803	+	0.262972i	$0.915297\pi$
$702$	−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	$-0.865700\pi$
$709$		−	1.09625e7i		−	0.819019i	0.912306	−	0.409509i	$-0.134300\pi$
$710$		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	$-0.853595\pi$
$733$	−2.60697e7			−1.79216			−0.896078	+	0.443898i	$0.853595\pi$
$734$	−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	$-0.994987\pi$
$739$		−	467568.i		−	0.0314944i	0.999876	−	0.0157472i	$-0.00501270\pi$
$740$		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	$-0.475727\pi$
$757$	2.40224e6			0.152362			0.0761811	+	0.997094i	$0.475727\pi$
$758$	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	$-0.104426\pi$
$773$	3.14540e7			1.89334			0.946668	+	0.322211i	$0.104426\pi$
$774$	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	$-0.720340\pi$
$787$	−2.21797e7			−1.27650			−0.638248	+	0.769831i	$0.720340\pi$
$788$	−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	$-0.694452\pi$
$797$	−2.05722e7			−1.14719			−0.573595	+	0.819139i	$0.694452\pi$
$798$	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	$0.225690\pi$
$811$			2.43908e7i			1.30219i	−0.758997	+	0.651094i	$0.774310\pi$
$812$	−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	$0.0477376\pi$
$821$			5.77124e6i			0.298821i	−0.988775	+	0.149410i	$0.952262\pi$
$822$	−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	$-0.387394\pi$
$827$	1.36273e7			0.692859			0.346430	+	0.938076i	$0.387394\pi$
$828$	206036.	−	740531.i	0.0104440	−	0.0375377i
$829$			5.64154e6i			0.285109i	0.989787	+	0.142555i	$0.0455317\pi$
$829$			5.64154e6i			0.285109i	−0.989787	+	0.142555i	$0.954468\pi$
$830$		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	$-0.564793\pi$
$853$	−8.59170e6			−0.404302			−0.202151	+	0.979354i	$0.564793\pi$
$854$	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	$-0.979123\pi$
$859$		−	2.83473e6i		−	0.131078i	0.997850	−	0.0655389i	$-0.0208767\pi$
$860$		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	$-0.286827\pi$
$877$	2.82780e7			1.24151			0.620754	+	0.784006i	$0.286827\pi$
$878$	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	$-0.700310\pi$
$883$	−2.72729e7			−1.17714			−0.588572	+	0.808445i	$0.700310\pi$
$884$	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	$-0.422840\pi$
$907$	1.18940e7			0.480077			0.240038	+	0.970763i	$0.422840\pi$
$908$	−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	$0.328099\pi$
$941$			4.65943e7i			1.71537i	−0.514174	+	0.857686i	$0.671901\pi$
$942$	−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	$-0.682907\pi$
$947$	−2.99997e7			−1.08703			−0.543516	+	0.839399i	$0.682907\pi$
$948$	−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	$0.187884\pi$
$971$			3.27040e7i			1.11315i	−0.830799	+	0.556573i	$0.812116\pi$
$972$	−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	$-0.674012\pi$
$997$	−3.26322e7			−1.03970			−0.519850	+	0.854257i	$0.674012\pi$
$998$	−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.b.149.1		20
4.3	odd	2		800.6.f.c.49.5		20
5.2	odd	4		40.6.d.a.21.11	✓	20
5.3	odd	4		200.6.d.b.101.10		20
5.4	even	2		200.6.f.c.149.20		20
8.3	odd	2		800.6.f.b.49.15		20
8.5	even	2		200.6.f.c.149.19		20
15.2	even	4		360.6.k.b.181.10		20
20.3	even	4		800.6.d.c.401.5		20
20.7	even	4		160.6.d.a.81.16		20
20.19	odd	2		800.6.f.b.49.16		20
40.3	even	4		800.6.d.c.401.16		20
40.13	odd	4		200.6.d.b.101.9		20
40.19	odd	2		800.6.f.c.49.6		20
40.27	even	4		160.6.d.a.81.5		20
40.29	even	2	inner	200.6.f.b.149.2		20
40.37	odd	4		40.6.d.a.21.12	yes	20
120.77	even	4		360.6.k.b.181.9		20

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

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

\(f(q)\)	\(=\)	\(q+(-5.60486 - 0.765181i) q^{2} +17.3148 q^{3} +(30.8290 + 8.57748i) q^{4} +(-97.0471 - 13.2490i) q^{6} +9.19080i q^{7} +(-166.229 - 71.6654i) q^{8} +56.8021 q^{9} +O(q^{10})\)	\(q+(-5.60486 - 0.765181i) q^{2} +17.3148 q^{3} +(30.8290 + 8.57748i) q^{4} +(-97.0471 - 13.2490i) q^{6} +9.19080i q^{7} +(-166.229 - 71.6654i) q^{8} +56.8021 q^{9} -160.480i q^{11} +(533.798 + 148.517i) q^{12} -368.546 q^{13} +(7.03263 - 51.5132i) q^{14} +(876.854 + 528.870i) q^{16} +1261.09i q^{17} +(-318.368 - 43.4639i) q^{18} +2486.75i q^{19} +159.137i q^{21} +(-122.796 + 899.467i) q^{22} -422.882i q^{23} +(-2878.22 - 1240.87i) q^{24} +(2065.65 + 282.005i) q^{26} -3223.98 q^{27} +(-78.8339 + 283.343i) q^{28} +5666.05i q^{29} +9387.13 q^{31} +(-4509.96 - 3635.20i) q^{32} -2778.67i q^{33} +(964.961 - 7068.23i) q^{34} +(1751.15 + 487.219i) q^{36} -3566.43 q^{37} +(1902.81 - 13937.9i) q^{38} -6381.30 q^{39} -5949.95 q^{41} +(121.769 - 891.941i) q^{42} -10658.5 q^{43} +(1376.51 - 4947.43i) q^{44} +(-323.581 + 2370.20i) q^{46} -9243.94i q^{47} +(15182.5 + 9157.27i) q^{48} +16722.5 q^{49} +21835.5i q^{51} +(-11361.9 - 3161.20i) q^{52} -8976.82 q^{53} +(18070.0 + 2466.93i) q^{54} +(658.662 - 1527.78i) q^{56} +43057.5i q^{57} +(4335.55 - 31757.4i) q^{58} +27435.6i q^{59} +50515.3i q^{61} +(-52613.6 - 7182.86i) q^{62} +522.057i q^{63} +(22496.2 + 23825.7i) q^{64} +(-2126.19 + 15574.1i) q^{66} -5964.39 q^{67} +(-10817.0 + 38878.1i) q^{68} -7322.11i q^{69} +67286.3 q^{71} +(-9442.16 - 4070.75i) q^{72} +85768.5i q^{73} +(19989.3 + 2728.96i) q^{74} +(-21330.0 + 76663.9i) q^{76} +1474.94 q^{77} +(35766.3 + 4882.86i) q^{78} -56567.2 q^{79} -69625.4 q^{81} +(33348.6 + 4552.79i) q^{82} +30208.1 q^{83} +(-1364.99 + 4906.03i) q^{84} +(59739.7 + 8155.72i) q^{86} +98106.4i q^{87} +(-11500.8 + 26676.4i) q^{88} -113965. q^{89} -3387.24i q^{91} +(3627.26 - 13037.0i) q^{92} +162536. q^{93} +(-7073.29 + 51811.0i) q^{94} +(-78089.1 - 62942.7i) q^{96} +138806. i q^{97} +(-93727.5 - 12795.8i) q^{98} -9115.59i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 36 q^{3} + 32 q^{4} + 204 q^{6} - 248 q^{8} + 1620 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 - 36 * q^3 + 32 * q^4 + 204 * q^6 - 248 * q^8 + 1620 * q^9	\( 20 q - 2 q^{2} - 36 q^{3} + 32 q^{4} + 204 q^{6} - 248 q^{8} + 1620 q^{9} - 1252 q^{12} - 2708 q^{14} + 3080 q^{16} - 2070 q^{18} - 8244 q^{22} - 1032 q^{24} - 8084 q^{26} - 11664 q^{27} - 22924 q^{28} + 7160 q^{31} - 14792 q^{32} - 21132 q^{34} + 18344 q^{36} + 3608 q^{37} + 16884 q^{38} + 44904 q^{39} + 11608 q^{41} + 49444 q^{42} + 51772 q^{43} - 72296 q^{44} - 28516 q^{46} + 85048 q^{48} - 18756 q^{49} + 111624 q^{52} - 928 q^{53} + 100584 q^{54} - 53624 q^{56} - 152344 q^{58} - 228648 q^{62} + 11264 q^{64} - 56688 q^{66} + 161604 q^{67} - 359040 q^{68} - 200312 q^{71} - 563448 q^{72} - 78876 q^{74} - 153872 q^{76} - 26008 q^{77} + 624640 q^{78} - 282080 q^{79} + 65172 q^{81} + 410576 q^{82} + 99092 q^{83} + 297128 q^{84} + 27452 q^{86} + 464496 q^{88} + 3160 q^{89} + 519244 q^{92} - 293472 q^{93} - 148820 q^{94} + 395168 q^{96} - 663674 q^{98}+O(q^{100}) \) 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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