LMFDB - Embedded newform 200.6.f.b.149.3

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			149.3
Root			$3.46430 - 1.99965i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.6.f.b.149.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.46395 - 1.46465i) q^{2} -29.2080 q^{3} +(27.7096 + 16.0056i) q^{4} +(159.591 + 42.7797i) q^{6} +168.173i q^{7} +(-127.961 - 128.039i) q^{8} +610.110 q^{9} +O(q^{10})$	\(q+(-5.46395 - 1.46465i) q^{2} -29.2080 q^{3} +(27.7096 + 16.0056i) q^{4} +(159.591 + 42.7797i) q^{6} +168.173i q^{7} +(-127.961 - 128.039i) q^{8} +610.110 q^{9} +514.493i q^{11} +(-809.342 - 467.493i) q^{12} +491.622 q^{13} +(246.316 - 918.892i) q^{14} +(511.641 + 887.017i) q^{16} -183.094i q^{17} +(-3333.61 - 893.600i) q^{18} -1250.96i q^{19} -4912.01i q^{21} +(753.554 - 2811.16i) q^{22} -423.498i q^{23} +(3737.49 + 3739.76i) q^{24} +(-2686.20 - 720.056i) q^{26} -10722.5 q^{27} +(-2691.72 + 4660.01i) q^{28} -3463.40i q^{29} +2343.92 q^{31} +(-1496.41 - 5596.00i) q^{32} -15027.3i q^{33} +(-268.170 + 1000.42i) q^{34} +(16905.9 + 9765.18i) q^{36} +7388.25 q^{37} +(-1832.23 + 6835.20i) q^{38} -14359.3 q^{39} +4240.39 q^{41} +(-7194.41 + 26839.0i) q^{42} +15159.4 q^{43} +(-8234.77 + 14256.4i) q^{44} +(-620.279 + 2313.98i) q^{46} +15357.8i q^{47} +(-14944.0 - 25908.0i) q^{48} -11475.3 q^{49} +5347.82i q^{51} +(13622.6 + 7868.71i) q^{52} +11393.9 q^{53} +(58587.5 + 15704.8i) q^{54} +(21532.7 - 21519.7i) q^{56} +36538.2i q^{57} +(-5072.68 + 18923.8i) q^{58} -11978.0i q^{59} +41454.0i q^{61} +(-12807.1 - 3433.03i) q^{62} +102604. i q^{63} +(-19.9046 + 32768.0i) q^{64} +(-22009.8 + 82108.6i) q^{66} +66524.9 q^{67} +(2930.53 - 5073.46i) q^{68} +12369.6i q^{69} -26214.5 q^{71} +(-78070.3 - 78117.7i) q^{72} -86291.9i q^{73} +(-40369.0 - 10821.2i) q^{74} +(20022.4 - 34663.7i) q^{76} -86524.0 q^{77} +(78458.6 + 21031.4i) q^{78} +19799.4 q^{79} +164928. q^{81} +(-23169.3 - 6210.70i) q^{82} +8370.24 q^{83} +(78619.8 - 136110. i) q^{84} +(-82830.0 - 22203.2i) q^{86} +101159. i q^{87} +(65875.1 - 65835.1i) q^{88} +3824.45 q^{89} +82677.7i q^{91} +(6778.35 - 11735.0i) q^{92} -68461.3 q^{93} +(22493.9 - 83914.4i) q^{94} +(43707.1 + 163448. i) q^{96} -35158.5i q^{97} +(62700.4 + 16807.3i) q^{98} +313897. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.46395	−	1.46465i	−0.965900	−	0.258917i
$2$	−5.46395	−	1.46465i	−0.965900	−	0.258917i
$3$	−29.2080			−1.87370			−0.936848	−	0.349736i	$-0.886271\pi$
$3$	−29.2080			−1.87370			−0.936848	+	0.349736i	$0.886271\pi$
$4$	27.7096	+	16.0056i	0.865924	+	0.500175i
$5$		0			0
$5$		0			0
$6$	159.591	+	42.7797i	1.80980	+	0.485132i
$7$			168.173i			1.29722i	0.761123	+	0.648608i	$0.224648\pi$
$7$			168.173i			1.29722i	−0.761123	+	0.648608i	$0.775352\pi$
$8$	−127.961	−	128.039i	−0.706892	−	0.707322i
$9$	610.110			2.51074
$10$		0			0
$11$			514.493i			1.28203i	0.767529	+	0.641014i	$0.221486\pi$
$11$			514.493i			1.28203i	−0.767529	+	0.641014i	$0.778514\pi$
$12$	−809.342	−	467.493i	−1.62248	−	0.937177i
$13$	491.622			0.806813			0.403406	−	0.915021i	$-0.367826\pi$
$13$	491.622			0.806813			0.403406	+	0.915021i	$0.367826\pi$
$14$	246.316	−	918.892i	0.335871	−	1.25298i
$15$		0			0
$16$	511.641	+	887.017i	0.499649	+	0.866228i
$17$		−	183.094i		−	0.153657i	−0.997044	−	0.0768284i	$-0.975521\pi$
$17$		−	183.094i		−	0.153657i	0.997044	−	0.0768284i	$-0.0244794\pi$
$18$	−3333.61	−	893.600i	−2.42512	−	0.650073i
$19$		−	1250.96i		−	0.794988i	−0.917605	−	0.397494i	$-0.869880\pi$
$19$		−	1250.96i		−	0.794988i	0.917605	−	0.397494i	$-0.130120\pi$
$20$		0			0
$21$		−	4912.01i		−	2.43059i
$22$	753.554	−	2811.16i	0.331939	−	1.23831i
$23$		−	423.498i		−	0.166929i	−0.996511	−	0.0834646i	$-0.973401\pi$
$23$		−	423.498i		−	0.166929i	0.996511	−	0.0834646i	$-0.0265985\pi$
$24$	3737.49	+	3739.76i	1.32450	+	1.32531i
$25$		0			0
$26$	−2686.20	−	720.056i	−0.779300	−	0.208897i
$27$	−10722.5			−2.83067
$28$	−2691.72	+	4660.01i	−0.648835	+	1.12329i
$29$		−	3463.40i		−	0.764729i	−0.924012	−	0.382364i	$-0.875110\pi$
$29$		−	3463.40i		−	0.764729i	0.924012	−	0.382364i	$-0.124890\pi$
$30$		0			0
$31$	2343.92			0.438065			0.219032	−	0.975718i	$-0.429710\pi$
$31$	2343.92			0.438065			0.219032	+	0.975718i	$0.429710\pi$
$32$	−1496.41	−	5596.00i	−0.258330	−	0.966057i
$33$		−	15027.3i		−	2.40213i
$34$	−268.170	+	1000.42i	−0.0397843	+	0.148417i
$35$		0			0
$36$	16905.9	+	9765.18i	2.17411	+	1.25581i
$37$	7388.25			0.887232			0.443616	−	0.896217i	$-0.353695\pi$
$37$	7388.25			0.887232			0.443616	+	0.896217i	$0.353695\pi$
$38$	−1832.23	+	6835.20i	−0.205836	+	0.767879i
$39$	−14359.3			−1.51172
$40$		0			0
$41$	4240.39			0.393954			0.196977	−	0.980408i	$-0.436888\pi$
$41$	4240.39			0.393954			0.196977	+	0.980408i	$0.436888\pi$
$42$	−7194.41	+	26839.0i	−0.629320	+	2.34770i
$43$	15159.4			1.25029			0.625143	−	0.780510i	$-0.285040\pi$
$43$	15159.4			1.25029			0.625143	+	0.780510i	$0.285040\pi$
$44$	−8234.77	+	14256.4i	−0.641239	+	1.11014i
$45$		0			0
$46$	−620.279	+	2313.98i	−0.0432208	+	0.161237i
$47$			15357.8i			1.01411i	0.861914	+	0.507055i	$0.169266\pi$
$47$			15357.8i			1.01411i	−0.861914	+	0.507055i	$0.830734\pi$
$48$	−14944.0	−	25908.0i	−0.936191	−	1.62305i
$49$	−11475.3			−0.682768
$50$		0			0
$51$			5347.82i			0.287906i
$52$	13622.6	+	7868.71i	0.698639	+	0.403548i
$53$	11393.9			0.557162			0.278581	−	0.960413i	$-0.410136\pi$
$53$	11393.9			0.557162			0.278581	+	0.960413i	$0.410136\pi$
$54$	58587.5	+	15704.8i	2.73414	+	0.732907i
$55$		0			0
$56$	21532.7	−	21519.7i	0.917548	−	0.916991i
$57$			36538.2i			1.48957i
$58$	−5072.68	+	18923.8i	−0.198001	+	0.738651i
$59$		−	11978.0i		−	0.447974i	−0.974592	−	0.223987i	$-0.928093\pi$
$59$		−	11978.0i		−	0.447974i	0.974592	−	0.223987i	$-0.0719074\pi$
$60$		0			0
$61$			41454.0i			1.42640i	0.700960	+	0.713200i	$0.252755\pi$
$61$			41454.0i			1.42640i	−0.700960	+	0.713200i	$0.747245\pi$
$62$	−12807.1	−	3433.03i	−0.423127	−	0.113422i
$63$			102604.i			3.25697i
$64$	−19.9046	+	32768.0i	−0.000607441	+	1.00000i
$65$		0			0
$66$	−22009.8	+	82108.6i	−0.621952	+	2.32022i
$67$	66524.9			1.81049			0.905247	−	0.424885i	$-0.139685\pi$
$67$	66524.9			1.81049			0.905247	+	0.424885i	$0.139685\pi$
$68$	2930.53	−	5073.46i	0.0768553	−	0.133055i
$69$			12369.6i			0.312775i
$70$		0			0
$71$	−26214.5			−0.617157			−0.308579	−	0.951199i	$-0.599853\pi$
$71$	−26214.5			−0.617157			−0.308579	+	0.951199i	$0.599853\pi$
$72$	−78070.3	−	78117.7i	−1.77482	−	1.77590i
$73$		−	86291.9i		−	1.89523i	−0.319409	−	0.947617i	$-0.603484\pi$
$73$		−	86291.9i		−	1.89523i	0.319409	−	0.947617i	$-0.396516\pi$
$74$	−40369.0	−	10821.2i	−0.856977	−	0.229719i
$75$		0			0
$76$	20022.4	−	34663.7i	0.397633	−	0.688399i
$77$	−86524.0			−1.66307
$78$	78458.6	+	21031.4i	1.46017	+	0.391410i
$79$	19799.4			0.356931			0.178466	−	0.983946i	$-0.442887\pi$
$79$	19799.4			0.356931			0.178466	+	0.983946i	$0.442887\pi$
$80$		0			0
$81$	164928.			2.79307
$82$	−23169.3	−	6210.70i	−0.380520	−	0.102001i
$83$	8370.24			0.133365			0.0666826	−	0.997774i	$-0.478759\pi$
$83$	8370.24			0.133365			0.0666826	+	0.997774i	$0.478759\pi$
$84$	78619.8	−	136110.i	1.21572	−	2.10471i
$85$		0			0
$86$	−82830.0	−	22203.2i	−1.20765	−	0.323720i
$87$			101159.i			1.43287i
$88$	65875.1	−	65835.1i	0.906806	−	0.906255i
$89$	3824.45			0.0511793			0.0255896	−	0.999673i	$-0.491854\pi$
$89$	3824.45			0.0511793			0.0255896	+	0.999673i	$0.491854\pi$
$90$		0			0
$91$			82677.7i			1.04661i
$92$	6778.35	−	11735.0i	0.0834939	−	0.144548i
$93$	−68461.3			−0.820801
$94$	22493.9	−	83914.4i	0.262570	−	0.979528i
$95$		0			0
$96$	43707.1	+	163448.i	0.484032	+	1.81010i
$97$		−	35158.5i		−	0.379403i	−0.981842	−	0.189702i	$-0.939248\pi$
$97$		−	35158.5i		−	0.379403i	0.981842	−	0.189702i	$-0.0607520\pi$
$98$	62700.4	+	16807.3i	0.659486	+	0.176780i
$99$			313897.i			3.21884i
$100$		0			0
$101$		−	99536.3i		−	0.970908i	−0.874262	−	0.485454i	$-0.838654\pi$
$101$		−	99536.3i		−	0.970908i	0.874262	−	0.485454i	$-0.161346\pi$
$102$	7832.71	−	29220.2i	0.0745438	−	0.278089i
$103$			46921.2i			0.435789i	0.975972	+	0.217895i	$0.0699189\pi$
$103$			46921.2i			0.435789i	−0.975972	+	0.217895i	$0.930081\pi$
$104$	−62908.5	−	62946.7i	−0.570329	−	0.570676i
$105$		0			0
$106$	−62255.5	−	16688.1i	−0.538162	−	0.144259i
$107$	−38381.3			−0.324086			−0.162043	−	0.986784i	$-0.551808\pi$
$107$	−38381.3			−0.324086			−0.162043	+	0.986784i	$0.551808\pi$
$108$	−297117.	−	171621.i	−2.45114	−	1.41583i
$109$			14288.7i			0.115193i	0.998340	+	0.0575966i	$0.0183437\pi$
$109$			14288.7i			0.115193i	−0.998340	+	0.0575966i	$0.981656\pi$
$110$		0			0
$111$	−215796.			−1.66240
$112$	−149173.	+	86044.4i	−1.12368	+	0.648153i
$113$			130552.i			0.961804i	0.876774	+	0.480902i	$0.159691\pi$
$113$			130552.i			0.961804i	−0.876774	+	0.480902i	$0.840309\pi$
$114$	53515.8	−	199643.i	0.385674	−	1.43877i
$115$		0			0
$116$	55433.8	−	95969.3i	0.382498	−	0.662197i
$117$	299943.			2.02570
$118$	−17543.6	+	65447.1i	−0.115988	+	0.432698i
$119$	30791.5			0.199326
$120$		0			0
$121$	−103652.			−0.643596
$122$	60715.7	−	226503.i	0.369319	−	1.37776i
$123$	−123853.			−0.738151
$124$	64949.0	+	37515.9i	0.379331	+	0.219109i
$125$		0			0
$126$	150280.	−	560624.i	0.843284	−	3.14591i
$127$			327594.i			1.80230i	0.433508	+	0.901150i	$0.357276\pi$
$127$			327594.i			1.80230i	−0.433508	+	0.901150i	$0.642724\pi$
$128$	48102.6	−	179014.i	0.259504	−	0.965742i
$129$	−442775.			−2.34266
$130$		0			0
$131$			116999.i			0.595669i	0.954618	+	0.297834i	$0.0962643\pi$
$131$			116999.i			0.595669i	−0.954618	+	0.297834i	$0.903736\pi$
$132$	240522.	−	416401.i	1.20149	−	2.08006i
$133$	210379.			1.03127
$134$	−363489.	−	97436.0i	−1.74876	−	0.468768i
$135$		0			0
$136$	−23443.1	+	23428.9i	−0.108685	+	0.108619i
$137$			74409.1i			0.338707i	0.985555	+	0.169354i	$0.0541680\pi$
$137$			74409.1i			0.338707i	−0.985555	+	0.169354i	$0.945832\pi$
$138$	18117.1	−	67586.7i	0.0809826	−	0.302109i
$139$		−	80434.5i		−	0.353106i	−0.984291	−	0.176553i	$-0.943505\pi$
$139$		−	80434.5i		−	0.353106i	0.984291	−	0.176553i	$-0.0564947\pi$
$140$		0			0
$141$		−	448572.i		−	1.90013i
$142$	143235.	+	38395.2i	0.596112	+	0.159792i
$143$			252936.i			1.03436i
$144$	312157.	+	541178.i	1.25449	+	2.17487i
$145$		0			0
$146$	−126388.	+	471495.i	−0.490708	+	1.83061i
$147$	335171.			1.27930
$148$	204725.	+	118253.i	0.768275	+	0.443771i
$149$			57917.4i			0.213719i	0.994274	+	0.106860i	$0.0340795\pi$
$149$			57917.4i			0.213719i	−0.994274	+	0.106860i	$0.965920\pi$
$150$		0			0
$151$	450813.			1.60899			0.804497	−	0.593957i	$-0.202435\pi$
$151$	450813.			1.60899			0.804497	+	0.593957i	$0.202435\pi$
$152$	−160172.	+	160075.i	−0.562312	+	0.561971i
$153$		−	111707.i		−	0.385792i
$154$	472763.	+	126728.i	1.60636	+	0.430596i
$155$		0			0
$156$	−397890.	−	229829.i	−1.30904	−	0.756126i
$157$	72067.3			0.233340			0.116670	−	0.993171i	$-0.462778\pi$
$157$	72067.3			0.233340			0.116670	+	0.993171i	$0.462778\pi$
$158$	−108183.	−	28999.3i	−0.344760	−	0.0924155i
$159$	−332792.			−1.04395
$160$		0			0
$161$	71221.2			0.216543
$162$	−901159.	−	241563.i	−2.69783	−	0.723173i
$163$	−471144.			−1.38895			−0.694473	−	0.719519i	$-0.744362\pi$
$163$	−471144.			−1.38895			−0.694473	+	0.719519i	$0.744362\pi$
$164$	117499.	+	67870.0i	0.341134	+	0.197046i
$165$		0			0
$166$	−45734.6	−	12259.5i	−0.128817	−	0.0345305i
$167$		−	519164.i		−	1.44050i	−0.693715	−	0.720250i	$-0.744027\pi$
$167$		−	519164.i		−	1.44050i	0.693715	−	0.720250i	$-0.255973\pi$
$168$	−628929.	+	628547.i	−1.71921	+	1.71816i
$169$	−129601.			−0.349053
$170$		0			0
$171$		−	763225.i		−	1.99601i
$172$	420059.	+	242635.i	1.08265	+	0.625363i
$173$	726898.			1.84654			0.923269	−	0.384153i	$-0.125506\pi$
$173$	726898.			1.84654			0.923269	+	0.384153i	$0.125506\pi$
$174$	148163.	−	552728.i	0.370994	−	1.38401i
$175$		0			0
$176$	−456364.	+	263236.i	−1.11053	+	0.640564i
$177$			349853.i			0.839368i
$178$	−20896.6	−	5601.50i	−0.0494340	−	0.0132512i
$179$		−	327278.i		−	0.763457i	−0.924274	−	0.381729i	$-0.875329\pi$
$179$		−	327278.i		−	0.763457i	0.924274	−	0.381729i	$-0.124671\pi$
$180$		0			0
$181$			651584.i			1.47834i	0.673519	+	0.739170i	$0.264782\pi$
$181$			651584.i			1.47834i	−0.673519	+	0.739170i	$0.735218\pi$
$182$	121094.	−	451747.i	0.270985	−	1.01092i
$183$		−	1.21079e6i		−	2.67264i
$184$	−54224.3	+	54191.3i	−0.118073	+	0.118001i
$185$		0			0
$186$	374069.	+	100272.i	0.792811	+	0.212519i
$187$	94200.5			0.196992
$188$	−245811.	+	425558.i	−0.507232	+	0.878142i
$189$		−	1.80325e6i		−	3.67198i
$190$		0			0
$191$	−427987.			−0.848882			−0.424441	−	0.905456i	$-0.639529\pi$
$191$	−427987.			−0.848882			−0.424441	+	0.905456i	$0.639529\pi$
$192$	581.375	−	957089.i	0.00113816	−	1.87370i
$193$			560696.i			1.08351i	0.840535	+	0.541757i	$0.182241\pi$
$193$			560696.i			1.08351i	−0.840535	+	0.541757i	$0.817759\pi$
$194$	−51495.1	+	192104.i	−0.0982339	+	0.366465i
$195$		0			0
$196$	−317975.	−	183669.i	−0.591226	−	0.341504i
$197$	−268824.			−0.493518			−0.246759	−	0.969077i	$-0.579366\pi$
$197$	−268824.			−0.493518			−0.246759	+	0.969077i	$0.579366\pi$
$198$	459751.	−	1.71512e6i	0.833411	−	3.10907i
$199$	−512715.			−0.917789			−0.458895	−	0.888491i	$-0.651754\pi$
$199$	−512715.			−0.917789			−0.458895	+	0.888491i	$0.651754\pi$
$200$		0			0
$201$	−1.94306e6			−3.39232
$202$	−145786.	+	543862.i	−0.251384	+	0.937799i
$203$	582451.			0.992018
$204$	−85595.1	+	148186.i	−0.144004	+	0.249305i
$205$		0			0
$206$	68723.4	−	256376.i	0.112833	−	0.420929i
$207$		−	258380.i		−	0.419116i
$208$	251534.	+	436077.i	0.403123	+	0.698884i
$209$	643612.			1.01920
$210$		0			0
$211$			661872.i			1.02345i	0.859148	+	0.511726i	$0.170994\pi$
$211$			661872.i			1.02345i	−0.859148	+	0.511726i	$0.829006\pi$
$212$	315719.	+	182366.i	0.482460	+	0.278679i
$213$	765674.			1.15637
$214$	209713.	+	56215.3i	0.313034	+	0.0839112i
$215$		0			0
$216$	1.37207e6	+	1.37290e6i	2.00098	+	2.00219i
$217$			394185.i			0.568265i
$218$	20928.0	−	78072.9i	0.0298255	−	0.111265i
$219$			2.52042e6i			3.55109i
$220$		0			0
$221$		−	90013.0i		−	0.123972i
$222$	1.17910e6	+	316067.i	1.60571	+	0.430424i
$223$			1.06479e6i			1.43384i	0.697153	+	0.716922i	$0.254450\pi$
$223$			1.06479e6i			1.43384i	−0.697153	+	0.716922i	$0.745550\pi$
$224$	941098.	−	251656.i	1.25318	−	0.335110i
$225$		0			0
$226$	191213.	−	713329.i	0.249027	−	0.929006i
$227$	−619730.			−0.798248			−0.399124	−	0.916897i	$-0.630686\pi$
$227$	−619730.			−0.798248			−0.399124	+	0.916897i	$0.630686\pi$
$228$	−584816.	+	1.01246e6i	−0.745044	+	1.28985i
$229$			434907.i			0.548035i	0.961725	+	0.274017i	$0.0883525\pi$
$229$			434907.i			0.548035i	−0.961725	+	0.274017i	$0.911647\pi$
$230$		0			0
$231$	2.52720e6			3.11608
$232$	−443450.	+	443180.i	−0.540909	+	0.540581i
$233$			793810.i			0.957915i	0.877838	+	0.478957i	$0.158985\pi$
$233$			793810.i			0.957915i	−0.877838	+	0.478957i	$0.841015\pi$
$234$	−1.63888e6	−	439313.i	−1.95662	−	0.524487i
$235$		0			0
$236$	191715.	−	331904.i	0.224066	−	0.387912i
$237$	−578302.			−0.668781
$238$	−168244.	−	45099.0i	−0.192529	−	0.0516089i
$239$	1.64777e6			1.86596			0.932978	−	0.359933i	$-0.117200\pi$
$239$	1.64777e6			1.86596			0.932978	+	0.359933i	$0.117200\pi$
$240$		0			0
$241$	592599.			0.657231			0.328616	−	0.944464i	$-0.393418\pi$
$241$	592599.			0.657231			0.328616	+	0.944464i	$0.393418\pi$
$242$	566349.	+	151814.i	0.621649	+	0.166638i
$243$	−2.21164e6			−2.40270
$244$	−663496.	+	1.14867e6i	−0.713450	+	1.23515i
$245$		0			0
$246$	676729.	+	181402.i	0.712979	+	0.191120i
$247$		−	615001.i		−	0.641406i
$248$	−299930.	−	300113.i	−0.309665	−	0.309853i
$249$	−244478.			−0.249886
$250$		0			0
$251$			1.64581e6i			1.64890i	0.565933	+	0.824451i	$0.308516\pi$
$251$			1.64581e6i			1.64890i	−0.565933	+	0.824451i	$0.691484\pi$
$252$	−1.64224e6	+	2.84312e6i	−1.62906	+	2.82029i
$253$	217887.			0.214008
$254$	479813.	−	1.78996e6i	0.466646	−	1.74084i
$255$		0			0
$256$	−525023.	+	907669.i	−0.500701	+	0.865620i
$257$			1.18756e6i			1.12156i	0.827966	+	0.560779i	$0.189498\pi$
$257$			1.18756e6i			1.12156i	−0.827966	+	0.560779i	$0.810502\pi$
$258$	2.41930e6	+	648513.i	2.26277	+	0.606554i
$259$			1.24251e6i			1.15093i
$260$		0			0
$261$		−	2.11305e6i		−	1.92003i
$262$	171364.	−	639279.i	0.154229	−	0.575356i
$263$		−	1.62916e6i		−	1.45236i	−0.687505	−	0.726180i	$-0.741294\pi$
$263$		−	1.62916e6i		−	1.45236i	0.687505	−	0.726180i	$-0.258706\pi$
$264$	−1.92408e6	+	1.92291e6i	−1.69908	+	1.69805i
$265$		0			0
$266$	−1.14950e6	−	308132.i	−0.996104	−	0.267013i
$267$	−111705.			−0.0958944
$268$	1.84338e6	+	1.06477e6i	1.56775	+	0.905565i
$269$		−	895226.i		−	0.754314i	−0.926149	−	0.377157i	$-0.876902\pi$
$269$		−	895226.i		−	0.754314i	0.926149	−	0.377157i	$-0.123098\pi$
$270$		0			0
$271$	16721.4			0.0138309			0.00691545	−	0.999976i	$-0.497799\pi$
$271$	16721.4			0.0138309			0.00691545	+	0.999976i	$0.497799\pi$
$272$	162408.	−	93678.4i	0.133102	−	0.0767745i
$273$		−	2.41485e6i		−	1.96103i
$274$	108984.	−	406568.i	0.0876970	−	0.327157i
$275$		0			0
$276$	−197982.	+	342755.i	−0.156442	+	0.270839i
$277$	573914.			0.449415			0.224708	−	0.974426i	$-0.427857\pi$
$277$	573914.			0.449415			0.224708	+	0.974426i	$0.427857\pi$
$278$	−117809.	+	439490.i	−0.0914251	+	0.341065i
$279$	1.43005e6			1.09987
$280$		0			0
$281$	1.95965e6			1.48052			0.740258	−	0.672322i	$-0.234703\pi$
$281$	1.95965e6			1.48052			0.740258	+	0.672322i	$0.234703\pi$
$282$	−657003.	+	2.45097e6i	−0.491976	+	1.83534i
$283$	−2.04454e6			−1.51751			−0.758753	−	0.651378i	$-0.774191\pi$
$283$	−2.04454e6			−1.51751			−0.758753	+	0.651378i	$0.774191\pi$
$284$	−726393.	−	419579.i	−0.534411	−	0.308687i
$285$		0			0
$286$	370464.	−	1.38203e6i	0.267812	−	0.999085i
$287$			713120.i			0.511044i
$288$	−912972.	−	3.41417e6i	−0.648599	−	2.42552i
$289$	1.38633e6			0.976390
$290$		0			0
$291$			1.02691e6i			0.710886i
$292$	1.38115e6	−	2.39111e6i	0.947949	−	1.64113i
$293$	−2.25113e6			−1.53190			−0.765951	−	0.642899i	$-0.777731\pi$
$293$	−2.25113e6			−1.53190			−0.765951	+	0.642899i	$0.777731\pi$
$294$	−1.83136e6	−	490909.i	−1.23568	−	0.331232i
$295$		0			0
$296$	−945408.	−	945983.i	−0.627177	−	0.627558i
$297$		−	5.51667e6i		−	3.62899i
$298$	84829.1	−	316458.i	0.0553355	−	0.206431i
$299$		−	208201.i		−	0.134681i
$300$		0			0
$301$			2.54940e6i			1.62189i
$302$	−2.46322e6	−	660286.i	−1.55413	−	0.416596i
$303$			2.90726e6i			1.81919i
$304$	1.10963e6	−	640044.i	0.688641	−	0.397215i
$305$		0			0
$306$	−163613.	+	610364.i	−0.0998881	+	0.372636i
$307$	−572436.			−0.346642			−0.173321	−	0.984865i	$-0.555450\pi$
$307$	−572436.			−0.346642			−0.173321	+	0.984865i	$0.555450\pi$
$308$	−2.39754e6	−	1.38487e6i	−1.44009	−	0.831825i
$309$		−	1.37048e6i		−	0.816537i
$310$		0			0
$311$	−2.86177e6			−1.67778			−0.838889	−	0.544303i	$-0.816794\pi$
$311$	−2.86177e6			−1.67778			−0.838889	+	0.544303i	$0.816794\pi$
$312$	1.83743e6	+	1.83855e6i	1.06862	+	1.06927i
$313$		−	345643.i		−	0.199419i	−0.995017	−	0.0997095i	$-0.968209\pi$
$313$		−	345643.i		−	0.199419i	0.995017	−	0.0997095i	$-0.0317913\pi$
$314$	−393772.	−	105554.i	−0.225383	−	0.0604156i
$315$		0			0
$316$	548633.	+	316902.i	0.309075	+	0.178528i
$317$	−2.84370e6			−1.58941			−0.794706	−	0.606995i	$-0.792375\pi$
$317$	−2.84370e6			−1.58941			−0.794706	+	0.606995i	$0.792375\pi$
$318$	1.81836e6	+	487426.i	1.00835	+	0.270297i
$319$	1.78189e6			0.980404
$320$		0			0
$321$	1.12104e6			0.607238
$322$	−389149.	−	104314.i	−0.209159	−	0.0560667i
$323$	−229044.			−0.122155
$324$	4.57008e6	+	2.63977e6i	2.41859	+	1.39702i
$325$		0			0
$326$	2.57431e6	+	690064.i	1.34158	+	0.359621i
$327$		−	417345.i		−	0.215837i
$328$	−542605.	−	542934.i	−0.278483	−	0.278652i
$329$	−2.58278e6			−1.31552
$330$		0			0
$331$		−	2.20630e6i		−	1.10686i	−0.832895	−	0.553431i	$-0.813318\pi$
$331$		−	2.20630e6i		−	1.10686i	0.832895	−	0.553431i	$-0.186682\pi$
$332$	231936.	+	133971.i	0.115484	+	0.0667060i
$333$	4.50764e6			2.22761
$334$	−760396.	+	2.83669e6i	−0.372970	+	1.39138i
$335$		0			0
$336$	4.35704e6	−	2.51319e6i	2.10544	−	1.21444i
$337$			210820.i			0.101120i	0.998721	+	0.0505599i	$0.0161006\pi$
$337$			210820.i			0.101120i	−0.998721	+	0.0505599i	$0.983899\pi$
$338$	708134.	+	189821.i	0.337150	+	0.0903758i
$339$		−	3.81316e6i		−	1.80213i
$340$		0			0
$341$			1.20593e6i			0.561611i
$342$	−1.11786e6	+	4.17022e6i	−0.516800	+	1.92794i
$343$			896652.i			0.411518i
$344$	−1.93981e6	−	1.94099e6i	−0.883818	−	0.884355i
$345$		0			0
$346$	−3.97174e6	−	1.06466e6i	−1.78357	−	0.478100i
$347$	−2.39916e6			−1.06963			−0.534817	−	0.844968i	$-0.679619\pi$
$347$	−2.39916e6			−1.06963			−0.534817	+	0.844968i	$0.679619\pi$
$348$	−1.61911e6	+	2.80307e6i	−0.716686	+	1.24076i
$349$		−	1.76207e6i		−	0.774392i	−0.921997	−	0.387196i	$-0.873444\pi$
$349$		−	1.76207e6i		−	0.774392i	0.921997	−	0.387196i	$-0.126556\pi$
$350$		0			0
$351$	−5.27144e6			−2.28382
$352$	2.87910e6	−	769891.i	1.23851	−	0.331186i
$353$		−	2.11387e6i		−	0.902904i	−0.892296	−	0.451452i	$-0.850906\pi$
$353$		−	2.11387e6i		−	0.902904i	0.892296	−	0.451452i	$-0.149094\pi$
$354$	512414.	−	1.91158e6i	0.217327	−	0.810745i
$355$		0			0
$356$	105974.	+	61212.7i	0.0443174	+	0.0255986i
$357$	−899360.			−0.373476
$358$	−479350.	+	1.78823e6i	−0.197672	+	0.737423i
$359$	25391.5			0.0103981			0.00519903	−	0.999986i	$-0.498345\pi$
$359$	25391.5			0.0103981			0.00519903	+	0.999986i	$0.498345\pi$
$360$		0			0
$361$	911190.			0.367994
$362$	954346.	−	3.56023e6i	0.382767	−	1.42793i
$363$	3.02747e6			1.20590
$364$	−1.32331e6	+	2.29096e6i	−0.523489	+	0.906285i
$365$		0			0
$366$	−1.77339e6	+	6.61569e6i	−0.691992	+	2.58150i
$367$		−	1.55872e6i		−	0.604091i	−0.953293	−	0.302046i	$-0.902330\pi$
$367$		−	1.55872e6i		−	0.604091i	0.953293	−	0.302046i	$-0.0976695\pi$
$368$	375650.	−	216679.i	0.144599	−	0.0834060i
$369$	2.58710e6			0.989116
$370$		0			0
$371$			1.91614e6i			0.722759i
$372$	−1.89703e6	−	1.09576e6i	−0.710751	−	0.410544i
$373$	741743.			0.276046			0.138023	−	0.990429i	$-0.455925\pi$
$373$	741743.			0.276046			0.138023	+	0.990429i	$0.455925\pi$
$374$	−514707.	−	137971.i	−0.190275	−	0.0510046i
$375$		0			0
$376$	1.96640e6	−	1.96520e6i	0.717301	−	0.716866i
$377$		−	1.70268e6i		−	0.616993i
$378$	−2.64113e6	+	9.85286e6i	−0.950738	+	3.54677i
$379$			2.61039e6i			0.933487i	0.884393	+	0.466743i	$0.154573\pi$
$379$			2.61039e6i			0.933487i	−0.884393	+	0.466743i	$0.845427\pi$
$380$		0			0
$381$		−	9.56839e6i		−	3.37696i
$382$	2.33850e6	+	626853.i	0.819935	+	0.219790i
$383$		−	3.05949e6i		−	1.06574i	−0.846197	−	0.532871i	$-0.821113\pi$
$383$		−	3.05949e6i		−	1.06574i	0.846197	−	0.532871i	$-0.178887\pi$
$384$	−1.40498e6	+	5.22864e6i	−0.486231	+	1.80951i
$385$		0			0
$386$	821227.	−	3.06362e6i	0.280540	−	1.04657i
$387$	9.24887e6			3.13914
$388$	562733.	−	974227.i	0.189768	−	0.328534i
$389$			498203.i			0.166929i	0.996511	+	0.0834646i	$0.0265985\pi$
$389$			498203.i			0.166929i	−0.996511	+	0.0834646i	$0.973401\pi$
$390$		0			0
$391$	−77540.0			−0.0256498
$392$	1.46839e6	+	1.46928e6i	0.482643	+	0.482937i
$393$		−	3.41732e6i		−	1.11610i
$394$	1.46884e6	+	393735.i	0.476689	+	0.127780i
$395$		0			0
$396$	−5.02411e6	+	8.69795e6i	−1.60998	+	2.78727i
$397$	3.95290e6			1.25875			0.629376	−	0.777101i	$-0.283311\pi$
$397$	3.95290e6			1.25875			0.629376	+	0.777101i	$0.283311\pi$
$398$	2.80145e6	+	750950.i	0.886492	+	0.237631i
$399$	−6.14475e6			−1.93229
$400$		0			0
$401$	−1.15248e6			−0.357909			−0.178955	−	0.983857i	$-0.557272\pi$
$401$	−1.15248e6			−0.357909			−0.178955	+	0.983857i	$0.557272\pi$
$402$	1.06168e7	+	2.84591e6i	3.27664	+	0.878328i
$403$	1.15232e6			0.353436
$404$	1.59314e6	−	2.75811e6i	0.485624	−	0.840732i
$405$		0			0
$406$	−3.18249e6	−	853090.i	−0.958190	−	0.256850i
$407$			3.80120e6i			1.13746i
$408$	684728.	−	684313.i	0.203642	−	0.203519i
$409$	−2.54459e6			−0.752159			−0.376079	−	0.926587i	$-0.622728\pi$
$409$	−2.54459e6			−0.752159			−0.376079	+	0.926587i	$0.622728\pi$
$410$		0			0
$411$		−	2.17334e6i		−	0.634635i
$412$	−751003.	+	1.30017e6i	−0.217971	+	0.377360i
$413$	2.01438e6			0.581119
$414$	−378438.	+	1.41178e6i	−0.108516	+	0.404824i
$415$		0			0
$416$	−735667.	−	2.75111e6i	−0.208424	−	0.779427i
$417$			2.34933e6i			0.661614i
$418$	−3.51666e6	−	942669.i	−0.984442	−	0.263887i
$419$			62820.4i			0.0174810i	0.999962	+	0.00874049i	$0.00278222\pi$
$419$			62820.4i			0.0174810i	−0.999962	+	0.00874049i	$0.997218\pi$
$420$		0			0
$421$			1.89940e6i			0.522289i	0.965300	+	0.261145i	$0.0841000\pi$
$421$			1.89940e6i			0.522289i	−0.965300	+	0.261145i	$0.915900\pi$
$422$	969414.	−	3.61644e6i	0.264989	−	0.988553i
$423$			9.36995e6i			2.54616i
$424$	−1.45797e6	−	1.45886e6i	−0.393853	−	0.394092i
$425$		0			0
$426$	−4.18361e6	−	1.12145e6i	−1.11693	−	0.299402i
$427$	−6.97145e6			−1.85035
$428$	−1.06353e6	−	614316.i	−0.280634	−	0.162100i
$429$		−	7.38776e6i		−	1.93807i
$430$		0			0
$431$	5.91659e6			1.53419			0.767094	−	0.641535i	$-0.221702\pi$
$431$	5.91659e6			1.53419			0.767094	+	0.641535i	$0.221702\pi$
$432$	−5.48609e6	−	9.51109e6i	−1.41434	−	2.45200i
$433$		−	1.64308e6i		−	0.421153i	−0.977577	−	0.210577i	$-0.932466\pi$
$433$		−	1.64308e6i		−	0.421153i	0.977577	−	0.210577i	$-0.0675341\pi$
$434$	577345.	−	2.15381e6i	0.147133	−	0.548886i
$435$		0			0
$436$	−228700.	+	395934.i	−0.0576168	+	0.0997486i
$437$	−529781.			−0.132707
$438$	3.69154e6	−	1.37714e7i	0.919438	−	3.43000i
$439$	4.34976e6			1.07722			0.538610	−	0.842555i	$-0.318950\pi$
$439$	4.34976e6			1.07722			0.538610	+	0.842555i	$0.318950\pi$
$440$		0			0
$441$	−7.00118e6			−1.71425
$442$	−131838.	+	491827.i	−0.0320985	+	0.119745i
$443$	2.27280e6			0.550239			0.275119	−	0.961410i	$-0.411283\pi$
$443$	2.27280e6			0.550239			0.275119	+	0.961410i	$0.411283\pi$
$444$	−5.97962e6	−	3.45395e6i	−1.43951	−	0.831493i
$445$		0			0
$446$	1.55955e6	−	5.81796e6i	0.371246	−	1.38495i
$447$		−	1.69165e6i		−	0.400445i
$448$	−5.51070e6	−	3347.43i	−1.29722	−	0.000787982i
$449$	−7.36304e6			−1.72362			−0.861809	−	0.507233i	$-0.830669\pi$
$449$	−7.36304e6			−1.72362			−0.861809	+	0.507233i	$0.830669\pi$
$450$		0			0
$451$			2.18165e6i			0.505060i
$452$	−2.08956e6	+	3.61753e6i	−0.481071	+	0.832849i
$453$	−1.31674e7			−3.01477
$454$	3.38618e6	+	907690.i	0.771027	+	0.206680i
$455$		0			0
$456$	4.67831e6	−	4.67547e6i	1.05360	−	1.05296i
$457$			6.23984e6i			1.39760i	0.715317	+	0.698800i	$0.246282\pi$
$457$			6.23984e6i			1.39760i	−0.715317	+	0.698800i	$0.753718\pi$
$458$	636989.	−	2.37631e6i	0.141895	−	0.529346i
$459$			1.96323e6i			0.434951i
$460$		0			0
$461$			832291.i			0.182399i	0.995833	+	0.0911996i	$0.0290701\pi$
$461$			832291.i			0.182399i	−0.995833	+	0.0911996i	$0.970930\pi$
$462$	−1.38085e7	−	3.70147e6i	−3.00982	−	0.806806i
$463$		−	3.61852e6i		−	0.784474i	−0.919864	−	0.392237i	$-0.871701\pi$
$463$		−	3.61852e6i		−	0.784474i	0.919864	−	0.392237i	$-0.128299\pi$
$464$	3.07209e6	−	1.77202e6i	0.662429	−	0.382096i
$465$		0			0
$466$	1.16266e6	−	4.33734e6i	0.248020	−	0.925249i
$467$	286010.			0.0606861			0.0303431	−	0.999540i	$-0.490340\pi$
$467$	286010.			0.0606861			0.0303431	+	0.999540i	$0.490340\pi$
$468$	8.31130e6	+	4.80077e6i	1.75410	+	1.01320i
$469$			1.11877e7i			2.34860i
$470$		0			0
$471$	−2.10494e6			−0.437208
$472$	−1.53365e6	+	1.53271e6i	−0.316862	+	0.316670i
$473$			7.79938e6i			1.60290i
$474$	3.15981e6	+	847013.i	0.645975	+	0.173159i
$475$		0			0
$476$	853220.	+	492837.i	0.172601	+	0.0996980i
$477$	6.95150e6			1.39889
$478$	−9.00333e6	−	2.41341e6i	−1.80233	−	0.483128i
$479$	2.28996e6			0.456026			0.228013	−	0.973658i	$-0.426777\pi$
$479$	2.28996e6			0.456026			0.228013	+	0.973658i	$0.426777\pi$
$480$		0			0
$481$	3.63222e6			0.715830
$482$	−3.23793e6	−	867953.i	−0.634820	−	0.170168i
$483$	−2.08023e6			−0.405736
$484$	−2.87215e6	−	1.65901e6i	−0.557306	−	0.321911i
$485$		0			0
$486$	1.20843e7	+	3.23930e6i	2.32077	+	0.622100i
$487$		−	6.55915e6i		−	1.25321i	−0.779335	−	0.626607i	$-0.784443\pi$
$487$		−	6.55915e6i		−	1.25321i	0.779335	−	0.626607i	$-0.215557\pi$
$488$	5.30772e6	−	5.30450e6i	1.00892	−	1.00831i
$489$	1.37612e7			2.60246
$490$		0			0
$491$		−	3.50573e6i		−	0.656257i	−0.944633	−	0.328129i	$-0.893582\pi$
$491$		−	3.50573e6i		−	0.656257i	0.944633	−	0.328129i	$-0.106418\pi$
$492$	−3.43192e6	−	1.98235e6i	−0.639183	−	0.369205i
$493$	−634127.			−0.117506
$494$	−900764.	+	3.36034e6i	−0.166071	+	0.619534i
$495$		0			0
$496$	1.19924e6	+	2.07910e6i	0.218879	+	0.379464i
$497$		−	4.40858e6i		−	0.800586i
$498$	1.33582e6	+	358076.i	0.241365	+	0.0646997i
$499$			1.11789e6i			0.200977i	0.994938	+	0.100489i	$0.0320406\pi$
$499$			1.11789e6i			0.200977i	−0.994938	+	0.100489i	$0.967959\pi$
$500$		0			0
$501$			1.51638e7i			2.69906i
$502$	2.41054e6	−	8.99262e6i	0.426929	−	1.59267i
$503$		−	3.97264e6i		−	0.700098i	−0.936731	−	0.350049i	$-0.886165\pi$
$503$		−	3.97264e6i		−	0.700098i	0.936731	−	0.350049i	$-0.113835\pi$
$504$	1.31373e7	−	1.31293e7i	2.30372	−	2.30233i
$505$		0			0
$506$	−1.19052e6	−	319129.i	−0.206710	−	0.0554102i
$507$	3.78539e6			0.654020
$508$	−5.24335e6	+	9.07750e6i	−0.901466	+	1.56065i
$509$			5.19239e6i			0.888327i	0.895946	+	0.444164i	$0.146499\pi$
$509$			5.19239e6i			0.888327i	−0.895946	+	0.444164i	$0.853501\pi$
$510$		0			0
$511$	1.45120e7			2.45853
$512$	4.19812e6	−	4.19048e6i	0.707751	−	0.706462i
$513$			1.34135e7i			2.25035i
$514$	1.73936e6	−	6.48875e6i	0.290390	−	1.08331i
$515$		0			0
$516$	−1.22691e7	−	7.08689e6i	−2.02856	−	1.17174i
$517$	−7.90148e6			−1.30012
$518$	1.81984e6	−	6.78900e6i	0.297995	−	1.11168i
$519$	−2.12313e7			−3.45985
$520$		0			0
$521$	1.09827e6			0.177262			0.0886311	−	0.996065i	$-0.471751\pi$
$521$	1.09827e6			0.177262			0.0886311	+	0.996065i	$0.471751\pi$
$522$	−3.09489e6	+	1.15456e7i	−0.497129	+	1.85456i
$523$	−8.67189e6			−1.38631			−0.693154	−	0.720790i	$-0.743779\pi$
$523$	−8.67189e6			−1.38631			−0.693154	+	0.720790i	$0.743779\pi$
$524$	−1.87264e6	+	3.24200e6i	−0.297939	+	0.515804i
$525$		0			0
$526$	−2.38616e6	+	8.90165e6i	−0.376040	+	1.40283i
$527$		−	429158.i		−	0.0673116i
$528$	1.33295e7	−	7.68859e6i	2.08079	−	1.20022i
$529$	6.25699e6			0.972135
$530$		0			0
$531$		−	7.30787e6i		−	1.12475i
$532$	5.82950e6	+	3.36724e6i	0.893002	+	0.515816i
$533$	2.08467e6			0.317847
$534$	610349.	+	163609.i	0.0926244	+	0.0248287i
$535$		0			0
$536$	−8.51260e6	−	8.51777e6i	−1.27982	−	1.28060i
$537$			9.55916e6i			1.43049i
$538$	−1.31120e6	+	4.89148e6i	−0.195305	+	0.728592i
$539$		−	5.90395e6i		−	0.875328i
$540$		0			0
$541$		−	746497.i		−	0.109657i	−0.998496	−	0.0548283i	$-0.982539\pi$
$541$		−	746497.i		−	0.109657i	0.998496	−	0.0548283i	$-0.0174612\pi$
$542$	−91365.2	−	24491.1i	−0.0133593	−	0.00358105i
$543$		−	1.90315e7i		−	2.76996i
$544$	−1.02459e6	+	273983.i	−0.148441	+	0.0396942i
$545$		0			0
$546$	−3.53693e6	+	1.31946e7i	−0.507744	+	1.89416i
$547$	−2.52087e6			−0.360231			−0.180116	−	0.983645i	$-0.557647\pi$
$547$	−2.52087e6			−0.360231			−0.180116	+	0.983645i	$0.557647\pi$
$548$	−1.19096e6	+	2.06184e6i	−0.169413	+	0.293295i
$549$			2.52915e7i			3.58132i
$550$		0			0
$551$	−4.33258e6			−0.607950
$552$	1.58378e6	−	1.58282e6i	0.221232	−	0.221098i
$553$			3.32973e6i			0.463017i
$554$	−3.13584e6	−	840586.i	−0.434090	−	0.116361i
$555$		0			0
$556$	1.28740e6	−	2.22880e6i	0.176615	−	0.305763i
$557$	186236.			0.0254347			0.0127173	−	0.999919i	$-0.495952\pi$
$557$	186236.			0.0254347			0.0127173	+	0.999919i	$0.495952\pi$
$558$	−7.81371e6	−	2.09453e6i	−1.06236	−	0.284774i
$559$	7.45267e6			1.00875
$560$		0			0
$561$	−2.75141e6			−0.369104
$562$	−1.07075e7	−	2.87021e6i	−1.43003	−	0.383331i
$563$	−358662.			−0.0476886			−0.0238443	−	0.999716i	$-0.507591\pi$
$563$	−358662.			−0.0476886			−0.0238443	+	0.999716i	$0.507591\pi$
$564$	7.17966e6	−	1.24297e7i	0.950400	−	1.64537i
$565$		0			0
$566$	1.11713e7	+	2.99455e6i	1.46576	+	0.392908i
$567$			2.77365e7i			3.62321i
$568$	3.35444e6	+	3.35648e6i	0.436263	+	0.436529i
$569$	−1.08964e7			−1.41093			−0.705463	−	0.708747i	$-0.749261\pi$
$569$	−1.08964e7			−1.41093			−0.705463	+	0.708747i	$0.749261\pi$
$570$		0			0
$571$			1.93042e6i			0.247778i	0.992296	+	0.123889i	$0.0395366\pi$
$571$			1.93042e6i			0.247778i	−0.992296	+	0.123889i	$0.960463\pi$
$572$	−4.04839e6	+	7.00874e6i	−0.517360	+	0.895674i
$573$	1.25007e7			1.59055
$574$	1.04447e6	−	3.89645e6i	0.132318	−	0.493617i
$575$		0			0
$576$	−12144.0	+	1.99921e7i	−0.00152513	+	2.51074i
$577$			1.33310e7i			1.66695i	0.552555	+	0.833477i	$0.313653\pi$
$577$			1.33310e7i			1.66695i	−0.552555	+	0.833477i	$0.686347\pi$
$578$	−7.57486e6	−	2.03050e6i	−0.943094	−	0.252804i
$579$		−	1.63768e7i		−	2.03018i
$580$		0			0
$581$			1.40765e6i			0.173003i
$582$	1.50407e6	−	5.61099e6i	0.184060	−	0.686645i
$583$			5.86206e6i			0.714297i
$584$	−1.10487e7	+	1.10420e7i	−1.34054	+	1.33973i
$585$		0			0
$586$	1.23001e7	+	3.29712e6i	1.47966	+	0.396635i
$587$	7.15350e6			0.856887			0.428443	−	0.903569i	$-0.359062\pi$
$587$	7.15350e6			0.856887			0.428443	+	0.903569i	$0.359062\pi$
$588$	9.28743e6	+	5.36461e6i	1.10778	+	0.639875i
$589$		−	2.93216e6i		−	0.348256i
$590$		0			0
$591$	7.85183e6			0.924703
$592$	3.78013e6	+	6.55350e6i	0.443305	+	0.768545i
$593$			1.46858e7i			1.71499i	0.514490	+	0.857496i	$0.327981\pi$
$593$			1.46858e7i			1.71499i	−0.514490	+	0.857496i	$0.672019\pi$
$594$	−8.08002e6	+	3.01428e7i	−0.939608	+	3.50524i
$595$		0			0
$596$	−927004.	+	1.60487e6i	−0.106897	+	0.185065i
$597$	1.49754e7			1.71966
$598$	−304943.	+	1.13760e6i	−0.0348711	+	0.130088i
$599$	9.83597e6			1.12008			0.560042	−	0.828465i	$-0.310785\pi$
$599$	9.83597e6			1.12008			0.560042	+	0.828465i	$0.310785\pi$
$600$		0			0
$601$	2.68643e6			0.303381			0.151691	−	0.988428i	$-0.451528\pi$
$601$	2.68643e6			0.303381			0.151691	+	0.988428i	$0.451528\pi$
$602$	3.73399e6	−	1.39298e7i	0.419935	−	1.56658i
$603$	4.05875e7			4.54568
$604$	1.24918e7	+	7.21554e6i	1.39327	+	0.804779i
$605$		0			0
$606$	4.25813e6	−	1.58851e7i	0.471018	−	1.75715i
$607$		−	387079.i		−	0.0426411i	−0.999773	−	0.0213205i	$-0.993213\pi$
$607$		−	387079.i		−	0.0426411i	0.999773	−	0.0213205i	$-0.00678705\pi$
$608$	−7.00039e6	+	1.87195e6i	−0.768003	+	0.205369i
$609$	−1.70123e7			−1.85874
$610$		0			0
$611$			7.55024e6i			0.818196i
$612$	1.78795e6	−	3.09536e6i	0.192964	−	0.334067i
$613$	−1.37500e7			−1.47792			−0.738962	−	0.673748i	$-0.764684\pi$
$613$	−1.37500e7			−1.47792			−0.738962	+	0.673748i	$0.764684\pi$
$614$	3.12777e6	+	838422.i	0.334821	+	0.0897515i
$615$		0			0
$616$	1.10717e7	+	1.10784e7i	1.17561	+	1.17632i
$617$			1.13239e7i			1.19752i	0.800930	+	0.598758i	$0.204339\pi$
$617$			1.13239e7i			1.19752i	−0.800930	+	0.598758i	$0.795661\pi$
$618$	−2.00728e6	+	7.48823e6i	−0.211415	+	0.788693i
$619$			6.62505e6i			0.694965i	0.937687	+	0.347482i	$0.112963\pi$
$619$			6.62505e6i			0.694965i	−0.937687	+	0.347482i	$0.887037\pi$
$620$		0			0
$621$			4.54098e6i			0.472521i
$622$	1.56366e7	+	4.19151e6i	1.62057	+	0.434405i
$623$			643171.i			0.0663905i
$624$	−7.34681e6	−	1.27370e7i	−0.755331	−	1.30950i
$625$		0			0
$626$	−506247.	+	1.88857e6i	−0.0516329	+	0.192619i
$627$	−1.87986e7			−1.90967
$628$	1.99695e6	+	1.15348e6i	0.202055	+	0.116711i
$629$		−	1.35274e6i		−	0.136329i
$630$		0			0
$631$	−1.12049e7			−1.12030			−0.560152	−	0.828390i	$-0.689257\pi$
$631$	−1.12049e7			−1.12030			−0.560152	+	0.828390i	$0.689257\pi$
$632$	−2.53355e6	−	2.53509e6i	−0.252312	−	0.252465i
$633$		−	1.93320e7i		−	1.91764i
$634$	1.55379e7	+	4.16505e6i	1.53521	+	0.411525i
$635$		0			0
$636$	−9.22153e6	−	5.32654e6i	−0.903983	−	0.522159i
$637$	−5.64150e6			−0.550866
$638$	−9.73618e6	−	2.60986e6i	−0.946972	−	0.253843i
$639$	−1.59937e7			−1.54952
$640$		0			0
$641$	−5.35866e6			−0.515123			−0.257562	−	0.966262i	$-0.582919\pi$
$641$	−5.35866e6			−0.515123			−0.257562	+	0.966262i	$0.582919\pi$
$642$	−6.12532e6	−	1.64194e6i	−0.586531	−	0.157224i
$643$	5.64079e6			0.538038			0.269019	−	0.963135i	$-0.413301\pi$
$643$	5.64079e6			0.538038			0.269019	+	0.963135i	$0.413301\pi$
$644$	1.97351e6	+	1.13994e6i	0.187510	+	0.108310i
$645$		0			0
$646$	1.25148e6	+	335470.i	0.117990	+	0.0316281i
$647$		−	5.67405e6i		−	0.532884i	−0.963851	−	0.266442i	$-0.914152\pi$
$647$		−	5.67405e6i		−	0.532884i	0.963851	−	0.266442i	$-0.0858480\pi$
$648$	−2.11044e7	−	2.11172e7i	−1.97440	−	1.97560i
$649$	6.16258e6			0.574316
$650$		0			0
$651$		−	1.15134e7i		−	1.06476i
$652$	−1.30552e7	−	7.54096e6i	−1.20272	−	0.694716i
$653$	1.50064e7			1.37719			0.688593	−	0.725148i	$-0.258229\pi$
$653$	1.50064e7			1.37719			0.688593	+	0.725148i	$0.258229\pi$
$654$	−611267.	+	2.28036e6i	−0.0558839	+	0.208477i
$655$		0			0
$656$	2.16955e6	+	3.76130e6i	0.196839	+	0.341254i
$657$		−	5.26475e7i		−	4.75844i
$658$	1.41122e7	+	3.78287e6i	1.27066	+	0.340610i
$659$		−	7.48265e6i		−	0.671184i	−0.942007	−	0.335592i	$-0.891064\pi$
$659$		−	7.48265e6i		−	0.671184i	0.942007	−	0.335592i	$-0.108936\pi$
$660$		0			0
$661$		−	1.85142e7i		−	1.64817i	−0.566467	−	0.824084i	$-0.691690\pi$
$661$		−	1.85142e7i		−	1.64817i	0.566467	−	0.824084i	$-0.308310\pi$
$662$	−3.23146e6	+	1.20551e7i	−0.286585	+	1.06912i
$663$			2.62910e6i			0.232286i
$664$	−1.07107e6	−	1.07172e6i	−0.0942748	−	0.0943321i
$665$		0			0
$666$	−2.46295e7	−	6.60214e6i	−2.15164	−	0.576765i
$667$	−1.46674e6			−0.127656
$668$	8.30953e6	−	1.43858e7i	0.720502	−	1.24736i
$669$		−	3.11004e7i		−	2.68659i
$670$		0			0
$671$	−2.13278e7			−1.82869
$672$	−2.74876e7	+	7.35038e6i	−2.34809	+	0.627894i
$673$		−	4.62662e6i		−	0.393755i	−0.980428	−	0.196878i	$-0.936920\pi$
$673$		−	4.62662e6i		−	0.393755i	0.980428	−	0.196878i	$-0.0630802\pi$
$674$	308778.	−	1.15191e6i	0.0261816	−	0.0976716i
$675$		0			0
$676$	−3.59119e6	−	2.07434e6i	−0.302254	−	0.174588i
$677$	1.21437e7			1.01831			0.509155	−	0.860675i	$-0.329958\pi$
$677$	1.21437e7			1.01831			0.509155	+	0.860675i	$0.329958\pi$
$678$	−5.58496e6	+	2.08349e7i	−0.466601	+	1.74068i
$679$	5.91272e6			0.492168
$680$		0			0
$681$	1.81011e7			1.49567
$682$	1.76627e6	−	6.58914e6i	0.145411	−	0.542460i
$683$	−9.19906e6			−0.754557			−0.377278	−	0.926100i	$-0.623140\pi$
$683$	−9.19906e6			−0.754557			−0.377278	+	0.926100i	$0.623140\pi$
$684$	1.22159e7	−	2.11486e7i	0.998354	−	1.72839i
$685$		0			0
$686$	1.31329e6	−	4.89927e6i	0.106549	−	0.397485i
$687$		−	1.27028e7i		−	1.02685i
$688$	7.75615e6	+	1.34466e7i	0.624705	+	1.08303i
$689$	5.60147e6			0.449525
$690$		0			0
$691$			1.02344e7i			0.815394i	0.913117	+	0.407697i	$0.133668\pi$
$691$			1.02344e7i			0.815394i	−0.913117	+	0.407697i	$0.866332\pi$
$692$	2.01420e7	+	1.16345e7i	1.59896	+	0.923593i
$693$	−5.27891e7			−4.17553
$694$	1.31089e7	+	3.51394e6i	1.03316	+	0.276946i
$695$		0			0
$696$	1.29523e7	−	1.29444e7i	1.01350	−	1.01288i
$697$		−	776389.i		−	0.0605338i
$698$	−2.58083e6	+	9.62789e6i	−0.200503	+	0.747985i
$699$		−	2.31856e7i		−	1.79484i
$700$		0			0
$701$		−	1.23863e6i		−	0.0952023i	−0.998866	−	0.0476011i	$-0.984842\pi$
$701$		−	1.23863e6i		−	0.0952023i	0.998866	−	0.0476011i	$-0.0151576\pi$
$702$	2.88029e7	+	7.72084e6i	2.20594	+	0.591319i
$703$		−	9.24242e6i		−	0.705339i
$704$	−1.68589e7	−	10240.8i	−1.28203	−	0.000778757i
$705$		0			0
$706$	−3.09609e6	+	1.15501e7i	−0.233777	+	0.872114i
$707$	1.67394e7			1.25948
$708$	−5.59961e6	+	9.69428e6i	−0.419831	+	0.726829i
$709$			2.52759e7i			1.88839i	0.329386	+	0.944195i	$0.393158\pi$
$709$			2.52759e7i			1.88839i	−0.329386	+	0.944195i	$0.606842\pi$
$710$		0			0
$711$	1.20798e7			0.896161
$712$	−489381.	−	489678.i	−0.0361782	−	0.0362002i
$713$		−	992646.i		−	0.0731258i
$714$	4.91406e6	+	1.31725e6i	0.360741	+	0.0966993i
$715$		0			0
$716$	5.23829e6	−	9.06874e6i	0.381863	−	0.661096i
$717$	−4.81281e7			−3.49624
$718$	−138738.	−	37189.8i	−0.0100435	−	0.00269223i
$719$	5.23203e6			0.377440			0.188720	−	0.982031i	$-0.439566\pi$
$719$	5.23203e6			0.377440			0.188720	+	0.982031i	$0.439566\pi$
$720$		0			0
$721$	−7.89090e6			−0.565313
$722$	−4.97870e6	−	1.33458e6i	−0.355445	−	0.0952799i
$723$	−1.73087e7			−1.23145
$724$	−1.04290e7	+	1.80551e7i	−0.739429	+	1.28013i
$725$		0			0
$726$	−1.65419e7	−	4.43419e6i	−1.16478	−	0.312229i
$727$		−	1.79530e7i		−	1.25980i	−0.776677	−	0.629899i	$-0.783096\pi$
$727$		−	1.79530e7i		−	1.25980i	0.776677	−	0.629899i	$-0.216904\pi$
$728$	1.05860e7	−	1.05795e7i	0.740290	−	0.739840i
$729$	2.45203e7			1.70886
$730$		0			0
$731$		−	2.77559e6i		−	0.192115i
$732$	1.93794e7	−	3.35504e7i	1.33679	−	2.31430i
$733$	−2.06019e6			−0.141627			−0.0708137	−	0.997490i	$-0.522560\pi$
$733$	−2.06019e6			−0.141627			−0.0708137	+	0.997490i	$0.522560\pi$
$734$	−2.28299e6	+	8.51677e6i	−0.156409	+	0.583492i
$735$		0			0
$736$	−2.36990e6	+	633726.i	−0.161263	+	0.0431228i
$737$			3.42266e7i			2.32111i
$738$	−1.41358e7	−	3.78921e6i	−0.955387	−	0.256099i
$739$			1.47746e6i			0.0995187i	0.998761	+	0.0497594i	$0.0158454\pi$
$739$			1.47746e6i			0.0995187i	−0.998761	+	0.0497594i	$0.984155\pi$
$740$		0			0
$741$			1.79630e7i			1.20180i
$742$	2.80649e6	−	1.04697e7i	0.187134	−	0.698112i
$743$			2.46543e7i			1.63840i	0.573508	+	0.819200i	$0.305582\pi$
$743$			2.46543e7i			1.63840i	−0.573508	+	0.819200i	$0.694418\pi$
$744$	8.76038e6	+	8.76570e6i	0.580217	+	0.580570i
$745$		0			0
$746$	−4.05285e6	−	1.08640e6i	−0.266633	−	0.0714729i
$747$	5.10676e6			0.334845
$748$	2.61026e6	+	1.50774e6i	0.170580	+	0.0985307i
$749$		−	6.45471e6i		−	0.420409i
$750$		0			0
$751$	−6.30342e6			−0.407827			−0.203914	−	0.978989i	$-0.565366\pi$
$751$	−6.30342e6			−0.407827			−0.203914	+	0.978989i	$0.565366\pi$
$752$	−1.36226e7	+	7.85768e6i	−0.878450	+	0.506699i
$753$		−	4.80708e7i		−	3.08954i
$754$	−2.49384e6	+	9.30338e6i	−0.159750	+	0.595953i
$755$		0			0
$756$	2.88621e7	−	4.99672e7i	1.83664	−	3.17966i
$757$	1.44827e7			0.918567			0.459284	−	0.888290i	$-0.348106\pi$
$757$	1.44827e7			0.918567			0.459284	+	0.888290i	$0.348106\pi$
$758$	3.82333e6	−	1.42631e7i	0.241695	−	0.901655i
$759$	−6.36405e6			−0.400986
$760$		0			0
$761$	9.50962e6			0.595253			0.297626	−	0.954682i	$-0.403805\pi$
$761$	9.50962e6			0.595253			0.297626	+	0.954682i	$0.403805\pi$
$762$	−1.40144e7	+	5.22812e7i	−0.874353	+	3.26181i
$763$	−2.40298e6			−0.149430
$764$	−1.18593e7	−	6.85020e6i	−0.735067	−	0.424590i
$765$		0			0
$766$	−4.48109e6	+	1.67169e7i	−0.275938	+	1.02940i
$767$		−	5.88863e6i		−	0.361431i
$768$	1.53349e7	−	2.65112e7i	0.938162	−	1.62191i
$769$	−2.88208e6			−0.175748			−0.0878741	−	0.996132i	$-0.528007\pi$
$769$	−2.88208e6			−0.175748			−0.0878741	+	0.996132i	$0.528007\pi$
$770$		0			0
$771$		−	3.46862e7i		−	2.10146i
$772$	−8.97429e6	+	1.55367e7i	−0.541947	+	0.938241i
$773$	1.83423e7			1.10409			0.552044	−	0.833815i	$-0.313848\pi$
$773$	1.83423e7			1.10409			0.552044	+	0.833815i	$0.313848\pi$
$774$	−5.05354e7	−	1.35464e7i	−3.03210	−	0.812777i
$775$		0			0
$776$	−4.50165e6	+	4.49892e6i	−0.268360	+	0.268197i
$777$		−	3.62912e7i		−	2.15650i
$778$	729695.	−	2.72216e6i	0.0432208	−	0.161237i
$779$		−	5.30457e6i		−	0.313189i
$780$		0			0
$781$		−	1.34872e7i		−	0.791213i
$782$	423675.	+	113569.i	0.0247751	+	0.00664117i
$783$			3.71365e7i			2.16469i
$784$	−5.87123e6	−	1.01788e7i	−0.341145	−	0.591433i
$785$		0			0
$786$	−5.00519e6	+	1.86721e7i	−0.288978	+	1.07804i
$787$	1.35279e7			0.778564			0.389282	−	0.921119i	$-0.372723\pi$
$787$	1.35279e7			0.778564			0.389282	+	0.921119i	$0.372723\pi$
$788$	−7.44901e6	−	4.30270e6i	−0.427349	−	0.246846i
$789$			4.75846e7i			2.72128i
$790$		0			0
$791$	−2.19553e7			−1.24767
$792$	4.01910e7	−	4.01666e7i	2.27675	−	2.27537i
$793$			2.03797e7i			1.15084i
$794$	−2.15985e7	−	5.78964e6i	−1.21583	−	0.325912i
$795$		0			0
$796$	−1.42071e7	−	8.20631e6i	−0.794736	−	0.459056i
$797$	3.10994e7			1.73423			0.867115	−	0.498109i	$-0.165972\pi$
$797$	3.10994e7			1.73423			0.867115	+	0.498109i	$0.165972\pi$
$798$	3.35746e7	+	8.99994e6i	1.86640	+	0.500302i
$799$	2.81192e6			0.155825
$800$		0			0
$801$	2.33333e6			0.128498
$802$	6.29710e6	+	1.68799e6i	0.345704	+	0.0926687i
$803$	4.43965e7			2.42974
$804$	−5.38414e7	−	3.10999e7i	−2.93749	−	1.69675i
$805$		0			0
$806$	−6.29623e6	−	1.68775e6i	−0.341384	−	0.0915106i
$807$			2.61478e7i			1.41336i
$808$	−1.27445e7	+	1.27368e7i	−0.686744	+	0.686327i
$809$	−1.19594e6			−0.0642449			−0.0321225	−	0.999484i	$-0.510227\pi$
$809$	−1.19594e6			−0.0642449			−0.0321225	+	0.999484i	$0.510227\pi$
$810$		0			0
$811$			5.59211e6i			0.298554i	0.988795	+	0.149277i	$0.0476947\pi$
$811$			5.59211e6i			0.298554i	−0.988795	+	0.149277i	$0.952305\pi$
$812$	1.61395e7	+	9.32249e6i	0.859012	+	0.496183i
$813$	−488400.			−0.0259149
$814$	5.56744e6	−	2.07696e7i	0.294507	−	1.09867i
$815$		0			0
$816$	−4.74361e6	+	2.73616e6i	−0.249392	+	0.143852i
$817$		−	1.89638e7i		−	0.993963i
$818$	1.39035e7	+	3.72694e6i	0.726510	+	0.194747i
$819$			5.04424e7i			2.62776i
$820$		0			0
$821$			2.42817e7i			1.25725i	0.777708	+	0.628625i	$0.216382\pi$
$821$			2.42817e7i			1.25725i	−0.777708	+	0.628625i	$0.783618\pi$
$822$	−3.18320e6	+	1.18750e7i	−0.164318	+	0.612993i
$823$		−	1.21094e7i		−	0.623193i	−0.950214	−	0.311597i	$-0.899136\pi$
$823$		−	1.21094e7i		−	0.623193i	0.950214	−	0.311597i	$-0.100864\pi$
$824$	6.00774e6	−	6.00410e6i	0.308243	−	0.308056i
$825$		0			0
$826$	−1.10065e7	−	2.95037e6i	−0.561303	−	0.150462i
$827$	−2.18004e7			−1.10841			−0.554205	−	0.832380i	$-0.686977\pi$
$827$	−2.18004e7			−1.10841			−0.554205	+	0.832380i	$0.686977\pi$
$828$	4.13554e6	−	7.15961e6i	0.209631	−	0.362922i
$829$		−	2.81218e7i		−	1.42121i	−0.703593	−	0.710603i	$-0.748422\pi$
$829$		−	2.81218e7i		−	1.42121i	0.703593	−	0.710603i	$-0.251578\pi$
$830$		0			0
$831$	−1.67629e7			−0.842067
$832$	−9785.55	+	1.61095e7i	−0.000490091	+	0.806813i
$833$			2.10106e6i			0.104912i
$834$	3.44096e6	−	1.28366e7i	0.171303	−	0.639052i
$835$		0			0
$836$	1.78342e7	+	1.03014e7i	0.882547	+	0.509777i
$837$	−2.51328e7			−1.24002
$838$	92010.2	−	343248.i	0.00452612	−	0.0168849i
$839$	−1.77035e6			−0.0868270			−0.0434135	−	0.999057i	$-0.513823\pi$
$839$	−1.77035e6			−0.0868270			−0.0434135	+	0.999057i	$0.513823\pi$
$840$		0			0
$841$	8.51602e6			0.415190
$842$	2.78197e6	−	1.03782e7i	0.135230	−	0.504479i
$843$	−5.72376e7			−2.77404
$844$	−1.05937e7	+	1.83402e7i	−0.511906	+	0.886233i
$845$		0			0
$846$	1.37237e7	−	5.11970e7i	0.659245	−	2.45934i
$847$		−	1.74315e7i		−	0.834883i
$848$	5.82956e6	+	1.01066e7i	0.278385	+	0.482629i
$849$	5.97171e7			2.84335
$850$		0			0
$851$		−	3.12891e6i		−	0.148105i
$852$	2.12165e7	+	1.22551e7i	1.00132	+	0.578385i
$853$	−2.98606e7			−1.40516			−0.702581	−	0.711604i	$-0.747969\pi$
$853$	−2.98606e7			−1.40516			−0.702581	+	0.711604i	$0.747969\pi$
$854$	3.80917e7	+	1.02108e7i	1.78725	+	0.479087i
$855$		0			0
$856$	4.91131e6	+	4.91429e6i	0.229094	+	0.229233i
$857$			1.59538e7i			0.742012i	0.928630	+	0.371006i	$0.120987\pi$
$857$			1.59538e7i			0.742012i	−0.928630	+	0.371006i	$0.879013\pi$
$858$	−1.08205e7	+	4.03664e7i	−0.501799	+	1.87198i
$859$		−	2.68382e7i		−	1.24099i	−0.784209	−	0.620497i	$-0.786931\pi$
$859$		−	2.68382e7i		−	1.24099i	0.784209	−	0.620497i	$-0.213069\pi$
$860$		0			0
$861$		−	2.08288e7i		−	0.957541i
$862$	−3.23280e7	−	8.66576e6i	−1.48187	−	0.397227i
$863$			1.99512e7i			0.911891i	0.890008	+	0.455946i	$0.150699\pi$
$863$			1.99512e7i			0.911891i	−0.890008	+	0.455946i	$0.849301\pi$
$864$	1.60453e7	+	6.00034e7i	0.731246	+	2.73458i
$865$		0			0
$866$	−2.40655e6	+	8.97773e6i	−0.109044	+	0.406792i
$867$	−4.04921e7			−1.82946
$868$	−6.30917e6	+	1.09227e7i	−0.284232	+	0.492074i
$869$			1.01867e7i			0.457596i
$870$		0			0
$871$	3.27051e7			1.46073
$872$	1.82951e6	−	1.82840e6i	0.0814787	−	0.0814292i
$873$		−	2.14505e7i		−	0.952582i
$874$	2.89470e6	+	775946.i	0.128181	+	0.0343600i
$875$		0			0
$876$	−4.03408e7	+	6.98397e7i	−1.77617	+	3.07498i
$877$	2.73500e7			1.20077			0.600384	−	0.799712i	$-0.295014\pi$
$877$	2.73500e7			1.20077			0.600384	+	0.799712i	$0.295014\pi$
$878$	−2.37669e7	−	6.37090e6i	−1.04049	−	0.278910i
$879$	6.57510e7			2.87032
$880$		0			0
$881$	−3.29524e7			−1.43037			−0.715184	−	0.698937i	$-0.753657\pi$
$881$	−3.29524e7			−1.43037			−0.715184	+	0.698937i	$0.753657\pi$
$882$	3.82541e7	+	1.02543e7i	1.65580	+	0.443849i
$883$	1.45135e7			0.626429			0.313214	−	0.949682i	$-0.398594\pi$
$883$	1.45135e7			0.626429			0.313214	+	0.949682i	$0.398594\pi$
$884$	1.44071e6	−	2.49422e6i	0.0620079	−	0.107351i
$885$		0			0
$886$	−1.24185e7	−	3.32886e6i	−0.531475	−	0.142466i
$887$		−	2.89058e7i		−	1.23360i	−0.787118	−	0.616802i	$-0.788428\pi$
$887$		−	2.89058e7i		−	1.23360i	0.787118	−	0.616802i	$-0.211572\pi$
$888$	2.76135e7	+	2.76303e7i	1.17514	+	1.17585i
$889$	−5.50926e7			−2.33797
$890$		0			0
$891$			8.48543e7i			3.58079i
$892$	−1.70426e7	+	2.95049e7i	−0.717173	+	1.24160i
$893$	1.92121e7			0.806205
$894$	−2.47769e6	+	9.24312e6i	−0.103682	+	0.386790i
$895$		0			0
$896$	3.01053e7	+	8.08957e6i	1.25278	+	0.336632i
$897$			6.08114e6i			0.252351i
$898$	4.02313e7	+	1.07843e7i	1.66484	+	0.446274i
$899$		−	8.11793e6i		−	0.335001i
$900$		0			0
$901$		−	2.08615e6i		−	0.0856117i
$902$	3.19536e6	−	1.19204e7i	0.130769	−	0.487838i
$903$		−	7.44630e7i		−	3.03893i
$904$	1.67157e7	−	1.67055e7i	0.680305	−	0.679892i
$905$		0			0
$906$	7.19459e7	+	1.92857e7i	2.91196	+	0.780574i
$907$	−1.75219e7			−0.707233			−0.353617	−	0.935390i	$-0.615048\pi$
$907$	−1.75219e7			−0.707233			−0.353617	+	0.935390i	$0.615048\pi$
$908$	−1.71724e7	−	9.91915e6i	−0.691222	−	0.399264i
$909$		−	6.07280e7i		−	2.43770i
$910$		0			0
$911$	−5.49598e6			−0.219406			−0.109703	−	0.993964i	$-0.534990\pi$
$911$	−5.49598e6			−0.219406			−0.109703	+	0.993964i	$0.534990\pi$
$912$	−3.24100e7	+	1.86944e7i	−1.29030	+	0.744261i
$913$			4.30643e6i			0.170978i
$914$	9.13922e6	−	3.40942e7i	0.361862	−	1.34994i
$915$		0			0
$916$	−6.96096e6	+	1.20511e7i	−0.274113	+	0.474556i
$917$	−1.96762e7			−0.772711
$918$	2.87546e6	−	1.07270e7i	0.112616	−	0.420119i
$919$	−1.89582e6			−0.0740472			−0.0370236	−	0.999314i	$-0.511788\pi$
$919$	−1.89582e6			−0.0740472			−0.0370236	+	0.999314i	$0.511788\pi$
$920$		0			0
$921$	1.67197e7			0.649502
$922$	1.21902e6	−	4.54760e6i	0.0472262	−	0.176179i
$923$	−1.28876e7			−0.497930
$924$	7.00275e7	+	4.04493e7i	2.69829	+	1.55859i
$925$		0			0
$926$	−5.29988e6	+	1.97714e7i	−0.203114	+	0.757723i
$927$			2.86271e7i			1.09415i
$928$	−1.93812e7	+	5.18266e6i	−0.738771	+	0.197552i
$929$	−3.44700e7			−1.31040			−0.655198	−	0.755457i	$-0.727415\pi$
$929$	−3.44700e7			−1.31040			−0.655198	+	0.755457i	$0.727415\pi$
$930$		0			0
$931$			1.43552e7i			0.542793i
$932$	−1.27054e7	+	2.19961e7i	−0.479125	+	0.829481i
$933$	8.35868e7			3.14365
$934$	−1.56275e6	−	418906.i	−0.0586167	−	0.0157127i
$935$		0			0
$936$	−3.83811e7	−	3.84044e7i	−1.43195	−	1.43282i
$937$		−	3.96544e7i		−	1.47551i	−0.675068	−	0.737756i	$-0.735886\pi$
$937$		−	3.96544e7i		−	1.47551i	0.675068	−	0.737756i	$-0.264114\pi$
$938$	1.63861e7	−	6.11292e7i	0.608093	−	2.26851i
$939$			1.00955e7i			0.373651i
$940$		0			0
$941$		−	1.88367e7i		−	0.693474i	−0.937962	−	0.346737i	$-0.887290\pi$
$941$		−	1.88367e7i		−	0.693474i	0.937962	−	0.346737i	$-0.112710\pi$
$942$	1.15013e7	+	3.08302e6i	0.422299	+	0.113201i
$943$		−	1.79580e6i		−	0.0657625i
$944$	1.06247e7	−	6.12842e6i	0.388048	−	0.223830i
$945$		0			0
$946$	1.14234e7	−	4.26154e7i	0.415019	−	1.54824i
$947$	4.04648e6			0.146623			0.0733115	−	0.997309i	$-0.476643\pi$
$947$	4.04648e6			0.146623			0.0733115	+	0.997309i	$0.476643\pi$
$948$	−1.60245e7	−	9.25607e6i	−0.579113	−	0.334508i
$949$		−	4.24230e7i		−	1.52910i
$950$		0			0
$951$	8.30590e7			2.97807
$952$	−3.94012e6	−	3.94251e6i	−0.140902	−	0.140988i
$953$			4.74092e7i			1.69095i	0.534016	+	0.845474i	$0.320682\pi$
$953$			4.74092e7i			1.69095i	−0.534016	+	0.845474i	$0.679318\pi$
$954$	−3.79827e7	−	1.01816e7i	−1.35118	−	0.362195i
$955$		0			0
$956$	4.56590e7	+	2.63735e7i	1.61578	+	0.933305i
$957$	−5.20456e7			−1.83698
$958$	−1.25123e7	−	3.35401e6i	−0.440476	−	0.118073i
$959$	−1.25136e7			−0.439376
$960$		0			0
$961$	−2.31352e7			−0.808099
$962$	−1.98463e7	−	5.31995e6i	−0.691420	−	0.185340i
$963$	−2.34168e7			−0.813695
$964$	1.64207e7	+	9.48491e6i	0.569112	+	0.328731i
$965$		0			0
$966$	1.13663e7	+	3.04682e6i	0.391900	+	0.105052i
$967$			1.05815e7i			0.363898i	0.983308	+	0.181949i	$0.0582406\pi$
$967$			1.05815e7i			0.363898i	−0.983308	+	0.181949i	$0.941759\pi$
$968$	1.32634e7	+	1.32715e7i	0.454953	+	0.455229i
$969$	6.68992e6			0.228882
$970$		0			0
$971$		−	3.45206e7i		−	1.17498i	−0.809232	−	0.587489i	$-0.800116\pi$
$971$		−	3.45206e7i		−	1.17498i	0.809232	−	0.587489i	$-0.199884\pi$
$972$	−6.12837e7	−	3.53987e7i	−2.08056	−	1.20177i
$973$	1.35269e7			0.458055
$974$	−9.60689e6	+	3.58389e7i	−0.324478	+	1.21048i
$975$		0			0
$976$	−3.67704e7	+	2.12095e7i	−1.23559	+	0.712700i
$977$			1.80039e7i			0.603433i	0.953398	+	0.301717i	$0.0975596\pi$
$977$			1.80039e7i			0.603433i	−0.953398	+	0.301717i	$0.902440\pi$
$978$	−7.51906e7	−	2.01554e7i	−2.51372	−	0.673821i
$979$			1.96765e6i			0.0656133i
$980$		0			0
$981$			8.71768e6i			0.289220i
$982$	−5.13468e6	+	1.91551e7i	−0.169916	+	0.633879i
$983$		−	2.71815e7i		−	0.897200i	−0.893733	−	0.448600i	$-0.851923\pi$
$983$		−	2.71815e7i		−	0.897200i	0.893733	−	0.448600i	$-0.148077\pi$
$984$	1.58484e7	+	1.58580e7i	0.521793	+	0.522110i
$985$		0			0
$986$	3.46484e6	+	928778.i	0.113499	+	0.0304242i
$987$	7.54378e7			2.46488
$988$	9.84346e6	−	1.70414e7i	0.320816	−	0.555409i
$989$		−	6.41996e6i		−	0.208709i
$990$		0			0
$991$	−2.26954e7			−0.734097			−0.367048	−	0.930202i	$-0.619632\pi$
$991$	−2.26954e7			−0.734097			−0.367048	+	0.930202i	$0.619632\pi$
$992$	−3.50746e6	−	1.31166e7i	−0.113165	−	0.423195i
$993$			6.44416e7i			2.07393i
$994$	−6.45705e6	+	2.40883e7i	−0.207285	+	0.773286i
$995$		0			0
$996$	−6.77439e6	−	3.91302e6i	−0.216382	−	0.124987i
$997$	2.28102e7			0.726762			0.363381	−	0.931641i	$-0.381622\pi$
$997$	2.28102e7			0.726762			0.363381	+	0.931641i	$0.381622\pi$
$998$	1.63732e6	−	6.10809e6i	0.0520364	−	0.194124i
$999$	−7.92208e7			−2.51146

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.f.b.149.3		20
4.3	odd	2		800.6.f.c.49.19		20
5.2	odd	4		40.6.d.a.21.13	✓	20
5.3	odd	4		200.6.d.b.101.8		20
5.4	even	2		200.6.f.c.149.18		20
8.3	odd	2		800.6.f.b.49.1		20
8.5	even	2		200.6.f.c.149.17		20
15.2	even	4		360.6.k.b.181.8		20
20.3	even	4		800.6.d.c.401.20		20
20.7	even	4		160.6.d.a.81.1		20
20.19	odd	2		800.6.f.b.49.2		20
40.3	even	4		800.6.d.c.401.1		20
40.13	odd	4		200.6.d.b.101.7		20
40.19	odd	2		800.6.f.c.49.20		20
40.27	even	4		160.6.d.a.81.20		20
40.29	even	2	inner	200.6.f.b.149.4		20
40.37	odd	4		40.6.d.a.21.14	yes	20
120.77	even	4		360.6.k.b.181.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.13	✓	20	5.2	odd	4
40.6.d.a.21.14	yes	20	40.37	odd	4
160.6.d.a.81.1		20	20.7	even	4
160.6.d.a.81.20		20	40.27	even	4
200.6.d.b.101.7		20	40.13	odd	4
200.6.d.b.101.8		20	5.3	odd	4
200.6.f.b.149.3		20	1.1	even	1	trivial
200.6.f.b.149.4		20	40.29	even	2	inner
200.6.f.c.149.17		20	8.5	even	2
200.6.f.c.149.18		20	5.4	even	2
360.6.k.b.181.7		20	120.77	even	4
360.6.k.b.181.8		20	15.2	even	4
800.6.d.c.401.1		20	40.3	even	4
800.6.d.c.401.20		20	20.3	even	4
800.6.f.b.49.1		20	8.3	odd	2
800.6.f.b.49.2		20	20.19	odd	2
800.6.f.c.49.19		20	4.3	odd	2
800.6.f.c.49.20		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)

\(f(q)\)	\(=\)	\(q+(-5.46395 - 1.46465i) q^{2} -29.2080 q^{3} +(27.7096 + 16.0056i) q^{4} +(159.591 + 42.7797i) q^{6} +168.173i q^{7} +(-127.961 - 128.039i) q^{8} +610.110 q^{9} +O(q^{10})\)	\(q+(-5.46395 - 1.46465i) q^{2} -29.2080 q^{3} +(27.7096 + 16.0056i) q^{4} +(159.591 + 42.7797i) q^{6} +168.173i q^{7} +(-127.961 - 128.039i) q^{8} +610.110 q^{9} +514.493i q^{11} +(-809.342 - 467.493i) q^{12} +491.622 q^{13} +(246.316 - 918.892i) q^{14} +(511.641 + 887.017i) q^{16} -183.094i q^{17} +(-3333.61 - 893.600i) q^{18} -1250.96i q^{19} -4912.01i q^{21} +(753.554 - 2811.16i) q^{22} -423.498i q^{23} +(3737.49 + 3739.76i) q^{24} +(-2686.20 - 720.056i) q^{26} -10722.5 q^{27} +(-2691.72 + 4660.01i) q^{28} -3463.40i q^{29} +2343.92 q^{31} +(-1496.41 - 5596.00i) q^{32} -15027.3i q^{33} +(-268.170 + 1000.42i) q^{34} +(16905.9 + 9765.18i) q^{36} +7388.25 q^{37} +(-1832.23 + 6835.20i) q^{38} -14359.3 q^{39} +4240.39 q^{41} +(-7194.41 + 26839.0i) q^{42} +15159.4 q^{43} +(-8234.77 + 14256.4i) q^{44} +(-620.279 + 2313.98i) q^{46} +15357.8i q^{47} +(-14944.0 - 25908.0i) q^{48} -11475.3 q^{49} +5347.82i q^{51} +(13622.6 + 7868.71i) q^{52} +11393.9 q^{53} +(58587.5 + 15704.8i) q^{54} +(21532.7 - 21519.7i) q^{56} +36538.2i q^{57} +(-5072.68 + 18923.8i) q^{58} -11978.0i q^{59} +41454.0i q^{61} +(-12807.1 - 3433.03i) q^{62} +102604. i q^{63} +(-19.9046 + 32768.0i) q^{64} +(-22009.8 + 82108.6i) q^{66} +66524.9 q^{67} +(2930.53 - 5073.46i) q^{68} +12369.6i q^{69} -26214.5 q^{71} +(-78070.3 - 78117.7i) q^{72} -86291.9i q^{73} +(-40369.0 - 10821.2i) q^{74} +(20022.4 - 34663.7i) q^{76} -86524.0 q^{77} +(78458.6 + 21031.4i) q^{78} +19799.4 q^{79} +164928. q^{81} +(-23169.3 - 6210.70i) q^{82} +8370.24 q^{83} +(78619.8 - 136110. i) q^{84} +(-82830.0 - 22203.2i) q^{86} +101159. i q^{87} +(65875.1 - 65835.1i) q^{88} +3824.45 q^{89} +82677.7i q^{91} +(6778.35 - 11735.0i) q^{92} -68461.3 q^{93} +(22493.9 - 83914.4i) q^{94} +(43707.1 + 163448. i) q^{96} -35158.5i q^{97} +(62700.4 + 16807.3i) q^{98} +313897. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 36 q^{3} + 32 q^{4} + 204 q^{6} - 248 q^{8} + 1620 q^{9}+O(q^{10}) \) 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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