LMFDB - Embedded newform 200.6.d.b.101.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,6,Mod(101,200)]

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, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("200.101");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.d (of order $2$, degree $1$, 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^{12} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.8
Root			$3.46430 + 1.99965i$ of defining polynomial
Character	$\chi$	$=$	200.101
Dual form			200.6.d.b.101.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.46465 + 5.46395i) q^{2} -29.2080i q^{3} +(-27.7096 - 16.0056i) q^{4} +(159.591 + 42.7797i) q^{6} +168.173 q^{7} +(128.039 - 127.961i) q^{8} -610.110 q^{9} +514.493i q^{11} +(-467.493 + 809.342i) q^{12} +491.622i q^{13} +(-246.316 + 918.892i) q^{14} +(511.641 + 887.017i) q^{16} -183.094 q^{17} +(893.600 - 3333.61i) q^{18} +1250.96i q^{19} -4912.01i q^{21} +(-2811.16 - 753.554i) q^{22} +423.498 q^{23} +(-3737.49 - 3739.76i) q^{24} +(-2686.20 - 720.056i) q^{26} +10722.5i q^{27} +(-4660.01 - 2691.72i) q^{28} +3463.40i q^{29} +2343.92 q^{31} +(-5596.00 + 1496.41i) q^{32} +15027.3 q^{33} +(268.170 - 1000.42i) q^{34} +(16905.9 + 9765.18i) q^{36} -7388.25i q^{37} +(-6835.20 - 1832.23i) q^{38} +14359.3 q^{39} +4240.39 q^{41} +(26839.0 + 7194.41i) q^{42} +15159.4i q^{43} +(8234.77 - 14256.4i) q^{44} +(-620.279 + 2313.98i) q^{46} +15357.8 q^{47} +(25908.0 - 14944.0i) q^{48} +11475.3 q^{49} +5347.82i q^{51} +(7868.71 - 13622.6i) q^{52} +11393.9i q^{53} +(-58587.5 - 15704.8i) q^{54} +(21532.7 - 21519.7i) q^{56} +36538.2 q^{57} +(-18923.8 - 5072.68i) q^{58} +11978.0i q^{59} +41454.0i q^{61} +(-3433.03 + 12807.1i) q^{62} -102604. q^{63} +(19.9046 - 32768.0i) q^{64} +(-22009.8 + 82108.6i) q^{66} -66524.9i q^{67} +(5073.46 + 2930.53i) q^{68} -12369.6i q^{69} -26214.5 q^{71} +(-78117.7 + 78070.3i) q^{72} +86291.9 q^{73} +(40369.0 + 10821.2i) q^{74} +(20022.4 - 34663.7i) q^{76} +86524.0i q^{77} +(-21031.4 + 78458.6i) q^{78} -19799.4 q^{79} +164928. q^{81} +(-6210.70 + 23169.3i) q^{82} +8370.24i q^{83} +(-78619.8 + 136110. i) q^{84} +(-82830.0 - 22203.2i) q^{86} +101159. q^{87} +(65835.1 + 65875.1i) q^{88} -3824.45 q^{89} +82677.7i q^{91} +(-11735.0 - 6778.35i) q^{92} -68461.3i q^{93} +(-22493.9 + 83914.4i) q^{94} +(43707.1 + 163448. i) q^{96} -35158.5 q^{97} +(-16807.3 + 62700.4i) q^{98} -313897. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 32 q^{4} + 204 q^{6} + 196 q^{7} - 248 q^{8} - 1620 q^{9} + 1876 q^{12} + 2708 q^{14} + 3080 q^{16} + 5294 q^{18} - 13836 q^{22} + 4676 q^{23} + 1032 q^{24} - 8084 q^{26} - 2108 q^{28}+ \cdots - 216942 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 32 * q^4 + 204 * q^6 + 196 * q^7 - 248 * q^8 - 1620 * q^9 + 1876 * q^12 + 2708 * q^14 + 3080 * q^16 + 5294 * q^18 - 13836 * q^22 + 4676 * q^23 + 1032 * q^24 - 8084 * q^26 - 2108 * q^28 + 7160 * q^31 - 6792 * q^32 - 5672 * q^33 + 21132 * q^34 + 18344 * q^36 + 19580 * q^38 - 44904 * q^39 + 11608 * q^41 + 17116 * q^42 + 72296 * q^44 - 28516 * q^46 - 44180 * q^47 + 88856 * q^48 + 18756 * q^49 + 39680 * q^52 - 100584 * q^54 - 53624 * q^56 - 5032 * q^57 - 59496 * q^58 - 59824 * q^62 - 240620 * q^63 - 11264 * q^64 - 56688 * q^66 - 11576 * q^68 - 200312 * q^71 - 235912 * q^72 + 105136 * q^73 + 78876 * q^74 - 153872 * q^76 - 95864 * q^78 + 282080 * q^79 + 65172 * q^81 + 223032 * q^82 - 297128 * q^84 + 27452 * q^86 + 332592 * q^87 - 86896 * q^88 - 3160 * q^89 - 107916 * q^92 + 148820 * q^94 + 395168 * q^96 - 147376 * q^97 - 216942 * q^98

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.46465	+	5.46395i	−0.258917	+	0.965900i
$2$	−1.46465	+	5.46395i	−0.258917	+	0.965900i
$3$		−	29.2080i		−	1.87370i	−0.349736	−	0.936848i	$-0.613729\pi$
$3$		−	29.2080i		−	1.87370i	0.349736	−	0.936848i	$-0.386271\pi$
$4$	−27.7096	−	16.0056i	−0.865924	−	0.500175i
$5$		0			0
$5$		0			0
$6$	159.591	+	42.7797i	1.80980	+	0.485132i
$7$	168.173			1.29722			0.648608	−	0.761123i	$-0.275352\pi$
$7$	168.173			1.29722			0.648608	+	0.761123i	$0.275352\pi$
$8$	128.039	−	127.961i	0.707322	−	0.706892i
$9$	−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	$0.778514\pi$
$12$	−467.493	+	809.342i	−0.937177	+	1.62248i
$13$			491.622i			0.806813i	0.915021	+	0.403406i	$0.132174\pi$
$13$			491.622i			0.806813i	−0.915021	+	0.403406i	$0.867826\pi$
$14$	−246.316	+	918.892i	−0.335871	+	1.25298i
$15$		0			0
$16$	511.641	+	887.017i	0.499649	+	0.866228i
$17$	−183.094			−0.153657			−0.0768284	−	0.997044i	$-0.524479\pi$
$17$	−183.094			−0.153657			−0.0768284	+	0.997044i	$0.524479\pi$
$18$	893.600	−	3333.61i	0.650073	−	2.42512i
$19$			1250.96i			0.794988i	0.917605	+	0.397494i	$0.130120\pi$
$19$			1250.96i			0.794988i	−0.917605	+	0.397494i	$0.869880\pi$
$20$		0			0
$21$		−	4912.01i		−	2.43059i
$22$	−2811.16	−	753.554i	−1.23831	−	0.331939i
$23$	423.498			0.166929			0.0834646	−	0.996511i	$-0.473401\pi$
$23$	423.498			0.166929			0.0834646	+	0.996511i	$0.473401\pi$
$24$	−3737.49	−	3739.76i	−1.32450	−	1.32531i
$25$		0			0
$26$	−2686.20	−	720.056i	−0.779300	−	0.208897i
$27$			10722.5i			2.83067i
$28$	−4660.01	−	2691.72i	−1.12329	−	0.648835i
$29$			3463.40i			0.764729i	0.924012	+	0.382364i	$0.124890\pi$
$29$			3463.40i			0.764729i	−0.924012	+	0.382364i	$0.875110\pi$
$30$		0			0
$31$	2343.92			0.438065			0.219032	−	0.975718i	$-0.429710\pi$
$31$	2343.92			0.438065			0.219032	+	0.975718i	$0.429710\pi$
$32$	−5596.00	+	1496.41i	−0.966057	+	0.258330i
$33$	15027.3			2.40213
$34$	268.170	−	1000.42i	0.0397843	−	0.148417i
$35$		0			0
$36$	16905.9	+	9765.18i	2.17411	+	1.25581i
$37$		−	7388.25i		−	0.887232i	−0.896217	−	0.443616i	$-0.853695\pi$
$37$		−	7388.25i		−	0.887232i	0.896217	−	0.443616i	$-0.146305\pi$
$38$	−6835.20	−	1832.23i	−0.767879	−	0.205836i
$39$	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	$0.436888\pi$
$42$	26839.0	+	7194.41i	2.34770	+	0.629320i
$43$			15159.4i			1.25029i	0.780510	+	0.625143i	$0.214960\pi$
$43$			15159.4i			1.25029i	−0.780510	+	0.625143i	$0.785040\pi$
$44$	8234.77	−	14256.4i	0.641239	−	1.11014i
$45$		0			0
$46$	−620.279	+	2313.98i	−0.0432208	+	0.161237i
$47$	15357.8			1.01411			0.507055	−	0.861914i	$-0.330734\pi$
$47$	15357.8			1.01411			0.507055	+	0.861914i	$0.330734\pi$
$48$	25908.0	−	14944.0i	1.62305	−	0.936191i
$49$	11475.3			0.682768
$50$		0			0
$51$			5347.82i			0.287906i
$52$	7868.71	−	13622.6i	0.403548	−	0.698639i
$53$			11393.9i			0.557162i	0.960413	+	0.278581i	$0.0898640\pi$
$53$			11393.9i			0.557162i	−0.960413	+	0.278581i	$0.910136\pi$
$54$	−58587.5	−	15704.8i	−2.73414	−	0.732907i
$55$		0			0
$56$	21532.7	−	21519.7i	0.917548	−	0.916991i
$57$	36538.2			1.48957
$58$	−18923.8	−	5072.68i	−0.738651	−	0.198001i
$59$			11978.0i			0.447974i	0.974592	+	0.223987i	$0.0719074\pi$
$59$			11978.0i			0.447974i	−0.974592	+	0.223987i	$0.928093\pi$
$60$		0			0
$61$			41454.0i			1.42640i	0.700960	+	0.713200i	$0.252755\pi$
$61$			41454.0i			1.42640i	−0.700960	+	0.713200i	$0.747245\pi$
$62$	−3433.03	+	12807.1i	−0.113422	+	0.423127i
$63$	−102604.			−3.25697
$64$	19.9046	−	32768.0i	0.000607441	−	1.00000i
$65$		0			0
$66$	−22009.8	+	82108.6i	−0.621952	+	2.32022i
$67$		−	66524.9i		−	1.81049i	−0.424885	−	0.905247i	$-0.639685\pi$
$67$		−	66524.9i		−	1.81049i	0.424885	−	0.905247i	$-0.360315\pi$
$68$	5073.46	+	2930.53i	0.133055	+	0.0768553i
$69$		−	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	$0.599853\pi$
$72$	−78117.7	+	78070.3i	−1.77590	+	1.77482i
$73$	86291.9			1.89523			0.947617	−	0.319409i	$-0.103484\pi$
$73$	86291.9			1.89523			0.947617	+	0.319409i	$0.103484\pi$
$74$	40369.0	+	10821.2i	0.856977	+	0.229719i
$75$		0			0
$76$	20022.4	−	34663.7i	0.397633	−	0.688399i
$77$			86524.0i			1.66307i
$78$	−21031.4	+	78458.6i	−0.391410	+	1.46017i
$79$	−19799.4			−0.356931			−0.178466	−	0.983946i	$-0.557113\pi$
$79$	−19799.4			−0.356931			−0.178466	+	0.983946i	$0.557113\pi$
$80$		0			0
$81$	164928.			2.79307
$82$	−6210.70	+	23169.3i	−0.102001	+	0.380520i
$83$			8370.24i			0.133365i	0.997774	+	0.0666826i	$0.0212415\pi$
$83$			8370.24i			0.133365i	−0.997774	+	0.0666826i	$0.978759\pi$
$84$	−78619.8	+	136110.i	−1.21572	+	2.10471i
$85$		0			0
$86$	−82830.0	−	22203.2i	−1.20765	−	0.323720i
$87$	101159.			1.43287
$88$	65835.1	+	65875.1i	0.906255	+	0.906806i
$89$	−3824.45			−0.0511793			−0.0255896	−	0.999673i	$-0.508146\pi$
$89$	−3824.45			−0.0511793			−0.0255896	+	0.999673i	$0.508146\pi$
$90$		0			0
$91$			82677.7i			1.04661i
$92$	−11735.0	−	6778.35i	−0.144548	−	0.0834939i
$93$		−	68461.3i		−	0.820801i
$94$	−22493.9	+	83914.4i	−0.262570	+	0.979528i
$95$		0			0
$96$	43707.1	+	163448.i	0.484032	+	1.81010i
$97$	−35158.5			−0.379403			−0.189702	−	0.981842i	$-0.560752\pi$
$97$	−35158.5			−0.379403			−0.189702	+	0.981842i	$0.560752\pi$
$98$	−16807.3	+	62700.4i	−0.176780	+	0.659486i
$99$		−	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	$-0.161346\pi$
$102$	−29220.2	−	7832.71i	−0.278089	−	0.0745438i
$103$	−46921.2			−0.435789			−0.217895	−	0.975972i	$-0.569919\pi$
$103$	−46921.2			−0.435789			−0.217895	+	0.975972i	$0.569919\pi$
$104$	62908.5	+	62946.7i	0.570329	+	0.570676i
$105$		0			0
$106$	−62255.5	−	16688.1i	−0.538162	−	0.144259i
$107$			38381.3i			0.324086i	0.986784	+	0.162043i	$0.0518083\pi$
$107$			38381.3i			0.324086i	−0.986784	+	0.162043i	$0.948192\pi$
$108$	171621.	−	297117.i	1.41583	−	2.45114i
$109$		−	14288.7i		−	0.115193i	−0.998340	−	0.0575966i	$-0.981656\pi$
$109$		−	14288.7i		−	0.115193i	0.998340	−	0.0575966i	$-0.0183437\pi$
$110$		0			0
$111$	−215796.			−1.66240
$112$	86044.4	+	149173.i	0.648153	+	1.12368i
$113$	−130552.			−0.961804			−0.480902	−	0.876774i	$-0.659691\pi$
$113$	−130552.			−0.961804			−0.480902	+	0.876774i	$0.659691\pi$
$114$	−53515.8	+	199643.i	−0.385674	+	1.43877i
$115$		0			0
$116$	55433.8	−	95969.3i	0.382498	−	0.662197i
$117$		−	299943.i		−	2.02570i
$118$	−65447.1	−	17543.6i	−0.432698	−	0.115988i
$119$	−30791.5			−0.199326
$120$		0			0
$121$	−103652.			−0.643596
$122$	−226503.	−	60715.7i	−1.37776	−	0.369319i
$123$		−	123853.i		−	0.738151i
$124$	−64949.0	−	37515.9i	−0.379331	−	0.219109i
$125$		0			0
$126$	150280.	−	560624.i	0.843284	−	3.14591i
$127$	327594.			1.80230			0.901150	−	0.433508i	$-0.142724\pi$
$127$	327594.			1.80230			0.901150	+	0.433508i	$0.142724\pi$
$128$	179014.	+	48102.6i	0.965742	+	0.259504i
$129$	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	$0.903736\pi$
$132$	−416401.	−	240522.i	−2.08006	−	1.20149i
$133$			210379.i			1.03127i
$134$	363489.	+	97436.0i	1.74876	+	0.468768i
$135$		0			0
$136$	−23443.1	+	23428.9i	−0.108685	+	0.108619i
$137$	74409.1			0.338707			0.169354	−	0.985555i	$-0.445832\pi$
$137$	74409.1			0.338707			0.169354	+	0.985555i	$0.445832\pi$
$138$	67586.7	+	18117.1i	0.302109	+	0.0809826i
$139$			80434.5i			0.353106i	0.984291	+	0.176553i	$0.0564947\pi$
$139$			80434.5i			0.353106i	−0.984291	+	0.176553i	$0.943505\pi$
$140$		0			0
$141$		−	448572.i		−	1.90013i
$142$	38395.2	−	143235.i	0.159792	−	0.596112i
$143$	−252936.			−1.03436
$144$	−312157.	−	541178.i	−1.25449	−	2.17487i
$145$		0			0
$146$	−126388.	+	471495.i	−0.490708	+	1.83061i
$147$		−	335171.i		−	1.27930i
$148$	−118253.	+	204725.i	−0.443771	+	0.768275i
$149$		−	57917.4i		−	0.213719i	−0.994274	−	0.106860i	$-0.965920\pi$
$149$		−	57917.4i		−	0.213719i	0.994274	−	0.106860i	$-0.0340795\pi$
$150$		0			0
$151$	450813.			1.60899			0.804497	−	0.593957i	$-0.202435\pi$
$151$	450813.			1.60899			0.804497	+	0.593957i	$0.202435\pi$
$152$	160075.	+	160172.i	0.561971	+	0.562312i
$153$	111707.			0.385792
$154$	−472763.	−	126728.i	−1.60636	−	0.430596i
$155$		0			0
$156$	−397890.	−	229829.i	−1.30904	−	0.756126i
$157$		−	72067.3i		−	0.233340i	−0.993171	−	0.116670i	$-0.962778\pi$
$157$		−	72067.3i		−	0.233340i	0.993171	−	0.116670i	$-0.0372220\pi$
$158$	28999.3	−	108183.i	0.0924155	−	0.344760i
$159$	332792.			1.04395
$160$		0			0
$161$	71221.2			0.216543
$162$	−241563.	+	901159.i	−0.723173	+	2.69783i
$163$		−	471144.i		−	1.38895i	−0.719519	−	0.694473i	$-0.755638\pi$
$163$		−	471144.i		−	1.38895i	0.719519	−	0.694473i	$-0.244362\pi$
$164$	−117499.	−	67870.0i	−0.341134	−	0.197046i
$165$		0			0
$166$	−45734.6	−	12259.5i	−0.128817	−	0.0345305i
$167$	−519164.			−1.44050			−0.720250	−	0.693715i	$-0.755973\pi$
$167$	−519164.			−1.44050			−0.720250	+	0.693715i	$0.755973\pi$
$168$	−628547.	−	628929.i	−1.71816	−	1.71921i
$169$	129601.			0.349053
$170$		0			0
$171$		−	763225.i		−	1.99601i
$172$	242635.	−	420059.i	0.625363	−	1.08265i
$173$			726898.i			1.84654i	0.384153	+	0.923269i	$0.374494\pi$
$173$			726898.i			1.84654i	−0.384153	+	0.923269i	$0.625506\pi$
$174$	−148163.	+	552728.i	−0.370994	+	1.38401i
$175$		0			0
$176$	−456364.	+	263236.i	−1.11053	+	0.640564i
$177$	349853.			0.839368
$178$	5601.50	−	20896.6i	0.0132512	−	0.0494340i
$179$			327278.i			0.763457i	0.924274	+	0.381729i	$0.124671\pi$
$179$			327278.i			0.763457i	−0.924274	+	0.381729i	$0.875329\pi$
$180$		0			0
$181$			651584.i			1.47834i	0.673519	+	0.739170i	$0.264782\pi$
$181$			651584.i			1.47834i	−0.673519	+	0.739170i	$0.735218\pi$
$182$	−451747.	−	121094.i	−1.01092	−	0.270985i
$183$	1.21079e6			2.67264
$184$	54224.3	−	54191.3i	0.118073	−	0.118001i
$185$		0			0
$186$	374069.	+	100272.i	0.792811	+	0.212519i
$187$		−	94200.5i		−	0.196992i
$188$	−425558.	−	245811.i	−0.878142	−	0.507232i
$189$			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	$0.639529\pi$
$192$	−957089.	−	581.375i	−1.87370	−	0.00113816i
$193$	−560696.			−1.08351			−0.541757	−	0.840535i	$-0.682241\pi$
$193$	−560696.			−1.08351			−0.541757	+	0.840535i	$0.682241\pi$
$194$	51495.1	−	192104.i	0.0982339	−	0.366465i
$195$		0			0
$196$	−317975.	−	183669.i	−0.591226	−	0.341504i
$197$			268824.i			0.493518i	0.969077	+	0.246759i	$0.0793656\pi$
$197$			268824.i			0.493518i	−0.969077	+	0.246759i	$0.920634\pi$
$198$	1.71512e6	+	459751.i	3.10907	+	0.833411i
$199$	512715.			0.917789			0.458895	−	0.888491i	$-0.348246\pi$
$199$	512715.			0.917789			0.458895	+	0.888491i	$0.348246\pi$
$200$		0			0
$201$	−1.94306e6			−3.39232
$202$	543862.	+	145786.i	0.937799	+	0.251384i
$203$			582451.i			0.992018i
$204$	85595.1	−	148186.i	0.144004	−	0.249305i
$205$		0			0
$206$	68723.4	−	256376.i	0.112833	−	0.420929i
$207$	−258380.			−0.419116
$208$	−436077.	+	251534.i	−0.698884	+	0.403123i
$209$	−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	$0.829006\pi$
$212$	182366.	−	315719.i	0.278679	−	0.482460i
$213$			765674.i			1.15637i
$214$	−209713.	−	56215.3i	−0.313034	−	0.0839112i
$215$		0			0
$216$	1.37207e6	+	1.37290e6i	2.00098	+	2.00219i
$217$	394185.			0.568265
$218$	78072.9	+	20928.0i	0.111265	+	0.0298255i
$219$		−	2.52042e6i		−	3.55109i
$220$		0			0
$221$		−	90013.0i		−	0.123972i
$222$	316067.	−	1.17910e6i	0.430424	−	1.60571i
$223$	−1.06479e6			−1.43384			−0.716922	−	0.697153i	$-0.754450\pi$
$223$	−1.06479e6			−1.43384			−0.716922	+	0.697153i	$0.754450\pi$
$224$	−941098.	+	251656.i	−1.25318	+	0.335110i
$225$		0			0
$226$	191213.	−	713329.i	0.249027	−	0.929006i
$227$			619730.i			0.798248i	0.916897	+	0.399124i	$0.130686\pi$
$227$			619730.i			0.798248i	−0.916897	+	0.399124i	$0.869314\pi$
$228$	−1.01246e6	−	584816.i	−1.28985	−	0.745044i
$229$		−	434907.i		−	0.548035i	−0.961725	−	0.274017i	$-0.911647\pi$
$229$		−	434907.i		−	0.548035i	0.961725	−	0.274017i	$-0.0883525\pi$
$230$		0			0
$231$	2.52720e6			3.11608
$232$	443180.	+	443450.i	0.540581	+	0.540909i
$233$	−793810.			−0.957915			−0.478957	−	0.877838i	$-0.658985\pi$
$233$	−793810.			−0.957915			−0.478957	+	0.877838i	$0.658985\pi$
$234$	1.63888e6	+	439313.i	1.95662	+	0.524487i
$235$		0			0
$236$	191715.	−	331904.i	0.224066	−	0.387912i
$237$			578302.i			0.668781i
$238$	45099.0	−	168244.i	0.0516089	−	0.192529i
$239$	−1.64777e6			−1.86596			−0.932978	−	0.359933i	$-0.882800\pi$
$239$	−1.64777e6			−1.86596			−0.932978	+	0.359933i	$0.882800\pi$
$240$		0			0
$241$	592599.			0.657231			0.328616	−	0.944464i	$-0.393418\pi$
$241$	592599.			0.657231			0.328616	+	0.944464i	$0.393418\pi$
$242$	151814.	−	566349.i	0.166638	−	0.621649i
$243$		−	2.21164e6i		−	2.40270i
$244$	663496.	−	1.14867e6i	0.713450	−	1.23515i
$245$		0			0
$246$	676729.	+	181402.i	0.712979	+	0.191120i
$247$	−615001.			−0.641406
$248$	300113.	−	299930.i	0.309853	−	0.309665i
$249$	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	$0.691484\pi$
$252$	2.84312e6	+	1.64224e6i	2.82029	+	1.62906i
$253$			217887.i			0.214008i
$254$	−479813.	+	1.78996e6i	−0.466646	+	1.74084i
$255$		0			0
$256$	−525023.	+	907669.i	−0.500701	+	0.865620i
$257$	1.18756e6			1.12156			0.560779	−	0.827966i	$-0.310502\pi$
$257$	1.18756e6			1.12156			0.560779	+	0.827966i	$0.310502\pi$
$258$	−648513.	+	2.41930e6i	−0.606554	+	2.26277i
$259$		−	1.24251e6i		−	1.15093i
$260$		0			0
$261$		−	2.11305e6i		−	1.92003i
$262$	−639279.	−	171364.i	−0.575356	−	0.154229i
$263$	1.62916e6			1.45236			0.726180	−	0.687505i	$-0.241294\pi$
$263$	1.62916e6			1.45236			0.726180	+	0.687505i	$0.241294\pi$
$264$	1.92408e6	−	1.92291e6i	1.69908	−	1.69805i
$265$		0			0
$266$	−1.14950e6	−	308132.i	−0.996104	−	0.267013i
$267$			111705.i			0.0958944i
$268$	−1.06477e6	+	1.84338e6i	−0.905565	+	1.56775i
$269$			895226.i			0.754314i	0.926149	+	0.377157i	$0.123098\pi$
$269$			895226.i			0.754314i	−0.926149	+	0.377157i	$0.876902\pi$
$270$		0			0
$271$	16721.4			0.0138309			0.00691545	−	0.999976i	$-0.497799\pi$
$271$	16721.4			0.0138309			0.00691545	+	0.999976i	$0.497799\pi$
$272$	−93678.4	−	162408.i	−0.0767745	−	0.133102i
$273$	2.41485e6			1.96103
$274$	−108984.	+	406568.i	−0.0876970	+	0.327157i
$275$		0			0
$276$	−197982.	+	342755.i	−0.156442	+	0.270839i
$277$		−	573914.i		−	0.449415i	−0.974426	−	0.224708i	$-0.927857\pi$
$277$		−	573914.i		−	0.449415i	0.974426	−	0.224708i	$-0.0721427\pi$
$278$	−439490.	−	117809.i	−0.341065	−	0.0914251i
$279$	−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	$0.234703\pi$
$282$	2.45097e6	+	657003.i	1.83534	+	0.491976i
$283$		−	2.04454e6i		−	1.51751i	−0.651378	−	0.758753i	$-0.725809\pi$
$283$		−	2.04454e6i		−	1.51751i	0.651378	−	0.758753i	$-0.274191\pi$
$284$	726393.	+	419579.i	0.534411	+	0.308687i
$285$		0			0
$286$	370464.	−	1.38203e6i	0.267812	−	0.999085i
$287$	713120.			0.511044
$288$	3.41417e6	−	912972.i	2.42552	−	0.648599i
$289$	−1.38633e6			−0.976390
$290$		0			0
$291$			1.02691e6i			0.710886i
$292$	−2.39111e6	−	1.38115e6i	−1.64113	−	0.947949i
$293$		−	2.25113e6i		−	1.53190i	−0.642899	−	0.765951i	$-0.722269\pi$
$293$		−	2.25113e6i		−	1.53190i	0.642899	−	0.765951i	$-0.277731\pi$
$294$	1.83136e6	+	490909.i	1.23568	+	0.331232i
$295$		0			0
$296$	−945408.	−	945983.i	−0.627177	−	0.627558i
$297$	−5.51667e6			−3.62899
$298$	316458.	+	84829.1i	0.206431	+	0.0553355i
$299$			208201.i			0.134681i
$300$		0			0
$301$			2.54940e6i			1.62189i
$302$	−660286.	+	2.46322e6i	−0.416596	+	1.55413i
$303$	−2.90726e6			−1.81919
$304$	−1.10963e6	+	640044.i	−0.688641	+	0.397215i
$305$		0			0
$306$	−163613.	+	610364.i	−0.0998881	+	0.372636i
$307$			572436.i			0.346642i	0.984865	+	0.173321i	$0.0554498\pi$
$307$			572436.i			0.346642i	−0.984865	+	0.173321i	$0.944550\pi$
$308$	1.38487e6	−	2.39754e6i	0.831825	−	1.44009i
$309$			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	$0.816794\pi$
$312$	1.83855e6	−	1.83743e6i	1.06927	−	1.06862i
$313$	345643.			0.199419			0.0997095	−	0.995017i	$-0.468209\pi$
$313$	345643.			0.199419			0.0997095	+	0.995017i	$0.468209\pi$
$314$	393772.	+	105554.i	0.225383	+	0.0604156i
$315$		0			0
$316$	548633.	+	316902.i	0.309075	+	0.178528i
$317$			2.84370e6i			1.58941i	0.606995	+	0.794706i	$0.292375\pi$
$317$			2.84370e6i			1.58941i	−0.606995	+	0.794706i	$0.707625\pi$
$318$	−487426.	+	1.81836e6i	−0.270297	+	1.00835i
$319$	−1.78189e6			−0.980404
$320$		0			0
$321$	1.12104e6			0.607238
$322$	−104314.	+	389149.i	−0.0560667	+	0.209159i
$323$		−	229044.i		−	0.122155i
$324$	−4.57008e6	−	2.63977e6i	−2.41859	−	1.39702i
$325$		0			0
$326$	2.57431e6	+	690064.i	1.34158	+	0.359621i
$327$	−417345.			−0.215837
$328$	542934.	−	542605.i	0.278652	−	0.278483i
$329$	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	$-0.186682\pi$
$332$	133971.	−	231936.i	0.0667060	−	0.115484i
$333$			4.50764e6i			2.22761i
$334$	760396.	−	2.83669e6i	0.372970	−	1.39138i
$335$		0			0
$336$	4.35704e6	−	2.51319e6i	2.10544	−	1.21444i
$337$	210820.			0.101120			0.0505599	−	0.998721i	$-0.483899\pi$
$337$	210820.			0.101120			0.0505599	+	0.998721i	$0.483899\pi$
$338$	−189821.	+	708134.i	−0.0903758	+	0.337150i
$339$			3.81316e6i			1.80213i
$340$		0			0
$341$			1.20593e6i			0.561611i
$342$	4.17022e6	+	1.11786e6i	1.92794	+	0.516800i
$343$	−896652.			−0.411518
$344$	1.93981e6	+	1.94099e6i	0.883818	+	0.884355i
$345$		0			0
$346$	−3.97174e6	−	1.06466e6i	−1.78357	−	0.478100i
$347$			2.39916e6i			1.06963i	0.844968	+	0.534817i	$0.179619\pi$
$347$			2.39916e6i			1.06963i	−0.844968	+	0.534817i	$0.820381\pi$
$348$	−2.80307e6	−	1.61911e6i	−1.24076	−	0.716686i
$349$			1.76207e6i			0.774392i	0.921997	+	0.387196i	$0.126556\pi$
$349$			1.76207e6i			0.774392i	−0.921997	+	0.387196i	$0.873444\pi$
$350$		0			0
$351$	−5.27144e6			−2.28382
$352$	−769891.	−	2.87910e6i	−0.331186	−	1.23851i
$353$	2.11387e6			0.902904			0.451452	−	0.892296i	$-0.350906\pi$
$353$	2.11387e6			0.902904			0.451452	+	0.892296i	$0.350906\pi$
$354$	−512414.	+	1.91158e6i	−0.217327	+	0.810745i
$355$		0			0
$356$	105974.	+	61212.7i	0.0443174	+	0.0255986i
$357$			899360.i			0.373476i
$358$	−1.78823e6	−	479350.i	−0.737423	−	0.197672i
$359$	−25391.5			−0.0103981			−0.00519903	−	0.999986i	$-0.501655\pi$
$359$	−25391.5			−0.0103981			−0.00519903	+	0.999986i	$0.501655\pi$
$360$		0			0
$361$	911190.			0.367994
$362$	−3.56023e6	−	954346.i	−1.42793	−	0.382767i
$363$			3.02747e6i			1.20590i
$364$	1.32331e6	−	2.29096e6i	0.523489	−	0.906285i
$365$		0			0
$366$	−1.77339e6	+	6.61569e6i	−0.691992	+	2.58150i
$367$	−1.55872e6			−0.604091			−0.302046	−	0.953293i	$-0.597670\pi$
$367$	−1.55872e6			−0.604091			−0.302046	+	0.953293i	$0.597670\pi$
$368$	216679.	+	375650.i	0.0834060	+	0.144599i
$369$	−2.58710e6			−0.989116
$370$		0			0
$371$			1.91614e6i			0.722759i
$372$	−1.09576e6	+	1.89703e6i	−0.410544	+	0.710751i
$373$			741743.i			0.276046i	0.990429	+	0.138023i	$0.0440748\pi$
$373$			741743.i			0.276046i	−0.990429	+	0.138023i	$0.955925\pi$
$374$	514707.	+	137971.i	0.190275	+	0.0510046i
$375$		0			0
$376$	1.96640e6	−	1.96520e6i	0.717301	−	0.716866i
$377$	−1.70268e6			−0.616993
$378$	−9.85286e6	−	2.64113e6i	−3.54677	−	0.950738i
$379$		−	2.61039e6i		−	0.933487i	−0.884393	−	0.466743i	$-0.845427\pi$
$379$		−	2.61039e6i		−	0.933487i	0.884393	−	0.466743i	$-0.154573\pi$
$380$		0			0
$381$		−	9.56839e6i		−	3.37696i
$382$	626853.	−	2.33850e6i	0.219790	−	0.819935i
$383$	3.05949e6			1.06574			0.532871	−	0.846197i	$-0.321113\pi$
$383$	3.05949e6			1.06574			0.532871	+	0.846197i	$0.321113\pi$
$384$	1.40498e6	−	5.22864e6i	0.486231	−	1.80951i
$385$		0			0
$386$	821227.	−	3.06362e6i	0.280540	−	1.04657i
$387$		−	9.24887e6i		−	3.13914i
$388$	974227.	+	562733.i	0.328534	+	0.189768i
$389$		−	498203.i		−	0.166929i	−0.996511	−	0.0834646i	$-0.973401\pi$
$389$		−	498203.i		−	0.166929i	0.996511	−	0.0834646i	$-0.0265985\pi$
$390$		0			0
$391$	−77540.0			−0.0256498
$392$	1.46928e6	−	1.46839e6i	0.482937	−	0.482643i
$393$	3.41732e6			1.11610
$394$	−1.46884e6	−	393735.i	−0.476689	−	0.127780i
$395$		0			0
$396$	−5.02411e6	+	8.69795e6i	−1.60998	+	2.78727i
$397$		−	3.95290e6i		−	1.25875i	−0.777101	−	0.629376i	$-0.783311\pi$
$397$		−	3.95290e6i		−	1.25875i	0.777101	−	0.629376i	$-0.216689\pi$
$398$	−750950.	+	2.80145e6i	−0.237631	+	0.886492i
$399$	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	$0.557272\pi$
$402$	2.84591e6	−	1.06168e7i	0.878328	−	3.27664i
$403$			1.15232e6i			0.353436i
$404$	−1.59314e6	+	2.75811e6i	−0.485624	+	0.840732i
$405$		0			0
$406$	−3.18249e6	−	853090.i	−0.958190	−	0.256850i
$407$	3.80120e6			1.13746
$408$	684313.	+	684728.i	0.203519	+	0.203642i
$409$	2.54459e6			0.752159			0.376079	−	0.926587i	$-0.377272\pi$
$409$	2.54459e6			0.752159			0.376079	+	0.926587i	$0.377272\pi$
$410$		0			0
$411$		−	2.17334e6i		−	0.634635i
$412$	1.30017e6	+	751003.i	0.377360	+	0.217971i
$413$			2.01438e6i			0.581119i
$414$	378438.	−	1.41178e6i	0.108516	−	0.404824i
$415$		0			0
$416$	−735667.	−	2.75111e6i	−0.208424	−	0.779427i
$417$	2.34933e6			0.661614
$418$	942669.	−	3.51666e6i	0.263887	−	0.984442i
$419$		−	62820.4i		−	0.0174810i	−0.999962	−	0.00874049i	$-0.997218\pi$
$419$		−	62820.4i		−	0.0174810i	0.999962	−	0.00874049i	$-0.00278222\pi$
$420$		0			0
$421$			1.89940e6i			0.522289i	0.965300	+	0.261145i	$0.0841000\pi$
$421$			1.89940e6i			0.522289i	−0.965300	+	0.261145i	$0.915900\pi$
$422$	−3.61644e6	−	969414.i	−0.988553	−	0.264989i
$423$	−9.36995e6			−2.54616
$424$	1.45797e6	+	1.45886e6i	0.393853	+	0.394092i
$425$		0			0
$426$	−4.18361e6	−	1.12145e6i	−1.11693	−	0.299402i
$427$			6.97145e6i			1.85035i
$428$	614316.	−	1.06353e6i	0.162100	−	0.280634i
$429$			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	$0.221702\pi$
$432$	−9.51109e6	+	5.48609e6i	−2.45200	+	1.41434i
$433$	1.64308e6			0.421153			0.210577	−	0.977577i	$-0.432466\pi$
$433$	1.64308e6			0.421153			0.210577	+	0.977577i	$0.432466\pi$
$434$	−577345.	+	2.15381e6i	−0.147133	+	0.548886i
$435$		0			0
$436$	−228700.	+	395934.i	−0.0576168	+	0.0997486i
$437$			529781.i			0.132707i
$438$	1.37714e7	+	3.69154e6i	3.43000	+	0.919438i
$439$	−4.34976e6			−1.07722			−0.538610	−	0.842555i	$-0.681050\pi$
$439$	−4.34976e6			−1.07722			−0.538610	+	0.842555i	$0.681050\pi$
$440$		0			0
$441$	−7.00118e6			−1.71425
$442$	491827.	+	131838.i	0.119745	+	0.0320985i
$443$			2.27280e6i			0.550239i	0.961410	+	0.275119i	$0.0887174\pi$
$443$			2.27280e6i			0.550239i	−0.961410	+	0.275119i	$0.911283\pi$
$444$	5.97962e6	+	3.45395e6i	1.43951	+	0.831493i
$445$		0			0
$446$	1.55955e6	−	5.81796e6i	0.371246	−	1.38495i
$447$	−1.69165e6			−0.400445
$448$	3347.43	−	5.51070e6i	0.000787982	−	1.29722i
$449$	7.36304e6			1.72362			0.861809	−	0.507233i	$-0.169331\pi$
$449$	7.36304e6			1.72362			0.861809	+	0.507233i	$0.169331\pi$
$450$		0			0
$451$			2.18165e6i			0.505060i
$452$	3.61753e6	+	2.08956e6i	0.832849	+	0.481071i
$453$		−	1.31674e7i		−	3.01477i
$454$	−3.38618e6	−	907690.i	−0.771027	−	0.206680i
$455$		0			0
$456$	4.67831e6	−	4.67547e6i	1.05360	−	1.05296i
$457$	6.23984e6			1.39760			0.698800	−	0.715317i	$-0.253718\pi$
$457$	6.23984e6			1.39760			0.698800	+	0.715317i	$0.253718\pi$
$458$	2.37631e6	+	636989.i	0.529346	+	0.141895i
$459$		−	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	$0.970930\pi$
$462$	−3.70147e6	+	1.38085e7i	−0.806806	+	3.00982i
$463$	3.61852e6			0.784474			0.392237	−	0.919864i	$-0.371701\pi$
$463$	3.61852e6			0.784474			0.392237	+	0.919864i	$0.371701\pi$
$464$	−3.07209e6	+	1.77202e6i	−0.662429	+	0.382096i
$465$		0			0
$466$	1.16266e6	−	4.33734e6i	0.248020	−	0.925249i
$467$		−	286010.i		−	0.0606861i	−0.999540	−	0.0303431i	$-0.990340\pi$
$467$		−	286010.i		−	0.0606861i	0.999540	−	0.0303431i	$-0.00965998\pi$
$468$	−4.80077e6	+	8.31130e6i	−1.01320	+	1.75410i
$469$		−	1.11877e7i		−	2.34860i
$470$		0			0
$471$	−2.10494e6			−0.437208
$472$	1.53271e6	+	1.53365e6i	0.316670	+	0.316862i
$473$	−7.79938e6			−1.60290
$474$	−3.15981e6	−	847013.i	−0.645975	−	0.173159i
$475$		0			0
$476$	853220.	+	492837.i	0.172601	+	0.0996980i
$477$		−	6.95150e6i		−	1.39889i
$478$	2.41341e6	−	9.00333e6i	0.483128	−	1.80233i
$479$	−2.28996e6			−0.456026			−0.228013	−	0.973658i	$-0.573223\pi$
$479$	−2.28996e6			−0.456026			−0.228013	+	0.973658i	$0.573223\pi$
$480$		0			0
$481$	3.63222e6			0.715830
$482$	−867953.	+	3.23793e6i	−0.170168	+	0.634820i
$483$		−	2.08023e6i		−	0.405736i
$484$	2.87215e6	+	1.65901e6i	0.557306	+	0.321911i
$485$		0			0
$486$	1.20843e7	+	3.23930e6i	2.32077	+	0.622100i
$487$	−6.55915e6			−1.25321			−0.626607	−	0.779335i	$-0.715557\pi$
$487$	−6.55915e6			−1.25321			−0.626607	+	0.779335i	$0.715557\pi$
$488$	5.30450e6	+	5.30772e6i	1.00831	+	1.00892i
$489$	−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	$-0.106418\pi$
$492$	−1.98235e6	+	3.43192e6i	−0.369205	+	0.639183i
$493$		−	634127.i		−	0.117506i
$494$	900764.	−	3.36034e6i	0.166071	−	0.619534i
$495$		0			0
$496$	1.19924e6	+	2.07910e6i	0.218879	+	0.379464i
$497$	−4.40858e6			−0.800586
$498$	−358076.	+	1.33582e6i	−0.0646997	+	0.241365i
$499$		−	1.11789e6i		−	0.200977i	−0.994938	−	0.100489i	$-0.967959\pi$
$499$		−	1.11789e6i		−	0.200977i	0.994938	−	0.100489i	$-0.0320406\pi$
$500$		0			0
$501$			1.51638e7i			2.69906i
$502$	−8.99262e6	−	2.41054e6i	−1.59267	−	0.426929i
$503$	3.97264e6			0.700098			0.350049	−	0.936731i	$-0.386165\pi$
$503$	3.97264e6			0.700098			0.350049	+	0.936731i	$0.386165\pi$
$504$	−1.31373e7	+	1.31293e7i	−2.30372	+	2.30233i
$505$		0			0
$506$	−1.19052e6	−	319129.i	−0.206710	−	0.0554102i
$507$		−	3.78539e6i		−	0.654020i
$508$	−9.07750e6	−	5.24335e6i	−1.56065	−	0.901466i
$509$		−	5.19239e6i		−	0.888327i	−0.895946	−	0.444164i	$-0.853501\pi$
$509$		−	5.19239e6i		−	0.888327i	0.895946	−	0.444164i	$-0.146499\pi$
$510$		0			0
$511$	1.45120e7			2.45853
$512$	−4.19048e6	−	4.19812e6i	−0.706462	−	0.707751i
$513$	−1.34135e7			−2.25035
$514$	−1.73936e6	+	6.48875e6i	−0.290390	+	1.08331i
$515$		0			0
$516$	−1.22691e7	−	7.08689e6i	−2.02856	−	1.17174i
$517$			7.90148e6i			1.30012i
$518$	6.78900e6	+	1.81984e6i	1.11168	+	0.297995i
$519$	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	$0.471751\pi$
$522$	1.15456e7	+	3.09489e6i	1.85456	+	0.497129i
$523$		−	8.67189e6i		−	1.38631i	−0.720790	−	0.693154i	$-0.756221\pi$
$523$		−	8.67189e6i		−	1.38631i	0.720790	−	0.693154i	$-0.243779\pi$
$524$	1.87264e6	−	3.24200e6i	0.297939	−	0.515804i
$525$		0			0
$526$	−2.38616e6	+	8.90165e6i	−0.376040	+	1.40283i
$527$	−429158.			−0.0673116
$528$	7.68859e6	+	1.33295e7i	1.20022	+	2.08079i
$529$	−6.25699e6			−0.972135
$530$		0			0
$531$		−	7.30787e6i		−	1.12475i
$532$	3.36724e6	−	5.82950e6i	0.515816	−	0.893002i
$533$			2.08467e6i			0.317847i
$534$	−610349.	−	163609.i	−0.0926244	−	0.0248287i
$535$		0			0
$536$	−8.51260e6	−	8.51777e6i	−1.27982	−	1.28060i
$537$	9.55916e6			1.43049
$538$	−4.89148e6	−	1.31120e6i	−0.728592	−	0.195305i
$539$			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	$-0.0174612\pi$
$542$	−24491.1	+	91365.2i	−0.00358105	+	0.0133593i
$543$	1.90315e7			2.76996
$544$	1.02459e6	−	273983.i	0.148441	−	0.0396942i
$545$		0			0
$546$	−3.53693e6	+	1.31946e7i	−0.507744	+	1.89416i
$547$			2.52087e6i			0.360231i	0.983645	+	0.180116i	$0.0576472\pi$
$547$			2.52087e6i			0.360231i	−0.983645	+	0.180116i	$0.942353\pi$
$548$	−2.06184e6	−	1.19096e6i	−0.293295	−	0.169413i
$549$		−	2.52915e7i		−	3.58132i
$550$		0			0
$551$	−4.33258e6			−0.607950
$552$	−1.58282e6	−	1.58378e6i	−0.221098	−	0.221232i
$553$	−3.32973e6			−0.463017
$554$	3.13584e6	+	840586.i	0.434090	+	0.116361i
$555$		0			0
$556$	1.28740e6	−	2.22880e6i	0.176615	−	0.305763i
$557$		−	186236.i		−	0.0254347i	−0.999919	−	0.0127173i	$-0.995952\pi$
$557$		−	186236.i		−	0.0254347i	0.999919	−	0.0127173i	$-0.00404816\pi$
$558$	2.09453e6	−	7.81371e6i	0.284774	−	1.06236i
$559$	−7.45267e6			−1.00875
$560$		0			0
$561$	−2.75141e6			−0.369104
$562$	−2.87021e6	+	1.07075e7i	−0.383331	+	1.43003i
$563$		−	358662.i		−	0.0476886i	−0.999716	−	0.0238443i	$-0.992409\pi$
$563$		−	358662.i		−	0.0476886i	0.999716	−	0.0238443i	$-0.00759059\pi$
$564$	−7.17966e6	+	1.24297e7i	−0.950400	+	1.64537i
$565$		0			0
$566$	1.11713e7	+	2.99455e6i	1.46576	+	0.392908i
$567$	2.77365e7			3.62321
$568$	−3.35648e6	+	3.35444e6i	−0.436529	+	0.436263i
$569$	1.08964e7			1.41093			0.705463	−	0.708747i	$-0.250739\pi$
$569$	1.08964e7			1.41093			0.705463	+	0.708747i	$0.250739\pi$
$570$		0			0
$571$			1.93042e6i			0.247778i	0.992296	+	0.123889i	$0.0395366\pi$
$571$			1.93042e6i			0.247778i	−0.992296	+	0.123889i	$0.960463\pi$
$572$	7.00874e6	+	4.04839e6i	0.895674	+	0.517360i
$573$			1.25007e7i			1.59055i
$574$	−1.04447e6	+	3.89645e6i	−0.132318	+	0.493617i
$575$		0			0
$576$	−12144.0	+	1.99921e7i	−0.00152513	+	2.51074i
$577$	1.33310e7			1.66695			0.833477	−	0.552555i	$-0.186347\pi$
$577$	1.33310e7			1.66695			0.833477	+	0.552555i	$0.186347\pi$
$578$	2.03050e6	−	7.57486e6i	0.252804	−	0.943094i
$579$			1.63768e7i			2.03018i
$580$		0			0
$581$			1.40765e6i			0.173003i
$582$	−5.61099e6	−	1.50407e6i	−0.686645	−	0.184060i
$583$	−5.86206e6			−0.714297
$584$	1.10487e7	−	1.10420e7i	1.34054	−	1.33973i
$585$		0			0
$586$	1.23001e7	+	3.29712e6i	1.47966	+	0.396635i
$587$		−	7.15350e6i		−	0.856887i	−0.903569	−	0.428443i	$-0.859062\pi$
$587$		−	7.15350e6i		−	0.856887i	0.903569	−	0.428443i	$-0.140938\pi$
$588$	−5.36461e6	+	9.28743e6i	−0.639875	+	1.10778i
$589$			2.93216e6i			0.348256i
$590$		0			0
$591$	7.85183e6			0.924703
$592$	6.55350e6	−	3.78013e6i	0.768545	−	0.443305i
$593$	−1.46858e7			−1.71499			−0.857496	−	0.514490i	$-0.827981\pi$
$593$	−1.46858e7			−1.71499			−0.857496	+	0.514490i	$0.827981\pi$
$594$	8.08002e6	−	3.01428e7i	0.939608	−	3.50524i
$595$		0			0
$596$	−927004.	+	1.60487e6i	−0.106897	+	0.185065i
$597$		−	1.49754e7i		−	1.71966i
$598$	−1.13760e6	−	304943.i	−0.130088	−	0.0348711i
$599$	−9.83597e6			−1.12008			−0.560042	−	0.828465i	$-0.689215\pi$
$599$	−9.83597e6			−1.12008			−0.560042	+	0.828465i	$0.689215\pi$
$600$		0			0
$601$	2.68643e6			0.303381			0.151691	−	0.988428i	$-0.451528\pi$
$601$	2.68643e6			0.303381			0.151691	+	0.988428i	$0.451528\pi$
$602$	−1.39298e7	−	3.73399e6i	−1.56658	−	0.419935i
$603$			4.05875e7i			4.54568i
$604$	−1.24918e7	−	7.21554e6i	−1.39327	−	0.804779i
$605$		0			0
$606$	4.25813e6	−	1.58851e7i	0.471018	−	1.75715i
$607$	−387079.			−0.0426411			−0.0213205	−	0.999773i	$-0.506787\pi$
$607$	−387079.			−0.0426411			−0.0213205	+	0.999773i	$0.506787\pi$
$608$	−1.87195e6	−	7.00039e6i	−0.205369	−	0.768003i
$609$	1.70123e7			1.85874
$610$		0			0
$611$			7.55024e6i			0.818196i
$612$	−3.09536e6	−	1.78795e6i	−0.334067	−	0.192964i
$613$		−	1.37500e7i		−	1.47792i	−0.673748	−	0.738962i	$-0.735316\pi$
$613$		−	1.37500e7i		−	1.47792i	0.673748	−	0.738962i	$-0.264684\pi$
$614$	−3.12777e6	−	838422.i	−0.334821	−	0.0897515i
$615$		0			0
$616$	1.10717e7	+	1.10784e7i	1.17561	+	1.17632i
$617$	1.13239e7			1.19752			0.598758	−	0.800930i	$-0.295661\pi$
$617$	1.13239e7			1.19752			0.598758	+	0.800930i	$0.295661\pi$
$618$	−7.48823e6	−	2.00728e6i	−0.788693	−	0.211415i
$619$		−	6.62505e6i		−	0.694965i	−0.937687	−	0.347482i	$-0.887037\pi$
$619$		−	6.62505e6i		−	0.694965i	0.937687	−	0.347482i	$-0.112963\pi$
$620$		0			0
$621$			4.54098e6i			0.472521i
$622$	4.19151e6	−	1.56366e7i	0.434405	−	1.62057i
$623$	−643171.			−0.0663905
$624$	7.34681e6	+	1.27370e7i	0.755331	+	1.30950i
$625$		0			0
$626$	−506247.	+	1.88857e6i	−0.0516329	+	0.192619i
$627$			1.87986e7i			1.90967i
$628$	−1.15348e6	+	1.99695e6i	−0.116711	+	0.202055i
$629$			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	$0.689257\pi$
$632$	−2.53509e6	+	2.53355e6i	−0.252465	+	0.252312i
$633$	1.93320e7			1.91764
$634$	−1.55379e7	−	4.16505e6i	−1.53521	−	0.411525i
$635$		0			0
$636$	−9.22153e6	−	5.32654e6i	−0.903983	−	0.522159i
$637$			5.64150e6i			0.550866i
$638$	2.60986e6	−	9.73618e6i	0.253843	−	0.946972i
$639$	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	$0.582919\pi$
$642$	−1.64194e6	+	6.12532e6i	−0.157224	+	0.586531i
$643$			5.64079e6i			0.538038i	0.963135	+	0.269019i	$0.0866994\pi$
$643$			5.64079e6i			0.538038i	−0.963135	+	0.269019i	$0.913301\pi$
$644$	−1.97351e6	−	1.13994e6i	−0.187510	−	0.108310i
$645$		0			0
$646$	1.25148e6	+	335470.i	0.117990	+	0.0316281i
$647$	−5.67405e6			−0.532884			−0.266442	−	0.963851i	$-0.585848\pi$
$647$	−5.67405e6			−0.532884			−0.266442	+	0.963851i	$0.585848\pi$
$648$	2.11172e7	−	2.11044e7i	1.97560	−	1.97440i
$649$	−6.16258e6			−0.574316
$650$		0			0
$651$		−	1.15134e7i		−	1.06476i
$652$	−7.54096e6	+	1.30552e7i	−0.694716	+	1.20272i
$653$			1.50064e7i			1.37719i	0.725148	+	0.688593i	$0.241771\pi$
$653$			1.50064e7i			1.37719i	−0.725148	+	0.688593i	$0.758229\pi$
$654$	611267.	−	2.28036e6i	0.0558839	−	0.208477i
$655$		0			0
$656$	2.16955e6	+	3.76130e6i	0.196839	+	0.341254i
$657$	−5.26475e7			−4.75844
$658$	−3.78287e6	+	1.41122e7i	−0.340610	+	1.27066i
$659$			7.48265e6i			0.671184i	0.942007	+	0.335592i	$0.108936\pi$
$659$			7.48265e6i			0.671184i	−0.942007	+	0.335592i	$0.891064\pi$
$660$		0			0
$661$		−	1.85142e7i		−	1.64817i	−0.566467	−	0.824084i	$-0.691690\pi$
$661$		−	1.85142e7i		−	1.64817i	0.566467	−	0.824084i	$-0.308310\pi$
$662$	1.20551e7	+	3.23146e6i	1.06912	+	0.286585i
$663$	−2.62910e6			−0.232286
$664$	1.07107e6	+	1.07172e6i	0.0942748	+	0.0943321i
$665$		0			0
$666$	−2.46295e7	−	6.60214e6i	−2.15164	−	0.576765i
$667$			1.46674e6i			0.127656i
$668$	1.43858e7	+	8.30953e6i	1.24736	+	0.720502i
$669$			3.11004e7i			2.68659i
$670$		0			0
$671$	−2.13278e7			−1.82869
$672$	7.35038e6	+	2.74876e7i	0.627894	+	2.34809i
$673$	4.62662e6			0.393755			0.196878	−	0.980428i	$-0.436920\pi$
$673$	4.62662e6			0.393755			0.196878	+	0.980428i	$0.436920\pi$
$674$	−308778.	+	1.15191e6i	−0.0261816	+	0.0976716i
$675$		0			0
$676$	−3.59119e6	−	2.07434e6i	−0.302254	−	0.174588i
$677$		−	1.21437e7i		−	1.01831i	−0.860675	−	0.509155i	$-0.829958\pi$
$677$		−	1.21437e7i		−	1.01831i	0.860675	−	0.509155i	$-0.170042\pi$
$678$	−2.08349e7	−	5.58496e6i	−1.74068	−	0.466601i
$679$	−5.91272e6			−0.492168
$680$		0			0
$681$	1.81011e7			1.49567
$682$	−6.58914e6	−	1.76627e6i	−0.542460	−	0.145411i
$683$		−	9.19906e6i		−	0.754557i	−0.926100	−	0.377278i	$-0.876860\pi$
$683$		−	9.19906e6i		−	0.754557i	0.926100	−	0.377278i	$-0.123140\pi$
$684$	−1.22159e7	+	2.11486e7i	−0.998354	+	1.72839i
$685$		0			0
$686$	1.31329e6	−	4.89927e6i	0.106549	−	0.397485i
$687$	−1.27028e7			−1.02685
$688$	−1.34466e7	+	7.75615e6i	−1.08303	+	0.624705i
$689$	−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	$0.866332\pi$
$692$	1.16345e7	−	2.01420e7i	0.923593	−	1.59896i
$693$		−	5.27891e7i		−	4.17553i
$694$	−1.31089e7	−	3.51394e6i	−1.03316	−	0.276946i
$695$		0			0
$696$	1.29523e7	−	1.29444e7i	1.01350	−	1.01288i
$697$	−776389.			−0.0605338
$698$	−9.62789e6	−	2.58083e6i	−0.747985	−	0.200503i
$699$			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	$-0.0151576\pi$
$702$	7.72084e6	−	2.88029e7i	0.591319	−	2.20594i
$703$	9.24242e6			0.705339
$704$	1.68589e7	+	10240.8i	1.28203	+	0.000778757i
$705$		0			0
$706$	−3.09609e6	+	1.15501e7i	−0.233777	+	0.872114i
$707$		−	1.67394e7i		−	1.25948i
$708$	−9.69428e6	−	5.59961e6i	−0.726829	−	0.419831i
$709$		−	2.52759e7i		−	1.88839i	−0.329386	−	0.944195i	$-0.606842\pi$
$709$		−	2.52759e7i		−	1.88839i	0.329386	−	0.944195i	$-0.393158\pi$
$710$		0			0
$711$	1.20798e7			0.896161
$712$	−489678.	+	489381.i	−0.0362002	+	0.0361782i
$713$	992646.			0.0731258
$714$	−4.91406e6	−	1.31725e6i	−0.360741	−	0.0966993i
$715$		0			0
$716$	5.23829e6	−	9.06874e6i	0.381863	−	0.661096i
$717$			4.81281e7i			3.49624i
$718$	37189.8	−	138738.i	0.00269223	−	0.0100435i
$719$	−5.23203e6			−0.377440			−0.188720	−	0.982031i	$-0.560434\pi$
$719$	−5.23203e6			−0.377440			−0.188720	+	0.982031i	$0.560434\pi$
$720$		0			0
$721$	−7.89090e6			−0.565313
$722$	−1.33458e6	+	4.97870e6i	−0.0952799	+	0.355445i
$723$		−	1.73087e7i		−	1.23145i
$724$	1.04290e7	−	1.80551e7i	0.739429	−	1.28013i
$725$		0			0
$726$	−1.65419e7	−	4.43419e6i	−1.16478	−	0.312229i
$727$	−1.79530e7			−1.25980			−0.629899	−	0.776677i	$-0.716904\pi$
$727$	−1.79530e7			−1.25980			−0.629899	+	0.776677i	$0.716904\pi$
$728$	1.05795e7	+	1.05860e7i	0.739840	+	0.740290i
$729$	−2.45203e7			−1.70886
$730$		0			0
$731$		−	2.77559e6i		−	0.192115i
$732$	−3.35504e7	−	1.93794e7i	−2.31430	−	1.33679i
$733$		−	2.06019e6i		−	0.141627i	−0.997490	−	0.0708137i	$-0.977440\pi$
$733$		−	2.06019e6i		−	0.141627i	0.997490	−	0.0708137i	$-0.0225596\pi$
$734$	2.28299e6	−	8.51677e6i	0.156409	−	0.583492i
$735$		0			0
$736$	−2.36990e6	+	633726.i	−0.161263	+	0.0431228i
$737$	3.42266e7			2.32111
$738$	3.78921e6	−	1.41358e7i	0.256099	−	0.955387i
$739$		−	1.47746e6i		−	0.0995187i	−0.998761	−	0.0497594i	$-0.984155\pi$
$739$		−	1.47746e6i		−	0.0995187i	0.998761	−	0.0497594i	$-0.0158454\pi$
$740$		0			0
$741$			1.79630e7i			1.20180i
$742$	−1.04697e7	−	2.80649e6i	−0.698112	−	0.187134i
$743$	−2.46543e7			−1.63840			−0.819200	−	0.573508i	$-0.805582\pi$
$743$	−2.46543e7			−1.63840			−0.819200	+	0.573508i	$0.805582\pi$
$744$	−8.76038e6	−	8.76570e6i	−0.580217	−	0.580570i
$745$		0			0
$746$	−4.05285e6	−	1.08640e6i	−0.266633	−	0.0714729i
$747$		−	5.10676e6i		−	0.334845i
$748$	−1.50774e6	+	2.61026e6i	−0.0985307	+	0.170580i
$749$			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	$0.565366\pi$
$752$	7.85768e6	+	1.36226e7i	0.506699	+	0.878450i
$753$	4.80708e7			3.08954
$754$	2.49384e6	−	9.30338e6i	0.159750	−	0.595953i
$755$		0			0
$756$	2.88621e7	−	4.99672e7i	1.83664	−	3.17966i
$757$		−	1.44827e7i		−	0.918567i	−0.888290	−	0.459284i	$-0.848106\pi$
$757$		−	1.44827e7i		−	0.918567i	0.888290	−	0.459284i	$-0.151894\pi$
$758$	1.42631e7	+	3.82333e6i	0.901655	+	0.241695i
$759$	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	$0.403805\pi$
$762$	5.22812e7	+	1.40144e7i	3.26181	+	0.874353i
$763$		−	2.40298e6i		−	0.149430i
$764$	1.18593e7	+	6.85020e6i	0.735067	+	0.424590i
$765$		0			0
$766$	−4.48109e6	+	1.67169e7i	−0.275938	+	1.02940i
$767$	−5.88863e6			−0.361431
$768$	2.65112e7	+	1.53349e7i	1.62191	+	0.938162i
$769$	2.88208e6			0.175748			0.0878741	−	0.996132i	$-0.471993\pi$
$769$	2.88208e6			0.175748			0.0878741	+	0.996132i	$0.471993\pi$
$770$		0			0
$771$		−	3.46862e7i		−	2.10146i
$772$	1.55367e7	+	8.97429e6i	0.938241	+	0.541947i
$773$			1.83423e7i			1.10409i	0.833815	+	0.552044i	$0.186152\pi$
$773$			1.83423e7i			1.10409i	−0.833815	+	0.552044i	$0.813848\pi$
$774$	5.05354e7	+	1.35464e7i	3.03210	+	0.812777i
$775$		0			0
$776$	−4.50165e6	+	4.49892e6i	−0.268360	+	0.268197i
$777$	−3.62912e7			−2.15650
$778$	2.72216e6	+	729695.i	0.161237	+	0.0432208i
$779$			5.30457e6i			0.313189i
$780$		0			0
$781$		−	1.34872e7i		−	0.791213i
$782$	113569.	−	423675.i	0.00664117	−	0.0247751i
$783$	−3.71365e7			−2.16469
$784$	5.87123e6	+	1.01788e7i	0.341145	+	0.591433i
$785$		0			0
$786$	−5.00519e6	+	1.86721e7i	−0.288978	+	1.07804i
$787$		−	1.35279e7i		−	0.778564i	−0.921119	−	0.389282i	$-0.872723\pi$
$787$		−	1.35279e7i		−	0.778564i	0.921119	−	0.389282i	$-0.127277\pi$
$788$	4.30270e6	−	7.44901e6i	0.246846	−	0.427349i
$789$		−	4.75846e7i		−	2.72128i
$790$		0			0
$791$	−2.19553e7			−1.24767
$792$	−4.01666e7	−	4.01910e7i	−2.27537	−	2.27675i
$793$	−2.03797e7			−1.15084
$794$	2.15985e7	+	5.78964e6i	1.21583	+	0.325912i
$795$		0			0
$796$	−1.42071e7	−	8.20631e6i	−0.794736	−	0.459056i
$797$		−	3.10994e7i		−	1.73423i	−0.498109	−	0.867115i	$-0.665972\pi$
$797$		−	3.10994e7i		−	1.73423i	0.498109	−	0.867115i	$-0.334028\pi$
$798$	−8.99994e6	+	3.35746e7i	−0.500302	+	1.86640i
$799$	−2.81192e6			−0.155825
$800$		0			0
$801$	2.33333e6			0.128498
$802$	1.68799e6	−	6.29710e6i	0.0926687	−	0.345704i
$803$			4.43965e7i			2.42974i
$804$	5.38414e7	+	3.10999e7i	2.93749	+	1.69675i
$805$		0			0
$806$	−6.29623e6	−	1.68775e6i	−0.341384	−	0.0915106i
$807$	2.61478e7			1.41336
$808$	−1.27368e7	−	1.27445e7i	−0.686327	−	0.686744i
$809$	1.19594e6			0.0642449			0.0321225	−	0.999484i	$-0.489773\pi$
$809$	1.19594e6			0.0642449			0.0321225	+	0.999484i	$0.489773\pi$
$810$		0			0
$811$			5.59211e6i			0.298554i	0.988795	+	0.149277i	$0.0476947\pi$
$811$			5.59211e6i			0.298554i	−0.988795	+	0.149277i	$0.952305\pi$
$812$	9.32249e6	−	1.61395e7i	0.496183	−	0.859012i
$813$		−	488400.i		−	0.0259149i
$814$	−5.56744e6	+	2.07696e7i	−0.294507	+	1.09867i
$815$		0			0
$816$	−4.74361e6	+	2.73616e6i	−0.249392	+	0.143852i
$817$	−1.89638e7			−0.993963
$818$	−3.72694e6	+	1.39035e7i	−0.194747	+	0.726510i
$819$		−	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	$0.783618\pi$
$822$	1.18750e7	+	3.18320e6i	0.612993	+	0.164318i
$823$	1.21094e7			0.623193			0.311597	−	0.950214i	$-0.399136\pi$
$823$	1.21094e7			0.623193			0.311597	+	0.950214i	$0.399136\pi$
$824$	−6.00774e6	+	6.00410e6i	−0.308243	+	0.308056i
$825$		0			0
$826$	−1.10065e7	−	2.95037e6i	−0.561303	−	0.150462i
$827$			2.18004e7i			1.10841i	0.832380	+	0.554205i	$0.186977\pi$
$827$			2.18004e7i			1.10841i	−0.832380	+	0.554205i	$0.813023\pi$
$828$	7.15961e6	+	4.13554e6i	0.362922	+	0.209631i
$829$			2.81218e7i			1.42121i	0.703593	+	0.710603i	$0.251578\pi$
$829$			2.81218e7i			1.42121i	−0.703593	+	0.710603i	$0.748422\pi$
$830$		0			0
$831$	−1.67629e7			−0.842067
$832$	1.61095e7	+	9785.55i	0.806813	+	0.000490091i
$833$	−2.10106e6			−0.104912
$834$	−3.44096e6	+	1.28366e7i	−0.171303	+	0.639052i
$835$		0			0
$836$	1.78342e7	+	1.03014e7i	0.882547	+	0.509777i
$837$			2.51328e7i			1.24002i
$838$	343248.	+	92010.2i	0.0168849	+	0.00452612i
$839$	1.77035e6			0.0868270			0.0434135	−	0.999057i	$-0.486177\pi$
$839$	1.77035e6			0.0868270			0.0434135	+	0.999057i	$0.486177\pi$
$840$		0			0
$841$	8.51602e6			0.415190
$842$	−1.03782e7	−	2.78197e6i	−0.504479	−	0.135230i
$843$		−	5.72376e7i		−	2.77404i
$844$	1.05937e7	−	1.83402e7i	0.511906	−	0.886233i
$845$		0			0
$846$	1.37237e7	−	5.11970e7i	0.659245	−	2.45934i
$847$	−1.74315e7			−0.834883
$848$	−1.01066e7	+	5.82956e6i	−0.482629	+	0.278385i
$849$	−5.97171e7			−2.84335
$850$		0			0
$851$		−	3.12891e6i		−	0.148105i
$852$	1.22551e7	−	2.12165e7i	0.578385	−	1.00132i
$853$		−	2.98606e7i		−	1.40516i	−0.711604	−	0.702581i	$-0.752031\pi$
$853$		−	2.98606e7i		−	1.40516i	0.711604	−	0.702581i	$-0.247969\pi$
$854$	−3.80917e7	−	1.02108e7i	−1.78725	−	0.479087i
$855$		0			0
$856$	4.91131e6	+	4.91429e6i	0.229094	+	0.229233i
$857$	1.59538e7			0.742012			0.371006	−	0.928630i	$-0.379013\pi$
$857$	1.59538e7			0.742012			0.371006	+	0.928630i	$0.379013\pi$
$858$	−4.03664e7	−	1.08205e7i	−1.87198	−	0.501799i
$859$			2.68382e7i			1.24099i	0.784209	+	0.620497i	$0.213069\pi$
$859$			2.68382e7i			1.24099i	−0.784209	+	0.620497i	$0.786931\pi$
$860$		0			0
$861$		−	2.08288e7i		−	0.957541i
$862$	−8.66576e6	+	3.23280e7i	−0.397227	+	1.48187i
$863$	−1.99512e7			−0.911891			−0.455946	−	0.890008i	$-0.650699\pi$
$863$	−1.99512e7			−0.911891			−0.455946	+	0.890008i	$0.650699\pi$
$864$	−1.60453e7	−	6.00034e7i	−0.731246	−	2.73458i
$865$		0			0
$866$	−2.40655e6	+	8.97773e6i	−0.109044	+	0.406792i
$867$			4.04921e7i			1.82946i
$868$	−1.09227e7	−	6.30917e6i	−0.492074	−	0.284232i
$869$		−	1.01867e7i		−	0.457596i
$870$		0			0
$871$	3.27051e7			1.46073
$872$	−1.82840e6	−	1.82951e6i	−0.0814292	−	0.0814787i
$873$	2.14505e7			0.952582
$874$	−2.89470e6	−	775946.i	−0.128181	−	0.0343600i
$875$		0			0
$876$	−4.03408e7	+	6.98397e7i	−1.77617	+	3.07498i
$877$		−	2.73500e7i		−	1.20077i	−0.799712	−	0.600384i	$-0.795014\pi$
$877$		−	2.73500e7i		−	1.20077i	0.799712	−	0.600384i	$-0.204986\pi$
$878$	6.37090e6	−	2.37669e7i	0.278910	−	1.04049i
$879$	−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	$0.753657\pi$
$882$	1.02543e7	−	3.82541e7i	0.443849	−	1.65580i
$883$			1.45135e7i			0.626429i	0.949682	+	0.313214i	$0.101406\pi$
$883$			1.45135e7i			0.626429i	−0.949682	+	0.313214i	$0.898594\pi$
$884$	−1.44071e6	+	2.49422e6i	−0.0620079	+	0.107351i
$885$		0			0
$886$	−1.24185e7	−	3.32886e6i	−0.531475	−	0.142466i
$887$	−2.89058e7			−1.23360			−0.616802	−	0.787118i	$-0.711572\pi$
$887$	−2.89058e7			−1.23360			−0.616802	+	0.787118i	$0.711572\pi$
$888$	−2.76303e7	+	2.76135e7i	−1.17585	+	1.17514i
$889$	5.50926e7			2.33797
$890$		0			0
$891$			8.48543e7i			3.58079i
$892$	2.95049e7	+	1.70426e7i	1.24160	+	0.717173i
$893$			1.92121e7i			0.806205i
$894$	2.47769e6	−	9.24312e6i	0.103682	−	0.386790i
$895$		0			0
$896$	3.01053e7	+	8.08957e6i	1.25278	+	0.336632i
$897$	6.08114e6			0.252351
$898$	−1.07843e7	+	4.02313e7i	−0.446274	+	1.66484i
$899$			8.11793e6i			0.335001i
$900$		0			0
$901$		−	2.08615e6i		−	0.0856117i
$902$	−1.19204e7	−	3.19536e6i	−0.487838	−	0.130769i
$903$	7.44630e7			3.03893
$904$	−1.67157e7	+	1.67055e7i	−0.680305	+	0.679892i
$905$		0			0
$906$	7.19459e7	+	1.92857e7i	2.91196	+	0.780574i
$907$			1.75219e7i			0.707233i	0.935390	+	0.353617i	$0.115048\pi$
$907$			1.75219e7i			0.707233i	−0.935390	+	0.353617i	$0.884952\pi$
$908$	9.91915e6	−	1.71724e7i	0.399264	−	0.691222i
$909$			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	$0.534990\pi$
$912$	1.86944e7	+	3.24100e7i	0.744261	+	1.29030i
$913$	−4.30643e6			−0.170978
$914$	−9.13922e6	+	3.40942e7i	−0.361862	+	1.34994i
$915$		0			0
$916$	−6.96096e6	+	1.20511e7i	−0.274113	+	0.474556i
$917$			1.96762e7i			0.772711i
$918$	1.07270e7	+	2.87546e6i	0.420119	+	0.112616i
$919$	1.89582e6			0.0740472			0.0370236	−	0.999314i	$-0.488212\pi$
$919$	1.89582e6			0.0740472			0.0370236	+	0.999314i	$0.488212\pi$
$920$		0			0
$921$	1.67197e7			0.649502
$922$	−4.54760e6	−	1.21902e6i	−0.176179	−	0.0472262i
$923$		−	1.28876e7i		−	0.497930i
$924$	−7.00275e7	−	4.04493e7i	−2.69829	−	1.55859i
$925$		0			0
$926$	−5.29988e6	+	1.97714e7i	−0.203114	+	0.757723i
$927$	2.86271e7			1.09415
$928$	−5.18266e6	−	1.93812e7i	−0.197552	−	0.738771i
$929$	3.44700e7			1.31040			0.655198	−	0.755457i	$-0.272585\pi$
$929$	3.44700e7			1.31040			0.655198	+	0.755457i	$0.272585\pi$
$930$		0			0
$931$			1.43552e7i			0.542793i
$932$	2.19961e7	+	1.27054e7i	0.829481	+	0.479125i
$933$			8.35868e7i			3.14365i
$934$	1.56275e6	+	418906.i	0.0586167	+	0.0157127i
$935$		0			0
$936$	−3.83811e7	−	3.84044e7i	−1.43195	−	1.43282i
$937$	−3.96544e7			−1.47551			−0.737756	−	0.675068i	$-0.764114\pi$
$937$	−3.96544e7			−1.47551			−0.737756	+	0.675068i	$0.764114\pi$
$938$	6.11292e7	+	1.63861e7i	2.26851	+	0.608093i
$939$		−	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	$-0.112710\pi$
$942$	3.08302e6	−	1.15013e7i	0.113201	−	0.422299i
$943$	1.79580e6			0.0657625
$944$	−1.06247e7	+	6.12842e6i	−0.388048	+	0.223830i
$945$		0			0
$946$	1.14234e7	−	4.26154e7i	0.415019	−	1.54824i
$947$		−	4.04648e6i		−	0.146623i	−0.997309	−	0.0733115i	$-0.976643\pi$
$947$		−	4.04648e6i		−	0.146623i	0.997309	−	0.0733115i	$-0.0233567\pi$
$948$	9.25607e6	−	1.60245e7i	0.334508	−	0.579113i
$949$			4.24230e7i			1.52910i
$950$		0			0
$951$	8.30590e7			2.97807
$952$	−3.94251e6	+	3.94012e6i	−0.140988	+	0.140902i
$953$	−4.74092e7			−1.69095			−0.845474	−	0.534016i	$-0.820682\pi$
$953$	−4.74092e7			−1.69095			−0.845474	+	0.534016i	$0.820682\pi$
$954$	3.79827e7	+	1.01816e7i	1.35118	+	0.362195i
$955$		0			0
$956$	4.56590e7	+	2.63735e7i	1.61578	+	0.933305i
$957$			5.20456e7i			1.83698i
$958$	3.35401e6	−	1.25123e7i	0.118073	−	0.440476i
$959$	1.25136e7			0.439376
$960$		0			0
$961$	−2.31352e7			−0.808099
$962$	−5.31995e6	+	1.98463e7i	−0.185340	+	0.691420i
$963$		−	2.34168e7i		−	0.813695i
$964$	−1.64207e7	−	9.48491e6i	−0.569112	−	0.328731i
$965$		0			0
$966$	1.13663e7	+	3.04682e6i	0.391900	+	0.105052i
$967$	1.05815e7			0.363898			0.181949	−	0.983308i	$-0.441759\pi$
$967$	1.05815e7			0.363898			0.181949	+	0.983308i	$0.441759\pi$
$968$	−1.32715e7	+	1.32634e7i	−0.455229	+	0.454953i
$969$	−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	$-0.199884\pi$
$972$	−3.53987e7	+	6.12837e7i	−1.20177	+	2.08056i
$973$			1.35269e7i			0.458055i
$974$	9.60689e6	−	3.58389e7i	0.324478	−	1.21048i
$975$		0			0
$976$	−3.67704e7	+	2.12095e7i	−1.23559	+	0.712700i
$977$	1.80039e7			0.603433			0.301717	−	0.953398i	$-0.402440\pi$
$977$	1.80039e7			0.603433			0.301717	+	0.953398i	$0.402440\pi$
$978$	2.01554e7	−	7.51906e7i	0.673821	−	2.51372i
$979$		−	1.96765e6i		−	0.0656133i
$980$		0			0
$981$			8.71768e6i			0.289220i
$982$	1.91551e7	+	5.13468e6i	0.633879	+	0.169916i
$983$	2.71815e7			0.897200			0.448600	−	0.893733i	$-0.351923\pi$
$983$	2.71815e7			0.897200			0.448600	+	0.893733i	$0.351923\pi$
$984$	−1.58484e7	−	1.58580e7i	−0.521793	−	0.522110i
$985$		0			0
$986$	3.46484e6	+	928778.i	0.113499	+	0.0304242i
$987$		−	7.54378e7i		−	2.46488i
$988$	1.70414e7	+	9.84346e6i	0.555409	+	0.320816i
$989$			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	$0.619632\pi$
$992$	−1.31166e7	+	3.50746e6i	−0.423195	+	0.113165i
$993$	−6.44416e7			−2.07393
$994$	6.45705e6	−	2.40883e7i	0.207285	−	0.773286i
$995$		0			0
$996$	−6.77439e6	−	3.91302e6i	−0.216382	−	0.124987i
$997$		−	2.28102e7i		−	0.726762i	−0.931641	−	0.363381i	$-0.881622\pi$
$997$		−	2.28102e7i		−	0.726762i	0.931641	−	0.363381i	$-0.118378\pi$
$998$	6.10809e6	+	1.63732e6i	0.194124	+	0.0520364i
$999$	7.92208e7			2.51146

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.13	✓	20	5.4	even	2
40.6.d.a.21.14	yes	20	40.29	even	2
160.6.d.a.81.1		20	20.19	odd	2
160.6.d.a.81.20		20	40.19	odd	2
200.6.d.b.101.7		20	8.5	even	2	inner
200.6.d.b.101.8		20	1.1	even	1	trivial
200.6.f.b.149.3		20	5.2	odd	4
200.6.f.b.149.4		20	40.13	odd	4
200.6.f.c.149.17		20	40.37	odd	4
200.6.f.c.149.18		20	5.3	odd	4
360.6.k.b.181.7		20	120.29	odd	2
360.6.k.b.181.8		20	15.14	odd	2
800.6.d.c.401.1		20	8.3	odd	2
800.6.d.c.401.20		20	4.3	odd	2
800.6.f.b.49.1		20	40.27	even	4
800.6.f.b.49.2		20	20.3	even	4
800.6.f.c.49.19		20	20.7	even	4
800.6.f.c.49.20		20	40.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	200.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46465 + 5.46395i) q^{2} -29.2080i q^{3} +(-27.7096 - 16.0056i) q^{4} +(159.591 + 42.7797i) q^{6} +168.173 q^{7} +(128.039 - 127.961i) q^{8} -610.110 q^{9} +514.493i q^{11} +(-467.493 + 809.342i) q^{12} +491.622i q^{13} +(-246.316 + 918.892i) q^{14} +(511.641 + 887.017i) q^{16} -183.094 q^{17} +(893.600 - 3333.61i) q^{18} +1250.96i q^{19} -4912.01i q^{21} +(-2811.16 - 753.554i) q^{22} +423.498 q^{23} +(-3737.49 - 3739.76i) q^{24} +(-2686.20 - 720.056i) q^{26} +10722.5i q^{27} +(-4660.01 - 2691.72i) q^{28} +3463.40i q^{29} +2343.92 q^{31} +(-5596.00 + 1496.41i) q^{32} +15027.3 q^{33} +(268.170 - 1000.42i) q^{34} +(16905.9 + 9765.18i) q^{36} -7388.25i q^{37} +(-6835.20 - 1832.23i) q^{38} +14359.3 q^{39} +4240.39 q^{41} +(26839.0 + 7194.41i) q^{42} +15159.4i q^{43} +(8234.77 - 14256.4i) q^{44} +(-620.279 + 2313.98i) q^{46} +15357.8 q^{47} +(25908.0 - 14944.0i) q^{48} +11475.3 q^{49} +5347.82i q^{51} +(7868.71 - 13622.6i) q^{52} +11393.9i q^{53} +(-58587.5 - 15704.8i) q^{54} +(21532.7 - 21519.7i) q^{56} +36538.2 q^{57} +(-18923.8 - 5072.68i) q^{58} +11978.0i q^{59} +41454.0i q^{61} +(-3433.03 + 12807.1i) q^{62} -102604. q^{63} +(19.9046 - 32768.0i) q^{64} +(-22009.8 + 82108.6i) q^{66} -66524.9i q^{67} +(5073.46 + 2930.53i) q^{68} -12369.6i q^{69} -26214.5 q^{71} +(-78117.7 + 78070.3i) q^{72} +86291.9 q^{73} +(40369.0 + 10821.2i) q^{74} +(20022.4 - 34663.7i) q^{76} +86524.0i q^{77} +(-21031.4 + 78458.6i) q^{78} -19799.4 q^{79} +164928. q^{81} +(-6210.70 + 23169.3i) q^{82} +8370.24i q^{83} +(-78619.8 + 136110. i) q^{84} +(-82830.0 - 22203.2i) q^{86} +101159. q^{87} +(65835.1 + 65875.1i) q^{88} -3824.45 q^{89} +82677.7i q^{91} +(-11735.0 - 6778.35i) q^{92} -68461.3i q^{93} +(-22493.9 + 83914.4i) q^{94} +(43707.1 + 163448. i) q^{96} -35158.5 q^{97} +(-16807.3 + 62700.4i) q^{98} -313897. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 32 q^{4} + 204 q^{6} + 196 q^{7} - 248 q^{8} - 1620 q^{9} + 1876 q^{12} + 2708 q^{14} + 3080 q^{16} + 5294 q^{18} - 13836 q^{22} + 4676 q^{23} + 1032 q^{24} - 8084 q^{26} - 2108 q^{28}+ \cdots - 216942 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 32 * q^4 + 204 * q^6 + 196 * q^7 - 248 * q^8 - 1620 * q^9 + 1876 * q^12 + 2708 * q^14 + 3080 * q^16 + 5294 * q^18 - 13836 * q^22 + 4676 * q^23 + 1032 * q^24 - 8084 * q^26 - 2108 * q^28 + 7160 * q^31 - 6792 * q^32 - 5672 * q^33 + 21132 * q^34 + 18344 * q^36 + 19580 * q^38 - 44904 * q^39 + 11608 * q^41 + 17116 * q^42 + 72296 * q^44 - 28516 * q^46 - 44180 * q^47 + 88856 * q^48 + 18756 * q^49 + 39680 * q^52 - 100584 * q^54 - 53624 * q^56 - 5032 * q^57 - 59496 * q^58 - 59824 * q^62 - 240620 * q^63 - 11264 * q^64 - 56688 * q^66 - 11576 * q^68 - 200312 * q^71 - 235912 * q^72 + 105136 * q^73 + 78876 * q^74 - 153872 * q^76 - 95864 * q^78 + 282080 * q^79 + 65172 * q^81 + 223032 * q^82 - 297128 * q^84 + 27452 * q^86 + 332592 * q^87 - 86896 * q^88 - 3160 * q^89 - 107916 * q^92 + 148820 * q^94 + 395168 * q^96 - 147376 * q^97 - 216942 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more