LMFDB - Embedded newform 360.6.k.b.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,6,Mod(181,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("360.181");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	360.k (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:	$57.7381751327$
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^{42}\cdot 3^{8}\cdot 5^{12} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.1
Root			$2.93366 - 2.71913i$ of defining polynomial
Character	$\chi$	$=$	360.181
Dual form			360.6.k.b.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.65278 - 0.214529i) q^{2} +(31.9080 + 2.42537i) q^{4} -25.0000i q^{5} -107.536 q^{7} +(-179.848 - 20.5552i) q^{8} +O(q^{10})$	\(q+(-5.65278 - 0.214529i) q^{2} +(31.9080 + 2.42537i) q^{4} -25.0000i q^{5} -107.536 q^{7} +(-179.848 - 20.5552i) q^{8} +(-5.36321 + 141.320i) q^{10} -272.206i q^{11} -198.402i q^{13} +(607.879 + 23.0696i) q^{14} +(1012.24 + 154.777i) q^{16} -2065.79 q^{17} -1891.04i q^{19} +(60.6342 - 797.699i) q^{20} +(-58.3959 + 1538.72i) q^{22} +987.677 q^{23} -625.000 q^{25} +(-42.5629 + 1121.52i) q^{26} +(-3431.26 - 260.815i) q^{28} +8015.26i q^{29} +827.342 q^{31} +(-5688.74 - 1092.07i) q^{32} +(11677.5 + 443.170i) q^{34} +2688.40i q^{35} -9426.30i q^{37} +(-405.681 + 10689.6i) q^{38} +(-513.881 + 4496.21i) q^{40} +8221.07 q^{41} +9301.63i q^{43} +(660.198 - 8685.52i) q^{44} +(-5583.12 - 211.885i) q^{46} -13837.9 q^{47} -5242.97 q^{49} +(3532.99 + 134.080i) q^{50} +(481.198 - 6330.60i) q^{52} -27751.2i q^{53} -6805.14 q^{55} +(19340.2 + 2210.43i) q^{56} +(1719.50 - 45308.5i) q^{58} -25106.1i q^{59} -26404.6i q^{61} +(-4676.79 - 177.488i) q^{62} +(31923.0 + 7393.66i) q^{64} -4960.05 q^{65} +38563.9i q^{67} +(-65915.1 - 5010.29i) q^{68} +(576.739 - 15197.0i) q^{70} +71073.0 q^{71} +18622.0 q^{73} +(-2022.21 + 53284.8i) q^{74} +(4586.46 - 60339.1i) q^{76} +29271.9i q^{77} -75599.4 q^{79} +(3869.43 - 25305.9i) q^{80} +(-46471.9 - 1763.65i) q^{82} +125298. i q^{83} +51644.7i q^{85} +(1995.47 - 52580.1i) q^{86} +(-5595.25 + 48955.8i) q^{88} -30341.5 q^{89} +21335.4i q^{91} +(31514.7 + 2395.48i) q^{92} +(78222.6 + 2968.62i) q^{94} -47275.9 q^{95} +15635.2 q^{97} +(29637.4 + 1124.77i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 32 q^{4} - 196 q^{7} - 248 q^{8}+O(q^{10}) $ 20 * q - 2 * q^2 - 32 * q^4 - 196 * q^7 - 248 * q^8	$ 20 q - 2 q^{2} - 32 q^{4} - 196 q^{7} - 248 q^{8} - 50 q^{10} - 2708 q^{14} + 3080 q^{16} + 1900 q^{20} + 13836 q^{22} + 4676 q^{23} - 12500 q^{25} + 8084 q^{26} + 2108 q^{28} + 7160 q^{31} - 6792 q^{32} + 21132 q^{34} + 19580 q^{38} + 6200 q^{40} - 11608 q^{41} - 72296 q^{44} - 28516 q^{46} - 44180 q^{47} + 18756 q^{49} + 1250 q^{50} - 39680 q^{52} - 24200 q^{55} + 53624 q^{56} + 59496 q^{58} - 59824 q^{62} - 11264 q^{64} - 11576 q^{68} + 29800 q^{70} + 200312 q^{71} - 105136 q^{73} - 78876 q^{74} - 153872 q^{76} + 282080 q^{79} - 16000 q^{80} - 223032 q^{82} - 27452 q^{86} + 86896 q^{88} + 3160 q^{89} - 107916 q^{92} + 148820 q^{94} - 144400 q^{95} + 147376 q^{97} - 216942 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 32 * q^4 - 196 * q^7 - 248 * q^8 - 50 * q^10 - 2708 * q^14 + 3080 * q^16 + 1900 * q^20 + 13836 * q^22 + 4676 * q^23 - 12500 * q^25 + 8084 * q^26 + 2108 * q^28 + 7160 * q^31 - 6792 * q^32 + 21132 * q^34 + 19580 * q^38 + 6200 * q^40 - 11608 * q^41 - 72296 * q^44 - 28516 * q^46 - 44180 * q^47 + 18756 * q^49 + 1250 * q^50 - 39680 * q^52 - 24200 * q^55 + 53624 * q^56 + 59496 * q^58 - 59824 * q^62 - 11264 * q^64 - 11576 * q^68 + 29800 * q^70 + 200312 * q^71 - 105136 * q^73 - 78876 * q^74 - 153872 * q^76 + 282080 * q^79 - 16000 * q^80 - 223032 * q^82 - 27452 * q^86 + 86896 * q^88 + 3160 * q^89 - 107916 * q^92 + 148820 * q^94 - 144400 * q^95 + 147376 * q^97 - 216942 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$1$	$1$

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 $

$2$	−5.65278	−	0.214529i	−0.999281	−	0.0379236i
$2$	−5.65278	−	0.214529i	−0.999281	−	0.0379236i
$3$		0			0
$3$		0			0
$4$	31.9080	+	2.42537i	0.997124	+	0.0757927i
$5$		−	25.0000i		−	0.447214i
$5$		−	25.0000i		−	0.447214i
$6$		0			0
$7$	−107.536			−0.829487			−0.414743	−	0.909938i	$-0.636129\pi$
$7$	−107.536			−0.829487			−0.414743	+	0.909938i	$0.636129\pi$
$8$	−179.848	−	20.5552i	−0.993532	−	0.113553i
$9$		0			0
$10$	−5.36321	+	141.320i	−0.0169600	+	0.446892i
$11$		−	272.206i		−	0.678290i	−0.940734	−	0.339145i	$-0.889862\pi$
$11$		−	272.206i		−	0.678290i	0.940734	−	0.339145i	$-0.110138\pi$
$12$		0			0
$13$		−	198.402i		−	0.325602i	−0.986659	−	0.162801i	$-0.947947\pi$
$13$		−	198.402i		−	0.325602i	0.986659	−	0.162801i	$-0.0520529\pi$
$14$	607.879	+	23.0696i	0.828890	+	0.0314572i
$15$		0			0
$16$	1012.24	+	154.777i	0.988511	+	0.151149i
$17$	−2065.79			−1.73366			−0.866829	−	0.498606i	$-0.833846\pi$
$17$	−2065.79			−1.73366			−0.866829	+	0.498606i	$0.833846\pi$
$18$		0			0
$19$		−	1891.04i		−	1.20176i	−0.799341	−	0.600878i	$-0.794818\pi$
$19$		−	1891.04i		−	1.20176i	0.799341	−	0.600878i	$-0.205182\pi$
$20$	60.6342	−	797.699i	0.0338955	−	0.445927i
$21$		0			0
$22$	−58.3959	+	1538.72i	−0.0257232	+	0.677802i
$23$	987.677			0.389310			0.194655	−	0.980872i	$-0.437641\pi$
$23$	987.677			0.389310			0.194655	+	0.980872i	$0.437641\pi$
$24$		0			0
$25$	−625.000			−0.200000
$26$	−42.5629	+	1121.52i	−0.0123480	+	0.325368i
$27$		0			0
$28$	−3431.26	−	260.815i	−0.827101	−	0.0628690i
$29$			8015.26i			1.76979i	0.465788	+	0.884896i	$0.345771\pi$
$29$			8015.26i			1.76979i	−0.465788	+	0.884896i	$0.654229\pi$
$30$		0			0
$31$	827.342			0.154625			0.0773127	−	0.997007i	$-0.475366\pi$
$31$	827.342			0.154625			0.0773127	+	0.997007i	$0.475366\pi$
$32$	−5688.74	−	1092.07i	−0.982068	−	0.188529i
$33$		0			0
$34$	11677.5	+	443.170i	1.73241	+	0.0657466i
$35$			2688.40i			0.370958i
$36$		0			0
$37$		−	9426.30i		−	1.13198i	−0.824414	−	0.565988i	$-0.808495\pi$
$37$		−	9426.30i		−	1.13198i	0.824414	−	0.565988i	$-0.191505\pi$
$38$	−405.681	+	10689.6i	−0.0455749	+	1.20089i
$39$		0			0
$40$	−513.881	+	4496.21i	−0.0507823	+	0.444321i
$41$	8221.07			0.763780			0.381890	−	0.924208i	$-0.375273\pi$
$41$	8221.07			0.763780			0.381890	+	0.924208i	$0.375273\pi$
$42$		0			0
$43$			9301.63i			0.767164i	0.923507	+	0.383582i	$0.125310\pi$
$43$			9301.63i			0.767164i	−0.923507	+	0.383582i	$0.874690\pi$
$44$	660.198	−	8685.52i	0.0514094	−	0.676339i
$45$		0			0
$46$	−5583.12	−	211.885i	−0.389030	−	0.0147640i
$47$	−13837.9			−0.913745			−0.456873	−	0.889532i	$-0.651031\pi$
$47$	−13837.9			−0.913745			−0.456873	+	0.889532i	$0.651031\pi$
$48$		0			0
$49$	−5242.97			−0.311952
$50$	3532.99	+	134.080i	0.199856	+	0.00758473i
$51$		0			0
$52$	481.198	−	6330.60i	0.0246783	−	0.324666i
$53$		−	27751.2i		−	1.35704i	−0.734582	−	0.678520i	$-0.762622\pi$
$53$		−	27751.2i		−	1.35704i	0.734582	−	0.678520i	$-0.237378\pi$
$54$		0			0
$55$	−6805.14			−0.303340
$56$	19340.2	+	2210.43i	0.824122	+	0.0941905i
$57$		0			0
$58$	1719.50	−	45308.5i	0.0671170	−	1.76852i
$59$		−	25106.1i		−	0.938965i	−0.882942	−	0.469482i	$-0.844441\pi$
$59$		−	25106.1i		−	0.938965i	0.882942	−	0.469482i	$-0.155559\pi$
$60$		0			0
$61$		−	26404.6i		−	0.908563i	−0.890858	−	0.454282i	$-0.849896\pi$
$61$		−	26404.6i		−	0.908563i	0.890858	−	0.454282i	$-0.150104\pi$
$62$	−4676.79	−	177.488i	−0.154514	−	0.00586396i
$63$		0			0
$64$	31923.0	+	7393.66i	0.974212	+	0.225637i
$65$	−4960.05			−0.145614
$66$		0			0
$67$			38563.9i			1.04953i	0.851248	+	0.524764i	$0.175846\pi$
$67$			38563.9i			1.04953i	−0.851248	+	0.524764i	$0.824154\pi$
$68$	−65915.1	−	5010.29i	−1.72867	−	0.131399i
$69$		0			0
$70$	576.739	−	15197.0i	0.0140681	−	0.370691i
$71$	71073.0			1.67324			0.836621	−	0.547782i	$-0.184528\pi$
$71$	71073.0			1.67324			0.836621	+	0.547782i	$0.184528\pi$
$72$		0			0
$73$	18622.0			0.408996			0.204498	−	0.978867i	$-0.434444\pi$
$73$	18622.0			0.408996			0.204498	+	0.978867i	$0.434444\pi$
$74$	−2022.21	+	53284.8i	−0.0429286	+	1.13116i
$75$		0			0
$76$	4586.46	−	60339.1i	0.0910843	−	1.19830i
$77$			29271.9i			0.562632i
$78$		0			0
$79$	−75599.4			−1.36286			−0.681429	−	0.731884i	$-0.738641\pi$
$79$	−75599.4			−1.36286			−0.681429	+	0.731884i	$0.738641\pi$
$80$	3869.43	−	25305.9i	0.0675961	−	0.442076i
$81$		0			0
$82$	−46471.9	−	1763.65i	−0.763231	−	0.0289653i
$83$			125298.i			1.99641i	0.0599304	+	0.998203i	$0.480912\pi$
$83$			125298.i			1.99641i	−0.0599304	+	0.998203i	$0.519088\pi$
$84$		0			0
$85$			51644.7i			0.775315i
$86$	1995.47	−	52580.1i	0.0290936	−	0.766612i
$87$		0			0
$88$	−5595.25	+	48955.8i	−0.0770217	+	0.673903i
$89$	−30341.5			−0.406034			−0.203017	−	0.979175i	$-0.565075\pi$
$89$	−30341.5			−0.406034			−0.203017	+	0.979175i	$0.565075\pi$
$90$		0			0
$91$			21335.4i			0.270083i
$92$	31514.7	+	2395.48i	0.388190	+	0.0295068i
$93$		0			0
$94$	78222.6	+	2968.62i	0.913088	+	0.0346526i
$95$	−47275.9			−0.537441
$96$		0			0
$97$	15635.2			0.168723			0.0843617	−	0.996435i	$-0.473115\pi$
$97$	15635.2			0.168723			0.0843617	+	0.996435i	$0.473115\pi$
$98$	29637.4	+	1124.77i	0.311727	+	0.0118303i
$99$		0			0
$100$	−19942.5	−	1515.85i	−0.199425	−	0.0151585i
$101$			102692.i			1.00169i	0.865538	+	0.500843i	$0.166976\pi$
$101$			102692.i			1.00169i	−0.865538	+	0.500843i	$0.833024\pi$
$102$		0			0
$103$	−35981.8			−0.334187			−0.167093	−	0.985941i	$-0.553438\pi$
$103$	−35981.8			−0.334187			−0.167093	+	0.985941i	$0.553438\pi$
$104$	−4078.20	+	35682.3i	−0.0369730	+	0.323496i
$105$		0			0
$106$	−5953.43	+	156872.i	−0.0514639	+	1.35606i
$107$			94984.6i			0.802035i	0.916070	+	0.401018i	$0.131343\pi$
$107$			94984.6i			0.802035i	−0.916070	+	0.401018i	$0.868657\pi$
$108$		0			0
$109$			173158.i			1.39597i	0.716113	+	0.697984i	$0.245919\pi$
$109$			173158.i			1.39597i	−0.716113	+	0.697984i	$0.754081\pi$
$110$	38468.0	+	1459.90i	0.303122	+	0.0115038i
$111$		0			0
$112$	−108852.	−	16644.1i	−0.819957	−	0.125376i
$113$	237780.			1.75178			0.875891	−	0.482510i	$-0.160275\pi$
$113$	237780.			1.75178			0.875891	+	0.482510i	$0.160275\pi$
$114$		0			0
$115$		−	24691.9i		−	0.174105i
$116$	−19439.9	+	255750.i	−0.134137	+	1.76470i
$117$		0			0
$118$	−5385.97	+	141919.i	−0.0356090	+	0.938289i
$119$	222147.			1.43805
$120$		0			0
$121$	86955.1			0.539923
$122$	−5664.54	+	149260.i	−0.0344560	+	0.907910i
$123$		0			0
$124$	26398.8	+	2006.61i	0.154181	+	0.0117195i
$125$			15625.0i			0.0894427i
$126$		0			0
$127$	−63282.9			−0.348158			−0.174079	−	0.984732i	$-0.555695\pi$
$127$	−63282.9			−0.348158			−0.174079	+	0.984732i	$0.555695\pi$
$128$	−178867.	−	48643.2i	−0.964954	−	0.262420i
$129$		0			0
$130$	28038.1	+	1064.07i	0.145509	+	0.00552221i
$131$			180082.i			0.916835i	0.888737	+	0.458417i	$0.151584\pi$
$131$			180082.i			0.916835i	−0.888737	+	0.458417i	$0.848416\pi$
$132$		0			0
$133$			203355.i			0.996840i
$134$	8273.05	−	217993.i	0.0398019	−	1.04877i
$135$		0			0
$136$	371529.	+	42462.8i	1.72244	+	0.196862i
$137$	−365739.			−1.66483			−0.832414	−	0.554155i	$-0.813042\pi$
$137$	−365739.			−1.66483			−0.832414	+	0.554155i	$0.813042\pi$
$138$		0			0
$139$			111886.i			0.491180i	0.969374	+	0.245590i	$0.0789817\pi$
$139$			111886.i			0.491180i	−0.969374	+	0.245590i	$0.921018\pi$
$140$	−6520.37	+	85781.5i	−0.0281159	+	0.369891i
$141$		0			0
$142$	−401760.	−	15247.2i	−1.67204	−	0.0634554i
$143$	−54006.1			−0.220853
$144$		0			0
$145$	200381.			0.791475
$146$	−105266.	−	3994.95i	−0.408702	−	0.0155106i
$147$		0			0
$148$	22862.2	−	300774.i	0.0857955	−	1.12872i
$149$			136480.i			0.503621i	0.967777	+	0.251811i	$0.0810260\pi$
$149$			136480.i			0.503621i	−0.967777	+	0.251811i	$0.918974\pi$
$150$		0			0
$151$	186354.			0.665115			0.332557	−	0.943083i	$-0.392088\pi$
$151$	186354.			0.665115			0.332557	+	0.943083i	$0.392088\pi$
$152$	−38870.7	+	340100.i	−0.136463	+	1.19398i
$153$		0			0
$154$	6279.67	−	165468.i	0.0213371	−	0.562228i
$155$		−	20683.6i		−	0.0691506i
$156$		0			0
$157$			74689.6i			0.241830i	0.992663	+	0.120915i	$0.0385829\pi$
$157$			74689.6i			0.241830i	−0.992663	+	0.120915i	$0.961417\pi$
$158$	427347.	+	16218.2i	1.36188	+	0.0516845i
$159$		0			0
$160$	−27301.9	+	142219.i	−0.0843126	+	0.439194i
$161$	−106211.			−0.322927
$162$		0			0
$163$			548779.i			1.61781i	0.587937	+	0.808907i	$0.299940\pi$
$163$			548779.i			1.61781i	−0.587937	+	0.808907i	$0.700060\pi$
$164$	262317.	+	19939.1i	0.761583	+	0.0578890i
$165$		0			0
$166$	26880.0	−	708282.i	0.0757109	−	1.99497i
$167$	−224312.			−0.622387			−0.311194	−	0.950347i	$-0.600729\pi$
$167$	−224312.			−0.622387			−0.311194	+	0.950347i	$0.600729\pi$
$168$		0			0
$169$	331930.			0.893983
$170$	11079.3	−	291936.i	0.0294028	−	0.774758i
$171$		0			0
$172$	−22559.9	+	296796.i	−0.0581454	+	0.764957i
$173$			165260.i			0.419809i	0.977722	+	0.209905i	$0.0673154\pi$
$173$			165260.i			0.419809i	−0.977722	+	0.209905i	$0.932685\pi$
$174$		0			0
$175$	67210.1			0.165897
$176$	42131.2	−	275536.i	0.102523	−	0.670497i
$177$		0			0
$178$	171514.	+	6509.12i	0.405742	+	0.0153983i
$179$			431975.i			1.00769i	0.863795	+	0.503844i	$0.168081\pi$
$179$			431975.i			1.00769i	−0.863795	+	0.503844i	$0.831919\pi$
$180$		0			0
$181$			216944.i			0.492210i	0.969243	+	0.246105i	$0.0791508\pi$
$181$			216944.i			0.492210i	−0.969243	+	0.246105i	$0.920849\pi$
$182$	4577.05	−	120604.i	0.0102425	−	0.269889i
$183$		0			0
$184$	−177632.	−	20301.9i	−0.386792	−	0.0442072i
$185$	−235658.			−0.506235
$186$		0			0
$187$			562319.i			1.17592i
$188$	−441539.	−	33562.0i	−0.911117	−	0.0692552i
$189$		0			0
$190$	267241.	+	10142.0i	0.537055	+	0.0203817i
$191$	34566.0			0.0685592			0.0342796	−	0.999412i	$-0.489086\pi$
$191$	34566.0			0.0685592			0.0342796	+	0.999412i	$0.489086\pi$
$192$		0			0
$193$	−473601.			−0.915208			−0.457604	−	0.889156i	$-0.651292\pi$
$193$	−473601.			−0.915208			−0.457604	+	0.889156i	$0.651292\pi$
$194$	−88382.7	−	3354.21i	−0.168602	−	0.00639861i
$195$		0			0
$196$	−167293.	−	12716.1i	−0.311055	−	0.0236437i
$197$		−	394784.i		−	0.724760i	−0.932030	−	0.362380i	$-0.881964\pi$
$197$		−	394784.i		−	0.724760i	0.932030	−	0.362380i	$-0.118036\pi$
$198$		0			0
$199$	−477089.			−0.854017			−0.427009	−	0.904248i	$-0.640433\pi$
$199$	−477089.			−0.854017			−0.427009	+	0.904248i	$0.640433\pi$
$200$	112405.	+	12847.0i	0.198706	+	0.0227106i
$201$		0			0
$202$	22030.3	−	580493.i	0.0379875	−	1.00096i
$203$		−	861930.i		−	1.46802i
$204$		0			0
$205$		−	205527.i		−	0.341573i
$206$	203397.	+	7719.11i	0.333946	+	0.0126736i
$207$		0			0
$208$	30708.1	−	200829.i	0.0492146	−	0.321862i
$209$	−514751.			−0.815139
$210$		0			0
$211$		−	435894.i		−	0.674023i	−0.941500	−	0.337012i	$-0.890584\pi$
$211$		−	435894.i		−	0.674023i	0.941500	−	0.337012i	$-0.109416\pi$
$212$	67306.9	−	885485.i	0.102854	−	1.35314i
$213$		0			0
$214$	20376.9	−	536927.i	0.0304161	−	0.801458i
$215$	232541.			0.343086
$216$		0			0
$217$	−88969.2			−0.128260
$218$	37147.3	−	978823.i	0.0529402	−	1.39496i
$219$		0			0
$220$	−217138.	−	16505.0i	−0.302468	−	0.0229910i
$221$			409856.i			0.564483i
$222$		0			0
$223$	1.14075e6			1.53613			0.768067	−	0.640369i	$-0.221219\pi$
$223$	1.14075e6			1.53613			0.768067	+	0.640369i	$0.221219\pi$
$224$	611746.	+	117437.i	0.814612	+	0.156382i
$225$		0			0
$226$	−1.34412e6	−	51010.7i	−1.75052	−	0.0664339i
$227$			1.08895e6i			1.40262i	0.712854	+	0.701312i	$0.247402\pi$
$227$			1.08895e6i			1.40262i	−0.712854	+	0.701312i	$0.752598\pi$
$228$		0			0
$229$		−	474386.i		−	0.597783i	−0.954287	−	0.298891i	$-0.903383\pi$
$229$		−	474386.i		−	0.597783i	0.954287	−	0.298891i	$-0.0966168\pi$
$230$	−5297.12	+	139578.i	−0.00660268	+	0.173979i
$231$		0			0
$232$	164756.	−	1.44153e6i	0.200965	−	1.75835i
$233$	271057.			0.327093			0.163547	−	0.986536i	$-0.447707\pi$
$233$	271057.			0.327093			0.163547	+	0.986536i	$0.447707\pi$
$234$		0			0
$235$			345947.i			0.408639i
$236$	60891.5	−	801084.i	0.0711667	−	0.936264i
$237$		0			0
$238$	−1.25575e6	−	47656.8i	−1.43701	−	0.0545359i
$239$	824404.			0.933567			0.466784	−	0.884372i	$-0.345413\pi$
$239$	824404.			0.933567			0.466784	+	0.884372i	$0.345413\pi$
$240$		0			0
$241$	−86717.2			−0.0961750			−0.0480875	−	0.998843i	$-0.515313\pi$
$241$	−86717.2			−0.0961750			−0.0480875	+	0.998843i	$0.515313\pi$
$242$	−491539.	−	18654.4i	−0.539535	−	0.0204758i
$243$		0			0
$244$	64040.9	−	842517.i	0.0688625	−	0.905950i
$245$			131074.i			0.139509i
$246$		0			0
$247$	−375186.			−0.391294
$248$	−148796.	−	17006.2i	−0.153625	−	0.0175581i
$249$		0			0
$250$	3352.01	−	88324.8i	0.00339199	−	0.0893784i
$251$			411977.i			0.412751i	0.978473	+	0.206376i	$0.0661669\pi$
$251$			411977.i			0.412751i	−0.978473	+	0.206376i	$0.933833\pi$
$252$		0			0
$253$		−	268851.i		−	0.264065i
$254$	357725.	+	13576.0i	0.347908	+	0.0132034i
$255$		0			0
$256$	1.00066e6	+	313341.i	0.954308	+	0.298826i
$257$	88057.5			0.0831637			0.0415818	−	0.999135i	$-0.486760\pi$
$257$	88057.5			0.0831637			0.0415818	+	0.999135i	$0.486760\pi$
$258$		0			0
$259$			1.01367e6i			0.938958i
$260$	−158265.	−	12029.9i	−0.145195	−	0.0110365i
$261$		0			0
$262$	38632.6	−	1.01796e6i	0.0347697	−	0.916175i
$263$	126284.			0.112579			0.0562896	−	0.998414i	$-0.482073\pi$
$263$	126284.			0.112579			0.0562896	+	0.998414i	$0.482073\pi$
$264$		0			0
$265$	−693781.			−0.606886
$266$	43625.4	−	1.14952e6i	0.0378038	−	0.996123i
$267$		0			0
$268$	−93531.6	+	1.23049e6i	−0.0795465	+	1.04651i
$269$		−	1.88178e6i		−	1.58558i	−0.609495	−	0.792790i	$-0.708628\pi$
$269$		−	1.88178e6i		−	1.58558i	0.609495	−	0.792790i	$-0.291372\pi$
$270$		0			0
$271$	−1.17095e6			−0.968532			−0.484266	−	0.874921i	$-0.660913\pi$
$271$	−1.17095e6			−0.968532			−0.484266	+	0.874921i	$0.660913\pi$
$272$	−2.09106e6	−	319736.i	−1.71374	−	0.262041i
$273$		0			0
$274$	2.06744e6	+	78461.3i	1.66363	+	0.0631363i
$275$			170128.i			0.135658i
$276$		0			0
$277$			1.11420e6i			0.872496i	0.899827	+	0.436248i	$0.143693\pi$
$277$			1.11420e6i			0.872496i	−0.899827	+	0.436248i	$0.856307\pi$
$278$	24002.8	−	632470.i	0.0186273	−	0.490826i
$279$		0			0
$280$	55260.8	−	483505.i	0.0421233	−	0.368558i
$281$	1.87861e6			1.41929			0.709646	−	0.704558i	$-0.248855\pi$
$281$	1.87861e6			1.41929			0.709646	+	0.704558i	$0.248855\pi$
$282$		0			0
$283$			3072.89i			0.00228077i	0.999999	+	0.00114038i	$0.000362996\pi$
$283$			3072.89i			0.00228077i	−0.999999	+	0.00114038i	$0.999637\pi$
$284$	2.26779e6	+	172378.i	1.66843	+	0.126820i
$285$		0			0
$286$	305285.	+	11585.9i	0.220694	+	0.00837554i
$287$	−884062.			−0.633546
$288$		0			0
$289$	2.84762e6			2.00557
$290$	−1.13271e6	−	42987.5i	−0.790906	−	0.0300156i
$291$		0			0
$292$	594190.	+	45165.2i	0.407820	+	0.0309989i
$293$		−	2.45968e6i		−	1.67382i	−0.547339	−	0.836911i	$-0.684359\pi$
$293$		−	2.45968e6i		−	1.67382i	0.547339	−	0.836911i	$-0.315641\pi$
$294$		0			0
$295$	−627653.			−0.419918
$296$	−193760.	+	1.69531e6i	−0.128539	+	1.12465i
$297$		0			0
$298$	29278.9	−	771493.i	0.0190992	−	0.503259i
$299$		−	195957.i		−	0.126760i
$300$		0			0
$301$		−	1.00026e6i		−	0.636352i
$302$	−1.05342e6	−	39978.3i	−0.664636	−	0.0252236i
$303$		0			0
$304$	292689.	−	1.91417e6i	0.181645	−	1.18795i
$305$	−660115.			−0.406322
$306$		0			0
$307$			257478.i			0.155917i	0.996957	+	0.0779585i	$0.0248402\pi$
$307$			257478.i			0.155917i	−0.996957	+	0.0779585i	$0.975160\pi$
$308$	−70995.2	+	934008.i	−0.0426434	+	0.561014i
$309$		0			0
$310$	−4437.21	+	116920.i	−0.00262244	+	0.0691009i
$311$	−2.43192e6			−1.42576			−0.712882	−	0.701284i	$-0.752610\pi$
$311$	−2.43192e6			−1.42576			−0.712882	+	0.701284i	$0.752610\pi$
$312$		0			0
$313$	−2.62542e6			−1.51474			−0.757369	−	0.652987i	$-0.773515\pi$
$313$	−2.62542e6			−1.51474			−0.757369	+	0.652987i	$0.773515\pi$
$314$	16023.0	−	422204.i	0.00917109	−	0.241656i
$315$		0			0
$316$	−2.41222e6	−	183356.i	−1.35894	−	0.103295i
$317$		−	2.54754e6i		−	1.42388i	−0.702240	−	0.711940i	$-0.747817\pi$
$317$		−	2.54754e6i		−	1.42388i	0.702240	−	0.711940i	$-0.252183\pi$
$318$		0			0
$319$	2.18180e6			1.20043
$320$	184841.	−	798074.i	0.100908	−	0.435681i
$321$		0			0
$322$	600388.	+	22785.3i	0.322695	+	0.0122466i
$323$			3.90648e6i			2.08343i
$324$		0			0
$325$			124001.i			0.0651205i
$326$	117729.	−	3.10213e6i	0.0613534	−	1.61665i
$327$		0			0
$328$	−1.47855e6	−	168986.i	−0.758840	−	0.0867294i
$329$	1.48807e6			0.757940
$330$		0			0
$331$			2.11710e6i			1.06211i	0.847336	+	0.531057i	$0.178205\pi$
$331$			2.11710e6i			1.06211i	−0.847336	+	0.531057i	$0.821795\pi$
$332$	−303893.	+	3.99800e6i	−0.151313	+	1.99066i
$333$		0			0
$334$	1.26799e6	+	48121.2i	0.621940	+	0.0236032i
$335$	964097.			0.469363
$336$		0			0
$337$	−1.56954e6			−0.752832			−0.376416	−	0.926451i	$-0.622844\pi$
$337$	−1.56954e6			−0.752832			−0.376416	+	0.926451i	$0.622844\pi$
$338$	−1.87633e6	−	71208.4i	−0.893340	−	0.0339031i
$339$		0			0
$340$	−125257.	+	1.64788e6i	−0.0587633	+	0.773085i
$341$		−	225207.i		−	0.104881i
$342$		0			0
$343$	2.37117e6			1.08825
$344$	191197.	−	1.67288e6i	0.0871136	−	0.762202i
$345$		0			0
$346$	35452.9	−	934178.i	0.0159207	−	0.419507i
$347$		−	428538.i		−	0.191058i	−0.995427	−	0.0955292i	$-0.969546\pi$
$347$		−	428538.i		−	0.191058i	0.995427	−	0.0955292i	$-0.0304543\pi$
$348$		0			0
$349$		−	522898.i		−	0.229802i	−0.993377	−	0.114901i	$-0.963345\pi$
$349$		−	522898.i		−	0.229802i	0.993377	−	0.114901i	$-0.0366551\pi$
$350$	−379924.	−	14418.5i	−0.165778	−	0.00629143i
$351$		0			0
$352$	−297269.	+	1.54851e6i	−0.127877	+	0.666126i
$353$	−1.89389e6			−0.808943			−0.404472	−	0.914550i	$-0.632545\pi$
$353$	−1.89389e6			−0.808943			−0.404472	+	0.914550i	$0.632545\pi$
$354$		0			0
$355$		−	1.77682e6i		−	0.748297i
$356$	−968136.	−	73589.3i	−0.404866	−	0.0307744i
$357$		0			0
$358$	92671.0	−	2.44186e6i	0.0382152	−	1.00696i
$359$	2.57094e6			1.05282			0.526412	−	0.850229i	$-0.323537\pi$
$359$	2.57094e6			1.05282			0.526412	+	0.850229i	$0.323537\pi$
$360$		0			0
$361$	−1.09992e6			−0.444216
$362$	46540.6	−	1.22634e6i	0.0186664	−	0.491856i
$363$		0			0
$364$	−51746.1	+	680768.i	−0.0204703	+	0.269306i
$365$		−	465550.i		−	0.182909i
$366$		0			0
$367$	−2.47263e6			−0.958282			−0.479141	−	0.877738i	$-0.659052\pi$
$367$	−2.47263e6			−0.958282			−0.479141	+	0.877738i	$0.659052\pi$
$368$	999761.	+	152870.i	0.384837	+	0.0588439i
$369$		0			0
$370$	1.33212e6	+	50555.3i	0.505871	+	0.0191983i
$371$			2.98426e6i			1.12565i
$372$		0			0
$373$			2.62533e6i			0.977038i	0.872553	+	0.488519i	$0.162463\pi$
$373$			2.62533e6i			0.977038i	−0.872553	+	0.488519i	$0.837537\pi$
$374$	120633.	−	3.17867e6i	0.0445953	−	1.17508i
$375$		0			0
$376$	2.48872e6	+	284441.i	0.907835	+	0.103758i
$377$	1.59024e6			0.576249
$378$		0			0
$379$			2.14283e6i			0.766284i	0.923689	+	0.383142i	$0.125158\pi$
$379$			2.14283e6i			0.766284i	−0.923689	+	0.383142i	$0.874842\pi$
$380$	−1.50848e6	−	114661.i	−0.535896	−	0.0407341i
$381$		0			0
$382$	−195394.	−	7415.39i	−0.0685098	−	0.00260001i
$383$	641783.			0.223559			0.111779	−	0.993733i	$-0.464345\pi$
$383$	641783.			0.223559			0.111779	+	0.993733i	$0.464345\pi$
$384$		0			0
$385$	731799.			0.251617
$386$	2.67717e6	+	101601.i	0.914549	+	0.0347080i
$387$		0			0
$388$	498889.	+	37921.2i	0.168238	+	0.0127880i
$389$			2.36321e6i			0.791823i	0.918289	+	0.395911i	$0.129571\pi$
$389$			2.36321e6i			0.791823i	−0.918289	+	0.395911i	$0.870429\pi$
$390$		0			0
$391$	−2.04033e6			−0.674930
$392$	942941.	+	107771.i	0.309934	+	0.0354230i
$393$		0			0
$394$	−84692.5	+	2.23163e6i	−0.0274855	+	0.724239i
$395$			1.88998e6i			0.609489i
$396$		0			0
$397$		−	403888.i		−	0.128613i	−0.997930	−	0.0643065i	$-0.979516\pi$
$397$		−	403888.i		−	0.128613i	0.997930	−	0.0643065i	$-0.0204835\pi$
$398$	2.69688e6	+	102349.i	0.853403	+	0.0323874i
$399$		0			0
$400$	−632647.	−	96735.6i	−0.197702	−	0.0302299i
$401$	−2.28335e6			−0.709108			−0.354554	−	0.935036i	$-0.615367\pi$
$401$	−2.28335e6			−0.709108			−0.354554	+	0.935036i	$0.615367\pi$
$402$		0			0
$403$		−	164146.i		−	0.0503464i
$404$	−249065.	+	3.27668e6i	−0.0759204	+	0.998804i
$405$		0			0
$406$	−184909.	+	4.87230e6i	−0.0556726	+	1.46696i
$407$	−2.56589e6			−0.767807
$408$		0			0
$409$	3.27964e6			0.969435			0.484717	−	0.874671i	$-0.338922\pi$
$409$	3.27964e6			0.969435			0.484717	+	0.874671i	$0.338922\pi$
$410$	−44091.3	+	1.16180e6i	−0.0129537	+	0.341327i
$411$		0			0
$412$	−1.14810e6	−	87269.0i	−0.333226	−	0.0253289i
$413$			2.69981e6i			0.778859i
$414$		0			0
$415$	3.13245e6			0.892820
$416$	−216670.	+	1.12866e6i	−0.0613854	+	0.319764i
$417$		0			0
$418$	2.90978e6	+	110429.i	0.814552	+	0.0309130i
$419$		−	604670.i		−	0.168261i	−0.996455	−	0.0841305i	$-0.973189\pi$
$419$		−	604670.i		−	0.168261i	0.996455	−	0.0841305i	$-0.0268113\pi$
$420$		0			0
$421$		−	3.46346e6i		−	0.952367i	−0.879346	−	0.476184i	$-0.842020\pi$
$421$		−	3.46346e6i		−	0.952367i	0.879346	−	0.476184i	$-0.157980\pi$
$422$	−93511.7	+	2.46402e6i	−0.0255614	+	0.673538i
$423$		0			0
$424$	−570433.	+	4.99102e6i	−0.154096	+	1.34826i
$425$	1.29112e6			0.346732
$426$		0			0
$427$			2.83945e6i			0.753641i
$428$	−230372.	+	3.03076e6i	−0.0607884	+	0.799728i
$429$		0			0
$430$	−1.31450e6	−	49886.6i	−0.342839	−	0.0130111i
$431$	−5.00345e6			−1.29741			−0.648704	−	0.761041i	$-0.724689\pi$
$431$	−5.00345e6			−1.29741			−0.648704	+	0.761041i	$0.724689\pi$
$432$		0			0
$433$	−4.11259e6			−1.05413			−0.527067	−	0.849824i	$-0.676708\pi$
$433$	−4.11259e6			−1.05413			−0.527067	+	0.849824i	$0.676708\pi$
$434$	502924.	+	19086.4i	0.128167	+	0.00486408i
$435$		0			0
$436$	−419971.	+	5.52511e6i	−0.105804	+	1.39195i
$437$		−	1.86773e6i		−	0.467855i
$438$		0			0
$439$	4.20313e6			1.04091			0.520454	−	0.853890i	$-0.325763\pi$
$439$	4.20313e6			1.04091			0.520454	+	0.853890i	$0.325763\pi$
$440$	1.22389e6	+	139881.i	0.301378	+	0.0344451i
$441$		0			0
$442$	87925.9	−	2.31683e6i	0.0214073	−	0.564077i
$443$		−	1.32165e6i		−	0.319969i	−0.987120	−	0.159984i	$-0.948856\pi$
$443$		−	1.32165e6i		−	0.319969i	0.987120	−	0.159984i	$-0.0511443\pi$
$444$		0			0
$445$			758538.i			0.181584i
$446$	−6.44843e6	−	244724.i	−1.53503	−	0.0582558i
$447$		0			0
$448$	−3.43287e6	−	795086.i	−0.808095	−	0.187163i
$449$	5.52202e6			1.29265			0.646327	−	0.763061i	$-0.276304\pi$
$449$	5.52202e6			1.29265			0.646327	+	0.763061i	$0.276304\pi$
$450$		0			0
$451$		−	2.23782e6i		−	0.518064i
$452$	7.58709e6	+	576705.i	1.74674	+	0.132772i
$453$		0			0
$454$	233610.	−	6.15557e6i	0.0531926	−	1.40162i
$455$	533385.			0.120785
$456$		0			0
$457$	3.46838e6			0.776849			0.388424	−	0.921481i	$-0.373019\pi$
$457$	3.46838e6			0.776849			0.388424	+	0.921481i	$0.373019\pi$
$458$	−101769.	+	2.68160e6i	−0.0226701	+	0.597352i
$459$		0			0
$460$	59887.0	−	787869.i	0.0131959	−	0.173604i
$461$		−	2.42345e6i		−	0.531107i	−0.964096	−	0.265554i	$-0.914445\pi$
$461$		−	2.42345e6i		−	0.531107i	0.964096	−	0.265554i	$-0.0855547\pi$
$462$		0			0
$463$	−6.58501e6			−1.42759			−0.713796	−	0.700354i	$-0.753026\pi$
$463$	−6.58501e6			−1.42759			−0.713796	+	0.700354i	$0.753026\pi$
$464$	−1.24058e6	+	8.11332e6i	−0.267503	+	1.74946i
$465$		0			0
$466$	−1.53223e6	−	58149.5i	−0.326858	−	0.0124046i
$467$			1.15697e6i			0.245488i	0.992438	+	0.122744i	$0.0391694\pi$
$467$			1.15697e6i			0.245488i	−0.992438	+	0.122744i	$0.960831\pi$
$468$		0			0
$469$		−	4.14701e6i		−	0.870569i
$470$	74215.5	−	1.95557e6i	0.0154971	−	0.408345i
$471$		0			0
$472$	−516062.	+	4.51529e6i	−0.106622	+	0.932891i
$473$	2.53196e6			0.520359
$474$		0			0
$475$			1.18190e6i			0.240351i
$476$	7.08825e6	+	538788.i	1.43391	+	0.108993i
$477$		0			0
$478$	−4.66018e6	−	176858.i	−0.932896	−	0.0354043i
$479$	380517.			0.0757767			0.0378883	−	0.999282i	$-0.487937\pi$
$479$	380517.			0.0757767			0.0378883	+	0.999282i	$0.487937\pi$
$480$		0			0
$481$	−1.87020e6			−0.368574
$482$	490193.	+	18603.3i	0.0961059	+	0.00364731i
$483$		0			0
$484$	2.77456e6	+	210898.i	0.538370	+	0.0409222i
$485$		−	390881.i		−	0.0754554i
$486$		0			0
$487$	2.67715e6			0.511505			0.255753	−	0.966742i	$-0.417677\pi$
$487$	2.67715e6			0.511505			0.255753	+	0.966742i	$0.417677\pi$
$488$	−542753.	+	4.74883e6i	−0.103170	+	0.902687i
$489$		0			0
$490$	28119.2	−	740935.i	0.00529069	−	0.139409i
$491$			5.10695e6i			0.956000i	0.878360	+	0.478000i	$0.158638\pi$
$491$			5.10695e6i			0.956000i	−0.878360	+	0.478000i	$0.841362\pi$
$492$		0			0
$493$		−	1.65578e7i		−	3.06822i
$494$	2.12084e6	+	80488.0i	0.391013	+	0.0148393i
$495$		0			0
$496$	837465.	+	128054.i	0.152849	+	0.0233715i
$497$	−7.64292e6			−1.38793
$498$		0			0
$499$			259376.i			0.0466313i	0.999728	+	0.0233157i	$0.00742228\pi$
$499$			259376.i			0.0466313i	−0.999728	+	0.0233157i	$0.992578\pi$
$500$	−37896.4	+	498562.i	−0.00677911	+	0.0891854i
$501$		0			0
$502$	88380.7	−	2.32882e6i	0.0156530	−	0.412454i
$503$	324388.			0.0571669			0.0285835	−	0.999591i	$-0.490900\pi$
$503$	324388.			0.0571669			0.0285835	+	0.999591i	$0.490900\pi$
$504$		0			0
$505$	2.56729e6			0.447967
$506$	−57676.2	+	1.51976e6i	−0.0100143	+	0.263875i
$507$		0			0
$508$	−2.01923e6	−	153484.i	−0.347157	−	0.0263879i
$509$		−	1.13575e7i		−	1.94307i	−0.236890	−	0.971537i	$-0.576128\pi$
$509$		−	1.13575e7i		−	1.94307i	0.236890	−	0.971537i	$-0.423872\pi$
$510$		0			0
$511$	−2.00254e6			−0.339257
$512$	−5.58932e6	−	1.98592e6i	−0.942289	−	0.334802i
$513$		0			0
$514$	−497770.	−	18890.8i	−0.0831038	−	0.00315387i
$515$			899544.i			0.149453i
$516$		0			0
$517$			3.76675e6i			0.619784i
$518$	217461.	−	5.73005e6i	0.0356087	−	0.938283i
$519$		0			0
$520$	892057.	+	101955.i	0.144672	+	0.0165348i
$521$	−9.15918e6			−1.47830			−0.739149	−	0.673541i	$-0.764772\pi$
$521$	−9.15918e6			−1.47830			−0.739149	+	0.673541i	$0.764772\pi$
$522$		0			0
$523$			7.08351e6i			1.13238i	0.824273	+	0.566192i	$0.191584\pi$
$523$			7.08351e6i			1.13238i	−0.824273	+	0.566192i	$0.808416\pi$
$524$	−436764.	+	5.74604e6i	−0.0694894	+	0.914198i
$525$		0			0
$526$	−713855.	−	27091.5i	−0.112498	−	0.00426942i
$527$	−1.70911e6			−0.268068
$528$		0			0
$529$	−5.46084e6			−0.848438
$530$	3.92179e6	+	148836.i	0.606450	+	0.0230153i
$531$		0			0
$532$	−493210.	+	6.48864e6i	−0.0755532	+	0.993973i
$533$		−	1.63108e6i		−	0.248689i
$534$		0			0
$535$	2.37461e6			0.358681
$536$	792690.	−	6.93566e6i	0.119177	−	1.04274i
$537$		0			0
$538$	−403696.	+	1.06373e7i	−0.0601310	+	1.58444i
$539$			1.42717e6i			0.211594i
$540$		0			0
$541$		−	2.53136e6i		−	0.371843i	−0.982565	−	0.185922i	$-0.940473\pi$
$541$		−	2.53136e6i		−	0.371843i	0.982565	−	0.185922i	$-0.0595271\pi$
$542$	6.61911e6	+	251201.i	0.967835	+	0.0367303i
$543$		0			0
$544$	1.17517e7	+	2.25599e6i	1.70257	+	0.326844i
$545$	4.32894e6			0.624296
$546$		0			0
$547$		−	1.30020e7i		−	1.85798i	−0.370108	−	0.928989i	$-0.620679\pi$
$547$		−	1.30020e7i		−	1.85798i	0.370108	−	0.928989i	$-0.379321\pi$
$548$	−1.16700e7	−	887050.i	−1.66004	−	0.126182i
$549$		0			0
$550$	36497.4	−	961700.i	0.00514464	−	0.135560i
$551$	1.51571e7			2.12686
$552$		0			0
$553$	8.12967e6			1.13047
$554$	239027.	−	6.29833e6i	0.0330882	−	0.871868i
$555$		0			0
$556$	−271366.	+	3.57007e6i	−0.0372279	+	0.489767i
$557$		−	5.70438e6i		−	0.779059i	−0.921014	−	0.389530i	$-0.872638\pi$
$557$		−	5.70438e6i		−	0.779059i	0.921014	−	0.389530i	$-0.127362\pi$
$558$		0			0
$559$	1.84546e6			0.249790
$560$	−416103.	+	2.72130e6i	−0.0560700	+	0.366696i
$561$		0			0
$562$	−1.06194e7	−	403016.i	−1.41827	−	0.0538247i
$563$			1.98939e6i			0.264514i	0.991215	+	0.132257i	$0.0422224\pi$
$563$			1.98939e6i			0.264514i	−0.991215	+	0.132257i	$0.957778\pi$
$564$		0			0
$565$		−	5.94451e6i		−	0.783420i
$566$	659.223	−	17370.4i	8.64951e−5	−	0.00227913i
$567$		0			0
$568$	−1.27824e7	−	1.46092e6i	−1.66242	−	0.190001i
$569$	−1.30277e6			−0.168689			−0.0843447	−	0.996437i	$-0.526880\pi$
$569$	−1.30277e6			−0.168689			−0.0843447	+	0.996437i	$0.526880\pi$
$570$		0			0
$571$		−	2.90628e6i		−	0.373033i	−0.982452	−	0.186517i	$-0.940280\pi$
$571$		−	2.90628e6i		−	0.373033i	0.982452	−	0.186517i	$-0.0597199\pi$
$572$	−1.72322e6	−	130985.i	−0.220218	−	0.0167390i
$573$		0			0
$574$	4.99741e6	+	189656.i	0.633090	+	0.0240264i
$575$	−617298.			−0.0778619
$576$		0			0
$577$	4.01853e6			0.502490			0.251245	−	0.967923i	$-0.419160\pi$
$577$	4.01853e6			0.502490			0.251245	+	0.967923i	$0.419160\pi$
$578$	−1.60970e7	−	610896.i	−2.00413	−	0.0760585i
$579$		0			0
$580$	6.39376e6	+	485998.i	0.789199	+	0.0599881i
$581$		−	1.34741e7i		−	1.65599i
$582$		0			0
$583$	−7.55404e6			−0.920466
$584$	−3.34914e6	−	382780.i	−0.406351	−	0.0464426i
$585$		0			0
$586$	−527671.	+	1.39040e7i	−0.0634774	+	1.67262i
$587$			1.29654e7i			1.55307i	0.630074	+	0.776535i	$0.283025\pi$
$587$			1.29654e7i			1.55307i	−0.630074	+	0.776535i	$0.716975\pi$
$588$		0			0
$589$		−	1.56454e6i		−	0.185822i
$590$	3.54798e6	+	134649.i	0.419616	+	0.0159248i
$591$		0			0
$592$	1.45897e6	−	9.54163e6i	0.171097	−	1.11897i
$593$	107000.			0.0124953			0.00624767	−	0.999980i	$-0.498011\pi$
$593$	107000.			0.0124953			0.00624767	+	0.999980i	$0.498011\pi$
$594$		0			0
$595$		−	5.55367e6i		−	0.643114i
$596$	−331015.	+	4.35480e6i	−0.0381708	+	0.502173i
$597$		0			0
$598$	−42038.4	+	1.10770e6i	−0.00480721	+	0.126669i
$599$	−1.06394e7			−1.21157			−0.605785	−	0.795629i	$-0.707141\pi$
$599$	−1.06394e7			−1.21157			−0.605785	+	0.795629i	$0.707141\pi$
$600$		0			0
$601$	−6.42705e6			−0.725814			−0.362907	−	0.931825i	$-0.618216\pi$
$601$	−6.42705e6			−0.725814			−0.362907	+	0.931825i	$0.618216\pi$
$602$	−214585.	+	5.65427e6i	−0.0241328	+	0.635894i
$603$		0			0
$604$	5.94618e6	+	451977.i	0.663202	+	0.0504109i
$605$		−	2.17388e6i		−	0.241461i
$606$		0			0
$607$	1.96807e6			0.216805			0.108403	−	0.994107i	$-0.465426\pi$
$607$	1.96807e6			0.216805			0.108403	+	0.994107i	$0.465426\pi$
$608$	−2.06515e6	+	1.07576e7i	−0.226565	+	1.18021i
$609$		0			0
$610$	3.73149e6	+	141614.i	0.406030	+	0.0154092i
$611$			2.74546e6i			0.297518i
$612$		0			0
$613$			8.12485e6i			0.873301i	0.899631	+	0.436651i	$0.143835\pi$
$613$			8.12485e6i			0.873301i	−0.899631	+	0.436651i	$0.856165\pi$
$614$	55236.3	−	1.45547e6i	0.00591294	−	0.155805i
$615$		0			0
$616$	601692.	−	5.26451e6i	0.0638885	−	0.558993i
$617$	−1.40750e6			−0.148846			−0.0744229	−	0.997227i	$-0.523711\pi$
$617$	−1.40750e6			−0.148846			−0.0744229	+	0.997227i	$0.523711\pi$
$618$		0			0
$619$		−	5.01827e6i		−	0.526414i	−0.964739	−	0.263207i	$-0.915220\pi$
$619$		−	5.01827e6i		−	0.526414i	0.964739	−	0.263207i	$-0.0847802\pi$
$620$	50165.2	−	659970.i	0.00524111	−	0.0689517i
$621$		0			0
$622$	1.37471e7	+	521715.i	1.42474	+	0.0540702i
$623$	3.26281e6			0.336800
$624$		0			0
$625$	390625.			0.0400000
$626$	1.48409e7	+	563227.i	1.51365	+	0.0574444i
$627$		0			0
$628$	−181150.	+	2.38319e6i	−0.0183290	+	0.241135i
$629$			1.94727e7i			1.96246i
$630$		0			0
$631$	5.59458e6			0.559363			0.279682	−	0.960093i	$-0.409771\pi$
$631$	5.59458e6			0.559363			0.279682	+	0.960093i	$0.409771\pi$
$632$	1.35964e7	+	1.55396e6i	1.35404	+	0.154756i
$633$		0			0
$634$	−546521.	+	1.44007e7i	−0.0539987	+	1.42286i
$635$			1.58207e6i			0.155701i
$636$		0			0
$637$			1.04022e6i			0.101572i
$638$	−1.23332e7	−	468058.i	−1.19957	−	0.0455248i
$639$		0			0
$640$	−1.21608e6	+	4.47169e6i	−0.117358	+	0.431540i
$641$	−3.70806e6			−0.356453			−0.178226	−	0.983990i	$-0.557036\pi$
$641$	−3.70806e6			−0.356453			−0.178226	+	0.983990i	$0.557036\pi$
$642$		0			0
$643$		−	1.36989e6i		−	0.130665i	−0.997864	−	0.0653325i	$-0.979189\pi$
$643$		−	1.36989e6i		−	0.130665i	0.997864	−	0.0653325i	$-0.0208108\pi$
$644$	−3.38897e6	−	257601.i	−0.321998	−	0.0244755i
$645$		0			0
$646$	838052.	−	2.20825e7i	0.0790114	−	2.08193i
$647$	1.38641e7			1.30206			0.651028	−	0.759053i	$-0.274338\pi$
$647$	1.38641e7			1.30206			0.651028	+	0.759053i	$0.274338\pi$
$648$		0			0
$649$	−6.83402e6			−0.636890
$650$	26601.8	−	700952.i	0.00246961	−	0.0650736i
$651$		0			0
$652$	−1.33099e6	+	1.75104e7i	−0.122618	+	1.61316i
$653$		−	1.00652e7i		−	0.923714i	−0.886954	−	0.461857i	$-0.847183\pi$
$653$		−	1.00652e7i		−	0.923714i	0.886954	−	0.461857i	$-0.152817\pi$
$654$		0			0
$655$	4.50204e6			0.410021
$656$	8.32165e6	+	1.27243e6i	0.755005	+	0.115445i
$657$		0			0
$658$	−8.41176e6	−	319234.i	−0.757394	−	0.0287438i
$659$		−	2.94962e6i		−	0.264578i	−0.991211	−	0.132289i	$-0.957767\pi$
$659$		−	2.94962e6i		−	0.264578i	0.991211	−	0.132289i	$-0.0422326\pi$
$660$		0			0
$661$			2.46213e6i			0.219184i	0.993977	+	0.109592i	$0.0349544\pi$
$661$			2.46213e6i			0.219184i	−0.993977	+	0.109592i	$0.965046\pi$
$662$	454178.	−	1.19675e7i	0.0402793	−	1.06135i
$663$		0			0
$664$	2.57553e6	−	2.25346e7i	0.226697	−	1.98349i
$665$	5.08387e6			0.445801
$666$		0			0
$667$			7.91648e6i			0.688997i
$668$	−7.15733e6	−	544038.i	−0.620597	−	0.0471724i
$669$		0			0
$670$	−5.44983e6	−	206826.i	−0.469025	−	0.0178000i
$671$	−7.18748e6			−0.616269
$672$		0			0
$673$	8.46100e6			0.720085			0.360043	−	0.932936i	$-0.382762\pi$
$673$	8.46100e6			0.720085			0.360043	+	0.932936i	$0.382762\pi$
$674$	8.87229e6	+	336712.i	0.752291	+	0.0285501i
$675$		0			0
$676$	1.05912e7	+	805051.i	0.891412	+	0.0677574i
$677$		−	2.01968e7i		−	1.69360i	−0.531913	−	0.846799i	$-0.678527\pi$
$677$		−	2.01968e7i		−	1.69360i	0.531913	−	0.846799i	$-0.321473\pi$
$678$		0			0
$679$	−1.68135e6			−0.139954
$680$	1.06157e6	−	9.28822e6i	0.0880392	−	0.770301i
$681$		0			0
$682$	−48313.4	+	1.27305e6i	−0.00397746	+	0.104805i
$683$		−	5.52541e6i		−	0.453224i	−0.973985	−	0.226612i	$-0.927235\pi$
$683$		−	5.52541e6i		−	0.453224i	0.973985	−	0.226612i	$-0.0727649\pi$
$684$		0			0
$685$			9.14346e6i			0.744534i
$686$	−1.34037e7	−	508683.i	−1.08746	−	0.0412703i
$687$		0			0
$688$	−1.43968e6	+	9.41544e6i	−0.115956	+	0.758350i
$689$	−5.50590e6			−0.441855
$690$		0			0
$691$			1.66737e7i			1.32843i	0.747543	+	0.664214i	$0.231234\pi$
$691$			1.66737e7i			1.32843i	−0.747543	+	0.664214i	$0.768766\pi$
$692$	−400816.	+	5.27310e6i	−0.0318185	+	0.418602i
$693$		0			0
$694$	−91933.7	+	2.42244e6i	−0.00724563	+	0.190921i
$695$	2.79716e6			0.219662
$696$		0			0
$697$	−1.69830e7			−1.32413
$698$	−112177.	+	2.95583e6i	−0.00871493	+	0.229637i
$699$		0			0
$700$	2.14454e6	+	163009.i	0.165420	+	0.0125738i
$701$			1.49989e7i			1.15283i	0.817157	+	0.576415i	$0.195549\pi$
$701$			1.49989e7i			1.15283i	−0.817157	+	0.576415i	$0.804451\pi$
$702$		0			0
$703$	−1.78255e7			−1.36036
$704$	2.01260e6	−	8.68961e6i	0.153047	−	0.660798i
$705$		0			0
$706$	1.07058e7	+	406294.i	0.808362	+	0.0306781i
$707$		−	1.10431e7i		−	0.830884i
$708$		0			0
$709$		−	1.84405e7i		−	1.37771i	−0.724900	−	0.688854i	$-0.758114\pi$
$709$		−	1.84405e7i		−	1.37771i	0.724900	−	0.688854i	$-0.241886\pi$
$710$	−381180.	+	1.00440e7i	−0.0283781	+	0.747758i
$711$		0			0
$712$	5.45688e6	+	623677.i	0.403408	+	0.0461063i
$713$	817147.			0.0601972
$714$		0			0
$715$			1.35015e6i			0.0987684i
$716$	−1.04770e6	+	1.37834e7i	−0.0763754	+	1.00479i
$717$		0			0
$718$	−1.45330e7	−	551540.i	−1.05207	−	0.0399269i
$719$	334083.			0.0241009			0.0120504	−	0.999927i	$-0.496164\pi$
$719$	334083.			0.0241009			0.0120504	+	0.999927i	$0.496164\pi$
$720$		0			0
$721$	3.86934e6			0.277204
$722$	6.21763e6	+	235965.i	0.443897	+	0.0168463i
$723$		0			0
$724$	−526168.	+	6.92223e6i	−0.0373059	+	0.490794i
$725$		−	5.00953e6i		−	0.353959i
$726$		0			0
$727$	−2.11438e7			−1.48370			−0.741851	−	0.670564i	$-0.766052\pi$
$727$	−2.11438e7			−1.48370			−0.741851	+	0.670564i	$0.766052\pi$
$728$	438554.	−	3.83714e6i	0.0306686	−	0.268336i
$729$		0			0
$730$	−99873.7	+	2.63165e6i	−0.00693656	+	0.182777i
$731$		−	1.92152e7i		−	1.33000i
$732$		0			0
$733$		−	1.48236e6i		−	0.101904i	−0.998701	−	0.0509521i	$-0.983774\pi$
$733$		−	1.48236e6i		−	0.101904i	0.998701	−	0.0509521i	$-0.0162256\pi$
$734$	1.39772e7	+	530449.i	0.957593	+	0.0363415i
$735$		0			0
$736$	−5.61864e6	−	1.07862e6i	−0.382328	−	0.0733960i
$737$	1.04973e7			0.711884
$738$		0			0
$739$			1.69772e7i			1.14355i	0.820411	+	0.571775i	$0.193745\pi$
$739$			1.69772e7i			1.14355i	−0.820411	+	0.571775i	$0.806255\pi$
$740$	−7.51935e6	−	571556.i	−0.504779	−	0.0383689i
$741$		0			0
$742$	640209.	−	1.68694e7i	0.0426886	−	1.12484i
$743$	2.01294e7			1.33770			0.668849	−	0.743399i	$-0.266787\pi$
$743$	2.01294e7			1.33770			0.668849	+	0.743399i	$0.266787\pi$
$744$		0			0
$745$	3.41201e6			0.225226
$746$	563208.	−	1.48404e7i	0.0370529	−	0.976336i
$747$		0			0
$748$	−1.36383e6	+	1.79424e7i	−0.0891264	+	1.17254i
$749$		−	1.02143e7i		−	0.665278i
$750$		0			0
$751$	−1.16155e7			−0.751514			−0.375757	−	0.926718i	$-0.622617\pi$
$751$	−1.16155e7			−0.751514			−0.375757	+	0.926718i	$0.622617\pi$
$752$	−1.40072e7	−	2.14179e6i	−0.903247	−	0.138112i
$753$		0			0
$754$	−8.98930e6	−	341152.i	−0.575834	−	0.0218534i
$755$		−	4.65885e6i		−	0.297448i
$756$		0			0
$757$		−	9.97313e6i		−	0.632545i	−0.948668	−	0.316273i	$-0.897569\pi$
$757$		−	9.97313e6i		−	0.632545i	0.948668	−	0.316273i	$-0.102431\pi$
$758$	459698.	−	1.21130e7i	0.0290603	−	0.765733i
$759$		0			0
$760$	8.50251e6	+	971768.i	0.533965	+	0.0610280i
$761$	−2.00566e7			−1.25544			−0.627719	−	0.778440i	$-0.716011\pi$
$761$	−2.00566e7			−1.25544			−0.627719	+	0.778440i	$0.716011\pi$
$762$		0			0
$763$		−	1.86207e7i		−	1.15794i
$764$	1.10293e6	+	83835.2i	0.0683620	+	0.00519628i
$765$		0			0
$766$	−3.62786e6	−	137681.i	−0.223398	−	0.00847816i
$767$	−4.98110e6			−0.305729
$768$		0			0
$769$	2.63971e7			1.60968			0.804842	−	0.593489i	$-0.202250\pi$
$769$	2.63971e7			1.60968			0.804842	+	0.593489i	$0.202250\pi$
$770$	−4.13670e6	−	156992.i	−0.251436	−	0.00954223i
$771$		0			0
$772$	−1.51117e7	−	1.14866e6i	−0.912575	−	0.0693661i
$773$			902367.i			0.0543169i	0.999631	+	0.0271584i	$0.00864586\pi$
$773$			902367.i			0.0543169i	−0.999631	+	0.0271584i	$0.991354\pi$
$774$		0			0
$775$	−517089.			−0.0309251
$776$	−2.81198e6	−	321386.i	−0.167632	−	0.0191590i
$777$		0			0
$778$	506976.	−	1.33587e7i	0.0300288	−	0.791253i
$779$		−	1.55463e7i		−	0.917877i
$780$		0			0
$781$		−	1.93465e7i		−	1.13494i
$782$	1.15335e7	+	437709.i	0.674444	+	0.0255958i
$783$		0			0
$784$	−5.30712e6	−	811492.i	−0.308368	−	0.0471513i
$785$	1.86724e6			0.108150
$786$		0			0
$787$		−	1.59032e7i		−	0.915269i	−0.889140	−	0.457635i	$-0.848697\pi$
$787$		−	1.59032e7i		−	0.915269i	0.889140	−	0.457635i	$-0.151303\pi$
$788$	957497.	−	1.25968e7i	0.0549315	−	0.722675i
$789$		0			0
$790$	405456.	−	1.06837e7i	0.0231140	−	0.609050i
$791$	−2.55700e7			−1.45308
$792$		0			0
$793$	−5.23873e6			−0.295830
$794$	−86645.5	+	2.28309e6i	−0.00487747	+	0.128520i
$795$		0			0
$796$	−1.52229e7	−	1.15712e6i	−0.851561	−	0.0647283i
$797$			2.52099e7i			1.40580i	0.711287	+	0.702902i	$0.248113\pi$
$797$			2.52099e7i			1.40580i	−0.711287	+	0.702902i	$0.751887\pi$
$798$		0			0
$799$	2.85861e7			1.58412
$800$	3.55546e6	+	682546.i	0.196414	+	0.0377057i
$801$		0			0
$802$	1.29073e7	+	489845.i	0.708598	+	0.0268920i
$803$		−	5.06901e6i		−	0.277418i
$804$		0			0
$805$			2.65527e6i			0.144417i
$806$	−35214.1	+	927884.i	−0.00190932	+	0.0503102i
$807$		0			0
$808$	2.11085e6	−	1.84689e7i	0.113744	−	0.995206i
$809$	1.43630e7			0.771570			0.385785	−	0.922589i	$-0.373931\pi$
$809$	1.43630e7			0.771570			0.385785	+	0.922589i	$0.373931\pi$
$810$		0			0
$811$		−	1.49512e7i		−	0.798222i	−0.916903	−	0.399111i	$-0.869319\pi$
$811$		−	1.49512e7i		−	0.798222i	0.916903	−	0.399111i	$-0.130681\pi$
$812$	2.09050e6	−	2.75024e7i	0.111265	−	1.46380i
$813$		0			0
$814$	1.45044e7	+	550457.i	0.767255	+	0.0291180i
$815$	1.37195e7			0.723508
$816$		0			0
$817$	1.75897e7			0.921943
$818$	−1.85391e7	−	703577.i	−0.968737	−	0.0367645i
$819$		0			0
$820$	498477.	−	6.55793e6i	0.0258887	−	0.340590i
$821$			2.49701e7i			1.29289i	0.762960	+	0.646446i	$0.223746\pi$
$821$			2.49701e7i			1.29289i	−0.762960	+	0.646446i	$0.776254\pi$
$822$		0			0
$823$	2.50946e7			1.29146			0.645729	−	0.763567i	$-0.276554\pi$
$823$	2.50946e7			1.29146			0.645729	+	0.763567i	$0.276554\pi$
$824$	6.47126e6	+	739614.i	0.332025	+	0.0379478i
$825$		0			0
$826$	579187.	−	1.52615e7i	0.0295372	−	0.778298i
$827$			2.47367e7i			1.25770i	0.777526	+	0.628850i	$0.216474\pi$
$827$			2.47367e7i			1.25770i	−0.777526	+	0.628850i	$0.783526\pi$
$828$		0			0
$829$			1.02078e7i			0.515878i	0.966161	+	0.257939i	$0.0830434\pi$
$829$			1.02078e7i			0.515878i	−0.966161	+	0.257939i	$0.916957\pi$
$830$	−1.77071e7	−	671999.i	−0.892177	−	0.0338590i
$831$		0			0
$832$	1.46692e6	−	6.33358e6i	0.0734678	−	0.317206i
$833$	1.08309e7			0.540818
$834$		0			0
$835$			5.60779e6i			0.278340i
$836$	−1.64246e7	−	1.24846e6i	−0.812794	−	0.0617816i
$837$		0			0
$838$	−129719.	+	3.41807e6i	−0.00638107	+	0.168140i
$839$	−2.64451e7			−1.29700			−0.648501	−	0.761214i	$-0.724604\pi$
$839$	−2.64451e7			−1.29700			−0.648501	+	0.761214i	$0.724604\pi$
$840$		0			0
$841$	−4.37332e7			−2.13217
$842$	−743010.	+	1.95782e7i	−0.0361172	+	0.951682i
$843$		0			0
$844$	1.05720e6	−	1.39085e7i	0.0510860	−	0.672084i
$845$		−	8.29824e6i		−	0.399801i
$846$		0			0
$847$	−9.35082e6			−0.447859
$848$	4.29525e6	−	2.80908e7i	0.205116	−	1.34145i
$849$		0			0
$850$	−7.29841e6	−	276981.i	−0.346482	−	0.0131493i
$851$		−	9.31014e6i		−	0.440689i
$852$		0			0
$853$			2.30070e7i			1.08265i	0.840814	+	0.541324i	$0.182077\pi$
$853$			2.30070e7i			1.08265i	−0.840814	+	0.541324i	$0.817923\pi$
$854$	609143.	−	1.60508e7i	0.0285808	−	0.753099i
$855$		0			0
$856$	1.95243e6	−	1.70828e7i	0.0910733	−	0.796848i
$857$	1.81332e7			0.843379			0.421689	−	0.906740i	$-0.361437\pi$
$857$	1.81332e7			0.843379			0.421689	+	0.906740i	$0.361437\pi$
$858$		0			0
$859$			1.83891e6i			0.0850310i	0.999096	+	0.0425155i	$0.0135372\pi$
$859$			1.83891e6i			0.0850310i	−0.999096	+	0.0425155i	$0.986463\pi$
$860$	7.41990e6	+	563997.i	0.342099	+	0.0260034i
$861$		0			0
$862$	2.82834e7	+	1.07338e6i	1.29647	+	0.0492024i
$863$	−1.14230e7			−0.522097			−0.261049	−	0.965326i	$-0.584068\pi$
$863$	−1.14230e7			−0.522097			−0.261049	+	0.965326i	$0.584068\pi$
$864$		0			0
$865$	4.13150e6			0.187744
$866$	2.32476e7	+	882268.i	1.05338	+	0.0399766i
$867$		0			0
$868$	−2.83883e6	−	215783.i	−0.127891	−	0.00972116i
$869$			2.05786e7i			0.924413i
$870$		0			0
$871$	7.65115e6			0.341729
$872$	3.55930e6	−	3.11421e7i	0.158516	−	1.38694i
$873$		0			0
$874$	−400682.	+	1.05579e7i	−0.0177428	+	0.467519i
$875$		−	1.68025e6i		−	0.0741915i
$876$		0			0
$877$			2.12365e7i			0.932362i	0.884689	+	0.466181i	$0.154370\pi$
$877$			2.12365e7i			0.932362i	−0.884689	+	0.466181i	$0.845630\pi$
$878$	−2.37594e7	−	901692.i	−1.04016	−	0.0394750i
$879$		0			0
$880$	−6.88840e6	−	1.05328e6i	−0.299855	−	0.0458497i
$881$	−1.35067e7			−0.586287			−0.293143	−	0.956069i	$-0.594701\pi$
$881$	−1.35067e7			−0.586287			−0.293143	+	0.956069i	$0.594701\pi$
$882$		0			0
$883$			2.44466e7i			1.05515i	0.849507	+	0.527577i	$0.176900\pi$
$883$			2.44466e7i			1.05515i	−0.849507	+	0.527577i	$0.823100\pi$
$884$	−994052.	+	1.30777e7i	−0.0427837	+	0.562859i
$885$		0			0
$886$	−283532.	+	7.47100e6i	−0.0121344	+	0.319738i
$887$	−8.02242e6			−0.342371			−0.171185	−	0.985239i	$-0.554760\pi$
$887$	−8.02242e6			−0.342371			−0.171185	+	0.985239i	$0.554760\pi$
$888$		0			0
$889$	6.80520e6			0.288793
$890$	162728.	−	4.28785e6i	0.00688632	−	0.181453i
$891$		0			0
$892$	3.63991e7	+	2.76674e6i	1.53172	+	0.116428i
$893$			2.61680e7i			1.09810i
$894$		0			0
$895$	1.07994e7			0.450652
$896$	1.92347e7	+	5.23090e6i	0.800416	+	0.217674i
$897$		0			0
$898$	−3.12148e7	−	1.18463e6i	−1.29172	−	0.0490221i
$899$			6.63136e6i			0.273655i
$900$		0			0
$901$			5.73281e7i			2.35264i
$902$	−480076.	+	1.26499e7i	−0.0196469	+	0.517692i
$903$		0			0
$904$	−4.27644e7	−	4.88763e6i	−1.74045	−	0.198920i
$905$	5.42359e6			0.220123
$906$		0			0
$907$		−	2.02868e7i		−	0.818831i	−0.912348	−	0.409416i	$-0.865733\pi$
$907$		−	2.02868e7i		−	0.818831i	0.912348	−	0.409416i	$-0.134267\pi$
$908$	−2.64109e6	+	3.47460e7i	−0.106309	+	1.39859i
$909$		0			0
$910$	−3.01511e6	−	114426.i	−0.120698	−	0.00458060i
$911$	−1.72893e7			−0.690209			−0.345104	−	0.938564i	$-0.612156\pi$
$911$	−1.72893e7			−0.690209			−0.345104	+	0.938564i	$0.612156\pi$
$912$		0			0
$913$	3.41068e7			1.35414
$914$	−1.96060e7	−	744067.i	−0.776290	−	0.0294609i
$915$		0			0
$916$	1.15056e6	−	1.51367e7i	0.0453076	−	0.596063i
$917$		−	1.93653e7i		−	0.760502i
$918$		0			0
$919$	−2.14060e7			−0.836079			−0.418039	−	0.908429i	$-0.637283\pi$
$919$	−2.14060e7			−0.836079			−0.418039	+	0.908429i	$0.637283\pi$
$920$	−507548.	+	4.44080e6i	−0.0197701	+	0.172978i
$921$		0			0
$922$	−519900.	+	1.36993e7i	−0.0201415	+	0.530725i
$923$		−	1.41010e7i		−	0.544812i
$924$		0			0
$925$			5.89144e6i			0.226395i
$926$	3.72237e7	+	1.41267e6i	1.42656	+	0.0541395i
$927$		0			0
$928$	8.75326e6	−	4.55967e7i	0.333657	−	1.73806i
$929$	−4.14158e7			−1.57444			−0.787221	−	0.616670i	$-0.788481\pi$
$929$	−4.14158e7			−1.57444			−0.787221	+	0.616670i	$0.788481\pi$
$930$		0			0
$931$			9.91466e6i			0.374890i
$932$	8.64889e6	+	657414.i	0.326152	+	0.0247913i
$933$		0			0
$934$	248203.	−	6.54010e6i	0.00930979	−	0.245311i
$935$	1.40580e7			0.525889
$936$		0			0
$937$	1.39335e7			0.518455			0.259228	−	0.965816i	$-0.416532\pi$
$937$	1.39335e7			0.518455			0.259228	+	0.965816i	$0.416532\pi$
$938$	−889652.	+	2.34422e7i	−0.0330151	+	0.869943i
$939$		0			0
$940$	−839049.	+	1.10385e7i	−0.0309719	+	0.407464i
$941$		−	1.51311e7i		−	0.557051i	−0.960429	−	0.278526i	$-0.910154\pi$
$941$		−	1.51311e7i		−	0.557051i	0.960429	−	0.278526i	$-0.0898457\pi$
$942$		0			0
$943$	8.11975e6			0.297347
$944$	3.88585e6	−	2.54133e7i	0.141924	−	0.928177i
$945$		0			0
$946$	−1.43126e7	−	543177.i	−0.519985	−	0.0197339i
$947$			2.72196e7i			0.986296i	0.869945	+	0.493148i	$0.164154\pi$
$947$			2.72196e7i			0.986296i	−0.869945	+	0.493148i	$0.835846\pi$
$948$		0			0
$949$		−	3.69464e6i		−	0.133170i
$950$	253551.	−	6.68102e6i	0.00911499	−	0.240178i
$951$		0			0
$952$	−3.99528e7	−	4.56628e6i	−1.42874	−	0.163294i
$953$	2.79494e7			0.996873			0.498437	−	0.866926i	$-0.333908\pi$
$953$	2.79494e7			0.996873			0.498437	+	0.866926i	$0.333908\pi$
$954$		0			0
$955$		−	864150.i		−	0.0306606i
$956$	2.63051e7	+	1.99948e6i	0.930882	+	0.0707576i
$957$		0			0
$958$	−2.15098e6	−	81631.8i	−0.0757221	−	0.00287373i
$959$	3.93301e7			1.38095
$960$		0			0
$961$	−2.79447e7			−0.976091
$962$	1.05718e7	+	401210.i	0.368309	+	0.0139777i
$963$		0			0
$964$	−2.76697e6	−	210321.i	−0.0958984	−	0.00728937i
$965$			1.18400e7i			0.409293i
$966$		0			0
$967$	3.73167e7			1.28333			0.641663	−	0.766987i	$-0.278245\pi$
$967$	3.73167e7			1.28333			0.641663	+	0.766987i	$0.278245\pi$
$968$	−1.56387e7	−	1.78738e6i	−0.536431	−	0.0613097i
$969$		0			0
$970$	−83855.2	+	2.20957e6i	−0.00286154	+	0.0754011i
$971$			1.77774e7i			0.605091i	0.953135	+	0.302545i	$0.0978364\pi$
$971$			1.77774e7i			0.605091i	−0.953135	+	0.302545i	$0.902164\pi$
$972$		0			0
$973$		−	1.20318e7i		−	0.407427i
$974$	−1.51333e7	−	574325.i	−0.511137	−	0.0193981i
$975$		0			0
$976$	4.08683e6	−	2.67277e7i	0.137329	−	0.898125i
$977$	−1.67378e7			−0.561000			−0.280500	−	0.959854i	$-0.590500\pi$
$977$	−1.67378e7			−0.561000			−0.280500	+	0.959854i	$0.590500\pi$
$978$		0			0
$979$			8.25913e6i			0.275409i
$980$	−317903.	+	4.18232e6i	−0.0105738	+	0.139108i
$981$		0			0
$982$	1.09559e6	−	2.88685e7i	0.0362550	−	0.955312i
$983$	2.99351e7			0.988091			0.494045	−	0.869436i	$-0.335518\pi$
$983$	2.99351e7			0.988091			0.494045	+	0.869436i	$0.335518\pi$
$984$		0			0
$985$	−9.86961e6			−0.324123
$986$	−3.55212e6	+	9.35978e7i	−0.116358	+	3.06601i
$987$		0			0
$988$	−1.19714e7	−	909963.i	−0.390169	−	0.0296573i
$989$			9.18701e6i			0.298664i
$990$		0			0
$991$	1.30589e7			0.422398			0.211199	−	0.977443i	$-0.432263\pi$
$991$	1.30589e7			0.422398			0.211199	+	0.977443i	$0.432263\pi$
$992$	−4.70654e6	−	903519.i	−0.151853	−	0.0291513i
$993$		0			0
$994$	4.32038e7	+	1.63962e6i	1.38693	+	0.0526354i
$995$			1.19272e7i			0.381928i
$996$		0			0
$997$			7.99417e6i			0.254704i	0.991858	+	0.127352i	$0.0406477\pi$
$997$			7.99417e6i			0.254704i	−0.991858	+	0.127352i	$0.959352\pi$
$998$	55643.4	−	1.46619e6i	0.00176843	−	0.0465978i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.6.k.b.181.1		20
3.2	odd	2		40.6.d.a.21.20	yes	20
8.5	even	2	inner	360.6.k.b.181.2		20
12.11	even	2		160.6.d.a.81.4		20
15.2	even	4		200.6.f.b.149.12		20
15.8	even	4		200.6.f.c.149.9		20
15.14	odd	2		200.6.d.b.101.1		20
24.5	odd	2		40.6.d.a.21.19	✓	20
24.11	even	2		160.6.d.a.81.17		20
60.23	odd	4		800.6.f.b.49.17		20
60.47	odd	4		800.6.f.c.49.4		20
60.59	even	2		800.6.d.c.401.17		20
120.29	odd	2		200.6.d.b.101.2		20
120.53	even	4		200.6.f.b.149.11		20
120.59	even	2		800.6.d.c.401.4		20
120.77	even	4		200.6.f.c.149.10		20
120.83	odd	4		800.6.f.c.49.3		20
120.107	odd	4		800.6.f.b.49.18		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.19	✓	20	24.5	odd	2
40.6.d.a.21.20	yes	20	3.2	odd	2
160.6.d.a.81.4		20	12.11	even	2
160.6.d.a.81.17		20	24.11	even	2
200.6.d.b.101.1		20	15.14	odd	2
200.6.d.b.101.2		20	120.29	odd	2
200.6.f.b.149.11		20	120.53	even	4
200.6.f.b.149.12		20	15.2	even	4
200.6.f.c.149.9		20	15.8	even	4
200.6.f.c.149.10		20	120.77	even	4
360.6.k.b.181.1		20	1.1	even	1	trivial
360.6.k.b.181.2		20	8.5	even	2	inner
800.6.d.c.401.4		20	120.59	even	2
800.6.d.c.401.17		20	60.59	even	2
800.6.f.b.49.17		20	60.23	odd	4
800.6.f.b.49.18		20	120.107	odd	4
800.6.f.c.49.3		20	120.83	odd	4
800.6.f.c.49.4		20	60.47	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	360.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.65278 - 0.214529i) q^{2} +(31.9080 + 2.42537i) q^{4} -25.0000i q^{5} -107.536 q^{7} +(-179.848 - 20.5552i) q^{8} +O(q^{10})\)	\(q+(-5.65278 - 0.214529i) q^{2} +(31.9080 + 2.42537i) q^{4} -25.0000i q^{5} -107.536 q^{7} +(-179.848 - 20.5552i) q^{8} +(-5.36321 + 141.320i) q^{10} -272.206i q^{11} -198.402i q^{13} +(607.879 + 23.0696i) q^{14} +(1012.24 + 154.777i) q^{16} -2065.79 q^{17} -1891.04i q^{19} +(60.6342 - 797.699i) q^{20} +(-58.3959 + 1538.72i) q^{22} +987.677 q^{23} -625.000 q^{25} +(-42.5629 + 1121.52i) q^{26} +(-3431.26 - 260.815i) q^{28} +8015.26i q^{29} +827.342 q^{31} +(-5688.74 - 1092.07i) q^{32} +(11677.5 + 443.170i) q^{34} +2688.40i q^{35} -9426.30i q^{37} +(-405.681 + 10689.6i) q^{38} +(-513.881 + 4496.21i) q^{40} +8221.07 q^{41} +9301.63i q^{43} +(660.198 - 8685.52i) q^{44} +(-5583.12 - 211.885i) q^{46} -13837.9 q^{47} -5242.97 q^{49} +(3532.99 + 134.080i) q^{50} +(481.198 - 6330.60i) q^{52} -27751.2i q^{53} -6805.14 q^{55} +(19340.2 + 2210.43i) q^{56} +(1719.50 - 45308.5i) q^{58} -25106.1i q^{59} -26404.6i q^{61} +(-4676.79 - 177.488i) q^{62} +(31923.0 + 7393.66i) q^{64} -4960.05 q^{65} +38563.9i q^{67} +(-65915.1 - 5010.29i) q^{68} +(576.739 - 15197.0i) q^{70} +71073.0 q^{71} +18622.0 q^{73} +(-2022.21 + 53284.8i) q^{74} +(4586.46 - 60339.1i) q^{76} +29271.9i q^{77} -75599.4 q^{79} +(3869.43 - 25305.9i) q^{80} +(-46471.9 - 1763.65i) q^{82} +125298. i q^{83} +51644.7i q^{85} +(1995.47 - 52580.1i) q^{86} +(-5595.25 + 48955.8i) q^{88} -30341.5 q^{89} +21335.4i q^{91} +(31514.7 + 2395.48i) q^{92} +(78222.6 + 2968.62i) q^{94} -47275.9 q^{95} +15635.2 q^{97} +(29637.4 + 1124.77i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 32 q^{4} - 196 q^{7} - 248 q^{8}+O(q^{10}) \) 20 * q - 2 * q^2 - 32 * q^4 - 196 * q^7 - 248 * q^8	\( 20 q - 2 q^{2} - 32 q^{4} - 196 q^{7} - 248 q^{8} - 50 q^{10} - 2708 q^{14} + 3080 q^{16} + 1900 q^{20} + 13836 q^{22} + 4676 q^{23} - 12500 q^{25} + 8084 q^{26} + 2108 q^{28} + 7160 q^{31} - 6792 q^{32} + 21132 q^{34} + 19580 q^{38} + 6200 q^{40} - 11608 q^{41} - 72296 q^{44} - 28516 q^{46} - 44180 q^{47} + 18756 q^{49} + 1250 q^{50} - 39680 q^{52} - 24200 q^{55} + 53624 q^{56} + 59496 q^{58} - 59824 q^{62} - 11264 q^{64} - 11576 q^{68} + 29800 q^{70} + 200312 q^{71} - 105136 q^{73} - 78876 q^{74} - 153872 q^{76} + 282080 q^{79} - 16000 q^{80} - 223032 q^{82} - 27452 q^{86} + 86896 q^{88} + 3160 q^{89} - 107916 q^{92} + 148820 q^{94} - 144400 q^{95} + 147376 q^{97} - 216942 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 32 * q^4 - 196 * q^7 - 248 * q^8 - 50 * q^10 - 2708 * q^14 + 3080 * q^16 + 1900 * q^20 + 13836 * q^22 + 4676 * q^23 - 12500 * q^25 + 8084 * q^26 + 2108 * q^28 + 7160 * q^31 - 6792 * q^32 + 21132 * q^34 + 19580 * q^38 + 6200 * q^40 - 11608 * q^41 - 72296 * q^44 - 28516 * q^46 - 44180 * q^47 + 18756 * q^49 + 1250 * q^50 - 39680 * q^52 - 24200 * q^55 + 53624 * q^56 + 59496 * q^58 - 59824 * q^62 - 11264 * q^64 - 11576 * q^68 + 29800 * q^70 + 200312 * q^71 - 105136 * q^73 - 78876 * q^74 - 153872 * q^76 + 282080 * q^79 - 16000 * q^80 - 223032 * q^82 - 27452 * q^86 + 86896 * q^88 + 3160 * q^89 - 107916 * q^92 + 148820 * q^94 - 144400 * q^95 + 147376 * q^97 - 216942 * q^98

Introduction

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