LMFDB - Embedded newform 882.4.g.j.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,4,Mod(361,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("882.361");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	882.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$52.0396846251$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 294)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	882.361
Dual form			882.4.g.j.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(4.00000 + 6.92820i) q^{5} +8.00000 q^{8} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(4.00000 + 6.92820i) q^{5} +8.00000 q^{8} +(8.00000 - 13.8564i) q^{10} +(20.0000 - 34.6410i) q^{11} +4.00000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-42.0000 + 72.7461i) q^{17} +(-74.0000 - 128.172i) q^{19} -32.0000 q^{20} -80.0000 q^{22} +(42.0000 + 72.7461i) q^{23} +(30.5000 - 52.8275i) q^{25} +(-4.00000 - 6.92820i) q^{26} -58.0000 q^{29} +(68.0000 - 117.779i) q^{31} +(-16.0000 + 27.7128i) q^{32} +168.000 q^{34} +(111.000 + 192.258i) q^{37} +(-148.000 + 256.344i) q^{38} +(32.0000 + 55.4256i) q^{40} -420.000 q^{41} -164.000 q^{43} +(80.0000 + 138.564i) q^{44} +(84.0000 - 145.492i) q^{46} +(244.000 + 422.620i) q^{47} -122.000 q^{50} +(-8.00000 + 13.8564i) q^{52} +(239.000 - 413.960i) q^{53} +320.000 q^{55} +(58.0000 + 100.459i) q^{58} +(274.000 - 474.582i) q^{59} +(-346.000 - 599.290i) q^{61} -272.000 q^{62} +64.0000 q^{64} +(16.0000 + 27.7128i) q^{65} +(454.000 - 786.351i) q^{67} +(-168.000 - 290.985i) q^{68} +524.000 q^{71} +(-220.000 + 381.051i) q^{73} +(222.000 - 384.515i) q^{74} +592.000 q^{76} +(-608.000 - 1053.09i) q^{79} +(64.0000 - 110.851i) q^{80} +(420.000 + 727.461i) q^{82} +684.000 q^{83} -672.000 q^{85} +(164.000 + 284.056i) q^{86} +(160.000 - 277.128i) q^{88} +(302.000 + 523.079i) q^{89} -336.000 q^{92} +(488.000 - 845.241i) q^{94} +(592.000 - 1025.37i) q^{95} -832.000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{4} + 8 q^{5} + 16 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 - 4 * q^4 + 8 * q^5 + 16 * q^8	$ 2 q - 2 q^{2} - 4 q^{4} + 8 q^{5} + 16 q^{8} + 16 q^{10} + 40 q^{11} + 8 q^{13} - 16 q^{16} - 84 q^{17} - 148 q^{19} - 64 q^{20} - 160 q^{22} + 84 q^{23} + 61 q^{25} - 8 q^{26} - 116 q^{29} + 136 q^{31} - 32 q^{32} + 336 q^{34} + 222 q^{37} - 296 q^{38} + 64 q^{40} - 840 q^{41} - 328 q^{43} + 160 q^{44} + 168 q^{46} + 488 q^{47} - 244 q^{50} - 16 q^{52} + 478 q^{53} + 640 q^{55} + 116 q^{58} + 548 q^{59} - 692 q^{61} - 544 q^{62} + 128 q^{64} + 32 q^{65} + 908 q^{67} - 336 q^{68} + 1048 q^{71} - 440 q^{73} + 444 q^{74} + 1184 q^{76} - 1216 q^{79} + 128 q^{80} + 840 q^{82} + 1368 q^{83} - 1344 q^{85} + 328 q^{86} + 320 q^{88} + 604 q^{89} - 672 q^{92} + 976 q^{94} + 1184 q^{95} - 1664 q^{97}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^4 + 8 * q^5 + 16 * q^8 + 16 * q^10 + 40 * q^11 + 8 * q^13 - 16 * q^16 - 84 * q^17 - 148 * q^19 - 64 * q^20 - 160 * q^22 + 84 * q^23 + 61 * q^25 - 8 * q^26 - 116 * q^29 + 136 * q^31 - 32 * q^32 + 336 * q^34 + 222 * q^37 - 296 * q^38 + 64 * q^40 - 840 * q^41 - 328 * q^43 + 160 * q^44 + 168 * q^46 + 488 * q^47 - 244 * q^50 - 16 * q^52 + 478 * q^53 + 640 * q^55 + 116 * q^58 + 548 * q^59 - 692 * q^61 - 544 * q^62 + 128 * q^64 + 32 * q^65 + 908 * q^67 - 336 * q^68 + 1048 * q^71 - 440 * q^73 + 444 * q^74 + 1184 * q^76 - 1216 * q^79 + 128 * q^80 + 840 * q^82 + 1368 * q^83 - 1344 * q^85 + 328 * q^86 + 320 * q^88 + 604 * q^89 - 672 * q^92 + 976 * q^94 + 1184 * q^95 - 1664 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	4.00000	+	6.92820i	0.357771	+	0.619677i	0.987588	−	0.157066i	$-0.0502036\pi$
$5$	4.00000	+	6.92820i	0.357771	+	0.619677i	−0.629817	+	0.776743i	$0.716870\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	8.00000			0.353553
$9$		0			0
$10$	8.00000	−	13.8564i	0.252982	−	0.438178i
$11$	20.0000	−	34.6410i	0.548202	−	0.949514i	−0.450195	−	0.892930i	$-0.648646\pi$
$11$	20.0000	−	34.6410i	0.548202	−	0.949514i	0.998398	−	0.0565844i	$-0.0180210\pi$
$12$		0			0
$13$	4.00000			0.0853385			0.0426692	−	0.999089i	$-0.486414\pi$
$13$	4.00000			0.0853385			0.0426692	+	0.999089i	$0.486414\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−42.0000	+	72.7461i	−0.599206	+	1.03785i	0.393733	+	0.919225i	$0.371183\pi$
$17$	−42.0000	+	72.7461i	−0.599206	+	1.03785i	−0.992939	+	0.118630i	$0.962150\pi$
$18$		0			0
$19$	−74.0000	−	128.172i	−0.893514	−	1.54761i	−0.835633	−	0.549288i	$-0.814899\pi$
$19$	−74.0000	−	128.172i	−0.893514	−	1.54761i	−0.0578808	−	0.998324i	$-0.518434\pi$
$20$	−32.0000			−0.357771
$21$		0			0
$22$	−80.0000			−0.775275
$23$	42.0000	+	72.7461i	0.380765	+	0.659505i	0.991172	−	0.132583i	$-0.0423272\pi$
$23$	42.0000	+	72.7461i	0.380765	+	0.659505i	−0.610406	+	0.792088i	$0.708994\pi$
$24$		0			0
$25$	30.5000	−	52.8275i	0.244000	−	0.422620i
$26$	−4.00000	−	6.92820i	−0.0301717	−	0.0522589i
$27$		0			0
$28$		0			0
$29$	−58.0000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−58.0000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	68.0000	−	117.779i	0.393973	−	0.682381i	−0.598997	−	0.800752i	$-0.704434\pi$
$31$	68.0000	−	117.779i	0.393973	−	0.682381i	0.992970	+	0.118370i	$0.0377670\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$		0			0
$34$	168.000			0.847405
$35$		0			0
$36$		0			0
$37$	111.000	+	192.258i	0.493197	+	0.854242i	0.999969	−	0.00783774i	$-0.00249486\pi$
$37$	111.000	+	192.258i	0.493197	+	0.854242i	−0.506772	+	0.862080i	$0.669162\pi$
$38$	−148.000	+	256.344i	−0.631810	+	1.09433i
$39$		0			0
$40$	32.0000	+	55.4256i	0.126491	+	0.219089i
$41$	−420.000			−1.59983			−0.799914	−	0.600114i	$-0.795122\pi$
$41$	−420.000			−1.59983			−0.799914	+	0.600114i	$0.795122\pi$
$42$		0			0
$43$	−164.000			−0.581622			−0.290811	−	0.956780i	$-0.593925\pi$
$43$	−164.000			−0.581622			−0.290811	+	0.956780i	$0.593925\pi$
$44$	80.0000	+	138.564i	0.274101	+	0.474757i
$45$		0			0
$46$	84.0000	−	145.492i	0.269242	−	0.466341i
$47$	244.000	+	422.620i	0.757257	+	1.31161i	0.944245	+	0.329245i	$0.106794\pi$
$47$	244.000	+	422.620i	0.757257	+	1.31161i	−0.186988	+	0.982362i	$0.559873\pi$
$48$		0			0
$49$		0			0
$50$	−122.000			−0.345068
$51$		0			0
$52$	−8.00000	+	13.8564i	−0.0213346	+	0.0369527i
$53$	239.000	−	413.960i	0.619418	−	1.07286i	−0.370174	−	0.928963i	$-0.620702\pi$
$53$	239.000	−	413.960i	0.619418	−	1.07286i	0.989592	−	0.143902i	$-0.0459649\pi$
$54$		0			0
$55$	320.000			0.784523
$56$		0			0
$57$		0			0
$58$	58.0000	+	100.459i	0.131306	+	0.227429i
$59$	274.000	−	474.582i	0.604606	−	1.04721i	−0.387507	−	0.921867i	$-0.626664\pi$
$59$	274.000	−	474.582i	0.604606	−	1.04721i	0.992114	−	0.125342i	$-0.0400028\pi$
$60$		0			0
$61$	−346.000	−	599.290i	−0.726242	−	1.25789i	−0.958461	−	0.285224i	$-0.907932\pi$
$61$	−346.000	−	599.290i	−0.726242	−	1.25789i	0.232219	−	0.972664i	$-0.425401\pi$
$62$	−272.000			−0.557162
$63$		0			0
$64$	64.0000			0.125000
$65$	16.0000	+	27.7128i	0.0305316	+	0.0528823i
$66$		0			0
$67$	454.000	−	786.351i	0.827835	−	1.43385i	−0.0718987	−	0.997412i	$-0.522906\pi$
$67$	454.000	−	786.351i	0.827835	−	1.43385i	0.899733	−	0.436440i	$-0.143761\pi$
$68$	−168.000	−	290.985i	−0.299603	−	0.518927i
$69$		0			0
$70$		0			0
$71$	524.000			0.875878			0.437939	−	0.899005i	$-0.355709\pi$
$71$	524.000			0.875878			0.437939	+	0.899005i	$0.355709\pi$
$72$		0			0
$73$	−220.000	+	381.051i	−0.352727	+	0.610941i	−0.986726	−	0.162393i	$-0.948079\pi$
$73$	−220.000	+	381.051i	−0.352727	+	0.610941i	0.633999	+	0.773334i	$0.281412\pi$
$74$	222.000	−	384.515i	0.348743	−	0.604040i
$75$		0			0
$76$	592.000			0.893514
$77$		0			0
$78$		0			0
$79$	−608.000	−	1053.09i	−0.865890	−	1.49977i	−0.866160	−	0.499766i	$-0.833419\pi$
$79$	−608.000	−	1053.09i	−0.865890	−	1.49977i	0.000269874	−	1.00000i	$-0.499914\pi$
$80$	64.0000	−	110.851i	0.0894427	−	0.154919i
$81$		0			0
$82$	420.000	+	727.461i	0.565625	+	0.979691i
$83$	684.000			0.904563			0.452282	−	0.891875i	$-0.350610\pi$
$83$	684.000			0.904563			0.452282	+	0.891875i	$0.350610\pi$
$84$		0			0
$85$	−672.000			−0.857513
$86$	164.000	+	284.056i	0.205635	+	0.356170i
$87$		0			0
$88$	160.000	−	277.128i	0.193819	−	0.335704i
$89$	302.000	+	523.079i	0.359685	+	0.622992i	0.987908	−	0.155041i	$-0.0495509\pi$
$89$	302.000	+	523.079i	0.359685	+	0.622992i	−0.628223	+	0.778033i	$0.716218\pi$
$90$		0			0
$91$		0			0
$92$	−336.000			−0.380765
$93$		0			0
$94$	488.000	−	845.241i	0.535461	−	0.927446i
$95$	592.000	−	1025.37i	0.639347	−	1.10738i
$96$		0			0
$97$	−832.000			−0.870895			−0.435447	−	0.900214i	$-0.643410\pi$
$97$	−832.000			−0.870895			−0.435447	+	0.900214i	$0.643410\pi$
$98$		0			0
$99$		0			0
$100$	122.000	+	211.310i	0.122000	+	0.211310i
$101$	232.000	−	401.836i	0.228563	−	0.395883i	−0.728819	−	0.684706i	$-0.759931\pi$
$101$	232.000	−	401.836i	0.228563	−	0.395883i	0.957382	+	0.288823i	$0.0932640\pi$
$102$		0			0
$103$	316.000	+	547.328i	0.302295	+	0.523591i	0.976655	−	0.214812i	$-0.0689138\pi$
$103$	316.000	+	547.328i	0.302295	+	0.523591i	−0.674360	+	0.738402i	$0.735580\pi$
$104$	32.0000			0.0301717
$105$		0			0
$106$	−956.000			−0.875990
$107$	−80.0000	−	138.564i	−0.0722794	−	0.125192i	0.827621	−	0.561288i	$-0.189694\pi$
$107$	−80.0000	−	138.564i	−0.0722794	−	0.125192i	−0.899900	+	0.436096i	$0.856361\pi$
$108$		0			0
$109$	1099.00	−	1903.52i	0.965735	−	1.67270i	0.258108	−	0.966116i	$-0.416901\pi$
$109$	1099.00	−	1903.52i	0.965735	−	1.67270i	0.707627	−	0.706586i	$-0.249766\pi$
$110$	−320.000	−	554.256i	−0.277371	−	0.480421i
$111$		0			0
$112$		0			0
$113$	−770.000			−0.641022			−0.320511	−	0.947245i	$-0.603855\pi$
$113$	−770.000			−0.641022			−0.320511	+	0.947245i	$0.603855\pi$
$114$		0			0
$115$	−336.000	+	581.969i	−0.272454	+	0.471903i
$116$	116.000	−	200.918i	0.0928477	−	0.160817i
$117$		0			0
$118$	−1096.00			−0.855042
$119$		0			0
$120$		0			0
$121$	−134.500	−	232.961i	−0.101052	−	0.175027i
$122$	−692.000	+	1198.58i	−0.513531	+	0.889461i
$123$		0			0
$124$	272.000	+	471.118i	0.196986	+	0.341191i
$125$	1488.00			1.06473
$126$		0			0
$127$	−184.000			−0.128562			−0.0642809	−	0.997932i	$-0.520475\pi$
$127$	−184.000			−0.128562			−0.0642809	+	0.997932i	$0.520475\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	32.0000	−	55.4256i	0.0215891	−	0.0373935i
$131$	−726.000	−	1257.47i	−0.484205	−	0.838668i	0.515630	−	0.856811i	$-0.327558\pi$
$131$	−726.000	−	1257.47i	−0.484205	−	0.838668i	−0.999835	+	0.0181429i	$0.994225\pi$
$132$		0			0
$133$		0			0
$134$	−1816.00			−1.17074
$135$		0			0
$136$	−336.000	+	581.969i	−0.211851	+	0.366937i
$137$	323.000	−	559.452i	0.201429	−	0.348885i	−0.747560	−	0.664194i	$-0.768775\pi$
$137$	323.000	−	559.452i	0.201429	−	0.348885i	0.948989	+	0.315309i	$0.102108\pi$
$138$		0			0
$139$	−3012.00			−1.83795			−0.918973	−	0.394320i	$-0.870980\pi$
$139$	−3012.00			−1.83795			−0.918973	+	0.394320i	$0.870980\pi$
$140$		0			0
$141$		0			0
$142$	−524.000	−	907.595i	−0.309670	−	0.536364i
$143$	80.0000	−	138.564i	0.0467828	−	0.0810301i
$144$		0			0
$145$	−232.000	−	401.836i	−0.132873	−	0.230142i
$146$	880.000			0.498831
$147$		0			0
$148$	−888.000			−0.493197
$149$	−1585.00	−	2745.30i	−0.871465	−	1.50942i	−0.860482	−	0.509482i	$-0.829837\pi$
$149$	−1585.00	−	2745.30i	−0.871465	−	1.50942i	−0.0109833	−	0.999940i	$-0.503496\pi$
$150$		0			0
$151$	940.000	−	1628.13i	0.506597	−	0.877451i	−0.493374	−	0.869817i	$-0.664237\pi$
$151$	940.000	−	1628.13i	0.506597	−	0.877451i	0.999971	−	0.00763414i	$-0.00243005\pi$
$152$	−592.000	−	1025.37i	−0.315905	−	0.547163i
$153$		0			0
$154$		0			0
$155$	1088.00			0.563808
$156$		0			0
$157$	−302.000	+	523.079i	−0.153517	+	0.265900i	−0.932518	−	0.361123i	$-0.882393\pi$
$157$	−302.000	+	523.079i	−0.153517	+	0.265900i	0.779001	+	0.627023i	$0.215727\pi$
$158$	−1216.00	+	2106.17i	−0.612277	+	1.06049i
$159$		0			0
$160$	−256.000			−0.126491
$161$		0			0
$162$		0			0
$163$	−558.000	−	966.484i	−0.268135	−	0.464423i	0.700246	−	0.713902i	$-0.253074\pi$
$163$	−558.000	−	966.484i	−0.268135	−	0.464423i	−0.968380	+	0.249479i	$0.919741\pi$
$164$	840.000	−	1454.92i	0.399957	−	0.692746i
$165$		0			0
$166$	−684.000	−	1184.72i	−0.319811	−	0.553930i
$167$	1784.00			0.826647			0.413324	−	0.910584i	$-0.364368\pi$
$167$	1784.00			0.826647			0.413324	+	0.910584i	$0.364368\pi$
$168$		0			0
$169$	−2181.00			−0.992717
$170$	672.000	+	1163.94i	0.303177	+	0.525118i
$171$		0			0
$172$	328.000	−	568.113i	0.145406	−	0.251850i
$173$	−172.000	−	297.913i	−0.0755891	−	0.130924i	0.825753	−	0.564032i	$-0.190750\pi$
$173$	−172.000	−	297.913i	−0.0755891	−	0.130924i	−0.901342	+	0.433107i	$0.857417\pi$
$174$		0			0
$175$		0			0
$176$	−640.000			−0.274101
$177$		0			0
$178$	604.000	−	1046.16i	0.254335	−	0.440522i
$179$	696.000	−	1205.51i	0.290623	−	0.503373i	−0.683334	−	0.730106i	$-0.739471\pi$
$179$	696.000	−	1205.51i	0.290623	−	0.503373i	0.973957	+	0.226732i	$0.0728042\pi$
$180$		0			0
$181$	4052.00			1.66399			0.831997	−	0.554781i	$-0.187198\pi$
$181$	4052.00			1.66399			0.831997	+	0.554781i	$0.187198\pi$
$182$		0			0
$183$		0			0
$184$	336.000	+	581.969i	0.134621	+	0.233170i
$185$	−888.000	+	1538.06i	−0.352903	+	0.611246i
$186$		0			0
$187$	1680.00	+	2909.85i	0.656972	+	1.13791i
$188$	−1952.00			−0.757257
$189$		0			0
$190$	−2368.00			−0.904173
$191$	−1554.00	−	2691.61i	−0.588709	−	1.01967i	−0.994402	−	0.105665i	$-0.966303\pi$
$191$	−1554.00	−	2691.61i	−0.588709	−	1.01967i	0.405692	−	0.914010i	$-0.367030\pi$
$192$		0			0
$193$	−25.0000	+	43.3013i	−0.00932404	+	0.0161497i	−0.870650	−	0.491903i	$-0.836301\pi$
$193$	−25.0000	+	43.3013i	−0.00932404	+	0.0161497i	0.861326	+	0.508053i	$0.169635\pi$
$194$	832.000	+	1441.07i	0.307908	+	0.533312i
$195$		0			0
$196$		0			0
$197$	162.000			0.0585889			0.0292945	−	0.999571i	$-0.490674\pi$
$197$	162.000			0.0585889			0.0292945	+	0.999571i	$0.490674\pi$
$198$		0			0
$199$	−772.000	+	1337.14i	−0.275003	+	0.476319i	−0.970136	−	0.242562i	$-0.922012\pi$
$199$	−772.000	+	1337.14i	−0.275003	+	0.476319i	0.695133	+	0.718881i	$0.255346\pi$
$200$	244.000	−	422.620i	0.0862670	−	0.149419i
$201$		0			0
$202$	−928.000			−0.323237
$203$		0			0
$204$		0			0
$205$	−1680.00	−	2909.85i	−0.572372	−	0.991378i
$206$	632.000	−	1094.66i	0.213755	−	0.370234i
$207$		0			0
$208$	−32.0000	−	55.4256i	−0.0106673	−	0.0184763i
$209$	−5920.00			−1.95931
$210$		0			0
$211$	−1204.00			−0.392828			−0.196414	−	0.980521i	$-0.562930\pi$
$211$	−1204.00			−0.392828			−0.196414	+	0.980521i	$0.562930\pi$
$212$	956.000	+	1655.84i	0.309709	+	0.536432i
$213$		0			0
$214$	−160.000	+	277.128i	−0.0511092	+	0.0885238i
$215$	−656.000	−	1136.23i	−0.208088	−	0.360418i
$216$		0			0
$217$		0			0
$218$	−4396.00			−1.36576
$219$		0			0
$220$	−640.000	+	1108.51i	−0.196131	+	0.339709i
$221$	−168.000	+	290.985i	−0.0511353	+	0.0885690i
$222$		0			0
$223$	2000.00			0.600583			0.300291	−	0.953848i	$-0.402916\pi$
$223$	2000.00			0.600583			0.300291	+	0.953848i	$0.402916\pi$
$224$		0			0
$225$		0			0
$226$	770.000	+	1333.68i	0.226636	+	0.392544i
$227$	194.000	−	336.018i	0.0567235	−	0.0982480i	−0.836269	−	0.548319i	$-0.815268\pi$
$227$	194.000	−	336.018i	0.0567235	−	0.0982480i	0.892993	+	0.450071i	$0.148601\pi$
$228$		0			0
$229$	−2090.00	−	3619.99i	−0.603105	−	1.04461i	−0.992348	−	0.123474i	$-0.960597\pi$
$229$	−2090.00	−	3619.99i	−0.603105	−	1.04461i	0.389243	−	0.921135i	$-0.372737\pi$
$230$	1344.00			0.385308
$231$		0			0
$232$	−464.000			−0.131306
$233$	−661.000	−	1144.89i	−0.185852	−	0.321905i	0.758011	−	0.652242i	$-0.226171\pi$
$233$	−661.000	−	1144.89i	−0.185852	−	0.321905i	−0.943863	+	0.330336i	$0.892838\pi$
$234$		0			0
$235$	−1952.00	+	3380.96i	−0.541849	+	0.938509i
$236$	1096.00	+	1898.33i	0.302303	+	0.523604i
$237$		0			0
$238$		0			0
$239$	−2412.00			−0.652800			−0.326400	−	0.945232i	$-0.605836\pi$
$239$	−2412.00			−0.652800			−0.326400	+	0.945232i	$0.605836\pi$
$240$		0			0
$241$	2168.00	−	3755.09i	0.579474	−	1.00368i	−0.416066	−	0.909334i	$-0.636591\pi$
$241$	2168.00	−	3755.09i	0.579474	−	1.00368i	0.995540	−	0.0943434i	$-0.0300752\pi$
$242$	−269.000	+	465.922i	−0.0714544	+	0.123763i
$243$		0			0
$244$	2768.00			0.726242
$245$		0			0
$246$		0			0
$247$	−296.000	−	512.687i	−0.0762511	−	0.132071i
$248$	544.000	−	942.236i	0.139290	−	0.241258i
$249$		0			0
$250$	−1488.00	−	2577.29i	−0.376438	−	0.652009i
$251$	−764.000			−0.192125			−0.0960623	−	0.995375i	$-0.530625\pi$
$251$	−764.000			−0.192125			−0.0960623	+	0.995375i	$0.530625\pi$
$252$		0			0
$253$	3360.00			0.834946
$254$	184.000	+	318.697i	0.0454535	+	0.0787278i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	2150.00	+	3723.91i	0.521842	+	0.903856i	0.999677	+	0.0254070i	$0.00808817\pi$
$257$	2150.00	+	3723.91i	0.521842	+	0.903856i	−0.477835	+	0.878449i	$0.658579\pi$
$258$		0			0
$259$		0			0
$260$	−128.000			−0.0305316
$261$		0			0
$262$	−1452.00	+	2514.94i	−0.342385	+	0.593028i
$263$	−1930.00	+	3342.86i	−0.452505	+	0.783762i	−0.998541	−	0.0539998i	$-0.982803\pi$
$263$	−1930.00	+	3342.86i	−0.452505	+	0.783762i	0.546036	+	0.837762i	$0.316136\pi$
$264$		0			0
$265$	3824.00			0.886439
$266$		0			0
$267$		0			0
$268$	1816.00	+	3145.40i	0.413917	+	0.716926i
$269$	−1400.00	+	2424.87i	−0.317322	+	0.549617i	−0.979928	−	0.199350i	$-0.936117\pi$
$269$	−1400.00	+	2424.87i	−0.317322	+	0.549617i	0.662607	+	0.748968i	$0.269450\pi$
$270$		0			0
$271$	2440.00	+	4226.20i	0.546935	+	0.947320i	0.998482	+	0.0550723i	$0.0175389\pi$
$271$	2440.00	+	4226.20i	0.546935	+	0.947320i	−0.451547	+	0.892247i	$0.649128\pi$
$272$	1344.00			0.299603
$273$		0			0
$274$	−1292.00			−0.284863
$275$	−1220.00	−	2113.10i	−0.267523	−	0.463363i
$276$		0			0
$277$	3337.00	−	5779.85i	0.723830	−	1.25371i	−0.235624	−	0.971844i	$-0.575713\pi$
$277$	3337.00	−	5779.85i	0.723830	−	1.25371i	0.959454	−	0.281866i	$-0.0909533\pi$
$278$	3012.00	+	5216.94i	0.649812	+	1.12551i
$279$		0			0
$280$		0			0
$281$	9402.00			1.99600			0.998001	−	0.0632056i	$-0.0201324\pi$
$281$	9402.00			1.99600			0.998001	+	0.0632056i	$0.0201324\pi$
$282$		0			0
$283$	4550.00	−	7880.83i	0.955722	−	1.65536i	0.223016	−	0.974815i	$-0.428410\pi$
$283$	4550.00	−	7880.83i	0.955722	−	1.65536i	0.732706	−	0.680545i	$-0.238257\pi$
$284$	−1048.00	+	1815.19i	−0.218970	+	0.379266i
$285$		0			0
$286$	−320.000			−0.0661608
$287$		0			0
$288$		0			0
$289$	−1071.50	−	1855.89i	−0.218095	−	0.377751i
$290$	−464.000	+	803.672i	−0.0939552	+	0.162735i
$291$		0			0
$292$	−880.000	−	1524.20i	−0.176363	−	0.305470i
$293$	−5952.00			−1.18676			−0.593378	−	0.804924i	$-0.702206\pi$
$293$	−5952.00			−1.18676			−0.593378	+	0.804924i	$0.702206\pi$
$294$		0			0
$295$	4384.00			0.865242
$296$	888.000	+	1538.06i	0.174371	+	0.302020i
$297$		0			0
$298$	−3170.00	+	5490.60i	−0.616219	+	1.06732i
$299$	168.000	+	290.985i	0.0324939	+	0.0562812i
$300$		0			0
$301$		0			0
$302$	−3760.00			−0.716436
$303$		0			0
$304$	−1184.00	+	2050.75i	−0.223378	+	0.386903i
$305$	2768.00	−	4794.32i	0.519656	−	0.900071i
$306$		0			0
$307$	−3004.00			−0.558460			−0.279230	−	0.960224i	$-0.590079\pi$
$307$	−3004.00			−0.558460			−0.279230	+	0.960224i	$0.590079\pi$
$308$		0			0
$309$		0			0
$310$	−1088.00	−	1884.47i	−0.199336	−	0.345261i
$311$	344.000	−	595.825i	0.0627217	−	0.108637i	−0.832959	−	0.553334i	$-0.813355\pi$
$311$	344.000	−	595.825i	0.0627217	−	0.108637i	0.895681	+	0.444697i	$0.146689\pi$
$312$		0			0
$313$	−2796.00	−	4842.81i	−0.504918	−	0.874543i	−0.999984	−	0.00568790i	$-0.998189\pi$
$313$	−2796.00	−	4842.81i	−0.504918	−	0.874543i	0.495066	−	0.868855i	$-0.335144\pi$
$314$	1208.00			0.217106
$315$		0			0
$316$	4864.00			0.865890
$317$	−1461.00	−	2530.53i	−0.258858	−	0.448355i	0.707078	−	0.707135i	$-0.250013\pi$
$317$	−1461.00	−	2530.53i	−0.258858	−	0.448355i	−0.965936	+	0.258780i	$0.916679\pi$
$318$		0			0
$319$	−1160.00	+	2009.18i	−0.203597	+	0.352641i
$320$	256.000	+	443.405i	0.0447214	+	0.0774597i
$321$		0			0
$322$		0			0
$323$	12432.0			2.14159
$324$		0			0
$325$	122.000	−	211.310i	0.0208226	−	0.0360658i
$326$	−1116.00	+	1932.97i	−0.189600	+	0.328396i
$327$		0			0
$328$	−3360.00			−0.565625
$329$		0			0
$330$		0			0
$331$	3746.00	+	6488.26i	0.622051	+	1.07742i	0.989103	+	0.147223i	$0.0470336\pi$
$331$	3746.00	+	6488.26i	0.622051	+	1.07742i	−0.367053	+	0.930200i	$0.619633\pi$
$332$	−1368.00	+	2369.45i	−0.226141	+	0.391687i
$333$		0			0
$334$	−1784.00	−	3089.98i	−0.292264	−	0.506216i
$335$	7264.00			1.18470
$336$		0			0
$337$	10766.0			1.74024			0.870121	−	0.492839i	$-0.164041\pi$
$337$	10766.0			1.74024			0.870121	+	0.492839i	$0.164041\pi$
$338$	2181.00	+	3777.60i	0.350979	+	0.607913i
$339$		0			0
$340$	1344.00	−	2327.88i	0.214378	−	0.371314i
$341$	−2720.00	−	4711.18i	−0.431954	−	0.748166i
$342$		0			0
$343$		0			0
$344$	−1312.00			−0.205635
$345$		0			0
$346$	−344.000	+	595.825i	−0.0534496	+	0.0925774i
$347$	−1992.00	+	3450.25i	−0.308173	+	0.533772i	−0.977963	−	0.208779i	$-0.933051\pi$
$347$	−1992.00	+	3450.25i	−0.308173	+	0.533772i	0.669789	+	0.742551i	$0.266384\pi$
$348$		0			0
$349$	−180.000			−0.0276080			−0.0138040	−	0.999905i	$-0.504394\pi$
$349$	−180.000			−0.0276080			−0.0138040	+	0.999905i	$0.504394\pi$
$350$		0			0
$351$		0			0
$352$	640.000	+	1108.51i	0.0969094	+	0.167852i
$353$	−5214.00	+	9030.91i	−0.786156	+	1.36166i	0.142149	+	0.989845i	$0.454599\pi$
$353$	−5214.00	+	9030.91i	−0.786156	+	1.36166i	−0.928306	+	0.371818i	$0.878735\pi$
$354$		0			0
$355$	2096.00	+	3630.38i	0.313364	+	0.542762i
$356$	−2416.00			−0.359685
$357$		0			0
$358$	−2784.00			−0.411003
$359$	4342.00	+	7520.56i	0.638334	+	1.10563i	0.985798	+	0.167934i	$0.0537096\pi$
$359$	4342.00	+	7520.56i	0.638334	+	1.10563i	−0.347464	+	0.937693i	$0.612957\pi$
$360$		0			0
$361$	−7522.50	+	13029.4i	−1.09673	+	1.89960i
$362$	−4052.00	−	7018.27i	−0.588310	−	1.01898i
$363$		0			0
$364$		0			0
$365$	−3520.00			−0.504781
$366$		0			0
$367$	−2824.00	+	4891.31i	−0.401666	+	0.695707i	−0.993927	−	0.110040i	$-0.964902\pi$
$367$	−2824.00	+	4891.31i	−0.401666	+	0.695707i	0.592261	+	0.805746i	$0.298236\pi$
$368$	672.000	−	1163.94i	0.0951914	−	0.164876i
$369$		0			0
$370$	3552.00			0.499080
$371$		0			0
$372$		0			0
$373$	1273.00	+	2204.90i	0.176712	+	0.306074i	0.940752	−	0.339095i	$-0.110121\pi$
$373$	1273.00	+	2204.90i	0.176712	+	0.306074i	−0.764041	+	0.645168i	$0.776787\pi$
$374$	3360.00	−	5819.69i	0.464549	−	0.804623i
$375$		0			0
$376$	1952.00	+	3380.96i	0.267731	+	0.463723i
$377$	−232.000			−0.0316939
$378$		0			0
$379$	8268.00			1.12058			0.560288	−	0.828298i	$-0.310690\pi$
$379$	8268.00			1.12058			0.560288	+	0.828298i	$0.310690\pi$
$380$	2368.00	+	4101.50i	0.319673	+	0.553690i
$381$		0			0
$382$	−3108.00	+	5383.21i	−0.416280	+	0.721019i
$383$	−5436.00	−	9415.43i	−0.725239	−	1.25615i	−0.958875	−	0.283827i	$-0.908396\pi$
$383$	−5436.00	−	9415.43i	−0.725239	−	1.25615i	0.233636	−	0.972324i	$-0.424938\pi$
$384$		0			0
$385$		0			0
$386$	100.000			0.0131862
$387$		0			0
$388$	1664.00	−	2882.13i	0.217724	−	0.377109i
$389$	5217.00	−	9036.11i	0.679980	−	1.17776i	−0.295006	−	0.955495i	$-0.595322\pi$
$389$	5217.00	−	9036.11i	0.679980	−	1.17776i	0.974986	−	0.222265i	$-0.0713451\pi$
$390$		0			0
$391$	−7056.00			−0.912627
$392$		0			0
$393$		0			0
$394$	−162.000	−	280.592i	−0.0207143	−	0.0358783i
$395$	4864.00	−	8424.70i	0.619581	−	1.07315i
$396$		0			0
$397$	1522.00	+	2636.18i	0.192411	+	0.333265i	0.946049	−	0.324025i	$-0.105036\pi$
$397$	1522.00	+	2636.18i	0.192411	+	0.333265i	−0.753638	+	0.657290i	$0.771703\pi$
$398$	3088.00			0.388913
$399$		0			0
$400$	−976.000			−0.122000
$401$	4455.00	+	7716.29i	0.554793	+	0.960930i	0.997920	+	0.0644709i	$0.0205360\pi$
$401$	4455.00	+	7716.29i	0.554793	+	0.960930i	−0.443126	+	0.896459i	$0.646131\pi$
$402$		0			0
$403$	272.000	−	471.118i	0.0336211	−	0.0582334i
$404$	928.000	+	1607.34i	0.114281	+	0.197941i
$405$		0			0
$406$		0			0
$407$	8880.00			1.08149
$408$		0			0
$409$	−2808.00	+	4863.60i	−0.339478	+	0.587994i	−0.984335	−	0.176310i	$-0.943584\pi$
$409$	−2808.00	+	4863.60i	−0.339478	+	0.587994i	0.644856	+	0.764304i	$0.276917\pi$
$410$	−3360.00	+	5819.69i	−0.404728	+	0.701010i
$411$		0			0
$412$	−2528.00			−0.302295
$413$		0			0
$414$		0			0
$415$	2736.00	+	4738.89i	0.323626	+	0.560537i
$416$	−64.0000	+	110.851i	−0.00754293	+	0.0130647i
$417$		0			0
$418$	5920.00	+	10253.7i	0.692719	+	1.19983i
$419$	8932.00			1.04142			0.520712	−	0.853732i	$-0.325666\pi$
$419$	8932.00			1.04142			0.520712	+	0.853732i	$0.325666\pi$
$420$		0			0
$421$	−5538.00			−0.641106			−0.320553	−	0.947231i	$-0.603869\pi$
$421$	−5538.00			−0.641106			−0.320553	+	0.947231i	$0.603869\pi$
$422$	1204.00	+	2085.39i	0.138886	+	0.240557i
$423$		0			0
$424$	1912.00	−	3311.68i	0.218997	−	0.379315i
$425$	2562.00	+	4437.51i	0.292412	+	0.506473i
$426$		0			0
$427$		0			0
$428$	640.000			0.0722794
$429$		0			0
$430$	−1312.00	+	2272.45i	−0.147140	+	0.254854i
$431$	−3350.00	+	5802.37i	−0.374394	+	0.648469i	−0.990236	−	0.139400i	$-0.955483\pi$
$431$	−3350.00	+	5802.37i	−0.374394	+	0.648469i	0.615842	+	0.787870i	$0.288816\pi$
$432$		0			0
$433$	−5048.00			−0.560257			−0.280129	−	0.959962i	$-0.590377\pi$
$433$	−5048.00			−0.560257			−0.280129	+	0.959962i	$0.590377\pi$
$434$		0			0
$435$		0			0
$436$	4396.00	+	7614.10i	0.482867	+	0.836351i
$437$	6216.00	−	10766.4i	0.680438	−	1.17855i
$438$		0			0
$439$	672.000	+	1163.94i	0.0730588	+	0.126542i	0.900240	−	0.435393i	$-0.143391\pi$
$439$	672.000	+	1163.94i	0.0730588	+	0.126542i	−0.827182	+	0.561935i	$0.810057\pi$
$440$	2560.00			0.277371
$441$		0			0
$442$	672.000			0.0723162
$443$	−2196.00	−	3803.58i	−0.235519	−	0.407932i	0.723904	−	0.689901i	$-0.242346\pi$
$443$	−2196.00	−	3803.58i	−0.235519	−	0.407932i	−0.959424	+	0.281969i	$0.909012\pi$
$444$		0			0
$445$	−2416.00	+	4184.63i	−0.257369	+	0.445777i
$446$	−2000.00	−	3464.10i	−0.212338	−	0.367780i
$447$		0			0
$448$		0			0
$449$	−3666.00			−0.385321			−0.192661	−	0.981265i	$-0.561712\pi$
$449$	−3666.00			−0.385321			−0.192661	+	0.981265i	$0.561712\pi$
$450$		0			0
$451$	−8400.00	+	14549.2i	−0.877030	+	1.51906i
$452$	1540.00	−	2667.36i	0.160256	−	0.277571i
$453$		0			0
$454$	−776.000			−0.0802191
$455$		0			0
$456$		0			0
$457$	−13.0000	−	22.5167i	−0.00133067	−	0.00230478i	0.865359	−	0.501152i	$-0.167090\pi$
$457$	−13.0000	−	22.5167i	−0.00133067	−	0.00230478i	−0.866690	+	0.498847i	$0.833757\pi$
$458$	−4180.00	+	7239.97i	−0.426460	+	0.738650i
$459$		0			0
$460$	−1344.00	−	2327.88i	−0.136227	−	0.235952i
$461$	−7656.00			−0.773483			−0.386741	−	0.922188i	$-0.626399\pi$
$461$	−7656.00			−0.773483			−0.386741	+	0.922188i	$0.626399\pi$
$462$		0			0
$463$	12608.0			1.26554			0.632768	−	0.774341i	$-0.281919\pi$
$463$	12608.0			1.26554			0.632768	+	0.774341i	$0.281919\pi$
$464$	464.000	+	803.672i	0.0464238	+	0.0804084i
$465$		0			0
$466$	−1322.00	+	2289.77i	−0.131417	+	0.227621i
$467$	−1534.00	−	2656.97i	−0.152002	−	0.263276i	0.779961	−	0.625828i	$-0.215239\pi$
$467$	−1534.00	−	2656.97i	−0.152002	−	0.263276i	−0.931963	+	0.362552i	$0.881905\pi$
$468$		0			0
$469$		0			0
$470$	7808.00			0.766290
$471$		0			0
$472$	2192.00	−	3796.66i	0.213761	−	0.370244i
$473$	−3280.00	+	5681.13i	−0.318847	+	0.552259i
$474$		0			0
$475$	−9028.00			−0.872070
$476$		0			0
$477$		0			0
$478$	2412.00	+	4177.71i	0.230800	+	0.399757i
$479$	3228.00	−	5591.06i	0.307915	−	0.533324i	−0.669991	−	0.742369i	$-0.733702\pi$
$479$	3228.00	−	5591.06i	0.307915	−	0.533324i	0.977906	+	0.209045i	$0.0670356\pi$
$480$		0			0
$481$	444.000	+	769.031i	0.0420887	+	0.0728997i
$482$	−8672.00			−0.819500
$483$		0			0
$484$	1076.00			0.101052
$485$	−3328.00	−	5764.27i	−0.311581	−	0.539674i
$486$		0			0
$487$	−5948.00	+	10302.2i	−0.553449	+	0.958602i	0.444574	+	0.895742i	$0.353355\pi$
$487$	−5948.00	+	10302.2i	−0.553449	+	0.958602i	−0.998022	+	0.0628592i	$0.979978\pi$
$488$	−2768.00	−	4794.32i	−0.256765	−	0.444731i
$489$		0			0
$490$		0			0
$491$	264.000			0.0242651			0.0121325	−	0.999926i	$-0.496138\pi$
$491$	264.000			0.0242651			0.0121325	+	0.999926i	$0.496138\pi$
$492$		0			0
$493$	2436.00	−	4219.28i	0.222539	−	0.385450i
$494$	−592.000	+	1025.37i	−0.0539177	+	0.0933882i
$495$		0			0
$496$	−2176.00			−0.196986
$497$		0			0
$498$		0			0
$499$	1314.00	+	2275.91i	0.117881	+	0.204176i	0.918928	−	0.394426i	$-0.129056\pi$
$499$	1314.00	+	2275.91i	0.117881	+	0.204176i	−0.801047	+	0.598602i	$0.795723\pi$
$500$	−2976.00	+	5154.58i	−0.266182	+	0.461040i
$501$		0			0
$502$	764.000	+	1323.29i	0.0679263	+	0.117652i
$503$	13568.0			1.20272			0.601359	−	0.798979i	$-0.294626\pi$
$503$	13568.0			1.20272			0.601359	+	0.798979i	$0.294626\pi$
$504$		0			0
$505$	3712.00			0.327093
$506$	−3360.00	−	5819.69i	−0.295198	−	0.511298i
$507$		0			0
$508$	368.000	−	637.395i	0.0321405	−	0.0556689i
$509$	10328.0	+	17888.6i	0.899372	+	1.55776i	0.828298	+	0.560288i	$0.189309\pi$
$509$	10328.0	+	17888.6i	0.899372	+	1.55776i	0.0710743	+	0.997471i	$0.477357\pi$
$510$		0			0
$511$		0			0
$512$	512.000			0.0441942
$513$		0			0
$514$	4300.00	−	7447.82i	0.368998	−	0.639123i
$515$	−2528.00	+	4378.62i	−0.216305	+	0.374651i
$516$		0			0
$517$	19520.0			1.66052
$518$		0			0
$519$		0			0
$520$	128.000	+	221.703i	0.0107946	+	0.0186967i
$521$	1814.00	−	3141.94i	0.152539	−	0.264205i	−0.779621	−	0.626251i	$-0.784588\pi$
$521$	1814.00	−	3141.94i	0.152539	−	0.264205i	0.932160	+	0.362046i	$0.117922\pi$
$522$		0			0
$523$	−2426.00	−	4201.96i	−0.202833	−	0.351317i	0.746607	−	0.665265i	$-0.231681\pi$
$523$	−2426.00	−	4201.96i	−0.202833	−	0.351317i	−0.949440	+	0.313948i	$0.898348\pi$
$524$	5808.00			0.484205
$525$		0			0
$526$	7720.00			0.639939
$527$	5712.00	+	9893.47i	0.472142	+	0.817773i
$528$		0			0
$529$	2555.50	−	4426.26i	0.210035	−	0.363792i
$530$	−3824.00	−	6623.36i	−0.313404	−	0.542831i
$531$		0			0
$532$		0			0
$533$	−1680.00			−0.136527
$534$		0			0
$535$	640.000	−	1108.51i	0.0517189	−	0.0895798i
$536$	3632.00	−	6290.81i	0.292684	−	0.506943i
$537$		0			0
$538$	5600.00			0.448760
$539$		0			0
$540$		0			0
$541$	3565.00	+	6174.76i	0.283311	+	0.490709i	0.972198	−	0.234159i	$-0.0752338\pi$
$541$	3565.00	+	6174.76i	0.283311	+	0.490709i	−0.688887	+	0.724869i	$0.741900\pi$
$542$	4880.00	−	8452.41i	0.386742	−	0.669856i
$543$		0			0
$544$	−1344.00	−	2327.88i	−0.105926	−	0.183469i
$545$	17584.0			1.38205
$546$		0			0
$547$	−12788.0			−0.999589			−0.499795	−	0.866144i	$-0.666591\pi$
$547$	−12788.0			−0.999589			−0.499795	+	0.866144i	$0.666591\pi$
$548$	1292.00	+	2237.81i	0.100714	+	0.174443i
$549$		0			0
$550$	−2440.00	+	4226.20i	−0.189167	+	0.327647i
$551$	4292.00	+	7433.96i	0.331843	+	0.574768i
$552$		0			0
$553$		0			0
$554$	−13348.0			−1.02365
$555$		0			0
$556$	6024.00	−	10433.9i	0.459487	−	0.795854i
$557$	1203.00	−	2083.66i	0.0915130	−	0.158505i	−0.816635	−	0.577155i	$-0.804163\pi$
$557$	1203.00	−	2083.66i	0.0915130	−	0.158505i	0.908148	+	0.418649i	$0.137496\pi$
$558$		0			0
$559$	−656.000			−0.0496348
$560$		0			0
$561$		0			0
$562$	−9402.00	−	16284.7i	−0.705693	−	1.22230i
$563$	−12706.0	+	22007.4i	−0.951144	+	1.64743i	−0.208189	+	0.978089i	$0.566757\pi$
$563$	−12706.0	+	22007.4i	−0.951144	+	1.64743i	−0.742955	+	0.669341i	$0.766577\pi$
$564$		0			0
$565$	−3080.00	−	5334.72i	−0.229339	−	0.397227i
$566$	−18200.0			−1.35160
$567$		0			0
$568$	4192.00			0.309670
$569$	−4845.00	−	8391.79i	−0.356965	−	0.618281i	0.630487	−	0.776199i	$-0.282855\pi$
$569$	−4845.00	−	8391.79i	−0.356965	−	0.618281i	−0.987452	+	0.157918i	$0.949522\pi$
$570$		0			0
$571$	−2802.00	+	4853.21i	−0.205359	+	0.355692i	−0.950247	−	0.311497i	$-0.899170\pi$
$571$	−2802.00	+	4853.21i	−0.205359	+	0.355692i	0.744888	+	0.667190i	$0.232503\pi$
$572$	320.000	+	554.256i	0.0233914	+	0.0405151i
$573$		0			0
$574$		0			0
$575$	5124.00			0.371627
$576$		0			0
$577$	10784.0	−	18678.4i	0.778066	−	1.34765i	−0.154990	−	0.987916i	$-0.549534\pi$
$577$	10784.0	−	18678.4i	0.778066	−	1.34765i	0.933055	−	0.359733i	$-0.117132\pi$
$578$	−2143.00	+	3711.78i	−0.154216	+	0.267111i
$579$		0			0
$580$	1856.00			0.132873
$581$		0			0
$582$		0			0
$583$	−9560.00	−	16558.4i	−0.679133	−	1.17629i
$584$	−1760.00	+	3048.41i	−0.124708	+	0.216000i
$585$		0			0
$586$	5952.00	+	10309.2i	0.419582	+	0.726737i
$587$	−20300.0			−1.42738			−0.713689	−	0.700463i	$-0.752977\pi$
$587$	−20300.0			−1.42738			−0.713689	+	0.700463i	$0.752977\pi$
$588$		0			0
$589$	−20128.0			−1.40808
$590$	−4384.00	−	7593.31i	−0.305909	−	0.529850i
$591$		0			0
$592$	1776.00	−	3076.12i	0.123299	−	0.213561i
$593$	6906.00	+	11961.5i	0.478238	+	0.828333i	0.999689	−	0.0249483i	$-0.00794212\pi$
$593$	6906.00	+	11961.5i	0.478238	+	0.828333i	−0.521450	+	0.853282i	$0.674609\pi$
$594$		0			0
$595$		0			0
$596$	12680.0			0.871465
$597$		0			0
$598$	336.000	−	581.969i	0.0229767	−	0.0397968i
$599$	−10998.0	+	19049.1i	−0.750194	+	1.29937i	0.197535	+	0.980296i	$0.436706\pi$
$599$	−10998.0	+	19049.1i	−0.750194	+	1.29937i	−0.947728	+	0.319078i	$0.896627\pi$
$600$		0			0
$601$	8368.00			0.567950			0.283975	−	0.958832i	$-0.408347\pi$
$601$	8368.00			0.567950			0.283975	+	0.958832i	$0.408347\pi$
$602$		0			0
$603$		0			0
$604$	3760.00	+	6512.51i	0.253298	+	0.438726i
$605$	1076.00	−	1863.69i	0.0723068	−	0.125239i
$606$		0			0
$607$	−10752.0	−	18623.0i	−0.718962	−	1.24528i	−0.961411	−	0.275115i	$-0.911284\pi$
$607$	−10752.0	−	18623.0i	−0.718962	−	1.24528i	0.242449	−	0.970164i	$-0.422049\pi$
$608$	4736.00			0.315905
$609$		0			0
$610$	−11072.0			−0.734905
$611$	976.000	+	1690.48i	0.0646231	+	0.111931i
$612$		0			0
$613$	5135.00	−	8894.08i	0.338337	−	0.586017i	−0.645783	−	0.763521i	$-0.723469\pi$
$613$	5135.00	−	8894.08i	0.338337	−	0.586017i	0.984120	+	0.177504i	$0.0568022\pi$
$614$	3004.00	+	5203.08i	0.197446	+	0.341986i
$615$		0			0
$616$		0			0
$617$	−28358.0			−1.85032			−0.925162	−	0.379572i	$-0.876071\pi$
$617$	−28358.0			−1.85032			−0.925162	+	0.379572i	$0.876071\pi$
$618$		0			0
$619$	−8146.00	+	14109.3i	−0.528942	+	0.916155i	0.470488	+	0.882406i	$0.344078\pi$
$619$	−8146.00	+	14109.3i	−0.528942	+	0.916155i	−0.999430	+	0.0337488i	$0.989255\pi$
$620$	−2176.00	+	3768.94i	−0.140952	+	0.244136i
$621$		0			0
$622$	−1376.00			−0.0887019
$623$		0			0
$624$		0			0
$625$	2139.50	+	3705.72i	0.136928	+	0.237166i
$626$	−5592.00	+	9685.63i	−0.357031	+	0.618395i
$627$		0			0
$628$	−1208.00	−	2092.32i	−0.0767587	−	0.132950i
$629$	−18648.0			−1.18211
$630$		0			0
$631$	11256.0			0.710134			0.355067	−	0.934841i	$-0.384458\pi$
$631$	11256.0			0.710134			0.355067	+	0.934841i	$0.384458\pi$
$632$	−4864.00	−	8424.70i	−0.306138	−	0.530247i
$633$		0			0
$634$	−2922.00	+	5061.05i	−0.183040	+	0.317035i
$635$	−736.000	−	1274.79i	−0.0459957	−	0.0796669i
$636$		0			0
$637$		0			0
$638$	4640.00			0.287930
$639$		0			0
$640$	512.000	−	886.810i	0.0316228	−	0.0547723i
$641$	7759.00	−	13439.0i	0.478100	−	0.828093i	−0.521585	−	0.853199i	$-0.674659\pi$
$641$	7759.00	−	13439.0i	0.478100	−	0.828093i	0.999685	+	0.0251060i	$0.00799233\pi$
$642$		0			0
$643$	−10452.0			−0.641037			−0.320518	−	0.947242i	$-0.603857\pi$
$643$	−10452.0			−0.641037			−0.320518	+	0.947242i	$0.603857\pi$
$644$		0			0
$645$		0			0
$646$	−12432.0	−	21532.9i	−0.757168	−	1.31145i
$647$	36.0000	−	62.3538i	0.00218749	−	0.00378884i	−0.864930	−	0.501893i	$-0.832637\pi$
$647$	36.0000	−	62.3538i	0.00218749	−	0.00378884i	0.867117	+	0.498104i	$0.165970\pi$
$648$		0			0
$649$	−10960.0	−	18983.3i	−0.662893	−	1.14816i
$650$	−488.000			−0.0294476
$651$		0			0
$652$	4464.00			0.268135
$653$	5981.00	+	10359.4i	0.358430	+	0.620819i	0.987699	−	0.156369i	$-0.0499789\pi$
$653$	5981.00	+	10359.4i	0.358430	+	0.620819i	−0.629269	+	0.777188i	$0.716646\pi$
$654$		0			0
$655$	5808.00	−	10059.8i	0.346469	−	0.600102i
$656$	3360.00	+	5819.69i	0.199979	+	0.346373i
$657$		0			0
$658$		0			0
$659$	6016.00			0.355615			0.177807	−	0.984065i	$-0.443100\pi$
$659$	6016.00			0.355615			0.177807	+	0.984065i	$0.443100\pi$
$660$		0			0
$661$	−13034.0	+	22575.6i	−0.766965	+	1.32842i	0.172236	+	0.985056i	$0.444901\pi$
$661$	−13034.0	+	22575.6i	−0.766965	+	1.32842i	−0.939201	+	0.343367i	$0.888433\pi$
$662$	7492.00	−	12976.5i	0.439856	−	0.761853i
$663$		0			0
$664$	5472.00			0.319811
$665$		0			0
$666$		0			0
$667$	−2436.00	−	4219.28i	−0.141413	−	0.244934i
$668$	−3568.00	+	6179.96i	−0.206662	+	0.357949i
$669$		0			0
$670$	−7264.00	−	12581.6i	−0.418855	−	0.725478i
$671$	−27680.0			−1.59251
$672$		0			0
$673$	−20530.0			−1.17589			−0.587945	−	0.808901i	$-0.700063\pi$
$673$	−20530.0			−1.17589			−0.587945	+	0.808901i	$0.700063\pi$
$674$	−10766.0	−	18647.3i	−0.615268	−	1.06568i
$675$		0			0
$676$	4362.00	−	7555.21i	0.248179	−	0.429859i
$677$	−5028.00	−	8708.75i	−0.285438	−	0.494394i	0.687277	−	0.726395i	$-0.258806\pi$
$677$	−5028.00	−	8708.75i	−0.285438	−	0.494394i	−0.972715	+	0.232002i	$0.925473\pi$
$678$		0			0
$679$		0			0
$680$	−5376.00			−0.303177
$681$		0			0
$682$	−5440.00	+	9422.36i	−0.305437	+	0.529033i
$683$	3076.00	−	5327.79i	0.172328	−	0.298480i	−0.766905	−	0.641760i	$-0.778205\pi$
$683$	3076.00	−	5327.79i	0.172328	−	0.298480i	0.939233	+	0.343280i	$0.111538\pi$
$684$		0			0
$685$	5168.00			0.288262
$686$		0			0
$687$		0			0
$688$	1312.00	+	2272.45i	0.0727028	+	0.125925i
$689$	956.000	−	1655.84i	0.0528602	−	0.0915566i
$690$		0			0
$691$	7358.00	+	12744.4i	0.405082	+	0.701622i	0.994331	−	0.106329i	$-0.0339097\pi$
$691$	7358.00	+	12744.4i	0.405082	+	0.701622i	−0.589249	+	0.807951i	$0.700576\pi$
$692$	1376.00			0.0755891
$693$		0			0
$694$	7968.00			0.435823
$695$	−12048.0	−	20867.7i	−0.657564	−	1.13893i
$696$		0			0
$697$	17640.0	−	30553.4i	0.958626	−	1.66039i
$698$	180.000	+	311.769i	0.00976089	+	0.0169064i
$699$		0			0
$700$		0			0
$701$	−28202.0			−1.51951			−0.759754	−	0.650211i	$-0.774681\pi$
$701$	−28202.0			−1.51951			−0.759754	+	0.650211i	$0.774681\pi$
$702$		0			0
$703$	16428.0	−	28454.1i	0.881357	−	1.52655i
$704$	1280.00	−	2217.03i	0.0685253	−	0.118689i
$705$		0			0
$706$	20856.0			1.11179
$707$		0			0
$708$		0			0
$709$	−11057.0	−	19151.3i	−0.585690	−	1.01445i	−0.994789	−	0.101955i	$-0.967490\pi$
$709$	−11057.0	−	19151.3i	−0.585690	−	1.01445i	0.409099	−	0.912490i	$-0.365843\pi$
$710$	4192.00	−	7260.76i	0.221582	−	0.383791i
$711$		0			0
$712$	2416.00	+	4184.63i	0.127168	+	0.220261i
$713$	11424.0			0.600045
$714$		0			0
$715$	1280.00			0.0669501
$716$	2784.00	+	4822.03i	0.145311	+	0.251687i
$717$		0			0
$718$	8684.00	−	15041.1i	0.451370	−	0.781797i
$719$	−4644.00	−	8043.64i	−0.240879	−	0.417215i	0.720086	−	0.693885i	$-0.244102\pi$
$719$	−4644.00	−	8043.64i	−0.240879	−	0.417215i	−0.960965	+	0.276670i	$0.910769\pi$
$720$		0			0
$721$		0			0
$722$	30090.0			1.55102
$723$		0			0
$724$	−8104.00	+	14036.5i	−0.415998	+	0.720530i
$725$	−1769.00	+	3064.00i	−0.0906193	+	0.156957i
$726$		0			0
$727$	23848.0			1.21661			0.608304	−	0.793704i	$-0.291850\pi$
$727$	23848.0			1.21661			0.608304	+	0.793704i	$0.291850\pi$
$728$		0			0
$729$		0			0
$730$	3520.00	+	6096.82i	0.178467	+	0.309114i
$731$	6888.00	−	11930.4i	0.348511	−	0.603640i
$732$		0			0
$733$	17378.0	+	30099.6i	0.875677	+	1.51672i	0.856040	+	0.516909i	$0.172918\pi$
$733$	17378.0	+	30099.6i	0.875677	+	1.51672i	0.0196367	+	0.999807i	$0.493749\pi$
$734$	11296.0			0.568042
$735$		0			0
$736$	−2688.00			−0.134621
$737$	−18160.0	−	31454.0i	−0.907642	−	1.57208i
$738$		0			0
$739$	−13022.0	+	22554.8i	−0.648203	+	1.12272i	0.335349	+	0.942094i	$0.391146\pi$
$739$	−13022.0	+	22554.8i	−0.648203	+	1.12272i	−0.983552	+	0.180626i	$0.942187\pi$
$740$	−3552.00	−	6152.24i	−0.176452	−	0.305623i
$741$		0			0
$742$		0			0
$743$	−36204.0			−1.78761			−0.893806	−	0.448454i	$-0.851975\pi$
$743$	−36204.0			−1.78761			−0.893806	+	0.448454i	$0.851975\pi$
$744$		0			0
$745$	12680.0	−	21962.4i	0.623569	−	1.08005i
$746$	2546.00	−	4409.80i	0.124954	−	0.216427i
$747$		0			0
$748$	−13440.0			−0.656972
$749$		0			0
$750$		0			0
$751$	5712.00	+	9893.47i	0.277542	+	0.480716i	0.970773	−	0.239999i	$-0.0771470\pi$
$751$	5712.00	+	9893.47i	0.277542	+	0.480716i	−0.693232	+	0.720715i	$0.743814\pi$
$752$	3904.00	−	6761.93i	0.189314	−	0.327902i
$753$		0			0
$754$	232.000	+	401.836i	0.0112055	+	0.0194085i
$755$	15040.0			0.724982
$756$		0			0
$757$	−16622.0			−0.798067			−0.399034	−	0.916936i	$-0.630654\pi$
$757$	−16622.0			−0.798067			−0.399034	+	0.916936i	$0.630654\pi$
$758$	−8268.00	−	14320.6i	−0.396184	−	0.686210i
$759$		0			0
$760$	4736.00	−	8202.99i	0.226043	−	0.391518i
$761$	−19262.0	−	33362.8i	−0.917539	−	1.58922i	−0.803141	−	0.595789i	$-0.796840\pi$
$761$	−19262.0	−	33362.8i	−0.917539	−	1.58922i	−0.114397	−	0.993435i	$-0.536494\pi$
$762$		0			0
$763$		0			0
$764$	12432.0			0.588709
$765$		0			0
$766$	−10872.0	+	18830.9i	−0.512822	+	0.888233i
$767$	1096.00	−	1898.33i	0.0515962	−	0.0893672i
$768$		0			0
$769$	−18440.0			−0.864712			−0.432356	−	0.901703i	$-0.642318\pi$
$769$	−18440.0			−0.864712			−0.432356	+	0.901703i	$0.642318\pi$
$770$		0			0
$771$		0			0
$772$	−100.000	−	173.205i	−0.00466202	−	0.00807485i
$773$	−6984.00	+	12096.6i	−0.324964	+	0.562854i	−0.981505	−	0.191436i	$-0.938685\pi$
$773$	−6984.00	+	12096.6i	−0.324964	+	0.562854i	0.656541	+	0.754290i	$0.272019\pi$
$774$		0			0
$775$	−4148.00	−	7184.55i	−0.192259	−	0.333002i
$776$	−6656.00			−0.307908
$777$		0			0
$778$	−20868.0			−0.961638
$779$	31080.0	+	53832.1i	1.42947	+	2.47591i
$780$		0			0
$781$	10480.0	−	18151.9i	0.480159	−	0.831659i
$782$	7056.00	+	12221.4i	0.322662	+	0.558868i
$783$		0			0
$784$		0			0
$785$	−4832.00			−0.219696
$786$		0			0
$787$	−5458.00	+	9453.53i	−0.247213	+	0.428186i	−0.962752	−	0.270388i	$-0.912848\pi$
$787$	−5458.00	+	9453.53i	−0.247213	+	0.428186i	0.715538	+	0.698573i	$0.246181\pi$
$788$	−324.000	+	561.184i	−0.0146472	+	0.0253698i
$789$		0			0
$790$	−19456.0			−0.876220
$791$		0			0
$792$		0			0
$793$	−1384.00	−	2397.16i	−0.0619764	−	0.107346i
$794$	3044.00	−	5272.36i	0.136055	−	0.235654i
$795$		0			0
$796$	−3088.00	−	5348.57i	−0.137502	−	0.238160i
$797$	−12360.0			−0.549327			−0.274664	−	0.961540i	$-0.588566\pi$
$797$	−12360.0			−0.549327			−0.274664	+	0.961540i	$0.588566\pi$
$798$		0			0
$799$	−40992.0			−1.81501
$800$	976.000	+	1690.48i	0.0431335	+	0.0747094i
$801$		0			0
$802$	8910.00	−	15432.6i	0.392298	−	0.679480i
$803$	8800.00	+	15242.0i	0.386731	+	0.669838i
$804$		0			0
$805$		0			0
$806$	−1088.00			−0.0475474
$807$		0			0
$808$	1856.00	−	3214.69i	0.0808092	−	0.139966i
$809$	1701.00	−	2946.22i	0.0739233	−	0.128039i	−0.826694	−	0.562651i	$-0.809781\pi$
$809$	1701.00	−	2946.22i	0.0739233	−	0.128039i	0.900618	+	0.434612i	$0.143115\pi$
$810$		0			0
$811$	292.000			0.0126430			0.00632152	−	0.999980i	$-0.497988\pi$
$811$	292.000			0.0126430			0.00632152	+	0.999980i	$0.497988\pi$
$812$		0			0
$813$		0			0
$814$	−8880.00	−	15380.6i	−0.382363	−	0.662273i
$815$	4464.00	−	7731.87i	0.191861	−	0.332314i
$816$		0			0
$817$	12136.0	+	21020.2i	0.519688	+	0.900126i
$818$	11232.0			0.480095
$819$		0			0
$820$	13440.0			0.572372
$821$	3455.00	+	5984.24i	0.146870	+	0.254386i	0.930069	−	0.367385i	$-0.119747\pi$
$821$	3455.00	+	5984.24i	0.146870	+	0.254386i	−0.783199	+	0.621771i	$0.786413\pi$
$822$		0			0
$823$	−284.000	+	491.902i	−0.0120287	+	0.0208343i	−0.871977	−	0.489547i	$-0.837162\pi$
$823$	−284.000	+	491.902i	−0.0120287	+	0.0208343i	0.859948	+	0.510381i	$0.170496\pi$
$824$	2528.00	+	4378.62i	0.106877	+	0.185117i
$825$		0			0
$826$		0			0
$827$	12144.0			0.510627			0.255313	−	0.966858i	$-0.417821\pi$
$827$	12144.0			0.510627			0.255313	+	0.966858i	$0.417821\pi$
$828$		0			0
$829$	−7414.00	+	12841.4i	−0.310614	+	0.537999i	−0.978495	−	0.206269i	$-0.933868\pi$
$829$	−7414.00	+	12841.4i	−0.310614	+	0.537999i	0.667882	+	0.744268i	$0.267201\pi$
$830$	5472.00	−	9477.78i	0.228838	−	0.396360i
$831$		0			0
$832$	256.000			0.0106673
$833$		0			0
$834$		0			0
$835$	7136.00	+	12359.9i	0.295750	+	0.512254i
$836$	11840.0	−	20507.5i	0.489827	−	0.848404i
$837$		0			0
$838$	−8932.00	−	15470.7i	−0.368199	−	0.637739i
$839$	22824.0			0.939180			0.469590	−	0.882885i	$-0.344402\pi$
$839$	22824.0			0.939180			0.469590	+	0.882885i	$0.344402\pi$
$840$		0			0
$841$	−21025.0			−0.862069
$842$	5538.00	+	9592.10i	0.226665	+	0.392596i
$843$		0			0
$844$	2408.00	−	4170.78i	0.0982071	−	0.170100i
$845$	−8724.00	−	15110.4i	−0.355165	−	0.615164i
$846$		0			0
$847$		0			0
$848$	−7648.00			−0.309709
$849$		0			0
$850$	5124.00	−	8875.03i	0.206767	−	0.358131i
$851$	−9324.00	+	16149.6i	−0.375585	+	0.650532i
$852$		0			0
$853$	−41780.0			−1.67705			−0.838523	−	0.544866i	$-0.816580\pi$
$853$	−41780.0			−1.67705			−0.838523	+	0.544866i	$0.816580\pi$
$854$		0			0
$855$		0			0
$856$	−640.000	−	1108.51i	−0.0255546	−	0.0442619i
$857$	−10710.0	+	18550.3i	−0.426892	+	0.739399i	−0.996595	−	0.0824518i	$-0.973725\pi$
$857$	−10710.0	+	18550.3i	−0.426892	+	0.739399i	0.569703	+	0.821851i	$0.307058\pi$
$858$		0			0
$859$	9066.00	+	15702.8i	0.360102	+	0.623716i	0.987977	−	0.154599i	$-0.0494084\pi$
$859$	9066.00	+	15702.8i	0.360102	+	0.623716i	−0.627875	+	0.778314i	$0.716075\pi$
$860$	5248.00			0.208088
$861$		0			0
$862$	13400.0			0.529473
$863$	12018.0	+	20815.8i	0.474041	+	0.821063i	0.999558	−	0.0297197i	$-0.00946147\pi$
$863$	12018.0	+	20815.8i	0.474041	+	0.821063i	−0.525517	+	0.850783i	$0.676128\pi$
$864$		0			0
$865$	1376.00	−	2383.30i	0.0540872	−	0.0936817i
$866$	5048.00	+	8743.39i	0.198081	+	0.343086i
$867$		0			0
$868$		0			0
$869$	−48640.0			−1.89873
$870$		0			0
$871$	1816.00	−	3145.40i	0.0706462	−	0.122363i
$872$	8792.00	−	15228.2i	0.341439	−	0.591389i
$873$		0			0
$874$	−24864.0			−0.962285
$875$		0			0
$876$		0			0
$877$	2187.00	+	3788.00i	0.0842072	+	0.145851i	0.905053	−	0.425299i	$-0.139831\pi$
$877$	2187.00	+	3788.00i	0.0842072	+	0.145851i	−0.820846	+	0.571150i	$0.806498\pi$
$878$	1344.00	−	2327.88i	0.0516604	−	0.0894784i
$879$		0			0
$880$	−2560.00	−	4434.05i	−0.0980654	−	0.169854i
$881$	46348.0			1.77242			0.886211	−	0.463282i	$-0.153328\pi$
$881$	46348.0			1.77242			0.886211	+	0.463282i	$0.153328\pi$
$882$		0			0
$883$	−20660.0			−0.787389			−0.393694	−	0.919241i	$-0.628803\pi$
$883$	−20660.0			−0.787389			−0.393694	+	0.919241i	$0.628803\pi$
$884$	−672.000	−	1163.94i	−0.0255677	−	0.0442845i
$885$		0			0
$886$	−4392.00	+	7607.17i	−0.166537	+	0.288451i
$887$	−900.000	−	1558.85i	−0.0340688	−	0.0590089i	0.848488	−	0.529214i	$-0.177513\pi$
$887$	−900.000	−	1558.85i	−0.0340688	−	0.0590089i	−0.882557	+	0.470205i	$0.844180\pi$
$888$		0			0
$889$		0			0
$890$	9664.00			0.363975
$891$		0			0
$892$	−4000.00	+	6928.20i	−0.150146	+	0.260060i
$893$	36112.0	−	62547.8i	1.35324	−	2.34388i
$894$		0			0
$895$	11136.0			0.415906
$896$		0			0
$897$		0			0
$898$	3666.00	+	6349.70i	0.136232	+	0.235960i
$899$	−3944.00	+	6831.21i	−0.146318	+	0.253430i
$900$		0			0
$901$	20076.0	+	34772.7i	0.742318	+	1.28573i
$902$	33600.0			1.24031
$903$		0			0
$904$	−6160.00			−0.226636
$905$	16208.0	+	28073.1i	0.595328	+	1.03114i
$906$		0			0
$907$	20998.0	−	36369.6i	0.768718	−	1.33146i	−0.169540	−	0.985523i	$-0.554228\pi$
$907$	20998.0	−	36369.6i	0.768718	−	1.33146i	0.938258	−	0.345935i	$-0.112438\pi$
$908$	776.000	+	1344.07i	0.0283617	+	0.0491240i
$909$		0			0
$910$		0			0
$911$	41308.0			1.50230			0.751150	−	0.660132i	$-0.229500\pi$
$911$	41308.0			1.50230			0.751150	+	0.660132i	$0.229500\pi$
$912$		0			0
$913$	13680.0	−	23694.5i	0.495884	−	0.858896i
$914$	−26.0000	+	45.0333i	−0.000940923	+	0.00162973i
$915$		0			0
$916$	16720.0			0.603105
$917$		0			0
$918$		0			0
$919$	−1968.00	−	3408.68i	−0.0706402	−	0.122352i	0.828542	−	0.559927i	$-0.189171\pi$
$919$	−1968.00	−	3408.68i	−0.0706402	−	0.122352i	−0.899182	+	0.437575i	$0.855838\pi$
$920$	−2688.00	+	4655.75i	−0.0963269	+	0.166843i
$921$		0			0
$922$	7656.00	+	13260.6i	0.273467	+	0.473659i
$923$	2096.00			0.0747461
$924$		0			0
$925$	13542.0			0.481360
$926$	−12608.0	−	21837.7i	−0.447435	−	0.774980i
$927$		0			0
$928$	928.000	−	1607.34i	0.0328266	−	0.0568574i
$929$	−3606.00	−	6245.78i	−0.127351	−	0.220578i	0.795299	−	0.606218i	$-0.207314\pi$
$929$	−3606.00	−	6245.78i	−0.127351	−	0.220578i	−0.922649	+	0.385640i	$0.873981\pi$
$930$		0			0
$931$		0			0
$932$	5288.00			0.185852
$933$		0			0
$934$	−3068.00	+	5313.93i	−0.107482	+	0.186164i
$935$	−13440.0	+	23278.8i	−0.470091	+	0.814221i
$936$		0			0
$937$	−38976.0			−1.35890			−0.679451	−	0.733721i	$-0.737782\pi$
$937$	−38976.0			−1.35890			−0.679451	+	0.733721i	$0.737782\pi$
$938$		0			0
$939$		0			0
$940$	−7808.00	−	13523.9i	−0.270924	−	0.469255i
$941$	26772.0	−	46370.5i	0.927463	−	1.60641i	0.139910	−	0.990164i	$-0.455319\pi$
$941$	26772.0	−	46370.5i	0.927463	−	1.60641i	0.787552	−	0.616248i	$-0.211348\pi$
$942$		0			0
$943$	−17640.0	−	30553.4i	−0.609160	−	1.05510i
$944$	−8768.00			−0.302303
$945$		0			0
$946$	13120.0			0.450918
$947$	−10696.0	−	18526.0i	−0.367026	−	0.635707i	0.622073	−	0.782959i	$-0.286291\pi$
$947$	−10696.0	−	18526.0i	−0.367026	−	0.635707i	−0.989099	+	0.147252i	$0.952957\pi$
$948$		0			0
$949$	−880.000	+	1524.20i	−0.0301012	+	0.0521368i
$950$	9028.00	+	15637.0i	0.308323	+	0.534031i
$951$		0			0
$952$		0			0
$953$	−21162.0			−0.719312			−0.359656	−	0.933085i	$-0.617106\pi$
$953$	−21162.0			−0.719312			−0.359656	+	0.933085i	$0.617106\pi$
$954$		0			0
$955$	12432.0	−	21532.9i	0.421246	−	0.729620i
$956$	4824.00	−	8355.41i	0.163200	−	0.282671i
$957$		0			0
$958$	−12912.0			−0.435457
$959$		0			0
$960$		0			0
$961$	5647.50	+	9781.76i	0.189571	+	0.328346i
$962$	888.000	−	1538.06i	0.0297612	−	0.0515479i
$963$		0			0
$964$	8672.00	+	15020.3i	0.289737	+	0.501839i
$965$	−400.000			−0.0133435
$966$		0			0
$967$	8224.00			0.273491			0.136746	−	0.990606i	$-0.456336\pi$
$967$	8224.00			0.273491			0.136746	+	0.990606i	$0.456336\pi$
$968$	−1076.00	−	1863.69i	−0.0357272	−	0.0618814i
$969$		0			0
$970$	−6656.00	+	11528.5i	−0.220321	+	0.381607i
$971$	−4070.00	−	7049.45i	−0.134513	−	0.232984i	0.790898	−	0.611948i	$-0.209614\pi$
$971$	−4070.00	−	7049.45i	−0.134513	−	0.232984i	−0.925411	+	0.378964i	$0.876280\pi$
$972$		0			0
$973$		0			0
$974$	23792.0			0.782695
$975$		0			0
$976$	−5536.00	+	9588.63i	−0.181560	+	0.314472i
$977$	16079.0	−	27849.6i	0.526523	−	0.911964i	−0.473000	−	0.881063i	$-0.656829\pi$
$977$	16079.0	−	27849.6i	0.526523	−	0.911964i	0.999522	−	0.0309016i	$-0.00983786\pi$
$978$		0			0
$979$	24160.0			0.788720
$980$		0			0
$981$		0			0
$982$	−264.000	−	457.261i	−0.00857900	−	0.0148593i
$983$	−20708.0	+	35867.3i	−0.671905	+	1.16377i	0.305458	+	0.952205i	$0.401190\pi$
$983$	−20708.0	+	35867.3i	−0.671905	+	1.16377i	−0.977363	+	0.211568i	$0.932143\pi$
$984$		0			0
$985$	648.000	+	1122.37i	0.0209614	+	0.0363062i
$986$	−9744.00			−0.314718
$987$		0			0
$988$	2368.00			0.0762511
$989$	−6888.00	−	11930.4i	−0.221462	−	0.383583i
$990$		0			0
$991$	−6148.00	+	10648.6i	−0.197071	+	0.341338i	−0.947578	−	0.319526i	$-0.896476\pi$
$991$	−6148.00	+	10648.6i	−0.197071	+	0.341338i	0.750506	+	0.660863i	$0.229810\pi$
$992$	2176.00	+	3768.94i	0.0696452	+	0.120629i
$993$		0			0
$994$		0			0
$995$	−12352.0			−0.393552
$996$		0			0
$997$	−28826.0	+	49928.1i	−0.915676	+	1.58600i	−0.109766	+	0.993957i	$0.535010\pi$
$997$	−28826.0	+	49928.1i	−0.915676	+	1.58600i	−0.805909	+	0.592039i	$0.798323\pi$
$998$	2628.00	−	4551.83i	0.0833546	−	0.144374i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.g.j.361.1		2
3.2	odd	2		294.4.e.f.67.1		2
7.2	even	3	inner	882.4.g.j.667.1		2
7.3	odd	6		882.4.a.q.1.1		1
7.4	even	3		882.4.a.j.1.1		1
7.5	odd	6		882.4.g.c.667.1		2
7.6	odd	2		882.4.g.c.361.1		2
21.2	odd	6		294.4.e.f.79.1		2
21.5	even	6		294.4.e.j.79.1		2
21.11	odd	6		294.4.a.f.1.1	yes	1
21.17	even	6		294.4.a.b.1.1	✓	1
21.20	even	2		294.4.e.j.67.1		2
84.11	even	6		2352.4.a.m.1.1		1
84.59	odd	6		2352.4.a.z.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.4.a.b.1.1	✓	1	21.17	even	6
294.4.a.f.1.1	yes	1	21.11	odd	6
294.4.e.f.67.1		2	3.2	odd	2
294.4.e.f.79.1		2	21.2	odd	6
294.4.e.j.67.1		2	21.20	even	2
294.4.e.j.79.1		2	21.5	even	6
882.4.a.j.1.1		1	7.4	even	3
882.4.a.q.1.1		1	7.3	odd	6
882.4.g.c.361.1		2	7.6	odd	2
882.4.g.c.667.1		2	7.5	odd	6
882.4.g.j.361.1		2	1.1	even	1	trivial
882.4.g.j.667.1		2	7.2	even	3	inner
2352.4.a.m.1.1		1	84.11	even	6
2352.4.a.z.1.1		1	84.59	odd	6

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	882.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(4.00000 + 6.92820i) q^{5} +8.00000 q^{8} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(4.00000 + 6.92820i) q^{5} +8.00000 q^{8} +(8.00000 - 13.8564i) q^{10} +(20.0000 - 34.6410i) q^{11} +4.00000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-42.0000 + 72.7461i) q^{17} +(-74.0000 - 128.172i) q^{19} -32.0000 q^{20} -80.0000 q^{22} +(42.0000 + 72.7461i) q^{23} +(30.5000 - 52.8275i) q^{25} +(-4.00000 - 6.92820i) q^{26} -58.0000 q^{29} +(68.0000 - 117.779i) q^{31} +(-16.0000 + 27.7128i) q^{32} +168.000 q^{34} +(111.000 + 192.258i) q^{37} +(-148.000 + 256.344i) q^{38} +(32.0000 + 55.4256i) q^{40} -420.000 q^{41} -164.000 q^{43} +(80.0000 + 138.564i) q^{44} +(84.0000 - 145.492i) q^{46} +(244.000 + 422.620i) q^{47} -122.000 q^{50} +(-8.00000 + 13.8564i) q^{52} +(239.000 - 413.960i) q^{53} +320.000 q^{55} +(58.0000 + 100.459i) q^{58} +(274.000 - 474.582i) q^{59} +(-346.000 - 599.290i) q^{61} -272.000 q^{62} +64.0000 q^{64} +(16.0000 + 27.7128i) q^{65} +(454.000 - 786.351i) q^{67} +(-168.000 - 290.985i) q^{68} +524.000 q^{71} +(-220.000 + 381.051i) q^{73} +(222.000 - 384.515i) q^{74} +592.000 q^{76} +(-608.000 - 1053.09i) q^{79} +(64.0000 - 110.851i) q^{80} +(420.000 + 727.461i) q^{82} +684.000 q^{83} -672.000 q^{85} +(164.000 + 284.056i) q^{86} +(160.000 - 277.128i) q^{88} +(302.000 + 523.079i) q^{89} -336.000 q^{92} +(488.000 - 845.241i) q^{94} +(592.000 - 1025.37i) q^{95} -832.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{4} + 8 q^{5} + 16 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 - 4 * q^4 + 8 * q^5 + 16 * q^8	\( 2 q - 2 q^{2} - 4 q^{4} + 8 q^{5} + 16 q^{8} + 16 q^{10} + 40 q^{11} + 8 q^{13} - 16 q^{16} - 84 q^{17} - 148 q^{19} - 64 q^{20} - 160 q^{22} + 84 q^{23} + 61 q^{25} - 8 q^{26} - 116 q^{29} + 136 q^{31} - 32 q^{32} + 336 q^{34} + 222 q^{37} - 296 q^{38} + 64 q^{40} - 840 q^{41} - 328 q^{43} + 160 q^{44} + 168 q^{46} + 488 q^{47} - 244 q^{50} - 16 q^{52} + 478 q^{53} + 640 q^{55} + 116 q^{58} + 548 q^{59} - 692 q^{61} - 544 q^{62} + 128 q^{64} + 32 q^{65} + 908 q^{67} - 336 q^{68} + 1048 q^{71} - 440 q^{73} + 444 q^{74} + 1184 q^{76} - 1216 q^{79} + 128 q^{80} + 840 q^{82} + 1368 q^{83} - 1344 q^{85} + 328 q^{86} + 320 q^{88} + 604 q^{89} - 672 q^{92} + 976 q^{94} + 1184 q^{95} - 1664 q^{97}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^4 + 8 * q^5 + 16 * q^8 + 16 * q^10 + 40 * q^11 + 8 * q^13 - 16 * q^16 - 84 * q^17 - 148 * q^19 - 64 * q^20 - 160 * q^22 + 84 * q^23 + 61 * q^25 - 8 * q^26 - 116 * q^29 + 136 * q^31 - 32 * q^32 + 336 * q^34 + 222 * q^37 - 296 * q^38 + 64 * q^40 - 840 * q^41 - 328 * q^43 + 160 * q^44 + 168 * q^46 + 488 * q^47 - 244 * q^50 - 16 * q^52 + 478 * q^53 + 640 * q^55 + 116 * q^58 + 548 * q^59 - 692 * q^61 - 544 * q^62 + 128 * q^64 + 32 * q^65 + 908 * q^67 - 336 * q^68 + 1048 * q^71 - 440 * q^73 + 444 * q^74 + 1184 * q^76 - 1216 * q^79 + 128 * q^80 + 840 * q^82 + 1368 * q^83 - 1344 * q^85 + 328 * q^86 + 320 * q^88 + 604 * q^89 - 672 * q^92 + 976 * q^94 + 1184 * q^95 - 1664 * q^97

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