LMFDB - Embedded newform 882.4.g.y.361.2

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 7^{2} $
Twist minimal:	no (minimal twist has level 294)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	882.361
Dual form			882.4.g.y.667.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(1.94975 + 3.37706i) q^{5} +8.00000 q^{8} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(1.94975 + 3.37706i) q^{5} +8.00000 q^{8} +(3.89949 - 6.75412i) q^{10} +(-30.6985 + 53.1713i) q^{11} -53.6985 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-16.0503 + 27.7999i) q^{17} +(-27.8995 - 48.3233i) q^{19} -15.5980 q^{20} +122.794 q^{22} +(-47.3015 - 81.9286i) q^{23} +(54.8970 - 95.0843i) q^{25} +(53.6985 + 93.0085i) q^{26} -138.191 q^{29} +(66.3015 - 114.838i) q^{31} +(-16.0000 + 27.7128i) q^{32} +64.2010 q^{34} +(-74.6030 - 129.216i) q^{37} +(-55.7990 + 96.6467i) q^{38} +(15.5980 + 27.0165i) q^{40} +427.497 q^{41} +437.588 q^{43} +(-122.794 - 212.685i) q^{44} +(-94.6030 + 163.857i) q^{46} +(-28.5025 - 49.3678i) q^{47} -219.588 q^{50} +(107.397 - 186.017i) q^{52} +(-131.794 + 228.274i) q^{53} -239.417 q^{55} +(138.191 + 239.354i) q^{58} +(-225.899 + 391.269i) q^{59} +(289.653 + 501.694i) q^{61} -265.206 q^{62} +64.0000 q^{64} +(-104.698 - 181.343i) q^{65} +(-154.794 + 268.111i) q^{67} +(-64.2010 - 111.199i) q^{68} +1058.98 q^{71} +(596.829 - 1033.74i) q^{73} +(-149.206 + 258.432i) q^{74} +223.196 q^{76} +(-659.779 - 1142.77i) q^{79} +(31.1960 - 54.0330i) q^{80} +(-427.497 - 740.447i) q^{82} +1190.33 q^{83} -125.176 q^{85} +(-437.588 - 757.924i) q^{86} +(-245.588 + 425.371i) q^{88} +(116.543 + 201.858i) q^{89} +378.412 q^{92} +(-57.0051 + 98.7356i) q^{94} +(108.794 - 188.437i) q^{95} +1609.44 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 8 q^{4} - 12 q^{5} + 32 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 - 8 * q^4 - 12 * q^5 + 32 * q^8	$ 4 q - 4 q^{2} - 8 q^{4} - 12 q^{5} + 32 q^{8} - 24 q^{10} - 4 q^{11} - 96 q^{13} - 32 q^{16} - 84 q^{17} - 72 q^{19} + 96 q^{20} + 16 q^{22} - 308 q^{23} - 18 q^{25} + 96 q^{26} + 160 q^{29} + 384 q^{31} - 64 q^{32} + 336 q^{34} - 536 q^{37} - 144 q^{38} - 96 q^{40} + 1512 q^{41} + 800 q^{43} - 16 q^{44} - 616 q^{46} - 312 q^{47} + 72 q^{50} + 192 q^{52} - 52 q^{53} - 2304 q^{55} - 160 q^{58} - 864 q^{59} + 1416 q^{61} - 1536 q^{62} + 256 q^{64} - 300 q^{65} - 144 q^{67} - 336 q^{68} + 3048 q^{71} + 744 q^{73} - 1072 q^{74} + 576 q^{76} - 976 q^{79} - 192 q^{80} - 1512 q^{82} - 624 q^{83} + 1400 q^{85} - 800 q^{86} - 32 q^{88} - 108 q^{89} + 2464 q^{92} - 624 q^{94} - 40 q^{95} + 1488 q^{97}+O(q^{100}) $ 4 * q - 4 * q^2 - 8 * q^4 - 12 * q^5 + 32 * q^8 - 24 * q^10 - 4 * q^11 - 96 * q^13 - 32 * q^16 - 84 * q^17 - 72 * q^19 + 96 * q^20 + 16 * q^22 - 308 * q^23 - 18 * q^25 + 96 * q^26 + 160 * q^29 + 384 * q^31 - 64 * q^32 + 336 * q^34 - 536 * q^37 - 144 * q^38 - 96 * q^40 + 1512 * q^41 + 800 * q^43 - 16 * q^44 - 616 * q^46 - 312 * q^47 + 72 * q^50 + 192 * q^52 - 52 * q^53 - 2304 * q^55 - 160 * q^58 - 864 * q^59 + 1416 * q^61 - 1536 * q^62 + 256 * q^64 - 300 * q^65 - 144 * q^67 - 336 * q^68 + 3048 * q^71 + 744 * q^73 - 1072 * q^74 + 576 * q^76 - 976 * q^79 - 192 * q^80 - 1512 * q^82 - 624 * q^83 + 1400 * q^85 - 800 * q^86 - 32 * q^88 - 108 * q^89 + 2464 * q^92 - 624 * q^94 - 40 * q^95 + 1488 * 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
$5$	1.94975	+	3.37706i	0.174391	+	0.302054i	0.939950	−	0.341311i	$-0.110871\pi$
$5$	1.94975	+	3.37706i	0.174391	+	0.302054i	−0.765560	+	0.643365i	$0.777538\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	8.00000			0.353553
$9$		0			0
$10$	3.89949	−	6.75412i	0.123313	−	0.213584i
$11$	−30.6985	+	53.1713i	−0.841449	+	1.45743i	0.0472203	+	0.998885i	$0.484964\pi$
$11$	−30.6985	+	53.1713i	−0.841449	+	1.45743i	−0.888669	+	0.458548i	$0.848370\pi$
$12$		0			0
$13$	−53.6985			−1.14564			−0.572818	−	0.819682i	$-0.694150\pi$
$13$	−53.6985			−1.14564			−0.572818	+	0.819682i	$0.694150\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−16.0503	+	27.7999i	−0.228986	+	0.396615i	−0.957508	−	0.288407i	$-0.906874\pi$
$17$	−16.0503	+	27.7999i	−0.228986	+	0.396615i	0.728522	+	0.685022i	$0.240208\pi$
$18$		0			0
$19$	−27.8995	−	48.3233i	−0.336873	−	0.583481i	0.646970	−	0.762515i	$-0.276036\pi$
$19$	−27.8995	−	48.3233i	−0.336873	−	0.583481i	−0.983843	+	0.179035i	$0.942703\pi$
$20$	−15.5980			−0.174391
$21$		0			0
$22$	122.794			1.18999
$23$	−47.3015	−	81.9286i	−0.428828	−	0.742752i	0.567941	−	0.823069i	$-0.307740\pi$
$23$	−47.3015	−	81.9286i	−0.428828	−	0.742752i	−0.996769	+	0.0803170i	$0.974407\pi$
$24$		0			0
$25$	54.8970	−	95.0843i	0.439176	−	0.760675i
$26$	53.6985	+	93.0085i	0.405044	+	0.701556i
$27$		0			0
$28$		0			0
$29$	−138.191			−0.884876			−0.442438	−	0.896799i	$-0.645886\pi$
$29$	−138.191			−0.884876			−0.442438	+	0.896799i	$0.645886\pi$
$30$		0			0
$31$	66.3015	−	114.838i	0.384132	−	0.665337i	−0.607516	−	0.794307i	$-0.707834\pi$
$31$	66.3015	−	114.838i	0.384132	−	0.665337i	0.991648	+	0.128971i	$0.0411673\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$		0			0
$34$	64.2010			0.323835
$35$		0			0
$36$		0			0
$37$	−74.6030	−	129.216i	−0.331477	−	0.574136i	0.651324	−	0.758799i	$-0.274214\pi$
$37$	−74.6030	−	129.216i	−0.331477	−	0.574136i	−0.982802	+	0.184664i	$0.940880\pi$
$38$	−55.7990	+	96.6467i	−0.238205	+	0.412583i
$39$		0			0
$40$	15.5980	+	27.0165i	0.0616564	+	0.106792i
$41$	427.497			1.62839			0.814194	−	0.580593i	$-0.197179\pi$
$41$	427.497			1.62839			0.814194	+	0.580593i	$0.197179\pi$
$42$		0			0
$43$	437.588			1.55190			0.775948	−	0.630797i	$-0.217272\pi$
$43$	437.588			1.55190			0.775948	+	0.630797i	$0.217272\pi$
$44$	−122.794	−	212.685i	−0.420725	−	0.728716i
$45$		0			0
$46$	−94.6030	+	163.857i	−0.303227	+	0.525205i
$47$	−28.5025	−	49.3678i	−0.0884579	−	0.153214i	0.818402	−	0.574647i	$-0.194861\pi$
$47$	−28.5025	−	49.3678i	−0.0884579	−	0.153214i	−0.906859	+	0.421433i	$0.861527\pi$
$48$		0			0
$49$		0			0
$50$	−219.588			−0.621088
$51$		0			0
$52$	107.397	−	186.017i	0.286409	−	0.496075i
$53$	−131.794	+	228.274i	−0.341572	+	0.591619i	−0.984725	−	0.174118i	$-0.944292\pi$
$53$	−131.794	+	228.274i	−0.341572	+	0.591619i	0.643153	+	0.765737i	$0.277626\pi$
$54$		0			0
$55$	−239.417			−0.586964
$56$		0			0
$57$		0			0
$58$	138.191	+	239.354i	0.312851	+	0.541874i
$59$	−225.899	+	391.269i	−0.498468	+	0.863372i	−0.999998	−	0.00176815i	$-0.999437\pi$
$59$	−225.899	+	391.269i	−0.498468	+	0.863372i	0.501530	+	0.865140i	$0.332771\pi$
$60$		0			0
$61$	289.653	+	501.694i	0.607972	+	1.05304i	0.991574	+	0.129540i	$0.0413501\pi$
$61$	289.653	+	501.694i	0.607972	+	1.05304i	−0.383602	+	0.923499i	$0.625317\pi$
$62$	−265.206			−0.543245
$63$		0			0
$64$	64.0000			0.125000
$65$	−104.698	−	181.343i	−0.199788	−	0.346044i
$66$		0			0
$67$	−154.794	+	268.111i	−0.282255	+	0.488880i	−0.971940	−	0.235230i	$-0.924416\pi$
$67$	−154.794	+	268.111i	−0.282255	+	0.488880i	0.689685	+	0.724110i	$0.257749\pi$
$68$	−64.2010	−	111.199i	−0.114493	−	0.198307i
$69$		0			0
$70$		0			0
$71$	1058.98			1.77012			0.885059	−	0.465479i	$-0.154118\pi$
$71$	1058.98			1.77012			0.885059	+	0.465479i	$0.154118\pi$
$72$		0			0
$73$	596.829	−	1033.74i	0.956898	−	1.65740i	0.226934	−	0.973910i	$-0.427130\pi$
$73$	596.829	−	1033.74i	0.956898	−	1.65740i	0.729964	−	0.683486i	$-0.239537\pi$
$74$	−149.206	+	258.432i	−0.234390	+	0.405975i
$75$		0			0
$76$	223.196			0.336873
$77$		0			0
$78$		0			0
$79$	−659.779	−	1142.77i	−0.939632	−	1.62749i	−0.766159	−	0.642651i	$-0.777834\pi$
$79$	−659.779	−	1142.77i	−0.939632	−	1.62749i	−0.173473	−	0.984839i	$-0.555499\pi$
$80$	31.1960	−	54.0330i	0.0435977	−	0.0755134i
$81$		0			0
$82$	−427.497	−	740.447i	−0.575722	−	0.997180i
$83$	1190.33			1.57417			0.787083	−	0.616847i	$-0.211590\pi$
$83$	1190.33			1.57417			0.787083	+	0.616847i	$0.211590\pi$
$84$		0			0
$85$	−125.176			−0.159732
$86$	−437.588	−	757.924i	−0.548678	−	0.950338i
$87$		0			0
$88$	−245.588	+	425.371i	−0.297497	+	0.515280i
$89$	116.543	+	201.858i	0.138803	+	0.240414i	0.927044	−	0.374953i	$-0.122341\pi$
$89$	116.543	+	201.858i	0.138803	+	0.240414i	−0.788241	+	0.615367i	$0.789008\pi$
$90$		0			0
$91$		0			0
$92$	378.412			0.428828
$93$		0			0
$94$	−57.0051	+	98.7356i	−0.0625492	+	0.108338i
$95$	108.794	−	188.437i	0.117495	−	0.203507i
$96$		0			0
$97$	1609.44			1.68468			0.842338	−	0.538950i	$-0.181179\pi$
$97$	1609.44			1.68468			0.842338	+	0.538950i	$0.181179\pi$
$98$		0			0
$99$		0			0
$100$	219.588	+	380.337i	0.219588	+	0.380337i
$101$	739.628	−	1281.07i	0.728671	−	1.26209i	−0.228774	−	0.973479i	$-0.573472\pi$
$101$	739.628	−	1281.07i	0.728671	−	1.26209i	0.957445	−	0.288615i	$-0.0931948\pi$
$102$		0			0
$103$	−572.673	−	991.899i	−0.547837	−	0.948881i	−0.998422	−	0.0561477i	$-0.982118\pi$
$103$	−572.673	−	991.899i	−0.547837	−	0.948881i	0.450586	−	0.892733i	$-0.351215\pi$
$104$	−429.588			−0.405044
$105$		0			0
$106$	527.176			0.483055
$107$	218.477	+	378.414i	0.197392	+	0.341894i	0.947682	−	0.319215i	$-0.103419\pi$
$107$	218.477	+	378.414i	0.197392	+	0.341894i	−0.750290	+	0.661109i	$0.770086\pi$
$108$		0			0
$109$	83.1758	−	144.065i	0.0730898	−	0.126595i	−0.827164	−	0.561960i	$-0.810047\pi$
$109$	83.1758	−	144.065i	0.0730898	−	0.126595i	0.900254	+	0.435365i	$0.143381\pi$
$110$	239.417	+	414.683i	0.207523	+	0.359440i
$111$		0			0
$112$		0			0
$113$	−490.824			−0.408609			−0.204305	−	0.978907i	$-0.565493\pi$
$113$	−490.824			−0.408609			−0.204305	+	0.978907i	$0.565493\pi$
$114$		0			0
$115$	184.452	−	319.480i	0.149567	−	0.259058i
$116$	276.382	−	478.707i	0.221219	−	0.383163i
$117$		0			0
$118$	903.598			0.704940
$119$		0			0
$120$		0			0
$121$	−1219.29	−	2111.88i	−0.916074	−	1.58669i
$122$	579.307	−	1003.39i	0.429901	−	0.744611i
$123$		0			0
$124$	265.206	+	459.350i	0.192066	+	0.332668i
$125$	915.578			0.655134
$126$		0			0
$127$	−2616.70			−1.82831			−0.914153	−	0.405369i	$-0.867143\pi$
$127$	−2616.70			−1.82831			−0.914153	+	0.405369i	$0.867143\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−209.397	+	362.686i	−0.141272	+	0.244690i
$131$	−88.7939	−	153.796i	−0.0592211	−	0.102574i	0.834895	−	0.550409i	$-0.185528\pi$
$131$	−88.7939	−	153.796i	−0.0592211	−	0.102574i	−0.894116	+	0.447835i	$0.852195\pi$
$132$		0			0
$133$		0			0
$134$	619.176			0.399169
$135$		0			0
$136$	−128.402	+	222.399i	−0.0809587	+	0.140225i
$137$	13.5076	−	23.3958i	0.00842358	−	0.0145901i	−0.861783	−	0.507277i	$-0.830652\pi$
$137$	13.5076	−	23.3958i	0.00842358	−	0.0145901i	0.870206	+	0.492687i	$0.163985\pi$
$138$		0			0
$139$	922.754			0.563071			0.281536	−	0.959551i	$-0.409156\pi$
$139$	922.754			0.563071			0.281536	+	0.959551i	$0.409156\pi$
$140$		0			0
$141$		0			0
$142$	−1058.98	−	1834.22i	−0.625831	−	1.08397i
$143$	1648.46	−	2855.22i	0.963995	−	1.66969i
$144$		0			0
$145$	−269.437	−	466.679i	−0.154314	−	0.267280i
$146$	−2387.32			−1.35326
$147$		0			0
$148$	596.824			0.331477
$149$	373.352	+	646.664i	0.205276	+	0.355549i	0.950221	−	0.311578i	$-0.100857\pi$
$149$	373.352	+	646.664i	0.205276	+	0.355549i	−0.744945	+	0.667126i	$0.767524\pi$
$150$		0			0
$151$	−1036.57	+	1795.40i	−0.558643	+	0.967598i	0.438967	+	0.898503i	$0.355344\pi$
$151$	−1036.57	+	1795.40i	−0.558643	+	0.967598i	−0.997610	+	0.0690949i	$0.977989\pi$
$152$	−223.196	−	386.587i	−0.119103	−	0.206292i
$153$		0			0
$154$		0			0
$155$	517.085			0.267956
$156$		0			0
$157$	783.110	−	1356.39i	0.398083	−	0.689500i	−0.595407	−	0.803425i	$-0.703009\pi$
$157$	783.110	−	1356.39i	0.398083	−	0.689500i	0.993489	+	0.113925i	$0.0363423\pi$
$158$	−1319.56	+	2285.54i	−0.664420	+	1.15081i
$159$		0			0
$160$	−124.784			−0.0616564
$161$		0			0
$162$		0			0
$163$	−49.3667	−	85.5056i	−0.0237221	−	0.0410878i	0.853921	−	0.520403i	$-0.174218\pi$
$163$	−49.3667	−	85.5056i	−0.0237221	−	0.0410878i	−0.877643	+	0.479315i	$0.840885\pi$
$164$	−854.995	+	1480.89i	−0.407097	+	0.705112i
$165$		0			0
$166$	−1190.33	−	2061.71i	−0.556552	−	0.963976i
$167$	−2231.36			−1.03394			−0.516969	−	0.856004i	$-0.672940\pi$
$167$	−2231.36			−1.03394			−0.516969	+	0.856004i	$0.672940\pi$
$168$		0			0
$169$	686.527			0.312484
$170$	125.176	+	216.811i	0.0564738	+	0.0978155i
$171$		0			0
$172$	−875.176	+	1515.85i	−0.387974	+	0.671991i
$173$	−1050.42	−	1819.38i	−0.461631	−	0.799568i	0.537412	−	0.843320i	$-0.319402\pi$
$173$	−1050.42	−	1819.38i	−0.461631	−	0.799568i	−0.999042	+	0.0437522i	$0.986069\pi$
$174$		0			0
$175$		0			0
$176$	982.352			0.420725
$177$		0			0
$178$	233.085	−	403.716i	0.0981488	−	0.169999i
$179$	861.271	−	1491.77i	0.359634	−	0.622904i	−0.628266	−	0.777999i	$-0.716235\pi$
$179$	861.271	−	1491.77i	0.359634	−	0.622904i	0.987900	+	0.155095i	$0.0495683\pi$
$180$		0			0
$181$	−1655.00			−0.679644			−0.339822	−	0.940490i	$-0.610367\pi$
$181$	−1655.00			−0.679644			−0.339822	+	0.940490i	$0.610367\pi$
$182$		0			0
$183$		0			0
$184$	−378.412	−	655.429i	−0.151614	−	0.262603i
$185$	290.914	−	503.878i	0.115613	−	0.200248i
$186$		0			0
$187$	−985.437	−	1706.83i	−0.385360	−	0.667463i
$188$	228.020			0.0884579
$189$		0			0
$190$	−435.176			−0.166163
$191$	−503.844	−	872.683i	−0.190874	−	0.330603i	0.754666	−	0.656109i	$-0.227799\pi$
$191$	−503.844	−	872.683i	−0.190874	−	0.330603i	−0.945540	+	0.325506i	$0.894465\pi$
$192$		0			0
$193$	3.82424	−	6.62378i	0.00142630	−	0.00247042i	−0.865311	−	0.501235i	$-0.832879\pi$
$193$	3.82424	−	6.62378i	0.00142630	−	0.00247042i	0.866738	+	0.498764i	$0.166213\pi$
$194$	−1609.44	−	2787.63i	−0.595623	−	1.03165i
$195$		0			0
$196$		0			0
$197$	−2689.88			−0.972822			−0.486411	−	0.873730i	$-0.661694\pi$
$197$	−2689.88			−0.972822			−0.486411	+	0.873730i	$0.661694\pi$
$198$		0			0
$199$	433.748	−	751.274i	0.154511	−	0.267620i	−0.778370	−	0.627806i	$-0.783953\pi$
$199$	433.748	−	751.274i	0.154511	−	0.267620i	0.932881	+	0.360185i	$0.117287\pi$
$200$	439.176	−	760.675i	0.155272	−	0.268939i
$201$		0			0
$202$	−2958.51			−1.03050
$203$		0			0
$204$		0			0
$205$	833.512	+	1443.69i	0.283976	+	0.491860i
$206$	−1145.35	+	1983.80i	−0.387379	+	0.670960i
$207$		0			0
$208$	429.588	+	744.068i	0.143205	+	0.248038i
$209$	3425.89			1.13385
$210$		0			0
$211$	162.030			0.0528655			0.0264328	−	0.999651i	$-0.491585\pi$
$211$	162.030			0.0528655			0.0264328	+	0.999651i	$0.491585\pi$
$212$	−527.176	−	913.095i	−0.170786	−	0.295810i
$213$		0			0
$214$	436.955	−	756.827i	0.139578	−	0.241755i
$215$	853.186	+	1477.76i	0.270636	+	0.468756i
$216$		0			0
$217$		0			0
$218$	−332.703			−0.103365
$219$		0			0
$220$	478.834	−	829.365i	0.146741	−	0.254163i
$221$	861.874	−	1492.81i	0.262335	−	0.454377i
$222$		0			0
$223$	4577.85			1.37469			0.687344	−	0.726332i	$-0.258777\pi$
$223$	4577.85			1.37469			0.687344	+	0.726332i	$0.258777\pi$
$224$		0			0
$225$		0			0
$226$	490.824	+	850.133i	0.144465	+	0.250221i
$227$	1109.10	−	1921.01i	0.324287	−	0.561682i	−0.657080	−	0.753820i	$-0.728209\pi$
$227$	1109.10	−	1921.01i	0.324287	−	0.561682i	0.981368	+	0.192138i	$0.0615422\pi$
$228$		0			0
$229$	392.608	+	680.018i	0.113294	+	0.196231i	0.917096	−	0.398665i	$-0.130527\pi$
$229$	392.608	+	680.018i	0.113294	+	0.196231i	−0.803803	+	0.594896i	$0.797193\pi$
$230$	−737.808			−0.211520
$231$		0			0
$232$	−1105.53			−0.312851
$233$	−2684.56	−	4649.80i	−0.754813	−	1.30738i	−0.945467	−	0.325718i	$-0.894394\pi$
$233$	−2684.56	−	4649.80i	−0.754813	−	1.30738i	0.190654	−	0.981657i	$-0.438939\pi$
$234$		0			0
$235$	111.145	−	192.510i	0.0308525	−	0.0534380i
$236$	−903.598	−	1565.08i	−0.249234	−	0.431686i
$237$		0			0
$238$		0			0
$239$	−3713.28			−1.00499			−0.502493	−	0.864581i	$-0.667584\pi$
$239$	−3713.28			−1.00499			−0.502493	+	0.864581i	$0.667584\pi$
$240$		0			0
$241$	3499.31	−	6060.99i	0.935313	−	1.62001i	0.161238	−	0.986915i	$-0.448451\pi$
$241$	3499.31	−	6060.99i	0.935313	−	1.62001i	0.774075	−	0.633094i	$-0.218215\pi$
$242$	−2438.59	+	4223.76i	−0.647762	+	1.12196i
$243$		0			0
$244$	−2317.23			−0.607972
$245$		0			0
$246$		0			0
$247$	1498.16	+	2594.89i	0.385934	+	0.668457i
$248$	530.412	−	918.701i	0.135811	−	0.235232i
$249$		0			0
$250$	−915.578	−	1585.83i	−0.231625	−	0.401186i
$251$	3722.75			0.936168			0.468084	−	0.883684i	$-0.344945\pi$
$251$	3722.75			0.936168			0.468084	+	0.883684i	$0.344945\pi$
$252$		0			0
$253$	5808.34			1.44335
$254$	2616.70	+	4532.26i	0.646404	+	1.11960i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−615.075	−	1065.34i	−0.149289	−	0.258576i	0.781676	−	0.623685i	$-0.214365\pi$
$257$	−615.075	−	1065.34i	−0.149289	−	0.258576i	−0.930965	+	0.365109i	$0.881032\pi$
$258$		0			0
$259$		0			0
$260$	837.588			0.199788
$261$		0			0
$262$	−177.588	+	307.591i	−0.0418756	+	0.0725307i
$263$	1194.32	−	2068.62i	0.280018	−	0.485005i	−0.691371	−	0.722500i	$-0.742993\pi$
$263$	1194.32	−	2068.62i	0.280018	−	0.485005i	0.971389	+	0.237495i	$0.0763262\pi$
$264$		0			0
$265$	−1027.86			−0.238268
$266$		0			0
$267$		0			0
$268$	−619.176	−	1072.44i	−0.141128	−	0.244440i
$269$	−3351.16	+	5804.37i	−0.759567	+	1.31561i	0.183504	+	0.983019i	$0.441256\pi$
$269$	−3351.16	+	5804.37i	−0.759567	+	1.31561i	−0.943071	+	0.332590i	$0.892077\pi$
$270$		0			0
$271$	2475.19	+	4287.15i	0.554822	+	0.960980i	0.997917	+	0.0645056i	$0.0205470\pi$
$271$	2475.19	+	4287.15i	0.554822	+	0.960980i	−0.443095	+	0.896475i	$0.646120\pi$
$272$	513.608			0.114493
$273$		0			0
$274$	−54.0303			−0.0119127
$275$	3370.51	+	5837.89i	0.739088	+	1.28014i
$276$		0			0
$277$	1852.59	−	3208.78i	0.401846	−	0.696017i	−0.592103	−	0.805862i	$-0.701702\pi$
$277$	1852.59	−	3208.78i	0.401846	−	0.696017i	0.993949	+	0.109845i	$0.0350355\pi$
$278$	−922.754	−	1598.26i	−0.199076	−	0.344809i
$279$		0			0
$280$		0			0
$281$	−9324.74			−1.97960			−0.989800	−	0.142465i	$-0.954497\pi$
$281$	−9324.74			−1.97960			−0.989800	+	0.142465i	$0.954497\pi$
$282$		0			0
$283$	−2784.74	+	4823.32i	−0.584932	+	1.01313i	0.409952	+	0.912107i	$0.365546\pi$
$283$	−2784.74	+	4823.32i	−0.584932	+	1.01313i	−0.994884	+	0.101025i	$0.967788\pi$
$284$	−2117.97	+	3668.43i	−0.442530	+	0.766484i
$285$		0			0
$286$	−6593.85			−1.36330
$287$		0			0
$288$		0			0
$289$	1941.28	+	3362.39i	0.395131	+	0.684387i
$290$	−538.875	+	933.358i	−0.109117	+	0.188996i
$291$		0			0
$292$	2387.32	+	4134.95i	0.478449	+	0.828698i
$293$	−1665.31			−0.332042			−0.166021	−	0.986122i	$-0.553092\pi$
$293$	−1665.31			−0.332042			−0.166021	+	0.986122i	$0.553092\pi$
$294$		0			0
$295$	−1761.79			−0.347713
$296$	−596.824	−	1033.73i	−0.117195	−	0.202988i
$297$		0			0
$298$	746.703	−	1293.33i	0.145152	−	0.251411i
$299$	2540.02	+	4399.44i	0.491281	+	0.850924i
$300$		0			0
$301$		0			0
$302$	4146.29			0.790040
$303$		0			0
$304$	−446.392	+	773.173i	−0.0842182	+	0.145870i
$305$	−1129.50	+	1956.35i	−0.212049	+	0.367280i
$306$		0			0
$307$	5303.32			0.985916			0.492958	−	0.870053i	$-0.335916\pi$
$307$	5303.32			0.985916			0.492958	+	0.870053i	$0.335916\pi$
$308$		0			0
$309$		0			0
$310$	−517.085	−	895.617i	−0.0947369	−	0.164089i
$311$	−562.994	+	975.135i	−0.102651	+	0.177797i	−0.912776	−	0.408460i	$-0.866066\pi$
$311$	−562.994	+	975.135i	−0.102651	+	0.177797i	0.810125	+	0.586257i	$0.199399\pi$
$312$		0			0
$313$	−4149.75	−	7187.58i	−0.749386	−	1.29798i	−0.948117	−	0.317921i	$-0.897015\pi$
$313$	−4149.75	−	7187.58i	−0.749386	−	1.29798i	0.198731	−	0.980054i	$-0.436318\pi$
$314$	−3132.44			−0.562974
$315$		0			0
$316$	5278.23			0.939632
$317$	−2139.38	−	3705.52i	−0.379053	−	0.656538i	0.611872	−	0.790957i	$-0.290417\pi$
$317$	−2139.38	−	3705.52i	−0.379053	−	0.656538i	−0.990925	+	0.134418i	$0.957083\pi$
$318$		0			0
$319$	4242.25	−	7347.80i	0.744578	−	1.28965i
$320$	124.784	+	216.132i	0.0217988	+	0.0377567i
$321$		0			0
$322$		0			0
$323$	1791.18			0.308556
$324$		0			0
$325$	−2947.88	+	5105.89i	−0.503136	+	0.871457i
$326$	−98.7333	+	171.011i	−0.0167740	+	0.0290535i
$327$		0			0
$328$	3419.98			0.575722
$329$		0			0
$330$		0			0
$331$	853.558	+	1478.41i	0.141739	+	0.245500i	0.928152	−	0.372202i	$-0.121397\pi$
$331$	853.558	+	1478.41i	0.141739	+	0.245500i	−0.786412	+	0.617702i	$0.788064\pi$
$332$	−2380.66	+	4123.43i	−0.393542	+	0.681634i
$333$		0			0
$334$	2231.36	+	3864.82i	0.365552	+	0.633155i
$335$	−1207.24			−0.196891
$336$		0			0
$337$	1710.67			0.276517			0.138259	−	0.990396i	$-0.455849\pi$
$337$	1710.67			0.276517			0.138259	+	0.990396i	$0.455849\pi$
$338$	−686.527	−	1189.10i	−0.110480	−	0.191357i
$339$		0			0
$340$	250.352	−	433.622i	0.0399330	−	0.0691660i
$341$	4070.71	+	7050.68i	0.646456	+	1.11969i
$342$		0			0
$343$		0			0
$344$	3500.70			0.548678
$345$		0			0
$346$	−2100.84	+	3638.77i	−0.326422	+	0.565380i
$347$	4455.15	−	7716.55i	0.689236	−	1.19379i	−0.282849	−	0.959164i	$-0.591280\pi$
$347$	4455.15	−	7716.55i	0.689236	−	1.19379i	0.972085	−	0.234628i	$-0.0753871\pi$
$348$		0			0
$349$	−5378.68			−0.824969			−0.412485	−	0.910965i	$-0.635339\pi$
$349$	−5378.68			−0.824969			−0.412485	+	0.910965i	$0.635339\pi$
$350$		0			0
$351$		0			0
$352$	−982.352	−	1701.48i	−0.148749	−	0.257640i
$353$	2126.28	−	3682.83i	0.320596	−	0.555289i	−0.660015	−	0.751253i	$-0.729450\pi$
$353$	2126.28	−	3682.83i	0.320596	−	0.555289i	0.980611	+	0.195963i	$0.0627833\pi$
$354$		0			0
$355$	2064.75	+	3576.26i	0.308692	+	0.534670i
$356$	−932.341			−0.138803
$357$		0			0
$358$	−3445.08			−0.508599
$359$	2451.94	+	4246.89i	0.360470	+	0.624352i	0.988038	−	0.154209i	$-0.0492831\pi$
$359$	2451.94	+	4246.89i	0.360470	+	0.624352i	−0.627568	+	0.778561i	$0.715950\pi$
$360$		0			0
$361$	1872.74	−	3243.67i	0.273033	−	0.472908i
$362$	1655.00	+	2866.55i	0.240290	+	0.416195i
$363$		0			0
$364$		0			0
$365$	4654.66			0.667497
$366$		0			0
$367$	−2020.78	+	3500.10i	−0.287423	+	0.497830i	−0.973194	−	0.229987i	$-0.926132\pi$
$367$	−2020.78	+	3500.10i	−0.287423	+	0.497830i	0.685771	+	0.727817i	$0.259465\pi$
$368$	−756.824	+	1310.86i	−0.107207	+	0.185688i
$369$		0			0
$370$	−1163.66			−0.163502
$371$		0			0
$372$		0			0
$373$	3725.67	+	6453.05i	0.517180	+	0.895781i	0.999801	+	0.0199523i	$0.00635144\pi$
$373$	3725.67	+	6453.05i	0.517180	+	0.895781i	−0.482621	+	0.875829i	$0.660315\pi$
$374$	−1970.87	+	3413.65i	−0.272491	+	0.471967i
$375$		0			0
$376$	−228.020	−	394.943i	−0.0312746	−	0.0541692i
$377$	7420.64			1.01375
$378$		0			0
$379$	−12564.4			−1.70288			−0.851438	−	0.524456i	$-0.824269\pi$
$379$	−12564.4			−1.70288			−0.851438	+	0.524456i	$0.824269\pi$
$380$	435.176	+	753.747i	0.0587475	+	0.101754i
$381$		0			0
$382$	−1007.69	+	1745.37i	−0.134968	+	0.233772i
$383$	2144.96	+	3715.19i	0.286169	+	0.495659i	0.972892	−	0.231260i	$-0.0742849\pi$
$383$	2144.96	+	3715.19i	0.286169	+	0.495659i	−0.686723	+	0.726919i	$0.740952\pi$
$384$		0			0
$385$		0			0
$386$	−15.2970			−0.00201709
$387$		0			0
$388$	−3218.87	+	5575.25i	−0.421169	+	0.729486i
$389$	2831.39	−	4904.11i	0.369041	−	0.639198i	−0.620375	−	0.784306i	$-0.713019\pi$
$389$	2831.39	−	4904.11i	0.369041	−	0.639198i	0.989416	+	0.145108i	$0.0463528\pi$
$390$		0			0
$391$	3036.81			0.392782
$392$		0			0
$393$		0			0
$394$	2689.88	+	4659.01i	0.343945	+	0.595729i
$395$	2572.80	−	4456.23i	0.327726	−	0.567638i
$396$		0			0
$397$	7280.69	+	12610.5i	0.920421	+	1.59422i	0.798764	+	0.601644i	$0.205487\pi$
$397$	7280.69	+	12610.5i	0.920421	+	1.59422i	0.121657	+	0.992572i	$0.461179\pi$
$398$	−1734.99			−0.218511
$399$		0			0
$400$	−1756.70			−0.219588
$401$	−1871.10	−	3240.83i	−0.233013	−	0.403590i	0.725681	−	0.688032i	$-0.241525\pi$
$401$	−1871.10	−	3240.83i	−0.233013	−	0.403590i	−0.958693	+	0.284442i	$0.908192\pi$
$402$		0			0
$403$	−3560.29	+	6166.60i	−0.440076	+	0.762234i
$404$	2958.51	+	5124.29i	0.364335	+	0.631047i
$405$		0			0
$406$		0			0
$407$	9160.80			1.11569
$408$		0			0
$409$	−1758.59	+	3045.96i	−0.212608	+	0.368247i	−0.952530	−	0.304445i	$-0.901529\pi$
$409$	−1758.59	+	3045.96i	−0.212608	+	0.368247i	0.739922	+	0.672692i	$0.234862\pi$
$410$	1667.02	−	2887.37i	0.200801	−	0.347798i
$411$		0			0
$412$	4581.39			0.547837
$413$		0			0
$414$		0			0
$415$	2320.85	+	4019.82i	0.274520	+	0.475483i
$416$	859.176	−	1488.14i	0.101261	−	0.175389i
$417$		0			0
$418$	−3425.89	−	5933.81i	−0.400875	−	0.694336i
$419$	−7579.52			−0.883732			−0.441866	−	0.897081i	$-0.645683\pi$
$419$	−7579.52			−0.883732			−0.441866	+	0.897081i	$0.645683\pi$
$420$		0			0
$421$	−4980.87			−0.576610			−0.288305	−	0.957539i	$-0.593092\pi$
$421$	−4980.87			−0.576610			−0.288305	+	0.957539i	$0.593092\pi$
$422$	−162.030	−	280.645i	−0.0186908	−	0.0323734i
$423$		0			0
$424$	−1054.35	+	1826.19i	−0.120764	+	0.209169i
$425$	1762.22	+	3052.26i	0.201130	+	0.348367i
$426$		0			0
$427$		0			0
$428$	−1747.82			−0.197392
$429$		0			0
$430$	1706.37	−	2955.52i	0.191369	−	0.331460i
$431$	7101.66	−	12300.4i	0.793678	−	1.37469i	−0.129998	−	0.991514i	$-0.541497\pi$
$431$	7101.66	−	12300.4i	0.793678	−	1.37469i	0.923676	−	0.383176i	$-0.125170\pi$
$432$		0			0
$433$	−3874.82			−0.430051			−0.215026	−	0.976608i	$-0.568983\pi$
$433$	−3874.82			−0.430051			−0.215026	+	0.976608i	$0.568983\pi$
$434$		0			0
$435$		0			0
$436$	332.703	+	576.259i	0.0365449	+	0.0632977i
$437$	−2639.38	+	4571.53i	−0.288921	+	0.500426i
$438$		0			0
$439$	3881.91	+	6723.66i	0.422035	+	0.730986i	0.996138	−	0.0877966i	$-0.0279826\pi$
$439$	3881.91	+	6723.66i	0.422035	+	0.730986i	−0.574103	+	0.818783i	$0.694649\pi$
$440$	−1915.34			−0.207523
$441$		0			0
$442$	−3447.50			−0.370997
$443$	4831.12	+	8367.74i	0.518134	+	0.897435i	0.999778	+	0.0210676i	$0.00670653\pi$
$443$	4831.12	+	8367.74i	0.518134	+	0.897435i	−0.481644	+	0.876367i	$0.659960\pi$
$444$		0			0
$445$	−454.458	+	787.144i	−0.0484120	+	0.0838521i
$446$	−4577.85	−	7929.07i	−0.486026	−	0.841821i
$447$		0			0
$448$		0			0
$449$	10942.6			1.15014			0.575069	−	0.818105i	$-0.304975\pi$
$449$	10942.6			1.15014			0.575069	+	0.818105i	$0.304975\pi$
$450$		0			0
$451$	−13123.5	+	22730.6i	−1.37021	+	2.37327i
$452$	981.648	−	1700.27i	0.102152	−	0.176933i
$453$		0			0
$454$	−4436.38			−0.458612
$455$		0			0
$456$		0			0
$457$	−6809.17	−	11793.8i	−0.696979	−	1.20720i	−0.969509	−	0.245056i	$-0.921194\pi$
$457$	−6809.17	−	11793.8i	−0.696979	−	1.20720i	0.272530	−	0.962147i	$-0.412140\pi$
$458$	785.217	−	1360.04i	0.0801108	−	0.138756i
$459$		0			0
$460$	737.808	+	1277.92i	0.0747836	+	0.129529i
$461$	11955.8			1.20789			0.603947	−	0.797025i	$-0.293594\pi$
$461$	11955.8			1.20789			0.603947	+	0.797025i	$0.293594\pi$
$462$		0			0
$463$	648.503			0.0650939			0.0325470	−	0.999470i	$-0.489638\pi$
$463$	648.503			0.0650939			0.0325470	+	0.999470i	$0.489638\pi$
$464$	1105.53	+	1914.83i	0.110610	+	0.191581i
$465$		0			0
$466$	−5369.12	+	9299.60i	−0.533734	+	0.924454i
$467$	−1392.37	−	2411.66i	−0.137969	−	0.238969i	0.788759	−	0.614703i	$-0.210724\pi$
$467$	−1392.37	−	2411.66i	−0.137969	−	0.238969i	−0.926728	+	0.375734i	$0.877391\pi$
$468$		0			0
$469$		0			0
$470$	−444.582			−0.0436320
$471$		0			0
$472$	−1807.20	+	3130.16i	−0.176235	+	0.305248i
$473$	−13433.3	+	23267.1i	−1.30584	+	2.26178i
$474$		0			0
$475$	−6126.39			−0.591785
$476$		0			0
$477$		0			0
$478$	3713.28	+	6431.58i	0.355316	+	0.615426i
$479$	−5556.70	+	9624.49i	−0.530046	+	0.918067i	0.469339	+	0.883018i	$0.344492\pi$
$479$	−5556.70	+	9624.49i	−0.530046	+	0.918067i	−0.999386	+	0.0350493i	$0.988841\pi$
$480$		0			0
$481$	4006.07	+	6938.72i	0.379753	+	0.657751i
$482$	−13997.2			−1.32273
$483$		0			0
$484$	9754.35			0.916074
$485$	3138.00	+	5435.17i	0.293792	+	0.508862i
$486$		0			0
$487$	1893.14	−	3279.01i	0.176152	−	0.305105i	−0.764407	−	0.644734i	$-0.776968\pi$
$487$	1893.14	−	3279.01i	0.176152	−	0.305105i	0.940559	+	0.339629i	$0.110302\pi$
$488$	2317.23	+	4013.55i	0.214951	+	0.372305i
$489$		0			0
$490$		0			0
$491$	9582.12			0.880723			0.440361	−	0.897821i	$-0.354850\pi$
$491$	9582.12			0.880723			0.440361	+	0.897821i	$0.354850\pi$
$492$		0			0
$493$	2218.00	−	3841.69i	0.202624	−	0.350955i
$494$	2996.32	−	5189.78i	0.272896	−	0.472671i
$495$		0			0
$496$	−2121.65			−0.192066
$497$		0			0
$498$		0			0
$499$	−2790.77	−	4833.76i	−0.250365	−	0.433645i	0.713261	−	0.700898i	$-0.247217\pi$
$499$	−2790.77	−	4833.76i	−0.250365	−	0.433645i	−0.963626	+	0.267253i	$0.913884\pi$
$500$	−1831.16	+	3171.65i	−0.163784	+	0.283681i
$501$		0			0
$502$	−3722.75	−	6448.00i	−0.330985	−	0.573283i
$503$	−14116.3			−1.25132			−0.625661	−	0.780095i	$-0.715171\pi$
$503$	−14116.3			−1.25132			−0.625661	+	0.780095i	$0.715171\pi$
$504$		0			0
$505$	5768.35			0.508294
$506$	−5808.34	−	10060.3i	−0.510301	−	0.883867i
$507$		0			0
$508$	5233.41	−	9064.53i	0.457076	−	0.791680i
$509$	−8393.81	−	14538.5i	−0.730941	−	1.26603i	−0.956481	−	0.291793i	$-0.905748\pi$
$509$	−8393.81	−	14538.5i	−0.730941	−	1.26603i	0.225540	−	0.974234i	$-0.427585\pi$
$510$		0			0
$511$		0			0
$512$	512.000			0.0441942
$513$		0			0
$514$	−1230.15	+	2130.68i	−0.105563	+	0.182841i
$515$	2233.14	−	3867.91i	0.191075	−	0.330952i
$516$		0			0
$517$	3499.94			0.297731
$518$		0			0
$519$		0			0
$520$	−837.588	−	1450.74i	−0.0706359	−	0.122345i
$521$	2799.31	−	4848.54i	0.235393	−	0.407713i	−0.723994	−	0.689807i	$-0.757696\pi$
$521$	2799.31	−	4848.54i	0.235393	−	0.407713i	0.959387	+	0.282094i	$0.0910289\pi$
$522$		0			0
$523$	−6635.37	−	11492.8i	−0.554769	−	0.960889i	−0.997921	−	0.0644422i	$-0.979473\pi$
$523$	−6635.37	−	11492.8i	−0.554769	−	0.960889i	0.443152	−	0.896446i	$-0.353860\pi$
$524$	710.352			0.0592211
$525$		0			0
$526$	−4777.27			−0.396005
$527$	2128.31	+	3686.34i	0.175922	+	0.304705i
$528$		0			0
$529$	1608.63	−	2786.23i	0.132213	−	0.228999i
$530$	1027.86	+	1780.31i	0.0842403	+	0.145909i
$531$		0			0
$532$		0			0
$533$	−22956.0			−1.86554
$534$		0			0
$535$	−851.951	+	1475.62i	−0.0688468	+	0.119246i
$536$	−1238.35	+	2144.89i	−0.0997922	+	0.172845i
$537$		0			0
$538$	13404.6			1.07419
$539$		0			0
$540$		0			0
$541$	11508.8	+	19933.8i	0.914603	+	1.58414i	0.807482	+	0.589893i	$0.200830\pi$
$541$	11508.8	+	19933.8i	0.914603	+	1.58414i	0.107121	+	0.994246i	$0.465837\pi$
$542$	4950.37	−	8574.29i	0.392319	−	0.679516i
$543$		0			0
$544$	−513.608	−	889.595i	−0.0404793	−	0.0701123i
$545$	648.687			0.0509848
$546$		0			0
$547$	4475.84			0.349859			0.174930	−	0.984581i	$-0.444030\pi$
$547$	4475.84			0.349859			0.174930	+	0.984581i	$0.444030\pi$
$548$	54.0303	+	93.5832i	0.00421179	+	0.00729503i
$549$		0			0
$550$	6741.02	−	11675.8i	0.522614	−	0.905194i
$551$	3855.46	+	6677.85i	0.298091	+	0.516308i
$552$		0			0
$553$		0			0
$554$	−7410.35			−0.568295
$555$		0			0
$556$	−1845.51	+	3196.51i	−0.140768	+	0.243817i
$557$	770.848	−	1335.15i	0.0586390	−	0.101566i	−0.835216	−	0.549922i	$-0.814657\pi$
$557$	770.848	−	1335.15i	0.0586390	−	0.101566i	0.893855	+	0.448357i	$0.147991\pi$
$558$		0			0
$559$	−23497.8			−1.77791
$560$		0			0
$561$		0			0
$562$	9324.74	+	16150.9i	0.699894	+	1.21225i
$563$	−6539.83	+	11327.3i	−0.489557	+	0.847938i	−0.999928	−	0.0120164i	$-0.996175\pi$
$563$	−6539.83	+	11327.3i	−0.489557	+	0.847938i	0.510370	+	0.859955i	$0.329508\pi$
$564$		0			0
$565$	−956.983	−	1657.54i	−0.0712577	−	0.123422i
$566$	11139.0			0.827219
$567$		0			0
$568$	8471.88			0.625831
$569$	5705.59	+	9882.37i	0.420370	+	0.728102i	0.995976	−	0.0896251i	$-0.0285669\pi$
$569$	5705.59	+	9882.37i	0.420370	+	0.728102i	−0.575605	+	0.817728i	$0.695234\pi$
$570$		0			0
$571$	−1155.87	+	2002.03i	−0.0847139	+	0.146729i	−0.905269	−	0.424838i	$-0.860331\pi$
$571$	−1155.87	+	2002.03i	−0.0847139	+	0.146729i	0.820555	+	0.571567i	$0.193664\pi$
$572$	6593.85	+	11420.9i	0.481998	+	0.834844i
$573$		0			0
$574$		0			0
$575$	−10386.8			−0.753324
$576$		0			0
$577$	12548.5	−	21734.6i	0.905373	−	1.56815i	0.0849578	−	0.996385i	$-0.472924\pi$
$577$	12548.5	−	21734.6i	0.905373	−	1.56815i	0.820415	−	0.571768i	$-0.193742\pi$
$578$	3882.56	−	6724.79i	0.279400	−	0.483935i
$579$		0			0
$580$	2155.50			0.154314
$581$		0			0
$582$		0			0
$583$	−8091.75	−	14015.3i	−0.574830	−	0.995635i
$584$	4774.63	−	8269.91i	0.338315	−	0.585978i
$585$		0			0
$586$	1665.31	+	2884.40i	0.117395	+	0.203333i
$587$	19789.1			1.39145			0.695726	−	0.718307i	$-0.255083\pi$
$587$	19789.1			1.39145			0.695726	+	0.718307i	$0.255083\pi$
$588$		0			0
$589$	−7399.12			−0.517615
$590$	1761.79	+	3051.51i	0.122935	+	0.212930i
$591$		0			0
$592$	−1193.65	+	2067.46i	−0.0828693	+	0.143534i
$593$	1387.07	+	2402.47i	0.0960540	+	0.166370i	0.910048	−	0.414503i	$-0.136045\pi$
$593$	1387.07	+	2402.47i	0.0960540	+	0.166370i	−0.813994	+	0.580873i	$0.802711\pi$
$594$		0			0
$595$		0			0
$596$	−2986.81			−0.205276
$597$		0			0
$598$	5080.04	−	8798.89i	0.347388	−	0.601694i
$599$	−13095.2	+	22681.5i	−0.893245	+	1.54715i	−0.0572831	+	0.998358i	$0.518244\pi$
$599$	−13095.2	+	22681.5i	−0.893245	+	1.54715i	−0.835962	+	0.548788i	$0.815090\pi$
$600$		0			0
$601$	11038.6			0.749211			0.374605	−	0.927184i	$-0.377778\pi$
$601$	11038.6			0.749211			0.374605	+	0.927184i	$0.377778\pi$
$602$		0			0
$603$		0			0
$604$	−4146.29	−	7181.59i	−0.279321	−	0.483799i
$605$	4754.63	−	8235.26i	0.319509	−	0.553407i
$606$		0			0
$607$	−927.197	−	1605.95i	−0.0619996	−	0.107386i	0.833360	−	0.552731i	$-0.186414\pi$
$607$	−927.197	−	1605.95i	−0.0619996	−	0.107386i	−0.895359	+	0.445345i	$0.853081\pi$
$608$	1785.57			0.119103
$609$		0			0
$610$	4518.01			0.299883
$611$	1530.54	+	2650.98i	0.101341	+	0.175527i
$612$		0			0
$613$	7428.42	−	12866.4i	0.489447	−	0.847747i	−0.510479	−	0.859890i	$-0.670532\pi$
$613$	7428.42	−	12866.4i	0.489447	−	0.847747i	0.999926	+	0.0121428i	$0.00386527\pi$
$614$	−5303.32	−	9185.61i	−0.348574	−	0.603748i
$615$		0			0
$616$		0			0
$617$	−7600.00			−0.495890			−0.247945	−	0.968774i	$-0.579755\pi$
$617$	−7600.00			−0.495890			−0.247945	+	0.968774i	$0.579755\pi$
$618$		0			0
$619$	11342.6	−	19646.0i	0.736509	−	1.27567i	−0.217549	−	0.976049i	$-0.569806\pi$
$619$	11342.6	−	19646.0i	0.736509	−	1.27567i	0.954058	−	0.299622i	$-0.0968606\pi$
$620$	−1034.17	+	1791.23i	−0.0669891	+	0.116029i
$621$		0			0
$622$	2251.98			0.145171
$623$		0			0
$624$		0			0
$625$	−5076.98	−	8793.58i	−0.324926	−	0.562789i
$626$	−8299.51	+	14375.2i	−0.529896	+	0.917807i
$627$		0			0
$628$	3132.44	+	5425.55i	0.199041	+	0.344750i
$629$	4789.59			0.303614
$630$		0			0
$631$	−12024.1			−0.758595			−0.379297	−	0.925275i	$-0.623834\pi$
$631$	−12024.1			−0.758595			−0.379297	+	0.925275i	$0.623834\pi$
$632$	−5278.23	−	9142.16i	−0.332210	−	0.575405i
$633$		0			0
$634$	−4278.76	+	7411.04i	−0.268031	+	0.464243i
$635$	−5101.91	−	8836.77i	−0.318840	−	0.552246i
$636$		0			0
$637$		0			0
$638$	−16969.0			−1.05299
$639$		0			0
$640$	249.568	−	432.264i	0.0154141	−	0.0266980i
$641$	5660.28	−	9803.89i	0.348779	−	0.604104i	−0.637253	−	0.770654i	$-0.719930\pi$
$641$	5660.28	−	9803.89i	0.348779	−	0.604104i	0.986033	+	0.166551i	$0.0532629\pi$
$642$		0			0
$643$	−16843.6			−1.03304			−0.516521	−	0.856275i	$-0.672773\pi$
$643$	−16843.6			−1.03304			−0.516521	+	0.856275i	$0.672773\pi$
$644$		0			0
$645$		0			0
$646$	−1791.18	−	3102.41i	−0.109091	−	0.188951i
$647$	−3859.66	+	6685.13i	−0.234527	+	0.406212i	−0.959135	−	0.282949i	$-0.908687\pi$
$647$	−3859.66	+	6685.13i	−0.234527	+	0.406212i	0.724608	+	0.689161i	$0.242021\pi$
$648$		0			0
$649$	−13869.5	−	24022.8i	−0.838871	−	1.45297i
$650$	11791.5			0.711542
$651$		0			0
$652$	394.933			0.0237221
$653$	−15401.6	−	26676.3i	−0.922987	−	1.59866i	−0.794768	−	0.606914i	$-0.792407\pi$
$653$	−15401.6	−	26676.3i	−0.922987	−	1.59866i	−0.128219	−	0.991746i	$-0.540926\pi$
$654$		0			0
$655$	346.252	−	599.725i	0.0206552	−	0.0357759i
$656$	−3419.98	−	5923.58i	−0.203548	−	0.352556i
$657$		0			0
$658$		0			0
$659$	−9760.68			−0.576968			−0.288484	−	0.957485i	$-0.593151\pi$
$659$	−9760.68			−0.576968			−0.288484	+	0.957485i	$0.593151\pi$
$660$		0			0
$661$	9035.53	−	15650.0i	0.531682	−	0.920899i	−0.467635	−	0.883922i	$-0.654894\pi$
$661$	9035.53	−	15650.0i	0.531682	−	0.920899i	0.999316	−	0.0369775i	$-0.0117730\pi$
$662$	1707.12	−	2956.81i	0.100225	−	0.173595i
$663$		0			0
$664$	9522.65			0.556552
$665$		0			0
$666$		0			0
$667$	6536.64	+	11321.8i	0.379460	+	0.657244i
$668$	4462.71	−	7729.65i	0.258484	−	0.447708i
$669$		0			0
$670$	1207.24	+	2090.99i	0.0696114	+	0.120570i
$671$	−35567.7			−2.04631
$672$		0			0
$673$	26591.1			1.52305			0.761524	−	0.648137i	$-0.224451\pi$
$673$	26591.1			1.52305			0.761524	+	0.648137i	$0.224451\pi$
$674$	−1710.67	−	2962.97i	−0.0977636	−	0.169331i
$675$		0			0
$676$	−1373.05	+	2378.20i	−0.0781210	+	0.135310i
$677$	−16540.1	−	28648.3i	−0.938979	−	1.62636i	−0.767380	−	0.641192i	$-0.778440\pi$
$677$	−16540.1	−	28648.3i	−0.938979	−	1.62636i	−0.171599	−	0.985167i	$-0.554893\pi$
$678$		0			0
$679$		0			0
$680$	−1001.41			−0.0564738
$681$		0			0
$682$	8141.42	−	14101.4i	0.457113	−	0.791743i
$683$	−5233.04	+	9063.89i	−0.293172	+	0.507789i	−0.974558	−	0.224135i	$-0.928044\pi$
$683$	−5233.04	+	9063.89i	−0.293172	+	0.507789i	0.681386	+	0.731924i	$0.261378\pi$
$684$		0			0
$685$	105.345			0.00587597
$686$		0			0
$687$		0			0
$688$	−3500.70	−	6063.40i	−0.193987	−	0.335995i
$689$	7077.13	−	12258.0i	0.391317	−	0.677781i
$690$		0			0
$691$	6634.95	+	11492.1i	0.365275	+	0.632675i	0.988820	−	0.149112i	$-0.0476415\pi$
$691$	6634.95	+	11492.1i	0.365275	+	0.632675i	−0.623545	+	0.781787i	$0.714308\pi$
$692$	8403.38			0.461631
$693$		0			0
$694$	−17820.6			−0.974727
$695$	1799.14	+	3116.20i	0.0981944	+	0.170078i
$696$		0			0
$697$	−6861.44	+	11884.4i	−0.372878	+	0.645843i
$698$	5378.68	+	9316.15i	0.291671	+	0.505189i
$699$		0			0
$700$		0			0
$701$	15169.9			0.817344			0.408672	−	0.912681i	$-0.365992\pi$
$701$	15169.9			0.817344			0.408672	+	0.912681i	$0.365992\pi$
$702$		0			0
$703$	−4162.77	+	7210.14i	−0.223331	+	0.386821i
$704$	−1964.70	+	3402.97i	−0.105181	+	0.182179i
$705$		0			0
$706$	−8505.13			−0.453392
$707$		0			0
$708$		0			0
$709$	−13158.9	−	22791.8i	−0.697026	−	1.20728i	−0.969493	−	0.245119i	$-0.921173\pi$
$709$	−13158.9	−	22791.8i	−0.697026	−	1.20728i	0.272467	−	0.962165i	$-0.412160\pi$
$710$	4129.51	−	7152.51i	0.218278	−	0.378069i
$711$		0			0
$712$	932.341	+	1614.86i	0.0490744	+	0.0849994i
$713$	−12544.6			−0.658907
$714$		0			0
$715$	12856.3			0.672447
$716$	3445.08	+	5967.06i	0.179817	+	0.311452i
$717$		0			0
$718$	4903.89	−	8493.78i	0.254891	−	0.441484i
$719$	−11506.5	−	19929.9i	−0.596831	−	1.03374i	−0.993286	−	0.115687i	$-0.963093\pi$
$719$	−11506.5	−	19929.9i	−0.596831	−	1.03374i	0.396455	−	0.918054i	$-0.370240\pi$
$720$		0			0
$721$		0			0
$722$	−7490.95			−0.386128
$723$		0			0
$724$	3310.01	−	5733.10i	0.169911	−	0.294294i
$725$	−7586.26	+	13139.8i	−0.388616	+	0.673103i
$726$		0			0
$727$	16265.4			0.829780			0.414890	−	0.909872i	$-0.363820\pi$
$727$	16265.4			0.829780			0.414890	+	0.909872i	$0.363820\pi$
$728$		0			0
$729$		0			0
$730$	−4654.66	−	8062.11i	−0.235996	−	0.408756i
$731$	−7023.40	+	12164.9i	−0.355362	+	0.615505i
$732$		0			0
$733$	−433.222	−	750.362i	−0.0218300	−	0.0378107i	0.854904	−	0.518786i	$-0.173616\pi$
$733$	−433.222	−	750.362i	−0.0218300	−	0.0378107i	−0.876734	+	0.480975i	$0.840283\pi$
$734$	8083.14			0.406477
$735$		0			0
$736$	3027.30			0.151614
$737$	−9503.88	−	16461.2i	−0.475007	−	0.822736i
$738$		0			0
$739$	−5495.03	+	9517.68i	−0.273529	+	0.473766i	−0.969763	−	0.244049i	$-0.921524\pi$
$739$	−5495.03	+	9517.68i	−0.273529	+	0.473766i	0.696234	+	0.717815i	$0.254858\pi$
$740$	1163.66	+	2015.51i	0.0578066	+	0.100124i
$741$		0			0
$742$		0			0
$743$	22416.4			1.10683			0.553417	−	0.832905i	$-0.313324\pi$
$743$	22416.4			1.10683			0.553417	+	0.832905i	$0.313324\pi$
$744$		0			0
$745$	−1455.88	+	2521.66i	−0.0715965	+	0.124009i
$746$	7451.35	−	12906.1i	0.365701	−	0.633413i
$747$		0			0
$748$	7883.49			0.385360
$749$		0			0
$750$		0			0
$751$	9858.97	+	17076.2i	0.479040	+	0.829722i	0.999711	−	0.0240358i	$-0.00765155\pi$
$751$	9858.97	+	17076.2i	0.479040	+	0.829722i	−0.520671	+	0.853757i	$0.674318\pi$
$752$	−456.040	+	789.885i	−0.0221145	+	0.0383034i
$753$		0			0
$754$	−7420.64	−	12852.9i	−0.358414	−	0.620791i
$755$	−8084.22			−0.389689
$756$		0			0
$757$	839.321			0.0402981			0.0201490	−	0.999797i	$-0.493586\pi$
$757$	839.321			0.0402981			0.0201490	+	0.999797i	$0.493586\pi$
$758$	12564.4	+	21762.2i	0.602057	+	1.04279i
$759$		0			0
$760$	870.352	−	1507.49i	0.0415407	−	0.0719507i
$761$	−9182.25	−	15904.1i	−0.437393	−	0.757587i	0.560094	−	0.828429i	$-0.310765\pi$
$761$	−9182.25	−	15904.1i	−0.437393	−	0.757587i	−0.997488	+	0.0708415i	$0.977432\pi$
$762$		0			0
$763$		0			0
$764$	4030.75			0.190874
$765$		0			0
$766$	4289.93	−	7430.38i	0.202352	−	0.350484i
$767$	12130.5	−	21010.6i	0.571063	−	0.989111i
$768$		0			0
$769$	14890.8			0.698277			0.349138	−	0.937071i	$-0.386474\pi$
$769$	14890.8			0.698277			0.349138	+	0.937071i	$0.386474\pi$
$770$		0			0
$771$		0			0
$772$	15.2970	+	26.4951i	0.000713148	+	0.00123521i
$773$	8303.10	−	14381.4i	0.386341	−	0.669163i	−0.605613	−	0.795759i	$-0.707072\pi$
$773$	8303.10	−	14381.4i	0.386341	−	0.669163i	0.991954	+	0.126597i	$0.0404053\pi$
$774$		0			0
$775$	−7279.50	−	12608.5i	−0.337403	−	0.584400i
$776$	12875.5			0.595623
$777$		0			0
$778$	−11325.5			−0.521903
$779$	−11927.0	−	20658.1i	−0.548559	−	0.950133i
$780$		0			0
$781$	−32509.2	+	56307.6i	−1.48946	+	2.57983i
$782$	−3036.81	−	5259.90i	−0.138869	−	0.240529i
$783$		0			0
$784$		0			0
$785$	6107.47			0.277688
$786$		0			0
$787$	1578.10	−	2733.35i	0.0714781	−	0.123804i	−0.828071	−	0.560623i	$-0.810562\pi$
$787$	1578.10	−	2733.35i	0.0714781	−	0.123804i	0.899549	+	0.436819i	$0.143895\pi$
$788$	5379.76	−	9318.01i	0.243205	−	0.421244i
$789$		0			0
$790$	−10291.2			−0.463475
$791$		0			0
$792$		0			0
$793$	−15553.9	−	26940.2i	−0.696515	−	1.20640i
$794$	14561.4	−	25221.0i	0.650836	−	1.12728i
$795$		0			0
$796$	1734.99	+	3005.10i	0.0772553	+	0.133810i
$797$	−13514.8			−0.600652			−0.300326	−	0.953837i	$-0.597096\pi$
$797$	−13514.8			−0.600652			−0.300326	+	0.953837i	$0.597096\pi$
$798$		0			0
$799$	1829.89			0.0810224
$800$	1756.70	+	3042.70i	0.0776360	+	0.134470i
$801$		0			0
$802$	−3742.19	+	6481.66i	−0.164765	+	0.285381i
$803$	36643.5	+	63468.4i	1.61036	+	2.78923i
$804$		0			0
$805$		0			0
$806$	14241.2			0.622362
$807$		0			0
$808$	5917.02	−	10248.6i	0.257624	−	0.446218i
$809$	−13379.1	+	23173.2i	−0.581437	+	1.00708i	0.413872	+	0.910335i	$0.364176\pi$
$809$	−13379.1	+	23173.2i	−0.581437	+	1.00708i	−0.995309	+	0.0967438i	$0.969157\pi$
$810$		0			0
$811$	15920.7			0.689338			0.344669	−	0.938724i	$-0.387991\pi$
$811$	15920.7			0.689338			0.344669	+	0.938724i	$0.387991\pi$
$812$		0			0
$813$		0			0
$814$	−9160.80	−	15867.0i	−0.394454	−	0.683215i
$815$	192.505	−	333.429i	0.00827381	−	0.0143307i
$816$		0			0
$817$	−12208.5	−	21145.7i	−0.522792	−	0.905501i
$818$	7034.35			0.300673
$819$		0			0
$820$	−6668.10			−0.283976
$821$	−9653.11	−	16719.7i	−0.410348	−	0.710744i	0.584580	−	0.811336i	$-0.301259\pi$
$821$	−9653.11	−	16719.7i	−0.410348	−	0.710744i	−0.994928	+	0.100593i	$0.967926\pi$
$822$		0			0
$823$	−395.500	+	685.026i	−0.0167512	+	0.0290140i	−0.874280	−	0.485423i	$-0.838666\pi$
$823$	−395.500	+	685.026i	−0.0167512	+	0.0290140i	0.857528	+	0.514437i	$0.171999\pi$
$824$	−4581.39	−	7935.19i	−0.193689	−	0.335480i
$825$		0			0
$826$		0			0
$827$	−29537.6			−1.24199			−0.620993	−	0.783816i	$-0.713270\pi$
$827$	−29537.6			−1.24199			−0.620993	+	0.783816i	$0.713270\pi$
$828$		0			0
$829$	−2883.26	+	4993.96i	−0.120796	+	0.209225i	−0.920082	−	0.391726i	$-0.871878\pi$
$829$	−2883.26	+	4993.96i	−0.120796	+	0.209225i	0.799286	+	0.600951i	$0.205211\pi$
$830$	4641.69	−	8039.64i	0.194115	−	0.336217i
$831$		0			0
$832$	−3436.70			−0.143205
$833$		0			0
$834$		0			0
$835$	−4350.58	−	7535.43i	−0.180309	−	0.312305i
$836$	−6851.78	+	11867.6i	−0.283461	+	0.490969i
$837$		0			0
$838$	7579.52	+	13128.1i	0.312446	+	0.541173i
$839$	29726.4			1.22321			0.611603	−	0.791165i	$-0.290525\pi$
$839$	29726.4			1.22321			0.611603	+	0.791165i	$0.290525\pi$
$840$		0			0
$841$	−5292.27			−0.216994
$842$	4980.87	+	8627.12i	0.203862	+	0.353100i
$843$		0			0
$844$	−324.061	+	561.289i	−0.0132164	+	0.0228914i
$845$	1338.55	+	2318.44i	0.0544943	+	0.0943869i
$846$		0			0
$847$		0			0
$848$	4217.41			0.170786
$849$		0			0
$850$	3524.44	−	6104.51i	0.142220	−	0.246333i
$851$	−7057.67	+	12224.2i	−0.284294	+	0.492411i
$852$		0			0
$853$	17829.6			0.715677			0.357838	−	0.933784i	$-0.383514\pi$
$853$	17829.6			0.715677			0.357838	+	0.933784i	$0.383514\pi$
$854$		0			0
$855$		0			0
$856$	1747.82	+	3027.31i	0.0697888	+	0.120878i
$857$	19841.2	−	34366.0i	0.790856	−	1.36980i	−0.134582	−	0.990902i	$-0.542969\pi$
$857$	19841.2	−	34366.0i	0.790856	−	1.36980i	0.925438	−	0.378900i	$-0.123697\pi$
$858$		0			0
$859$	−1097.57	−	1901.04i	−0.0435955	−	0.0755096i	0.843404	−	0.537279i	$-0.180548\pi$
$859$	−1097.57	−	1901.04i	−0.0435955	−	0.0755096i	−0.887000	+	0.461770i	$0.847215\pi$
$860$	−6825.49			−0.270636
$861$		0			0
$862$	−28406.6			−1.12243
$863$	15958.5	+	27641.0i	0.629472	+	1.09028i	0.987658	+	0.156627i	$0.0500622\pi$
$863$	15958.5	+	27641.0i	0.629472	+	1.09028i	−0.358186	+	0.933650i	$0.616604\pi$
$864$		0			0
$865$	4096.12	−	7094.68i	0.161008	−	0.278874i
$866$	3874.82	+	6711.39i	0.152046	+	0.263351i
$867$		0			0
$868$		0			0
$869$	81016.8			3.16261
$870$		0			0
$871$	8312.20	−	14397.2i	0.323362	−	0.560079i
$872$	665.406	−	1152.52i	0.0258412	−	0.0447582i
$873$		0			0
$874$	10557.5			0.408596
$875$		0			0
$876$		0			0
$877$	−14421.4	−	24978.6i	−0.555276	−	0.961766i	−0.997882	−	0.0650500i	$-0.979279\pi$
$877$	−14421.4	−	24978.6i	−0.555276	−	0.961766i	0.442606	−	0.896716i	$-0.354054\pi$
$878$	7763.82	−	13447.3i	0.298424	−	0.516885i
$879$		0			0
$880$	1915.34	+	3317.46i	0.0733705	+	0.127081i
$881$	−15350.2			−0.587015			−0.293508	−	0.955957i	$-0.594823\pi$
$881$	−15350.2			−0.587015			−0.293508	+	0.955957i	$0.594823\pi$
$882$		0			0
$883$	6089.64			0.232087			0.116043	−	0.993244i	$-0.462979\pi$
$883$	6089.64			0.232087			0.116043	+	0.993244i	$0.462979\pi$
$884$	3447.50	+	5971.24i	0.131167	+	0.227188i
$885$		0			0
$886$	9662.24	−	16735.5i	0.366376	−	0.634582i
$887$	192.221	+	332.936i	0.00727637	+	0.0126030i	0.869641	−	0.493685i	$-0.164351\pi$
$887$	192.221	+	332.936i	0.00727637	+	0.0126030i	−0.862364	+	0.506288i	$0.831017\pi$
$888$		0			0
$889$		0			0
$890$	1817.83			0.0684650
$891$		0			0
$892$	−9155.70	+	15858.1i	−0.343672	+	0.595257i
$893$	−1590.41	+	2754.67i	−0.0595981	+	0.103227i
$894$		0			0
$895$	6717.05			0.250867
$896$		0			0
$897$		0			0
$898$	−10942.6	−	18953.1i	−0.406636	−	0.704313i
$899$	−9162.27	+	15869.5i	−0.339910	+	0.588741i
$900$		0			0
$901$	−4230.65	−	7327.70i	−0.156430	−	0.270945i
$902$	52494.1			1.93776
$903$		0			0
$904$	−3926.59			−0.144465
$905$	−3226.84	−	5589.05i	−0.118524	−	0.205289i
$906$		0			0
$907$	3633.97	−	6294.21i	0.133036	−	0.230426i	−0.791809	−	0.610768i	$-0.790861\pi$
$907$	3633.97	−	6294.21i	0.133036	−	0.230426i	0.924846	+	0.380343i	$0.124194\pi$
$908$	4436.38	+	7684.04i	0.162144	+	0.280841i
$909$		0			0
$910$		0			0
$911$	8535.12			0.310408			0.155204	−	0.987882i	$-0.450397\pi$
$911$	8535.12			0.310408			0.155204	+	0.987882i	$0.450397\pi$
$912$		0			0
$913$	−36541.4	+	63291.5i	−1.32458	+	2.29424i
$914$	−13618.3	+	23587.7i	−0.492839	+	0.853622i
$915$		0			0
$916$	−3140.87			−0.113294
$917$		0			0
$918$		0			0
$919$	5425.86	+	9397.87i	0.194758	+	0.337331i	0.946821	−	0.321760i	$-0.104275\pi$
$919$	5425.86	+	9397.87i	0.194758	+	0.337331i	−0.752063	+	0.659091i	$0.770941\pi$
$920$	1475.62	−	2555.84i	0.0528800	−	0.0915909i
$921$		0			0
$922$	−11955.8	−	20708.1i	−0.427055	−	0.739681i
$923$	−56865.9			−2.02791
$924$		0			0
$925$	−16381.9			−0.582307
$926$	−648.503	−	1123.24i	−0.0230142	−	0.0398617i
$927$		0			0
$928$	2211.05	−	3829.66i	0.0782127	−	0.135468i
$929$	780.319	+	1351.55i	0.0275581	+	0.0477320i	0.879476	−	0.475944i	$-0.157894\pi$
$929$	780.319	+	1351.55i	0.0275581	+	0.0477320i	−0.851917	+	0.523676i	$0.824560\pi$
$930$		0			0
$931$		0			0
$932$	21476.5			0.754813
$933$		0			0
$934$	−2784.74	+	4823.32i	−0.0975585	+	0.168976i
$935$	3842.71	−	6655.76i	0.134406	−	0.232799i
$936$		0			0
$937$	−11978.4			−0.417627			−0.208813	−	0.977956i	$-0.566960\pi$
$937$	−11978.4			−0.417627			−0.208813	+	0.977956i	$0.566960\pi$
$938$		0			0
$939$		0			0
$940$	444.582	+	770.038i	0.0154262	+	0.0267190i
$941$	−12298.8	+	21302.2i	−0.426068	+	0.737972i	−0.996520	−	0.0833594i	$-0.973435\pi$
$941$	−12298.8	+	21302.2i	−0.426068	+	0.737972i	0.570451	+	0.821332i	$0.306768\pi$
$942$		0			0
$943$	−20221.3	−	35024.3i	−0.698298	−	1.20949i
$944$	7228.78			0.249234
$945$		0			0
$946$	53733.1			1.84674
$947$	−5417.32	−	9383.07i	−0.185891	−	0.321973i	0.757985	−	0.652272i	$-0.226184\pi$
$947$	−5417.32	−	9383.07i	−0.185891	−	0.321973i	−0.943877	+	0.330298i	$0.892851\pi$
$948$		0			0
$949$	−32048.8	+	55510.2i	−1.09626	+	1.89877i
$950$	6126.39	+	10611.2i	0.209228	+	0.362393i
$951$		0			0
$952$		0			0
$953$	−701.418			−0.0238417			−0.0119209	−	0.999929i	$-0.503795\pi$
$953$	−701.418			−0.0238417			−0.0119209	+	0.999929i	$0.503795\pi$
$954$		0			0
$955$	1964.74	−	3403.02i	0.0665732	−	0.115308i
$956$	7426.55	−	12863.2i	0.251247	−	0.435172i
$957$		0			0
$958$	22226.8			0.749599
$959$		0			0
$960$		0			0
$961$	6103.72	+	10571.9i	0.204885	+	0.354871i
$962$	8012.14	−	13877.4i	0.268526	−	0.465100i
$963$		0			0
$964$	13997.2	+	24243.9i	0.467657	+	0.810005i
$965$	29.8252			0.000994931
$966$		0			0
$967$	42402.5			1.41011			0.705053	−	0.709154i	$-0.250923\pi$
$967$	42402.5			1.41011			0.705053	+	0.709154i	$0.250923\pi$
$968$	−9754.35	−	16895.0i	−0.323881	−	0.560978i
$969$		0			0
$970$	6275.99	−	10870.3i	0.207742	−	0.359820i
$971$	−7731.69	−	13391.7i	−0.255532	−	0.442595i	0.709508	−	0.704698i	$-0.248917\pi$
$971$	−7731.69	−	13391.7i	−0.255532	−	0.442595i	−0.965040	+	0.262103i	$0.915584\pi$
$972$		0			0
$973$		0			0
$974$	−7572.55			−0.249117
$975$		0			0
$976$	4634.45	−	8027.11i	0.151993	−	0.263260i
$977$	−17242.1	+	29864.1i	−0.564609	+	0.977931i	0.432477	+	0.901645i	$0.357640\pi$
$977$	−17242.1	+	29864.1i	−0.564609	+	0.977931i	−0.997086	+	0.0762860i	$0.975694\pi$
$978$		0			0
$979$	−14310.7			−0.467184
$980$		0			0
$981$		0			0
$982$	−9582.12	−	16596.7i	−0.311383	−	0.539330i
$983$	−3667.68	+	6352.61i	−0.119004	+	0.206121i	−0.919373	−	0.393386i	$-0.871303\pi$
$983$	−3667.68	+	6352.61i	−0.119004	+	0.206121i	0.800369	+	0.599507i	$0.204637\pi$
$984$		0			0
$985$	−5244.58	−	9083.89i	−0.169651	−	0.293844i
$986$	−8872.00			−0.286554
$987$		0			0
$988$	−11985.3			−0.385934
$989$	−20698.6	−	35851.0i	−0.665497	−	1.15267i
$990$		0			0
$991$	5061.48	−	8766.74i	0.162243	−	0.281014i	−0.773430	−	0.633882i	$-0.781460\pi$
$991$	5061.48	−	8766.74i	0.162243	−	0.281014i	0.935673	+	0.352869i	$0.114794\pi$
$992$	2121.65	+	3674.80i	0.0679057	+	0.117616i
$993$		0			0
$994$		0			0
$995$	3382.80			0.107781
$996$		0			0
$997$	28334.6	−	49076.9i	0.900066	−	1.55896i	0.0726582	−	0.997357i	$-0.476852\pi$
$997$	28334.6	−	49076.9i	0.900066	−	1.55896i	0.827407	−	0.561602i	$-0.189815\pi$
$998$	−5581.55	+	9667.52i	−0.177035	+	0.306633i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.4.g.y.361.2		4
3.2	odd	2		294.4.e.n.67.1		4
7.2	even	3	inner	882.4.g.y.667.2		4
7.3	odd	6		882.4.a.bc.1.2		2
7.4	even	3		882.4.a.bi.1.1		2
7.5	odd	6		882.4.g.bd.667.1		4
7.6	odd	2		882.4.g.bd.361.1		4
21.2	odd	6		294.4.e.n.79.1		4
21.5	even	6		294.4.e.o.79.2		4
21.11	odd	6		294.4.a.k.1.2	yes	2
21.17	even	6		294.4.a.j.1.1	✓	2
21.20	even	2		294.4.e.o.67.2		4
84.11	even	6		2352.4.a.bn.1.2		2
84.59	odd	6		2352.4.a.cd.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.4.a.j.1.1	✓	2	21.17	even	6
294.4.a.k.1.2	yes	2	21.11	odd	6
294.4.e.n.67.1		4	3.2	odd	2
294.4.e.n.79.1		4	21.2	odd	6
294.4.e.o.67.2		4	21.20	even	2
294.4.e.o.79.2		4	21.5	even	6
882.4.a.bc.1.2		2	7.3	odd	6
882.4.a.bi.1.1		2	7.4	even	3
882.4.g.y.361.2		4	1.1	even	1	trivial
882.4.g.y.667.2		4	7.2	even	3	inner
882.4.g.bd.361.1		4	7.6	odd	2
882.4.g.bd.667.1		4	7.5	odd	6
2352.4.a.bn.1.2		2	84.11	even	6
2352.4.a.cd.1.1		2	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(1.94975 + 3.37706i) q^{5} +8.00000 q^{8} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(1.94975 + 3.37706i) q^{5} +8.00000 q^{8} +(3.89949 - 6.75412i) q^{10} +(-30.6985 + 53.1713i) q^{11} -53.6985 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-16.0503 + 27.7999i) q^{17} +(-27.8995 - 48.3233i) q^{19} -15.5980 q^{20} +122.794 q^{22} +(-47.3015 - 81.9286i) q^{23} +(54.8970 - 95.0843i) q^{25} +(53.6985 + 93.0085i) q^{26} -138.191 q^{29} +(66.3015 - 114.838i) q^{31} +(-16.0000 + 27.7128i) q^{32} +64.2010 q^{34} +(-74.6030 - 129.216i) q^{37} +(-55.7990 + 96.6467i) q^{38} +(15.5980 + 27.0165i) q^{40} +427.497 q^{41} +437.588 q^{43} +(-122.794 - 212.685i) q^{44} +(-94.6030 + 163.857i) q^{46} +(-28.5025 - 49.3678i) q^{47} -219.588 q^{50} +(107.397 - 186.017i) q^{52} +(-131.794 + 228.274i) q^{53} -239.417 q^{55} +(138.191 + 239.354i) q^{58} +(-225.899 + 391.269i) q^{59} +(289.653 + 501.694i) q^{61} -265.206 q^{62} +64.0000 q^{64} +(-104.698 - 181.343i) q^{65} +(-154.794 + 268.111i) q^{67} +(-64.2010 - 111.199i) q^{68} +1058.98 q^{71} +(596.829 - 1033.74i) q^{73} +(-149.206 + 258.432i) q^{74} +223.196 q^{76} +(-659.779 - 1142.77i) q^{79} +(31.1960 - 54.0330i) q^{80} +(-427.497 - 740.447i) q^{82} +1190.33 q^{83} -125.176 q^{85} +(-437.588 - 757.924i) q^{86} +(-245.588 + 425.371i) q^{88} +(116.543 + 201.858i) q^{89} +378.412 q^{92} +(-57.0051 + 98.7356i) q^{94} +(108.794 - 188.437i) q^{95} +1609.44 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 8 q^{4} - 12 q^{5} + 32 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 - 8 * q^4 - 12 * q^5 + 32 * q^8	\( 4 q - 4 q^{2} - 8 q^{4} - 12 q^{5} + 32 q^{8} - 24 q^{10} - 4 q^{11} - 96 q^{13} - 32 q^{16} - 84 q^{17} - 72 q^{19} + 96 q^{20} + 16 q^{22} - 308 q^{23} - 18 q^{25} + 96 q^{26} + 160 q^{29} + 384 q^{31} - 64 q^{32} + 336 q^{34} - 536 q^{37} - 144 q^{38} - 96 q^{40} + 1512 q^{41} + 800 q^{43} - 16 q^{44} - 616 q^{46} - 312 q^{47} + 72 q^{50} + 192 q^{52} - 52 q^{53} - 2304 q^{55} - 160 q^{58} - 864 q^{59} + 1416 q^{61} - 1536 q^{62} + 256 q^{64} - 300 q^{65} - 144 q^{67} - 336 q^{68} + 3048 q^{71} + 744 q^{73} - 1072 q^{74} + 576 q^{76} - 976 q^{79} - 192 q^{80} - 1512 q^{82} - 624 q^{83} + 1400 q^{85} - 800 q^{86} - 32 q^{88} - 108 q^{89} + 2464 q^{92} - 624 q^{94} - 40 q^{95} + 1488 q^{97}+O(q^{100}) \) 4 * q - 4 * q^2 - 8 * q^4 - 12 * q^5 + 32 * q^8 - 24 * q^10 - 4 * q^11 - 96 * q^13 - 32 * q^16 - 84 * q^17 - 72 * q^19 + 96 * q^20 + 16 * q^22 - 308 * q^23 - 18 * q^25 + 96 * q^26 + 160 * q^29 + 384 * q^31 - 64 * q^32 + 336 * q^34 - 536 * q^37 - 144 * q^38 - 96 * q^40 + 1512 * q^41 + 800 * q^43 - 16 * q^44 - 616 * q^46 - 312 * q^47 + 72 * q^50 + 192 * q^52 - 52 * q^53 - 2304 * q^55 - 160 * q^58 - 864 * q^59 + 1416 * q^61 - 1536 * q^62 + 256 * q^64 - 300 * q^65 - 144 * q^67 - 336 * q^68 + 3048 * q^71 + 744 * q^73 - 1072 * q^74 + 576 * q^76 - 976 * q^79 - 192 * q^80 - 1512 * q^82 - 624 * q^83 + 1400 * q^85 - 800 * q^86 - 32 * q^88 - 108 * q^89 + 2464 * q^92 - 624 * q^94 - 40 * q^95 + 1488 * q^97

Introduction

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