LMFDB - Embedded newform 882.4.g.bd.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.bd.667.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(7.94975 + 13.7694i) q^{5} +8.00000 q^{8} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(7.94975 + 13.7694i) q^{5} +8.00000 q^{8} +(15.8995 - 27.5387i) q^{10} +(28.6985 - 49.7072i) q^{11} -5.69848 q^{13} +(-8.00000 - 13.8564i) q^{16} +(25.9497 - 44.9463i) q^{17} +(8.10051 + 14.0305i) q^{19} -63.5980 q^{20} -114.794 q^{22} +(-106.698 - 184.807i) q^{23} +(-63.8970 + 110.673i) q^{25} +(5.69848 + 9.87007i) q^{26} +218.191 q^{29} +(-125.698 + 217.716i) q^{31} +(-16.0000 + 27.7128i) q^{32} -103.799 q^{34} +(-193.397 - 334.973i) q^{37} +(16.2010 - 28.0610i) q^{38} +(63.5980 + 110.155i) q^{40} -328.503 q^{41} -37.5879 q^{43} +(114.794 + 198.829i) q^{44} +(-213.397 + 369.614i) q^{46} +(127.497 + 220.832i) q^{47} +255.588 q^{50} +(11.3970 - 19.7401i) q^{52} +(105.794 - 183.240i) q^{53} +912.583 q^{55} +(-218.191 - 377.918i) q^{58} +(206.101 - 356.977i) q^{59} +(-418.347 - 724.598i) q^{61} +502.794 q^{62} +64.0000 q^{64} +(-45.3015 - 78.4645i) q^{65} +(82.7939 - 143.403i) q^{67} +(103.799 + 179.785i) q^{68} +465.015 q^{71} +(224.829 - 389.415i) q^{73} +(-386.794 + 669.947i) q^{74} -64.8040 q^{76} +(171.779 + 297.530i) q^{79} +(127.196 - 220.310i) q^{80} +(328.503 + 568.983i) q^{82} +1502.33 q^{83} +825.176 q^{85} +(37.5879 + 65.1041i) q^{86} +(229.588 - 397.658i) q^{88} +(170.543 + 295.389i) q^{89} +853.588 q^{92} +(254.995 - 441.664i) q^{94} +(-128.794 + 223.078i) q^{95} +865.437 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	7.94975	+	13.7694i	0.711047	+	1.23157i	0.964464	+	0.264213i	$0.0851120\pi$
$5$	7.94975	+	13.7694i	0.711047	+	1.23157i	−0.253417	+	0.967357i	$0.581555\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	8.00000			0.353553
$9$		0			0
$10$	15.8995	−	27.5387i	0.502786	−	0.870851i
$11$	28.6985	−	49.7072i	0.786629	−	1.36248i	−0.141392	−	0.989954i	$-0.545158\pi$
$11$	28.6985	−	49.7072i	0.786629	−	1.36248i	0.928021	−	0.372528i	$-0.121509\pi$
$12$		0			0
$13$	−5.69848			−0.121575			−0.0607875	−	0.998151i	$-0.519361\pi$
$13$	−5.69848			−0.121575			−0.0607875	+	0.998151i	$0.519361\pi$
$14$		0			0
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	25.9497	−	44.9463i	0.370220	−	0.641240i	−0.619379	−	0.785092i	$-0.712616\pi$
$17$	25.9497	−	44.9463i	0.370220	−	0.641240i	0.989599	+	0.143852i	$0.0459490\pi$
$18$		0			0
$19$	8.10051	+	14.0305i	0.0978096	+	0.169411i	0.910778	−	0.412897i	$-0.135483\pi$
$19$	8.10051	+	14.0305i	0.0978096	+	0.169411i	−0.812968	+	0.582308i	$0.802150\pi$
$20$	−63.5980			−0.711047
$21$		0			0
$22$	−114.794			−1.11246
$23$	−106.698	−	184.807i	−0.967312	−	1.67543i	−0.703271	−	0.710922i	$-0.748278\pi$
$23$	−106.698	−	184.807i	−0.967312	−	1.67543i	−0.264041	−	0.964512i	$-0.585055\pi$
$24$		0			0
$25$	−63.8970	+	110.673i	−0.511176	+	0.885382i
$26$	5.69848	+	9.87007i	0.0429833	+	0.0744492i
$27$		0			0
$28$		0			0
$29$	218.191			1.39714			0.698570	−	0.715542i	$-0.253820\pi$
$29$	218.191			1.39714			0.698570	+	0.715542i	$0.253820\pi$
$30$		0			0
$31$	−125.698	+	217.716i	−0.728262	+	1.26139i	0.229356	+	0.973343i	$0.426338\pi$
$31$	−125.698	+	217.716i	−0.728262	+	1.26139i	−0.957617	+	0.288044i	$0.906995\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−103.799			−0.523570
$35$		0			0
$36$		0			0
$37$	−193.397	−	334.973i	−0.859304	−	1.48836i	−0.872593	−	0.488447i	$-0.837563\pi$
$37$	−193.397	−	334.973i	−0.859304	−	1.48836i	0.0132889	−	0.999912i	$-0.495770\pi$
$38$	16.2010	−	28.0610i	0.0691619	−	0.119792i
$39$		0			0
$40$	63.5980	+	110.155i	0.251393	+	0.435426i
$41$	−328.503			−1.25130			−0.625652	−	0.780102i	$-0.715167\pi$
$41$	−328.503			−1.25130			−0.625652	+	0.780102i	$0.715167\pi$
$42$		0			0
$43$	−37.5879			−0.133305			−0.0666523	−	0.997776i	$-0.521232\pi$
$43$	−37.5879			−0.133305			−0.0666523	+	0.997776i	$0.521232\pi$
$44$	114.794	+	198.829i	0.393314	+	0.681241i
$45$		0			0
$46$	−213.397	+	369.614i	−0.683993	+	1.18471i
$47$	127.497	+	220.832i	0.395690	+	0.685355i	0.993189	−	0.116515i	$-0.0371722\pi$
$47$	127.497	+	220.832i	0.395690	+	0.685355i	−0.597499	+	0.801869i	$0.703839\pi$
$48$		0			0
$49$		0			0
$50$	255.588			0.722912
$51$		0			0
$52$	11.3970	−	19.7401i	0.0303938	−	0.0526435i
$53$	105.794	−	183.240i	0.274187	−	0.474906i	−0.695743	−	0.718291i	$-0.744925\pi$
$53$	105.794	−	183.240i	0.274187	−	0.474906i	0.969930	+	0.243385i	$0.0782579\pi$
$54$		0			0
$55$	912.583			2.23732
$56$		0			0
$57$		0			0
$58$	−218.191	−	377.918i	−0.493963	−	0.855569i
$59$	206.101	−	356.977i	0.454780	−	0.787701i	−0.543896	−	0.839153i	$-0.683051\pi$
$59$	206.101	−	356.977i	0.454780	−	0.787701i	0.998676	+	0.0514512i	$0.0163847\pi$
$60$		0			0
$61$	−418.347	−	724.598i	−0.878095	−	1.52091i	−0.853429	−	0.521210i	$-0.825481\pi$
$61$	−418.347	−	724.598i	−0.878095	−	1.52091i	−0.0246666	−	0.999696i	$-0.507852\pi$
$62$	502.794			1.02992
$63$		0			0
$64$	64.0000			0.125000
$65$	−45.3015	−	78.4645i	−0.0864456	−	0.149728i
$66$		0			0
$67$	82.7939	−	143.403i	0.150969	−	0.261485i	−0.780615	−	0.625012i	$-0.785094\pi$
$67$	82.7939	−	143.403i	0.150969	−	0.261485i	0.931584	+	0.363527i	$0.118427\pi$
$68$	103.799	+	179.785i	0.185110	+	0.320620i
$69$		0			0
$70$		0			0
$71$	465.015			0.777284			0.388642	−	0.921389i	$-0.372944\pi$
$71$	465.015			0.777284			0.388642	+	0.921389i	$0.372944\pi$
$72$		0			0
$73$	224.829	−	389.415i	0.360469	−	0.624351i	−0.627569	−	0.778561i	$-0.715950\pi$
$73$	224.829	−	389.415i	0.360469	−	0.624351i	0.988038	+	0.154210i	$0.0492833\pi$
$74$	−386.794	+	669.947i	−0.607620	+	1.05243i
$75$		0			0
$76$	−64.8040			−0.0978096
$77$		0			0
$78$		0			0
$79$	171.779	+	297.530i	0.244641	+	0.423730i	0.962031	−	0.272942i	$-0.0879966\pi$
$79$	171.779	+	297.530i	0.244641	+	0.423730i	−0.717390	+	0.696672i	$0.754663\pi$
$80$	127.196	−	220.310i	0.177762	−	0.307892i
$81$		0			0
$82$	328.503	+	568.983i	0.442403	+	0.766264i
$83$	1502.33			1.98677			0.993387	−	0.114812i	$-0.0366265\pi$
$83$	1502.33			1.98677			0.993387	+	0.114812i	$0.0366265\pi$
$84$		0			0
$85$	825.176			1.05298
$86$	37.5879	+	65.1041i	0.0471303	+	0.0816321i
$87$		0			0
$88$	229.588	−	397.658i	0.278115	−	0.481710i
$89$	170.543	+	295.389i	0.203118	+	0.351810i	0.949531	−	0.313672i	$-0.101559\pi$
$89$	170.543	+	295.389i	0.203118	+	0.351810i	−0.746414	+	0.665482i	$0.768226\pi$
$90$		0			0
$91$		0			0
$92$	853.588			0.967312
$93$		0			0
$94$	254.995	−	441.664i	0.279795	−	0.484619i
$95$	−128.794	+	223.078i	−0.139095	+	0.240919i
$96$		0			0
$97$	865.437			0.905895			0.452947	−	0.891537i	$-0.350373\pi$
$97$	865.437			0.905895			0.452947	+	0.891537i	$0.350373\pi$
$98$		0			0
$99$		0			0
$100$	−255.588	−	442.691i	−0.255588	−	0.442691i
$101$	121.628	−	210.666i	0.119826	−	0.207545i	−0.799873	−	0.600170i	$-0.795100\pi$
$101$	121.628	−	210.666i	0.119826	−	0.207545i	0.919699	+	0.392625i	$0.128433\pi$
$102$		0			0
$103$	−476.673	−	825.622i	−0.456000	−	0.789815i	0.542745	−	0.839898i	$-0.317385\pi$
$103$	−476.673	−	825.622i	−0.456000	−	0.789815i	−0.998745	+	0.0500822i	$0.984052\pi$
$104$	−45.5879			−0.0429833
$105$		0			0
$106$	−423.176			−0.387759
$107$	−672.477	−	1164.76i	−0.607578	−	1.05236i	−0.991638	−	0.129048i	$-0.958808\pi$
$107$	−672.477	−	1164.76i	−0.607578	−	1.05236i	0.384061	−	0.923308i	$-0.374525\pi$
$108$		0			0
$109$	−867.176	+	1501.99i	−0.762022	+	1.31986i	0.179785	+	0.983706i	$0.442460\pi$
$109$	−867.176	+	1501.99i	−0.762022	+	1.31986i	−0.941807	+	0.336155i	$0.890874\pi$
$110$	−912.583	−	1580.64i	−0.791012	−	1.37007i
$111$		0			0
$112$		0			0
$113$	−1441.18			−1.19977			−0.599887	−	0.800085i	$-0.704788\pi$
$113$	−1441.18			−1.19977			−0.599887	+	0.800085i	$0.704788\pi$
$114$		0			0
$115$	1696.45	−	2938.34i	1.37561	−	2.38262i
$116$	−436.382	+	755.835i	−0.349285	+	0.604979i
$117$		0			0
$118$	−824.402			−0.643156
$119$		0			0
$120$		0			0
$121$	−981.706	−	1700.36i	−0.737570	−	1.27751i
$122$	−836.693	+	1449.20i	−0.620907	+	1.07544i
$123$		0			0
$124$	−502.794	−	870.865i	−0.364131	−	0.630693i
$125$	−44.4222			−0.0317860
$126$		0			0
$127$	1184.70			0.827759			0.413880	−	0.910332i	$-0.364173\pi$
$127$	1184.70			0.827759			0.413880	+	0.910332i	$0.364173\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−90.6030	+	156.929i	−0.0611262	+	0.105874i
$131$	−148.794	−	257.719i	−0.0992381	−	0.171885i	0.812131	−	0.583475i	$-0.198307\pi$
$131$	−148.794	−	257.719i	−0.0992381	−	0.171885i	−0.911369	+	0.411589i	$0.864974\pi$
$132$		0			0
$133$		0			0
$134$	−331.176			−0.213502
$135$		0			0
$136$	207.598	−	359.570i	0.130892	−	0.226712i
$137$	310.492	−	537.789i	0.193629	−	0.335375i	−0.752821	−	0.658225i	$-0.771308\pi$
$137$	310.492	−	537.789i	0.193629	−	0.335375i	0.946450	+	0.322850i	$0.104641\pi$
$138$		0			0
$139$	898.754			0.548426			0.274213	−	0.961669i	$-0.411583\pi$
$139$	898.754			0.548426			0.274213	+	0.961669i	$0.411583\pi$
$140$		0			0
$141$		0			0
$142$	−465.015	−	805.430i	−0.274811	−	0.475987i
$143$	−163.538	+	283.256i	−0.0956344	+	0.165644i
$144$		0			0
$145$	1734.56	+	3004.35i	0.993432	+	1.72067i
$146$	−899.316			−0.509780
$147$		0			0
$148$	1547.18			0.859304
$149$	−1527.35	−	2645.45i	−0.839769	−	1.45452i	−0.890088	−	0.455789i	$-0.849357\pi$
$149$	−1527.35	−	2645.45i	−0.839769	−	1.45452i	0.0503195	−	0.998733i	$-0.483976\pi$
$150$		0			0
$151$	32.5727	−	56.4176i	0.0175545	−	0.0304053i	−0.857115	−	0.515126i	$-0.827745\pi$
$151$	32.5727	−	56.4176i	0.0175545	−	0.0304053i	0.874669	+	0.484720i	$0.161079\pi$
$152$	64.8040	+	112.244i	0.0345809	+	0.0598959i
$153$		0			0
$154$		0			0
$155$	−3997.08			−2.07131
$156$		0			0
$157$	771.110	−	1335.60i	0.391983	−	0.678934i	−0.600728	−	0.799453i	$-0.705123\pi$
$157$	771.110	−	1335.60i	0.391983	−	0.678934i	0.992711	+	0.120519i	$0.0384559\pi$
$158$	343.558	−	595.059i	0.172987	−	0.299623i
$159$		0			0
$160$	−508.784			−0.251393
$161$		0			0
$162$		0			0
$163$	1257.37	+	2177.82i	0.604200	+	1.04650i	0.992177	+	0.124836i	$0.0398404\pi$
$163$	1257.37	+	2177.82i	0.604200	+	1.04650i	−0.387978	+	0.921669i	$0.626826\pi$
$164$	657.005	−	1137.97i	0.312826	−	0.541831i
$165$		0			0
$166$	−1502.33	−	2602.11i	−0.702431	−	1.21665i
$167$	528.643			0.244956			0.122478	−	0.992471i	$-0.460916\pi$
$167$	528.643			0.244956			0.122478	+	0.992471i	$0.460916\pi$
$168$		0			0
$169$	−2164.53			−0.985220
$170$	−825.176	−	1429.25i	−0.372283	−	0.644813i
$171$		0			0
$172$	75.1758	−	130.208i	0.0333261	−	0.0577226i
$173$	−48.4220	−	83.8693i	−0.0212801	−	0.0368582i	0.855189	−	0.518316i	$-0.173441\pi$
$173$	−48.4220	−	83.8693i	−0.0212801	−	0.0368582i	−0.876469	+	0.481458i	$0.840108\pi$
$174$		0			0
$175$		0			0
$176$	−918.352			−0.393314
$177$		0			0
$178$	341.085	−	590.777i	0.143626	−	0.248768i
$179$	−267.271	+	462.927i	−0.111602	+	0.193301i	−0.916416	−	0.400226i	$-0.868932\pi$
$179$	−267.271	+	462.927i	−0.111602	+	0.193301i	0.804814	+	0.593527i	$0.202265\pi$
$180$		0			0
$181$	−2087.00			−0.857049			−0.428524	−	0.903530i	$-0.640966\pi$
$181$	−2087.00			−0.857049			−0.428524	+	0.903530i	$0.640966\pi$
$182$		0			0
$183$		0			0
$184$	−853.588	−	1478.46i	−0.341996	−	0.592355i
$185$	3074.91	−	5325.91i	1.22201	−	2.11659i
$186$		0			0
$187$	−1489.44	−	2579.78i	−0.582451	−	1.00884i
$188$	−1019.98			−0.395690
$189$		0			0
$190$	515.176			0.196709
$191$	1693.84	+	2933.82i	0.641687	+	1.11143i	0.985056	+	0.172234i	$0.0550986\pi$
$191$	1693.84	+	2933.82i	0.641687	+	1.11143i	−0.343369	+	0.939201i	$0.611568\pi$
$192$		0			0
$193$	954.176	−	1652.68i	0.355871	−	0.616386i	−0.631396	−	0.775461i	$-0.717518\pi$
$193$	954.176	−	1652.68i	0.355871	−	0.616386i	0.987267	+	0.159074i	$0.0508510\pi$
$194$	−865.437	−	1498.98i	−0.320282	−	0.554745i
$195$		0			0
$196$		0			0
$197$	2061.88			0.745699			0.372850	−	0.927892i	$-0.378381\pi$
$197$	2061.88			0.745699			0.372850	+	0.927892i	$0.378381\pi$
$198$		0			0
$199$	1585.75	−	2746.60i	0.564878	−	0.978397i	−0.432183	−	0.901786i	$-0.642257\pi$
$199$	1585.75	−	2746.60i	0.564878	−	0.978397i	0.997061	−	0.0766115i	$-0.0244101\pi$
$200$	−511.176	+	885.382i	−0.180728	+	0.313030i
$201$		0			0
$202$	−486.512			−0.169460
$203$		0			0
$204$		0			0
$205$	−2611.51	−	4523.27i	−0.889736	−	1.54107i
$206$	−953.346	+	1651.24i	−0.322441	+	0.558484i
$207$		0			0
$208$	45.5879	+	78.9605i	0.0151969	+	0.0263218i
$209$	929.889			0.307760
$210$		0			0
$211$	1349.97			0.440454			0.220227	−	0.975449i	$-0.429320\pi$
$211$	1349.97			0.440454			0.220227	+	0.975449i	$0.429320\pi$
$212$	423.176	+	732.962i	0.137094	+	0.237453i
$213$		0			0
$214$	−1344.95	+	2329.53i	−0.429622	+	0.744128i
$215$	−298.814	−	517.561i	−0.0947858	−	0.164174i
$216$		0			0
$217$		0			0
$218$	3468.70			1.07766
$219$		0			0
$220$	−1825.17	+	3161.28i	−0.559330	+	0.968788i
$221$	−147.874	+	256.126i	−0.0450095	+	0.0779587i
$222$		0			0
$223$	1361.85			0.408951			0.204476	−	0.978872i	$-0.434451\pi$
$223$	1361.85			0.408951			0.204476	+	0.978872i	$0.434451\pi$
$224$		0			0
$225$		0			0
$226$	1441.18	+	2496.19i	0.424184	+	0.734708i
$227$	−930.905	+	1612.37i	−0.272186	+	0.471441i	−0.969421	−	0.245402i	$-0.921080\pi$
$227$	−930.905	+	1612.37i	−0.272186	+	0.471441i	0.697235	+	0.716843i	$0.254413\pi$
$228$		0			0
$229$	−2679.39	−	4640.84i	−0.773184	−	1.33919i	−0.935809	−	0.352506i	$-0.885329\pi$
$229$	−2679.39	−	4640.84i	−0.773184	−	1.33919i	0.162625	−	0.986688i	$-0.448004\pi$
$230$	−6785.81			−1.94540
$231$		0			0
$232$	1745.53			0.493963
$233$	2720.56	+	4712.15i	0.764935	+	1.32491i	0.940281	+	0.340400i	$0.110562\pi$
$233$	2720.56	+	4712.15i	0.764935	+	1.32491i	−0.175345	+	0.984507i	$0.556104\pi$
$234$		0			0
$235$	−2027.15	+	3511.12i	−0.562708	+	0.974639i
$236$	824.402	+	1427.91i	0.227390	+	0.393851i
$237$		0			0
$238$		0			0
$239$	1157.28			0.313213			0.156607	−	0.987661i	$-0.449945\pi$
$239$	1157.28			0.313213			0.156607	+	0.987661i	$0.449945\pi$
$240$		0			0
$241$	−1984.69	+	3437.58i	−0.530477	+	0.918814i	0.468890	+	0.883256i	$0.344654\pi$
$241$	−1984.69	+	3437.58i	−0.530477	+	0.918814i	−0.999368	+	0.0355573i	$0.988679\pi$
$242$	−1963.41	+	3400.73i	−0.521541	+	0.903335i
$243$		0			0
$244$	3346.77			0.878095
$245$		0			0
$246$		0			0
$247$	−46.1606	−	79.9525i	−0.0118912	−	0.0205962i
$248$	−1005.59	+	1741.73i	−0.257479	+	0.445967i
$249$		0			0
$250$	44.4222	+	76.9415i	0.0112380	+	0.0194648i
$251$	5978.75			1.50349			0.751744	−	0.659455i	$-0.229213\pi$
$251$	5978.75			1.50349			0.751744	+	0.659455i	$0.229213\pi$
$252$		0			0
$253$	−12248.3			−3.04366
$254$	−1184.70	−	2051.97i	−0.292657	−	0.506897i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−2325.07	−	4027.15i	−0.564335	−	0.977458i	−0.997111	−	0.0759560i	$-0.975799\pi$
$257$	−2325.07	−	4027.15i	−0.564335	−	0.977458i	0.432776	−	0.901502i	$-0.357534\pi$
$258$		0			0
$259$		0			0
$260$	362.412			0.0864456
$261$		0			0
$262$	−297.588	+	515.437i	−0.0701719	+	0.121541i
$263$	1847.68	−	3200.28i	0.433205	−	0.750334i	−0.563942	−	0.825815i	$-0.690716\pi$
$263$	1847.68	−	3200.28i	0.433205	−	0.750334i	0.997147	+	0.0754807i	$0.0240491\pi$
$264$		0			0
$265$	3364.14			0.779840
$266$		0			0
$267$		0			0
$268$	331.176	+	573.613i	0.0754843	+	0.130743i
$269$	3578.84	−	6198.74i	0.811175	−	1.40500i	−0.100868	−	0.994900i	$-0.532162\pi$
$269$	3578.84	−	6198.74i	0.811175	−	1.40500i	0.912042	−	0.410096i	$-0.134505\pi$
$270$		0			0
$271$	2019.19	+	3497.33i	0.452608	+	0.783940i	0.998547	−	0.0538847i	$-0.0171604\pi$
$271$	2019.19	+	3497.33i	0.452608	+	0.783940i	−0.545939	+	0.837825i	$0.683827\pi$
$272$	−830.392			−0.185110
$273$		0			0
$274$	−1241.97			−0.273833
$275$	3667.49	+	6352.28i	0.804211	+	1.39293i
$276$		0			0
$277$	1377.41	−	2385.75i	0.298775	−	0.517493i	−0.677081	−	0.735909i	$-0.736755\pi$
$277$	1377.41	−	2385.75i	0.298775	−	0.517493i	0.975856	+	0.218415i	$0.0700887\pi$
$278$	−898.754	−	1556.69i	−0.193898	−	0.335841i
$279$		0			0
$280$		0			0
$281$	772.742			0.164050			0.0820248	−	0.996630i	$-0.473861\pi$
$281$	772.742			0.164050			0.0820248	+	0.996630i	$0.473861\pi$
$282$		0			0
$283$	−3372.74	+	5841.76i	−0.708441	+	1.22706i	0.256995	+	0.966413i	$0.417268\pi$
$283$	−3372.74	+	5841.76i	−0.708441	+	1.22706i	−0.965435	+	0.260643i	$0.916066\pi$
$284$	−930.030	+	1610.86i	−0.194321	+	0.336574i
$285$		0			0
$286$	654.152			0.135248
$287$		0			0
$288$		0			0
$289$	1109.72	+	1922.09i	0.225874	+	0.391226i
$290$	3469.13	−	6008.70i	0.702462	−	1.21670i
$291$		0			0
$292$	899.316	+	1557.66i	0.180235	+	0.312175i
$293$	1922.69			0.383362			0.191681	−	0.981457i	$-0.438606\pi$
$293$	1922.69			0.383362			0.191681	+	0.981457i	$0.438606\pi$
$294$		0			0
$295$	6553.79			1.29348
$296$	−1547.18	−	2679.79i	−0.303810	−	0.526214i
$297$		0			0
$298$	−3054.70	+	5290.90i	−0.593806	+	1.02850i
$299$	608.020	+	1053.12i	0.117601	+	0.203691i
$300$		0			0
$301$		0			0
$302$	−130.291			−0.0248258
$303$		0			0
$304$	129.608	−	224.488i	0.0244524	−	0.0423528i
$305$	6651.50	−	11520.7i	1.24873	−	2.16287i
$306$		0			0
$307$	−2016.68			−0.374913			−0.187456	−	0.982273i	$-0.560024\pi$
$307$	−2016.68			−0.374913			−0.187456	+	0.982273i	$0.560024\pi$
$308$		0			0
$309$		0			0
$310$	3997.08	+	6923.15i	0.732320	+	1.26842i
$311$	−3574.99	+	6192.07i	−0.651831	+	1.12900i	0.330848	+	0.943684i	$0.392665\pi$
$311$	−3574.99	+	6192.07i	−0.651831	+	1.12900i	−0.982678	+	0.185320i	$0.940668\pi$
$312$		0			0
$313$	4298.25	+	7444.78i	0.776202	+	1.34442i	0.934116	+	0.356969i	$0.116190\pi$
$313$	4298.25	+	7444.78i	0.776202	+	1.34442i	−0.157914	+	0.987453i	$0.550477\pi$
$314$	−3084.44			−0.554347
$315$		0			0
$316$	−1374.23			−0.244641
$317$	−1426.62	−	2470.98i	−0.252766	−	0.437804i	0.711520	−	0.702666i	$-0.248007\pi$
$317$	−1426.62	−	2470.98i	−0.252766	−	0.437804i	−0.964286	+	0.264862i	$0.914674\pi$
$318$		0			0
$319$	6261.75	−	10845.7i	1.09903	−	1.90358i
$320$	508.784	+	881.239i	0.0888809	+	0.153946i
$321$		0			0
$322$		0			0
$323$	840.824			0.144844
$324$		0			0
$325$	364.116	−	630.667i	0.0621462	−	0.107640i
$326$	2514.73	−	4355.65i	0.427234	−	0.739991i
$327$		0			0
$328$	−2628.02			−0.442403
$329$		0			0
$330$		0			0
$331$	−809.558	−	1402.19i	−0.134433	−	0.232845i	0.790948	−	0.611884i	$-0.209588\pi$
$331$	−809.558	−	1402.19i	−0.134433	−	0.232845i	−0.925381	+	0.379039i	$0.876255\pi$
$332$	−3004.66	+	5204.23i	−0.496694	+	0.860299i
$333$		0			0
$334$	−528.643	−	915.637i	−0.0866050	−	0.150004i
$335$	2632.76			0.429383
$336$		0			0
$337$	−3278.67			−0.529972			−0.264986	−	0.964252i	$-0.585367\pi$
$337$	−3278.67			−0.529972			−0.264986	+	0.964252i	$0.585367\pi$
$338$	2164.53	+	3749.07i	0.348328	+	0.603321i
$339$		0			0
$340$	−1650.35	+	2858.49i	−0.263244	+	0.455952i
$341$	7214.71	+	12496.2i	1.14574	+	1.98449i
$342$		0			0
$343$		0			0
$344$	−300.703			−0.0471303
$345$		0			0
$346$	−96.8439	+	167.739i	−0.0150473	+	0.0260627i
$347$	−1425.15	+	2468.43i	−0.220479	+	0.381880i	−0.954953	−	0.296756i	$-0.904095\pi$
$347$	−1425.15	+	2468.43i	−0.220479	+	0.381880i	0.734475	+	0.678636i	$0.237429\pi$
$348$		0			0
$349$	4725.32			0.724758			0.362379	−	0.932031i	$-0.381965\pi$
$349$	4725.32			0.724758			0.362379	+	0.932031i	$0.381965\pi$
$350$		0			0
$351$		0			0
$352$	918.352	+	1590.63i	0.139058	+	0.240855i
$353$	−3363.72	+	5826.13i	−0.507175	+	0.878452i	0.492791	+	0.870148i	$0.335977\pi$
$353$	−3363.72	+	5826.13i	−0.507175	+	0.878452i	−0.999966	+	0.00830453i	$0.997357\pi$
$354$		0			0
$355$	3696.75	+	6402.96i	0.552685	+	0.957279i
$356$	−1364.34			−0.203118
$357$		0			0
$358$	1069.08			0.157829
$359$	−3665.94	−	6349.60i	−0.538945	−	0.933479i	−0.998961	−	0.0455691i	$-0.985490\pi$
$359$	−3665.94	−	6349.60i	−0.538945	−	0.933479i	0.460017	−	0.887910i	$-0.347843\pi$
$360$		0			0
$361$	3298.26	−	5712.76i	0.480867	−	0.832885i
$362$	2087.00	+	3614.80i	0.303012	+	0.524833i
$363$		0			0
$364$		0			0
$365$	7149.34			1.02524
$366$		0			0
$367$	1387.22	−	2402.73i	0.197308	−	0.341748i	−0.750347	−	0.661045i	$-0.770113\pi$
$367$	1387.22	−	2402.73i	0.197308	−	0.341748i	0.947655	+	0.319297i	$0.103447\pi$
$368$	−1707.18	+	2956.92i	−0.241828	+	0.418858i
$369$		0			0
$370$	−12299.7			−1.72819
$371$		0			0
$372$		0			0
$373$	−1263.67	−	2188.75i	−0.175417	−	0.303831i	0.764889	−	0.644163i	$-0.222794\pi$
$373$	−1263.67	−	2188.75i	−0.175417	−	0.303831i	−0.940305	+	0.340332i	$0.889461\pi$
$374$	−2978.87	+	5159.56i	−0.411855	+	0.713354i
$375$		0			0
$376$	1019.98	+	1766.66i	0.139897	+	0.242309i
$377$	−1243.36			−0.169857
$378$		0			0
$379$	3116.40			0.422371			0.211186	−	0.977446i	$-0.432268\pi$
$379$	3116.40			0.422371			0.211186	+	0.977446i	$0.432268\pi$
$380$	−515.176	−	892.311i	−0.0695473	−	0.120459i
$381$		0			0
$382$	3387.69	−	5867.65i	0.453741	−	0.785903i
$383$	−759.035	−	1314.69i	−0.101266	−	0.175398i	0.810940	−	0.585129i	$-0.198956\pi$
$383$	−759.035	−	1314.69i	−0.101266	−	0.175398i	−0.912207	+	0.409731i	$0.865623\pi$
$384$		0			0
$385$		0			0
$386$	−3816.70			−0.503277
$387$		0			0
$388$	−1730.87	+	2997.96i	−0.226474	+	0.392264i
$389$	−1623.39	+	2811.79i	−0.211591	+	0.366487i	−0.952213	−	0.305436i	$-0.901198\pi$
$389$	−1623.39	+	2811.79i	−0.211591	+	0.366487i	0.740622	+	0.671922i	$0.234531\pi$
$390$		0			0
$391$	−11075.2			−1.43247
$392$		0			0
$393$		0			0
$394$	−2061.88	−	3571.28i	−0.263645	−	0.456646i
$395$	−2731.20	+	4730.57i	−0.347902	+	0.602584i
$396$		0			0
$397$	−915.312	−	1585.37i	−0.115713	−	0.200421i	0.802351	−	0.596852i	$-0.203582\pi$
$397$	−915.312	−	1585.37i	−0.115713	−	0.200421i	−0.918065	+	0.396431i	$0.870249\pi$
$398$	−6342.99			−0.798858
$399$		0			0
$400$	2044.70			0.255588
$401$	−1692.90	−	2932.20i	−0.210822	−	0.365154i	0.741150	−	0.671339i	$-0.234281\pi$
$401$	−1692.90	−	2932.20i	−0.210822	−	0.365154i	−0.951972	+	0.306185i	$0.900947\pi$
$402$		0			0
$403$	716.291	−	1240.65i	0.0885384	−	0.153353i
$404$	486.512	+	842.664i	0.0599131	+	0.103772i
$405$		0			0
$406$		0			0
$407$	−22200.8			−2.70382
$408$		0			0
$409$	−4626.59	+	8013.48i	−0.559340	+	0.968805i	0.438212	+	0.898872i	$0.355612\pi$
$409$	−4626.59	+	8013.48i	−0.559340	+	0.968805i	−0.997552	+	0.0699333i	$0.977721\pi$
$410$	−5223.02	+	9046.54i	−0.629138	+	1.08970i
$411$		0			0
$412$	3813.39			0.456000
$413$		0			0
$414$		0			0
$415$	11943.2	+	20686.2i	1.41269	+	2.44685i
$416$	91.1758	−	157.921i	0.0107458	−	0.0186123i
$417$		0			0
$418$	−929.889	−	1610.61i	−0.108809	−	0.188464i
$419$	−3547.52			−0.413622			−0.206811	−	0.978381i	$-0.566308\pi$
$419$	−3547.52			−0.413622			−0.206811	+	0.978381i	$0.566308\pi$
$420$		0			0
$421$	7848.87			0.908624			0.454312	−	0.890843i	$-0.349885\pi$
$421$	7848.87			0.908624			0.454312	+	0.890843i	$0.349885\pi$
$422$	−1349.97	−	2338.22i	−0.155724	−	0.269722i
$423$		0			0
$424$	846.352	−	1465.92i	0.0969398	−	0.167905i
$425$	3316.22	+	5743.86i	0.378495	+	0.655572i
$426$		0			0
$427$		0			0
$428$	5379.82			0.607578
$429$		0			0
$430$	−597.628	+	1035.12i	−0.0670237	+	0.116088i
$431$	−2223.66	+	3851.50i	−0.248515	+	0.430441i	−0.963114	−	0.269094i	$-0.913276\pi$
$431$	−2223.66	+	3851.50i	−0.248515	+	0.430441i	0.714599	+	0.699534i	$0.246609\pi$
$432$		0			0
$433$	−6994.82			−0.776327			−0.388164	−	0.921590i	$-0.626890\pi$
$433$	−6994.82			−0.776327			−0.388164	+	0.921590i	$0.626890\pi$
$434$		0			0
$435$		0			0
$436$	−3468.70	−	6007.97i	−0.381011	−	0.659930i
$437$	1728.62	−	2994.06i	0.189225	−	0.327747i
$438$		0			0
$439$	−318.091	−	550.950i	−0.0345823	−	0.0598984i	0.848216	−	0.529650i	$-0.177677\pi$
$439$	−318.091	−	550.950i	−0.0345823	−	0.0598984i	−0.882799	+	0.469752i	$0.844343\pi$
$440$	7300.66			0.791012
$441$		0			0
$442$	591.497			0.0636530
$443$	−2237.12	−	3874.80i	−0.239929	−	0.415570i	0.720764	−	0.693180i	$-0.243791\pi$
$443$	−2237.12	−	3874.80i	−0.239929	−	0.415570i	−0.960694	+	0.277610i	$0.910458\pi$
$444$		0			0
$445$	−2711.54	+	4696.53i	−0.288853	+	0.500308i
$446$	−1361.85	−	2358.79i	−0.144586	−	0.250430i
$447$		0			0
$448$		0			0
$449$	2389.42			0.251144			0.125572	−	0.992085i	$-0.459923\pi$
$449$	2389.42			0.251144			0.125572	+	0.992085i	$0.459923\pi$
$450$		0			0
$451$	−9427.52	+	16329.0i	−0.984312	+	1.70488i
$452$	2882.35	−	4992.38i	0.299943	−	0.519517i
$453$		0			0
$454$	3723.62			0.384930
$455$		0			0
$456$		0			0
$457$	2219.17	+	3843.71i	0.227152	+	0.393438i	0.956963	−	0.290210i	$-0.0937253\pi$
$457$	2219.17	+	3843.71i	0.227152	+	0.393438i	−0.729811	+	0.683649i	$0.760392\pi$
$458$	−5358.78	+	9281.68i	−0.546724	+	0.946953i
$459$		0			0
$460$	6785.81	+	11753.4i	0.687804	+	1.19131i
$461$	14079.8			1.42248			0.711240	−	0.702949i	$-0.248134\pi$
$461$	14079.8			1.42248			0.711240	+	0.702949i	$0.248134\pi$
$462$		0			0
$463$	4687.50			0.470511			0.235255	−	0.971934i	$-0.424407\pi$
$463$	4687.50			0.470511			0.235255	+	0.971934i	$0.424407\pi$
$464$	−1745.53	−	3023.34i	−0.174642	−	0.302489i
$465$		0			0
$466$	5441.12	−	9424.30i	0.540891	−	0.936851i
$467$	4223.63	+	7315.54i	0.418514	+	0.724888i	0.995790	−	0.0916611i	$-0.0292176\pi$
$467$	4223.63	+	7315.54i	0.418514	+	0.724888i	−0.577276	+	0.816549i	$0.695884\pi$
$468$		0			0
$469$		0			0
$470$	8108.58			0.795789
$471$		0			0
$472$	1648.80	−	2855.81i	0.160789	−	0.278495i
$473$	−1078.72	+	1868.39i	−0.104861	+	0.181625i
$474$		0			0
$475$	−2070.39			−0.199992
$476$		0			0
$477$		0			0
$478$	−1157.28	−	2004.46i	−0.110738	−	0.191803i
$479$	−2184.70	+	3784.02i	−0.208396	+	0.360952i	−0.951209	−	0.308546i	$-0.900158\pi$
$479$	−2184.70	+	3784.02i	−0.208396	+	0.360952i	0.742814	+	0.669498i	$0.233491\pi$
$480$		0			0
$481$	1102.07	+	1908.84i	0.104470	+	0.180947i
$482$	7938.75			0.750208
$483$		0			0
$484$	7853.65			0.737570
$485$	6880.00	+	11916.5i	0.644134	+	1.11567i
$486$		0			0
$487$	7238.86	−	12538.1i	0.673561	−	1.16664i	−0.303326	−	0.952887i	$-0.598097\pi$
$487$	7238.86	−	12538.1i	0.673561	−	1.16664i	0.976887	−	0.213755i	$-0.0685695\pi$
$488$	−3346.77	−	5796.78i	−0.310454	−	0.537721i
$489$		0			0
$490$		0			0
$491$	−9306.12			−0.855355			−0.427677	−	0.903931i	$-0.640668\pi$
$491$	−9306.12			−0.855355			−0.427677	+	0.903931i	$0.640668\pi$
$492$		0			0
$493$	5662.00	−	9806.87i	0.517249	−	0.895901i
$494$	−92.3212	+	159.905i	−0.00840836	+	0.0145637i
$495$		0			0
$496$	4022.35			0.364131
$497$		0			0
$498$		0			0
$499$	6118.77	+	10598.0i	0.548926	+	0.950767i	0.998349	+	0.0574479i	$0.0182963\pi$
$499$	6118.77	+	10598.0i	0.548926	+	0.950767i	−0.449423	+	0.893319i	$0.648370\pi$
$500$	88.8444	−	153.883i	0.00794649	−	0.0137637i
$501$		0			0
$502$	−5978.75	−	10355.5i	−0.531563	−	0.920695i
$503$	−5524.30			−0.489694			−0.244847	−	0.969562i	$-0.578738\pi$
$503$	−5524.30			−0.489694			−0.244847	+	0.969562i	$0.578738\pi$
$504$		0			0
$505$	3867.65			0.340808
$506$	12248.3	+	21214.7i	1.07610	+	1.86385i
$507$		0			0
$508$	−2369.41	+	4103.93i	−0.206940	+	0.358430i
$509$	−5039.81	−	8729.20i	−0.438871	−	0.760148i	0.558731	−	0.829349i	$-0.311288\pi$
$509$	−5039.81	−	8729.20i	−0.438871	−	0.760148i	−0.997603	+	0.0692012i	$0.977955\pi$
$510$		0			0
$511$		0			0
$512$	512.000			0.0441942
$513$		0			0
$514$	−4650.15	+	8054.30i	−0.399045	+	0.691167i
$515$	7578.86	−	13127.0i	0.648475	−	1.12319i
$516$		0			0
$517$	14635.9			1.24504
$518$		0			0
$519$		0			0
$520$	−362.412	−	627.716i	−0.0305631	−	0.0529369i
$521$	2853.31	−	4942.07i	0.239934	−	0.415578i	−0.720761	−	0.693184i	$-0.756208\pi$
$521$	2853.31	−	4942.07i	0.239934	−	0.415578i	0.960695	+	0.277606i	$0.0895409\pi$
$522$		0			0
$523$	5328.63	+	9229.46i	0.445516	+	0.771656i	0.998088	−	0.0618088i	$-0.0196869\pi$
$523$	5328.63	+	9229.46i	0.445516	+	0.771656i	−0.552572	+	0.833465i	$0.686354\pi$
$524$	1190.35			0.0992381
$525$		0			0
$526$	−7390.73			−0.612645
$527$	6523.69	+	11299.4i	0.539234	+	0.933981i
$528$		0			0
$529$	−16685.6	+	28900.4i	−1.37138	+	2.37531i
$530$	−3364.14	−	5826.86i	−0.275715	−	0.477552i
$531$		0			0
$532$		0			0
$533$	1871.97			0.152127
$534$		0			0
$535$	10692.0	−	18519.2i	0.864033	−	1.49655i
$536$	662.352	−	1147.23i	0.0533754	−	0.0924489i
$537$		0			0
$538$	−14315.4			−1.14717
$539$		0			0
$540$		0			0
$541$	2005.24	+	3473.18i	0.159357	+	0.276014i	0.934637	−	0.355603i	$-0.115725\pi$
$541$	2005.24	+	3473.18i	0.159357	+	0.276014i	−0.775280	+	0.631618i	$0.782391\pi$
$542$	4038.37	−	6994.66i	0.320042	−	0.554329i
$543$		0			0
$544$	830.392	+	1438.28i	0.0654462	+	0.113356i
$545$	−27575.3			−2.16733
$546$		0			0
$547$	−17619.8			−1.37728			−0.688638	−	0.725105i	$-0.741791\pi$
$547$	−17619.8			−1.37728			−0.688638	+	0.725105i	$0.741791\pi$
$548$	1241.97	+	2151.15i	0.0968144	+	0.167688i
$549$		0			0
$550$	7334.98	−	12704.6i	0.568663	−	0.984954i
$551$	1767.46	+	3061.32i	0.136654	+	0.236691i
$552$		0			0
$553$		0			0
$554$	−5509.65			−0.422532
$555$		0			0
$556$	−1797.51	+	3113.37i	−0.137107	+	0.237476i
$557$	−5168.85	+	8952.71i	−0.393198	+	0.681038i	−0.992869	−	0.119208i	$-0.961965\pi$
$557$	−5168.85	+	8952.71i	−0.393198	+	0.681038i	0.599672	+	0.800246i	$0.295298\pi$
$558$		0			0
$559$	214.194			0.0162065
$560$		0			0
$561$		0			0
$562$	−772.742	−	1338.43i	−0.0580003	−	0.100459i
$563$	−12011.8	+	20805.1i	−0.899180	+	1.55742i	−0.0706347	+	0.997502i	$0.522502\pi$
$563$	−12011.8	+	20805.1i	−0.899180	+	1.55742i	−0.828545	+	0.559923i	$0.810831\pi$
$564$		0			0
$565$	−11457.0	−	19844.1i	−0.853095	−	1.47760i
$566$	13491.0			1.00189
$567$		0			0
$568$	3720.12			0.274811
$569$	−6589.59	−	11413.5i	−0.485501	−	0.840912i	0.514361	−	0.857574i	$-0.328029\pi$
$569$	−6589.59	−	11413.5i	−0.485501	−	0.840912i	−0.999861	+	0.0166623i	$0.994696\pi$
$570$		0			0
$571$	−3888.13	+	6734.44i	−0.284962	+	0.493568i	−0.972600	−	0.232485i	$-0.925314\pi$
$571$	−3888.13	+	6734.44i	−0.284962	+	0.493568i	0.687638	+	0.726054i	$0.258648\pi$
$572$	−654.152	−	1133.02i	−0.0478172	−	0.0828219i
$573$		0			0
$574$		0			0
$575$	27270.8			1.97787
$576$		0			0
$577$	−10083.5	+	17465.2i	−0.727525	+	1.26011i	0.230401	+	0.973096i	$0.425996\pi$
$577$	−10083.5	+	17465.2i	−0.727525	+	1.26011i	−0.957926	+	0.287015i	$0.907337\pi$
$578$	2219.44	−	3844.19i	0.159717	−	0.276639i
$579$		0			0
$580$	−13876.5			−0.993432
$581$		0			0
$582$		0			0
$583$	−6072.25	−	10517.4i	−0.431367	−	0.747150i
$584$	1798.63	−	3115.32i	0.127445	−	0.220741i
$585$		0			0
$586$	−1922.69	−	3330.20i	−0.135539	−	0.234760i
$587$	8365.08			0.588184			0.294092	−	0.955777i	$-0.404983\pi$
$587$	8365.08			0.588184			0.294092	+	0.955777i	$0.404983\pi$
$588$		0			0
$589$	−4072.88			−0.284924
$590$	−6553.79	−	11351.5i	−0.457314	−	0.792091i
$591$		0			0
$592$	−3094.35	+	5359.57i	−0.214826	+	0.372090i
$593$	−13810.9	−	23921.2i	−0.956403	−	1.65654i	−0.731124	−	0.682244i	$-0.761004\pi$
$593$	−13810.9	−	23921.2i	−0.956403	−	1.65654i	−0.225279	−	0.974294i	$-0.572329\pi$
$594$		0			0
$595$		0			0
$596$	12218.8			0.839769
$597$		0			0
$598$	1216.04	−	2106.24i	0.0831564	−	0.144031i
$599$	269.159	−	466.197i	0.0183598	−	0.0318002i	−0.856700	−	0.515816i	$-0.827489\pi$
$599$	269.159	−	466.197i	0.0183598	−	0.0318002i	0.875059	+	0.484016i	$0.160822\pi$
$600$		0			0
$601$	6958.64			0.472294			0.236147	−	0.971717i	$-0.424115\pi$
$601$	6958.64			0.472294			0.236147	+	0.971717i	$0.424115\pi$
$602$		0			0
$603$		0			0
$604$	130.291	+	225.670i	0.00877725	+	0.0152027i
$605$	15608.6	−	27034.9i	1.04889	−	1.81674i
$606$		0			0
$607$	8648.80	+	14980.2i	0.578326	+	1.00169i	0.995671	+	0.0929425i	$0.0296273\pi$
$607$	8648.80	+	14980.2i	0.578326	+	1.00169i	−0.417345	+	0.908748i	$0.637039\pi$
$608$	−518.432			−0.0345809
$609$		0			0
$610$	−26606.0			−1.76598
$611$	−726.542	−	1258.41i	−0.0481060	−	0.0833220i
$612$		0			0
$613$	419.579	−	726.732i	0.0276454	−	0.0478832i	−0.851872	−	0.523751i	$-0.824532\pi$
$613$	419.579	−	726.732i	0.0276454	−	0.0478832i	0.879517	+	0.475867i	$0.157866\pi$
$614$	2016.68	+	3493.00i	0.132552	+	0.229586i
$615$		0			0
$616$		0			0
$617$	16040.0			1.04659			0.523295	−	0.852152i	$-0.324703\pi$
$617$	16040.0			1.04659			0.523295	+	0.852152i	$0.324703\pi$
$618$		0			0
$619$	2714.64	−	4701.90i	0.176269	−	0.305307i	−0.764331	−	0.644825i	$-0.776930\pi$
$619$	2714.64	−	4701.90i	0.176269	−	0.305307i	0.940600	+	0.339517i	$0.110264\pi$
$620$	7994.17	−	13846.3i	0.517828	−	0.896905i
$621$		0			0
$622$	14300.0			0.921828
$623$		0			0
$624$		0			0
$625$	7633.98	+	13222.4i	0.488574	+	0.846236i
$626$	8596.49	−	14889.6i	0.548858	−	0.950649i
$627$		0			0
$628$	3084.44	+	5342.41i	0.195991	+	0.339467i
$629$	−20074.4			−1.27253
$630$		0			0
$631$	−1807.86			−0.114057			−0.0570284	−	0.998373i	$-0.518163\pi$
$631$	−1807.86			−0.114057			−0.0570284	+	0.998373i	$0.518163\pi$
$632$	1374.23	+	2380.24i	0.0864936	+	0.149811i
$633$		0			0
$634$	−2853.24	+	4941.95i	−0.178733	+	0.309574i
$635$	9418.09	+	16312.6i	0.588576	+	1.01944i
$636$		0			0
$637$		0			0
$638$	−25047.0			−1.55426
$639$		0			0
$640$	1017.57	−	1762.48i	0.0628483	−	0.108856i
$641$	−2952.28	+	5113.50i	−0.181916	+	0.315087i	−0.942533	−	0.334113i	$-0.891563\pi$
$641$	−2952.28	+	5113.50i	−0.181916	+	0.315087i	0.760617	+	0.649201i	$0.224897\pi$
$642$		0			0
$643$	8092.42			0.496320			0.248160	−	0.968719i	$-0.420174\pi$
$643$	8092.42			0.496320			0.248160	+	0.968719i	$0.420174\pi$
$644$		0			0
$645$		0			0
$646$	−840.824	−	1456.35i	−0.0512102	−	0.0886987i
$647$	10096.3	−	17487.4i	0.613490	−	1.06260i	−0.377157	−	0.926149i	$-0.623098\pi$
$647$	10096.3	−	17487.4i	0.613490	−	1.06260i	0.990647	−	0.136447i	$-0.0435683\pi$
$648$		0			0
$649$	−11829.5	−	20489.4i	−0.715486	−	1.23926i
$650$	−1456.46			−0.0878880
$651$		0			0
$652$	−10058.9			−0.604200
$653$	−10590.4	−	18343.2i	−0.634664	−	1.09927i	−0.986586	−	0.163240i	$-0.947805\pi$
$653$	−10590.4	−	18343.2i	−0.634664	−	1.09927i	0.351923	−	0.936029i	$-0.385528\pi$
$654$		0			0
$655$	2365.75	−	4097.60i	0.141126	−	0.244437i
$656$	2628.02	+	4551.86i	0.156413	+	0.270915i
$657$		0			0
$658$		0			0
$659$	−28411.3			−1.67944			−0.839718	−	0.543023i	$-0.817280\pi$
$659$	−28411.3			−1.67944			−0.839718	+	0.543023i	$0.817280\pi$
$660$		0			0
$661$	−8352.47	+	14466.9i	−0.491488	+	0.851282i	−0.999952	−	0.00980149i	$-0.996880\pi$
$661$	−8352.47	+	14466.9i	−0.491488	+	0.851282i	0.508464	+	0.861083i	$0.330213\pi$
$662$	−1619.12	+	2804.39i	−0.0950585	+	0.164646i
$663$		0			0
$664$	12018.7			0.702431
$665$		0			0
$666$		0			0
$667$	−23280.6	−	40323.3i	−1.35147	−	2.34081i
$668$	−1057.29	+	1831.27i	−0.0612390	+	0.106069i
$669$		0			0
$670$	−2632.76	−	4560.08i	−0.151810	−	0.262942i
$671$	−48023.7			−2.76294
$672$		0			0
$673$	−9047.09			−0.518187			−0.259093	−	0.965852i	$-0.583424\pi$
$673$	−9047.09			−0.518187			−0.259093	+	0.965852i	$0.583424\pi$
$674$	3278.67	+	5678.83i	0.187374	+	0.324540i
$675$		0			0
$676$	4329.05	−	7498.14i	0.246305	−	0.426613i
$677$	−3922.13	−	6793.32i	−0.222658	−	0.385655i	0.732956	−	0.680276i	$-0.238140\pi$
$677$	−3922.13	−	6793.32i	−0.222658	−	0.385655i	−0.955614	+	0.294621i	$0.904807\pi$
$678$		0			0
$679$		0			0
$680$	6601.41			0.372283
$681$		0			0
$682$	14429.4	−	24992.5i	0.810163	−	1.40324i
$683$	12883.0	−	22314.1i	0.721751	−	1.25011i	−0.238547	−	0.971131i	$-0.576671\pi$
$683$	12883.0	−	22314.1i	0.721751	−	1.25011i	0.960298	−	0.278978i	$-0.0899956\pi$
$684$		0			0
$685$	9873.35			0.550717
$686$		0			0
$687$		0			0
$688$	300.703	+	520.833i	0.0166631	+	0.0288613i
$689$	−602.865	+	1044.19i	−0.0333343	+	0.0577367i
$690$		0			0
$691$	−12337.1	−	21368.4i	−0.679195	−	1.17640i	−0.975224	−	0.221221i	$-0.928996\pi$
$691$	−12337.1	−	21368.4i	−0.679195	−	1.17640i	0.296029	−	0.955179i	$-0.404338\pi$
$692$	387.376			0.0212801
$693$		0			0
$694$	5700.60			0.311804
$695$	7144.86	+	12375.3i	0.389957	+	0.675425i
$696$		0			0
$697$	−8524.56	+	14765.0i	−0.463258	+	0.802386i
$698$	−4725.32	−	8184.49i	−0.256241	−	0.443822i
$699$		0			0
$700$		0			0
$701$	−29377.9			−1.58286			−0.791431	−	0.611258i	$-0.790664\pi$
$701$	−29377.9			−1.58286			−0.791431	+	0.611258i	$0.790664\pi$
$702$		0			0
$703$	3133.23	−	5426.91i	0.168097	−	0.291152i
$704$	1836.70	−	3181.26i	0.0983286	−	0.170310i
$705$		0			0
$706$	13454.9			0.717253
$707$		0			0
$708$		0			0
$709$	−15297.1	−	26495.4i	−0.810291	−	1.40347i	−0.912660	−	0.408719i	$-0.865976\pi$
$709$	−15297.1	−	26495.4i	−0.810291	−	1.40347i	0.102369	−	0.994746i	$-0.467358\pi$
$710$	7393.51	−	12805.9i	0.390808	−	0.676898i
$711$		0			0
$712$	1364.34	+	2363.11i	0.0718130	+	0.124384i
$713$	53647.4			2.81782
$714$		0			0
$715$	−5200.34			−0.272002
$716$	−1069.08	−	1851.71i	−0.0558011	−	0.0966503i
$717$		0			0
$718$	−7331.89	+	12699.2i	−0.381091	+	0.660070i
$719$	973.469	+	1686.10i	0.0504927	+	0.0874559i	0.890167	−	0.455634i	$-0.150588\pi$
$719$	973.469	+	1686.10i	0.0504927	+	0.0874559i	−0.839674	+	0.543090i	$0.817254\pi$
$720$		0			0
$721$		0			0
$722$	−13193.1			−0.680048
$723$		0			0
$724$	4174.01	−	7229.60i	0.214262	−	0.371113i
$725$	−13941.7	+	24147.8i	−0.714184	+	1.23700i
$726$		0			0
$727$	−15750.6			−0.803518			−0.401759	−	0.915745i	$-0.631601\pi$
$727$	−15750.6			−0.803518			−0.401759	+	0.915745i	$0.631601\pi$
$728$		0			0
$729$		0			0
$730$	−7149.34	−	12383.0i	−0.362478	−	0.627830i
$731$	−975.396	+	1689.44i	−0.0493520	+	0.0854802i
$732$		0			0
$733$	7174.78	+	12427.1i	0.361537	+	0.626200i	0.988214	−	0.153079i	$-0.0489189\pi$
$733$	7174.78	+	12427.1i	0.361537	+	0.626200i	−0.626677	+	0.779279i	$0.715586\pi$
$734$	−5548.86			−0.279036
$735$		0			0
$736$	6828.70			0.341996
$737$	−4752.12	−	8230.92i	−0.237512	−	0.411384i
$738$		0			0
$739$	8879.03	−	15378.9i	0.441976	−	0.765525i	−0.555860	−	0.831276i	$-0.687611\pi$
$739$	8879.03	−	15378.9i	0.441976	−	0.765525i	0.997836	+	0.0657506i	$0.0209442\pi$
$740$	12299.7	+	21303.6i	0.611006	+	1.05829i
$741$		0			0
$742$		0			0
$743$	29187.6			1.44117			0.720586	−	0.693366i	$-0.243873\pi$
$743$	29187.6			1.44117			0.720586	+	0.693366i	$0.243873\pi$
$744$		0			0
$745$	24284.1	−	42061.3i	1.19423	−	2.06847i
$746$	−2527.35	+	4377.49i	−0.124038	+	0.214841i
$747$		0			0
$748$	11915.5			0.582451
$749$		0			0
$750$		0			0
$751$	−6890.97	−	11935.5i	−0.334827	−	0.579938i	0.648624	−	0.761109i	$-0.275345\pi$
$751$	−6890.97	−	11935.5i	−0.334827	−	0.579938i	−0.983452	+	0.181171i	$0.942011\pi$
$752$	2039.96	−	3533.31i	0.0989224	−	0.171339i
$753$		0			0
$754$	1243.36	+	2153.56i	0.0600536	+	0.104016i
$755$	1035.78			0.0499283
$756$		0			0
$757$	36952.7			1.77420			0.887099	−	0.461579i	$-0.152717\pi$
$757$	36952.7			1.77420			0.887099	+	0.461579i	$0.152717\pi$
$758$	−3116.40	−	5397.76i	−0.149331	−	0.258649i
$759$		0			0
$760$	−1030.35	+	1784.62i	−0.0491773	+	0.0851776i
$761$	−14408.2	−	24955.8i	−0.686332	−	1.18876i	−0.973016	−	0.230737i	$-0.925886\pi$
$761$	−14408.2	−	24955.8i	−0.686332	−	1.18876i	0.286684	−	0.958025i	$-0.407447\pi$
$762$		0			0
$763$		0			0
$764$	−13550.8			−0.641687
$765$		0			0
$766$	−1518.07	+	2629.38i	−0.0716059	+	0.124025i
$767$	−1174.46	+	2034.23i	−0.0552898	+	0.0957648i
$768$		0			0
$769$	−25285.2			−1.18571			−0.592854	−	0.805310i	$-0.701999\pi$
$769$	−25285.2			−1.18571			−0.592854	+	0.805310i	$0.701999\pi$
$770$		0			0
$771$		0			0
$772$	3816.70	+	6610.72i	0.177935	+	0.308193i
$773$	9209.10	−	15950.6i	0.428497	−	0.742179i	−0.568243	−	0.822861i	$-0.692376\pi$
$773$	9209.10	−	15950.6i	0.428497	−	0.742179i	0.996740	+	0.0806820i	$0.0257098\pi$
$774$		0			0
$775$	−16063.5	−	27822.8i	−0.744540	−	1.28958i
$776$	6923.49			0.320282
$777$		0			0
$778$	6493.55			0.299235
$779$	−2661.04	−	4609.05i	−0.122390	−	0.211985i
$780$		0			0
$781$	13345.2	−	23114.6i	0.611434	−	1.05903i
$782$	11075.2	+	19182.8i	0.506455	+	0.877207i
$783$		0			0
$784$		0			0
$785$	24520.5			1.11487
$786$		0			0
$787$	−5537.90	+	9591.92i	−0.250832	+	0.434454i	−0.963755	−	0.266788i	$-0.914038\pi$
$787$	−5537.90	+	9591.92i	−0.250832	+	0.434454i	0.712923	+	0.701242i	$0.247371\pi$
$788$	−4123.76	+	7142.56i	−0.186425	+	0.322897i
$789$		0			0
$790$	10924.8			0.492008
$791$		0			0
$792$		0			0
$793$	2383.94	+	4129.11i	0.106754	+	0.184904i
$794$	−1830.62	+	3170.74i	−0.0818217	+	0.141719i
$795$		0			0
$796$	6342.99	+	10986.4i	0.282439	+	0.489199i
$797$	−4838.83			−0.215057			−0.107528	−	0.994202i	$-0.534294\pi$
$797$	−4838.83			−0.215057			−0.107528	+	0.994202i	$0.534294\pi$
$798$		0			0
$799$	13234.1			0.585969
$800$	−2044.70	−	3541.53i	−0.0903640	−	0.156515i
$801$		0			0
$802$	−3385.81	+	5864.39i	−0.149074	+	0.258203i
$803$	−12904.5	−	22351.3i	−0.567111	−	0.982265i
$804$		0			0
$805$		0			0
$806$	−2865.16			−0.125212
$807$		0			0
$808$	973.024	−	1685.33i	0.0423649	−	0.0733782i
$809$	−15754.9	+	27288.4i	−0.684690	+	1.18592i	0.288844	+	0.957376i	$0.406729\pi$
$809$	−15754.9	+	27288.4i	−0.684690	+	1.18592i	−0.973534	+	0.228542i	$0.926604\pi$
$810$		0			0
$811$	−29463.3			−1.27570			−0.637851	−	0.770160i	$-0.720177\pi$
$811$	−29463.3			−1.27570			−0.637851	+	0.770160i	$0.720177\pi$
$812$		0			0
$813$		0			0
$814$	22200.8	+	38452.9i	0.955943	+	1.65574i
$815$	−19991.5	+	34626.3i	−0.859229	+	1.48823i
$816$		0			0
$817$	−304.481	−	527.376i	−0.0130385	−	0.0225833i
$818$	18506.3			0.791026
$819$		0			0
$820$	20892.1			0.889736
$821$	1751.11	+	3033.01i	0.0744386	+	0.128932i	0.900842	−	0.434147i	$-0.142950\pi$
$821$	1751.11	+	3033.01i	0.0744386	+	0.128932i	−0.826403	+	0.563079i	$0.809617\pi$
$822$		0			0
$823$	−19996.5	+	34635.0i	−0.846943	+	1.46695i	0.0369799	+	0.999316i	$0.488226\pi$
$823$	−19996.5	+	34635.0i	−0.846943	+	1.46695i	−0.883923	+	0.467632i	$0.845107\pi$
$824$	−3813.39	−	6604.98i	−0.161220	−	0.279242i
$825$		0			0
$826$		0			0
$827$	10733.6			0.451322			0.225661	−	0.974206i	$-0.427546\pi$
$827$	10733.6			0.451322			0.225661	+	0.974206i	$0.427546\pi$
$828$		0			0
$829$	7268.74	−	12589.8i	0.304528	−	0.527458i	−0.672628	−	0.739981i	$-0.734835\pi$
$829$	7268.74	−	12589.8i	0.304528	−	0.527458i	0.977156	+	0.212523i	$0.0681679\pi$
$830$	23886.3	−	41372.3i	0.998923	−	1.73018i
$831$		0			0
$832$	−364.703			−0.0151969
$833$		0			0
$834$		0			0
$835$	4202.58	+	7279.09i	0.174175	+	0.301680i
$836$	−1859.78	+	3221.23i	−0.0769399	+	0.133264i
$837$		0			0
$838$	3547.52	+	6144.48i	0.146237	+	0.253291i
$839$	−7353.57			−0.302591			−0.151295	−	0.988489i	$-0.548344\pi$
$839$	−7353.57			−0.302591			−0.151295	+	0.988489i	$0.548344\pi$
$840$		0			0
$841$	23218.3			0.951998
$842$	−7848.87	−	13594.6i	−0.321247	−	0.556416i
$843$		0			0
$844$	−2699.94	+	4676.43i	−0.110113	+	0.190722i
$845$	−17207.4	−	29804.2i	−0.700537	−	1.21337i
$846$		0			0
$847$		0			0
$848$	−3385.41			−0.137094
$849$		0			0
$850$	6632.44	−	11487.7i	0.267636	−	0.463560i
$851$	−41270.3	+	71482.3i	−1.66243	+	2.87941i
$852$		0			0
$853$	19293.6			0.774442			0.387221	−	0.921987i	$-0.373435\pi$
$853$	19293.6			0.774442			0.387221	+	0.921987i	$0.373435\pi$
$854$		0			0
$855$		0			0
$856$	−5379.82	−	9318.12i	−0.214811	−	0.372064i
$857$	−7080.78	+	12264.3i	−0.282234	+	0.488844i	−0.971935	−	0.235251i	$-0.924409\pi$
$857$	−7080.78	+	12264.3i	−0.282234	+	0.488844i	0.689701	+	0.724095i	$0.257742\pi$
$858$		0			0
$859$	−4109.57	−	7117.98i	−0.163232	−	0.282727i	0.772794	−	0.634657i	$-0.218859\pi$
$859$	−4109.57	−	7117.98i	−0.163232	−	0.282727i	−0.936026	+	0.351930i	$0.885525\pi$
$860$	2390.51			0.0947858
$861$		0			0
$862$	8894.65			0.351454
$863$	1287.47	+	2229.97i	0.0507835	+	0.0879595i	0.890300	−	0.455375i	$-0.150495\pi$
$863$	1287.47	+	2229.97i	0.0507835	+	0.0879595i	−0.839516	+	0.543335i	$0.817161\pi$
$864$		0			0
$865$	769.885	−	1333.48i	0.0302623	−	0.0524158i
$866$	6994.82	+	12115.4i	0.274473	+	0.475401i
$867$		0			0
$868$		0			0
$869$	19719.2			0.769766
$870$		0			0
$871$	−471.800	+	817.182i	−0.0183540	+	0.0317901i
$872$	−6937.41	+	12015.9i	−0.269415	+	0.466641i
$873$		0			0
$874$	−6914.49			−0.267604
$875$		0			0
$876$		0			0
$877$	−15490.6	−	26830.5i	−0.596442	−	1.03307i	−0.993342	−	0.115206i	$-0.963247\pi$
$877$	−15490.6	−	26830.5i	−0.596442	−	1.03307i	0.396900	−	0.917862i	$-0.370086\pi$
$878$	−636.182	+	1101.90i	−0.0244534	+	0.0423546i
$879$		0			0
$880$	−7300.66	−	12645.1i	−0.279665	−	0.484394i
$881$	41781.8			1.59780			0.798902	−	0.601461i	$-0.205415\pi$
$881$	41781.8			1.59780			0.798902	+	0.601461i	$0.205415\pi$
$882$		0			0
$883$	−39289.6			−1.49740			−0.748699	−	0.662911i	$-0.769321\pi$
$883$	−39289.6			−1.49740			−0.748699	+	0.662911i	$0.769321\pi$
$884$	−591.497	−	1024.50i	−0.0225047	−	0.0389794i
$885$		0			0
$886$	−4474.24	+	7749.61i	−0.169656	+	0.293852i
$887$	2916.22	+	5051.04i	0.110391	+	0.191203i	0.915928	−	0.401342i	$-0.131456\pi$
$887$	2916.22	+	5051.04i	0.110391	+	0.191203i	−0.805537	+	0.592546i	$0.798123\pi$
$888$		0			0
$889$		0			0
$890$	10846.2			0.408499
$891$		0			0
$892$	−2723.70	+	4717.58i	−0.102238	+	0.177081i
$893$	−2065.59	+	3577.70i	−0.0774045	+	0.134069i
$894$		0			0
$895$	−8498.95			−0.317418
$896$		0			0
$897$		0			0
$898$	−2389.42	−	4138.59i	−0.0887928	−	0.153794i
$899$	−27426.3	+	47503.7i	−1.01748	+	1.76233i
$900$		0			0
$901$	−5490.65	−	9510.09i	−0.203019	−	0.351639i
$902$	37710.1			1.39203
$903$		0			0
$904$	−11529.4			−0.424184
$905$	−16591.2	−	28736.7i	−0.609402	−	1.05552i
$906$		0			0
$907$	−21194.0	+	36709.0i	−0.775892	+	1.34388i	0.158400	+	0.987375i	$0.449367\pi$
$907$	−21194.0	+	36709.0i	−0.775892	+	1.34388i	−0.934292	+	0.356509i	$0.883967\pi$
$908$	−3723.62	−	6449.50i	−0.136093	−	0.235720i
$909$		0			0
$910$		0			0
$911$	−2275.12			−0.0827423			−0.0413711	−	0.999144i	$-0.513173\pi$
$911$	−2275.12			−0.0827423			−0.0413711	+	0.999144i	$0.513173\pi$
$912$		0			0
$913$	43114.6	−	74676.7i	1.56285	−	2.70694i
$914$	4438.34	−	7687.43i	0.160621	−	0.278203i
$915$		0			0
$916$	21435.1			0.773184
$917$		0			0
$918$		0			0
$919$	15642.1	+	27093.0i	0.561465	+	0.972486i	0.997369	+	0.0724930i	$0.0230955\pi$
$919$	15642.1	+	27093.0i	0.561465	+	0.972486i	−0.435904	+	0.899993i	$0.643571\pi$
$920$	13571.6	−	23506.7i	0.486351	−	0.842385i
$921$		0			0
$922$	−14079.8	−	24387.0i	−0.502923	−	0.871088i
$923$	−2649.88			−0.0944983
$924$		0			0
$925$	49429.9			1.75702
$926$	−4687.50	−	8118.98i	−0.166351	−	0.288128i
$927$		0			0
$928$	−3491.05	+	6046.68i	−0.123491	+	0.213892i
$929$	16098.3	+	27883.1i	0.568535	+	0.984731i	0.996711	+	0.0810358i	$0.0258228\pi$
$929$	16098.3	+	27883.1i	0.568535	+	0.984731i	−0.428176	+	0.903695i	$0.640844\pi$
$930$		0			0
$931$		0			0
$932$	−21764.5			−0.764935
$933$		0			0
$934$	8447.26	−	14631.1i	0.295934	−	0.512573i
$935$	23681.3	−	41017.2i	0.828301	−	1.43466i
$936$		0			0
$937$	22293.6			0.777269			0.388635	−	0.921392i	$-0.372947\pi$
$937$	22293.6			0.777269			0.388635	+	0.921392i	$0.372947\pi$
$938$		0			0
$939$		0			0
$940$	−8108.58	−	14044.5i	−0.281354	−	0.487319i
$941$	−15904.8	+	27548.0i	−0.550991	+	0.954345i	0.447212	+	0.894428i	$0.352417\pi$
$941$	−15904.8	+	27548.0i	−0.550991	+	0.954345i	−0.998203	+	0.0599168i	$0.980916\pi$
$942$		0			0
$943$	35050.7	+	60709.6i	1.21040	+	2.09648i
$944$	−6595.22			−0.227390
$945$		0			0
$946$	4314.86			0.148296
$947$	9491.32	+	16439.4i	0.325688	+	0.564108i	0.981651	−	0.190685i	$-0.0610708\pi$
$947$	9491.32	+	16439.4i	0.325688	+	0.564108i	−0.655963	+	0.754793i	$0.727737\pi$
$948$		0			0
$949$	−1281.18	+	2219.08i	−0.0438240	+	0.0759055i
$950$	2070.39	+	3586.02i	0.0707077	+	0.122469i
$951$		0			0
$952$		0			0
$953$	−9254.58			−0.314570			−0.157285	−	0.987553i	$-0.550274\pi$
$953$	−9254.58			−0.314570			−0.157285	+	0.987553i	$0.550274\pi$
$954$		0			0
$955$	−26931.3	+	46646.3i	−0.912539	+	1.58056i
$956$	−2314.55	+	4008.92i	−0.0783033	+	0.135625i
$957$		0			0
$958$	8738.81			0.294716
$959$		0			0
$960$		0			0
$961$	−16704.7	−	28933.4i	−0.560730	−	0.971213i
$962$	2204.14	−	3817.68i	0.0738714	−	0.127949i
$963$		0			0
$964$	−7938.75	−	13750.3i	−0.265239	−	0.459407i
$965$	30341.8			1.01216
$966$		0			0
$967$	15317.5			0.509387			0.254694	−	0.967022i	$-0.418025\pi$
$967$	15317.5			0.509387			0.254694	+	0.967022i	$0.418025\pi$
$968$	−7853.65	−	13602.9i	−0.260770	−	0.451668i
$969$		0			0
$970$	13760.0	−	23833.0i	0.455471	−	0.788900i
$971$	11216.3	+	19427.2i	0.370699	+	0.642069i	0.989673	−	0.143342i	$-0.0457849\pi$
$971$	11216.3	+	19427.2i	0.370699	+	0.642069i	−0.618974	+	0.785411i	$0.712452\pi$
$972$		0			0
$973$		0			0
$974$	−28955.5			−0.952559
$975$		0			0
$976$	−6693.55	+	11593.6i	−0.219524	+	0.380226i
$977$	−313.932	+	543.746i	−0.0102800	+	0.0178055i	−0.871120	−	0.491071i	$-0.836606\pi$
$977$	−313.932	+	543.746i	−0.0102800	+	0.0178055i	0.860840	+	0.508876i	$0.169939\pi$
$978$		0			0
$979$	19577.3			0.639114
$980$		0			0
$981$		0			0
$982$	9306.12	+	16118.7i	0.302414	+	0.523796i
$983$	22516.3	−	38999.4i	0.730579	−	1.26540i	−0.226057	−	0.974114i	$-0.572584\pi$
$983$	22516.3	−	38999.4i	0.730579	−	1.26540i	0.956636	−	0.291286i	$-0.0940830\pi$
$984$		0			0
$985$	16391.4	+	28390.8i	0.530227	+	0.918381i
$986$	−22648.0			−0.731500
$987$		0			0
$988$	369.285			0.0118912
$989$	4010.57	+	6946.51i	0.128947	+	0.223343i
$990$		0			0
$991$	15990.5	−	27696.4i	0.512569	−	0.887795i	−0.487325	−	0.873221i	$-0.662027\pi$
$991$	15990.5	−	27696.4i	0.512569	−	0.887795i	0.999894	−	0.0145745i	$-0.00463937\pi$
$992$	−4022.35	−	6966.92i	−0.128740	−	0.222984i
$993$		0			0
$994$		0			0
$995$	50425.2			1.60662
$996$		0			0
$997$	−6189.41	+	10720.4i	−0.196611	+	0.340539i	−0.947427	−	0.319971i	$-0.896327\pi$
$997$	−6189.41	+	10720.4i	−0.196611	+	0.340539i	0.750817	+	0.660511i	$0.229660\pi$
$998$	12237.5	−	21196.1i	0.388149	−	0.672294i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(7.94975 + 13.7694i) q^{5} +8.00000 q^{8} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(7.94975 + 13.7694i) q^{5} +8.00000 q^{8} +(15.8995 - 27.5387i) q^{10} +(28.6985 - 49.7072i) q^{11} -5.69848 q^{13} +(-8.00000 - 13.8564i) q^{16} +(25.9497 - 44.9463i) q^{17} +(8.10051 + 14.0305i) q^{19} -63.5980 q^{20} -114.794 q^{22} +(-106.698 - 184.807i) q^{23} +(-63.8970 + 110.673i) q^{25} +(5.69848 + 9.87007i) q^{26} +218.191 q^{29} +(-125.698 + 217.716i) q^{31} +(-16.0000 + 27.7128i) q^{32} -103.799 q^{34} +(-193.397 - 334.973i) q^{37} +(16.2010 - 28.0610i) q^{38} +(63.5980 + 110.155i) q^{40} -328.503 q^{41} -37.5879 q^{43} +(114.794 + 198.829i) q^{44} +(-213.397 + 369.614i) q^{46} +(127.497 + 220.832i) q^{47} +255.588 q^{50} +(11.3970 - 19.7401i) q^{52} +(105.794 - 183.240i) q^{53} +912.583 q^{55} +(-218.191 - 377.918i) q^{58} +(206.101 - 356.977i) q^{59} +(-418.347 - 724.598i) q^{61} +502.794 q^{62} +64.0000 q^{64} +(-45.3015 - 78.4645i) q^{65} +(82.7939 - 143.403i) q^{67} +(103.799 + 179.785i) q^{68} +465.015 q^{71} +(224.829 - 389.415i) q^{73} +(-386.794 + 669.947i) q^{74} -64.8040 q^{76} +(171.779 + 297.530i) q^{79} +(127.196 - 220.310i) q^{80} +(328.503 + 568.983i) q^{82} +1502.33 q^{83} +825.176 q^{85} +(37.5879 + 65.1041i) q^{86} +(229.588 - 397.658i) q^{88} +(170.543 + 295.389i) q^{89} +853.588 q^{92} +(254.995 - 441.664i) q^{94} +(-128.794 + 223.078i) q^{95} +865.437 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 8 q^{4} + 12 q^{5} + 32 q^{8}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more