LMFDB - Embedded newform 405.3.i.d.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,3,Mod(26,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("405.26");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	405.i (of order $6$, 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:	$11.0354507066$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} + 7x^{4} + 36x^{2} + 81 $ x^8 + 4x^6 + 7x^4 + 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.1
Root			$-1.40294 + 1.01575i$ of defining polynomial
Character	$\chi$	$=$	405.26
Dual form			405.3.i.d.296.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.16124 - 1.82514i) q^{2} +(4.66228 + 8.07530i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-3.58114 + 6.20271i) q^{7} -19.4361i q^{8} -8.16228 q^{10} +(-4.70023 - 2.71368i) q^{11} +(-4.90569 - 8.49691i) q^{13} +(22.6417 - 13.0722i) q^{14} +(-16.8246 + 29.1410i) q^{16} -12.2317i q^{17} +6.32456 q^{19} +(18.0569 + 10.4252i) q^{20} +(9.90569 + 17.1572i) q^{22} +(-10.4265 + 6.01972i) q^{23} +(2.50000 - 4.33013i) q^{25} +35.8143i q^{26} -66.7851 q^{28} +(38.9608 + 22.4940i) q^{29} +(29.1359 + 50.4649i) q^{31} +(39.0441 - 22.5421i) q^{32} +(-22.3246 + 38.6673i) q^{34} +16.0153i q^{35} +66.4605 q^{37} +(-19.9934 - 11.5432i) q^{38} +(-21.7302 - 37.6379i) q^{40} +(14.2672 - 8.23717i) q^{41} +(21.8114 - 37.7784i) q^{43} -50.6077i q^{44} +43.9473 q^{46} +(-34.6904 - 20.0285i) q^{47} +(-1.14911 - 1.99032i) q^{49} +(-15.8062 + 9.12570i) q^{50} +(45.7434 - 79.2299i) q^{52} +13.2242i q^{53} -12.1359 q^{55} +(120.557 + 69.6035i) q^{56} +(-82.1096 - 142.218i) q^{58} +(21.7822 - 12.5759i) q^{59} +(17.8377 - 30.8958i) q^{61} -212.709i q^{62} -29.9737 q^{64} +(-18.9997 - 10.9695i) q^{65} +(-13.3509 - 23.1244i) q^{67} +(98.7746 - 57.0275i) q^{68} +(29.2302 - 50.6283i) q^{70} +92.7301i q^{71} +60.3246 q^{73} +(-210.097 - 121.300i) q^{74} +(29.4868 + 51.0727i) q^{76} +(33.6644 - 19.4361i) q^{77} +(48.1096 - 83.3283i) q^{79} +75.2417i q^{80} -60.1359 q^{82} +(68.5212 + 39.5607i) q^{83} +(-13.6754 - 23.6866i) q^{85} +(-137.902 + 79.6177i) q^{86} +(-52.7434 + 91.3543i) q^{88} -107.443i q^{89} +70.2719 q^{91} +(-97.2221 - 56.1312i) q^{92} +(73.1096 + 126.630i) q^{94} +(12.2474 - 7.07107i) q^{95} +(0.539501 - 0.934443i) q^{97} +8.38915i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{4} - 16 q^{7} - 40 q^{10} + 24 q^{13} - 84 q^{16} + 16 q^{22} + 20 q^{25} - 256 q^{28} + 56 q^{31} - 128 q^{34} + 304 q^{37} - 60 q^{40} + 48 q^{43} + 48 q^{46} + 92 q^{49} + 328 q^{52} + 80 q^{55}+ \cdots + 232 q^{97}+O(q^{100}) $ 8 * q + 12 * q^4 - 16 * q^7 - 40 * q^10 + 24 * q^13 - 84 * q^16 + 16 * q^22 + 20 * q^25 - 256 * q^28 + 56 * q^31 - 128 * q^34 + 304 * q^37 - 60 * q^40 + 48 * q^43 + 48 * q^46 + 92 * q^49 + 328 * q^52 + 80 * q^55 - 328 * q^58 + 168 * q^61 - 88 * q^64 - 208 * q^67 + 120 * q^70 + 432 * q^73 + 160 * q^76 + 56 * q^79 - 304 * q^82 - 160 * q^85 - 384 * q^88 + 208 * q^91 + 256 * q^94 + 232 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−3.16124	−	1.82514i	−1.58062	−	0.912570i	−0.994769	−	0.102150i	$-0.967428\pi$
$2$	−3.16124	−	1.82514i	−1.58062	−	0.912570i	−0.585849	−	0.810420i	$-0.699239\pi$
$3$		0			0
$3$		0			0
$4$	4.66228	+	8.07530i	1.16557	+	2.01883i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$6$		0			0
$7$	−3.58114	+	6.20271i	−0.511591	+	0.886102i	0.488318	+	0.872666i	$0.337610\pi$
$7$	−3.58114	+	6.20271i	−0.511591	+	0.886102i	−0.999910	+	0.0134366i	$0.995723\pi$
$8$		−	19.4361i		−	2.42952i
$9$		0			0
$10$	−8.16228			−0.816228
$11$	−4.70023	−	2.71368i	−0.427294	−	0.246698i	0.270899	−	0.962608i	$-0.412679\pi$
$11$	−4.70023	−	2.71368i	−0.427294	−	0.246698i	−0.698193	+	0.715910i	$0.746012\pi$
$12$		0			0
$13$	−4.90569	−	8.49691i	−0.377361	−	0.653609i	0.613316	−	0.789837i	$-0.289835\pi$
$13$	−4.90569	−	8.49691i	−0.377361	−	0.653609i	−0.990677	+	0.136229i	$0.956502\pi$
$14$	22.6417	−	13.0722i	1.61726	−	0.933726i
$15$		0			0
$16$	−16.8246	+	29.1410i	−1.05153	+	1.82131i
$17$		−	12.2317i		−	0.719511i	−0.933047	−	0.359756i	$-0.882860\pi$
$17$		−	12.2317i		−	0.719511i	0.933047	−	0.359756i	$-0.117140\pi$
$18$		0			0
$19$	6.32456			0.332871			0.166436	−	0.986052i	$-0.446774\pi$
$19$	6.32456			0.332871			0.166436	+	0.986052i	$0.446774\pi$
$20$	18.0569	+	10.4252i	0.902846	+	0.521258i
$21$		0			0
$22$	9.90569	+	17.1572i	0.450259	+	0.779871i
$23$	−10.4265	+	6.01972i	−0.453324	+	0.261727i	−0.709233	−	0.704974i	$-0.750959\pi$
$23$	−10.4265	+	6.01972i	−0.453324	+	0.261727i	0.255909	+	0.966701i	$0.417625\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$			35.8143i			1.37747i
$27$		0			0
$28$	−66.7851			−2.38518
$29$	38.9608	+	22.4940i	1.34348	+	0.775657i	0.987316	−	0.158768i	$-0.0507521\pi$
$29$	38.9608	+	22.4940i	1.34348	+	0.775657i	0.356161	+	0.934425i	$0.384085\pi$
$30$		0			0
$31$	29.1359	+	50.4649i	0.939869	+	1.62790i	0.765712	+	0.643183i	$0.222387\pi$
$31$	29.1359	+	50.4649i	0.939869	+	1.62790i	0.174157	+	0.984718i	$0.444280\pi$
$32$	39.0441	−	22.5421i	1.22013	−	0.704441i
$33$		0			0
$34$	−22.3246	+	38.6673i	−0.656605	+	1.13727i
$35$			16.0153i			0.457581i
$36$		0			0
$37$	66.4605			1.79623			0.898115	−	0.439761i	$-0.144937\pi$
$37$	66.4605			1.79623			0.898115	+	0.439761i	$0.144937\pi$
$38$	−19.9934	−	11.5432i	−0.526143	−	0.303769i
$39$		0			0
$40$	−21.7302	−	37.6379i	−0.543256	−	0.940947i
$41$	14.2672	−	8.23717i	0.347980	−	0.200906i	−0.315815	−	0.948821i	$-0.602278\pi$
$41$	14.2672	−	8.23717i	0.347980	−	0.200906i	0.663795	+	0.747914i	$0.268945\pi$
$42$		0			0
$43$	21.8114	−	37.7784i	0.507242	−	0.878568i	−0.492723	−	0.870186i	$-0.663999\pi$
$43$	21.8114	−	37.7784i	0.507242	−	0.878568i	0.999965	−	0.00838215i	$-0.00266815\pi$
$44$		−	50.6077i		−	1.15018i
$45$		0			0
$46$	43.9473			0.955377
$47$	−34.6904	−	20.0285i	−0.738093	−	0.426138i	0.0832828	−	0.996526i	$-0.473460\pi$
$47$	−34.6904	−	20.0285i	−0.738093	−	0.426138i	−0.821375	+	0.570388i	$0.806793\pi$
$48$		0			0
$49$	−1.14911	−	1.99032i	−0.0234512	−	0.0406187i
$50$	−15.8062	+	9.12570i	−0.316124	+	0.182514i
$51$		0			0
$52$	45.7434	−	79.2299i	0.879681	−	1.52365i
$53$			13.2242i			0.249512i	0.992187	+	0.124756i	$0.0398149\pi$
$53$			13.2242i			0.249512i	−0.992187	+	0.124756i	$0.960185\pi$
$54$		0			0
$55$	−12.1359			−0.220654
$56$	120.557	+	69.6035i	2.15280	+	1.24292i
$57$		0			0
$58$	−82.1096	−	142.218i	−1.41568	−	2.45203i
$59$	21.7822	−	12.5759i	0.369189	−	0.213151i	−0.303915	−	0.952699i	$-0.598294\pi$
$59$	21.7822	−	12.5759i	0.369189	−	0.213151i	0.673104	+	0.739548i	$0.264961\pi$
$60$		0			0
$61$	17.8377	−	30.8958i	0.292422	−	0.506489i	−0.681960	−	0.731389i	$-0.738872\pi$
$61$	17.8377	−	30.8958i	0.292422	−	0.506489i	0.974382	+	0.224900i	$0.0722056\pi$
$62$		−	212.709i		−	3.43079i
$63$		0			0
$64$	−29.9737			−0.468339
$65$	−18.9997	−	10.9695i	−0.292303	−	0.168761i
$66$		0			0
$67$	−13.3509	−	23.1244i	−0.199267	−	0.345141i	0.749024	−	0.662543i	$-0.230523\pi$
$67$	−13.3509	−	23.1244i	−0.199267	−	0.345141i	−0.948291	+	0.317402i	$0.897189\pi$
$68$	98.7746	−	57.0275i	1.45257	−	0.838640i
$69$		0			0
$70$	29.2302	−	50.6283i	0.417575	−	0.723261i
$71$			92.7301i			1.30606i	0.757333	+	0.653029i	$0.226502\pi$
$71$			92.7301i			1.30606i	−0.757333	+	0.653029i	$0.773498\pi$
$72$		0			0
$73$	60.3246			0.826364			0.413182	−	0.910649i	$-0.364417\pi$
$73$	60.3246			0.826364			0.413182	+	0.910649i	$0.364417\pi$
$74$	−210.097	−	121.300i	−2.83915	−	1.63919i
$75$		0			0
$76$	29.4868	+	51.0727i	0.387985	+	0.672009i
$77$	33.6644	−	19.4361i	0.437199	−	0.252417i
$78$		0			0
$79$	48.1096	−	83.3283i	0.608982	−	1.05479i	−0.382426	−	0.923986i	$-0.624911\pi$
$79$	48.1096	−	83.3283i	0.608982	−	1.05479i	0.991408	−	0.130802i	$-0.0417553\pi$
$80$			75.2417i			0.940521i
$81$		0			0
$82$	−60.1359			−0.733365
$83$	68.5212	+	39.5607i	0.825557	+	0.476635i	0.852329	−	0.523006i	$-0.175190\pi$
$83$	68.5212	+	39.5607i	0.825557	+	0.476635i	−0.0267722	+	0.999642i	$0.508523\pi$
$84$		0			0
$85$	−13.6754	−	23.6866i	−0.160888	−	0.278665i
$86$	−137.902	+	79.6177i	−1.60351	+	0.925787i
$87$		0			0
$88$	−52.7434	+	91.3543i	−0.599357	+	1.03812i
$89$		−	107.443i		−	1.20722i	−0.797278	−	0.603612i	$-0.793728\pi$
$89$		−	107.443i		−	1.20722i	0.797278	−	0.603612i	$-0.206272\pi$
$90$		0			0
$91$	70.2719			0.772219
$92$	−97.2221	−	56.1312i	−1.05676	−	0.610122i
$93$		0			0
$94$	73.1096	+	126.630i	0.777762	+	1.34712i
$95$	12.2474	−	7.07107i	0.128921	−	0.0744323i
$96$		0			0
$97$	0.539501	−	0.934443i	0.00556187	−	0.00963344i	−0.863231	−	0.504809i	$-0.831563\pi$
$97$	0.539501	−	0.934443i	0.00556187	−	0.00963344i	0.868793	+	0.495176i	$0.164896\pi$
$98$			8.38915i			0.0856036i
$99$		0			0
$100$	46.6228			0.466228
$101$	147.469	+	85.1412i	1.46009	+	0.842982i	0.999015	−	0.0443800i	$-0.0141312\pi$
$101$	147.469	+	85.1412i	1.46009	+	0.842982i	0.461073	+	0.887362i	$0.347465\pi$
$102$		0			0
$103$	64.2302	+	111.250i	0.623595	+	1.08010i	0.988811	+	0.149175i	$0.0476617\pi$
$103$	64.2302	+	111.250i	0.623595	+	1.08010i	−0.365216	+	0.930923i	$0.619005\pi$
$104$	−165.147	+	95.3477i	−1.58795	+	0.916805i
$105$		0			0
$106$	24.1359	−	41.8047i	0.227698	−	0.394384i
$107$			76.3675i			0.713715i	0.934159	+	0.356858i	$0.116152\pi$
$107$			76.3675i			0.713715i	−0.934159	+	0.356858i	$0.883848\pi$
$108$		0			0
$109$	−13.0790			−0.119991			−0.0599954	−	0.998199i	$-0.519109\pi$
$109$	−13.0790			−0.119991			−0.0599954	+	0.998199i	$0.519109\pi$
$110$	38.3646	+	22.1498i	0.348769	+	0.201362i
$111$		0			0
$112$	−120.502	−	208.716i	−1.07591	−	1.86353i
$113$	−17.9414	+	10.3585i	−0.158774	+	0.0916680i	−0.577282	−	0.816545i	$-0.695887\pi$
$113$	−17.9414	+	10.3585i	−0.158774	+	0.0916680i	0.418508	+	0.908213i	$0.362553\pi$
$114$		0			0
$115$	−13.4605	+	23.3143i	−0.117048	+	0.202733i
$116$			419.494i			3.61633i
$117$		0			0
$118$	−91.8114			−0.778063
$119$	75.8697	+	43.8034i	0.637560	+	0.368096i
$120$		0			0
$121$	−45.7719	−	79.2792i	−0.378280	−	0.655200i
$122$	−112.779	+	65.1127i	−0.924414	+	0.533711i
$123$		0			0
$124$	−271.680	+	470.563i	−2.19097	+	3.79486i
$125$		−	11.1803i		−	0.0894427i
$126$		0			0
$127$	−38.0306			−0.299454			−0.149727	−	0.988727i	$-0.547839\pi$
$127$	−38.0306			−0.299454			−0.149727	+	0.988727i	$0.547839\pi$
$128$	−61.4225	−	35.4623i	−0.479863	−	0.277049i
$129$		0			0
$130$	40.0416	+	69.3542i	0.308013	+	0.533493i
$131$	−72.6949	+	41.9704i	−0.554923	+	0.320385i	−0.751105	−	0.660182i	$-0.770479\pi$
$131$	−72.6949	+	41.9704i	−0.554923	+	0.320385i	0.196182	+	0.980567i	$0.437146\pi$
$132$		0			0
$133$	−22.6491	+	39.2294i	−0.170294	+	0.294958i
$134$			97.4690i			0.727381i
$135$		0			0
$136$	−237.737			−1.74806
$137$	−13.5044	−	7.79680i	−0.0985726	−	0.0569109i	0.449903	−	0.893077i	$-0.351458\pi$
$137$	−13.5044	−	7.79680i	−0.0985726	−	0.0569109i	−0.548476	+	0.836166i	$0.684792\pi$
$138$		0			0
$139$	−33.9210	−	58.7529i	−0.244036	−	0.422683i	0.717824	−	0.696224i	$-0.245138\pi$
$139$	−33.9210	−	58.7529i	−0.244036	−	0.422683i	−0.961860	+	0.273542i	$0.911805\pi$
$140$	−129.329	+	74.6680i	−0.923776	+	0.533343i
$141$		0			0
$142$	169.246	−	293.142i	1.19187	−	2.06438i
$143$			53.2499i			0.372377i
$144$		0			0
$145$	100.596			0.693769
$146$	−190.700	−	110.101i	−1.30617	−	0.754115i
$147$		0			0
$148$	309.857	+	536.689i	2.09363	+	3.62627i
$149$	202.153	−	116.713i	1.35673	−	0.783308i	0.367548	−	0.930005i	$-0.380197\pi$
$149$	202.153	−	116.713i	1.35673	−	0.783308i	0.989182	+	0.146697i	$0.0468642\pi$
$150$		0			0
$151$	−92.6754	+	160.519i	−0.613745	+	1.06304i	0.376859	+	0.926271i	$0.377004\pi$
$151$	−92.6754	+	160.519i	−0.613745	+	1.06304i	−0.990603	+	0.136766i	$0.956329\pi$
$152$		−	122.925i		−	0.808716i
$153$		0			0
$154$	−141.895			−0.921394
$155$	112.843	+	65.1500i	0.728020	+	0.420322i
$156$		0			0
$157$	55.6381	+	96.3680i	0.354383	+	0.613809i	0.987012	−	0.160646i	$-0.0513577\pi$
$157$	55.6381	+	96.3680i	0.354383	+	0.613809i	−0.632629	+	0.774455i	$0.718024\pi$
$158$	−304.172	+	175.614i	−1.92514	+	1.11148i
$159$		0			0
$160$	50.4057	−	87.3052i	0.315036	−	0.545658i
$161$		−	86.2298i		−	0.535589i
$162$		0			0
$163$	118.763			0.728607			0.364304	−	0.931280i	$-0.381307\pi$
$163$	118.763			0.728607			0.364304	+	0.931280i	$0.381307\pi$
$164$	133.035	+	76.8079i	0.811190	+	0.468341i
$165$		0			0
$166$	−144.408	−	250.122i	−0.869927	−	1.50676i
$167$	191.560	−	110.597i	1.14706	−	0.662258i	0.198894	−	0.980021i	$-0.436265\pi$
$167$	191.560	−	110.597i	1.14706	−	0.662258i	0.948170	+	0.317763i	$0.102932\pi$
$168$		0			0
$169$	36.3683	−	62.9918i	0.215197	−	0.372733i
$170$			99.8384i			0.587285i
$171$		0			0
$172$	406.763			2.36490
$173$	−165.244	−	95.4036i	−0.955166	−	0.551466i	−0.0604844	−	0.998169i	$-0.519265\pi$
$173$	−165.244	−	95.4036i	−0.955166	−	0.551466i	−0.894682	+	0.446704i	$0.852598\pi$
$174$		0			0
$175$	17.9057	+	31.0136i	0.102318	+	0.177220i
$176$	158.159	−	91.3129i	0.898628	−	0.518823i
$177$		0			0
$178$	−196.099	+	339.653i	−1.10168	+	1.90816i
$179$		−	58.1005i		−	0.324584i	−0.986743	−	0.162292i	$-0.948111\pi$
$179$		−	58.1005i		−	0.324584i	0.986743	−	0.162292i	$-0.0518886\pi$
$180$		0			0
$181$	−162.921			−0.900116			−0.450058	−	0.892999i	$-0.648597\pi$
$181$	−162.921			−0.900116			−0.450058	+	0.892999i	$0.648597\pi$
$182$	−222.146	−	128.256i	−1.22058	−	0.704704i
$183$		0			0
$184$	117.000	+	202.650i	0.635870	+	1.10136i
$185$	128.700	−	74.3051i	0.695677	−	0.401649i
$186$		0			0
$187$	−33.1929	+	57.4918i	−0.177502	+	0.307443i
$188$		−	373.513i		−	1.98677i
$189$		0			0
$190$	−51.6228			−0.271699
$191$	−86.6561	−	50.0309i	−0.453697	−	0.261942i	0.255693	−	0.966758i	$-0.417696\pi$
$191$	−86.6561	−	50.0309i	−0.453697	−	0.261942i	−0.709390	+	0.704816i	$0.751030\pi$
$192$		0			0
$193$	30.9473	+	53.6024i	0.160349	+	0.277732i	0.934994	−	0.354664i	$-0.115405\pi$
$193$	30.9473	+	53.6024i	0.160349	+	0.277732i	−0.774645	+	0.632396i	$0.782071\pi$
$194$	−3.41098	+	1.96933i	−0.0175824	+	0.0101512i
$195$		0			0
$196$	10.7149	−	18.5588i	0.0546681	−	0.0946879i
$197$		−	24.8791i		−	0.126290i	−0.998004	−	0.0631449i	$-0.979887\pi$
$197$		−	24.8791i		−	0.126290i	0.998004	−	0.0631449i	$-0.0201130\pi$
$198$		0			0
$199$	−156.491			−0.786387			−0.393194	−	0.919456i	$-0.628630\pi$
$199$	−156.491			−0.786387			−0.393194	+	0.919456i	$0.628630\pi$
$200$	−84.1609	−	48.5903i	−0.420804	−	0.242952i
$201$		0			0
$202$	−310.789	−	538.303i	−1.53856	−	2.66487i
$203$	−279.048	+	161.109i	−1.37462	+	0.793639i
$204$		0			0
$205$	18.4189	−	31.9024i	0.0898481	−	0.155621i
$206$		−	468.917i		−	2.27630i
$207$		0			0
$208$	330.144			1.58723
$209$	−29.7269	−	17.1628i	−0.142234	−	0.0821187i
$210$		0			0
$211$	−118.895	−	205.932i	−0.563482	−	0.975979i	−0.997189	−	0.0749253i	$-0.976128\pi$
$211$	−118.895	−	205.932i	−0.563482	−	0.975979i	0.433707	−	0.901054i	$-0.357205\pi$
$212$	−106.789	+	61.6547i	−0.503722	+	0.290824i
$213$		0			0
$214$	139.381	−	241.416i	0.651315	−	1.12811i
$215$		−	97.5435i		−	0.453691i
$216$		0			0
$217$	−417.359			−1.92332
$218$	41.3458	+	23.8710i	0.189660	+	0.109500i
$219$		0			0
$220$	−56.5811	−	98.0014i	−0.257187	−	0.445461i
$221$	−103.932	+	60.0049i	−0.470279	+	0.271516i
$222$		0			0
$223$	91.1512	−	157.879i	0.408750	−	0.707976i	−0.586000	−	0.810311i	$-0.699298\pi$
$223$	91.1512	−	157.879i	0.408750	−	0.707976i	0.994750	+	0.102335i	$0.0326315\pi$
$224$			322.906i			1.44154i
$225$		0			0
$226$	75.6228			0.334614
$227$	351.674	+	203.039i	1.54922	+	0.894444i	0.998201	+	0.0599528i	$0.0190950\pi$
$227$	351.674	+	203.039i	1.54922	+	0.894444i	0.551021	+	0.834491i	$0.314238\pi$
$228$		0			0
$229$	13.6491	+	23.6410i	0.0596031	+	0.103236i	0.894287	−	0.447493i	$-0.147683\pi$
$229$	13.6491	+	23.6410i	0.0596031	+	0.103236i	−0.834684	+	0.550729i	$0.814350\pi$
$230$	85.1036	−	49.1346i	0.370016	−	0.213629i
$231$		0			0
$232$	437.197	−	757.248i	1.88447	−	3.26400i
$233$			356.382i			1.52954i	0.644306	+	0.764768i	$0.277146\pi$
$233$			356.382i			1.52954i	−0.644306	+	0.764768i	$0.722854\pi$
$234$		0			0
$235$	−89.5701			−0.381149
$236$	203.109	+	117.265i	0.860631	+	0.496886i
$237$		0			0
$238$	−159.895	−	276.946i	−0.671826	−	1.16364i
$239$	235.290	−	135.845i	0.984479	−	0.568389i	0.0808596	−	0.996725i	$-0.474233\pi$
$239$	235.290	−	135.845i	0.984479	−	0.568389i	0.903619	+	0.428336i	$0.140900\pi$
$240$		0			0
$241$	112.219	−	194.369i	0.465640	−	0.806512i	−0.533590	−	0.845743i	$-0.679158\pi$
$241$	112.219	−	194.369i	0.465640	−	0.806512i	0.999230	+	0.0392311i	$0.0124909\pi$
$242$			334.161i			1.38083i
$243$		0			0
$244$	332.658			1.36335
$245$	−4.45049	−	2.56949i	−0.0181653	−	0.0104877i
$246$		0			0
$247$	−31.0263	−	53.7392i	−0.125613	−	0.217568i
$248$	980.843	−	566.290i	3.95501	−	2.28343i
$249$		0			0
$250$	−20.4057	+	35.3437i	−0.0816228	+	0.141375i
$251$			318.775i			1.27002i	0.772504	+	0.635010i	$0.219004\pi$
$251$			318.775i			1.27002i	−0.772504	+	0.635010i	$0.780996\pi$
$252$		0			0
$253$	65.3423			0.258270
$254$	120.224	+	69.4112i	0.473322	+	0.273272i
$255$		0			0
$256$	189.395	+	328.041i	0.739823	+	1.28141i
$257$	−322.140	+	185.988i	−1.25346	+	0.723688i	−0.971796	−	0.235824i	$-0.924221\pi$
$257$	−322.140	+	185.988i	−1.25346	+	0.723688i	−0.281668	+	0.959512i	$0.590888\pi$
$258$		0			0
$259$	−238.004	+	412.235i	−0.918935	+	1.59164i
$260$		−	204.571i		−	0.786811i
$261$		0			0
$262$	306.408			1.16950
$263$	206.590	+	119.275i	0.785512	+	0.453515i	0.838380	−	0.545086i	$-0.183503\pi$
$263$	206.590	+	119.275i	0.785512	+	0.453515i	−0.0528683	+	0.998601i	$0.516836\pi$
$264$		0			0
$265$	14.7851	+	25.6085i	0.0557927	+	0.0966357i
$266$	143.198	−	82.6756i	0.538340	−	0.310811i
$267$		0			0
$268$	124.491	−	215.625i	0.464519	−	0.804571i
$269$		−	125.871i		−	0.467922i	−0.972246	−	0.233961i	$-0.924831\pi$
$269$		−	125.871i		−	0.467922i	0.972246	−	0.233961i	$-0.0751688\pi$
$270$		0			0
$271$	−258.649			−0.954425			−0.477212	−	0.878788i	$-0.658353\pi$
$271$	−258.649			−0.954425			−0.477212	+	0.878788i	$0.658353\pi$
$272$	356.443	+	205.793i	1.31045	+	0.756591i
$273$		0			0
$274$	28.4605	+	49.2950i	0.103870	+	0.179909i
$275$	−23.5012	+	13.5684i	−0.0854587	+	0.0493396i
$276$		0			0
$277$	−113.857	+	197.207i	−0.411037	+	0.711937i	−0.995003	−	0.0998406i	$-0.968167\pi$
$277$	−113.857	+	197.207i	−0.411037	+	0.711937i	0.583966	+	0.811778i	$0.301500\pi$
$278$			247.642i			0.890800i
$279$		0			0
$280$	311.276			1.11170
$281$	−209.044	−	120.692i	−0.743930	−	0.429508i	0.0795665	−	0.996830i	$-0.474646\pi$
$281$	−209.044	−	120.692i	−0.743930	−	0.429508i	−0.823496	+	0.567321i	$0.807980\pi$
$282$		0			0
$283$	−104.167	−	180.422i	−0.368080	−	0.637533i	0.621186	−	0.783663i	$-0.286651\pi$
$283$	−104.167	−	180.422i	−0.368080	−	0.637533i	−0.989265	+	0.146131i	$0.953318\pi$
$284$	−748.824	+	432.334i	−2.63670	+	1.52230i
$285$		0			0
$286$	97.1886	−	168.336i	0.339820	−	0.588586i
$287$			117.994i			0.411128i
$288$		0			0
$289$	139.386			0.482304
$290$	−318.009	−	183.603i	−1.09658	−	0.633113i
$291$		0			0
$292$	281.250	+	487.139i	0.963184	+	1.66828i
$293$	174.671	−	100.847i	0.596148	−	0.344186i	−0.171377	−	0.985206i	$-0.554822\pi$
$293$	174.671	−	100.847i	0.596148	−	0.344186i	0.767525	+	0.641020i	$0.221488\pi$
$294$		0			0
$295$	28.1206	−	48.7064i	0.0953242	−	0.165106i
$296$		−	1291.73i		−	4.36397i
$297$		0			0
$298$	−852.070			−2.85929
$299$	102.298	+	59.0618i	0.342134	+	0.197531i
$300$		0			0
$301$	156.219	+	270.580i	0.519001	+	0.898936i
$302$	585.938	−	338.291i	1.94019	−	1.12017i
$303$		0			0
$304$	−106.408	+	184.304i	−0.350026	+	0.606262i
$305$		−	79.7727i		−	0.261550i
$306$		0			0
$307$	342.824			1.11669			0.558346	−	0.829608i	$-0.311436\pi$
$307$	342.824			1.11669			0.558346	+	0.829608i	$0.311436\pi$
$308$	313.905	+	181.233i	1.01917	+	0.588420i
$309$		0			0
$310$	−237.816	−	411.909i	−0.767147	−	1.32874i
$311$	188.482	−	108.820i	0.606050	−	0.349903i	−0.165368	−	0.986232i	$-0.552881\pi$
$311$	188.482	−	108.820i	0.606050	−	0.349903i	0.771418	+	0.636329i	$0.219548\pi$
$312$		0			0
$313$	−140.947	+	244.128i	−0.450311	+	0.779961i	−0.998405	−	0.0564552i	$-0.982020\pi$
$313$	−140.947	+	244.128i	−0.450311	+	0.779961i	0.548094	+	0.836417i	$0.315354\pi$
$314$		−	406.189i		−	1.29360i
$315$		0			0
$316$	897.201			2.83925
$317$	13.3379	+	7.70067i	0.0420756	+	0.0242923i	0.520890	−	0.853624i	$-0.325600\pi$
$317$	13.3379	+	7.70067i	0.0420756	+	0.0242923i	−0.478815	+	0.877916i	$0.658933\pi$
$318$		0			0
$319$	−122.083	−	211.454i	−0.382706	−	0.662867i
$320$	−58.0438	+	33.5116i	−0.181387	+	0.104724i
$321$		0			0
$322$	−157.381	+	272.593i	−0.488762	+	0.846561i
$323$		−	77.3600i		−	0.239505i
$324$		0			0
$325$	−49.0569			−0.150944
$326$	−375.438	−	216.759i	−1.15165	−	0.664905i
$327$		0			0
$328$	−160.099	−	277.299i	−0.488105	−	0.845423i
$329$	248.462	−	143.450i	0.755203	−	0.436017i
$330$		0			0
$331$	−187.759	+	325.208i	−0.567247	+	0.982500i	0.429590	+	0.903024i	$0.358658\pi$
$331$	−187.759	+	325.208i	−0.567247	+	0.982500i	−0.996837	+	0.0794763i	$0.974675\pi$
$332$			737.773i			2.22221i
$333$		0			0
$334$	−807.421			−2.41743
$335$	−51.7078	−	29.8535i	−0.154352	−	0.0891149i
$336$		0			0
$337$	−94.0569	−	162.911i	−0.279101	−	0.483417i	0.692061	−	0.721839i	$-0.256703\pi$
$337$	−94.0569	−	162.911i	−0.279101	−	0.483417i	−0.971162	+	0.238423i	$0.923370\pi$
$338$	−229.938	+	132.755i	−0.680289	+	0.392765i
$339$		0			0
$340$	127.517	−	220.867i	0.375051	−	0.649608i
$341$		−	316.262i		−	0.927456i
$342$		0			0
$343$	−334.491			−0.975193
$344$	−734.266	−	423.929i	−2.13450	−	1.23235i
$345$		0			0
$346$	348.250	+	603.186i	1.00650	+	1.74331i
$347$	−444.958	+	256.897i	−1.28230	+	0.740336i	−0.977268	−	0.212006i	$-0.932000\pi$
$347$	−444.958	+	256.897i	−1.28230	+	0.740336i	−0.305032	+	0.952342i	$0.598667\pi$
$348$		0			0
$349$	−56.2676	+	97.4584i	−0.161225	+	0.279250i	−0.935308	−	0.353834i	$-0.884878\pi$
$349$	−56.2676	+	97.4584i	−0.161225	+	0.279250i	0.774083	+	0.633084i	$0.218211\pi$
$350$		−	130.722i		−	0.373490i
$351$		0			0
$352$	−244.688			−0.695137
$353$	−370.807	−	214.086i	−1.05045	−	0.606475i	−0.127672	−	0.991816i	$-0.540750\pi$
$353$	−370.807	−	214.086i	−1.05045	−	0.606475i	−0.922774	+	0.385341i	$0.874084\pi$
$354$		0			0
$355$	103.675	+	179.571i	0.292044	+	0.505834i
$356$	867.635	−	500.929i	2.43718	−	1.40710i
$357$		0			0
$358$	−106.042	+	183.670i	−0.296206	+	0.513043i
$359$			56.1961i			0.156535i	0.996932	+	0.0782676i	$0.0249389\pi$
$359$			56.1961i			0.156535i	−0.996932	+	0.0782676i	$0.975061\pi$
$360$		0			0
$361$	−321.000			−0.889197
$362$	515.032	+	297.354i	1.42274	+	0.821419i
$363$		0			0
$364$	327.627	+	567.467i	0.900074	+	1.55897i
$365$	116.818	−	67.4449i	0.320049	−	0.184781i
$366$		0			0
$367$	77.1819	−	133.683i	0.210305	−	0.364259i	−0.741505	−	0.670947i	$-0.765888\pi$
$367$	77.1819	−	133.683i	0.210305	−	0.364259i	0.951810	+	0.306689i	$0.0992210\pi$
$368$		−	405.116i		−	1.10086i
$369$		0			0
$370$	−542.469			−1.46613
$371$	−82.0257	−	47.3575i	−0.221093	−	0.127648i
$372$		0			0
$373$	−278.642	−	482.623i	−0.747030	−	1.29389i	−0.949240	−	0.314552i	$-0.898146\pi$
$373$	−278.642	−	482.623i	−0.747030	−	1.29389i	0.202210	−	0.979342i	$-0.435188\pi$
$374$	209.861	−	121.163i	0.561126	−	0.323966i
$375$		0			0
$376$	−389.276	+	674.246i	−1.03531	+	1.79321i
$377$		−	441.396i		−	1.17081i
$378$		0			0
$379$	147.404			0.388928			0.194464	−	0.980910i	$-0.437703\pi$
$379$	147.404			0.388928			0.194464	+	0.980910i	$0.437703\pi$
$380$	114.202	+	65.9346i	0.300532	+	0.173512i
$381$		0			0
$382$	182.627	+	316.319i	0.478081	+	0.828061i
$383$	−637.931	+	368.310i	−1.66562	+	0.961644i	−0.695657	+	0.718374i	$0.744887\pi$
$383$	−637.931	+	368.310i	−1.66562	+	0.961644i	−0.969959	+	0.243270i	$0.921780\pi$
$384$		0			0
$385$	43.4605	−	75.2758i	0.112884	−	0.195522i
$386$		−	225.933i		−	0.585319i
$387$		0			0
$388$	10.0612			0.0259310
$389$	256.697	+	148.204i	0.659889	+	0.380987i	0.792235	−	0.610216i	$-0.208918\pi$
$389$	256.697	+	148.204i	0.659889	+	0.380987i	−0.132345	+	0.991204i	$0.542251\pi$
$390$		0			0
$391$	73.6313	+	127.533i	0.188315	+	0.326172i
$392$	−38.6841	+	22.3343i	−0.0986839	+	0.0569752i
$393$		0			0
$394$	−45.4078	+	78.6487i	−0.115248	+	0.199616i
$395$		−	215.153i		−	0.544690i
$396$		0			0
$397$	−457.057			−1.15128			−0.575638	−	0.817704i	$-0.695246\pi$
$397$	−457.057			−1.15128			−0.575638	+	0.817704i	$0.695246\pi$
$398$	494.705	+	285.618i	1.24298	+	0.717634i
$399$		0			0
$400$	84.1228	+	145.705i	0.210307	+	0.364262i
$401$	−338.738	+	195.571i	−0.844734	+	0.487707i	−0.858871	−	0.512193i	$-0.828833\pi$
$401$	−338.738	+	195.571i	−0.844734	+	0.487707i	0.0141366	+	0.999900i	$0.495500\pi$
$402$		0			0
$403$	285.864	−	495.131i	0.709340	−	1.22861i
$404$			1587.81i			3.93022i
$405$		0			0
$406$	1176.18			2.89700
$407$	−312.380	−	180.352i	−0.767518	−	0.443127i
$408$		0			0
$409$	205.921	+	356.666i	0.503474	+	0.872043i	0.999992	+	0.00401646i	$0.00127848\pi$
$409$	205.921	+	356.666i	0.503474	+	0.872043i	−0.496518	+	0.868027i	$0.665388\pi$
$410$	−116.453	+	67.2340i	−0.284031	+	0.163985i
$411$		0			0
$412$	−598.919	+	1037.36i	−1.45369	+	2.51786i
$413$			180.145i			0.436186i
$414$		0			0
$415$	176.921			0.426316
$416$	−383.077	−	221.169i	−0.920857	−	0.531657i
$417$		0			0
$418$	62.6491	+	108.511i	0.149878	+	0.259597i
$419$	565.902	−	326.724i	1.35060	−	0.779770i	0.362267	−	0.932074i	$-0.382003\pi$
$419$	565.902	−	326.724i	1.35060	−	0.779770i	0.988334	+	0.152304i	$0.0486694\pi$
$420$		0			0
$421$	−62.5174	+	108.283i	−0.148497	+	0.257205i	−0.930672	−	0.365854i	$-0.880777\pi$
$421$	−62.5174	+	108.283i	−0.148497	+	0.257205i	0.782175	+	0.623059i	$0.214110\pi$
$422$			867.998i			2.05687i
$423$		0			0
$424$	257.026			0.606194
$425$	−52.9648	−	30.5792i	−0.124623	−	0.0719511i
$426$		0			0
$427$	127.759	+	221.285i	0.299201	+	0.518231i
$428$	−616.691	+	356.047i	−1.44087	+	0.831885i
$429$		0			0
$430$	−178.031	+	308.358i	−0.414025	+	0.717112i
$431$			397.208i			0.921596i	0.887505	+	0.460798i	$0.152437\pi$
$431$			397.208i			0.921596i	−0.887505	+	0.460798i	$0.847563\pi$
$432$		0			0
$433$	560.114			1.29357			0.646783	−	0.762674i	$-0.276114\pi$
$433$	560.114			1.29357			0.646783	+	0.762674i	$0.276114\pi$
$434$	1319.37	+	761.740i	3.04003	+	1.75516i
$435$		0			0
$436$	−60.9779	−	105.617i	−0.139858	−	0.242241i
$437$	−65.9427	+	38.0720i	−0.150899	+	0.0871214i
$438$		0			0
$439$	332.193	−	575.375i	0.756704	−	1.31065i	−0.187819	−	0.982204i	$-0.560142\pi$
$439$	332.193	−	575.375i	0.756704	−	1.31065i	0.944523	−	0.328446i	$-0.106525\pi$
$440$			235.876i			0.536081i
$441$		0			0
$442$	438.070			0.991108
$443$	−321.560	−	185.653i	−0.725868	−	0.419080i	0.0910405	−	0.995847i	$-0.470981\pi$
$443$	−321.560	−	185.653i	−0.725868	−	0.419080i	−0.816909	+	0.576767i	$0.804314\pi$
$444$		0			0
$445$	−120.125	−	208.062i	−0.269944	−	0.467556i
$446$	−576.301	+	332.728i	−1.29216	+	0.746026i
$447$		0			0
$448$	107.340	−	185.918i	0.239598	−	0.414996i
$449$		−	585.471i		−	1.30395i	−0.758243	−	0.651973i	$-0.773942\pi$
$449$		−	585.471i		−	1.30395i	0.758243	−	0.651973i	$-0.226058\pi$
$450$		0			0
$451$	−89.4121			−0.198253
$452$	−167.296	−	96.5883i	−0.370123	−	0.213691i
$453$		0			0
$454$	−741.149	−	1283.71i	−1.63249	−	2.82755i
$455$	136.081	−	78.5664i	0.299079	−	0.172673i
$456$		0			0
$457$	−84.3203	+	146.047i	−0.184508	+	0.319578i	−0.943411	−	0.331627i	$-0.892403\pi$
$457$	−84.3203	+	146.047i	−0.184508	+	0.319578i	0.758902	+	0.651204i	$0.225736\pi$
$458$		−	99.6462i		−	0.217568i
$459$		0			0
$460$	−251.026			−0.545709
$461$	−258.501	−	149.246i	−0.560741	−	0.323744i	0.192702	−	0.981257i	$-0.438275\pi$
$461$	−258.501	−	149.246i	−0.560741	−	0.323744i	−0.753443	+	0.657514i	$0.771608\pi$
$462$		0			0
$463$	297.642	+	515.532i	0.642856	+	1.11346i	0.984792	+	0.173736i	$0.0555840\pi$
$463$	297.642	+	515.532i	0.642856	+	1.11346i	−0.341936	+	0.939723i	$0.611083\pi$
$464$	−1311.00	+	756.905i	−2.82543	+	1.63126i
$465$		0			0
$466$	650.447	−	1126.61i	1.39581	−	2.41761i
$467$			623.655i			1.33545i	0.744408	+	0.667725i	$0.232732\pi$
$467$			623.655i			1.33545i	−0.744408	+	0.667725i	$0.767268\pi$
$468$		0			0
$469$	191.246			0.407773
$470$	283.152	+	163.478i	0.602452	+	0.347826i
$471$		0			0
$472$	−244.427	−	423.361i	−0.517855	−	0.896951i
$473$	−205.037	+	118.378i	−0.433482	+	0.250271i
$474$		0			0
$475$	15.8114	−	27.3861i	0.0332871	−	0.0576550i
$476$			816.894i			1.71616i
$477$		0			0
$478$	−991.745			−2.07478
$479$	114.192	+	65.9285i	0.238396	+	0.137638i	0.614439	−	0.788964i	$-0.289382\pi$
$479$	114.192	+	65.9285i	0.238396	+	0.137638i	−0.376043	+	0.926602i	$0.622716\pi$
$480$		0			0
$481$	−326.035	−	564.709i	−0.677827	−	1.17403i
$482$	−709.503	+	409.632i	−1.47200	+	0.849858i
$483$		0			0
$484$	426.802	−	739.244i	0.881823	−	1.52736i
$485$		−	2.41272i		−	0.00497468i
$486$		0			0
$487$	41.8028			0.0858375			0.0429187	−	0.999079i	$-0.486334\pi$
$487$	41.8028			0.0858375			0.0429187	+	0.999079i	$0.486334\pi$
$488$	−600.495	−	346.696i	−1.23052	−	0.710443i
$489$		0			0
$490$	9.37936	+	16.2455i	0.0191416	+	0.0331541i
$491$	−154.860	+	89.4085i	−0.315397	+	0.182095i	−0.649339	−	0.760499i	$-0.724954\pi$
$491$	−154.860	+	89.4085i	−0.315397	+	0.182095i	0.333942	+	0.942594i	$0.391621\pi$
$492$		0			0
$493$	275.140	−	476.557i	0.558094	−	0.966647i
$494$			226.510i			0.458522i
$495$		0			0
$496$	−1960.80			−3.95322
$497$	−575.179	−	332.079i	−1.15730	−	0.668168i
$498$		0			0
$499$	19.5480	+	33.8582i	0.0391744	+	0.0678521i	0.884948	−	0.465690i	$-0.154194\pi$
$499$	19.5480	+	33.8582i	0.0391744	+	0.0678521i	−0.845773	+	0.533542i	$0.820861\pi$
$500$	90.2846	−	52.1258i	0.180569	−	0.104252i
$501$		0			0
$502$	581.809	−	1007.72i	1.15898	−	2.00742i
$503$			578.698i			1.15049i	0.817980	+	0.575247i	$0.195094\pi$
$503$			578.698i			1.15049i	−0.817980	+	0.575247i	$0.804906\pi$
$504$		0			0
$505$	380.763			0.753986
$506$	−206.563	−	119.259i	−0.408226	−	0.235690i
$507$		0			0
$508$	−177.309	−	307.109i	−0.349034	−	0.604545i
$509$	308.082	−	177.871i	0.605270	−	0.349453i	−0.165842	−	0.986152i	$-0.553034\pi$
$509$	308.082	−	177.871i	0.605270	−	0.349453i	0.771112	+	0.636700i	$0.219701\pi$
$510$		0			0
$511$	−216.031	+	374.176i	−0.422760	+	0.732243i
$512$		−	1098.99i		−	2.14646i
$513$		0			0
$514$	1357.81			2.64166
$515$	248.763	+	143.623i	0.483034	+	0.278880i
$516$		0			0
$517$	108.702	+	188.277i	0.210255	+	0.364172i
$518$	1504.78	−	868.783i	2.90497	−	1.67719i
$519$		0			0
$520$	−213.204	+	369.280i	−0.410008	+	0.710154i
$521$		−	810.952i		−	1.55653i	−0.627936	−	0.778265i	$-0.716100\pi$
$521$		−	810.952i		−	1.55653i	0.627936	−	0.778265i	$-0.283900\pi$
$522$		0			0
$523$	720.483			1.37760			0.688798	−	0.724953i	$-0.258139\pi$
$523$	720.483			1.37760			0.688798	+	0.724953i	$0.258139\pi$
$524$	−677.848	−	391.356i	−1.29360	−	0.746862i
$525$		0			0
$526$	−435.386	−	754.110i	−0.827730	−	1.43367i
$527$	617.271	−	356.382i	1.17129	−	0.676246i
$528$		0			0
$529$	−192.026	+	332.599i	−0.362998	+	0.628731i
$530$		−	107.939i		−	0.203659i
$531$		0			0
$532$	−422.386			−0.793958
$533$	−139.981	−	80.8180i	−0.262628	−	0.151629i
$534$		0			0
$535$	85.3815	+	147.885i	0.159592	+	0.276421i
$536$	−449.449	+	259.490i	−0.838524	+	0.484122i
$537$		0			0
$538$	−229.732	+	397.908i	−0.427012	+	0.739606i
$539$			12.4733i			0.0231415i
$540$		0			0
$541$	347.149			0.641680			0.320840	−	0.947133i	$-0.396035\pi$
$541$	347.149			0.641680			0.320840	+	0.947133i	$0.396035\pi$
$542$	817.651	+	472.071i	1.50858	+	0.870980i
$543$		0			0
$544$	−275.728	−	477.575i	−0.506853	−	0.877895i
$545$	−25.3274	+	14.6228i	−0.0464723	+	0.0268308i
$546$		0			0
$547$	360.416	−	624.259i	0.658896	−	1.14124i	−0.322005	−	0.946738i	$-0.604357\pi$
$547$	360.416	−	624.259i	0.658896	−	1.14124i	0.980902	−	0.194504i	$-0.0623098\pi$
$548$		−	145.403i		−	0.265334i
$549$		0			0
$550$	99.0569			0.180104
$551$	246.410	+	142.265i	0.447205	+	0.258194i
$552$		0			0
$553$	344.574	+	596.820i	0.623100	+	1.07924i
$554$	719.860	−	415.611i	1.29939	−	0.750201i
$555$		0			0
$556$	316.298	−	547.845i	0.568882	−	0.985332i
$557$		−	429.102i		−	0.770380i	−0.922837	−	0.385190i	$-0.874136\pi$
$557$		−	429.102i		−	0.770380i	0.922837	−	0.385190i	$-0.125864\pi$
$558$		0			0
$559$	−428.000			−0.765653
$560$	−466.703	−	269.451i	−0.833398	−	0.481162i
$561$		0			0
$562$	440.559	+	763.071i	0.783913	+	1.35778i
$563$	−580.948	+	335.410i	−1.03188	+	0.595755i	−0.917522	−	0.397685i	$-0.869814\pi$
$563$	−580.948	+	335.410i	−1.03188	+	0.595755i	−0.114356	+	0.993440i	$0.536480\pi$
$564$		0			0
$565$	−23.1623	+	40.1182i	−0.0409952	+	0.0710057i
$566$			760.474i			1.34359i
$567$		0			0
$568$	1802.31			3.17309
$569$	−319.271	−	184.331i	−0.561110	−	0.323957i	0.192481	−	0.981301i	$-0.438347\pi$
$569$	−319.271	−	184.331i	−0.561110	−	0.323957i	−0.753591	+	0.657344i	$0.771680\pi$
$570$		0			0
$571$	−62.1445	−	107.637i	−0.108834	−	0.188507i	0.806464	−	0.591283i	$-0.201379\pi$
$571$	−62.1445	−	107.637i	−0.108834	−	0.188507i	−0.915298	+	0.402777i	$0.868045\pi$
$572$	−430.009	+	248.266i	−0.751764	+	0.434031i
$573$		0			0
$574$	215.355	−	373.006i	0.375183	−	0.649836i
$575$			60.1972i			0.104691i
$576$		0			0
$577$	504.236			0.873893			0.436947	−	0.899487i	$-0.356060\pi$
$577$	504.236			0.873893			0.436947	+	0.899487i	$0.356060\pi$
$578$	−440.631	−	254.399i	−0.762338	−	0.440136i
$579$		0			0
$580$	469.009	+	812.347i	0.808635	+	1.40060i
$581$	−490.768	+	283.345i	−0.844695	+	0.487685i
$582$		0			0
$583$	35.8861	−	62.1566i	0.0615542	−	0.106615i
$584$		−	1172.48i		−	2.00766i
$585$		0			0
$586$	−736.236			−1.25638
$587$	−33.9703	−	19.6128i	−0.0578711	−	0.0334119i	0.470785	−	0.882248i	$-0.343971\pi$
$587$	−33.9703	−	19.6128i	−0.0578711	−	0.0334119i	−0.528656	+	0.848836i	$0.677304\pi$
$588$		0			0
$589$	184.272	+	319.168i	0.312855	+	0.541882i
$590$	−177.792	+	102.648i	−0.301342	+	0.173980i
$591$		0			0
$592$	−1118.17	+	1936.72i	−1.88880	+	3.27149i
$593$		−	621.670i		−	1.04835i	−0.851611	−	0.524174i	$-0.824374\pi$
$593$		−	621.670i		−	1.04835i	0.851611	−	0.524174i	$-0.175626\pi$
$594$		0			0
$595$	195.895			0.329235
$596$	1884.98	+	1088.30i	3.16272	+	1.82600i
$597$		0			0
$598$	−215.592	−	373.417i	−0.360522	−	0.624442i
$599$	−969.750	+	559.886i	−1.61895	+	0.934701i	−0.631756	+	0.775167i	$0.717666\pi$
$599$	−969.750	+	559.886i	−1.61895	+	0.934701i	−0.987193	+	0.159534i	$0.949001\pi$
$600$		0			0
$601$	161.895	−	280.410i	0.269375	−	0.466572i	−0.699325	−	0.714804i	$-0.746516\pi$
$601$	161.895	−	280.410i	0.269375	−	0.466572i	0.968701	+	0.248232i	$0.0798494\pi$
$602$		−	1140.49i		−	1.89450i
$603$		0			0
$604$	−1728.31			−2.86145
$605$	−177.274	−	102.349i	−0.293014	−	0.169172i
$606$		0			0
$607$	−512.813	−	888.218i	−0.844832	−	1.46329i	−0.885767	−	0.464131i	$-0.846367\pi$
$607$	−512.813	−	888.218i	−0.844832	−	1.46329i	0.0409345	−	0.999162i	$-0.486966\pi$
$608$	246.936	−	142.569i	0.406145	−	0.234488i
$609$		0			0
$610$	−145.596	+	252.180i	−0.238683	+	0.413411i
$611$			393.014i			0.643232i
$612$		0			0
$613$	904.153			1.47496			0.737482	−	0.675367i	$-0.236015\pi$
$613$	904.153			1.47496			0.737482	+	0.675367i	$0.236015\pi$
$614$	−1083.75	−	625.702i	−1.76506	−	1.01906i
$615$		0			0
$616$	−377.763	−	654.305i	−0.613252	−	1.06218i
$617$	615.498	−	355.358i	0.997566	−	0.575945i	0.0900390	−	0.995938i	$-0.471301\pi$
$617$	615.498	−	355.358i	0.997566	−	0.575945i	0.907527	+	0.419993i	$0.137968\pi$
$618$		0			0
$619$	291.868	−	505.531i	0.471516	−	0.816689i	−0.527953	−	0.849274i	$-0.677040\pi$
$619$	291.868	−	505.531i	0.471516	−	0.816689i	0.999469	+	0.0325841i	$0.0103737\pi$
$620$			1214.99i			1.95966i
$621$		0			0
$622$	−794.447			−1.27725
$623$	666.438	+	384.768i	1.06972	+	0.617606i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	891.136	−	514.497i	1.42354	−	0.821881i
$627$		0			0
$628$	−518.800	+	898.589i	−0.826115	+	1.43087i
$629$		−	812.924i		−	1.29241i
$630$		0			0
$631$	−20.0968			−0.0318491			−0.0159246	−	0.999873i	$-0.505069\pi$
$631$	−20.0968			−0.0318491			−0.0159246	+	0.999873i	$0.505069\pi$
$632$	−1619.58	−	935.064i	−2.56263	−	1.47953i
$633$		0			0
$634$	−28.1096	−	48.6873i	−0.0443369	−	0.0767938i
$635$	−73.6460	+	42.5195i	−0.115978	+	0.0669599i
$636$		0			0
$637$	−11.2744	+	19.5278i	−0.0176992	+	0.0306559i
$638$			891.277i			1.39699i
$639$		0			0
$640$	−158.592			−0.247800
$641$	295.840	+	170.803i	0.461529	+	0.266464i	0.712687	−	0.701482i	$-0.247478\pi$
$641$	295.840	+	170.803i	0.461529	+	0.266464i	−0.251158	+	0.967946i	$0.580811\pi$
$642$		0			0
$643$	234.846	+	406.766i	0.365235	+	0.632606i	0.988814	−	0.149155i	$-0.0476552\pi$
$643$	234.846	+	406.766i	0.365235	+	0.632606i	−0.623579	+	0.781761i	$0.714322\pi$
$644$	696.332	−	402.027i	1.08126	−	0.624266i
$645$		0			0
$646$	−141.193	+	244.553i	−0.218565	+	0.378565i
$647$			572.099i			0.884234i	0.896957	+	0.442117i	$0.145772\pi$
$647$			572.099i			0.884234i	−0.896957	+	0.442117i	$0.854228\pi$
$648$		0			0
$649$	−136.508			−0.210336
$650$	155.081	+	89.5358i	0.238586	+	0.137747i
$651$		0			0
$652$	553.706	+	959.047i	0.849242	+	1.47093i
$653$	−184.931	+	106.770i	−0.283203	+	0.163507i	−0.634872	−	0.772617i	$-0.718947\pi$
$653$	−184.931	+	106.770i	−0.283203	+	0.163507i	0.351670	+	0.936124i	$0.385614\pi$
$654$		0			0
$655$	−93.8488	+	162.551i	−0.143281	+	0.248169i
$656$			554.347i			0.845040i
$657$		0			0
$658$	−1047.26			−1.59158
$659$	−364.582	−	210.491i	−0.553235	−	0.319410i	0.197191	−	0.980365i	$-0.436818\pi$
$659$	−364.582	−	210.491i	−0.553235	−	0.319410i	−0.750426	+	0.660955i	$0.770151\pi$
$660$		0			0
$661$	−217.136	−	376.090i	−0.328496	−	0.568972i	0.653718	−	0.756739i	$-0.273208\pi$
$661$	−217.136	−	376.090i	−0.328496	−	0.568972i	−0.982214	+	0.187767i	$0.939875\pi$
$662$	1187.10	−	685.372i	1.79320	−	1.03531i
$663$		0			0
$664$	768.907	−	1331.79i	1.15799	−	2.00570i
$665$			101.290i			0.152316i
$666$		0			0
$667$	−541.631			−0.812041
$668$	1786.21	+	1031.27i	2.67397	+	1.54381i
$669$		0			0
$670$	108.974	+	188.748i	0.162647	+	0.281713i
$671$	−167.683	+	96.8117i	−0.249900	+	0.144280i
$672$		0			0
$673$	−36.3900	+	63.0294i	−0.0540714	+	0.0936544i	−0.891794	−	0.452441i	$-0.850553\pi$
$673$	−36.3900	+	63.0294i	−0.0540714	+	0.0936544i	0.837723	+	0.546096i	$0.183887\pi$
$674$			686.669i			1.01880i
$675$		0			0
$676$	678.237			1.00331
$677$	149.048	+	86.0531i	0.220160	+	0.127109i	0.606024	−	0.795446i	$-0.292763\pi$
$677$	149.048	+	86.0531i	0.220160	+	0.127109i	−0.385864	+	0.922556i	$0.626097\pi$
$678$		0			0
$679$	3.86406	+	6.69274i	0.00569080	+	0.00985676i
$680$	−460.375	+	265.798i	−0.677022	+	0.390879i
$681$		0			0
$682$	−577.223	+	999.780i	−0.846369	+	1.46595i
$683$			792.592i			1.16046i	0.814454	+	0.580228i	$0.197037\pi$
$683$			792.592i			1.16046i	−0.814454	+	0.580228i	$0.802963\pi$
$684$		0			0
$685$	−34.8683			−0.0509027
$686$	1057.41	+	610.493i	1.54141	+	0.889932i
$687$		0			0
$688$	733.934	+	1271.21i	1.06676	+	1.84769i
$689$	112.364	−	64.8737i	0.163083	−	0.0941563i
$690$		0			0
$691$	−77.4256	+	134.105i	−0.112049	+	0.194074i	−0.916596	−	0.399814i	$-0.869075\pi$
$691$	−77.4256	+	134.105i	−0.112049	+	0.194074i	0.804547	+	0.593888i	$0.202408\pi$
$692$		−	1779.19i		−	2.57109i
$693$		0			0
$694$	1875.49			2.70244
$695$	−131.375	−	75.8497i	−0.189029	−	0.109136i
$696$		0			0
$697$	−100.754	−	174.512i	−0.144554	−	0.250376i
$698$	355.750	−	205.393i	0.509671	−	0.294259i
$699$		0			0
$700$	−166.963	+	289.188i	−0.238518	+	0.413125i
$701$			950.544i			1.35598i	0.735070	+	0.677991i	$0.237149\pi$
$701$			950.544i			1.35598i	−0.735070	+	0.677991i	$0.762851\pi$
$702$		0			0
$703$	420.333			0.597913
$704$	140.883	+	81.3389i	0.200118	+	0.115538i
$705$		0			0
$706$	781.473	+	1353.55i	1.10690	+	1.91721i
$707$	−1056.21	+	609.805i	−1.49394	+	0.862525i
$708$		0			0
$709$	−195.175	+	338.053i	−0.275282	+	0.476803i	−0.970206	−	0.242280i	$-0.922105\pi$
$709$	−195.175	+	338.053i	−0.275282	+	0.476803i	0.694924	+	0.719083i	$0.255438\pi$
$710$		−	756.889i		−	1.06604i
$711$		0			0
$712$	−2088.28			−2.93297
$713$	−607.569	−	350.780i	−0.852131	−	0.491978i
$714$		0			0
$715$	59.5352	+	103.118i	0.0832661	+	0.144221i
$716$	469.179	−	270.881i	0.655278	−	0.378325i
$717$		0			0
$718$	102.566	−	177.649i	0.142849	−	0.247422i
$719$		−	655.227i		−	0.911303i	−0.890158	−	0.455651i	$-0.849406\pi$
$719$		−	655.227i		−	0.911303i	0.890158	−	0.455651i	$-0.150594\pi$
$720$		0			0
$721$	−920.070			−1.27610
$722$	1014.76	+	585.870i	1.40548	+	0.811455i
$723$		0			0
$724$	−759.583	−	1315.64i	−1.04915	−	1.81718i
$725$	194.804	−	112.470i	0.268695	−	0.155131i
$726$		0			0
$727$	−712.125	+	1233.44i	−0.979539	+	1.69661i	−0.315478	+	0.948933i	$0.602165\pi$
$727$	−712.125	+	1233.44i	−0.979539	+	1.69661i	−0.664061	+	0.747679i	$0.731168\pi$
$728$		−	1365.81i		−	1.87612i
$729$		0			0
$730$	−492.386			−0.674501
$731$	−462.094	−	266.790i	−0.632140	−	0.364966i
$732$		0			0
$733$	473.375	+	819.909i	0.645805	+	1.11857i	0.984115	+	0.177532i	$0.0568113\pi$
$733$	473.375	+	819.909i	0.645805	+	1.11857i	−0.338311	+	0.941035i	$0.609855\pi$
$734$	−487.980	+	281.735i	−0.664823	+	0.383836i
$735$		0			0
$736$	−271.394	+	470.069i	−0.368742	+	0.638680i
$737$			144.920i			0.196635i
$738$		0			0
$739$	591.429			0.800310			0.400155	−	0.916447i	$-0.368956\pi$
$739$	591.429			0.800310			0.400155	+	0.916447i	$0.368956\pi$
$740$	1200.07	+	692.862i	1.62172	+	0.936300i
$741$		0			0
$742$	172.868	+	299.417i	0.232976	+	0.403527i
$743$	634.106	−	366.101i	0.853440	−	0.492734i	−0.00837016	−	0.999965i	$-0.502664\pi$
$743$	634.106	−	366.101i	0.853440	−	0.492734i	0.861810	+	0.507231i	$0.169331\pi$
$744$		0			0
$745$	260.978	−	452.027i	0.350306	−	0.606748i
$746$			2034.25i			2.72687i
$747$		0			0
$748$	−619.018			−0.827564
$749$	−473.686	−	273.483i	−0.632425	−	0.365130i
$750$		0			0
$751$	107.680	+	186.507i	0.143382	+	0.248345i	0.928768	−	0.370661i	$-0.120869\pi$
$751$	107.680	+	186.507i	0.143382	+	0.248345i	−0.785386	+	0.619006i	$0.787536\pi$
$752$	1167.30	−	673.941i	1.55226	−	0.896198i
$753$		0			0
$754$	−805.609	+	1395.36i	−1.06845	+	1.85061i
$755$			414.457i			0.548950i
$756$		0			0
$757$	276.258			0.364938			0.182469	−	0.983212i	$-0.441591\pi$
$757$	276.258			0.364938			0.182469	+	0.983212i	$0.441591\pi$
$758$	−465.978	−	269.032i	−0.614746	−	0.354924i
$759$		0			0
$760$	−137.434	−	238.043i	−0.180834	−	0.313214i
$761$	773.684	−	446.687i	1.01667	−	0.586973i	0.103531	−	0.994626i	$-0.466986\pi$
$761$	773.684	−	446.687i	1.01667	−	0.586973i	0.913137	+	0.407653i	$0.133653\pi$
$762$		0			0
$763$	46.8377	−	81.1253i	0.0613863	−	0.106324i
$764$		−	933.033i		−	1.22125i
$765$		0			0
$766$	2688.87			3.51027
$767$	−213.713	−	123.387i	−0.278635	−	0.160870i
$768$		0			0
$769$	−142.158	−	246.225i	−0.184861	−	0.320188i	0.758669	−	0.651477i	$-0.225850\pi$
$769$	−142.158	−	246.225i	−0.184861	−	0.320188i	−0.943530	+	0.331288i	$0.892517\pi$
$770$	−274.778	+	158.643i	−0.356854	+	0.206030i
$771$		0			0
$772$	−288.570	+	499.818i	−0.373795	+	0.647433i
$773$		−	1059.64i		−	1.37081i	−0.728162	−	0.685405i	$-0.759625\pi$
$773$		−	1059.64i		−	1.37081i	0.728162	−	0.685405i	$-0.240375\pi$
$774$		0			0
$775$	291.359			0.375948
$776$	−18.1620	−	10.4858i	−0.0234046	−	0.0135126i
$777$		0			0
$778$	−540.986	−	937.016i	−0.695355	−	1.20439i
$779$	90.2336	−	52.0964i	0.115833	−	0.0668760i
$780$		0			0
$781$	251.640	−	435.853i	0.322202	−	0.558070i
$782$		−	537.550i		−	0.687404i
$783$		0			0
$784$	77.3331			0.0986392
$785$	215.485	+	124.411i	0.274504	+	0.158485i
$786$		0			0
$787$	437.759	+	758.220i	0.556237	+	0.963431i	0.997806	+	0.0662038i	$0.0210888\pi$
$787$	437.759	+	758.220i	0.556237	+	0.963431i	−0.441569	+	0.897227i	$0.645578\pi$
$788$	200.906	−	115.993i	0.254957	−	0.147199i
$789$		0			0
$790$	−392.684	+	680.149i	−0.497068	+	0.860948i
$791$		−	148.381i		−	0.187586i
$792$		0			0
$793$	−350.026			−0.441394
$794$	1444.87	+	834.193i	1.81973	+	1.05062i
$795$		0			0
$796$	−729.605	−	1263.71i	−0.916589	−	1.58758i
$797$	642.980	−	371.225i	0.806750	−	0.465777i	−0.0390760	−	0.999236i	$-0.512441\pi$
$797$	642.980	−	371.225i	0.806750	−	0.465777i	0.845826	+	0.533459i	$0.179108\pi$
$798$		0			0
$799$	−244.982	+	424.322i	−0.306611	+	0.531066i
$800$		−	225.421i		−	0.281776i
$801$		0			0
$802$	1427.78			1.78027
$803$	−283.539	−	163.702i	−0.353100	−	0.203862i
$804$		0			0
$805$	−96.4078	−	166.983i	−0.119761	−	0.207433i
$806$	−1807.37	+	1043.48i	−2.24239	+	1.29465i
$807$		0			0
$808$	1654.81	−	2866.22i	2.04804	−	3.54731i
$809$			113.720i			0.140568i	0.997527	+	0.0702842i	$0.0223906\pi$
$809$			113.720i			0.140568i	−0.997527	+	0.0702842i	$0.977609\pi$
$810$		0			0
$811$	−1466.03			−1.80769			−0.903844	−	0.427863i	$-0.859267\pi$
$811$	−1466.03			−1.80769			−0.903844	+	0.427863i	$0.859267\pi$
$812$	−2602.00	−	1502.27i	−3.20444	−	1.85008i
$813$		0			0
$814$	658.337	+	1140.27i	0.808768	+	1.40083i
$815$	229.984	−	132.781i	0.282188	−	0.162922i
$816$		0			0
$817$	137.947	−	238.932i	0.168846	−	0.292450i
$818$		−	1503.34i		−	1.83782i
$819$		0			0
$820$	343.495			0.418897
$821$	−476.377	−	275.036i	−0.580240	−	0.335002i	0.180989	−	0.983485i	$-0.442070\pi$
$821$	−476.377	−	275.036i	−0.580240	−	0.335002i	−0.761229	+	0.648483i	$0.775404\pi$
$822$		0			0
$823$	−696.256	−	1205.95i	−0.845997	−	1.46531i	−0.884752	−	0.466062i	$-0.845672\pi$
$823$	−696.256	−	1205.95i	−0.845997	−	1.46531i	0.0387547	−	0.999249i	$-0.487661\pi$
$824$	2162.27	−	1248.39i	2.62411	−	1.51503i
$825$		0			0
$826$	328.789	−	569.480i	0.398050	−	0.689443i
$827$		−	955.922i		−	1.15589i	−0.816075	−	0.577945i	$-0.803855\pi$
$827$		−	955.922i		−	1.15589i	0.816075	−	0.577945i	$-0.196145\pi$
$828$		0			0
$829$	−1652.69			−1.99360			−0.996798	−	0.0799552i	$-0.974522\pi$
$829$	−1652.69			−1.99360			−0.996798	+	0.0799552i	$0.974522\pi$
$830$	−559.289	−	322.906i	−0.673842	−	0.389043i
$831$		0			0
$832$	147.042	+	254.684i	0.176733	+	0.306110i
$833$	−24.3450	+	14.0556i	−0.0292256	+	0.0168734i
$834$		0			0
$835$	247.302	−	428.340i	0.296171	−	0.512983i
$836$		−	320.071i		−	0.382860i
$837$		0			0
$838$	−2385.27			−2.84638
$839$	1358.03	+	784.057i	1.61863	+	0.934514i	0.987276	+	0.159015i	$0.0508319\pi$
$839$	1358.03	+	784.057i	1.61863	+	0.934514i	0.631349	+	0.775499i	$0.282501\pi$
$840$		0			0
$841$	591.464	+	1024.45i	0.703287	+	1.21813i
$842$	395.265	−	228.206i	0.469436	−	0.271029i
$843$		0			0
$844$	1108.64	−	1920.22i	1.31355	−	2.27514i
$845$		−	162.644i		−	0.192478i
$846$		0			0
$847$	655.662			0.774099
$848$	−385.365	−	222.491i	−0.454440	−	0.262371i
$849$		0			0
$850$	111.623	+	193.336i	0.131321	+	0.227454i
$851$	−692.948	+	400.073i	−0.814274	+	0.470122i
$852$		0			0
$853$	325.616	−	563.983i	0.381730	−	0.661176i	−0.609579	−	0.792725i	$-0.708662\pi$
$853$	325.616	−	563.983i	0.381730	−	0.661176i	0.991310	+	0.131549i	$0.0419950\pi$
$854$		−	932.711i		−	1.09217i
$855$		0			0
$856$	1484.29			1.73398
$857$	259.055	+	149.565i	0.302281	+	0.174522i	0.643467	−	0.765474i	$-0.277495\pi$
$857$	259.055	+	149.565i	0.302281	+	0.174522i	−0.341186	+	0.939996i	$0.610829\pi$
$858$		0			0
$859$	−547.860	−	948.921i	−0.637788	−	1.10468i	−0.985917	−	0.167234i	$-0.946516\pi$
$859$	−547.860	−	948.921i	−0.637788	−	1.10468i	0.348129	−	0.937447i	$-0.386817\pi$
$860$	787.693	−	454.775i	0.915922	−	0.528808i
$861$		0			0
$862$	724.960	−	1255.67i	0.841021	−	1.45669i
$863$		−	1221.95i		−	1.41593i	−0.706247	−	0.707965i	$-0.749613\pi$
$863$		−	1221.95i		−	1.41593i	0.706247	−	0.707965i	$-0.250387\pi$
$864$		0			0
$865$	−426.658			−0.493246
$866$	−1770.65	−	1022.29i	−2.04463	−	1.18047i
$867$		0			0
$868$	−1945.85	−	3370.30i	−2.24176	−	3.88284i
$869$	−452.253	+	261.108i	−0.520429	+	0.300470i
$870$		0			0
$871$	−130.991	+	226.883i	−0.150391	+	0.260485i
$872$			254.205i			0.291520i
$873$		0			0
$874$	277.947			0.318018
$875$	69.3485	+	40.0383i	0.0792554	+	0.0457581i
$876$		0			0
$877$	−383.200	−	663.721i	−0.436944	−	0.756809i	0.560508	−	0.828149i	$-0.310606\pi$
$877$	−383.200	−	663.721i	−0.436944	−	0.756809i	−0.997452	+	0.0713401i	$0.977272\pi$
$878$	−2100.28	+	1212.60i	−2.39212	+	1.38109i
$879$		0			0
$880$	204.182	−	353.653i	0.232025	−	0.401879i
$881$			310.097i			0.351983i	0.984392	+	0.175992i	$0.0563132\pi$
$881$			310.097i			0.351983i	−0.984392	+	0.175992i	$0.943687\pi$
$882$		0			0
$883$	−122.236			−0.138433			−0.0692165	−	0.997602i	$-0.522050\pi$
$883$	−122.236			−0.138433			−0.0692165	+	0.997602i	$0.522050\pi$
$884$	−969.116	−	559.519i	−1.09628	−	0.632940i
$885$		0			0
$886$	677.684	+	1173.78i	0.764880	+	1.32481i
$887$	−229.882	+	132.722i	−0.259167	+	0.149630i	−0.623955	−	0.781460i	$-0.714475\pi$
$887$	−229.882	+	132.722i	−0.259167	+	0.149630i	0.364787	+	0.931091i	$0.381142\pi$
$888$		0			0
$889$	136.193	−	235.893i	0.153198	−	0.265346i
$890$			876.980i			0.985370i
$891$		0			0
$892$	1699.89			1.90571
$893$	−219.401	−	126.671i	−0.245690	−	0.141849i
$894$		0			0
$895$	−64.9584	−	112.511i	−0.0725792	−	0.125711i
$896$	439.925	−	253.991i	0.490988	−	0.283472i
$897$		0			0
$898$	−1068.57	+	1850.81i	−1.18994	+	2.06104i
$899$			2621.54i			2.91606i
$900$		0			0
$901$	161.754			0.179527
$902$	282.653	+	163.190i	0.313362	+	0.180920i
$903$		0			0
$904$	201.329	+	348.712i	0.222709	+	0.385743i
$905$	−315.495	+	182.151i	−0.348613	+	0.201272i
$906$		0			0
$907$	−336.311	+	582.508i	−0.370795	+	0.642236i	−0.989688	−	0.143240i	$-0.954248\pi$
$907$	−336.311	+	582.508i	−0.370795	+	0.642236i	0.618893	+	0.785475i	$0.287581\pi$
$908$			3786.49i			4.17015i
$909$		0			0
$910$	−573.579			−0.630306
$911$	1214.58	+	701.239i	1.33324	+	0.769746i	0.985795	−	0.167955i	$-0.0537162\pi$
$911$	1214.58	+	701.239i	1.33324	+	0.769746i	0.347444	+	0.937701i	$0.387050\pi$
$912$		0			0
$913$	−214.710	−	371.889i	−0.235170	−	0.407327i
$914$	533.113	−	307.793i	0.583274	−	0.336754i
$915$		0			0
$916$	−127.272	+	220.441i	−0.138943	+	0.240657i
$917$		−	601.208i		−	0.655625i
$918$		0			0
$919$	−338.255			−0.368068			−0.184034	−	0.982920i	$-0.558916\pi$
$919$	−338.255			−0.368068			−0.184034	+	0.982920i	$0.558916\pi$
$920$	453.139	+	261.620i	0.492542	+	0.284370i
$921$		0			0
$922$	544.789	+	943.603i	0.590878	+	1.02343i
$923$	787.920	−	454.906i	0.853651	−	0.492856i
$924$		0			0
$925$	166.151	−	287.782i	0.179623	−	0.311116i
$926$		−	2172.96i		−	2.34661i
$927$		0			0
$928$	2028.25			2.18562
$929$	128.351	+	74.1033i	0.138160	+	0.0797667i	0.567487	−	0.823383i	$-0.307916\pi$
$929$	128.351	+	74.1033i	0.138160	+	0.0797667i	−0.429327	+	0.903149i	$0.641249\pi$
$930$		0			0
$931$	−7.26761	−	12.5879i	−0.00780624	−	0.0135208i
$932$	−2877.89	+	1661.55i	−3.08787	+	1.78278i
$933$		0			0
$934$	1138.26	−	1971.52i	1.21869	−	2.11084i
$935$			148.443i			0.158763i
$936$		0			0
$937$	−1416.72			−1.51197			−0.755987	−	0.654587i	$-0.772843\pi$
$937$	−1416.72			−1.51197			−0.755987	+	0.654587i	$0.772843\pi$
$938$	−604.572	−	349.050i	−0.644534	−	0.372122i
$939$		0			0
$940$	−417.601	−	723.306i	−0.444256	−	0.769474i
$941$	1211.50	−	699.461i	1.28746	−	0.743317i	0.309262	−	0.950977i	$-0.399918\pi$
$941$	1211.50	−	699.461i	1.28746	−	0.743317i	0.978201	+	0.207660i	$0.0665847\pi$
$942$		0			0
$943$	−99.1708	+	171.769i	−0.105165	+	0.182152i
$944$			846.338i			0.896544i
$945$		0			0
$946$	864.228			0.913560
$947$	909.824	+	525.287i	0.960744	+	0.554686i	0.896402	−	0.443242i	$-0.146172\pi$
$947$	909.824	+	525.287i	0.960744	+	0.554686i	0.0643418	+	0.997928i	$0.479505\pi$
$948$		0			0
$949$	−295.934	−	512.572i	−0.311838	−	0.540118i
$950$	−99.9671	+	57.7160i	−0.105229	+	0.0607537i
$951$		0			0
$952$	851.368	−	1474.61i	0.894294	−	1.54896i
$953$			551.928i			0.579148i	0.957156	+	0.289574i	$0.0935136\pi$
$953$			551.928i			0.579148i	−0.957156	+	0.289574i	$0.906486\pi$
$954$		0			0
$955$	−223.745			−0.234288
$956$	2193.98	+	1266.69i	2.29496	+	1.32499i
$957$		0			0
$958$	−240.658	−	416.831i	−0.251208	−	0.435106i
$959$	96.7226	−	55.8428i	0.100858	−	0.0582303i
$960$		0			0
$961$	−1217.31	+	2108.44i	−1.26671	+	2.19400i
$962$			2380.24i			2.47426i
$963$		0			0
$964$	2092.79			2.17094
$965$	119.859	+	69.2003i	0.124206	+	0.0717102i
$966$		0			0
$967$	178.546	+	309.251i	0.184639	+	0.319805i	0.943455	−	0.331501i	$-0.107555\pi$
$967$	178.546	+	309.251i	0.184639	+	0.319805i	−0.758816	+	0.651306i	$0.774222\pi$
$968$	−1540.88	+	889.628i	−1.59182	+	0.919037i
$969$		0			0
$970$	−4.40356	+	7.62719i	−0.00453975	+	0.00786308i
$971$		−	308.206i		−	0.317411i	−0.987326	−	0.158705i	$-0.949268\pi$
$971$		−	308.206i		−	0.317411i	0.987326	−	0.158705i	$-0.0507320\pi$
$972$		0			0
$973$	485.903			0.499387
$974$	−132.149	−	76.2961i	−0.135676	−	0.0783327i
$975$		0			0
$976$	600.223	+	1039.62i	0.614983	+	1.06518i
$977$	−219.347	+	126.640i	−0.224511	+	0.129621i	−0.608037	−	0.793909i	$-0.708043\pi$
$977$	−219.347	+	126.640i	−0.224511	+	0.129621i	0.383526	+	0.923530i	$0.374710\pi$
$978$		0			0
$979$	−291.566	+	505.007i	−0.297820	+	0.515839i
$980$		−	47.9187i		−	0.0488966i
$981$		0			0
$982$	652.732			0.664697
$983$	925.551	+	534.367i	0.941558	+	0.543609i	0.890448	−	0.455084i	$-0.150391\pi$
$983$	925.551	+	534.367i	0.941558	+	0.543609i	0.0511096	+	0.998693i	$0.483724\pi$
$984$		0			0
$985$	−27.8157	−	48.1781i	−0.0282393	−	0.0489118i
$986$	−1739.57	+	1004.34i	−1.76427	+	1.01860i
$987$		0			0
$988$	289.307	−	501.094i	0.292821	−	0.507180i
$989$			525.194i			0.531035i
$990$		0			0
$991$	280.631			0.283179			0.141590	−	0.989925i	$-0.454779\pi$
$991$	280.631			0.283179			0.141590	+	0.989925i	$0.454779\pi$
$992$	2275.17	+	1313.57i	2.29352	+	1.32416i
$993$		0			0
$994$	1212.18	+	2099.56i	1.21950	+	2.11224i
$995$	−303.044	+	174.962i	−0.304567	+	0.175842i
$996$		0			0
$997$	178.287	−	308.802i	0.178824	−	0.309732i	−0.762654	−	0.646806i	$-0.776104\pi$
$997$	178.287	−	308.802i	0.178824	−	0.309732i	0.941478	+	0.337075i	$0.109438\pi$
$998$		−	142.712i		−	0.142998i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.3.i.d.26.1		8
3.2	odd	2	inner	405.3.i.d.26.4		8
9.2	odd	6		45.3.c.a.26.1	✓	4
9.4	even	3	inner	405.3.i.d.296.4		8
9.5	odd	6	inner	405.3.i.d.296.1		8
9.7	even	3		45.3.c.a.26.4	yes	4
36.7	odd	6		720.3.l.a.161.3		4
36.11	even	6		720.3.l.a.161.1		4
45.2	even	12		225.3.d.b.224.8		8
45.7	odd	12		225.3.d.b.224.2		8
45.29	odd	6		225.3.c.c.26.4		4
45.34	even	6		225.3.c.c.26.1		4
45.38	even	12		225.3.d.b.224.1		8
45.43	odd	12		225.3.d.b.224.7		8
72.11	even	6		2880.3.l.c.1601.3		4
72.29	odd	6		2880.3.l.g.1601.4		4
72.43	odd	6		2880.3.l.c.1601.1		4
72.61	even	6		2880.3.l.g.1601.2		4
180.7	even	12		3600.3.c.i.449.1		8
180.43	even	12		3600.3.c.i.449.7		8
180.47	odd	12		3600.3.c.i.449.2		8
180.79	odd	6		3600.3.l.v.1601.3		4
180.83	odd	12		3600.3.c.i.449.8		8
180.119	even	6		3600.3.l.v.1601.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.c.a.26.1	✓	4	9.2	odd	6
45.3.c.a.26.4	yes	4	9.7	even	3
225.3.c.c.26.1		4	45.34	even	6
225.3.c.c.26.4		4	45.29	odd	6
225.3.d.b.224.1		8	45.38	even	12
225.3.d.b.224.2		8	45.7	odd	12
225.3.d.b.224.7		8	45.43	odd	12
225.3.d.b.224.8		8	45.2	even	12
405.3.i.d.26.1		8	1.1	even	1	trivial
405.3.i.d.26.4		8	3.2	odd	2	inner
405.3.i.d.296.1		8	9.5	odd	6	inner
405.3.i.d.296.4		8	9.4	even	3	inner
720.3.l.a.161.1		4	36.11	even	6
720.3.l.a.161.3		4	36.7	odd	6
2880.3.l.c.1601.1		4	72.43	odd	6
2880.3.l.c.1601.3		4	72.11	even	6
2880.3.l.g.1601.2		4	72.61	even	6
2880.3.l.g.1601.4		4	72.29	odd	6
3600.3.c.i.449.1		8	180.7	even	12
3600.3.c.i.449.2		8	180.47	odd	12
3600.3.c.i.449.7		8	180.43	even	12
3600.3.c.i.449.8		8	180.83	odd	12
3600.3.l.v.1601.3		4	180.79	odd	6
3600.3.l.v.1601.4		4	180.119	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	405.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.16124 - 1.82514i) q^{2} +(4.66228 + 8.07530i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-3.58114 + 6.20271i) q^{7} -19.4361i q^{8} -8.16228 q^{10} +(-4.70023 - 2.71368i) q^{11} +(-4.90569 - 8.49691i) q^{13} +(22.6417 - 13.0722i) q^{14} +(-16.8246 + 29.1410i) q^{16} -12.2317i q^{17} +6.32456 q^{19} +(18.0569 + 10.4252i) q^{20} +(9.90569 + 17.1572i) q^{22} +(-10.4265 + 6.01972i) q^{23} +(2.50000 - 4.33013i) q^{25} +35.8143i q^{26} -66.7851 q^{28} +(38.9608 + 22.4940i) q^{29} +(29.1359 + 50.4649i) q^{31} +(39.0441 - 22.5421i) q^{32} +(-22.3246 + 38.6673i) q^{34} +16.0153i q^{35} +66.4605 q^{37} +(-19.9934 - 11.5432i) q^{38} +(-21.7302 - 37.6379i) q^{40} +(14.2672 - 8.23717i) q^{41} +(21.8114 - 37.7784i) q^{43} -50.6077i q^{44} +43.9473 q^{46} +(-34.6904 - 20.0285i) q^{47} +(-1.14911 - 1.99032i) q^{49} +(-15.8062 + 9.12570i) q^{50} +(45.7434 - 79.2299i) q^{52} +13.2242i q^{53} -12.1359 q^{55} +(120.557 + 69.6035i) q^{56} +(-82.1096 - 142.218i) q^{58} +(21.7822 - 12.5759i) q^{59} +(17.8377 - 30.8958i) q^{61} -212.709i q^{62} -29.9737 q^{64} +(-18.9997 - 10.9695i) q^{65} +(-13.3509 - 23.1244i) q^{67} +(98.7746 - 57.0275i) q^{68} +(29.2302 - 50.6283i) q^{70} +92.7301i q^{71} +60.3246 q^{73} +(-210.097 - 121.300i) q^{74} +(29.4868 + 51.0727i) q^{76} +(33.6644 - 19.4361i) q^{77} +(48.1096 - 83.3283i) q^{79} +75.2417i q^{80} -60.1359 q^{82} +(68.5212 + 39.5607i) q^{83} +(-13.6754 - 23.6866i) q^{85} +(-137.902 + 79.6177i) q^{86} +(-52.7434 + 91.3543i) q^{88} -107.443i q^{89} +70.2719 q^{91} +(-97.2221 - 56.1312i) q^{92} +(73.1096 + 126.630i) q^{94} +(12.2474 - 7.07107i) q^{95} +(0.539501 - 0.934443i) q^{97} +8.38915i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{4} - 16 q^{7} - 40 q^{10} + 24 q^{13} - 84 q^{16} + 16 q^{22} + 20 q^{25} - 256 q^{28} + 56 q^{31} - 128 q^{34} + 304 q^{37} - 60 q^{40} + 48 q^{43} + 48 q^{46} + 92 q^{49} + 328 q^{52} + 80 q^{55}+ \cdots + 232 q^{97}+O(q^{100}) \) 8 * q + 12 * q^4 - 16 * q^7 - 40 * q^10 + 24 * q^13 - 84 * q^16 + 16 * q^22 + 20 * q^25 - 256 * q^28 + 56 * q^31 - 128 * q^34 + 304 * q^37 - 60 * q^40 + 48 * q^43 + 48 * q^46 + 92 * q^49 + 328 * q^52 + 80 * q^55 - 328 * q^58 + 168 * q^61 - 88 * q^64 - 208 * q^67 + 120 * q^70 + 432 * q^73 + 160 * q^76 + 56 * q^79 - 304 * q^82 - 160 * q^85 - 384 * q^88 + 208 * q^91 + 256 * q^94 + 232 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more