LMFDB - Embedded newform 208.4.w.e.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,4,Mod(17,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("208.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	208.w (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:	$12.2723972812$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 340 x^{18} + 48278 x^{16} + 3724852 x^{14} + 170209937 x^{12} + 4703455168 x^{10} + \cdots + 549543481344 $ x^20 + 340x^18 + 48278x^16 + 3724852x^14 + 170209937x^12 + 4703455168x^10 + 76591569568x^8 + 674465272704x^6 + 2596745246976x^4 + 2244726908928*x^2 + 549543481344
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{40} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.4
Root			$-4.48142i$ of defining polynomial
Character	$\chi$	$=$	208.49
Dual form			208.4.w.e.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.74071 - 3.01500i) q^{3} -11.3595i q^{5} +(-15.7942 - 9.11877i) q^{7} +(7.43985 - 12.8862i) q^{9} +O(q^{10})$	\(q+(-1.74071 - 3.01500i) q^{3} -11.3595i q^{5} +(-15.7942 - 9.11877i) q^{7} +(7.43985 - 12.8862i) q^{9} +(-24.0779 + 13.9014i) q^{11} +(25.5232 + 39.3137i) q^{13} +(-34.2489 + 19.7736i) q^{15} +(-18.6370 + 32.2803i) q^{17} +(-69.3954 - 40.0655i) q^{19} +63.4926i q^{21} +(27.3556 + 47.3813i) q^{23} -4.03856 q^{25} -145.801 q^{27} +(-86.8799 - 150.480i) q^{29} +204.307i q^{31} +(83.8253 + 48.3966i) q^{33} +(-103.585 + 179.414i) q^{35} +(-316.009 + 182.448i) q^{37} +(74.1021 - 145.386i) q^{39} +(-238.555 + 137.730i) q^{41} +(165.415 - 286.508i) q^{43} +(-146.381 - 84.5131i) q^{45} +29.1876i q^{47} +(-5.19611 - 8.99992i) q^{49} +129.767 q^{51} -306.420 q^{53} +(157.913 + 273.513i) q^{55} +278.970i q^{57} +(-57.7012 - 33.3138i) q^{59} +(265.204 - 459.347i) q^{61} +(-235.013 + 135.685i) q^{63} +(446.584 - 289.932i) q^{65} +(781.364 - 451.121i) q^{67} +(95.2363 - 164.954i) q^{69} +(54.5127 + 31.4729i) q^{71} +108.377i q^{73} +(7.02997 + 12.1763i) q^{75} +507.054 q^{77} -720.440 q^{79} +(52.9211 + 91.6621i) q^{81} -789.483i q^{83} +(366.689 + 211.708i) q^{85} +(-302.466 + 523.886i) q^{87} +(510.945 - 294.994i) q^{89} +(-44.6263 - 853.667i) q^{91} +(615.984 - 355.639i) q^{93} +(-455.124 + 788.298i) q^{95} +(-616.136 - 355.726i) q^{97} +413.697i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{3} + 54 q^{7} - 72 q^{9}+O(q^{10}) $ 20 * q + 6 * q^3 + 54 * q^7 - 72 * q^9	$ 20 q + 6 q^{3} + 54 q^{7} - 72 q^{9} + 42 q^{11} + 24 q^{13} - 70 q^{17} + 102 q^{19} - 90 q^{23} - 628 q^{25} - 708 q^{27} + 170 q^{29} - 678 q^{33} + 544 q^{35} + 582 q^{37} - 1162 q^{39} + 438 q^{41} - 270 q^{43} + 540 q^{45} + 92 q^{49} + 444 q^{51} - 592 q^{53} + 288 q^{55} - 90 q^{59} + 746 q^{61} + 1068 q^{63} - 1412 q^{65} - 846 q^{67} + 682 q^{69} + 1038 q^{71} - 722 q^{75} + 2812 q^{77} + 1008 q^{79} + 694 q^{81} - 180 q^{85} + 338 q^{87} + 2466 q^{89} - 690 q^{91} - 4764 q^{93} + 2592 q^{95} - 846 q^{97}+O(q^{100}) $ 20 * q + 6 * q^3 + 54 * q^7 - 72 * q^9 + 42 * q^11 + 24 * q^13 - 70 * q^17 + 102 * q^19 - 90 * q^23 - 628 * q^25 - 708 * q^27 + 170 * q^29 - 678 * q^33 + 544 * q^35 + 582 * q^37 - 1162 * q^39 + 438 * q^41 - 270 * q^43 + 540 * q^45 + 92 * q^49 + 444 * q^51 - 592 * q^53 + 288 * q^55 - 90 * q^59 + 746 * q^61 + 1068 * q^63 - 1412 * q^65 - 846 * q^67 + 682 * q^69 + 1038 * q^71 - 722 * q^75 + 2812 * q^77 + 1008 * q^79 + 694 * q^81 - 180 * q^85 + 338 * q^87 + 2466 * q^89 - 690 * q^91 - 4764 * q^93 + 2592 * q^95 - 846 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−1.74071	−	3.01500i	−0.335000	−	0.580237i	0.648485	−	0.761228i	$-0.275403\pi$
$3$	−1.74071	−	3.01500i	−0.335000	−	0.580237i	−0.983485	+	0.180991i	$0.942070\pi$
$4$		0			0
$5$		−	11.3595i		−	1.01603i	−0.861349	−	0.508013i	$-0.830380\pi$
$5$		−	11.3595i		−	1.01603i	0.861349	−	0.508013i	$-0.169620\pi$
$6$		0			0
$7$	−15.7942	−	9.11877i	−0.852805	−	0.492367i	0.00879124	−	0.999961i	$-0.497202\pi$
$7$	−15.7942	−	9.11877i	−0.852805	−	0.492367i	−0.861596	+	0.507594i	$0.830535\pi$
$8$		0			0
$9$	7.43985	−	12.8862i	0.275550	−	0.477267i
$10$		0			0
$11$	−24.0779	+	13.9014i	−0.659978	+	0.381039i	−0.792269	−	0.610172i	$-0.791100\pi$
$11$	−24.0779	+	13.9014i	−0.659978	+	0.381039i	0.132290	+	0.991211i	$0.457767\pi$
$12$		0			0
$13$	25.5232	+	39.3137i	0.544529	+	0.838742i
$13$	25.5232	+	39.3137i	0.544529	+	0.838742i
$14$		0			0
$15$	−34.2489	+	19.7736i	−0.589536	+	0.340369i
$16$		0			0
$17$	−18.6370	+	32.2803i	−0.265891	+	0.460537i	−0.967797	−	0.251733i	$-0.918999\pi$
$17$	−18.6370	+	32.2803i	−0.265891	+	0.460537i	0.701906	+	0.712270i	$0.252333\pi$
$18$		0			0
$19$	−69.3954	−	40.0655i	−0.837916	−	0.483771i	0.0186394	−	0.999826i	$-0.494067\pi$
$19$	−69.3954	−	40.0655i	−0.837916	−	0.483771i	−0.856555	+	0.516055i	$0.827400\pi$
$20$		0			0
$21$			63.4926i			0.659772i
$22$		0			0
$23$	27.3556	+	47.3813i	0.248001	+	0.429551i	0.962971	−	0.269604i	$-0.0868929\pi$
$23$	27.3556	+	47.3813i	0.248001	+	0.429551i	−0.714970	+	0.699155i	$0.753560\pi$
$24$		0			0
$25$	−4.03856			−0.0323085
$26$		0			0
$27$	−145.801			−1.03924
$28$		0			0
$29$	−86.8799	−	150.480i	−0.556317	−	0.963569i	−0.997800	−	0.0662996i	$-0.978881\pi$
$29$	−86.8799	−	150.480i	−0.556317	−	0.963569i	0.441483	−	0.897270i	$-0.354453\pi$
$30$		0			0
$31$			204.307i			1.18370i	0.806050	+	0.591848i	$0.201601\pi$
$31$			204.307i			1.18370i	−0.806050	+	0.591848i	$0.798399\pi$
$32$		0			0
$33$	83.8253	+	48.3966i	0.442185	+	0.255296i
$34$		0			0
$35$	−103.585	+	179.414i	−0.500258	+	0.866472i
$36$		0			0
$37$	−316.009	+	182.448i	−1.40409	+	0.810654i	−0.994810	−	0.101753i	$-0.967555\pi$
$37$	−316.009	+	182.448i	−1.40409	+	0.810654i	−0.409284	+	0.912407i	$0.634222\pi$
$38$		0			0
$39$	74.1021	−	145.386i	0.304252	−	0.596934i
$40$		0			0
$41$	−238.555	+	137.730i	−0.908684	+	0.524629i	−0.880008	−	0.474960i	$-0.842463\pi$
$41$	−238.555	+	137.730i	−0.908684	+	0.524629i	−0.0286765	+	0.999589i	$0.509129\pi$
$42$		0			0
$43$	165.415	−	286.508i	0.586642	−	1.01609i	−0.408027	−	0.912970i	$-0.633783\pi$
$43$	165.415	−	286.508i	0.586642	−	1.01609i	0.994669	−	0.103123i	$-0.0328837\pi$
$44$		0			0
$45$	−146.381	−	84.5131i	−0.484915	−	0.279966i
$46$		0			0
$47$			29.1876i			0.0905839i	0.998974	+	0.0452920i	$0.0144218\pi$
$47$			29.1876i			0.0905839i	−0.998974	+	0.0452920i	$0.985578\pi$
$48$		0			0
$49$	−5.19611	−	8.99992i	−0.0151490	−	0.0262388i
$50$		0			0
$51$	129.767			0.356294
$52$		0			0
$53$	−306.420			−0.794152			−0.397076	−	0.917786i	$-0.629975\pi$
$53$	−306.420			−0.794152			−0.397076	+	0.917786i	$0.629975\pi$
$54$		0			0
$55$	157.913	+	273.513i	0.387145	+	0.670555i
$56$		0			0
$57$			278.970i			0.648253i
$58$		0			0
$59$	−57.7012	−	33.3138i	−0.127323	−	0.0735099i	0.434986	−	0.900437i	$-0.356753\pi$
$59$	−57.7012	−	33.3138i	−0.127323	−	0.0735099i	−0.562309	+	0.826927i	$0.690087\pi$
$60$		0			0
$61$	265.204	−	459.347i	0.556654	−	0.964153i	−0.441119	−	0.897449i	$-0.645418\pi$
$61$	265.204	−	459.347i	0.556654	−	0.964153i	0.997773	−	0.0667041i	$-0.0212483\pi$
$62$		0			0
$63$	−235.013	+	135.685i	−0.469981	+	0.271344i
$64$		0			0
$65$	446.584	−	289.932i	0.852184	−	0.553255i
$66$		0			0
$67$	781.364	−	451.121i	1.42476	−	0.822585i	0.428058	−	0.903751i	$-0.359198\pi$
$67$	781.364	−	451.121i	1.42476	−	0.822585i	0.996701	+	0.0811662i	$0.0258644\pi$
$68$		0			0
$69$	95.2363	−	164.954i	0.166161	−	0.287799i
$70$		0			0
$71$	54.5127	+	31.4729i	0.0911193	+	0.0526077i	0.544867	−	0.838522i	$-0.316580\pi$
$71$	54.5127	+	31.4729i	0.0911193	+	0.0526077i	−0.453748	+	0.891130i	$0.649913\pi$
$72$		0			0
$73$			108.377i			0.173761i	0.996219	+	0.0868803i	$0.0276898\pi$
$73$			108.377i			0.173761i	−0.996219	+	0.0868803i	$0.972310\pi$
$74$		0			0
$75$	7.02997	+	12.1763i	0.0108233	+	0.0187466i
$76$		0			0
$77$	507.054			0.750444
$78$		0			0
$79$	−720.440			−1.02602			−0.513012	−	0.858382i	$-0.671470\pi$
$79$	−720.440			−1.02602			−0.513012	+	0.858382i	$0.671470\pi$
$80$		0			0
$81$	52.9211	+	91.6621i	0.0725942	+	0.125737i
$82$		0			0
$83$		−	789.483i		−	1.04406i	−0.852927	−	0.522030i	$-0.825175\pi$
$83$		−	789.483i		−	1.04406i	0.852927	−	0.522030i	$-0.174825\pi$
$84$		0			0
$85$	366.689	+	211.708i	0.467917	+	0.270152i
$86$		0			0
$87$	−302.466	+	523.886i	−0.372732	+	0.645591i
$88$		0			0
$89$	510.945	−	294.994i	0.608540	−	0.351341i	−0.163854	−	0.986485i	$-0.552393\pi$
$89$	510.945	−	294.994i	0.608540	−	0.351341i	0.772394	+	0.635144i	$0.219059\pi$
$90$		0			0
$91$	−44.6263	−	853.667i	−0.0514077	−	0.983392i
$92$		0			0
$93$	615.984	−	355.639i	0.686824	−	0.396538i
$94$		0			0
$95$	−455.124	+	788.298i	−0.491524	+	0.851344i
$96$		0			0
$97$	−616.136	−	355.726i	−0.644940	−	0.372356i	0.141575	−	0.989928i	$-0.454783\pi$
$97$	−616.136	−	355.726i	−0.644940	−	0.372356i	−0.786515	+	0.617571i	$0.788117\pi$
$98$		0			0
$99$			413.697i			0.419981i
$100$		0			0
$101$	155.036	+	268.531i	0.152739	+	0.264552i	0.932234	−	0.361857i	$-0.117857\pi$
$101$	155.036	+	268.531i	0.152739	+	0.264552i	−0.779494	+	0.626409i	$0.784524\pi$
$102$		0			0
$103$	1005.76			0.962143			0.481071	−	0.876681i	$-0.340248\pi$
$103$	1005.76			0.962143			0.481071	+	0.876681i	$0.340248\pi$
$104$		0			0
$105$	721.245			0.670345
$106$		0			0
$107$	−683.455	−	1183.78i	−0.617496	−	1.06953i	−0.989941	−	0.141480i	$-0.954814\pi$
$107$	−683.455	−	1183.78i	−0.617496	−	1.06953i	0.372445	−	0.928054i	$-0.378520\pi$
$108$		0			0
$109$			2078.10i			1.82611i	0.407835	+	0.913056i	$0.366284\pi$
$109$			2078.10i			1.82611i	−0.407835	+	0.913056i	$0.633716\pi$
$110$		0			0
$111$	1100.16	+	635.177i	0.940743	+	0.543138i
$112$		0			0
$113$	931.831	−	1613.98i	0.775746	−	1.34363i	−0.158629	−	0.987338i	$-0.550707\pi$
$113$	931.831	−	1613.98i	0.775746	−	1.34363i	0.934374	−	0.356293i	$-0.115959\pi$
$114$		0			0
$115$	538.228	−	310.746i	0.436435	−	0.251976i
$116$		0			0
$117$	696.493	−	36.4098i	0.550349	−	0.0287700i
$118$		0			0
$119$	588.713	−	339.894i	0.453506	−	0.261832i
$120$		0			0
$121$	−279.003	+	483.247i	−0.209619	+	0.363071i
$122$		0			0
$123$	830.511	+	479.496i	0.608818	+	0.351501i
$124$		0			0
$125$		−	1374.06i		−	0.983200i
$126$		0			0
$127$	−4.27569	−	7.40571i	−0.00298745	−	0.00517442i	0.864528	−	0.502585i	$-0.167618\pi$
$127$	−4.27569	−	7.40571i	−0.00298745	−	0.00517442i	−0.867515	+	0.497411i	$0.834284\pi$
$128$		0			0
$129$	−1151.76			−0.786100
$130$		0			0
$131$	−1675.92			−1.11775			−0.558877	−	0.829250i	$-0.688768\pi$
$131$	−1675.92			−1.11775			−0.558877	+	0.829250i	$0.688768\pi$
$132$		0			0
$133$	730.695	+	1265.60i	0.476386	+	0.825125i
$134$		0			0
$135$			1656.23i			1.05589i
$136$		0			0
$137$	−1338.09	−	772.544i	−0.834456	−	0.481773i	0.0209202	−	0.999781i	$-0.493340\pi$
$137$	−1338.09	−	772.544i	−0.834456	−	0.481773i	−0.855376	+	0.518008i	$0.826674\pi$
$138$		0			0
$139$	931.606	−	1613.59i	0.568473	−	0.984624i	−0.428244	−	0.903663i	$-0.640868\pi$
$139$	931.606	−	1613.59i	0.568473	−	0.984624i	0.996717	−	0.0809611i	$-0.0257990\pi$
$140$		0			0
$141$	88.0005	−	50.8071i	0.0525601	−	0.0303456i
$142$		0			0
$143$	−1161.06	−	591.782i	−0.678970	−	0.346065i
$144$		0			0
$145$	−1709.38	+	986.914i	−0.979011	+	0.565232i
$146$		0			0
$147$	−18.0898	+	31.3325i	−0.0101498	+	0.0175800i
$148$		0			0
$149$	−2810.05	−	1622.38i	−1.54502	−	0.892019i	−0.998510	−	0.0545687i	$-0.982622\pi$
$149$	−2810.05	−	1622.38i	−1.54502	−	0.892019i	−0.546513	−	0.837451i	$-0.684045\pi$
$150$		0			0
$151$			2019.09i			1.08815i	0.839035	+	0.544077i	$0.183120\pi$
$151$			2019.09i			1.08815i	−0.839035	+	0.544077i	$0.816880\pi$
$152$		0			0
$153$	277.314	+	480.321i	0.146533	+	0.253802i
$154$		0			0
$155$	2320.82			1.20267
$156$		0			0
$157$	−1337.75			−0.680027			−0.340013	−	0.940421i	$-0.610432\pi$
$157$	−1337.75			−0.680027			−0.340013	+	0.940421i	$0.610432\pi$
$158$		0			0
$159$	533.389	+	923.856i	0.266041	+	0.460796i
$160$		0			0
$161$		−	997.797i		−	0.488431i
$162$		0			0
$163$	−3382.04	−	1952.62i	−1.62517	−	0.938290i	−0.985508	−	0.169629i	$-0.945743\pi$
$163$	−3382.04	−	1952.62i	−1.62517	−	0.938290i	−0.639657	−	0.768660i	$-0.720924\pi$
$164$		0			0
$165$	549.762	−	952.215i	0.259387	−	0.449272i
$166$		0			0
$167$	3441.53	−	1986.97i	1.59469	−	0.920696i	0.602206	−	0.798341i	$-0.294289\pi$
$167$	3441.53	−	1986.97i	1.59469	−	0.920696i	0.992486	−	0.122355i	$-0.0390448\pi$
$168$		0			0
$169$	−894.128	+	2006.82i	−0.406977	+	0.913438i
$170$		0			0
$171$	−1032.58	+	596.162i	−0.461776	+	0.266606i
$172$		0			0
$173$	452.748	−	784.182i	0.198970	−	0.344626i	−0.749225	−	0.662316i	$-0.769574\pi$
$173$	452.748	−	784.182i	0.198970	−	0.344626i	0.948195	+	0.317690i	$0.102907\pi$
$174$		0			0
$175$	63.7857	+	36.8267i	0.0275528	+	0.0159076i
$176$		0			0
$177$			231.959i			0.0985033i
$178$		0			0
$179$	−310.724	−	538.190i	−0.129746	−	0.224727i	0.793832	−	0.608137i	$-0.208083\pi$
$179$	−310.724	−	538.190i	−0.129746	−	0.224727i	−0.923578	+	0.383410i	$0.874750\pi$
$180$		0			0
$181$	−3256.91			−1.33748			−0.668740	−	0.743496i	$-0.733166\pi$
$181$	−3256.91			−1.33748			−0.668740	+	0.743496i	$0.733166\pi$
$182$		0			0
$183$	−1846.57			−0.745916
$184$		0			0
$185$	2072.52	+	3589.70i	0.823646	+	1.42660i
$186$		0			0
$187$		−	1036.32i		−	0.405259i
$188$		0			0
$189$	2302.80	+	1329.52i	0.886266	+	0.511686i
$190$		0			0
$191$	−2118.85	+	3669.96i	−0.802696	+	1.39031i	0.115139	+	0.993349i	$0.463269\pi$
$191$	−2118.85	+	3669.96i	−0.802696	+	1.39031i	−0.917835	+	0.396961i	$0.870065\pi$
$192$		0			0
$193$	−861.254	+	497.245i	−0.321214	+	0.185453i	−0.651934	−	0.758276i	$-0.726042\pi$
$193$	−861.254	+	497.245i	−0.321214	+	0.185453i	0.330719	+	0.943729i	$0.392709\pi$
$194$		0			0
$195$	−1651.52	−	841.764i	−0.606501	−	0.309128i
$196$		0			0
$197$	−561.512	+	324.189i	−0.203076	+	0.117246i	−0.598090	−	0.801429i	$-0.704073\pi$
$197$	−561.512	+	324.189i	−0.203076	+	0.117246i	0.395013	+	0.918675i	$0.370740\pi$
$198$		0			0
$199$	−1997.99	+	3460.62i	−0.711727	+	1.23275i	0.252482	+	0.967602i	$0.418753\pi$
$199$	−1997.99	+	3460.62i	−0.711727	+	1.23275i	−0.964209	+	0.265145i	$0.914580\pi$
$200$		0			0
$201$	−2720.26	−	1570.54i	−0.954588	−	0.551132i
$202$		0			0
$203$			3168.95i			1.09565i
$204$		0			0
$205$	1564.54	+	2709.87i	0.533037	+	0.923246i
$206$		0			0
$207$	814.086			0.273347
$208$		0			0
$209$	2227.86			0.737342
$210$		0			0
$211$	741.690	+	1284.65i	0.241991	+	0.419140i	0.961281	−	0.275569i	$-0.0888663\pi$
$211$	741.690	+	1284.65i	0.241991	+	0.419140i	−0.719290	+	0.694709i	$0.755533\pi$
$212$		0			0
$213$		−	219.141i		−	0.0704943i
$214$		0			0
$215$	−3254.59	−	1879.04i	−1.03238	−	0.596043i
$216$		0			0
$217$	1863.03	−	3226.85i	0.582813	−	1.00946i
$218$		0			0
$219$	326.756	−	188.652i	0.100822	−	0.0582098i
$220$		0			0
$221$	−1744.73	+	91.2077i	−0.531057	+	0.0277615i
$222$		0			0
$223$	−2374.16	+	1370.72i	−0.712939	+	0.411615i	−0.812148	−	0.583451i	$-0.801702\pi$
$223$	−2374.16	+	1370.72i	−0.712939	+	0.411615i	0.0992096	+	0.995067i	$0.468369\pi$
$224$		0			0
$225$	−30.0463	+	52.0417i	−0.00890261	+	0.0154198i
$226$		0			0
$227$	−90.2304	−	52.0946i	−0.0263824	−	0.0152319i	0.486751	−	0.873541i	$-0.338182\pi$
$227$	−90.2304	−	52.0946i	−0.0263824	−	0.0152319i	−0.513133	+	0.858309i	$0.671515\pi$
$228$		0			0
$229$		−	224.940i		−	0.0649102i	−0.999473	−	0.0324551i	$-0.989667\pi$
$229$		−	224.940i		−	0.0649102i	0.999473	−	0.0324551i	$-0.0103326\pi$
$230$		0			0
$231$	−882.634	−	1528.77i	−0.251399	−	0.435435i
$232$		0			0
$233$	7093.79			1.99455			0.997273	−	0.0737947i	$-0.0235109\pi$
$233$	7093.79			1.99455			0.997273	+	0.0737947i	$0.0235109\pi$
$234$		0			0
$235$	331.557			0.0920356
$236$		0			0
$237$	1254.08	+	2172.13i	0.343718	+	0.595337i
$238$		0			0
$239$		−	355.202i		−	0.0961343i	−0.998844	−	0.0480671i	$-0.984694\pi$
$239$		−	355.202i		−	0.0961343i	0.998844	−	0.0480671i	$-0.0153061\pi$
$240$		0			0
$241$	893.697	+	515.976i	0.238872	+	0.137913i	0.614658	−	0.788794i	$-0.289294\pi$
$241$	893.697	+	515.976i	0.238872	+	0.137913i	−0.375786	+	0.926706i	$0.622627\pi$
$242$		0			0
$243$	−1784.07	+	3090.10i	−0.470980	+	0.815762i
$244$		0			0
$245$	−102.235	+	59.0252i	−0.0266593	+	0.0153918i
$246$		0			0
$247$	−196.076	−	3750.79i	−0.0505102	−	0.966223i
$248$		0			0
$249$	−2380.29	+	1374.26i	−0.605802	+	0.349760i
$250$		0			0
$251$	3158.21	−	5470.18i	0.794200	−	1.37560i	−0.129146	−	0.991626i	$-0.541223\pi$
$251$	3158.21	−	5470.18i	0.794200	−	1.37560i	0.923346	−	0.383970i	$-0.125443\pi$
$252$		0			0
$253$	−1317.33	−	760.561i	−0.327351	−	0.188996i
$254$		0			0
$255$		−	1474.09i		−	0.362004i
$256$		0			0
$257$	−3439.23	−	5956.92i	−0.834760	−	1.44585i	−0.894226	−	0.447616i	$-0.852273\pi$
$257$	−3439.23	−	5956.92i	−0.834760	−	1.44585i	0.0594657	−	0.998230i	$-0.481060\pi$
$258$		0			0
$259$	6654.79			1.59656
$260$		0			0
$261$	−2585.50			−0.613173
$262$		0			0
$263$	−2262.34	−	3918.49i	−0.530426	−	0.918725i	−0.999370	−	0.0354970i	$-0.988699\pi$
$263$	−2262.34	−	3918.49i	−0.530426	−	0.918725i	0.468944	−	0.883228i	$-0.344635\pi$
$264$		0			0
$265$			3480.78i			0.806879i
$266$		0			0
$267$	−1778.82	−	1027.00i	−0.407722	−	0.235398i
$268$		0			0
$269$	3164.82	−	5481.62i	0.717332	−	1.24245i	−0.244722	−	0.969593i	$-0.578697\pi$
$269$	3164.82	−	5481.62i	0.717332	−	1.24245i	0.962053	−	0.272861i	$-0.0879701\pi$
$270$		0			0
$271$	5054.63	−	2918.29i	1.13301	−	0.654146i	0.188322	−	0.982107i	$-0.439695\pi$
$271$	5054.63	−	2918.29i	1.13301	−	0.654146i	0.944691	+	0.327962i	$0.106362\pi$
$272$		0			0
$273$	−2496.12	+	1620.54i	−0.553379	+	0.359265i
$274$		0			0
$275$	97.2401	−	56.1416i	0.0213229	−	0.0123108i
$276$		0			0
$277$	3576.38	−	6194.48i	0.775755	−	1.34365i	−0.158615	−	0.987341i	$-0.550703\pi$
$277$	3576.38	−	6194.48i	0.775755	−	1.34365i	0.934369	−	0.356306i	$-0.115964\pi$
$278$		0			0
$279$	2632.74	+	1520.01i	0.564939	+	0.326167i
$280$		0			0
$281$		−	1517.96i		−	0.322256i	−0.986934	−	0.161128i	$-0.948487\pi$
$281$		−	1517.96i		−	0.322256i	0.986934	−	0.161128i	$-0.0515132\pi$
$282$		0			0
$283$	837.216	+	1450.10i	0.175856	+	0.304592i	0.940457	−	0.339912i	$-0.110397\pi$
$283$	837.216	+	1450.10i	0.175856	+	0.304592i	−0.764601	+	0.644504i	$0.777064\pi$
$284$		0			0
$285$	3168.96			0.658642
$286$		0			0
$287$	5023.71			1.03324
$288$		0			0
$289$	1761.82	+	3051.56i	0.358604	+	0.621120i
$290$		0			0
$291$			2476.87i			0.498957i
$292$		0			0
$293$	−483.616	−	279.216i	−0.0964271	−	0.0556722i	0.451011	−	0.892518i	$-0.351064\pi$
$293$	−483.616	−	279.216i	−0.0964271	−	0.0556722i	−0.547438	+	0.836846i	$0.684397\pi$
$294$		0			0
$295$	−378.428	+	655.457i	−0.0746880	+	0.129363i
$296$		0			0
$297$	3510.58	−	2026.83i	0.685874	−	0.395989i
$298$		0			0
$299$	−1164.53	+	2284.77i	−0.225239	+	0.441912i
$300$		0			0
$301$	−5225.20	+	3016.77i	−1.00058	+	0.577686i
$302$		0			0
$303$	539.747	−	934.868i	0.102335	−	0.177250i
$304$		0			0
$305$	−5217.96	−	3012.59i	−0.979604	−	0.565575i
$306$		0			0
$307$			5611.63i			1.04323i	0.853180	+	0.521617i	$0.174671\pi$
$307$			5611.63i			1.04323i	−0.853180	+	0.521617i	$0.825329\pi$
$308$		0			0
$309$	−1750.74	−	3032.37i	−0.322318	−	0.558271i
$310$		0			0
$311$	5535.90			1.00936			0.504682	−	0.863305i	$-0.331610\pi$
$311$	5535.90			1.00936			0.504682	+	0.863305i	$0.331610\pi$
$312$		0			0
$313$	8163.45			1.47420			0.737101	−	0.675782i	$-0.236194\pi$
$313$	8163.45			1.47420			0.737101	+	0.675782i	$0.236194\pi$
$314$		0			0
$315$	1541.31	+	2669.63i	0.275692	+	0.477513i
$316$		0			0
$317$			8717.93i			1.54463i	0.635240	+	0.772315i	$0.280901\pi$
$317$			8717.93i			1.54463i	−0.635240	+	0.772315i	$0.719099\pi$
$318$		0			0
$319$	4183.77	+	2415.50i	0.734314	+	0.423957i
$320$		0			0
$321$	−2379.39	+	4121.23i	−0.413722	+	0.716588i
$322$		0			0
$323$	2586.65	−	1493.40i	0.445589	−	0.257261i
$324$		0			0
$325$	−103.077	−	158.771i	−0.0175929	−	0.0270985i
$326$		0			0
$327$	6265.48	−	3617.38i	1.05958	−	0.611747i
$328$		0			0
$329$	266.155	−	460.994i	0.0446006	−	0.0772504i
$330$		0			0
$331$	620.574	+	358.289i	0.103051	+	0.0594965i	0.550640	−	0.834743i	$-0.314384\pi$
$331$	620.574	+	358.289i	0.103051	+	0.0594965i	−0.447589	+	0.894239i	$0.647717\pi$
$332$		0			0
$333$			5429.53i			0.893503i
$334$		0			0
$335$	−5124.51	−	8875.92i	−0.835768	−	1.44759i
$336$		0			0
$337$	−731.387			−0.118223			−0.0591116	−	0.998251i	$-0.518827\pi$
$337$	−731.387			−0.118223			−0.0591116	+	0.998251i	$0.518827\pi$
$338$		0			0
$339$	−6488.19			−1.03950
$340$		0			0
$341$	−2840.15	−	4919.28i	−0.451034	−	0.781213i
$342$		0			0
$343$			6445.00i			1.01457i
$344$		0			0
$345$	−1873.80	−	1081.84i	−0.292411	−	0.168824i
$346$		0			0
$347$	864.720	−	1497.74i	0.133777	−	0.231709i	−0.791353	−	0.611360i	$-0.790623\pi$
$347$	864.720	−	1497.74i	0.133777	−	0.231709i	0.925130	+	0.379651i	$0.123956\pi$
$348$		0			0
$349$	7429.54	−	4289.45i	1.13952	−	0.657905i	0.193212	−	0.981157i	$-0.438110\pi$
$349$	7429.54	−	4289.45i	1.13952	−	0.657905i	0.946313	+	0.323252i	$0.104776\pi$
$350$		0			0
$351$	−3721.31	−	5731.97i	−0.565894	−	0.871652i
$352$		0			0
$353$	−557.187	+	321.692i	−0.0840115	+	0.0485041i	−0.541417	−	0.840754i	$-0.682112\pi$
$353$	−557.187	+	321.692i	−0.0840115	+	0.0485041i	0.457406	+	0.889258i	$0.348779\pi$
$354$		0			0
$355$	357.517	−	619.238i	0.0534508	−	0.0925795i
$356$		0			0
$357$	−2049.56	−	1183.31i	−0.303849	−	0.175427i
$358$		0			0
$359$		−	5958.85i		−	0.876033i	−0.898967	−	0.438017i	$-0.855681\pi$
$359$		−	5958.85i		−	0.876033i	0.898967	−	0.438017i	$-0.144319\pi$
$360$		0			0
$361$	−219.017	−	379.349i	−0.0319314	−	0.0553068i
$362$		0			0
$363$	1942.65			0.280889
$364$		0			0
$365$	1231.11			0.176545
$366$		0			0
$367$	3107.39	+	5382.15i	0.441974	+	0.765521i	0.997836	−	0.0657535i	$-0.0209451\pi$
$367$	3107.39	+	5382.15i	0.441974	+	0.765521i	−0.555862	+	0.831274i	$0.687612\pi$
$368$		0			0
$369$			4098.76i			0.578246i
$370$		0			0
$371$	4839.65	+	2794.17i	0.677257	+	0.391014i
$372$		0			0
$373$	270.918	−	469.245i	0.0376076	−	0.0651382i	−0.846609	−	0.532215i	$-0.821360\pi$
$373$	270.918	−	469.245i	0.0376076	−	0.0651382i	0.884217	+	0.467077i	$0.154693\pi$
$374$		0			0
$375$	−4142.80	+	2391.85i	−0.570489	+	0.329372i
$376$		0			0
$377$	3698.48	−	7256.32i	0.505256	−	0.991298i
$378$		0			0
$379$	−10708.6	+	6182.59i	−1.45135	+	0.837937i	−0.998558	−	0.0536789i	$-0.982905\pi$
$379$	−10708.6	+	6182.59i	−1.45135	+	0.837937i	−0.452792	+	0.891616i	$0.649572\pi$
$380$		0			0
$381$	−14.8855	+	25.7824i	−0.00200159	+	0.00346686i
$382$		0			0
$383$	−11454.3	−	6613.17i	−1.52817	−	0.882290i	−0.999439	−	0.0335008i	$-0.989334\pi$
$383$	−11454.3	−	6613.17i	−1.52817	−	0.882290i	−0.528732	−	0.848789i	$-0.677332\pi$
$384$		0			0
$385$		−	5759.89i		−	0.762470i
$386$		0			0
$387$	−2461.33	−	4263.15i	−0.323298	−	0.559969i
$388$		0			0
$389$	926.895			0.120811			0.0604055	−	0.998174i	$-0.480761\pi$
$389$	926.895			0.120811			0.0604055	+	0.998174i	$0.480761\pi$
$390$		0			0
$391$	−2039.31			−0.263765
$392$		0			0
$393$	2917.29	+	5052.90i	0.374448	+	0.648562i
$394$		0			0
$395$			8183.85i			1.04247i
$396$		0			0
$397$	3782.25	+	2183.68i	0.478151	+	0.276060i	0.719645	−	0.694342i	$-0.244304\pi$
$397$	3782.25	+	2183.68i	0.478151	+	0.276060i	−0.241495	+	0.970402i	$0.577638\pi$
$398$		0			0
$399$	2543.86	−	4406.09i	0.319178	−	0.552833i
$400$		0			0
$401$	−10400.8	+	6004.90i	−1.29524	+	0.747806i	−0.979578	−	0.201066i	$-0.935559\pi$
$401$	−10400.8	+	6004.90i	−1.29524	+	0.747806i	−0.315660	+	0.948872i	$0.602226\pi$
$402$		0			0
$403$	−8032.04	+	5214.57i	−0.992815	+	0.644556i
$404$		0			0
$405$	1041.24	−	601.158i	0.127752	−	0.0737575i
$406$		0			0
$407$	5072.55	−	8785.91i	0.617781	−	1.07003i
$408$		0			0
$409$	6058.28	+	3497.75i	0.732426	+	0.422867i	0.819309	−	0.573352i	$-0.194357\pi$
$409$	6058.28	+	3497.75i	0.732426	+	0.422867i	−0.0868827	+	0.996219i	$0.527691\pi$
$410$		0			0
$411$			5379.10i			0.645576i
$412$		0			0
$413$	607.561	+	1052.33i	0.0723878	+	0.125379i
$414$		0			0
$415$	−8968.14			−1.06079
$416$		0			0
$417$	−6486.62			−0.761754
$418$		0			0
$419$	938.917	+	1626.25i	0.109473	+	0.189612i	0.915557	−	0.402189i	$-0.131750\pi$
$419$	938.917	+	1626.25i	0.109473	+	0.189612i	−0.806084	+	0.591801i	$0.798417\pi$
$420$		0			0
$421$			13004.8i			1.50549i	0.658310	+	0.752747i	$0.271272\pi$
$421$			13004.8i			1.50549i	−0.658310	+	0.752747i	$0.728728\pi$
$422$		0			0
$423$	376.117	+	217.151i	0.0432327	+	0.0249604i
$424$		0			0
$425$	75.2668	−	130.366i	0.00859054	−	0.0148792i
$426$		0			0
$427$	−8377.35	+	4836.67i	−0.949434	+	0.548156i
$428$		0			0
$429$	236.848	+	4530.72i	0.0266553	+	0.509895i
$430$		0			0
$431$	561.118	−	323.962i	0.0627103	−	0.0362058i	−0.468317	−	0.883560i	$-0.655139\pi$
$431$	561.118	−	323.962i	0.0627103	−	0.0362058i	0.531027	+	0.847355i	$0.321806\pi$
$432$		0			0
$433$	4821.12	−	8350.42i	0.535076	−	0.926780i	−0.464083	−	0.885792i	$-0.653616\pi$
$433$	4821.12	−	8350.42i	0.535076	−	0.926780i	0.999160	−	0.0409880i	$-0.0130505\pi$
$434$		0			0
$435$	5951.09	+	3435.86i	0.655937	+	0.378706i
$436$		0			0
$437$		−	4384.06i		−	0.479904i
$438$		0			0
$439$	87.6026	+	151.732i	0.00952402	+	0.0164961i	0.870748	−	0.491729i	$-0.163635\pi$
$439$	87.6026	+	151.732i	0.00952402	+	0.0164961i	−0.861224	+	0.508225i	$0.830302\pi$
$440$		0			0
$441$	−154.633			−0.0166972
$442$		0			0
$443$	−14450.4			−1.54980			−0.774900	−	0.632084i	$-0.782200\pi$
$443$	−14450.4			−1.54980			−0.774900	+	0.632084i	$0.782200\pi$
$444$		0			0
$445$	−3350.99	−	5804.09i	−0.356971	−	0.618293i
$446$		0			0
$447$			11296.4i			1.19531i
$448$		0			0
$449$	−9134.96	−	5274.07i	−0.960146	−	0.554341i	−0.0639281	−	0.997955i	$-0.520363\pi$
$449$	−9134.96	−	5274.07i	−0.960146	−	0.554341i	−0.896218	+	0.443614i	$0.853696\pi$
$450$		0			0
$451$	3829.27	−	6632.49i	0.399808	−	0.692487i
$452$		0			0
$453$	6087.56	−	3514.65i	0.631387	−	0.364531i
$454$		0			0
$455$	−9697.25	+	506.933i	−0.999151	+	0.0522316i
$456$		0			0
$457$	−2835.35	+	1636.99i	−0.290224	+	0.167561i	−0.638043	−	0.770001i	$-0.720256\pi$
$457$	−2835.35	+	1636.99i	−0.290224	+	0.167561i	0.347819	+	0.937562i	$0.386922\pi$
$458$		0			0
$459$	2717.30	−	4706.50i	0.276324	−	0.478607i
$460$		0			0
$461$	10839.0	+	6257.93i	1.09506	+	0.632236i	0.934920	−	0.354858i	$-0.115471\pi$
$461$	10839.0	+	6257.93i	1.09506	+	0.632236i	0.160144	+	0.987094i	$0.448804\pi$
$462$		0			0
$463$		−	6519.56i		−	0.654406i	−0.944954	−	0.327203i	$-0.893894\pi$
$463$		−	6519.56i		−	0.654406i	0.944954	−	0.327203i	$-0.106106\pi$
$464$		0			0
$465$	−4039.88	−	6997.28i	−0.402893	−	0.697831i
$466$		0			0
$467$	14366.4			1.42355			0.711774	−	0.702408i	$-0.247892\pi$
$467$	14366.4			1.42355			0.711774	+	0.702408i	$0.247892\pi$
$468$		0			0
$469$	−16454.7			−1.62006
$470$		0			0
$471$	2328.64	+	4033.32i	0.227809	+	0.394577i
$472$		0			0
$473$			9198.01i			0.894133i
$474$		0			0
$475$	280.258	+	161.807i	0.0270718	+	0.0156299i
$476$		0			0
$477$	−2279.72	+	3948.59i	−0.218829	+	0.379022i
$478$		0			0
$479$	9612.26	−	5549.64i	0.916901	−	0.529373i	0.0342556	−	0.999413i	$-0.489094\pi$
$479$	9612.26	−	5549.64i	0.916901	−	0.529373i	0.882645	+	0.470040i	$0.155761\pi$
$480$		0			0
$481$	−15238.2	−	7766.80i	−1.44450	−	0.736248i
$482$		0			0
$483$	−3008.36	+	1736.88i	−0.283406	+	0.163624i
$484$		0			0
$485$	−4040.88	+	6999.01i	−0.378323	+	0.655275i
$486$		0			0
$487$	−5365.96	−	3098.04i	−0.499291	−	0.288266i	0.229130	−	0.973396i	$-0.426412\pi$
$487$	−5365.96	−	3098.04i	−0.499291	−	0.288266i	−0.728421	+	0.685130i	$0.759745\pi$
$488$		0			0
$489$			13595.8i			1.25731i
$490$		0			0
$491$	4689.11	+	8121.78i	0.430991	+	0.746499i	0.996959	−	0.0779287i	$-0.0248306\pi$
$491$	4689.11	+	8121.78i	0.430991	+	0.746499i	−0.565968	+	0.824427i	$0.691497\pi$
$492$		0			0
$493$	6476.74			0.591679
$494$		0			0
$495$	4699.40			0.426712
$496$		0			0
$497$	−573.989	−	994.178i	−0.0518046	−	0.0897283i
$498$		0			0
$499$			6307.30i			0.565839i	0.959144	+	0.282919i	$0.0913029\pi$
$499$			6307.30i			0.565839i	−0.959144	+	0.282919i	$0.908697\pi$
$500$		0			0
$501$	−11981.4	−	6917.47i	−1.06844	−	0.616866i
$502$		0			0
$503$	2164.98	−	3749.85i	0.191911	−	0.332400i	−0.753972	−	0.656906i	$-0.771865\pi$
$503$	2164.98	−	3749.85i	0.191911	−	0.332400i	0.945884	+	0.324506i	$0.105198\pi$
$504$		0			0
$505$	3050.38	−	1761.14i	0.268792	−	0.155187i
$506$		0			0
$507$	7606.99	−	797.505i	0.666348	−	0.0698588i
$508$		0			0
$509$	−3170.52	+	1830.50i	−0.276092	+	0.159402i	−0.631653	−	0.775251i	$-0.717623\pi$
$509$	−3170.52	+	1830.50i	−0.276092	+	0.159402i	0.355561	+	0.934653i	$0.384290\pi$
$510$		0			0
$511$	988.262	−	1711.72i	0.0855541	−	0.148184i
$512$		0			0
$513$	10117.9	+	5841.58i	0.870793	+	0.502753i
$514$		0			0
$515$		−	11425.0i		−	0.977562i
$516$		0			0
$517$	−405.748	−	702.776i	−0.0345160	−	0.0597834i
$518$		0			0
$519$	−3152.41			−0.266619
$520$		0			0
$521$	−16209.4			−1.36304			−0.681521	−	0.731799i	$-0.738681\pi$
$521$	−16209.4			−1.36304			−0.681521	+	0.731799i	$0.738681\pi$
$522$		0			0
$523$	3431.04	+	5942.73i	0.286862	+	0.496859i	0.973059	−	0.230556i	$-0.0740546\pi$
$523$	3431.04	+	5942.73i	0.286862	+	0.496859i	−0.686197	+	0.727416i	$0.740721\pi$
$524$		0			0
$525$		−	256.419i		−	0.0213162i
$526$		0			0
$527$	−6595.08	−	3807.67i	−0.545135	−	0.314734i
$528$		0			0
$529$	4586.84	−	7944.65i	0.376991	−	0.652967i
$530$		0			0
$531$	−858.576	+	495.699i	−0.0701677	+	0.0405113i
$532$		0			0
$533$	−11503.4	−	5863.16i	−0.934833	−	0.476476i
$534$		0			0
$535$	−13447.2	+	7763.72i	−1.08667	+	0.627392i
$536$		0			0
$537$	−1081.76	+	1873.66i	−0.0869300	+	0.150567i
$538$		0			0
$539$	250.223	+	144.466i	0.0199960	+	0.0115447i
$540$		0			0
$541$			7852.96i			0.624076i	0.950070	+	0.312038i	$0.101012\pi$
$541$			7852.96i			0.624076i	−0.950070	+	0.312038i	$0.898988\pi$
$542$		0			0
$543$	5669.33	+	9819.57i	0.448056	+	0.776056i
$544$		0			0
$545$	23606.2			1.85538
$546$		0			0
$547$	15588.1			1.21846			0.609232	−	0.792992i	$-0.291478\pi$
$547$	15588.1			1.21846			0.609232	+	0.792992i	$0.291478\pi$
$548$		0			0
$549$	−3946.16	−	6834.94i	−0.306772	−	0.531345i
$550$		0			0
$551$			13923.5i			1.07652i
$552$		0			0
$553$	11378.8	+	6569.53i	0.874998	+	0.505180i
$554$		0			0
$555$	7215.30	−	12497.3i	0.551842	−	0.955819i
$556$		0			0
$557$	14022.2	−	8095.73i	1.06668	−	0.615848i	0.139407	−	0.990235i	$-0.455480\pi$
$557$	14022.2	−	8095.73i	1.06668	−	0.615848i	0.927272	+	0.374387i	$0.122147\pi$
$558$		0			0
$559$	15485.6	−	809.524i	1.17168	−	0.0612509i
$560$		0			0
$561$	−3124.51	+	1803.94i	−0.235146	+	0.135762i
$562$		0			0
$563$	−2443.27	+	4231.87i	−0.182898	+	0.316789i	−0.942866	−	0.333172i	$-0.891881\pi$
$563$	−2443.27	+	4231.87i	−0.182898	+	0.316789i	0.759968	+	0.649960i	$0.225215\pi$
$564$		0			0
$565$	−18334.0	−	10585.1i	−1.36516	−	0.788178i
$566$		0			0
$567$		−	1930.30i		−	0.142972i
$568$		0			0
$569$	6785.81	+	11753.4i	0.499958	+	0.865952i	1.00000		4.88065e-5i	$-1.55356e-5\pi$
$569$	6785.81	+	11753.4i	0.499958	+	0.865952i	−0.500042	+	0.866001i	$0.666682\pi$
$570$		0			0
$571$	−13416.6			−0.983304			−0.491652	−	0.870792i	$-0.663607\pi$
$571$	−13416.6			−0.983304			−0.491652	+	0.870792i	$0.663607\pi$
$572$		0			0
$573$	14753.3			1.07561
$574$		0			0
$575$	−110.477	−	191.352i	−0.00801255	−	0.0138781i
$576$		0			0
$577$		−	11145.0i		−	0.804111i	−0.915615	−	0.402056i	$-0.868296\pi$
$577$		−	11145.0i		−	0.804111i	0.915615	−	0.402056i	$-0.131704\pi$
$578$		0			0
$579$	2998.39	+	1731.12i	0.215214	+	0.124254i
$580$		0			0
$581$	−7199.11	+	12469.2i	−0.514061	+	0.890380i
$582$		0			0
$583$	7377.95	−	4259.66i	0.524123	−	0.302602i
$584$		0			0
$585$	−413.598	−	7911.82i	−0.0292311	−	0.559169i
$586$		0			0
$587$	3027.56	−	1747.96i	0.212880	−	0.122906i	−0.389769	−	0.920913i	$-0.627445\pi$
$587$	3027.56	−	1747.96i	0.212880	−	0.122906i	0.602649	+	0.798006i	$0.294112\pi$
$588$		0			0
$589$	8185.64	−	14177.9i	0.572637	−	0.991837i
$590$		0			0
$591$	1954.86	+	1128.64i	0.136061	+	0.0785549i
$592$		0			0
$593$		−	6694.81i		−	0.463614i	−0.972762	−	0.231807i	$-0.925536\pi$
$593$		−	6694.81i		−	0.463614i	0.972762	−	0.231807i	$-0.0744637\pi$
$594$		0			0
$595$	−3861.03	−	6687.50i	−0.266028	−	0.460774i
$596$		0			0
$597$	13911.7			0.953713
$598$		0			0
$599$	2122.48			0.144778			0.0723892	−	0.997376i	$-0.476938\pi$
$599$	2122.48			0.144778			0.0723892	+	0.997376i	$0.476938\pi$
$600$		0			0
$601$	7325.37	+	12687.9i	0.497185	+	0.861150i	0.999995	−	0.00324727i	$-0.00103364\pi$
$601$	7325.37	+	12687.9i	0.497185	+	0.861150i	−0.502810	+	0.864397i	$0.667700\pi$
$602$		0			0
$603$		−	13425.1i		−	0.906654i
$604$		0			0
$605$	5489.46	+	3169.34i	0.368889	+	0.212978i
$606$		0			0
$607$	7002.49	−	12128.7i	0.468241	−	0.811017i	−0.531100	−	0.847309i	$-0.678221\pi$
$607$	7002.49	−	12128.7i	0.468241	−	0.811017i	0.999341	+	0.0362916i	$0.0115545\pi$
$608$		0			0
$609$	9554.39	−	5516.23i	0.635736	−	0.367042i
$610$		0			0
$611$	−1147.47	+	744.962i	−0.0759766	+	0.0493256i
$612$		0			0
$613$	10014.7	−	5781.99i	0.659853	−	0.380966i	−0.132368	−	0.991201i	$-0.542258\pi$
$613$	10014.7	−	5781.99i	0.659853	−	0.380966i	0.792221	+	0.610234i	$0.208925\pi$
$614$		0			0
$615$	5446.84	−	9434.20i	0.357134	−	0.618575i
$616$		0			0
$617$	20721.2	+	11963.4i	1.35203	+	0.780596i	0.988534	−	0.150999i	$-0.0482492\pi$
$617$	20721.2	+	11963.4i	1.35203	+	0.780596i	0.363498	+	0.931595i	$0.381583\pi$
$618$		0			0
$619$		−	10200.8i		−	0.662367i	−0.943566	−	0.331184i	$-0.892552\pi$
$619$		−	10200.8i		−	0.662367i	0.943566	−	0.331184i	$-0.107448\pi$
$620$		0			0
$621$	−3988.47	−	6908.23i	−0.257732	−	0.446405i
$622$		0			0
$623$	−10759.9			−0.691955
$624$		0			0
$625$	−16113.5			−1.03126
$626$		0			0
$627$	−3878.06	−	6717.00i	−0.247009	−	0.427833i
$628$		0			0
$629$		−	13601.1i		−	0.862183i
$630$		0			0
$631$	−10643.7	−	6145.12i	−0.671501	−	0.387691i	0.125144	−	0.992139i	$-0.460061\pi$
$631$	−10643.7	−	6145.12i	−0.671501	−	0.387691i	−0.796645	+	0.604447i	$0.793394\pi$
$632$		0			0
$633$	2582.14	−	4472.39i	0.162134	−	0.280824i
$634$		0			0
$635$	−84.1253	+	48.5698i	−0.00525734	+	0.00303533i
$636$		0			0
$637$	221.198	−	433.985i	0.0137585	−	0.0269939i
$638$		0			0
$639$	811.133	−	468.308i	0.0502158	−	0.0289921i
$640$		0			0
$641$	−1903.34	+	3296.68i	−0.117281	+	0.203137i	−0.918689	−	0.394981i	$-0.870751\pi$
$641$	−1903.34	+	3296.68i	−0.117281	+	0.203137i	0.801408	+	0.598118i	$0.204085\pi$
$642$		0			0
$643$	−23701.9	−	13684.3i	−1.45367	−	0.839277i	−0.454983	−	0.890500i	$-0.650355\pi$
$643$	−23701.9	−	13684.3i	−1.45367	−	0.839277i	−0.998687	+	0.0512236i	$0.983688\pi$
$644$		0			0
$645$			13083.4i			0.798698i
$646$		0			0
$647$	11019.1	+	19085.7i	0.669562	+	1.15972i	0.978027	+	0.208480i	$0.0668515\pi$
$647$	11019.1	+	19085.7i	0.669562	+	1.15972i	−0.308465	+	0.951236i	$0.599815\pi$
$648$		0			0
$649$	1852.43			0.112040
$650$		0			0
$651$	−12972.0			−0.780969
$652$		0			0
$653$	−2015.67	−	3491.25i	−0.120795	−	0.209224i	0.799286	−	0.600950i	$-0.205211\pi$
$653$	−2015.67	−	3491.25i	−0.120795	−	0.209224i	−0.920082	+	0.391727i	$0.871878\pi$
$654$		0			0
$655$			19037.6i			1.13567i
$656$		0			0
$657$	1396.56	+	806.307i	0.0829302	+	0.0478798i
$658$		0			0
$659$	6876.09	−	11909.7i	0.406456	−	0.704002i	−0.588034	−	0.808836i	$-0.700098\pi$
$659$	6876.09	−	11909.7i	0.406456	−	0.704002i	0.994490	+	0.104834i	$0.0334311\pi$
$660$		0			0
$661$	2061.25	−	1190.06i	0.121291	−	0.0700273i	−0.438127	−	0.898913i	$-0.644358\pi$
$661$	2061.25	−	1190.06i	0.121291	−	0.0700273i	0.559418	+	0.828886i	$0.311025\pi$
$662$		0			0
$663$	3312.07	+	5101.61i	0.194012	+	0.298839i
$664$		0			0
$665$	14376.6	−	8300.34i	0.838348	−	0.484020i
$666$		0			0
$667$	4753.30	−	8232.96i	0.275935	−	0.477933i
$668$		0			0
$669$	8265.44	+	4772.05i	0.477669	+	0.275782i
$670$		0			0
$671$			14746.8i			0.848427i
$672$		0			0
$673$	518.865	+	898.701i	0.0297188	+	0.0514745i	0.880502	−	0.474042i	$-0.157205\pi$
$673$	518.865	+	898.701i	0.0297188	+	0.0514745i	−0.850783	+	0.525516i	$0.823872\pi$
$674$		0			0
$675$	588.826			0.0335762
$676$		0			0
$677$	−5888.62			−0.334296			−0.167148	−	0.985932i	$-0.553456\pi$
$677$	−5888.62			−0.334296			−0.167148	+	0.985932i	$0.553456\pi$
$678$		0			0
$679$	6487.57	+	11236.8i	0.366672	+	0.635094i
$680$		0			0
$681$			362.726i			0.0204107i
$682$		0			0
$683$	18472.4	+	10665.0i	1.03488	+	0.597491i	0.918380	−	0.395700i	$-0.129498\pi$
$683$	18472.4	+	10665.0i	1.03488	+	0.597491i	0.116504	+	0.993190i	$0.462831\pi$
$684$		0			0
$685$	−8775.73	+	15200.0i	−0.489494	+	0.847828i
$686$		0			0
$687$	−678.194	+	391.555i	−0.0376633	+	0.0217449i
$688$		0			0
$689$	−7820.83	−	12046.5i	−0.432438	−	0.666088i
$690$		0			0
$691$	−20897.6	+	12065.2i	−1.15048	+	0.664230i	−0.949004	−	0.315264i	$-0.897907\pi$
$691$	−20897.6	+	12065.2i	−1.15048	+	0.664230i	−0.201475	+	0.979494i	$0.564574\pi$
$692$		0			0
$693$	3772.41	−	6534.00i	0.206785	−	0.358162i
$694$		0			0
$695$	−18329.6	−	10582.6i	−1.00040	−	0.577583i
$696$		0			0
$697$		−	10267.5i		−	0.557977i
$698$		0			0
$699$	−12348.2	−	21387.8i	−0.668173	−	1.15731i
$700$		0			0
$701$	2110.53			0.113714			0.0568570	−	0.998382i	$-0.481892\pi$
$701$	2110.53			0.113714			0.0568570	+	0.998382i	$0.481892\pi$
$702$		0			0
$703$	29239.4			1.56868
$704$		0			0
$705$	−577.144	−	999.643i	−0.0308319	−	0.0534025i
$706$		0			0
$707$		−	5654.96i		−	0.300816i
$708$		0			0
$709$	2579.40	+	1489.22i	0.136631	+	0.0788838i	0.566757	−	0.823885i	$-0.308198\pi$
$709$	2579.40	+	1489.22i	0.136631	+	0.0788838i	−0.430126	+	0.902769i	$0.641531\pi$
$710$		0			0
$711$	−5359.97	+	9283.74i	−0.282721	+	0.489687i
$712$		0			0
$713$	−9680.31	+	5588.93i	−0.508458	+	0.293558i
$714$		0			0
$715$	−6722.36	+	13189.1i	−0.351611	+	0.689851i
$716$		0			0
$717$	−1070.93	+	618.304i	−0.0557807	+	0.0322050i
$718$		0			0
$719$	−12805.5	+	22179.8i	−0.664208	+	1.15044i	0.315292	+	0.948995i	$0.397898\pi$
$719$	−12805.5	+	22179.8i	−0.664208	+	1.15044i	−0.979499	+	0.201447i	$0.935436\pi$
$720$		0			0
$721$	−15885.2	−	9171.32i	−0.820520	−	0.473728i
$722$		0			0
$723$		−	3592.66i		−	0.184803i
$724$		0			0
$725$	350.870	+	607.724i	0.0179738	+	0.0311315i
$726$		0			0
$727$	23623.3			1.20515			0.602573	−	0.798064i	$-0.294142\pi$
$727$	23623.3			1.20515			0.602573	+	0.798064i	$0.294142\pi$
$728$		0			0
$729$	15279.9			0.776302
$730$		0			0
$731$	6165.70	+	10679.3i	0.311966	+	0.540340i
$732$		0			0
$733$		−	9925.29i		−	0.500135i	−0.968228	−	0.250067i	$-0.919547\pi$
$733$		−	9925.29i		−	0.500135i	0.968228	−	0.250067i	$-0.0804528\pi$
$734$		0			0
$735$	355.922	+	205.492i	0.0178617	+	0.0103125i
$736$		0			0
$737$	−12542.4	+	21724.1i	−0.626873	+	1.08578i
$738$		0			0
$739$	11238.7	−	6488.66i	0.559434	−	0.322990i	−0.193484	−	0.981103i	$-0.561979\pi$
$739$	11238.7	−	6488.66i	0.559434	−	0.322990i	0.752918	+	0.658114i	$0.228645\pi$
$740$		0			0
$741$	−10967.3	+	7120.21i	−0.543717	+	0.352992i
$742$		0			0
$743$	−11221.3	+	6478.61i	−0.554063	+	0.319889i	−0.750759	−	0.660576i	$-0.770312\pi$
$743$	−11221.3	+	6478.61i	−0.554063	+	0.319889i	0.196696	+	0.980465i	$0.436979\pi$
$744$		0			0
$745$	−18429.5	+	31920.8i	−0.906315	+	1.56978i
$746$		0			0
$747$	−10173.4	−	5873.64i	−0.498295	−	0.287691i
$748$		0			0
$749$			24929.1i			1.21614i
$750$		0			0
$751$	−8888.17	−	15394.8i	−0.431869	−	0.748019i	0.565165	−	0.824978i	$-0.308812\pi$
$751$	−8888.17	−	15394.8i	−0.431869	−	0.748019i	−0.997034	+	0.0769585i	$0.975479\pi$
$752$		0			0
$753$	−21990.1			−1.06423
$754$		0			0
$755$	22935.9			1.10559
$756$		0			0
$757$	18151.9	+	31440.0i	0.871523	+	1.50952i	0.860422	+	0.509583i	$0.170200\pi$
$757$	18151.9	+	31440.0i	0.871523	+	1.50952i	0.0111010	+	0.999938i	$0.496466\pi$
$758$		0			0
$759$			5295.67i			0.253255i
$760$		0			0
$761$	−25388.8	−	14658.2i	−1.20939	−	0.698240i	−0.246761	−	0.969076i	$-0.579366\pi$
$761$	−25388.8	−	14658.2i	−1.20939	−	0.698240i	−0.962625	+	0.270836i	$0.912700\pi$
$762$		0			0
$763$	18949.7	−	32821.9i	0.899117	−	1.55732i
$764$		0			0
$765$	5456.22	−	3150.15i	0.257869	−	0.148881i
$766$		0			0
$767$	−163.034	−	3118.72i	−0.00767512	−	0.146819i
$768$		0			0
$769$	9806.59	−	5661.84i	0.459863	−	0.265502i	−0.252124	−	0.967695i	$-0.581129\pi$
$769$	9806.59	−	5661.84i	0.459863	−	0.265502i	0.711987	+	0.702193i	$0.247796\pi$
$770$		0			0
$771$	−11973.4	+	20738.6i	−0.559289	+	0.968717i
$772$		0			0
$773$	−25685.4	−	14829.5i	−1.19514	−	0.690012i	−0.235668	−	0.971834i	$-0.575728\pi$
$773$	−25685.4	−	14829.5i	−1.19514	−	0.690012i	−0.959467	+	0.281822i	$0.909061\pi$
$774$		0			0
$775$		−	825.105i		−	0.0382434i
$776$		0			0
$777$	−11584.1	−	20064.2i	−0.534847	−	0.926382i
$778$		0			0
$779$	22072.8			1.01520
$780$		0			0
$781$	−1750.07			−0.0801823
$782$		0			0
$783$	12667.2	+	21940.2i	0.578145	+	1.00138i
$784$		0			0
$785$			15196.2i			0.690925i
$786$		0			0
$787$	23620.8	+	13637.5i	1.06987	+	0.617692i	0.928147	−	0.372214i	$-0.121401\pi$
$787$	23620.8	+	13637.5i	1.06987	+	0.617692i	0.141726	+	0.989906i	$0.454735\pi$
$788$		0			0
$789$	−7876.17	+	13641.9i	−0.355385	+	0.615546i
$790$		0			0
$791$	−29435.0	+	16994.3i	−1.32312	+	0.763903i
$792$		0			0
$793$	24827.5	−	1297.88i	1.11179	−	0.0581198i
$794$		0			0
$795$	10494.6	−	6059.04i	0.468181	−	0.270304i
$796$		0			0
$797$	−7582.15	+	13132.7i	−0.336981	+	0.583668i	−0.983863	−	0.178922i	$-0.942739\pi$
$797$	−7582.15	+	13132.7i	−0.336981	+	0.583668i	0.646883	+	0.762590i	$0.276072\pi$
$798$		0			0
$799$	−942.184	−	543.970i	−0.0417172	−	0.0240855i
$800$		0			0
$801$		−	8778.86i		−	0.387248i
$802$		0			0
$803$	−1506.59	−	2609.48i	−0.0662095	−	0.114678i
$804$		0			0
$805$	−11334.5			−0.496259
$806$		0			0
$807$	−22036.1			−0.961224
$808$		0			0
$809$	−19607.3	−	33960.8i	−0.852107	−	1.47589i	−0.879303	−	0.476263i	$-0.841991\pi$
$809$	−19607.3	−	33960.8i	−0.852107	−	1.47589i	0.0271954	−	0.999630i	$-0.491342\pi$
$810$		0			0
$811$		−	24559.6i		−	1.06339i	−0.846937	−	0.531693i	$-0.821556\pi$
$811$		−	24559.6i		−	1.06339i	0.846937	−	0.531693i	$-0.178444\pi$
$812$		0			0
$813$	−17597.3	−	10159.8i	−0.759119	−	0.438277i
$814$		0			0
$815$	−22180.8	+	38418.3i	−0.953326	+	1.65121i
$816$		0			0
$817$	−22958.1	+	13254.9i	−0.983113	+	0.567600i
$818$		0			0
$819$	−11332.5	−	5776.10i	−0.483506	−	0.246438i
$820$		0			0
$821$	715.224	−	412.935i	0.0304038	−	0.0175536i	−0.484721	−	0.874669i	$-0.661079\pi$
$821$	715.224	−	412.935i	0.0304038	−	0.0175536i	0.515125	+	0.857115i	$0.327746\pi$
$822$		0			0
$823$	10925.5	−	18923.5i	0.462744	−	0.801497i	−0.536352	−	0.843994i	$-0.680198\pi$
$823$	10925.5	−	18923.5i	0.462744	−	0.801497i	0.999097	+	0.0424975i	$0.0135314\pi$
$824$		0			0
$825$	−338.534	−	195.453i	−0.0142863	−	0.00824822i
$826$		0			0
$827$			35044.2i			1.47353i	0.676150	+	0.736764i	$0.263647\pi$
$827$			35044.2i			1.47353i	−0.676150	+	0.736764i	$0.736353\pi$
$828$		0			0
$829$	−1005.91	−	1742.30i	−0.0421434	−	0.0729945i	0.844184	−	0.536053i	$-0.180085\pi$
$829$	−1005.91	−	1742.30i	−0.0421434	−	0.0729945i	−0.886328	+	0.463059i	$0.846752\pi$
$830$		0			0
$831$	−24901.8			−1.03951
$832$		0			0
$833$	387.360			0.0161119
$834$		0			0
$835$	−22571.0	−	39094.1i	−0.935451	−	1.62025i
$836$		0			0
$837$		−	29788.1i		−	1.23014i
$838$		0			0
$839$	−32487.2	−	18756.5i	−1.33681	−	0.771808i	−0.350477	−	0.936571i	$-0.613981\pi$
$839$	−32487.2	−	18756.5i	−1.33681	−	0.771808i	−0.986333	+	0.164764i	$0.947314\pi$
$840$		0			0
$841$	−2901.74	+	5025.96i	−0.118977	+	0.206075i
$842$		0			0
$843$	−4576.65	+	2642.33i	−0.186985	+	0.107956i
$844$		0			0
$845$	22796.5	+	10156.9i	0.928077	+	0.413499i
$846$		0			0
$847$	8813.24	−	5088.33i	0.357528	−	0.206419i
$848$		0			0
$849$	2914.70	−	5048.41i	0.117824	−	0.204077i
$850$		0			0
$851$	−17289.2	−	9981.92i	−0.696435	−	0.402087i
$852$		0			0
$853$			2229.31i			0.0894845i	0.998999	+	0.0447423i	$0.0142467\pi$
$853$			2229.31i			0.0894845i	−0.998999	+	0.0447423i	$0.985753\pi$
$854$		0			0
$855$	6772.11	+	11729.6i	0.270879	+	0.469176i
$856$		0			0
$857$	30245.0			1.20554			0.602770	−	0.797915i	$-0.294064\pi$
$857$	30245.0			1.20554			0.602770	+	0.797915i	$0.294064\pi$
$858$		0			0
$859$	−599.221			−0.0238011			−0.0119005	−	0.999929i	$-0.503788\pi$
$859$	−599.221			−0.0238011			−0.0119005	+	0.999929i	$0.503788\pi$
$860$		0			0
$861$	−8744.82	−	15146.5i	−0.346135	−	0.599524i
$862$		0			0
$863$		−	35921.9i		−	1.41691i	−0.705754	−	0.708457i	$-0.749392\pi$
$863$		−	35921.9i		−	1.41691i	0.705754	−	0.708457i	$-0.250608\pi$
$864$		0			0
$865$	−8907.93	−	5142.99i	−0.350149	−	0.202158i
$866$		0			0
$867$	6133.64	−	10623.8i	0.240265	−	0.416150i
$868$		0			0
$869$	17346.7	−	10015.1i	0.677153	−	0.390955i
$870$		0			0
$871$	37678.2	+	19204.2i	1.46576	+	0.747084i
$872$		0			0
$873$	−9167.93	+	5293.10i	−0.355426	+	0.205206i
$874$		0			0
$875$	−12529.8	+	21702.2i	−0.484095	+	0.838478i
$876$		0			0
$877$	8421.91	+	4862.39i	0.324273	+	0.187219i	0.653296	−	0.757103i	$-0.273386\pi$
$877$	8421.91	+	4862.39i	0.324273	+	0.187219i	−0.329022	+	0.944322i	$0.606719\pi$
$878$		0			0
$879$			1944.14i			0.0746007i
$880$		0			0
$881$	11977.6	+	20745.8i	0.458042	+	0.793351i	0.998857	−	0.0477897i	$-0.0152177\pi$
$881$	11977.6	+	20745.8i	0.458042	+	0.793351i	−0.540816	+	0.841141i	$0.681884\pi$
$882$		0			0
$883$	−20633.7			−0.786386			−0.393193	−	0.919456i	$-0.628630\pi$
$883$	−20633.7			−0.786386			−0.393193	+	0.919456i	$0.628630\pi$
$884$		0			0
$885$	2634.94			0.100082
$886$		0			0
$887$	13502.1	+	23386.3i	0.511111	+	0.885269i	0.999917	+	0.0128772i	$0.00409905\pi$
$887$	13502.1	+	23386.3i	0.511111	+	0.885269i	−0.488807	+	0.872392i	$0.662568\pi$
$888$		0			0
$889$			155.956i			0.00588369i
$890$		0			0
$891$	−2548.46	−	1471.35i	−0.0958211	−	0.0553224i
$892$		0			0
$893$	1169.41	−	2025.48i	0.0438219	−	0.0759017i
$894$		0			0
$895$	−6113.57	+	3529.67i	−0.228329	+	0.131826i
$896$		0			0
$897$	8915.69	−	466.076i	0.331869	−	0.0173487i
$898$		0			0
$899$	30744.2	−	17750.1i	1.14057	−	0.658510i
$900$		0			0
$901$	5710.76	−	9891.33i	0.211158	−	0.365736i
$902$		0			0
$903$	18191.1	+	10502.6i	0.670390	+	0.387050i
$904$		0			0
$905$			36996.9i			1.35891i
$906$		0			0
$907$	−8885.66	−	15390.4i	−0.325296	−	0.563429i	0.656276	−	0.754521i	$-0.272131\pi$
$907$	−8885.66	−	15390.4i	−0.325296	−	0.563429i	−0.981572	+	0.191092i	$0.938797\pi$
$908$		0			0
$909$	4613.79			0.168349
$910$		0			0
$911$	−29859.8			−1.08595			−0.542974	−	0.839750i	$-0.682702\pi$
$911$	−29859.8			−1.08595			−0.542974	+	0.839750i	$0.682702\pi$
$912$		0			0
$913$	10974.9	+	19009.1i	0.397827	+	0.689057i
$914$		0			0
$915$			20976.2i			0.757870i
$916$		0			0
$917$	26469.8	+	15282.3i	0.953227	+	0.550346i
$918$		0			0
$919$	−7704.41	+	13344.4i	−0.276545	+	0.478991i	−0.970524	−	0.241005i	$-0.922523\pi$
$919$	−7704.41	+	13344.4i	−0.276545	+	0.478991i	0.693978	+	0.719996i	$0.255856\pi$
$920$		0			0
$921$	16919.1	−	9768.22i	0.605322	−	0.349483i
$922$		0			0
$923$	154.025	+	2946.39i	0.00549274	+	0.105072i
$924$		0			0
$925$	1276.22	−	736.826i	0.0453642	−	0.0261910i
$926$		0			0
$927$	7482.72	−	12960.5i	0.265119	−	0.459199i
$928$		0			0
$929$	13100.5	+	7563.56i	0.462662	+	0.267118i	0.713163	−	0.700998i	$-0.247262\pi$
$929$	13100.5	+	7563.56i	0.462662	+	0.267118i	−0.250501	+	0.968116i	$0.580595\pi$
$930$		0			0
$931$			832.738i			0.0293146i
$932$		0			0
$933$	−9636.40	−	16690.7i	−0.338137	−	0.585670i
$934$		0			0
$935$	−11772.1			−0.411754
$936$		0			0
$937$	21478.8			0.748861			0.374431	−	0.927255i	$-0.377838\pi$
$937$	21478.8			0.748861			0.374431	+	0.927255i	$0.377838\pi$
$938$		0			0
$939$	−14210.2	−	24612.8i	−0.493858	−	0.855387i
$940$		0			0
$941$			6948.64i			0.240722i	0.992730	+	0.120361i	$0.0384052\pi$
$941$			6948.64i			0.240722i	−0.992730	+	0.120361i	$0.961595\pi$
$942$		0			0
$943$	−13051.6	−	7535.36i	−0.450710	−	0.260217i
$944$		0			0
$945$	15102.8	−	26158.7i	0.519886	−	0.900470i
$946$		0			0
$947$	−20758.8	+	11985.1i	−0.712323	+	0.411260i	−0.811921	−	0.583768i	$-0.801578\pi$
$947$	−20758.8	+	11985.1i	−0.712323	+	0.411260i	0.0995977	+	0.995028i	$0.468244\pi$
$948$		0			0
$949$	−4260.68	+	2766.12i	−0.145740	+	0.0946177i
$950$		0			0
$951$	26284.6	−	15175.4i	0.896251	−	0.517451i
$952$		0			0
$953$	3482.64	−	6032.11i	0.118377	−	0.205036i	−0.800747	−	0.599002i	$-0.795564\pi$
$953$	3482.64	−	6032.11i	0.118377	−	0.205036i	0.919125	+	0.393966i	$0.128897\pi$
$954$		0			0
$955$	41689.0	+	24069.2i	1.41259	+	0.815560i
$956$		0			0
$957$		−	16818.8i		−	0.568102i
$958$		0			0
$959$	14089.3	+	24403.4i	0.474419	+	0.821717i
$960$		0			0
$961$	−11950.2			−0.401135
$962$		0			0
$963$	−20339.2			−0.680605
$964$		0			0
$965$	5648.46	+	9783.42i	0.188425	+	0.326362i
$966$		0			0
$967$		−	19955.8i		−	0.663635i	−0.943344	−	0.331818i	$-0.892338\pi$
$967$		−	19955.8i		−	0.663635i	0.943344	−	0.331818i	$-0.107662\pi$
$968$		0			0
$969$	−9005.22	−	5199.17i	−0.298544	−	0.172365i
$970$		0			0
$971$	−21661.6	+	37519.0i	−0.715915	+	1.24000i	0.246690	+	0.969094i	$0.420657\pi$
$971$	−21661.6	+	37519.0i	−0.715915	+	1.24000i	−0.962605	+	0.270907i	$0.912676\pi$
$972$		0			0
$973$	−29427.9	+	16990.2i	−0.969593	+	0.559795i
$974$		0			0
$975$	−299.266	+	587.151i	−0.00982992	+	0.0192860i
$976$		0			0
$977$	−16700.0	+	9641.77i	−0.546859	+	0.315729i	−0.747854	−	0.663863i	$-0.768916\pi$
$977$	−16700.0	+	9641.77i	−0.546859	+	0.315729i	0.200995	+	0.979592i	$0.435582\pi$
$978$		0			0
$979$	−8201.66	+	14205.7i	−0.267749	+	0.463755i
$980$		0			0
$981$	26778.9	+	15460.8i	0.871542	+	0.503185i
$982$		0			0
$983$		−	34064.0i		−	1.10526i	−0.833426	−	0.552631i	$-0.813624\pi$
$983$		−	34064.0i		−	1.10526i	0.833426	−	0.552631i	$-0.186376\pi$
$984$		0			0
$985$	3682.63	+	6378.50i	0.119125	+	0.206331i
$986$		0			0
$987$	−1853.19			−0.0597647
$988$		0			0
$989$	18100.1			0.581952
$990$		0			0
$991$	−14366.1	−	24882.9i	−0.460500	−	0.797610i	0.538486	−	0.842635i	$-0.318997\pi$
$991$	−14366.1	−	24882.9i	−0.460500	−	0.797610i	−0.998986	+	0.0450249i	$0.985663\pi$
$992$		0			0
$993$		−	2494.71i		−	0.0797252i
$994$		0			0
$995$	39310.9	+	22696.2i	1.25250	+	0.723133i
$996$		0			0
$997$	21698.5	−	37583.0i	0.689268	−	1.19385i	−0.282808	−	0.959177i	$-0.591266\pi$
$997$	21698.5	−	37583.0i	0.689268	−	1.19385i	0.972075	−	0.234670i	$-0.0754009\pi$
$998$		0			0
$999$	46074.3	−	26601.0i	1.45919	−	0.842462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.4.w.e.49.4		20
4.3	odd	2		104.4.o.a.49.7	yes	20
13.4	even	6	inner	208.4.w.e.17.4		20
52.11	even	12		1352.4.a.o.1.4		10
52.15	even	12		1352.4.a.p.1.4		10
52.43	odd	6		104.4.o.a.17.7	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.4.o.a.17.7	✓	20	52.43	odd	6
104.4.o.a.49.7	yes	20	4.3	odd	2
208.4.w.e.17.4		20	13.4	even	6	inner
208.4.w.e.49.4		20	1.1	even	1	trivial
1352.4.a.o.1.4		10	52.11	even	12
1352.4.a.p.1.4		10	52.15	even	12

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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	208.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.74071 - 3.01500i) q^{3} -11.3595i q^{5} +(-15.7942 - 9.11877i) q^{7} +(7.43985 - 12.8862i) q^{9} +O(q^{10})\)	\(q+(-1.74071 - 3.01500i) q^{3} -11.3595i q^{5} +(-15.7942 - 9.11877i) q^{7} +(7.43985 - 12.8862i) q^{9} +(-24.0779 + 13.9014i) q^{11} +(25.5232 + 39.3137i) q^{13} +(-34.2489 + 19.7736i) q^{15} +(-18.6370 + 32.2803i) q^{17} +(-69.3954 - 40.0655i) q^{19} +63.4926i q^{21} +(27.3556 + 47.3813i) q^{23} -4.03856 q^{25} -145.801 q^{27} +(-86.8799 - 150.480i) q^{29} +204.307i q^{31} +(83.8253 + 48.3966i) q^{33} +(-103.585 + 179.414i) q^{35} +(-316.009 + 182.448i) q^{37} +(74.1021 - 145.386i) q^{39} +(-238.555 + 137.730i) q^{41} +(165.415 - 286.508i) q^{43} +(-146.381 - 84.5131i) q^{45} +29.1876i q^{47} +(-5.19611 - 8.99992i) q^{49} +129.767 q^{51} -306.420 q^{53} +(157.913 + 273.513i) q^{55} +278.970i q^{57} +(-57.7012 - 33.3138i) q^{59} +(265.204 - 459.347i) q^{61} +(-235.013 + 135.685i) q^{63} +(446.584 - 289.932i) q^{65} +(781.364 - 451.121i) q^{67} +(95.2363 - 164.954i) q^{69} +(54.5127 + 31.4729i) q^{71} +108.377i q^{73} +(7.02997 + 12.1763i) q^{75} +507.054 q^{77} -720.440 q^{79} +(52.9211 + 91.6621i) q^{81} -789.483i q^{83} +(366.689 + 211.708i) q^{85} +(-302.466 + 523.886i) q^{87} +(510.945 - 294.994i) q^{89} +(-44.6263 - 853.667i) q^{91} +(615.984 - 355.639i) q^{93} +(-455.124 + 788.298i) q^{95} +(-616.136 - 355.726i) q^{97} +413.697i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{3} + 54 q^{7} - 72 q^{9}+O(q^{10}) \) 20 * q + 6 * q^3 + 54 * q^7 - 72 * q^9	\( 20 q + 6 q^{3} + 54 q^{7} - 72 q^{9} + 42 q^{11} + 24 q^{13} - 70 q^{17} + 102 q^{19} - 90 q^{23} - 628 q^{25} - 708 q^{27} + 170 q^{29} - 678 q^{33} + 544 q^{35} + 582 q^{37} - 1162 q^{39} + 438 q^{41} - 270 q^{43} + 540 q^{45} + 92 q^{49} + 444 q^{51} - 592 q^{53} + 288 q^{55} - 90 q^{59} + 746 q^{61} + 1068 q^{63} - 1412 q^{65} - 846 q^{67} + 682 q^{69} + 1038 q^{71} - 722 q^{75} + 2812 q^{77} + 1008 q^{79} + 694 q^{81} - 180 q^{85} + 338 q^{87} + 2466 q^{89} - 690 q^{91} - 4764 q^{93} + 2592 q^{95} - 846 q^{97}+O(q^{100}) \) 20 * q + 6 * q^3 + 54 * q^7 - 72 * q^9 + 42 * q^11 + 24 * q^13 - 70 * q^17 + 102 * q^19 - 90 * q^23 - 628 * q^25 - 708 * q^27 + 170 * q^29 - 678 * q^33 + 544 * q^35 + 582 * q^37 - 1162 * q^39 + 438 * q^41 - 270 * q^43 + 540 * q^45 + 92 * q^49 + 444 * q^51 - 592 * q^53 + 288 * q^55 - 90 * q^59 + 746 * q^61 + 1068 * q^63 - 1412 * q^65 - 846 * q^67 + 682 * q^69 + 1038 * q^71 - 722 * q^75 + 2812 * q^77 + 1008 * q^79 + 694 * q^81 - 180 * q^85 + 338 * q^87 + 2466 * q^89 - 690 * q^91 - 4764 * q^93 + 2592 * q^95 - 846 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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