LMFDB - Embedded newform 108.4.b.a.107.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(107,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("108.107");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.b (of order $2$, degree $1$, 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:	$6.37220628062$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 12x^{10} + 112x^{8} - 368x^{6} + 928x^{4} - 256x^{2} + 64 $ x^12 - 12x^10 + 112x^8 - 368x^6 + 928x^4 - 256*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			107.4
Root			$0.456937 + 0.263813i$ of defining polynomial
Character	$\chi$	$=$	108.107
Dual form			108.4.b.a.107.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.51859 + 2.38619i) q^{2} +(-3.38780 - 7.24726i) q^{4} +13.1987i q^{5} +4.49091i q^{7} +(22.4380 + 2.92167i) q^{8} +O(q^{10})$	\(q+(-1.51859 + 2.38619i) q^{2} +(-3.38780 - 7.24726i) q^{4} +13.1987i q^{5} +4.49091i q^{7} +(22.4380 + 2.92167i) q^{8} +(-31.4945 - 20.0433i) q^{10} -22.3519 q^{11} -73.5402 q^{13} +(-10.7162 - 6.81984i) q^{14} +(-41.0457 + 49.1045i) q^{16} +42.6199i q^{17} -122.563i q^{19} +(95.6542 - 44.7144i) q^{20} +(33.9433 - 53.3359i) q^{22} -197.965 q^{23} -49.2047 q^{25} +(111.677 - 175.481i) q^{26} +(32.5468 - 15.2143i) q^{28} -14.6816i q^{29} +147.133i q^{31} +(-54.8412 - 172.512i) q^{32} +(-101.699 - 64.7220i) q^{34} -59.2740 q^{35} +234.154 q^{37} +(292.458 + 186.122i) q^{38} +(-38.5622 + 296.152i) q^{40} +396.340i q^{41} +280.764i q^{43} +(75.7238 + 161.990i) q^{44} +(300.627 - 472.382i) q^{46} -534.237 q^{47} +322.832 q^{49} +(74.7216 - 117.412i) q^{50} +(249.139 + 532.965i) q^{52} +337.497i q^{53} -295.016i q^{55} +(-13.1210 + 100.767i) q^{56} +(35.0330 + 22.2952i) q^{58} +672.928 q^{59} -80.8693 q^{61} +(-351.087 - 223.434i) q^{62} +(494.928 + 131.113i) q^{64} -970.632i q^{65} -251.791i q^{67} +(308.878 - 144.388i) q^{68} +(90.0127 - 141.439i) q^{70} +95.8124 q^{71} -251.422 q^{73} +(-355.583 + 558.737i) q^{74} +(-888.245 + 415.218i) q^{76} -100.381i q^{77} +499.839i q^{79} +(-648.114 - 541.748i) q^{80} +(-945.742 - 601.876i) q^{82} -16.1731 q^{83} -562.526 q^{85} +(-669.957 - 426.365i) q^{86} +(-501.533 - 65.3050i) q^{88} -321.011i q^{89} -330.263i q^{91} +(670.665 + 1434.71i) q^{92} +(811.285 - 1274.79i) q^{94} +1617.67 q^{95} -210.036 q^{97} +(-490.248 + 770.337i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4}+O(q^{10}) $ 12 * q - 12 * q^4	$ 12 q - 12 q^{4} + 24 q^{10} + 36 q^{13} + 24 q^{16} + 120 q^{22} - 132 q^{25} + 420 q^{28} - 360 q^{34} + 516 q^{37} - 1152 q^{40} - 696 q^{46} - 720 q^{49} + 204 q^{52} + 2832 q^{58} - 972 q^{61} + 2496 q^{64} - 1848 q^{70} + 660 q^{73} - 5004 q^{76} - 3888 q^{82} + 1056 q^{85} + 3168 q^{88} + 7608 q^{94} + 2532 q^{97}+O(q^{100}) $ 12 * q - 12 * q^4 + 24 * q^10 + 36 * q^13 + 24 * q^16 + 120 * q^22 - 132 * q^25 + 420 * q^28 - 360 * q^34 + 516 * q^37 - 1152 * q^40 - 696 * q^46 - 720 * q^49 + 204 * q^52 + 2832 * q^58 - 972 * q^61 + 2496 * q^64 - 1848 * q^70 + 660 * q^73 - 5004 * q^76 - 3888 * q^82 + 1056 * q^85 + 3168 * q^88 + 7608 * q^94 + 2532 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.51859	+	2.38619i	−0.536901	+	0.843645i
$2$	−1.51859	+	2.38619i	−0.536901	+	0.843645i
$3$		0			0
$3$		0			0
$4$	−3.38780	−	7.24726i	−0.423474	−	0.905908i
$5$			13.1987i			1.18052i	0.807212	+	0.590262i	$0.200976\pi$
$5$			13.1987i			1.18052i	−0.807212	+	0.590262i	$0.799024\pi$
$6$		0			0
$7$			4.49091i			0.242486i	0.992623	+	0.121243i	$0.0386881\pi$
$7$			4.49091i			0.242486i	−0.992623	+	0.121243i	$0.961312\pi$
$8$	22.4380	+	2.92167i	0.991629	+	0.129121i
$9$		0			0
$10$	−31.4945	−	20.0433i	−0.995944	−	0.633825i
$11$	−22.3519			−0.612669			−0.306335	−	0.951924i	$-0.599103\pi$
$11$	−22.3519			−0.612669			−0.306335	+	0.951924i	$0.599103\pi$
$12$		0			0
$13$	−73.5402			−1.56895			−0.784476	−	0.620159i	$-0.787068\pi$
$13$	−73.5402			−1.56895			−0.784476	+	0.620159i	$0.787068\pi$
$14$	−10.7162	−	6.81984i	−0.204573	−	0.130191i
$15$		0			0
$16$	−41.0457	+	49.1045i	−0.641339	+	0.767258i
$17$			42.6199i			0.608050i	0.952664	+	0.304025i	$0.0983307\pi$
$17$			42.6199i			0.608050i	−0.952664	+	0.304025i	$0.901669\pi$
$18$		0			0
$19$		−	122.563i		−	1.47989i	−0.672669	−	0.739943i	$-0.734852\pi$
$19$		−	122.563i		−	1.47989i	0.672669	−	0.739943i	$-0.265148\pi$
$20$	95.6542	−	44.7144i	1.06945	−	0.499922i
$21$		0			0
$22$	33.9433	−	53.3359i	0.328943	−	0.516875i
$23$	−197.965			−1.79472			−0.897360	−	0.441299i	$-0.854518\pi$
$23$	−197.965			−1.79472			−0.897360	+	0.441299i	$0.854518\pi$
$24$		0			0
$25$	−49.2047			−0.393638
$26$	111.677	−	175.481i	0.842372	−	1.32364i
$27$		0			0
$28$	32.5468	−	15.2143i	0.219670	−	0.102687i
$29$		−	14.6816i		−	0.0940102i	−0.998895	−	0.0470051i	$-0.985032\pi$
$29$		−	14.6816i		−	0.0940102i	0.998895	−	0.0470051i	$-0.0149677\pi$
$30$		0			0
$31$			147.133i			0.852448i	0.904618	+	0.426224i	$0.140156\pi$
$31$			147.133i			0.852448i	−0.904618	+	0.426224i	$0.859844\pi$
$32$	−54.8412	−	172.512i	−0.302958	−	0.953004i
$33$		0			0
$34$	−101.699	−	64.7220i	−0.512979	−	0.326463i
$35$	−59.2740			−0.286261
$36$		0			0
$37$	234.154			1.04040			0.520199	−	0.854045i	$-0.325858\pi$
$37$	234.154			1.04040			0.520199	+	0.854045i	$0.325858\pi$
$38$	292.458	+	186.122i	1.24850	+	0.794553i
$39$		0			0
$40$	−38.5622	+	296.152i	−0.152430	+	1.17064i
$41$			396.340i			1.50970i	0.655895	+	0.754852i	$0.272292\pi$
$41$			396.340i			1.50970i	−0.655895	+	0.754852i	$0.727708\pi$
$42$		0			0
$43$			280.764i			0.995725i	0.867256	+	0.497863i	$0.165882\pi$
$43$			280.764i			0.995725i	−0.867256	+	0.497863i	$0.834118\pi$
$44$	75.7238	+	161.990i	0.259450	+	0.555022i
$45$		0			0
$46$	300.627	−	472.382i	0.963587	−	1.51411i
$47$	−534.237			−1.65801			−0.829006	−	0.559240i	$-0.811093\pi$
$47$	−534.237			−1.65801			−0.829006	+	0.559240i	$0.811093\pi$
$48$		0			0
$49$	322.832			0.941200
$50$	74.7216	−	117.412i	0.211345	−	0.332091i
$51$		0			0
$52$	249.139	+	532.965i	0.664411	+	1.42133i
$53$			337.497i			0.874695i	0.899293	+	0.437347i	$0.144082\pi$
$53$			337.497i			0.874695i	−0.899293	+	0.437347i	$0.855918\pi$
$54$		0			0
$55$		−	295.016i		−	0.723271i
$56$	−13.1210	+	100.767i	−0.0313101	+	0.240457i
$57$		0			0
$58$	35.0330	+	22.2952i	0.0793113	+	0.0504742i
$59$	672.928			1.48488			0.742439	−	0.669914i	$-0.233669\pi$
$59$	672.928			1.48488			0.742439	+	0.669914i	$0.233669\pi$
$60$		0			0
$61$	−80.8693			−0.169742			−0.0848709	−	0.996392i	$-0.527048\pi$
$61$	−80.8693			−0.169742			−0.0848709	+	0.996392i	$0.527048\pi$
$62$	−351.087	−	223.434i	−0.719164	−	0.457680i
$63$		0			0
$64$	494.928	+	131.113i	0.966656	+	0.256080i
$65$		−	970.632i		−	1.85219i
$66$		0			0
$67$		−	251.791i		−	0.459121i	−0.973294	−	0.229560i	$-0.926271\pi$
$67$		−	251.791i		−	0.459121i	0.973294	−	0.229560i	$-0.0737289\pi$
$68$	308.878	−	144.388i	0.550838	−	0.257494i
$69$		0			0
$70$	90.0127	−	141.439i	0.153694	−	0.241503i
$71$	95.8124			0.160153			0.0800763	−	0.996789i	$-0.474484\pi$
$71$	95.8124			0.160153			0.0800763	+	0.996789i	$0.474484\pi$
$72$		0			0
$73$	−251.422			−0.403106			−0.201553	−	0.979478i	$-0.564599\pi$
$73$	−251.422			−0.403106			−0.201553	+	0.979478i	$0.564599\pi$
$74$	−355.583	+	558.737i	−0.558591	+	0.877727i
$75$		0			0
$76$	−888.245	+	415.218i	−1.34064	+	0.626694i
$77$		−	100.381i		−	0.148564i
$78$		0			0
$79$			499.839i			0.711852i	0.934514	+	0.355926i	$0.115835\pi$
$79$			499.839i			0.711852i	−0.934514	+	0.355926i	$0.884165\pi$
$80$	−648.114	−	541.748i	−0.905766	−	0.757116i
$81$		0			0
$82$	−945.742	−	601.876i	−1.27366	−	0.810562i
$83$	−16.1731			−0.0213882			−0.0106941	−	0.999943i	$-0.503404\pi$
$83$	−16.1731			−0.0213882			−0.0106941	+	0.999943i	$0.503404\pi$
$84$		0			0
$85$	−562.526			−0.717818
$86$	−669.957	−	426.365i	−0.840039	−	0.534606i
$87$		0			0
$88$	−501.533	−	65.3050i	−0.607540	−	0.0791084i
$89$		−	321.011i		−	0.382327i	−0.981558	−	0.191164i	$-0.938774\pi$
$89$		−	321.011i		−	0.382327i	0.981558	−	0.191164i	$-0.0612261\pi$
$90$		0			0
$91$		−	330.263i		−	0.380450i
$92$	670.665	+	1434.71i	0.760018	+	1.62585i
$93$		0			0
$94$	811.285	−	1274.79i	0.890188	−	1.39877i
$95$	1617.67			1.74704
$96$		0			0
$97$	−210.036			−0.219855			−0.109928	−	0.993940i	$-0.535062\pi$
$97$	−210.036			−0.219855			−0.109928	+	0.993940i	$0.535062\pi$
$98$	−490.248	+	770.337i	−0.505331	+	0.794039i
$99$		0			0
$100$	166.696	+	356.600i	0.166696	+	0.356600i
$101$		−	1568.74i		−	1.54550i	−0.634713	−	0.772748i	$-0.718882\pi$
$101$		−	1568.74i		−	1.54550i	0.634713	−	0.772748i	$-0.281118\pi$
$102$		0			0
$103$			544.057i			0.520462i	0.965546	+	0.260231i	$0.0837987\pi$
$103$			544.057i			0.520462i	−0.965546	+	0.260231i	$0.916201\pi$
$104$	−1650.09	−	214.860i	−1.55582	−	0.202585i
$105$		0			0
$106$	−805.333	−	512.519i	−0.737932	−	0.469625i
$107$	1105.78			0.999064			0.499532	−	0.866295i	$-0.333505\pi$
$107$	1105.78			0.999064			0.499532	+	0.866295i	$0.333505\pi$
$108$		0			0
$109$	17.6601			0.0155186			0.00775932	−	0.999970i	$-0.497530\pi$
$109$	17.6601			0.0155186			0.00775932	+	0.999970i	$0.497530\pi$
$110$	703.963	+	448.007i	0.610184	+	0.388325i
$111$		0			0
$112$	−220.524	−	184.333i	−0.186050	−	0.155516i
$113$			1603.29i			1.33473i	0.744729	+	0.667367i	$0.232579\pi$
$113$			1603.29i			1.33473i	−0.744729	+	0.667367i	$0.767421\pi$
$114$		0			0
$115$		−	2612.87i		−	2.11871i
$116$	−106.401	+	49.7381i	−0.0851646	+	0.0398109i
$117$		0			0
$118$	−1021.90	+	1605.73i	−0.797233	+	1.25271i
$119$	−191.402			−0.147444
$120$		0			0
$121$	−831.391			−0.624636
$122$	122.807	−	192.969i	0.0911345	−	0.143202i
$123$		0			0
$124$	1066.31	−	498.457i	0.772240	−	0.360990i
$125$			1000.40i			0.715825i
$126$		0			0
$127$			2080.04i			1.45334i	0.686988	+	0.726669i	$0.258932\pi$
$127$			2080.04i			1.45334i	−0.686988	+	0.726669i	$0.741068\pi$
$128$	−1064.45	+	981.885i	−0.735039	+	0.678025i
$129$		0			0
$130$	2316.11	+	1473.99i	1.56259	+	0.994441i
$131$	−1093.35			−0.729213			−0.364606	−	0.931162i	$-0.618796\pi$
$131$	−1093.35			−0.729213			−0.364606	+	0.931162i	$0.618796\pi$
$132$		0			0
$133$	550.419			0.358853
$134$	600.820	+	382.365i	0.387335	+	0.246503i
$135$		0			0
$136$	−124.521	+	956.306i	−0.0785120	+	0.602960i
$137$		−	1344.61i		−	0.838522i	−0.907866	−	0.419261i	$-0.862289\pi$
$137$		−	1344.61i		−	0.838522i	0.907866	−	0.419261i	$-0.137711\pi$
$138$		0			0
$139$		−	805.378i		−	0.491448i	−0.969340	−	0.245724i	$-0.920974\pi$
$139$		−	805.378i		−	0.491448i	0.969340	−	0.245724i	$-0.0790257\pi$
$140$	200.808	+	429.575i	0.121224	+	0.259326i
$141$		0			0
$142$	−145.499	+	228.627i	−0.0859862	+	0.135112i
$143$	1643.77			0.961249
$144$		0			0
$145$	193.777			0.110981
$146$	381.806	−	599.941i	0.216428	−	0.340079i
$147$		0			0
$148$	−793.267	−	1696.98i	−0.440582	−	0.942505i
$149$		−	879.365i		−	0.483493i	−0.970339	−	0.241746i	$-0.922280\pi$
$149$		−	879.365i		−	0.483493i	0.970339	−	0.241746i	$-0.0777202\pi$
$150$		0			0
$151$			1826.20i			0.984197i	0.870540	+	0.492098i	$0.163770\pi$
$151$			1826.20i			0.984197i	−0.870540	+	0.492098i	$0.836230\pi$
$152$	358.089	−	2750.07i	0.191084	−	1.46750i
$153$		0			0
$154$	239.527	+	152.437i	0.125335	+	0.0797642i
$155$	−1941.96			−1.00634
$156$		0			0
$157$	3417.81			1.73740			0.868698	−	0.495342i	$-0.164957\pi$
$157$	3417.81			1.73740			0.868698	+	0.495342i	$0.164957\pi$
$158$	−1192.71	−	759.049i	−0.600551	−	0.382194i
$159$		0			0
$160$	2276.93	−	723.831i	1.12504	−	0.357649i
$161$		−	889.044i		−	0.435195i
$162$		0			0
$163$			1190.78i			0.572204i	0.958199	+	0.286102i	$0.0923596\pi$
$163$			1190.78i			0.572204i	−0.958199	+	0.286102i	$0.907640\pi$
$164$	2872.38	−	1342.72i	1.36765	−	0.639321i
$165$		0			0
$166$	24.5602	−	38.5920i	0.0114834	−	0.0180441i
$167$	−2123.75			−0.984077			−0.492039	−	0.870573i	$-0.663748\pi$
$167$	−2123.75			−0.984077			−0.492039	+	0.870573i	$0.663748\pi$
$168$		0			0
$169$	3211.16			1.46161
$170$	854.244	−	1342.29i	0.385397	−	0.605584i
$171$		0			0
$172$	2034.77	−	951.173i	0.902035	−	0.421664i
$173$			1769.12i			0.777477i	0.921348	+	0.388738i	$0.127089\pi$
$173$			1769.12i			0.777477i	−0.921348	+	0.388738i	$0.872911\pi$
$174$		0			0
$175$		−	220.974i		−	0.0954519i
$176$	917.450	−	1097.58i	0.392929	−	0.470075i
$177$		0			0
$178$	765.993	+	487.483i	0.322548	+	0.205272i
$179$	−3685.89			−1.53909			−0.769543	−	0.638595i	$-0.779516\pi$
$179$	−3685.89			−1.53909			−0.769543	+	0.638595i	$0.779516\pi$
$180$		0			0
$181$	−2425.51			−0.996059			−0.498030	−	0.867160i	$-0.665943\pi$
$181$	−2425.51			−0.996059			−0.498030	+	0.867160i	$0.665943\pi$
$182$	788.069	+	501.532i	0.320965	+	0.204264i
$183$		0			0
$184$	−4441.94	−	578.389i	−1.77970	−	0.231736i
$185$			3090.52i			1.22822i
$186$		0			0
$187$		−	952.638i		−	0.372534i
$188$	1809.89	+	3871.76i	0.702125	+	1.50201i
$189$		0			0
$190$	−2456.56	+	3860.06i	−0.937989	+	1.47388i
$191$	1367.60			0.518096			0.259048	−	0.965865i	$-0.416591\pi$
$191$	1367.60			0.518096			0.259048	+	0.965865i	$0.416591\pi$
$192$		0			0
$193$	−1240.32			−0.462591			−0.231296	−	0.972883i	$-0.574296\pi$
$193$	−1240.32			−0.462591			−0.231296	+	0.972883i	$0.574296\pi$
$194$	318.958	−	501.187i	0.118041	−	0.185480i
$195$		0			0
$196$	−1093.69	−	2339.65i	−0.398574	−	0.852641i
$197$			2889.56i			1.04504i	0.852628	+	0.522519i	$0.175008\pi$
$197$			2889.56i			1.04504i	−0.852628	+	0.522519i	$0.824992\pi$
$198$		0			0
$199$			1851.53i			0.659555i	0.944059	+	0.329777i	$0.106974\pi$
$199$			1851.53i			0.659555i	−0.944059	+	0.329777i	$0.893026\pi$
$200$	−1104.06	−	143.760i	−0.390343	−	0.0508269i
$201$		0			0
$202$	3743.30	+	2382.26i	1.30385	+	0.829778i
$203$	65.9336			0.0227962
$204$		0			0
$205$	−5231.16			−1.78224
$206$	−1298.22	−	826.198i	−0.439085	−	0.279437i
$207$		0			0
$208$	3018.51	−	3611.15i	1.00623	−	1.20379i
$209$			2739.52i			0.906681i
$210$		0			0
$211$		−	4177.37i		−	1.36295i	−0.731843	−	0.681474i	$-0.761339\pi$
$211$		−	4177.37i		−	1.36295i	0.731843	−	0.681474i	$-0.238661\pi$
$212$	2445.93	−	1143.37i	0.792393	−	0.370411i
$213$		0			0
$214$	−1679.22	+	2638.60i	−0.536399	+	0.842856i
$215$	−3705.72			−1.17548
$216$		0			0
$217$	−660.762			−0.206707
$218$	−26.8184	+	42.1404i	−0.00833198	+	0.0130922i
$219$		0			0
$220$	−2138.06	+	999.453i	−0.655217	+	0.306287i
$221$		−	3134.28i		−	0.954002i
$222$		0			0
$223$		−	1155.67i		−	0.347039i	−0.984830	−	0.173519i	$-0.944486\pi$
$223$		−	1155.67i		−	0.347039i	0.984830	−	0.173519i	$-0.0555139\pi$
$224$	774.737	−	246.287i	0.231091	−	0.0734632i
$225$		0			0
$226$	−3825.76	−	2434.74i	−1.12604	−	0.716620i
$227$	−1499.50			−0.438437			−0.219218	−	0.975676i	$-0.570351\pi$
$227$	−1499.50			−0.438437			−0.219218	+	0.975676i	$0.570351\pi$
$228$		0			0
$229$	−320.011			−0.0923445			−0.0461723	−	0.998933i	$-0.514702\pi$
$229$	−320.011			−0.0923445			−0.0461723	+	0.998933i	$0.514702\pi$
$230$	6234.81	+	3967.87i	1.78744	+	1.13754i
$231$		0			0
$232$	42.8947	−	329.425i	0.0121387	−	0.0932233i
$233$		−	1446.64i		−	0.406749i	−0.979101	−	0.203374i	$-0.934809\pi$
$233$		−	1446.64i		−	0.406749i	0.979101	−	0.203374i	$-0.0651909\pi$
$234$		0			0
$235$		−	7051.22i		−	1.95732i
$236$	−2279.74	−	4876.89i	−0.628808	−	1.34516i
$237$		0			0
$238$	290.661	−	456.722i	0.0791628	−	0.124390i
$239$	1432.06			0.387582			0.193791	−	0.981043i	$-0.437922\pi$
$239$	1432.06			0.387582			0.193791	+	0.981043i	$0.437922\pi$
$240$		0			0
$241$	−1148.97			−0.307102			−0.153551	−	0.988141i	$-0.549071\pi$
$241$	−1148.97			−0.307102			−0.153551	+	0.988141i	$0.549071\pi$
$242$	1262.54	−	1983.86i	0.335368	−	0.526972i
$243$		0			0
$244$	273.968	+	586.081i	0.0718813	+	0.153770i
$245$			4260.95i			1.11111i
$246$		0			0
$247$			9013.30i			2.32187i
$248$	−429.875	+	3301.37i	−0.110069	+	0.845312i
$249$		0			0
$250$	−2387.13	−	1519.19i	−0.603903	−	0.384327i
$251$	3652.62			0.918531			0.459266	−	0.888299i	$-0.348113\pi$
$251$	3652.62			0.918531			0.459266	+	0.888299i	$0.348113\pi$
$252$		0			0
$253$	4424.90			1.09957
$254$	−4963.37	−	3158.72i	−1.22610	−	0.780298i
$255$		0			0
$256$	−726.503	−	4031.06i	−0.177369	−	0.984144i
$257$		−	5362.37i		−	1.30154i	−0.759275	−	0.650770i	$-0.774446\pi$
$257$		−	5362.37i		−	1.30154i	0.759275	−	0.650770i	$-0.225554\pi$
$258$		0			0
$259$			1051.57i			0.252283i
$260$	−7034.43	+	3288.30i	−1.67791	+	0.784354i
$261$		0			0
$262$	1660.35	−	2608.95i	0.391515	−	0.615197i
$263$	1096.98			0.257196			0.128598	−	0.991697i	$-0.458952\pi$
$263$	1096.98			0.257196			0.128598	+	0.991697i	$0.458952\pi$
$264$		0			0
$265$	−4454.51			−1.03260
$266$	−835.859	+	1313.40i	−0.192668	+	0.302744i
$267$		0			0
$268$	−1824.79	+	853.015i	−0.415921	+	0.194426i
$269$		−	5602.35i		−	1.26982i	−0.772586	−	0.634910i	$-0.781037\pi$
$269$		−	5602.35i		−	1.26982i	0.772586	−	0.634910i	$-0.218963\pi$
$270$		0			0
$271$			1051.62i			0.235725i	0.993030	+	0.117862i	$0.0376041\pi$
$271$			1051.62i			0.235725i	−0.993030	+	0.117862i	$0.962396\pi$
$272$	−2092.83	−	1749.36i	−0.466531	−	0.389966i
$273$		0			0
$274$	3208.48	+	2041.90i	0.707415	+	0.450203i
$275$	1099.82			0.241170
$276$		0			0
$277$	2739.10			0.594139			0.297069	−	0.954856i	$-0.403991\pi$
$277$	2739.10			0.594139			0.297069	+	0.954856i	$0.403991\pi$
$278$	1921.78	+	1223.04i	0.414608	+	0.263859i
$279$		0			0
$280$	−1329.99	−	173.179i	−0.283865	−	0.0369623i
$281$		−	423.244i		−	0.0898528i	−0.998990	−	0.0449264i	$-0.985695\pi$
$281$		−	423.244i		−	0.0898528i	0.998990	−	0.0449264i	$-0.0143053\pi$
$282$		0			0
$283$		−	1630.51i		−	0.342486i	−0.985229	−	0.171243i	$-0.945222\pi$
$283$		−	1630.51i		−	0.342486i	0.985229	−	0.171243i	$-0.0547783\pi$
$284$	−324.593	−	694.378i	−0.0678206	−	0.145084i
$285$		0			0
$286$	−2496.20	+	3922.33i	−0.516096	+	0.810953i
$287$	−1779.93			−0.366083
$288$		0			0
$289$	3096.54			0.630275
$290$	−294.267	+	462.388i	−0.0595860	+	0.0936289i
$291$		0			0
$292$	851.767	+	1822.12i	0.170705	+	0.365177i
$293$		−	2352.75i		−	0.469109i	−0.972103	−	0.234554i	$-0.924637\pi$
$293$		−	2352.75i		−	0.469109i	0.972103	−	0.234554i	$-0.0753631\pi$
$294$		0			0
$295$			8881.76i			1.75293i
$296$	5253.96	+	684.122i	1.03169	+	0.134337i
$297$		0			0
$298$	2098.33	+	1335.39i	0.407896	+	0.259588i
$299$	14558.4			2.81583
$300$		0			0
$301$	−1260.89			−0.241450
$302$	−4357.65	−	2773.23i	−0.830313	−	0.528416i
$303$		0			0
$304$	6018.39	+	5030.68i	1.13545	+	0.949109i
$305$		−	1067.37i		−	0.200384i
$306$		0			0
$307$		−	10088.6i		−	1.87554i	−0.347263	−	0.937768i	$-0.612889\pi$
$307$		−	10088.6i		−	1.87554i	0.347263	−	0.937768i	$-0.387111\pi$
$308$	−727.485	+	340.069i	−0.134585	+	0.0629131i
$309$		0			0
$310$	2949.03	−	4633.89i	0.540303	−	0.848990i
$311$	−3970.97			−0.724029			−0.362015	−	0.932172i	$-0.617911\pi$
$311$	−3970.97			−0.724029			−0.362015	+	0.932172i	$0.617911\pi$
$312$		0			0
$313$	4539.33			0.819738			0.409869	−	0.912144i	$-0.365574\pi$
$313$	4539.33			0.819738			0.409869	+	0.912144i	$0.365574\pi$
$314$	−5190.24	+	8155.55i	−0.932810	+	1.46575i
$315$		0			0
$316$	3622.47	−	1693.35i	0.644873	−	0.301451i
$317$			4211.47i			0.746181i	0.927795	+	0.373091i	$0.121702\pi$
$317$			4211.47i			0.746181i	−0.927795	+	0.373091i	$0.878298\pi$
$318$		0			0
$319$			328.161i			0.0575972i
$320$	−1730.52	+	6532.38i	−0.302309	+	1.14116i
$321$		0			0
$322$	2121.43	+	1350.09i	0.367151	+	0.233657i
$323$	5223.62			0.899846
$324$		0			0
$325$	3618.52			0.617599
$326$	−2841.43	−	1808.30i	−0.482737	−	0.307217i
$327$		0			0
$328$	−1157.98	+	8893.08i	−0.194934	+	1.49707i
$329$		−	2399.21i		−	0.402045i
$330$		0			0
$331$		−	3143.43i		−	0.521990i	−0.965340	−	0.260995i	$-0.915949\pi$
$331$		−	3143.43i		−	0.521990i	0.965340	−	0.260995i	$-0.0840506\pi$
$332$	54.7910	+	117.210i	0.00905738	+	0.0193758i
$333$		0			0
$334$	3225.10	−	5067.68i	0.528352	−	0.830212i
$335$	3323.30			0.542004
$336$		0			0
$337$	7102.24			1.14802			0.574012	−	0.818847i	$-0.305386\pi$
$337$	7102.24			1.14802			0.574012	+	0.818847i	$0.305386\pi$
$338$	−4876.42	+	7662.43i	−0.784741	+	1.23308i
$339$		0			0
$340$	1905.72	+	4076.78i	0.303978	+	0.650277i
$341$		−	3288.71i		−	0.522269i
$342$		0			0
$343$			2990.19i			0.470715i
$344$	−820.302	+	6299.79i	−0.128569	+	0.987390i
$345$		0			0
$346$	−4221.45	−	2686.56i	−0.655915	−	0.417428i
$347$	−4871.70			−0.753678			−0.376839	−	0.926279i	$-0.622989\pi$
$347$	−4871.70			−0.753678			−0.376839	+	0.926279i	$0.622989\pi$
$348$		0			0
$349$	−7245.91			−1.11136			−0.555680	−	0.831396i	$-0.687542\pi$
$349$	−7245.91			−1.11136			−0.555680	+	0.831396i	$0.687542\pi$
$350$	527.286	+	335.568i	0.0805275	+	0.0512482i
$351$		0			0
$352$	1225.81	+	3855.98i	0.185613	+	0.583876i
$353$			9352.32i			1.41012i	0.709146	+	0.705062i	$0.249081\pi$
$353$			9352.32i			1.41012i	−0.709146	+	0.705062i	$0.750919\pi$
$354$		0			0
$355$			1264.60i			0.189064i
$356$	−2326.45	+	1087.52i	−0.346353	+	0.161906i
$357$		0			0
$358$	5597.34	−	8795.24i	0.826337	−	1.29844i
$359$	5162.08			0.758898			0.379449	−	0.925213i	$-0.376114\pi$
$359$	5162.08			0.758898			0.379449	+	0.925213i	$0.376114\pi$
$360$		0			0
$361$	−8162.66			−1.19006
$362$	3683.34	−	5787.73i	0.534785	−	0.840321i
$363$		0			0
$364$	−2393.50	+	1118.86i	−0.344652	+	0.161111i
$365$		−	3318.44i		−	0.475877i
$366$		0			0
$367$			3138.93i			0.446460i	0.974766	+	0.223230i	$0.0716600\pi$
$367$			3138.93i			0.446460i	−0.974766	+	0.223230i	$0.928340\pi$
$368$	8125.61	−	9720.97i	1.15102	−	1.37701i
$369$		0			0
$370$	−7374.58	−	4693.23i	−1.03618	−	0.659430i
$371$	−1515.67			−0.212102
$372$		0			0
$373$	3085.24			0.428278			0.214139	−	0.976803i	$-0.431305\pi$
$373$	3085.24			0.428278			0.214139	+	0.976803i	$0.431305\pi$
$374$	2273.17	+	1446.66i	0.314286	+	0.200014i
$375$		0			0
$376$	−11987.2	−	1560.87i	−1.64413	−	0.214084i
$377$			1079.68i			0.147498i
$378$		0			0
$379$			13468.6i			1.82542i	0.408611	+	0.912709i	$0.366013\pi$
$379$			13468.6i			1.82542i	−0.408611	+	0.912709i	$0.633987\pi$
$380$	−5480.32	−	11723.7i	−0.739828	−	1.58266i
$381$		0			0
$382$	−2076.82	+	3263.36i	−0.278166	+	0.437089i
$383$	−1100.69			−0.146847			−0.0734235	−	0.997301i	$-0.523392\pi$
$383$	−1100.69			−0.146847			−0.0734235	+	0.997301i	$0.523392\pi$
$384$		0			0
$385$	1324.89			0.175383
$386$	1883.53	−	2959.64i	0.248366	−	0.390263i
$387$		0			0
$388$	711.560	+	1522.19i	0.0931031	+	0.199169i
$389$		−	10089.1i		−	1.31501i	−0.753452	−	0.657503i	$-0.771613\pi$
$389$		−	10089.1i		−	1.31501i	0.753452	−	0.657503i	$-0.228387\pi$
$390$		0			0
$391$		−	8437.26i		−	1.09128i
$392$	7243.70	+	943.208i	0.933321	+	0.121529i
$393$		0			0
$394$	−6895.03	−	4388.04i	−0.881641	−	0.561082i
$395$	−6597.21			−0.840359
$396$		0			0
$397$	1596.47			0.201825			0.100912	−	0.994895i	$-0.467824\pi$
$397$	1596.47			0.201825			0.100912	+	0.994895i	$0.467824\pi$
$398$	−4418.10	−	2811.70i	−0.556430	−	0.354116i
$399$		0			0
$400$	2019.64	−	2416.17i	0.252455	−	0.302022i
$401$		−	4818.54i		−	0.600066i	−0.953929	−	0.300033i	$-0.903002\pi$
$401$		−	4818.54i		−	0.600066i	0.953929	−	0.300033i	$-0.0969977\pi$
$402$		0			0
$403$		−	10820.2i		−	1.33745i
$404$	−11369.0	+	5314.56i	−1.40008	+	0.654478i
$405$		0			0
$406$	−100.126	+	157.330i	−0.0122393	+	0.0192319i
$407$	−5233.80			−0.637420
$408$		0			0
$409$	−4223.57			−0.510617			−0.255308	−	0.966860i	$-0.582177\pi$
$409$	−4223.57			−0.510617			−0.255308	+	0.966860i	$0.582177\pi$
$410$	7943.96	−	12482.5i	0.956888	−	1.50358i
$411$		0			0
$412$	3942.93	−	1843.16i	0.471491	−	0.220402i
$413$			3022.06i			0.360063i
$414$		0			0
$415$		−	213.463i		−	0.0252493i
$416$	4033.03	+	12686.6i	0.475326	+	1.49522i
$417$		0			0
$418$	−6537.00	−	4160.19i	−0.764917	−	0.486798i
$419$	1165.75			0.135921			0.0679604	−	0.997688i	$-0.478351\pi$
$419$	1165.75			0.135921			0.0679604	+	0.997688i	$0.478351\pi$
$420$		0			0
$421$	−9114.56			−1.05515			−0.527573	−	0.849510i	$-0.676898\pi$
$421$	−9114.56			−1.05515			−0.527573	+	0.849510i	$0.676898\pi$
$422$	9967.99	+	6343.69i	1.14984	+	0.731768i
$423$		0			0
$424$	−986.057	+	7572.77i	−0.112941	+	0.867373i
$425$		−	2097.10i		−	0.239352i
$426$		0			0
$427$		−	363.177i		−	0.0411601i
$428$	−3746.16	−	8013.88i	−0.423078	−	0.905060i
$429$		0			0
$430$	5627.45	−	8842.54i	0.631115	−	0.991686i
$431$	−6631.38			−0.741120			−0.370560	−	0.928809i	$-0.620834\pi$
$431$	−6631.38			−0.741120			−0.370560	+	0.928809i	$0.620834\pi$
$432$		0			0
$433$	−15681.8			−1.74046			−0.870230	−	0.492646i	$-0.836030\pi$
$433$	−15681.8			−1.74046			−0.870230	+	0.492646i	$0.836030\pi$
$434$	1003.42	−	1576.70i	0.110981	−	0.174388i
$435$		0			0
$436$	−59.8289	−	127.988i	−0.00657175	−	0.0140585i
$437$			24263.2i			2.65598i
$438$		0			0
$439$		−	7923.17i		−	0.861395i	−0.902496	−	0.430697i	$-0.858268\pi$
$439$		−	7923.17i		−	0.861395i	0.902496	−	0.430697i	$-0.141732\pi$
$440$	861.939	−	6619.56i	0.0933894	−	0.717216i
$441$		0			0
$442$	7478.98	+	4759.67i	0.804839	+	0.512205i
$443$	−14013.0			−1.50289			−0.751445	−	0.659796i	$-0.770643\pi$
$443$	−14013.0			−1.50289			−0.751445	+	0.659796i	$0.770643\pi$
$444$		0			0
$445$	4236.92			0.451346
$446$	2757.65	+	1754.99i	0.292777	+	0.186325i
$447$		0			0
$448$	−588.817	+	2222.68i	−0.0620959	+	0.234401i
$449$			5967.60i			0.627235i	0.949549	+	0.313617i	$0.101541\pi$
$449$			5967.60i			0.627235i	−0.949549	+	0.313617i	$0.898459\pi$
$450$		0			0
$451$		−	8858.96i		−	0.924950i
$452$	11619.5	−	5431.62i	1.20915	−	0.565226i
$453$		0			0
$454$	2277.12	−	3578.09i	0.235397	−	0.369885i
$455$	4359.02			0.449130
$456$		0			0
$457$	12901.4			1.32057			0.660285	−	0.751015i	$-0.270435\pi$
$457$	12901.4			1.32057			0.660285	+	0.751015i	$0.270435\pi$
$458$	485.963	−	763.606i	0.0495799	−	0.0779060i
$459$		0			0
$460$	−18936.2	+	8851.88i	−1.91936	+	0.897220i
$461$			9801.20i			0.990212i	0.868833	+	0.495106i	$0.164871\pi$
$461$			9801.20i			0.990212i	−0.868833	+	0.495106i	$0.835129\pi$
$462$		0			0
$463$			3427.68i			0.344056i	0.985092	+	0.172028i	$0.0550320\pi$
$463$			3427.68i			0.344056i	−0.985092	+	0.172028i	$0.944968\pi$
$464$	720.930	+	602.615i	0.0721301	+	0.0602924i
$465$		0			0
$466$	3451.96	+	2196.85i	0.343152	+	0.218384i
$467$	−13777.2			−1.36517			−0.682583	−	0.730808i	$-0.739144\pi$
$467$	−13777.2			−1.36517			−0.682583	+	0.730808i	$0.739144\pi$
$468$		0			0
$469$	1130.77			0.111331
$470$	16825.5	+	10707.9i	1.65129	+	1.05089i
$471$		0			0
$472$	15099.2	+	1966.08i	1.47245	+	0.191729i
$473$		−	6275.63i		−	0.610050i
$474$		0			0
$475$			6030.67i			0.582539i
$476$	648.432	+	1387.14i	0.0624387	+	0.133571i
$477$		0			0
$478$	−2174.70	+	3417.16i	−0.208093	+	0.326982i
$479$	−2793.91			−0.266507			−0.133254	−	0.991082i	$-0.542542\pi$
$479$	−2793.91			−0.266507			−0.133254	+	0.991082i	$0.542542\pi$
$480$		0			0
$481$	−17219.8			−1.63234
$482$	1744.81	−	2741.66i	0.164883	−	0.259085i
$483$		0			0
$484$	2816.58	+	6025.31i	0.264518	+	0.565863i
$485$		−	2772.20i		−	0.259545i
$486$		0			0
$487$			17643.8i			1.64172i	0.571131	+	0.820859i	$0.306505\pi$
$487$			17643.8i			1.64172i	−0.571131	+	0.820859i	$0.693495\pi$
$488$	−1814.54	−	236.273i	−0.168321	−	0.0219172i
$489$		0			0
$490$	−10167.4	−	6470.61i	−0.937383	−	0.596556i
$491$	4816.53			0.442703			0.221351	−	0.975194i	$-0.428953\pi$
$491$	4816.53			0.442703			0.221351	+	0.975194i	$0.428953\pi$
$492$		0			0
$493$	625.727			0.0571629
$494$	−21507.4	−	13687.5i	−1.95884	−	1.24662i
$495$		0			0
$496$	−7224.90	−	6039.18i	−0.654047	−	0.546708i
$497$			430.285i			0.0388349i
$498$		0			0
$499$		−	9504.01i		−	0.852621i	−0.904577	−	0.426311i	$-0.859813\pi$
$499$		−	9504.01i		−	0.852621i	0.904577	−	0.426311i	$-0.140187\pi$
$500$	7250.14	−	3389.14i	0.648472	−	0.303134i
$501$		0			0
$502$	−5546.82	+	8715.84i	−0.493161	+	0.774915i
$503$	13840.8			1.22690			0.613452	−	0.789732i	$-0.289780\pi$
$503$	13840.8			1.22690			0.613452	+	0.789732i	$0.289780\pi$
$504$		0			0
$505$	20705.2			1.82450
$506$	−6719.59	+	10558.7i	−0.590360	+	0.927647i
$507$		0			0
$508$	15074.6	−	7046.75i	1.31659	−	0.615451i
$509$			8144.19i			0.709204i	0.935017	+	0.354602i	$0.115384\pi$
$509$			8144.19i			0.709204i	−0.935017	+	0.354602i	$0.884616\pi$
$510$		0			0
$511$		−	1129.12i		−	0.0977478i
$512$	10722.1	+	4387.93i	0.925498	+	0.378752i
$513$		0			0
$514$	12795.6	+	8143.22i	1.09804	+	0.698798i
$515$	−7180.83			−0.614418
$516$		0			0
$517$	11941.2			1.01581
$518$	−2509.24	−	1596.89i	−0.212837	−	0.135451i
$519$		0			0
$520$	2835.87	−	21779.0i	0.239156	−	1.83668i
$521$			21121.1i			1.77607i	0.459779	+	0.888034i	$0.347929\pi$
$521$			21121.1i			1.77607i	−0.459779	+	0.888034i	$0.652071\pi$
$522$		0			0
$523$			15414.6i			1.28878i	0.764696	+	0.644391i	$0.222889\pi$
$523$			15414.6i			1.28878i	−0.764696	+	0.644391i	$0.777111\pi$
$524$	3704.06	+	7923.83i	0.308803	+	0.660600i
$525$		0			0
$526$	−1665.85	+	2617.59i	−0.138089	+	0.216982i
$527$	−6270.81			−0.518331
$528$		0			0
$529$	27023.2			2.22102
$530$	6764.56	−	10629.3i	0.554403	−	0.871147i
$531$		0			0
$532$	−1864.71	−	3989.03i	−0.151965	−	0.325087i
$533$		−	29146.9i		−	2.36865i
$534$		0			0
$535$			14594.8i			1.17942i
$536$	735.649	−	5649.68i	0.0592821	−	0.455278i
$537$		0			0
$538$	13368.3	+	8507.65i	1.07128	+	0.681767i
$539$	−7215.91			−0.576644
$540$		0			0
$541$	−3269.66			−0.259840			−0.129920	−	0.991524i	$-0.541472\pi$
$541$	−3269.66			−0.259840			−0.129920	+	0.991524i	$0.541472\pi$
$542$	−2509.36	−	1596.97i	−0.198868	−	0.126561i
$543$		0			0
$544$	7352.46	−	2337.33i	0.579474	−	0.184214i
$545$			233.090i			0.0183201i
$546$		0			0
$547$		−	2028.46i		−	0.158557i	−0.996853	−	0.0792784i	$-0.974738\pi$
$547$		−	2028.46i		−	0.158557i	0.996853	−	0.0792784i	$-0.0252616\pi$
$548$	−9744.72	+	4555.25i	−0.759624	+	0.355092i
$549$		0			0
$550$	−1670.17	+	2624.38i	−0.129484	+	0.203462i
$551$	−1799.41			−0.139124
$552$		0			0
$553$	−2244.74			−0.172615
$554$	−4159.56	+	6536.01i	−0.318994	+	0.501242i
$555$		0			0
$556$	−5836.79	+	2728.45i	−0.445207	+	0.208116i
$557$		−	5968.99i		−	0.454065i	−0.973887	−	0.227032i	$-0.927098\pi$
$557$		−	5968.99i		−	0.454065i	0.973887	−	0.227032i	$-0.0729023\pi$
$558$		0			0
$559$		−	20647.5i		−	1.56225i
$560$	2432.94	−	2910.62i	0.183590	−	0.219636i
$561$		0			0
$562$	1009.94	+	642.733i	0.0758039	+	0.0482421i
$563$	13107.0			0.981161			0.490581	−	0.871396i	$-0.336785\pi$
$563$	13107.0			0.981161			0.490581	+	0.871396i	$0.336785\pi$
$564$		0			0
$565$	−21161.3			−1.57569
$566$	3890.70	+	2476.06i	0.288937	+	0.183881i
$567$		0			0
$568$	2149.84	+	279.932i	0.158812	+	0.0206791i
$569$		−	20162.7i		−	1.48553i	−0.669553	−	0.742764i	$-0.733514\pi$
$569$		−	20162.7i		−	1.48553i	0.669553	−	0.742764i	$-0.266486\pi$
$570$		0			0
$571$			9396.23i			0.688652i	0.938850	+	0.344326i	$0.111892\pi$
$571$			9396.23i			0.688652i	−0.938850	+	0.344326i	$0.888108\pi$
$572$	−5568.74	−	11912.8i	−0.407064	−	0.870803i
$573$		0			0
$574$	2702.97	−	4247.24i	0.196550	−	0.308844i
$575$	9740.82			0.706470
$576$		0			0
$577$	−3349.25			−0.241648			−0.120824	−	0.992674i	$-0.538554\pi$
$577$	−3349.25			−0.241648			−0.120824	+	0.992674i	$0.538554\pi$
$578$	−4702.36	+	7388.93i	−0.338395	+	0.531728i
$579$		0			0
$580$	−656.477	−	1404.35i	−0.0469978	−	0.100539i
$581$		−	72.6318i		−	0.00518636i
$582$		0			0
$583$		−	7543.72i		−	0.535899i
$584$	−5641.41	−	734.573i	−0.399732	−	0.0520494i
$585$		0			0
$586$	5614.10	+	3572.85i	0.395762	+	0.251865i
$587$	−5156.24			−0.362557			−0.181278	−	0.983432i	$-0.558023\pi$
$587$	−5156.24			−0.362557			−0.181278	+	0.983432i	$0.558023\pi$
$588$		0			0
$589$	18033.1			1.26153
$590$	−21193.5	−	13487.7i	−1.47886	−	0.941153i
$591$		0			0
$592$	−9611.03	+	11498.0i	−0.667248	+	0.798254i
$593$		−	19449.0i		−	1.34684i	−0.739261	−	0.673419i	$-0.764825\pi$
$593$		−	19449.0i		−	1.34684i	0.739261	−	0.673419i	$-0.235175\pi$
$594$		0			0
$595$		−	2526.26i		−	0.174061i
$596$	−6372.99	+	2979.11i	−0.438000	+	0.204747i
$597$		0			0
$598$	−22108.2	+	34739.1i	−1.51182	+	2.37556i
$599$	25726.7			1.75486			0.877432	−	0.479701i	$-0.159255\pi$
$599$	25726.7			1.75486			0.877432	+	0.479701i	$0.159255\pi$
$600$		0			0
$601$	−11668.4			−0.791952			−0.395976	−	0.918261i	$-0.629594\pi$
$601$	−11668.4			−0.791952			−0.395976	+	0.918261i	$0.629594\pi$
$602$	1914.77	−	3008.72i	0.129635	−	0.203698i
$603$		0			0
$604$	13234.9	−	6186.78i	0.891592	−	0.416782i
$605$		−	10973.3i		−	0.737399i
$606$		0			0
$607$		−	26441.9i		−	1.76811i	−0.467382	−	0.884055i	$-0.654803\pi$
$607$		−	26441.9i		−	1.76811i	0.467382	−	0.884055i	$-0.345197\pi$
$608$	−21143.6	+	6721.50i	−1.41034	+	0.448343i
$609$		0			0
$610$	2546.94	+	1620.89i	0.169053	+	0.107587i
$611$	39287.9			2.60134
$612$		0			0
$613$	−4001.56			−0.263656			−0.131828	−	0.991273i	$-0.542085\pi$
$613$	−4001.56			−0.263656			−0.131828	+	0.991273i	$0.542085\pi$
$614$	24073.4	+	15320.5i	1.58229	+	1.00698i
$615$		0			0
$616$	293.279	−	2252.34i	0.0191827	−	0.147320i
$617$			25511.2i			1.66457i	0.554347	+	0.832286i	$0.312968\pi$
$617$			25511.2i			1.66457i	−0.554347	+	0.832286i	$0.687032\pi$
$618$		0			0
$619$			25105.1i			1.63014i	0.579361	+	0.815071i	$0.303302\pi$
$619$			25105.1i			1.63014i	−0.579361	+	0.815071i	$0.696698\pi$
$620$	6578.97	+	14073.9i	0.426157	+	0.911648i
$621$		0			0
$622$	6030.26	−	9475.48i	0.388732	−	0.610824i
$623$	1441.63			0.0927091
$624$		0			0
$625$	−19354.5			−1.23869
$626$	−6893.36	+	10831.7i	−0.440118	+	0.691568i
$627$		0			0
$628$	−11578.8	−	24769.8i	−0.735743	−	1.57392i
$629$			9979.65i			0.632614i
$630$		0			0
$631$		−	10090.6i		−	0.636612i	−0.947988	−	0.318306i	$-0.896886\pi$
$631$		−	10090.6i		−	0.636612i	0.947988	−	0.318306i	$-0.103114\pi$
$632$	−1460.37	+	11215.4i	−0.0919150	+	0.705893i
$633$		0			0
$634$	−10049.4	−	6395.47i	−0.629512	−	0.400626i
$635$	−27453.8			−1.71570
$636$		0			0
$637$	−23741.1			−1.47670
$638$	−783.055	−	498.341i	−0.0485916	−	0.0309240i
$639$		0			0
$640$	−12959.6	−	14049.3i	−0.800425	−	0.867732i
$641$		−	155.209i		−	0.00956376i	−0.999989	−	0.00478188i	$-0.998478\pi$
$641$		−	155.209i		−	0.00956376i	0.999989	−	0.00478188i	$-0.00152213\pi$
$642$		0			0
$643$			8048.26i			0.493612i	0.969065	+	0.246806i	$0.0793810\pi$
$643$			8048.26i			0.493612i	−0.969065	+	0.246806i	$0.920619\pi$
$644$	−6443.14	+	3011.90i	−0.394247	+	0.184294i
$645$		0			0
$646$	−7932.52	+	12464.5i	−0.483128	+	0.759150i
$647$	−17128.5			−1.04079			−0.520394	−	0.853926i	$-0.674215\pi$
$647$	−17128.5			−1.04079			−0.520394	+	0.853926i	$0.674215\pi$
$648$		0			0
$649$	−15041.2			−0.909739
$650$	−5495.04	+	8634.48i	−0.331590	+	0.521034i
$651$		0			0
$652$	8629.91	−	4034.13i	0.518364	−	0.242314i
$653$		−	5854.10i		−	0.350825i	−0.984495	−	0.175412i	$-0.943874\pi$
$653$		−	5854.10i		−	0.350825i	0.984495	−	0.175412i	$-0.0561259\pi$
$654$		0			0
$655$		−	14430.8i		−	0.860853i
$656$	−19462.1	−	16268.0i	−1.15833	−	0.968232i
$657$		0			0
$658$	5724.98	+	3643.41i	0.339184	+	0.215859i
$659$	22130.6			1.30817			0.654086	−	0.756420i	$-0.273053\pi$
$659$	22130.6			1.30817			0.654086	+	0.756420i	$0.273053\pi$
$660$		0			0
$661$	19160.0			1.12744			0.563721	−	0.825965i	$-0.309369\pi$
$661$	19160.0			1.12744			0.563721	+	0.825965i	$0.309369\pi$
$662$	7500.82	+	4773.57i	0.440374	+	0.280257i
$663$		0			0
$664$	−362.891	−	47.2524i	−0.0212092	−	0.00276167i
$665$			7264.80i			0.423634i
$666$		0			0
$667$			2906.44i			0.168722i
$668$	7194.84	+	15391.4i	0.416732	+	0.891484i
$669$		0			0
$670$	−5046.71	+	7930.02i	−0.291002	+	0.457259i
$671$	1807.58			0.103996
$672$		0			0
$673$	24302.6			1.39197			0.695984	−	0.718057i	$-0.254968\pi$
$673$	24302.6			1.39197			0.695984	+	0.718057i	$0.254968\pi$
$674$	−10785.4	+	16947.3i	−0.616375	+	0.968524i
$675$		0			0
$676$	−10878.8	−	23272.1i	−0.618955	−	1.32409i
$677$			16656.4i			0.945581i	0.881175	+	0.472791i	$0.156753\pi$
$677$			16656.4i			0.945581i	−0.881175	+	0.472791i	$0.843247\pi$
$678$		0			0
$679$		−	943.255i		−	0.0533120i
$680$	−12622.0	−	1643.52i	−0.711809	−	0.0926853i
$681$		0			0
$682$	7847.48	+	4994.19i	0.440610	+	0.280407i
$683$	24952.6			1.39793			0.698964	−	0.715157i	$-0.253645\pi$
$683$	24952.6			1.39793			0.698964	+	0.715157i	$0.253645\pi$
$684$		0			0
$685$	17747.0			0.989895
$686$	−7135.16	−	4540.86i	−0.397116	−	0.252727i
$687$		0			0
$688$	−13786.8	−	11524.2i	−0.763978	−	0.638597i
$689$		−	24819.6i		−	1.37235i
$690$		0			0
$691$			15536.7i			0.855346i	0.903934	+	0.427673i	$0.140666\pi$
$691$			15536.7i			0.855346i	−0.903934	+	0.427673i	$0.859334\pi$
$692$	12821.3	−	5993.41i	0.704323	−	0.329242i
$693$		0			0
$694$	7398.09	−	11624.8i	0.404651	−	0.635837i
$695$	10629.9			0.580166
$696$		0			0
$697$	−16892.0			−0.917976
$698$	11003.5	−	17290.1i	0.596691	−	0.937594i
$699$		0			0
$700$	−1601.46	+	748.615i	−0.0864706	+	0.0404214i
$701$		−	9683.38i		−	0.521735i	−0.965375	−	0.260868i	$-0.915991\pi$
$701$		−	9683.38i		−	0.521735i	0.965375	−	0.260868i	$-0.0840086\pi$
$702$		0			0
$703$		−	28698.6i		−	1.53967i
$704$	−11062.6	−	2930.63i	−0.592240	−	0.156892i
$705$		0			0
$706$	−22316.4	−	14202.3i	−1.18964	−	0.757097i
$707$	7045.06			0.374762
$708$		0			0
$709$	−15665.5			−0.829801			−0.414901	−	0.909867i	$-0.636184\pi$
$709$	−15665.5			−0.829801			−0.414901	+	0.909867i	$0.636184\pi$
$710$	−3017.56	−	1920.40i	−0.159503	−	0.101509i
$711$		0			0
$712$	937.889	−	7202.85i	0.0493664	−	0.379127i
$713$		−	29127.2i		−	1.52991i
$714$		0			0
$715$			21695.5i			1.13478i
$716$	12487.0	+	26712.6i	0.651764	+	1.39427i
$717$		0			0
$718$	−7839.06	+	12317.7i	−0.407453	+	0.640240i
$719$	−15944.3			−0.827015			−0.413507	−	0.910501i	$-0.635696\pi$
$719$	−15944.3			−0.827015			−0.413507	+	0.910501i	$0.635696\pi$
$720$		0			0
$721$	−2443.31			−0.126205
$722$	12395.7	−	19477.6i	0.638947	−	1.00399i
$723$		0			0
$724$	8217.13	+	17578.3i	0.421806	+	0.902338i
$725$			722.402i			0.0370060i
$726$		0			0
$727$			23773.6i			1.21281i	0.795156	+	0.606405i	$0.207389\pi$
$727$			23773.6i			1.21281i	−0.795156	+	0.606405i	$0.792611\pi$
$728$	964.919	−	7410.43i	0.0491240	−	0.377265i
$729$		0			0
$730$	7918.42	+	5039.33i	0.401471	+	0.255499i
$731$	−11966.2			−0.605451
$732$		0			0
$733$	−16190.1			−0.815818			−0.407909	−	0.913023i	$-0.633742\pi$
$733$	−16190.1			−0.815818			−0.407909	+	0.913023i	$0.633742\pi$
$734$	−7490.07	−	4766.73i	−0.376653	−	0.239705i
$735$		0			0
$736$	10856.6	+	34151.4i	0.543724	+	1.71038i
$737$			5628.00i			0.281289i
$738$		0			0
$739$		−	3013.13i		−	0.149986i	−0.997184	−	0.0749930i	$-0.976107\pi$
$739$		−	3013.13i		−	0.149986i	0.997184	−	0.0749930i	$-0.0238934\pi$
$740$	22397.9	−	10470.1i	1.11265	−	0.520118i
$741$		0			0
$742$	2301.68	−	3616.68i	0.113878	−	0.178939i
$743$	−14363.7			−0.709225			−0.354613	−	0.935013i	$-0.615387\pi$
$743$	−14363.7			−0.709225			−0.354613	+	0.935013i	$0.615387\pi$
$744$		0			0
$745$	11606.4			0.570775
$746$	−4685.20	+	7361.97i	−0.229943	+	0.361315i
$747$		0			0
$748$	−6904.02	+	3227.34i	−0.337481	+	0.157758i
$749$			4965.96i			0.242260i
$750$		0			0
$751$		−	21754.9i		−	1.05705i	−0.848917	−	0.528526i	$-0.822745\pi$
$751$		−	21754.9i		−	1.05705i	0.848917	−	0.528526i	$-0.177255\pi$
$752$	21928.1	−	26233.5i	1.06335	−	1.27212i
$753$		0			0
$754$	−2576.33	−	1639.59i	−0.124436	−	0.0791916i
$755$	−24103.3			−1.16187
$756$		0			0
$757$	25070.4			1.20370			0.601848	−	0.798611i	$-0.294431\pi$
$757$	25070.4			1.20370			0.601848	+	0.798611i	$0.294431\pi$
$758$	−32138.5	−	20453.2i	−1.54000	−	0.980069i
$759$		0			0
$760$	36297.2	+	4726.29i	1.73242	+	0.225580i
$761$			20326.9i			0.968263i	0.874995	+	0.484132i	$0.160864\pi$
$761$			20326.9i			0.968263i	−0.874995	+	0.484132i	$0.839136\pi$
$762$		0			0
$763$			79.3101i			0.00376306i
$764$	−4633.16	−	9911.38i	−0.219400	−	0.469347i
$765$		0			0
$766$	1671.48	−	2626.44i	0.0788423	−	0.123887i
$767$	−49487.3			−2.32970
$768$		0			0
$769$	−4680.89			−0.219502			−0.109751	−	0.993959i	$-0.535005\pi$
$769$	−4680.89			−0.219502			−0.109751	+	0.993959i	$0.535005\pi$
$770$	−2011.96	+	3161.44i	−0.0941636	+	0.147961i
$771$		0			0
$772$	4201.95	+	8988.92i	0.195896	+	0.419065i
$773$			2385.68i			0.111005i	0.998459	+	0.0555025i	$0.0176761\pi$
$773$			2385.68i			0.111005i	−0.998459	+	0.0555025i	$0.982324\pi$
$774$		0			0
$775$		−	7239.65i		−	0.335556i
$776$	−4712.80	−	613.658i	−0.218015	−	0.0283879i
$777$		0			0
$778$	24074.5	+	15321.2i	1.10940	+	0.706028i
$779$	48576.6			2.23419
$780$		0			0
$781$	−2141.59			−0.0981206
$782$	20132.9	+	12812.7i	0.920653	+	0.585909i
$783$		0			0
$784$	−13250.8	+	15852.5i	−0.603628	+	0.722143i
$785$			45110.6i			2.05104i
$786$		0			0
$787$			8714.78i			0.394725i	0.980331	+	0.197362i	$0.0632375\pi$
$787$			8714.78i			0.394725i	−0.980331	+	0.197362i	$0.936762\pi$
$788$	20941.4	−	9789.23i	0.946708	−	0.442547i
$789$		0			0
$790$	10018.4	−	15742.2i	0.451190	−	0.708965i
$791$	−7200.24			−0.323655
$792$		0			0
$793$	5947.14			0.266317
$794$	−2424.37	+	3809.48i	−0.108360	+	0.170269i
$795$		0			0
$796$	13418.5	−	6272.60i	0.597496	−	0.279304i
$797$		−	15364.9i		−	0.682876i	−0.939904	−	0.341438i	$-0.889086\pi$
$797$		−	15364.9i		−	0.682876i	0.939904	−	0.341438i	$-0.110914\pi$
$798$		0			0
$799$		−	22769.2i		−	1.00815i
$800$	2698.45	+	8488.41i	0.119256	+	0.375138i
$801$		0			0
$802$	11497.9	+	7317.37i	0.506243	+	0.322176i
$803$	5619.77			0.246971
$804$		0			0
$805$	11734.2			0.513759
$806$	25819.0	+	16431.4i	1.12833	+	0.718079i
$807$		0			0
$808$	4583.33	−	35199.3i	0.199556	−	1.53256i
$809$		−	25153.9i		−	1.09316i	−0.837408	−	0.546578i	$-0.815930\pi$
$809$		−	25153.9i		−	1.09316i	0.837408	−	0.546578i	$-0.184070\pi$
$810$		0			0
$811$			20366.0i			0.881807i	0.897554	+	0.440904i	$0.145342\pi$
$811$			20366.0i			0.881807i	−0.897554	+	0.440904i	$0.854658\pi$
$812$	−223.370	−	477.838i	−0.00965361	−	0.0206513i
$813$		0			0
$814$	7947.98	−	12488.8i	0.342232	−	0.537756i
$815$	−15716.7			−0.675501
$816$		0			0
$817$	34411.3			1.47356
$818$	6413.86	−	10078.2i	0.274151	−	0.430779i
$819$		0			0
$820$	17722.1	+	37911.6i	0.754734	+	1.61455i
$821$			781.431i			0.0332182i	0.999862	+	0.0166091i	$0.00528708\pi$
$821$			781.431i			0.0332182i	−0.999862	+	0.0166091i	$0.994713\pi$
$822$		0			0
$823$			32821.3i			1.39013i	0.718945	+	0.695067i	$0.244625\pi$
$823$			32821.3i			1.39013i	−0.718945	+	0.695067i	$0.755375\pi$
$824$	−1589.56	+	12207.6i	−0.0672025	+	0.516105i
$825$		0			0
$826$	−7211.21	−	4589.26i	−0.303765	−	0.193318i
$827$	−43717.4			−1.83821			−0.919106	−	0.394010i	$-0.871087\pi$
$827$	−43717.4			−1.83821			−0.919106	+	0.394010i	$0.871087\pi$
$828$		0			0
$829$	13211.9			0.553521			0.276761	−	0.960939i	$-0.410739\pi$
$829$	13211.9			0.553521			0.276761	+	0.960939i	$0.410739\pi$
$830$	509.363	+	324.162i	0.0213015	+	0.0135564i
$831$		0			0
$832$	−36397.1	−	9642.07i	−1.51664	−	0.401777i
$833$			13759.1i			0.572297i
$834$		0			0
$835$		−	28030.7i		−	1.16173i
$836$	19854.0	−	9280.92i	0.821370	−	0.383956i
$837$		0			0
$838$	−1770.30	+	2781.71i	−0.0729760	+	0.114669i
$839$	33876.0			1.39396			0.696978	−	0.717092i	$-0.254527\pi$
$839$	33876.0			1.39396			0.696978	+	0.717092i	$0.254527\pi$
$840$		0			0
$841$	24173.5			0.991162
$842$	13841.2	−	21749.1i	0.566509	−	0.890169i
$843$		0			0
$844$	−30274.5	+	14152.1i	−1.23471	+	0.577173i
$845$			42383.0i			1.72547i
$846$		0			0
$847$		−	3733.70i		−	0.151466i
$848$	−16572.6	−	13852.8i	−0.671116	−	0.560976i
$849$		0			0
$850$	5004.08	+	3184.63i	0.201928	+	0.128508i
$851$	−46354.4			−1.86722
$852$		0			0
$853$	−14748.5			−0.592005			−0.296002	−	0.955187i	$-0.595654\pi$
$853$	−14748.5			−0.592005			−0.296002	+	0.955187i	$0.595654\pi$
$854$	866.608	+	551.515i	0.0347245	+	0.0220989i
$855$		0			0
$856$	24811.5	+	3230.73i	0.990701	+	0.129000i
$857$			24382.3i			0.971859i	0.873998	+	0.485929i	$0.161519\pi$
$857$			24382.3i			0.971859i	−0.873998	+	0.485929i	$0.838481\pi$
$858$		0			0
$859$			21247.2i			0.843942i	0.906609	+	0.421971i	$0.138662\pi$
$859$			21247.2i			0.843942i	−0.906609	+	0.421971i	$0.861338\pi$
$860$	12554.2	+	26856.3i	0.497785	+	1.06487i
$861$		0			0
$862$	10070.3	−	15823.7i	0.397908	−	0.625242i
$863$	4434.51			0.174916			0.0874581	−	0.996168i	$-0.472126\pi$
$863$	4434.51			0.174916			0.0874581	+	0.996168i	$0.472126\pi$
$864$		0			0
$865$	−23350.0			−0.917830
$866$	23814.2	−	37419.7i	0.934455	−	1.46833i
$867$		0			0
$868$	2238.53	+	4788.72i	0.0875352	+	0.187258i
$869$		−	11172.4i		−	0.436130i
$870$		0			0
$871$			18516.7i			0.720339i
$872$	396.258	+	51.5971i	0.0153887	+	0.00200378i
$873$		0			0
$874$	−57896.5	−	36845.7i	−2.24071	−	1.42600i
$875$	−4492.69			−0.173578
$876$		0			0
$877$	−13985.9			−0.538507			−0.269253	−	0.963069i	$-0.586777\pi$
$877$	−13985.9			−0.538507			−0.269253	+	0.963069i	$0.586777\pi$
$878$	18906.2	+	12032.0i	0.726711	+	0.462484i
$879$		0			0
$880$	14486.6	+	12109.1i	0.554935	+	0.463862i
$881$		−	4428.74i		−	0.169362i	−0.996408	−	0.0846812i	$-0.973013\pi$
$881$		−	4428.74i		−	0.169362i	0.996408	−	0.0846812i	$-0.0269872\pi$
$882$		0			0
$883$			40519.1i			1.54426i	0.635467	+	0.772128i	$0.280808\pi$
$883$			40519.1i			1.54426i	−0.635467	+	0.772128i	$0.719192\pi$
$884$	−22714.9	+	10618.3i	−0.864238	+	0.403995i
$885$		0			0
$886$	21280.0	−	33437.8i	0.806903	−	1.26791i
$887$	−31161.7			−1.17960			−0.589802	−	0.807548i	$-0.700794\pi$
$887$	−31161.7			−1.17960			−0.589802	+	0.807548i	$0.700794\pi$
$888$		0			0
$889$	−9341.29			−0.352415
$890$	−6434.12	+	10110.1i	−0.242328	+	0.380776i
$891$		0			0
$892$	−8375.47	+	3915.18i	−0.314385	+	0.146962i
$893$			65477.7i			2.45367i
$894$		0			0
$895$		−	48648.9i		−	1.81693i
$896$	−4409.56	−	4780.35i	−0.164412	−	0.178237i
$897$		0			0
$898$	−14239.8	−	9062.31i	−0.529164	−	0.336763i
$899$	2160.14			0.0801388
$900$		0			0
$901$	−14384.1			−0.531858
$902$	21139.2	+	13453.1i	0.780329	+	0.496607i
$903$		0			0
$904$	−4684.29	+	35974.7i	−0.172342	+	1.32356i
$905$		−	32013.5i		−	1.17587i
$906$		0			0
$907$			24021.4i			0.879402i	0.898144	+	0.439701i	$0.144916\pi$
$907$			24021.4i			0.879402i	−0.898144	+	0.439701i	$0.855084\pi$
$908$	5079.99	+	10867.3i	0.185667	+	0.397184i
$909$		0			0
$910$	−6619.55	+	10401.5i	−0.241138	+	0.378907i
$911$	33057.5			1.20225			0.601123	−	0.799157i	$-0.294720\pi$
$911$	33057.5			1.20225			0.601123	+	0.799157i	$0.294720\pi$
$912$		0			0
$913$	361.499			0.0131039
$914$	−19591.8	+	30785.1i	−0.709016	+	1.11409i
$915$		0			0
$916$	1084.13	+	2319.20i	0.0391055	+	0.0836556i
$917$		−	4910.16i		−	0.176824i
$918$		0			0
$919$			10303.3i			0.369831i	0.982754	+	0.184915i	$0.0592011\pi$
$919$			10303.3i			0.369831i	−0.982754	+	0.184915i	$0.940799\pi$
$920$	7633.96	−	58627.7i	0.273570	−	2.10098i
$921$		0			0
$922$	−23387.5	−	14884.0i	−0.835387	−	0.531646i
$923$	−7046.06			−0.251272
$924$		0			0
$925$	−11521.5			−0.409540
$926$	−8179.10	−	5205.23i	−0.290261	−	0.184724i
$927$		0			0
$928$	−2532.75	+	805.154i	−0.0895921	+	0.0284811i
$929$		−	7704.91i		−	0.272110i	−0.990701	−	0.136055i	$-0.956558\pi$
$929$		−	7704.91i		−	0.272110i	0.990701	−	0.136055i	$-0.0434424\pi$
$930$		0			0
$931$		−	39567.2i		−	1.39287i
$932$	−10484.2	+	4900.92i	−0.368477	+	0.172248i
$933$		0			0
$934$	20921.9	−	32875.0i	0.732959	−	1.15172i
$935$	12573.5			0.439785
$936$		0			0
$937$	−44189.8			−1.54068			−0.770340	−	0.637633i	$-0.779914\pi$
$937$	−44189.8			−1.54068			−0.770340	+	0.637633i	$0.779914\pi$
$938$	−1717.17	+	2698.23i	−0.0597735	+	0.0939236i
$939$		0			0
$940$	−51102.1	+	23888.1i	−1.77315	+	0.828876i
$941$		−	51448.1i		−	1.78232i	−0.453691	−	0.891159i	$-0.649893\pi$
$941$		−	51448.1i		−	1.78232i	0.453691	−	0.891159i	$-0.350107\pi$
$942$		0			0
$943$		−	78461.5i		−	2.70950i
$944$	−27620.8	+	33043.8i	−0.952310	+	1.13928i
$945$		0			0
$946$	14974.8	+	9530.08i	0.514666	+	0.327537i
$947$	17691.3			0.607066			0.303533	−	0.952821i	$-0.401834\pi$
$947$	17691.3			0.607066			0.303533	+	0.952821i	$0.401834\pi$
$948$		0			0
$949$	18489.6			0.632454
$950$	−14390.3	−	9158.09i	−0.491457	−	0.312766i
$951$		0			0
$952$	−4294.69	−	559.215i	−0.146210	−	0.0190381i
$953$		−	27331.2i		−	0.929007i	−0.885571	−	0.464504i	$-0.846233\pi$
$953$		−	27331.2i		−	0.929007i	0.885571	−	0.464504i	$-0.153767\pi$
$954$		0			0
$955$			18050.5i			0.611624i
$956$	−4851.52	−	10378.5i	−0.164131	−	0.351114i
$957$		0			0
$958$	4242.79	−	6666.79i	0.143088	−	0.224837i
$959$	6038.51			0.203330
$960$		0			0
$961$	8142.84			0.273332
$962$	26149.7	−	41089.6i	0.876403	−	1.37711i
$963$		0			0
$964$	3892.47	+	8326.88i	0.130050	+	0.278206i
$965$		−	16370.6i		−	0.546101i
$966$		0			0
$967$		−	48045.3i		−	1.59776i	−0.601492	−	0.798879i	$-0.705427\pi$
$967$		−	48045.3i		−	1.59776i	0.601492	−	0.798879i	$-0.294573\pi$
$968$	−18654.8	−	2429.05i	−0.619408	−	0.0806536i
$969$		0			0
$970$	6614.99	+	4209.82i	0.218964	+	0.139350i
$971$	6999.70			0.231340			0.115670	−	0.993288i	$-0.463099\pi$
$971$	6999.70			0.231340			0.115670	+	0.993288i	$0.463099\pi$
$972$		0			0
$973$	3616.88			0.119169
$974$	−42101.4	−	26793.6i	−1.38503	−	0.881440i
$975$		0			0
$976$	3319.33	−	3971.04i	0.108862	−	0.130236i
$977$			42914.1i			1.40527i	0.711552	+	0.702633i	$0.247992\pi$
$977$			42914.1i			1.40527i	−0.711552	+	0.702633i	$0.752008\pi$
$978$		0			0
$979$			7175.22i			0.234240i
$980$	30880.2	−	14435.2i	1.00656	−	0.470527i
$981$		0			0
$982$	−7314.31	+	11493.2i	−0.237688	+	0.373484i
$983$	−1615.78			−0.0524266			−0.0262133	−	0.999656i	$-0.508345\pi$
$983$	−1615.78			−0.0524266			−0.0262133	+	0.999656i	$0.508345\pi$
$984$		0			0
$985$	−38138.3			−1.23369
$986$	−950.220	+	1493.10i	−0.0306908	+	0.0482252i
$987$		0			0
$988$	65321.7	−	30535.2i	2.10340	−	0.983253i
$989$		−	55581.6i		−	1.78705i
$990$		0			0
$991$			15725.6i			0.504076i	0.967717	+	0.252038i	$0.0811008\pi$
$991$			15725.6i			0.504076i	−0.967717	+	0.252038i	$0.918899\pi$
$992$	25382.3	−	8068.96i	0.812386	−	0.258256i
$993$		0			0
$994$	−1026.74	−	653.425i	−0.0327628	−	0.0208505i
$995$	−24437.7			−0.778620
$996$		0			0
$997$	−22555.5			−0.716489			−0.358244	−	0.933628i	$-0.616625\pi$
$997$	−22555.5			−0.716489			−0.358244	+	0.933628i	$0.616625\pi$
$998$	22678.4	+	14432.7i	0.719310	+	0.457773i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.b.a.107.4	yes	12
3.2	odd	2	inner	108.4.b.a.107.9	yes	12
4.3	odd	2	inner	108.4.b.a.107.10	yes	12
8.3	odd	2		1728.4.c.i.1727.3		12
8.5	even	2		1728.4.c.i.1727.4		12
12.11	even	2	inner	108.4.b.a.107.3	✓	12
24.5	odd	2		1728.4.c.i.1727.10		12
24.11	even	2		1728.4.c.i.1727.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.b.a.107.3	✓	12	12.11	even	2	inner
108.4.b.a.107.4	yes	12	1.1	even	1	trivial
108.4.b.a.107.9	yes	12	3.2	odd	2	inner
108.4.b.a.107.10	yes	12	4.3	odd	2	inner
1728.4.c.i.1727.3		12	8.3	odd	2
1728.4.c.i.1727.4		12	8.5	even	2
1728.4.c.i.1727.9		12	24.11	even	2
1728.4.c.i.1727.10		12	24.5	odd	2

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.51859 + 2.38619i) q^{2} +(-3.38780 - 7.24726i) q^{4} +13.1987i q^{5} +4.49091i q^{7} +(22.4380 + 2.92167i) q^{8} +O(q^{10})\)	\(q+(-1.51859 + 2.38619i) q^{2} +(-3.38780 - 7.24726i) q^{4} +13.1987i q^{5} +4.49091i q^{7} +(22.4380 + 2.92167i) q^{8} +(-31.4945 - 20.0433i) q^{10} -22.3519 q^{11} -73.5402 q^{13} +(-10.7162 - 6.81984i) q^{14} +(-41.0457 + 49.1045i) q^{16} +42.6199i q^{17} -122.563i q^{19} +(95.6542 - 44.7144i) q^{20} +(33.9433 - 53.3359i) q^{22} -197.965 q^{23} -49.2047 q^{25} +(111.677 - 175.481i) q^{26} +(32.5468 - 15.2143i) q^{28} -14.6816i q^{29} +147.133i q^{31} +(-54.8412 - 172.512i) q^{32} +(-101.699 - 64.7220i) q^{34} -59.2740 q^{35} +234.154 q^{37} +(292.458 + 186.122i) q^{38} +(-38.5622 + 296.152i) q^{40} +396.340i q^{41} +280.764i q^{43} +(75.7238 + 161.990i) q^{44} +(300.627 - 472.382i) q^{46} -534.237 q^{47} +322.832 q^{49} +(74.7216 - 117.412i) q^{50} +(249.139 + 532.965i) q^{52} +337.497i q^{53} -295.016i q^{55} +(-13.1210 + 100.767i) q^{56} +(35.0330 + 22.2952i) q^{58} +672.928 q^{59} -80.8693 q^{61} +(-351.087 - 223.434i) q^{62} +(494.928 + 131.113i) q^{64} -970.632i q^{65} -251.791i q^{67} +(308.878 - 144.388i) q^{68} +(90.0127 - 141.439i) q^{70} +95.8124 q^{71} -251.422 q^{73} +(-355.583 + 558.737i) q^{74} +(-888.245 + 415.218i) q^{76} -100.381i q^{77} +499.839i q^{79} +(-648.114 - 541.748i) q^{80} +(-945.742 - 601.876i) q^{82} -16.1731 q^{83} -562.526 q^{85} +(-669.957 - 426.365i) q^{86} +(-501.533 - 65.3050i) q^{88} -321.011i q^{89} -330.263i q^{91} +(670.665 + 1434.71i) q^{92} +(811.285 - 1274.79i) q^{94} +1617.67 q^{95} -210.036 q^{97} +(-490.248 + 770.337i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4}+O(q^{10}) \) 12 * q - 12 * q^4	\( 12 q - 12 q^{4} + 24 q^{10} + 36 q^{13} + 24 q^{16} + 120 q^{22} - 132 q^{25} + 420 q^{28} - 360 q^{34} + 516 q^{37} - 1152 q^{40} - 696 q^{46} - 720 q^{49} + 204 q^{52} + 2832 q^{58} - 972 q^{61} + 2496 q^{64} - 1848 q^{70} + 660 q^{73} - 5004 q^{76} - 3888 q^{82} + 1056 q^{85} + 3168 q^{88} + 7608 q^{94} + 2532 q^{97}+O(q^{100}) \) 12 * q - 12 * q^4 + 24 * q^10 + 36 * q^13 + 24 * q^16 + 120 * q^22 - 132 * q^25 + 420 * q^28 - 360 * q^34 + 516 * q^37 - 1152 * q^40 - 696 * q^46 - 720 * q^49 + 204 * q^52 + 2832 * q^58 - 972 * q^61 + 2496 * q^64 - 1848 * q^70 + 660 * q^73 - 5004 * q^76 - 3888 * q^82 + 1056 * q^85 + 3168 * q^88 + 7608 * q^94 + 2532 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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