LMFDB - Embedded newform 336.4.bc.f.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(17,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("336.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.bc (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:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	336.17
Dual form			336.4.bc.f.257.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.62731 + 3.72057i) q^{3} +(0.263312 + 0.456070i) q^{5} +(16.6747 + 8.05944i) q^{7} +(-0.685212 - 26.9913i) q^{9} +O(q^{10})$	\(q+(-3.62731 + 3.72057i) q^{3} +(0.263312 + 0.456070i) q^{5} +(16.6747 + 8.05944i) q^{7} +(-0.685212 - 26.9913i) q^{9} +(9.84572 + 5.68443i) q^{11} -65.8264i q^{13} +(-2.65195 - 0.674638i) q^{15} +(0.339033 - 0.587223i) q^{17} +(19.0112 - 10.9761i) q^{19} +(-90.4700 + 32.8052i) q^{21} +(6.60693 - 3.81451i) q^{23} +(62.3613 - 108.013i) q^{25} +(102.908 + 95.3565i) q^{27} +165.699i q^{29} +(110.323 + 63.6953i) q^{31} +(-56.8628 + 16.0124i) q^{33} +(0.714981 + 9.72697i) q^{35} +(-95.9053 - 166.113i) q^{37} +(244.911 + 238.773i) q^{39} +508.434 q^{41} +25.2052 q^{43} +(12.1295 - 7.41964i) q^{45} +(167.209 + 289.614i) q^{47} +(213.091 + 268.777i) q^{49} +(0.955021 + 3.39143i) q^{51} +(376.298 + 217.256i) q^{53} +5.98711i q^{55} +(-28.1222 + 110.546i) q^{57} +(-208.919 + 361.858i) q^{59} +(-288.511 + 166.572i) q^{61} +(206.109 - 455.594i) q^{63} +(30.0214 - 17.3329i) q^{65} +(68.6985 - 118.989i) q^{67} +(-9.77326 + 38.4180i) q^{69} -718.257i q^{71} +(1009.78 + 582.997i) q^{73} +(175.665 + 623.816i) q^{75} +(118.361 + 174.137i) q^{77} +(-189.187 - 327.682i) q^{79} +(-728.061 + 36.9895i) q^{81} -539.610 q^{83} +0.357086 q^{85} +(-616.495 - 601.043i) q^{87} +(457.610 + 792.604i) q^{89} +(530.524 - 1097.64i) q^{91} +(-637.160 + 179.423i) q^{93} +(10.0117 + 5.78029i) q^{95} -29.2850i q^{97} +(146.684 - 269.644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{7} + 14 q^{9}+O(q^{10}) $ 48 * q - 12 * q^7 + 14 * q^9	$ 48 q - 12 q^{7} + 14 q^{9} + 88 q^{15} + 270 q^{19} + 50 q^{21} - 438 q^{25} - 216 q^{31} - 372 q^{33} + 66 q^{37} - 242 q^{39} - 900 q^{43} - 294 q^{45} + 60 q^{49} + 138 q^{51} + 1384 q^{57} + 108 q^{61} - 1096 q^{63} - 6 q^{67} - 1206 q^{73} + 594 q^{75} + 588 q^{79} - 54 q^{81} - 240 q^{85} + 3522 q^{87} - 234 q^{91} - 608 q^{93} - 1988 q^{99}+O(q^{100}) $ 48 * q - 12 * q^7 + 14 * q^9 + 88 * q^15 + 270 * q^19 + 50 * q^21 - 438 * q^25 - 216 * q^31 - 372 * q^33 + 66 * q^37 - 242 * q^39 - 900 * q^43 - 294 * q^45 + 60 * q^49 + 138 * q^51 + 1384 * q^57 + 108 * q^61 - 1096 * q^63 - 6 * q^67 - 1206 * q^73 + 594 * q^75 + 588 * q^79 - 54 * q^81 - 240 * q^85 + 3522 * q^87 - 234 * q^91 - 608 * q^93 - 1988 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.62731	+	3.72057i	−0.698077	+	0.716023i
$3$	−3.62731	+	3.72057i	−0.698077	+	0.716023i
$4$		0			0
$5$	0.263312	+	0.456070i	0.0235513	+	0.0407921i	0.877561	−	0.479465i	$-0.159169\pi$
$5$	0.263312	+	0.456070i	0.0235513	+	0.0407921i	−0.854010	+	0.520257i	$0.825836\pi$
$6$		0			0
$7$	16.6747	+	8.05944i	0.900349	+	0.435169i
$7$	16.6747	+	8.05944i	0.900349	+	0.435169i
$8$		0			0
$9$	−0.685212	−	26.9913i	−0.0253782	−	0.999678i
$10$		0			0
$11$	9.84572	+	5.68443i	0.269872	+	0.155811i	0.628830	−	0.777543i	$-0.283534\pi$
$11$	9.84572	+	5.68443i	0.269872	+	0.155811i	−0.358957	+	0.933354i	$0.616868\pi$
$12$		0			0
$13$		−	65.8264i		−	1.40438i	−0.711989	−	0.702191i	$-0.752205\pi$
$13$		−	65.8264i		−	1.40438i	0.711989	−	0.702191i	$-0.247795\pi$
$14$		0			0
$15$	−2.65195	−	0.674638i	−0.0456487	−	0.0116127i
$16$		0			0
$17$	0.339033	−	0.587223i	0.00483692	−	0.00837779i	−0.863597	−	0.504183i	$-0.831794\pi$
$17$	0.339033	−	0.587223i	0.00483692	−	0.00837779i	0.868434	+	0.495805i	$0.165127\pi$
$18$		0			0
$19$	19.0112	−	10.9761i	0.229551	−	0.132531i	−0.380814	−	0.924652i	$-0.624356\pi$
$19$	19.0112	−	10.9761i	0.229551	−	0.132531i	0.610365	+	0.792120i	$0.291023\pi$
$20$		0			0
$21$	−90.4700	+	32.8052i	−0.940103	+	0.340890i
$22$		0			0
$23$	6.60693	−	3.81451i	0.0598974	−	0.0345818i	−0.469752	−	0.882798i	$-0.655657\pi$
$23$	6.60693	−	3.81451i	0.0598974	−	0.0345818i	0.529650	+	0.848217i	$0.322323\pi$
$24$		0			0
$25$	62.3613	−	108.013i	0.498891	−	0.864104i
$26$		0			0
$27$	102.908	+	95.3565i	0.733508	+	0.679680i
$28$		0			0
$29$			165.699i			1.06102i	0.847679	+	0.530510i	$0.178000\pi$
$29$			165.699i			1.06102i	−0.847679	+	0.530510i	$0.822000\pi$
$30$		0			0
$31$	110.323	+	63.6953i	0.639183	+	0.369033i	0.784300	−	0.620382i	$-0.213022\pi$
$31$	110.323	+	63.6953i	0.639183	+	0.369033i	−0.145117	+	0.989415i	$0.546356\pi$
$32$		0			0
$33$	−56.8628	+	16.0124i	−0.299956	+	0.0844669i
$34$		0			0
$35$	0.714981	+	9.72697i	0.00345297	+	0.0469759i
$36$		0			0
$37$	−95.9053	−	166.113i	−0.426128	−	0.738075i	0.570397	−	0.821369i	$-0.306789\pi$
$37$	−95.9053	−	166.113i	−0.426128	−	0.738075i	−0.996525	+	0.0832937i	$0.973456\pi$
$38$		0			0
$39$	244.911	+	238.773i	1.00557	+	0.980366i
$40$		0			0
$41$	508.434			1.93668			0.968342	−	0.249627i	$-0.0803080\pi$
$41$	508.434			1.93668			0.968342	+	0.249627i	$0.0803080\pi$
$42$		0			0
$43$	25.2052			0.0893898			0.0446949	−	0.999001i	$-0.485768\pi$
$43$	25.2052			0.0893898			0.0446949	+	0.999001i	$0.485768\pi$
$44$		0			0
$45$	12.1295	−	7.41964i	0.0401813	−	0.0245790i
$46$		0			0
$47$	167.209	+	289.614i	0.518934	+	0.898820i	0.999758	+	0.0220031i	$0.00700436\pi$
$47$	167.209	+	289.614i	0.518934	+	0.898820i	−0.480824	+	0.876817i	$0.659662\pi$
$48$		0			0
$49$	213.091	+	268.777i	0.621256	+	0.783607i
$50$		0			0
$51$	0.955021	+	3.39143i	0.00262215	+	0.00931168i
$52$		0			0
$53$	376.298	+	217.256i	0.975255	+	0.563064i	0.900834	−	0.434163i	$-0.142956\pi$
$53$	376.298	+	217.256i	0.975255	+	0.563064i	0.0744207	+	0.997227i	$0.476289\pi$
$54$		0			0
$55$			5.98711i			0.0146782i
$56$		0			0
$57$	−28.1222	+	110.546i	−0.0653487	+	0.256881i
$58$		0			0
$59$	−208.919	+	361.858i	−0.460998	+	0.798473i	−0.999011	−	0.0444641i	$-0.985842\pi$
$59$	−208.919	+	361.858i	−0.460998	+	0.798473i	0.538012	+	0.842937i	$0.319175\pi$
$60$		0			0
$61$	−288.511	+	166.572i	−0.605576	+	0.349629i	−0.771232	−	0.636554i	$-0.780359\pi$
$61$	−288.511	+	166.572i	−0.605576	+	0.349629i	0.165656	+	0.986184i	$0.447026\pi$
$62$		0			0
$63$	206.109	−	455.594i	0.412179	−	0.911103i
$64$		0			0
$65$	30.0214	−	17.3329i	0.0572877	−	0.0330751i
$66$		0			0
$67$	68.6985	−	118.989i	0.125266	−	0.216968i	−0.796571	−	0.604546i	$-0.793355\pi$
$67$	68.6985	−	118.989i	0.125266	−	0.216968i	0.921837	+	0.387578i	$0.126688\pi$
$68$		0			0
$69$	−9.77326	+	38.4180i	−0.0170516	+	0.0670287i
$70$		0			0
$71$		−	718.257i		−	1.20058i	−0.799781	−	0.600292i	$-0.795051\pi$
$71$		−	718.257i		−	1.20058i	0.799781	−	0.600292i	$-0.204949\pi$
$72$		0			0
$73$	1009.78	+	582.997i	1.61898	+	0.934721i	0.987183	+	0.159591i	$0.0510176\pi$
$73$	1009.78	+	582.997i	1.61898	+	0.934721i	0.631802	+	0.775130i	$0.282316\pi$
$74$		0			0
$75$	175.665	+	623.816i	0.270455	+	0.960428i
$76$		0			0
$77$	118.361	+	174.137i	0.175175	+	0.257724i
$78$		0			0
$79$	−189.187	−	327.682i	−0.269433	−	0.466672i	0.699282	−	0.714846i	$-0.253503\pi$
$79$	−189.187	−	327.682i	−0.269433	−	0.466672i	−0.968716	+	0.248174i	$0.920170\pi$
$80$		0			0
$81$	−728.061	+	36.9895i	−0.998712	+	0.0507401i
$82$		0			0
$83$	−539.610			−0.713613			−0.356806	−	0.934178i	$-0.616134\pi$
$83$	−539.610			−0.713613			−0.356806	+	0.934178i	$0.616134\pi$
$84$		0			0
$85$	0.357086			0.000455663
$86$		0			0
$87$	−616.495	−	601.043i	−0.759715	−	0.740673i
$88$		0			0
$89$	457.610	+	792.604i	0.545018	+	0.943998i	0.998606	+	0.0527868i	$0.0168104\pi$
$89$	457.610	+	792.604i	0.545018	+	0.943998i	−0.453588	+	0.891211i	$0.649856\pi$
$90$		0			0
$91$	530.524	−	1097.64i	0.611143	−	1.26443i
$92$		0			0
$93$	−637.160	+	179.423i	−0.710435	+	0.200057i
$94$		0			0
$95$	10.0117	+	5.78029i	0.0108125	+	0.00624258i
$96$		0			0
$97$		−	29.2850i		−	0.0306541i	−0.999883	−	0.0153270i	$-0.995121\pi$
$97$		−	29.2850i		−	0.0306541i	0.999883	−	0.0153270i	$-0.00487894\pi$
$98$		0			0
$99$	146.684	−	269.644i	0.148912	−	0.273740i
$100$		0			0
$101$	502.651	−	870.617i	0.495204	−	0.857719i	−0.504780	−	0.863248i	$-0.668427\pi$
$101$	502.651	−	870.617i	0.495204	−	0.857719i	0.999985	+	0.00552879i	$0.00175988\pi$
$102$		0			0
$103$	209.321	−	120.852i	0.200243	−	0.115610i	−0.396526	−	0.918024i	$-0.629784\pi$
$103$	209.321	−	120.852i	0.200243	−	0.115610i	0.596769	+	0.802413i	$0.296451\pi$
$104$		0			0
$105$	−38.7833	−	32.6226i	−0.0360463	−	0.0303204i
$106$		0			0
$107$	−1253.93	+	723.958i	−1.13292	+	0.654090i	−0.944667	−	0.328031i	$-0.893615\pi$
$107$	−1253.93	+	723.958i	−1.13292	+	0.654090i	−0.188250	+	0.982121i	$0.560282\pi$
$108$		0			0
$109$	945.124	−	1637.00i	0.830518	−	1.43850i	−0.0671095	−	0.997746i	$-0.521378\pi$
$109$	945.124	−	1637.00i	0.830518	−	1.43850i	0.897628	−	0.440754i	$-0.145289\pi$
$110$		0			0
$111$	965.912	+	245.721i	0.825949	+	0.210116i
$112$		0			0
$113$		−	751.341i		−	0.625488i	−0.949837	−	0.312744i	$-0.898752\pi$
$113$		−	751.341i		−	0.625488i	0.949837	−	0.312744i	$-0.101248\pi$
$114$		0			0
$115$	3.47937	+	2.00881i	0.00282133	+	0.00162889i
$116$		0			0
$117$	−1776.74	+	45.1050i	−1.40393	+	0.0356407i
$118$		0			0
$119$	10.3860	−	7.05934i	0.00800066	−	0.00543806i
$120$		0			0
$121$	−600.875	−	1040.75i	−0.451446	−	0.781927i
$122$		0			0
$123$	−1844.25	+	1891.66i	−1.35195	+	1.38671i
$124$		0			0
$125$	131.510			0.0941008
$126$		0			0
$127$	2243.48			1.56753			0.783767	−	0.621054i	$-0.213295\pi$
$127$	2243.48			1.56753			0.783767	+	0.621054i	$0.213295\pi$
$128$		0			0
$129$	−91.4272	+	93.7777i	−0.0624009	+	0.0640052i
$130$		0			0
$131$	−1038.92	−	1799.47i	−0.692909	−	1.20015i	−0.970881	−	0.239564i	$-0.922996\pi$
$131$	−1038.92	−	1799.47i	−0.692909	−	1.20015i	0.277972	−	0.960589i	$-0.410338\pi$
$132$		0			0
$133$	405.467	−	29.8039i	0.264349	−	0.0194310i
$134$		0			0
$135$	−16.3922	+	72.0419i	−0.0104505	+	0.0459287i
$136$		0			0
$137$	−1954.66	−	1128.52i	−1.21896	−	0.703767i	−0.254265	−	0.967135i	$-0.581834\pi$
$137$	−1954.66	−	1128.52i	−1.21896	−	0.703767i	−0.964696	+	0.263367i	$0.915167\pi$
$138$		0			0
$139$			1086.52i			0.663004i	0.943455	+	0.331502i	$0.107555\pi$
$139$			1086.52i			0.663004i	−0.943455	+	0.331502i	$0.892445\pi$
$140$		0			0
$141$	−1684.05	−	428.410i	−1.00583	−	0.255877i
$142$		0			0
$143$	374.186	−	648.108i	0.218818	−	0.379004i
$144$		0			0
$145$	−75.5704	+	43.6306i	−0.0432813	+	0.0249884i
$146$		0			0
$147$	−1772.95	−	182.121i	−0.994766	−	0.102184i
$148$		0			0
$149$	−2547.94	+	1471.06i	−1.40091	+	0.808816i	−0.994486	−	0.104869i	$-0.966558\pi$
$149$	−2547.94	+	1471.06i	−1.40091	+	0.808816i	−0.406424	+	0.913685i	$0.633224\pi$
$150$		0			0
$151$	−1167.06	+	2021.40i	−0.628965	+	1.08940i	0.358795	+	0.933417i	$0.383188\pi$
$151$	−1167.06	+	2021.40i	−0.628965	+	1.08940i	−0.987760	+	0.155983i	$0.950145\pi$
$152$		0			0
$153$	−16.0822	−	8.74857i	−0.00849784	−	0.00462275i
$154$		0			0
$155$			67.0869i			0.0347648i
$156$		0			0
$157$	2616.30	+	1510.52i	1.32996	+	0.767852i	0.985293	−	0.170873i	$-0.0546588\pi$
$157$	2616.30	+	1510.52i	1.32996	+	0.767852i	0.344666	+	0.938725i	$0.387992\pi$
$158$		0			0
$159$	−2173.26	+	611.987i	−1.08397	+	0.305244i
$160$		0			0
$161$	140.911	−	10.3577i	0.0689775	−	0.00507019i
$162$		0			0
$163$	1190.49	+	2061.98i	0.572062	+	0.990840i	0.996354	+	0.0853146i	$0.0271895\pi$
$163$	1190.49	+	2061.98i	0.572062	+	0.990840i	−0.424292	+	0.905525i	$0.639477\pi$
$164$		0			0
$165$	−22.2754	−	21.7171i	−0.0105099	−	0.0102465i
$166$		0			0
$167$	3474.90			1.61015			0.805077	−	0.593171i	$-0.202124\pi$
$167$	3474.90			1.61015			0.805077	+	0.593171i	$0.202124\pi$
$168$		0			0
$169$	−2136.12			−0.972288
$170$		0			0
$171$	−309.286	−	505.616i	−0.138314	−	0.226114i
$172$		0			0
$173$	−231.181	−	400.417i	−0.101597	−	0.175972i	0.810746	−	0.585399i	$-0.199062\pi$
$173$	−231.181	−	400.417i	−0.101597	−	0.175972i	−0.912343	+	0.409427i	$0.865729\pi$
$174$		0			0
$175$	1910.38	−	1298.49i	0.825207	−	0.560893i
$176$		0			0
$177$	−588.502	−	2089.87i	−0.249913	−	0.887481i
$178$		0			0
$179$	−1687.55	−	974.309i	−0.704657	−	0.406834i	0.104423	−	0.994533i	$-0.466701\pi$
$179$	−1687.55	−	974.309i	−0.704657	−	0.406834i	−0.809080	+	0.587699i	$0.800034\pi$
$180$		0			0
$181$		−	615.018i		−	0.252563i	−0.991994	−	0.126282i	$-0.959696\pi$
$181$		−	615.018i		−	0.252563i	0.991994	−	0.126282i	$-0.0403043\pi$
$182$		0			0
$183$	426.779	−	1677.64i	0.172396	−	0.677674i
$184$		0			0
$185$	50.5060	−	87.4790i	0.0200718	−	0.0347653i
$186$		0			0
$187$	6.67605	−	3.85442i	0.00261070	−	0.00150729i
$188$		0			0
$189$	947.446	+	2419.42i	0.364638	+	0.931149i
$190$		0			0
$191$	1933.30	−	1116.19i	0.732400	−	0.422851i	−0.0868995	−	0.996217i	$-0.527696\pi$
$191$	1933.30	−	1116.19i	0.732400	−	0.422851i	0.819300	+	0.573366i	$0.194363\pi$
$192$		0			0
$193$	692.298	−	1199.09i	0.258200	−	0.447216i	−0.707559	−	0.706654i	$-0.750204\pi$
$193$	692.298	−	1199.09i	0.258200	−	0.447216i	0.965760	+	0.259438i	$0.0835372\pi$
$194$		0			0
$195$	−44.4090	+	174.568i	−0.0163087	+	0.0641082i
$196$		0			0
$197$		−	3912.85i		−	1.41512i	−0.706652	−	0.707562i	$-0.749795\pi$
$197$		−	3912.85i		−	1.41512i	0.706652	−	0.707562i	$-0.250205\pi$
$198$		0			0
$199$	−3069.79	−	1772.34i	−1.09353	−	0.631347i	−0.159013	−	0.987277i	$-0.550831\pi$
$199$	−3069.79	−	1772.34i	−1.09353	−	0.631347i	−0.934513	+	0.355929i	$0.884164\pi$
$200$		0			0
$201$	193.516	+	687.208i	0.0679084	+	0.241154i
$202$		0			0
$203$	−1335.44	+	2762.99i	−0.461723	+	0.955289i
$204$		0			0
$205$	133.877	+	231.881i	0.0456115	+	0.0790014i
$206$		0			0
$207$	−107.486	−	175.716i	−0.0360907	−	0.0590005i
$208$		0			0
$209$	249.572			0.0825993
$210$		0			0
$211$	2180.84			0.711542			0.355771	−	0.934573i	$-0.384218\pi$
$211$	2180.84			0.711542			0.355771	+	0.934573i	$0.384218\pi$
$212$		0			0
$213$	2672.32	+	2605.34i	0.859646	+	0.838099i
$214$		0			0
$215$	6.63684	+	11.4953i	0.00210525	+	0.00364640i
$216$		0			0
$217$	1326.26	+	1951.24i	0.414896	+	0.610411i
$218$		0			0
$219$	−5831.87	+	1642.24i	−1.79946	+	0.506723i
$220$		0			0
$221$	−38.6548	−	22.3173i	−0.0117656	−	0.00679288i
$222$		0			0
$223$		−	3793.00i		−	1.13900i	−0.821990	−	0.569502i	$-0.807136\pi$
$223$		−	3793.00i		−	1.13900i	0.821990	−	0.569502i	$-0.192864\pi$
$224$		0			0
$225$	−2958.14	−	1609.20i	−0.876487	−	0.476801i
$226$		0			0
$227$	−2487.54	+	4308.54i	−0.727329	+	1.25977i	0.230680	+	0.973030i	$0.425905\pi$
$227$	−2487.54	+	4308.54i	−0.727329	+	1.25977i	−0.958008	+	0.286740i	$0.907428\pi$
$228$		0			0
$229$	226.277	−	130.641i	0.0652961	−	0.0376987i	−0.466997	−	0.884259i	$-0.654664\pi$
$229$	226.277	−	130.641i	0.0652961	−	0.0376987i	0.532293	+	0.846560i	$0.321331\pi$
$230$		0			0
$231$	−1077.22	−	191.279i	−0.306822	−	0.0544817i
$232$		0			0
$233$	−3952.64	+	2282.06i	−1.11136	+	0.641643i	−0.939181	−	0.343423i	$-0.888413\pi$
$233$	−3952.64	+	2282.06i	−1.11136	+	0.641643i	−0.172177	+	0.985066i	$0.555080\pi$
$234$		0			0
$235$	−88.0561	+	152.518i	−0.0244432	+	0.0423368i
$236$		0			0
$237$	1905.40	+	484.721i	0.522233	+	0.132852i
$238$		0			0
$239$		−	4367.13i		−	1.18195i	−0.806689	−	0.590976i	$-0.798743\pi$
$239$		−	4367.13i		−	1.18195i	0.806689	−	0.590976i	$-0.201257\pi$
$240$		0			0
$241$	1154.96	+	666.815i	0.308703	+	0.178230i	0.646346	−	0.763045i	$-0.276296\pi$
$241$	1154.96	+	666.815i	0.308703	+	0.178230i	−0.337643	+	0.941274i	$0.609630\pi$
$242$		0			0
$243$	2503.28	−	2842.97i	0.660846	−	0.750521i
$244$		0			0
$245$	−66.4718	+	167.957i	−0.0173336	+	0.0437973i
$246$		0			0
$247$	−722.519	−	1251.44i	−0.186125	−	0.322377i
$248$		0			0
$249$	1957.33	−	2007.65i	0.498156	−	0.510963i
$250$		0			0
$251$	3117.15			0.783875			0.391938	−	0.919992i	$-0.371805\pi$
$251$	3117.15			0.783875			0.391938	+	0.919992i	$0.371805\pi$
$252$		0			0
$253$	86.7333			0.0215529
$254$		0			0
$255$	−1.29526	+	1.32856i	−0.000318088	+	0.000326266i
$256$		0			0
$257$	554.639	+	960.663i	0.134620	+	0.233169i	0.925452	−	0.378864i	$-0.123685\pi$
$257$	554.639	+	960.663i	0.134620	+	0.233169i	−0.790832	+	0.612033i	$0.790352\pi$
$258$		0			0
$259$	−260.415	−	3542.82i	−0.0624766	−	0.849963i
$260$		0			0
$261$	4472.44	−	113.539i	1.06068	−	0.0269268i
$262$		0			0
$263$	4538.61	+	2620.37i	1.06412	+	0.614368i	0.926568	−	0.376127i	$-0.122744\pi$
$263$	4538.61	+	2620.37i	1.06412	+	0.614368i	0.137549	+	0.990495i	$0.456078\pi$
$264$		0			0
$265$			228.824i			0.0530436i
$266$		0			0
$267$	−4608.83	−	1172.45i	−1.05639	−	0.268738i
$268$		0			0
$269$	−1654.06	+	2864.92i	−0.374907	+	0.649358i	−0.990313	−	0.138852i	$-0.955659\pi$
$269$	−1654.06	+	2864.92i	−0.374907	+	0.649358i	0.615406	+	0.788210i	$0.288992\pi$
$270$		0			0
$271$	2978.05	−	1719.38i	0.667541	−	0.385405i	−0.127603	−	0.991825i	$-0.540728\pi$
$271$	2978.05	−	1719.38i	0.667541	−	0.385405i	0.795144	+	0.606420i	$0.207395\pi$
$272$		0			0
$273$	2159.45	+	5955.32i	0.478739	+	1.32026i
$274$		0			0
$275$	1227.98	−	708.977i	0.269274	−	0.155465i
$276$		0			0
$277$	1792.98	−	3105.53i	0.388915	−	0.673621i	−0.603389	−	0.797447i	$-0.706183\pi$
$277$	1792.98	−	3105.53i	0.388915	−	0.673621i	0.992304	+	0.123826i	$0.0395166\pi$
$278$		0			0
$279$	1643.62	−	3021.42i	0.352692	−	0.648343i
$280$		0			0
$281$		−	536.879i		−	0.113977i	−0.998375	−	0.0569884i	$-0.981850\pi$
$281$		−	536.879i		−	0.113977i	0.998375	−	0.0569884i	$-0.0181498\pi$
$282$		0			0
$283$	−1693.93	−	977.990i	−0.355808	−	0.205426i	0.311433	−	0.950268i	$-0.399191\pi$
$283$	−1693.93	−	977.990i	−0.355808	−	0.205426i	−0.667240	+	0.744843i	$0.732525\pi$
$284$		0			0
$285$	−57.8217	+	16.2825i	−0.0120178	+	0.00338417i
$286$		0			0
$287$	8477.98	+	4097.69i	1.74369	+	0.842784i
$288$		0			0
$289$	2456.27	+	4254.38i	0.499953	+	0.865944i
$290$		0			0
$291$	108.957	+	106.226i	0.0219490	+	0.0213989i
$292$		0			0
$293$	8428.11			1.68046			0.840232	−	0.542228i	$-0.182419\pi$
$293$	8428.11			1.68046			0.840232	+	0.542228i	$0.182419\pi$
$294$		0			0
$295$	−220.043			−0.0434285
$296$		0			0
$297$	471.160	+	1523.83i	0.0920521	+	0.297715i
$298$		0			0
$299$	−251.096	−	434.911i	−0.0485660	−	0.0841188i
$300$		0			0
$301$	420.289	+	203.140i	0.0804820	+	0.0388996i
$302$		0			0
$303$	1415.92	+	5028.14i	0.268456	+	0.953331i
$304$		0			0
$305$	−151.937	−	87.7209i	−0.0285242	−	0.0164685i
$306$		0			0
$307$			4651.20i			0.864684i	0.901710	+	0.432342i	$0.142313\pi$
$307$			4651.20i			0.864684i	−0.901710	+	0.432342i	$0.857687\pi$
$308$		0			0
$309$	−309.637	+	1217.16i	−0.0570053	+	0.224084i
$310$		0			0
$311$	−1839.99	+	3186.96i	−0.335486	+	0.581080i	−0.983578	−	0.180483i	$-0.942234\pi$
$311$	−1839.99	+	3186.96i	−0.335486	+	0.581080i	0.648092	+	0.761562i	$0.275567\pi$
$312$		0			0
$313$	−929.740	+	536.786i	−0.167898	+	0.0969358i	−0.581594	−	0.813479i	$-0.697571\pi$
$313$	−929.740	+	536.786i	−0.167898	+	0.0969358i	0.413696	+	0.910415i	$0.364237\pi$
$314$		0			0
$315$	262.054	−	25.9633i	0.0468732	−	0.00464402i
$316$		0			0
$317$	−2312.94	+	1335.38i	−0.409804	+	0.236600i	−0.690706	−	0.723136i	$-0.742700\pi$
$317$	−2312.94	+	1335.38i	−0.409804	+	0.236600i	0.280902	+	0.959737i	$0.409367\pi$
$318$		0			0
$319$	−941.906	+	1631.43i	−0.165319	+	0.286340i
$320$		0			0
$321$	1854.87	−	7291.36i	0.322519	−	1.26780i
$322$		0			0
$323$		−	14.8851i		−	0.00256417i
$324$		0			0
$325$	−7110.11	−	4105.02i	−1.21353	−	0.700633i
$326$		0			0
$327$	2662.32	+	9454.32i	0.450234	+	1.59885i
$328$		0			0
$329$	454.029	+	6176.84i	0.0760833	+	1.03508i
$330$		0			0
$331$	4779.06	+	8277.58i	0.793599	+	1.37455i	0.923725	+	0.383056i	$0.125128\pi$
$331$	4779.06	+	8277.58i	0.793599	+	1.37455i	−0.130127	+	0.991497i	$0.541538\pi$
$332$		0			0
$333$	−4417.89	+	2702.43i	−0.727023	+	0.444722i
$334$		0			0
$335$	72.3565			0.0118008
$336$		0			0
$337$	−305.593			−0.0493968			−0.0246984	−	0.999695i	$-0.507863\pi$
$337$	−305.593			−0.0493968			−0.0246984	+	0.999695i	$0.507863\pi$
$338$		0			0
$339$	2795.41	+	2725.35i	0.447864	+	0.436639i
$340$		0			0
$341$	724.143	+	1254.25i	0.114999	+	0.199183i
$342$		0			0
$343$	1387.03	+	6199.17i	0.218346	+	0.975871i
$344$		0			0
$345$	−20.0947	+	5.65862i	−0.00313583	+	0.000883043i
$346$		0			0
$347$	−4993.59	−	2883.05i	−0.772536	−	0.446024i	0.0612428	−	0.998123i	$-0.480494\pi$
$347$	−4993.59	−	2883.05i	−0.772536	−	0.446024i	−0.833778	+	0.552099i	$0.813827\pi$
$348$		0			0
$349$		−	6896.44i		−	1.05776i	−0.848697	−	0.528880i	$-0.822612\pi$
$349$		−	6896.44i		−	1.05776i	0.848697	−	0.528880i	$-0.177388\pi$
$350$		0			0
$351$	6276.98	−	6774.09i	0.954531	−	1.03013i
$352$		0			0
$353$	4688.32	−	8120.40i	0.706895	−	1.22438i	−0.259108	−	0.965848i	$-0.583429\pi$
$353$	4688.32	−	8120.40i	0.706895	−	1.22438i	0.966003	−	0.258530i	$-0.0832380\pi$
$354$		0			0
$355$	327.575	−	189.126i	0.0489743	−	0.0282753i
$356$		0			0
$357$	−11.4084	+	64.2481i	−0.00169130	+	0.00952484i
$358$		0			0
$359$	−1644.06	+	949.198i	−0.241700	+	0.139545i	−0.615958	−	0.787779i	$-0.711231\pi$
$359$	−1644.06	+	949.198i	−0.241700	+	0.139545i	0.374258	+	0.927325i	$0.377897\pi$
$360$		0			0
$361$	−3188.55	+	5522.73i	−0.464871	+	0.805180i
$362$		0			0
$363$	6051.72	+	1539.52i	0.875022	+	0.222599i
$364$		0			0
$365$			614.040i			0.0880557i
$366$		0			0
$367$	−3072.05	−	1773.65i	−0.436947	−	0.252271i	0.265355	−	0.964151i	$-0.414511\pi$
$367$	−3072.05	−	1773.65i	−0.436947	−	0.252271i	−0.702302	+	0.711879i	$0.747844\pi$
$368$		0			0
$369$	−348.385	−	13723.3i	−0.0491496	−	1.93606i
$370$		0			0
$371$	4523.70	+	6655.42i	0.633042	+	0.931354i
$372$		0			0
$373$	−2099.26	−	3636.02i	−0.291408	−	0.504734i	0.682735	−	0.730666i	$-0.260791\pi$
$373$	−2099.26	−	3636.02i	−0.291408	−	0.504734i	−0.974143	+	0.225932i	$0.927457\pi$
$374$		0			0
$375$	−477.027	+	489.291i	−0.0656896	+	0.0673784i
$376$		0			0
$377$	10907.4			1.49008
$378$		0			0
$379$	−11748.8			−1.59233			−0.796165	−	0.605080i	$-0.793141\pi$
$379$	−11748.8			−1.59233			−0.796165	+	0.605080i	$0.793141\pi$
$380$		0			0
$381$	−8137.81	+	8347.02i	−1.09426	+	1.12239i
$382$		0			0
$383$	−5111.95	−	8854.16i	−0.682006	−	1.18127i	−0.974368	−	0.224962i	$-0.927774\pi$
$383$	−5111.95	−	8854.16i	−0.682006	−	1.18127i	0.292361	−	0.956308i	$-0.405559\pi$
$384$		0			0
$385$	−48.2527	+	99.8332i	−0.00638750	+	0.0132155i
$386$		0			0
$387$	−17.2709	−	680.322i	−0.00226855	−	0.0893610i
$388$		0			0
$389$	−3605.15	−	2081.43i	−0.469893	−	0.271293i	0.246302	−	0.969193i	$-0.420784\pi$
$389$	−3605.15	−	2081.43i	−0.469893	−	0.271293i	−0.716195	+	0.697901i	$0.754118\pi$
$390$		0			0
$391$		−	5.17299i		−	0.000669077i
$392$		0			0
$393$	10463.5	+	2661.85i	1.34304	+	0.341660i
$394$		0			0
$395$	99.6305	−	172.565i	0.0126910	−	0.0219815i
$396$		0			0
$397$	3962.92	−	2287.99i	0.500991	−	0.289247i	−0.228132	−	0.973630i	$-0.573262\pi$
$397$	3962.92	−	2287.99i	0.500991	−	0.289247i	0.729123	+	0.684383i	$0.239928\pi$
$398$		0			0
$399$	−1359.87	+	1616.68i	−0.170623	+	0.202845i
$400$		0			0
$401$	−5375.54	+	3103.57i	−0.669430	+	0.386496i	−0.795861	−	0.605480i	$-0.792981\pi$
$401$	−5375.54	+	3103.57i	−0.669430	+	0.386496i	0.126431	+	0.991975i	$0.459648\pi$
$402$		0			0
$403$	4192.83	−	7262.20i	0.518263	−	0.897657i
$404$		0			0
$405$	−208.577	−	322.307i	−0.0255908	−	0.0395446i
$406$		0			0
$407$		−	2180.67i		−	0.265582i
$408$		0			0
$409$	−10290.0	−	5940.92i	−1.24403	−	0.718238i	−0.274114	−	0.961697i	$-0.588385\pi$
$409$	−10290.0	−	5940.92i	−1.24403	−	0.718238i	−0.969911	+	0.243459i	$0.921718\pi$
$410$		0			0
$411$	11288.9	−	3178.93i	1.35484	−	0.381521i
$412$		0			0
$413$	−6400.03	+	4350.10i	−0.762530	+	0.518292i
$414$		0			0
$415$	−142.086	−	246.100i	−0.0168065	−	0.0291098i
$416$		0			0
$417$	−4042.47	−	3941.15i	−0.474726	−	0.462827i
$418$		0			0
$419$	347.837			0.0405560			0.0202780	−	0.999794i	$-0.493545\pi$
$419$	347.837			0.0405560			0.0202780	+	0.999794i	$0.493545\pi$
$420$		0			0
$421$	−7639.03			−0.884331			−0.442166	−	0.896933i	$-0.645790\pi$
$421$	−7639.03			−0.884331			−0.442166	+	0.896933i	$0.645790\pi$
$422$		0			0
$423$	7702.49	−	4711.63i	0.885361	−	0.541577i
$424$		0			0
$425$	−42.2851	−	73.2400i	−0.00482619	−	0.00835920i
$426$		0			0
$427$	−6153.32	+	452.300i	−0.697377	+	0.0512607i
$428$		0			0
$429$	1054.04	+	3743.07i	0.118624	+	0.421252i
$430$		0			0
$431$	−13282.3	−	7668.55i	−1.48442	−	0.857032i	−0.484580	−	0.874747i	$-0.661028\pi$
$431$	−13282.3	−	7668.55i	−1.48442	−	0.857032i	−0.999843	+	0.0177146i	$0.994361\pi$
$432$		0			0
$433$			11113.0i			1.23339i	0.787202	+	0.616696i	$0.211529\pi$
$433$			11113.0i			1.23339i	−0.787202	+	0.616696i	$0.788471\pi$
$434$		0			0
$435$	111.787	−	439.426i	0.0123213	−	0.0484342i
$436$		0			0
$437$	83.7371	−	145.037i	0.00916634	−	0.0158766i
$438$		0			0
$439$	−7997.97	+	4617.63i	−0.869527	+	0.502022i	−0.867191	−	0.497976i	$-0.834077\pi$
$439$	−7997.97	+	4617.63i	−0.869527	+	0.502022i	−0.00233599	+	0.999997i	$0.500744\pi$
$440$		0			0
$441$	7108.64	−	5935.77i	0.767589	−	0.640943i
$442$		0			0
$443$	−2636.02	+	1521.91i	−0.282712	+	0.163224i	−0.634650	−	0.772799i	$-0.718856\pi$
$443$	−2636.02	+	1521.91i	−0.282712	+	0.163224i	0.351939	+	0.936023i	$0.385523\pi$
$444$		0			0
$445$	−240.988	+	417.404i	−0.0256718	+	0.0444648i
$446$		0			0
$447$	3769.03	−	14815.8i	0.398812	−	1.56770i
$448$		0			0
$449$		−	9732.40i		−	1.02294i	−0.859301	−	0.511470i	$-0.829101\pi$
$449$		−	9732.40i		−	1.02294i	0.859301	−	0.511470i	$-0.170899\pi$
$450$		0			0
$451$	5005.90	+	2890.16i	0.522657	+	0.301756i
$452$		0			0
$453$	−3287.48	−	11674.4i	−0.340969	−	1.21084i
$454$		0			0
$455$	640.291	−	47.0646i	0.0659721	−	0.00484928i
$456$		0			0
$457$	9550.15	+	16541.3i	0.977543	+	1.69315i	0.671274	+	0.741210i	$0.265748\pi$
$457$	9550.15	+	16541.3i	0.977543	+	1.69315i	0.306270	+	0.951945i	$0.400919\pi$
$458$		0			0
$459$	90.8848	−	28.1011i	0.00924214	−	0.00285762i
$460$		0			0
$461$	1672.67			0.168989			0.0844946	−	0.996424i	$-0.473072\pi$
$461$	1672.67			0.168989			0.0844946	+	0.996424i	$0.473072\pi$
$462$		0			0
$463$	−12242.9			−1.22889			−0.614445	−	0.788960i	$-0.710620\pi$
$463$	−12242.9			−1.22889			−0.614445	+	0.788960i	$0.710620\pi$
$464$		0			0
$465$	−249.601	−	243.345i	−0.0248924	−	0.0242685i
$466$		0			0
$467$	−8378.07	−	14511.2i	−0.830173	−	1.43790i	−0.897901	−	0.440197i	$-0.854908\pi$
$467$	−8378.07	−	14511.2i	−0.830173	−	1.43790i	0.0677283	−	0.997704i	$-0.478425\pi$
$468$		0			0
$469$	2104.51	−	1430.44i	0.207201	−	0.140835i
$470$		0			0
$471$	−15110.1	+	4254.98i	−1.47821	+	0.416262i
$472$		0			0
$473$	248.164	+	143.277i	0.0241238	+	0.0139279i
$474$		0			0
$475$		−	2737.94i		−	0.264474i
$476$		0			0
$477$	5606.17	−	10305.6i	0.538132	−	0.989230i
$478$		0			0
$479$	−8971.99	+	15539.9i	−0.855826	+	1.48233i	0.0200500	+	0.999799i	$0.493617\pi$
$479$	−8971.99	+	15539.9i	−0.855826	+	1.48233i	−0.875876	+	0.482536i	$0.839716\pi$
$480$		0			0
$481$	−10934.6	+	6313.10i	−1.03654	+	0.598446i
$482$		0			0
$483$	−472.593	+	561.841i	−0.0445212	+	0.0529289i
$484$		0			0
$485$	13.3560	−	7.71109i	0.00125044	−	0.000721944i
$486$		0			0
$487$	4293.67	−	7436.85i	0.399517	−	0.691983i	−0.594150	−	0.804355i	$-0.702511\pi$
$487$	4293.67	−	7436.85i	0.399517	−	0.691983i	0.993666	+	0.112371i	$0.0358446\pi$
$488$		0			0
$489$	−11990.0	−	3050.17i	−1.10881	−	0.282073i
$490$		0			0
$491$		−	7844.47i		−	0.721010i	−0.932757	−	0.360505i	$-0.882604\pi$
$491$		−	7844.47i		−	0.721010i	0.932757	−	0.360505i	$-0.117396\pi$
$492$		0			0
$493$	97.3024	+	56.1776i	0.00888900	+	0.00513207i
$494$		0			0
$495$	161.600	−	4.10244i	0.0146735	−	0.000372507i
$496$		0			0
$497$	5788.75	−	11976.7i	0.522456	−	1.08094i
$498$		0			0
$499$	−7889.58	−	13665.2i	−0.707788	−	1.22593i	−0.965676	−	0.259750i	$-0.916360\pi$
$499$	−7889.58	−	13665.2i	−0.707788	−	1.22593i	0.257888	−	0.966175i	$-0.416974\pi$
$500$		0			0
$501$	−12604.5	+	12928.6i	−1.12401	+	1.15291i
$502$		0			0
$503$	−15535.1			−1.37709			−0.688543	−	0.725196i	$-0.741749\pi$
$503$	−15535.1			−1.37709			−0.688543	+	0.725196i	$0.741749\pi$
$504$		0			0
$505$	529.416			0.0466509
$506$		0			0
$507$	7748.36	−	7947.56i	0.678732	−	0.696181i
$508$		0			0
$509$	5913.59	+	10242.6i	0.514961	+	0.891939i	0.999849	+	0.0173626i	$0.00552698\pi$
$509$	5913.59	+	10242.6i	0.514961	+	0.891939i	−0.484888	+	0.874576i	$0.661140\pi$
$510$		0			0
$511$	12139.2	+	17859.6i	1.05089	+	1.54611i
$512$		0			0
$513$	3003.06	+	683.307i	0.258456	+	0.0588084i
$514$		0			0
$515$	110.234	+	63.6434i	0.00943199	+	0.00544556i
$516$		0			0
$517$			3801.94i			0.323422i
$518$		0			0
$519$	2328.34	+	592.314i	0.196923	+	0.0500957i
$520$		0			0
$521$	−4803.81	+	8320.44i	−0.403951	+	0.699664i	−0.994199	−	0.107558i	$-0.965697\pi$
$521$	−4803.81	+	8320.44i	−0.403951	+	0.699664i	0.590248	+	0.807222i	$0.299030\pi$
$522$		0			0
$523$	−6854.71	+	3957.57i	−0.573108	+	0.330884i	−0.758390	−	0.651801i	$-0.774014\pi$
$523$	−6854.71	+	3957.57i	−0.573108	+	0.330884i	0.185282	+	0.982685i	$0.440680\pi$
$524$		0			0
$525$	−2098.44	+	11817.7i	−0.174445	+	0.982414i
$526$		0			0
$527$	74.8066	−	43.1896i	0.00618335	−	0.00356996i
$528$		0			0
$529$	−6054.40	+	10486.5i	−0.497608	+	0.861883i
$530$		0			0
$531$	9910.17	+	5391.04i	0.809915	+	0.440586i
$532$		0			0
$533$		−	33468.4i		−	2.71984i
$534$		0			0
$535$	−660.350	−	381.253i	−0.0533634	−	0.0308094i
$536$		0			0
$537$	9746.26	−	2744.53i	0.783207	−	0.220549i
$538$		0			0
$539$	570.188	+	3857.61i	0.0455653	+	0.308272i
$540$		0			0
$541$	−2198.76	−	3808.36i	−0.174736	−	0.302651i	0.765334	−	0.643633i	$-0.222574\pi$
$541$	−2198.76	−	3808.36i	−0.174736	−	0.302651i	−0.940070	+	0.340982i	$0.889240\pi$
$542$		0			0
$543$	2288.21	+	2230.86i	0.180841	+	0.176308i
$544$		0			0
$545$	995.450			0.0782392
$546$		0			0
$547$	−16800.1			−1.31320			−0.656598	−	0.754240i	$-0.728005\pi$
$547$	−16800.1			−1.31320			−0.656598	+	0.754240i	$0.728005\pi$
$548$		0			0
$549$	4693.69	+	7673.16i	0.364885	+	0.596508i
$550$		0			0
$551$	1818.74	+	3150.14i	0.140618	+	0.243558i
$552$		0			0
$553$	−513.707	−	6988.74i	−0.0395028	−	0.537416i
$554$		0			0
$555$	142.270	+	505.225i	0.0108811	+	0.0386407i
$556$		0			0
$557$	18844.8	+	10880.1i	1.43354	+	0.827654i	0.997389	−	0.0722198i	$-0.0230083\pi$
$557$	18844.8	+	10880.1i	1.43354	+	0.827654i	0.436150	+	0.899874i	$0.356342\pi$
$558$		0			0
$559$		−	1659.17i		−	0.125537i
$560$		0			0
$561$	−9.87550	+	38.8199i	−0.000743215	+	0.00292152i
$562$		0			0
$563$	4741.56	−	8212.63i	0.354943	−	0.614780i	−0.632165	−	0.774834i	$-0.717833\pi$
$563$	4741.56	−	8212.63i	0.354943	−	0.614780i	0.987108	+	0.160054i	$0.0511668\pi$
$564$		0			0
$565$	342.664	−	197.837i	0.0255150	−	0.0147311i
$566$		0			0
$567$	−12438.3	−	5250.97i	−0.921270	−	0.388924i
$568$		0			0
$569$	−17650.5	+	10190.5i	−1.30043	+	0.750805i	−0.980478	−	0.196627i	$-0.937001\pi$
$569$	−17650.5	+	10190.5i	−1.30043	+	0.750805i	−0.319955	+	0.947433i	$0.603668\pi$
$570$		0			0
$571$	8194.57	−	14193.4i	0.600582	−	1.04024i	−0.392151	−	0.919901i	$-0.628269\pi$
$571$	8194.57	−	14193.4i	0.600582	−	1.04024i	0.992733	−	0.120337i	$-0.0383977\pi$
$572$		0			0
$573$	−2859.81	+	11241.7i	−0.208500	+	0.819598i
$574$		0			0
$575$		−	951.513i		−	0.0690101i
$576$		0			0
$577$	−3432.41	−	1981.70i	−0.247648	−	0.142980i	0.371039	−	0.928617i	$-0.379002\pi$
$577$	−3432.41	−	1981.70i	−0.247648	−	0.142980i	−0.618687	+	0.785638i	$0.712335\pi$
$578$		0			0
$579$	1950.13	+	6925.23i	0.139973	+	0.497069i
$580$		0			0
$581$	−8997.83	−	4348.95i	−0.642501	−	0.310542i
$582$		0			0
$583$	2469.95	+	4278.08i	0.175463	+	0.303911i
$584$		0			0
$585$	−488.408	−	798.441i	−0.0345183	−	0.0564298i
$586$		0			0
$587$	25463.9			1.79047			0.895236	−	0.445593i	$-0.147007\pi$
$587$	25463.9			1.79047			0.895236	+	0.445593i	$0.147007\pi$
$588$		0			0
$589$	2796.51			0.195633
$590$		0			0
$591$	14558.0	+	14193.1i	1.01326	+	0.987864i
$592$		0			0
$593$	5111.63	+	8853.61i	0.353979	+	0.613110i	0.986943	−	0.161072i	$-0.0514950\pi$
$593$	5111.63	+	8853.61i	0.353979	+	0.613110i	−0.632964	+	0.774182i	$0.718162\pi$
$594$		0			0
$595$	5.95430	+	2.87791i	0.000410256	+	0.000198290i
$596$		0			0
$597$	17729.2	−	4992.51i	1.21542	−	0.342261i
$598$		0			0
$599$	−9148.27	−	5281.76i	−0.624020	−	0.360278i	0.154412	−	0.988007i	$-0.450652\pi$
$599$	−9148.27	−	5281.76i	−0.624020	−	0.360278i	−0.778433	+	0.627728i	$0.783985\pi$
$600$		0			0
$601$			8886.76i			0.603159i	0.953441	+	0.301579i	$0.0975138\pi$
$601$			8886.76i			0.603159i	−0.953441	+	0.301579i	$0.902486\pi$
$602$		0			0
$603$	−3258.75	−	1772.73i	−0.220077	−	0.119720i
$604$		0			0
$605$	316.435	−	548.081i	0.0212643	−	0.0368309i
$606$		0			0
$607$	−20595.0	+	11890.5i	−1.37714	+	0.795093i	−0.991815	−	0.127686i	$-0.959245\pi$
$607$	−20595.0	+	11890.5i	−1.37714	+	0.795093i	−0.385328	+	0.922780i	$0.625912\pi$
$608$		0			0
$609$	−5435.80	−	14990.8i	−0.361691	−	0.997469i
$610$		0			0
$611$	19064.3	−	11006.8i	1.26229	−	0.728782i
$612$		0			0
$613$	6975.41	−	12081.8i	0.459599	−	0.796048i	−0.539341	−	0.842088i	$-0.681327\pi$
$613$	6975.41	−	12081.8i	0.459599	−	0.796048i	0.998940	+	0.0460392i	$0.0146599\pi$
$614$		0			0
$615$	−1348.34	−	343.009i	−0.0884072	−	0.0224902i
$616$		0			0
$617$			17793.8i			1.16103i	0.814251	+	0.580513i	$0.197148\pi$
$617$			17793.8i			1.16103i	−0.814251	+	0.580513i	$0.802852\pi$
$618$		0			0
$619$	15053.4	+	8691.09i	0.977459	+	0.564336i	0.901502	−	0.432775i	$-0.142465\pi$
$619$	15053.4	+	8691.09i	0.977459	+	0.564336i	0.0759571	+	0.997111i	$0.475799\pi$
$620$		0			0
$621$	1043.65	+	237.468i	0.0674398	+	0.0153451i
$622$		0			0
$623$	1242.57	+	16904.5i	0.0799075	+	1.08710i
$624$		0			0
$625$	−7760.54	−	13441.6i	−0.496674	−	0.860265i
$626$		0			0
$627$	−905.275	+	928.548i	−0.0576606	+	0.0591430i
$628$		0			0
$629$	−130.060			−0.00824459
$630$		0			0
$631$	23727.0			1.49692			0.748461	−	0.663178i	$-0.230793\pi$
$631$	23727.0			1.49692			0.748461	+	0.663178i	$0.230793\pi$
$632$		0			0
$633$	−7910.59	+	8113.96i	−0.496710	+	0.509480i
$634$		0			0
$635$	590.736	+	1023.18i	0.0369175	+	0.0639430i
$636$		0			0
$637$	17692.6	−	14027.0i	1.10048	−	0.872481i
$638$		0			0
$639$	−19386.7	+	492.158i	−1.20020	+	0.0304687i
$640$		0			0
$641$	−17207.0	−	9934.44i	−1.06027	−	0.612148i	−0.134764	−	0.990878i	$-0.543028\pi$
$641$	−17207.0	−	9934.44i	−1.06027	−	0.612148i	−0.925507	+	0.378730i	$0.876361\pi$
$642$		0			0
$643$			12150.0i			0.745178i	0.927997	+	0.372589i	$0.121530\pi$
$643$			12150.0i			0.745178i	−0.927997	+	0.372589i	$0.878470\pi$
$644$		0			0
$645$	−66.8430	−	17.0044i	−0.00408053	−	0.00103806i
$646$		0			0
$647$	1830.02	−	3169.69i	0.111199	−	0.192602i	−0.805055	−	0.593200i	$-0.797864\pi$
$647$	1830.02	−	3169.69i	0.111199	−	0.192602i	0.916254	+	0.400598i	$0.131198\pi$
$648$		0			0
$649$	−4113.91	+	2375.17i	−0.248821	+	0.143657i
$650$		0			0
$651$	−12070.5	−	2143.33i	−0.726698	−	0.129038i
$652$		0			0
$653$	−12672.4	+	7316.41i	−0.759432	+	0.438458i	−0.829092	−	0.559113i	$-0.811142\pi$
$653$	−12672.4	+	7316.41i	−0.759432	+	0.438458i	0.0696600	+	0.997571i	$0.477809\pi$
$654$		0			0
$655$	547.121	−	947.641i	0.0326378	−	0.0565304i
$656$		0			0
$657$	15043.9	−	27654.8i	0.893333	−	1.64218i
$658$		0			0
$659$			28047.8i			1.65795i	0.559286	+	0.828975i	$0.311075\pi$
$659$			28047.8i			1.65795i	−0.559286	+	0.828975i	$0.688925\pi$
$660$		0			0
$661$	−25318.8	−	14617.8i	−1.48985	−	0.860162i	−0.489912	−	0.871772i	$-0.662971\pi$
$661$	−25318.8	−	14617.8i	−1.48985	−	0.860162i	−0.999933	+	0.0116092i	$0.996305\pi$
$662$		0			0
$663$	223.246	−	62.8656i	0.0130772	−	0.00368250i
$664$		0			0
$665$	120.357	+	177.074i	0.00701841	+	0.0103257i
$666$		0			0
$667$	632.062	+	1094.76i	0.0366920	+	0.0635524i
$668$		0			0
$669$	14112.1	+	13758.4i	0.815553	+	0.795112i
$670$		0			0
$671$	−3787.47			−0.217904
$672$		0			0
$673$	8911.77			0.510436			0.255218	−	0.966883i	$-0.417853\pi$
$673$	8911.77			0.510436			0.255218	+	0.966883i	$0.417853\pi$
$674$		0			0
$675$	16717.2	−	5168.88i	0.953255	−	0.294741i
$676$		0			0
$677$	−4990.32	−	8643.48i	−0.283299	−	0.490688i	0.688896	−	0.724860i	$-0.258096\pi$
$677$	−4990.32	−	8643.48i	−0.283299	−	0.490688i	−0.972195	+	0.234172i	$0.924762\pi$
$678$		0			0
$679$	236.021	−	488.319i	0.0133397	−	0.0275993i
$680$		0			0
$681$	−7007.13	−	24883.5i	−0.394293	−	1.40020i
$682$		0			0
$683$	15066.1	+	8698.39i	0.844051	+	0.487313i	0.858639	−	0.512581i	$-0.171310\pi$
$683$	15066.1	+	8698.39i	0.844051	+	0.487313i	−0.0145884	+	0.999894i	$0.504644\pi$
$684$		0			0
$685$		−	1188.61i		−	0.0662986i
$686$		0			0
$687$	−334.719	+	1315.75i	−0.0185885	+	0.0730701i
$688$		0			0
$689$	14301.2	−	24770.4i	0.790756	−	1.36963i
$690$		0			0
$691$	5002.68	−	2888.30i	0.275414	−	0.159010i	−0.355932	−	0.934512i	$-0.615836\pi$
$691$	5002.68	−	2888.30i	0.275414	−	0.159010i	0.631345	+	0.775502i	$0.282503\pi$
$692$		0			0
$693$	4619.08	−	3314.04i	0.253195	−	0.181659i
$694$		0			0
$695$	−495.529	+	286.094i	−0.0270453	+	0.0156146i
$696$		0			0
$697$	172.376	−	298.564i	0.00936758	−	0.0162251i
$698$		0			0
$699$	5846.92	−	22983.8i	0.316382	−	1.24367i
$700$		0			0
$701$			15013.5i			0.808916i	0.914557	+	0.404458i	$0.132540\pi$
$701$			15013.5i			0.808916i	−0.914557	+	0.404458i	$0.867460\pi$
$702$		0			0
$703$	−3646.55	−	2105.34i	−0.195636	−	0.112951i
$704$		0			0
$705$	−248.045	−	880.848i	−0.0132509	−	0.0470562i
$706$		0			0
$707$	15398.2	−	10466.2i	0.819109	−	0.556749i
$708$		0			0
$709$	2499.40	+	4329.10i	0.132394	+	0.229313i	0.924599	−	0.380942i	$-0.124400\pi$
$709$	2499.40	+	4329.10i	0.132394	+	0.229313i	−0.792205	+	0.610255i	$0.791067\pi$
$710$		0			0
$711$	−8714.93	+	5330.94i	−0.459684	+	0.281190i
$712$		0			0
$713$	971.866			0.0510472
$714$		0			0
$715$	394.110			0.0206138
$716$		0			0
$717$	16248.2	+	15841.0i	0.846305	+	0.825093i
$718$		0			0
$719$	3748.62	+	6492.79i	0.194436	+	0.336774i	0.946716	−	0.322071i	$-0.104379\pi$
$719$	3748.62	+	6492.79i	0.194436	+	0.336774i	−0.752279	+	0.658844i	$0.771046\pi$
$720$		0			0
$721$	4464.37	−	328.154i	0.230599	−	0.0169502i
$722$		0			0
$723$	−6670.32	+	1878.35i	−0.343115	+	0.0966203i
$724$		0			0
$725$	17897.7	+	10333.2i	0.916832	+	0.529333i
$726$		0			0
$727$			2079.71i			0.106096i	0.998592	+	0.0530482i	$0.0168937\pi$
$727$			2079.71i			0.106096i	−0.998592	+	0.0530482i	$0.983106\pi$
$728$		0			0
$729$	1497.27	+	19626.0i	0.0760693	+	0.997103i
$730$		0			0
$731$	8.54541	−	14.8011i	0.000432371	−	0.000748889i
$732$		0			0
$733$	−331.894	+	191.619i	−0.0167241	+	0.00965567i	−0.508339	−	0.861157i	$-0.669740\pi$
$733$	−331.894	+	191.619i	−0.0167241	+	0.00965567i	0.491615	+	0.870813i	$0.336407\pi$
$734$		0			0
$735$	−383.779	−	856.543i	−0.0192597	−	0.0429851i
$736$		0			0
$737$	1352.77	−	781.023i	0.0676119	−	0.0390358i
$738$		0			0
$739$	−1523.42	+	2638.64i	−0.0758320	+	0.131345i	−0.901448	−	0.432888i	$-0.857495\pi$
$739$	−1523.42	+	2638.64i	−0.0758320	+	0.131345i	0.825616	+	0.564233i	$0.190828\pi$
$740$		0			0
$741$	7276.86	+	1851.18i	0.360759	+	0.0917745i
$742$		0			0
$743$			7608.81i			0.375694i	0.982198	+	0.187847i	$0.0601508\pi$
$743$			7608.81i			0.375694i	−0.982198	+	0.187847i	$0.939849\pi$
$744$		0			0
$745$	−1341.81	−	774.693i	−0.0659866	−	0.0380974i
$746$		0			0
$747$	369.747	+	14564.8i	0.0181102	+	0.713383i
$748$		0			0
$749$	−26743.6	+	1965.79i	−1.30466	+	0.0958991i
$750$		0			0
$751$	−6607.85	−	11445.1i	−0.321070	−	0.556110i	0.659639	−	0.751583i	$-0.270709\pi$
$751$	−6607.85	−	11445.1i	−0.321070	−	0.556110i	−0.980709	+	0.195473i	$0.937376\pi$
$752$		0			0
$753$	−11306.9	+	11597.6i	−0.547205	+	0.561273i
$754$		0			0
$755$	−1229.20			−0.0592519
$756$		0			0
$757$	24928.8			1.19690			0.598449	−	0.801161i	$-0.295784\pi$
$757$	24928.8			1.19690			0.598449	+	0.801161i	$0.295784\pi$
$758$		0			0
$759$	−314.609	+	322.697i	−0.0150456	+	0.0154324i
$760$		0			0
$761$	18141.8	+	31422.6i	0.864179	+	1.49680i	0.867860	+	0.496810i	$0.165495\pi$
$761$	18141.8	+	31422.6i	0.864179	+	1.49680i	−0.00368010	+	0.999993i	$0.501171\pi$
$762$		0			0
$763$	28953.0	−	19679.4i	1.37375	−	0.933736i
$764$		0			0
$765$	−0.244679	−	9.63821i	−1.15639e−5	−	0.000455517i
$766$		0			0
$767$	23819.8	+	13752.4i	1.12136	+	0.647418i
$768$		0			0
$769$			19079.7i			0.894708i	0.894357	+	0.447354i	$0.147634\pi$
$769$			19079.7i			0.894708i	−0.894357	+	0.447354i	$0.852366\pi$
$770$		0			0
$771$	−5586.06	−	1421.05i	−0.260930	−	0.0663787i
$772$		0			0
$773$	−1279.58	+	2216.29i	−0.0595383	+	0.103123i	−0.894258	−	0.447551i	$-0.852296\pi$
$773$	−1279.58	+	2216.29i	−0.0595383	+	0.103123i	0.834720	+	0.550675i	$0.185630\pi$
$774$		0			0
$775$	13759.8	−	7944.25i	0.637765	−	0.368214i
$776$		0			0
$777$	14125.9	+	11882.0i	0.652207	+	0.548605i
$778$		0			0
$779$	9665.94	−	5580.63i	0.444568	−	0.256671i
$780$		0			0
$781$	4082.88	−	7071.76i	0.187064	−	0.324004i
$782$		0			0
$783$	−15800.5	+	17051.8i	−0.721155	+	0.778267i
$784$		0			0
$785$			1590.95i			0.0723358i
$786$		0			0
$787$	−32921.5	−	19007.2i	−1.49114	−	0.860908i	−0.491188	−	0.871053i	$-0.663437\pi$
$787$	−32921.5	−	19007.2i	−1.49114	−	0.860908i	−0.999949	+	0.0101450i	$0.996771\pi$
$788$		0			0
$789$	−26212.2	+	7381.31i	−1.18274	+	0.333056i
$790$		0			0
$791$	6055.38	−	12528.4i	0.272193	−	0.563158i
$792$		0			0
$793$	10964.9	+	18991.7i	0.491013	+	0.850459i
$794$		0			0
$795$	−851.355	−	830.016i	−0.0379804	−	0.0370285i
$796$		0			0
$797$	264.307			0.0117468			0.00587342	−	0.999983i	$-0.498130\pi$
$797$	264.307			0.0117468			0.00587342	+	0.999983i	$0.498130\pi$
$798$		0			0
$799$	226.757			0.0100402
$800$		0			0
$801$	21079.9	−	12894.6i	0.929863	−	0.568799i
$802$		0			0
$803$	6628.01	+	11480.1i	0.291279	+	0.504511i
$804$		0			0
$805$	41.8275	+	61.5381i	0.00183134	+	0.00269433i
$806$		0			0
$807$	−4659.32	−	16546.0i	−0.203242	−	0.721744i
$808$		0			0
$809$	−22385.9	−	12924.5i	−0.972865	−	0.561684i	−0.0727566	−	0.997350i	$-0.523180\pi$
$809$	−22385.9	−	12924.5i	−0.972865	−	0.561684i	−0.900109	+	0.435666i	$0.856513\pi$
$810$		0			0
$811$			29501.8i			1.27737i	0.769468	+	0.638686i	$0.220522\pi$
$811$			29501.8i			1.27737i	−0.769468	+	0.638686i	$0.779478\pi$
$812$		0			0
$813$	−4405.26	+	17316.7i	−0.190036	+	0.747017i
$814$		0			0
$815$	−626.938	+	1085.89i	−0.0269456	+	0.0466712i
$816$		0			0
$817$	479.182	−	276.656i	0.0205195	−	0.0118469i
$818$		0			0
$819$	−29990.1	−	13567.4i	−1.27954	−	0.578857i
$820$		0			0
$821$	19688.6	−	11367.2i	0.836953	−	0.483215i	−0.0192746	−	0.999814i	$-0.506136\pi$
$821$	19688.6	−	11367.2i	0.836953	−	0.483215i	0.856227	+	0.516599i	$0.172802\pi$
$822$		0			0
$823$	10968.7	−	18998.4i	0.464577	−	0.804670i	−0.534606	−	0.845102i	$-0.679540\pi$
$823$	10968.7	−	18998.4i	0.464577	−	0.804670i	0.999182	+	0.0404314i	$0.0128732\pi$
$824$		0			0
$825$	−1816.49	+	7140.48i	−0.0766569	+	0.301333i
$826$		0			0
$827$		−	14680.4i		−	0.617276i	−0.951180	−	0.308638i	$-0.900127\pi$
$827$		−	14680.4i		−	0.617276i	0.951180	−	0.308638i	$-0.0998731\pi$
$828$		0			0
$829$	22703.0	+	13107.6i	0.951155	+	0.549150i	0.893440	−	0.449183i	$-0.148285\pi$
$829$	22703.0	+	13107.6i	0.951155	+	0.549150i	0.0577157	+	0.998333i	$0.481618\pi$
$830$		0			0
$831$	5050.63	+	17935.6i	0.210836	+	0.748711i
$832$		0			0
$833$	230.077	−	34.0074i	0.00956986	−	0.00141451i
$834$		0			0
$835$	914.982	+	1584.79i	0.0379213	+	0.0656815i
$836$		0			0
$837$	5279.45	+	17074.8i	0.218022	+	0.705129i
$838$		0			0
$839$	−20763.2			−0.854382			−0.427191	−	0.904161i	$-0.640497\pi$
$839$	−20763.2			−0.854382			−0.427191	+	0.904161i	$0.640497\pi$
$840$		0			0
$841$	−3067.27			−0.125764
$842$		0			0
$843$	1997.49	+	1947.43i	0.0816101	+	0.0795646i
$844$		0			0
$845$	−562.465	−	974.218i	−0.0228987	−	0.0396617i
$846$		0			0
$847$	−1631.58	−	22196.8i	−0.0661885	−	0.900463i
$848$		0			0
$849$	9783.08	−	2754.89i	0.395470	−	0.111364i
$850$		0			0
$851$	−1267.28	−	731.664i	−0.0510479	−	0.0294725i
$852$		0			0
$853$			36.8279i			0.00147827i	1.00000		0.000739134i	$0.000235274\pi$
$853$			36.8279i			0.00147827i	−1.00000		0.000739134i	$0.999765\pi$
$854$		0			0
$855$	149.157	−	274.191i	0.00596616	−	0.0109674i
$856$		0			0
$857$	12324.1	−	21345.9i	0.491228	−	0.850832i	−0.508721	−	0.860931i	$-0.669882\pi$
$857$	12324.1	−	21345.9i	0.491228	−	0.850832i	0.999949	+	0.0100996i	$0.00321487\pi$
$858$		0			0
$859$	16681.8	−	9631.21i	0.662601	−	0.382553i	−0.130666	−	0.991426i	$-0.541712\pi$
$859$	16681.8	−	9631.21i	0.662601	−	0.382553i	0.793267	+	0.608874i	$0.208378\pi$
$860$		0			0
$861$	−45998.0	+	16679.3i	−1.82068	+	0.660195i
$862$		0			0
$863$	−1795.72	+	1036.76i	−0.0708307	+	0.0408941i	−0.534997	−	0.844854i	$-0.679687\pi$
$863$	−1795.72	+	1036.76i	−0.0708307	+	0.0408941i	0.464166	+	0.885748i	$0.346354\pi$
$864$		0			0
$865$	121.745	−	210.869i	0.00478551	−	0.00828874i
$866$		0			0
$867$	−24738.4	−	6293.27i	−0.969042	−	0.246517i
$868$		0			0
$869$		−	4301.68i		−	0.167922i
$870$		0			0
$871$	−7832.64	−	4522.17i	−0.304706	−	0.175922i
$872$		0			0
$873$	−790.441	+	20.0664i	−0.0306442	+	0.000777945i
$874$		0			0
$875$	2192.89	+	1059.90i	0.0847236	+	0.0409497i
$876$		0			0
$877$	−9254.98	−	16030.1i	−0.356349	−	0.617215i	0.630999	−	0.775784i	$-0.282645\pi$
$877$	−9254.98	−	16030.1i	−0.356349	−	0.617215i	−0.987348	+	0.158569i	$0.949312\pi$
$878$		0			0
$879$	−30571.4	+	31357.3i	−1.17309	+	1.20325i
$880$		0			0
$881$	−18519.0			−0.708197			−0.354098	−	0.935208i	$-0.615212\pi$
$881$	−18519.0			−0.708197			−0.354098	+	0.935208i	$0.615212\pi$
$882$		0			0
$883$	17433.5			0.664421			0.332210	−	0.943205i	$-0.392206\pi$
$883$	17433.5			0.664421			0.332210	+	0.943205i	$0.392206\pi$
$884$		0			0
$885$	798.165	−	818.685i	0.0303164	−	0.0310958i
$886$		0			0
$887$	−6522.36	−	11297.1i	−0.246899	−	0.427642i	0.715765	−	0.698341i	$-0.246078\pi$
$887$	−6522.36	−	11297.1i	−0.246899	−	0.427642i	−0.962664	+	0.270700i	$0.912745\pi$
$888$		0			0
$889$	37409.4	+	18081.2i	1.41133	+	0.682142i
$890$		0			0
$891$	−7378.55	−	3774.42i	−0.277431	−	0.141917i
$892$		0			0
$893$	6357.68	+	3670.61i	0.238244	+	0.137550i
$894$		0			0
$895$		−	1026.19i		−	0.0383259i
$896$		0			0
$897$	2528.92	+	643.338i	0.0941338	+	0.0239470i
$898$		0			0
$899$	−10554.3	+	18280.5i	−0.391551	+	0.678186i
$900$		0			0
$901$	255.155	−	147.314i	0.00943446	−	0.00544699i
$902$		0			0
$903$	−2280.32	+	826.862i	−0.0840356	+	0.0304720i
$904$		0			0
$905$	280.491	−	161.941i	0.0103026	−	0.00594820i
$906$		0			0
$907$	−4239.49	+	7343.01i	−0.155204	+	0.268821i	−0.933133	−	0.359531i	$-0.882937\pi$
$907$	−4239.49	+	7343.01i	−0.155204	+	0.268821i	0.777929	+	0.628352i	$0.216270\pi$
$908$		0			0
$909$	−23843.5	−	12970.6i	−0.870010	−	0.473277i
$910$		0			0
$911$			2461.64i			0.0895256i	0.998998	+	0.0447628i	$0.0142532\pi$
$911$			2461.64i			0.0895256i	−0.998998	+	0.0447628i	$0.985747\pi$
$912$		0			0
$913$	−5312.85	−	3067.37i	−0.192584	−	0.111189i
$914$		0			0
$915$	877.494	−	247.101i	0.0317039	−	0.00892775i
$916$		0			0
$917$	−2821.02	−	38378.7i	−0.101590	−	1.38209i
$918$		0			0
$919$	19763.8	+	34232.0i	0.709411	+	1.22874i	0.965076	+	0.261970i	$0.0843722\pi$
$919$	19763.8	+	34232.0i	0.709411	+	1.22874i	−0.255665	+	0.966765i	$0.582294\pi$
$920$		0			0
$921$	−17305.1	−	16871.4i	−0.619134	−	0.603616i
$922$		0			0
$923$	−47280.3			−1.68608
$924$		0			0
$925$	−23923.1			−0.850365
$926$		0			0
$927$	−3405.38	−	5567.05i	−0.120655	−	0.197245i
$928$		0			0
$929$	−16359.4	−	28335.2i	−0.577754	−	1.00070i	−0.995736	−	0.0922440i	$-0.970596\pi$
$929$	−16359.4	−	28335.2i	−0.577754	−	1.00070i	0.417983	−	0.908455i	$-0.362737\pi$
$930$		0			0
$931$	7001.25	+	2770.87i	0.246462	+	0.0975419i
$932$		0			0
$933$	−5183.06	−	18405.9i	−0.181871	−	0.645854i
$934$		0			0
$935$	3.51577	+	2.02983i	0.000122971	+	7.09973e-5i
$936$		0			0
$937$			21523.1i			0.750406i	0.926943	+	0.375203i	$0.122427\pi$
$937$			21523.1i			0.750406i	−0.926943	+	0.375203i	$0.877573\pi$
$938$		0			0
$939$	1375.31	−	5406.25i	0.0477972	−	0.187887i
$940$		0			0
$941$	−21454.9	+	37161.0i	−0.743263	+	1.28737i	0.207738	+	0.978184i	$0.433390\pi$
$941$	−21454.9	+	37161.0i	−0.743263	+	1.28737i	−0.951002	+	0.309186i	$0.899944\pi$
$942$		0			0
$943$	3359.19	−	1939.43i	0.116002	−	0.0669740i
$944$		0			0
$945$	−853.952	+	1069.16i	−0.0293958	+	0.0368042i
$946$		0			0
$947$	8938.35	−	5160.56i	0.306713	−	0.177081i	−0.338741	−	0.940879i	$-0.610001\pi$
$947$	8938.35	−	5160.56i	0.306713	−	0.177081i	0.645455	+	0.763798i	$0.276668\pi$
$948$		0			0
$949$	38376.6	−	66470.2i	1.31271	−	2.27367i
$950$		0			0
$951$	3421.41	−	13449.3i	0.116663	−	0.458594i
$952$		0			0
$953$			55448.9i			1.88475i	0.334558	+	0.942375i	$0.391413\pi$
$953$			55448.9i			1.88475i	−0.334558	+	0.942375i	$0.608587\pi$
$954$		0			0
$955$	1018.12	+	587.812i	0.0344980	+	0.0199174i
$956$		0			0
$957$	−2653.25	−	9422.12i	−0.0896211	−	0.318259i
$958$		0			0
$959$	−23498.1	−	34571.2i	−0.791232	−	1.16409i
$960$		0			0
$961$	−6781.32	−	11745.6i	−0.227630	−	0.394266i
$962$		0			0
$963$	20399.8	+	33349.2i	0.682631	+	1.11595i
$964$		0			0
$965$	729.161			0.0243239
$966$		0			0
$967$	14843.5			0.493626			0.246813	−	0.969063i	$-0.420617\pi$
$967$	14843.5			0.493626			0.246813	+	0.969063i	$0.420617\pi$
$968$		0			0
$969$	55.3809	+	53.9928i	0.00183601	+	0.00178999i
$970$		0			0
$971$	−11922.3	−	20650.1i	−0.394033	−	0.682485i	0.598944	−	0.800791i	$-0.295587\pi$
$971$	−11922.3	−	20650.1i	−0.394033	−	0.682485i	−0.992977	+	0.118306i	$0.962254\pi$
$972$		0			0
$973$	−8756.75	+	18117.4i	−0.288519	+	0.596935i
$974$		0			0
$975$	41063.6	−	11563.4i	1.34881	−	0.379821i
$976$		0			0
$977$	11571.6	+	6680.87i	0.378923	+	0.218772i	0.677350	−	0.735661i	$-0.263128\pi$
$977$	11571.6	+	6680.87i	0.378923	+	0.218772i	−0.298426	+	0.954433i	$0.596462\pi$
$978$		0			0
$979$			10405.0i			0.339679i
$980$		0			0
$981$	−44832.5	−	24388.4i	−1.45911	−	0.793744i
$982$		0			0
$983$	2649.18	−	4588.51i	0.0859569	−	0.148882i	−0.819842	−	0.572590i	$-0.805939\pi$
$983$	2649.18	−	4588.51i	0.0859569	−	0.148882i	0.905799	+	0.423709i	$0.139272\pi$
$984$		0			0
$985$	1784.53	−	1030.30i	0.0577258	−	0.0333280i
$986$		0			0
$987$	−24628.2	−	20716.1i	−0.794250	−	0.668085i
$988$		0			0
$989$	166.529	−	96.1457i	0.00535422	−	0.00309126i
$990$		0			0
$991$	8526.29	−	14768.0i	0.273306	−	0.473381i	−0.696400	−	0.717654i	$-0.745216\pi$
$991$	8526.29	−	14768.0i	0.273306	−	0.473381i	0.969706	+	0.244273i	$0.0785494\pi$
$992$		0			0
$993$	−48132.4	−	12244.6i	−1.53820	−	0.391308i
$994$		0			0
$995$		−	1866.72i		−	0.0594763i
$996$		0			0
$997$	2682.03	+	1548.47i	0.0851963	+	0.0491881i	0.541993	−	0.840383i	$-0.317670\pi$
$997$	2682.03	+	1548.47i	0.0851963	+	0.0491881i	−0.456797	+	0.889571i	$0.651003\pi$
$998$		0			0
$999$	5970.48	−	26239.6i	0.189087	−	0.831015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bc.f.17.6		48
3.2	odd	2	inner	336.4.bc.f.17.15		48
4.3	odd	2		168.4.u.a.17.19	yes	48
7.5	odd	6	inner	336.4.bc.f.257.15		48
12.11	even	2		168.4.u.a.17.10	✓	48
21.5	even	6	inner	336.4.bc.f.257.6		48
28.19	even	6		168.4.u.a.89.10	yes	48
84.47	odd	6		168.4.u.a.89.19	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.u.a.17.10	✓	48	12.11	even	2
168.4.u.a.17.19	yes	48	4.3	odd	2
168.4.u.a.89.10	yes	48	28.19	even	6
168.4.u.a.89.19	yes	48	84.47	odd	6
336.4.bc.f.17.6		48	1.1	even	1	trivial
336.4.bc.f.17.15		48	3.2	odd	2	inner
336.4.bc.f.257.6		48	21.5	even	6	inner
336.4.bc.f.257.15		48	7.5	odd	6	inner

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.62731 + 3.72057i) q^{3} +(0.263312 + 0.456070i) q^{5} +(16.6747 + 8.05944i) q^{7} +(-0.685212 - 26.9913i) q^{9} +O(q^{10})\)	\(q+(-3.62731 + 3.72057i) q^{3} +(0.263312 + 0.456070i) q^{5} +(16.6747 + 8.05944i) q^{7} +(-0.685212 - 26.9913i) q^{9} +(9.84572 + 5.68443i) q^{11} -65.8264i q^{13} +(-2.65195 - 0.674638i) q^{15} +(0.339033 - 0.587223i) q^{17} +(19.0112 - 10.9761i) q^{19} +(-90.4700 + 32.8052i) q^{21} +(6.60693 - 3.81451i) q^{23} +(62.3613 - 108.013i) q^{25} +(102.908 + 95.3565i) q^{27} +165.699i q^{29} +(110.323 + 63.6953i) q^{31} +(-56.8628 + 16.0124i) q^{33} +(0.714981 + 9.72697i) q^{35} +(-95.9053 - 166.113i) q^{37} +(244.911 + 238.773i) q^{39} +508.434 q^{41} +25.2052 q^{43} +(12.1295 - 7.41964i) q^{45} +(167.209 + 289.614i) q^{47} +(213.091 + 268.777i) q^{49} +(0.955021 + 3.39143i) q^{51} +(376.298 + 217.256i) q^{53} +5.98711i q^{55} +(-28.1222 + 110.546i) q^{57} +(-208.919 + 361.858i) q^{59} +(-288.511 + 166.572i) q^{61} +(206.109 - 455.594i) q^{63} +(30.0214 - 17.3329i) q^{65} +(68.6985 - 118.989i) q^{67} +(-9.77326 + 38.4180i) q^{69} -718.257i q^{71} +(1009.78 + 582.997i) q^{73} +(175.665 + 623.816i) q^{75} +(118.361 + 174.137i) q^{77} +(-189.187 - 327.682i) q^{79} +(-728.061 + 36.9895i) q^{81} -539.610 q^{83} +0.357086 q^{85} +(-616.495 - 601.043i) q^{87} +(457.610 + 792.604i) q^{89} +(530.524 - 1097.64i) q^{91} +(-637.160 + 179.423i) q^{93} +(10.0117 + 5.78029i) q^{95} -29.2850i q^{97} +(146.684 - 269.644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{7} + 14 q^{9}+O(q^{10}) \) 48 * q - 12 * q^7 + 14 * q^9	\( 48 q - 12 q^{7} + 14 q^{9} + 88 q^{15} + 270 q^{19} + 50 q^{21} - 438 q^{25} - 216 q^{31} - 372 q^{33} + 66 q^{37} - 242 q^{39} - 900 q^{43} - 294 q^{45} + 60 q^{49} + 138 q^{51} + 1384 q^{57} + 108 q^{61} - 1096 q^{63} - 6 q^{67} - 1206 q^{73} + 594 q^{75} + 588 q^{79} - 54 q^{81} - 240 q^{85} + 3522 q^{87} - 234 q^{91} - 608 q^{93} - 1988 q^{99}+O(q^{100}) \) 48 * q - 12 * q^7 + 14 * q^9 + 88 * q^15 + 270 * q^19 + 50 * q^21 - 438 * q^25 - 216 * q^31 - 372 * q^33 + 66 * q^37 - 242 * q^39 - 900 * q^43 - 294 * q^45 + 60 * q^49 + 138 * q^51 + 1384 * q^57 + 108 * q^61 - 1096 * q^63 - 6 * q^67 - 1206 * q^73 + 594 * q^75 + 588 * q^79 - 54 * q^81 - 240 * q^85 + 3522 * q^87 - 234 * q^91 - 608 * q^93 - 1988 * q^99

Introduction

L-functions

Modular forms

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Database

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