LMFDB - Embedded newform 336.4.bc.f.17.3

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			17.3
Character	$\chi$	$=$	336.17
Dual form			336.4.bc.f.257.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.99832 - 1.42013i) q^{3} +(-6.11124 - 10.5850i) q^{5} +(-4.39164 + 17.9920i) q^{7} +(22.9665 + 14.1965i) q^{9} +O(q^{10})$	\(q+(-4.99832 - 1.42013i) q^{3} +(-6.11124 - 10.5850i) q^{5} +(-4.39164 + 17.9920i) q^{7} +(22.9665 + 14.1965i) q^{9} +(47.3827 + 27.3564i) q^{11} -27.0247i q^{13} +(15.5139 + 61.5859i) q^{15} +(20.3052 - 35.1697i) q^{17} +(48.4879 - 27.9945i) q^{19} +(47.5018 - 83.6934i) q^{21} +(-93.3394 + 53.8895i) q^{23} +(-12.1945 + 21.1215i) q^{25} +(-94.6330 - 103.574i) q^{27} +38.2431i q^{29} +(-257.992 - 148.952i) q^{31} +(-197.985 - 204.026i) q^{33} +(217.284 - 63.4683i) q^{35} +(-142.286 - 246.447i) q^{37} +(-38.3785 + 135.078i) q^{39} +28.3958 q^{41} -212.817 q^{43} +(9.91619 - 329.858i) q^{45} +(125.209 + 216.869i) q^{47} +(-304.427 - 158.029i) q^{49} +(-151.438 + 146.954i) q^{51} +(294.863 + 170.239i) q^{53} -668.727i q^{55} +(-282.114 + 71.0665i) q^{57} +(451.101 - 781.329i) q^{59} +(499.851 - 288.589i) q^{61} +(-356.285 + 350.868i) q^{63} +(-286.056 + 165.154i) q^{65} +(184.464 - 319.500i) q^{67} +(543.070 - 136.803i) q^{69} -1184.28i q^{71} +(-407.399 - 235.212i) q^{73} +(90.9474 - 88.2544i) q^{75} +(-700.286 + 732.373i) q^{77} +(20.0802 + 34.7799i) q^{79} +(325.918 + 652.088i) q^{81} -855.263 q^{83} -496.361 q^{85} +(54.3102 - 191.152i) q^{87} +(322.110 + 557.910i) q^{89} +(486.229 + 118.683i) q^{91} +(1078.00 + 1110.89i) q^{93} +(-592.642 - 342.162i) q^{95} -748.863i q^{97} +(699.848 + 1300.95i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−4.99832	−	1.42013i	−0.961928	−	0.273304i
$3$	−4.99832	−	1.42013i	−0.961928	−	0.273304i
$4$		0			0
$5$	−6.11124	−	10.5850i	−0.546606	−	0.946749i	−0.998504	−	0.0546796i	$-0.982586\pi$
$5$	−6.11124	−	10.5850i	−0.546606	−	0.946749i	0.451898	−	0.892070i	$-0.350747\pi$
$6$		0			0
$7$	−4.39164	+	17.9920i	−0.237126	+	0.971479i
$7$	−4.39164	+	17.9920i	−0.237126	+	0.971479i
$8$		0			0
$9$	22.9665	+	14.1965i	0.850610	+	0.525797i
$10$		0			0
$11$	47.3827	+	27.3564i	1.29877	+	0.749843i	0.980191	−	0.198054i	$-0.0634623\pi$
$11$	47.3827	+	27.3564i	1.29877	+	0.749843i	0.318575	+	0.947898i	$0.396796\pi$
$12$		0			0
$13$		−	27.0247i		−	0.576561i	−0.957546	−	0.288281i	$-0.906916\pi$
$13$		−	27.0247i		−	0.576561i	0.957546	−	0.288281i	$-0.0930836\pi$
$14$		0			0
$15$	15.5139	+	61.5859i	0.267045	+	1.06009i
$16$		0			0
$17$	20.3052	−	35.1697i	0.289691	−	0.501759i	−0.684045	−	0.729440i	$-0.739781\pi$
$17$	20.3052	−	35.1697i	0.289691	−	0.501759i	0.973736	+	0.227680i	$0.0731142\pi$
$18$		0			0
$19$	48.4879	−	27.9945i	0.585467	−	0.338020i	−0.177836	−	0.984060i	$-0.556910\pi$
$19$	48.4879	−	27.9945i	0.585467	−	0.338020i	0.763303	+	0.646040i	$0.223576\pi$
$20$		0			0
$21$	47.5018	−	83.6934i	0.493607	−	0.869685i
$22$		0			0
$23$	−93.3394	+	53.8895i	−0.846200	+	0.488554i	−0.859367	−	0.511359i	$-0.829142\pi$
$23$	−93.3394	+	53.8895i	−0.846200	+	0.488554i	0.0131667	+	0.999913i	$0.495809\pi$
$24$		0			0
$25$	−12.1945	+	21.1215i	−0.0975561	+	0.168972i
$26$		0			0
$27$	−94.6330	−	103.574i	−0.674523	−	0.738254i
$28$		0			0
$29$			38.2431i			0.244882i	0.992476	+	0.122441i	$0.0390722\pi$
$29$			38.2431i			0.244882i	−0.992476	+	0.122441i	$0.960928\pi$
$30$		0			0
$31$	−257.992	−	148.952i	−1.49473	−	0.862985i	−0.494753	−	0.869034i	$-0.664741\pi$
$31$	−257.992	−	148.952i	−1.49473	−	0.862985i	−0.999982	+	0.00604814i	$0.998075\pi$
$32$		0			0
$33$	−197.985	−	204.026i	−1.04438	−	1.07625i
$34$		0			0
$35$	217.284	−	63.4683i	1.04936	−	0.306517i
$36$		0			0
$37$	−142.286	−	246.447i	−0.632209	−	1.09502i	−0.987099	−	0.160110i	$-0.948815\pi$
$37$	−142.286	−	246.447i	−0.632209	−	1.09502i	0.354890	−	0.934908i	$-0.384518\pi$
$38$		0			0
$39$	−38.3785	+	135.078i	−0.157576	+	0.554610i
$40$		0			0
$41$	28.3958			0.108163			0.0540815	−	0.998537i	$-0.482777\pi$
$41$	28.3958			0.108163			0.0540815	+	0.998537i	$0.482777\pi$
$42$		0			0
$43$	−212.817			−0.754752			−0.377376	−	0.926060i	$-0.623173\pi$
$43$	−212.817			−0.754752			−0.377376	+	0.926060i	$0.623173\pi$
$44$		0			0
$45$	9.91619	−	329.858i	0.0328493	−	1.09272i
$46$		0			0
$47$	125.209	+	216.869i	0.388588	+	0.673055i	0.992260	−	0.124178i	$-0.0396295\pi$
$47$	125.209	+	216.869i	0.388588	+	0.673055i	−0.603672	+	0.797233i	$0.706296\pi$
$48$		0			0
$49$	−304.427	−	158.029i	−0.887542	−	0.460726i
$50$		0			0
$51$	−151.438	+	146.954i	−0.415794	+	0.403483i
$52$		0			0
$53$	294.863	+	170.239i	0.764198	+	0.441210i	0.830801	−	0.556570i	$-0.187883\pi$
$53$	294.863	+	170.239i	0.764198	+	0.441210i	−0.0666029	+	0.997780i	$0.521216\pi$
$54$		0			0
$55$		−	668.727i		−	1.63947i
$56$		0			0
$57$	−282.114	+	71.0665i	−0.655559	+	0.165140i
$58$		0			0
$59$	451.101	−	781.329i	0.995395	−	1.72407i	0.414681	−	0.909967i	$-0.363893\pi$
$59$	451.101	−	781.329i	0.995395	−	1.72407i	0.580714	−	0.814108i	$-0.302774\pi$
$60$		0			0
$61$	499.851	−	288.589i	1.04917	−	0.605739i	0.126753	−	0.991934i	$-0.459544\pi$
$61$	499.851	−	288.589i	1.04917	−	0.605739i	0.922417	+	0.386196i	$0.126211\pi$
$62$		0			0
$63$	−356.285	+	350.868i	−0.712502	+	0.701670i
$64$		0			0
$65$	−286.056	+	165.154i	−0.545859	+	0.315152i
$66$		0			0
$67$	184.464	−	319.500i	0.336355	−	0.582585i	−0.647389	−	0.762160i	$-0.724139\pi$
$67$	184.464	−	319.500i	0.336355	−	0.582585i	0.983744	+	0.179575i	$0.0574723\pi$
$68$		0			0
$69$	543.070	−	136.803i	0.947507	−	0.238684i
$70$		0			0
$71$		−	1184.28i		−	1.97955i	−0.142648	−	0.989773i	$-0.545562\pi$
$71$		−	1184.28i		−	1.97955i	0.142648	−	0.989773i	$-0.454438\pi$
$72$		0			0
$73$	−407.399	−	235.212i	−0.653184	−	0.377116i	0.136491	−	0.990641i	$-0.456417\pi$
$73$	−407.399	−	235.212i	−0.653184	−	0.377116i	−0.789675	+	0.613526i	$0.789751\pi$
$74$		0			0
$75$	90.9474	−	88.2544i	0.140023	−	0.135877i
$76$		0			0
$77$	−700.286	+	732.373i	−1.03643	+	1.08392i
$78$		0			0
$79$	20.0802	+	34.7799i	0.0285974	+	0.0495321i	0.879970	−	0.475029i	$-0.157563\pi$
$79$	20.0802	+	34.7799i	0.0285974	+	0.0495321i	−0.851373	+	0.524562i	$0.824229\pi$
$80$		0			0
$81$	325.918	+	652.088i	0.447075	+	0.894496i
$82$		0			0
$83$	−855.263			−1.13105			−0.565526	−	0.824731i	$-0.691327\pi$
$83$	−855.263			−1.13105			−0.565526	+	0.824731i	$0.691327\pi$
$84$		0			0
$85$	−496.361			−0.633387
$86$		0			0
$87$	54.3102	−	191.152i	0.0669271	−	0.235559i
$88$		0			0
$89$	322.110	+	557.910i	0.383636	+	0.664476i	0.991579	−	0.129504i	$-0.0413386\pi$
$89$	322.110	+	557.910i	0.383636	+	0.664476i	−0.607943	+	0.793980i	$0.708005\pi$
$90$		0			0
$91$	486.229	+	118.683i	0.560117	+	0.136718i
$92$		0			0
$93$	1078.00	+	1110.89i	1.20197	+	1.23865i
$94$		0			0
$95$	−592.642	−	342.162i	−0.640040	−	0.369527i
$96$		0			0
$97$		−	748.863i		−	0.783872i	−0.919993	−	0.391936i	$-0.871806\pi$
$97$		−	748.863i		−	0.783872i	0.919993	−	0.391936i	$-0.128194\pi$
$98$		0			0
$99$	699.848	+	1300.95i	0.710479	+	1.32071i
$100$		0			0
$101$	−639.339	+	1107.37i	−0.629867	+	1.09096i	0.357711	+	0.933832i	$0.383557\pi$
$101$	−639.339	+	1107.37i	−0.629867	+	1.09096i	−0.987578	+	0.157130i	$0.949776\pi$
$102$		0			0
$103$	48.6627	−	28.0954i	0.0465523	−	0.0268770i	−0.476543	−	0.879151i	$-0.658110\pi$
$103$	48.6627	−	28.0954i	0.0465523	−	0.0268770i	0.523096	+	0.852274i	$0.324777\pi$
$104$		0			0
$105$	−1176.19	+	8.66453i	−1.09318	+	0.00805306i
$106$		0			0
$107$	−96.0313	+	55.4437i	−0.0867635	+	0.0500930i	−0.542754	−	0.839892i	$-0.682618\pi$
$107$	−96.0313	+	55.4437i	−0.0867635	+	0.0500930i	0.455991	+	0.889985i	$0.349285\pi$
$108$		0			0
$109$	486.042	−	841.850i	0.427105	−	0.739767i	−0.569510	−	0.821985i	$-0.692867\pi$
$109$	486.042	−	841.850i	0.427105	−	0.739767i	0.996614	+	0.0822175i	$0.0262002\pi$
$110$		0			0
$111$	361.207	+	1433.89i	0.308867	+	1.22611i
$112$		0			0
$113$		−	1949.29i		−	1.62277i	−0.584510	−	0.811387i	$-0.698713\pi$
$113$		−	1949.29i		−	1.62277i	0.584510	−	0.811387i	$-0.301287\pi$
$114$		0			0
$115$	1140.84	+	658.664i	0.925076	+	0.534093i
$116$		0			0
$117$	383.656	−	620.662i	0.303154	−	0.490429i
$118$		0			0
$119$	543.602	+	519.785i	0.418755	+	0.400409i
$120$		0			0
$121$	831.249	+	1439.76i	0.624529	+	1.08172i
$122$		0			0
$123$	−141.932	−	40.3257i	−0.104045	−	0.0295614i
$124$		0			0
$125$	−1229.72			−0.879913
$126$		0			0
$127$	−2659.56			−1.85825			−0.929124	−	0.369768i	$-0.879437\pi$
$127$	−2659.56			−1.85825			−0.929124	+	0.369768i	$0.879437\pi$
$128$		0			0
$129$	1063.73	+	302.228i	0.726016	+	0.206276i
$130$		0			0
$131$	999.107	+	1730.50i	0.666354	+	1.15416i	0.978916	+	0.204262i	$0.0654793\pi$
$131$	999.107	+	1730.50i	0.666354	+	1.15416i	−0.312562	+	0.949897i	$0.601187\pi$
$132$		0			0
$133$	290.737	+	995.337i	0.189549	+	0.648922i
$134$		0			0
$135$	−518.005	+	1634.65i	−0.330243	+	1.04214i
$136$		0			0
$137$	1334.65	+	770.561i	0.832314	+	0.480537i	0.854644	−	0.519214i	$-0.173775\pi$
$137$	1334.65	+	770.561i	0.832314	+	0.480537i	−0.0223305	+	0.999751i	$0.507109\pi$
$138$		0			0
$139$		−	2926.53i		−	1.78579i	−0.450261	−	0.892897i	$-0.648669\pi$
$139$		−	2926.53i		−	1.78579i	0.450261	−	0.892897i	$-0.351331\pi$
$140$		0			0
$141$	−317.855	−	1261.79i	−0.189846	−	0.753633i
$142$		0			0
$143$	739.299	−	1280.50i	0.432331	−	0.748818i
$144$		0			0
$145$	404.803	−	233.713i	0.231842	−	0.133854i
$146$		0			0
$147$	1297.20	+	1222.21i	0.727834	+	0.685754i
$148$		0			0
$149$	2078.26	−	1199.89i	1.14267	−	0.659721i	0.195580	−	0.980688i	$-0.437341\pi$
$149$	2078.26	−	1199.89i	1.14267	−	0.659721i	0.947090	+	0.320967i	$0.104008\pi$
$150$		0			0
$151$	−89.6992	+	155.363i	−0.0483418	+	0.0837305i	−0.889184	−	0.457550i	$-0.848727\pi$
$151$	−89.6992	+	155.363i	−0.0483418	+	0.0837305i	0.840842	+	0.541281i	$0.182060\pi$
$152$		0			0
$153$	965.627	−	519.461i	0.510237	−	0.274483i
$154$		0			0
$155$			3641.12i			1.88685i
$156$		0			0
$157$	−1609.18	−	929.062i	−0.818004	−	0.472275i	0.0317234	−	0.999497i	$-0.489900\pi$
$157$	−1609.18	−	929.062i	−0.818004	−	0.472275i	−0.849728	+	0.527222i	$0.823234\pi$
$158$		0			0
$159$	−1232.06	−	1269.65i	−0.614519	−	0.633270i
$160$		0			0
$161$	−559.670	−	1916.03i	−0.273964	−	0.937915i
$162$		0			0
$163$	1512.28	+	2619.35i	0.726693	+	1.25867i	0.958274	+	0.285853i	$0.0922768\pi$
$163$	1512.28	+	2619.35i	0.726693	+	1.25867i	−0.231581	+	0.972816i	$0.574390\pi$
$164$		0			0
$165$	−949.678	+	3342.51i	−0.448075	+	1.57706i
$166$		0			0
$167$	1811.37			0.839329			0.419664	−	0.907679i	$-0.362148\pi$
$167$	1811.37			0.839329			0.419664	+	0.907679i	$0.362148\pi$
$168$		0			0
$169$	1466.67			0.667577
$170$		0			0
$171$	1511.02	+	45.4243i	0.675734	+	0.0203139i
$172$		0			0
$173$	−554.616	−	960.623i	−0.243738	−	0.422167i	0.718038	−	0.696004i	$-0.245040\pi$
$173$	−554.616	−	960.623i	−0.243738	−	0.422167i	−0.961776	+	0.273837i	$0.911707\pi$
$174$		0			0
$175$	−326.465	−	312.162i	−0.141020	−	0.134841i
$176$		0			0
$177$	−3364.33	+	3264.72i	−1.42869	+	1.38639i
$178$		0			0
$179$	−3272.96	−	1889.64i	−1.36666	−	0.789043i	−0.376162	−	0.926554i	$-0.622756\pi$
$179$	−3272.96	−	1889.64i	−1.36666	−	0.789043i	−0.990500	+	0.137512i	$0.956090\pi$
$180$		0			0
$181$		−	1180.13i		−	0.484634i	−0.970197	−	0.242317i	$-0.922093\pi$
$181$		−	1180.13i		−	0.484634i	0.970197	−	0.242317i	$-0.0779074\pi$
$182$		0			0
$183$	−2908.25	+	732.610i	−1.17478	+	0.295935i
$184$		0			0
$185$	−1739.09	+	3012.19i	−0.691138	+	1.19709i
$186$		0			0
$187$	1924.24	−	1110.96i	0.752481	−	0.434445i
$188$		0			0
$189$	2279.10	−	1247.78i	0.877145	−	0.480226i
$190$		0			0
$191$	−2714.53	+	1567.24i	−1.02836	+	0.593724i	−0.916514	−	0.400002i	$-0.869010\pi$
$191$	−2714.53	+	1567.24i	−1.02836	+	0.593724i	−0.111846	+	0.993726i	$0.535676\pi$
$192$		0			0
$193$	−406.923	+	704.811i	−0.151767	+	0.262867i	−0.931877	−	0.362775i	$-0.881830\pi$
$193$	−406.923	+	704.811i	−0.151767	+	0.262867i	0.780110	+	0.625642i	$0.215163\pi$
$194$		0			0
$195$	1664.34	−	419.259i	0.611209	−	0.153968i
$196$		0			0
$197$		−	2665.95i		−	0.964168i	−0.876125	−	0.482084i	$-0.839880\pi$
$197$		−	2665.95i		−	0.964168i	0.876125	−	0.482084i	$-0.160120\pi$
$198$		0			0
$199$	−1849.89	−	1068.03i	−0.658970	−	0.380457i	0.132914	−	0.991128i	$-0.457567\pi$
$199$	−1849.89	−	1068.03i	−0.658970	−	0.380457i	−0.791885	+	0.610671i	$0.790900\pi$
$200$		0			0
$201$	−1375.74	+	1335.00i	−0.482772	+	0.468477i
$202$		0			0
$203$	−688.072	−	167.950i	−0.237898	−	0.0580679i
$204$		0			0
$205$	−173.534	−	300.569i	−0.0591226	−	0.102403i
$206$		0			0
$207$	−2908.72	−	87.4419i	−0.976667	−	0.0293606i
$208$		0			0
$209$	3063.32			1.01385
$210$		0			0
$211$	1542.44			0.503250			0.251625	−	0.967825i	$-0.419035\pi$
$211$	1542.44			0.503250			0.251625	+	0.967825i	$0.419035\pi$
$212$		0			0
$213$	−1681.82	+	5919.40i	−0.541018	+	1.90418i
$214$		0			0
$215$	1300.58	+	2252.67i	0.412552	+	0.714560i
$216$		0			0
$217$	3812.96	−	3987.66i	1.19281	−	1.24747i
$218$		0			0
$219$	1702.28	+	1754.22i	0.525248	+	0.541276i
$220$		0			0
$221$	−950.450	−	548.743i	−0.289295	−	0.167025i
$222$		0			0
$223$			1581.82i			0.475008i	0.971387	+	0.237504i	$0.0763292\pi$
$223$			1581.82i			0.475008i	−0.971387	+	0.237504i	$0.923671\pi$
$224$		0			0
$225$	−579.917	+	311.967i	−0.171827	+	0.0924347i
$226$		0			0
$227$	1283.03	−	2222.27i	0.375143	−	0.649767i	−0.615206	−	0.788367i	$-0.710927\pi$
$227$	1283.03	−	2222.27i	0.375143	−	0.649767i	0.990348	+	0.138600i	$0.0442603\pi$
$228$		0			0
$229$	−1499.61	+	865.802i	−0.432739	+	0.249842i	−0.700513	−	0.713640i	$-0.747045\pi$
$229$	−1499.61	+	865.802i	−0.432739	+	0.249842i	0.267774	+	0.963482i	$0.413712\pi$
$230$		0			0
$231$	4540.32	−	2666.14i	1.29321	−	0.759390i
$232$		0			0
$233$	2637.07	−	1522.51i	0.741460	−	0.428082i	−0.0811399	−	0.996703i	$-0.525856\pi$
$233$	2637.07	−	1522.51i	0.741460	−	0.428082i	0.822600	+	0.568621i	$0.192523\pi$
$234$		0			0
$235$	1530.37	−	2650.67i	0.424809	−	0.735791i
$236$		0			0
$237$	−50.9753	−	202.357i	−0.0139713	−	0.0554621i
$238$		0			0
$239$			660.825i			0.178850i	0.995994	+	0.0894251i	$0.0285030\pi$
$239$			660.825i			0.178850i	−0.995994	+	0.0894251i	$0.971497\pi$
$240$		0			0
$241$	419.293	+	242.079i	0.112071	+	0.0647041i	0.554988	−	0.831859i	$-0.312723\pi$
$241$	419.293	+	242.079i	0.112071	+	0.0647041i	−0.442917	+	0.896563i	$0.646056\pi$
$242$		0			0
$243$	−702.994	−	3722.19i	−0.185585	−	0.982628i
$244$		0			0
$245$	187.694	+	4188.11i	0.0489441	+	1.09212i
$246$		0			0
$247$	−756.542	−	1310.37i	−0.194889	−	0.337558i
$248$		0			0
$249$	4274.88	+	1214.58i	1.08799	+	0.309121i
$250$		0			0
$251$	2610.69			0.656514			0.328257	−	0.944588i	$-0.393539\pi$
$251$	2610.69			0.656514			0.328257	+	0.944588i	$0.393539\pi$
$252$		0			0
$253$	−5896.90			−1.46536
$254$		0			0
$255$	2480.97	+	704.896i	0.609273	+	0.173107i
$256$		0			0
$257$	729.496	+	1263.52i	0.177061	+	0.306679i	0.940873	−	0.338760i	$-0.110008\pi$
$257$	729.496	+	1263.52i	0.177061	+	0.306679i	−0.763812	+	0.645439i	$0.776674\pi$
$258$		0			0
$259$	5058.96	−	1477.72i	1.21370	−	0.354520i
$260$		0			0
$261$	−542.919	+	878.310i	−0.128758	+	0.208299i
$262$		0			0
$263$	−4410.38	−	2546.33i	−1.03405	−	0.597010i	−0.115909	−	0.993260i	$-0.536978\pi$
$263$	−4410.38	−	2546.33i	−1.03405	−	0.597010i	−0.918143	+	0.396249i	$0.870312\pi$
$264$		0			0
$265$		−	4161.49i		−	0.964672i
$266$		0			0
$267$	−817.704	−	3246.05i	−0.187426	−	0.744027i
$268$		0			0
$269$	−487.624	+	844.590i	−0.110524	+	0.191433i	−0.915982	−	0.401220i	$-0.868586\pi$
$269$	−487.624	+	844.590i	−0.110524	+	0.191433i	0.805458	+	0.592653i	$0.201920\pi$
$270$		0			0
$271$	−3190.71	+	1842.16i	−0.715209	+	0.412926i	−0.812987	−	0.582282i	$-0.802160\pi$
$271$	−3190.71	+	1842.16i	−0.715209	+	0.412926i	0.0977775	+	0.995208i	$0.468827\pi$
$272$		0			0
$273$	−2261.79	−	1283.72i	−0.501427	−	0.284595i
$274$		0			0
$275$	−1155.62	+	667.197i	−0.253405	+	0.146304i
$276$		0			0
$277$	−1650.60	+	2858.93i	−0.358033	+	0.620132i	−0.987632	−	0.156789i	$-0.949886\pi$
$277$	−1650.60	+	2858.93i	−0.358033	+	0.620132i	0.629599	+	0.776920i	$0.283219\pi$
$278$		0			0
$279$	−3810.57	−	7083.49i	−0.817681	−	1.51999i
$280$		0			0
$281$		−	444.621i		−	0.0943910i	−0.998886	−	0.0471955i	$-0.984972\pi$
$281$		−	444.621i		−	0.0943910i	0.998886	−	0.0471955i	$-0.0150284\pi$
$282$		0			0
$283$	−1569.80	−	906.327i	−0.329736	−	0.190373i	0.325988	−	0.945374i	$-0.394303\pi$
$283$	−1569.80	−	906.327i	−0.329736	−	0.190373i	−0.655724	+	0.755001i	$0.727636\pi$
$284$		0			0
$285$	2476.30	+	2551.86i	0.514679	+	0.530384i
$286$		0			0
$287$	−124.704	+	510.899i	−0.0256483	+	0.105078i
$288$		0			0
$289$	1631.89	+	2826.52i	0.332158	+	0.575315i
$290$		0			0
$291$	−1063.48	+	3743.06i	−0.214235	+	0.754028i
$292$		0			0
$293$	693.371			0.138250			0.0691248	−	0.997608i	$-0.477979\pi$
$293$	693.371			0.138250			0.0691248	+	0.997608i	$0.477979\pi$
$294$		0			0
$295$	−11027.1			−2.17636
$296$		0			0
$297$	−1650.55	−	7496.44i	−0.322474	−	1.46461i
$298$		0			0
$299$	1456.35	+	2522.47i	0.281681	+	0.487886i
$300$		0			0
$301$	934.615	−	3829.02i	0.178971	−	0.733225i
$302$		0			0
$303$	4768.23	−	4627.04i	0.904051	−	0.877282i
$304$		0			0
$305$	−6109.42	−	3527.28i	−1.14697	−	0.662201i
$306$		0			0
$307$		−	5574.91i		−	1.03641i	−0.855257	−	0.518203i	$-0.826601\pi$
$307$		−	5574.91i		−	1.03641i	0.855257	−	0.518203i	$-0.173399\pi$
$308$		0			0
$309$	−283.131	+	71.3228i	−0.0521255	+	0.0131308i
$310$		0			0
$311$	484.794	−	839.688i	0.0883927	−	0.153101i	−0.818439	−	0.574593i	$-0.805160\pi$
$311$	484.794	−	839.688i	0.0883927	−	0.153101i	0.906832	+	0.421492i	$0.138494\pi$
$312$		0			0
$313$	−1698.97	+	980.901i	−0.306810	+	0.177137i	−0.645498	−	0.763762i	$-0.723350\pi$
$313$	−1698.97	+	980.901i	−0.306810	+	0.177137i	0.338688	+	0.940899i	$0.390017\pi$
$314$		0			0
$315$	5891.27	+	1627.03i	1.05376	+	0.291024i
$316$		0			0
$317$	8969.01	−	5178.26i	1.58912	−	0.917476i	0.595662	−	0.803235i	$-0.296890\pi$
$317$	8969.01	−	5178.26i	1.58912	−	0.917476i	0.993453	−	0.114241i	$-0.0364437\pi$
$318$		0			0
$319$	−1046.20	+	1812.06i	−0.183623	+	0.318044i
$320$		0			0
$321$	558.733	−	140.749i	0.0971509	−	0.0244730i
$322$		0			0
$323$		−	2273.74i		−	0.391685i
$324$		0			0
$325$	570.802	+	329.553i	0.0974228	+	0.0562471i
$326$		0			0
$327$	−3624.93	+	3517.60i	−0.613025	+	0.594873i
$328$		0			0
$329$	−4451.79	+	1300.36i	−0.746003	+	0.217907i
$330$		0			0
$331$	−1990.22	−	3447.16i	−0.330491	−	0.572427i	0.652117	−	0.758118i	$-0.273881\pi$
$331$	−1990.22	−	3447.16i	−0.330491	−	0.572427i	−0.982608	+	0.185691i	$0.940548\pi$
$332$		0			0
$333$	230.876	−	7679.99i	0.0379938	−	1.26385i
$334$		0			0
$335$	−4509.21			−0.735415
$336$		0			0
$337$	−8369.88			−1.35293			−0.676463	−	0.736476i	$-0.736488\pi$
$337$	−8369.88			−1.35293			−0.676463	+	0.736476i	$0.736488\pi$
$338$		0			0
$339$	−2768.24	+	9743.16i	−0.443510	+	1.56099i
$340$		0			0
$341$	−8149.58	−	14115.5i	−1.29421	−	2.24163i
$342$		0			0
$343$	4180.20	−	4783.26i	0.658045	−	0.752979i
$344$		0			0
$345$	−4766.89	−	4912.35i	−0.743887	−	0.766586i
$346$		0			0
$347$	4876.37	+	2815.37i	0.754401	+	0.435554i	0.827282	−	0.561787i	$-0.189886\pi$
$347$	4876.37	+	2815.37i	0.754401	+	0.435554i	−0.0728808	+	0.997341i	$0.523219\pi$
$348$		0			0
$349$		−	10150.9i		−	1.55691i	−0.627698	−	0.778457i	$-0.716003\pi$
$349$		−	10150.9i		−	1.55691i	0.627698	−	0.778457i	$-0.283997\pi$
$350$		0			0
$351$	−2799.06	+	2557.43i	−0.425648	+	0.388904i
$352$		0			0
$353$	1284.89	−	2225.50i	0.193733	−	0.335556i	−0.752751	−	0.658305i	$-0.771274\pi$
$353$	1284.89	−	2225.50i	0.193733	−	0.335556i	0.946485	+	0.322749i	$0.104607\pi$
$354$		0			0
$355$	−12535.5	+	7237.40i	−1.87413	+	1.08203i
$356$		0			0
$357$	−1978.94	−	3370.04i	−0.293379	−	0.499612i
$358$		0			0
$359$	1588.86	−	917.327i	0.233584	−	0.134860i	−0.378640	−	0.925544i	$-0.623608\pi$
$359$	1588.86	−	917.327i	0.233584	−	0.134860i	0.612224	+	0.790684i	$0.290275\pi$
$360$		0			0
$361$	−1862.12	+	3225.28i	−0.271485	+	0.470226i
$362$		0			0
$363$	−2110.20	−	8376.89i	−0.305115	−	1.21122i
$364$		0			0
$365$			5749.74i			0.824535i
$366$		0			0
$367$	6793.91	+	3922.47i	0.966320	+	0.557905i	0.898112	−	0.439766i	$-0.144939\pi$
$367$	6793.91	+	3922.47i	0.966320	+	0.557905i	0.0682076	+	0.997671i	$0.478272\pi$
$368$		0			0
$369$	652.152	+	403.122i	0.0920046	+	0.0568718i
$370$		0			0
$371$	−4357.88	+	4557.55i	−0.609837	+	0.637780i
$372$		0			0
$373$	2429.11	+	4207.33i	0.337197	+	0.584042i	0.983904	−	0.178696i	$-0.0571880\pi$
$373$	2429.11	+	4207.33i	0.337197	+	0.584042i	−0.646708	+	0.762738i	$0.723855\pi$
$374$		0			0
$375$	6146.52	+	1746.35i	0.846413	+	0.240483i
$376$		0			0
$377$	1033.51			0.141189
$378$		0			0
$379$	10589.6			1.43523			0.717616	−	0.696439i	$-0.245233\pi$
$379$	10589.6			1.43523			0.717616	+	0.696439i	$0.245233\pi$
$380$		0			0
$381$	13293.3	+	3776.91i	1.78750	+	0.507866i
$382$		0			0
$383$	1948.54	+	3374.96i	0.259962	+	0.450268i	0.966231	−	0.257676i	$-0.0829566\pi$
$383$	1948.54	+	3374.96i	0.259962	+	0.450268i	−0.706269	+	0.707943i	$0.749623\pi$
$384$		0			0
$385$	12031.8	+	2936.80i	1.59272	+	0.388762i
$386$		0			0
$387$	−4887.66	−	3021.26i	−0.641999	−	0.396846i
$388$		0			0
$389$	7782.20	+	4493.06i	1.01433	+	0.585622i	0.912456	−	0.409175i	$-0.134184\pi$
$389$	7782.20	+	4493.06i	1.01433	+	0.585622i	0.101872	+	0.994798i	$0.467517\pi$
$390$		0			0
$391$			4376.96i			0.566118i
$392$		0			0
$393$	−2536.32	−	10068.5i	−0.325548	−	1.29233i
$394$		0			0
$395$	245.429	−	425.096i	0.0312630	−	0.0541491i
$396$		0			0
$397$	−2777.60	+	1603.65i	−0.351143	+	0.202733i	−0.665189	−	0.746675i	$-0.731649\pi$
$397$	−2777.60	+	1603.65i	−0.351143	+	0.202733i	0.314045	+	0.949408i	$0.398316\pi$
$398$		0			0
$399$	−39.6906	−	5387.90i	−0.00497999	−	0.676021i
$400$		0			0
$401$	−7566.81	+	4368.70i	−0.942315	+	0.544046i	−0.890685	−	0.454620i	$-0.849775\pi$
$401$	−7566.81	+	4368.70i	−0.942315	+	0.544046i	−0.0516300	+	0.998666i	$0.516442\pi$
$402$		0			0
$403$	−4025.38	+	6972.16i	−0.497564	+	0.861806i
$404$		0			0
$405$	4910.57	−	7434.90i	0.602490	−	0.912205i
$406$		0			0
$407$		−	15569.8i		−	1.89623i
$408$		0			0
$409$	10056.2	+	5805.94i	1.21576	+	0.701920i	0.964009	−	0.265871i	$-0.0856596\pi$
$409$	10056.2	+	5805.94i	1.21576	+	0.701920i	0.251753	+	0.967792i	$0.418993\pi$
$410$		0			0
$411$	−5576.72	−	5746.89i	−0.669293	−	0.689716i
$412$		0			0
$413$	12076.6	+	11547.5i	1.43887	+	1.37583i
$414$		0			0
$415$	5226.72	+	9052.94i	0.618240	+	1.07082i
$416$		0			0
$417$	−4156.05	+	14627.8i	−0.488064	+	1.71781i
$418$		0			0
$419$	10111.6			1.17896			0.589482	−	0.807782i	$-0.299332\pi$
$419$	10111.6			1.17896			0.589482	+	0.807782i	$0.299332\pi$
$420$		0			0
$421$	−8005.12			−0.926711			−0.463356	−	0.886172i	$-0.653355\pi$
$421$	−8005.12			−0.926711			−0.463356	+	0.886172i	$0.653355\pi$
$422$		0			0
$423$	−203.166	+	6758.25i	−0.0233529	+	0.776826i
$424$		0			0
$425$	495.225	+	857.755i	0.0565222	+	0.0978994i
$426$		0			0
$427$	2997.14	+	10260.7i	0.339677	+	1.16288i
$428$		0			0
$429$	−5513.73	+	5350.47i	−0.620526	+	0.602152i
$430$		0			0
$431$	13312.3	+	7685.84i	1.48777	+	0.858965i	0.999903	−	0.0139531i	$-0.00444154\pi$
$431$	13312.3	+	7685.84i	1.48777	+	0.858965i	0.487868	+	0.872918i	$0.337775\pi$
$432$		0			0
$433$			15508.4i			1.72121i	0.509272	+	0.860606i	$0.329915\pi$
$433$			15508.4i			1.72121i	−0.509272	+	0.860606i	$0.670085\pi$
$434$		0			0
$435$	−2355.24	+	593.301i	−0.259598	+	0.0653946i
$436$		0			0
$437$	−3017.22	+	5225.97i	−0.330282	+	0.572065i
$438$		0			0
$439$	13707.7	−	7914.13i	1.49028	−	0.860412i	0.490339	−	0.871532i	$-0.336873\pi$
$439$	13707.7	−	7914.13i	1.49028	−	0.860412i	0.999938	+	0.0111193i	$0.00353947\pi$
$440$		0			0
$441$	−4748.16	−	7951.17i	−0.512704	−	0.858565i
$442$		0			0
$443$	−5655.01	+	3264.92i	−0.606495	+	0.350160i	−0.771593	−	0.636117i	$-0.780540\pi$
$443$	−5655.01	+	3264.92i	−0.606495	+	0.350160i	0.165097	+	0.986277i	$0.447206\pi$
$444$		0			0
$445$	3936.98	−	6819.05i	0.419395	−	0.726413i
$446$		0			0
$447$	−12091.8	+	3046.02i	−1.27947	+	0.322308i
$448$		0			0
$449$			12934.7i			1.35952i	0.733434	+	0.679761i	$0.237917\pi$
$449$			12934.7i			1.35952i	−0.733434	+	0.679761i	$0.762083\pi$
$450$		0			0
$451$	1345.47	+	776.809i	0.140479	+	0.0811053i
$452$		0			0
$453$	668.981	−	649.173i	0.0693852	−	0.0673307i
$454$		0			0
$455$	−1715.21	−	5872.02i	−0.176726	−	0.605021i
$456$		0			0
$457$	4806.68	+	8325.42i	0.492007	+	0.852181i	0.999958	−	0.00920512i	$-0.00293012\pi$
$457$	4806.68	+	8325.42i	0.492007	+	0.852181i	−0.507951	+	0.861386i	$0.669597\pi$
$458$		0			0
$459$	−5564.22	+	1225.12i	−0.565829	+	0.124583i
$460$		0			0
$461$	−11205.4			−1.13207			−0.566037	−	0.824380i	$-0.691524\pi$
$461$	−11205.4			−1.13207			−0.566037	+	0.824380i	$0.691524\pi$
$462$		0			0
$463$	−4300.85			−0.431701			−0.215850	−	0.976426i	$-0.569252\pi$
$463$	−4300.85			−0.431701			−0.215850	+	0.976426i	$0.569252\pi$
$464$		0			0
$465$	5170.86	−	18199.5i	0.515684	−	1.81502i
$466$		0			0
$467$	−7282.65	−	12613.9i	−0.721630	−	1.24990i	−0.960346	−	0.278810i	$-0.910060\pi$
$467$	−7282.65	−	12613.9i	−0.721630	−	1.24990i	0.238717	−	0.971089i	$-0.423273\pi$
$468$		0			0
$469$	4938.37	+	4722.01i	0.486210	+	0.464908i
$470$		0			0
$471$	6723.82	+	6928.99i	0.657787	+	0.677858i
$472$		0			0
$473$	−10083.9	−	5821.92i	−0.980246	−	0.565945i
$474$		0			0
$475$			1365.52i			0.131904i
$476$		0			0
$477$	4355.15	+	8095.81i	0.418048	+	0.777111i
$478$		0			0
$479$	−937.775	+	1624.27i	−0.0894531	+	0.154937i	−0.907280	−	0.420527i	$-0.861845\pi$
$479$	−937.775	+	1624.27i	−0.0894531	+	0.154937i	0.817827	+	0.575464i	$0.195179\pi$
$480$		0			0
$481$	−6660.15	+	3845.24i	−0.631345	+	0.364507i
$482$		0			0
$483$	76.4046	+	10371.7i	0.00719779	+	0.977081i
$484$		0			0
$485$	−7926.70	+	4576.48i	−0.742130	+	0.428469i
$486$		0			0
$487$	615.525	−	1066.12i	0.0572733	−	0.0992002i	−0.835967	−	0.548779i	$-0.815093\pi$
$487$	615.525	−	1066.12i	0.0572733	−	0.0992002i	0.893240	+	0.449579i	$0.148426\pi$
$488$		0			0
$489$	−3839.06	−	15240.0i	−0.355027	−	1.40936i
$490$		0			0
$491$		−	6644.33i		−	0.610702i	−0.952240	−	0.305351i	$-0.901226\pi$
$491$		−	6644.33i		−	0.610702i	0.952240	−	0.305351i	$-0.0987737\pi$
$492$		0			0
$493$	1345.00	+	776.536i	0.122872	+	0.0709400i
$494$		0			0
$495$	9493.59	−	15358.3i	0.862031	−	1.39455i
$496$		0			0
$497$	21307.6	+	5200.91i	1.92309	+	0.469402i
$498$		0			0
$499$	7276.93	+	12604.0i	0.652826	+	1.13073i	0.982434	+	0.186609i	$0.0597499\pi$
$499$	7276.93	+	12604.0i	0.652826	+	1.13073i	−0.329609	+	0.944118i	$0.606917\pi$
$500$		0			0
$501$	−9053.81	−	2572.37i	−0.807374	−	0.229392i
$502$		0			0
$503$	6799.96			0.602774			0.301387	−	0.953502i	$-0.402550\pi$
$503$	6799.96			0.602774			0.301387	+	0.953502i	$0.402550\pi$
$504$		0			0
$505$	15628.6			1.37716
$506$		0			0
$507$	−7330.87	−	2082.85i	−0.642161	−	0.182451i
$508$		0			0
$509$	1924.80	+	3333.85i	0.167614	+	0.290315i	0.937580	−	0.347769i	$-0.113061\pi$
$509$	1924.80	+	3333.85i	0.167614	+	0.290315i	−0.769967	+	0.638084i	$0.779727\pi$
$510$		0			0
$511$	6021.09	−	6296.97i	0.521247	−	0.545130i
$512$		0			0
$513$	−7488.06	−	2372.89i	−0.644456	−	0.204221i
$514$		0			0
$515$	−594.779	−	343.396i	−0.0508915	−	0.0293822i
$516$		0			0
$517$			13701.1i			1.16552i
$518$		0			0
$519$	1407.94	+	5589.13i	0.119079	+	0.472708i
$520$		0			0
$521$	−5682.32	+	9842.06i	−0.477825	+	0.827617i	−0.999677	−	0.0254190i	$-0.991908\pi$
$521$	−5682.32	+	9842.06i	−0.477825	+	0.827617i	0.521852	+	0.853036i	$0.325241\pi$
$522$		0			0
$523$	−10037.3	+	5795.05i	−0.839200	+	0.484512i	−0.856992	−	0.515330i	$-0.827670\pi$
$523$	−10037.3	+	5795.05i	−0.839200	+	0.484512i	0.0177924	+	0.999842i	$0.494336\pi$
$524$		0			0
$525$	1188.47	+	2023.91i	0.0987982	+	0.168249i
$526$		0			0
$527$	−10477.2	+	6049.01i	−0.866022	+	0.499998i
$528$		0			0
$529$	−275.341	+	476.904i	−0.0226301	+	0.0391965i
$530$		0			0
$531$	21452.3	−	11540.3i	1.75321	−	0.943140i
$532$		0			0
$533$		−	767.389i		−	0.0623626i
$534$		0			0
$535$	1173.74	+	677.660i	0.0948509	+	0.0547622i
$536$		0			0
$537$	13675.8	+	14093.1i	1.09898	+	1.13252i
$538$		0			0
$539$	−10101.5	−	15815.9i	−0.807238	−	1.26389i
$540$		0			0
$541$	−2756.37	−	4774.17i	−0.219049	−	0.379404i	0.735468	−	0.677559i	$-0.236962\pi$
$541$	−2756.37	−	4774.17i	−0.219049	−	0.379404i	−0.954518	+	0.298155i	$0.903629\pi$
$542$		0			0
$543$	−1675.94	+	5898.69i	−0.132452	+	0.466183i
$544$		0			0
$545$	−11881.3			−0.933832
$546$		0			0
$547$	−19797.4			−1.54749			−0.773746	−	0.633497i	$-0.781619\pi$
$547$	−19797.4			−1.54749			−0.773746	+	0.633497i	$0.781619\pi$
$548$		0			0
$549$	15576.8	+	468.269i	1.21093	+	0.0364030i
$550$		0			0
$551$	1070.60	+	1854.33i	0.0827749	+	0.143370i
$552$		0			0
$553$	−713.945	+	208.543i	−0.0549006	+	0.0160364i
$554$		0			0
$555$	12970.2	−	12586.2i	0.991993	−	0.962620i
$556$		0			0
$557$	−4626.61	−	2671.18i	−0.351950	−	0.203198i	0.313594	−	0.949557i	$-0.398467\pi$
$557$	−4626.61	−	2671.18i	−0.351950	−	0.203198i	−0.665544	+	0.746359i	$0.731800\pi$
$558$		0			0
$559$			5751.32i			0.435161i
$560$		0			0
$561$	−11195.7	+	2820.27i	−0.842568	+	0.212249i
$562$		0			0
$563$	5595.50	−	9691.69i	0.418867	−	0.725499i	−0.576959	−	0.816773i	$-0.695761\pi$
$563$	5595.50	−	9691.69i	0.418867	−	0.725499i	0.995826	+	0.0912740i	$0.0290939\pi$
$564$		0			0
$565$	−20633.2	+	11912.6i	−1.53636	+	0.887018i
$566$		0			0
$567$	−13163.7	+	3000.19i	−0.974998	+	0.222216i
$568$		0			0
$569$	13960.7	−	8060.21i	1.02858	−	0.593852i	0.112004	−	0.993708i	$-0.464273\pi$
$569$	13960.7	−	8060.21i	1.02858	−	0.593852i	0.916578	+	0.399856i	$0.130940\pi$
$570$		0			0
$571$	−4187.14	+	7252.34i	−0.306876	+	0.531525i	−0.977677	−	0.210112i	$-0.932617\pi$
$571$	−4187.14	+	7252.34i	−0.306876	+	0.531525i	0.670801	+	0.741637i	$0.265950\pi$
$572$		0			0
$573$	15793.8	−	3978.57i	1.15148	−	0.290065i
$574$		0			0
$575$		−	2628.63i		−	0.190646i
$576$		0			0
$577$	−10723.1	−	6190.98i	−0.773671	−	0.446679i	0.0605115	−	0.998167i	$-0.480727\pi$
$577$	−10723.1	−	6190.98i	−0.773671	−	0.446679i	−0.834183	+	0.551488i	$0.814060\pi$
$578$		0			0
$579$	3034.85	−	2944.99i	0.217831	−	0.211381i
$580$		0			0
$581$	3756.00	−	15387.9i	0.268202	−	1.09879i
$582$		0			0
$583$	9314.26	+	16132.8i	0.661677	+	1.14606i
$584$		0			0
$585$	−8914.31	−	267.982i	−0.630019	−	0.0189396i
$586$		0			0
$587$	−12886.6			−0.906112			−0.453056	−	0.891482i	$-0.649666\pi$
$587$	−12886.6			−0.906112			−0.453056	+	0.891482i	$0.649666\pi$
$588$		0			0
$589$	−16679.3			−1.16682
$590$		0			0
$591$	−3785.99	+	13325.3i	−0.263511	+	0.927460i
$592$		0			0
$593$	−1510.79	−	2616.76i	−0.104622	−	0.181210i	0.808962	−	0.587861i	$-0.200030\pi$
$593$	−1510.79	−	2616.76i	−0.104622	−	0.181210i	−0.913584	+	0.406651i	$0.866696\pi$
$594$		0			0
$595$	2179.84	−	8930.54i	0.150193	−	0.615322i
$596$		0			0
$597$	7729.59	+	7965.45i	0.529902	+	0.546071i
$598$		0			0
$599$	7770.56	+	4486.34i	0.530044	+	0.306021i	0.741035	−	0.671467i	$-0.234335\pi$
$599$	7770.56	+	4486.34i	0.530044	+	0.306021i	−0.210990	+	0.977488i	$0.567669\pi$
$600$		0			0
$601$		−	14238.3i		−	0.966374i	−0.875517	−	0.483187i	$-0.839479\pi$
$601$		−	14238.3i		−	0.966374i	0.875517	−	0.483187i	$-0.160521\pi$
$602$		0			0
$603$	8772.27	−	4719.05i	0.592429	−	0.318698i
$604$		0			0
$605$	10159.9	−	17597.5i	0.682743	−	1.18255i
$606$		0			0
$607$	3552.68	−	2051.14i	0.237560	−	0.137155i	−0.376495	−	0.926419i	$-0.622871\pi$
$607$	3552.68	−	2051.14i	0.237560	−	0.137155i	0.614055	+	0.789264i	$0.289537\pi$
$608$		0			0
$609$	3200.70	+	1816.62i	0.212970	+	0.120875i
$610$		0			0
$611$	5860.81	−	3383.74i	0.388057	−	0.224045i
$612$		0			0
$613$	3234.01	−	5601.47i	0.213084	−	0.369072i	−0.739594	−	0.673053i	$-0.764983\pi$
$613$	3234.01	−	5601.47i	0.213084	−	0.369072i	0.952678	+	0.303981i	$0.0983159\pi$
$614$		0			0
$615$	440.531	+	1748.78i	0.0288844	+	0.114663i
$616$		0			0
$617$		−	6608.54i		−	0.431199i	−0.976482	−	0.215600i	$-0.930829\pi$
$617$		−	6608.54i		−	0.431199i	0.976482	−	0.215600i	$-0.0691706\pi$
$618$		0			0
$619$	−18325.1	−	10580.0i	−1.18990	−	0.686990i	−0.231617	−	0.972807i	$-0.574402\pi$
$619$	−18325.1	−	10580.0i	−1.18990	−	0.686990i	−0.958284	+	0.285817i	$0.907735\pi$
$620$		0			0
$621$	14414.5	+	4567.82i	0.931458	+	0.295169i
$622$		0			0
$623$	−11452.5	+	3345.27i	−0.736495	+	0.215129i
$624$		0			0
$625$	9039.40	+	15656.7i	0.578522	+	1.00203i
$626$		0			0
$627$	−15311.4	−	4350.30i	−0.975248	−	0.277088i
$628$		0			0
$629$	−11556.6			−0.732580
$630$		0			0
$631$	7741.19			0.488387			0.244193	−	0.969727i	$-0.421477\pi$
$631$	7741.19			0.488387			0.244193	+	0.969727i	$0.421477\pi$
$632$		0			0
$633$	−7709.60	−	2190.46i	−0.484090	−	0.137540i
$634$		0			0
$635$	16253.2	+	28151.4i	1.01573	+	1.75930i
$636$		0			0
$637$	−4270.68	+	8227.04i	−0.265637	+	0.511723i
$638$		0			0
$639$	16812.6	−	27198.7i	1.04084	−	1.68382i
$640$		0			0
$641$	−12037.2	−	6949.67i	−0.741716	−	0.428230i	0.0809769	−	0.996716i	$-0.474196\pi$
$641$	−12037.2	−	6949.67i	−0.741716	−	0.428230i	−0.822693	+	0.568486i	$0.807529\pi$
$642$		0			0
$643$		−	3191.05i		−	0.195712i	−0.995201	−	0.0978560i	$-0.968802\pi$
$643$		−	3191.05i		−	0.195712i	0.995201	−	0.0978560i	$-0.0311985\pi$
$644$		0			0
$645$	−3301.63	−	13106.5i	−0.201553	−	0.800107i
$646$		0			0
$647$	−14331.5	+	24822.9i	−0.870835	+	1.50833i	−0.00970044	+	0.999953i	$0.503088\pi$
$647$	−14331.5	+	24822.9i	−0.870835	+	1.50833i	−0.861134	+	0.508377i	$0.830246\pi$
$648$		0			0
$649$	42748.8	−	24681.0i	2.58557	−	1.49278i
$650$		0			0
$651$	−24721.4	+	14516.8i	−1.48834	+	0.873973i
$652$		0			0
$653$	−12927.5	+	7463.67i	−0.774717	+	0.447283i	−0.834555	−	0.550925i	$-0.814275\pi$
$653$	−12927.5	+	7463.67i	−0.774717	+	0.447283i	0.0598375	+	0.998208i	$0.480942\pi$
$654$		0			0
$655$	12211.6	−	21151.0i	0.728466	−	1.26174i
$656$		0			0
$657$	−6017.32	−	11185.6i	−0.357318	−	0.664220i
$658$		0			0
$659$			20808.5i			1.23002i	0.788518	+	0.615012i	$0.210849\pi$
$659$			20808.5i			1.23002i	−0.788518	+	0.615012i	$0.789151\pi$
$660$		0			0
$661$	−12905.7	−	7451.11i	−0.759415	−	0.438448i	0.0696706	−	0.997570i	$-0.477805\pi$
$661$	−12905.7	−	7451.11i	−0.759415	−	0.438448i	−0.829086	+	0.559122i	$0.811139\pi$
$662$		0			0
$663$	3971.37	+	4092.55i	0.232632	+	0.239731i
$664$		0			0
$665$	8758.86	−	9160.19i	0.510758	−	0.534161i
$666$		0			0
$667$	−2060.90	−	3569.59i	−0.119638	−	0.207219i
$668$		0			0
$669$	2246.39	−	7906.46i	0.129821	−	0.456923i
$670$		0			0
$671$	31579.1			1.81684
$672$		0			0
$673$	20032.6			1.14740			0.573699	−	0.819066i	$-0.305508\pi$
$673$	20032.6			1.14740			0.573699	+	0.819066i	$0.305508\pi$
$674$		0			0
$675$	3341.65	−	735.756i	0.190548	−	0.0419545i
$676$		0			0
$677$	2839.67	+	4918.45i	0.161207	+	0.279219i	0.935302	−	0.353851i	$-0.115128\pi$
$677$	2839.67	+	4918.45i	0.161207	+	0.279219i	−0.774095	+	0.633070i	$0.781795\pi$
$678$		0			0
$679$	13473.6	+	3288.74i	0.761515	+	0.185876i
$680$		0			0
$681$	−9568.88	+	9285.55i	−0.538444	+	0.522501i
$682$		0			0
$683$	14522.3	+	8384.43i	0.813585	+	0.469724i	0.848199	−	0.529677i	$-0.177687\pi$
$683$	14522.3	+	8384.43i	0.813585	+	0.469724i	−0.0346143	+	0.999401i	$0.511020\pi$
$684$		0			0
$685$		−	18836.3i		−	1.05066i
$686$		0			0
$687$	8725.10	−	2197.92i	0.484546	−	0.122061i
$688$		0			0
$689$	4600.66	−	7968.57i	0.254385	−	0.440607i
$690$		0			0
$691$	−8348.57	+	4820.05i	−0.459616	+	0.265359i	−0.711883	−	0.702298i	$-0.752157\pi$
$691$	−8348.57	+	4820.05i	−0.459616	+	0.265359i	0.252267	+	0.967658i	$0.418824\pi$
$692$		0			0
$693$	−26480.2	+	6878.40i	−1.45152	+	0.377040i
$694$		0			0
$695$	−30977.3	+	17884.8i	−1.69070	+	0.976126i
$696$		0			0
$697$	576.584	−	998.674i	0.0313338	−	0.0542718i
$698$		0			0
$699$	−15343.1	+	3865.04i	−0.830227	+	0.209140i
$700$		0			0
$701$		−	4109.58i		−	0.221422i	−0.993853	−	0.110711i	$-0.964687\pi$
$701$		−	4109.58i		−	0.221422i	0.993853	−	0.110711i	$-0.0353127\pi$
$702$		0			0
$703$	−13798.3	−	7966.46i	−0.740275	−	0.427398i
$704$		0			0
$705$	−11413.6	+	11075.6i	−0.609730	+	0.591676i
$706$		0			0
$707$	−17116.1	−	16366.2i	−0.910489	−	0.870598i
$708$		0			0
$709$	−4208.59	−	7289.49i	−0.222929	−	0.386125i	0.732767	−	0.680480i	$-0.238229\pi$
$709$	−4208.59	−	7289.49i	−0.222929	−	0.386125i	−0.955696	+	0.294355i	$0.904895\pi$
$710$		0			0
$711$	−32.5824	+	1083.84i	−0.00171861	+	0.0571690i
$712$		0			0
$713$	32107.8			1.68646
$714$		0			0
$715$	−18072.1			−0.945258
$716$		0			0
$717$	938.456	−	3303.02i	0.0488804	−	0.172041i
$718$		0			0
$719$	5394.98	+	9344.38i	0.279831	+	0.484682i	0.971343	−	0.237684i	$-0.0763881\pi$
$719$	5394.98	+	9344.38i	0.279831	+	0.484682i	−0.691511	+	0.722366i	$0.743055\pi$
$720$		0			0
$721$	291.785	+	998.927i	0.0150716	+	0.0515978i
$722$		0			0
$723$	−1751.98	−	1805.44i	−0.0901201	−	0.0928700i
$724$		0			0
$725$	−807.753	−	466.357i	−0.0413782	−	0.0238897i
$726$		0			0
$727$		−	7138.00i		−	0.364146i	−0.983285	−	0.182073i	$-0.941719\pi$
$727$		−	7138.00i		−	0.364146i	0.983285	−	0.182073i	$-0.0582807\pi$
$728$		0			0
$729$	−1772.19	+	19603.1i	−0.0900368	+	0.995938i
$730$		0			0
$731$	−4321.30	+	7484.72i	−0.218645	+	0.378704i
$732$		0			0
$733$	−5673.59	+	3275.65i	−0.285892	+	0.165060i	−0.636088	−	0.771617i	$-0.719448\pi$
$733$	−5673.59	+	3275.65i	−0.285892	+	0.165060i	0.350196	+	0.936677i	$0.386115\pi$
$734$		0			0
$735$	5009.49	−	21200.1i	0.251399	−	1.06391i
$736$		0			0
$737$	17480.8	−	10092.5i	0.873694	−	0.504428i
$738$		0			0
$739$	11962.1	−	20718.9i	0.595443	−	1.03134i	−0.398041	−	0.917368i	$-0.630310\pi$
$739$	11962.1	−	20718.9i	0.595443	−	1.03134i	0.993484	−	0.113970i	$-0.0363568\pi$
$740$		0			0
$741$	1920.55	+	7624.03i	0.0952134	+	0.377970i
$742$		0			0
$743$		−	33097.2i		−	1.63421i	−0.576489	−	0.817105i	$-0.695578\pi$
$743$		−	33097.2i		−	1.63421i	0.576489	−	0.817105i	$-0.304422\pi$
$744$		0			0
$745$	−25401.5	−	14665.6i	−1.24918	−	0.721215i
$746$		0			0
$747$	−19642.4	−	12141.8i	−0.962084	−	0.594703i
$748$		0			0
$749$	−575.811	−	1971.29i	−0.0280904	−	0.0961673i
$750$		0			0
$751$	−8613.02	−	14918.2i	−0.418500	−	0.724863i	0.577289	−	0.816540i	$-0.304111\pi$
$751$	−8613.02	−	14918.2i	−0.418500	−	0.724863i	−0.995789	+	0.0916766i	$0.970777\pi$
$752$		0			0
$753$	−13049.1	−	3707.51i	−0.631519	−	0.179428i
$754$		0			0
$755$	2192.69			0.105696
$756$		0			0
$757$	−34314.7			−1.64754			−0.823770	−	0.566924i	$-0.808133\pi$
$757$	−34314.7			−1.64754			−0.823770	+	0.566924i	$0.808133\pi$
$758$		0			0
$759$	29474.6	+	8374.35i	1.40957	+	0.400487i
$760$		0			0
$761$	−14662.6	−	25396.4i	−0.698448	−	1.20975i	−0.969004	−	0.247043i	$-0.920541\pi$
$761$	−14662.6	−	25396.4i	−0.698448	−	1.20975i	0.270556	−	0.962704i	$-0.412792\pi$
$762$		0			0
$763$	13012.1	+	12442.0i	0.617391	+	0.590341i
$764$		0			0
$765$	−11399.7	−	7046.60i	−0.538765	−	0.333033i
$766$		0			0
$767$	−21115.2	−	12190.8i	−0.994035	−	0.573906i
$768$		0			0
$769$			41511.3i			1.94660i	0.229539	+	0.973299i	$0.426278\pi$
$769$			41511.3i			1.94660i	−0.229539	+	0.973299i	$0.573722\pi$
$770$		0			0
$771$	−1851.89	−	7351.48i	−0.0865035	−	0.343394i
$772$		0			0
$773$	−12697.7	+	21993.1i	−0.590821	+	1.02333i	0.403301	+	0.915068i	$0.367863\pi$
$773$	−12697.7	+	21993.1i	−0.590821	+	1.02333i	−0.994122	+	0.108265i	$0.965470\pi$
$774$		0			0
$775$	6292.18	−	3632.79i	0.291641	−	0.168379i
$776$		0			0
$777$	−27384.8	+	201.734i	−1.26438	+	0.00931423i
$778$		0			0
$779$	1376.85	−	794.927i	0.0633259	−	0.0365612i
$780$		0			0
$781$	32397.6	−	56114.3i	1.48435	−	2.57097i
$782$		0			0
$783$	3961.00	−	3619.06i	0.180785	−	0.165178i
$784$		0			0
$785$			22710.9i			1.03259i
$786$		0			0
$787$	−33979.6	−	19618.1i	−1.53906	−	0.888578i	−0.998894	−	0.0470205i	$-0.985027\pi$
$787$	−33979.6	−	19618.1i	−1.53906	−	0.888578i	−0.540168	−	0.841557i	$-0.681639\pi$
$788$		0			0
$789$	18428.4	+	18990.7i	0.831519	+	0.856891i
$790$		0			0
$791$	35071.6	+	8560.55i	1.57649	+	0.384802i
$792$		0			0
$793$	−7799.03	−	13508.3i	−0.349246	−	0.604911i
$794$		0			0
$795$	−5909.84	+	20800.5i	−0.263648	+	0.927945i
$796$		0			0
$797$	28857.2			1.28253			0.641264	−	0.767321i	$-0.278410\pi$
$797$	28857.2			1.28253			0.641264	+	0.767321i	$0.278410\pi$
$798$		0			0
$799$	10169.6			0.450282
$800$		0			0
$801$	−522.660	+	17386.1i	−0.0230553	+	0.766925i
$802$		0			0
$803$	−12869.1	−	22289.9i	−0.565555	−	0.979571i
$804$		0			0
$805$	−16860.8	+	17633.4i	−0.738220	+	0.772045i
$806$		0			0
$807$	3636.73	−	3529.05i	0.158636	−	0.153938i
$808$		0			0
$809$	29443.3	+	16999.1i	1.27957	+	0.738759i	0.976769	−	0.214296i	$-0.0687457\pi$
$809$	29443.3	+	16999.1i	1.27957	+	0.738759i	0.302799	+	0.953055i	$0.402079\pi$
$810$		0			0
$811$		−	1300.27i		−	0.0562990i	−0.999604	−	0.0281495i	$-0.991039\pi$
$811$		−	1300.27i		−	0.0562990i	0.999604	−	0.0281495i	$-0.00896145\pi$
$812$		0			0
$813$	18564.3	−	4676.48i	0.800834	−	0.201736i
$814$		0			0
$815$	18483.8	−	32014.9i	0.794429	−	1.37599i
$816$		0			0
$817$	−10319.1	+	5957.71i	−0.441882	+	0.255121i
$818$		0			0
$819$	9482.09	+	9628.48i	0.404556	+	0.410801i
$820$		0			0
$821$	10717.9	−	6187.98i	0.455611	−	0.263047i	−0.254586	−	0.967050i	$-0.581939\pi$
$821$	10717.9	−	6187.98i	0.455611	−	0.263047i	0.710197	+	0.704003i	$0.248606\pi$
$822$		0			0
$823$	2282.79	−	3953.90i	0.0966864	−	0.167466i	−0.813625	−	0.581390i	$-0.802509\pi$
$823$	2282.79	−	3953.90i	0.0966864	−	0.167466i	0.910311	+	0.413925i	$0.135842\pi$
$824$		0			0
$825$	6723.66	−	1693.74i	0.283743	−	0.0714769i
$826$		0			0
$827$			13907.2i			0.584765i	0.956301	+	0.292383i	$0.0944481\pi$
$827$			13907.2i			0.584765i	−0.956301	+	0.292383i	$0.905552\pi$
$828$		0			0
$829$	−26.4048	−	15.2448i	−0.00110624	−	0.000638690i	0.499447	−	0.866345i	$-0.333537\pi$
$829$	−26.4048	−	15.2448i	−0.00110624	−	0.000638690i	−0.500553	+	0.865706i	$0.666870\pi$
$830$		0			0
$831$	12310.3	−	11945.8i	0.513886	−	0.498670i
$832$		0			0
$833$	−11739.3	+	7497.80i	−0.488286	+	0.311865i
$834$		0			0
$835$	−11069.7	−	19173.3i	−0.458782	−	0.794634i
$836$		0			0
$837$	8987.02	+	40817.1i	0.371131	+	1.68560i
$838$		0			0
$839$	−18157.8			−0.747173			−0.373587	−	0.927595i	$-0.621872\pi$
$839$	−18157.8			−0.747173			−0.373587	+	0.927595i	$0.621872\pi$
$840$		0			0
$841$	22926.5			0.940033
$842$		0			0
$843$	−631.419	+	2222.36i	−0.0257974	+	0.0907973i
$844$		0			0
$845$	−8963.15	−	15524.6i	−0.364902	−	0.632028i
$846$		0			0
$847$	−29554.8	+	8632.94i	−1.19896	+	0.350214i
$848$		0			0
$849$	6559.29	+	6759.44i	0.265152	+	0.273243i
$850$		0			0
$851$	26561.8	+	15335.5i	1.06995	+	0.617736i
$852$		0			0
$853$			13489.4i			0.541464i	0.962655	+	0.270732i	$0.0872657\pi$
$853$			13489.4i			0.541464i	−0.962655	+	0.270732i	$0.912734\pi$
$854$		0			0
$855$	−8753.39	−	16271.7i	−0.350128	−	0.650855i
$856$		0			0
$857$	−1188.83	+	2059.12i	−0.0473859	+	0.0820748i	−0.888746	−	0.458401i	$-0.848422\pi$
$857$	−1188.83	+	2059.12i	−0.0473859	+	0.0820748i	0.841360	+	0.540476i	$0.181756\pi$
$858$		0			0
$859$	16353.2	−	9441.53i	0.649551	−	0.375019i	−0.138733	−	0.990330i	$-0.544303\pi$
$859$	16353.2	−	9441.53i	0.649551	−	0.375019i	0.788284	+	0.615311i	$0.210970\pi$
$860$		0			0
$861$	1348.85	−	2376.54i	0.0533900	−	0.0940678i
$862$		0			0
$863$	−10869.9	+	6275.72i	−0.428754	+	0.247541i	−0.698816	−	0.715302i	$-0.746289\pi$
$863$	−10869.9	+	6275.72i	−0.428754	+	0.247541i	0.270062	+	0.962843i	$0.412956\pi$
$864$		0			0
$865$	−6778.78	+	11741.2i	−0.266457	+	0.461518i
$866$		0			0
$867$	−4142.71	−	16445.4i	−0.162277	−	0.644192i
$868$		0			0
$869$			2197.29i			0.0857742i
$870$		0			0
$871$	−8634.39	−	4985.07i	−0.335896	−	0.193930i
$872$		0			0
$873$	10631.3	−	17198.8i	0.412157	−	0.666769i
$874$		0			0
$875$	5400.46	−	22125.1i	0.208650	−	0.854817i
$876$		0			0
$877$	−20663.8	−	35790.8i	−0.795630	−	1.37807i	−0.922439	−	0.386144i	$-0.873807\pi$
$877$	−20663.8	−	35790.8i	−0.795630	−	1.37807i	0.126809	−	0.991927i	$-0.459526\pi$
$878$		0			0
$879$	−3465.69	−	984.675i	−0.132986	−	0.0377841i
$880$		0			0
$881$	−31002.4			−1.18558			−0.592791	−	0.805357i	$-0.701974\pi$
$881$	−31002.4			−1.18558			−0.592791	+	0.805357i	$0.701974\pi$
$882$		0			0
$883$	42592.8			1.62329			0.811643	−	0.584154i	$-0.198574\pi$
$883$	42592.8			1.62329			0.811643	+	0.584154i	$0.198574\pi$
$884$		0			0
$885$	55117.2	+	15659.9i	2.09350	+	0.594806i
$886$		0			0
$887$	3129.31	+	5420.12i	0.118458	+	0.205175i	0.919157	−	0.393892i	$-0.128872\pi$
$887$	3129.31	+	5420.12i	0.118458	+	0.205175i	−0.800699	+	0.599067i	$0.795538\pi$
$888$		0			0
$889$	11679.8	−	47850.9i	0.440639	−	1.80525i
$890$		0			0
$891$	−2395.92	+	39813.6i	−0.0900857	+	1.49698i
$892$		0			0
$893$	12142.3	+	7010.34i	0.455011	+	0.262701i
$894$		0			0
$895$			46192.3i			1.72518i
$896$		0			0
$897$	−3697.07	−	14676.3i	−0.137616	−	0.546296i
$898$		0			0
$899$	5696.39	−	9866.43i	0.211329	−	0.366033i
$900$		0			0
$901$	11974.5	−	6913.49i	0.442762	−	0.255629i
$902$		0			0
$903$	−10109.2	+	17811.4i	−0.372551	+	0.656396i
$904$		0			0
$905$	−12491.7	+	7212.08i	−0.458827	+	0.264904i
$906$		0			0
$907$	6082.91	−	10535.9i	0.222690	−	0.385710i	−0.732934	−	0.680300i	$-0.761850\pi$
$907$	6082.91	−	10535.9i	0.222690	−	0.385710i	0.955624	+	0.294589i	$0.0951829\pi$
$908$		0			0
$909$	−30404.1	+	16355.9i	−1.10940	+	0.596801i
$910$		0			0
$911$			30486.2i			1.10873i	0.832273	+	0.554366i	$0.187039\pi$
$911$			30486.2i			1.10873i	−0.832273	+	0.554366i	$0.812961\pi$
$912$		0			0
$913$	−40524.7	−	23396.9i	−1.46897	−	0.848111i
$914$		0			0
$915$	25527.7	+	26306.6i	0.922316	+	0.950459i
$916$		0			0
$917$	−35523.0	+	10376.2i	−1.27925	+	0.373668i
$918$		0			0
$919$	7103.12	+	12303.0i	0.254962	+	0.441608i	0.964885	−	0.262672i	$-0.0846036\pi$
$919$	7103.12	+	12303.0i	0.254962	+	0.441608i	−0.709923	+	0.704279i	$0.751270\pi$
$920$		0			0
$921$	−7917.08	+	27865.2i	−0.283254	+	0.996948i
$922$		0			0
$923$	−32004.7			−1.14133
$924$		0			0
$925$	6940.45			0.246703
$926$		0			0
$927$	1516.47	+	45.5881i	0.0537296	+	0.00161522i
$928$		0			0
$929$	−19290.5	−	33412.2i	−0.681272	−	1.18000i	−0.974593	−	0.223984i	$-0.928094\pi$
$929$	−19290.5	−	33412.2i	−0.681272	−	1.18000i	0.293321	−	0.956014i	$-0.405240\pi$
$930$		0			0
$931$	−19185.0	+	859.791i	−0.675362	+	0.0302669i
$932$		0			0
$933$	−3615.62	+	3508.56i	−0.126870	+	0.123114i
$934$		0			0
$935$	−23518.9	−	13578.7i	−0.822622	−	0.474941i
$936$		0			0
$937$			20630.2i			0.719272i	0.933093	+	0.359636i	$0.117099\pi$
$937$			20630.2i			0.719272i	−0.933093	+	0.359636i	$0.882901\pi$
$938$		0			0
$939$	9885.01	−	2490.11i	0.343541	−	0.0865405i
$940$		0			0
$941$	−8820.50	+	15277.5i	−0.305569	+	0.529260i	−0.977388	−	0.211455i	$-0.932180\pi$
$941$	−8820.50	+	15277.5i	−0.305569	+	0.529260i	0.671819	+	0.740715i	$0.265513\pi$
$942$		0			0
$943$	−2650.45	+	1530.24i	−0.0915276	+	0.0528435i
$944$		0			0
$945$	−27135.9	−	16498.8i	−0.934106	−	0.567942i
$946$		0			0
$947$	11311.5	−	6530.68i	0.388145	−	0.224096i	−0.293211	−	0.956048i	$-0.594724\pi$
$947$	11311.5	−	6530.68i	0.388145	−	0.224096i	0.681356	+	0.731952i	$0.261391\pi$
$948$		0			0
$949$	−6356.52	+	11009.8i	−0.217430	+	0.376600i
$950$		0			0
$951$	−52183.8	+	13145.5i	−1.77936	+	0.448235i
$952$		0			0
$953$			12172.7i			0.413757i	0.978367	+	0.206879i	$0.0663306\pi$
$953$			12172.7i			0.413757i	−0.978367	+	0.206879i	$0.933669\pi$
$954$		0			0
$955$	33178.3	+	19155.5i	1.12422	+	0.649066i
$956$		0			0
$957$	7802.59	−	7571.55i	0.263555	−	0.255751i
$958$		0			0
$959$	−19725.3	+	20629.1i	−0.664194	+	0.694627i
$960$		0			0
$961$	29477.8	+	51057.1i	0.989488	+	1.71384i
$962$		0			0
$963$	−2992.61	−	89.9638i	−0.100141	−	0.00301043i
$964$		0			0
$965$	9947.21			0.331826
$966$		0			0
$967$	3592.90			0.119483			0.0597413	−	0.998214i	$-0.480972\pi$
$967$	3592.90			0.119483			0.0597413	+	0.998214i	$0.480972\pi$
$968$		0			0
$969$	−3229.00	+	11364.9i	−0.107049	+	0.376773i
$970$		0			0
$971$	8552.13	+	14812.7i	0.282648	+	0.489560i	0.972036	−	0.234832i	$-0.0754539\pi$
$971$	8552.13	+	14812.7i	0.282648	+	0.489560i	−0.689388	+	0.724392i	$0.742121\pi$
$972$		0			0
$973$	52654.3	+	12852.3i	1.73486	+	0.423458i
$974$		0			0
$975$	−2385.05	−	2457.82i	−0.0783412	−	0.0807316i
$976$		0			0
$977$	−2706.99	−	1562.88i	−0.0886431	−	0.0511781i	0.455023	−	0.890480i	$-0.349631\pi$
$977$	−2706.99	−	1562.88i	−0.0886431	−	0.0511781i	−0.543666	+	0.839301i	$0.682964\pi$
$978$		0			0
$979$			35247.1i			1.15067i
$980$		0			0
$981$	23114.0	−	12434.2i	0.752267	−	0.404683i
$982$		0			0
$983$	13385.5	−	23184.4i	0.434314	−	0.752254i	−0.562925	−	0.826508i	$-0.690324\pi$
$983$	13385.5	−	23184.4i	0.434314	−	0.752254i	0.997239	+	0.0742535i	$0.0236574\pi$
$984$		0			0
$985$	−28219.0	+	16292.3i	−0.912825	+	0.527020i
$986$		0			0
$987$	24098.1	−	177.522i	0.777155	−	0.00572501i
$988$		0			0
$989$	19864.2	−	11468.6i	0.638671	−	0.368737i
$990$		0			0
$991$	18555.4	−	32138.9i	0.594785	−	1.03020i	−0.398792	−	0.917041i	$-0.630571\pi$
$991$	18555.4	−	32138.9i	0.594785	−	1.03020i	0.993577	−	0.113156i	$-0.0360961\pi$
$992$		0			0
$993$	5052.35	+	20056.4i	0.161462	+	0.640958i
$994$		0			0
$995$			26108.0i			0.831839i
$996$		0			0
$997$	39407.8	+	22752.1i	1.25181	+	0.722734i	0.971469	−	0.237165i	$-0.0762183\pi$
$997$	39407.8	+	22752.1i	1.25181	+	0.722734i	0.280344	+	0.959900i	$0.409552\pi$
$998$		0			0
$999$	−12060.6	+	38059.2i	−0.381961	+	1.20535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bc.f.17.3		48
3.2	odd	2	inner	336.4.bc.f.17.5		48
4.3	odd	2		168.4.u.a.17.22	yes	48
7.5	odd	6	inner	336.4.bc.f.257.5		48
12.11	even	2		168.4.u.a.17.20	✓	48
21.5	even	6	inner	336.4.bc.f.257.3		48
28.19	even	6		168.4.u.a.89.20	yes	48
84.47	odd	6		168.4.u.a.89.22	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.u.a.17.20	✓	48	12.11	even	2
168.4.u.a.17.22	yes	48	4.3	odd	2
168.4.u.a.89.20	yes	48	28.19	even	6
168.4.u.a.89.22	yes	48	84.47	odd	6
336.4.bc.f.17.3		48	1.1	even	1	trivial
336.4.bc.f.17.5		48	3.2	odd	2	inner
336.4.bc.f.257.3		48	21.5	even	6	inner
336.4.bc.f.257.5		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)

\(f(q)\)	\(=\)	\(q+(-4.99832 - 1.42013i) q^{3} +(-6.11124 - 10.5850i) q^{5} +(-4.39164 + 17.9920i) q^{7} +(22.9665 + 14.1965i) q^{9} +O(q^{10})\)	\(q+(-4.99832 - 1.42013i) q^{3} +(-6.11124 - 10.5850i) q^{5} +(-4.39164 + 17.9920i) q^{7} +(22.9665 + 14.1965i) q^{9} +(47.3827 + 27.3564i) q^{11} -27.0247i q^{13} +(15.5139 + 61.5859i) q^{15} +(20.3052 - 35.1697i) q^{17} +(48.4879 - 27.9945i) q^{19} +(47.5018 - 83.6934i) q^{21} +(-93.3394 + 53.8895i) q^{23} +(-12.1945 + 21.1215i) q^{25} +(-94.6330 - 103.574i) q^{27} +38.2431i q^{29} +(-257.992 - 148.952i) q^{31} +(-197.985 - 204.026i) q^{33} +(217.284 - 63.4683i) q^{35} +(-142.286 - 246.447i) q^{37} +(-38.3785 + 135.078i) q^{39} +28.3958 q^{41} -212.817 q^{43} +(9.91619 - 329.858i) q^{45} +(125.209 + 216.869i) q^{47} +(-304.427 - 158.029i) q^{49} +(-151.438 + 146.954i) q^{51} +(294.863 + 170.239i) q^{53} -668.727i q^{55} +(-282.114 + 71.0665i) q^{57} +(451.101 - 781.329i) q^{59} +(499.851 - 288.589i) q^{61} +(-356.285 + 350.868i) q^{63} +(-286.056 + 165.154i) q^{65} +(184.464 - 319.500i) q^{67} +(543.070 - 136.803i) q^{69} -1184.28i q^{71} +(-407.399 - 235.212i) q^{73} +(90.9474 - 88.2544i) q^{75} +(-700.286 + 732.373i) q^{77} +(20.0802 + 34.7799i) q^{79} +(325.918 + 652.088i) q^{81} -855.263 q^{83} -496.361 q^{85} +(54.3102 - 191.152i) q^{87} +(322.110 + 557.910i) q^{89} +(486.229 + 118.683i) q^{91} +(1078.00 + 1110.89i) q^{93} +(-592.642 - 342.162i) q^{95} -748.863i q^{97} +(699.848 + 1300.95i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{7} + 14 q^{9}+O(q^{10}) \) 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

Varieties

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Representations

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Database

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