LMFDB - Embedded newform 336.4.bc.f.17.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,4,Mod(17,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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			17.2
Character	$\chi$	$=$	336.17
Dual form			336.4.bc.f.257.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.12717 - 0.843898i) q^{3} +(-8.29692 - 14.3707i) q^{5} +(-9.36640 - 15.9772i) q^{7} +(25.5757 + 8.65361i) q^{9} +(-36.0346 - 20.8046i) q^{11} -71.9408i q^{13} +(30.4123 + 80.6827i) q^{15} +(46.0996 - 79.8469i) q^{17} +(-86.6129 + 50.0060i) q^{19} +(34.5400 + 89.8220i) q^{21} +(74.8424 - 43.2103i) q^{23} +(-75.1779 + 130.212i) q^{25} +(-123.828 - 65.9517i) q^{27} -45.0841i q^{29} +(110.666 + 63.8931i) q^{31} +(167.198 + 137.078i) q^{33} +(-151.891 + 267.163i) q^{35} +(188.322 + 326.183i) q^{37} +(-60.7106 + 368.852i) q^{39} -298.098 q^{41} -154.234 q^{43} +(-87.8411 - 439.338i) q^{45} +(-103.187 - 178.724i) q^{47} +(-167.541 + 299.297i) q^{49} +(-303.743 + 370.485i) q^{51} +(-191.437 - 110.526i) q^{53} +690.456i q^{55} +(486.279 - 183.297i) q^{57} +(303.149 - 525.070i) q^{59} +(-291.647 + 168.383i) q^{61} +(-101.292 - 489.681i) q^{63} +(-1033.84 + 596.887i) q^{65} +(-15.4896 + 26.8287i) q^{67} +(-420.195 + 158.387i) q^{69} -450.864i q^{71} +(613.551 + 354.234i) q^{73} +(495.335 - 604.176i) q^{75} +(5.11567 + 770.596i) q^{77} +(372.522 + 645.226i) q^{79} +(579.230 + 442.644i) q^{81} +1057.78 q^{83} -1529.94 q^{85} +(-38.0464 + 231.154i) q^{87} +(333.644 + 577.888i) q^{89} +(-1149.41 + 673.826i) q^{91} +(-513.484 - 420.981i) q^{93} +(1437.24 + 829.791i) q^{95} -1165.89i q^{97} +(-741.575 - 843.921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

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
$3$	−5.12717	−	0.843898i	−0.986724	−	0.162408i
$3$	−5.12717	−	0.843898i	−0.986724	−	0.162408i
$4$		0			0
$5$	−8.29692	−	14.3707i	−0.742099	−	1.28535i	−0.951538	−	0.307532i	$-0.900497\pi$
$5$	−8.29692	−	14.3707i	−0.742099	−	1.28535i	0.209438	−	0.977822i	$-0.432836\pi$
$6$		0			0
$7$	−9.36640	−	15.9772i	−0.505738	−	0.862687i
$7$	−9.36640	−	15.9772i	−0.505738	−	0.862687i
$8$		0			0
$9$	25.5757	+	8.65361i	0.947247	+	0.320504i
$10$		0			0
$11$	−36.0346	−	20.8046i	−0.987713	−	0.570256i	−0.0831231	−	0.996539i	$-0.526489\pi$
$11$	−36.0346	−	20.8046i	−0.987713	−	0.570256i	−0.904590	+	0.426283i	$0.859823\pi$
$12$		0			0
$13$		−	71.9408i		−	1.53483i	−0.641151	−	0.767414i	$-0.721543\pi$
$13$		−	71.9408i		−	1.53483i	0.641151	−	0.767414i	$-0.278457\pi$
$14$		0			0
$15$	30.4123	+	80.6827i	0.523495	+	1.38881i
$16$		0			0
$17$	46.0996	−	79.8469i	0.657694	−	1.13916i	−0.323517	−	0.946222i	$-0.604865\pi$
$17$	46.0996	−	79.8469i	0.657694	−	1.13916i	0.981211	−	0.192937i	$-0.0618013\pi$
$18$		0			0
$19$	−86.6129	+	50.0060i	−1.04581	+	0.603798i	−0.921473	−	0.388443i	$-0.873013\pi$
$19$	−86.6129	+	50.0060i	−1.04581	+	0.603798i	−0.124335	+	0.992240i	$0.539680\pi$
$20$		0			0
$21$	34.5400	+	89.8220i	0.358916	+	0.933370i
$22$		0			0
$23$	74.8424	−	43.2103i	0.678510	−	0.391738i	−0.120784	−	0.992679i	$-0.538541\pi$
$23$	74.8424	−	43.2103i	0.678510	−	0.391738i	0.799293	+	0.600941i	$0.205207\pi$
$24$		0			0
$25$	−75.1779	+	130.212i	−0.601423	+	1.04170i
$26$		0			0
$27$	−123.828	−	65.9517i	−0.882619	−	0.470090i
$28$		0			0
$29$		−	45.0841i		−	0.288687i	−0.989528	−	0.144343i	$-0.953893\pi$
$29$		−	45.0841i		−	0.288687i	0.989528	−	0.144343i	$-0.0461070\pi$
$30$		0			0
$31$	110.666	+	63.8931i	0.641168	+	0.370179i	0.785064	−	0.619414i	$-0.212630\pi$
$31$	110.666	+	63.8931i	0.641168	+	0.370179i	−0.143896	+	0.989593i	$0.545963\pi$
$32$		0			0
$33$	167.198	+	137.078i	0.881985	+	0.723098i
$34$		0			0
$35$	−151.891	+	267.163i	−0.733550	+	1.29025i
$36$		0			0
$37$	188.322	+	326.183i	0.836756	+	1.44930i	0.892593	+	0.450863i	$0.148884\pi$
$37$	188.322	+	326.183i	0.836756	+	1.44930i	−0.0558374	+	0.998440i	$0.517783\pi$
$38$		0			0
$39$	−60.7106	+	368.852i	−0.249269	+	1.51445i
$40$		0			0
$41$	−298.098			−1.13549			−0.567745	−	0.823205i	$-0.692184\pi$
$41$	−298.098			−1.13549			−0.567745	+	0.823205i	$0.692184\pi$
$42$		0			0
$43$	−154.234			−0.546987			−0.273494	−	0.961874i	$-0.588179\pi$
$43$	−154.234			−0.546987			−0.273494	+	0.961874i	$0.588179\pi$
$44$		0			0
$45$	−87.8411	−	439.338i	−0.290991	−	1.45539i
$46$		0			0
$47$	−103.187	−	178.724i	−0.320240	−	0.554673i	0.660297	−	0.751005i	$-0.270430\pi$
$47$	−103.187	−	178.724i	−0.320240	−	0.554673i	−0.980538	+	0.196332i	$0.937097\pi$
$48$		0			0
$49$	−167.541	+	299.297i	−0.488458	+	0.872587i
$50$		0			0
$51$	−303.743	+	370.485i	−0.833971	+	1.01722i
$52$		0			0
$53$	−191.437	−	110.526i	−0.496148	−	0.286451i	0.230973	−	0.972960i	$-0.425809\pi$
$53$	−191.437	−	110.526i	−0.496148	−	0.286451i	−0.727122	+	0.686509i	$0.759142\pi$
$54$		0			0
$55$			690.456i			1.69275i
$56$		0			0
$57$	486.279	−	183.297i	1.12999	−	0.425934i
$58$		0			0
$59$	303.149	−	525.070i	0.668927	−	1.15862i	−0.309278	−	0.950972i	$-0.600087\pi$
$59$	303.149	−	525.070i	0.668927	−	1.15862i	0.978205	−	0.207643i	$-0.0665794\pi$
$60$		0			0
$61$	−291.647	+	168.383i	−0.612157	+	0.353429i	−0.773809	−	0.633419i	$-0.781651\pi$
$61$	−291.647	+	168.383i	−0.612157	+	0.353429i	0.161652	+	0.986848i	$0.448318\pi$
$62$		0			0
$63$	−101.292	−	489.681i	−0.202564	−	0.979269i
$64$		0			0
$65$	−1033.84	+	596.887i	−1.97280	+	1.13900i
$66$		0			0
$67$	−15.4896	+	26.8287i	−0.0282441	+	0.0489202i	−0.879802	−	0.475340i	$-0.842325\pi$
$67$	−15.4896	+	26.8287i	−0.0282441	+	0.0489202i	0.851558	+	0.524261i	$0.175658\pi$
$68$		0			0
$69$	−420.195	+	158.387i	−0.733123	+	0.276341i
$70$		0			0
$71$		−	450.864i		−	0.753629i	−0.926289	−	0.376814i	$-0.877019\pi$
$71$		−	450.864i		−	0.753629i	0.926289	−	0.376814i	$-0.122981\pi$
$72$		0			0
$73$	613.551	+	354.234i	0.983709	+	0.567944i	0.903388	−	0.428825i	$-0.141072\pi$
$73$	613.551	+	354.234i	0.983709	+	0.567944i	0.0803209	+	0.996769i	$0.474405\pi$
$74$		0			0
$75$	495.335	−	604.176i	0.762618	−	0.930189i
$76$		0			0
$77$	5.11567	+	770.596i	0.00757123	+	1.14049i
$78$		0			0
$79$	372.522	+	645.226i	0.530531	+	0.918907i	0.999365	+	0.0356206i	$0.0113408\pi$
$79$	372.522	+	645.226i	0.530531	+	0.918907i	−0.468834	+	0.883286i	$0.655326\pi$
$80$		0			0
$81$	579.230	+	442.644i	0.794554	+	0.607193i
$82$		0			0
$83$	1057.78			1.39888			0.699439	−	0.714693i	$-0.253433\pi$
$83$	1057.78			1.39888			0.699439	+	0.714693i	$0.253433\pi$
$84$		0			0
$85$	−1529.94			−1.95230
$86$		0			0
$87$	−38.0464	+	231.154i	−0.0468851	+	0.284854i
$88$		0			0
$89$	333.644	+	577.888i	0.397373	+	0.688270i	0.993401	−	0.114694i	$-0.0365886\pi$
$89$	333.644	+	577.888i	0.397373	+	0.688270i	−0.596028	+	0.802964i	$0.703255\pi$
$90$		0			0
$91$	−1149.41	+	673.826i	−1.32408	+	0.776221i
$92$		0			0
$93$	−513.484	−	420.981i	−0.572536	−	0.469395i
$94$		0			0
$95$	1437.24	+	829.791i	1.55219	+	0.896156i
$96$		0			0
$97$		−	1165.89i		−	1.22039i	−0.792251	−	0.610195i	$-0.791091\pi$
$97$		−	1165.89i		−	1.22039i	0.792251	−	0.610195i	$-0.208909\pi$
$98$		0			0
$99$	−741.575	−	843.921i	−0.752839	−	0.856740i
$100$		0			0
$101$	569.548	−	986.486i	0.561110	−	0.971871i	−0.436290	−	0.899806i	$-0.643708\pi$
$101$	569.548	−	986.486i	0.561110	−	0.971871i	0.997400	−	0.0720650i	$-0.0229589\pi$
$102$		0			0
$103$	920.316	−	531.345i	0.880402	−	0.508301i	0.00961128	−	0.999954i	$-0.496941\pi$
$103$	920.316	−	531.345i	0.880402	−	0.508301i	0.870791	+	0.491653i	$0.163607\pi$
$104$		0			0
$105$	1004.23	−	1241.61i	0.933359	−	1.15399i
$106$		0			0
$107$	402.972	−	232.656i	0.364082	−	0.210203i	−0.306788	−	0.951778i	$-0.599254\pi$
$107$	402.972	−	232.656i	0.364082	−	0.210203i	0.670870	+	0.741575i	$0.265921\pi$
$108$		0			0
$109$	−18.3377	+	31.7618i	−0.0161141	+	0.0279104i	−0.873970	−	0.485980i	$-0.838463\pi$
$109$	−18.3377	+	31.7618i	−0.0161141	+	0.0279104i	0.857856	+	0.513890i	$0.171796\pi$
$110$		0			0
$111$	−690.293	−	1831.32i	−0.590268	−	1.56596i
$112$		0			0
$113$			553.407i			0.460709i	0.973107	+	0.230355i	$0.0739886\pi$
$113$			553.407i			0.460709i	−0.973107	+	0.230355i	$0.926011\pi$
$114$		0			0
$115$	−1241.92	−	717.025i	−1.00704	−	0.581417i
$116$		0			0
$117$	622.547	−	1839.93i	0.491919	−	1.45386i
$118$		0			0
$119$	−1707.52	+	11.3355i	−1.31536	+	0.00873213i
$120$		0			0
$121$	200.162	+	346.691i	0.150385	+	0.260474i
$122$		0			0
$123$	1528.40	+	251.564i	1.12041	+	0.184413i
$124$		0			0
$125$	420.750			0.301064
$126$		0			0
$127$	−158.835			−0.110979			−0.0554894	−	0.998459i	$-0.517672\pi$
$127$	−158.835			−0.110979			−0.0554894	+	0.998459i	$0.517672\pi$
$128$		0			0
$129$	790.783	+	130.158i	0.539725	+	0.0888352i
$130$		0			0
$131$	224.990	+	389.695i	0.150057	+	0.259907i	0.931248	−	0.364385i	$-0.118721\pi$
$131$	224.990	+	389.695i	0.150057	+	0.259907i	−0.781191	+	0.624292i	$0.785388\pi$
$132$		0			0
$133$	1610.21	+	915.454i	1.04979	+	0.596842i
$134$		0			0
$135$	79.6192	+	2326.69i	0.0507595	+	1.48333i
$136$		0			0
$137$	−1739.78	−	1004.46i	−1.08496	−	0.626401i	−0.152729	−	0.988268i	$-0.548806\pi$
$137$	−1739.78	−	1004.46i	−1.08496	−	0.626401i	−0.932230	+	0.361867i	$0.882139\pi$
$138$		0			0
$139$		−	2400.58i		−	1.46485i	−0.680847	−	0.732426i	$-0.738388\pi$
$139$		−	2400.58i		−	1.46485i	0.680847	−	0.732426i	$-0.261612\pi$
$140$		0			0
$141$	378.229	+	1003.43i	0.225905	+	0.599318i
$142$		0			0
$143$	−1496.70	+	2592.36i	−0.875246	+	1.51597i
$144$		0			0
$145$	−647.890	+	374.060i	−0.371065	+	0.214234i
$146$		0			0
$147$	1111.59	−	1393.16i	0.623688	−	0.781673i
$148$		0			0
$149$	1841.72	−	1063.32i	1.01261	−	0.584633i	0.100658	−	0.994921i	$-0.467905\pi$
$149$	1841.72	−	1063.32i	1.01261	−	0.584633i	0.911956	+	0.410288i	$0.134572\pi$
$150$		0			0
$151$	−764.888	+	1324.83i	−0.412223	+	0.713992i	−0.995133	−	0.0985455i	$-0.968581\pi$
$151$	−764.888	+	1324.83i	−0.412223	+	0.713992i	0.582909	+	0.812537i	$0.301914\pi$
$152$		0			0
$153$	1869.99	−	1643.21i	0.988104	−	0.868272i
$154$		0			0
$155$		−	2120.46i		−	1.09884i
$156$		0			0
$157$	−633.214	−	365.586i	−0.321885	−	0.185840i	0.330347	−	0.943859i	$-0.392834\pi$
$157$	−633.214	−	365.586i	−0.321885	−	0.185840i	−0.652232	+	0.758019i	$0.726167\pi$
$158$		0			0
$159$	888.255	+	728.239i	0.443039	+	0.363227i
$160$		0			0
$161$	−1391.38	−	791.047i	−0.681095	−	0.387225i
$162$		0			0
$163$	−407.288	−	705.443i	−0.195713	−	0.338985i	0.751421	−	0.659823i	$-0.229369\pi$
$163$	−407.288	−	705.443i	−0.195713	−	0.338985i	−0.947134	+	0.320838i	$0.896035\pi$
$164$		0			0
$165$	582.674	−	3540.08i	0.274916	−	1.67027i
$166$		0			0
$167$	−993.394			−0.460306			−0.230153	−	0.973154i	$-0.573923\pi$
$167$	−993.394			−0.460306			−0.230153	+	0.973154i	$0.573923\pi$
$168$		0			0
$169$	−2978.47			−1.35570
$170$		0			0
$171$	−2647.91	+	529.423i	−1.18416	+	0.236760i
$172$		0			0
$173$	1849.86	+	3204.06i	0.812963	+	1.40809i	0.910782	+	0.412888i	$0.135480\pi$
$173$	1849.86	+	3204.06i	0.812963	+	1.40809i	−0.0978189	+	0.995204i	$0.531187\pi$
$174$		0			0
$175$	2784.57	−	18.4856i	1.20282	−	0.00798503i
$176$		0			0
$177$	−1997.40	+	2436.29i	−0.848214	+	1.03459i
$178$		0			0
$179$	−1460.09	−	842.981i	−0.609676	−	0.351997i	0.163163	−	0.986599i	$-0.447830\pi$
$179$	−1460.09	−	842.981i	−0.609676	−	0.351997i	−0.772839	+	0.634603i	$0.781164\pi$
$180$		0			0
$181$		−	624.165i		−	0.256320i	−0.991754	−	0.128160i	$-0.959093\pi$
$181$		−	624.165i		−	0.256320i	0.991754	−	0.128160i	$-0.0409070\pi$
$182$		0			0
$183$	1637.42	−	617.205i	0.661430	−	0.249318i
$184$		0			0
$185$	3124.99	−	5412.64i	1.24191	−	2.15105i
$186$		0			0
$187$	−3322.36	+	1918.17i	−1.29923	+	0.750108i
$188$		0			0
$189$	106.099	+	2596.15i	0.0408337	+	0.999166i
$190$		0			0
$191$	2436.36	−	1406.63i	0.922979	−	0.532882i	0.0383946	−	0.999263i	$-0.487776\pi$
$191$	2436.36	−	1406.63i	0.922979	−	0.532882i	0.884584	+	0.466381i	$0.154442\pi$
$192$		0			0
$193$	271.698	−	470.594i	0.101333	−	0.175513i	−0.810901	−	0.585183i	$-0.801023\pi$
$193$	271.698	−	470.594i	0.101333	−	0.175513i	0.912234	+	0.409670i	$0.134356\pi$
$194$		0			0
$195$	5804.37	−	2187.89i	2.13159	−	0.803475i
$196$		0			0
$197$			1301.71i			0.470777i	0.971901	+	0.235388i	$0.0756362\pi$
$197$			1301.71i			0.470777i	−0.971901	+	0.235388i	$0.924364\pi$
$198$		0			0
$199$	−415.849	−	240.091i	−0.148135	−	0.0855256i	0.424101	−	0.905615i	$-0.360590\pi$
$199$	−415.849	−	240.091i	−0.148135	−	0.0855256i	−0.572235	+	0.820089i	$0.693924\pi$
$200$		0			0
$201$	102.058	−	124.484i	0.0358141	−	0.0436836i
$202$		0			0
$203$	−720.318	+	422.276i	−0.249046	+	0.146000i
$204$		0			0
$205$	2473.30	+	4283.87i	0.842646	+	1.45951i
$206$		0			0
$207$	2288.07	−	457.475i	0.768270	−	0.153607i
$208$		0			0
$209$	4161.41			1.37728
$210$		0			0
$211$	−92.6723			−0.0302361			−0.0151181	−	0.999886i	$-0.504812\pi$
$211$	−92.6723			−0.0302361			−0.0151181	+	0.999886i	$0.504812\pi$
$212$		0			0
$213$	−380.483	+	2311.65i	−0.122395	+	0.743624i
$214$		0			0
$215$	1279.67	+	2216.45i	0.405919	+	0.703072i
$216$		0			0
$217$	−15.7108	−	2366.58i	−0.00491482	−	0.740341i
$218$		0			0
$219$	−2846.84	−	2333.99i	−0.878410	−	0.720167i
$220$		0			0
$221$	−5744.24	−	3316.44i	−1.74841	−	1.00945i
$222$		0			0
$223$			3120.21i			0.936972i	0.883471	+	0.468486i	$0.155200\pi$
$223$			3120.21i			0.936972i	−0.883471	+	0.468486i	$0.844800\pi$
$224$		0			0
$225$	−3049.53	+	2679.70i	−0.903564	+	0.793984i
$226$		0			0
$227$	−1912.66	+	3312.83i	−0.559242	+	0.968635i	0.438318	+	0.898820i	$0.355574\pi$
$227$	−1912.66	+	3312.83i	−0.559242	+	0.968635i	−0.997560	+	0.0698153i	$0.977759\pi$
$228$		0			0
$229$	1989.41	−	1148.59i	0.574080	−	0.331445i	−0.184697	−	0.982795i	$-0.559131\pi$
$229$	1989.41	−	1148.59i	0.574080	−	0.331445i	0.758777	+	0.651350i	$0.225797\pi$
$230$		0			0
$231$	624.075	−	3955.29i	0.177754	−	1.12658i
$232$		0			0
$233$	−4451.29	+	2569.95i	−1.25156	+	0.722589i	−0.971419	−	0.237370i	$-0.923715\pi$
$233$	−4451.29	+	2569.95i	−1.25156	+	0.722589i	−0.280141	+	0.959959i	$0.590381\pi$
$234$		0			0
$235$	−1712.26	+	2965.72i	−0.475300	+	0.823245i
$236$		0			0
$237$	−1365.48	−	3622.55i	−0.374250	−	0.992870i
$238$		0			0
$239$		−	4561.23i		−	1.23448i	−0.786774	−	0.617241i	$-0.788250\pi$
$239$		−	4561.23i		−	1.23448i	0.786774	−	0.617241i	$-0.211750\pi$
$240$		0			0
$241$	−2097.55	−	1211.02i	−0.560644	−	0.323688i	0.192760	−	0.981246i	$-0.438256\pi$
$241$	−2097.55	−	1211.02i	−0.560644	−	0.323688i	−0.753404	+	0.657558i	$0.771589\pi$
$242$		0			0
$243$	−2596.26	−	2758.32i	−0.685393	−	0.728174i
$244$		0			0
$245$	5691.19	−	75.5663i	1.48407	−	0.0197051i
$246$		0			0
$247$	3597.47	+	6231.00i	0.926726	+	1.60514i
$248$		0			0
$249$	−5423.43	−	892.661i	−1.38031	−	0.227189i
$250$		0			0
$251$	−2323.52			−0.584301			−0.292150	−	0.956372i	$-0.594371\pi$
$251$	−2323.52			−0.584301			−0.292150	+	0.956372i	$0.594371\pi$
$252$		0			0
$253$	−3595.89			−0.893564
$254$		0			0
$255$	7844.26	+	1291.11i	1.92638	+	0.317069i
$256$		0			0
$257$	2408.92	+	4172.36i	0.584685	+	1.01270i	0.994915	+	0.100722i	$0.0321152\pi$
$257$	2408.92	+	4172.36i	0.584685	+	1.01270i	−0.410230	+	0.911982i	$0.634551\pi$
$258$		0			0
$259$	3447.59	−	6064.02i	0.827116	−	1.45483i
$260$		0			0
$261$	390.140	−	1153.06i	0.0925252	−	0.273458i
$262$		0			0
$263$	−4099.29	−	2366.73i	−0.961114	−	0.554900i	−0.0645984	−	0.997911i	$-0.520577\pi$
$263$	−4099.29	−	2366.73i	−0.961114	−	0.554900i	−0.896516	+	0.443012i	$0.853910\pi$
$264$		0			0
$265$			3668.10i			0.850302i
$266$		0			0
$267$	−1222.97	−	3244.49i	−0.280317	−	0.743669i
$268$		0			0
$269$	−3176.43	+	5501.75i	−0.719965	+	1.24702i	0.241048	+	0.970513i	$0.422509\pi$
$269$	−3176.43	+	5501.75i	−0.719965	+	1.24702i	−0.961013	+	0.276503i	$0.910824\pi$
$270$		0			0
$271$	2207.33	−	1274.40i	0.494781	−	0.285662i	−0.231775	−	0.972769i	$-0.574453\pi$
$271$	2207.33	−	1274.40i	0.494781	−	0.285662i	0.726556	+	0.687108i	$0.241120\pi$
$272$		0			0
$273$	6461.86	−	2484.83i	1.43256	−	0.550875i
$274$		0			0
$275$	5418.01	−	3128.09i	1.18807	−	0.685931i
$276$		0			0
$277$	−2364.68	+	4095.75i	−0.512925	+	0.888411i	0.486963	+	0.873423i	$0.338105\pi$
$277$	−2364.68	+	4095.75i	−0.512925	+	0.888411i	−0.999888	+	0.0149889i	$0.995229\pi$
$278$		0			0
$279$	2277.45	+	2591.77i	0.488701	+	0.556147i
$280$		0			0
$281$		−	3104.55i		−	0.659082i	−0.944141	−	0.329541i	$-0.893106\pi$
$281$		−	3104.55i		−	0.659082i	0.944141	−	0.329541i	$-0.106894\pi$
$282$		0			0
$283$	−2706.64	−	1562.68i	−0.568527	−	0.328239i	0.188034	−	0.982163i	$-0.439789\pi$
$283$	−2706.64	−	1562.68i	−0.568527	−	0.328239i	−0.756561	+	0.653923i	$0.773122\pi$
$284$		0			0
$285$	−6668.71	−	5467.36i	−1.38604	−	1.13635i
$286$		0			0
$287$	2792.10	+	4762.77i	0.574260	+	0.979572i
$288$		0			0
$289$	−1793.85	−	3107.04i	−0.365123	−	0.632411i
$290$		0			0
$291$	−983.888	+	5977.69i	−0.198201	+	1.20419i
$292$		0			0
$293$	−3473.05			−0.692483			−0.346242	−	0.938145i	$-0.612542\pi$
$293$	−3473.05			−0.692483			−0.346242	+	0.938145i	$0.612542\pi$
$294$		0			0
$295$	−10060.8			−1.98564
$296$		0			0
$297$	3089.99	+	4952.74i	0.603702	+	0.967632i
$298$		0			0
$299$	−3108.58	−	5384.22i	−0.601251	−	1.04140i
$300$		0			0
$301$	1444.62	+	2464.22i	0.276632	+	0.471879i
$302$		0			0
$303$	−3752.66	+	4577.24i	−0.711500	+	0.867839i
$304$		0			0
$305$	4839.55	+	2794.12i	0.908563	+	0.524559i
$306$		0			0
$307$		−	5831.84i		−	1.08417i	−0.840323	−	0.542086i	$-0.817635\pi$
$307$		−	5831.84i		−	1.08417i	0.840323	−	0.542086i	$-0.182365\pi$
$308$		0			0
$309$	−5167.01	+	1947.64i	−0.951266	+	0.358568i
$310$		0			0
$311$	−4948.29	+	8570.70i	−0.902225	+	1.56270i	−0.0776259	+	0.996983i	$0.524734\pi$
$311$	−4948.29	+	8570.70i	−0.902225	+	1.56270i	−0.824599	+	0.565717i	$0.808599\pi$
$312$		0			0
$313$	−7417.35	+	4282.41i	−1.33947	+	0.773342i	−0.986728	−	0.162380i	$-0.948083\pi$
$313$	−7417.35	+	4282.41i	−1.33947	+	0.773342i	−0.352739	+	0.935722i	$0.614750\pi$
$314$		0			0
$315$	−6196.64	+	5518.47i	−1.10838	+	0.987082i
$316$		0			0
$317$	3265.61	−	1885.40i	0.578596	−	0.334053i	−0.181979	−	0.983302i	$-0.558250\pi$
$317$	3265.61	−	1885.40i	0.578596	−	0.334053i	0.760575	+	0.649250i	$0.224917\pi$
$318$		0			0
$319$	−937.957	+	1624.59i	−0.164625	+	0.285140i
$320$		0			0
$321$	−2262.44	+	852.799i	−0.393387	+	0.148282i
$322$		0			0
$323$			9221.02i			1.58846i
$324$		0			0
$325$	9367.54	+	5408.35i	1.59882	+	0.923082i
$326$		0			0
$327$	120.824	−	147.373i	0.0204330	−	0.0249228i
$328$		0			0
$329$	−1889.03	+	3322.63i	−0.316551	+	0.556786i
$330$		0			0
$331$	5400.43	+	9353.82i	0.896781	+	1.55327i	0.831585	+	0.555397i	$0.187434\pi$
$331$	5400.43	+	9353.82i	0.896781	+	1.55327i	0.0651951	+	0.997873i	$0.479233\pi$
$332$		0			0
$333$	1993.80	+	9972.02i	0.328107	+	1.64103i
$334$		0			0
$335$	514.064			0.0838397
$336$		0			0
$337$	8729.29			1.41102			0.705511	−	0.708699i	$-0.250717\pi$
$337$	8729.29			1.41102			0.705511	+	0.708699i	$0.250717\pi$
$338$		0			0
$339$	467.019	−	2837.41i	0.0748230	−	0.454593i
$340$		0			0
$341$	−2658.54	−	4604.72i	−0.422193	−	0.731260i
$342$		0			0
$343$	6351.19	−	126.504i	0.999802	−	0.0199142i
$344$		0			0
$345$	5762.45	+	4724.36i	0.899247	+	0.737250i
$346$		0			0
$347$	2951.55	+	1704.08i	0.456621	+	0.263630i	0.710622	−	0.703574i	$-0.248414\pi$
$347$	2951.55	+	1704.08i	0.456621	+	0.263630i	−0.254002	+	0.967204i	$0.581747\pi$
$348$		0			0
$349$		−	6078.23i		−	0.932265i	−0.884715	−	0.466132i	$-0.845647\pi$
$349$		−	6078.23i		−	0.932265i	0.884715	−	0.466132i	$-0.154353\pi$
$350$		0			0
$351$	−4744.62	+	8908.28i	−0.721507	+	1.35467i
$352$		0			0
$353$	3444.86	−	5966.67i	0.519409	−	0.899643i	−0.480336	−	0.877084i	$-0.659485\pi$
$353$	3444.86	−	5966.67i	0.519409	−	0.899643i	0.999746	−	0.0225588i	$-0.00718130\pi$
$354$		0			0
$355$	−6479.22	+	3740.78i	−0.968680	+	0.559268i
$356$		0			0
$357$	8764.28	+	1382.85i	1.29931	+	0.205009i
$358$		0			0
$359$	−6338.74	+	3659.67i	−0.931883	+	0.538023i	−0.887407	−	0.460987i	$-0.847495\pi$
$359$	−6338.74	+	3659.67i	−0.931883	+	0.538023i	−0.0444765	+	0.999010i	$0.514162\pi$
$360$		0			0
$361$	1571.69	−	2722.25i	0.229143	−	0.396888i
$362$		0			0
$363$	−733.692	−	1946.46i	−0.106085	−	0.281439i
$364$		0			0
$365$		−	11756.2i		−	1.68588i
$366$		0			0
$367$	7729.26	+	4462.49i	1.09936	+	0.634714i	0.936052	−	0.351861i	$-0.114451\pi$
$367$	7729.26	+	4462.49i	1.09936	+	0.634714i	0.163305	+	0.986576i	$0.447784\pi$
$368$		0			0
$369$	−7624.05	−	2579.62i	−1.07559	−	0.363929i
$370$		0			0
$371$	27.1774	+	4093.85i	0.00380318	+	0.572890i
$372$		0			0
$373$	425.459	+	736.916i	0.0590601	+	0.102295i	0.894044	−	0.447980i	$-0.147856\pi$
$373$	425.459	+	736.916i	0.0590601	+	0.102295i	−0.834984	+	0.550275i	$0.814523\pi$
$374$		0			0
$375$	−2157.25	−	355.070i	−0.297067	−	0.0488952i
$376$		0			0
$377$	−3243.39			−0.443085
$378$		0			0
$379$	−3715.61			−0.503584			−0.251792	−	0.967781i	$-0.581020\pi$
$379$	−3715.61			−0.503584			−0.251792	+	0.967781i	$0.581020\pi$
$380$		0			0
$381$	814.372	+	134.040i	0.109505	+	0.0180239i
$382$		0			0
$383$	−4703.20	−	8146.19i	−0.627474	−	1.08682i	−0.988057	−	0.154090i	$-0.950756\pi$
$383$	−4703.20	−	8146.19i	−0.627474	−	1.08682i	0.360583	−	0.932727i	$-0.382578\pi$
$384$		0			0
$385$	11031.6	−	6467.09i	1.46031	−	0.856087i
$386$		0			0
$387$	−3944.64	−	1334.68i	−0.518132	−	0.175312i
$388$		0			0
$389$	850.130	+	490.823i	0.110805	+	0.0639735i	0.554379	−	0.832265i	$-0.312956\pi$
$389$	850.130	+	490.823i	0.110805	+	0.0639735i	−0.443573	+	0.896238i	$0.646289\pi$
$390$		0			0
$391$		−	7967.91i		−	1.03057i
$392$		0			0
$393$	−824.700	−	2187.90i	−0.105854	−	0.280827i
$394$		0			0
$395$	6181.57	−	10706.8i	0.787413	−	1.36384i
$396$		0			0
$397$	−8976.10	+	5182.35i	−1.13475	+	0.655151i	−0.945126	−	0.326705i	$-0.894061\pi$
$397$	−8976.10	+	5182.35i	−1.13475	+	0.655151i	−0.189628	+	0.981856i	$0.560728\pi$
$398$		0			0
$399$	−7483.24	−	6052.54i	−0.938924	−	0.759413i
$400$		0			0
$401$	−6115.22	+	3530.62i	−0.761545	+	0.439678i	−0.829850	−	0.557986i	$-0.811574\pi$
$401$	−6115.22	+	3530.62i	−0.761545	+	0.439678i	0.0683051	+	0.997664i	$0.478241\pi$
$402$		0			0
$403$	4596.52	−	7961.40i	0.568161	−	0.984083i
$404$		0			0
$405$	1555.27	−	11996.5i	0.190819	−	1.47188i
$406$		0			0
$407$		−	15671.9i		−	1.90866i
$408$		0			0
$409$	−7226.85	−	4172.42i	−0.873703	−	0.504433i	−0.00512627	−	0.999987i	$-0.501632\pi$
$409$	−7226.85	−	4172.42i	−0.873703	−	0.504433i	−0.868577	+	0.495554i	$0.834965\pi$
$410$		0			0
$411$	8072.47	+	6618.24i	0.968821	+	0.794291i
$412$		0			0
$413$	−11228.6	+	74.5418i	−1.33782	+	0.00888127i
$414$		0			0
$415$	−8776.35	−	15201.1i	−1.03811	−	1.79805i
$416$		0			0
$417$	−2025.84	+	12308.2i	−0.237904	+	1.44540i
$418$		0			0
$419$	4034.43			0.470393			0.235197	−	0.971948i	$-0.424427\pi$
$419$	4034.43			0.470393			0.235197	+	0.971948i	$0.424427\pi$
$420$		0			0
$421$	−474.967			−0.0549845			−0.0274923	−	0.999622i	$-0.508752\pi$
$421$	−474.967			−0.0549845			−0.0274923	+	0.999622i	$0.508752\pi$
$422$		0			0
$423$	−1092.46	−	5463.93i	−0.125572	−	0.628051i
$424$		0			0
$425$	6931.34	+	12005.4i	0.791105	+	1.37023i
$426$		0			0
$427$	5421.96	+	3082.56i	0.614490	+	0.349358i
$428$		0			0
$429$	9861.50	−	12028.4i	1.10983	−	1.35370i
$430$		0			0
$431$	2530.47	+	1460.97i	0.282804	+	0.163277i	0.634692	−	0.772765i	$-0.281127\pi$
$431$	2530.47	+	1460.97i	0.282804	+	0.163277i	−0.351888	+	0.936042i	$0.614460\pi$
$432$		0			0
$433$		−	12182.0i		−	1.35203i	−0.736888	−	0.676015i	$-0.763706\pi$
$433$		−	12182.0i		−	1.35203i	0.736888	−	0.676015i	$-0.236294\pi$
$434$		0			0
$435$	3637.51	−	1371.11i	0.400932	−	0.151126i
$436$		0			0
$437$	−4321.55	+	7485.14i	−0.473061	+	0.819365i
$438$		0			0
$439$	2146.15	−	1239.08i	0.233326	−	0.134711i	−0.378779	−	0.925487i	$-0.623656\pi$
$439$	2146.15	−	1239.08i	0.233326	−	0.134711i	0.612106	+	0.790776i	$0.290323\pi$
$440$		0			0
$441$	−6874.98	+	6204.90i	−0.742358	+	0.670003i
$442$		0			0
$443$	8956.89	−	5171.27i	0.960621	−	0.554615i	0.0642566	−	0.997933i	$-0.479532\pi$
$443$	8956.89	−	5171.27i	0.960621	−	0.554615i	0.896364	+	0.443319i	$0.146199\pi$
$444$		0			0
$445$	5536.44	−	9589.39i	0.589780	−	1.02153i
$446$		0			0
$447$	−10340.1	+	3897.58i	−1.09412	+	0.412414i
$448$		0			0
$449$		−	10545.1i		−	1.10837i	−0.832395	−	0.554183i	$-0.813031\pi$
$449$		−	10545.1i		−	1.10837i	0.832395	−	0.554183i	$-0.186969\pi$
$450$		0			0
$451$	10741.8	+	6201.80i	1.12154	+	0.647520i
$452$		0			0
$453$	5039.73	−	6147.11i	0.522709	−	0.637564i
$454$		0			0
$455$	19219.9	+	10927.2i	1.98032	+	1.12587i
$456$		0			0
$457$	−1930.75	−	3344.16i	−0.197629	−	0.342304i	0.750130	−	0.661291i	$-0.229991\pi$
$457$	−1930.75	−	3344.16i	−0.197629	−	0.342304i	−0.947759	+	0.318986i	$0.896658\pi$
$458$		0			0
$459$	−10974.5	+	6846.93i	−1.11600	+	0.696268i
$460$		0			0
$461$	11520.2			1.16388			0.581942	−	0.813230i	$-0.302293\pi$
$461$	11520.2			1.16388			0.581942	+	0.813230i	$0.302293\pi$
$462$		0			0
$463$	−292.312			−0.0293411			−0.0146705	−	0.999892i	$-0.504670\pi$
$463$	−292.312			−0.0293411			−0.0146705	+	0.999892i	$0.504670\pi$
$464$		0			0
$465$	−1789.45	+	10872.0i	−0.178460	+	1.08425i
$466$		0			0
$467$	−3883.43	−	6726.30i	−0.384805	−	0.666501i	0.606937	−	0.794750i	$-0.292398\pi$
$467$	−3883.43	−	6726.30i	−0.384805	−	0.666501i	−0.991742	+	0.128248i	$0.959065\pi$
$468$		0			0
$469$	573.730	−	3.80876i	0.0564869	−	0.000374994i
$470$		0			0
$471$	2938.07	+	2408.79i	0.287430	+	0.235650i
$472$		0			0
$473$	5557.76	+	3208.77i	0.540266	+	0.311923i
$474$		0			0
$475$		−	15037.4i		−	1.45255i
$476$		0			0
$477$	−3939.67	−	4483.40i	−0.378166	−	0.430358i
$478$		0			0
$479$	5271.30	−	9130.15i	0.502822	−	0.870913i	−0.497173	−	0.867652i	$-0.665628\pi$
$479$	5271.30	−	9130.15i	0.502822	−	0.870913i	0.999995	−	0.00326151i	$-0.00103817\pi$
$480$		0			0
$481$	23465.9	−	13548.0i	2.22443	−	1.28428i
$482$		0			0
$483$	6466.29	+	5230.01i	0.609164	+	0.492699i
$484$		0			0
$485$	−16754.6	+	9673.27i	−1.56863	+	0.905650i
$486$		0			0
$487$	3779.59	−	6546.44i	0.351683	−	0.609133i	−0.634861	−	0.772626i	$-0.718943\pi$
$487$	3779.59	−	6546.44i	0.351683	−	0.609133i	0.986544	+	0.163493i	$0.0522762\pi$
$488$		0			0
$489$	1492.91	+	3960.63i	0.138061	+	0.366270i
$490$		0			0
$491$			19617.4i			1.80310i	0.432674	+	0.901550i	$0.357570\pi$
$491$			19617.4i			1.80310i	−0.432674	+	0.901550i	$0.642430\pi$
$492$		0			0
$493$	−3599.83	−	2078.36i	−0.328860	−	0.189868i
$494$		0			0
$495$	−5974.94	+	17658.9i	−0.542532	+	1.60345i
$496$		0			0
$497$	−7203.53	+	4222.97i	−0.650146	+	0.381139i
$498$		0			0
$499$	−599.984	−	1039.20i	−0.0538256	−	0.0932286i	0.837857	−	0.545889i	$-0.183808\pi$
$499$	−599.984	−	1039.20i	−0.0538256	−	0.0932286i	−0.891683	+	0.452661i	$0.850475\pi$
$500$		0			0
$501$	5093.30	+	838.323i	0.454195	+	0.0747575i
$502$		0			0
$503$	2879.14			0.255218			0.127609	−	0.991825i	$-0.459270\pi$
$503$	2879.14			0.255218			0.127609	+	0.991825i	$0.459270\pi$
$504$		0			0
$505$	−18902.0			−1.66560
$506$		0			0
$507$	15271.1	+	2513.53i	1.33770	+	0.220177i
$508$		0			0
$509$	−7735.46	−	13398.2i	−0.673611	−	1.16673i	−0.976873	−	0.213821i	$-0.931409\pi$
$509$	−7735.46	−	13398.2i	−0.673611	−	1.16673i	0.303262	−	0.952907i	$-0.401924\pi$
$510$		0			0
$511$	−87.1031	−	13120.7i	−0.00754054	−	1.13586i
$512$		0			0
$513$	14023.1	−	479.869i	1.20689	−	0.0412996i
$514$		0			0
$515$	−15271.6	−	8817.05i	−1.30669	−	0.754419i
$516$		0			0
$517$			8587.01i			0.730477i
$518$		0			0
$519$	−6780.66	−	17988.8i	−0.573484	−	1.52143i
$520$		0			0
$521$	1287.45	−	2229.93i	0.108262	−	0.187515i	−0.806804	−	0.590819i	$-0.798805\pi$
$521$	1287.45	−	2229.93i	0.108262	−	0.187515i	0.915066	+	0.403304i	$0.132138\pi$
$522$		0			0
$523$	−1320.42	+	762.347i	−0.110398	+	0.0637382i	−0.554182	−	0.832395i	$-0.686969\pi$
$523$	−1320.42	+	762.347i	−0.110398	+	0.0637382i	0.443784	+	0.896134i	$0.353636\pi$
$524$		0			0
$525$	−14292.5	−	2255.11i	−1.18815	−	0.187469i
$526$		0			0
$527$	10203.3	−	5890.89i	0.843385	−	0.486928i
$528$		0			0
$529$	−2349.24	+	4069.00i	−0.193083	+	0.334429i
$530$		0			0
$531$	12297.0	−	10805.7i	1.00498	−	0.883101i
$532$		0			0
$533$			21445.4i			1.74278i
$534$		0			0
$535$	−6686.86	−	3860.66i	−0.540370	−	0.311983i
$536$		0			0
$537$	6774.72	+	5554.27i	0.544415	+	0.446340i
$538$		0			0
$539$	12264.0	−	7299.44i	0.980055	−	0.583320i
$540$		0			0
$541$	10053.1	+	17412.4i	0.798920	+	1.38377i	0.920320	+	0.391166i	$0.127928\pi$
$541$	10053.1	+	17412.4i	0.798920	+	1.38377i	−0.121400	+	0.992604i	$0.538738\pi$
$542$		0			0
$543$	−526.732	+	3200.20i	−0.0416284	+	0.252917i
$544$		0			0
$545$	608.586			0.0478330
$546$		0			0
$547$	3946.90			0.308514			0.154257	−	0.988031i	$-0.450702\pi$
$547$	3946.90			0.308514			0.154257	+	0.988031i	$0.450702\pi$
$548$		0			0
$549$	−8916.19	+	1782.70i	−0.693140	+	0.138586i
$550$		0			0
$551$	2254.48	+	3904.87i	0.174308	+	0.301911i
$552$		0			0
$553$	6819.72	−	11995.3i	0.524419	−	0.922408i
$554$		0			0
$555$	−20590.0	+	25114.3i	−1.57477	+	1.92080i
$556$		0			0
$557$	18086.0	+	10442.0i	1.37582	+	0.794328i	0.991653	−	0.128938i	$-0.0411567\pi$
$557$	18086.0	+	10442.0i	1.37582	+	0.794328i	0.384163	+	0.923265i	$0.374490\pi$
$558$		0			0
$559$			11095.7i			0.839532i
$560$		0			0
$561$	18653.0	−	7031.03i	1.40380	−	0.529145i
$562$		0			0
$563$	−4026.52	+	6974.13i	−0.301416	+	0.522069i	−0.976457	−	0.215712i	$-0.930793\pi$
$563$	−4026.52	+	6974.13i	−0.301416	+	0.522069i	0.675041	+	0.737781i	$0.264126\pi$
$564$		0			0
$565$	7952.84	−	4591.58i	0.592175	−	0.341892i
$566$		0			0
$567$	1646.90	−	13400.4i	0.121981	−	0.992532i
$568$		0			0
$569$	−3249.15	+	1875.90i	−0.239387	+	0.138210i	−0.614895	−	0.788609i	$-0.710802\pi$
$569$	−3249.15	+	1875.90i	−0.239387	+	0.138210i	0.375508	+	0.926819i	$0.377468\pi$
$570$		0			0
$571$	7068.28	−	12242.6i	0.518036	−	0.897264i	−0.481745	−	0.876312i	$-0.659997\pi$
$571$	7068.28	−	12242.6i	0.518036	−	0.897264i	0.999780	−	0.0209525i	$-0.00666987\pi$
$572$		0			0
$573$	−13678.7	+	5156.01i	−0.997269	+	0.375908i
$574$		0			0
$575$			12993.8i			0.942401i
$576$		0			0
$577$	−13804.0	−	7969.72i	−0.995956	−	0.575015i	−0.0889067	−	0.996040i	$-0.528337\pi$
$577$	−13804.0	−	7969.72i	−0.995956	−	0.575015i	−0.907049	+	0.421025i	$0.861671\pi$
$578$		0			0
$579$	−1790.17	+	2183.53i	−0.128492	+	0.156726i
$580$		0			0
$581$	−9907.62	−	16900.4i	−0.707466	−	1.20679i
$582$		0			0
$583$	4598.90	+	7965.53i	0.326701	+	0.565863i
$584$		0			0
$585$	−31606.3	+	6319.35i	−2.23378	+	0.446621i
$586$		0			0
$587$	−26116.9			−1.83639			−0.918196	−	0.396127i	$-0.870354\pi$
$587$	−26116.9			−1.83639			−0.918196	+	0.396127i	$0.870354\pi$
$588$		0			0
$589$	−12780.1			−0.894052
$590$		0			0
$591$	1098.51	−	6674.09i	0.0764580	−	0.464527i
$592$		0			0
$593$	−5150.35	−	8920.66i	−0.356660	−	0.617753i	0.630741	−	0.775994i	$-0.282751\pi$
$593$	−5150.35	−	8920.66i	−0.356660	−	0.617753i	−0.987401	+	0.158240i	$0.949418\pi$
$594$		0			0
$595$	14330.0	+	24444.1i	0.987351	+	1.68422i
$596$		0			0
$597$	1929.52	+	1581.92i	0.132278	+	0.108448i
$598$		0			0
$599$	−3319.39	−	1916.45i	−0.226421	−	0.130725i	0.382499	−	0.923956i	$-0.375064\pi$
$599$	−3319.39	−	1916.45i	−0.226421	−	0.130725i	−0.608920	+	0.793232i	$0.708397\pi$
$600$		0			0
$601$		−	19446.0i		−	1.31983i	−0.751339	−	0.659916i	$-0.770592\pi$
$601$		−	19446.0i		−	1.31983i	0.751339	−	0.659916i	$-0.229408\pi$
$602$		0			0
$603$	−628.322	+	552.122i	−0.0424332	+	0.0372872i
$604$		0			0
$605$	3321.46	−	5752.93i	0.223201	−	0.386595i
$606$		0			0
$607$	14174.9	−	8183.87i	0.947842	−	0.547237i	0.0554324	−	0.998462i	$-0.482346\pi$
$607$	14174.9	−	8183.87i	0.947842	−	0.547237i	0.892410	+	0.451225i	$0.149013\pi$
$608$		0			0
$609$	4049.55	−	1557.21i	0.269451	−	0.103614i
$610$		0			0
$611$	−12857.6	+	7423.32i	−0.851328	+	0.491514i
$612$		0			0
$613$	10423.9	−	18054.7i	0.686814	−	1.18960i	−0.286049	−	0.958215i	$-0.592342\pi$
$613$	10423.9	−	18054.7i	0.686814	−	1.18960i	0.972863	−	0.231381i	$-0.0743245\pi$
$614$		0			0
$615$	−9065.85	−	24051.3i	−0.594423	−	1.57698i
$616$		0			0
$617$			2420.87i			0.157959i	0.996876	+	0.0789793i	$0.0251661\pi$
$617$			2420.87i			0.157959i	−0.996876	+	0.0789793i	$0.974834\pi$
$618$		0			0
$619$	−18668.5	−	10778.2i	−1.21220	−	0.699862i	−0.248959	−	0.968514i	$-0.580088\pi$
$619$	−18668.5	−	10778.2i	−1.21220	−	0.699862i	−0.963237	+	0.268653i	$0.913422\pi$
$620$		0			0
$621$	−12117.4	+	414.656i	−0.783017	+	0.0267948i
$622$		0			0
$623$	6107.99	−	10743.4i	0.392795	−	0.690893i
$624$		0			0
$625$	5906.31	+	10230.0i	0.378004	+	0.654722i
$626$		0			0
$627$	−21336.3	−	3511.81i	−1.35899	−	0.223681i
$628$		0			0
$629$	34726.3			2.20132
$630$		0			0
$631$	−24199.6			−1.52674			−0.763368	−	0.645964i	$-0.776456\pi$
$631$	−24199.6			−1.52674			−0.763368	+	0.645964i	$0.776456\pi$
$632$		0			0
$633$	475.146	+	78.2059i	0.0298347	+	0.00491060i
$634$		0			0
$635$	1317.84	+	2282.57i	0.0823573	+	0.142647i
$636$		0			0
$637$	21531.7	+	12053.0i	1.33927	+	0.749700i
$638$		0			0
$639$	3901.60	−	11531.1i	0.241541	−	0.713873i
$640$		0			0
$641$	731.695	+	422.445i	0.0450862	+	0.0260305i	0.522374	−	0.852717i	$-0.325047\pi$
$641$	731.695	+	422.445i	0.0450862	+	0.0260305i	−0.477287	+	0.878747i	$0.658380\pi$
$642$		0			0
$643$			27219.9i			1.66944i	0.550676	+	0.834719i	$0.314370\pi$
$643$			27219.9i			1.66944i	−0.550676	+	0.834719i	$0.685630\pi$
$644$		0			0
$645$	−4690.61	−	12444.0i	−0.286345	−	0.759662i
$646$		0			0
$647$	−4462.47	+	7729.23i	−0.271156	+	0.469656i	−0.969158	−	0.246440i	$-0.920739\pi$
$647$	−4462.47	+	7729.23i	−0.271156	+	0.469656i	0.698002	+	0.716096i	$0.254073\pi$
$648$		0			0
$649$	−21847.7	+	12613.8i	−1.32142	+	0.762919i
$650$		0			0
$651$	−1916.60	+	12147.1i	−0.115388	+	0.731310i
$652$		0			0
$653$	2771.82	−	1600.31i	0.166110	−	0.0959036i	−0.414640	−	0.909985i	$-0.636093\pi$
$653$	2771.82	−	1600.31i	0.166110	−	0.0959036i	0.580750	+	0.814082i	$0.302759\pi$
$654$		0			0
$655$	3733.45	−	6466.53i	0.222715	−	0.385753i
$656$		0			0
$657$	12626.6	+	14369.2i	0.749787	+	0.853266i
$658$		0			0
$659$			23233.0i			1.37334i	0.726972	+	0.686668i	$0.240927\pi$
$659$			23233.0i			1.37334i	−0.726972	+	0.686668i	$0.759073\pi$
$660$		0			0
$661$	20885.6	+	12058.3i	1.22898	+	0.709551i	0.966816	−	0.255473i	$-0.0822313\pi$
$661$	20885.6	+	12058.3i	1.22898	+	0.709551i	0.262162	+	0.965024i	$0.415565\pi$
$662$		0			0
$663$	26653.0	+	21851.5i	1.56126	+	1.28000i
$664$		0			0
$665$	−204.039	−	30735.2i	−0.0118982	−	1.79227i
$666$		0			0
$667$	−1948.10	−	3374.21i	−0.113090	−	0.195877i
$668$		0			0
$669$	2633.14	−	15997.8i	0.152172	−	0.924532i
$670$		0			0
$671$	14012.5			0.806181
$672$		0			0
$673$	2234.31			0.127974			0.0639869	−	0.997951i	$-0.479618\pi$
$673$	2234.31			0.127974			0.0639869	+	0.997951i	$0.479618\pi$
$674$		0			0
$675$	17896.8	−	11165.8i	1.02052	−	0.636697i
$676$		0			0
$677$	17006.4	+	29456.0i	0.965449	+	1.67221i	0.708403	+	0.705808i	$0.249416\pi$
$677$	17006.4	+	29456.0i	0.965449	+	1.67221i	0.257046	+	0.966399i	$0.417251\pi$
$678$		0			0
$679$	−18627.6	+	10920.2i	−1.05281	+	0.617198i
$680$		0			0
$681$	12602.2	−	15371.3i	0.709131	−	0.864950i
$682$		0			0
$683$	11045.9	+	6377.33i	0.618826	+	0.357279i	0.776412	−	0.630226i	$-0.217038\pi$
$683$	11045.9	+	6377.33i	0.618826	+	0.357279i	−0.157586	+	0.987505i	$0.550371\pi$
$684$		0			0
$685$			33335.8i			1.85941i
$686$		0			0
$687$	−11169.4	+	4210.15i	−0.620287	+	0.233809i
$688$		0			0
$689$	−7951.33	+	13772.1i	−0.439654	+	0.761503i
$690$		0			0
$691$	−13341.2	+	7702.57i	−0.734479	+	0.424051i	−0.820058	−	0.572280i	$-0.806059\pi$
$691$	−13341.2	+	7702.57i	−0.734479	+	0.424051i	0.0855797	+	0.996331i	$0.472726\pi$
$692$		0			0
$693$	−6537.60	+	19752.8i	−0.358359	+	1.08275i
$694$		0			0
$695$	−34498.0	+	19917.4i	−1.88285	+	1.08707i
$696$		0			0
$697$	−13742.2	+	23802.2i	−0.746805	+	1.29350i
$698$		0			0
$699$	24991.3	−	9420.14i	1.35230	−	0.509732i
$700$		0			0
$701$		−	28790.5i		−	1.55122i	−0.631215	−	0.775608i	$-0.717443\pi$
$701$		−	28790.5i		−	1.55122i	0.631215	−	0.775608i	$-0.282557\pi$
$702$		0			0
$703$	−32622.2	−	18834.5i	−1.75017	−	1.01046i
$704$		0			0
$705$	11281.8	−	13760.8i	0.602692	−	0.735122i
$706$		0			0
$707$	−21095.9	+	140.047i	−1.12220	+	0.00744980i
$708$		0			0
$709$	−4358.50	−	7549.15i	−0.230870	−	0.399879i	0.727194	−	0.686432i	$-0.240824\pi$
$709$	−4358.50	−	7549.15i	−0.230870	−	0.399879i	−0.958064	+	0.286553i	$0.907491\pi$
$710$		0			0
$711$	3943.96	+	19725.8i	0.208031	+	1.04047i
$712$		0			0
$713$	11043.4			0.580052
$714$		0			0
$715$	49672.0			2.59808
$716$		0			0
$717$	−3849.21	+	23386.2i	−0.200490	+	1.21809i
$718$		0			0
$719$	−11357.0	−	19670.9i	−0.589075	−	1.02031i	−0.994354	−	0.106114i	$-0.966159\pi$
$719$	−11357.0	−	19670.9i	−0.589075	−	1.02031i	0.405279	−	0.914193i	$-0.367174\pi$
$720$		0			0
$721$	−17109.4	−	9727.28i	−0.883757	−	0.502445i
$722$		0			0
$723$	9732.52	+	7979.23i	0.500631	+	0.410444i
$724$		0			0
$725$	5870.49	+	3389.33i	0.300724	+	0.173623i
$726$		0			0
$727$			3053.19i			0.155759i	0.996963	+	0.0778794i	$0.0248149\pi$
$727$			3053.19i			0.155759i	−0.996963	+	0.0778794i	$0.975185\pi$
$728$		0			0
$729$	10983.7	+	16333.3i	0.558032	+	0.829820i
$730$		0			0
$731$	−7110.12	+	12315.1i	−0.359750	+	0.623106i
$732$		0			0
$733$	−19325.0	+	11157.3i	−0.973787	+	0.562216i	−0.900389	−	0.435086i	$-0.856718\pi$
$733$	−19325.0	+	11157.3i	−0.973787	+	0.562216i	−0.0733987	+	0.997303i	$0.523385\pi$
$734$		0			0
$735$	−29243.4	−	4415.34i	−1.46757	−	0.221581i
$736$		0			0
$737$	1116.32	−	644.509i	0.0557941	−	0.0322127i
$738$		0			0
$739$	−3328.38	+	5764.91i	−0.165678	+	0.286963i	−0.936896	−	0.349608i	$-0.886315\pi$
$739$	−3328.38	+	5764.91i	−0.165678	+	0.286963i	0.771218	+	0.636572i	$0.219648\pi$
$740$		0			0
$741$	−13186.5	−	34983.2i	−0.653735	−	1.73433i
$742$		0			0
$743$		−	15251.1i		−	0.753041i	−0.926408	−	0.376520i	$-0.877120\pi$
$743$		−	15251.1i		−	0.753041i	0.926408	−	0.376520i	$-0.122880\pi$
$744$		0			0
$745$	−30561.2	−	17644.5i	−1.50292	−	0.867711i
$746$		0			0
$747$	27053.5	+	9153.64i	1.32508	+	0.448346i
$748$		0			0
$749$	−7491.59	−	4259.21i	−0.365470	−	0.207781i
$750$		0			0
$751$	15011.8	+	26001.2i	0.729411	+	1.26338i	0.957132	+	0.289651i	$0.0935392\pi$
$751$	15011.8	+	26001.2i	0.729411	+	1.26338i	−0.227721	+	0.973726i	$0.573128\pi$
$752$		0			0
$753$	11913.1	+	1960.82i	0.576544	+	0.0948952i
$754$		0			0
$755$	25384.9			1.22364
$756$		0			0
$757$	28779.9			1.38180			0.690901	−	0.722949i	$-0.257214\pi$
$757$	28779.9			1.38180			0.690901	+	0.722949i	$0.257214\pi$
$758$		0			0
$759$	18436.7	+	3034.56i	0.881701	+	0.145122i
$760$		0			0
$761$	−14841.5	−	25706.2i	−0.706969	−	1.22451i	−0.965976	−	0.258631i	$-0.916729\pi$
$761$	−14841.5	−	25706.2i	−0.706969	−	1.22451i	0.259007	−	0.965875i	$-0.416605\pi$
$762$		0			0
$763$	679.223	−	4.50908i	0.0322274	−	0.000213945i
$764$		0			0
$765$	−39129.2	−	13239.5i	−1.84931	−	0.625719i
$766$		0			0
$767$	−37773.9	−	21808.8i	−1.77828	−	1.02669i
$768$		0			0
$769$			16261.1i			0.762534i	0.924465	+	0.381267i	$0.124512\pi$
$769$			16261.1i			0.762534i	−0.924465	+	0.381267i	$0.875488\pi$
$770$		0			0
$771$	−8829.86	−	23425.3i	−0.412451	−	1.09422i
$772$		0			0
$773$	8515.09	−	14748.6i	0.396205	−	0.686248i	−0.597049	−	0.802205i	$-0.703660\pi$
$773$	8515.09	−	14748.6i	0.396205	−	0.686248i	0.993254	+	0.115957i	$0.0369935\pi$
$774$		0			0
$775$	−16639.3	+	9606.69i	−0.771226	+	0.445268i
$776$		0			0
$777$	−22793.8	+	28181.8i	−1.05241	+	1.30118i
$778$		0			0
$779$	25819.1	−	14906.7i	1.18750	−	0.685606i
$780$		0			0
$781$	−9380.03	+	16246.7i	−0.429762	+	0.744369i
$782$		0			0
$783$	−2973.38	+	5582.68i	−0.135709	+	0.254800i
$784$		0			0
$785$			12133.0i			0.551648i
$786$		0			0
$787$	14775.6	+	8530.69i	0.669242	+	0.386387i	0.795789	−	0.605574i	$-0.207056\pi$
$787$	14775.6	+	8530.69i	0.669242	+	0.386387i	−0.126548	+	0.991961i	$0.540390\pi$
$788$		0			0
$789$	19020.5	+	15594.0i	0.858234	+	0.703625i
$790$		0			0
$791$	8841.89	−	5183.43i	0.397448	−	0.232998i
$792$		0			0
$793$	12113.6	+	20981.3i	0.542453	+	0.939557i
$794$		0			0
$795$	3095.50	−	18807.0i	0.138096	−	0.839013i
$796$		0			0
$797$	−29152.4			−1.29565			−0.647823	−	0.761791i	$-0.724321\pi$
$797$	−29152.4			−1.29565			−0.647823	+	0.761791i	$0.724321\pi$
$798$		0			0
$799$	−19027.4			−0.842481
$800$		0			0
$801$	3532.35	+	17667.1i	0.155817	+	0.779321i
$802$		0			0
$803$	−14739.4	−	25529.4i	−0.647748	−	1.12193i
$804$		0			0
$805$	176.310	+	26558.4i	0.00771941	+	1.16281i
$806$		0			0
$807$	20929.0	−	25527.8i	0.912932	−	1.11353i
$808$		0			0
$809$	−23571.9	−	13609.3i	−1.02441	−	0.591441i	−0.109029	−	0.994039i	$-0.534774\pi$
$809$	−23571.9	−	13609.3i	−1.02441	−	0.591441i	−0.915377	+	0.402598i	$0.868107\pi$
$810$		0			0
$811$			36722.8i			1.59003i	0.606591	+	0.795014i	$0.292537\pi$
$811$			36722.8i			1.59003i	−0.606591	+	0.795014i	$0.707463\pi$
$812$		0			0
$813$	−12392.8	+	4671.31i	−0.534606	+	0.201513i
$814$		0			0
$815$	−6758.47	+	11706.0i	−0.290477	+	0.503121i
$816$		0			0
$817$	13358.6	−	7712.61i	0.572044	−	0.330270i
$818$		0			0
$819$	−35228.0	+	7287.00i	−1.50301	+	0.310902i
$820$		0			0
$821$	−19548.0	+	11286.0i	−0.830974	+	0.479763i	−0.854186	−	0.519967i	$-0.825944\pi$
$821$	−19548.0	+	11286.0i	−0.830974	+	0.479763i	0.0232120	+	0.999731i	$0.492611\pi$
$822$		0			0
$823$	17102.5	−	29622.4i	0.724370	−	1.25465i	−0.234863	−	0.972029i	$-0.575464\pi$
$823$	17102.5	−	29622.4i	0.724370	−	1.25465i	0.959233	−	0.282617i	$-0.0912027\pi$
$824$		0			0
$825$	−30418.8	+	11466.0i	−1.28369	+	0.483872i
$826$		0			0
$827$		−	24956.1i		−	1.04935i	−0.851304	−	0.524674i	$-0.824187\pi$
$827$		−	24956.1i		−	1.04935i	0.851304	−	0.524674i	$-0.175813\pi$
$828$		0			0
$829$	−27970.1	−	16148.5i	−1.17182	−	0.676552i	−0.217714	−	0.976013i	$-0.569860\pi$
$829$	−27970.1	−	16148.5i	−1.17182	−	0.676552i	−0.954109	+	0.299460i	$0.903193\pi$
$830$		0			0
$831$	15580.5	−	19004.1i	0.650400	−	0.793313i
$832$		0			0
$833$	16174.4	+	27175.1i	0.672760	+	1.13033i
$834$		0			0
$835$	8242.12	+	14275.8i	0.341593	+	0.591657i
$836$		0			0
$837$	−9489.69	−	15210.4i	−0.391890	−	0.628133i
$838$		0			0
$839$	−23250.5			−0.956731			−0.478365	−	0.878161i	$-0.658771\pi$
$839$	−23250.5			−0.956731			−0.478365	+	0.878161i	$0.658771\pi$
$840$		0			0
$841$	22356.4			0.916660
$842$		0			0
$843$	−2619.92	+	15917.5i	−0.107040	+	0.650332i
$844$		0			0
$845$	24712.2	+	42802.7i	1.00606	+	1.74255i
$846$		0			0
$847$	3664.34	−	6445.27i	0.148652	−	0.261466i
$848$		0			0
$849$	12558.7	+	10296.3i	0.507671	+	0.416215i
$850$		0			0
$851$	28189.0	+	16274.9i	1.13549	+	0.655578i
$852$		0			0
$853$			6705.16i			0.269145i	0.990904	+	0.134572i	$0.0429661\pi$
$853$			6705.16i			0.269145i	−0.990904	+	0.134572i	$0.957034\pi$
$854$		0			0
$855$	29577.7	+	33659.8i	1.18308	+	1.34636i
$856$		0			0
$857$	3136.56	−	5432.69i	0.125021	−	0.216543i	−0.796720	−	0.604348i	$-0.793434\pi$
$857$	3136.56	−	5432.69i	0.125021	−	0.216543i	0.921741	+	0.387806i	$0.126767\pi$
$858$		0			0
$859$	9239.39	−	5334.37i	0.366990	−	0.211882i	−0.305153	−	0.952303i	$-0.598708\pi$
$859$	9239.39	−	5334.37i	0.366990	−	0.211882i	0.672142	+	0.740422i	$0.265374\pi$
$860$		0			0
$861$	−10296.3	−	26775.7i	−0.407546	−	1.05983i
$862$		0			0
$863$	17034.3	−	9834.75i	0.671905	−	0.387925i	−0.124893	−	0.992170i	$-0.539859\pi$
$863$	17034.3	−	9834.75i	0.671905	−	0.387925i	0.796798	+	0.604246i	$0.206525\pi$
$864$		0			0
$865$	30696.4	−	53167.7i	1.20660	−	2.08989i
$866$		0			0
$867$	6575.34	+	17444.1i	0.257566	+	0.683314i
$868$		0			0
$869$		−	31000.6i		−	1.21015i
$870$		0			0
$871$	1930.08	+	1114.33i	0.0750841	+	0.0433498i
$872$		0			0
$873$	10089.1	−	29818.3i	0.391140	−	1.15601i
$874$		0			0
$875$	−3940.91	−	6722.40i	−0.152259	−	0.259724i
$876$		0			0
$877$	−4189.33	−	7256.13i	−0.161304	−	0.279386i	0.774033	−	0.633146i	$-0.218237\pi$
$877$	−4189.33	−	7256.13i	−0.161304	−	0.279386i	−0.935337	+	0.353759i	$0.884903\pi$
$878$		0			0
$879$	17806.9	+	2930.90i	0.683289	+	0.112465i
$880$		0			0
$881$	−24758.7			−0.946814			−0.473407	−	0.880844i	$-0.656976\pi$
$881$	−24758.7			−0.946814			−0.473407	+	0.880844i	$0.656976\pi$
$882$		0			0
$883$	−34812.0			−1.32675			−0.663374	−	0.748288i	$-0.730876\pi$
$883$	−34812.0			−1.32675			−0.663374	+	0.748288i	$0.730876\pi$
$884$		0			0
$885$	51583.5	+	8490.31i	1.95928	+	0.322484i
$886$		0			0
$887$	7366.01	+	12758.3i	0.278835	+	0.482956i	0.971095	−	0.238692i	$-0.0767185\pi$
$887$	7366.01	+	12758.3i	0.278835	+	0.482956i	−0.692261	+	0.721647i	$0.743385\pi$
$888$		0			0
$889$	1487.71	+	2537.73i	0.0561262	+	0.0957399i
$890$		0			0
$891$	−11663.3	−	28001.1i	−0.438536	−	1.05283i
$892$		0			0
$893$	17874.6	+	10319.9i	0.669820	+	0.386721i
$894$		0			0
$895$			27976.6i			1.04487i
$896$		0			0
$897$	11394.5	+	30229.1i	0.424137	+	1.12522i
$898$		0			0
$899$	2880.56	−	4989.28i	0.106866	−	0.185097i
$900$		0			0
$901$	−17650.3	+	10190.4i	−0.652627	+	0.376795i
$902$		0			0
$903$	−5327.24	−	13853.6i	−0.196323	−	0.510541i
$904$		0			0
$905$	−8969.69	+	5178.65i	−0.329461	+	0.190215i
$906$		0			0
$907$	−16011.0	+	27731.8i	−0.586147	+	1.01524i	0.408584	+	0.912721i	$0.366023\pi$
$907$	−16011.0	+	27731.8i	−0.586147	+	1.01524i	−0.994731	+	0.102516i	$0.967311\pi$
$908$		0			0
$909$	23103.2	−	20301.4i	0.842999	−	0.740764i
$910$		0			0
$911$			20643.5i			0.750767i	0.926869	+	0.375384i	$0.122489\pi$
$911$			20643.5i			0.750767i	−0.926869	+	0.375384i	$0.877511\pi$
$912$		0			0
$913$	−38116.8	−	22006.8i	−1.38169	−	0.797719i
$914$		0			0
$915$	−22455.2	−	18410.0i	−0.811308	−	0.665153i
$916$		0			0
$917$	4118.87	−	7244.75i	0.148328	−	0.260897i
$918$		0			0
$919$	−18121.5	−	31387.4i	−0.650462	−	1.12663i	−0.983011	−	0.183547i	$-0.941242\pi$
$919$	−18121.5	−	31387.4i	−0.650462	−	1.12663i	0.332549	−	0.943086i	$-0.392091\pi$
$920$		0			0
$921$	−4921.48	+	29900.8i	−0.176078	+	1.06978i
$922$		0			0
$923$	−32435.5			−1.15669
$924$		0			0
$925$	−56630.6			−2.01298
$926$		0			0
$927$	28135.8	−	5625.45i	0.996871	−	0.199314i
$928$		0			0
$929$	16984.4	+	29417.9i	0.599828	+	1.03893i	0.992846	+	0.119402i	$0.0380977\pi$
$929$	16984.4	+	29417.9i	0.599828	+	1.03893i	−0.393018	+	0.919531i	$0.628569\pi$
$930$		0			0
$931$	−455.442	−	34301.1i	−0.0160328	−	1.20749i
$932$		0			0
$933$	32603.5	−	39767.5i	1.14404	−	1.39542i
$934$		0			0
$935$	55130.8	+	31829.8i	1.92831	+	1.11331i
$936$		0			0
$937$			14636.9i			0.510318i	0.966899	+	0.255159i	$0.0821279\pi$
$937$			14636.9i			0.510318i	−0.966899	+	0.255159i	$0.917872\pi$
$938$		0			0
$939$	41643.9	−	15697.1i	1.44728	−	0.545534i
$940$		0			0
$941$	16015.3	−	27739.3i	0.554818	−	0.960973i	−0.443099	−	0.896472i	$-0.646121\pi$
$941$	16015.3	−	27739.3i	0.554818	−	0.960973i	0.997918	−	0.0645009i	$-0.0205455\pi$
$942$		0			0
$943$	−22310.4	+	12880.9i	−0.770441	+	0.444814i
$944$		0			0
$945$	36428.2	−	23064.8i	1.25398	−	0.793966i
$946$		0			0
$947$	4795.10	−	2768.45i	0.164540	−	0.0949974i	−0.415469	−	0.909608i	$-0.636382\pi$
$947$	4795.10	−	2768.45i	0.164540	−	0.0949974i	0.580009	+	0.814610i	$0.303049\pi$
$948$		0			0
$949$	25483.9	−	44139.3i	0.871698	−	1.50982i
$950$		0			0
$951$	−18334.4	+	6910.92i	−0.625167	+	0.235649i
$952$		0			0
$953$			36036.5i			1.22491i	0.790506	+	0.612454i	$0.209818\pi$
$953$			36036.5i			1.22491i	−0.790506	+	0.612454i	$0.790182\pi$
$954$		0			0
$955$	−40428.6	−	23341.5i	−1.36988	−	0.790903i
$956$		0			0
$957$	6180.05	−	7538.00i	0.208749	−	0.254617i
$958$		0			0
$959$	246.988	+	37205.0i	0.00831666	+	1.25277i
$960$		0			0
$961$	−6730.85	−	11658.2i	−0.225936	−	0.391332i
$962$		0			0
$963$	12319.6	−	2463.17i	0.412247	−	0.0824244i
$964$		0			0
$965$	−9017.02			−0.300796
$966$		0			0
$967$	56255.8			1.87080			0.935400	−	0.353591i	$-0.115040\pi$
$967$	56255.8			1.87080			0.935400	+	0.353591i	$0.115040\pi$
$968$		0			0
$969$	7781.60	−	47277.7i	0.257978	−	1.56737i
$970$		0			0
$971$	13498.6	+	23380.2i	0.446128	+	0.772716i	0.998130	−	0.0611266i	$-0.0194693\pi$
$971$	13498.6	+	23380.2i	0.446128	+	0.772716i	−0.552002	+	0.833843i	$0.686136\pi$
$972$		0			0
$973$	−38354.5	+	22484.8i	−1.26371	+	0.740831i
$974$		0			0
$975$	−43464.9	−	35634.8i	−1.42768	−	1.17049i
$976$		0			0
$977$	2971.88	+	1715.82i	0.0973172	+	0.0561861i	0.547869	−	0.836564i	$-0.315439\pi$
$977$	2971.88	+	1715.82i	0.0973172	+	0.0561861i	−0.450552	+	0.892750i	$0.648773\pi$
$978$		0			0
$979$		−	27765.3i		−	0.906418i
$980$		0			0
$981$	−743.854	+	653.643i	−0.0242094	+	0.0212734i
$982$		0			0
$983$	17017.3	−	29474.7i	0.552153	−	0.956357i	−0.445966	−	0.895050i	$-0.647140\pi$
$983$	17017.3	−	29474.7i	0.552153	−	0.956357i	0.998119	−	0.0613068i	$-0.0195268\pi$
$984$		0			0
$985$	18706.5	−	10800.2i	0.605115	−	0.349363i
$986$		0			0
$987$	12489.3	−	15441.6i	0.402775	−	0.497984i
$988$		0			0
$989$	−11543.2	+	6664.49i	−0.371136	+	0.214276i
$990$		0			0
$991$	−8251.21	+	14291.5i	−0.264489	+	0.458108i	−0.967430	−	0.253140i	$-0.918537\pi$
$991$	−8251.21	+	14291.5i	−0.264489	+	0.458108i	0.702941	+	0.711248i	$0.251870\pi$
$992$		0			0
$993$	−19795.2	−	52516.0i	−0.632611	−	1.67829i
$994$		0			0
$995$			7968.06i			0.253874i
$996$		0			0
$997$	43733.5	+	25249.5i	1.38922	+	0.802067i	0.993227	−	0.116186i	$-0.0370670\pi$
$997$	43733.5	+	25249.5i	1.38922	+	0.802067i	0.395993	+	0.918253i	$0.370400\pi$
$998$		0			0
$999$	−1807.18	−	52810.8i	−0.0572339	−	1.67253i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.bc.f.17.2		48
3.2	odd	2	inner	336.4.bc.f.17.7		48
4.3	odd	2		168.4.u.a.17.23	yes	48
7.5	odd	6	inner	336.4.bc.f.257.7		48
12.11	even	2		168.4.u.a.17.18	✓	48
21.5	even	6	inner	336.4.bc.f.257.2		48
28.19	even	6		168.4.u.a.89.18	yes	48
84.47	odd	6		168.4.u.a.89.23	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.u.a.17.18	✓	48	12.11	even	2
168.4.u.a.17.23	yes	48	4.3	odd	2
168.4.u.a.89.18	yes	48	28.19	even	6
168.4.u.a.89.23	yes	48	84.47	odd	6
336.4.bc.f.17.2		48	1.1	even	1	trivial
336.4.bc.f.17.7		48	3.2	odd	2	inner
336.4.bc.f.257.2		48	21.5	even	6	inner
336.4.bc.f.257.7		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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-5.12717 - 0.843898i) q^{3} +(-8.29692 - 14.3707i) q^{5} +(-9.36640 - 15.9772i) q^{7} +(25.5757 + 8.65361i) q^{9} +(-36.0346 - 20.8046i) q^{11} -71.9408i q^{13} +(30.4123 + 80.6827i) q^{15} +(46.0996 - 79.8469i) q^{17} +(-86.6129 + 50.0060i) q^{19} +(34.5400 + 89.8220i) q^{21} +(74.8424 - 43.2103i) q^{23} +(-75.1779 + 130.212i) q^{25} +(-123.828 - 65.9517i) q^{27} -45.0841i q^{29} +(110.666 + 63.8931i) q^{31} +(167.198 + 137.078i) q^{33} +(-151.891 + 267.163i) q^{35} +(188.322 + 326.183i) q^{37} +(-60.7106 + 368.852i) q^{39} -298.098 q^{41} -154.234 q^{43} +(-87.8411 - 439.338i) q^{45} +(-103.187 - 178.724i) q^{47} +(-167.541 + 299.297i) q^{49} +(-303.743 + 370.485i) q^{51} +(-191.437 - 110.526i) q^{53} +690.456i q^{55} +(486.279 - 183.297i) q^{57} +(303.149 - 525.070i) q^{59} +(-291.647 + 168.383i) q^{61} +(-101.292 - 489.681i) q^{63} +(-1033.84 + 596.887i) q^{65} +(-15.4896 + 26.8287i) q^{67} +(-420.195 + 158.387i) q^{69} -450.864i q^{71} +(613.551 + 354.234i) q^{73} +(495.335 - 604.176i) q^{75} +(5.11567 + 770.596i) q^{77} +(372.522 + 645.226i) q^{79} +(579.230 + 442.644i) q^{81} +1057.78 q^{83} -1529.94 q^{85} +(-38.0464 + 231.154i) q^{87} +(333.644 + 577.888i) q^{89} +(-1149.41 + 673.826i) q^{91} +(-513.484 - 420.981i) q^{93} +(1437.24 + 829.791i) q^{95} -1165.89i q^{97} +(-741.575 - 843.921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{7} + 14 q^{9} + 88 q^{15} + 270 q^{19} + 50 q^{21} - 438 q^{25} - 216 q^{31} - 372 q^{33} + 66 q^{37} - 242 q^{39} - 900 q^{43} - 294 q^{45} + 60 q^{49} + 138 q^{51} + 1384 q^{57} + 108 q^{61}+ \cdots - 1988 q^{99}+O(q^{100}) \) 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

Fields

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Database

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