LMFDB - Embedded newform 252.4.w.a.5.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(5,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 5]))

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

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

chi := DirichletCharacter("252.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.w (of order $6$, degree $2$, 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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.17
Character	$\chi$	$=$	252.5
Dual form			252.4.w.a.101.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.04499 - 4.21047i) q^{3} +(-4.90701 - 8.49919i) q^{5} +(13.1134 - 13.0781i) q^{7} +(-8.45605 - 25.6417i) q^{9} +O(q^{10})$	\(q+(3.04499 - 4.21047i) q^{3} +(-4.90701 - 8.49919i) q^{5} +(13.1134 - 13.0781i) q^{7} +(-8.45605 - 25.6417i) q^{9} +(-0.742316 - 0.428576i) q^{11} +(-7.39720 - 4.27078i) q^{13} +(-50.7274 - 5.21917i) q^{15} +(47.9292 + 83.0157i) q^{17} +(-129.161 - 74.5714i) q^{19} +(-15.1348 - 95.0365i) q^{21} +(30.7416 - 17.7487i) q^{23} +(14.3425 - 24.8420i) q^{25} +(-133.712 - 42.4748i) q^{27} +(-76.3034 + 44.0538i) q^{29} -39.0048i q^{31} +(-4.06485 + 1.82048i) q^{33} +(-175.501 - 47.2790i) q^{35} +(-107.015 + 185.355i) q^{37} +(-40.5064 + 18.1412i) q^{39} +(101.831 - 176.376i) q^{41} +(-58.4055 - 101.161i) q^{43} +(-176.440 + 197.694i) q^{45} +110.820 q^{47} +(0.924207 - 342.999i) q^{49} +(495.479 + 50.9782i) q^{51} +(-324.375 + 187.278i) q^{53} +8.41211i q^{55} +(-707.276 + 316.761i) q^{57} +592.918 q^{59} -580.381i q^{61} +(-446.233 - 225.661i) q^{63} +83.8270i q^{65} -199.385 q^{67} +(18.8777 - 183.481i) q^{69} -469.212i q^{71} +(444.818 - 256.816i) q^{73} +(-60.9234 - 136.032i) q^{75} +(-15.3393 + 4.08801i) q^{77} +195.541 q^{79} +(-585.990 + 433.654i) q^{81} +(210.760 + 365.047i) q^{83} +(470.378 - 814.718i) q^{85} +(-46.8563 + 455.417i) q^{87} +(-261.110 + 452.257i) q^{89} +(-152.857 + 40.7372i) q^{91} +(-164.228 - 118.769i) q^{93} +1463.69i q^{95} +(585.915 - 338.278i) q^{97} +(-4.71235 + 22.6583i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 12 * q^9	$ 48 q + 6 q^{7} + 12 q^{9} + 12 q^{11} - 36 q^{13} + 66 q^{15} - 72 q^{17} + 24 q^{21} + 30 q^{23} - 600 q^{25} - 396 q^{27} + 42 q^{29} + 390 q^{35} + 84 q^{37} - 840 q^{39} - 618 q^{41} - 42 q^{43} + 366 q^{45} + 396 q^{47} + 318 q^{49} - 738 q^{51} - 1620 q^{53} + 492 q^{57} + 1500 q^{59} + 672 q^{63} - 588 q^{67} - 924 q^{69} + 564 q^{75} - 2472 q^{77} + 1608 q^{79} + 2592 q^{81} - 360 q^{85} + 2640 q^{87} + 1722 q^{89} + 540 q^{91} + 660 q^{93} - 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 12 * q^9 + 12 * q^11 - 36 * q^13 + 66 * q^15 - 72 * q^17 + 24 * q^21 + 30 * q^23 - 600 * q^25 - 396 * q^27 + 42 * q^29 + 390 * q^35 + 84 * q^37 - 840 * q^39 - 618 * q^41 - 42 * q^43 + 366 * q^45 + 396 * q^47 + 318 * q^49 - 738 * q^51 - 1620 * q^53 + 492 * q^57 + 1500 * q^59 + 672 * q^63 - 588 * q^67 - 924 * q^69 + 564 * q^75 - 2472 * q^77 + 1608 * q^79 + 2592 * q^81 - 360 * q^85 + 2640 * q^87 + 1722 * q^89 + 540 * q^91 + 660 * q^93 - 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	3.04499	−	4.21047i	0.586009	−	0.810305i
$3$	3.04499	−	4.21047i	0.586009	−	0.810305i
$4$		0			0
$5$	−4.90701	−	8.49919i	−0.438896	−	0.760191i	0.558708	−	0.829364i	$-0.311297\pi$
$5$	−4.90701	−	8.49919i	−0.438896	−	0.760191i	−0.997605	+	0.0691735i	$0.977964\pi$
$6$		0			0
$7$	13.1134	−	13.0781i	0.708059	−	0.706153i
$7$	13.1134	−	13.0781i	0.708059	−	0.706153i
$8$		0			0
$9$	−8.45605	−	25.6417i	−0.313187	−	0.949691i
$10$		0			0
$11$	−0.742316	−	0.428576i	−0.0203470	−	0.0117473i	0.489792	−	0.871839i	$-0.337073\pi$
$11$	−0.742316	−	0.428576i	−0.0203470	−	0.0117473i	−0.510139	+	0.860092i	$0.670406\pi$
$12$		0			0
$13$	−7.39720	−	4.27078i	−0.157817	−	0.0911154i	0.419012	−	0.907981i	$-0.362377\pi$
$13$	−7.39720	−	4.27078i	−0.157817	−	0.0911154i	−0.576828	+	0.816865i	$0.695710\pi$
$14$		0			0
$15$	−50.7274	−	5.21917i	−0.873183	−	0.0898389i
$16$		0			0
$17$	47.9292	+	83.0157i	0.683796	+	1.18437i	0.973814	+	0.227348i	$0.0730055\pi$
$17$	47.9292	+	83.0157i	0.683796	+	1.18437i	−0.290018	+	0.957021i	$0.593661\pi$
$18$		0			0
$19$	−129.161	−	74.5714i	−1.55956	−	0.900413i	−0.997299	−	0.0734546i	$-0.976598\pi$
$19$	−129.161	−	74.5714i	−1.55956	−	0.900413i	−0.562263	−	0.826959i	$-0.690069\pi$
$20$		0			0
$21$	−15.1348	−	95.0365i	−0.157271	−	0.987556i
$22$		0			0
$23$	30.7416	−	17.7487i	0.278699	−	0.160907i	−0.354135	−	0.935194i	$-0.615225\pi$
$23$	30.7416	−	17.7487i	0.278699	−	0.160907i	0.632834	+	0.774287i	$0.281892\pi$
$24$		0			0
$25$	14.3425	−	24.8420i	0.114740	−	0.198736i
$26$		0			0
$27$	−133.712	−	42.4748i	−0.953070	−	0.302751i
$28$		0			0
$29$	−76.3034	+	44.0538i	−0.488593	+	0.282089i	−0.723991	−	0.689810i	$-0.757694\pi$
$29$	−76.3034	+	44.0538i	−0.488593	+	0.282089i	0.235398	+	0.971899i	$0.424361\pi$
$30$		0			0
$31$		−	39.0048i		−	0.225983i	−0.993596	−	0.112991i	$-0.963957\pi$
$31$		−	39.0048i		−	0.225983i	0.993596	−	0.112991i	$-0.0360432\pi$
$32$		0			0
$33$	−4.06485	+	1.82048i	−0.0214424	+	0.00960320i
$34$		0			0
$35$	−175.501	−	47.2790i	−0.847576	−	0.228332i
$36$		0			0
$37$	−107.015	+	185.355i	−0.475489	+	0.823571i	−0.999606	−	0.0280751i	$-0.991062\pi$
$37$	−107.015	+	185.355i	−0.475489	+	0.823571i	0.524117	+	0.851646i	$0.324396\pi$
$38$		0			0
$39$	−40.5064	+	18.1412i	−0.166313	+	0.0744850i
$40$		0			0
$41$	101.831	−	176.376i	0.387886	−	0.671837i	−0.604279	−	0.796772i	$-0.706539\pi$
$41$	101.831	−	176.376i	0.387886	−	0.671837i	0.992165	+	0.124935i	$0.0398723\pi$
$42$		0			0
$43$	−58.4055	−	101.161i	−0.207134	−	0.358766i	0.743677	−	0.668539i	$-0.233080\pi$
$43$	−58.4055	−	101.161i	−0.207134	−	0.358766i	−0.950810	+	0.309773i	$0.899747\pi$
$44$		0			0
$45$	−176.440	+	197.694i	−0.584490	+	0.654898i
$46$		0			0
$47$	110.820			0.343932			0.171966	−	0.985103i	$-0.444988\pi$
$47$	110.820			0.343932			0.171966	+	0.985103i	$0.444988\pi$
$48$		0			0
$49$	0.924207	−	342.999i	0.00269448	−	0.999996i
$50$		0			0
$51$	495.479	+	50.9782i	1.36041	+	0.139968i
$52$		0			0
$53$	−324.375	+	187.278i	−0.840685	+	0.485370i	−0.857497	−	0.514489i	$-0.827982\pi$
$53$	−324.375	+	187.278i	−0.840685	+	0.485370i	0.0168119	+	0.999859i	$0.494648\pi$
$54$		0			0
$55$			8.41211i			0.0206234i
$56$		0			0
$57$	−707.276	+	316.761i	−1.64353	+	0.736070i
$58$		0			0
$59$	592.918			1.30833			0.654164	−	0.756353i	$-0.273021\pi$
$59$	592.918			1.30833			0.654164	+	0.756353i	$0.273021\pi$
$60$		0			0
$61$		−	580.381i		−	1.21820i	−0.793093	−	0.609100i	$-0.791531\pi$
$61$		−	580.381i		−	1.21820i	0.793093	−	0.609100i	$-0.208469\pi$
$62$		0			0
$63$	−446.233	−	225.661i	−0.892383	−	0.451279i
$64$		0			0
$65$			83.8270i			0.159961i
$66$		0			0
$67$	−199.385			−0.363563			−0.181782	−	0.983339i	$-0.558186\pi$
$67$	−199.385			−0.363563			−0.181782	+	0.983339i	$0.558186\pi$
$68$		0			0
$69$	18.8777	−	183.481i	0.0329364	−	0.320124i
$70$		0			0
$71$		−	469.212i		−	0.784299i	−0.919902	−	0.392149i	$-0.871732\pi$
$71$		−	469.212i		−	0.784299i	0.919902	−	0.392149i	$-0.128268\pi$
$72$		0			0
$73$	444.818	−	256.816i	0.713179	−	0.411754i	−0.0990581	−	0.995082i	$-0.531583\pi$
$73$	444.818	−	256.816i	0.713179	−	0.411754i	0.812237	+	0.583328i	$0.198250\pi$
$74$		0			0
$75$	−60.9234	−	136.032i	−0.0937977	−	0.209435i
$76$		0			0
$77$	−15.3393	+	4.08801i	−0.0227023	+	0.00605028i
$78$		0			0
$79$	195.541			0.278483			0.139241	−	0.990258i	$-0.455534\pi$
$79$	195.541			0.278483			0.139241	+	0.990258i	$0.455534\pi$
$80$		0			0
$81$	−585.990	+	433.654i	−0.803828	+	0.594862i
$82$		0			0
$83$	210.760	+	365.047i	0.278722	+	0.482761i	0.971067	−	0.238805i	$-0.0767558\pi$
$83$	210.760	+	365.047i	0.278722	+	0.482761i	−0.692345	+	0.721566i	$0.743422\pi$
$84$		0			0
$85$	470.378	−	814.718i	0.600231	−	1.03963i
$86$		0			0
$87$	−46.8563	+	455.417i	−0.0577416	+	0.561216i
$88$		0			0
$89$	−261.110	+	452.257i	−0.310985	+	0.538642i	−0.978576	−	0.205887i	$-0.933992\pi$
$89$	−261.110	+	452.257i	−0.310985	+	0.538642i	0.667591	+	0.744528i	$0.267326\pi$
$90$		0			0
$91$	−152.857	+	40.7372i	−0.176085	+	0.0469276i
$92$		0			0
$93$	−164.228	−	118.769i	−0.183115	−	0.132428i
$94$		0			0
$95$			1463.69i			1.58075i
$96$		0			0
$97$	585.915	−	338.278i	0.613305	−	0.354092i	−0.160953	−	0.986962i	$-0.551457\pi$
$97$	585.915	−	338.278i	0.613305	−	0.354092i	0.774258	+	0.632870i	$0.218123\pi$
$98$		0			0
$99$	−4.71235	+	22.6583i	−0.00478393	+	0.0230024i
$100$		0			0
$101$	383.917	−	664.964i	0.378229	−	0.655113i	−0.612575	−	0.790412i	$-0.709866\pi$
$101$	383.917	−	664.964i	0.378229	−	0.655113i	0.990805	+	0.135300i	$0.0431997\pi$
$102$		0			0
$103$	1716.44	−	990.987i	1.64200	−	0.948008i	0.661875	−	0.749614i	$-0.269761\pi$
$103$	1716.44	−	990.987i	1.64200	−	0.948008i	0.980122	−	0.198394i	$-0.0635726\pi$
$104$		0			0
$105$	−733.467	+	594.979i	−0.681705	+	0.552990i
$106$		0			0
$107$	1814.21	+	1047.44i	1.63913	+	0.946351i	0.981135	+	0.193326i	$0.0619276\pi$
$107$	1814.21	+	1047.44i	1.63913	+	0.946351i	0.657993	+	0.753024i	$0.271406\pi$
$108$		0			0
$109$	736.566	+	1275.77i	0.647249	+	1.12107i	0.983777	+	0.179395i	$0.0574141\pi$
$109$	736.566	+	1275.77i	0.647249	+	1.12107i	−0.336528	+	0.941674i	$0.609253\pi$
$110$		0			0
$111$	454.571	+	1014.99i	0.388703	+	0.867911i
$112$		0			0
$113$	1952.03	+	1127.00i	1.62506	+	0.938226i	0.985539	+	0.169449i	$0.0541989\pi$
$113$	1952.03	+	1127.00i	1.62506	+	0.938226i	0.639517	+	0.768777i	$0.279134\pi$
$114$		0			0
$115$	−301.699	−	174.186i	−0.244640	−	0.141243i
$116$		0			0
$117$	−46.9587	+	225.791i	−0.0371055	+	0.178413i
$118$		0			0
$119$	1714.21	+	461.797i	1.32051	+	0.355738i
$120$		0			0
$121$	−665.133	−	1152.04i	−0.499724	−	0.865547i
$122$		0			0
$123$	−432.552	−	965.819i	−0.317089	−	0.708008i
$124$		0			0
$125$	−1508.27			−1.07923
$126$		0			0
$127$	−1292.13			−0.902821			−0.451410	−	0.892316i	$-0.649079\pi$
$127$	−1292.13			−0.902821			−0.451410	+	0.892316i	$0.649079\pi$
$128$		0			0
$129$	−603.780	−	62.1209i	−0.412092	−	0.0423988i
$130$		0			0
$131$	1373.51	+	2378.99i	0.916063	+	1.58667i	0.805338	+	0.592816i	$0.201984\pi$
$131$	1373.51	+	2378.99i	0.916063	+	1.58667i	0.110725	+	0.993851i	$0.464683\pi$
$132$		0			0
$133$	−2669.01	+	711.305i	−1.74009	+	0.463744i
$134$		0			0
$135$	295.125	+	1344.87i	0.188150	+	0.857391i
$136$		0			0
$137$	−837.319	−	483.426i	−0.522168	−	0.301474i	0.215653	−	0.976470i	$-0.430812\pi$
$137$	−837.319	−	483.426i	−0.522168	−	0.301474i	−0.737821	+	0.674996i	$0.764145\pi$
$138$		0			0
$139$	1274.68	+	735.938i	0.777821	+	0.449075i	0.835657	−	0.549251i	$-0.185087\pi$
$139$	1274.68	+	735.938i	0.777821	+	0.449075i	−0.0578366	+	0.998326i	$0.518420\pi$
$140$		0			0
$141$	337.446	−	466.605i	0.201547	−	0.278689i
$142$		0			0
$143$	3.66071	+	6.34053i	0.00214072	+	0.00370784i
$144$		0			0
$145$	748.844	+	432.345i	0.428883	+	0.247616i
$146$		0			0
$147$	−1441.37	−	1048.32i	−0.808723	−	0.588190i
$148$		0			0
$149$	646.020	−	372.980i	0.355195	−	0.205072i	−0.311776	−	0.950156i	$-0.600924\pi$
$149$	646.020	−	372.980i	0.355195	−	0.205072i	0.666971	+	0.745084i	$0.267591\pi$
$150$		0			0
$151$	980.874	−	1698.92i	0.528625	−	0.915606i	−0.470818	−	0.882231i	$-0.656041\pi$
$151$	980.874	−	1698.92i	0.528625	−	0.915606i	0.999443	−	0.0333753i	$-0.0106257\pi$
$152$		0			0
$153$	1723.37	−	1930.97i	0.910629	−	1.02032i
$154$		0			0
$155$	−331.509	+	191.397i	−0.171790	+	0.0991830i
$156$		0			0
$157$			707.562i			0.359679i	0.983696	+	0.179839i	$0.0575578\pi$
$157$			707.562i			0.359679i	−0.983696	+	0.179839i	$0.942442\pi$
$158$		0			0
$159$	−199.192	+	1936.03i	−0.0993517	+	0.965642i
$160$		0			0
$161$	171.008	−	634.789i	0.0837102	−	0.310735i
$162$		0			0
$163$	−326.853	+	566.126i	−0.157062	+	0.272039i	−0.933808	−	0.357775i	$-0.883536\pi$
$163$	−326.853	+	566.126i	−0.157062	+	0.272039i	0.776746	+	0.629814i	$0.216869\pi$
$164$		0			0
$165$	35.4189	+	25.6148i	0.0167113	+	0.0120855i
$166$		0			0
$167$	1281.22	−	2219.13i	0.593673	−	1.02827i	−0.400060	−	0.916489i	$-0.631011\pi$
$167$	1281.22	−	2219.13i	0.593673	−	1.02827i	0.993733	−	0.111783i	$-0.0356561\pi$
$168$		0			0
$169$	−1062.02	−	1839.47i	−0.483396	−	0.837266i
$170$		0			0
$171$	−819.939	+	3942.49i	−0.366680	+	1.76310i
$172$		0			0
$173$	−2744.02			−1.20592			−0.602959	−	0.797772i	$-0.706012\pi$
$173$	−2744.02			−1.20592			−0.602959	+	0.797772i	$0.706012\pi$
$174$		0			0
$175$	−136.807	−	513.337i	−0.0590951	−	0.221741i
$176$		0			0
$177$	1805.43	−	2496.46i	0.766692	−	1.06014i
$178$		0			0
$179$	−393.647	+	227.272i	−0.164372	+	0.0949002i	−0.579929	−	0.814667i	$-0.696920\pi$
$179$	−393.647	+	227.272i	−0.164372	+	0.0949002i	0.415557	+	0.909567i	$0.363587\pi$
$180$		0			0
$181$		−	3158.80i		−	1.29719i	−0.761132	−	0.648597i	$-0.775356\pi$
$181$		−	3158.80i		−	1.29719i	0.761132	−	0.648597i	$-0.224644\pi$
$182$		0			0
$183$	−2443.68	−	1767.26i	−0.987113	−	0.713876i
$184$		0			0
$185$	2100.49			0.834762
$186$		0			0
$187$		−	82.1652i		−	0.0321311i
$188$		0			0
$189$	−2308.91	+	1191.71i	−0.888618	+	0.458648i
$190$		0			0
$191$			1238.93i			0.469349i	0.972074	+	0.234675i	$0.0754024\pi$
$191$			1238.93i			0.469349i	−0.972074	+	0.234675i	$0.924598\pi$
$192$		0			0
$193$	811.724			0.302742			0.151371	−	0.988477i	$-0.451631\pi$
$193$	811.724			0.302742			0.151371	+	0.988477i	$0.451631\pi$
$194$		0			0
$195$	352.951	+	255.253i	0.129617	+	0.0937385i
$196$		0			0
$197$		−	4779.36i		−	1.72850i	−0.503060	−	0.864251i	$-0.667793\pi$
$197$		−	4779.36i		−	1.72850i	0.503060	−	0.864251i	$-0.332207\pi$
$198$		0			0
$199$	2804.07	−	1618.93i	0.998870	−	0.576698i	0.0909561	−	0.995855i	$-0.471008\pi$
$199$	2804.07	−	1618.93i	0.998870	−	0.576698i	0.907914	+	0.419157i	$0.137674\pi$
$200$		0			0
$201$	−607.125	+	839.503i	−0.213051	+	0.294597i
$202$		0			0
$203$	−424.458	+	1575.60i	−0.146754	+	0.544757i
$204$		0			0
$205$	−1998.74			−0.680966
$206$		0			0
$207$	−715.058	−	638.182i	−0.240097	−	0.214284i
$208$		0			0
$209$	63.9190	+	110.711i	0.0211549	+	0.0366413i
$210$		0			0
$211$	−198.197	+	343.288i	−0.0646657	+	0.112004i	−0.896546	−	0.442951i	$-0.853931\pi$
$211$	−198.197	+	343.288i	−0.0646657	+	0.112004i	0.831880	+	0.554956i	$0.187265\pi$
$212$		0			0
$213$	−1975.60	−	1428.75i	−0.635521	−	0.459606i
$214$		0			0
$215$	−573.192	+	992.798i	−0.181820	+	0.314922i
$216$		0			0
$217$	−510.110	−	511.486i	−0.159578	−	0.160009i
$218$		0			0
$219$	273.153	−	2654.90i	0.0842830	−	0.819184i
$220$		0			0
$221$		−	818.779i		−	0.249217i
$222$		0			0
$223$	2308.64	−	1332.90i	0.693265	−	0.400257i	−0.111569	−	0.993757i	$-0.535588\pi$
$223$	2308.64	−	1332.90i	0.693265	−	0.400257i	0.804834	+	0.593500i	$0.202254\pi$
$224$		0			0
$225$	−758.270	−	157.701i	−0.224673	−	0.0467262i
$226$		0			0
$227$	−2062.54	+	3572.43i	−0.603065	+	1.04454i	0.389289	+	0.921116i	$0.372721\pi$
$227$	−2062.54	+	3572.43i	−0.603065	+	1.04454i	−0.992354	+	0.123424i	$0.960613\pi$
$228$		0			0
$229$	−5468.65	+	3157.33i	−1.57807	+	0.911100i	−0.582944	+	0.812512i	$0.698099\pi$
$229$	−5468.65	+	3157.33i	−1.57807	+	0.911100i	−0.995128	+	0.0985879i	$0.968567\pi$
$230$		0			0
$231$	−29.4956	+	77.0335i	−0.00840115	+	0.0219413i
$232$		0			0
$233$	−4654.11	−	2687.05i	−1.30859	−	0.755513i	−0.326726	−	0.945119i	$-0.605945\pi$
$233$	−4654.11	−	2687.05i	−1.30859	−	0.755513i	−0.981860	+	0.189607i	$0.939279\pi$
$234$		0			0
$235$	−543.796	−	941.882i	−0.150950	−	0.261454i
$236$		0			0
$237$	595.422	−	823.320i	0.163193	−	0.225656i
$238$		0			0
$239$	−5514.37	−	3183.72i	−1.49245	−	0.861665i	−0.492484	−	0.870321i	$-0.663911\pi$
$239$	−5514.37	−	3183.72i	−1.49245	−	0.861665i	−0.999963	+	0.00865664i	$0.997244\pi$
$240$		0			0
$241$	2480.83	+	1432.31i	0.663088	+	0.382834i	0.793452	−	0.608632i	$-0.208282\pi$
$241$	2480.83	+	1432.31i	0.663088	+	0.382834i	−0.130365	+	0.991466i	$0.541615\pi$
$242$		0			0
$243$	41.5512	+	3787.77i	0.0109692	+	0.999940i
$244$		0			0
$245$	−2919.75	+	1675.24i	−0.761371	+	0.436846i
$246$		0			0
$247$	636.956	+	1103.24i	0.164083	+	0.284200i
$248$		0			0
$249$	2178.78	+	224.168i	0.554517	+	0.0570524i
$250$		0			0
$251$	4570.07			1.14925			0.574623	−	0.818418i	$-0.305149\pi$
$251$	4570.07			1.14925			0.574623	+	0.818418i	$0.305149\pi$
$252$		0			0
$253$	−30.4266			−0.00756089
$254$		0			0
$255$	−1998.05	−	4461.32i	−0.490677	−	1.09560i
$256$		0			0
$257$	396.198	+	686.235i	0.0961640	+	0.166561i	0.910094	−	0.414402i	$-0.136009\pi$
$257$	396.198	+	686.235i	0.0961640	+	0.166561i	−0.813930	+	0.580963i	$0.802676\pi$
$258$		0			0
$259$	1020.77	+	3830.19i	0.244894	+	0.918905i
$260$		0			0
$261$	1774.84	+	1584.03i	0.420919	+	0.375666i
$262$		0			0
$263$	−133.195	−	76.9004i	−0.0312288	−	0.0180300i	0.484304	−	0.874900i	$-0.339073\pi$
$263$	−133.195	−	76.9004i	−0.0312288	−	0.0180300i	−0.515533	+	0.856870i	$0.672406\pi$
$264$		0			0
$265$	3183.42	+	1837.95i	0.737947	+	0.426054i
$266$		0			0
$267$	1109.13	+	2476.51i	0.254224	+	0.567641i
$268$		0			0
$269$	−315.805	−	546.990i	−0.0715798	−	0.123980i	0.828014	−	0.560707i	$-0.189471\pi$
$269$	−315.805	−	546.990i	−0.0715798	−	0.123980i	−0.899594	+	0.436727i	$0.856137\pi$
$270$		0			0
$271$	−2574.64	−	1486.47i	−0.577116	−	0.333198i	0.182871	−	0.983137i	$-0.441461\pi$
$271$	−2574.64	−	1486.47i	−0.577116	−	0.333198i	−0.759986	+	0.649939i	$0.774794\pi$
$272$		0			0
$273$	−293.925	+	767.642i	−0.0651616	+	0.170182i
$274$		0			0
$275$	−21.2933	+	12.2937i	−0.00466922	+	0.00269578i
$276$		0			0
$277$	−2184.07	+	3782.93i	−0.473748	+	0.820556i	−0.999548	−	0.0300519i	$-0.990433\pi$
$277$	−2184.07	+	3782.93i	−0.473748	+	0.820556i	0.525800	+	0.850608i	$0.323766\pi$
$278$		0			0
$279$	−1000.15	+	329.826i	−0.214614	+	0.0707748i
$280$		0			0
$281$	−2133.94	+	1232.03i	−0.453026	+	0.261555i	−0.709107	−	0.705100i	$-0.750902\pi$
$281$	−2133.94	+	1232.03i	−0.453026	+	0.261555i	0.256081	+	0.966655i	$0.417569\pi$
$282$		0			0
$283$		−	2201.28i		−	0.462376i	−0.972909	−	0.231188i	$-0.925739\pi$
$283$		−	2201.28i		−	0.462376i	0.972909	−	0.231188i	$-0.0742612\pi$
$284$		0			0
$285$	6162.82	+	4456.92i	1.28089	+	0.926335i
$286$		0			0
$287$	−971.322	−	3644.66i	−0.199775	−	0.749607i
$288$		0			0
$289$	−2137.91	+	3702.97i	−0.435154	+	0.753708i
$290$		0			0
$291$	359.797	−	3497.03i	0.0724801	−	0.704465i
$292$		0			0
$293$	3509.21	−	6078.13i	0.699693	−	1.21190i	−0.268879	−	0.963174i	$-0.586653\pi$
$293$	3509.21	−	6078.13i	0.699693	−	1.21190i	0.968573	−	0.248731i	$-0.0800134\pi$
$294$		0			0
$295$	−2909.45	−	5039.32i	−0.574220	−	0.994579i
$296$		0			0
$297$	81.0528	+	88.8354i	0.0158356	+	0.0173561i
$298$		0			0
$299$	−303.203			−0.0586443
$300$		0			0
$301$	−2088.90	−	562.736i	−0.400007	−	0.107759i
$302$		0			0
$303$	−1630.78	−	3641.28i	−0.309195	−	0.690383i
$304$		0			0
$305$	−4932.77	+	2847.94i	−0.926064	+	0.534663i
$306$		0			0
$307$			1466.87i			0.272700i	0.990661	+	0.136350i	$0.0435371\pi$
$307$			1466.87i			0.272700i	−0.990661	+	0.136350i	$0.956463\pi$
$308$		0			0
$309$	1054.03	−	10244.6i	0.194050	−	1.88606i
$310$		0			0
$311$	9341.69			1.70327			0.851637	−	0.524132i	$-0.175610\pi$
$311$	9341.69			1.70327			0.851637	+	0.524132i	$0.175610\pi$
$312$		0			0
$313$			8503.31i			1.53558i	0.640703	+	0.767789i	$0.278643\pi$
$313$			8503.31i			1.53558i	−0.640703	+	0.767789i	$0.721357\pi$
$314$		0			0
$315$	271.737	+	4899.94i	0.0486052	+	0.876446i
$316$		0			0
$317$			2634.37i			0.466754i	0.972386	+	0.233377i	$0.0749777\pi$
$317$			2634.37i			0.466754i	−0.972386	+	0.233377i	$0.925022\pi$
$318$		0			0
$319$	75.5216			0.0132552
$320$		0			0
$321$	9934.46	−	4449.25i	1.72738	−	0.773622i
$322$		0			0
$323$		−	14296.6i		−	2.46280i
$324$		0			0
$325$	−212.189	+	122.507i	−0.0362158	+	0.0209092i
$326$		0			0
$327$	7614.42	+	783.422i	1.28770	+	0.132487i
$328$		0			0
$329$	1453.23	−	1449.32i	0.243524	−	0.242868i
$330$		0			0
$331$	4161.10			0.690980			0.345490	−	0.938422i	$-0.387713\pi$
$331$	4161.10			0.690980			0.345490	+	0.938422i	$0.387713\pi$
$332$		0			0
$333$	5657.73	+	1176.66i	0.931056	+	0.193636i
$334$		0			0
$335$	978.383	+	1694.61i	0.159567	+	0.276377i
$336$		0			0
$337$	−4779.71	+	8278.70i	−0.772604	+	1.33819i	0.163527	+	0.986539i	$0.447713\pi$
$337$	−4779.71	+	8278.70i	−0.772604	+	1.33819i	−0.936131	+	0.351650i	$0.885621\pi$
$338$		0			0
$339$	10689.1	−	4787.23i	1.71255	−	0.766981i
$340$		0			0
$341$	−16.7165	+	28.9538i	−0.00265469	+	0.00459806i
$342$		0			0
$343$	−4473.67	−	4509.98i	−0.704243	−	0.709959i
$344$		0			0
$345$	−1652.07	+	739.898i	−0.257811	+	0.115463i
$346$		0			0
$347$			1458.91i			0.225702i	0.993612	+	0.112851i	$0.0359982\pi$
$347$			1458.91i			0.225702i	−0.993612	+	0.112851i	$0.964002\pi$
$348$		0			0
$349$	−1446.76	+	835.287i	−0.221901	+	0.128114i	−0.606830	−	0.794832i	$-0.707559\pi$
$349$	−1446.76	+	835.287i	−0.221901	+	0.128114i	0.384929	+	0.922946i	$0.374226\pi$
$350$		0			0
$351$	807.695	+	885.249i	0.122825	+	0.134618i
$352$		0			0
$353$	−4648.03	+	8050.62i	−0.700820	+	1.21386i	0.267359	+	0.963597i	$0.413849\pi$
$353$	−4648.03	+	8050.62i	−0.700820	+	1.21386i	−0.968179	+	0.250259i	$0.919484\pi$
$354$		0			0
$355$	−3987.92	+	2302.43i	−0.596216	+	0.344226i
$356$		0			0
$357$	7164.13	−	5811.45i	1.06209	−	0.861553i
$358$		0			0
$359$	−5344.51	−	3085.65i	−0.785717	−	0.453634i	0.0527356	−	0.998609i	$-0.483206\pi$
$359$	−5344.51	−	3085.65i	−0.785717	−	0.453634i	−0.838453	+	0.544975i	$0.816539\pi$
$360$		0			0
$361$	7692.28	+	13323.4i	1.12149	+	1.94247i
$362$		0			0
$363$	−6875.96	−	707.445i	−0.994200	−	0.102290i
$364$		0			0
$365$	−4365.46	−	2520.40i	−0.626023	−	0.361435i
$366$		0			0
$367$	9263.14	+	5348.08i	1.31753	+	0.760674i	0.983330	−	0.181830i	$-0.0582020\pi$
$367$	9263.14	+	5348.08i	1.31753	+	0.760674i	0.334196	+	0.942504i	$0.391535\pi$
$368$		0			0
$369$	−5383.67	−	1119.67i	−0.759519	−	0.157961i
$370$		0			0
$371$	−1804.42	+	6698.08i	−0.252509	+	0.937323i
$372$		0			0
$373$	369.480	+	639.959i	0.0512894	+	0.0888359i	0.890530	−	0.454924i	$-0.150334\pi$
$373$	369.480	+	639.959i	0.0512894	+	0.0888359i	−0.839241	+	0.543760i	$0.817000\pi$
$374$		0			0
$375$	−4592.66	+	6350.51i	−0.632438	+	0.874504i
$376$		0			0
$377$	752.576			0.102811
$378$		0			0
$379$	−3002.36			−0.406915			−0.203457	−	0.979084i	$-0.565218\pi$
$379$	−3002.36			−0.406915			−0.203457	+	0.979084i	$0.565218\pi$
$380$		0			0
$381$	−3934.53	+	5440.48i	−0.529061	+	0.731560i
$382$		0			0
$383$	309.117	+	535.407i	0.0412406	+	0.0714309i	0.885909	−	0.463859i	$-0.153536\pi$
$383$	309.117	+	535.407i	0.0412406	+	0.0714309i	−0.844668	+	0.535290i	$0.820202\pi$
$384$		0			0
$385$	110.015	+	110.312i	0.0145633	+	0.0146026i
$386$		0			0
$387$	−2100.06	+	2353.04i	−0.275846	+	0.309074i
$388$		0			0
$389$	−529.948	−	305.966i	−0.0690731	−	0.0398794i	0.465066	−	0.885276i	$-0.346031\pi$
$389$	−529.948	−	305.966i	−0.0690731	−	0.0398794i	−0.534139	+	0.845397i	$0.679364\pi$
$390$		0			0
$391$	2946.84	+	1701.36i	0.381146	+	0.220055i
$392$		0			0
$393$	14199.0	+	1460.89i	1.82250	+	0.187511i
$394$		0			0
$395$	−959.524	−	1661.94i	−0.122225	−	0.211700i
$396$		0			0
$397$	10005.9	+	5776.92i	1.26494	+	0.730316i	0.974027	−	0.226433i	$-0.0727063\pi$
$397$	10005.9	+	5776.92i	1.26494	+	0.730316i	0.290917	+	0.956748i	$0.406040\pi$
$398$		0			0
$399$	−5132.17	+	13403.7i	−0.643935	+	1.68176i
$400$		0			0
$401$	3610.56	−	2084.56i	0.449633	−	0.259596i	−0.258042	−	0.966134i	$-0.583077\pi$
$401$	3610.56	−	2084.56i	0.449633	−	0.259596i	0.707675	+	0.706538i	$0.249744\pi$
$402$		0			0
$403$	−166.581	+	288.526i	−0.0205905	+	0.0356638i
$404$		0			0
$405$	6561.17	+	2852.50i	0.805006	+	0.349980i
$406$		0			0
$407$	158.877	−	91.7278i	0.0193495	−	0.0111714i
$408$		0			0
$409$		−	6671.93i		−	0.806615i	−0.915065	−	0.403307i	$-0.867861\pi$
$409$		−	6671.93i		−	0.806615i	0.915065	−	0.403307i	$-0.132139\pi$
$410$		0			0
$411$	−4585.08	+	2053.47i	−0.550280	+	0.246449i
$412$		0			0
$413$	7775.19	−	7754.27i	0.926373	−	0.923880i
$414$		0			0
$415$	2068.41	−	3582.58i	0.244660	−	0.423764i
$416$		0			0
$417$	6980.04	−	3126.08i	0.819698	−	0.367110i
$418$		0			0
$419$	−7527.22	+	13037.5i	−0.877634	+	1.52011i	−0.0237046	+	0.999719i	$0.507546\pi$
$419$	−7527.22	+	13037.5i	−0.877634	+	1.52011i	−0.853930	+	0.520388i	$0.825787\pi$
$420$		0			0
$421$	−300.115	−	519.814i	−0.0347427	−	0.0601762i	0.848131	−	0.529786i	$-0.177728\pi$
$421$	−300.115	−	519.814i	−0.0347427	−	0.0601762i	−0.882874	+	0.469610i	$0.844395\pi$
$422$		0			0
$423$	−937.101	−	2841.61i	−0.107715	−	0.326629i
$424$		0			0
$425$	2749.70			0.313835
$426$		0			0
$427$	−7590.31	−	7610.79i	−0.860236	−	0.862557i
$428$		0			0
$429$	37.8434	+	3.89358i	0.00425897	+	0.000438191i
$430$		0			0
$431$	−1212.37	+	699.964i	−0.135494	+	0.0782275i	−0.566215	−	0.824258i	$-0.691593\pi$
$431$	−1212.37	+	699.964i	−0.135494	+	0.0782275i	0.430721	+	0.902485i	$0.358259\pi$
$432$		0			0
$433$		−	8313.72i		−	0.922707i	−0.887217	−	0.461353i	$-0.847364\pi$
$433$		−	8313.72i		−	0.922707i	0.887217	−	0.461353i	$-0.152636\pi$
$434$		0			0
$435$	4100.60	−	1836.49i	0.451974	−	0.202421i
$436$		0			0
$437$	−5294.17			−0.579530
$438$		0			0
$439$			7100.28i			0.771932i	0.922513	+	0.385966i	$0.126132\pi$
$439$			7100.28i			0.771932i	−0.922513	+	0.385966i	$0.873868\pi$
$440$		0			0
$441$	−8802.88	+	2876.72i	−0.950532	+	0.310627i
$442$		0			0
$443$		−	163.702i		−	0.0175569i	−0.999961	−	0.00877846i	$-0.997206\pi$
$443$		−	163.702i		−	0.0175569i	0.999961	−	0.00877846i	$-0.00279431\pi$
$444$		0			0
$445$	5125.09			0.545960
$446$		0			0
$447$	396.707	−	3855.77i	0.0419767	−	0.407990i
$448$		0			0
$449$			995.044i			0.104586i	0.998632	+	0.0522929i	$0.0166529\pi$
$449$			995.044i			0.104586i	−0.998632	+	0.0522929i	$0.983347\pi$
$450$		0			0
$451$	−151.181	+	87.2845i	−0.0157846	+	0.00911323i
$452$		0			0
$453$	−4166.51	−	9303.15i	−0.432140	−	0.964901i
$454$		0			0
$455$	1096.30	+	1099.26i	0.112957	+	0.113262i
$456$		0			0
$457$	15381.8			1.57447			0.787233	−	0.616656i	$-0.211513\pi$
$457$	15381.8			1.57447			0.787233	+	0.616656i	$0.211513\pi$
$458$		0			0
$459$	−2882.63	−	13136.0i	−0.293136	−	1.33581i
$460$		0			0
$461$	−6149.43	−	10651.1i	−0.621274	−	1.07608i	−0.989249	−	0.146243i	$-0.953282\pi$
$461$	−6149.43	−	10651.1i	−0.621274	−	1.07608i	0.367974	−	0.929836i	$-0.380051\pi$
$462$		0			0
$463$	−5826.42	+	10091.7i	−0.584831	+	1.01296i	0.410065	+	0.912056i	$0.365506\pi$
$463$	−5826.42	+	10091.7i	−0.584831	+	1.01296i	−0.994896	+	0.100901i	$0.967827\pi$
$464$		0			0
$465$	−203.572	+	1978.61i	−0.0203020	+	0.197324i
$466$		0			0
$467$	8069.36	−	13976.6i	0.799584	−	1.38492i	−0.120303	−	0.992737i	$-0.538387\pi$
$467$	8069.36	−	13976.6i	0.799584	−	1.38492i	0.919887	−	0.392183i	$-0.128280\pi$
$468$		0			0
$469$	−2614.62	+	2607.58i	−0.257424	+	0.256731i
$470$		0			0
$471$	2979.16	+	2154.52i	0.291449	+	0.210775i
$472$		0			0
$473$			100.125i			0.00973307i
$474$		0			0
$475$	−3705.00	+	2139.08i	−0.357888	+	0.206627i
$476$		0			0
$477$	7545.05	+	6733.88i	0.724243	+	0.646380i
$478$		0			0
$479$	−7046.13	+	12204.3i	−0.672121	+	1.16415i	0.305180	+	0.952295i	$0.401283\pi$
$479$	−7046.13	+	12204.3i	−0.672121	+	1.16415i	−0.977301	+	0.211853i	$0.932050\pi$
$480$		0			0
$481$	1583.22	−	914.071i	0.150080	−	0.0866488i
$482$		0			0
$483$	−2152.04	−	2652.95i	−0.202735	−	0.249924i
$484$		0			0
$485$	−5750.18	−	3319.87i	−0.538355	−	0.310819i
$486$		0			0
$487$	−4125.25	−	7145.13i	−0.383845	−	0.664840i	0.607763	−	0.794119i	$-0.292067\pi$
$487$	−4125.25	−	7145.13i	−0.383845	−	0.664840i	−0.991608	+	0.129279i	$0.958734\pi$
$488$		0			0
$489$	1388.39	+	3100.05i	0.128395	+	0.286685i
$490$		0			0
$491$	5432.80	+	3136.63i	0.499346	+	0.288297i	0.728443	−	0.685106i	$-0.240244\pi$
$491$	5432.80	+	3136.63i	0.499346	+	0.288297i	−0.229098	+	0.973403i	$0.573578\pi$
$492$		0			0
$493$	−7314.32	−	4222.93i	−0.668196	−	0.385783i
$494$		0			0
$495$	215.701	−	71.1332i	0.0195859	−	0.00645899i
$496$		0			0
$497$	−6136.42	−	6152.98i	−0.553835	−	0.555329i
$498$		0			0
$499$	2319.50	+	4017.49i	0.208086	+	0.360416i	0.951112	−	0.308847i	$-0.0999431\pi$
$499$	2319.50	+	4017.49i	0.208086	+	0.360416i	−0.743025	+	0.669263i	$0.766610\pi$
$500$		0			0
$501$	−5442.28	−	12151.7i	−0.485316	−	1.08363i
$502$		0			0
$503$	−1130.74			−0.100233			−0.0501164	−	0.998743i	$-0.515959\pi$
$503$	−1130.74			−0.100233			−0.0501164	+	0.998743i	$0.515959\pi$
$504$		0			0
$505$	−7535.54			−0.664014
$506$		0			0
$507$	−10978.9	−	1129.58i	−0.961715	−	0.0989476i
$508$		0			0
$509$	−6470.95	−	11208.0i	−0.563497	−	0.976005i	−0.997188	−	0.0749432i	$-0.976122\pi$
$509$	−6470.95	−	11208.0i	−0.563497	−	0.976005i	0.433691	−	0.901062i	$-0.357211\pi$
$510$		0			0
$511$	2474.42	−	9185.14i	0.214211	−	0.795160i
$512$		0			0
$513$	14103.0	+	15457.2i	1.21377	+	1.33032i
$514$		0			0
$515$	−16845.2	−	9725.56i	−1.44133	−	0.832154i
$516$		0			0
$517$	−82.2635	−	47.4949i	−0.00699796	−	0.00404027i
$518$		0			0
$519$	−8355.51	+	11553.6i	−0.706679	+	0.977161i
$520$		0			0
$521$	8837.84	+	15307.6i	0.743173	+	1.28721i	0.951044	+	0.309057i	$0.100013\pi$
$521$	8837.84	+	15307.6i	0.743173	+	1.28721i	−0.207871	+	0.978156i	$0.566653\pi$
$522$		0			0
$523$	−13250.2	−	7650.02i	−1.10782	−	0.639602i	−0.169559	−	0.985520i	$-0.554234\pi$
$523$	−13250.2	−	7650.02i	−1.10782	−	0.639602i	−0.938265	+	0.345918i	$0.887568\pi$
$524$		0			0
$525$	−2577.96	−	987.084i	−0.214308	−	0.0820569i
$526$		0			0
$527$	3238.01	−	1869.47i	0.267647	−	0.154526i
$528$		0			0
$529$	−5453.47	+	9445.69i	−0.448218	+	0.776336i
$530$		0			0
$531$	−5013.74	−	15203.4i	−0.409751	−	1.24251i
$532$		0			0
$533$	−1506.53	+	869.794i	−0.122430	+	0.0706847i
$534$		0			0
$535$		−	20559.1i		−	1.66140i
$536$		0			0
$537$	−241.730	+	2349.48i	−0.0194254	+	0.188804i
$538$		0			0
$539$	−147.687	+	254.217i	−0.0118021	+	0.0203152i
$540$		0			0
$541$	−8179.80	+	14167.8i	−0.650050	+	1.12592i	0.333060	+	0.942906i	$0.391919\pi$
$541$	−8179.80	+	14167.8i	−0.650050	+	1.12592i	−0.983110	+	0.183014i	$0.941415\pi$
$542$		0			0
$543$	−13300.0	−	9618.53i	−1.05112	−	0.760167i
$544$		0			0
$545$	7228.67	−	12520.4i	0.568151	−	0.984066i
$546$		0			0
$547$	−7057.62	−	12224.2i	−0.551667	−	0.955516i	−0.998154	−	0.0607256i	$-0.980659\pi$
$547$	−7057.62	−	12224.2i	−0.551667	−	0.955516i	0.446487	−	0.894790i	$-0.352675\pi$
$548$		0			0
$549$	−14881.9	+	4907.73i	−1.15691	+	0.381524i
$550$		0			0
$551$	13140.6			1.01599
$552$		0			0
$553$	2564.22	−	2557.32i	0.197182	−	0.196651i
$554$		0			0
$555$	6395.97	−	8844.03i	0.489178	−	0.676411i
$556$		0			0
$557$	−18113.4	+	10457.8i	−1.37790	+	0.795530i	−0.991906	−	0.126972i	$-0.959474\pi$
$557$	−18113.4	+	10457.8i	−1.37790	+	0.795530i	−0.385992	+	0.922502i	$0.626141\pi$
$558$		0			0
$559$			997.747i			0.0754923i
$560$		0			0
$561$	−345.954	−	250.192i	−0.0260360	−	0.0188291i
$562$		0			0
$563$	26144.4			1.95711			0.978556	−	0.205980i	$-0.0660381\pi$
$563$	26144.4			1.95711			0.978556	+	0.205980i	$0.0660381\pi$
$564$		0			0
$565$		−	22120.9i		−	1.64714i
$566$		0			0
$567$	−2012.95	+	13350.4i	−0.149093	+	0.988823i
$568$		0			0
$569$		−	13959.6i		−	1.02850i	−0.857639	−	0.514252i	$-0.828070\pi$
$569$		−	13959.6i		−	1.02850i	0.857639	−	0.514252i	$-0.171930\pi$
$570$		0			0
$571$	11549.0			0.846426			0.423213	−	0.906030i	$-0.360902\pi$
$571$	11549.0			0.846426			0.423213	+	0.906030i	$0.360902\pi$
$572$		0			0
$573$	5216.46	+	3772.52i	0.380316	+	0.275043i
$574$		0			0
$575$		−	1018.24i		−	0.0738498i
$576$		0			0
$577$	9173.20	−	5296.15i	0.661847	−	0.382117i	−0.131134	−	0.991365i	$-0.541862\pi$
$577$	9173.20	−	5296.15i	0.661847	−	0.382117i	0.792980	+	0.609247i	$0.208528\pi$
$578$		0			0
$579$	2471.69	−	3417.74i	0.177409	−	0.245313i
$580$		0			0
$581$	7537.93	+	2030.67i	0.538255	+	0.145003i
$582$		0			0
$583$	321.051			0.0228072
$584$		0			0
$585$	2149.46	−	708.845i	0.151914	−	0.0500977i
$586$		0			0
$587$	12223.3	+	21171.3i	0.859469	+	1.48864i	0.872436	+	0.488729i	$0.162539\pi$
$587$	12223.3	+	21171.3i	0.859469	+	1.48864i	−0.0129666	+	0.999916i	$0.504128\pi$
$588$		0			0
$589$	−2908.64	+	5037.91i	−0.203478	+	0.352434i
$590$		0			0
$591$	−20123.3	−	14553.1i	−1.40061	−	1.01292i
$592$		0			0
$593$	3759.70	−	6512.00i	0.260358	−	0.450954i	−0.705979	−	0.708233i	$-0.749493\pi$
$593$	3759.70	−	6512.00i	0.260358	−	0.450954i	0.966337	+	0.257279i	$0.0828260\pi$
$594$		0			0
$595$	−4486.74	−	16835.4i	−0.309140	−	1.15997i
$596$		0			0
$597$	1721.92	−	16736.1i	0.118046	−	1.14734i
$598$		0			0
$599$			21525.2i			1.46827i	0.679003	+	0.734135i	$0.262412\pi$
$599$			21525.2i			1.46827i	−0.679003	+	0.734135i	$0.737588\pi$
$600$		0			0
$601$	−15936.3	+	9200.82i	−1.08162	+	0.624474i	−0.931333	−	0.364168i	$-0.881353\pi$
$601$	−15936.3	+	9200.82i	−1.08162	+	0.624474i	−0.150288	+	0.988642i	$0.548020\pi$
$602$		0			0
$603$	1686.01	+	5112.56i	0.113863	+	0.345273i
$604$		0			0
$605$	−6527.62	+	11306.2i	−0.438654	+	0.759771i
$606$		0			0
$607$	−10691.0	+	6172.46i	−0.714885	+	0.412739i	−0.812867	−	0.582449i	$-0.802095\pi$
$607$	−10691.0	+	6172.46i	−0.714885	+	0.412739i	0.0979821	+	0.995188i	$0.468761\pi$
$608$		0			0
$609$	5341.56	+	6584.87i	0.355420	+	0.438148i
$610$		0			0
$611$	−819.759	−	473.288i	−0.0542781	−	0.0313375i
$612$		0			0
$613$	6988.28	+	12104.1i	0.460447	+	0.797518i	0.998983	−	0.0450846i	$-0.0143557\pi$
$613$	6988.28	+	12104.1i	0.460447	+	0.797518i	−0.538536	+	0.842603i	$0.681022\pi$
$614$		0			0
$615$	−6086.15	+	8415.63i	−0.399052	+	0.551790i
$616$		0			0
$617$	7538.77	+	4352.51i	0.491895	+	0.283996i	0.725360	−	0.688369i	$-0.241673\pi$
$617$	7538.77	+	4352.51i	0.491895	+	0.283996i	−0.233465	+	0.972365i	$0.575006\pi$
$618$		0			0
$619$	−10273.7	−	5931.54i	−0.667101	−	0.385151i	0.127876	−	0.991790i	$-0.459184\pi$
$619$	−10273.7	−	5931.54i	−0.667101	−	0.385151i	−0.794977	+	0.606639i	$0.792517\pi$
$620$		0			0
$621$	−4864.39	+	1067.47i	−0.314334	+	0.0689791i
$622$		0			0
$623$	2490.62	+	9345.48i	0.160168	+	0.600993i
$624$		0			0
$625$	5608.27	+	9713.81i	0.358929	+	0.621684i
$626$		0			0
$627$	660.778	+	67.9852i	0.0420876	+	0.00433025i
$628$		0			0
$629$	−20516.5			−1.30055
$630$		0			0
$631$	19449.0			1.22703			0.613514	−	0.789684i	$-0.289756\pi$
$631$	19449.0			1.22703			0.613514	+	0.789684i	$0.289756\pi$
$632$		0			0
$633$	841.893	+	1879.81i	0.0528629	+	0.118034i
$634$		0			0
$635$	6340.51	+	10982.1i	0.396245	+	0.686316i
$636$		0			0
$637$	−1471.71	+	2533.28i	−0.0915403	+	0.157570i
$638$		0			0
$639$	−12031.4	+	3967.68i	−0.744842	+	0.245632i
$640$		0			0
$641$	8810.19	+	5086.57i	0.542873	+	0.313428i	0.746243	−	0.665674i	$-0.231856\pi$
$641$	8810.19	+	5086.57i	0.542873	+	0.313428i	−0.203369	+	0.979102i	$0.565189\pi$
$642$		0			0
$643$	12352.8	+	7131.91i	0.757618	+	0.437411i	0.828440	−	0.560078i	$-0.189229\pi$
$643$	12352.8	+	7131.91i	0.757618	+	0.437411i	−0.0708218	+	0.997489i	$0.522562\pi$
$644$		0			0
$645$	2434.78	+	5436.47i	0.148635	+	0.331877i
$646$		0			0
$647$	8796.63	+	15236.2i	0.534515	+	0.925807i	0.999187	+	0.0403240i	$0.0128390\pi$
$647$	8796.63	+	15236.2i	0.534515	+	0.925807i	−0.464672	+	0.885483i	$0.653828\pi$
$648$		0			0
$649$	−440.132	−	254.110i	−0.0266205	−	0.0153693i
$650$		0			0
$651$	−3706.88	+	590.329i	−0.223170	+	0.0355404i
$652$		0			0
$653$	−10790.4	+	6229.82i	−0.646646	+	0.373341i	−0.787170	−	0.616736i	$-0.788455\pi$
$653$	−10790.4	+	6229.82i	−0.646646	+	0.373341i	0.140524	+	0.990077i	$0.455121\pi$
$654$		0			0
$655$	13479.7	−	23347.5i	0.804113	−	1.39276i
$656$		0			0
$657$	−10346.6	−	9234.24i	−0.614398	−	0.548344i
$658$		0			0
$659$	15153.7	−	8748.99i	0.895758	−	0.517166i	0.0199364	−	0.999801i	$-0.493654\pi$
$659$	15153.7	−	8748.99i	0.895758	−	0.517166i	0.875821	+	0.482635i	$0.160320\pi$
$660$		0			0
$661$		−	18098.9i		−	1.06500i	−0.846431	−	0.532499i	$-0.821253\pi$
$661$		−	18098.9i		−	1.06500i	0.846431	−	0.532499i	$-0.178747\pi$
$662$		0			0
$663$	−3447.44	−	2493.18i	−0.201942	−	0.146044i
$664$		0			0
$665$	19142.4	+	19194.0i	1.11625	+	1.11927i
$666$		0			0
$667$	−1563.79	+	2708.57i	−0.0907801	+	0.157236i
$668$		0			0
$669$	1417.69	−	13779.1i	0.0819297	−	0.796310i
$670$		0			0
$671$	−248.738	+	430.826i	−0.0143106	+	0.0247867i
$672$		0			0
$673$	5468.21	+	9471.21i	0.313200	+	0.542479i	0.979053	−	0.203604i	$-0.0652655\pi$
$673$	5468.21	+	9471.21i	0.313200	+	0.542479i	−0.665853	+	0.746083i	$0.731932\pi$
$674$		0			0
$675$	−2972.92	+	2712.47i	−0.169523	+	0.154671i
$676$		0			0
$677$	11281.3			0.640435			0.320218	−	0.947344i	$-0.396244\pi$
$677$	11281.3			0.640435			0.320218	+	0.947344i	$0.396244\pi$
$678$		0			0
$679$	3259.30	−	12098.7i	0.184213	−	0.683806i
$680$		0			0
$681$	8761.17	+	19562.3i	0.492994	+	1.10078i
$682$		0			0
$683$	−5497.71	+	3174.10i	−0.308000	+	0.177824i	−0.646031	−	0.763311i	$-0.723572\pi$
$683$	−5497.71	+	3174.10i	−0.308000	+	0.177824i	0.338031	+	0.941135i	$0.390239\pi$
$684$		0			0
$685$			9488.71i			0.529263i
$686$		0			0
$687$	−3358.18	+	32639.6i	−0.186496	+	1.81263i
$688$		0			0
$689$	3199.29			0.176899
$690$		0			0
$691$		−	22460.0i		−	1.23650i	−0.785983	−	0.618248i	$-0.787843\pi$
$691$		−	22460.0i		−	1.23650i	0.785983	−	0.618248i	$-0.212157\pi$
$692$		0			0
$693$	234.533	+	358.756i	0.0128560	+	0.0196653i
$694$		0			0
$695$		−	14445.0i		−	0.788390i
$696$		0			0
$697$	19522.7			1.06094
$698$		0			0
$699$	−25485.4	+	11413.9i	−1.37904	+	0.617616i
$700$		0			0
$701$		−	9083.18i		−	0.489397i	−0.969599	−	0.244698i	$-0.921311\pi$
$701$		−	9083.18i		−	0.489397i	0.969599	−	0.244698i	$-0.0786889\pi$
$702$		0			0
$703$	27644.3	−	15960.5i	1.48311	−	0.856273i
$704$		0			0
$705$	−5621.61	−	578.389i	−0.300315	−	0.0308984i
$706$		0			0
$707$	−3662.02	−	13740.9i	−0.194801	−	0.730946i
$708$		0			0
$709$	−17749.0			−0.940167			−0.470083	−	0.882622i	$-0.655776\pi$
$709$	−17749.0			−0.940167			−0.470083	+	0.882622i	$0.655776\pi$
$710$		0			0
$711$	−1653.51	−	5014.01i	−0.0872171	−	0.264473i
$712$		0			0
$713$	−692.283	−	1199.07i	−0.0363621	−	0.0629811i
$714$		0			0
$715$	35.9262	−	62.2261i	0.00187911	−	0.00325472i
$716$		0			0
$717$	−30196.2	+	13523.7i	−1.57280	+	0.704393i
$718$		0			0
$719$	−9644.87	+	16705.4i	−0.500268	+	0.866490i	0.499732	+	0.866180i	$0.333432\pi$
$719$	−9644.87	+	16705.4i	−0.500268	+	0.866490i	−1.00000		0.000309855i	$0.999901\pi$
$720$		0			0
$721$	9548.14	−	35443.1i	0.493192	−	1.83075i
$722$		0			0
$723$	13584.8	−	6084.08i	0.698787	−	0.312959i
$724$		0			0
$725$			2527.37i			0.129468i
$726$		0			0
$727$	−16662.6	+	9620.16i	−0.850043	+	0.490773i	−0.860666	−	0.509171i	$-0.829952\pi$
$727$	−16662.6	+	9620.16i	−0.850043	+	0.490773i	0.0106220	+	0.999944i	$0.496619\pi$
$728$		0			0
$729$	16074.8	+	11358.8i	0.816684	+	0.577085i
$730$		0			0
$731$	5598.65	−	9697.15i	0.283274	−	0.490646i
$732$		0			0
$733$	23096.4	−	13334.7i	1.16383	−	0.671935i	0.211607	−	0.977355i	$-0.432130\pi$
$733$	23096.4	−	13334.7i	1.16383	−	0.671935i	0.952218	+	0.305420i	$0.0987968\pi$
$734$		0			0
$735$	−1837.05	+	17394.6i	−0.0921913	+	0.872938i
$736$		0			0
$737$	148.006	+	85.4516i	0.00739740	+	0.00427089i
$738$		0			0
$739$	19504.2	+	33782.2i	0.970868	+	1.68159i	0.692945	+	0.720990i	$0.256313\pi$
$739$	19504.2	+	33782.2i	0.970868	+	1.68159i	0.277923	+	0.960603i	$0.410354\pi$
$740$		0			0
$741$	6584.68	+	677.475i	0.326443	+	0.0335866i
$742$		0			0
$743$	16513.4	+	9534.00i	0.815366	+	0.470752i	0.848816	−	0.528689i	$-0.177316\pi$
$743$	16513.4	+	9534.00i	0.815366	+	0.470752i	−0.0334501	+	0.999440i	$0.510649\pi$
$744$		0			0
$745$	−6340.06	−	3660.43i	−0.311788	−	0.180011i
$746$		0			0
$747$	7578.23	−	8491.10i	0.371182	−	0.415895i
$748$		0			0
$749$	37489.1	−	9991.06i	1.82887	−	0.487404i
$750$		0			0
$751$	−5772.91	−	9998.97i	−0.280501	−	0.485842i	0.691007	−	0.722848i	$-0.257167\pi$
$751$	−5772.91	−	9998.97i	−0.280501	−	0.485842i	−0.971508	+	0.237006i	$0.923834\pi$
$752$		0			0
$753$	13915.8	−	19242.1i	0.673468	−	0.931239i
$754$		0			0
$755$	−19252.6			−0.928047
$756$		0			0
$757$	−29253.9			−1.40456			−0.702279	−	0.711901i	$-0.747834\pi$
$757$	−29253.9			−1.40456			−0.702279	+	0.711901i	$0.747834\pi$
$758$		0			0
$759$	−92.6488	+	128.110i	−0.00443075	+	0.00612663i
$760$		0			0
$761$	−5635.28	−	9760.60i	−0.268435	−	0.464943i	0.700023	−	0.714120i	$-0.253173\pi$
$761$	−5635.28	−	9760.60i	−0.268435	−	0.464943i	−0.968458	+	0.249178i	$0.919840\pi$
$762$		0			0
$763$	26343.6	+	7096.80i	1.24994	+	0.336725i
$764$		0			0
$765$	−24868.3	−	5171.97i	−1.17531	−	0.244435i
$766$		0			0
$767$	−4385.93	−	2532.22i	−0.206476	−	0.119209i
$768$		0			0
$769$	−6649.65	−	3839.18i	−0.311824	−	0.180031i	0.335919	−	0.941891i	$-0.390953\pi$
$769$	−6649.65	−	3839.18i	−0.311824	−	0.180031i	−0.647742	+	0.761860i	$0.724287\pi$
$770$		0			0
$771$	4095.79	+	421.402i	0.191318	+	0.0196841i
$772$		0			0
$773$	6301.53	+	10914.6i	0.293209	+	0.507852i	0.974567	−	0.224098i	$-0.0719436\pi$
$773$	6301.53	+	10914.6i	0.293209	+	0.507852i	−0.681358	+	0.731950i	$0.738610\pi$
$774$		0			0
$775$	−968.954	−	559.426i	−0.0449108	−	0.0259293i
$776$		0			0
$777$	19235.1	+	7364.99i	0.888103	+	0.340048i
$778$		0			0
$779$	−26305.2	+	15187.3i	−1.20986	+	0.698514i
$780$		0			0
$781$	−201.093	+	348.303i	−0.00921341	+	0.0159581i
$782$		0			0
$783$	12073.9	−	2649.55i	0.551066	−	0.120929i
$784$		0			0
$785$	6013.70	−	3472.01i	0.273424	−	0.157862i
$786$		0			0
$787$		−	1271.00i		−	0.0575684i	−0.999586	−	0.0287842i	$-0.990836\pi$
$787$		−	1271.00i		−	0.0575684i	0.999586	−	0.0287842i	$-0.00916357\pi$
$788$		0			0
$789$	−729.366	+	326.654i	−0.0329101	+	0.0147391i
$790$		0			0
$791$	40336.9	−	10750.0i	1.81317	−	0.483219i
$792$		0			0
$793$	−2478.68	+	4293.20i	−0.110997	+	0.192252i
$794$		0			0
$795$	17432.1	−	7807.15i	0.777677	−	0.348291i
$796$		0			0
$797$	−11823.9	+	20479.6i	−0.525502	+	0.910196i	0.474057	+	0.880494i	$0.342789\pi$
$797$	−11823.9	+	20479.6i	−0.525502	+	0.910196i	−0.999559	+	0.0297018i	$0.990544\pi$
$798$		0			0
$799$	5311.52	+	9199.82i	0.235179	+	0.407342i
$800$		0			0
$801$	13804.6	+	2871.00i	0.608940	+	0.126644i
$802$		0			0
$803$	−440.261			−0.0193480
$804$		0			0
$805$	−6234.33	+	1661.49i	−0.272958	+	0.0727449i
$806$		0			0
$807$	−3264.71	−	335.895i	−0.142408	−	0.0146519i
$808$		0			0
$809$	−20728.1	+	11967.4i	−0.900819	+	0.520088i	−0.877466	−	0.479639i	$-0.840768\pi$
$809$	−20728.1	+	11967.4i	−0.900819	+	0.520088i	−0.0233532	+	0.999727i	$0.507434\pi$
$810$		0			0
$811$			22831.6i			0.988565i	0.869301	+	0.494283i	$0.164569\pi$
$811$			22831.6i			0.988565i	−0.869301	+	0.494283i	$0.835431\pi$
$812$		0			0
$813$	−14098.5	+	6314.15i	−0.608187	+	0.272382i
$814$		0			0
$815$	6415.48			0.275736
$816$		0			0
$817$			17421.5i			0.746024i
$818$		0			0
$819$	2337.13	+	3575.02i	0.0997143	+	0.152529i
$820$		0			0
$821$		−	11354.3i		−	0.482666i	−0.970442	−	0.241333i	$-0.922415\pi$
$821$		−	11354.3i		−	0.482666i	0.970442	−	0.241333i	$-0.0775846\pi$
$822$		0			0
$823$	16190.0			0.685722			0.342861	−	0.939386i	$-0.388604\pi$
$823$	16190.0			0.685722			0.342861	+	0.939386i	$0.388604\pi$
$824$		0			0
$825$	−13.0758	+	127.089i	−0.000551806	+	0.00536324i
$826$		0			0
$827$		−	29074.8i		−	1.22253i	−0.791427	−	0.611264i	$-0.790662\pi$
$827$		−	29074.8i		−	1.22253i	0.791427	−	0.611264i	$-0.209338\pi$
$828$		0			0
$829$	8006.47	−	4622.54i	0.335436	−	0.193664i	−0.322816	−	0.946462i	$-0.604630\pi$
$829$	8006.47	−	4622.54i	0.335436	−	0.193664i	0.658252	+	0.752798i	$0.271296\pi$
$830$		0			0
$831$	9277.40	+	20715.0i	0.387280	+	0.864734i
$832$		0			0
$833$	28518.6	−	16362.9i	1.18621	−	0.680602i
$834$		0			0
$835$	−25147.7			−1.04224
$836$		0			0
$837$	−1656.72	+	5215.40i	−0.0684164	+	0.215377i
$838$		0			0
$839$	−2083.58	−	3608.87i	−0.0857368	−	0.148501i	0.819968	−	0.572409i	$-0.193991\pi$
$839$	−2083.58	−	3608.87i	−0.0857368	−	0.148501i	−0.905705	+	0.423909i	$0.860658\pi$
$840$		0			0
$841$	−8313.02	+	14398.6i	−0.340851	+	0.590372i
$842$		0			0
$843$	−1310.41	+	12736.4i	−0.0535384	+	0.520363i
$844$		0			0
$845$	−10422.7	+	18052.6i	−0.424321	+	0.734946i
$846$		0			0
$847$	−23788.8	−	6408.54i	−0.965043	−	0.259977i
$848$		0			0
$849$	−9268.41	−	6702.87i	−0.374665	−	0.270956i
$850$		0			0
$851$			7597.47i			0.306038i
$852$		0			0
$853$	23733.0	−	13702.3i	0.952641	−	0.550008i	0.0587407	−	0.998273i	$-0.481291\pi$
$853$	23733.0	−	13702.3i	0.952641	−	0.550008i	0.893900	+	0.448266i	$0.147958\pi$
$854$		0			0
$855$	37531.5	−	12377.0i	1.50123	−	0.495071i
$856$		0			0
$857$	5936.78	−	10282.8i	0.236635	−	0.409864i	−0.723111	−	0.690731i	$-0.757289\pi$
$857$	5936.78	−	10282.8i	0.236635	−	0.409864i	0.959747	+	0.280867i	$0.0906220\pi$
$858$		0			0
$859$	8655.05	−	4996.99i	0.343779	−	0.198481i	−0.318163	−	0.948036i	$-0.603066\pi$
$859$	8655.05	−	4996.99i	0.343779	−	0.198481i	0.661942	+	0.749555i	$0.269732\pi$
$860$		0			0
$861$	−18303.4	−	7008.23i	−0.724480	−	0.277398i
$862$		0			0
$863$	37488.7	+	21644.1i	1.47871	+	0.853735i	0.999710	−	0.0240781i	$-0.00766505\pi$
$863$	37488.7	+	21644.1i	1.47871	+	0.853735i	0.479003	+	0.877813i	$0.340998\pi$
$864$		0			0
$865$	13464.9	+	23321.9i	0.529273	+	0.916727i
$866$		0			0
$867$	9081.30	+	20277.1i	0.355729	+	0.794287i
$868$		0			0
$869$	−145.153	−	83.8044i	−0.00566627	−	0.00327143i
$870$		0			0
$871$	1474.89	+	851.528i	0.0573763	+	0.0331262i
$872$		0			0
$873$	−13628.5	−	12163.3i	−0.528357	−	0.471554i
$874$		0			0
$875$	−19778.6	+	19725.3i	−0.764157	+	0.762101i
$876$		0			0
$877$	−21376.5	−	37025.1i	−0.823069	−	1.42560i	−0.903386	−	0.428828i	$-0.858927\pi$
$877$	−21376.5	−	37025.1i	−0.823069	−	1.42560i	0.0803167	−	0.996769i	$-0.474407\pi$
$878$		0			0
$879$	−14906.2	−	33283.3i	−0.571985	−	1.27715i
$880$		0			0
$881$	−40289.2			−1.54072			−0.770362	−	0.637606i	$-0.779925\pi$
$881$	−40289.2			−1.54072			−0.770362	+	0.637606i	$0.779925\pi$
$882$		0			0
$883$	−15292.6			−0.582827			−0.291414	−	0.956597i	$-0.594126\pi$
$883$	−15292.6			−0.582827			−0.291414	+	0.956597i	$0.594126\pi$
$884$		0			0
$885$	−30077.2	−	3094.54i	−1.14241	−	0.117539i
$886$		0			0
$887$	−18953.2	−	32827.8i	−0.717457	−	1.24267i	−0.962004	−	0.273035i	$-0.911973\pi$
$887$	−18953.2	−	32827.8i	−0.717457	−	1.24267i	0.244547	−	0.969637i	$-0.421361\pi$
$888$		0			0
$889$	−16944.3	+	16898.7i	−0.639250	+	0.637530i
$890$		0			0
$891$	620.844	−	70.7670i	0.0233435	−	0.00266081i
$892$		0			0
$893$	−14313.7	−	8264.01i	−0.536382	−	0.309680i
$894$		0			0
$895$	3863.26	+	2230.46i	0.144285	+	0.0833027i
$896$		0			0
$897$	−923.249	+	1276.62i	−0.0343661	+	0.0475198i
$898$		0			0
$899$	1718.31	+	2976.20i	0.0637473	+	0.110414i
$900$		0			0
$901$	−31094.0	−	17952.1i	−1.14971	−	0.663788i
$902$		0			0
$903$	−8730.06	+	7081.71i	−0.321725	+	0.260979i
$904$		0			0
$905$	−26847.3	+	15500.3i	−0.986114	+	0.569333i
$906$		0			0
$907$	15052.1	−	26071.0i	0.551045	−	0.954437i	−0.447155	−	0.894457i	$-0.647563\pi$
$907$	15052.1	−	26071.0i	0.551045	−	0.954437i	0.998200	−	0.0599807i	$-0.0191039\pi$
$908$		0			0
$909$	−20297.2	−	4221.31i	−0.740611	−	0.154028i
$910$		0			0
$911$	−6812.51	+	3933.20i	−0.247759	+	0.143044i	−0.618738	−	0.785598i	$-0.712356\pi$
$911$	−6812.51	+	3933.20i	−0.247759	+	0.143044i	0.370979	+	0.928641i	$0.379022\pi$
$912$		0			0
$913$		−	361.307i		−	0.0130970i
$914$		0			0
$915$	−3029.11	+	29441.2i	−0.109442	+	1.06371i
$916$		0			0
$917$	49124.2	+	13233.8i	1.76906	+	0.476573i
$918$		0			0
$919$	−15193.4	+	26315.8i	−0.545359	+	0.944589i	0.453226	+	0.891396i	$0.350273\pi$
$919$	−15193.4	+	26315.8i	−0.545359	+	0.944589i	−0.998584	+	0.0531930i	$0.983060\pi$
$920$		0			0
$921$	6176.22	+	4466.61i	0.220970	+	0.159805i
$922$		0			0
$923$	−2003.90	+	3470.86i	−0.0714617	+	0.123775i
$924$		0			0
$925$	3069.72	+	5316.91i	0.109115	+	0.188993i
$926$		0			0
$927$	−39924.8	−	35632.5i	−1.41457	−	1.26249i
$928$		0			0
$929$	2532.11			0.0894249			0.0447124	−	0.999000i	$-0.485763\pi$
$929$	2532.11			0.0894249			0.0447124	+	0.999000i	$0.485763\pi$
$930$		0			0
$931$	−25697.3	+	44233.3i	−0.904612	+	1.55713i
$932$		0			0
$933$	28445.4	−	39332.9i	0.998134	−	1.38017i
$934$		0			0
$935$	−698.337	+	403.185i	−0.0244258	+	0.0141022i
$936$		0			0
$937$		−	25100.9i		−	0.875145i	−0.899183	−	0.437572i	$-0.855838\pi$
$937$		−	25100.9i		−	0.875145i	0.899183	−	0.437572i	$-0.144162\pi$
$938$		0			0
$939$	35802.9	+	25892.5i	1.24429	+	0.899862i
$940$		0			0
$941$	−38318.8			−1.32748			−0.663739	−	0.747964i	$-0.731031\pi$
$941$	−38318.8			−1.32748			−0.663739	+	0.747964i	$0.731031\pi$
$942$		0			0
$943$		−	7229.45i		−	0.249654i
$944$		0			0
$945$	21458.5	+	13776.1i	0.738671	+	0.474220i
$946$		0			0
$947$		−	23999.0i		−	0.823509i	−0.911295	−	0.411755i	$-0.864916\pi$
$947$		−	23999.0i		−	0.823509i	0.911295	−	0.411755i	$-0.135084\pi$
$948$		0			0
$949$	−4387.22			−0.150069
$950$		0			0
$951$	11091.9	+	8021.65i	0.378213	+	0.273522i
$952$		0			0
$953$			31381.6i			1.06668i	0.845900	+	0.533342i	$0.179064\pi$
$953$			31381.6i			1.06668i	−0.845900	+	0.533342i	$0.820936\pi$
$954$		0			0
$955$	10529.9	−	6079.43i	0.356795	−	0.205996i
$956$		0			0
$957$	229.963	−	317.981i	0.00776765	−	0.0107407i
$958$		0			0
$959$	−17302.4	+	4611.20i	−0.582612	+	0.155269i
$960$		0			0
$961$	28269.6			0.948932
$962$		0			0
$963$	11516.9	−	55376.6i	0.385388	−	1.85305i
$964$		0			0
$965$	−3983.14	−	6899.00i	−0.132872	−	0.230142i
$966$		0			0
$967$	−19405.7	+	33611.6i	−0.645341	+	1.11776i	0.338881	+	0.940829i	$0.389951\pi$
$967$	−19405.7	+	33611.6i	−0.645341	+	1.11776i	−0.984223	+	0.176935i	$0.943382\pi$
$968$		0			0
$969$	−60195.3	−	43533.0i	−1.99561	−	1.44322i
$970$		0			0
$971$	9434.09	−	16340.3i	0.311797	−	0.540048i	−0.666955	−	0.745098i	$-0.732403\pi$
$971$	9434.09	−	16340.3i	0.311797	−	0.540048i	0.978751	+	0.205051i	$0.0657359\pi$
$972$		0			0
$973$	26340.2	−	7019.80i	0.867859	−	0.231289i
$974$		0			0
$975$	−130.301	+	1266.45i	−0.00427996	+	0.0415988i
$976$		0			0
$977$		−	41014.1i		−	1.34305i	−0.740983	−	0.671523i	$-0.765640\pi$
$977$		−	41014.1i		−	1.34305i	0.740983	−	0.671523i	$-0.234360\pi$
$978$		0			0
$979$	387.653	−	223.811i	0.0126552	−	0.00730648i
$980$		0			0
$981$	26484.4	−	29674.7i	0.861960	−	0.965792i
$982$		0			0
$983$	−8260.99	+	14308.4i	−0.268041	+	0.464261i	−0.968356	−	0.249573i	$-0.919710\pi$
$983$	−8260.99	+	14308.4i	−0.268041	+	0.464261i	0.700315	+	0.713834i	$0.253043\pi$
$984$		0			0
$985$	−40620.7	+	23452.3i	−1.31399	+	0.758633i
$986$		0			0
$987$	−1677.24	−	10532.0i	−0.0540903	−	0.339651i
$988$		0			0
$989$	−3590.96	−	2073.24i	−0.115456	−	0.0666584i
$990$		0			0
$991$	−16706.9	−	28937.2i	−0.535531	−	0.927567i	−0.999137	−	0.0415257i	$-0.986778\pi$
$991$	−16706.9	−	28937.2i	−0.535531	−	0.927567i	0.463606	−	0.886041i	$-0.346555\pi$
$992$		0			0
$993$	12670.5	−	17520.1i	0.404921	−	0.559904i
$994$		0			0
$995$	−27519.2	−	15888.2i	−0.876801	−	0.506221i
$996$		0			0
$997$	19002.2	+	10970.9i	0.603616	+	0.348498i	0.770463	−	0.637485i	$-0.220025\pi$
$997$	19002.2	+	10970.9i	0.603616	+	0.348498i	−0.166847	+	0.985983i	$0.553359\pi$
$998$		0			0
$999$	22182.0	−	20238.7i	0.702511	−	0.640966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.w.a.5.17	✓	48
3.2	odd	2		756.4.w.a.341.19		48
7.3	odd	6		252.4.bm.a.185.23	yes	48
9.2	odd	6		252.4.bm.a.173.23	yes	48
9.7	even	3		756.4.bm.a.89.19		48
21.17	even	6		756.4.bm.a.17.19		48
63.38	even	6	inner	252.4.w.a.101.17	yes	48
63.52	odd	6		756.4.w.a.521.19		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.17	✓	48	1.1	even	1	trivial
252.4.w.a.101.17	yes	48	63.38	even	6	inner
252.4.bm.a.173.23	yes	48	9.2	odd	6
252.4.bm.a.185.23	yes	48	7.3	odd	6
756.4.w.a.341.19		48	3.2	odd	2
756.4.w.a.521.19		48	63.52	odd	6
756.4.bm.a.17.19		48	21.17	even	6
756.4.bm.a.89.19		48	9.7	even	3

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.04499 - 4.21047i) q^{3} +(-4.90701 - 8.49919i) q^{5} +(13.1134 - 13.0781i) q^{7} +(-8.45605 - 25.6417i) q^{9} +O(q^{10})\)	\(q+(3.04499 - 4.21047i) q^{3} +(-4.90701 - 8.49919i) q^{5} +(13.1134 - 13.0781i) q^{7} +(-8.45605 - 25.6417i) q^{9} +(-0.742316 - 0.428576i) q^{11} +(-7.39720 - 4.27078i) q^{13} +(-50.7274 - 5.21917i) q^{15} +(47.9292 + 83.0157i) q^{17} +(-129.161 - 74.5714i) q^{19} +(-15.1348 - 95.0365i) q^{21} +(30.7416 - 17.7487i) q^{23} +(14.3425 - 24.8420i) q^{25} +(-133.712 - 42.4748i) q^{27} +(-76.3034 + 44.0538i) q^{29} -39.0048i q^{31} +(-4.06485 + 1.82048i) q^{33} +(-175.501 - 47.2790i) q^{35} +(-107.015 + 185.355i) q^{37} +(-40.5064 + 18.1412i) q^{39} +(101.831 - 176.376i) q^{41} +(-58.4055 - 101.161i) q^{43} +(-176.440 + 197.694i) q^{45} +110.820 q^{47} +(0.924207 - 342.999i) q^{49} +(495.479 + 50.9782i) q^{51} +(-324.375 + 187.278i) q^{53} +8.41211i q^{55} +(-707.276 + 316.761i) q^{57} +592.918 q^{59} -580.381i q^{61} +(-446.233 - 225.661i) q^{63} +83.8270i q^{65} -199.385 q^{67} +(18.8777 - 183.481i) q^{69} -469.212i q^{71} +(444.818 - 256.816i) q^{73} +(-60.9234 - 136.032i) q^{75} +(-15.3393 + 4.08801i) q^{77} +195.541 q^{79} +(-585.990 + 433.654i) q^{81} +(210.760 + 365.047i) q^{83} +(470.378 - 814.718i) q^{85} +(-46.8563 + 455.417i) q^{87} +(-261.110 + 452.257i) q^{89} +(-152.857 + 40.7372i) q^{91} +(-164.228 - 118.769i) q^{93} +1463.69i q^{95} +(585.915 - 338.278i) q^{97} +(-4.71235 + 22.6583i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 12 * q^9	\( 48 q + 6 q^{7} + 12 q^{9} + 12 q^{11} - 36 q^{13} + 66 q^{15} - 72 q^{17} + 24 q^{21} + 30 q^{23} - 600 q^{25} - 396 q^{27} + 42 q^{29} + 390 q^{35} + 84 q^{37} - 840 q^{39} - 618 q^{41} - 42 q^{43} + 366 q^{45} + 396 q^{47} + 318 q^{49} - 738 q^{51} - 1620 q^{53} + 492 q^{57} + 1500 q^{59} + 672 q^{63} - 588 q^{67} - 924 q^{69} + 564 q^{75} - 2472 q^{77} + 1608 q^{79} + 2592 q^{81} - 360 q^{85} + 2640 q^{87} + 1722 q^{89} + 540 q^{91} + 660 q^{93} - 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 12 * q^9 + 12 * q^11 - 36 * q^13 + 66 * q^15 - 72 * q^17 + 24 * q^21 + 30 * q^23 - 600 * q^25 - 396 * q^27 + 42 * q^29 + 390 * q^35 + 84 * q^37 - 840 * q^39 - 618 * q^41 - 42 * q^43 + 366 * q^45 + 396 * q^47 + 318 * q^49 - 738 * q^51 - 1620 * q^53 + 492 * q^57 + 1500 * q^59 + 672 * q^63 - 588 * q^67 - 924 * q^69 + 564 * q^75 - 2472 * q^77 + 1608 * q^79 + 2592 * q^81 - 360 * q^85 + 2640 * q^87 + 1722 * q^89 + 540 * q^91 + 660 * q^93 - 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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