LMFDB - Embedded newform 252.4.x.a.209.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(41,252)]

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, 3]))

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

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

chi := DirichletCharacter("252.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.x (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			209.10
Character	$\chi$	$=$	252.209
Dual form			252.4.x.a.41.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.494604 + 5.17256i) q^{3} +(2.99997 + 5.19610i) q^{5} +(-0.375477 - 18.5165i) q^{7} +(-26.5107 - 5.11673i) q^{9} +O(q^{10})$	\(q+(-0.494604 + 5.17256i) q^{3} +(2.99997 + 5.19610i) q^{5} +(-0.375477 - 18.5165i) q^{7} +(-26.5107 - 5.11673i) q^{9} +(-39.3810 - 22.7366i) q^{11} +(-22.7627 + 13.1421i) q^{13} +(-28.3609 + 12.9475i) q^{15} -19.7249 q^{17} -27.9162i q^{19} +(95.9632 + 7.21613i) q^{21} +(-60.3466 + 34.8411i) q^{23} +(44.5004 - 77.0769i) q^{25} +(39.5789 - 134.598i) q^{27} +(-119.031 - 68.7227i) q^{29} +(138.202 - 79.7908i) q^{31} +(137.085 - 192.455i) q^{33} +(95.0869 - 57.4998i) q^{35} -287.829 q^{37} +(-56.7196 - 124.242i) q^{39} +(-20.4288 - 35.3837i) q^{41} +(55.4158 - 95.9830i) q^{43} +(-52.9443 - 153.102i) q^{45} +(109.666 - 189.948i) q^{47} +(-342.718 + 13.9050i) q^{49} +(9.75601 - 102.028i) q^{51} +209.770i q^{53} -272.837i q^{55} +(144.398 + 13.8074i) q^{57} +(413.880 + 716.860i) q^{59} +(-594.209 - 343.066i) q^{61} +(-84.7896 + 492.806i) q^{63} +(-136.575 - 78.8515i) q^{65} +(-171.449 - 296.958i) q^{67} +(-150.370 - 329.379i) q^{69} -387.476i q^{71} +220.721i q^{73} +(376.675 + 268.303i) q^{75} +(-406.215 + 737.734i) q^{77} +(242.301 - 419.677i) q^{79} +(676.638 + 271.297i) q^{81} +(-354.323 + 613.706i) q^{83} +(-59.1741 - 102.493i) q^{85} +(414.346 - 581.706i) q^{87} -140.929 q^{89} +(251.891 + 416.550i) q^{91} +(344.368 + 754.321i) q^{93} +(145.055 - 83.7476i) q^{95} +(-1304.31 - 753.041i) q^{97} +(927.683 + 804.267i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 60 * q^9	$ 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.494604	+	5.17256i	−0.0951865	+	0.995459i
$3$	−0.494604	+	5.17256i	−0.0951865	+	0.995459i
$4$		0			0
$5$	2.99997	+	5.19610i	0.268325	+	0.464753i	0.968430	−	0.249288i	$-0.0801964\pi$
$5$	2.99997	+	5.19610i	0.268325	+	0.464753i	−0.700104	+	0.714041i	$0.746863\pi$
$6$		0			0
$7$	−0.375477	−	18.5165i	−0.0202739	−	0.999794i
$7$	−0.375477	−	18.5165i	−0.0202739	−	0.999794i
$8$		0			0
$9$	−26.5107	−	5.11673i	−0.981879	−	0.189509i
$10$		0			0
$11$	−39.3810	−	22.7366i	−1.07944	−	0.623214i	−0.148694	−	0.988883i	$-0.547507\pi$
$11$	−39.3810	−	22.7366i	−1.07944	−	0.623214i	−0.930745	+	0.365669i	$0.880840\pi$
$12$		0			0
$13$	−22.7627	+	13.1421i	−0.485634	+	0.280381i	−0.722761	−	0.691098i	$-0.757127\pi$
$13$	−22.7627	+	13.1421i	−0.485634	+	0.280381i	0.237127	+	0.971479i	$0.423794\pi$
$14$		0			0
$15$	−28.3609	+	12.9475i	−0.488184	+	0.222869i
$16$		0			0
$17$	−19.7249			−0.281411			−0.140706	−	0.990051i	$-0.544937\pi$
$17$	−19.7249			−0.281411			−0.140706	+	0.990051i	$0.544937\pi$
$18$		0			0
$19$		−	27.9162i		−	0.337074i	−0.985695	−	0.168537i	$-0.946096\pi$
$19$		−	27.9162i		−	0.337074i	0.985695	−	0.168537i	$-0.0539043\pi$
$20$		0			0
$21$	95.9632	+	7.21613i	0.997185	+	0.0749852i
$22$		0			0
$23$	−60.3466	+	34.8411i	−0.547093	+	0.315864i	−0.747949	−	0.663757i	$-0.768961\pi$
$23$	−60.3466	+	34.8411i	−0.547093	+	0.315864i	0.200856	+	0.979621i	$0.435628\pi$
$24$		0			0
$25$	44.5004	−	77.0769i	0.356003	−	0.616615i
$26$		0			0
$27$	39.5789	−	134.598i	0.282110	−	0.959382i
$28$		0			0
$29$	−119.031	−	68.7227i	−0.762191	−	0.440051i	0.0678907	−	0.997693i	$-0.478373\pi$
$29$	−119.031	−	68.7227i	−0.762191	−	0.440051i	−0.830082	+	0.557641i	$0.811706\pi$
$30$		0			0
$31$	138.202	−	79.7908i	0.800702	−	0.462286i	−0.0430146	−	0.999074i	$-0.513696\pi$
$31$	138.202	−	79.7908i	0.800702	−	0.462286i	0.843717	+	0.536789i	$0.180363\pi$
$32$		0			0
$33$	137.085	−	192.455i	0.723133	−	1.01522i
$34$		0			0
$35$	95.0869	−	57.4998i	0.459218	−	0.277693i
$36$		0			0
$37$	−287.829			−1.27889			−0.639443	−	0.768839i	$-0.720835\pi$
$37$	−287.829			−1.27889			−0.639443	+	0.768839i	$0.720835\pi$
$38$		0			0
$39$	−56.7196	−	124.242i	−0.232882	−	0.510117i
$40$		0			0
$41$	−20.4288	−	35.3837i	−0.0778157	−	0.134781i	0.824492	−	0.565874i	$-0.191461\pi$
$41$	−20.4288	−	35.3837i	−0.0778157	−	0.134781i	−0.902307	+	0.431093i	$0.858128\pi$
$42$		0			0
$43$	55.4158	−	95.9830i	0.196531	−	0.340402i	−0.750870	−	0.660450i	$-0.770366\pi$
$43$	55.4158	−	95.9830i	0.196531	−	0.340402i	0.947401	+	0.320048i	$0.103699\pi$
$44$		0			0
$45$	−52.9443	−	153.102i	−0.175388	−	0.507181i
$46$		0			0
$47$	109.666	−	189.948i	0.340351	−	0.589504i	−0.644147	−	0.764902i	$-0.722788\pi$
$47$	109.666	−	189.948i	0.340351	−	0.589504i	0.984498	+	0.175397i	$0.0561209\pi$
$48$		0			0
$49$	−342.718	+	13.9050i	−0.999178	+	0.0405394i
$50$		0			0
$51$	9.75601	−	102.028i	0.0267866	−	0.280133i
$52$		0			0
$53$			209.770i			0.543664i	0.962345	+	0.271832i	$0.0876295\pi$
$53$			209.770i			0.543664i	−0.962345	+	0.271832i	$0.912371\pi$
$54$		0			0
$55$		−	272.837i		−	0.668897i
$56$		0			0
$57$	144.398	+	13.8074i	0.335544	+	0.0320849i
$58$		0			0
$59$	413.880	+	716.860i	0.913263	+	1.58182i	0.809425	+	0.587224i	$0.199779\pi$
$59$	413.880	+	716.860i	0.913263	+	1.58182i	0.103839	+	0.994594i	$0.466887\pi$
$60$		0			0
$61$	−594.209	−	343.066i	−1.24722	−	0.720085i	−0.276668	−	0.960965i	$-0.589230\pi$
$61$	−594.209	−	343.066i	−1.24722	−	0.720085i	−0.970555	+	0.240881i	$0.922564\pi$
$62$		0			0
$63$	−84.7896	+	492.806i	−0.169563	+	0.985519i
$64$		0			0
$65$	−136.575	−	78.8515i	−0.260616	−	0.150467i
$66$		0			0
$67$	−171.449	−	296.958i	−0.312624	−	0.541480i	0.666306	−	0.745679i	$-0.267875\pi$
$67$	−171.449	−	296.958i	−0.312624	−	0.541480i	−0.978930	+	0.204198i	$0.934541\pi$
$68$		0			0
$69$	−150.370	−	329.379i	−0.262354	−	0.574675i
$70$		0			0
$71$		−	387.476i		−	0.647675i	−0.946113	−	0.323838i	$-0.895027\pi$
$71$		−	387.476i		−	0.647675i	0.946113	−	0.323838i	$-0.104973\pi$
$72$		0			0
$73$			220.721i			0.353882i	0.984221	+	0.176941i	$0.0566202\pi$
$73$			220.721i			0.353882i	−0.984221	+	0.176941i	$0.943380\pi$
$74$		0			0
$75$	376.675	+	268.303i	0.579929	+	0.413080i
$76$		0			0
$77$	−406.215	+	737.734i	−0.601202	+	1.09185i
$78$		0			0
$79$	242.301	−	419.677i	0.345076	−	0.597688i	−0.640292	−	0.768132i	$-0.721187\pi$
$79$	242.301	−	419.677i	0.345076	−	0.597688i	0.985367	+	0.170443i	$0.0545200\pi$
$80$		0			0
$81$	676.638	+	271.297i	0.928173	+	0.372149i
$82$		0			0
$83$	−354.323	+	613.706i	−0.468579	+	0.811602i	−0.999355	−	0.0359099i	$-0.988567\pi$
$83$	−354.323	+	613.706i	−0.468579	+	0.811602i	0.530776	+	0.847512i	$0.321900\pi$
$84$		0			0
$85$	−59.1741	−	102.493i	−0.0755098	−	0.130787i
$86$		0			0
$87$	414.346	−	581.706i	0.510604	−	0.716844i
$88$		0			0
$89$	−140.929			−0.167848			−0.0839240	−	0.996472i	$-0.526745\pi$
$89$	−140.929			−0.167848			−0.0839240	+	0.996472i	$0.526745\pi$
$90$		0			0
$91$	251.891	+	416.550i	0.290169	+	0.479850i
$92$		0			0
$93$	344.368	+	754.321i	0.383970	+	0.841070i
$94$		0			0
$95$	145.055	−	83.7476i	0.156656	−	0.0904455i
$96$		0			0
$97$	−1304.31	−	753.041i	−1.36528	−	0.788245i	−0.374960	−	0.927041i	$-0.622343\pi$
$97$	−1304.31	−	753.041i	−1.36528	−	0.788245i	−0.990321	+	0.138796i	$0.955677\pi$
$98$		0			0
$99$	927.683	+	804.267i	0.941774	+	0.816484i
$100$		0			0
$101$	−923.516	+	1599.58i	−0.909834	+	1.57588i	−0.0955414	+	0.995425i	$0.530458\pi$
$101$	−923.516	+	1599.58i	−0.909834	+	1.57588i	−0.814293	+	0.580454i	$0.802875\pi$
$102$		0			0
$103$	−696.481	+	402.114i	−0.666275	+	0.384674i	−0.794664	−	0.607050i	$-0.792353\pi$
$103$	−696.481	+	402.114i	−0.666275	+	0.384674i	0.128389	+	0.991724i	$0.459019\pi$
$104$		0			0
$105$	250.391	+	520.282i	0.232720	+	0.483565i
$106$		0			0
$107$			282.997i			0.255685i	0.991794	+	0.127843i	$0.0408053\pi$
$107$			282.997i			0.255685i	−0.991794	+	0.127843i	$0.959195\pi$
$108$		0			0
$109$	1826.43			1.60496			0.802478	−	0.596681i	$-0.203514\pi$
$109$	1826.43			1.60496			0.802478	+	0.596681i	$0.203514\pi$
$110$		0			0
$111$	142.361	−	1488.81i	0.121733	−	1.27308i
$112$		0			0
$113$	−815.811	+	471.008i	−0.679159	+	0.392113i	−0.799538	−	0.600615i	$-0.794922\pi$
$113$	−815.811	+	471.008i	−0.679159	+	0.392113i	0.120379	+	0.992728i	$0.461589\pi$
$114$		0			0
$115$	−362.076	−	209.044i	−0.293598	−	0.169509i
$116$		0			0
$117$	670.701	−	231.935i	0.529968	−	0.183268i
$118$		0			0
$119$	7.40625	+	365.235i	0.00570529	+	0.281353i
$120$		0			0
$121$	368.410	+	638.105i	0.276792	+	0.479418i
$122$		0			0
$123$	193.129	−	88.1683i	0.141576	−	0.0646331i
$124$		0			0
$125$	1283.99			0.918749
$126$		0			0
$127$	320.551			0.223971			0.111985	−	0.993710i	$-0.464279\pi$
$127$	320.551			0.223971			0.111985	+	0.993710i	$0.464279\pi$
$128$		0			0
$129$	469.069	+	334.115i	0.320149	+	0.228040i
$130$		0			0
$131$	306.907	+	531.578i	0.204691	+	0.354536i	0.950034	−	0.312145i	$-0.101048\pi$
$131$	306.907	+	531.578i	0.204691	+	0.354536i	−0.745343	+	0.666681i	$0.767714\pi$
$132$		0			0
$133$	−516.908	+	10.4819i	−0.337005	+	0.00683379i
$134$		0			0
$135$	818.118	−	198.133i	0.521573	−	0.126315i
$136$		0			0
$137$	1515.86	+	875.182i	0.945318	+	0.545780i	0.891623	−	0.452778i	$-0.149567\pi$
$137$	1515.86	+	875.182i	0.945318	+	0.545780i	0.0536948	+	0.998557i	$0.482900\pi$
$138$		0			0
$139$	−1120.72	+	647.048i	−0.683872	+	0.394834i	−0.801312	−	0.598246i	$-0.795865\pi$
$139$	−1120.72	+	647.048i	−0.683872	+	0.394834i	0.117440	+	0.993080i	$0.462531\pi$
$140$		0			0
$141$	928.274	+	661.204i	0.554431	+	0.394918i
$142$		0			0
$143$	1195.23			0.698950
$144$		0			0
$145$		−	824.664i		−	0.472308i
$146$		0			0
$147$	97.5851	−	1779.61i	0.0547530	−	0.998500i
$148$		0			0
$149$	−2499.23	+	1442.93i	−1.37413	+	0.793352i	−0.991445	−	0.130528i	$-0.958333\pi$
$149$	−2499.23	+	1442.93i	−1.37413	+	0.793352i	−0.382681	+	0.923880i	$0.624999\pi$
$150$		0			0
$151$	1540.63	−	2668.45i	0.830297	−	1.43812i	−0.0675056	−	0.997719i	$-0.521504\pi$
$151$	1540.63	−	2668.45i	0.830297	−	1.43812i	0.897803	−	0.440398i	$-0.145163\pi$
$152$		0			0
$153$	522.922	+	100.927i	0.276312	+	0.0533298i
$154$		0			0
$155$	829.202	+	478.740i	0.429697	+	0.248086i
$156$		0			0
$157$	−1090.13	+	629.388i	−0.554153	+	0.319941i	−0.750795	−	0.660535i	$-0.770330\pi$
$157$	−1090.13	+	629.388i	−0.554153	+	0.319941i	0.196642	+	0.980475i	$0.436996\pi$
$158$		0			0
$159$	−1085.05	−	103.753i	−0.541195	−	0.0517495i
$160$		0			0
$161$	667.793	+	1104.32i	0.326891	+	0.540576i
$162$		0			0
$163$	−2906.94			−1.39687			−0.698434	−	0.715675i	$-0.746119\pi$
$163$	−2906.94			−1.39687			−0.698434	+	0.715675i	$0.746119\pi$
$164$		0			0
$165$	1411.27	+	134.946i	0.665860	+	0.0636700i
$166$		0			0
$167$	−286.775	−	496.709i	−0.132882	−	0.230159i	0.791904	−	0.610645i	$-0.209090\pi$
$167$	−286.775	−	496.709i	−0.132882	−	0.230159i	−0.924786	+	0.380487i	$0.875756\pi$
$168$		0			0
$169$	−753.072	+	1304.36i	−0.342773	+	0.593700i
$170$		0			0
$171$	−142.840	+	740.078i	−0.0638785	+	0.330966i
$172$		0			0
$173$	−1931.13	+	3344.82i	−0.848679	+	1.46995i	0.0337092	+	0.999432i	$0.489268\pi$
$173$	−1931.13	+	3344.82i	−0.848679	+	1.46995i	−0.882388	+	0.470523i	$0.844065\pi$
$174$		0			0
$175$	−1443.90	−	795.048i	−0.623706	−	0.343429i
$176$		0			0
$177$	−3912.71	+	1786.25i	−1.66157	+	0.758549i
$178$		0			0
$179$		−	2248.26i		−	0.938787i	−0.882989	−	0.469394i	$-0.844473\pi$
$179$		−	2248.26i		−	0.938787i	0.882989	−	0.469394i	$-0.155527\pi$
$180$		0			0
$181$		−	166.407i		−	0.0683368i	−0.999416	−	0.0341684i	$-0.989122\pi$
$181$		−	166.407i		−	0.0683368i	0.999416	−	0.0341684i	$-0.0108783\pi$
$182$		0			0
$183$	2068.43	−	2903.90i	0.835534	−	1.17302i
$184$		0			0
$185$	−863.478	−	1495.59i	−0.343157	−	0.594366i
$186$		0			0
$187$	776.787	+	448.478i	0.303766	+	0.175379i
$188$		0			0
$189$	−2507.13	−	682.323i	−0.964904	−	0.262601i
$190$		0			0
$191$	−1758.88	−	1015.49i	−0.666324	−	0.384703i	0.128358	−	0.991728i	$-0.459029\pi$
$191$	−1758.88	−	1015.49i	−0.666324	−	0.384703i	−0.794682	+	0.607025i	$0.792363\pi$
$192$		0			0
$193$	251.118	+	434.949i	0.0936573	+	0.162219i	0.909047	−	0.416693i	$-0.136811\pi$
$193$	251.118	+	434.949i	0.0936573	+	0.162219i	−0.815390	+	0.578912i	$0.803478\pi$
$194$		0			0
$195$	475.415	−	667.441i	0.174591	−	0.245110i
$196$		0			0
$197$		−	3949.11i		−	1.42823i	−0.700026	−	0.714117i	$-0.746828\pi$
$197$		−	3949.11i		−	1.42823i	0.700026	−	0.714117i	$-0.253172\pi$
$198$		0			0
$199$		−	629.709i		−	0.224316i	−0.993690	−	0.112158i	$-0.964224\pi$
$199$		−	629.709i		−	0.224316i	0.993690	−	0.112158i	$-0.0357763\pi$
$200$		0			0
$201$	1620.83	−	739.952i	0.568779	−	0.259663i
$202$		0			0
$203$	−1227.81	+	2229.84i	−0.424508	+	0.770956i
$204$		0			0
$205$	122.572	−	212.300i	0.0417599	−	0.0723302i
$206$		0			0
$207$	1778.10	−	614.886i	0.597038	−	0.206462i
$208$		0			0
$209$	−634.720	+	1099.37i	−0.210069	+	0.363851i
$210$		0			0
$211$	−1494.95	−	2589.33i	−0.487757	−	0.844820i	0.512144	−	0.858900i	$-0.328851\pi$
$211$	−1494.95	−	2589.33i	−0.487757	−	0.844820i	−0.999901	+	0.0140797i	$0.995518\pi$
$212$		0			0
$213$	2004.24	+	191.647i	0.644735	+	0.0616500i
$214$		0			0
$215$	664.983			0.210937
$216$		0			0
$217$	−1529.33	−	2529.05i	−0.478424	−	0.791165i
$218$		0			0
$219$	−1141.69	−	109.169i	−0.352275	−	0.0336848i
$220$		0			0
$221$	448.992	−	259.226i	0.136663	−	0.0789023i
$222$		0			0
$223$	2829.72	+	1633.74i	0.849740	+	0.490598i	0.860563	−	0.509344i	$-0.170112\pi$
$223$	2829.72	+	1633.74i	0.849740	+	0.490598i	−0.0108230	+	0.999941i	$0.503445\pi$
$224$		0			0
$225$	−1574.12	+	1815.67i	−0.466406	+	0.537976i
$226$		0			0
$227$	2836.86	−	4913.59i	0.829468	−	1.43668i	−0.0689889	−	0.997617i	$-0.521977\pi$
$227$	2836.86	−	4913.59i	0.829468	−	1.43668i	0.898457	−	0.439063i	$-0.144689\pi$
$228$		0			0
$229$	4528.48	−	2614.52i	1.30677	−	0.754465i	0.325215	−	0.945640i	$-0.394563\pi$
$229$	4528.48	−	2614.52i	1.30677	−	0.754465i	0.981556	+	0.191175i	$0.0612298\pi$
$230$		0			0
$231$	−3615.06	−	2466.06i	−1.02967	−	0.702402i
$232$		0			0
$233$		−	3433.84i		−	0.965487i	−0.875762	−	0.482743i	$-0.839640\pi$
$233$		−	3433.84i		−	0.965487i	0.875762	−	0.482743i	$-0.160360\pi$
$234$		0			0
$235$	1315.98			0.365299
$236$		0			0
$237$	2050.96	+	1460.89i	0.562128	+	0.400401i
$238$		0			0
$239$	469.677	−	271.168i	0.127117	−	0.0733908i	−0.435093	−	0.900385i	$-0.643285\pi$
$239$	469.677	−	271.168i	0.127117	−	0.0733908i	0.562210	+	0.826995i	$0.309951\pi$
$240$		0			0
$241$	−3110.33	−	1795.75i	−0.831343	−	0.479976i	0.0229693	−	0.999736i	$-0.492688\pi$
$241$	−3110.33	−	1795.75i	−0.831343	−	0.479976i	−0.854312	+	0.519760i	$0.826021\pi$
$242$		0			0
$243$	−1737.97	+	3365.77i	−0.458809	+	0.888535i
$244$		0			0
$245$	−1100.40	−	1739.08i	−0.286946	−	0.453493i
$246$		0			0
$247$	366.876	+	635.448i	0.0945092	+	0.163695i
$248$		0			0
$249$	−2999.18	−	2136.30i	−0.763315	−	0.543705i
$250$		0			0
$251$	4334.39			1.08998			0.544988	−	0.838444i	$-0.316534\pi$
$251$	4334.39			1.08998			0.544988	+	0.838444i	$0.316534\pi$
$252$		0			0
$253$	3168.68			0.787404
$254$		0			0
$255$	559.416	−	255.388i	0.137380	−	0.0627178i
$256$		0			0
$257$	−3282.88	−	5686.12i	−0.796812	−	1.38012i	−0.921682	−	0.387946i	$-0.873185\pi$
$257$	−3282.88	−	5686.12i	−0.796812	−	1.38012i	0.124870	−	0.992173i	$-0.460148\pi$
$258$		0			0
$259$	108.073	+	5329.57i	0.0259279	+	1.27862i
$260$		0			0
$261$	2803.97	+	2430.94i	0.664986	+	0.576519i
$262$		0			0
$263$	6274.79	+	3622.75i	1.47118	+	0.849386i	0.999476	−	0.0323711i	$-0.0103058\pi$
$263$	6274.79	+	3622.75i	1.47118	+	0.849386i	0.471704	+	0.881757i	$0.343639\pi$
$264$		0			0
$265$	−1089.99	+	629.305i	−0.252669	+	0.145879i
$266$		0			0
$267$	69.7041	−	728.965i	0.0159769	−	0.167086i
$268$		0			0
$269$	−3455.87			−0.783302			−0.391651	−	0.920114i	$-0.628096\pi$
$269$	−3455.87			−0.783302			−0.391651	+	0.920114i	$0.628096\pi$
$270$		0			0
$271$		−	2471.30i		−	0.553951i	−0.960877	−	0.276975i	$-0.910668\pi$
$271$		−	2471.30i		−	0.553951i	0.960877	−	0.276975i	$-0.0893321\pi$
$272$		0			0
$273$	−2279.22	+	1096.89i	−0.505291	+	0.243176i
$274$		0			0
$275$	−3504.94	+	2023.58i	−0.768567	+	0.443732i
$276$		0			0
$277$	2256.85	−	3908.97i	0.489533	−	0.847897i	−0.510394	−	0.859941i	$-0.670500\pi$
$277$	2256.85	−	3908.97i	0.489533	−	0.847897i	0.999927	+	0.0120440i	$0.00383381\pi$
$278$		0			0
$279$	−4072.10	+	1408.17i	−0.873800	+	0.302169i
$280$		0			0
$281$	2090.48	+	1206.94i	0.443799	+	0.256228i	0.705208	−	0.709001i	$-0.250854\pi$
$281$	2090.48	+	1206.94i	0.443799	+	0.256228i	−0.261409	+	0.965228i	$0.584187\pi$
$282$		0			0
$283$	3893.62	−	2247.98i	0.817851	−	0.472187i	−0.0318238	−	0.999493i	$-0.510132\pi$
$283$	3893.62	−	2247.98i	0.817851	−	0.472187i	0.849675	+	0.527307i	$0.176798\pi$
$284$		0			0
$285$	361.445	+	791.728i	0.0751233	+	0.164554i
$286$		0			0
$287$	−647.511	+	391.555i	−0.133175	+	0.0805322i
$288$		0			0
$289$	−4523.93			−0.920808
$290$		0			0
$291$	4540.27	−	6374.14i	0.914622	−	1.28405i
$292$		0			0
$293$	1569.64	+	2718.69i	0.312966	+	0.542073i	0.979003	−	0.203845i	$-0.0653440\pi$
$293$	1569.64	+	2718.69i	0.312966	+	0.542073i	−0.666037	+	0.745919i	$0.732011\pi$
$294$		0			0
$295$	−2483.25	+	4301.12i	−0.490103	+	0.848884i
$296$		0			0
$297$	−4618.96	+	4400.70i	−0.902421	+	0.859779i
$298$		0			0
$299$	915.768	−	1586.16i	0.177125	−	0.306789i
$300$		0			0
$301$	−1798.07	−	990.065i	−0.344316	−	0.189589i
$302$		0			0
$303$	−7817.13	−	5568.10i	−1.48212	−	1.05571i
$304$		0			0
$305$		−	4116.75i		−	0.772868i
$306$		0			0
$307$			10294.0i			1.91371i	0.290560	+	0.956857i	$0.406158\pi$
$307$			10294.0i			1.91371i	−0.290560	+	0.956857i	$0.593842\pi$
$308$		0			0
$309$	−1735.47	−	3801.48i	−0.319507	−	0.699865i
$310$		0			0
$311$	−3940.59	−	6825.30i	−0.718489	−	1.24446i	−0.961598	−	0.274461i	$-0.911501\pi$
$311$	−3940.59	−	6825.30i	−0.718489	−	1.24446i	0.243109	−	0.969999i	$-0.421833\pi$
$312$		0			0
$313$	7096.84	+	4097.36i	1.28159	+	0.739925i	0.977139	−	0.212604i	$-0.0681943\pi$
$313$	7096.84	+	4097.36i	1.28159	+	0.739925i	0.304449	+	0.952529i	$0.401528\pi$
$314$		0			0
$315$	−2815.03	+	1037.83i	−0.503521	+	0.185635i
$316$		0			0
$317$	7590.80	+	4382.55i	1.34493	+	0.776494i	0.987526	−	0.157457i	$-0.0503295\pi$
$317$	7590.80	+	4382.55i	1.34493	+	0.776494i	0.357401	+	0.933951i	$0.383663\pi$
$318$		0			0
$319$	3125.05	+	5412.74i	0.548493	+	0.950017i
$320$		0			0
$321$	−1463.82	−	139.971i	−0.254524	−	0.0243378i
$322$		0			0
$323$			550.644i			0.0948564i
$324$		0			0
$325$			2339.31i			0.399266i
$326$		0			0
$327$	−903.359	+	9447.32i	−0.152770	+	1.59767i
$328$		0			0
$329$	−3558.33	−	1959.31i	−0.596283	−	0.328329i
$330$		0			0
$331$	−3431.76	+	5943.98i	−0.569869	+	0.987041i	0.426710	+	0.904389i	$0.359673\pi$
$331$	−3431.76	+	5943.98i	−0.569869	+	0.987041i	−0.996578	+	0.0826527i	$0.973661\pi$
$332$		0			0
$333$	7630.55	+	1472.74i	1.25571	+	0.242360i
$334$		0			0
$335$	1028.68	−	1781.73i	0.167770	−	0.290586i
$336$		0			0
$337$	2323.81	+	4024.96i	0.375627	+	0.650605i	0.990421	−	0.138083i	$-0.0440941\pi$
$337$	2323.81	+	4024.96i	0.375627	+	0.650605i	−0.614794	+	0.788688i	$0.710761\pi$
$338$		0			0
$339$	−2032.82	−	4452.79i	−0.325686	−	0.713399i
$340$		0			0
$341$	−7256.70			−1.15241
$342$		0			0
$343$	386.154	+	6340.70i	0.0607882	+	0.998151i
$344$		0			0
$345$	1260.38	−	1769.46i	0.196686	−	0.276130i
$346$		0			0
$347$	8295.04	−	4789.14i	1.28329	−	0.740907i	0.305840	−	0.952083i	$-0.401063\pi$
$347$	8295.04	−	4789.14i	1.28329	−	0.740907i	0.977448	+	0.211176i	$0.0677294\pi$
$348$		0			0
$349$	−755.168	−	435.997i	−0.115826	−	0.0668721i	0.440968	−	0.897523i	$-0.354635\pi$
$349$	−755.168	−	435.997i	−0.115826	−	0.0668721i	−0.556794	+	0.830651i	$0.687969\pi$
$350$		0			0
$351$	867.966	+	3583.96i	0.131990	+	0.545007i
$352$		0			0
$353$	−4148.63	+	7185.64i	−0.625523	+	1.08344i	0.362917	+	0.931821i	$0.381781\pi$
$353$	−4148.63	+	7185.64i	−0.625523	+	1.08344i	−0.988440	+	0.151615i	$0.951552\pi$
$354$		0			0
$355$	2013.36	−	1162.42i	0.301009	−	0.173788i
$356$		0			0
$357$	−1892.86	−	142.337i	−0.280619	−	0.0211017i
$358$		0			0
$359$			976.696i			0.143588i	0.997419	+	0.0717939i	$0.0228724\pi$
$359$			976.696i			0.143588i	−0.997419	+	0.0717939i	$0.977128\pi$
$360$		0			0
$361$	6079.69			0.886381
$362$		0			0
$363$	−3482.85	+	1590.01i	−0.503588	+	0.229901i
$364$		0			0
$365$	−1146.89	+	662.155i	−0.164468	+	0.0949556i
$366$		0			0
$367$	6001.51	+	3464.97i	0.853614	+	0.492834i	0.861868	−	0.507132i	$-0.169294\pi$
$367$	6001.51	+	3464.97i	0.853614	+	0.492834i	−0.00825490	+	0.999966i	$0.502628\pi$
$368$		0			0
$369$	360.534	+	1042.58i	0.0508635	+	0.147085i
$370$		0			0
$371$	3884.20	−	78.7640i	0.543552	−	0.0110222i
$372$		0			0
$373$	2259.68	+	3913.89i	0.313678	+	0.543307i	0.979156	−	0.203111i	$-0.0651053\pi$
$373$	2259.68	+	3913.89i	0.313678	+	0.543307i	−0.665477	+	0.746418i	$0.731772\pi$
$374$		0			0
$375$	−635.067	+	6641.52i	−0.0874525	+	0.914578i
$376$		0			0
$377$	3612.63			0.493528
$378$		0			0
$379$	2781.32			0.376958			0.188479	−	0.982077i	$-0.439644\pi$
$379$	2781.32			0.376958			0.188479	+	0.982077i	$0.439644\pi$
$380$		0			0
$381$	−158.546	+	1658.07i	−0.0213190	+	0.222954i
$382$		0			0
$383$	−5449.44	−	9438.71i	−0.727033	−	1.25926i	−0.958132	−	0.286327i	$-0.907566\pi$
$383$	−5449.44	−	9438.71i	−0.727033	−	1.25926i	0.231099	−	0.972930i	$-0.425768\pi$
$384$		0			0
$385$	−5051.97	+	102.444i	−0.668759	+	0.0135611i
$386$		0			0
$387$	−1960.23	+	2261.03i	−0.257479	+	0.296989i
$388$		0			0
$389$	1922.09	+	1109.72i	0.250524	+	0.144640i	0.620004	−	0.784598i	$-0.287131\pi$
$389$	1922.09	+	1109.72i	0.250524	+	0.144640i	−0.369480	+	0.929239i	$0.620464\pi$
$390$		0			0
$391$	1190.33	−	687.237i	0.153958	−	0.0888877i
$392$		0			0
$393$	−2901.41	+	1324.57i	−0.372410	+	0.170015i
$394$		0			0
$395$	2907.58			0.370370
$396$		0			0
$397$		−	10873.7i		−	1.37464i	−0.726354	−	0.687321i	$-0.758786\pi$
$397$		−	10873.7i		−	1.37464i	0.726354	−	0.687321i	$-0.241214\pi$
$398$		0			0
$399$	201.447	−	2678.92i	0.0252756	−	0.336125i
$400$		0			0
$401$	−5301.00	+	3060.53i	−0.660147	+	0.381136i	−0.792333	−	0.610089i	$-0.791134\pi$
$401$	−5301.00	+	3060.53i	−0.660147	+	0.381136i	0.132186	+	0.991225i	$0.457800\pi$
$402$		0			0
$403$	−2097.23	+	3632.51i	−0.259232	+	0.449003i
$404$		0			0
$405$	620.209	+	4329.76i	0.0760949	+	0.531228i
$406$		0			0
$407$	11335.0	+	6544.26i	1.38048	+	0.797020i
$408$		0			0
$409$	12155.0	−	7017.69i	1.46950	−	0.848416i	0.470085	−	0.882621i	$-0.344223\pi$
$409$	12155.0	−	7017.69i	1.46950	−	0.848416i	0.999415	+	0.0342045i	$0.0108898\pi$
$410$		0			0
$411$	−5276.68	+	7408.00i	−0.633283	+	0.889075i
$412$		0			0
$413$	13118.3	−	7932.75i	1.56298	−	0.945145i
$414$		0			0
$415$	−4251.83			−0.502926
$416$		0			0
$417$	−2792.58	−	6117.03i	−0.327946	−	0.718350i
$418$		0			0
$419$	−4144.18	−	7177.94i	−0.483190	−	0.836910i	0.516624	−	0.856213i	$-0.327189\pi$
$419$	−4144.18	−	7177.94i	−0.483190	−	0.836910i	−0.999814	+	0.0193028i	$0.993855\pi$
$420$		0			0
$421$	7767.30	−	13453.4i	0.899181	−	1.55743i	0.0706368	−	0.997502i	$-0.477497\pi$
$421$	7767.30	−	13453.4i	0.899181	−	1.55743i	0.828544	−	0.559924i	$-0.189170\pi$
$422$		0			0
$423$	−3879.25	+	4474.52i	−0.445899	+	0.514323i
$424$		0			0
$425$	−877.765	+	1520.33i	−0.100183	+	0.173522i
$426$		0			0
$427$	−6129.26	+	11131.4i	−0.694651	+	1.26157i
$428$		0			0
$429$	−591.163	+	6182.37i	−0.0665306	+	0.695776i
$430$		0			0
$431$		−	3167.89i		−	0.354041i	−0.984207	−	0.177021i	$-0.943354\pi$
$431$		−	3167.89i		−	0.354041i	0.984207	−	0.177021i	$-0.0566459\pi$
$432$		0			0
$433$		−	2187.70i		−	0.242804i	−0.992603	−	0.121402i	$-0.961261\pi$
$433$		−	2187.70i		−	0.242804i	0.992603	−	0.121402i	$-0.0387391\pi$
$434$		0			0
$435$	4265.62	+	407.882i	0.470163	+	0.0449573i
$436$		0			0
$437$	972.630	+	1684.65i	0.106470	+	0.184411i
$438$		0			0
$439$	1703.79	+	983.684i	0.185234	+	0.106945i	0.589749	−	0.807586i	$-0.299227\pi$
$439$	1703.79	+	983.684i	0.185234	+	0.106945i	−0.404516	+	0.914531i	$0.632560\pi$
$440$		0			0
$441$	9156.86	+	1384.96i	0.988754	+	0.149548i
$442$		0			0
$443$	2229.21	+	1287.04i	0.239081	+	0.138034i	0.614754	−	0.788719i	$-0.289255\pi$
$443$	2229.21	+	1287.04i	0.239081	+	0.138034i	−0.375673	+	0.926752i	$0.622588\pi$
$444$		0			0
$445$	−422.783	−	732.282i	−0.0450379	−	0.0780079i
$446$		0			0
$447$	−6227.51	−	13641.1i	−0.658952	−	1.44340i
$448$		0			0
$449$		−	9168.11i		−	0.963630i	−0.876273	−	0.481815i	$-0.839978\pi$
$449$		−	9168.11i		−	0.963630i	0.876273	−	0.481815i	$-0.160022\pi$
$450$		0			0
$451$			1857.93i			0.193983i
$452$		0			0
$453$	13040.7	+	9288.84i	1.35255	+	0.963416i
$454$		0			0
$455$	−1408.77	+	2558.49i	−0.145152	+	0.263613i
$456$		0			0
$457$	449.418	−	778.415i	0.0460019	−	0.0796777i	−0.842108	−	0.539310i	$-0.818685\pi$
$457$	449.418	−	778.415i	0.0460019	−	0.0796777i	0.888110	+	0.459632i	$0.152019\pi$
$458$		0			0
$459$	−780.690	+	2654.92i	−0.0793889	+	0.269981i
$460$		0			0
$461$	−750.955	+	1300.69i	−0.0758686	+	0.131408i	−0.901464	−	0.432855i	$-0.857506\pi$
$461$	−750.955	+	1300.69i	−0.0758686	+	0.131408i	0.825595	+	0.564263i	$0.190840\pi$
$462$		0			0
$463$	515.882	+	893.534i	0.0517820	+	0.0896891i	0.890755	−	0.454485i	$-0.150177\pi$
$463$	515.882	+	893.534i	0.0517820	+	0.0896891i	−0.838973	+	0.544174i	$0.816843\pi$
$464$		0			0
$465$	−2886.44	+	4052.31i	−0.287861	+	0.404132i
$466$		0			0
$467$	−8619.68			−0.854114			−0.427057	−	0.904225i	$-0.640450\pi$
$467$	−8619.68			−0.854114			−0.427057	+	0.904225i	$0.640450\pi$
$468$		0			0
$469$	−5434.23	+	3286.12i	−0.535031	+	0.323537i
$470$		0			0
$471$	−2716.37	−	5950.07i	−0.265740	−	0.582091i
$472$		0			0
$473$	−4364.66	+	2519.94i	−0.424286	+	0.244962i
$474$		0			0
$475$	−2151.69	−	1242.28i	−0.207845	−	0.119999i
$476$		0			0
$477$	1073.34	−	5561.17i	0.103029	−	0.533812i
$478$		0			0
$479$	−2037.51	+	3529.07i	−0.194355	+	0.336634i	−0.946689	−	0.322149i	$-0.895595\pi$
$479$	−2037.51	+	3529.07i	−0.194355	+	0.336634i	0.752334	+	0.658782i	$0.228928\pi$
$480$		0			0
$481$	6551.77	−	3782.66i	0.621070	−	0.358575i
$482$		0			0
$483$	−6042.47	+	2907.99i	−0.569237	+	0.273951i
$484$		0			0
$485$		−	9036.40i		−	0.846025i
$486$		0			0
$487$	−14817.8			−1.37876			−0.689381	−	0.724399i	$-0.742117\pi$
$487$	−14817.8			−1.37876			−0.689381	+	0.724399i	$0.742117\pi$
$488$		0			0
$489$	1437.78	−	15036.3i	0.132963	−	1.39052i
$490$		0			0
$491$	−6217.36	+	3589.59i	−0.571457	+	0.329931i	−0.757731	−	0.652567i	$-0.773692\pi$
$491$	−6217.36	+	3589.59i	−0.571457	+	0.329931i	0.186274	+	0.982498i	$0.440359\pi$
$492$		0			0
$493$	2347.88	+	1355.55i	0.214489	+	0.123835i
$494$		0			0
$495$	−1396.03	+	7233.11i	−0.126762	+	0.656776i
$496$		0			0
$497$	−7174.68	+	145.488i	−0.647542	+	0.0131309i
$498$		0			0
$499$	−5380.59	−	9319.46i	−0.482702	−	0.836065i	0.517100	−	0.855925i	$-0.327011\pi$
$499$	−5380.59	−	9319.46i	−0.482702	−	0.836065i	−0.999803	+	0.0198598i	$0.993678\pi$
$500$		0			0
$501$	2711.09	−	1237.69i	0.241762	−	0.110371i
$502$		0			0
$503$	11285.3			1.00037			0.500186	−	0.865918i	$-0.333265\pi$
$503$	11285.3			1.00037			0.500186	+	0.865918i	$0.333265\pi$
$504$		0			0
$505$	−11082.1			−0.976527
$506$		0			0
$507$	−6374.41	−	4540.45i	−0.558377	−	0.397729i
$508$		0			0
$509$	−5404.52	−	9360.91i	−0.470631	−	0.815157i	0.528805	−	0.848744i	$-0.322640\pi$
$509$	−5404.52	−	9360.91i	−0.470631	−	0.815157i	−0.999436	+	0.0335864i	$0.989307\pi$
$510$		0			0
$511$	4086.96	−	82.8755i	0.353809	−	0.00717456i
$512$		0			0
$513$	−3757.45	−	1104.89i	−0.323383	−	0.0950919i
$514$		0			0
$515$	−4178.84	−	2412.66i	−0.357557	−	0.206436i
$516$		0			0
$517$	−8637.54	+	4986.89i	−0.734775	+	0.424223i
$518$		0			0
$519$	−16346.1	−	11643.3i	−1.38250	−	0.984745i
$520$		0			0
$521$	−3085.93			−0.259495			−0.129747	−	0.991547i	$-0.541417\pi$
$521$	−3085.93			−0.259495			−0.129747	+	0.991547i	$0.541417\pi$
$522$		0			0
$523$		−	2155.94i		−	0.180254i	−0.995930	−	0.0901268i	$-0.971273\pi$
$523$		−	2155.94i		−	0.180254i	0.995930	−	0.0901268i	$-0.0287272\pi$
$524$		0			0
$525$	4826.59	−	7075.42i	0.401238	−	0.588184i
$526$		0			0
$527$	−2726.01	+	1573.87i	−0.225327	+	0.130092i
$528$		0			0
$529$	−3655.69	+	6331.85i	−0.300460	+	0.520412i
$530$		0			0
$531$	−7304.27	−	21122.2i	−0.596946	−	1.72623i
$532$		0			0
$533$	930.030	+	536.953i	0.0755799	+	0.0436361i
$534$		0			0
$535$	−1470.48	+	848.982i	−0.118831	+	0.0686069i
$536$		0			0
$537$	11629.3	+	1112.00i	0.934525	+	0.0893599i
$538$		0			0
$539$	13812.7	+	7244.67i	1.10382	+	0.578942i
$540$		0			0
$541$	19410.4			1.54255			0.771273	−	0.636504i	$-0.219620\pi$
$541$	19410.4			1.54255			0.771273	+	0.636504i	$0.219620\pi$
$542$		0			0
$543$	860.752	+	82.3057i	0.0680265	+	0.00650475i
$544$		0			0
$545$	5479.23	+	9490.31i	0.430651	+	0.745909i
$546$		0			0
$547$	−2279.16	+	3947.62i	−0.178153	+	0.308570i	−0.941248	−	0.337716i	$-0.890346\pi$
$547$	−2279.16	+	3947.62i	−0.178153	+	0.308570i	0.763095	+	0.646286i	$0.223679\pi$
$548$		0			0
$549$	13997.5	+	12135.4i	1.08816	+	0.943396i
$550$		0			0
$551$	−1918.48	+	3322.90i	−0.148330	+	0.256915i
$552$		0			0
$553$	−7861.91	−	4328.97i	−0.604561	−	0.332887i
$554$		0			0
$555$	8163.09	−	3726.67i	0.624331	−	0.285024i
$556$		0			0
$557$		−	4710.38i		−	0.358322i	−0.983820	−	0.179161i	$-0.942662\pi$
$557$		−	4710.38i		−	0.358322i	0.983820	−	0.179161i	$-0.0573383\pi$
$558$		0			0
$559$			2913.11i			0.220414i
$560$		0			0
$561$	−2703.98	+	3796.16i	−0.203498	+	0.285693i
$562$		0			0
$563$	2316.26	+	4011.87i	0.173390	+	0.300320i	0.939603	−	0.342267i	$-0.111195\pi$
$563$	2316.26	+	4011.87i	0.173390	+	0.300320i	−0.766213	+	0.642587i	$0.777861\pi$
$564$		0			0
$565$	−4894.81	−	2826.02i	−0.364471	−	0.210428i
$566$		0			0
$567$	4769.39	−	12630.8i	0.353255	−	0.935527i
$568$		0			0
$569$	−6667.01	−	3849.20i	−0.491205	−	0.283597i	0.233869	−	0.972268i	$-0.424861\pi$
$569$	−6667.01	−	3849.20i	−0.491205	−	0.283597i	−0.725074	+	0.688671i	$0.758195\pi$
$570$		0			0
$571$	−8556.34	−	14820.0i	−0.627096	−	1.08616i	−0.988132	−	0.153610i	$-0.950910\pi$
$571$	−8556.34	−	14820.0i	−0.627096	−	1.08616i	0.361036	−	0.932552i	$-0.382423\pi$
$572$		0			0
$573$	6122.62	−	8595.64i	0.446381	−	0.626680i
$574$		0			0
$575$			6201.77i			0.449794i
$576$		0			0
$577$		−	2389.01i		−	0.172367i	−0.996279	−	0.0861834i	$-0.972533\pi$
$577$		−	2389.01i		−	0.172367i	0.996279	−	0.0861834i	$-0.0274671\pi$
$578$		0			0
$579$	−2374.00	+	1083.79i	−0.170398	+	0.0777910i
$580$		0			0
$581$	11496.7	+	6330.38i	0.820935	+	0.452028i
$582$		0			0
$583$	4769.48	−	8260.97i	0.338819	−	0.586852i
$584$		0			0
$585$	3217.24	+	2789.23i	0.227379	+	0.197129i
$586$		0			0
$587$	7877.22	−	13643.7i	0.553880	−	0.959348i	−0.444110	−	0.895972i	$-0.646480\pi$
$587$	7877.22	−	13643.7i	0.553880	−	0.959348i	0.997990	−	0.0633757i	$-0.0201866\pi$
$588$		0			0
$589$	−2227.45	−	3858.06i	−0.155824	−	0.269896i
$590$		0			0
$591$	20427.0	+	1953.24i	1.42175	+	0.135949i
$592$		0			0
$593$	−14439.8			−0.999953			−0.499976	−	0.866039i	$-0.666658\pi$
$593$	−14439.8			−0.999953			−0.499976	+	0.866039i	$0.666658\pi$
$594$		0			0
$595$	−1875.58	+	1134.18i	−0.129229	+	0.0781458i
$596$		0			0
$597$	3257.21	+	311.457i	0.223298	+	0.0213519i
$598$		0			0
$599$	−13069.6	+	7545.75i	−0.891504	+	0.514710i	−0.874434	−	0.485145i	$-0.838767\pi$
$599$	−13069.6	+	7545.75i	−0.891504	+	0.514710i	−0.0170695	+	0.999854i	$0.505434\pi$
$600$		0			0
$601$	−21885.4	−	12635.5i	−1.48540	−	0.857595i	−0.485536	−	0.874217i	$-0.661376\pi$
$601$	−21885.4	−	12635.5i	−1.48540	−	0.857595i	−0.999862	+	0.0166219i	$0.994709\pi$
$602$		0			0
$603$	3025.78	+	8749.83i	0.204343	+	0.590913i
$604$		0			0
$605$	−2210.44	+	3828.59i	−0.148541	+	0.257280i
$606$		0			0
$607$	16922.0	−	9769.93i	1.13154	−	0.653293i	0.187216	−	0.982319i	$-0.440053\pi$
$607$	16922.0	−	9769.93i	1.13154	−	0.653293i	0.944321	+	0.329025i	$0.106720\pi$
$608$		0			0
$609$	−10926.7	−	7453.79i	−0.727048	−	0.495965i
$610$		0			0
$611$			5764.97i			0.381711i
$612$		0			0
$613$	22968.2			1.51334			0.756671	−	0.653796i	$-0.226825\pi$
$613$	22968.2			1.51334			0.756671	+	0.653796i	$0.226825\pi$
$614$		0			0
$615$	1037.51	+	739.013i	0.0680268	+	0.0484551i
$616$		0			0
$617$	−24539.5	+	14167.9i	−1.60117	+	0.924437i	−0.609920	+	0.792463i	$0.708798\pi$
$617$	−24539.5	+	14167.9i	−1.60117	+	0.924437i	−0.991253	+	0.131974i	$0.957868\pi$
$618$		0			0
$619$	−17347.3	−	10015.5i	−1.12641	−	0.650332i	−0.183379	−	0.983042i	$-0.558703\pi$
$619$	−17347.3	−	10015.5i	−1.12641	−	0.650332i	−0.943029	+	0.332710i	$0.892037\pi$
$620$		0			0
$621$	2301.08	+	9501.48i	0.148694	+	0.613979i
$622$		0			0
$623$	52.9157	+	2609.51i	0.00340292	+	0.167813i
$624$		0			0
$625$	−1710.61	−	2962.87i	−0.109479	−	0.189624i
$626$		0			0
$627$	−5372.61	−	3826.88i	−0.342203	−	0.243749i
$628$		0			0
$629$	5677.39			0.359893
$630$		0			0
$631$	7219.42			0.455469			0.227734	−	0.973723i	$-0.426868\pi$
$631$	7219.42			0.455469			0.227734	+	0.973723i	$0.426868\pi$
$632$		0			0
$633$	14132.9	−	6452.03i	0.887412	−	0.405127i
$634$		0			0
$635$	961.643	+	1665.61i	0.0600970	+	0.104091i
$636$		0			0
$637$	7618.45	−	4820.54i	0.473868	−	0.299838i
$638$		0			0
$639$	−1982.61	+	10272.3i	−0.122740	+	0.635939i
$640$		0			0
$641$	−14946.4	−	8629.29i	−0.920976	−	0.531726i	−0.0370299	−	0.999314i	$-0.511790\pi$
$641$	−14946.4	−	8629.29i	−0.920976	−	0.531726i	−0.883946	+	0.467588i	$0.845123\pi$
$642$		0			0
$643$	−21951.3	+	12673.6i	−1.34631	+	0.777291i	−0.987724	−	0.156206i	$-0.950074\pi$
$643$	−21951.3	+	12673.6i	−1.34631	+	0.777291i	−0.358584	+	0.933498i	$0.616740\pi$
$644$		0			0
$645$	−328.903	+	3439.66i	−0.0200784	+	0.209979i
$646$		0			0
$647$	6799.46			0.413160			0.206580	−	0.978430i	$-0.433767\pi$
$647$	6799.46			0.413160			0.206580	+	0.978430i	$0.433767\pi$
$648$		0			0
$649$		−	37640.9i		−	2.27663i
$650$		0			0
$651$	13838.1	−	6659.70i	0.833112	−	0.400943i
$652$		0			0
$653$	19452.8	−	11231.1i	1.16577	−	0.673058i	0.213090	−	0.977033i	$-0.431647\pi$
$653$	19452.8	−	11231.1i	1.16577	−	0.673058i	0.952680	+	0.303975i	$0.0983139\pi$
$654$		0			0
$655$	−1841.42	+	3189.43i	−0.109848	+	0.190262i
$656$		0			0
$657$	1129.37	−	5851.47i	0.0670637	−	0.347470i
$658$		0			0
$659$	3236.46	+	1868.57i	0.191312	+	0.110454i	0.592597	−	0.805499i	$-0.298103\pi$
$659$	3236.46	+	1868.57i	0.191312	+	0.110454i	−0.401285	+	0.915953i	$0.631436\pi$
$660$		0			0
$661$	−10205.8	+	5892.33i	−0.600545	+	0.346725i	−0.769256	−	0.638941i	$-0.779373\pi$
$661$	−10205.8	+	5892.33i	−0.600545	+	0.346725i	0.168711	+	0.985666i	$0.446040\pi$
$662$		0			0
$663$	1118.79	+	2450.65i	0.0655356	+	0.143553i
$664$		0			0
$665$	−1605.17	−	2654.46i	−0.0936030	−	0.154790i
$666$		0			0
$667$	9577.50			0.555986
$668$		0			0
$669$	−9850.20	+	13828.8i	−0.569254	+	0.799184i
$670$		0			0
$671$	15600.4	+	27020.6i	0.897534	+	1.55457i
$672$		0			0
$673$	5712.35	−	9894.08i	0.327184	−	0.566699i	−0.654768	−	0.755830i	$-0.727234\pi$
$673$	5712.35	−	9894.08i	0.327184	−	0.566699i	0.981952	+	0.189131i	$0.0605670\pi$
$674$		0			0
$675$	−8613.09	−	9040.26i	−0.491138	−	0.515496i
$676$		0			0
$677$	−15013.5	+	26004.1i	−0.852312	+	1.47625i	0.0268044	+	0.999641i	$0.491467\pi$
$677$	−15013.5	+	26004.1i	−0.852312	+	1.47625i	−0.879116	+	0.476607i	$0.841866\pi$
$678$		0			0
$679$	−13453.9	+	24433.9i	−0.760404	+	1.38098i
$680$		0			0
$681$	24012.7	+	17104.1i	1.35120	+	0.962454i
$682$		0			0
$683$			18482.4i			1.03545i	0.855548	+	0.517723i	$0.173220\pi$
$683$			18482.4i			1.03545i	−0.855548	+	0.517723i	$0.826780\pi$
$684$		0			0
$685$			10502.1i			0.585786i
$686$		0			0
$687$	11284.0	+	24717.0i	0.626652	+	1.37265i
$688$		0			0
$689$	−2756.82	−	4774.94i	−0.152433	−	0.264022i
$690$		0			0
$691$	16408.4	+	9473.38i	0.903334	+	0.521540i	0.878280	−	0.478146i	$-0.158691\pi$
$691$	16408.4	+	9473.38i	0.903334	+	0.521540i	0.0250537	+	0.999686i	$0.492024\pi$
$692$		0			0
$693$	14543.9	−	17479.4i	0.797223	−	0.958134i
$694$		0			0
$695$	−6724.25	−	3882.25i	−0.367001	−	0.211888i
$696$		0			0
$697$	402.956	+	697.941i	0.0218982	+	0.0379288i
$698$		0			0
$699$	17761.7	+	1698.39i	0.961103	+	0.0919013i
$700$		0			0
$701$		−	9045.09i		−	0.487344i	−0.969858	−	0.243672i	$-0.921648\pi$
$701$		−	9045.09i		−	0.487344i	0.969858	−	0.243672i	$-0.0783521\pi$
$702$		0			0
$703$			8035.08i			0.431079i
$704$		0			0
$705$	−650.890	+	6807.00i	−0.0347715	+	0.363640i
$706$		0			0
$707$	29965.2	+	16499.6i	1.59400	+	0.877698i
$708$		0			0
$709$	−1866.89	+	3233.55i	−0.0988893	+	0.171281i	−0.911225	−	0.411909i	$-0.864862\pi$
$709$	−1866.89	+	3233.55i	−0.0988893	+	0.171281i	0.812336	+	0.583190i	$0.198196\pi$
$710$		0			0
$711$	−8570.95	+	9886.16i	−0.452089	+	0.521463i
$712$		0			0
$713$	−5560.00	+	9630.20i	−0.292039	+	0.505826i
$714$		0			0
$715$	3585.64	+	6210.51i	0.187546	+	0.324839i
$716$		0			0
$717$	1170.33	+	2563.55i	0.0609578	+	0.133525i
$718$		0			0
$719$	−35410.2			−1.83669			−0.918343	−	0.395785i	$-0.870473\pi$
$719$	−35410.2			−1.83669			−0.918343	+	0.395785i	$0.870473\pi$
$720$		0			0
$721$	7707.23	+	12745.4i	0.398103	+	0.658339i
$722$		0			0
$723$	10827.0	−	15200.2i	0.556929	−	0.781881i
$724$		0			0
$725$	−10593.9	+	6116.37i	−0.542685	+	0.313319i
$726$		0			0
$727$	2328.92	+	1344.60i	0.118810	+	0.0685951i	0.558227	−	0.829688i	$-0.311482\pi$
$727$	2328.92	+	1344.60i	0.118810	+	0.0685951i	−0.439417	+	0.898283i	$0.644815\pi$
$728$		0			0
$729$	−16550.0	−	10654.5i	−0.840828	−	0.541302i
$730$		0			0
$731$	−1093.07	+	1893.25i	−0.0553060	+	0.0957928i
$732$		0			0
$733$	10520.4	−	6073.96i	0.530123	−	0.306066i	−0.210944	−	0.977498i	$-0.567654\pi$
$733$	10520.4	−	6073.96i	0.530123	−	0.306066i	0.741066	+	0.671432i	$0.234320\pi$
$734$		0			0
$735$	9539.76	−	4831.70i	0.478748	−	0.242476i
$736$		0			0
$737$			15592.7i			0.779326i
$738$		0			0
$739$	−33517.3			−1.66841			−0.834204	−	0.551456i	$-0.814072\pi$
$739$	−33517.3			−1.66841			−0.834204	+	0.551456i	$0.814072\pi$
$740$		0			0
$741$	−3468.35	+	1583.39i	−0.171947	+	0.0784985i
$742$		0			0
$743$	21381.5	−	12344.6i	1.05573	−	0.609529i	0.131485	−	0.991318i	$-0.458025\pi$
$743$	21381.5	−	12344.6i	1.05573	−	0.609529i	0.924249	+	0.381790i	$0.124692\pi$
$744$		0			0
$745$	−14995.2	−	8657.49i	−0.737426	−	0.425753i
$746$		0			0
$747$	12533.5	−	14456.8i	0.613893	−	0.708095i
$748$		0			0
$749$	5240.10	−	106.259i	0.255633	−	0.00518373i
$750$		0			0
$751$	−4794.74	−	8304.74i	−0.232973	−	0.403521i	0.725709	−	0.688002i	$-0.241512\pi$
$751$	−4794.74	−	8304.74i	−0.232973	−	0.403521i	−0.958682	+	0.284481i	$0.908179\pi$
$752$		0			0
$753$	−2143.80	+	22419.9i	−0.103751	+	1.08503i
$754$		0			0
$755$	18487.4			0.891159
$756$		0			0
$757$	−13621.8			−0.654022			−0.327011	−	0.945021i	$-0.606041\pi$
$757$	−13621.8			−0.654022			−0.327011	+	0.945021i	$0.606041\pi$
$758$		0			0
$759$	−1567.24	+	16390.2i	−0.0749502	+	0.783829i
$760$		0			0
$761$	839.906	+	1454.76i	0.0400086	+	0.0692970i	0.885336	−	0.464951i	$-0.153928\pi$
$761$	839.906	+	1454.76i	0.0400086	+	0.0692970i	−0.845328	+	0.534248i	$0.820595\pi$
$762$		0			0
$763$	−685.783	−	33819.0i	−0.0325387	−	1.60463i
$764$		0			0
$765$	1044.32	+	3019.93i	0.0493562	+	0.142727i
$766$		0			0
$767$	−18842.0	−	10878.5i	−0.887023	−	0.512123i
$768$		0			0
$769$	−30695.1	+	17721.8i	−1.43939	+	0.831034i	−0.997807	−	0.0661849i	$-0.978917\pi$
$769$	−30695.1	+	17721.8i	−1.43939	+	0.831034i	−0.441586	+	0.897219i	$0.645584\pi$
$770$		0			0
$771$	31035.5	−	14168.5i	1.44970	−	0.661825i
$772$		0			0
$773$	−13901.4			−0.646829			−0.323415	−	0.946257i	$-0.604831\pi$
$773$	−13901.4			−0.646829			−0.323415	+	0.946257i	$0.604831\pi$
$774$		0			0
$775$		−	14202.9i		−	0.658300i
$776$		0			0
$777$	−27621.0	−	2077.01i	−1.27529	−	0.0958974i
$778$		0			0
$779$	−987.778	+	570.294i	−0.0454311	+	0.0262297i
$780$		0			0
$781$	−8809.91	+	15259.2i	−0.403641	+	0.699126i
$782$		0			0
$783$	−13961.0	+	13301.3i	−0.637199	+	0.607090i
$784$		0			0
$785$	−6540.73	−	3776.29i	−0.297387	−	0.171696i
$786$		0			0
$787$	3906.63	−	2255.49i	0.176946	−	0.102160i	−0.408911	−	0.912574i	$-0.634091\pi$
$787$	3906.63	−	2255.49i	0.176946	−	0.102160i	0.585857	+	0.810415i	$0.300758\pi$
$788$		0			0
$789$	−21842.4	+	30664.9i	−0.985566	+	1.38365i
$790$		0			0
$791$	9027.72	+	14929.1i	0.405801	+	0.671070i
$792$		0			0
$793$	18034.4			0.807592
$794$		0			0
$795$	−2716.00	−	5949.28i	−0.121166	−	0.265408i
$796$		0			0
$797$	15620.6	+	27055.6i	0.694240	+	1.20246i	0.970436	+	0.241358i	$0.0775928\pi$
$797$	15620.6	+	27055.6i	0.694240	+	1.20246i	−0.276196	+	0.961101i	$0.589074\pi$
$798$		0			0
$799$	−2163.16	+	3746.70i	−0.0957785	+	0.165893i
$800$		0			0
$801$	3736.14	+	721.097i	0.164806	+	0.0318086i
$802$		0			0
$803$	5018.45	−	8692.21i	0.220544	−	0.381994i
$804$		0			0
$805$	−3734.81	+	6782.85i	−0.163521	+	0.296974i
$806$		0			0
$807$	1709.29	−	17875.7i	0.0745598	−	0.779745i
$808$		0			0
$809$			42276.5i			1.83728i	0.395091	+	0.918642i	$0.370713\pi$
$809$			42276.5i			1.83728i	−0.395091	+	0.918642i	$0.629287\pi$
$810$		0			0
$811$			29402.1i			1.27305i	0.771254	+	0.636527i	$0.219630\pi$
$811$			29402.1i			1.27305i	−0.771254	+	0.636527i	$0.780370\pi$
$812$		0			0
$813$	12782.9	+	1222.31i	0.551436	+	0.0527286i
$814$		0			0
$815$	−8720.74	−	15104.8i	−0.374815	−	0.649198i
$816$		0			0
$817$	−2679.48	−	1547.00i	−0.114741	−	0.0662455i
$818$		0			0
$819$	−4546.44	−	12331.9i	−0.193975	−	0.526144i
$820$		0			0
$821$	36104.3	+	20844.8i	1.53477	+	0.886103i	0.999132	+	0.0416579i	$0.0132640\pi$
$821$	36104.3	+	20844.8i	1.53477	+	0.886103i	0.535643	+	0.844445i	$0.320069\pi$
$822$		0			0
$823$	4162.09	+	7208.95i	0.176284	+	0.305332i	0.940605	−	0.339504i	$-0.110259\pi$
$823$	4162.09	+	7208.95i	0.176284	+	0.305332i	−0.764321	+	0.644836i	$0.776926\pi$
$824$		0			0
$825$	−8733.52	−	19130.4i	−0.368560	−	0.807315i
$826$		0			0
$827$			7260.76i			0.305298i	0.988280	+	0.152649i	$0.0487804\pi$
$827$			7260.76i			0.305298i	−0.988280	+	0.152649i	$0.951220\pi$
$828$		0			0
$829$		−	26509.9i		−	1.11065i	−0.831634	−	0.555324i	$-0.812594\pi$
$829$		−	26509.9i		−	1.11065i	0.831634	−	0.555324i	$-0.187406\pi$
$830$		0			0
$831$	19103.1	+	13607.1i	0.797450	+	0.568019i
$832$		0			0
$833$	6760.08	−	274.275i	0.281180	−	0.0114082i
$834$		0			0
$835$	1720.63	−	2980.22i	0.0713113	−	0.123515i
$836$		0			0
$837$	−5269.78	−	21759.7i	−0.217623	−	0.898594i
$838$		0			0
$839$	4438.40	−	7687.53i	0.182635	−	0.316332i	−0.760142	−	0.649757i	$-0.774871\pi$
$839$	4438.40	−	7687.53i	0.182635	−	0.316332i	0.942777	+	0.333424i	$0.108204\pi$
$840$		0			0
$841$	−2748.88	−	4761.19i	−0.112710	−	0.195219i
$842$		0			0
$843$	−7276.92	+	10216.2i	−0.297308	+	0.417395i
$844$		0			0
$845$	−9036.78			−0.367899
$846$		0			0
$847$	11677.1	−	7061.25i	0.473708	−	0.286455i
$848$		0			0
$849$	9702.03	+	21251.9i	0.392194	+	0.859083i
$850$		0			0
$851$	17369.5	−	10028.3i	0.699669	−	0.403954i
$852$		0			0
$853$	13168.8	+	7603.02i	0.528596	+	0.305185i	0.740444	−	0.672118i	$-0.234615\pi$
$853$	13168.8	+	7603.02i	0.528596	+	0.305185i	−0.211849	+	0.977302i	$0.567948\pi$
$854$		0			0
$855$	−4274.03	+	1478.00i	−0.170958	+	0.0591189i
$856$		0			0
$857$	11826.9	−	20484.8i	0.471410	−	0.816506i	−0.528055	−	0.849210i	$-0.677078\pi$
$857$	11826.9	−	20484.8i	0.471410	−	0.816506i	0.999465	+	0.0327038i	$0.0104118\pi$
$858$		0			0
$859$	25545.4	−	14748.7i	1.01467	−	0.585818i	0.102112	−	0.994773i	$-0.467440\pi$
$859$	25545.4	−	14748.7i	1.01467	−	0.585818i	0.912555	+	0.408954i	$0.134107\pi$
$860$		0			0
$861$	−1705.08	−	3542.95i	−0.0674901	−	0.140236i
$862$		0			0
$863$		−	36862.0i		−	1.45399i	−0.686640	−	0.726997i	$-0.740915\pi$
$863$		−	36862.0i		−	1.45399i	0.686640	−	0.726997i	$-0.259085\pi$
$864$		0			0
$865$	−23173.4			−0.910888
$866$		0			0
$867$	2237.55	−	23400.3i	0.0876485	−	0.916627i
$868$		0			0
$869$	−19084.1	+	11018.2i	−0.744976	+	0.430112i
$870$		0			0
$871$	7805.27	+	4506.38i	0.303641	+	0.175307i
$872$		0			0
$873$	30725.0	+	26637.5i	1.19116	+	1.03269i
$874$		0			0
$875$	−482.109	−	23775.0i	−0.0186266	−	0.918560i
$876$		0			0
$877$	4353.93	+	7541.22i	0.167642	+	0.290364i	0.937590	−	0.347742i	$-0.113052\pi$
$877$	4353.93	+	7541.22i	0.167642	+	0.290364i	−0.769949	+	0.638106i	$0.779718\pi$
$878$		0			0
$879$	−14838.9	+	6774.36i	−0.569402	+	0.259947i
$880$		0			0
$881$	18950.2			0.724685			0.362342	−	0.932045i	$-0.381977\pi$
$881$	18950.2			0.724685			0.362342	+	0.932045i	$0.381977\pi$
$882$		0			0
$883$	5510.89			0.210030			0.105015	−	0.994471i	$-0.466511\pi$
$883$	5510.89			0.210030			0.105015	+	0.994471i	$0.466511\pi$
$884$		0			0
$885$	−21019.6	−	14972.1i	−0.798378	−	0.568680i
$886$		0			0
$887$	−12652.8	−	21915.3i	−0.478962	−	0.829586i	0.520747	−	0.853711i	$-0.325653\pi$
$887$	−12652.8	−	21915.3i	−0.478962	−	0.829586i	−0.999709	+	0.0241247i	$0.992320\pi$
$888$		0			0
$889$	−120.359	−	5935.47i	−0.00454075	−	0.223925i
$890$		0			0
$891$	−20478.3	−	26068.4i	−0.769977	−	0.980163i
$892$		0			0
$893$	−5302.61	−	3061.46i	−0.198707	−	0.114723i
$894$		0			0
$895$	11682.2	−	6744.71i	0.436304	−	0.251900i
$896$		0			0
$897$	7751.55	+	5521.38i	0.288536	+	0.205522i
$898$		0			0
$899$	−21933.8			−0.813717
$900$		0			0
$901$		−	4137.70i		−	0.152993i
$902$		0			0
$903$	6010.50	−	8810.94i	0.221503	−	0.324706i
$904$		0			0
$905$	864.669	−	499.217i	0.0317598	−	0.0183365i
$906$		0			0
$907$	9256.41	−	16032.6i	0.338869	−	0.586938i	−0.645351	−	0.763886i	$-0.723289\pi$
$907$	9256.41	−	16032.6i	0.338869	−	0.586938i	0.984220	+	0.176948i	$0.0566224\pi$
$908$		0			0
$909$	32667.7	−	37680.6i	1.19199	−	1.37490i
$910$		0			0
$911$	−27338.9	−	15784.1i	−0.994266	−	0.574040i	−0.0877196	−	0.996145i	$-0.527958\pi$
$911$	−27338.9	−	15784.1i	−0.994266	−	0.574040i	−0.906547	+	0.422105i	$0.861291\pi$
$912$		0			0
$913$	27907.2	−	16112.2i	1.01160	−	0.584050i
$914$		0			0
$915$	21294.2	+	2036.16i	0.769359	+	0.0735666i
$916$		0			0
$917$	9727.70	−	5882.42i	0.350313	−	0.211837i
$918$		0			0
$919$	2352.27			0.0844332			0.0422166	−	0.999108i	$-0.486558\pi$
$919$	2352.27			0.0844332			0.0422166	+	0.999108i	$0.486558\pi$
$920$		0			0
$921$	−53246.4	−	5091.45i	−1.90502	−	0.182160i
$922$		0			0
$923$	5092.23	+	8820.01i	0.181596	+	0.314533i
$924$		0			0
$925$	−12808.5	+	22185.0i	−0.455287	+	0.788580i
$926$		0			0
$927$	20521.7	−	7096.62i	0.727100	−	0.251439i
$928$		0			0
$929$	4728.40	−	8189.83i	0.166990	−	0.289235i	−0.770370	−	0.637597i	$-0.779929\pi$
$929$	4728.40	−	8189.83i	0.166990	−	0.289235i	0.937360	+	0.348362i	$0.113262\pi$
$930$		0			0
$931$	388.174	+	9567.38i	0.0136648	+	0.336797i
$932$		0			0
$933$	37253.3	−	17007.1i	1.30720	−	0.596771i
$934$		0			0
$935$			5381.68i			0.188235i
$936$		0			0
$937$			34791.9i			1.21302i	0.795075	+	0.606511i	$0.207431\pi$
$937$			34791.9i			1.21302i	−0.795075	+	0.606511i	$0.792569\pi$
$938$		0			0
$939$	−24704.0	+	34682.2i	−0.858555	+	1.20534i
$940$		0			0
$941$	−5515.38	−	9552.92i	−0.191069	−	0.330942i	0.754535	−	0.656259i	$-0.227862\pi$
$941$	−5515.38	−	9552.92i	−0.191069	−	0.330942i	−0.945605	+	0.325317i	$0.894529\pi$
$942$		0			0
$943$	2465.62	+	1423.52i	0.0851448	+	0.0491584i
$944$		0			0
$945$	−3975.90	−	15074.2i	−0.136863	−	0.518905i
$946$		0			0
$947$	−26402.6	−	15243.5i	−0.905985	−	0.523071i	−0.0268478	−	0.999640i	$-0.508547\pi$
$947$	−26402.6	−	15243.5i	−0.905985	−	0.523071i	−0.879137	+	0.476569i	$0.841880\pi$
$948$		0			0
$949$	−2900.72	−	5024.20i	−0.0992218	−	0.171857i
$950$		0			0
$951$	−26423.4	+	37096.2i	−0.900987	+	1.26491i
$952$		0			0
$953$		−	21378.9i		−	0.726685i	−0.931656	−	0.363343i	$-0.881635\pi$
$953$		−	21378.9i		−	0.726685i	0.931656	−	0.363343i	$-0.118365\pi$
$954$		0			0
$955$		−	12185.7i		−	0.412902i
$956$		0			0
$957$	−29543.4	+	13487.3i	−0.997912	+	0.455573i
$958$		0			0
$959$	15636.1	−	28396.9i	0.526502	−	0.956189i
$960$		0			0
$961$	−2162.36	+	3745.31i	−0.0725842	+	0.125720i
$962$		0			0
$963$	1448.02	−	7502.45i	0.0484546	−	0.251052i
$964$		0			0
$965$	−1506.69	+	2609.67i	−0.0502613	+	0.0870550i
$966$		0			0
$967$	1999.31	+	3462.91i	0.0664877	+	0.115160i	0.897353	−	0.441314i	$-0.145487\pi$
$967$	1999.31	+	3462.91i	0.0664877	+	0.115160i	−0.830865	+	0.556474i	$0.812154\pi$
$968$		0			0
$969$	−2848.24	−	272.350i	−0.0944257	−	0.00902905i
$970$		0			0
$971$	−48223.6			−1.59379			−0.796895	−	0.604118i	$-0.793525\pi$
$971$	−48223.6			−1.59379			−0.796895	+	0.604118i	$0.793525\pi$
$972$		0			0
$973$	12401.8	+	20508.8i	0.408618	+	0.675727i
$974$		0			0
$975$	−12100.2	−	1157.03i	−0.397453	−	0.0380047i
$976$		0			0
$977$	−3157.95	+	1823.24i	−0.103410	+	0.0597038i	−0.550813	−	0.834629i	$-0.685682\pi$
$977$	−3157.95	+	1823.24i	−0.103410	+	0.0597038i	0.447403	+	0.894332i	$0.352349\pi$
$978$		0			0
$979$	5549.94	+	3204.26i	0.181182	+	0.104605i
$980$		0			0
$981$	−48420.0	−	9345.36i	−1.57587	−	0.304153i
$982$		0			0
$983$	−10473.4	+	18140.5i	−0.339828	+	0.588600i	−0.984400	−	0.175944i	$-0.943702\pi$
$983$	−10473.4	+	18140.5i	−0.339828	+	0.588600i	0.644572	+	0.764544i	$0.277036\pi$
$984$		0			0
$985$	20519.9	−	11847.2i	0.663776	−	0.383232i
$986$		0			0
$987$	11894.6	−	17436.6i	0.383596	−	0.562324i
$988$		0			0
$989$			7722.99i			0.248308i
$990$		0			0
$991$	6732.72			0.215814			0.107907	−	0.994161i	$-0.465585\pi$
$991$	6732.72			0.215814			0.107907	+	0.994161i	$0.465585\pi$
$992$		0			0
$993$	−29048.2	−	20690.9i	−0.928316	−	0.661234i
$994$		0			0
$995$	3272.03	−	1889.11i	0.104252	−	0.0601897i
$996$		0			0
$997$	35961.0	+	20762.1i	1.14232	+	0.659520i	0.947005	−	0.321220i	$-0.104093\pi$
$997$	35961.0	+	20762.1i	1.14232	+	0.659520i	0.195318	+	0.980740i	$0.437426\pi$
$998$		0			0
$999$	−11392.0	+	38741.1i	−0.360786	+	1.22694i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.x.a.209.10	yes	48
3.2	odd	2		756.4.x.a.629.9		48
7.6	odd	2	inner	252.4.x.a.209.15	yes	48
9.2	odd	6		2268.4.f.a.1133.31		48
9.4	even	3		756.4.x.a.125.16		48
9.5	odd	6	inner	252.4.x.a.41.15	yes	48
9.7	even	3		2268.4.f.a.1133.18		48
21.20	even	2		756.4.x.a.629.16		48
63.13	odd	6		756.4.x.a.125.9		48
63.20	even	6		2268.4.f.a.1133.17		48
63.34	odd	6		2268.4.f.a.1133.32		48
63.41	even	6	inner	252.4.x.a.41.10	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.x.a.41.10	✓	48	63.41	even	6	inner
252.4.x.a.41.15	yes	48	9.5	odd	6	inner
252.4.x.a.209.10	yes	48	1.1	even	1	trivial
252.4.x.a.209.15	yes	48	7.6	odd	2	inner
756.4.x.a.125.9		48	63.13	odd	6
756.4.x.a.125.16		48	9.4	even	3
756.4.x.a.629.9		48	3.2	odd	2
756.4.x.a.629.16		48	21.20	even	2
2268.4.f.a.1133.17		48	63.20	even	6
2268.4.f.a.1133.18		48	9.7	even	3
2268.4.f.a.1133.31		48	9.2	odd	6
2268.4.f.a.1133.32		48	63.34	odd	6

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.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.494604 + 5.17256i) q^{3} +(2.99997 + 5.19610i) q^{5} +(-0.375477 - 18.5165i) q^{7} +(-26.5107 - 5.11673i) q^{9} +O(q^{10})\)	\(q+(-0.494604 + 5.17256i) q^{3} +(2.99997 + 5.19610i) q^{5} +(-0.375477 - 18.5165i) q^{7} +(-26.5107 - 5.11673i) q^{9} +(-39.3810 - 22.7366i) q^{11} +(-22.7627 + 13.1421i) q^{13} +(-28.3609 + 12.9475i) q^{15} -19.7249 q^{17} -27.9162i q^{19} +(95.9632 + 7.21613i) q^{21} +(-60.3466 + 34.8411i) q^{23} +(44.5004 - 77.0769i) q^{25} +(39.5789 - 134.598i) q^{27} +(-119.031 - 68.7227i) q^{29} +(138.202 - 79.7908i) q^{31} +(137.085 - 192.455i) q^{33} +(95.0869 - 57.4998i) q^{35} -287.829 q^{37} +(-56.7196 - 124.242i) q^{39} +(-20.4288 - 35.3837i) q^{41} +(55.4158 - 95.9830i) q^{43} +(-52.9443 - 153.102i) q^{45} +(109.666 - 189.948i) q^{47} +(-342.718 + 13.9050i) q^{49} +(9.75601 - 102.028i) q^{51} +209.770i q^{53} -272.837i q^{55} +(144.398 + 13.8074i) q^{57} +(413.880 + 716.860i) q^{59} +(-594.209 - 343.066i) q^{61} +(-84.7896 + 492.806i) q^{63} +(-136.575 - 78.8515i) q^{65} +(-171.449 - 296.958i) q^{67} +(-150.370 - 329.379i) q^{69} -387.476i q^{71} +220.721i q^{73} +(376.675 + 268.303i) q^{75} +(-406.215 + 737.734i) q^{77} +(242.301 - 419.677i) q^{79} +(676.638 + 271.297i) q^{81} +(-354.323 + 613.706i) q^{83} +(-59.1741 - 102.493i) q^{85} +(414.346 - 581.706i) q^{87} -140.929 q^{89} +(251.891 + 416.550i) q^{91} +(344.368 + 754.321i) q^{93} +(145.055 - 83.7476i) q^{95} +(-1304.31 - 753.041i) q^{97} +(927.683 + 804.267i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 60 * q^9	\( 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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