LMFDB - Embedded newform 504.3.g.d.379.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,3,Mod(379,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 0])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.379"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	504.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.7330053238$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.1
Character	$\chi$	$=$	504.379
Dual form			504.3.g.d.379.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.97309 - 0.326994i) q^{2} +(3.78615 + 1.29038i) q^{4} -4.09875i q^{5} +2.64575i q^{7} +(-7.04846 - 3.78407i) q^{8} +(-1.34027 + 8.08719i) q^{10} -3.52638 q^{11} +12.2733i q^{13} +(0.865145 - 5.22030i) q^{14} +(12.6699 + 9.77111i) q^{16} -3.97553 q^{17} -6.32165 q^{19} +(5.28893 - 15.5185i) q^{20} +(6.95787 + 1.15311i) q^{22} +39.8630i q^{23} +8.20025 q^{25} +(4.01329 - 24.2163i) q^{26} +(-3.41401 + 10.0172i) q^{28} +0.832427i q^{29} -23.7963i q^{31} +(-21.8037 - 23.4222i) q^{32} +(7.84407 + 1.29998i) q^{34} +10.8443 q^{35} -9.82415i q^{37} +(12.4732 + 2.06714i) q^{38} +(-15.5100 + 28.8899i) q^{40} +47.1852 q^{41} -31.2784 q^{43} +(-13.3514 - 4.55036i) q^{44} +(13.0350 - 78.6532i) q^{46} +87.1081i q^{47} -7.00000 q^{49} +(-16.1798 - 2.68143i) q^{50} +(-15.8372 + 46.4685i) q^{52} +25.5892i q^{53} +14.4538i q^{55} +(10.0117 - 18.6485i) q^{56} +(0.272198 - 1.64245i) q^{58} -26.9359 q^{59} +58.4964i q^{61} +(-7.78124 + 46.9521i) q^{62} +(35.3616 + 53.3438i) q^{64} +50.3052 q^{65} +99.8159 q^{67} +(-15.0520 - 5.12993i) q^{68} +(-21.3967 - 3.54601i) q^{70} +77.8151i q^{71} +119.267 q^{73} +(-3.21244 + 19.3839i) q^{74} +(-23.9347 - 8.15731i) q^{76} -9.32994i q^{77} +142.651i q^{79} +(40.0493 - 51.9306i) q^{80} +(-93.1006 - 15.4293i) q^{82} +90.4847 q^{83} +16.2947i q^{85} +(61.7150 + 10.2278i) q^{86} +(24.8556 + 13.3441i) q^{88} -64.1455 q^{89} -32.4721 q^{91} +(-51.4382 + 150.927i) q^{92} +(28.4838 - 171.872i) q^{94} +25.9109i q^{95} -81.1434 q^{97} +(13.8116 + 2.28896i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} + 10 q^{4} - 10 q^{8} + 12 q^{10} - 32 q^{11} + 14 q^{14} + 66 q^{16} - 16 q^{17} - 64 q^{19} - 20 q^{20} + 12 q^{22} - 72 q^{25} - 100 q^{26} - 14 q^{28} - 98 q^{32} - 108 q^{34} + 72 q^{38}+ \cdots - 14 q^{98}+O(q^{100}) $ 24 * q + 2 * q^2 + 10 * q^4 - 10 * q^8 + 12 * q^10 - 32 * q^11 + 14 * q^14 + 66 * q^16 - 16 * q^17 - 64 * q^19 - 20 * q^20 + 12 * q^22 - 72 * q^25 - 100 * q^26 - 14 * q^28 - 98 * q^32 - 108 * q^34 + 72 * q^38 - 332 * q^40 + 80 * q^41 + 32 * q^43 + 292 * q^44 - 168 * q^49 - 46 * q^50 - 4 * q^52 - 98 * q^56 - 96 * q^58 + 16 * q^62 - 182 * q^64 + 192 * q^65 - 32 * q^67 - 188 * q^68 - 84 * q^70 - 240 * q^73 - 208 * q^74 + 8 * q^76 - 484 * q^80 - 372 * q^82 + 320 * q^83 + 604 * q^86 + 468 * q^88 - 400 * q^89 - 352 * q^92 - 72 * q^94 + 144 * q^97 - 14 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$	−1.97309	−	0.326994i	−0.986544	−	0.163497i
$2$	−1.97309	−	0.326994i	−0.986544	−	0.163497i
$3$		0			0
$3$		0			0
$4$	3.78615	+	1.29038i	0.946537	+	0.322594i
$5$		−	4.09875i		−	0.819750i	−0.912142	−	0.409875i	$-0.865572\pi$
$5$		−	4.09875i		−	0.819750i	0.912142	−	0.409875i	$-0.134428\pi$
$6$		0			0
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	−7.04846	−	3.78407i	−0.881058	−	0.473009i
$9$		0			0
$10$	−1.34027	+	8.08719i	−0.134027	+	0.808719i
$11$	−3.52638			−0.320580			−0.160290	−	0.987070i	$-0.551243\pi$
$11$	−3.52638			−0.320580			−0.160290	+	0.987070i	$0.551243\pi$
$12$		0			0
$13$			12.2733i			0.944099i	0.881572	+	0.472050i	$0.156486\pi$
$13$			12.2733i			0.944099i	−0.881572	+	0.472050i	$0.843514\pi$
$14$	0.865145	−	5.22030i	0.0617960	−	0.372879i
$15$		0			0
$16$	12.6699	+	9.77111i	0.791866	+	0.610694i
$17$	−3.97553			−0.233855			−0.116927	−	0.993140i	$-0.537304\pi$
$17$	−3.97553			−0.233855			−0.116927	+	0.993140i	$0.537304\pi$
$18$		0			0
$19$	−6.32165			−0.332719			−0.166359	−	0.986065i	$-0.553201\pi$
$19$	−6.32165			−0.332719			−0.166359	+	0.986065i	$0.553201\pi$
$20$	5.28893	−	15.5185i	0.264446	−	0.775924i
$21$		0			0
$22$	6.95787	+	1.15311i	0.316267	+	0.0524139i
$23$			39.8630i			1.73317i	0.499026	+	0.866587i	$0.333691\pi$
$23$			39.8630i			1.73317i	−0.499026	+	0.866587i	$0.666309\pi$
$24$		0			0
$25$	8.20025			0.328010
$26$	4.01329	−	24.2163i	0.154357	−	0.931395i
$27$		0			0
$28$	−3.41401	+	10.0172i	−0.121929	+	0.357758i
$29$			0.832427i			0.0287044i	0.999897	+	0.0143522i	$0.00456860\pi$
$29$			0.832427i			0.0287044i	−0.999897	+	0.0143522i	$0.995431\pi$
$30$		0			0
$31$		−	23.7963i		−	0.767622i	−0.923412	−	0.383811i	$-0.874611\pi$
$31$		−	23.7963i		−	0.767622i	0.923412	−	0.383811i	$-0.125389\pi$
$32$	−21.8037	−	23.4222i	−0.681364	−	0.731945i
$33$		0			0
$34$	7.84407	+	1.29998i	0.230708	+	0.0382346i
$35$	10.8443			0.309836
$36$		0			0
$37$		−	9.82415i		−	0.265518i	−0.991148	−	0.132759i	$-0.957616\pi$
$37$		−	9.82415i		−	0.265518i	0.991148	−	0.132759i	$-0.0423836\pi$
$38$	12.4732	+	2.06714i	0.328242	+	0.0543985i
$39$		0			0
$40$	−15.5100	+	28.8899i	−0.387749	+	0.722247i
$41$	47.1852			1.15086			0.575429	−	0.817851i	$-0.304835\pi$
$41$	47.1852			1.15086			0.575429	+	0.817851i	$0.304835\pi$
$42$		0			0
$43$	−31.2784			−0.727404			−0.363702	−	0.931515i	$-0.618487\pi$
$43$	−31.2784			−0.727404			−0.363702	+	0.931515i	$0.618487\pi$
$44$	−13.3514	−	4.55036i	−0.303441	−	0.103417i
$45$		0			0
$46$	13.0350	−	78.6532i	0.283369	−	1.70985i
$47$			87.1081i			1.85336i	0.375845	+	0.926682i	$0.377352\pi$
$47$			87.1081i			1.85336i	−0.375845	+	0.926682i	$0.622648\pi$
$48$		0			0
$49$	−7.00000			−0.142857
$50$	−16.1798	−	2.68143i	−0.323596	−	0.0536286i
$51$		0			0
$52$	−15.8372	+	46.4685i	−0.304561	+	0.893625i
$53$			25.5892i			0.482816i	0.970424	+	0.241408i	$0.0776091\pi$
$53$			25.5892i			0.482816i	−0.970424	+	0.241408i	$0.922391\pi$
$54$		0			0
$55$			14.4538i			0.262796i
$56$	10.0117	−	18.6485i	0.178781	−	0.333008i
$57$		0			0
$58$	0.272198	−	1.64245i	0.00469308	−	0.0283181i
$59$	−26.9359			−0.456540			−0.228270	−	0.973598i	$-0.573307\pi$
$59$	−26.9359			−0.456540			−0.228270	+	0.973598i	$0.573307\pi$
$60$		0			0
$61$			58.4964i			0.958957i	0.877554	+	0.479478i	$0.159174\pi$
$61$			58.4964i			0.958957i	−0.877554	+	0.479478i	$0.840826\pi$
$62$	−7.78124	+	46.9521i	−0.125504	+	0.757293i
$63$		0			0
$64$	35.3616	+	53.3438i	0.552525	+	0.833496i
$65$	50.3052			0.773925
$66$		0			0
$67$	99.8159			1.48979			0.744895	−	0.667182i	$-0.232500\pi$
$67$	99.8159			1.48979			0.744895	+	0.667182i	$0.232500\pi$
$68$	−15.0520	−	5.12993i	−0.221352	−	0.0754401i
$69$		0			0
$70$	−21.3967	−	3.54601i	−0.305667	−	0.0506573i
$71$			77.8151i			1.09599i	0.836482	+	0.547994i	$0.184608\pi$
$71$			77.8151i			1.09599i	−0.836482	+	0.547994i	$0.815392\pi$
$72$		0			0
$73$	119.267			1.63380			0.816898	−	0.576781i	$-0.195692\pi$
$73$	119.267			1.63380			0.816898	+	0.576781i	$0.195692\pi$
$74$	−3.21244	+	19.3839i	−0.0434113	+	0.261945i
$75$		0			0
$76$	−23.9347	−	8.15731i	−0.314931	−	0.107333i
$77$		−	9.32994i		−	0.121168i
$78$		0			0
$79$			142.651i			1.80571i	0.429944	+	0.902856i	$0.358533\pi$
$79$			142.651i			1.80571i	−0.429944	+	0.902856i	$0.641467\pi$
$80$	40.0493	−	51.9306i	0.500617	−	0.649133i
$81$		0			0
$82$	−93.1006	−	15.4293i	−1.13537	−	0.188162i
$83$	90.4847			1.09018			0.545089	−	0.838378i	$-0.316496\pi$
$83$	90.4847			1.09018			0.545089	+	0.838378i	$0.316496\pi$
$84$		0			0
$85$			16.2947i			0.191703i
$86$	61.7150	+	10.2278i	0.717616	+	0.118928i
$87$		0			0
$88$	24.8556	+	13.3441i	0.282450	+	0.151637i
$89$	−64.1455			−0.720736			−0.360368	−	0.932810i	$-0.617349\pi$
$89$	−64.1455			−0.720736			−0.360368	+	0.932810i	$0.617349\pi$
$90$		0			0
$91$	−32.4721			−0.356836
$92$	−51.4382	+	150.927i	−0.559111	+	1.64051i
$93$		0			0
$94$	28.4838	−	171.872i	0.303020	−	1.82843i
$95$			25.9109i			0.272746i
$96$		0			0
$97$	−81.1434			−0.836530			−0.418265	−	0.908325i	$-0.637362\pi$
$97$	−81.1434			−0.836530			−0.418265	+	0.908325i	$0.637362\pi$
$98$	13.8116	+	2.28896i	0.140935	+	0.0233567i
$99$		0			0
$100$	31.0474	+	10.5814i	0.310474	+	0.105814i
$101$			24.8807i			0.246343i	0.992385	+	0.123172i	$0.0393065\pi$
$101$			24.8807i			0.246343i	−0.992385	+	0.123172i	$0.960693\pi$
$102$		0			0
$103$			49.7695i			0.483199i	0.970376	+	0.241600i	$0.0776721\pi$
$103$			49.7695i			0.483199i	−0.970376	+	0.241600i	$0.922328\pi$
$104$	46.4430	−	86.5078i	0.446567	−	0.831806i
$105$		0			0
$106$	8.36752	−	50.4898i	0.0789389	−	0.476319i
$107$	168.829			1.57784			0.788920	−	0.614496i	$-0.210641\pi$
$107$	168.829			1.57784			0.788920	+	0.614496i	$0.210641\pi$
$108$		0			0
$109$			23.9528i			0.219750i	0.993945	+	0.109875i	$0.0350451\pi$
$109$			23.9528i			0.219750i	−0.993945	+	0.109875i	$0.964955\pi$
$110$	4.72630	−	28.5186i	0.0429663	−	0.259260i
$111$		0			0
$112$	−25.8519	+	33.5213i	−0.230821	+	0.299297i
$113$	−171.416			−1.51696			−0.758478	−	0.651699i	$-0.774056\pi$
$113$	−171.416			−1.51696			−0.758478	+	0.651699i	$0.774056\pi$
$114$		0			0
$115$	163.388			1.42077
$116$	−1.07414	+	3.15169i	−0.00925985	+	0.0271698i
$117$		0			0
$118$	53.1468	+	8.80787i	0.450397	+	0.0746429i
$119$		−	10.5183i		−	0.0883888i
$120$		0			0
$121$	−108.565			−0.897228
$122$	19.1280	−	115.418i	0.156787	−	0.946053i
$123$		0			0
$124$	30.7061	−	90.0963i	0.247630	−	0.726583i
$125$		−	136.080i		−	1.08864i
$126$		0			0
$127$			63.2004i			0.497641i	0.968550	+	0.248821i	$0.0800429\pi$
$127$			63.2004i			0.497641i	−0.968550	+	0.248821i	$0.919957\pi$
$128$	−52.3284	−	116.815i	−0.408816	−	0.912617i
$129$		0			0
$130$	−99.2565	−	16.4495i	−0.763511	−	0.126534i
$131$	−126.893			−0.968650			−0.484325	−	0.874888i	$-0.660935\pi$
$131$	−126.893			−0.968650			−0.484325	+	0.874888i	$0.660935\pi$
$132$		0			0
$133$		−	16.7255i		−	0.125756i
$134$	−196.946	−	32.6392i	−1.46974	−	0.243576i
$135$		0			0
$136$	28.0214	+	15.0437i	0.206040	+	0.110615i
$137$	145.277			1.06041			0.530207	−	0.847869i	$-0.322114\pi$
$137$	145.277			1.06041			0.530207	+	0.847869i	$0.322114\pi$
$138$		0			0
$139$	−81.0035			−0.582759			−0.291379	−	0.956608i	$-0.594114\pi$
$139$	−81.0035			−0.582759			−0.291379	+	0.956608i	$0.594114\pi$
$140$	41.0580	+	13.9932i	0.293272	+	0.0999513i
$141$		0			0
$142$	25.4451	−	153.536i	0.179191	−	1.08124i
$143$		−	43.2803i		−	0.302660i
$144$		0			0
$145$	3.41191			0.0235304
$146$	−235.325	−	38.9996i	−1.61181	−	0.267121i
$147$		0			0
$148$	12.6768	−	37.1957i	0.0856543	−	0.251322i
$149$		−	144.331i		−	0.968664i	−0.874884	−	0.484332i	$-0.839063\pi$
$149$		−	144.331i		−	0.968664i	0.874884	−	0.484332i	$-0.160937\pi$
$150$		0			0
$151$			100.770i			0.667348i	0.942689	+	0.333674i	$0.108288\pi$
$151$			100.770i			0.667348i	−0.942689	+	0.333674i	$0.891712\pi$
$152$	44.5579	+	23.9216i	0.293144	+	0.157379i
$153$		0			0
$154$	−3.05083	+	18.4088i	−0.0198106	+	0.119538i
$155$	−97.5350			−0.629258
$156$		0			0
$157$		−	274.593i		−	1.74900i	−0.485023	−	0.874501i	$-0.661189\pi$
$157$		−	274.593i		−	1.74900i	0.485023	−	0.874501i	$-0.338811\pi$
$158$	46.6461	−	281.463i	0.295228	−	1.78141i
$159$		0			0
$160$	−96.0019	+	89.3677i	−0.600012	+	0.558548i
$161$	−105.468			−0.655078
$162$		0			0
$163$	−111.290			−0.682764			−0.341382	−	0.939925i	$-0.610895\pi$
$163$	−111.290			−0.682764			−0.341382	+	0.939925i	$0.610895\pi$
$164$	178.650	+	60.8866i	1.08933	+	0.371260i
$165$		0			0
$166$	−178.534	−	29.5879i	−1.07551	−	0.178241i
$167$			145.281i			0.869947i	0.900443	+	0.434974i	$0.143242\pi$
$167$			145.281i			0.869947i	−0.900443	+	0.434974i	$0.856758\pi$
$168$		0			0
$169$	18.3663			0.108677
$170$	5.32827	−	32.1509i	0.0313428	−	0.189123i
$171$		0			0
$172$	−118.425	−	40.3608i	−0.688515	−	0.234656i
$173$		−	19.2583i		−	0.111319i	−0.998450	−	0.0556597i	$-0.982274\pi$
$173$		−	19.2583i		−	0.111319i	0.998450	−	0.0556597i	$-0.0177262\pi$
$174$		0			0
$175$			21.6958i			0.123976i
$176$	−44.6788	−	34.4567i	−0.253857	−	0.195777i
$177$		0			0
$178$	126.565	+	20.9752i	0.711038	+	0.117838i
$179$	−122.983			−0.687056			−0.343528	−	0.939142i	$-0.611622\pi$
$179$	−122.983			−0.687056			−0.343528	+	0.939142i	$0.611622\pi$
$180$		0			0
$181$		−	321.748i		−	1.77761i	−0.458281	−	0.888807i	$-0.651535\pi$
$181$		−	321.748i		−	1.77761i	0.458281	−	0.888807i	$-0.348465\pi$
$182$	64.0702	+	10.6182i	0.352034	+	0.0583416i
$183$		0			0
$184$	150.844	−	280.973i	0.819807	−	1.52703i
$185$	−40.2667			−0.217658
$186$		0			0
$187$	14.0193			0.0749693
$188$	−112.402	+	329.804i	−0.597884	+	1.75428i
$189$		0			0
$190$	8.47270	−	51.1244i	0.0445932	−	0.269076i
$191$		−	176.871i		−	0.926026i	−0.886351	−	0.463013i	$-0.846768\pi$
$191$		−	176.871i		−	0.926026i	0.886351	−	0.463013i	$-0.153232\pi$
$192$		0			0
$193$	−304.692			−1.57871			−0.789357	−	0.613935i	$-0.789586\pi$
$193$	−304.692			−1.57871			−0.789357	+	0.613935i	$0.789586\pi$
$194$	160.103	+	26.5334i	0.825274	+	0.136770i
$195$		0			0
$196$	−26.5030	−	9.03263i	−0.135220	−	0.0460848i
$197$			388.291i			1.97102i	0.169609	+	0.985511i	$0.445749\pi$
$197$			388.291i			1.97102i	−0.169609	+	0.985511i	$0.554251\pi$
$198$		0			0
$199$		−	122.637i		−	0.616265i	−0.951343	−	0.308132i	$-0.900296\pi$
$199$		−	122.637i		−	0.616265i	0.951343	−	0.308132i	$-0.0997040\pi$
$200$	−57.7991	−	31.0303i	−0.288996	−	0.155152i
$201$		0			0
$202$	8.13582	−	49.0917i	0.0402763	−	0.243028i
$203$	−2.20239			−0.0108492
$204$		0			0
$205$		−	193.400i		−	0.943417i
$206$	16.2743	−	98.1997i	0.0790016	−	0.476697i
$207$		0			0
$208$	−119.924	+	155.501i	−0.576556	+	0.747600i
$209$	22.2926			0.106663
$210$		0			0
$211$	−284.157			−1.34672			−0.673358	−	0.739316i	$-0.735149\pi$
$211$	−284.157			−1.34672			−0.673358	+	0.739316i	$0.735149\pi$
$212$	−33.0197	+	96.8847i	−0.155753	+	0.457003i
$213$		0			0
$214$	−333.114	−	55.2060i	−1.55661	−	0.257972i
$215$			128.202i			0.596289i
$216$		0			0
$217$	62.9590			0.290134
$218$	7.83241	−	47.2609i	0.0359285	−	0.216793i
$219$		0			0
$220$	−18.6508	+	54.7241i	−0.0847763	+	0.248746i
$221$		−	48.7929i		−	0.220782i
$222$		0			0
$223$			307.496i			1.37891i	0.724331	+	0.689453i	$0.242149\pi$
$223$			307.496i			1.37891i	−0.724331	+	0.689453i	$0.757851\pi$
$224$	61.9694	−	57.6870i	0.276649	−	0.257531i
$225$		0			0
$226$	338.219	+	56.0520i	1.49654	+	0.248018i
$227$	227.172			1.00076			0.500378	−	0.865807i	$-0.333194\pi$
$227$	227.172			1.00076			0.500378	+	0.865807i	$0.333194\pi$
$228$		0			0
$229$		−	323.439i		−	1.41240i	−0.708014	−	0.706198i	$-0.750409\pi$
$229$		−	323.439i		−	1.41240i	0.708014	−	0.706198i	$-0.249591\pi$
$230$	−322.380	−	53.4270i	−1.40165	−	0.232291i
$231$		0			0
$232$	3.14996	−	5.86733i	0.0135774	−	0.0252902i
$233$	215.163			0.923448			0.461724	−	0.887024i	$-0.347231\pi$
$233$	215.163			0.923448			0.461724	+	0.887024i	$0.347231\pi$
$234$		0			0
$235$	357.035			1.51930
$236$	−101.983	−	34.7574i	−0.432132	−	0.147277i
$237$		0			0
$238$	−3.43941	+	20.7535i	−0.0144513	+	0.0871995i
$239$		−	343.504i		−	1.43726i	−0.695395	−	0.718628i	$-0.744771\pi$
$239$		−	343.504i		−	1.43726i	0.695395	−	0.718628i	$-0.255229\pi$
$240$		0			0
$241$	300.189			1.24560			0.622800	−	0.782381i	$-0.285995\pi$
$241$	300.189			1.24560			0.622800	+	0.782381i	$0.285995\pi$
$242$	214.207	+	35.5000i	0.885155	+	0.146694i
$243$		0			0
$244$	−75.4823	+	221.476i	−0.309354	+	0.907689i
$245$			28.6913i			0.117107i
$246$		0			0
$247$		−	77.5875i		−	0.314119i
$248$	−90.0468	+	167.727i	−0.363092	+	0.676319i
$249$		0			0
$250$	−44.4972	+	268.497i	−0.177989	+	1.07399i
$251$	176.192			0.701959			0.350979	−	0.936383i	$-0.385849\pi$
$251$	176.192			0.701959			0.350979	+	0.936383i	$0.385849\pi$
$252$		0			0
$253$		−	140.572i		−	0.555622i
$254$	20.6662	−	124.700i	0.0813628	−	0.490945i
$255$		0			0
$256$	65.0508	+	247.597i	0.254105	+	0.967177i
$257$	72.9213			0.283741			0.141870	−	0.989885i	$-0.454688\pi$
$257$	72.9213			0.283741			0.141870	+	0.989885i	$0.454688\pi$
$258$		0			0
$259$	25.9923			0.100356
$260$	190.463	+	64.9125i	0.732549	+	0.249664i
$261$		0			0
$262$	250.371	+	41.4933i	0.955616	+	0.158371i
$263$			74.1913i			0.282096i	0.990003	+	0.141048i	$0.0450472\pi$
$263$			74.1913i			0.282096i	−0.990003	+	0.141048i	$0.954953\pi$
$264$		0			0
$265$	104.884			0.395788
$266$	−5.46915	+	33.0009i	−0.0205607	+	0.124064i
$267$		0			0
$268$	377.918	+	128.800i	1.41014	+	0.480597i
$269$		−	34.4460i		−	0.128052i	−0.997948	−	0.0640259i	$-0.979606\pi$
$269$		−	34.4460i		−	0.128052i	0.997948	−	0.0640259i	$-0.0203940\pi$
$270$		0			0
$271$			337.074i			1.24382i	0.783090	+	0.621908i	$0.213642\pi$
$271$			337.074i			1.24382i	−0.783090	+	0.621908i	$0.786358\pi$
$272$	−50.3695	−	38.8454i	−0.185182	−	0.142814i
$273$		0			0
$274$	−286.643	−	47.5046i	−1.04614	−	0.173374i
$275$	−28.9172			−0.105154
$276$		0			0
$277$		−	63.1547i		−	0.227995i	−0.993481	−	0.113998i	$-0.963634\pi$
$277$		−	63.1547i		−	0.227995i	0.993481	−	0.113998i	$-0.0363657\pi$
$278$	159.827	+	26.4876i	0.574917	+	0.0952793i
$279$		0			0
$280$	−76.4354	−	41.0355i	−0.272984	−	0.146555i
$281$	−64.2556			−0.228668			−0.114334	−	0.993442i	$-0.536473\pi$
$281$	−64.2556			−0.228668			−0.114334	+	0.993442i	$0.536473\pi$
$282$		0			0
$283$	168.359			0.594910			0.297455	−	0.954736i	$-0.403862\pi$
$283$	168.359			0.594910			0.297455	+	0.954736i	$0.403862\pi$
$284$	−100.411	+	294.620i	−0.353559	+	1.03739i
$285$		0			0
$286$	−14.1524	+	85.3959i	−0.0494839	+	0.298587i
$287$			124.840i			0.434984i
$288$		0			0
$289$	−273.195			−0.945312
$290$	−6.73200	−	1.11567i	−0.0232138	−	0.00384715i
$291$		0			0
$292$	451.563	+	153.899i	1.54645	+	0.527053i
$293$		−	109.708i		−	0.374431i	−0.982319	−	0.187215i	$-0.940054\pi$
$293$		−	109.708i		−	0.374431i	0.982319	−	0.187215i	$-0.0599462\pi$
$294$		0			0
$295$			110.403i			0.374249i
$296$	−37.1753	+	69.2451i	−0.125592	+	0.233936i
$297$		0			0
$298$	−47.1953	+	284.778i	−0.158374	+	0.955629i
$299$	−489.250			−1.63629
$300$		0			0
$301$		−	82.7548i		−	0.274933i
$302$	32.9510	−	198.827i	0.109109	−	0.658368i
$303$		0			0
$304$	−80.0945	−	61.7696i	−0.263469	−	0.203189i
$305$	239.762			0.786105
$306$		0			0
$307$	−309.446			−1.00797			−0.503984	−	0.863713i	$-0.668133\pi$
$307$	−309.446			−1.00797			−0.503984	+	0.863713i	$0.668133\pi$
$308$	12.0391	−	35.3245i	0.0390881	−	0.114690i
$309$		0			0
$310$	192.445	+	31.8934i	0.620791	+	0.102882i
$311$		−	115.287i		−	0.370699i	−0.982673	−	0.185350i	$-0.940658\pi$
$311$		−	115.287i		−	0.370699i	0.982673	−	0.185350i	$-0.0593418\pi$
$312$		0			0
$313$	215.554			0.688672			0.344336	−	0.938846i	$-0.388104\pi$
$313$	215.554			0.688672			0.344336	+	0.938846i	$0.388104\pi$
$314$	−89.7904	+	541.797i	−0.285957	+	1.72547i
$315$		0			0
$316$	−184.074	+	540.099i	−0.582511	+	1.70917i
$317$		−	177.444i		−	0.559760i	−0.960035	−	0.279880i	$-0.909705\pi$
$317$		−	177.444i		−	0.559760i	0.960035	−	0.279880i	$-0.0902947\pi$
$318$		0			0
$319$		−	2.93546i		−	0.00920206i
$320$	218.643	−	144.938i	0.683259	−	0.452932i
$321$		0			0
$322$	208.097	+	34.4873i	0.646263	+	0.107103i
$323$	25.1319			0.0778079
$324$		0			0
$325$			100.644i			0.309674i
$326$	219.586	+	36.3913i	0.673576	+	0.111630i
$327$		0			0
$328$	−332.583	−	178.552i	−1.01397	−	0.544367i
$329$	−230.466			−0.700506
$330$		0			0
$331$	225.169			0.680270			0.340135	−	0.940377i	$-0.389527\pi$
$331$	225.169			0.680270			0.340135	+	0.940377i	$0.389527\pi$
$332$	342.589	+	116.759i	1.03189	+	0.351684i
$333$		0			0
$334$	47.5061	−	286.653i	0.142234	−	0.858241i
$335$		−	409.121i		−	1.22126i
$336$		0			0
$337$	−244.467			−0.725421			−0.362710	−	0.931902i	$-0.618149\pi$
$337$	−244.467			−0.725421			−0.362710	+	0.931902i	$0.618149\pi$
$338$	−36.2384	−	6.00569i	−0.107214	−	0.0177683i
$339$		0			0
$340$	−21.0263	+	61.6942i	−0.0618421	+	0.181454i
$341$			83.9148i			0.246085i
$342$		0			0
$343$		−	18.5203i		−	0.0539949i
$344$	220.464	+	118.360i	0.640885	+	0.344069i
$345$		0			0
$346$	−6.29734	+	37.9982i	−0.0182004	+	0.109822i
$347$	−453.748			−1.30763			−0.653816	−	0.756654i	$-0.726833\pi$
$347$	−453.748			−1.30763			−0.653816	+	0.756654i	$0.726833\pi$
$348$		0			0
$349$			523.107i			1.49888i	0.662075	+	0.749438i	$0.269676\pi$
$349$			523.107i			1.49888i	−0.662075	+	0.749438i	$0.730324\pi$
$350$	7.09440	−	42.8077i	0.0202697	−	0.122308i
$351$		0			0
$352$	76.8881	+	82.5958i	0.218432	+	0.234647i
$353$	−145.415			−0.411941			−0.205971	−	0.978558i	$-0.566035\pi$
$353$	−145.415			−0.411941			−0.205971	+	0.978558i	$0.566035\pi$
$354$		0			0
$355$	318.945			0.898436
$356$	−242.865	−	82.7718i	−0.682204	−	0.232505i
$357$		0			0
$358$	242.656	+	40.2147i	0.677811	+	0.112332i
$359$			325.591i			0.906938i	0.891272	+	0.453469i	$0.149814\pi$
$359$			325.591i			0.906938i	−0.891272	+	0.453469i	$0.850186\pi$
$360$		0			0
$361$	−321.037			−0.889298
$362$	−105.210	+	634.838i	−0.290635	+	1.75370i
$363$		0			0
$364$	−122.944	−	41.9012i	−0.337759	−	0.115113i
$365$		−	488.846i		−	1.33931i
$366$		0			0
$367$			232.973i			0.634805i	0.948291	+	0.317403i	$0.102811\pi$
$367$			232.973i			0.634805i	−0.948291	+	0.317403i	$0.897189\pi$
$368$	−389.506	+	505.059i	−1.05844	+	1.37244i
$369$		0			0
$370$	79.4498	+	13.1670i	0.214729	+	0.0355864i
$371$	−67.7027			−0.182487
$372$		0			0
$373$			463.330i			1.24217i	0.783743	+	0.621086i	$0.213308\pi$
$373$			463.330i			1.24217i	−0.783743	+	0.621086i	$0.786692\pi$
$374$	−27.6612	−	4.58421i	−0.0739605	−	0.0122573i
$375$		0			0
$376$	329.623	−	613.978i	0.876658	−	1.63292i
$377$	−10.2166			−0.0270998
$378$		0			0
$379$	−633.928			−1.67263			−0.836316	−	0.548248i	$-0.815295\pi$
$379$	−633.928			−1.67263			−0.836316	+	0.548248i	$0.815295\pi$
$380$	−33.4348	+	98.1025i	−0.0879862	+	0.258164i
$381$		0			0
$382$	−57.8358	+	348.982i	−0.151403	+	0.913566i
$383$			100.562i			0.262565i	0.991345	+	0.131282i	$0.0419095\pi$
$383$			100.562i			0.262565i	−0.991345	+	0.131282i	$0.958091\pi$
$384$		0			0
$385$	−38.2411			−0.0993275
$386$	601.183	+	99.6323i	1.55747	+	0.258115i
$387$		0			0
$388$	−307.221	−	104.705i	−0.791807	−	0.269860i
$389$		−	410.986i		−	1.05652i	−0.849083	−	0.528260i	$-0.822845\pi$
$389$		−	410.986i		−	1.05652i	0.849083	−	0.528260i	$-0.177155\pi$
$390$		0			0
$391$		−	158.477i		−	0.405311i
$392$	49.3392	+	26.4885i	0.125865	+	0.0675727i
$393$		0			0
$394$	126.969	−	766.133i	0.322256	−	1.94450i
$395$	584.692			1.48023
$396$		0			0
$397$		−	369.869i		−	0.931659i	−0.884874	−	0.465830i	$-0.845756\pi$
$397$		−	369.869i		−	0.931659i	0.884874	−	0.465830i	$-0.154244\pi$
$398$	−40.1015	+	241.973i	−0.100757	+	0.607972i
$399$		0			0
$400$	103.896	+	80.1255i	0.259740	+	0.200314i
$401$	−344.696			−0.859590			−0.429795	−	0.902926i	$-0.641414\pi$
$401$	−344.696			−0.859590			−0.429795	+	0.902926i	$0.641414\pi$
$402$		0			0
$403$	292.059			0.724711
$404$	−32.1054	+	94.2019i	−0.0794688	+	0.233173i
$405$		0			0
$406$	4.34552	+	0.720169i	0.0107032	+	0.00177382i
$407$			34.6437i			0.0851197i
$408$		0			0
$409$	327.650			0.801099			0.400550	−	0.916275i	$-0.368819\pi$
$409$	327.650			0.801099			0.400550	+	0.916275i	$0.368819\pi$
$410$	−63.2408	+	381.596i	−0.154246	+	0.930722i
$411$		0			0
$412$	−64.2214	+	188.435i	−0.155877	+	0.457366i
$413$		−	71.2656i		−	0.172556i
$414$		0			0
$415$		−	370.874i		−	0.893673i
$416$	287.468	−	267.603i	0.691028	−	0.643275i
$417$		0			0
$418$	−43.9852	−	7.28954i	−0.105228	−	0.0174391i
$419$	780.119			1.86186			0.930929	−	0.365199i	$-0.118999\pi$
$419$	780.119			1.86186			0.930929	+	0.365199i	$0.118999\pi$
$420$		0			0
$421$			682.087i			1.62016i	0.586320	+	0.810079i	$0.300576\pi$
$421$			682.087i			1.62016i	−0.586320	+	0.810079i	$0.699424\pi$
$422$	560.667	+	92.9177i	1.32859	+	0.220184i
$423$		0			0
$424$	96.8315	−	180.365i	0.228376	−	0.425388i
$425$	−32.6003			−0.0767067
$426$		0			0
$427$	−154.767			−0.362452
$428$	639.211	+	217.853i	1.49348	+	0.509001i
$429$		0			0
$430$	41.9214	−	252.954i	0.0974915	−	0.588266i
$431$		−	222.883i		−	0.517131i	−0.965994	−	0.258565i	$-0.916750\pi$
$431$		−	222.883i		−	0.517131i	0.965994	−	0.258565i	$-0.0832497\pi$
$432$		0			0
$433$	827.262			1.91054			0.955268	−	0.295743i	$-0.0955671\pi$
$433$	827.262			1.91054			0.955268	+	0.295743i	$0.0955671\pi$
$434$	−124.224	−	20.5872i	−0.286230	−	0.0474360i
$435$		0			0
$436$	−30.9081	+	90.6888i	−0.0708901	+	0.208002i
$437$		−	252.000i		−	0.576659i
$438$		0			0
$439$		−	624.321i		−	1.42214i	−0.703120	−	0.711072i	$-0.748210\pi$
$439$		−	624.321i		−	1.42214i	0.703120	−	0.711072i	$-0.251790\pi$
$440$	54.6941	−	101.877i	0.124305	−	0.231538i
$441$		0			0
$442$	−15.9550	+	96.2726i	−0.0360972	+	0.217811i
$443$	−331.608			−0.748550			−0.374275	−	0.927318i	$-0.622108\pi$
$443$	−331.608			−0.748550			−0.374275	+	0.927318i	$0.622108\pi$
$444$		0			0
$445$			262.917i			0.590824i
$446$	100.549	−	606.717i	0.225447	−	1.36035i
$447$		0			0
$448$	−141.134	+	93.5580i	−0.315032	+	0.208835i
$449$	−14.2571			−0.0317530			−0.0158765	−	0.999874i	$-0.505054\pi$
$449$	−14.2571			−0.0317530			−0.0158765	+	0.999874i	$0.505054\pi$
$450$		0			0
$451$	−166.393			−0.368943
$452$	−649.006	−	221.191i	−1.43585	−	0.489360i
$453$		0			0
$454$	−448.230	−	74.2838i	−0.987290	−	0.163621i
$455$			133.095i			0.292516i
$456$		0			0
$457$	−188.688			−0.412885			−0.206443	−	0.978459i	$-0.566189\pi$
$457$	−188.688			−0.412885			−0.206443	+	0.978459i	$0.566189\pi$
$458$	−105.762	+	638.173i	−0.230922	+	1.39339i
$459$		0			0
$460$	618.613	+	210.832i	1.34481	+	0.458331i
$461$			197.385i			0.428168i	0.976815	+	0.214084i	$0.0686766\pi$
$461$			197.385i			0.428168i	−0.976815	+	0.214084i	$0.931323\pi$
$462$		0			0
$463$			112.628i			0.243257i	0.992576	+	0.121629i	$0.0388117\pi$
$463$			112.628i			0.243257i	−0.992576	+	0.121629i	$0.961188\pi$
$464$	−8.13373	+	10.5467i	−0.0175296	+	0.0227300i
$465$		0			0
$466$	−424.536	−	70.3571i	−0.911022	−	0.150981i
$467$	−449.374			−0.962256			−0.481128	−	0.876650i	$-0.659773\pi$
$467$	−449.374			−0.962256			−0.481128	+	0.876650i	$0.659773\pi$
$468$		0			0
$469$			264.088i			0.563088i
$470$	−704.460	−	116.748i	−1.49885	−	0.248400i
$471$		0			0
$472$	189.856	+	101.927i	0.402238	+	0.215948i
$473$	110.300			0.233191
$474$		0			0
$475$	−51.8391			−0.109135
$476$	13.5725	−	39.8238i	0.0285137	−	0.0836633i
$477$		0			0
$478$	−112.324	+	677.763i	−0.234987	+	1.41792i
$479$		−	455.307i		−	0.950536i	−0.879841	−	0.475268i	$-0.842351\pi$
$479$		−	455.307i		−	0.950536i	0.879841	−	0.475268i	$-0.157649\pi$
$480$		0			0
$481$	120.575			0.250675
$482$	−592.300	−	98.1601i	−1.22884	−	0.203652i
$483$		0			0
$484$	−411.042	−	140.089i	−0.849260	−	0.289440i
$485$			332.587i			0.685746i
$486$		0			0
$487$		−	966.691i		−	1.98499i	−0.122278	−	0.992496i	$-0.539020\pi$
$487$		−	966.691i		−	1.98499i	0.122278	−	0.992496i	$-0.460980\pi$
$488$	221.354	−	412.309i	0.453595	−	0.844896i
$489$		0			0
$490$	9.38187	−	56.6104i	0.0191467	−	0.115531i
$491$	−119.359			−0.243093			−0.121547	−	0.992586i	$-0.538785\pi$
$491$	−119.359			−0.243093			−0.121547	+	0.992586i	$0.538785\pi$
$492$		0			0
$493$		−	3.30934i		−	0.00671266i
$494$	−25.3706	+	153.087i	−0.0513576	+	0.309893i
$495$		0			0
$496$	232.516	−	301.496i	0.468782	−	0.607854i
$497$	−205.879			−0.414244
$498$		0			0
$499$	668.069			1.33882			0.669408	−	0.742895i	$-0.266548\pi$
$499$	668.069			1.33882			0.669408	+	0.742895i	$0.266548\pi$
$500$	175.594	−	515.217i	0.351187	−	1.03043i
$501$		0			0
$502$	−347.641	−	57.6136i	−0.692513	−	0.114768i
$503$			195.247i			0.388166i	0.980985	+	0.194083i	$0.0621731\pi$
$503$			195.247i			0.388166i	−0.980985	+	0.194083i	$0.937827\pi$
$504$		0			0
$505$	101.980			0.201940
$506$	−45.9663	+	277.361i	−0.0908424	+	0.548145i
$507$		0			0
$508$	−81.5523	+	239.286i	−0.160536	+	0.471036i
$509$		−	996.859i		−	1.95847i	−0.202737	−	0.979233i	$-0.564984\pi$
$509$		−	996.859i		−	1.95847i	0.202737	−	0.979233i	$-0.435016\pi$
$510$		0			0
$511$			315.551i			0.617517i
$512$	−47.3882	−	509.802i	−0.0925550	−	0.995708i
$513$		0			0
$514$	−143.880	−	23.8448i	−0.279922	−	0.0463907i
$515$	203.993			0.396103
$516$		0			0
$517$		−	307.177i		−	0.594152i
$518$	−51.2850	−	8.49931i	−0.0990058	−	0.0164079i
$519$		0			0
$520$	−354.574	−	190.358i	−0.681873	−	0.366074i
$521$	−2.00334			−0.00384517			−0.00192259	−	0.999998i	$-0.500612\pi$
$521$	−2.00334			−0.00384517			−0.00192259	+	0.999998i	$0.500612\pi$
$522$		0			0
$523$	−508.847			−0.972938			−0.486469	−	0.873698i	$-0.661715\pi$
$523$	−508.847			−0.972938			−0.486469	+	0.873698i	$0.661715\pi$
$524$	−480.436	−	163.740i	−0.916863	−	0.312481i
$525$		0			0
$526$	24.2601	−	146.386i	0.0461219	−	0.278300i
$527$			94.6029i			0.179512i
$528$		0			0
$529$	−1060.06			−2.00389
$530$	−206.945	−	34.2964i	−0.390462	−	0.0647102i
$531$		0			0
$532$	21.5822	−	63.3253i	0.0405681	−	0.119033i
$533$			579.118i			1.08652i
$534$		0			0
$535$		−	691.987i		−	1.29343i
$536$	−703.549	−	377.711i	−1.31259	−	0.704684i
$537$		0			0
$538$	−11.2636	+	67.9649i	−0.0209361	+	0.126329i
$539$	24.6847			0.0457972
$540$		0			0
$541$		−	311.490i		−	0.575766i	−0.957666	−	0.287883i	$-0.907049\pi$
$541$		−	311.490i		−	0.575766i	0.957666	−	0.287883i	$-0.0929515\pi$
$542$	110.221	−	665.077i	0.203360	−	1.22708i
$543$		0			0
$544$	86.6811	+	93.1158i	0.159340	+	0.171169i
$545$	98.1764			0.180140
$546$		0			0
$547$	−417.585			−0.763410			−0.381705	−	0.924284i	$-0.624663\pi$
$547$	−417.585			−0.763410			−0.381705	+	0.924284i	$0.624663\pi$
$548$	550.039	+	187.461i	1.00372	+	0.342083i
$549$		0			0
$550$	57.0562	+	9.45576i	0.103739	+	0.0171923i
$551$		−	5.26231i		−	0.00955048i
$552$		0			0
$553$	−377.420			−0.682495
$554$	−20.6512	+	124.610i	−0.0372766	+	0.224927i
$555$		0			0
$556$	−306.691	−	104.525i	−0.551603	−	0.187994i
$557$			605.617i			1.08728i	0.839317	+	0.543642i	$0.182955\pi$
$557$			605.617i			1.08728i	−0.839317	+	0.543642i	$0.817045\pi$
$558$		0			0
$559$		−	383.889i		−	0.686742i
$560$	137.395	+	105.961i	0.245349	+	0.189215i
$561$		0			0
$562$	126.782	+	21.0112i	0.225591	+	0.0373865i
$563$	382.574			0.679528			0.339764	−	0.940511i	$-0.389653\pi$
$563$	382.574			0.679528			0.339764	+	0.940511i	$0.389653\pi$
$564$		0			0
$565$			702.591i			1.24352i
$566$	−332.188	−	55.0525i	−0.586905	−	0.0972660i
$567$		0			0
$568$	294.458	−	548.477i	0.518412	−	0.965628i
$569$	−766.912			−1.34782			−0.673912	−	0.738812i	$-0.735387\pi$
$569$	−766.912			−1.34782			−0.673912	+	0.738812i	$0.735387\pi$
$570$		0			0
$571$	379.036			0.663810			0.331905	−	0.943313i	$-0.392309\pi$
$571$	379.036			0.663810			0.331905	+	0.943313i	$0.392309\pi$
$572$	55.8479	−	163.866i	0.0976362	−	0.286479i
$573$		0			0
$574$	40.8220	−	246.321i	0.0711185	−	0.429131i
$575$			326.886i			0.568498i
$576$		0			0
$577$	37.2041			0.0644784			0.0322392	−	0.999480i	$-0.489736\pi$
$577$	37.2041			0.0644784			0.0322392	+	0.999480i	$0.489736\pi$
$578$	539.038	+	89.3332i	0.932592	+	0.154556i
$579$		0			0
$580$	12.9180	+	4.40264i	0.0222724	+	0.00759076i
$581$			239.400i			0.412048i
$582$		0			0
$583$		−	90.2375i		−	0.154781i
$584$	−840.650	−	451.316i	−1.43947	−	0.772801i
$585$		0			0
$586$	−35.8739	+	216.464i	−0.0612183	+	0.369392i
$587$	701.870			1.19569			0.597845	−	0.801612i	$-0.296024\pi$
$587$	701.870			1.19569			0.597845	+	0.801612i	$0.296024\pi$
$588$		0			0
$589$			150.432i			0.255402i
$590$	36.1013	−	217.836i	0.0611886	−	0.369213i
$591$		0			0
$592$	95.9928	−	124.471i	0.162150	−	0.210254i
$593$	933.086			1.57350			0.786750	−	0.617272i	$-0.211762\pi$
$593$	933.086			1.57350			0.786750	+	0.617272i	$0.211762\pi$
$594$		0			0
$595$	−43.1118			−0.0724568
$596$	186.241	−	546.458i	0.312485	−	0.916877i
$597$		0			0
$598$	965.333	+	159.982i	1.61427	+	0.267528i
$599$			85.2304i			0.142288i	0.997466	+	0.0711439i	$0.0226649\pi$
$599$			85.2304i			0.142288i	−0.997466	+	0.0711439i	$0.977335\pi$
$600$		0			0
$601$	928.450			1.54484			0.772421	−	0.635111i	$-0.219046\pi$
$601$	928.450			1.54484			0.772421	+	0.635111i	$0.219046\pi$
$602$	−27.0603	+	163.282i	−0.0449507	+	0.271233i
$603$		0			0
$604$	−130.031	+	381.529i	−0.215282	+	0.631670i
$605$			444.979i			0.735503i
$606$		0			0
$607$		−	186.121i		−	0.306624i	−0.988178	−	0.153312i	$-0.951006\pi$
$607$		−	186.121i		−	0.306624i	0.988178	−	0.153312i	$-0.0489940\pi$
$608$	137.835	+	148.067i	0.226703	+	0.243532i
$609$		0			0
$610$	−473.071	−	78.4007i	−0.775527	−	0.128526i
$611$	−1069.10			−1.74976
$612$		0			0
$613$			208.018i			0.339345i	0.985501	+	0.169672i	$0.0542709\pi$
$613$			208.018i			0.339345i	−0.985501	+	0.169672i	$0.945729\pi$
$614$	610.564	+	101.187i	0.994405	+	0.164800i
$615$		0			0
$616$	−35.3052	+	65.7617i	−0.0573136	+	0.106756i
$617$	26.3994			0.0427867			0.0213934	−	0.999771i	$-0.493190\pi$
$617$	26.3994			0.0427867			0.0213934	+	0.999771i	$0.493190\pi$
$618$		0			0
$619$	301.410			0.486930			0.243465	−	0.969910i	$-0.421716\pi$
$619$	301.410			0.486930			0.243465	+	0.969910i	$0.421716\pi$
$620$	−369.282	−	125.857i	−0.595616	−	0.202995i
$621$		0			0
$622$	−37.6983	+	227.472i	−0.0606082	+	0.365711i
$623$		−	169.713i		−	0.272413i
$624$		0			0
$625$	−352.750			−0.564400
$626$	−425.308	−	70.4850i	−0.679406	−	0.112596i
$627$		0			0
$628$	354.329	−	1039.65i	0.564217	−	1.65550i
$629$			39.0562i			0.0620926i
$630$		0			0
$631$		−	124.227i		−	0.196873i	−0.995143	−	0.0984364i	$-0.968616\pi$
$631$		−	124.227i		−	0.196873i	0.995143	−	0.0984364i	$-0.0313841\pi$
$632$	539.802	−	1005.47i	0.854118	−	1.59094i
$633$		0			0
$634$	−58.0231	+	350.112i	−0.0915190	+	0.552228i
$635$	259.043			0.407941
$636$		0			0
$637$		−	85.9130i		−	0.134871i
$638$	−0.959876	+	5.79191i	−0.00150451	+	0.00907823i
$639$		0			0
$640$	−478.795	+	214.481i	−0.748118	+	0.335127i
$641$	849.868			1.32585			0.662924	−	0.748687i	$-0.269315\pi$
$641$	849.868			1.32585			0.662924	+	0.748687i	$0.269315\pi$
$642$		0			0
$643$	−192.307			−0.299078			−0.149539	−	0.988756i	$-0.547779\pi$
$643$	−192.307			−0.299078			−0.149539	+	0.988756i	$0.547779\pi$
$644$	−399.316	−	136.093i	−0.620056	−	0.211324i
$645$		0			0
$646$	−49.5875	−	8.21799i	−0.0767609	−	0.0127214i
$647$			455.619i			0.704203i	0.935962	+	0.352101i	$0.114533\pi$
$647$			455.619i			0.704203i	−0.935962	+	0.352101i	$0.885467\pi$
$648$		0			0
$649$	94.9862			0.146358
$650$	32.9100	−	198.579i	0.0506307	−	0.305507i
$651$		0			0
$652$	−421.362	−	143.607i	−0.646261	−	0.220255i
$653$			664.401i			1.01746i	0.860926	+	0.508729i	$0.169885\pi$
$653$			664.401i			1.01746i	−0.860926	+	0.508729i	$0.830115\pi$
$654$		0			0
$655$			520.103i			0.794051i
$656$	597.830	+	461.052i	0.911326	+	0.702823i
$657$		0			0
$658$	454.731	+	75.3611i	0.691080	+	0.114531i
$659$	−782.869			−1.18797			−0.593983	−	0.804478i	$-0.702445\pi$
$659$	−782.869			−1.18797			−0.593983	+	0.804478i	$0.702445\pi$
$660$		0			0
$661$			134.657i			0.203718i	0.994799	+	0.101859i	$0.0324790\pi$
$661$			134.657i			0.203718i	−0.994799	+	0.101859i	$0.967521\pi$
$662$	−444.279	−	73.6290i	−0.671116	−	0.111222i
$663$		0			0
$664$	−637.778	−	342.401i	−0.960509	−	0.515664i
$665$	−68.5538			−0.103088
$666$		0			0
$667$	−33.1830			−0.0497497
$668$	−187.467	+	550.056i	−0.280640	+	0.823438i
$669$		0			0
$670$	−133.780	+	807.231i	−0.199672	+	1.20482i
$671$		−	206.281i		−	0.307423i
$672$		0			0
$673$	799.458			1.18790			0.593951	−	0.804501i	$-0.297567\pi$
$673$	799.458			1.18790			0.593951	+	0.804501i	$0.297567\pi$
$674$	482.354	+	79.9392i	0.715659	+	0.118604i
$675$		0			0
$676$	69.5378	+	23.6995i	0.102866	+	0.0350584i
$677$			1095.53i			1.61821i	0.587667	+	0.809103i	$0.300047\pi$
$677$			1095.53i			1.61821i	−0.587667	+	0.809103i	$0.699953\pi$
$678$		0			0
$679$		−	214.685i		−	0.316179i
$680$	61.6604	−	114.853i	0.0906770	−	0.168901i
$681$		0			0
$682$	27.4396	−	165.571i	0.0402341	−	0.242773i
$683$	435.002			0.636899			0.318450	−	0.947940i	$-0.396838\pi$
$683$	435.002			0.636899			0.318450	+	0.947940i	$0.396838\pi$
$684$		0			0
$685$		−	595.452i		−	0.869274i
$686$	−6.05601	+	36.5421i	−0.00882801	+	0.0532684i
$687$		0			0
$688$	−396.293	−	305.624i	−0.576007	−	0.444222i
$689$	−314.064			−0.455826
$690$		0			0
$691$	−1149.83			−1.66401			−0.832003	−	0.554771i	$-0.812806\pi$
$691$	−1149.83			−1.66401			−0.832003	+	0.554771i	$0.812806\pi$
$692$	24.8504	−	72.9147i	0.0359110	−	0.105368i
$693$		0			0
$694$	895.285	+	148.373i	1.29004	+	0.213794i
$695$			332.013i			0.477717i
$696$		0			0
$697$	−187.586			−0.269134
$698$	171.053	−	1032.14i	0.245062	−	1.47871i
$699$		0			0
$700$	−27.9957	+	82.1436i	−0.0399939	+	0.117348i
$701$			199.358i			0.284390i	0.989839	+	0.142195i	$0.0454161\pi$
$701$			199.358i			0.284390i	−0.989839	+	0.142195i	$0.954584\pi$
$702$		0			0
$703$			62.1049i			0.0883426i
$704$	−124.699	−	188.111i	−0.177129	−	0.267203i
$705$		0			0
$706$	286.917	+	47.5499i	0.406398	+	0.0673511i
$707$	−65.8280			−0.0931089
$708$		0			0
$709$			919.307i			1.29663i	0.761374	+	0.648313i	$0.224525\pi$
$709$			919.307i			1.29663i	−0.761374	+	0.648313i	$0.775475\pi$
$710$	−629.306	−	104.293i	−0.886346	−	0.146892i
$711$		0			0
$712$	452.127	+	242.731i	0.635010	+	0.340915i
$713$	948.591			1.33042
$714$		0			0
$715$	−177.395			−0.248105
$716$	−465.632	−	158.694i	−0.650324	−	0.221640i
$717$		0			0
$718$	106.466	−	642.419i	0.148282	−	0.894734i
$719$		−	682.855i		−	0.949728i	−0.880059	−	0.474864i	$-0.842497\pi$
$719$		−	682.855i		−	0.949728i	0.880059	−	0.474864i	$-0.157503\pi$
$720$		0			0
$721$	−131.678			−0.182632
$722$	633.434	+	104.977i	0.877332	+	0.145398i
$723$		0			0
$724$	415.176	−	1218.19i	0.573448	−	1.68258i
$725$			6.82610i			0.00941531i
$726$		0			0
$727$		−	298.077i		−	0.410010i	−0.978761	−	0.205005i	$-0.934279\pi$
$727$		−	298.077i		−	0.410010i	0.978761	−	0.205005i	$-0.0657211\pi$
$728$	228.878	+	122.877i	0.314393	+	0.168787i
$729$		0			0
$730$	−159.850	+	964.537i	−0.218972	+	1.32128i
$731$	124.348			0.170107
$732$		0			0
$733$			891.569i			1.21633i	0.793811	+	0.608164i	$0.208094\pi$
$733$			891.569i			1.21633i	−0.793811	+	0.608164i	$0.791906\pi$
$734$	76.1809	−	459.677i	0.103789	−	0.626263i
$735$		0			0
$736$	933.680	−	869.159i	1.26859	−	1.18092i
$737$	−351.989			−0.477598
$738$		0			0
$739$	390.305			0.528153			0.264077	−	0.964502i	$-0.414933\pi$
$739$	390.305			0.528153			0.264077	+	0.964502i	$0.414933\pi$
$740$	−152.456	−	51.9592i	−0.206021	−	0.0702151i
$741$		0			0
$742$	133.583	+	22.1384i	0.180032	+	0.0298361i
$743$			805.058i			1.08352i	0.840532	+	0.541762i	$0.182242\pi$
$743$			805.058i			1.08352i	−0.840532	+	0.541762i	$0.817758\pi$
$744$		0			0
$745$	−591.576			−0.794062
$746$	151.506	−	914.191i	0.203091	−	1.22546i
$747$		0			0
$748$	53.0790	+	18.0901i	0.0709612	+	0.0241846i
$749$			446.679i			0.596367i
$750$		0			0
$751$			548.399i			0.730224i	0.930964	+	0.365112i	$0.118969\pi$
$751$			548.399i			0.730224i	−0.930964	+	0.365112i	$0.881031\pi$
$752$	−851.143	+	1103.65i	−1.13184	+	1.46762i
$753$		0			0
$754$	20.1583	+	3.34077i	0.0267351	+	0.00443073i
$755$	413.029			0.547059
$756$		0			0
$757$		−	928.292i		−	1.22628i	−0.789975	−	0.613138i	$-0.789907\pi$
$757$		−	928.292i		−	1.22628i	0.789975	−	0.613138i	$-0.210093\pi$
$758$	1250.79	+	207.290i	1.65013	+	0.273470i
$759$		0			0
$760$	98.0487	−	182.632i	0.129011	−	0.240305i
$761$	1213.56			1.59469			0.797344	−	0.603526i	$-0.206238\pi$
$761$	1213.56			1.59469			0.797344	+	0.603526i	$0.206238\pi$
$762$		0			0
$763$	−63.3731			−0.0830578
$764$	228.230	−	669.660i	0.298730	−	0.876519i
$765$		0			0
$766$	32.8833	−	198.418i	0.0429285	−	0.259032i
$767$		−	330.592i		−	0.431019i
$768$		0			0
$769$	843.497			1.09688			0.548438	−	0.836191i	$-0.315223\pi$
$769$	843.497			1.09688			0.548438	+	0.836191i	$0.315223\pi$
$770$	75.4530	+	12.5046i	0.0979909	+	0.0162397i
$771$		0			0
$772$	−1153.61	−	393.167i	−1.49431	−	0.509283i
$773$			891.060i			1.15273i	0.817192	+	0.576365i	$0.195529\pi$
$773$			891.060i			1.15273i	−0.817192	+	0.576365i	$0.804471\pi$
$774$		0			0
$775$		−	195.135i		−	0.251788i
$776$	571.936	+	307.053i	0.737031	+	0.395686i
$777$		0			0
$778$	−134.390	+	810.912i	−0.172738	+	1.04230i
$779$	−298.289			−0.382912
$780$		0			0
$781$		−	274.406i		−	0.351352i
$782$	−51.8209	+	312.688i	−0.0662671	+	0.399857i
$783$		0			0
$784$	−88.6890	−	68.3978i	−0.113124	−	0.0872421i
$785$	−1125.49			−1.43374
$786$		0			0
$787$	−265.122			−0.336877			−0.168438	−	0.985712i	$-0.553872\pi$
$787$	−265.122			−0.336877			−0.168438	+	0.985712i	$0.553872\pi$
$788$	−501.042	+	1470.13i	−0.635840	+	1.86565i
$789$		0			0
$790$	−1153.65	−	191.191i	−1.46031	−	0.242013i
$791$		−	453.524i		−	0.573355i
$792$		0			0
$793$	−717.943			−0.905350
$794$	−120.945	+	729.783i	−0.152323	+	0.919122i
$795$		0			0
$796$	158.247	−	464.321i	0.198803	−	0.583318i
$797$		−	918.018i		−	1.15184i	−0.817505	−	0.575921i	$-0.804644\pi$
$797$		−	918.018i		−	1.15184i	0.817505	−	0.575921i	$-0.195356\pi$
$798$		0			0
$799$		−	346.301i		−	0.433418i
$800$	−178.795	−	192.068i	−0.223494	−	0.240085i
$801$		0			0
$802$	680.115	+	112.713i	0.848023	+	0.140540i
$803$	−420.582			−0.523763
$804$		0			0
$805$			432.285i			0.537000i
$806$	−576.257	−	95.5014i	−0.714959	−	0.118488i
$807$		0			0
$808$	94.1502	−	175.370i	0.116522	−	0.217042i
$809$	−181.129			−0.223893			−0.111947	−	0.993714i	$-0.535709\pi$
$809$	−181.129			−0.223893			−0.111947	+	0.993714i	$0.535709\pi$
$810$		0			0
$811$	879.121			1.08400			0.541998	−	0.840380i	$-0.317668\pi$
$811$	879.121			1.08400			0.541998	+	0.840380i	$0.317668\pi$
$812$	−8.33859	−	2.84191i	−0.0102692	−	0.00349990i
$813$		0			0
$814$	11.3283	−	68.3551i	0.0139168	−	0.0839743i
$815$			456.152i			0.559696i
$816$		0			0
$817$	197.731			0.242021
$818$	−646.481	−	107.139i	−0.790320	−	0.130977i
$819$		0			0
$820$	249.559	−	732.243i	0.304340	−	0.892979i
$821$			1271.70i			1.54896i	0.632598	+	0.774480i	$0.281988\pi$
$821$			1271.70i			1.54896i	−0.632598	+	0.774480i	$0.718012\pi$
$822$		0			0
$823$			542.745i			0.659471i	0.944073	+	0.329736i	$0.106960\pi$
$823$			542.745i			0.659471i	−0.944073	+	0.329736i	$0.893040\pi$
$824$	188.332	−	350.799i	0.228558	−	0.425727i
$825$		0			0
$826$	−23.3034	+	140.613i	−0.0282124	+	0.170234i
$827$	−171.607			−0.207506			−0.103753	−	0.994603i	$-0.533085\pi$
$827$	−171.607			−0.207506			−0.103753	+	0.994603i	$0.533085\pi$
$828$		0			0
$829$			862.620i			1.04056i	0.853997	+	0.520278i	$0.174172\pi$
$829$			862.620i			1.04056i	−0.853997	+	0.520278i	$0.825828\pi$
$830$	−121.274	+	731.767i	−0.146113	+	0.881647i
$831$		0			0
$832$	−654.704	+	434.003i	−0.786903	+	0.521638i
$833$	27.8287			0.0334078
$834$		0			0
$835$	595.471			0.713139
$836$	84.4031	+	28.7658i	0.100961	+	0.0344089i
$837$		0			0
$838$	−1539.24	−	255.094i	−1.83681	−	0.304408i
$839$		−	992.896i		−	1.18343i	−0.806148	−	0.591714i	$-0.798452\pi$
$839$		−	992.896i		−	1.18343i	0.806148	−	0.591714i	$-0.201548\pi$
$840$		0			0
$841$	840.307			0.999176
$842$	223.038	−	1345.82i	0.264891	−	1.59836i
$843$		0			0
$844$	−1075.86	−	366.669i	−1.27472	−	0.434442i
$845$		−	75.2791i		−	0.0890877i
$846$		0			0
$847$		−	287.235i		−	0.339120i
$848$	−250.035	+	324.212i	−0.294853	+	0.382326i
$849$		0			0
$850$	64.3233	+	10.6601i	0.0756745	+	0.0125413i
$851$	391.620			0.460188
$852$		0			0
$853$			790.557i			0.926796i	0.886150	+	0.463398i	$0.153370\pi$
$853$			790.557i			0.926796i	−0.886150	+	0.463398i	$0.846630\pi$
$854$	305.369	+	50.6078i	0.357574	+	0.0592597i
$855$		0			0
$856$	−1189.98	−	638.860i	−1.39017	−	0.746332i
$857$	592.166			0.690976			0.345488	−	0.938423i	$-0.387713\pi$
$857$	592.166			0.690976			0.345488	+	0.938423i	$0.387713\pi$
$858$		0			0
$859$	−1167.30			−1.35890			−0.679451	−	0.733721i	$-0.737782\pi$
$859$	−1167.30			−1.35890			−0.679451	+	0.733721i	$0.737782\pi$
$860$	−165.429	+	485.393i	−0.192359	+	0.564410i
$861$		0			0
$862$	−72.8815	+	439.768i	−0.0845493	+	0.510172i
$863$		−	1290.28i		−	1.49511i	−0.664200	−	0.747555i	$-0.731228\pi$
$863$		−	1290.28i		−	1.49511i	0.664200	−	0.747555i	$-0.268772\pi$
$864$		0			0
$865$	−78.9348			−0.0912541
$866$	−1632.26	−	270.510i	−1.88483	−	0.312367i
$867$		0			0
$868$	238.372	+	81.2408i	0.274623	+	0.0935954i
$869$		−	503.043i		−	0.578876i
$870$		0			0
$871$			1225.07i			1.40651i
$872$	90.6390	−	168.830i	0.103944	−	0.193613i
$873$		0			0
$874$	−82.4025	+	497.218i	−0.0942821	+	0.568900i
$875$	360.033			0.411466
$876$		0			0
$877$		−	795.949i		−	0.907581i	−0.891108	−	0.453791i	$-0.850071\pi$
$877$		−	795.949i		−	0.907581i	0.891108	−	0.453791i	$-0.149929\pi$
$878$	−204.149	+	1231.84i	−0.232516	+	1.40301i
$879$		0			0
$880$	−141.229	+	183.127i	−0.160488	+	0.208099i
$881$	−44.6577			−0.0506898			−0.0253449	−	0.999679i	$-0.508068\pi$
$881$	−44.6577			−0.0506898			−0.0253449	+	0.999679i	$0.508068\pi$
$882$		0			0
$883$	1361.40			1.54179			0.770894	−	0.636963i	$-0.219810\pi$
$883$	1361.40			1.54179			0.770894	+	0.636963i	$0.219810\pi$
$884$	62.9611	−	184.737i	0.0712230	−	0.208979i
$885$		0			0
$886$	654.291	+	108.434i	0.738477	+	0.122386i
$887$		−	157.476i		−	0.177538i	−0.996052	−	0.0887690i	$-0.971707\pi$
$887$		−	157.476i		−	0.177538i	0.996052	−	0.0887690i	$-0.0282933\pi$
$888$		0			0
$889$	−167.213			−0.188091
$890$	85.9721	−	518.757i	0.0965979	−	0.582873i
$891$		0			0
$892$	−396.785	+	1164.23i	−0.444827	+	1.30519i
$893$		−	550.668i		−	0.616649i
$894$		0			0
$895$			504.077i			0.563214i
$896$	309.063	−	138.448i	0.344937	−	0.154518i
$897$		0			0
$898$	28.1305	+	4.66199i	0.0313258	+	0.00519153i
$899$	19.8087			0.0220341
$900$		0			0
$901$		−	101.731i		−	0.112909i
$902$	328.308	+	54.4096i	0.363978	+	0.0603210i
$903$		0			0
$904$	1208.22	+	648.650i	1.33652	+	0.717533i
$905$	−1318.77			−1.45720
$906$		0			0
$907$	1773.43			1.95527			0.977637	−	0.210300i	$-0.0674441\pi$
$907$	1773.43			1.95527			0.977637	+	0.210300i	$0.0674441\pi$
$908$	860.106	+	293.137i	0.947254	+	0.322838i
$909$		0			0
$910$	43.5212	−	262.608i	0.0478255	−	0.288580i
$911$		−	575.398i		−	0.631612i	−0.948824	−	0.315806i	$-0.897725\pi$
$911$		−	575.398i		−	0.631612i	0.948824	−	0.315806i	$-0.102275\pi$
$912$		0			0
$913$	−319.084			−0.349489
$914$	372.299	+	61.7000i	0.407329	+	0.0675054i
$915$		0			0
$916$	417.357	−	1224.59i	0.455630	−	1.33689i
$917$		−	335.728i		−	0.366115i
$918$		0			0
$919$			46.2676i			0.0503455i	0.999683	+	0.0251728i	$0.00801359\pi$
$919$			46.2676i			0.0503455i	−0.999683	+	0.0251728i	$0.991986\pi$
$920$	−1151.64	−	618.274i	−1.25178	−	0.672037i
$921$		0			0
$922$	64.5438	−	389.458i	0.0700041	−	0.422406i
$923$	−955.047			−1.03472
$924$		0			0
$925$		−	80.5604i		−	0.0870924i
$926$	36.8287	−	222.225i	0.0397719	−	0.239984i
$927$		0			0
$928$	19.4973	−	18.1499i	0.0210100	−	0.0195581i
$929$	78.7228			0.0847393			0.0423696	−	0.999102i	$-0.486509\pi$
$929$	78.7228			0.0847393			0.0423696	+	0.999102i	$0.486509\pi$
$930$		0			0
$931$	44.2516			0.0475312
$932$	814.641	+	277.642i	0.874078	+	0.297899i
$933$		0			0
$934$	886.654	+	146.942i	0.949308	+	0.157326i
$935$		−	57.4614i		−	0.0614561i
$936$		0			0
$937$	−771.207			−0.823060			−0.411530	−	0.911396i	$-0.635005\pi$
$937$	−771.207			−0.823060			−0.411530	+	0.911396i	$0.635005\pi$
$938$	86.3552	−	521.069i	0.0920631	−	0.555511i
$939$		0			0
$940$	1351.79	+	460.709i	1.43807	+	0.490116i
$941$		−	1287.41i		−	1.36813i	−0.729420	−	0.684066i	$-0.760210\pi$
$941$		−	1287.41i		−	1.36813i	0.729420	−	0.684066i	$-0.239790\pi$
$942$		0			0
$943$			1880.94i			1.99464i
$944$	−341.274	−	263.193i	−0.361519	−	0.278807i
$945$		0			0
$946$	−217.631	−	36.0673i	−0.230054	−	0.0381261i
$947$	−117.702			−0.124290			−0.0621448	−	0.998067i	$-0.519794\pi$
$947$	−117.702			−0.124290			−0.0621448	+	0.998067i	$0.519794\pi$
$948$		0			0
$949$			1463.80i			1.54247i
$950$	102.283	+	16.9511i	0.107666	+	0.0178432i
$951$		0			0
$952$	−39.8019	+	74.1376i	−0.0418087	+	0.0778757i
$953$	−128.384			−0.134715			−0.0673577	−	0.997729i	$-0.521457\pi$
$953$	−128.384			−0.134715			−0.0673577	+	0.997729i	$0.521457\pi$
$954$		0			0
$955$	−724.950			−0.759110
$956$	443.249	−	1300.56i	0.463650	−	1.36042i
$957$		0			0
$958$	−148.883	+	898.361i	−0.155410	+	0.937746i
$959$			384.366i			0.400798i
$960$		0			0
$961$	394.737			0.410757
$962$	−237.904	−	39.4272i	−0.247302	−	0.0409846i
$963$		0			0
$964$	1136.56	+	387.357i	1.17901	+	0.401823i
$965$			1248.85i			1.29415i
$966$		0			0
$967$			510.697i			0.528125i	0.964506	+	0.264062i	$0.0850625\pi$
$967$			510.697i			0.528125i	−0.964506	+	0.264062i	$0.914938\pi$
$968$	765.213	+	410.816i	0.790510	+	0.424397i
$969$		0			0
$970$	108.754	−	656.223i	0.112117	−	0.676518i
$971$	−427.761			−0.440537			−0.220268	−	0.975439i	$-0.570693\pi$
$971$	−427.761			−0.440537			−0.220268	+	0.975439i	$0.570693\pi$
$972$		0			0
$973$		−	214.315i		−	0.220262i
$974$	−316.102	+	1907.37i	−0.324540	+	1.95828i
$975$		0			0
$976$	−571.574	+	741.141i	−0.585630	+	0.759366i
$977$	−30.5283			−0.0312470			−0.0156235	−	0.999878i	$-0.504973\pi$
$977$	−30.5283			−0.0312470			−0.0156235	+	0.999878i	$0.504973\pi$
$978$		0			0
$979$	226.202			0.231054
$980$	−37.0225	+	108.629i	−0.0377780	+	0.110846i
$981$		0			0
$982$	235.505	+	39.0296i	0.239822	+	0.0397450i
$983$		−	1521.29i		−	1.54760i	−0.633432	−	0.773799i	$-0.718354\pi$
$983$		−	1521.29i		−	1.54760i	0.633432	−	0.773799i	$-0.281646\pi$
$984$		0			0
$985$	1591.51			1.61575
$986$	−1.08213	+	6.52962i	−0.00109750	+	0.00662233i
$987$		0			0
$988$	100.117	−	293.758i	0.101333	−	0.297326i
$989$		−	1246.85i		−	1.26072i
$990$		0			0
$991$		−	826.002i		−	0.833503i	−0.909020	−	0.416752i	$-0.863168\pi$
$991$		−	826.002i		−	0.833503i	0.909020	−	0.416752i	$-0.136832\pi$
$992$	−557.362	+	518.846i	−0.561857	+	0.523030i
$993$		0			0
$994$	406.218	+	67.3213i	0.408670	+	0.0677277i
$995$	−502.657			−0.505183
$996$		0			0
$997$		−	149.882i		−	0.150333i	−0.997171	−	0.0751665i	$-0.976051\pi$
$997$		−	149.882i		−	0.150333i	0.997171	−	0.0751665i	$-0.0239488\pi$
$998$	−1318.16	−	218.454i	−1.32080	−	0.218892i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.3.g.d.379.1		24
3.2	odd	2		168.3.g.a.43.24	yes	24
4.3	odd	2		2016.3.g.d.1135.6		24
8.3	odd	2	inner	504.3.g.d.379.2		24
8.5	even	2		2016.3.g.d.1135.19		24
12.11	even	2		672.3.g.a.463.23		24
24.5	odd	2		672.3.g.a.463.14		24
24.11	even	2		168.3.g.a.43.23	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.g.a.43.23	✓	24	24.11	even	2
168.3.g.a.43.24	yes	24	3.2	odd	2
504.3.g.d.379.1		24	1.1	even	1	trivial
504.3.g.d.379.2		24	8.3	odd	2	inner
672.3.g.a.463.14		24	24.5	odd	2
672.3.g.a.463.23		24	12.11	even	2
2016.3.g.d.1135.6		24	4.3	odd	2
2016.3.g.d.1135.19		24	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	504.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.97309 - 0.326994i) q^{2} +(3.78615 + 1.29038i) q^{4} -4.09875i q^{5} +2.64575i q^{7} +(-7.04846 - 3.78407i) q^{8} +(-1.34027 + 8.08719i) q^{10} -3.52638 q^{11} +12.2733i q^{13} +(0.865145 - 5.22030i) q^{14} +(12.6699 + 9.77111i) q^{16} -3.97553 q^{17} -6.32165 q^{19} +(5.28893 - 15.5185i) q^{20} +(6.95787 + 1.15311i) q^{22} +39.8630i q^{23} +8.20025 q^{25} +(4.01329 - 24.2163i) q^{26} +(-3.41401 + 10.0172i) q^{28} +0.832427i q^{29} -23.7963i q^{31} +(-21.8037 - 23.4222i) q^{32} +(7.84407 + 1.29998i) q^{34} +10.8443 q^{35} -9.82415i q^{37} +(12.4732 + 2.06714i) q^{38} +(-15.5100 + 28.8899i) q^{40} +47.1852 q^{41} -31.2784 q^{43} +(-13.3514 - 4.55036i) q^{44} +(13.0350 - 78.6532i) q^{46} +87.1081i q^{47} -7.00000 q^{49} +(-16.1798 - 2.68143i) q^{50} +(-15.8372 + 46.4685i) q^{52} +25.5892i q^{53} +14.4538i q^{55} +(10.0117 - 18.6485i) q^{56} +(0.272198 - 1.64245i) q^{58} -26.9359 q^{59} +58.4964i q^{61} +(-7.78124 + 46.9521i) q^{62} +(35.3616 + 53.3438i) q^{64} +50.3052 q^{65} +99.8159 q^{67} +(-15.0520 - 5.12993i) q^{68} +(-21.3967 - 3.54601i) q^{70} +77.8151i q^{71} +119.267 q^{73} +(-3.21244 + 19.3839i) q^{74} +(-23.9347 - 8.15731i) q^{76} -9.32994i q^{77} +142.651i q^{79} +(40.0493 - 51.9306i) q^{80} +(-93.1006 - 15.4293i) q^{82} +90.4847 q^{83} +16.2947i q^{85} +(61.7150 + 10.2278i) q^{86} +(24.8556 + 13.3441i) q^{88} -64.1455 q^{89} -32.4721 q^{91} +(-51.4382 + 150.927i) q^{92} +(28.4838 - 171.872i) q^{94} +25.9109i q^{95} -81.1434 q^{97} +(13.8116 + 2.28896i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} + 10 q^{4} - 10 q^{8} + 12 q^{10} - 32 q^{11} + 14 q^{14} + 66 q^{16} - 16 q^{17} - 64 q^{19} - 20 q^{20} + 12 q^{22} - 72 q^{25} - 100 q^{26} - 14 q^{28} - 98 q^{32} - 108 q^{34} + 72 q^{38}+ \cdots - 14 q^{98}+O(q^{100}) \) 24 * q + 2 * q^2 + 10 * q^4 - 10 * q^8 + 12 * q^10 - 32 * q^11 + 14 * q^14 + 66 * q^16 - 16 * q^17 - 64 * q^19 - 20 * q^20 + 12 * q^22 - 72 * q^25 - 100 * q^26 - 14 * q^28 - 98 * q^32 - 108 * q^34 + 72 * q^38 - 332 * q^40 + 80 * q^41 + 32 * q^43 + 292 * q^44 - 168 * q^49 - 46 * q^50 - 4 * q^52 - 98 * q^56 - 96 * q^58 + 16 * q^62 - 182 * q^64 + 192 * q^65 - 32 * q^67 - 188 * q^68 - 84 * q^70 - 240 * q^73 - 208 * q^74 + 8 * q^76 - 484 * q^80 - 372 * q^82 + 320 * q^83 + 604 * q^86 + 468 * q^88 - 400 * q^89 - 352 * q^92 - 72 * q^94 + 144 * q^97 - 14 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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