LMFDB - Embedded newform 360.4.m.c.179.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,4,Mod(179,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))

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

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

chi := DirichletCharacter("360.179");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	360.m (of order $2$, degree $1$, 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:	$21.2406876021$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			179.22
Character	$\chi$	$=$	360.179
Dual form			360.4.m.c.179.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.51905 - 2.38589i) q^{2} +(-3.38496 + 7.24859i) q^{4} +(6.07981 + 9.38275i) q^{5} +14.2510 q^{7} +(22.4363 - 2.93483i) q^{8} +O(q^{10})$	\(q+(-1.51905 - 2.38589i) q^{2} +(-3.38496 + 7.24859i) q^{4} +(6.07981 + 9.38275i) q^{5} +14.2510 q^{7} +(22.4363 - 2.93483i) q^{8} +(13.1507 - 28.7586i) q^{10} -27.1398i q^{11} -26.3714 q^{13} +(-21.6479 - 34.0012i) q^{14} +(-41.0841 - 49.0724i) q^{16} +85.4877 q^{17} -42.9911 q^{19} +(-88.5916 + 12.3098i) q^{20} +(-64.7526 + 41.2268i) q^{22} +192.381i q^{23} +(-51.0719 + 114.091i) q^{25} +(40.0596 + 62.9194i) q^{26} +(-48.2389 + 103.299i) q^{28} +237.502 q^{29} -232.950i q^{31} +(-54.6726 + 172.566i) q^{32} +(-129.860 - 203.964i) q^{34} +(86.6431 + 133.713i) q^{35} +214.767 q^{37} +(65.3057 + 102.572i) q^{38} +(163.945 + 192.671i) q^{40} +427.145i q^{41} +317.252i q^{43} +(196.725 + 91.8672i) q^{44} +(459.001 - 292.237i) q^{46} -78.8688i q^{47} -139.910 q^{49} +(349.789 - 51.4576i) q^{50} +(89.2663 - 191.156i) q^{52} -49.0487i q^{53} +(254.646 - 165.005i) q^{55} +(319.738 - 41.8241i) q^{56} +(-360.778 - 566.654i) q^{58} -386.301i q^{59} +11.0694i q^{61} +(-555.793 + 353.863i) q^{62} +(494.774 - 131.693i) q^{64} +(-160.333 - 247.437i) q^{65} -275.513i q^{67} +(-289.373 + 619.665i) q^{68} +(187.410 - 409.838i) q^{70} +965.571 q^{71} +816.521i q^{73} +(-326.242 - 512.410i) q^{74} +(145.523 - 311.625i) q^{76} -386.768i q^{77} +332.287i q^{79} +(210.651 - 683.832i) q^{80} +(1019.12 - 648.856i) q^{82} +459.444 q^{83} +(519.749 + 802.110i) q^{85} +(756.929 - 481.922i) q^{86} +(-79.6507 - 608.916i) q^{88} +1055.50i q^{89} -375.818 q^{91} +(-1394.49 - 651.203i) q^{92} +(-188.172 + 119.806i) q^{94} +(-261.377 - 403.374i) q^{95} +329.837i q^{97} +(212.531 + 333.811i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 76 q^{4}+O(q^{10}) $ 64 * q + 76 * q^4	$ 64 q + 76 q^{4} + 72 q^{10} - 236 q^{16} - 48 q^{19} + 1000 q^{25} - 192 q^{34} + 1284 q^{40} + 336 q^{46} + 784 q^{49} + 4228 q^{64} - 768 q^{70} + 648 q^{76} + 4304 q^{91} - 5944 q^{94}+O(q^{100}) $ 64 * q + 76 * q^4 + 72 * q^10 - 236 * q^16 - 48 * q^19 + 1000 * q^25 - 192 * q^34 + 1284 * q^40 + 336 * q^46 + 784 * q^49 + 4228 * q^64 - 768 * q^70 + 648 * q^76 + 4304 * q^91 - 5944 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	−1.51905	−	2.38589i	−0.537066	−	0.843540i
$2$	−1.51905	−	2.38589i	−0.537066	−	0.843540i
$3$		0			0
$3$		0			0
$4$	−3.38496	+	7.24859i	−0.423120	+	0.906074i
$5$	6.07981	+	9.38275i	0.543795	+	0.839218i
$5$	6.07981	+	9.38275i	0.543795	+	0.839218i
$6$		0			0
$7$	14.2510			0.769479			0.384740	−	0.923025i	$-0.374291\pi$
$7$	14.2510			0.769479			0.384740	+	0.923025i	$0.374291\pi$
$8$	22.4363	−	2.93483i	0.991553	−	0.129702i
$9$		0			0
$10$	13.1507	−	28.7586i	0.415861	−	0.909428i
$11$		−	27.1398i		−	0.743905i	−0.928252	−	0.371953i	$-0.878688\pi$
$11$		−	27.1398i		−	0.743905i	0.928252	−	0.371953i	$-0.121312\pi$
$12$		0			0
$13$	−26.3714			−0.562625			−0.281312	−	0.959616i	$-0.590770\pi$
$13$	−26.3714			−0.562625			−0.281312	+	0.959616i	$0.590770\pi$
$14$	−21.6479	−	34.0012i	−0.413261	−	0.649087i
$15$		0			0
$16$	−41.0841	−	49.0724i	−0.641939	−	0.766756i
$17$	85.4877			1.21964			0.609818	−	0.792541i	$-0.291242\pi$
$17$	85.4877			1.21964			0.609818	+	0.792541i	$0.291242\pi$
$18$		0			0
$19$	−42.9911			−0.519096			−0.259548	−	0.965730i	$-0.583574\pi$
$19$	−42.9911			−0.519096			−0.259548	+	0.965730i	$0.583574\pi$
$20$	−88.5916	+	12.3098i	−0.990484	+	0.137628i
$21$		0			0
$22$	−64.7526	+	41.2268i	−0.627514	+	0.399526i
$23$			192.381i			1.74410i	0.489418	+	0.872049i	$0.337209\pi$
$23$			192.381i			1.74410i	−0.489418	+	0.872049i	$0.662791\pi$
$24$		0			0
$25$	−51.0719	+	114.091i	−0.408575	+	0.912725i
$26$	40.0596	+	62.9194i	0.302167	+	0.474597i
$27$		0			0
$28$	−48.2389	+	103.299i	−0.325582	+	0.697205i
$29$	237.502			1.52079			0.760397	−	0.649459i	$-0.225005\pi$
$29$	237.502			1.52079			0.760397	+	0.649459i	$0.225005\pi$
$30$		0			0
$31$		−	232.950i		−	1.34965i	−0.737980	−	0.674823i	$-0.764220\pi$
$31$		−	232.950i		−	1.34965i	0.737980	−	0.674823i	$-0.235780\pi$
$32$	−54.6726	+	172.566i	−0.302026	+	0.953300i
$33$		0			0
$34$	−129.860	−	203.964i	−0.655025	−	1.02881i
$35$	86.6431	+	133.713i	0.418439	+	0.645761i
$36$		0			0
$37$	214.767			0.954254			0.477127	−	0.878834i	$-0.341678\pi$
$37$	214.767			0.954254			0.477127	+	0.878834i	$0.341678\pi$
$38$	65.3057	+	102.572i	0.278789	+	0.437878i
$39$		0			0
$40$	163.945	+	192.671i	0.648050	+	0.761598i
$41$			427.145i			1.62705i	0.581533	+	0.813523i	$0.302453\pi$
$41$			427.145i			1.62705i	−0.581533	+	0.813523i	$0.697547\pi$
$42$		0			0
$43$			317.252i			1.12513i	0.826754	+	0.562563i	$0.190185\pi$
$43$			317.252i			1.12513i	−0.826754	+	0.562563i	$0.809815\pi$
$44$	196.725	+	91.8672i	0.674033	+	0.314761i
$45$		0			0
$46$	459.001	−	292.237i	1.47122	−	0.936696i
$47$		−	78.8688i		−	0.244770i	−0.992483	−	0.122385i	$-0.960946\pi$
$47$		−	78.8688i		−	0.244770i	0.992483	−	0.122385i	$-0.0390543\pi$
$48$		0			0
$49$	−139.910			−0.407902
$50$	349.789	−	51.4576i	0.989352	−	0.145544i
$51$		0			0
$52$	89.2663	−	191.156i	0.238058	−	0.509779i
$53$		−	49.0487i		−	0.127120i	−0.997978	−	0.0635600i	$-0.979755\pi$
$53$		−	49.0487i		−	0.127120i	0.997978	−	0.0635600i	$-0.0202454\pi$
$54$		0			0
$55$	254.646	−	165.005i	0.624299	−	0.404532i
$56$	319.738	−	41.8241i	0.762979	−	0.0998033i
$57$		0			0
$58$	−360.778	−	566.654i	−0.816766	−	1.28285i
$59$		−	386.301i		−	0.852408i	−0.904627	−	0.426204i	$-0.859851\pi$
$59$		−	386.301i		−	0.852408i	0.904627	−	0.426204i	$-0.140149\pi$
$60$		0			0
$61$			11.0694i			0.0232343i	0.999933	+	0.0116172i	$0.00369794\pi$
$61$			11.0694i			0.0232343i	−0.999933	+	0.0116172i	$0.996302\pi$
$62$	−555.793	+	353.863i	−1.13848	+	0.724849i
$63$		0			0
$64$	494.774	−	131.693i	0.966355	−	0.257214i
$65$	−160.333	−	247.437i	−0.305952	−	0.472165i
$66$		0			0
$67$		−	275.513i		−	0.502378i	−0.967938	−	0.251189i	$-0.919178\pi$
$67$		−	275.513i		−	0.502378i	0.967938	−	0.251189i	$-0.0808215\pi$
$68$	−289.373	+	619.665i	−0.516053	+	1.10508i
$69$		0			0
$70$	187.410	−	409.838i	0.319996	−	0.699786i
$71$	965.571			1.61397			0.806987	−	0.590569i	$-0.201097\pi$
$71$	965.571			1.61397			0.806987	+	0.590569i	$0.201097\pi$
$72$		0			0
$73$			816.521i			1.30913i	0.756005	+	0.654566i	$0.227149\pi$
$73$			816.521i			1.30913i	−0.756005	+	0.654566i	$0.772851\pi$
$74$	−326.242	−	512.410i	−0.512497	−	0.804952i
$75$		0			0
$76$	145.523	−	311.625i	0.219640	−	0.470339i
$77$		−	386.768i		−	0.572420i
$78$		0			0
$79$			332.287i			0.473231i	0.971603	+	0.236615i	$0.0760382\pi$
$79$			332.287i			0.473231i	−0.971603	+	0.236615i	$0.923962\pi$
$80$	210.651	−	683.832i	0.294393	−	0.955684i
$81$		0			0
$82$	1019.12	−	648.856i	1.37248	−	0.873831i
$83$	459.444			0.607596			0.303798	−	0.952736i	$-0.401745\pi$
$83$	459.444			0.607596			0.303798	+	0.952736i	$0.401745\pi$
$84$		0			0
$85$	519.749	+	802.110i	0.663232	+	1.02354i
$86$	756.929	−	481.922i	0.949090	−	0.604267i
$87$		0			0
$88$	−79.6507	−	608.916i	−0.0964862	−	0.737621i
$89$			1055.50i			1.25710i	0.777767	+	0.628552i	$0.216352\pi$
$89$			1055.50i			1.25710i	−0.777767	+	0.628552i	$0.783648\pi$
$90$		0			0
$91$	−375.818			−0.432928
$92$	−1394.49	−	651.203i	−1.58028	−	0.737963i
$93$		0			0
$94$	−188.172	+	119.806i	−0.206473	+	0.131458i
$95$	−261.377	−	403.374i	−0.282282	−	0.435635i
$96$		0			0
$97$			329.837i			0.345257i	0.984987	+	0.172628i	$0.0552260\pi$
$97$			329.837i			0.345257i	−0.984987	+	0.172628i	$0.944774\pi$
$98$	212.531	+	333.811i	0.219070	+	0.344082i
$99$		0			0
$100$	−654.119	−	756.391i	−0.654119	−	0.756391i
$101$	329.167			0.324291			0.162145	−	0.986767i	$-0.448159\pi$
$101$	329.167			0.324291			0.162145	+	0.986767i	$0.448159\pi$
$102$		0			0
$103$	665.986			0.637103			0.318551	−	0.947906i	$-0.396804\pi$
$103$	665.986			0.637103			0.318551	+	0.947906i	$0.396804\pi$
$104$	−591.677	+	77.3957i	−0.557872	+	0.0729738i
$105$		0			0
$106$	−117.025	+	74.5075i	−0.107231	+	0.0682718i
$107$	1423.11			1.28577			0.642885	−	0.765963i	$-0.277737\pi$
$107$	1423.11			1.28577			0.642885	+	0.765963i	$0.277737\pi$
$108$		0			0
$109$		−	146.977i		−	0.129155i	−0.997913	−	0.0645773i	$-0.979430\pi$
$109$		−	146.977i		−	0.129155i	0.997913	−	0.0645773i	$-0.0205699\pi$
$110$	−780.504	−	356.907i	−0.676528	−	0.309361i
$111$		0			0
$112$	−585.487	−	699.328i	−0.493958	−	0.590003i
$113$	921.869			0.767452			0.383726	−	0.923447i	$-0.374641\pi$
$113$	921.869			0.767452			0.383726	+	0.923447i	$0.374641\pi$
$114$		0			0
$115$	−1805.06	+	1169.64i	−1.46368	+	0.948431i
$116$	−803.935	+	1721.55i	−0.643478	+	1.37795i
$117$		0			0
$118$	−921.672	+	586.811i	−0.719040	+	0.457799i
$119$	1218.28			0.938485
$120$		0			0
$121$	594.431			0.446605
$122$	26.4104	−	16.8150i	0.0195991	−	0.0124784i
$123$		0			0
$124$	1688.56	+	788.526i	1.22288	+	0.571062i
$125$	−1380.99	+	214.455i	−0.988156	+	0.153451i
$126$		0			0
$127$	1032.44			0.721372			0.360686	−	0.932687i	$-0.382543\pi$
$127$	1032.44			0.721372			0.360686	+	0.932687i	$0.382543\pi$
$128$	−1065.79	−	980.427i	−0.735966	−	0.677018i
$129$		0			0
$130$	−346.802	+	758.407i	−0.233974	+	0.511667i
$131$			975.161i			0.650383i	0.945648	+	0.325192i	$0.105429\pi$
$131$			975.161i			0.650383i	−0.945648	+	0.325192i	$0.894571\pi$
$132$		0			0
$133$	−612.664			−0.399434
$134$	−657.345	+	418.519i	−0.423776	+	0.269810i
$135$		0			0
$136$	1918.03	−	250.892i	1.20933	−	0.158190i
$137$	−1625.08			−1.01343			−0.506716	−	0.862113i	$-0.669141\pi$
$137$	−1625.08			−1.01343			−0.506716	+	0.862113i	$0.669141\pi$
$138$		0			0
$139$	−1926.97			−1.17585			−0.587927	−	0.808914i	$-0.700056\pi$
$139$	−1926.97			−1.17585			−0.587927	+	0.808914i	$0.700056\pi$
$140$	−1262.51	+	175.426i	−0.762157	+	0.105902i
$141$		0			0
$142$	−1466.75	−	2303.75i	−0.866811	−	1.36145i
$143$			715.716i			0.418540i
$144$		0			0
$145$	1443.97	+	2228.42i	0.826999	+	1.27628i
$146$	1948.13	−	1240.34i	1.10431	−	0.703090i
$147$		0			0
$148$	−726.976	+	1556.75i	−0.403764	+	0.864624i
$149$	−2988.95			−1.64339			−0.821693	−	0.569931i	$-0.806970\pi$
$149$	−2988.95			−1.64339			−0.821693	+	0.569931i	$0.806970\pi$
$150$		0			0
$151$			430.216i			0.231858i	0.993258	+	0.115929i	$0.0369845\pi$
$151$			430.216i			0.231858i	−0.993258	+	0.115929i	$0.963016\pi$
$152$	−964.560	+	126.171i	−0.514711	+	0.0673280i
$153$		0			0
$154$	−922.787	+	587.521i	−0.482859	+	0.307427i
$155$	2185.71	−	1416.29i	1.13265	−	0.733930i
$156$		0			0
$157$	−916.124			−0.465698			−0.232849	−	0.972513i	$-0.574805\pi$
$157$	−916.124			−0.465698			−0.232849	+	0.972513i	$0.574805\pi$
$158$	792.802	−	504.762i	0.399189	−	0.254156i
$159$		0			0
$160$	−1951.54	+	536.187i	−0.964267	+	0.264933i
$161$			2741.62i			1.34205i
$162$		0			0
$163$			791.874i			0.380517i	0.981734	+	0.190259i	$0.0609327\pi$
$163$			791.874i			0.380517i	−0.981734	+	0.190259i	$0.939067\pi$
$164$	−3096.20	−	1445.87i	−1.47422	−	0.688436i
$165$		0			0
$166$	−697.919	−	1096.18i	−0.326319	−	0.512532i
$167$		−	661.753i		−	0.306634i	−0.988177	−	0.153317i	$-0.951004\pi$
$167$		−	661.753i		−	0.306634i	0.988177	−	0.153317i	$-0.0489956\pi$
$168$		0			0
$169$	−1501.55			−0.683453
$170$	1124.22	−	2458.51i	0.507199	−	1.10917i
$171$		0			0
$172$	−2299.63	−	1073.89i	−1.01945	−	0.476064i
$173$		−	3826.45i		−	1.68161i	−0.541335	−	0.840807i	$-0.682081\pi$
$173$		−	3826.45i		−	1.68161i	0.541335	−	0.840807i	$-0.317919\pi$
$174$		0			0
$175$	−727.823	+	1625.90i	−0.314390	+	0.702323i
$176$	−1331.81	+	1115.01i	−0.570394	+	0.477541i
$177$		0			0
$178$	2518.30	−	1603.35i	1.06042	−	0.675148i
$179$		−	4057.24i		−	1.69415i	−0.531476	−	0.847074i	$-0.678362\pi$
$179$		−	4057.24i		−	1.69415i	0.531476	−	0.847074i	$-0.321638\pi$
$180$		0			0
$181$			1166.97i			0.479229i	0.970868	+	0.239614i	$0.0770210\pi$
$181$			1166.97i			0.479229i	−0.970868	+	0.239614i	$0.922979\pi$
$182$	570.887	+	896.662i	0.232511	+	0.365192i
$183$		0			0
$184$	564.606	+	4316.32i	0.226214	+	1.72937i
$185$	1305.74	+	2015.10i	0.518918	+	0.800827i
$186$		0			0
$187$		−	2320.12i		−	0.907294i
$188$	571.687	+	266.968i	0.221780	+	0.103567i
$189$		0			0
$190$	−565.362	+	1236.36i	−0.215872	+	0.472081i
$191$	−632.306			−0.239540			−0.119770	−	0.992802i	$-0.538216\pi$
$191$	−632.306			−0.239540			−0.119770	+	0.992802i	$0.538216\pi$
$192$		0			0
$193$			2485.26i			0.926905i	0.886122	+	0.463453i	$0.153390\pi$
$193$			2485.26i			0.926905i	−0.886122	+	0.463453i	$0.846610\pi$
$194$	786.956	−	501.040i	0.291238	−	0.185426i
$195$		0			0
$196$	473.591	−	1014.15i	0.172591	−	0.369589i
$197$		−	1040.02i		−	0.376132i	−0.982156	−	0.188066i	$-0.939778\pi$
$197$		−	1040.02i		−	0.376132i	0.982156	−	0.188066i	$-0.0602219\pi$
$198$		0			0
$199$		−	2340.35i		−	0.833682i	−0.908979	−	0.416841i	$-0.863137\pi$
$199$		−	2340.35i		−	0.833682i	0.908979	−	0.416841i	$-0.136863\pi$
$200$	−811.026	+	2709.66i	−0.286741	+	0.958008i
$201$		0			0
$202$	−500.022	−	785.357i	−0.174165	−	0.273552i
$203$	3384.63			1.17022
$204$		0			0
$205$	−4007.79	+	2596.96i	−1.36545	+	0.884778i
$206$	−1011.67	−	1588.97i	−0.342166	−	0.537422i
$207$		0			0
$208$	1083.45	+	1294.11i	0.361171	+	0.431396i
$209$			1166.77i			0.386158i
$210$		0			0
$211$	−2314.80			−0.755247			−0.377623	−	0.925959i	$-0.623259\pi$
$211$	−2314.80			−0.755247			−0.377623	+	0.925959i	$0.623259\pi$
$212$	355.534	+	166.028i	0.115180	+	0.0537870i
$213$		0			0
$214$	−2161.78	−	3395.39i	−0.690543	−	1.08460i
$215$	−2976.69	+	1928.83i	−0.944227	+	0.611838i
$216$		0			0
$217$		−	3319.76i		−	1.03852i
$218$	−350.672	+	223.266i	−0.108947	+	0.0693646i
$219$		0			0
$220$	334.085	+	2404.36i	0.102382	+	0.736826i
$221$	−2254.43			−0.686198
$222$		0			0
$223$	−965.597			−0.289960			−0.144980	−	0.989435i	$-0.546312\pi$
$223$	−965.597			−0.289960			−0.144980	+	0.989435i	$0.546312\pi$
$224$	−779.137	+	2459.23i	−0.232403	+	0.733544i
$225$		0			0
$226$	−1400.37	−	2199.48i	−0.412172	−	0.647377i
$227$	−5640.42			−1.64920			−0.824599	−	0.565718i	$-0.808599\pi$
$227$	−5640.42			−1.64920			−0.824599	+	0.565718i	$0.808599\pi$
$228$		0			0
$229$			1173.09i			0.338514i	0.985572	+	0.169257i	$0.0541368\pi$
$229$			1173.09i			0.338514i	−0.985572	+	0.169257i	$0.945863\pi$
$230$	5532.62	+	2529.94i	1.58613	+	0.725302i
$231$		0			0
$232$	5328.66	−	697.028i	1.50795	−	0.197250i
$233$	−3425.36			−0.963101			−0.481550	−	0.876418i	$-0.659926\pi$
$233$	−3425.36			−0.963101			−0.481550	+	0.876418i	$0.659926\pi$
$234$		0			0
$235$	740.006	−	479.507i	0.205416	−	0.133105i
$236$	2800.13	+	1307.61i	0.772344	+	0.360671i
$237$		0			0
$238$	−1850.63	−	2906.69i	−0.504028	−	0.791650i
$239$	6506.95			1.76109			0.880543	−	0.473966i	$-0.157178\pi$
$239$	6506.95			1.76109			0.880543	+	0.473966i	$0.157178\pi$
$240$		0			0
$241$	7055.61			1.88586			0.942929	−	0.332995i	$-0.108059\pi$
$241$	7055.61			1.88586			0.942929	+	0.332995i	$0.108059\pi$
$242$	−902.972	−	1418.25i	−0.239856	−	0.376729i
$243$		0			0
$244$	−80.2376	−	37.4695i	−0.0210520	−	0.00983090i
$245$	−850.628	−	1312.74i	−0.221815	−	0.342319i
$246$		0			0
$247$	1133.74			0.292056
$248$	−683.668	−	5226.53i	−0.175052	−	1.33824i
$249$		0			0
$250$	2609.46	+	2969.13i	0.660147	+	0.751136i
$251$		−	5819.61i		−	1.46347i	−0.681590	−	0.731735i	$-0.738711\pi$
$251$		−	5819.61i		−	1.46347i	0.681590	−	0.731735i	$-0.261289\pi$
$252$		0			0
$253$	5221.19			1.29744
$254$	−1568.33	−	2463.29i	−0.387424	−	0.608506i
$255$		0			0
$256$	−720.199	+	4032.19i	−0.175830	+	0.984421i
$257$	−7218.05			−1.75194			−0.875971	−	0.482363i	$-0.839779\pi$
$257$	−7218.05			−1.75194			−0.875971	+	0.482363i	$0.839779\pi$
$258$		0			0
$259$	3060.63			0.734279
$260$	2336.29	−	324.627i	0.557271	−	0.0774327i
$261$		0			0
$262$	2326.63	−	1481.32i	0.548625	−	0.349299i
$263$			487.506i			0.114300i	0.998366	+	0.0571500i	$0.0182013\pi$
$263$			487.506i			0.114300i	−0.998366	+	0.0571500i	$0.981799\pi$
$264$		0			0
$265$	460.211	−	298.207i	0.106681	−	0.0691271i
$266$	930.668	+	1461.75i	0.214522	+	0.336938i
$267$		0			0
$268$	1997.08	+	932.602i	0.455191	+	0.212566i
$269$	6032.92			1.36741			0.683706	−	0.729758i	$-0.260367\pi$
$269$	6032.92			1.36741			0.683706	+	0.729758i	$0.260367\pi$
$270$		0			0
$271$		−	7588.58i		−	1.70101i	−0.525968	−	0.850504i	$-0.676297\pi$
$271$		−	7588.58i		−	1.70101i	0.525968	−	0.850504i	$-0.323703\pi$
$272$	−3512.18	−	4195.09i	−0.782932	−	0.935164i
$273$		0			0
$274$	2468.59	+	3877.28i	0.544280	+	0.854871i
$275$	3096.40	+	1386.08i	0.678981	+	0.303941i
$276$		0			0
$277$	−663.460			−0.143911			−0.0719557	−	0.997408i	$-0.522924\pi$
$277$	−663.460			−0.143911			−0.0719557	+	0.997408i	$0.522924\pi$
$278$	2927.17	+	4597.55i	0.631511	+	0.991880i
$279$		0			0
$280$	2336.37	+	2745.74i	0.498661	+	0.586034i
$281$			2615.72i			0.555306i	0.960681	+	0.277653i	$0.0895565\pi$
$281$			2615.72i			0.555306i	−0.960681	+	0.277653i	$0.910443\pi$
$282$		0			0
$283$		−	8796.74i		−	1.84775i	−0.382699	−	0.923873i	$-0.625006\pi$
$283$		−	8796.74i		−	1.84775i	0.382699	−	0.923873i	$-0.374994\pi$
$284$	−3268.42	+	6999.02i	−0.682905	+	1.46238i
$285$		0			0
$286$	1707.62	−	1087.21i	0.353055	−	0.224783i
$287$			6087.23i			1.25198i
$288$		0			0
$289$	2395.15			0.487513
$290$	3123.31	−	6830.23i	0.632438	−	1.38305i
$291$		0			0
$292$	−5918.63	−	2763.89i	−1.18617	−	0.553920i
$293$			5597.48i			1.11607i	0.829818	+	0.558034i	$0.188444\pi$
$293$			5597.48i			1.11607i	−0.829818	+	0.558034i	$0.811556\pi$
$294$		0			0
$295$	3624.56	−	2348.63i	0.715356	−	0.463535i
$296$	4818.56	−	630.303i	0.946193	−	0.123769i
$297$		0			0
$298$	4540.37	+	7131.31i	0.882606	+	1.38626i
$299$		−	5073.37i		−	0.981273i
$300$		0			0
$301$			4521.14i			0.865762i
$302$	1026.45	−	653.521i	0.195581	−	0.124523i
$303$		0			0
$304$	1766.25	+	2109.67i	0.333228	+	0.398020i
$305$	−103.861	+	67.2999i	−0.0194987	+	0.0126347i
$306$		0			0
$307$		−	10085.9i		−	1.87503i	−0.347945	−	0.937515i	$-0.613121\pi$
$307$		−	10085.9i		−	1.87503i	0.347945	−	0.937515i	$-0.386879\pi$
$308$	2803.52	+	1309.19i	0.518654	+	0.242202i
$309$		0			0
$310$	−6699.32	−	3063.45i	−1.22741	−	0.561265i
$311$	2356.75			0.429707			0.214853	−	0.976646i	$-0.431073\pi$
$311$	2356.75			0.429707			0.214853	+	0.976646i	$0.431073\pi$
$312$		0			0
$313$			2299.30i			0.415221i	0.978212	+	0.207610i	$0.0665686\pi$
$313$			2299.30i			0.415221i	−0.978212	+	0.207610i	$0.933431\pi$
$314$	1391.64	+	2185.77i	0.250111	+	0.392835i
$315$		0			0
$316$	−2408.61	−	1124.78i	−0.428782	−	0.200234i
$317$			2952.43i			0.523107i	0.965189	+	0.261554i	$0.0842348\pi$
$317$			2952.43i			0.523107i	−0.965189	+	0.261554i	$0.915765\pi$
$318$		0			0
$319$		−	6445.75i		−	1.13133i
$320$	4243.77	+	3841.66i	0.741357	+	0.671111i
$321$		0			0
$322$	6541.20	−	4164.66i	1.13207	−	0.720768i
$323$	−3675.21			−0.633109
$324$		0			0
$325$	1346.84	−	3008.73i	0.229874	−	0.513522i
$326$	1889.33	−	1202.90i	0.320982	−	0.204363i
$327$		0			0
$328$	1253.60	+	9583.55i	0.211032	+	1.61330i
$329$		−	1123.96i		−	0.188346i
$330$		0			0
$331$	−712.205			−0.118267			−0.0591334	−	0.998250i	$-0.518834\pi$
$331$	−712.205			−0.118267			−0.0591334	+	0.998250i	$0.518834\pi$
$332$	−1555.20	+	3330.32i	−0.257086	+	0.550527i
$333$		0			0
$334$	−1578.87	+	1005.24i	−0.258658	+	0.164683i
$335$	2585.07	−	1675.07i	0.421605	−	0.273190i
$336$		0			0
$337$		−	6426.35i		−	1.03877i	−0.854540	−	0.519385i	$-0.826161\pi$
$337$		−	6426.35i		−	1.03877i	0.854540	−	0.519385i	$-0.173839\pi$
$338$	2280.93	+	3582.53i	0.367060	+	0.576520i
$339$		0			0
$340$	−7573.49	+	1052.34i	−1.20803	+	0.167856i
$341$	−6322.21			−1.00401
$342$		0			0
$343$	−6881.93			−1.08335
$344$	931.080	+	7117.95i	0.145932	+	1.11562i
$345$		0			0
$346$	−9129.49	+	5812.57i	−1.41851	+	0.903138i
$347$	3605.09			0.557727			0.278863	−	0.960331i	$-0.410042\pi$
$347$	3605.09			0.557727			0.278863	+	0.960331i	$0.410042\pi$
$348$		0			0
$349$		−	12427.6i		−	1.90611i	−0.302794	−	0.953056i	$-0.597919\pi$
$349$		−	12427.6i		−	1.90611i	0.302794	−	0.953056i	$-0.402081\pi$
$350$	4984.82	−	733.320i	0.761286	−	0.111993i
$351$		0			0
$352$	4683.40	+	1483.80i	0.709164	+	0.224679i
$353$	2166.24			0.326622			0.163311	−	0.986575i	$-0.447783\pi$
$353$	2166.24			0.326622			0.163311	+	0.986575i	$0.447783\pi$
$354$		0			0
$355$	5870.48	+	9059.70i	0.877670	+	1.35448i
$356$	−7650.85	−	3572.81i	−1.13903	−	0.531906i
$357$		0			0
$358$	−9680.14	+	6163.16i	−1.42908	+	0.909869i
$359$	5106.99			0.750799			0.375399	−	0.926863i	$-0.377506\pi$
$359$	5106.99			0.750799			0.375399	+	0.926863i	$0.377506\pi$
$360$		0			0
$361$	−5010.77			−0.730539
$362$	2784.27	−	1772.69i	0.404249	−	0.257377i
$363$		0			0
$364$	1272.13	−	2724.15i	0.183181	−	0.392265i
$365$	−7661.21	+	4964.29i	−1.09865	+	0.711899i
$366$		0			0
$367$	715.146			0.101717			0.0508587	−	0.998706i	$-0.483804\pi$
$367$	715.146			0.101717			0.0508587	+	0.998706i	$0.483804\pi$
$368$	9440.61	−	7903.80i	1.33730	−	1.11960i
$369$		0			0
$370$	2824.32	−	6176.39i	0.396837	−	0.867826i
$371$		−	698.991i		−	0.0978161i
$372$		0			0
$373$	−8490.68			−1.17863			−0.589317	−	0.807902i	$-0.700603\pi$
$373$	−8490.68			−1.17863			−0.589317	+	0.807902i	$0.700603\pi$
$374$	−5535.55	+	3524.38i	−0.765339	+	0.487277i
$375$		0			0
$376$	−231.466	−	1769.52i	−0.0317473	−	0.242703i
$377$	−6263.27			−0.855636
$378$		0			0
$379$	−9763.26			−1.32323			−0.661616	−	0.749843i	$-0.730129\pi$
$379$	−9763.26			−1.32323			−0.661616	+	0.749843i	$0.730129\pi$
$380$	3808.65	−	529.211i	0.514156	−	0.0714420i
$381$		0			0
$382$	960.506	+	1508.61i	0.128649	+	0.202061i
$383$			9959.88i			1.32879i	0.747382	+	0.664394i	$0.231310\pi$
$383$			9959.88i			1.32879i	−0.747382	+	0.664394i	$0.768690\pi$
$384$		0			0
$385$	3628.95	−	2351.48i	0.480385	−	0.311279i
$386$	5929.55	−	3775.23i	0.781882	−	0.497809i
$387$		0			0
$388$	−2390.85	−	1116.49i	−0.312828	−	0.146085i
$389$	11833.4			1.54236			0.771181	−	0.636616i	$-0.219666\pi$
$389$	11833.4			1.54236			0.771181	+	0.636616i	$0.219666\pi$
$390$		0			0
$391$			16446.2i			2.12717i
$392$	−3139.07	+	410.613i	−0.404456	+	0.0529058i
$393$		0			0
$394$	−2481.36	+	1579.84i	−0.317283	+	0.202008i
$395$	−3117.77	+	2020.24i	−0.397144	+	0.257340i
$396$		0			0
$397$	−3397.10			−0.429460			−0.214730	−	0.976673i	$-0.568887\pi$
$397$	−3397.10			−0.429460			−0.214730	+	0.976673i	$0.568887\pi$
$398$	−5583.81	+	3555.11i	−0.703244	+	0.447742i
$399$		0			0
$400$	7696.94	−	2181.09i	0.962117	−	0.272636i
$401$		−	7148.32i		−	0.890200i	−0.895481	−	0.445100i	$-0.853168\pi$
$401$		−	7148.32i		−	0.890200i	0.895481	−	0.445100i	$-0.146832\pi$
$402$		0			0
$403$			6143.22i			0.759344i
$404$	−1114.22	+	2386.00i	−0.137214	+	0.293831i
$405$		0			0
$406$	−5141.43	−	8075.36i	−0.628485	−	0.987127i
$407$		−	5828.72i		−	0.709874i
$408$		0			0
$409$	11240.5			1.35894			0.679469	−	0.733705i	$-0.262210\pi$
$409$	11240.5			1.35894			0.679469	+	0.733705i	$0.262210\pi$
$410$	12284.1	+	5617.25i	1.47968	+	0.676625i
$411$		0			0
$412$	−2254.34	+	4827.46i	−0.269571	+	0.577262i
$413$		−	5505.15i		−	0.655910i
$414$		0			0
$415$	2793.33	+	4310.84i	0.330408	+	0.509906i
$416$	1441.80	−	4550.81i	0.169927	−	0.536350i
$417$		0			0
$418$	2783.78	−	1772.38i	0.325740	−	0.207392i
$419$			1378.51i			0.160727i	0.996766	+	0.0803634i	$0.0256081\pi$
$419$			1378.51i			0.160727i	−0.996766	+	0.0803634i	$0.974392\pi$
$420$		0			0
$421$		−	2220.90i		−	0.257102i	−0.991703	−	0.128551i	$-0.958967\pi$
$421$		−	2220.90i		−	0.257102i	0.991703	−	0.128551i	$-0.0410327\pi$
$422$	3516.29	+	5522.85i	0.405617	+	0.637081i
$423$		0			0
$424$	−143.950	−	1100.47i	−0.0164878	−	0.126046i
$425$	−4366.02	+	9753.35i	−0.498313	+	1.11319i
$426$		0			0
$427$			157.750i			0.0178783i
$428$	−4817.18	+	10315.5i	−0.544035	+	1.16500i
$429$		0			0
$430$	9123.73	+	4172.08i	1.02322	+	0.467896i
$431$	−14662.1			−1.63863			−0.819315	−	0.573343i	$-0.805646\pi$
$431$	−14662.1			−1.63863			−0.819315	+	0.573343i	$0.805646\pi$
$432$		0			0
$433$			2962.95i			0.328846i	0.986390	+	0.164423i	$0.0525762\pi$
$433$			2962.95i			0.328846i	−0.986390	+	0.164423i	$0.947424\pi$
$434$	−7920.58	+	5042.88i	−0.876037	+	0.557756i
$435$		0			0
$436$	1065.38	+	497.512i	0.117024	+	0.0546479i
$437$		−	8270.68i		−	0.905355i
$438$		0			0
$439$		−	8021.35i		−	0.872069i	−0.899930	−	0.436034i	$-0.856383\pi$
$439$		−	8021.35i		−	0.872069i	0.899930	−	0.436034i	$-0.143617\pi$
$440$	5229.05	−	4449.44i	0.566557	−	0.482088i
$441$		0			0
$442$	3424.60	+	5378.84i	0.368533	+	0.578835i
$443$	170.590			0.0182957			0.00914784	−	0.999958i	$-0.497088\pi$
$443$	170.590			0.0182957			0.00914784	+	0.999958i	$0.497088\pi$
$444$		0			0
$445$	−9903.45	+	6417.21i	−1.05499	+	0.683607i
$446$	1466.79	+	2303.81i	0.155728	+	0.244593i
$447$		0			0
$448$	7051.00	−	1876.76i	0.743590	−	0.197920i
$449$		−	8908.83i		−	0.936378i	−0.883628	−	0.468189i	$-0.844907\pi$
$449$		−	8908.83i		−	0.936378i	0.883628	−	0.468189i	$-0.155093\pi$
$450$		0			0
$451$	11592.6			1.21037
$452$	−3120.49	+	6682.25i	−0.324725	+	0.695368i
$453$		0			0
$454$	8568.09	+	13457.4i	0.885728	+	1.39116i
$455$	−2284.90	−	3526.21i	−0.235424	−	0.363321i
$456$		0			0
$457$		−	9835.04i		−	1.00670i	−0.864082	−	0.503352i	$-0.832100\pi$
$457$		−	9835.04i		−	1.00670i	0.864082	−	0.503352i	$-0.167900\pi$
$458$	2798.86	−	1781.98i	0.285550	−	0.181804i
$459$		0			0
$460$	−2368.17	−	17043.4i	−0.240036	−	1.72750i
$461$	−10228.8			−1.03341			−0.516705	−	0.856163i	$-0.672842\pi$
$461$	−10228.8			−1.03341			−0.516705	+	0.856163i	$0.672842\pi$
$462$		0			0
$463$	−11692.9			−1.17369			−0.586844	−	0.809700i	$-0.699630\pi$
$463$	−11692.9			−1.17369			−0.586844	+	0.809700i	$0.699630\pi$
$464$	−9757.55	−	11654.8i	−0.976256	−	1.16608i
$465$		0			0
$466$	5203.29	+	8172.53i	0.517249	+	0.812414i
$467$	−10856.6			−1.07577			−0.537885	−	0.843018i	$-0.680777\pi$
$467$	−10856.6			−1.07577			−0.537885	+	0.843018i	$0.680777\pi$
$468$		0			0
$469$		−	3926.33i		−	0.386569i
$470$	−2268.16	−	1037.18i	−0.222601	−	0.101790i
$471$		0			0
$472$	−1133.73	−	8667.15i	−0.110559	−	0.845208i
$473$	8610.15			0.836988
$474$		0			0
$475$	2195.63	−	4904.88i	0.212090	−	0.473792i
$476$	−4123.84	+	8830.82i	−0.397092	+	0.850336i
$477$		0			0
$478$	−9884.39	−	15524.9i	−0.945819	−	1.48555i
$479$	1508.75			0.143917			0.0719586	−	0.997408i	$-0.477075\pi$
$479$	1508.75			0.143917			0.0719586	+	0.997408i	$0.477075\pi$
$480$		0			0
$481$	−5663.70			−0.536887
$482$	−10717.8	−	16833.9i	−1.01283	−	1.59080i
$483$		0			0
$484$	−2012.13	+	4308.79i	−0.188968	+	0.404657i
$485$	−3094.78	+	2005.35i	−0.289746	+	0.187749i
$486$		0			0
$487$	9639.21			0.896908			0.448454	−	0.893806i	$-0.351975\pi$
$487$	9639.21			0.896908			0.448454	+	0.893806i	$0.351975\pi$
$488$	32.4868	+	248.356i	0.00301354	+	0.0230380i
$489$		0			0
$490$	−1839.91	+	4023.63i	−0.169630	+	0.370957i
$491$			8332.44i			0.765861i	0.923777	+	0.382930i	$0.125085\pi$
$491$			8332.44i			0.765861i	−0.923777	+	0.382930i	$0.874915\pi$
$492$		0			0
$493$	20303.5			1.85481
$494$	−1722.20	−	2704.97i	−0.156854	−	0.246361i
$495$		0			0
$496$	−11431.4	+	9570.52i	−1.03485	+	0.866389i
$497$	13760.3			1.24192
$498$		0			0
$499$	−10857.6			−0.974053			−0.487027	−	0.873387i	$-0.661919\pi$
$499$	−10857.6			−0.974053			−0.487027	+	0.873387i	$0.661919\pi$
$500$	3120.11	−	10736.2i	0.279071	−	0.960271i
$501$		0			0
$502$	−13885.0	+	8840.30i	−1.23450	+	0.785980i
$503$		−	2858.57i		−	0.253394i	−0.991941	−	0.126697i	$-0.959562\pi$
$503$		−	2858.57i		−	0.253394i	0.991941	−	0.126697i	$-0.0404376\pi$
$504$		0			0
$505$	2001.27	+	3088.49i	0.176347	+	0.272151i
$506$	−7931.26	−	12457.2i	−0.696813	−	1.09445i
$507$		0			0
$508$	−3494.77	+	7483.73i	−0.305227	+	0.653616i
$509$	9992.20			0.870130			0.435065	−	0.900399i	$-0.356725\pi$
$509$	9992.20			0.870130			0.435065	+	0.900399i	$0.356725\pi$
$510$		0			0
$511$			11636.2i			1.00735i
$512$	10714.4	−	4406.78i	0.924831	−	0.380379i
$513$		0			0
$514$	10964.6	+	17221.5i	0.940909	+	1.47783i
$515$	4049.07	+	6248.78i	0.346453	+	0.534668i
$516$		0			0
$517$	−2140.48			−0.182086
$518$	−4649.25	−	7302.33i	−0.394356	−	0.619394i
$519$		0			0
$520$	−4323.47	−	5081.01i	−0.364609	−	0.428494i
$521$		−	5734.27i		−	0.482194i	−0.970501	−	0.241097i	$-0.922493\pi$
$521$		−	5734.27i		−	0.482194i	0.970501	−	0.241097i	$-0.0775072\pi$
$522$		0			0
$523$		−	5345.64i		−	0.446938i	−0.974711	−	0.223469i	$-0.928262\pi$
$523$		−	5345.64i		−	0.446938i	0.974711	−	0.223469i	$-0.0717382\pi$
$524$	−7068.54	−	3300.88i	−0.589295	−	0.275190i
$525$		0			0
$526$	1163.14	−	740.547i	0.0964167	−	0.0613867i
$527$		−	19914.3i		−	1.64608i
$528$		0			0
$529$	−24843.6			−2.04188
$530$	−1410.57	−	645.023i	−0.115606	−	0.0528642i
$531$		0			0
$532$	2073.84	−	4440.95i	0.169008	−	0.361916i
$533$		−	11264.4i		−	0.915416i
$534$		0			0
$535$	8652.24	+	13352.7i	0.699195	+	1.07904i
$536$	−808.584	−	6181.49i	−0.0651596	−	0.498134i
$537$		0			0
$538$	−9164.33	−	14393.9i	−0.734391	−	1.15347i
$539$			3797.14i			0.303440i
$540$		0			0
$541$			2869.81i			0.228064i	0.993477	+	0.114032i	$0.0363767\pi$
$541$			2869.81i			0.228064i	−0.993477	+	0.114032i	$0.963623\pi$
$542$	−18105.5	+	11527.4i	−1.43487	+	0.913554i
$543$		0			0
$544$	−4673.84	+	14752.2i	−0.368362	+	1.16268i
$545$	1379.05	−	893.593i	0.108389	−	0.0702336i
$546$		0			0
$547$			13243.3i			1.03518i	0.855628	+	0.517591i	$0.173171\pi$
$547$			13243.3i			1.03518i	−0.855628	+	0.517591i	$0.826829\pi$
$548$	5500.85	−	11779.6i	0.428804	−	0.918245i
$549$		0			0
$550$	−1396.55	−	9493.19i	−0.108271	−	0.735984i
$551$	−10210.5			−0.789438
$552$		0			0
$553$			4735.41i			0.364141i
$554$	1007.83	+	1582.94i	0.0772899	+	0.121395i
$555$		0			0
$556$	6522.73	−	13967.8i	0.497527	−	1.06541i
$557$			22760.2i			1.73138i	0.500580	+	0.865690i	$0.333120\pi$
$557$			22760.2i			1.73138i	−0.500580	+	0.865690i	$0.666880\pi$
$558$		0			0
$559$		−	8366.39i		−	0.633024i
$560$	3001.97	−	9745.26i	0.226529	−	0.735379i
$561$		0			0
$562$	6240.83	−	3973.42i	0.468423	−	0.298236i
$563$	−13426.4			−1.00507			−0.502535	−	0.864557i	$-0.667599\pi$
$563$	−13426.4			−1.00507			−0.502535	+	0.864557i	$0.667599\pi$
$564$		0			0
$565$	5604.78	+	8649.66i	0.417336	+	0.644060i
$566$	−20988.1	+	13362.7i	−1.55865	+	0.992361i
$567$		0			0
$568$	21663.8	−	2833.79i	1.60034	−	0.209336i
$569$		−	22984.8i		−	1.69345i	−0.532032	−	0.846724i	$-0.678571\pi$
$569$		−	22984.8i		−	1.69345i	0.532032	−	0.846724i	$-0.321429\pi$
$570$		0			0
$571$	−259.713			−0.0190344			−0.00951722	−	0.999955i	$-0.503029\pi$
$571$	−259.713			−0.0190344			−0.00951722	+	0.999955i	$0.503029\pi$
$572$	−5187.93	−	2422.67i	−0.379228	−	0.177093i
$573$		0			0
$574$	14523.5	−	9246.81i	1.05609	−	0.672395i
$575$	−21948.9	−	9825.27i	−1.59188	−	0.712595i
$576$		0			0
$577$			6679.10i			0.481897i	0.970538	+	0.240949i	$0.0774585\pi$
$577$			6679.10i			0.481897i	−0.970538	+	0.240949i	$0.922541\pi$
$578$	−3638.36	−	5714.57i	−0.261827	−	0.411237i
$579$		0			0
$580$	−21040.7	+	2923.60i	−1.50632	+	0.209303i
$581$	6547.51			0.467533
$582$		0			0
$583$	−1331.17			−0.0945652
$584$	2396.35	+	18319.7i	0.169797	+	1.29807i
$585$		0			0
$586$	13355.0	−	8502.86i	0.941449	−	0.599402i
$587$	23879.5			1.67907			0.839535	−	0.543306i	$-0.182828\pi$
$587$	23879.5			1.67907			0.839535	+	0.543306i	$0.182828\pi$
$588$		0			0
$589$			10014.8i			0.700596i
$590$	−11109.5	−	5080.12i	−0.775204	−	0.354483i
$591$		0			0
$592$	−8823.48	−	10539.1i	−0.612572	−	0.731680i
$593$	5523.78			0.382520			0.191260	−	0.981539i	$-0.438743\pi$
$593$	5523.78			0.382520			0.191260	+	0.981539i	$0.438743\pi$
$594$		0			0
$595$	7406.92	+	11430.8i	0.510343	+	0.787594i
$596$	10117.5	−	21665.7i	0.695350	−	1.48903i
$597$		0			0
$598$	−12104.5	+	7706.72i	−0.827743	+	0.527008i
$599$	15958.3			1.08854			0.544271	−	0.838909i	$-0.316806\pi$
$599$	15958.3			1.08854			0.544271	+	0.838909i	$0.316806\pi$
$600$		0			0
$601$	−15279.9			−1.03707			−0.518535	−	0.855056i	$-0.673522\pi$
$601$	−15279.9			−1.03707			−0.518535	+	0.855056i	$0.673522\pi$
$602$	10787.0	−	6867.85i	0.730305	−	0.464971i
$603$		0			0
$604$	−3118.46	−	1456.27i	−0.210080	−	0.0981037i
$605$	3614.03	+	5577.40i	0.242861	+	0.374799i
$606$		0			0
$607$	−20079.6			−1.34268			−0.671339	−	0.741151i	$-0.734280\pi$
$607$	−20079.6			−1.34268			−0.671339	+	0.741151i	$0.734280\pi$
$608$	2350.43	−	7418.78i	0.156781	−	0.494854i
$609$		0			0
$610$	318.341	+	145.570i	0.0211299	+	0.00966224i
$611$			2079.88i			0.137714i
$612$		0			0
$613$	22571.0			1.48717			0.743584	−	0.668643i	$-0.233125\pi$
$613$	22571.0			1.48717			0.743584	+	0.668643i	$0.233125\pi$
$614$	−24063.9	+	15321.0i	−1.58166	+	1.00701i
$615$		0			0
$616$	−1135.10	−	8677.64i	−0.0742442	−	0.567584i
$617$	15222.8			0.993270			0.496635	−	0.867959i	$-0.334569\pi$
$617$	15222.8			0.993270			0.496635	+	0.867959i	$0.334569\pi$
$618$		0			0
$619$	24010.5			1.55907			0.779535	−	0.626358i	$-0.215455\pi$
$619$	24010.5			1.55907			0.779535	+	0.626358i	$0.215455\pi$
$620$	2867.56	+	20637.4i	0.185748	+	1.33680i
$621$		0			0
$622$	−3580.02	−	5622.94i	−0.230781	−	0.362475i
$623$			15041.8i			0.967316i
$624$		0			0
$625$	−10408.3	−	11653.6i	−0.666133	−	0.745833i
$626$	5485.88	−	3492.76i	0.350255	−	0.223001i
$627$		0			0
$628$	3101.04	−	6640.60i	0.197046	−	0.421957i
$629$	18359.9			1.16384
$630$		0			0
$631$		−	10267.3i		−	0.647758i	−0.946098	−	0.323879i	$-0.895013\pi$
$631$		−	10267.3i		−	0.647758i	0.946098	−	0.323879i	$-0.104987\pi$
$632$	975.206	+	7455.29i	0.0613792	+	0.469234i
$633$		0			0
$634$	7044.18	−	4484.89i	0.441262	−	0.280943i
$635$	6277.04	+	9687.12i	0.392278	+	0.605388i
$636$		0			0
$637$	3689.64			0.229496
$638$	−15378.9	+	9791.44i	−0.954319	+	0.607597i
$639$		0			0
$640$	2719.28	−	15960.9i	0.167952	−	0.985795i
$641$			21967.0i			1.35358i	0.736177	+	0.676789i	$0.236629\pi$
$641$			21967.0i			1.35358i	−0.736177	+	0.676789i	$0.763371\pi$
$642$		0			0
$643$		−	3689.93i		−	0.226309i	−0.993577	−	0.113154i	$-0.963905\pi$
$643$		−	3689.93i		−	0.226309i	0.993577	−	0.113154i	$-0.0360955\pi$
$644$	−19872.9	−	9280.27i	−1.21599	−	0.567847i
$645$		0			0
$646$	5582.83	+	8768.65i	0.340021	+	0.534053i
$647$			5518.50i			0.335324i	0.985845	+	0.167662i	$0.0536217\pi$
$647$			5518.50i			0.335324i	−0.985845	+	0.167662i	$0.946378\pi$
$648$		0			0
$649$	−10484.1			−0.634111
$650$	−9224.43	+	1357.01i	−0.556634	+	0.0818867i
$651$		0			0
$652$	−5739.97	−	2680.46i	−0.344777	−	0.161005i
$653$		−	24118.2i		−	1.44536i	−0.691185	−	0.722678i	$-0.742911\pi$
$653$		−	24118.2i		−	1.44536i	0.691185	−	0.722678i	$-0.257089\pi$
$654$		0			0
$655$	−9149.69	+	5928.79i	−0.545814	+	0.353675i
$656$	20961.0	−	17548.9i	1.24755	−	1.04446i
$657$		0			0
$658$	−2681.64	+	1707.35i	−0.158877	+	0.101154i
$659$			24826.8i			1.46755i	0.679392	+	0.733775i	$0.262243\pi$
$659$			24826.8i			1.46755i	−0.679392	+	0.733775i	$0.737757\pi$
$660$		0			0
$661$			8774.46i			0.516319i	0.966102	+	0.258160i	$0.0831160\pi$
$661$			8774.46i			0.516319i	−0.966102	+	0.258160i	$0.916884\pi$
$662$	1081.88	+	1699.24i	0.0635171	+	0.0997629i
$663$		0			0
$664$	10308.2	−	1348.39i	0.602464	−	0.0788067i
$665$	−3724.88	−	5748.47i	−0.217210	−	0.335212i
$666$		0			0
$667$			45690.9i			2.65241i
$668$	4796.77	+	2240.01i	0.277833	+	0.129743i
$669$		0			0
$670$	−7923.39	−	3623.19i	−0.456876	−	0.208919i
$671$	300.421			0.0172841
$672$		0			0
$673$			11665.9i			0.668185i	0.942540	+	0.334093i	$0.108430\pi$
$673$			11665.9i			0.668185i	−0.942540	+	0.334093i	$0.891570\pi$
$674$	−15332.6	+	9761.96i	−0.876244	+	0.557888i
$675$		0			0
$676$	5082.68	−	10884.1i	0.289183	−	0.619259i
$677$			166.449i			0.00944929i	0.999989	+	0.00472464i	$0.00150391\pi$
$677$			166.449i			0.00944929i	−0.999989	+	0.00472464i	$0.998496\pi$
$678$		0			0
$679$			4700.50i			0.265668i
$680$	14015.3	+	16471.0i	0.790385	+	0.928873i
$681$		0			0
$682$	9603.76	+	15084.1i	0.539219	+	0.846921i
$683$	−31424.7			−1.76052			−0.880259	−	0.474493i	$-0.842632\pi$
$683$	−31424.7			−1.76052			−0.880259	+	0.474493i	$0.842632\pi$
$684$		0			0
$685$	−9880.20	−	15247.8i	−0.551099	−	0.850491i
$686$	10454.0	+	16419.5i	0.581831	+	0.913850i
$687$		0			0
$688$	15568.3	−	13034.0i	0.862698	−	0.722262i
$689$			1293.48i			0.0715208i
$690$		0			0
$691$	−1044.70			−0.0575143			−0.0287572	−	0.999586i	$-0.509155\pi$
$691$	−1044.70			−0.0575143			−0.0287572	+	0.999586i	$0.509155\pi$
$692$	27736.3	+	12952.4i	1.52367	+	0.711525i
$693$		0			0
$694$	−5476.31	−	8601.35i	−0.299536	−	0.470465i
$695$	−11715.6	−	18080.3i	−0.639423	−	0.986798i
$696$		0			0
$697$			36515.7i			1.98440i
$698$	−29650.9	+	18878.1i	−1.60788	+	1.02371i
$699$		0			0
$700$	−9321.83	−	10779.3i	−0.503331	−	0.582027i
$701$	17851.8			0.961842			0.480921	−	0.876764i	$-0.340302\pi$
$701$	17851.8			0.961842			0.480921	+	0.876764i	$0.340302\pi$
$702$		0			0
$703$	−9233.04			−0.495350
$704$	−3574.13	−	13428.1i	−0.191342	−	0.718876i
$705$		0			0
$706$	−3290.64	−	5168.42i	−0.175417	−	0.275519i
$707$	4690.94			0.249535
$708$		0			0
$709$		−	30275.7i		−	1.60371i	−0.597520	−	0.801854i	$-0.703847\pi$
$709$		−	30275.7i		−	1.60371i	0.597520	−	0.801854i	$-0.296153\pi$
$710$	12697.9	−	27768.5i	0.671189	−	1.46779i
$711$		0			0
$712$	3097.70	+	23681.4i	0.163049	+	1.24649i
$713$	44815.2			2.35391
$714$		0			0
$715$	−6715.38	+	4351.41i	−0.351246	+	0.227600i
$716$	29409.3	+	13733.6i	1.53502	+	0.716828i
$717$		0			0
$718$	−7757.79	−	12184.7i	−0.403228	−	0.633329i
$719$	1883.54			0.0976969			0.0488485	−	0.998806i	$-0.484445\pi$
$719$	1883.54			0.0976969			0.0488485	+	0.998806i	$0.484445\pi$
$720$		0			0
$721$	9490.94			0.490237
$722$	7611.62	+	11955.2i	0.392348	+	0.616239i
$723$		0			0
$724$	−8458.90	−	3950.16i	−0.434216	−	0.202771i
$725$	−12129.7	+	27096.7i	−0.621358	+	1.38807i
$726$		0			0
$727$	29666.6			1.51344			0.756721	−	0.653738i	$-0.226800\pi$
$727$	29666.6			1.51344			0.756721	+	0.653738i	$0.226800\pi$
$728$	−8431.96	+	1102.96i	−0.429271	+	0.0561518i
$729$		0			0
$730$	23482.1	+	10737.8i	1.19056	+	0.544417i
$731$			27121.1i			1.37225i
$732$		0			0
$733$	13472.2			0.678864			0.339432	−	0.940631i	$-0.389765\pi$
$733$	13472.2			0.678864			0.339432	+	0.940631i	$0.389765\pi$
$734$	−1086.34	−	1706.26i	−0.0546290	−	0.0858028i
$735$		0			0
$736$	−33198.4	−	10518.0i	−1.66265	−	0.526764i
$737$	−7477.37			−0.373721
$738$		0			0
$739$	−17576.4			−0.874907			−0.437454	−	0.899241i	$-0.644120\pi$
$739$	−17576.4			−0.874907			−0.437454	+	0.899241i	$0.644120\pi$
$740$	−19026.5	+	2643.73i	−0.945173	+	0.131332i
$741$		0			0
$742$	−1667.72	+	1061.80i	−0.0825118	+	0.0525337i
$743$		−	14438.0i		−	0.712894i	−0.934316	−	0.356447i	$-0.883988\pi$
$743$		−	14438.0i		−	0.712894i	0.934316	−	0.356447i	$-0.116012\pi$
$744$		0			0
$745$	−18172.2	−	28044.6i	−0.893664	−	1.37916i
$746$	12897.8	+	20257.8i	0.633004	+	0.994225i
$747$		0			0
$748$	16817.6	+	7853.52i	0.822075	+	0.383894i
$749$	20280.7			0.989373
$750$		0			0
$751$			3329.07i			0.161757i	0.996724	+	0.0808785i	$0.0257726\pi$
$751$			3329.07i			0.161757i	−0.996724	+	0.0808785i	$0.974227\pi$
$752$	−3870.28	+	3240.25i	−0.187679	+	0.157127i
$753$		0			0
$754$	9514.23	+	14943.5i	0.459533	+	0.721763i
$755$	−4036.61	+	2615.63i	−0.194579	+	0.126083i
$756$		0			0
$757$	−13097.9			−0.628867			−0.314433	−	0.949280i	$-0.601814\pi$
$757$	−13097.9			−0.628867			−0.314433	+	0.949280i	$0.601814\pi$
$758$	14830.9	+	23294.1i	0.710663	+	1.11620i
$759$		0			0
$760$	−7048.17	−	8283.12i	−0.336400	−	0.395343i
$761$		−	11190.4i		−	0.533051i	−0.963828	−	0.266525i	$-0.914124\pi$
$761$		−	11190.4i		−	0.533051i	0.963828	−	0.266525i	$-0.0858756\pi$
$762$		0			0
$763$		−	2094.56i		−	0.0993818i
$764$	2140.33	−	4583.33i	0.101354	−	0.217040i
$765$		0			0
$766$	23763.2	−	15129.6i	1.12089	−	0.713647i
$767$			10187.3i			0.479586i
$768$		0			0
$769$	−22078.4			−1.03533			−0.517664	−	0.855584i	$-0.673198\pi$
$769$	−22078.4			−1.03533			−0.517664	+	0.855584i	$0.673198\pi$
$770$	−11122.9	−	5086.26i	−0.520574	−	0.238047i
$771$		0			0
$772$	−18014.6	−	8412.50i	−0.839844	−	0.392192i
$773$			7769.19i			0.361499i	0.983529	+	0.180749i	$0.0578523\pi$
$773$			7769.19i			0.361499i	−0.983529	+	0.180749i	$0.942148\pi$
$774$		0			0
$775$	26577.4	+	11897.2i	1.23185	+	0.551431i
$776$	968.016	+	7400.32i	0.0447806	+	0.342340i
$777$		0			0
$778$	−17975.6	−	28233.3i	−0.828350	−	1.30104i
$779$		−	18363.4i		−	0.844593i
$780$		0			0
$781$		−	26205.4i		−	1.20064i
$782$	39238.9	−	24982.7i	1.79435	−	1.14243i
$783$		0			0
$784$	5748.08	+	6865.73i	0.261848	+	0.312761i
$785$	−5569.86	−	8595.76i	−0.253244	−	0.390822i
$786$		0			0
$787$			1689.20i			0.0765102i	0.999268	+	0.0382551i	$0.0121800\pi$
$787$			1689.20i			0.0765102i	−0.999268	+	0.0382551i	$0.987820\pi$
$788$	7538.64	+	3520.41i	0.340803	+	0.159149i
$789$		0			0
$790$	9556.13	+	4369.80i	0.430370	+	0.196798i
$791$	13137.5			0.590539
$792$		0			0
$793$		−	291.916i		−	0.0130722i
$794$	5160.38	+	8105.12i	0.230649	+	0.362267i
$795$		0			0
$796$	16964.2	+	7921.98i	0.755377	+	0.352748i
$797$			8716.02i			0.387374i	0.981063	+	0.193687i	$0.0620447\pi$
$797$			8716.02i			0.387374i	−0.981063	+	0.193687i	$0.937955\pi$
$798$		0			0
$799$		−	6742.31i		−	0.298531i
$800$	−16895.9	−	15050.9i	−0.746700	−	0.665161i
$801$		0			0
$802$	−17055.1	+	10858.7i	−0.750920	+	0.478096i
$803$	22160.2			0.973870
$804$		0			0
$805$	−25723.9	+	16668.5i	−1.12627	+	0.729798i
$806$	14657.1	−	9331.87i	0.640537	−	0.407818i
$807$		0			0
$808$	7385.28	−	966.049i	0.321551	−	0.0420612i
$809$		−	23509.5i		−	1.02170i	−0.859671	−	0.510848i	$-0.829332\pi$
$809$		−	23509.5i		−	1.02170i	0.859671	−	0.510848i	$-0.170668\pi$
$810$		0			0
$811$	9230.48			0.399662			0.199831	−	0.979830i	$-0.435961\pi$
$811$	9230.48			0.399662			0.199831	+	0.979830i	$0.435961\pi$
$812$	−11456.8	+	24533.8i	−0.495143	+	1.06030i
$813$		0			0
$814$	−13906.7	+	8854.13i	−0.598808	+	0.381249i
$815$	−7429.95	+	4814.44i	−0.319337	+	0.206923i
$816$		0			0
$817$		−	13639.0i		−	0.584049i
$818$	−17074.9	−	26818.5i	−0.729839	−	1.14632i
$819$		0			0
$820$	−5258.07	−	37841.5i	−0.223926	−	1.61156i
$821$	9012.19			0.383103			0.191552	−	0.981483i	$-0.438648\pi$
$821$	9012.19			0.383103			0.191552	+	0.981483i	$0.438648\pi$
$822$		0			0
$823$	−24464.7			−1.03619			−0.518096	−	0.855323i	$-0.673359\pi$
$823$	−24464.7			−1.03619			−0.518096	+	0.855323i	$0.673359\pi$
$824$	14942.3	−	1954.56i	0.631721	−	0.0826337i
$825$		0			0
$826$	−13134.7	+	8362.62i	−0.553287	+	0.352267i
$827$	−21129.7			−0.888453			−0.444226	−	0.895915i	$-0.646521\pi$
$827$	−21129.7			−0.888453			−0.444226	+	0.895915i	$0.646521\pi$
$828$		0			0
$829$		−	15474.1i		−	0.648295i	−0.946007	−	0.324147i	$-0.894923\pi$
$829$		−	15474.1i		−	0.648295i	0.946007	−	0.324147i	$-0.105077\pi$
$830$	6041.99	−	13213.0i	0.252676	−	0.552565i
$831$		0			0
$832$	−13047.9	+	3472.94i	−0.543695	+	0.144715i
$833$	−11960.6			−0.497492
$834$		0			0
$835$	6209.06	−	4023.33i	0.257333	−	0.166746i
$836$	−8457.43	−	3949.47i	−0.349888	−	0.163391i
$837$		0			0
$838$	3288.97	−	2094.03i	0.135580	−	0.0863209i
$839$	16117.8			0.663229			0.331615	−	0.943415i	$-0.392407\pi$
$839$	16117.8			0.663229			0.331615	+	0.943415i	$0.392407\pi$
$840$		0			0
$841$	32018.2			1.31281
$842$	−5298.83	+	3373.67i	−0.216876	+	0.138081i
$843$		0			0
$844$	7835.49	−	16779.0i	0.319560	−	0.684309i
$845$	−9129.12	−	14088.6i	−0.371658	−	0.573567i
$846$		0			0
$847$	8471.22			0.343653
$848$	−2406.94	+	2015.12i	−0.0974700	+	0.0816032i
$849$		0			0
$850$	29902.6	−	4398.99i	1.20665	−	0.177511i
$851$			41317.1i			1.66431i
$852$		0			0
$853$	48785.0			1.95823			0.979113	−	0.203319i	$-0.0651729\pi$
$853$	48785.0			1.95823			0.979113	+	0.203319i	$0.0651729\pi$
$854$	376.374	−	239.630i	0.0150811	−	0.00960183i
$855$		0			0
$856$	31929.3	−	4176.59i	1.27491	−	0.166767i
$857$	10323.1			0.411469			0.205735	−	0.978608i	$-0.434042\pi$
$857$	10323.1			0.411469			0.205735	+	0.978608i	$0.434042\pi$
$858$		0			0
$859$	4548.06			0.180649			0.0903246	−	0.995912i	$-0.471210\pi$
$859$	4548.06			0.180649			0.0903246	+	0.995912i	$0.471210\pi$
$860$	−3905.30	−	28105.8i	−0.154849	−	1.11442i
$861$		0			0
$862$	22272.5	+	34982.2i	0.880053	+	1.38225i
$863$			46077.7i			1.81750i	0.417342	+	0.908750i	$0.362962\pi$
$863$			46077.7i			1.81750i	−0.417342	+	0.908750i	$0.637038\pi$
$864$		0			0
$865$	35902.6	−	23264.1i	1.41124	−	0.914453i
$866$	7069.28	−	4500.88i	0.277395	−	0.176612i
$867$		0			0
$868$	24063.5	+	11237.2i	0.940979	+	0.439420i
$869$	9018.21			0.352039
$870$		0			0
$871$			7265.68i			0.282650i
$872$	−431.353	−	3297.62i	−0.0167517	−	0.128064i
$873$		0			0
$874$	−19732.9	+	12563.6i	−0.763703	+	0.486235i
$875$	−19680.4	+	3056.18i	−0.760366	+	0.118078i
$876$		0			0
$877$	12784.3			0.492239			0.246120	−	0.969239i	$-0.420844\pi$
$877$	12784.3			0.492239			0.246120	+	0.969239i	$0.420844\pi$
$878$	−19138.1	+	12184.9i	−0.735625	+	0.468359i
$879$		0			0
$880$	−18559.1	−	5717.01i	−0.710939	−	0.219001i
$881$		−	30010.2i		−	1.14764i	−0.818982	−	0.573819i	$-0.805461\pi$
$881$		−	30010.2i		−	1.14764i	0.818982	−	0.573819i	$-0.194539\pi$
$882$		0			0
$883$		−	50889.7i		−	1.93950i	−0.244108	−	0.969748i	$-0.578495\pi$
$883$		−	50889.7i		−	1.93950i	0.244108	−	0.969748i	$-0.421505\pi$
$884$	7631.18	−	16341.5i	0.290344	−	0.621746i
$885$		0			0
$886$	−259.136	−	407.010i	−0.00982599	−	0.0154331i
$887$		−	26060.4i		−	0.986497i	−0.869888	−	0.493248i	$-0.835809\pi$
$887$		−	26060.4i		−	0.986497i	0.869888	−	0.493248i	$-0.164191\pi$
$888$		0			0
$889$	14713.3			0.555081
$890$	30354.6	+	13880.5i	1.14325	+	0.522781i
$891$		0			0
$892$	3268.51	−	6999.21i	0.122688	−	0.262725i
$893$			3390.65i			0.127059i
$894$		0			0
$895$	38068.0	−	24667.2i	1.42176	−	0.921268i
$896$	−15188.6	−	13972.0i	−0.566311	−	0.520952i
$897$		0			0
$898$	−21255.5	+	13533.0i	−0.789872	+	0.502897i
$899$		−	55326.0i		−	2.05253i
$900$		0			0
$901$		−	4193.06i		−	0.155040i
$902$	−17609.8	−	27658.8i	−0.650047	−	1.02099i
$903$		0			0
$904$	20683.3	−	2705.53i	0.760970	−	0.0995404i
$905$	−10949.4	+	7094.97i	−0.402177	+	0.260602i
$906$		0			0
$907$			24506.9i			0.897176i	0.893739	+	0.448588i	$0.148073\pi$
$907$			24506.9i			0.897176i	−0.893739	+	0.448588i	$0.851927\pi$
$908$	19092.6	−	40885.1i	0.697809	−	1.49429i
$909$		0			0
$910$	−4942.26	+	10808.0i	−0.180038	+	0.393717i
$911$	8487.84			0.308688			0.154344	−	0.988017i	$-0.450674\pi$
$911$	8487.84			0.308688			0.154344	+	0.988017i	$0.450674\pi$
$912$		0			0
$913$		−	12469.2i		−	0.451994i
$914$	−23465.3	+	14939.9i	−0.849195	+	0.540666i
$915$		0			0
$916$	−8503.21	−	3970.85i	−0.306718	−	0.143232i
$917$			13897.0i			0.500457i
$918$		0			0
$919$			49134.1i			1.76364i	0.471586	+	0.881820i	$0.343682\pi$
$919$			49134.1i			1.76364i	−0.471586	+	0.881820i	$0.656318\pi$
$920$	−37066.2	+	31540.0i	−1.32830	+	1.13026i
$921$		0			0
$922$	15538.1	+	24404.8i	0.555010	+	0.871723i
$923$	−25463.5			−0.908062
$924$		0			0
$925$	−10968.5	+	24502.8i	−0.389884	+	0.870971i
$926$	17762.2	+	27898.1i	0.630347	+	0.990052i
$927$		0			0
$928$	−12984.8	+	40984.7i	−0.459319	+	1.44977i
$929$			29735.2i			1.05014i	0.851059	+	0.525069i	$0.175961\pi$
$929$			29735.2i			1.05014i	−0.851059	+	0.525069i	$0.824039\pi$
$930$		0			0
$931$	6014.89			0.211740
$932$	11594.7	−	24829.0i	0.407507	−	0.872640i
$933$		0			0
$934$	16491.8	+	25902.7i	0.577760	+	0.907456i
$935$	21769.1	−	14105.9i	0.761418	−	0.493381i
$936$		0			0
$937$		−	19681.8i		−	0.686208i	−0.939297	−	0.343104i	$-0.888522\pi$
$937$		−	19681.8i		−	0.686208i	0.939297	−	0.343104i	$-0.111478\pi$
$938$	−9367.79	+	5964.30i	−0.326087	+	0.207613i
$939$		0			0
$940$	970.858	+	6987.11i	0.0336871	+	0.242441i
$941$	13157.3			0.455807			0.227904	−	0.973684i	$-0.426813\pi$
$941$	13157.3			0.455807			0.227904	+	0.973684i	$0.426813\pi$
$942$		0			0
$943$	−82174.7			−2.83773
$944$	−18956.7	+	15870.8i	−0.653589	+	0.547194i
$945$		0			0
$946$	−13079.3	−	20542.9i	−0.449518	−	0.706033i
$947$	33324.5			1.14351			0.571753	−	0.820426i	$-0.306264\pi$
$947$	33324.5			1.14351			0.571753	+	0.820426i	$0.306264\pi$
$948$		0			0
$949$		−	21532.8i		−	0.736550i
$950$	−15037.8	+	2212.22i	−0.513569	+	0.0755514i
$951$		0			0
$952$	27333.7	−	3575.45i	0.930557	−	0.121724i
$953$	−56910.2			−1.93442			−0.967210	−	0.253980i	$-0.918260\pi$
$953$	−56910.2			−1.93442			−0.967210	+	0.253980i	$0.918260\pi$
$954$		0			0
$955$	−3844.30	−	5932.77i	−0.130260	−	0.201026i
$956$	−22025.8	+	47166.2i	−0.745151	+	1.59567i
$957$		0			0
$958$	−2291.86	−	3599.70i	−0.0772930	−	0.121400i
$959$	−23159.0			−0.779816
$960$		0			0
$961$	−24474.6			−0.821542
$962$	8603.46	+	13513.0i	0.288344	+	0.452886i
$963$		0			0
$964$	−23883.0	+	51143.2i	−0.797944	+	1.70873i
$965$	−23318.5	+	15109.9i	−0.777876	+	0.504046i
$966$		0			0
$967$	12101.8			0.402450			0.201225	−	0.979545i	$-0.435508\pi$
$967$	12101.8			0.402450			0.201225	+	0.979545i	$0.435508\pi$
$968$	13336.8	−	1744.55i	0.442833	−	0.0579257i
$969$		0			0
$970$	9485.67	+	4337.58i	0.313986	+	0.143579i
$971$		−	24142.2i		−	0.797899i	−0.916973	−	0.398949i	$-0.869375\pi$
$971$		−	24142.2i		−	0.797899i	0.916973	−	0.398949i	$-0.130625\pi$
$972$		0			0
$973$	−27461.2			−0.904795
$974$	−14642.5	−	22998.1i	−0.481699	−	0.756578i
$975$		0			0
$976$	543.202	−	454.776i	0.0178150	−	0.0149150i
$977$	21384.9			0.700271			0.350135	−	0.936699i	$-0.386136\pi$
$977$	21384.9			0.700271			0.350135	+	0.936699i	$0.386136\pi$
$978$		0			0
$979$	28645.9			0.935167
$980$	12394.9	−	1722.27i	0.404020	−	0.0561385i
$981$		0			0
$982$	19880.3	−	12657.4i	0.646035	−	0.411318i
$983$		−	2538.22i		−	0.0823566i	−0.999152	−	0.0411783i	$-0.986889\pi$
$983$		−	2538.22i		−	0.0823566i	0.999152	−	0.0411783i	$-0.0131112\pi$
$984$		0			0
$985$	9758.20	−	6323.09i	0.315657	−	0.204539i
$986$	−30842.1	−	48442.0i	−0.996158	−	1.56461i
$987$		0			0
$988$	−3837.65	+	8217.99i	−0.123575	+	0.264625i
$989$	−61033.3			−1.96233
$990$		0			0
$991$		−	30753.6i		−	0.985792i	−0.870088	−	0.492896i	$-0.835938\pi$
$991$		−	30753.6i		−	0.985792i	0.870088	−	0.492896i	$-0.164062\pi$
$992$	40199.1	+	12736.0i	1.28662	+	0.407628i
$993$		0			0
$994$	−20902.6	−	32830.6i	−0.666993	−	1.04761i
$995$	21958.9	−	14228.9i	0.699641	−	0.453352i
$996$		0			0
$997$	−56847.7			−1.80580			−0.902902	−	0.429847i	$-0.858567\pi$
$997$	−56847.7			−1.80580			−0.902902	+	0.429847i	$0.858567\pi$
$998$	16493.2	+	25905.0i	0.523131	+	0.821653i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.4.m.c.179.22	yes	64
3.2	odd	2	inner	360.4.m.c.179.43	yes	64
4.3	odd	2		1440.4.m.c.719.39		64
5.4	even	2	inner	360.4.m.c.179.44	yes	64
8.3	odd	2	inner	360.4.m.c.179.23	yes	64
8.5	even	2		1440.4.m.c.719.26		64
12.11	even	2		1440.4.m.c.719.25		64
15.14	odd	2	inner	360.4.m.c.179.21	✓	64
20.19	odd	2		1440.4.m.c.719.38		64
24.5	odd	2		1440.4.m.c.719.40		64
24.11	even	2	inner	360.4.m.c.179.42	yes	64
40.19	odd	2	inner	360.4.m.c.179.41	yes	64
40.29	even	2		1440.4.m.c.719.27		64
60.59	even	2		1440.4.m.c.719.28		64
120.29	odd	2		1440.4.m.c.719.37		64
120.59	even	2	inner	360.4.m.c.179.24	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.4.m.c.179.21	✓	64	15.14	odd	2	inner
360.4.m.c.179.22	yes	64	1.1	even	1	trivial
360.4.m.c.179.23	yes	64	8.3	odd	2	inner
360.4.m.c.179.24	yes	64	120.59	even	2	inner
360.4.m.c.179.41	yes	64	40.19	odd	2	inner
360.4.m.c.179.42	yes	64	24.11	even	2	inner
360.4.m.c.179.43	yes	64	3.2	odd	2	inner
360.4.m.c.179.44	yes	64	5.4	even	2	inner
1440.4.m.c.719.25		64	12.11	even	2
1440.4.m.c.719.26		64	8.5	even	2
1440.4.m.c.719.27		64	40.29	even	2
1440.4.m.c.719.28		64	60.59	even	2
1440.4.m.c.719.37		64	120.29	odd	2
1440.4.m.c.719.38		64	20.19	odd	2
1440.4.m.c.719.39		64	4.3	odd	2
1440.4.m.c.719.40		64	24.5	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	360.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.51905 - 2.38589i) q^{2} +(-3.38496 + 7.24859i) q^{4} +(6.07981 + 9.38275i) q^{5} +14.2510 q^{7} +(22.4363 - 2.93483i) q^{8} +O(q^{10})\)	\(q+(-1.51905 - 2.38589i) q^{2} +(-3.38496 + 7.24859i) q^{4} +(6.07981 + 9.38275i) q^{5} +14.2510 q^{7} +(22.4363 - 2.93483i) q^{8} +(13.1507 - 28.7586i) q^{10} -27.1398i q^{11} -26.3714 q^{13} +(-21.6479 - 34.0012i) q^{14} +(-41.0841 - 49.0724i) q^{16} +85.4877 q^{17} -42.9911 q^{19} +(-88.5916 + 12.3098i) q^{20} +(-64.7526 + 41.2268i) q^{22} +192.381i q^{23} +(-51.0719 + 114.091i) q^{25} +(40.0596 + 62.9194i) q^{26} +(-48.2389 + 103.299i) q^{28} +237.502 q^{29} -232.950i q^{31} +(-54.6726 + 172.566i) q^{32} +(-129.860 - 203.964i) q^{34} +(86.6431 + 133.713i) q^{35} +214.767 q^{37} +(65.3057 + 102.572i) q^{38} +(163.945 + 192.671i) q^{40} +427.145i q^{41} +317.252i q^{43} +(196.725 + 91.8672i) q^{44} +(459.001 - 292.237i) q^{46} -78.8688i q^{47} -139.910 q^{49} +(349.789 - 51.4576i) q^{50} +(89.2663 - 191.156i) q^{52} -49.0487i q^{53} +(254.646 - 165.005i) q^{55} +(319.738 - 41.8241i) q^{56} +(-360.778 - 566.654i) q^{58} -386.301i q^{59} +11.0694i q^{61} +(-555.793 + 353.863i) q^{62} +(494.774 - 131.693i) q^{64} +(-160.333 - 247.437i) q^{65} -275.513i q^{67} +(-289.373 + 619.665i) q^{68} +(187.410 - 409.838i) q^{70} +965.571 q^{71} +816.521i q^{73} +(-326.242 - 512.410i) q^{74} +(145.523 - 311.625i) q^{76} -386.768i q^{77} +332.287i q^{79} +(210.651 - 683.832i) q^{80} +(1019.12 - 648.856i) q^{82} +459.444 q^{83} +(519.749 + 802.110i) q^{85} +(756.929 - 481.922i) q^{86} +(-79.6507 - 608.916i) q^{88} +1055.50i q^{89} -375.818 q^{91} +(-1394.49 - 651.203i) q^{92} +(-188.172 + 119.806i) q^{94} +(-261.377 - 403.374i) q^{95} +329.837i q^{97} +(212.531 + 333.811i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 76 q^{4}+O(q^{10}) \) 64 * q + 76 * q^4	\( 64 q + 76 q^{4} + 72 q^{10} - 236 q^{16} - 48 q^{19} + 1000 q^{25} - 192 q^{34} + 1284 q^{40} + 336 q^{46} + 784 q^{49} + 4228 q^{64} - 768 q^{70} + 648 q^{76} + 4304 q^{91} - 5944 q^{94}+O(q^{100}) \) 64 * q + 76 * q^4 + 72 * q^10 - 236 * q^16 - 48 * q^19 + 1000 * q^25 - 192 * q^34 + 1284 * q^40 + 336 * q^46 + 784 * q^49 + 4228 * q^64 - 768 * q^70 + 648 * q^76 + 4304 * q^91 - 5944 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more