LMFDB - Embedded newform 252.4.i.a.25.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(25,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 4, 4]))

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

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

chi := DirichletCharacter("252.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.12
Character	$\chi$	$=$	252.25
Dual form			252.4.i.a.121.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.977623 - 5.10336i) q^{3} +(-6.36172 + 11.0188i) q^{5} +(5.55536 - 17.6674i) q^{7} +(-25.0885 + 9.97831i) q^{9} +O(q^{10})$	\(q+(-0.977623 - 5.10336i) q^{3} +(-6.36172 + 11.0188i) q^{5} +(5.55536 - 17.6674i) q^{7} +(-25.0885 + 9.97831i) q^{9} +(-2.97902 - 5.15982i) q^{11} +(6.61455 + 11.4567i) q^{13} +(62.4524 + 21.6939i) q^{15} +(-58.1225 + 100.671i) q^{17} +(2.84809 + 4.93303i) q^{19} +(-95.5942 - 11.0789i) q^{21} +(-10.9608 + 18.9847i) q^{23} +(-18.4430 - 31.9442i) q^{25} +(75.4500 + 118.281i) q^{27} +(-67.1546 + 116.315i) q^{29} +133.596 q^{31} +(-23.4200 + 20.2474i) q^{33} +(159.333 + 173.609i) q^{35} +(133.049 + 230.447i) q^{37} +(52.0013 - 44.9568i) q^{39} +(180.928 + 313.377i) q^{41} +(-72.1763 + 125.013i) q^{43} +(49.6568 - 339.925i) q^{45} +29.4217 q^{47} +(-281.276 - 196.298i) q^{49} +(570.582 + 198.201i) q^{51} +(95.0340 - 164.604i) q^{53} +75.8068 q^{55} +(22.3907 - 19.3574i) q^{57} +328.174 q^{59} -420.104 q^{61} +(36.9154 + 498.683i) q^{63} -168.320 q^{65} -916.379 q^{67} +(107.601 + 37.3771i) q^{69} -803.107 q^{71} +(-230.631 + 399.464i) q^{73} +(-144.992 + 125.351i) q^{75} +(-107.710 + 23.9670i) q^{77} -395.966 q^{79} +(529.867 - 500.682i) q^{81} +(-524.406 + 908.298i) q^{83} +(-739.518 - 1280.88i) q^{85} +(659.250 + 229.002i) q^{87} +(-95.0573 - 164.644i) q^{89} +(239.157 - 53.2158i) q^{91} +(-130.607 - 681.789i) q^{93} -72.4749 q^{95} +(897.554 - 1554.61i) q^{97} +(126.225 + 99.7265i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9}+O(q^{10}) $ 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9	$ 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9} + 4 q^{11} - 12 q^{13} - 26 q^{15} + 112 q^{17} + 60 q^{19} - 80 q^{21} + 10 q^{23} - 600 q^{25} + 194 q^{29} + 60 q^{31} - 472 q^{33} + 394 q^{35} - 84 q^{37} + 604 q^{39} + 210 q^{41} + 42 q^{43} + 254 q^{45} - 132 q^{47} - 78 q^{49} - 58 q^{51} - 468 q^{53} + 612 q^{55} + 1476 q^{57} - 916 q^{59} - 804 q^{61} - 444 q^{63} + 1656 q^{65} - 588 q^{67} - 28 q^{69} - 2228 q^{71} - 336 q^{73} - 668 q^{75} - 1216 q^{77} - 768 q^{79} - 104 q^{81} + 1024 q^{83} + 360 q^{85} + 2188 q^{87} + 2922 q^{89} - 120 q^{91} - 1292 q^{93} + 2428 q^{95} - 264 q^{97} - 2246 q^{99}+O(q^{100}) $ 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9 + 4 * q^11 - 12 * q^13 - 26 * q^15 + 112 * q^17 + 60 * q^19 - 80 * q^21 + 10 * q^23 - 600 * q^25 + 194 * q^29 + 60 * q^31 - 472 * q^33 + 394 * q^35 - 84 * q^37 + 604 * q^39 + 210 * q^41 + 42 * q^43 + 254 * q^45 - 132 * q^47 - 78 * q^49 - 58 * q^51 - 468 * q^53 + 612 * q^55 + 1476 * q^57 - 916 * q^59 - 804 * q^61 - 444 * q^63 + 1656 * q^65 - 588 * q^67 - 28 * q^69 - 2228 * q^71 - 336 * q^73 - 668 * q^75 - 1216 * q^77 - 768 * q^79 - 104 * q^81 + 1024 * q^83 + 360 * q^85 + 2188 * q^87 + 2922 * q^89 - 120 * q^91 - 1292 * q^93 + 2428 * q^95 - 264 * q^97 - 2246 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.977623	−	5.10336i	−0.188144	−	0.982142i
$3$	−0.977623	−	5.10336i	−0.188144	−	0.982142i
$4$		0			0
$5$	−6.36172	+	11.0188i	−0.569010	+	0.985554i	0.427655	+	0.903942i	$0.359340\pi$
$5$	−6.36172	+	11.0188i	−0.569010	+	0.985554i	−0.996664	+	0.0816114i	$0.973993\pi$
$6$		0			0
$7$	5.55536	−	17.6674i	0.299961	−	0.953951i
$7$	5.55536	−	17.6674i	0.299961	−	0.953951i
$8$		0			0
$9$	−25.0885	+	9.97831i	−0.929204	+	0.369567i
$10$		0			0
$11$	−2.97902	−	5.15982i	−0.0816553	−	0.141431i	0.822306	−	0.569046i	$-0.192687\pi$
$11$	−2.97902	−	5.15982i	−0.0816553	−	0.141431i	−0.903961	+	0.427615i	$0.859354\pi$
$12$		0			0
$13$	6.61455	+	11.4567i	0.141119	+	0.244425i	0.927918	−	0.372784i	$-0.121597\pi$
$13$	6.61455	+	11.4567i	0.141119	+	0.244425i	−0.786799	+	0.617209i	$0.788263\pi$
$14$		0			0
$15$	62.4524	+	21.6939i	1.07501	+	0.373422i
$16$		0			0
$17$	−58.1225	+	100.671i	−0.829222	+	1.43625i	0.0694279	+	0.997587i	$0.477883\pi$
$17$	−58.1225	+	100.671i	−0.829222	+	1.43625i	−0.898650	+	0.438667i	$0.855451\pi$
$18$		0			0
$19$	2.84809	+	4.93303i	0.0343893	+	0.0595640i	0.882708	−	0.469922i	$-0.155718\pi$
$19$	2.84809	+	4.93303i	0.0343893	+	0.0595640i	−0.848319	+	0.529486i	$0.822385\pi$
$20$		0			0
$21$	−95.5942	−	11.0789i	−0.993351	−	0.115125i
$22$		0			0
$23$	−10.9608	+	18.9847i	−0.0993690	+	0.172112i	−0.911424	−	0.411469i	$-0.865016\pi$
$23$	−10.9608	+	18.9847i	−0.0993690	+	0.172112i	0.812055	+	0.583581i	$0.198349\pi$
$24$		0			0
$25$	−18.4430	−	31.9442i	−0.147544	−	0.255554i
$26$		0			0
$27$	75.4500	+	118.281i	0.537791	+	0.843078i
$28$		0			0
$29$	−67.1546	+	116.315i	−0.430010	+	0.744799i	−0.996874	−	0.0790123i	$-0.974823\pi$
$29$	−67.1546	+	116.315i	−0.430010	+	0.744799i	0.566863	+	0.823812i	$0.308157\pi$
$30$		0			0
$31$	133.596			0.774018			0.387009	−	0.922076i	$-0.373508\pi$
$31$	133.596			0.774018			0.387009	+	0.922076i	$0.373508\pi$
$32$		0			0
$33$	−23.4200	+	20.2474i	−0.123543	+	0.106806i
$34$		0			0
$35$	159.333	+	173.609i	0.769489	+	0.838435i
$36$		0			0
$37$	133.049	+	230.447i	0.591165	+	1.02393i	0.994076	+	0.108688i	$0.0346650\pi$
$37$	133.049	+	230.447i	0.591165	+	1.02393i	−0.402911	+	0.915239i	$0.632002\pi$
$38$		0			0
$39$	52.0013	−	44.9568i	0.213510	−	0.184586i
$40$		0			0
$41$	180.928	+	313.377i	0.689176	+	1.19369i	0.972105	+	0.234547i	$0.0753608\pi$
$41$	180.928	+	313.377i	0.689176	+	1.19369i	−0.282928	+	0.959141i	$0.591306\pi$
$42$		0			0
$43$	−72.1763	+	125.013i	−0.255972	+	0.443356i	−0.965159	−	0.261664i	$-0.915729\pi$
$43$	−72.1763	+	125.013i	−0.255972	+	0.443356i	0.709187	+	0.705020i	$0.249062\pi$
$44$		0			0
$45$	49.6568	−	339.925i	0.164498	−	1.12607i
$46$		0			0
$47$	29.4217			0.0913106			0.0456553	−	0.998957i	$-0.485462\pi$
$47$	29.4217			0.0913106			0.0456553	+	0.998957i	$0.485462\pi$
$48$		0			0
$49$	−281.276	−	196.298i	−0.820047	−	0.572297i
$50$		0			0
$51$	570.582	+	198.201i	1.56662	+	0.544191i
$52$		0			0
$53$	95.0340	−	164.604i	0.246301	−	0.426605i	−0.716196	−	0.697899i	$-0.754118\pi$
$53$	95.0340	−	164.604i	0.246301	−	0.426605i	0.962496	+	0.271294i	$0.0874517\pi$
$54$		0			0
$55$	75.8068			0.185851
$56$		0			0
$57$	22.3907	−	19.3574i	0.0520301	−	0.0449817i
$58$		0			0
$59$	328.174			0.724145			0.362073	−	0.932150i	$-0.382069\pi$
$59$	328.174			0.724145			0.362073	+	0.932150i	$0.382069\pi$
$60$		0			0
$61$	−420.104			−0.881784			−0.440892	−	0.897560i	$-0.645338\pi$
$61$	−420.104			−0.881784			−0.440892	+	0.897560i	$0.645338\pi$
$62$		0			0
$63$	36.9154	+	498.683i	0.0738239	+	0.997271i
$64$		0			0
$65$	−168.320			−0.321192
$66$		0			0
$67$	−916.379			−1.67095			−0.835474	−	0.549529i	$-0.814807\pi$
$67$	−916.379			−1.67095			−0.835474	+	0.549529i	$0.814807\pi$
$68$		0			0
$69$	107.601	+	37.3771i	0.187734	+	0.0652126i
$70$		0			0
$71$	−803.107			−1.34241			−0.671206	−	0.741271i	$-0.734224\pi$
$71$	−803.107			−1.34241			−0.671206	+	0.741271i	$0.734224\pi$
$72$		0			0
$73$	−230.631	+	399.464i	−0.369771	+	0.640462i	−0.989530	−	0.144331i	$-0.953897\pi$
$73$	−230.631	+	399.464i	−0.369771	+	0.640462i	0.619759	+	0.784792i	$0.287230\pi$
$74$		0			0
$75$	−144.992	+	125.351i	−0.223230	+	0.192990i
$76$		0			0
$77$	−107.710	+	23.9670i	−0.159412	+	0.0354713i
$78$		0			0
$79$	−395.966			−0.563919			−0.281960	−	0.959426i	$-0.590984\pi$
$79$	−395.966			−0.563919			−0.281960	+	0.959426i	$0.590984\pi$
$80$		0			0
$81$	529.867	−	500.682i	0.726840	−	0.686807i
$82$		0			0
$83$	−524.406	+	908.298i	−0.693507	+	1.20119i	0.277175	+	0.960820i	$0.410602\pi$
$83$	−524.406	+	908.298i	−0.693507	+	1.20119i	−0.970681	+	0.240370i	$0.922731\pi$
$84$		0			0
$85$	−739.518	−	1280.88i	−0.943670	−	1.63448i
$86$		0			0
$87$	659.250	+	229.002i	0.812402	+	0.282202i
$88$		0			0
$89$	−95.0573	−	164.644i	−0.113214	−	0.196093i	0.803850	−	0.594832i	$-0.202781\pi$
$89$	−95.0573	−	164.644i	−0.113214	−	0.196093i	−0.917064	+	0.398739i	$0.869448\pi$
$90$		0			0
$91$	239.157	−	53.2158i	0.275500	−	0.0613026i
$92$		0			0
$93$	−130.607	−	681.789i	−0.145627	−	0.760196i
$94$		0			0
$95$	−72.4749			−0.0782713
$96$		0			0
$97$	897.554	−	1554.61i	0.939513	−	1.62728i	0.173133	−	0.984899i	$-0.444611\pi$
$97$	897.554	−	1554.61i	0.939513	−	1.62728i	0.766381	−	0.642386i	$-0.222056\pi$
$98$		0			0
$99$	126.225	+	99.7265i	0.128143	+	0.101241i
$100$		0			0
$101$	557.810	+	966.155i	0.549546	+	0.951842i	0.998306	+	0.0581893i	$0.0185327\pi$
$101$	557.810	+	966.155i	0.549546	+	0.951842i	−0.448759	+	0.893653i	$0.648134\pi$
$102$		0			0
$103$	647.191	−	1120.97i	0.619122	−	1.07235i	−0.370524	−	0.928823i	$-0.620822\pi$
$103$	647.191	−	1120.97i	0.619122	−	1.07235i	0.989646	−	0.143528i	$-0.0458449\pi$
$104$		0			0
$105$	730.220	−	982.855i	0.678688	−	0.913494i
$106$		0			0
$107$	−422.888	−	732.463i	−0.382076	−	0.661774i	0.609283	−	0.792953i	$-0.291457\pi$
$107$	−422.888	−	732.463i	−0.382076	−	0.661774i	−0.991359	+	0.131178i	$0.958124\pi$
$108$		0			0
$109$	−103.985	+	180.107i	−0.0913754	+	0.158267i	−0.908090	−	0.418775i	$-0.862460\pi$
$109$	−103.985	+	180.107i	−0.0913754	+	0.158267i	0.816715	+	0.577042i	$0.195793\pi$
$110$		0			0
$111$	1045.98	−	904.286i	0.894418	−	0.773253i
$112$		0			0
$113$	−227.865	−	394.673i	−0.189696	−	0.328564i	0.755453	−	0.655203i	$-0.227417\pi$
$113$	−227.865	−	394.673i	−0.189696	−	0.328564i	−0.945149	+	0.326640i	$0.894084\pi$
$114$		0			0
$115$	−139.459	−	241.550i	−0.113084	−	0.195867i
$116$		0			0
$117$	−280.268	−	221.430i	−0.221460	−	0.174968i
$118$		0			0
$119$	1455.71	+	1586.14i	1.12138	+	1.22186i
$120$		0			0
$121$	647.751	−	1121.94i	0.486665	−	0.842928i
$122$		0			0
$123$	1422.39	−	1229.70i	1.04271	−	0.901453i
$124$		0			0
$125$	−1121.11			−0.802204
$126$		0			0
$127$	−2848.91			−1.99055			−0.995275	−	0.0970955i	$-0.969045\pi$
$127$	−2848.91			−1.99055			−0.995275	+	0.0970955i	$0.969045\pi$
$128$		0			0
$129$	708.548	+	246.126i	0.483598	+	0.167986i
$130$		0			0
$131$	350.020	−	606.253i	0.233446	−	0.404340i	−0.725374	−	0.688355i	$-0.758333\pi$
$131$	350.020	−	606.253i	0.233446	−	0.404340i	0.958820	+	0.284015i	$0.0916665\pi$
$132$		0			0
$133$	102.976	−	22.9136i	0.0671366	−	0.0149388i
$134$		0			0
$135$	−1783.30	+	78.9020i	−1.13691	+	0.0503023i
$136$		0			0
$137$	476.767	+	825.784i	0.297321	+	0.514974i	0.975522	−	0.219902i	$-0.0705737\pi$
$137$	476.767	+	825.784i	0.297321	+	0.514974i	−0.678201	+	0.734876i	$0.737240\pi$
$138$		0			0
$139$	438.423	+	759.370i	0.267529	+	0.463374i	0.968223	−	0.250088i	$-0.0804596\pi$
$139$	438.423	+	759.370i	0.267529	+	0.463374i	−0.700694	+	0.713462i	$0.747126\pi$
$140$		0			0
$141$	−28.7633	−	150.150i	−0.0171795	−	0.0896799i
$142$		0			0
$143$	39.4098	−	68.2597i	0.0230462	−	0.0399173i
$144$		0			0
$145$	−854.438	−	1479.93i	−0.489360	−	0.847596i
$146$		0			0
$147$	−726.796	+	1627.36i	−0.407790	+	0.913076i
$148$		0			0
$149$	−1387.70	+	2403.56i	−0.762983	+	1.32153i	0.178323	+	0.983972i	$0.442933\pi$
$149$	−1387.70	+	2403.56i	−0.762983	+	1.32153i	−0.941306	+	0.337554i	$0.890400\pi$
$150$		0			0
$151$	933.325	+	1616.57i	0.502999	+	0.871221i	0.999994	+	0.00346697i	$0.00110357\pi$
$151$	933.325	+	1616.57i	0.502999	+	0.871221i	−0.496995	+	0.867754i	$0.665563\pi$
$152$		0			0
$153$	453.679	−	3105.65i	0.239724	−	1.64103i
$154$		0			0
$155$	−849.901	+	1472.07i	−0.440424	+	0.762837i
$156$		0			0
$157$	−2541.47			−1.29192			−0.645960	−	0.763371i	$-0.723543\pi$
$157$	−2541.47			−1.29192			−0.645960	+	0.763371i	$0.723543\pi$
$158$		0			0
$159$	−932.939	−	324.072i	−0.465326	−	0.161639i
$160$		0			0
$161$	274.519	+	299.116i	0.134380	+	0.146420i
$162$		0			0
$163$	−170.783	−	295.805i	−0.0820660	−	0.142142i	0.822071	−	0.569385i	$-0.192818\pi$
$163$	−170.783	−	295.805i	−0.0820660	−	0.142142i	−0.904137	+	0.427242i	$0.859485\pi$
$164$		0			0
$165$	−74.1104	−	386.869i	−0.0349666	−	0.182532i
$166$		0			0
$167$	274.336	+	475.164i	0.127118	+	0.220176i	0.922559	−	0.385856i	$-0.126094\pi$
$167$	274.336	+	475.164i	0.127118	+	0.220176i	−0.795441	+	0.606032i	$0.792761\pi$
$168$		0			0
$169$	1011.00	−	1751.10i	0.460171	−	0.797039i
$170$		0			0
$171$	−120.678	−	95.3433i	−0.0539675	−	0.0426379i
$172$		0			0
$173$	2645.56			1.16265			0.581324	−	0.813672i	$-0.302535\pi$
$173$	2645.56			1.16265			0.581324	+	0.813672i	$0.302535\pi$
$174$		0			0
$175$	−666.829	+	148.379i	−0.288043	+	0.0640936i
$176$		0			0
$177$	−320.830	−	1674.79i	−0.136243	−	0.711213i
$178$		0			0
$179$	1423.56	−	2465.69i	0.594426	−	1.02958i	−0.399202	−	0.916863i	$-0.630713\pi$
$179$	1423.56	−	2465.69i	0.594426	−	1.02958i	0.993628	−	0.112713i	$-0.0359540\pi$
$180$		0			0
$181$	3748.80			1.53948			0.769741	−	0.638357i	$-0.220385\pi$
$181$	3748.80			1.53948			0.769741	+	0.638357i	$0.220385\pi$
$182$		0			0
$183$	410.703	+	2143.94i	0.165902	+	0.866037i
$184$		0			0
$185$	−3385.68			−1.34551
$186$		0			0
$187$	692.592			0.270841
$188$		0			0
$189$	2508.87	−	675.916i	0.965572	−	0.260136i
$190$		0			0
$191$	−2806.50			−1.06320			−0.531600	−	0.846995i	$-0.678409\pi$
$191$	−2806.50			−1.06320			−0.531600	+	0.846995i	$0.678409\pi$
$192$		0			0
$193$	−2905.52			−1.08365			−0.541824	−	0.840492i	$-0.682266\pi$
$193$	−2905.52			−1.08365			−0.541824	+	0.840492i	$0.682266\pi$
$194$		0			0
$195$	164.553	+	858.996i	0.0604303	+	0.315456i
$196$		0			0
$197$	1860.10			0.672724			0.336362	−	0.941733i	$-0.390803\pi$
$197$	1860.10			0.672724			0.336362	+	0.941733i	$0.390803\pi$
$198$		0			0
$199$	−2069.28	+	3584.09i	−0.737122	+	1.27673i	0.216665	+	0.976246i	$0.430482\pi$
$199$	−2069.28	+	3584.09i	−0.737122	+	1.27673i	−0.953786	+	0.300486i	$0.902851\pi$
$200$		0			0
$201$	895.873	+	4676.61i	0.314378	+	1.64111i
$202$		0			0
$203$	1681.92	+	1832.62i	0.581516	+	0.633620i
$204$		0			0
$205$	−4604.06			−1.56859
$206$		0			0
$207$	85.5553	−	585.668i	0.0287271	−	0.196651i
$208$		0			0
$209$	16.9690	−	29.3912i	0.00561613	−	0.00972743i
$210$		0			0
$211$	2381.28	+	4124.50i	0.776939	+	1.34570i	0.933698	+	0.358061i	$0.116562\pi$
$211$	2381.28	+	4124.50i	0.776939	+	1.34570i	−0.156759	+	0.987637i	$0.550105\pi$
$212$		0			0
$213$	785.136	+	4098.54i	0.252566	+	1.31844i
$214$		0			0
$215$	−918.331	−	1590.60i	−0.291301	−	0.504548i
$216$		0			0
$217$	742.174	−	2360.30i	0.232175	−	0.738376i
$218$		0			0
$219$	2264.08	+	786.465i	0.698594	+	0.242669i
$220$		0			0
$221$	−1537.82			−0.468076
$222$		0			0
$223$	1550.19	−	2685.01i	0.465510	−	0.806286i	−0.533715	−	0.845665i	$-0.679204\pi$
$223$	1550.19	−	2685.01i	0.465510	−	0.806286i	0.999224	+	0.0393782i	$0.0125377\pi$
$224$		0			0
$225$	781.456	+	617.402i	0.231543	+	0.182934i
$226$		0			0
$227$	2179.62	+	3775.22i	0.637298	+	1.10383i	0.986023	+	0.166608i	$0.0532814\pi$
$227$	2179.62	+	3775.22i	0.637298	+	1.10383i	−0.348725	+	0.937225i	$0.613385\pi$
$228$		0			0
$229$	−1591.33	+	2756.26i	−0.459205	+	0.795366i	−0.998919	−	0.0464821i	$-0.985199\pi$
$229$	−1591.33	+	2756.26i	−0.459205	+	0.795366i	0.539714	+	0.841848i	$0.318532\pi$
$230$		0			0
$231$	227.612	+	526.253i	0.0648302	+	0.149891i
$232$		0			0
$233$	−2474.84	−	4286.55i	−0.695846	−	1.20524i	−0.969895	−	0.243525i	$-0.921696\pi$
$233$	−2474.84	−	4286.55i	−0.695846	−	1.20524i	0.274049	−	0.961716i	$-0.411637\pi$
$234$		0			0
$235$	−187.173	+	324.193i	−0.0519566	+	0.0899915i
$236$		0			0
$237$	387.105	+	2020.75i	0.106098	+	0.553849i
$238$		0			0
$239$	−316.378	−	547.982i	−0.0856266	−	0.148310i	0.820031	−	0.572318i	$-0.193956\pi$
$239$	−316.378	−	547.982i	−0.0856266	−	0.148310i	−0.905658	+	0.424009i	$0.860623\pi$
$240$		0			0
$241$	1350.91	+	2339.84i	0.361078	+	0.625405i	0.988138	−	0.153565i	$-0.0490756\pi$
$241$	1350.91	+	2339.84i	0.361078	+	0.625405i	−0.627061	+	0.778970i	$0.715742\pi$
$242$		0			0
$243$	−3073.17	−	2214.62i	−0.811292	−	0.584642i
$244$		0			0
$245$	3952.37	−	1850.54i	1.03064	−	0.482557i
$246$		0			0
$247$	−37.6776	+	65.2596i	−0.00970596	+	0.0168112i
$248$		0			0
$249$	5148.04	+	1788.26i	1.31022	+	0.455126i
$250$		0			0
$251$	3634.77			0.914043			0.457021	−	0.889456i	$-0.348916\pi$
$251$	3634.77			0.914043			0.457021	+	0.889456i	$0.348916\pi$
$252$		0			0
$253$	130.610			0.0324560
$254$		0			0
$255$	−5813.83	+	5026.24i	−1.42775	+	1.23434i
$256$		0			0
$257$	−1740.66	+	3014.91i	−0.422487	+	0.731770i	−0.996182	−	0.0872995i	$-0.972176\pi$
$257$	−1740.66	+	3014.91i	−0.422487	+	0.731770i	0.573695	+	0.819069i	$0.305510\pi$
$258$		0			0
$259$	4810.54	−	1070.41i	1.15410	−	0.256804i
$260$		0			0
$261$	524.179	−	3588.26i	0.124314	−	0.850988i
$262$		0			0
$263$	−1891.38	−	3275.96i	−0.443450	−	0.768078i	0.554493	−	0.832189i	$-0.312912\pi$
$263$	−1891.38	−	3275.96i	−0.443450	−	0.768078i	−0.997943	+	0.0641105i	$0.979579\pi$
$264$		0			0
$265$	1209.16	+	2094.33i	0.280295	+	0.485485i
$266$		0			0
$267$	−747.307	+	646.071i	−0.171290	+	0.148086i
$268$		0			0
$269$	−2607.09	+	4515.60i	−0.590917	+	1.02350i	0.403192	+	0.915116i	$0.367901\pi$
$269$	−2607.09	+	4515.60i	−0.590917	+	1.02350i	−0.994109	+	0.108384i	$0.965433\pi$
$270$		0			0
$271$	1744.57	+	3021.69i	0.391053	+	0.677323i	0.992589	−	0.121523i	$-0.0387777\pi$
$271$	1744.57	+	3021.69i	0.391053	+	0.677323i	−0.601536	+	0.798846i	$0.705444\pi$
$272$		0			0
$273$	−505.385	−	1168.48i	−0.112041	−	0.259046i
$274$		0			0
$275$	−109.884	+	190.325i	−0.0240955	+	0.0417346i
$276$		0			0
$277$	774.411	+	1341.32i	0.167978	+	0.290946i	0.937709	−	0.347422i	$-0.112943\pi$
$277$	774.411	+	1341.32i	0.167978	+	0.290946i	−0.769731	+	0.638368i	$0.779610\pi$
$278$		0			0
$279$	−3351.73	+	1333.06i	−0.719221	+	0.286052i
$280$		0			0
$281$	981.207	−	1699.50i	0.208306	−	0.360796i	−0.742875	−	0.669430i	$-0.766538\pi$
$281$	981.207	−	1699.50i	0.208306	−	0.360796i	0.951181	+	0.308634i	$0.0998718\pi$
$282$		0			0
$283$	8811.64			1.85088			0.925438	−	0.378899i	$-0.123697\pi$
$283$	8811.64			1.85088			0.925438	+	0.378899i	$0.123697\pi$
$284$		0			0
$285$	70.8531	+	369.866i	0.0147262	+	0.0768735i
$286$		0			0
$287$	6541.68	−	1455.61i	1.34545	−	0.299380i
$288$		0			0
$289$	−4299.94	−	7447.72i	−0.875217	−	1.51592i
$290$		0			0
$291$	−8811.19	−	3060.72i	−1.77499	−	0.616572i
$292$		0			0
$293$	−1715.97	−	2972.15i	−0.342144	−	0.592611i	0.642686	−	0.766129i	$-0.277820\pi$
$293$	−1715.97	−	2972.15i	−0.342144	−	0.592611i	−0.984831	+	0.173518i	$0.944486\pi$
$294$		0			0
$295$	−2087.75	+	3616.09i	−0.412046	+	0.713684i
$296$		0			0
$297$	385.539	−	741.668i	0.0753240	−	0.144902i
$298$		0			0
$299$	−290.003			−0.0560914
$300$		0			0
$301$	1807.69	+	1969.66i	0.346159	+	0.377174i
$302$		0			0
$303$	4385.31	−	3791.24i	0.831450	−	0.718815i
$304$		0			0
$305$	2672.58	−	4629.05i	0.501743	−	0.869045i
$306$		0			0
$307$	6786.87			1.26172			0.630858	−	0.775898i	$-0.282703\pi$
$307$	6786.87			1.26172			0.630858	+	0.775898i	$0.282703\pi$
$308$		0			0
$309$	−6353.41	−	2206.96i	−1.16968	−	0.406310i
$310$		0			0
$311$	−8338.45			−1.52035			−0.760177	−	0.649716i	$-0.774888\pi$
$311$	−8338.45			−1.52035			−0.760177	+	0.649716i	$0.774888\pi$
$312$		0			0
$313$	−7074.59			−1.27757			−0.638786	−	0.769385i	$-0.720563\pi$
$313$	−7074.59			−1.27757			−0.638786	+	0.769385i	$0.720563\pi$
$314$		0			0
$315$	−5729.74	−	2765.71i	−1.02487	−	0.494700i
$316$		0			0
$317$	4147.10			0.734777			0.367388	−	0.930068i	$-0.380252\pi$
$317$	4147.10			0.734777			0.367388	+	0.930068i	$0.380252\pi$
$318$		0			0
$319$	800.220			0.140450
$320$		0			0
$321$	−3324.60	+	2874.22i	−0.578071	+	0.499761i
$322$		0			0
$323$	−662.151			−0.114065
$324$		0			0
$325$	243.984	−	422.593i	0.0416425	−	0.0721269i
$326$		0			0
$327$	1020.81	+	354.594i	0.172632	+	0.0599667i
$328$		0			0
$329$	163.448	−	519.806i	0.0273896	−	0.0871059i
$330$		0			0
$331$	2364.62			0.392663			0.196332	−	0.980538i	$-0.437097\pi$
$331$	2364.62			0.392663			0.196332	+	0.980538i	$0.437097\pi$
$332$		0			0
$333$	−5637.47	−	4453.98i	−0.927722	−	0.732962i
$334$		0			0
$335$	5829.75	−	10097.4i	0.950786	−	1.64681i
$336$		0			0
$337$	1766.23	+	3059.20i	0.285498	+	0.494497i	0.972730	−	0.231941i	$-0.0745077\pi$
$337$	1766.23	+	3059.20i	0.285498	+	0.494497i	−0.687232	+	0.726438i	$0.741174\pi$
$338$		0			0
$339$	−1791.39	+	1548.72i	−0.287006	+	0.248126i
$340$		0			0
$341$	−397.986	−	689.331i	−0.0632027	−	0.109470i
$342$		0			0
$343$	−5030.67	+	3878.92i	−0.791926	+	0.610618i
$344$		0			0
$345$	−1096.38	+	947.855i	−0.171093	+	0.147915i
$346$		0			0
$347$	−2434.74			−0.376668			−0.188334	−	0.982105i	$-0.560309\pi$
$347$	−2434.74			−0.376668			−0.188334	+	0.982105i	$0.560309\pi$
$348$		0			0
$349$	−4613.73	+	7991.21i	−0.707642	+	1.22567i	0.258087	+	0.966122i	$0.416908\pi$
$349$	−4613.73	+	7991.21i	−0.707642	+	1.22567i	−0.965730	+	0.259551i	$0.916426\pi$
$350$		0			0
$351$	−856.042	+	1646.78i	−0.130177	+	0.250424i
$352$		0			0
$353$	−45.2898	−	78.4442i	−0.00682870	−	0.0118277i	0.862591	−	0.505902i	$-0.168840\pi$
$353$	−45.2898	−	78.4442i	−0.00682870	−	0.0118277i	−0.869420	+	0.494075i	$0.835507\pi$
$354$		0			0
$355$	5109.14	−	8849.30i	0.763846	−	1.32302i
$356$		0			0
$357$	6671.50	−	8979.64i	0.989056	−	1.33124i
$358$		0			0
$359$	−3305.71	−	5725.65i	−0.485985	−	0.841751i	0.513885	−	0.857859i	$-0.328206\pi$
$359$	−3305.71	−	5725.65i	−0.485985	−	0.841751i	−0.999870	+	0.0161082i	$0.994872\pi$
$360$		0			0
$361$	3413.28	−	5911.97i	0.497635	−	0.861929i
$362$		0			0
$363$	−6358.90	−	2208.87i	−0.919438	−	0.319382i
$364$		0			0
$365$	−2934.42	−	5082.56i	−0.420806	−	0.728858i
$366$		0			0
$367$	2218.07	+	3841.80i	0.315482	+	0.546432i	0.979540	−	0.201250i	$-0.0645003\pi$
$367$	2218.07	+	3841.80i	0.315482	+	0.546432i	−0.664057	+	0.747682i	$0.731167\pi$
$368$		0			0
$369$	−7666.19	−	6056.80i	−1.08153	−	0.854483i
$370$		0			0
$371$	−2380.18	−	2593.44i	−0.333080	−	0.362924i
$372$		0			0
$373$	4305.45	−	7457.26i	0.597662	−	1.03518i	−0.395503	−	0.918464i	$-0.629430\pi$
$373$	4305.45	−	7457.26i	0.597662	−	1.03518i	0.993165	−	0.116716i	$-0.0372368\pi$
$374$		0			0
$375$	1096.03	+	5721.44i	0.150929	+	0.787878i
$376$		0			0
$377$	−1776.79			−0.242730
$378$		0			0
$379$	6008.89			0.814396			0.407198	−	0.913340i	$-0.366506\pi$
$379$	6008.89			0.814396			0.407198	+	0.913340i	$0.366506\pi$
$380$		0			0
$381$	2785.16	+	14539.0i	0.374509	+	1.95500i
$382$		0			0
$383$	3703.77	−	6415.12i	0.494135	−	0.855867i	−0.505842	−	0.862626i	$-0.668818\pi$
$383$	3703.77	−	6415.12i	0.494135	−	0.855867i	0.999977	+	0.00675896i	$0.00215146\pi$
$384$		0			0
$385$	421.134	−	1339.31i	0.0557480	−	0.177292i
$386$		0			0
$387$	563.377	−	3856.59i	0.0740001	−	0.506567i
$388$		0			0
$389$	7465.35	+	12930.4i	0.973028	+	1.68533i	0.686293	+	0.727325i	$0.259237\pi$
$389$	7465.35	+	12930.4i	0.973028	+	1.68533i	0.286735	+	0.958010i	$0.407430\pi$
$390$		0			0
$391$	−1274.14	−	2206.87i	−0.164798	−	0.285438i
$392$		0			0
$393$	−3436.11	−	1193.59i	−0.441041	−	0.153203i
$394$		0			0
$395$	2519.02	−	4363.08i	0.320876	−	0.555773i
$396$		0			0
$397$	6136.95	+	10629.5i	0.775831	+	1.34378i	0.934327	+	0.356418i	$0.116002\pi$
$397$	6136.95	+	10629.5i	0.775831	+	1.34378i	−0.158496	+	0.987360i	$0.550664\pi$
$398$		0			0
$399$	−217.608	−	503.123i	−0.0273033	−	0.0631270i
$400$		0			0
$401$	−7161.07	+	12403.3i	−0.891787	+	1.54462i	−0.0540564	+	0.998538i	$0.517215\pi$
$401$	−7161.07	+	12403.3i	−0.891787	+	1.54462i	−0.837731	+	0.546083i	$0.816118\pi$
$402$		0			0
$403$	883.679	+	1530.58i	0.109229	+	0.189190i
$404$		0			0
$405$	2146.06	+	9023.71i	0.263306	+	1.10714i
$406$		0			0
$407$	792.710	−	1373.01i	0.0965435	−	0.167218i
$408$		0			0
$409$	−5293.13			−0.639922			−0.319961	−	0.947431i	$-0.603670\pi$
$409$	−5293.13			−0.639922			−0.319961	+	0.947431i	$0.603670\pi$
$410$		0			0
$411$	3748.17	−	3240.41i	0.449839	−	0.388900i
$412$		0			0
$413$	1823.12	−	5797.98i	0.217215	−	0.690799i
$414$		0			0
$415$	−6672.25	−	11556.7i	−0.789224	−	1.36698i
$416$		0			0
$417$	3446.73	−	2979.80i	0.404765	−	0.349932i
$418$		0			0
$419$	−6845.56	−	11856.9i	−0.798156	−	1.38245i	−0.920816	−	0.389998i	$-0.872476\pi$
$419$	−6845.56	−	11856.9i	−0.798156	−	1.38245i	0.122660	−	0.992449i	$-0.460858\pi$
$420$		0			0
$421$	1657.47	−	2870.82i	0.191877	−	0.332340i	−0.753995	−	0.656880i	$-0.771876\pi$
$421$	1657.47	−	2870.82i	0.191877	−	0.332340i	0.945872	+	0.324539i	$0.105209\pi$
$422$		0			0
$423$	−738.147	+	293.579i	−0.0848462	+	0.0337454i
$424$		0			0
$425$	4287.81			0.489386
$426$		0			0
$427$	−2333.83	+	7422.16i	−0.264501	+	0.841179i
$428$		0			0
$429$	−386.882	−	134.390i	−0.0435404	−	0.0151245i
$430$		0			0
$431$	8332.28	−	14431.9i	0.931211	−	1.61290i	0.149955	−	0.988693i	$-0.452087\pi$
$431$	8332.28	−	14431.9i	0.931211	−	1.61290i	0.781255	−	0.624211i	$-0.214580\pi$
$432$		0			0
$433$	13408.2			1.48812			0.744061	−	0.668112i	$-0.232897\pi$
$433$	13408.2			1.48812			0.744061	+	0.668112i	$0.232897\pi$
$434$		0			0
$435$	−6717.29	+	5807.31i	−0.740389	+	0.640090i
$436$		0			0
$437$	−124.869			−0.0136689
$438$		0			0
$439$	−1354.93			−0.147306			−0.0736528	−	0.997284i	$-0.523466\pi$
$439$	−1354.93			−0.147306			−0.0736528	+	0.997284i	$0.523466\pi$
$440$		0			0
$441$	9015.52	+	2118.16i	0.973493	+	0.228718i
$442$		0			0
$443$	−2541.89			−0.272616			−0.136308	−	0.990667i	$-0.543524\pi$
$443$	−2541.89			−0.272616			−0.136308	+	0.990667i	$0.543524\pi$
$444$		0			0
$445$	2418.91			0.257680
$446$		0			0
$447$	13622.9	+	4732.14i	1.44148	+	0.500721i
$448$		0			0
$449$	−4353.76			−0.457609			−0.228805	−	0.973472i	$-0.573482\pi$
$449$	−4353.76			−0.457609			−0.228805	+	0.973472i	$0.573482\pi$
$450$		0			0
$451$	1077.98	−	1867.11i	0.112550	−	0.194942i
$452$		0			0
$453$	7337.48	−	6343.48i	0.761026	−	0.657931i
$454$		0			0
$455$	−935.077	+	2973.78i	−0.0963452	+	0.306402i
$456$		0			0
$457$	−12497.1			−1.27919			−0.639594	−	0.768713i	$-0.720898\pi$
$457$	−12497.1			−1.27919			−0.639594	+	0.768713i	$0.720898\pi$
$458$		0			0
$459$	−16292.8	+	720.871i	−1.65682	+	0.0733058i
$460$		0			0
$461$	5473.38	−	9480.17i	0.552973	−	0.957778i	−0.445085	−	0.895488i	$-0.646826\pi$
$461$	5473.38	−	9480.17i	0.552973	−	0.957778i	0.998058	−	0.0622894i	$-0.0198402\pi$
$462$		0			0
$463$	188.815	+	327.038i	0.0189525	+	0.0328266i	0.875346	−	0.483497i	$-0.160634\pi$
$463$	188.815	+	327.038i	0.0189525	+	0.0328266i	−0.856394	+	0.516324i	$0.827300\pi$
$464$		0			0
$465$	8343.39	+	2898.22i	0.832076	+	0.289036i
$466$		0			0
$467$	−8348.57	−	14460.2i	−0.827250	−	1.43284i	−0.900187	−	0.435503i	$-0.856570\pi$
$467$	−8348.57	−	14460.2i	−0.827250	−	1.43284i	0.0729368	−	0.997337i	$-0.476763\pi$
$468$		0			0
$469$	−5090.82	+	16190.1i	−0.501220	+	1.59400i
$470$		0			0
$471$	2484.60	+	12970.0i	0.243066	+	1.26885i
$472$		0			0
$473$	860.059			0.0836058
$474$		0			0
$475$	105.054	−	181.960i	0.0101479	−	0.0175766i
$476$		0			0
$477$	−741.794	+	5077.94i	−0.0712042	+	0.487428i
$478$		0			0
$479$	−1189.57	−	2060.39i	−0.113471	−	0.196538i	0.803696	−	0.595040i	$-0.202864\pi$
$479$	−1189.57	−	2060.39i	−0.113471	−	0.196538i	−0.917168	+	0.398502i	$0.869530\pi$
$480$		0			0
$481$	−1760.12	+	3048.61i	−0.166849	+	0.288991i
$482$		0			0
$483$	1258.12	−	1693.39i	0.118523	−	0.159528i
$484$		0			0
$485$	11420.0	+	19780.0i	1.06918	+	1.85188i
$486$		0			0
$487$	−633.989	+	1098.10i	−0.0589913	+	0.102176i	−0.894013	−	0.448041i	$-0.852122\pi$
$487$	−633.989	+	1098.10i	−0.0589913	+	0.102176i	0.835022	+	0.550217i	$0.185455\pi$
$488$		0			0
$489$	−1342.64	+	1160.75i	−0.124164	+	0.107344i
$490$		0			0
$491$	1507.12	+	2610.41i	0.138524	+	0.239931i	0.926938	−	0.375214i	$-0.122431\pi$
$491$	1507.12	+	2610.41i	0.138524	+	0.239931i	−0.788414	+	0.615145i	$0.789098\pi$
$492$		0			0
$493$	−7806.38	−	13521.0i	−0.713148	−	1.23521i
$494$		0			0
$495$	−1901.88	+	756.424i	−0.172693	+	0.0686843i
$496$		0			0
$497$	−4461.55	+	14188.8i	−0.402672	+	1.28060i
$498$		0			0
$499$	−4401.90	+	7624.32i	−0.394902	+	0.683991i	−0.993089	−	0.117366i	$-0.962555\pi$
$499$	−4401.90	+	7624.32i	−0.394902	+	0.683991i	0.598186	+	0.801357i	$0.295888\pi$
$500$		0			0
$501$	2156.74	−	1864.57i	0.192327	−	0.166273i
$502$		0			0
$503$	5806.02			0.514667			0.257334	−	0.966323i	$-0.417156\pi$
$503$	5806.02			0.514667			0.257334	+	0.966323i	$0.417156\pi$
$504$		0			0
$505$	−14194.5			−1.25079
$506$		0			0
$507$	−9924.84	−	3447.56i	−0.869384	−	0.301995i
$508$		0			0
$509$	−9982.84	+	17290.8i	−0.869315	+	1.50570i	−0.00661795	+	0.999978i	$0.502107\pi$
$509$	−9982.84	+	17290.8i	−0.869315	+	1.50570i	−0.862697	+	0.505720i	$0.831227\pi$
$510$		0			0
$511$	5776.26	+	6293.82i	0.500053	+	0.544857i
$512$		0			0
$513$	−368.594	+	709.071i	−0.0317228	+	0.0610258i
$514$		0			0
$515$	8234.49	+	14262.6i	0.704573	+	1.22036i
$516$		0			0
$517$	−87.6479	−	151.811i	−0.00745600	−	0.0129142i
$518$		0			0
$519$	−2586.36	−	13501.2i	−0.218745	−	1.14189i
$520$		0			0
$521$	7113.28	−	12320.6i	0.598154	−	1.03603i	−0.394939	−	0.918707i	$-0.629234\pi$
$521$	7113.28	−	12320.6i	0.598154	−	1.03603i	0.993093	−	0.117327i	$-0.0374324\pi$
$522$		0			0
$523$	6978.53	+	12087.2i	0.583461	+	1.01058i	0.995065	+	0.0992212i	$0.0316351\pi$
$523$	6978.53	+	12087.2i	0.583461	+	1.01058i	−0.411605	+	0.911363i	$0.635032\pi$
$524$		0			0
$525$	1409.14	+	3258.01i	0.117142	+	0.270840i
$526$		0			0
$527$	−7764.94	+	13449.3i	−0.641833	+	1.11169i
$528$		0			0
$529$	5843.22	+	10120.8i	0.480252	+	0.831820i
$530$		0			0
$531$	−8233.39	+	3274.62i	−0.672879	+	0.267620i
$532$		0			0
$533$	−2393.52	+	4145.69i	−0.194512	+	0.336904i
$534$		0			0
$535$	10761.2			0.869619
$536$		0			0
$537$	−13975.0	−	4854.45i	−1.12303	−	0.390102i
$538$		0			0
$539$	−174.934	+	2036.11i	−0.0139794	+	0.162711i
$540$		0			0
$541$	−3778.15	−	6543.95i	−0.300251	−	0.520049i	0.675942	−	0.736955i	$-0.263737\pi$
$541$	−3778.15	−	6543.95i	−0.300251	−	0.520049i	−0.976193	+	0.216906i	$0.930404\pi$
$542$		0			0
$543$	−3664.91	−	19131.5i	−0.289643	−	1.51199i
$544$		0			0
$545$	−1323.04	−	2291.58i	−0.103987	−	0.180111i
$546$		0			0
$547$	4631.75	−	8022.42i	0.362046	−	0.627082i	−0.626251	−	0.779621i	$-0.715412\pi$
$547$	4631.75	−	8022.42i	0.362046	−	0.627082i	0.988297	+	0.152539i	$0.0487450\pi$
$548$		0			0
$549$	10539.8	−	4191.93i	0.819357	−	0.325878i
$550$		0			0
$551$	−765.049			−0.0591509
$552$		0			0
$553$	−2199.73	+	6995.70i	−0.169154	+	0.537952i
$554$		0			0
$555$	3309.91	+	17278.3i	0.253150	+	1.32148i
$556$		0			0
$557$	−9660.73	+	16732.9i	−0.734898	+	1.27288i	0.219870	+	0.975529i	$0.429437\pi$
$557$	−9660.73	+	16732.9i	−0.734898	+	1.27288i	−0.954768	+	0.297351i	$0.903897\pi$
$558$		0			0
$559$	−1909.66			−0.144490
$560$		0			0
$561$	−677.094	−	3534.55i	−0.0509571	−	0.266005i
$562$		0			0
$563$	−13468.6			−1.00823			−0.504117	−	0.863635i	$-0.668182\pi$
$563$	−13468.6			−1.00823			−0.504117	+	0.863635i	$0.668182\pi$
$564$		0			0
$565$	5798.44			0.431756
$566$		0			0
$567$	−5902.16	−	12142.8i	−0.437156	−	0.899386i
$568$		0			0
$569$	−2823.33			−0.208014			−0.104007	−	0.994577i	$-0.533166\pi$
$569$	−2823.33			−0.208014			−0.104007	+	0.994577i	$0.533166\pi$
$570$		0			0
$571$	−16811.2			−1.23210			−0.616050	−	0.787707i	$-0.711268\pi$
$571$	−16811.2			−1.23210			−0.616050	+	0.787707i	$0.711268\pi$
$572$		0			0
$573$	2743.70	+	14322.6i	0.200034	+	1.04421i
$574$		0			0
$575$	808.600			0.0586452
$576$		0			0
$577$	12849.4	−	22255.8i	0.927085	−	1.60576i	0.138912	−	0.990305i	$-0.455639\pi$
$577$	12849.4	−	22255.8i	0.927085	−	1.60576i	0.788173	−	0.615454i	$-0.211027\pi$
$578$		0			0
$579$	2840.50	+	14827.9i	0.203881	+	1.06430i
$580$		0			0
$581$	13134.0	+	14310.8i	0.937851	+	1.02188i
$582$		0			0
$583$	−1132.43			−0.0804470
$584$		0			0
$585$	4222.89	−	1679.55i	0.298453	−	0.118702i
$586$		0			0
$587$	1572.98	−	2724.48i	0.110603	−	0.191570i	−0.805411	−	0.592717i	$-0.798055\pi$
$587$	1572.98	−	2724.48i	0.110603	−	0.191570i	0.916013	+	0.401147i	$0.131389\pi$
$588$		0			0
$589$	380.493	+	659.034i	0.0266179	+	0.0461036i
$590$		0			0
$591$	−1818.48	−	9492.75i	−0.126569	−	0.660710i
$592$		0			0
$593$	5615.42	+	9726.19i	0.388866	+	0.673536i	0.992297	−	0.123879i	$-0.0395336\pi$
$593$	5615.42	+	9726.19i	0.388866	+	0.673536i	−0.603431	+	0.797415i	$0.706200\pi$
$594$		0			0
$595$	−26738.2	+	5949.61i	−1.84228	+	0.409933i
$596$		0			0
$597$	20313.9	+	7056.37i	1.39262	+	0.483749i
$598$		0			0
$599$	26625.6			1.81618			0.908091	−	0.418773i	$-0.137540\pi$
$599$	26625.6			1.81618			0.908091	+	0.418773i	$0.137540\pi$
$600$		0			0
$601$	6127.09	−	10612.4i	0.415856	−	0.720283i	−0.579662	−	0.814857i	$-0.696815\pi$
$601$	6127.09	−	10612.4i	0.415856	−	0.720283i	0.995518	+	0.0945737i	$0.0301488\pi$
$602$		0			0
$603$	22990.6	−	9143.92i	1.55265	−	0.617528i
$604$		0			0
$605$	8241.62	+	14274.9i	0.553834	+	0.959268i
$606$		0			0
$607$	1015.04	−	1758.10i	0.0678733	−	0.117560i	−0.830092	−	0.557627i	$-0.811712\pi$
$607$	1015.04	−	1758.10i	0.0678733	−	0.117560i	0.897965	+	0.440067i	$0.145045\pi$
$608$		0			0
$609$	7708.24	−	10375.1i	0.512896	−	0.690343i
$610$		0			0
$611$	194.612	+	337.077i	0.0128857	+	0.0223186i
$612$		0			0
$613$	−328.977	+	569.806i	−0.0216758	+	0.0375436i	−0.876660	−	0.481111i	$-0.840233\pi$
$613$	−328.977	+	569.806i	−0.0216758	+	0.0375436i	0.854984	+	0.518654i	$0.173567\pi$
$614$		0			0
$615$	4501.03	+	23496.1i	0.295120	+	1.54058i
$616$		0			0
$617$	−5043.45	−	8735.51i	−0.329079	−	0.569981i	0.653251	−	0.757142i	$-0.273405\pi$
$617$	−5043.45	−	8735.51i	−0.329079	−	0.569981i	−0.982329	+	0.187161i	$0.940071\pi$
$618$		0			0
$619$	469.313	+	812.875i	0.0304738	+	0.0527822i	0.880860	−	0.473377i	$-0.156965\pi$
$619$	469.313	+	812.875i	0.0304738	+	0.0527822i	−0.850386	+	0.526159i	$0.823632\pi$
$620$		0			0
$621$	−3072.51	+	135.943i	−0.198544	+	0.00878453i
$622$		0			0
$623$	−3436.91	+	764.761i	−0.221023	+	0.0491806i
$624$		0			0
$625$	9437.59	−	16346.4i	0.604005	−	1.04617i
$626$		0			0
$627$	−166.583	−	57.8655i	−0.0106104	−	0.00368568i
$628$		0			0
$629$	−30932.5			−1.96083
$630$		0			0
$631$	13891.3			0.876392			0.438196	−	0.898880i	$-0.355618\pi$
$631$	13891.3			0.876392			0.438196	+	0.898880i	$0.355618\pi$
$632$		0			0
$633$	18720.8	−	16184.7i	1.17549	−	1.01625i
$634$		0			0
$635$	18124.0	−	31391.6i	1.13264	−	1.96179i
$636$		0			0
$637$	388.419	−	4520.93i	0.0241597	−	0.281202i
$638$		0			0
$639$	20148.8	−	8013.66i	1.24738	−	0.496112i
$640$		0			0
$641$	3343.53	+	5791.17i	0.206024	+	0.356845i	0.950459	−	0.310851i	$-0.100614\pi$
$641$	3343.53	+	5791.17i	0.206024	+	0.356845i	−0.744434	+	0.667696i	$0.767281\pi$
$642$		0			0
$643$	−5425.64	−	9397.48i	−0.332762	−	0.576361i	0.650290	−	0.759686i	$-0.274647\pi$
$643$	−5425.64	−	9397.48i	−0.332762	−	0.576361i	−0.983052	+	0.183325i	$0.941314\pi$
$644$		0			0
$645$	−7219.60	+	6241.58i	−0.440731	+	0.381026i
$646$		0			0
$647$	−11880.7	+	20578.0i	−0.721915	+	1.25039i	0.238316	+	0.971188i	$0.423405\pi$
$647$	−11880.7	+	20578.0i	−0.721915	+	1.25039i	−0.960231	+	0.279206i	$0.909929\pi$
$648$		0			0
$649$	−977.636	−	1693.32i	−0.0591303	−	0.102417i
$650$		0			0
$651$	−12771.0	−	1480.10i	−0.768872	−	0.0891085i
$652$		0			0
$653$	−7241.08	+	12541.9i	−0.433944	+	0.751613i	−0.997209	−	0.0746632i	$-0.976212\pi$
$653$	−7241.08	+	12541.9i	−0.433944	+	0.751613i	0.563265	+	0.826277i	$0.309545\pi$
$654$		0			0
$655$	4453.46	+	7713.62i	0.265666	+	0.460147i
$656$		0			0
$657$	1800.20	−	12323.3i	0.106899	−	0.731775i
$658$		0			0
$659$	−8267.96	+	14320.5i	−0.488731	+	0.846507i	−0.999916	−	0.0129636i	$-0.995873\pi$
$659$	−8267.96	+	14320.5i	−0.488731	+	0.846507i	0.511185	+	0.859471i	$0.329207\pi$
$660$		0			0
$661$	−1815.84			−0.106850			−0.0534251	−	0.998572i	$-0.517014\pi$
$661$	−1815.84			−0.106850			−0.0534251	+	0.998572i	$0.517014\pi$
$662$		0			0
$663$	1503.40	+	7848.03i	0.0880654	+	0.459717i
$664$		0			0
$665$	−402.624	+	1280.45i	−0.0234784	+	0.0746670i
$666$		0			0
$667$	−1472.14	−	2549.82i	−0.0854594	−	0.148020i
$668$		0			0
$669$	−15218.1	−	5286.26i	−0.879470	−	0.305499i
$670$		0			0
$671$	1251.50	+	2167.66i	0.0720023	+	0.124712i
$672$		0			0
$673$	10086.0	−	17469.5i	0.577693	−	1.00059i	−0.418050	−	0.908424i	$-0.637286\pi$
$673$	10086.0	−	17469.5i	0.577693	−	1.00059i	0.995743	−	0.0921702i	$-0.0293804\pi$
$674$		0			0
$675$	2386.85	−	4591.64i	0.136104	−	0.261825i
$676$		0			0
$677$	−15541.0			−0.882258			−0.441129	−	0.897444i	$-0.645422\pi$
$677$	−15541.0			−0.882258			−0.441129	+	0.897444i	$0.645422\pi$
$678$		0			0
$679$	−22479.7	−	24493.9i	−1.27053	−	1.38437i
$680$		0			0
$681$	17135.4	−	14814.1i	0.964217	−	0.833596i
$682$		0			0
$683$	7300.36	−	12644.6i	0.408991	−	0.708392i	−0.585786	−	0.810466i	$-0.699214\pi$
$683$	7300.36	−	12644.6i	0.408991	−	0.708392i	0.994777	+	0.102073i	$0.0325476\pi$
$684$		0			0
$685$	−12132.2			−0.676713
$686$		0			0
$687$	15621.9	+	5426.53i	0.867559	+	0.301361i
$688$		0			0
$689$	2514.43			0.139031
$690$		0			0
$691$	7676.25			0.422602			0.211301	−	0.977421i	$-0.432230\pi$
$691$	7676.25			0.422602			0.211301	+	0.977421i	$0.432230\pi$
$692$		0			0
$693$	2463.14	−	1676.06i	0.135017	−	0.0918735i
$694$		0			0
$695$	−11156.5			−0.608906
$696$		0			0
$697$	−42064.0			−2.28592
$698$		0			0
$699$	−19456.3	+	16820.6i	−1.05280	+	0.910177i
$700$		0			0
$701$	−18086.7			−0.974499			−0.487250	−	0.873263i	$-0.662000\pi$
$701$	−18086.7			−0.974499			−0.487250	+	0.873263i	$0.662000\pi$
$702$		0			0
$703$	−757.869	+	1312.67i	−0.0406594	+	0.0704242i
$704$		0			0
$705$	1837.46	+	638.271i	0.0981597	+	0.0340974i
$706$		0			0
$707$	20168.3	−	4487.73i	1.07285	−	0.238725i
$708$		0			0
$709$	−972.392			−0.0515077			−0.0257538	−	0.999668i	$-0.508199\pi$
$709$	−972.392			−0.0515077			−0.0257538	+	0.999668i	$0.508199\pi$
$710$		0			0
$711$	9934.19	−	3951.07i	0.523996	−	0.208406i
$712$		0			0
$713$	−1464.32	+	2536.28i	−0.0769134	+	0.133218i
$714$		0			0
$715$	501.428	+	868.499i	0.0262271	+	0.0454266i
$716$		0			0
$717$	−2487.25	+	2150.31i	−0.129551	+	0.112001i
$718$		0			0
$719$	−235.037	−	407.095i	−0.0121911	−	0.0211156i	0.859866	−	0.510521i	$-0.170547\pi$
$719$	−235.037	−	407.095i	−0.0121911	−	0.0211156i	−0.872057	+	0.489405i	$0.837214\pi$
$720$		0			0
$721$	−16209.2	−	17661.6i	−0.837258	−	0.912277i
$722$		0			0
$723$	10620.4	−	9181.66i	0.546302	−	0.472295i
$724$		0			0
$725$	4954.13			0.253782
$726$		0			0
$727$	461.041	−	798.547i	0.0235201	−	0.0407379i	−0.854026	−	0.520231i	$-0.825846\pi$
$727$	461.041	−	798.547i	0.0235201	−	0.0407379i	0.877546	+	0.479493i	$0.159179\pi$
$728$		0			0
$729$	−8297.60	+	17848.5i	−0.421562	+	0.906800i
$730$		0			0
$731$	−8390.13	−	14532.1i	−0.424515	−	0.735281i
$732$		0			0
$733$	−8092.12	+	14016.0i	−0.407762	+	0.706264i	−0.994639	−	0.103412i	$-0.967024\pi$
$733$	−8092.12	+	14016.0i	−0.407762	+	0.706264i	0.586877	+	0.809676i	$0.300357\pi$
$734$		0			0
$735$	−13307.9	−	18361.2i	−0.667849	−	0.921448i
$736$		0			0
$737$	2729.91	+	4728.35i	0.136442	+	0.236324i
$738$		0			0
$739$	−13769.2	+	23848.9i	−0.685396	+	1.18714i	0.287917	+	0.957655i	$0.407037\pi$
$739$	−13769.2	+	23848.9i	−0.685396	+	1.18714i	−0.973312	+	0.229484i	$0.926296\pi$
$740$		0			0
$741$	369.878	+	128.483i	0.0183371	+	0.00636970i
$742$		0			0
$743$	7569.28	+	13110.4i	0.373741	+	0.647339i	0.990138	−	0.140097i	$-0.0447414\pi$
$743$	7569.28	+	13110.4i	0.373741	+	0.647339i	−0.616396	+	0.787436i	$0.711408\pi$
$744$		0			0
$745$	−17656.3	−	30581.6i	−0.868290	−	1.50392i
$746$		0			0
$747$	4093.29	−	28020.5i	0.200489	−	1.37245i
$748$		0			0
$749$	−15290.0	+	3402.24i	−0.745908	+	0.165975i
$750$		0			0
$751$	5468.05	−	9470.94i	0.265689	−	0.460186i	−0.702055	−	0.712122i	$-0.747734\pi$
$751$	5468.05	−	9470.94i	0.265689	−	0.460186i	0.967744	+	0.251936i	$0.0810674\pi$
$752$		0			0
$753$	−3553.43	−	18549.5i	−0.171971	−	0.897719i
$754$		0			0
$755$	−23750.2			−1.14485
$756$		0			0
$757$	−20595.1			−0.988825			−0.494413	−	0.869227i	$-0.664617\pi$
$757$	−20595.1			−0.988825			−0.494413	+	0.869227i	$0.664617\pi$
$758$		0			0
$759$	−127.687	−	666.549i	−0.00610639	−	0.0318764i
$760$		0			0
$761$	11653.0	−	20183.6i	0.555088	−	0.961441i	−0.442809	−	0.896616i	$-0.646018\pi$
$761$	11653.0	−	20183.6i	0.555088	−	0.961441i	0.997897	−	0.0648245i	$-0.0206488\pi$
$762$		0			0
$763$	2604.35	+	2837.70i	0.123570	+	0.134642i
$764$		0			0
$765$	31334.4	+	24756.3i	1.48091	+	1.17002i
$766$		0			0
$767$	2170.72	+	3759.80i	0.102191	+	0.176999i
$768$		0			0
$769$	6295.02	+	10903.3i	0.295194	+	0.511291i	0.975030	−	0.222073i	$-0.0712824\pi$
$769$	6295.02	+	10903.3i	0.295194	+	0.511291i	−0.679836	+	0.733364i	$0.737949\pi$
$770$		0			0
$771$	17087.9	+	5935.76i	0.798190	+	0.277265i
$772$		0			0
$773$	10030.7	−	17373.7i	0.466727	−	0.808395i	−0.532550	−	0.846398i	$-0.678766\pi$
$773$	10030.7	−	17373.7i	0.466727	−	0.808395i	0.999278	+	0.0380030i	$0.0120996\pi$
$774$		0			0
$775$	−2463.91	−	4267.62i	−0.114202	−	0.197803i
$776$		0			0
$777$	−10165.6	−	23503.5i	−0.469355	−	1.08518i
$778$		0			0
$779$	−1030.60	+	1785.05i	−0.0474005	+	0.0821001i
$780$		0			0
$781$	2392.47	+	4143.88i	0.109615	+	0.189859i
$782$		0			0
$783$	−18824.6	+	832.893i	−0.859180	+	0.0380143i
$784$		0			0
$785$	16168.1	−	28004.0i	0.735115	−	1.27326i
$786$		0			0
$787$	10521.9			0.476578			0.238289	−	0.971194i	$-0.423413\pi$
$787$	10521.9			0.476578			0.238289	+	0.971194i	$0.423413\pi$
$788$		0			0
$789$	−14869.4	+	12855.0i	−0.670929	+	0.580040i
$790$		0			0
$791$	−8238.72	+	1833.23i	−0.370335	+	0.0824047i
$792$		0			0
$793$	−2778.80	−	4813.02i	−0.124436	−	0.215530i
$794$		0			0
$795$	9505.99	−	8218.24i	0.424079	−	0.366630i
$796$		0			0
$797$	−8005.64	−	13866.2i	−0.355802	−	0.616268i	0.631453	−	0.775414i	$-0.282459\pi$
$797$	−8005.64	−	13866.2i	−0.355802	−	0.616268i	−0.987255	+	0.159147i	$0.949126\pi$
$798$		0			0
$799$	−1710.06	+	2961.92i	−0.0757167	+	0.131145i
$800$		0			0
$801$	4027.72	+	3182.16i	0.177668	+	0.140370i
$802$		0			0
$803$	2748.21			0.120775
$804$		0			0
$805$	−5042.32	+	1121.99i	−0.220768	+	0.0491240i
$806$		0			0
$807$	25593.5	+	8890.33i	1.11640	+	0.387800i
$808$		0			0
$809$	967.725	−	1676.15i	0.0420561	−	0.0728434i	−0.844231	−	0.535979i	$-0.819943\pi$
$809$	967.725	−	1676.15i	0.0420561	−	0.0728434i	0.886287	+	0.463136i	$0.153276\pi$
$810$		0			0
$811$	23212.1			1.00504			0.502521	−	0.864565i	$-0.332406\pi$
$811$	23212.1			1.00504			0.502521	+	0.864565i	$0.332406\pi$
$812$		0			0
$813$	13715.2	−	11857.2i	0.591653	−	0.511503i
$814$		0			0
$815$	4345.89			0.186785
$816$		0			0
$817$	−822.258			−0.0352107
$818$		0			0
$819$	−5469.10	+	3721.49i	−0.233340	+	0.158778i
$820$		0			0
$821$	16753.5			0.712183			0.356091	−	0.934451i	$-0.384109\pi$
$821$	16753.5			0.712183			0.356091	+	0.934451i	$0.384109\pi$
$822$		0			0
$823$	12051.8			0.510450			0.255225	−	0.966882i	$-0.417851\pi$
$823$	12051.8			0.510450			0.255225	+	0.966882i	$0.417851\pi$
$824$		0			0
$825$	1078.72	+	374.712i	0.0455227	+	0.0158131i
$826$		0			0
$827$	38044.6			1.59969			0.799843	−	0.600209i	$-0.204916\pi$
$827$	38044.6			1.59969			0.799843	+	0.600209i	$0.204916\pi$
$828$		0			0
$829$	−4691.40	+	8125.74i	−0.196549	+	0.340432i	−0.947407	−	0.320031i	$-0.896307\pi$
$829$	−4691.40	+	8125.74i	−0.196549	+	0.340432i	0.750858	+	0.660463i	$0.229640\pi$
$830$		0			0
$831$	6088.15	−	5263.40i	0.254146	−	0.219718i
$832$		0			0
$833$	36110.0	−	16907.0i	1.50196	−	0.703234i
$834$		0			0
$835$	−6981.00			−0.289326
$836$		0			0
$837$	10079.8	+	15801.8i	0.416260	+	0.652558i
$838$		0			0
$839$	−13946.5	+	24156.0i	−0.573880	+	0.993990i	0.422282	+	0.906465i	$0.361229\pi$
$839$	−13946.5	+	24156.0i	−0.573880	+	0.993990i	−0.996162	+	0.0875253i	$0.972104\pi$
$840$		0			0
$841$	3175.02	+	5499.30i	0.130182	+	0.225483i
$842$		0			0
$843$	−9632.40	−	3345.98i	−0.393544	−	0.136704i
$844$		0			0
$845$	12863.3	+	22280.0i	0.523683	+	0.907046i
$846$		0			0
$847$	−16223.3	−	17676.9i	−0.658132	−	0.717100i
$848$		0			0
$849$	−8614.46	−	44969.0i	−0.348230	−	1.81782i
$850$		0			0
$851$	−5833.29			−0.234974
$852$		0			0
$853$	6676.05	−	11563.3i	0.267976	−	0.464148i	−0.700363	−	0.713787i	$-0.746978\pi$
$853$	6676.05	−	11563.3i	0.267976	−	0.464148i	0.968339	+	0.249639i	$0.0803118\pi$
$854$		0			0
$855$	1818.29	−	723.178i	0.0727300	−	0.0289265i
$856$		0			0
$857$	−21456.5	−	37163.7i	−0.855239	−	1.48132i	−0.876423	−	0.481541i	$-0.840077\pi$
$857$	−21456.5	−	37163.7i	−0.855239	−	1.48132i	0.0211848	−	0.999776i	$-0.493256\pi$
$858$		0			0
$859$	7929.69	−	13734.6i	0.314968	−	0.545541i	−0.664463	−	0.747321i	$-0.731340\pi$
$859$	7929.69	−	13734.6i	0.314968	−	0.545541i	0.979431	+	0.201781i	$0.0646729\pi$
$860$		0			0
$861$	−13823.8	−	31961.5i	−0.547171	−	1.26509i
$862$		0			0
$863$	20096.3	+	34807.7i	0.792682	+	1.37297i	0.924301	+	0.381665i	$0.124649\pi$
$863$	20096.3	+	34807.7i	0.792682	+	1.37297i	−0.131619	+	0.991300i	$0.542017\pi$
$864$		0			0
$865$	−16830.3	+	29151.0i	−0.661558	+	1.14585i
$866$		0			0
$867$	−33804.6	+	29225.2i	−1.32418	+	1.14480i
$868$		0			0
$869$	1179.59	+	2043.11i	0.0460470	+	0.0797558i
$870$		0			0
$871$	−6061.44	−	10498.7i	−0.235803	−	0.408422i
$872$		0			0
$873$	−7005.91	+	47958.9i	−0.271609	+	1.85929i
$874$		0			0
$875$	−6228.19	+	19807.2i	−0.240630	+	0.765263i
$876$		0			0
$877$	25230.1	−	43699.8i	0.971448	−	1.68260i	0.280259	−	0.959924i	$-0.409580\pi$
$877$	25230.1	−	43699.8i	0.971448	−	1.68260i	0.691189	−	0.722674i	$-0.257087\pi$
$878$		0			0
$879$	−13490.4	+	11662.9i	−0.517656	+	0.447530i
$880$		0			0
$881$	−49909.2			−1.90861			−0.954304	−	0.298837i	$-0.903401\pi$
$881$	−49909.2			−1.90861			−0.954304	+	0.298837i	$0.903401\pi$
$882$		0			0
$883$	48516.9			1.84906			0.924532	−	0.381104i	$-0.124456\pi$
$883$	48516.9			1.84906			0.924532	+	0.381104i	$0.124456\pi$
$884$		0			0
$885$	20495.2	+	7119.36i	0.778462	+	0.270412i
$886$		0			0
$887$	−9780.12	+	16939.7i	−0.370219	+	0.641238i	−0.989599	−	0.143853i	$-0.954051\pi$
$887$	−9780.12	+	16939.7i	−0.370219	+	0.641238i	0.619380	+	0.785091i	$0.287384\pi$
$888$		0			0
$889$	−15826.7	+	50332.9i	−0.597088	+	1.89889i
$890$		0			0
$891$	−4161.91	−	1242.47i	−0.156486	−	0.0467164i
$892$		0			0
$893$	83.7956	+	145.138i	0.00314010	+	0.00543882i
$894$		0			0
$895$	18112.6	+	31372.0i	0.676468	+	1.17168i
$896$		0			0
$897$	283.514	+	1479.99i	0.0105532	+	0.0550897i
$898$		0			0
$899$	−8971.59	+	15539.3i	−0.332836	+	0.576488i
$900$		0			0
$901$	11047.2	+	19134.4i	0.408475	+	0.707500i
$902$		0			0
$903$	8284.65	−	11150.9i	0.305311	−	0.410940i
$904$		0			0
$905$	−23848.8	+	41307.4i	−0.875980	+	1.51724i
$906$		0			0
$907$	16519.5	+	28612.7i	0.604766	+	1.04749i	0.992088	+	0.125541i	$0.0400666\pi$
$907$	16519.5	+	28612.7i	0.604766	+	1.04749i	−0.387323	+	0.921944i	$0.626600\pi$
$908$		0			0
$909$	−23635.2	−	18673.4i	−0.862410	−	0.681361i
$910$		0			0
$911$	−9492.76	+	16441.9i	−0.345235	+	0.597965i	−0.985396	−	0.170276i	$-0.945534\pi$
$911$	−9492.76	+	16441.9i	−0.345235	+	0.597965i	0.640161	+	0.768241i	$0.278868\pi$
$912$		0			0
$913$	6248.87			0.226514
$914$		0			0
$915$	−26236.5	−	9113.69i	−0.947925	−	0.329278i
$916$		0			0
$917$	−8766.44	−	9551.91i	−0.315696	−	0.343982i
$918$		0			0
$919$	73.9734	+	128.126i	0.00265523	+	0.00459900i	0.867350	−	0.497699i	$-0.165821\pi$
$919$	73.9734	+	128.126i	0.00265523	+	0.00459900i	−0.864695	+	0.502298i	$0.832488\pi$
$920$		0			0
$921$	−6634.99	−	34635.8i	−0.237384	−	1.23918i
$922$		0			0
$923$	−5312.20	−	9200.99i	−0.189440	−	0.328120i
$924$		0			0
$925$	4907.63	−	8500.27i	0.174445	−	0.302148i
$926$		0			0
$927$	−5051.69	+	34581.3i	−0.178985	+	1.22524i
$928$		0			0
$929$	46909.5			1.65668			0.828338	−	0.560229i	$-0.189287\pi$
$929$	46909.5			1.65668			0.828338	+	0.560229i	$0.189287\pi$
$930$		0			0
$931$	167.245	−	1946.62i	0.00588747	−	0.0685261i
$932$		0			0
$933$	8151.85	+	42554.1i	0.286045	+	1.49320i
$934$		0			0
$935$	−4406.08	+	7631.55i	−0.154111	+	0.266929i
$936$		0			0
$937$	46549.5			1.62295			0.811475	−	0.584387i	$-0.198665\pi$
$937$	46549.5			1.62295			0.811475	+	0.584387i	$0.198665\pi$
$938$		0			0
$939$	6916.28	+	36104.2i	0.240367	+	1.25476i
$940$		0			0
$941$	−2600.39			−0.0900853			−0.0450427	−	0.998985i	$-0.514342\pi$
$941$	−2600.39			−0.0900853			−0.0450427	+	0.998985i	$0.514342\pi$
$942$		0			0
$943$	−7932.48			−0.273931
$944$		0			0
$945$	−8512.90	+	31944.7i	−0.293042	+	1.09964i
$946$		0			0
$947$	−32801.0			−1.12554			−0.562772	−	0.826612i	$-0.690265\pi$
$947$	−32801.0			−1.12554			−0.562772	+	0.826612i	$0.690265\pi$
$948$		0			0
$949$	−6102.07			−0.208727
$950$		0			0
$951$	−4054.30	−	21164.1i	−0.138244	−	0.721655i
$952$		0			0
$953$	34401.7			1.16934			0.584670	−	0.811271i	$-0.301224\pi$
$953$	34401.7			1.16934			0.584670	+	0.811271i	$0.301224\pi$
$954$		0			0
$955$	17854.2	−	30924.3i	0.604971	−	1.04784i
$956$		0			0
$957$	−782.313	−	4083.81i	−0.0264249	−	0.137942i
$958$		0			0
$959$	17238.1	−	3835.71i	0.580445	−	0.129157i
$960$		0			0
$961$	−11943.1			−0.400896
$962$		0			0
$963$	17918.4	+	14156.7i	0.599596	+	0.473721i
$964$		0			0
$965$	18484.1	−	32015.4i	0.616606	−	1.06799i
$966$		0			0
$967$	−1923.97	−	3332.42i	−0.0639822	−	0.110820i	0.832260	−	0.554386i	$-0.187047\pi$
$967$	−1923.97	−	3332.42i	−0.0639822	−	0.110820i	−0.896242	+	0.443565i	$0.853713\pi$
$968$		0			0
$969$	647.334	+	3379.20i	0.0214606	+	0.112028i
$970$		0			0
$971$	19825.2	+	34338.2i	0.655221	+	1.13488i	0.981838	+	0.189719i	$0.0607578\pi$
$971$	19825.2	+	34338.2i	0.655221	+	1.13488i	−0.326617	+	0.945157i	$0.605909\pi$
$972$		0			0
$973$	15851.7	−	3527.22i	0.522284	−	0.116215i
$974$		0			0
$975$	−2395.17	−	832.002i	−0.0786736	−	0.0273286i
$976$		0			0
$977$	−6953.36			−0.227695			−0.113847	−	0.993498i	$-0.536317\pi$
$977$	−6953.36			−0.227695			−0.113847	+	0.993498i	$0.536317\pi$
$978$		0			0
$979$	−566.355	+	980.956i	−0.0184891	+	0.0320240i
$980$		0			0
$981$	811.658	−	5556.20i	0.0264162	−	0.180831i
$982$		0			0
$983$	−24385.9	−	42237.7i	−0.791241	−	1.37047i	−0.925199	−	0.379483i	$-0.876102\pi$
$983$	−24385.9	−	42237.7i	−0.791241	−	1.37047i	0.133957	−	0.990987i	$-0.457231\pi$
$984$		0			0
$985$	−11833.4	+	20496.1i	−0.382786	+	0.663005i
$986$		0			0
$987$	−2812.55	−	325.961i	−0.0907035	−	0.0105121i
$988$		0			0
$989$	−1582.22	−	2740.49i	−0.0508713	−	0.0881117i
$990$		0			0
$991$	−3263.23	+	5652.07i	−0.104601	+	0.181175i	−0.913575	−	0.406670i	$-0.866690\pi$
$991$	−3263.23	+	5652.07i	−0.104601	+	0.181175i	0.808974	+	0.587844i	$0.200023\pi$
$992$		0			0
$993$	−2311.71	−	12067.5i	−0.0738770	−	0.385651i
$994$		0			0
$995$	−26328.3	−	45602.0i	−0.838859	−	1.45295i
$996$		0			0
$997$	264.654	+	458.395i	0.00840691	+	0.0145612i	0.870198	−	0.492702i	$-0.163991\pi$
$997$	264.654	+	458.395i	0.00840691	+	0.0145612i	−0.861791	+	0.507263i	$0.830657\pi$
$998$		0			0
$999$	−17218.9	+	33124.3i	−0.545328	+	1.04906i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.i.a.25.12	✓	48
3.2	odd	2		756.4.i.a.613.21		48
7.2	even	3		252.4.l.a.205.22	yes	48
9.4	even	3		252.4.l.a.193.22	yes	48
9.5	odd	6		756.4.l.a.361.4		48
21.2	odd	6		756.4.l.a.289.4		48
63.23	odd	6		756.4.i.a.37.21		48
63.58	even	3	inner	252.4.i.a.121.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.i.a.25.12	✓	48	1.1	even	1	trivial
252.4.i.a.121.12	yes	48	63.58	even	3	inner
252.4.l.a.193.22	yes	48	9.4	even	3
252.4.l.a.205.22	yes	48	7.2	even	3
756.4.i.a.37.21		48	63.23	odd	6
756.4.i.a.613.21		48	3.2	odd	2
756.4.l.a.289.4		48	21.2	odd	6
756.4.l.a.361.4		48	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.977623 - 5.10336i) q^{3} +(-6.36172 + 11.0188i) q^{5} +(5.55536 - 17.6674i) q^{7} +(-25.0885 + 9.97831i) q^{9} +O(q^{10})\)	\(q+(-0.977623 - 5.10336i) q^{3} +(-6.36172 + 11.0188i) q^{5} +(5.55536 - 17.6674i) q^{7} +(-25.0885 + 9.97831i) q^{9} +(-2.97902 - 5.15982i) q^{11} +(6.61455 + 11.4567i) q^{13} +(62.4524 + 21.6939i) q^{15} +(-58.1225 + 100.671i) q^{17} +(2.84809 + 4.93303i) q^{19} +(-95.5942 - 11.0789i) q^{21} +(-10.9608 + 18.9847i) q^{23} +(-18.4430 - 31.9442i) q^{25} +(75.4500 + 118.281i) q^{27} +(-67.1546 + 116.315i) q^{29} +133.596 q^{31} +(-23.4200 + 20.2474i) q^{33} +(159.333 + 173.609i) q^{35} +(133.049 + 230.447i) q^{37} +(52.0013 - 44.9568i) q^{39} +(180.928 + 313.377i) q^{41} +(-72.1763 + 125.013i) q^{43} +(49.6568 - 339.925i) q^{45} +29.4217 q^{47} +(-281.276 - 196.298i) q^{49} +(570.582 + 198.201i) q^{51} +(95.0340 - 164.604i) q^{53} +75.8068 q^{55} +(22.3907 - 19.3574i) q^{57} +328.174 q^{59} -420.104 q^{61} +(36.9154 + 498.683i) q^{63} -168.320 q^{65} -916.379 q^{67} +(107.601 + 37.3771i) q^{69} -803.107 q^{71} +(-230.631 + 399.464i) q^{73} +(-144.992 + 125.351i) q^{75} +(-107.710 + 23.9670i) q^{77} -395.966 q^{79} +(529.867 - 500.682i) q^{81} +(-524.406 + 908.298i) q^{83} +(-739.518 - 1280.88i) q^{85} +(659.250 + 229.002i) q^{87} +(-95.0573 - 164.644i) q^{89} +(239.157 - 53.2158i) q^{91} +(-130.607 - 681.789i) q^{93} -72.4749 q^{95} +(897.554 - 1554.61i) q^{97} +(126.225 + 99.7265i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9}+O(q^{10}) \) 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9	\( 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9} + 4 q^{11} - 12 q^{13} - 26 q^{15} + 112 q^{17} + 60 q^{19} - 80 q^{21} + 10 q^{23} - 600 q^{25} + 194 q^{29} + 60 q^{31} - 472 q^{33} + 394 q^{35} - 84 q^{37} + 604 q^{39} + 210 q^{41} + 42 q^{43} + 254 q^{45} - 132 q^{47} - 78 q^{49} - 58 q^{51} - 468 q^{53} + 612 q^{55} + 1476 q^{57} - 916 q^{59} - 804 q^{61} - 444 q^{63} + 1656 q^{65} - 588 q^{67} - 28 q^{69} - 2228 q^{71} - 336 q^{73} - 668 q^{75} - 1216 q^{77} - 768 q^{79} - 104 q^{81} + 1024 q^{83} + 360 q^{85} + 2188 q^{87} + 2922 q^{89} - 120 q^{91} - 1292 q^{93} + 2428 q^{95} - 264 q^{97} - 2246 q^{99}+O(q^{100}) \) 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9 + 4 * q^11 - 12 * q^13 - 26 * q^15 + 112 * q^17 + 60 * q^19 - 80 * q^21 + 10 * q^23 - 600 * q^25 + 194 * q^29 + 60 * q^31 - 472 * q^33 + 394 * q^35 - 84 * q^37 + 604 * q^39 + 210 * q^41 + 42 * q^43 + 254 * q^45 - 132 * q^47 - 78 * q^49 - 58 * q^51 - 468 * q^53 + 612 * q^55 + 1476 * q^57 - 916 * q^59 - 804 * q^61 - 444 * q^63 + 1656 * q^65 - 588 * q^67 - 28 * q^69 - 2228 * q^71 - 336 * q^73 - 668 * q^75 - 1216 * q^77 - 768 * q^79 - 104 * q^81 + 1024 * q^83 + 360 * q^85 + 2188 * q^87 + 2922 * q^89 - 120 * q^91 - 1292 * q^93 + 2428 * q^95 - 264 * q^97 - 2246 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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