LMFDB - Embedded newform 76.4.i.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,4,Mod(5,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 16]))

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

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

chi := DirichletCharacter("76.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	76.i (of order $9$, degree $6$, 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:	$4.48414516044$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.1
Character	$\chi$	$=$	76.25
Dual form			76.4.i.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.30252 - 3.02187i) q^{3} +(2.68735 + 15.2407i) q^{5} +(13.2377 - 22.9284i) q^{7} +(39.1169 + 32.8230i) q^{9} +O(q^{10})$	\(q+(-8.30252 - 3.02187i) q^{3} +(2.68735 + 15.2407i) q^{5} +(13.2377 - 22.9284i) q^{7} +(39.1169 + 32.8230i) q^{9} +(17.8101 + 30.8481i) q^{11} +(81.8311 - 29.7841i) q^{13} +(23.7437 - 134.657i) q^{15} +(-60.6275 + 50.8725i) q^{17} +(55.9965 + 61.0196i) q^{19} +(-179.193 + 150.361i) q^{21} +(-0.619729 + 3.51466i) q^{23} +(-107.597 + 39.1620i) q^{25} +(-106.305 - 184.125i) q^{27} +(-14.1436 - 11.8679i) q^{29} +(35.4073 - 61.3272i) q^{31} +(-54.6501 - 309.936i) q^{33} +(385.021 + 140.136i) q^{35} +218.640 q^{37} -769.408 q^{39} +(234.319 + 85.2851i) q^{41} +(-2.56953 - 14.5725i) q^{43} +(-395.125 + 684.377i) q^{45} +(-16.4781 - 13.8267i) q^{47} +(-178.975 - 309.995i) q^{49} +(657.091 - 239.162i) q^{51} +(58.9875 - 334.535i) q^{53} +(-422.285 + 354.339i) q^{55} +(-280.519 - 675.830i) q^{57} +(-215.121 + 180.508i) q^{59} +(-85.9322 + 487.346i) q^{61} +(1270.40 - 462.387i) q^{63} +(673.841 + 1167.13i) q^{65} +(-35.8009 - 30.0405i) q^{67} +(15.7662 - 27.3078i) q^{69} +(-77.7722 - 441.068i) q^{71} +(610.761 + 222.299i) q^{73} +1011.66 q^{75} +943.063 q^{77} +(-946.589 - 344.530i) q^{79} +(86.7835 + 492.173i) q^{81} +(-136.496 + 236.417i) q^{83} +(-938.262 - 787.295i) q^{85} +(81.5641 + 141.273i) q^{87} +(-891.322 + 324.415i) q^{89} +(400.356 - 2270.53i) q^{91} +(-479.292 + 402.174i) q^{93} +(-779.501 + 1017.41i) q^{95} +(-616.533 + 517.333i) q^{97} +(-315.848 + 1791.26i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9	$ 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9} + 42 q^{11} - 42 q^{13} + 78 q^{15} + 30 q^{17} + 282 q^{19} + 198 q^{21} - 300 q^{23} - 276 q^{25} + 219 q^{27} + 216 q^{29} + 30 q^{31} - 597 q^{33} - 636 q^{35} + 60 q^{37} - 2172 q^{39} - 63 q^{41} - 246 q^{43} - 882 q^{45} + 762 q^{47} - 525 q^{49} + 2613 q^{51} + 882 q^{53} + 1350 q^{55} + 924 q^{57} + 2085 q^{59} + 1530 q^{61} + 2424 q^{63} + 1530 q^{65} - 3609 q^{67} + 756 q^{69} - 4962 q^{71} - 2394 q^{73} - 3516 q^{77} - 630 q^{79} - 3723 q^{81} - 2382 q^{83} + 3228 q^{85} - 1110 q^{87} + 2196 q^{89} + 6036 q^{91} + 5010 q^{93} + 6204 q^{95} + 6459 q^{97} + 6189 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9 + 42 * q^11 - 42 * q^13 + 78 * q^15 + 30 * q^17 + 282 * q^19 + 198 * q^21 - 300 * q^23 - 276 * q^25 + 219 * q^27 + 216 * q^29 + 30 * q^31 - 597 * q^33 - 636 * q^35 + 60 * q^37 - 2172 * q^39 - 63 * q^41 - 246 * q^43 - 882 * q^45 + 762 * q^47 - 525 * q^49 + 2613 * q^51 + 882 * q^53 + 1350 * q^55 + 924 * q^57 + 2085 * q^59 + 1530 * q^61 + 2424 * q^63 + 1530 * q^65 - 3609 * q^67 + 756 * q^69 - 4962 * q^71 - 2394 * q^73 - 3516 * q^77 - 630 * q^79 - 3723 * q^81 - 2382 * q^83 + 3228 * q^85 - 1110 * q^87 + 2196 * q^89 + 6036 * q^91 + 5010 * q^93 + 6204 * q^95 + 6459 * q^97 + 6189 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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
$3$	−8.30252	−	3.02187i	−1.59782	−	0.581559i	−0.618841	−	0.785517i	$-0.712397\pi$
$3$	−8.30252	−	3.02187i	−1.59782	−	0.581559i	−0.978980	+	0.203958i	$0.934620\pi$
$4$		0			0
$5$	2.68735	+	15.2407i	0.240364	+	1.36317i	0.831017	+	0.556247i	$0.187759\pi$
$5$	2.68735	+	15.2407i	0.240364	+	1.36317i	−0.590653	+	0.806926i	$0.701130\pi$
$6$		0			0
$7$	13.2377	−	22.9284i	0.714771	−	1.23802i	−0.248277	−	0.968689i	$-0.579864\pi$
$7$	13.2377	−	22.9284i	0.714771	−	1.23802i	0.963048	−	0.269330i	$-0.0868023\pi$
$8$		0			0
$9$	39.1169	+	32.8230i	1.44877	+	1.21567i
$10$		0			0
$11$	17.8101	+	30.8481i	0.488178	+	0.845549i	0.999908	−	0.0135977i	$-0.00432840\pi$
$11$	17.8101	+	30.8481i	0.488178	+	0.845549i	−0.511730	+	0.859147i	$0.670995\pi$
$12$		0			0
$13$	81.8311	−	29.7841i	1.74584	−	0.635433i	0.746292	−	0.665618i	$-0.231832\pi$
$13$	81.8311	−	29.7841i	1.74584	−	0.635433i	0.999544	+	0.0301859i	$0.00960993\pi$
$14$		0			0
$15$	23.7437	−	134.657i	0.408707	−	2.31789i
$16$		0			0
$17$	−60.6275	+	50.8725i	−0.864961	+	0.725788i	−0.963031	−	0.269391i	$-0.913178\pi$
$17$	−60.6275	+	50.8725i	−0.864961	+	0.725788i	0.0980701	+	0.995180i	$0.468733\pi$
$18$		0			0
$19$	55.9965	+	61.0196i	0.676131	+	0.736781i
$19$	55.9965	+	61.0196i	0.676131	+	0.736781i
$20$		0			0
$21$	−179.193	+	150.361i	−1.86206	+	1.56245i
$22$		0			0
$23$	−0.619729	+	3.51466i	−0.00561837	+	0.0318633i	−0.987488	−	0.157694i	$-0.949594\pi$
$23$	−0.619729	+	3.51466i	−0.00561837	+	0.0318633i	0.981870	+	0.189557i	$0.0607052\pi$
$24$		0			0
$25$	−107.597	+	39.1620i	−0.860773	+	0.313296i
$26$		0			0
$27$	−106.305	−	184.125i	−0.757717	−	1.31240i
$28$		0			0
$29$	−14.1436	−	11.8679i	−0.0905653	−	0.0759933i	0.596381	−	0.802702i	$-0.296605\pi$
$29$	−14.1436	−	11.8679i	−0.0905653	−	0.0759933i	−0.686946	+	0.726708i	$0.741049\pi$
$30$		0			0
$31$	35.4073	−	61.3272i	0.205140	−	0.355313i	−0.745037	−	0.667023i	$-0.767568\pi$
$31$	35.4073	−	61.3272i	0.205140	−	0.355313i	0.950177	+	0.311710i	$0.100902\pi$
$32$		0			0
$33$	−54.6501	−	309.936i	−0.288284	−	1.63494i
$34$		0			0
$35$	385.021	+	140.136i	1.85944	+	0.676781i
$36$		0			0
$37$	218.640			0.971464			0.485732	−	0.874108i	$-0.338553\pi$
$37$	218.640			0.971464			0.485732	+	0.874108i	$0.338553\pi$
$38$		0			0
$39$	−769.408			−3.15907
$40$		0			0
$41$	234.319	+	85.2851i	0.892548	+	0.324861i	0.747262	−	0.664529i	$-0.231368\pi$
$41$	234.319	+	85.2851i	0.892548	+	0.324861i	0.145285	+	0.989390i	$0.453590\pi$
$42$		0			0
$43$	−2.56953	−	14.5725i	−0.00911277	−	0.0516811i	0.979912	−	0.199429i	$-0.0639087\pi$
$43$	−2.56953	−	14.5725i	−0.00911277	−	0.0516811i	−0.989025	+	0.147748i	$0.952798\pi$
$44$		0			0
$45$	−395.125	+	684.377i	−1.30893	+	2.26713i
$46$		0			0
$47$	−16.4781	−	13.8267i	−0.0511398	−	0.0429114i	0.616859	−	0.787073i	$-0.288405\pi$
$47$	−16.4781	−	13.8267i	−0.0511398	−	0.0429114i	−0.667999	+	0.744162i	$0.732849\pi$
$48$		0			0
$49$	−178.975	−	309.995i	−0.521794	−	0.903774i
$50$		0			0
$51$	657.091	−	239.162i	1.80414	−	0.656653i
$52$		0			0
$53$	58.9875	−	334.535i	0.152878	−	0.867017i	−0.807821	−	0.589427i	$-0.799353\pi$
$53$	58.9875	−	334.535i	0.152878	−	0.867017i	0.960700	−	0.277589i	$-0.0895354\pi$
$54$		0			0
$55$	−422.285	+	354.339i	−1.03529	+	0.868710i
$56$		0			0
$57$	−280.519	−	675.830i	−0.651854	−	1.57045i
$58$		0			0
$59$	−215.121	+	180.508i	−0.474685	+	0.398308i	−0.848500	−	0.529195i	$-0.822494\pi$
$59$	−215.121	+	180.508i	−0.474685	+	0.398308i	0.373815	+	0.927503i	$0.378049\pi$
$60$		0			0
$61$	−85.9322	+	487.346i	−0.180369	+	1.02292i	0.751394	+	0.659854i	$0.229382\pi$
$61$	−85.9322	+	487.346i	−0.180369	+	1.02292i	−0.931763	+	0.363068i	$0.881729\pi$
$62$		0			0
$63$	1270.40	−	462.387i	2.54056	−	0.924688i
$64$		0			0
$65$	673.841	+	1167.13i	1.28584	+	2.22714i
$66$		0			0
$67$	−35.8009	−	30.0405i	−0.0652803	−	0.0547767i	0.609564	−	0.792737i	$-0.291345\pi$
$67$	−35.8009	−	30.0405i	−0.0652803	−	0.0547767i	−0.674844	+	0.737960i	$0.735789\pi$
$68$		0			0
$69$	15.7662	−	27.3078i	0.0275076	−	0.0476445i
$70$		0			0
$71$	−77.7722	−	441.068i	−0.129998	−	0.737256i	−0.978213	−	0.207604i	$-0.933434\pi$
$71$	−77.7722	−	441.068i	−0.129998	−	0.737256i	0.848215	−	0.529652i	$-0.177678\pi$
$72$		0			0
$73$	610.761	+	222.299i	0.979235	+	0.356412i	0.781543	−	0.623852i	$-0.214433\pi$
$73$	610.761	+	222.299i	0.979235	+	0.356412i	0.197692	+	0.980264i	$0.436655\pi$
$74$		0			0
$75$	1011.66			1.55756
$76$		0			0
$77$	943.063			1.39574
$78$		0			0
$79$	−946.589	−	344.530i	−1.34810	−	0.490667i	−0.435743	−	0.900071i	$-0.643514\pi$
$79$	−946.589	−	344.530i	−1.34810	−	0.490667i	−0.912353	+	0.409404i	$0.865737\pi$
$80$		0			0
$81$	86.7835	+	492.173i	0.119045	+	0.675135i
$82$		0			0
$83$	−136.496	+	236.417i	−0.180510	+	0.312653i	−0.942054	−	0.335460i	$-0.891108\pi$
$83$	−136.496	+	236.417i	−0.180510	+	0.312653i	0.761544	+	0.648113i	$0.224442\pi$
$84$		0			0
$85$	−938.262	−	787.295i	−1.19728	−	1.00464i
$86$		0			0
$87$	81.5641	+	141.273i	0.100512	+	0.174093i
$88$		0			0
$89$	−891.322	+	324.415i	−1.06157	+	0.386381i	−0.813019	−	0.582238i	$-0.802177\pi$
$89$	−891.322	+	324.415i	−1.06157	+	0.386381i	−0.248553	+	0.968618i	$0.579955\pi$
$90$		0			0
$91$	400.356	−	2270.53i	0.461195	−	2.61557i
$92$		0			0
$93$	−479.292	+	402.174i	−0.534412	+	0.448425i
$94$		0			0
$95$	−779.501	+	1017.41i	−0.841843	+	1.09878i
$96$		0			0
$97$	−616.533	+	517.333i	−0.645355	+	0.541517i	−0.905658	−	0.424010i	$-0.860622\pi$
$97$	−616.533	+	517.333i	−0.645355	+	0.541517i	0.260303	+	0.965527i	$0.416178\pi$
$98$		0			0
$99$	−315.848	+	1791.26i	−0.320645	+	1.81847i
$100$		0			0
$101$	1331.52	−	484.634i	1.31180	−	0.477455i	0.410976	−	0.911646i	$-0.365188\pi$
$101$	1331.52	−	484.634i	1.31180	−	0.477455i	0.900821	+	0.434192i	$0.142966\pi$
$102$		0			0
$103$	116.179	+	201.229i	0.111141	+	0.192501i	0.916230	−	0.400652i	$-0.131216\pi$
$103$	116.179	+	201.229i	0.111141	+	0.192501i	−0.805090	+	0.593153i	$0.797883\pi$
$104$		0			0
$105$	−2773.17	−	2326.96i	−2.57746	−	2.16275i
$106$		0			0
$107$	−133.197	+	230.704i	−0.120342	+	0.208439i	−0.919903	−	0.392147i	$-0.871733\pi$
$107$	−133.197	+	230.704i	−0.120342	+	0.208439i	0.799560	+	0.600586i	$0.205066\pi$
$108$		0			0
$109$	−118.085	−	669.694i	−0.103766	−	0.588487i	−0.991706	−	0.128527i	$-0.958975\pi$
$109$	−118.085	−	669.694i	−0.103766	−	0.588487i	0.887940	−	0.459960i	$-0.152136\pi$
$110$		0			0
$111$	−1815.26	−	660.701i	−1.55222	−	0.564963i
$112$		0			0
$113$	−1157.41			−0.963536			−0.481768	−	0.876299i	$-0.660005\pi$
$113$	−1157.41			−0.963536			−0.481768	+	0.876299i	$0.660005\pi$
$114$		0			0
$115$	−55.2314			−0.0447857
$116$		0			0
$117$	4178.58	+	1520.88i	3.30180	+	1.20176i
$118$		0			0
$119$	363.856	+	2063.53i	0.280291	+	1.58961i
$120$		0			0
$121$	31.0985	−	53.8642i	0.0233648	−	0.0404689i
$122$		0			0
$123$	−1687.72	−	1416.16i	−1.23720	−	1.03814i
$124$		0			0
$125$	81.2336	+	140.701i	0.0581260	+	0.100677i
$126$		0			0
$127$	845.783	−	307.840i	0.590954	−	0.215089i	−0.0291952	−	0.999574i	$-0.509294\pi$
$127$	845.783	−	307.840i	0.590954	−	0.215089i	0.620149	+	0.784484i	$0.287072\pi$
$128$		0			0
$129$	−22.7027	+	128.753i	−0.0154950	+	0.0878767i
$130$		0			0
$131$	−172.260	+	144.544i	−0.114889	+	0.0964033i	−0.698422	−	0.715686i	$-0.746114\pi$
$131$	−172.260	+	144.544i	−0.114889	+	0.0964033i	0.583533	+	0.812089i	$0.301670\pi$
$132$		0			0
$133$	2140.35	−	476.152i	1.39543	−	0.310433i
$134$		0			0
$135$	2520.53	−	2114.97i	1.60691	−	1.34835i
$136$		0			0
$137$	463.579	−	2629.09i	0.289097	−	1.63955i	−0.401177	−	0.916001i	$-0.631399\pi$
$137$	463.579	−	2629.09i	0.289097	−	1.63955i	0.690273	−	0.723549i	$-0.257490\pi$
$138$		0			0
$139$	−2557.25	+	930.763i	−1.56045	+	0.567959i	−0.970841	−	0.239726i	$-0.922942\pi$
$139$	−2557.25	+	930.763i	−1.56045	+	0.567959i	−0.589614	+	0.807685i	$0.700720\pi$
$140$		0			0
$141$	95.0268	+	164.591i	0.0567568	+	0.0983056i
$142$		0			0
$143$	2376.20	+	1993.87i	1.38957	+	1.16599i
$144$		0			0
$145$	142.866	−	247.451i	0.0818234	−	0.141722i
$146$		0			0
$147$	549.184	+	3114.58i	0.308135	+	1.74752i
$148$		0			0
$149$	−2237.01	−	814.205i	−1.22995	−	0.447666i	−0.356371	−	0.934344i	$-0.615986\pi$
$149$	−2237.01	−	814.205i	−1.22995	−	0.447666i	−0.873581	+	0.486678i	$0.838208\pi$
$150$		0			0
$151$	−2211.66			−1.19194			−0.595969	−	0.803007i	$-0.703232\pi$
$151$	−2211.66			−1.19194			−0.595969	+	0.803007i	$0.703232\pi$
$152$		0			0
$153$	−4041.35			−2.13545
$154$		0			0
$155$	1029.82	+	374.825i	0.533661	+	0.194237i
$156$		0			0
$157$	62.7494	+	355.869i	0.0318977	+	0.180901i	0.996594	−	0.0824637i	$-0.0262788\pi$
$157$	62.7494	+	355.869i	0.0318977	+	0.180901i	−0.964696	+	0.263365i	$0.915168\pi$
$158$		0			0
$159$	−1500.66	+	2599.23i	−0.748494	+	1.29643i
$160$		0			0
$161$	72.3818	+	60.7355i	0.0354316	+	0.0297306i
$162$		0			0
$163$	966.846	+	1674.63i	0.464596	+	0.804704i	0.999183	−	0.0404091i	$-0.0128661\pi$
$163$	966.846	+	1674.63i	0.464596	+	0.804704i	−0.534587	+	0.845113i	$0.679533\pi$
$164$		0			0
$165$	4576.79	−	1665.82i	2.15941	−	0.785962i
$166$		0			0
$167$	584.320	−	3313.85i	0.270755	−	1.53553i	−0.481376	−	0.876514i	$-0.659863\pi$
$167$	584.320	−	3313.85i	0.270755	−	1.53553i	0.752131	−	0.659014i	$-0.229026\pi$
$168$		0			0
$169$	4126.24	−	3462.33i	1.87813	−	1.57594i
$170$		0			0
$171$	187.568	+	4224.87i	0.0838811	+	1.88938i
$172$		0			0
$173$	1032.83	−	866.644i	0.453898	−	0.380866i	−0.386982	−	0.922087i	$-0.626482\pi$
$173$	1032.83	−	866.644i	0.453898	−	0.380866i	0.840880	+	0.541222i	$0.182038\pi$
$174$		0			0
$175$	−526.413	+	2985.44i	−0.227389	+	1.28959i
$176$		0			0
$177$	2331.52	−	848.605i	0.990101	−	0.360367i
$178$		0			0
$179$	743.775	+	1288.26i	0.310572	+	0.537926i	0.978486	−	0.206312i	$-0.0661462\pi$
$179$	743.775	+	1288.26i	0.310572	+	0.537926i	−0.667915	+	0.744238i	$0.732813\pi$
$180$		0			0
$181$	−515.271	−	432.364i	−0.211601	−	0.177554i	0.530827	−	0.847480i	$-0.321881\pi$
$181$	−515.271	−	432.364i	−0.211601	−	0.177554i	−0.742428	+	0.669926i	$0.766326\pi$
$182$		0			0
$183$	2186.15	−	3786.52i	0.883086	−	1.52955i
$184$		0			0
$185$	587.562	+	3332.23i	0.233505	+	1.32427i
$186$		0			0
$187$	−2649.10	−	964.194i	−1.03594	−	0.377053i
$188$		0			0
$189$	−5628.94			−2.16638
$190$		0			0
$191$	5207.47			1.97277			0.986386	−	0.164449i	$-0.0525847\pi$
$191$	5207.47			1.97277			0.986386	+	0.164449i	$0.0525847\pi$
$192$		0			0
$193$	−776.597	−	282.658i	−0.289641	−	0.105421i	0.193114	−	0.981176i	$-0.438141\pi$
$193$	−776.597	−	282.658i	−0.289641	−	0.105421i	−0.482754	+	0.875756i	$0.660364\pi$
$194$		0			0
$195$	−2067.67	−	11726.3i	−0.759328	−	4.30636i
$196$		0			0
$197$	−1220.88	+	2114.63i	−0.441545	+	0.764779i	−0.997804	−	0.0662302i	$-0.978903\pi$
$197$	−1220.88	+	2114.63i	−0.441545	+	0.764779i	0.556259	+	0.831009i	$0.312236\pi$
$198$		0			0
$199$	2031.00	+	1704.21i	0.723485	+	0.607076i	0.928347	−	0.371715i	$-0.121230\pi$
$199$	2031.00	+	1704.21i	0.723485	+	0.607076i	−0.204862	+	0.978791i	$0.565675\pi$
$200$		0			0
$201$	206.459	+	357.598i	0.0724503	+	0.125488i
$202$		0			0
$203$	−459.340	+	167.186i	−0.158815	+	0.0578038i
$204$		0			0
$205$	−670.110	+	3800.38i	−0.228305	+	1.29478i
$206$		0			0
$207$	−139.603	+	117.141i	−0.0468749	+	0.0393327i
$208$		0			0
$209$	−885.029	+	2814.15i	−0.292913	+	0.931382i
$210$		0			0
$211$	−1430.18	+	1200.07i	−0.466625	+	0.391545i	−0.845562	−	0.533878i	$-0.820734\pi$
$211$	−1430.18	+	1200.07i	−0.466625	+	0.391545i	0.378937	+	0.925423i	$0.376290\pi$
$212$		0			0
$213$	−687.145	+	3896.99i	−0.221044	+	1.25360i
$214$		0			0
$215$	215.191	−	78.3230i	0.0682599	−	0.0248446i
$216$		0			0
$217$	−937.424	−	1623.67i	−0.293256	−	0.507934i
$218$		0			0
$219$	−4399.10	−	3691.28i	−1.35737	−	1.13897i
$220$		0			0
$221$	−3446.03	+	5968.69i	−1.04889	+	1.81673i
$222$		0			0
$223$	−159.839	−	906.495i	−0.0479984	−	0.272212i	0.951358	−	0.308088i	$-0.0996891\pi$
$223$	−159.839	−	906.495i	−0.0479984	−	0.272212i	−0.999356	+	0.0358756i	$0.988578\pi$
$224$		0			0
$225$	−5494.26	−	1999.75i	−1.62793	−	0.592517i
$226$		0			0
$227$	−1036.03			−0.302925			−0.151463	−	0.988463i	$-0.548398\pi$
$227$	−1036.03			−0.302925			−0.151463	+	0.988463i	$0.548398\pi$
$228$		0			0
$229$	−2109.77			−0.608810			−0.304405	−	0.952543i	$-0.598458\pi$
$229$	−2109.77			−0.608810			−0.304405	+	0.952543i	$0.598458\pi$
$230$		0			0
$231$	−7829.80	−	2849.81i	−2.23014	−	0.811706i
$232$		0			0
$233$	−887.489	−	5033.20i	−0.249534	−	1.41518i	−0.809723	−	0.586812i	$-0.800383\pi$
$233$	−887.489	−	5033.20i	−0.249534	−	1.41518i	0.560190	−	0.828364i	$-0.310728\pi$
$234$		0			0
$235$	166.447	−	288.295i	0.0462035	−	0.0800268i
$236$		0			0
$237$	6817.95	+	5720.94i	1.86866	+	1.56799i
$238$		0			0
$239$	−3131.50	−	5423.92i	−0.847531	−	1.46797i	−0.883405	−	0.468610i	$-0.844755\pi$
$239$	−3131.50	−	5423.92i	−0.847531	−	1.46797i	0.0358743	−	0.999356i	$-0.488578\pi$
$240$		0			0
$241$	3226.40	−	1174.31i	0.862369	−	0.313877i	0.127296	−	0.991865i	$-0.459370\pi$
$241$	3226.40	−	1174.31i	0.862369	−	0.313877i	0.735073	+	0.677988i	$0.237148\pi$
$242$		0			0
$243$	−230.057	+	1304.72i	−0.0607332	+	0.344435i
$244$		0			0
$245$	4243.57	−	3560.78i	1.10658	−	0.928531i
$246$		0			0
$247$	6399.67	+	3325.49i	1.64859	+	0.856664i
$248$		0			0
$249$	1847.68	−	1550.39i	0.470249	−	0.394586i
$250$		0			0
$251$	357.213	−	2025.85i	0.0898290	−	0.509445i	−0.906381	−	0.422462i	$-0.861166\pi$
$251$	357.213	−	2025.85i	0.0898290	−	0.509445i	0.996210	−	0.0869837i	$-0.0277228\pi$
$252$		0			0
$253$	−119.458	+	43.4791i	−0.0296848	+	0.0108044i
$254$		0			0
$255$	5410.83	+	9371.84i	1.32878	+	2.30152i
$256$		0			0
$257$	−5911.98	−	4960.74i	−1.43494	−	1.20406i	−0.942720	−	0.333585i	$-0.891742\pi$
$257$	−5911.98	−	4960.74i	−1.43494	−	1.20406i	−0.492219	−	0.870471i	$-0.663814\pi$
$258$		0			0
$259$	2894.30	−	5013.07i	0.694374	−	1.20269i
$260$		0			0
$261$	−163.714	−	928.468i	−0.0388262	−	0.220194i
$262$		0			0
$263$	−4650.63	−	1692.69i	−1.09038	−	0.396866i	−0.266618	−	0.963802i	$-0.585906\pi$
$263$	−4650.63	−	1692.69i	−1.09038	−	0.396866i	−0.823762	+	0.566936i	$0.808129\pi$
$264$		0			0
$265$	5257.08			1.21864
$266$		0			0
$267$	8380.55			1.92090
$268$		0			0
$269$	6048.27	+	2201.39i	1.37089	+	0.498964i	0.919404	−	0.393314i	$-0.128671\pi$
$269$	6048.27	+	2201.39i	1.37089	+	0.498964i	0.451487	+	0.892278i	$0.350894\pi$
$270$		0			0
$271$	1278.80	+	7252.41i	0.286647	+	1.62565i	0.699343	+	0.714786i	$0.253476\pi$
$271$	1278.80	+	7252.41i	0.286647	+	1.62565i	−0.412696	+	0.910869i	$0.635413\pi$
$272$		0			0
$273$	−10185.2	+	17641.3i	−2.25801	+	3.91099i
$274$		0			0
$275$	−3124.38	−	2621.67i	−0.685117	−	0.574881i
$276$		0			0
$277$	−1143.19	−	1980.07i	−0.247970	−	0.429497i	0.714992	−	0.699132i	$-0.246430\pi$
$277$	−1143.19	−	1980.07i	−0.247970	−	0.429497i	−0.962963	+	0.269635i	$0.913097\pi$
$278$		0			0
$279$	3397.96	−	1236.76i	0.729143	−	0.265386i
$280$		0			0
$281$	−945.774	+	5363.75i	−0.200784	+	1.13870i	0.703155	+	0.711037i	$0.251774\pi$
$281$	−945.774	+	5363.75i	−0.200784	+	1.13870i	−0.903938	+	0.427663i	$0.859337\pi$
$282$		0			0
$283$	−4815.09	+	4040.34i	−1.01140	+	0.848669i	−0.988523	−	0.151070i	$-0.951728\pi$
$283$	−4815.09	+	4040.34i	−1.01140	+	0.848669i	−0.0228806	+	0.999738i	$0.507284\pi$
$284$		0			0
$285$	9546.30	−	6091.51i	1.98412	−	1.26607i
$286$		0			0
$287$	5057.30	−	4243.58i	1.04015	−	0.872790i
$288$		0			0
$289$	234.548	−	1330.19i	0.0477403	−	0.270749i
$290$		0			0
$291$	6682.09	−	2432.08i	1.34609	−	0.489935i
$292$		0			0
$293$	−2633.67	−	4561.64i	−0.525121	−	0.909536i	−0.999572	−	0.0292541i	$-0.990687\pi$
$293$	−2633.67	−	4561.64i	−0.525121	−	0.909536i	0.474451	−	0.880282i	$-0.342647\pi$
$294$		0			0
$295$	−3329.19	−	2793.52i	−0.657060	−	0.551339i
$296$		0			0
$297$	3786.60	−	6558.59i	0.739801	−	1.28137i
$298$		0			0
$299$	53.9678	+	306.067i	0.0104383	+	0.0591983i
$300$		0			0
$301$	−368.140	−	133.992i	−0.0704957	−	0.0256583i
$302$		0			0
$303$	−12519.5			−2.37368
$304$		0			0
$305$	−7658.44			−1.43777
$306$		0			0
$307$	5915.83	+	2153.18i	1.09978	+	0.400289i	0.827237	−	0.561853i	$-0.189911\pi$
$307$	5915.83	+	2153.18i	1.09978	+	0.400289i	0.272548	+	0.962142i	$0.412134\pi$
$308$		0			0
$309$	−356.495	−	2021.78i	−0.0656320	−	0.372218i
$310$		0			0
$311$	4719.46	−	8174.34i	0.860502	−	1.49043i	−0.0109437	−	0.999940i	$-0.503484\pi$
$311$	4719.46	−	8174.34i	0.860502	−	1.49043i	0.871445	−	0.490493i	$-0.163183\pi$
$312$		0			0
$313$	765.034	+	641.939i	0.138154	+	0.115925i	0.709246	−	0.704961i	$-0.249036\pi$
$313$	765.034	+	641.939i	0.138154	+	0.115925i	−0.571092	+	0.820886i	$0.693480\pi$
$314$		0			0
$315$	10461.1	+	18119.2i	1.87117	+	3.24096i
$316$		0			0
$317$	−5779.46	+	2103.55i	−1.02400	+	0.372704i	−0.798792	−	0.601608i	$-0.794527\pi$
$317$	−5779.46	+	2103.55i	−1.02400	+	0.372704i	−0.225204	+	0.974312i	$0.572305\pi$
$318$		0			0
$319$	114.202	−	647.669i	0.0200441	−	0.113676i
$320$		0			0
$321$	1803.03	−	1512.92i	0.313505	−	0.263062i
$322$		0			0
$323$	−6499.15	−	850.779i	−1.11957	−	0.146559i
$324$		0			0
$325$	−7638.35	+	6409.33i	−1.30369	+	1.09393i
$326$		0			0
$327$	−1043.32	+	5916.98i	−0.176440	+	1.00064i
$328$		0			0
$329$	−535.158	+	194.782i	−0.0896784	+	0.0326403i
$330$		0			0
$331$	−3272.89	−	5668.80i	−0.543487	−	0.941346i	−0.998700	−	0.0509643i	$-0.983771\pi$
$331$	−3272.89	−	5668.80i	−0.543487	−	0.941346i	0.455214	−	0.890382i	$-0.349563\pi$
$332$		0			0
$333$	8552.51	+	7176.41i	1.40743	+	1.18098i
$334$		0			0
$335$	361.630	−	626.362i	0.0589790	−	0.102155i
$336$		0			0
$337$	−1149.51	−	6519.18i	−0.185809	−	1.05378i	−0.924911	−	0.380183i	$-0.875861\pi$
$337$	−1149.51	−	6519.18i	−0.185809	−	1.05378i	0.739102	−	0.673593i	$-0.235250\pi$
$338$		0			0
$339$	9609.38	+	3497.53i	1.53956	+	0.560353i
$340$		0			0
$341$	2522.43			0.400579
$342$		0			0
$343$	−395.830			−0.0623115
$344$		0			0
$345$	458.560	+	166.902i	0.0715595	+	0.0260455i
$346$		0			0
$347$	856.361	+	4856.67i	0.132484	+	0.751353i	0.976579	+	0.215159i	$0.0690271\pi$
$347$	856.361	+	4856.67i	0.132484	+	0.751353i	−0.844095	+	0.536193i	$0.819862\pi$
$348$		0			0
$349$	1654.37	−	2865.46i	0.253744	−	0.439497i	−0.710810	−	0.703384i	$-0.751671\pi$
$349$	1654.37	−	2865.46i	0.253744	−	0.439497i	0.964554	+	0.263887i	$0.0850047\pi$
$350$		0			0
$351$	−14183.0	−	11901.0i	−2.15679	−	1.80977i
$352$		0			0
$353$	−3540.92	−	6133.06i	−0.533893	−	0.924730i	−0.999216	−	0.0395893i	$-0.987395\pi$
$353$	−3540.92	−	6133.06i	−0.533893	−	0.924730i	0.465323	−	0.885141i	$-0.345938\pi$
$354$		0			0
$355$	6513.20	−	2370.61i	0.973760	−	0.354420i
$356$		0			0
$357$	3214.80	−	18232.0i	0.476597	−	2.70292i
$358$		0			0
$359$	−2446.10	+	2052.52i	−0.359611	+	0.301749i	−0.804636	−	0.593769i	$-0.797639\pi$
$359$	−2446.10	+	2052.52i	−0.359611	+	0.301749i	0.445025	+	0.895518i	$0.353195\pi$
$360$		0			0
$361$	−587.774	+	6833.77i	−0.0856938	+	0.996322i
$362$		0			0
$363$	−420.966	+	353.233i	−0.0608678	+	0.0510741i
$364$		0			0
$365$	−1746.67	+	9905.84i	−0.250479	+	1.42054i
$366$		0			0
$367$	192.947	−	70.2268i	0.0274434	−	0.00998859i	−0.328262	−	0.944587i	$-0.606463\pi$
$367$	192.947	−	70.2268i	0.0274434	−	0.00998859i	0.355705	+	0.934598i	$0.384241\pi$
$368$		0			0
$369$	6366.52	+	11027.1i	0.898178	+	1.55569i
$370$		0			0
$371$	−6889.50	−	5780.97i	−0.964110	−	0.808984i
$372$		0			0
$373$	3895.03	−	6746.39i	0.540689	−	0.936501i	−0.458175	−	0.888862i	$-0.651497\pi$
$373$	3895.03	−	6746.39i	0.540689	−	0.936501i	0.998865	−	0.0476396i	$-0.0151699\pi$
$374$		0			0
$375$	−249.264	−	1413.65i	−0.0343252	−	0.194668i
$376$		0			0
$377$	−1510.86	−	549.907i	−0.206401	−	0.0751238i
$378$		0			0
$379$	−11635.5			−1.57698			−0.788491	−	0.615046i	$-0.789138\pi$
$379$	−11635.5			−1.57698			−0.788491	+	0.615046i	$0.789138\pi$
$380$		0			0
$381$	−7952.38			−1.06932
$382$		0			0
$383$	−2403.51	−	874.805i	−0.320662	−	0.116711i	0.176674	−	0.984269i	$-0.443466\pi$
$383$	−2403.51	−	874.805i	−0.320662	−	0.116711i	−0.497336	+	0.867558i	$0.665688\pi$
$384$		0			0
$385$	2534.34	+	14373.0i	0.335486	+	1.90264i
$386$		0			0
$387$	377.801	−	654.371i	0.0496246	−	0.0859523i
$388$		0			0
$389$	−6708.11	−	5628.77i	−0.874330	−	0.733650i	0.0906751	−	0.995881i	$-0.471098\pi$
$389$	−6708.11	−	5628.77i	−0.874330	−	0.733650i	−0.965005	+	0.262230i	$0.915542\pi$
$390$		0			0
$391$	−141.227	−	244.612i	−0.0182664	−	0.0316383i
$392$		0			0
$393$	1866.99	−	679.528i	0.239636	−	0.0872205i
$394$		0			0
$395$	2707.08	−	15352.6i	0.344830	−	1.95563i
$396$		0			0
$397$	−6949.49	+	5831.31i	−0.878551	+	0.737192i	−0.965881	−	0.258987i	$-0.916611\pi$
$397$	−6949.49	+	5831.31i	−0.878551	+	0.737192i	0.0873293	+	0.996179i	$0.472167\pi$
$398$		0			0
$399$	−19209.2	−	2514.60i	−2.41018	−	0.315507i
$400$		0			0
$401$	−111.258	+	93.3563i	−0.0138552	+	0.0116259i	−0.649689	−	0.760200i	$-0.725101\pi$
$401$	−111.258	+	93.3563i	−0.0138552	+	0.0116259i	0.635834	+	0.771826i	$0.280656\pi$
$402$		0			0
$403$	1070.84	−	6073.05i	0.132363	−	0.750670i
$404$		0			0
$405$	−7267.87	+	2645.29i	−0.891712	+	0.324556i
$406$		0			0
$407$	3894.00	+	6744.61i	0.474247	+	0.821420i
$408$		0			0
$409$	2892.12	+	2426.77i	0.349648	+	0.293389i	0.800649	−	0.599134i	$-0.204488\pi$
$409$	2892.12	+	2426.77i	0.349648	+	0.293389i	−0.451001	+	0.892523i	$0.648933\pi$
$410$		0			0
$411$	−11793.6	+	20427.2i	−1.41542	+	2.45158i
$412$		0			0
$413$	1291.05	+	7321.92i	0.153822	+	0.872368i
$414$		0			0
$415$	−3969.99	−	1444.96i	−0.469588	−	0.170916i
$416$		0			0
$417$	24044.3			2.82363
$418$		0			0
$419$	5805.97			0.676945			0.338473	−	0.940976i	$-0.390090\pi$
$419$	5805.97			0.676945			0.338473	+	0.940976i	$0.390090\pi$
$420$		0			0
$421$	6140.79	+	2235.07i	0.710888	+	0.258742i	0.672053	−	0.740503i	$-0.265413\pi$
$421$	6140.79	+	2235.07i	0.710888	+	0.258742i	0.0388357	+	0.999246i	$0.487635\pi$
$422$		0			0
$423$	−190.736	−	1081.72i	−0.0219241	−	0.124338i
$424$		0			0
$425$	4531.05	−	7848.00i	0.517148	−	0.895727i
$426$		0			0
$427$	10036.5	+	8421.65i	1.13747	+	0.954455i
$428$		0			0
$429$	−13703.3	−	23734.7i	−1.54219	−	2.67115i
$430$		0			0
$431$	4299.62	−	1564.94i	0.480524	−	0.174896i	−0.0903900	−	0.995906i	$-0.528811\pi$
$431$	4299.62	−	1564.94i	0.480524	−	0.174896i	0.570914	+	0.821010i	$0.306589\pi$
$432$		0			0
$433$	412.232	−	2337.88i	0.0457520	−	0.259472i	−0.953349	−	0.301871i	$-0.902389\pi$
$433$	412.232	−	2337.88i	0.0457520	−	0.259472i	0.999101	+	0.0423985i	$0.0134999\pi$
$434$		0			0
$435$	−1933.91	+	1622.75i	−0.213159	+	0.178862i
$436$		0			0
$437$	−249.166	+	158.993i	−0.0272751	+	0.0174043i
$438$		0			0
$439$	−7433.59	+	6237.52i	−0.808169	+	0.678134i	−0.950170	−	0.311732i	$-0.899091\pi$
$439$	−7433.59	+	6237.52i	−0.808169	+	0.678134i	0.142001	+	0.989866i	$0.454646\pi$
$440$		0			0
$441$	3173.98	−	18000.5i	0.342725	−	1.94369i
$442$		0			0
$443$	9617.55	−	3500.50i	1.03148	−	0.375426i	0.229833	−	0.973230i	$-0.426182\pi$
$443$	9617.55	−	3500.50i	1.03148	−	0.375426i	0.801642	+	0.597804i	$0.203960\pi$
$444$		0			0
$445$	−7339.61	−	12712.6i	−0.781867	−	1.35423i
$446$		0			0
$447$	16112.4	+	13519.9i	1.70490	+	1.43058i
$448$		0			0
$449$	−9144.54	+	15838.8i	−0.961152	+	1.66476i	−0.241537	+	0.970392i	$0.577652\pi$
$449$	−9144.54	+	15838.8i	−0.961152	+	1.66476i	−0.719615	+	0.694373i	$0.755682\pi$
$450$		0			0
$451$	1542.37	+	8747.22i	0.161036	+	0.913282i
$452$		0			0
$453$	18362.4	+	6683.36i	1.90450	+	0.693182i
$454$		0			0
$455$	35680.5			3.67633
$456$		0			0
$457$	−4252.19			−0.435249			−0.217625	−	0.976033i	$-0.569831\pi$
$457$	−4252.19			−0.435249			−0.217625	+	0.976033i	$0.569831\pi$
$458$		0			0
$459$	15811.9	+	5755.06i	1.60792	+	0.585236i
$460$		0			0
$461$	649.180	+	3681.68i	0.0655864	+	0.371959i	0.999881	+	0.0154558i	$0.00491992\pi$
$461$	649.180	+	3681.68i	0.0655864	+	0.371959i	−0.934294	+	0.356503i	$0.883969\pi$
$462$		0			0
$463$	4322.00	−	7485.92i	0.433824	−	0.751404i	−0.563375	−	0.826201i	$-0.690497\pi$
$463$	4322.00	−	7485.92i	0.433824	−	0.751404i	0.997199	+	0.0747967i	$0.0238308\pi$
$464$		0			0
$465$	−7417.46	−	6223.98i	−0.739734	−	0.620710i
$466$		0			0
$467$	388.026	+	672.081i	0.0384490	+	0.0665957i	0.884610	−	0.466332i	$-0.154425\pi$
$467$	388.026	+	672.081i	0.0384490	+	0.0665957i	−0.846161	+	0.532928i	$0.821092\pi$
$468$		0			0
$469$	−1162.71	+	423.190i	−0.114475	+	0.0416655i
$470$		0			0
$471$	554.413	−	3144.23i	0.0542378	−	0.307598i
$472$		0			0
$473$	403.770	−	338.803i	0.0392502	−	0.0329349i
$474$		0			0
$475$	−8414.68	−	4372.56i	−0.812825	−	0.422372i
$476$		0			0
$477$	13287.8	−	11149.8i	1.27549	−	1.07026i
$478$		0			0
$479$	−3065.58	+	17385.7i	−0.292421	+	1.65840i	0.385081	+	0.922883i	$0.374173\pi$
$479$	−3065.58	+	17385.7i	−0.292421	+	1.65840i	−0.677503	+	0.735520i	$0.736938\pi$
$480$		0			0
$481$	17891.5	−	6511.99i	1.69602	−	0.617300i
$482$		0			0
$483$	−417.416	−	722.986i	−0.0393232	−	0.0681098i
$484$		0			0
$485$	−9541.37	−	8006.16i	−0.893302	−	0.749569i
$486$		0			0
$487$	−4827.82	+	8362.03i	−0.449219	+	0.778069i	−0.998335	−	0.0576763i	$-0.981631\pi$
$487$	−4827.82	+	8362.03i	−0.449219	+	0.778069i	0.549117	+	0.835746i	$0.314964\pi$
$488$		0			0
$489$	−2966.75	−	16825.3i	−0.274358	−	1.55596i
$490$		0			0
$491$	234.605	+	85.3893i	0.0215633	+	0.00784840i	0.352779	−	0.935707i	$-0.385237\pi$
$491$	234.605	+	85.3893i	0.0215633	+	0.00784840i	−0.331216	+	0.943555i	$0.607459\pi$
$492$		0			0
$493$	1461.24			0.133490
$494$		0			0
$495$	−28148.9			−2.55596
$496$		0			0
$497$	−11142.5	−	4055.55i	−1.00566	−	0.366029i
$498$		0			0
$499$	−366.242	−	2077.06i	−0.0328562	−	0.186337i	0.963963	−	0.266038i	$-0.0857146\pi$
$499$	−366.242	−	2077.06i	−0.0328562	−	0.186337i	−0.996819	+	0.0797009i	$0.974603\pi$
$500$		0			0
$501$	−14865.3	+	25747.5i	−1.32562	+	2.29604i
$502$		0			0
$503$	3811.57	+	3198.29i	0.337872	+	0.283508i	0.795898	−	0.605430i	$-0.206999\pi$
$503$	3811.57	+	3198.29i	0.337872	+	0.283508i	−0.458026	+	0.888939i	$0.651443\pi$
$504$		0			0
$505$	10964.5	+	18991.0i	0.966162	+	1.67344i
$506$		0			0
$507$	−44720.9	+	16277.1i	−3.91741	+	1.42582i
$508$		0			0
$509$	−2671.38	+	15150.1i	−0.232626	+	1.31929i	0.614930	+	0.788582i	$0.289184\pi$
$509$	−2671.38	+	15150.1i	−0.232626	+	1.31929i	−0.847556	+	0.530706i	$0.821927\pi$
$510$		0			0
$511$	13182.1	−	11061.1i	1.14117	−	0.957559i
$512$		0			0
$513$	5282.54	−	16797.0i	0.454639	−	1.44563i
$514$		0			0
$515$	−2754.66	+	2311.43i	−0.235698	+	0.197774i
$516$		0			0
$517$	133.051	−	754.572i	0.0113184	−	0.0641896i
$518$		0			0
$519$	−11193.9	+	4074.26i	−0.946743	+	0.344586i
$520$		0			0
$521$	−103.467	−	179.211i	−0.00870055	−	0.0150698i	0.861642	−	0.507516i	$-0.169436\pi$
$521$	−103.467	−	179.211i	−0.00870055	−	0.0150698i	−0.870343	+	0.492446i	$0.836103\pi$
$522$		0			0
$523$	−2538.70	−	2130.22i	−0.212256	−	0.178104i	0.530461	−	0.847709i	$-0.322019\pi$
$523$	−2538.70	−	2130.22i	−0.212256	−	0.178104i	−0.742717	+	0.669606i	$0.766463\pi$
$524$		0			0
$525$	13392.2	−	23195.9i	1.11330	−	1.92829i
$526$		0			0
$527$	973.214	+	5519.37i	0.0804438	+	0.456219i
$528$		0			0
$529$	11421.3	+	4157.00i	0.938709	+	0.341662i
$530$		0			0
$531$	−14339.7			−1.17192
$532$		0			0
$533$	21714.7			1.76467
$534$		0			0
$535$	−3874.04	−	1410.04i	−0.313064	−	0.113946i
$536$		0			0
$537$	−2282.26	−	12943.4i	−0.183402	−	1.04012i
$538$		0			0
$539$	6375.15	−	11042.1i	0.509457	−	0.882405i
$540$		0			0
$541$	203.520	+	170.773i	0.0161738	+	0.0135714i	0.650839	−	0.759216i	$-0.274417\pi$
$541$	203.520	+	170.773i	0.0161738	+	0.0135714i	−0.634665	+	0.772787i	$0.718862\pi$
$542$		0			0
$543$	2971.50	+	5146.79i	0.234842	+	0.406759i
$544$		0			0
$545$	9889.29	−	3599.41i	0.777267	−	0.282902i
$546$		0			0
$547$	3920.28	−	22233.0i	0.306433	−	1.73787i	−0.310249	−	0.950655i	$-0.600412\pi$
$547$	3920.28	−	22233.0i	0.306433	−	1.73787i	0.616682	−	0.787213i	$-0.288477\pi$
$548$		0			0
$549$	−19357.5	+	16242.9i	−1.50485	+	1.26272i
$550$		0			0
$551$	−67.8192	−	1527.59i	−0.00524355	−	0.118108i
$552$		0			0
$553$	−20430.2	+	17143.0i	−1.57103	+	1.31825i
$554$		0			0
$555$	5191.32	−	29441.4i	0.397044	−	2.25175i
$556$		0			0
$557$	−18289.4	+	6656.80i	−1.39129	+	0.506387i	−0.925580	−	0.378551i	$-0.876422\pi$
$557$	−18289.4	+	6656.80i	−1.39129	+	0.506387i	−0.465708	+	0.884939i	$0.654200\pi$
$558$		0			0
$559$	−644.296	−	1115.95i	−0.0487493	−	0.0844362i
$560$		0			0
$561$	19080.5	+	16010.5i	1.43597	+	1.20493i
$562$		0			0
$563$	2972.67	−	5148.82i	0.222528	−	0.385429i	−0.733047	−	0.680178i	$-0.761903\pi$
$563$	2972.67	−	5148.82i	0.222528	−	0.385429i	0.955575	+	0.294748i	$0.0952359\pi$
$564$		0			0
$565$	−3110.36	−	17639.7i	−0.231600	−	1.31347i
$566$		0			0
$567$	12433.6	+	4525.45i	0.920920	+	0.335187i
$568$		0			0
$569$	−10615.3			−0.782103			−0.391051	−	0.920369i	$-0.627888\pi$
$569$	−10615.3			−0.782103			−0.391051	+	0.920369i	$0.627888\pi$
$570$		0			0
$571$	18071.4			1.32446			0.662230	−	0.749301i	$-0.269610\pi$
$571$	18071.4			1.32446			0.662230	+	0.749301i	$0.269610\pi$
$572$		0			0
$573$	−43235.1	−	15736.3i	−3.15213	−	1.14728i
$574$		0			0
$575$	−70.9602	−	402.435i	−0.00514651	−	0.0291873i
$576$		0			0
$577$	12247.6	−	21213.4i	0.883662	−	1.53055i	0.0364233	−	0.999336i	$-0.488404\pi$
$577$	12247.6	−	21213.4i	0.883662	−	1.53055i	0.847239	−	0.531212i	$-0.178263\pi$
$578$		0			0
$579$	5593.55	+	4693.55i	0.401486	+	0.336886i
$580$		0			0
$581$	3613.79	+	6259.26i	0.258047	+	0.446950i
$582$		0			0
$583$	11370.3	−	4138.46i	0.807737	−	0.293992i
$584$		0			0
$585$	−11950.0	+	67771.8i	−0.844567	+	4.78978i
$586$		0			0
$587$	−11378.5	+	9547.68i	−0.800069	+	0.671337i	−0.948215	−	0.317628i	$-0.897114\pi$
$587$	−11378.5	+	9547.68i	−0.800069	+	0.671337i	0.148147	+	0.988965i	$0.452669\pi$
$588$		0			0
$589$	5724.84	−	1273.57i	0.400489	−	0.0890946i
$590$		0			0
$591$	16526.6	−	13867.4i	1.15027	−	0.965194i
$592$		0			0
$593$	−995.592	+	5646.28i	−0.0689444	+	0.391003i	0.930735	+	0.365694i	$0.119168\pi$
$593$	−995.592	+	5646.28i	−0.0689444	+	0.391003i	−0.999680	+	0.0253095i	$0.991943\pi$
$594$		0			0
$595$	−30471.9	+	11090.9i	−2.09954	+	0.764171i
$596$		0			0
$597$	−11712.5	−	20286.6i	−0.802948	−	1.39075i
$598$		0			0
$599$	11450.8	+	9608.40i	0.781083	+	0.655407i	0.943521	−	0.331312i	$-0.107491\pi$
$599$	11450.8	+	9608.40i	0.781083	+	0.655407i	−0.162438	+	0.986719i	$0.551936\pi$
$600$		0			0
$601$	3798.35	−	6578.94i	0.257800	−	0.446523i	−0.707852	−	0.706361i	$-0.750336\pi$
$601$	3798.35	−	6578.94i	0.257800	−	0.446523i	0.965652	+	0.259838i	$0.0836690\pi$
$602$		0			0
$603$	−414.401	−	2350.19i	−0.0279863	−	0.158718i
$604$		0			0
$605$	904.502	+	329.212i	0.0607822	+	0.0221229i
$606$		0			0
$607$	−24917.7			−1.66619			−0.833095	−	0.553130i	$-0.813433\pi$
$607$	−24917.7			−1.66619			−0.833095	+	0.553130i	$0.813433\pi$
$608$		0			0
$609$	4318.89			0.287373
$610$		0			0
$611$	−1760.24	−	640.673i	−0.116549	−	0.0424204i
$612$		0			0
$613$	3584.42	+	20328.2i	0.236172	+	1.33940i	0.840132	+	0.542382i	$0.182477\pi$
$613$	3584.42	+	20328.2i	0.236172	+	1.33940i	−0.603961	+	0.797014i	$0.706412\pi$
$614$		0			0
$615$	17047.9	−	29527.8i	1.11778	−	1.93606i
$616$		0			0
$617$	21621.9	+	18142.9i	1.41080	+	1.18380i	0.956056	+	0.293183i	$0.0947144\pi$
$617$	21621.9	+	18142.9i	1.41080	+	1.18380i	0.454746	+	0.890621i	$0.349730\pi$
$618$		0			0
$619$	−13505.1	−	23391.6i	−0.876927	−	1.51888i	−0.854696	−	0.519129i	$-0.826256\pi$
$619$	−13505.1	−	23391.6i	−0.876927	−	1.51888i	−0.0222312	−	0.999753i	$-0.507077\pi$
$620$		0			0
$621$	713.017	−	259.517i	0.0460747	−	0.0167698i
$622$		0			0
$623$	−4360.77	+	24731.1i	−0.280434	+	1.59042i
$624$		0			0
$625$	−12890.3	+	10816.2i	−0.824977	+	0.692238i
$626$		0			0
$627$	15852.0	−	20690.1i	1.00968	−	1.31784i
$628$		0			0
$629$	−13255.6	+	11122.8i	−0.840278	+	0.705077i
$630$		0			0
$631$	−601.464	+	3411.07i	−0.0379459	+	0.215202i	−0.997885	−	0.0650075i	$-0.979293\pi$
$631$	−601.464	+	3411.07i	−0.0379459	+	0.215202i	0.959939	+	0.280210i	$0.0904040\pi$
$632$		0			0
$633$	15500.6	−	5641.75i	0.973290	−	0.354248i
$634$		0			0
$635$	6964.62	+	12063.1i	0.435248	+	0.753872i
$636$		0			0
$637$	−23878.7	−	20036.6i	−1.48525	−	1.24628i
$638$		0			0
$639$	11435.0	−	19805.9i	0.707919	−	1.22615i
$640$		0			0
$641$	−4085.46	−	23169.8i	−0.251741	−	1.42769i	−0.804301	−	0.594222i	$-0.797460\pi$
$641$	−4085.46	−	23169.8i	−0.251741	−	1.42769i	0.552560	−	0.833473i	$-0.313651\pi$
$642$		0			0
$643$	−15841.3	−	5765.76i	−0.971570	−	0.353623i	−0.193013	−	0.981196i	$-0.561826\pi$
$643$	−15841.3	−	5765.76i	−0.971570	−	0.353623i	−0.778557	+	0.627574i	$0.784048\pi$
$644$		0			0
$645$	−2023.31			−0.123516
$646$		0			0
$647$	5338.90			0.324411			0.162205	−	0.986757i	$-0.448139\pi$
$647$	5338.90			0.324411			0.162205	+	0.986757i	$0.448139\pi$
$648$		0			0
$649$	−9399.67	−	3421.20i	−0.568520	−	0.206924i
$650$		0			0
$651$	2876.47	+	16313.3i	0.173177	+	0.982133i
$652$		0			0
$653$	466.792	−	808.508i	0.0279740	−	0.0484523i	−0.851700	−	0.524030i	$-0.824428\pi$
$653$	466.792	−	808.508i	0.0279740	−	0.0484523i	0.879673	+	0.475578i	$0.157761\pi$
$654$		0			0
$655$	−2665.88	−	2236.94i	−0.159030	−	0.133442i
$656$		0			0
$657$	16594.6	+	28742.6i	0.985412	+	1.70678i
$658$		0			0
$659$	2720.00	−	989.999i	0.160783	−	0.0585203i	−0.260375	−	0.965508i	$-0.583846\pi$
$659$	2720.00	−	989.999i	0.160783	−	0.0585203i	0.421158	+	0.906987i	$0.361624\pi$
$660$		0			0
$661$	−2146.05	+	12170.9i	−0.126281	+	0.716176i	0.854258	+	0.519850i	$0.174012\pi$
$661$	−2146.05	+	12170.9i	−0.126281	+	0.716176i	−0.980539	+	0.196326i	$0.937099\pi$
$662$		0			0
$663$	46647.3	−	39141.7i	2.73248	−	2.29282i
$664$		0			0
$665$	13008.8	+	31340.9i	0.758585	+	1.82759i
$666$		0			0
$667$	50.4766	−	42.3549i	0.00293023	−	0.00245875i
$668$		0			0
$669$	−1412.24	+	8009.20i	−0.0816148	+	0.462860i
$670$		0			0
$671$	−16564.1	+	6028.85i	−0.952983	+	0.346857i
$672$		0			0
$673$	−11423.7	−	19786.5i	−0.654313	−	1.13330i	−0.982065	−	0.188540i	$-0.939624\pi$
$673$	−11423.7	−	19786.5i	−0.654313	−	1.13330i	0.327752	−	0.944764i	$-0.393709\pi$
$674$		0			0
$675$	18648.7	+	15648.1i	1.06339	+	0.892292i
$676$		0			0
$677$	3421.65	−	5926.47i	0.194246	−	0.336444i	−0.752407	−	0.658698i	$-0.771107\pi$
$677$	3421.65	−	5926.47i	0.194246	−	0.336444i	0.946653	+	0.322254i	$0.104441\pi$
$678$		0			0
$679$	3700.12	+	20984.4i	0.209128	+	1.18602i
$680$		0			0
$681$	8601.69	+	3130.76i	0.484020	+	0.176169i
$682$		0			0
$683$	26766.1			1.49952			0.749762	−	0.661707i	$-0.230168\pi$
$683$	26766.1			1.49952			0.749762	+	0.661707i	$0.230168\pi$
$684$		0			0
$685$	41315.1			2.30448
$686$		0			0
$687$	17516.4	+	6375.44i	0.972768	+	0.354059i
$688$		0			0
$689$	−5136.80	−	29132.2i	−0.284030	−	1.61081i
$690$		0			0
$691$	866.184	−	1500.27i	0.0476862	−	0.0825950i	−0.841197	−	0.540729i	$-0.818149\pi$
$691$	866.184	−	1500.27i	0.0476862	−	0.0825950i	0.888883	+	0.458134i	$0.151482\pi$
$692$		0			0
$693$	36889.7	+	30954.2i	2.02211	+	1.69675i
$694$		0			0
$695$	−21057.8	−	36473.1i	−1.14930	−	1.99065i
$696$		0			0
$697$	−18544.8	+	6749.77i	−1.00780	+	0.366809i
$698$		0			0
$699$	−7841.28	+	44470.1i	−0.424298	+	2.40632i
$700$		0			0
$701$	22866.8	−	19187.5i	1.23205	−	1.03381i	0.233946	−	0.972250i	$-0.424836\pi$
$701$	22866.8	−	19187.5i	1.23205	−	1.03381i	0.998103	−	0.0615624i	$-0.0196083\pi$
$702$		0			0
$703$	12243.1	+	13341.3i	0.656837	+	0.715756i
$704$		0			0
$705$	−2253.12	+	1890.59i	−0.120365	+	0.100998i
$706$		0			0
$707$	6514.43	−	36945.2i	0.346535	−	1.96530i
$708$		0			0
$709$	−11025.6	+	4013.00i	−0.584028	+	0.212569i	−0.617101	−	0.786884i	$-0.711693\pi$
$709$	−11025.6	+	4013.00i	−0.584028	+	0.212569i	0.0330729	+	0.999453i	$0.489471\pi$
$710$		0			0
$711$	−25719.1	−	44546.8i	−1.35660	−	2.34970i
$712$		0			0
$713$	193.601	+	162.451i	0.0101689	+	0.00853272i
$714$		0			0
$715$	−24002.4	+	41573.3i	−1.25544	+	2.17448i
$716$		0			0
$717$	9608.96	+	54495.1i	0.500493	+	2.83844i
$718$		0			0
$719$	9111.64	+	3316.37i	0.472610	+	0.172016i	0.567334	−	0.823487i	$-0.307975\pi$
$719$	9111.64	+	3316.37i	0.472610	+	0.172016i	−0.0947241	+	0.995504i	$0.530197\pi$
$720$		0			0
$721$	6151.81			0.317761
$722$		0			0
$723$	−30335.9			−1.56045
$724$		0			0
$725$	1986.57	+	723.051i	0.101764	+	0.0370392i
$726$		0			0
$727$	−1122.05	−	6363.44i	−0.0572413	−	0.324631i	0.942719	−	0.333589i	$-0.108260\pi$
$727$	−1122.05	−	6363.44i	−0.0572413	−	0.324631i	−0.999960	+	0.00895759i	$0.997149\pi$
$728$		0			0
$729$	12599.6	−	21823.1i	0.640125	−	1.10873i
$730$		0			0
$731$	897.125	+	752.777i	0.0453917	+	0.0380882i
$732$		0			0
$733$	−11330.1	−	19624.3i	−0.570924	−	0.988869i	−0.996471	−	0.0839329i	$-0.973252\pi$
$733$	−11330.1	−	19624.3i	−0.570924	−	0.988869i	0.425548	−	0.904936i	$-0.360081\pi$
$734$		0			0
$735$	−45992.6	+	16739.9i	−2.30811	+	0.840084i
$736$		0			0
$737$	289.073	−	1639.41i	0.0144480	−	0.0819384i
$738$		0			0
$739$	24575.7	−	20621.4i	1.22332	−	1.02648i	0.224671	−	0.974435i	$-0.427869\pi$
$739$	24575.7	−	20621.4i	1.22332	−	1.02648i	0.998645	−	0.0520492i	$-0.0165753\pi$
$740$		0			0
$741$	−43084.2	−	46948.9i	−2.13595	−	2.32755i
$742$		0			0
$743$	−5623.42	+	4718.61i	−0.277663	+	0.232987i	−0.770975	−	0.636866i	$-0.780231\pi$
$743$	−5623.42	+	4718.61i	−0.277663	+	0.232987i	0.493312	+	0.869852i	$0.335786\pi$
$744$		0			0
$745$	6397.45	−	36281.7i	0.314610	−	1.78424i
$746$		0			0
$747$	−13099.2	+	4767.72i	−0.641600	+	0.233523i
$748$		0			0
$749$	3526.45	+	6107.99i	0.172034	+	0.297972i
$750$		0			0
$751$	23305.9	+	19556.0i	1.13242	+	0.950210i	0.999164	−	0.0408725i	$-0.0130138\pi$
$751$	23305.9	+	19556.0i	1.13242	+	0.950210i	0.133251	+	0.991082i	$0.457458\pi$
$752$		0			0
$753$	−9087.63	+	15740.2i	−0.439803	+	0.761761i
$754$		0			0
$755$	−5943.52	−	33707.4i	−0.286499	−	1.62482i
$756$		0			0
$757$	−11203.5	−	4077.73i	−0.537908	−	0.195783i	0.0587576	−	0.998272i	$-0.481286\pi$
$757$	−11203.5	−	4077.73i	−0.537908	−	0.195783i	−0.596666	+	0.802490i	$0.703508\pi$
$758$		0			0
$759$	1123.19			0.0537143
$760$		0			0
$761$	−5576.45			−0.265632			−0.132816	−	0.991141i	$-0.542402\pi$
$761$	−5576.45			−0.265632			−0.132816	+	0.991141i	$0.542402\pi$
$762$		0			0
$763$	−16918.2	−	6157.73i	−0.802727	−	0.292169i
$764$		0			0
$765$	−10860.5	−	61593.1i	−0.513285	−	2.91099i
$766$		0			0
$767$	−12227.4	+	21178.4i	−0.575625	+	0.997011i
$768$		0			0
$769$	−8348.43	−	7005.17i	−0.391485	−	0.328495i	0.425706	−	0.904861i	$-0.360026\pi$
$769$	−8348.43	−	7005.17i	−0.391485	−	0.328495i	−0.817191	+	0.576366i	$0.804470\pi$
$770$		0			0
$771$	34093.6	+	59051.9i	1.59254	+	2.75837i
$772$		0			0
$773$	−12402.3	+	4514.05i	−0.577074	+	0.210038i	−0.614035	−	0.789279i	$-0.710455\pi$
$773$	−12402.3	+	4514.05i	−0.577074	+	0.210038i	0.0369609	+	0.999317i	$0.488232\pi$
$774$		0			0
$775$	−1408.01	+	7985.22i	−0.0652609	+	0.370113i
$776$		0			0
$777$	−39178.8	+	32874.9i	−1.80892	+	1.51786i
$778$		0			0
$779$	7916.99	+	19073.7i	0.364128	+	0.877261i
$780$		0			0
$781$	12221.0	−	10254.6i	0.559924	−	0.469832i
$782$		0			0
$783$	−681.644	+	3865.80i	−0.0311111	+	0.176440i
$784$		0			0
$785$	−5255.08	+	1912.69i	−0.238932	+	0.0869643i
$786$		0			0
$787$	6873.88	+	11905.9i	0.311344	+	0.539263i	0.978654	−	0.205517i	$-0.0658876\pi$
$787$	6873.88	+	11905.9i	0.311344	+	0.539263i	−0.667310	+	0.744780i	$0.732554\pi$
$788$		0			0
$789$	33496.8	+	28107.2i	1.51143	+	1.26824i
$790$		0			0
$791$	−15321.4	+	26537.5i	−0.688707	+	1.19288i
$792$		0			0
$793$	7483.23	+	42439.5i	0.335104	+	1.90047i
$794$		0			0
$795$	−43647.0	−	15886.2i	−1.94717	−	0.708711i
$796$		0			0
$797$	−21384.3			−0.950403			−0.475201	−	0.879877i	$-0.657625\pi$
$797$	−21384.3			−0.950403			−0.475201	+	0.879877i	$0.657625\pi$
$798$		0			0
$799$	1702.43			0.0753786
$800$		0			0
$801$	−45514.0	−	16565.7i	−2.00769	−	0.730739i
$802$		0			0
$803$	4020.25	+	22800.0i	0.176677	+	1.00198i
$804$		0			0
$805$	−731.139	+	1266.37i	−0.0320115	+	0.0554456i
$806$		0			0
$807$	−43563.6	−	36554.2i	−1.90026	−	1.59451i
$808$		0			0
$809$	−12839.7	−	22239.1i	−0.557999	−	0.966483i	−0.997663	−	0.0683205i	$-0.978236\pi$
$809$	−12839.7	−	22239.1i	−0.557999	−	0.966483i	0.439664	−	0.898162i	$-0.355097\pi$
$810$		0			0
$811$	−7409.52	+	2696.84i	−0.320818	+	0.116768i	−0.497409	−	0.867516i	$-0.665715\pi$
$811$	−7409.52	+	2696.84i	−0.320818	+	0.116768i	0.176591	+	0.984284i	$0.443493\pi$
$812$		0			0
$813$	11298.6	−	64077.6i	0.487404	−	2.76421i
$814$		0			0
$815$	−22924.3	+	19235.7i	−0.985279	+	0.826747i
$816$		0			0
$817$	745.324	−	972.802i	0.0319162	−	0.0416573i
$818$		0			0
$819$	90186.4	−	75675.4i	3.84782	−	3.22871i
$820$		0			0
$821$	−920.383	+	5219.75i	−0.0391250	+	0.221889i	−0.998101	−	0.0615984i	$-0.980380\pi$
$821$	−920.383	+	5219.75i	−0.0391250	+	0.221889i	0.958976	+	0.283487i	$0.0914913\pi$
$822$		0			0
$823$	25035.5	−	9112.18i	1.06037	−	0.385942i	0.247801	−	0.968811i	$-0.420292\pi$
$823$	25035.5	−	9112.18i	1.06037	−	0.385942i	0.812567	+	0.582868i	$0.198070\pi$
$824$		0			0
$825$	18017.9	+	31207.9i	0.760366	+	1.31699i
$826$		0			0
$827$	−24379.9	−	20457.2i	−1.02512	−	0.860176i	−0.0348559	−	0.999392i	$-0.511097\pi$
$827$	−24379.9	−	20457.2i	−1.02512	−	0.860176i	−0.990262	+	0.139216i	$0.955542\pi$
$828$		0			0
$829$	9600.30	−	16628.2i	0.402210	−	0.696648i	−0.591782	−	0.806098i	$-0.701576\pi$
$829$	9600.30	−	16628.2i	0.402210	−	0.696648i	0.993992	+	0.109450i	$0.0349089\pi$
$830$		0			0
$831$	3507.87	+	19894.1i	0.146434	+	0.830468i
$832$		0			0
$833$	26621.0	+	9689.27i	1.10728	+	0.403017i
$834$		0			0
$835$	52075.7			2.15827
$836$		0			0
$837$	−15055.8			−0.621752
$838$		0			0
$839$	18841.6	+	6857.79i	0.775310	+	0.282190i	0.699215	−	0.714911i	$-0.253533\pi$
$839$	18841.6	+	6857.79i	0.775310	+	0.282190i	0.0760941	+	0.997101i	$0.475755\pi$
$840$		0			0
$841$	−4175.91	−	23682.8i	−0.171221	−	0.971043i
$842$		0			0
$843$	24060.9	−	41674.6i	0.983037	−	1.70267i
$844$		0			0
$845$	63857.1	+	53582.5i	2.59971	+	2.18141i
$846$		0			0
$847$	−823.347	−	1426.08i	−0.0334009	−	0.0578520i
$848$		0			0
$849$	52186.7	−	18994.4i	2.10959	−	0.767829i
$850$		0			0
$851$	−135.497	+	768.444i	−0.00545804	+	0.0309541i
$852$		0			0
$853$	12458.1	−	10453.6i	0.500069	−	0.419608i	−0.357550	−	0.933894i	$-0.616388\pi$
$853$	12458.1	−	10453.6i	0.500069	−	0.419608i	0.857618	+	0.514287i	$0.171943\pi$
$854$		0			0
$855$	−63886.1	+	14212.4i	−2.55539	+	0.568483i
$856$		0			0
$857$	−13997.9	+	11745.7i	−0.557947	+	0.468173i	−0.877622	−	0.479354i	$-0.840871\pi$
$857$	−13997.9	+	11745.7i	−0.557947	+	0.468173i	0.319674	+	0.947527i	$0.396426\pi$
$858$		0			0
$859$	−3668.55	+	20805.4i	−0.145715	+	0.826391i	0.821075	+	0.570820i	$0.193375\pi$
$859$	−3668.55	+	20805.4i	−0.145715	+	0.826391i	−0.966790	+	0.255571i	$0.917737\pi$
$860$		0			0
$861$	−54811.9	+	19949.9i	−2.16955	+	0.789653i
$862$		0			0
$863$	−7926.28	−	13728.7i	−0.312646	−	0.541520i	0.666288	−	0.745695i	$-0.267882\pi$
$863$	−7926.28	−	13728.7i	−0.312646	−	0.541520i	−0.978934	+	0.204175i	$0.934549\pi$
$864$		0			0
$865$	15983.9	+	13412.1i	0.628287	+	0.527195i
$866$		0			0
$867$	−5967.00	+	10335.1i	−0.233737	+	0.404844i
$868$		0			0
$869$	−6230.79	−	35336.6i	−0.243228	−	1.37941i
$870$		0			0
$871$	−3824.36	−	1391.95i	−0.148776	−	0.0541499i
$872$		0			0
$873$	−41097.3			−1.59328
$874$		0			0
$875$	4301.39			0.166187
$876$		0			0
$877$	9532.22	+	3469.45i	0.367024	+	0.133586i	0.518947	−	0.854806i	$-0.326324\pi$
$877$	9532.22	+	3469.45i	0.367024	+	0.133586i	−0.151923	+	0.988392i	$0.548546\pi$
$878$		0			0
$879$	8081.37	+	45831.7i	0.310100	+	1.75866i
$880$		0			0
$881$	9591.97	−	16613.8i	0.366812	−	0.635337i	−0.622253	−	0.782816i	$-0.713782\pi$
$881$	9591.97	−	16613.8i	0.366812	−	0.635337i	0.989065	+	0.147479i	$0.0471158\pi$
$882$		0			0
$883$	−22888.4	−	19205.6i	−0.872315	−	0.731959i	0.0922691	−	0.995734i	$-0.470588\pi$
$883$	−22888.4	−	19205.6i	−0.872315	−	0.731959i	−0.964584	+	0.263775i	$0.915032\pi$
$884$		0			0
$885$	19199.0	+	33253.6i	0.729228	+	1.26306i
$886$		0			0
$887$	−15391.1	+	5601.92i	−0.582620	+	0.212056i	−0.616480	−	0.787370i	$-0.711442\pi$
$887$	−15391.1	+	5601.92i	−0.582620	+	0.212056i	0.0338604	+	0.999427i	$0.489220\pi$
$888$		0			0
$889$	4137.97	−	23467.6i	0.156111	−	0.885351i
$890$		0			0
$891$	−13637.0	+	11442.8i	−0.512745	+	0.430244i
$892$		0			0
$893$	−79.0132	−	1779.73i	−0.00296089	−	0.0666926i
$894$		0			0
$895$	−17635.2	+	14797.7i	−0.658636	+	0.552661i
$896$		0			0
$897$	476.825	−	2704.21i	0.0177488	−	0.100659i
$898$		0			0
$899$	−1228.61	+	447.177i	−0.0455799	+	0.0165897i
$900$		0			0
$901$	13442.4	+	23282.9i	0.497037	+	0.860893i
$902$		0			0
$903$	2651.58	+	2224.94i	0.0977177	+	0.0819949i
$904$		0			0
$905$	5204.83	−	9015.02i	0.191176	−	0.331127i
$906$		0			0
$907$	6307.53	+	35771.8i	0.230913	+	1.30957i	0.851053	+	0.525081i	$0.175965\pi$
$907$	6307.53	+	35771.8i	0.230913	+	1.30957i	−0.620140	+	0.784491i	$0.712924\pi$
$908$		0			0
$909$	67992.2	+	24747.1i	2.48092	+	0.902982i
$910$		0			0
$911$	−9813.73			−0.356908			−0.178454	−	0.983948i	$-0.557110\pi$
$911$	−9813.73			−0.356908			−0.178454	+	0.983948i	$0.557110\pi$
$912$		0			0
$913$	−9724.02			−0.352484
$914$		0			0
$915$	63584.3	+	23142.8i	2.29730	+	0.836150i
$916$		0			0
$917$	1033.82	+	5863.09i	0.0372299	+	0.211141i
$918$		0			0
$919$	1160.95	−	2010.83i	0.0416717	−	0.0721775i	−0.844437	−	0.535654i	$-0.820065\pi$
$919$	1160.95	−	2010.83i	0.0416717	−	0.0721775i	0.886109	+	0.463477i	$0.153398\pi$
$920$		0			0
$921$	−42609.6	−	35753.7i	−1.52447	−	1.27918i
$922$		0			0
$923$	−19501.0	−	33776.7i	−0.695432	−	1.20452i
$924$		0			0
$925$	−23524.9	+	8562.36i	−0.836209	+	0.304355i
$926$		0			0
$927$	−2060.34	+	11684.8i	−0.0729996	+	0.414001i
$928$		0			0
$929$	11627.5	−	9756.65i	0.410642	−	0.344570i	−0.413948	−	0.910301i	$-0.635850\pi$
$929$	11627.5	−	9756.65i	0.410642	−	0.344570i	0.824590	+	0.565731i	$0.191406\pi$
$930$		0			0
$931$	8893.72	−	28279.6i	0.313083	−	0.995518i
$932$		0			0
$933$	−63885.2	+	53606.0i	−2.24170	+	1.88101i
$934$		0			0
$935$	7575.96	−	42965.4i	0.264984	−	1.50280i
$936$		0			0
$937$	38177.4	−	13895.4i	1.33106	−	0.484466i	0.424073	−	0.905628i	$-0.360600\pi$
$937$	38177.4	−	13895.4i	1.33106	−	0.484466i	0.906985	+	0.421162i	$0.138378\pi$
$938$		0			0
$939$	−4411.85	−	7641.55i	−0.153328	−	0.265572i
$940$		0			0
$941$	−4788.53	−	4018.05i	−0.165889	−	0.139197i	0.556064	−	0.831139i	$-0.312311\pi$
$941$	−4788.53	−	4018.05i	−0.165889	−	0.139197i	−0.721953	+	0.691942i	$0.756755\pi$
$942$		0			0
$943$	−444.962	+	770.697i	−0.0153658	+	0.0266144i
$944$		0			0
$945$	−15126.9	−	85789.1i	−0.520719	−	2.95314i
$946$		0			0
$947$	19402.8	+	7062.04i	0.665793	+	0.242329i	0.652736	−	0.757586i	$-0.273621\pi$
$947$	19402.8	+	7062.04i	0.665793	+	0.242329i	0.0130577	+	0.999915i	$0.495843\pi$
$948$		0			0
$949$	56600.2			1.93606
$950$		0			0
$951$	54340.7			1.85291
$952$		0			0
$953$	10632.5	+	3869.92i	0.361407	+	0.131541i	0.516340	−	0.856384i	$-0.327294\pi$
$953$	10632.5	+	3869.92i	0.361407	+	0.131541i	−0.154933	+	0.987925i	$0.549516\pi$
$954$		0			0
$955$	13994.3	+	79365.7i	0.474183	+	2.68923i
$956$		0			0
$957$	−2905.33	+	5032.18i	−0.0981359	+	0.169976i
$958$		0			0
$959$	−54144.2	−	45432.3i	−1.82316	−	1.52981i
$960$		0			0
$961$	12388.1	+	21456.9i	0.415835	+	0.720248i
$962$		0			0
$963$	−12782.6	+	4652.50i	−0.427741	+	0.155685i
$964$		0			0
$965$	2220.93	−	12595.5i	0.0740873	−	0.420170i
$966$		0			0
$967$	5376.29	−	4511.25i	0.178790	−	0.150023i	−0.549001	−	0.835822i	$-0.684992\pi$
$967$	5376.29	−	4511.25i	0.178790	−	0.150023i	0.727791	+	0.685799i	$0.240547\pi$
$968$		0			0
$969$	51388.4	+	26703.2i	1.70365	+	0.885273i
$970$		0			0
$971$	−25600.0	+	21481.0i	−0.846080	+	0.709945i	−0.958923	−	0.283668i	$-0.908449\pi$
$971$	−25600.0	+	21481.0i	−0.846080	+	0.709945i	0.112843	+	0.993613i	$0.464004\pi$
$972$		0			0
$973$	−12511.3	+	70955.0i	−0.412223	+	2.33783i
$974$		0			0
$975$	82785.7	−	30131.5i	2.71924	−	0.989724i
$976$		0			0
$977$	−18225.6	−	31567.7i	−0.596817	−	1.03372i	−0.993288	−	0.115670i	$-0.963099\pi$
$977$	−18225.6	−	31567.7i	−0.596817	−	1.03372i	0.396471	−	0.918047i	$-0.370235\pi$
$978$		0			0
$979$	−25882.1	−	21717.7i	−0.844940	−	0.708989i
$980$		0			0
$981$	17362.2	−	30072.3i	0.565070	−	0.978729i
$982$		0			0
$983$	−686.318	−	3892.31i	−0.0222687	−	0.126292i	0.971647	−	0.236437i	$-0.0759797\pi$
$983$	−686.318	−	3892.31i	−0.0222687	−	0.126292i	−0.993916	+	0.110145i	$0.964869\pi$
$984$		0			0
$985$	−35509.5	−	12924.4i	−1.14866	−	0.418077i
$986$		0			0
$987$	5031.76			0.162272
$988$		0			0
$989$	52.8098			0.00169793
$990$		0			0
$991$	25774.5	+	9381.13i	0.826188	+	0.300708i	0.720293	−	0.693669i	$-0.244007\pi$
$991$	25774.5	+	9381.13i	0.826188	+	0.300708i	0.105895	+	0.994377i	$0.466229\pi$
$992$		0			0
$993$	10042.8	+	56955.6i	0.320945	+	1.82017i
$994$		0			0
$995$	−20515.4	+	35533.7i	−0.653649	+	1.13215i
$996$		0			0
$997$	9826.39	+	8245.32i	0.312141	+	0.261918i	0.785376	−	0.619019i	$-0.212469\pi$
$997$	9826.39	+	8245.32i	0.312141	+	0.261918i	−0.473235	+	0.880936i	$0.656914\pi$
$998$		0			0
$999$	−23242.4	−	40257.1i	−0.736094	−	1.27495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.4.i.a.25.1	✓	30
19.4	even	9		1444.4.a.j.1.15		15
19.15	odd	18		1444.4.a.k.1.1		15
19.16	even	9	inner	76.4.i.a.73.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.4.i.a.25.1	✓	30	1.1	even	1	trivial
76.4.i.a.73.1	yes	30	19.16	even	9	inner
1444.4.a.j.1.15		15	19.4	even	9
1444.4.a.k.1.1		15	19.15	odd	18

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	76.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.30252 - 3.02187i) q^{3} +(2.68735 + 15.2407i) q^{5} +(13.2377 - 22.9284i) q^{7} +(39.1169 + 32.8230i) q^{9} +O(q^{10})\)	\(q+(-8.30252 - 3.02187i) q^{3} +(2.68735 + 15.2407i) q^{5} +(13.2377 - 22.9284i) q^{7} +(39.1169 + 32.8230i) q^{9} +(17.8101 + 30.8481i) q^{11} +(81.8311 - 29.7841i) q^{13} +(23.7437 - 134.657i) q^{15} +(-60.6275 + 50.8725i) q^{17} +(55.9965 + 61.0196i) q^{19} +(-179.193 + 150.361i) q^{21} +(-0.619729 + 3.51466i) q^{23} +(-107.597 + 39.1620i) q^{25} +(-106.305 - 184.125i) q^{27} +(-14.1436 - 11.8679i) q^{29} +(35.4073 - 61.3272i) q^{31} +(-54.6501 - 309.936i) q^{33} +(385.021 + 140.136i) q^{35} +218.640 q^{37} -769.408 q^{39} +(234.319 + 85.2851i) q^{41} +(-2.56953 - 14.5725i) q^{43} +(-395.125 + 684.377i) q^{45} +(-16.4781 - 13.8267i) q^{47} +(-178.975 - 309.995i) q^{49} +(657.091 - 239.162i) q^{51} +(58.9875 - 334.535i) q^{53} +(-422.285 + 354.339i) q^{55} +(-280.519 - 675.830i) q^{57} +(-215.121 + 180.508i) q^{59} +(-85.9322 + 487.346i) q^{61} +(1270.40 - 462.387i) q^{63} +(673.841 + 1167.13i) q^{65} +(-35.8009 - 30.0405i) q^{67} +(15.7662 - 27.3078i) q^{69} +(-77.7722 - 441.068i) q^{71} +(610.761 + 222.299i) q^{73} +1011.66 q^{75} +943.063 q^{77} +(-946.589 - 344.530i) q^{79} +(86.7835 + 492.173i) q^{81} +(-136.496 + 236.417i) q^{83} +(-938.262 - 787.295i) q^{85} +(81.5641 + 141.273i) q^{87} +(-891.322 + 324.415i) q^{89} +(400.356 - 2270.53i) q^{91} +(-479.292 + 402.174i) q^{93} +(-779.501 + 1017.41i) q^{95} +(-616.533 + 517.333i) q^{97} +(-315.848 + 1791.26i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9	\( 30 q - 3 q^{3} + 6 q^{7} + 15 q^{9} + 42 q^{11} - 42 q^{13} + 78 q^{15} + 30 q^{17} + 282 q^{19} + 198 q^{21} - 300 q^{23} - 276 q^{25} + 219 q^{27} + 216 q^{29} + 30 q^{31} - 597 q^{33} - 636 q^{35} + 60 q^{37} - 2172 q^{39} - 63 q^{41} - 246 q^{43} - 882 q^{45} + 762 q^{47} - 525 q^{49} + 2613 q^{51} + 882 q^{53} + 1350 q^{55} + 924 q^{57} + 2085 q^{59} + 1530 q^{61} + 2424 q^{63} + 1530 q^{65} - 3609 q^{67} + 756 q^{69} - 4962 q^{71} - 2394 q^{73} - 3516 q^{77} - 630 q^{79} - 3723 q^{81} - 2382 q^{83} + 3228 q^{85} - 1110 q^{87} + 2196 q^{89} + 6036 q^{91} + 5010 q^{93} + 6204 q^{95} + 6459 q^{97} + 6189 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 + 6 * q^7 + 15 * q^9 + 42 * q^11 - 42 * q^13 + 78 * q^15 + 30 * q^17 + 282 * q^19 + 198 * q^21 - 300 * q^23 - 276 * q^25 + 219 * q^27 + 216 * q^29 + 30 * q^31 - 597 * q^33 - 636 * q^35 + 60 * q^37 - 2172 * q^39 - 63 * q^41 - 246 * q^43 - 882 * q^45 + 762 * q^47 - 525 * q^49 + 2613 * q^51 + 882 * q^53 + 1350 * q^55 + 924 * q^57 + 2085 * q^59 + 1530 * q^61 + 2424 * q^63 + 1530 * q^65 - 3609 * q^67 + 756 * q^69 - 4962 * q^71 - 2394 * q^73 - 3516 * q^77 - 630 * q^79 - 3723 * q^81 - 2382 * q^83 + 3228 * q^85 - 1110 * q^87 + 2196 * q^89 + 6036 * q^91 + 5010 * q^93 + 6204 * q^95 + 6459 * q^97 + 6189 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more