LMFDB - Embedded newform 380.2.d.b.379.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(379,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("380.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.3
Character	$\chi$	$=$	380.379
Dual form			380.2.d.b.379.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39672 + 0.221721i) q^{2} +2.04365i q^{3} +(1.90168 - 0.619368i) q^{4} +(0.665544 - 2.13473i) q^{5} +(-0.453121 - 2.85442i) q^{6} -2.07881 q^{7} +(-2.51879 + 1.28673i) q^{8} -1.17650 q^{9} +O(q^{10})$	\(q+(-1.39672 + 0.221721i) q^{2} +2.04365i q^{3} +(1.90168 - 0.619368i) q^{4} +(0.665544 - 2.13473i) q^{5} +(-0.453121 - 2.85442i) q^{6} -2.07881 q^{7} +(-2.51879 + 1.28673i) q^{8} -1.17650 q^{9} +(-0.456267 + 3.12919i) q^{10} +4.08691i q^{11} +(1.26577 + 3.88637i) q^{12} +4.52166 q^{13} +(2.90352 - 0.460916i) q^{14} +(4.36263 + 1.36014i) q^{15} +(3.23277 - 2.35568i) q^{16} +6.58081i q^{17} +(1.64325 - 0.260856i) q^{18} +(-4.31870 + 0.590625i) q^{19} +(-0.0565286 - 4.47178i) q^{20} -4.24835i q^{21} +(-0.906157 - 5.70829i) q^{22} +7.09670 q^{23} +(-2.62962 - 5.14753i) q^{24} +(-4.11410 - 2.84151i) q^{25} +(-6.31551 + 1.00255i) q^{26} +3.72659i q^{27} +(-3.95323 + 1.28755i) q^{28} +5.90320i q^{29} +(-6.39496 - 0.932450i) q^{30} +1.69936 q^{31} +(-3.99298 + 4.00701i) q^{32} -8.35222 q^{33} +(-1.45911 - 9.19158i) q^{34} +(-1.38354 + 4.43768i) q^{35} +(-2.23733 + 0.728688i) q^{36} -1.81756 q^{37} +(5.90108 - 1.78249i) q^{38} +9.24068i q^{39} +(1.07044 + 6.23331i) q^{40} -1.10137i q^{41} +(0.941951 + 5.93378i) q^{42} +7.73444 q^{43} +(2.53130 + 7.77200i) q^{44} +(-0.783014 + 2.51151i) q^{45} +(-9.91214 + 1.57349i) q^{46} -9.98526 q^{47} +(4.81418 + 6.60664i) q^{48} -2.67856 q^{49} +(6.37629 + 3.05662i) q^{50} -13.4489 q^{51} +(8.59874 - 2.80057i) q^{52} -2.18817 q^{53} +(-0.826265 - 5.20502i) q^{54} +(8.72444 + 2.72002i) q^{55} +(5.23609 - 2.67486i) q^{56} +(-1.20703 - 8.82591i) q^{57} +(-1.30887 - 8.24514i) q^{58} +9.39966 q^{59} +(9.13875 - 0.115525i) q^{60} +4.95794 q^{61} +(-2.37353 + 0.376784i) q^{62} +2.44572 q^{63} +(4.68866 - 6.48201i) q^{64} +(3.00936 - 9.65250i) q^{65} +(11.6657 - 1.85187i) q^{66} -13.3041i q^{67} +(4.07594 + 12.5146i) q^{68} +14.5032i q^{69} +(0.948492 - 6.50498i) q^{70} -4.67605 q^{71} +(2.96337 - 1.51384i) q^{72} +6.18455i q^{73} +(2.53863 - 0.402992i) q^{74} +(5.80704 - 8.40778i) q^{75} +(-7.84697 + 3.79804i) q^{76} -8.49591i q^{77} +(-2.04886 - 12.9067i) q^{78} +4.04921 q^{79} +(-2.87717 - 8.46888i) q^{80} -11.1453 q^{81} +(0.244198 + 1.53831i) q^{82} -7.46362 q^{83} +(-2.63129 - 8.07901i) q^{84} +(14.0482 + 4.37982i) q^{85} +(-10.8029 + 1.71489i) q^{86} -12.0641 q^{87} +(-5.25875 - 10.2941i) q^{88} -0.553472i q^{89} +(0.536800 - 3.68150i) q^{90} -9.39966 q^{91} +(13.4956 - 4.39547i) q^{92} +3.47289i q^{93} +(13.9467 - 2.21395i) q^{94} +(-1.61346 + 9.61232i) q^{95} +(-8.18892 - 8.16025i) q^{96} +12.4166 q^{97} +(3.74121 - 0.593894i) q^{98} -4.80826i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9}+O(q^{10}) $ 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9	$ 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9} - 8 q^{16} - 20 q^{20} - 40 q^{24} - 84 q^{25} - 24 q^{26} + 24 q^{30} + 24 q^{36} - 40 q^{44} - 12 q^{45} + 128 q^{49} - 120 q^{54} + 24 q^{61} + 72 q^{64} + 112 q^{66} + 32 q^{74} + 56 q^{76} + 96 q^{80} - 72 q^{81} + 44 q^{85} - 40 q^{96}+O(q^{100}) $ 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9 - 8 * q^16 - 20 * q^20 - 40 * q^24 - 84 * q^25 - 24 * q^26 + 24 * q^30 + 24 * q^36 - 40 * q^44 - 12 * q^45 + 128 * q^49 - 120 * q^54 + 24 * q^61 + 72 * q^64 + 112 * q^66 + 32 * q^74 + 56 * q^76 + 96 * q^80 - 72 * q^81 + 44 * q^85 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.39672	+	0.221721i	−0.987633	+	0.156781i
$2$	−1.39672	+	0.221721i	−0.987633	+	0.156781i
$3$			2.04365i			1.17990i	0.807439	+	0.589951i	$0.200853\pi$
$3$			2.04365i			1.17990i	−0.807439	+	0.589951i	$0.799147\pi$
$4$	1.90168	−	0.619368i	0.950840	−	0.309684i
$5$	0.665544	−	2.13473i	0.297640	−	0.954678i
$5$	0.665544	−	2.13473i	0.297640	−	0.954678i
$6$	−0.453121	−	2.85442i	−0.184986	−	1.16531i
$7$	−2.07881			−0.785715			−0.392858	−	0.919599i	$-0.628514\pi$
$7$	−2.07881			−0.785715			−0.392858	+	0.919599i	$0.628514\pi$
$8$	−2.51879	+	1.28673i	−0.890528	+	0.454927i
$9$	−1.17650			−0.392167
$10$	−0.456267	+	3.12919i	−0.144284	+	0.989536i
$11$			4.08691i			1.23225i	0.787648	+	0.616125i	$0.211299\pi$
$11$			4.08691i			1.23225i	−0.787648	+	0.616125i	$0.788701\pi$
$12$	1.26577	+	3.88637i	0.365396	+	1.12190i
$13$	4.52166			1.25408			0.627041	−	0.778986i	$-0.284266\pi$
$13$	4.52166			1.25408			0.627041	+	0.778986i	$0.284266\pi$
$14$	2.90352	−	0.460916i	0.775999	−	0.123185i
$15$	4.36263	+	1.36014i	1.12643	+	0.351186i
$16$	3.23277	−	2.35568i	0.808192	−	0.588919i
$17$			6.58081i			1.59608i	0.602604	+	0.798041i	$0.294130\pi$
$17$			6.58081i			1.59608i	−0.602604	+	0.798041i	$0.705870\pi$
$18$	1.64325	−	0.260856i	0.387318	−	0.0614843i
$19$	−4.31870	+	0.590625i	−0.990778	+	0.135499i
$19$	−4.31870	+	0.590625i	−0.990778	+	0.135499i
$20$	−0.0565286	−	4.47178i	−0.0126402	−	0.999920i
$21$		−	4.24835i		−	0.927067i
$22$	−0.906157	−	5.70829i	−0.193193	−	1.21701i
$23$	7.09670			1.47976			0.739882	−	0.672736i	$-0.234881\pi$
$23$	7.09670			1.47976			0.739882	+	0.672736i	$0.234881\pi$
$24$	−2.62962	−	5.14753i	−0.536770	−	1.05074i
$25$	−4.11410	−	2.84151i	−0.822820	−	0.568301i
$26$	−6.31551	+	1.00255i	−1.23857	+	0.196616i
$27$			3.72659i			0.717183i
$28$	−3.95323	+	1.28755i	−0.747089	+	0.243323i
$29$			5.90320i			1.09620i	0.836414	+	0.548098i	$0.184648\pi$
$29$			5.90320i			1.09620i	−0.836414	+	0.548098i	$0.815352\pi$
$30$	−6.39496	−	0.932450i	−1.16756	−	0.170241i
$31$	1.69936			0.305214			0.152607	−	0.988287i	$-0.451233\pi$
$31$	1.69936			0.305214			0.152607	+	0.988287i	$0.451233\pi$
$32$	−3.99298	+	4.00701i	−0.705866	+	0.708345i
$33$	−8.35222			−1.45393
$34$	−1.45911	−	9.19158i	−0.250235	−	1.57634i
$35$	−1.38354	+	4.43768i	−0.233861	+	0.750105i
$36$	−2.23733	+	0.728688i	−0.372888	+	0.121448i
$37$	−1.81756			−0.298805			−0.149403	−	0.988776i	$-0.547735\pi$
$37$	−1.81756			−0.298805			−0.149403	+	0.988776i	$0.547735\pi$
$38$	5.90108	−	1.78249i	0.957281	−	0.289158i
$39$			9.24068i			1.47969i
$40$	1.07044	+	6.23331i	0.169252	+	0.985573i
$41$		−	1.10137i		−	0.172005i	−0.996295	−	0.0860027i	$-0.972591\pi$
$41$		−	1.10137i		−	0.172005i	0.996295	−	0.0860027i	$-0.0274094\pi$
$42$	0.941951	+	5.93378i	0.145346	+	0.915602i
$43$	7.73444			1.17949			0.589746	−	0.807589i	$-0.299228\pi$
$43$	7.73444			1.17949			0.589746	+	0.807589i	$0.299228\pi$
$44$	2.53130	+	7.77200i	0.381608	+	1.17167i
$45$	−0.783014	+	2.51151i	−0.116725	+	0.374394i
$46$	−9.91214	+	1.57349i	−1.46146	+	0.231999i
$47$	−9.98526			−1.45650			−0.728250	−	0.685312i	$-0.759666\pi$
$47$	−9.98526			−1.45650			−0.728250	+	0.685312i	$0.759666\pi$
$48$	4.81418	+	6.60664i	0.694867	+	0.953587i
$49$	−2.67856			−0.382651
$50$	6.37629	+	3.05662i	0.901744	+	0.432271i
$51$	−13.4489			−1.88322
$52$	8.59874	−	2.80057i	1.19243	−	0.388369i
$53$	−2.18817			−0.300568			−0.150284	−	0.988643i	$-0.548019\pi$
$53$	−2.18817			−0.300568			−0.150284	+	0.988643i	$0.548019\pi$
$54$	−0.826265	−	5.20502i	−0.112440	−	0.708313i
$55$	8.72444	+	2.72002i	1.17640	+	0.366768i
$56$	5.23609	−	2.67486i	0.699702	−	0.357444i
$57$	−1.20703	−	8.82591i	−0.159875	−	1.16902i
$58$	−1.30887	−	8.24514i	−0.171863	−	1.08264i
$59$	9.39966			1.22373			0.611866	−	0.790962i	$-0.290419\pi$
$59$	9.39966			1.22373			0.611866	+	0.790962i	$0.290419\pi$
$60$	9.13875	−	0.115525i	1.17981	−	0.0149142i
$61$	4.95794			0.634800			0.317400	−	0.948292i	$-0.397190\pi$
$61$	4.95794			0.634800			0.317400	+	0.948292i	$0.397190\pi$
$62$	−2.37353	+	0.376784i	−0.301439	+	0.0478516i
$63$	2.44572			0.308132
$64$	4.68866	−	6.48201i	0.586082	−	0.810252i
$65$	3.00936	−	9.65250i	0.373266	−	1.19724i
$66$	11.6657	−	1.85187i	1.43595	−	0.227949i
$67$		−	13.3041i		−	1.62536i	−0.582713	−	0.812678i	$-0.698009\pi$
$67$		−	13.3041i		−	1.62536i	0.582713	−	0.812678i	$-0.301991\pi$
$68$	4.07594	+	12.5146i	0.494281	+	1.51762i
$69$			14.5032i			1.74598i
$70$	0.948492	−	6.50498i	0.113366	−	0.777494i
$71$	−4.67605			−0.554945			−0.277472	−	0.960734i	$-0.589497\pi$
$71$	−4.67605			−0.554945			−0.277472	+	0.960734i	$0.589497\pi$
$72$	2.96337	−	1.51384i	0.349236	−	0.178408i
$73$			6.18455i			0.723846i	0.932208	+	0.361923i	$0.117880\pi$
$73$			6.18455i			0.723846i	−0.932208	+	0.361923i	$0.882120\pi$
$74$	2.53863	−	0.402992i	0.295110	−	0.0468469i
$75$	5.80704	−	8.40778i	0.670540	−	0.970847i
$76$	−7.84697	+	3.79804i	−0.900109	+	0.435665i
$77$		−	8.49591i		−	0.968199i
$78$	−2.04886	−	12.9067i	−0.231988	−	1.46139i
$79$	4.04921			0.455572			0.227786	−	0.973711i	$-0.426851\pi$
$79$	4.04921			0.455572			0.227786	+	0.973711i	$0.426851\pi$
$80$	−2.87717	−	8.46888i	−0.321678	−	0.946849i
$81$	−11.1453			−1.23837
$82$	0.244198	+	1.53831i	0.0269671	+	0.169878i
$83$	−7.46362			−0.819238			−0.409619	−	0.912257i	$-0.634338\pi$
$83$	−7.46362			−0.819238			−0.409619	+	0.912257i	$0.634338\pi$
$84$	−2.63129	−	8.07901i	−0.287098	−	0.881492i
$85$	14.0482	+	4.37982i	1.52374	+	0.475058i
$86$	−10.8029	+	1.71489i	−1.16491	+	0.184922i
$87$	−12.0641			−1.29340
$88$	−5.25875	−	10.2941i	−0.560585	−	1.09735i
$89$		−	0.553472i		−	0.0586680i	−0.999570	−	0.0293340i	$-0.990661\pi$
$89$		−	0.553472i		−	0.0586680i	0.999570	−	0.0293340i	$-0.00933864\pi$
$90$	0.536800	−	3.68150i	0.0565836	−	0.388064i
$91$	−9.39966			−0.985352
$92$	13.4956	−	4.39547i	1.40702	−	0.458259i
$93$			3.47289i			0.360122i
$94$	13.9467	−	2.21395i	1.43849	−	0.228351i
$95$	−1.61346	+	9.61232i	−0.165538	+	0.986203i
$96$	−8.18892	−	8.16025i	−0.835778	−	0.832852i
$97$	12.4166			1.26071			0.630355	−	0.776307i	$-0.282909\pi$
$97$	12.4166			1.26071			0.630355	+	0.776307i	$0.282909\pi$
$98$	3.74121	−	0.593894i	0.377919	−	0.0599923i
$99$		−	4.80826i		−	0.483249i
$100$	−9.58364	−	2.85549i	−0.958364	−	0.285549i
$101$	9.53915			0.949181			0.474591	−	0.880207i	$-0.342596\pi$
$101$	9.53915			0.949181			0.474591	+	0.880207i	$0.342596\pi$
$102$	18.7844	−	2.98190i	1.85993	−	0.295252i
$103$		−	14.1699i		−	1.39620i	−0.715998	−	0.698102i	$-0.754028\pi$
$103$		−	14.1699i		−	1.39620i	0.715998	−	0.698102i	$-0.245972\pi$
$104$	−11.3891	+	5.81815i	−1.11680	+	0.570517i
$105$	−9.06907	−	2.82747i	−0.885050	−	0.275933i
$106$	3.05626	−	0.485163i	0.296851	−	0.0471232i
$107$		−	2.59574i		−	0.250940i	−0.992097	−	0.125470i	$-0.959956\pi$
$107$		−	2.59574i		−	0.250940i	0.992097	−	0.125470i	$-0.0400438\pi$
$108$	2.30813	+	7.08678i	0.222100	+	0.681926i
$109$		−	12.6595i		−	1.21256i	−0.795251	−	0.606280i	$-0.792661\pi$
$109$		−	12.6595i		−	1.21256i	0.795251	−	0.606280i	$-0.207339\pi$
$110$	−12.7887	−	1.86473i	−1.21936	−	0.177795i
$111$		−	3.71446i		−	0.352561i
$112$	−6.72030	+	4.89700i	−0.635009	+	0.462723i
$113$	12.9394			1.21724			0.608620	−	0.793461i	$-0.291723\pi$
$113$	12.9394			1.21724			0.608620	+	0.793461i	$0.291723\pi$
$114$	3.64278	+	12.0597i	0.341178	+	1.12950i
$115$	4.72317	−	15.1495i	0.440438	−	1.41270i
$116$	3.65625	+	11.2260i	0.339474	+	1.04231i
$117$	−5.31974			−0.491810
$118$	−13.1287	+	2.08411i	−1.20860	+	0.191858i
$119$		−	13.6802i		−	1.25407i
$120$	−12.7387	+	2.18761i	−1.16288	+	0.199701i
$121$	−5.70286			−0.518442
$122$	−6.92488	+	1.09928i	−0.626949	+	0.0995244i
$123$	2.25082			0.202949
$124$	3.23163	−	1.05253i	0.290209	−	0.0945197i
$125$	−8.80395	+	6.89133i	−0.787449	+	0.616379i
$126$	−3.41600	+	0.542269i	−0.304322	+	0.0483092i
$127$			7.32119i			0.649651i	0.945774	+	0.324825i	$0.105305\pi$
$127$			7.32119i			0.649651i	−0.945774	+	0.324825i	$0.894695\pi$
$128$	−5.11156	+	10.0932i	−0.451802	+	0.892118i
$129$			15.8065i			1.39168i
$130$	−2.06308	+	14.1491i	−0.180945	+	1.24096i
$131$		−	11.3901i		−	0.995160i	−0.867418	−	0.497580i	$-0.834222\pi$
$131$		−	11.3901i		−	0.995160i	0.867418	−	0.497580i	$-0.165778\pi$
$132$	−15.8832	+	5.17309i	−1.38246	+	0.450260i
$133$	8.97775	−	1.22780i	0.778469	−	0.106463i
$134$	2.94981	+	18.5822i	0.254825	+	1.60526i
$135$	7.95524	+	2.48021i	0.684678	+	0.213462i
$136$	−8.46772	−	16.5757i	−0.726101	−	1.42136i
$137$			7.24081i			0.618624i	0.950961	+	0.309312i	$0.100099\pi$
$137$			7.24081i			0.618624i	−0.950961	+	0.309312i	$0.899901\pi$
$138$	−3.21566	−	20.2569i	−0.273736	−	1.72438i
$139$			0.0394231i			0.00334382i	0.999999	+	0.00167191i	$0.000532186\pi$
$139$			0.0394231i			0.00334382i	−0.999999	+	0.00167191i	$0.999468\pi$
$140$	0.117512	+	9.29597i	0.00993158	+	0.785653i
$141$		−	20.4064i		−	1.71853i
$142$	6.53115	−	1.03678i	0.548082	−	0.0870047i
$143$			18.4796i			1.54534i
$144$	−3.80336	+	2.77146i	−0.316947	+	0.230955i
$145$	12.6017	+	3.92884i	1.04651	+	0.326272i
$146$	−1.37125	−	8.63811i	−0.113485	−	0.714895i
$147$		−	5.47403i		−	0.451491i
$148$	−3.45642	+	1.12574i	−0.284116	+	0.0925352i
$149$	7.71138			0.631741			0.315870	−	0.948802i	$-0.397704\pi$
$149$	7.71138			0.631741			0.315870	+	0.948802i	$0.397704\pi$
$150$	−6.24666	+	13.0309i	−0.510037	+	1.06397i
$151$	8.63740			0.702902			0.351451	−	0.936206i	$-0.385688\pi$
$151$	8.63740			0.702902			0.351451	+	0.936206i	$0.385688\pi$
$152$	10.1179	−	7.04466i	0.820674	−	0.571397i
$153$		−	7.74234i		−	0.625931i
$154$	1.88373	+	11.8664i	0.151795	+	0.956225i
$155$	1.13100	−	3.62766i	0.0908439	−	0.291381i
$156$	5.72338	+	17.5728i	0.458237	+	1.40695i
$157$		−	17.2555i		−	1.37714i	−0.725169	−	0.688571i	$-0.758238\pi$
$157$		−	17.2555i		−	1.37714i	0.725169	−	0.688571i	$-0.241762\pi$
$158$	−5.65563	+	0.897797i	−0.449938	+	0.0714249i
$159$		−	4.47184i		−	0.354640i
$160$	5.89635	+	11.1908i	0.466148	+	0.884707i
$161$	−14.7527			−1.16267
$162$	15.5670	−	2.47116i	1.22306	−	0.194153i
$163$	−5.21280			−0.408298			−0.204149	−	0.978940i	$-0.565443\pi$
$163$	−5.21280			−0.408298			−0.204149	+	0.978940i	$0.565443\pi$
$164$	−0.682154	−	2.09446i	−0.0532673	−	0.163549i
$165$	−5.55877	+	17.8297i	−0.432750	+	1.38804i
$166$	10.4246	−	1.65484i	0.809107	−	0.128441i
$167$			14.1450i			1.09457i	0.836946	+	0.547285i	$0.184339\pi$
$167$			14.1450i			1.09457i	−0.836946	+	0.547285i	$0.815661\pi$
$168$	5.46648	+	10.7007i	0.421748	+	0.825579i
$169$	7.44540			0.572723
$170$	−20.5926	−	3.00261i	−1.57938	−	0.230290i
$171$	5.08096	−	0.694871i	0.388551	−	0.0531381i
$172$	14.7084	−	4.79046i	1.12151	−	0.365269i
$173$	−5.48227			−0.416809			−0.208405	−	0.978043i	$-0.566827\pi$
$173$	−5.48227			−0.416809			−0.208405	+	0.978043i	$0.566827\pi$
$174$	16.8502	−	2.67486i	1.27741	−	0.202781i
$175$	8.55243	+	5.90695i	0.646503	+	0.446523i
$176$	9.62745	+	13.2120i	0.725696	+	0.995895i
$177$			19.2096i			1.44388i
$178$	0.122717	+	0.773049i	0.00919801	+	0.0579424i
$179$	1.18947			0.0889053			0.0444527	−	0.999011i	$-0.485846\pi$
$179$	1.18947			0.0889053			0.0444527	+	0.999011i	$0.485846\pi$
$180$	0.0665060	+	5.26106i	0.00495706	+	0.392136i
$181$		−	5.10146i		−	0.379189i	−0.981863	−	0.189594i	$-0.939283\pi$
$181$		−	5.10146i		−	0.379189i	0.981863	−	0.189594i	$-0.0607173\pi$
$182$	13.1287	−	2.08411i	0.973167	−	0.154484i
$183$			10.1323i			0.749001i
$184$	−17.8751	+	9.13153i	−1.31777	+	0.673186i
$185$	−1.20967	+	3.87999i	−0.0889365	+	0.285263i
$186$	−0.770014	−	4.85067i	−0.0564602	−	0.355668i
$187$	−26.8952			−1.96677
$188$	−18.9888	+	6.18455i	−1.38490	+	0.451054i
$189$		−	7.74686i		−	0.563501i
$190$	0.122305	−	13.7835i	0.00887295	−	0.999961i
$191$		−	4.80768i		−	0.347872i	−0.984757	−	0.173936i	$-0.944351\pi$
$191$		−	4.80768i		−	0.347872i	0.984757	−	0.173936i	$-0.0556486\pi$
$192$	13.2470	+	9.58197i	0.956017	+	0.691519i
$193$	−22.0347			−1.58609			−0.793045	−	0.609163i	$-0.791506\pi$
$193$	−22.0347			−1.58609			−0.793045	+	0.609163i	$0.791506\pi$
$194$	−17.3425	+	2.75302i	−1.24512	+	0.197655i
$195$	19.7263	+	6.15008i	1.41263	+	0.440417i
$196$	−5.09376	+	1.65901i	−0.363840	+	0.118501i
$197$		−	15.9745i		−	1.13814i	−0.822290	−	0.569069i	$-0.807304\pi$
$197$		−	15.9745i		−	1.13814i	0.822290	−	0.569069i	$-0.192696\pi$
$198$	1.06610	+	6.71582i	0.0757641	+	0.477273i
$199$			12.4990i			0.886030i	0.896514	+	0.443015i	$0.146091\pi$
$199$			12.4990i			0.886030i	−0.896514	+	0.443015i	$0.853909\pi$
$200$	14.0188	+	1.86344i	0.991281	+	0.131765i
$201$	27.1889			1.91776
$202$	−13.3236	+	2.11504i	−0.937443	+	0.148813i
$203$		−	12.2716i		−	0.861298i
$204$	−25.5754	+	8.32980i	−1.79064	+	0.583202i
$205$	−2.35113	−	0.733011i	−0.164210	−	0.0511957i
$206$	3.14178	+	19.7915i	0.218898	+	1.37894i
$207$	−8.34929			−0.580315
$208$	14.6175	−	10.6516i	1.01354	−	0.738553i
$209$	−2.41383	−	17.6502i	−0.166968	−	1.22089i
$210$	13.2939	+	1.93839i	0.917366	+	0.133761i
$211$	−9.66236			−0.665184			−0.332592	−	0.943071i	$-0.607923\pi$
$211$	−9.66236			−0.665184			−0.332592	+	0.943071i	$0.607923\pi$
$212$	−4.16119	+	1.35528i	−0.285792	+	0.0930810i
$213$		−	9.55620i		−	0.654780i
$214$	0.575531	+	3.62553i	0.0393425	+	0.247836i
$215$	5.14761	−	16.5109i	0.351064	−	1.12603i
$216$	−4.79511	−	9.38651i	−0.326266	−	0.638671i
$217$	−3.53264			−0.239811
$218$	2.80688	+	17.6818i	0.190106	+	1.19757i
$219$	−12.6390			−0.854068
$220$	18.2758	−	0.231027i	1.23215	−	0.0155759i
$221$			29.7562i			2.00162i
$222$	0.823575	+	5.18807i	0.0552747	+	0.348201i
$223$			8.38081i			0.561220i	0.959822	+	0.280610i	$0.0905368\pi$
$223$			8.38081i			0.561220i	−0.959822	+	0.280610i	$0.909463\pi$
$224$	8.30064	−	8.32980i	0.554610	−	0.556558i
$225$	4.84025	+	3.34304i	0.322683	+	0.222869i
$226$	−18.0728	+	2.86895i	−1.20219	+	0.190840i
$227$		−	7.85463i		−	0.521330i	−0.965429	−	0.260665i	$-0.916058\pi$
$227$		−	7.85463i		−	0.521330i	0.965429	−	0.260665i	$-0.0839418\pi$
$228$	−7.76186	−	16.0364i	−0.514042	−	1.06204i
$229$	−12.6232			−0.834162			−0.417081	−	0.908869i	$-0.636947\pi$
$229$	−12.6232			−0.834162			−0.417081	+	0.908869i	$0.636947\pi$
$230$	−3.23799	+	22.2069i	−0.213507	+	1.46428i
$231$	17.3627			1.14238
$232$	−7.59582	−	14.8689i	−0.498690	−	0.976194i
$233$		−	7.08234i		−	0.463980i	−0.972718	−	0.231990i	$-0.925476\pi$
$233$		−	7.08234i		−	0.463980i	0.972718	−	0.231990i	$-0.0745236\pi$
$234$	7.43021	−	1.17950i	0.485728	−	0.0771064i
$235$	−6.64563	+	21.3158i	−0.433513	+	1.39049i
$236$	17.8751	−	5.82185i	1.16357	−	0.378970i
$237$			8.27517i			0.537530i
$238$	3.03320	+	19.1075i	0.196613	+	1.23856i
$239$		−	17.5612i		−	1.13594i	−0.823050	−	0.567969i	$-0.807729\pi$
$239$		−	17.5612i		−	1.13594i	0.823050	−	0.567969i	$-0.192271\pi$
$240$	17.3074	−	5.87994i	1.11719	−	0.379548i
$241$			25.5078i			1.64310i	0.570134	+	0.821552i	$0.306891\pi$
$241$			25.5078i			1.64310i	−0.570134	+	0.821552i	$0.693109\pi$
$242$	7.96533	−	1.26445i	0.512031	−	0.0812818i
$243$		−	11.5974i		−	0.743975i
$244$	9.42842	−	3.07079i	0.603593	−	0.196587i
$245$	−1.78270	+	5.71799i	−0.113892	+	0.365309i
$246$	−3.14377	+	0.499055i	−0.200440	+	0.0318186i
$247$	−19.5277	+	2.67060i	−1.24252	+	0.169926i
$248$	−4.28033	+	2.18661i	−0.271801	+	0.138850i
$249$		−	15.2530i		−	0.966620i
$250$	10.7687	−	11.5773i	0.681075	−	0.732214i
$251$		−	17.7479i		−	1.12024i	−0.828412	−	0.560120i	$-0.810755\pi$
$251$		−	17.7479i		−	1.12024i	0.828412	−	0.560120i	$-0.189245\pi$
$252$	4.65098	−	1.51480i	0.292984	−	0.0954235i
$253$			29.0036i			1.82344i
$254$	−1.62327	−	10.2257i	−0.101853	−	0.641617i
$255$	−8.95082	+	28.7096i	−0.560522	+	1.79787i
$256$	4.90157	−	15.2307i	0.306348	−	0.951920i
$257$	−11.6378			−0.725947			−0.362974	−	0.931799i	$-0.618238\pi$
$257$	−11.6378			−0.725947			−0.362974	+	0.931799i	$0.618238\pi$
$258$	−3.50464	−	22.0773i	−0.218189	−	1.37447i
$259$	3.77836			0.234776
$260$	−0.255603	−	20.2199i	−0.0158518	−	1.25398i
$261$		−	6.94513i		−	0.429893i
$262$	2.52544	+	15.9089i	0.156022	+	0.982854i
$263$	−27.2166			−1.67825			−0.839123	−	0.543942i	$-0.816931\pi$
$263$	−27.2166			−1.67825			−0.839123	+	0.543942i	$0.816931\pi$
$264$	21.0375	−	10.7470i	1.29477	−	0.661435i
$265$	−1.45632	+	4.67113i	−0.0894611	+	0.286945i
$266$	−12.2672	+	3.70545i	−0.752151	+	0.227196i
$267$	1.13110			0.0692224
$268$	−8.24014	−	25.3002i	−0.503347	−	1.54545i
$269$		−	20.4064i		−	1.24420i	−0.782939	−	0.622099i	$-0.786280\pi$
$269$		−	20.4064i		−	1.24420i	0.782939	−	0.622099i	$-0.213720\pi$
$270$	−11.6612	−	1.70032i	−0.709678	−	0.103478i
$271$			2.86027i			0.173749i	0.996219	+	0.0868746i	$0.0276879\pi$
$271$			2.86027i			0.173749i	−0.996219	+	0.0868746i	$0.972312\pi$
$272$	15.5023	+	21.2742i	0.939963	+	1.28994i
$273$		−	19.2096i		−	1.16262i
$274$	−1.60544	−	10.1134i	−0.0969883	−	0.610974i
$275$	11.6130	−	16.8140i	0.700290	−	1.01392i
$276$	8.98279	+	27.5804i	0.540701	+	1.66014i
$277$			0.796560i			0.0478606i	0.999714	+	0.0239303i	$0.00761799\pi$
$277$			0.796560i			0.0478606i	−0.999714	+	0.0239303i	$0.992382\pi$
$278$	−0.00874094	−	0.0550632i	−0.000524247	−	0.00330247i
$279$	−1.99930			−0.119695
$280$	−2.22525	−	12.9579i	−0.132984	−	0.774380i
$281$			8.04650i			0.480014i	0.970771	+	0.240007i	$0.0771497\pi$
$281$			8.04650i			0.480014i	−0.970771	+	0.240007i	$0.922850\pi$
$282$	4.52453	+	28.5021i	0.269432	+	1.69727i
$283$	29.0701			1.72804			0.864019	−	0.503459i	$-0.167939\pi$
$283$	29.0701			1.72804			0.864019	+	0.503459i	$0.167939\pi$
$284$	−8.89234	+	2.89619i	−0.527663	+	0.171857i
$285$	−19.6442	−	3.29735i	−1.16362	−	0.195318i
$286$	−4.09733	−	25.8110i	−0.242280	−	1.52623i
$287$			2.28954i			0.135147i
$288$	4.69775	−	4.71425i	0.276818	−	0.277790i
$289$	−26.3071			−1.54748
$290$	−18.4722	−	2.69344i	−1.08473	−	0.158164i
$291$			25.3751i			1.48751i
$292$	3.83051	+	11.7610i	0.224164	+	0.688262i
$293$	−0.297923			−0.0174048			−0.00870242	−	0.999962i	$-0.502770\pi$
$293$	−0.297923			−0.0174048			−0.00870242	+	0.999962i	$0.502770\pi$
$294$	1.21371	+	7.64572i	0.0707851	+	0.445907i
$295$	6.25589	−	20.0657i	0.364232	−	1.16827i
$296$	4.57806	−	2.33871i	0.266095	−	0.135935i
$297$	−15.2303			−0.883749
$298$	−10.7707	+	1.70978i	−0.623928	+	0.0990448i
$299$	32.0889			1.85575
$300$	5.83563	−	19.5856i	0.336920	−	1.13078i
$301$	−16.0784			−0.926745
$302$	−12.0641	+	1.91510i	−0.694209	+	0.110201i
$303$			19.4947i			1.11994i
$304$	−12.5700	+	12.0828i	−0.720941	+	0.692997i
$305$	3.29973	−	10.5838i	0.188942	−	0.606029i
$306$	1.71664	+	10.8139i	0.0981340	+	0.618190i
$307$		−	18.1387i		−	1.03523i	−0.855613	−	0.517616i	$-0.826819\pi$
$307$		−	18.1387i		−	1.03523i	0.855613	−	0.517616i	$-0.173181\pi$
$308$	−5.26209	−	16.1565i	−0.299835	−	0.920602i
$309$	28.9584			1.64738
$310$	−0.775361	+	5.31761i	−0.0440376	+	0.302020i
$311$		−	3.19194i		−	0.180998i	−0.995897	−	0.0904991i	$-0.971154\pi$
$311$		−	3.19194i		−	0.180998i	0.995897	−	0.0904991i	$-0.0288462\pi$
$312$	−11.8903	−	23.2754i	−0.673153	−	1.31771i
$313$			5.38799i			0.304547i	0.988338	+	0.152274i	$0.0486595\pi$
$313$			5.38799i			0.304547i	−0.988338	+	0.152274i	$0.951341\pi$
$314$	3.82593	+	24.1012i	0.215909	+	1.36011i
$315$	1.62774	−	5.22094i	0.0917125	−	0.294167i
$316$	7.70030	−	2.50795i	0.433176	−	0.141083i
$317$	19.5632			1.09878			0.549389	−	0.835567i	$-0.314861\pi$
$317$	19.5632			1.09878			0.549389	+	0.835567i	$0.314861\pi$
$318$	0.991504	+	6.24593i	0.0556008	+	0.350255i
$319$	−24.1259			−1.35079
$320$	−10.7168	−	14.3231i	−0.599088	−	0.800683i
$321$	5.30478			0.296084
$322$	20.6054	−	3.27099i	1.14830	−	0.182285i
$323$	−3.88679	−	28.4205i	−0.216267	−	1.58136i
$324$	−21.1949	+	6.90307i	−1.17749	+	0.383504i
$325$	−18.6026	−	12.8483i	−1.03188	−	0.712697i
$326$	7.28084	−	1.15579i	0.403249	−	0.0640133i
$327$	25.8716			1.43070
$328$	1.41717	+	2.77413i	0.0782500	+	0.153176i
$329$	20.7574			1.14439
$330$	3.81084	−	26.1357i	0.209780	−	1.43872i
$331$	4.81147			0.264462			0.132231	−	0.991219i	$-0.457786\pi$
$331$	4.81147			0.264462			0.132231	+	0.991219i	$0.457786\pi$
$332$	−14.1934	+	4.62272i	−0.778964	+	0.253705i
$333$	2.13837			0.117182
$334$	−3.13624	−	19.7566i	−0.171608	−	1.08103i
$335$	−28.4006	−	8.85448i	−1.55169	−	0.483772i
$336$	−10.0078	−	13.7339i	−0.545968	−	0.749248i
$337$	2.60018			0.141641			0.0708205	−	0.997489i	$-0.477438\pi$
$337$	2.60018			0.141641			0.0708205	+	0.997489i	$0.477438\pi$
$338$	−10.3992	+	1.65080i	−0.565640	+	0.0897919i
$339$			26.4437i			1.43622i
$340$	29.4279	−	0.372004i	1.59595	−	0.0201747i
$341$			6.94513i			0.376100i
$342$	−6.94263	+	2.09710i	−0.375415	+	0.113398i
$343$	20.1199			1.08637
$344$	−19.4815	+	9.95213i	−1.05037	+	0.536583i
$345$	30.9603	+	9.65250i	1.66685	+	0.519673i
$346$	7.65722	−	1.21554i	0.411655	−	0.0653476i
$347$	7.24605			0.388988			0.194494	−	0.980904i	$-0.437694\pi$
$347$	7.24605			0.388988			0.194494	+	0.980904i	$0.437694\pi$
$348$	−22.9420	+	7.47209i	−1.22982	+	0.400546i
$349$	3.34575			0.179094			0.0895469	−	0.995983i	$-0.471458\pi$
$349$	3.34575			0.179094			0.0895469	+	0.995983i	$0.471458\pi$
$350$	−13.2551	−	6.35412i	−0.708514	−	0.339642i
$351$			16.8504i			0.899406i
$352$	−16.3763	−	16.3190i	−0.872859	−	0.869804i
$353$		−	12.2638i		−	0.652738i	−0.945243	−	0.326369i	$-0.894175\pi$
$353$		−	12.2638i		−	0.652738i	0.945243	−	0.326369i	$-0.105825\pi$
$354$	−4.25918	−	26.8305i	−0.226373	−	1.42603i
$355$	−3.11212	+	9.98207i	−0.165174	+	0.529794i
$356$	−0.342803	−	1.05253i	−0.0181685	−	0.0557838i
$357$	27.9576			1.47967
$358$	−1.66136	+	0.263732i	−0.0878059	+	0.0139386i
$359$		−	4.98189i		−	0.262934i	−0.991321	−	0.131467i	$-0.958031\pi$
$359$		−	4.98189i		−	0.262934i	0.991321	−	0.131467i	$-0.0419688\pi$
$360$	−1.25938	−	7.33350i	−0.0663752	−	0.386510i
$361$	18.3023	−	5.10146i	0.963280	−	0.268498i
$362$	1.13110	+	7.12534i	0.0594495	+	0.374499i
$363$		−	11.6547i		−	0.611711i
$364$	−17.8751	+	5.82185i	−0.936912	+	0.305148i
$365$	13.2023	+	4.11609i	0.691040	+	0.215446i
$366$	−2.24655	−	14.1520i	−0.117429	−	0.739739i
$367$	0.268098			0.0139946			0.00699731	−	0.999976i	$-0.497773\pi$
$367$	0.268098			0.0139946			0.00699731	+	0.999976i	$0.497773\pi$
$368$	22.9420	−	16.7175i	1.19593	−	0.871462i
$369$			1.29577i			0.0674549i
$370$	0.829294	−	5.68749i	0.0431129	−	0.295679i
$371$	4.54878			0.236161
$372$	2.15100	+	6.60432i	0.111524	+	0.342418i
$373$	37.5031			1.94183			0.970917	−	0.239415i	$-0.0769558\pi$
$373$	37.5031			1.94183			0.970917	+	0.239415i	$0.0769558\pi$
$374$	37.5652	−	5.96325i	1.94245	−	0.308352i
$375$	−14.0835	−	17.9922i	−0.727267	−	0.929113i
$376$	25.1508	−	12.8483i	1.29705	−	0.662602i
$377$			26.6922i			1.37472i
$378$	1.71765	+	10.8202i	0.0883462	+	0.556533i
$379$	−13.5658			−0.696829			−0.348415	−	0.937340i	$-0.613280\pi$
$379$	−13.5658			−0.696829			−0.348415	+	0.937340i	$0.613280\pi$
$380$	2.88527	+	19.2789i	0.148011	+	0.988986i
$381$	−14.9619			−0.766524
$382$	1.06597	+	6.71501i	0.0545396	+	0.343570i
$383$			21.0817i			1.07722i	0.842554	+	0.538612i	$0.181051\pi$
$383$			21.0817i			1.07722i	−0.842554	+	0.538612i	$0.818949\pi$
$384$	−20.6269	−	10.4462i	−1.05261	−	0.533082i
$385$	−18.1364	−	5.65440i	−0.924318	−	0.288175i
$386$	30.7764	−	4.88556i	1.56648	−	0.248669i
$387$	−9.09959			−0.462558
$388$	23.6123	−	7.69042i	1.19873	−	0.390422i
$389$	−4.88919			−0.247892			−0.123946	−	0.992289i	$-0.539555\pi$
$389$	−4.88919			−0.247892			−0.123946	+	0.992289i	$0.539555\pi$
$390$	−28.9158	−	4.21622i	−1.46421	−	0.213497i
$391$			46.7021i			2.36182i
$392$	6.74674	−	3.44658i	0.340762	−	0.174079i
$393$	23.2774			1.17419
$394$	3.54189	+	22.3120i	0.178438	+	1.12406i
$395$	2.69493	−	8.64395i	0.135597	−	0.434925i
$396$	−2.97808	−	9.14378i	−0.149654	−	0.459492i
$397$		−	3.22742i		−	0.161980i	−0.996715	−	0.0809899i	$-0.974192\pi$
$397$		−	3.22742i		−	0.161980i	0.996715	−	0.0809899i	$-0.0258081\pi$
$398$	−2.77130	−	17.4577i	−0.138912	−	0.875073i
$399$	2.50918	+	18.3474i	0.125616	+	0.918517i
$400$	−19.9936	+	0.505566i	−0.999680	+	0.0252783i
$401$		−	22.8549i		−	1.14132i	−0.821187	−	0.570659i	$-0.806688\pi$
$401$		−	22.8549i		−	1.14132i	0.821187	−	0.570659i	$-0.193312\pi$
$402$	−37.9755	+	6.02837i	−1.89404	+	0.300668i
$403$	7.68391			0.382763
$404$	18.1404	−	5.90824i	0.902519	−	0.293946i
$405$	−7.41772	+	23.7923i	−0.368590	+	1.18225i
$406$	2.72088	+	17.1401i	0.135035	+	0.850647i
$407$		−	7.42822i		−	0.368203i
$408$	33.8749	−	17.3051i	1.67706	−	0.856728i
$409$		−	35.2947i		−	1.74521i	−0.488425	−	0.872606i	$-0.662428\pi$
$409$		−	35.2947i		−	1.74521i	0.488425	−	0.872606i	$-0.337572\pi$
$410$	3.44640	+	0.502520i	0.170206	+	0.0248177i
$411$	−14.7977			−0.729915
$412$	−8.77639	−	26.9466i	−0.432382	−	1.32757i
$413$	−19.5401			−0.961505
$414$	11.6617	−	1.85122i	0.573139	−	0.0909823i
$415$	−4.96737	+	15.9328i	−0.243838	+	0.782109i
$416$	−18.0549	+	18.1183i	−0.885214	+	0.888323i
$417$	−0.0805669			−0.00394538
$418$	7.28488	+	24.1172i	0.356315	+	1.17961i
$419$			0.942419i			0.0460402i	0.999735	+	0.0230201i	$0.00732817\pi$
$419$			0.942419i			0.0460402i	−0.999735	+	0.0230201i	$0.992672\pi$
$420$	−18.9977	+	0.240153i	−0.926993	+	0.0117183i
$421$			6.45110i			0.314407i	0.987566	+	0.157204i	$0.0502479\pi$
$421$			6.45110i			0.314407i	−0.987566	+	0.157204i	$0.949752\pi$
$422$	13.4956	−	2.14235i	0.656958	−	0.104288i
$423$	11.7477			0.571192
$424$	5.51154	−	2.81558i	0.267664	−	0.136737i
$425$	18.6994	−	27.0741i	0.907055	−	1.31329i
$426$	2.11881	+	13.3474i	0.102657	+	0.646683i
$427$	−10.3066			−0.498772
$428$	−1.60772	−	4.93626i	−0.0777120	−	0.238603i
$429$	−37.7659			−1.82335
$430$	−3.52897	+	24.2025i	−0.170182	+	1.16715i
$431$	40.4739			1.94956			0.974779	−	0.223172i	$-0.0716410\pi$
$431$	40.4739			1.94956			0.974779	+	0.223172i	$0.0716410\pi$
$432$	8.77864	+	12.0472i	0.422363	+	0.579621i
$433$	−10.3942			−0.499516			−0.249758	−	0.968308i	$-0.580351\pi$
$433$	−10.3942			−0.499516			−0.249758	+	0.968308i	$0.580351\pi$
$434$	4.93412	−	0.783262i	0.236845	−	0.0375978i
$435$	−8.02917	+	25.7535i	−0.384969	+	1.23478i
$436$	−7.84089	−	24.0743i	−0.375510	−	1.15295i
$437$	−30.6485	+	4.19149i	−1.46612	+	0.200506i
$438$	17.6533	−	2.80235i	0.843506	−	0.133901i
$439$	−13.7355			−0.655558			−0.327779	−	0.944754i	$-0.606300\pi$
$439$	−13.7355			−0.655558			−0.327779	+	0.944754i	$0.606300\pi$
$440$	−25.4750	+	4.37481i	−1.21447	+	0.208561i
$441$	3.15133			0.150063
$442$	−6.59759	−	41.5612i	−0.313815	−	1.97686i
$443$	−13.5116			−0.641953			−0.320977	−	0.947087i	$-0.604011\pi$
$443$	−13.5116			−0.641953			−0.320977	+	0.947087i	$0.604011\pi$
$444$	−2.30062	−	7.06371i	−0.109182	−	0.335229i
$445$	−1.18151	−	0.368360i	−0.0560090	−	0.0174620i
$446$	−1.85821	−	11.7057i	−0.0879886	−	0.554280i
$447$			15.7594i			0.745392i
$448$	−9.74681	+	13.4749i	−0.460494	+	0.636627i
$449$			32.5385i			1.53559i	0.640697	+	0.767794i	$0.278645\pi$
$449$			32.5385i			1.53559i	−0.640697	+	0.767794i	$0.721355\pi$
$450$	−7.50172	−	3.59612i	−0.353635	−	0.169523i
$451$	4.50121			0.211954
$452$	24.6067	−	8.01428i	1.15740	−	0.376960i
$453$			17.6518i			0.829355i
$454$	1.74154	+	10.9708i	0.0817346	+	0.514883i
$455$	−6.25589	+	20.0657i	−0.293281	+	0.940694i
$456$	14.3968	+	20.6775i	0.674193	+	0.968314i
$457$		−	4.01741i		−	0.187927i	−0.995576	−	0.0939634i	$-0.970046\pi$
$457$		−	4.01741i		−	0.187927i	0.995576	−	0.0939634i	$-0.0299537\pi$
$458$	17.6311	−	2.79882i	0.823846	−	0.130780i
$459$	−24.5240			−1.14468
$460$	−0.401166	−	31.7349i	−0.0187045	−	1.47965i
$461$	−8.79412			−0.409583			−0.204792	−	0.978806i	$-0.565652\pi$
$461$	−8.79412			−0.409583			−0.204792	+	0.978806i	$0.565652\pi$
$462$	−24.2508	+	3.84967i	−1.12825	+	0.179103i
$463$	12.4815			0.580065			0.290032	−	0.957017i	$-0.406334\pi$
$463$	12.4815			0.580065			0.290032	+	0.957017i	$0.406334\pi$
$464$	13.9060	+	19.0837i	0.645571	+	0.885937i
$465$	7.41367	+	2.31136i	0.343801	+	0.107187i
$466$	1.57031	+	9.89208i	0.0727431	+	0.458242i
$467$	6.35790			0.294209			0.147104	−	0.989121i	$-0.453005\pi$
$467$	6.35790			0.294209			0.147104	+	0.989121i	$0.453005\pi$
$468$	−10.1164	+	3.29488i	−0.467633	+	0.152306i
$469$			27.6567i			1.27707i
$470$	4.55595	−	31.2458i	0.210150	−	1.44126i
$471$	35.2643			1.62489
$472$	−23.6758	+	12.0948i	−1.08977	+	0.556709i
$473$			31.6100i			1.45343i
$474$	−1.83478	−	11.5581i	−0.0842744	−	0.530883i
$475$	19.4458	+	9.84172i	0.892236	+	0.451569i
$476$	−8.47310	−	26.0154i	−0.388364	−	1.19242i
$477$	2.57438			0.117873
$478$	3.89369	+	24.5281i	0.178093	+	1.12189i
$479$			26.0062i			1.18825i	0.804372	+	0.594127i	$0.202502\pi$
$479$			26.0062i			1.18825i	−0.804372	+	0.594127i	$0.797498\pi$
$480$	−22.8700	+	12.0501i	−1.04387	+	0.550008i
$481$	−8.21839			−0.374726
$482$	−5.65563	−	35.6274i	−0.257607	−	1.62278i
$483$		−	30.1493i		−	1.37184i
$484$	−10.8450	+	3.53217i	−0.492955	+	0.160553i
$485$	8.26377	−	26.5059i	0.375238	−	1.20357i
$486$	2.57140	+	16.1984i	0.116641	+	0.734774i
$487$		−	9.02248i		−	0.408848i	−0.978882	−	0.204424i	$-0.934468\pi$
$487$		−	9.02248i		−	0.408848i	0.978882	−	0.204424i	$-0.0655321\pi$
$488$	−12.4880	+	6.37953i	−0.565307	+	0.288788i
$489$		−	10.6531i		−	0.481751i
$490$	1.22214	−	8.38171i	0.0552106	−	0.378647i
$491$		−	33.0190i		−	1.49013i	−0.666994	−	0.745063i	$-0.732419\pi$
$491$		−	33.0190i		−	1.49013i	0.666994	−	0.745063i	$-0.267581\pi$
$492$	4.28033	−	1.39408i	0.192972	−	0.0628501i
$493$	−38.8478			−1.74962
$494$	26.6827	−	8.05980i	1.20051	−	0.362628i
$495$	−10.2643	−	3.20011i	−0.461347	−	0.143834i
$496$	5.49363	−	4.00314i	0.246671	−	0.179746i
$497$	9.72060			0.436029
$498$	3.38192	+	21.3043i	0.151547	+	0.954667i
$499$			13.3058i			0.595649i	0.954621	+	0.297824i	$0.0962610\pi$
$499$			13.3058i			0.595649i	−0.954621	+	0.297824i	$0.903739\pi$
$500$	−12.4740	+	18.5580i	−0.557855	+	0.829938i
$501$	−28.9073			−1.29148
$502$	3.93510	+	24.7890i	0.175632	+	1.10639i
$503$	−11.5983			−0.517144			−0.258572	−	0.965992i	$-0.583252\pi$
$503$	−11.5983			−0.517144			−0.258572	+	0.965992i	$0.583252\pi$
$504$	−6.16027	+	3.14698i	−0.274400	+	0.140178i
$505$	6.34873	−	20.3635i	0.282515	−	0.906163i
$506$	−6.43072	−	40.5101i	−0.285881	−	1.80089i
$507$			15.2158i			0.675756i
$508$	4.53451	+	13.9226i	0.201186	+	0.617713i
$509$			15.7154i			0.696571i	0.937389	+	0.348285i	$0.113236\pi$
$509$			15.7154i			0.696571i	−0.937389	+	0.348285i	$0.886764\pi$
$510$	6.13628	−	42.0841i	0.271719	−	1.86351i
$511$		−	12.8565i		−	0.568737i
$512$	−3.46916	+	22.3599i	−0.153317	+	0.988177i
$513$	−2.20102	−	16.0940i	−0.0971772	−	0.710568i
$514$	16.2548	−	2.58035i	0.716970	−	0.113815i
$515$	−30.2489	−	9.43071i	−1.33293	−	0.415567i
$516$	9.79003	+	30.0589i	0.430982	+	1.32327i
$517$		−	40.8089i		−	1.79477i
$518$	−5.27733	+	0.837744i	−0.231873	+	0.0368083i
$519$		−	11.2038i		−	0.491794i
$520$	4.84018	+	28.1849i	0.212256	+	1.23599i
$521$			33.8676i			1.48377i	0.670529	+	0.741883i	$0.266067\pi$
$521$			33.8676i			1.48377i	−0.670529	+	0.741883i	$0.733933\pi$
$522$	1.53988	+	9.70043i	0.0673989	+	0.424576i
$523$			33.9095i			1.48276i	0.671086	+	0.741379i	$0.265828\pi$
$523$			33.9095i			1.48276i	−0.671086	+	0.741379i	$0.734172\pi$
$524$	−7.05468	−	21.6604i	−0.308185	−	0.946238i
$525$	−12.0717	+	17.4782i	−0.526853	+	0.762810i
$526$	38.0140	−	6.03450i	1.65749	−	0.263117i
$527$			11.1831i			0.487146i
$528$	−27.0008	+	19.6751i	−1.17506	+	0.856250i
$529$	27.3632			1.18970
$530$	0.998388	−	6.84718i	0.0433672	−	0.297423i
$531$	−11.0587			−0.479908
$532$	16.3123	−	7.89540i	0.707229	−	0.342309i
$533$		−	4.98003i		−	0.215709i
$534$	−1.57984	+	0.250790i	−0.0683664	+	0.0108527i
$535$	−5.54119	−	1.72758i	−0.239567	−	0.0746898i
$536$	17.1188	+	33.5103i	0.739419	+	1.44743i
$537$			2.43086i			0.104900i
$538$	4.52453	+	28.5021i	0.195066	+	1.22881i
$539$		−	10.9470i		−	0.471522i
$540$	16.6645	−	0.210659i	0.717125	−	0.00906531i
$541$	12.8556			0.552705			0.276352	−	0.961056i	$-0.410874\pi$
$541$	12.8556			0.552705			0.276352	+	0.961056i	$0.410874\pi$
$542$	−0.634184	−	3.99501i	−0.0272405	−	0.171601i
$543$	10.4256			0.447405
$544$	−26.3694	−	26.2771i	−1.13058	−	1.12662i
$545$	−27.0246	−	8.42546i	−1.15760	−	0.360907i
$546$	4.25918	+	26.8305i	0.182276	+	1.14824i
$547$		−	14.9025i		−	0.637187i	−0.947892	−	0.318593i	$-0.896790\pi$
$547$		−	14.9025i		−	0.637187i	0.947892	−	0.318593i	$-0.103210\pi$
$548$	4.48472	+	13.7697i	0.191578	+	0.588212i
$549$	−5.83303			−0.248948
$550$	−12.4921	+	26.0594i	−0.532666	+	1.11117i
$551$	−3.48657	−	25.4941i	−0.148533	−	1.08609i
$552$	−18.6617	−	36.5305i	−0.794293	−	1.55484i
$553$	−8.41753			−0.357950
$554$	−0.176614	−	1.11257i	−0.00750363	−	0.0472688i
$555$	−7.92935	−	2.47214i	−0.336582	−	0.104936i
$556$	0.0244174	+	0.0749700i	0.00103553	+	0.00317944i
$557$		−	10.7020i		−	0.453458i	−0.973958	−	0.226729i	$-0.927197\pi$
$557$		−	10.7020i		−	0.453458i	0.973958	−	0.226729i	$-0.0728032\pi$
$558$	2.79247	−	0.443287i	0.118215	−	0.0187658i
$559$	34.9725			1.47918
$560$	5.98109	+	17.6052i	0.252747	+	0.743954i
$561$		−	54.9644i		−	2.32060i
$562$	−1.78408	−	11.2387i	−0.0752569	−	0.474078i
$563$			27.6932i			1.16713i	0.812066	+	0.583565i	$0.198343\pi$
$563$			27.6932i			1.16713i	−0.812066	+	0.583565i	$0.801657\pi$
$564$	−12.6390	−	38.8064i	−0.532200	−	1.63404i
$565$	8.61177	−	27.6222i	0.362300	−	1.16207i
$566$	−40.6029	+	6.44547i	−1.70667	+	0.270923i
$567$	23.1690			0.973008
$568$	11.7780	−	6.01681i	0.494194	−	0.252460i
$569$			32.1609i			1.34825i	0.738616	+	0.674127i	$0.235480\pi$
$569$			32.1609i			1.34825i	−0.738616	+	0.674127i	$0.764520\pi$
$570$	28.1687	+	0.249949i	1.17986	+	0.0104692i
$571$			44.0887i			1.84506i	0.385930	+	0.922528i	$0.373881\pi$
$571$			44.0887i			1.84506i	−0.385930	+	0.922528i	$0.626119\pi$
$572$	11.4457	+	35.1423i	0.478568	+	1.46937i
$573$	9.82522			0.410455
$574$	−0.507640	−	3.19786i	−0.0211885	−	0.133476i
$575$	−29.1966	−	20.1653i	−1.21758	−	0.840952i
$576$	−5.51621	+	7.62611i	−0.229842	+	0.317754i
$577$			36.7343i			1.52927i	0.644465	+	0.764633i	$0.277080\pi$
$577$			36.7343i			1.52927i	−0.644465	+	0.764633i	$0.722920\pi$
$578$	36.7437	−	5.83285i	1.52834	−	0.242614i
$579$		−	45.0311i		−	1.87143i
$580$	26.3978	−	0.333699i	1.09611	−	0.0138561i
$581$	15.5154			0.643688
$582$	−5.62620	−	35.4420i	−0.233214	−	1.46912i
$583$		−	8.94284i		−	0.370375i
$584$	−7.95784	−	15.5776i	−0.329298	−	0.644606i
$585$	−3.54052	+	11.3562i	−0.146383	+	0.469521i
$586$	0.416116	−	0.0660559i	0.0171896	−	0.00272874i
$587$	16.3518			0.674912			0.337456	−	0.941341i	$-0.390434\pi$
$587$	16.3518			0.674912			0.337456	+	0.941341i	$0.390434\pi$
$588$	−3.39044	−	10.4099i	−0.139819	−	0.429295i
$589$	−7.33901	+	1.00368i	−0.302399	+	0.0413560i
$590$	−4.28876	+	29.4133i	−0.176565	+	1.21093i
$591$	32.6463			1.34289
$592$	−5.87575	+	4.28159i	−0.241492	+	0.175972i
$593$			15.2822i			0.627565i	0.949495	+	0.313782i	$0.101596\pi$
$593$			15.2822i			0.627565i	−0.949495	+	0.313782i	$0.898404\pi$
$594$	21.2725	−	3.37687i	0.872820	−	0.138555i
$595$	−29.2036	−	9.10480i	−1.19723	−	0.373261i
$596$	14.6646	−	4.77618i	0.600684	−	0.195640i
$597$	−25.5436			−1.04543
$598$	−44.8193	+	7.11479i	−1.83280	+	0.290945i
$599$	18.0855			0.738954			0.369477	−	0.929240i	$-0.379537\pi$
$599$	18.0855			0.738954			0.369477	+	0.929240i	$0.379537\pi$
$600$	−3.80821	+	28.6496i	−0.155470	+	1.16961i
$601$		−	7.44723i		−	0.303779i	−0.988397	−	0.151889i	$-0.951464\pi$
$601$		−	7.44723i		−	0.303779i	0.988397	−	0.151889i	$-0.0485358\pi$
$602$	22.4571	−	3.56493i	0.915284	−	0.145296i
$603$			15.6523i			0.637412i
$604$	16.4256	−	5.34973i	0.668347	−	0.217677i
$605$	−3.79551	+	12.1740i	−0.154309	+	0.494945i
$606$	−4.32239	−	27.2287i	−0.175585	−	1.10609i
$607$			14.8938i			0.604520i	0.953226	+	0.302260i	$0.0977410\pi$
$607$			14.8938i			0.604520i	−0.953226	+	0.302260i	$0.902259\pi$
$608$	14.8778	−	19.6634i	0.603376	−	0.797457i
$609$	25.0789			1.01625
$610$	−2.26215	+	15.5143i	−0.0915917	+	0.628157i
$611$	−45.1499			−1.82657
$612$	−4.79536	−	14.7234i	−0.193841	−	0.595160i
$613$		−	22.5813i		−	0.912048i	−0.889967	−	0.456024i	$-0.849273\pi$
$613$		−	22.5813i		−	0.912048i	0.889967	−	0.456024i	$-0.150727\pi$
$614$	4.02175	+	25.3348i	0.162305	+	1.02243i
$615$	1.49802	−	4.80488i	0.0604059	−	0.193751i
$616$	10.9319	+	21.3995i	0.440460	+	0.862208i
$617$		−	22.8933i		−	0.921651i	−0.887491	−	0.460826i	$-0.847553\pi$
$617$		−	22.8933i		−	0.921651i	0.887491	−	0.460826i	$-0.152447\pi$
$618$	−40.4468	+	6.42069i	−1.62701	+	0.258278i
$619$		−	20.8399i		−	0.837627i	−0.908072	−	0.418813i	$-0.862446\pi$
$619$		−	20.8399i		−	0.837627i	0.908072	−	0.418813i	$-0.137554\pi$
$620$	−0.0960622	−	7.59915i	−0.00385795	−	0.305189i
$621$			26.4465i			1.06126i
$622$	0.707721	+	4.45826i	0.0283770	+	0.178760i
$623$			1.15056i			0.0460963i
$624$	21.7681	+	29.8730i	0.871420	+	1.19588i
$625$	8.85167	+	23.3805i	0.354067	+	0.935220i
$626$	−1.19463	−	7.52553i	−0.0477471	−	0.300781i
$627$	36.0707	−	4.93303i	1.44053	−	0.197006i
$628$	−10.6875	−	32.8145i	−0.426479	−	1.30944i
$629$		−	11.9610i		−	0.476917i
$630$	−1.11590	+	7.65313i	−0.0444586	+	0.304908i
$631$		−	39.1233i		−	1.55747i	−0.627352	−	0.778736i	$-0.715861\pi$
$631$		−	39.1233i		−	1.55747i	0.627352	−	0.778736i	$-0.284139\pi$
$632$	−10.1991	+	5.21024i	−0.405700	+	0.207252i
$633$		−	19.7465i		−	0.784852i
$634$	−27.3244	+	4.33758i	−1.08519	+	0.172267i
$635$	15.6287	+	4.87257i	0.620207	+	0.193362i
$636$	−2.76972	−	8.50401i	−0.109826	−	0.337206i
$637$	−12.1115			−0.479876
$638$	33.6972	−	5.34922i	1.33408	−	0.211778i
$639$	5.50138			0.217631
$640$	18.1442	+	17.6292i	0.717211	+	0.696856i
$641$		−	31.6593i		−	1.25047i	−0.780438	−	0.625233i	$-0.785004\pi$
$641$		−	31.6593i		−	1.25047i	0.780438	−	0.625233i	$-0.214996\pi$
$642$	−7.40932	+	1.17618i	−0.292423	+	0.0464203i
$643$	41.4100			1.63305			0.816525	−	0.577310i	$-0.195898\pi$
$643$	41.4100			1.63305			0.816525	+	0.577310i	$0.195898\pi$
$644$	−28.0549	+	9.13733i	−1.10552	+	0.360061i
$645$	33.7425	+	10.5199i	1.32861	+	0.414221i
$646$	11.7302	+	38.8339i	0.461519	+	1.52790i
$647$	10.3940			0.408632			0.204316	−	0.978905i	$-0.434503\pi$
$647$	10.3940			0.408632			0.204316	+	0.978905i	$0.434503\pi$
$648$	28.0728	−	14.3410i	1.10281	−	0.563370i
$649$			38.4156i			1.50794i
$650$	28.8314	+	13.8210i	1.13086	+	0.542104i
$651$		−	7.21947i		−	0.282953i
$652$	−9.91307	+	3.22864i	−0.388226	+	0.126443i
$653$			10.9657i			0.429122i	0.976711	+	0.214561i	$0.0688321\pi$
$653$			10.9657i			0.429122i	−0.976711	+	0.214561i	$0.931168\pi$
$654$	−36.1355	+	5.73629i	−1.41301	+	0.224307i
$655$	−24.3148	−	7.58063i	−0.950058	−	0.296200i
$656$	−2.59448	−	3.56048i	−0.101297	−	0.139013i
$657$		−	7.27613i		−	0.283869i
$658$	−28.9924	+	4.60237i	−1.13024	+	0.179419i
$659$	−4.33670			−0.168934			−0.0844668	−	0.996426i	$-0.526919\pi$
$659$	−4.33670			−0.168934			−0.0844668	+	0.996426i	$0.526919\pi$
$660$	0.472139	+	37.3493i	0.0183780	+	1.45382i
$661$			37.7050i			1.46655i	0.679930	+	0.733277i	$0.262010\pi$
$661$			37.7050i			1.46655i	−0.679930	+	0.733277i	$0.737990\pi$
$662$	−6.72030	+	1.06681i	−0.261192	+	0.0414626i
$663$	−60.8112			−2.36171
$664$	18.7993	−	9.60365i	0.729555	−	0.372694i
$665$	3.35408	−	19.9822i	0.130066	−	0.774875i
$666$	−2.98671	+	0.474122i	−0.115733	+	0.0183718i
$667$			41.8932i			1.62211i
$668$	8.76093	+	26.8992i	0.338971	+	1.04076i
$669$	−17.1274			−0.662185
$670$	41.6311	+	6.07023i	1.60835	+	0.234514i
$671$			20.2627i			0.782232i
$672$	17.0232	+	16.9636i	0.656684	+	0.654385i
$673$	−6.00665			−0.231539			−0.115770	−	0.993276i	$-0.536933\pi$
$673$	−6.00665			−0.231539			−0.115770	+	0.993276i	$0.536933\pi$
$674$	−3.63174	+	0.576517i	−0.139889	+	0.0222066i
$675$	10.5891	−	15.3316i	0.407576	−	0.590112i
$676$	14.1588	−	4.61144i	0.544567	−	0.177363i
$677$	−19.6709			−0.756013			−0.378007	−	0.925803i	$-0.623390\pi$
$677$	−19.6709			−0.756013			−0.378007	+	0.925803i	$0.623390\pi$
$678$	−5.86314	−	36.9346i	−0.225172	−	1.41846i
$679$	−25.8116			−0.990560
$680$	−41.0202	+	7.04439i	−1.57305	+	0.270140i
$681$	16.0521			0.615118
$682$	−1.53988	−	9.70043i	−0.0589652	−	0.371449i
$683$		−	38.4534i		−	1.47138i	−0.677319	−	0.735690i	$-0.736858\pi$
$683$		−	38.4534i		−	1.47138i	0.677319	−	0.735690i	$-0.263142\pi$
$684$	9.23197	−	4.46840i	0.352993	−	0.170854i
$685$	15.4571	+	4.81908i	0.590587	+	0.184127i
$686$	−28.1019	+	4.46101i	−1.07294	+	0.170322i
$687$		−	25.7973i		−	0.984228i
$688$	25.0036	−	18.2198i	0.953255	−	0.694625i
$689$	−9.89414			−0.376937
$690$	−45.3831	−	6.61732i	−1.72771	−	0.251917i
$691$		−	30.3813i		−	1.15576i	−0.816121	−	0.577880i	$-0.803880\pi$
$691$		−	30.3813i		−	1.15576i	0.816121	−	0.577880i	$-0.196120\pi$
$692$	−10.4255	+	3.39554i	−0.396319	+	0.129079i
$693$			9.99546i			0.379696i
$694$	−10.1207	+	1.60660i	−0.384178	+	0.0609859i
$695$	0.0841574	+	0.0262378i	0.00319227	+	0.000995256i
$696$	30.3869	−	15.5232i	1.15181	−	0.588405i
$697$	7.24792			0.274535
$698$	−4.67309	+	0.741824i	−0.176879	+	0.0280785i
$699$	14.4738			0.547450
$700$	19.9225	+	5.93602i	0.753001	+	0.224360i
$701$	9.48317			0.358175			0.179087	−	0.983833i	$-0.442686\pi$
$701$	9.48317			0.358175			0.179087	+	0.983833i	$0.442686\pi$
$702$	−3.73609	−	23.5353i	−0.141010	−	0.888283i
$703$	7.84950	−	1.07350i	0.296050	−	0.0404877i
$704$	26.4914	+	19.1621i	0.998433	+	0.722200i
$705$	−43.5620	−	13.5813i	−1.64064	−	0.511503i
$706$	2.71915	+	17.1292i	0.102337	+	0.644665i
$707$	−19.8301			−0.745786
$708$	11.8978	+	36.5305i	0.447147	+	1.37290i
$709$	35.7244			1.34166			0.670829	−	0.741612i	$-0.265938\pi$
$709$	35.7244			1.34166			0.670829	+	0.741612i	$0.265938\pi$
$710$	2.13353	−	14.6322i	0.0800699	−	0.549138i
$711$	−4.76391			−0.178660
$712$	0.712169	+	1.39408i	0.0266897	+	0.0522455i
$713$	12.0598			0.451644
$714$	−39.0491	+	6.19880i	−1.46138	+	0.231984i
$715$	39.4489	+	12.2990i	1.47531	+	0.459957i
$716$	2.26199	−	0.736721i	0.0845347	−	0.0275325i
$717$	35.8889			1.34030
$718$	1.10459	+	6.95833i	0.0412230	+	0.259683i
$719$			6.57919i			0.245362i	0.992446	+	0.122681i	$0.0391492\pi$
$719$			6.57919i			0.245362i	−0.992446	+	0.122681i	$0.960851\pi$
$720$	3.38500	+	9.96365i	0.126152	+	0.371323i
$721$			29.4565i			1.09702i
$722$	−24.4322	+	11.1834i	−0.909272	+	0.416201i
$723$	−52.1291			−1.93870
$724$	−3.15968	−	9.70134i	−0.117429	−	0.360548i
$725$	16.7740	−	24.2864i	0.622970	−	0.901973i
$726$	2.58409	+	16.2783i	0.0959045	+	0.604146i
$727$	1.20206			0.0445818			0.0222909	−	0.999752i	$-0.492904\pi$
$727$	1.20206			0.0445818			0.0222909	+	0.999752i	$0.492904\pi$
$728$	23.6758	−	12.0948i	0.877484	−	0.448264i
$729$	−9.73500			−0.360555
$730$	−19.3526	−	2.82181i	−0.716272	−	0.104440i
$731$			50.8989i			1.88256i
$732$	6.27562	+	19.2684i	0.231954	+	0.712180i
$733$			34.8374i			1.28675i	0.765551	+	0.643375i	$0.222466\pi$
$733$			34.8374i			1.28675i	−0.765551	+	0.643375i	$0.777534\pi$
$734$	−0.374460	+	0.0594432i	−0.0138216	+	0.00219409i
$735$	−11.6856	−	3.64321i	−0.431028	−	0.134382i
$736$	−28.3370	+	28.4365i	−1.04452	+	1.04818i
$737$	54.3728			2.00285
$738$	−0.287299	−	1.80983i	−0.0105756	−	0.0666207i
$739$			10.0566i			0.369939i	0.982744	+	0.184969i	$0.0592186\pi$
$739$			10.0566i			0.369939i	−0.982744	+	0.184969i	$0.940781\pi$
$740$	0.102744	+	8.12773i	0.00377695	+	0.298781i
$741$	−5.45778	−	39.9077i	−0.200496	−	1.46605i
$742$	−6.35339	+	1.00856i	−0.233240	+	0.0370255i
$743$		−	33.2676i		−	1.22047i	−0.792220	−	0.610235i	$-0.791075\pi$
$743$		−	33.2676i		−	1.22047i	0.792220	−	0.610235i	$-0.208925\pi$
$744$	−4.46867	−	8.74750i	−0.163829	−	0.320699i
$745$	5.13226	−	16.4617i	0.188032	−	0.603109i
$746$	−52.3814	+	8.31523i	−1.91782	+	0.304442i
$747$	8.78096			0.321279
$748$	−51.1461	+	16.6580i	−1.87009	+	0.609078i
$749$			5.39604i			0.197167i
$750$	23.6600	+	22.0075i	0.863940	+	0.803601i
$751$	35.0253			1.27809			0.639045	−	0.769169i	$-0.279330\pi$
$751$	35.0253			1.27809			0.639045	+	0.769169i	$0.279330\pi$
$752$	−32.2800	+	23.5220i	−1.17713	+	0.857761i
$753$	36.2705			1.32177
$754$	−5.91824	−	37.2817i	−0.215530	−	1.35772i
$755$	5.74857	−	18.4385i	0.209212	−	0.671045i
$756$	−4.79816	−	14.7320i	−0.174507	−	0.535799i
$757$		−	15.6212i		−	0.567764i	−0.958859	−	0.283882i	$-0.908378\pi$
$757$		−	15.6212i		−	0.567764i	0.958859	−	0.283882i	$-0.0916224\pi$
$758$	18.9477	−	3.00783i	0.688212	−	0.109249i
$759$	−59.2732			−2.15148
$760$	−8.30447	−	26.2876i	−0.301235	−	0.953550i
$761$	−39.5461			−1.43355			−0.716773	−	0.697307i	$-0.754381\pi$
$761$	−39.5461			−1.43355			−0.716773	+	0.697307i	$0.754381\pi$
$762$	20.8977	−	3.31738i	0.757044	−	0.120176i
$763$			26.3167i			0.952728i
$764$	−2.97772	−	9.14267i	−0.107730	−	0.330770i
$765$	−16.5278	−	5.15287i	−0.597563	−	0.186302i
$766$	−4.67426	−	29.4453i	−0.168888	−	1.06390i
$767$	42.5020			1.53466
$768$	31.1262	+	10.0171i	1.12317	+	0.361460i
$769$	−22.9425			−0.827327			−0.413664	−	0.910430i	$-0.635751\pi$
$769$	−22.9425			−0.827327			−0.413664	+	0.910430i	$0.635751\pi$
$770$	26.5853	+	3.87641i	0.958068	+	0.139696i
$771$		−	23.7836i		−	0.856546i
$772$	−41.9029	+	13.6476i	−1.50812	+	0.491187i
$773$	−19.3863			−0.697276			−0.348638	−	0.937258i	$-0.613356\pi$
$773$	−19.3863			−0.697276			−0.348638	+	0.937258i	$0.613356\pi$
$774$	12.7096	−	2.01757i	0.456838	−	0.0725202i
$775$	−6.99133	−	4.82874i	−0.251136	−	0.173453i
$776$	−31.2748	+	15.9767i	−1.12270	+	0.573532i
$777$			7.72164i			0.277012i
$778$	6.82885	−	1.08404i	0.244826	−	0.0388647i
$779$	0.650497	+	4.75649i	0.0233065	+	0.170419i
$780$	41.3223	−	0.522362i	1.47958	−	0.0187036i
$781$		−	19.1106i		−	0.683831i
$782$	−10.3548	−	65.2299i	−0.370289	−	2.33262i
$783$	−21.9988			−0.786173
$784$	−8.65915	+	6.30982i	−0.309256	+	0.225351i
$785$	−36.8359	−	11.4843i	−1.31473	−	0.409893i
$786$	−32.5122	+	5.16111i	−1.15967	+	0.184091i
$787$			29.3498i			1.04621i	0.852269	+	0.523104i	$0.175226\pi$
$787$			29.3498i			1.04621i	−0.852269	+	0.523104i	$0.824774\pi$
$788$	−9.89410	−	30.3784i	−0.352463	−	1.08219i
$789$		−	55.6211i		−	1.98016i
$790$	−1.84752	+	12.6707i	−0.0657319	+	0.450805i
$791$	−26.8986			−0.956405
$792$	6.18693	+	12.1110i	0.219843	+	0.430347i
$793$	22.4181			0.796091
$794$	0.715589	+	4.50782i	0.0253953	+	0.159977i
$795$	−9.54616	−	2.97621i	−0.338567	−	0.105555i
$796$	7.74147	+	23.7691i	0.274389	+	0.842473i
$797$	31.3818			1.11160			0.555801	−	0.831315i	$-0.312412\pi$
$797$	31.3818			1.11160			0.555801	+	0.831315i	$0.312412\pi$
$798$	−7.57264	−	25.0699i	−0.268069	−	0.887464i
$799$		−	65.7111i		−	2.32469i
$800$	27.8135	−	5.13915i	0.983355	−	0.181696i
$801$			0.651162i			0.0230077i
$802$	5.06742	+	31.9220i	0.178937	+	1.12720i
$803$	−25.2757			−0.891960
$804$	51.7047	−	16.8400i	1.82348	−	0.593899i
$805$	−9.81856	+	31.4929i	−0.346059	+	1.10998i
$806$	−10.7323	+	1.70369i	−0.378030	+	0.0600099i
$807$	41.7035			1.46803
$808$	−24.0272	+	12.2743i	−0.845273	+	0.431809i
$809$	−23.5494			−0.827952			−0.413976	−	0.910288i	$-0.635860\pi$
$809$	−23.5494			−0.827952			−0.413976	+	0.910288i	$0.635860\pi$
$810$	5.08526	−	34.8759i	0.178678	−	1.22541i
$811$	−47.4895			−1.66758			−0.833790	−	0.552081i	$-0.813834\pi$
$811$	−47.4895			−1.66758			−0.833790	+	0.552081i	$0.813834\pi$
$812$	−7.60064	−	23.3367i	−0.266730	−	0.818957i
$813$	−5.84539			−0.205007
$814$	1.64700	+	10.3752i	0.0577272	+	0.363650i
$815$	−3.46935	+	11.1279i	−0.121526	+	0.389793i
$816$	−43.4771	+	31.6812i	−1.52200	+	1.10906i
$817$	−33.4027	+	4.56815i	−1.16861	+	0.159819i
$818$	7.82560	+	49.2970i	0.273616	+	1.72363i
$819$	11.0587			0.386423
$820$	−4.92509	+	0.0622589i	−0.171992	+	0.00217418i
$821$	47.3269			1.65172			0.825861	−	0.563874i	$-0.190690\pi$
$821$	47.3269			1.65172			0.825861	+	0.563874i	$0.190690\pi$
$822$	20.6683	−	3.28096i	0.720889	−	0.114437i
$823$	−4.33210			−0.151007			−0.0755037	−	0.997146i	$-0.524056\pi$
$823$	−4.33210			−0.151007			−0.0755037	+	0.997146i	$0.524056\pi$
$824$	18.2329	+	35.6911i	0.635172	+	1.24336i
$825$	34.3619	+	23.7329i	1.19633	+	0.826273i
$826$	27.2921	−	4.33246i	0.949614	−	0.150745i
$827$		−	31.5182i		−	1.09599i	−0.836480	−	0.547997i	$-0.815391\pi$
$827$		−	31.5182i		−	1.09599i	0.836480	−	0.547997i	$-0.184609\pi$
$828$	−15.8777	+	5.17128i	−0.551787	+	0.179714i
$829$		−	17.6063i		−	0.611493i	−0.952113	−	0.305747i	$-0.901094\pi$
$829$		−	17.6063i		−	0.611493i	0.952113	−	0.305747i	$-0.0989060\pi$
$830$	3.40540	−	23.3551i	0.118203	−	0.810666i
$831$	−1.62789			−0.0564708
$832$	21.2005	−	29.3095i	0.734995	−	1.01612i
$833$		−	17.6271i		−	0.610742i
$834$	0.112530	−	0.0178634i	0.00389659	−	0.000618559i
$835$	30.1956	+	9.41409i	1.04496	+	0.325788i
$836$	−15.5223	−	32.0699i	−0.536849	−	1.10916i
$837$			6.33281i			0.218894i
$838$	−0.208955	−	1.31630i	−0.00721822	−	0.0454708i
$839$	26.0009			0.897652			0.448826	−	0.893619i	$-0.351842\pi$
$839$	26.0009			0.897652			0.448826	+	0.893619i	$0.351842\pi$
$840$	26.4813	−	4.54763i	0.913692	−	0.156908i
$841$	−5.84775			−0.201646
$842$	−1.43035	−	9.01041i	−0.0492930	−	0.310519i
$843$	−16.4442			−0.566369
$844$	−18.3747	+	5.98455i	−0.632483	+	0.205997i
$845$	4.95524	−	15.8939i	0.170465	−	0.546766i
$846$	−16.4083	+	2.60471i	−0.564128	+	0.0895519i
$847$	11.8552			0.407348
$848$	−7.07383	+	5.15461i	−0.242916	+	0.177010i
$849$			59.4091i			2.03892i
$850$	−20.1150	+	41.9612i	−0.689940	+	1.43926i
$851$	−12.8987			−0.442161
$852$	−5.91880	−	18.1728i	−0.202775	−	0.622591i
$853$		−	46.2282i		−	1.58282i	−0.611284	−	0.791411i	$-0.709347\pi$
$853$		−	46.2282i		−	1.58282i	0.611284	−	0.791411i	$-0.290653\pi$
$854$	14.3955	−	2.28520i	0.492604	−	0.0781979i
$855$	1.89824	−	11.3089i	0.0649185	−	0.386757i
$856$	3.34001	+	6.53814i	0.114159	+	0.223469i
$857$	−30.9917			−1.05866			−0.529329	−	0.848417i	$-0.677556\pi$
$857$	−30.9917			−1.05866			−0.529329	+	0.848417i	$0.677556\pi$
$858$	52.7485	−	8.37351i	1.80081	−	0.285867i
$859$			15.3528i			0.523829i	0.965091	+	0.261915i	$0.0843539\pi$
$859$			15.3528i			0.523829i	−0.965091	+	0.261915i	$0.915646\pi$
$860$	−0.437217	−	34.5867i	−0.0149090	−	1.17940i
$861$	−4.67902			−0.159460
$862$	−56.5309	+	8.97393i	−1.92545	+	0.305653i
$863$		−	21.0012i		−	0.714889i	−0.933934	−	0.357445i	$-0.883648\pi$
$863$		−	21.0012i		−	0.714889i	0.933934	−	0.357445i	$-0.116352\pi$
$864$	−14.9325	−	14.8802i	−0.508013	−	0.506235i
$865$	−3.64869	+	11.7031i	−0.124059	+	0.397918i
$866$	14.5179	−	2.30463i	0.493338	−	0.0783144i
$867$		−	53.7624i		−	1.82587i
$868$	−6.71794	+	2.18800i	−0.228022	+	0.0742656i
$869$			16.5488i			0.561379i
$870$	5.50444	−	37.7507i	0.186618	−	1.27987i
$871$		−	60.1567i		−	2.03833i
$872$	16.2894	+	31.8867i	0.551627	+	1.07982i
$873$	−14.6081			−0.494410
$874$	41.8782	−	12.6498i	1.41655	−	0.427885i
$875$	18.3017	−	14.3257i	0.618711	−	0.484299i
$876$	−24.0354	+	7.82822i	−0.812081	+	0.264491i
$877$	−18.6172			−0.628657			−0.314328	−	0.949314i	$-0.601779\pi$
$877$	−18.6172			−0.628657			−0.314328	+	0.949314i	$0.601779\pi$
$878$	19.1847	−	3.04545i	0.647451	−	0.102779i
$879$		−	0.608850i		−	0.0205360i
$880$	34.6116	−	11.7588i	1.16676	−	0.396388i
$881$	42.3381			1.42641			0.713203	−	0.700958i	$-0.247244\pi$
$881$	42.3381			1.42641			0.713203	+	0.700958i	$0.247244\pi$
$882$	−4.40154	+	0.698718i	−0.148208	+	0.0235270i
$883$	13.6012			0.457718			0.228859	−	0.973460i	$-0.426501\pi$
$883$	13.6012			0.457718			0.228859	+	0.973460i	$0.426501\pi$
$884$	18.4300	+	56.5867i	0.619869	+	1.90322i
$885$	41.0072	+	12.7848i	1.37844	+	0.429758i
$886$	18.8719	−	2.99580i	0.634015	−	0.100646i
$887$		−	24.8694i		−	0.835032i	−0.908670	−	0.417516i	$-0.862901\pi$
$887$		−	24.8694i		−	0.835032i	0.908670	−	0.417516i	$-0.137099\pi$
$888$	4.77950	+	9.35596i	0.160390	+	0.313965i
$889$		−	15.2193i		−	0.510441i
$890$	1.73192	+	0.252531i	0.0580541	+	0.00846487i
$891$		−	45.5501i		−	1.52599i
$892$	5.19080	+	15.9376i	0.173801	+	0.533631i
$893$	43.1233	−	5.89754i	1.44307	−	0.197354i
$894$	−3.49419	−	22.0115i	−0.116863	−	0.736174i
$895$	0.791646	−	2.53920i	0.0264618	−	0.0848760i
$896$	10.6259	−	20.9817i	0.354988	−	0.700951i
$897$			65.5784i			2.18960i
$898$	−7.21449	−	45.4473i	−0.240751	−	1.51660i
$899$			10.0316i			0.334574i
$900$	11.2752	+	3.35949i	0.375839	+	0.111983i
$901$		−	14.3999i		−	0.479730i
$902$	−6.28695	+	0.998015i	−0.209333	+	0.0332303i
$903$		−	32.8586i		−	1.09347i
$904$	−32.5918	+	16.6496i	−1.08399	+	0.553756i
$905$	−10.8902	−	3.39525i	−0.362003	−	0.112862i
$906$	−3.91379	−	24.6547i	−0.130027	−	0.819098i
$907$			7.43282i			0.246803i	0.992357	+	0.123401i	$0.0393803\pi$
$907$			7.43282i			0.246803i	−0.992357	+	0.123401i	$0.960620\pi$
$908$	−4.86491	−	14.9370i	−0.161448	−	0.495701i
$909$	−11.2228			−0.372238
$910$	4.28876	−	29.4133i	0.142171	−	0.975042i
$911$	−15.0373			−0.498210			−0.249105	−	0.968477i	$-0.580136\pi$
$911$	−15.0373			−0.498210			−0.249105	+	0.968477i	$0.580136\pi$
$912$	−24.6930	−	25.6887i	−0.817668	−	0.850639i
$913$		−	30.5032i		−	1.00951i
$914$	0.890747	+	5.61122i	0.0294633	+	0.185603i
$915$	21.6297	+	6.74349i	0.715055	+	0.222933i
$916$	−24.0052	+	7.81837i	−0.793154	+	0.258326i
$917$			23.6779i			0.781913i
$918$	34.2533	−	5.43749i	1.13053	−	0.179464i
$919$			32.5833i			1.07482i	0.843320	+	0.537412i	$0.180598\pi$
$919$			32.5833i			1.07482i	−0.843320	+	0.537412i	$0.819402\pi$
$920$	7.59662	+	44.2359i	0.250453	+	1.45842i
$921$	37.0692			1.22147
$922$	12.2830	−	1.94985i	0.404518	−	0.0642148i
$923$	−21.1435			−0.695946
$924$	33.0182	−	10.7539i	1.08622	−	0.353776i
$925$	7.47763	+	5.16461i	0.245863	+	0.169811i
$926$	−17.4332	+	2.76742i	−0.572892	+	0.0909430i
$927$			16.6709i			0.547546i
$928$	−23.6542	−	23.5714i	−0.776486	−	0.773768i
$929$	−21.5135			−0.705834			−0.352917	−	0.935655i	$-0.614810\pi$
$929$	−21.5135			−0.705834			−0.352917	+	0.935655i	$0.614810\pi$
$930$	−10.8673	−	1.58457i	−0.356354	−	0.0519600i
$931$	11.5679	−	1.58202i	0.379122	−	0.0518487i
$932$	−4.38658	−	13.4683i	−0.143687	−	0.441170i
$933$	6.52320			0.213560
$934$	−8.88024	+	1.40968i	−0.290570	+	0.0461263i
$935$	−17.8999	+	57.4139i	−0.585391	+	1.87763i
$936$	13.3993	−	6.84507i	0.437971	−	0.223738i
$937$			7.82422i			0.255606i	0.991800	+	0.127803i	$0.0407925\pi$
$937$			7.82422i			0.255606i	−0.991800	+	0.127803i	$0.959207\pi$
$938$	−6.13209	−	38.6288i	−0.200220	−	1.26127i
$939$	−11.0112			−0.359335
$940$	0.564452	+	44.6519i	0.0184104	+	1.45638i
$941$		−	8.43169i		−	0.274865i	−0.990511	−	0.137433i	$-0.956115\pi$
$941$		−	8.43169i		−	0.274865i	0.990511	−	0.137433i	$-0.0438851\pi$
$942$	−49.2545	+	7.81885i	−1.60480	+	0.254752i
$943$		−	7.81611i		−	0.254527i
$944$	30.3869	−	22.1426i	0.989010	−	0.720679i
$945$	−16.5374	−	5.15588i	−0.537962	−	0.167721i
$946$	−7.00862	−	44.1505i	−0.227870	−	1.43546i
$947$	40.8976			1.32899			0.664497	−	0.747291i	$-0.268646\pi$
$947$	40.8976			1.32899			0.664497	+	0.747291i	$0.268646\pi$
$948$	5.12537	+	15.7367i	0.166464	+	0.511105i
$949$			27.9644i			0.907763i
$950$	−29.3426	−	9.43462i	−0.952000	−	0.306099i
$951$			39.9803i			1.29645i
$952$	17.6028	+	34.4577i	0.570509	+	1.11678i
$953$	−47.6805			−1.54452			−0.772262	−	0.635305i	$-0.780875\pi$
$953$	−47.6805			−1.54452			−0.772262	+	0.635305i	$0.780875\pi$
$954$	−3.59570	+	0.570796i	−0.116415	+	0.0184802i
$955$	−10.2631	−	3.19973i	−0.332106	−	0.103541i
$956$	−10.8768	−	33.3957i	−0.351782	−	1.08010i
$957$		−	49.3048i		−	1.59380i
$958$	−5.76613	−	36.3235i	−0.186295	−	1.17356i
$959$		−	15.0522i		−	0.486062i
$960$	29.2713	−	21.9014i	0.944727	−	0.706865i
$961$	−28.1122			−0.906845
$962$	11.4788	−	1.82219i	0.370092	−	0.0587499i
$963$			3.05389i			0.0984104i
$964$	15.7987	+	48.5077i	0.508843	+	1.56233i
$965$	−14.6650	+	47.0380i	−0.472085	+	1.51421i
$966$	6.68475	+	42.1103i	0.215078	+	1.35488i
$967$	10.0525			0.323267			0.161634	−	0.986851i	$-0.448324\pi$
$967$	10.0525			0.323267			0.161634	+	0.986851i	$0.448324\pi$
$968$	14.3643	−	7.33804i	0.461688	−	0.235854i
$969$	58.0816	−	7.94324i	1.86585	−	0.255173i
$970$	−5.66527	+	38.8537i	−0.181901	+	1.24752i
$971$	−26.8896			−0.862928			−0.431464	−	0.902130i	$-0.642003\pi$
$971$	−26.8896			−0.862928			−0.431464	+	0.902130i	$0.642003\pi$
$972$	−7.18307	−	22.0546i	−0.230397	−	0.707400i
$973$		−	0.0819530i		−	0.00262729i
$974$	2.00048	+	12.6019i	0.0640994	+	0.403792i
$975$	26.2575	−	38.0171i	0.840912	−	1.21752i
$976$	16.0279	−	11.6793i	0.513040	−	0.373846i
$977$	−7.48027			−0.239315			−0.119658	−	0.992815i	$-0.538180\pi$
$977$	−7.48027			−0.239315			−0.119658	+	0.992815i	$0.538180\pi$
$978$	2.36203	+	14.8795i	0.0755293	+	0.475794i
$979$	2.26199			0.0722936
$980$	0.151415	+	11.9779i	0.00483678	+	0.382621i
$981$			14.8939i			0.475527i
$982$	7.32102	+	46.1185i	0.233623	+	1.47170i
$983$			22.7801i			0.726572i	0.931678	+	0.363286i	$0.118345\pi$
$983$			22.7801i			0.726572i	−0.931678	+	0.363286i	$0.881655\pi$
$984$	−5.66935	+	2.89619i	−0.180732	+	0.0923272i
$985$	−34.1012	−	10.6317i	−1.08655	−	0.338756i
$986$	54.2597	−	8.61340i	1.72798	−	0.274307i
$987$			42.4209i			1.35027i
$988$	−35.4813	+	17.1734i	−1.12881	+	0.546360i
$989$	54.8890			1.74537
$990$	15.0460	+	2.19385i	0.478192	+	0.0697252i
$991$	11.3141			0.359406			0.179703	−	0.983721i	$-0.442486\pi$
$991$	11.3141			0.359406			0.179703	+	0.983721i	$0.442486\pi$
$992$	−6.78550	+	6.80934i	−0.215440	+	0.216197i
$993$			9.83296i			0.312040i
$994$	−13.5770	+	2.15527i	−0.430636	+	0.0683609i
$995$	26.6819	+	8.31863i	0.845874	+	0.263718i
$996$	−9.44722	−	29.0063i	−0.299347	−	0.919101i
$997$			57.7071i			1.82760i	0.406161	+	0.913802i	$0.366867\pi$
$997$			57.7071i			1.82760i	−0.406161	+	0.913802i	$0.633133\pi$
$998$	−2.95018	−	18.5845i	−0.0933863	−	0.588283i
$999$		−	6.77331i		−	0.214298i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.d.b.379.3	yes	40
4.3	odd	2	inner	380.2.d.b.379.1	✓	40
5.4	even	2	inner	380.2.d.b.379.38	yes	40
19.18	odd	2	inner	380.2.d.b.379.37	yes	40
20.19	odd	2	inner	380.2.d.b.379.40	yes	40
76.75	even	2	inner	380.2.d.b.379.39	yes	40
95.94	odd	2	inner	380.2.d.b.379.4	yes	40
380.379	even	2	inner	380.2.d.b.379.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.d.b.379.1	✓	40	4.3	odd	2	inner
380.2.d.b.379.2	yes	40	380.379	even	2	inner
380.2.d.b.379.3	yes	40	1.1	even	1	trivial
380.2.d.b.379.4	yes	40	95.94	odd	2	inner
380.2.d.b.379.37	yes	40	19.18	odd	2	inner
380.2.d.b.379.38	yes	40	5.4	even	2	inner
380.2.d.b.379.39	yes	40	76.75	even	2	inner
380.2.d.b.379.40	yes	40	20.19	odd	2	inner

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39672 + 0.221721i) q^{2} +2.04365i q^{3} +(1.90168 - 0.619368i) q^{4} +(0.665544 - 2.13473i) q^{5} +(-0.453121 - 2.85442i) q^{6} -2.07881 q^{7} +(-2.51879 + 1.28673i) q^{8} -1.17650 q^{9} +O(q^{10})\)	\(q+(-1.39672 + 0.221721i) q^{2} +2.04365i q^{3} +(1.90168 - 0.619368i) q^{4} +(0.665544 - 2.13473i) q^{5} +(-0.453121 - 2.85442i) q^{6} -2.07881 q^{7} +(-2.51879 + 1.28673i) q^{8} -1.17650 q^{9} +(-0.456267 + 3.12919i) q^{10} +4.08691i q^{11} +(1.26577 + 3.88637i) q^{12} +4.52166 q^{13} +(2.90352 - 0.460916i) q^{14} +(4.36263 + 1.36014i) q^{15} +(3.23277 - 2.35568i) q^{16} +6.58081i q^{17} +(1.64325 - 0.260856i) q^{18} +(-4.31870 + 0.590625i) q^{19} +(-0.0565286 - 4.47178i) q^{20} -4.24835i q^{21} +(-0.906157 - 5.70829i) q^{22} +7.09670 q^{23} +(-2.62962 - 5.14753i) q^{24} +(-4.11410 - 2.84151i) q^{25} +(-6.31551 + 1.00255i) q^{26} +3.72659i q^{27} +(-3.95323 + 1.28755i) q^{28} +5.90320i q^{29} +(-6.39496 - 0.932450i) q^{30} +1.69936 q^{31} +(-3.99298 + 4.00701i) q^{32} -8.35222 q^{33} +(-1.45911 - 9.19158i) q^{34} +(-1.38354 + 4.43768i) q^{35} +(-2.23733 + 0.728688i) q^{36} -1.81756 q^{37} +(5.90108 - 1.78249i) q^{38} +9.24068i q^{39} +(1.07044 + 6.23331i) q^{40} -1.10137i q^{41} +(0.941951 + 5.93378i) q^{42} +7.73444 q^{43} +(2.53130 + 7.77200i) q^{44} +(-0.783014 + 2.51151i) q^{45} +(-9.91214 + 1.57349i) q^{46} -9.98526 q^{47} +(4.81418 + 6.60664i) q^{48} -2.67856 q^{49} +(6.37629 + 3.05662i) q^{50} -13.4489 q^{51} +(8.59874 - 2.80057i) q^{52} -2.18817 q^{53} +(-0.826265 - 5.20502i) q^{54} +(8.72444 + 2.72002i) q^{55} +(5.23609 - 2.67486i) q^{56} +(-1.20703 - 8.82591i) q^{57} +(-1.30887 - 8.24514i) q^{58} +9.39966 q^{59} +(9.13875 - 0.115525i) q^{60} +4.95794 q^{61} +(-2.37353 + 0.376784i) q^{62} +2.44572 q^{63} +(4.68866 - 6.48201i) q^{64} +(3.00936 - 9.65250i) q^{65} +(11.6657 - 1.85187i) q^{66} -13.3041i q^{67} +(4.07594 + 12.5146i) q^{68} +14.5032i q^{69} +(0.948492 - 6.50498i) q^{70} -4.67605 q^{71} +(2.96337 - 1.51384i) q^{72} +6.18455i q^{73} +(2.53863 - 0.402992i) q^{74} +(5.80704 - 8.40778i) q^{75} +(-7.84697 + 3.79804i) q^{76} -8.49591i q^{77} +(-2.04886 - 12.9067i) q^{78} +4.04921 q^{79} +(-2.87717 - 8.46888i) q^{80} -11.1453 q^{81} +(0.244198 + 1.53831i) q^{82} -7.46362 q^{83} +(-2.63129 - 8.07901i) q^{84} +(14.0482 + 4.37982i) q^{85} +(-10.8029 + 1.71489i) q^{86} -12.0641 q^{87} +(-5.25875 - 10.2941i) q^{88} -0.553472i q^{89} +(0.536800 - 3.68150i) q^{90} -9.39966 q^{91} +(13.4956 - 4.39547i) q^{92} +3.47289i q^{93} +(13.9467 - 2.21395i) q^{94} +(-1.61346 + 9.61232i) q^{95} +(-8.18892 - 8.16025i) q^{96} +12.4166 q^{97} +(3.74121 - 0.593894i) q^{98} -4.80826i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9}+O(q^{10}) \) 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9	\( 40 q - 4 q^{5} + 8 q^{6} - 8 q^{9} - 8 q^{16} - 20 q^{20} - 40 q^{24} - 84 q^{25} - 24 q^{26} + 24 q^{30} + 24 q^{36} - 40 q^{44} - 12 q^{45} + 128 q^{49} - 120 q^{54} + 24 q^{61} + 72 q^{64} + 112 q^{66} + 32 q^{74} + 56 q^{76} + 96 q^{80} - 72 q^{81} + 44 q^{85} - 40 q^{96}+O(q^{100}) \) 40 * q - 4 * q^5 + 8 * q^6 - 8 * q^9 - 8 * q^16 - 20 * q^20 - 40 * q^24 - 84 * q^25 - 24 * q^26 + 24 * q^30 + 24 * q^36 - 40 * q^44 - 12 * q^45 + 128 * q^49 - 120 * q^54 + 24 * q^61 + 72 * q^64 + 112 * q^66 + 32 * q^74 + 56 * q^76 + 96 * q^80 - 72 * q^81 + 44 * q^85 - 40 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more