LMFDB - Embedded newform 380.2.d.b.379.4

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			379.4
Character	$\chi$	$=$	380.379
Dual form			380.2.d.b.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39672 + 0.221721i) q^{2} +2.04365i q^{3} +(1.90168 - 0.619368i) q^{4} +(0.665544 + 2.13473i) q^{5} +(-0.453121 - 2.85442i) q^{6} +2.07881 q^{7} +(-2.51879 + 1.28673i) q^{8} -1.17650 q^{9} +O(q^{10})$	\(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} +(-1.40290 - 2.83406i) 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} +(2.58783 + 3.64735i) 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} +(5.79182 - 2.86703i) 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} +(-6.16299 + 0.132608i) q^{38} +9.24068i q^{39} +(-4.42318 - 4.52056i) 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} +(5.11624 - 4.88099i) 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} +(-7.45390 + 5.28862i) 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} +(-2.91635 - 5.89146i) 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} +(8.57859 - 1.55168i) q^{76} +8.49591i q^{77} +(-2.04886 - 12.9067i) q^{78} -4.04921 q^{79} +(7.18027 + 5.33326i) 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} +(1.65051 + 3.33428i) 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	$-0.371486\pi$
$7$	2.07881			0.785715			0.392858	+	0.919599i	$0.371486\pi$
$8$	−2.51879	+	1.28673i	−0.890528	+	0.454927i
$9$	−1.17650			−0.392167
$10$	−1.40290	−	2.83406i	−0.443635	−	0.896208i
$11$			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	$-0.705870\pi$
$17$		−	6.58081i		−	1.59608i	0.602604	−	0.798041i	$-0.294130\pi$
$18$	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
$20$	2.58783	+	3.64735i	0.578657	+	0.815571i
$21$			4.24835i			0.927067i
$22$	−0.906157	−	5.70829i	−0.193193	−	1.21701i
$23$	−7.09670			−1.47976			−0.739882	−	0.672736i	$-0.765119\pi$
$23$	−7.09670			−1.47976			−0.739882	+	0.672736i	$0.765119\pi$
$24$	−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	$-0.815352\pi$
$29$		−	5.90320i		−	1.09620i	0.836414	−	0.548098i	$-0.184648\pi$
$30$	5.79182	−	2.86703i	1.05744	−	0.523445i
$31$	−1.69936			−0.305214			−0.152607	−	0.988287i	$-0.548767\pi$
$31$	−1.69936			−0.305214			−0.152607	+	0.988287i	$0.548767\pi$
$32$	−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	$0.547735\pi$
$38$	−6.16299	+	0.132608i	−0.999769	+	0.0215119i
$39$			9.24068i			1.47969i
$40$	−4.42318	−	4.52056i	−0.699367	−	0.714763i
$41$			1.10137i			0.172005i	0.996295	+	0.0860027i	$0.0274094\pi$
$41$			1.10137i			0.172005i	−0.996295	+	0.0860027i	$0.972591\pi$
$42$	−0.941951	−	5.93378i	−0.145346	−	0.915602i
$43$	−7.73444			−1.17949			−0.589746	−	0.807589i	$-0.700772\pi$
$43$	−7.73444			−1.17949			−0.589746	+	0.807589i	$0.700772\pi$
$44$	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	$-0.240334\pi$
$47$	9.98526			1.45650			0.728250	+	0.685312i	$0.240334\pi$
$48$	4.81418	+	6.60664i	0.694867	+	0.953587i
$49$	−2.67856			−0.382651
$50$	5.11624	−	4.88099i	0.723546	−	0.690276i
$51$	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	$-0.709581\pi$
$59$	−9.39966			−1.22373			−0.611866	+	0.790962i	$0.709581\pi$
$60$	−7.45390	+	5.28862i	−0.962294	+	0.682758i
$61$	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
$70$	−2.91635	−	5.89146i	−0.348571	−	0.704164i
$71$	4.67605			0.554945			0.277472	−	0.960734i	$-0.410503\pi$
$71$	4.67605			0.554945			0.277472	+	0.960734i	$0.410503\pi$
$72$	2.96337	−	1.51384i	0.349236	−	0.178408i
$73$		−	6.18455i		−	0.723846i	−0.932208	−	0.361923i	$-0.882120\pi$
$73$		−	6.18455i		−	0.723846i	0.932208	−	0.361923i	$-0.117880\pi$
$74$	2.53863	−	0.402992i	0.295110	−	0.0468469i
$75$	−5.80704	−	8.40778i	−0.670540	−	0.970847i
$76$	8.57859	−	1.55168i	0.984032	−	0.177990i
$77$			8.49591i			0.968199i
$78$	−2.04886	−	12.9067i	−0.231988	−	1.46139i
$79$	−4.04921			−0.455572			−0.227786	−	0.973711i	$-0.573149\pi$
$79$	−4.04921			−0.455572			−0.227786	+	0.973711i	$0.573149\pi$
$80$	7.18027	+	5.33326i	0.802779	+	0.596277i
$81$	−11.1453			−1.23837
$82$	−0.244198	−	1.53831i	−0.0269671	−	0.169878i
$83$	7.46362			0.819238			0.409619	−	0.912257i	$-0.365662\pi$
$83$	7.46362			0.819238			0.409619	+	0.912257i	$0.365662\pi$
$84$	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	$0.00933864\pi$
$89$			0.553472i			0.0586680i	−0.999570	+	0.0293340i	$0.990661\pi$
$90$	1.65051	+	3.33428i	0.173979	+	0.351463i
$91$	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
$100$	−6.06376	+	7.95178i	−0.606376	+	0.795178i
$101$	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	$0.207339\pi$
$109$			12.6595i			1.21256i	−0.795251	+	0.606280i	$0.792661\pi$
$110$	11.5825	−	5.73352i	1.10435	−	0.546669i
$111$		−	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	$0.291723\pi$
$114$	−0.271005	−	12.5950i	−0.0253819	−	1.17963i
$115$	−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
$120$	9.23844	−	9.03943i	0.843350	−	0.825184i
$121$	−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
$130$	−6.34342	−	12.8146i	−0.556355	−	1.12392i
$131$		−	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	$-0.899901\pi$
$137$		−	7.24081i		−	0.618624i	0.950961	−	0.309312i	$-0.100099\pi$
$138$	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	$0.999468\pi$
$140$	5.37960	+	7.58213i	0.454659	+	0.640807i
$141$			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	$0.397704\pi$
$150$	9.97503	+	10.4558i	0.814458	+	0.853713i
$151$	−8.63740			−0.702902			−0.351451	−	0.936206i	$-0.614312\pi$
$151$	−8.63740			−0.702902			−0.351451	+	0.936206i	$0.614312\pi$
$152$	−11.6379	+	4.06933i	−0.943958	+	0.330067i
$153$			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	$0.241762\pi$
$157$			17.2555i			1.37714i	−0.725169	+	0.688571i	$0.758238\pi$
$158$	5.65563	−	0.897797i	0.449938	−	0.0714249i
$159$		−	4.47184i		−	0.354640i
$160$	−11.2114	−	5.85708i	−0.886336	−	0.463043i
$161$	−14.7527			−1.16267
$162$	15.5670	−	2.47116i	1.22306	−	0.194153i
$163$	5.21280			0.408298			0.204149	−	0.978940i	$-0.434557\pi$
$163$	5.21280			0.408298			0.204149	+	0.978940i	$0.434557\pi$
$164$	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
$170$	−18.6504	+	9.23220i	−1.43042	+	0.708077i
$171$	−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	$-0.514154\pi$
$179$	−1.18947			−0.0889053			−0.0444527	+	0.999011i	$0.514154\pi$
$180$	−3.04459	−	4.29111i	−0.226930	−	0.319841i
$181$			5.10146i			0.379189i	0.981863	+	0.189594i	$0.0607173\pi$
$181$			5.10146i			0.379189i	−0.981863	+	0.189594i	$0.939283\pi$
$182$	−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
$190$	−4.38482	−	13.0680i	−0.318108	−	0.948054i
$191$		−	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	$0.192696\pi$
$197$			15.9745i			1.13814i	−0.822290	+	0.569069i	$0.807304\pi$
$198$	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	$0.853909\pi$
$200$	6.70633	−	12.4509i	0.474209	−	0.880412i
$201$	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
$210$	12.0401	−	5.96000i	0.830844	−	0.411279i
$211$	9.66236			0.665184			0.332592	−	0.943071i	$-0.392077\pi$
$211$	9.66236			0.665184			0.332592	+	0.943071i	$0.392077\pi$
$212$	−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
$220$	−14.9064	+	10.5762i	−1.00499	+	0.713050i
$221$		−	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	$-0.0839418\pi$
$228$	3.17110	+	17.5316i	0.210011	+	1.16106i
$229$	−12.6232			−0.834162			−0.417081	−	0.908869i	$-0.636947\pi$
$229$	−12.6232			−0.834162			−0.417081	+	0.908869i	$0.636947\pi$
$230$	9.95594	+	20.1125i	0.656475	+	1.32618i
$231$	−17.3627			−1.14238
$232$	7.59582	+	14.8689i	0.498690	+	0.976194i
$233$			7.08234i			0.463980i	0.972718	+	0.231990i	$0.0745236\pi$
$233$			7.08234i			0.463980i	−0.972718	+	0.231990i	$0.925476\pi$
$234$	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	$-0.192271\pi$
$240$	−10.8993	+	14.6740i	−0.703548	+	0.947200i
$241$		−	25.5078i		−	1.64310i	−0.570134	−	0.821552i	$-0.693109\pi$
$241$		−	25.5078i		−	1.64310i	0.570134	−	0.821552i	$-0.306891\pi$
$242$	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
$250$	13.8247	+	7.67326i	0.874348	+	0.485300i
$251$		−	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
$260$	11.7013	+	16.4921i	0.725683	+	1.02279i
$261$			6.94513i			0.429893i
$262$	2.52544	+	15.9089i	0.156022	+	0.982854i
$263$	27.2166			1.67825			0.839123	−	0.543942i	$-0.183069\pi$
$263$	27.2166			1.67825			0.839123	+	0.543942i	$0.183069\pi$
$264$	21.0375	−	10.7470i	1.29477	−	0.661435i
$265$	−1.45632	−	4.67113i	−0.0894611	−	0.286945i
$266$	−12.8117	+	0.275667i	−0.785534	+	0.0169022i
$267$	−1.13110			−0.0692224
$268$	−8.24014	−	25.3002i	−0.503347	−	1.54545i
$269$			20.4064i			1.24420i	0.782939	+	0.622099i	$0.213720\pi$
$269$			20.4064i			1.24420i	−0.782939	+	0.622099i	$0.786280\pi$
$270$	10.5614	−	5.22802i	0.642744	−	0.318167i
$271$			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	$-0.992382\pi$
$277$		−	0.796560i		−	0.0478606i	0.999714	−	0.0239303i	$-0.00761799\pi$
$278$	−0.00874094	−	0.0550632i	−0.000524247	−	0.00330247i
$279$	1.99930			0.119695
$280$	−9.19495	−	9.39737i	−0.549503	−	0.561601i
$281$		−	8.04650i		−	0.480014i	−0.970771	−	0.240007i	$-0.922850\pi$
$281$		−	8.04650i		−	0.480014i	0.970771	−	0.240007i	$-0.0771497\pi$
$282$	−4.52453	−	28.5021i	−0.269432	−	1.69727i
$283$	−29.0701			−1.72804			−0.864019	−	0.503459i	$-0.832061\pi$
$283$	−29.0701			−1.72804			−0.864019	+	0.503459i	$0.832061\pi$
$284$	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
$290$	−16.7300	+	8.28157i	−0.982420	+	0.486311i
$291$			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
$300$	−16.2506	−	12.3922i	−0.938231	−	0.715464i
$301$	−16.0784			−0.926745
$302$	12.0641	−	1.91510i	0.694209	−	0.110201i
$303$			19.4947i			1.11994i
$304$	15.3527	−	8.26411i	0.880536	−	0.473979i
$305$	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
$310$	2.38402	+	4.81608i	0.135403	+	0.273535i
$311$		−	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	$-0.951341\pi$
$313$		−	5.38799i		−	0.304547i	0.988338	−	0.152274i	$-0.0486595\pi$
$314$	−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
$320$	16.9578	+	5.69492i	0.947971	+	0.318356i
$321$	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
$330$	11.7173	+	23.6707i	0.645016	+	1.30303i
$331$	−4.81147			−0.264462			−0.132231	−	0.991219i	$-0.542214\pi$
$331$	−4.81147			−0.264462			−0.132231	+	0.991219i	$0.542214\pi$
$332$	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
$340$	24.0025	−	17.0300i	1.30172	−	0.923583i
$341$		−	6.94513i		−	0.376100i
$342$	7.25077	−	0.156014i	0.392077	−	0.00843627i
$343$	−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	$-0.562306\pi$
$347$	−7.24605			−0.388988			−0.194494	+	0.980904i	$0.562306\pi$
$348$	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	$0.471458\pi$
$350$	10.6357	−	10.1466i	0.568501	−	0.542360i
$351$			16.8504i			0.899406i
$352$	−16.3763	−	16.3190i	−0.872859	−	0.869804i
$353$			12.2638i			0.652738i	0.945243	+	0.326369i	$0.105825\pi$
$353$			12.2638i			0.652738i	−0.945243	+	0.326369i	$0.894175\pi$
$354$	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	$-0.0419688\pi$
$360$	5.20388	+	5.31845i	0.274269	+	0.280307i
$361$	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	$-0.502227\pi$
$367$	−0.268098			−0.0139946			−0.00699731	+	0.999976i	$0.502227\pi$
$368$	−22.9420	+	16.7175i	−1.19593	+	0.871462i
$369$		−	1.29577i		−	0.0674549i
$370$	2.54985	+	5.15107i	0.132560	+	0.267792i
$371$	−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	$-0.386720\pi$
$379$	13.5658			0.696829			0.348415	+	0.937340i	$0.386720\pi$
$380$	9.02185	+	17.2802i	0.462811	+	0.886457i
$381$	−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	$0.539555\pi$
$390$	26.1886	−	12.9637i	1.32611	−	0.656443i
$391$			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	$0.0258081\pi$
$397$			3.22742i			0.161980i	−0.996715	+	0.0809899i	$0.974192\pi$
$398$	−2.77130	−	17.4577i	−0.138912	−	0.875073i
$399$	−2.50918	+	18.3474i	−0.125616	+	0.918517i
$400$	−6.60626	+	18.8774i	−0.330313	+	0.943871i
$401$			22.8549i			1.14132i	0.821187	+	0.570659i	$0.193312\pi$
$401$			22.8549i			1.14132i	−0.821187	+	0.570659i	$0.806688\pi$
$402$	−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	$0.337572\pi$
$409$			35.2947i			1.74521i	−0.488425	+	0.872606i	$0.662428\pi$
$410$	3.12135	−	1.54511i	0.154153	−	0.0763075i
$411$	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
$418$	−0.541959	−	25.1876i	−0.0265081	−	1.23197i
$419$			0.942419i			0.0460402i	0.999735	+	0.0230201i	$0.00732817\pi$
$419$			0.942419i			0.0460402i	−0.999735	+	0.0230201i	$0.992672\pi$
$420$	−15.4952	+	10.9940i	−0.756089	+	0.536453i
$421$		−	6.45110i		−	0.314407i	−0.987566	−	0.157204i	$-0.949752\pi$
$421$		−	6.45110i		−	0.314407i	0.987566	−	0.157204i	$-0.0502479\pi$
$422$	−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
$430$	10.8506	+	21.9199i	0.523263	+	1.05707i
$431$	−40.4739			−1.94956			−0.974779	−	0.223172i	$-0.928359\pi$
$431$	−40.4739			−1.94956			−0.974779	+	0.223172i	$0.928359\pi$
$432$	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	$-0.393700\pi$
$439$	13.7355			0.655558			0.327779	+	0.944754i	$0.393700\pi$
$440$	18.4751	−	18.0772i	0.880768	−	0.861795i
$441$	3.15133			0.150063
$442$	6.59759	+	41.5612i	0.313815	+	1.97686i
$443$	13.5116			0.641953			0.320977	−	0.947087i	$-0.395989\pi$
$443$	13.5116			0.641953			0.320977	+	0.947087i	$0.395989\pi$
$444$	−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	$-0.721355\pi$
$449$		−	32.5385i		−	1.53559i	0.640697	−	0.767794i	$-0.278645\pi$
$450$	−6.01927	+	5.74249i	−0.283751	+	0.270704i
$451$	−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
$456$	−8.31629	−	23.7838i	−0.389446	−	1.11378i
$457$			4.01741i			0.187927i	0.995576	+	0.0939634i	$0.0299537\pi$
$457$			4.01741i			0.187927i	−0.995576	+	0.0939634i	$0.970046\pi$
$458$	17.6311	−	2.79882i	0.823846	−	0.130780i
$459$	24.5240			1.14468
$460$	−18.3651	−	25.8841i	−0.856276	−	1.20685i
$461$	−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	$-0.593666\pi$
$463$	−12.4815			−0.580065			−0.290032	+	0.957017i	$0.593666\pi$
$464$	−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	$-0.546995\pi$
$467$	−6.35790			−0.294209			−0.147104	+	0.989121i	$0.546995\pi$
$468$	−10.1164	+	3.29488i	−0.467633	+	0.152306i
$469$		−	27.6567i		−	1.27707i
$470$	−14.0083	−	28.2988i	−0.646154	−	1.30533i
$471$	−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	$0.797498\pi$
$480$	11.9698	−	22.9121i	0.546345	−	1.04579i
$481$	−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
$490$	3.75774	+	7.59119i	0.169757	+	0.342935i
$491$		−	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
$494$	−27.8669	+	0.599610i	−1.25379	+	0.0269777i
$495$	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	$0.903739\pi$
$500$	−21.0106	−	7.65221i	−0.939621	−	0.342217i
$501$	−28.9073			−1.29148
$502$	3.93510	+	24.7890i	0.175632	+	1.10639i
$503$	11.5983			0.517144			0.258572	−	0.965992i	$-0.416748\pi$
$503$	11.5983			0.517144			0.258572	+	0.965992i	$0.416748\pi$
$504$	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	$-0.886764\pi$
$509$		−	15.7154i		−	0.696571i	0.937389	−	0.348285i	$-0.113236\pi$
$510$	−18.8674	−	38.1149i	−0.835461	−	1.68775i
$511$		−	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
$520$	−20.0001	−	20.4404i	−0.877063	−	0.896372i
$521$		−	33.8676i		−	1.48377i	−0.670529	−	0.741883i	$-0.733933\pi$
$521$		−	33.8676i		−	1.48377i	0.670529	−	0.741883i	$-0.266067\pi$
$522$	−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
$530$	3.06977	+	6.20139i	0.133342	+	0.269371i
$531$	11.0587			0.479908
$532$	17.8332	−	3.22565i	0.773169	−	0.139850i
$533$			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
$540$	−13.5922	+	9.64378i	−0.584913	+	0.415002i
$541$	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
$550$	19.9482	+	20.9097i	0.850593	+	0.891590i
$551$	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	$0.0728032\pi$
$557$			10.7020i			0.453458i	−0.973958	+	0.226729i	$0.927197\pi$
$558$	−2.79247	+	0.443287i	−0.118215	+	0.0187658i
$559$	−34.9725			−1.47918
$560$	14.9264	+	11.0868i	0.630756	+	0.468504i
$561$			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	$-0.764520\pi$
$569$		−	32.1609i		−	1.34825i	0.738616	−	0.674127i	$-0.235480\pi$
$570$	26.7065	−	8.96104i	1.11861	−	0.375337i
$571$			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	$-0.722920\pi$
$577$		−	36.7343i		−	1.52927i	0.644465	−	0.764633i	$-0.277080\pi$
$578$	36.7437	−	5.83285i	1.52834	−	0.242614i
$579$		−	45.0311i		−	1.87143i
$580$	21.5310	−	15.2765i	0.894026	−	0.634321i
$581$	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	$-0.609566\pi$
$587$	−16.3518			−0.674912			−0.337456	+	0.941341i	$0.609566\pi$
$588$	−3.39044	−	10.4099i	−0.139819	−	0.429295i
$589$	−7.33901	−	1.00368i	−0.302399	−	0.0413560i
$590$	13.1867	+	26.6392i	0.542890	+	1.09672i
$591$	−32.6463			−1.34289
$592$	−5.87575	+	4.28159i	−0.241492	+	0.175972i
$593$		−	15.2822i		−	0.627565i	−0.949495	−	0.313782i	$-0.898404\pi$
$593$		−	15.2822i		−	0.627565i	0.949495	−	0.313782i	$-0.101596\pi$
$594$	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	$-0.620463\pi$
$599$	−18.0855			−0.738954			−0.369477	+	0.929240i	$0.620463\pi$
$600$	25.4453	+	13.7054i	1.03880	+	0.559520i
$601$			7.44723i			0.303779i	0.988397	+	0.151889i	$0.0485358\pi$
$601$			7.44723i			0.303779i	−0.988397	+	0.151889i	$0.951464\pi$
$602$	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	$0.902259\pi$
$608$	−19.6111	+	14.9467i	−0.795336	+	0.606169i
$609$	25.0789			1.01625
$610$	−6.95548	−	14.0511i	−0.281619	−	0.568912i
$611$	45.1499			1.82657
$612$	4.79536	+	14.7234i	0.193841	+	0.595160i
$613$			22.5813i			0.912048i	0.889967	+	0.456024i	$0.150727\pi$
$613$			22.5813i			0.912048i	−0.889967	+	0.456024i	$0.849273\pi$
$614$	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	$0.152447\pi$
$617$			22.8933i			0.921651i	−0.887491	+	0.460826i	$0.847553\pi$
$618$	−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	$-0.137554\pi$
$620$	−4.39765	−	6.19814i	−0.176614	−	0.248923i
$621$		−	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
$630$	3.43109	+	6.93132i	0.136698	+	0.276150i
$631$		−	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
$640$	−24.9481	−	4.19433i	−0.986160	−	0.165795i
$641$			31.6593i			1.25047i	0.780438	+	0.625233i	$0.214996\pi$
$641$			31.6593i			1.25047i	−0.780438	+	0.625233i	$0.785004\pi$
$642$	−7.40932	+	1.17618i	−0.292423	+	0.0464203i
$643$	−41.4100			−1.63305			−0.816525	−	0.577310i	$-0.804102\pi$
$643$	−41.4100			−1.63305			−0.816525	+	0.577310i	$0.804102\pi$
$644$	−28.0549	+	9.13733i	−1.10552	+	0.360061i
$645$	33.7425	−	10.5199i	1.32861	−	0.414221i
$646$	0.872670	+	40.5575i	0.0343348	+	1.59571i
$647$	−10.3940			−0.408632			−0.204316	−	0.978905i	$-0.565497\pi$
$647$	−10.3940			−0.408632			−0.204316	+	0.978905i	$0.565497\pi$
$648$	28.0728	−	14.3410i	1.10281	−	0.563370i
$649$		−	38.4156i		−	1.50794i
$650$	23.1339	−	22.0702i	0.907387	−	0.865663i
$651$		−	7.21947i		−	0.282953i
$652$	9.91307	−	3.22864i	0.388226	−	0.126443i
$653$		−	10.9657i		−	0.429122i	−0.976711	−	0.214561i	$-0.931168\pi$
$653$		−	10.9657i		−	0.429122i	0.976711	−	0.214561i	$-0.0688321\pi$
$654$	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	$-0.473081\pi$
$659$	4.33670			0.168934			0.0844668	+	0.996426i	$0.473081\pi$
$660$	−21.6141	−	30.4634i	−0.841329	−	1.18579i
$661$		−	37.7050i		−	1.46655i	−0.679930	−	0.733277i	$-0.737990\pi$
$661$		−	37.7050i		−	1.46655i	0.679930	−	0.733277i	$-0.262010\pi$
$662$	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
$670$	−37.7046	+	18.6643i	−1.45666	+	0.721065i
$671$			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
$680$	−29.7490	+	29.1081i	−1.14082	+	1.11625i
$681$	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	$-0.263142\pi$
$684$	−10.0927	+	1.82556i	−0.385905	+	0.0698020i
$685$	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
$690$	−41.1028	+	20.3464i	−1.56476	+	0.774576i
$691$		−	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
$700$	−12.6054	+	16.5302i	−0.476439	+	0.624783i
$701$	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	$0.265938\pi$
$710$	−6.56001	−	13.2522i	−0.246193	−	0.497346i
$711$	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	$0.960851\pi$
$720$	−8.44761	−	6.27460i	−0.314824	−	0.233840i
$721$		−	29.4565i		−	1.09702i
$722$	−26.6944	−	3.06732i	−0.993463	−	0.114154i
$723$	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	$-0.507096\pi$
$727$	−1.20206			−0.0445818			−0.0222909	+	0.999752i	$0.507096\pi$
$728$	−23.6758	+	12.0948i	−0.877484	+	0.448264i
$729$	−9.73500			−0.360555
$730$	−17.5274	+	8.67628i	−0.648717	+	0.321123i
$731$			50.8989i			1.88256i
$732$	6.27562	+	19.2684i	0.231954	+	0.712180i
$733$		−	34.8374i		−	1.28675i	−0.765551	−	0.643375i	$-0.777534\pi$
$733$		−	34.8374i		−	1.28675i	0.765551	−	0.643375i	$-0.222466\pi$
$734$	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	$0.940781\pi$
$740$	−4.70354	−	6.62927i	−0.172906	−	0.243697i
$741$	−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
$750$	−15.6815	+	28.2527i	−0.572606	+	1.03164i
$751$	−35.0253			−1.27809			−0.639045	−	0.769169i	$-0.720670\pi$
$751$	−35.0253			−1.27809			−0.639045	+	0.769169i	$0.720670\pi$
$752$	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	$0.0916224\pi$
$757$			15.6212i			0.567764i	−0.958859	+	0.283882i	$0.908378\pi$
$758$	−18.9477	+	3.00783i	−0.688212	+	0.109249i
$759$	59.2732			2.15148
$760$	−16.4324	−	22.1354i	−0.596067	−	0.802935i
$761$	−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	$0.635751\pi$
$770$	24.0779	−	11.9189i	0.867707	−	0.429527i
$771$		−	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
$780$	−33.7040	+	23.9133i	−1.20680	+	0.856235i
$781$			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
$790$	5.68062	+	11.4757i	0.202108	+	0.408287i
$791$	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	$0.312412\pi$
$798$	−0.563367	−	26.1826i	−0.0199430	−	0.926852i
$799$		−	65.7111i		−	2.32469i
$800$	5.04160	−	27.8313i	0.178247	−	0.983986i
$801$		−	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	$0.635860\pi$
$810$	15.6358	+	31.5866i	0.549385	+	1.10984i
$811$	47.4895			1.66758			0.833790	−	0.552081i	$-0.186166\pi$
$811$	47.4895			1.66758			0.833790	+	0.552081i	$0.186166\pi$
$812$	−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
$820$	−4.01708	+	2.85016i	−0.140283	+	0.0995320i
$821$	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	$-0.475944\pi$
$823$	4.33210			0.151007			0.0755037	+	0.997146i	$0.475944\pi$
$824$	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	$0.0989060\pi$
$829$			17.6063i			0.611493i	−0.952113	+	0.305747i	$0.901094\pi$
$830$	−10.4707	−	21.1523i	−0.363443	−	0.734208i
$831$	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
$836$	6.34160	+	35.0600i	0.219329	+	1.21257i
$837$		−	6.33281i		−	0.218894i
$838$	−0.208955	−	1.31630i	−0.00721822	−	0.0454708i
$839$	−26.0009			−0.897652			−0.448826	−	0.893619i	$-0.648158\pi$
$839$	−26.0009			−0.897652			−0.448826	+	0.893619i	$0.648158\pi$
$840$	19.2049	−	18.7912i	0.662633	−	0.648360i
$841$	−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
$850$	−32.1209	−	33.6690i	−1.10174	−	1.15484i
$851$	12.8987			0.442161
$852$	5.91880	+	18.1728i	0.202775	+	0.622591i
$853$			46.2282i			1.58282i	0.611284	+	0.791411i	$0.290653\pi$
$853$			46.2282i			1.58282i	−0.611284	+	0.791411i	$0.709347\pi$
$854$	−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	$0.915646\pi$
$860$	−20.0154	−	28.2102i	−0.682520	−	0.961959i
$861$	−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
$870$	−16.9246	−	34.1903i	−0.573799	−	1.15916i
$871$		−	60.1567i		−	2.03833i
$872$	−16.2894	−	31.8867i	−0.551627	−	1.07982i
$873$	−14.6081			−0.494410
$874$	43.7369	−	0.941082i	1.47942	−	0.0318326i
$875$	−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
$880$	−21.7966	+	29.3452i	−0.734763	+	0.989225i
$881$	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	$-0.573499\pi$
$883$	−13.6012			−0.457718			−0.228859	+	0.973460i	$0.573499\pi$
$884$	−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
$890$	1.56857	−	0.776464i	0.0525787	−	0.0260271i
$891$		−	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
$900$	7.13403	−	9.35528i	0.237801	−	0.311843i
$901$			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
$910$	−13.1867	−	26.6392i	−0.437136	−	0.883080i
$911$	15.0373			0.498210			0.249105	−	0.968477i	$-0.419864\pi$
$911$	15.0373			0.498210			0.249105	+	0.968477i	$0.419864\pi$
$912$	16.8889	+	31.3755i	0.559249	+	1.03895i
$913$			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	$0.819402\pi$
$920$	31.3900	+	32.0811i	1.03490	+	1.05768i
$921$	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	$0.614810\pi$
$930$	−9.84237	+	4.87210i	−0.322744	+	0.159763i
$931$	−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	$-0.959207\pi$
$937$		−	7.82422i		−	0.255606i	0.991800	−	0.127803i	$-0.0407925\pi$
$938$	6.13209	+	38.6288i	0.200220	+	1.26127i
$939$	11.0112			0.359335
$940$	25.8402	+	36.4197i	0.842813	+	1.18788i
$941$			8.43169i			0.274865i	0.990511	+	0.137433i	$0.0438851\pi$
$941$			8.43169i			0.274865i	−0.990511	+	0.137433i	$0.956115\pi$
$942$	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	$-0.731354\pi$
$947$	−40.8976			−1.32899			−0.664497	+	0.747291i	$0.731354\pi$
$948$	−5.12537	−	15.7367i	−0.166464	−	0.511105i
$949$		−	27.9644i		−	0.907763i
$950$	24.9784	−	18.0577i	0.810405	−	0.585870i
$951$			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
$960$	−11.6384	+	34.6558i	−0.375629	+	1.11851i
$961$	−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	$-0.551676\pi$
$967$	−10.0525			−0.323267			−0.161634	+	0.986851i	$0.551676\pi$
$968$	14.3643	−	7.33804i	0.461688	−	0.235854i
$969$	58.0816	+	7.94324i	1.86585	+	0.255173i
$970$	−17.4191	−	35.1892i	−0.559295	−	1.12986i
$971$	26.8896			0.862928			0.431464	−	0.902130i	$-0.357997\pi$
$971$	26.8896			0.862928			0.431464	+	0.902130i	$0.357997\pi$
$972$	−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
$980$	−6.93166	−	9.76963i	−0.221424	−	0.312079i
$981$		−	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
$988$	38.7895	−	7.01619i	1.23406	−	0.223215i
$989$	54.8890			1.74537
$990$	−13.6269	+	6.74549i	−0.433091	+	0.214386i
$991$	−11.3141			−0.359406			−0.179703	−	0.983721i	$-0.557514\pi$
$991$	−11.3141			−0.359406			−0.179703	+	0.983721i	$0.557514\pi$
$992$	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	$-0.633133\pi$
$997$		−	57.7071i		−	1.82760i	0.406161	−	0.913802i	$-0.366867\pi$
$998$	−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.379.4	yes	40
4.3	odd	2	inner	380.2.d.b.379.2	yes	40
5.4	even	2	inner	380.2.d.b.379.37	yes	40
19.18	odd	2	inner	380.2.d.b.379.38	yes	40
20.19	odd	2	inner	380.2.d.b.379.39	yes	40
76.75	even	2	inner	380.2.d.b.379.40	yes	40
95.94	odd	2	inner	380.2.d.b.379.3	yes	40
380.379	even	2	inner	380.2.d.b.379.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.d.b.379.1	✓	40	380.379	even	2	inner
380.2.d.b.379.2	yes	40	4.3	odd	2	inner
380.2.d.b.379.3	yes	40	95.94	odd	2	inner
380.2.d.b.379.4	yes	40	1.1	even	1	trivial
380.2.d.b.379.37	yes	40	5.4	even	2	inner
380.2.d.b.379.38	yes	40	19.18	odd	2	inner
380.2.d.b.379.39	yes	40	20.19	odd	2	inner
380.2.d.b.379.40	yes	40	76.75	even	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} +(-1.40290 - 2.83406i) 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} +(2.58783 + 3.64735i) 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} +(5.79182 - 2.86703i) 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} +(-6.16299 + 0.132608i) q^{38} +9.24068i q^{39} +(-4.42318 - 4.52056i) 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} +(5.11624 - 4.88099i) 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} +(-7.45390 + 5.28862i) 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} +(-2.91635 - 5.89146i) 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} +(8.57859 - 1.55168i) q^{76} +8.49591i q^{77} +(-2.04886 - 12.9067i) q^{78} -4.04921 q^{79} +(7.18027 + 5.33326i) 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} +(1.65051 + 3.33428i) 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

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Database

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