LMFDB - Embedded newform 961.2.g.g.448.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			448.1
Root			$-0.104528 + 0.994522i$ of defining polynomial
Character	$\chi$	$=$	961.448
Dual form			961.2.g.g.547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 1.53884i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(0.190983 - 0.330792i) q^{5} +(-0.809017 - 1.40126i) q^{6} +(-0.313585 + 2.98357i) q^{7} +(1.80902 - 1.31433i) q^{8} +(0.209057 + 1.98904i) q^{9} +(-0.413545 - 0.459289i) q^{10} +(4.78339 - 2.12970i) q^{11} +(-0.604528 + 0.128496i) q^{12} +(-1.81359 - 0.385489i) q^{13} +(4.43444 + 1.97434i) q^{14} +(-0.118034 - 0.363271i) q^{15} +(-1.50000 - 4.61653i) q^{16} +(3.86984 + 1.72296i) q^{17} +(3.16535 + 0.672816i) q^{18} +(-4.89074 + 1.03956i) q^{19} +(-0.215659 + 0.0960175i) q^{20} +(2.00739 + 2.22943i) q^{21} +(-0.885579 - 8.42572i) q^{22} +(2.80902 - 2.04087i) q^{23} +(0.233733 - 2.22382i) q^{24} +(2.42705 + 4.20378i) q^{25} +(-1.50000 + 2.59808i) q^{26} +(4.04508 + 2.93893i) q^{27} +(1.24064 - 1.37787i) q^{28} +(1.97214 - 6.06961i) q^{29} -0.618034 q^{30} -3.38197 q^{32} +(1.61803 - 4.97980i) q^{33} +(4.58629 - 5.09359i) q^{34} +(0.927051 + 0.673542i) q^{35} +(0.618034 - 1.07047i) q^{36} +(-2.11803 - 3.66854i) q^{37} +(-0.845653 + 8.04585i) q^{38} +(-1.50000 + 1.08981i) q^{39} +(-0.0892780 - 0.849423i) q^{40} +(-1.65418 - 1.83716i) q^{41} +(4.43444 - 1.97434i) q^{42} +(-2.32991 + 0.495239i) q^{43} +(-3.16535 - 0.672816i) q^{44} +(0.697887 + 0.310719i) q^{45} +(-1.73607 - 5.34307i) q^{46} +(-1.73607 - 5.34307i) q^{47} +(-4.43444 - 1.97434i) q^{48} +(-1.95630 - 0.415823i) q^{49} +(7.68247 - 1.63296i) q^{50} +(3.86984 - 1.72296i) q^{51} +(0.766755 + 0.851568i) q^{52} +(0.0740275 + 0.704324i) q^{53} +(6.54508 - 4.75528i) q^{54} +(0.209057 - 1.98904i) q^{55} +(3.35410 + 5.80948i) q^{56} +(-2.50000 + 4.33013i) q^{57} +(-8.35410 - 6.06961i) q^{58} +(0.353210 - 0.392279i) q^{59} +(-0.0729490 + 0.224514i) q^{60} -10.9443 q^{61} -6.00000 q^{63} +(1.30902 - 4.02874i) q^{64} +(-0.473881 + 0.526298i) q^{65} +(-6.85410 - 4.97980i) q^{66} +(-0.118034 + 0.204441i) q^{67} +(-1.30902 - 2.26728i) q^{68} +(0.362937 - 3.45312i) q^{69} +(1.50000 - 1.08981i) q^{70} +(1.15924 + 11.0294i) q^{71} +(2.99244 + 3.32344i) q^{72} +(-10.5627 + 4.70281i) q^{73} +(-6.70432 + 1.42505i) q^{74} +(4.74803 + 1.00922i) q^{75} +(2.82301 + 1.25689i) q^{76} +(4.85410 + 14.9394i) q^{77} +(0.927051 + 2.85317i) q^{78} +(-1.81359 - 0.385489i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-3.65418 + 1.62695i) q^{82} +(-4.74425 - 5.26902i) q^{83} +(-0.193806 - 1.84395i) q^{84} +(1.30902 - 0.951057i) q^{85} +(-0.402863 + 3.83299i) q^{86} +(-3.19098 - 5.52694i) q^{87} +(5.85410 - 10.1396i) q^{88} +(-6.97214 - 5.06555i) q^{89} +(0.827091 - 0.918578i) q^{90} +(1.71885 - 5.29007i) q^{91} -2.14590 q^{92} -9.09017 q^{94} +(-0.590170 + 1.81636i) q^{95} +(-2.26298 + 2.51329i) q^{96} +(15.1353 + 10.9964i) q^{97} +(-1.61803 + 2.80252i) q^{98} +(5.23607 + 9.06914i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + q^{3} - 4 q^{4} + 6 q^{5} - 2 q^{6} + 3 q^{7} + 10 q^{8} - 2 q^{9} + 3 q^{10} + 8 q^{11} - 3 q^{12} - 9 q^{13} + 9 q^{14} + 8 q^{15} - 12 q^{16} + 7 q^{17} + 4 q^{18} + 5 q^{19} - 3 q^{20}+ \cdots + 24 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 + q^3 - 4 * q^4 + 6 * q^5 - 2 * q^6 + 3 * q^7 + 10 * q^8 - 2 * q^9 + 3 * q^10 + 8 * q^11 - 3 * q^12 - 9 * q^13 + 9 * q^14 + 8 * q^15 - 12 * q^16 + 7 * q^17 + 4 * q^18 + 5 * q^19 - 3 * q^20 + 3 * q^21 + 14 * q^22 + 18 * q^23 - 5 * q^24 + 6 * q^25 - 12 * q^26 + 10 * q^27 - 9 * q^28 - 20 * q^29 + 4 * q^30 - 36 * q^32 + 4 * q^33 - 4 * q^34 - 6 * q^35 - 4 * q^36 - 8 * q^37 + 15 * q^38 - 12 * q^39 + 5 * q^40 + 12 * q^41 + 9 * q^42 + 6 * q^43 - 4 * q^44 - 2 * q^45 + 4 * q^46 + 4 * q^47 - 9 * q^48 + 2 * q^49 + 3 * q^50 + 7 * q^51 + 12 * q^52 - 9 * q^53 + 30 * q^54 - 2 * q^55 - 20 * q^57 - 40 * q^58 + 15 * q^59 - 14 * q^60 - 16 * q^61 - 48 * q^63 + 6 * q^64 + 21 * q^65 - 28 * q^66 + 8 * q^67 - 6 * q^68 - 9 * q^69 + 12 * q^70 - 18 * q^71 - 10 * q^72 - 24 * q^73 - 4 * q^74 + 6 * q^75 + 10 * q^76 + 12 * q^77 - 6 * q^78 - 9 * q^80 + q^81 - 4 * q^82 + 11 * q^83 + 6 * q^84 + 6 * q^85 + 8 * q^86 - 30 * q^87 + 20 * q^88 - 20 * q^89 - 6 * q^90 + 54 * q^91 - 44 * q^92 - 28 * q^94 + 40 * q^95 - 7 * q^96 + 54 * q^97 - 4 * q^98 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{15}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	1.53884i	0.353553	−	1.08813i	−0.603290	−	0.797522i	$-0.706144\pi$
$2$	0.500000	−	1.53884i	0.353553	−	1.08813i	0.956844	−	0.290604i	$-0.0938561\pi$
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i	−0.518346	−	0.855171i	$-0.673452\pi$
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i	0.904668	+	0.426116i	$0.140119\pi$
$4$	−0.500000	−	0.363271i	−0.250000	−	0.181636i
$5$	0.190983	−	0.330792i	0.0854102	−	0.147935i	−0.820156	−	0.572140i	$-0.806113\pi$
$5$	0.190983	−	0.330792i	0.0854102	−	0.147935i	0.905566	+	0.424206i	$0.139447\pi$
$6$	−0.809017	−	1.40126i	−0.330280	−	0.572061i
$7$	−0.313585	+	2.98357i	−0.118524	+	1.12768i	0.759980	+	0.649947i	$0.225209\pi$
$7$	−0.313585	+	2.98357i	−0.118524	+	1.12768i	−0.878504	+	0.477735i	$0.841458\pi$
$8$	1.80902	−	1.31433i	0.639584	−	0.464685i
$9$	0.209057	+	1.98904i	0.0696856	+	0.663015i
$10$	−0.413545	−	0.459289i	−0.130775	−	0.145240i
$11$	4.78339	−	2.12970i	1.44225	−	0.642129i	0.471418	−	0.881910i	$-0.343742\pi$
$11$	4.78339	−	2.12970i	1.44225	−	0.642129i	0.970827	+	0.239781i	$0.0770756\pi$
$12$	−0.604528	+	0.128496i	−0.174512	+	0.0370937i
$13$	−1.81359	−	0.385489i	−0.502998	−	0.106916i	−0.0505773	−	0.998720i	$-0.516106\pi$
$13$	−1.81359	−	0.385489i	−0.502998	−	0.106916i	−0.452421	+	0.891805i	$0.649439\pi$
$14$	4.43444	+	1.97434i	1.18515	+	0.527665i
$15$	−0.118034	−	0.363271i	−0.0304762	−	0.0937962i
$16$	−1.50000	−	4.61653i	−0.375000	−	1.15413i
$17$	3.86984	+	1.72296i	0.938574	+	0.417880i	0.818255	−	0.574855i	$-0.194942\pi$
$17$	3.86984	+	1.72296i	0.938574	+	0.417880i	0.120319	+	0.992735i	$0.461608\pi$
$18$	3.16535	+	0.672816i	0.746081	+	0.158584i
$19$	−4.89074	+	1.03956i	−1.12201	+	0.238491i	−0.731323	−	0.682031i	$-0.761097\pi$
$19$	−4.89074	+	1.03956i	−1.12201	+	0.238491i	−0.390689	+	0.920523i	$0.627763\pi$
$20$	−0.215659	+	0.0960175i	−0.0482228	+	0.0214702i
$21$	2.00739	+	2.22943i	0.438049	+	0.486502i
$22$	−0.885579	−	8.42572i	−0.188806	−	1.79637i
$23$	2.80902	−	2.04087i	0.585721	−	0.425551i	−0.255061	−	0.966925i	$-0.582096\pi$
$23$	2.80902	−	2.04087i	0.585721	−	0.425551i	0.840782	+	0.541374i	$0.182096\pi$
$24$	0.233733	−	2.22382i	0.0477105	−	0.453935i
$25$	2.42705	+	4.20378i	0.485410	+	0.840755i
$26$	−1.50000	+	2.59808i	−0.294174	+	0.509525i
$27$	4.04508	+	2.93893i	0.778477	+	0.565597i
$28$	1.24064	−	1.37787i	0.234458	−	0.260392i
$29$	1.97214	−	6.06961i	0.366216	−	1.12710i	−0.582999	−	0.812473i	$-0.698121\pi$
$29$	1.97214	−	6.06961i	0.366216	−	1.12710i	0.949216	−	0.314626i	$-0.101879\pi$
$30$	−0.618034			−0.112837
$31$		0			0
$31$		0			0
$32$	−3.38197			−0.597853
$33$	1.61803	−	4.97980i	0.281664	−	0.866871i
$34$	4.58629	−	5.09359i	0.786542	−	0.873544i
$35$	0.927051	+	0.673542i	0.156700	+	0.113849i
$36$	0.618034	−	1.07047i	0.103006	−	0.178411i
$37$	−2.11803	−	3.66854i	−0.348203	−	0.603105i	0.637728	−	0.770262i	$-0.279875\pi$
$37$	−2.11803	−	3.66854i	−0.348203	−	0.603105i	−0.985930	+	0.167157i	$0.946541\pi$
$38$	−0.845653	+	8.04585i	−0.137183	+	1.30521i
$39$	−1.50000	+	1.08981i	−0.240192	+	0.174510i
$40$	−0.0892780	−	0.849423i	−0.0141161	−	0.134306i
$41$	−1.65418	−	1.83716i	−0.258340	−	0.286915i	0.599997	−	0.800002i	$-0.295168\pi$
$41$	−1.65418	−	1.83716i	−0.258340	−	0.286915i	−0.858337	+	0.513087i	$0.828502\pi$
$42$	4.43444	−	1.97434i	0.684249	−	0.304647i
$43$	−2.32991	+	0.495239i	−0.355309	+	0.0755232i	−0.382108	−	0.924118i	$-0.624802\pi$
$43$	−2.32991	+	0.495239i	−0.355309	+	0.0755232i	0.0267994	+	0.999641i	$0.491468\pi$
$44$	−3.16535	−	0.672816i	−0.477195	−	0.101431i
$45$	0.697887	+	0.310719i	0.104035	+	0.0463193i
$46$	−1.73607	−	5.34307i	−0.255969	−	0.787792i
$47$	−1.73607	−	5.34307i	−0.253232	−	0.779367i	−0.994173	−	0.107797i	$-0.965620\pi$
$47$	−1.73607	−	5.34307i	−0.253232	−	0.779367i	0.740941	−	0.671570i	$-0.234380\pi$
$48$	−4.43444	−	1.97434i	−0.640057	−	0.284972i
$49$	−1.95630	−	0.415823i	−0.279471	−	0.0594033i
$50$	7.68247	−	1.63296i	1.08647	−	0.230935i
$51$	3.86984	−	1.72296i	0.541886	−	0.241263i
$52$	0.766755	+	0.851568i	0.106330	+	0.118091i
$53$	0.0740275	+	0.704324i	0.0101685	+	0.0967464i	0.998429	−	0.0560315i	$-0.0178447\pi$
$53$	0.0740275	+	0.704324i	0.0101685	+	0.0967464i	−0.988261	+	0.152778i	$0.951178\pi$
$54$	6.54508	−	4.75528i	0.890673	−	0.647112i
$55$	0.209057	−	1.98904i	0.0281892	−	0.268203i
$56$	3.35410	+	5.80948i	0.448211	+	0.776324i
$57$	−2.50000	+	4.33013i	−0.331133	+	0.573539i
$58$	−8.35410	−	6.06961i	−1.09695	−	0.796979i
$59$	0.353210	−	0.392279i	0.0459840	−	0.0510704i	−0.719714	−	0.694271i	$-0.755727\pi$
$59$	0.353210	−	0.392279i	0.0459840	−	0.0510704i	0.765698	+	0.643200i	$0.222394\pi$
$60$	−0.0729490	+	0.224514i	−0.00941768	+	0.0289846i
$61$	−10.9443			−1.40127			−0.700635	−	0.713520i	$-0.747100\pi$
$61$	−10.9443			−1.40127			−0.700635	+	0.713520i	$0.747100\pi$
$62$		0			0
$63$	−6.00000			−0.755929
$64$	1.30902	−	4.02874i	0.163627	−	0.503593i
$65$	−0.473881	+	0.526298i	−0.0587777	+	0.0652792i
$66$	−6.85410	−	4.97980i	−0.843682	−	0.612971i
$67$	−0.118034	+	0.204441i	−0.0144201	+	0.0249764i	−0.873145	−	0.487460i	$-0.837924\pi$
$67$	−0.118034	+	0.204441i	−0.0144201	+	0.0249764i	0.858725	+	0.512436i	$0.171257\pi$
$68$	−1.30902	−	2.26728i	−0.158742	−	0.274949i
$69$	0.362937	−	3.45312i	0.0436925	−	0.415706i
$70$	1.50000	−	1.08981i	0.179284	−	0.130258i
$71$	1.15924	+	11.0294i	0.137576	+	1.30895i	0.817611	+	0.575771i	$0.195298\pi$
$71$	1.15924	+	11.0294i	0.137576	+	1.30895i	−0.680035	+	0.733180i	$0.738035\pi$
$72$	2.99244	+	3.32344i	0.352663	+	0.391672i
$73$	−10.5627	+	4.70281i	−1.23627	+	0.550423i	−0.917623	−	0.397451i	$-0.869895\pi$
$73$	−10.5627	+	4.70281i	−1.23627	+	0.550423i	−0.318646	+	0.947874i	$0.603228\pi$
$74$	−6.70432	+	1.42505i	−0.779362	+	0.165658i
$75$	4.74803	+	1.00922i	0.548255	+	0.116535i
$76$	2.82301	+	1.25689i	0.323822	+	0.144175i
$77$	4.85410	+	14.9394i	0.553176	+	1.70250i
$78$	0.927051	+	2.85317i	0.104968	+	0.323058i
$79$		0			0		0.406737	−	0.913545i	$-0.366667\pi$
$79$		0			0		−0.406737	+	0.913545i	$0.633333\pi$
$80$	−1.81359	−	0.385489i	−0.202765	−	0.0430990i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	−3.65418	+	1.62695i	−0.403537	+	0.179666i
$83$	−4.74425	−	5.26902i	−0.520749	−	0.578350i	0.424200	−	0.905569i	$-0.360555\pi$
$83$	−4.74425	−	5.26902i	−0.520749	−	0.578350i	−0.944949	+	0.327218i	$0.893889\pi$
$84$	−0.193806	−	1.84395i	−0.0211460	−	0.201191i
$85$	1.30902	−	0.951057i	0.141983	−	0.103157i
$86$	−0.402863	+	3.83299i	−0.0434419	+	0.413322i
$87$	−3.19098	−	5.52694i	−0.342109	−	0.592551i
$88$	5.85410	−	10.1396i	0.624049	−	1.08089i
$89$	−6.97214	−	5.06555i	−0.739045	−	0.536948i	0.153367	−	0.988169i	$-0.450988\pi$
$89$	−6.97214	−	5.06555i	−0.739045	−	0.536948i	−0.892412	+	0.451222i	$0.850988\pi$
$90$	0.827091	−	0.918578i	0.0871830	−	0.0968266i
$91$	1.71885	−	5.29007i	0.180184	−	0.554550i
$92$	−2.14590			−0.223725
$93$		0			0
$94$	−9.09017			−0.937579
$95$	−0.590170	+	1.81636i	−0.0605502	+	0.186354i
$96$	−2.26298	+	2.51329i	−0.230964	+	0.256512i
$97$	15.1353	+	10.9964i	1.53675	+	1.11652i	0.952331	+	0.305065i	$0.0986782\pi$
$97$	15.1353	+	10.9964i	1.53675	+	1.11652i	0.584421	+	0.811451i	$0.301322\pi$
$98$	−1.61803	+	2.80252i	−0.163446	+	0.283097i
$99$	5.23607	+	9.06914i	0.526245	+	0.911482i
$100$	0.313585	−	2.98357i	0.0313585	−	0.298357i
$101$	−7.47214	+	5.42882i	−0.743505	+	0.540188i	−0.893807	−	0.448452i	$-0.851976\pi$
$101$	−7.47214	+	5.42882i	−0.743505	+	0.540188i	0.150302	+	0.988640i	$0.451976\pi$
$102$	−0.716449	−	6.81655i	−0.0709390	−	0.674939i
$103$	−4.58629	−	5.09359i	−0.451901	−	0.501886i	0.473544	−	0.880770i	$-0.342975\pi$
$103$	−4.58629	−	5.09359i	−0.451901	−	0.501886i	−0.925444	+	0.378884i	$0.876308\pi$
$104$	−3.78747	+	1.68629i	−0.371392	+	0.165354i
$105$	1.12086	−	0.238246i	0.109384	−	0.0232504i
$106$	1.12086	+	0.238246i	0.108867	+	0.0231405i
$107$	−9.21783	−	4.10404i	−0.891121	−	0.396753i	−0.0904810	−	0.995898i	$-0.528840\pi$
$107$	−9.21783	−	4.10404i	−0.891121	−	0.396753i	−0.800640	+	0.599145i	$0.795507\pi$
$108$	−0.954915	−	2.93893i	−0.0918867	−	0.282798i
$109$	5.69098	+	17.5150i	0.545097	+	1.67764i	0.720758	+	0.693186i	$0.243794\pi$
$109$	5.69098	+	17.5150i	0.545097	+	1.67764i	−0.175661	+	0.984451i	$0.556206\pi$
$110$	−2.95630	−	1.31623i	−0.281872	−	0.125497i
$111$	−4.14350	−	0.880728i	−0.393284	−	0.0835950i
$112$	14.2441	−	3.02767i	1.34594	−	0.286088i
$113$	4.43444	−	1.97434i	0.417157	−	0.185730i	−0.187415	−	0.982281i	$-0.560011\pi$
$113$	4.43444	−	1.97434i	0.417157	−	0.185730i	0.604572	+	0.796550i	$0.293344\pi$
$114$	5.41338	+	6.01217i	0.507010	+	0.563091i
$115$	−0.138630	−	1.31897i	−0.0129273	−	0.122995i
$116$	−3.19098	+	2.31838i	−0.296275	+	0.215257i
$117$	0.387613	−	3.68789i	0.0358348	−	0.340946i
$118$	−0.427051	−	0.739674i	−0.0393132	−	0.0680925i
$119$	−6.35410	+	11.0056i	−0.582480	+	1.00888i
$120$	−0.690983	−	0.502029i	−0.0630778	−	0.0458287i
$121$	10.9847	−	12.1998i	0.998611	−	1.10907i
$122$	−5.47214	+	16.8415i	−0.495424	+	1.52476i
$123$	−2.47214			−0.222905
$124$		0			0
$125$	3.76393			0.336656
$126$	−3.00000	+	9.23305i	−0.267261	+	0.822546i
$127$	−3.85682	+	4.28344i	−0.342238	+	0.380094i	−0.889552	−	0.456834i	$-0.848984\pi$
$127$	−3.85682	+	4.28344i	−0.342238	+	0.380094i	0.547314	+	0.836927i	$0.315650\pi$
$128$	−11.0172	−	8.00448i	−0.973794	−	0.707503i
$129$	−1.19098	+	2.06284i	−0.104860	+	0.181623i
$130$	0.572949	+	0.992377i	0.0502510	+	0.0870372i
$131$	1.15924	−	11.0294i	0.101283	−	0.963645i	−0.819371	−	0.573264i	$-0.805677\pi$
$131$	1.15924	−	11.0294i	0.101283	−	0.963645i	0.920654	−	0.390380i	$-0.127656\pi$
$132$	−2.61803	+	1.90211i	−0.227871	+	0.165558i
$133$	−1.56793	−	14.9178i	−0.135957	−	1.29354i
$134$	0.255585	+	0.283856i	0.0220792	+	0.0245214i
$135$	1.74472	−	0.776798i	0.150161	−	0.0668561i
$136$	9.26515	−	1.96937i	0.794480	−	0.168872i
$137$	2.41811	+	0.513986i	0.206593	+	0.0439128i	0.310046	−	0.950722i	$-0.399656\pi$
$137$	2.41811	+	0.513986i	0.206593	+	0.0439128i	−0.103452	+	0.994634i	$0.532989\pi$
$138$	−5.13233	−	2.28506i	−0.436893	−	0.194517i
$139$	0.263932	+	0.812299i	0.0223864	+	0.0688983i	0.961626	−	0.274365i	$-0.0884677\pi$
$139$	0.263932	+	0.812299i	0.0223864	+	0.0688983i	−0.939239	+	0.343263i	$0.888468\pi$
$140$	−0.218847	−	0.673542i	−0.0184960	−	0.0569247i
$141$	−5.13233	−	2.28506i	−0.432220	−	0.192437i
$142$	17.5521	+	3.73082i	1.47294	+	0.313084i
$143$	−9.49606	+	2.01845i	−0.794100	+	0.168791i
$144$	8.86889	−	3.94868i	0.739074	−	0.329057i
$145$	−1.63114	−	1.81156i	−0.135458	−	0.150442i
$146$	1.95554	+	18.6057i	0.161842	+	1.53982i
$147$	−1.61803	+	1.17557i	−0.133453	+	0.0969594i
$148$	−0.273659	+	2.60369i	−0.0224946	+	0.214022i
$149$	−6.01722	−	10.4221i	−0.492950	−	0.853814i	0.507017	−	0.861936i	$-0.330748\pi$
$149$	−6.01722	−	10.4221i	−0.492950	−	0.853814i	−0.999967	+	0.00812166i	$0.997415\pi$
$150$	3.92705	−	6.80185i	0.320642	−	0.555369i
$151$	14.9721	+	10.8779i	1.21842	+	0.885230i	0.995968	−	0.0897142i	$-0.0285954\pi$
$151$	14.9721	+	10.8779i	1.21842	+	0.885230i	0.222448	+	0.974945i	$0.428595\pi$
$152$	−7.48111	+	8.30861i	−0.606798	+	0.673917i
$153$	−2.61803	+	8.05748i	−0.211656	+	0.651409i
$154$	25.4164			2.04811
$155$		0			0
$156$	1.14590			0.0917453
$157$	−1.14590	+	3.52671i	−0.0914526	+	0.281462i	−0.986313	−	0.164884i	$-0.947275\pi$
$157$	−1.14590	+	3.52671i	−0.0914526	+	0.281462i	0.894860	+	0.446346i	$0.147275\pi$
$158$		0			0
$159$	0.572949	+	0.416272i	0.0454378	+	0.0330125i
$160$	−0.645898	+	1.11873i	−0.0510627	+	0.0884432i
$161$	5.20820	+	9.02087i	0.410464	+	0.710944i
$162$	−0.169131	+	1.60917i	−0.0132882	+	0.126428i
$163$	−0.572949	+	0.416272i	−0.0448768	+	0.0326049i	−0.609998	−	0.792403i	$-0.708830\pi$
$163$	−0.572949	+	0.416272i	−0.0448768	+	0.0326049i	0.565121	+	0.825008i	$0.308830\pi$
$164$	0.159705	+	1.51949i	0.0124709	+	0.118653i
$165$	−1.33826	−	1.48629i	−0.104183	−	0.115707i
$166$	−10.4803	+	4.66614i	−0.813430	+	0.362163i
$167$	−4.65983	+	0.990477i	−0.360588	+	0.0766454i	−0.384643	−	0.923065i	$-0.625676\pi$
$167$	−4.65983	+	0.990477i	−0.360588	+	0.0766454i	0.0240551	+	0.999711i	$0.492342\pi$
$168$	6.56161	+	1.39471i	0.506239	+	0.107605i
$169$	−8.73560	−	3.88934i	−0.671969	−	0.299180i
$170$	−0.809017	−	2.48990i	−0.0620488	−	0.190966i
$171$	−3.09017	−	9.51057i	−0.236311	−	0.727291i
$172$	1.34486	+	0.598772i	0.102545	+	0.0456559i
$173$	−11.8260	−	2.51369i	−0.899112	−	0.191112i	−0.264904	−	0.964275i	$-0.585340\pi$
$173$	−11.8260	−	2.51369i	−0.899112	−	0.191112i	−0.634208	+	0.773163i	$0.718674\pi$
$174$	−10.1006	+	2.14695i	−0.765723	+	0.162760i
$175$	−13.3033	+	5.92302i	−1.00564	+	0.447738i
$176$	−17.0069	−	18.8881i	−1.28194	−	1.42374i
$177$	−0.0551768	−	0.524972i	−0.00414734	−	0.0394593i
$178$	−11.2812	+	8.19624i	−0.845558	+	0.614334i
$179$	−0.501567	+	4.77209i	−0.0374889	+	0.356683i	0.959656	+	0.281175i	$0.0907243\pi$
$179$	−0.501567	+	4.77209i	−0.0374889	+	0.356683i	−0.997145	+	0.0755072i	$0.975942\pi$
$180$	−0.236068	−	0.408882i	−0.0175955	−	0.0304762i
$181$	8.50000	−	14.7224i	0.631800	−	1.09431i	−0.355383	−	0.934721i	$-0.615650\pi$
$181$	8.50000	−	14.7224i	0.631800	−	1.09431i	0.987184	−	0.159589i	$-0.0510169\pi$
$182$	−7.28115	−	5.29007i	−0.539715	−	0.392126i
$183$	−7.32315	+	8.13318i	−0.541343	+	0.601222i
$184$	2.39919	−	7.38394i	0.176870	−	0.544351i
$185$	−1.61803			−0.118960
$186$		0			0
$187$	22.1803			1.62199
$188$	−1.07295	+	3.30220i	−0.0782528	+	0.240838i
$189$	−10.0370	+	11.1472i	−0.730081	+	0.810837i
$190$	2.50000	+	1.81636i	0.181369	+	0.131772i
$191$	2.45492	−	4.25204i	0.177631	−	0.307667i	−0.763437	−	0.645882i	$-0.776490\pi$
$191$	2.45492	−	4.25204i	0.177631	−	0.307667i	0.941069	+	0.338215i	$0.109823\pi$
$192$	−2.11803	−	3.66854i	−0.152856	−	0.264754i
$193$	0.482716	−	4.59274i	0.0347467	−	0.330592i	−0.963316	−	0.268371i	$-0.913515\pi$
$193$	0.482716	−	4.59274i	0.0347467	−	0.330592i	0.998062	−	0.0622216i	$-0.0198186\pi$
$194$	24.4894	−	17.7926i	1.75823	−	1.27743i
$195$	0.0740275	+	0.704324i	0.00530122	+	0.0504377i
$196$	0.827091	+	0.918578i	0.0590779	+	0.0656127i
$197$	9.51586	−	4.23673i	0.677977	−	0.301855i	−0.0387092	−	0.999251i	$-0.512325\pi$
$197$	9.51586	−	4.23673i	0.677977	−	0.301855i	0.716686	+	0.697396i	$0.245658\pi$
$198$	16.5740	−	3.52291i	1.17786	−	0.250362i
$199$	−13.0013	−	2.76352i	−0.921640	−	0.195901i	−0.277427	−	0.960747i	$-0.589482\pi$
$199$	−13.0013	−	2.76352i	−0.921640	−	0.195901i	−0.644213	+	0.764846i	$0.722815\pi$
$200$	9.91572	+	4.41476i	0.701147	+	0.312171i
$201$	0.0729490	+	0.224514i	0.00514543	+	0.0158360i
$202$	4.61803	+	14.2128i	0.324924	+	1.00001i
$203$	17.4906	+	7.78734i	1.22760	+	0.546564i
$204$	−2.56082	−	0.544320i	−0.179294	−	0.0381100i
$205$	−0.923637	+	0.196325i	−0.0645096	+	0.0137119i
$206$	−10.1314	+	4.51078i	−0.705886	+	0.314281i
$207$	4.64662	+	5.16060i	0.322963	+	0.358686i
$208$	0.940756	+	8.95070i	0.0652297	+	0.620619i
$209$	−21.1803	+	15.3884i	−1.46507	+	1.06444i
$210$	0.193806	−	1.84395i	0.0133739	−	0.127244i
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	0.970229	−	0.242190i	$-0.0778659\pi$
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	−0.694857	+	0.719148i	$0.744533\pi$
$212$	0.218847	−	0.379054i	0.0150305	−	0.0260336i
$213$	8.97214	+	6.51864i	0.614761	+	0.446650i
$214$	−10.9244	+	12.1328i	−0.746776	+	0.829378i
$215$	−0.281153	+	0.865300i	−0.0191745	+	0.0590130i
$216$	11.1803			0.760726
$217$		0			0
$218$	29.7984			2.01820
$219$	−3.57295	+	10.9964i	−0.241438	+	0.743068i
$220$	−0.827091	+	0.918578i	−0.0557625	+	0.0619305i
$221$	−6.35410	−	4.61653i	−0.427423	−	0.310541i
$222$	−3.42705	+	5.93583i	−0.230009	+	0.398387i
$223$	−6.35410	−	11.0056i	−0.425502	−	0.736991i	0.570965	−	0.820974i	$-0.306569\pi$
$223$	−6.35410	−	11.0056i	−0.425502	−	0.736991i	−0.996467	+	0.0839830i	$0.973236\pi$
$224$	1.06054	−	10.0903i	0.0708600	−	0.674188i
$225$	−7.85410	+	5.70634i	−0.523607	+	0.380423i
$226$	−0.820977	−	7.81108i	−0.0546106	−	0.519585i
$227$	14.5487	+	16.1579i	0.965629	+	1.07244i	0.997336	+	0.0729426i	$0.0232390\pi$
$227$	14.5487	+	16.1579i	0.965629	+	1.07244i	−0.0317070	+	0.999497i	$0.510094\pi$
$228$	2.82301	−	1.25689i	0.186958	−	0.0832393i
$229$	−2.70353	+	0.574654i	−0.178655	+	0.0379742i	−0.296370	−	0.955073i	$-0.595776\pi$
$229$	−2.70353	+	0.574654i	−0.178655	+	0.0379742i	0.117716	+	0.993047i	$0.462443\pi$
$230$	−2.09901	−	0.446157i	−0.138404	−	0.0294187i
$231$	14.3502	+	6.38910i	0.944171	+	0.420372i
$232$	−4.40983	−	13.5721i	−0.289520	−	0.891049i
$233$	−1.79180	−	5.51458i	−0.117384	−	0.361272i	0.875052	−	0.484028i	$-0.160827\pi$
$233$	−1.79180	−	5.51458i	−0.117384	−	0.361272i	−0.992437	+	0.122756i	$0.960827\pi$
$234$	−5.48127	−	2.44042i	−0.358322	−	0.159535i
$235$	−2.09901	−	0.446157i	−0.136924	−	0.0291041i
$236$	−0.319109	+	0.0678287i	−0.0207722	+	0.00441527i
$237$		0			0
$238$	13.7589	+	15.2808i	0.891855	+	0.990505i
$239$	1.40240	+	13.3429i	0.0907135	+	0.863081i	0.941374	+	0.337365i	$0.109536\pi$
$239$	1.40240	+	13.3429i	0.0907135	+	0.863081i	−0.850660	+	0.525716i	$0.823798\pi$
$240$	−1.50000	+	1.08981i	−0.0968246	+	0.0703472i
$241$	−1.82634	+	17.3764i	−0.117645	+	1.11931i	0.763284	+	0.646064i	$0.223586\pi$
$241$	−1.82634	+	17.3764i	−0.117645	+	1.11931i	−0.880928	+	0.473250i	$0.843081\pi$
$242$	−13.2812	−	23.0036i	−0.853745	−	1.47873i
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$	5.47214	+	3.97574i	0.350318	+	0.254521i
$245$	−0.511170	+	0.567712i	−0.0326575	+	0.0362698i
$246$	−1.23607	+	3.80423i	−0.0788088	+	0.242549i
$247$	9.27051			0.589868
$248$		0			0
$249$	−7.09017			−0.449321
$250$	1.88197	−	5.79210i	0.119026	−	0.366324i
$251$	11.3379	−	12.5920i	0.715644	−	0.794803i	−0.270140	−	0.962821i	$-0.587070\pi$
$251$	11.3379	−	12.5920i	0.715644	−	0.794803i	0.985784	+	0.168018i	$0.0537367\pi$
$252$	3.00000	+	2.17963i	0.188982	+	0.137304i
$253$	9.09017	−	15.7446i	0.571494	−	0.989857i
$254$	4.66312	+	8.07676i	0.292590	+	0.506781i
$255$	0.169131	−	1.60917i	0.0105914	−	0.100770i
$256$	−10.9721	+	7.97172i	−0.685758	+	0.498233i
$257$	2.65674	+	25.2772i	0.165723	+	1.57675i	0.689113	+	0.724654i	$0.258000\pi$
$257$	2.65674	+	25.2772i	0.165723	+	1.57675i	−0.523390	+	0.852093i	$0.675333\pi$
$258$	2.57890	+	2.86416i	0.160555	+	0.178315i
$259$	11.6095	−	5.16889i	0.721381	−	0.321179i
$260$	0.428129	−	0.0910017i	0.0265515	−	0.00564369i
$261$	12.4850	+	2.65377i	0.772803	+	0.164264i
$262$	−16.3929	−	7.29859i	−1.01276	−	0.450909i
$263$	−4.26393	−	13.1230i	−0.262925	−	0.809201i	−0.992164	−	0.124942i	$-0.960126\pi$
$263$	−4.26393	−	13.1230i	−0.262925	−	0.809201i	0.729239	−	0.684259i	$-0.239874\pi$
$264$	−3.61803	−	11.1352i	−0.222675	−	0.685322i
$265$	0.247123	+	0.110026i	0.0151806	+	0.00675886i
$266$	−23.7401	−	5.04612i	−1.45560	−	0.309398i
$267$	−8.42971	+	1.79179i	−0.515890	+	0.109656i
$268$	0.133284	−	0.0593421i	0.00814165	−	0.00362489i
$269$	2.42094	+	2.68872i	0.147607	+	0.163934i	0.812414	−	0.583081i	$-0.198153\pi$
$269$	2.42094	+	2.68872i	0.147607	+	0.163934i	−0.664807	+	0.747015i	$0.731486\pi$
$270$	−0.323011	−	3.07324i	−0.0196578	−	0.187032i
$271$	−8.54508	+	6.20837i	−0.519077	+	0.377131i	−0.816256	−	0.577690i	$-0.803954\pi$
$271$	−8.54508	+	6.20837i	−0.519077	+	0.377131i	0.297179	+	0.954822i	$0.403954\pi$
$272$	2.14935	−	20.4497i	0.130323	−	1.23994i
$273$	−2.78115	−	4.81710i	−0.168323	−	0.291544i
$274$	2.00000	−	3.46410i	0.120824	−	0.209274i
$275$	20.5623	+	14.9394i	1.23995	+	0.900879i
$276$	−1.43589	+	1.59471i	−0.0864302	+	0.0959904i
$277$	0.718847	−	2.21238i	0.0431913	−	0.132929i	−0.927136	−	0.374726i	$-0.877737\pi$
$277$	0.718847	−	2.21238i	0.0431913	−	0.132929i	0.970327	+	0.241797i	$0.0777368\pi$
$278$	1.38197			0.0828848
$279$		0			0
$280$	2.56231			0.153127
$281$	−3.10081	+	9.54332i	−0.184979	+	0.569307i	−0.999948	−	0.0101977i	$-0.996754\pi$
$281$	−3.10081	+	9.54332i	−0.184979	+	0.569307i	0.814969	+	0.579505i	$0.196754\pi$
$282$	−6.08251	+	6.75531i	−0.362208	+	0.402273i
$283$	10.9721	+	7.97172i	0.652226	+	0.473870i	0.864029	−	0.503443i	$-0.167933\pi$
$283$	10.9721	+	7.97172i	0.652226	+	0.473870i	−0.211803	+	0.977312i	$0.567933\pi$
$284$	3.42705	−	5.93583i	0.203358	−	0.352226i
$285$	0.954915	+	1.65396i	0.0565643	+	0.0979722i
$286$	−1.64195	+	15.6222i	−0.0970908	+	0.923757i
$287$	6.00000	−	4.35926i	0.354169	−	0.257319i
$288$	−0.707023	−	6.72688i	−0.0416618	−	0.396385i
$289$	0.631841	+	0.701731i	0.0371671	+	0.0412783i
$290$	−3.60327	+	1.60428i	−0.211591	+	0.0942066i
$291$	18.2994	−	3.88965i	1.07273	−	0.228016i
$292$	6.98974	+	1.48572i	0.409044	+	0.0869449i
$293$	−3.43852	−	1.53093i	−0.200881	−	0.0894378i	0.303831	−	0.952726i	$-0.401734\pi$
$293$	−3.43852	−	1.53093i	−0.200881	−	0.0894378i	−0.504711	+	0.863288i	$0.668401\pi$
$294$	1.00000	+	3.07768i	0.0583212	+	0.179494i
$295$	−0.0623059	−	0.191758i	−0.00362759	−	0.0111646i
$296$	−8.65323	−	3.85266i	−0.502959	−	0.223932i
$297$	25.6082	+	5.44320i	1.48594	+	0.315846i
$298$	−19.0466	+	4.04848i	−1.10334	+	0.234522i
$299$	−5.88113	+	2.61845i	−0.340114	+	0.151429i
$300$	−2.00739	−	2.22943i	−0.115897	−	0.128716i
$301$	−0.746950	−	7.10675i	−0.0430535	−	0.409626i
$302$	24.2254	−	17.6008i	1.39402	−	1.01281i
$303$	−0.965432	+	9.18547i	−0.0554626	+	0.527692i
$304$	12.1353	+	21.0189i	0.696005	+	1.20552i
$305$	−2.09017	+	3.62028i	−0.119683	+	0.207297i
$306$	11.0902	+	8.05748i	0.633983	+	0.460615i
$307$	−3.40599	+	3.78273i	−0.194390	+	0.215892i	−0.832458	−	0.554088i	$-0.813067\pi$
$307$	−3.40599	+	3.78273i	−0.194390	+	0.215892i	0.638068	+	0.769980i	$0.279734\pi$
$308$	3.00000	−	9.23305i	0.170941	−	0.526102i
$309$	−6.85410			−0.389916
$310$		0			0
$311$	7.52786			0.426866			0.213433	−	0.976958i	$-0.431535\pi$
$311$	7.52786			0.426866			0.213433	+	0.976958i	$0.431535\pi$
$312$	−1.28115	+	3.94298i	−0.0725310	+	0.223227i
$313$	2.16535	−	2.40487i	0.122393	−	0.135931i	−0.678834	−	0.734292i	$-0.737514\pi$
$313$	2.16535	−	2.40487i	0.122393	−	0.135931i	0.801227	+	0.598361i	$0.204181\pi$
$314$	4.85410	+	3.52671i	0.273933	+	0.199024i
$315$	−1.14590	+	1.98475i	−0.0645640	+	0.111828i
$316$		0			0
$317$	1.03363	−	9.83437i	0.0580547	−	0.552353i	−0.926378	−	0.376594i	$-0.877095\pi$
$317$	1.03363	−	9.83437i	0.0580547	−	0.552353i	0.984433	−	0.175760i	$-0.0562381\pi$
$318$	0.927051	−	0.673542i	0.0519864	−	0.0377704i
$319$	−3.49297	−	33.2333i	−0.195569	−	1.86071i
$320$	−1.08268	−	1.20243i	−0.0605234	−	0.0672181i
$321$	−9.21783	+	4.10404i	−0.514489	+	0.229065i
$322$	16.4858	−	3.50416i	0.918718	−	0.195279i
$323$	−20.7175	−	4.40364i	−1.15275	−	0.245025i
$324$	0.564602	+	0.251377i	0.0313668	+	0.0139654i
$325$	−2.78115	−	8.55951i	−0.154271	−	0.474796i
$326$	0.354102	+	1.08981i	0.0196119	+	0.0603592i
$327$	16.8242	+	7.49063i	0.930382	+	0.414233i
$328$	−5.40707	−	1.14931i	−0.298555	−	0.0634599i
$329$	16.4858	−	3.50416i	0.908892	−	0.193191i
$330$	−2.95630	+	1.31623i	−0.162739	+	0.0724559i
$331$	14.9019	+	16.5502i	0.819081	+	0.909682i	0.997234	−	0.0743208i	$-0.0236789\pi$
$331$	14.9019	+	16.5502i	0.819081	+	0.909682i	−0.178153	+	0.984003i	$0.557012\pi$
$332$	0.458040	+	4.35796i	0.0251382	+	0.239174i
$333$	6.85410	−	4.97980i	0.375602	−	0.272891i
$334$	−0.805727	+	7.66598i	−0.0440874	+	0.419464i
$335$	0.0450850	+	0.0780895i	0.00246326	+	0.00426648i
$336$	7.28115	−	12.6113i	0.397219	−	0.688004i
$337$	−22.6353	−	16.4455i	−1.23302	−	0.895842i	−0.235908	−	0.971775i	$-0.575806\pi$
$337$	−22.6353	−	16.4455i	−1.23302	−	0.895842i	−0.997113	+	0.0759333i	$0.975806\pi$
$338$	−10.3529	+	11.4980i	−0.563122	+	0.625411i
$339$	1.50000	−	4.61653i	0.0814688	−	0.250735i
$340$	−1.00000			−0.0542326
$341$		0			0
$342$	−16.1803			−0.874933
$343$	−4.63525	+	14.2658i	−0.250280	+	0.770283i
$344$	−3.56395	+	3.95817i	−0.192155	+	0.213410i
$345$	−1.07295	−	0.779543i	−0.0577656	−	0.0419692i
$346$	−9.78115	+	16.9415i	−0.525838	+	0.910778i
$347$	−16.0623	−	27.8207i	−0.862270	−	1.49350i	−0.869733	−	0.493523i	$-0.835709\pi$
$347$	−16.0623	−	27.8207i	−0.862270	−	1.49350i	0.00746305	−	0.999972i	$-0.497624\pi$
$348$	−0.412289	+	3.92266i	−0.0221010	+	0.210277i
$349$	2.66312	−	1.93487i	0.142553	−	0.103571i	−0.514223	−	0.857657i	$-0.671920\pi$
$349$	2.66312	−	1.93487i	0.142553	−	0.103571i	0.656776	+	0.754085i	$0.271920\pi$
$350$	2.46293	+	23.4332i	0.131649	+	1.25256i
$351$	−6.20318	−	6.88933i	−0.331101	−	0.367725i
$352$	−16.1772	+	7.20258i	−0.862250	+	0.383899i
$353$	−33.8615	+	7.19749i	−1.80227	+	0.383084i	−0.981998	−	0.188892i	$-0.939510\pi$
$353$	−33.8615	+	7.19749i	−1.80227	+	0.383084i	−0.820270	+	0.571976i	$0.806177\pi$
$354$	−0.835438	−	0.177578i	−0.0444030	−	0.00943815i
$355$	3.86984	+	1.72296i	0.205390	+	0.0914454i
$356$	1.64590	+	5.06555i	0.0872324	+	0.268474i
$357$	3.92705	+	12.0862i	0.207842	+	0.639671i
$358$	7.09270	+	3.15788i	0.374861	+	0.166899i
$359$	9.46237	+	2.01129i	0.499405	+	0.106152i	0.450725	−	0.892663i	$-0.351165\pi$
$359$	9.46237	+	2.01129i	0.499405	+	0.106152i	0.0486794	+	0.998814i	$0.484499\pi$
$360$	1.67088	−	0.355156i	0.0880629	−	0.0187183i
$361$	5.48127	−	2.44042i	0.288488	−	0.128443i
$362$	−18.4055	−	20.4414i	−0.967371	−	1.07437i
$363$	−1.71598	−	16.3265i	−0.0900657	−	0.856918i
$364$	−2.78115	+	2.02063i	−0.145772	+	0.105910i
$365$	−0.461640	+	4.39221i	−0.0241634	+	0.229899i
$366$	8.85410	+	15.3358i	0.462811	+	0.801613i
$367$	−1.36475	+	2.36381i	−0.0712391	+	0.123390i	−0.899445	−	0.437035i	$-0.856029\pi$
$367$	−1.36475	+	2.36381i	−0.0712391	+	0.123390i	0.828206	+	0.560425i	$0.189362\pi$
$368$	−13.6353	−	9.90659i	−0.710787	−	0.516417i
$369$	3.30836	−	3.67431i	0.172227	−	0.191277i
$370$	−0.809017	+	2.48990i	−0.0420588	+	0.129444i
$371$	−2.12461			−0.110304
$372$		0			0
$373$	−31.6525			−1.63890			−0.819452	−	0.573148i	$-0.805722\pi$
$373$	−31.6525			−1.63890			−0.819452	+	0.573148i	$0.805722\pi$
$374$	11.0902	−	34.1320i	0.573459	−	1.76493i
$375$	2.51856	−	2.79715i	0.130058	−	0.144444i
$376$	−10.1631	−	7.38394i	−0.524123	−	0.380798i
$377$	−5.91641	+	10.2475i	−0.304711	+	0.527774i
$378$	12.1353	+	21.0189i	0.624170	+	1.08109i
$379$	−0.879754	+	8.37030i	−0.0451899	+	0.429954i	0.948414	+	0.317034i	$0.102687\pi$
$379$	−0.879754	+	8.37030i	−0.0451899	+	0.429954i	−0.993604	+	0.112920i	$0.963980\pi$
$380$	0.954915	−	0.693786i	0.0489861	−	0.0355905i
$381$	0.602495	+	5.73236i	0.0308668	+	0.293678i
$382$	−5.31576	−	5.90374i	−0.271978	−	0.302062i
$383$	9.26874	−	4.12671i	0.473610	−	0.210865i	−0.156029	−	0.987752i	$-0.549869\pi$
$383$	9.26874	−	4.12671i	0.473610	−	0.210865i	0.629639	+	0.776888i	$0.283203\pi$
$384$	−13.3204	+	2.83135i	−0.679756	+	0.144487i
$385$	5.86889	+	1.24747i	0.299106	+	0.0635770i
$386$	−6.82614	−	3.03919i	−0.347441	−	0.154691i
$387$	−1.47214	−	4.53077i	−0.0748329	−	0.230312i
$388$	−3.57295	−	10.9964i	−0.181389	−	0.558258i
$389$	−26.5557	−	11.8234i	−1.34643	−	0.599469i	−0.398271	−	0.917268i	$-0.630390\pi$
$389$	−26.5557	−	11.8234i	−1.34643	−	0.599469i	−0.948158	+	0.317798i	$0.897056\pi$
$390$	1.12086	+	0.238246i	0.0567568	+	0.0120640i
$391$	14.3868	−	3.05801i	0.727571	−	0.154650i
$392$	−4.08550	+	1.81898i	−0.206349	+	0.0918724i
$393$	−7.42077	−	8.24160i	−0.374328	−	0.415734i
$394$	−1.76173	−	16.7618i	−0.0887548	−	0.844446i
$395$		0			0
$396$	0.676522	−	6.43668i	0.0339965	−	0.323455i
$397$	−14.8541	−	25.7281i	−0.745506	−	1.29125i	−0.949958	−	0.312378i	$-0.898875\pi$
$397$	−14.8541	−	25.7281i	−0.745506	−	1.29125i	0.204452	−	0.978877i	$-0.434459\pi$
$398$	−10.7533	+	18.6252i	−0.539014	+	0.933599i
$399$	−12.1353	−	8.81678i	−0.607523	−	0.441391i
$400$	15.7663	−	17.5102i	0.788313	−	0.875510i
$401$	−7.36475	+	22.6664i	−0.367778	+	1.13190i	0.580445	+	0.814299i	$0.302878\pi$
$401$	−7.36475	+	22.6664i	−0.367778	+	1.13190i	−0.948223	+	0.317605i	$0.897122\pi$
$402$	0.381966			0.0190507
$403$		0			0
$404$	5.70820			0.283994
$405$	−0.118034	+	0.363271i	−0.00586516	+	0.0180511i
$406$	20.7288	−	23.0217i	1.02875	−	1.14255i
$407$	−17.9443	−	13.0373i	−0.889465	−	0.646234i
$408$	4.73607	−	8.20311i	0.234470	−	0.406114i
$409$	8.09017	+	14.0126i	0.400033	+	0.692878i	0.993729	−	0.111811i	$-0.0356653\pi$
$409$	8.09017	+	14.0126i	0.400033	+	0.692878i	−0.593696	+	0.804689i	$0.702332\pi$
$410$	−0.159705	+	1.51949i	−0.00788728	+	0.0750425i
$411$	2.00000	−	1.45309i	0.0986527	−	0.0716754i
$412$	0.442790	+	4.21286i	0.0218147	+	0.207553i
$413$	1.05963	+	1.17684i	0.0521410	+	0.0579084i
$414$	10.2647	−	4.57012i	0.504480	−	0.224609i
$415$	−2.64902	+	0.563067i	−0.130035	+	0.0276399i
$416$	6.13348	+	1.30371i	0.300719	+	0.0639198i
$417$	0.780261	+	0.347395i	0.0382095	+	0.0170120i
$418$	13.0902	+	40.2874i	0.640261	+	1.97052i
$419$	−1.38197	−	4.25325i	−0.0675135	−	0.207785i	0.911608	−	0.411060i	$-0.134841\pi$
$419$	−1.38197	−	4.25325i	−0.0675135	−	0.207785i	−0.979122	+	0.203275i	$0.934841\pi$
$420$	−0.646976	−	0.288052i	−0.0315692	−	0.0140555i
$421$	−18.8157	−	3.99940i	−0.917022	−	0.194919i	−0.274857	−	0.961485i	$-0.588630\pi$
$421$	−18.8157	−	3.99940i	−0.917022	−	0.194919i	−0.642165	+	0.766566i	$0.721964\pi$
$422$	12.6614	−	2.69127i	0.616348	−	0.131009i
$423$	10.2647	−	4.57012i	0.499085	−	0.222207i
$424$	1.05963	+	1.17684i	0.0514602	+	0.0571523i
$425$	2.14935	+	20.4497i	0.104259	+	0.991954i
$426$	14.5172	−	10.5474i	0.703362	−	0.511022i
$427$	3.43196	−	32.6530i	0.166084	−	1.58019i
$428$	3.11803	+	5.40059i	0.150716	+	0.261048i
$429$	−4.85410	+	8.40755i	−0.234358	+	0.405920i
$430$	1.19098	+	0.865300i	0.0574343	+	0.0417285i
$431$	16.5703	−	18.4032i	0.798163	−	0.886450i	−0.197421	−	0.980319i	$-0.563257\pi$
$431$	16.5703	−	18.4032i	0.798163	−	0.886450i	0.995585	+	0.0938684i	$0.0299233\pi$
$432$	7.50000	−	23.0826i	0.360844	−	1.11056i
$433$	−27.4164			−1.31755			−0.658774	−	0.752341i	$-0.728925\pi$
$433$	−27.4164			−1.31755			−0.658774	+	0.752341i	$0.728925\pi$
$434$		0			0
$435$	−2.43769			−0.116878
$436$	3.51722	−	10.8249i	0.168444	−	0.518418i
$437$	−11.6166	+	12.9015i	−0.555696	+	0.617162i
$438$	15.1353	+	10.9964i	0.723190	+	0.525429i
$439$	5.91641	−	10.2475i	0.282375	−	0.489087i	−0.689594	−	0.724196i	$-0.742211\pi$
$439$	5.91641	−	10.2475i	0.282375	−	0.489087i	0.971969	+	0.235108i	$0.0755445\pi$
$440$	−2.23607	−	3.87298i	−0.106600	−	0.184637i
$441$	0.418114	−	3.97809i	0.0199102	−	0.189433i
$442$	−10.2812	+	7.46969i	−0.489025	+	0.355297i
$443$	0.0915030	+	0.870593i	0.00434744	+	0.0413631i	0.996481	−	0.0838243i	$-0.0267135\pi$
$443$	0.0915030	+	0.870593i	0.00434744	+	0.0413631i	−0.992133	+	0.125187i	$0.960047\pi$
$444$	1.75181	+	1.94558i	0.0831371	+	0.0923331i
$445$	−3.00721	+	1.33889i	−0.142555	+	0.0634697i
$446$	−20.1130	+	4.27514i	−0.952377	+	0.202434i
$447$	−11.7715	−	2.50210i	−0.556771	−	0.118345i
$448$	11.6095	+	5.16889i	0.548498	+	0.244207i
$449$	10.5279	+	32.4014i	0.496841	+	1.52912i	0.814069	+	0.580769i	$0.197248\pi$
$449$	10.5279	+	32.4014i	0.496841	+	1.52912i	−0.317228	+	0.948349i	$0.602752\pi$
$450$	4.85410	+	14.9394i	0.228825	+	0.704250i
$451$	−11.8252	−	5.26491i	−0.556826	−	0.247915i
$452$	−2.93444	−	0.623735i	−0.138025	−	0.0293380i
$453$	18.1022	−	3.84773i	0.850514	−	0.180782i
$454$	32.1388	−	14.3091i	1.50835	−	0.671561i
$455$	−1.42164	−	1.57889i	−0.0666476	−	0.0740197i
$456$	1.16866	+	11.1191i	0.0547277	+	0.520699i
$457$	21.6353	−	15.7189i	1.01205	−	0.735301i	0.0474155	−	0.998875i	$-0.484902\pi$
$457$	21.6353	−	15.7189i	1.01205	−	0.735301i	0.964639	+	0.263575i	$0.0849015\pi$
$458$	−0.467465	+	4.44764i	−0.0218432	+	0.207824i
$459$	10.5902	+	18.3427i	0.494307	+	0.856164i
$460$	−0.409830	+	0.709846i	−0.0191084	+	0.0330968i
$461$	−25.6803	−	18.6579i	−1.19605	−	0.868983i	−0.202162	−	0.979352i	$-0.564797\pi$
$461$	−25.6803	−	18.6579i	−1.19605	−	0.868983i	−0.993891	+	0.110369i	$0.964797\pi$
$462$	17.0069	−	18.8881i	0.791232	−	0.878753i
$463$	−2.81966	+	8.67802i	−0.131041	+	0.403302i	−0.994953	−	0.100340i	$-0.968007\pi$
$463$	−2.81966	+	8.67802i	−0.131041	+	0.403302i	0.863912	+	0.503642i	$0.168007\pi$
$464$	−30.9787			−1.43815
$465$		0			0
$466$	−9.38197			−0.434611
$467$	11.9828	−	36.8792i	0.554497	−	1.70657i	−0.142771	−	0.989756i	$-0.545601\pi$
$467$	11.9828	−	36.8792i	0.554497	−	1.70657i	0.697268	−	0.716810i	$-0.254399\pi$
$468$	−1.53351	+	1.70314i	−0.0708866	+	0.0787275i
$469$	−0.572949	−	0.416272i	−0.0264563	−	0.0192216i
$470$	−1.73607	+	3.00696i	−0.0800788	+	0.138701i
$471$	1.85410	+	3.21140i	0.0854325	+	0.147973i
$472$	0.123379	−	1.17387i	0.00567898	−	0.0540319i
$473$	−10.0902	+	7.33094i	−0.463947	+	0.337077i
$474$		0			0
$475$	−16.2401	−	18.0365i	−0.745149	−	0.827572i
$476$	7.17508	−	3.19455i	0.328869	−	0.146422i
$477$	−1.38546	+	0.294488i	−0.0634357	+	0.0134837i
$478$	21.2338	+	4.51339i	0.971213	+	0.206438i
$479$	8.17100	+	3.63796i	0.373342	+	0.166223i	0.584826	−	0.811159i	$-0.301163\pi$
$479$	8.17100	+	3.63796i	0.373342	+	0.166223i	−0.211483	+	0.977382i	$0.567829\pi$
$480$	0.399187	+	1.22857i	0.0182203	+	0.0560763i
$481$	2.42705	+	7.46969i	0.110664	+	0.340589i
$482$	25.8264	+	11.4987i	1.17636	+	0.523749i
$483$	10.1888	+	2.16569i	0.463606	+	0.0985424i
$484$	−9.92419	+	2.10945i	−0.451099	+	0.0958841i
$485$	6.52810	−	2.90650i	0.296426	−	0.131977i
$486$	17.3228	+	19.2389i	0.785779	+	0.872696i
$487$	−4.38215	−	41.6933i	−0.198574	−	1.88930i	−0.410262	−	0.911968i	$-0.634563\pi$
$487$	−4.38215	−	41.6933i	−0.198574	−	1.88930i	0.211688	−	0.977337i	$-0.432104\pi$
$488$	−19.7984	+	14.3844i	−0.896230	+	0.651149i
$489$	−0.0740275	+	0.704324i	−0.00334764	+	0.0318506i
$490$	0.618034	+	1.07047i	0.0279199	+	0.0483587i
$491$	10.7984	−	18.7033i	0.487324	−	0.844070i	−0.512570	−	0.858645i	$-0.671306\pi$
$491$	10.7984	−	18.7033i	0.487324	−	0.844070i	0.999894	+	0.0145759i	$0.00463981\pi$
$492$	1.23607	+	0.898056i	0.0557262	+	0.0404875i
$493$	18.0896	−	20.0905i	0.814713	−	0.904831i
$494$	4.63525	−	14.2658i	0.208550	−	0.641851i
$495$	4.00000			0.179787
$496$		0			0
$497$	−33.2705			−1.49239
$498$	−3.54508	+	10.9106i	−0.158859	+	0.488918i
$499$	−7.26281	+	8.06617i	−0.325128	+	0.361091i	−0.883444	−	0.468537i	$-0.844781\pi$
$499$	−7.26281	+	8.06617i	−0.325128	+	0.361091i	0.558316	+	0.829629i	$0.311448\pi$
$500$	−1.88197	−	1.36733i	−0.0841641	−	0.0611488i
$501$	−2.38197	+	4.12569i	−0.106418	+	0.184322i
$502$	−13.7082	−	23.7433i	−0.611827	−	1.05972i
$503$	−2.07532	+	19.7453i	−0.0925339	+	0.880401i	0.845527	+	0.533932i	$0.179286\pi$
$503$	−2.07532	+	19.7453i	−0.0925339	+	0.880401i	−0.938061	+	0.346469i	$0.887381\pi$
$504$	−10.8541	+	7.88597i	−0.483480	+	0.351269i
$505$	0.368762	+	3.50854i	0.0164097	+	0.156128i
$506$	−19.6834	−	21.8607i	−0.875035	−	0.971824i
$507$	−8.73560	+	3.88934i	−0.387962	+	0.172732i
$508$	3.48446	−	0.740645i	0.154598	−	0.0328608i
$509$	−12.8041	−	2.72160i	−0.567533	−	0.120633i	−0.0847959	−	0.996398i	$-0.527024\pi$
$509$	−12.8041	−	2.72160i	−0.567533	−	0.120633i	−0.482737	+	0.875766i	$0.660357\pi$
$510$	−2.39169	−	1.06485i	−0.105906	−	0.0471524i
$511$	−10.7188	−	32.9892i	−0.474174	−	1.45936i
$512$	−1.63525	−	5.03280i	−0.0722687	−	0.222420i
$513$	−22.8386	−	10.1684i	−1.00835	−	0.448947i
$514$	40.2259	+	8.55029i	1.77429	+	0.377137i
$515$	−2.56082	+	0.544320i	−0.112843	+	0.0239856i
$516$	1.34486	−	0.598772i	0.0592043	−	0.0263595i
$517$	−19.6834	−	21.8607i	−0.865676	−	0.961430i
$518$	−2.14935	−	20.4497i	−0.0944369	−	0.898507i
$519$	−9.78115	+	7.10642i	−0.429345	+	0.311937i
$520$	−0.165530	+	1.57492i	−0.00725899	+	0.0690647i
$521$	13.5344	+	23.4423i	0.592955	+	1.02703i	0.993832	+	0.110896i	$0.0353720\pi$
$521$	13.5344	+	23.4423i	0.592955	+	1.02703i	−0.400877	+	0.916132i	$0.631295\pi$
$522$	10.3262	−	17.8856i	0.451967	−	0.782830i
$523$	−4.95492	−	3.59996i	−0.216663	−	0.157415i	0.474160	−	0.880439i	$-0.342752\pi$
$523$	−4.95492	−	3.59996i	−0.216663	−	0.157415i	−0.690823	+	0.723024i	$0.742752\pi$
$524$	−4.58629	+	5.09359i	−0.200353	+	0.222515i
$525$	−4.50000	+	13.8496i	−0.196396	+	0.604445i
$526$	−22.3262			−0.973470
$527$		0			0
$528$	−25.4164			−1.10611
$529$	−3.38197	+	10.4086i	−0.147042	+	0.452549i
$530$	0.292875	−	0.325270i	0.0127217	−	0.0141288i
$531$	0.854102	+	0.620541i	0.0370649	+	0.0269292i
$532$	−4.63525	+	8.02850i	−0.200964	+	0.348079i
$533$	2.29180	+	3.96951i	0.0992687	+	0.171938i
$534$	−1.45757	+	13.8679i	−0.0630754	+	0.600122i
$535$	−3.11803	+	2.26538i	−0.134804	+	0.0979411i
$536$	0.0551768	+	0.524972i	0.00238328	+	0.0226754i
$537$	3.21074	+	3.56589i	0.138554	+	0.153879i
$538$	5.34799	−	2.38108i	0.230568	−	0.102656i
$539$	−10.2433	+	2.17728i	−0.441210	+	0.0937821i
$540$	−1.15455	−	0.245406i	−0.0496838	−	0.0105606i
$541$	20.0980	+	8.94821i	0.864081	+	0.384713i	0.790417	−	0.612570i	$-0.209864\pi$
$541$	20.0980	+	8.94821i	0.864081	+	0.384713i	0.0736639	+	0.997283i	$0.476531\pi$
$542$	5.28115	+	16.2537i	0.226845	+	0.698157i
$543$	−5.25329	−	16.1680i	−0.225440	−	0.693834i
$544$	−13.0877	−	5.82701i	−0.561129	−	0.249831i
$545$	6.88072	+	1.46254i	0.294738	+	0.0626484i
$546$	−8.80333	+	1.87121i	−0.376748	+	0.0800802i
$547$	−9.40202	+	4.18605i	−0.402001	+	0.178983i	−0.597770	−	0.801667i	$-0.703946\pi$
$547$	−9.40202	+	4.18605i	−0.402001	+	0.178983i	0.195769	+	0.980650i	$0.437280\pi$
$548$	−1.02234	−	1.13542i	−0.0436722	−	0.0485029i
$549$	−2.28798	−	21.7686i	−0.0976484	−	0.929063i
$550$	33.2705	−	24.1724i	1.41866	−	1.03072i
$551$	−3.33549	+	31.7350i	−0.142096	+	1.35196i
$552$	−3.88197	−	6.72376i	−0.165227	−	0.286182i
$553$		0			0
$554$	−3.04508	−	2.21238i	−0.129373	−	0.0939952i
$555$	−1.08268	+	1.20243i	−0.0459570	+	0.0510405i
$556$	0.163119	−	0.502029i	0.00691778	−	0.0212908i
$557$	−0.111456			−0.00472255			−0.00236127	−	0.999997i	$-0.500752\pi$
$557$	−0.111456			−0.00472255			−0.00236127	+	0.999997i	$0.500752\pi$
$558$		0			0
$559$	4.41641			0.186794
$560$	1.71885	−	5.29007i	0.0726345	−	0.223546i
$561$	14.8415	−	16.4832i	0.626610	−	0.695921i
$562$	13.1353	+	9.54332i	0.554077	+	0.402561i
$563$	−5.78115	+	10.0133i	−0.243647	+	0.422008i	−0.961750	−	0.273928i	$-0.911677\pi$
$563$	−5.78115	+	10.0133i	−0.243647	+	0.422008i	0.718104	+	0.695936i	$0.245010\pi$
$564$	1.73607	+	3.00696i	0.0731016	+	0.126616i
$565$	0.193806	−	1.84395i	0.00815350	−	0.0775753i
$566$	17.7533	−	12.8985i	0.746226	−	0.542165i
$567$	−0.313585	−	2.98357i	−0.0131693	−	0.125298i
$568$	16.5934	+	18.4288i	0.696242	+	0.773255i
$569$	−22.3564	+	9.95371i	−0.937229	+	0.417281i	−0.817762	−	0.575557i	$-0.804785\pi$
$569$	−22.3564	+	9.95371i	−0.937229	+	0.417281i	−0.119468	+	0.992838i	$0.538119\pi$
$570$	3.02264	−	0.642482i	0.126605	−	0.0269106i
$571$	6.84703	+	1.45538i	0.286539	+	0.0609058i	0.348939	−	0.937145i	$-0.386542\pi$
$571$	6.84703	+	1.45538i	0.286539	+	0.0609058i	−0.0623997	+	0.998051i	$0.519875\pi$
$572$	5.48127	+	2.44042i	0.229184	+	0.102039i
$573$	−1.51722	−	4.66953i	−0.0633828	−	0.195072i
$574$	−3.70820	−	11.4127i	−0.154777	−	0.476356i
$575$	15.3970	+	6.85518i	0.642099	+	0.285881i
$576$	8.28700	+	1.76146i	0.345292	+	0.0733940i
$577$	7.80436	−	1.65887i	0.324900	−	0.0690596i	−0.0425744	−	0.999093i	$-0.513556\pi$
$577$	7.80436	−	1.65887i	0.324900	−	0.0690596i	0.367474	+	0.930034i	$0.380223\pi$
$578$	1.39577	−	0.621438i	0.0580565	−	0.0258484i
$579$	−3.09007	−	3.43187i	−0.128419	−	0.142624i
$580$	0.157480	+	1.49832i	0.00653901	+	0.0622145i
$581$	17.2082	−	12.5025i	0.713917	−	0.518691i
$582$	3.16413	−	30.1047i	0.131157	−	1.24788i
$583$	1.85410	+	3.21140i	0.0767891	+	0.133003i
$584$	−12.9271	+	22.3903i	−0.534925	+	0.926518i
$585$	−1.14590	−	0.832544i	−0.0473771	−	0.0344214i
$586$	−4.07512	+	4.52588i	−0.168342	+	0.186962i
$587$	12.3647	−	38.0548i	0.510348	−	1.57069i	−0.281243	−	0.959637i	$-0.590747\pi$
$587$	12.3647	−	38.0548i	0.510348	−	1.57069i	0.791591	−	0.611052i	$-0.209253\pi$
$588$	1.23607			0.0509746
$589$		0			0
$590$	−0.326238			−0.0134310
$591$	3.21885	−	9.90659i	0.132406	−	0.407503i
$592$	−13.7589	+	15.2808i	−0.565486	+	0.628036i
$593$	−33.8885	−	24.6215i	−1.39164	−	1.01108i	−0.995684	−	0.0928113i	$-0.970415\pi$
$593$	−33.8885	−	24.6215i	−1.39164	−	1.01108i	−0.395952	−	0.918271i	$-0.629585\pi$
$594$	21.1803	−	36.6854i	0.869040	−	1.50522i
$595$	2.42705	+	4.20378i	0.0994994	+	0.172338i
$596$	−0.777451	+	7.39695i	−0.0318456	+	0.302991i
$597$	−10.7533	+	7.81272i	−0.440103	+	0.319753i
$598$	1.08881	+	10.3593i	0.0445248	+	0.423625i
$599$	3.48057	+	3.86556i	0.142212	+	0.157943i	0.810043	−	0.586371i	$-0.199444\pi$
$599$	3.48057	+	3.86556i	0.142212	+	0.157943i	−0.667831	+	0.744313i	$0.732777\pi$
$600$	9.91572	−	4.41476i	0.404807	−	0.180232i
$601$	21.5192	−	4.57406i	0.877788	−	0.186580i	0.253087	−	0.967443i	$-0.418554\pi$
$601$	21.5192	−	4.57406i	0.877788	−	0.186580i	0.624701	+	0.780864i	$0.285221\pi$
$602$	−11.3096	−	2.40394i	−0.460947	−	0.0979772i
$603$	−0.431318	−	0.192035i	−0.0175646	−	0.00782027i
$604$	−3.53444	−	10.8779i	−0.143814	−	0.442615i
$605$	−1.93769	−	5.96361i	−0.0787785	−	0.242455i
$606$	13.6523	+	6.07838i	0.554586	+	0.246917i
$607$	−1.38546	−	0.294488i	−0.0562339	−	0.0119529i	0.179709	−	0.983720i	$-0.442484\pi$
$607$	−1.38546	−	0.294488i	−0.0562339	−	0.0119529i	−0.235943	+	0.971767i	$0.575818\pi$
$608$	16.5403	−	3.51575i	0.670798	−	0.142583i
$609$	17.4906	−	7.78734i	0.708757	−	0.315559i
$610$	4.52595	+	5.02658i	0.183251	+	0.203520i
$611$	1.08881	+	10.3593i	0.0440486	+	0.419094i
$612$	4.23607	−	3.07768i	0.171233	−	0.124408i
$613$	4.48890	−	42.7090i	0.181305	−	1.72500i	−0.404491	−	0.914542i	$-0.632551\pi$
$613$	4.48890	−	42.7090i	0.181305	−	1.72500i	0.585796	−	0.810459i	$-0.300782\pi$
$614$	4.11803	+	7.13264i	0.166190	+	0.287850i
$615$	−0.472136	+	0.817763i	−0.0190384	+	0.0329754i
$616$	28.4164	+	20.6457i	1.14493	+	0.831840i
$617$	−6.53335	+	7.25602i	−0.263023	+	0.292116i	−0.860162	−	0.510022i	$-0.829637\pi$
$617$	−6.53335	+	7.25602i	−0.263023	+	0.292116i	0.597139	+	0.802138i	$0.296304\pi$
$618$	−3.42705	+	10.5474i	−0.137856	+	0.424278i
$619$	40.0000			1.60774			0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$		0			0
$621$	17.3607			0.696660
$622$	3.76393	−	11.5842i	0.150920	−	0.464484i
$623$	17.2998	−	19.2133i	0.693101	−	0.769766i
$624$	7.28115	+	5.29007i	0.291479	+	0.211772i
$625$	−11.4164	+	19.7738i	−0.456656	+	0.790952i
$626$	−2.61803	−	4.53457i	−0.104638	−	0.181238i
$627$	−2.73659	+	26.0369i	−0.109289	+	1.03981i
$628$	1.85410	−	1.34708i	0.0739867	−	0.0537545i
$629$	−1.87569	−	17.8460i	−0.0747885	−	0.711565i
$630$	2.48127	+	2.75573i	0.0988563	+	0.109791i
$631$	38.6160	−	17.1930i	1.53728	−	0.684441i	0.548822	−	0.835939i	$-0.315076\pi$
$631$	38.6160	−	17.1930i	1.53728	−	0.684441i	0.988458	+	0.151498i	$0.0484097\pi$
$632$		0			0
$633$	7.82518	+	1.66329i	0.311023	+	0.0661100i
$634$	−14.6167	−	6.50779i	−0.580504	−	0.258457i
$635$	0.680340	+	2.09387i	0.0269985	+	0.0830927i
$636$	−0.135255	−	0.416272i	−0.00536321	−	0.0165063i
$637$	3.38761	+	1.50826i	0.134222	+	0.0597595i
$638$	−52.8873	−	11.2416i	−2.09383	−	0.445057i
$639$	−21.6956	+	4.61155i	−0.858267	+	0.182430i
$640$	−4.75192	+	2.11569i	−0.187836	+	0.0836301i
$641$	20.0136	+	22.2273i	0.790489	+	0.877927i	0.994890	−	0.100960i	$-0.0321915\pi$
$641$	20.0136	+	22.2273i	0.790489	+	0.877927i	−0.204401	+	0.978887i	$0.565525\pi$
$642$	1.70656	+	16.2368i	0.0673524	+	0.640815i
$643$	12.0172	−	8.73102i	0.473913	−	0.344318i	−0.325051	−	0.945696i	$-0.605382\pi$
$643$	12.0172	−	8.73102i	0.473913	−	0.344318i	0.798964	+	0.601378i	$0.205382\pi$
$644$	0.672922	−	6.40243i	0.0265169	−	0.252291i
$645$	0.454915	+	0.787936i	0.0179123	+	0.0310249i
$646$	−17.1353	+	29.6791i	−0.674178	+	1.16771i
$647$	4.76393	+	3.46120i	0.187289	+	0.136074i	0.677479	−	0.735542i	$-0.263072\pi$
$647$	4.76393	+	3.46120i	0.187289	+	0.136074i	−0.490190	+	0.871616i	$0.663072\pi$
$648$	−1.49622	+	1.66172i	−0.0587771	+	0.0652786i
$649$	0.854102	−	2.62866i	0.0335264	−	0.103184i
$650$	−14.5623			−0.571181
$651$		0			0
$652$	0.437694			0.0171414
$653$	2.57953	−	7.93897i	0.100945	−	0.310676i	−0.887813	−	0.460205i	$-0.847776\pi$
$653$	2.57953	−	7.93897i	0.100945	−	0.310676i	0.988757	+	0.149529i	$0.0477759\pi$
$654$	19.9390	−	22.1445i	0.779677	−	0.865919i
$655$	−3.42705	−	2.48990i	−0.133906	−	0.0972884i
$656$	−6.00000	+	10.3923i	−0.234261	+	0.405751i
$657$	−11.5623	−	20.0265i	−0.451089	−	0.781308i
$658$	2.85054	−	27.1211i	0.111126	−	1.05729i
$659$	30.4894	−	22.1518i	1.18770	−	0.862912i	0.194678	−	0.980867i	$-0.437634\pi$
$659$	30.4894	−	22.1518i	1.18770	−	0.862912i	0.993019	+	0.117955i	$0.0376339\pi$
$660$	0.129204	+	1.22930i	0.00502927	+	0.0478503i
$661$	−9.62341	−	10.6879i	−0.374307	−	0.415710i	0.526331	−	0.850280i	$-0.323567\pi$
$661$	−9.62341	−	10.6879i	−0.374307	−	0.415710i	−0.900638	+	0.434569i	$0.856901\pi$
$662$	32.9191	−	14.6565i	1.27944	−	0.569642i
$663$	−7.68247	+	1.63296i	−0.298362	+	0.0634189i
$664$	−15.5077	−	3.29625i	−0.601814	−	0.127919i
$665$	−5.23415	−	2.33039i	−0.202972	−	0.0903688i
$666$	−4.23607	−	13.0373i	−0.164144	−	0.505184i
$667$	−6.84752	−	21.0745i	−0.265137	−	0.816008i
$668$	2.68973	+	1.19754i	0.104069	+	0.0463343i
$669$	−12.4305	−	2.64218i	−0.480591	−	0.102153i
$670$	0.142710	−	0.0303339i	0.00551336	−	0.00117190i
$671$	−52.3507	+	23.3080i	−2.02098	+	0.899796i
$672$	−6.78893	−	7.53987i	−0.261889	−	0.290857i
$673$	2.34315	+	22.2936i	0.0903219	+	0.859355i	0.942073	+	0.335408i	$0.108874\pi$
$673$	2.34315	+	22.2936i	0.0903219	+	0.859355i	−0.851751	+	0.523947i	$0.824459\pi$
$674$	−36.6246	+	26.6093i	−1.41073	+	1.02495i
$675$	−2.53696	+	24.1376i	−0.0976476	+	0.929055i
$676$	2.95492	+	5.11806i	0.113651	+	0.196849i
$677$	−1.32624	+	2.29711i	−0.0509715	+	0.0882852i	−0.890385	−	0.455207i	$-0.849565\pi$
$677$	−1.32624	+	2.29711i	−0.0509715	+	0.0882852i	0.839414	+	0.543493i	$0.182898\pi$
$678$	−6.35410	−	4.61653i	−0.244028	−	0.177297i
$679$	−37.5547	+	41.7087i	−1.44122	+	1.60063i
$680$	1.11803	−	3.44095i	0.0428746	−	0.131955i
$681$	21.7426			0.833180
$682$		0			0
$683$	27.9443			1.06926			0.534629	−	0.845087i	$-0.320451\pi$
$683$	27.9443			1.06926			0.534629	+	0.845087i	$0.320451\pi$
$684$	−1.90983	+	5.87785i	−0.0730242	+	0.224745i
$685$	0.631841	−	0.701731i	0.0241414	−	0.0268118i
$686$	19.6353	+	14.2658i	0.749678	+	0.544673i
$687$	−1.38197	+	2.39364i	−0.0527253	+	0.0913229i
$688$	5.78115	+	10.0133i	0.220404	+	0.381752i
$689$	0.137254	−	1.30589i	0.00522898	−	0.0497504i
$690$	−1.73607	+	1.26133i	−0.0660910	+	0.0480179i
$691$	5.20895	+	49.5598i	0.198158	+	1.88534i	0.416006	+	0.909362i	$0.363430\pi$
$691$	5.20895	+	49.5598i	0.198158	+	1.88534i	−0.217848	+	0.975983i	$0.569904\pi$
$692$	4.99983	+	5.55288i	0.190065	+	0.211089i
$693$	−28.7003	+	12.7782i	−1.09023	+	0.485404i
$694$	−50.8429	+	10.8070i	−1.92997	+	0.410227i
$695$	0.319109	+	0.0678287i	0.0121045	+	0.00257289i
$696$	−13.0368	−	5.80434i	−0.494157	−	0.220013i
$697$	−3.23607	−	9.95959i	−0.122575	−	0.377246i
$698$	−1.64590	−	5.06555i	−0.0622982	−	0.191734i
$699$	−5.29708	−	2.35841i	−0.200354	−	0.0892033i
$700$	8.80333	+	1.87121i	0.332735	+	0.0707249i
$701$	0.944458	−	0.200751i	0.0356717	−	0.00758225i	−0.190041	−	0.981776i	$-0.560862\pi$
$701$	0.944458	−	0.200751i	0.0356717	−	0.00758225i	0.225713	+	0.974194i	$0.427529\pi$
$702$	−13.7032	+	6.10105i	−0.517193	+	0.230269i
$703$	14.1724	+	15.7401i	0.534523	+	0.593648i
$704$	−2.31848	−	22.0588i	−0.0873809	−	0.831374i
$705$	−1.73607	+	1.26133i	−0.0653841	+	0.0475043i
$706$	−5.85497	+	55.7063i	−0.220355	+	2.09653i
$707$	−13.8541	−	23.9960i	−0.521037	−	0.902463i
$708$	−0.163119	+	0.282530i	−0.00613039	+	0.0106181i
$709$	8.78115	+	6.37988i	0.329783	+	0.239601i	0.740339	−	0.672234i	$-0.234665\pi$
$709$	8.78115	+	6.37988i	0.329783	+	0.239601i	−0.410555	+	0.911836i	$0.634665\pi$
$710$	4.58629	−	5.09359i	0.172120	−	0.191159i
$711$		0			0
$712$	−19.2705			−0.722193
$713$		0			0
$714$	20.5623			0.769525
$715$	−1.14590	+	3.52671i	−0.0428542	+	0.131892i
$716$	1.98435	−	2.20384i	0.0741585	−	0.0823613i
$717$	10.8541	+	7.88597i	0.405354	+	0.294507i
$718$	7.82624	−	13.5554i	0.292073	−	0.505885i
$719$	−21.8090	−	37.7743i	−0.813339	−	1.40874i	−0.910514	−	0.413477i	$-0.864314\pi$
$719$	−21.8090	−	37.7743i	−0.813339	−	1.40874i	0.0971753	−	0.995267i	$-0.469019\pi$
$720$	0.387613	−	3.68789i	0.0144455	−	0.137440i
$721$	16.6353	−	12.0862i	0.619529	−	0.450114i
$722$	−1.01478	−	9.65502i	−0.0377663	−	0.359323i
$723$	11.6911	+	12.9843i	0.434798	+	0.482892i
$724$	−9.59824	+	4.27341i	−0.356716	+	0.158820i
$725$	30.3018	−	6.44084i	1.12538	−	0.239207i
$726$	−25.9819	−	5.52261i	−0.964277	−	0.204963i
$727$	27.2536	+	12.1341i	1.01078	+	0.450029i	0.844217	−	0.536002i	$-0.180066\pi$
$727$	27.2536	+	12.1341i	1.01078	+	0.450029i	0.166564	+	0.986031i	$0.446733\pi$
$728$	−3.84346	−	11.8290i	−0.142448	−	0.438410i
$729$	4.01722	+	12.3637i	0.148786	+	0.457916i
$730$	6.52810	+	2.90650i	0.241616	+	0.107574i
$731$	−9.86968	−	2.09786i	−0.365043	−	0.0775923i
$732$	6.61612	−	1.40630i	0.244539	−	0.0519784i
$733$	9.18636	−	4.09003i	0.339306	−	0.151069i	−0.230008	−	0.973189i	$-0.573875\pi$
$733$	9.18636	−	4.09003i	0.339306	−	0.151069i	0.569314	+	0.822120i	$0.307209\pi$
$734$	2.95515	+	3.28203i	0.109077	+	0.121142i
$735$	0.0798526	+	0.759747i	0.00294541	+	0.0280237i
$736$	−9.50000	+	6.90215i	−0.350175	+	0.254417i
$737$	−0.129204	+	1.22930i	−0.00475930	+	0.0452817i
$738$	−4.00000	−	6.92820i	−0.147242	−	0.255031i
$739$	4.14590	−	7.18091i	0.152509	−	0.264154i	−0.779640	−	0.626228i	$-0.784598\pi$
$739$	4.14590	−	7.18091i	0.152509	−	0.264154i	0.932149	+	0.362074i	$0.117931\pi$
$740$	0.809017	+	0.587785i	0.0297401	+	0.0216074i
$741$	6.20318	−	6.88933i	0.227880	−	0.253086i
$742$	−1.06231	+	3.26944i	−0.0389985	+	0.120025i
$743$	23.5623			0.864417			0.432209	−	0.901774i	$-0.357734\pi$
$743$	23.5623			0.864417			0.432209	+	0.901774i	$0.357734\pi$
$744$		0			0
$745$	−4.59675			−0.168412
$746$	−15.8262	+	48.7082i	−0.579440	+	1.78333i
$747$	9.48850	−	10.5380i	0.347166	−	0.385567i
$748$	−11.0902	−	8.05748i	−0.405497	−	0.294611i
$749$	15.1353	−	26.2150i	0.553030	−	0.957876i
$750$	−3.04508	−	5.27424i	−0.111191	−	0.192588i
$751$	−1.44592	+	13.7570i	−0.0527625	+	0.502001i	0.935945	+	0.352145i	$0.114548\pi$
$751$	−1.44592	+	13.7570i	−0.0527625	+	0.502001i	−0.988708	+	0.149856i	$0.952119\pi$
$752$	−22.0623	+	16.0292i	−0.804530	+	0.584525i
$753$	−1.77116	−	16.8514i	−0.0645446	−	0.614101i
$754$	12.8111	+	14.2282i	0.466553	+	0.518160i
$755$	6.45775	−	2.87517i	0.235021	−	0.104638i
$756$	9.06793	−	1.92745i	0.329797	−	0.0701006i
$757$	2.81255	+	0.597827i	0.102224	+	0.0217284i	0.258740	−	0.965947i	$-0.416693\pi$
$757$	2.81255	+	0.597827i	0.102224	+	0.0217284i	−0.156516	+	0.987675i	$0.550026\pi$
$758$	12.4407	+	5.53895i	0.451866	+	0.201184i
$759$	−5.61803	−	17.2905i	−0.203922	−	0.627607i
$760$	1.31966	+	4.06150i	0.0478691	+	0.147326i
$761$	31.5233	+	14.0351i	1.14272	+	0.508772i	0.888728	−	0.458435i	$-0.151590\pi$
$761$	31.5233	+	14.0351i	1.14272	+	0.508772i	0.253992	+	0.967206i	$0.418256\pi$
$762$	9.12244	+	1.93903i	0.330471	+	0.0702438i
$763$	−54.0419	+	11.4870i	−1.95645	+	0.415856i
$764$	−2.77210	+	1.23422i	−0.100291	+	0.0446525i
$765$	2.16535	+	2.40487i	0.0782885	+	0.0869482i
$766$	−1.71598	−	16.3265i	−0.0620009	−	0.589900i
$767$	−0.791796	+	0.575274i	−0.0285901	+	0.0207719i
$768$	−1.41765	+	13.4880i <

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 1.53884i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.500000 - 0.363271i) q^{4} +(0.190983 - 0.330792i) q^{5} +(-0.809017 - 1.40126i) q^{6} +(-0.313585 + 2.98357i) q^{7} +(1.80902 - 1.31433i) q^{8} +(0.209057 + 1.98904i) q^{9} +(-0.413545 - 0.459289i) q^{10} +(4.78339 - 2.12970i) q^{11} +(-0.604528 + 0.128496i) q^{12} +(-1.81359 - 0.385489i) q^{13} +(4.43444 + 1.97434i) q^{14} +(-0.118034 - 0.363271i) q^{15} +(-1.50000 - 4.61653i) q^{16} +(3.86984 + 1.72296i) q^{17} +(3.16535 + 0.672816i) q^{18} +(-4.89074 + 1.03956i) q^{19} +(-0.215659 + 0.0960175i) q^{20} +(2.00739 + 2.22943i) q^{21} +(-0.885579 - 8.42572i) q^{22} +(2.80902 - 2.04087i) q^{23} +(0.233733 - 2.22382i) q^{24} +(2.42705 + 4.20378i) q^{25} +(-1.50000 + 2.59808i) q^{26} +(4.04508 + 2.93893i) q^{27} +(1.24064 - 1.37787i) q^{28} +(1.97214 - 6.06961i) q^{29} -0.618034 q^{30} -3.38197 q^{32} +(1.61803 - 4.97980i) q^{33} +(4.58629 - 5.09359i) q^{34} +(0.927051 + 0.673542i) q^{35} +(0.618034 - 1.07047i) q^{36} +(-2.11803 - 3.66854i) q^{37} +(-0.845653 + 8.04585i) q^{38} +(-1.50000 + 1.08981i) q^{39} +(-0.0892780 - 0.849423i) q^{40} +(-1.65418 - 1.83716i) q^{41} +(4.43444 - 1.97434i) q^{42} +(-2.32991 + 0.495239i) q^{43} +(-3.16535 - 0.672816i) q^{44} +(0.697887 + 0.310719i) q^{45} +(-1.73607 - 5.34307i) q^{46} +(-1.73607 - 5.34307i) q^{47} +(-4.43444 - 1.97434i) q^{48} +(-1.95630 - 0.415823i) q^{49} +(7.68247 - 1.63296i) q^{50} +(3.86984 - 1.72296i) q^{51} +(0.766755 + 0.851568i) q^{52} +(0.0740275 + 0.704324i) q^{53} +(6.54508 - 4.75528i) q^{54} +(0.209057 - 1.98904i) q^{55} +(3.35410 + 5.80948i) q^{56} +(-2.50000 + 4.33013i) q^{57} +(-8.35410 - 6.06961i) q^{58} +(0.353210 - 0.392279i) q^{59} +(-0.0729490 + 0.224514i) q^{60} -10.9443 q^{61} -6.00000 q^{63} +(1.30902 - 4.02874i) q^{64} +(-0.473881 + 0.526298i) q^{65} +(-6.85410 - 4.97980i) q^{66} +(-0.118034 + 0.204441i) q^{67} +(-1.30902 - 2.26728i) q^{68} +(0.362937 - 3.45312i) q^{69} +(1.50000 - 1.08981i) q^{70} +(1.15924 + 11.0294i) q^{71} +(2.99244 + 3.32344i) q^{72} +(-10.5627 + 4.70281i) q^{73} +(-6.70432 + 1.42505i) q^{74} +(4.74803 + 1.00922i) q^{75} +(2.82301 + 1.25689i) q^{76} +(4.85410 + 14.9394i) q^{77} +(0.927051 + 2.85317i) q^{78} +(-1.81359 - 0.385489i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-3.65418 + 1.62695i) q^{82} +(-4.74425 - 5.26902i) q^{83} +(-0.193806 - 1.84395i) q^{84} +(1.30902 - 0.951057i) q^{85} +(-0.402863 + 3.83299i) q^{86} +(-3.19098 - 5.52694i) q^{87} +(5.85410 - 10.1396i) q^{88} +(-6.97214 - 5.06555i) q^{89} +(0.827091 - 0.918578i) q^{90} +(1.71885 - 5.29007i) q^{91} -2.14590 q^{92} -9.09017 q^{94} +(-0.590170 + 1.81636i) q^{95} +(-2.26298 + 2.51329i) q^{96} +(15.1353 + 10.9964i) q^{97} +(-1.61803 + 2.80252i) q^{98} +(5.23607 + 9.06914i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + q^{3} - 4 q^{4} + 6 q^{5} - 2 q^{6} + 3 q^{7} + 10 q^{8} - 2 q^{9} + 3 q^{10} + 8 q^{11} - 3 q^{12} - 9 q^{13} + 9 q^{14} + 8 q^{15} - 12 q^{16} + 7 q^{17} + 4 q^{18} + 5 q^{19} - 3 q^{20}+ \cdots + 24 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + q^3 - 4 * q^4 + 6 * q^5 - 2 * q^6 + 3 * q^7 + 10 * q^8 - 2 * q^9 + 3 * q^10 + 8 * q^11 - 3 * q^12 - 9 * q^13 + 9 * q^14 + 8 * q^15 - 12 * q^16 + 7 * q^17 + 4 * q^18 + 5 * q^19 - 3 * q^20 + 3 * q^21 + 14 * q^22 + 18 * q^23 - 5 * q^24 + 6 * q^25 - 12 * q^26 + 10 * q^27 - 9 * q^28 - 20 * q^29 + 4 * q^30 - 36 * q^32 + 4 * q^33 - 4 * q^34 - 6 * q^35 - 4 * q^36 - 8 * q^37 + 15 * q^38 - 12 * q^39 + 5 * q^40 + 12 * q^41 + 9 * q^42 + 6 * q^43 - 4 * q^44 - 2 * q^45 + 4 * q^46 + 4 * q^47 - 9 * q^48 + 2 * q^49 + 3 * q^50 + 7 * q^51 + 12 * q^52 - 9 * q^53 + 30 * q^54 - 2 * q^55 - 20 * q^57 - 40 * q^58 + 15 * q^59 - 14 * q^60 - 16 * q^61 - 48 * q^63 + 6 * q^64 + 21 * q^65 - 28 * q^66 + 8 * q^67 - 6 * q^68 - 9 * q^69 + 12 * q^70 - 18 * q^71 - 10 * q^72 - 24 * q^73 - 4 * q^74 + 6 * q^75 + 10 * q^76 + 12 * q^77 - 6 * q^78 - 9 * q^80 + q^81 - 4 * q^82 + 11 * q^83 + 6 * q^84 + 6 * q^85 + 8 * q^86 - 30 * q^87 + 20 * q^88 - 20 * q^89 - 6 * q^90 + 54 * q^91 - 44 * q^92 - 28 * q^94 + 40 * q^95 - 7 * q^96 + 54 * q^97 - 4 * q^98 + 24 * q^99

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