LMFDB - Embedded newform 260.2.o.a.27.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(27,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("260.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.o (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.9
Character	$\chi$	$=$	260.27
Dual form			260.2.o.a.183.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08734 + 0.904262i) q^{2} +(1.78782 + 1.78782i) q^{3} +(0.364619 - 1.96648i) q^{4} +(-1.34049 + 1.78972i) q^{5} +(-3.56063 - 0.327311i) q^{6} +(2.34459 - 2.34459i) q^{7} +(1.38175 + 2.46795i) q^{8} +3.39260i q^{9} +O(q^{10})$	\(q+(-1.08734 + 0.904262i) q^{2} +(1.78782 + 1.78782i) q^{3} +(0.364619 - 1.96648i) q^{4} +(-1.34049 + 1.78972i) q^{5} +(-3.56063 - 0.327311i) q^{6} +(2.34459 - 2.34459i) q^{7} +(1.38175 + 2.46795i) q^{8} +3.39260i q^{9} +(-0.160802 - 3.15819i) q^{10} +5.90452i q^{11} +(4.16759 - 2.86384i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(-0.429245 + 4.66950i) q^{14} +(-5.59625 + 0.803133i) q^{15} +(-3.73411 - 1.43404i) q^{16} +(-0.975710 - 0.975710i) q^{17} +(-3.06780 - 3.68891i) q^{18} +2.12103 q^{19} +(3.03068 + 3.28862i) q^{20} +8.38342 q^{21} +(-5.33924 - 6.42023i) q^{22} +(-3.10133 - 3.10133i) q^{23} +(-1.94193 + 6.88257i) q^{24} +(-1.40617 - 4.79820i) q^{25} +(0.129456 - 1.40828i) q^{26} +(-0.701895 + 0.701895i) q^{27} +(-3.75572 - 5.46549i) q^{28} -5.56185i q^{29} +(5.35878 - 5.93375i) q^{30} +7.23441i q^{31} +(5.35699 - 1.81733i) q^{32} +(-10.5562 + 10.5562i) q^{33} +(1.94323 + 0.178631i) q^{34} +(1.05325 + 7.33907i) q^{35} +(6.67149 + 1.23701i) q^{36} +(-2.19333 - 2.19333i) q^{37} +(-2.30628 + 1.91796i) q^{38} -2.52836 q^{39} +(-6.26915 - 0.835322i) q^{40} -0.538879 q^{41} +(-9.11564 + 7.58081i) q^{42} +(5.78842 + 5.78842i) q^{43} +(11.6111 + 2.15290i) q^{44} +(-6.07179 - 4.54775i) q^{45} +(6.17662 + 0.567787i) q^{46} +(3.98616 - 3.98616i) q^{47} +(-4.11211 - 9.23970i) q^{48} -3.99424i q^{49} +(5.86781 + 3.94573i) q^{50} -3.48879i q^{51} +(1.13269 + 1.64834i) q^{52} +(7.09286 - 7.09286i) q^{53} +(0.128502 - 1.39790i) q^{54} +(-10.5674 - 7.91496i) q^{55} +(9.02598 + 2.54669i) q^{56} +(3.79201 + 3.79201i) q^{57} +(5.02937 + 6.04762i) q^{58} -3.05954 q^{59} +(-0.461154 + 11.2978i) q^{60} +8.82521 q^{61} +(-6.54180 - 7.86626i) q^{62} +(7.95427 + 7.95427i) q^{63} +(-4.18153 + 6.82017i) q^{64} +(-0.317650 - 2.21339i) q^{65} +(1.93262 - 21.0238i) q^{66} +(2.58148 - 2.58148i) q^{67} +(-2.27448 + 1.56295i) q^{68} -11.0892i q^{69} +(-7.78168 - 7.02765i) q^{70} -8.53161i q^{71} +(-8.37276 + 4.68772i) q^{72} +(2.76749 - 2.76749i) q^{73} +(4.36825 + 0.401552i) q^{74} +(6.06434 - 11.0923i) q^{75} +(0.773367 - 4.17096i) q^{76} +(13.8437 + 13.8437i) q^{77} +(2.74919 - 2.28630i) q^{78} +7.02598 q^{79} +(7.57205 - 4.76068i) q^{80} +7.66807 q^{81} +(0.585945 - 0.487288i) q^{82} +(-6.93558 - 6.93558i) q^{83} +(3.05676 - 16.4859i) q^{84} +(3.05417 - 0.438313i) q^{85} +(-11.5282 - 1.05974i) q^{86} +(9.94358 - 9.94358i) q^{87} +(-14.5721 + 8.15857i) q^{88} +9.42448i q^{89} +(10.7145 - 0.545537i) q^{90} +3.31576i q^{91} +(-7.22952 + 4.96791i) q^{92} +(-12.9338 + 12.9338i) q^{93} +(-0.729780 + 7.93885i) q^{94} +(-2.84322 + 3.79603i) q^{95} +(12.8264 + 6.32828i) q^{96} +(-11.8148 - 11.8148i) q^{97} +(3.61184 + 4.34310i) q^{98} -20.0317 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 - 12 * q^8	$ 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) $ 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.08734	+	0.904262i	−0.768866	+	0.639410i
$2$	−1.08734	+	0.904262i	−0.768866	+	0.639410i
$3$	1.78782	+	1.78782i	1.03220	+	1.03220i	0.999464	+	0.0327341i	$0.0104214\pi$
$3$	1.78782	+	1.78782i	1.03220	+	1.03220i	0.0327341	+	0.999464i	$0.489579\pi$
$4$	0.364619	−	1.96648i	0.182310	−	0.983241i
$5$	−1.34049	+	1.78972i	−0.599486	+	0.800385i
$5$	−1.34049	+	1.78972i	−0.599486	+	0.800385i
$6$	−3.56063	−	0.327311i	−1.45362	−	0.133624i
$7$	2.34459	−	2.34459i	0.886173	−	0.886173i	−0.107980	−	0.994153i	$-0.534438\pi$
$7$	2.34459	−	2.34459i	0.886173	−	0.886173i	0.994153	+	0.107980i	$0.0344382\pi$
$8$	1.38175	+	2.46795i	0.488522	+	0.872551i
$9$			3.39260i			1.13087i
$10$	−0.160802	−	3.15819i	−0.0508501	−	0.998706i
$11$			5.90452i			1.78028i	0.455687	+	0.890140i	$0.349394\pi$
$11$			5.90452i			1.78028i	−0.455687	+	0.890140i	$0.650606\pi$
$12$	4.16759	−	2.86384i	1.20308	−	0.826720i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$13$	−0.707107	+	0.707107i	−0.196116	+	0.196116i
$14$	−0.429245	+	4.66950i	−0.114720	+	1.24798i
$15$	−5.59625	+	0.803133i	−1.44494	+	0.207368i
$16$	−3.73411	−	1.43404i	−0.933526	−	0.358509i
$17$	−0.975710	−	0.975710i	−0.236644	−	0.236644i	0.578815	−	0.815459i	$-0.303515\pi$
$17$	−0.975710	−	0.975710i	−0.236644	−	0.236644i	−0.815459	+	0.578815i	$0.803515\pi$
$18$	−3.06780	−	3.68891i	−0.723087	−	0.869485i
$19$	2.12103			0.486597			0.243298	−	0.969952i	$-0.421771\pi$
$19$	2.12103			0.486597			0.243298	+	0.969952i	$0.421771\pi$
$20$	3.03068	+	3.28862i	0.677680	+	0.735357i
$21$	8.38342			1.82941
$22$	−5.33924	−	6.42023i	−1.13833	−	1.36880i
$23$	−3.10133	−	3.10133i	−0.646673	−	0.646673i	0.305515	−	0.952187i	$-0.401171\pi$
$23$	−3.10133	−	3.10133i	−0.646673	−	0.646673i	−0.952187	+	0.305515i	$0.901171\pi$
$24$	−1.94193	+	6.88257i	−0.396394	+	1.40490i
$25$	−1.40617	−	4.79820i	−0.281233	−	0.959639i
$26$	0.129456	−	1.40828i	0.0253884	−	0.276186i
$27$	−0.701895	+	0.701895i	−0.135080	+	0.135080i
$28$	−3.75572	−	5.46549i	−0.709764	−	1.03288i
$29$		−	5.56185i		−	1.03281i	−0.856345	−	0.516405i	$-0.827270\pi$
$29$		−	5.56185i		−	1.03281i	0.856345	−	0.516405i	$-0.172730\pi$
$30$	5.35878	−	5.93375i	0.978375	−	1.08335i
$31$			7.23441i			1.29934i	0.760217	+	0.649669i	$0.225092\pi$
$31$			7.23441i			1.29934i	−0.760217	+	0.649669i	$0.774908\pi$
$32$	5.35699	−	1.81733i	0.946991	−	0.321261i
$33$	−10.5562	+	10.5562i	−1.83760	+	1.83760i
$34$	1.94323	+	0.178631i	0.333261	+	0.0306350i
$35$	1.05325	+	7.33907i	0.178032	+	1.24053i
$36$	6.67149	+	1.23701i	1.11191	+	0.206168i
$37$	−2.19333	−	2.19333i	−0.360582	−	0.360582i	0.503445	−	0.864027i	$-0.332066\pi$
$37$	−2.19333	−	2.19333i	−0.360582	−	0.360582i	−0.864027	+	0.503445i	$0.832066\pi$
$38$	−2.30628	+	1.91796i	−0.374128	+	0.311135i
$39$	−2.52836			−0.404861
$40$	−6.26915	−	0.835322i	−0.991240	−	0.132076i
$41$	−0.538879			−0.0841588			−0.0420794	−	0.999114i	$-0.513398\pi$
$41$	−0.538879			−0.0841588			−0.0420794	+	0.999114i	$0.513398\pi$
$42$	−9.11564	+	7.58081i	−1.40657	+	1.16974i
$43$	5.78842	+	5.78842i	0.882726	+	0.882726i	0.993811	−	0.111085i	$-0.0354325\pi$
$43$	5.78842	+	5.78842i	0.882726	+	0.882726i	−0.111085	+	0.993811i	$0.535432\pi$
$44$	11.6111	+	2.15290i	1.75044	+	0.324562i
$45$	−6.07179	−	4.54775i	−0.905129	−	0.677938i
$46$	6.17662	+	0.567787i	0.910693	+	0.0837156i
$47$	3.98616	−	3.98616i	0.581441	−	0.581441i	−0.353858	−	0.935299i	$-0.615130\pi$
$47$	3.98616	−	3.98616i	0.581441	−	0.581441i	0.935299	+	0.353858i	$0.115130\pi$
$48$	−4.11211	−	9.23970i	−0.593532	−	1.33364i
$49$		−	3.99424i		−	0.570606i
$50$	5.86781	+	3.94573i	0.829834	+	0.558011i
$51$		−	3.48879i		−	0.488528i
$52$	1.13269	+	1.64834i	0.157076	+	0.228583i
$53$	7.09286	−	7.09286i	0.974279	−	0.974279i	−0.0253982	−	0.999677i	$-0.508085\pi$
$53$	7.09286	−	7.09286i	0.974279	−	0.974279i	0.999677	+	0.0253982i	$0.00808537\pi$
$54$	0.128502	−	1.39790i	0.0174869	−	0.190230i
$55$	−10.5674	−	7.91496i	−1.42491	−	1.06725i
$56$	9.02598	+	2.54669i	1.20615	+	0.340316i
$57$	3.79201	+	3.79201i	0.502264	+	0.502264i
$58$	5.02937	+	6.04762i	0.660388	+	0.794092i
$59$	−3.05954			−0.398319			−0.199159	−	0.979967i	$-0.563821\pi$
$59$	−3.05954			−0.398319			−0.199159	+	0.979967i	$0.563821\pi$
$60$	−0.461154	+	11.2978i	−0.0595347	+	1.45853i
$61$	8.82521			1.12995			0.564976	−	0.825107i	$-0.308885\pi$
$61$	8.82521			1.12995			0.564976	+	0.825107i	$0.308885\pi$
$62$	−6.54180	−	7.86626i	−0.830809	−	0.999016i
$63$	7.95427	+	7.95427i	1.00214	+	1.00214i
$64$	−4.18153	+	6.82017i	−0.522692	+	0.852522i
$65$	−0.317650	−	2.21339i	−0.0393996	−	0.274537i
$66$	1.93262	−	21.0238i	0.237889	−	2.58785i
$67$	2.58148	−	2.58148i	0.315378	−	0.315378i	−0.531611	−	0.846989i	$-0.678413\pi$
$67$	2.58148	−	2.58148i	0.315378	−	0.315378i	0.846989	+	0.531611i	$0.178413\pi$
$68$	−2.27448	+	1.56295i	−0.275821	+	0.189536i
$69$		−	11.0892i		−	1.33499i
$70$	−7.78168	−	7.02765i	−0.930089	−	0.839965i
$71$		−	8.53161i		−	1.01252i	−0.862382	−	0.506258i	$-0.831028\pi$
$71$		−	8.53161i		−	1.01252i	0.862382	−	0.506258i	$-0.168972\pi$
$72$	−8.37276	+	4.68772i	−0.986739	+	0.552454i
$73$	2.76749	−	2.76749i	0.323910	−	0.323910i	−0.526355	−	0.850265i	$-0.676442\pi$
$73$	2.76749	−	2.76749i	0.323910	−	0.323910i	0.850265	+	0.526355i	$0.176442\pi$
$74$	4.36825	+	0.401552i	0.507798	+	0.0466795i
$75$	6.06434	−	11.0923i	0.700250	−	1.28083i
$76$	0.773367	−	4.17096i	0.0887113	−	0.478442i
$77$	13.8437	+	13.8437i	1.57764	+	1.57764i
$78$	2.74919	−	2.28630i	0.311284	−	0.258872i
$79$	7.02598			0.790484			0.395242	−	0.918577i	$-0.370661\pi$
$79$	7.02598			0.790484			0.395242	+	0.918577i	$0.370661\pi$
$80$	7.57205	−	4.76068i	0.846581	−	0.532260i
$81$	7.66807			0.852008
$82$	0.585945	−	0.487288i	0.0647068	−	0.0538120i
$83$	−6.93558	−	6.93558i	−0.761279	−	0.761279i	0.215275	−	0.976554i	$-0.430935\pi$
$83$	−6.93558	−	6.93558i	−0.761279	−	0.761279i	−0.976554	+	0.215275i	$0.930935\pi$
$84$	3.05676	−	16.4859i	0.333520	−	1.79875i
$85$	3.05417	−	0.438313i	0.331272	−	0.0475417i
$86$	−11.5282	−	1.05974i	−1.24312	−	0.114274i
$87$	9.94358	−	9.94358i	1.06606	−	1.06606i
$88$	−14.5721	+	8.15857i	−1.55339	+	0.869707i
$89$			9.42448i			0.998993i	0.866316	+	0.499496i	$0.166482\pi$
$89$			9.42448i			0.998993i	−0.866316	+	0.499496i	$0.833518\pi$
$90$	10.7145	−	0.545537i	1.12940	−	0.0575046i
$91$			3.31576i			0.347586i
$92$	−7.22952	+	4.96791i	−0.753730	+	0.517940i
$93$	−12.9338	+	12.9338i	−1.34117	+	1.34117i
$94$	−0.729780	+	7.93885i	−0.0752710	+	0.818829i
$95$	−2.84322	+	3.79603i	−0.291708	+	0.389465i
$96$	12.8264	+	6.32828i	1.30909	+	0.645877i
$97$	−11.8148	−	11.8148i	−1.19961	−	1.19961i	−0.974284	−	0.225322i	$-0.927657\pi$
$97$	−11.8148	−	11.8148i	−1.19961	−	1.19961i	−0.225322	−	0.974284i	$-0.572343\pi$
$98$	3.61184	+	4.34310i	0.364851	+	0.438720i
$99$	−20.0317			−2.01326
$100$	−9.94829	+	1.01569i	−0.994829	+	0.101569i
$101$	−4.69937			−0.467605			−0.233803	−	0.972284i	$-0.575117\pi$
$101$	−4.69937			−0.467605			−0.233803	+	0.972284i	$0.575117\pi$
$102$	3.15478	+	3.79350i	0.312369	+	0.375612i
$103$	−0.855000	−	0.855000i	−0.0842456	−	0.0842456i	0.663728	−	0.747974i	$-0.268973\pi$
$103$	−0.855000	−	0.855000i	−0.0842456	−	0.0842456i	−0.747974	+	0.663728i	$0.768973\pi$
$104$	−2.72215	−	0.768058i	−0.266929	−	0.0753143i
$105$	−11.2379	+	15.0039i	−1.09671	+	1.46424i
$106$	−1.29855	+	14.1262i	−0.126126	+	1.37205i
$107$	−12.9913	+	12.9913i	−1.25591	+	1.25591i	−0.302889	+	0.953026i	$0.597951\pi$
$107$	−12.9913	+	12.9913i	−1.25591	+	1.25591i	−0.953026	+	0.302889i	$0.902049\pi$
$108$	1.12434	+	1.63619i	0.108190	+	0.157442i
$109$			2.62288i			0.251226i	0.992079	+	0.125613i	$0.0400898\pi$
$109$			2.62288i			0.251226i	−0.992079	+	0.125613i	$0.959910\pi$
$110$	18.6476	−	0.949459i	1.77798	−	0.0905273i
$111$		−	7.84257i		−	0.744383i
$112$	−12.1172	+	5.39273i	−1.14497	+	0.509565i
$113$	10.8980	−	10.8980i	1.02520	−	1.02520i	0.0255277	−	0.999674i	$-0.491873\pi$
$113$	10.8980	−	10.8980i	1.02520	−	1.02520i	0.999674	−	0.0255277i	$-0.00812660\pi$
$114$	−7.55218	−	0.694235i	−0.707326	−	0.0650211i
$115$	9.70781	−	1.39320i	0.905258	−	0.129916i
$116$	−10.9373	−	2.02796i	−1.01550	−	0.188291i
$117$	−2.39893	−	2.39893i	−0.221781	−	0.221781i
$118$	3.32677	−	2.76663i	0.306254	−	0.254689i
$119$	−4.57529			−0.419416
$120$	−9.71470	−	12.7015i	−0.886827	−	1.15948i
$121$	−23.8634			−2.16940
$122$	−9.59601	+	7.98031i	−0.868782	+	0.722503i
$123$	−0.963419	−	0.963419i	−0.0868685	−	0.0868685i
$124$	14.2263	+	2.63781i	1.27756	+	0.236882i
$125$	10.4724	+	3.91530i	0.936677	+	0.350195i
$126$	−15.8417	−	1.45625i	−1.41129	−	0.129733i
$127$	4.31384	−	4.31384i	0.382792	−	0.382792i	−0.489315	−	0.872107i	$-0.662753\pi$
$127$	4.31384	−	4.31384i	0.382792	−	0.382792i	0.872107	+	0.489315i	$0.162753\pi$
$128$	−1.62048	−	11.1971i	−0.143231	−	0.989689i
$129$			20.6973i			1.82230i
$130$	2.34688	+	2.11947i	0.205835	+	0.185890i
$131$			6.36243i			0.555888i	0.960597	+	0.277944i	$0.0896529\pi$
$131$			6.36243i			0.555888i	−0.960597	+	0.277944i	$0.910347\pi$
$132$	16.9096	+	24.6076i	1.47179	+	2.14182i
$133$	4.97294	−	4.97294i	0.431209	−	0.431209i
$134$	−0.472614	+	5.14129i	−0.0408276	+	0.444140i
$135$	−0.315309	−	2.19708i	−0.0271375	−	0.189094i
$136$	1.05981	−	3.75619i	0.0908783	−	0.322090i
$137$	−0.675923	−	0.675923i	−0.0577480	−	0.0577480i	0.677643	−	0.735391i	$-0.263001\pi$
$137$	−0.675923	−	0.675923i	−0.0577480	−	0.0577480i	−0.735391	+	0.677643i	$0.763001\pi$
$138$	10.0276	+	12.0578i	0.853605	+	1.02643i
$139$	−4.46061			−0.378344			−0.189172	−	0.981944i	$-0.560580\pi$
$139$	−4.46061			−0.378344			−0.189172	+	0.981944i	$0.560580\pi$
$140$	14.8162	+	0.604769i	1.25220	+	0.0511124i
$141$	14.2531			1.20032
$142$	7.71481	+	9.27677i	0.647413	+	0.778489i
$143$	−4.17513	−	4.17513i	−0.349142	−	0.349142i
$144$	4.86511	−	12.6683i	0.405426	−	1.05569i
$145$	9.95413	+	7.45561i	0.826645	+	0.619155i
$146$	−0.506668	+	5.51174i	−0.0419321	+	0.456155i
$147$	7.14099	−	7.14099i	0.588979	−	0.588979i
$148$	−5.11288	+	3.51342i	−0.420276	+	0.288801i
$149$			7.40369i			0.606534i	0.952906	+	0.303267i	$0.0980775\pi$
$149$			7.40369i			0.606534i	−0.952906	+	0.303267i	$0.901923\pi$
$150$	3.43633	+	17.5448i	0.280575	+	1.43253i
$151$		−	8.25499i		−	0.671782i	−0.941901	−	0.335891i	$-0.890963\pi$
$151$		−	8.25499i		−	0.671782i	0.941901	−	0.335891i	$-0.109037\pi$
$152$	2.93073	+	5.23458i	0.237713	+	0.424581i
$153$	3.31019	−	3.31019i	0.267613	−	0.267613i
$154$	−27.5712	−	2.53448i	−2.22175	−	0.204235i
$155$	−12.9475	−	9.69766i	−1.03997	−	0.778935i
$156$	−0.921889	+	4.97197i	−0.0738102	+	0.398076i
$157$	−14.4491	−	14.4491i	−1.15316	−	1.15316i	−0.985915	−	0.167249i	$-0.946512\pi$
$157$	−14.4491	−	14.4491i	−1.15316	−	1.15316i	−0.167249	−	0.985915i	$-0.553488\pi$
$158$	−7.63963	+	6.35333i	−0.607776	+	0.505444i
$159$	25.3615			2.01130
$160$	−3.92850	+	12.0236i	−0.310575	+	0.950549i
$161$	−14.5427			−1.14613
$162$	−8.33781	+	6.93395i	−0.655080	+	0.544782i
$163$	9.14075	+	9.14075i	0.715959	+	0.715959i	0.967775	−	0.251816i	$-0.0810278\pi$
$163$	9.14075	+	9.14075i	0.715959	+	0.715959i	−0.251816	+	0.967775i	$0.581028\pi$
$164$	−0.196486	+	1.05970i	−0.0153430	+	0.0827484i
$165$	−4.74212	−	33.0432i	−0.369173	−	2.57241i
$166$	13.8129	+	1.26976i	1.07209	+	0.0985521i
$167$	2.67668	−	2.67668i	0.207128	−	0.207128i	−0.595918	−	0.803046i	$-0.703212\pi$
$167$	2.67668	−	2.67668i	0.207128	−	0.207128i	0.803046	+	0.595918i	$0.203212\pi$
$168$	11.5838	+	20.6899i	0.893709	+	1.59626i
$169$		−	1.00000i		−	0.0769231i
$170$	−2.92458	+	3.23837i	−0.224305	+	0.248372i
$171$			7.19579i			0.550276i
$172$	13.4934	−	9.27226i	1.02886	−	0.707003i
$173$	−4.31314	+	4.31314i	−0.327922	+	0.327922i	−0.851796	−	0.523874i	$-0.824486\pi$
$173$	−4.31314	+	4.31314i	−0.327922	+	0.327922i	0.523874	+	0.851796i	$0.324486\pi$
$174$	−1.82045	+	19.8037i	−0.138008	+	1.50131i
$175$	−14.5467	−	7.95294i	−1.09963	−	0.601185i
$176$	8.46729	−	22.0481i	0.638246	−	1.66194i
$177$	−5.46991	−	5.46991i	−0.411144	−	0.411144i
$178$	−8.52220	−	10.2476i	−0.638766	−	0.768092i
$179$	10.4807			0.783364			0.391682	−	0.920101i	$-0.371893\pi$
$179$	10.4807			0.783364			0.391682	+	0.920101i	$0.371893\pi$
$180$	−11.1570	+	10.2819i	−0.831591	+	0.766365i
$181$	−15.5219			−1.15374			−0.576868	−	0.816837i	$-0.695725\pi$
$181$	−15.5219			−1.15374			−0.576868	+	0.816837i	$0.695725\pi$
$182$	−2.99831	−	3.60536i	−0.222250	−	0.267247i
$183$	15.7779	+	15.7779i	1.16633	+	1.16633i
$184$	3.36866	−	11.9392i	0.248341	−	0.880169i
$185$	6.86559	−	0.985299i	0.504768	−	0.0724406i
$186$	2.36790	−	25.7590i	0.173623	−	1.88874i
$187$	5.76110	−	5.76110i	0.421293	−	0.421293i
$188$	−6.38528	−	9.29214i	−0.465694	−	0.677699i
$189$			3.29132i			0.239408i
$190$	−0.341065	−	6.69859i	−0.0247435	−	0.485967i
$191$			13.2435i			0.958268i	0.877742	+	0.479134i	$0.159049\pi$
$191$			13.2435i			0.958268i	−0.877742	+	0.479134i	$0.840951\pi$
$192$	−19.6691	+	4.71742i	−1.41949	+	0.340450i
$193$	−14.6402	+	14.6402i	−1.05383	+	1.05383i	−0.0553595	+	0.998466i	$0.517630\pi$
$193$	−14.6402	+	14.6402i	−1.05383	+	1.05383i	−0.998466	+	0.0553595i	$0.982370\pi$
$194$	23.5303	+	2.16303i	1.68938	+	0.155296i
$195$	3.38924	−	4.52504i	0.242709	−	0.324045i
$196$	−7.85461	−	1.45638i	−0.561044	−	0.104027i
$197$	−17.4045	−	17.4045i	−1.24002	−	1.24002i	−0.959991	−	0.280030i	$-0.909656\pi$
$197$	−17.4045	−	17.4045i	−1.24002	−	1.24002i	−0.280030	−	0.959991i	$-0.590344\pi$
$198$	21.7813	−	18.1139i	1.54793	−	1.28730i
$199$	−26.2930			−1.86386			−0.931930	−	0.362639i	$-0.881876\pi$
$199$	−26.2930			−1.86386			−0.931930	+	0.362639i	$0.881876\pi$
$200$	9.89873	−	10.1003i	0.699946	−	0.714196i
$201$	9.23045			0.651066
$202$	5.10982	−	4.24947i	0.359526	−	0.298991i
$203$	−13.0403	−	13.0403i	−0.915248	−	0.915248i
$204$	−6.86064	−	1.27208i	−0.480341	−	0.0890634i
$205$	0.722363	−	0.964440i	0.0504520	−	0.0673594i
$206$	1.70282	+	0.156532i	0.118641	+	0.0109061i
$207$	10.5216	−	10.5216i	0.731300	−	0.731300i
$208$	3.65443	−	1.62639i	0.253389	−	0.112770i
$209$			12.5236i			0.866278i
$210$	−1.34807	−	26.4764i	−0.0930258	−	1.82705i
$211$		−	6.67079i		−	0.459236i	−0.973281	−	0.229618i	$-0.926252\pi$
$211$		−	6.67079i		−	0.459236i	0.973281	−	0.229618i	$-0.0737477\pi$
$212$	−11.3618	−	16.5342i	−0.780331	−	1.13557i
$213$	15.2530	−	15.2530i	1.04512	−	1.04512i
$214$	2.37842	−	25.8735i	0.162586	−	1.76867i
$215$	−18.1190	+	2.60030i	−1.23570	+	0.177339i
$216$	−2.70209	−	0.762397i	−0.183854	−	0.0518746i
$217$	16.9617	+	16.9617i	1.15144	+	1.15144i
$218$	−2.37177	−	2.85196i	−0.160636	−	0.193159i
$219$	9.89555			0.668679
$220$	−19.4177	+	17.8947i	−1.30914	+	1.20646i
$221$	1.37986			0.0928195
$222$	7.09174	+	8.52754i	0.475966	+	0.572331i
$223$	3.91569	+	3.91569i	0.262214	+	0.262214i	0.825953	−	0.563739i	$-0.190638\pi$
$223$	3.91569	+	3.91569i	0.262214	+	0.262214i	−0.563739	+	0.825953i	$0.690638\pi$
$224$	8.29907	−	16.8209i	0.554505	−	1.12389i
$225$	16.2784	−	4.77056i	1.08522	−	0.318037i
$226$	−1.99520	+	21.7046i	−0.132719	+	1.44377i
$227$	0.441036	−	0.441036i	0.0292726	−	0.0292726i	−0.692319	−	0.721592i	$-0.743411\pi$
$227$	0.441036	−	0.441036i	0.0292726	−	0.0292726i	0.721592	+	0.692319i	$0.243411\pi$
$228$	8.83956	−	6.07428i	0.585414	−	0.402279i
$229$			6.34608i			0.419361i	0.977770	+	0.209680i	$0.0672423\pi$
$229$			6.34608i			0.419361i	−0.977770	+	0.209680i	$0.932758\pi$
$230$	−9.29589	+	10.2933i	−0.612953	+	0.678719i
$231$			49.5001i			3.25687i
$232$	13.7263	−	7.68508i	0.901179	−	0.504550i
$233$	6.40187	−	6.40187i	0.419401	−	0.419401i	−0.465596	−	0.884997i	$-0.654160\pi$
$233$	6.40187	−	6.40187i	0.419401	−	0.419401i	0.884997	+	0.465596i	$0.154160\pi$
$234$	4.77771	+	0.439192i	0.312329	+	0.0287109i
$235$	1.79068	+	12.4775i	0.116811	+	0.813943i
$236$	−1.11557	+	6.01654i	−0.0726173	+	0.391643i
$237$	12.5612	+	12.5612i	0.815936	+	0.815936i
$238$	4.97489	−	4.13726i	0.322475	−	0.268179i
$239$	−16.6919			−1.07971			−0.539855	−	0.841758i	$-0.681521\pi$
$239$	−16.6919			−1.07971			−0.539855	+	0.841758i	$0.681521\pi$
$240$	22.0487	+	5.02623i	1.42324	+	0.324442i
$241$	−4.87302			−0.313899			−0.156950	−	0.987607i	$-0.550166\pi$
$241$	−4.87302			−0.313899			−0.156950	+	0.987607i	$0.550166\pi$
$242$	25.9476	−	21.5787i	1.66798	−	1.38713i
$243$	15.8148	+	15.8148i	1.01452	+	1.01452i
$244$	3.21784	−	17.3546i	0.206001	−	1.11102i
$245$	7.14856	+	5.35425i	0.456705	+	0.342070i
$246$	1.91875	+	0.176381i	0.122335	+	0.0112457i
$247$	−1.49979	+	1.49979i	−0.0954294	+	0.0954294i
$248$	−17.8541	+	9.99614i	−1.13374	+	0.634756i
$249$		−	24.7991i		−	1.57158i
$250$	−14.9275	+	5.21250i	−0.944097	+	0.329667i
$251$		−	3.80662i		−	0.240271i	−0.992757	−	0.120136i	$-0.961667\pi$
$251$		−	3.80662i		−	0.240271i	0.992757	−	0.120136i	$-0.0383330\pi$
$252$	18.5422	−	12.7416i	1.16805	−	0.802648i
$253$	18.3119	−	18.3119i	1.15126	−	1.15126i
$254$	−0.789771	+	8.59146i	−0.0495547	+	0.539076i
$255$	6.24394	+	4.67669i	0.391010	+	0.292865i
$256$	11.8871	+	10.7097i	0.742943	+	0.669355i
$257$	15.4246	+	15.4246i	0.962160	+	0.962160i	0.999310	−	0.0371497i	$-0.0118278\pi$
$257$	15.4246	+	15.4246i	0.962160	+	0.962160i	−0.0371497	+	0.999310i	$0.511828\pi$
$258$	−18.7158	−	22.5050i	−1.16519	−	1.40110i
$259$	−10.2850			−0.639076
$260$	−4.46842	−	0.182393i	−0.277119	−	0.0113115i
$261$	18.8691			1.16797
$262$	−5.75330	−	6.91813i	−0.355440	−	0.427403i
$263$	2.06774	+	2.06774i	0.127502	+	0.127502i	0.767978	−	0.640476i	$-0.221263\pi$
$263$	2.06774	+	2.06774i	0.127502	+	0.127502i	−0.640476	+	0.767978i	$0.721263\pi$
$264$	−40.6383	−	11.4661i	−2.50111	−	0.705692i
$265$	3.18629	+	22.2021i	0.195732	+	1.36387i
$266$	−0.910439	+	9.90413i	−0.0558226	+	0.607261i
$267$	−16.8493	+	16.8493i	−1.03116	+	1.03116i
$268$	−4.13518	−	6.01770i	−0.252596	−	0.367589i
$269$		−	1.08783i		−	0.0663260i	−0.999450	−	0.0331630i	$-0.989442\pi$
$269$		−	1.08783i		−	0.0663260i	0.999450	−	0.0331630i	$-0.0105580\pi$
$270$	2.32958	+	2.10385i	0.141774	+	0.128036i
$271$			18.6868i			1.13514i	0.823325	+	0.567570i	$0.192116\pi$
$271$			18.6868i			1.13514i	−0.823325	+	0.567570i	$0.807884\pi$
$272$	2.24420	+	5.04260i	0.136075	+	0.305753i
$273$	−5.92798	+	5.92798i	−0.358777	+	0.358777i
$274$	1.34617	+	0.123747i	0.0813251	+	0.00747582i
$275$	28.3311	−	8.30274i	1.70843	−	0.500674i
$276$	−21.8068	−	4.04336i	−1.31262	−	0.243381i
$277$	1.31820	+	1.31820i	0.0792032	+	0.0792032i	0.745599	−	0.666395i	$-0.232164\pi$
$277$	1.31820	+	1.31820i	0.0792032	+	0.0792032i	−0.666395	+	0.745599i	$0.732164\pi$
$278$	4.85020	−	4.03356i	0.290896	−	0.241917i
$279$	−24.5434			−1.46938
$280$	−16.6571	+	12.7401i	−0.995452	+	0.761368i
$281$	−7.34919			−0.438416			−0.219208	−	0.975678i	$-0.570347\pi$
$281$	−7.34919			−0.438416			−0.219208	+	0.975678i	$0.570347\pi$
$282$	−15.4979	+	12.8885i	−0.922889	+	0.767500i
$283$	7.05023	+	7.05023i	0.419093	+	0.419093i	0.884891	−	0.465798i	$-0.154233\pi$
$283$	7.05023	+	7.05023i	0.419093	+	0.419093i	−0.465798	+	0.884891i	$0.654233\pi$
$284$	−16.7773	−	3.11079i	−0.995547	−	0.184592i
$285$	−11.8698	+	1.70347i	−0.703105	+	0.100905i
$286$	8.31520	+	0.764376i	0.491688	+	0.0451985i
$287$	−1.26345	+	1.26345i	−0.0745793	+	0.0745793i
$288$	6.16546	+	18.1741i	0.363303	+	1.07092i
$289$		−	15.0960i		−	0.887999i
$290$	−17.5654	+	0.894356i	−1.03147	+	0.0525184i
$291$		−	42.2453i		−	2.47646i
$292$	−4.43314	−	6.45130i	−0.259430	−	0.377534i
$293$	−11.9457	+	11.9457i	−0.697876	+	0.697876i	−0.963952	−	0.266076i	$-0.914273\pi$
$293$	−11.9457	+	11.9457i	−0.697876	+	0.697876i	0.266076	+	0.963952i	$0.414273\pi$
$294$	−1.30736	+	14.2220i	−0.0762468	+	0.829445i
$295$	4.10129	−	5.47571i	0.238786	−	0.318808i
$296$	2.38239	−	8.44367i	0.138474	−	0.490778i
$297$	−4.14436	−	4.14436i	−0.240480	−	0.240480i
$298$	−6.69488	−	8.05034i	−0.387824	−	0.466344i
$299$	4.38595			0.253646
$300$	−19.6016	−	15.9699i	−1.13170	−	0.922021i
$301$	27.1430			1.56450
$302$	7.46468	+	8.97599i	0.429544	+	0.516510i
$303$	−8.40163	−	8.40163i	−0.482661	−	0.482661i
$304$	−7.92013	−	3.04163i	−0.454251	−	0.174449i
$305$	−11.8301	+	15.7946i	−0.677391	+	0.904397i
$306$	−0.606024	+	6.59259i	−0.0346441	+	0.376873i
$307$	0.789610	−	0.789610i	0.0450654	−	0.0450654i	−0.684215	−	0.729280i	$-0.739855\pi$
$307$	0.789610	−	0.789610i	0.0450654	−	0.0450654i	0.729280	+	0.684215i	$0.239855\pi$
$308$	32.2711	−	22.1757i	1.83882	−	1.26358i
$309$		−	3.05717i		−	0.173916i
$310$	22.8476	−	1.16331i	1.29766	−	0.0660714i
$311$			18.0187i			1.02174i	0.859657	+	0.510872i	$0.170677\pi$
$311$			18.0187i			1.02174i	−0.859657	+	0.510872i	$0.829323\pi$
$312$	−3.49356	−	6.23986i	−0.197784	−	0.353262i
$313$	19.4426	−	19.4426i	1.09896	−	1.09896i	0.104427	−	0.994533i	$-0.466699\pi$
$313$	19.4426	−	19.4426i	1.09896	−	1.09896i	0.994533	−	0.104427i	$-0.0333008\pi$
$314$	28.7769	+	2.64532i	1.62397	+	0.149284i
$315$	−24.8985	+	3.57325i	−1.40287	+	0.201330i
$316$	2.56181	−	13.8165i	0.144113	−	0.777237i
$317$	−9.02608	−	9.02608i	−0.506955	−	0.506955i	0.406635	−	0.913591i	$-0.366702\pi$
$317$	−9.02608	−	9.02608i	−0.506955	−	0.506955i	−0.913591	+	0.406635i	$0.866702\pi$
$318$	−27.5766	+	22.9335i	−1.54642	+	1.28604i
$319$	32.8400			1.83869
$320$	−6.60087	−	16.6261i	−0.369000	−	0.929430i
$321$	−46.4521			−2.59271
$322$	15.8129	−	13.1504i	0.881219	−	0.732846i
$323$	−2.06950	−	2.06950i	−0.115150	−	0.115150i
$324$	2.79593	−	15.0791i	0.155329	−	0.837729i
$325$	4.38715	+	2.39853i	0.243355	+	0.133046i
$326$	−18.2048	−	1.67347i	−1.00827	−	0.0926852i
$327$	−4.68923	+	4.68923i	−0.259315	+	0.259315i
$328$	−0.744596	−	1.32993i	−0.0411134	−	0.0734328i
$329$		−	18.6919i		−	1.03052i
$330$	35.0360	+	31.6411i	1.92867	+	1.74178i
$331$		−	2.06198i		−	0.113336i	−0.998393	−	0.0566682i	$-0.981952\pi$
$331$		−	2.06198i		−	0.113336i	0.998393	−	0.0566682i	$-0.0180477\pi$
$332$	−16.1675	+	11.1099i	−0.887309	+	0.609732i
$333$	7.44110	−	7.44110i	0.407770	−	0.407770i
$334$	−0.490043	+	5.33089i	−0.0268139	+	0.291693i
$335$	1.15967	+	8.08057i	0.0633593	+	0.441489i
$336$	−31.3046	−	12.0221i	−1.70781	−	0.655861i
$337$	9.46896	+	9.46896i	0.515807	+	0.515807i	0.916300	−	0.400493i	$-0.131161\pi$
$337$	9.46896	+	9.46896i	0.515807	+	0.515807i	−0.400493	+	0.916300i	$0.631161\pi$
$338$	0.904262	+	1.08734i	0.0491854	+	0.0591435i
$339$	38.9675			2.11642
$340$	0.251677	−	6.16579i	0.0136491	−	0.334387i
$341$	−42.7157			−2.31319
$342$	−6.50688	−	7.82427i	−0.351852	−	0.423088i
$343$	7.04728	+	7.04728i	0.380517	+	0.380517i
$344$	−6.28737	+	22.2837i	−0.338992	+	1.20146i
$345$	19.8466	+	14.8650i	1.06851	+	0.800307i
$346$	0.789644	−	8.59007i	0.0424515	−	0.461805i
$347$	−7.60949	+	7.60949i	−0.408499	+	0.408499i	−0.881215	−	0.472716i	$-0.843274\pi$
$347$	−7.60949	+	7.60949i	−0.408499	+	0.408499i	0.472716	+	0.881215i	$0.343274\pi$
$348$	−15.9283	−	23.1795i	−0.853844	−	1.24255i
$349$		−	4.69447i		−	0.251289i	−0.992075	−	0.125644i	$-0.959900\pi$
$349$		−	4.69447i		−	0.251289i	0.992075	−	0.125644i	$-0.0400999\pi$
$350$	23.0088	−	4.50650i	1.22987	−	0.240882i
$351$		−	0.992630i		−	0.0529827i
$352$	10.7304	+	31.6305i	0.571934	+	1.68591i
$353$	7.77497	−	7.77497i	0.413820	−	0.413820i	−0.469247	−	0.883067i	$-0.655475\pi$
$353$	7.77497	−	7.77497i	0.413820	−	0.413820i	0.883067	+	0.469247i	$0.155475\pi$
$354$	10.8939	+	1.00142i	0.579004	+	0.0532250i
$355$	15.2692	+	11.4365i	0.810403	+	0.606989i
$356$	18.5331	+	3.43635i	0.982251	+	0.182126i
$357$	−8.17979	−	8.17979i	−0.432920	−	0.432920i
$358$	−11.3961	+	9.47730i	−0.602302	+	0.500891i
$359$	−22.3596			−1.18009			−0.590046	−	0.807369i	$-0.700891\pi$
$359$	−22.3596			−1.18009			−0.590046	+	0.807369i	$0.700891\pi$
$360$	2.83391	−	21.2687i	0.149360	−	1.12096i
$361$	−14.5013			−0.763224
$362$	16.8776	−	14.0359i	0.887068	−	0.737710i
$363$	−42.6634	−	42.6634i	−2.23925	−	2.23925i
$364$	6.52038	+	1.20899i	0.341761	+	0.0633683i
$365$	1.24323	+	8.66282i	0.0650734	+	0.453433i
$366$	−31.4233	−	2.88859i	−1.64252	−	0.150989i
$367$	10.2028	−	10.2028i	0.532580	−	0.532580i	−0.388760	−	0.921339i	$-0.627096\pi$
$367$	10.2028	−	10.2028i	0.532580	−	0.532580i	0.921339	+	0.388760i	$0.127096\pi$
$368$	7.13328	+	16.0281i	0.371848	+	0.835524i
$369$		−	1.82820i		−	0.0951723i
$370$	−6.57426	+	7.27965i	−0.341780	+	0.378451i
$371$		−	33.2598i		−	1.72676i
$372$	20.7182	+	30.1500i	1.07419	+	1.56321i
$373$	−17.6595	+	17.6595i	−0.914372	+	0.914372i	−0.996613	−	0.0822402i	$-0.973793\pi$
$373$	−17.6595	+	17.6595i	−0.914372	+	0.914372i	0.0822402	+	0.996613i	$0.473793\pi$
$374$	−1.05473	+	11.4738i	−0.0545389	+	0.593297i
$375$	11.7228	+	25.7226i	0.605365	+	1.32831i
$376$	15.3455	+	4.32976i	0.791384	+	0.223290i
$377$	3.93282	+	3.93282i	0.202551	+	0.202551i
$378$	−2.97622	−	3.57879i	−0.153080	−	0.184073i
$379$	−6.98725			−0.358911			−0.179456	−	0.983766i	$-0.557434\pi$
$379$	−6.98725			−0.358911			−0.179456	+	0.983766i	$0.557434\pi$
$380$	6.42814	+	6.97524i	0.329757	+	0.357822i
$381$	15.4247			0.790233
$382$	−11.9756	−	14.4002i	−0.612726	−	0.736779i
$383$	−8.29838	−	8.29838i	−0.424028	−	0.424028i	0.462560	−	0.886588i	$-0.346931\pi$
$383$	−8.29838	−	8.29838i	−0.424028	−	0.424028i	−0.886588	+	0.462560i	$0.846931\pi$
$384$	17.1212	−	22.9154i	0.873713	−	1.16940i
$385$	−43.3337	+	6.21894i	−2.20849	+	0.316946i
$386$	2.68031	−	29.1575i	0.136424	−	1.48408i
$387$	−19.6378	+	19.6378i	−0.998245	+	0.998245i
$388$	−27.5414	+	18.9256i	−1.39820	+	0.960802i
$389$		−	8.88726i		−	0.450602i	−0.974289	−	0.225301i	$-0.927663\pi$
$389$		−	8.88726i		−	0.450602i	0.974289	−	0.225301i	$-0.0723365\pi$
$390$	0.406565	+	7.98503i	0.0205872	+	0.404338i
$391$			6.05200i			0.306063i
$392$	9.85759	−	5.51905i	0.497883	−	0.278754i
$393$	−11.3749	+	11.3749i	−0.573786	+	0.573786i
$394$	34.6629	+	3.18639i	1.74629	+	0.160528i
$395$	−9.41826	+	12.5745i	−0.473884	+	0.632692i
$396$	−7.30394	+	39.3919i	−0.367037	+	1.97952i
$397$	15.3788	+	15.3788i	0.771838	+	0.771838i	0.978428	−	0.206590i	$-0.0662365\pi$
$397$	15.3788	+	15.3788i	0.771838	+	0.771838i	−0.206590	+	0.978428i	$0.566237\pi$
$398$	28.5894	−	23.7757i	1.43306	−	1.19177i
$399$	17.7815			0.890186
$400$	−1.63001	+	19.9335i	−0.0815006	+	0.996673i
$401$	−7.73585			−0.386310			−0.193155	−	0.981168i	$-0.561872\pi$
$401$	−7.73585			−0.386310			−0.193155	+	0.981168i	$0.561872\pi$
$402$	−10.0366	+	8.34675i	−0.500582	+	0.416298i
$403$	−5.11550	−	5.11550i	−0.254821	−	0.254821i
$404$	−1.71348	+	9.24124i	−0.0852490	+	0.459769i
$405$	−10.2790	+	13.7237i	−0.510767	+	0.681935i
$406$	25.9711	+	2.38739i	1.28892	+	0.118484i
$407$	12.9506	−	12.9506i	0.641936	−	0.641936i
$408$	8.61014	−	4.82063i	0.426265	−	0.238657i
$409$			7.27059i			0.359508i	0.983712	+	0.179754i	$0.0575301\pi$
$409$			7.27059i			0.359508i	−0.983712	+	0.179754i	$0.942470\pi$
$410$	0.0866528	+	1.70188i	0.00427948	+	0.0840499i
$411$		−	2.41686i		−	0.119215i
$412$	−1.99309	+	1.36959i	−0.0981926	+	0.0674750i
$413$	−7.17339	+	7.17339i	−0.352979	+	0.352979i
$414$	−1.92627	+	20.9548i	−0.0946712	+	1.02987i
$415$	21.7098	−	3.11563i	1.06569	−	0.152941i
$416$	−2.50292	+	5.07301i	−0.122716	+	0.248725i
$417$	−7.97477	−	7.97477i	−0.390526	−	0.390526i
$418$	−11.3247	−	13.6175i	−0.553907	−	0.666052i
$419$	28.5271			1.39364			0.696819	−	0.717247i	$-0.254598\pi$
$419$	28.5271			1.39364			0.696819	+	0.717247i	$0.254598\pi$
$420$	25.4074	+	27.5699i	1.23976	+	1.34527i
$421$	29.4919			1.43735			0.718674	−	0.695347i	$-0.244749\pi$
$421$	29.4919			1.43735			0.718674	+	0.695347i	$0.244749\pi$
$422$	6.03214	+	7.25342i	0.293640	+	0.353091i
$423$	13.5234	+	13.5234i	0.657532	+	0.657532i
$424$	27.3054	+	7.70425i	1.32607	+	0.374151i
$425$	−3.30964	+	6.05366i	−0.160541	+	0.293645i
$426$	−2.79249	+	30.3779i	−0.135297	+	1.47181i
$427$	20.6915	−	20.6915i	1.00133	−	1.00133i
$428$	20.8103	+	30.2840i	1.00590	+	1.46383i
$429$		−	14.9287i		−	0.720767i
$430$	17.3501	−	19.2117i	0.836698	−	0.926471i
$431$			22.3840i			1.07820i	0.842242	+	0.539099i	$0.181235\pi$
$431$			22.3840i			1.07820i	−0.842242	+	0.539099i	$0.818765\pi$
$432$	3.62749	−	1.61441i	0.174528	−	0.0776733i
$433$	−9.07817	+	9.07817i	−0.436269	+	0.436269i	−0.890754	−	0.454485i	$-0.849823\pi$
$433$	−9.07817	+	9.07817i	−0.436269	+	0.436269i	0.454485	+	0.890754i	$0.349823\pi$
$434$	−33.7811	−	3.10533i	−1.62154	−	0.149061i
$435$	4.46690	+	31.1255i	0.214172	+	1.49235i
$436$	5.15784	+	0.956352i	0.247016	+	0.0458010i
$437$	−6.57801	−	6.57801i	−0.314669	−	0.314669i
$438$	−10.7598	+	8.94817i	−0.514125	+	0.427560i
$439$	0.367210			0.0175260			0.00876298	−	0.999962i	$-0.497211\pi$
$439$	0.367210			0.0175260			0.00876298	+	0.999962i	$0.497211\pi$
$440$	4.93218	−	37.0163i	0.235132	−	1.76468i
$441$	13.5509			0.645279
$442$	−1.50038	+	1.24776i	−0.0713658	+	0.0593497i
$443$	−15.4141	−	15.4141i	−0.732348	−	0.732348i	0.238736	−	0.971084i	$-0.423267\pi$
$443$	−15.4141	−	15.4141i	−0.732348	−	0.732348i	−0.971084	+	0.238736i	$0.923267\pi$
$444$	−15.4223	−	2.85955i	−0.731908	−	0.135708i
$445$	−16.8671	−	12.6334i	−0.799579	−	0.598882i
$446$	−7.79851	−	0.716879i	−0.369270	−	0.0339452i
$447$	−13.2365	+	13.2365i	−0.626064	+	0.626064i
$448$	6.18654	+	25.7945i	0.292287	+	1.21868i
$449$		−	40.2066i		−	1.89747i	−0.316079	−	0.948733i	$-0.602366\pi$
$449$		−	40.2066i		−	1.89747i	0.316079	−	0.948733i	$-0.397634\pi$
$450$	−13.3863	+	19.9071i	−0.631035	+	0.938431i
$451$		−	3.18182i		−	0.149826i
$452$	−17.4572	−	25.4045i	−0.821116	−	1.19492i
$453$	14.7584	−	14.7584i	0.693412	−	0.693412i
$454$	−0.0807442	+	0.878368i	−0.00378951	+	0.0412239i
$455$	−5.93426	−	4.44474i	−0.278203	−	0.208373i
$456$	−4.11887	+	14.5981i	−0.192884	+	0.683619i
$457$	9.15479	+	9.15479i	0.428243	+	0.428243i	0.888029	−	0.459787i	$-0.152074\pi$
$457$	9.15479	+	9.15479i	0.428243	+	0.428243i	−0.459787	+	0.888029i	$0.652074\pi$
$458$	−5.73852	−	6.90035i	−0.268143	−	0.322432i
$459$	1.36969			0.0639318
$460$	0.799964	−	19.5982i	0.0372985	−	0.913772i
$461$	28.6420			1.33399			0.666995	−	0.745062i	$-0.267580\pi$
$461$	28.6420			1.33399			0.666995	+	0.745062i	$0.267580\pi$
$462$	−44.7611	−	53.8235i	−2.08247	−	2.50409i
$463$	−20.4203	−	20.4203i	−0.949010	−	0.949010i	0.0497517	−	0.998762i	$-0.484157\pi$
$463$	−20.4203	−	20.4203i	−0.949010	−	0.949010i	−0.998762	+	0.0497517i	$0.984157\pi$
$464$	−7.97589	+	20.7685i	−0.370271	+	0.964154i
$465$	−5.81019	−	40.4855i	−0.269441	−	1.87747i
$466$	−1.17204	+	12.7500i	−0.0542939	+	0.590632i
$467$	−21.3596	+	21.3596i	−0.988406	+	0.988406i	−0.999934	−	0.0115276i	$-0.996331\pi$
$467$	−21.3596	+	21.3596i	−0.988406	+	0.988406i	0.0115276	+	0.999934i	$0.496331\pi$
$468$	−5.59215	+	3.84276i	−0.258497	+	0.177631i
$469$		−	12.1051i		−	0.558959i
$470$	−13.2300	−	11.9481i	−0.610255	−	0.551123i
$471$		−	51.6648i		−	2.38059i
$472$	−4.22752	−	7.55079i	−0.194588	−	0.347553i
$473$	−34.1779	+	34.1779i	−1.57150	+	1.57150i
$474$	−25.0169	−	2.29968i	−1.14906	−	0.105628i
$475$	−2.98251	−	10.1771i	−0.136847	−	0.466957i
$476$	−1.66824	+	8.99722i	−0.0764636	+	0.412387i
$477$	24.0632	+	24.0632i	1.10178	+	1.10178i
$478$	18.1498	−	15.0939i	0.830153	−	0.690378i
$479$	4.14375			0.189333			0.0946664	−	0.995509i	$-0.469822\pi$
$479$	4.14375			0.189333			0.0946664	+	0.995509i	$0.469822\pi$
$480$	−28.5195	+	14.4726i	−1.30173	+	0.660580i
$481$	3.10184			0.141432
$482$	5.29864	−	4.40649i	0.241346	−	0.200710i
$483$	−25.9998	−	25.9998i	−1.18303	−	1.18303i
$484$	−8.70105	+	46.9269i	−0.395502	+	2.13304i
$485$	36.9826	−	5.30748i	1.67929	−	0.241000i
$486$	−31.4968	−	2.89535i	−1.42873	−	0.131336i
$487$	−24.6973	+	24.6973i	−1.11914	+	1.11914i	−0.127273	+	0.991868i	$0.540622\pi$
$487$	−24.6973	+	24.6973i	−1.11914	+	1.11914i	−0.991868	+	0.127273i	$0.959378\pi$
$488$	12.1942	+	21.7802i	0.552007	+	0.985942i
$489$			32.6840i			1.47802i
$490$	−12.6146	+	0.642283i	−0.569868	+	0.0290154i
$491$		−	19.3185i		−	0.871832i	−0.899987	−	0.435916i	$-0.856424\pi$
$491$		−	19.3185i		−	0.871832i	0.899987	−	0.435916i	$-0.143576\pi$
$492$	−2.24583	+	1.54326i	−0.101250	+	0.0695757i
$493$	−5.42675	+	5.42675i	−0.244408	+	0.244408i
$494$	0.274579	−	2.98699i	0.0123539	−	0.134391i
$495$	26.8523	−	35.8510i	1.20692	−	1.61138i
$496$	10.3744	−	27.0140i	0.465824	−	1.21297i
$497$	−20.0032	−	20.0032i	−0.897265	−	0.897265i
$498$	22.4249	+	26.9651i	1.00488	+	1.20834i
$499$	−4.80183			−0.214959			−0.107480	−	0.994207i	$-0.534278\pi$
$499$	−4.80183			−0.214959			−0.107480	+	0.994207i	$0.534278\pi$
$500$	11.5178	−	19.1661i	0.515092	−	0.857135i
$501$	9.57085			0.427594
$502$	3.44218	+	4.13909i	0.153632	+	0.184737i
$503$	−7.80160	−	7.80160i	−0.347856	−	0.347856i	0.511454	−	0.859310i	$-0.329107\pi$
$503$	−7.80160	−	7.80160i	−0.347856	−	0.347856i	−0.859310	+	0.511454i	$0.829107\pi$
$504$	−8.63991	+	30.6215i	−0.384852	+	1.36399i
$505$	6.29947	−	8.41055i	0.280323	−	0.374264i
$506$	−3.35251	+	36.4700i	−0.149037	+	1.62129i
$507$	1.78782	−	1.78782i	0.0793999	−	0.0793999i
$508$	−6.91018	−	10.0560i	−0.306590	−	0.446163i
$509$			41.1405i			1.82352i	0.410725	+	0.911759i	$0.365276\pi$
$509$			41.1405i			1.82352i	−0.410725	+	0.911759i	$0.634724\pi$
$510$	−11.0182	+	0.561004i	−0.487896	+	0.0248417i
$511$		−	12.9773i		−	0.574081i
$512$	−22.6097	−	0.896029i	−0.999216	−	0.0395992i
$513$	−1.48874	+	1.48874i	−0.0657294	+	0.0657294i
$514$	−30.7197	−	2.82391i	−1.35499	−	0.124557i
$515$	2.67633	−	0.384087i	0.117933	−	0.0169249i
$516$	40.7009	+	7.54664i	1.79176	+	0.332222i
$517$	23.5364	+	23.5364i	1.03513	+	1.03513i
$518$	11.1832	−	9.30029i	0.491364	−	0.408631i
$519$	−15.4222			−0.676962
$520$	5.02362	−	3.84230i	0.220300	−	0.168496i
$521$	17.4587			0.764881			0.382441	−	0.923980i	$-0.375084\pi$
$521$	17.4587			0.764881			0.382441	+	0.923980i	$0.375084\pi$
$522$	−20.5172	+	17.0626i	−0.898012	+	0.746811i
$523$	20.3908	+	20.3908i	0.891627	+	0.891627i	0.994676	−	0.103050i	$-0.0328600\pi$
$523$	20.3908	+	20.3908i	0.891627	+	0.891627i	−0.103050	+	0.994676i	$0.532860\pi$
$524$	12.5116	+	2.31987i	0.546572	+	0.101344i
$525$	−11.7885	−	40.2253i	−0.514492	−	1.75558i
$526$	−4.11812	−	0.378559i	−0.179559	−	0.0165060i
$527$	7.05868	−	7.05868i	0.307481	−	0.307481i
$528$	54.5560	−	24.2800i	2.37425	−	1.05665i
$529$		−	3.76347i		−	0.163629i
$530$	−23.5411	−	21.2600i	−1.02256	−	0.923477i
$531$		−	10.3798i		−	0.450445i
$532$	−7.96597	−	11.5924i	−0.345369	−	0.502596i
$533$	0.381045	−	0.381045i	0.0165049	−	0.0165049i
$534$	3.08474	−	33.5571i	0.133490	−	1.45216i
$535$	−5.83600	−	40.6654i	−0.252312	−	1.75812i
$536$	9.93792	+	2.80400i	0.429253	+	0.121114i
$537$	18.7376	+	18.7376i	0.808587	+	0.808587i
$538$	0.983681	+	1.18284i	0.0424095	+	0.0509958i
$539$	23.5841			1.01584
$540$	−4.43548	−	0.181048i	−0.190873	−	0.00779108i
$541$	−13.3562			−0.574228			−0.287114	−	0.957896i	$-0.592696\pi$
$541$	−13.3562			−0.574228			−0.287114	+	0.957896i	$0.592696\pi$
$542$	−16.8977	−	20.3189i	−0.725820	−	0.872770i
$543$	−27.7504	−	27.7504i	−1.19088	−	1.19088i
$544$	−7.00005	−	3.45368i	−0.300125	−	0.148075i
$545$	−4.69421	−	3.51594i	−0.201078	−	0.150607i
$546$	1.08528	−	11.8062i	0.0464459	−	0.505258i
$547$	−16.3289	+	16.3289i	−0.698175	+	0.698175i	−0.964017	−	0.265842i	$-0.914350\pi$
$547$	−16.3289	+	16.3289i	−0.698175	+	0.698175i	0.265842	+	0.964017i	$0.414350\pi$
$548$	−1.57565	+	1.08274i	−0.0673082	+	0.0462522i
$549$			29.9404i			1.27783i
$550$	−23.2977	+	34.6466i	−0.993415	+	1.47734i
$551$		−	11.7968i		−	0.502561i
$552$	27.3677	−	15.3226i	1.16485	−	0.652172i
$553$	16.4731	−	16.4731i	0.700506	−	0.700506i
$554$	−2.62534	−	0.241335i	−0.111540	−	0.0102533i
$555$	14.0360	+	10.5129i	0.595794	+	0.446247i
$556$	−1.62643	+	8.77171i	−0.0689758	+	0.372003i
$557$	−3.94925	−	3.94925i	−0.167335	−	0.167335i	0.618472	−	0.785807i	$-0.287752\pi$
$557$	−3.94925	−	3.94925i	−0.167335	−	0.167335i	−0.785807	+	0.618472i	$0.787752\pi$
$558$	26.6871	−	22.1937i	1.12975	−	0.939534i
$559$	−8.18607			−0.346234
$560$	6.59154	−	28.9152i	0.278543	−	1.22189i
$561$	20.5996			0.869716
$562$	7.99107	−	6.64559i	0.337083	−	0.280327i
$563$	28.4131	+	28.4131i	1.19747	+	1.19747i	0.974922	+	0.222547i	$0.0714371\pi$
$563$	28.4131	+	28.4131i	1.19747	+	1.19747i	0.222547	+	0.974922i	$0.428563\pi$
$564$	5.19695	−	28.0284i	0.218831	−	1.18021i
$565$	4.89567	+	34.1131i	0.205962	+	1.43515i
$566$	−14.0413	−	1.29075i	−0.590198	−	0.0542541i
$567$	17.9785	−	17.9785i	0.755027	−	0.755027i
$568$	21.0556	−	11.7886i	0.883472	−	0.494637i
$569$		−	1.74697i		−	0.0732369i	−0.999329	−	0.0366184i	$-0.988341\pi$
$569$		−	1.74697i		−	0.0732369i	0.999329	−	0.0366184i	$-0.0116586\pi$
$570$	11.3661	−	12.5856i	0.476074	−	0.527155i
$571$		−	15.3998i		−	0.644460i	−0.946661	−	0.322230i	$-0.895568\pi$
$571$		−	15.3998i		−	0.644460i	0.946661	−	0.322230i	$-0.104432\pi$
$572$	−9.73265	+	6.68798i	−0.406942	+	0.279639i
$573$	−23.6770	+	23.6770i	−0.989122	+	0.989122i
$574$	0.231311	−	2.51630i	0.00965473	−	0.105028i
$575$	−10.5198	+	19.2418i	−0.438707	+	0.802438i
$576$	−23.1381	−	14.1863i	−0.964088	−	0.591094i
$577$	−1.31527	−	1.31527i	−0.0547554	−	0.0547554i	0.679199	−	0.733954i	$-0.262327\pi$
$577$	−1.31527	−	1.31527i	−0.0547554	−	0.0547554i	−0.733954	+	0.679199i	$0.762327\pi$
$578$	13.6507	+	16.4145i	0.567795	+	0.682752i
$579$	−52.3481			−2.17551
$580$	18.2908	−	16.8562i	0.759484	−	0.699914i
$581$	−32.5223			−1.34925
$582$	38.2008	+	45.9350i	1.58348	+	1.90407i
$583$	41.8799	+	41.8799i	1.73449	+	1.73449i
$584$	10.6540	+	3.00604i	0.440866	+	0.124391i
$585$	7.50915	−	1.07766i	0.310465	−	0.0445557i
$586$	2.18700	−	23.7911i	0.0903443	−	0.982802i
$587$	6.86501	−	6.86501i	0.283349	−	0.283349i	−0.551094	−	0.834443i	$-0.685789\pi$
$587$	6.86501	−	6.86501i	0.283349	−	0.283349i	0.834443	+	0.551094i	$0.185789\pi$
$588$	−11.4389	−	16.6464i	−0.471732	−	0.686485i
$589$			15.3444i			0.632253i
$590$	0.491981	+	9.66261i	0.0202545	+	0.397803i
$591$		−	62.2323i		−	2.55990i
$592$	5.04482	+	11.3355i	0.207341	+	0.465884i
$593$	27.3416	−	27.3416i	1.12279	−	1.12279i	0.131466	−	0.991321i	$-0.458032\pi$
$593$	27.3416	−	27.3416i	1.12279	−	1.12279i	0.991321	−	0.131466i	$-0.0419683\pi$
$594$	8.25391	+	0.758742i	0.338662	+	0.0311316i
$595$	6.13313	−	8.18846i	0.251434	−	0.335694i
$596$	14.5592	+	2.69953i	0.596369	+	0.110577i
$597$	−47.0071	−	47.0071i	−1.92387	−	1.92387i
$598$	−4.76902	+	3.96605i	−0.195020	+	0.162184i
$599$	−29.1119			−1.18948			−0.594740	−	0.803918i	$-0.702745\pi$
$599$	−29.1119			−1.18948			−0.594740	+	0.803918i	$0.702745\pi$
$600$	35.7546	−	0.360292i	1.45967	−	0.0147088i
$601$	18.6652			0.761370			0.380685	−	0.924705i	$-0.375688\pi$
$601$	18.6652			0.761370			0.380685	+	0.924705i	$0.375688\pi$
$602$	−29.5137	+	24.5444i	−1.20289	+	1.00035i
$603$	8.75793	+	8.75793i	0.356651	+	0.356651i
$604$	−16.2333	−	3.00993i	−0.660523	−	0.122472i
$605$	31.9886	−	42.7087i	1.30052	−	1.73635i
$606$	16.7327	+	1.53816i	0.679720	+	0.0624834i
$607$	−11.4008	+	11.4008i	−0.462745	+	0.462745i	−0.899554	−	0.436809i	$-0.856108\pi$
$607$	−11.4008	+	11.4008i	−0.462745	+	0.462745i	0.436809	+	0.899554i	$0.356108\pi$
$608$	11.3623	−	3.85459i	0.460802	−	0.156324i
$609$		−	46.6273i		−	1.88943i
$610$	−1.41911	−	27.8717i	−0.0574581	−	1.12849i
$611$			5.63728i			0.228060i
$612$	−5.30247	−	7.71639i	−0.214340	−	0.311917i
$613$	−7.48848	+	7.48848i	−0.302457	+	0.302457i	−0.841974	−	0.539517i	$-0.818607\pi$
$613$	−7.48848	+	7.48848i	−0.302457	+	0.302457i	0.539517	+	0.841974i	$0.318607\pi$
$614$	−0.144561	+	1.57259i	−0.00583399	+	0.0634645i
$615$	3.01570	−	0.432791i	0.121605	−	0.0174518i
$616$	−15.0370	+	53.2941i	−0.605858	+	2.14728i
$617$	−4.44176	−	4.44176i	−0.178818	−	0.178818i	0.612022	−	0.790841i	$-0.290356\pi$
$617$	−4.44176	−	4.44176i	−0.178818	−	0.178818i	−0.790841	+	0.612022i	$0.790356\pi$
$618$	2.76448	+	3.32419i	0.111204	+	0.133718i
$619$	29.5686			1.18846			0.594231	−	0.804294i	$-0.297456\pi$
$619$	29.5686			1.18846			0.594231	+	0.804294i	$0.297456\pi$
$620$	−23.7912	+	21.9251i	−0.955477	+	0.880535i
$621$	4.35362			0.174705
$622$	−16.2936	−	19.5924i	−0.653314	−	0.785585i
$623$	22.0966	+	22.0966i	0.885281	+	0.885281i
$624$	9.44116	+	3.62576i	0.377949	+	0.145146i
$625$	−21.0454	+	13.4941i	−0.841816	+	0.539765i
$626$	−3.55952	+	38.7219i	−0.142267	+	1.54764i
$627$	−22.3900	+	22.3900i	−0.894171	+	0.894171i
$628$	−33.6823	+	23.1455i	−1.34407	+	0.923605i
$629$			4.28011i			0.170659i
$630$	23.8420	−	26.4001i	0.949888	−	1.05181i
$631$			7.08057i			0.281873i	0.990019	+	0.140937i	$0.0450113\pi$
$631$			7.08057i			0.281873i	−0.990019	+	0.140937i	$0.954989\pi$
$632$	9.70815	+	17.3397i	0.386169	+	0.689738i
$633$	11.9262	−	11.9262i	0.474023	−	0.474023i
$634$	17.9764	+	1.65248i	0.713933	+	0.0656284i
$635$	1.93788	+	13.5032i	0.0769026	+	0.535859i
$636$	9.24730	−	49.8730i	0.366679	−	1.97759i
$637$	2.82436	+	2.82436i	0.111905	+	0.111905i
$638$	−35.7083	+	29.6960i	−1.41371	+	1.17568i
$639$	28.9443			1.14502
$640$	22.2118	+	12.1094i	0.877998	+	0.478665i
$641$	47.7079			1.88435			0.942174	−	0.335124i	$-0.108778\pi$
$641$	47.7079			1.88435			0.942174	+	0.335124i	$0.108778\pi$
$642$	50.5093	−	42.0049i	1.99344	−	1.65780i
$643$	7.14982	+	7.14982i	0.281961	+	0.281961i	0.833891	−	0.551929i	$-0.186108\pi$
$643$	7.14982	+	7.14982i	0.281961	+	0.281961i	−0.551929	+	0.833891i	$0.686108\pi$
$644$	−5.30256	+	28.5980i	−0.208950	+	1.12692i
$645$	−37.0423	−	27.7446i	−1.45854	−	1.09244i
$646$	4.12163	+	0.378882i	0.162163	+	0.0149069i
$647$	10.5716	−	10.5716i	0.415614	−	0.415614i	−0.468075	−	0.883689i	$-0.655052\pi$
$647$	10.5716	−	10.5716i	0.415614	−	0.415614i	0.883689	+	0.468075i	$0.155052\pi$
$648$	10.5954	+	18.9244i	0.416225	+	0.743421i
$649$		−	18.0651i		−	0.709119i
$650$	−6.93922	+	1.35912i	−0.272179	+	0.0533089i
$651$			60.6491i			2.37703i
$652$	21.3080	−	14.6422i	0.834487	−	0.573434i
$653$	13.5641	−	13.5641i	0.530805	−	0.530805i	−0.390007	−	0.920812i	$-0.627527\pi$
$653$	13.5641	−	13.5641i	0.530805	−	0.530805i	0.920812	+	0.390007i	$0.127527\pi$
$654$	0.858497	−	9.33909i	0.0335699	−	0.365187i
$655$	−11.3869	−	8.52878i	−0.444924	−	0.333247i
$656$	2.01223	+	0.772772i	0.0785644	+	0.0301717i
$657$	9.38899	+	9.38899i	0.366299	+	0.366299i
$658$	16.9023	+	20.3244i	0.658922	+	0.792328i
$659$	12.8543			0.500732			0.250366	−	0.968151i	$-0.419449\pi$
$659$	12.8543			0.500732			0.250366	+	0.968151i	$0.419449\pi$
$660$	−66.7078	−	2.72289i	−2.59660	−	0.105988i
$661$	−21.0808			−0.819949			−0.409975	−	0.912097i	$-0.634462\pi$
$661$	−21.0808			−0.819949			−0.409975	+	0.912097i	$0.634462\pi$
$662$	1.86457	+	2.24207i	0.0724685	+	0.0871405i
$663$	2.46694	+	2.46694i	0.0958082	+	0.0958082i
$664$	7.53341	−	26.6999i	0.292353	−	1.03616i
$665$	2.23397	+	15.5663i	0.0866296	+	0.603637i
$666$	−1.36230	+	14.8197i	−0.0527882	+	0.574252i
$667$	−17.2491	+	17.2491i	−0.667889	+	0.667889i
$668$	−4.28768	−	6.23962i	−0.165895	−	0.241418i
$669$			14.0011i			0.541314i
$670$	−8.56791	−	7.73769i	−0.331007	−	0.298933i
$671$			52.1087i			2.01163i
$672$	44.9099	−	15.2354i	1.73244	−	0.587719i
$673$	4.99164	−	4.99164i	0.192414	−	0.192414i	−0.604325	−	0.796738i	$-0.706557\pi$
$673$	4.99164	−	4.99164i	0.192414	−	0.192414i	0.796738	+	0.604325i	$0.206557\pi$
$674$	−18.8584	−	1.73356i	−0.726399	−	0.0667743i
$675$	4.35481	+	2.38085i	0.167617	+	0.0916390i
$676$	−1.96648	−	0.364619i	−0.0756339	−	0.0140238i
$677$	−23.8899	−	23.8899i	−0.918164	−	0.918164i	0.0787317	−	0.996896i	$-0.474913\pi$
$677$	−23.8899	−	23.8899i	−0.918164	−	0.918164i	−0.996896	+	0.0787317i	$0.974913\pi$
$678$	−42.3709	+	35.2368i	−1.62725	+	1.35326i
$679$	−55.4016			−2.12612
$680$	5.30184	+	6.93190i	0.203316	+	0.265826i
$681$	1.57699			0.0604302
$682$	46.4465	−	38.6262i	1.77853	−	1.47907i
$683$	−28.7712	−	28.7712i	−1.10090	−	1.10090i	−0.994302	−	0.106598i	$-0.966004\pi$
$683$	−28.7712	−	28.7712i	−1.10090	−	1.10090i	−0.106598	−	0.994302i	$-0.533996\pi$
$684$	14.1504	+	2.62372i	0.541054	+	0.100321i
$685$	2.11578	−	0.303641i	0.0808398	−	0.0116015i
$686$	−14.0354	−	1.29020i	−0.535873	−	0.0492602i
$687$	−11.3456	+	11.3456i	−0.432863	+	0.432863i
$688$	−13.3138	−	29.9154i	−0.507583	−	1.14051i
$689$			10.0308i			0.382144i
$690$	−35.0219	+	1.78317i	−1.33326	+	0.0678842i
$691$		−	14.3829i		−	0.547153i	−0.961850	−	0.273576i	$-0.911793\pi$
$691$		−	14.3829i		−	0.547153i	0.961850	−	0.273576i	$-0.0882067\pi$
$692$	6.90906	+	10.0544i	0.262643	+	0.382210i
$693$	−46.9661	+	46.9661i	−1.78410	+	1.78410i
$694$	1.39313	−	15.1551i	0.0528826	−	0.575279i
$695$	5.97941	−	7.98323i	0.226812	−	0.302821i
$696$	38.2798	+	10.8007i	1.45099	+	0.409399i
$697$	0.525789	+	0.525789i	0.0199157	+	0.0199157i
$698$	4.24503	+	5.10448i	0.160677	+	0.193208i
$699$	22.8908			0.865809
$700$	−20.9433	+	25.7061i	−0.791583	+	0.971598i
$701$	−0.729357			−0.0275474			−0.0137737	−	0.999905i	$-0.504384\pi$
$701$	−0.729357			−0.0275474			−0.0137737	+	0.999905i	$0.504384\pi$
$702$	0.897598	+	1.07933i	0.0338777	+	0.0407366i
$703$	−4.65211	−	4.65211i	−0.175458	−	0.175458i
$704$	−40.2699	−	24.6900i	−1.51773	−	0.930538i
$705$	−19.1061	+	25.5089i	−0.719578	+	0.960722i
$706$	−1.42343	+	15.4847i	−0.0535715	+	0.582773i
$707$	−11.0181	+	11.0181i	−0.414379	+	0.414379i
$708$	−12.7509	+	8.76205i	−0.479209	+	0.329298i
$709$		−	34.6107i		−	1.29983i	−0.760006	−	0.649916i	$-0.774804\pi$
$709$		−	34.6107i		−	1.29983i	0.760006	−	0.649916i	$-0.225196\pi$
$710$	−26.9444	+	1.37190i	−1.01121	+	0.0514865i
$711$			23.8363i			0.893932i
$712$	−23.2591	+	13.0223i	−0.871673	+	0.488030i
$713$	22.4363	−	22.4363i	0.840246	−	0.840246i
$714$	16.2909	+	1.49754i	0.609671	+	0.0560441i
$715$	13.0690	−	1.87557i	0.488753	−	0.0701424i
$716$	3.82147	−	20.6101i	0.142815	−	0.770236i
$717$	−29.8421	−	29.8421i	−1.11448	−	1.11448i
$718$	24.3125	−	20.2189i	0.907333	−	0.754563i
$719$	18.2520			0.680684			0.340342	−	0.940302i	$-0.389457\pi$
$719$	18.2520			0.680684			0.340342	+	0.940302i	$0.389457\pi$
$720$	16.1511	+	25.6889i	0.601915	+	0.957370i
$721$	−4.00926			−0.149312
$722$	15.7678	−	13.1129i	0.586817	−	0.488013i
$723$	−8.71209	−	8.71209i	−0.324006	−	0.324006i
$724$	−5.65960	+	30.5236i	−0.210337	+	1.13440i
$725$	−26.6868	+	7.82088i	−0.991124	+	0.290460i
$726$	84.9686	+	7.81075i	3.15348	+	0.289884i
$727$	−4.69639	+	4.69639i	−0.174179	+	0.174179i	−0.788813	−	0.614633i	$-0.789304\pi$
$727$	−4.69639	+	4.69639i	−0.174179	+	0.174179i	0.614633	+	0.788813i	$0.289304\pi$
$728$	−8.18312	+	4.58155i	−0.303286	+	0.169803i
$729$			33.5439i			1.24237i
$730$	−9.18527	−	8.29523i	−0.339962	−	0.307020i
$731$		−	11.2956i		−	0.417784i
$732$	36.7799	−	25.2740i	1.35942	−	0.934154i
$733$	−2.92353	+	2.92353i	−0.107983	+	0.107983i	−0.759034	−	0.651051i	$-0.774328\pi$
$733$	−2.92353	+	2.92353i	−0.107983	+	0.107983i	0.651051	+	0.759034i	$0.274328\pi$
$734$	−1.86790	+	20.3198i	−0.0689456	+	0.750019i
$735$	3.20791	+	22.3528i	0.118326	+	0.824495i
$736$	−22.2499	−	10.9777i	−0.820143	−	0.404642i
$737$	15.2424	+	15.2424i	0.561462	+	0.561462i
$738$	1.65317	+	1.98788i	0.0608541	+	0.0731748i
$739$	−41.5292			−1.52768			−0.763838	−	0.645408i	$-0.776687\pi$
$739$	−41.5292			−1.52768			−0.763838	+	0.645408i	$0.776687\pi$
$740$	0.565753	−	13.8603i	0.0207975	−	0.509515i
$741$	−5.36271			−0.197004
$742$	30.0755	+	36.1647i	1.10411	+	1.32765i
$743$	0.495864	+	0.495864i	0.0181915	+	0.0181915i	0.716144	−	0.697953i	$-0.245905\pi$
$743$	0.495864	+	0.495864i	0.0181915	+	0.0181915i	−0.697953	+	0.716144i	$0.745905\pi$
$744$	−49.7913	−	14.0487i	−1.82544	−	0.515050i
$745$	−13.2505	−	9.92459i	−0.485461	−	0.363609i
$746$	3.23307	−	35.1706i	0.118371	−	1.28769i
$747$	23.5296	−	23.5296i	0.860905	−	0.860905i
$748$	−9.22849	−	13.4297i	−0.337427	−	0.491039i
$749$			60.9186i			2.22592i
$750$	−36.0067	−	17.3687i	−1.31478	−	0.634214i
$751$		−	51.0434i		−	1.86260i	−0.364251	−	0.931301i	$-0.618675\pi$
$751$		−	51.0434i		−	1.86260i	0.364251	−	0.931301i	$-0.381325\pi$
$752$	−20.6010	+	9.16844i	−0.751242	+	0.334339i
$753$	6.80554	−	6.80554i	0.248008	−	0.248008i
$754$	−7.83262	−	0.720014i	−0.285247	−	0.0262214i
$755$	14.7741	+	11.0657i	0.537684	+	0.402724i
$756$	6.47232	+	1.20008i	0.235396	+	0.0436465i
$757$	33.0450	+	33.0450i	1.20104	+	1.20104i	0.973850	+	0.227190i	$0.0729539\pi$
$757$	33.0450	+	33.0450i	1.20104	+	1.20104i	0.227190	+	0.973850i	$0.427046\pi$
$758$	7.59752	−	6.31831i	0.275954	−	0.229491i
$759$	65.4767			2.37665
$760$	−13.2970	−	1.77174i	−0.482334	−	0.0642677i
$761$	−53.2090			−1.92882			−0.964412	−	0.264406i	$-0.914824\pi$
$761$	−53.2090			−1.92882			−0.964412	+	0.264406i	$0.914824\pi$
$762$	−16.7719	+	13.9480i	−0.607584	+	0.505283i
$763$	6.14958	+	6.14958i	0.222630	+	0.222630i
$764$	26.0432	+	4.82885i	0.942208	+	0.174702i
$765$	1.48702	+	10.3616i	0.0537633	+	0.374624i
$766$	16.5271	+	1.51926i	0.597148	+	0.0548929i
$767$	2.16342	−	2.16342i	0.0781167	−	0.0781167i
$768$	2.10499	+	40.3989i	0.0759572	+	1.45777i
$769$		−	42.2296i		−	1.52284i	−0.648259	−	0.761420i	$-0.724503\pi$
$769$		−	42.2296i		−	1.52284i	0.648259	−	0.761420i	$-0.275497\pi$
$770$	41.4949	−	45.9471i	1.49537	−	1.65582i
$771$			55.1528i			1.98628i
$772$	23.4516	+	34.1278i	0.844042	+	1.22829i
$773$	−7.25976	+	7.25976i	−0.261115	+	0.261115i	−0.825507	−	0.564392i	$-0.809111\pi$
$773$	−7.25976	+	7.25976i	−0.261115	+	0.261115i	0.564392	+	0.825507i	$0.309111\pi$
$774$	3.59526	−	39.1107i	0.129229	−	1.40580i
$775$	34.7121	−	10.1728i	1.24690	−	0.365417i
$776$	12.8332	−	45.4832i	0.460683	−	1.63275i
$777$	−18.3876	−	18.3876i	−0.659653	−	0.659653i
$778$	8.03641	+	9.66348i	0.288119	+	0.346452i
$779$	−1.14298			−0.0409514
$780$	−7.66264	−	8.31481i	−0.274366	−	0.297718i
$781$	50.3751			1.80256
$782$	−5.47260	−	6.58059i	−0.195700	−	0.235321i
$783$	3.90384	+	3.90384i	0.139512	+	0.139512i
$784$	−5.72789	+	14.9149i	−0.204567	+	0.532676i
$785$	45.2287	−	6.49089i	1.61428	−	0.231670i
$786$	2.08249	−	22.6542i	0.0742801	−	0.808050i
$787$	2.28033	−	2.28033i	0.0812851	−	0.0812851i	−0.665295	−	0.746580i	$-0.731694\pi$
$787$	2.28033	−	2.28033i	0.0812851	−	0.0812851i	0.746580	+	0.665295i	$0.231694\pi$
$788$	−40.5717	+	27.8797i	−1.44531	+	0.993172i
$789$			7.39350i			0.263216i
$790$	−1.12979	−	22.1894i	−0.0401962	−	0.789462i
$791$		−	51.1030i		−	1.81701i
$792$	−27.6788	−	49.4371i	−0.983522	−	1.75667i
$793$	−6.24037	+	6.24037i	−0.221602	+	0.221602i
$794$	−30.6284	−	2.81552i	−1.08696	−	0.0999190i
$795$	−33.9969	+	45.3899i	−1.20575	+	1.60981i
$796$	−9.58693	+	51.7047i	−0.339800	+	1.83262i
$797$	−23.7266	−	23.7266i	−0.840439	−	0.840439i	0.148477	−	0.988916i	$-0.452563\pi$
$797$	−23.7266	−	23.7266i	−0.840439	−	0.840439i	−0.988916	+	0.148477i	$0.952563\pi$
$798$	−19.3345	+	16.0791i	−0.684434	+	0.569194i
$799$	−7.77867			−0.275189
$800$	−16.2527	−	23.1484i	−0.574620	−	0.818420i
$801$	−31.9735			−1.12973
$802$	8.41151	−	6.99524i	0.297021	−	0.247011i
$803$	16.3407	+	16.3407i	0.576651	+	0.576651i
$804$	3.36560	−	18.1515i	0.118696	−	0.640154i
$805$	19.4944	−	26.0274i	0.687088	−	0.917344i
$806$	10.1880	+	0.936537i	0.358858	+	0.0329881i
$807$	1.94484	−	1.94484i	0.0684615	−	0.0684615i
$808$	−6.49336	−	11.5978i	−0.228436	−	0.408010i
$809$			46.5795i			1.63765i	0.574045	+	0.818824i	$0.305373\pi$
$809$			46.5795i			1.63765i	−0.574045	+	0.818824i	$0.694627\pi$
$810$	−1.23304	−	24.2172i	−0.0433246	−	0.850906i
$811$			14.5241i			0.510010i	0.966940	+	0.255005i	$0.0820770\pi$
$811$			14.5241i			0.510010i	−0.966940	+	0.255005i	$0.917923\pi$
$812$	−30.3982	+	20.8887i	−1.06677	+	0.733051i
$813$	−33.4086	+	33.4086i	−1.17169	+	1.17169i
$814$	−2.37097	+	25.7924i	−0.0831025	+	0.904024i
$815$	−28.6125	+	4.10625i	−1.00225	+	0.143836i
$816$	−5.00304	+	13.0275i	−0.175142	+	0.456053i
$817$	12.2774	+	12.2774i	0.429532	+	0.429532i
$818$	−6.57452	−	7.90561i	−0.229873	−	0.276413i
$819$	−11.2490			−0.393073
$820$	−1.63317	−	1.77217i	−0.0570327	−	0.0618868i
$821$	11.3924			0.397597			0.198799	−	0.980040i	$-0.436296\pi$
$821$	11.3924			0.397597			0.198799	+	0.980040i	$0.436296\pi$
$822$	2.18547	+	2.62795i	0.0762271	+	0.0916602i
$823$	−31.8998	−	31.8998i	−1.11196	−	1.11196i	−0.992886	−	0.119072i	$-0.962008\pi$
$823$	−31.8998	−	31.8998i	−1.11196	−	1.11196i	−0.119072	−	0.992886i	$-0.537992\pi$
$824$	0.928699	−	3.29149i	0.0323528	−	0.114665i
$825$	65.4946	+	35.8070i	2.28023	+	1.24664i
$826$	1.31329	−	14.2865i	0.0456953	−	0.497092i
$827$	−3.71377	+	3.71377i	−0.129141	+	0.129141i	−0.768723	−	0.639582i	$-0.779107\pi$
$827$	−3.71377	+	3.71377i	−0.129141	+	0.129141i	0.639582	+	0.768723i	$0.279107\pi$
$828$	−16.8541	−	24.5269i	−0.585721	−	0.852368i
$829$			52.6592i			1.82893i	0.404666	+	0.914465i	$0.367388\pi$
$829$			52.6592i			1.82893i	−0.404666	+	0.914465i	$0.632612\pi$
$830$	−20.7886	+	23.0191i	−0.721583	+	0.799005i
$831$			4.71342i			0.163507i
$832$	−1.86580	−	7.77938i	−0.0646850	−	0.269702i
$833$	−3.89722	+	3.89722i	−0.135031	+	0.135031i
$834$	15.8826	+	1.46001i	0.549969	+	0.0505559i
$835$	1.20243	+	8.37857i	0.0416119	+	0.289952i
$836$	24.6275	+	4.56636i	0.851760	+	0.157931i
$837$	−5.07780	−	5.07780i	−0.175514	−	0.175514i
$838$	−31.0186	+	25.7960i	−1.07152	+	0.891106i
$839$	49.5149			1.70944			0.854721	−	0.519087i	$-0.173728\pi$
$839$	49.5149			1.70944			0.854721	+	0.519087i	$0.173728\pi$
$840$	−52.5569	−	7.00286i	−1.81339	−	0.241622i
$841$	−1.93415			−0.0666947
$842$	−32.0678	+	26.6684i	−1.10513	+	0.919055i
$843$	−13.1390	−	13.1390i	−0.452532	−	0.452532i
$844$	−13.1180	−	2.43230i	−0.451540	−	0.0837232i
$845$	1.78972	+	1.34049i	0.0615681	+	0.0461143i
$846$	−26.9333	−	2.47585i	−0.925987	−	0.0851215i
$847$	−55.9499	+	55.9499i	−1.92246	+	1.92246i
$848$	−36.6569	+	16.3141i	−1.25880	+	0.560228i
$849$			25.2091i			0.865174i
$850$	−1.87539	−	9.57517i	−0.0643254	−	0.328426i
$851$			13.6045i			0.466357i
$852$	−24.4332	−	35.5563i	−0.837067	−	1.21814i
$853$	3.77420	−	3.77420i	0.129226	−	0.129226i	−0.639535	−	0.768762i	$-0.720873\pi$
$853$	3.77420	−	3.77420i	0.129226	−	0.129226i	0.768762	+	0.639535i	$0.220873\pi$
$854$	−3.78817	+	41.2093i	−0.129629	+	1.41015i
$855$	−12.8784	−	9.64589i	−0.440433	−	0.329882i
$856$	−50.0125	−	14.1111i	−1.70939	−	0.482307i
$857$	5.34477	+	5.34477i	0.182574	+	0.182574i	0.792476	−	0.609903i	$-0.208791\pi$
$857$	5.34477	+	5.34477i	0.182574	+	0.182574i	−0.609903	+	0.792476i	$0.708791\pi$
$858$	13.4995	+	16.2326i	0.460865	+	0.554173i
$859$	−16.2616			−0.554840			−0.277420	−	0.960749i	$-0.589479\pi$
$859$	−16.2616			−0.554840			−0.277420	+	0.960749i	$0.589479\pi$
$860$	−1.49308	+	36.5787i	−0.0509135	+	1.24732i
$861$	−4.51765			−0.153961
$862$	−20.2410	−	24.3390i	−0.689411	−	0.828990i
$863$	0.381854	+	0.381854i	0.0129985	+	0.0129985i	0.713576	−	0.700578i	$-0.247074\pi$
$863$	0.381854	+	0.381854i	0.0129985	+	0.0129985i	−0.700578	+	0.713576i	$0.747074\pi$
$864$	−2.48447	+	5.03562i	−0.0845235	+	0.171315i
$865$	−1.93757	−	13.5010i	−0.0658794	−	0.459049i
$866$	1.66202	−	18.0801i	0.0564777	−	0.614387i
$867$	26.9889	−	26.9889i	0.916591	−	0.916591i
$868$	39.5396	−	27.1704i	1.34206	−	0.922223i
$869$			41.4850i			1.40728i
$870$	−33.0026	−	29.8047i	−1.11889	−	1.01048i
$871$			3.65077i			0.123702i
$872$	−6.47313	+	3.62416i	−0.219208	+	0.122730i
$873$	40.0827	−	40.0827i	1.35659	−	1.35659i
$874$	13.1008	+	1.20429i	0.443140	+	0.0407357i
$875$	33.7332	−	15.3736i	1.14039	−	0.519724i
$876$	3.60811	−	19.4594i	0.121907	−	0.657473i
$877$	−23.3288	−	23.3288i	−0.787756	−	0.787756i	0.193370	−	0.981126i	$-0.438058\pi$
$877$	−23.3288	−	23.3288i	−0.787756	−	0.787756i	−0.981126	+	0.193370i	$0.938058\pi$
$878$	−0.399282	+	0.332054i	−0.0134751	+	0.0112063i
$879$	−42.7136			−1.44069
$880$	28.1095	+	44.7093i	0.947571	+	1.50715i
$881$	−1.58726			−0.0534761			−0.0267380	−	0.999642i	$-0.508512\pi$
$881$	−1.58726			−0.0534761			−0.0267380	+	0.999642i	$0.508512\pi$
$882$	−14.7344	+	12.2535i	−0.496133	+	0.412598i
$883$	6.47019	+	6.47019i	0.217739	+	0.217739i	0.807545	−	0.589806i	$-0.200796\pi$
$883$	6.47019	+	6.47019i	0.217739	+	0.217739i	−0.589806	+	0.807545i	$0.700796\pi$
$884$	0.503124	−	2.71347i	0.0169219	−	0.0912640i
$885$	17.1220	−	2.45722i	0.575548	−	0.0825985i
$886$	30.6989	+	2.82200i	1.03135	+	0.0948068i
$887$	−9.17801	+	9.17801i	−0.308167	+	0.308167i	−0.844198	−	0.536031i	$-0.819923\pi$
$887$	−9.17801	+	9.17801i	−0.308167	+	0.308167i	0.536031	+	0.844198i	$0.319923\pi$
$888$	19.3550	−	10.8365i	0.649513	−	0.363648i
$889$		−	20.2284i		−	0.678439i
$890$	29.7643	−	1.51548i	0.997700	−	0.0507988i
$891$			45.2763i			1.51681i
$892$	9.12788	−	6.27241i	0.305624	−	0.210016i
$893$	8.45474	−	8.45474i	0.282927	−	0.282927i
$894$	2.42331	−	26.3618i	0.0810477	−	0.881670i
$895$	−14.0493	+	18.7575i	−0.469616	+	0.626993i
$896$	−30.0519	−	22.4532i	−1.00396	−	0.750109i
$897$	7.84128	+	7.84128i	0.261813	+	0.261813i
$898$	36.3573	+	43.7183i	1.21326	+	1.45890i
$899$	40.2367			1.34197
$900$	−3.44581	−	33.7505i	−0.114860	−	1.12502i
$901$	−13.8411			−0.461115
$902$	2.87720	+	3.45973i	0.0958004	+	0.115196i
$903$	48.5268	+	48.5268i	1.61487	+	1.61487i
$904$	41.9542	+	11.8374i	1.39538	+	0.393707i
$905$	20.8070	−	27.7798i	0.691648	−	0.923433i
$906$	−2.70195	+	29.3929i	−0.0897663	+	0.976515i
$907$	12.0107	−	12.0107i	0.398810	−	0.398810i	−0.479003	−	0.877813i	$-0.659002\pi$
$907$	12.0107	−	12.0107i	0.398810	−	0.398810i	0.877813	+	0.479003i	$0.159002\pi$
$908$	−0.706479	−	1.02810i	−0.0234453	−	0.0341187i
$909$		−	15.9431i		−	0.528799i
$910$	10.4718	−	0.533180i	0.347136	−	0.0176748i
$911$			14.8483i			0.491947i	0.969277	+	0.245974i	$0.0791076\pi$
$911$			14.8483i			0.491947i	−0.969277	+	0.245974i	$0.920892\pi$
$912$	−8.72189	−	19.5976i	−0.288811	−	0.648943i
$913$	40.9513	−	40.9513i	1.35529	−	1.35529i
$914$	−18.2327	−	1.67604i	−0.603084	−	0.0554386i
$915$	−49.3881	+	7.08782i	−1.63272	+	0.234316i
$916$	12.4794	+	2.31390i	0.412333	+	0.0764535i
$917$	14.9173	+	14.9173i	0.492613	+	0.492613i
$918$	−1.48932	+	1.23856i	−0.0491550	+	0.0408786i
$919$	11.8992			0.392517			0.196259	−	0.980552i	$-0.437121\pi$
$919$	11.8992			0.392517			0.196259	+	0.980552i	$0.437121\pi$
$920$	16.8521	+	22.0333i	0.555598	+	0.726417i
$921$	2.82336			0.0930329
$922$	−31.1436	+	25.8999i	−1.02566	+	0.852967i
$923$	6.03276	+	6.03276i	0.198571	+	0.198571i
$924$	97.3411	+	18.0487i	3.20229	+	0.593759i
$925$	−7.43985	+	13.6082i	−0.244621	+	0.447436i
$926$	40.6690	+	3.73851i	1.33647	+	0.122855i
$927$	2.90067	−	2.90067i	0.0952705	−	0.0952705i
$928$	−10.1077	−	29.7948i	−0.331801	−	0.978061i
$929$		−	48.4616i		−	1.58998i	−0.606626	−	0.794988i	$-0.707477\pi$
$929$		−	48.4616i		−	1.58998i	0.606626	−	0.794988i	$-0.292523\pi$
$930$	42.9272	+	38.7676i	1.40764	+	1.27124i
$931$		−	8.47189i		−	0.277655i
$932$	−10.2549	−	14.9234i	−0.335911	−	0.488833i
$933$	−32.2141	+	32.2141i	−1.05464	+	1.05464i
$934$	3.91049	−	42.5399i	0.127955	−	1.39195i
$935$	2.58803	+	18.0334i	0.0846376	+	0.589756i
$936$	2.60571	−	9.23515i	0.0851704	−	0.301860i
$937$	−9.15329	−	9.15329i	−0.299025	−	0.299025i	0.541607	−	0.840632i	$-0.317816\pi$
$937$	−9.15329	−	9.15329i	−0.299025	−	0.299025i	−0.840632	+	0.541607i	$0.817816\pi$
$938$	10.9461	+	13.1623i	0.357404	+	0.429765i
$939$	69.5196			2.26869
$940$	25.1897	+	1.02820i	0.821598	+	0.0335361i
$941$	2.89295			0.0943076			0.0471538	−	0.998888i	$-0.484985\pi$
$941$	2.89295			0.0943076			0.0471538	+	0.998888i	$0.484985\pi$
$942$	46.7185	+	56.1772i	1.52217	+	1.83035i
$943$	1.67124	+	1.67124i	0.0544232	+	0.0544232i
$944$	11.4247	+	4.38749i	0.371841	+	0.142801i
$945$	−5.89053	−	4.41199i	−0.191619	−	0.143522i
$946$	6.25723	−	68.0687i	0.203440	−	2.21311i
$947$	−26.8015	+	26.8015i	−0.870932	+	0.870932i	−0.992574	−	0.121642i	$-0.961184\pi$
$947$	−26.8015	+	26.8015i	−0.870932	+	0.870932i	0.121642	+	0.992574i	$0.461184\pi$
$948$	29.2814	−	20.1213i	0.951015	−	0.653509i
$949$			3.91382i			0.127048i
$950$	12.4458	+	8.36900i	0.403794	+	0.271526i
$951$		−	32.2740i		−	1.04656i
$952$	−6.32190	−	11.2916i	−0.204894	−	0.365962i
$953$	3.36852	−	3.36852i	0.109117	−	0.109117i	−0.650440	−	0.759557i	$-0.725416\pi$
$953$	3.36852	−	3.36852i	0.109117	−	0.109117i	0.759557	+	0.650440i	$0.225416\pi$
$954$	−47.9244	−	4.40546i	−1.55161	−	0.142632i
$955$	−23.7021	−	17.7528i	−0.766983	−	0.574468i
$956$	−6.08620	+	32.8244i	−0.196842	+	1.06162i
$957$	58.7121	+	58.7121i	1.89789	+	1.89789i
$958$	−4.50567	+	3.74704i	−0.145572	+	0.121061i
$959$	−3.16953			−0.102349
$960$	17.9234	−	41.5257i	0.578475	−	1.34024i
$961$	−21.3366			−0.688278
$962$	−3.37276	+	2.80488i	−0.108742	+	0.0904329i
$963$	−44.0742	−	44.0742i	−1.42027	−	1.42027i
$964$	−1.77680	+	9.58272i	−0.0572269	+	0.308639i
$965$	−6.57675	−	45.8269i	−0.211713	−	1.47522i
$966$	51.7813	+	4.76000i	1.66603	+	0.153150i
$967$	−8.63935	+	8.63935i	−0.277823	+	0.277823i	−0.832239	−	0.554417i	$-0.812941\pi$
$967$	−8.63935	+	8.63935i	−0.277823	+	0.277823i	0.554417	+	0.832239i	$0.312941\pi$
$968$	−32.9732	−	58.8936i	−1.05980	−	1.89291i
$969$		−	7.39980i		−	0.237716i
$970$	−35.4134	+	39.2130i	−1.13705	+	1.25905i
$971$		−	0.617122i		−	0.0198044i	−0.999951	−	0.00990220i	$-0.996848\pi$
$971$		−	0.617122i		−	0.0198044i	0.999951	−	0.00990220i	$-0.00315202\pi$
$972$	36.8659	−	25.3332i	1.18248	−	0.812562i
$973$	−10.4583	+	10.4583i	−0.335278	+	0.335278i
$974$	4.52154	−	49.1872i	0.144879	−	1.57606i
$975$	3.55529	+	12.1316i	0.113861	+	0.388521i
$976$	−32.9543	−	12.6557i	−1.05484	−	0.405098i
$977$	−33.6160	−	33.6160i	−1.07547	−	1.07547i	−0.996909	−	0.0785608i	$-0.974968\pi$
$977$	−33.6160	−	33.6160i	−1.07547	−	1.07547i	−0.0785608	−	0.996909i	$-0.525032\pi$
$978$	−29.5549	−	35.5387i	−0.945063	−	1.13640i
$979$	−55.6470			−1.77849
$980$	13.1355	−	12.1053i	0.419600	−	0.386688i
$981$	−8.89837			−0.284103
$982$	17.4690	+	21.0058i	0.557458	+	0.670322i
$983$	−27.8829	−	27.8829i	−0.889327	−	0.889327i	0.105131	−	0.994458i	$-0.466474\pi$
$983$	−27.8829	−	27.8829i	−0.889327	−	0.889327i	−0.994458	+	0.105131i	$0.966474\pi$
$984$	1.04646	−	3.70887i	0.0333600	−	0.118234i
$985$	54.4798	−	7.81855i	1.73587	−	0.249120i
$986$	0.993520	−	10.8079i	0.0316401	−	0.344194i
$987$	33.4177	−	33.4177i	1.06370	−	1.06370i
$988$	2.40246	+	3.49617i	0.0764324	+	0.111228i
$989$		−	35.9036i		−	1.14167i
$990$	3.22113	+	63.2638i	0.102374	+	2.01065i
$991$		−	1.39819i		−	0.0444150i	−0.999753	−	0.0222075i	$-0.992931\pi$
$991$		−	1.39819i		−	0.0444150i	0.999753	−	0.0222075i	$-0.00706945\pi$
$992$	13.1473	+	38.7546i	0.417426	+	1.23046i
$993$	3.68644	−	3.68644i	0.116986	−	0.116986i
$994$	39.8384	+	3.66215i	1.26360	+	0.116156i
$995$	35.2455	−	47.0570i	1.11736	−	1.49181i
$996$	−48.7671	−	9.04225i	−1.54524	−	0.286515i
$997$	−24.4024	−	24.4024i	−0.772832	−	0.772832i	0.205769	−	0.978601i	$-0.434030\pi$
$997$	−24.4024	−	24.4024i	−0.772832	−	0.772832i	−0.978601	+	0.205769i	$0.934030\pi$
$998$	5.22122	−	4.34211i	0.165275	−	0.137447i
$999$	3.07898			0.0974146

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.o.a.27.9	✓	72
4.3	odd	2	inner	260.2.o.a.27.26	yes	72
5.3	odd	4	inner	260.2.o.a.183.26	yes	72
20.3	even	4	inner	260.2.o.a.183.9	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.o.a.27.9	✓	72	1.1	even	1	trivial
260.2.o.a.27.26	yes	72	4.3	odd	2	inner
260.2.o.a.183.9	yes	72	20.3	even	4	inner
260.2.o.a.183.26	yes	72	5.3	odd	4	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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08734 + 0.904262i) q^{2} +(1.78782 + 1.78782i) q^{3} +(0.364619 - 1.96648i) q^{4} +(-1.34049 + 1.78972i) q^{5} +(-3.56063 - 0.327311i) q^{6} +(2.34459 - 2.34459i) q^{7} +(1.38175 + 2.46795i) q^{8} +3.39260i q^{9} +O(q^{10})\)	\(q+(-1.08734 + 0.904262i) q^{2} +(1.78782 + 1.78782i) q^{3} +(0.364619 - 1.96648i) q^{4} +(-1.34049 + 1.78972i) q^{5} +(-3.56063 - 0.327311i) q^{6} +(2.34459 - 2.34459i) q^{7} +(1.38175 + 2.46795i) q^{8} +3.39260i q^{9} +(-0.160802 - 3.15819i) q^{10} +5.90452i q^{11} +(4.16759 - 2.86384i) q^{12} +(-0.707107 + 0.707107i) q^{13} +(-0.429245 + 4.66950i) q^{14} +(-5.59625 + 0.803133i) q^{15} +(-3.73411 - 1.43404i) q^{16} +(-0.975710 - 0.975710i) q^{17} +(-3.06780 - 3.68891i) q^{18} +2.12103 q^{19} +(3.03068 + 3.28862i) q^{20} +8.38342 q^{21} +(-5.33924 - 6.42023i) q^{22} +(-3.10133 - 3.10133i) q^{23} +(-1.94193 + 6.88257i) q^{24} +(-1.40617 - 4.79820i) q^{25} +(0.129456 - 1.40828i) q^{26} +(-0.701895 + 0.701895i) q^{27} +(-3.75572 - 5.46549i) q^{28} -5.56185i q^{29} +(5.35878 - 5.93375i) q^{30} +7.23441i q^{31} +(5.35699 - 1.81733i) q^{32} +(-10.5562 + 10.5562i) q^{33} +(1.94323 + 0.178631i) q^{34} +(1.05325 + 7.33907i) q^{35} +(6.67149 + 1.23701i) q^{36} +(-2.19333 - 2.19333i) q^{37} +(-2.30628 + 1.91796i) q^{38} -2.52836 q^{39} +(-6.26915 - 0.835322i) q^{40} -0.538879 q^{41} +(-9.11564 + 7.58081i) q^{42} +(5.78842 + 5.78842i) q^{43} +(11.6111 + 2.15290i) q^{44} +(-6.07179 - 4.54775i) q^{45} +(6.17662 + 0.567787i) q^{46} +(3.98616 - 3.98616i) q^{47} +(-4.11211 - 9.23970i) q^{48} -3.99424i q^{49} +(5.86781 + 3.94573i) q^{50} -3.48879i q^{51} +(1.13269 + 1.64834i) q^{52} +(7.09286 - 7.09286i) q^{53} +(0.128502 - 1.39790i) q^{54} +(-10.5674 - 7.91496i) q^{55} +(9.02598 + 2.54669i) q^{56} +(3.79201 + 3.79201i) q^{57} +(5.02937 + 6.04762i) q^{58} -3.05954 q^{59} +(-0.461154 + 11.2978i) q^{60} +8.82521 q^{61} +(-6.54180 - 7.86626i) q^{62} +(7.95427 + 7.95427i) q^{63} +(-4.18153 + 6.82017i) q^{64} +(-0.317650 - 2.21339i) q^{65} +(1.93262 - 21.0238i) q^{66} +(2.58148 - 2.58148i) q^{67} +(-2.27448 + 1.56295i) q^{68} -11.0892i q^{69} +(-7.78168 - 7.02765i) q^{70} -8.53161i q^{71} +(-8.37276 + 4.68772i) q^{72} +(2.76749 - 2.76749i) q^{73} +(4.36825 + 0.401552i) q^{74} +(6.06434 - 11.0923i) q^{75} +(0.773367 - 4.17096i) q^{76} +(13.8437 + 13.8437i) q^{77} +(2.74919 - 2.28630i) q^{78} +7.02598 q^{79} +(7.57205 - 4.76068i) q^{80} +7.66807 q^{81} +(0.585945 - 0.487288i) q^{82} +(-6.93558 - 6.93558i) q^{83} +(3.05676 - 16.4859i) q^{84} +(3.05417 - 0.438313i) q^{85} +(-11.5282 - 1.05974i) q^{86} +(9.94358 - 9.94358i) q^{87} +(-14.5721 + 8.15857i) q^{88} +9.42448i q^{89} +(10.7145 - 0.545537i) q^{90} +3.31576i q^{91} +(-7.22952 + 4.96791i) q^{92} +(-12.9338 + 12.9338i) q^{93} +(-0.729780 + 7.93885i) q^{94} +(-2.84322 + 3.79603i) q^{95} +(12.8264 + 6.32828i) q^{96} +(-11.8148 - 11.8148i) q^{97} +(3.61184 + 4.34310i) q^{98} -20.0317 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} - 12 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 - 12 * q^8	\( 72 q - 8 q^{6} - 12 q^{8} - 8 q^{10} - 8 q^{12} - 8 q^{16} + 28 q^{18} - 16 q^{21} - 8 q^{22} - 20 q^{28} - 32 q^{30} - 40 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 8 q^{40} - 40 q^{42} - 8 q^{46} + 60 q^{48} + 40 q^{50} + 8 q^{52} - 48 q^{53} + 8 q^{56} - 60 q^{58} + 20 q^{60} - 64 q^{61} + 60 q^{62} + 8 q^{66} - 16 q^{68} - 60 q^{70} + 40 q^{72} - 16 q^{73} - 72 q^{76} + 48 q^{77} - 20 q^{80} + 8 q^{81} - 12 q^{82} + 48 q^{85} + 48 q^{86} + 12 q^{88} + 44 q^{90} - 36 q^{92} + 16 q^{93} + 32 q^{96} - 80 q^{97} - 32 q^{98}+O(q^{100}) \) 72 * q - 8 * q^6 - 12 * q^8 - 8 * q^10 - 8 * q^12 - 8 * q^16 + 28 * q^18 - 16 * q^21 - 8 * q^22 - 20 * q^28 - 32 * q^30 - 40 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 8 * q^40 - 40 * q^42 - 8 * q^46 + 60 * q^48 + 40 * q^50 + 8 * q^52 - 48 * q^53 + 8 * q^56 - 60 * q^58 + 20 * q^60 - 64 * q^61 + 60 * q^62 + 8 * q^66 - 16 * q^68 - 60 * q^70 + 40 * q^72 - 16 * q^73 - 72 * q^76 + 48 * q^77 - 20 * q^80 + 8 * q^81 - 12 * q^82 + 48 * q^85 + 48 * q^86 + 12 * q^88 + 44 * q^90 - 36 * q^92 + 16 * q^93 + 32 * q^96 - 80 * q^97 - 32 * q^98

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