LMFDB - Embedded newform 425.2.p.a.16.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(16,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("425.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.p (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$42$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			16.17
Character	$\chi$	$=$	425.16
Dual form			425.2.p.a.186.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.484961 - 0.352344i) q^{2} +(-0.406117 + 0.131955i) q^{3} +(-0.506994 - 1.56037i) q^{4} +(1.58222 + 1.58005i) q^{5} +(0.243445 + 0.0790999i) q^{6} +1.28394i q^{7} +(-0.674391 + 2.07556i) q^{8} +(-2.27953 + 1.65618i) q^{9} +(-0.210594 - 1.32375i) q^{10} +(-1.22857 + 1.69099i) q^{11} +(0.411798 + 0.566791i) q^{12} +(-1.13980 + 0.828112i) q^{13} +(0.452388 - 0.622658i) q^{14} +(-0.851065 - 0.432903i) q^{15} +(-1.59629 + 1.15977i) q^{16} +(3.68812 - 1.84330i) q^{17} +1.68903 q^{18} +(-1.63955 + 5.04601i) q^{19} +(1.66328 - 3.26993i) q^{20} +(-0.169422 - 0.521428i) q^{21} +(1.19162 - 0.387181i) q^{22} +(1.00437 - 1.38240i) q^{23} -0.931911i q^{24} +(0.00686804 + 5.00000i) q^{25} +0.844538 q^{26} +(1.46020 - 2.00979i) q^{27} +(2.00341 - 0.650947i) q^{28} +(-6.37622 + 2.07176i) q^{29} +(0.260202 + 0.509809i) q^{30} +(5.60602 + 1.82151i) q^{31} +5.54753 q^{32} +(0.275810 - 0.848856i) q^{33} +(-2.43807 - 0.405559i) q^{34} +(-2.02869 + 2.03147i) q^{35} +(3.73995 + 2.71723i) q^{36} +(5.76316 + 7.93230i) q^{37} +(2.57305 - 1.86943i) q^{38} +(0.353618 - 0.486713i) q^{39} +(-4.34654 + 2.21843i) q^{40} +(3.01287 + 4.14686i) q^{41} +(-0.101559 + 0.312567i) q^{42} -9.46065 q^{43} +(3.26144 + 1.05971i) q^{44} +(-6.22358 - 0.981337i) q^{45} +(-0.974160 + 0.316524i) q^{46} +(-1.98465 - 6.10811i) q^{47} +(0.495242 - 0.681642i) q^{48} +5.35151 q^{49} +(1.75839 - 2.42722i) q^{50} +(-1.25457 + 1.23526i) q^{51} +(1.87003 + 1.35866i) q^{52} +(-0.388660 - 1.19617i) q^{53} +(-1.41628 + 0.460176i) q^{54} +(-4.61573 + 0.734310i) q^{55} +(-2.66489 - 0.865875i) q^{56} -2.26562i q^{57} +(3.82219 + 1.24190i) q^{58} +(0.686944 - 0.499094i) q^{59} +(-0.244003 + 1.54745i) q^{60} +(-1.13552 + 1.56291i) q^{61} +(-2.07690 - 2.85861i) q^{62} +(-2.12642 - 2.92677i) q^{63} +(0.502243 + 0.364901i) q^{64} +(-3.11188 - 0.490683i) q^{65} +(-0.432847 + 0.314482i) q^{66} +(1.69284 - 5.21003i) q^{67} +(-4.74608 - 4.82028i) q^{68} +(-0.225477 + 0.693947i) q^{69} +(1.69961 - 0.270389i) q^{70} +(-7.27731 + 2.36454i) q^{71} +(-1.90020 - 5.84823i) q^{72} +(4.87278 - 6.70681i) q^{73} -5.87747i q^{74} +(-0.662566 - 2.02968i) q^{75} +8.70487 q^{76} +(-2.17112 - 1.57741i) q^{77} +(-0.342982 + 0.111441i) q^{78} +(-5.42721 + 1.76341i) q^{79} +(-4.35818 - 0.687201i) q^{80} +(2.28430 - 7.03036i) q^{81} -3.07263i q^{82} +(1.29766 - 3.99378i) q^{83} +(-0.727723 + 0.528722i) q^{84} +(8.74795 + 2.91090i) q^{85} +(4.58804 + 3.33341i) q^{86} +(2.31611 - 1.68275i) q^{87} +(-2.68121 - 3.69037i) q^{88} +(-6.66491 - 4.84234i) q^{89} +(2.67242 + 2.66875i) q^{90} +(-1.06324 - 1.46343i) q^{91} +(-2.66626 - 0.866319i) q^{92} -2.51706 q^{93} +(-1.18968 + 3.66147i) q^{94} +(-10.5671 + 5.39335i) q^{95} +(-2.25295 + 0.732027i) q^{96} +(6.68210 - 2.17115i) q^{97} +(-2.59527 - 1.88557i) q^{98} -5.88940i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9} - 18 q^{13} - 10 q^{15} - 28 q^{16} + 2 q^{17} - 60 q^{18} - 8 q^{19} + 32 q^{21} + 6 q^{25} + 52 q^{26} - 54 q^{30} + 44 q^{32} - 24 q^{33} + 26 q^{35} + 34 q^{36}+ \cdots - 36 q^{98}+O(q^{100}) $ 168 * q - 8 * q^2 - 44 * q^4 - 4 * q^8 + 28 * q^9 - 18 * q^13 - 10 * q^15 - 28 * q^16 + 2 * q^17 - 60 * q^18 - 8 * q^19 + 32 * q^21 + 6 * q^25 + 52 * q^26 - 54 * q^30 + 44 * q^32 - 24 * q^33 + 26 * q^35 + 34 * q^36 - 18 * q^38 + 80 * q^42 - 8 * q^43 - 40 * q^47 - 84 * q^49 - 82 * q^50 - 36 * q^51 - 30 * q^52 - 42 * q^53 - 18 * q^55 - 18 * q^59 + 28 * q^60 - 16 * q^64 - 140 * q^66 - 62 * q^67 + 144 * q^68 + 44 * q^69 + 4 * q^70 - 6 * q^72 + 72 * q^76 + 48 * q^77 - 28 * q^81 - 14 * q^83 + 24 * q^84 + 62 * q^85 + 82 * q^86 + 48 * q^87 + 90 * q^89 - 224 * q^93 + 26 * q^94 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.484961	−	0.352344i	−0.342919	−	0.249145i	0.402973	−	0.915212i	$-0.367977\pi$
$2$	−0.484961	−	0.352344i	−0.342919	−	0.249145i	−0.745892	+	0.666067i	$0.767977\pi$
$3$	−0.406117	+	0.131955i	−0.234472	+	0.0761845i	−0.423896	−	0.905711i	$-0.639338\pi$
$3$	−0.406117	+	0.131955i	−0.234472	+	0.0761845i	0.189424	+	0.981895i	$0.439338\pi$
$4$	−0.506994	−	1.56037i	−0.253497	−	0.780183i
$5$	1.58222	+	1.58005i	0.707592	+	0.706621i
$5$	1.58222	+	1.58005i	0.707592	+	0.706621i
$6$	0.243445	+	0.0790999i	0.0993858	+	0.0322924i
$7$			1.28394i			0.485282i	0.970116	+	0.242641i	$0.0780137\pi$
$7$			1.28394i			0.485282i	−0.970116	+	0.242641i	$0.921986\pi$
$8$	−0.674391	+	2.07556i	−0.238433	+	0.733822i
$9$	−2.27953	+	1.65618i	−0.759844	+	0.552059i
$10$	−0.210594	−	1.32375i	−0.0665956	−	0.418607i
$11$	−1.22857	+	1.69099i	−0.370429	+	0.509852i	−0.953017	−	0.302915i	$-0.902040\pi$
$11$	−1.22857	+	1.69099i	−0.370429	+	0.509852i	0.582588	+	0.812767i	$0.302040\pi$
$12$	0.411798	+	0.566791i	0.118876	+	0.163618i
$13$	−1.13980	+	0.828112i	−0.316123	+	0.229677i	−0.734519	−	0.678588i	$-0.762592\pi$
$13$	−1.13980	+	0.828112i	−0.316123	+	0.229677i	0.418396	+	0.908265i	$0.362592\pi$
$14$	0.452388	−	0.622658i	0.120906	−	0.166412i
$15$	−0.851065	−	0.432903i	−0.219744	−	0.111775i
$16$	−1.59629	+	1.15977i	−0.399072	+	0.289943i
$17$	3.68812	−	1.84330i	0.894501	−	0.447067i
$17$	3.68812	−	1.84330i	0.894501	−	0.447067i
$18$	1.68903			0.398108
$19$	−1.63955	+	5.04601i	−0.376138	+	1.15763i	0.566569	+	0.824014i	$0.308270\pi$
$19$	−1.63955	+	5.04601i	−0.376138	+	1.15763i	−0.942708	+	0.333620i	$0.891730\pi$
$20$	1.66328	−	3.26993i	0.371921	−	0.731178i
$21$	−0.169422	−	0.521428i	−0.0369710	−	0.113785i
$22$	1.19162	−	0.387181i	0.254054	−	0.0825472i
$23$	1.00437	−	1.38240i	0.209426	−	0.288250i	−0.691363	−	0.722508i	$-0.742989\pi$
$23$	1.00437	−	1.38240i	0.209426	−	0.288250i	0.900789	+	0.434258i	$0.142989\pi$
$24$		−	0.931911i		−	0.190226i
$25$	0.00686804	+	5.00000i	0.00137361	+	0.999999i
$26$	0.844538			0.165628
$27$	1.46020	−	2.00979i	0.281015	−	0.386784i
$28$	2.00341	−	0.650947i	0.378609	−	0.123017i
$29$	−6.37622	+	2.07176i	−1.18403	+	0.384716i	−0.833864	−	0.551970i	$-0.813876\pi$
$29$	−6.37622	+	2.07176i	−1.18403	+	0.384716i	−0.350170	+	0.936686i	$0.613876\pi$
$30$	0.260202	+	0.509809i	0.0475061	+	0.0930780i
$31$	5.60602	+	1.82151i	1.00687	+	0.327152i	0.765608	−	0.643308i	$-0.222438\pi$
$31$	5.60602	+	1.82151i	1.00687	+	0.327152i	0.241263	+	0.970460i	$0.422438\pi$
$32$	5.54753			0.980674
$33$	0.275810	−	0.848856i	0.0480124	−	0.147767i
$34$	−2.43807	−	0.405559i	−0.418126	−	0.0695529i
$35$	−2.02869	+	2.03147i	−0.342910	+	0.343382i
$36$	3.73995	+	2.71723i	0.623325	+	0.452872i
$37$	5.76316	+	7.93230i	0.947457	+	1.30406i	0.952648	+	0.304076i	$0.0983477\pi$
$37$	5.76316	+	7.93230i	0.947457	+	1.30406i	−0.00519083	+	0.999987i	$0.501652\pi$
$38$	2.57305	−	1.86943i	0.417404	−	0.303262i
$39$	0.353618	−	0.486713i	0.0566242	−	0.0779365i
$40$	−4.34654	+	2.21843i	−0.687248	+	0.350765i
$41$	3.01287	+	4.14686i	0.470532	+	0.647631i	0.976651	−	0.214832i	$-0.0689204\pi$
$41$	3.01287	+	4.14686i	0.470532	+	0.647631i	−0.506119	+	0.862464i	$0.668920\pi$
$42$	−0.101559	+	0.312567i	−0.0156709	+	0.0482301i
$43$	−9.46065			−1.44274			−0.721368	−	0.692552i	$-0.756486\pi$
$43$	−9.46065			−1.44274			−0.721368	+	0.692552i	$0.756486\pi$
$44$	3.26144	+	1.05971i	0.491681	+	0.159757i
$45$	−6.22358	−	0.981337i	−0.927756	−	0.146289i
$46$	−0.974160	+	0.316524i	−0.143632	+	0.0466689i
$47$	−1.98465	−	6.10811i	−0.289490	−	0.890960i	−0.985017	−	0.172459i	$-0.944829\pi$
$47$	−1.98465	−	6.10811i	−0.289490	−	0.890960i	0.695526	−	0.718501i	$-0.255171\pi$
$48$	0.495242	−	0.681642i	0.0714820	−	0.0983865i
$49$	5.35151			0.764501
$50$	1.75839	−	2.42722i	0.248674	−	0.343261i
$51$	−1.25457	+	1.23526i	−0.175676	+	0.172972i
$52$	1.87003	+	1.35866i	0.259327	+	0.188412i
$53$	−0.388660	−	1.19617i	−0.0533865	−	0.164307i	0.920808	−	0.390015i	$-0.127530\pi$
$53$	−0.388660	−	1.19617i	−0.0533865	−	0.164307i	−0.974195	+	0.225708i	$0.927530\pi$
$54$	−1.41628	+	0.460176i	−0.192731	+	0.0626221i
$55$	−4.61573	+	0.734310i	−0.622385	+	0.0990143i
$56$	−2.66489	−	0.865875i	−0.356111	−	0.115707i
$57$		−	2.26562i		−	0.300089i
$58$	3.82219	+	1.24190i	0.501878	+	0.163070i
$59$	0.686944	−	0.499094i	0.0894324	−	0.0649765i	−0.542170	−	0.840269i	$-0.682397\pi$
$59$	0.686944	−	0.499094i	0.0894324	−	0.0649765i	0.631603	+	0.775292i	$0.282397\pi$
$60$	−0.244003	+	1.54745i	−0.0315007	+	0.199775i
$61$	−1.13552	+	1.56291i	−0.145388	+	0.200110i	−0.875500	−	0.483218i	$-0.839468\pi$
$61$	−1.13552	+	1.56291i	−0.145388	+	0.200110i	0.730112	+	0.683328i	$0.239468\pi$
$62$	−2.07690	−	2.85861i	−0.263767	−	0.363044i
$63$	−2.12642	−	2.92677i	−0.267904	−	0.368739i
$64$	0.502243	+	0.364901i	0.0627804	+	0.0456126i
$65$	−3.11188	−	0.490683i	−0.385981	−	0.0608617i
$66$	−0.432847	+	0.314482i	−0.0532797	+	0.0387100i
$67$	1.69284	−	5.21003i	0.206813	−	0.636506i	−0.792821	−	0.609455i	$-0.791388\pi$
$67$	1.69284	−	5.21003i	0.206813	−	0.636506i	0.999634	−	0.0270511i	$-0.00861168\pi$
$68$	−4.74608	−	4.82028i	−0.575547	−	0.584544i
$69$	−0.225477	+	0.693947i	−0.0271443	+	0.0835414i
$70$	1.69961	−	0.270389i	0.203142	−	0.0323176i
$71$	−7.27731	+	2.36454i	−0.863658	+	0.280619i	−0.707155	−	0.707058i	$-0.750022\pi$
$71$	−7.27731	+	2.36454i	−0.863658	+	0.280619i	−0.156502	+	0.987678i	$0.550022\pi$
$72$	−1.90020	−	5.84823i	−0.223941	−	0.689220i
$73$	4.87278	−	6.70681i	0.570316	−	0.784973i	−0.422276	−	0.906467i	$-0.638769\pi$
$73$	4.87278	−	6.70681i	0.570316	−	0.784973i	0.992592	+	0.121494i	$0.0387687\pi$
$74$		−	5.87747i		−	0.683242i
$75$	−0.662566	−	2.02968i	−0.0765065	−	0.234367i
$76$	8.70487			0.998517
$77$	−2.17112	−	1.57741i	−0.247422	−	0.179763i
$78$	−0.342982	+	0.111441i	−0.0388350	+	0.0126183i
$79$	−5.42721	+	1.76341i	−0.610609	+	0.198399i	−0.597966	−	0.801521i	$-0.704024\pi$
$79$	−5.42721	+	1.76341i	−0.610609	+	0.198399i	−0.0126426	+	0.999920i	$0.504024\pi$
$80$	−4.35818	−	0.687201i	−0.487260	−	0.0768314i
$81$	2.28430	−	7.03036i	0.253811	−	0.781151i
$82$		−	3.07263i		−	0.339316i
$83$	1.29766	−	3.99378i	0.142436	−	0.438374i	−0.854236	−	0.519885i	$-0.825975\pi$
$83$	1.29766	−	3.99378i	0.142436	−	0.438374i	0.996672	+	0.0815111i	$0.0259746\pi$
$84$	−0.727723	+	0.528722i	−0.0794011	+	0.0576883i
$85$	8.74795	+	2.91090i	0.948848	+	0.315732i
$86$	4.58804	+	3.33341i	0.494741	+	0.359451i
$87$	2.31611	−	1.68275i	0.248313	−	0.180410i
$88$	−2.68121	−	3.69037i	−0.285818	−	0.393395i
$89$	−6.66491	−	4.84234i	−0.706479	−	0.513287i	0.175557	−	0.984469i	$-0.443827\pi$
$89$	−6.66491	−	4.84234i	−0.706479	−	0.513287i	−0.882036	+	0.471182i	$0.843827\pi$
$90$	2.67242	+	2.66875i	0.281698	+	0.281311i
$91$	−1.06324	−	1.46343i	−0.111458	−	0.153409i
$92$	−2.66626	−	0.866319i	−0.277976	−	0.0903200i
$93$	−2.51706			−0.261007
$94$	−1.18968	+	3.66147i	−0.122707	+	0.377652i
$95$	−10.5671	+	5.39335i	−1.08416	+	0.553346i
$96$	−2.25295	+	0.732027i	−0.229940	+	0.0747122i
$97$	6.68210	−	2.17115i	0.678464	−	0.220446i	0.0505414	−	0.998722i	$-0.483905\pi$
$97$	6.68210	−	2.17115i	0.678464	−	0.220446i	0.627923	+	0.778276i	$0.283905\pi$
$98$	−2.59527	−	1.88557i	−0.262162	−	0.190472i
$99$		−	5.88940i		−	0.591907i
$100$	7.79834	−	2.54568i	0.779834	−	0.254568i
$101$	6.85446			0.682044			0.341022	−	0.940055i	$-0.389227\pi$
$101$	6.85446			0.682044			0.341022	+	0.940055i	$0.389227\pi$
$102$	1.04366	−	0.157012i	0.103338	−	0.0155465i
$103$	−2.69357	−	8.28996i	−0.265405	−	0.816834i	−0.991600	−	0.129344i	$-0.958713\pi$
$103$	−2.69357	−	8.28996i	−0.265405	−	0.816834i	0.726194	−	0.687489i	$-0.241287\pi$
$104$	−0.950129	−	2.92420i	−0.0931678	−	0.286741i
$105$	0.555820	−	1.09271i	0.0542425	−	0.106638i
$106$	−0.232980	+	0.717039i	−0.0226290	+	0.0696449i
$107$			9.62269i			0.930261i	0.885242	+	0.465130i	$0.153993\pi$
$107$			9.62269i			0.930261i	−0.885242	+	0.465130i	$0.846007\pi$
$108$	−3.87632	−	1.25949i	−0.372999	−	0.121195i
$109$	−4.17136	−	5.74138i	−0.399544	−	0.549925i	0.561086	−	0.827758i	$-0.310384\pi$
$109$	−4.17136	−	5.74138i	−0.399544	−	0.549925i	−0.960629	+	0.277833i	$0.910384\pi$
$110$	2.49718	+	1.27022i	0.238096	+	0.121110i
$111$	−3.38723	−	2.46096i	−0.321501	−	0.233584i
$112$	−1.48907	−	2.04953i	−0.140704	−	0.193662i
$113$	5.22816	+	7.19594i	0.491824	+	0.676937i	0.980723	−	0.195403i	$-0.0626015\pi$
$113$	5.22816	+	7.19594i	0.491824	+	0.676937i	−0.488899	+	0.872340i	$0.662601\pi$
$114$	−0.798278	+	1.09874i	−0.0747656	+	0.102906i
$115$	3.77340	−	0.600305i	0.351871	−	0.0559787i
$116$	6.46541	+	8.89887i	0.600298	+	0.826239i
$117$	1.22671	−	3.77542i	0.113409	−	0.349037i
$118$	−0.508993			−0.0468566
$119$	2.36668	+	4.73531i	0.216953	+	0.434085i
$120$	1.47247	−	1.47449i	0.134417	−	0.134602i
$121$	2.04914	+	6.30661i	0.186286	+	0.573329i
$122$	1.10136	−	0.357855i	0.0997128	−	0.0323987i
$123$	−1.77078	−	1.28655i	−0.159666	−	0.116004i
$124$		−	9.67094i		−	0.868476i
$125$	−7.88939	+	7.92197i	−0.705648	+	0.708562i
$126$			2.16860i			0.193194i
$127$	4.61858	+	3.35559i	0.409833	+	0.297761i	0.773534	−	0.633755i	$-0.218487\pi$
$127$	4.61858	+	3.35559i	0.409833	+	0.297761i	−0.363701	+	0.931516i	$0.618487\pi$
$128$	−3.54356	−	10.9060i	−0.313209	−	0.963959i
$129$	3.84213	−	1.24838i	0.338281	−	0.109914i
$130$	1.33625	+	1.33441i	0.117197	+	0.117036i
$131$	−18.4074	−	5.98094i	−1.60827	−	0.522557i	−0.639133	−	0.769096i	$-0.720707\pi$
$131$	−18.4074	−	5.98094i	−1.60827	−	0.522557i	−0.969133	+	0.246539i	$0.920707\pi$
$132$	−1.46436			−0.127456
$133$	−6.47875	−	2.10507i	−0.561779	−	0.182533i
$134$	−2.65668	+	1.93019i	−0.229503	+	0.166743i
$135$	5.48593	−	0.872749i	0.472154	−	0.0751143i
$136$	1.33866	+	8.89804i	0.114789	+	0.763000i
$137$	2.44928	−	1.77951i	0.209257	−	0.152034i	−0.478221	−	0.878240i	$-0.658718\pi$
$137$	2.44928	−	1.77951i	0.209257	−	0.152034i	0.687477	+	0.726206i	$0.258718\pi$
$138$	0.353856	−	0.257091i	0.0301222	−	0.0218851i
$139$	−3.13723	+	4.31803i	−0.266096	+	0.366250i	−0.921067	−	0.389404i	$-0.872681\pi$
$139$	−3.13723	+	4.31803i	−0.266096	+	0.366250i	0.654971	+	0.755654i	$0.272681\pi$
$140$	4.19838	+	2.13555i	0.354827	+	0.180487i
$141$	1.61200	+	2.21872i	0.135755	+	0.186850i
$142$	4.36234	+	1.41741i	0.366080	+	0.118946i
$143$		−	2.94478i		−	0.246255i
$144$	1.71800	−	5.28747i	0.143167	−	0.440623i
$145$	−13.3621	−	6.79677i	−1.10966	−	0.564441i
$146$	−4.72622	+	1.53564i	−0.391144	+	0.127091i
$147$	−2.17334	+	0.706161i	−0.179254	+	0.0582432i
$148$	9.45542	−	13.0143i	0.777230	−	1.06977i
$149$	−6.79725			−0.556852			−0.278426	−	0.960458i	$-0.589813\pi$
$149$	−6.79725			−0.556852			−0.278426	+	0.960458i	$0.589813\pi$
$150$	−0.393827	+	1.21776i	−0.0321559	+	0.0994301i
$151$	10.0322			0.816410			0.408205	−	0.912890i	$-0.366155\pi$
$151$	10.0322			0.816410			0.408205	+	0.912890i	$0.366155\pi$
$152$	−9.36762	−	6.80597i	−0.759814	−	0.552037i
$153$	−5.35435	+	10.3100i	−0.432874	+	0.833518i
$154$	0.497115	+	1.52996i	0.0400587	+	0.123288i
$155$	5.99191	+	11.7398i	0.481282	+	0.942967i
$156$	−0.938733	−	0.305013i	−0.0751588	−	0.0244206i
$157$	−0.798735			−0.0637460			−0.0318730	−	0.999492i	$-0.510147\pi$
$157$	−0.798735			−0.0637460			−0.0318730	+	0.999492i	$0.510147\pi$
$158$	3.25331	+	1.05706i	0.258819	+	0.0840955i
$159$	0.315683	+	0.434500i	0.0250353	+	0.0344581i
$160$	8.77744	+	8.76539i	0.693917	+	0.692965i
$161$	1.77491	+	1.28955i	0.139882	+	0.101631i
$162$	−3.58491	+	2.60459i	−0.281657	+	0.204636i
$163$	0.0365633	+	0.0503250i	0.00286386	+	0.00394176i	0.810447	−	0.585813i	$-0.199225\pi$
$163$	0.0365633	+	0.0503250i	0.00286386	+	0.00394176i	−0.807583	+	0.589754i	$0.799225\pi$
$164$	4.94312	−	6.80362i	0.385993	−	0.531274i
$165$	1.77763	−	0.907286i	0.138388	−	0.0706322i
$166$	−2.03650	+	1.47960i	−0.158063	+	0.114839i
$167$	−2.69098	−	0.874351i	−0.208234	−	0.0676593i	0.203043	−	0.979170i	$-0.434917\pi$
$167$	−2.69098	−	0.874351i	−0.208234	−	0.0676593i	−0.411277	+	0.911511i	$0.634917\pi$
$168$	1.19651			0.0923131
$169$	−3.40385	+	10.4760i	−0.261835	+	0.805844i
$170$	−3.21677	−	4.49397i	−0.246715	−	0.344671i
$171$	−4.61968	−	14.2179i	−0.353276	−	1.08727i
$172$	4.79649	+	14.7621i	0.365729	+	1.12560i
$173$	10.3186	−	14.2024i	0.784512	−	1.07979i	−0.210258	−	0.977646i	$-0.567430\pi$
$173$	10.3186	−	14.2024i	0.784512	−	1.07979i	0.994770	−	0.102142i	$-0.0325696\pi$
$174$	−1.71613			−0.130100
$175$	−6.41967	+	0.00881812i	−0.485281	+	0.000666587i
$176$		−	4.12417i		−	0.310871i
$177$	−0.213121	+	0.293336i	−0.0160192	+	0.0220485i
$178$	1.52605	+	4.69669i	0.114382	+	0.352032i
$179$	−7.64958	−	23.5430i	−0.571756	−	1.75968i	−0.646968	−	0.762517i	$-0.723963\pi$
$179$	−7.64958	−	23.5430i	−0.571756	−	1.75968i	0.0752117	−	0.997168i	$-0.476037\pi$
$180$	1.62407	+	10.2086i	0.121051	+	0.760904i
$181$	25.2703	+	8.21082i	1.87833	+	0.610306i	0.987880	+	0.155220i	$0.0496086\pi$
$181$	25.2703	+	8.21082i	1.87833	+	0.610306i	0.890448	+	0.455086i	$0.150391\pi$
$182$			1.08433i			0.0803761i
$183$	0.254920	−	0.784562i	0.0188442	−	0.0579965i
$184$	2.19191	+	3.01691i	0.161590	+	0.222410i
$185$	−3.41485	+	21.6568i	−0.251065	+	1.59224i
$186$	1.22067	+	0.886872i	0.0895042	+	0.0650286i
$187$	−1.41413	+	8.50120i	−0.103411	+	0.621669i
$188$	−8.52469	+	6.19355i	−0.621727	+	0.451711i
$189$	2.58044	+	1.87480i	0.187699	+	0.136372i
$190$	7.02494	+	1.10770i	0.509643	+	0.0803607i
$191$	−11.5843	+	8.41646i	−0.838208	+	0.608994i	−0.921870	−	0.387500i	$-0.873339\pi$
$191$	−11.5843	+	8.41646i	−0.838208	+	0.608994i	0.0836613	+	0.996494i	$0.473339\pi$
$192$	−0.252120	−	0.0819188i	−0.0181952	−	0.00591198i
$193$			17.2918i			1.24469i	0.782744	+	0.622344i	$0.213819\pi$
$193$			17.2918i			1.24469i	−0.782744	+	0.622344i	$0.786181\pi$
$194$	−4.00555	−	1.30148i	−0.287581	−	0.0934409i
$195$	1.32854	−	0.211355i	0.0951384	−	0.0151354i
$196$	−2.71318	−	8.35032i	−0.193799	−	0.596451i
$197$	17.8873	−	5.81193i	1.27442	−	0.414083i	0.407806	−	0.913069i	$-0.366294\pi$
$197$	17.8873	−	5.81193i	1.27442	−	0.414083i	0.866610	+	0.498986i	$0.166294\pi$
$198$	−2.07510	+	2.85613i	−0.147471	+	0.202976i
$199$			13.0129i			0.922462i	0.887280	+	0.461231i	$0.152592\pi$
$199$			13.0129i			0.922462i	−0.887280	+	0.461231i	$0.847408\pi$
$200$	−10.3824	−	3.35770i	−0.734149	−	0.237425i
$201$			2.33926i			0.164999i
$202$	−3.32414	−	2.41513i	−0.233886	−	0.169928i
$203$	−2.66000	−	8.18665i	−0.186696	−	0.574590i
$204$	2.56353	+	1.33133i	0.179483	+	0.0932114i
$205$	−1.78522	+	11.3218i	−0.124685	+	0.790747i
$206$	−1.61464	+	4.96937i	−0.112498	+	0.346232i
$207$			4.81463i			0.334640i
$208$	0.859026	−	2.64381i	0.0595628	−	0.183315i
$209$	−6.51843	−	8.97186i	−0.450890	−	0.620596i
$210$	−0.654562	+	0.334082i	−0.0451691	+	0.0230539i
$211$	14.0920	−	19.3960i	0.970133	−	1.33527i	0.0281540	−	0.999604i	$-0.491037\pi$
$211$	14.0920	−	19.3960i	0.970133	−	1.33527i	0.941979	−	0.335671i	$-0.108963\pi$
$212$	−1.66942	+	1.21290i	−0.114656	+	0.0833026i
$213$	2.64343	−	1.92056i	0.181125	−	0.131595i
$214$	3.39050	−	4.66663i	0.231770	−	0.319004i
$215$	−14.9689	−	14.9483i	−1.02087	−	1.01947i
$216$	3.18670	+	4.38612i	0.216828	+	0.298438i
$217$	−2.33870	+	7.19777i	−0.158761	+	0.488616i
$218$			4.25410i			0.288124i
$219$	−1.09392	+	3.36674i	−0.0739203	+	0.227503i
$220$	3.48594	+	6.82994i	0.235022	+	0.460474i
$221$	−2.67725	+	5.15517i	−0.180092	+	0.346775i
$222$	0.775564	+	2.38694i	0.0520525	+	0.160201i
$223$	18.8989	+	13.7309i	1.26556	+	0.919487i	0.999017	−	0.0443349i	$-0.0141169\pi$
$223$	18.8989	+	13.7309i	1.26556	+	0.919487i	0.266548	+	0.963822i	$0.414117\pi$
$224$			7.12267i			0.475903i
$225$	−8.29653	−	11.3863i	−0.553102	−	0.759085i
$226$		−	5.33186i		−	0.354670i
$227$	1.96489	−	2.70444i	0.130414	−	0.179500i	−0.738816	−	0.673907i	$-0.764615\pi$
$227$	1.96489	−	2.70444i	0.130414	−	0.179500i	0.869230	+	0.494407i	$0.164615\pi$
$228$	−3.53520	+	1.14865i	−0.234124	+	0.0760715i
$229$	9.00106	+	27.7024i	0.594807	+	1.83063i	0.555684	+	0.831393i	$0.312456\pi$
$229$	9.00106	+	27.7024i	0.594807	+	1.83063i	0.0391226	+	0.999234i	$0.487544\pi$
$230$	−2.04146	−	1.03841i	−0.134610	−	0.0684709i
$231$	1.08988	+	0.354122i	0.0717086	+	0.0232995i
$232$		−	14.6314i		−	0.960600i
$233$	19.8220	+	6.44056i	1.29858	+	0.421935i	0.875088	−	0.483964i	$-0.160803\pi$
$233$	19.8220	+	6.44056i	1.29858	+	0.421935i	0.423494	+	0.905899i	$0.360803\pi$
$234$	−1.92515	+	1.39871i	−0.125851	+	0.0914362i
$235$	6.51099	−	12.8003i	0.424730	−	0.834996i
$236$	−1.12705	−	0.818846i	−0.0733644	−	0.0533024i
$237$	1.97139	−	1.43230i	0.128056	−	0.0930379i
$238$	0.520712	−	3.13033i	0.0337528	−	0.202909i
$239$	13.5993	+	9.88044i	0.879663	+	0.639113i	0.933162	−	0.359455i	$-0.117037\pi$
$239$	13.5993	+	9.88044i	0.879663	+	0.639113i	−0.0534993	+	0.998568i	$0.517037\pi$
$240$	1.86061	−	0.296002i	0.120102	−	0.0191069i
$241$	5.57107	+	7.66792i	0.358864	+	0.493934i	0.949832	−	0.312761i	$-0.101254\pi$
$241$	5.57107	+	7.66792i	0.358864	+	0.493934i	−0.590967	+	0.806695i	$0.701254\pi$
$242$	1.22835	−	3.78046i	0.0789611	−	0.243017i
$243$			10.6093i			0.680586i
$244$	3.01441	+	0.979442i	0.192978	+	0.0627023i
$245$	8.46729	+	8.45567i	0.540955	+	0.540213i
$246$	0.405451	+	1.24785i	0.0258506	+	0.0795600i
$247$	−2.30991	−	7.10917i	−0.146976	−	0.452346i
$248$	−7.56130	+	10.4072i	−0.480143	+	0.660861i
$249$			1.79318i			0.113638i
$250$	6.61730	−	1.06206i	0.418515	−	0.0671705i
$251$	−6.03874			−0.381162			−0.190581	−	0.981671i	$-0.561037\pi$
$251$	−6.03874			−0.381162			−0.190581	+	0.981671i	$0.561037\pi$
$252$	−3.48875	+	4.80186i	−0.219771	+	0.302489i
$253$	1.10367	+	3.39676i	0.0693873	+	0.213552i
$254$	−1.05750	−	3.25466i	−0.0663537	−	0.204216i
$255$	−3.93680	−	0.0278285i	−0.246532	−	0.00174269i
$256$	−1.74049	+	5.35666i	−0.108780	+	0.334792i
$257$	22.7235			1.41745			0.708727	−	0.705483i	$-0.249270\pi$
$257$	22.7235			1.41745			0.708727	+	0.705483i	$0.249270\pi$
$258$	−2.30314	−	0.748337i	−0.143387	−	0.0465894i
$259$	−10.1846	+	7.39952i	−0.632838	+	0.459784i
$260$	0.812059	+	5.10445i	0.0503617	+	0.316564i
$261$	11.1036	−	15.2828i	0.687295	−	0.945981i
$262$	6.81953	+	9.38628i	0.421312	+	0.579886i
$263$	19.3258	−	14.0410i	1.19168	−	0.865806i	0.198239	−	0.980154i	$-0.436478\pi$
$263$	19.3258	−	14.0410i	1.19168	−	0.865806i	0.993441	+	0.114348i	$0.0364779\pi$
$264$	1.57585	+	1.14492i	0.0969869	+	0.0704651i
$265$	1.27507	−	2.50672i	0.0783268	−	0.153986i
$266$	2.40023	+	3.30363i	0.147167	+	0.202559i
$267$	3.34571	+	1.08709i	0.204754	+	0.0665286i
$268$	−8.98781			−0.549018
$269$	−5.73108	−	1.86214i	−0.349430	−	0.113537i	0.129043	−	0.991639i	$-0.458809\pi$
$269$	−5.73108	−	1.86214i	−0.349430	−	0.113537i	−0.478473	+	0.878102i	$0.658809\pi$
$270$	−2.96797	−	1.50969i	−0.180625	−	0.0918768i
$271$	−8.68762	−	26.7377i	−0.527735	−	1.62420i	−0.758843	−	0.651274i	$-0.774235\pi$
$271$	−8.68762	−	26.7377i	−0.527735	−	1.62420i	0.231107	−	0.972928i	$-0.425765\pi$
$272$	−3.74949	+	7.21982i	−0.227346	+	0.437766i
$273$	0.624908	+	0.454023i	0.0378212	+	0.0274787i
$274$	−1.81481			−0.109636
$275$	−8.46337	−	6.13125i	−0.510360	−	0.369728i
$276$	1.19713			0.0720586
$277$	−12.7386	+	17.5332i	−0.765391	+	1.05347i	0.231356	+	0.972869i	$0.425684\pi$
$277$	−12.7386	+	17.5332i	−0.765391	+	1.05347i	−0.996746	+	0.0806010i	$0.974316\pi$
$278$	3.04287	−	0.988687i	0.182499	−	0.0592975i
$279$	−15.7958	+	5.13238i	−0.945672	+	0.307268i
$280$	−2.84832	−	5.58067i	−0.170220	−	0.333509i
$281$	2.44645	−	7.52939i	0.145943	−	0.449166i	−0.851188	−	0.524860i	$-0.824117\pi$
$281$	2.44645	−	7.52939i	0.145943	−	0.449166i	0.997131	+	0.0756949i	$0.0241175\pi$
$282$		−	1.64397i		−	0.0978971i
$283$	20.2802	+	6.58942i	1.20553	+	0.391701i	0.841793	−	0.539801i	$-0.181500\pi$
$283$	20.2802	+	6.58942i	1.20553	+	0.391701i	0.363738	+	0.931501i	$0.381500\pi$
$284$	7.37910	+	10.1565i	0.437869	+	0.602675i
$285$	3.57980	−	3.58472i	0.212049	−	0.212340i
$286$	−1.03758	+	1.42810i	−0.0613533	+	0.0844455i
$287$	−5.32431	+	3.86833i	−0.314284	+	0.228341i
$288$	−12.6458	+	9.18769i	−0.745159	+	0.541390i
$289$	10.2045	−	13.5966i	0.600263	−	0.799803i
$290$	4.08528	+	8.00423i	0.239896	+	0.470024i
$291$	−2.42722	+	1.76348i	−0.142286	+	0.103377i
$292$	−12.9356	−	4.20302i	−0.756996	−	0.245963i
$293$	−10.2566			−0.599195			−0.299597	−	0.954066i	$-0.596852\pi$
$293$	−10.2566			−0.599195			−0.299597	+	0.954066i	$0.596852\pi$
$294$	1.30280	+	0.423304i	0.0759806	+	0.0246876i
$295$	1.87549	+	0.295729i	0.109195	+	0.0172180i
$296$	−20.3506	+	6.61232i	−1.18286	+	0.384333i
$297$	1.60457	+	4.93835i	0.0931065	+	0.286552i
$298$	3.29640	+	2.39497i	0.190955	+	0.138737i
$299$			2.40739i			0.139223i
$300$	−2.83112	+	2.06288i	−0.163455	+	0.119100i
$301$		−	12.1469i		−	0.700133i
$302$	−4.86523	−	3.53479i	−0.279962	−	0.203405i
$303$	−2.78371	+	0.904483i	−0.159920	+	0.0519612i
$304$	−3.23503	−	9.95639i	−0.185541	−	0.571038i
$305$	−4.26612	+	0.678692i	−0.244278	+	0.0388618i
$306$	6.22934	−	3.11339i	0.356108	−	0.177981i
$307$	−2.59295			−0.147988			−0.0739938	−	0.997259i	$-0.523575\pi$
$307$	−2.59295			−0.147988			−0.0739938	+	0.997259i	$0.523575\pi$
$308$	−1.36059	+	4.18748i	−0.0775270	+	0.238604i
$309$	2.18781	+	3.01126i	0.124460	+	0.171305i
$310$	1.23063	−	7.80457i	0.0698950	−	0.443270i
$311$	5.80001	−	7.98303i	0.328888	−	0.452676i	−0.612267	−	0.790651i	$-0.709742\pi$
$311$	5.80001	−	7.98303i	0.328888	−	0.452676i	0.941155	+	0.337975i	$0.109742\pi$
$312$	0.771727	+	1.06219i	0.0436905	+	0.0601348i
$313$	−11.3679	−	15.6466i	−0.642554	−	0.884400i	0.356194	−	0.934412i	$-0.384074\pi$
$313$	−11.3679	−	15.6466i	−0.642554	−	0.884400i	−0.998749	+	0.0500117i	$0.984074\pi$
$314$	0.387355	+	0.281430i	0.0218597	+	0.0158820i
$315$	1.25997	−	7.99067i	0.0709914	−	0.450223i
$316$	5.50313	+	7.57440i	0.309575	+	0.426093i
$317$	−12.9756	−	4.21604i	−0.728784	−	0.236796i	−0.0789568	−	0.996878i	$-0.525159\pi$
$317$	−12.9756	−	4.21604i	−0.728784	−	0.236796i	−0.649828	+	0.760082i	$0.725159\pi$
$318$		−	0.321945i		−	0.0180538i
$319$	4.33034	−	13.3274i	0.242452	−	0.746192i
$320$	0.218099	+	1.37093i	0.0121921	+	0.0766371i
$321$	−1.26977	−	3.90794i	−0.0708715	−	0.218120i
$322$	−0.406396	−	1.25076i	−0.0226476	−	0.0697020i
$323$	3.25448	+	21.6325i	0.181084	+	1.20366i
$324$	−12.1281			−0.673782
$325$	−4.14839	−	5.69330i	−0.230111	−	0.315808i
$326$		−	0.0372885i		−	0.00206522i
$327$	2.45167	+	1.78124i	0.135578	+	0.0985028i
$328$	−10.6389	+	3.45680i	−0.587437	+	0.190870i
$329$	7.84242	−	2.54816i	0.432367	−	0.140485i
$330$	−1.18176	−	0.186340i	−0.0650536	−	0.0102577i
$331$	−1.76571	+	5.43430i	−0.0970523	+	0.298696i	−0.987783	−	0.155835i	$-0.950193\pi$
$331$	−1.76571	+	5.43430i	−0.0970523	+	0.298696i	0.890731	+	0.454531i	$0.150193\pi$
$332$	−6.88967			−0.378120
$333$	−26.2746	−	8.53713i	−1.43984	−	0.467832i
$334$	0.996944	+	1.37218i	0.0545504	+	0.0750821i
$335$	10.9106	−	5.56865i	0.596108	−	0.304248i
$336$	0.875184	+	0.635858i	0.0477452	+	0.0346889i
$337$	−14.4019	−	19.8225i	−0.784521	−	1.07980i	−0.994769	−	0.102152i	$-0.967427\pi$
$337$	−14.4019	−	19.8225i	−0.784521	−	1.07980i	0.210248	−	0.977648i	$-0.432573\pi$
$338$	5.34188	−	3.88111i	0.290560	−	0.211104i
$339$	−3.07279	−	2.23251i	−0.166891	−	0.121253i
$340$	0.106922	−	15.1258i	0.00579864	−	0.820313i
$341$	−9.96756	+	7.24185i	−0.539774	+	0.392168i
$342$	−2.76924	+	8.52285i	−0.149744	+	0.460863i
$343$			15.8585i			0.856281i
$344$	6.38018	−	19.6362i	0.343996	−	1.05871i
$345$	−1.45323	+	0.741715i	−0.0782392	+	0.0399326i
$346$	−10.0083	+	3.25188i	−0.538048	+	0.174822i
$347$	−13.9522	+	4.53336i	−0.748996	+	0.243364i	−0.658549	−	0.752538i	$-0.728830\pi$
$347$	−13.9522	+	4.53336i	−0.748996	+	0.243364i	−0.0904469	+	0.995901i	$0.528830\pi$
$348$	−3.79997	−	2.76084i	−0.203700	−	0.147996i
$349$	−5.23006			−0.279959			−0.139979	−	0.990154i	$-0.544704\pi$
$349$	−5.23006			−0.279959			−0.139979	+	0.990154i	$0.544704\pi$
$350$	3.11639	+	2.25766i	0.166578	+	0.120677i
$351$			3.49996i			0.186814i
$352$	−6.81555	+	9.38080i	−0.363270	+	0.499998i
$353$	−4.43583	−	13.6521i	−0.236095	−	0.726627i	−0.996974	−	0.0777329i	$-0.975232\pi$
$353$	−4.43583	−	13.6521i	−0.236095	−	0.726627i	0.760879	−	0.648894i	$-0.224768\pi$
$354$	0.206711	−	0.0671645i	0.0109866	−	0.00356975i
$355$	−15.2504	−	7.75730i	−0.809409	−	0.411715i
$356$	−4.17676	+	12.8547i	−0.221368	+	0.681300i
$357$	−1.58600	−	1.61079i	−0.0839400	−	0.0852522i
$358$	−4.58549	+	14.1127i	−0.242351	+	0.745879i
$359$	20.7091	−	15.0460i	1.09298	−	0.794099i	0.113083	−	0.993585i	$-0.463927\pi$
$359$	20.7091	−	15.0460i	1.09298	−	0.794099i	0.979901	+	0.199486i	$0.0639273\pi$
$360$	6.23395	−	12.2556i	0.328558	−	0.645928i
$361$	−7.40278	−	5.37844i	−0.389620	−	0.283076i
$362$	−9.36207	−	12.8858i	−0.492059	−	0.677262i
$363$	−1.66438	−	2.29083i	−0.0873575	−	0.120237i
$364$	−1.74443	+	2.40100i	−0.0914328	+	0.125846i
$365$	18.3070	−	2.91243i	0.958230	−	0.152443i
$366$	−0.400062	+	0.290662i	−0.0209116	+	0.0151931i
$367$	3.58646	+	1.16531i	0.187212	+	0.0608288i	0.401122	−	0.916024i	$-0.368620\pi$
$367$	3.58646	+	1.16531i	0.187212	+	0.0608288i	−0.213911	+	0.976853i	$0.568620\pi$
$368$			3.37154i			0.175754i
$369$	−13.7359	−	4.46306i	−0.715062	−	0.232338i
$370$	9.28671	−	9.29948i	0.482793	−	0.483457i
$371$	1.53581	−	0.499014i	0.0797352	−	0.0259075i
$372$	1.27613	+	3.92753i	0.0661644	+	0.203633i
$373$	19.1656	+	13.9246i	0.992356	+	0.720989i	0.960436	−	0.278502i	$-0.0898379\pi$
$373$	19.1656	+	13.9246i	0.992356	+	0.720989i	0.0319199	+	0.999490i	$0.489838\pi$
$374$	3.68115	−	3.62449i	0.190348	−	0.187418i
$375$	2.15867	−	4.25829i	0.111473	−	0.219897i
$376$	14.0162			0.722831
$377$	5.55196	−	7.64161i	0.285940	−	0.393563i
$378$	−0.590837	−	1.81841i	−0.0303894	−	0.0935288i
$379$	8.80862	−	2.86209i	0.452468	−	0.147016i	−0.0739125	−	0.997265i	$-0.523549\pi$
$379$	8.80862	−	2.86209i	0.452468	−	0.147016i	0.526381	+	0.850249i	$0.323549\pi$
$380$	13.7731	+	13.7541i	0.706543	+	0.705573i
$381$	−2.31847	−	0.753317i	−0.118779	−	0.0385936i
$382$	8.58341			0.439165
$383$	0.139346	−	0.428864i	0.00712026	−	0.0219139i	−0.947433	−	0.319953i	$-0.896333\pi$
$383$	0.139346	−	0.428864i	0.00712026	−	0.0219139i	0.954554	+	0.298040i	$0.0963327\pi$
$384$	2.87820	+	3.96150i	0.146878	+	0.202160i
$385$	−0.942806	−	5.92630i	−0.0480499	−	0.302032i
$386$	6.09265	−	8.38582i	0.310108	−	0.426827i
$387$	21.5658	−	15.6685i	1.09625	−	0.796475i
$388$	−6.77557	−	9.32577i	−0.343977	−	0.473444i
$389$	7.42943	+	5.39780i	0.376687	+	0.273679i	0.759978	−	0.649948i	$-0.225209\pi$
$389$	7.42943	+	5.39780i	0.376687	+	0.273679i	−0.383291	+	0.923627i	$0.625209\pi$
$390$	−0.718757	−	0.365603i	−0.0363957	−	0.0185130i
$391$	1.15606	−	6.94981i	0.0584646	−	0.351467i
$392$	−3.60901	+	11.1074i	−0.182283	+	0.561008i
$393$	8.26480			0.416904
$394$	−10.7224	−	3.48393i	−0.540188	−	0.175518i
$395$	−11.3733	−	5.78517i	−0.572255	−	0.291084i
$396$	−9.18962	+	2.98589i	−0.461796	+	0.150047i
$397$	11.5545	−	3.75429i	0.579904	−	0.188422i	−0.00435337	−	0.999991i	$-0.501386\pi$
$397$	11.5545	−	3.75429i	0.579904	−	0.188422i	0.584258	+	0.811568i	$0.301386\pi$
$398$	4.58503	−	6.31075i	0.229827	−	0.316330i
$399$	2.90891			0.145628
$400$	−5.80981	−	7.97347i	−0.290491	−	0.398673i
$401$		−	35.4769i		−	1.77163i	−0.464038	−	0.885815i	$-0.653600\pi$
$401$		−	35.4769i		−	1.77163i	0.464038	−	0.885815i	$-0.346400\pi$
$402$	0.824225	−	1.13445i	0.0411086	−	0.0565812i
$403$	−7.89815	+	2.56626i	−0.393435	+	0.127835i
$404$	−3.47517	−	10.6955i	−0.172896	−	0.532119i
$405$	14.7226	−	7.51429i	0.731573	−	0.373388i
$406$	−1.59452	+	4.90744i	−0.0791349	+	0.243552i
$407$	−20.4939			−1.01584
$408$	−1.71780	−	3.43700i	−0.0850436	−	0.170157i
$409$	14.9082	−	10.8314i	0.737163	−	0.535580i	−0.154658	−	0.987968i	$-0.549428\pi$
$409$	14.9082	−	10.8314i	0.737163	−	0.535580i	0.891821	+	0.452388i	$0.149428\pi$
$410$	4.85492	−	4.86160i	0.239768	−	0.240097i
$411$	−0.759881	+	1.04589i	−0.0374821	+	0.0515897i
$412$	−11.5697	+	8.40591i	−0.570001	+	0.414130i
$413$	0.640804	+	0.881991i	0.0315319	+	0.0433999i
$414$	1.69641	−	2.33491i	0.0833740	−	0.114754i
$415$	8.36357	−	4.26869i	0.410551	−	0.209542i
$416$	−6.32307	+	4.59398i	−0.310014	+	0.225238i
$417$	0.704296	−	2.16760i	0.0344895	−	0.106148i
$418$			6.64773i			0.325151i
$419$	27.8681	+	9.05488i	1.36144	+	0.442360i	0.896525	−	0.442993i	$-0.146083\pi$
$419$	27.8681	+	9.05488i	1.36144	+	0.442360i	0.464919	+	0.885353i	$0.346083\pi$
$420$	−1.98683	−	0.313284i	−0.0969473	−	0.0152867i
$421$	−6.40352	−	19.7080i	−0.312088	−	0.960509i	−0.976936	−	0.213530i	$-0.931504\pi$
$421$	−6.40352	−	19.7080i	−0.312088	−	0.960509i	0.664848	−	0.746979i	$-0.268496\pi$
$422$	−13.6681	+	4.44104i	−0.665354	+	0.216187i
$423$	14.6402	+	10.6367i	0.711830	+	0.517175i
$424$	2.74484			0.133301
$425$	9.24184	+	18.4279i	0.448295	+	0.893886i
$426$	−1.95866			−0.0948972
$427$	−2.00667	−	1.45793i	−0.0971097	−	0.0705544i
$428$	15.0149	−	4.87865i	0.725774	−	0.235818i
$429$	0.388580	+	1.19593i	0.0187608	+	0.0577399i
$430$	1.99235	+	12.5235i	0.0960798	+	0.603939i
$431$	−9.57710	−	3.11179i	−0.461312	−	0.149889i	0.0691350	−	0.997607i	$-0.477976\pi$
$431$	−9.57710	−	3.11179i	−0.461312	−	0.149889i	−0.530447	+	0.847718i	$0.677976\pi$
$432$			4.90170i			0.235833i
$433$	−11.9766	+	36.8603i	−0.575561	+	1.77139i	0.0587022	+	0.998276i	$0.481304\pi$
$433$	−11.9766	+	36.8603i	−0.575561	+	1.77139i	−0.634263	+	0.773118i	$0.718696\pi$
$434$	3.67027	−	2.66661i	0.176179	−	0.128001i
$435$	6.32345	+	0.997084i	0.303186	+	0.0478065i
$436$	−6.84381	+	9.41970i	−0.327759	+	0.451122i
$437$	5.32888	+	7.33457i	0.254915	+	0.350860i
$438$	1.71676	−	1.24730i	0.0820300	−	0.0595983i
$439$	−23.0636	+	31.7443i	−1.10077	+	1.51507i	−0.266401	+	0.963862i	$0.585834\pi$
$439$	−23.0636	+	31.7443i	−1.10077	+	1.51507i	−0.834365	+	0.551212i	$0.814166\pi$
$440$	1.58870	−	10.0755i	0.0757384	−	0.480328i
$441$	−12.1989	+	8.86305i	−0.580902	+	0.422050i
$442$	3.11476	−	1.55674i	0.148154	−	0.0740466i
$443$	30.4433			1.44640			0.723202	−	0.690637i	$-0.242670\pi$
$443$	30.4433			1.44640			0.723202	+	0.690637i	$0.242670\pi$
$444$	−2.12270	+	6.53301i	−0.100739	+	0.310043i
$445$	−2.89423	−	18.1926i	−0.137200	−	0.862411i
$446$	−4.32723	−	13.3179i	−0.204900	−	0.630619i
$447$	2.76048	−	0.896934i	0.130566	−	0.0424235i
$448$	−0.468509	+	0.644848i	−0.0221350	+	0.0304662i
$449$			26.2185i			1.23733i	0.785656	+	0.618663i	$0.212325\pi$
$449$			26.2185i			1.23733i	−0.785656	+	0.618663i	$0.787675\pi$
$450$	0.0116003	+	8.44513i	0.000546844	+	0.398107i
$451$	−10.7138			−0.504495
$452$	8.57766	−	11.8061i	0.403459	−	0.555314i
$453$	−4.07425	+	1.32381i	−0.191425	+	0.0621978i
$454$	−1.90579	+	0.619228i	−0.0894430	+	0.0290618i
$455$	0.630005	−	3.99545i	0.0295351	−	0.187310i
$456$	4.70244	+	1.52791i	0.220212	+	0.0715511i
$457$	0.978163			0.0457565			0.0228783	−	0.999738i	$-0.492717\pi$
$457$	0.978163			0.0457565			0.0228783	+	0.999738i	$0.492717\pi$
$458$	5.39564	−	16.6061i	0.252121	−	0.775950i
$459$	1.68073	−	10.1039i	0.0784499	−	0.471611i
$460$	−2.84979	−	5.58354i	−0.132872	−	0.260334i
$461$	14.1109	+	10.2522i	0.657209	+	0.477490i	0.865719	−	0.500530i	$-0.166861\pi$
$461$	14.1109	+	10.2522i	0.657209	+	0.477490i	−0.208510	+	0.978020i	$0.566861\pi$
$462$	−0.403774	−	0.555747i	−0.0187853	−	0.0258557i
$463$	18.0422	−	13.1085i	0.838494	−	0.609201i	−0.0834558	−	0.996511i	$-0.526596\pi$
$463$	18.0422	−	13.1085i	0.838494	−	0.609201i	0.921949	+	0.387310i	$0.126596\pi$
$464$	7.77551	−	10.7021i	0.360969	−	0.496831i
$465$	−3.98255	−	3.97708i	−0.184686	−	0.184433i
$466$	−7.34359	−	10.1076i	−0.340185	−	0.468225i
$467$	−2.42925	+	7.47647i	−0.112412	+	0.345970i	−0.991399	−	0.130877i	$-0.958221\pi$
$467$	−2.42925	+	7.47647i	−0.112412	+	0.345970i	0.878986	+	0.476847i	$0.158221\pi$
$468$	−6.51297			−0.301062
$469$	6.68934	+	2.17350i	0.308885	+	0.100363i
$470$	−7.66767	+	3.91351i	−0.353683	+	0.180517i
$471$	0.324380	−	0.105397i	0.0149466	−	0.00485646i
$472$	0.572632	+	1.76238i	0.0263575	+	0.0811201i
$473$	11.6231	−	15.9978i	0.534431	−	0.735581i
$474$	−1.46071			−0.0670927
$475$	−25.2413	−	8.16308i	−1.15815	−	0.374548i
$476$	6.18892	−	6.09366i	0.283669	−	0.279303i
$477$	2.86704	+	2.08302i	0.131273	+	0.0953751i
$478$	−3.11379	−	9.58325i	−0.142421	−	0.438328i
$479$	4.30745	−	1.39958i	0.196813	−	0.0639483i	−0.208952	−	0.977926i	$-0.567005\pi$
$479$	4.30745	−	1.39958i	0.196813	−	0.0639483i	0.405765	+	0.913978i	$0.367005\pi$
$480$	−4.72131	−	2.40154i	−0.215497	−	0.109615i
$481$	−13.1377	−	4.26869i	−0.599027	−	0.194636i
$482$		−	5.68158i		−	0.258789i
$483$	−0.890984	−	0.289498i	−0.0405412	−	0.0131726i
$484$	8.80173	−	6.39483i	0.400079	−	0.290674i
$485$	14.0031	+	7.12283i	0.635848	+	0.323431i
$486$	3.73812	−	5.14509i	0.169565	−	0.233386i
$487$	−24.9662	−	34.3631i	−1.13133	−	1.55714i	−0.785522	−	0.618833i	$-0.787606\pi$
$487$	−24.9662	−	34.3631i	−1.13133	−	1.55714i	−0.345806	−	0.938306i	$-0.612394\pi$
$488$	−2.47813	−	3.41085i	−0.112180	−	0.154402i
$489$	−0.0214896	−	0.0156131i	−0.000971795	−	0.000706050i
$490$	−1.12699	−	7.08407i	−0.0509124	−	0.320026i
$491$	−34.8256	+	25.3023i	−1.57166	+	1.14188i	−0.646109	+	0.763245i	$0.723605\pi$
$491$	−34.8256	+	25.3023i	−1.57166	+	1.14188i	−0.925548	+	0.378630i	$0.876395\pi$
$492$	−1.10971	+	3.41534i	−0.0500296	+	0.153975i
$493$	−19.6974	+	19.3942i	−0.887125	+	0.873471i
$494$	−1.38466	+	4.26155i	−0.0622989	+	0.191736i
$495$	9.30556	−	9.31835i	0.418254	−	0.418829i
$496$	−11.0614	+	3.59405i	−0.496669	+	0.161378i
$497$	−3.03592	−	9.34360i	−0.136180	−	0.419118i
$498$	0.631816	−	0.869619i	0.0283123	−	0.0389686i
$499$		−	1.73339i		−	0.0775972i	−0.999247	−	0.0387986i	$-0.987647\pi$
$499$		−	1.73339i		−	0.0775972i	0.999247	−	0.0387986i	$-0.0123531\pi$
$500$	16.3610	+	8.29395i	0.731688	+	0.370917i
$501$	1.20823			0.0539796
$502$	2.92855	+	2.12772i	0.130708	+	0.0949646i
$503$	−26.5762	+	8.63512i	−1.18497	+	0.385021i	−0.834212	−	0.551444i	$-0.814077\pi$
$503$	−26.5762	+	8.63512i	−1.18497	+	0.385021i	−0.350761	+	0.936465i	$0.614077\pi$
$504$	7.50874	−	2.43974i	0.334466	−	0.108675i
$505$	10.8453	+	10.8304i	0.482609	+	0.481947i
$506$	0.661590	−	2.03617i	0.0294113	−	0.0905186i
$507$		−	4.70363i		−	0.208895i
$508$	2.89437	−	8.90794i	0.128417	−	0.395226i
$509$	10.8041	−	7.84960i	0.478881	−	0.347928i	−0.322011	−	0.946736i	$-0.604359\pi$
$509$	10.8041	−	7.84960i	0.478881	−	0.347928i	0.800892	+	0.598808i	$0.204359\pi$
$510$	1.89939	+	1.40061i	0.0841063	+	0.0620199i
$511$	8.61111	+	6.25634i	0.380933	+	0.276764i
$512$	−15.8229	+	11.4960i	−0.699278	+	0.508055i
$513$	7.74736	+	10.6633i	0.342054	+	0.470797i
$514$	−11.0200	−	8.00651i	−0.486072	−	0.353152i
$515$	8.83673	−	17.3726i	0.389393	−	0.765526i
$516$	−3.89587	−	5.36221i	−0.171506	−	0.236058i
$517$	12.7670	+	4.14826i	0.561493	+	0.182440i
$518$	7.54629			0.331565
$519$	−2.31649	+	7.12944i	−0.101683	+	0.312947i
$520$	3.11707	−	6.12799i	0.136692	−	0.268730i
$521$	−10.1243	+	3.28959i	−0.443555	+	0.144120i	−0.522275	−	0.852777i	$-0.674917\pi$
$521$	−10.1243	+	3.28959i	−0.443555	+	0.144120i	0.0787203	+	0.996897i	$0.474917\pi$
$522$	−10.7696	+	3.49926i	−0.471373	+	0.153158i
$523$	−3.75430	−	2.72766i	−0.164164	−	0.119272i	0.502670	−	0.864478i	$-0.332351\pi$
$523$	−3.75430	−	2.72766i	−0.164164	−	0.119272i	−0.666834	+	0.745206i	$0.732351\pi$
$524$			31.7547i			1.38721i
$525$	2.60597	−	0.850692i	0.113734	−	0.0371272i
$526$	−14.3195			−0.624361
$527$	24.0333	−	3.61566i	1.04691	−	0.157501i
$528$	0.544206	+	1.67490i	0.0236835	+	0.0728905i
$529$	6.20513	+	19.0974i	0.269788	+	0.830323i
$530$	−1.50159	+	0.766395i	−0.0652247	+	0.0332901i
$531$	−0.739322	+	2.27540i	−0.0320839	+	0.0987440i
$532$			11.1765i			0.484562i
$533$	−6.86814	−	2.23159i	−0.297492	−	0.0966611i
$534$	−1.23951	−	1.70603i	−0.0536387	−	0.0738273i
$535$	−15.2044	+	15.2253i	−0.657342	+	0.658245i
$536$	9.67210	+	7.02719i	0.417771	+	0.303529i
$537$	6.21325	+	8.55180i	0.268121	+	0.369038i
$538$	2.12323	+	2.92238i	0.0915390	+	0.125993i
$539$	−6.57473	+	9.04934i	−0.283194	+	0.389783i
$540$	−4.14314	−	8.11759i	−0.178293	−	0.349326i
$541$	19.4594	+	26.7836i	0.836625	+	1.15152i	0.986654	+	0.162834i	$0.0520635\pi$
$541$	19.4594	+	26.7836i	0.836625	+	1.15152i	−0.150029	+	0.988682i	$0.547937\pi$
$542$	−5.20774	+	16.0278i	−0.223692	+	0.688452i
$543$	−11.3462			−0.486911
$544$	20.4600	−	10.2258i	0.877213	−	0.438427i
$545$	2.47166	−	15.6751i	0.105874	−	0.671449i
$546$	−0.143084	−	0.440366i	−0.00612341	−	0.0188459i
$547$	−40.3698	+	13.1169i	−1.72609	+	0.560840i	−0.992875	−	0.119160i	$-0.961980\pi$
$547$	−40.3698	+	13.1169i	−1.72609	+	0.560840i	−0.733212	+	0.680000i	$0.761980\pi$
$548$	−4.01846	−	2.91958i	−0.171660	−	0.124718i
$549$		−	5.44332i		−	0.232315i
$550$	1.94409	+	5.95544i	0.0828961	+	0.253941i
$551$		−	35.5712i		−	1.51538i
$552$	−1.28827	−	0.935984i	−0.0548325	−	0.0398381i
$553$	−2.26410	−	6.96819i	−0.0962794	−	0.296318i
$554$	12.3555	−	4.01454i	0.524934	−	0.170561i
$555$	−1.47090	−	9.24579i	−0.0624362	−	0.392462i
$556$	8.32826	+	2.70602i	0.353197	+	0.114761i
$557$	−41.2279			−1.74688			−0.873441	−	0.486931i	$-0.838116\pi$
$557$	−41.2279			−1.74688			−0.873441	+	0.486931i	$0.838116\pi$
$558$	9.46873	+	3.07658i	0.400843	+	0.130242i
$559$	10.7832	−	7.83448i	0.456082	−	0.331363i
$560$	0.882321	−	5.59563i	0.0372849	−	0.236458i
$561$	−0.547478	−	3.63909i	−0.0231146	−	0.153642i
$562$	−3.83937	+	2.78946i	−0.161954	+	0.117666i
$563$	−16.8479	+	12.2407i	−0.710054	+	0.515885i	−0.883191	−	0.469013i	$-0.844610\pi$
$563$	−16.8479	+	12.2407i	−0.710054	+	0.515885i	0.173137	+	0.984898i	$0.444610\pi$
$564$	2.64475	−	3.64019i	0.111364	−	0.153280i
$565$	−3.09785	+	19.6464i	−0.130327	+	0.826528i
$566$	−7.51333	−	10.3412i	−0.315809	−	0.434674i
$567$	9.02653	+	2.93290i	0.379079	+	0.123170i
$568$		−	16.6991i		−	0.700681i
$569$	−0.410542	+	1.26352i	−0.0172108	+	0.0529694i	−0.959293	−	0.282412i	$-0.908865\pi$
$569$	−0.410542	+	1.26352i	−0.0172108	+	0.0529694i	0.942082	+	0.335382i	$0.108865\pi$
$570$	−2.99912	+	0.477125i	−0.125619	+	0.0199846i
$571$	−5.38997	+	1.75131i	−0.225563	+	0.0732900i	−0.419618	−	0.907701i	$-0.637836\pi$
$571$	−5.38997	+	1.75131i	−0.225563	+	0.0732900i	0.194055	+	0.980991i	$0.437836\pi$
$572$	−4.59494	+	1.49299i	−0.192124	+	0.0624249i
$573$	3.59397	−	4.94668i	0.150140	−	0.206650i
$574$	3.94506			0.164664
$575$	6.91888	+	5.01235i	0.288537	+	0.209030i
$576$	−1.74922			−0.0728842
$577$	14.0341	+	10.1964i	0.584247	+	0.424481i	0.840253	−	0.542195i	$-0.182407\pi$
$577$	14.0341	+	10.1964i	0.584247	+	0.424481i	−0.256005	+	0.966675i	$0.582407\pi$
$578$	−9.73947	+	2.99835i	−0.405108	+	0.124715i
$579$	−2.28174	−	7.02248i	−0.0948259	−	0.291844i
$580$	−3.83096	+	24.2957i	−0.159072	+	1.00882i
$581$	5.12776	+	1.66611i	0.212735	+	0.0691218i
$582$	1.79846			0.0745485
$583$	2.50021	+	0.812367i	0.103548	+	0.0336448i
$584$	10.6342	+	14.6368i	0.440048	+	0.605675i
$585$	7.90629	−	4.03530i	0.326885	−	0.166839i
$586$	4.97403	+	3.61384i	0.205475	+	0.149286i
$587$	6.04435	−	4.39148i	0.249477	−	0.181256i	−0.456018	−	0.889971i	$-0.650725\pi$
$587$	6.04435	−	4.39148i	0.249477	−	0.181256i	0.705495	+	0.708715i	$0.250725\pi$
$588$	2.20374	+	3.03319i	0.0908807	+	0.125087i
$589$	−18.3827	+	25.3016i	−0.757445	+	1.04253i
$590$	−0.805342	−	0.804236i	−0.0331554	−	0.0331099i
$591$	−6.49742	+	4.72065i	−0.267268	+	0.194182i
$592$	−18.3993	−	5.97830i	−0.756207	−	0.245707i
$593$	−27.1161			−1.11352			−0.556762	−	0.830672i	$-0.687957\pi$
$593$	−27.1161			−1.11352			−0.556762	+	0.830672i	$0.687957\pi$
$594$	0.961849	−	2.96027i	0.0394651	−	0.121461i
$595$	−3.73741	+	11.2318i	−0.153219	+	0.460459i
$596$	3.44616	+	10.6062i	0.141160	+	0.434447i
$597$	−1.71713	−	5.28477i	−0.0702773	−	0.216291i
$598$	0.848229	−	1.16749i	0.0346867	−	0.0477421i
$599$	47.3421			1.93435			0.967173	−	0.254120i	$-0.0817859\pi$
$599$	47.3421			1.93435			0.967173	+	0.254120i	$0.0817859\pi$
$600$	4.65955	−	0.00640040i	0.190225	−	0.000261295i
$601$			0.700391i			0.0285695i	0.999898	+	0.0142848i	$0.00454714\pi$
$601$			0.700391i			0.0285695i	−0.999898	+	0.0142848i	$0.995453\pi$
$602$	−4.27988	+	5.89075i	−0.174435	+	0.240089i
$603$	4.76984	+	14.6801i	0.194243	+	0.597818i
$604$	−5.08627	−	15.6539i	−0.206957	−	0.636949i
$605$	−6.72258	+	13.2162i	−0.273312	+	0.537316i
$606$	1.66868	+	0.542187i	0.0677855	+	0.0220248i
$607$			4.68665i			0.190225i	0.995467	+	0.0951126i	$0.0303211\pi$
$607$			4.68665i			0.190225i	−0.995467	+	0.0951126i	$0.969679\pi$
$608$	−9.09544	+	27.9929i	−0.368869	+	1.13526i
$609$	2.16055	+	2.97374i	0.0875498	+	0.120502i
$610$	2.30804	+	1.17401i	0.0934496	+	0.0475341i
$611$	7.32030	+	5.31851i	0.296148	+	0.215164i
$612$	18.8021	+	3.12762i	0.760029	+	0.126427i
$613$	10.0241	−	7.28297i	0.404871	−	0.294156i	−0.366651	−	0.930359i	$-0.619496\pi$
$613$	10.0241	−	7.28297i	0.404871	−	0.294156i	0.771522	+	0.636202i	$0.219496\pi$
$614$	1.25748	+	0.913612i	0.0507478	+	0.0368704i
$615$	−0.768960	−	4.83353i	−0.0310075	−	0.194907i
$616$	4.73820	−	3.44250i	0.190907	−	0.138702i
$617$	36.0308	+	11.7071i	1.45054	+	0.471310i	0.925167	−	0.379560i	$-0.123925\pi$
$617$	36.0308	+	11.7071i	1.45054	+	0.471310i	0.525376	+	0.850870i	$0.323925\pi$
$618$		−	2.23121i		−	0.0897523i
$619$	6.85882	+	2.22857i	0.275679	+	0.0895736i	0.443594	−	0.896228i	$-0.353703\pi$
$619$	6.85882	+	2.22857i	0.275679	+	0.0895736i	−0.167915	+	0.985802i	$0.553703\pi$
$620$	15.2806	−	15.3016i	0.613683	−	0.614527i
$621$	−1.31175	−	4.03715i	−0.0526387	−	0.162005i
$622$	−5.62555	+	1.82785i	−0.225564	+	0.0732902i
$623$	6.21725	−	8.55731i	0.249089	−	0.342841i
$624$			1.18705i			0.0475200i
$625$	−24.9999	+	0.0686803i	−0.999996	+	0.00274721i
$626$			11.5934i			0.463367i
$627$	3.83113	+	2.78348i	0.153001	+	0.111162i
$628$	0.404954	+	1.24632i	0.0161594	+	0.0497336i
$629$	35.8769	+	18.6320i	1.43050	+	0.742908i
$630$	−3.42651	+	3.43122i	−0.136515	+	0.136703i
$631$	7.59070	−	23.3618i	0.302181	−	0.930017i	−0.678533	−	0.734570i	$-0.737384\pi$
$631$	7.59070	−	23.3618i	0.302181	−	0.930017i	0.980714	−	0.195448i	$-0.0626159\pi$
$632$		−	12.4537i		−	0.495384i
$633$	−3.16360	+	9.73656i	−0.125742	+	0.386993i
$634$	4.80717	+	6.61651i	0.190917	+	0.262775i
$635$	2.00561	+	12.6069i	0.0795903	+	0.500289i
$636$	0.517930	−	0.712870i	0.0205373	−	0.0282671i
$637$	−6.09965	+	4.43165i	−0.241677	+	0.175588i
$638$	−6.79588	+	4.93750i	−0.269052	+	0.195477i
$639$	12.6728	−	17.4426i	0.501327	−	0.690017i
$640$	11.6253	−	22.8547i	0.459529	−	0.903410i
$641$	1.32010	+	1.81696i	0.0521407	+	0.0717655i	0.834291	−	0.551324i	$-0.185877\pi$
$641$	1.32010	+	1.81696i	0.0521407	+	0.0717655i	−0.782150	+	0.623090i	$0.785877\pi$
$642$	−0.761154	+	2.34259i	−0.0300404	+	0.0924547i
$643$			11.0302i			0.434989i	0.976062	+	0.217494i	$0.0697884\pi$
$643$			11.0302i			0.434989i	−0.976062	+	0.217494i	$0.930212\pi$
$644$	1.11230	−	3.42330i	0.0438307	−	0.134897i
$645$	8.05163	+	4.09555i	0.317032	+	0.161262i
$646$	6.04379	−	11.6376i	0.237790	−	0.457875i
$647$	−2.21118	−	6.80530i	−0.0869303	−	0.267544i	0.898136	−	0.439717i	$-0.144921\pi$
$647$	−2.21118	−	6.80530i	−0.0869303	−	0.267544i	−0.985067	+	0.172173i	$0.944921\pi$
$648$	13.0514	+	9.48243i	0.512709	+	0.372505i
$649$			1.77479i			0.0696665i
$650$	0.00580032	+	4.22269i	0.000227507	+	0.165627i
$651$		−	3.23174i		−	0.126662i
$652$	0.0599882	−	0.0825666i	0.00234932	−	0.00323356i
$653$	3.34656	−	1.08736i	0.130961	−	0.0425518i	−0.242803	−	0.970076i	$-0.578067\pi$
$653$	3.34656	−	1.08736i	0.130961	−	0.0425518i	0.373764	+	0.927524i	$0.378067\pi$
$654$	−0.561352	−	1.72766i	−0.0219506	−	0.0675570i
$655$	−19.6745	−	38.5479i	−0.768747	−	1.50619i
$656$	−9.61883	−	3.12535i	−0.375552	−	0.122024i
$657$			23.3586i			0.911305i
$658$	−4.70110	−	1.52748i	−0.183268	−	0.0595473i
$659$	−16.9020	+	12.2800i	−0.658407	+	0.478360i	−0.866124	−	0.499828i	$-0.833396\pi$
$659$	−16.9020	+	12.2800i	−0.658407	+	0.478360i	0.207718	+	0.978189i	$0.433396\pi$
$660$	−2.31695	−	2.31377i	−0.0901871	−	0.0900633i
$661$	−12.5969	−	9.15221i	−0.489964	−	0.355980i	0.315207	−	0.949023i	$-0.397926\pi$
$661$	−12.5969	−	9.15221i	−0.489964	−	0.355980i	−0.805170	+	0.593043i	$0.797926\pi$
$662$	2.77105	−	2.01328i	0.107700	−	0.0782485i
$663$	0.407025	−	2.44688i	0.0158076	−	0.0950290i
$664$	7.41422	+	5.38674i	0.287727	+	0.209046i
$665$	−6.92471	−	13.5675i	−0.268529	−	0.526124i
$666$	9.73413	+	13.3979i	0.377190	+	0.519157i
$667$	−3.54009	+	10.8953i	−0.137073	+	0.421867i
$668$			4.64220i			0.179612i
$669$	−9.48704	−	3.08252i	−0.366790	−	0.119177i
$670$	−7.25328	−	1.14370i	−0.280219	−	0.0441850i
$671$	−1.24779	−	3.84030i	−0.0481703	−	0.148253i
$672$	−0.939875	−	2.89264i	−0.0362565	−	0.111586i
$673$	−11.5336	+	15.8746i	−0.444587	+	0.611922i	−0.971224	−	0.238169i	$-0.923453\pi$
$673$	−11.5336	+	15.8746i	−0.444587	+	0.611922i	0.526637	+	0.850090i	$0.323453\pi$
$674$			14.6876i			0.565743i
$675$	10.0590	+	7.28718i	0.387170	+	0.280484i
$676$	18.0721			0.695080
$677$	23.4410	−	32.2638i	0.900910	−	1.24000i	−0.0692665	−	0.997598i	$-0.522066\pi$
$677$	23.4410	−	32.2638i	0.900910	−	1.24000i	0.970177	−	0.242398i	$-0.0779341\pi$
$678$	0.703568	+	2.16536i	0.0270204	+	0.0831601i
$679$	2.78761	+	8.57938i	0.106979	+	0.329246i
$680$	−11.9413	+	16.1938i	−0.457928	+	0.621005i
$681$	−0.441110	+	1.35760i	−0.0169034	+	0.0520232i
$682$	7.38550			0.282805
$683$	26.3962	+	8.57664i	1.01002	+	0.328176i	0.766863	−	0.641810i	$-0.221816\pi$
$683$	26.3962	+	8.57664i	1.01002	+	0.328176i	0.243159	+	0.969987i	$0.421816\pi$
$684$	−19.8430	+	14.4168i	−0.758717	+	0.551240i
$685$	6.68704	+	1.05442i	0.255499	+	0.0402871i
$686$	5.58767	−	7.69077i	0.213338	−	0.293635i
$687$	−7.31097	−	10.0627i	−0.278931	−	0.383916i
$688$	15.1019	−	10.9722i	0.575755	−	0.418311i
$689$	1.43356	+	1.04154i	0.0546143	+	0.0396796i
$690$	0.966098	+	0.152335i	0.0367787	+	0.00579928i
$691$	28.5613	+	39.3112i	1.08652	+	1.49547i	0.852132	+	0.523327i	$0.175309\pi$
$691$	28.5613	+	39.3112i	1.08652	+	1.49547i	0.234391	+	0.972142i	$0.424691\pi$
$692$	−27.3924	−	8.90034i	−1.04130	−	0.338340i
$693$	7.56160			0.287242
$694$	8.36360	+	2.71750i	0.317478	+	0.103155i
$695$	−11.7865	+	1.87510i	−0.447088	+	0.0711266i
$696$	1.93070	+	5.94207i	0.0731828	+	0.225234i
$697$	18.7558	+	9.74050i	0.710425	+	0.368948i
$698$	2.53637	+	1.84278i	0.0960032	+	0.0697504i
$699$	−8.89992			−0.336626
$700$	3.26849	+	10.0126i	0.123537	+	0.378440i
$701$	11.2558			0.425126			0.212563	−	0.977147i	$-0.431819\pi$
$701$	11.2558			0.425126			0.212563	+	0.977147i	$0.431819\pi$
$702$	1.23319	−	1.69734i	0.0465439	−	0.0640622i
$703$	−49.4755	+	16.0756i	−1.86600	+	0.606301i
$704$	−1.23409	+	0.400979i	−0.0465114	+	0.0151125i
$705$	−0.955159	+	6.05756i	−0.0359734	+	0.228141i
$706$	−2.65903	+	8.18366i	−0.100074	+	0.307996i
$707$			8.80068i			0.330984i
$708$	0.565764	+	0.183828i	0.0212627	+	0.00690867i
$709$	−15.6490	−	21.5390i	−0.587711	−	0.808915i	0.406803	−	0.913516i	$-0.366643\pi$
$709$	−15.6490	−	21.5390i	−0.587711	−	0.808915i	−0.994514	+	0.104601i	$0.966643\pi$
$710$	4.66262	+	9.13539i	0.174985	+	0.342845i
$711$	9.45099	−	13.0082i	0.354440	−	0.487844i
$712$	14.5453	−	10.5678i	0.545110	−	0.396045i
$713$	8.14857	−	5.92028i	0.305166	−	0.221716i
$714$	0.201593	+	1.33999i	0.00754444	+	0.0501478i
$715$	4.65291	−	4.65931i	0.174009	−	0.174248i
$716$	−32.8574	+	23.8723i	−1.22794	+	0.892149i
$717$	−6.82667	−	2.21812i	−0.254947	−	0.0828372i
$718$	−15.3445			−0.572651
$719$	−6.34248	−	2.06080i	−0.236535	−	0.0768547i	0.188351	−	0.982102i	$-0.439686\pi$
$719$	−6.34248	−	2.06080i	−0.236535	−	0.0768547i	−0.424886	+	0.905247i	$0.639686\pi$
$720$	11.0727	−	5.65143i	0.412657	−	0.210616i
$721$	10.6438	−	3.45837i	0.396395	−	0.128796i
$722$	1.69500	+	5.21666i	0.0630812	+	0.194144i
$723$	−3.27433	−	2.37894i	−0.121774	−	0.0884738i
$724$		−	43.5938i		−	1.62015i
$725$	−10.4026	−	31.8668i	−0.386342	−	1.18350i
$726$			1.69740i			0.0629963i
$727$	1.63088	+	1.18491i	0.0604862	+	0.0439458i	0.617617	−	0.786479i	$-0.288098\pi$
$727$	1.63088	+	1.18491i	0.0604862	+	0.0439458i	−0.557131	+	0.830424i	$0.688098\pi$
$728$	3.75448	−	1.21990i	0.139150	−	0.0452127i
$729$	5.45295	+	16.7825i	0.201961	+	0.621573i
$730$	−9.90433	−	5.03794i	−0.366576	−	0.186463i
$731$	−34.8920	+	17.4388i	−1.29053	+	0.644999i
$732$	−1.35345			−0.0500248
$733$	3.17719	−	9.77839i	0.117352	−	0.361173i	−0.875078	−	0.483982i	$-0.839190\pi$
$733$	3.17719	−	9.77839i	0.117352	−	0.361173i	0.992430	+	0.122809i	$0.0391901\pi$
$734$	−1.32870	−	1.82880i	−0.0490432	−	0.0675022i
$735$	−4.55448	−	2.31669i	−0.167995	−	0.0854523i
$736$	5.57177	−	7.66889i	0.205378	−	0.282679i
$737$	6.73031	+	9.26348i	0.247914	+	0.341225i
$738$	5.08883	+	7.00417i	0.187322	+	0.257827i
$739$	−37.0596	−	26.9254i	−1.36326	−	0.990466i	−0.998230	−	0.0594698i	$-0.981059\pi$
$739$	−37.0596	−	26.9254i	−1.36326	−	0.990466i	−0.365029	−	0.930996i	$-0.618941\pi$
$740$	35.5238	−	5.65143i	1.30588	−	0.207751i
$741$	1.87619	+	2.58235i	0.0689235	+	0.0948650i
$742$	−0.920631	−	0.299131i	−0.0337974	−	0.0109815i
$743$		−	5.96009i		−	0.218654i	−0.994006	−	0.109327i	$-0.965130\pi$
$743$		−	5.96009i		−	0.218654i	0.994006	−	0.109327i	$-0.0348696\pi$
$744$	1.69748	−	5.22431i	0.0622327	−	0.191533i
$745$	−10.7548	−	10.7400i	−0.394024	−	0.393484i
$746$	−4.38829	−	13.5058i	−0.160667	−	0.494481i
$747$	3.65635	+	11.2531i	0.133779	+	0.411729i
$748$	13.9819	−	2.10350i	0.511231	−	0.0769116i
$749$	−12.3549			−0.451439
$750$	−2.54726	+	1.30451i	−0.0930126	+	0.0476340i
$751$		−	26.7328i		−	0.975493i	−0.872985	−	0.487747i	$-0.837819\pi$
$751$		−	26.7328i		−	0.975493i	0.872985	−	0.487747i	$-0.162181\pi$
$752$	10.2521	+	7.44857i	0.373855	+	0.271622i
$753$	2.45244	−	0.796845i	0.0893717	−	0.0290386i
$754$	−5.38496	+	1.74968i	−0.196109	+	0.0637196i
$755$	15.8732	+	15.8514i	0.577685	+	0.576892i
$756$	1.61711	−	4.97695i	0.0588136	−	0.181010i
$757$	−8.89664			−0.323354			−0.161677	−	0.986844i	$-0.551690\pi$
$757$	−8.89664			−0.323354			−0.161677	+	0.986844i	$0.551690\pi$
$758$	−5.28028	−	1.71567i	−0.191788	−	0.0623158i
$759$	−0.896441	−	1.23384i	−0.0325387	−	0.0447857i
$760$	−4.06788	−	25.5699i	−0.147557	−	0.927518i
$761$	−4.24486	−	3.08407i	−0.153876	−	0.111797i	0.508183	−	0.861249i	$-0.330317\pi$
$761$	−4.24486	−	3.08407i	−0.153876	−	0.111797i	−0.662059	+	0.749452i	$0.730317\pi$
$762$	0.858940	+	1.18223i	0.0311161	+	0.0428277i
$763$	7.37157	−	5.35576i	0.266869	−	0.193891i
$764$	19.0059	+	13.8086i	0.687610	+	0.499578i
$765$	−24.7622	+	7.85265i	−0.895279	+	0.283913i
$766$	−0.218685	+	0.158884i	−0.00790142	+	0.00574072i
$767$	−0.369672	+	1.13773i	−0.0133481	+	0.0410812i
$768$		−	2.40510i		−	0.0867866i
$769$	−0.862743	+	2.65525i	−0.0311113	+	0.0957507i	−0.965406	−	0.260750i	$-0.916030\pi$
$769$	−0.862743	+	2.65525i	−0.0311113	+	0.0957507i	0.934295	+	0.356501i	$0.116030\pi$
$770$	−1.63087	+	3.20621i	−0.0587726	+	0.115544i
$771$	−9.22841	+	2.99849i	−0.332353	+	0.107988i

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.484961 - 0.352344i) q^{2} +(-0.406117 + 0.131955i) q^{3} +(-0.506994 - 1.56037i) q^{4} +(1.58222 + 1.58005i) q^{5} +(0.243445 + 0.0790999i) q^{6} +1.28394i q^{7} +(-0.674391 + 2.07556i) q^{8} +(-2.27953 + 1.65618i) q^{9} +(-0.210594 - 1.32375i) q^{10} +(-1.22857 + 1.69099i) q^{11} +(0.411798 + 0.566791i) q^{12} +(-1.13980 + 0.828112i) q^{13} +(0.452388 - 0.622658i) q^{14} +(-0.851065 - 0.432903i) q^{15} +(-1.59629 + 1.15977i) q^{16} +(3.68812 - 1.84330i) q^{17} +1.68903 q^{18} +(-1.63955 + 5.04601i) q^{19} +(1.66328 - 3.26993i) q^{20} +(-0.169422 - 0.521428i) q^{21} +(1.19162 - 0.387181i) q^{22} +(1.00437 - 1.38240i) q^{23} -0.931911i q^{24} +(0.00686804 + 5.00000i) q^{25} +0.844538 q^{26} +(1.46020 - 2.00979i) q^{27} +(2.00341 - 0.650947i) q^{28} +(-6.37622 + 2.07176i) q^{29} +(0.260202 + 0.509809i) q^{30} +(5.60602 + 1.82151i) q^{31} +5.54753 q^{32} +(0.275810 - 0.848856i) q^{33} +(-2.43807 - 0.405559i) q^{34} +(-2.02869 + 2.03147i) q^{35} +(3.73995 + 2.71723i) q^{36} +(5.76316 + 7.93230i) q^{37} +(2.57305 - 1.86943i) q^{38} +(0.353618 - 0.486713i) q^{39} +(-4.34654 + 2.21843i) q^{40} +(3.01287 + 4.14686i) q^{41} +(-0.101559 + 0.312567i) q^{42} -9.46065 q^{43} +(3.26144 + 1.05971i) q^{44} +(-6.22358 - 0.981337i) q^{45} +(-0.974160 + 0.316524i) q^{46} +(-1.98465 - 6.10811i) q^{47} +(0.495242 - 0.681642i) q^{48} +5.35151 q^{49} +(1.75839 - 2.42722i) q^{50} +(-1.25457 + 1.23526i) q^{51} +(1.87003 + 1.35866i) q^{52} +(-0.388660 - 1.19617i) q^{53} +(-1.41628 + 0.460176i) q^{54} +(-4.61573 + 0.734310i) q^{55} +(-2.66489 - 0.865875i) q^{56} -2.26562i q^{57} +(3.82219 + 1.24190i) q^{58} +(0.686944 - 0.499094i) q^{59} +(-0.244003 + 1.54745i) q^{60} +(-1.13552 + 1.56291i) q^{61} +(-2.07690 - 2.85861i) q^{62} +(-2.12642 - 2.92677i) q^{63} +(0.502243 + 0.364901i) q^{64} +(-3.11188 - 0.490683i) q^{65} +(-0.432847 + 0.314482i) q^{66} +(1.69284 - 5.21003i) q^{67} +(-4.74608 - 4.82028i) q^{68} +(-0.225477 + 0.693947i) q^{69} +(1.69961 - 0.270389i) q^{70} +(-7.27731 + 2.36454i) q^{71} +(-1.90020 - 5.84823i) q^{72} +(4.87278 - 6.70681i) q^{73} -5.87747i q^{74} +(-0.662566 - 2.02968i) q^{75} +8.70487 q^{76} +(-2.17112 - 1.57741i) q^{77} +(-0.342982 + 0.111441i) q^{78} +(-5.42721 + 1.76341i) q^{79} +(-4.35818 - 0.687201i) q^{80} +(2.28430 - 7.03036i) q^{81} -3.07263i q^{82} +(1.29766 - 3.99378i) q^{83} +(-0.727723 + 0.528722i) q^{84} +(8.74795 + 2.91090i) q^{85} +(4.58804 + 3.33341i) q^{86} +(2.31611 - 1.68275i) q^{87} +(-2.68121 - 3.69037i) q^{88} +(-6.66491 - 4.84234i) q^{89} +(2.67242 + 2.66875i) q^{90} +(-1.06324 - 1.46343i) q^{91} +(-2.66626 - 0.866319i) q^{92} -2.51706 q^{93} +(-1.18968 + 3.66147i) q^{94} +(-10.5671 + 5.39335i) q^{95} +(-2.25295 + 0.732027i) q^{96} +(6.68210 - 2.17115i) q^{97} +(-2.59527 - 1.88557i) q^{98} -5.88940i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 8 q^{2} - 44 q^{4} - 4 q^{8} + 28 q^{9} - 18 q^{13} - 10 q^{15} - 28 q^{16} + 2 q^{17} - 60 q^{18} - 8 q^{19} + 32 q^{21} + 6 q^{25} + 52 q^{26} - 54 q^{30} + 44 q^{32} - 24 q^{33} + 26 q^{35} + 34 q^{36}+ \cdots - 36 q^{98}+O(q^{100}) \) 168 * q - 8 * q^2 - 44 * q^4 - 4 * q^8 + 28 * q^9 - 18 * q^13 - 10 * q^15 - 28 * q^16 + 2 * q^17 - 60 * q^18 - 8 * q^19 + 32 * q^21 + 6 * q^25 + 52 * q^26 - 54 * q^30 + 44 * q^32 - 24 * q^33 + 26 * q^35 + 34 * q^36 - 18 * q^38 + 80 * q^42 - 8 * q^43 - 40 * q^47 - 84 * q^49 - 82 * q^50 - 36 * q^51 - 30 * q^52 - 42 * q^53 - 18 * q^55 - 18 * q^59 + 28 * q^60 - 16 * q^64 - 140 * q^66 - 62 * q^67 + 144 * q^68 + 44 * q^69 + 4 * q^70 - 6 * q^72 + 72 * q^76 + 48 * q^77 - 28 * q^81 - 14 * q^83 + 24 * q^84 + 62 * q^85 + 82 * q^86 + 48 * q^87 + 90 * q^89 - 224 * q^93 + 26 * q^94 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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