LMFDB - Embedded newform 425.2.p.a.16.18

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			16.18
Character	$\chi$	$=$	425.16
Dual form			425.2.p.a.186.18

$q$-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} +(-1.90029 - 3.65909i) 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} +(-0.367695 + 2.44407i) 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} +(-2.77487 + 8.79205i) 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	−0.189424	−	0.981895i	$-0.560662\pi$
$3$	0.406117	−	0.131955i	0.234472	−	0.0761845i	0.423896	+	0.905711i	$0.360662\pi$
$4$	−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	$-0.921986\pi$
$7$		−	1.28394i		−	0.485282i	0.970116	−	0.242641i	$-0.0780137\pi$
$8$	−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	−0.582588	−	0.812767i	$-0.697960\pi$
$11$	1.22857	−	1.69099i	0.370429	−	0.509852i	0.953017	+	0.302915i	$0.0979600\pi$
$12$	−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
$17$	−1.90029	−	3.65909i	−0.460887	−	0.887459i
$17$	−1.90029	−	3.65909i	−0.460887	−	0.887459i
$18$	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	−0.900789	−	0.434258i	$-0.857011\pi$
$23$	−1.00437	+	1.38240i	−0.209426	+	0.288250i	0.691363	+	0.722508i	$0.257011\pi$
$24$			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	0.350170	−	0.936686i	$-0.386124\pi$
$29$	6.37622	−	2.07176i	1.18403	−	0.384716i	0.833864	+	0.551970i	$0.186124\pi$
$30$	0.260202	+	0.509809i	0.0475061	+	0.0930780i
$31$	−5.60602	−	1.82151i	−1.00687	−	0.327152i	−0.241263	−	0.970460i	$-0.577562\pi$
$31$	−5.60602	−	1.82151i	−1.00687	−	0.327152i	−0.765608	+	0.643308i	$0.777562\pi$
$32$	5.54753			0.980674
$33$	0.275810	−	0.848856i	0.0480124	−	0.147767i
$34$	−0.367695	+	2.44407i	−0.0630592	+	0.419154i
$35$	−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	$-0.901652\pi$
$37$	−5.76316	−	7.93230i	−0.947457	−	1.30406i	0.00519083	−	0.999987i	$-0.498348\pi$
$38$	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	0.506119	−	0.862464i	$-0.331080\pi$
$41$	−3.01287	−	4.14686i	−0.470532	−	0.647631i	−0.976651	+	0.214832i	$0.931080\pi$
$42$	−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	−0.730112	−	0.683328i	$-0.760532\pi$
$61$	1.13552	−	1.56291i	0.145388	−	0.200110i	0.875500	+	0.483218i	$0.160532\pi$
$62$	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	0.156502	−	0.987678i	$-0.449978\pi$
$71$	7.27731	−	2.36454i	0.863658	−	0.280619i	0.707155	+	0.707058i	$0.249978\pi$
$72$	−1.90020	−	5.84823i	−0.223941	−	0.689220i
$73$	−4.87278	+	6.70681i	−0.570316	+	0.784973i	−0.992592	−	0.121494i	$-0.961231\pi$
$73$	−4.87278	+	6.70681i	−0.570316	+	0.784973i	0.422276	+	0.906467i	$0.361231\pi$
$74$			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	0.0126426	−	0.999920i	$-0.495976\pi$
$79$	5.42721	−	1.76341i	0.610609	−	0.198399i	0.597966	+	0.801521i	$0.295976\pi$
$80$	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
$85$	−2.77487	+	8.79205i	−0.300977	+	0.953631i
$86$	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	−0.627923	−	0.778276i	$-0.716095\pi$
$97$	−6.68210	+	2.17115i	−0.678464	+	0.220446i	−0.0505414	+	0.998722i	$0.516095\pi$
$98$	−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	$0.389227\pi$
$102$	0.173181	+	1.04110i	0.0171474	+	0.103084i
$103$	−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	$-0.846007\pi$
$107$		−	9.62269i		−	0.930261i	0.885242	−	0.465130i	$-0.153993\pi$
$108$	3.87632	+	1.25949i	0.372999	+	0.121195i
$109$	4.17136	+	5.74138i	0.399544	+	0.549925i	0.960629	−	0.277833i	$-0.0896162\pi$
$109$	4.17136	+	5.74138i	0.399544	+	0.549925i	−0.561086	+	0.827758i	$0.689616\pi$
$110$	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	0.488899	−	0.872340i	$-0.337399\pi$
$113$	−5.22816	−	7.19594i	−0.491824	−	0.676937i	−0.980723	+	0.195403i	$0.937399\pi$
$114$	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
$119$	−4.69803	+	2.43984i	−0.430668	+	0.223660i
$120$	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	0.969133	−	0.246539i	$-0.0792933\pi$
$131$	18.4074	+	5.98094i	1.60827	+	0.522557i	0.639133	+	0.769096i	$0.279293\pi$
$132$	−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
$136$	8.87620	−	1.47651i	0.761128	−	0.126609i
$137$	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	−0.654971	−	0.755654i	$-0.727319\pi$
$139$	3.13723	−	4.31803i	0.266096	−	0.366250i	0.921067	+	0.389404i	$0.127319\pi$
$140$	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
$153$	10.3919	+	5.19380i	0.840132	+	0.419893i
$154$	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	0.807583	−	0.589754i	$-0.200775\pi$
$163$	−0.0365633	−	0.0503250i	−0.00286386	−	0.00394176i	−0.810447	+	0.585813i	$0.800775\pi$
$164$	−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	0.411277	−	0.911511i	$-0.365083\pi$
$167$	2.69098	+	0.874351i	0.208234	+	0.0676593i	−0.203043	+	0.979170i	$0.565083\pi$
$168$	1.19651			0.0923131
$169$	−3.40385	+	10.4760i	−0.261835	+	0.805844i
$170$	4.44353	−	3.28609i	0.340803	−	0.252031i
$171$	−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	$0.432570\pi$
$173$	−10.3186	+	14.2024i	−0.784512	+	1.07979i	−0.994770	+	0.102142i	$0.967430\pi$
$174$	−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	$-0.950391\pi$
$181$	−25.2703	−	8.21082i	−1.87833	−	0.610306i	−0.890448	−	0.455086i	$-0.849609\pi$
$182$		−	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
$187$	−8.52211	−	1.28210i	−0.623199	−	0.0937565i
$188$	−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	$-0.786181\pi$
$193$		−	17.2918i		−	1.24469i	0.782744	−	0.622344i	$-0.213819\pi$
$194$	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	−0.866610	−	0.498986i	$-0.833706\pi$
$197$	−17.8873	+	5.81193i	−1.27442	+	0.414083i	−0.407806	+	0.913069i	$0.633706\pi$
$198$	2.07510	−	2.85613i	0.147471	−	0.202976i
$199$		−	13.0129i		−	0.922462i	−0.887280	−	0.461231i	$-0.847408\pi$
$199$		−	13.0129i		−	0.922462i	0.887280	−	0.461231i	$-0.152592\pi$
$200$	−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
$204$	−1.29140	+	2.58387i	−0.0904164	+	0.180907i
$205$	−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	$0.508963\pi$
$211$	−14.0920	+	19.3960i	−0.970133	+	1.33527i	−0.941979	+	0.335671i	$0.891037\pi$
$212$	−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
$221$	5.19608	+	2.59697i	0.349526	+	0.174691i
$222$	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	−0.869230	−	0.494407i	$-0.835385\pi$
$227$	−1.96489	+	2.70444i	−0.130414	+	0.179500i	0.738816	+	0.673907i	$0.235385\pi$
$228$	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	−0.423494	−	0.905899i	$-0.639197\pi$
$233$	−19.8220	−	6.44056i	−1.29858	−	0.421935i	−0.875088	+	0.483964i	$0.839197\pi$
$234$	−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
$238$	3.13803	+	0.472097i	0.203408	+	0.0306015i
$239$	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	0.590967	−	0.806695i	$-0.298746\pi$
$241$	−5.57107	−	7.66792i	−0.358864	−	0.493934i	−0.949832	+	0.312761i	$0.898746\pi$
$242$	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
$255$	0.0332361	+	3.93676i	0.00208133	+	0.246529i
$256$	−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	0.478473	−	0.878102i	$-0.341191\pi$
$269$	5.73108	+	1.86214i	0.349430	+	0.113537i	−0.129043	+	0.991639i	$0.541191\pi$
$270$	−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	$-0.425765\pi$
$272$	7.27711	+	3.63706i	0.441239	+	0.220529i
$273$	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	$-0.574316\pi$
$277$	12.7386	−	17.5332i	0.765391	−	1.05347i	0.996746	−	0.0806010i	$-0.0256839\pi$
$278$	−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	−0.363738	−	0.931501i	$-0.618500\pi$
$283$	−20.2802	−	6.58942i	−1.20553	−	0.391701i	−0.841793	+	0.539801i	$0.818500\pi$
$284$	−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
$289$	−9.77783	+	13.9066i	−0.575166	+	0.818036i
$290$	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
$306$	−3.20964	−	6.18030i	−0.183483	−	0.353304i
$307$	−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	−0.941155	−	0.337975i	$-0.890258\pi$
$311$	−5.80001	+	7.98303i	−0.328888	+	0.452676i	0.612267	+	0.790651i	$0.290258\pi$
$312$	−0.771727	−	1.06219i	−0.0436905	−	0.0601348i
$313$	11.3679	+	15.6466i	0.642554	+	0.884400i	0.998749	−	0.0500117i	$-0.0159259\pi$
$313$	11.3679	+	15.6466i	0.642554	+	0.884400i	−0.356194	+	0.934412i	$0.615926\pi$
$314$	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	0.649828	−	0.760082i	$-0.274841\pi$
$317$	12.9756	+	4.21604i	0.728784	+	0.236796i	0.0789568	+	0.996878i	$0.474841\pi$
$318$			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
$323$	21.5794	−	3.58961i	1.20071	−	0.199731i
$324$	−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	$0.0325728\pi$
$337$	14.4019	+	19.8225i	0.784521	+	1.07980i	−0.210248	+	0.977648i	$0.567427\pi$
$338$	5.34188	−	3.88111i	0.290560	−	0.211104i
$339$	−3.07279	−	2.23251i	−0.166891	−	0.121253i
$340$	15.1257	−	0.127698i	0.820304	−	0.00692542i
$341$	−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	0.0904469	−	0.995901i	$-0.471170\pi$
$347$	13.9522	−	4.53336i	0.748996	−	0.243364i	0.658549	+	0.752538i	$0.271170\pi$
$348$	−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	0.213911	−	0.976853i	$-0.431380\pi$
$367$	−3.58646	−	1.16531i	−0.187212	−	0.0608288i	−0.401122	+	0.916024i	$0.631380\pi$
$368$		−	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	−0.526381	−	0.850249i	$-0.676451\pi$
$379$	−8.80862	+	2.86209i	−0.452468	+	0.147016i	0.0739125	+	0.997265i	$0.476451\pi$
$380$	−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
$391$	6.96690	+	1.04813i	0.352331	+	0.0530061i
$392$	−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	−0.584258	−	0.811568i	$-0.698614\pi$
$397$	−11.5545	+	3.75429i	−0.579904	+	0.188422i	0.00435337	+	0.999991i	$0.498614\pi$
$398$	−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	$0.346400\pi$
$401$			35.4769i			1.77163i	−0.464038	+	0.885815i	$0.653600\pi$
$402$	−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
$408$	3.40994	−	1.77090i	0.168817	−	0.0876725i
$409$	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	−0.464919	−	0.885353i	$-0.653917\pi$
$419$	−27.8681	−	9.05488i	−1.36144	−	0.442360i	−0.896525	+	0.442993i	$0.853917\pi$
$420$	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
$425$	18.2824	−	9.52655i	0.886825	−	0.462106i
$426$	−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	0.530447	−	0.847718i	$-0.322024\pi$
$431$	9.57710	+	3.11179i	0.461312	+	0.149889i	−0.0691350	+	0.997607i	$0.522024\pi$
$432$		−	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	$-0.414166\pi$
$439$	23.0636	−	31.7443i	1.10077	−	1.51507i	0.834365	−	0.551212i	$-0.185834\pi$
$440$	1.58870	−	10.0755i	0.0757384	−	0.480328i
$441$	−12.1989	+	8.86305i	−0.580902	+	0.422050i
$442$	−1.60486	−	3.09024i	−0.0763356	−	0.146988i
$443$	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	$-0.787675\pi$
$449$		−	26.2185i		−	1.23733i	0.785656	−	0.618663i	$-0.212325\pi$
$450$	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
$459$	10.1288	+	1.52382i	0.472771	+	0.0711256i
$460$	−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	−0.405765	−	0.913978i	$-0.632995\pi$
$479$	−4.30745	+	1.39958i	−0.196813	+	0.0639483i	0.208952	+	0.977926i	$0.432995\pi$
$480$	−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	$0.212394\pi$
$487$	24.9662	+	34.3631i	1.13133	+	1.55714i	0.345806	+	0.938306i	$0.387606\pi$
$488$	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	$0.0123531\pi$
$499$			1.73339i			0.0775972i	−0.999247	+	0.0387986i	$0.987647\pi$
$500$	−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	0.350761	−	0.936465i	$-0.385923\pi$
$503$	26.5762	−	8.63512i	1.18497	−	0.385021i	0.834212	+	0.551444i	$0.185923\pi$
$504$	−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	$0.204359\pi$
$510$	1.37098	−	1.92088i	0.0607079	−	0.0850582i
$511$	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	−0.0787203	−	0.996897i	$-0.525083\pi$
$521$	10.1243	−	3.28959i	0.443555	−	0.144120i	0.522275	+	0.852777i	$0.325083\pi$
$522$	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
$527$	3.98799	+	23.9743i	0.173720	+	1.04434i
$528$	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	$-0.947937\pi$
$541$	−19.4594	−	26.7836i	−0.836625	−	1.15152i	0.150029	−	0.988682i	$-0.452063\pi$
$542$	−5.20774	+	16.0278i	−0.223692	+	0.688452i
$543$	−11.3462			−0.486911
$544$	−10.5419	−	20.2989i	−0.451980	−	0.870308i
$545$	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	0.733212	−	0.680000i	$-0.238020\pi$
$547$	40.3698	−	13.1169i	1.72609	−	0.560840i	0.992875	+	0.119160i	$0.0380201\pi$
$548$	−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
$561$	−3.63016	+	0.603856i	−0.153265	+	0.0254948i
$562$	−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	−0.194055	−	0.980991i	$-0.562164\pi$
$571$	5.38997	−	1.75131i	0.225563	−	0.0732900i	0.419618	+	0.907701i	$0.362164\pi$
$572$	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	$0.582407\pi$
$578$	9.64178	−	3.29900i	0.401045	−	0.137220i
$579$	−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
$595$	11.2884	+	3.56275i	0.462780	+	0.146059i
$596$	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	$-0.995453\pi$
$601$		−	0.700391i		−	0.0285695i	0.999898	−	0.0142848i	$-0.00454714\pi$
$602$	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	$-0.969679\pi$
$607$		−	4.68665i		−	0.190225i	0.995467	−	0.0951126i	$-0.0303211\pi$
$608$	−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
$612$	2.83562	−	18.8483i	0.114623	−	0.761899i
$613$	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	−0.525376	−	0.850870i	$-0.676075\pi$
$617$	−36.0308	−	11.7071i	−1.45054	−	0.471310i	−0.925167	+	0.379560i	$0.876075\pi$
$618$			2.23121i			0.0897523i
$619$	−6.85882	−	2.22857i	−0.275679	−	0.0895736i	0.167915	−	0.985802i	$-0.446297\pi$
$619$	−6.85882	−	2.22857i	−0.275679	−	0.0895736i	−0.443594	+	0.896228i	$0.646297\pi$
$620$	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
$629$	−18.0733	+	36.1615i	−0.720631	+	1.44185i
$630$	−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	0.782150	−	0.623090i	$-0.214123\pi$
$641$	−1.32010	−	1.81696i	−0.0521407	−	0.0717655i	−0.834291	+	0.551324i	$0.814123\pi$
$642$	−0.761154	+	2.34259i	−0.0300404	+	0.0924547i
$643$		−	11.0302i		−	0.434989i	−0.976062	−	0.217494i	$-0.930212\pi$
$643$		−	11.0302i		−	0.434989i	0.976062	−	0.217494i	$-0.0697884\pi$
$644$	1.11230	−	3.42330i	0.0438307	−	0.134897i
$645$	8.05163	+	4.09555i	0.317032	+	0.161262i
$646$	−11.7299	−	5.86256i	−0.461508	−	0.230659i
$647$	−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	−0.373764	−	0.927524i	$-0.621933\pi$
$653$	−3.34656	+	1.08736i	−0.130961	+	0.0425518i	0.242803	+	0.970076i	$0.421933\pi$
$654$	−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
$663$	2.45290	+	0.369024i	0.0952628	+	0.0143317i
$664$	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	−0.526637	−	0.850090i	$-0.676547\pi$
$673$	11.5336	−	15.8746i	0.444587	−	0.611922i	0.971224	+	0.238169i	$0.0765472\pi$
$674$		−	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	$0.477934\pi$
$677$	−23.4410	+	32.2638i	−0.900910	+	1.24000i	−0.970177	+	0.242398i	$0.922066\pi$
$678$	0.703568	+	2.16536i	0.0270204	+	0.0831601i
$679$	2.78761	+	8.57938i	0.106979	+	0.329246i
$680$	−16.3771	−	11.6887i	−0.628033	−	0.448241i
$681$	−0.441110	+	1.35760i	−0.0169034	+	0.0520232i
$682$	7.38550			0.282805
$683$	−26.3962	−	8.57664i	−1.01002	−	0.328176i	−0.243159	−	0.969987i	$-0.578184\pi$
$683$	−26.3962	−	8.57664i	−1.01002	−	0.328176i	−0.766863	+	0.641810i	$0.778184\pi$
$684$	−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	$-0.824691\pi$
$691$	−28.5613	−	39.3112i	−1.08652	−	1.49547i	−0.234391	−	0.972142i	$-0.575309\pi$
$692$	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
$697$	−9.44842	+	18.9046i	−0.357884	+	0.716062i
$698$	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	0.994514	−	0.104601i	$-0.0333566\pi$
$709$	15.6490	+	21.5390i	0.587711	+	0.808915i	−0.406803	+	0.913516i	$0.633357\pi$
$710$	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
$714$	1.33670	−	0.222353i	0.0500248	−	0.00832135i
$715$	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	0.424886	−	0.905247i	$-0.360314\pi$
$719$	6.34248	+	2.06080i	0.236535	+	0.0768547i	−0.188351	+	0.982102i	$0.560314\pi$
$720$	−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
$731$	17.9779	+	34.6173i	0.664938	+	1.28037i
$732$	−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	$0.0348696\pi$
$743$			5.96009i			0.218654i	−0.994006	+	0.109327i	$0.965130\pi$
$744$	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
$748$	2.32011	+	13.9476i	0.0848317	+	0.509976i
$749$	−12.3549			−0.451439
$750$	−2.54726	+	1.30451i	−0.0930126	+	0.0476340i
$751$			26.7328i			0.975493i	0.872985	+	0.487747i	$0.162181\pi$
$751$			26.7328i			0.975493i	−0.872985	+	0.487747i	$0.837819\pi$
$752$	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
$765$	−8.23578	−	24.6374i	−0.297765	−	0.890768i
$766$	−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

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} +(-1.90029 - 3.65909i) 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} +(-0.367695 + 2.44407i) 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} +(-2.77487 + 8.79205i) 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

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