LMFDB - Embedded newform 702.2.w.d.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(79,702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(702, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("702.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.w (of order $9$, degree $6$, 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:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			79.2
Character	$\chi$	$=$	702.79
Dual form			702.2.w.d.391.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 + 0.984808i) q^{2} +(-1.55499 - 0.762899i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.368840 + 0.309494i) q^{5} +(1.02133 - 1.39889i) q^{6} +(-0.0350928 + 0.0127727i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.83597 + 2.37260i) q^{9} +(-0.240744 - 0.416980i) q^{10} +(-1.22890 - 1.03117i) q^{11} +(1.20028 + 1.24873i) q^{12} +(0.173648 + 0.984808i) q^{13} +(-0.00648489 - 0.0367776i) q^{14} +(0.809655 - 0.199871i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-2.84400 - 4.92596i) q^{17} +(-2.65536 + 1.39608i) q^{18} +(0.721260 - 1.24926i) q^{19} +(0.452450 - 0.164678i) q^{20} +(0.0643132 + 0.00691081i) q^{21} +(1.22890 - 1.03117i) q^{22} +(8.01307 + 2.91652i) q^{23} +(-1.43818 + 0.965209i) q^{24} +(-0.827984 + 4.69573i) q^{25} -1.00000 q^{26} +(-1.04486 - 5.09002i) q^{27} +0.0373450 q^{28} +(-0.722801 + 4.09921i) q^{29} +(0.0562396 + 0.832061i) q^{30} +(8.19771 + 2.98372i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(1.12424 + 2.54098i) q^{33} +(5.34498 - 1.94541i) q^{34} +(0.00899056 - 0.0155721i) q^{35} +(-0.913773 - 2.85745i) q^{36} +(3.21107 + 5.56174i) q^{37} +(1.10503 + 0.927234i) q^{38} +(0.481288 - 1.66384i) q^{39} +(0.0836093 + 0.474172i) q^{40} +(-0.304760 - 1.72838i) q^{41} +(-0.0179737 + 0.0621361i) q^{42} +(9.34743 + 7.84342i) q^{43} +(0.802106 + 1.38929i) q^{44} +(-1.41148 - 0.306887i) q^{45} +(-4.26366 + 7.38488i) q^{46} +(10.2441 - 3.72856i) q^{47} +(-0.700808 - 1.58394i) q^{48} +(-5.36124 + 4.49862i) q^{49} +(-4.48061 - 1.63081i) q^{50} +(0.664382 + 9.82949i) q^{51} +(0.173648 - 0.984808i) q^{52} -1.74510 q^{53} +(5.19413 - 0.145116i) q^{54} +0.772408 q^{55} +(-0.00648489 + 0.0367776i) q^{56} +(-2.07461 + 1.39233i) q^{57} +(-3.91142 - 1.42364i) q^{58} +(-6.81878 + 5.72164i) q^{59} +(-0.829187 - 0.0891008i) q^{60} +(9.25156 - 3.36729i) q^{61} +(-4.36191 + 7.55505i) q^{62} +(-0.0947339 - 0.0598107i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.368840 - 0.309494i) q^{65} +(-2.69760 + 0.665928i) q^{66} +(0.0256044 + 0.145210i) q^{67} +(0.987712 + 5.60159i) q^{68} +(-10.2352 - 10.6483i) q^{69} +(0.0137743 + 0.0115580i) q^{70} +(0.488931 + 0.846853i) q^{71} +(2.97271 - 0.403700i) q^{72} +(-1.32294 + 2.29141i) q^{73} +(-6.03484 + 2.19650i) q^{74} +(4.86987 - 6.67013i) q^{75} +(-1.10503 + 0.927234i) q^{76} +(0.0562963 + 0.0204902i) q^{77} +(1.55499 + 0.762899i) q^{78} +(2.40733 - 13.6527i) q^{79} -0.481487 q^{80} +(-2.25842 + 8.71203i) q^{81} +1.75505 q^{82} +(1.13955 - 6.46269i) q^{83} +(-0.0580710 - 0.0284904i) q^{84} +(2.57354 + 0.936691i) q^{85} +(-9.34743 + 7.84342i) q^{86} +(4.25123 - 5.82280i) q^{87} +(-1.50747 + 0.548673i) q^{88} +(-0.176290 + 0.305343i) q^{89} +(0.547327 - 1.33675i) q^{90} +(-0.0186725 - 0.0323417i) q^{91} +(-6.53231 - 5.48126i) q^{92} +(-10.4711 - 10.8937i) q^{93} +(1.89304 + 10.7360i) q^{94} +(0.120608 + 0.684003i) q^{95} +(1.68157 - 0.415112i) q^{96} +(14.4735 + 12.1447i) q^{97} +(-3.49930 - 6.06097i) q^{98} +(0.190323 - 4.80887i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 3 q^{5} + 9 q^{6} - 3 q^{7} + 33 q^{8} - 6 q^{9} - 9 q^{10} - 3 q^{11} + 3 q^{14} - 27 q^{15} + 12 q^{17} - 12 q^{18} - 21 q^{19} - 6 q^{20} - 18 q^{21} + 3 q^{22} - 3 q^{25} - 66 q^{26} + 9 q^{27}+ \cdots - 15 q^{99}+O(q^{100}) $ 66 * q + 3 * q^5 + 9 * q^6 - 3 * q^7 + 33 * q^8 - 6 * q^9 - 9 * q^10 - 3 * q^11 + 3 * q^14 - 27 * q^15 + 12 * q^17 - 12 * q^18 - 21 * q^19 - 6 * q^20 - 18 * q^21 + 3 * q^22 - 3 * q^25 - 66 * q^26 + 9 * q^27 + 18 * q^28 + 39 * q^29 + 9 * q^30 - 9 * q^31 + 15 * q^33 - 6 * q^34 - 9 * q^35 - 3 * q^36 - 21 * q^37 + 6 * q^38 - 3 * q^40 + 6 * q^41 + 9 * q^42 - 6 * q^43 + 3 * q^44 - 9 * q^45 - 9 * q^46 - 36 * q^47 + 9 * q^48 - 9 * q^49 + 3 * q^50 + 21 * q^51 - 60 * q^53 + 27 * q^54 + 84 * q^55 + 3 * q^56 + 87 * q^57 + 24 * q^58 - 30 * q^59 + 6 * q^60 - 12 * q^61 + 21 * q^62 - 60 * q^63 - 33 * q^64 + 3 * q^65 + 24 * q^66 - 3 * q^67 + 15 * q^68 - 87 * q^69 - 21 * q^70 + 3 * q^71 + 6 * q^72 - 15 * q^73 + 6 * q^74 - 117 * q^75 - 6 * q^76 + 27 * q^77 + 27 * q^79 - 18 * q^80 + 78 * q^81 + 24 * q^82 - 24 * q^83 + 33 * q^84 + 45 * q^85 + 6 * q^86 + 18 * q^87 - 6 * q^88 + 36 * q^89 - 87 * q^90 - 9 * q^91 - 63 * q^93 - 36 * q^94 + 63 * q^95 - 102 * q^97 + 72 * q^98 - 15 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	−1.55499	−	0.762899i	−0.897772	−	0.440460i
$3$	−1.55499	−	0.762899i	−0.897772	−	0.440460i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−0.368840	+	0.309494i	−0.164950	+	0.138410i	−0.721527	−	0.692387i	$-0.756559\pi$
$5$	−0.368840	+	0.309494i	−0.164950	+	0.138410i	0.556576	+	0.830797i	$0.312115\pi$
$6$	1.02133	−	1.39889i	0.416956	−	0.571093i
$7$	−0.0350928	+	0.0127727i	−0.0132638	+	0.00482764i	−0.348644	−	0.937255i	$-0.613358\pi$
$7$	−0.0350928	+	0.0127727i	−0.0132638	+	0.00482764i	0.335380	+	0.942083i	$0.391135\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	1.83597	+	2.37260i	0.611990	+	0.790865i
$10$	−0.240744	−	0.416980i	−0.0761298	−	0.131861i
$11$	−1.22890	−	1.03117i	−0.370527	−	0.310909i	0.438443	−	0.898759i	$-0.355530\pi$
$11$	−1.22890	−	1.03117i	−0.370527	−	0.310909i	−0.808970	+	0.587850i	$0.799974\pi$
$12$	1.20028	+	1.24873i	0.346492	+	0.360477i
$13$	0.173648	+	0.984808i	0.0481613	+	0.273137i
$13$	0.173648	+	0.984808i	0.0481613	+	0.273137i
$14$	−0.00648489	−	0.0367776i	−0.00173316	−	0.00982924i
$15$	0.809655	−	0.199871i	0.209052	−	0.0516065i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−2.84400	−	4.92596i	−0.689772	−	1.19472i	−0.971911	−	0.235347i	$-0.924377\pi$
$17$	−2.84400	−	4.92596i	−0.689772	−	1.19472i	0.282139	−	0.959373i	$-0.408956\pi$
$18$	−2.65536	+	1.39608i	−0.625875	+	0.329060i
$19$	0.721260	−	1.24926i	0.165468	−	0.286600i	−0.771353	−	0.636407i	$-0.780420\pi$
$19$	0.721260	−	1.24926i	0.165468	−	0.286600i	0.936821	+	0.349808i	$0.113753\pi$
$20$	0.452450	−	0.164678i	0.101171	−	0.0368232i
$21$	0.0643132	+	0.00691081i	0.0140343	+	0.00150806i
$22$	1.22890	−	1.03117i	0.262002	−	0.219846i
$23$	8.01307	+	2.91652i	1.67084	+	0.608136i	0.992010	−	0.126159i	$-0.0402651\pi$
$23$	8.01307	+	2.91652i	1.67084	+	0.608136i	0.678830	+	0.734295i	$0.262487\pi$
$24$	−1.43818	+	0.965209i	−0.293568	+	0.197022i
$25$	−0.827984	+	4.69573i	−0.165597	+	0.939146i
$26$	−1.00000			−0.196116
$27$	−1.04486	−	5.09002i	−0.201084	−	0.979574i
$28$	0.0373450			0.00705754
$29$	−0.722801	+	4.09921i	−0.134221	+	0.761204i	0.841178	+	0.540758i	$0.181863\pi$
$29$	−0.722801	+	4.09921i	−0.134221	+	0.761204i	−0.975399	+	0.220446i	$0.929249\pi$
$30$	0.0562396	+	0.832061i	0.0102679	+	0.151913i
$31$	8.19771	+	2.98372i	1.47235	+	0.535892i	0.948738	−	0.316064i	$-0.102361\pi$
$31$	8.19771	+	2.98372i	1.47235	+	0.535892i	0.523614	+	0.851956i	$0.324583\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	1.12424	+	2.54098i	0.195706	+	0.442327i
$34$	5.34498	−	1.94541i	0.916656	−	0.333636i
$35$	0.00899056	−	0.0155721i	0.00151968	−	0.00263217i
$36$	−0.913773	−	2.85745i	−0.152295	−	0.476242i
$37$	3.21107	+	5.56174i	0.527897	+	0.914344i	0.999471	+	0.0325176i	$0.0103525\pi$
$37$	3.21107	+	5.56174i	0.527897	+	0.914344i	−0.471575	+	0.881826i	$0.656314\pi$
$38$	1.10503	+	0.927234i	0.179260	+	0.150417i
$39$	0.481288	−	1.66384i	0.0770677	−	0.266428i
$40$	0.0836093	+	0.474172i	0.0132198	+	0.0749732i
$41$	−0.304760	−	1.72838i	−0.0475956	−	0.269928i	0.951718	−	0.306974i	$-0.0993164\pi$
$41$	−0.304760	−	1.72838i	−0.0475956	−	0.269928i	−0.999314	+	0.0370458i	$0.988205\pi$
$42$	−0.0179737	+	0.0621361i	−0.00277340	+	0.00958780i
$43$	9.34743	+	7.84342i	1.42547	+	1.19611i	0.948331	+	0.317283i	$0.102770\pi$
$43$	9.34743	+	7.84342i	1.42547	+	1.19611i	0.477138	+	0.878828i	$0.341674\pi$
$44$	0.802106	+	1.38929i	0.120922	+	0.209443i
$45$	−1.41148	−	0.306887i	−0.210412	−	0.0457481i
$46$	−4.26366	+	7.38488i	−0.628643	+	1.08884i
$47$	10.2441	−	3.72856i	1.49426	−	0.543867i	0.539695	−	0.841861i	$-0.318540\pi$
$47$	10.2441	−	3.72856i	1.49426	−	0.543867i	0.954568	+	0.297994i	$0.0963175\pi$
$48$	−0.700808	−	1.58394i	−0.101153	−	0.228622i
$49$	−5.36124	+	4.49862i	−0.765892	+	0.642660i
$50$	−4.48061	−	1.63081i	−0.633655	−	0.230631i
$51$	0.664382	+	9.82949i	0.0930321	+	1.37640i
$52$	0.173648	−	0.984808i	0.0240807	−	0.136568i
$53$	−1.74510			−0.239708			−0.119854	−	0.992792i	$-0.538243\pi$
$53$	−1.74510			−0.239708			−0.119854	+	0.992792i	$0.538243\pi$
$54$	5.19413	−	0.145116i	0.706831	−	0.0197477i
$55$	0.772408			0.104151
$56$	−0.00648489	+	0.0367776i	−0.000866580	+	0.00491462i
$57$	−2.07461	+	1.39233i	−0.274788	+	0.184419i
$58$	−3.91142	−	1.42364i	−0.513595	−	0.186933i
$59$	−6.81878	+	5.72164i	−0.887730	+	0.744894i	−0.967753	−	0.251899i	$-0.918945\pi$
$59$	−6.81878	+	5.72164i	−0.887730	+	0.744894i	0.0800237	+	0.996793i	$0.474500\pi$
$60$	−0.829187	−	0.0891008i	−0.107048	−	0.0115029i
$61$	9.25156	−	3.36729i	1.18454	−	0.431138i	0.326737	−	0.945115i	$-0.394051\pi$
$61$	9.25156	−	3.36729i	1.18454	−	0.431138i	0.857804	+	0.513978i	$0.171829\pi$
$62$	−4.36191	+	7.55505i	−0.553963	+	0.959492i
$63$	−0.0947339	−	0.0598107i	−0.0119354	−	0.00753544i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.368840	−	0.309494i	−0.0457490	−	0.0383880i
$66$	−2.69760	+	0.665928i	−0.332051	+	0.0819701i
$67$	0.0256044	+	0.145210i	0.00312808	+	0.0177402i	0.986332	−	0.164771i	$-0.0526885\pi$
$67$	0.0256044	+	0.145210i	0.00312808	+	0.0177402i	−0.983204	+	0.182511i	$0.941577\pi$
$68$	0.987712	+	5.60159i	0.119778	+	0.679293i
$69$	−10.2352	−	10.6483i	−1.23217	−	1.28191i
$70$	0.0137743	+	0.0115580i	0.00164635	+	0.00138145i
$71$	0.488931	+	0.846853i	0.0580254	+	0.100503i	0.893579	−	0.448906i	$-0.148186\pi$
$71$	0.488931	+	0.846853i	0.0580254	+	0.100503i	−0.835554	+	0.549409i	$0.814853\pi$
$72$	2.97271	−	0.403700i	0.350338	−	0.0475765i
$73$	−1.32294	+	2.29141i	−0.154839	+	0.268189i	−0.933000	−	0.359875i	$-0.882819\pi$
$73$	−1.32294	+	2.29141i	−0.154839	+	0.268189i	0.778161	+	0.628064i	$0.216153\pi$
$74$	−6.03484	+	2.19650i	−0.701536	+	0.255338i
$75$	4.86987	−	6.67013i	0.562324	−	0.770201i
$76$	−1.10503	+	0.927234i	−0.126756	+	0.106361i
$77$	0.0562963	+	0.0204902i	0.00641556	+	0.00233507i
$78$	1.55499	+	0.762899i	0.176068	+	0.0863813i
$79$	2.40733	−	13.6527i	0.270846	−	1.53604i	−0.481010	−	0.876715i	$-0.659730\pi$
$79$	2.40733	−	13.6527i	0.270846	−	1.53604i	0.751856	−	0.659328i	$-0.229159\pi$
$80$	−0.481487			−0.0538319
$81$	−2.25842	+	8.71203i	−0.250936	+	0.968004i
$82$	1.75505			0.193812
$83$	1.13955	−	6.46269i	0.125081	−	0.709372i	−0.856178	−	0.516681i	$-0.827167\pi$
$83$	1.13955	−	6.46269i	0.125081	−	0.709372i	0.981259	−	0.192691i	$-0.0617216\pi$
$84$	−0.0580710	−	0.0284904i	−0.00633606	−	0.00310856i
$85$	2.57354	+	0.936691i	0.279139	+	0.101598i
$86$	−9.34743	+	7.84342i	−1.00796	+	0.845778i
$87$	4.25123	−	5.82280i	0.455780	−	0.624269i
$88$	−1.50747	+	0.548673i	−0.160696	+	0.0584887i
$89$	−0.176290	+	0.305343i	−0.0186867	+	0.0323663i	−0.875218	−	0.483730i	$-0.839282\pi$
$89$	−0.176290	+	0.305343i	−0.0186867	+	0.0323663i	0.856531	+	0.516096i	$0.172615\pi$
$90$	0.547327	−	1.33675i	0.0576933	−	0.140906i
$91$	−0.0186725	−	0.0323417i	−0.00195741	−	0.00339033i
$92$	−6.53231	−	5.48126i	−0.681041	−	0.571461i
$93$	−10.4711	−	10.8937i	−1.08580	−	1.12962i
$94$	1.89304	+	10.7360i	0.195252	+	1.10733i
$95$	0.120608	+	0.684003i	0.0123741	+	0.0701772i
$96$	1.68157	−	0.415112i	0.171625	−	0.0423672i
$97$	14.4735	+	12.1447i	1.46956	+	1.23310i	0.916545	+	0.399932i	$0.130966\pi$
$97$	14.4735	+	12.1447i	1.46956	+	1.23310i	0.553012	+	0.833173i	$0.313478\pi$
$98$	−3.49930	−	6.06097i	−0.353483	−	0.612250i
$99$	0.190323	−	4.80887i	0.0191282	−	0.483310i
$100$	2.38409	−	4.12936i	0.238409	−	0.412936i
$101$	−7.72979	+	2.81341i	−0.769143	+	0.279945i	−0.696638	−	0.717423i	$-0.745322\pi$
$101$	−7.72979	+	2.81341i	−0.769143	+	0.279945i	−0.0725050	+	0.997368i	$0.523099\pi$
$102$	−9.79552	−	1.05258i	−0.969901	−	0.104221i
$103$	10.3497	−	8.68447i	1.01979	−	0.855706i	0.0301893	−	0.999544i	$-0.490389\pi$
$103$	10.3497	−	8.68447i	1.01979	−	0.855706i	0.989601	+	0.143838i	$0.0459445\pi$
$104$	0.939693	+	0.342020i	0.0921444	+	0.0335378i
$105$	−0.0258602	+	0.0173555i	−0.00252369	+	0.00169373i
$106$	0.303034	−	1.71859i	0.0294332	−	0.166924i
$107$	−15.8582			−1.53307			−0.766535	−	0.642203i	$-0.778021\pi$
$107$	−15.8582			−1.53307			−0.766535	+	0.642203i	$0.778021\pi$
$108$	−0.759039	+	5.14041i	−0.0730386	+	0.494637i
$109$	−6.99918			−0.670400			−0.335200	−	0.942147i	$-0.608804\pi$
$109$	−6.99918			−0.670400			−0.335200	+	0.942147i	$0.608804\pi$
$110$	−0.134127	+	0.760673i	−0.0127885	+	0.0725273i
$111$	−0.750131	−	11.0982i	−0.0711993	−	1.05339i
$112$	−0.0350928	−	0.0127727i	−0.00331596	−	0.00120691i
$113$	9.32724	−	7.82649i	0.877433	−	0.736254i	−0.0882165	−	0.996101i	$-0.528117\pi$
$113$	9.32724	−	7.82649i	0.877433	−	0.736254i	0.965650	+	0.259847i	$0.0836723\pi$
$114$	−1.01093	−	2.28487i	−0.0946821	−	0.213997i
$115$	−3.85819	+	1.40427i	−0.359778	+	0.130948i
$116$	2.08122	−	3.60479i	0.193237	−	0.334696i
$117$	−2.01774	+	2.22008i	−0.186540	+	0.205246i
$118$	−4.45064	−	7.70874i	−0.409715	−	0.709647i
$119$	0.162722	+	0.136540i	0.0149167	+	0.0125166i
$120$	0.231734	−	0.801117i	0.0211543	−	0.0731317i
$121$	−1.46325	−	8.29848i	−0.133022	−	0.754408i
$122$	1.70962	+	9.69573i	0.154782	+	0.877810i
$123$	−0.844682	+	2.92011i	−0.0761624	+	0.263298i
$124$	−6.68283	−	5.60756i	−0.600136	−	0.503574i
$125$	−2.35162	−	4.07313i	−0.210336	−	0.364312i
$126$	0.0753524	−	0.0829087i	0.00671292	−	0.00738609i
$127$	−7.84671	+	13.5909i	−0.696283	+	1.20600i	0.273464	+	0.961882i	$0.411831\pi$
$127$	−7.84671	+	13.5909i	−0.696283	+	1.20600i	−0.969746	+	0.244115i	$0.921503\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	−8.55139	−	19.3276i	−0.752908	−	1.70170i
$130$	0.368840	−	0.309494i	0.0323494	−	0.0271444i
$131$	7.80836	+	2.84201i	0.682220	+	0.248308i	0.659800	−	0.751441i	$-0.270641\pi$
$131$	7.80836	+	2.84201i	0.682220	+	0.248308i	0.0224193	+	0.999749i	$0.492863\pi$
$132$	−0.187378	−	2.77225i	−0.0163092	−	0.241294i
$133$	−0.00935458	+	0.0530525i	−0.000811145	+	0.00460023i
$134$	−0.147450			−0.0127377
$135$	1.96072	+	1.55403i	0.168752	+	0.133749i
$136$	−5.68801			−0.487742
$137$	0.391707	−	2.22148i	0.0334658	−	0.189794i	−0.963492	−	0.267737i	$-0.913724\pi$
$137$	0.391707	−	2.22148i	0.0334658	−	0.189794i	0.996958	+	0.0779431i	$0.0248352\pi$
$138$	12.2639	−	8.23065i	1.04397	−	0.700640i
$139$	−6.84838	−	2.49260i	−0.580872	−	0.211420i	0.0348382	−	0.999393i	$-0.488908\pi$
$139$	−6.84838	−	2.49260i	−0.580872	−	0.211420i	−0.615710	+	0.787973i	$0.711131\pi$
$140$	−0.0137743	+	0.0115580i	−0.00116414	+	0.000976833i
$141$	−18.7740	−	2.01738i	−1.58106	−	0.169894i
$142$	−0.918889	+	0.334448i	−0.0771114	+	0.0280663i
$143$	0.802106	−	1.38929i	0.0670755	−	0.116178i
$144$	−0.118640	+	2.99765i	−0.00988664	+	0.249804i
$145$	−1.00208	−	1.73566i	−0.0832184	−	0.144138i
$146$	−2.02687	−	1.70074i	−0.167745	−	0.140755i
$147$	11.7687	−	2.90521i	0.970662	−	0.239617i
$148$	−1.11519	−	6.32457i	−0.0916683	−	0.519877i
$149$	2.29272	+	13.0027i	0.187827	+	1.06522i	0.922269	+	0.386549i	$0.126333\pi$
$149$	2.29272	+	13.0027i	0.187827	+	1.06522i	−0.734442	+	0.678672i	$0.762556\pi$
$150$	5.72316	+	5.95414i	0.467294	+	0.486154i
$151$	10.3685	+	8.70020i	0.843776	+	0.708012i	0.958410	−	0.285396i	$-0.0921251\pi$
$151$	10.3685	+	8.70020i	0.843776	+	0.708012i	−0.114634	+	0.993408i	$0.536570\pi$
$152$	−0.721260	−	1.24926i	−0.0585019	−	0.101328i
$153$	6.46580	−	15.7916i	0.522729	−	1.27667i
$154$	−0.0299546	+	0.0518830i	−0.00241381	+	0.00418085i
$155$	−3.94709	+	1.43662i	−0.317038	+	0.115392i
$156$	−1.02133	+	1.39889i	−0.0817718	+	0.112001i
$157$	1.04089	−	0.873409i	0.0830719	−	0.0697056i	−0.600306	−	0.799770i	$-0.704955\pi$
$157$	1.04089	−	0.873409i	0.0830719	−	0.0697056i	0.683378	+	0.730065i	$0.260510\pi$
$158$	13.0272	+	4.74152i	1.03639	+	0.377215i
$159$	2.71361	+	1.33134i	0.215203	+	0.105582i
$160$	0.0836093	−	0.474172i	0.00660990	−	0.0374866i
$161$	−0.318453			−0.0250976
$162$	−8.18751	−	3.73694i	−0.643271	−	0.293602i
$163$	20.6396			1.61662			0.808308	−	0.588760i	$-0.200384\pi$
$163$	20.6396			1.61662			0.808308	+	0.588760i	$0.200384\pi$
$164$	−0.304760	+	1.72838i	−0.0237978	+	0.134964i
$165$	−1.20108	−	0.589269i	−0.0935043	−	0.0458745i
$166$	6.16663	+	2.24447i	0.478623	+	0.174205i
$167$	−15.7874	+	13.2472i	−1.22166	+	1.02510i	−0.222928	+	0.974835i	$0.571561\pi$
$167$	−15.7874	+	13.2472i	−1.22166	+	1.02510i	−0.998736	+	0.0502624i	$0.983994\pi$
$168$	0.0381415	−	0.0522414i	0.00294268	−	0.00403051i
$169$	−0.939693	+	0.342020i	−0.0722840	+	0.0263092i
$170$	−1.36935	+	2.37178i	−0.105024	+	0.181908i
$171$	4.28820	−	0.582345i	0.327927	−	0.0445330i
$172$	−6.10110	−	10.5674i	−0.465205	−	0.805758i
$173$	−4.79667	−	4.02488i	−0.364684	−	0.306006i	0.441970	−	0.897030i	$-0.354280\pi$
$173$	−4.79667	−	4.02488i	−0.364684	−	0.306006i	−0.806654	+	0.591023i	$0.798724\pi$
$174$	4.99612	+	5.19776i	0.378755	+	0.394041i
$175$	−0.0309211	−	0.175362i	−0.00233741	−	0.0132561i
$176$	−0.278569	−	1.57984i	−0.0209979	−	0.119085i
$177$	14.9681	−	3.69503i	1.12507	−	0.277736i
$178$	−0.270092	−	0.226634i	−0.0202442	−	0.0169869i
$179$	−12.3294	−	21.3551i	−0.921540	−	1.59615i	−0.797033	−	0.603936i	$-0.793598\pi$
$179$	−12.3294	−	21.3551i	−0.921540	−	1.59615i	−0.124507	−	0.992219i	$-0.539735\pi$
$180$	1.22140	+	0.771136i	0.0910378	+	0.0574771i
$181$	−3.53195	+	6.11751i	−0.262528	+	0.454711i	−0.966913	−	0.255107i	$-0.917889\pi$
$181$	−3.53195	+	6.11751i	−0.262528	+	0.454711i	0.704385	+	0.709818i	$0.251223\pi$
$182$	0.0350928	−	0.0127727i	0.00260125	−	0.000946778i
$183$	−16.9550	−	1.82191i	−1.25335	−	0.134679i
$184$	6.53231	−	5.48126i	0.481568	−	0.404084i
$185$	−2.90570	−	1.05759i	−0.213631	−	0.0777553i
$186$	12.5465	−	8.42031i	0.919950	−	0.617407i
$187$	−1.58450	+	8.98615i	−0.115870	+	0.657132i
$188$	−10.9016			−0.795080
$189$	0.101681	+	0.165277i	0.00739617	+	0.0120221i
$190$	−0.694554			−0.0503883
$191$	2.20776	−	12.5208i	0.159748	−	0.905976i	−0.794567	−	0.607176i	$-0.792302\pi$
$191$	2.20776	−	12.5208i	0.159748	−	0.905976i	0.954316	−	0.298801i	$-0.0965865\pi$
$192$	0.116804	+	1.72811i	0.00842960	+	0.124715i
$193$	−15.1561	−	5.51635i	−1.09096	−	0.397076i	−0.266982	−	0.963702i	$-0.586026\pi$
$193$	−15.1561	−	5.51635i	−1.09096	−	0.397076i	−0.823975	+	0.566626i	$0.808248\pi$
$194$	−14.4735	+	12.1447i	−1.03913	+	0.871937i
$195$	0.337430	+	0.762647i	0.0241638	+	0.0546143i
$196$	6.57654	−	2.39366i	0.469753	−	0.170976i
$197$	5.42715	−	9.40010i	0.386669	−	0.669730i	−0.605331	−	0.795974i	$-0.706959\pi$
$197$	5.42715	−	9.40010i	0.386669	−	0.669730i	0.991999	+	0.126245i	$0.0402924\pi$
$198$	4.70277	+	1.02248i	0.334211	+	0.0726648i
$199$	−7.03545	−	12.1858i	−0.498730	−	0.863826i	0.501269	−	0.865291i	$-0.332867\pi$
$199$	−7.03545	−	12.1858i	−0.498730	−	0.863826i	−0.999999	+	0.00146596i	$0.999533\pi$
$200$	3.65263	+	3.06492i	0.258280	+	0.216723i
$201$	0.0709659	−	0.245333i	0.00500555	−	0.0173045i
$202$	−1.42841	−	8.10090i	−0.100502	−	0.569977i
$203$	−0.0269930	−	0.153085i	−0.00189454	−	0.0107445i
$204$	2.73757	−	9.46393i	0.191668	−	0.662608i
$205$	0.647332	+	0.543176i	0.0452116	+	0.0379370i
$206$	6.75532	+	11.7005i	0.470665	+	0.815216i
$207$	7.79204	+	24.3664i	0.541584	+	1.69358i
$208$	−0.500000	+	0.866025i	−0.0346688	+	0.0600481i
$209$	−2.17455	+	0.791472i	−0.150417	+	0.0547472i
$210$	−0.0126013	−	0.0284810i	−0.000869573	−	0.00196538i
$211$	−2.04007	+	1.71183i	−0.140444	+	0.117847i	−0.710303	−	0.703896i	$-0.751442\pi$
$211$	−2.04007	+	1.71183i	−0.140444	+	0.117847i	0.569859	+	0.821743i	$0.306998\pi$
$212$	1.63986	+	0.596860i	0.112626	+	0.0409925i
$213$	−0.114218	−	1.68985i	−0.00782609	−	0.115787i
$214$	2.75375	−	15.6173i	0.188242	−	1.06757i
$215$	−5.87520			−0.400685
$216$	−4.93051	−	1.64013i	−0.335479	−	0.111597i
$217$	−0.325791			−0.0221161
$218$	1.21539	−	6.89284i	0.0823169	−	0.466842i
$219$	3.80527	−	2.55384i	0.257137	−	0.172572i
$220$	−0.725826	−	0.264179i	−0.0489352	−	0.0178109i
$221$	4.35727	−	3.65618i	0.293101	−	0.245941i
$222$	11.0598	+	1.18844i	0.742285	+	0.0797628i
$223$	22.8775	−	8.32674i	1.53199	−	0.557600i	0.567885	−	0.823108i	$-0.307762\pi$
$223$	22.8775	−	8.32674i	1.53199	−	0.557600i	0.964109	+	0.265508i	$0.0855397\pi$
$224$	0.0186725	−	0.0323417i	0.00124761	−	0.00216092i
$225$	−12.6612	+	6.65675i	−0.844082	+	0.443784i
$226$	6.08793	+	10.5446i	0.404963	+	0.701416i
$227$	20.1143	+	16.8779i	1.33503	+	1.12022i	0.982873	+	0.184285i	$0.0589969\pi$
$227$	20.1143	+	16.8779i	1.33503	+	1.12022i	0.352159	+	0.935940i	$0.385448\pi$
$228$	2.42570	−	0.598807i	0.160646	−	0.0396570i
$229$	−1.47265	−	8.35183i	−0.0973157	−	0.551905i	−0.994013	−	0.109261i	$-0.965152\pi$
$229$	−1.47265	−	8.35183i	−0.0973157	−	0.551905i	0.896697	−	0.442644i	$-0.145959\pi$
$230$	−0.712964	−	4.04342i	−0.0470115	−	0.266615i
$231$	−0.0719081	−	0.0748104i	−0.00473121	−	0.00492216i
$232$	3.18862	+	2.67557i	0.209343	+	0.175660i
$233$	11.8242	+	20.4800i	0.774626	+	1.34169i	0.935004	+	0.354637i	$0.115395\pi$
$233$	11.8242	+	20.4800i	0.774626	+	1.34169i	−0.160378	+	0.987056i	$0.551271\pi$
$234$	−1.83597	−	2.37260i	−0.120021	−	0.155101i
$235$	−2.62449	+	4.54575i	−0.171203	+	0.296532i
$236$	8.36447	−	3.04442i	0.544481	−	0.198175i
$237$	−14.1590	+	19.3931i	−0.919723	+	1.25972i
$238$	−0.162722	+	0.136540i	−0.0105477	+	0.00885057i
$239$	19.4005	+	7.06121i	1.25492	+	0.456752i	0.882060	−	0.471137i	$-0.156156\pi$
$239$	19.4005	+	7.06121i	1.25492	+	0.456752i	0.372856	+	0.927889i	$0.378379\pi$
$240$	0.748706	+	0.367326i	0.0483288	+	0.0237108i
$241$	−1.76688	+	10.0205i	−0.113814	+	0.645474i	0.873516	+	0.486796i	$0.161834\pi$
$241$	−1.76688	+	10.0205i	−0.113814	+	0.645474i	−0.987330	+	0.158678i	$0.949277\pi$
$242$	8.42650			0.541676
$243$	10.1582	−	11.8242i	0.651650	−	0.758520i
$244$	−9.84530			−0.630281
$245$	0.585149	−	3.31854i	0.0373838	−	0.212014i
$246$	−2.72907	−	1.33892i	−0.173999	−	0.0853665i
$247$	1.35552	+	0.493371i	0.0862500	+	0.0313924i
$248$	6.68283	−	5.60756i	0.424360	−	0.356081i
$249$	−6.70236	+	9.18004i	−0.424745	+	0.581762i
$250$	4.41961	−	1.60861i	0.279520	−	0.101737i
$251$	4.42487	−	7.66411i	0.279296	−	0.483754i	−0.691914	−	0.721980i	$-0.743232\pi$
$251$	4.42487	−	7.66411i	0.279296	−	0.483754i	0.971210	+	0.238226i	$0.0765657\pi$
$252$	0.0685643	+	0.0886046i	0.00431915	+	0.00558156i
$253$	−6.83982	−	11.8469i	−0.430016	−	0.744810i
$254$	−12.0219	−	10.0875i	−0.754318	−	0.632948i
$255$	−3.28722	−	3.41989i	−0.205854	−	0.214162i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−0.413462	−	2.34486i	−0.0257910	−	0.146268i	0.969193	−	0.246303i	$-0.0792158\pi$
$257$	−0.413462	−	2.34486i	−0.0257910	−	0.146268i	−0.994984	+	0.100035i	$0.968105\pi$
$258$	20.5189	−	5.06528i	1.27745	−	0.315351i
$259$	−0.183724	−	0.154163i	−0.0114161	−	0.00957921i
$260$	0.240744	+	0.416980i	0.0149303	+	0.0258600i
$261$	−11.0528	+	5.81112i	−0.684152	+	0.359699i
$262$	−4.15474	+	7.19622i	−0.256681	+	0.444584i
$263$	−8.65958	+	3.15183i	−0.533972	+	0.194350i	−0.594911	−	0.803791i	$-0.702813\pi$
$263$	−8.65958	+	3.15183i	−0.533972	+	0.194350i	0.0609388	+	0.998142i	$0.480591\pi$
$264$	2.76267	+	0.296865i	0.170031	+	0.0182708i
$265$	0.643664	−	0.540099i	0.0395400	−	0.0331780i
$266$	−0.0506221	−	0.0184249i	−0.00310384	−	0.00112970i
$267$	0.507074	−	0.340313i	0.0310324	−	0.0208268i
$268$	0.0256044	−	0.145210i	0.00156404	−	0.00887010i
$269$	−15.7633			−0.961106			−0.480553	−	0.876966i	$-0.659564\pi$
$269$	−15.7633			−0.961106			−0.480553	+	0.876966i	$0.659564\pi$
$270$	−1.87089	+	1.66107i	−0.113859	+	0.101090i
$271$	−15.9114			−0.966550			−0.483275	−	0.875469i	$-0.660553\pi$
$271$	−15.9114			−0.966550			−0.483275	+	0.875469i	$0.660553\pi$
$272$	0.987712	−	5.60159i	0.0598888	−	0.339646i
$273$	0.00436204	+	0.0645362i	0.000264003	+	0.00390591i
$274$	2.11971	+	0.771513i	0.128057	+	0.0466088i
$275$	5.85960	−	4.91678i	0.353347	−	0.296493i
$276$	5.97602	+	13.5068i	0.359714	+	0.813013i
$277$	−17.9884	+	6.54724i	−1.08082	+	0.393385i	−0.820212	−	0.572060i	$-0.806144\pi$
$277$	−17.9884	+	6.54724i	−1.08082	+	0.393385i	−0.260606	+	0.965445i	$0.583922\pi$
$278$	3.64394	−	6.31150i	0.218549	−	0.378538i
$279$	7.97159	+	24.9279i	0.477247	+	1.49239i
$280$	−0.00899056	−	0.0155721i	−0.000537289	−	0.000930612i
$281$	−6.26440	−	5.25646i	−0.373703	−	0.313574i	0.436522	−	0.899694i	$-0.356210\pi$
$281$	−6.26440	−	5.25646i	−0.373703	−	0.313574i	−0.810224	+	0.586120i	$0.800655\pi$
$282$	5.24680	−	18.1385i	0.312443	−	1.08013i
$283$	1.31422	+	7.45334i	0.0781226	+	0.443055i	0.998630	+	0.0523297i	$0.0166647\pi$
$283$	1.31422	+	7.45334i	0.0781226	+	0.443055i	−0.920507	+	0.390725i	$0.872224\pi$
$284$	−0.169804	−	0.963005i	−0.0100760	−	0.0571438i
$285$	0.334281	−	1.15563i	0.0198011	−	0.0684534i
$286$	1.22890	+	1.03117i	0.0726663	+	0.0609742i
$287$	0.0327711	+	0.0567612i	0.00193442	+	0.00335051i
$288$	−2.93151	−	0.637374i	−0.172741	−	0.0375576i
$289$	−7.67671	+	13.2964i	−0.451571	+	0.782144i
$290$	1.88330	−	0.685465i	0.110591	−	0.0402519i
$291$	−13.2409	−	29.9266i	−0.776195	−	1.75433i
$292$	2.02687	−	1.70074i	0.118614	−	0.0995286i
$293$	5.62704	+	2.04808i	0.328735	+	0.119650i	0.501115	−	0.865381i	$-0.332923\pi$
$293$	5.62704	+	2.04808i	0.328735	+	0.119650i	−0.172380	+	0.985031i	$0.555146\pi$
$294$	0.817465	+	12.0943i	0.0476755	+	0.705357i
$295$	0.744231	−	4.22074i	0.0433308	−	0.245741i
$296$	6.42214			0.373279
$297$	−3.96463	+	7.33254i	−0.230051	+	0.425477i
$298$	−13.2033			−0.764844
$299$	−1.48075	+	8.39778i	−0.0856343	+	0.485656i
$300$	−6.85750	+	4.60228i	−0.395918	+	0.265713i
$301$	−0.428209	−	0.155855i	−0.0246816	−	0.00898336i
$302$	−10.3685	+	8.70020i	−0.596640	+	0.500640i
$303$	14.1661	+	1.52222i	0.813820	+	0.0874495i
$304$	1.35552	−	0.493371i	0.0777447	−	0.0282968i
$305$	−2.37019	+	4.10529i	−0.135717	+	0.235068i
$306$	14.4289	+	9.10975i	0.824845	+	0.520770i
$307$	−4.56552	−	7.90771i	−0.260568	−	0.451317i	0.705825	−	0.708386i	$-0.250576\pi$
$307$	−4.56552	−	7.90771i	−0.260568	−	0.451317i	−0.966393	+	0.257069i	$0.917243\pi$
$308$	−0.0458932	−	0.0385090i	−0.00261501	−	0.00219425i
$309$	−22.7191	+	5.60843i	−1.29244	+	0.319052i
$310$	−0.729393	−	4.13659i	−0.0414267	−	0.234943i
$311$	−0.00301328	−	0.0170892i	−0.000170867	−	0.000969037i	0.984722	−	0.174133i	$-0.0557122\pi$
$311$	−0.00301328	−	0.0170892i	−0.000170867	−	0.000969037i	−0.984893	+	0.173164i	$0.944601\pi$
$312$	−1.20028	−	1.24873i	−0.0679527	−	0.0706953i
$313$	−2.13352	−	1.79024i	−0.120594	−	0.101190i	0.580496	−	0.814263i	$-0.302859\pi$
$313$	−2.13352	−	1.79024i	−0.120594	−	0.101190i	−0.701090	+	0.713073i	$0.747303\pi$
$314$	0.679391	+	1.17674i	0.0383403	+	0.0664073i
$315$	0.0534527	−	0.00725898i	0.00301172	−	0.000408997i
$316$	−6.93163	+	12.0059i	−0.389935	+	0.675387i
$317$	16.9768	−	6.17905i	0.953513	−	0.347050i	0.182025	−	0.983294i	$-0.441735\pi$
$317$	16.9768	−	6.17905i	0.953513	−	0.347050i	0.771488	+	0.636244i	$0.219513\pi$
$318$	−1.78232	+	2.44120i	−0.0999478	+	0.136896i
$319$	5.11522	−	4.29218i	0.286398	−	0.240316i
$320$	0.452450	+	0.164678i	0.0252927	+	0.00920579i
$321$	24.6593	+	12.0982i	1.37635	+	0.675256i
$322$	0.0552988	−	0.313615i	0.00308168	−	0.0174771i
$323$	−8.20506			−0.456542
$324$	5.10191	−	7.41421i	0.283440	−	0.411900i
$325$	−4.76817			−0.264490
$326$	−3.58402	+	20.3260i	−0.198501	+	1.12575i
$327$	10.8836	+	5.33966i	0.601866	+	0.295284i
$328$	−1.64920	−	0.600261i	−0.0910620	−	0.0331439i
$329$	−0.311872	+	0.261692i	−0.0171941	+	0.0144275i
$330$	0.788882	−	1.08051i	0.0434265	−	0.0594802i
$331$	−24.9383	+	9.07682i	−1.37074	+	0.498907i	−0.919356	−	0.393426i	$-0.871290\pi$
$331$	−24.9383	+	9.07682i	−1.37074	+	0.498907i	−0.451379	+	0.892332i	$0.649068\pi$
$332$	−3.28119	+	5.68319i	−0.180079	+	0.311906i
$333$	−7.30032	+	17.8298i	−0.400055	+	0.977065i
$334$	−10.3045	−	17.8479i	−0.563836	−	0.976592i
$335$	−0.0543855	−	0.0456349i	−0.00297140	−	0.00249330i
$336$	0.0448246	+	0.0466337i	0.00244538	+	0.00254408i
$337$	0.761421	+	4.31823i	0.0414772	+	0.235229i	0.998498	−	0.0547908i	$-0.0174492\pi$
$337$	0.761421	+	4.31823i	0.0414772	+	0.235229i	−0.957021	+	0.290020i	$0.906338\pi$
$338$	−0.173648	−	0.984808i	−0.00944522	−	0.0535665i
$339$	−20.4746	+	5.05434i	−1.11203	+	0.274514i
$340$	−2.09797	−	1.76040i	−0.113778	−	0.0954713i
$341$	−6.99743	−	12.1199i	−0.378932	−	0.656330i
$342$	−0.171140	+	4.32417i	−0.00925419	+	0.233824i
$343$	0.261389	−	0.452739i	0.0141137	−	0.0244456i
$344$	11.4663	−	4.17340i	0.618222	−	0.225015i
$345$	7.07075	+	0.759791i	0.380676	+	0.0409058i
$346$	4.79667	−	4.02488i	0.257871	−	0.216379i
$347$	−2.56597	−	0.933936i	−0.137748	−	0.0501363i	0.272226	−	0.962233i	$-0.412240\pi$
$347$	−2.56597	−	0.933936i	−0.137748	−	0.0501363i	−0.409974	+	0.912097i	$0.634462\pi$
$348$	−5.98636	+	4.01763i	−0.320903	+	0.215368i
$349$	−5.69363	+	32.2902i	−0.304773	+	1.72845i	0.319798	+	0.947486i	$0.396385\pi$
$349$	−5.69363	+	32.2902i	−0.304773	+	1.72845i	−0.624571	+	0.780968i	$0.714726\pi$
$350$	0.178067			0.00951810
$351$	4.83125	−	1.91286i	0.257873	−	0.102101i
$352$	1.60421			0.0855048
$353$	0.909765	−	5.15953i	0.0484219	−	0.274614i	−0.950978	−	0.309259i	$-0.899919\pi$
$353$	0.909765	−	5.15953i	0.0484219	−	0.274614i	0.999400	+	0.0346450i	$0.0110300\pi$
$354$	1.03971	+	15.3824i	0.0552597	+	0.817564i
$355$	−0.442433	−	0.161032i	−0.0234819	−	0.00854672i
$356$	0.270092	−	0.226634i	0.0143148	−	0.0120116i
$357$	−0.148864	−	0.336458i	−0.00787874	−	0.0178073i
$358$	23.1716	−	8.43378i	1.22466	−	0.445739i
$359$	−17.2269	+	29.8378i	−0.909199	+	1.57478i	−0.0940201	+	0.995570i	$0.529972\pi$
$359$	−17.2269	+	29.8378i	−0.909199	+	1.57478i	−0.815179	+	0.579209i	$0.803362\pi$
$360$	−0.971514	+	1.06894i	−0.0512033	+	0.0563380i
$361$	8.45957	+	14.6524i	0.445240	+	0.771179i
$362$	−5.41126	−	4.54058i	−0.284409	−	0.238648i
$363$	−4.05557	+	14.0203i	−0.212862	+	0.735877i
$364$	0.00648489	+	0.0367776i	0.000339901	+	0.00192767i
$365$	−0.221221	−	1.25461i	−0.0115792	−	0.0656691i
$366$	4.73842	−	16.3810i	0.247681	−	0.856249i
$367$	−2.24284	−	1.88196i	−0.117075	−	0.0982377i	0.582371	−	0.812923i	$-0.302125\pi$
$367$	−2.24284	−	1.88196i	−0.117075	−	0.0982377i	−0.699446	+	0.714686i	$0.746570\pi$
$368$	4.26366	+	7.38488i	0.222259	+	0.384964i
$369$	3.54122	−	3.89633i	0.184349	−	0.202835i
$370$	1.54609	−	2.67790i	0.0803773	−	0.139218i
$371$	0.0612405	−	0.0222897i	0.00317945	−	0.00115723i
$372$	6.11372	+	13.8180i	0.316982	+	0.716431i
$373$	−4.10872	+	3.44762i	−0.212741	+	0.178511i	−0.742931	−	0.669368i	$-0.766565\pi$
$373$	−4.10872	+	3.44762i	−0.212741	+	0.178511i	0.530190	+	0.847879i	$0.322121\pi$
$374$	−8.57448	−	3.12086i	−0.443376	−	0.161376i
$375$	0.549358	+	8.12772i	0.0283687	+	0.419714i
$376$	1.89304	−	10.7360i	0.0976262	−	0.553666i
$377$	−4.16245			−0.214377
$378$	−0.180423	+	0.0714357i	−0.00927995	+	0.00367426i
$379$	−0.557961			−0.0286606			−0.0143303	−	0.999897i	$-0.504562\pi$
$379$	−0.557961			−0.0286606			−0.0143303	+	0.999897i	$0.504562\pi$
$380$	0.120608	−	0.684003i	0.00618706	−	0.0350886i
$381$	22.5700	−	15.1474i	1.15630	−	0.776026i
$382$	11.9472	+	4.34844i	0.611274	+	0.222486i
$383$	8.41516	−	7.06116i	0.429995	−	0.360808i	−0.401955	−	0.915659i	$-0.631669\pi$
$383$	8.41516	−	7.06116i	0.429995	−	0.360808i	0.831950	+	0.554851i	$0.187225\pi$
$384$	−1.72214	−	0.185053i	−0.0878824	−	0.00944346i
$385$	−0.0271059	+	0.00986576i	−0.00138145	+	0.000502806i
$386$	8.06437	−	13.9679i	0.410466	−	0.710947i
$387$	−1.44766	+	36.5780i	−0.0735889	+	1.85936i
$388$	−9.44688	−	16.3625i	−0.479593	−	0.830679i
$389$	−3.22891	−	2.70937i	−0.163712	−	0.137371i	0.557251	−	0.830344i	$-0.311856\pi$
$389$	−3.22891	−	2.70937i	−0.163712	−	0.137371i	−0.720963	+	0.692973i	$0.756300\pi$
$390$	−0.809655	+	0.199871i	−0.0409985	+	0.0101209i
$391$	−8.42254	−	47.7666i	−0.425946	−	2.41566i
$392$	1.21530	+	6.89228i	0.0613817	+	0.348113i
$393$	−9.97373	−	10.3763i	−0.503108	−	0.523414i
$394$	8.31488	+	6.97701i	0.418898	+	0.351497i
$395$	3.33749	+	5.78070i	0.167927	+	0.290859i
$396$	−1.82358	+	4.45377i	−0.0916382	+	0.223810i
$397$	−8.76730	+	15.1854i	−0.440018	+	0.762134i	−0.997690	−	0.0679273i	$-0.978361\pi$
$397$	−8.76730	+	15.1854i	−0.440018	+	0.762134i	0.557672	+	0.830061i	$0.311695\pi$
$398$	13.2223	−	4.81253i	0.662775	−	0.241230i
$399$	0.0550199	−	0.0753593i	0.00275444	−	0.00377268i
$400$	−3.65263	+	3.06492i	−0.182632	+	0.153246i
$401$	31.5815	+	11.4947i	1.57710	+	0.574019i	0.974572	−	0.224075i	$-0.0719362\pi$
$401$	31.5815	+	11.4947i	1.57710	+	0.574019i	0.602532	+	0.798094i	$0.294158\pi$
$402$	0.229283	+	0.112489i	0.0114356	+	0.00561046i
$403$	−1.51488	+	8.59128i	−0.0754613	+	0.427962i
$404$	8.22587			0.409252
$405$	−1.86332	−	3.91232i	−0.0925893	−	0.194405i
$406$	0.155447			0.00771468
$407$	1.78901	−	10.1460i	0.0886778	−	0.502917i
$408$	8.84478	+	4.33937i	0.437882	+	0.214831i
$409$	10.7728	+	3.92096i	0.532679	+	0.193879i	0.594334	−	0.804218i	$-0.297416\pi$
$409$	10.7728	+	3.92096i	0.532679	+	0.193879i	−0.0616553	+	0.998098i	$0.519638\pi$
$410$	−0.647332	+	0.543176i	−0.0319694	+	0.0268255i
$411$	−2.30387	+	3.15554i	−0.113641	+	0.155652i
$412$	−12.6958	+	4.62091i	−0.625479	+	0.227656i
$413$	0.166209	−	0.287883i	0.00817862	−	0.0141658i
$414$	−25.3493	+	3.44248i	−1.24585	+	0.169189i
$415$	1.57985	+	2.73638i	0.0775519	+	0.134324i
$416$	−0.766044	−	0.642788i	−0.0375584	−	0.0315153i
$417$	8.74753	+	9.10059i	0.428369	+	0.445658i
$418$	−0.401841	−	2.27895i	−0.0196547	−	0.111467i
$419$	1.01044	+	5.73047i	0.0493631	+	0.279952i	0.999491	−	0.0319092i	$-0.0101587\pi$
$419$	1.01044	+	5.73047i	0.0493631	+	0.279952i	−0.950128	+	0.311861i	$0.899048\pi$
$420$	0.0302365	−	0.00746419i	0.00147539	−	0.000364215i
$421$	−17.8740	−	14.9980i	−0.871123	−	0.730959i	0.0932112	−	0.995646i	$-0.470287\pi$
$421$	−17.8740	−	14.9980i	−0.871123	−	0.730959i	−0.964334	+	0.264687i	$0.914731\pi$
$422$	−1.33156	−	2.30634i	−0.0648195	−	0.112271i
$423$	27.6543	+	17.4597i	1.34460	+	0.848919i
$424$	−0.872551	+	1.51130i	−0.0423748	+	0.0733954i
$425$	25.4858	−	9.27606i	1.23624	−	0.449955i
$426$	1.68401	+	0.180956i	0.0815906	+	0.00876737i
$427$	−0.281654	+	0.236335i	−0.0136302	+	0.0114371i
$428$	14.9018	+	5.42382i	0.720307	+	0.262170i
$429$	−2.30715	+	1.54840i	−0.111390	+	0.0747575i
$430$	1.02022	−	5.78594i	0.0491993	−	0.279023i
$431$	11.9642			0.576295			0.288148	−	0.957586i	$-0.406961\pi$
$431$	11.9642			0.576295			0.288148	+	0.957586i	$0.406961\pi$
$432$	2.47139	−	4.57080i	0.118905	−	0.219913i
$433$	17.8832			0.859414			0.429707	−	0.902968i	$-0.358617\pi$
$433$	17.8832			0.859414			0.429707	+	0.902968i	$0.358617\pi$
$434$	0.0565730	−	0.320841i	0.00271559	−	0.0154009i
$435$	0.234094	+	3.46341i	0.0112240	+	0.166058i
$436$	6.57707	+	2.39386i	0.314985	+	0.114645i
$437$	9.42299	−	7.90682i	0.450763	−	0.378235i
$438$	1.85426	+	4.19093i	0.0885999	+	0.200250i
$439$	−7.21436	+	2.62581i	−0.344323	+	0.125323i	−0.508392	−	0.861126i	$-0.669760\pi$
$439$	−7.21436	+	2.62581i	−0.344323	+	0.125323i	0.164070	+	0.986449i	$0.447538\pi$
$440$	0.386204	−	0.668925i	0.0184115	−	0.0318897i
$441$	−20.5165	−	4.46073i	−0.976975	−	0.212416i
$442$	2.84400	+	4.92596i	0.135275	+	0.234304i
$443$	23.4632	+	19.6880i	1.11477	+	0.935405i	0.998329	−	0.0577926i	$-0.0184062\pi$
$443$	23.4632	+	19.6880i	1.11477	+	0.935405i	0.116443	+	0.993197i	$0.462851\pi$
$444$	−3.09090	+	10.6854i	−0.146688	+	0.507107i
$445$	−0.0294789	−	0.167183i	−0.00139744	−	0.00792525i
$446$	4.22760	+	23.9759i	0.200183	+	1.13529i
$447$	6.35457	−	21.9681i	0.300561	−	1.03906i
$448$	0.0286079	+	0.0240049i	0.00135160	+	0.00113412i
$449$	−19.3567	−	33.5268i	−0.913500	−	1.58223i	−0.809083	−	0.587695i	$-0.800035\pi$
$449$	−19.3567	−	33.5268i	−0.913500	−	1.58223i	−0.104418	−	0.994534i	$-0.533298\pi$
$450$	−4.35703	−	13.6248i	−0.205392	−	0.642280i
$451$	−1.40773	+	2.43826i	−0.0662875	+	0.114813i
$452$	−11.4416	+	4.16439i	−0.538166	+	0.195876i
$453$	−9.48550	−	21.4388i	−0.445668	−	1.00728i
$454$	−20.1143	+	16.8779i	−0.944010	+	0.792119i
$455$	0.0168967	+	0.00614991i	0.000792131	+	0.000288312i
$456$	0.168492	+	2.49283i	0.00789036	+	0.116737i
$457$	0.713370	−	4.04572i	0.0333700	−	0.189251i	−0.963566	−	0.267470i	$-0.913812\pi$
$457$	0.713370	−	4.04572i	0.0333700	−	0.189251i	0.996936	+	0.0782193i	$0.0249234\pi$
$458$	8.48067			0.396276
$459$	−22.1016	+	19.6230i	−1.03162	+	0.915922i
$460$	4.10580			0.191434
$461$	1.73568	−	9.84353i	0.0808386	−	0.458459i	−0.917339	−	0.398108i	$-0.869667\pi$
$461$	1.73568	−	9.84353i	0.0808386	−	0.458459i	0.998177	−	0.0603508i	$-0.0192219\pi$
$462$	0.0861606	−	0.0578250i	0.00400855	−	0.00269026i
$463$	−6.00349	−	2.18509i	−0.279006	−	0.101550i	0.198727	−	0.980055i	$-0.436319\pi$
$463$	−6.00349	−	2.18509i	−0.279006	−	0.101550i	−0.477733	+	0.878505i	$0.658541\pi$
$464$	−3.18862	+	2.67557i	−0.148028	+	0.124210i
$465$	7.23367	+	0.777299i	0.335454	+	0.0360464i
$466$	−22.2222	+	8.08820i	−1.02942	+	0.374679i
$467$	2.59290	−	4.49103i	0.119985	−	0.207820i	−0.799777	−	0.600298i	$-0.795049\pi$
$467$	2.59290	−	4.49103i	0.119985	−	0.207820i	0.919761	+	0.392478i	$0.128382\pi$
$468$	2.65536	−	1.39608i	0.122744	−	0.0645339i
$469$	−0.00275326	−	0.00476878i	−0.000127134	−	0.000220202i
$470$	−4.02095	−	3.37398i	−0.185473	−	0.155630i
$471$	−2.28489	+	0.564047i	−0.105282	+	0.0259899i
$472$	1.54569	+	8.76606i	0.0711463	+	0.403490i
$473$	−3.39915	−	19.2775i	−0.156293	−	0.886382i
$474$	−16.6398	−	17.3114i	−0.764293	−	0.795141i
$475$	5.26899	+	4.42121i	0.241758	+	0.202859i
$476$	−0.106209	−	0.183960i	−0.00486809	−	0.00843178i
$477$	−3.20396	−	4.14042i	−0.146699	−	0.189577i
$478$	−10.3228	+	17.8796i	−0.472154	+	0.817795i
$479$	14.7248	−	5.35939i	0.672794	−	0.244877i	0.0170436	−	0.999855i	$-0.494575\pi$
$479$	14.7248	−	5.35939i	0.672794	−	0.244877i	0.655750	+	0.754978i	$0.272352\pi$
$480$	−0.491757	+	0.673546i	−0.0224455	+	0.0307430i
$481$	−4.91964	+	4.12807i	−0.224316	+	0.188224i
$482$	−9.56140	−	3.48007i	−0.435510	−	0.158513i
$483$	0.495190	+	0.242947i	0.0225319	+	0.0110545i
$484$	−1.46325	+	8.29848i	−0.0665112	+	0.377204i
$485$	−9.09710			−0.413078
$486$	9.88057	+	12.0571i	0.448192	+	0.546923i
$487$	36.3603			1.64764			0.823822	−	0.566848i	$-0.191837\pi$
$487$	36.3603			1.64764			0.823822	+	0.566848i	$0.191837\pi$
$488$	1.70962	−	9.69573i	0.0773908	−	0.438905i
$489$	−32.0943	−	15.7459i	−1.45135	−	0.712054i
$490$	3.16652	+	1.15252i	0.143049	+	0.0520655i
$491$	−1.59611	+	1.33929i	−0.0720313	+	0.0604414i	−0.678092	−	0.734977i	$-0.737193\pi$
$491$	−1.59611	+	1.33929i	−0.0720313	+	0.0604414i	0.606061	+	0.795418i	$0.292749\pi$
$492$	1.79248	−	2.45511i	0.0808112	−	0.110685i
$493$	22.2482	−	8.09768i	1.00201	−	0.364701i
$494$	−0.721260	+	1.24926i	−0.0324510	+	0.0562068i
$495$	1.41812	+	1.83261i	0.0637397	+	0.0823697i
$496$	4.36191	+	7.55505i	0.195856	+	0.339232i
$497$	−0.0279746	−	0.0234735i	−0.00125483	−	0.00105293i
$498$	−7.87672	−	8.19463i	−0.352964	−	0.367210i
$499$	−2.86197	−	16.2310i	−0.128119	−	0.726600i	−0.979406	−	0.201900i	$-0.935288\pi$
$499$	−2.86197	−	16.2310i	−0.128119	−	0.726600i	0.851287	−	0.524701i	$-0.175823\pi$
$500$	0.816710	+	4.63179i	0.0365244	+	0.207140i
$501$	34.6554	−	8.55503i	1.54829	−	0.382210i
$502$	6.77930	+	5.68851i	0.302575	+	0.253891i
$503$	5.06194	+	8.76754i	0.225701	+	0.390925i	0.956529	−	0.291636i	$-0.0941995\pi$
$503$	5.06194	+	8.76754i	0.225701	+	0.390925i	−0.730829	+	0.682561i	$0.760866\pi$
$504$	−0.0991645	+	0.0521367i	−0.00441714	+	0.00232235i
$505$	1.98032	−	3.43002i	0.0881233	−	0.152634i
$506$	12.8547	−	4.67871i	0.571459	−	0.207994i
$507$	1.72214	+	0.185053i	0.0764828	+	0.00821851i
$508$	12.0219	−	10.0875i	0.533384	−	0.447562i
$509$	26.9474	+	9.80805i	1.19442	+	0.434734i	0.861274	−	0.508141i	$-0.169667\pi$
$509$	26.9474	+	9.80805i	1.19442	+	0.434734i	0.333148	+	0.942875i	$0.391889\pi$
$510$	3.93875	−	2.64342i	0.174411	−	0.117053i
$511$	0.0171583	−	0.0973095i	0.000759038	−	0.00430472i
$512$	−1.00000			−0.0441942
$513$	−7.11236	−	2.36592i	−0.314018	−	0.104458i
$514$	2.38103			0.105023
$515$	−1.12961	+	6.40636i	−0.0497768	+	0.282298i
$516$	1.42527	+	21.0867i	0.0627438	+	0.928291i
$517$	−16.4338	−	5.98141i	−0.722757	−	0.263062i
$518$	0.183724	−	0.154163i	0.00807237	−	0.00677352i
$519$	4.38818	+	9.91802i	0.192620	+	0.435353i
$520$	−0.452450	+	0.164678i	−0.0198412	+	0.00722162i
$521$	2.37684	−	4.11680i	0.104131	−	0.180360i	−0.809252	−	0.587462i	$-0.800127\pi$
$521$	2.37684	−	4.11680i	0.104131	−	0.180360i	0.913383	+	0.407102i	$0.133461\pi$
$522$	−3.80353	−	11.8940i	−0.166476	−	0.520586i
$523$	−17.0764	−	29.5773i	−0.746701	−	1.29332i	−0.949396	−	0.314082i	$-0.898303\pi$
$523$	−17.0764	−	29.5773i	−0.746701	−	1.29332i	0.202695	−	0.979242i	$-0.435030\pi$
$524$	−6.36543	−	5.34123i	−0.278075	−	0.233333i
$525$	−0.0857016	+	0.296275i	−0.00374032	+	0.0129305i
$526$	−1.60023	−	9.07533i	−0.0697731	−	0.395703i
$527$	−8.61662	−	48.8673i	−0.375346	−	2.12869i
$528$	−0.772088	+	2.66915i	−0.0336008	+	0.116160i
$529$	38.0841	+	31.9564i	1.65583	+	1.38941i
$530$	0.420122	+	0.727673i	0.0182489	+	0.0316081i
$531$	−26.0942	−	5.67345i	−1.13239	−	0.246207i
$532$	0.0269354	−	0.0466535i	0.00116780	−	0.00202269i
$533$	1.64920	−	0.600261i	0.0714349	−	0.0260002i
$534$	0.247090	+	0.558465i	0.0106926	+	0.0241671i
$535$	5.84914	−	4.90801i	0.252881	−	0.212192i
$536$	0.138558	+	0.0504309i	0.00598478	+	0.00217828i
$537$	2.88024	+	42.6130i	0.124291	+	1.83888i
$538$	2.73727	−	15.5238i	0.118012	−	0.669280i
$539$	11.2273			0.483592
$540$	−1.31096	−	2.13091i	−0.0564148	−	0.0916998i
$541$	−1.44184			−0.0619896			−0.0309948	−	0.999520i	$-0.509868\pi$
$541$	−1.44184			−0.0619896			−0.0309948	+	0.999520i	$0.509868\pi$
$542$	2.76299	−	15.6697i	0.118681	−	0.673071i
$543$	10.1592	−	6.81813i	0.435972	−	0.292594i
$544$	5.34498	+	1.94541i	0.229164	+	0.0834089i
$545$	2.58158	−	2.16620i	0.110583	−	0.0927899i
$546$	−0.0643132	−	0.00691081i	−0.00275235	−	0.000295756i
$547$	8.95865	−	3.26068i	0.383044	−	0.139417i	−0.143319	−	0.989677i	$-0.545777\pi$
$547$	8.95865	−	3.26068i	0.383044	−	0.139417i	0.526363	+	0.850260i	$0.323555\pi$
$548$	−1.12788	+	1.95354i	−0.0481805	+	0.0834510i
$549$	24.9748	+	15.7680i	1.06590	+	0.672960i
$550$	3.82458	+	6.62437i	0.163081	+	0.282464i
$551$	4.59965	+	3.85956i	0.195952	+	0.164423i
$552$	−14.3393	+	3.53980i	−0.610322	+	0.150664i
$553$	0.0899017	+	0.509858i	0.00382301	+	0.0216814i
$554$	−3.32412	−	18.8520i	−0.141228	−	0.800945i
$555$	3.71149	+	3.86129i	0.157544	+	0.163902i
$556$	5.58285	+	4.68456i	0.236765	+	0.198670i
$557$	−16.4525	−	28.4965i	−0.697113	−	1.20744i	−0.969463	−	0.245237i	$-0.921134\pi$
$557$	−16.4525	−	28.4965i	−0.697113	−	1.20744i	0.272350	−	0.962198i	$-0.412199\pi$
$558$	−25.9334	+	3.52180i	−1.09785	+	0.149090i
$559$	−6.10110	+	10.5674i	−0.258049	+	0.446954i
$560$	0.0168967	−	0.00614991i	0.000714017	−	0.000259881i
$561$	9.31940	−	12.7645i	0.393465	−	0.538919i
$562$	6.26440	−	5.25646i	0.264248	−	0.221730i
$563$	−29.2277	−	10.6380i	−1.23180	−	0.448339i	−0.357587	−	0.933880i	$-0.616400\pi$
$563$	−29.2277	−	10.6380i	−1.23180	−	0.448339i	−0.874214	+	0.485541i	$0.838623\pi$
$564$	16.9518	+	8.31681i	0.713801	+	0.350201i
$565$	−1.01801	+	5.77345i	−0.0428282	+	0.242891i
$566$	−7.56832			−0.318120
$567$	−0.0320222	−	0.334576i	−0.00134481	−	0.0140509i
$568$	0.977861			0.0410301
$569$	0.753201	−	4.27161i	0.0315758	−	0.179075i	−0.964941	−	0.262467i	$-0.915464\pi$
$569$	0.753201	−	4.27161i	0.0315758	−	0.179075i	0.996517	+	0.0833913i	$0.0265751\pi$
$570$	1.08002	+	0.529875i	0.0452372	+	0.0221940i
$571$	−41.3582	−	15.0532i	−1.73079	−	0.629955i	−0.732100	−	0.681197i	$-0.761460\pi$
$571$	−41.3582	−	15.0532i	−1.73079	−	0.629955i	−0.998686	+	0.0512421i	$0.983682\pi$
$572$	−1.22890	+	1.03117i	−0.0513828	+	0.0431153i
$573$	−12.9852	+	17.7855i	−0.542464	+	0.742998i
$574$	−0.0615895	+	0.0224167i	−0.00257069	+	0.000935656i
$575$	−20.3299	+	35.2124i	−0.847814	+	1.46846i
$576$	1.13674	−	2.77630i	0.0473643	−	0.115679i
$577$	−10.6628	−	18.4685i	−0.443899	−	0.768856i	0.554076	−	0.832466i	$-0.313072\pi$
$577$	−10.6628	−	18.4685i	−0.443899	−	0.768856i	−0.997975	+	0.0636106i	$0.979738\pi$
$578$	−11.7614	−	9.86898i	−0.489210	−	0.410496i
$579$	19.3591	+	20.1404i	0.804535	+	0.837006i
$580$	0.348020	+	1.97372i	0.0144507	+	0.0819541i
$581$	0.0425564	+	0.241349i	0.00176554	+	0.0100128i
$582$	31.7712	−	7.84303i	1.31696	−	0.325104i
$583$	2.14455	+	1.79949i	0.0888183	+	0.0745274i
$584$	1.32294	+	2.29141i	0.0547438	+	0.0948191i
$585$	0.0571235	−	1.44333i	0.00236176	−	0.0596744i
$586$	−2.99409	+	5.18591i	−0.123685	+	0.214228i
$587$	−7.17383	+	2.61106i	−0.296096	+	0.107770i	−0.485797	−	0.874072i	$-0.661470\pi$
$587$	−7.17383	+	2.61106i	−0.296096	+	0.107770i	0.189701	+	0.981842i	$0.439248\pi$
$588$	−12.0526	−	1.29512i	−0.497039	−	0.0534096i
$589$	9.64012	−	8.08902i	0.397214	−	0.333302i
$590$	4.02739	+	1.46585i	0.165805	+	0.0603480i
$591$	−15.6105	+	10.4767i	−0.642129	+	0.430953i
$592$	−1.11519	+	6.32457i	−0.0458341	+	0.259938i
$593$	36.1782			1.48566			0.742831	−	0.669479i	$-0.233483\pi$
$593$	36.1782			1.48566			0.742831	+	0.669479i	$0.233483\pi$
$594$	−6.53269	−	5.17768i	−0.268040	−	0.212443i
$595$	−0.102277			−0.00419294
$596$	2.29272	−	13.0027i	0.0939135	−	0.532610i
$597$	1.64354	+	24.3160i	0.0672655	+	0.995189i
$598$	−8.01307	−	2.91652i	−0.327679	−	0.119265i
$599$	−5.84972	+	4.90850i	−0.239013	+	0.200556i	−0.754424	−	0.656387i	$-0.772084\pi$
$599$	−5.84972	+	4.90850i	−0.239013	+	0.200556i	0.515411	+	0.856943i	$0.327639\pi$
$600$	−3.34157	−	7.55250i	−0.136419	−	0.308330i
$601$	−0.447861	+	0.163008i	−0.0182686	+	0.00664924i	−0.351138	−	0.936324i	$-0.614205\pi$
$601$	−0.447861	+	0.163008i	−0.0182686	+	0.00664924i	0.332870	+	0.942973i	$0.391983\pi$
$602$	0.227845	−	0.394640i	0.00928629	−	0.0160843i
$603$	−0.297515	+	0.327350i	−0.0121158	+	0.0133307i
$604$	−6.76755	−	11.7217i	−0.275368	−	0.476951i
$605$	3.10803	+	2.60795i	0.126360	+	0.106028i
$606$	−3.95901	+	13.6865i	−0.160824	+	0.555977i
$607$	1.26004	+	7.14603i	0.0511433	+	0.290048i	0.999643	−	0.0267309i	$-0.00850971\pi$
$607$	1.26004	+	7.14603i	0.0511433	+	0.290048i	−0.948499	+	0.316779i	$0.897399\pi$
$608$	0.250491	+	1.42060i	0.0101587	+	0.0576131i
$609$	−0.0748145	+	0.258638i	−0.00303164	+	0.0104805i
$610$	−3.63135	−	3.04706i	−0.147029	−	0.123372i
$611$	5.45080	+	9.44106i	0.220516	+	0.381944i
$612$	−11.4769	+	12.6278i	−0.463926	+	0.510449i
$613$	14.4105	−	24.9598i	0.582036	−	1.00812i	−0.413201	−	0.910640i	$-0.635589\pi$
$613$	14.4105	−	24.9598i	0.582036	−	1.00812i	0.995238	−	0.0974770i	$-0.0310772\pi$
$614$	8.58037	−	3.12300i	0.346275	−	0.126034i
$615$	−0.592204	−	1.33848i	−0.0238800	−	0.0539727i
$616$	0.0458932	−	0.0385090i	0.00184909	−	0.00155157i
$617$	16.0605	+	5.84555i	0.646572	+	0.235333i	0.644428	−	0.764665i	$-0.277095\pi$
$617$	16.0605	+	5.84555i	0.646572	+	0.235333i	0.00214359	+	0.999998i	$0.499318\pi$
$618$	−1.57810	−	23.3478i	−0.0634803	−	0.939187i
$619$	2.93858	−	16.6655i	0.118111	−	0.669843i	−0.867051	−	0.498219i	$-0.833987\pi$
$619$	2.93858	−	16.6655i	0.118111	−	0.669843i	0.985163	−	0.171624i	$-0.0549014\pi$
$620$	4.20041			0.168692
$621$	6.47258	−	43.8340i	0.259736	−	1.75900i
$622$	0.0173528			0.000695783
$623$	0.00228644	−	0.0129670i	9.16042e−5	−	0.000519514i
$624$	1.43818	−	0.965209i	0.0575734	−	0.0386393i
$625$	−20.2751	−	7.37953i	−0.811004	−	0.295181i
$626$	2.13352	−	1.79024i	0.0852727	−	0.0715523i
$627$	3.98521	+	0.428233i	0.159154	+	0.0171020i
$628$	−1.27684	+	0.464731i	−0.0509514	+	0.0185448i
$629$	18.2646	−	31.6352i	0.728257	−	1.26138i
$630$	−0.00213327	+	0.0539012i	−8.49917e−5	+	0.00214747i
$631$	−8.42901	−	14.5995i	−0.335554	−	0.581196i	0.648037	−	0.761608i	$-0.275590\pi$
$631$	−8.42901	−	14.5995i	−0.335554	−	0.581196i	−0.983591	+	0.180413i	$0.942257\pi$
$632$	−10.6199	−	8.91113i	−0.422436	−	0.354466i
$633$	4.47824	−	1.10550i	0.177994	−	0.0439396i
$634$	3.13719	+	17.7919i	0.124594	+	0.706606i
$635$	−1.31212	−	7.44138i	−0.0520697	−	0.295302i
$636$	−2.09462	−	2.17916i	−0.0830570	−	0.0864092i
$637$	−5.36124	−	4.49862i	−0.212420	−	0.178242i
$638$	3.33873	+	5.78284i	0.132181	+	0.228945i
$639$	−1.11158	+	2.71483i	−0.0439733	+	0.107397i
$640$	−0.240744	+	0.416980i	−0.00951622	+	0.0164826i
$641$	−20.4127	+	7.42961i	−0.806252	+	0.293452i	−0.712075	−	0.702104i	$-0.752244\pi$
$641$	−20.4127	+	7.42961i	−0.806252	+	0.293452i	−0.0941775	+	0.995555i	$0.530022\pi$
$642$	−16.1964	+	22.1838i	−0.639223	+	0.875526i
$643$	27.8181	−	23.3421i	1.09704	−	0.920523i	0.0998147	−	0.995006i	$-0.468175\pi$
$643$	27.8181	−	23.3421i	1.09704	−	0.920523i	0.997222	+	0.0744827i	$0.0237306\pi$
$644$	0.299248	+	0.108917i	0.0117920	+	0.00429194i
$645$	9.13586	+	4.48218i	0.359724	+	0.176486i
$646$	1.42479	−	8.08041i	0.0560578	−	0.317919i
$647$	2.30387			0.0905745			0.0452873	−	0.998974i	$-0.485580\pi$
$647$	2.30387			0.0905745			0.0452873	+	0.998974i	$0.485580\pi$
$648$	6.41563	+	6.31187i	0.252030	+	0.247954i
$649$	14.2796			0.560522
$650$	0.827984	−	4.69573i	0.0324762	−	0.184182i
$651$	0.506601	+	0.248545i	0.0198552	+	0.00974126i
$652$	−19.3949	−	7.05915i	−0.759561	−	0.276458i
$653$	−14.4372	+	12.1143i	−0.564972	+	0.474068i	−0.879973	−	0.475023i	$-0.842440\pi$
$653$	−14.4372	+	12.1143i	−0.564972	+	0.474068i	0.315001	+	0.949091i	$0.397995\pi$
$654$	−7.14846	+	9.79106i	−0.279527	+	0.382861i
$655$	−3.75962	+	1.36839i	−0.146901	+	0.0534675i
$656$	0.877523	−	1.51991i	0.0342615	−	0.0593427i
$657$	−7.86547	+	1.06814i	−0.306861	+	0.0416723i
$658$	−0.203560	−	0.352576i	−0.00793559	−	0.0137449i
$659$	−10.1940	−	8.55376i	−0.397101	−	0.333207i	0.422271	−	0.906470i	$-0.361233\pi$
$659$	−10.1940	−	8.55376i	−0.397101	−	0.333207i	−0.819372	+	0.573263i	$0.805677\pi$
$660$	0.927108	+	0.964526i	0.0360876	+	0.0375441i
$661$	2.89101	+	16.3957i	0.112447	+	0.637719i	0.987983	+	0.154565i	$0.0493977\pi$
$661$	2.89101	+	16.3957i	0.112447	+	0.637719i	−0.875536	+	0.483154i	$0.839491\pi$
$662$	−4.60842	−	26.1356i	−0.179111	−	1.01579i
$663$	−9.56479	+	2.36116i	−0.371466	+	0.0916999i
$664$	−5.02708	−	4.21822i	−0.195089	−	0.163699i
$665$	−0.0129691	−	0.0224631i	−0.000502919	−	0.000871081i
$666$	−16.2912	−	10.2855i	−0.631271	−	0.398556i
$667$	−17.7473	+	30.7392i	−0.687177	+	1.19023i
$668$	19.3661	−	7.04868i	0.749296	−	0.272721i
$669$	−41.9267	−	4.50527i	−1.62098	−	0.174184i
$670$	0.0543855	−	0.0456349i	0.00210110	−	0.00176303i
$671$	−14.8415	−	5.40185i	−0.572948	−	0.208536i
$672$	−0.0537089	+	0.0360457i	−0.00207187	+	0.00139049i
$673$	−6.48209	+	36.7617i	−0.249866	+	1.41706i	0.559048	+	0.829135i	$0.311167\pi$
$673$	−6.48209	+	36.7617i	−0.249866	+	1.41706i	−0.808915	+	0.587926i	$0.799945\pi$
$674$	−4.38485			−0.168898
$675$	24.7665	−	0.691936i	0.953262	−	0.0266326i
$676$	1.00000			0.0384615
$677$	−1.62624	+	9.22286i	−0.0625014	+	0.354463i	0.937478	+	0.348045i	$0.113154\pi$
$677$	−1.62624	+	9.22286i	−0.0625014	+	0.354463i	−0.999979	+	0.00641857i	$0.997957\pi$
$678$	−1.42219	−	21.0412i	−0.0546188	−	0.808082i
$679$	−0.663035	−	0.241325i	−0.0254450	−	0.00926121i
$680$	2.09797	−	1.76040i	0.0804534	−	0.0675084i
$681$	−18.4013	−	41.5901i	−0.705141	−	1.59373i
$682$	13.1509	−	4.78652i	0.503573	−	0.183285i
$683$	−8.41351	+	14.5726i	−0.321934	+	0.557606i	−0.980887	−	0.194578i	$-0.937666\pi$
$683$	−8.41351	+	14.5726i	−0.321934	+	0.557606i	0.658953	+	0.752184i	$0.271000\pi$
$684$	−4.22876	−	0.919425i	−0.161691	−	0.0351551i
$685$	0.543058	+	0.940604i	0.0207492	+	0.0359386i
$686$	0.400471	+	0.336035i	0.0152901	+	0.0128299i
$687$	−4.08165	+	14.1105i	−0.155724	+	0.538348i
$688$	2.11889	+	12.0168i	0.0807819	+	0.458137i
$689$	−0.303034	−	1.71859i	−0.0115447	−	0.0654731i
$690$	−1.97607	+	6.83139i	−0.0752277	+	0.260067i
$691$	−21.2519	−	17.8324i	−0.808460	−	0.678378i	0.141780	−	0.989898i	$-0.454717\pi$
$691$	−21.2519	−	17.8324i	−0.808460	−	0.678378i	−0.950240	+	0.311520i	$0.899162\pi$
$692$	3.13080	+	5.42271i	0.119015	+	0.206141i
$693$	0.0547435	+	0.171188i	0.00207953	+	0.00650289i
$694$	1.36532	−	2.36481i	0.0518269	−	0.0897669i
$695$	3.29740	−	1.20016i	0.125078	−	0.0455245i
$696$	−2.91707	−	6.59307i	−0.110571	−	0.249910i
$697$	−7.64720	+	6.41676i	−0.289658	+	0.243052i
$698$	−30.8109	−	11.2143i	−1.16621	−	0.424466i
$699$	−2.76222	−	40.8668i	−0.104477	−	1.54573i
$700$	−0.0309211	+	0.175362i	−0.00116871	+	0.00662806i
$701$	−38.7348			−1.46299			−0.731496	−	0.681845i	$-0.761178\pi$
$701$	−38.7348			−1.46299			−0.731496	+	0.681845i	$0.761178\pi$
$702$	1.04486	+	5.09002i	0.0394358	+	0.192110i
$703$	9.26406			0.349401
$704$	−0.278569	+	1.57984i	−0.0104989	+	0.0595425i
$705$	7.54899	−	5.06636i	0.284311	−	0.190810i
$706$	4.92317	+	1.79189i	0.185286	+	0.0674386i
$707$	0.235325	−	0.197461i	0.00885031	−	0.00742629i
$708$	−15.3292	−	1.64721i	−0.576108	−	0.0619060i
$709$	−43.5995	+	15.8689i	−1.63741	+	0.595970i	−0.986584	−	0.163253i	$-0.947801\pi$
$709$	−43.5995	+	15.8689i	−1.63741	+	0.595970i	−0.650830	+	0.759223i	$0.725579\pi$
$710$	0.235414	−	0.407748i	0.00883492	−	0.0153025i
$711$	36.8120	−	19.3542i	1.38056	−	0.725841i
$712$	0.176290	+	0.305343i	0.00660674	+	0.0114432i
$713$	56.9867	+	47.8175i	2.13417	+	1.79078i
$714$	0.357197	−	0.0881775i	0.0133678	−	0.00329996i
$715$	0.134127	+	0.760673i	0.00501607	+	0.0284476i
$716$	4.28194	+	24.2841i	0.160024	+	0.907540i
$717$	−24.7806	−	25.7807i	−0.925448	−	0.962799i
$718$	−26.3931	−	22.1464i	−0.984981	−	0.826497i
$719$	−18.3488	−	31.7811i	−0.684296	−	1.18524i	−0.973658	−	0.228015i	$-0.926776\pi$
$719$	−18.3488	−	31.7811i	−0.684296	−	1.18524i	0.289362	−	0.957220i	$-0.406557\pi$
$720$	−0.883996	−	1.14237i	−0.0329446	−	0.0425738i
$721$	−0.252277	+	0.436957i	−0.00939529	+	0.0162731i
$722$	−15.8988	+	5.78669i	−0.591692	+	0.215358i
$723$	10.3921	−	14.2337i	0.386485	−	0.529358i
$724$	5.41126	−	4.54058i	0.201108	−	0.168749i
$725$	−18.6503	−	6.78816i	−0.692656	−	0.252106i
$726$	−13.1031	−	6.42857i	−0.486302	−	0.238587i
$727$	1.02648	−	5.82147i	0.0380701	−	0.215906i	−0.959838	−	0.280555i	$-0.909482\pi$
$727$	1.02648	−	5.82147i	0.0380701	−	0.215906i	0.997908	+	0.0646485i	$0.0205926\pi$
$728$	−0.0373450			−0.00138410
$729$	−24.8165	+	10.6367i	−0.919131	+	0.393953i
$730$	1.27396			0.0471514
$731$	12.0523	−	68.3518i	0.445769	−	2.52808i
$732$	15.3093	+	7.51097i	0.565849	+	0.277613i
$733$	−2.18666	−	0.795879i	−0.0807661	−	0.0293965i	0.301321	−	0.953523i	$-0.402572\pi$
$733$	−2.18666	−	0.795879i	−0.0807661	−	0.0293965i	−0.382087	+	0.924126i	$0.624795\pi$
$734$	2.24284	−	1.88196i	0.0827846	−	0.0694645i
$735$	−3.44161	+	4.71388i	−0.126946	+	0.173874i
$736$	−8.01307	+	2.91652i	−0.295366	+	0.107504i
$737$	0.118271	−	0.204851i	0.00435655	−	0.00754577i
$738$	3.22221	+	4.16401i	0.118611	+	0.153279i
$739$	2.67932	+	4.64071i	0.0985602	+	0.170711i	0.911089	−	0.412210i	$-0.135243\pi$
$739$	2.67932	+	4.64071i	0.0985602	+	0.170711i	−0.812529	+	0.582921i	$0.801910\pi$
$740$	2.36874	+	1.98761i	0.0870768	+	0.0730661i
$741$	−1.73143	−	1.80131i	−0.0636057	−	0.0661729i
$742$	0.0113168	+	0.0641807i	0.000415453	+	0.00235615i
$743$	−2.58787	−	14.6766i	−0.0949399	−	0.538431i	−0.994766	−	0.102182i	$-0.967418\pi$
$743$	−2.58787	−	14.6766i	−0.0949399	−	0.538431i	0.899826	−	0.436249i	$-0.143693\pi$
$744$	−14.6697	+	3.62136i	−0.537818	+	0.132766i
$745$	−4.86990	−	4.08633i	−0.178419	−	0.149711i
$746$	−2.68178	−	4.64497i	−0.0981868	−	0.170065i
$747$	17.4255	−	9.16163i	0.637567	−	0.335206i
$748$	4.56239	−	7.90228i	0.166817	−	0.288936i
$749$	0.556509	−	0.202553i	0.0203344	−	0.00740111i
$750$	−8.09963	−	0.870351i	−0.295757	−	0.0317807i
$751$	−18.1866	+	15.2604i	−0.663638	+	0.556858i	−0.911175	−	0.412020i	$-0.864823\pi$
$751$	−18.1866	+	15.2604i	−0.663638	+	0.556858i	0.247537	+	0.968878i	$0.420379\pi$
$752$	10.2441	+	3.72856i	0.373566	+	0.135967i
$753$	−12.7276	+	8.54186i	−0.463818	+	0.311283i
$754$	0.722801	−	4.09921i	0.0263229	−	0.149284i
$755$	−6.51698			−0.237177
$756$	−0.0390203	−	0.190087i	−0.00141916	−	0.00691338i
$757$	49.8321			1.81118			0.905589	−	0.424157i	$-0.139430\pi$
$757$	49.8321			1.81118			0.905589	+	0.424157i	$0.139430\pi$
$758$	0.0968890	−	0.549485i	0.00351917	−	0.0199582i
$759$	1.59784	+	23.6399i	0.0579978	+	0.858074i
$760$	0.652668	+	0.237552i	0.0236747	+	0.00861690i
$761$	−2.96278	+	2.48607i	−0.107401	+	0.0901198i	−0.694907	−	0.719100i	$-0.744554\pi$
$761$	−2.96278	+	2.48607i	−0.107401	+	0.0901198i	0.587506	+	0.809220i	$0.300110\pi$
$762$	10.9981	+	24.8574i	0.398418	+	0.900490i
$763$	0.245621	−	0.0893987i	0.00889207	−	0.00323645i
$764$	−6.35700	+	11.0106i	−0.229988	+	0.398351i
$765$	2.50255	+	7.82570i	0.0904799	+	0.282939i
$766$	5.49261	+	9.51347i	0.198456	+	0.343736i
$767$	−6.81878	−	5.72164i	−0.246212	−	0.206596i
$768$	0.481288	−	1.66384i	0.0173670	−	0.0600386i
$769$	−7.86395	−	44.5987i	−0.283581	−	1.60827i	−0.710309	−	0.703890i	$-0.751445\pi$
$769$	−7.86395	−	44.5987i	−0.283581	−	1.60827i	0.426728	−	0.904380i	$-0.359666\pi$
$770$	−0.00500898	−	0.0284073i	−0.000180511	−	0.00102373i
$771$	−1.14596	+	3.96165i	−0.0412708	+	0.142675i
$772$	12.3553	+	10.3674i	0.444678	+	0.373129i
$773$	0.350111	+	0.606410i	0.0125926	+	0.0218110i	0.872253	−	0.489055i	$-0.162658\pi$
$773$	0.350111	+	0.606410i	0.0125926	+	0.0218110i	−0.859660	+	0.510866i	$0.829325\pi$
$774$	−35.7709	−	7.77737i	−1.28576	−	0.279552i
$775$	−20.7983	+	36.0238i	−0.747098	+	1.29401i
$776$	17.7543	−	6.46205i	0.637343	−	0.231974i
$777$	0.168078	+	0.379884i	0.00602976	+	0.0136283i
$778$	3.22891	−	2.70937i	0.115762	−	0.0971357i
$779$	−2.37901	−	0.865888i	−0.0852368	−	0.0310237i
$780$	−0.0562396	−	0.832061i	−0.00201370	−	0.0297926i
$781$	0.272401	−	1.54486i	0.00974729	−	0.0552796i
$782$	48.5035			1.73448
$783$	21.6203	−	0.604037i	0.772646	−	0.0215865i
$784$	−6.99861			−0.249950
$785$	−0.113607	+	0.644297i	−0.00405480	+	0.0229959i
$786$	11.9506	−	8.02039i	0.426262	−	0.286078i
$787$	13.3832	+	4.87109i	0.477060	+	0.173635i	0.569348	−	0.822097i	$-0.307196\pi$
$787$	13.3832	+	4.87109i	0.477060	+	0.173635i	−0.0922881	+	0.995732i	$0.529418\pi$
$788$	−8.31488	+	6.97701i	−0.296205	+	0.248546i
$789$	15.8701	+	1.70533i	0.564989	+	0.0607113i
$790$	−6.27243	+	2.28298i	−0.223163	+	0.0812247i
$791$	−0.227353	+	0.393788i	−0.00808376	+	0.0140015i
$792$	−4.06944	−	2.56926i	−0.144601	−	0.0912947i
$793$	4.92265	+	8.52628i	0.174808	+	0.302777i
$794$	−13.4323	−	11.2710i	−0.476694	−	0.399994i
$795$	−1.41293	+	0.348796i	−0.0501115	+	0.0123705i
$796$	2.44339	+	13.8571i	0.0866035	+	0.491153i
$797$	−2.84866	−	16.1555i	−0.100905	−	0.572258i	−0.992777	−	0.119972i	$-0.961720\pi$
$797$	−2.84866	−	16.1555i	−0.100905	−	0.572258i	0.891873	−	0.452287i	$-0.149392\pi$
$798$	0.0646603	+	0.0672700i	0.00228895	+	0.00238133i
$799$	−47.5011	−	39.8582i	−1.68047	−	1.41008i
$800$	−2.38409	−	4.12936i	−0.0842901	−	0.145995i
$801$	−1.04812	+	0.142336i	−0.0370334	+	0.00502920i
$802$	−16.8042	+	29.1057i	−0.593375	+	1.02776i
$803$	3.98859	−	1.45173i	0.140754	−	0.0512304i
$804$	−0.150595	+	0.206266i	−0.00531108	+	0.00727444i
$805$	0.117458	−	0.0985592i	0.00413986	−	0.00347376i
$806$	−8.19771	−	2.98372i	−0.288752	−	0.105097i
$807$	24.5117	+	12.0258i	0.862854	+	0.423328i
$808$	−1.42841	+	8.10090i	−0.0502512	+	0.284989i
$809$	−24.5383			−0.862719			−0.431360	−	0.902180i	$-0.641966\pi$
$809$	−24.5383			−0.862719			−0.431360	+	0.902180i	$0.641966\pi$
$810$	4.17644	−	1.15565i	0.146745	−	0.0406054i
$811$	24.9380			0.875690			0.437845	−	0.899050i	$-0.355742\pi$
$811$	24.9380			0.875690			0.437845	+	0.899050i	$0.355742\pi$
$812$	−0.0269930	+	0.153085i	−0.000947269	+	0.00537223i
$813$	24.7421	+	12.1388i	0.867742	+	0.425726i
$814$	9.68116	+	3.52365i	0.339325	+	0.123504i
$815$	−7.61271	+	6.38782i	−0.266662	+	0.223756i
$816$	−5.80933	+	7.95688i	−0.203367	+	0.278547i
$817$	16.5404	−	6.02021i	0.578675	−	0.210620i
$818$	−5.73207	+	9.92823i	−0.200417	+	0.347132i
$819$	0.0424516	−	0.103681i	0.00148338	−	0.00362290i
$820$	−0.422516	−	0.731819i	−0.0147549	−	0.0255562i
$821$	39.4475	+	33.1004i	1.37673	+	1.15521i	0.970405	+	0.241482i	$0.0776336\pi$
$821$	39.4475	+	33.1004i	1.37673	+	1.15521i	0.406323	+	0.913730i	$0.366811\pi$
$822$	−2.70754	−	2.81682i	−0.0944364	−	0.0982479i
$823$	−6.53638	−	37.0697i	−0.227844	−	1.29217i	−0.857173	−	0.515028i	$-0.827781\pi$
$823$	−6.53638	−	37.0697i	−0.227844	−	1.29217i	0.629329	−	0.777139i	$-0.283330\pi$
$824$	−2.34610	−	13.3054i	−0.0817301	−	0.463515i
$825$	−12.8626	+	3.17526i	−0.447818	+	0.110548i
$826$	0.254647	+	0.213674i	0.00886031	+	0.00743469i
$827$	19.7718	+	34.2457i	0.687531	+	1.19084i	0.972634	+	0.232342i	$0.0746388\pi$
$827$	19.7718	+	34.2457i	0.687531	+	1.19084i	−0.285103	+	0.958497i	$0.592028\pi$
$828$	1.01168	−	25.5620i	0.0351583	−	0.888340i
$829$	6.12893	−	10.6156i	0.212867	−	0.368696i	−0.739744	−	0.672889i	$-0.765053\pi$
$829$	6.12893	−	10.6156i	0.212867	−	0.368696i	0.952611	+	0.304193i	$0.0983867\pi$
$830$	−2.96915	+	1.08068i	−0.103061	+	0.0375110i
$831$	32.9666	+	3.54245i	1.14360	+	0.122886i
$832$	0.766044	−	0.642788i	0.0265578	−	0.0222847i
$833$	37.4074	+	13.6152i	1.29609	+	0.471738i
$834$	−10.4813	+	7.03434i	−0.362938	+	0.243579i
$835$	1.72310	−	9.77219i	0.0596304	−	0.338181i
$836$	2.31411			0.0800351
$837$	6.62172	−	44.8440i	0.228880	−	1.55004i
$838$	−5.81888			−0.201010
$839$	−6.71673	+	38.0925i	−0.231887	+	1.31510i	0.617184	+	0.786819i	$0.288273\pi$
$839$	−6.71673	+	38.0925i	−0.231887	+	1.31510i	−0.849071	+	0.528279i	$0.822838\pi$
$840$	0.00210027	+	0.0310733i	7.24661e−5	+	0.00107213i
$841$	10.9700	+	3.99275i	0.378276	+	0.137681i
$842$	17.8740	−	14.9980i	0.615977	−	0.516866i
$843$	5.73092	+	12.9528i	0.197383	+	0.446119i
$844$	2.50252	−	0.910843i	0.0861403	−	0.0313525i
$845$	0.240744	−	0.416980i	0.00828183	−	0.0143445i
$846$	−21.9966	+	24.2024i	−0.756257	+	0.832094i
$847$	0.157344	+	0.272527i	0.00540640	+	0.00936415i
$848$	−1.33683	−	1.12173i	−0.0459068	−	0.0385204i
$849$	3.64254	−	12.5925i	0.125012	−	0.432172i
$850$	4.70958	+	26.7093i	0.161537	+	0.916123i
$851$	9.50962	+	53.9317i	0.325985	+	1.84876i
$852$	−0.470633	+	1.62700i	−0.0161236	+	0.0557402i
$853$	0.538959	+	0.452241i	0.0184536	+	0.0154844i	0.651968	−	0.758247i	$-0.273944\pi$
$853$	0.538959	+	0.452241i	0.0184536	+	0.0154844i	−0.633514	+	0.773731i	$0.718388\pi$
$854$	−0.183836	−	0.318414i	−0.00629075	−	0.0108959i
$855$	−1.40143	+	1.54196i	−0.0479278	+	0.0527340i
$856$	−7.92910	+	13.7336i	−0.271011	+	0.469405i
$857$	−33.4379	+	12.1704i	−1.14222	+	0.415733i	−0.842713	−	0.538363i	$-0.819043\pi$
$857$	−33.4379	+	12.1704i	−1.14222	+	0.415733i	−0.299503	+	0.954095i	$0.596821\pi$
$858$	−1.12424	−	2.54098i	−0.0383811	−	0.0867476i
$859$	18.2482	−	15.3121i	0.622621	−	0.522441i	−0.276005	−	0.961156i	$-0.589011\pi$
$859$	18.2482	−	15.3121i	0.622621	−	0.522441i	0.898626	+	0.438715i	$0.144566\pi$
$860$	5.52088	+	2.00944i	0.188261	+	0.0685212i
$861$	−0.00765558	−	0.113264i	−0.000260902	−	0.00386002i
$862$	−2.07756	+	11.7824i	−0.0707620	+	0.401311i
$863$	−50.7596			−1.72788			−0.863939	−	0.503597i	$-0.832010\pi$
$863$	−50.7596			−1.72788			−0.863939	+	0.503597i	$0.832010\pi$
$864$	4.07221	+	3.22755i	0.138539	+	0.109804i
$865$	3.01488			0.102509
$866$	−3.10539	+	17.6116i	−0.105526	+	0.598465i
$867$	22.0810	−	14.8193i	0.749911	−	0.503288i
$868$	0.306143	+	0.111427i	0.0103912	+	0.00378208i
$869$	−17.0365	+	14.2954i	−0.577925	+	0.484937i
$870$	−3.45145	−	0.370877i	−0.117015	−	0.0125739i
$871$	−0.138558	+	0.0504309i	−0.00469485	+	0.00170878i
$872$	−3.49959	+	6.06147i	−0.118511	+	0.205267i
$873$	−2.24155	+	56.6369i	−0.0758649	+	1.91687i
$874$	6.15042	+	10.6528i	0.208041	+	0.360338i
$875$	0.134550	+	0.112901i	0.00454862	+	0.00381675i
$876$	−4.44925	+	1.09834i	−0.150326	+	0.0371095i
$877$	−6.32522	−	35.8721i	−0.213588	−	1.21131i	−0.883341	−	0.468731i	$-0.844711\pi$
$877$	−6.32522	−	35.8721i	−0.213588	−	1.21131i	0.669753	−	0.742584i	$-0.266400\pi$
$878$	−1.33316	−	7.56073i	−0.0449920	−	0.255162i
$879$	−7.18750	−	7.47759i	−0.242428	−	0.252213i
$880$	0.591698	+	0.496494i	0.0199462	+	0.0167368i
$881$	21.2486	+	36.8037i	0.715885	+	1.23995i	0.962617	+	0.270865i	$0.0873097\pi$
$881$	21.2486	+	36.8037i	0.715885	+	1.23995i	−0.246733	+	0.969084i	$0.579357\pi$
$882$	7.95561	−	19.4302i	0.267879	−	0.654249i
$883$	−2.59330	+	4.49173i	−0.0872715	+	0.151159i	−0.906357	−	0.422513i	$-0.861148\pi$
$883$	−2.59330	+	4.49173i	−0.0872715	+	0.151159i	0.819085	+	0.573672i	$0.194481\pi$
$884$	−5.34498	+	1.94541i	−0.179771	+	0.0654313i
$885$	−4.37727	+	5.99543i	−0.147140	+	0.201534i
$886$	−23.4632	+	19.6880i	−0.788263	+	0.661431i
$887$	−42.6490	−	15.5230i	−1.43201	−	0.521210i	−0.494505	−	0.869175i	$-0.664650\pi$
$887$	−42.6490	−	15.5230i	−1.43201	−	0.521210i	−0.937507	+	0.347965i	$0.886873\pi$
$888$	−9.98635	−	4.89944i	−0.335120	−	0.164415i
$889$	0.101770	−	0.577167i	0.00341326	−	0.0193576i
$890$	0.169762			0.00569045
$891$	11.7589	−	8.37739i	0.393939	−	0.280653i
$892$	−24.3458			−0.815157
$893$	2.73075	−	15.4869i	0.0913811	−	0.518248i
$894$	20.5309	+	10.0727i	0.686656	+	0.336883i
$895$	11.1568	+	4.06076i	0.372932	+	0.135736i
$896$	−0.0286079	+	0.0240049i	−0.000955724	+	0.000801947i
$897$	8.70921	−	11.9288i	0.290792	−	0.398290i
$898$	36.3787	−	13.2408i	1.21397	−	0.441850i
$899$	−18.1562	+	31.4475i	−0.605544	+	1.04883i
$900$	14.1744	−	1.92491i	0.472480	−	0.0641636i
$901$	4.96308	+	8.59630i	0.165344	+	0.286384i
$902$	−2.15677	−	1.80975i	−0.0718126	−	0.0602580i
$903$	0.546958	+	0.569034i	0.0182016	+	0.0189363i
$904$	−2.11431	−	11.9909i	−0.0703210	−	0.398810i
$905$	−0.590607	−	3.34950i	−0.0196325	−	0.111341i
$906$	22.7602	−	5.61859i	0.756158	−	0.186665i
$907$	−17.7861	−	14.9243i	−0.590576	−	0.495552i	0.297825	−	0.954621i	$-0.403739\pi$
$907$	−17.7861	−	14.9243i	−0.590576	−	0.495552i	−0.888401	+	0.459068i	$0.848183\pi$
$908$	−13.1287	−	22.7395i	−0.435690	−	0.754637i
$909$	−20.8668	−	13.1743i	−0.692107	−	0.436965i
$910$	−0.00899056	+	0.0155721i	−0.000298034	+	0.000516210i
$911$	−41.0536	+	14.9423i	−1.36017	+	0.495060i	−0.916106	−	0.400937i	$-0.868685\pi$
$911$	−41.0536	+	14.9423i	−1.36017	+	0.495060i	−0.444060	+	0.895997i	$0.646462\pi$
$912$	−2.48422	−	0.266943i	−0.0822606	−	0.00883937i
$913$	−8.06451	+	6.76692i	−0.266896	+	0.223953i
$914$	3.86038	+	1.40506i	0.127690	+	0.0464754i
$915$	6.81754	−	4.57546i	0.225381	−	0.151260i
$916$	−1.47265	+	8.35183i	−0.0486578	+	0.275952i
$917$	−0.310318			−0.0102476
$918$	−15.4869	−	25.1733i	−0.511145	−	0.830844i
$919$	33.6906			1.11135			0.555675	−	0.831399i	$-0.312460\pi$
$919$	33.6906			1.11135			0.555675	+	0.831399i	$0.312460\pi$
$920$	−0.712964	+	4.04342i	−0.0235057	+	0.133308i
$921$	1.06654	+	15.7794i	0.0351437	+	0.519949i
$922$	9.39258	+	3.41862i	0.309328	+	0.112586i
$923$	−0.749085	+	0.628557i	−0.0246564	+	0.0206892i
$924$	0.0419849	+	0.0948928i	0.00138120	+	0.00312174i
$925$	−28.7751	+	10.4733i	−0.946121	+	0.344360i
$926$	3.19439	−	5.53285i	0.104974	−	0.181821i
$927$	39.6066	+	8.61133i	1.30085	+	0.282833i
$928$	−2.08122	−	3.60479i	−0.0683195	−	0.118333i
$929$	8.45867	+	7.09766i	0.277520	+	0.232867i	0.770914	−	0.636939i	$-0.219800\pi$
$929$	8.45867	+	7.09766i	0.277520	+	0.232867i	−0.493394	+	0.869806i	$0.664244\pi$
$930$	−2.02160	+	6.98880i	−0.0662910	+	0.229172i
$931$	1.75309	+	9.94225i	0.0574551	+	0.325844i
$932$	−4.10649	−	23.2890i	−0.134512	−	0.762858i
$933$	−0.00835168	+	0.0288722i	−0.000273422	+	0.000945235i
$934$	3.97255	+	3.33336i	0.129986	+	0.109071i
$935$	−2.19673	−	3.80485i	−0.0718407	−	0.124432i
$936$	0.913773	+	2.85745i	0.0298676	+	0.0933987i
$937$	10.0538	−	17.4136i	0.328442	−	0.568879i	−0.653761	−	0.756702i	$-0.726810\pi$
$937$	10.0538	−	17.4136i	0.328442	−	0.568879i	0.982203	+	0.187822i	$0.0601430\pi$
$938$	0.00517443	−	0.00188334i	0.000168951	−	6.14932e-5i
$939$	1.95183	+	4.41146i	0.0636956	+	0.143963i
$940$	4.02095	−	3.37398i	0.131149	−	0.110047i
$941$	−0.352721	−	0.128380i	−0.0114984	−	0.00418506i	0.336265	−	0.941768i	$-0.390836\pi$
$941$	−0.352721	−	0.128380i	−0.0114984	−	0.00418506i	−0.347763	+	0.937583i	$0.613059\pi$
$942$	−0.158711	−	2.34812i	−0.00517109	−	0.0765060i
$943$	2.59879	−	14.7385i	0.0846283	−	0.479951i
$944$	−8.90129			−0.289712
$945$	−0.0886562	−	0.0294914i	−0.00288399	−	0.000959356i
$946$	19.5749			0.636436
$947$	−6.20819	+	35.2084i	−0.201739	+	1.14412i	0.700750	+	0.713407i	$0.252849\pi$
$947$	−6.20819	+	35.2084i	−0.201739	+	1.14412i	−0.902489	+	0.430713i	$0.858262\pi$
$948$	19.9379	−	13.3809i	0.647553	−	0.434593i
$949$	−2.48632	−	0.904947i	−0.0807094	−	0.0293758i
$950$	−5.26899	+	4.42121i	−0.170949	+	0.143443i
$951$	−31.1127	−	3.34324i	−1.00890	−	0.108412i
$952$	0.199608	−	0.0726514i	0.00646934	−	0.00235465i
$953$	9.14377	−	15.8375i	0.296196	−	0.513026i	−0.679067	−	0.734077i	$-0.737615\pi$
$953$	9.14377	−	15.8375i	0.296196	−	0.513026i	0.975262	+	0.221050i	$0.0709486\pi$
$954$	4.63388	−	2.43631i	0.150027	−	0.0788783i
$955$	3.06081	+	5.30148i	0.0990456	+	0.171552i
$956$	−15.8155	−	13.2707i	−0.511508	−	0.429207i
$957$	−11.2286	+	2.77189i	−0.362969	+	0.0896025i
$958$	2.72104	+	15.4318i	0.0879127	+	0.498578i
$959$	0.0146283	+	0.0829612i	0.000472373	+	0.00267896i
$960$	−0.577921	−	0.601246i	−0.0186523	−	0.0194051i
$961$	34.5524	+	28.9929i	1.11459	+	0.935256i
$962$	−3.21107	−	5.56174i	−0.103529	−	0.179318i
$963$	−29.1152	−	37.6251i	−0.938224	−	1.21245i
$964$	5.08752	−	8.81184i	0.163858	−	0.283810i
$965$	7.29744	−	2.65605i	0.234913	−	0.0855013i
$966$	−0.325245	+	0.445480i	−0.0104646	+	0.0143331i
$967$	−2.21195	+	1.85605i	−0.0711315	+	0.0596864i	−0.677660	−	0.735375i	$-0.737006\pi$
$967$	−2.21195	+	1.85605i	−0.0711315	+	0.0596864i	0.606529	+	0.795062i	$0.292562\pi$
$968$	−7.91832	−	2.88203i	−0.254504	−	0.0926321i
$969$	12.7588	+	6.25963i	0.409871	+	0.201088i
$970$	1.57969	−	8.95889i	0.0507209	−	0.287653i
$971$	28.9452			0.928895			0.464448	−	0.885601i	$-0.346253\pi$
$971$	28.9452			0.928895			0.464448	+	0.885601i	$0.346253\pi$
$972$	−13.5897	+	7.63676i	−0.435890	+	0.244949i
$973$	0.272166			0.00872525
$974$	−6.31391	+	35.8079i	−0.202311	+	1.14736i
$975$	7.41444	+	3.63763i	0.237452	+	0.116497i
$976$	9.25156	+	3.36729i	0.296135	+	0.107784i
$977$	4.86613	−	4.08317i	0.155681	−	0.130632i	−0.561620	−	0.827395i	$-0.689822\pi$
$977$	4.86613	−	4.08317i	0.155681	−	0.130632i	0.717301	+	0.696763i	$0.245377\pi$
$978$	21.0798	−	28.8724i	0.674058	−	0.923239i
$979$	0.531502	−	0.193451i	0.0169869	−	0.00618272i
$980$	−1.68487	+	2.91828i	−0.0538212	+	0.0932210i
$981$	−12.8503	−	16.6062i	−0.410278	−	0.530196i
$982$	−1.04178	−	1.80442i	−0.0332447	−	0.0575815i
$983$	41.5259	+	34.8444i	1.32447	+	1.11136i	0.985336	+	0.170625i	$0.0545785\pi$
$983$	41.5259	+	34.8444i	1.32447	+	1.11136i	0.339134	+	0.940738i	$0.389866\pi$
$984$	2.10655	+	2.19157i	0.0671544	+	0.0698648i
$985$	0.907521	+	5.14681i	0.0289160	+	0.163991i
$986$	4.11130	+	23.3163i	0.130930	+	0.742543i
$987$	0.684601	−	0.169000i	0.0217911	−	0.00537934i
$988$	−1.10503	−	0.927234i	−0.0351558	−	0.0294992i
$989$	52.0261	+	90.1118i	1.65433	+	2.86539i
$990$	−2.05102	+	1.07834i	−0.0651858	+	0.0342720i
$991$	15.3730	−	26.6268i	0.488340	−	0.845829i	−0.511570	−	0.859241i	$-0.670936\pi$
$991$	15.3730	−	26.6268i	0.488340	−	0.845829i	0.999910	+	0.0134121i	$0.00426935\pi$
$992$	−8.19771	+	2.98372i	−0.260277	+	0.0947333i
$993$	45.7035	+	4.91110i	1.45036	+	0.155849i
$994$	0.0279746	−	0.0234735i	0.000887299	−	0.000744533i
$995$	6.36638	+	2.31717i	0.201828	+	0.0734593i
$996$	9.43792	−	6.33408i	0.299052	−	0.200703i
$997$	−6.56327	+	37.2222i	−0.207861	+	1.17884i	0.685013	+	0.728531i	$0.259796\pi$
$997$	−6.56327	+	37.2222i	−0.207861	+	1.17884i	−0.892874	+	0.450307i	$0.851315\pi$
$998$	16.4814			0.521710
$999$	24.9542	−	22.1556i	0.789516	−	0.700973i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.w.d.79.2	✓	66
27.13	even	9	inner	702.2.w.d.391.2	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
702.2.w.d.79.2	✓	66	1.1	even	1	trivial
702.2.w.d.391.2	yes	66	27.13	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-1.55499 - 0.762899i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.368840 + 0.309494i) q^{5} +(1.02133 - 1.39889i) q^{6} +(-0.0350928 + 0.0127727i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.83597 + 2.37260i) q^{9} +(-0.240744 - 0.416980i) q^{10} +(-1.22890 - 1.03117i) q^{11} +(1.20028 + 1.24873i) q^{12} +(0.173648 + 0.984808i) q^{13} +(-0.00648489 - 0.0367776i) q^{14} +(0.809655 - 0.199871i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-2.84400 - 4.92596i) q^{17} +(-2.65536 + 1.39608i) q^{18} +(0.721260 - 1.24926i) q^{19} +(0.452450 - 0.164678i) q^{20} +(0.0643132 + 0.00691081i) q^{21} +(1.22890 - 1.03117i) q^{22} +(8.01307 + 2.91652i) q^{23} +(-1.43818 + 0.965209i) q^{24} +(-0.827984 + 4.69573i) q^{25} -1.00000 q^{26} +(-1.04486 - 5.09002i) q^{27} +0.0373450 q^{28} +(-0.722801 + 4.09921i) q^{29} +(0.0562396 + 0.832061i) q^{30} +(8.19771 + 2.98372i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(1.12424 + 2.54098i) q^{33} +(5.34498 - 1.94541i) q^{34} +(0.00899056 - 0.0155721i) q^{35} +(-0.913773 - 2.85745i) q^{36} +(3.21107 + 5.56174i) q^{37} +(1.10503 + 0.927234i) q^{38} +(0.481288 - 1.66384i) q^{39} +(0.0836093 + 0.474172i) q^{40} +(-0.304760 - 1.72838i) q^{41} +(-0.0179737 + 0.0621361i) q^{42} +(9.34743 + 7.84342i) q^{43} +(0.802106 + 1.38929i) q^{44} +(-1.41148 - 0.306887i) q^{45} +(-4.26366 + 7.38488i) q^{46} +(10.2441 - 3.72856i) q^{47} +(-0.700808 - 1.58394i) q^{48} +(-5.36124 + 4.49862i) q^{49} +(-4.48061 - 1.63081i) q^{50} +(0.664382 + 9.82949i) q^{51} +(0.173648 - 0.984808i) q^{52} -1.74510 q^{53} +(5.19413 - 0.145116i) q^{54} +0.772408 q^{55} +(-0.00648489 + 0.0367776i) q^{56} +(-2.07461 + 1.39233i) q^{57} +(-3.91142 - 1.42364i) q^{58} +(-6.81878 + 5.72164i) q^{59} +(-0.829187 - 0.0891008i) q^{60} +(9.25156 - 3.36729i) q^{61} +(-4.36191 + 7.55505i) q^{62} +(-0.0947339 - 0.0598107i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.368840 - 0.309494i) q^{65} +(-2.69760 + 0.665928i) q^{66} +(0.0256044 + 0.145210i) q^{67} +(0.987712 + 5.60159i) q^{68} +(-10.2352 - 10.6483i) q^{69} +(0.0137743 + 0.0115580i) q^{70} +(0.488931 + 0.846853i) q^{71} +(2.97271 - 0.403700i) q^{72} +(-1.32294 + 2.29141i) q^{73} +(-6.03484 + 2.19650i) q^{74} +(4.86987 - 6.67013i) q^{75} +(-1.10503 + 0.927234i) q^{76} +(0.0562963 + 0.0204902i) q^{77} +(1.55499 + 0.762899i) q^{78} +(2.40733 - 13.6527i) q^{79} -0.481487 q^{80} +(-2.25842 + 8.71203i) q^{81} +1.75505 q^{82} +(1.13955 - 6.46269i) q^{83} +(-0.0580710 - 0.0284904i) q^{84} +(2.57354 + 0.936691i) q^{85} +(-9.34743 + 7.84342i) q^{86} +(4.25123 - 5.82280i) q^{87} +(-1.50747 + 0.548673i) q^{88} +(-0.176290 + 0.305343i) q^{89} +(0.547327 - 1.33675i) q^{90} +(-0.0186725 - 0.0323417i) q^{91} +(-6.53231 - 5.48126i) q^{92} +(-10.4711 - 10.8937i) q^{93} +(1.89304 + 10.7360i) q^{94} +(0.120608 + 0.684003i) q^{95} +(1.68157 - 0.415112i) q^{96} +(14.4735 + 12.1447i) q^{97} +(-3.49930 - 6.06097i) q^{98} +(0.190323 - 4.80887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 3 q^{5} + 9 q^{6} - 3 q^{7} + 33 q^{8} - 6 q^{9} - 9 q^{10} - 3 q^{11} + 3 q^{14} - 27 q^{15} + 12 q^{17} - 12 q^{18} - 21 q^{19} - 6 q^{20} - 18 q^{21} + 3 q^{22} - 3 q^{25} - 66 q^{26} + 9 q^{27}+ \cdots - 15 q^{99}+O(q^{100}) \) 66 * q + 3 * q^5 + 9 * q^6 - 3 * q^7 + 33 * q^8 - 6 * q^9 - 9 * q^10 - 3 * q^11 + 3 * q^14 - 27 * q^15 + 12 * q^17 - 12 * q^18 - 21 * q^19 - 6 * q^20 - 18 * q^21 + 3 * q^22 - 3 * q^25 - 66 * q^26 + 9 * q^27 + 18 * q^28 + 39 * q^29 + 9 * q^30 - 9 * q^31 + 15 * q^33 - 6 * q^34 - 9 * q^35 - 3 * q^36 - 21 * q^37 + 6 * q^38 - 3 * q^40 + 6 * q^41 + 9 * q^42 - 6 * q^43 + 3 * q^44 - 9 * q^45 - 9 * q^46 - 36 * q^47 + 9 * q^48 - 9 * q^49 + 3 * q^50 + 21 * q^51 - 60 * q^53 + 27 * q^54 + 84 * q^55 + 3 * q^56 + 87 * q^57 + 24 * q^58 - 30 * q^59 + 6 * q^60 - 12 * q^61 + 21 * q^62 - 60 * q^63 - 33 * q^64 + 3 * q^65 + 24 * q^66 - 3 * q^67 + 15 * q^68 - 87 * q^69 - 21 * q^70 + 3 * q^71 + 6 * q^72 - 15 * q^73 + 6 * q^74 - 117 * q^75 - 6 * q^76 + 27 * q^77 + 27 * q^79 - 18 * q^80 + 78 * q^81 + 24 * q^82 - 24 * q^83 + 33 * q^84 + 45 * q^85 + 6 * q^86 + 18 * q^87 - 6 * q^88 + 36 * q^89 - 87 * q^90 - 9 * q^91 - 63 * q^93 - 36 * q^94 + 63 * q^95 - 102 * q^97 + 72 * q^98 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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