LMFDB - Embedded newform 966.2.y.c.163.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			163.5
Character	$\chi$	$=$	966.163
Dual form			966.2.y.c.403.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.888835 + 0.458227i) q^{2} +(0.786053 - 0.618159i) q^{3} +(0.580057 - 0.814576i) q^{4} +(-0.514242 + 0.490329i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(1.98444 + 1.74985i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.235759 - 0.971812i) q^{9} +O(q^{10})$	\(q+(-0.888835 + 0.458227i) q^{2} +(0.786053 - 0.618159i) q^{3} +(0.580057 - 0.814576i) q^{4} +(-0.514242 + 0.490329i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(1.98444 + 1.74985i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.235759 - 0.971812i) q^{9} +(0.232395 - 0.671461i) q^{10} +(-3.31785 - 1.71047i) q^{11} +(-0.0475819 - 0.998867i) q^{12} +(0.811507 + 0.936529i) q^{13} +(-2.56567 - 0.646009i) q^{14} +(-0.101120 + 0.703308i) q^{15} +(-0.327068 - 0.945001i) q^{16} +(0.773673 - 0.0738768i) q^{17} +(0.235759 + 0.971812i) q^{18} +(8.55910 + 0.817295i) q^{19} +(0.101120 + 0.703308i) q^{20} +(2.64156 + 0.148778i) q^{21} +3.73280 q^{22} +(2.54285 + 4.06619i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.213887 + 4.49004i) q^{25} +(-1.15044 - 0.460566i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(2.57648 - 0.601463i) q^{28} +(1.47949 - 3.23962i) q^{29} +(-0.232395 - 0.671461i) q^{30} +(-5.22242 + 2.09074i) q^{31} +(0.723734 + 0.690079i) q^{32} +(-3.66534 + 0.706437i) q^{33} +(-0.653816 + 0.420182i) q^{34} +(-1.87849 + 0.0731802i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-0.284485 + 1.17266i) q^{37} +(-7.98214 + 3.19557i) q^{38} +(1.21681 + 0.234521i) q^{39} +(-0.412154 - 0.578789i) q^{40} +(6.63468 + 1.94812i) q^{41} +(-2.41609 + 1.07820i) q^{42} +(-0.577413 - 4.01599i) q^{43} +(-3.31785 + 1.71047i) q^{44} +(0.355270 + 0.615346i) q^{45} +(-4.12341 - 2.44898i) q^{46} +(6.33543 - 10.9733i) q^{47} +(-0.841254 - 0.540641i) q^{48} +(0.876018 + 6.94497i) q^{49} +(-1.86735 - 4.08892i) q^{50} +(0.562481 - 0.536324i) q^{51} +(1.23359 - 0.117794i) q^{52} +(-6.09417 - 1.17456i) q^{53} +(0.786053 + 0.618159i) q^{54} +(2.54487 - 0.747241i) q^{55} +(-2.01446 + 1.71521i) q^{56} +(7.23312 - 4.64845i) q^{57} +(0.169461 + 3.55743i) q^{58} +(-3.10600 + 8.97420i) q^{59} +(0.514242 + 0.490329i) q^{60} +(11.4977 + 9.04189i) q^{61} +(3.68384 - 4.25138i) q^{62} +(2.16838 - 1.51596i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-0.876519 - 0.0836974i) q^{65} +(2.93418 - 2.30746i) q^{66} +(-0.276430 + 5.80297i) q^{67} +(0.388596 - 0.673068i) q^{68} +(4.51237 + 1.62436i) q^{69} +(1.63613 - 0.925818i) q^{70} +(12.1678 + 7.81980i) q^{71} +(0.928368 + 0.371662i) q^{72} +(8.60900 - 12.0896i) q^{73} +(-0.284485 - 1.17266i) q^{74} +(2.60743 + 3.66163i) q^{75} +(5.63051 - 6.49796i) q^{76} +(-3.59100 - 9.20007i) q^{77} +(-1.18901 + 0.349125i) q^{78} +(12.7262 - 2.45277i) q^{79} +(0.631553 + 0.325588i) q^{80} +(-0.888835 - 0.458227i) q^{81} +(-6.78982 + 1.30863i) q^{82} +(-10.6051 + 3.11395i) q^{83} +(1.65345 - 2.06546i) q^{84} +(-0.361631 + 0.417345i) q^{85} +(2.35346 + 3.30497i) q^{86} +(-0.839647 - 3.46107i) q^{87} +(2.16524 - 3.04065i) q^{88} +(-5.21252 - 2.08678i) q^{89} +(-0.597745 - 0.384147i) q^{90} +(-0.0284011 + 3.27851i) q^{91} +(4.78722 + 0.287279i) q^{92} +(-2.81269 + 4.87172i) q^{93} +(-0.602904 + 12.6565i) q^{94} +(-4.80219 + 3.77649i) q^{95} +(0.995472 + 0.0950560i) q^{96} +(-8.60141 - 2.52560i) q^{97} +(-3.96101 - 5.77152i) q^{98} +(-2.44447 + 2.82106i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{12} - 4 q^{13} + 9 q^{14} - 18 q^{15} + 8 q^{16} - 21 q^{17} + 8 q^{18} + 4 q^{19} + 18 q^{20} - 15 q^{21} + 116 q^{22} + 14 q^{23} + 80 q^{24} + 2 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 46 q^{29} - 2 q^{30} + q^{31} + 8 q^{32} - 8 q^{33} - 68 q^{34} - 84 q^{35} - 16 q^{36} + 19 q^{37} - 7 q^{38} - 2 q^{39} - 9 q^{40} + 38 q^{41} + 2 q^{42} + 28 q^{43} + 8 q^{44} + 24 q^{45} - 8 q^{46} - 26 q^{47} + 16 q^{48} - 6 q^{49} - 4 q^{50} + 21 q^{51} + 2 q^{52} - 20 q^{53} - 8 q^{54} + 46 q^{55} - 2 q^{56} - 14 q^{57} - 21 q^{58} + 36 q^{59} - 2 q^{60} + 40 q^{61} - 24 q^{62} - 2 q^{63} - 16 q^{64} - 10 q^{65} - 8 q^{66} + 6 q^{67} + 34 q^{68} + 6 q^{69} - 20 q^{70} + 132 q^{71} + 8 q^{72} - 36 q^{73} + 19 q^{74} - 2 q^{75} - 8 q^{76} - 75 q^{77} - 18 q^{78} + 34 q^{79} + 2 q^{80} + 8 q^{81} + 47 q^{82} + 74 q^{83} + 13 q^{84} + 2 q^{85} + 30 q^{86} + 10 q^{87} - 3 q^{88} - 12 q^{89} - 4 q^{90} - 30 q^{91} - 50 q^{92} + 10 q^{93} - 4 q^{94} + 27 q^{95} - 8 q^{96} + 24 q^{97} + 7 q^{98} - 16 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^12 - 4 * q^13 + 9 * q^14 - 18 * q^15 + 8 * q^16 - 21 * q^17 + 8 * q^18 + 4 * q^19 + 18 * q^20 - 15 * q^21 + 116 * q^22 + 14 * q^23 + 80 * q^24 + 2 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 46 * q^29 - 2 * q^30 + q^31 + 8 * q^32 - 8 * q^33 - 68 * q^34 - 84 * q^35 - 16 * q^36 + 19 * q^37 - 7 * q^38 - 2 * q^39 - 9 * q^40 + 38 * q^41 + 2 * q^42 + 28 * q^43 + 8 * q^44 + 24 * q^45 - 8 * q^46 - 26 * q^47 + 16 * q^48 - 6 * q^49 - 4 * q^50 + 21 * q^51 + 2 * q^52 - 20 * q^53 - 8 * q^54 + 46 * q^55 - 2 * q^56 - 14 * q^57 - 21 * q^58 + 36 * q^59 - 2 * q^60 + 40 * q^61 - 24 * q^62 - 2 * q^63 - 16 * q^64 - 10 * q^65 - 8 * q^66 + 6 * q^67 + 34 * q^68 + 6 * q^69 - 20 * q^70 + 132 * q^71 + 8 * q^72 - 36 * q^73 + 19 * q^74 - 2 * q^75 - 8 * q^76 - 75 * q^77 - 18 * q^78 + 34 * q^79 + 2 * q^80 + 8 * q^81 + 47 * q^82 + 74 * q^83 + 13 * q^84 + 2 * q^85 + 30 * q^86 + 10 * q^87 - 3 * q^88 - 12 * q^89 - 4 * q^90 - 30 * q^91 - 50 * q^92 + 10 * q^93 - 4 * q^94 + 27 * q^95 - 8 * q^96 + 24 * q^97 + 7 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{11}\right)$

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 $

$2$	−0.888835	+	0.458227i	−0.628502	+	0.324015i
$2$	−0.888835	+	0.458227i	−0.628502	+	0.324015i
$3$	0.786053	−	0.618159i	0.453828	−	0.356894i
$3$	0.786053	−	0.618159i	0.453828	−	0.356894i
$4$	0.580057	−	0.814576i	0.290028	−	0.407288i
$5$	−0.514242	+	0.490329i	−0.229976	+	0.219282i	−0.796301	−	0.604900i	$-0.793213\pi$
$5$	−0.514242	+	0.490329i	−0.229976	+	0.219282i	0.566325	+	0.824182i	$0.308365\pi$
$6$	−0.415415	+	0.909632i	−0.169592	+	0.371356i
$7$	1.98444	+	1.74985i	0.750048	+	0.661383i
$7$	1.98444	+	1.74985i	0.750048	+	0.661383i
$8$	−0.142315	+	0.989821i	−0.0503159	+	0.349955i
$9$	0.235759	−	0.971812i	0.0785863	−	0.323937i
$10$	0.232395	−	0.671461i	0.0734897	−	0.212335i
$11$	−3.31785	−	1.71047i	−1.00037	−	0.515726i	−0.121399	−	0.992604i	$-0.538738\pi$
$11$	−3.31785	−	1.71047i	−1.00037	−	0.515726i	−0.878969	+	0.476878i	$0.841768\pi$
$12$	−0.0475819	−	0.998867i	−0.0137357	−	0.288348i
$13$	0.811507	+	0.936529i	0.225072	+	0.259746i	0.857043	−	0.515246i	$-0.172299\pi$
$13$	0.811507	+	0.936529i	0.225072	+	0.259746i	−0.631971	+	0.774992i	$0.717754\pi$
$14$	−2.56567	−	0.646009i	−0.685705	−	0.172653i
$15$	−0.101120	+	0.703308i	−0.0261092	+	0.181593i
$16$	−0.327068	−	0.945001i	−0.0817670	−	0.236250i
$17$	0.773673	−	0.0738768i	0.187643	−	0.0179178i	−0.000811276	−	1.00000i	$-0.500258\pi$
$17$	0.773673	−	0.0738768i	0.187643	−	0.0179178i	0.188455	+	0.982082i	$0.439652\pi$
$18$	0.235759	+	0.971812i	0.0555689	+	0.229058i
$19$	8.55910	+	0.817295i	1.96359	+	0.187500i	0.997498	−	0.0706920i	$-0.0225208\pi$
$19$	8.55910	+	0.817295i	1.96359	+	0.187500i	0.966094	+	0.258192i	$0.0831268\pi$
$20$	0.101120	+	0.703308i	0.0226112	+	0.157264i
$21$	2.64156	+	0.148778i	0.576437	+	0.0324660i
$22$	3.73280			0.795836
$23$	2.54285	+	4.06619i	0.530221	+	0.847860i
$23$	2.54285	+	4.06619i	0.530221	+	0.847860i
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.213887	+	4.49004i	−0.0427774	+	0.898008i
$26$	−1.15044	−	0.460566i	−0.225620	−	0.0903245i
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$	2.57648	−	0.601463i	0.486909	−	0.113666i
$29$	1.47949	−	3.23962i	0.274734	−	0.601583i	−0.721094	−	0.692837i	$-0.756360\pi$
$29$	1.47949	−	3.23962i	0.274734	−	0.601583i	0.995828	+	0.0912547i	$0.0290877\pi$
$30$	−0.232395	−	0.671461i	−0.0424293	−	0.122591i
$31$	−5.22242	+	2.09074i	−0.937974	+	0.375508i	−0.789738	−	0.613444i	$-0.789784\pi$
$31$	−5.22242	+	2.09074i	−0.937974	+	0.375508i	−0.148236	+	0.988952i	$0.547360\pi$
$32$	0.723734	+	0.690079i	0.127939	+	0.121990i
$33$	−3.66534	+	0.706437i	−0.638055	+	0.122975i
$34$	−0.653816	+	0.420182i	−0.112128	+	0.0720606i
$35$	−1.87849	+	0.0731802i	−0.317522	+	0.0123697i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	−0.284485	+	1.17266i	−0.0467691	+	0.192785i	−0.990404	−	0.138204i	$-0.955867\pi$
$37$	−0.284485	+	1.17266i	−0.0467691	+	0.192785i	0.943635	+	0.330989i	$0.107382\pi$
$38$	−7.98214	+	3.19557i	−1.29487	+	0.518389i
$39$	1.21681	+	0.234521i	0.194846	+	0.0375535i
$40$	−0.412154	−	0.578789i	−0.0651672	−	0.0915146i
$41$	6.63468	+	1.94812i	1.03616	+	0.304245i	0.755214	−	0.655478i	$-0.227533\pi$
$41$	6.63468	+	1.94812i	1.03616	+	0.304245i	0.280949	+	0.959723i	$0.409351\pi$
$42$	−2.41609	+	1.07820i	−0.372811	+	0.166369i
$43$	−0.577413	−	4.01599i	−0.0880546	−	0.612433i	−0.985291	−	0.170883i	$-0.945338\pi$
$43$	−0.577413	−	4.01599i	−0.0880546	−	0.612433i	0.897237	−	0.441550i	$-0.145571\pi$
$44$	−3.31785	+	1.71047i	−0.500184	+	0.257863i
$45$	0.355270	+	0.615346i	0.0529606	+	0.0917304i
$46$	−4.12341	−	2.44898i	−0.607964	−	0.361082i
$47$	6.33543	−	10.9733i	0.924118	−	1.60062i	0.131144	−	0.991363i	$-0.458135\pi$
$47$	6.33543	−	10.9733i	0.924118	−	1.60062i	0.792974	−	0.609256i	$-0.208532\pi$
$48$	−0.841254	−	0.540641i	−0.121424	−	0.0780348i
$49$	0.876018	+	6.94497i	0.125145	+	0.992138i
$50$	−1.86735	−	4.08892i	−0.264083	−	0.578260i
$51$	0.562481	−	0.536324i	0.0787630	−	0.0751004i
$52$	1.23359	−	0.117794i	0.171069	−	0.0163351i
$53$	−6.09417	−	1.17456i	−0.837099	−	0.161338i	−0.247352	−	0.968926i	$-0.579560\pi$
$53$	−6.09417	−	1.17456i	−0.837099	−	0.161338i	−0.589747	+	0.807588i	$0.700773\pi$
$54$	0.786053	+	0.618159i	0.106968	+	0.0841208i
$55$	2.54487	−	0.747241i	0.343150	−	0.100758i
$56$	−2.01446	+	1.71521i	−0.269193	+	0.229205i
$57$	7.23312	−	4.64845i	0.958051	−	0.615702i
$58$	0.169461	+	3.55743i	0.0222514	+	0.467113i
$59$	−3.10600	+	8.97420i	−0.404367	+	1.16834i	0.540630	+	0.841261i	$0.318186\pi$
$59$	−3.10600	+	8.97420i	−0.404367	+	1.16834i	−0.944997	+	0.327080i	$0.893935\pi$
$60$	0.514242	+	0.490329i	0.0663884	+	0.0633012i
$61$	11.4977	+	9.04189i	1.47213	+	1.15770i	0.952988	+	0.303007i	$0.0979905\pi$
$61$	11.4977	+	9.04189i	1.47213	+	1.15770i	0.519141	+	0.854689i	$0.326252\pi$
$62$	3.68384	−	4.25138i	0.467848	−	0.539925i
$63$	2.16838	−	1.51596i	0.273190	−	0.190993i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−0.876519	−	0.0836974i	−0.108719	−	0.0103814i
$66$	2.93418	−	2.30746i	0.361173	−	0.284029i
$67$	−0.276430	+	5.80297i	−0.0337713	+	0.708946i	0.916969	+	0.398958i	$0.130628\pi$
$67$	−0.276430	+	5.80297i	−0.0337713	+	0.708946i	−0.950740	+	0.309988i	$0.899675\pi$
$68$	0.388596	−	0.673068i	0.0471242	−	0.0816215i
$69$	4.51237	+	1.62436i	0.543225	+	0.195550i
$70$	1.63613	−	0.925818i	0.195555	−	0.110656i
$71$	12.1678	+	7.81980i	1.44406	+	0.928040i	0.999478	+	0.0323002i	$0.0102832\pi$
$71$	12.1678	+	7.81980i	1.44406	+	0.928040i	0.444580	+	0.895739i	$0.353353\pi$
$72$	0.928368	+	0.371662i	0.109409	+	0.0438008i
$73$	8.60900	−	12.0896i	1.00761	−	1.41499i	0.100086	−	0.994979i	$-0.468088\pi$
$73$	8.60900	−	12.0896i	1.00761	−	1.41499i	0.907521	−	0.420007i	$-0.137972\pi$
$74$	−0.284485	−	1.17266i	−0.0330708	−	0.136320i
$75$	2.60743	+	3.66163i	0.301080	+	0.422808i
$76$	5.63051	−	6.49796i	0.645864	−	0.745367i
$77$	−3.59100	−	9.20007i	−0.409233	−	1.04845i
$78$	−1.18901	+	0.349125i	−0.134629	+	0.0395306i
$79$	12.7262	−	2.45277i	1.43181	−	0.275958i	0.586374	−	0.810040i	$-0.300555\pi$
$79$	12.7262	−	2.45277i	1.43181	−	0.275958i	0.845433	+	0.534082i	$0.179343\pi$
$80$	0.631553	+	0.325588i	0.0706098	+	0.0364019i
$81$	−0.888835	−	0.458227i	−0.0987595	−	0.0509141i
$82$	−6.78982	+	1.30863i	−0.749810	+	0.144514i
$83$	−10.6051	+	3.11395i	−1.16406	+	0.341800i	−0.806010	−	0.591901i	$-0.798377\pi$
$83$	−10.6051	+	3.11395i	−1.16406	+	0.341800i	−0.358053	+	0.933701i	$0.616559\pi$
$84$	1.65345	−	2.06546i	0.180406	−	0.225360i
$85$	−0.361631	+	0.417345i	−0.0392244	+	0.0452674i
$86$	2.35346	+	3.30497i	0.253780	+	0.356384i
$87$	−0.839647	−	3.46107i	−0.0900196	−	0.371066i
$88$	2.16524	−	3.04065i	0.230815	−	0.324134i
$89$	−5.21252	−	2.08678i	−0.552526	−	0.221198i	0.0785620	−	0.996909i	$-0.474967\pi$
$89$	−5.21252	−	2.08678i	−0.552526	−	0.221198i	−0.631088	+	0.775711i	$0.717391\pi$
$90$	−0.597745	−	0.384147i	−0.0630078	−	0.0404927i
$91$	−0.0284011	+	3.27851i	−0.00297724	+	0.343681i
$92$	4.78722	+	0.287279i	0.499102	+	0.0299510i
$93$	−2.81269	+	4.87172i	−0.291662	+	0.505174i
$94$	−0.602904	+	12.6565i	−0.0621848	+	1.30542i
$95$	−4.80219	+	3.77649i	−0.492695	+	0.387459i
$96$	0.995472	+	0.0950560i	0.101600	+	0.00970162i
$97$	−8.60141	−	2.52560i	−0.873341	−	0.256436i	−0.185805	−	0.982587i	$-0.559489\pi$
$97$	−8.60141	−	2.52560i	−0.873341	−	0.256436i	−0.687536	+	0.726150i	$0.741308\pi$
$98$	−3.96101	−	5.77152i	−0.400122	−	0.583012i
$99$	−2.44447	+	2.82106i	−0.245678	+	0.283528i
$100$	3.53341	+	2.77871i	0.353341	+	0.277871i
$101$	−4.74431	−	4.52369i	−0.472076	−	0.450124i	0.416309	−	0.909223i	$-0.363324\pi$
$101$	−4.74431	−	4.52369i	−0.472076	−	0.450124i	−0.888385	+	0.459100i	$0.848172\pi$
$102$	−0.254195	+	0.734447i	−0.0251690	+	0.0727211i
$103$	−0.102854	−	2.15918i	−0.0101345	−	0.212750i	−0.998254	−	0.0590638i	$-0.981188\pi$
$103$	−0.102854	−	2.15918i	−0.0101345	−	0.212750i	0.988120	−	0.153686i	$-0.0491146\pi$
$104$	−1.04249	+	0.669965i	−0.102224	+	0.0656955i
$105$	−1.43135	+	1.21873i	−0.139686	+	0.118936i
$106$	5.95493	−	1.74853i	0.578394	−	0.169832i
$107$	1.96796	+	1.54762i	0.190250	+	0.149614i	0.708741	−	0.705469i	$-0.249264\pi$
$107$	1.96796	+	1.54762i	0.190250	+	0.149614i	−0.518491	+	0.855083i	$0.673506\pi$
$108$	−0.981929	−	0.189251i	−0.0944861	−	0.0182107i
$109$	−4.16875	+	0.398068i	−0.399294	+	0.0381280i	−0.292772	−	0.956182i	$-0.594578\pi$
$109$	−4.16875	+	0.398068i	−0.399294	+	0.0381280i	−0.106522	+	0.994310i	$0.533972\pi$
$110$	−1.91956	+	1.83030i	−0.183023	+	0.174512i
$111$	0.501273	+	1.09763i	0.0475787	+	0.104183i
$112$	1.00457	−	2.44762i	0.0949226	−	0.231278i
$113$	3.34910	+	2.15233i	0.315056	+	0.202474i	0.688606	−	0.725136i	$-0.258223\pi$
$113$	3.34910	+	2.15233i	0.315056	+	0.202474i	−0.373549	+	0.927610i	$0.621859\pi$
$114$	−4.29902	+	7.44611i	−0.402640	+	0.697392i
$115$	−3.30141	−	0.844175i	−0.307858	−	0.0787198i
$116$	−1.78073	−	3.08432i	−0.165337	−	0.286372i
$117$	1.10145	−	0.567837i	0.101829	−	0.0524965i
$118$	−1.35149	−	9.39984i	−0.124415	−	0.865325i
$119$	1.66458	+	1.20721i	0.152592	+	0.110665i
$120$	−0.681758	−	0.200182i	−0.0622357	−	0.0182741i
$121$	1.70177	+	2.38981i	0.154707	+	0.217255i
$122$	−14.3628	−	2.76820i	−1.30035	−	0.250621i
$123$	6.41946	−	2.56996i	0.578823	−	0.231726i
$124$	−1.32623	+	5.46681i	−0.119099	+	0.490934i
$125$	−4.41813	−	5.09880i	−0.395170	−	0.456050i
$126$	−1.23268	+	2.34105i	−0.109816	+	0.208557i
$127$	4.88246	−	3.13776i	0.433248	−	0.278431i	−0.305785	−	0.952100i	$-0.598919\pi$
$127$	4.88246	−	3.13776i	0.433248	−	0.278431i	0.739033	+	0.673669i	$0.235283\pi$
$128$	0.981929	−	0.189251i	0.0867911	−	0.0167276i
$129$	−2.93640	−	2.79985i	−0.258536	−	0.246513i
$130$	0.817433	−	0.327251i	0.0716936	−	0.0287018i
$131$	1.86174	+	5.37913i	0.162661	+	0.469977i	0.996648	−	0.0818062i	$-0.0260689\pi$
$131$	1.86174	+	5.37913i	0.162661	+	0.469977i	−0.833988	+	0.551783i	$0.813948\pi$
$132$	−1.55066	+	3.39548i	−0.134968	+	0.295538i
$133$	15.5549	+	16.5990i	1.34878	+	1.43932i
$134$	−2.41338	−	5.28456i	−0.208484	−	0.456516i
$135$	0.659643	+	0.264081i	0.0567730	+	0.0227285i
$136$	−0.0369803	+	0.776312i	−0.00317103	+	0.0665682i
$137$	10.0440	+	17.3968i	0.858119	+	1.48630i	0.873721	+	0.486427i	$0.161700\pi$
$137$	10.0440	+	17.3968i	0.858119	+	1.48630i	−0.0156028	+	0.999878i	$0.504967\pi$
$138$	−4.75508	+	0.623899i	−0.404779	+	0.0531098i
$139$	−17.3207			−1.46912			−0.734562	−	0.678541i	$-0.762613\pi$
$139$	−17.3207			−1.46912			−0.734562	+	0.678541i	$0.762613\pi$
$140$	−1.03002	+	1.57262i	−0.0870525	+	0.132911i
$141$	−1.80325	−	12.5419i	−0.151861	−	1.05622i
$142$	−14.3985	−	1.37489i	−1.20829	−	0.115378i
$143$	−1.09055	−	4.49532i	−0.0911966	−	0.375917i
$144$	−0.995472	+	0.0950560i	−0.0829560	+	0.00792134i
$145$	0.827666	+	2.39138i	0.0687339	+	0.198594i
$146$	−2.11219	+	14.6906i	−0.174806	+	1.21580i
$147$	4.98169	+	4.91760i	0.410883	+	0.405596i
$148$	0.790207	+	0.911947i	0.0649546	+	0.0749616i
$149$	0.159511	+	3.34854i	0.0130676	+	0.274323i	0.995939	+	0.0900304i	$0.0286964\pi$
$149$	0.159511	+	3.34854i	0.0130676	+	0.274323i	−0.982871	+	0.184293i	$0.941001\pi$
$150$	−3.99543	−	2.05979i	−0.326226	−	0.168181i
$151$	3.69630	−	10.6798i	0.300801	−	0.869106i	−0.688760	−	0.724989i	$-0.741845\pi$
$151$	3.69630	−	10.6798i	0.300801	−	0.869106i	0.989561	−	0.144117i	$-0.0460342\pi$
$152$	−2.02706	+	8.35567i	−0.164416	+	0.677734i
$153$	0.110606	−	0.769282i	0.00894196	−	0.0621927i
$154$	7.40753	+	6.53186i	0.596916	+	0.526352i
$155$	1.66044	−	3.63585i	0.133370	−	0.292039i
$156$	0.896855	−	0.855150i	0.0718059	−	0.0684668i
$157$	8.32750	−	11.6943i	0.664607	−	0.933310i	−0.335355	−	0.942092i	$-0.608856\pi$
$157$	8.32750	−	11.6943i	0.664607	−	0.933310i	0.999961	+	0.00878217i	$0.00279549\pi$
$158$	−10.1876	+	8.01158i	−0.810478	+	0.637367i
$159$	−5.51641	+	2.84391i	−0.437479	+	0.225536i
$160$	−0.710540			−0.0561731
$161$	−2.06911	+	12.5187i	−0.163069	+	0.986615i
$162$	1.00000			0.0785674
$163$	−11.9160	+	6.14314i	−0.933336	+	0.481168i	−0.856656	−	0.515888i	$-0.827462\pi$
$163$	−11.9160	+	6.14314i	−0.933336	+	0.481168i	−0.0766795	+	0.997056i	$0.524432\pi$
$164$	5.43538	−	4.27443i	0.424432	−	0.333777i
$165$	1.53849	−	2.16050i	0.119771	−	0.168195i
$166$	7.99932	−	7.62733i	0.620867	−	0.591996i
$167$	−8.47146	+	18.5499i	−0.655542	+	1.43544i	0.231077	+	0.972935i	$0.425775\pi$
$167$	−8.47146	+	18.5499i	−0.655542	+	1.43544i	−0.886619	+	0.462501i	$0.846952\pi$
$168$	−0.523198	+	2.59350i	−0.0403656	+	0.200093i
$169$	1.63155	−	11.3477i	0.125504	−	0.872898i
$170$	0.130192	−	0.536660i	0.00998530	−	0.0411600i
$171$	2.81214	−	8.12515i	0.215050	−	0.621345i
$172$	−3.60626	−	1.85916i	−0.274975	−	0.141759i
$173$	−0.262681	−	5.51436i	−0.0199713	−	0.419249i	−0.986609	−	0.163102i	$-0.947850\pi$
$173$	−0.262681	−	5.51436i	−0.0199713	−	0.419249i	0.966638	−	0.256147i	$-0.0824530\pi$
$174$	2.33226	+	2.69157i	0.176808	+	0.204048i
$175$	−8.28136	+	8.53595i	−0.626012	+	0.645257i
$176$	−0.531233	+	3.69481i	−0.0400432	+	0.278507i
$177$	3.10600	+	8.97420i	0.233461	+	0.674542i
$178$	5.58929	−	0.533713i	0.418935	−	0.0400035i
$179$	−5.30865	−	21.8826i	−0.396787	−	1.63558i	−0.723405	−	0.690424i	$-0.757424\pi$
$179$	−5.30865	−	21.8826i	−0.396787	−	1.63558i	0.326618	−	0.945157i	$-0.394091\pi$
$180$	0.707323	+	0.0675412i	0.0527207	+	0.00503422i
$181$	1.28822	+	8.95978i	0.0957528	+	0.665975i	0.980006	+	0.198968i	$0.0637588\pi$
$181$	1.28822	+	8.95978i	0.0957528	+	0.665975i	−0.884253	+	0.467008i	$0.845332\pi$
$182$	−1.47706	−	2.92707i	−0.109487	−	0.216969i
$183$	14.6271			1.08127
$184$	−4.38669	+	1.93829i	−0.323391	+	0.142892i
$185$	−0.428697	−	0.742525i	−0.0315184	−	0.0545915i
$186$	0.267666	−	5.61901i	0.0196262	−	0.412006i
$187$	−2.69329	−	1.07823i	−0.196953	−	0.0788481i
$188$	−5.26367	−	11.5258i	−0.383892	−	0.840607i
$189$	0.767357	−	2.53203i	0.0558170	−	0.184178i
$190$	2.53787	−	5.55717i	0.184117	−	0.403159i
$191$	−3.34130	−	9.65405i	−0.241768	−	0.698543i	−0.998971	−	0.0453627i	$-0.985556\pi$
$191$	−3.34130	−	9.65405i	−0.241768	−	0.698543i	0.757203	−	0.653180i	$-0.226566\pi$
$192$	−0.928368	+	0.371662i	−0.0669992	+	0.0268224i
$193$	−18.6792	−	17.8106i	−1.34456	−	1.28203i	−0.927832	−	0.372999i	$-0.878330\pi$
$193$	−18.6792	−	17.8106i	−1.34456	−	1.28203i	−0.416724	−	0.909033i	$-0.636822\pi$
$194$	8.80254	−	1.69655i	0.631986	−	0.121805i
$195$	−0.740729	+	0.476037i	−0.0530447	+	0.0340897i
$196$	6.16535	+	3.31489i	0.440382	+	0.236778i
$197$	−7.10626	−	8.20107i	−0.506300	−	0.584302i	0.443847	−	0.896102i	$-0.353613\pi$
$197$	−7.10626	−	8.20107i	−0.506300	−	0.584302i	−0.950148	+	0.311801i	$0.899068\pi$
$198$	0.880041	−	3.62758i	0.0625418	−	0.257801i
$199$	5.44506	−	2.17987i	0.385990	−	0.154527i	−0.170548	−	0.985349i	$-0.554554\pi$
$199$	5.44506	−	2.17987i	0.385990	−	0.154527i	0.556538	+	0.830822i	$0.312129\pi$
$200$	−4.41390	−	0.850709i	−0.312110	−	0.0601542i
$201$	3.36987	+	4.73232i	0.237692	+	0.333792i
$202$	6.28978	+	1.84685i	0.442548	+	0.129944i
$203$	8.60482	−	3.83996i	0.603940	−	0.269512i
$204$	−0.110606	−	0.769282i	−0.00774397	−	0.0538605i
$205$	−4.36705	+	2.25137i	−0.305008	+	0.157243i
$206$	1.08081	+	1.87203i	0.0753039	+	0.130430i
$207$	4.55107	−	1.51253i	0.316321	−	0.105128i
$208$	0.619603	−	1.07318i	0.0429617	−	0.0744119i
$209$	−26.9998	−	17.3517i	−1.86762	−	1.20024i
$210$	0.713785	−	1.73913i	0.0492559	−	0.120012i
$211$	−2.71823	−	5.95209i	−0.187131	−	0.409759i	0.792694	−	0.609620i	$-0.208678\pi$
$211$	−2.71823	−	5.95209i	−0.187131	−	0.409759i	−0.979824	+	0.199861i	$0.935951\pi$
$212$	−4.49173	+	4.28286i	−0.308493	+	0.294148i
$213$	14.3985	−	1.37489i	0.986566	−	0.0942056i
$214$	−2.45835	−	0.473809i	−0.168050	−	0.0323889i
$215$	2.26609	+	1.78207i	0.154546	+	0.121536i
$216$	0.959493	−	0.281733i	0.0652852	−	0.0191695i
$217$	−14.0221	−	4.98952i	−0.951881	−	0.338711i
$218$	3.52293	−	2.26405i	0.238603	−	0.153341i
$219$	−0.706194	−	14.8248i	−0.0477201	−	1.00177i
$220$	0.867484	−	2.50643i	0.0584858	−	0.168984i
$221$	0.697029	+	0.664616i	0.0468873	+	0.0447069i
$222$	−0.948514	−	0.745920i	−0.0636601	−	0.0500629i
$223$	−14.8301	+	17.1148i	−0.993094	+	1.14609i	−0.00382398	+	0.999993i	$0.501217\pi$
$223$	−14.8301	+	17.1148i	−0.993094	+	1.14609i	−0.989270	+	0.146099i	$0.953328\pi$
$224$	0.228670	+	2.63585i	0.0152787	+	0.176115i
$225$	4.31305	+	1.26643i	0.287537	+	0.0844283i
$226$	−3.96305	−	0.378426i	−0.263618	−	0.0251725i
$227$	−5.53778	+	4.35496i	−0.367555	+	0.289049i	−0.784804	−	0.619743i	$-0.787237\pi$
$227$	−5.53778	+	4.35496i	−0.367555	+	0.289049i	0.417249	+	0.908792i	$0.362994\pi$
$228$	0.409111	−	8.58829i	0.0270940	−	0.568774i
$229$	11.9701	−	20.7329i	0.791009	−	1.37007i	−0.134334	−	0.990936i	$-0.542889\pi$
$229$	11.9701	−	20.7329i	0.791009	−	1.37007i	0.925343	−	0.379131i	$-0.123777\pi$
$230$	3.32124	−	0.762462i	0.218996	−	0.0502752i
$231$	−8.50983	−	5.01194i	−0.559905	−	0.329761i
$232$	2.99609	+	1.92547i	0.196703	+	0.126413i
$233$	4.84808	+	1.94088i	0.317608	+	0.127151i	0.524989	−	0.851109i	$-0.324070\pi$
$233$	4.84808	+	1.94088i	0.317608	+	0.127151i	−0.207380	+	0.978260i	$0.566494\pi$
$234$	−0.718810	+	1.00943i	−0.0469901	+	0.0659883i
$235$	2.12258	+	8.74938i	0.138462	+	0.570746i
$236$	5.50851	+	7.73562i	0.358573	+	0.503546i
$237$	8.48725	−	9.79481i	0.551306	−	0.636241i
$238$	−2.03272	−	0.310256i	−0.131761	−	0.0201109i
$239$	3.59796	−	1.05646i	0.232733	−	0.0683365i	−0.163287	−	0.986579i	$-0.552210\pi$
$239$	3.59796	−	1.05646i	0.232733	−	0.0683365i	0.396019	+	0.918242i	$0.370391\pi$
$240$	0.697700	−	0.134471i	0.0450363	−	0.00868004i
$241$	−3.82785	−	1.97339i	−0.246573	−	0.127117i	0.330510	−	0.943802i	$-0.392779\pi$
$241$	−3.82785	−	1.97339i	−0.246573	−	0.127117i	−0.577084	+	0.816685i	$0.695809\pi$
$242$	−2.60767	−	1.34435i	−0.167627	−	0.0864180i
$243$	−0.981929	+	0.189251i	−0.0629908	+	0.0121405i
$244$	14.0346	−	4.12094i	0.898475	−	0.263816i
$245$	−3.85581	−	3.14186i	−0.246338	−	0.200726i
$246$	−4.52822	+	5.22584i	−0.288709	+	0.333187i
$247$	6.18035	+	8.67909i	0.393246	+	0.552237i
$248$	−1.32623	−	5.46681i	−0.0842159	−	0.347143i
$249$	−6.41128	+	9.00338i	−0.406298	+	0.570566i
$250$	6.26340	+	2.50749i	0.396132	+	0.158587i
$251$	−11.5794	−	7.44165i	−0.730887	−	0.469713i	0.121522	−	0.992589i	$-0.461223\pi$
$251$	−11.5794	−	7.44165i	−0.730887	−	0.469713i	−0.852409	+	0.522876i	$0.824859\pi$
$252$	0.0229188	−	2.64565i	0.00144375	−	0.166660i
$253$	−1.48169	−	17.8405i	−0.0931529	−	1.12162i
$254$	−2.90189	+	5.02623i	−0.182081	+	0.315373i
$255$	−0.0262760	+	0.551601i	−0.00164547	+	0.0345426i
$256$	−0.786053	+	0.618159i	−0.0491283	+	0.0386349i
$257$	−27.7284	−	2.64774i	−1.72965	−	0.165162i	−0.817750	−	0.575574i	$-0.804779\pi$
$257$	−27.7284	−	2.64774i	−1.72965	−	0.165162i	−0.911900	+	0.410412i	$0.865385\pi$
$258$	3.89294	+	1.14307i	0.242364	+	0.0711645i
$259$	−2.61654	+	1.82928i	−0.162584	+	0.113666i
$260$	−0.576609	+	0.665442i	−0.0357597	+	0.0412689i
$261$	−2.79950	−	2.20155i	−0.173285	−	0.136273i
$262$	−4.11964	−	3.92807i	−0.254512	−	0.242677i
$263$	−0.502023	+	1.45050i	−0.0309561	+	0.0894417i	−0.959420	−	0.281981i	$-0.909009\pi$
$263$	−0.502023	+	1.45050i	−0.0309561	+	0.0894417i	0.928464	+	0.371422i	$0.121130\pi$
$264$	−0.177614	−	3.72857i	−0.0109314	−	0.229478i
$265$	3.70980	−	2.38414i	0.227891	−	0.146457i
$266$	−21.4319	−	7.62616i	−1.31407	−	0.467590i
$267$	−5.38728	+	1.58185i	−0.329696	+	0.0968075i
$268$	4.56662	+	3.59123i	0.278951	+	0.219369i
$269$	−21.4470	−	4.13357i	−1.30765	−	0.252028i	−0.512627	−	0.858611i	$-0.671328\pi$
$269$	−21.4470	−	4.13357i	−1.30765	−	0.252028i	−0.795020	+	0.606583i	$0.792540\pi$
$270$	−0.707323	+	0.0675412i	−0.0430463	+	0.00411042i
$271$	−15.4711	+	14.7516i	−0.939799	+	0.896097i	−0.994744	−	0.102392i	$-0.967350\pi$
$271$	−15.4711	+	14.7516i	−0.939799	+	0.896097i	0.0549446	+	0.998489i	$0.482502\pi$
$272$	−0.322857	−	0.706959i	−0.0195761	−	0.0428657i
$273$	2.00431	+	2.59464i	0.121307	+	0.157035i
$274$	−16.8991	−	10.8604i	−1.02091	−	0.656102i
$275$	8.38972	−	14.5314i	0.505919	−	0.876277i
$276$	3.94059	−	2.73345i	0.237196	−	0.164534i
$277$	−13.9962	−	24.2422i	−0.840952	−	1.45657i	−0.889091	−	0.457730i	$-0.848663\pi$
$277$	−13.9962	−	24.2422i	−0.840952	−	1.45657i	0.0481394	−	0.998841i	$-0.484671\pi$
$278$	15.3953	−	7.93682i	0.923347	−	0.476019i
$279$	0.800575	+	5.56812i	0.0479292	+	0.333355i
$280$	0.194901	−	1.86978i	0.0116476	−	0.111741i
$281$	28.7935	+	8.45455i	1.71768	+	0.504356i	0.984456	−	0.175633i	$-0.0561971\pi$
$281$	28.7935	+	8.45455i	1.71768	+	0.504356i	0.733223	+	0.679989i	$0.238015\pi$
$282$	7.34982	+	10.3214i	0.437676	+	0.614629i
$283$	−16.8404	−	3.24573i	−1.00106	−	0.192938i	−0.337712	−	0.941250i	$-0.609653\pi$
$283$	−16.8404	−	3.24573i	−1.00106	−	0.192938i	−0.663348	+	0.748311i	$0.730865\pi$
$284$	13.4279	−	5.37571i	0.796797	−	0.318989i
$285$	−1.44031	+	5.93704i	−0.0853166	+	0.351680i
$286$	3.02920	+	3.49588i	0.179120	+	0.206716i
$287$	9.75721	+	15.4757i	0.575950	+	0.913499i
$288$	0.841254	−	0.540641i	0.0495713	−	0.0318576i
$289$	−16.0997	+	3.10296i	−0.947040	+	0.182527i
$290$	−1.83145	−	1.74629i	−0.107547	−	0.102546i
$291$	−8.32239	+	3.33178i	−0.487867	+	0.195313i
$292$	−4.85423	−	14.0254i	−0.284072	−	0.820772i
$293$	3.47589	−	7.61114i	0.203064	−	0.444648i	−0.780513	−	0.625140i	$-0.785042\pi$
$293$	3.47589	−	7.61114i	0.203064	−	0.444648i	0.983576	+	0.180492i	$0.0577691\pi$
$294$	−6.68128	−	2.08819i	−0.389660	−	0.121786i
$295$	−2.80307	−	6.13787i	−0.163201	−	0.357361i
$296$	−1.12024	−	0.448477i	−0.0651128	−	0.0260672i
$297$	−0.177614	+	3.72857i	−0.0103062	+	0.216354i
$298$	−1.67617	−	2.90321i	−0.0970979	−	0.168178i
$299$	−1.74457	+	5.68120i	−0.100891	+	0.328552i
$300$	4.49513			0.259527
$301$	5.88156	−	8.97989i	0.339008	−	0.517592i
$302$	1.60835	+	11.1863i	0.0925499	+	0.643699i
$303$	−6.52564	−	0.623123i	−0.374888	−	0.0357975i
$304$	−2.02706	−	8.35567i	−0.116260	−	0.479230i
$305$	−10.3461	+	0.987933i	−0.592416	+	0.0565689i
$306$	0.254195	+	0.734447i	0.0145313	+	0.0419856i
$307$	−0.0755016	+	0.525125i	−0.00430910	+	0.0299705i	−0.991863	−	0.127313i	$-0.959365\pi$
$307$	−0.0755016	+	0.525125i	−0.00430910	+	0.0299705i	0.987553	+	0.157284i	$0.0502737\pi$
$308$	−9.57714	−	2.41142i	−0.545708	−	0.137404i
$309$	−1.41557	−	1.63365i	−0.0805287	−	0.0929351i
$310$	0.190188	+	3.99253i	0.0108019	+	0.226761i
$311$	−25.2004	−	12.9917i	−1.42899	−	0.736693i	−0.441927	−	0.897051i	$-0.645705\pi$
$311$	−25.2004	−	12.9917i	−1.42899	−	0.736693i	−0.987059	+	0.160358i	$0.948735\pi$
$312$	−0.405304	+	1.17105i	−0.0229458	+	0.0662977i
$313$	0.907074	−	3.73901i	0.0512708	−	0.211341i	−0.940414	−	0.340032i	$-0.889562\pi$
$313$	0.907074	−	3.73901i	0.0512708	−	0.211341i	0.991685	+	0.128690i	$0.0410773\pi$
$314$	−2.04312	+	14.2102i	−0.115300	+	0.801929i
$315$	−0.371753	+	1.84279i	−0.0209459	+	0.103829i
$316$	5.38394	−	11.7892i	0.302870	−	0.663193i
$317$	10.0756	−	9.60704i	0.565901	−	0.539585i	−0.352204	−	0.935923i	$-0.614568\pi$
$317$	10.0756	−	9.60704i	0.565901	−	0.539585i	0.918105	+	0.396338i	$0.129719\pi$
$318$	3.60002	−	5.05553i	0.201879	−	0.283500i
$319$	−10.4500	+	8.21795i	−0.585086	+	0.460117i
$320$	0.631553	−	0.325588i	0.0353049	−	0.0182009i
$321$	2.50360			0.139737
$322$	−3.89732	−	12.0752i	−0.217189	−	0.672926i
$323$	6.68232			0.371814
$324$	−0.888835	+	0.458227i	−0.0493797	+	0.0254570i
$325$	−4.37863	+	3.44339i	−0.242882	+	0.191005i
$326$	7.77644	−	10.9205i	0.430697	−	0.604830i
$327$	−3.03079	+	2.88985i	−0.167603	+	0.159809i
$328$	−2.87250	+	6.28990i	−0.158607	+	0.347302i
$329$	31.7740	−	10.6898i	1.75176	−	0.589346i
$330$	−0.377463	+	2.62531i	−0.0207786	+	0.144519i
$331$	−2.95042	+	12.1618i	−0.162170	+	0.668473i	0.831441	+	0.555613i	$0.187516\pi$
$331$	−2.95042	+	12.1618i	−0.162170	+	0.668473i	−0.993611	+	0.112860i	$0.963999\pi$
$332$	−3.61503	+	10.4449i	−0.198401	+	0.573241i
$333$	1.07254	+	0.552932i	0.0587748	+	0.0303005i
$334$	−0.970327	−	20.3697i	−0.0530939	−	1.11458i
$335$	−2.70321	−	3.11968i	−0.147692	−	0.170446i
$336$	−0.723376	−	2.54494i	−0.0394634	−	0.138838i
$337$	−2.24644	+	15.6243i	−0.122371	+	0.851111i	0.832486	+	0.554046i	$0.186917\pi$
$337$	−2.24644	+	15.6243i	−0.122371	+	0.851111i	−0.954857	+	0.297065i	$0.903992\pi$
$338$	3.74963	+	10.8338i	0.203953	+	0.589283i
$339$	3.96305	−	0.378426i	0.215243	−	0.0205533i
$340$	0.130192	+	0.536660i	0.00706067	+	0.0291045i
$341$	20.9033	+	1.99603i	1.13198	+	0.108091i
$342$	1.22363	+	8.51051i	0.0661662	+	0.460196i
$343$	−10.4143	+	15.3148i	−0.562318	+	0.826921i
$344$	4.05729			0.218754
$345$	−3.11692	+	1.37723i	−0.167809	+	0.0741476i
$346$	2.76031	+	4.78099i	0.148395	+	0.257028i
$347$	−1.14236	+	23.9811i	−0.0613252	+	1.28737i	0.733145	+	0.680072i	$0.238052\pi$
$347$	−1.14236	+	23.9811i	−0.0613252	+	1.28737i	−0.794471	+	0.607303i	$0.792252\pi$
$348$	−3.30635	−	1.32366i	−0.177239	−	0.0709557i
$349$	0.624835	+	1.36820i	0.0334466	+	0.0732379i	0.925618	−	0.378459i	$-0.123546\pi$
$349$	0.624835	+	1.36820i	0.0334466	+	0.0732379i	−0.892171	+	0.451697i	$0.850819\pi$
$350$	3.44937	−	11.3818i	0.184377	−	0.608383i
$351$	0.514785	−	1.12722i	0.0274772	−	0.0601666i
$352$	−1.22088	−	3.52750i	−0.0650731	−	0.188016i
$353$	14.2293	−	5.69655i	0.757349	−	0.303197i	0.0393353	−	0.999226i	$-0.487476\pi$
$353$	14.2293	−	5.69655i	0.757349	−	0.303197i	0.718013	+	0.696029i	$0.245052\pi$
$354$	−6.87294	−	6.55333i	−0.365293	−	0.348306i
$355$	−10.0915	+	1.94498i	−0.535601	+	0.103229i
$356$	−4.72340	+	3.03554i	−0.250340	+	0.160884i
$357$	2.05470	−	0.0800449i	0.108746	−	0.00423642i
$358$	14.7457	+	17.0174i	0.779334	+	0.899400i
$359$	−5.24839	+	21.6341i	−0.276999	+	1.14181i	0.647940	+	0.761691i	$0.275631\pi$
$359$	−5.24839	+	21.6341i	−0.276999	+	1.14181i	−0.924939	+	0.380115i	$0.875884\pi$
$360$	−0.659643	+	0.264081i	−0.0347662	+	0.0139183i
$361$	53.9335	+	10.3948i	2.83861	+	0.547097i
$362$	−5.25063	−	7.37347i	−0.275967	−	0.387541i
$363$	2.81497	+	0.826549i	0.147747	+	0.0433826i
$364$	2.65412	+	1.92486i	0.139114	+	0.100890i
$365$	1.50079	+	10.4382i	0.0785551	+	0.546363i
$366$	−13.0011	+	6.70254i	−0.679579	+	0.350347i
$367$	6.70633	+	11.6157i	0.350068	+	0.606335i	0.986261	−	0.165195i	$-0.0528253\pi$
$367$	6.70633	+	11.6157i	0.350068	+	0.606335i	−0.636193	+	0.771530i	$0.719492\pi$
$368$	3.01087	−	3.73292i	0.156952	−	0.194592i
$369$	3.45739	−	5.98837i	0.179984	−	0.311742i
$370$	0.721286	+	0.463542i	0.0374979	+	0.0240984i
$371$	−10.0382	−	12.9948i	−0.521159	−	0.674654i
$372$	2.33687	+	5.11702i	0.121161	+	0.265305i
$373$	3.91989	−	3.73761i	0.202964	−	0.193526i	−0.581779	−	0.813347i	$-0.697643\pi$
$373$	3.91989	−	3.73761i	0.202964	−	0.193526i	0.784743	+	0.619821i	$0.212795\pi$
$374$	2.88797	−	0.275768i	0.149333	−	0.0142596i
$375$	−6.62475	−	1.27682i	−0.342101	−	0.0659345i
$376$	9.95997	+	7.83261i	0.513646	+	0.403936i
$377$	4.23461	−	1.24339i	0.218094	−	0.0640381i
$378$	0.478188	+	2.60218i	0.0245954	+	0.133842i
$379$	−6.57223	+	4.22372i	−0.337593	+	0.216958i	−0.698442	−	0.715666i	$-0.746123\pi$
$379$	−6.57223	+	4.22372i	−0.337593	+	0.216958i	0.360849	+	0.932624i	$0.382487\pi$
$380$	0.290690	+	6.10233i	0.0149121	+	0.313043i
$381$	1.89823	−	5.48458i	0.0972494	−	0.280984i
$382$	7.39361	+	7.04979i	0.378290	+	0.360699i
$383$	−7.76686	−	6.10793i	−0.396868	−	0.312101i	0.399704	−	0.916644i	$-0.369113\pi$
$383$	−7.76686	−	6.10793i	−0.396868	−	0.312101i	−0.796572	+	0.604544i	$0.793355\pi$
$384$	0.654861	−	0.755750i	0.0334182	−	0.0385667i
$385$	6.35771	+	2.97029i	0.324019	+	0.151380i
$386$	24.7640	+	7.27136i	1.26045	+	0.370102i
$387$	−4.03892	−	0.385670i	−0.205310	−	0.0196047i
$388$	−7.04660	+	5.54151i	−0.357737	+	0.281328i
$389$	1.42843	−	29.9865i	0.0724245	−	1.52038i	−0.611745	−	0.791055i	$-0.709532\pi$
$389$	1.42843	−	29.9865i	0.0724245	−	1.52038i	0.684170	−	0.729323i	$-0.260165\pi$
$390$	0.440253	−	0.762540i	0.0222931	−	0.0386127i
$391$	2.26773	+	2.95805i	0.114684	+	0.149595i
$392$	−6.99895	−	0.121270i	−0.353500	−	0.00612507i
$393$	4.78858	+	3.07743i	0.241552	+	0.155236i
$394$	10.0742	+	4.03312i	0.507533	+	0.203186i
$395$	−5.34167	+	7.50133i	−0.268769	+	0.377433i
$396$	0.880041	+	3.62758i	0.0442237	+	0.182293i
$397$	−13.4660	−	18.9103i	−0.675838	−	0.949082i	−0.999995	−	0.00307855i	$-0.999020\pi$
$397$	−13.4660	−	18.9103i	−0.675838	−	0.949082i	0.324157	−	0.946003i	$-0.394919\pi$
$398$	−3.84088	+	4.43262i	−0.192526	+	0.222187i
$399$	22.4878	+	3.43234i	1.12580	+	0.171832i
$400$	4.31305	−	1.26643i	0.215652	−	0.0633213i
$401$	11.4294	−	2.20284i	0.570757	−	0.110004i	0.104296	−	0.994546i	$-0.466741\pi$
$401$	11.4294	−	2.20284i	0.570757	−	0.110004i	0.466461	+	0.884542i	$0.345529\pi$
$402$	−5.16374	−	2.66209i	−0.257544	−	0.132773i
$403$	−6.19607	−	3.19430i	−0.308648	−	0.159119i
$404$	−6.43686	+	1.24060i	−0.320246	+	0.0617223i
$405$	0.681758	−	0.200182i	0.0338769	−	0.00994714i
$406$	−5.88870	+	7.35604i	−0.292251	+	0.365074i
$407$	2.94969	−	3.40412i	0.146210	−	0.168736i
$408$	0.450816	+	0.633082i	0.0223187	+	0.0313422i
$409$	2.26633	+	9.34193i	0.112063	+	0.461929i	0.999998	+	0.00196044i	$0.000624028\pi$
$409$	2.26633	+	9.34193i	0.112063	+	0.461929i	−0.887935	+	0.459968i	$0.847861\pi$
$410$	2.84995	−	4.00220i	0.140749	−	0.197654i
$411$	18.6491	+	7.46597i	0.919892	+	0.368269i
$412$	−1.81848	−	1.16866i	−0.0895900	−	0.0575760i
$413$	−21.8672	+	12.3737i	−1.07602	+	0.608871i
$414$	−3.35207	+	3.42981i	−0.164745	+	0.168566i
$415$	3.92674	−	6.80132i	0.192756	−	0.333864i
$416$	−0.0589638	+	1.23780i	−0.00289094	+	0.0606882i
$417$	−13.6150	+	10.7070i	−0.666730	+	0.524322i
$418$	31.9494	+	3.05080i	1.56270	+	0.149219i
$419$	1.32280	+	0.388409i	0.0646229	+	0.0189750i	0.313884	−	0.949461i	$-0.398370\pi$
$419$	1.32280	+	0.388409i	0.0646229	+	0.0189750i	−0.249261	+	0.968436i	$0.580188\pi$
$420$	0.162479	+	1.87288i	0.00792818	+	0.0913871i
$421$	16.7072	−	19.2811i	0.814258	−	0.939703i	−0.184814	−	0.982773i	$-0.559168\pi$
$421$	16.7072	−	19.2811i	0.814258	−	0.939703i	0.999072	+	0.0430700i	$0.0137139\pi$
$422$	5.14346	+	4.04487i	0.250380	+	0.196901i
$423$	−9.17034	−	8.74390i	−0.445877	−	0.425143i
$424$	2.02989	−	5.86499i	0.0985803	−	0.284829i
$425$	0.166231	+	3.48963i	0.00806340	+	0.169272i
$426$	−12.1678	+	7.81980i	−0.589534	+	0.378871i
$427$	6.99452	+	38.0624i	0.338489	+	1.84197i
$428$	2.40218	−	0.705345i	0.116114	−	0.0340941i
$429$	−3.63605	−	2.85942i	−0.175550	−	0.138054i
$430$	−2.83077	−	0.545587i	−0.136512	−	0.0263105i
$431$	25.8341	−	2.46686i	1.24439	−	0.118824i	0.547991	−	0.836484i	$-0.315393\pi$
$431$	25.8341	−	2.46686i	1.24439	−	0.118824i	0.696394	+	0.717660i	$0.254787\pi$
$432$	−0.723734	+	0.690079i	−0.0348207	+	0.0332014i
$433$	−2.97997	−	6.52522i	−0.143208	−	0.313582i	0.824413	−	0.565988i	$-0.191505\pi$
$433$	−2.97997	−	6.52522i	−0.143208	−	0.313582i	−0.967621	+	0.252406i	$0.918778\pi$
$434$	14.7497	−	1.99043i	0.708006	−	0.0955436i
$435$	2.12885	+	1.36813i	0.102070	+	0.0655966i
$436$	−2.09386	+	3.62667i	−0.100278	+	0.173686i
$437$	18.4412	+	36.8812i	0.882163	+	1.76427i
$438$	7.42082	+	12.8532i	0.354581	+	0.614151i
$439$	−19.4916	+	10.0486i	−0.930285	+	0.479595i	−0.855615	−	0.517613i	$-0.826821\pi$
$439$	−19.4916	+	10.0486i	−0.930285	+	0.479595i	−0.0746698	+	0.997208i	$0.523790\pi$
$440$	0.377463	+	2.62531i	0.0179948	+	0.125157i
$441$	6.95573	+	0.786014i	0.331225	+	0.0374292i
$442$	−0.924089	−	0.271337i	−0.0439544	−	0.0129062i
$443$	2.08601	+	2.92939i	0.0991093	+	0.139180i	0.861153	−	0.508347i	$-0.169743\pi$
$443$	2.08601	+	2.92939i	0.0991093	+	0.139180i	−0.762043	+	0.647526i	$0.775804\pi$
$444$	1.18487	+	0.228366i	0.0562316	+	0.0108378i
$445$	3.70371	−	1.48274i	0.175573	−	0.0702886i
$446$	5.33903	−	22.0078i	0.252810	−	1.04210i
$447$	2.19531	+	2.53353i	0.103835	+	0.119832i
$448$	−1.41107	−	2.23805i	−0.0666666	−	0.105738i
$449$	18.5742	−	11.9369i	0.876570	−	0.563337i	−0.0231859	−	0.999731i	$-0.507381\pi$
$449$	18.5742	−	11.9369i	0.876570	−	0.563337i	0.899756	+	0.436394i	$0.143745\pi$
$450$	−4.41390	+	0.850709i	−0.208073	+	0.0401028i
$451$	−18.6807	−	17.8120i	−0.879638	−	0.838733i
$452$	3.69591	−	1.47962i	0.173841	−	0.0695953i
$453$	−3.69630	−	10.6798i	−0.173667	−	0.501779i
$454$	2.92662	−	6.40840i	0.137353	−	0.300761i
$455$	−1.59294	−	1.69987i	−0.0746783	−	0.0796913i
$456$	3.57175	+	7.82104i	0.167263	+	0.366254i
$457$	−26.4446	−	10.5868i	−1.23703	−	0.495230i	−0.341349	−	0.939937i	$-0.610884\pi$
$457$	−26.4446	−	10.5868i	−1.23703	−	0.495230i	−0.895676	+	0.444706i	$0.853308\pi$
$458$	−1.13912	+	23.9132i	−0.0532278	+	1.11739i
$459$	−0.388596	−	0.673068i	−0.0181381	−	0.0314161i
$460$	−2.60265	+	2.19958i	−0.121349	+	0.102556i
$461$	35.6167			1.65883			0.829416	−	0.558631i	$-0.188673\pi$
$461$	35.6167			1.65883			0.829416	+	0.558631i	$0.188673\pi$
$462$	9.86044	+	0.555359i	0.458749	+	0.0258376i
$463$	1.02660	+	7.14013i	0.0477099	+	0.331830i	0.999672	+	0.0256137i	$0.00815398\pi$
$463$	1.02660	+	7.14013i	0.0477099	+	0.331830i	−0.951962	+	0.306216i	$0.900937\pi$
$464$	−3.54534	−	0.338539i	−0.164588	−	0.0157163i
$465$	−0.942342	−	3.88439i	−0.0437001	−	0.180134i
$466$	−5.19851	+	0.496397i	−0.240816	+	0.0229952i
$467$	5.12539	+	14.8088i	0.237175	+	0.685271i	0.999284	+	0.0378234i	$0.0120424\pi$
$467$	5.12539	+	14.8088i	0.237175	+	0.685271i	−0.762110	+	0.647448i	$0.775836\pi$
$468$	0.176357	−	1.22659i	0.00815212	−	0.0566993i
$469$	−10.7029	+	11.0320i	−0.494215	+	0.509408i
$470$	−5.89582	−	6.80413i	−0.271954	−	0.313851i
$471$	−0.683103	−	14.3401i	−0.0314757	−	0.660757i
$472$	−8.44082	−	4.35155i	−0.388520	−	0.200296i
$473$	−4.95346	+	14.3121i	−0.227761	+	0.658071i
$474$	−3.05553	+	12.5951i	−0.140345	+	0.578510i
$475$	−5.50037	+	38.2559i	−0.252374	+	1.75530i
$476$	1.94892	−	0.655678i	0.0893285	−	0.0300530i
$477$	−2.57820	+	5.64548i	−0.118048	+	0.258489i
$478$	−2.71390	+	2.58770i	−0.124131	+	0.118359i
$479$	1.15125	−	1.61671i	0.0526022	−	0.0738694i	−0.787437	−	0.616395i	$-0.788592\pi$
$479$	1.15125	−	1.61671i	0.0526022	−	0.0738694i	0.840039	+	0.542526i	$0.182532\pi$
$480$	−0.558522	+	0.439227i	−0.0254929	+	0.0200479i
$481$	−1.32910	+	0.685197i	−0.0606016	+	0.0312423i
$482$	4.30659			0.196160
$483$	6.11214	+	11.1194i	0.278112	+	0.505952i
$484$	2.93381			0.133355
$485$	5.66159	−	2.91875i	0.257079	−	0.132534i
$486$	0.786053	−	0.618159i	0.0356561	−	0.0280403i
$487$	−10.5885	+	14.8694i	−0.479809	+	0.673797i	−0.981547	−	0.191223i	$-0.938755\pi$
$487$	−10.5885	+	14.8694i	−0.479809	+	0.673797i	0.501738	+	0.865020i	$0.332694\pi$
$488$	−10.5861	+	10.0939i	−0.479212	+	0.456928i
$489$	−5.56920	+	12.1948i	−0.251848	+	0.551470i
$490$	4.86686	+	1.02576i	0.219862	+	0.0463393i
$491$	−0.346328	+	2.40876i	−0.0156296	+	0.108706i	−0.996143	−	0.0877472i	$-0.972033\pi$
$491$	−0.346328	+	2.40876i	−0.0156296	+	0.108706i	0.980513	+	0.196453i	$0.0629423\pi$
$492$	1.63022	−	6.71986i	0.0734960	−	0.302955i
$493$	0.905305	−	2.61571i	0.0407729	−	0.117806i
$494$	−9.47030	−	4.88228i	−0.426089	−	0.219664i
$495$	−0.126202	−	2.64930i	−0.00567235	−	0.119077i
$496$	3.68384	+	4.25138i	0.165409	+	0.190892i
$497$	10.4629	+	36.8099i	0.469324	+	1.65115i
$498$	1.57298	−	10.9403i	0.0704871	−	0.490248i
$499$	3.92756	+	11.3479i	0.175822	+	0.508004i	0.998136	−	0.0610300i	$-0.0194385\pi$
$499$	3.92756	+	11.3479i	0.175822	+	0.508004i	−0.822314	+	0.569034i	$0.807317\pi$
$500$	−6.71613	+	0.641312i	−0.300354	+	0.0286804i
$501$	4.80778	+	19.8179i	0.214796	+	0.885400i
$502$	13.7022	+	1.30840i	0.611558	+	0.0583967i
$503$	−5.53844	−	38.5207i	−0.246947	−	1.71755i	−0.615663	−	0.788010i	$-0.711112\pi$
$503$	−5.53844	−	38.5207i	−0.246947	−	1.71755i	0.368716	−	0.929542i	$-0.379798\pi$
$504$	1.19194	+	2.36205i	0.0530931	+	0.105214i
$505$	4.65782			0.207270
$506$	9.49195	+	15.1783i	0.421969	+	0.674757i
$507$	−5.73218	−	9.92843i	−0.254575	−	0.440937i
$508$	0.276155	−	5.79721i	0.0122524	−	0.257210i
$509$	−5.52147	−	2.21046i	−0.244735	−	0.0979771i	0.246052	−	0.969257i	$-0.420867\pi$
$509$	−5.52147	−	2.21046i	−0.244735	−	0.0979771i	−0.490787	+	0.871279i	$0.663291\pi$
$510$	−0.229403	−	0.502323i	−0.0101581	−	0.0222432i
$511$	38.2392	−	8.92670i	1.69160	−	0.394894i
$512$	0.415415	−	0.909632i	0.0183589	−	0.0402004i
$513$	−2.81214	−	8.12515i	−0.124159	−	0.358734i
$514$	25.8592	−	10.3525i	1.14060	−	0.456628i
$515$	1.11160	+	1.05991i	0.0489830	+	0.0467052i
$516$	−3.98397	+	0.767847i	−0.175385	+	0.0338026i
$517$	−39.7895	+	25.5711i	−1.74994	+	1.12462i
$518$	1.48745	−	2.82489i	0.0653547	−	0.124119i
$519$	−3.61523	−	4.17220i	−0.158691	−	0.183139i
$520$	0.207587	−	0.855686i	0.00910330	−	0.0375243i
$521$	22.8382	−	9.14302i	1.00056	−	0.400563i	0.187197	−	0.982322i	$-0.440060\pi$
$521$	22.8382	−	9.14302i	1.00056	−	0.400563i	0.813361	+	0.581760i	$0.197636\pi$
$522$	3.49710	+	0.674011i	0.153064	+	0.0295007i
$523$	−19.3902	−	27.2298i	−0.847876	−	1.19068i	−0.979912	−	0.199430i	$-0.936091\pi$
$523$	−19.3902	−	27.2298i	−0.847876	−	1.19068i	0.132036	−	0.991245i	$-0.457849\pi$
$524$	5.46162	+	1.60368i	0.238592	+	0.0700570i
$525$	−1.23302	+	11.8289i	−0.0538132	+	0.516256i
$526$	−0.218442	−	1.51930i	−0.00952452	−	0.0662445i
$527$	−3.88599	+	2.00337i	−0.169276	+	0.0872680i
$528$	1.86640	+	3.23270i	0.0812247	+	0.140685i
$529$	−10.0678	+	20.6794i	−0.437732	+	0.899105i
$530$	−2.20492	+	3.81904i	−0.0957758	+	0.165889i
$531$	7.98896	+	5.13419i	0.346691	+	0.222805i
$532$	22.5439	−	3.04224i	0.977402	−	0.131898i
$533$	3.55962	+	7.79448i	0.154184	+	0.337617i
$534$	4.06356	−	3.87460i	0.175847	−	0.167670i
$535$	−1.77085	+	0.169096i	−0.0765606	+	0.00731065i
$536$	−5.70457	−	1.09947i	−0.246400	−	0.0474897i
$537$	−17.6998	−	13.9193i	−0.763802	−	0.600661i
$538$	20.9570	−	6.15352i	0.903519	−	0.265297i
$539$	8.97266	−	24.5407i	0.386480	−	1.05704i
$540$	0.597745	−	0.384147i	0.0257228	−	0.0165311i
$541$	−2.05689	−	43.1794i	−0.0884326	−	1.85643i	−0.413208	−	0.910637i	$-0.635592\pi$
$541$	−2.05689	−	43.1794i	−0.0884326	−	1.85643i	0.324775	−	0.945791i	$-0.394711\pi$
$542$	6.99164	−	20.2010i	0.300317	−	0.867708i
$543$	6.55118	+	6.24654i	0.281138	+	0.268065i
$544$	0.610914	+	0.480428i	0.0261927	+	0.0205982i
$545$	1.94856	−	2.24876i	0.0834673	−	0.0963264i
$546$	−2.97044	−	1.38778i	−0.127123	−	0.0593913i
$547$	23.0566	+	6.77002i	0.985828	+	0.289465i	0.734628	−	0.678470i	$-0.237357\pi$
$547$	23.0566	+	6.77002i	0.985828	+	0.289465i	0.251200	+	0.967935i	$0.419175\pi$
$548$	19.9971	+	1.90949i	0.854233	+	0.0815694i
$549$	11.4977	−	9.04189i	0.490710	−	0.385898i
$550$	−0.798398	+	16.7604i	−0.0340438	+	0.714667i
$551$	15.3108	−	26.5191i	0.652261	−	1.12975i
$552$	−2.25000	+	4.23527i	−0.0957664	+	0.180265i
$553$	29.5463	+	17.4016i	1.25644	+	0.739990i
$554$	23.5487	+	15.1339i	1.00049	+	0.642976i
$555$	−0.795977	−	0.318661i	−0.0337874	−	0.0135264i
$556$	−10.0470	+	14.1090i	−0.426088	+	0.598357i
$557$	4.50603	+	18.5741i	0.190927	+	0.787011i	0.984042	+	0.177939i	$0.0569428\pi$
$557$	4.50603	+	18.5741i	0.190927	+	0.787011i	−0.793115	+	0.609072i	$0.791542\pi$
$558$	−3.26304	−	4.58230i	−0.138135	−	0.193984i
$559$	3.29252	−	3.79977i	0.139259	−	0.160713i
$560$	0.683549	+	1.75124i	0.0288852	+	0.0740033i
$561$	−2.78359	+	0.817336i	−0.117523	+	0.0345079i
$562$	−29.4668	+	5.67926i	−1.24298	+	0.239565i
$563$	−18.6303	−	9.60460i	−0.785174	−	0.404786i	0.0185195	−	0.999828i	$-0.494105\pi$
$563$	−18.6303	−	9.60460i	−0.785174	−	0.404786i	−0.803694	+	0.595043i	$0.797135\pi$
$564$	−11.2623	−	5.80613i	−0.474229	−	0.244482i
$565$	−2.77760	+	0.535338i	−0.116854	+	0.0225218i
$566$	16.4556	−	4.83181i	0.691682	−	0.203096i
$567$	−0.962012	−	2.46466i	−0.0404007	−	0.103506i
$568$	−9.47187	+	10.9311i	−0.397431	+	0.458660i
$569$	17.0152	+	23.8945i	0.713315	+	1.00171i	0.999058	+	0.0434047i	$0.0138205\pi$
$569$	17.0152	+	23.8945i	0.713315	+	1.00171i	−0.285742	+	0.958306i	$0.592240\pi$
$570$	−1.44031	−	5.93704i	−0.0603279	−	0.248675i
$571$	−17.1871	+	24.1359i	−0.719258	+	1.01006i	0.279495	+	0.960147i	$0.409833\pi$
$571$	−17.1871	+	24.1359i	−0.719258	+	1.01006i	−0.998754	+	0.0499100i	$0.984107\pi$
$572$	−4.29436	−	1.71920i	−0.179556	−	0.0718835i
$573$	−8.59418	−	5.52314i	−0.359027	−	0.230733i
$574$	−15.7639	−	9.28429i	−0.657973	−	0.387519i
$575$	−18.8013	+	10.5478i	−0.784066	+	0.439873i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	0.855037	−	17.9494i	0.0355956	−	0.747245i	−0.908562	−	0.417750i	$-0.862819\pi$
$577$	0.855037	−	17.9494i	0.0355956	−	0.747245i	0.944158	−	0.329494i	$-0.106878\pi$
$578$	12.8881	−	10.1353i	0.536074	−	0.421574i
$579$	−25.6926	−	2.45334i	−1.06775	−	0.101957i
$580$	2.42806	+	0.712942i	0.100820	+	0.0296033i
$581$	−26.4942	−	12.3780i	−1.09916	−	0.513525i
$582$	5.87053	−	6.77495i	0.243341	−	0.280831i
$583$	18.2105	+	14.3209i	0.754201	+	0.593111i
$584$	10.7414	+	10.2419i	0.444482	+	0.423813i
$585$	−0.287985	+	0.832079i	−0.0119067	+	0.0344022i
$586$	0.398131	+	8.35780i	0.0164466	+	0.345257i
$587$	−13.6712	+	8.78596i	−0.564272	+	0.362635i	−0.791465	−	0.611214i	$-0.790681\pi$
$587$	−13.6712	+	8.78596i	−0.564272	+	0.362635i	0.227194	+	0.973850i	$0.427045\pi$
$588$	6.89542	−	1.20548i	0.284362	−	0.0497132i
$589$	−46.4080	+	13.6266i	−1.91221	+	0.561475i
$590$	5.30401	+	4.17112i	0.218363	+	0.171722i
$591$	−10.6555	−	2.05367i	−0.438307	−	0.0844768i
$592$	1.20122	−	0.114702i	0.0493697	−	0.00471423i
$593$	10.5319	−	10.0421i	0.432493	−	0.412381i	−0.442308	−	0.896863i	$-0.645840\pi$
$593$	10.5319	−	10.0421i	0.432493	−	0.412381i	0.874801	+	0.484482i	$0.160992\pi$
$594$	−1.55066	−	3.39548i	−0.0636244	−	0.139318i
$595$	−1.44793	+	0.195394i	−0.0593593	+	0.00801039i
$596$	2.82017	+	1.81241i	0.115519	+	0.0742392i
$597$	2.93260	−	5.07941i	0.120023	−	0.207886i
$598$	−1.05264	−	5.84906i	−0.0430457	−	0.239186i
$599$	3.84356	+	6.65725i	0.157044	+	0.272008i	0.933801	−	0.357792i	$-0.116470\pi$
$599$	3.84356	+	6.65725i	0.157044	+	0.272008i	−0.776758	+	0.629800i	$0.783137\pi$
$600$	−3.99543	+	2.05979i	−0.163113	+	0.0840905i
$601$	−0.654052	−	4.54903i	−0.0266793	−	0.185559i	0.972124	−	0.234468i	$-0.0753347\pi$
$601$	−0.654052	−	4.54903i	−0.0266793	−	0.185559i	−0.998803	+	0.0489089i	$0.984426\pi$
$602$	−1.11292	+	10.6767i	−0.0453591	+	0.435151i
$603$	5.57423	+	1.63674i	0.227000	+	0.0666532i
$604$	−6.55541	−	9.20578i	−0.266736	−	0.374578i
$605$	−2.04692	−	0.394511i	−0.0832190	−	0.0160391i
$606$	6.08575	−	2.43637i	0.247217	−	0.0989706i
$607$	−1.24472	+	5.13081i	−0.0505217	+	0.208253i	−0.991478	−	0.130275i	$-0.958414\pi$
$607$	−1.24472	+	5.13081i	−0.0505217	+	0.208253i	0.940956	+	0.338528i	$0.109929\pi$
$608$	5.63051	+	6.49796i	0.228347	+	0.263527i
$609$	4.39014	−	8.33755i	0.177897	−	0.337855i
$610$	8.74329	−	5.61897i	0.354005	−	0.227505i
$611$	15.4181	−	2.97159i	0.623748	−	0.120218i
$612$	−0.562481	−	0.536324i	−0.0227369	−	0.0216796i
$613$	43.4699	−	17.4027i	1.75573	−	0.702890i	0.756956	−	0.653466i	$-0.226686\pi$
$613$	43.4699	−	17.4027i	1.75573	−	0.702890i	0.998778	−	0.0494234i	$-0.0157384\pi$
$614$	−0.173518	−	0.501346i	−0.00700260	−	0.0202327i
$615$	−2.04103	+	4.46923i	−0.0823022	+	0.180217i
$616$	9.61748	−	2.24514i	0.387499	−	0.0904594i
$617$	18.1089	+	39.6529i	0.729035	+	1.59636i	0.800793	+	0.598942i	$0.204412\pi$
$617$	18.1089	+	39.6529i	0.729035	+	1.59636i	−0.0717576	+	0.997422i	$0.522861\pi$
$618$	2.00679	+	0.803396i	0.0807248	+	0.0323173i
$619$	1.48102	−	31.0905i	0.0595273	−	1.24963i	−0.749557	−	0.661940i	$-0.769733\pi$
$619$	1.48102	−	31.0905i	0.0595273	−	1.24963i	0.809084	−	0.587693i	$-0.199964\pi$
$620$	−1.99853	−	3.46155i	−0.0802629	−	0.139019i
$621$	2.64240	−	4.00221i	0.106036	−	0.160603i
$622$	28.3522			1.13682
$623$	−6.69239	−	13.2622i	−0.268125	−	0.531341i
$624$	−0.176357	−	1.22659i	−0.00705994	−	0.0491030i
$625$	−17.6018	−	1.68077i	−0.704072	−	0.0672308i
$626$	0.907074	+	3.73901i	0.0362540	+	0.149441i
$627$	−31.9494	+	3.05080i	−1.27594	+	0.121837i
$628$	−4.69550	−	13.5668i	−0.187371	−	0.541373i
$629$	−0.133466	+	0.928276i	−0.00532164	+	0.0370128i
$630$	−0.513988	−	1.80828i	−0.0204778	−	0.0720437i
$631$	−25.2601	−	29.1517i	−1.00559	−	1.16051i	−0.987006	−	0.160684i	$-0.948630\pi$
$631$	−25.2601	−	29.1517i	−1.00559	−	1.16051i	−0.0185828	−	0.999827i	$-0.505915\pi$
$632$	0.616680	+	12.9457i	0.0245302	+	0.514953i
$633$	−5.81601	−	2.99836i	−0.231166	−	0.119174i
$634$	−4.55333	+	13.1560i	−0.180836	+	0.522490i
$635$	−0.972228	+	4.00758i	−0.0385817	+	0.159036i
$636$	−0.883253	+	6.14316i	−0.0350233	+	0.243592i
$637$	−5.79327	+	6.45631i	−0.229538	+	0.255808i
$638$	5.52262	−	12.0929i	0.218643	−	0.478761i
$639$	10.4681	−	9.98127i	0.414110	−	0.394853i
$640$	−0.412154	+	0.578789i	−0.0162918	+	0.0228786i
$641$	−4.33890	+	3.41215i	−0.171376	+	0.134772i	−0.700163	−	0.713983i	$-0.746889\pi$
$641$	−4.33890	+	3.41215i	−0.171376	+	0.134772i	0.528787	+	0.848755i	$0.322647\pi$
$642$	−2.22529	+	1.14721i	−0.0878250	+	0.0452769i
$643$	17.9810			0.709100			0.354550	−	0.935037i	$-0.384634\pi$
$643$	17.9810			0.709100			0.354550	+	0.935037i	$0.384634\pi$
$644$	8.99726	+	8.94703i	0.354542	+	0.352562i
$645$	2.88287			0.113513
$646$	−5.93949	+	3.06202i	−0.233686	+	0.120473i
$647$	−25.8127	+	20.2993i	−1.01480	+	0.798049i	−0.979524	−	0.201328i	$-0.935474\pi$
$647$	−25.8127	+	20.2993i	−1.01480	+	0.798049i	−0.0352783	+	0.999378i	$0.511232\pi$
$648$	0.580057	−	0.814576i	0.0227868	−	0.0319996i
$649$	25.6553	−	24.4623i	1.00706	−	0.960229i
$650$	2.31403	−	5.06701i	0.0907635	−	0.198744i
$651$	−14.1064	+	4.74585i	−0.552874	+	0.186004i
$652$	−1.90792	+	13.2699i	−0.0747200	+	0.519689i
$653$	−2.43638	+	10.0429i	−0.0953430	+	0.393009i	−0.999409	−	0.0343844i	$-0.989053\pi$
$653$	−2.43638	+	10.0429i	−0.0953430	+	0.393009i	0.904066	+	0.427394i	$0.140568\pi$
$654$	1.36967	−	3.95739i	0.0535582	−	0.154746i
$655$	−3.59493	−	1.85331i	−0.140465	−	0.0724150i
$656$	−0.329018	−	6.90695i	−0.0128460	−	0.269671i
$657$	−9.71921	−	11.2166i	−0.379182	−	0.437600i
$658$	−23.3435	+	24.0611i	−0.910024	+	0.938000i
$659$	−2.01179	+	13.9923i	−0.0783681	+	0.545062i	0.912380	+	0.409345i	$0.134243\pi$
$659$	−2.01179	+	13.9923i	−0.0783681	+	0.545062i	−0.990748	+	0.135717i	$0.956666\pi$
$660$	−0.867484	−	2.50643i	−0.0337668	−	0.0975627i
$661$	−4.69787	+	0.448592i	−0.182726	+	0.0174482i	−0.186018	−	0.982546i	$-0.559558\pi$
$661$	−4.69787	+	0.448592i	−0.182726	+	0.0174482i	0.00329197	+	0.999995i	$0.498952\pi$
$662$	−2.95042	−	12.1618i	−0.114671	−	0.472681i
$663$	0.958740	+	0.0915486i	0.0372344	+	0.00355545i
$664$	−1.57298	−	10.9403i	−0.0610436	−	0.424567i
$665$	−16.1380	−	0.908922i	−0.625804	−	0.0352465i
$666$	−1.20668			−0.0467579
$667$	16.9350	−	2.22199i	0.655727	−	0.0860360i
$668$	10.1964	+	17.6607i	0.394510	+	0.683311i
$669$	−1.07755	+	22.6205i	−0.0416603	+	0.874558i
$670$	3.83223	+	1.53419i	0.148052	+	0.0592711i
$671$	−22.6817	−	49.6661i	−0.875618	−	1.91734i
$672$	1.80912	+	1.93056i	0.0697884	+	0.0744731i
$673$	−6.85420	+	15.0086i	−0.264210	+	0.578540i	−0.994516	−	0.104580i	$-0.966650\pi$
$673$	−6.85420	+	15.0086i	−0.264210	+	0.578540i	0.730306	+	0.683120i	$0.239377\pi$
$674$	−5.16277	−	14.9168i	−0.198862	−	0.574575i
$675$	4.17314	−	1.67067i	0.160624	−	0.0643042i
$676$	−8.29715	−	7.91132i	−0.319121	−	0.304282i
$677$	9.14775	−	1.76308i	0.351577	−	0.0677608i	−0.0104055	−	0.999946i	$-0.503312\pi$
$677$	9.14775	−	1.76308i	0.351577	−	0.0677608i	0.361982	+	0.932185i	$0.382100\pi$
$678$	−3.34910	+	2.15233i	−0.128621	+	0.0826599i
$679$	−12.6496	−	20.0631i	−0.485446	−	0.769952i
$680$	−0.361631	−	0.417345i	−0.0138679	−	0.0160044i
$681$	−1.66093	+	6.84645i	−0.0636471	+	0.262357i
$682$	−19.4943	+	7.80432i	−0.746474	+	0.298843i
$683$	49.7109	+	9.58099i	1.90214	+	0.366607i	0.998142	−	0.0609385i	$-0.0194094\pi$
$683$	49.7109	+	9.58099i	1.90214	+	0.366607i	0.903994	+	0.427545i	$0.140621\pi$
$684$	−4.98735	−	7.00375i	−0.190696	−	0.267795i
$685$	−13.6952	−	4.02127i	−0.523266	−	0.153645i
$686$	2.23894	−	18.3844i	0.0854829	−	0.701921i
$687$	−3.40706	−	23.6966i	−0.129987	−	0.904081i
$688$	−3.60626	+	1.85916i	−0.137488	+	0.0708797i
$689$	−3.84546	−	6.66053i	−0.146500	−	0.253746i
$690$	2.13935	−	2.65239i	0.0814435	−	0.100975i
$691$	−0.973985	+	1.68699i	−0.0370521	+	0.0641762i	−0.883957	−	0.467569i	$-0.845130\pi$
$691$	−0.973985	+	1.68699i	−0.0370521	+	0.0641762i	0.846905	+	0.531745i	$0.178463\pi$
$692$	−4.64423	−	2.98467i	−0.176547	−	0.113460i
$693$	−9.78735	+	1.32078i	−0.371791	+	0.0501722i
$694$	−9.97342	−	21.8387i	−0.378586	−	0.828987i
$695$	8.90705	−	8.49285i	0.337864	−	0.322152i
$696$	3.54534	−	0.338539i	0.134386	−	0.0128323i
$697$	5.27699	+	1.01706i	0.199880	+	0.0385238i
$698$	−1.18232	−	0.929786i	−0.0447515	−	0.0351929i
$699$	5.01062	−	1.47125i	0.189519	−	0.0556478i
$700$	2.14952	+	11.6971i	0.0812442	+	0.442110i
$701$	8.61985	−	5.53964i	0.325567	−	0.209229i	−0.367639	−	0.929969i	$-0.619834\pi$
$701$	8.61985	−	5.53964i	0.325567	−	0.209229i	0.693206	+	0.720739i	$0.256197\pi$
$702$	0.0589638	+	1.23780i	0.00222544	+	0.0467178i
$703$	−3.39335	+	9.80445i	−0.127983	+	0.369782i
$704$	2.70156	+	2.57593i	0.101819	+	0.0970839i
$705$	7.07696	+	5.56538i	0.266534	+	0.209605i
$706$	−10.0372	+	11.5835i	−0.377754	+	0.435952i
$707$	−1.49901	−	17.2788i	−0.0563759	−	0.649838i
$708$	9.11182	+	2.67547i	0.342443	+	0.100550i
$709$	19.3044	+	1.84335i	0.724993	+	0.0692284i	0.451026	−	0.892511i	$-0.351058\pi$
$709$	19.3044	+	1.84335i	0.724993	+	0.0692284i	0.273967	+	0.961739i	$0.411664\pi$
$710$	8.07844	−	6.35295i	0.303178	−	0.238422i
$711$	0.616680	−	12.9457i	0.0231273	−	0.485502i
$712$	2.80736	−	4.86249i	0.105210	−	0.182229i
$713$	−21.7812	−	15.9189i	−0.815712	−	0.596168i
$714$	−1.78961	+	1.01266i	−0.0669745	+	0.0378980i
$715$	2.76499	+	1.77695i	0.103405	+	0.0664543i
$716$	−20.9043	−	8.36884i	−0.781232	−	0.312758i
$717$	2.17513	−	3.05454i	0.0812317	−	0.114074i
$718$	−5.24839	−	21.6341i	−0.195868	−	0.807379i
$719$	17.1543	+	24.0899i	0.639749	+	0.898402i	0.999398	−	0.0346855i	$-0.0110430\pi$
$719$	17.1543	+	24.0899i	0.639749	+	0.898402i	−0.359649	+	0.933088i	$0.617104\pi$
$720$	0.465305	−	0.536991i	0.0173409	−	0.0200125i
$721$	3.57414	−	4.46475i	0.133108	−	0.166276i
$722$	−52.7012	+	15.4745i	−1.96134	+	0.575900i
$723$	−4.22876	+	0.815027i	−0.157269	+	0.0303112i
$724$	8.04566	+	4.14783i	0.299015	+	0.154153i
$725$	14.2296	+	7.33586i	0.528474	+	0.272447i
$726$	−2.88079	+	0.555226i	−0.106916	+	0.0206064i
$727$	3.58059	−	1.05136i	0.132797	−	0.0389927i	−0.214659	−	0.976689i	$-0.568864\pi$
$727$	3.58059	−	1.05136i	0.132797	−	0.0389927i	0.347456	+	0.937696i	$0.387046\pi$
$728$	−3.24109	−	0.494692i	−0.120123	−	0.0183345i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	−6.11704	−	8.59018i	−0.226402	−	0.317937i
$731$	−0.743418	−	3.06441i	−0.0274963	−	0.113341i
$732$	8.48457	−	11.9149i	0.313599	−	0.440388i
$733$	33.6580	+	13.4746i	1.24318	+	0.497696i	0.897650	−	0.440710i	$-0.145273\pi$
$733$	33.6580	+	13.4746i	1.24318	+	0.497696i	0.345535	+	0.938406i	$0.387697\pi$
$734$	−11.2834	−	7.25143i	−0.416480	−	0.267655i
$735$	−4.97304	−	0.0861674i	−0.183433	−	0.00317833i
$736$	−0.965648	+	4.69761i	−0.0355942	+	0.173156i
$737$	10.8430	−	18.7806i	0.399405	−	0.691791i
$738$	−0.329018	+	6.90695i	−0.0121113	+	0.254248i
$739$	22.4975	−	17.6922i	0.827585	−	0.650820i	−0.111783	−	0.993733i	$-0.535656\pi$
$739$	22.4975	−	17.6922i	0.827585	−	0.650820i	0.939367	+	0.342913i	$0.111414\pi$
$740$	−0.853512	−	0.0815005i	−0.0313757	−	0.00299602i
$741$	10.2231	+	3.00178i	0.375556	+	0.110273i
$742$	14.8769	+	6.95041i	0.546147	+	0.255158i
$743$	14.4085	−	16.6283i	0.528596	−	0.610032i	−0.427166	−	0.904173i	$-0.640488\pi$
$743$	14.4085	−	16.6283i	0.528596	−	0.610032i	0.955762	+	0.294141i	$0.0950336\pi$
$744$	−4.42185	−	3.47738i	−0.162113	−	0.127487i
$745$	−1.72391	−	1.64375i	−0.0631593	−	0.0602223i
$746$	−1.77147	+	5.11831i	−0.0648580	+	0.187395i
$747$	0.525915	+	11.0403i	0.0192422	+	0.403944i
$748$	−2.44056	+	1.56846i	−0.0892359	+	0.0573484i
$749$	1.19719	+	6.51481i	0.0437444	+	0.238046i
$750$	6.47339	−	1.90076i	0.236375	−	0.0694059i
$751$	18.9356	+	14.8911i	0.690971	+	0.543385i	0.900736	−	0.434366i	$-0.143028\pi$
$751$	18.9356	+	14.8911i	0.690971	+	0.543385i	−0.209766	+	0.977752i	$0.567270\pi$
$752$	−12.4419	−	2.39798i	−0.453709	−	0.0874452i
$753$	−13.7022	+	1.30840i	−0.499335	+	0.0476807i
$754$	−3.19412	+	3.04558i	−0.116323	+	0.110914i
$755$	3.33580	+	7.30439i	0.121402	+	0.265834i
$756$	−1.61742	−	2.09379i	−0.0588249	−	0.0761504i
$757$	−9.60693	−	6.17400i	−0.349170	−	0.224398i	0.354285	−	0.935137i	$-0.384724\pi$
$757$	−9.60693	−	6.17400i	−0.349170	−	0.224398i	−0.703455	+	0.710739i	$0.748360\pi$
$758$	3.90622	−	6.76576i	0.141880	−	0.245744i
$759$	−12.1929	−	13.1076i	−0.442575	−	0.475777i
$760$	−3.05462	−	5.29076i	−0.110803	−	0.191916i
$761$	−16.4358	+	8.47326i	−0.595799	+	0.307155i	−0.729623	−	0.683850i	$-0.760304\pi$
$761$	−16.4358	+	8.47326i	−0.595799	+	0.307155i	0.133825	+	0.991005i	$0.457274\pi$
$762$	0.825965	+	5.74471i	0.0299215	+	0.208109i
$763$	−8.96921	−	6.50477i	−0.324707	−	0.235488i
$764$	−9.80210	−	2.87816i	−0.354628	−	0.104128i
$765$	0.320323	+	0.449830i	0.0115813	+	0.0162637i
$766$	9.70228	+	1.86996i	0.350557	+	0.0675644i
$767$	−10.9251	+	4.37377i	−0.394484	+	0.157928i
$768$	−0.235759	+	0.971812i	−0.00850722	+	0.0350672i
$769$	24.0530	+	27.7586i	0.867373	+	1.00100i	0.999952	+	0.00982931i	$0.00312882\pi$
$769$	24.0530	+	27.7586i	0.867373	+	1.00100i	−0.132579	+	0.991172i	$0.542326\pi$
$770$	−7.01202	+	0.273167i	−0.252696	+	0.00984427i
$771$	−23.4327	+	15.0593i	−0.843909	+	0.542347i
$772$	−25.3430	+	4.88447i	−0.912116	+	0.175796i
$773$	−2.98303	−	2.84431i	−0.107292	−	0.102303i	0.634535	−	0.772895i	$-0.281192\pi$
$773$	−2.98303	−	2.84431i	−0.107292	−	0.102303i	−0.741827	+	0.670592i	$0.766040\pi$
$774$	3.76666	−	1.50794i	0.135390	−	0.0542019i
$775$	−8.27051	−	23.8961i	−0.297085	−	0.858372i
$776$	3.72400	−	8.15443i	0.133684	−	0.292727i
$777$	−0.925954	+	3.05535i	−0.0332184	+	0.109610i
$778$	12.4710	+	27.3076i	0.447106	+	0.979026i
$779$	55.1947	+	22.0966i	1.97756	+	0.791694i
$780$	−0.0418961	+	0.879508i	−0.00150012	+	0.0314915i
$781$	−26.9955	−	46.7576i	−0.965976	−	1.67312i
$782$	−3.37109	−	1.59008i	−0.120550	−	0.0568612i
$783$	−3.56146			−0.127276
$784$	6.27648	−	3.09931i	0.224160	−	0.110690i
$785$	1.45172	+	10.0969i	0.0518141	+	0.360375i
$786$	−5.66642	−	0.541078i	−0.202115	−	0.0192996i
$787$	5.99058	+	24.6935i	0.213541	+	0.880228i	0.973210	+	0.229918i	$0.0738458\pi$
$787$	5.99058	+	24.6935i	0.213541	+	0.880228i	−0.759669	+	0.650310i	$0.774639\pi$
$788$	−10.8024	+	1.03151i	−0.384821	+	0.0367459i
$789$	0.502023	+	1.45050i	0.0178725	+	0.0516392i
$790$	1.31056	−	9.11515i	0.0466276	−	0.324302i
$791$	2.87982	+	10.1316i	0.102394	+	0.360239i
$792$	−2.44447	−	2.82106i	−0.0868603	−	0.100242i
$793$	0.862471	+	18.1055i	0.0306272	+	0.642945i
$794$	20.6342	+	10.6377i	0.732282	+	0.377518i
$795$	1.44232	−	4.16731i	0.0511538	−	0.147799i
$796$	1.38277	−	5.69986i	0.0490110	−	0.202026i
$797$	3.09073	−	21.4965i	0.109479	−	0.761445i	−0.858933	−	0.512089i	$-0.828872\pi$
$797$	3.09073	−	21.4965i	0.109479	−	0.761445i	0.968412	−	0.249356i	$-0.0802190\pi$
$798$	−21.5608	+	7.25373i	−0.763243	+	0.256779i
$799$	4.09088	−	8.95778i	0.144725	−	0.316904i
$800$	−3.25328	+	3.10200i	−0.115021	+	0.109672i
$801$	−3.25685	+	4.57361i	−0.115075	+	0.161601i
$802$	−9.14946	+	7.19521i	−0.323079	+	0.254072i
$803$	−49.2423	+	25.3862i	−1.73772	+	0.895858i
$804$	5.80955			0.204887
$805$	−5.07428	−	7.45221i	−0.178845	−	0.262656i
$806$	6.97100			0.245543
$807$	−19.4137	+	10.0085i	−0.683394	+	0.352314i
$808$	5.15283	−	4.05223i	0.181276	−	0.142557i
$809$	−4.67239	+	6.56145i	−0.164272	+	0.230688i	−0.888504	−	0.458868i	$-0.848255\pi$
$809$	−4.67239	+	6.56145i	−0.164272	+	0.230688i	0.724232	+	0.689556i	$0.242194\pi$
$810$	−0.514242	+	0.490329i	−0.0180686	+	0.0172284i
$811$	7.32391	−	16.0371i	0.257177	−	0.563140i	−0.736367	−	0.676582i	$-0.763460\pi$
$811$	7.32391	−	16.0371i	0.257177	−	0.563140i	0.993545	+	0.113442i	$0.0361877\pi$
$812$	1.86335	−	9.23667i	0.0653907	−	0.324144i
$813$	−3.04222	+	21.1591i	−0.106695	+	0.742083i
$814$	−1.06193	+	4.37733i	−0.0372205	+	0.153425i
$815$	3.11557	−	9.00184i	0.109134	−	0.315321i
$816$	−0.690796	−	0.356130i	−0.0241827	−	0.0124670i
$817$	−1.65988	−	34.8452i	−0.0580719	−	1.21908i
$818$	−6.29511	−	7.26495i	−0.220103	−	0.254013i
$819$	3.17940	+	0.800538i	0.111097	+	0.0279731i
$820$	−0.699225	+	4.86322i	−0.0244180	+	0.169831i
$821$	−7.28162	−	21.0388i	−0.254130	−	0.734261i	−0.997836	−	0.0657537i	$-0.979055\pi$
$821$	−7.28162	−	21.0388i	−0.254130	−	0.734261i	0.743706	−	0.668507i	$-0.233066\pi$
$822$	−19.9971	+	1.90949i	−0.697478	+	0.0666011i
$823$	−0.281001	−	1.15830i	−0.00979509	−	0.0403759i	0.966704	−	0.255896i	$-0.0823705\pi$
$823$	−0.281001	−	1.15830i	−0.00979509	−	0.0403759i	−0.976499	+	0.215520i	$0.930855\pi$
$824$	2.15184	+	0.205476i	0.0749629	+	0.00715809i
$825$	−2.38796	−	16.6086i	−0.0831382	−	0.578239i
$826$	13.7664	−	21.0183i	0.478994	−	0.731322i
$827$	−12.2116			−0.424639			−0.212319	−	0.977200i	$-0.568102\pi$
$827$	−12.2116			−0.424639			−0.212319	+	0.977200i	$0.568102\pi$
$828$	1.40781	−	4.58455i	0.0489248	−	0.159324i
$829$	−19.2386	−	33.3223i	−0.668186	−	1.15733i	−0.978411	−	0.206669i	$-0.933738\pi$
$829$	−19.2386	−	33.3223i	−0.668186	−	1.15733i	0.310225	−	0.950663i	$-0.399595\pi$
$830$	−0.373684	+	7.84459i	−0.0129708	+	0.272290i
$831$	−25.9873	−	10.4037i	−0.901489	−	0.360902i
$832$	−0.514785	−	1.12722i	−0.0178469	−	0.0390794i
$833$	1.19082	+	5.30842i	0.0412596	+	0.183926i
$834$	7.19529	−	15.7555i	0.249153	−	0.545568i
$835$	−4.73918	−	13.6930i	−0.164006	−	0.473864i
$836$	−29.7957	+	11.9284i	−1.03051	+	0.412553i
$837$	4.07128	+	3.88196i	0.140724	+	0.134180i
$838$	−1.35373	+	0.260910i	−0.0467638	+	0.00901299i
$839$	25.5856	−	16.4428i	0.883311	−	0.567670i	−0.0184859	−	0.999829i	$-0.505885\pi$
$839$	25.5856	−	16.4428i	0.883311	−	0.567670i	0.901797	+	0.432159i	$0.142248\pi$
$840$	−1.00262	−	1.59023i	−0.0345937	−	0.0548681i
$841$	10.6847	+	12.3308i	0.368438	+	0.425200i
$842$	−6.01481	+	24.7934i	−0.207284	+	0.854437i
$843$	27.8595	−	11.1533i	0.959532	−	0.384139i
$844$	−6.42516	−	1.23835i	−0.221163	−	0.0426257i
$845$	4.72508	+	6.63545i	0.162548	+	0.228266i
$846$	12.1576	+	3.56980i	0.417987	+	0.122732i
$847$	−0.804744	+	7.72029i	−0.0276513	+	0.265272i
$848$	0.883253	+	6.14316i	0.0303310	+	0.210957i
$849$	−15.2438	+	7.85875i	−0.523167	+	0.269712i
$850$	−1.74679	−	3.02553i	−0.0599144	−	0.103775i
$851$	−5.49168	+	1.82514i	−0.188253	+	0.0625649i
$852$	7.23197	−	12.5261i	0.247763	−	0.429139i
$853$	−42.8133	−	27.5145i	−1.46590	−	0.942077i	−0.998309	−	0.0581326i	$-0.981485\pi$
$853$	−42.8133	−	27.5145i	−1.46590	−	0.942077i	−0.467592	−	0.883945i	$-0.654878\pi$
$854$	−23.6582	−	30.6261i	−0.809566	−	1.04800i
$855$	2.53787	+	5.55717i	0.0867934	+	0.190051i
$856$	−1.81194	+	1.72768i	−0.0619308	+	0.0590509i
$857$	−27.4208	+	2.61837i	−0.936678	+	0.0894419i	−0.552218	−	0.833700i	$-0.686218\pi$
$857$	−27.4208	+	2.61837i	−0.936678	+	0.0894419i	−0.384460	+	0.923142i	$0.625612\pi$
$858$	4.54212	+	0.875421i	0.155065	+	0.0298864i
$859$	5.57563	+	4.38472i	0.190238	+	0.149605i	0.708735	−	0.705474i	$-0.249266\pi$
$859$	5.57563	+	4.38472i	0.190238	+	0.149605i	−0.518497	+	0.855079i	$0.673508\pi$
$860$	2.76609	−	0.812198i	0.0943230	−	0.0276957i
$861$	17.2361	+	6.13317i	0.587405	+	0.209018i
$862$	−21.8319	+	14.0305i	−0.743597	+	0.477881i
$863$	−1.34504	−	28.2359i	−0.0457857	−	0.961160i	−0.898552	−	0.438867i	$-0.855380\pi$
$863$	−1.34504	−	28.2359i	−0.0457857	−	0.961160i	0.852766	−	0.522293i	$-0.174923\pi$
$864$	0.327068	−	0.945001i	0.0111271	−	0.0321496i
$865$	2.83893	+	2.70692i	0.0965266	+	0.0920379i
$866$	5.63873	+	4.43434i	0.191612	+	0.150685i
$867$	−10.7371	+	12.3912i	−0.364650	+	0.420829i
$868$	−12.1980	+	8.52785i	−0.414025	+	0.289454i
$869$	−46.4189	−	13.6298i	−1.57465	−	0.462360i
$870$	−2.51910	−	0.240545i	−0.0854057	−	0.00815525i
$871$	−5.65898	+	4.45027i	−0.191747	+	0.150792i
$872$	0.199260	−	4.18297i	0.00674778	−	0.141653i
$873$	−4.48227	+	7.76352i	−0.151702	+	0.262755i
$874$	−33.2911	−	24.3311i	−1.12609	−	0.823010i
$875$	0.154626	−	17.8494i	0.00522730	−	0.603418i
$876$	−12.4856	−	8.02400i	−0.421849	−	0.271106i
$877$	−1.65870	−	0.664042i	−0.0560102	−	0.0224231i	0.343488	−	0.939157i	$-0.388391\pi$
$877$	−1.65870	−	0.664042i	−0.0560102	−	0.0224231i	−0.399498	+	0.916734i	$0.630816\pi$
$878$	12.7203	−	17.8632i	0.429289	−	0.602852i
$879$	−1.97266	−	8.13141i	−0.0665362	−	0.274266i
$880$	−1.53849	−	2.16050i	−0.0518624	−	0.0728306i
$881$	7.58343	−	8.75174i	0.255492	−	0.294854i	−0.613484	−	0.789707i	$-0.710233\pi$
$881$	7.58343	−	8.75174i	0.255492	−	0.294854i	0.868977	+	0.494853i	$0.164778\pi$
$882$	−6.54267	+	2.48866i	−0.220303	+	0.0837977i
$883$	4.14653	−	1.21753i	0.139542	−	0.0409732i	−0.211216	−	0.977439i	$-0.567742\pi$
$883$	4.14653	−	1.21753i	0.139542	−	0.0409732i	0.350758	+	0.936466i	$0.385924\pi$
$884$	0.945697	−	0.182268i	0.0318072	−	0.00613034i
$885$	−5.99755	−	3.09195i	−0.201605	−	0.103935i
$886$	−3.19644	−	1.64788i	−0.107387	−	0.0553616i
$887$	−4.86146	+	0.936970i	−0.163232	+	0.0314604i	−0.270212	−	0.962801i	$-0.587094\pi$
$887$	−4.86146	+	0.936970i	−0.163232	+	0.0314604i	0.106980	+	0.994261i	$0.465882\pi$
$888$	−1.15780	+	0.339961i	−0.0388532	+	0.0114083i
$889$	15.1796	+	2.31688i	0.509107	+	0.0777056i
$890$	−2.61256	+	3.01505i	−0.0875730	+	0.101065i
$891$	2.16524	+	3.04065i	0.0725382	+	0.101866i
$892$	5.33903	+	22.0078i	0.178764	+	0.736874i
$893$	63.1940	−	88.7436i	2.11471	−	2.96969i
$894$	−3.11220	−	1.24594i	−0.104088	−	0.0416704i
$895$	13.4596	+	8.64996i	0.449905	+	0.289136i
$896$	2.27974	+	1.34267i	0.0761609	+	0.0448556i
$897$	2.14056	+	5.54414i	0.0714712	+	0.185114i
$898$	−11.0396	+	19.1211i	−0.368396	+	0.638080i
$899$	−0.953284	+	20.0119i	−0.0317938	+	0.667434i
$900$	3.53341	−	2.77871i	0.117780	−	0.0926235i
$901$	−4.80167	−	0.458504i	−0.159967	−	0.0152750i
$902$	24.7659	+	7.27194i	0.824616	+	0.242129i
$903$	−0.927782	−	10.6944i	−0.0308746	−	0.355888i
$904$	−2.60705	+	3.00870i	−0.0867092	+	0.100068i
$905$	−5.05570	−	3.97584i	−0.168057	−	0.132162i
$906$	8.17915	+	7.79880i	0.271734	+	0.259098i
$907$	−16.9430	+	48.9536i	−0.562584	+	1.62548i	0.200872	+	0.979618i	$0.435623\pi$
$907$	−16.9430	+	48.9536i	−0.562584	+	1.62548i	−0.763455	+	0.645861i	$0.776499\pi$
$908$	0.335217	+	7.03706i	0.0111246	+	0.233533i
$909$	−5.51469	+	3.54407i	−0.182911	+	0.117549i
$910$	2.19479	+	0.780979i	0.0727566	+	0.0258892i
$911$	25.5938	−	7.51501i	0.847960	−	0.248983i	0.171245	−	0.985229i	$-0.445221\pi$
$911$	25.5938	−	7.51501i	0.847960	−	0.248983i	0.676715	+	0.736245i	$0.263403\pi$
$912$	−6.75851	−	5.31495i	−0.223797	−	0.175996i
$913$	40.5125	+	7.80814i	1.34077	+	0.258412i
$914$	28.3560	−	2.70767i	0.937935	−	0.0895619i
$915$	−7.52189	+	7.17210i	−0.248666	+	0.237102i
$916$	−9.94515	−	21.7768i	−0.328597	−	0.719527i
$917$	−5.71819	+	13.9323i	−0.188831	+	0.460086i
$918$	0.653816	+	0.420182i	0.0215791	+	0.0138681i
$919$	−18.1664	+	31.4651i	−0.599254	+	1.03794i	0.393677	+	0.919249i	$0.371203\pi$
$919$	−18.1664	+	31.4651i	−0.599254	+	1.03794i	−0.992931	+	0.118690i	$0.962130\pi$
$920$	1.30542	−	3.14767i	0.0430385	−	0.103776i
$921$	0.265262	+	0.459448i	0.00874069	+	0.0151393i
$922$	−31.6573	+	16.3205i	−1.04258	+	0.537487i
$923$	2.55082	+	17.7414i	0.0839614	+	0.583964i
$924$	−9.01879	+	4.02469i	−0.296696	+	0.132403i
$925$	−5.20447	−	1.52817i	−0.171122	−	0.0502459i
$926$	−4.18427	−	5.87599i	−0.137504	−	0.193097i
$927$	−2.12257	−	0.409091i	−0.0697142	−	0.0134363i
$928$	3.30635	−	1.32366i	0.108536	−	0.0434513i
$929$	−0.274783	+	1.13267i	−0.00901533	+	0.0371617i	−0.976142	−	0.217135i	$-0.930329\pi$
$929$	−0.274783	+	1.13267i	−0.00901533	+	0.0371617i	0.967126	+	0.254297i	$0.0818440\pi$
$930$	2.61752	+	3.02077i	0.0858317	+	0.0990551i
$931$	1.82184	+	60.1586i	0.0597084	+	1.97162i
$932$	4.39316	−	2.82331i	0.143903	−	0.0924806i
$933$	−27.8398	+	5.36569i	−0.911435	+	0.175665i
$934$	−11.3414	−	10.8140i	−0.371103	−	0.353846i
$935$	1.91369	−	0.766127i	0.0625845	−	0.0250550i
$936$	0.405304	+	1.17105i	0.0132478	+	0.0382770i
$937$	5.74542	−	12.5807i	0.187695	−	0.410994i	−0.792269	−	0.610173i	$-0.791100\pi$
$937$	5.74542	−	12.5807i	0.187695	−	0.410994i	0.979963	+	0.199179i	$0.0638274\pi$
$938$	4.45800	−	14.7100i	0.145559	−	0.480297i
$939$	−1.59829	−	3.49978i	−0.0521584	−	0.114211i
$940$	8.35825	+	3.34614i	0.272616	+	0.109139i
$941$	0.149972	−	3.14830i	0.00488895	−	0.102632i	−0.995104	−	0.0988350i	$-0.968488\pi$
$941$	0.149972	−	3.14830i	0.00488895	−	0.102632i	0.999993	−	0.00379678i	$-0.00120856\pi$
$942$	7.17818	+	12.4330i	0.233878	+	0.405088i
$943$	8.94957	+	31.9317i	0.291438	+	1.03984i
$944$	9.49650			0.309085
$945$	0.846919	+	1.67833i	0.0275503	+	0.0545962i
$946$	−2.15537	−	14.9909i	−0.0700770	−	0.487396i
$947$	22.6032	+	2.15834i	0.734505	+	0.0701367i	0.455603	−	0.890183i	$-0.349424\pi$
$947$	22.6032	+	2.15834i	0.734505	+	0.0701367i	0.278902	+	0.960320i	$0.410030\pi$
$948$	−3.05553	−	12.5951i	−0.0992389	−	0.409068i
$949$	18.3086	−	1.74826i	0.594321	−	0.0567508i
$950$	−12.6409	−	36.5236i	−0.410126	−	1.18498i
$951$	1.98126	−	13.7799i	0.0642467	−	0.446845i
$952$	−1.43182	+	1.47584i	−0.0464055	+	0.0478321i
$953$	−20.8790	−	24.0957i	−0.676338	−	0.780536i	0.309016	−	0.951057i	$-0.400000\pi$
$953$	−20.8790	−	24.0957i	−0.676338	−	0.780536i	−0.985354	+	0.170521i	$0.945455\pi$
$954$	−0.295309	−	6.19930i	−0.00956098	−	0.200710i
$955$	6.45190	+	3.32619i	0.208779	+	0.107633i
$956$	1.22646	−	3.54362i	0.0396665	−	0.114609i
$957$	−3.13423	+	12.9195i	−0.101315	+	0.417628i
$958$	−0.282456	+	1.96453i	−0.00912574	+	0.0634709i
$959$	−10.5100	+	52.0984i	−0.339386	+	1.68235i
$960$	0.295169	−	0.646330i	0.00952654	−	0.0208602i
$961$	0.466720	−	0.445017i	0.0150555	−	0.0143554i
$962$	0.867373	−	1.21805i	0.0279652	−	0.0392717i
$963$	1.96796	−	1.54762i	0.0634166	−	0.0498714i
$964$	−3.82785	+	1.97339i	−0.123287	+	0.0635587i
$965$	18.3386			0.590342
$966$	−10.5279	−	7.08260i	−0.338730	−	0.227879i
$967$	−40.9236			−1.31601			−0.658007	−	0.753012i	$-0.728600\pi$
$967$	−40.9236			−1.31601			−0.658007	+	0.753012i	$0.728600\pi$
$968$	−2.60767	+	1.34435i	−0.0838137	+	0.0432090i
$969$	5.25266	−	4.13074i	0.168740	−	0.132698i
$970$	−3.69477	+	5.18858i	−0.118632	+	0.166595i
$971$	28.3683	−	27.0491i	0.910381	−	0.868047i	−0.0813098	−	0.996689i	$-0.525910\pi$
$971$	28.3683	−	27.0491i	0.910381	−	0.868047i	0.991691	+	0.128642i	$0.0410618\pi$
$972$	−0.415415	+	0.909632i	−0.0133244	+	0.0291765i
$973$	−34.3720	−	30.3088i	−1.10191	−	0.971654i
$974$	2.59784	−	18.0684i	0.0832401	−	0.578948i
$975$	−1.31327	+	5.41337i	−0.0420583	+	0.173367i
$976$	4.78406	−	13.8226i	0.153134	−	0.442452i
$977$	−6.37552	−	3.28681i	−0.203971	−	0.105154i	0.353215	−	0.935542i	$-0.385089\pi$
$977$	−6.37552	−	3.28681i	−0.203971	−	0.105154i	−0.557186	+	0.830388i	$0.688119\pi$
$978$	−0.637899	−	13.3912i	−0.0203978	−	0.428202i
$979$	13.7250	+	15.8395i	0.438652	+	0.506232i
$980$	−4.79587	+	1.31839i	−0.153198	+	0.0421144i
$981$	−0.595974	+	4.14509i	−0.0190280	+	0.132343i
$982$	−0.795930	−	2.29969i	−0.0253992	−	0.0733861i
$983$	−0.300422	+	0.0286869i	−0.00958199	+	0.000914969i	−0.0998459	−	0.995003i	$-0.531835\pi$
$983$	−0.300422	+	0.0286869i	−0.00958199	+	0.000914969i	0.0902639	+	0.995918i	$0.471229\pi$
$984$	1.63022	+	6.71986i	0.0519695	+	0.214221i
$985$	7.67556	+	0.732927i	0.244564	+	0.0233530i
$986$	0.393919	+	2.73977i	0.0125449	+	0.0872520i
$987$	18.3680	−	28.0441i	0.584661	−	0.892653i
$988$	10.6547			0.338972
$989$	14.8615	−	12.5599i	0.472569	−	0.399383i
$990$	1.32615	+	2.29696i	0.0421479	+	0.0730023i
$991$	2.25599	−	47.3590i	0.0716638	−	1.50441i	−0.621378	−	0.783511i	$-0.713427\pi$
$991$	2.25599	−	47.3590i	0.0716638	−	1.50441i	0.693042	−	0.720897i	$-0.256270\pi$
$992$	−5.22242	−	2.09074i	−0.165812	−	0.0663811i
$993$	5.19874	+	11.3836i	0.164977	+	0.361249i
$994$	−26.1670	−	27.9236i	−0.829968	−	0.885682i
$995$	−1.73122	+	3.79085i	−0.0548835	+	0.120178i
$996$	3.61503	+	10.4449i	0.114547	+	0.330961i
$997$	1.76864	−	0.708058i	0.0560135	−	0.0224244i	−0.343487	−	0.939158i	$-0.611608\pi$
$997$	1.76864	−	0.708058i	0.0560135	−	0.0224244i	0.399500	+	0.916733i	$0.369184\pi$
$998$	−8.69089	−	8.28674i	−0.275105	−	0.262312i
$999$	1.18487	−	0.228366i	0.0374877	−	0.00722517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.c.163.5	yes	160
7.4	even	3	inner	966.2.y.c.25.5	✓	160
23.12	even	11	inner	966.2.y.c.541.5	yes	160
161.81	even	33	inner	966.2.y.c.403.5	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.c.25.5	✓	160	7.4	even	3	inner
966.2.y.c.163.5	yes	160	1.1	even	1	trivial
966.2.y.c.403.5	yes	160	161.81	even	33	inner
966.2.y.c.541.5	yes	160	23.12	even	11	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.888835 + 0.458227i) q^{2} +(0.786053 - 0.618159i) q^{3} +(0.580057 - 0.814576i) q^{4} +(-0.514242 + 0.490329i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(1.98444 + 1.74985i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.235759 - 0.971812i) q^{9} +O(q^{10})\)	\(q+(-0.888835 + 0.458227i) q^{2} +(0.786053 - 0.618159i) q^{3} +(0.580057 - 0.814576i) q^{4} +(-0.514242 + 0.490329i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(1.98444 + 1.74985i) q^{7} +(-0.142315 + 0.989821i) q^{8} +(0.235759 - 0.971812i) q^{9} +(0.232395 - 0.671461i) q^{10} +(-3.31785 - 1.71047i) q^{11} +(-0.0475819 - 0.998867i) q^{12} +(0.811507 + 0.936529i) q^{13} +(-2.56567 - 0.646009i) q^{14} +(-0.101120 + 0.703308i) q^{15} +(-0.327068 - 0.945001i) q^{16} +(0.773673 - 0.0738768i) q^{17} +(0.235759 + 0.971812i) q^{18} +(8.55910 + 0.817295i) q^{19} +(0.101120 + 0.703308i) q^{20} +(2.64156 + 0.148778i) q^{21} +3.73280 q^{22} +(2.54285 + 4.06619i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.213887 + 4.49004i) q^{25} +(-1.15044 - 0.460566i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(2.57648 - 0.601463i) q^{28} +(1.47949 - 3.23962i) q^{29} +(-0.232395 - 0.671461i) q^{30} +(-5.22242 + 2.09074i) q^{31} +(0.723734 + 0.690079i) q^{32} +(-3.66534 + 0.706437i) q^{33} +(-0.653816 + 0.420182i) q^{34} +(-1.87849 + 0.0731802i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-0.284485 + 1.17266i) q^{37} +(-7.98214 + 3.19557i) q^{38} +(1.21681 + 0.234521i) q^{39} +(-0.412154 - 0.578789i) q^{40} +(6.63468 + 1.94812i) q^{41} +(-2.41609 + 1.07820i) q^{42} +(-0.577413 - 4.01599i) q^{43} +(-3.31785 + 1.71047i) q^{44} +(0.355270 + 0.615346i) q^{45} +(-4.12341 - 2.44898i) q^{46} +(6.33543 - 10.9733i) q^{47} +(-0.841254 - 0.540641i) q^{48} +(0.876018 + 6.94497i) q^{49} +(-1.86735 - 4.08892i) q^{50} +(0.562481 - 0.536324i) q^{51} +(1.23359 - 0.117794i) q^{52} +(-6.09417 - 1.17456i) q^{53} +(0.786053 + 0.618159i) q^{54} +(2.54487 - 0.747241i) q^{55} +(-2.01446 + 1.71521i) q^{56} +(7.23312 - 4.64845i) q^{57} +(0.169461 + 3.55743i) q^{58} +(-3.10600 + 8.97420i) q^{59} +(0.514242 + 0.490329i) q^{60} +(11.4977 + 9.04189i) q^{61} +(3.68384 - 4.25138i) q^{62} +(2.16838 - 1.51596i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-0.876519 - 0.0836974i) q^{65} +(2.93418 - 2.30746i) q^{66} +(-0.276430 + 5.80297i) q^{67} +(0.388596 - 0.673068i) q^{68} +(4.51237 + 1.62436i) q^{69} +(1.63613 - 0.925818i) q^{70} +(12.1678 + 7.81980i) q^{71} +(0.928368 + 0.371662i) q^{72} +(8.60900 - 12.0896i) q^{73} +(-0.284485 - 1.17266i) q^{74} +(2.60743 + 3.66163i) q^{75} +(5.63051 - 6.49796i) q^{76} +(-3.59100 - 9.20007i) q^{77} +(-1.18901 + 0.349125i) q^{78} +(12.7262 - 2.45277i) q^{79} +(0.631553 + 0.325588i) q^{80} +(-0.888835 - 0.458227i) q^{81} +(-6.78982 + 1.30863i) q^{82} +(-10.6051 + 3.11395i) q^{83} +(1.65345 - 2.06546i) q^{84} +(-0.361631 + 0.417345i) q^{85} +(2.35346 + 3.30497i) q^{86} +(-0.839647 - 3.46107i) q^{87} +(2.16524 - 3.04065i) q^{88} +(-5.21252 - 2.08678i) q^{89} +(-0.597745 - 0.384147i) q^{90} +(-0.0284011 + 3.27851i) q^{91} +(4.78722 + 0.287279i) q^{92} +(-2.81269 + 4.87172i) q^{93} +(-0.602904 + 12.6565i) q^{94} +(-4.80219 + 3.77649i) q^{95} +(0.995472 + 0.0950560i) q^{96} +(-8.60141 - 2.52560i) q^{97} +(-3.96101 - 5.77152i) q^{98} +(-2.44447 + 2.82106i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{12} - 4 q^{13} + 9 q^{14} - 18 q^{15} + 8 q^{16} - 21 q^{17} + 8 q^{18} + 4 q^{19} + 18 q^{20} - 15 q^{21} + 116 q^{22} + 14 q^{23} + 80 q^{24} + 2 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 46 q^{29} - 2 q^{30} + q^{31} + 8 q^{32} - 8 q^{33} - 68 q^{34} - 84 q^{35} - 16 q^{36} + 19 q^{37} - 7 q^{38} - 2 q^{39} - 9 q^{40} + 38 q^{41} + 2 q^{42} + 28 q^{43} + 8 q^{44} + 24 q^{45} - 8 q^{46} - 26 q^{47} + 16 q^{48} - 6 q^{49} - 4 q^{50} + 21 q^{51} + 2 q^{52} - 20 q^{53} - 8 q^{54} + 46 q^{55} - 2 q^{56} - 14 q^{57} - 21 q^{58} + 36 q^{59} - 2 q^{60} + 40 q^{61} - 24 q^{62} - 2 q^{63} - 16 q^{64} - 10 q^{65} - 8 q^{66} + 6 q^{67} + 34 q^{68} + 6 q^{69} - 20 q^{70} + 132 q^{71} + 8 q^{72} - 36 q^{73} + 19 q^{74} - 2 q^{75} - 8 q^{76} - 75 q^{77} - 18 q^{78} + 34 q^{79} + 2 q^{80} + 8 q^{81} + 47 q^{82} + 74 q^{83} + 13 q^{84} + 2 q^{85} + 30 q^{86} + 10 q^{87} - 3 q^{88} - 12 q^{89} - 4 q^{90} - 30 q^{91} - 50 q^{92} + 10 q^{93} - 4 q^{94} + 27 q^{95} - 8 q^{96} + 24 q^{97} + 7 q^{98} - 16 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^12 - 4 * q^13 + 9 * q^14 - 18 * q^15 + 8 * q^16 - 21 * q^17 + 8 * q^18 + 4 * q^19 + 18 * q^20 - 15 * q^21 + 116 * q^22 + 14 * q^23 + 80 * q^24 + 2 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 46 * q^29 - 2 * q^30 + q^31 + 8 * q^32 - 8 * q^33 - 68 * q^34 - 84 * q^35 - 16 * q^36 + 19 * q^37 - 7 * q^38 - 2 * q^39 - 9 * q^40 + 38 * q^41 + 2 * q^42 + 28 * q^43 + 8 * q^44 + 24 * q^45 - 8 * q^46 - 26 * q^47 + 16 * q^48 - 6 * q^49 - 4 * q^50 + 21 * q^51 + 2 * q^52 - 20 * q^53 - 8 * q^54 + 46 * q^55 - 2 * q^56 - 14 * q^57 - 21 * q^58 + 36 * q^59 - 2 * q^60 + 40 * q^61 - 24 * q^62 - 2 * q^63 - 16 * q^64 - 10 * q^65 - 8 * q^66 + 6 * q^67 + 34 * q^68 + 6 * q^69 - 20 * q^70 + 132 * q^71 + 8 * q^72 - 36 * q^73 + 19 * q^74 - 2 * q^75 - 8 * q^76 - 75 * q^77 - 18 * q^78 + 34 * q^79 + 2 * q^80 + 8 * q^81 + 47 * q^82 + 74 * q^83 + 13 * q^84 + 2 * q^85 + 30 * q^86 + 10 * q^87 - 3 * q^88 - 12 * q^89 - 4 * q^90 - 30 * q^91 - 50 * q^92 + 10 * q^93 - 4 * q^94 + 27 * q^95 - 8 * q^96 + 24 * q^97 + 7 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

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