LMFDB - Embedded newform 72.2.l.b.11.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,2,Mod(11,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("72.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	72.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.574922894553$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + \cdots + 256 $ x^16 - 3x^15 + 7x^14 - 12x^13 + 16x^12 - 12x^11 - 8x^10 + 36x^9 - 68x^8 + 72x^7 - 32x^6 - 96x^5 + 256x^4 - 384x^3 + 448x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.7
Root			$0.867527 + 1.11687i$ of defining polynomial
Character	$\chi$	$=$	72.11
Dual form			72.2.l.b.59.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.533474 - 1.30973i) q^{2} +(0.925606 + 1.46399i) q^{3} +(-1.43081 - 1.39742i) q^{4} +(-0.895377 - 1.55084i) q^{5} +(2.41122 - 0.431300i) q^{6} +(2.08793 + 1.20546i) q^{7} +(-2.59355 + 1.12850i) q^{8} +(-1.28651 + 2.71015i) q^{9} +(-2.50885 + 0.345375i) q^{10} +(-1.36975 - 0.790826i) q^{11} +(0.721434 - 3.38815i) q^{12} +(-5.35491 + 3.09166i) q^{13} +(2.69269 - 2.09155i) q^{14} +(1.44164 - 2.74629i) q^{15} +(0.0944399 + 3.99888i) q^{16} -3.69943i q^{17} +(2.86326 + 3.13078i) q^{18} +3.12941 q^{19} +(-0.886056 + 3.47017i) q^{20} +(0.167814 + 4.17248i) q^{21} +(-1.76650 + 1.37212i) q^{22} +(1.36036 + 2.35622i) q^{23} +(-4.05271 - 2.75238i) q^{24} +(0.896599 - 1.55296i) q^{25} +(1.19255 + 8.66283i) q^{26} +(-5.15842 + 0.625100i) q^{27} +(-1.30289 - 4.64250i) q^{28} +(2.55291 - 4.42177i) q^{29} +(-2.82783 - 3.35324i) q^{30} +(5.95312 - 3.43703i) q^{31} +(5.28786 + 2.00961i) q^{32} +(-0.110092 - 2.73729i) q^{33} +(-4.84528 - 1.97355i) q^{34} -4.31738i q^{35} +(5.62796 - 2.07992i) q^{36} -5.24328i q^{37} +(1.66946 - 4.09870i) q^{38} +(-9.48268 - 4.97786i) q^{39} +(4.07232 + 3.01175i) q^{40} +(-5.32220 + 3.07278i) q^{41} +(5.55436 + 2.00612i) q^{42} +(-0.452455 + 0.783675i) q^{43} +(0.854739 + 3.04564i) q^{44} +(5.35491 - 0.431438i) q^{45} +(3.81174 - 0.524733i) q^{46} +(-4.88993 + 8.46960i) q^{47} +(-5.76690 + 3.83965i) q^{48} +(-0.593711 - 1.02834i) q^{49} +(-1.55565 - 2.00277i) q^{50} +(5.41592 - 3.42422i) q^{51} +(11.9822 + 3.05948i) q^{52} +7.05913 q^{53} +(-1.93317 + 7.08963i) q^{54} +2.83235i q^{55} +(-6.77550 - 0.770215i) q^{56} +(2.89660 + 4.58141i) q^{57} +(-4.42944 - 5.70254i) q^{58} +(-6.10118 + 3.52252i) q^{59} +(-5.90042 + 1.91484i) q^{60} +(3.05109 + 1.76155i) q^{61} +(-1.32577 - 9.63057i) q^{62} +(-5.95312 + 4.10775i) q^{63} +(5.45299 - 5.85362i) q^{64} +(9.58933 + 5.53640i) q^{65} +(-3.64385 - 1.31608i) q^{66} +(1.03786 + 1.79762i) q^{67} +(-5.16966 + 5.29319i) q^{68} +(-2.19031 + 4.17248i) q^{69} +(-5.65463 - 2.30321i) q^{70} -3.31507 q^{71} +(0.278229 - 8.48072i) q^{72} +0.631029 q^{73} +(-6.86730 - 2.79715i) q^{74} +(3.10340 - 0.124816i) q^{75} +(-4.47759 - 4.37310i) q^{76} +(-1.90662 - 3.30237i) q^{77} +(-11.5784 + 9.76424i) q^{78} +(-7.82515 - 4.51785i) q^{79} +(6.11707 - 3.72697i) q^{80} +(-5.68980 - 6.97325i) q^{81} +(1.18526 + 8.60992i) q^{82} +(13.5542 + 7.82551i) q^{83} +(5.59059 - 6.20453i) q^{84} +(-5.73722 + 3.31239i) q^{85} +(0.785033 + 1.01067i) q^{86} +(8.83640 - 0.355393i) q^{87} +(4.44496 + 0.505287i) q^{88} +1.16402i q^{89} +(2.29164 - 7.24368i) q^{90} -14.9075 q^{91} +(1.34620 - 5.27230i) q^{92} +(10.5420 + 5.53394i) q^{93} +(8.48428 + 10.9228i) q^{94} +(-2.80200 - 4.85321i) q^{95} +(1.95243 + 9.60146i) q^{96} +(-6.72981 + 11.6564i) q^{97} +(-1.66358 + 0.229013i) q^{98} +(3.90545 - 2.69482i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} - 6 q^{3} - 5 q^{4} - 3 q^{6} - 6 q^{9} + 12 q^{11} - 6 q^{12} - 18 q^{14} + 7 q^{16} - 4 q^{19} + 18 q^{20} - q^{22} + 21 q^{24} - 14 q^{25} - 36 q^{27} - 12 q^{28} + 12 q^{30} + 27 q^{32}+ \cdots - 6 q^{99}+O(q^{100}) $ 16 * q - 3 * q^2 - 6 * q^3 - 5 * q^4 - 3 * q^6 - 6 * q^9 + 12 * q^11 - 6 * q^12 - 18 * q^14 + 7 * q^16 - 4 * q^19 + 18 * q^20 - q^22 + 21 * q^24 - 14 * q^25 - 36 * q^27 - 12 * q^28 + 12 * q^30 + 27 * q^32 + 12 * q^33 - 13 * q^34 + 27 * q^36 - 15 * q^38 - 12 * q^40 - 36 * q^41 + 42 * q^42 + 8 * q^43 + 12 * q^46 - 27 * q^48 + 10 * q^49 + 51 * q^50 + 18 * q^51 - 18 * q^52 + 39 * q^54 - 66 * q^56 + 18 * q^57 + 12 * q^58 + 12 * q^59 - 72 * q^60 + 34 * q^64 - 6 * q^65 - 24 * q^66 - 16 * q^67 - 9 * q^68 + 18 * q^70 - 21 * q^72 - 4 * q^73 - 60 * q^74 + 78 * q^75 - 7 * q^76 - 72 * q^78 - 6 * q^81 - 22 * q^82 + 54 * q^83 + 12 * q^84 - 51 * q^86 - 13 * q^88 - 66 * q^90 - 36 * q^91 + 84 * q^92 + 24 * q^94 + 42 * q^96 + 8 * q^97 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.533474	−	1.30973i	0.377223	−	0.926122i
$2$	0.533474	−	1.30973i	0.377223	−	0.926122i
$3$	0.925606	+	1.46399i	0.534399	+	0.845232i
$3$	0.925606	+	1.46399i	0.534399	+	0.845232i
$4$	−1.43081	−	1.39742i	−0.715405	−	0.698710i
$5$	−0.895377	−	1.55084i	−0.400425	−	0.693556i	0.593352	−	0.804943i	$-0.297804\pi$
$5$	−0.895377	−	1.55084i	−0.400425	−	0.693556i	−0.993777	+	0.111387i	$0.964471\pi$
$6$	2.41122	−	0.431300i	0.984376	−	0.176078i
$7$	2.08793	+	1.20546i	0.789162	+	0.455623i	0.839667	−	0.543101i	$-0.182750\pi$
$7$	2.08793	+	1.20546i	0.789162	+	0.455623i	−0.0505056	+	0.998724i	$0.516083\pi$
$8$	−2.59355	+	1.12850i	−0.916958	+	0.398984i
$9$	−1.28651	+	2.71015i	−0.428836	+	0.903382i
$10$	−2.50885	+	0.345375i	−0.793368	+	0.109217i
$11$	−1.36975	−	0.790826i	−0.412995	−	0.238443i	0.279081	−	0.960268i	$-0.409970\pi$
$11$	−1.36975	−	0.790826i	−0.412995	−	0.238443i	−0.692076	+	0.721825i	$0.743304\pi$
$12$	0.721434	−	3.38815i	0.208260	−	0.978073i
$13$	−5.35491	+	3.09166i	−1.48519	+	0.857472i	−0.999858	−	0.0168604i	$-0.994633\pi$
$13$	−5.35491	+	3.09166i	−1.48519	+	0.857472i	−0.485327	+	0.874332i	$0.661300\pi$
$14$	2.69269	−	2.09155i	0.719652	−	0.558989i
$15$	1.44164	−	2.74629i	0.372230	−	0.709088i
$16$	0.0944399	+	3.99888i	0.0236100	+	0.999721i
$17$		−	3.69943i		−	0.897244i	−0.893722	−	0.448622i	$-0.851915\pi$
$17$		−	3.69943i		−	0.897244i	0.893722	−	0.448622i	$-0.148085\pi$
$18$	2.86326	+	3.13078i	0.674876	+	0.737931i
$19$	3.12941			0.717936			0.358968	−	0.933350i	$-0.383129\pi$
$19$	3.12941			0.717936			0.358968	+	0.933350i	$0.383129\pi$
$20$	−0.886056	+	3.47017i	−0.198128	+	0.775955i
$21$	0.167814	+	4.17248i	0.0366200	+	0.910509i
$22$	−1.76650	+	1.37212i	−0.376619	+	0.292538i
$23$	1.36036	+	2.35622i	0.283655	+	0.491305i	0.972282	−	0.233811i	$-0.0751196\pi$
$23$	1.36036	+	2.35622i	0.283655	+	0.491305i	−0.688627	+	0.725116i	$0.741786\pi$
$24$	−4.05271	−	2.75238i	−0.827255	−	0.561826i
$25$	0.896599	−	1.55296i	0.179320	−	0.310591i
$26$	1.19255	+	8.66283i	0.233878	+	1.69892i
$27$	−5.15842	+	0.625100i	−0.992738	+	0.120301i
$28$	−1.30289	−	4.64250i	−0.246223	−	0.877350i
$29$	2.55291	−	4.42177i	0.474064	−	0.821102i	−0.525495	−	0.850796i	$-0.676120\pi$
$29$	2.55291	−	4.42177i	0.474064	−	0.821102i	0.999559	+	0.0296942i	$0.00945336\pi$
$30$	−2.82783	−	3.35324i	−0.516288	−	0.612215i
$31$	5.95312	−	3.43703i	1.06921	−	0.617310i	0.141246	−	0.989975i	$-0.454889\pi$
$31$	5.95312	−	3.43703i	1.06921	−	0.617310i	0.927966	+	0.372665i	$0.121556\pi$
$32$	5.28786	+	2.00961i	0.934770	+	0.355252i
$33$	−0.110092	−	2.73729i	−0.0191645	−	0.476501i
$34$	−4.84528	−	1.97355i	−0.830958	−	0.338461i
$35$		−	4.31738i		−	0.729771i
$36$	5.62796	−	2.07992i	0.937993	−	0.346653i
$37$		−	5.24328i		−	0.861990i	−0.902354	−	0.430995i	$-0.858163\pi$
$37$		−	5.24328i		−	0.861990i	0.902354	−	0.430995i	$-0.141837\pi$
$38$	1.66946	−	4.09870i	0.270822	−	0.664896i
$39$	−9.48268	−	4.97786i	−1.51844	−	0.797095i
$40$	4.07232	+	3.01175i	0.643890	+	0.476199i
$41$	−5.32220	+	3.07278i	−0.831189	+	0.479887i	−0.854260	−	0.519847i	$-0.825989\pi$
$41$	−5.32220	+	3.07278i	−0.831189	+	0.479887i	0.0230708	+	0.999734i	$0.492656\pi$
$42$	5.55436	+	2.00612i	0.857057	+	0.309551i
$43$	−0.452455	+	0.783675i	−0.0689987	+	0.119509i	−0.898461	−	0.439054i	$-0.855314\pi$
$43$	−0.452455	+	0.783675i	−0.0689987	+	0.119509i	0.829462	+	0.558563i	$0.188647\pi$
$44$	0.854739	+	3.04564i	0.128857	+	0.459147i
$45$	5.35491	−	0.431438i	0.798263	−	0.0643150i
$46$	3.81174	−	0.524733i	0.562010	−	0.0773677i
$47$	−4.88993	+	8.46960i	−0.713269	+	1.23542i	0.250354	+	0.968154i	$0.419453\pi$
$47$	−4.88993	+	8.46960i	−0.713269	+	1.23542i	−0.963623	+	0.267264i	$0.913880\pi$
$48$	−5.76690	+	3.83965i	−0.832380	+	0.554206i
$49$	−0.593711	−	1.02834i	−0.0848159	−	0.146905i
$50$	−1.55565	−	2.00277i	−0.220002	−	0.283234i
$51$	5.41592	−	3.42422i	0.758380	−	0.479486i
$52$	11.9822	+	3.05948i	1.66163	+	0.424273i
$53$	7.05913			0.969646			0.484823	−	0.874612i	$-0.338884\pi$
$53$	7.05913			0.969646			0.484823	+	0.874612i	$0.338884\pi$
$54$	−1.93317	+	7.08963i	−0.263071	+	0.964777i
$55$			2.83235i			0.381914i
$56$	−6.77550	−	0.770215i	−0.905414	−	0.102924i
$57$	2.89660	+	4.58141i	0.383664	+	0.606822i
$58$	−4.42944	−	5.70254i	−0.581613	−	0.748780i
$59$	−6.10118	+	3.52252i	−0.794306	+	0.458593i	−0.841476	−	0.540294i	$-0.818313\pi$
$59$	−6.10118	+	3.52252i	−0.794306	+	0.458593i	0.0471702	+	0.998887i	$0.484980\pi$
$60$	−5.90042	+	1.91484i	−0.761742	+	0.247205i
$61$	3.05109	+	1.76155i	0.390652	+	0.225543i	0.682443	−	0.730939i	$-0.260918\pi$
$61$	3.05109	+	1.76155i	0.390652	+	0.225543i	−0.291790	+	0.956482i	$0.594251\pi$
$62$	−1.32577	−	9.63057i	−0.168373	−	1.22308i
$63$	−5.95312	+	4.10775i	−0.750022	+	0.517527i
$64$	5.45299	−	5.85362i	0.681624	−	0.731703i
$65$	9.58933	+	5.53640i	1.18941	+	0.686706i
$66$	−3.64385	−	1.31608i	−0.448527	−	0.161998i
$67$	1.03786	+	1.79762i	0.126794	+	0.219614i	0.922433	−	0.386158i	$-0.126198\pi$
$67$	1.03786	+	1.79762i	0.126794	+	0.219614i	−0.795639	+	0.605772i	$0.792865\pi$
$68$	−5.16966	+	5.29319i	−0.626913	+	0.641893i
$69$	−2.19031	+	4.17248i	−0.263682	+	0.502307i
$70$	−5.65463	−	2.30321i	−0.675857	−	0.275286i
$71$	−3.31507			−0.393426			−0.196713	−	0.980461i	$-0.563027\pi$
$71$	−3.31507			−0.393426			−0.196713	+	0.980461i	$0.563027\pi$
$72$	0.278229	−	8.48072i	0.0327896	−	0.999462i
$73$	0.631029			0.0738563			0.0369282	−	0.999318i	$-0.488243\pi$
$73$	0.631029			0.0738563			0.0369282	+	0.999318i	$0.488243\pi$
$74$	−6.86730	−	2.79715i	−0.798308	−	0.325162i
$75$	3.10340	−	0.124816i	0.358350	−	0.0144125i
$76$	−4.47759	−	4.37310i	−0.513615	−	0.501628i
$77$	−1.90662	−	3.30237i	−0.217280	−	0.376340i
$78$	−11.5784	+	9.76424i	−1.31100	+	1.10558i
$79$	−7.82515	−	4.51785i	−0.880398	−	0.508298i	−0.00960849	−	0.999954i	$-0.503059\pi$
$79$	−7.82515	−	4.51785i	−0.880398	−	0.508298i	−0.870790	+	0.491656i	$0.836392\pi$
$80$	6.11707	−	3.72697i	0.683909	−	0.416688i
$81$	−5.68980	−	6.97325i	−0.632200	−	0.774806i
$82$	1.18526	+	8.60992i	0.130891	+	0.950807i
$83$	13.5542	+	7.82551i	1.48776	+	0.858961i	0.999903	−	0.0139604i	$-0.00444387\pi$
$83$	13.5542	+	7.82551i	1.48776	+	0.858961i	0.487861	+	0.872921i	$0.337777\pi$
$84$	5.59059	−	6.20453i	0.609983	−	0.676970i
$85$	−5.73722	+	3.31239i	−0.622289	+	0.359279i
$86$	0.785033	+	1.01067i	0.0846523	+	0.108983i
$87$	8.83640	−	0.355393i	0.947361	−	0.0381021i
$88$	4.44496	+	0.505287i	0.473834	+	0.0538638i
$89$			1.16402i			0.123386i	0.998095	+	0.0616929i	$0.0196499\pi$
$89$			1.16402i			0.123386i	−0.998095	+	0.0616929i	$0.980350\pi$
$90$	2.29164	−	7.24368i	0.241560	−	0.763550i
$91$	−14.9075			−1.56274
$92$	1.34620	−	5.27230i	0.140351	−	0.549675i
$93$	10.5420	+	5.53394i	1.09316	+	0.573843i
$94$	8.48428	+	10.9228i	0.875087	+	1.12660i
$95$	−2.80200	−	4.85321i	−0.287479	−	0.497929i
$96$	1.95243	+	9.60146i	0.199270	+	0.979945i
$97$	−6.72981	+	11.6564i	−0.683309	+	1.18353i	0.290656	+	0.956827i	$0.406126\pi$
$97$	−6.72981	+	11.6564i	−0.683309	+	1.18353i	−0.973965	+	0.226698i	$0.927207\pi$
$98$	−1.66358	+	0.229013i	−0.168047	+	0.0231338i
$99$	3.90545	−	2.69482i	0.392512	−	0.270840i
$100$	−3.45299	+	0.969060i	−0.345299	+	0.0969060i
$101$	−3.28047	+	5.68195i	−0.326419	+	0.565375i	−0.981799	−	0.189925i	$-0.939175\pi$
$101$	−3.28047	+	5.68195i	−0.326419	+	0.565375i	0.655379	+	0.755300i	$0.272509\pi$
$102$	−1.59557	−	8.92014i	−0.157985	−	0.883226i
$103$	5.12167	−	2.95700i	0.504653	−	0.291361i	−0.225980	−	0.974132i	$-0.572558\pi$
$103$	5.12167	−	2.95700i	0.504653	−	0.291361i	0.730633	+	0.682771i	$0.239225\pi$
$104$	10.3993	−	14.0614i	1.01974	−	1.37883i
$105$	6.32058	−	3.99619i	0.616826	−	0.389989i
$106$	3.76586	−	9.24559i	0.365773	−	0.898011i
$107$			1.01487i			0.0981111i	0.998796	+	0.0490555i	$0.0156211\pi$
$107$			1.01487i			0.0981111i	−0.998796	+	0.0490555i	$0.984379\pi$
$108$	8.25424	+	6.31407i	0.794265	+	0.607572i
$109$		−	4.46314i		−	0.427491i	−0.976889	−	0.213746i	$-0.931434\pi$
$109$		−	4.46314i		−	0.427491i	0.976889	−	0.213746i	$-0.0685664\pi$
$110$	3.70963	+	1.51098i	0.353699	+	0.144067i
$111$	7.67608	−	4.85321i	0.728582	−	0.460646i
$112$	−4.62333	+	8.46322i	−0.436864	+	0.799699i
$113$	7.35628	−	4.24715i	0.692021	−	0.399538i	−0.112348	−	0.993669i	$-0.535837\pi$
$113$	7.35628	−	4.24715i	0.692021	−	0.399538i	0.804369	+	0.594131i	$0.202504\pi$
$114$	7.54569	−	1.34971i	0.706719	−	0.126412i
$115$	2.43607	−	4.21940i	0.227165	−	0.393462i
$116$	−9.83180	+	2.75923i	−0.912860	+	0.256188i
$117$	−1.48972	−	18.4900i	−0.137725	−	1.70941i
$118$	1.35874	+	9.87010i	0.125082	+	0.908616i
$119$	4.45953	−	7.72414i	0.408805	−	0.708071i
$120$	−0.639790	+	8.74951i	−0.0584046	+	0.798717i
$121$	−4.24919	−	7.35981i	−0.386290	−	0.669074i
$122$	3.93484	−	3.05638i	0.356244	−	0.276712i
$123$	−9.42476	−	4.94745i	−0.849802	−	0.446097i
$124$	−13.3208	−	3.40125i	−1.19624	−	0.305442i
$125$	−12.1650			−1.08807
$126$	2.20423	+	9.98838i	0.196368	+	0.889836i
$127$			15.9098i			1.41176i	0.708329	+	0.705882i	$0.249449\pi$
$127$			15.9098i			1.41176i	−0.708329	+	0.705882i	$0.750551\pi$
$128$	−4.75766	−	10.2647i	−0.420522	−	0.907282i
$129$	−1.56608	+	0.0629866i	−0.137886	+	0.00554566i
$130$	12.3669	−	9.60596i	1.08465	−	0.842498i
$131$	1.38769	−	0.801182i	0.121243	−	0.0699996i	−0.438152	−	0.898901i	$-0.644367\pi$
$131$	1.38769	−	0.801182i	0.121243	−	0.0699996i	0.559395	+	0.828901i	$0.311034\pi$
$132$	−3.66762	+	4.07038i	−0.319225	+	0.354281i
$133$	6.53397	+	3.77239i	0.566567	+	0.327108i
$134$	2.90807	−	0.400333i	0.251219	−	0.0345835i
$135$	5.58816	+	7.44017i	0.480952	+	0.640348i
$136$	4.17480	+	9.59466i	0.357986	+	0.822735i
$137$	−10.6153	−	6.12877i	−0.906930	−	0.523616i	−0.0274877	−	0.999622i	$-0.508751\pi$
$137$	−10.6153	−	6.12877i	−0.906930	−	0.523616i	−0.879442	+	0.476006i	$0.842084\pi$
$138$	4.29637	+	5.09463i	0.365731	+	0.433684i
$139$	−0.618940	−	1.07204i	−0.0524978	−	0.0909289i	0.838582	−	0.544775i	$-0.183385\pi$
$139$	−0.618940	−	1.07204i	−0.0524978	−	0.0909289i	−0.891080	+	0.453846i	$0.850052\pi$
$140$	−6.03319	+	6.17736i	−0.509898	+	0.522082i
$141$	−16.9255	+	0.680731i	−1.42539	+	0.0573279i
$142$	−1.76850	+	4.34186i	−0.148409	+	0.364361i
$143$	9.77985			0.817832
$144$	−10.9591	−	4.88865i	−0.913255	−	0.407387i
$145$	−9.14327			−0.759307
$146$	0.336637	−	0.826480i	0.0278603	−	0.0684000i
$147$	0.955929	−	1.82102i	0.0788437	−	0.150195i
$148$	−7.32706	+	7.50214i	−0.602280	+	0.616672i
$149$	2.96982	+	5.14387i	0.243297	+	0.421402i	0.961651	−	0.274275i	$-0.0884378\pi$
$149$	2.96982	+	5.14387i	0.243297	+	0.421402i	−0.718355	+	0.695677i	$0.755104\pi$
$150$	1.49211	−	4.13122i	0.121830	−	0.337313i
$151$	−11.9663	−	6.90874i	−0.973803	−	0.562226i	−0.0734098	−	0.997302i	$-0.523388\pi$
$151$	−11.9663	−	6.90874i	−0.973803	−	0.562226i	−0.900394	+	0.435076i	$0.856721\pi$
$152$	−8.11627	+	3.53153i	−0.658317	+	0.286445i
$153$	10.0260	+	4.75935i	0.810555	+	0.384770i
$154$	−5.34236	+	0.735444i	−0.430500	+	0.0592637i
$155$	−10.6606	−	6.15488i	−0.856278	−	0.494372i
$156$	6.61178	+	20.3737i	0.529366	+	1.63120i
$157$	4.98995	−	2.88095i	0.398241	−	0.229925i	−0.287483	−	0.957786i	$-0.592819\pi$
$157$	4.98995	−	2.88095i	0.398241	−	0.229925i	0.685725	+	0.727861i	$0.259485\pi$
$158$	−10.0917	+	7.83871i	−0.802853	+	0.623615i
$159$	6.53397	+	10.3345i	0.518178	+	0.819576i
$160$	−1.61805	−	9.99998i	−0.127918	−	0.790568i
$161$			6.55947i			0.516959i
$162$	−12.1685	+	3.73208i	−0.956045	+	0.293220i
$163$	11.2888			0.884209			0.442104	−	0.896964i	$-0.354232\pi$
$163$	11.2888			0.884209			0.442104	+	0.896964i	$0.354232\pi$
$164$	11.9090	+	3.04079i	0.929939	+	0.237446i
$165$	−4.14652	+	2.62164i	−0.322806	+	0.204094i
$166$	17.4801	−	13.5777i	1.35672	−	1.05383i
$167$	0.378448	+	0.655492i	0.0292852	+	0.0507235i	0.880297	−	0.474424i	$-0.157344\pi$
$167$	0.378448	+	0.655492i	0.0292852	+	0.0507235i	−0.851011	+	0.525147i	$0.824010\pi$
$168$	−5.14386	−	10.6321i	−0.396857	−	0.820288i
$169$	12.6167	−	21.8528i	0.970517	−	1.68098i
$170$	1.27769	+	9.28132i	0.0979943	+	0.711844i
$171$	−4.02601	+	8.48116i	−0.307876	+	0.648570i
$172$	1.74250	−	0.489021i	0.132864	−	0.0372875i
$173$	−4.62735	+	8.01480i	−0.351811	+	0.609354i	−0.986567	−	0.163359i	$-0.947767\pi$
$173$	−4.62735	+	8.01480i	−0.351811	+	0.609354i	0.634756	+	0.772713i	$0.281101\pi$
$174$	4.24852	−	11.7629i	0.322079	−	0.891745i
$175$	3.74406	−	2.16164i	0.283025	−	0.163404i
$176$	3.03306	−	5.55216i	0.228626	−	0.418510i
$177$	−10.8042	−	5.67158i	−0.812094	−	0.426302i
$178$	1.52456	+	0.620974i	0.114270	+	0.0465439i
$179$		−	1.56530i		−	0.116996i	−0.998288	−	0.0584980i	$-0.981369\pi$
$179$		−	1.56530i		−	0.116996i	0.998288	−	0.0584980i	$-0.0186311\pi$
$180$	−8.26477	−	6.86575i	−0.616019	−	0.511743i
$181$		−	3.68300i		−	0.273755i	−0.990588	−	0.136878i	$-0.956293\pi$
$181$		−	3.68300i		−	0.273755i	0.990588	−	0.136878i	$-0.0437067\pi$
$182$	−7.95279	+	19.5249i	−0.589500	+	1.44728i
$183$	0.245227	+	6.09726i	0.0181277	+	0.450722i
$184$	−6.18715	−	4.57580i	−0.456122	−	0.337332i
$185$	−8.13148	+	4.69471i	−0.597838	+	0.345162i
$186$	12.8719	−	10.8550i	0.943812	−	0.795929i
$187$	−2.92561	+	5.06730i	−0.213941	+	0.370558i
$188$	18.8321	−	5.28512i	1.37348	−	0.385457i
$189$	−11.5239	−	4.91312i	−0.838242	−	0.357377i
$190$	−7.85121	+	1.08082i	−0.569587	+	0.0784108i
$191$	11.8678	−	20.5556i	0.858722	−	1.48735i	−0.0144258	−	0.999896i	$-0.504592\pi$
$191$	11.8678	−	20.5556i	0.858722	−	1.48735i	0.873148	−	0.487455i	$-0.162075\pi$
$192$	13.6169	+	2.56496i	0.982718	+	0.185110i
$193$	12.8012	+	22.1723i	0.921451	+	1.59600i	0.797172	+	0.603752i	$0.206328\pi$
$193$	12.8012	+	22.1723i	0.921451	+	1.59600i	0.124279	+	0.992247i	$0.460338\pi$
$194$	11.6766	+	15.0326i	0.838330	+	1.07928i
$195$	0.770728	+	19.1632i	0.0551929	+	1.37230i
$196$	−0.587531	+	2.30102i	−0.0419665	+	0.164359i
$197$	−5.76656			−0.410850			−0.205425	−	0.978673i	$-0.565858\pi$
$197$	−5.76656			−0.410850			−0.205425	+	0.978673i	$0.565858\pi$
$198$	−1.44605	−	6.55272i	−0.102766	−	0.465681i
$199$		−	1.24163i		−	0.0880169i	−0.999031	−	0.0440085i	$-0.985987\pi$
$199$		−	1.24163i		−	0.0880169i	0.999031	−	0.0440085i	$-0.0140129\pi$
$200$	−0.572870	+	5.03947i	−0.0405080	+	0.356345i
$201$	−1.67104	+	3.18329i	−0.117866	+	0.224532i
$202$	5.69180	+	7.32772i	0.400473	+	0.515577i
$203$	10.6606	−	6.15488i	0.748226	−	0.431988i
$204$	−12.5342	−	2.66890i	−0.877571	−	0.186860i
$205$	9.53076	+	5.50259i	0.665657	+	0.384317i
$206$	−1.14060	−	8.28550i	−0.0794696	−	0.577278i
$207$	−8.13581	+	0.655492i	−0.565478	+	0.0455598i
$208$	−12.8689	−	21.1217i	−0.892298	−	1.46453i
$209$	−4.28651	−	2.47482i	−0.296504	−	0.171187i
$210$	−1.86209	−	10.4102i	−0.128496	−	0.718369i
$211$	1.62194	+	2.80928i	0.111659	+	0.193399i	0.916439	−	0.400174i	$-0.131050\pi$
$211$	1.62194	+	2.80928i	0.111659	+	0.193399i	−0.804780	+	0.593573i	$0.797717\pi$
$212$	−10.1003	−	9.86456i	−0.693690	−	0.677501i
$213$	−3.06844	−	4.85321i	−0.210246	−	0.332536i
$214$	1.32921	+	0.541406i	0.0908629	+	0.0370098i
$215$	1.62047			0.110515
$216$	12.6732	−	7.44248i	0.862301	−	0.506397i
$217$	16.5729			1.12504
$218$	−5.84553	−	2.38097i	−0.395909	−	0.161260i
$219$	0.584084	+	0.923817i	0.0394687	+	0.0624258i
$220$	3.95798	−	4.05256i	0.266847	−	0.273223i
$221$	11.4374	+	19.8101i	0.769362	+	1.33257i
$222$	−2.26143	−	12.6427i	−0.151777	−	0.848522i
$223$	−12.1221	−	6.99871i	−0.811758	−	0.468669i	0.0358081	−	0.999359i	$-0.488599\pi$
$223$	−12.1221	−	6.99871i	−0.811758	−	0.468669i	−0.847566	+	0.530690i	$0.821933\pi$
$224$	8.61815	+	10.5702i	0.575824	+	0.706254i
$225$	3.05526	+	4.42780i	0.203684	+	0.295187i
$226$	−1.63826	−	11.9005i	−0.108975	−	0.791611i
$227$	−8.75366	−	5.05393i	−0.581001	−	0.335441i	0.180530	−	0.983569i	$-0.442219\pi$
$227$	−8.75366	−	5.05393i	−0.581001	−	0.335441i	−0.761531	+	0.648128i	$0.775552\pi$
$228$	2.25766	−	10.6029i	0.149517	−	0.702194i
$229$	9.93043	−	5.73334i	0.656221	−	0.378869i	−0.134615	−	0.990898i	$-0.542980\pi$
$229$	9.93043	−	5.73334i	0.656221	−	0.378869i	0.790836	+	0.612029i	$0.209646\pi$
$230$	−4.22672	−	5.44155i	−0.278702	−	0.358805i
$231$	3.06984	−	5.84796i	0.201981	−	0.384768i
$232$	−1.63115	+	14.3490i	−0.107090	+	0.942060i
$233$		−	6.74860i		−	0.442115i	−0.975261	−	0.221058i	$-0.929049\pi$
$233$		−	6.74860i		−	0.442115i	0.975261	−	0.221058i	$-0.0709509\pi$
$234$	−25.0118	−	7.91282i	−1.63507	−	0.517277i
$235$	17.5133			1.14244
$236$	13.6521	+	3.48585i	0.888674	+	0.226909i
$237$	−0.628934	−	15.6377i	−0.0408537	−	1.01578i
$238$	−7.73753	−	9.96144i	−0.501550	−	0.645704i
$239$	0.0677896	+	0.117415i	0.00438494	+	0.00759495i	0.868210	−	0.496198i	$-0.165271\pi$
$239$	0.0677896	+	0.117415i	0.00438494	+	0.00759495i	−0.863825	+	0.503793i	$0.831938\pi$
$240$	11.1182	+	5.50559i	0.717678	+	0.355384i
$241$	−9.71742	+	16.8311i	−0.625954	+	1.08418i	0.362401	+	0.932022i	$0.381957\pi$
$241$	−9.71742	+	16.8311i	−0.625954	+	1.08418i	−0.988355	+	0.152163i	$0.951376\pi$
$242$	−11.9062	+	1.63904i	−0.765362	+	0.105362i
$243$	4.94223	−	14.7843i	0.317044	−	0.948411i
$244$	−1.90391	−	6.78410i	−0.121886	−	0.434307i
$245$	−1.06319	+	1.84150i	−0.0679248	+	0.117649i
$246$	−11.5077	+	9.70461i	−0.733705	+	0.618743i
$247$	−16.7577	+	9.67507i	−1.06627	+	0.615610i
$248$	−11.5610	+	15.6322i	−0.734126	+	0.992645i
$249$	1.08940	+	27.0864i	0.0690376	+	1.71653i
$250$	−6.48969	+	15.9329i	−0.410444	+	1.00768i
$251$			18.7837i			1.18561i	0.805344	+	0.592807i	$0.201980\pi$
$251$			18.7837i			1.18561i	−0.805344	+	0.592807i	$0.798020\pi$
$252$	14.2580	+	2.44159i	0.898171	+	0.153806i
$253$		−	4.30324i		−	0.270542i
$254$	20.8376	+	8.48745i	1.30747	+	0.532550i
$255$	−10.1597	−	5.33325i	−0.636225	−	0.333981i
$256$	−15.9822	+	0.755308i	−0.998885	+	0.0472068i
$257$	18.6937	−	10.7928i	1.16608	−	0.673238i	0.213329	−	0.976981i	$-0.431570\pi$
$257$	18.6937	−	10.7928i	1.16608	−	0.673238i	0.952754	+	0.303742i	$0.0982362\pi$
$258$	−0.752969	+	2.08476i	−0.0468778	+	0.129791i
$259$	6.32058	−	10.9476i	0.392742	−	0.680249i
$260$	−5.98385	−	21.3219i	−0.371102	−	1.32233i
$261$	8.69931	+	12.6074i	0.538474	+	0.780379i
$262$	−0.309041	−	2.24491i	−0.0190926	−	0.138691i
$263$	−8.56995	+	14.8436i	−0.528446	+	0.915295i	0.471004	+	0.882131i	$0.343892\pi$
$263$	−8.56995	+	14.8436i	−0.528446	+	0.915295i	−0.999450	+	0.0331642i	$0.989442\pi$
$264$	3.37455	+	6.97505i	0.207689	+	0.429285i
$265$	−6.32058	−	10.9476i	−0.388270	−	0.672504i
$266$	8.42654	−	6.54530i	0.516664	−	0.401318i
$267$	−1.70411	+	1.07742i	−0.104290	+	0.0659372i
$268$	1.02705	−	4.02237i	0.0627371	−	0.245705i
$269$	20.1271			1.22717			0.613585	−	0.789629i	$-0.289727\pi$
$269$	20.1271			1.22717			0.613585	+	0.789629i	$0.289727\pi$
$270$	12.7258	−	3.34987i	0.774467	−	0.203866i
$271$			6.20336i			0.376827i	0.982090	+	0.188414i	$0.0603345\pi$
$271$			6.20336i			0.376827i	−0.982090	+	0.188414i	$0.939665\pi$
$272$	14.7936	−	0.349374i	0.896994	−	0.0211839i
$273$	−13.7985	−	21.8244i	−0.835124	−	1.32087i
$274$	−13.6901	+	10.6337i	−0.827047	+	0.642408i
$275$	−2.45623	+	1.41811i	−0.148116	+	0.0855151i
$276$	8.96462	−	2.90925i	0.539606	−	0.175116i
$277$	10.6060	+	6.12340i	0.637256	+	0.367920i	0.783557	−	0.621320i	$-0.213403\pi$
$277$	10.6060	+	6.12340i	0.637256	+	0.367920i	−0.146301	+	0.989240i	$0.546737\pi$
$278$	−1.73427	+	0.238744i	−0.104015	+	0.0143189i
$279$	1.65614	+	20.5556i	0.0991504	+	1.23063i
$280$	4.87215	+	11.1973i	0.291167	+	0.669169i
$281$	−15.1623	−	8.75399i	−0.904510	−	0.522219i	−0.0258492	−	0.999666i	$-0.508229\pi$
$281$	−15.1623	−	8.75399i	−0.904510	−	0.522219i	−0.878661	+	0.477447i	$0.841562\pi$
$282$	−8.13775	+	22.5311i	−0.484596	+	1.34171i
$283$	−3.79698	−	6.57656i	−0.225707	−	0.390936i	0.730824	−	0.682565i	$-0.239136\pi$
$283$	−3.79698	−	6.57656i	−0.225707	−	0.390936i	−0.956531	+	0.291630i	$0.905802\pi$
$284$	4.74323	+	4.63254i	0.281459	+	0.274890i
$285$	4.51148	−	8.59425i	0.267237	−	0.509079i
$286$	5.21730	−	12.8090i	0.308505	−	0.757413i
$287$	−14.8165			−0.874590
$288$	−12.2492	+	11.7455i	−0.721792	+	0.692110i
$289$	3.31420			0.194953
$290$	−4.87770	+	11.9753i	−0.286428	+	0.703212i
$291$	−23.2939	+	0.936863i	−1.36551	+	0.0549199i
$292$	−0.902883	−	0.881812i	−0.0528372	−	0.0516041i
$293$	−12.6164	−	21.8523i	−0.737061	−	1.27663i	−0.953813	−	0.300400i	$-0.902880\pi$
$293$	−12.6164	−	21.8523i	−0.737061	−	1.27663i	0.216753	−	0.976227i	$-0.430454\pi$
$294$	−1.87509	−	2.22348i	−0.109357	−	0.129676i
$295$	10.9257	+	6.30797i	0.636120	+	0.367264i
$296$	5.91702	+	13.5987i	0.343920	+	0.790408i
$297$	7.56008	+	3.22318i	0.438681	+	0.187028i
$298$	8.32143	−	1.14555i	0.482047	−	0.0663599i
$299$	−14.5692	−	8.41155i	−0.842561	−	0.486453i
$300$	−4.61480	−	4.15816i	−0.266436	−	0.240072i
$301$	−1.88938	+	1.09084i	−0.108902	+	0.0628748i
$302$	−15.4323	+	11.9870i	−0.888031	+	0.689777i
$303$	−11.3547	+	0.456678i	−0.652311	+	0.0262354i
$304$	0.295541	+	12.5141i	0.0169504	+	0.717735i
$305$		−	6.30900i		−	0.361253i
$306$	11.5821	−	10.5924i	0.662105	−	0.605529i
$307$	−29.5997			−1.68934			−0.844671	−	0.535286i	$-0.820204\pi$
$307$	−29.5997			−1.68934			−0.844671	+	0.535286i	$0.820204\pi$
$308$	−1.88678	+	7.38942i	−0.107509	+	0.421051i
$309$	9.06964	+	4.76103i	0.515954	+	0.270846i
$310$	−13.7484	+	10.6791i	−0.780857	+	0.606529i
$311$	−10.3607	−	17.9453i	−0.587502	−	1.01758i	−0.994558	−	0.104180i	$-0.966778\pi$
$311$	−10.3607	−	17.9453i	−0.587502	−	1.01758i	0.407057	−	0.913403i	$-0.366555\pi$
$312$	30.2113	+	2.20914i	1.71038	+	0.125068i
$313$	1.73680	−	3.00823i	0.0981700	−	0.170035i	−0.812757	−	0.582603i	$-0.802034\pi$
$313$	1.73680	−	3.00823i	0.0981700	−	0.170035i	0.910927	+	0.412567i	$0.135368\pi$
$314$	−1.11127	−	8.07242i	−0.0627126	−	0.455553i
$315$	11.7007	+	5.55434i	0.659262	+	0.312952i
$316$	4.88298	+	17.3992i	0.274689	+	0.978782i
$317$	7.64385	−	13.2395i	0.429321	−	0.743606i	−0.567492	−	0.823379i	$-0.692086\pi$
$317$	7.64385	−	13.2395i	0.429321	−	0.743606i	0.996813	+	0.0797728i	$0.0254195\pi$
$318$	17.0211	−	3.04460i	0.954497	−	0.170733i
$319$	−6.99370	+	4.03781i	−0.391572	+	0.226074i
$320$	−13.9605	−	3.21551i	−0.780416	−	0.179753i
$321$	−1.48575	+	0.939368i	−0.0829267	+	0.0524304i
$322$	8.59117	+	3.49931i	0.478767	+	0.195009i
$323$		−	11.5770i		−	0.644164i
$324$	−1.60353	+	17.9284i	−0.0890849	+	0.996024i
$325$			11.0879i			0.615047i
$326$	6.02229	−	14.7854i	0.333544	−	0.818885i
$327$	6.53397	−	4.13111i	0.361329	−	0.228451i
$328$	10.3358	−	13.9755i	0.570698	−	0.771667i
$329$	−20.4196	+	11.7893i	−1.12577	+	0.649963i
$330$	1.22159	+	6.82942i	0.0672464	+	0.375947i
$331$	3.09986	−	5.36912i	0.170384	−	0.295114i	−0.768170	−	0.640246i	$-0.778833\pi$
$331$	3.09986	−	5.36912i	0.170384	−	0.295114i	0.938554	+	0.345132i	$0.112166\pi$
$332$	−8.45795	−	30.1377i	−0.464190	−	1.65402i
$333$	14.2101	+	6.74552i	0.778706	+	0.369652i
$334$	1.06041	−	0.145979i	0.0580232	−	0.00798763i
$335$	1.85854	−	3.21909i	0.101543	−	0.175878i
$336$	−16.6694	+	1.06512i	−0.909391	+	0.0581068i
$337$	−9.63097	−	16.6813i	−0.524632	−	0.908690i	−0.999589	−	0.0286803i	$-0.990870\pi$
$337$	−9.63097	−	16.6813i	−0.524632	−	0.908690i	0.474956	−	0.880009i	$-0.342464\pi$
$338$	−21.8907	−	28.1825i	−1.19070	−	1.53292i
$339$	13.0268	+	6.83830i	0.707518	+	0.371406i
$340$	12.8377	+	3.27791i	0.696221	+	0.177769i
$341$	−10.8724			−0.588772
$342$	8.96030	+	9.79748i	0.484517	+	0.529787i
$343$		−	19.7393i		−	1.06582i
$344$	0.289090	−	2.54309i	0.0155867	−	0.137114i
$345$	8.43199	−	0.339128i	0.453963	−	0.0182580i
$346$	8.02870	+	10.3363i	0.431625	+	0.555682i
$347$	22.9191	−	13.2323i	1.23036	−	0.710349i	0.263255	−	0.964726i	$-0.415204\pi$
$347$	22.9191	−	13.2323i	1.23036	−	0.710349i	0.967105	+	0.254378i	$0.0818706\pi$
$348$	−13.1398	−	11.8396i	−0.704370	−	0.634672i
$349$	−14.8362	−	8.56568i	−0.794164	−	0.458511i	0.0472627	−	0.998882i	$-0.484950\pi$
$349$	−14.8362	−	8.56568i	−0.794164	−	0.458511i	−0.841426	+	0.540372i	$0.818284\pi$
$350$	−0.833810	−	6.05691i	−0.0445690	−	0.323755i
$351$	25.6903	−	19.2954i	1.37124	−	1.02991i
$352$	−5.65380	−	6.93444i	−0.301348	−	0.369607i
$353$	26.8134	+	15.4807i	1.42713	+	0.823955i	0.996894	−	0.0787597i	$-0.0250960\pi$
$353$	26.8134	+	15.4807i	1.42713	+	0.823955i	0.430239	+	0.902715i	$0.358429\pi$
$354$	−13.1920	+	11.1250i	−0.701148	+	0.591287i
$355$	2.96823	+	5.14113i	0.157538	+	0.272863i
$356$	1.62662	−	1.66549i	0.0862108	−	0.0882708i
$357$	15.4358	−	0.620816i	0.816949	−	0.0328570i
$358$	−2.05013	−	0.835047i	−0.108353	−	0.0441336i
$359$	6.43781			0.339775			0.169887	−	0.985463i	$-0.445660\pi$
$359$	6.43781			0.339775			0.169887	+	0.985463i	$0.445660\pi$
$360$	−13.4013	+	7.16195i	−0.706313	+	0.377468i
$361$	−9.20680			−0.484569
$362$	−4.82376	−	1.96479i	−0.253531	−	0.103267i
$363$	6.84158	−	13.0330i	0.359090	−	0.684057i
$364$	21.3299	+	20.8321i	1.11799	+	1.09190i
$365$	−0.565009	−	0.978624i	−0.0295739	−	0.0512235i
$366$	8.11661	+	2.93155i	0.424262	+	0.153234i
$367$	23.8725	+	13.7828i	1.24614	+	0.719457i	0.970337	−	0.241758i	$-0.0777241\pi$
$367$	23.8725	+	13.7828i	1.24614	+	0.719457i	0.275800	+	0.961215i	$0.411057\pi$
$368$	−9.29376	+	5.66245i	−0.484471	+	0.295176i
$369$	−1.48062	−	18.3771i	−0.0770780	−	0.956674i
$370$	1.81089	+	13.1546i	0.0941439	+	0.683875i
$371$	14.7389	+	8.50953i	0.765208	+	0.441793i
$372$	−7.35039	−	22.6496i	−0.381100	−	1.17433i
$373$	−23.2547	+	13.4261i	−1.20408	+	0.695178i	−0.961461	−	0.274942i	$-0.911341\pi$
$373$	−23.2547	+	13.4261i	−1.20408	+	0.695178i	−0.242623	+	0.970121i	$0.578008\pi$
$374$	5.07608	+	6.53504i	0.262478	+	0.337919i
$375$	−11.2599	−	17.8093i	−0.581461	−	0.919669i
$376$	3.12435	−	27.4846i	0.161126	−	1.41741i
$377$			31.5709i			1.62599i
$378$	−12.5826	+	12.4723i	−0.647179	+	0.641504i
$379$	4.63966			0.238323			0.119162	−	0.992875i	$-0.461979\pi$
$379$	4.63966			0.238323			0.119162	+	0.992875i	$0.461979\pi$
$380$	−2.77283	+	10.8596i	−0.142243	+	0.557085i
$381$	−23.2917	+	14.7262i	−1.19327	+	0.754445i
$382$	−20.5912	−	26.5095i	−1.05354	−	1.35635i
$383$	17.7531	+	30.7493i	0.907141	+	1.57122i	0.818017	+	0.575195i	$0.195074\pi$
$383$	17.7531	+	30.7493i	0.907141	+	1.57122i	0.0891248	+	0.996020i	$0.471593\pi$
$384$	10.6237	−	16.4662i	0.542138	−	0.840289i
$385$	−3.41430	+	5.91373i	−0.174009	+	0.301392i
$386$	35.8690	−	4.93782i	1.82568	−	0.251328i
$387$	−1.54179	−	2.23442i	−0.0783735	−	0.113582i
$388$	25.9179	−	7.27370i	1.31578	−	0.369266i
$389$	3.19920	−	5.54117i	0.162206	−	0.280949i	−0.773454	−	0.633853i	$-0.781473\pi$
$389$	3.19920	−	5.54117i	0.162206	−	0.280949i	0.935659	+	0.352904i	$0.114806\pi$
$390$	25.5098	+	9.21361i	1.29174	+	0.466549i
$391$	8.71666	−	5.03257i	0.440821	−	0.254508i
$392$	2.70029	+	1.99704i	0.136385	+	0.100866i
$393$	2.45737	+	1.28998i	0.123958	+	0.0650707i
$394$	−3.07631	+	7.55266i	−0.154982	+	0.380498i
$395$			16.1807i			0.814141i
$396$	−9.35375	−	1.60177i	−0.470044	−	0.0804918i
$397$		−	3.01894i		−	0.151516i	−0.997126	−	0.0757581i	$-0.975862\pi$
$397$		−	3.01894i		−	0.151516i	0.997126	−	0.0757581i	$-0.0241377\pi$
$398$	−1.62621	−	0.662378i	−0.0815144	−	0.0332020i
$399$	0.525158	+	13.0574i	0.0262908	+	0.653687i
$400$	6.29476	+	3.43874i	0.314738	+	0.171937i
$401$	25.1191	−	14.5025i	1.25439	−	0.724222i	0.282411	−	0.959294i	$-0.408866\pi$
$401$	25.1191	−	14.5025i	1.25439	−	0.724222i	0.971978	+	0.235072i	$0.0755326\pi$
$402$	3.27781	+	3.88683i	0.163482	+	0.193857i
$403$	−21.2523	+	36.8100i	−1.05865	+	1.83364i
$404$	12.6338	−	3.54560i	0.628555	−	0.176400i
$405$	−5.71987	+	15.0676i	−0.284223	+	0.748717i
$406$	−2.37413	−	17.2460i	−0.117826	−	0.855904i
$407$	−4.14652	+	7.18198i	−0.205535	+	0.355998i
$408$	−10.1822	+	14.9927i	−0.504095	+	0.742250i
$409$	−0.662169	−	1.14691i	−0.0327422	−	0.0567111i	0.849190	−	0.528087i	$-0.177091\pi$
$409$	−0.662169	−	1.14691i	−0.0327422	−	0.0567111i	−0.881932	+	0.471376i	$0.843757\pi$
$410$	12.2913	−	9.54728i	0.607026	−	0.471507i
$411$	−0.853191	−	21.2135i	−0.0420848	−	1.04639i
$412$	−11.4603	−	2.92621i	−0.564608	−	0.144164i
$413$	−16.9851			−0.835781
$414$	−3.48172	+	11.0054i	−0.171117	+	0.540888i
$415$		−	28.0271i		−	1.37580i
$416$	−34.5291	+	5.58698i	−1.69293	+	0.273924i
$417$	0.996550	−	1.89840i	0.0488013	−	0.0929651i
$418$	−5.52809	+	4.29394i	−0.270388	+	0.210023i
$419$	−27.2974	+	15.7602i	−1.33357	+	0.769935i	−0.985844	−	0.167663i	$-0.946378\pi$
$419$	−27.2974	+	15.7602i	−1.33357	+	0.769935i	−0.347722	+	0.937598i	$0.613045\pi$
$420$	−14.6279	−	3.11471i	−0.713769	−	0.151982i
$421$	−30.9851	−	17.8893i	−1.51012	−	0.871869i	−0.999930	−	0.0118087i	$-0.996241\pi$
$421$	−30.9851	−	17.8893i	−1.51012	−	0.871869i	−0.510192	−	0.860061i	$-0.670426\pi$
$422$	4.54468	−	0.625632i	0.221231	−	0.0304553i
$423$	−16.6629	−	24.1486i	−0.810180	−	1.17415i
$424$	−18.3082	+	7.96620i	−0.889125	+	0.386873i
$425$	−5.74505	−	3.31691i	−0.278676	−	0.160894i
$426$	−7.99335	+	1.42979i	−0.387279	+	0.0692735i
$427$	4.24697	+	7.35597i	0.205525	+	0.355980i
$428$	1.41820	−	1.45209i	0.0685511	−	0.0701892i
$429$	9.05229	+	14.3176i	0.437049	+	0.691259i
$430$	0.864479	−	2.12239i	0.0416889	−	0.102351i
$431$	−17.1129			−0.824301			−0.412150	−	0.911116i	$-0.635222\pi$
$431$	−17.1129			−0.824301			−0.412150	+	0.911116i	$0.635222\pi$
$432$	−2.98686	−	20.5689i	−0.143705	−	0.989620i
$433$	−19.1099			−0.918363			−0.459182	−	0.888342i	$-0.651857\pi$
$433$	−19.1099			−0.918363			−0.459182	+	0.888342i	$0.651857\pi$
$434$	8.84121	−	21.7061i	0.424391	−	1.04193i
$435$	−8.46307	−	13.3856i	−0.405773	−	0.641791i
$436$	−6.23688	+	6.38591i	−0.298692	+	0.305830i
$437$	4.25713	+	7.37356i	0.203646	+	0.352725i
$438$	1.52155	−	0.272163i	0.0727024	−	0.0130044i
$439$	29.4886	+	17.0253i	1.40742	+	0.812572i	0.995138	−	0.0984868i	$-0.0314002\pi$
$439$	29.4886	+	17.0253i	1.40742	+	0.812572i	0.412277	+	0.911058i	$0.364734\pi$
$440$	−3.19630	−	7.34584i	−0.152377	−	0.350199i
$441$	3.55076	−	0.286080i	0.169084	−	0.0136229i
$442$	32.0476	−	4.41175i	1.52435	−	0.209846i
$443$	17.1586	+	9.90651i	0.815229	+	0.470673i	0.848768	−	0.528765i	$-0.177345\pi$
$443$	17.1586	+	9.90651i	0.815229	+	0.470673i	−0.0335394	+	0.999437i	$0.510678\pi$
$444$	−17.7650	−	3.78268i	−0.843089	−	0.179518i
$445$	1.80521	−	1.04224i	0.0855749	−	0.0494067i
$446$	−15.6333	+	12.1431i	−0.740258	+	0.574995i
$447$	−4.78167	+	9.10896i	−0.226165	+	0.430839i
$448$	18.4418	−	5.64854i	0.871292	−	0.266868i
$449$			8.73916i			0.412426i	0.978507	+	0.206213i	$0.0661140\pi$
$449$			8.73916i			0.412426i	−0.978507	+	0.206213i	$0.933886\pi$
$450$	7.42915	−	1.63946i	0.350213	−	0.0772847i
$451$	9.72012			0.457703
$452$	−16.4605	−	4.20294i	−0.774237	−	0.197690i
$453$	−0.961772	−	23.9133i	−0.0451880	−	1.12354i
$454$	−11.2892	+	8.76883i	−0.529826	+	0.411542i
$455$	13.3479	+	23.1192i	0.625758	+	1.08384i
$456$	−12.6826	−	8.61331i	−0.593916	−	0.403355i
$457$	−1.25081	+	2.16647i	−0.0585104	+	0.101343i	−0.893797	−	0.448472i	$-0.851968\pi$
$457$	−1.25081	+	2.16647i	−0.0585104	+	0.101343i	0.835287	+	0.549815i	$0.185302\pi$
$458$	−2.21152	−	16.0648i	−0.103338	−	0.750659i
$459$	2.31252	+	19.0832i	0.107939	+	0.890728i
$460$	−9.38184	+	2.63295i	−0.437430	+	0.122762i
$461$	−2.63419	+	4.56255i	−0.122686	+	0.212499i	−0.920826	−	0.389973i	$-0.872484\pi$
$461$	−2.63419	+	4.56255i	−0.122686	+	0.212499i	0.798140	+	0.602472i	$0.205818\pi$
$462$	−6.02160	−	7.14041i	−0.280150	−	0.332202i
$463$	15.2227	−	8.78883i	0.707459	−	0.408451i	−0.102661	−	0.994716i	$-0.532736\pi$
$463$	15.2227	−	8.78883i	0.707459	−	0.408451i	0.810119	+	0.586265i	$0.199402\pi$
$464$	17.9232	+	9.79120i	0.832066	+	0.454545i
$465$	−0.856827	−	21.3039i	−0.0397344	−	0.987946i
$466$	−8.83888	−	3.60020i	−0.409453	−	0.166776i
$467$			2.29842i			0.106358i	0.998585	+	0.0531791i	$0.0169354\pi$
$467$			2.29842i			0.106358i	−0.998585	+	0.0531791i	$0.983065\pi$
$468$	−23.7068	+	28.5375i	−1.09585	+	1.31915i
$469$			5.00439i			0.231081i
$470$	9.34290	−	22.9378i	0.430956	−	1.05804i
$471$	8.83640	+	4.63859i	0.407160	+	0.213735i
$472$	11.8486	−	16.0210i	0.545374	−	0.737425i
$473$	1.23950	−	0.715626i	0.0569923	−	0.0329045i
$474$	−20.8167	−	7.51855i	−0.956143	−	0.345338i
$475$	2.80582	−	4.85983i	0.128740	−	0.222984i
$476$	−17.1746	+	4.81995i	−0.787197	+	0.220922i
$477$	−9.08162	+	19.1313i	−0.415819	+	0.875961i
$478$	0.189947	−	0.0261485i	0.00868795	−	0.00119601i
$479$	−18.0219	+	31.2149i	−0.823442	+	1.42624i	0.0796622	+	0.996822i	$0.474616\pi$
$479$	−18.0219	+	31.2149i	−0.823442	+	1.42624i	−0.903104	+	0.429422i	$0.858717\pi$
$480$	13.1422	−	11.6248i	0.599854	−	0.530599i
$481$	16.2104	+	28.0773i	0.739132	+	1.28021i
$482$	16.8603	+	21.7062i	0.767963	+	0.988690i
$483$	−9.60297	+	6.07149i	−0.436950	+	0.276262i
$484$	−4.20496	+	16.4684i	−0.191134	+	0.748564i
$485$	24.1029			1.09446
$486$	−16.7269	−	14.3600i	−0.758748	−	0.651384i
$487$		−	2.72292i		−	0.123387i	−0.998095	−	0.0616937i	$-0.980350\pi$
$487$		−	2.72292i		−	0.123387i	0.998095	−	0.0616937i	$-0.0196502\pi$
$488$	−9.90106	−	1.12552i	−0.448200	−	0.0509498i
$489$	10.4490	+	16.5267i	0.472520	+	0.747362i
$490$	1.84469	+	2.37489i	0.0833347	+	0.107287i
$491$	13.1715	−	7.60457i	0.594421	−	0.343189i	−0.172422	−	0.985023i	$-0.555159\pi$
$491$	13.1715	−	7.60457i	0.594421	−	0.343189i	0.766844	+	0.641834i	$0.221826\pi$
$492$	6.57139	+	20.2492i	0.296261	+	0.912905i
$493$	−16.3580	−	9.44432i	−0.736729	−	0.425351i
$494$	3.73197	+	27.1095i	0.167909	+	1.21972i
$495$	−7.67608	−	3.64384i	−0.345014	−	0.163778i
$496$	14.3065	+	23.4812i	0.642382	+	1.05434i
$497$	−6.92161	−	3.99619i	−0.310477	−	0.179254i
$498$	36.0572	+	13.0231i	1.61576	+	0.583579i
$499$	−19.7305	−	34.1743i	−0.883260	−	1.52985i	−0.847695	−	0.530483i	$-0.822010\pi$
$499$	−19.7305	−	34.1743i	−0.883260	−	1.52985i	−0.0355642	−	0.999367i	$-0.511323\pi$
$500$	17.4057	+	16.9995i	0.778409	+	0.760242i
$501$	−0.609336	+	1.16077i	−0.0272231	+	0.0518594i
$502$	24.6016	+	10.0206i	1.09802	+	0.447241i
$503$	18.4749			0.823756			0.411878	−	0.911239i	$-0.364873\pi$
$503$	18.4749			0.823756			0.411878	+	0.911239i	$0.364873\pi$
$504$	10.8041	−	17.3717i	0.481254	−	0.773798i
$505$	11.7490			0.522826
$506$	−5.63610	−	2.29566i	−0.250555	−	0.102055i
$507$	43.6703	−	1.75638i	1.93947	−	0.0780038i
$508$	22.2326	−	22.7639i	0.986413	−	1.00998i
$509$	−17.0068	−	29.4566i	−0.753813	−	1.30564i	−0.945962	−	0.324277i	$-0.894879\pi$
$509$	−17.0068	−	29.4566i	−0.753813	−	1.30564i	0.192149	−	0.981366i	$-0.438454\pi$
$510$	−12.4051	+	10.4614i	−0.549306	+	0.463237i
$511$	1.31754	+	0.760683i	0.0582846	+	0.0336506i
$512$	−7.53681	+	21.3353i	−0.333083	+	0.942897i
$513$	−16.1428	+	1.95619i	−0.712722	+	0.0863680i
$514$	−4.16313	−	30.2415i	−0.183628	−	1.33390i
$515$	−9.17165	−	5.29525i	−0.404151	−	0.233337i
$516$	2.32879	+	2.09835i	0.102519	+	0.0923748i
$517$	13.3960	−	7.73416i	0.589153	−	0.340148i
$518$	−10.9666	−	14.1185i	−0.481843	−	0.620333i
$519$	−16.0167	+	0.644177i	−0.703053	+	0.0282762i
$520$	−31.1182	−	3.53741i	−1.36462	−	0.155126i
$521$		−	12.0788i		−	0.529182i	−0.964361	−	0.264591i	$-0.914763\pi$
$521$		−	12.0788i		−	0.529182i	0.964361	−	0.264591i	$-0.0852369\pi$
$522$	21.1532	−	4.66807i	0.925851	−	0.204316i
$523$	5.27483			0.230652			0.115326	−	0.993328i	$-0.463209\pi$
$523$	5.27483			0.230652			0.115326	+	0.993328i	$0.463209\pi$
$524$	−3.10511	−	0.792842i	−0.135647	−	0.0346354i
$525$	6.63013	+	3.48043i	0.289363	+	0.151899i
$526$	14.8693	+	19.1430i	0.648333	+	0.834676i
$527$	−12.7151	−	22.0232i	−0.553877	−	0.959344i
$528$	10.9357	−	0.698752i	0.475915	−	0.0304093i
$529$	7.79883	−	13.5080i	0.339080	−	0.587303i
$530$	−17.7103	+	2.43804i	−0.769286	+	0.105902i
$531$	−1.69733	−	21.0668i	−0.0736578	−	0.914223i
$532$	−4.07727	−	14.5283i	−0.176772	−	0.629881i
$533$	19.0000	−	32.9089i	0.822980	−	1.42544i
$534$	0.502041	+	2.80670i	0.0217254	+	0.121458i
$535$	1.57390	−	0.908690i	0.0680455	−	0.0392861i
$536$	−4.72033	−	3.49099i	−0.203887	−	0.150788i
$537$	2.29158	−	1.44885i	0.0988889	−	0.0625226i
$538$	10.7373	−	26.3611i	0.462917	−	1.13651i
$539$			1.87809i			0.0808950i
$540$	2.40144	−	18.4545i	0.103342	−	0.794154i
$541$			23.6734i			1.01780i	0.860826	+	0.508900i	$0.169948\pi$
$541$			23.6734i			1.01780i	−0.860826	+	0.508900i	$0.830052\pi$
$542$	8.12475	+	3.30933i	0.348988	+	0.142148i
$543$	5.39186	−	3.40901i	0.231387	−	0.146295i
$544$	7.43442	−	19.5621i	0.318748	−	0.838717i
$545$	−6.92161	+	3.99619i	−0.296489	+	0.171178i
$546$	−35.9454	+	6.42962i	−1.53832	+	0.275163i
$547$	10.5319	−	18.2418i	0.450312	−	0.779964i	−0.548093	−	0.836417i	$-0.684646\pi$
$547$	10.5319	−	18.2418i	0.450312	−	0.779964i	0.998405	+	0.0564536i	$0.0179793\pi$
$548$	6.62409	+	23.6032i	0.282967	+	1.00828i
$549$	−8.69931	+	6.00266i	−0.371278	+	0.256187i
$550$	0.547007	+	3.97354i	0.0233245	+	0.169432i
$551$	7.98910	−	13.8375i	0.340347	−	0.589498i
$552$	0.972044	−	13.2933i	0.0413729	−	0.565800i
$553$	−10.8922	−	18.8659i	−0.463184	−	0.802259i
$554$	13.6781	−	10.6244i	0.581126	−	0.451389i
$555$	−14.3995	−	7.55892i	−0.611226	−	0.320858i
$556$	−0.612497	+	2.39880i	−0.0259756	+	0.101732i
$557$	9.64427			0.408641			0.204321	−	0.978904i	$-0.434502\pi$
$557$	9.64427			0.408641			0.204321	+	0.978904i	$0.434502\pi$
$558$	27.8059	+	8.79677i	1.17712	+	0.372397i
$559$		−	5.59535i		−	0.236658i
$560$	17.2647	−	0.407733i	0.729567	−	0.0172299i
$561$	−10.1264	+	0.407276i	−0.427537	+	0.0171952i
$562$	−19.5541	+	15.1886i	−0.824841	+	0.640694i
$563$	−36.8534	+	21.2773i	−1.55319	+	0.896733i	−0.555307	+	0.831645i	$0.687399\pi$
$563$	−36.8534	+	21.2773i	−1.55319	+	0.896733i	−0.997880	+	0.0650873i	$0.979267\pi$
$564$	25.1685	+	22.6780i	1.05978	+	0.954918i
$565$	−13.1733	−	7.60561i	−0.554205	−	0.319970i
$566$	−10.6391	+	1.46461i	−0.447196	+	0.0615622i
$567$	−3.47387	−	21.4185i	−0.145889	−	0.899491i
$568$	8.59779	−	3.74104i	0.360755	−	0.156971i
$569$	−8.25996	−	4.76889i	−0.346275	−	0.199922i	0.316768	−	0.948503i	$-0.397402\pi$
$569$	−8.25996	−	4.76889i	−0.346275	−	0.199922i	−0.663044	+	0.748581i	$0.730736\pi$
$570$	−8.84943	−	10.4936i	−0.370662	−	0.439531i
$571$	13.4455	+	23.2882i	0.562675	+	0.974582i	0.997262	+	0.0739518i	$0.0235611\pi$
$571$	13.4455	+	23.2882i	0.562675	+	0.974582i	−0.434587	+	0.900630i	$0.643106\pi$
$572$	−13.9931	−	13.6666i	−0.585082	−	0.571427i
$573$	41.0780	−	1.65212i	1.71606	−	0.0690185i
$574$	−7.90421	+	19.4057i	−0.329915	+	0.809977i
$575$	4.87880			0.203460
$576$	8.84886	+	22.3091i	0.368702	+	0.929547i
$577$	−8.52363			−0.354843			−0.177422	−	0.984135i	$-0.556776\pi$
$577$	−8.52363			−0.354843			−0.177422	+	0.984135i	$0.556776\pi$
$578$	1.76804	−	4.34072i	0.0735407	−	0.180550i
$579$	−20.6111	+	39.2636i	−0.856569	+	1.63174i
$580$	13.0823	+	12.7770i	0.543213	+	0.530535i
$581$	18.8667	+	32.6781i	0.782724	+	1.35572i
$582$	−11.1997	+	31.0086i	−0.464241	+	1.28535i
$583$	−9.66924	−	5.58254i	−0.400459	−	0.231205i
$584$	−1.63660	+	0.712114i	−0.0677232	+	0.0294675i
$585$	−27.3412	+	18.8659i	−1.13042	+	0.780008i
$586$	−35.3513	+	4.86655i	−1.46035	+	0.201035i
$587$	−19.4568	−	11.2334i	−0.803067	−	0.463651i	0.0414756	−	0.999140i	$-0.486794\pi$
$587$	−19.4568	−	11.2334i	−0.803067	−	0.463651i	−0.844542	+	0.535489i	$0.820127\pi$
$588$	−3.91248	+	1.26970i	−0.161348	+	0.0523616i
$589$	18.6297	−	10.7559i	0.767625	−	0.443189i
$590$	14.0903	−	10.9447i	0.580090	−	0.450584i
$591$	−5.33756	−	8.44216i	−0.219558	−	0.347264i
$592$	20.9673	−	0.495174i	0.861749	−	0.0203515i
$593$		−	28.8424i		−	1.18442i	−0.805785	−	0.592208i	$-0.798257\pi$
$593$		−	28.8424i		−	1.18442i	0.805785	−	0.592208i	$-0.201743\pi$
$594$	8.25462	−	8.18223i	0.338691	−	0.335721i
$595$	−15.9719			−0.654783
$596$	2.93890	−	11.5100i	0.120382	−	0.471467i
$597$	1.81773	−	1.14926i	0.0743947	−	0.0470361i
$598$	−18.7892	+	14.5945i	−0.768348	+	0.596813i
$599$	−8.40225	−	14.5531i	−0.343307	−	0.594625i	0.641738	−	0.766924i	$-0.278214\pi$
$599$	−8.40225	−	14.5531i	−0.343307	−	0.594625i	−0.985045	+	0.172299i	$0.944880\pi$
$600$	−7.90797	+	3.82589i	−0.322841	+	0.156191i
$601$	14.8802	−	25.7732i	0.606974	−	1.05131i	−0.384762	−	0.923016i	$-0.625716\pi$
$601$	14.8802	−	25.7732i	0.606974	−	1.05131i	0.991736	−	0.128294i	$-0.0409502\pi$
$602$	0.420769	+	3.05653i	0.0171493	+	0.124575i
$603$	−6.20702	+	0.500092i	−0.252769	+	0.0203653i
$604$	7.46710	+	26.6070i	0.303832	+	1.08263i
$605$	−7.60926	+	13.1796i	−0.309360	+	0.535828i
$606$	−5.45932	+	15.1153i	−0.221770	+	0.614017i
$607$	−20.9599	+	12.1012i	−0.850737	+	0.491173i	−0.860899	−	0.508775i	$-0.830098\pi$
$607$	−20.9599	+	12.1012i	−0.850737	+	0.491173i	0.0101625	+	0.999948i	$0.496765\pi$
$608$	16.5479	+	6.28889i	0.671105	+	0.255048i
$609$	18.8782	+	9.90993i	0.764981	+	0.401571i
$610$	−8.26312	−	3.36569i	−0.334564	−	0.136273i
$611$		−	60.4720i		−	2.44643i
$612$	−7.69452	−	20.8203i	−0.311032	−	0.841609i
$613$			38.3189i			1.54769i	0.633377	+	0.773843i	$0.281668\pi$
$613$			38.3189i			1.54769i	−0.633377	+	0.773843i	$0.718332\pi$
$614$	−15.7906	+	38.7677i	−0.637259	+	1.56454i
$615$	0.766020	+	19.0461i	0.0308889	+	0.768014i
$616$	8.67163	+	6.41324i	0.349390	+	0.258397i
$617$	−7.31357	+	4.22249i	−0.294433	+	0.169991i	−0.639939	−	0.768425i	$-0.721041\pi$
$617$	−7.31357	+	4.22249i	−0.294433	+	0.169991i	0.345506	+	0.938417i	$0.387707\pi$
$618$	11.0741	−	9.33894i	0.445466	−	0.375667i
$619$	4.12431	−	7.14352i	0.165770	−	0.287122i	−0.771158	−	0.636643i	$-0.780322\pi$
$619$	4.12431	−	7.14352i	0.165770	−	0.287122i	0.936929	+	0.349521i	$0.113656\pi$
$620$	6.65231	+	23.7038i	0.267163	+	0.951966i
$621$	−8.49018	−	11.3040i	−0.340699	−	0.453613i
$622$	−29.0307	+	3.99644i	−1.16403	+	0.160243i
$623$	−1.40318	+	2.43038i	−0.0562173	+	0.0973713i
$624$	19.0103	−	38.3903i	0.761022	−	1.53684i
$625$	6.40923	+	11.1011i	0.256369	+	0.444044i
$626$	−3.01345	−	3.87957i	−0.120442	−	0.155059i
$627$	−0.344521	−	8.56609i	−0.0137589	−	0.342097i
$628$	−11.1656	−	2.85096i	−0.445555	−	0.113766i
$629$	−19.3972			−0.773415
$630$	13.5168	−	12.3618i	0.538521	−	0.492505i
$631$			34.0954i			1.35732i	0.734454	+	0.678659i	$0.237439\pi$
$631$			34.0954i			1.35732i	−0.734454	+	0.678659i	$0.762561\pi$
$632$	25.3933	+	2.88662i	1.01009	+	0.114824i
$633$	−2.61147	+	4.97478i	−0.103797	+	0.197730i
$634$	−13.2625	−	17.0744i	−0.526721	−	0.678110i
$635$	24.6735	−	14.2452i	0.979138	−	0.565305i
$636$	5.09270	−	23.9174i	0.201939	−	0.948385i
$637$	6.35854	+	3.67111i	0.251935	+	0.145455i
$638$	1.55751	+	11.3140i	0.0616624	+	0.447924i
$639$	4.26486	−	8.98432i	0.168715	−	0.355414i
$640$	−11.6590	+	16.5692i	−0.460864	+	0.654954i
$641$	20.9715	+	12.1079i	0.828324	+	0.478233i	0.853279	−	0.521455i	$-0.174611\pi$
$641$	20.9715	+	12.1079i	0.828324	+	0.478233i	−0.0249544	+	0.999689i	$0.507944\pi$
$642$	0.437713	+	2.44707i	0.0172752	+	0.0965782i
$643$	11.3299	+	19.6240i	0.446808	+	0.773895i	0.998176	−	0.0603676i	$-0.0192273\pi$
$643$	11.3299	+	19.6240i	0.446808	+	0.773895i	−0.551368	+	0.834262i	$0.685894\pi$
$644$	9.16633	−	9.38536i	0.361204	−	0.369835i
$645$	1.49992	+	2.37235i	0.0590592	+	0.0934110i
$646$	−15.1628	−	6.17605i	−0.596574	−	0.242993i
$647$	−38.6020			−1.51760			−0.758800	−	0.651323i	$-0.774214\pi$
$647$	−38.6020			−1.51760			−0.758800	+	0.651323i	$0.774214\pi$
$648$	22.6261	+	11.6646i	0.888835	+	0.458227i
$649$	11.1428			0.437393
$650$	14.5222	+	5.91512i	0.569609	+	0.232010i
$651$	15.3400	+	24.2625i	0.601221	+	0.950921i
$652$	−16.1522	−	15.7752i	−0.632568	−	0.617805i
$653$	−13.1416	−	22.7619i	−0.514271	−	0.890743i	−0.999863	−	0.0165576i	$-0.994729\pi$
$653$	−13.1416	−	22.7619i	−0.514271	−	0.890743i	0.485592	−	0.874185i	$-0.338604\pi$
$654$	−1.92495	−	10.7616i	−0.0752716	−	0.420812i
$655$	−2.48501	−	1.43472i	−0.0970973	−	0.0560592i
$656$	−12.7903	−	20.9927i	−0.499378	−	0.819627i
$657$	−0.811823	+	1.71018i	−0.0316722	+	0.0667205i
$658$	4.54748	+	33.0335i	0.177279	+	1.28778i
$659$	33.1862	+	19.1601i	1.29275	+	0.746370i	0.979141	−	0.203182i	$-0.0651283\pi$
$659$	33.1862	+	19.1601i	1.29275	+	0.746370i	0.313610	+	0.949552i	$0.398462\pi$
$660$	9.59641	+	2.04335i	0.373540	+	0.0795374i
$661$	38.7145	−	22.3518i	1.50582	−	0.869385i	0.505842	−	0.862626i	$-0.331182\pi$
$661$	38.7145	−	22.3518i	1.50582	−	0.869385i	0.999977	−	0.00675901i	$-0.00215148\pi$
$662$	−5.37843	−	6.92429i	−0.209039	−	0.269120i
$663$	−18.4152	+	35.0805i	−0.715189	+	1.36242i
$664$	−43.9845	−	5.00000i	−1.70693	−	0.194038i
$665$		−	13.5109i		−	0.523928i
$666$	16.4155	−	15.0128i	0.636089	−	0.581736i
$667$	13.8915			0.537882
$668$	0.374509	−	1.46674i	0.0144902	−	0.0567497i
$669$	−0.974297	−	24.2247i	−0.0376685	−	0.936580i
$670$	−3.22467	−	4.15150i	−0.124580	−	0.160387i
$671$	−2.78616	−	4.82576i	−0.107558	−	0.186297i
$672$	−7.49768	+	22.4007i	−0.289229	+	0.864127i
$673$	−12.8138	+	22.1942i	−0.493937	+	0.855524i	−0.999976	−	0.00698696i	$-0.997776\pi$
$673$	−12.8138	+	22.1942i	−0.493937	+	0.855524i	0.506039	+	0.862511i	$0.331109\pi$
$674$	−26.9860	+	3.71496i	−1.03946	+	0.143095i
$675$	−3.65428	+	8.57125i	−0.140653	+	0.329908i
$676$	−48.5897	+	13.6364i	−1.86883	+	0.524476i
$677$	−11.1613	+	19.3320i	−0.428964	+	0.742988i	−0.996781	−	0.0801666i	$-0.974455\pi$
$677$	−11.1613	+	19.3320i	−0.428964	+	0.742988i	0.567817	+	0.823155i	$0.307788\pi$
$678$	15.9058	−	13.4136i	0.610859	−	0.515145i
$679$	−28.1027	+	16.2251i	−1.07848	+	0.622662i
$680$	11.1418	−	15.0653i	0.427267	−	0.577727i
$681$	−0.703562	−	17.4932i	−0.0269605	−	0.670340i
$682$	−5.80013	+	14.2399i	−0.222099	+	0.545275i
$683$		−	20.5229i		−	0.785288i	−0.919691	−	0.392644i	$-0.871560\pi$
$683$		−	20.5229i		−	0.785288i	0.919691	−	0.392644i	$-0.128440\pi$
$684$	17.6122	−	6.50891i	0.673419	−	0.248875i
$685$			21.9502i			0.838676i
$686$	−25.8532	−	10.5304i	−0.987081	−	0.402053i
$687$	17.5852	+	9.23119i	0.670917	+	0.352192i
$688$	−3.17656	−	1.73530i	−0.121105	−	0.0661579i
$689$	−37.8010	+	21.8244i	−1.44010	+	0.831444i
$690$	4.05408	−	11.2246i	0.154336	−	0.427313i
$691$	−5.97960	+	10.3570i	−0.227475	+	0.393998i	−0.957059	−	0.289893i	$-0.906380\pi$
$691$	−5.97960	+	10.3570i	−0.227475	+	0.393998i	0.729584	+	0.683891i	$0.239714\pi$
$692$	17.8209	−	5.00132i	0.677449	−	0.190122i
$693$	11.4028	−	0.918709i	0.433156	−	0.0348989i
$694$	−5.10412	−	37.0770i	−0.193750	−	1.40742i
$695$	−1.10837	+	1.91975i	−0.0420429	+	0.0728204i
$696$	−22.5166	+	10.8936i	−0.853488	+	0.412920i
$697$	11.3675	+	19.6891i	0.430576	+	0.745779i
$698$	−19.1335	+	14.8619i	−0.724214	+	0.562532i
$699$	9.87985	−	6.24654i	0.373690	−	0.236266i
$700$	−8.37776	−	2.13913i	−0.316650	−	0.0808516i
$701$	41.9171			1.58319			0.791593	−	0.611049i	$-0.209252\pi$
$701$	41.9171			1.58319			0.791593	+	0.611049i	$0.209252\pi$
$702$	−11.5668	−	43.9410i	−0.436561	−	1.65845i
$703$		−	16.4084i		−	0.618853i
$704$	−12.0984	+	3.70563i	−0.455977	+	0.139661i
$705$	16.2104	+	25.6392i	0.610520	+	0.965630i
$706$	34.5799	−	26.8599i	1.30143	−	1.01088i
$707$	−13.6988	+	7.90899i	−0.515195	+	0.297448i
$708$	7.53320	+	23.2130i	0.283115	+	0.872396i
$709$	4.41486	+	2.54892i	0.165803	+	0.0957266i	0.580606	−	0.814185i	$-0.302816\pi$
$709$	4.41486	+	2.54892i	0.165803	+	0.0957266i	−0.414802	+	0.909912i	$0.636149\pi$
$710$	8.31700	−	1.14494i	0.312131	−	0.0429688i
$711$	22.3112	−	15.3951i	0.836734	−	0.577360i
$712$	−1.31359	−	3.01894i	−0.0492289	−	0.113140i
$713$	16.1968	+	9.35122i	0.606575	+	0.350206i
$714$	7.42149	−	20.5480i	0.277742	−	0.768989i
$715$	−8.75666	−	15.1670i	−0.327480	−	0.567213i
$716$	−2.18738	+	2.23965i	−0.0817463	+	0.0836996i
$717$	−0.109147	+	0.207923i	−0.00407619	+	0.00776503i
$718$	3.43441	−	8.43183i	0.128171	−	0.314673i
$719$	35.1676			1.31153			0.655765	−	0.754965i	$-0.272346\pi$
$719$	35.1676			1.31153			0.655765	+	0.754965i	$0.272346\pi$
$720$	2.23099	+	21.3729i	0.0831441	+	0.796522i
$721$	14.2582			0.531003
$722$	−4.91159	+	12.0585i	−0.182790	+	0.448770i
$723$	−33.6350	+	1.35277i	−1.25090	+	0.0503101i
$724$	−5.14670	+	5.26968i	−0.191275	+	0.195846i
$725$	−4.57787	−	7.92911i	−0.170018	−	0.294480i
$726$	−13.4200	−	15.9134i	−0.498064	−	0.590604i
$727$	−19.9209	−	11.5013i	−0.738826	−	0.426561i	0.0828164	−	0.996565i	$-0.473609\pi$
$727$	−19.9209	−	11.5013i	−0.738826	−	0.426561i	−0.821642	+	0.570003i	$0.806942\pi$
$728$	38.6634	−	16.8231i	1.43296	−	0.623506i
$729$	26.2185	−	6.44905i	0.971056	−	0.238854i
$730$	−1.58316	+	0.217941i	−0.0585952	+	0.00806637i
$731$	2.89915	+	1.67383i	0.107229	+	0.0619087i
$732$	8.16955	−	9.06670i	0.301955	−	0.335115i
$733$	−7.38177	+	4.26187i	−0.272652	+	0.157416i	−0.630092	−	0.776520i	$-0.716983\pi$
$733$	−7.38177	+	4.26187i	−0.272652	+	0.157416i	0.357440	+	0.933936i	$0.383650\pi$
$734$	30.7872	−	23.9139i	1.13638	−	0.882679i
$735$	−3.68003	+	0.148008i	−0.135740	+	0.00545935i
$736$	2.45833	+	15.1931i	0.0906152	+	0.560027i
$737$		−	3.28305i		−	0.120933i
$738$	−24.8590	−	7.86449i	−0.915073	−	0.289496i
$739$	32.3956			1.19169			0.595846	−	0.803099i	$-0.296817\pi$
$739$	32.3956			1.19169			0.595846	+	0.803099i	$0.296817\pi$
$740$	18.1951	+	4.64584i	0.668865	+	0.170784i
$741$	−29.6752	−	15.5777i	−1.09015	−	0.572263i
$742$	19.0081	−	14.7645i	0.697808	−	0.542021i
$743$	−2.22350	−	3.85122i	−0.0815725	−	0.141288i	0.822353	−	0.568978i	$-0.192661\pi$
$743$	−2.22350	−	3.85122i	−0.0815725	−	0.141288i	−0.903926	+	0.427690i	$0.859328\pi$
$744$	−33.5862	−	2.45593i	−1.23133	−	0.0900386i
$745$	5.31821	−	9.21141i	0.194844	−	0.337480i
$746$	5.17887	+	37.6200i	0.189612	+	1.37737i
$747$	−38.6458	+	26.6662i	−1.41398	+	0.975666i
$748$	11.2671	−	3.16205i	0.411967	−	0.115616i
$749$	−1.22339	+	2.11897i	−0.0447016	+	0.0774255i
$750$	−29.3324	+	5.24674i	−1.07107	+	0.191584i
$751$	−32.3801	+	18.6946i	−1.18157	+	0.682177i	−0.956376	−	0.292138i	$-0.905633\pi$
$751$	−32.3801	+	18.6946i	−1.18157	+	0.682177i	−0.225189	+	0.974315i	$0.572300\pi$
$752$	−34.3308	−	18.7544i	−1.25191	−	0.683902i
$753$	−27.4990	+	17.3863i	−1.00212	+	0.633591i
$754$	41.3495	+	16.8423i	1.50586	+	0.613359i
$755$			24.7437i			0.900517i
$756$	9.62286	+	23.1335i	0.349980	+	0.841357i
$757$		−	46.7837i		−	1.70038i	−0.526474	−	0.850191i	$-0.676486\pi$
$757$		−	46.7837i		−	1.70038i	0.526474	−	0.850191i	$-0.323514\pi$
$758$	2.47514	−	6.07673i	0.0899011	−	0.220717i
$759$	6.29988	−	3.98310i	0.228671	−	0.144577i
$760$	12.7440	+	9.42499i	0.462272	+	0.341880i
$761$	5.83226	−	3.36726i	0.211419	−	0.122063i	−0.390552	−	0.920581i	$-0.627716\pi$
$761$	5.83226	−	3.36726i	0.211419	−	0.122063i	0.601971	+	0.798518i	$0.294382\pi$
$762$	6.86189	+	38.3620i	0.248580	+	1.38971i
$763$	5.38016	−	9.31870i	0.194775	−	0.337360i
$764$	−45.7053	+	12.8269i	−1.65356	+	0.464061i
$765$	−1.59608	−	19.8101i	−0.0577063	−	0.716237i
$766$	49.7442	−	6.84792i	1.79733	−	0.247425i
$767$	21.7809	−	37.7255i	0.786461	−	1.36219i
$768$	−15.8989	−	22.6985i	−0.573704	−	0.819063i
$769$	−8.91160	−	15.4353i	−0.321361	−	0.556613i	0.659408	−	0.751785i	$-0.270807\pi$
$769$	−8.91160	−	15.4353i	−0.321361	−	0.556613i	−0.980769	+	0.195172i	$0.937473\pi$
$770$	5.92399	+	7.62665i	0.213486	+	0.274845i
$771$	33.1036	+	17.3774i	1.19220	+	0.625833i
$772$	12.6679	−	49.6131i	0.455929	−	1.78561i
$773$	−18.9682			−0.682237			−0.341119	−	0.940020i	$-0.610806\pi$
$773$	−18.9682			−0.682237			−0.341119	+	0.940020i	$0.610806\pi$
$774$	−3.74901	+	0.827326i	−0.134755	+	0.0297376i
$775$		−	12.3266i		−	0.442783i
$776$	4.29992	−	37.8259i	0.154358	−	1.35787i
$777$	21.8775	−	0.879894i	0.784850	−	0.0315660i
$778$	−5.55078	−	7.14617i	−0.199005	−	0.256203i
$779$	−16.6554	+	9.61597i	−0.596740	+	0.344528i
$780$	25.6762	−	28.4959i	0.919356	−	1.02032i
$781$	4.54081	+	2.62164i	0.162483	+	0.0938096i
$782$	−1.94122	−	14.1013i	−0.0694178	−	0.504260i
$783$	−10.4049	+	24.4052i	−0.371842	+	0.872169i
$784$	4.05614	−	2.47130i	0.144862	−	0.0882607i
$785$	−8.93578	−	5.15907i	−0.318932	−	0.184135i
$786$	3.00047	−	2.53034i	0.107023	−	0.0902541i
$787$	−1.03810	−	1.79804i	−0.0370041	−	0.0640931i	0.846930	−	0.531704i	$-0.178448\pi$
$787$	−1.03810	−	1.79804i	−0.0370041	−	0.0640931i	−0.883934	+	0.467611i	$0.845115\pi$
$788$	8.25085	+	8.05830i	0.293924	+	0.287065i
$789$	−29.6632	+	1.19303i	−1.05604	+	0.0424730i
$790$	21.1925	+	8.63200i	0.753994	+	0.307113i
$791$	20.4792			0.728155
$792$	−7.08787	+	11.3964i	−0.251857	+	0.404955i
$793$	−21.7844			−0.773588
$794$	−3.95401	−	1.61053i	−0.140323	−	0.0571554i
$795$	10.1767	−	19.3864i	0.360931	−	0.687564i
$796$	−1.73508	+	1.77654i	−0.0614982	+	0.0629678i
$797$	17.7593	+	30.7601i	0.629068	+	1.08958i	0.987739	+	0.156113i	$0.0498965\pi$
$797$	17.7593	+	30.7601i	0.629068	+	1.08958i	−0.358671	+	0.933464i	$0.616770\pi$
$798$	17.3819	+	6.27796i	0.615312	+	0.222237i
$799$	31.3327	+	18.0900i	1.10847	+	0.639977i
$800$	7.86192	−	6.40999i	0.277961	−	0.226628i
$801$	−3.15466	−	1.49752i	−0.111464	−	0.0529122i
$802$	−5.59407	−	40.6361i	−0.197533	−	1.43491i
$803$	−0.864352	−	0.499034i	−0.0305023	−	0.0176105i
$804$	6.83934	−	2.21954i	0.241205	−	0.0782772i
$805$	10.1727	−	5.87320i	0.358540	−	0.207003i
$806$	36.8738	+	47.4720i	1.29883	+	1.67213i
$807$	18.6297	+	29.4657i	0.655798	+	1.03724i
$808$	2.09601	−	18.4384i	0.0737375	−	0.648661i
$809$		−	41.7225i		−	1.46688i	−0.679752	−	0.733442i	$-0.737913\pi$
$809$		−	41.7225i		−	1.46688i	0.679752	−	0.733442i	$-0.262087\pi$
$810$	16.6832	+	15.5297i	0.586189	+	0.545659i
$811$	−3.03064			−0.106420			−0.0532102	−	0.998583i	$-0.516945\pi$
$811$	−3.03064			−0.106420			−0.0532102	+	0.998583i	$0.516945\pi$
$812$	−23.8542	−	6.09081i	−0.837119	−	0.213746i
$813$	−9.08162	+	5.74186i	−0.318506	+	0.201376i
$814$	7.19443	+	9.26224i	0.252165	+	0.324641i
$815$	−10.1078	−	17.5071i	−0.354059	−	0.613248i
$816$	14.2045	+	21.3342i	0.497258	+	0.746848i
$817$	−1.41592	+	2.45244i	−0.0495366	+	0.0858000i
$818$	−1.85540	+	0.255419i	−0.0648725	+	0.00893052i
$819$	19.1787	−	40.4016i	0.670157	−	1.41175i
$820$	−5.94730	−	21.1916i	−0.207689	−	0.740044i
$821$	−25.9259	+	44.9049i	−0.904819	+	1.56719i	−0.0836589	+	0.996494i	$0.526661\pi$
$821$	−25.9259	+	44.9049i	−0.904819	+	1.56719i	−0.821160	+	0.570698i	$0.806673\pi$
$822$	−28.2393	−	10.1994i	−0.984957	−	0.355745i
$823$	28.3812	−	16.3859i	0.989307	−	0.571177i	0.0842401	−	0.996445i	$-0.473154\pi$
$823$	28.3812	−	16.3859i	0.989307	−	0.571177i	0.905067	+	0.425269i	$0.139820\pi$
$824$	−9.94633	+	13.4489i	−0.346497	+	0.468514i
$825$	−4.34959	−	2.28328i	−0.151433	−	0.0794937i
$826$	−9.06110	+	22.2460i	−0.315276	+	0.774036i
$827$			52.8295i			1.83706i	0.395350	+	0.918531i	$0.370623\pi$
$827$			52.8295i			1.83706i	−0.395350	+	0.918531i	$0.629377\pi$
$828$	12.5568	+	10.4312i	0.436379	+	0.362511i
$829$		−	0.0144624i		−	0.000502300i	−1.00000		0.000251150i	$-0.999920\pi$
$829$		−	0.0144624i		−	0.000502300i	1.00000		0.000251150i	$-7.99435e-5\pi$
$830$	−36.7081	−	14.9517i	−1.27416	−	0.518982i
$831$	0.852444	+	21.1950i	0.0295710	+	0.735245i
$832$	−11.1029	+	48.2044i	−0.384923	+	1.67119i
$833$	−3.80427	+	2.19639i	−0.131810	+	0.0761006i
$834$	−1.95477	−	2.31796i	−0.0676881	−	0.0802645i
$835$	0.677708	−	1.17382i	0.0234531	−	0.0406219i
$836$	2.67483	+	9.53104i	0.0925108	+	0.329638i
$837$	−28.5602	+	21.4509i	−0.987184	+	0.741453i
$838$	6.07919	+	44.1600i	0.210002	+	1.52548i
$839$	16.6802	−	28.8909i	0.575864	−	0.997425i	−0.420083	−	0.907486i	$-0.637999\pi$
$839$	16.6802	−	28.8909i	0.575864	−	0.997425i	0.995947	−	0.0899399i	$-0.0286675\pi$
$840$	−11.8831	+	17.4971i	−0.410004	+	0.603707i
$841$	1.46530	+	2.53797i	0.0505275	+	0.0875162i
$842$	−39.9599	+	31.0388i	−1.37711	+	1.06967i
$843$	−1.21865	−	30.3002i	−0.0419725	−	1.04359i
$844$	1.60505	−	6.28608i	0.0552483	−	0.216376i
$845$	−45.1869			−1.55448
$846$	−40.5175	+	8.94137i	−1.39302	+	0.307411i
$847$		−	20.4890i		−	0.704010i
$848$	0.666663	+	28.2286i	0.0228933	+	0.969376i
$849$	6.11348	−	11.6460i	0.209814	−	0.399690i
$850$	−7.40911	+	5.75501i	−0.254130	+	0.197395i
$851$	12.3543	−	7.13276i	0.423500	−	0.244508i
$852$	−2.39160	+	11.2319i	−0.0819349	+	0.384799i
$853$	32.7219	+	18.8920i	1.12038	+	0.646850i	0.941497	−	0.337021i	$-0.109419\pi$
$853$	32.7219	+	18.8920i	1.12038	+	0.646850i	0.178880	+	0.983871i	$0.442753\pi$
$854$	11.9000	−	1.63819i	0.407210	−	0.0560576i
$855$	16.7577	−	1.35015i	0.573101	−	0.0461741i
$856$	−1.14528	−	2.63211i	−0.0391447	−	0.0899637i
$857$	9.00665	+	5.19999i	0.307661	+	0.177628i	0.645879	−	0.763439i	$-0.276491\pi$
$857$	9.00665	+	5.19999i	0.307661	+	0.177628i	−0.338218	+	0.941068i	$0.609824\pi$
$858$	23.5814	−	4.21805i	0.805055	−	0.144002i
$859$	−10.3547	−	17.9348i	−0.353297	−	0.611929i	0.633528	−	0.773720i	$-0.281606\pi$
$859$	−10.3547	−	17.9348i	−0.353297	−	0.611929i	−0.986825	+	0.161791i	$0.948273\pi$
$860$	−2.31859	−	2.26448i	−0.0790632	−	0.0772180i
$861$	−13.7142	−	21.6911i	−0.467380	−	0.739232i
$862$	−9.12930	+	22.4134i	−0.310945	+	0.763404i
$863$	4.67705			0.159209			0.0796043	−	0.996827i	$-0.474634\pi$
$863$	4.67705			0.159209			0.0796043	+	0.996827i	$0.474634\pi$
$864$	−28.5332	−	7.06096i	−0.970719	−	0.240219i
$865$	16.5729			0.563495
$866$	−10.1946	+	25.0289i	−0.346428	+	0.850517i
$867$	3.06764	+	4.85194i	0.104183	+	0.164780i
$868$	−23.7127	−	23.1593i	−0.804861	−	0.786077i
$869$	7.14567	+	12.3767i	0.242400	+	0.419849i
$870$	−22.0464	+	3.94349i	−0.747444	+	0.133697i
$871$	−11.1152	−	6.41739i	−0.376626	−	0.217445i
$872$	5.03664	+	11.5754i	0.170562	+	0.391992i
$873$	−22.9325	−	33.2348i	−0.776149	−	1.12483i
$874$	11.9285	−	1.64211i	0.403487	−	0.0555450i
$875$	−25.3995	−	14.6644i	−0.858660	−	0.495748i
$876$	0.455246	−	2.13802i	0.0153813	−	0.0722369i
$877$	−9.04467	+	5.22194i	−0.305417	+	0.176333i	−0.644874	−	0.764289i	$-0.723090\pi$
$877$	−9.04467	+	5.22194i	−0.305417	+	0.176333i	0.339457	+	0.940622i	$0.389757\pi$
$878$	38.0300	−	29.5397i	1.28345	−	0.996918i
$879$	20.3136	−	38.6969i	0.685162	−	1.30522i
$880$	−11.3262	+	0.267487i	−0.381807	+	0.00901697i
$881$			29.7734i			1.00309i	0.865131	+	0.501546i	$0.167235\pi$
$881$			29.7734i			1.00309i	−0.865131	+	0.501546i	$0.832765\pi$
$882$	1.51955	−	4.80317i	0.0511659	−	0.161731i
$883$	−52.9294			−1.78122			−0.890608	−	0.454772i	$-0.849721\pi$
$883$	−52.9294			−1.78122			−0.890608	+	0.454772i	$0.849721\pi$
$884$	11.3183	−	44.3274i	0.380676	−	1.49089i
$885$	0.878137	+	21.8338i	0.0295183	+	0.733935i
$886$	22.1286	−	17.1883i	0.743424	−	0.577453i
$887$	22.4416	+	38.8700i	0.753515	+	1.30513i	0.946109	+	0.323848i	$0.104977\pi$
$887$	22.4416	+	38.8700i	0.753515	+	1.30513i	−0.192594	+	0.981278i	$0.561690\pi$
$888$	−14.4315	+	21.2495i	−0.484288	+	0.713085i
$889$	−19.1787	+	33.2184i	−0.643232	+	1.11411i
$890$	−0.402022	−	2.92035i	−0.0134758	−	0.0978902i
$891$	2.27898	+	14.0512i	0.0763486	+	0.470734i
$892$	7.56434	+	26.9535i	0.253273	+	0.902471i
$893$	−15.3026	+	26.5048i	−0.512081	+	0.886951i
$894$	9.37943	+	11.1221i	0.313695	+	0.371979i
$895$	−2.42753	+	1.40153i	−0.0811434	+	0.0468481i
$896$	2.44012	−	27.1672i	0.0815188	−	0.907592i
$897$	−1.17098	−	29.1149i	−0.0390979	−	0.972119i
$898$	11.4460	+	4.66211i	0.381957	+	0.155577i
$899$		−	35.0978i		−	1.17058i
$900$	1.81600	−	10.6048i	0.0605335	−	0.353494i
$901$		−	26.1148i		−	0.870009i
$902$	5.18543	−	12.7308i	0.172656	−	0.423889i
$903$	−3.34579	−	1.75635i	−0.111341	−	0.0584475i
$904$	−14.2860	+	19.3167i	−0.475145	+	0.642465i
$905$	−5.71174	+	3.29768i	−0.189865	+	0.109618i
$906$	−31.8331	−	11.4974i	−1.05758	−	0.381977i
$907$	−8.19627	+	14.1964i	−0.272153	+	0.471382i	−0.969413	−	0.245436i	$-0.921069\pi$
$907$	−8.19627	+	14.1964i	−0.272153	+	0.471382i	0.697260	+	0.716818i	$0.254402\pi$
$908$	5.46238	+	19.4637i	0.181275	+	0.645927i
$909$	−11.1786	−	16.2004i	−0.370769	−	0.537335i
$910$	37.4008	−	5.14869i	1.23982	−	0.170677i
$911$	−13.4518	+	23.2991i	−0.445677	+	0.771935i	−0.998099	−	0.0616295i	$-0.980370\pi$
$911$	−13.4518	+	23.2991i	−0.445677	+	0.771935i	0.552422	+	0.833564i	$0.313704\pi$
$912$	−18.0470	+	12.0158i	−0.597595	+	0.397884i
$913$	−12.3772	−	21.4380i	−0.409626	−	0.709493i
$914$	2.17022	+	2.79398i	0.0717846	+	0.0924168i
$915$	9.23629	−	5.83965i	0.305342	−	0.193053i
$916$	−22.2204	−	5.67365i	−0.734184	−	0.187463i
$917$	3.86319			0.127574
$918$	26.2276	+	7.15162i	0.865640	+	0.236038i
$919$		−	22.2518i		−	0.734020i	−0.930217	−	0.367010i	$-0.880381\pi$
$919$		−	22.2518i		−	0.734020i	0.930217	−	0.367010i	$-0.119619\pi$
$920$	−1.55650	+	13.6923i	−0.0513162	+	0.451423i
$921$	−27.3976	−	43.3335i	−0.902782	−	1.42789i
$922$	4.57046	+	5.88409i	0.150520	+	0.193782i
$923$	17.7519	−	10.2491i	0.584310	−	0.337352i
$924$	−12.5644	+	4.07748i	−0.413339	+	0.134139i
$925$	−8.14257	−	4.70112i	−0.267726	−	0.154572i
$926$	−3.39012	−	24.6263i	−0.111406	−	0.809271i
$927$	1.42483	+	17.6847i	0.0467976	+	0.580841i
$928$	22.3855	−	18.2513i	0.734839	−	0.599130i
$929$	−8.55489	−	4.93917i	−0.280677	−	0.162049i	0.353053	−	0.935603i	$-0.385144\pi$
$929$	−8.55489	−	4.93917i	−0.280677	−	0.162049i	−0.633730	+	0.773555i	$0.718477\pi$
$930$	−28.3596	−	10.2429i	−0.929947	−	0.335877i
$931$	−1.85796	−	3.21809i	−0.0608923	−	0.105469i
$932$	−9.43062	+	9.65597i	−0.308910	+	0.316292i
$933$	16.6817	−	31.7782i	0.546134	−	1.04037i
$934$	3.01032	+	1.22615i	0.0985006	+	0.0401207i
$935$	10.4781			0.342670
$936$	24.7296	+	46.2737i	0.808312	+	1.51250i
$937$	−2.11802			−0.0691926			−0.0345963	−	0.999401i	$-0.511015\pi$
$937$	−2.11802			−0.0691926			−0.0345963	+	0.999401i	$0.511015\pi$
$938$	6.55442	+	2.66971i	0.214010	+	0.0871692i
$939$	6.01161	−	0.241782i	0.196181	−	0.00789026i
$940$	−25.0582	−	24.4734i	−0.817310	−	0.798236i
$941$	3.56180	+	6.16922i	0.116111	+	0.201111i	0.918223	−	0.396063i	$-0.129624\pi$
$941$	3.56180	+	6.16922i	0.116111	+	0.201111i	−0.802112	+	0.597173i	$0.796290\pi$
$942$	10.7893	−	9.09877i	0.351535	−	0.296454i
$943$	−14.4803	−	8.36018i	−0.471542	−	0.272245i
$944$	−14.6623	−	24.0653i	−0.477219	−	0.783257i
$945$	2.69879	+	22.2708i	0.0877918	+	0.724471i
$946$	−0.276039	−	2.00518i	−0.00897480	−	0.0651942i
$947$	44.5581	+	25.7256i	1.44794	+	0.835970i	0.998359	−	0.0572679i	$-0.0182389\pi$
$947$	44.5581	+	25.7256i	1.44794	+	0.835970i	0.449584	+	0.893238i	$0.351572\pi$
$948$	−20.9525	+	23.2534i	−0.680505	+	0.755236i
$949$	−3.37910	+	1.95093i	−0.109690	+	0.0633297i
$950$	−4.86826	−	6.26748i	−0.157947	−	0.203344i
$951$	26.4577	−	1.06411i	0.857949	−	0.0345060i
$952$	−2.84936	+	25.0655i	−0.0923482	+	0.812378i
$953$			45.3652i			1.46952i	0.678326	+	0.734761i	$0.262706\pi$
$953$			45.3652i			1.46952i	−0.678326	+	0.734761i	$0.737294\pi$
$954$	20.2121	+	22.1006i	0.654391	+	0.715532i
$955$	−42.5046			−1.37542
$956$	0.0670839	−	0.262729i	0.00216965	−	0.00849727i
$957$	−12.3847	−	6.50125i	−0.400341	−	0.210156i
$958$	31.2690	+	40.2562i	1.01025	+	1.30062i
$959$	−14.7760	−	25.5928i	−0.477143	−	0.826436i
$960$	−8.21446	−	23.4143i	−0.265121	−	0.755693i
$961$	8.12641	−	14.0754i	0.262142	−	0.454044i
$962$	45.4216	−	6.25286i	1.46445	−	0.201600i
$963$	−2.75044	−	1.30564i	−0.0886318	−	0.0420735i
$964$	37.4239	−	10.5028i	1.20534	−	0.338271i
$965$	22.9238	−	39.7052i	0.737944	−	1.27816i
$966$	2.82910	+	15.8163i	0.0910248	+	0.508882i
$967$	−2.55341	+	1.47421i	−0.0821121	+	0.0474075i	−0.540494	−	0.841348i	$-0.681763\pi$
$967$	−2.55341	+	1.47421i	−0.0821121	+	0.0474075i	0.458382	+	0.888755i	$0.348429\pi$
$968$	19.3260	+	14.2928i	0.621161	+	0.459389i
$969$	16.9486	−	10.7158i	0.544468	−	0.344240i
$970$	12.8583	−	31.5684i	0.412854	−	1.01360i
$971$			21.8052i			0.699763i	0.936794	+	0.349882i	$0.113778\pi$
$971$			21.8052i			0.699763i	−0.936794	+	0.349882i	$0.886222\pi$
$972$	−27.7312	+	14.2471i	−0.889479	+	0.456977i
$973$		−	2.98444i		−	0.0956768i
$974$	−3.56631	−	1.45261i	−0.114272	−	0.0465446i
$975$	−16.2325	+	10.2630i	−0.519858	+	0.328680i
$976$	−6.75609	+	12.3673i	−0.216257	+	0.395869i
$977$	26.7110	−	15.4216i	0.854560	−	0.493381i	−0.00762657	−	0.999971i	$-0.502428\pi$
$977$	26.7110	−	15.4216i	0.854560	−	0.493381i	0.862187	+	0.506590i	$0.169094\pi$
$978$	27.2198	−	4.86887i	0.870394	−	0.155689i
$979$	0.920536	−	1.59441i	0.0294204	−	0.0509577i
$980$	4.09457	−	1.14912i	0.130796	−	0.0367072i
$981$	12.0958	+	5.74186i	0.386188	+	0.183324i
$982$	−2.93332	−	21.3080i	−0.0936059	−	0.679966i
$983$	−6.49316	+	11.2465i	−0.207100	+	0.358707i	−0.950800	−	0.309806i	$-0.899736\pi$
$983$	−6.49316	+	11.2465i	−0.207100	+	0.358707i	0.743700	+	0.668513i	$0.233069\pi$
$984$	30.0268	+	2.19565i	0.957218	+	0.0699946i
$985$	5.16324	+	8.94300i	0.164515	+	0.284948i
$986$	−21.0961	+	16.3864i	−0.671838	+	0.521849i
$987$	−36.1598	−	18.9818i	−1.15098	−	0.604197i
$988$	37.4972	+	9.57435i	1.19295	+	0.304601i
$989$	−2.46201			−0.0782873
$990$	−8.86745	+	8.10974i	−0.281826	+	0.257744i
$991$			47.5865i			1.51163i	0.654783	+	0.755817i	$0.272760\pi$
$991$			47.5865i			1.51163i	−0.654783	+	0.755817i	$0.727240\pi$
$992$	38.3864	−	6.21111i	1.21877	−	0.197203i
$993$	10.7296	−	0.431535i	0.340493	−	0.0136943i
$994$	−8.92645	+	6.93361i	−0.283130	+	0.219921i
$995$	−1.92557	+	1.11173i	−0.0610447	+	0.0352442i
$996$	36.2924	−	40.2779i	1.14997	−	1.27625i
$997$	−7.41748	−	4.28248i	−0.234914	−	0.135628i	0.377923	−	0.925837i	$-0.376638\pi$
$997$	−7.41748	−	4.28248i	−0.234914	−	0.135628i	−0.612837	+	0.790209i	$0.709972\pi$
$998$	−55.2850	+	7.61067i	−1.75001	+	0.240912i
$999$	3.27757	+	27.0470i	0.103698	+	0.855729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.2.l.b.11.7	yes	16
3.2	odd	2		216.2.l.b.35.2		16
4.3	odd	2		288.2.p.b.47.1		16
8.3	odd	2	inner	72.2.l.b.11.3	✓	16
8.5	even	2		288.2.p.b.47.2		16
9.2	odd	6		648.2.f.b.323.15		16
9.4	even	3		216.2.l.b.179.6		16
9.5	odd	6	inner	72.2.l.b.59.3	yes	16
9.7	even	3		648.2.f.b.323.2		16
12.11	even	2		864.2.p.b.143.6		16
24.5	odd	2		864.2.p.b.143.3		16
24.11	even	2		216.2.l.b.35.6		16
36.7	odd	6		2592.2.f.b.1295.12		16
36.11	even	6		2592.2.f.b.1295.6		16
36.23	even	6		288.2.p.b.239.2		16
36.31	odd	6		864.2.p.b.719.3		16
72.5	odd	6		288.2.p.b.239.1		16
72.11	even	6		648.2.f.b.323.1		16
72.13	even	6		864.2.p.b.719.6		16
72.29	odd	6		2592.2.f.b.1295.11		16
72.43	odd	6		648.2.f.b.323.16		16
72.59	even	6	inner	72.2.l.b.59.7	yes	16
72.61	even	6		2592.2.f.b.1295.5		16
72.67	odd	6		216.2.l.b.179.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.l.b.11.3	✓	16	8.3	odd	2	inner
72.2.l.b.11.7	yes	16	1.1	even	1	trivial
72.2.l.b.59.3	yes	16	9.5	odd	6	inner
72.2.l.b.59.7	yes	16	72.59	even	6	inner
216.2.l.b.35.2		16	3.2	odd	2
216.2.l.b.35.6		16	24.11	even	2
216.2.l.b.179.2		16	72.67	odd	6
216.2.l.b.179.6		16	9.4	even	3
288.2.p.b.47.1		16	4.3	odd	2
288.2.p.b.47.2		16	8.5	even	2
288.2.p.b.239.1		16	72.5	odd	6
288.2.p.b.239.2		16	36.23	even	6
648.2.f.b.323.1		16	72.11	even	6
648.2.f.b.323.2		16	9.7	even	3
648.2.f.b.323.15		16	9.2	odd	6
648.2.f.b.323.16		16	72.43	odd	6
864.2.p.b.143.3		16	24.5	odd	2
864.2.p.b.143.6		16	12.11	even	2
864.2.p.b.719.3		16	36.31	odd	6
864.2.p.b.719.6		16	72.13	even	6
2592.2.f.b.1295.5		16	72.61	even	6
2592.2.f.b.1295.6		16	36.11	even	6
2592.2.f.b.1295.11		16	72.29	odd	6
2592.2.f.b.1295.12		16	36.7	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	72.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.533474 - 1.30973i) q^{2} +(0.925606 + 1.46399i) q^{3} +(-1.43081 - 1.39742i) q^{4} +(-0.895377 - 1.55084i) q^{5} +(2.41122 - 0.431300i) q^{6} +(2.08793 + 1.20546i) q^{7} +(-2.59355 + 1.12850i) q^{8} +(-1.28651 + 2.71015i) q^{9} +(-2.50885 + 0.345375i) q^{10} +(-1.36975 - 0.790826i) q^{11} +(0.721434 - 3.38815i) q^{12} +(-5.35491 + 3.09166i) q^{13} +(2.69269 - 2.09155i) q^{14} +(1.44164 - 2.74629i) q^{15} +(0.0944399 + 3.99888i) q^{16} -3.69943i q^{17} +(2.86326 + 3.13078i) q^{18} +3.12941 q^{19} +(-0.886056 + 3.47017i) q^{20} +(0.167814 + 4.17248i) q^{21} +(-1.76650 + 1.37212i) q^{22} +(1.36036 + 2.35622i) q^{23} +(-4.05271 - 2.75238i) q^{24} +(0.896599 - 1.55296i) q^{25} +(1.19255 + 8.66283i) q^{26} +(-5.15842 + 0.625100i) q^{27} +(-1.30289 - 4.64250i) q^{28} +(2.55291 - 4.42177i) q^{29} +(-2.82783 - 3.35324i) q^{30} +(5.95312 - 3.43703i) q^{31} +(5.28786 + 2.00961i) q^{32} +(-0.110092 - 2.73729i) q^{33} +(-4.84528 - 1.97355i) q^{34} -4.31738i q^{35} +(5.62796 - 2.07992i) q^{36} -5.24328i q^{37} +(1.66946 - 4.09870i) q^{38} +(-9.48268 - 4.97786i) q^{39} +(4.07232 + 3.01175i) q^{40} +(-5.32220 + 3.07278i) q^{41} +(5.55436 + 2.00612i) q^{42} +(-0.452455 + 0.783675i) q^{43} +(0.854739 + 3.04564i) q^{44} +(5.35491 - 0.431438i) q^{45} +(3.81174 - 0.524733i) q^{46} +(-4.88993 + 8.46960i) q^{47} +(-5.76690 + 3.83965i) q^{48} +(-0.593711 - 1.02834i) q^{49} +(-1.55565 - 2.00277i) q^{50} +(5.41592 - 3.42422i) q^{51} +(11.9822 + 3.05948i) q^{52} +7.05913 q^{53} +(-1.93317 + 7.08963i) q^{54} +2.83235i q^{55} +(-6.77550 - 0.770215i) q^{56} +(2.89660 + 4.58141i) q^{57} +(-4.42944 - 5.70254i) q^{58} +(-6.10118 + 3.52252i) q^{59} +(-5.90042 + 1.91484i) q^{60} +(3.05109 + 1.76155i) q^{61} +(-1.32577 - 9.63057i) q^{62} +(-5.95312 + 4.10775i) q^{63} +(5.45299 - 5.85362i) q^{64} +(9.58933 + 5.53640i) q^{65} +(-3.64385 - 1.31608i) q^{66} +(1.03786 + 1.79762i) q^{67} +(-5.16966 + 5.29319i) q^{68} +(-2.19031 + 4.17248i) q^{69} +(-5.65463 - 2.30321i) q^{70} -3.31507 q^{71} +(0.278229 - 8.48072i) q^{72} +0.631029 q^{73} +(-6.86730 - 2.79715i) q^{74} +(3.10340 - 0.124816i) q^{75} +(-4.47759 - 4.37310i) q^{76} +(-1.90662 - 3.30237i) q^{77} +(-11.5784 + 9.76424i) q^{78} +(-7.82515 - 4.51785i) q^{79} +(6.11707 - 3.72697i) q^{80} +(-5.68980 - 6.97325i) q^{81} +(1.18526 + 8.60992i) q^{82} +(13.5542 + 7.82551i) q^{83} +(5.59059 - 6.20453i) q^{84} +(-5.73722 + 3.31239i) q^{85} +(0.785033 + 1.01067i) q^{86} +(8.83640 - 0.355393i) q^{87} +(4.44496 + 0.505287i) q^{88} +1.16402i q^{89} +(2.29164 - 7.24368i) q^{90} -14.9075 q^{91} +(1.34620 - 5.27230i) q^{92} +(10.5420 + 5.53394i) q^{93} +(8.48428 + 10.9228i) q^{94} +(-2.80200 - 4.85321i) q^{95} +(1.95243 + 9.60146i) q^{96} +(-6.72981 + 11.6564i) q^{97} +(-1.66358 + 0.229013i) q^{98} +(3.90545 - 2.69482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} - 6 q^{3} - 5 q^{4} - 3 q^{6} - 6 q^{9} + 12 q^{11} - 6 q^{12} - 18 q^{14} + 7 q^{16} - 4 q^{19} + 18 q^{20} - q^{22} + 21 q^{24} - 14 q^{25} - 36 q^{27} - 12 q^{28} + 12 q^{30} + 27 q^{32}+ \cdots - 6 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - 6 * q^3 - 5 * q^4 - 3 * q^6 - 6 * q^9 + 12 * q^11 - 6 * q^12 - 18 * q^14 + 7 * q^16 - 4 * q^19 + 18 * q^20 - q^22 + 21 * q^24 - 14 * q^25 - 36 * q^27 - 12 * q^28 + 12 * q^30 + 27 * q^32 + 12 * q^33 - 13 * q^34 + 27 * q^36 - 15 * q^38 - 12 * q^40 - 36 * q^41 + 42 * q^42 + 8 * q^43 + 12 * q^46 - 27 * q^48 + 10 * q^49 + 51 * q^50 + 18 * q^51 - 18 * q^52 + 39 * q^54 - 66 * q^56 + 18 * q^57 + 12 * q^58 + 12 * q^59 - 72 * q^60 + 34 * q^64 - 6 * q^65 - 24 * q^66 - 16 * q^67 - 9 * q^68 + 18 * q^70 - 21 * q^72 - 4 * q^73 - 60 * q^74 + 78 * q^75 - 7 * q^76 - 72 * q^78 - 6 * q^81 - 22 * q^82 + 54 * q^83 + 12 * q^84 - 51 * q^86 - 13 * q^88 - 66 * q^90 - 36 * q^91 + 84 * q^92 + 24 * q^94 + 42 * q^96 + 8 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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