LMFDB - Embedded newform 72.2.l.b.11.3

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			11.3
Root			$-0.533474 - 1.30973i$ of defining polynomial
Character	$\chi$	$=$	72.11
Dual form			72.2.l.b.59.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.867527 + 1.11687i) q^{2} +(0.925606 + 1.46399i) q^{3} +(-0.494795 - 1.93783i) q^{4} +(0.895377 + 1.55084i) q^{5} +(-2.43807 - 0.236266i) 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} +(2.37897 - 2.51804i) q^{12} +(5.35491 - 3.09166i) q^{13} +(3.15768 - 1.28617i) q^{14} +(-1.44164 + 2.74629i) q^{15} +(-3.51036 + 1.91766i) q^{16} -3.69943i q^{17} +(-1.91080 - 3.78799i) q^{18} +3.12941 q^{19} +(2.56223 - 2.50243i) q^{20} +(-0.167814 - 4.17248i) q^{21} +(2.07154 - 0.843770i) q^{22} +(-1.36036 - 2.35622i) q^{23} +(0.748502 + 4.84146i) 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} +(-1.81658 - 3.99260i) q^{30} +(-5.95312 + 3.43703i) q^{31} +(0.903557 - 5.58423i) q^{32} +(-0.110092 - 2.73729i) q^{33} +(4.13178 + 3.20936i) q^{34} -4.31738i q^{35} +(5.88836 + 1.15206i) q^{36} +5.24328i q^{37} +(-2.71485 + 3.49514i) q^{38} +(9.48268 + 4.97786i) q^{39} +(0.572089 + 5.03261i) q^{40} +(-5.32220 + 3.07278i) q^{41} +(4.80570 + 3.43231i) 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} +(-6.05663 - 3.36412i) q^{48} +(-0.593711 - 1.02834i) q^{49} +(0.956625 + 2.34861i) q^{50} +(5.41592 - 3.42422i) q^{51} +(-8.64069 - 8.84716i) q^{52} -7.05913 q^{53} +(3.77691 - 6.30357i) q^{54} -2.83235i q^{55} +(-4.05478 - 5.48265i) q^{56} +(2.89660 + 4.58141i) q^{57} +(-2.72382 - 6.68727i) q^{58} +(-6.10118 + 3.52252i) q^{59} +(6.03514 + 1.43480i) 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} +(3.15270 + 2.25171i) q^{66} +(1.03786 + 1.79762i) q^{67} +(-7.16886 + 1.83046i) q^{68} +(2.19031 - 4.17248i) q^{69} +(4.82195 + 3.74544i) q^{70} +3.31507 q^{71} +(-6.39501 + 5.57708i) q^{72} +0.631029 q^{73} +(-5.85606 - 4.54868i) q^{74} +(3.10340 - 0.124816i) q^{75} +(-1.54842 - 6.06426i) q^{76} +(1.90662 + 3.30237i) q^{77} +(-13.7861 + 6.27250i) 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} +(-8.00251 + 2.38972i) q^{84} +(5.73722 - 3.31239i) q^{85} +(-0.482746 - 1.18519i) q^{86} +(-8.83640 + 0.355393i) q^{87} +(-2.66007 - 3.59680i) q^{88} +1.16402i q^{89} +(4.16367 - 6.35502i) q^{90} -14.9075 q^{91} +(-3.89284 + 3.80199i) q^{92} +(-10.5420 - 5.53394i) q^{93} +(5.21730 + 12.8090i) q^{94} +(2.80200 + 4.85321i) q^{95} +(9.01156 - 3.84600i) 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 $

$2$	−0.867527	+	1.11687i	−0.613434	+	0.789746i
$2$	−0.867527	+	1.11687i	−0.613434	+	0.789746i
$3$	0.925606	+	1.46399i	0.534399	+	0.845232i
$3$	0.925606	+	1.46399i	0.534399	+	0.845232i
$4$	−0.494795	−	1.93783i	−0.247397	−	0.968914i
$5$	0.895377	+	1.55084i	0.400425	+	0.693556i	0.993777	−	0.111387i	$-0.0355292\pi$
$5$	0.895377	+	1.55084i	0.400425	+	0.693556i	−0.593352	+	0.804943i	$0.702196\pi$
$6$	−2.43807	−	0.236266i	−0.995337	−	0.0964550i
$7$	−2.08793	−	1.20546i	−0.789162	−	0.455623i	0.0505056	−	0.998724i	$-0.483917\pi$
$7$	−2.08793	−	1.20546i	−0.789162	−	0.455623i	−0.839667	+	0.543101i	$0.817250\pi$
$8$	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	$0.743304\pi$
$12$	2.37897	−	2.51804i	0.686749	−	0.726895i
$13$	5.35491	−	3.09166i	1.48519	−	0.857472i	0.485327	−	0.874332i	$-0.338700\pi$
$13$	5.35491	−	3.09166i	1.48519	−	0.857472i	0.999858	+	0.0168604i	$0.00536707\pi$
$14$	3.15768	−	1.28617i	0.843925	−	0.343743i
$15$	−1.44164	+	2.74629i	−0.372230	+	0.709088i
$16$	−3.51036	+	1.91766i	−0.877589	+	0.479414i
$17$		−	3.69943i		−	0.897244i	−0.893722	−	0.448622i	$-0.851915\pi$
$17$		−	3.69943i		−	0.897244i	0.893722	−	0.448622i	$-0.148085\pi$
$18$	−1.91080	−	3.78799i	−0.450380	−	0.892837i
$19$	3.12941			0.717936			0.358968	−	0.933350i	$-0.383129\pi$
$19$	3.12941			0.717936			0.358968	+	0.933350i	$0.383129\pi$
$20$	2.56223	−	2.50243i	0.572932	−	0.559561i
$21$	−0.167814	−	4.17248i	−0.0366200	−	0.910509i
$22$	2.07154	−	0.843770i	0.441655	−	0.179892i
$23$	−1.36036	−	2.35622i	−0.283655	−	0.491305i	0.688627	−	0.725116i	$-0.258214\pi$
$23$	−1.36036	−	2.35622i	−0.283655	−	0.491305i	−0.972282	+	0.233811i	$0.924880\pi$
$24$	0.748502	+	4.84146i	0.152787	+	0.988259i
$25$	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	−0.999559	−	0.0296942i	$-0.990547\pi$
$29$	−2.55291	+	4.42177i	−0.474064	+	0.821102i	0.525495	+	0.850796i	$0.323880\pi$
$30$	−1.81658	−	3.99260i	−0.331661	−	0.728945i
$31$	−5.95312	+	3.43703i	−1.06921	+	0.617310i	−0.927966	−	0.372665i	$-0.878444\pi$
$31$	−5.95312	+	3.43703i	−1.06921	+	0.617310i	−0.141246	+	0.989975i	$0.545111\pi$
$32$	0.903557	−	5.58423i	0.159728	−	0.987161i
$33$	−0.110092	−	2.73729i	−0.0191645	−	0.476501i
$34$	4.13178	+	3.20936i	0.708595	+	0.550400i
$35$		−	4.31738i		−	0.729771i
$36$	5.88836	+	1.15206i	0.981393	+	0.192011i
$37$			5.24328i			0.861990i	0.902354	+	0.430995i	$0.141837\pi$
$37$			5.24328i			0.861990i	−0.902354	+	0.430995i	$0.858163\pi$
$38$	−2.71485	+	3.49514i	−0.440406	+	0.566987i
$39$	9.48268	+	4.97786i	1.51844	+	0.797095i
$40$	0.572089	+	5.03261i	0.0904552	+	0.795725i
$41$	−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	$0.492656\pi$
$42$	4.80570	+	3.43231i	0.741535	+	0.529617i
$43$	−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	$-0.580547\pi$
$47$	4.88993	−	8.46960i	0.713269	−	1.23542i	0.963623	−	0.267264i	$-0.0861196\pi$
$48$	−6.05663	−	3.36412i	−0.874199	−	0.485569i
$49$	−0.593711	−	1.02834i	−0.0848159	−	0.146905i
$50$	0.956625	+	2.34861i	0.135287	+	0.332144i
$51$	5.41592	−	3.42422i	0.758380	−	0.479486i
$52$	−8.64069	−	8.84716i	−1.19825	−	1.22688i
$53$	−7.05913			−0.969646			−0.484823	−	0.874612i	$-0.661116\pi$
$53$	−7.05913			−0.969646			−0.484823	+	0.874612i	$0.661116\pi$
$54$	3.77691	−	6.30357i	0.513972	−	0.857807i
$55$		−	2.83235i		−	0.381914i
$56$	−4.05478	−	5.48265i	−0.541842	−	0.732650i
$57$	2.89660	+	4.58141i	0.383664	+	0.606822i
$58$	−2.72382	−	6.68727i	−0.357655	−	0.878082i
$59$	−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	$0.484980\pi$
$60$	6.03514	+	1.43480i	0.779134	+	0.185232i
$61$	−3.05109	−	1.76155i	−0.390652	−	0.225543i	0.291790	−	0.956482i	$-0.405749\pi$
$61$	−3.05109	−	1.76155i	−0.390652	−	0.225543i	−0.682443	+	0.730939i	$0.739082\pi$
$62$	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
$66$	3.15270	+	2.25171i	0.388071	+	0.277167i
$67$	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	$0.792865\pi$
$68$	−7.16886	+	1.83046i	−0.869353	+	0.221976i
$69$	2.19031	−	4.17248i	0.263682	−	0.502307i
$70$	4.82195	+	3.74544i	0.576334	+	0.447666i
$71$	3.31507			0.393426			0.196713	−	0.980461i	$-0.436973\pi$
$71$	3.31507			0.393426			0.196713	+	0.980461i	$0.436973\pi$
$72$	−6.39501	+	5.57708i	−0.753659	+	0.657265i
$73$	0.631029			0.0738563			0.0369282	−	0.999318i	$-0.488243\pi$
$73$	0.631029			0.0738563			0.0369282	+	0.999318i	$0.488243\pi$
$74$	−5.85606	−	4.54868i	−0.680753	−	0.528774i
$75$	3.10340	−	0.124816i	0.358350	−	0.0144125i
$76$	−1.54842	−	6.06426i	−0.177615	−	0.695618i
$77$	1.90662	+	3.30237i	0.217280	+	0.376340i
$78$	−13.7861	+	6.27250i	−1.56097	+	0.710220i
$79$	7.82515	+	4.51785i	0.880398	+	0.508298i	0.870790	−	0.491656i	$-0.163608\pi$
$79$	7.82515	+	4.51785i	0.880398	+	0.508298i	0.00960849	+	0.999954i	$0.496941\pi$
$80$	−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	$0.337777\pi$
$84$	−8.00251	+	2.38972i	−0.873146	+	0.260739i
$85$	5.73722	−	3.31239i	0.622289	−	0.359279i
$86$	−0.482746	−	1.18519i	−0.0520558	−	0.127803i
$87$	−8.83640	+	0.355393i	−0.947361	+	0.0381021i
$88$	−2.66007	−	3.59680i	−0.283564	−	0.383420i
$89$			1.16402i			0.123386i	0.998095	+	0.0616929i	$0.0196499\pi$
$89$			1.16402i			0.123386i	−0.998095	+	0.0616929i	$0.980350\pi$
$90$	4.16367	−	6.35502i	0.438889	−	0.669878i
$91$	−14.9075			−1.56274
$92$	−3.89284	+	3.80199i	−0.405857	+	0.396385i
$93$	−10.5420	−	5.53394i	−1.09316	−	0.573843i
$94$	5.21730	+	12.8090i	0.538123	+	1.32115i
$95$	2.80200	+	4.85321i	0.287479	+	0.497929i
$96$	9.01156	−	3.84600i	0.919739	−	0.392531i
$97$	−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	−0.655379	−	0.755300i	$-0.727491\pi$
$101$	3.28047	−	5.68195i	0.326419	−	0.565375i	0.981799	+	0.189925i	$0.0608245\pi$
$102$	−0.874048	+	9.01947i	−0.0865437	+	0.893061i
$103$	−5.12167	+	2.95700i	−0.504653	+	0.291361i	−0.730633	−	0.682771i	$-0.760775\pi$
$103$	−5.12167	+	2.95700i	−0.504653	+	0.291361i	0.225980	+	0.974132i	$0.427442\pi$
$104$	17.3772	−	1.97537i	1.70397	−	0.193701i
$105$	6.32058	−	3.99619i	0.616826	−	0.389989i
$106$	6.12398	−	7.88413i	0.594814	−	0.765774i
$107$			1.01487i			0.0981111i	0.998796	+	0.0490555i	$0.0156211\pi$
$107$			1.01487i			0.0981111i	−0.998796	+	0.0490555i	$0.984379\pi$
$108$	3.76369	+	9.68683i	0.362162	+	0.932115i
$109$			4.46314i			0.427491i	0.976889	+	0.213746i	$0.0685664\pi$
$109$			4.46314i			0.427491i	−0.976889	+	0.213746i	$0.931434\pi$
$110$	3.16336	+	2.45714i	0.301615	+	0.234279i
$111$	−7.67608	+	4.85321i	−0.728582	+	0.460646i
$112$	9.64103	+	0.227688i	0.910991	+	0.0215145i
$113$	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	$0.202504\pi$
$114$	−7.62971	−	0.739371i	−0.714588	−	0.0692485i
$115$	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
$120$	−6.83813	+	5.49574i	−0.624233	+	0.501690i
$121$	−4.24919	−	7.35981i	−0.386290	−	0.669074i
$122$	4.61432	−	1.87948i	0.417761	−	0.170160i
$123$	−9.42476	−	4.94745i	−0.849802	−	0.446097i
$124$	9.60595	+	9.83549i	0.862640	+	0.883253i
$125$	12.1650			1.08807
$126$	−0.576671	+	10.2124i	−0.0513740	+	0.909796i
$127$		−	15.9098i		−	1.41176i	−0.708329	−	0.705882i	$-0.750551\pi$
$127$		−	15.9098i		−	1.41176i	0.708329	−	0.705882i	$-0.249449\pi$
$128$	−11.2683	+	1.01211i	−0.995991	+	0.0894587i
$129$	−1.56608	+	0.0629866i	−0.137886	+	0.00554566i
$130$	−14.5024	+	5.90706i	−1.27195	+	0.518083i
$131$	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	$0.311034\pi$
$132$	−5.24992	+	1.56773i	−0.456947	+	0.136454i
$133$	−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	$0.842084\pi$
$138$	2.75996	+	6.06602i	0.234944	+	0.516374i
$139$	−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	$0.850052\pi$
$140$	−8.36634	+	2.13622i	−0.707085	+	0.180543i
$141$	16.9255	−	0.680731i	1.42539	−	0.0573279i
$142$	−2.87591	+	3.70250i	−0.241341	+	0.310707i
$143$	−9.77985			−0.817832
$144$	−0.681029	−	11.9807i	−0.0567524	−	0.998388i
$145$	−9.14327			−0.759307
$146$	−0.547434	+	0.704777i	−0.0453060	+	0.0583277i
$147$	0.955929	−	1.82102i	0.0788437	−	0.150195i
$148$	10.1606	−	2.59435i	0.835194	−	0.213254i
$149$	−2.96982	−	5.14387i	−0.243297	−	0.421402i	0.718355	−	0.695677i	$-0.244896\pi$
$149$	−2.96982	−	5.14387i	−0.243297	−	0.421402i	−0.961651	+	0.274275i	$0.911562\pi$
$150$	−2.55288	+	3.57438i	−0.208442	+	0.291847i
$151$	11.9663	+	6.90874i	0.973803	+	0.562226i	0.900394	−	0.435076i	$-0.143279\pi$
$151$	11.9663	+	6.90874i	0.973803	+	0.562226i	0.0734098	+	0.997302i	$0.476612\pi$
$152$	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
$156$	4.95424	−	20.8388i	0.396657	−	1.66844i
$157$	−4.98995	+	2.88095i	−0.398241	+	0.229925i	−0.685725	−	0.727861i	$-0.740515\pi$
$157$	−4.98995	+	2.88095i	−0.398241	+	0.229925i	0.287483	+	0.957786i	$0.407181\pi$
$158$	−11.8344	+	4.82031i	−0.941493	+	0.383484i
$159$	−6.53397	−	10.3345i	−0.518178	−	0.819576i
$160$	9.46926	−	3.59872i	0.748611	−	0.284504i
$161$			6.55947i			0.516959i
$162$	12.7243	−	0.305281i	0.999712	−	0.0239851i
$163$	11.2888			0.884209			0.442104	−	0.896964i	$-0.354232\pi$
$163$	11.2888			0.884209			0.442104	+	0.896964i	$0.354232\pi$
$164$	8.58791	+	8.79312i	0.670603	+	0.686628i
$165$	4.14652	−	2.62164i	0.322806	−	0.204094i
$166$	−20.4987	+	8.34941i	−1.59101	+	0.648040i
$167$	−0.378448	−	0.655492i	−0.0292852	−	0.0507235i	0.851011	−	0.525147i	$-0.175990\pi$
$167$	−0.378448	−	0.655492i	−0.0292852	−	0.0507235i	−0.880297	+	0.474424i	$0.842656\pi$
$168$	4.27339	−	11.0109i	0.329699	−	0.849510i
$169$	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	−0.634756	−	0.772713i	$-0.718899\pi$
$173$	4.62735	−	8.01480i	0.351811	−	0.609354i	0.986567	+	0.163359i	$0.0522327\pi$
$174$	7.26888	−	10.1774i	0.551053	−	0.771548i
$175$	−3.74406	+	2.16164i	−0.283025	+	0.163404i
$176$	6.32484	+	0.149371i	0.476753	+	0.0112593i
$177$	−10.8042	−	5.67158i	−0.812094	−	0.426302i
$178$	−1.30006	−	1.00982i	−0.0974434	−	0.0756890i
$179$		−	1.56530i		−	0.116996i	−0.998288	−	0.0584980i	$-0.981369\pi$
$179$		−	1.56530i		−	0.116996i	0.998288	−	0.0584980i	$-0.0186311\pi$
$180$	3.48564	+	10.1634i	0.259804	+	0.757537i
$181$			3.68300i			0.273755i	0.990588	+	0.136878i	$0.0437067\pi$
$181$			3.68300i			0.273755i	−0.990588	+	0.136878i	$0.956293\pi$
$182$	12.9327	−	16.6498i	0.958635	−	1.23416i
$183$	−0.245227	−	6.09726i	−0.0181277	−	0.450722i
$184$	−0.869185	−	7.64613i	−0.0640771	−	0.563680i
$185$	−8.13148	+	4.69471i	−0.597838	+	0.345162i
$186$	15.3262	−	6.97321i	1.12377	−	0.511300i
$187$	−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	$0.495408\pi$
$191$	−11.8678	+	20.5556i	−0.858722	+	1.48735i	−0.873148	+	0.487455i	$0.837925\pi$
$192$	−3.52229	+	13.4012i	−0.254200	+	0.967152i
$193$	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	$0.460338\pi$
$194$	−7.18036	−	17.6285i	−0.515520	−	1.26566i
$195$	0.770728	+	19.1632i	0.0551929	+	1.37230i
$196$	−1.69898	+	1.65933i	−0.121355	+	0.118523i
$197$	5.76656			0.410850			0.205425	−	0.978673i	$-0.434142\pi$
$197$	5.76656			0.410850			0.205425	+	0.978673i	$0.434142\pi$
$198$	−0.378316	+	6.69970i	−0.0268857	+	0.476127i
$199$			1.24163i			0.0880169i	0.999031	+	0.0440085i	$0.0140129\pi$
$199$			1.24163i			0.0880169i	−0.999031	+	0.0440085i	$0.985987\pi$
$200$	4.07788	−	3.01586i	0.288349	−	0.213253i
$201$	−1.67104	+	3.18329i	−0.117866	+	0.224532i
$202$	3.50010	+	8.59310i	0.246266	+	0.604609i
$203$	10.6606	−	6.15488i	0.748226	−	0.431988i
$204$	−9.31531	−	8.80083i	−0.652202	−	0.616181i
$205$	−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
$210$	−1.02005	+	10.5261i	−0.0703900	+	0.726368i
$211$	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	$0.797717\pi$
$212$	3.49282	+	13.6794i	0.239888	+	0.939504i
$213$	3.06844	+	4.85321i	0.210246	+	0.332536i
$214$	−1.13348	−	0.880426i	−0.0774828	−	0.0601847i
$215$	−1.62047			−0.110515
$216$	−14.0840	−	4.20003i	−0.958297	−	0.285776i
$217$	16.5729			1.12504
$218$	−4.98474	−	3.87189i	−0.337610	−	0.262238i
$219$	0.584084	+	0.923817i	0.0394687	+	0.0624258i
$220$	−5.48861	+	1.40143i	−0.370042	+	0.0944845i
$221$	−11.4374	−	19.8101i	−0.769362	−	1.33257i
$222$	1.23881	−	12.7835i	0.0831432	−	0.857970i
$223$	12.1221	+	6.99871i	0.811758	+	0.468669i	0.847566	−	0.530690i	$-0.178067\pi$
$223$	12.1221	+	6.99871i	0.811758	+	0.468669i	−0.0358081	+	0.999359i	$0.511401\pi$
$224$	−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	$0.775552\pi$
$228$	7.44476	−	7.87997i	0.493041	−	0.521864i
$229$	−9.93043	+	5.73334i	−0.656221	+	0.378869i	−0.790836	−	0.612029i	$-0.790354\pi$
$229$	−9.93043	+	5.73334i	−0.656221	+	0.378869i	0.134615	+	0.990898i	$0.457020\pi$
$230$	2.59916	+	6.38122i	0.171384	+	0.420765i
$231$	−3.06984	+	5.84796i	−0.201981	+	0.384768i
$232$	−11.6110	+	8.58713i	−0.762303	+	0.563773i
$233$		−	6.74860i		−	0.442115i	−0.975261	−	0.221058i	$-0.929049\pi$
$233$		−	6.74860i		−	0.442115i	0.975261	−	0.221058i	$-0.0709509\pi$
$234$	−21.9433	−	14.3768i	−1.43448	−	0.939840i
$235$	17.5133			1.14244
$236$	9.84487	+	10.0801i	0.640846	+	0.656160i
$237$	0.628934	+	15.6377i	0.0408537	+	1.01578i
$238$	−4.75809	−	11.6816i	−0.308421	−	0.757207i
$239$	−0.0677896	−	0.117415i	−0.00438494	−	0.00759495i	0.863825	−	0.503793i	$-0.168062\pi$
$239$	−0.0677896	−	0.117415i	−0.00438494	−	0.00759495i	−0.868210	+	0.496198i	$0.834729\pi$
$240$	−0.205761	−	12.4050i	−0.0132818	−	0.800740i
$241$	−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
$246$	13.7019	−	6.23419i	0.873601	−	0.397477i
$247$	16.7577	−	9.67507i	1.06627	−	0.615610i
$248$	−19.3184	+	2.19605i	−1.22672	+	0.139449i
$249$	1.08940	+	27.0864i	0.0690376	+	1.71653i
$250$	−10.5534	+	13.5867i	−0.667457	+	0.859296i
$251$			18.7837i			1.18561i	0.805344	+	0.592807i	$0.201980\pi$
$251$			18.7837i			1.18561i	−0.805344	+	0.592807i	$0.798020\pi$
$252$	−10.9057	−	9.50363i	−0.686993	−	0.598672i
$253$			4.30324i			0.270542i
$254$	17.7691	+	13.8022i	1.11494	+	0.866024i
$255$	10.1597	+	5.33325i	0.636225	+	0.333981i
$256$	8.64520	−	13.4633i	0.540325	−	0.841457i
$257$	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	$0.0982362\pi$
$258$	1.28827	−	1.80375i	0.0802043	−	0.112297i
$259$	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	$-0.656108\pi$
$263$	8.56995	−	14.8436i	0.528446	−	0.915295i	0.999450	−	0.0331642i	$-0.0105584\pi$
$264$	2.80349	−	7.22353i	0.172543	−	0.444577i
$265$	−6.32058	−	10.9476i	−0.388270	−	0.672504i
$266$	9.88166	−	4.02494i	0.605884	−	0.246785i
$267$	−1.70411	+	1.07742i	−0.104290	+	0.0659372i
$268$	2.96995	−	2.90064i	0.181419	−	0.177185i
$269$	−20.1271			−1.22717			−0.613585	−	0.789629i	$-0.710273\pi$
$269$	−20.1271			−1.22717			−0.613585	+	0.789629i	$0.710273\pi$
$270$	13.1576	+	0.213305i	0.800745	+	0.0129813i
$271$		−	6.20336i		−	0.376827i	−0.982090	−	0.188414i	$-0.939665\pi$
$271$		−	6.20336i		−	0.376827i	0.982090	−	0.188414i	$-0.0603345\pi$
$272$	7.09424	+	12.9863i	0.430151	+	0.787412i
$273$	−13.7985	−	21.8244i	−0.835124	−	1.32087i
$274$	16.0541	−	6.53908i	0.969865	−	0.395040i
$275$	−2.45623	+	1.41811i	−0.148116	+	0.0855151i
$276$	−9.16930	−	2.17992i	−0.551927	−	0.131216i
$277$	−10.6060	−	6.12340i	−0.637256	−	0.367920i	0.146301	−	0.989240i	$-0.453263\pi$
$277$	−10.6060	−	6.12340i	−0.637256	−	0.367920i	−0.783557	+	0.621320i	$0.786597\pi$
$278$	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	$0.841562\pi$
$282$	−13.9231	+	19.4941i	−0.829106	+	1.16086i
$283$	−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	$0.905802\pi$
$284$	−1.64028	−	6.42403i	−0.0973326	−	0.381196i
$285$	−4.51148	+	8.59425i	−0.267237	+	0.509079i
$286$	8.48428	−	10.9228i	0.501686	−	0.645880i
$287$	14.8165			0.874590
$288$	13.9716	+	9.63292i	0.823287	+	0.567625i
$289$	3.31420			0.194953
$290$	7.93203	−	10.2118i	0.465785	−	0.599660i
$291$	−23.2939	+	0.936863i	−1.36551	+	0.0549199i
$292$	−0.312230	−	1.22283i	−0.0182719	−	0.0715604i
$293$	12.6164	+	21.8523i	0.737061	+	1.27663i	0.953813	+	0.300400i	$0.0971202\pi$
$293$	12.6164	+	21.8523i	0.737061	+	1.27663i	−0.216753	+	0.976227i	$0.569546\pi$
$294$	1.20455	+	2.64743i	0.0702507	+	0.154401i
$295$	−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
$300$	−1.77742	−	5.95210i	−0.102619	−	0.343645i
$301$	1.88938	−	1.09084i	0.108902	−	0.0628748i
$302$	−18.0972	+	7.37127i	−1.04138	+	0.424169i
$303$	11.3547	−	0.456678i	0.652311	−	0.0262354i
$304$	−10.9853	+	6.00113i	−0.630052	+	0.344188i
$305$		−	6.30900i		−	0.361253i
$306$	−14.0134	+	7.06888i	−0.801093	+	0.404101i
$307$	−29.5997			−1.68934			−0.844671	−	0.535286i	$-0.820204\pi$
$307$	−29.5997			−1.68934			−0.844671	+	0.535286i	$0.820204\pi$
$308$	5.45604	−	5.32871i	0.310887	−	0.303631i
$309$	−9.06964	−	4.76103i	−0.515954	−	0.270846i
$310$	16.1225	−	6.56694i	0.915698	−	0.372977i
$311$	10.3607	+	17.9453i	0.587502	+	1.01758i	0.994558	+	0.104180i	$0.0332218\pi$
$311$	10.3607	+	17.9453i	0.587502	+	1.01758i	−0.407057	+	0.913403i	$0.633445\pi$
$312$	18.9763	+	23.6115i	1.07432	+	1.33674i
$313$	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	−0.996813	−	0.0797728i	$-0.974581\pi$
$317$	−7.64385	+	13.2395i	−0.429321	+	0.743606i	0.567492	+	0.823379i	$0.307914\pi$
$318$	17.2106	+	1.66783i	0.965125	+	0.0935272i
$319$	6.99370	−	4.03781i	0.391572	−	0.226074i
$320$	−4.19554	+	13.6979i	−0.234538	+	0.765737i
$321$	−1.48575	+	0.939368i	−0.0829267	+	0.0524304i
$322$	−7.32607	−	5.69052i	−0.408266	−	0.317120i
$323$		−	11.5770i		−	0.644164i
$324$	−10.6977	+	14.4762i	−0.594315	+	0.804232i
$325$		−	11.0879i		−	0.615047i
$326$	−9.79335	+	12.6081i	−0.542404	+	0.698300i
$327$	−6.53397	+	4.13111i	−0.361329	+	0.228451i
$328$	−17.2710	+	1.96331i	−0.953632	+	0.108406i
$329$	−20.4196	+	11.7893i	−1.12577	+	0.649963i
$330$	−0.669186	+	6.90546i	−0.0368375	+	0.380133i
$331$	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
$336$	8.59046	+	14.3251i	0.468648	+	0.781497i
$337$	−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	$-0.342464\pi$
$338$	13.4614	+	33.0491i	0.732203	+	1.79763i
$339$	13.0268	+	6.83830i	0.707518	+	0.371406i
$340$	−9.25759	−	9.47880i	−0.502063	−	0.514060i
$341$	10.8724			0.588772
$342$	−5.97968	−	11.8542i	−0.323344	−	0.640999i
$343$			19.7393i			1.06582i
$344$	−2.05784	+	1.52191i	−0.110951	+	0.0820556i
$345$	8.43199	−	0.339128i	0.453963	−	0.0182580i
$346$	4.93714	+	12.1212i	0.265422	+	0.651640i
$347$	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	$0.0818706\pi$
$348$	5.06089	+	16.9476i	0.271292	+	0.908485i
$349$	14.8362	+	8.56568i	0.794164	+	0.458511i	0.841426	−	0.540372i	$-0.181716\pi$
$349$	14.8362	+	8.56568i	0.794164	+	0.458511i	−0.0472627	+	0.998882i	$0.515050\pi$
$350$	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	$0.358429\pi$
$354$	15.7073	−	7.14664i	0.834836	−	0.379840i
$355$	2.96823	+	5.14113i	0.157538	+	0.272863i
$356$	2.25567	−	0.575950i	0.119550	−	0.0305253i
$357$	−15.4358	+	0.620816i	−0.816949	+	0.0328570i
$358$	1.74824	+	1.35794i	0.0923972	+	0.0717694i
$359$	−6.43781			−0.339775			−0.169887	−	0.985463i	$-0.554340\pi$
$359$	−6.43781			−0.339775			−0.169887	+	0.985463i	$0.554340\pi$
$360$	−14.3751	−	4.92404i	−0.757634	−	0.259520i
$361$	−9.20680			−0.484569
$362$	−4.11343	−	3.19510i	−0.216197	−	0.167931i
$363$	6.84158	−	13.0330i	0.359090	−	0.684057i
$364$	7.37618	+	28.8883i	0.386617	+	1.51416i
$365$	0.565009	+	0.978624i	0.0295739	+	0.0512235i
$366$	7.02258	+	5.01565i	0.367076	+	0.262172i
$367$	−23.8725	−	13.7828i	−1.24614	−	0.719457i	−0.275800	−	0.961215i	$-0.588943\pi$
$367$	−23.8725	−	13.7828i	−1.24614	−	0.719457i	−0.970337	+	0.241758i	$0.922276\pi$
$368$	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
$372$	−5.50769	+	23.1668i	−0.285560	+	1.20114i
$373$	23.2547	−	13.4261i	1.20408	−	0.695178i	0.242623	−	0.970121i	$-0.421992\pi$
$373$	23.2547	−	13.4261i	1.20408	−	0.695178i	0.961461	+	0.274942i	$0.0886587\pi$
$374$	−3.12147	−	7.66354i	−0.161407	−	0.396272i
$375$	11.2599	+	17.8093i	0.581461	+	0.919669i
$376$	22.2402	−	16.4481i	1.14695	−	0.848244i
$377$			31.5709i			1.62599i
$378$	−15.4846	+	8.60845i	−0.796443	+	0.442771i
$379$	4.63966			0.238323			0.119162	−	0.992875i	$-0.461979\pi$
$379$	4.63966			0.238323			0.119162	+	0.992875i	$0.461979\pi$
$380$	8.01827	−	7.83114i	0.411328	−	0.401729i
$381$	23.2917	−	14.7262i	1.19327	−	0.754445i
$382$	−12.6623	−	31.0873i	−0.647860	−	1.59056i
$383$	−17.7531	−	30.7493i	−0.907141	−	1.57122i	−0.818017	−	0.575195i	$-0.804926\pi$
$383$	−17.7531	−	30.7493i	−0.907141	−	1.57122i	−0.0891248	−	0.996020i	$-0.528407\pi$
$384$	−11.9118	−	15.5599i	−0.607870	−	0.794037i
$385$	−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	−0.935659	−	0.352904i	$-0.885194\pi$
$389$	−3.19920	+	5.54117i	−0.162206	+	0.280949i	0.773454	+	0.633853i	$0.218527\pi$
$390$	−22.0714	−	15.7638i	−1.11763	−	0.798229i
$391$	−8.71666	+	5.03257i	−0.440821	+	0.254508i
$392$	−0.379344	−	3.33705i	−0.0191597	−	0.168546i
$393$	2.45737	+	1.28998i	0.123958	+	0.0650707i
$394$	−5.00264	+	6.44049i	−0.252029	+	0.324467i
$395$			16.1807i			0.814141i
$396$	−7.15450	−	6.23470i	−0.359527	−	0.313306i
$397$			3.01894i			0.151516i	0.997126	+	0.0757581i	$0.0241377\pi$
$397$			3.01894i			0.151516i	−0.997126	+	0.0757581i	$0.975862\pi$
$398$	−1.38674	−	1.07715i	−0.0695110	−	0.0539926i
$399$	−0.525158	−	13.0574i	−0.0262908	−	0.653687i
$400$	−0.169349	+	7.17079i	−0.00846747	+	0.358540i
$401$	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	$0.0755326\pi$
$402$	−2.10565	−	4.62793i	−0.105020	−	0.230820i
$403$	−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
$408$	17.9107	−	2.76903i	0.886710	−	0.137088i
$409$	−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	$0.843757\pi$
$410$	14.4139	−	5.87098i	0.711850	−	0.289947i
$411$	−0.853191	−	21.2135i	−0.0420848	−	1.04639i
$412$	8.26432	+	8.46180i	0.407154	+	0.416883i
$413$	16.9851			0.835781
$414$	−6.32593	+	9.65529i	−0.310903	+	0.474532i
$415$			28.0271i			1.37580i
$416$	−12.4261	−	32.6965i	−0.609238	−	1.60308i
$417$	0.996550	−	1.89840i	0.0488013	−	0.0929651i
$418$	6.48271	−	2.64050i	0.317080	−	0.129151i
$419$	−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	$0.613045\pi$
$420$	−10.8713	−	10.2709i	−0.530467	−	0.501169i
$421$	30.9851	+	17.8893i	1.51012	+	0.871869i	0.999930	+	0.0118087i	$0.00375891\pi$
$421$	30.9851	+	17.8893i	1.51012	+	0.871869i	0.510192	+	0.860061i	$0.329574\pi$
$422$	−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
$426$	−8.08236	−	0.783236i	−0.391592	−	0.0379479i
$427$	4.24697	+	7.35597i	0.205525	+	0.355980i
$428$	1.96664	−	0.502152i	0.0950612	−	0.0242724i
$429$	−9.05229	−	14.3176i	−0.437049	−	0.691259i
$430$	1.40580	−	1.80985i	0.0677938	−	0.0872789i
$431$	17.1129			0.824301			0.412150	−	0.911116i	$-0.364778\pi$
$431$	17.1129			0.824301			0.412150	+	0.911116i	$0.364778\pi$
$432$	16.9091	−	12.0864i	0.813542	−	0.581506i
$433$	−19.1099			−0.918363			−0.459182	−	0.888342i	$-0.651857\pi$
$433$	−19.1099			−0.918363			−0.459182	+	0.888342i	$0.651857\pi$
$434$	−14.3774	+	18.5098i	−0.690138	+	0.888497i
$435$	−8.46307	−	13.3856i	−0.405773	−	0.641791i
$436$	8.64880	−	2.20834i	0.414202	−	0.105760i
$437$	−4.25713	−	7.37356i	−0.203646	−	0.352725i
$438$	−1.53849	−	0.149090i	−0.0735120	−	0.00712381i
$439$	−29.4886	−	17.0253i	−1.40742	−	0.812572i	−0.412277	−	0.911058i	$-0.635266\pi$
$439$	−29.4886	−	17.0253i	−1.40742	−	0.812572i	−0.995138	+	0.0984868i	$0.968600\pi$
$440$	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	$0.510678\pi$
$444$	13.2028	+	12.4736i	0.626576	+	0.591970i
$445$	−1.80521	+	1.04224i	−0.0855749	+	0.0494067i
$446$	−18.3329	+	7.46727i	−0.868089	+	0.353585i
$447$	4.78167	−	9.10896i	0.226165	−	0.430839i
$448$	−4.32911	−	18.7953i	−0.204531	−	0.887995i
$449$			8.73916i			0.412426i	0.978507	+	0.206213i	$0.0661140\pi$
$449$			8.73916i			0.412426i	−0.978507	+	0.206213i	$0.933886\pi$
$450$	−7.59579	−	0.428916i	−0.358069	−	0.0202193i
$451$	9.72012			0.457703
$452$	−11.8701	−	12.1537i	−0.558323	−	0.571664i
$453$	0.961772	+	23.9133i	0.0451880	+	1.12354i
$454$	13.2386	−	5.39228i	0.621319	−	0.253072i
$455$	−13.3479	−	23.1192i	−0.625758	−	1.08384i
$456$	2.34237	+	15.1509i	0.109691	+	0.709506i
$457$	−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	−0.798140	−	0.602472i	$-0.794182\pi$
$461$	2.63419	−	4.56255i	0.122686	−	0.212499i	0.920826	+	0.389973i	$0.127516\pi$
$462$	−3.86824	−	8.50187i	−0.179967	−	0.395543i
$463$	−15.2227	+	8.78883i	−0.707459	+	0.408451i	−0.810119	−	0.586265i	$-0.800598\pi$
$463$	−15.2227	+	8.78883i	−0.707459	+	0.408451i	0.102661	+	0.994716i	$0.467264\pi$
$464$	0.482193	−	20.4176i	0.0223852	−	0.947863i
$465$	−0.856827	−	21.3039i	−0.0397344	−	0.987946i
$466$	7.53731	+	5.85459i	0.349159	+	0.271209i
$467$			2.29842i			0.106358i	0.998585	+	0.0531791i	$0.0169354\pi$
$467$			2.29842i			0.106358i	−0.998585	+	0.0531791i	$0.983065\pi$
$468$	35.0934	−	12.0356i	1.62219	−	0.556346i
$469$		−	5.00439i		−	0.231081i
$470$	−15.1933	+	19.5601i	−0.700813	+	0.902240i
$471$	−8.83640	−	4.63859i	−0.407160	−	0.213735i
$472$	−19.7989	+	2.25066i	−0.911316	+	0.103595i
$473$	1.23950	−	0.715626i	0.0569923	−	0.0329045i
$474$	−18.0108	−	12.8636i	−0.827265	−	0.590847i
$475$	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	$-0.525384\pi$
$479$	18.0219	−	31.2149i	0.823442	−	1.42624i	0.903104	−	0.429422i	$-0.141283\pi$
$480$	14.0333	+	10.5319i	0.640528	+	0.480712i
$481$	16.2104	+	28.0773i	0.739132	+	1.28021i
$482$	−10.3680	−	25.4545i	−0.472249	−	1.15942i
$483$	−9.60297	+	6.07149i	−0.436950	+	0.276262i
$484$	−12.1596	+	11.8758i	−0.552708	+	0.539809i
$485$	−24.1029			−1.09446
$486$	12.2246	+	18.3456i	0.554518	+	0.832172i
$487$			2.72292i			0.123387i	0.998095	+	0.0616937i	$0.0196502\pi$
$487$			2.72292i			0.123387i	−0.998095	+	0.0616937i	$0.980350\pi$
$488$	−5.92526	−	8.01181i	−0.268224	−	0.362678i
$489$	10.4490	+	16.5267i	0.472520	+	0.747362i
$490$	1.13437	+	2.78500i	0.0512456	+	0.125813i
$491$	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	$0.221826\pi$
$492$	−4.92398	+	20.7115i	−0.221990	+	0.933749i
$493$	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
$498$	−31.1971	−	22.2815i	−1.39798	−	0.998458i
$499$	−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	$-0.511323\pi$
$500$	−6.01916	−	23.5736i	−0.269185	−	1.05424i
$501$	0.609336	−	1.16077i	0.0272231	−	0.0518594i
$502$	−20.9789	−	16.2953i	−0.936334	−	0.727296i
$503$	−18.4749			−0.823756			−0.411878	−	0.911239i	$-0.635127\pi$
$503$	−18.4749			−0.823756			−0.411878	+	0.911239i	$0.635127\pi$
$504$	20.0753	−	3.93557i	0.894224	−	0.175304i
$505$	11.7490			0.522826
$506$	−4.80615	−	3.73317i	−0.213660	−	0.165960i
$507$	43.6703	−	1.75638i	1.93947	−	0.0780038i
$508$	−30.8304	+	7.87208i	−1.36788	+	0.349267i
$509$	17.0068	+	29.4566i	0.753813	+	1.30564i	0.945962	+	0.324277i	$0.105121\pi$
$509$	17.0068	+	29.4566i	0.753813	+	1.30564i	−0.192149	+	0.981366i	$0.561546\pi$
$510$	−14.7703	+	6.72032i	−0.654042	+	0.297581i
$511$	−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
$516$	0.896947	+	3.00364i	0.0394859	+	0.132228i
$517$	−13.3960	+	7.73416i	−0.589153	+	0.340148i
$518$	6.74374	+	16.5566i	0.296303	+	0.727454i
$519$	16.0167	−	0.644177i	0.703053	−	0.0282762i
$520$	18.6226	+	25.1805i	0.816655	+	1.10424i
$521$		−	12.0788i		−	0.529182i	−0.964361	−	0.264591i	$-0.914763\pi$
$521$		−	12.0788i		−	0.529182i	0.964361	−	0.264591i	$-0.0852369\pi$
$522$	21.6277	+	1.22126i	0.946619	+	0.0534533i
$523$	5.27483			0.230652			0.115326	−	0.993328i	$-0.463209\pi$
$523$	5.27483			0.230652			0.115326	+	0.993328i	$0.463209\pi$
$524$	−2.23917	−	2.29268i	−0.0978188	−	0.100156i
$525$	−6.63013	−	3.48043i	−0.289363	−	0.151899i
$526$	9.14370	+	22.4487i	0.398684	+	0.978811i
$527$	12.7151	+	22.0232i	0.553877	+	0.959344i
$528$	5.63563	+	9.39773i	0.245259	+	0.408984i
$529$	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
$534$	0.275017	−	2.83796i	0.0119012	−	0.122810i
$535$	−1.57390	+	0.908690i	−0.0680455	+	0.0392861i
$536$	0.663123	+	5.83343i	0.0286426	+	0.251966i
$537$	2.29158	−	1.44885i	0.0988889	−	0.0625226i
$538$	17.4608	−	22.4793i	0.752787	−	0.969152i
$539$			1.87809i			0.0808950i
$540$	−11.6528	+	14.5102i	−0.501456	+	0.624422i
$541$		−	23.6734i		−	1.01780i	−0.860826	−	0.508900i	$-0.830052\pi$
$541$		−	23.6734i		−	1.01780i	0.860826	−	0.508900i	$-0.169948\pi$
$542$	6.92834	+	5.38158i	0.297598	+	0.231159i
$543$	−5.39186	+	3.40901i	−0.231387	+	0.146295i
$544$	−20.6585	−	3.34265i	−0.885725	−	0.143315i
$545$	−6.92161	+	3.99619i	−0.296489	+	0.171178i
$546$	36.3456	+	3.52214i	1.55545	+	0.150734i
$547$	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
$552$	10.3893	−	8.34977i	0.442198	−	0.355390i
$553$	−10.8922	−	18.8659i	−0.463184	−	0.802259i
$554$	16.0401	−	6.53335i	0.681477	−	0.277576i
$555$	−14.3995	−	7.55892i	−0.611226	−	0.320858i
$556$	−1.77117	+	1.72984i	−0.0751144	+	0.0733614i
$557$	−9.64427			−0.408641			−0.204321	−	0.978904i	$-0.565498\pi$
$557$	−9.64427			−0.408641			−0.204321	+	0.978904i	$0.565498\pi$
$558$	24.3947	+	15.9828i	1.03271	+	0.676607i
$559$			5.59535i			0.236658i
$560$	8.27925	+	15.1555i	0.349862	+	0.640439i
$561$	−10.1264	+	0.407276i	−0.427537	+	0.0171952i
$562$	22.9308	−	9.34005i	0.967277	−	0.393986i
$563$	−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	$0.979267\pi$
$564$	−9.69380	−	32.4619i	−0.408183	−	1.36689i
$565$	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	$0.730736\pi$
$570$	−5.68483	−	12.4945i	−0.238111	−	0.523336i
$571$	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	$0.643106\pi$
$572$	4.83902	+	18.9517i	0.202330	+	0.792409i
$573$	−41.0780	+	1.65212i	−1.71606	+	0.0690185i
$574$	−12.8537	+	16.5481i	−0.536503	+	0.690704i
$575$	−4.87880			−0.203460
$576$	−22.8795	+	7.24769i	−0.953312	+	0.301987i
$577$	−8.52363			−0.354843			−0.177422	−	0.984135i	$-0.556776\pi$
$577$	−8.52363			−0.354843			−0.177422	+	0.984135i	$0.556776\pi$
$578$	−2.87516	+	3.70153i	−0.119591	+	0.153963i
$579$	−20.6111	+	39.2636i	−0.856569	+	1.63174i
$580$	4.52404	+	17.7181i	0.187851	+	0.735704i
$581$	−18.8667	−	32.6781i	−0.782724	−	1.35572i
$582$	19.1617	−	26.8290i	0.794280	−	1.11210i
$583$	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	$0.820127\pi$
$588$	−4.00181	−	0.951395i	−0.165032	−	0.0392349i
$589$	−18.6297	+	10.7559i	−0.767625	+	0.443189i
$590$	16.5235	−	6.73027i	0.680263	−	0.277081i
$591$	5.33756	+	8.44216i	0.219558	+	0.347264i
$592$	−10.0548	−	18.4058i	−0.413250	−	0.756473i
$593$		−	28.8424i		−	1.18442i	−0.805785	−	0.592208i	$-0.798257\pi$
$593$		−	28.8424i		−	1.18442i	0.805785	−	0.592208i	$-0.201743\pi$
$594$	−10.1584	+	5.64744i	−0.416806	+	0.231717i
$595$	−15.9719			−0.654783
$596$	−8.49849	+	8.30015i	−0.348112	+	0.339987i
$597$	−1.81773	+	1.14926i	−0.0743947	+	0.0470361i
$598$	22.0338	−	8.97469i	0.901029	−	0.367002i
$599$	8.40225	+	14.5531i	0.343307	+	0.594625i	0.985045	−	0.172299i	$-0.0551196\pi$
$599$	8.40225	+	14.5531i	0.343307	+	0.594625i	−0.641738	+	0.766924i	$0.721786\pi$
$600$	8.18968	+	3.17846i	0.334342	+	0.129760i
$601$	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
$606$	−9.34047	+	13.0779i	−0.379431	+	0.531254i
$607$	20.9599	−	12.1012i	0.850737	−	0.491173i	−0.0101625	−	0.999948i	$-0.503235\pi$
$607$	20.9599	−	12.1012i	0.850737	−	0.491173i	0.860899	+	0.508775i	$0.169902\pi$
$608$	2.82760	−	17.4753i	0.114674	−	0.708718i
$609$	18.8782	+	9.90993i	0.764981	+	0.401571i
$610$	7.04633	+	5.47323i	0.285298	+	0.221605i
$611$		−	60.4720i		−	2.44643i
$612$	4.26198	−	21.7836i	0.172280	−	0.880549i
$613$		−	38.3189i		−	1.54769i	−0.633377	−	0.773843i	$-0.718332\pi$
$613$		−	38.3189i		−	1.54769i	0.633377	−	0.773843i	$-0.281668\pi$
$614$	25.6785	−	33.0589i	1.03630	−	1.33415i
$615$	−0.766020	−	19.0461i	−0.0308889	−	0.768014i
$616$	1.21821	+	10.7165i	0.0490831	+	0.431779i
$617$	−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	$0.387707\pi$
$618$	13.1856	−	5.99928i	0.530403	−	0.241327i
$619$	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
$624$	−42.8334	+	0.710473i	−1.71471	+	0.0284417i
$625$	6.40923	+	11.1011i	0.256369	+	0.444044i
$626$	1.85308	+	4.54951i	0.0740640	+	0.181835i
$627$	−0.344521	−	8.56609i	−0.0137589	−	0.342097i
$628$	8.05179	+	8.24419i	0.321301	+	0.328979i
$629$	19.3972			0.773415
$630$	−16.3542	+	8.24966i	−0.651566	+	0.328674i
$631$		−	34.0954i		−	1.35732i	−0.734454	−	0.678659i	$-0.762561\pi$
$631$		−	34.0954i		−	1.35732i	0.734454	−	0.678659i	$-0.237439\pi$
$632$	15.1965	+	20.5479i	0.604486	+	0.817353i
$633$	−2.61147	+	4.97478i	−0.103797	+	0.197730i
$634$	−8.15559	−	20.0228i	−0.323900	−	0.795208i
$635$	24.6735	−	14.2452i	0.979138	−	0.565305i
$636$	−16.7934	+	17.7752i	−0.665903	+	0.704831i
$637$	−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	$0.507944\pi$
$642$	0.239779	−	2.47432i	0.00946330	−	0.0976536i
$643$	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	$0.685894\pi$
$644$	12.7111	−	3.24559i	0.500889	−	0.127894i
$645$	−1.49992	−	2.37235i	−0.0590592	−	0.0934110i
$646$	12.9300	+	10.0434i	0.508726	+	0.395152i
$647$	38.6020			1.51760			0.758800	−	0.651323i	$-0.225786\pi$
$647$	38.6020			1.51760			0.758800	+	0.651323i	$0.225786\pi$
$648$	−6.88748	−	24.5064i	−0.270566	−	0.962701i
$649$	11.1428			0.437393
$650$	12.3838	+	9.61906i	0.485731	+	0.377291i
$651$	15.3400	+	24.2625i	0.601221	+	0.950921i
$652$	−5.58565	−	21.8758i	−0.218751	−	0.856722i
$653$	13.1416	+	22.7619i	0.514271	+	0.890743i	0.999863	+	0.0165576i	$0.00527069\pi$
$653$	13.1416	+	22.7619i	0.514271	+	0.890743i	−0.485592	+	0.874185i	$0.661396\pi$
$654$	1.05449	−	10.8814i	0.0412337	−	0.425498i
$655$	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	$0.398462\pi$
$660$	−7.13196	−	6.73807i	−0.277611	−	0.262279i
$661$	−38.7145	+	22.3518i	−1.50582	+	0.869385i	−0.505842	+	0.862626i	$0.668818\pi$
$661$	−38.7145	+	22.3518i	−1.50582	+	0.869385i	−0.999977	+	0.00675901i	$0.997849\pi$
$662$	3.30739	+	8.12000i	0.128546	+	0.315593i
$663$	18.4152	−	35.0805i	0.715189	−	1.36242i
$664$	26.3224	+	35.5917i	1.02151	+	1.38122i
$665$		−	13.5109i		−	0.523928i
$666$	19.8615	−	10.0189i	0.769616	−	0.388223i
$667$	13.8915			0.537882
$668$	−1.08298	+	1.05770i	−0.0419016	+	0.0409237i
$669$	0.974297	+	24.2247i	0.0376685	+	0.936580i
$670$	−1.98297	−	4.86840i	−0.0766088	−	0.188083i
$671$	2.78616	+	4.82576i	0.107558	+	0.186297i
$672$	−23.4517	−	2.83296i	−0.904669	−	0.109284i
$673$	−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	−0.567817	−	0.823155i	$-0.692212\pi$
$677$	11.1613	−	19.3320i	0.428964	−	0.742988i	0.996781	+	0.0801666i	$0.0255452\pi$
$678$	−18.9386	+	8.61681i	−0.727332	+	0.330927i
$679$	28.1027	−	16.2251i	1.07848	−	0.622662i
$680$	18.6178	−	2.11640i	0.713960	−	0.0811604i
$681$	−0.703562	−	17.4932i	−0.0269605	−	0.670340i
$682$	−9.43208	+	12.1430i	−0.361173	+	0.464981i
$683$		−	20.5229i		−	0.785288i	−0.919691	−	0.392644i	$-0.871560\pi$
$683$		−	20.5229i		−	0.785288i	0.919691	−	0.392644i	$-0.128440\pi$
$684$	18.4271	+	3.60528i	0.704577	+	0.137851i
$685$		−	21.9502i		−	0.838676i
$686$	−22.0462	−	17.1244i	−0.841728	−	0.653811i
$687$	−17.5852	−	9.23119i	−0.670917	−	0.352192i
$688$	0.0854595	−	3.61863i	0.00325811	−	0.137959i
$689$	−37.8010	+	21.8244i	−1.44010	+	0.831444i
$690$	−6.93622	+	9.71164i	−0.264057	+	0.369716i
$691$	−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
$696$	−23.3187	−	9.05011i	−0.883893	−	0.343044i
$697$	11.3675	+	19.6891i	0.430576	+	0.745779i
$698$	−22.4376	+	9.13914i	−0.849274	+	0.345922i
$699$	9.87985	−	6.24654i	0.373690	−	0.236266i
$700$	6.04142	+	6.18579i	0.228344	+	0.233801i
$701$	−41.9171			−1.58319			−0.791593	−	0.611049i	$-0.790748\pi$
$701$	−41.9171			−1.58319			−0.791593	+	0.611049i	$0.790748\pi$
$702$	0.736522	−	45.4320i	0.0277982	−	1.71472i
$703$			16.4084i			0.618853i
$704$	−2.84004	−	12.3304i	−0.107038	−	0.464718i
$705$	16.2104	+	25.6392i	0.610520	+	0.965630i
$706$	−40.5513	+	16.5171i	−1.52617	+	0.621630i
$707$	−13.6988	+	7.90899i	−0.515195	+	0.297448i
$708$	−5.64468	+	23.7430i	−0.212140	+	0.892315i
$709$	−4.41486	−	2.54892i	−0.165803	−	0.0957266i	0.414802	−	0.909912i	$-0.363851\pi$
$709$	−4.41486	−	2.54892i	−0.165803	−	0.0957266i	−0.580606	+	0.814185i	$0.697184\pi$
$710$	−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
$714$	12.6976	−	17.7783i	0.475196	−	0.665338i
$715$	−8.75666	−	15.1670i	−0.327480	−	0.567213i
$716$	−3.03328	+	0.774503i	−0.113359	+	0.0289445i
$717$	0.109147	−	0.207923i	0.00407619	−	0.00776503i
$718$	5.58497	−	7.19020i	0.208429	−	0.268336i
$719$	−35.1676			−1.31153			−0.655765	−	0.754965i	$-0.727654\pi$
$719$	−35.1676			−1.31153			−0.655765	+	0.754965i	$0.727654\pi$
$720$	17.9703	−	11.7834i	0.669713	−	0.439141i
$721$	14.2582			0.531003
$722$	7.98715	−	10.2828i	0.297251	−	0.382686i
$723$	−33.6350	+	1.35277i	−1.25090	+	0.0503101i
$724$	7.13702	−	1.82233i	0.265245	−	0.0677264i
$725$	4.57787	+	7.92911i	0.170018	+	0.294480i
$726$	8.62095	+	18.9477i	0.319953	+	0.703214i
$727$	19.9209	+	11.5013i	0.738826	+	0.426561i	0.821642	−	0.570003i	$-0.193058\pi$
$727$	19.9209	+	11.5013i	0.738826	+	0.426561i	−0.0828164	+	0.996565i	$0.526391\pi$
$728$	−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
$732$	−11.6941	+	3.49210i	−0.432226	+	0.129072i
$733$	7.38177	−	4.26187i	0.272652	−	0.157416i	−0.357440	−	0.933936i	$-0.616350\pi$
$733$	7.38177	−	4.26187i	0.272652	−	0.157416i	0.630092	+	0.776520i	$0.283017\pi$
$734$	36.1037	−	14.7055i	1.33261	−	0.542792i
$735$	3.68003	−	0.148008i	0.135740	−	0.00545935i
$736$	−14.3868	+	5.46759i	−0.530305	+	0.201538i
$737$		−	3.28305i		−	0.120933i
$738$	21.8093	+	14.2890i	0.802812	+	0.525984i
$739$	32.3956			1.19169			0.595846	−	0.803099i	$-0.296817\pi$
$739$	32.3956			1.19169			0.595846	+	0.803099i	$0.296817\pi$
$740$	13.1210	+	13.4345i	0.482336	+	0.493862i
$741$	29.6752	+	15.5777i	1.09015	+	0.572263i
$742$	−22.2905	+	9.07923i	−0.818308	+	0.333309i
$743$	2.22350	+	3.85122i	0.0815725	+	0.141288i	0.903926	−	0.427690i	$-0.140672\pi$
$743$	2.22350	+	3.85122i	0.0815725	+	0.141288i	−0.822353	+	0.568978i	$0.807339\pi$
$744$	−21.0962	−	26.2492i	−0.773424	−	0.962341i
$745$	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
$750$	−29.6590	−	2.87416i	−1.08299	−	0.104949i
$751$	32.3801	−	18.6946i	1.18157	−	0.682177i	0.225189	−	0.974315i	$-0.427700\pi$
$751$	32.3801	−	18.6946i	1.18157	−	0.682177i	0.956376	+	0.292138i	$0.0943666\pi$
$752$	−0.923608	+	39.1085i	−0.0336805	+	1.42614i
$753$	−27.4990	+	17.3863i	−1.00212	+	0.633591i
$754$	−35.2606	−	27.3886i	−1.28412	−	0.997435i
$755$			24.7437i			0.900517i
$756$	3.81881	−	24.7624i	0.138889	−	0.900599i
$757$			46.7837i			1.70038i	0.526474	+	0.850191i	$0.323514\pi$
$757$			46.7837i			1.70038i	−0.526474	+	0.850191i	$0.676486\pi$
$758$	−4.02503	+	5.18190i	−0.146196	+	0.188215i
$759$	−6.29988	+	3.98310i	−0.228671	+	0.144577i
$760$	1.79030	+	15.7491i	0.0649410	+	0.571279i
$761$	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	$0.294382\pi$
$762$	−3.75893	+	38.7891i	−0.136172	+	1.40518i
$763$	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
$768$	27.7121	+	0.194730i	0.999975	+	0.00702672i
$769$	−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	$0.937473\pi$
$770$	−3.64288	−	8.94364i	−0.131280	−	0.322307i
$771$	33.1036	+	17.3774i	1.19220	+	0.625833i
$772$	36.6322	−	35.7773i	1.31842	−	1.28765i
$773$	18.9682			0.682237			0.341119	−	0.940020i	$-0.389194\pi$
$773$	18.9682			0.682237			0.341119	+	0.940020i	$0.389194\pi$
$774$	3.83310	+	0.216446i	0.137778	+	0.00777999i
$775$			12.3266i			0.442783i
$776$	−30.6083	+	22.6368i	−1.09877	+	0.812614i
$777$	21.8775	−	0.879894i	0.784850	−	0.0315660i
$778$	−3.41338	−	8.38020i	−0.122375	−	0.300445i
$779$	−16.6554	+	9.61597i	−0.596740	+	0.344528i
$780$	36.7536	−	10.9754i	1.31599	−	0.392982i
$781$	−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
$786$	−3.57257	+	1.62547i	−0.127429	+	0.0579787i
$787$	−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	$0.845115\pi$
$788$	−2.85326	−	11.1746i	−0.101643	−	0.398079i
$789$	29.6632	−	1.19303i	1.05604	−	0.0424730i
$790$	−18.0718	−	14.0372i	−0.642965	−	0.499422i
$791$	−20.4792			−0.728155
$792$	13.1701	−	2.58187i	0.467978	−	0.0917427i
$793$	−21.7844			−0.773588
$794$	−3.37176	−	2.61901i	−0.119659	−	0.0929452i
$795$	10.1767	−	19.3864i	0.360931	−	0.687564i
$796$	2.40607	−	0.614353i	0.0852808	−	0.0217752i
$797$	−17.7593	−	30.7601i	−0.629068	−	1.08958i	−0.987739	−	0.156113i	$-0.950103\pi$
$797$	−17.7593	−	30.7601i	−0.629068	−	1.08958i	0.358671	−	0.933464i	$-0.383230\pi$
$798$	15.0390	+	10.7411i	0.532374	+	0.380231i
$799$	−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
$804$	6.99549	+	1.66312i	0.246712	+	0.0586536i
$805$	−10.1727	+	5.87320i	−0.358540	+	0.207003i
$806$	−22.6751	−	55.6697i	−0.798696	−	1.96088i
$807$	−18.6297	−	29.4657i	−0.655798	−	1.03724i
$808$	14.9201	−	11.0344i	0.524888	−	0.388189i
$809$		−	41.7225i		−	1.46688i	−0.679752	−	0.733442i	$-0.737913\pi$
$809$		−	41.7225i		−	1.46688i	0.679752	−	0.733442i	$-0.262087\pi$
$810$	11.8665	+	19.4599i	0.416945	+	0.683753i
$811$	−3.03064			−0.106420			−0.0532102	−	0.998583i	$-0.516945\pi$
$811$	−3.03064			−0.106420			−0.0532102	+	0.998583i	$0.516945\pi$
$812$	−17.2019	−	17.6130i	−0.603669	−	0.618093i
$813$	9.08162	−	5.74186i	0.318506	−	0.201376i
$814$	4.42412	+	10.8617i	0.155065	+	0.380702i
$815$	10.1078	+	17.5071i	0.354059	+	0.613248i
$816$	−12.4453	+	22.4061i	−0.435674	+	0.784370i
$817$	−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	$-0.473339\pi$
$821$	25.9259	−	44.9049i	0.904819	−	1.56719i	0.821160	−	0.570698i	$-0.193327\pi$
$822$	24.4329	+	17.4504i	0.852196	+	0.608653i
$823$	−28.3812	+	16.3859i	−0.989307	+	0.571177i	−0.905067	−	0.425269i	$-0.860180\pi$
$823$	−28.3812	+	16.3859i	−0.989307	+	0.571177i	−0.0842401	+	0.996445i	$0.526846\pi$
$824$	−16.6202	+	1.88933i	−0.578994	+	0.0658180i
$825$	−4.34959	−	2.28328i	−0.151433	−	0.0794937i
$826$	−14.7350	+	18.9701i	−0.512697	+	0.660055i
$827$			52.8295i			1.83706i	0.395350	+	0.918531i	$0.370623\pi$
$827$			52.8295i			1.83706i	−0.395350	+	0.918531i	$0.629377\pi$
$828$	−5.29579	−	15.4415i	−0.184041	−	0.536628i
$829$			0.0144624i			0.000502300i	1.00000		0.000251150i	$7.99435e-5\pi$
$829$			0.0144624i			0.000502300i	−1.00000		0.000251150i	$0.999920\pi$
$830$	−31.3026	−	24.3143i	−1.08653	−	0.843961i
$831$	−0.852444	−	21.1950i	−0.0295710	−	0.735245i
$832$	47.2977	+	14.4868i	1.63975	+	0.502240i
$833$	−3.80427	+	2.19639i	−0.131810	+	0.0761006i
$834$	1.25573	+	2.75993i	0.0434825	+	0.0955686i
$835$	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	$0.362001\pi$
$839$	−16.6802	+	28.8909i	−0.575864	+	0.997425i	−0.995947	+	0.0899399i	$0.971333\pi$
$840$	20.9024	−	3.23157i	0.721203	−	0.111500i
$841$	1.46530	+	2.53797i	0.0505275	+	0.0875162i
$842$	−46.8604	+	19.0869i	−1.61492	+	0.657779i
$843$	−1.21865	−	30.3002i	−0.0419725	−	1.04359i
$844$	4.64138	−	4.53306i	0.159763	−	0.156034i
$845$	45.1869			1.55448
$846$	−41.4264	−	2.33925i	−1.42427	−	0.0804250i
$847$			20.4890i			0.704010i
$848$	24.7801	−	13.5370i	0.850951	−	0.464862i
$849$	6.11348	−	11.6460i	0.209814	−	0.399690i
$850$	8.68854	−	3.53897i	0.298014	−	0.121386i
$851$	12.3543	−	7.13276i	0.423500	−	0.244508i
$852$	7.88643	−	8.34746i	0.270185	−	0.285979i
$853$	−32.7219	−	18.8920i	−1.12038	−	0.646850i	−0.178880	−	0.983871i	$-0.557247\pi$
$853$	−32.7219	−	18.8920i	−1.12038	−	0.646850i	−0.941497	+	0.337021i	$0.890581\pi$
$854$	−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	$0.609824\pi$
$858$	23.8440	+	2.31064i	0.814019	+	0.0788840i
$859$	−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	$0.948273\pi$
$860$	0.801801	+	3.14019i	0.0273412	+	0.107080i
$861$	13.7142	+	21.6911i	0.467380	+	0.739232i
$862$	−14.8459	+	19.1129i	−0.505654	+	0.650988i
$863$	−4.67705			−0.159209			−0.0796043	−	0.996827i	$-0.525366\pi$
$863$	−4.67705			−0.159209			−0.0796043	+	0.996827i	$0.525366\pi$
$864$	−1.17022	+	29.3706i	−0.0398118	+	0.999207i
$865$	16.5729			0.563495
$866$	16.5784	−	21.3433i	0.563355	−	0.725274i
$867$	3.06764	+	4.85194i	0.104183	+	0.164780i
$868$	−8.20018	−	32.1154i	−0.278332	−	1.09007i
$869$	−7.14567	−	12.3767i	−0.242400	−	0.419849i
$870$	22.2919	+	2.16024i	0.755767	+	0.0732390i
$871$	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
$876$	1.50120	−	1.58895i	0.0507207	−	0.0536858i
$877$	9.04467	−	5.22194i	0.305417	−	0.176333i	−0.339457	−	0.940622i	$-0.610243\pi$
$877$	9.04467	−	5.22194i	0.305417	−	0.176333i	0.644874	+	0.764289i	$0.276910\pi$
$878$	44.5972	−	18.1651i	1.50508	−	0.613042i
$879$	−20.3136	+	38.6969i	−0.685162	+	1.30522i
$880$	5.43147	+	9.94255i	0.183095	+	0.335163i
$881$			29.7734i			1.00309i	0.865131	+	0.501546i	$0.167235\pi$
$881$			29.7734i			1.00309i	−0.865131	+	0.501546i	$0.832765\pi$
$882$	−2.76087	+	4.21392i	−0.0929632	+	0.141890i
$883$	−52.9294			−1.78122			−0.890608	−	0.454772i	$-0.849721\pi$
$883$	−52.9294			−1.78122			−0.890608	+	0.454772i	$0.849721\pi$
$884$	−32.7295	+	31.9656i	−1.10081	+	1.07512i
$885$	−0.878137	−	21.8338i	−0.0295183	−	0.733935i
$886$	−25.9498	+	10.5697i	−0.871801	+	0.355097i
$887$	−22.4416	−	38.8700i	−0.753515	−	1.30513i	−0.946109	−	0.323848i	$-0.895023\pi$
$887$	−22.4416	−	38.8700i	−0.753515	−	1.30513i	0.192594	−	0.981278i	$-0.438310\pi$
$888$	−25.3851	+	3.92460i	−0.851869	+	0.131701i
$889$	−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
$894$	6.02529	+	13.2428i	0.201516	+	0.442905i
$895$	2.42753	−	1.40153i	0.0811434	−	0.0468481i
$896$	24.7475	+	11.4704i	0.826757	+	0.383199i
$897$	−1.17098	−	29.1149i	−0.0390979	−	0.972119i
$898$	−9.76050	−	7.58145i	−0.325712	−	0.252996i
$899$		−	35.0978i		−	1.17058i
$900$	7.06860	−	8.11142i	0.235620	−	0.270381i
$901$			26.1148i			0.870009i
$902$	−8.43246	+	10.8561i	−0.280770	+	0.361469i
$903$	3.34579	+	1.75635i	0.111341	+	0.0584475i
$904$	23.8718	−	2.71366i	0.793963	−	0.0902549i
$905$	−5.71174	+	3.29768i	−0.189865	+	0.109618i
$906$	−27.5424	−	19.6712i	−0.915033	−	0.653532i
$907$	−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	−0.552422	−	0.833564i	$-0.686296\pi$
$911$	13.4518	−	23.2991i	0.445677	−	0.771935i	0.998099	+	0.0616295i	$0.0196297\pi$
$912$	−18.9537	−	10.5277i	−0.627618	−	0.348607i
$913$	−12.3772	−	21.4380i	−0.409626	−	0.709493i
$914$	−1.33455	−	3.27646i	−0.0441430	−	0.108376i
$915$	9.23629	−	5.83965i	0.305342	−	0.193053i
$916$	16.0237	+	16.4066i	0.529439	+	0.542091i
$917$	−3.86319			−0.127574
$918$	−23.3196	−	13.9724i	−0.769662	−	0.461158i
$919$			22.2518i			0.734020i	0.930217	+	0.367010i	$0.119619\pi$
$919$			22.2518i			0.734020i	−0.930217	+	0.367010i	$0.880381\pi$
$920$	11.0797	−	8.19413i	0.365286	−	0.270153i
$921$	−27.3976	−	43.3335i	−0.902782	−	1.42789i
$922$	2.81054	+	6.90017i	0.0925603	+	0.227245i
$923$	17.7519	−	10.2491i	0.584310	−	0.337352i
$924$	12.8513	+	3.05528i	0.422776	+	0.100511i
$925$	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	$0.718477\pi$
$930$	24.5370	+	17.5248i	0.804601	+	0.574659i
$931$	−1.85796	−	3.21809i	−0.0608923	−	0.105469i
$932$	−13.0776	+	3.33917i	−0.428372	+	0.109378i
$933$	−16.6817	+	31.7782i	−0.546134	+	1.04037i
$934$	−2.56703	−	1.99394i	−0.0839959	−	0.0652437i
$935$	−10.4781			−0.342670
$936$	−17.0023	+	49.6360i	−0.555737	+	1.62240i
$937$	−2.11802			−0.0691926			−0.0345963	−	0.999401i	$-0.511015\pi$
$937$	−2.11802			−0.0691926			−0.0345963	+	0.999401i	$0.511015\pi$
$938$	5.58925	+	4.34144i	0.182496	+	0.141753i
$939$	6.01161	−	0.241782i	0.196181	−	0.00789026i
$940$	−8.66550	−	33.9378i	−0.282637	−	1.10693i
$941$	−3.56180	−	6.16922i	−0.116111	−	0.201111i	0.802112	−	0.597173i	$-0.203710\pi$
$941$	−3.56180	−	6.16922i	−0.116111	−	0.201111i	−0.918223	+	0.396063i	$0.870376\pi$
$942$	12.8465	−	5.84500i	0.418562	−	0.190440i
$943$	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	$0.351572\pi$
$948$	29.9919	−	8.95620i	0.974092	−	0.290884i
$949$	3.37910	−	1.95093i	0.109690	−	0.0633297i
$950$	2.99367	+	7.34977i	0.0971274	+	0.238458i
$951$	−26.4577	+	1.06411i	−0.857949	+	0.0345060i
$952$	−20.2827	+	15.0004i	−0.657366	+	0.486165i
$953$			45.3652i			1.46952i	0.678326	+	0.734761i	$0.262706\pi$
$953$			45.3652i			1.46952i	−0.678326	+	0.734761i	$0.737294\pi$
$954$	13.4886	+	26.7399i	0.436709	+	0.865736i
$955$	−42.5046			−1.37542
$956$	−0.193988	+	0.189461i	−0.00627403	+	0.00612761i
$957$	12.3847	+	6.50125i	0.400341	+	0.210156i
$958$	19.2284	+	47.2078i	0.621243	+	1.52522i
$959$	14.7760	+	25.5928i	0.477143	+	0.826436i
$960$	−23.9370	+	6.53666i	−0.772562	+	0.210970i
$961$	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
$966$	1.54978	−	15.9924i	0.0498633	−	0.514548i
$967$	2.55341	−	1.47421i	0.0821121	−	0.0474075i	−0.458382	−	0.888755i	$-0.651571\pi$
$967$	2.55341	−	1.47421i	0.0821121	−	0.0474075i	0.540494	+	0.841348i	$0.318237\pi$
$968$	−2.71496	−	23.8832i	−0.0872622	−	0.767636i
$969$	16.9486	−	10.7158i	0.544468	−	0.344240i
$970$	20.9099	−	26.9198i	0.671376	−	0.864342i
$971$			21.8052i			0.699763i	0.936794	+	0.349882i	$0.113778\pi$
$971$			21.8052i			0.699763i	−0.936794	+	0.349882i	$0.886222\pi$
$972$	−31.0947	−	2.26201i	−0.997364	−	0.0725540i
$973$			2.98444i			0.0956768i
$974$	−3.04115	−	2.36221i	−0.0974447	−	0.0756901i
$975$	16.2325	−	10.2630i	0.519858	−	0.328680i
$976$	14.0885	+	0.332721i	0.450961	+	0.0106501i
$977$	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	$0.169094\pi$
$978$	−27.5229	−	2.66716i	−0.880086	−	0.0852863i
$979$	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	−0.743700	−	0.668513i	$-0.766931\pi$
$983$	6.49316	−	11.2465i	0.207100	−	0.358707i	0.950800	+	0.309806i	$0.100264\pi$
$984$	−18.8604	−	23.4673i	−0.601248	−	0.748109i
$985$	5.16324	+	8.94300i	0.164515	+	0.284948i
$986$	−24.7391	+	10.0766i	−0.787854	+	0.320904i
$987$	−36.1598	−	18.9818i	−1.15098	−	0.604197i
$988$	−27.0402	−	27.6864i	−0.860265	−	0.880821i
$989$	2.46201			0.0782873
$990$	−10.7289	+	5.41206i	−0.340987	+	0.172006i
$991$		−	47.5865i		−	1.51163i	−0.654783	−	0.755817i	$-0.727240\pi$
$991$		−	47.5865i		−	1.51163i	0.654783	−	0.755817i	$-0.272760\pi$
$992$	13.8142	+	36.3491i	0.438601	+	1.15409i
$993$	10.7296	−	0.431535i	0.340493	−	0.0136943i
$994$	10.4679	−	4.26373i	0.332022	−	0.135237i
$995$	−1.92557	+	1.11173i	−0.0610447	+	0.0352442i
$996$	51.9499	−	15.5133i	1.64609	−	0.491558i
$997$	7.41748	+	4.28248i	0.234914	+	0.135628i	0.612837	−	0.790209i	$-0.290028\pi$
$997$	7.41748	+	4.28248i	0.234914	+	0.135628i	−0.377923	+	0.925837i	$0.623362\pi$
$998$	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.11.3	✓	16
3.2	odd	2		216.2.l.b.35.6		16
4.3	odd	2		288.2.p.b.47.2		16
8.3	odd	2	inner	72.2.l.b.11.7	yes	16
8.5	even	2		288.2.p.b.47.1		16
9.2	odd	6		648.2.f.b.323.1		16
9.4	even	3		216.2.l.b.179.2		16
9.5	odd	6	inner	72.2.l.b.59.7	yes	16
9.7	even	3		648.2.f.b.323.16		16
12.11	even	2		864.2.p.b.143.3		16
24.5	odd	2		864.2.p.b.143.6		16
24.11	even	2		216.2.l.b.35.2		16
36.7	odd	6		2592.2.f.b.1295.5		16
36.11	even	6		2592.2.f.b.1295.11		16
36.23	even	6		288.2.p.b.239.1		16
36.31	odd	6		864.2.p.b.719.6		16
72.5	odd	6		288.2.p.b.239.2		16
72.11	even	6		648.2.f.b.323.15		16
72.13	even	6		864.2.p.b.719.3		16
72.29	odd	6		2592.2.f.b.1295.6		16
72.43	odd	6		648.2.f.b.323.2		16
72.59	even	6	inner	72.2.l.b.59.3	yes	16
72.61	even	6		2592.2.f.b.1295.12		16
72.67	odd	6		216.2.l.b.179.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.l.b.11.3	✓	16	1.1	even	1	trivial
72.2.l.b.11.7	yes	16	8.3	odd	2	inner
72.2.l.b.59.3	yes	16	72.59	even	6	inner
72.2.l.b.59.7	yes	16	9.5	odd	6	inner
216.2.l.b.35.2		16	24.11	even	2
216.2.l.b.35.6		16	3.2	odd	2
216.2.l.b.179.2		16	9.4	even	3
216.2.l.b.179.6		16	72.67	odd	6
288.2.p.b.47.1		16	8.5	even	2
288.2.p.b.47.2		16	4.3	odd	2
288.2.p.b.239.1		16	36.23	even	6
288.2.p.b.239.2		16	72.5	odd	6
648.2.f.b.323.1		16	9.2	odd	6
648.2.f.b.323.2		16	72.43	odd	6
648.2.f.b.323.15		16	72.11	even	6
648.2.f.b.323.16		16	9.7	even	3
864.2.p.b.143.3		16	12.11	even	2
864.2.p.b.143.6		16	24.5	odd	2
864.2.p.b.719.3		16	72.13	even	6
864.2.p.b.719.6		16	36.31	odd	6
2592.2.f.b.1295.5		16	36.7	odd	6
2592.2.f.b.1295.6		16	72.29	odd	6
2592.2.f.b.1295.11		16	36.11	even	6
2592.2.f.b.1295.12		16	72.61	even	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+(-0.867527 + 1.11687i) q^{2} +(0.925606 + 1.46399i) q^{3} +(-0.494795 - 1.93783i) q^{4} +(0.895377 + 1.55084i) q^{5} +(-2.43807 - 0.236266i) 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} +(2.37897 - 2.51804i) q^{12} +(5.35491 - 3.09166i) q^{13} +(3.15768 - 1.28617i) q^{14} +(-1.44164 + 2.74629i) q^{15} +(-3.51036 + 1.91766i) q^{16} -3.69943i q^{17} +(-1.91080 - 3.78799i) q^{18} +3.12941 q^{19} +(2.56223 - 2.50243i) q^{20} +(-0.167814 - 4.17248i) q^{21} +(2.07154 - 0.843770i) q^{22} +(-1.36036 - 2.35622i) q^{23} +(0.748502 + 4.84146i) 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} +(-1.81658 - 3.99260i) q^{30} +(-5.95312 + 3.43703i) q^{31} +(0.903557 - 5.58423i) q^{32} +(-0.110092 - 2.73729i) q^{33} +(4.13178 + 3.20936i) q^{34} -4.31738i q^{35} +(5.88836 + 1.15206i) q^{36} +5.24328i q^{37} +(-2.71485 + 3.49514i) q^{38} +(9.48268 + 4.97786i) q^{39} +(0.572089 + 5.03261i) q^{40} +(-5.32220 + 3.07278i) q^{41} +(4.80570 + 3.43231i) 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} +(-6.05663 - 3.36412i) q^{48} +(-0.593711 - 1.02834i) q^{49} +(0.956625 + 2.34861i) q^{50} +(5.41592 - 3.42422i) q^{51} +(-8.64069 - 8.84716i) q^{52} -7.05913 q^{53} +(3.77691 - 6.30357i) q^{54} -2.83235i q^{55} +(-4.05478 - 5.48265i) q^{56} +(2.89660 + 4.58141i) q^{57} +(-2.72382 - 6.68727i) q^{58} +(-6.10118 + 3.52252i) q^{59} +(6.03514 + 1.43480i) 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} +(3.15270 + 2.25171i) q^{66} +(1.03786 + 1.79762i) q^{67} +(-7.16886 + 1.83046i) q^{68} +(2.19031 - 4.17248i) q^{69} +(4.82195 + 3.74544i) q^{70} +3.31507 q^{71} +(-6.39501 + 5.57708i) q^{72} +0.631029 q^{73} +(-5.85606 - 4.54868i) q^{74} +(3.10340 - 0.124816i) q^{75} +(-1.54842 - 6.06426i) q^{76} +(1.90662 + 3.30237i) q^{77} +(-13.7861 + 6.27250i) 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} +(-8.00251 + 2.38972i) q^{84} +(5.73722 - 3.31239i) q^{85} +(-0.482746 - 1.18519i) q^{86} +(-8.83640 + 0.355393i) q^{87} +(-2.66007 - 3.59680i) q^{88} +1.16402i q^{89} +(4.16367 - 6.35502i) q^{90} -14.9075 q^{91} +(-3.89284 + 3.80199i) q^{92} +(-10.5420 - 5.53394i) q^{93} +(5.21730 + 12.8090i) q^{94} +(2.80200 + 4.85321i) q^{95} +(9.01156 - 3.84600i) 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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Representations

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Database

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