LMFDB - Embedded newform 78.2.k.a.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,2,Mod(11,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 7]))

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

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

chi := DirichletCharacter("78.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	78.k (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.622833135766$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + 9297 x^{8} - 11276 x^{7} + 11224 x^{6} - 9024 x^{5} + 5736 x^{4} - 2780 x^{3} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			41.1
Root			$0.500000 - 0.410882i$ of defining polynomial
Character	$\chi$	$=$	78.41
Dual form			78.2.k.a.59.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.0795432 - 1.73022i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.02097 + 2.02097i) q^{5} +(1.69185 + 0.370982i) q^{6} +(3.46723 - 0.929042i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.98735 + 0.275255i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.0795432 - 1.73022i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.02097 + 2.02097i) q^{5} +(1.69185 + 0.370982i) q^{6} +(3.46723 - 0.929042i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.98735 + 0.275255i) q^{9} +(-2.47517 + 1.42904i) q^{10} +(-4.05922 - 1.08766i) q^{11} +(-0.796225 + 1.53819i) q^{12} +(-3.60121 - 0.176977i) q^{13} +3.58954i q^{14} +(3.33598 - 3.65748i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.72704 + 2.99132i) q^{17} +(0.507306 - 2.95680i) q^{18} +(0.581191 + 2.16903i) q^{19} +(-0.739726 - 2.76070i) q^{20} +(-1.88324 - 5.92518i) q^{21} +(2.10121 - 3.63939i) q^{22} +(-1.51618 - 2.62611i) q^{23} +(-1.27970 - 1.16721i) q^{24} +3.16864i q^{25} +(1.10301 - 3.43269i) q^{26} +(0.713876 + 5.14688i) q^{27} +(-3.46723 - 0.929042i) q^{28} +(1.74432 - 1.00708i) q^{29} +(2.66944 + 4.16893i) q^{30} +(1.21829 - 1.21829i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.55902 + 7.10987i) q^{33} +(-2.44240 - 2.44240i) q^{34} +(8.88473 + 5.12960i) q^{35} +(2.72474 + 1.25529i) q^{36} +(-1.25335 + 4.67758i) q^{37} -2.24555 q^{38} +(-0.0197576 + 6.24497i) q^{39} +2.85808 q^{40} +(2.05521 - 7.67015i) q^{41} +(6.21071 - 0.285524i) q^{42} +(-1.68905 - 0.975173i) q^{43} +(2.97155 + 2.97155i) q^{44} +(-6.59362 - 5.48105i) q^{45} +(2.92904 - 0.784834i) q^{46} +(-0.957390 + 0.957390i) q^{47} +(1.45865 - 0.933998i) q^{48} +(5.09639 - 2.94240i) q^{49} +(-3.06067 - 0.820104i) q^{50} +(5.31303 + 2.75023i) q^{51} +(3.03025 + 1.95387i) q^{52} +7.22186i q^{53} +(-5.15627 - 0.642559i) q^{54} +(-6.00542 - 10.4017i) q^{55} +(1.79477 - 3.10863i) q^{56} +(3.70668 - 1.17812i) q^{57} +(0.521304 + 1.94553i) q^{58} +(-2.66284 - 9.93785i) q^{59} +(-4.71778 + 1.49949i) q^{60} +(-0.137104 + 0.237470i) q^{61} +(0.861464 + 1.49210i) q^{62} +(-10.1021 + 3.72974i) q^{63} -1.00000i q^{64} +(-6.92026 - 7.63559i) q^{65} +(-6.46410 - 3.34607i) q^{66} +(4.10121 + 1.09891i) q^{67} +(2.99132 - 1.72704i) q^{68} +(-4.42315 + 2.83223i) q^{69} +(-7.25436 + 7.25436i) q^{70} +(10.6578 - 2.85575i) q^{71} +(-1.91774 + 2.30701i) q^{72} +(10.0822 + 10.0822i) q^{73} +(-4.19381 - 2.42130i) q^{74} +(5.48246 - 0.252044i) q^{75} +(0.581191 - 2.16903i) q^{76} -15.0847 q^{77} +(-6.02706 - 1.63540i) q^{78} +1.58051 q^{79} +(-0.739726 + 2.76070i) q^{80} +(8.84847 - 1.64456i) q^{81} +(6.87686 + 3.97036i) q^{82} +(-2.58938 - 2.58938i) q^{83} +(-1.33165 + 6.07298i) q^{84} +(-9.53567 + 2.55507i) q^{85} +(1.37910 - 1.37910i) q^{86} +(-1.88122 - 2.93795i) q^{87} +(-3.63939 + 2.10121i) q^{88} +(9.50933 + 2.54802i) q^{89} +(7.00085 - 4.95035i) q^{90} +(-12.6506 + 2.73205i) q^{91} +3.03237i q^{92} +(-2.20483 - 2.01101i) q^{93} +(-0.676977 - 1.17256i) q^{94} +(-3.20898 + 5.55812i) q^{95} +(0.524648 + 1.65068i) q^{96} +(-2.07638 - 7.74915i) q^{97} +(1.52310 + 5.68429i) q^{98} +(12.4257 + 2.13191i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} - 24 q^{10} - 24 q^{13} + 8 q^{16} - 16 q^{19} - 24 q^{21} - 8 q^{28} + 24 q^{30} + 16 q^{31} - 24 q^{33} + 24 q^{34} + 24 q^{36} + 16 q^{37} + 48 q^{39} + 24 q^{45} + 24 q^{46} + 24 q^{49} - 8 q^{52} - 24 q^{55} - 24 q^{57} - 24 q^{60} - 24 q^{61} - 24 q^{63} - 48 q^{66} + 32 q^{67} - 48 q^{69} - 24 q^{72} + 56 q^{73} - 16 q^{76} - 96 q^{79} + 24 q^{81} - 48 q^{82} - 24 q^{85} + 48 q^{87} - 16 q^{91} - 24 q^{93} - 24 q^{94} + 16 q^{97}+O(q^{100}) $ 16 * q + 8 * q^7 - 24 * q^10 - 24 * q^13 + 8 * q^16 - 16 * q^19 - 24 * q^21 - 8 * q^28 + 24 * q^30 + 16 * q^31 - 24 * q^33 + 24 * q^34 + 24 * q^36 + 16 * q^37 + 48 * q^39 + 24 * q^45 + 24 * q^46 + 24 * q^49 - 8 * q^52 - 24 * q^55 - 24 * q^57 - 24 * q^60 - 24 * q^61 - 24 * q^63 - 48 * q^66 + 32 * q^67 - 48 * q^69 - 24 * q^72 + 56 * q^73 - 16 * q^76 - 96 * q^79 + 24 * q^81 - 48 * q^82 - 24 * q^85 + 48 * q^87 - 16 * q^91 - 24 * q^93 - 24 * q^94 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$-1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−0.0795432	−	1.73022i	−0.0459243	−	0.998945i
$3$	−0.0795432	−	1.73022i	−0.0459243	−	0.998945i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	2.02097	+	2.02097i	0.903805	+	0.903805i	0.995763	−	0.0919576i	$-0.0293124\pi$
$5$	2.02097	+	2.02097i	0.903805	+	0.903805i	−0.0919576	+	0.995763i	$0.529312\pi$
$6$	1.69185	+	0.370982i	0.690697	+	0.151453i
$7$	3.46723	−	0.929042i	1.31049	−	0.351145i	0.465083	−	0.885267i	$-0.346025\pi$
$7$	3.46723	−	0.929042i	1.31049	−	0.351145i	0.845407	+	0.534122i	$0.179358\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.98735	+	0.275255i	−0.995782	+	0.0917517i
$10$	−2.47517	+	1.42904i	−0.782718	+	0.451903i
$11$	−4.05922	−	1.08766i	−1.22390	−	0.327943i	−0.411699	−	0.911320i	$-0.635064\pi$
$11$	−4.05922	−	1.08766i	−1.22390	−	0.327943i	−0.812201	+	0.583377i	$0.801731\pi$
$12$	−0.796225	+	1.53819i	−0.229850	+	0.444037i
$13$	−3.60121	−	0.176977i	−0.998795	−	0.0490845i
$13$	−3.60121	−	0.176977i	−0.998795	−	0.0490845i
$14$			3.58954i			0.959345i
$15$	3.33598	−	3.65748i	0.861345	−	0.944358i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.72704	+	2.99132i	−0.418869	+	0.725502i	−0.995826	−	0.0912724i	$-0.970907\pi$
$17$	−1.72704	+	2.99132i	−0.418869	+	0.725502i	0.576957	+	0.816774i	$0.304240\pi$
$18$	0.507306	−	2.95680i	0.119573	−	0.696923i
$19$	0.581191	+	2.16903i	0.133334	+	0.497611i	0.999999	−	0.00128023i	$-0.000407509\pi$
$19$	0.581191	+	2.16903i	0.133334	+	0.497611i	−0.866665	+	0.498891i	$0.833741\pi$
$20$	−0.739726	−	2.76070i	−0.165408	−	0.617310i
$21$	−1.88324	−	5.92518i	−0.410958	−	1.29298i
$22$	2.10121	−	3.63939i	0.447978	−	0.775921i
$23$	−1.51618	−	2.62611i	−0.316146	−	0.547581i	0.663534	−	0.748146i	$-0.269056\pi$
$23$	−1.51618	−	2.62611i	−0.316146	−	0.547581i	−0.979680	+	0.200565i	$0.935722\pi$
$24$	−1.27970	−	1.16721i	−0.261217	−	0.238255i
$25$			3.16864i			0.633728i
$26$	1.10301	−	3.43269i	0.216317	−	0.673206i
$27$	0.713876	+	5.14688i	0.137386	+	0.990518i
$28$	−3.46723	−	0.929042i	−0.655245	−	0.175572i
$29$	1.74432	−	1.00708i	0.323911	−	0.187010i	−0.329223	−	0.944252i	$-0.606787\pi$
$29$	1.74432	−	1.00708i	0.323911	−	0.187010i	0.653135	+	0.757242i	$0.273454\pi$
$30$	2.66944	+	4.16893i	0.487372	+	0.761139i
$31$	1.21829	−	1.21829i	0.218812	−	0.218812i	−0.589186	−	0.807998i	$-0.700551\pi$
$31$	1.21829	−	1.21829i	0.218812	−	0.218812i	0.807998	+	0.589186i	$0.200551\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−1.55902	+	7.10987i	−0.271390	+	1.23767i
$34$	−2.44240	−	2.44240i	−0.418869	−	0.418869i
$35$	8.88473	+	5.12960i	1.50179	+	0.867061i
$36$	2.72474	+	1.25529i	0.454124	+	0.209216i
$37$	−1.25335	+	4.67758i	−0.206050	+	0.768990i	0.783077	+	0.621925i	$0.213649\pi$
$37$	−1.25335	+	4.67758i	−0.206050	+	0.768990i	−0.989127	+	0.147065i	$0.953017\pi$
$38$	−2.24555			−0.364276
$39$	−0.0197576	+	6.24497i	−0.00316375	+	0.999995i
$40$	2.85808			0.451903
$41$	2.05521	−	7.67015i	0.320970	−	1.19788i	−0.597332	−	0.801994i	$-0.703772\pi$
$41$	2.05521	−	7.67015i	0.320970	−	1.19788i	0.918302	−	0.395881i	$-0.129561\pi$
$42$	6.21071	−	0.285524i	0.958333	−	0.0440573i
$43$	−1.68905	−	0.975173i	−0.257578	−	0.148712i	0.365651	−	0.930752i	$-0.380846\pi$
$43$	−1.68905	−	0.975173i	−0.257578	−	0.148712i	−0.623229	+	0.782039i	$0.714180\pi$
$44$	2.97155	+	2.97155i	0.447978	+	0.447978i
$45$	−6.59362	−	5.48105i	−0.982919	−	0.817067i
$46$	2.92904	−	0.784834i	0.431864	−	0.115718i
$47$	−0.957390	+	0.957390i	−0.139650	+	0.139650i	−0.773476	−	0.633826i	$-0.781484\pi$
$47$	−0.957390	+	0.957390i	−0.139650	+	0.139650i	0.633826	+	0.773476i	$0.281484\pi$
$48$	1.45865	−	0.933998i	0.210537	−	0.134811i
$49$	5.09639	−	2.94240i	0.728056	−	0.420343i
$50$	−3.06067	−	0.820104i	−0.432844	−	0.115980i
$51$	5.31303	+	2.75023i	0.743973	+	0.385109i
$52$	3.03025	+	1.95387i	0.420220	+	0.270953i
$53$			7.22186i			0.991999i	0.868323	+	0.495999i	$0.165198\pi$
$53$			7.22186i			0.991999i	−0.868323	+	0.495999i	$0.834802\pi$
$54$	−5.15627	−	0.642559i	−0.701679	−	0.0874413i
$55$	−6.00542	−	10.4017i	−0.809771	−	1.40256i
$56$	1.79477	−	3.10863i	0.239836	−	0.415409i
$57$	3.70668	−	1.17812i	0.490962	−	0.156046i
$58$	0.521304	+	1.94553i	0.0684505	+	0.255461i
$59$	−2.66284	−	9.93785i	−0.346672	−	1.29380i	−0.890647	−	0.454696i	$-0.849748\pi$
$59$	−2.66284	−	9.93785i	−0.346672	−	1.29380i	0.543975	−	0.839101i	$-0.316919\pi$
$60$	−4.71778	+	1.49949i	−0.609063	+	0.193583i
$61$	−0.137104	+	0.237470i	−0.0175543	+	0.0304050i	−0.874669	−	0.484720i	$-0.838921\pi$
$61$	−0.137104	+	0.237470i	−0.0175543	+	0.0304050i	0.857115	+	0.515125i	$0.172255\pi$
$62$	0.861464	+	1.49210i	0.109406	+	0.189497i
$63$	−10.1021	+	3.72974i	−1.27274	+	0.469903i
$64$		−	1.00000i		−	0.125000i
$65$	−6.92026	−	7.63559i	−0.858353	−	0.947079i
$66$	−6.46410	−	3.34607i	−0.795676	−	0.411872i
$67$	4.10121	+	1.09891i	0.501042	+	0.134254i	0.500484	−	0.865746i	$-0.333156\pi$
$67$	4.10121	+	1.09891i	0.501042	+	0.134254i	0.000558430		1.00000i	$0.499822\pi$
$68$	2.99132	−	1.72704i	0.362751	−	0.209434i
$69$	−4.42315	+	2.83223i	−0.532485	+	0.340960i
$70$	−7.25436	+	7.25436i	−0.867061	+	0.867061i
$71$	10.6578	−	2.85575i	1.26485	−	0.338915i	0.436793	−	0.899562i	$-0.356114\pi$
$71$	10.6578	−	2.85575i	1.26485	−	0.338915i	0.828055	+	0.560647i	$0.189447\pi$
$72$	−1.91774	+	2.30701i	−0.226008	+	0.271883i
$73$	10.0822	+	10.0822i	1.18003	+	1.18003i	0.979735	+	0.200296i	$0.0641903\pi$
$73$	10.0822	+	10.0822i	1.18003	+	1.18003i	0.200296	+	0.979735i	$0.435810\pi$
$74$	−4.19381	−	2.42130i	−0.487520	−	0.281470i
$75$	5.48246	−	0.252044i	0.633059	−	0.0291035i
$76$	0.581191	−	2.16903i	0.0666672	−	0.248805i
$77$	−15.0847			−1.71906
$78$	−6.02706	−	1.63540i	−0.682430	−	0.185173i
$79$	1.58051			0.177821			0.0889105	−	0.996040i	$-0.471661\pi$
$79$	1.58051			0.177821			0.0889105	+	0.996040i	$0.471661\pi$
$80$	−0.739726	+	2.76070i	−0.0827039	+	0.308655i
$81$	8.84847	−	1.64456i	0.983163	−	0.182729i
$82$	6.87686	+	3.97036i	0.759423	+	0.438453i
$83$	−2.58938	−	2.58938i	−0.284221	−	0.284221i	0.550569	−	0.834790i	$-0.314411\pi$
$83$	−2.58938	−	2.58938i	−0.284221	−	0.284221i	−0.834790	+	0.550569i	$0.814411\pi$
$84$	−1.33165	+	6.07298i	−0.145295	+	0.662617i
$85$	−9.53567	+	2.55507i	−1.03429	+	0.277137i
$86$	1.37910	−	1.37910i	0.148712	−	0.148712i
$87$	−1.88122	−	2.93795i	−0.201688	−	0.314981i
$88$	−3.63939	+	2.10121i	−0.387961	+	0.223989i
$89$	9.50933	+	2.54802i	1.00799	+	0.270089i	0.724788	−	0.688972i	$-0.241938\pi$
$89$	9.50933	+	2.54802i	1.00799	+	0.270089i	0.283199	+	0.959061i	$0.408604\pi$
$90$	7.00085	−	4.95035i	0.737954	−	0.521812i
$91$	−12.6506	+	2.73205i	−1.32615	+	0.286397i
$92$			3.03237i			0.316146i
$93$	−2.20483	−	2.01101i	−0.228630	−	0.208533i
$94$	−0.676977	−	1.17256i	−0.0698248	−	0.120940i
$95$	−3.20898	+	5.55812i	−0.329235	+	0.570251i
$96$	0.524648	+	1.65068i	0.0535466	+	0.168472i
$97$	−2.07638	−	7.74915i	−0.210824	−	0.786807i	−0.987595	−	0.157023i	$-0.949810\pi$
$97$	−2.07638	−	7.74915i	−0.210824	−	0.786807i	0.776771	−	0.629784i	$-0.216856\pi$
$98$	1.52310	+	5.68429i	0.153856	+	0.574200i
$99$	12.4257	+	2.13191i	1.24883	+	0.214265i
$100$	1.58432	−	2.74412i	0.158432	−	0.274412i
$101$	1.05342	+	1.82458i	0.104820	+	0.181553i	0.913665	−	0.406469i	$-0.133240\pi$
$101$	1.05342	+	1.82458i	0.104820	+	0.181553i	−0.808845	+	0.588022i	$0.799907\pi$
$102$	−4.03163	+	4.42018i	−0.399191	+	0.437663i
$103$		−	14.2629i		−	1.40537i	−0.711503	−	0.702683i	$-0.751985\pi$
$103$		−	14.2629i		−	1.40537i	0.711503	−	0.702683i	$-0.248015\pi$
$104$	−2.67158	+	2.42130i	−0.261970	+	0.237428i
$105$	8.16864	−	15.7806i	0.797178	−	1.54003i
$106$	−6.97578	−	1.86915i	−0.677548	−	0.181548i
$107$	−11.9906	+	6.92275i	−1.15917	+	0.669248i	−0.951105	−	0.308867i	$-0.900050\pi$
$107$	−11.9906	+	6.92275i	−1.15917	+	0.669248i	−0.208066	+	0.978115i	$0.566717\pi$
$108$	1.95521	−	4.81427i	0.188140	−	0.463253i
$109$	5.84220	−	5.84220i	0.559581	−	0.559581i	−0.369607	−	0.929188i	$-0.620508\pi$
$109$	5.84220	−	5.84220i	0.559581	−	0.559581i	0.929188	+	0.369607i	$0.120508\pi$
$110$	11.6016	−	3.10863i	1.10617	−	0.296397i
$111$	8.19296	+	1.79651i	0.777641	+	0.170518i
$112$	2.53819	+	2.53819i	0.239836	+	0.239836i
$113$	15.5920	+	9.00205i	1.46677	+	0.846841i	0.999309	−	0.0371710i	$-0.0118346\pi$
$113$	15.5920	+	9.00205i	1.46677	+	0.846841i	0.467463	+	0.884012i	$0.345168\pi$
$114$	0.178618	+	3.88530i	0.0167291	+	0.363892i
$115$	2.24312	−	8.37145i	0.209172	−	0.780641i
$116$	−2.01416			−0.187010
$117$	10.8068	−	0.462560i	0.999085	−	0.0427637i
$118$	10.2884			0.947125
$119$	−3.20898	+	11.9761i	−0.294167	+	1.09785i
$120$	−0.227341	−	4.94512i	−0.0207533	−	0.451426i
$121$	5.76795	+	3.33013i	0.524359	+	0.302739i
$122$	−0.193894	−	0.193894i	−0.0175543	−	0.0175543i
$123$	−13.4345	−	2.94586i	−1.21135	−	0.265620i
$124$	−1.66422	+	0.445927i	−0.149452	+	0.0400454i
$125$	3.70112	−	3.70112i	0.331039	−	0.331039i
$126$	−0.988040	−	10.7232i	−0.0880216	−	0.955299i
$127$	−17.9209	+	10.3466i	−1.59022	+	0.918114i	−0.596952	+	0.802277i	$0.703622\pi$
$127$	−17.9209	+	10.3466i	−1.59022	+	0.918114i	−0.993268	+	0.115837i	$0.963045\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−1.55291	+	3.00000i	−0.136726	+	0.264135i
$130$	9.16651	−	4.70822i	0.803956	−	0.412939i
$131$			4.68295i			0.409151i	0.978851	+	0.204576i	$0.0655814\pi$
$131$			4.68295i			0.409151i	−0.978851	+	0.204576i	$0.934419\pi$
$132$	4.90508	−	5.37782i	0.426933	−	0.468079i
$133$	4.03025	+	6.98059i	0.349467	+	0.605294i
$134$	−2.12294	+	3.67704i	−0.183394	+	0.317648i
$135$	−8.95897	+	11.8444i	−0.771065	+	1.01940i
$136$	0.893982	+	3.33639i	0.0766583	+	0.286093i
$137$	−1.41832	−	5.29326i	−0.121176	−	0.452234i	0.878499	−	0.477744i	$-0.158545\pi$
$137$	−1.41832	−	5.29326i	−0.121176	−	0.452234i	−0.999675	+	0.0255107i	$0.991879\pi$
$138$	−1.59092	−	5.00547i	−0.135428	−	0.426094i
$139$	−7.34662	+	12.7247i	−0.623132	+	1.07930i	0.365767	+	0.930706i	$0.380807\pi$
$139$	−7.34662	+	12.7247i	−0.623132	+	1.07930i	−0.988899	+	0.148590i	$0.952527\pi$
$140$	−5.12960	−	8.88473i	−0.433531	−	0.750897i
$141$	1.73265	+	1.58034i	0.145916	+	0.133089i
$142$			11.0338i			0.925933i
$143$	14.4256	+	4.63529i	1.20633	+	0.387622i
$144$	−1.73205	−	2.44949i	−0.144338	−	0.204124i
$145$	5.56049	+	1.48993i	0.461774	+	0.123732i
$146$	−12.3481	+	7.12919i	−1.02194	+	0.590016i
$147$	−5.49640	−	8.58385i	−0.453335	−	0.707984i
$148$	3.42423	−	3.42423i	0.281470	−	0.281470i
$149$	−9.98255	+	2.67482i	−0.817803	+	0.219130i	−0.643386	−	0.765542i	$-0.722471\pi$
$149$	−9.98255	+	2.67482i	−0.817803	+	0.219130i	−0.174417	+	0.984672i	$0.555804\pi$
$150$	−1.17551	+	5.36088i	−0.0959798	+	0.437714i
$151$	−6.48932	−	6.48932i	−0.528094	−	0.528094i	0.391910	−	0.920004i	$-0.371814\pi$
$151$	−6.48932	−	6.48932i	−0.528094	−	0.528094i	−0.920004	+	0.391910i	$0.871814\pi$
$152$	1.94470	+	1.12277i	0.157736	+	0.0910691i
$153$	4.33589	−	9.41149i	0.350536	−	0.760874i
$154$	3.90421	−	14.5707i	0.314611	−	1.17414i
$155$	4.92427			0.395527
$156$	3.13959	−	5.39842i	0.251369	−	0.432220i
$157$	−14.1431			−1.12874			−0.564372	−	0.825520i	$-0.690882\pi$
$157$	−14.1431			−1.12874			−0.564372	+	0.825520i	$0.690882\pi$
$158$	−0.409066	+	1.52665i	−0.0325435	+	0.121454i
$159$	12.4954	−	0.574450i	0.990952	−	0.0455568i
$160$	−2.47517	−	1.42904i	−0.195680	−	0.112976i
$161$	−7.69672	−	7.69672i	−0.606587	−	0.606587i
$162$	−0.701625	+	8.97261i	−0.0551249	+	0.704955i
$163$	1.07638	−	0.288415i	0.0843084	−	0.0225904i	−0.216418	−	0.976301i	$-0.569437\pi$
$163$	1.07638	−	0.288415i	0.0843084	−	0.0225904i	0.300727	+	0.953710i	$0.402771\pi$
$164$	−5.61494	+	5.61494i	−0.438453	+	0.438453i
$165$	−17.5196	+	11.2181i	−1.36390	+	0.873328i
$166$	3.17133	−	1.83097i	0.246143	−	0.142110i
$167$	5.39478	+	1.44553i	0.417461	+	0.111858i	0.461434	−	0.887174i	$-0.347335\pi$
$167$	5.39478	+	1.44553i	0.417461	+	0.111858i	−0.0439735	+	0.999033i	$0.514002\pi$
$168$	−5.52139	−	2.85808i	−0.425985	−	0.220506i
$169$	12.9374	+	1.27466i	0.995181	+	0.0980507i
$170$		−	9.87205i		−	0.757152i
$171$	−2.33326	−	6.31968i	−0.178429	−	0.483278i
$172$	0.975173	+	1.68905i	0.0743562	+	0.128789i
$173$	8.74765	−	15.1514i	0.665072	−	1.15194i	−0.314194	−	0.949359i	$-0.601734\pi$
$173$	8.74765	−	15.1514i	0.665072	−	1.15194i	0.979266	−	0.202579i	$-0.0649324\pi$
$174$	3.32474	−	1.05673i	0.252048	−	0.0801102i
$175$	2.94380	+	10.9864i	0.222530	+	0.830494i
$176$	−1.08766	−	4.05922i	−0.0819857	−	0.305975i
$177$	−16.9829	+	5.39779i	−1.27651	+	0.405723i
$178$	−4.92239	+	8.52583i	−0.368949	+	0.639038i
$179$	−4.60754	−	7.98049i	−0.344384	−	0.596490i	0.640858	−	0.767660i	$-0.278579\pi$
$179$	−4.60754	−	7.98049i	−0.344384	−	0.596490i	−0.985242	+	0.171169i	$0.945245\pi$
$180$	2.96971	+	8.04354i	0.221349	+	0.599530i
$181$		−	13.8110i		−	1.02656i	−0.858220	−	0.513282i	$-0.828429\pi$
$181$		−	13.8110i		−	1.02656i	0.858220	−	0.513282i	$-0.171571\pi$
$182$	0.635265	−	12.9267i	0.0470890	−	0.958189i
$183$	0.421783	+	0.218331i	0.0311791	+	0.0161395i
$184$	−2.92904	−	0.784834i	−0.215932	−	0.0578588i
$185$	−11.9862	+	6.92026i	−0.881246	+	0.508788i
$186$	2.51314	−	1.60921i	0.184273	−	0.117993i
$187$	10.2640	−	10.2640i	0.750577	−	0.750577i
$188$	1.30782	−	0.350429i	0.0953825	−	0.0255577i
$189$	7.25684	+	17.1822i	0.527857	+	1.24982i
$190$	−4.53819	−	4.53819i	−0.329235	−	0.329235i
$191$	−19.6614	−	11.3515i	−1.42265	−	0.821366i	−0.426123	−	0.904665i	$-0.640121\pi$
$191$	−19.6614	−	11.3515i	−1.42265	−	0.821366i	−0.996525	+	0.0832996i	$0.973454\pi$
$192$	−1.73022	+	0.0795432i	−0.124868	+	0.00574054i
$193$	−5.18821	+	19.3627i	−0.373456	+	1.39376i	0.482133	+	0.876098i	$0.339862\pi$
$193$	−5.18821	+	19.3627i	−0.373456	+	1.39376i	−0.855588	+	0.517657i	$0.826804\pi$
$194$	8.02251			0.575983
$195$	−12.6608	+	12.5810i	−0.906660	+	0.900941i
$196$	−5.88481			−0.420343
$197$	−4.82369	+	18.0023i	−0.343674	+	1.28261i	0.550480	+	0.834849i	$0.314445\pi$
$197$	−4.82369	+	18.0023i	−0.343674	+	1.28261i	−0.894154	+	0.447760i	$0.852222\pi$
$198$	−5.27526	+	11.4505i	−0.374897	+	0.813751i
$199$	−3.90611	−	2.25519i	−0.276897	−	0.159866i	0.355121	−	0.934820i	$-0.384440\pi$
$199$	−3.90611	−	2.25519i	−0.276897	−	0.159866i	−0.632018	+	0.774954i	$0.717773\pi$
$200$	2.24057	+	2.24057i	0.158432	+	0.158432i
$201$	1.57514	−	7.18341i	0.111102	−	0.506679i
$202$	−2.03506	+	0.545293i	−0.143186	+	0.0383667i
$203$	5.11233	−	5.11233i	0.358815	−	0.358815i
$204$	−3.22610	−	5.03828i	−0.225872	−	0.352750i
$205$	19.6547	−	11.3476i	1.37274	−	0.792552i
$206$	13.7769	+	3.69151i	0.959883	+	0.257200i
$207$	5.25221	+	7.42775i	0.365054	+	0.516264i
$208$	−1.64734	−	3.20722i	−0.114222	−	0.222381i
$209$		−	9.43672i		−	0.652752i
$210$	13.1287	+	11.9746i	0.905966	+	0.826327i
$211$	4.28841	+	7.42775i	0.295227	+	0.511348i	0.975038	−	0.222040i	$-0.0712715\pi$
$211$	4.28841	+	7.42775i	0.295227	+	0.511348i	−0.679811	+	0.733387i	$0.737938\pi$
$212$	3.61093	−	6.25431i	0.248000	−	0.429548i
$213$	−5.78884	−	18.2132i	−0.396645	−	1.24795i
$214$	−3.58348	−	13.3737i	−0.244962	−	0.914210i
$215$	−1.44272	−	5.38431i	−0.0983928	−	0.367207i
$216$	4.14418	+	3.13461i	0.281976	+	0.213283i
$217$	3.09226	−	5.35596i	0.209916	−	0.363586i
$218$	4.13106	+	7.15520i	0.279791	+	0.484612i
$219$	16.6425	−	18.2464i	1.12459	−	1.23298i
$220$			12.0108i			0.809771i
$221$	6.74882	−	10.4667i	0.453975	−	0.704067i
$222$	−3.85579	+	7.44882i	−0.258784	+	0.499932i
$223$	20.3575	+	5.45476i	1.36324	+	0.365278i	0.865004	−	0.501765i	$-0.167316\pi$
$223$	20.3575	+	5.45476i	1.36324	+	0.365278i	0.498232	+	0.867043i	$0.333983\pi$
$224$	−3.10863	+	1.79477i	−0.207704	+	0.119918i
$225$	−0.872184	−	9.46582i	−0.0581456	−	0.631055i
$226$	−12.7308	+	12.7308i	−0.846841	+	0.846841i
$227$	4.85544	−	1.30101i	0.322267	−	0.0863512i	−0.0940589	−	0.995567i	$-0.529984\pi$
$227$	4.85544	−	1.30101i	0.322267	−	0.0863512i	0.416326	+	0.909215i	$0.363318\pi$
$228$	−3.79914	−	0.833058i	−0.251604	−	0.0551706i
$229$	−9.92484	−	9.92484i	−0.655852	−	0.655852i	0.298544	−	0.954396i	$-0.403499\pi$
$229$	−9.92484	−	9.92484i	−0.655852	−	0.655852i	−0.954396	+	0.298544i	$0.903499\pi$
$230$	7.50563	+	4.33338i	0.494907	+	0.285735i
$231$	1.19989	+	26.0999i	0.0789468	+	1.71725i
$232$	0.521304	−	1.94553i	0.0342253	−	0.127730i
$233$	18.7944			1.23126			0.615630	−	0.788035i	$-0.288902\pi$
$233$	18.7944			1.23126			0.615630	+	0.788035i	$0.288902\pi$
$234$	−2.35020	+	10.5582i	−0.153637	+	0.690214i
$235$	−3.86971			−0.252432
$236$	−2.66284	+	9.93785i	−0.173336	+	0.646899i
$237$	−0.125719	−	2.73463i	−0.00816631	−	0.177633i
$238$	−10.7375	−	6.19928i	−0.696007	−	0.401840i
$239$	6.82142	+	6.82142i	0.441241	+	0.441241i	0.892429	−	0.451188i	$-0.149000\pi$
$239$	6.82142	+	6.82142i	0.441241	+	0.441241i	−0.451188	+	0.892429i	$0.649000\pi$
$240$	4.83546	+	1.06030i	0.312128	+	0.0684419i
$241$	8.18821	−	2.19402i	0.527449	−	0.141330i	0.0147390	−	0.999891i	$-0.495308\pi$
$241$	8.18821	−	2.19402i	0.527449	−	0.141330i	0.512710	+	0.858562i	$0.328642\pi$
$242$	−4.70951	+	4.70951i	−0.302739	+	0.302739i
$243$	−3.54930	−	15.1790i	−0.227688	−	0.973734i
$244$	0.237470	−	0.137104i	0.0152025	−	0.00877716i
$245$	16.2462	+	4.35315i	1.03793	+	0.278112i
$246$	6.32260	−	12.2143i	0.403114	−	0.778757i
$247$	−1.70912	−	7.91400i	−0.108749	−	0.503555i
$248$		−	1.72293i		−	0.109406i
$249$	−4.27423	+	4.68617i	−0.270868	+	0.296974i
$250$	2.61709	+	4.53293i	0.165519	+	0.286688i
$251$	−3.51988	+	6.09661i	−0.222173	+	0.384814i	−0.955467	−	0.295096i	$-0.904648\pi$
$251$	−3.51988	+	6.09661i	−0.222173	+	0.384814i	0.733295	+	0.679911i	$0.237982\pi$
$252$	10.6135	+	1.82100i	0.668590	+	0.114712i
$253$	3.29820	+	12.3090i	0.207356	+	0.773862i
$254$	−5.35580	−	19.9881i	−0.336053	−	1.25417i
$255$	5.17935	+	16.2956i	0.324343	+	1.02047i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.815993	−	1.41334i	−0.0509003	−	0.0881618i	0.839453	−	0.543433i	$-0.182876\pi$
$257$	−0.815993	−	1.41334i	−0.0509003	−	0.0881618i	−0.890353	+	0.455271i	$0.849542\pi$
$258$	−2.49585	−	2.27646i	−0.155385	−	0.141726i
$259$			17.3827i			1.08011i
$260$	2.17533	+	10.0727i	0.134908	+	0.624685i
$261$	−4.93367	+	3.48863i	−0.305387	+	0.215941i
$262$	−4.52338	−	1.21204i	−0.279455	−	0.0748799i
$263$	−9.15209	+	5.28396i	−0.564342	+	0.325823i	−0.754886	−	0.655856i	$-0.772308\pi$
$263$	−9.15209	+	5.28396i	−0.564342	+	0.325823i	0.190544	+	0.981679i	$0.438975\pi$
$264$	3.92504	+	6.12983i	0.241570	+	0.377265i
$265$	−14.5952	+	14.5952i	−0.896574	+	0.896574i
$266$	−7.78584	+	2.08621i	−0.477380	+	0.127914i
$267$	3.65223	−	16.6559i	0.223513	−	1.01933i
$268$	−3.00229	−	3.00229i	−0.183394	−	0.183394i
$269$	−7.46392	−	4.30930i	−0.455083	−	0.262742i	0.254891	−	0.966970i	$-0.417960\pi$
$269$	−7.46392	−	4.30930i	−0.455083	−	0.262742i	−0.709975	+	0.704227i	$0.751294\pi$
$270$	−9.12207	−	11.7193i	−0.555152	−	0.713211i
$271$	5.13290	−	19.1563i	0.311802	−	1.16366i	−0.615129	−	0.788427i	$-0.710896\pi$
$271$	5.13290	−	19.1563i	0.311802	−	1.16366i	0.926930	−	0.375233i	$-0.122437\pi$
$272$	−3.45408			−0.209434
$273$	5.73333	+	21.6711i	0.346997	+	1.31159i
$274$	5.47999			0.331058
$275$	3.44642	−	12.8622i	0.207827	−	0.775620i
$276$	5.24667	−	0.241204i	0.315813	−	0.0145188i
$277$	−13.4255	−	7.75123i	−0.806661	−	0.465726i	0.0391339	−	0.999234i	$-0.487540\pi$
$277$	−13.4255	−	7.75123i	−0.806661	−	0.465726i	−0.845795	+	0.533508i	$0.820873\pi$
$278$	−10.3897	−	10.3897i	−0.623132	−	0.623132i
$279$	−3.30413	+	3.97481i	−0.197813	+	0.237966i
$280$	9.90963	−	2.65528i	0.592214	−	0.158683i
$281$	−11.9452	+	11.9452i	−0.712591	+	0.712591i	−0.967077	−	0.254486i	$-0.918094\pi$
$281$	−11.9452	+	11.9452i	−0.712591	+	0.712591i	0.254486	+	0.967077i	$0.418094\pi$
$282$	−1.97494	+	1.26459i	−0.117606	+	0.0753052i
$283$	−1.36808	+	0.789860i	−0.0813237	+	0.0469523i	−0.540110	−	0.841594i	$-0.681618\pi$
$283$	−1.36808	+	0.789860i	−0.0813237	+	0.0469523i	0.458787	+	0.888546i	$0.348284\pi$
$284$	−10.6578	−	2.85575i	−0.632424	−	0.169458i
$285$	9.87205	+	5.11015i	0.584770	+	0.302699i
$286$	−8.21096	+	12.7343i	−0.485524	+	0.752997i
$287$		−	28.5035i		−	1.68251i
$288$	2.81431	−	1.03906i	0.165835	−	0.0612271i
$289$	2.53467	+	4.39017i	0.149098	+	0.258245i
$290$	−2.87832	+	4.98540i	−0.169021	+	0.292753i
$291$	−13.2426	+	4.20899i	−0.776295	+	0.246735i
$292$	−3.69034	−	13.7725i	−0.215961	−	0.805976i
$293$	−1.01073	−	3.77209i	−0.0590474	−	0.220368i	0.930097	−	0.367314i	$-0.119722\pi$
$293$	−1.01073	−	3.77209i	−0.0590474	−	0.220368i	−0.989145	+	0.146946i	$0.953056\pi$
$294$	9.71393	−	3.08745i	0.566528	−	0.180064i
$295$	14.7026	−	25.4656i	0.856017	−	1.48266i
$296$	2.42130	+	4.19381i	0.140735	+	0.243760i
$297$	2.70030	−	21.6688i	0.156687	−	1.25735i
$298$		−	10.3347i		−	0.598673i
$299$	4.99533	+	9.72548i	0.288887	+	0.562439i
$300$	−4.87397	−	2.52295i	−0.281399	−	0.145663i
$301$	−6.76230	−	1.81195i	−0.389772	−	0.104439i
$302$	7.94777	−	4.58864i	0.457343	−	0.264047i
$303$	3.07315	−	1.96779i	0.176548	−	0.113047i
$304$	−1.58784	+	1.58784i	−0.0910691	+	0.0910691i
$305$	−0.757003	+	0.202838i	−0.0433459	+	0.0116145i
$306$	7.96859	+	6.62402i	0.455534	+	0.378670i
$307$	21.7994	+	21.7994i	1.24416	+	1.24416i	0.958260	+	0.285899i	$0.0922920\pi$
$307$	21.7994	+	21.7994i	1.24416	+	1.24416i	0.285899	+	0.958260i	$0.407708\pi$
$308$	13.0638	+	7.54236i	0.744377	+	0.429766i
$309$	−24.6780	+	1.13452i	−1.40388	+	0.0645404i
$310$	−1.27450	+	4.75648i	−0.0723865	+	0.270150i
$311$	−20.9295			−1.18681			−0.593403	−	0.804906i	$-0.702216\pi$
$311$	−20.9295			−1.18681			−0.593403	+	0.804906i	$0.702216\pi$
$312$	4.40189	+	4.42983i	0.249208	+	0.250790i
$313$	−32.6685			−1.84653			−0.923267	−	0.384159i	$-0.874491\pi$
$313$	−32.6685			−1.84653			−0.923267	+	0.384159i	$0.874491\pi$
$314$	3.66051	−	13.6612i	0.206575	−	0.770947i
$315$	−27.9537	−	12.8783i	−1.57501	−	0.725612i
$316$	−1.36876	−	0.790254i	−0.0769988	−	0.0444553i
$317$	5.21085	+	5.21085i	0.292671	+	0.292671i	0.838134	−	0.545464i	$-0.183646\pi$
$317$	5.21085	+	5.21085i	0.292671	+	0.292671i	−0.545464	+	0.838134i	$0.683646\pi$
$318$	−2.67918	+	12.2183i	−0.150241	+	0.685170i
$319$	−8.17593	+	2.19073i	−0.457764	+	0.122657i
$320$	2.02097	−	2.02097i	0.112976	−	0.112976i
$321$	12.9317	+	20.1957i	0.721776	+	1.12721i
$322$	9.42652	−	5.44240i	0.525319	−	0.303293i
$323$	−7.49202	−	2.00748i	−0.416867	−	0.111699i
$324$	−8.48528	−	3.00000i	−0.471405	−	0.166667i
$325$	0.560775	−	11.4109i	0.0311062	−	0.632964i
$326$			1.11435i			0.0617181i
$327$	−10.5730	−	9.64360i	−0.584689	−	0.533292i
$328$	−3.97036	−	6.87686i	−0.219226	−	0.379711i
$329$	−2.43004	+	4.20895i	−0.133972	+	0.232047i
$330$	−6.30146	−	19.8261i	−0.346884	−	1.09139i
$331$	4.72013	+	17.6158i	0.259442	+	0.968251i	0.965565	+	0.260162i	$0.0837759\pi$
$331$	4.72013	+	17.6158i	0.259442	+	0.968251i	−0.706123	+	0.708089i	$0.749557\pi$
$332$	0.947777	+	3.53715i	0.0520160	+	0.194127i
$333$	2.45667	−	14.3186i	0.134625	−	0.784652i
$334$	−2.79254	+	4.83683i	−0.152801	+	0.264660i
$335$	6.06754	+	10.5093i	0.331505	+	0.574184i
$336$	4.18974	−	4.59353i	0.228569	−	0.250598i
$337$			4.92484i			0.268273i	0.990963	+	0.134136i	$0.0428260\pi$
$337$			4.92484i			0.268273i	−0.990963	+	0.134136i	$0.957174\pi$
$338$	−4.57966	+	12.1666i	−0.249101	+	0.661777i
$339$	14.3353	−	27.6937i	0.778587	−	1.50412i
$340$	9.53567	+	2.55507i	0.517144	+	0.138568i
$341$	−6.27042	+	3.62023i	−0.339562	+	0.196046i
$342$	6.70823	−	0.618099i	0.362740	−	0.0334230i
$343$	−2.83057	+	2.83057i	−0.152836	+	0.152836i
$344$	−1.88389	+	0.504787i	−0.101572	+	0.0272163i
$345$	−14.6629	−	3.21521i	−0.789424	−	0.173101i
$346$	12.3711	+	12.3711i	0.665072	+	0.665072i
$347$	12.9403	+	7.47108i	0.694671	+	0.401069i	0.805360	−	0.592787i	$-0.201972\pi$
$347$	12.9403	+	7.47108i	0.694671	+	0.401069i	−0.110688	+	0.993855i	$0.535306\pi$
$348$	0.160213	+	3.48495i	0.00858832	+	0.186813i
$349$	−8.08448	+	30.1717i	−0.432752	+	1.61505i	0.313636	+	0.949543i	$0.398453\pi$
$349$	−8.08448	+	30.1717i	−0.432752	+	1.61505i	−0.746388	+	0.665511i	$0.768214\pi$
$350$	−11.3740			−0.607964
$351$	−1.65994	−	18.6613i	−0.0886008	−	0.996067i
$352$	4.20241			0.223989
$353$	−2.67762	+	9.99302i	−0.142515	+	0.531875i	0.857338	+	0.514754i	$0.172117\pi$
$353$	−2.67762	+	9.99302i	−0.142515	+	0.531875i	−0.999853	+	0.0171211i	$0.994550\pi$
$354$	−0.818374	−	17.8013i	−0.0434961	−	0.946126i
$355$	27.3105	+	15.7677i	1.44949	+	0.836864i
$356$	−6.96131	−	6.96131i	−0.368949	−	0.368949i
$357$	20.9766	+	4.59964i	1.11020	+	0.243439i
$358$	8.90109	−	2.38504i	0.470437	−	0.126053i
$359$	−9.08944	+	9.08944i	−0.479722	+	0.479722i	−0.905043	−	0.425321i	$-0.860161\pi$
$359$	−9.08944	+	9.08944i	−0.479722	+	0.479722i	0.425321	+	0.905043i	$0.360161\pi$
$360$	−8.53808	+	0.786702i	−0.449996	+	0.0414628i
$361$	12.0876	−	6.97875i	0.636187	−	0.367303i
$362$	13.3404	+	3.57455i	0.701156	+	0.187874i
$363$	5.30306	−	10.2447i	0.278339	−	0.537709i
$364$	12.3218	+	3.95929i	0.645837	+	0.207523i
$365$			40.7516i			2.13304i
$366$	−0.320057	+	0.350903i	−0.0167296	+	0.0183420i
$367$	−0.823475	−	1.42630i	−0.0429850	−	0.0744522i	0.843732	−	0.536764i	$-0.180353\pi$
$367$	−0.823475	−	1.42630i	−0.0429850	−	0.0744522i	−0.886717	+	0.462312i	$0.847020\pi$
$368$	1.51618	−	2.62611i	0.0790365	−	0.136895i
$369$	−4.02837	+	23.4791i	−0.209709	+	1.22227i
$370$	−3.58219	−	13.3689i	−0.186229	−	0.695017i
$371$	6.70941	+	25.0398i	0.348335	+	1.30000i
$372$	0.903931	+	2.84400i	0.0468666	+	0.147455i
$373$	9.97578	−	17.2786i	0.516526	−	0.894650i	−0.483290	−	0.875461i	$-0.660558\pi$
$373$	9.97578	−	17.2786i	0.516526	−	0.894650i	0.999816	−	0.0191892i	$-0.00610849\pi$
$374$	7.25773	+	12.5708i	0.375288	+	0.650018i
$375$	−6.69817	−	6.10937i	−0.345892	−	0.315487i
$376$			1.35395i			0.0698248i
$377$	−6.45987	+	3.31800i	−0.332700	+	0.170886i
$378$	−18.4749	+	2.56249i	−0.950248	+	0.131800i
$379$	−11.8923	−	3.18653i	−0.610865	−	0.163681i	−0.0598936	−	0.998205i	$-0.519076\pi$
$379$	−11.8923	−	3.18653i	−0.610865	−	0.163681i	−0.550972	+	0.834524i	$0.685743\pi$
$380$	5.55812	−	3.20898i	0.285126	−	0.164617i
$381$	19.3274	+	30.1841i	0.990175	+	1.54638i
$382$	16.0534	−	16.0534i	0.821366	−	0.821366i
$383$	27.3800	−	7.33645i	1.39905	−	0.374875i	0.521048	−	0.853527i	$-0.325541\pi$
$383$	27.3800	−	7.33645i	1.39905	−	0.374875i	0.878005	+	0.478652i	$0.158875\pi$
$384$	0.370982	−	1.69185i	0.0189316	−	0.0863371i
$385$	−30.4858	−	30.4858i	−1.55370	−	1.55370i
$386$	−17.3601	−	10.0229i	−0.883605	−	0.510150i
$387$	5.31419	+	2.44826i	0.270136	+	0.124452i
$388$	−2.07638	+	7.74915i	−0.105412	+	0.393403i
$389$	15.9504			0.808717			0.404359	−	0.914601i	$-0.367495\pi$
$389$	15.9504			0.808717			0.404359	+	0.914601i	$0.367495\pi$
$390$	−8.87541	−	15.4856i	−0.449424	−	0.784144i
$391$	10.4740			0.529695
$392$	1.52310	−	5.68429i	0.0769282	−	0.287100i
$393$	8.10255	−	0.372497i	0.408720	−	0.0187900i
$394$	−16.1404	−	9.31866i	−0.813141	−	0.469467i
$395$	3.19416	+	3.19416i	0.160716	+	0.160716i
$396$	−9.69499	−	8.05912i	−0.487192	−	0.404986i
$397$	−12.2594	+	3.28489i	−0.615281	+	0.164864i	−0.552981	−	0.833194i	$-0.686510\pi$
$397$	−12.2594	+	3.28489i	−0.615281	+	0.164864i	−0.0622992	+	0.998058i	$0.519843\pi$
$398$	3.18933	−	3.18933i	0.159866	−	0.159866i
$399$	11.7574	−	7.52849i	0.588606	−	0.376896i
$400$	−2.74412	+	1.58432i	−0.137206	+	0.0792160i
$401$	−15.8603	−	4.24976i	−0.792027	−	0.212223i	−0.159946	−	0.987126i	$-0.551132\pi$
$401$	−15.8603	−	4.24976i	−0.792027	−	0.212223i	−0.632080	+	0.774903i	$0.717799\pi$
$402$	6.53097	+	3.38068i	0.325735	+	0.168613i
$403$	−4.60294	+	4.17172i	−0.229289	+	0.207808i
$404$		−	2.10685i		−	0.104820i
$405$	21.2061	+	14.5589i	1.05374	+	0.723436i
$406$	3.61496	+	6.26130i	0.179408	+	0.310743i
$407$	10.1753	−	17.6241i	0.504370	−	0.873594i
$408$	5.70158	−	1.81217i	0.282270	−	0.0897160i
$409$	−8.82005	−	32.9169i	−0.436123	−	1.62763i	−0.738364	−	0.674403i	$-0.764401\pi$
$409$	−8.82005	−	32.9169i	−0.436123	−	1.62763i	0.302240	−	0.953232i	$-0.402266\pi$
$410$	5.87396	+	21.9219i	0.290094	+	1.08265i
$411$	−9.04570	+	2.87506i	−0.446192	+	0.141816i
$412$	−7.13145	+	12.3520i	−0.351341	+	0.608541i
$413$	−18.4653	−	31.9829i	−0.908620	−	1.57378i
$414$	−8.53403	+	3.15081i	−0.419425	+	0.154854i
$415$		−	10.4661i		−	0.513761i
$416$	3.52430	−	0.761114i	0.172793	−	0.0373167i
$417$	22.6010	+	11.6991i	1.10677	+	0.572909i
$418$	9.11517	+	2.44240i	0.445838	+	0.119462i
$419$	28.4943	−	16.4512i	1.39204	−	0.803693i	0.398496	−	0.917170i	$-0.369532\pi$
$419$	28.4943	−	16.4512i	1.39204	−	0.803693i	0.993541	+	0.113477i	$0.0361989\pi$
$420$	−14.9646	+	9.58208i	−0.730195	+	0.467558i
$421$	17.0945	−	17.0945i	0.833137	−	0.833137i	−0.154808	−	0.987945i	$-0.549476\pi$
$421$	17.0945	−	17.0945i	0.833137	−	0.833137i	0.987945	+	0.154808i	$0.0494759\pi$
$422$	−8.28458	+	2.21985i	−0.403287	+	0.108060i
$423$	2.59653	−	3.12358i	0.126247	−	0.151874i
$424$	5.10662	+	5.10662i	0.248000	+	0.248000i
$425$	−9.47842	−	5.47237i	−0.459771	−	0.265449i
$426$	19.0909	−	0.877662i	0.924957	−	0.0425229i
$427$	−0.254750	+	0.950740i	−0.0123282	+	0.0460095i
$428$	13.8455			0.669248
$429$	6.87263	−	25.3282i	0.331813	−	1.22286i
$430$	5.57425			0.268814
$431$	−0.454427	+	1.69594i	−0.0218890	+	0.0816908i	−0.976006	−	0.217742i	$-0.930131\pi$
$431$	−0.454427	+	1.69594i	−0.0218890	+	0.0816908i	0.954117	+	0.299433i	$0.0967975\pi$
$432$	−4.10039	+	3.19168i	−0.197280	+	0.153560i
$433$	−8.87140	−	5.12190i	−0.426332	−	0.246143i	0.271451	−	0.962452i	$-0.412497\pi$
$433$	−8.87140	−	5.12190i	−0.426332	−	0.246143i	−0.697783	+	0.716309i	$0.745830\pi$
$434$	4.37312	+	4.37312i	0.209916	+	0.209916i
$435$	2.13561	−	9.73941i	0.102395	−	0.466969i
$436$	−7.98059	+	2.13839i	−0.382201	+	0.102410i
$437$	4.81492	−	4.81492i	0.230329	−	0.230329i
$438$	13.3173	+	20.7979i	0.636325	+	0.993763i
$439$	−4.67848	+	2.70112i	−0.223292	+	0.128917i	−0.607473	−	0.794340i	$-0.707817\pi$
$439$	−4.67848	+	2.70112i	−0.223292	+	0.128917i	0.384182	+	0.923257i	$0.374484\pi$
$440$	−11.6016	−	3.10863i	−0.553084	−	0.148198i
$441$	−14.4148	+	10.1928i	−0.686418	+	0.485371i
$442$	8.36335	+	9.22784i	0.397804	+	0.438924i
$443$			13.5731i			0.644876i	0.946591	+	0.322438i	$0.104502\pi$
$443$			13.5731i			0.644876i	−0.946591	+	0.322438i	$0.895498\pi$
$444$	−6.19705	−	5.65231i	−0.294099	−	0.268247i
$445$	14.0686	+	24.3675i	0.666916	+	1.15513i
$446$	−10.5378	+	18.2520i	−0.498979	+	0.864257i
$447$	5.42208	+	17.0593i	0.256455	+	0.806877i
$448$	−0.929042	−	3.46723i	−0.0438931	−	0.163811i
$449$	−0.525222	−	1.96016i	−0.0247868	−	0.0925055i	0.952424	−	0.304775i	$-0.0985812\pi$
$449$	−0.525222	−	1.96016i	−0.0247868	−	0.0925055i	−0.977211	+	0.212269i	$0.931915\pi$
$450$	9.36902	+	1.60747i	0.441660	+	0.0757769i
$451$	−16.6851	+	28.8994i	−0.785670	+	1.36082i
$452$	−9.00205	−	15.5920i	−0.423421	−	0.733386i
$453$	−10.7118	+	11.7442i	−0.503284	+	0.551789i
$454$			5.02672i			0.235916i
$455$	−31.0879	−	20.0451i	−1.45742	−	0.939731i
$456$	1.78796	−	3.45408i	0.0837291	−	0.161752i
$457$	−28.9328	−	7.75251i	−1.35342	−	0.362647i	−0.492022	−	0.870583i	$-0.663742\pi$
$457$	−28.9328	−	7.75251i	−1.35342	−	0.362647i	−0.861395	+	0.507936i	$0.830409\pi$
$458$	12.1554	−	7.01792i	0.567984	−	0.327926i
$459$	−16.6289	−	6.75344i	−0.776169	−	0.315223i
$460$	−6.12832	+	6.12832i	−0.285735	+	0.285735i
$461$	−15.5621	+	4.16985i	−0.724798	+	0.194209i	−0.602312	−	0.798261i	$-0.705754\pi$
$461$	−15.5621	+	4.16985i	−0.724798	+	0.194209i	−0.122487	+	0.992470i	$0.539087\pi$
$462$	−25.5212	−	5.59616i	−1.18735	−	0.260357i
$463$	−4.07041	−	4.07041i	−0.189168	−	0.189168i	0.606168	−	0.795336i	$-0.292706\pi$
$463$	−4.07041	−	4.07041i	−0.189168	−	0.189168i	−0.795336	+	0.606168i	$0.792706\pi$
$464$	1.74432	+	1.00708i	0.0809779	+	0.0467526i
$465$	−0.391693	−	8.52009i	−0.0181643	−	0.395110i
$466$	−4.86434	+	18.1540i	−0.225336	+	0.840966i
$467$	−36.8536			−1.70538			−0.852690	−	0.522417i	$-0.825030\pi$
$467$	−36.8536			−1.70538			−0.852690	+	0.522417i	$0.825030\pi$
$468$	−9.59021	−	5.00279i	−0.443308	−	0.231254i
$469$	15.2408			0.703753
$470$	1.00155	−	3.73785i	0.0461983	−	0.172414i
$471$	1.12499	+	24.4708i	0.0518368	+	1.12755i
$472$	−8.91003	−	5.14421i	−0.410117	−	0.236781i
$473$	5.79555	+	5.79555i	0.266480	+	0.266480i
$474$	2.67399	+	0.586340i	0.122820	+	0.0269315i
$475$	−6.87289	+	1.84159i	−0.315350	+	0.0844977i
$476$	8.76711	−	8.76711i	0.401840	−	0.401840i
$477$	−1.98785	−	21.5742i	−0.0910176	−	0.987814i
$478$	−8.35450	+	4.82347i	−0.382126	+	0.220621i
$479$	−14.5305	−	3.89342i	−0.663913	−	0.177895i	−0.0889019	−	0.996040i	$-0.528336\pi$
$479$	−14.5305	−	3.89342i	−0.663913	−	0.177895i	−0.575011	+	0.818145i	$0.695002\pi$
$480$	−2.27568	+	4.39627i	−0.103870	+	0.200661i
$481$	5.34141	−	16.6231i	0.243547	−	0.757949i
$482$			8.47706i			0.386119i
$483$	−12.7048	+	13.9293i	−0.578090	+	0.633804i
$484$	−3.33013	−	5.76795i	−0.151369	−	0.262180i
$485$	11.4645	−	19.8571i	0.520576	−	0.901664i
$486$	15.5804	+	0.500258i	0.706743	+	0.0226921i
$487$	4.33018	+	16.1605i	0.196219	+	0.732301i	0.991948	+	0.126647i	$0.0404216\pi$
$487$	4.33018	+	16.1605i	0.196219	+	0.732301i	−0.795728	+	0.605654i	$0.792912\pi$
$488$	0.0709701	+	0.264864i	0.00321266	+	0.0119898i
$489$	−0.584640	−	1.83943i	−0.0264383	−	0.0831820i
$490$	−8.40963	+	14.5659i	−0.379909	+	0.658021i
$491$	12.6333	+	21.8815i	0.570132	+	0.987498i	0.996552	+	0.0829727i	$0.0264414\pi$
$491$	12.6333	+	21.8815i	0.570132	+	0.987498i	−0.426419	+	0.904526i	$0.640225\pi$
$492$	10.1617	+	9.26846i	0.458126	+	0.417855i
$493$			6.95708i			0.313331i
$494$	8.08669	+	0.397410i	0.363837	+	0.0178803i
$495$	20.8034	+	29.4204i	0.935043	+	1.32235i
$496$	1.66422	+	0.445927i	0.0747258	+	0.0200227i
$497$	34.3000	−	19.8031i	1.53856	−	0.888290i
$498$	−3.42024	−	5.34146i	−0.153264	−	0.239357i
$499$	1.37946	−	1.37946i	0.0617533	−	0.0617533i	−0.675556	−	0.737309i	$-0.736096\pi$
$499$	1.37946	−	1.37946i	0.0617533	−	0.0617533i	0.737309	+	0.675556i	$0.236096\pi$
$500$	−5.05583	+	1.35471i	−0.226104	+	0.0605843i
$501$	2.07197	−	9.44916i	0.0925687	−	0.422157i
$502$	−4.97786	−	4.97786i	−0.222173	−	0.222173i
$503$	−9.77777	−	5.64520i	−0.435969	−	0.251707i	0.265917	−	0.963996i	$-0.414325\pi$
$503$	−9.77777	−	5.64520i	−0.435969	−	0.251707i	−0.701886	+	0.712289i	$0.747659\pi$
$504$	−4.50593	+	9.78058i	−0.200710	+	0.435662i
$505$	−1.55849	+	5.81637i	−0.0693520	+	0.258825i
$506$	−12.7433			−0.566507
$507$	1.17636	−	22.4859i	0.0522442	−	0.998634i
$508$	20.6932			0.918114
$509$	9.73260	−	36.3226i	0.431390	−	1.60997i	−0.318171	−	0.948033i	$-0.603069\pi$
$509$	9.73260	−	36.3226i	0.431390	−	1.60997i	0.749561	−	0.661936i	$-0.230265\pi$
$510$	−17.0808	+	0.785255i	−0.756353	+	0.0347717i
$511$	44.3241	+	25.5905i	1.96078	+	1.13206i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−10.7489	+	4.53974i	−0.474574	+	0.200435i
$514$	1.57638	−	0.422389i	0.0695311	−	0.0186308i
$515$	28.8249	−	28.8249i	1.27018	−	1.27018i
$516$	2.84486	−	1.82162i	0.125238	−	0.0801923i
$517$	4.92757	−	2.84493i	0.216714	−	0.125120i
$518$	−16.7904	−	4.49897i	−0.737727	−	0.197673i
$519$	−26.9111	−	13.9302i	−1.18127	−	0.611468i
$520$	−10.2925	−	0.505814i	−0.451358	−	0.0221814i
$521$		−	18.2111i		−	0.797843i	−0.916985	−	0.398922i	$-0.869385\pi$
$521$		−	18.2111i		−	0.797843i	0.916985	−	0.398922i	$-0.130615\pi$
$522$	−2.09283	−	5.66849i	−0.0916008	−	0.248103i
$523$	−16.9049	−	29.2801i	−0.739199	−	1.28033i	−0.952857	−	0.303421i	$-0.901871\pi$
$523$	−16.9049	−	29.2801i	−0.739199	−	1.28033i	0.213658	−	0.976909i	$-0.431462\pi$
$524$	2.34147	−	4.05555i	0.102288	−	0.177168i
$525$	18.7748	−	5.96732i	0.819398	−	0.260435i
$526$	−2.73518	−	10.2078i	−0.119260	−	0.445083i
$527$	1.54027	+	5.74835i	0.0670951	+	0.250402i
$528$	−6.93684	+	2.20478i	−0.301887	+	0.0959509i
$529$	6.90238	−	11.9553i	0.300103	−	0.519794i
$530$	−10.3203	−	17.8753i	−0.448287	−	0.776455i
$531$	10.6903	+	28.9548i	0.463918	+	1.25653i
$532$		−	8.06049i		−	0.349467i
$533$	−8.75867	+	27.2580i	−0.379380	+	1.18068i
$534$	15.1431	+	7.83866i	0.655307	+	0.339212i
$535$	−38.2233	−	10.2419i	−1.65254	−	0.442795i
$536$	3.67704	−	2.12294i	0.158824	−	0.0916970i
$537$	−13.4415	+	8.60687i	−0.580045	+	0.371414i
$538$	6.09426	−	6.09426i	0.262742	−	0.262742i
$539$	−23.8877	+	6.40069i	−1.02892	+	0.275697i
$540$	13.6809	−	5.77808i	0.588732	−	0.248649i
$541$	−4.97355	−	4.97355i	−0.213829	−	0.213829i	0.592063	−	0.805892i	$-0.298314\pi$
$541$	−4.97355	−	4.97355i	−0.213829	−	0.213829i	−0.805892	+	0.592063i	$0.798314\pi$
$542$	17.1750	+	9.91601i	0.737731	+	0.425929i
$543$	−23.8961	+	1.09857i	−1.02548	+	0.0471442i
$544$	0.893982	−	3.33639i	0.0383291	−	0.143046i
$545$	23.6138			1.01150
$546$	−22.4166	−	0.0709208i	−0.959340	−	0.00303513i
$547$	−2.15870			−0.0922995			−0.0461497	−	0.998935i	$-0.514695\pi$
$547$	−2.15870			−0.0922995			−0.0461497	+	0.998935i	$0.514695\pi$
$548$	−1.41832	+	5.29326i	−0.0605878	+	0.226117i
$549$	0.344211	−	0.747145i	0.0146906	−	0.0318874i
$550$	11.5319	+	6.65796i	0.491723	+	0.283897i
$551$	3.19818	+	3.19818i	0.136247	+	0.136247i
$552$	−1.12495	+	5.13032i	−0.0478812	+	0.218361i
$553$	5.47999	−	1.46836i	0.233033	−	0.0624409i
$554$	10.9619	−	10.9619i	0.465726	−	0.465726i
$555$	12.9270	+	20.1884i	0.548722	+	0.856951i
$556$	12.7247	−	7.34662i	0.539648	−	0.311566i
$557$	−2.17782	−	0.583545i	−0.0922772	−	0.0247256i	0.212385	−	0.977186i	$-0.431877\pi$
$557$	−2.17782	−	0.583545i	−0.0922772	−	0.0247256i	−0.304662	+	0.952460i	$0.598544\pi$
$558$	−2.98420	−	4.22030i	−0.126331	−	0.178659i
$559$	5.91003	+	3.81072i	0.249968	+	0.161176i
$560$			10.2592i			0.433531i
$561$	−18.5754	−	16.9426i	−0.784254	−	0.715315i
$562$	−8.44653	−	14.6298i	−0.356296	−	0.617122i
$563$	−18.1490	+	31.4349i	−0.764888	+	1.32482i	0.175418	+	0.984494i	$0.443872\pi$
$563$	−18.1490	+	31.4349i	−0.764888	+	1.32482i	−0.940306	+	0.340330i	$0.889461\pi$
$564$	−0.710348	−	2.23494i	−0.0299111	−	0.0941081i
$565$	13.3181	+	49.7038i	0.560297	+	2.09106i
$566$	−0.408861	−	1.52589i	−0.0171857	−	0.0641380i
$567$	29.1518	−	13.9227i	1.22426	−	0.584698i
$568$	5.51689	−	9.55553i	0.231483	−	0.400941i
$569$	19.5376	+	33.8400i	0.819057	+	1.41865i	0.906378	+	0.422468i	$0.138836\pi$
$569$	19.5376	+	33.8400i	0.819057	+	1.41865i	−0.0873209	+	0.996180i	$0.527831\pi$
$570$	−7.49110	+	8.21306i	−0.313768	+	0.344007i
$571$		−	31.9061i		−	1.33523i	−0.744508	−	0.667614i	$-0.767316\pi$
$571$		−	31.9061i		−	1.33523i	0.744508	−	0.667614i	$-0.232684\pi$
$572$	−10.1753	−	11.2271i	−0.425450	−	0.469427i
$573$	−18.0767	+	34.9215i	−0.755165	+	1.45887i
$574$	27.5323	+	7.37726i	1.14918	+	0.307921i
$575$	8.32119	−	4.80424i	0.347018	−	0.200351i
$576$	0.275255	+	2.98735i	0.0114690	+	0.124473i
$577$	9.31011	−	9.31011i	0.387585	−	0.387585i	−0.486240	−	0.873825i	$-0.661632\pi$
$577$	9.31011	−	9.31011i	0.387585	−	0.387585i	0.873825	+	0.486240i	$0.161632\pi$
$578$	−4.89660	+	1.31204i	−0.203672	+	0.0545736i
$579$	33.9144	+	7.43659i	1.40944	+	0.309054i
$580$	−4.07056	−	4.07056i	−0.169021	−	0.169021i
$581$	−11.3836	−	6.57233i	−0.472271	−	0.272666i
$582$	−0.638136	−	13.8807i	−0.0264516	−	0.575375i
$583$	7.85495	−	29.3151i	0.325319	−	1.21411i
$584$	14.2584			0.590016
$585$	22.7750	+	20.9053i	0.941629	+	0.864328i
$586$	3.90516			0.161321
$587$	7.58008	−	28.2892i	0.312863	−	1.16762i	−0.613099	−	0.790006i	$-0.710077\pi$
$587$	7.58008	−	28.2892i	0.312863	−	1.16762i	0.925962	−	0.377615i	$-0.123256\pi$
$588$	0.468097	+	10.1820i	0.0193040	+	0.419900i
$589$	3.35059	+	1.93446i	0.138058	+	0.0797081i
$590$	20.7926	+	20.7926i	0.856017	+	0.856017i
$591$	31.5316	+	6.91411i	1.29704	+	0.284408i
$592$	−4.67758	+	1.25335i	−0.192247	+	0.0515126i
$593$	−12.7368	+	12.7368i	−0.523037	+	0.523037i	−0.918487	−	0.395450i	$-0.870589\pi$
$593$	−12.7368	+	12.7368i	−0.523037	+	0.523037i	0.395450	+	0.918487i	$0.370589\pi$
$594$	20.2315	+	8.21658i	0.830110	+	0.337130i
$595$	−30.6886	+	17.7181i	−1.25811	+	0.726370i
$596$	9.98255	+	2.67482i	0.408901	+	0.109565i
$597$	−3.59128	+	6.93783i	−0.146981	+	0.283946i
$598$	−10.6870	+	2.30798i	−0.437023	+	0.0943802i
$599$			15.6579i			0.639764i	0.947457	+	0.319882i	$0.103643\pi$
$599$			15.6579i			0.639764i	−0.947457	+	0.319882i	$0.896357\pi$
$600$	3.69846	−	4.05490i	0.150989	−	0.165541i
$601$	−3.99832	−	6.92529i	−0.163095	−	0.282488i	0.772882	−	0.634549i	$-0.218814\pi$
$601$	−3.99832	−	6.92529i	−0.163095	−	0.282488i	−0.935977	+	0.352061i	$0.885481\pi$
$602$	3.50042	−	6.06291i	0.142667	−	0.247106i
$603$	−12.5542	−	2.15396i	−0.511247	−	0.0877160i
$604$	2.37526	+	8.86458i	0.0966478	+	0.360695i
$605$	4.92677	+	18.3869i	0.200302	+	0.747535i
$606$	1.10535	+	3.47773i	0.0449019	+	0.141273i
$607$	−2.24581	+	3.88985i	−0.0911545	+	0.157884i	−0.907997	−	0.418976i	$-0.862389\pi$
$607$	−2.24581	+	3.88985i	−0.0911545	+	0.157884i	0.816843	+	0.576860i	$0.195722\pi$
$608$	−1.12277	−	1.94470i	−0.0455345	−	0.0788681i
$609$	−9.25212	−	8.43882i	−0.374915	−	0.341958i
$610$		−	0.783707i		−	0.0317314i
$611$	3.61719	−	3.27832i	0.146336	−	0.132627i
$612$	−8.46073	+	5.98264i	−0.342005	+	0.241834i
$613$	30.5112	+	8.17546i	1.23234	+	0.330204i	0.815489	−	0.578773i	$-0.196468\pi$
$613$	30.5112	+	8.17546i	1.23234	+	0.330204i	0.416848	+	0.908976i	$0.363135\pi$
$614$	−26.6987	+	15.4145i	−1.07747	+	0.622079i
$615$	−21.1973	−	33.1043i	−0.854758	−	1.33489i
$616$	−10.6665	+	10.6665i	−0.429766	+	0.429766i
$617$	−5.23513	+	1.40275i	−0.210758	+	0.0564725i	−0.362653	−	0.931924i	$-0.618129\pi$
$617$	−5.23513	+	1.40275i	−0.210758	+	0.0564725i	0.151895	+	0.988397i	$0.451462\pi$
$618$	5.29128	−	24.1308i	0.212846	−	0.970682i
$619$	7.22455	+	7.22455i	0.290379	+	0.290379i	0.837230	−	0.546851i	$-0.184174\pi$
$619$	7.22455	+	7.22455i	0.290379	+	0.290379i	−0.546851	+	0.837230i	$0.684174\pi$
$620$	−4.26455	−	2.46214i	−0.171268	−	0.0988818i
$621$	12.4339	−	9.67833i	0.498955	−	0.388378i
$622$	5.41696	−	20.2164i	0.217200	−	0.810603i
$623$	35.3382			1.41580
$624$	−5.41818	+	3.10537i	−0.216901	+	0.124314i
$625$	30.8029			1.23212
$626$	8.45523	−	31.5554i	0.337939	−	1.26121i
$627$	−16.3276	+	0.750627i	−0.652063	+	0.0299772i
$628$	12.2483	+	7.07156i	0.488761	+	0.282186i
$629$	−11.8276	−	11.8276i	−0.471596	−	0.471596i
$630$	19.6745	−	23.6681i	0.783850	−	0.942958i
$631$	−20.2844	+	5.43520i	−0.807511	+	0.216372i	−0.638879	−	0.769307i	$-0.720602\pi$
$631$	−20.2844	+	5.43520i	−0.807511	+	0.216372i	−0.168632	+	0.985679i	$0.553935\pi$
$632$	1.11759	−	1.11759i	0.0444553	−	0.0444553i
$633$	12.5106	−	8.01074i	0.497250	−	0.318398i
$634$	−6.38197	+	3.68463i	−0.253460	+	0.146335i
$635$	−57.1277	−	15.3073i	−2.26705	−	0.607453i
$636$	−11.1086	−	5.75023i	−0.440484	−	0.228011i
$637$	−18.8739	+	9.69426i	−0.747811	+	0.384100i
$638$		−	8.46434i		−	0.335106i
$639$	−31.0525	+	11.4647i	−1.22842	+	0.453538i
$640$	1.42904	+	2.47517i	0.0564878	+	0.0978398i
$641$	−21.3437	+	36.9683i	−0.843024	+	1.46016i	0.0443019	+	0.999018i	$0.485894\pi$
$641$	−21.3437	+	36.9683i	−0.843024	+	1.46016i	−0.887326	+	0.461143i	$0.847440\pi$
$642$	−22.8545	+	7.26401i	−0.901995	+	0.286688i
$643$	−0.813185	−	3.03485i	−0.0320689	−	0.119683i	0.948036	−	0.318163i	$-0.103066\pi$
$643$	−0.813185	−	3.03485i	−0.0320689	−	0.119683i	−0.980105	+	0.198481i	$0.936399\pi$
$644$	2.81720	+	10.5139i	0.111013	+	0.414306i
$645$	−9.20130	+	2.92452i	−0.362301	+	0.115153i
$646$	3.87815	−	6.71716i	0.152584	−	0.264283i
$647$	18.2351	+	31.5841i	0.716895	+	1.24170i	0.962224	+	0.272258i	$0.0877705\pi$
$647$	18.2351	+	31.5841i	0.716895	+	1.24170i	−0.245329	+	0.969440i	$0.578896\pi$
$648$	5.09393	−	7.41970i	0.200108	−	0.291473i
$649$			43.2361i			1.69717i
$650$	10.8770	+	3.49503i	0.426630	+	0.137086i
$651$	−9.51297	−	4.92427i	−0.372843	−	0.192998i
$652$	−1.07638	−	0.288415i	−0.0421542	−	0.0112952i
$653$	39.3421	−	22.7142i	1.53957	−	0.888874i	0.540711	−	0.841208i	$-0.318155\pi$
$653$	39.3421	−	22.7142i	1.53957	−	0.888874i	0.998863	−	0.0476658i	$-0.0151782\pi$
$654$	12.0515	−	7.71680i	0.471251	−	0.301751i
$655$	−9.46410	+	9.46410i	−0.369793	+	0.369793i
$656$	7.67015	−	2.05521i	0.299469	−	0.0802424i
$657$	−32.8942	−	27.3438i	−1.28332	−	1.06678i
$658$	−3.43659	−	3.43659i	−0.133972	−	0.133972i
$659$	11.4858	+	6.63132i	0.447422	+	0.258319i	0.706741	−	0.707472i	$-0.250165\pi$
$659$	11.4858	+	6.63132i	0.447422	+	0.258319i	−0.259319	+	0.965792i	$0.583498\pi$
$660$	20.7814	−	0.955381i	0.808916	−	0.0371882i
$661$	2.40763	−	8.98541i	0.0936460	−	0.349492i	−0.903165	−	0.429294i	$-0.858762\pi$
$661$	2.40763	−	8.98541i	0.0936460	−	0.349492i	0.996811	+	0.0798025i	$0.0254290\pi$
$662$	−18.2372			−0.708809
$663$	−18.6466	−	10.8444i	−0.724173	−	0.421162i
$664$	−3.66193			−0.142110
$665$	−5.96256	+	22.2526i	−0.231218	+	0.862918i
$666$	13.1948	+	6.07888i	0.511289	+	0.235552i
$667$	−5.28941	−	3.05384i	−0.204807	−	0.118245i
$668$	−3.94925	−	3.94925i	−0.152801	−	0.152801i
$669$	7.81866	−	35.6568i	0.302287	−	1.37857i
$670$	−11.7216	+	3.14079i	−0.452844	+	0.121339i
$671$	0.814821	−	0.814821i	0.0314558	−	0.0314558i
$672$	3.35262	+	5.23587i	0.129330	+	0.201978i
$673$	−22.9273	+	13.2371i	−0.883782	+	0.510252i	−0.871904	−	0.489678i	$-0.837114\pi$
$673$	−22.9273	+	13.2371i	−0.883782	+	0.510252i	−0.0118785	+	0.999929i	$0.503781\pi$
$674$	−4.75703	−	1.27464i	−0.183234	−	0.0490973i
$675$	−16.3086	+	2.26202i	−0.627719	+	0.0870650i
$676$	−10.5668	−	7.57257i	−0.406414	−	0.291253i
$677$		−	41.0789i		−	1.57879i	−0.613885	−	0.789396i	$-0.710394\pi$
$677$		−	41.0789i		−	1.57879i	0.613885	−	0.789396i	$-0.289606\pi$
$678$	23.0398	+	21.0145i	0.884839	+	0.807057i
$679$	−14.3986	−	24.9390i	−0.552566	−	0.957073i
$680$	−4.93602	+	8.54944i	−0.189288	+	0.327856i
$681$	−2.63726	−	8.29751i	−0.101060	−	0.317961i
$682$	−1.87397	−	6.99374i	−0.0717579	−	0.267804i
$683$	1.54160	+	5.75334i	0.0589878	+	0.220145i	0.989128	−	0.147060i	$-0.0469812\pi$
$683$	1.54160	+	5.75334i	0.0589878	+	0.220145i	−0.930140	+	0.367206i	$0.880315\pi$
$684$	−1.13918	+	6.63963i	−0.0435577	+	0.253873i
$685$	7.83113	−	13.5639i	0.299212	−	0.518250i
$686$	−2.00152	−	3.46673i	−0.0764182	−	0.132360i
$687$	−16.3827	+	17.9616i	−0.625040	+	0.685279i
$688$		−	1.95035i		−	0.0743562i
$689$	1.27810	−	26.0074i	0.0486917	−	0.990803i
$690$	6.90069	−	13.3311i	0.262705	−	0.507507i
$691$	27.6429	+	7.40689i	1.05159	+	0.281771i	0.742907	−	0.669395i	$-0.233447\pi$
$691$	27.6429	+	7.40689i	1.05159	+	0.281771i	0.308679	+	0.951166i	$0.400113\pi$
$692$	−15.1514	+	8.74765i	−0.575969	+	0.332536i
$693$	45.0633	−	4.15215i	1.71181	−	0.157727i
$694$	−10.5657	+	10.5657i	−0.401069	+	0.401069i
$695$	−40.5636	+	10.8690i	−1.53866	+	0.412284i
$696$	−3.40767	−	0.747218i	−0.129167	−	0.0283232i
$697$	19.3944	+	19.3944i	0.734617	+	0.734617i
$698$	−27.0512	−	15.6180i	−1.02390	−	0.591151i
$699$	−1.49497	−	32.5185i	−0.0565448	−	1.22996i
$700$	2.94380	−	10.9864i	0.111265	−	0.415247i
$701$	−0.672924			−0.0254160			−0.0127080	−	0.999919i	$-0.504045\pi$
$701$	−0.672924			−0.0254160			−0.0127080	+	0.999919i	$0.504045\pi$
$702$	18.4551	+	3.22653i	0.696542	+	0.121777i
$703$	−10.8743			−0.410131
$704$	−1.08766	+	4.05922i	−0.0409929	+	0.152987i
$705$	0.307809	+	6.69546i	0.0115928	+	0.252166i
$706$	−8.95950	−	5.17277i	−0.337195	−	0.194680i
$707$	5.34758	+	5.34758i	0.201116	+	0.201116i
$708$	17.4065	+	3.81682i	0.654176	+	0.143445i
$709$	29.5534	−	7.91881i	1.10990	−	0.297397i	0.343111	−	0.939295i	$-0.388519\pi$
$709$	29.5534	−	7.91881i	1.10990	−	0.297397i	0.766790	+	0.641898i	$0.221853\pi$
$710$	−22.2989	+	22.2989i	−0.836864	+	0.836864i
$711$	−4.72152	+	0.435043i	−0.177071	+	0.0163154i
$712$	8.52583	−	4.92239i	0.319519	−	0.184474i
$713$	−5.04653	−	1.35221i	−0.188994	−	0.0506408i
$714$	−9.87205	+	19.0713i	−0.369452	+	0.713727i
$715$	19.7859	+	38.5214i	0.739950	+	1.44062i
$716$			9.21508i			0.344384i
$717$	11.2600	−	12.3452i	0.420512	−	0.461039i
$718$	−6.42720	−	11.1322i	−0.239861	−	0.415452i
$719$	11.5566	−	20.0165i	0.430987	−	0.746491i	−0.565972	−	0.824425i	$-0.691499\pi$
$719$	11.5566	−	20.0165i	0.430987	−	0.746491i	0.996959	+	0.0779336i	$0.0248322\pi$
$720$	1.44992	−	8.45077i	0.0540354	−	0.314942i
$721$	−13.2508	−	49.4528i	−0.493487	−	1.84172i
$722$	3.61247	+	13.4819i	0.134442	+	0.501745i
$723$	−4.44747	−	13.9929i	−0.165403	−	0.520402i
$724$	−6.90550	+	11.9607i	−0.256641	+	0.444515i
$725$	3.19108	+	5.52711i	0.118514	+	0.205272i
$726$	8.52312	+	7.77390i	0.316322	+	0.288516i
$727$			11.5379i			0.427917i	0.976843	+	0.213959i	$0.0686357\pi$
$727$			11.5379i			0.427917i	−0.976843	+	0.213959i	$0.931364\pi$
$728$	−7.01349	+	10.8772i	−0.259937	+	0.403136i
$729$	−25.9808	+	7.34847i	−0.962250	+	0.272166i
$730$	−39.3630	−	10.5473i	−1.45689	−	0.390373i
$731$	5.83411	−	3.36832i	0.215782	−	0.124582i
$732$	−0.256109	−	0.399971i	−0.00946606	−	0.0147834i
$733$	−0.910162	+	0.910162i	−0.0336176	+	0.0336176i	−0.723716	−	0.690098i	$-0.757567\pi$
$733$	−0.910162	+	0.910162i	−0.0336176	+	0.0336176i	0.690098	+	0.723716i	$0.257567\pi$
$734$	1.59083	−	0.426262i	0.0587186	−	0.0157336i
$735$	6.23964	−	28.4558i	0.230153	−	1.04961i
$736$	2.14421	+	2.14421i	0.0790365	+	0.0790365i
$737$	−15.4524	−	8.92147i	−0.569198	−	0.328626i
$738$	−21.6364	−	9.96794i	−0.796448	−	0.366925i
$739$	−3.23160	+	12.0605i	−0.118876	+	0.443652i	−0.999548	−	0.0300754i	$-0.990425\pi$
$739$	−3.23160	+	12.0605i	−0.118876	+	0.443652i	0.880671	+	0.473728i	$0.157092\pi$
$740$	13.8405			0.508788
$741$	−13.5570	+	3.58666i	−0.498030	+	0.131759i
$742$	−25.9232			−0.951669
$743$	−11.8573	+	44.2519i	−0.435001	+	1.62345i	0.306063	+	0.952011i	$0.400988\pi$
$743$	−11.8573	+	44.2519i	−0.435001	+	1.62345i	−0.741064	+	0.671435i	$0.765678\pi$
$744$	−2.98105	+	0.137047i	−0.109291	+	0.00502440i
$745$	−25.5802	−	14.7687i	−0.937185	−	0.541084i
$746$	14.1079	+	14.1079i	0.516526	+	0.516526i
$747$	8.44810	+	7.02262i	0.309100	+	0.256944i
$748$	−14.0209	+	3.75688i	−0.512653	+	0.137365i
$749$	−35.1425	+	35.1425i	−1.28408	+	1.28408i
$750$	7.63481	−	4.88871i	0.278784	−	0.178511i
$751$	13.8766	−	8.01168i	0.506366	−	0.292350i	−0.224973	−	0.974365i	$-0.572229\pi$
$751$	13.8766	−	8.01168i	0.506366	−	0.292350i	0.731338	+	0.682015i	$0.238896\pi$
$752$	−1.30782	−	0.350429i	−0.0476912	−	0.0127788i
$753$	10.8285	+	5.60523i	0.394611	+	0.204266i
$754$	−1.53301	−	7.09852i	−0.0558289	−	0.258513i
$755$		−	26.2295i		−	0.954588i
$756$	2.30649	−	18.5086i	0.0838864	−	0.673153i
$757$	15.6277	+	27.0680i	0.567998	+	0.983802i	0.996764	+	0.0803861i	$0.0256153\pi$
$757$	15.6277	+	27.0680i	0.567998	+	0.983802i	−0.428765	+	0.903416i	$0.641051\pi$
$758$	6.15590	−	10.6623i	0.223592	−	0.387273i
$759$	21.0350	−	6.68572i	0.763523	−	0.242676i
$760$	1.66109	+	6.19928i	0.0602542	+	0.224872i
$761$	4.45283	+	16.6182i	0.161415	+	0.602409i	0.998470	+	0.0552906i	$0.0176085\pi$
$761$	4.45283	+	16.6182i	0.161415	+	0.602409i	−0.837055	+	0.547118i	$0.815725\pi$
$762$	−34.1579	+	10.8567i	−1.23741	+	0.393295i
$763$	14.8286	−	25.6839i	0.536832	−	0.929820i
$764$	11.3515	+	19.6614i	0.410683	+	0.711324i
$765$	27.7830	−	10.2576i	1.00450	−	0.370865i
$766$			28.3459i			1.02418i
$767$	7.83066	+	36.2595i	0.282749	+

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	78.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.0795432 - 1.73022i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.02097 + 2.02097i) q^{5} +(1.69185 + 0.370982i) q^{6} +(3.46723 - 0.929042i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.98735 + 0.275255i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.0795432 - 1.73022i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.02097 + 2.02097i) q^{5} +(1.69185 + 0.370982i) q^{6} +(3.46723 - 0.929042i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.98735 + 0.275255i) q^{9} +(-2.47517 + 1.42904i) q^{10} +(-4.05922 - 1.08766i) q^{11} +(-0.796225 + 1.53819i) q^{12} +(-3.60121 - 0.176977i) q^{13} +3.58954i q^{14} +(3.33598 - 3.65748i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.72704 + 2.99132i) q^{17} +(0.507306 - 2.95680i) q^{18} +(0.581191 + 2.16903i) q^{19} +(-0.739726 - 2.76070i) q^{20} +(-1.88324 - 5.92518i) q^{21} +(2.10121 - 3.63939i) q^{22} +(-1.51618 - 2.62611i) q^{23} +(-1.27970 - 1.16721i) q^{24} +3.16864i q^{25} +(1.10301 - 3.43269i) q^{26} +(0.713876 + 5.14688i) q^{27} +(-3.46723 - 0.929042i) q^{28} +(1.74432 - 1.00708i) q^{29} +(2.66944 + 4.16893i) q^{30} +(1.21829 - 1.21829i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.55902 + 7.10987i) q^{33} +(-2.44240 - 2.44240i) q^{34} +(8.88473 + 5.12960i) q^{35} +(2.72474 + 1.25529i) q^{36} +(-1.25335 + 4.67758i) q^{37} -2.24555 q^{38} +(-0.0197576 + 6.24497i) q^{39} +2.85808 q^{40} +(2.05521 - 7.67015i) q^{41} +(6.21071 - 0.285524i) q^{42} +(-1.68905 - 0.975173i) q^{43} +(2.97155 + 2.97155i) q^{44} +(-6.59362 - 5.48105i) q^{45} +(2.92904 - 0.784834i) q^{46} +(-0.957390 + 0.957390i) q^{47} +(1.45865 - 0.933998i) q^{48} +(5.09639 - 2.94240i) q^{49} +(-3.06067 - 0.820104i) q^{50} +(5.31303 + 2.75023i) q^{51} +(3.03025 + 1.95387i) q^{52} +7.22186i q^{53} +(-5.15627 - 0.642559i) q^{54} +(-6.00542 - 10.4017i) q^{55} +(1.79477 - 3.10863i) q^{56} +(3.70668 - 1.17812i) q^{57} +(0.521304 + 1.94553i) q^{58} +(-2.66284 - 9.93785i) q^{59} +(-4.71778 + 1.49949i) q^{60} +(-0.137104 + 0.237470i) q^{61} +(0.861464 + 1.49210i) q^{62} +(-10.1021 + 3.72974i) q^{63} -1.00000i q^{64} +(-6.92026 - 7.63559i) q^{65} +(-6.46410 - 3.34607i) q^{66} +(4.10121 + 1.09891i) q^{67} +(2.99132 - 1.72704i) q^{68} +(-4.42315 + 2.83223i) q^{69} +(-7.25436 + 7.25436i) q^{70} +(10.6578 - 2.85575i) q^{71} +(-1.91774 + 2.30701i) q^{72} +(10.0822 + 10.0822i) q^{73} +(-4.19381 - 2.42130i) q^{74} +(5.48246 - 0.252044i) q^{75} +(0.581191 - 2.16903i) q^{76} -15.0847 q^{77} +(-6.02706 - 1.63540i) q^{78} +1.58051 q^{79} +(-0.739726 + 2.76070i) q^{80} +(8.84847 - 1.64456i) q^{81} +(6.87686 + 3.97036i) q^{82} +(-2.58938 - 2.58938i) q^{83} +(-1.33165 + 6.07298i) q^{84} +(-9.53567 + 2.55507i) q^{85} +(1.37910 - 1.37910i) q^{86} +(-1.88122 - 2.93795i) q^{87} +(-3.63939 + 2.10121i) q^{88} +(9.50933 + 2.54802i) q^{89} +(7.00085 - 4.95035i) q^{90} +(-12.6506 + 2.73205i) q^{91} +3.03237i q^{92} +(-2.20483 - 2.01101i) q^{93} +(-0.676977 - 1.17256i) q^{94} +(-3.20898 + 5.55812i) q^{95} +(0.524648 + 1.65068i) q^{96} +(-2.07638 - 7.74915i) q^{97} +(1.52310 + 5.68429i) q^{98} +(12.4257 + 2.13191i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} - 24 q^{10} - 24 q^{13} + 8 q^{16} - 16 q^{19} - 24 q^{21} - 8 q^{28} + 24 q^{30} + 16 q^{31} - 24 q^{33} + 24 q^{34} + 24 q^{36} + 16 q^{37} + 48 q^{39} + 24 q^{45} + 24 q^{46} + 24 q^{49} - 8 q^{52} - 24 q^{55} - 24 q^{57} - 24 q^{60} - 24 q^{61} - 24 q^{63} - 48 q^{66} + 32 q^{67} - 48 q^{69} - 24 q^{72} + 56 q^{73} - 16 q^{76} - 96 q^{79} + 24 q^{81} - 48 q^{82} - 24 q^{85} + 48 q^{87} - 16 q^{91} - 24 q^{93} - 24 q^{94} + 16 q^{97}+O(q^{100}) \) 16 * q + 8 * q^7 - 24 * q^10 - 24 * q^13 + 8 * q^16 - 16 * q^19 - 24 * q^21 - 8 * q^28 + 24 * q^30 + 16 * q^31 - 24 * q^33 + 24 * q^34 + 24 * q^36 + 16 * q^37 + 48 * q^39 + 24 * q^45 + 24 * q^46 + 24 * q^49 - 8 * q^52 - 24 * q^55 - 24 * q^57 - 24 * q^60 - 24 * q^61 - 24 * q^63 - 48 * q^66 + 32 * q^67 - 48 * q^69 - 24 * q^72 + 56 * q^73 - 16 * q^76 - 96 * q^79 + 24 * q^81 - 48 * q^82 - 24 * q^85 + 48 * q^87 - 16 * q^91 - 24 * q^93 - 24 * q^94 + 16 * q^97

Introduction

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