LMFDB - Embedded newform 78.2.k.a.59.1

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} + \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			59.1
Root			$0.500000 + 0.410882i$ of defining polynomial
Character	$\chi$	$=$	78.59
Dual form			78.2.k.a.41.1

$q$-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 $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

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	−0.0919576	−	0.995763i	$-0.529312\pi$
$5$	2.02097	−	2.02097i	0.903805	−	0.903805i	0.995763	+	0.0919576i	$0.0293124\pi$
$6$	1.69185	−	0.370982i	0.690697	−	0.151453i
$7$	3.46723	+	0.929042i	1.31049	+	0.351145i	0.845407	−	0.534122i	$-0.179358\pi$
$7$	3.46723	+	0.929042i	1.31049	+	0.351145i	0.465083	+	0.885267i	$0.346025\pi$
$8$	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	−0.812201	−	0.583377i	$-0.801731\pi$
$11$	−4.05922	+	1.08766i	−1.22390	+	0.327943i	−0.411699	+	0.911320i	$0.635064\pi$
$12$	−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	0.576957	−	0.816774i	$-0.304240\pi$
$17$	−1.72704	−	2.99132i	−0.418869	−	0.725502i	−0.995826	+	0.0912724i	$0.970907\pi$
$18$	0.507306	+	2.95680i	0.119573	+	0.696923i
$19$	0.581191	−	2.16903i	0.133334	−	0.497611i	−0.866665	−	0.498891i	$-0.833741\pi$
$19$	0.581191	−	2.16903i	0.133334	−	0.497611i	0.999999	+	0.00128023i	$0.000407509\pi$
$20$	−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	−0.979680	−	0.200565i	$-0.935722\pi$
$23$	−1.51618	+	2.62611i	−0.316146	+	0.547581i	0.663534	+	0.748146i	$0.269056\pi$
$24$	−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	0.653135	−	0.757242i	$-0.273454\pi$
$29$	1.74432	+	1.00708i	0.323911	+	0.187010i	−0.329223	+	0.944252i	$0.606787\pi$
$30$	2.66944	−	4.16893i	0.487372	−	0.761139i
$31$	1.21829	+	1.21829i	0.218812	+	0.218812i	0.807998	−	0.589186i	$-0.200551\pi$
$31$	1.21829	+	1.21829i	0.218812	+	0.218812i	−0.589186	+	0.807998i	$0.700551\pi$
$32$	−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	−0.989127	−	0.147065i	$-0.953017\pi$
$37$	−1.25335	−	4.67758i	−0.206050	−	0.768990i	0.783077	−	0.621925i	$-0.213649\pi$
$38$	−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	0.918302	+	0.395881i	$0.129561\pi$
$41$	2.05521	+	7.67015i	0.320970	+	1.19788i	−0.597332	+	0.801994i	$0.703772\pi$
$42$	6.21071	+	0.285524i	0.958333	+	0.0440573i
$43$	−1.68905	+	0.975173i	−0.257578	+	0.148712i	−0.623229	−	0.782039i	$-0.714180\pi$
$43$	−1.68905	+	0.975173i	−0.257578	+	0.148712i	0.365651	+	0.930752i	$0.380846\pi$
$44$	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	0.633826	−	0.773476i	$-0.281484\pi$
$47$	−0.957390	−	0.957390i	−0.139650	−	0.139650i	−0.773476	+	0.633826i	$0.781484\pi$
$48$	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	$-0.834802\pi$
$53$		−	7.22186i		−	0.991999i	0.868323	−	0.495999i	$-0.165198\pi$
$54$	−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	0.543975	+	0.839101i	$0.316919\pi$
$59$	−2.66284	+	9.93785i	−0.346672	+	1.29380i	−0.890647	+	0.454696i	$0.849748\pi$
$60$	−4.71778	−	1.49949i	−0.609063	−	0.193583i
$61$	−0.137104	−	0.237470i	−0.0175543	−	0.0304050i	0.857115	−	0.515125i	$-0.172255\pi$
$61$	−0.137104	−	0.237470i	−0.0175543	−	0.0304050i	−0.874669	+	0.484720i	$0.838921\pi$
$62$	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	0.000558430	−	1.00000i	$-0.499822\pi$
$67$	4.10121	−	1.09891i	0.501042	−	0.134254i	0.500484	+	0.865746i	$0.333156\pi$
$68$	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	0.828055	−	0.560647i	$-0.189447\pi$
$71$	10.6578	+	2.85575i	1.26485	+	0.338915i	0.436793	+	0.899562i	$0.356114\pi$
$72$	−1.91774	−	2.30701i	−0.226008	−	0.271883i
$73$	10.0822	−	10.0822i	1.18003	−	1.18003i	0.200296	−	0.979735i	$-0.435810\pi$
$73$	10.0822	−	10.0822i	1.18003	−	1.18003i	0.979735	−	0.200296i	$-0.0641903\pi$
$74$	−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	−0.834790	−	0.550569i	$-0.814411\pi$
$83$	−2.58938	+	2.58938i	−0.284221	+	0.284221i	0.550569	+	0.834790i	$0.314411\pi$
$84$	−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	0.283199	−	0.959061i	$-0.408604\pi$
$89$	9.50933	−	2.54802i	1.00799	−	0.270089i	0.724788	+	0.688972i	$0.241938\pi$
$90$	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	0.776771	+	0.629784i	$0.216856\pi$
$97$	−2.07638	+	7.74915i	−0.210824	+	0.786807i	−0.987595	+	0.157023i	$0.949810\pi$
$98$	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	−0.808845	−	0.588022i	$-0.799907\pi$
$101$	1.05342	−	1.82458i	0.104820	−	0.181553i	0.913665	+	0.406469i	$0.133240\pi$
$102$	−4.03163	−	4.42018i	−0.399191	−	0.437663i
$103$			14.2629i			1.40537i	0.711503	+	0.702683i	$0.248015\pi$
$103$			14.2629i			1.40537i	−0.711503	+	0.702683i	$0.751985\pi$
$104$	−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	−0.208066	−	0.978115i	$-0.566717\pi$
$107$	−11.9906	−	6.92275i	−1.15917	−	0.669248i	−0.951105	+	0.308867i	$0.900050\pi$
$108$	1.95521	+	4.81427i	0.188140	+	0.463253i
$109$	5.84220	+	5.84220i	0.559581	+	0.559581i	0.929188	−	0.369607i	$-0.120508\pi$
$109$	5.84220	+	5.84220i	0.559581	+	0.559581i	−0.369607	+	0.929188i	$0.620508\pi$
$110$	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	0.467463	−	0.884012i	$-0.345168\pi$
$113$	15.5920	−	9.00205i	1.46677	−	0.846841i	0.999309	+	0.0371710i	$0.0118346\pi$
$114$	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	−0.993268	−	0.115837i	$-0.963045\pi$
$127$	−17.9209	−	10.3466i	−1.59022	−	0.918114i	−0.596952	−	0.802277i	$-0.703622\pi$
$128$	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	$-0.934419\pi$
$131$		−	4.68295i		−	0.409151i	0.978851	−	0.204576i	$-0.0655814\pi$
$132$	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	−0.999675	−	0.0255107i	$-0.991879\pi$
$137$	−1.41832	+	5.29326i	−0.121176	+	0.452234i	0.878499	+	0.477744i	$0.158545\pi$
$138$	−1.59092	+	5.00547i	−0.135428	+	0.426094i
$139$	−7.34662	−	12.7247i	−0.623132	−	1.07930i	−0.988899	−	0.148590i	$-0.952527\pi$
$139$	−7.34662	−	12.7247i	−0.623132	−	1.07930i	0.365767	−	0.930706i	$-0.380807\pi$
$140$	−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	−0.174417	−	0.984672i	$-0.555804\pi$
$149$	−9.98255	−	2.67482i	−0.817803	−	0.219130i	−0.643386	+	0.765542i	$0.722471\pi$
$150$	−1.17551	−	5.36088i	−0.0959798	−	0.437714i
$151$	−6.48932	+	6.48932i	−0.528094	+	0.528094i	−0.920004	−	0.391910i	$-0.871814\pi$
$151$	−6.48932	+	6.48932i	−0.528094	+	0.528094i	0.391910	+	0.920004i	$0.371814\pi$
$152$	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	0.300727	−	0.953710i	$-0.402771\pi$
$163$	1.07638	+	0.288415i	0.0843084	+	0.0225904i	−0.216418	+	0.976301i	$0.569437\pi$
$164$	−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	−0.0439735	−	0.999033i	$-0.514002\pi$
$167$	5.39478	−	1.44553i	0.417461	−	0.111858i	0.461434	+	0.887174i	$0.347335\pi$
$168$	−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	0.979266	+	0.202579i	$0.0649324\pi$
$173$	8.74765	+	15.1514i	0.665072	+	1.15194i	−0.314194	+	0.949359i	$0.601734\pi$
$174$	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	−0.985242	−	0.171169i	$-0.945245\pi$
$179$	−4.60754	+	7.98049i	−0.344384	+	0.596490i	0.640858	+	0.767660i	$0.278579\pi$
$180$	2.96971	−	8.04354i	0.221349	−	0.599530i
$181$			13.8110i			1.02656i	0.858220	+	0.513282i	$0.171571\pi$
$181$			13.8110i			1.02656i	−0.858220	+	0.513282i	$0.828429\pi$
$182$	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	−0.996525	−	0.0832996i	$-0.973454\pi$
$191$	−19.6614	+	11.3515i	−1.42265	+	0.821366i	−0.426123	+	0.904665i	$0.640121\pi$
$192$	−1.73022	−	0.0795432i	−0.124868	−	0.00574054i
$193$	−5.18821	−	19.3627i	−0.373456	−	1.39376i	−0.855588	−	0.517657i	$-0.826804\pi$
$193$	−5.18821	−	19.3627i	−0.373456	−	1.39376i	0.482133	−	0.876098i	$-0.339862\pi$
$194$	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	−0.894154	−	0.447760i	$-0.852222\pi$
$197$	−4.82369	−	18.0023i	−0.343674	−	1.28261i	0.550480	−	0.834849i	$-0.314445\pi$
$198$	−5.27526	−	11.4505i	−0.374897	−	0.813751i
$199$	−3.90611	+	2.25519i	−0.276897	+	0.159866i	−0.632018	−	0.774954i	$-0.717773\pi$
$199$	−3.90611	+	2.25519i	−0.276897	+	0.159866i	0.355121	+	0.934820i	$0.384440\pi$
$200$	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	−0.679811	−	0.733387i	$-0.737938\pi$
$211$	4.28841	−	7.42775i	0.295227	−	0.511348i	0.975038	+	0.222040i	$0.0712715\pi$
$212$	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	0.498232	−	0.867043i	$-0.333983\pi$
$223$	20.3575	−	5.45476i	1.36324	−	0.365278i	0.865004	+	0.501765i	$0.167316\pi$
$224$	−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	0.416326	−	0.909215i	$-0.363318\pi$
$227$	4.85544	+	1.30101i	0.322267	+	0.0863512i	−0.0940589	+	0.995567i	$0.529984\pi$
$228$	−3.79914	+	0.833058i	−0.251604	+	0.0551706i
$229$	−9.92484	+	9.92484i	−0.655852	+	0.655852i	−0.954396	−	0.298544i	$-0.903499\pi$
$229$	−9.92484	+	9.92484i	−0.655852	+	0.655852i	0.298544	+	0.954396i	$0.403499\pi$
$230$	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	−0.451188	−	0.892429i	$-0.649000\pi$
$239$	6.82142	−	6.82142i	0.441241	−	0.441241i	0.892429	+	0.451188i	$0.149000\pi$
$240$	4.83546	−	1.06030i	0.312128	−	0.0684419i
$241$	8.18821	+	2.19402i	0.527449	+	0.141330i	0.512710	−	0.858562i	$-0.328642\pi$
$241$	8.18821	+	2.19402i	0.527449	+	0.141330i	0.0147390	+	0.999891i	$0.495308\pi$
$242$	−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	0.733295	−	0.679911i	$-0.237982\pi$
$251$	−3.51988	−	6.09661i	−0.222173	−	0.384814i	−0.955467	+	0.295096i	$0.904648\pi$
$252$	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	−0.890353	−	0.455271i	$-0.849542\pi$
$257$	−0.815993	+	1.41334i	−0.0509003	+	0.0881618i	0.839453	+	0.543433i	$0.182876\pi$
$258$	−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	0.190544	−	0.981679i	$-0.438975\pi$
$263$	−9.15209	−	5.28396i	−0.564342	−	0.325823i	−0.754886	+	0.655856i	$0.772308\pi$
$264$	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	−0.709975	−	0.704227i	$-0.751294\pi$
$269$	−7.46392	+	4.30930i	−0.455083	+	0.262742i	0.254891	+	0.966970i	$0.417960\pi$
$270$	−9.12207	+	11.7193i	−0.555152	+	0.713211i
$271$	5.13290	+	19.1563i	0.311802	+	1.16366i	0.926930	+	0.375233i	$0.122437\pi$
$271$	5.13290	+	19.1563i	0.311802	+	1.16366i	−0.615129	+	0.788427i	$0.710896\pi$
$272$	−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	−0.845795	−	0.533508i	$-0.820873\pi$
$277$	−13.4255	+	7.75123i	−0.806661	+	0.465726i	0.0391339	+	0.999234i	$0.487540\pi$
$278$	−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	0.254486	−	0.967077i	$-0.418094\pi$
$281$	−11.9452	−	11.9452i	−0.712591	−	0.712591i	−0.967077	+	0.254486i	$0.918094\pi$
$282$	−1.97494	−	1.26459i	−0.117606	−	0.0753052i
$283$	−1.36808	−	0.789860i	−0.0813237	−	0.0469523i	0.458787	−	0.888546i	$-0.348284\pi$
$283$	−1.36808	−	0.789860i	−0.0813237	−	0.0469523i	−0.540110	+	0.841594i	$0.681618\pi$
$284$	−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	−0.989145	−	0.146946i	$-0.953056\pi$
$293$	−1.01073	+	3.77209i	−0.0590474	+	0.220368i	0.930097	+	0.367314i	$0.119722\pi$
$294$	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	0.285899	−	0.958260i	$-0.407708\pi$
$307$	21.7994	−	21.7994i	1.24416	−	1.24416i	0.958260	−	0.285899i	$-0.0922920\pi$
$308$	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	−0.545464	−	0.838134i	$-0.683646\pi$
$317$	5.21085	−	5.21085i	0.292671	−	0.292671i	0.838134	+	0.545464i	$0.183646\pi$
$318$	−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	−0.706123	−	0.708089i	$-0.749557\pi$
$331$	4.72013	−	17.6158i	0.259442	−	0.968251i	0.965565	−	0.260162i	$-0.0837759\pi$
$332$	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	$-0.957174\pi$
$337$		−	4.92484i		−	0.268273i	0.990963	−	0.134136i	$-0.0428260\pi$
$338$	−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	−0.110688	−	0.993855i	$-0.535306\pi$
$347$	12.9403	−	7.47108i	0.694671	−	0.401069i	0.805360	+	0.592787i	$0.201972\pi$
$348$	0.160213	−	3.48495i	0.00858832	−	0.186813i
$349$	−8.08448	−	30.1717i	−0.432752	−	1.61505i	−0.746388	−	0.665511i	$-0.768214\pi$
$349$	−8.08448	−	30.1717i	−0.432752	−	1.61505i	0.313636	−	0.949543i	$-0.398453\pi$
$350$	−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	−0.999853	−	0.0171211i	$-0.994550\pi$
$353$	−2.67762	−	9.99302i	−0.142515	−	0.531875i	0.857338	−	0.514754i	$-0.172117\pi$
$354$	−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	0.425321	−	0.905043i	$-0.360161\pi$
$359$	−9.08944	−	9.08944i	−0.479722	−	0.479722i	−0.905043	+	0.425321i	$0.860161\pi$
$360$	−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	−0.886717	−	0.462312i	$-0.847020\pi$
$367$	−0.823475	+	1.42630i	−0.0429850	+	0.0744522i	0.843732	+	0.536764i	$0.180353\pi$
$368$	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	0.999816	+	0.0191892i	$0.00610849\pi$
$373$	9.97578	+	17.2786i	0.516526	+	0.894650i	−0.483290	+	0.875461i	$0.660558\pi$
$374$	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	−0.550972	−	0.834524i	$-0.685743\pi$
$379$	−11.8923	+	3.18653i	−0.610865	+	0.163681i	−0.0598936	+	0.998205i	$0.519076\pi$
$380$	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	0.878005	−	0.478652i	$-0.158875\pi$
$383$	27.3800	+	7.33645i	1.39905	+	0.374875i	0.521048	+	0.853527i	$0.325541\pi$
$384$	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	−0.0622992	−	0.998058i	$-0.519843\pi$
$397$	−12.2594	−	3.28489i	−0.615281	−	0.164864i	−0.552981	+	0.833194i	$0.686510\pi$
$398$	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	−0.632080	−	0.774903i	$-0.717799\pi$
$401$	−15.8603	+	4.24976i	−0.792027	+	0.212223i	−0.159946	+	0.987126i	$0.551132\pi$
$402$	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	0.302240	+	0.953232i	$0.402266\pi$
$409$	−8.82005	+	32.9169i	−0.436123	+	1.62763i	−0.738364	+	0.674403i	$0.764401\pi$
$410$	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	0.993541	−	0.113477i	$-0.0361989\pi$
$419$	28.4943	+	16.4512i	1.39204	+	0.803693i	0.398496	+	0.917170i	$0.369532\pi$
$420$	−14.9646	−	9.58208i	−0.730195	−	0.467558i
$421$	17.0945	+	17.0945i	0.833137	+	0.833137i	0.987945	−	0.154808i	$-0.0494759\pi$
$421$	17.0945	+	17.0945i	0.833137	+	0.833137i	−0.154808	+	0.987945i	$0.549476\pi$
$422$	−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	0.954117	−	0.299433i	$-0.0967975\pi$
$431$	−0.454427	−	1.69594i	−0.0218890	−	0.0816908i	−0.976006	+	0.217742i	$0.930131\pi$
$432$	−4.10039	−	3.19168i	−0.197280	−	0.153560i
$433$	−8.87140	+	5.12190i	−0.426332	+	0.246143i	−0.697783	−	0.716309i	$-0.745830\pi$
$433$	−8.87140	+	5.12190i	−0.426332	+	0.246143i	0.271451	+	0.962452i	$0.412497\pi$
$434$	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	0.384182	−	0.923257i	$-0.374484\pi$
$439$	−4.67848	−	2.70112i	−0.223292	−	0.128917i	−0.607473	+	0.794340i	$0.707817\pi$
$440$	−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	$-0.895498\pi$
$443$		−	13.5731i		−	0.644876i	0.946591	−	0.322438i	$-0.104502\pi$
$444$	−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	−0.977211	−	0.212269i	$-0.931915\pi$
$449$	−0.525222	+	1.96016i	−0.0247868	+	0.0925055i	0.952424	+	0.304775i	$0.0985812\pi$
$450$	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	−0.861395	−	0.507936i	$-0.830409\pi$
$457$	−28.9328	+	7.75251i	−1.35342	+	0.362647i	−0.492022	+	0.870583i	$0.663742\pi$
$458$	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	−0.122487	−	0.992470i	$-0.539087\pi$
$461$	−15.5621	−	4.16985i	−0.724798	−	0.194209i	−0.602312	+	0.798261i	$0.705754\pi$
$462$	−25.5212	+	5.59616i	−1.18735	+	0.260357i
$463$	−4.07041	+	4.07041i	−0.189168	+	0.189168i	−0.795336	−	0.606168i	$-0.792706\pi$
$463$	−4.07041	+	4.07041i	−0.189168	+	0.189168i	0.606168	+	0.795336i	$0.292706\pi$
$464$	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	−0.575011	−	0.818145i	$-0.695002\pi$
$479$	−14.5305	+	3.89342i	−0.663913	+	0.177895i	−0.0889019	+	0.996040i	$0.528336\pi$
$480$	−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	−0.795728	−	0.605654i	$-0.792912\pi$
$487$	4.33018	−	16.1605i	0.196219	−	0.732301i	0.991948	−	0.126647i	$-0.0404216\pi$
$488$	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	−0.426419	−	0.904526i	$-0.640225\pi$
$491$	12.6333	−	21.8815i	0.570132	−	0.987498i	0.996552	−	0.0829727i	$-0.0264414\pi$
$492$	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	0.737309	−	0.675556i	$-0.236096\pi$
$499$	1.37946	+	1.37946i	0.0617533	+	0.0617533i	−0.675556	+	0.737309i	$0.736096\pi$
$500$	−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	−0.701886	−	0.712289i	$-0.747659\pi$
$503$	−9.77777	+	5.64520i	−0.435969	+	0.251707i	0.265917	+	0.963996i	$0.414325\pi$
$504$	−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	0.749561	+	0.661936i	$0.230265\pi$
$509$	9.73260	+	36.3226i	0.431390	+	1.60997i	−0.318171	+	0.948033i	$0.603069\pi$
$510$	−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	$0.130615\pi$
$521$			18.2111i			0.797843i	−0.916985	+	0.398922i	$0.869385\pi$
$522$	−2.09283	+	5.66849i	−0.0916008	+	0.248103i
$523$	−16.9049	+	29.2801i	−0.739199	+	1.28033i	0.213658	+	0.976909i	$0.431462\pi$
$523$	−16.9049	+	29.2801i	−0.739199	+	1.28033i	−0.952857	+	0.303421i	$0.901871\pi$
$524$	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	−0.805892	−	0.592063i	$-0.798314\pi$
$541$	−4.97355	+	4.97355i	−0.213829	+	0.213829i	0.592063	+	0.805892i	$0.298314\pi$
$542$	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	−0.304662	−	0.952460i	$-0.598544\pi$
$557$	−2.17782	+	0.583545i	−0.0922772	+	0.0247256i	0.212385	+	0.977186i	$0.431877\pi$
$558$	−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	−0.940306	−	0.340330i	$-0.889461\pi$
$563$	−18.1490	−	31.4349i	−0.764888	−	1.32482i	0.175418	−	0.984494i	$-0.443872\pi$
$564$	−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	−0.0873209	−	0.996180i	$-0.527831\pi$
$569$	19.5376	−	33.8400i	0.819057	−	1.41865i	0.906378	−	0.422468i	$-0.138836\pi$
$570$	−7.49110	−	8.21306i	−0.313768	−	0.344007i
$571$			31.9061i			1.33523i	0.744508	+	0.667614i	$0.232684\pi$
$571$			31.9061i			1.33523i	−0.744508	+	0.667614i	$0.767316\pi$
$572$	−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	0.873825	−	0.486240i	$-0.161632\pi$
$577$	9.31011	+	9.31011i	0.387585	+	0.387585i	−0.486240	+	0.873825i	$0.661632\pi$
$578$	−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	0.925962	+	0.377615i	$0.123256\pi$
$587$	7.58008	+	28.2892i	0.312863	+	1.16762i	−0.613099	+	0.790006i	$0.710077\pi$
$588$	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	0.395450	−	0.918487i	$-0.370589\pi$
$593$	−12.7368	−	12.7368i	−0.523037	−	0.523037i	−0.918487	+	0.395450i	$0.870589\pi$
$594$	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	$-0.896357\pi$
$599$		−	15.6579i		−	0.639764i	0.947457	−	0.319882i	$-0.103643\pi$
$600$	3.69846	+	4.05490i	0.150989	+	0.165541i
$601$	−3.99832	+	6.92529i	−0.163095	+	0.282488i	−0.935977	−	0.352061i	$-0.885481\pi$
$601$	−3.99832	+	6.92529i	−0.163095	+	0.282488i	0.772882	+	0.634549i	$0.218814\pi$
$602$	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	0.816843	−	0.576860i	$-0.195722\pi$
$607$	−2.24581	−	3.88985i	−0.0911545	−	0.157884i	−0.907997	+	0.418976i	$0.862389\pi$
$608$	−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	0.416848	−	0.908976i	$-0.363135\pi$
$613$	30.5112	−	8.17546i	1.23234	−	0.330204i	0.815489	+	0.578773i	$0.196468\pi$
$614$	−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	0.151895	−	0.988397i	$-0.451462\pi$
$617$	−5.23513	−	1.40275i	−0.210758	−	0.0564725i	−0.362653	+	0.931924i	$0.618129\pi$
$618$	5.29128	+	24.1308i	0.212846	+	0.970682i
$619$	7.22455	−	7.22455i	0.290379	−	0.290379i	−0.546851	−	0.837230i	$-0.684174\pi$
$619$	7.22455	−	7.22455i	0.290379	−	0.290379i	0.837230	+	0.546851i	$0.184174\pi$
$620$	−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	−0.168632	−	0.985679i	$-0.553935\pi$
$631$	−20.2844	−	5.43520i	−0.807511	−	0.216372i	−0.638879	+	0.769307i	$0.720602\pi$
$632$	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	−0.887326	−	0.461143i	$-0.847440\pi$
$641$	−21.3437	−	36.9683i	−0.843024	−	1.46016i	0.0443019	−	0.999018i	$-0.485894\pi$
$642$	−22.8545	−	7.26401i	−0.901995	−	0.286688i
$643$	−0.813185	+	3.03485i	−0.0320689	+	0.119683i	−0.980105	−	0.198481i	$-0.936399\pi$
$643$	−0.813185	+	3.03485i	−0.0320689	+	0.119683i	0.948036	+	0.318163i	$0.103066\pi$
$644$	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	−0.245329	−	0.969440i	$-0.578896\pi$
$647$	18.2351	−	31.5841i	0.716895	−	1.24170i	0.962224	−	0.272258i	$-0.0877705\pi$
$648$	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	0.998863	+	0.0476658i	$0.0151782\pi$
$653$	39.3421	+	22.7142i	1.53957	+	0.888874i	0.540711	+	0.841208i	$0.318155\pi$
$654$	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	−0.259319	−	0.965792i	$-0.583498\pi$
$659$	11.4858	−	6.63132i	0.447422	−	0.258319i	0.706741	+	0.707472i	$0.250165\pi$
$660$	20.7814	+	0.955381i	0.808916	+	0.0371882i
$661$	2.40763	+	8.98541i	0.0936460	+	0.349492i	0.996811	−	0.0798025i	$-0.0254290\pi$
$661$	2.40763	+	8.98541i	0.0936460	+	0.349492i	−0.903165	+	0.429294i	$0.858762\pi$
$662$	−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	−0.0118785	−	0.999929i	$-0.503781\pi$
$673$	−22.9273	−	13.2371i	−0.883782	−	0.510252i	−0.871904	+	0.489678i	$0.837114\pi$
$674$	−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	$0.289606\pi$
$677$			41.0789i			1.57879i	−0.613885	+	0.789396i	$0.710394\pi$
$678$	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	−0.930140	−	0.367206i	$-0.880315\pi$
$683$	1.54160	−	5.75334i	0.0589878	−	0.220145i	0.989128	+	0.147060i	$0.0469812\pi$
$684$	−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	0.308679	−	0.951166i	$-0.400113\pi$
$691$	27.6429	−	7.40689i	1.05159	−	0.281771i	0.742907	+	0.669395i	$0.233447\pi$
$692$	−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	0.766790	−	0.641898i	$-0.221853\pi$
$709$	29.5534	+	7.91881i	1.10990	+	0.297397i	0.343111	+	0.939295i	$0.388519\pi$
$710$	−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	0.996959	−	0.0779336i	$-0.0248322\pi$
$719$	11.5566	+	20.0165i	0.430987	+	0.746491i	−0.565972	+	0.824425i	$0.691499\pi$
$720$	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	$-0.931364\pi$
$727$		−	11.5379i		−	0.427917i	0.976843	−	0.213959i	$-0.0686357\pi$
$728$	−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	0.690098	−	0.723716i	$-0.257567\pi$
$733$	−0.910162	−	0.910162i	−0.0336176	−	0.0336176i	−0.723716	+	0.690098i	$0.757567\pi$
$734$	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	0.880671	−	0.473728i	$-0.157092\pi$
$739$	−3.23160	−	12.0605i	−0.118876	−	0.443652i	−0.999548	+	0.0300754i	$0.990425\pi$
$740$	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	−0.741064	−	0.671435i	$-0.765678\pi$
$743$	−11.8573	−	44.2519i	−0.435001	−	1.62345i	0.306063	−	0.952011i	$-0.400988\pi$
$744$	−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	0.731338	−	0.682015i	$-0.238896\pi$
$751$	13.8766	+	8.01168i	0.506366	+	0.292350i	−0.224973	+	0.974365i	$0.572229\pi$
$752$	−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	−0.428765	−	0.903416i	$-0.641051\pi$
$757$	15.6277	−	27.0680i	0.567998	−	0.983802i	0.996764	−	0.0803861i	$-0.0256153\pi$
$758$	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	−0.837055	−	0.547118i	$-0.815725\pi$
$761$	4.45283	−	16.6182i	0.161415	−	0.602409i	0.998470	−	0.0552906i	$-0.0176085\pi$
$762$	−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	−	1.30925i
$768$	1.53819	−	0.796225i	0.0555046	−	0.0287313i
$769$	0.224553	−	0.0601687i	0.00809758	−	0.00216974i	−0.254768	−	0.967002i	$-0.581999\pi$
$769$	0.224553	−	0.0601687i	0.00809758	−	0.00216974i	0.262866	+	0.964832i	$0.415332\pi$
$770$	37.3373	+	21.5567i	1.34554	+	0.776850i
$771$	−2.38049	−	1.52427i	−0.0857313	−	0.0548953i
$772$	14.1745	+	14.1745i	0.510150	+	0.510150i
$773$	42.7466	+	11.4539i	1.53749	+	0.411968i	0.925453	−	0.378863i	$-0.123685\pi$
$773$	42.7466	+	11.4539i	1.53749	+	0.411968i	0.612034	+	0.790831i	$0.290352\pi$
$774$	−3.74025	−	4.49946i	−0.134441	−	0.161730i
$775$	3.86034	−	3.86034i	0.138667	−	0.138667i
$776$	−6.94770	+	4.01125i	−0.249408	+	0.143996i
$777$	30.0759	+	1.38267i	1.07897	+	0.0496032i
$778$	−4.12827	−	15.4069i	−0.148006	−	0.552364i
$779$	17.8313			0.638872
$780$	17.2551	+	4.56502i	0.617831	+	0.163454i
$781$	−46.3684			−1.65919
$782$	−2.71088	−	10.1171i	−0.0969409	−	0.361788i
$783$	6.42856	−	8.25886i	0.229738	−	0.295148i
$784$	5.09639	−	2.94240i	0.182014	−	0.105086i
$785$	−28.5828	+	28.5828i	−1.02017	+	1.02017i
$786$	−1.73729	−	7.92287i	−0.0619671	−	0.282599i
$787$	20.4083	+	5.46839i	0.727478	+	0.194927i	0.603506	−	0.797358i	$-0.293770\pi$
$787$	20.4083	+	5.46839i	0.727478	+	0.194927i	0.123972	+	0.992286i	$0.460437\pi$
$788$	13.1786	+	13.1786i	0.469467	+	0.469467i
$789$	9.87042	−	15.4149i	0.351396	−	0.548783i
$790$	−3.91203	−	2.25861i	−0.139184	−	0.0803578i
$791$	62.4244	−	16.7266i	2.21955	−	0.594728i
$792$	10.2938	+	7.27879i	0.365773	+	0.258640i
$793$	0.535765	+	0.830916i	0.0190256	+	0.0295067i
$794$			12.6918i			0.450417i
$795$	26.4138	−	24.0919i	0.936802	−	0.854453i
$796$	2.25519	−	3.90611i	0.0799332	−	0.138448i
$797$	−12.0370	−	20.8487i	−0.426373	−	0.738501i	0.570174	−	0.821524i	$-0.306876\pi$
$797$	−12.0370	−	20.8487i	−0.426373	−	0.738501i	−0.996548	+	0.0830233i	$0.973542\pi$
$798$	4.22892	−	13.3053i	0.149702	−	0.471002i
$799$	−1.21041	+	4.51731i	−0.0428212	+	0.159811i
$800$	−0.820104	+	3.06067i	−0.0289951	+	0.108211i
$801$	−29.1090	+	4.99431i	−1.02852	+	0.176465i
$802$	8.20991	+	14.2200i	0.289902	+	0.502125i
$803$	−29.9598	+	51.8918i	−1.05726	+	1.83122i
$804$	−4.95582	−	5.43345i	−0.174778	−	0.191623i
$805$			31.1097i			1.09647i
$806$	−2.83824	+	5.52582i	−0.0999729	+	0.194639i
$807$	−6.86234	−	13.2570i	−0.241566	−	0.466669i
$808$	2.03506	−	0.545293i	0.0715932	−	0.0191833i
$809$	−22.2703	−	12.8578i	−0.782982	−	0.452055i	0.0545042	−	0.998514i	$-0.482642\pi$
$809$	−22.2703	−	12.8578i	−0.782982	−	0.452055i	−0.837486	+	0.546459i	$0.815975\pi$
$810$	−19.5513	−	16.7154i	−0.686964	−	0.587320i
$811$	5.99463	+	5.99463i	0.210500	+	0.210500i	0.804480	−	0.593980i	$-0.202444\pi$
$811$	5.99463	+	5.99463i	0.210500	+	0.210500i	−0.593980	+	0.804480i	$0.702444\pi$
$812$	−6.98357	−	1.87124i	−0.245075	−	0.0656677i
$813$	−33.5529	+	7.35732i	−1.17675	+	0.258032i
$814$	14.3900	−	14.3900i	0.504370	−	0.504370i
$815$	2.75821	−	1.59245i	0.0966157	−	0.0557811i
$816$	0.274749	−	5.97633i	0.00961813	−	0.209213i
$817$	1.13352	+	4.23037i	0.0396570	+	0.148002i
$818$	34.0781			1.19151
$819$	37.0398	+	11.6437i	1.29427	+	0.406865i
$820$	−22.6952			−0.792552
$821$	13.7528	+	51.3262i	0.479977	+	1.79130i	0.601687	+	0.798732i	$0.294496\pi$
$821$	13.7528	+	51.3262i	0.479977	+	1.79130i	−0.121710	+	0.992566i	$0.538838\pi$
$822$	−0.435896	+	9.48160i	−0.0152036	+	0.330709i
$823$	−9.92634	+	5.73097i	−0.346010	+	0.199769i	−0.662927	−	0.748684i	$-0.730686\pi$
$823$	−9.92634	+	5.73097i	−0.346010	+	0.199769i	0.316916	+	0.948454i	$0.397353\pi$
$824$	−10.0854	+	10.0854i	−0.351341	+	0.351341i
$825$	−22.5286	+	4.93997i	−0.784346	+	0.171988i
$826$	35.6723	+	9.55837i	1.24120	+	0.332578i
$827$	−4.57665	−	4.57665i	−0.159146	−	0.159146i	0.623042	−	0.782188i	$-0.285896\pi$
$827$	−4.57665	−	4.57665i	−0.159146	−	0.159146i	−0.782188	+	0.623042i	$0.785896\pi$
$828$	−0.834675	+	9.05873i	−0.0290069	+	0.314813i
$829$	43.2625	+	24.9776i	1.50257	+	0.867509i	0.999996	+	0.00297446i	$0.000946803\pi$
$829$	43.2625	+	24.9776i	1.50257	+	0.867509i	0.502574	+	0.864534i	$0.332387\pi$
$830$	10.1095	−	2.70883i	0.350905	−	0.0940248i
$831$	−12.3434	−	23.8457i	−0.428189	−	0.827198i
$832$	−0.176977	−	3.60121i	−0.00613556	−	0.124849i
$833$		−	20.3266i		−	0.704275i
$834$	−17.1500	−	18.8029i	−0.593858	−	0.651091i
$835$	7.98133	−	13.8241i	0.276205	−	0.478401i
$836$	−4.71836	−	8.17244i	−0.163188	−	0.282650i
$837$	7.14013	−	5.40071i	0.246799	−	0.186676i
$838$	8.51576	−	31.7812i	0.294172	−	1.09786i
$839$	−3.00183	+	11.2030i	−0.103635	+	0.386770i	−0.998187	−	0.0601939i	$-0.980828\pi$
$839$	−3.00183	+	11.2030i	−0.103635	+	0.386770i	0.894552	+	0.446964i	$0.147495\pi$
$840$	−5.38247	+	16.9347i	−0.185713	+	0.584302i
$841$	−12.4716	−	21.6014i	−0.430054	−	0.744876i
$842$	12.0877	−	20.9364i	0.416568	−	0.721517i
$843$	21.6180	−	19.7177i	0.744564	−	0.679114i
$844$			8.57683i			0.295227i
$845$	23.5700	−	28.7221i	0.810832	−	0.988069i
$846$	2.34512	−	3.31649i	0.0806267	−	0.114023i
$847$	23.0926	−	6.18765i	0.793472	−	0.212610i
$848$	−6.25431	−	3.61093i	−0.214774	−	0.124000i
$849$	1.47545	−	2.30425i	0.0506375	−	0.0790817i
$850$	7.73910	+	7.73910i	0.265449	+	0.265449i
$851$	14.1841	+	3.80063i	0.486226	+	0.130284i
$852$	−4.09333	−	18.6675i	−0.140235	−	0.639539i
$853$	−1.56247	+	1.56247i	−0.0534978	+	0.0534978i	−0.733350	−	0.679852i	$-0.762044\pi$
$853$	−1.56247	+	1.56247i	−0.0534978	+	0.0534978i	0.679852	+	0.733350i	$0.262044\pi$
$854$	−0.852410	+	0.492139i	−0.0291689	+	0.0168407i
$855$	8.05644	+	17.4873i	0.275525	+	0.598054i
$856$	−3.58348	−	13.3737i	−0.122481	−	0.457105i
$857$	−21.5804			−0.737174			−0.368587	−	0.929593i	$-0.620158\pi$
$857$	−21.5804			−0.737174			−0.368587	+	0.929593i	$0.620158\pi$
$858$	22.6864	−	13.1939i	0.774500	−	0.450431i
$859$	10.5544			0.360110			0.180055	−	0.983657i	$-0.442372\pi$
$859$	10.5544			0.360110			0.180055	+	0.983657i	$0.442372\pi$
$860$	−1.44272	−	5.38431i	−0.0491964	−	0.183604i
$861$	−49.3175	−	2.26726i	−1.68074	−	0.0772681i
$862$	−1.52054	+	0.877885i	−0.0517899	+	0.0299009i
$863$	−21.4177	+	21.4177i	−0.729066	+	0.729066i	−0.970434	−	0.241368i	$-0.922404\pi$
$863$	−21.4177	+	21.4177i	−0.729066	+	0.729066i	0.241368	+	0.970434i	$0.422404\pi$
$864$	−2.02166	+	4.78674i	−0.0687783	+	0.162848i
$865$	48.2992	+	12.9417i	1.64222	+	0.440032i
$866$	7.24346	+	7.24346i	0.246143	+	0.246143i
$867$	7.39436	+	4.73475i	0.251126	+	0.160800i
$868$	−5.35596	−	3.09226i	−0.181793	−	0.104958i
$869$	−6.41562	+	1.71906i	−0.217635	+	0.0583152i
$870$	8.85481	−	4.58359i	0.300206	−	0.155398i
$871$	−14.5748	+	4.68323i	−0.493848	+	0.158685i
$872$			8.26212i			0.279791i
$873$	8.33585	−	22.5779i	0.282126	−	0.764144i
$874$	3.40467	−	5.89705i	0.115165	−	0.199471i
$875$	9.39415	+	16.2711i	0.317580	+	0.550065i
$876$	−23.5360	−	7.48062i	−0.795208	−	0.252747i
$877$	10.1109	−	37.7342i	0.341420	−	1.27419i	−0.555320	−	0.831637i	$-0.687404\pi$
$877$	10.1109	−	37.7342i	0.341420	−	1.27419i	0.896740	−	0.442558i	$-0.145929\pi$
$878$	−1.39820	+	5.21816i	−0.0471871	+	0.176105i
$879$	−6.44617	−	2.04883i	−0.217424	−	0.0691054i
$880$	6.00542	+	10.4017i	0.202443	+	0.350641i
$881$	−3.39708	+	5.88391i	−0.114450	+	0.198234i	−0.917560	−	0.397598i	$-0.869844\pi$
$881$	−3.39708	+	5.88391i	−0.114450	+	0.198234i	0.803110	+	0.595831i	$0.203177\pi$
$882$	−6.11466	+	16.5617i	−0.205891	+	0.557661i
$883$			40.6560i			1.36818i	0.729397	+	0.684091i	$0.239801\pi$
$883$			40.6560i			1.36818i	−0.729397	+	0.684091i	$0.760199\pi$
$884$	−11.0780	−	5.69003i	−0.372594	−	0.191376i
$885$	−45.2307	+	23.4131i	−1.52041	+	0.787023i
$886$	−13.1106	+	3.51297i	−0.440458	+	0.118020i
$887$	−9.04299	−	5.22097i	−0.303634	−	0.175303i	0.340440	−	0.940266i	$-0.389424\pi$
$887$	−9.04299	−	5.22097i	−0.303634	−	0.175303i	−0.644074	+	0.764963i	$0.722757\pi$
$888$	7.06362	+	4.52297i	0.237040	+	0.151781i
$889$	−52.5233	−	52.5233i	−1.76158	−	1.76158i
$890$	−27.1784	−	7.28244i	−0.911024	−	0.244108i
$891$	−37.7066	+	2.94852i	−1.26322	+	0.0987790i
$892$	−14.9027	+	14.9027i	−0.498979	+	0.498979i
$893$	−2.63304	+	1.52018i	−0.0881112	+	0.0508710i
$894$	−17.8813	−	0.822056i	−0.598042	−	0.0274937i
$895$	6.81664	+	25.4400i	0.227855	+	0.850367i
$896$	3.58954			0.119918
$897$	16.4299	+	9.41663i	0.548579	+	0.314412i
$898$	2.02930			0.0677187
$899$	0.898169	+	3.35201i	0.0299556	+	0.111796i
$900$	−3.97758	−	8.63374i	−0.132586	−	0.287791i
$901$	−21.6029	+	12.4724i	−0.719697	+	0.415517i
$902$	−23.5963	+	23.5963i	−0.785670	+	0.785670i
$903$	−2.59719	−	11.8444i	−0.0864290	−	0.394157i
$904$	17.3906	+	4.65980i	0.578403	+	0.154983i
$905$	27.9116	+	27.9116i	0.927814	+	0.927814i
$906$	−8.57157	+	13.3864i	−0.284771	+	0.444734i
$907$	−33.9759	−	19.6160i	−1.12815	−	0.651338i	−0.184681	−	0.982799i	$-0.559125\pi$
$907$	−33.9759	−	19.6160i	−1.12815	−	0.651338i	−0.943469	+	0.331461i	$0.892458\pi$
$908$	−4.85544	+	1.30101i	−0.161134	+	0.0431756i
$909$	−3.64917	+	5.16071i	−0.121035	+	0.171170i
$910$	27.4083	+	24.8406i	0.908575	+	0.823457i
$911$			32.0923i			1.06326i	0.846975	+	0.531632i	$0.178421\pi$
$911$			32.0923i			1.06326i	−0.846975	+	0.531632i	$0.821579\pi$
$912$	2.87363	−	2.62102i	0.0951553	−	0.0867907i
$913$	7.69447	−	13.3272i	0.254650	−	0.441066i
$914$	14.9767	+	25.9404i	0.495385	+	0.858032i
$915$	0.411170	−	1.29365i	0.0135929	−	0.0427667i
$916$	3.63274	−	13.5576i	0.120029	−	0.447955i
$917$	4.35066	−	16.2369i	0.143671	−	0.536189i
$918$	10.8272	+	14.3143i	0.357350	+	0.472443i
$919$	−16.6421	−	28.8249i	−0.548972	−	0.950847i	−0.998345	−	0.0575028i	$-0.981686\pi$
$919$	−16.6421	−	28.8249i	−0.548972	−	0.950847i	0.449374	−	0.893344i	$-0.351647\pi$
$920$	−4.33338	+	7.50563i	−0.142867	+	0.247453i
$921$	35.9839	+	39.4519i	1.18571	+	1.29998i
$922$			16.1111i			0.530589i
$923$	−38.8863	−	8.39796i	−1.27996	−	0.276422i
$924$	12.0108	+	23.2032i	0.395128	+	0.763328i
$925$	−14.8216	+	3.97143i	−0.487330	+	0.130580i
$926$	4.98521	+	2.87821i	0.163824	+	0.0945840i
$927$	3.92594	−	42.6082i	0.128945	−	1.39944i
$928$	−1.42423	−	1.42423i	−0.0467526	−	0.0467526i
$929$	−21.2156	−	5.68470i	−0.696060	−	0.186509i	−0.106595	−	0.994303i	$-0.533995\pi$
$929$	−21.2156	−	5.68470i	−0.696060	−	0.186509i	−0.589465	+	0.807794i	$0.700662\pi$
$930$	8.33116	−	1.82682i	0.273189	−	0.0599037i
$931$	9.34415	−	9.34415i	0.306242	−	0.306242i
$932$	−16.2764	+	9.39719i	−0.533151	+	0.307815i
$933$	1.66480	−	36.2128i	0.0545032	−	1.18555i
$934$	9.53841	+	35.5978i	0.312106	+	1.16480i
$935$	41.4864			1.35675
$936$	7.31445	+	7.96861i	0.239080	+	0.260462i
$937$	55.9423			1.82755			0.913777	−	0.406216i	$-0.133152\pi$
$937$	55.9423			1.82755			0.913777	+	0.406216i	$0.133152\pi$
$938$	−3.94460	−	14.7214i	−0.128796	−	0.480672i
$939$	2.59856	−	56.5238i	0.0848008	−	1.84459i
$940$	3.35127	−	1.93486i	0.109306	−	0.0631080i
$941$	17.1600	−	17.1600i	0.559401	−	0.559401i	−0.369736	−	0.929137i	$-0.620552\pi$
$941$	17.1600	−	17.1600i	0.559401	−	0.559401i	0.929137	+	0.369736i	$0.120552\pi$
$942$	−23.9281	+	5.24685i	−0.779620	+	0.170951i
$943$	−23.2587	−	6.23215i	−0.757407	−	0.202947i
$944$	7.27501	+	7.27501i	0.236781	+	0.236781i
$945$	−20.0589	−	49.3906i	−0.652515	−	1.60668i
$946$	−7.09808	−	4.09808i	−0.230778	−	0.133240i
$947$	46.0604	−	12.3419i	1.49676	−	0.401056i	0.584748	−	0.811215i	$-0.301193\pi$
$947$	46.0604	−	12.3419i	1.49676	−	0.401056i	0.912014	+	0.410159i	$0.134527\pi$
$948$	−1.25844	−	2.43112i	−0.0408722	−	0.0789591i
$949$	−34.5237	+	38.0924i	−1.12069	+	1.23653i
$950$			7.11534i			0.230852i
$951$	8.60145	+	9.43043i	0.278921	+	0.305803i
$952$	6.19928	−	10.7375i	0.200920	−	0.348003i
$953$	21.5278	+	37.2872i	0.697353	+	1.20785i	0.969381	+	0.245561i	$0.0789721\pi$
$953$	21.5278	+	37.2872i	0.697353	+	1.20785i	−0.272029	+	0.962289i	$0.587695\pi$
$954$	21.3536	−	3.66369i	0.691347	−	0.118616i
$955$	−16.7940	+	62.6761i	−0.543441	+	2.02815i
$956$	−2.49681	+	9.31824i	−0.0807527	+	0.301373i
$957$	4.44080	−	13.9719i	0.143551	−	0.451648i
$958$	7.52152	+	13.0276i	0.243009	+	0.420904i
$959$	−9.83532	+	17.0353i	−0.317599	+	0.550098i
$960$	−3.65748	+	3.33598i	−0.118045	+	0.107668i
$961$		−	28.0315i		−	0.904242i
$962$	14.6742	−	9.46179i	0.473117	−	0.305060i
$963$	33.9144	+	23.9811i	1.09288	+	0.772781i
$964$	−8.18821	+	2.19402i	−0.263724	+	0.0706648i
$965$	−49.6166	−	28.6461i	−1.59721	−	0.922152i
$966$	−10.1664	+	15.8771i	−0.327098	+	0.510837i
$967$	−4.96226	−	4.96226i	−0.159576	−	0.159576i	0.622803	−	0.782379i	$-0.285994\pi$
$967$	−4.96226	−	4.96226i	−0.159576	−	0.159576i	−0.782379	+	0.622803i	$0.785994\pi$
$968$	6.43331	+	1.72380i	0.206774	+	0.0554050i
$969$	−2.87745	−	13.1225i	−0.0924370	−	0.421557i
$970$	16.2132	−	16.2132i	0.520576	−	0.520576i
$971$	−27.5285	+	15.8936i	−0.883432	+	0.510050i	−0.871789	−	0.489882i	$-0.837040\pi$
$971$	−27.5285	+	15.8936i	−0.883432	+	0.510050i	−0.0116437	+	0.999932i	$0.503706\pi$
$972$	−4.51572	−	14.9201i	−0.144842	−	0.478561i
$973$	−13.6506	−	50.9448i	−0.437619	−	1.63322i
$974$	−16.7305			−0.536081
$975$	−19.7881	+	0.0626048i	−0.633725	+	0.00200496i
$976$	−0.274207			−0.00877716
$977$	1.80392	+	6.73232i	0.0577125	+	0.215386i	0.988760	−	0.149512i	$-0.0477704\pi$
$977$	1.80392	+	6.73232i	0.0577125	+	0.215386i	−0.931047	+	0.364898i	$0.881104\pi$
$978$	1.92807	+	0.0886389i	0.0616529	+	0.00283436i
$979$	−35.8290	+	20.6859i	−1.14510	+	0.661124i
$980$	−11.8930	+	11.8930i	−0.379909	+	0.379909i
$981$	−15.8446	−	19.0608i	−0.505878	−	0.608563i
$982$	−24.4056	−	6.53947i	−0.778815	−	0.208683i
$983$	10.5636	+	10.5636i	0.336926	+	0.336926i	0.855209	−	0.518283i	$-0.173429\pi$
$983$	10.5636	+	10.5636i	0.336926	+	0.336926i	−0.518283	+	0.855209i	$0.673429\pi$
$984$	−11.5827	−	7.41662i	−0.369243	−	0.236433i
$985$	−46.1306	−	26.6335i	−1.46984	−	0.848614i
$986$	−6.72002	+	1.80063i	−0.214009	+	0.0573436i
$987$	7.47571	−	3.86971i	0.237954	−	0.123174i
$988$	−2.47686	−	7.70828i	−0.0787993	−	0.245233i
$989$		−	5.91416i		−	0.188059i
$990$	−33.8023	−	12.4800i	−1.07431	−	0.396639i
$991$	−13.1927	+	22.8505i	−0.419081	+	0.725870i	−0.995847	−	0.0910396i	$-0.970981\pi$
$991$	−13.1927	+	22.8505i	−0.419081	+	0.725870i	0.576766	+	0.816909i	$0.304314\pi$
$992$	−0.861464	−	1.49210i	−0.0273515	−	0.0473742i
$993$	30.1038	+	9.56810i	0.955315	+	0.303635i
$994$	10.2508	−	38.2566i	0.325137	−	1.21343i
$995$	−3.33645	+	12.4518i	−0.105773	+	0.394749i
$996$	6.04468	+	1.92122i	0.191533	+	0.0608763i
$997$	−14.6325	−	25.3443i	−0.463416	−	0.802660i	0.535712	−	0.844401i	$-0.320043\pi$
$997$	−14.6325	−	25.3443i	−0.463416	−	0.802660i	−0.999129	+	0.0417401i	$0.986710\pi$
$998$	0.975428	−	1.68949i	0.0308766	−	0.0534799i
$999$	−24.9697	+	3.11165i	−0.790006	+	0.0984483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.2.k.a.59.1	yes	16
3.2	odd	2	inner	78.2.k.a.59.3	yes	16
4.3	odd	2		624.2.cn.d.449.3		16
12.11	even	2		624.2.cn.d.449.4		16
13.2	odd	12	inner	78.2.k.a.41.3	yes	16
13.4	even	6		1014.2.g.d.437.8		16
13.6	odd	12		1014.2.g.c.239.8		16
13.7	odd	12		1014.2.g.d.239.4		16
13.9	even	3		1014.2.g.c.437.4		16
39.2	even	12	inner	78.2.k.a.41.1	✓	16
39.17	odd	6		1014.2.g.d.437.4		16
39.20	even	12		1014.2.g.d.239.8		16
39.32	even	12		1014.2.g.c.239.4		16
39.35	odd	6		1014.2.g.c.437.8		16
52.15	even	12		624.2.cn.d.353.4		16
156.119	odd	12		624.2.cn.d.353.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.k.a.41.1	✓	16	39.2	even	12	inner
78.2.k.a.41.3	yes	16	13.2	odd	12	inner
78.2.k.a.59.1	yes	16	1.1	even	1	trivial
78.2.k.a.59.3	yes	16	3.2	odd	2	inner
624.2.cn.d.353.3		16	156.119	odd	12
624.2.cn.d.353.4		16	52.15	even	12
624.2.cn.d.449.3		16	4.3	odd	2
624.2.cn.d.449.4		16	12.11	even	2
1014.2.g.c.239.4		16	39.32	even	12
1014.2.g.c.239.8		16	13.6	odd	12
1014.2.g.c.437.4		16	13.9	even	3
1014.2.g.c.437.8		16	39.35	odd	6
1014.2.g.d.239.4		16	13.7	odd	12
1014.2.g.d.239.8		16	39.20	even	12
1014.2.g.d.437.4		16	39.17	odd	6
1014.2.g.d.437.8		16	13.4	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 $\F_{q}$

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

L-functions

Modular forms

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Database

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