LMFDB - Embedded newform 238.2.p.b.97.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [238,2,Mod(27,238)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(238, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 3]))

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

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

chi := DirichletCharacter("238.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 238 = 2 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	238.p (of order $16$, degree $8$, 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:	$1.90043956811$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			97.5
Character	$\chi$	$=$	238.97
Dual form			238.2.p.b.27.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.382683 + 0.923880i) q^{2} +(0.750734 + 1.12355i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(-0.521884 + 2.62369i) q^{5} +(-0.750734 + 1.12355i) q^{6} +(-2.49686 + 0.875034i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(0.449281 - 1.08466i) q^{9} +O(q^{10})$	\(q+(0.382683 + 0.923880i) q^{2} +(0.750734 + 1.12355i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(-0.521884 + 2.62369i) q^{5} +(-0.750734 + 1.12355i) q^{6} +(-2.49686 + 0.875034i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(0.449281 - 1.08466i) q^{9} +(-2.62369 + 0.521884i) q^{10} +(1.84587 - 2.76253i) q^{11} +(-1.32532 - 0.263623i) q^{12} +(-0.942965 + 0.942965i) q^{13} +(-1.76393 - 1.97194i) q^{14} +(-3.33965 + 1.38333i) q^{15} -1.00000i q^{16} +(-0.895150 + 4.02476i) q^{17} +1.17403 q^{18} +(5.89694 - 2.44259i) q^{19} +(-1.48620 - 2.22426i) q^{20} +(-2.85763 - 2.14844i) q^{21} +(3.25863 + 0.648182i) q^{22} +(6.35280 + 4.24480i) q^{23} +(-0.263623 - 1.32532i) q^{24} +(-1.99199 - 0.825109i) q^{25} +(-1.23204 - 0.510329i) q^{26} +(5.53193 - 1.10037i) q^{27} +(1.14680 - 2.38429i) q^{28} +(-0.344698 + 1.73291i) q^{29} +(-2.55606 - 2.55606i) q^{30} +(-8.12346 + 5.42792i) q^{31} +(0.923880 - 0.382683i) q^{32} +4.48961 q^{33} +(-4.06095 + 0.713199i) q^{34} +(-0.992746 - 7.00766i) q^{35} +(0.449281 + 1.08466i) q^{36} +(-0.850529 + 0.568305i) q^{37} +(4.51332 + 4.51332i) q^{38} +(-1.76739 - 0.351555i) q^{39} +(1.48620 - 2.22426i) q^{40} +(-1.48074 - 7.44419i) q^{41} +(0.891331 - 3.46227i) q^{42} +(-1.19420 + 2.88305i) q^{43} +(0.648182 + 3.25863i) q^{44} +(2.61134 + 1.74484i) q^{45} +(-1.49058 + 7.49364i) q^{46} +(7.44818 - 7.44818i) q^{47} +(1.12355 - 0.750734i) q^{48} +(5.46863 - 4.36968i) q^{49} -2.15611i q^{50} +(-5.19405 + 2.01578i) q^{51} -1.33355i q^{52} +(-4.22081 - 10.1899i) q^{53} +(3.13358 + 4.68974i) q^{54} +(6.28470 + 6.28470i) q^{55} +(2.64166 + 0.147081i) q^{56} +(7.17141 + 4.79179i) q^{57} +(-1.73291 + 0.344698i) q^{58} +(1.22220 - 2.95065i) q^{59} +(1.38333 - 3.33965i) q^{60} +(-3.79206 + 0.754288i) q^{61} +(-8.12346 - 5.42792i) q^{62} +(-0.172677 + 3.10138i) q^{63} +(0.707107 + 0.707107i) q^{64} +(-1.98193 - 2.96617i) q^{65} +(1.71810 + 4.14785i) q^{66} +4.08800i q^{67} +(-2.21297 - 3.47890i) q^{68} +10.3244i q^{69} +(6.09432 - 3.59889i) q^{70} +(9.18916 - 6.14000i) q^{71} +(-0.830163 + 0.830163i) q^{72} +(-1.09021 + 5.48087i) q^{73} +(-0.850529 - 0.568305i) q^{74} +(-0.568400 - 2.85754i) q^{75} +(-2.44259 + 5.89694i) q^{76} +(-2.19156 + 8.51286i) q^{77} +(-0.351555 - 1.76739i) q^{78} +(8.71748 - 13.0466i) q^{79} +(2.62369 + 0.521884i) q^{80} +(2.89884 + 2.89884i) q^{81} +(6.31088 - 4.21679i) q^{82} +(-3.20528 - 7.73824i) q^{83} +(3.53982 - 0.501472i) q^{84} +(-10.0926 - 4.44906i) q^{85} -3.12059 q^{86} +(-2.20580 + 0.913671i) q^{87} +(-2.76253 + 1.84587i) q^{88} +(-5.83406 - 5.83406i) q^{89} +(-0.612707 + 3.08029i) q^{90} +(1.52933 - 3.17958i) q^{91} +(-7.49364 + 1.49058i) q^{92} +(-12.1971 - 5.05221i) q^{93} +(9.73152 + 4.03093i) q^{94} +(3.33108 + 16.7465i) q^{95} +(1.12355 + 0.750734i) q^{96} +(-6.22576 - 1.23838i) q^{97} +(6.12981 + 3.38015i) q^{98} +(-2.16710 - 3.24329i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 16 q^{11} - 8 q^{14} + 64 q^{15} - 80 q^{18} - 48 q^{21} + 16 q^{22} - 16 q^{25} + 8 q^{28} + 32 q^{29} + 16 q^{39} - 24 q^{42} - 16 q^{43} + 16 q^{44} - 16 q^{46} + 16 q^{49} + 32 q^{51} - 48 q^{53} + 64 q^{57} + 16 q^{58} + 32 q^{60} - 104 q^{63} - 48 q^{65} + 16 q^{70} - 112 q^{71} - 16 q^{72} - 40 q^{77} - 64 q^{78} + 32 q^{79} + 112 q^{81} - 176 q^{85} + 32 q^{86} + 16 q^{88} + 80 q^{91} - 32 q^{93} - 32 q^{95} - 96 q^{99}+O(q^{100}) $ 48 * q - 16 * q^11 - 8 * q^14 + 64 * q^15 - 80 * q^18 - 48 * q^21 + 16 * q^22 - 16 * q^25 + 8 * q^28 + 32 * q^29 + 16 * q^39 - 24 * q^42 - 16 * q^43 + 16 * q^44 - 16 * q^46 + 16 * q^49 + 32 * q^51 - 48 * q^53 + 64 * q^57 + 16 * q^58 + 32 * q^60 - 104 * q^63 - 48 * q^65 + 16 * q^70 - 112 * q^71 - 16 * q^72 - 40 * q^77 - 64 * q^78 + 32 * q^79 + 112 * q^81 - 176 * q^85 + 32 * q^86 + 16 * q^88 + 80 * q^91 - 32 * q^93 - 32 * q^95 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/238\mathbb{Z}\right)^\times$.

$n$	$71$	$171$
$\chi(n)$	$e\left(\frac{13}{16}\right)$	$-1$

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 $

$2$	0.382683	+	0.923880i	0.270598	+	0.653281i
$2$	0.382683	+	0.923880i	0.270598	+	0.653281i
$3$	0.750734	+	1.12355i	0.433436	+	0.648683i	0.982319	−	0.187216i	$-0.0599465\pi$
$3$	0.750734	+	1.12355i	0.433436	+	0.648683i	−0.548882	+	0.835900i	$0.684947\pi$
$4$	−0.707107	+	0.707107i	−0.353553	+	0.353553i
$5$	−0.521884	+	2.62369i	−0.233394	+	1.17335i	0.669275	+	0.743015i	$0.266605\pi$
$5$	−0.521884	+	2.62369i	−0.233394	+	1.17335i	−0.902669	+	0.430335i	$0.858395\pi$
$6$	−0.750734	+	1.12355i	−0.306486	+	0.458688i
$7$	−2.49686	+	0.875034i	−0.943725	+	0.330732i
$7$	−2.49686	+	0.875034i	−0.943725	+	0.330732i
$8$	−0.923880	−	0.382683i	−0.326641	−	0.135299i
$9$	0.449281	−	1.08466i	0.149760	−	0.361554i
$10$	−2.62369	+	0.521884i	−0.829684	+	0.165034i
$11$	1.84587	−	2.76253i	0.556550	−	0.832935i	−0.441375	−	0.897323i	$-0.645509\pi$
$11$	1.84587	−	2.76253i	0.556550	−	0.832935i	0.997925	+	0.0643873i	$0.0205093\pi$
$12$	−1.32532	−	0.263623i	−0.382587	−	0.0761013i
$13$	−0.942965	+	0.942965i	−0.261531	+	0.261531i	−0.825676	−	0.564145i	$-0.809206\pi$
$13$	−0.942965	+	0.942965i	−0.261531	+	0.261531i	0.564145	+	0.825676i	$0.309206\pi$
$14$	−1.76393	−	1.97194i	−0.471431	−	0.527023i
$15$	−3.33965	+	1.38333i	−0.862294	+	0.357174i
$16$		−	1.00000i		−	0.250000i
$17$	−0.895150	+	4.02476i	−0.217106	+	0.976148i
$17$	−0.895150	+	4.02476i	−0.217106	+	0.976148i
$18$	1.17403			0.276721
$19$	5.89694	−	2.44259i	1.35285	−	0.560369i	0.415766	−	0.909472i	$-0.363513\pi$
$19$	5.89694	−	2.44259i	1.35285	−	0.560369i	0.937085	+	0.349102i	$0.113513\pi$
$20$	−1.48620	−	2.22426i	−0.332325	−	0.497359i
$21$	−2.85763	−	2.14844i	−0.623585	−	0.468827i
$22$	3.25863	+	0.648182i	0.694742	+	0.138193i
$23$	6.35280	+	4.24480i	1.32465	+	0.885103i	0.998192	−	0.0601086i	$-0.0191447\pi$
$23$	6.35280	+	4.24480i	1.32465	+	0.885103i	0.326458	+	0.945212i	$0.394145\pi$
$24$	−0.263623	−	1.32532i	−0.0538118	−	0.270530i
$25$	−1.99199	−	0.825109i	−0.398398	−	0.165022i
$26$	−1.23204	−	0.510329i	−0.241623	−	0.100084i
$27$	5.53193	−	1.10037i	1.06462	−	0.211766i
$28$	1.14680	−	2.38429i	0.216726	−	0.450588i
$29$	−0.344698	+	1.73291i	−0.0640088	+	0.321794i	−0.999502	−	0.0315502i	$-0.989956\pi$
$29$	−0.344698	+	1.73291i	−0.0640088	+	0.321794i	0.935493	+	0.353344i	$0.114956\pi$
$30$	−2.55606	−	2.55606i	−0.466670	−	0.466670i
$31$	−8.12346	+	5.42792i	−1.45902	+	0.974884i	−0.462940	+	0.886389i	$0.653206\pi$
$31$	−8.12346	+	5.42792i	−1.45902	+	0.974884i	−0.996077	+	0.0884947i	$0.971794\pi$
$32$	0.923880	−	0.382683i	0.163320	−	0.0676495i
$33$	4.48961			0.781540
$34$	−4.06095	+	0.713199i	−0.696448	+	0.122313i
$35$	−0.992746	−	7.00766i	−0.167805	−	1.18451i
$36$	0.449281	+	1.08466i	0.0748802	+	0.180777i
$37$	−0.850529	+	0.568305i	−0.139826	+	0.0934288i	−0.623516	−	0.781811i	$-0.714296\pi$
$37$	−0.850529	+	0.568305i	−0.139826	+	0.0934288i	0.483690	+	0.875240i	$0.339296\pi$
$38$	4.51332	+	4.51332i	0.732158	+	0.732158i
$39$	−1.76739	−	0.351555i	−0.283008	−	0.0562938i
$40$	1.48620	−	2.22426i	0.234989	−	0.351686i
$41$	−1.48074	−	7.44419i	−0.231253	−	1.16259i	−0.905587	−	0.424160i	$-0.860569\pi$
$41$	−1.48074	−	7.44419i	−0.231253	−	1.16259i	0.674334	−	0.738426i	$-0.264431\pi$
$42$	0.891331	−	3.46227i	0.137535	−	0.534240i
$43$	−1.19420	+	2.88305i	−0.182113	+	0.439661i	−0.988402	−	0.151862i	$-0.951473\pi$
$43$	−1.19420	+	2.88305i	−0.182113	+	0.439661i	0.806288	+	0.591523i	$0.201473\pi$
$44$	0.648182	+	3.25863i	0.0977171	+	0.491257i
$45$	2.61134	+	1.74484i	0.389276	+	0.260106i
$46$	−1.49058	+	7.49364i	−0.219774	+	1.10488i
$47$	7.44818	−	7.44818i	1.08643	−	1.08643i	0.0905359	−	0.995893i	$-0.471142\pi$
$47$	7.44818	−	7.44818i	1.08643	−	1.08643i	0.995893	−	0.0905359i	$-0.0288580\pi$
$48$	1.12355	−	0.750734i	0.162171	−	0.108359i
$49$	5.46863	−	4.36968i	0.781233	−	0.624240i
$50$		−	2.15611i		−	0.304920i
$51$	−5.19405	+	2.01578i	−0.727313	+	0.282265i
$52$		−	1.33355i		−	0.184931i
$53$	−4.22081	−	10.1899i	−0.579773	−	1.39970i	−0.893017	−	0.450024i	$-0.851415\pi$
$53$	−4.22081	−	10.1899i	−0.579773	−	1.39970i	0.313243	−	0.949673i	$-0.398585\pi$
$54$	3.13358	+	4.68974i	0.426427	+	0.638193i
$55$	6.28470	+	6.28470i	0.847429	+	0.847429i
$56$	2.64166	+	0.147081i	0.353007	+	0.0196545i
$57$	7.17141	+	4.79179i	0.949877	+	0.634687i
$58$	−1.73291	+	0.344698i	−0.227543	+	0.0452611i
$59$	1.22220	−	2.95065i	0.159117	−	0.384141i	−0.824135	−	0.566393i	$-0.808338\pi$
$59$	1.22220	−	2.95065i	0.159117	−	0.384141i	0.983252	+	0.182251i	$0.0583385\pi$
$60$	1.38333	−	3.33965i	0.178587	−	0.431147i
$61$	−3.79206	+	0.754288i	−0.485524	+	0.0965767i	−0.431782	−	0.901978i	$-0.642115\pi$
$61$	−3.79206	+	0.754288i	−0.485524	+	0.0965767i	−0.0537421	+	0.998555i	$0.517115\pi$
$62$	−8.12346	−	5.42792i	−1.03168	−	0.689347i
$63$	−0.172677	+	3.10138i	−0.0217553	+	0.390738i
$64$	0.707107	+	0.707107i	0.0883883	+	0.0883883i
$65$	−1.98193	−	2.96617i	−0.245828	−	0.367908i
$66$	1.71810	+	4.14785i	0.211483	+	0.510566i
$67$			4.08800i			0.499429i	0.968320	+	0.249714i	$0.0803367\pi$
$67$			4.08800i			0.499429i	−0.968320	+	0.249714i	$0.919663\pi$
$68$	−2.21297	−	3.47890i	−0.268362	−	0.421879i
$69$			10.3244i			1.24291i
$70$	6.09432	−	3.59889i	0.728411	−	0.430150i
$71$	9.18916	−	6.14000i	1.09055	−	0.728684i	0.125856	−	0.992049i	$-0.459832\pi$
$71$	9.18916	−	6.14000i	1.09055	−	0.728684i	0.964696	+	0.263365i	$0.0848323\pi$
$72$	−0.830163	+	0.830163i	−0.0978357	+	0.0978357i
$73$	−1.09021	+	5.48087i	−0.127600	+	0.641487i	0.863057	+	0.505107i	$0.168547\pi$
$73$	−1.09021	+	5.48087i	−0.127600	+	0.641487i	−0.990657	+	0.136380i	$0.956453\pi$
$74$	−0.850529	−	0.568305i	−0.0988720	−	0.0660642i
$75$	−0.568400	−	2.85754i	−0.0656332	−	0.329960i
$76$	−2.44259	+	5.89694i	−0.280185	+	0.676425i
$77$	−2.19156	+	8.51286i	−0.249751	+	0.970130i
$78$	−0.351555	−	1.76739i	−0.0398058	−	0.200117i
$79$	8.71748	−	13.0466i	0.980793	−	1.46786i	0.0996427	−	0.995023i	$-0.468230\pi$
$79$	8.71748	−	13.0466i	0.980793	−	1.46786i	0.881150	−	0.472837i	$-0.156770\pi$
$80$	2.62369	+	0.521884i	0.293337	+	0.0583484i
$81$	2.89884	+	2.89884i	0.322093	+	0.322093i
$82$	6.31088	−	4.21679i	0.696920	−	0.465667i
$83$	−3.20528	−	7.73824i	−0.351826	−	0.849382i	−0.996395	−	0.0848362i	$-0.972963\pi$
$83$	−3.20528	−	7.73824i	−0.351826	−	0.849382i	0.644569	−	0.764546i	$-0.277037\pi$
$84$	3.53982	−	0.501472i	0.386226	−	0.0547151i
$85$	−10.0926	−	4.44906i	−1.09469	−	0.482568i
$86$	−3.12059			−0.336502
$87$	−2.20580	+	0.913671i	−0.236486	+	0.0979558i
$88$	−2.76253	+	1.84587i	−0.294487	+	0.196770i
$89$	−5.83406	−	5.83406i	−0.618409	−	0.618409i	0.326714	−	0.945123i	$-0.394059\pi$
$89$	−5.83406	−	5.83406i	−0.618409	−	0.618409i	−0.945123	+	0.326714i	$0.894059\pi$
$90$	−0.612707	+	3.08029i	−0.0645850	+	0.324691i
$91$	1.52933	−	3.17958i	0.160317	−	0.333310i
$92$	−7.49364	+	1.49058i	−0.781266	+	0.155403i
$93$	−12.1971	−	5.05221i	−1.26478	−	0.523890i
$94$	9.73152	+	4.03093i	1.00373	+	0.415758i
$95$	3.33108	+	16.7465i	0.341762	+	1.71815i
$96$	1.12355	+	0.750734i	0.114672	+	0.0766214i
$97$	−6.22576	−	1.23838i	−0.632131	−	0.125739i	−0.131383	−	0.991332i	$-0.541942\pi$
$97$	−6.22576	−	1.23838i	−0.632131	−	0.125739i	−0.500748	+	0.865593i	$0.666942\pi$
$98$	6.12981	+	3.38015i	0.619204	+	0.341447i
$99$	−2.16710	−	3.24329i	−0.217802	−	0.325963i
$100$	1.99199	−	0.825109i	0.199199	−	0.0825109i
$101$	−13.0143			−1.29498			−0.647488	−	0.762076i	$-0.724180\pi$
$101$	−13.0143			−1.29498			−0.647488	+	0.762076i	$0.724180\pi$
$102$	−3.85001	−	4.02727i	−0.381208	−	0.398759i
$103$			1.91103i			0.188300i	0.995558	+	0.0941498i	$0.0300133\pi$
$103$			1.91103i			0.188300i	−0.995558	+	0.0941498i	$0.969987\pi$
$104$	1.23204	−	0.510329i	0.120812	−	0.0500419i
$105$	7.12818	−	6.37629i	0.695639	−	0.622262i
$106$	7.79905	−	7.79905i	0.757510	−	0.757510i
$107$	1.72938	+	0.343996i	0.167186	+	0.0332553i	0.277973	−	0.960589i	$-0.410337\pi$
$107$	1.72938	+	0.343996i	0.167186	+	0.0332553i	−0.110788	+	0.993844i	$0.535337\pi$
$108$	−3.13358	+	4.68974i	−0.301529	+	0.451270i
$109$	1.07244	−	0.213321i	0.102721	−	0.0204324i	−0.143462	−	0.989656i	$-0.545824\pi$
$109$	1.07244	−	0.213321i	0.102721	−	0.0204324i	0.246183	+	0.969223i	$0.420824\pi$
$110$	−3.40126	+	8.21136i	−0.324297	+	0.782922i
$111$	−1.27704	−	0.528968i	−0.121211	−	0.0502074i
$112$	0.875034	+	2.49686i	0.0826830	+	0.235931i
$113$	−3.93706	+	5.89223i	−0.370367	+	0.554294i	−0.969104	−	0.246652i	$-0.920670\pi$
$113$	−3.93706	+	5.89223i	−0.370367	+	0.554294i	0.598737	+	0.800946i	$0.295670\pi$
$114$	−1.68265	+	8.45926i	−0.157595	+	0.792282i
$115$	−14.4525	+	14.4525i	−1.34770	+	1.34770i
$116$	−0.981617	−	1.46909i	−0.0911409	−	0.136402i
$117$	0.599141	+	1.44645i	0.0553906	+	0.133725i
$118$	3.19376			0.294009
$119$	−1.28674	−	10.8326i	−0.117955	−	0.993019i
$120$	3.61481			0.329986
$121$	−0.0148529	−	0.0358581i	−0.00135026	−	0.00325983i
$122$	−2.14803	−	3.21475i	−0.194474	−	0.291050i
$123$	7.25229	−	7.25229i	0.653917	−	0.653917i
$124$	1.90603	−	9.58228i	0.171167	−	0.860514i
$125$	−4.22659	+	6.32554i	−0.378038	+	0.565773i
$126$	−2.93139	+	1.02732i	−0.261149	+	0.0915205i
$127$	−8.66090	−	3.58746i	−0.768530	−	0.318336i	−0.0362534	−	0.999343i	$-0.511542\pi$
$127$	−8.66090	−	3.58746i	−0.768530	−	0.318336i	−0.732277	+	0.681007i	$0.761542\pi$
$128$	−0.382683	+	0.923880i	−0.0338248	+	0.0816602i
$129$	−4.13578	+	0.822658i	−0.364135	+	0.0724310i
$130$	1.98193	−	2.96617i	0.173827	−	0.260150i
$131$	−5.28641	−	1.05153i	−0.461876	−	0.0918729i	−0.0413330	−	0.999145i	$-0.513160\pi$
$131$	−5.28641	−	1.05153i	−0.461876	−	0.0918729i	−0.420543	+	0.907273i	$0.638160\pi$
$132$	−3.17463	+	3.17463i	−0.276316	+	0.276316i
$133$	−12.5865	+	11.2588i	−1.09139	+	0.976265i
$134$	−3.77682	+	1.56441i	−0.326268	+	0.135144i
$135$			15.0883i			1.29860i
$136$	2.36722	−	3.37584i	0.202987	−	0.289476i
$137$	6.81092			0.581896			0.290948	−	0.956739i	$-0.406029\pi$
$137$	6.81092			0.581896			0.290948	+	0.956739i	$0.406029\pi$
$138$	−9.53852	+	3.95099i	−0.811973	+	0.336330i
$139$	8.52024	+	12.7514i	0.722677	+	1.08156i	0.992922	+	0.118771i	$0.0378955\pi$
$139$	8.52024	+	12.7514i	0.722677	+	1.08156i	−0.270244	+	0.962792i	$0.587104\pi$
$140$	5.65714	+	4.25318i	0.478115	+	0.359460i
$141$	13.9600	+	2.77682i	1.17565	+	0.233851i
$142$	9.18916	+	6.14000i	0.771137	+	0.515257i
$143$	0.864385	+	4.34556i	0.0722835	+	0.363394i
$144$	−1.08466	−	0.449281i	−0.0903884	−	0.0374401i
$145$	−4.36674	−	1.80876i	−0.362638	−	0.150209i
$146$	−5.48087	+	1.09021i	−0.453600	+	0.0902266i
$147$	9.01505	+	2.86383i	0.743549	+	0.236205i
$148$	0.199562	−	1.00327i	0.0164039	−	0.0824681i
$149$	−2.88350	−	2.88350i	−0.236225	−	0.236225i	0.579060	−	0.815285i	$-0.303420\pi$
$149$	−2.88350	−	2.88350i	−0.236225	−	0.236225i	−0.815285	+	0.579060i	$0.803420\pi$
$150$	2.42251	−	1.61867i	0.197797	−	0.132164i
$151$	−9.35644	+	3.87557i	−0.761416	+	0.315389i	−0.729390	−	0.684098i	$-0.760196\pi$
$151$	−9.35644	+	3.87557i	−0.761416	+	0.315389i	−0.0320264	+	0.999487i	$0.510196\pi$
$152$	−6.38280			−0.517714
$153$	3.96333	+	2.77918i	0.320416	+	0.224684i
$154$	−8.70353	+	1.23299i	−0.701350	+	0.0993574i
$155$	−10.0017	−	24.1462i	−0.803355	−	1.93947i
$156$	1.49832	−	1.00114i	0.119961	−	0.0801557i
$157$	−3.57101	−	3.57101i	−0.284997	−	0.284997i	0.550101	−	0.835098i	$-0.314589\pi$
$157$	−3.57101	−	3.57101i	−0.284997	−	0.284997i	−0.835098	+	0.550101i	$0.814589\pi$
$158$	15.3895	+	3.06117i	1.22433	+	0.243534i
$159$	8.28023	−	12.3922i	0.656665	−	0.982769i
$160$	0.521884	+	2.62369i	0.0412586	+	0.207421i
$161$	−19.5764	−	5.03977i	−1.54284	−	0.397190i
$162$	−1.56884	+	3.78751i	−0.123260	+	0.297575i
$163$	−0.592425	−	2.97832i	−0.0464023	−	0.233280i	0.950624	−	0.310346i	$-0.100445\pi$
$163$	−0.592425	−	2.97832i	−0.0464023	−	0.233280i	−0.997026	+	0.0770658i	$0.975445\pi$
$164$	6.31088	+	4.21679i	0.492797	+	0.329276i
$165$	−2.34306	+	11.7793i	−0.182407	+	0.917020i
$166$	5.92259	−	5.92259i	0.459682	−	0.459682i
$167$	17.5316	−	11.7142i	1.35664	−	0.906475i	0.357017	−	0.934098i	$-0.383794\pi$
$167$	17.5316	−	11.7142i	1.35664	−	0.906475i	0.999618	+	0.0276227i	$0.00879371\pi$
$168$	1.81793	+	3.07846i	0.140256	+	0.237509i
$169$			11.2216i			0.863203i
$170$	0.248136	−	11.0269i	0.0190312	−	0.845724i
$171$		−	7.49359i		−	0.573049i
$172$	−1.19420	−	2.88305i	−0.0910567	−	0.219830i
$173$	0.0981839	+	0.146943i	0.00746478	+	0.0111718i	0.835183	−	0.549972i	$-0.185362\pi$
$173$	0.0981839	+	0.146943i	0.00746478	+	0.0111718i	−0.827718	+	0.561144i	$0.810362\pi$
$174$	−1.68824	−	1.68824i	−0.127985	−	0.127985i
$175$	5.69572	+	0.317123i	0.430556	+	0.0239723i
$176$	−2.76253	−	1.84587i	−0.208234	−	0.139137i
$177$	4.23275	−	0.841947i	0.318153	−	0.0632846i
$178$	3.15737	−	7.62256i	0.236655	−	0.571335i
$179$	0.491656	−	1.18696i	0.0367481	−	0.0887178i	−0.904440	−	0.426601i	$-0.859711\pi$
$179$	0.491656	−	1.18696i	0.0367481	−	0.0887178i	0.941188	+	0.337883i	$0.109711\pi$
$180$	−3.08029	+	0.612707i	−0.229591	+	0.0456685i
$181$	17.5171	+	11.7045i	1.30203	+	0.869991i	0.996614	−	0.0822266i	$-0.0262031\pi$
$181$	17.5171	+	11.7045i	1.30203	+	0.869991i	0.305420	+	0.952218i	$0.401203\pi$
$182$	3.52280	+	0.196141i	0.261127	+	0.0145389i
$183$	−3.69431	−	3.69431i	−0.273091	−	0.273091i
$184$	−4.24480	−	6.35280i	−0.312931	−	0.468335i
$185$	−1.04718	−	2.52811i	−0.0769902	−	0.185871i
$186$		−	13.2021i		−	0.968022i
$187$	9.46621	+	9.90205i	0.692238	+	0.724110i
$188$			10.5333i			0.768221i
$189$	−12.8496	+	7.58809i	−0.934670	+	0.551952i
$190$	−14.1970	+	9.48613i	−1.02996	+	0.688196i
$191$	4.12179	−	4.12179i	0.298242	−	0.298242i	−0.542083	−	0.840325i	$-0.682364\pi$
$191$	4.12179	−	4.12179i	0.298242	−	0.298242i	0.840325	+	0.542083i	$0.182364\pi$
$192$	−0.263623	+	1.32532i	−0.0190253	+	0.0956468i
$193$	−1.65337	−	1.10475i	−0.119012	−	0.0795216i	0.494639	−	0.869098i	$-0.335300\pi$
$193$	−1.65337	−	1.10475i	−0.119012	−	0.0795216i	−0.613652	+	0.789577i	$0.710300\pi$
$194$	−1.23838	−	6.22576i	−0.0889106	−	0.446984i
$195$	1.84474	−	4.45360i	0.132105	−	0.318929i
$196$	−0.777076	+	6.95673i	−0.0555055	+	0.496910i
$197$	2.51918	+	12.6648i	0.179484	+	0.902328i	0.960599	+	0.277940i	$0.0896515\pi$
$197$	2.51918	+	12.6648i	0.179484	+	0.902328i	−0.781114	+	0.624388i	$0.785348\pi$
$198$	2.16710	−	3.24329i	0.154009	−	0.230491i
$199$	7.73221	+	1.53803i	0.548122	+	0.109028i	0.461380	−	0.887203i	$-0.347354\pi$
$199$	7.73221	+	1.53803i	0.548122	+	0.109028i	0.0867419	+	0.996231i	$0.472354\pi$
$200$	1.52460	+	1.52460i	0.107806	+	0.107806i
$201$	−4.59308	+	3.06900i	−0.323971	+	0.216471i
$202$	−4.98037	−	12.0237i	−0.350418	−	0.845984i
$203$	−0.655696	−	4.62847i	−0.0460209	−	0.324855i
$204$	2.24738	−	5.09812i	0.157348	−	0.356940i
$205$	20.3040			1.41809
$206$	−1.76556	+	0.731320i	−0.123013	+	0.0509535i
$207$	7.45837	−	4.98352i	0.518392	−	0.346379i
$208$	0.942965	+	0.942965i	0.0653828	+	0.0653828i
$209$	4.13722	−	20.7992i	0.286177	−	1.43871i
$210$	8.61876	+	4.14548i	0.594751	+	0.286065i
$211$	−21.3460	+	4.24598i	−1.46952	+	0.292305i	−0.863986	−	0.503516i	$-0.832039\pi$
$211$	−21.3460	+	4.24598i	−1.46952	+	0.292305i	−0.605531	+	0.795822i	$0.707039\pi$
$212$	10.1899	+	4.22081i	0.699848	+	0.289887i
$213$	13.7972	+	5.71500i	0.945370	+	0.391585i
$214$	0.343996	+	1.72938i	0.0235151	+	0.118218i
$215$	−6.94099	−	4.63782i	−0.473371	−	0.316297i
$216$	−5.53193	−	1.10037i	−0.376400	−	0.0748706i
$217$	15.5335	−	20.6611i	1.05449	−	1.40257i
$218$	0.607487	+	0.909168i	0.0411442	+	0.0615766i
$219$	−6.97650	+	2.88976i	−0.471428	+	0.195272i
$220$	−8.88791			−0.599223
$221$	−2.95111	−	4.63930i	−0.198513	−	0.312073i
$222$		−	1.38226i		−	0.0927712i
$223$	−6.41743	+	2.65819i	−0.429743	+	0.178005i	−0.587061	−	0.809543i	$-0.699715\pi$
$223$	−6.41743	+	2.65819i	−0.429743	+	0.178005i	0.157318	+	0.987548i	$0.449715\pi$
$224$	−1.97194	+	1.76393i	−0.131756	+	0.117858i
$225$	−1.78993	+	1.78993i	−0.119328	+	0.119328i
$226$	−6.95036	−	1.38251i	−0.462331	−	0.0919633i
$227$	0.319122	−	0.477600i	0.0211809	−	0.0316994i	−0.820728	−	0.571319i	$-0.806432\pi$
$227$	0.319122	−	0.477600i	0.0211809	−	0.0316994i	0.841909	+	0.539620i	$0.181432\pi$
$228$	−8.45926	+	1.68265i	−0.560228	+	0.111436i
$229$	1.34719	−	3.25241i	0.0890249	−	0.214925i	−0.873096	−	0.487548i	$-0.837891\pi$
$229$	1.34719	−	3.25241i	0.0890249	−	0.214925i	0.962121	+	0.272623i	$0.0878912\pi$
$230$	−18.8831	−	7.82163i	−1.24511	−	0.515743i
$231$	−11.2099	+	3.92856i	−0.737559	+	0.258480i
$232$	0.981617	−	1.46909i	0.0644463	−	0.0964507i
$233$	−3.84626	+	19.3365i	−0.251977	+	1.26677i	0.622851	+	0.782340i	$0.285974\pi$
$233$	−3.84626	+	19.3365i	−0.251977	+	1.26677i	−0.874828	+	0.484434i	$0.839026\pi$
$234$	−1.10707	+	1.10707i	−0.0723713	+	0.0723713i
$235$	15.6546	+	23.4288i	1.02120	+	1.52833i
$236$	1.22220	+	2.95065i	0.0795583	+	0.192071i
$237$	21.2031			1.37729
$238$	9.51556	−	5.33423i	0.616802	−	0.345767i
$239$	29.1497			1.88554			0.942770	−	0.333443i	$-0.108211\pi$
$239$	29.1497			1.88554			0.942770	+	0.333443i	$0.108211\pi$
$240$	1.38333	+	3.33965i	0.0892935	+	0.215573i
$241$	−12.9198	−	19.3358i	−0.832237	−	1.24553i	−0.967031	−	0.254657i	$-0.918037\pi$
$241$	−12.9198	−	19.3358i	−0.832237	−	1.24553i	0.134794	−	0.990874i	$-0.456963\pi$
$242$	0.0274446	−	0.0274446i	0.00176421	−	0.00176421i
$243$	2.22037	−	11.1625i	0.142436	−	0.716077i
$244$	2.14803	−	3.21475i	0.137514	−	0.205804i
$245$	8.61069	+	16.6285i	0.550117	+	1.06235i
$246$	9.47558	+	3.92491i	0.604141	+	0.250243i
$247$	−3.25733	+	7.86389i	−0.207259	+	0.500367i
$248$	9.58228	−	1.90603i	0.608475	−	0.121033i
$249$	6.28800	−	9.41066i	0.398486	−	0.596376i
$250$	−7.46148	−	1.48418i	−0.471905	−	0.0938678i
$251$	−12.6489	+	12.6489i	−0.798389	+	0.798389i	−0.982841	−	0.184453i	$-0.940949\pi$
$251$	−12.6489	+	12.6489i	−0.798389	+	0.798389i	0.184453	+	0.982841i	$0.440949\pi$
$252$	−2.07091	−	2.31511i	−0.130455	−	0.145838i
$253$	23.4528	−	9.71448i	1.47447	−	0.610744i
$254$		−	9.37449i		−	0.588208i
$255$	−2.57808	−	14.6796i	−0.161446	−	0.919271i
$256$	−1.00000			−0.0625000
$257$	15.0330	−	6.22689i	0.937735	−	0.388423i	0.139127	−	0.990274i	$-0.455570\pi$
$257$	15.0330	−	6.22689i	0.937735	−	0.388423i	0.798608	+	0.601852i	$0.205570\pi$
$258$	−2.34273	−	3.50614i	−0.145852	−	0.218283i
$259$	1.62637	−	2.16322i	0.101057	−	0.134416i
$260$	3.49883	+	0.695961i	0.216988	+	0.0431617i
$261$	1.72476	+	1.15245i	0.106760	+	0.0713346i
$262$	−1.05153	−	5.28641i	−0.0649639	−	0.326596i
$263$	−24.8051	−	10.2746i	−1.52955	−	0.633560i	−0.550072	−	0.835117i	$-0.685400\pi$
$263$	−24.8051	−	10.2746i	−1.52955	−	0.633560i	−0.979477	+	0.201557i	$0.935400\pi$
$264$	−4.14785	−	1.71810i	−0.255283	−	0.105742i
$265$	28.9380	−	5.75613i	1.77765	−	0.353596i
$266$	−15.2185	−	7.31983i	−0.933103	−	0.448807i
$267$	2.17505	−	10.9347i	0.133111	−	0.669192i
$268$	−2.89065	−	2.89065i	−0.176575	−	0.176575i
$269$	19.4844	−	13.0191i	1.18798	−	0.793786i	0.205232	−	0.978713i	$-0.434205\pi$
$269$	19.4844	−	13.0191i	1.18798	−	0.793786i	0.982752	+	0.184928i	$0.0592051\pi$
$270$	−13.9398	+	5.77405i	−0.848349	+	0.351398i
$271$	−2.10604			−0.127933			−0.0639665	−	0.997952i	$-0.520375\pi$
$271$	−2.10604			−0.127933			−0.0639665	+	0.997952i	$0.520375\pi$
$272$	4.02476	+	0.895150i	0.244037	+	0.0542765i
$273$	4.72054	−	0.668740i	0.285700	−	0.0404740i
$274$	2.60643	+	6.29247i	0.157460	+	0.380142i
$275$	−5.95633	+	3.97989i	−0.359180	+	0.239997i
$276$	−7.30047	−	7.30047i	−0.439437	−	0.439437i
$277$	−30.9615	−	6.15862i	−1.86030	−	0.370036i	−0.868272	−	0.496088i	$-0.834769\pi$
$277$	−30.9615	−	6.15862i	−1.86030	−	0.370036i	−0.992024	+	0.126052i	$0.959769\pi$
$278$	−8.52024	+	12.7514i	−0.511010	+	0.764781i
$279$	2.23774	+	11.2499i	0.133970	+	0.673512i
$280$	−1.76454	+	6.85414i	−0.105451	+	0.409613i
$281$	−1.16863	+	2.82133i	−0.0697149	+	0.168307i	−0.954896	−	0.296939i	$-0.904034\pi$
$281$	−1.16863	+	2.82133i	−0.0697149	+	0.168307i	0.885181	+	0.465246i	$0.154034\pi$
$282$	2.77682	+	13.9600i	0.165357	+	0.831308i
$283$	−3.39382	−	2.26768i	−0.201742	−	0.134799i	0.450596	−	0.892728i	$-0.351212\pi$
$283$	−3.39382	−	2.26768i	−0.201742	−	0.134799i	−0.652338	+	0.757929i	$0.726212\pi$
$284$	−2.15608	+	10.8393i	−0.127940	+	0.643197i
$285$	−16.3148	+	16.3148i	−0.966406	+	0.966406i
$286$	−3.68399	+	2.46156i	−0.217839	+	0.145555i
$287$	10.2111	+	17.2914i	0.602743	+	1.02068i
$288$		−	1.17403i		−	0.0691803i
$289$	−15.3974	−	7.20553i	−0.905730	−	0.423855i
$290$		−	4.72652i		−	0.277551i
$291$	−3.28251	−	7.92467i	−0.192424	−	0.464552i
$292$	−3.10466	−	4.64645i	−0.181687	−	0.271913i
$293$	−4.48920	−	4.48920i	−0.262262	−	0.262262i	0.563711	−	0.825972i	$-0.309373\pi$
$293$	−4.48920	−	4.48920i	−0.262262	−	0.262262i	−0.825972	+	0.563711i	$0.809373\pi$
$294$	0.804077	+	9.42476i	0.0468947	+	0.549663i
$295$	7.10374	+	4.74656i	0.413595	+	0.276356i
$296$	1.00327	−	0.199562i	0.0583137	−	0.0115993i
$297$	7.17139	−	17.3133i	0.416126	−	1.00462i
$298$	1.56054	−	3.76747i	0.0903995	−	0.218244i
$299$	−9.99317	+	1.98776i	−0.577920	+	0.114955i
$300$	2.42251	+	1.61867i	0.139863	+	0.0934538i
$301$	0.458979	−	8.24353i	0.0264551	−	0.475149i
$302$	−7.16111	−	7.16111i	−0.412076	−	0.412076i
$303$	−9.77031	−	14.6223i	−0.561290	−	0.840029i
$304$	−2.44259	−	5.89694i	−0.140092	−	0.338213i
$305$		−	10.3428i		−	0.592230i
$306$	−1.05093	+	4.72518i	−0.0600778	+	0.270121i
$307$		−	12.4845i		−	0.712528i	−0.934385	−	0.356264i	$-0.884050\pi$
$307$		−	12.4845i		−	0.712528i	0.934385	−	0.356264i	$-0.115950\pi$
$308$	−4.46983	−	7.56917i	−0.254692	−	0.431293i
$309$	−2.14715	+	1.43468i	−0.122147	+	0.0816159i
$310$	18.4807	−	18.4807i	1.04963	−	1.04963i
$311$	−3.85946	+	19.4028i	−0.218850	+	1.10023i	0.702555	+	0.711630i	$0.252043\pi$
$311$	−3.85946	+	19.4028i	−0.218850	+	1.10023i	−0.921405	+	0.388604i	$0.872957\pi$
$312$	1.49832	+	1.00114i	0.0848255	+	0.0566786i
$313$	2.76151	+	13.8830i	0.156090	+	0.784715i	0.976930	+	0.213558i	$0.0685053\pi$
$313$	2.76151	+	13.8830i	0.156090	+	0.784715i	−0.820841	+	0.571157i	$0.806495\pi$
$314$	1.93261	−	4.66574i	0.109064	−	0.263303i
$315$	−8.04695	−	2.07162i	−0.453394	−	0.116722i
$316$	3.06117	+	15.3895i	0.172204	+	0.865729i
$317$	6.06161	−	9.07184i	0.340454	−	0.509526i	−0.621251	−	0.783612i	$-0.713375\pi$
$317$	6.06161	−	9.07184i	0.340454	−	0.509526i	0.961705	+	0.274086i	$0.0883753\pi$
$318$	14.6176	+	2.90763i	0.819717	+	0.163052i
$319$	4.15097	+	4.15097i	0.232410	+	0.232410i
$320$	−2.22426	+	1.48620i	−0.124340	+	0.0830812i
$321$	0.911809	+	2.20130i	0.0508922	+	0.122865i
$322$	−2.83543	−	20.0149i	−0.158012	−	1.11539i
$323$	4.55221	+	25.9203i	0.253291	+	1.44224i
$324$	−4.09957			−0.227754
$325$	2.65642	−	1.10033i	0.147352	−	0.0610351i
$326$	2.52490	−	1.68708i	0.139841	−	0.0934389i
$327$	1.04479	+	1.04479i	0.0577771	+	0.0577771i
$328$	−1.48074	+	7.44419i	−0.0817602	+	0.411036i
$329$	−12.0797	+	25.1145i	−0.665973	+	1.38461i
$330$	−11.7793	+	2.34306i	−0.648431	+	0.128981i
$331$	2.80174	+	1.16052i	0.153998	+	0.0637880i	0.458351	−	0.888771i	$-0.348440\pi$
$331$	2.80174	+	1.16052i	0.153998	+	0.0637880i	−0.304353	+	0.952559i	$0.598440\pi$
$332$	7.73824	+	3.20528i	0.424691	+	0.175913i
$333$	0.234292	+	1.17786i	0.0128391	+	0.0645466i
$334$	17.5316	+	11.7142i	0.959286	+	0.640975i
$335$	−10.7256	−	2.13346i	−0.586005	−	0.116564i
$336$	−2.14844	+	2.85763i	−0.117207	+	0.155896i
$337$	2.48877	+	3.72470i	0.135572	+	0.202898i	0.893043	−	0.449971i	$-0.148566\pi$
$337$	2.48877	+	3.72470i	0.135572	+	0.202898i	−0.757472	+	0.652868i	$0.773566\pi$
$338$	−10.3674	+	4.29433i	−0.563914	+	0.233581i
$339$	−9.57591			−0.520092
$340$	10.2825	−	3.99056i	0.557646	−	0.216419i
$341$			32.4606i			1.75784i
$342$	6.92318	−	2.86767i	0.374362	−	0.155066i
$343$	−9.83079	+	15.6957i	−0.530813	+	0.847489i
$344$	2.20659	−	2.20659i	0.118971	−	0.118971i
$345$	−27.0881	−	5.38815i	−1.45837	−	0.290089i
$346$	−0.0981839	+	0.146943i	−0.00527840	+	0.00789968i
$347$	8.06571	−	1.60437i	0.432990	−	0.0861271i	0.0262169	−	0.999656i	$-0.491654\pi$
$347$	8.06571	−	1.60437i	0.432990	−	0.0861271i	0.406773	+	0.913529i	$0.366654\pi$
$348$	0.913671	−	2.20580i	0.0489779	−	0.118243i
$349$	−18.6118	−	7.70927i	−0.996268	−	0.412668i	−0.175841	−	0.984419i	$-0.556264\pi$
$349$	−18.6118	−	7.70927i	−0.996268	−	0.412668i	−0.820427	+	0.571751i	$0.806264\pi$
$350$	1.88667	+	5.38351i	0.100847	+	0.287761i
$351$	−4.17880	+	6.25402i	−0.223048	+	0.333815i
$352$	0.648182	−	3.25863i	0.0345482	−	0.173686i
$353$	19.9280	−	19.9280i	1.06066	−	1.06066i	0.0626256	−	0.998037i	$-0.480053\pi$
$353$	19.9280	−	19.9280i	1.06066	−	1.06066i	0.998037	−	0.0626256i	$-0.0199474\pi$
$354$	2.39766	+	3.58835i	0.127434	+	0.190719i
$355$	11.3138	+	27.3139i	0.600473	+	1.44967i
$356$	8.25060			0.437281
$357$	11.2049	−	9.57809i	0.593029	−	0.506926i
$358$	1.28476			0.0679017
$359$	6.28516	+	15.1737i	0.331718	+	0.800838i	0.998456	+	0.0555461i	$0.0176900\pi$
$359$	6.28516	+	15.1737i	0.331718	+	0.800838i	−0.666738	+	0.745292i	$0.732310\pi$
$360$	−1.74484	−	2.61134i	−0.0919613	−	0.137630i
$361$	15.3726	−	15.3726i	0.809085	−	0.809085i
$362$	−4.11009	+	20.6628i	−0.216021	+	1.08601i
$363$	0.0291379	−	0.0436079i	0.00152934	−	0.00228882i
$364$	1.16691	+	3.32970i	0.0611624	+	0.174524i
$365$	−13.8111	−	5.72076i	−0.722908	−	0.299438i
$366$	1.99935	−	4.82685i	0.104508	−	0.252303i
$367$	−22.3863	+	4.45292i	−1.16856	+	0.232441i	−0.740973	−	0.671535i	$-0.765635\pi$
$367$	−22.3863	+	4.45292i	−1.16856	+	0.232441i	−0.427584	+	0.903975i	$0.640635\pi$
$368$	4.24480	−	6.35280i	0.221276	−	0.331163i
$369$	−8.73969	−	1.73843i	−0.454970	−	0.0904991i
$370$	1.93494	−	1.93494i	0.100592	−	0.100592i
$371$	19.4553	+	21.7495i	1.01007	+	1.12918i
$372$	12.1971	−	5.05221i	0.632391	−	0.261945i
$373$			37.3870i			1.93582i	0.251290	+	0.967912i	$0.419145\pi$
$373$			37.3870i			1.93582i	−0.251290	+	0.967912i	$0.580855\pi$
$374$	−5.52574	+	12.5350i	−0.285729	+	0.648169i
$375$	−10.2801			−0.530863
$376$	−9.73152	+	4.03093i	−0.501865	+	0.207879i
$377$	−1.30904	−	1.95912i	−0.0674189	−	0.100900i
$378$	−11.9278	−	8.96764i	−0.613500	−	0.461245i
$379$	3.79898	+	0.755663i	0.195140	+	0.0388158i	0.291693	−	0.956512i	$-0.405782\pi$
$379$	3.79898	+	0.755663i	0.195140	+	0.0388158i	−0.0965524	+	0.995328i	$0.530782\pi$
$380$	−14.1970	−	9.48613i	−0.728290	−	0.486628i
$381$	−2.47133	−	12.4242i	−0.126610	−	0.636511i
$382$	5.38538	+	2.23070i	0.275540	+	0.114132i
$383$	−6.79376	−	2.81407i	−0.347145	−	0.143792i	0.202296	−	0.979324i	$-0.435160\pi$
$383$	−6.79376	−	2.81407i	−0.347145	−	0.143792i	−0.549442	+	0.835532i	$0.685160\pi$
$384$	−1.32532	+	0.263623i	−0.0676325	+	0.0134529i
$385$	−21.1914	−	10.1927i	−1.08001	−	0.519468i
$386$	0.387936	−	1.95029i	0.0197454	−	0.0992670i
$387$	2.59060	+	2.59060i	0.131687	+	0.131687i
$388$	5.27795	−	3.52661i	0.267947	−	0.179037i
$389$	3.25532	−	1.34840i	0.165051	−	0.0683665i	−0.298628	−	0.954370i	$-0.596529\pi$
$389$	3.25532	−	1.34840i	0.165051	−	0.0683665i	0.463679	+	0.886003i	$0.346529\pi$
$390$	4.82054			0.244098
$391$	−22.7710	+	21.7688i	−1.15158	+	1.10089i
$392$	−6.72456	+	1.94430i	−0.339642	+	0.0982021i
$393$	−2.78724	−	6.72899i	−0.140598	−	0.339432i
$394$	−10.7367	+	7.17402i	−0.540906	+	0.361422i
$395$	29.6808	+	29.6808i	1.49340	+	1.49340i
$396$	3.82572	+	0.760984i	0.192250	+	0.0382409i
$397$	−13.2462	+	19.8244i	−0.664808	+	0.994956i	0.333822	+	0.942636i	$0.391662\pi$
$397$	−13.2462	+	19.8244i	−0.664808	+	0.994956i	−0.998630	+	0.0523198i	$0.983338\pi$
$398$	1.53803	+	7.73221i	0.0770946	+	0.387581i
$399$	−22.0990	−	5.68919i	−1.10633	−	0.284816i
$400$	−0.825109	+	1.99199i	−0.0412554	+	0.0995994i
$401$	−0.852615	−	4.28639i	−0.0425776	−	0.214052i	0.953640	−	0.300951i	$-0.0973041\pi$
$401$	−0.852615	−	4.28639i	−0.0425776	−	0.214052i	−0.996217	+	0.0868993i	$0.972304\pi$
$402$	−4.59308	−	3.06900i	−0.229082	−	0.153068i
$403$	2.54180	−	12.7785i	0.126616	−	0.636542i
$404$	9.20253	−	9.20253i	0.457843	−	0.457843i
$405$	−9.11850	+	6.09279i	−0.453102	+	0.302753i
$406$	4.02522	−	2.37702i	0.199768	−	0.117970i
$407$			3.39863i			0.168464i
$408$	5.57008	+	0.125343i	0.275760	+	0.00620539i
$409$		−	17.8284i		−	0.881559i	−0.897615	−	0.440780i	$-0.854702\pi$
$409$		−	17.8284i		−	0.881559i	0.897615	−	0.440780i	$-0.145298\pi$
$410$	7.77001	+	18.7585i	0.383733	+	0.926414i
$411$	5.11319	+	7.65243i	0.252215	+	0.377466i
$412$	−1.35130	−	1.35130i	−0.0665740	−	0.0665740i
$413$	−0.469741	+	8.43682i	−0.0231145	+	0.415149i
$414$	7.45837	+	4.98352i	0.366559	+	0.244927i
$415$	21.9755	−	4.37120i	1.07874	−	0.214574i
$416$	−0.510329	+	1.23204i	−0.0250209	+	0.0604059i
$417$	−7.93048	+	19.1459i	−0.388357	+	0.937577i
$418$	20.7992	−	4.13722i	1.01732	−	0.202358i
$419$	−31.2312	−	20.8680i	−1.52574	−	1.01947i	−0.983844	−	0.179028i	$-0.942705\pi$
$419$	−31.2312	−	20.8680i	−1.52574	−	1.01947i	−0.541901	−	0.840442i	$-0.682295\pi$
$420$	−0.531670	+	9.54910i	−0.0259429	+	0.465948i
$421$	−19.2466	−	19.2466i	−0.938021	−	0.938021i	0.0601675	−	0.998188i	$-0.480837\pi$
$421$	−19.2466	−	19.2466i	−0.938021	−	0.938021i	−0.998188	+	0.0601675i	$0.980837\pi$
$422$	−12.0915	−	18.0962i	−0.588606	−	0.880911i
$423$	−4.73242	−	11.4251i	−0.230098	−	0.555506i
$424$			11.0295i			0.535641i
$425$	5.10399	−	7.27868i	0.247580	−	0.353068i
$426$			14.9340i			0.723555i
$427$	8.80822	−	5.20154i	0.426260	−	0.251720i
$428$	−1.46610	+	0.979617i	−0.0708666	+	0.0473516i
$429$	−4.23354	+	4.23354i	−0.204397	+	0.204397i
$430$	1.62859	−	8.18745i	0.0785374	−	0.394834i
$431$	−13.4038	−	8.95611i	−0.645637	−	0.431401i	0.189169	−	0.981944i	$-0.439420\pi$
$431$	−13.4038	−	8.95611i	−0.645637	−	0.431401i	−0.834806	+	0.550544i	$0.814420\pi$
$432$	−1.10037	−	5.53193i	−0.0529415	−	0.266155i
$433$	7.19807	−	17.3777i	0.345917	−	0.835118i	−0.651176	−	0.758927i	$-0.725724\pi$
$433$	7.19807	−	17.3777i	0.345917	−	0.835118i	0.997093	−	0.0761914i	$-0.0242760\pi$
$434$	25.0328	+	6.44446i	1.20161	+	0.309344i
$435$	−1.24602	−	6.26416i	−0.0597420	−	0.300343i
$436$	−0.607487	+	0.909168i	−0.0290933	+	0.0435413i
$437$	47.8304	+	9.51406i	2.28804	+	0.455119i
$438$	−5.33958	−	5.33958i	−0.255135	−	0.255135i
$439$	9.97277	−	6.66359i	0.475974	−	0.318036i	−0.294339	−	0.955701i	$-0.595100\pi$
$439$	9.97277	−	6.66359i	0.475974	−	0.318036i	0.770314	+	0.637665i	$0.220100\pi$
$440$	−3.40126	−	8.21136i	−0.162149	−	0.391461i
$441$	−2.28267	−	7.89482i	−0.108698	−	0.375944i
$442$	3.15682	−	4.50186i	0.150154	−	0.214132i
$443$	19.6927			0.935628			0.467814	−	0.883827i	$-0.345042\pi$
$443$	19.6927			0.935628			0.467814	+	0.883827i	$0.345042\pi$
$444$	1.27704	−	0.528968i	0.0606057	−	0.0251037i
$445$	18.3515	−	12.2621i	0.869943	−	0.581277i
$446$	−4.91169	−	4.91169i	−0.232575	−	0.232575i
$447$	1.07502	−	5.40450i	0.0508468	−	0.255624i
$448$	−2.38429	−	1.14680i	−0.112647	−	0.0541814i
$449$	1.30041	−	0.258668i	0.0613701	−	0.0122073i	−0.164310	−	0.986409i	$-0.552540\pi$
$449$	1.30041	−	0.258668i	0.0613701	−	0.0122073i	0.225680	+	0.974202i	$0.427540\pi$
$450$	−2.33865	−	0.968701i	−0.110245	−	0.0456650i
$451$	−23.2981	−	9.65037i	−1.09706	−	0.454418i
$452$	−1.38251	−	6.95036i	−0.0650279	−	0.326917i
$453$	−11.3786	−	7.60294i	−0.534613	−	0.357217i
$454$	0.563368	+	0.112061i	0.0264402	+	0.00525927i
$455$	7.54410	+	5.67185i	0.353673	+	0.265900i
$456$	−4.79179	−	7.17141i	−0.224396	−	0.335832i
$457$	3.60756	−	1.49430i	0.168755	−	0.0699005i	−0.296707	−	0.954969i	$-0.595888\pi$
$457$	3.60756	−	1.49430i	0.168755	−	0.0699005i	0.465461	+	0.885068i	$0.345888\pi$
$458$	3.52038			0.164497
$459$	−0.523184	+	23.2497i	−0.0244201	+	1.08520i
$460$		−	20.4389i		−	0.952968i
$461$	−1.77465	+	0.735084i	−0.0826537	+	0.0342363i	−0.423627	−	0.905837i	$-0.639243\pi$
$461$	−1.77465	+	0.735084i	−0.0826537	+	0.0342363i	0.340974	+	0.940073i	$0.389243\pi$
$462$	−7.91937	−	8.85322i	−0.368442	−	0.411889i
$463$	20.2179	−	20.2179i	0.939605	−	0.939605i	−0.0586719	−	0.998277i	$-0.518687\pi$
$463$	20.2179	−	20.2179i	0.939605	−	0.939605i	0.998277	+	0.0586719i	$0.0186866\pi$
$464$	1.73291	+	0.344698i	0.0804485	+	0.0160022i
$465$	19.6209	−	29.3648i	0.909898	−	1.36176i
$466$	−19.3365	+	3.84626i	−0.895744	+	0.178175i
$467$	−7.01930	+	16.9461i	−0.324815	+	0.784172i	0.674146	+	0.738598i	$0.264512\pi$
$467$	−7.01930	+	16.9461i	−0.324815	+	0.784172i	−0.998961	+	0.0455742i	$0.985488\pi$
$468$	−1.44645	−	0.599141i	−0.0668623	−	0.0276953i
$469$	−3.57714	−	10.2072i	−0.165177	−	0.471323i
$470$	−15.6546	+	23.4288i	−0.722094	+	1.08069i
$471$	1.33134	−	6.69309i	0.0613448	−	0.308401i
$472$	−2.25833	+	2.25833i	−0.103948	+	0.103948i
$473$	5.76019	+	8.62073i	0.264854	+	0.396381i
$474$	8.11407	+	19.5891i	0.372691	+	0.899757i
$475$	−13.7620			−0.631446
$476$	8.56964	+	6.74991i	0.392789	+	0.309382i
$477$	−12.9490			−0.592892
$478$	11.1551	+	26.9309i	0.510224	+	1.23179i
$479$	−17.5906	−	26.3262i	−0.803736	−	1.20288i	−0.975988	−	0.217824i	$-0.930104\pi$
$479$	−17.5906	−	26.3262i	−0.803736	−	1.20288i	0.172252	−	0.985053i	$-0.444896\pi$
$480$	−2.55606	+	2.55606i	−0.116668	+	0.116668i
$481$	0.266127	−	1.33791i	0.0121344	−	0.0610035i
$482$	12.9198	−	19.3358i	0.588481	−	0.880724i
$483$	−9.03422	−	25.7786i	−0.411071	−	1.17297i
$484$	0.0358581	+	0.0148529i	0.00162991	+	0.000675132i
$485$	6.49826	−	15.6882i	0.295071	−	0.712364i
$486$	11.1625	−	2.22037i	0.506343	−	0.100718i
$487$	12.3801	−	18.5281i	0.560995	−	0.839588i	−0.437217	−	0.899356i	$-0.644036\pi$
$487$	12.3801	−	18.5281i	0.560995	−	0.839588i	0.998212	+	0.0597675i	$0.0190359\pi$
$488$	3.79206	+	0.754288i	0.171659	+	0.0341450i
$489$	2.90155	−	2.90155i	0.131212	−	0.131212i
$490$	−12.0675	+	14.3187i	−0.545155	+	0.646852i
$491$	−23.5047	+	9.73598i	−1.06075	+	0.439379i	−0.843719	−	0.536785i	$-0.819639\pi$
$491$	−23.5047	+	9.73598i	−1.06075	+	0.439379i	−0.217035	+	0.976164i	$0.569639\pi$
$492$			10.2563i			0.462389i
$493$	−6.66601	−	2.93855i	−0.300222	−	0.132345i
$494$	−8.51181			−0.382964
$495$	9.64037	−	3.99317i	0.433302	−	0.179480i
$496$	5.42792	+	8.12346i	0.243721	+	0.364754i
$497$	−17.5713	+	23.3715i	−0.788182	+	1.04836i
$498$	11.1006	+	2.20805i	0.497431	+	0.0989452i
$499$	−25.6882	−	17.1643i	−1.14996	−	0.768380i	−0.173662	−	0.984805i	$-0.555560\pi$
$499$	−25.6882	−	17.1643i	−1.14996	−	0.768380i	−0.976299	+	0.216426i	$0.930560\pi$
$500$	−1.48418	−	7.46148i	−0.0663746	−	0.333687i
$501$	26.3231	+	10.9034i	1.17603	+	0.487128i
$502$	−16.5265	−	6.84551i	−0.737615	−	0.305530i
$503$	1.76490	−	0.351061i	0.0786931	−	0.0156530i	−0.155587	−	0.987822i	$-0.549727\pi$
$503$	1.76490	−	0.351061i	0.0786931	−	0.0156530i	0.234280	+	0.972169i	$0.424727\pi$
$504$	1.34638	−	2.79922i	0.0599726	−	0.124687i
$505$	6.79198	−	34.1456i	0.302239	−	1.51946i
$506$	17.9500	+	17.9500i	0.797976	+	0.797976i
$507$	−12.6081	+	8.42446i	−0.559945	+	0.374143i
$508$	8.66090	−	3.58746i	0.384265	−	0.159168i
$509$	7.37292			0.326799			0.163400	−	0.986560i	$-0.447754\pi$
$509$	7.37292			0.326799			0.163400	+	0.986560i	$0.447754\pi$
$510$	12.5756	−	7.99947i	0.556856	−	0.354222i
$511$	−2.07384	−	14.6389i	−0.0917412	−	0.647588i
$512$	−0.382683	−	0.923880i	−0.0169124	−	0.0408301i
$513$	29.9337	−	20.0010i	1.32160	−	0.883068i
$514$	11.5058	+	11.5058i	0.507499	+	0.507499i
$515$	−5.01396	−	0.997338i	−0.220941	−	0.0439480i
$516$	2.34273	−	3.50614i	0.103133	−	0.154349i
$517$	−6.82751	−	34.3242i	−0.300273	−	1.50958i
$518$	2.62094	+	0.674738i	0.115157	+	0.0296463i
$519$	−0.0913877	+	0.220630i	−0.00401148	+	0.00968456i
$520$	0.695961	+	3.49883i	0.0305199	+	0.153434i
$521$	24.9180	+	16.6497i	1.09168	+	0.729434i	0.964932	−	0.262501i	$-0.0845473\pi$
$521$	24.9180	+	16.6497i	1.09168	+	0.729434i	0.126744	+	0.991935i	$0.459547\pi$
$522$	−0.404685	+	2.03449i	−0.0177126	+	0.0890472i
$523$	1.31738	−	1.31738i	0.0576049	−	0.0576049i	−0.677718	−	0.735322i	$-0.737031\pi$
$523$	1.31738	−	1.31738i	0.0576049	−	0.0576049i	0.735322	+	0.677718i	$0.237031\pi$
$524$	4.48161	−	2.99451i	0.195780	−	0.130816i
$525$	3.91966	+	6.63751i	0.171068	+	0.289685i
$526$		−	26.8489i		−	1.17067i
$527$	−14.5744	−	37.5538i	−0.634870	−	1.63587i
$528$		−	4.48961i		−	0.195385i
$529$	13.5380	+	32.6836i	0.588607	+	1.42102i
$530$	16.3921	+	24.5325i	0.712027	+	1.06562i
$531$	−2.65134	−	2.65134i	−0.115058	−	0.115058i
$532$	0.938789	−	16.8612i	0.0407017	−	0.731025i
$533$	8.41589	+	5.62332i	0.364533	+	0.243573i
$534$	10.9347	−	2.17505i	0.473191	−	0.0941235i
$535$	−1.80508	+	4.35784i	−0.0780402	+	0.188406i
$536$	1.56441	−	3.77682i	0.0675722	−	0.163134i
$537$	1.70272	−	0.338692i	0.0734777	−	0.0146156i
$538$	19.4844	+	13.0191i	0.840032	+	0.561291i
$539$	−1.97702	−	23.1731i	−0.0851565	−	0.998137i
$540$	−10.6691	−	10.6691i	−0.459123	−	0.459123i
$541$	21.6871	+	32.4570i	0.932400	+	1.39544i	0.918452	+	0.395532i	$0.129440\pi$
$541$	21.6871	+	32.4570i	0.932400	+	1.39544i	0.0139480	+	0.999903i	$0.495560\pi$
$542$	−0.805948	−	1.94573i	−0.0346184	−	0.0835762i
$543$			28.4683i			1.22169i
$544$	0.713199	+	4.06095i	0.0305781	+	0.174112i
$545$			2.92507i			0.125296i
$546$	2.42431	+	4.10529i	0.103751	+	0.175690i
$547$	−1.86938	+	1.24908i	−0.0799287	+	0.0534067i	−0.594892	−	0.803805i	$-0.702805\pi$
$547$	−1.86938	+	1.24908i	−0.0799287	+	0.0534067i	0.514964	+	0.857212i	$0.327805\pi$
$548$	−4.81605	+	4.81605i	−0.205731	+	0.205731i
$549$	−0.885555	+	4.45199i	−0.0377946	+	0.190006i
$550$	−5.95633	−	3.97989i	−0.253979	−	0.169703i
$551$	2.20014	+	11.0608i	0.0937291	+	0.471208i
$552$	3.95099	−	9.53852i	0.168165	−	0.405986i
$553$	−10.3501	+	40.2037i	−0.440130	+	1.70964i
$554$	−6.15862	−	30.9615i	−0.261655	−	1.31543i
$555$	2.05432	−	3.07450i	0.0872009	−	0.130505i
$556$	−15.0413	−	2.99191i	−0.637895	−	0.126885i
$557$	−6.14133	−	6.14133i	−0.260217	−	0.260217i	0.564925	−	0.825142i	$-0.308905\pi$
$557$	−6.14133	−	6.14133i	−0.260217	−	0.260217i	−0.825142	+	0.564925i	$0.808905\pi$
$558$	−9.53718	+	6.37254i	−0.403741	+	0.269771i
$559$	−1.59253	−	3.84470i	−0.0673567	−	0.162613i
$560$	−7.00766	+	0.992746i	−0.296128	+	0.0419512i
$561$	−4.01887	+	18.0696i	−0.169677	+	0.762899i
$562$	−3.05379			−0.128816
$563$	5.58964	−	2.31530i	0.235575	−	0.0975784i	−0.261773	−	0.965129i	$-0.584307\pi$
$563$	5.58964	−	2.31530i	0.235575	−	0.0975784i	0.497348	+	0.867551i	$0.334307\pi$
$564$	−11.8347	+	7.90772i	−0.498332	+	0.332975i
$565$	−13.4047	−	13.4047i	−0.563939	−	0.563939i
$566$	0.796302	−	4.00328i	0.0334711	−	0.168271i
$567$	−9.77457	−	4.70141i	−0.410493	−	0.197441i
$568$	−10.8393	+	2.15608i	−0.454809	+	0.0904671i
$569$	34.8760	+	14.4461i	1.46208	+	0.605613i	0.965037	−	0.262114i	$-0.0844195\pi$
$569$	34.8760	+	14.4461i	1.46208	+	0.605613i	0.497042	+	0.867727i	$0.334420\pi$
$570$	−21.3163	−	8.82951i	−0.892843	−	0.369827i
$571$	−3.14490	−	15.8105i	−0.131610	−	0.661647i	−0.989112	−	0.147166i	$-0.952985\pi$
$571$	−3.14490	−	15.8105i	−0.131610	−	0.661647i	0.857502	−	0.514481i	$-0.172015\pi$
$572$	−3.68399	−	2.46156i	−0.154035	−	0.102923i
$573$	7.72542	+	1.53668i	0.322734	+	0.0641958i
$574$	−12.0675	+	16.0510i	−0.503689	+	0.669955i
$575$	−9.15228	−	13.6973i	−0.381676	−	0.571219i
$576$	1.08466	−	0.449281i	0.0451942	−	0.0187201i
$577$	23.6399			0.984143			0.492071	−	0.870555i	$-0.336240\pi$
$577$	23.6399			0.984143			0.492071	+	0.870555i	$0.336240\pi$
$578$	0.764709	−	16.9828i	0.0318077	−	0.706391i
$579$		−	2.68702i		−	0.111669i
$580$	4.36674	−	1.80876i	0.181319	−	0.0751047i
$581$	14.7744	+	16.5166i	0.612944	+	0.685223i
$582$	6.06528	−	6.06528i	0.251414	−	0.251414i
$583$	−35.9411	−	7.14913i	−1.48853	−	0.296087i
$584$	3.10466	−	4.64645i	0.128472	−	0.192272i
$585$	−4.10773	+	0.817078i	−0.169834	+	0.0337820i
$586$	2.42954	−	5.86542i	0.100363	−	0.242298i
$587$	24.5248	+	10.1585i	1.01225	+	0.419286i	0.826274	−	0.563269i	$-0.190456\pi$
$587$	24.5248	+	10.1585i	1.01225	+	0.419286i	0.185973	+	0.982555i	$0.440456\pi$
$588$	−8.39963	+	4.34957i	−0.346395	+	0.179373i
$589$	−34.6454	+	51.8505i	−1.42754	+	2.13646i
$590$	−1.66677	+	8.37943i	−0.0686199	+	0.344976i
$591$	−12.3383	+	12.3383i	−0.507530	+	0.507530i
$592$	0.568305	+	0.850529i	0.0233572	+	0.0349565i
$593$	−10.9957	−	26.5459i	−0.451538	−	1.09011i	−0.971737	−	0.236065i	$-0.924142\pi$
$593$	−10.9957	−	26.5459i	−0.451538	−	1.09011i	0.520199	−	0.854045i	$-0.325858\pi$
$594$	18.7397			0.768901
$595$	29.0928	+	2.27734i	1.19269	+	0.0933618i
$596$	4.07788			0.167036
$597$	4.07677	+	9.84220i	0.166851	+	0.402814i
$598$	−5.66067	−	8.47180i	−0.231482	−	0.346438i
$599$	−11.4591	+	11.4591i	−0.468207	+	0.468207i	−0.901333	−	0.433126i	$-0.857410\pi$
$599$	−11.4591	+	11.4591i	−0.468207	+	0.468207i	0.433126	+	0.901333i	$0.357410\pi$
$600$	−0.568400	+	2.85754i	−0.0232048	+	0.116659i
$601$	−6.86895	+	10.2801i	−0.280190	+	0.419334i	−0.944695	−	0.327949i	$-0.893642\pi$
$601$	−6.86895	+	10.2801i	−0.280190	+	0.419334i	0.664505	+	0.747284i	$0.268642\pi$
$602$	7.79167	−	2.73062i	0.317565	−	0.111292i
$603$	4.43409	+	1.83666i	0.180570	+	0.0747946i
$604$	3.87557	−	9.35644i	0.157695	−	0.380708i
$605$	0.101832	−	0.0202556i	0.00414006	−	0.000823509i
$606$	9.77031	−	14.6223i	0.396892	−	0.593990i
$607$	−5.31845	−	1.05791i	−0.215869	−	0.0429390i	0.0859708	−	0.996298i	$-0.472601\pi$
$607$	−5.31845	−	1.05791i	−0.215869	−	0.0429390i	−0.301840	+	0.953359i	$0.597601\pi$
$608$	4.51332	−	4.51332i	0.183039	−	0.183039i
$609$	4.70807	−	4.21146i	0.190781	−	0.170657i
$610$	9.55554	−	3.95804i	0.386893	−	0.160256i
$611$			14.0467i			0.568271i
$612$	−4.76768	+	0.837315i	−0.192722	+	0.0338465i
$613$	−42.1094			−1.70078			−0.850391	−	0.526151i	$-0.823634\pi$
$613$	−42.1094			−1.70078			−0.850391	+	0.526151i	$0.823634\pi$
$614$	11.5342	−	4.77761i	0.465482	−	0.192809i
$615$	15.2429	+	22.8126i	0.614653	+	0.919894i
$616$	5.28247	−	7.02618i	0.212837	−	0.283093i
$617$	−1.51205	−	0.300765i	−0.0608727	−	0.0121083i	0.164560	−	0.986367i	$-0.447380\pi$
$617$	−1.51205	−	0.300765i	−0.0608727	−	0.0121083i	−0.225433	+	0.974259i	$0.572380\pi$
$618$	−2.14715	−	1.43468i	−0.0863708	−	0.0577112i
$619$	8.23389	+	41.3946i	0.330948	+	1.66379i	0.684986	+	0.728557i	$0.259808\pi$
$619$	8.23389	+	41.3946i	0.330948	+	1.66379i	−0.354038	+	0.935231i	$0.615192\pi$
$620$	24.1462	+	10.0017i	0.969735	+	0.401677i
$621$	39.8141	+	16.4915i	1.59768	+	0.661782i
$622$	−19.4028	+	3.85946i	−0.777983	+	0.154750i
$623$	19.6718	+	9.46183i	0.788135	+	0.379080i
$624$	−0.351555	+	1.76739i	−0.0140735	+	0.0707521i
$625$	−22.0135	−	22.0135i	−0.880539	−	0.880539i
$626$	−11.7695	+	7.86411i	−0.470402	+	0.314313i
$627$	26.4749	−	10.9663i	1.05731	−	0.437951i
$628$	5.05016			0.201523
$629$	−1.52594	−	3.93190i	−0.0608433	−	0.156775i
$630$	−1.16551	−	8.22719i	−0.0464351	−	0.327779i
$631$	6.73324	+	16.2555i	0.268046	+	0.647120i	0.999391	−	0.0348871i	$-0.0111072\pi$
$631$	6.73324	+	16.2555i	0.268046	+	0.647120i	−0.731345	+	0.682007i	$0.761107\pi$
$632$	−13.0466	+	8.71748i	−0.518967	+	0.346763i
$633$	−20.7957	−	20.7957i	−0.826556	−	0.826556i
$634$	10.7010	+	2.12856i	0.424990	+	0.0845357i
$635$	13.9324	−	20.8513i	0.552889	−	0.827457i
$636$	2.90763	+	14.6176i	0.115295	+	0.579627i
$637$	−1.03627	+	9.27718i	−0.0410586	+	0.367575i
$638$	−2.24649	+	5.42350i	−0.0889393	+	0.214718i
$639$	−2.53130	−	12.7257i	−0.100137	−	0.503421i
$640$	−2.22426	−	1.48620i	−0.0879215	−	0.0587473i
$641$	−5.50489	+	27.6750i	−0.217430	+	1.09310i	0.705672	+	0.708539i	$0.250645\pi$
$641$	−5.50489	+	27.6750i	−0.217430	+	1.09310i	−0.923102	+	0.384556i	$0.874355\pi$
$642$	−1.68480	+	1.68480i	−0.0664939	+	0.0664939i
$643$	9.30652	−	6.21842i	0.367013	−	0.245230i	−0.358364	−	0.933582i	$-0.616665\pi$
$643$	9.30652	−	6.21842i	0.367013	−	0.245230i	0.725377	+	0.688352i	$0.241665\pi$
$644$	17.4063	−	10.2790i	0.685903	−	0.405048i
$645$		−	11.2803i		−	0.444163i
$646$	−22.2051	+	14.1249i	−0.873650	+	0.555739i
$647$			32.6407i			1.28324i	0.767024	+	0.641619i	$0.221737\pi$
$647$			32.6407i			1.28324i	−0.767024	+	0.641619i	$0.778263\pi$
$648$	−1.56884	−	3.78751i	−0.0616298	−	0.148787i
$649$	−5.89525	−	8.82286i	−0.231409	−	0.346328i
$650$	2.03314	+	2.03314i	0.0797462	+	0.0797462i
$651$	34.8754	+	1.94177i	1.36687	+	0.0761041i
$652$	2.52490	+	1.68708i	0.0988826	+	0.0660713i
$653$	24.6923	−	4.91159i	0.966282	−	0.192206i	0.313363	−	0.949633i	$-0.398544\pi$
$653$	24.6923	−	4.91159i	0.966282	−	0.192206i	0.652919	+	0.757428i	$0.273544\pi$
$654$	−0.565437	+	1.36509i	−0.0221103	+	0.0533791i
$655$	5.51779	−	13.3211i	0.215598	−	0.520500i
$656$	−7.44419	+	1.48074i	−0.290647	+	0.0578132i
$657$	5.45507	+	3.64496i	0.212823	+	0.142203i
$658$	−27.8255	−	1.54925i	−1.08475	−	0.0603961i
$659$	15.7771	+	15.7771i	0.614587	+	0.614587i	0.944138	−	0.329551i	$-0.106897\pi$
$659$	15.7771	+	15.7771i	0.614587	+	0.614587i	−0.329551	+	0.944138i	$0.606897\pi$
$660$	−6.67246	−	9.98604i	−0.259725	−	0.388706i
$661$	−9.44509	−	22.8025i	−0.367371	−	0.886913i	−0.994179	−	0.107739i	$-0.965639\pi$
$661$	−9.44509	−	22.8025i	−0.367371	−	0.886913i	0.626808	−	0.779174i	$-0.284361\pi$
$662$			3.03259i			0.117865i
$663$	2.99700	−	6.79861i	0.116394	−	0.264036i
$664$			8.37581i			0.325044i
$665$	−22.9710	−	38.8989i	−0.890778	−	1.50843i
$666$	−0.998545	+	0.667207i	−0.0386928	+	0.0258537i
$667$	−9.54568	+	9.54568i	−0.369610	+	0.369610i
$668$	−4.11349	+	20.6799i	−0.159156	+	0.800130i
$669$	−7.80439	−	5.21473i	−0.301735	−	0.201613i
$670$	−2.13346	−	10.7256i	−0.0824229	−	0.414368i
$671$	−4.91589	+	11.8680i	−0.189776	+	0.458160i
$672$	−3.46227	−	0.891331i	−0.133560	−	0.0343838i
$673$	−3.42642	−	17.2258i	−0.132079	−	0.664006i	−0.988923	−	0.148430i	$-0.952578\pi$
$673$	−3.42642	−	17.2258i	−0.132079	−	0.664006i	0.856844	−	0.515576i	$-0.172422\pi$
$674$	−2.48877	+	3.72470i	−0.0958637	+	0.143470i
$675$	−11.9275	−	2.37252i	−0.459088	−	0.0913183i
$676$	−7.93489	−	7.93489i	−0.305188	−	0.305188i
$677$	−33.0176	+	22.0617i	−1.26897	+	0.847898i	−0.993547	−	0.113425i	$-0.963818\pi$
$677$	−33.0176	+	22.0617i	−1.26897	+	0.847898i	−0.275423	+	0.961323i	$0.588818\pi$
$678$	−3.66454	−	8.84699i	−0.140736	−	0.339767i
$679$	16.6285	−	2.35569i	0.638143	−	0.0904031i
$680$	7.62173	+	7.97265i	0.292280	+	0.305737i
$681$	0.776184			0.0297435
$682$	−29.9896	+	12.4221i	−1.14836	+	0.475668i
$683$	−3.87736	+	2.59077i	−0.148363	+	0.0991331i	−0.627536	−	0.778587i	$-0.715937\pi$
$683$	−3.87736	+	2.59077i	−0.148363	+	0.0991331i	0.479173	+	0.877720i	$0.340937\pi$
$684$	5.29877	+	5.29877i	0.202603	+	0.202603i
$685$	−3.55451	+	17.8697i	−0.135811	+	0.682768i
$686$	−18.2630	−	3.07598i	−0.697286	−	0.117441i
$687$	4.66563	−	0.928052i	0.178005	−	0.0354074i
$688$	2.88305	+	1.19420i	0.109915	+	0.0455283i
$689$	13.5888	+	5.62868i	0.517694	+	0.214436i
$690$	−5.38815	−	27.0881i	−0.205124	−	1.03123i
$691$	−23.8051	−	15.9061i	−0.905588	−	0.605095i	0.0131708	−	0.999913i	$-0.495807\pi$
$691$	−23.8051	−	15.9061i	−0.905588	−	0.605095i	−0.918759	+	0.394818i	$0.870807\pi$
$692$	−0.173331	−	0.0344776i	−0.00658904	−	0.00131064i
$693$	8.24894	+	6.20177i	0.313351	+	0.235586i
$694$	4.56886	+	6.83778i	0.173432	+	0.259559i
$695$	−37.9024	+	15.6997i	−1.43772	+	0.595523i
$696$	2.38754			0.0904994
$697$	31.2866	+	0.704036i	1.18506	+	0.0266673i
$698$		−	20.1453i		−	0.762511i
$699$	−24.6131	+	10.1951i	−0.930951	+	0.385613i
$700$	−4.25172	+	3.80324i	−0.160700	+	0.143749i
$701$	3.90972	−	3.90972i	0.147668	−	0.147668i	−0.629407	−	0.777076i	$-0.716702\pi$
$701$	3.90972	−	3.90972i	0.147668	−	0.147668i	0.777076	+	0.629407i	$0.216702\pi$
$702$	−7.37712	−	1.46740i	−0.278431	−	0.0553835i
$703$	−3.62738	+	5.42876i	−0.136809	+	0.204750i
$704$	3.25863	−	0.648182i	0.122814	−	0.0244293i
$705$	−14.5710	+	35.1776i	−0.548777	+	1.32487i
$706$	26.0372	+	10.7850i	0.979925	+	0.405898i
$707$	32.4950	−	11.3880i	1.22210	−	0.428290i
$708$	−2.39766	+	3.58835i	−0.0901096	+	0.134859i
$709$	5.46667	−	27.4828i	0.205305	−	1.03214i	−0.731381	−	0.681969i	$-0.761124\pi$
$709$	5.46667	−	27.4828i	0.205305	−	1.03214i	0.936686	−	0.350170i	$-0.113876\pi$
$710$	−20.9051	+	20.9051i	−0.784555	+	0.784555i
$711$	−10.2346	−	15.3171i	−0.383826	−	0.574436i
$712$	3.15737	+	7.62256i	0.118327	+	0.285668i
$713$	−74.6472			−2.79556
$714$	13.1369	+	6.68665i	0.491638	+	0.250242i
$715$	−11.8525			−0.443259
$716$	0.491656	+	1.18696i	0.0183741	+	0.0443589i
$717$	21.8837	+	32.7513i	0.817262	+	1.22312i
$718$	−11.6135	+	11.6135i	−0.433411	+	0.433411i
$719$	9.90009	−	49.7711i	0.369211	−	1.85615i	−0.132597	−	0.991170i	$-0.542331\pi$
$719$	9.90009	−	49.7711i	0.369211	−	1.85615i	0.501808	−	0.864979i	$-0.332669\pi$
$720$	1.74484	−	2.61134i	0.0650264	−	0.0973189i
$721$	−1.67222	−	4.77158i	−0.0622767	−	0.177703i
$722$	20.0853	+	8.31960i	0.747497	+	0.309623i
$723$	12.0255	−	29.0321i	0.447233	−	1.07972i
$724$	−20.6628	+	4.11009i	−0.767927	+	0.152750i
$725$	2.11648	−	3.16753i	0.0786040	−	0.117639i
$726$	0.0514390	+	0.0102319i	0.00190908	+	0.000379740i
$727$	−4.11721	+	4.11721i	−0.152699	+	0.152699i	−0.779322	−	0.626623i	$-0.784436\pi$
$727$	−4.11721	+	4.11721i	−0.152699	+	0.152699i	0.626623	+	0.779322i	$0.284436\pi$
$728$	−2.62968	+	2.35230i	−0.0974626	+	0.0871820i
$729$	25.5711	−	10.5919i	0.947079	−	0.392293i
$730$		−	14.9491i		−	0.553290i
$731$	−10.5346	−	7.38712i	−0.389636	−	0.273222i
$732$	5.22454			0.193105
$733$	−9.56690	+	3.96274i	−0.353362	+	0.146367i	−0.552301	−	0.833645i	$-0.686250\pi$
$733$	−9.56690	+	3.96274i	−0.353362	+	0.146367i	0.198940	+	0.980012i	$0.436250\pi$
$734$	−12.6808	−	18.9782i	−0.468058	−	0.700499i
$735$	−12.2186	+	22.1581i	−0.450690	+	0.817314i
$736$	7.49364	+	1.49058i	0.276219	+	0.0549434i
$737$	11.2932	+	7.54590i	0.415992	+	0.277957i
$738$	−1.73843	−	8.73969i	−0.0639925	−	0.321712i
$739$	−26.6655	−	11.0452i	−0.980908	−	0.406305i	−0.166146	−	0.986101i	$-0.553132\pi$
$739$	−26.6655	−	11.0452i	−0.980908	−	0.406305i	−0.814762	+	0.579796i	$0.803132\pi$
$740$	2.52811	+	1.04718i	0.0929353	+	0.0384951i
$741$	−11.2809	+	2.24391i	−0.414413	+	0.0824319i
$742$	−12.6487	+	26.2976i	−0.464349	+	0.965414i
$743$	4.49352	−	22.5904i	0.164851	−	0.828762i	−0.806522	−	0.591204i	$-0.798653\pi$
$743$	4.49352	−	22.5904i	0.164851	−	0.828762i	0.971373	−	0.237559i	$-0.0763472\pi$
$744$	9.33527	+	9.33527i	0.342248	+	0.342248i
$745$	9.07025	−	6.06055i	0.332308	−	0.222041i
$746$	−34.5410	+	14.3074i	−1.26464	+	0.523830i
$747$	−9.83344			−0.359787
$748$	−13.6954	−	0.308186i	−0.500755	−	0.0112684i
$749$	−4.61904	+	0.654360i	−0.168776	+	0.0239098i
$750$	−3.93403	−	9.49759i	−0.143650	−	0.346803i
$751$	−23.0280	+	15.3868i	−0.840305	+	0.561474i	−0.899574	−	0.436768i	$-0.856123\pi$
$751$	−23.0280	+	15.3868i	−0.840305	+	0.561474i	0.0592691	+	0.998242i	$0.481123\pi$
$752$	−7.44818	−	7.44818i	−0.271607	−	0.271607i
$753$	−23.7076	−	4.71573i	−0.863952	−	0.171851i
$754$	1.30904	−	1.95912i	0.0476724	−	0.0713468i
$755$	−5.28530	−	26.5710i	−0.192352	−	0.967018i
$756$	3.72044	−	14.4516i	0.135311	−	0.525600i
$757$	−5.55241	+	13.4047i	−0.201806	+	0.487202i	−0.992089	−	0.125540i	$-0.959934\pi$
$757$	−5.55241	+	13.4047i	−0.201806	+	0.487202i	0.790283	+	0.612742i	$0.209934\pi$
$758$	0.755663	+	3.79898i	0.0274469	+	0.137985i
$759$	28.5216	+	19.0575i	1.03527	+	0.691743i
$760$	3.33108	−	16.7465i	0.120831	−	0.607459i
$761$	22.5304	−	22.5304i	0.816725	−	0.816725i	−0.168907	−	0.985632i	$-0.554024\pi$
$761$	22.5304	−	22.5304i	0.816725	−	0.816725i	0.985632	+	0.168907i	$0.0540237\pi$
$762$	10.5327	−	7.03775i	0.381561	−	0.254951i
$763$	−2.49106	+	1.47105i	−0.0901825	+	0.0532556i
$764$			5.82909i			0.210889i
$765$	−9.36012	+	8.94813i	−0.338416	+	0.323520i
$766$		−	7.35352i		−	0.265693i
$767$	1.62987	+	3.93485i	0.0588511	+	0.142079i
$768$	−0.750734	−	1.12355i	−0.0270898	−	0.0405427i
$769$	32.3185	+	32.3185i	1.16544	+	1.16544i	0.983267	+	0.182169i	$0.0583119\pi$
$769$	32.3185	+	32.3185i	1.16544	+	1.16544i	0.182169	+	0.983267i	$0.441688\pi$
$770$	1.30724	−	23.4788i	0.0471098	−	0.846119i
$771$	18.2820	+	12.2157i	0.658412	+	0.439937i
$772$	1.95029	−	0.387936i	0.0701924	−	0.0139621i
$773$	−12.0127	+	29.0012i	−0.432066	+	1.04310i	0.546554	+	0.837424i	$0.315939\pi$
$773$	−12.0127	+	29.0012i	−0.432066	+	1.04310i	−0.978620	+	0.205676i	$0.934061\pi$
$774$	−1.40202	+	3.38478i	−0.0503946	+	0.121663i
$775$	20.6605	−	4.10962i	0.742146	−	0.147622i
$776$	5.27795	+	3.52661i	0.189467	+	0.126598i
$777$	3.65146	+	0.203304i	0.130995	+	0.00729350i
$778$	2.49151	+	2.49151i	0.0893251	+	0.0893251i
$779$	−26.9150	−	40.2811i	−0.964328	−	1.44322i
$780$	1.84474	+	4.45360i	0.0660524	+	0.159465i
$781$		−	36.7190i		−	1.31391i
$782$	−28.8258	−	12.7071i	−1.03081	−	0.454407i
$783$			9.96565i			0.356143i
$784$	−4.36968	−	5.46863i	−0.156060	−	0.195308i
$785$	11.2329	−	7.50556i	0.400918	−	0.267885i
$786$	5.15014	−	5.15014i	0.183700	−	0.183700i
$787$	−2.16705	+	10.8945i	−0.0772471	+	0.388347i	0.922749	+	0.385402i	$0.125937\pi$
$787$	−2.16705	+	10.8945i	−0.0772471	+	0.388347i	−0.999996	+	0.00294478i	$0.999063\pi$
$788$	−10.7367	−	7.17402i	−0.382478	−	0.255564i
$789$	−7.07797	−	35.5834i	−0.251982	−	1.26680i
$790$	−16.0631	+	38.7798i	−0.571500	+	1.37972i
$791$	4.67439	−	18.1571i	0.166202	−	0.645593i
$792$	0.760984	+	3.82572i	0.0270404	+	0.135941i
$793$	2.86451	−	4.28705i	0.101722	−	0.152238i
$794$	−23.3844	−	4.65145i	−0.829882	−	0.165074i
$795$	28.1921	+	28.1921i	0.999870	+	0.999870i
$796$	−6.55505	+	4.37995i	−0.232338	+	0.155243i
$797$	8.28680	+	20.0061i	0.293533	+	0.708652i	1.00000		0.000905524i	$0.000288237\pi$
$797$	8.28680	+	20.0061i	0.293533	+	0.708652i	−0.706466	+	0.707747i	$0.749712\pi$
$798$	−3.20080	−	22.5940i	−0.113307	−	0.799818i
$799$	23.3099	+	36.6444i	0.824646	+	1.29639i
$800$	−2.15611			−0.0762301
$801$	−8.94911	+	3.70684i	−0.316201	+	0.130975i
$802$	3.63382	−	2.42804i	0.128315	−	0.0857372i
$803$	13.1287	+	13.1287i	0.463302	+	0.463302i
$804$	1.07769	−	5.41791i	0.0380072	−	0.191075i
$805$	23.4394	−	48.7322i	0.826131	−	1.71759i
$806$	12.7785	−	2.54180i	0.450103	−	0.0895310i
$807$	29.2552	+	12.1179i	1.02983	+	0.426570i
$808$	12.0237	+	4.98037i	0.422992	+	0.175209i
$809$	5.02362	+	25.2555i	0.176621	+	0.887934i	0.962858	+	0.270009i	$0.0870267\pi$
$809$	5.02362	+	25.2555i	0.176621	+	0.887934i	−0.786237	+	0.617925i	$0.787973\pi$
$810$	−9.11850	−	6.09279i	−0.320392	−	0.214079i
$811$	46.4733	+	9.24411i	1.63190	+	0.324605i	0.924199	−	0.381910i	$-0.124734\pi$
$811$	46.4733	+	9.24411i	1.63190	+	0.324605i	0.707698	+	0.706515i	$0.249734\pi$
$812$	3.73647	+	2.80917i	0.131124	+	0.0985827i
$813$	−1.58108	−	2.36625i	−0.0554508	−	0.0829880i
$814$	−3.13993	+	1.30060i	−0.110054	+	0.0455860i
$815$	8.12337			0.284549
$816$	2.01578	+	5.19405i	0.0705663	+	0.181828i
$817$			19.9181i			0.696846i
$818$	16.4713	−	6.82265i	0.575906	−	0.238548i
$819$	−2.76167	−	3.08732i	−0.0965005	−	0.107880i
$820$	−14.3571	+	14.3571i	−0.501372	+	0.501372i
$821$	−39.3829	−	7.83374i	−1.37447	−	0.273399i	−0.548047	−	0.836447i	$-0.684629\pi$
$821$	−39.3829	−	7.83374i	−1.37447	−	0.273399i	−0.826424	+	0.563048i	$0.809629\pi$
$822$	−5.11319	+	7.65243i	−0.178343	+	0.266909i
$823$	51.3366	−	10.2115i	1.78948	−	0.355950i	0.814834	−	0.579694i	$-0.196828\pi$
$823$	51.3366	−	10.2115i	1.78948	−	0.355950i	0.974648	+	0.223744i	$0.0718280\pi$
$824$	0.731320	−	1.76556i	0.0254768	−	0.0615063i
$825$	−8.94324	−	3.70441i	−0.311364	−	0.128971i
$826$	−7.97437	+	2.79465i	−0.277464	+	0.0972382i
$827$	−25.6495	+	38.3872i	−0.891920	+	1.33485i	0.0499073	+	0.998754i	$0.484107\pi$
$827$	−25.6495	+	38.3872i	−0.891920	+	1.33485i	−0.941827	+	0.336098i	$0.890893\pi$
$828$	−1.74998	+	8.79774i	−0.0608160	+	0.305743i
$829$	6.04797	−	6.04797i	0.210055	−	0.210055i	−0.594236	−	0.804291i	$-0.702545\pi$
$829$	6.04797	−	6.04797i	0.210055	−	0.210055i	0.804291	+	0.594236i	$0.202545\pi$
$830$	12.4481	+	18.6300i	0.432081	+	0.646655i
$831$	−16.3243	−	39.4104i	−0.566284	−	1.36713i
$832$	−1.33355			−0.0462327
$833$	12.6917	+	25.9215i	0.439740	+	0.898125i
$834$	−20.7233			−0.717591
$835$	21.5851	+	52.1110i	0.746982	+	1.80337i
$836$	11.7818	+	17.6327i	0.407482	+	0.609840i
$837$	−38.9657	+	38.9657i	−1.34685	+	1.34685i
$838$	7.32788	−	36.8397i	0.253137	−	1.27261i
$839$	−15.6236	+	23.3824i	−0.539387	+	0.807249i	−0.996624	−	0.0820954i	$-0.973839\pi$
$839$	−15.6236	+	23.3824i	−0.539387	+	0.807249i	0.457238	+	0.889344i	$0.348839\pi$
$840$	−9.02568	+	3.16308i	−0.311416	+	0.109137i
$841$	23.9083	+	9.90316i	0.824425	+	0.341488i
$842$	10.4162	−	25.1469i	0.358965	−	0.866618i
$843$	−4.04725	+	0.805048i	−0.139395	+	0.0277273i
$844$	12.0915	−	18.0962i	0.416207	−	0.622898i
$845$	−29.4421	−	5.85640i	−1.01284	−	0.201466i
$846$	8.74438	−	8.74438i	0.300638	−	0.300638i
$847$	0.0684627	+	0.0765359i	0.00235241	+	0.00262980i
$848$	−10.1899	+	4.22081i	−0.349924	+	0.144943i
$849$		−	5.51556i		−	0.189293i
$850$	8.67784	+	1.93004i	0.297647	+	0.0662000i
$851$	−7.81559			−0.267915
$852$	−13.7972	+	5.71500i	−0.472685	+	0.195793i
$853$	−24.2790	−	36.3360i	−0.831296	−	1.24412i	−0.967356	−	0.253422i	$-0.918444\pi$
$853$	−24.2790	−	36.3360i	−0.831296	−	1.24412i	0.136060	−	0.990701i	$-0.456556\pi$
$854$	8.17635	+	6.14720i	0.279789	+	0.210353i
$855$	19.6609	+	3.91079i	0.672387	+	0.133746i
$856$	−1.46610	−	0.979617i	−0.0501103	−	0.0334826i
$857$	4.63494	+	23.3014i	0.158327	+	0.795962i	0.975573	+	0.219674i	$0.0704993\pi$
$857$	4.63494	+	23.3014i	0.158327	+	0.795962i	−0.817247	+	0.576288i	$0.804501\pi$
$858$	−5.53139	−	2.29118i	−0.188838	−	0.0782194i
$859$	24.5537	+	10.1705i	0.837763	+	0.347013i	0.759971	−	0.649957i	$-0.225213\pi$
$859$	24.5537	+	10.1705i	0.837763	+	0.347013i	0.0777919	+	0.996970i	$0.475213\pi$
$860$	8.18745	−	1.62859i	0.279190	−	0.0555343i
$861$	−11.7620	+	24.4540i	−0.400847	+	0.833389i
$862$	3.14497	−	15.8108i	0.107118	−	0.538519i
$863$	32.2724	+	32.2724i	1.09856	+	1.09856i	0.994579	+	0.103985i	$0.0331594\pi$
$863$	32.2724	+	32.2724i	1.09856	+	1.09856i	0.103985	+	0.994579i	$0.466841\pi$
$864$	4.68974	−	3.13358i	0.159548	−	0.106607i
$865$	−0.436772	+	0.180917i	−0.0148507	+	0.00615136i
$866$	18.8095			0.639172
$867$	−3.46356	−	22.7092i	−0.117629	−	0.771246i
$868$	3.62572	+	25.5935i	0.123065	+	0.868699i
$869$	−19.9504	−	48.1646i	−0.676773	−	1.63387i
$870$	5.31050	−	3.54836i	0.180043	−	0.120301i
$871$	−3.85484	−	3.85484i	−0.130616	−	0.130616i
$872$	−1.07244	−	0.213321i	−0.0363173	−	0.00722396i
$873$	−4.14034	+	6.19646i	−0.140129	+	0.209718i
$874$	9.51406	+	47.8304i	0.321818	+	1.61789i
$875$	5.01814	−	19.4924i	0.169644	−	0.658963i
$876$	2.88976	−	6.97650i	0.0976360	−	0.235714i
$877$	1.58790	+	7.98290i	0.0536195	+	0.269564i	0.998290	−	0.0584577i	$-0.0186183\pi$
$877$	1.58790	+	7.98290i	0.0536195	+	0.269564i	−0.944670	+	0.328021i	$0.893618\pi$
$878$	9.97277	+	6.66359i	0.336565	+	0.224885i
$879$	1.67366	−	8.41404i	0.0564511	−	0.283799i
$880$	6.28470	−	6.28470i	0.211857	−	0.211857i
$881$	−9.68820	+	6.47345i	−0.326404	+	0.218096i	−0.707965	−	0.706248i	$-0.750387\pi$
$881$	−9.68820	+	6.47345i	−0.326404	+	0.218096i	0.381561	+	0.924344i	$0.375387\pi$
$882$	6.42033	−	5.13013i	0.216184	−	0.172740i
$883$		−	10.1047i		−	0.340052i	−0.985440	−	0.170026i	$-0.945615\pi$
$883$		−	10.1047i		−	0.340052i	0.985440	−	0.170026i	$-0.0543851\pi$
$884$	5.36724	+	1.19373i	0.180520	+	0.0401495i
$885$			11.5448i			0.388075i
$886$	7.53607	+	18.1937i	0.253179	+	0.611229i
$887$	−10.6506	−	15.9398i	−0.357613	−	0.535205i	0.608423	−	0.793613i	$-0.291802\pi$
$887$	−10.6506	−	15.9398i	−0.357613	−	0.535205i	−0.966036	+	0.258407i	$0.916802\pi$
$888$	0.977406	+	0.977406i	0.0327996	+	0.0327996i
$889$	24.7642	+	1.37881i	0.830565	+	0.0462438i
$890$	18.3515	+	12.2621i	0.615142	+	0.411025i
$891$	13.3590	−	2.65727i	0.447543	−	0.0890218i
$892$	2.65819	−	6.41743i	0.0890027	−	0.214871i
$893$	25.7286	−	62.1144i	0.860975	−	2.07858i
$894$	5.40450	−	1.07502i	0.180753	−	0.0359541i
$895$	2.85764	+	1.90941i	0.0955202	+	0.0638246i
$896$	0.147081	−	2.64166i	0.00491363	−	0.0882517i
$897$	−9.73557	−	9.73557i	−0.325061	−	0.325061i
$898$	0.736623	+	1.10243i	0.0245814	+	0.0367887i
$899$	−6.60599	−	15.9483i	−0.220322	−	0.531904i
$900$		−	2.53134i		−	0.0843779i
$901$	44.7904	−	7.86624i	1.49218	−	0.262062i
$902$		−	25.2176i		−	0.839656i
$903$	9.60661	−	5.67301i	0.319688	−	0.188786i
$904$	5.89223	−	3.93706i	0.195973	−	0.130945i
$905$	−39.8510	+	39.8510i	−1.32469	+	1.32469i
$906$	2.66980	−	13.4220i	0.0886980	−	0.445915i
$907$	−22.1913	−	14.8277i	−0.736849	−	0.492346i	0.129629	−	0.991563i	$-0.458621\pi$
$907$	−22.1913	−	14.8277i	−0.736849	−	0.492346i	−0.866478	+	0.499216i	$0.833621\pi$
$908$	0.112061	+	0.563368i	0.00371887	+	0.0186960i
$909$	−5.84710	+	14.1161i	−0.193936	+	0.468203i
$910$	−2.35310	+	9.14036i	−0.0780046	+	0.303000i
$911$	−2.41317	−	12.1318i	−0.0799519	−	0.401945i	−0.999950	−	0.0100220i	$-0.996810\pi$
$911$	−2.41317	−	12.1318i	−0.0799519	−	0.401945i	0.919998	−	0.391923i	$-0.128190\pi$
$912$	4.79179	−	7.17141i	0.158672	−	0.237469i
$913$	−27.2937	−	5.42905i	−0.903289	−	0.179675i
$914$	2.76111	+	2.76111i	0.0913294	+	0.0913294i
$915$	11.6207	−	7.76472i	0.384169	−	0.256694i
$916$	1.34719	+	3.25241i	0.0445125	+	0.107463i
$917$	14.1196	−	2.00026i	0.466269	−	0.0660545i
$918$	−21.6801	+	8.41391i	−0.715550	+	0.277700i
$919$	12.3612			0.407759			0.203880	−	0.978996i	$-0.434645\pi$
$919$	12.3612			0.407759			0.203880	+	0.978996i	$0.434645\pi$
$920$	18.8831	−	7.82163i	0.622556	−	0.257871i
$921$	14.0270	−	9.37254i	0.462205	−	0.308836i
$922$	−1.35826	−	1.35826i	−0.0447319	−	0.0447319i
$923$	−2.87525	+	14.4549i	−0.0946400	+	0.475787i
$924$	5.14870	−	10.7045i	0.169380	−	0.352153i
$925$	2.16316	−	0.430279i	0.0711242	−	0.0141475i
$926$	26.4160	+	10.9418i	0.868082	+	0.359571i
$927$	2.07282	+	0.858591i	0.0680804	+	0.0281998i
$928$	0.344698	+	1.73291i	0.0113153	+	0.0568857i
$929$	−7.85673	−	5.24970i	−0.257771	−	0.172237i	0.419970	−	0.907538i	$-0.362041\pi$
$929$	−7.85673	−	5.24970i	−0.257771	−	0.172237i	−0.677741	+	0.735301i	$0.737041\pi$
$930$	34.6381	+	6.88995i	1.13583	+	0.225930i
$931$	21.5748	−	39.1254i	0.707087	−	1.28228i
$932$	−10.9532	−	16.3927i	−0.358785	−	0.536960i
$933$	−24.6975	+	10.2301i	−0.808561	+	0.334917i
$934$	−18.3423			−0.600179
$935$	−30.9202	+	19.6687i	−1.01120	+	0.643235i
$936$		−	1.56563i		−	0.0511742i
$937$	27.9963	−	11.5964i	0.914599	−	0.378839i	0.124783	−	0.992184i	$-0.460176\pi$
$937$	27.9963	−	11.5964i	0.914599	−	0.378839i	0.789815	+	0.613345i	$0.210176\pi$
$938$	8.06128	−	7.21096i	0.263210	−	0.235446i
$939$	−13.5252	+	13.5252i	−0.441377	+	0.441377i
$940$	−27.6362	−	5.49718i	−0.901392	−	0.179298i
$941$	−1.49556	+	2.23826i	−0.0487538	+	0.0729653i	−0.855046	−	0.518553i	$-0.826471\pi$
$941$	−1.49556	+	2.23826i	−0.0487538	+	0.0729653i	0.806292	+	0.591518i	$0.201471\pi$
$942$	6.69309	−	1.33134i	0.218073	−	0.0433773i
$943$	22.1923	−	53.5769i	0.722680	−	1.74470i
$944$	−2.95065	−	1.22220i	−0.0960354	−	0.0397791i
$945$	−13.2028	−	37.6734i	−0.429487	−	1.22552i
$946$	−5.76019	+	8.62073i	−0.187280	+	0.280284i
$947$	−2.38357	+	11.9830i	−0.0774556	+	0.389395i	0.922538	+	0.385905i	$0.126111\pi$
$947$	−2.38357	+	11.9830i	−0.0774556	+	0.389395i	−0.999994	+	0.00349003i	$0.998889\pi$
$948$	−14.9928	+	14.9928i	−0.486945	+	0.486945i
$949$	−4.14023	−	6.19630i	−0.134398	−	0.201140i
$950$	−5.26650	−	12.7145i	−0.170868	−	0.412512i
$951$	14.7434			0.478086
$952$	−2.95665	+	10.5004i	−0.0958255	+	0.340320i
$953$	14.2431			0.461380			0.230690	−	0.973027i	$-0.425902\pi$
$953$	14.2431			0.461380			0.230690	+	0.973027i	$0.425902\pi$
$954$	−4.95536	−	11.9633i	−0.160436	−	0.387326i
$955$	8.66320	+	12.9654i	0.280335	+	0.419551i
$956$	−20.6120	+	20.6120i	−0.666639	+	0.666639i
$957$	−1.54756	+	7.78010i	−0.0500255	+	0.251495i
$958$	17.5906	−	26.3262i	0.568327	−	0.850562i
$959$	−17.0059	+	5.95979i	−0.549150	+	0.192452i
$960$	−3.33965	−	1.38333i	−0.107787	−	0.0446467i
$961$	24.6651	−	59.5468i	0.795649	−	1.92087i
$962$	1.33791	−	0.266127i	0.0431360	−	0.00858028i
$963$	1.15010	−	1.72124i	0.0370614	−	0.0554663i
$964$	22.8082	+	4.53683i	0.734602	+	0.146121i
$965$	3.76139	−	3.76139i	0.121083	−	0.121083i
$966$	20.3591	−	18.2116i	0.655044	−	0.585948i
$967$	29.8459	−	12.3626i	0.959780	−	0.397554i	0.152882	−	0.988244i	$-0.451145\pi$
$967$	29.8459	−	12.3626i	0.959780	−	0.397554i	0.806898	+	0.590691i	$0.201145\pi$
$968$			0.0388125i			0.00124748i
$969$	−25.7053	+	24.5739i	−0.825773	+	0.789426i
$970$	16.9808			0.545220
$971$	−5.54789	+	2.29801i	−0.178040	+	0.0737466i	−0.469923	−	0.882707i	$-0.655718\pi$
$971$	−5.54789	+	2.29801i	−0.178040	+	0.0737466i	0.291883	+	0.956454i	$0.405718\pi$
$972$	6.32307	+	9.46314i	0.202812	+	0.303530i
$973$	−32.4318	−	24.3831i	−1.03972	−	0.781685i
$974$	21.8554	+	4.34731i	0.700292	+	0.139297i
$975$	3.23054	+	2.15858i	0.103460	+	0.0691298i
$976$	0.754288	+	3.79206i	0.0241442	+	0.121381i
$977$	27.5685	+	11.4192i	0.881994	+	0.365334i	0.777270	−	0.629167i	$-0.216604\pi$
$977$	27.5685	+	11.4192i	0.881994	+	0.365334i	0.104724	+	0.994501i	$0.466604\pi$
$978$	3.79105	+	1.57031i	0.121224	+	0.0502128i
$979$	−26.8857	+	5.34789i	−0.859270	+	0.170919i
$980$	−17.8468	−	5.66942i	−0.570094	−	0.181103i
$981$	0.250445	−	1.25907i	0.00799609	−	0.0401991i
$982$	−17.9897	−	17.9897i	−0.574076	−	0.574076i
$983$	12.2312	−	8.17264i	0.390116	−	0.260667i	−0.345008	−	0.938600i	$-0.612124\pi$
$983$	12.2312	−	8.17264i	0.390116	−	0.260667i	0.735124	+	0.677933i	$0.237124\pi$
$984$	−9.47558	+	3.92491i	−0.302070	+	0.125122i
$985$	−34.5432			−1.10064
$986$	0.163891	−	7.28312i	0.00521935	−	0.231942i
$987$	−37.2861	+	5.28216i	−1.18683	+	0.168133i
$988$	−3.25733	−	7.86389i	−0.103629	−	0.250184i
$989$	−19.8245	+	13.2463i	−0.630381	+	0.421207i
$990$	7.37842	+	7.37842i	0.234502	+	0.234502i
$991$	−33.0405	−	6.57217i	−1.04957	−	0.208772i	−0.359969	−	0.932964i	$-0.617213\pi$
$991$	−33.0405	−	6.57217i	−1.04957	−	0.208772i	−0.689598	+	0.724192i	$0.742213\pi$
$992$	−5.42792	+	8.12346i	−0.172337	+	0.257920i
$993$	0.799459	+	4.01915i	0.0253701	+	0.127544i
$994$	−28.3168	−	7.28989i	−0.898153	−	0.231221i
$995$	−8.07064	+	19.4843i	−0.255857	+	0.617692i
$996$	2.20805	+	11.1006i	0.0699648	+	0.351737i
$997$	−27.3629	−	18.2833i	−0.866590	−	0.579037i	0.0408749	−	0.999164i	$-0.486985\pi$
$997$	−27.3629	−	18.2833i	−0.866590	−	0.579037i	−0.907465	+	0.420127i	$0.861985\pi$
$998$	6.02730	−	30.3013i	0.190791	−	0.959170i
$999$	−4.07972	+	4.07972i	−0.129077	+	0.129077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	238.2.p.b.97.5	yes	48
7.6	odd	2	inner	238.2.p.b.97.2	yes	48
17.10	odd	16	inner	238.2.p.b.27.2	✓	48
119.27	even	16	inner	238.2.p.b.27.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
238.2.p.b.27.2	✓	48	17.10	odd	16	inner
238.2.p.b.27.5	yes	48	119.27	even	16	inner
238.2.p.b.97.2	yes	48	7.6	odd	2	inner
238.2.p.b.97.5	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 238 = 2 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	238.p (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.382683 + 0.923880i) q^{2} +(0.750734 + 1.12355i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(-0.521884 + 2.62369i) q^{5} +(-0.750734 + 1.12355i) q^{6} +(-2.49686 + 0.875034i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(0.449281 - 1.08466i) q^{9} +O(q^{10})\)	\(q+(0.382683 + 0.923880i) q^{2} +(0.750734 + 1.12355i) q^{3} +(-0.707107 + 0.707107i) q^{4} +(-0.521884 + 2.62369i) q^{5} +(-0.750734 + 1.12355i) q^{6} +(-2.49686 + 0.875034i) q^{7} +(-0.923880 - 0.382683i) q^{8} +(0.449281 - 1.08466i) q^{9} +(-2.62369 + 0.521884i) q^{10} +(1.84587 - 2.76253i) q^{11} +(-1.32532 - 0.263623i) q^{12} +(-0.942965 + 0.942965i) q^{13} +(-1.76393 - 1.97194i) q^{14} +(-3.33965 + 1.38333i) q^{15} -1.00000i q^{16} +(-0.895150 + 4.02476i) q^{17} +1.17403 q^{18} +(5.89694 - 2.44259i) q^{19} +(-1.48620 - 2.22426i) q^{20} +(-2.85763 - 2.14844i) q^{21} +(3.25863 + 0.648182i) q^{22} +(6.35280 + 4.24480i) q^{23} +(-0.263623 - 1.32532i) q^{24} +(-1.99199 - 0.825109i) q^{25} +(-1.23204 - 0.510329i) q^{26} +(5.53193 - 1.10037i) q^{27} +(1.14680 - 2.38429i) q^{28} +(-0.344698 + 1.73291i) q^{29} +(-2.55606 - 2.55606i) q^{30} +(-8.12346 + 5.42792i) q^{31} +(0.923880 - 0.382683i) q^{32} +4.48961 q^{33} +(-4.06095 + 0.713199i) q^{34} +(-0.992746 - 7.00766i) q^{35} +(0.449281 + 1.08466i) q^{36} +(-0.850529 + 0.568305i) q^{37} +(4.51332 + 4.51332i) q^{38} +(-1.76739 - 0.351555i) q^{39} +(1.48620 - 2.22426i) q^{40} +(-1.48074 - 7.44419i) q^{41} +(0.891331 - 3.46227i) q^{42} +(-1.19420 + 2.88305i) q^{43} +(0.648182 + 3.25863i) q^{44} +(2.61134 + 1.74484i) q^{45} +(-1.49058 + 7.49364i) q^{46} +(7.44818 - 7.44818i) q^{47} +(1.12355 - 0.750734i) q^{48} +(5.46863 - 4.36968i) q^{49} -2.15611i q^{50} +(-5.19405 + 2.01578i) q^{51} -1.33355i q^{52} +(-4.22081 - 10.1899i) q^{53} +(3.13358 + 4.68974i) q^{54} +(6.28470 + 6.28470i) q^{55} +(2.64166 + 0.147081i) q^{56} +(7.17141 + 4.79179i) q^{57} +(-1.73291 + 0.344698i) q^{58} +(1.22220 - 2.95065i) q^{59} +(1.38333 - 3.33965i) q^{60} +(-3.79206 + 0.754288i) q^{61} +(-8.12346 - 5.42792i) q^{62} +(-0.172677 + 3.10138i) q^{63} +(0.707107 + 0.707107i) q^{64} +(-1.98193 - 2.96617i) q^{65} +(1.71810 + 4.14785i) q^{66} +4.08800i q^{67} +(-2.21297 - 3.47890i) q^{68} +10.3244i q^{69} +(6.09432 - 3.59889i) q^{70} +(9.18916 - 6.14000i) q^{71} +(-0.830163 + 0.830163i) q^{72} +(-1.09021 + 5.48087i) q^{73} +(-0.850529 - 0.568305i) q^{74} +(-0.568400 - 2.85754i) q^{75} +(-2.44259 + 5.89694i) q^{76} +(-2.19156 + 8.51286i) q^{77} +(-0.351555 - 1.76739i) q^{78} +(8.71748 - 13.0466i) q^{79} +(2.62369 + 0.521884i) q^{80} +(2.89884 + 2.89884i) q^{81} +(6.31088 - 4.21679i) q^{82} +(-3.20528 - 7.73824i) q^{83} +(3.53982 - 0.501472i) q^{84} +(-10.0926 - 4.44906i) q^{85} -3.12059 q^{86} +(-2.20580 + 0.913671i) q^{87} +(-2.76253 + 1.84587i) q^{88} +(-5.83406 - 5.83406i) q^{89} +(-0.612707 + 3.08029i) q^{90} +(1.52933 - 3.17958i) q^{91} +(-7.49364 + 1.49058i) q^{92} +(-12.1971 - 5.05221i) q^{93} +(9.73152 + 4.03093i) q^{94} +(3.33108 + 16.7465i) q^{95} +(1.12355 + 0.750734i) q^{96} +(-6.22576 - 1.23838i) q^{97} +(6.12981 + 3.38015i) q^{98} +(-2.16710 - 3.24329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 16 q^{11} - 8 q^{14} + 64 q^{15} - 80 q^{18} - 48 q^{21} + 16 q^{22} - 16 q^{25} + 8 q^{28} + 32 q^{29} + 16 q^{39} - 24 q^{42} - 16 q^{43} + 16 q^{44} - 16 q^{46} + 16 q^{49} + 32 q^{51} - 48 q^{53} + 64 q^{57} + 16 q^{58} + 32 q^{60} - 104 q^{63} - 48 q^{65} + 16 q^{70} - 112 q^{71} - 16 q^{72} - 40 q^{77} - 64 q^{78} + 32 q^{79} + 112 q^{81} - 176 q^{85} + 32 q^{86} + 16 q^{88} + 80 q^{91} - 32 q^{93} - 32 q^{95} - 96 q^{99}+O(q^{100}) \) 48 * q - 16 * q^11 - 8 * q^14 + 64 * q^15 - 80 * q^18 - 48 * q^21 + 16 * q^22 - 16 * q^25 + 8 * q^28 + 32 * q^29 + 16 * q^39 - 24 * q^42 - 16 * q^43 + 16 * q^44 - 16 * q^46 + 16 * q^49 + 32 * q^51 - 48 * q^53 + 64 * q^57 + 16 * q^58 + 32 * q^60 - 104 * q^63 - 48 * q^65 + 16 * q^70 - 112 * q^71 - 16 * q^72 - 40 * q^77 - 64 * q^78 + 32 * q^79 + 112 * q^81 - 176 * q^85 + 32 * q^86 + 16 * q^88 + 80 * q^91 - 32 * q^93 - 32 * q^95 - 96 * q^99

Introduction

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