LMFDB - Embedded newform 961.2.d.s.628.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [64,8,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			628.11
Character	$\chi$	$=$	961.628
Dual form			961.2.d.s.531.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0383721 - 0.118097i) q^{2} +(-0.457114 - 1.40685i) q^{3} +(1.60556 + 1.16651i) q^{4} -1.22944 q^{5} -0.183686 q^{6} +(-2.15767 - 1.56764i) q^{7} +(0.400289 - 0.290827i) q^{8} +(0.656767 - 0.477169i) q^{9} +(-0.0471763 + 0.145194i) q^{10} +(-4.55632 - 3.31036i) q^{11} +(0.907181 - 2.79201i) q^{12} +(0.00416104 + 0.0128063i) q^{13} +(-0.267928 + 0.194661i) q^{14} +(0.561997 + 1.72965i) q^{15} +(1.20755 + 3.71646i) q^{16} +(2.86784 - 2.08361i) q^{17} +(-0.0311508 - 0.0958723i) q^{18} +(-1.84293 + 5.67196i) q^{19} +(-1.97395 - 1.43416i) q^{20} +(-1.21914 + 3.75212i) q^{21} +(-0.565779 + 0.411063i) q^{22} +(-3.30863 + 2.40386i) q^{23} +(-0.592128 - 0.430206i) q^{24} -3.48847 q^{25} +0.00167206 q^{26} +(-4.56175 - 3.31430i) q^{27} +(-1.63561 - 5.03388i) q^{28} +(0.916226 - 2.81985i) q^{29} +0.225832 q^{30} +1.47481 q^{32} +(-2.57443 + 7.92329i) q^{33} +(-0.136023 - 0.418637i) q^{34} +(2.65274 + 1.92733i) q^{35} +1.61110 q^{36} -10.6352 q^{37} +(0.599125 + 0.435290i) q^{38} +(0.0161146 - 0.0117079i) q^{39} +(-0.492133 + 0.357555i) q^{40} +(-2.20784 + 6.79504i) q^{41} +(0.396333 + 0.287953i) q^{42} +(0.981323 - 3.02020i) q^{43} +(-3.45388 - 10.6300i) q^{44} +(-0.807459 + 0.586654i) q^{45} +(0.156930 + 0.482981i) q^{46} +(-3.03154 - 9.33014i) q^{47} +(4.67653 - 3.39770i) q^{48} +(0.0349290 + 0.107500i) q^{49} +(-0.133860 + 0.411978i) q^{50} +(-4.24227 - 3.08219i) q^{51} +(-0.00825791 + 0.0254152i) q^{52} +(6.39793 - 4.64837i) q^{53} +(-0.566454 + 0.411553i) q^{54} +(5.60174 + 4.06990i) q^{55} -1.31960 q^{56} +8.82205 q^{57} +(-0.297859 - 0.216407i) q^{58} +(-3.21097 - 9.88236i) q^{59} +(-1.11533 + 3.43263i) q^{60} -3.70951 q^{61} -2.16512 q^{63} +(-2.35851 + 7.25876i) q^{64} +(-0.00511576 - 0.0157447i) q^{65} +(0.836931 + 0.608066i) q^{66} +3.56973 q^{67} +7.03504 q^{68} +(4.89430 + 3.55592i) q^{69} +(0.329403 - 0.239325i) q^{70} +(-3.04327 + 2.21107i) q^{71} +(0.124123 - 0.382011i) q^{72} +(-2.87218 - 2.08676i) q^{73} +(-0.408096 + 1.25599i) q^{74} +(1.59463 + 4.90776i) q^{75} +(-9.57532 + 6.95688i) q^{76} +(4.64158 + 14.2853i) q^{77} +(-0.000764323 - 0.00235234i) q^{78} +(-2.63729 + 1.91611i) q^{79} +(-1.48462 - 4.56919i) q^{80} +(-1.82491 + 5.61650i) q^{81} +(0.717755 + 0.521480i) q^{82} +(-0.639738 + 1.96891i) q^{83} +(-6.33427 + 4.60211i) q^{84} +(-3.52586 + 2.56168i) q^{85} +(-0.319022 - 0.231783i) q^{86} -4.38594 q^{87} -2.78658 q^{88} +(7.12284 + 5.17504i) q^{89} +(0.0382982 + 0.117870i) q^{90} +(0.0110976 - 0.0341549i) q^{91} -8.11632 q^{92} -1.21819 q^{94} +(2.26578 - 6.97336i) q^{95} +(-0.674156 - 2.07484i) q^{96} +(-2.74054 - 1.99112i) q^{97} +0.0140358 q^{98} -4.57204 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{2} - 8 q^{4} - 64 q^{5} + 16 q^{7} - 8 q^{10} + 8 q^{14} + 8 q^{16} + 24 q^{18} + 32 q^{19} + 24 q^{20} + 8 q^{28} - 32 q^{32} + 32 q^{33} + 16 q^{35} - 160 q^{36} + 24 q^{38} + 32 q^{39} + 32 q^{41}+ \cdots + 64 q^{98}+O(q^{100}) $ 64 * q + 8 * q^2 - 8 * q^4 - 64 * q^5 + 16 * q^7 - 8 * q^10 + 8 * q^14 + 8 * q^16 + 24 * q^18 + 32 * q^19 + 24 * q^20 + 8 * q^28 - 32 * q^32 + 32 * q^33 + 16 * q^35 - 160 * q^36 + 24 * q^38 + 32 * q^39 + 32 * q^41 + 16 * q^45 + 32 * q^47 + 16 * q^49 + 32 * q^50 + 32 * q^51 - 192 * q^56 + 64 * q^59 - 64 * q^63 + 16 * q^64 + 64 * q^67 + 32 * q^69 - 88 * q^70 + 48 * q^71 - 48 * q^72 - 40 * q^76 - 32 * q^78 + 40 * q^80 + 16 * q^81 - 88 * q^82 - 128 * q^87 - 40 * q^90 - 128 * q^94 + 48 * q^95 + 64 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.0383721	−	0.118097i	0.0271332	−	0.0835073i	−0.936573	−	0.350473i	$-0.886021\pi$
$2$	0.0383721	−	0.118097i	0.0271332	−	0.0835073i	0.963706	+	0.266965i	$0.0860210\pi$
$3$	−0.457114	−	1.40685i	−0.263915	−	0.812247i	−0.991941	−	0.126698i	$-0.959562\pi$
$3$	−0.457114	−	1.40685i	−0.263915	−	0.812247i	0.728026	−	0.685549i	$-0.240438\pi$
$4$	1.60556	+	1.16651i	0.802780	+	0.583254i
$5$	−1.22944			−0.549824			−0.274912	−	0.961469i	$-0.588649\pi$
$5$	−1.22944			−0.549824			−0.274912	+	0.961469i	$0.588649\pi$
$6$	−0.183686			−0.0749894
$7$	−2.15767	−	1.56764i	−0.815523	−	0.592512i	0.0999038	−	0.994997i	$-0.468146\pi$
$7$	−2.15767	−	1.56764i	−0.815523	−	0.592512i	−0.915426	+	0.402485i	$0.868146\pi$
$8$	0.400289	−	0.290827i	0.141523	−	0.102823i
$9$	0.656767	−	0.477169i	0.218922	−	0.159056i
$10$	−0.0471763	+	0.145194i	−0.0149185	+	0.0459143i
$11$	−4.55632	−	3.31036i	−1.37378	−	0.998111i	−0.997431	−	0.0716336i	$-0.977179\pi$
$11$	−4.55632	−	3.31036i	−1.37378	−	0.998111i	−0.376351	−	0.926477i	$-0.622821\pi$
$12$	0.907181	−	2.79201i	0.261880	−	0.805985i
$13$	0.00416104	+	0.0128063i	0.00115406	+	0.00355184i	0.951632	−	0.307241i	$-0.0994056\pi$
$13$	0.00416104	+	0.0128063i	0.00115406	+	0.00355184i	−0.950478	+	0.310792i	$0.899406\pi$
$14$	−0.267928	+	0.194661i	−0.0716067	+	0.0520253i
$15$	0.561997	+	1.72965i	0.145107	+	0.446593i
$16$	1.20755	+	3.71646i	0.301888	+	0.929116i
$17$	2.86784	−	2.08361i	0.695554	−	0.505350i	−0.182927	−	0.983127i	$-0.558557\pi$
$17$	2.86784	−	2.08361i	0.695554	−	0.505350i	0.878481	+	0.477777i	$0.158557\pi$
$18$	−0.0311508	−	0.0958723i	−0.00734231	−	0.0225973i
$19$	−1.84293	+	5.67196i	−0.422797	+	1.30124i	0.482290	+	0.876012i	$0.339805\pi$
$19$	−1.84293	+	5.67196i	−0.422797	+	1.30124i	−0.905088	+	0.425225i	$0.860195\pi$
$20$	−1.97395	−	1.43416i	−0.441388	−	0.320687i
$21$	−1.21914	+	3.75212i	−0.266037	+	0.818779i
$22$	−0.565779	+	0.411063i	−0.120625	+	0.0876389i
$23$	−3.30863	+	2.40386i	−0.689897	+	0.501239i	−0.876626	−	0.481172i	$-0.840211\pi$
$23$	−3.30863	+	2.40386i	−0.689897	+	0.501239i	0.186729	+	0.982411i	$0.440211\pi$
$24$	−0.592128	−	0.430206i	−0.120868	−	0.0878155i
$25$	−3.48847			−0.697693
$26$	0.00167206			0.000327918
$27$	−4.56175	−	3.31430i	−0.877909	−	0.637838i
$28$	−1.63561	−	5.03388i	−0.309100	−	0.951313i
$29$	0.916226	−	2.81985i	0.170139	−	0.523633i	−0.829239	−	0.558894i	$-0.811226\pi$
$29$	0.916226	−	2.81985i	0.170139	−	0.523633i	0.999378	+	0.0352602i	$0.0112260\pi$
$30$	0.225832			0.0412310
$31$		0			0
$31$		0			0
$32$	1.47481			0.260712
$33$	−2.57443	+	7.92329i	−0.448151	+	1.37927i
$34$	−0.136023	−	0.418637i	−0.0233278	−	0.0717956i
$35$	2.65274	+	1.92733i	0.448394	+	0.325778i
$36$	1.61110			0.268517
$37$	−10.6352			−1.74842			−0.874211	−	0.485546i	$-0.838621\pi$
$37$	−10.6352			−1.74842			−0.874211	+	0.485546i	$0.838621\pi$
$38$	0.599125	+	0.435290i	0.0971909	+	0.0706133i
$39$	0.0161146	−	0.0117079i	0.00258040	−	0.00187477i
$40$	−0.492133	+	0.357555i	−0.0778130	+	0.0565345i
$41$	−2.20784	+	6.79504i	−0.344807	+	1.06121i	0.616880	+	0.787057i	$0.288396\pi$
$41$	−2.20784	+	6.79504i	−0.344807	+	1.06121i	−0.961687	+	0.274150i	$0.911604\pi$
$42$	0.396333	+	0.287953i	0.0611556	+	0.0444321i
$43$	0.981323	−	3.02020i	0.149650	−	0.460577i	−0.847929	−	0.530109i	$-0.822151\pi$
$43$	0.981323	−	3.02020i	0.149650	−	0.460577i	0.997580	+	0.0695329i	$0.0221509\pi$
$44$	−3.45388	−	10.6300i	−0.520692	−	1.60253i
$45$	−0.807459	+	0.586654i	−0.120369	+	0.0874531i
$46$	0.156930	+	0.482981i	0.0231381	+	0.0712116i
$47$	−3.03154	−	9.33014i	−0.442196	−	1.36094i	−0.885529	−	0.464583i	$-0.846204\pi$
$47$	−3.03154	−	9.33014i	−0.442196	−	1.36094i	0.443333	−	0.896357i	$-0.353796\pi$
$48$	4.67653	−	3.39770i	0.674999	−	0.490416i
$49$	0.0349290	+	0.107500i	0.00498985	+	0.0153572i
$50$	−0.133860	+	0.411978i	−0.0189306	+	0.0582624i
$51$	−4.24227	−	3.08219i	−0.594036	−	0.431593i
$52$	−0.00825791	+	0.0254152i	−0.00114517	+	0.00352446i
$53$	6.39793	−	4.64837i	0.878824	−	0.638503i	−0.0541162	−	0.998535i	$-0.517234\pi$
$53$	6.39793	−	4.64837i	0.878824	−	0.638503i	0.932940	+	0.360032i	$0.117234\pi$
$54$	−0.566454	+	0.411553i	−0.0770846	+	0.0560052i
$55$	5.60174	+	4.06990i	0.755339	+	0.548786i
$56$	−1.31960			−0.176339
$57$	8.82205			1.16851
$58$	−0.297859	−	0.216407i	−0.0391108	−	0.0284157i
$59$	−3.21097	−	9.88236i	−0.418033	−	1.28657i	−0.909510	−	0.415683i	$-0.863543\pi$
$59$	−3.21097	−	9.88236i	−0.418033	−	1.28657i	0.491476	−	0.870891i	$-0.336457\pi$
$60$	−1.11533	+	3.43263i	−0.143988	+	0.443150i
$61$	−3.70951			−0.474954			−0.237477	−	0.971393i	$-0.576320\pi$
$61$	−3.70951			−0.474954			−0.237477	+	0.971393i	$0.576320\pi$
$62$		0			0
$63$	−2.16512			−0.272779
$64$	−2.35851	+	7.25876i	−0.294814	+	0.907345i
$65$	−0.00511576	−	0.0157447i	−0.000634532	−	0.00195289i
$66$	0.836931	+	0.608066i	0.103019	+	0.0748477i
$67$	3.56973			0.436112			0.218056	−	0.975936i	$-0.430028\pi$
$67$	3.56973			0.436112			0.218056	+	0.975936i	$0.430028\pi$
$68$	7.03504			0.853124
$69$	4.89430	+	3.55592i	0.589205	+	0.428082i
$70$	0.329403	−	0.239325i	0.0393711	−	0.0286048i
$71$	−3.04327	+	2.21107i	−0.361170	+	0.262405i	−0.753540	−	0.657402i	$-0.771655\pi$
$71$	−3.04327	+	2.21107i	−0.361170	+	0.262405i	0.392370	+	0.919807i	$0.371655\pi$
$72$	0.124123	−	0.382011i	0.0146280	−	0.0450204i
$73$	−2.87218	−	2.08676i	−0.336163	−	0.244237i	0.406878	−	0.913482i	$-0.366617\pi$
$73$	−2.87218	−	2.08676i	−0.336163	−	0.244237i	−0.743041	+	0.669246i	$0.766617\pi$
$74$	−0.408096	+	1.25599i	−0.0474402	+	0.146006i
$75$	1.59463	+	4.90776i	0.184132	+	0.566699i
$76$	−9.57532	+	6.95688i	−1.09836	+	0.798008i
$77$	4.64158	+	14.2853i	0.528958	+	1.62796i
$78$	−0.000764323	−	0.00235234i	−8.65425e−5	−	0.000266351i
$79$	−2.63729	+	1.91611i	−0.296719	+	0.215579i	−0.726177	−	0.687508i	$-0.758705\pi$
$79$	−2.63729	+	1.91611i	−0.296719	+	0.215579i	0.429458	+	0.903087i	$0.358705\pi$
$80$	−1.48462	−	4.56919i	−0.165985	−	0.510851i
$81$	−1.82491	+	5.61650i	−0.202768	+	0.624056i
$82$	0.717755	+	0.521480i	0.0792628	+	0.0575878i
$83$	−0.639738	+	1.96891i	−0.0702204	+	0.216116i	−0.980008	−	0.198958i	$-0.936244\pi$
$83$	−0.639738	+	1.96891i	−0.0702204	+	0.216116i	0.909788	+	0.415074i	$0.136244\pi$
$84$	−6.33427	+	4.60211i	−0.691125	+	0.502132i
$85$	−3.52586	+	2.56168i	−0.382433	+	0.277854i
$86$	−0.319022	−	0.231783i	−0.0344010	−	0.0249938i
$87$	−4.38594			−0.470222
$88$	−2.78658			−0.297051
$89$	7.12284	+	5.17504i	0.755019	+	0.548553i	0.897379	−	0.441262i	$-0.145469\pi$
$89$	7.12284	+	5.17504i	0.755019	+	0.548553i	−0.142360	+	0.989815i	$0.545469\pi$
$90$	0.0382982	+	0.117870i	0.00403698	+	0.0124246i
$91$	0.0110976	−	0.0341549i	0.00116334	−	0.00358040i
$92$	−8.11632			−0.846185
$93$		0			0
$94$	−1.21819			−0.125647
$95$	2.26578	−	6.97336i	0.232464	−	0.715452i
$96$	−0.674156	−	2.07484i	−0.0688057	−	0.211762i
$97$	−2.74054	−	1.99112i	−0.278260	−	0.202168i	0.439898	−	0.898048i	$-0.355014\pi$
$97$	−2.74054	−	1.99112i	−0.278260	−	0.202168i	−0.718158	+	0.695880i	$0.755014\pi$
$98$	0.0140358			0.00141783
$99$	−4.57204			−0.459508
$100$	−5.60094	−	4.06932i	−0.560094	−	0.406932i
$101$	7.01285	−	5.09514i	0.697805	−	0.506985i	−0.181412	−	0.983407i	$-0.558067\pi$
$101$	7.01285	−	5.09514i	0.697805	−	0.506985i	0.879217	+	0.476422i	$0.158067\pi$
$102$	−0.526782	+	0.382730i	−0.0521592	+	0.0378959i
$103$	0.828462	−	2.54974i	0.0816308	−	0.251234i	−0.901909	−	0.431927i	$-0.857834\pi$
$103$	0.828462	−	2.54974i	0.0816308	−	0.251234i	0.983540	+	0.180693i	$0.0578340\pi$
$104$	0.00539004	+	0.00391610i	0.000528537	+	0.000384005i
$105$	1.49886	−	4.61302i	0.146274	−	0.450185i
$106$	−0.303457	−	0.933945i	−0.0294744	−	0.0907128i
$107$	6.45248	−	4.68800i	0.623784	−	0.453206i	−0.230457	−	0.973083i	$-0.574022\pi$
$107$	6.45248	−	4.68800i	0.623784	−	0.453206i	0.854241	+	0.519877i	$0.174022\pi$
$108$	−3.45800	−	10.6426i	−0.332746	−	1.02409i
$109$	1.94648	+	5.99066i	0.186439	+	0.573801i	0.999970	−	0.00772042i	$-0.00245751\pi$
$109$	1.94648	+	5.99066i	0.186439	+	0.573801i	−0.813531	+	0.581522i	$0.802458\pi$
$110$	0.695594	−	0.505379i	0.0663223	−	0.0481860i
$111$	4.86152	+	14.9622i	0.461435	+	1.42015i
$112$	3.22057	−	9.91191i	0.304316	−	0.936587i
$113$	2.22259	+	1.61481i	0.209084	+	0.151908i	0.687399	−	0.726280i	$-0.258752\pi$
$113$	2.22259	+	1.61481i	0.209084	+	0.151908i	−0.478315	+	0.878188i	$0.658752\pi$
$114$	0.338520	−	1.04186i	0.0317053	−	0.0975790i
$115$	4.06778	−	2.95541i	0.379322	−	0.275594i
$116$	4.76043	−	3.45866i	0.441995	−	0.321128i
$117$	0.00884363	+	0.00642527i	0.000817594	+	0.000594017i
$118$	−1.29029			−0.118781
$119$	−9.45421			−0.866666
$120$	0.727989	+	0.528915i	0.0664560	+	0.0482831i
$121$	6.40237	+	19.7045i	0.582034	+	1.79132i
$122$	−0.142342	+	0.438082i	−0.0128870	+	0.0396621i
$123$	10.5689			0.952962
$124$		0			0
$125$	10.4361			0.933433
$126$	−0.0830800	+	0.255694i	−0.00740136	+	0.0227790i
$127$	−0.536248	−	1.65040i	−0.0475844	−	0.146450i	0.924441	−	0.381325i	$-0.124532\pi$
$127$	−0.536248	−	1.65040i	−0.0475844	−	0.146450i	−0.972026	+	0.234875i	$0.924532\pi$
$128$	3.15303	+	2.29081i	0.278691	+	0.202481i
$129$	−4.69756			−0.413597
$130$	−0.00205571			−0.000180297
$131$	−5.71926	−	4.15529i	−0.499694	−	0.363049i	0.309206	−	0.950995i	$-0.399937\pi$
$131$	−5.71926	−	4.15529i	−0.499694	−	0.363049i	−0.808900	+	0.587946i	$0.799937\pi$
$132$	−13.3760	+	9.71821i	−1.16423	+	0.845862i
$133$	12.8680	−	9.34917i	1.11580	−	0.810676i
$134$	0.136978	−	0.421575i	0.0118331	−	0.0364185i
$135$	5.60842	+	4.07475i	0.482696	+	0.350699i
$136$	0.541996	−	1.66809i	0.0464758	−	0.143038i
$137$	2.94712	+	9.07032i	0.251790	+	0.774930i	0.994445	+	0.105256i	$0.0335661\pi$
$137$	2.94712	+	9.07032i	0.251790	+	0.774930i	−0.742655	+	0.669674i	$0.766434\pi$
$138$	0.607748	−	0.441555i	0.0517350	−	0.0375876i
$139$	−4.12488	−	12.6951i	−0.349868	−	1.07678i	−0.958926	−	0.283656i	$-0.908453\pi$
$139$	−4.12488	−	12.6951i	−0.349868	−	1.07678i	0.609059	−	0.793125i	$-0.291547\pi$
$140$	2.01089	+	6.18887i	0.169951	+	0.523055i
$141$	−11.7404	+	8.52988i	−0.988718	+	0.718345i
$142$	0.144344	+	0.444245i	0.0121131	+	0.0372802i
$143$	0.0234346	−	0.0721243i	0.00195970	−	0.00603134i
$144$	2.56646	+	1.86465i	0.213872	+	0.155387i
$145$	−1.12645	+	3.46685i	−0.0935465	+	0.287906i
$146$	−0.356652	+	0.259123i	−0.0295167	+	0.0214451i
$147$	0.135271	−	0.0982799i	0.0111569	−	0.00810599i
$148$	−17.0755	−	12.4061i	−1.40360	−	1.01977i
$149$	18.1985			1.49088			0.745440	−	0.666573i	$-0.232239\pi$
$149$	18.1985			1.49088			0.745440	+	0.666573i	$0.232239\pi$
$150$	0.640781			0.0523196
$151$	−5.33596	−	3.87680i	−0.434234	−	0.315490i	0.349106	−	0.937083i	$-0.386485\pi$
$151$	−5.33596	−	3.87680i	−0.434234	−	0.315490i	−0.783340	+	0.621594i	$0.786485\pi$
$152$	0.911853	+	2.80639i	0.0739610	+	0.227629i
$153$	0.889271	−	2.73690i	0.0718933	−	0.221265i
$154$	1.86516			0.150299
$155$		0			0
$156$	0.0395303			0.00316496
$157$	4.85934	−	14.9555i	0.387817	−	1.19358i	−0.546598	−	0.837395i	$-0.684078\pi$
$157$	4.85934	−	14.9555i	0.387817	−	1.19358i	0.934416	−	0.356184i	$-0.115922\pi$
$158$	0.125088	+	0.384982i	0.00995148	+	0.0306275i
$159$	−9.46417	−	6.87612i	−0.750557	−	0.545312i
$160$	−1.81319			−0.143346
$161$	10.9073			0.859617
$162$	0.593267	+	0.431034i	0.0466114	+	0.0338652i
$163$	5.82198	−	4.22992i	0.456013	−	0.331313i	−0.335952	−	0.941879i	$-0.609058\pi$
$163$	5.82198	−	4.22992i	0.456013	−	0.331313i	0.791965	+	0.610566i	$0.209058\pi$
$164$	−11.4713	+	8.33438i	−0.895757	+	0.650806i
$165$	3.16512	−	9.74124i	0.246404	−	0.758355i
$166$	0.207975	+	0.151102i	0.0161420	+	0.0117278i
$167$	−6.32566	+	19.4684i	−0.489494	+	1.50651i	0.335871	+	0.941908i	$0.390969\pi$
$167$	−6.32566	+	19.4684i	−0.489494	+	1.50651i	−0.825365	+	0.564599i	$0.809031\pi$
$168$	0.603209	+	1.85649i	0.0465386	+	0.143231i
$169$	10.5171	−	7.64110i	0.809006	−	0.587777i
$170$	0.167233	+	0.514691i	0.0128262	+	0.0394750i
$171$	1.49611	+	4.60455i	0.114410	+	0.352119i
$172$	5.09866	−	3.70439i	0.388769	−	0.282457i
$173$	−6.51019	−	20.0363i	−0.494960	−	1.52333i	−0.817018	−	0.576612i	$-0.804375\pi$
$173$	−6.51019	−	20.0363i	−0.494960	−	1.52333i	0.322058	−	0.946720i	$-0.395625\pi$
$174$	−0.168298	+	0.517967i	−0.0127586	+	0.0392670i
$175$	7.52696	+	5.46865i	0.568985	+	0.413391i
$176$	6.80084	−	20.9308i	0.512632	−	1.57772i
$177$	−12.4353	+	9.03474i	−0.934691	+	0.679093i
$178$	0.884475	−	0.642609i	0.0662942	−	0.0481656i
$179$	8.47762	+	6.15935i	0.633647	+	0.460371i	0.857662	−	0.514214i	$-0.171916\pi$
$179$	8.47762	+	6.15935i	0.633647	+	0.460371i	−0.224015	+	0.974586i	$0.571916\pi$
$180$	−1.98076			−0.147637
$181$	−9.53710			−0.708887			−0.354443	−	0.935077i	$-0.615330\pi$
$181$	−9.53710			−0.708887			−0.354443	+	0.935077i	$0.615330\pi$
$182$	−0.00360775	−	0.00262119i	−0.000267425	−	0.000194295i
$183$	1.69567	+	5.21873i	0.125348	+	0.385780i
$184$	−0.625300	+	1.92448i	−0.0460977	+	0.141874i
$185$	13.0754			0.961325
$186$		0			0
$187$	−19.9643			−1.45994
$188$	6.01635	−	18.5164i	0.438787	−	1.35045i
$189$	4.64712	+	14.3024i	0.338028	+	1.04034i
$190$	−0.736591	−	0.535165i	−0.0534379	−	0.0388249i
$191$	−10.0046			−0.723905			−0.361952	−	0.932197i	$-0.617890\pi$
$191$	−10.0046			−0.723905			−0.361952	+	0.932197i	$0.617890\pi$
$192$	11.2901			0.814794
$193$	16.7309	+	12.1557i	1.20432	+	0.874988i	0.994703	−	0.102795i	$-0.0327787\pi$
$193$	16.7309	+	12.1557i	1.20432	+	0.874988i	0.209616	+	0.977784i	$0.432779\pi$
$194$	−0.340306	+	0.247246i	−0.0244325	+	0.0177513i
$195$	−0.0198120	+	0.0143943i	−0.00141877	+	0.00103079i
$196$	−0.0693193	+	0.213343i	−0.00495138	+	0.0152388i
$197$	0.609421	+	0.442770i	0.0434194	+	0.0315461i	0.609283	−	0.792953i	$-0.291457\pi$
$197$	0.609421	+	0.442770i	0.0434194	+	0.0315461i	−0.565864	+	0.824499i	$0.691457\pi$
$198$	−0.175439	+	0.539945i	−0.0124679	+	0.0383722i
$199$	3.05637	+	9.40655i	0.216660	+	0.666812i	0.999032	+	0.0439998i	$0.0140101\pi$
$199$	3.05637	+	9.40655i	0.216660	+	0.666812i	−0.782371	+	0.622813i	$0.785990\pi$
$200$	−1.39639	+	1.01454i	−0.0987399	+	0.0717387i
$201$	−1.63177	−	5.02209i	−0.115096	−	0.354231i
$202$	−0.332623	−	1.02371i	−0.0234033	−	0.0720279i
$203$	−6.39742	+	4.64800i	−0.449011	+	0.326226i
$204$	−3.21582	−	9.89728i	−0.225152	−	0.692948i
$205$	2.71442	−	8.35413i	0.189583	−	0.583478i
$206$	−0.269328	−	0.195678i	−0.0187649	−	0.0136335i
$207$	−1.02595	+	3.15755i	−0.0713086	+	0.219465i
$208$	−0.0425697	+	0.0309287i	−0.00295168	+	0.00214452i
$209$	27.1732	−	19.7425i	1.87961	−	1.36562i
$210$	−0.487270	−	0.354022i	−0.0336248	−	0.0244299i
$211$	14.0629			0.968128			0.484064	−	0.875033i	$-0.339160\pi$
$211$	14.0629			0.968128			0.484064	+	0.875033i	$0.339160\pi$
$212$	15.6946			1.07791
$213$	4.50177	+	3.27073i	0.308456	+	0.224106i
$214$	−0.306044	−	0.941907i	−0.0209207	−	0.0643874i
$215$	−1.20648	+	3.71317i	−0.0822814	+	0.253236i
$216$	−2.78990			−0.189829
$217$		0			0
$218$	0.782170			0.0529753
$219$	−1.62285	+	4.99462i	−0.109662	+	0.337505i
$220$	4.24636	+	13.0689i	0.286289	+	0.881108i
$221$	0.0386167	+	0.0280566i	0.00259764	+	0.00188729i
$222$	1.95354			0.131113
$223$	9.89557			0.662656			0.331328	−	0.943516i	$-0.392503\pi$
$223$	9.89557			0.662656			0.331328	+	0.943516i	$0.392503\pi$
$224$	−3.18215	−	2.31197i	−0.212616	−	0.154475i
$225$	−2.29111	+	1.66459i	−0.152741	+	0.110973i
$226$	0.275990	−	0.200518i	0.0183586	−	0.0133383i
$227$	2.90617	−	8.94428i	0.192890	−	0.593653i	−0.807105	−	0.590408i	$-0.798967\pi$
$227$	2.90617	−	8.94428i	0.192890	−	0.593653i	0.999995	−	0.00324524i	$-0.00103299\pi$
$228$	14.1643	+	10.2910i	0.938055	+	0.681537i
$229$	−4.55942	+	14.0325i	−0.301295	+	0.927291i	0.679739	+	0.733454i	$0.262093\pi$
$229$	−4.55942	+	14.0325i	−0.301295	+	0.927291i	−0.981034	+	0.193837i	$0.937907\pi$
$230$	−0.192937	−	0.593798i	−0.0127219	−	0.0391539i
$231$	17.9756	−	13.0601i	1.18271	−	0.859289i
$232$	−0.453334	−	1.39522i	−0.0297628	−	0.0916005i
$233$	−8.83355	−	27.1869i	−0.578705	−	1.78107i	−0.623201	−	0.782062i	$-0.714168\pi$
$233$	−8.83355	−	27.1869i	−0.578705	−	1.78107i	0.0444952	−	0.999010i	$-0.485832\pi$
$234$	0.00109815		0.000797856i	7.17886e−5		5.21575e-5i
$235$	3.72712	+	11.4709i	0.243130	+	0.748278i
$236$	6.37244	−	19.6123i	0.414810	−	1.27665i
$237$	3.90123	+	2.83441i	0.253412	+	0.184114i
$238$	−0.362778	+	1.11652i	−0.0235154	+	0.0723729i
$239$	7.28824	−	5.29522i	0.471437	−	0.342519i	−0.326564	−	0.945175i	$-0.605891\pi$
$239$	7.28824	−	5.29522i	0.471437	−	0.342519i	0.798001	+	0.602656i	$0.205891\pi$
$240$	−5.74954	+	4.17728i	−0.371131	+	0.269642i
$241$	−0.637637	−	0.463270i	−0.0410738	−	0.0298419i	0.567059	−	0.823677i	$-0.308081\pi$
$241$	−0.637637	−	0.463270i	−0.0410738	−	0.0298419i	−0.608133	+	0.793835i	$0.708081\pi$
$242$	2.57271			0.165380
$243$	−8.18011			−0.524754
$244$	−5.95584	−	4.32717i	−0.381283	−	0.277019i
$245$	−0.0429432	−	0.132166i	−0.00274354	−	0.00844376i
$246$	0.405549	−	1.24815i	0.0258569	−	0.0795793i
$247$	−0.0803056			−0.00510972
$248$		0			0
$249$	3.06241			0.194072
$250$	0.400455	−	1.23247i	0.0253270	−	0.0779484i
$251$	−6.10982	−	18.8041i	−0.385648	−	1.18690i	−0.936009	−	0.351977i	$-0.885510\pi$
$251$	−6.10982	−	18.8041i	−0.385648	−	1.18690i	0.550360	−	0.834927i	$-0.314490\pi$
$252$	−3.47622	−	2.52562i	−0.218982	−	0.159099i
$253$	23.0328			1.44806
$254$	−0.215485			−0.0135207
$255$	5.21564	+	3.78938i	0.326616	+	0.237300i
$256$	−11.9578	+	8.68786i	−0.747363	+	0.542991i
$257$	7.30107	−	5.30454i	0.455428	−	0.330888i	−0.336307	−	0.941752i	$-0.609178\pi$
$257$	7.30107	−	5.30454i	0.455428	−	0.330888i	0.791735	+	0.610864i	$0.209178\pi$
$258$	−0.180255	+	0.554768i	−0.0112222	+	0.0345384i
$259$	22.9473	+	16.6722i	1.42588	+	1.03596i
$260$	0.0101526	−	0.0312466i	0.000629640	−	0.00193783i
$261$	−0.743800	−	2.28918i	−0.0460401	−	0.141697i
$262$	−0.710187	+	0.515981i	−0.0438755	+	0.0318774i
$263$	−0.966605	−	2.97490i	−0.0596034	−	0.183440i	0.916822	−	0.399297i	$-0.130746\pi$
$263$	−0.966605	−	2.97490i	−0.0596034	−	0.183440i	−0.976425	+	0.215856i	$0.930746\pi$
$264$	1.27379	+	3.92031i	0.0783962	+	0.241279i
$265$	−7.86591	+	5.71492i	−0.483199	+	0.351065i
$266$	−0.610337	−	1.87842i	−0.0374221	−	0.115174i
$267$	4.02458	−	12.3864i	0.246300	−	0.758034i
$268$	5.73141	+	4.16411i	0.350102	+	0.254364i
$269$	4.31932	−	13.2935i	0.263354	−	0.810519i	−0.728714	−	0.684818i	$-0.759882\pi$
$269$	4.31932	−	13.2935i	0.263354	−	0.810519i	0.992068	−	0.125702i	$-0.0401182\pi$
$270$	0.696423	−	0.505981i	0.0423830	−	0.0307930i
$271$	−11.3738	+	8.26352i	−0.690907	+	0.501973i	−0.876958	−	0.480567i	$-0.840431\pi$
$271$	−11.3738	+	8.26352i	−0.690907	+	0.501973i	0.186051	+	0.982540i	$0.440431\pi$
$272$	11.2067	+	8.14217i	0.679508	+	0.493692i
$273$	−0.0531238			−0.00321520
$274$	1.18427			0.0715441
$275$	15.8946	+	11.5481i	0.958478	+	0.696375i
$276$	3.71009	+	11.4185i	0.223321	+	0.687311i
$277$	6.80511	−	20.9440i	0.408880	−	1.25840i	−0.508732	−	0.860925i	$-0.669886\pi$
$277$	6.80511	−	20.9440i	0.408880	−	1.25840i	0.917612	−	0.397477i	$-0.130114\pi$
$278$	−1.65753			−0.0994121
$279$		0			0
$280$	1.62238			0.0969556
$281$	0.718851	−	2.21240i	0.0428830	−	0.131980i	−0.927323	−	0.374262i	$-0.877896\pi$
$281$	0.718851	−	2.21240i	0.0428830	−	0.131980i	0.970206	+	0.242282i	$0.0778959\pi$
$282$	0.556852	+	1.71381i	0.0331600	+	0.102056i
$283$	−11.2692	−	8.18754i	−0.669883	−	0.486699i	0.200103	−	0.979775i	$-0.435872\pi$
$283$	−11.2692	−	8.18754i	−0.669883	−	0.486699i	−0.869986	+	0.493076i	$0.835872\pi$
$284$	−7.46537			−0.442988
$285$	−10.8462			−0.642475
$286$	−0.00761844	−	0.00553512i	−0.000450488	−	0.000327299i
$287$	15.4160	−	11.2004i	0.909976	−	0.661136i
$288$	0.968606	−	0.703733i	0.0570756	−	0.0414679i
$289$	−1.37019	+	4.21702i	−0.0805995	+	0.248060i
$290$	0.366201	+	0.266061i	0.0215041	+	0.0156236i
$291$	−1.54847	+	4.76571i	−0.0907731	+	0.279371i
$292$	−2.17723	−	6.70083i	−0.127413	−	0.392136i
$293$	−20.9215	+	15.2004i	−1.22225	+	0.888014i	−0.996285	−	0.0861222i	$-0.972552\pi$
$293$	−20.9215	+	15.2004i	−1.22225	+	0.888014i	−0.225962	+	0.974136i	$0.572552\pi$
$294$	−0.00641595	−	0.0197463i	−0.000374186	−	0.00115163i
$295$	3.94771	+	12.1498i	0.229845	+	0.707390i
$296$	−4.25716	+	3.09301i	−0.247443	+	0.179778i
$297$	9.81324	+	30.2021i	0.569422	+	1.75250i
$298$	0.698315	−	2.14919i	0.0404523	−	0.124499i
$299$	−0.0445520	−	0.0323689i	−0.00257651	−	0.00187194i
$300$	−3.16467	+	9.73985i	−0.182712	+	0.562330i
$301$	−6.85196	+	4.97824i	−0.394940	+	0.286941i
$302$	−0.662591	+	0.481400i	−0.0381278	+	0.0277015i
$303$	−10.3738	−	7.53700i	−0.595959	−	0.432989i
$304$	−23.3051			−1.33664
$305$	4.56064			0.261141
$306$	−0.289096	−	0.210041i	−0.0165265	−	0.0120072i
$307$	−0.202611	−	0.623572i	−0.0115636	−	0.0355891i	0.945108	−	0.326757i	$-0.105956\pi$
$307$	−0.202611	−	0.623572i	−0.0115636	−	0.0355891i	−0.956672	+	0.291168i	$0.905956\pi$
$308$	−9.21160	+	28.3504i	−0.524879	+	1.61541i
$309$	−3.96582			−0.225608
$310$		0			0
$311$	−22.0394			−1.24974			−0.624869	−	0.780730i	$-0.714848\pi$
$311$	−22.0394			−1.24974			−0.624869	+	0.780730i	$0.714848\pi$
$312$	0.00304551	−	0.00937311i	0.000172418	−	0.000530648i
$313$	2.93979	+	9.04774i	0.166167	+	0.511409i	0.999120	−	0.0419342i	$-0.0133520\pi$
$313$	2.93979	+	9.04774i	0.166167	+	0.511409i	−0.832954	+	0.553343i	$0.813352\pi$
$314$	−1.57974	−	1.14775i	−0.0891498	−	0.0647711i
$315$	2.66189			0.149981
$316$	−6.46948			−0.363937
$317$	1.69492	+	1.23143i	0.0951959	+	0.0691639i	0.634365	−	0.773034i	$-0.281262\pi$
$317$	1.69492	+	1.23143i	0.0951959	+	0.0691639i	−0.539169	+	0.842198i	$0.681262\pi$
$318$	−1.17521	+	0.853840i	−0.0659025	+	0.0478809i
$319$	−13.5093	+	9.81511i	−0.756378	+	0.549541i
$320$	2.89966	−	8.92424i	0.162096	−	0.498880i
$321$	−9.54485	−	6.93474i	−0.532741	−	0.387059i
$322$	0.418536	−	1.28812i	0.0233241	−	0.0717842i
$323$	6.53292	+	20.1063i	0.363501	+	1.11874i
$324$	−9.48169	+	6.88885i	−0.526761	+	0.382714i
$325$	−0.0145156	−	0.0446745i	−0.000805182	−	0.00247810i
$326$	−0.276139	−	0.849870i	−0.0152939	−	0.0470699i
$327$	7.53822	−	5.47684i	0.416864	−	0.302870i
$328$	1.09240	+	3.36208i	0.0603180	+	0.185640i
$329$	−8.08521	+	24.8837i	−0.445752	+	1.37188i
$330$	−1.02896	−	0.747583i	−0.0566424	−	0.0411531i
$331$	0.774826	−	2.38467i	0.0425883	−	0.131073i	−0.927502	−	0.373819i	$-0.878048\pi$
$331$	0.774826	−	2.38467i	0.0425883	−	0.131073i	0.970090	+	0.242746i	$0.0780481\pi$
$332$	−3.32389	+	2.41495i	−0.182422	+	0.132537i
$333$	−6.98488	+	5.07481i	−0.382769	+	0.278098i
$334$	2.05643	+	1.49408i	0.112523	+	0.0817526i
$335$	−4.38878			−0.239785
$336$	−15.4168			−0.841054
$337$	22.0163	+	15.9958i	1.19931	+	0.871347i	0.994216	−	0.107396i	$-0.0342514\pi$
$337$	22.0163	+	15.9958i	1.19931	+	0.871347i	0.205090	+	0.978743i	$0.434251\pi$
$338$	−0.498830	−	1.53524i	−0.0271328	−	0.0835061i
$339$	1.25582	−	3.86501i	0.0682067	−	0.209919i
$340$	−8.64920			−0.469069
$341$		0			0
$342$	0.601193			0.0325088
$343$	−5.67594	+	17.4687i	−0.306472	+	0.943224i
$344$	−0.485543	−	1.49435i	−0.0261787	−	0.0805698i
$345$	−6.01727	−	4.37180i	−0.323959	−	0.235370i
$346$	−2.61604			−0.140639
$347$	24.3284			1.30602			0.653010	−	0.757350i	$-0.273506\pi$
$347$	24.3284			1.30602			0.653010	+	0.757350i	$0.273506\pi$
$348$	−7.04189	−	5.11623i	−0.377485	−	0.274259i
$349$	−9.84219	+	7.15077i	−0.526841	+	0.382772i	−0.819175	−	0.573544i	$-0.805568\pi$
$349$	−9.84219	+	7.15077i	−0.526841	+	0.382772i	0.292334	+	0.956316i	$0.405568\pi$
$350$	0.934657	−	0.679068i	0.0499595	−	0.0362977i
$351$	0.0234625	−	0.0722103i	0.00125234	−	0.00385430i
$352$	−6.71969	−	4.88214i	−0.358161	−	0.260219i
$353$	8.65725	−	26.6443i	0.460779	−	1.41813i	−0.403436	−	0.915008i	$-0.632184\pi$
$353$	8.65725	−	26.6443i	0.460779	−	1.41813i	0.864215	−	0.503123i	$-0.167816\pi$
$354$	0.589810	+	1.81525i	0.0313481	+	0.0964794i
$355$	3.74153	−	2.71838i	0.198580	−	0.144277i
$356$	5.39941	+	16.6177i	0.286168	+	0.880735i
$357$	4.32166	+	13.3007i	0.228726	+	0.703947i
$358$	1.05271	−	0.764835i	0.0556372	−	0.0404228i
$359$	−7.52044	−	23.1455i	−0.396913	−	1.22157i	−0.927461	−	0.373919i	$-0.878014\pi$
$359$	−7.52044	−	23.1455i	−0.396913	−	1.22157i	0.530548	−	0.847655i	$-0.321986\pi$
$360$	−0.152602	+	0.469661i	−0.00804284	+	0.0247533i
$361$	−13.4034	−	9.73815i	−0.705443	−	0.512534i
$362$	−0.365958	+	1.12630i	−0.0192343	+	0.0591972i
$363$	24.7947	−	18.0144i	1.30138	−	0.945511i
$364$	0.0576598	−	0.0418923i	0.00302219	−	0.00219575i
$365$	3.53118	+	2.56555i	0.184831	+	0.134287i
$366$	0.681384			0.0356165
$367$	−1.68920			−0.0881753			−0.0440876	−	0.999028i	$-0.514038\pi$
$367$	−1.68920			−0.0881753			−0.0440876	+	0.999028i	$0.514038\pi$
$368$	−12.9292	−	9.39362i	−0.673981	−	0.489676i
$369$	1.79235	+	5.51628i	0.0933058	+	0.287166i
$370$	0.501732	−	1.54417i	0.0260838	−	0.0802777i
$371$	−21.0916			−1.09502
$372$		0			0
$373$	24.2842			1.25739			0.628695	−	0.777652i	$-0.283589\pi$
$373$	24.2842			1.25739			0.628695	+	0.777652i	$0.283589\pi$
$374$	−0.766072	+	2.35773i	−0.0396126	+	0.121915i
$375$	−4.77049	−	14.6821i	−0.246347	−	0.758179i
$376$	−3.92695	−	2.85309i	−0.202517	−	0.147137i
$377$	0.0399245			0.00205621
$378$	1.86739			0.0960480
$379$	−10.7960	−	7.84372i	−0.554551	−	0.402905i	0.274910	−	0.961470i	$-0.411352\pi$
$379$	−10.7960	−	7.84372i	−0.554551	−	0.402905i	−0.829461	+	0.558565i	$0.811352\pi$
$380$	11.7723	−	8.55310i	0.603908	−	0.438765i
$381$	−2.07675	+	1.50885i	−0.106395	+	0.0773005i
$382$	−0.383896	+	1.18151i	−0.0196418	+	0.0604513i
$383$	−20.2614	−	14.7208i	−1.03531	−	0.752197i	−0.0659458	−	0.997823i	$-0.521006\pi$
$383$	−20.2614	−	14.7208i	−1.03531	−	0.752197i	−0.969365	+	0.245626i	$0.921006\pi$
$384$	1.78154	−	5.48301i	0.0909137	−	0.279804i
$385$	−5.70657	−	17.5630i	−0.290834	−	0.895094i
$386$	2.07756	−	1.50943i	0.105745	−	0.0768281i
$387$	−0.796647	−	2.45183i	−0.0404959	−	0.124633i
$388$	−2.07745	−	6.39372i	−0.105466	−	0.324592i
$389$	−17.7471	+	12.8940i	−0.899813	+	0.653752i	−0.938418	−	0.345502i	$-0.887709\pi$
$389$	−17.7471	+	12.8940i	−0.899813	+	0.653752i	0.0386049	+	0.999255i	$0.487709\pi$
$390$	0.000939693		0.00289208i	4.75832e−5		0.000146446i
$391$	−4.47993	+	13.7878i	−0.226560	+	0.697279i
$392$	0.0452456	+	0.0328729i	0.00228525	+	0.00166033i
$393$	−3.23152	+	9.94560i	−0.163009	+	0.501689i
$394$	0.0756746	−	0.0549808i	0.00381243	−	0.00276989i
$395$	3.24241	−	2.35575i	0.163143	−	0.118530i
$396$	−7.34069	−	5.33332i	−0.368883	−	0.268010i
$397$	2.21630			0.111233			0.0556165	−	0.998452i	$-0.482288\pi$
$397$	2.21630			0.111233			0.0556165	+	0.998452i	$0.482288\pi$
$398$	1.22817			0.0615624
$399$	−19.0351	−	13.8298i	−0.952945	−	0.692355i
$400$	−4.21250	−	12.9648i	−0.210625	−	0.648238i
$401$	−8.24135	+	25.3643i	−0.411553	+	1.26663i	0.503744	+	0.863853i	$0.331955\pi$
$401$	−8.24135	+	25.3643i	−0.411553	+	1.26663i	−0.915298	+	0.402778i	$0.868045\pi$
$402$	−0.655708			−0.0327038
$403$		0			0
$404$	17.2031			0.855885
$405$	2.24363	−	6.90518i	0.111487	−	0.343121i
$406$	0.303433	+	0.933871i	0.0150591	+	0.0463472i
$407$	48.4575	+	35.2065i	2.40195	+	1.74512i
$408$	−2.59451			−0.128448
$409$	−37.8777			−1.87293			−0.936465	−	0.350760i	$-0.885923\pi$
$409$	−37.8777			−1.87293			−0.936465	+	0.350760i	$0.885923\pi$
$410$	−0.882440	−	0.641130i	−0.0435806	−	0.0316632i
$411$	11.4134	−	8.29235i	0.562983	−	0.409031i
$412$	4.30444	−	3.12736i	0.212065	−	0.154074i
$413$	−8.56375	+	26.3565i	−0.421395	+	1.29692i
$414$	0.333530	+	0.242324i	0.0163921	+	0.0119096i
$415$	0.786523	−	2.42067i	0.0386089	−	0.118826i
$416$	0.00613673	+	0.0188869i	0.000300878	+	0.000926007i
$417$	−15.9746	+	11.6062i	−0.782278	+	0.568358i
$418$	−1.28884	−	3.96664i	−0.0630392	−	0.194015i
$419$	−2.83276	−	8.71835i	−0.138390	−	0.425919i	0.857712	−	0.514130i	$-0.171885\pi$
$419$	−2.83276	−	8.71835i	−0.138390	−	0.425919i	−0.996102	+	0.0882107i	$0.971885\pi$
$420$	7.78763	−	5.65805i	0.379998	−	0.276084i
$421$	−1.00989	−	3.10813i	−0.0492192	−	0.151481i	0.923426	−	0.383776i	$-0.125377\pi$
$421$	−1.00989	−	3.10813i	−0.0492192	−	0.151481i	−0.972645	+	0.232295i	$0.925377\pi$
$422$	0.539621	−	1.66078i	0.0262684	−	0.0808457i
$423$	−6.44308	−	4.68117i	−0.313273	−	0.227606i
$424$	1.20915	−	3.72138i	0.0587215	−	0.180726i
$425$	−10.0044	+	7.26861i	−0.485284	+	0.352579i
$426$	0.559005	−	0.406141i	0.0270839	−	0.0196776i
$427$	8.00389	+	5.81517i	0.387336	+	0.281416i
$428$	15.8284			0.765095
$429$	−0.112181			−0.00541613
$430$	0.392220	+	0.284964i	0.0189145	+	0.0137422i
$431$	−7.25281	−	22.3218i	−0.349355	−	1.07521i	−0.959211	−	0.282692i	$-0.908772\pi$
$431$	−7.25281	−	22.3218i	−0.349355	−	1.07521i	0.609855	−	0.792513i	$-0.291228\pi$
$432$	6.80894	−	20.9558i	0.327595	−	1.00824i
$433$	27.3421			1.31398			0.656990	−	0.753900i	$-0.271829\pi$
$433$	27.3421			1.31398			0.656990	+	0.753900i	$0.271829\pi$
$434$		0			0
$435$	5.39227			0.258540
$436$	−3.86295	+	11.8890i	−0.185002	+	0.569378i
$437$	−7.53702	−	23.1966i	−0.360545	−	1.10964i
$438$	0.527578	+	0.383308i	0.0252087	+	0.0183152i
$439$	−33.0439			−1.57710			−0.788551	−	0.614970i	$-0.789168\pi$
$439$	−33.0439			−1.57710			−0.788551	+	0.614970i	$0.789168\pi$
$440$	3.42595			0.163326
$441$	0.0742361	+	0.0539357i	0.00353505	+	0.00256836i
$442$	0.00479521	−	0.00348392i	0.000228085	−	0.000165713i
$443$	10.7814	−	7.83313i	0.512239	−	0.372163i	−0.301434	−	0.953487i	$-0.597465\pi$
$443$	10.7814	−	7.83313i	0.512239	−	0.372163i	0.813672	+	0.581324i	$0.197465\pi$
$444$	−9.64808	+	29.6937i	−0.457878	+	1.40920i
$445$	−8.75713	−	6.36243i	−0.415128	−	0.301608i
$446$	0.379713	−	1.16864i	0.0179800	−	0.0553366i
$447$	−8.31880	−	25.6026i	−0.393466	−	1.21096i
$448$	16.4680	−	11.9647i	0.778040	−	0.565279i
$449$	3.49014	+	10.7415i	0.164710	+	0.506924i	0.999015	−	0.0443786i	$-0.0141308\pi$
$449$	3.49014	+	10.7415i	0.164710	+	0.506924i	−0.834305	+	0.551303i	$0.814131\pi$
$450$	0.108668	+	0.334447i	0.00512268	+	0.0157660i
$451$	32.5537	−	23.6516i	1.53289	−	1.11371i
$452$	1.68482	+	5.18534i	0.0792472	+	0.243898i
$453$	−3.01495	+	9.27905i	−0.141655	+	0.435968i
$454$	−0.944778	−	0.686421i	−0.0443406	−	0.0322153i
$455$	−0.0136439	+	0.0419915i	−0.000639635	+	0.00196859i
$456$	3.53137	−	2.56569i	0.165371	−	0.120149i
$457$	−3.68158	+	2.67482i	−0.172217	+	0.125123i	−0.670555	−	0.741860i	$-0.733944\pi$
$457$	−3.68158	+	2.67482i	−0.172217	+	0.125123i	0.498338	+	0.866983i	$0.333944\pi$
$458$	1.48224	+	1.07691i	0.0692604	+	0.0503207i
$459$	−19.9881			−0.932965
$460$	9.97857			0.465253
$461$	−23.2966	−	16.9260i	−1.08503	−	0.788320i	−0.106477	−	0.994315i	$-0.533957\pi$
$461$	−23.2966	−	16.9260i	−1.08503	−	0.788320i	−0.978553	+	0.205995i	$0.933957\pi$
$462$	−0.852593	−	2.62401i	−0.0396662	−	0.122080i
$463$	3.72413	−	11.4617i	0.173075	−	0.532670i	−0.826465	−	0.562988i	$-0.809652\pi$
$463$	3.72413	−	11.4617i	0.173075	−	0.532670i	0.999540	+	0.0303177i	$0.00965190\pi$
$464$	11.5863			0.537879
$465$		0			0
$466$	−3.54965			−0.164435
$467$	−5.91149	+	18.1937i	−0.273551	+	0.841904i	0.716048	+	0.698051i	$0.245949\pi$
$467$	−5.91149	+	18.1937i	−0.273551	+	0.841904i	−0.989599	+	0.143853i	$0.954051\pi$
$468$	0.00670385	+	0.0206323i	0.000309885	+	0.000953729i
$469$	−7.70230	−	5.59605i	−0.355659	−	0.258401i
$470$	1.49770			0.0690836
$471$	−23.2615			−1.07183
$472$	−4.15937	−	3.02196i	−0.191451	−	0.139097i
$473$	−14.4692	+	10.5125i	−0.665293	+	0.483364i
$474$	0.484433	−	0.351961i	0.0222508	−	0.0161661i
$475$	6.42900	−	19.7864i	0.294983	−	0.907864i
$476$	−15.1793	−	11.0284i	−0.695742	−	0.505486i
$477$	1.98389	−	6.10580i	0.0908363	−	0.279565i
$478$	−0.345685	−	1.06391i	−0.0158113	−	0.0486621i
$479$	9.94368	−	7.22451i	0.454338	−	0.330096i	−0.336968	−	0.941516i	$-0.609401\pi$
$479$	9.94368	−	7.22451i	0.454338	−	0.330096i	0.791306	+	0.611420i	$0.209401\pi$
$480$	0.828837	+	2.55090i	0.0378311	+	0.116432i
$481$	−0.0442536	−	0.136199i	−0.00201779	−	0.00621012i
$482$	−0.0791783	+	0.0575264i	−0.00360647	+	0.00262026i
$483$	−4.98589	−	15.3450i	−0.226866	−	0.698221i
$484$	−12.7060	+	39.1051i	−0.577547	+	1.77751i
$485$	3.36934	+	2.44797i	0.152994	+	0.111157i
$486$	−0.313888	+	0.966047i	−0.0142382	+	0.0438208i
$487$	−12.2378	+	8.89125i	−0.554546	+	0.402901i	−0.829459	−	0.558568i	$-0.811351\pi$
$487$	−12.2378	+	8.89125i	−0.554546	+	0.402901i	0.274913	+	0.961469i	$0.411351\pi$
$488$	−1.48487	+	1.07882i	−0.0672171	+	0.0488361i
$489$	−8.61218	−	6.25712i	−0.389456	−	0.282957i
$490$	−0.0172562			−0.000779556
$491$	30.5340			1.37798			0.688990	−	0.724771i	$-0.258054\pi$
$491$	30.5340			1.37798			0.688990	+	0.724771i	$0.258054\pi$
$492$	16.9689	+	12.3287i	0.765019	+	0.555819i
$493$	−3.24788	−	9.99596i	−0.146277	−	0.450195i
$494$	−0.00308149	+	0.00948386i	−0.000138643	+	0.000426699i
$495$	5.62108			0.252649
$496$		0			0
$497$	10.0325			0.450020
$498$	0.117511	−	0.361661i	0.00526579	−	0.0162064i
$499$	8.90808	+	27.4163i	0.398781	+	1.22732i	0.925978	+	0.377577i	$0.123243\pi$
$499$	8.90808	+	27.4163i	0.398781	+	1.22732i	−0.527197	+	0.849743i	$0.676757\pi$
$500$	16.7558	+	12.1738i	0.749341	+	0.544428i
$501$	30.2807			1.35284
$502$	−2.45516			−0.109579
$503$	2.52240	+	1.83263i	0.112468	+	0.0817130i	0.642598	−	0.766204i	$-0.277857\pi$
$503$	2.52240	+	1.83263i	0.112468	+	0.0817130i	−0.530129	+	0.847917i	$0.677857\pi$
$504$	−0.866672	+	0.629674i	−0.0386046	+	0.0280479i
$505$	−8.62192	+	6.26419i	−0.383670	+	0.278753i
$506$	0.883817	−	2.72011i	0.0392904	−	0.120924i
$507$	−15.5574	−	11.3031i	−0.690929	−	0.501989i
$508$	1.06423	−	3.27536i	0.0472175	−	0.145321i
$509$	−4.10861	−	12.6450i	−0.182111	−	0.560479i	0.817776	−	0.575537i	$-0.195207\pi$
$509$	−4.10861	−	12.6450i	−0.182111	−	0.560479i	−0.999887	+	0.0150575i	$0.995207\pi$
$510$	0.647650	−	0.470545i	0.0286784	−	0.0208361i
$511$	2.92593	+	9.00507i	0.129435	+	0.398361i
$512$	2.97586	+	9.15876i	0.131516	+	0.404764i
$513$	27.2056	−	19.7660i	1.20116	−	0.872691i
$514$	−0.346293	−	1.06578i	−0.0152743	−	0.0470096i
$515$	−1.01855	+	3.13477i	−0.0448826	+	0.138134i
$516$	−7.54221	−	5.47974i	−0.332027	−	0.241232i
$517$	−17.0734	+	52.5466i	−0.750888	+	2.31100i
$518$	2.84948	−	2.07027i	0.125199	−	0.0909623i
$519$	−25.2122	+	18.3178i	−1.10669	+	0.804061i
$520$	−0.00662676	−	0.00481462i	−0.000290603	−	0.000211135i
$521$	8.44298			0.369894			0.184947	−	0.982749i	$-0.440789\pi$
$521$	8.44298			0.369894			0.184947	+	0.982749i	$0.440789\pi$
$522$	−0.298887			−0.0130819
$523$	−32.0890	−	23.3141i	−1.40316	−	1.01945i	−0.994274	−	0.106865i	$-0.965919\pi$
$523$	−32.0890	−	23.3141i	−1.40316	−	1.01945i	−0.408882	−	0.912587i	$-0.634081\pi$
$524$	−4.33544	−	13.3431i	−0.189395	−	0.582897i
$525$	4.25292	−	13.0891i	0.185612	−	0.571256i
$526$	−0.388418			−0.0169358
$527$		0			0
$528$	−32.5554			−1.41679
$529$	−1.93891	+	5.96734i	−0.0843002	+	0.259449i
$530$	0.373084	+	1.14823i	0.0162057	+	0.0498761i
$531$	−6.82442	−	4.95823i	−0.296155	−	0.215169i
$532$	31.5662			1.36857
$533$	−0.0962066			−0.00416717
$534$	−1.30836	−	0.950582i	−0.0566184	−	0.0411357i
$535$	−7.93296	+	5.76363i	−0.342972	+	0.249184i
$536$	1.42892	−	1.03817i	0.0617200	−	0.0448422i
$537$	4.79006	−	14.7423i	0.206706	−	0.636177i
$538$	−1.40418	−	1.02020i	−0.0605386	−	0.0439839i
$539$	0.196717	−	0.605433i	0.00847321	−	0.0260778i
$540$	4.25142	+	13.0845i	0.182952	+	0.563068i
$541$	−17.6602	+	12.8309i	−0.759270	+	0.551642i	−0.898686	−	0.438592i	$-0.855477\pi$
$541$	−17.6602	+	12.8309i	−0.759270	+	0.551642i	0.139416	+	0.990234i	$0.455477\pi$
$542$	0.539463	+	1.66030i	0.0231719	+	0.0713158i
$543$	4.35954	+	13.4173i	0.187086	+	0.575791i
$544$	4.22952	−	3.07293i	0.181339	−	0.131751i
$545$	−2.39309	−	7.36519i	−0.102509	−	0.315490i
$546$	−0.00203847	+	0.00627377i	−8.72385e−5	+	0.000268492i
$547$	−22.1186	−	16.0701i	−0.945725	−	0.687109i	0.00406722	−	0.999992i	$-0.498705\pi$
$547$	−22.1186	−	16.0701i	−0.945725	−	0.687109i	−0.949792	+	0.312883i	$0.898705\pi$
$548$	−5.84881	+	18.0008i	−0.249849	+	0.768955i
$549$	−2.43628	+	1.77006i	−0.103978	+	0.0755445i
$550$	1.97370	−	1.43398i	0.0841589	−	0.0611450i
$551$	14.3055	+	10.3936i	0.609437	+	0.442782i
$552$	2.99329			0.127403
$553$	8.69417			0.369714
$554$	−2.21230	−	1.60733i	−0.0939915	−	0.0682888i
$555$	−5.97697	−	18.3952i	−0.253708	−	0.780834i
$556$	8.18615	−	25.1944i	0.347170	−	1.06848i
$557$	−27.9171			−1.18289			−0.591443	−	0.806347i	$-0.701441\pi$
$557$	−27.9171			−1.18289			−0.591443	+	0.806347i	$0.701441\pi$
$558$		0			0
$559$	0.0427611			0.00180860
$560$	−3.95952	+	12.1861i	−0.167320	+	0.514959i
$561$	9.12598	+	28.0869i	0.385299	+	1.18583i
$562$	−0.233694	−	0.169788i	−0.00985777	−	0.00716209i
$563$	−25.7662			−1.08591			−0.542957	−	0.839760i	$-0.682695\pi$
$563$	−25.7662			−1.08591			−0.542957	+	0.839760i	$0.682695\pi$
$564$	−28.8000			−1.21270
$565$	−2.73255	−	1.98532i	−0.114959	−	0.0835229i
$566$	−1.39935	+	1.01668i	−0.0588189	+	0.0427344i
$567$	12.7422	−	9.25775i	0.535122	−	0.388789i
$568$	−0.575150	+	1.77013i	−0.0241327	+	0.0742729i
$569$	−13.1169	−	9.53000i	−0.549890	−	0.399518i	0.277855	−	0.960623i	$-0.410377\pi$
$569$	−13.1169	−	9.53000i	−0.549890	−	0.399518i	−0.827745	+	0.561105i	$0.810377\pi$
$570$	−0.416192	+	1.28091i	−0.0174324	+	0.0536513i
$571$	−2.89841	−	8.92039i	−0.121295	−	0.373307i	0.871913	−	0.489661i	$-0.162879\pi$
$571$	−2.89841	−	8.92039i	−0.121295	−	0.373307i	−0.993208	+	0.116354i	$0.962879\pi$
$572$	0.121759	−	0.0884633i	0.00509101	−	0.00369883i
$573$	4.57323	+	14.0750i	0.191049	+	0.587990i
$574$	−0.731187	−	2.25036i	−0.0305192	−	0.0939283i
$575$	11.5420	−	8.38578i	0.481336	−	0.349711i
$576$	1.91466	+	5.89273i	0.0797776	+	0.245530i
$577$	9.78854	−	30.1260i	0.407502	−	1.25416i	−0.511286	−	0.859411i	$-0.670831\pi$
$577$	9.78854	−	30.1260i	0.407502	−	1.25416i	0.918788	−	0.394752i	$-0.129169\pi$
$578$	0.445440	+	0.323631i	0.0185279	+	0.0134613i
$579$	9.45338	−	29.0945i	0.392869	−	1.20913i
$580$	−5.85269	+	4.25223i	−0.243020	+	0.176564i
$581$	4.46689	−	3.24538i	0.185318	−	0.134641i
$582$	0.503398	+	0.365740i	0.0208665	+	0.0151604i
$583$	−44.5388			−1.84461
$584$	−1.75658			−0.0726880
$585$	−0.0108728	−	0.00789952i	−0.000449533	−	0.000326605i
$586$	0.992316	+	3.05404i	0.0409922	+	0.126161i
$587$	−0.0577249	+	0.177659i	−0.00238256	+	0.00733278i	−0.952241	−	0.305348i	$-0.901227\pi$
$587$	−0.0577249	+	0.177659i	−0.00238256	+	0.00733278i	0.949858	+	0.312681i	$0.101227\pi$
$588$	0.331829			0.0136844
$589$		0			0
$590$	1.58634			0.0653086
$591$	0.344338	−	1.05976i	0.0141642	−	0.0435928i
$592$	−12.8426	−	39.5255i	−0.527828	−	1.62449i
$593$	10.8949	+	7.91559i	0.447399	+	0.325054i	0.788568	−	0.614948i	$-0.210823\pi$
$593$	10.8949	+	7.91559i	0.447399	+	0.325054i	−0.341169	+	0.940002i	$0.610823\pi$
$594$	3.94333			0.161797
$595$	11.6234			0.476514
$596$	29.2188	+	21.2287i	1.19685	+	0.869561i
$597$	11.8365	−	8.59974i	0.484437	−	0.351964i
$598$	−0.00553223	+	0.00401940i	−0.000226230	+	0.000164365i
$599$	−5.71417	+	17.5864i	−0.233475	+	0.718561i	0.763845	+	0.645399i	$0.223309\pi$
$599$	−5.71417	+	17.5864i	−0.233475	+	0.718561i	−0.997320	+	0.0731620i	$0.976691\pi$
$600$	2.06562	+	1.50076i	0.0843285	+	0.0612683i
$601$	5.51922	−	16.9864i	0.225134	−	0.692890i	−0.773144	−	0.634230i	$-0.781317\pi$
$601$	5.51922	−	16.9864i	0.225134	−	0.692890i	0.998278	−	0.0586601i	$-0.0186828\pi$
$602$	0.324992	+	1.00022i	0.0132457	+	0.0407660i
$603$	2.34448	−	1.70337i	0.0954747	−	0.0693664i
$604$	−4.04488	−	12.4489i	−0.164584	−	0.506537i
$605$	−7.87136	−	24.2256i	−0.320016	−	0.984909i
$606$	−1.28816	+	0.935904i	−0.0523280	+	0.0380185i
$607$	8.94927	+	27.5430i	0.363240	+	1.11794i	0.951076	+	0.308957i	$0.0999798\pi$
$607$	8.94927	+	27.5430i	0.363240	+	1.11794i	−0.587837	+	0.808980i	$0.700020\pi$
$608$	−2.71797	+	8.36505i	−0.110228	+	0.339248i
$609$	9.46341	+	6.87557i	0.383477	+	0.278612i
$610$	0.175001	−	0.538598i	0.00708558	−	0.0218072i
$611$	0.106871	−	0.0776461i	0.00432352	−	0.00314122i
$612$	4.62039	−	3.35691i	0.186768	−	0.135695i
$613$	−16.7017	−	12.1345i	−0.674575	−	0.490108i	0.196978	−	0.980408i	$-0.436887\pi$
$613$	−16.7017	−	12.1345i	−0.674575	−	0.490108i	−0.871554	+	0.490300i	$0.836887\pi$
$614$	−0.0814167			−0.00328571
$615$	−12.9938			−0.523962
$616$	6.01253	+	4.36836i	0.242252	+	0.176006i
$617$	0.215559	+	0.663421i	0.00867806	+	0.0267083i	0.955302	−	0.295632i	$-0.0955303\pi$
$617$	0.215559	+	0.663421i	0.00867806	+	0.0267083i	−0.946624	+	0.322341i	$0.895530\pi$
$618$	−0.152177	+	0.468352i	−0.00612145	+	0.0188399i
$619$	2.41091			0.0969026			0.0484513	−	0.998826i	$-0.484571\pi$
$619$	2.41091			0.0969026			0.0484513	+	0.998826i	$0.484571\pi$
$620$		0			0
$621$	23.0603			0.925376
$622$	−0.845696	+	2.60279i	−0.0339093	+	0.104362i
$623$	−7.25613	−	22.3321i	−0.290711	−	0.894715i
$624$	0.0629713	+	0.0457514i	0.00252087	+	0.00183152i
$625$	4.61172			0.184469
$626$	1.18132			0.0472150
$627$	−40.1961	−	29.2041i	−1.60528	−	1.16630i
$628$	25.2477	−	18.3435i	1.00749	−	0.731985i
$629$	−30.5002	+	22.1597i	−1.21612	+	0.883565i
$630$	0.102142	−	0.314362i	0.00406945	−	0.0125245i
$631$	29.4592	+	21.4034i	1.17275	+	0.852054i	0.991336	−	0.131352i	$-0.0419319\pi$
$631$	29.4592	+	21.4034i	1.17275	+	0.852054i	0.181416	+	0.983406i	$0.441932\pi$
$632$	−0.498424	+	1.53399i	−0.0198262	+	0.0610189i
$633$	−6.42834	−	19.7844i	−0.255504	−	0.786359i
$634$	0.210466	−	0.152912i	0.00835865	−	0.00607292i
$635$	0.659288	+	2.02908i	0.0261630	+	0.0805216i
$636$	−7.17424	−	22.0800i	−0.284477	−	0.875530i
$637$	−0.00123135		0.000894625i	−4.87877e−5		3.54463e-5i
$638$	0.640755	+	1.97204i	0.0253677	+	0.0780738i
$639$	−0.943668	+	2.90431i	−0.0373309	+	0.114893i
$640$	−3.87647	−	2.81642i	−0.153231	−	0.111329i
$641$	−0.664297	+	2.04450i	−0.0262382	+	0.0807527i	−0.963318	−	0.268362i	$-0.913518\pi$
$641$	−0.664297	+	2.04450i	−0.0262382	+	0.0807527i	0.937080	+	0.349115i	$0.113518\pi$
$642$	−1.18523	+	0.861118i	−0.0467772	+	0.0339856i
$643$	−14.3562	+	10.4304i	−0.566155	+	0.411336i	−0.833706	−	0.552208i	$-0.813785\pi$
$643$	−14.3562	+	10.4304i	−0.566155	+	0.411336i	0.267552	+	0.963544i	$0.413785\pi$
$644$	17.5123	+	12.7235i	0.690083	+	0.501375i
$645$	5.77539			0.227406
$646$	2.62517			0.103286
$647$	32.4985	+	23.6115i	1.27765	+	0.928265i	0.999479	−	0.0322678i	$-0.0102729\pi$
$647$	32.4985	+	23.6115i	1.27765	+	0.928265i	0.278168	+	0.960533i	$0.410273\pi$
$648$	0.902937	+	2.77895i	0.0354707	+	0.109168i
$649$	−18.0839	+	55.6567i	−0.709857	+	2.18471i
$650$	−0.00583292			−0.000228786
$651$		0			0
$652$	14.2818			0.559317
$653$	−0.746666	+	2.29800i	−0.0292193	+	0.0899278i	−0.964603	−	0.263708i	$-0.915055\pi$
$653$	−0.746666	+	2.29800i	−0.0292193	+	0.0899278i	0.935383	+	0.353635i	$0.115055\pi$
$654$	−0.357541	−	1.10040i	−0.0139810	−	0.0430290i
$655$	7.03152	+	5.10869i	0.274744	+	0.199613i
$656$	−27.9196			−1.09008
$657$	−2.88209			−0.112441
$658$	2.62845	+	1.90968i	0.102468	+	0.0744471i
$659$	−21.3322	+	15.4987i	−0.830983	+	0.603745i	−0.919837	−	0.392300i	$-0.871679\pi$
$659$	−21.3322	+	15.4987i	−0.830983	+	0.603745i	0.0888542	+	0.996045i	$0.471679\pi$
$660$	16.4450	−	11.9480i	0.640122	−	0.465076i
$661$	−11.6851	+	35.9630i	−0.454497	+	1.39880i	0.417227	+	0.908802i	$0.363002\pi$
$661$	−11.6851	+	35.9630i	−0.454497	+	1.39880i	−0.871724	+	0.489996i	$0.836998\pi$
$662$	−0.251891	−	0.183009i	−0.00979002	−	0.00711286i
$663$	0.0218194	−	0.0671531i	0.000847394	−	0.00260801i
$664$	0.316532	+	0.974186i	0.0122838	+	0.0378058i
$665$	−15.8205	+	11.4943i	−0.613494	+	0.445729i
$666$	0.331296	+	1.01962i	0.0128375	+	0.0395097i
$667$	3.74708	+	11.5323i	0.145087	+	0.446533i
$668$	−32.8662	+	23.8787i	−1.27163	+	0.923895i
$669$	−4.52341	−	13.9216i	−0.174885	−	0.538241i
$670$	−0.168407	+	0.518303i	−0.00650612	+	0.0200238i
$671$	16.9017	+	12.2798i	0.652483	+	0.474057i
$672$	−1.79799	+	5.53365i	−0.0693590	+	0.213465i
$673$	20.9368	−	15.2115i	0.807055	−	0.586360i	−0.105920	−	0.994375i	$-0.533779\pi$
$673$	20.9368	−	15.2115i	0.807055	−	0.586360i	0.912975	+	0.408015i	$0.133779\pi$
$674$	2.73387	−	1.98627i	0.105305	−	0.0765084i
$675$	15.9135	+	11.5618i	0.612511	+	0.445015i
$676$	25.7992			0.992276
$677$	19.9464			0.766602			0.383301	−	0.923623i	$-0.374787\pi$
$677$	19.9464			0.766602			0.383301	+	0.923623i	$0.374787\pi$
$678$	−0.408259	−	0.296617i	−0.0156791	−	0.0113915i
$679$	2.79183	+	8.59236i	0.107140	+	0.329744i
$680$	−0.666354	+	2.05083i	−0.0255535	+	0.0786456i
$681$	−13.9117			−0.533099
$682$		0			0
$683$	−10.3960			−0.397793			−0.198897	−	0.980020i	$-0.563736\pi$
$683$	−10.3960			−0.397793			−0.198897	+	0.980020i	$0.563736\pi$
$684$	−2.96915	+	9.13810i	−0.113528	+	0.349404i
$685$	−3.62333	−	11.1515i	−0.138440	−	0.426075i
$686$	1.84521	+	1.34062i	0.0704505	+	0.0511853i
$687$	21.8258			0.832706
$688$	12.4095			0.473107
$689$	0.0861507	+	0.0625921i	0.00328208	+	0.00238457i
$690$	−0.747193	+	0.542867i	−0.0284451	+	0.0206666i
$691$	10.8816	−	7.90591i	0.413954	−	0.300755i	−0.361247	−	0.932470i	$-0.617649\pi$
$691$	10.8816	−	7.90591i	0.413954	−	0.300755i	0.775201	+	0.631715i	$0.217649\pi$
$692$	12.9200	−	39.7636i	0.491144	−	1.51159i
$693$	9.86496	+	7.16731i	0.374739	+	0.272264i
$694$	0.933533	−	2.87312i	0.0354364	−	0.109062i
$695$	5.07131	+	15.6079i	0.192366	+	0.592041i
$696$	−1.75564	+	1.27555i	−0.0665474	+	0.0483495i
$697$	7.82647	+	24.0874i	0.296449	+	0.912376i
$698$	0.466820	+	1.43672i	0.0176694	+	0.0543808i
$699$	−34.2100	+	24.8550i	−1.29394	+	0.940104i
$700$	5.70575	+	17.5605i	0.215657	+	0.663725i
$701$	−0.470661	+	1.44855i	−0.0177766	+	0.0547109i	−0.959551	−	0.281534i	$-0.909157\pi$
$701$	−0.470661	+	1.44855i	−0.0177766	+	0.0547109i	0.941775	+	0.336245i	$0.109157\pi$
$702$	−0.00762752	−	0.00554172i	−0.000287882	−	0.000209159i
$703$	19.6000	−	60.3227i	0.739229	−	2.27511i
$704$	34.7752	−	25.2657i	1.31064	−	0.952236i
$705$	14.4341	−	10.4870i	0.543621	−	0.394964i
$706$	−2.81441	−	2.04479i	−0.105922	−	0.0769567i
$707$	−23.1188			−0.869471
$708$	−30.5046			−1.14643
$709$	1.24999	+	0.908169i	0.0469442	+	0.0341070i	0.611010	−	0.791623i	$-0.290764\pi$
$709$	1.24999	+	0.908169i	0.0469442	+	0.0341070i	−0.564066	+	0.825730i	$0.690764\pi$
$710$	−0.177463	−	0.546174i	−0.00666006	−	0.0204976i
$711$	−0.817781	+	2.51687i	−0.0306692	+	0.0943901i
$712$	4.35623			0.163257
$713$		0			0
$714$	1.73660			0.0649908
$715$	−0.0288116	+	0.0886729i	−0.00107749	+	0.00331618i
$716$	6.42639	+	19.7784i	0.240166	+	0.739154i
$717$	−10.7812	−	7.83297i	−0.402630	−	0.292528i
$718$	−3.02199			−0.112780
$719$	36.4715			1.36016			0.680079	−	0.733139i	$-0.261946\pi$
$719$	36.4715			1.36016			0.680079	+	0.733139i	$0.261946\pi$
$720$	−3.15533	−	2.29248i	−0.117592	−	0.0854356i
$721$	−5.78463	+	4.20278i	−0.215431	+	0.156520i
$722$	−1.66436	+	1.20923i	−0.0619412	+	0.0450029i
$723$	−0.360280	+	1.10883i	−0.0133990	+	0.0412378i
$724$	−15.3124	−	11.1251i	−0.569080	−	0.413461i
$725$	−3.19622	+	9.83696i	−0.118705	+	0.365335i
$726$	−1.17602	−	3.61943i	−0.0436464	−	0.134330i
$727$	−9.16225	+	6.65676i	−0.339809	+	0.246886i	−0.744581	−	0.667532i	$-0.767351\pi$
$727$	−9.16225	+	6.65676i	−0.339809	+	0.246886i	0.404772	+	0.914418i	$0.367351\pi$
$728$	−0.00549091	−	0.0168993i	−0.000203507	−	0.000626329i
$729$	9.21398	+	28.3577i	0.341259	+	1.05029i
$730$	0.438483	−	0.318577i	0.0162290	−	0.0117911i
$731$	−3.47864	−	10.7062i	−0.128662	−	0.395982i
$732$	−3.36519	+	10.3570i	−0.124381	+	0.382806i
$733$	−1.47532	−	1.07188i	−0.0544921	−	0.0395908i	0.560206	−	0.828353i	$-0.310722\pi$
$733$	−1.47532	−	1.07188i	−0.0544921	−	0.0395908i	−0.614698	+	0.788763i	$0.710722\pi$
$734$	−0.0648179	+	0.199489i	−0.00239247	+	0.00736328i
$735$	−0.166308	+	0.120830i	−0.00613436	+	0.00445687i
$736$	−4.87959	+	3.54523i	−0.179864	+	0.130679i
$737$	−16.2648	−	11.8171i	−0.599122	−	0.435288i
$738$	0.720232			0.0265121
$739$	−35.2840			−1.29794			−0.648971	−	0.760813i	$-0.724800\pi$
$739$	−35.2840			−1.29794			−0.648971	+	0.760813i	$0.724800\pi$
$740$	20.9934	+	15.2526i	0.771733	+	0.560697i
$741$	0.0367089	+	0.112978i	0.00134853	+	0.00415036i
$742$	−0.809328	+	2.49086i	−0.0297114	+	0.0914422i
$743$	−26.9859			−0.990018			−0.495009	−	0.868888i	$-0.664835\pi$
$743$	−26.9859			−0.990018			−0.495009	+	0.868888i	$0.664835\pi$
$744$		0			0
$745$	−22.3741			−0.819722
$746$	0.931837	−	2.86790i	0.0341170	−	0.105001i
$747$	0.519346	+	1.59838i	0.0190019	+	0.0584817i
$748$	−32.0539	−	23.2885i	−1.17201	−	0.851513i
$749$	−21.2714			−0.777240
$750$	−1.91696			−0.0699976
$751$	17.1193	+	12.4379i	0.624691	+	0.453865i	0.854557	−	0.519358i	$-0.173829\pi$
$751$	17.1193	+	12.4379i	0.624691	+	0.453865i	−0.229866	+	0.973222i	$0.573829\pi$
$752$	31.0144	−	22.5333i	1.13098	−	0.821703i
$753$	−23.6617	+	17.1912i	−0.862281	+	0.626484i
$754$	0.00153198	−	0.00471496i	5.57916e−5	−	0.000171709i
$755$	6.56027	+	4.76631i	0.238753	+	0.173464i
$756$	−9.22258	+	28.3842i	−0.335422	+	1.03232i
$757$	16.5689	+	50.9937i	0.602205	+	1.85340i	0.514966	+	0.857210i	$0.327804\pi$
$757$	16.5689	+	50.9937i	0.602205	+	1.85340i	0.0872392	+	0.996187i	$0.472196\pi$
$758$	−1.34058	+	0.973991i	−0.0486922	+	0.0353769i
$759$	−10.5286	−	32.4038i	−0.382165	−	1.17618i
$760$	−1.12107	−	3.45031i	−0.0406656	−	0.125156i
$761$	6.67260	−	4.84793i	0.241882	−	0.175737i	−0.460240	−	0.887795i	$-0.652236\pi$
$761$	6.67260	−	4.84793i	0.241882	−	0.175737i	0.702121	+	0.712057i	$0.252236\pi$
$762$	0.0985012	+	0.303156i	0.00356832	+	0.0109822i
$763$	5.19133	−	15.9773i	0.187939	−	0.578416i
$764$	−16.0629	−	11.6704i	−0.581136	−	0.422220i
$765$	−1.09331	+	3.36486i	−0.0395287	+	0.121657i
$766$	−2.51596	+	1.82795i	−0.0909052	+	0.0660465i
$767$	0.113196	−	0.0822417i	0.00408727	−	0.00296958i
$768$	17.6886	+	12.8515i	0.638284	+	0.463740i
$769$	26.3326			0.949577			0.474788	−	0.880100i	$-0.342525\pi$
$769$	26.3326			0.949577			0.474788	+	0.880100i	$0.342525\pi$
$770$	−2.29311			−0.0826381
$771$	−10.8001	−	7.84675i	−0.388957	−	0.282594i
$772$	12.6827	+	39.0335i	0.456462	+	1.40485i
$773$	−3.66000	+	11.2643i	−0.131641	+	0.405150i	−0.995052	−	0.0993508i	$-0.968323\pi$
$773$	−3.66000	+	11.2643i	−0.131641	+	0.405150i	0.863411	+	0.504501i	$0.168323\pi$
$774$	−0.320123			−0.0115066
$775$		0			0
$776$	−1.67608			−0.0601677
$777$	12.9658	−	39.9047i	0.465146	−	1.43157i
$778$	0.841753	+	2.59065i	0.0301783	+	0.0928793i
$779$	−34.4723	−	25.0456i	−1.23510	−	0.897351i
$780$	−0.0486004			−0.00174017
$781$	21.1855			0.758078
$782$	1.45639	+	1.05813i	0.0520806	+	0.0378387i
$783$	−13.5254	+	9.82681i	−0.483360	+	0.351181i
$784$	−0.357342	+	0.259624i	−0.0127622	+	0.00927230i
$785$	−5.97429	+	18.3870i	−0.213231	+	0.656259i
$786$	1.05055	+	0.763267i	0.0374718	+	0.0272248i
$787$	12.0136	−	36.9740i	0.428238	−	1.31798i	−0.471621	−	0.881801i	$-0.656331\pi$
$787$	12.0136	−	36.9740i	0.428238	−	1.31798i	0.899859	−	0.436180i	$-0.143669\pi$
$788$	0.461967	+	1.42179i	0.0164569	+	0.0506491i
$789$	−3.74340	+	2.71974i	−0.133269	+	0.0968254i
$790$	−0.153789	−	0.473314i	−0.00547157	−	0.0168397i
$791$	−2.26419	−	6.96845i	−0.0805052	−	0.247769i
$792$	−1.83014	+	1.32967i	−0.0650311	+	0.0472478i
$793$	−0.0154354	−	0.0475053i	−0.000548127	−	0.00168696i
$794$	0.0850441	−	0.261739i	0.00301810	−	0.00928876i
$795$	11.6357	+	8.45381i	0.412675	+	0.299826i
$796$	−6.06562	+	18.6681i	−0.214990	+	0.661672i
$797$	−42.1225	+	30.6038i	−1.49206	+	1.08404i	−0.518641	+	0.854992i	$0.673562\pi$
$797$	−42.1225	+	30.6038i	−1.49206	+	1.08404i	−0.973415	+	0.229050i	$0.926438\pi$
$798$	−2.36367	+	1.71731i	−0.0836731	+	0.0607921i
$799$	−28.1344	−	20.4408i	−0.995323	−	0.723144i
$800$	−5.14482			−0.181897
$801$	7.14742			0.252542
$802$	2.67921	+	1.94656i	0.0946061	+	0.0687354i
$803$	6.17863	+	19.0159i	0.218039	+	0.671056i
$804$	3.23839	−	9.96673i	0.114209	−	0.351500i
$805$	−13.4099			−0.472638
$806$		0			0
$807$	−20.6764			−0.727845
$808$	1.32536	−	4.07905i	0.0466261	−	0.143500i
$809$	9.64388	+	29.6808i	0.339061	+	1.04352i	0.964687	+	0.263399i	$0.0848435\pi$
$809$	9.64388	+	29.6808i	0.339061	+	1.04352i	−0.625626	+	0.780123i	$0.715157\pi$
$810$	−0.729389	−	0.529932i	−0.0256281	−	0.0186199i
$811$	16.4241			0.576729			0.288364	−	0.957521i	$-0.406889\pi$
$811$	16.4241			0.576729			0.288364	+	0.957521i	$0.406889\pi$
$812$	−15.6934			−0.550729
$813$	16.8247	+	12.2238i	0.590067	+	0.428709i
$814$	6.01720	−	4.37175i	0.210903	−	0.153230i
$815$	−7.15780	+	5.20045i	−0.250727	+	0.182164i
$816$	6.33208	−	19.4881i	0.221667	−	0.682222i
$817$	15.3220	+	11.1321i	0.536047	+	0.389461i
$818$	−1.45344	+	4.47324i	−0.0508185	+	0.156403i
$819$	−0.00900913	−	0.0277272i	−0.000314804	−	0.000968868i
$820$	14.1033	−	10.2467i	0.492509	−	0.357829i
$821$	−12.4433	−	38.2967i	−0.434275	−	1.33656i	−0.893827	−	0.448411i	$-0.851990\pi$
$821$	−12.4433	−	38.2967i	−0.434275	−	1.33656i	0.459552	−	0.888151i	$-0.348010\pi$
$822$	−0.541345	−	1.66609i	−0.0188816	−	0.0581115i
$823$	−18.8505	+	13.6957i	−0.657088	+	0.477402i	−0.865678	−	0.500601i	$-0.833112\pi$
$823$	−18.8505	+	13.6957i	−0.657088	+	0.477402i	0.208591	+	0.978003i	$0.433112\pi$
$824$	−0.409910	−	1.26157i	−0.0142799	−	0.0439490i
$825$	8.98082	−	27.6401i	0.312672	−	0.962305i
$826$	2.78402	+	2.02271i	0.0968684	+	0.0703790i
$827$	7.45869	−	22.9555i	0.259364	−	0.798240i	−0.733574	−	0.679609i	$-0.762149\pi$
$827$	7.45869	−	22.9555i	0.259364	−	0.798240i	0.992938	−	0.118631i	$-0.0378506\pi$
$828$	−5.33054	+	3.87286i	−0.185249	+	0.134591i
$829$	18.3804	−	13.3541i	0.638376	−	0.463807i	−0.220916	−	0.975293i	$-0.570905\pi$
$829$	18.3804	−	13.3541i	0.638376	−	0.463807i	0.859292	+	0.511485i	$0.170905\pi$
$830$	−0.255693	−	0.185772i	−0.00887525	−	0.00644825i
$831$	−32.5758			−1.13004
$832$	−0.102772			−0.00356298
$833$	0.324160	+	0.235516i	0.0112315	+	0.00816014i
$834$	0.757681	+	2.33190i	0.0262364	+	0.0807472i
$835$	7.77704	−	23.9353i	0.269136	−	0.828315i
$836$	66.6580			2.30541
$837$		0			0
$838$	−1.13831			−0.0393223
$839$	−1.85861	+	5.72022i	−0.0641664	+	0.197484i	−0.978000	−	0.208605i	$-0.933108\pi$
$839$	−1.85861	+	5.72022i	−0.0641664	+	0.197484i	0.913834	+	0.406089i	$0.133108\pi$
$840$	−0.741612	−	2.28245i	−0.0255881	−	0.0787519i
$841$	16.3494	+	11.8785i	0.563772	+	0.409605i
$842$	−0.405813			−0.0139852
$843$	−3.44111			−0.118518
$844$	22.5788	+	16.4044i	0.777193	+	0.564664i
$845$	−12.9302	+	9.39431i	−0.444811	+	0.323174i
$846$	−0.800067	+	0.581282i	−0.0275069	+	0.0199849i
$847$	17.0753	−	52.5524i	0.586714	−	1.80572i
$848$	25.0013	+	18.1645i	0.858550	+	0.623773i
$849$	−6.36736	+	19.5967i	−0.218527	+	0.672558i
$850$	0.474513	+	1.46040i	0.0162756	+	0.0500913i
$851$	35.1881	−	25.5656i	1.20623	−	0.876378i
$852$	3.41253	+	10.5027i	0.116911	+	0.359816i
$853$	3.34165	+	10.2845i	0.114416	+	0.352136i	0.991825	−	0.127607i	$-0.0407297\pi$
$853$	3.34165	+	10.2845i	0.114416	+	0.352136i	−0.877409	+	0.479744i	$0.840730\pi$
$854$	0.993881	−	0.722097i	0.0340099	−	0.0247096i
$855$	−1.83938	−	5.66104i	−0.0629056	−	0.193603i
$856$	1.21946	−	3.75310i	0.0416802	−	0.128278i
$857$	27.5745	+	20.0341i	0.941928	+	0.684351i	0.948884	−	0.315625i	$-0.102214\pi$
$857$	27.5745	+	20.0341i	0.941928	+	0.684351i	−0.00695590	+	0.999976i	$0.502214\pi$
$858$	−0.00430461	+	0.0132482i	−0.000146957	+	0.000452287i
$859$	6.08213	−	4.41893i	0.207520	−	0.150772i	−0.479171	−	0.877722i	$-0.659063\pi$
$859$	6.08213	−	4.41893i	0.207520	−	0.150772i	0.686691	+	0.726950i	$0.259063\pi$
$860$	−6.26852	+	4.55435i	−0.213755	+	0.155302i
$861$	−22.8041	−	16.5682i	−0.777162	−	0.564642i
$862$	−2.91445			−0.0992666
$863$	−22.2748			−0.758243			−0.379121	−	0.925347i	$-0.623774\pi$
$863$	−22.2748			−0.758243			−0.379121	+	0.925347i	$0.623774\pi$
$864$	−6.72770	−	4.88796i	−0.228881	−	0.166292i
$865$	8.00392	+	24.6335i	0.272141	+	0.837565i
$866$	1.04917	−	3.22903i	0.0356524	−	0.109727i
$867$	6.55906			0.222757
$868$		0			0
$869$	18.3594			0.622798
$870$	0.206913	−	0.636812i	0.00701499	−	0.0215899i
$871$	0.0148538	+	0.0457152i	0.000503301	+	0.00154900i
$872$	2.52140	+	1.83190i	0.0853854	+	0.0620361i
$873$	−2.75000			−0.0930734
$874$	−3.02866			−0.102446
$875$	−22.5177	−	16.3600i	−0.761236	−	0.553070i
$876$	−8.43184	+	6.12609i	−0.284886	+	0.206981i
$877$	21.9773	−	15.9675i	0.742122	−	0.539183i	−0.151253	−	0.988495i	$-0.548331\pi$
$877$	21.9773	−	15.9675i	0.742122	−	0.539183i	0.893375	+	0.449312i	$0.148331\pi$
$878$	−1.26796	+	3.90239i	−0.0427917	+	0.131699i
$879$	30.9482	+	22.4852i	1.04386	+	0.758406i
$880$	−8.36125	+	25.7333i	−0.281858	+	0.867469i
$881$	−7.03618	−	21.6551i	−0.237055	−	0.729580i	−0.996842	−	0.0794084i	$-0.974697\pi$
$881$	−7.03618	−	21.6551i	−0.237055	−	0.729580i	0.759787	−	0.650172i	$-0.225303\pi$
$882$	0.00921824	−	0.00669744i	0.000310394	−	0.000225515i
$883$	−6.34514	−	19.5283i	−0.213531	−	0.657180i	−0.999255	−	0.0386029i	$-0.987709\pi$
$883$	−6.34514	−	19.5283i	−0.213531	−	0.657180i	0.785724	−	0.618578i	$-0.212291\pi$
$884$	0.0292731	+	0.0900932i	0.000984560	+	0.00303016i
$885$	15.2885	−	11.1077i	0.513916	−	0.373382i
$886$	−0.511366	−	1.57382i	−0.0171797	−	0.0528736i
$887$	16.5966	−	51.0792i	0.557261	−	1.71507i	−0.132636	−	0.991165i	$-0.542344\pi$
$887$	16.5966	−	51.0792i	0.557261	−	1.71507i	0.689897	−	0.723908i	$-0.257656\pi$
$888$	6.29743	+	4.57535i	0.211328	+	0.153539i
$889$	−1.43019	+	4.40167i	−0.0479670	+	0.147627i
$890$	−1.08741	+	0.790052i	−0.0364502	+	0.0264826i
$891$	26.9075	−	19.5495i	0.901436	−	0.654931i
$892$	15.8879	+	11.5433i	0.531967	+	0.386497i
$893$	58.5071			1.95787
$894$	−3.34281			−0.111800
$895$	−10.4228	−	7.57258i	−0.348395	−	0.253123i
$896$	−3.21203	−	9.88561i	−0.107306	−	0.330255i
$897$	−0.0251730	+	0.0774744i	−0.000840501	+	0.00258680i
$898$	1.40247			0.0468010
$899$		0			0
$900$	−5.62027			−0.187342
$901$	8.66288	−	26.6616i	0.288602	−	0.888227i
$902$	−1.54404	−	4.75205i	−0.0514108	−	0.158226i
$903$	10.1358	+	7.36408i	0.337298	+	0.245061i
$904$	1.35931			0.0452099
$905$	11.7253			0.389763
$906$	0.980140	+	0.712113i	0.0325630	+	0.0236584i
$907$	−43.1601	+	31.3576i	−1.43311	+	1.04121i	−0.443679	+	0.896186i	$0.646327\pi$
$907$	−43.1601	+	31.3576i	−1.43311	+	1.04121i	−0.989428	+	0.145028i	$0.953673\pi$
$908$	15.0996	−	10.9705i	0.501098	−	0.364069i
$909$	2.17457	−	6.69264i	0.0721260	−	0.221981i
$910$	0.00443554	+	0.00322260i	0.000147037	+	0.000106828i
$911$	−13.7656	+	42.3662i	−0.456075	+	1.40365i	0.413794	+	0.910371i	$0.364203\pi$
$911$	−13.7656	+	42.3662i	−0.456075	+	1.40365i	−0.869869	+	0.493283i	$0.835797\pi$
$912$	10.6531	+	32.7868i	0.352759	+	1.08568i
$913$	9.43266	−	6.85323i	0.312175	−	0.226809i
$914$	0.174619	+	0.537422i	0.00577589	+	0.0177764i
$915$	−2.08473	−	6.41615i	−0.0689191	−	0.212111i
$916$	−23.6894	+	17.2113i	−0.782719	+	0.568679i
$917$	5.82629	+	17.9315i	0.192401	+	0.592149i
$918$	−0.766985	+	2.36054i	−0.0253143	+	0.0779094i
$919$	9.43229	+	6.85296i	0.311142	+	0.226058i	0.732387	−	0.680889i	$-0.238406\pi$
$919$	9.43229	+	6.85296i	0.311142	+	0.226058i	−0.421244	+	0.906947i	$0.638406\pi$
$920$	0.768772	−	2.36604i	0.0253457	−	0.0780059i
$921$	−0.784658	+	0.570088i	−0.0258554	+	0.0187850i
$922$	−2.89284	+	2.10177i	−0.0952707	+	0.0692182i
$923$	−0.0409788	−	0.0297729i	−0.00134883	−	0.000979986i
$924$	44.0956			1.45064
$925$	37.1007			1.21986
$926$	−1.21069	−	0.879618i	−0.0397857	−	0.0289060i
$927$	−0.672553	−	2.06991i	−0.0220895	−	0.0679846i
$928$	1.35126	−	4.15874i	0.0443572	−	0.136517i
$929$	16.1137			0.528675			0.264337	−	0.964430i	$-0.414847\pi$
$929$	16.1137			0.528675			0.264337	+	0.964430i	$0.414847\pi$
$930$		0			0
$931$	−0.674109			−0.0220930
$932$	17.5309	−	53.9546i	0.574244	−	1.76734i
$933$	10.0745	+	31.0062i	0.329825	+	1.01510i
$934$	1.92179	+	1.39626i	0.0628828	+	0.0456870i
$935$	24.5450			0.802708
$936$	0.00540865			0.000176787
$937$	−36.6391	−	26.6199i	−1.19695	−	0.869633i	−0.202966	−	0.979186i	$-0.565058\pi$
$937$	−36.6391	−	26.6199i	−1.19695	−	0.869633i	−0.993981	+	0.109553i	$0.965058\pi$
$938$	−0.956430	+	0.694887i	−0.0312285	+	0.0226889i
$939$	11.3850	−	8.27171i	0.371536	−	0.269937i
$940$	−7.39676	+	22.7649i	−0.241256	+	0.742509i
$941$	19.8280	+	14.4059i	0.646376	+	0.469619i	0.862035	−	0.506849i	$-0.169190\pi$
$941$	19.8280	+	14.4059i	0.646376	+	0.469619i	−0.215659	+	0.976469i	$0.569190\pi$
$942$	−0.892591	+	2.74711i	−0.0290822	+	0.0895058i
$943$	−9.02939	−	27.7896i	−0.294037	−	0.904954i
$944$	32.8500	−	23.8669i	1.06918	−	0.776803i
$945$	−5.71337	−	17.5840i	−0.185856	−	0.572006i
$946$	0.686280	+	2.11215i	0.0223129	+	0.0686720i
$947$	36.2065	−	26.3056i	1.17655	−	0.854816i	0.184775	−	0.982781i	$-0.440844\pi$
$947$	36.2065	−	26.3056i	1.17655	−	0.854816i	0.991779	+	0.127964i	$0.0408443\pi$
$948$	2.95729	+	9.10162i	0.0960485	+	0.295607i
$949$	0.0147725	−	0.0454652i	0.000479537	−	0.00147586i
$950$	−2.09003	−	1.51849i	−0.0678094	−	0.0492664i
$951$	0.957669	−	2.94740i	0.0310545	−	0.0955760i
$952$	−3.78441	+	2.74954i	−0.122654	+	0.0891130i
$953$	24.9268	−	18.1103i	0.807457	−	0.586652i	−0.105635	−	0.994405i	$-0.533688\pi$
$953$	24.9268	−	18.1103i	0.807457	−	0.586652i	0.913092	+	0.407753i	$0.133688\pi$
$954$	−0.644951	−	0.468584i	−0.0208811	−	0.0151710i
$955$	12.3001			0.398020
$956$	17.8786			0.578236
$957$	19.9837	+	14.5190i	0.645982	+	0.469334i
$958$	−0.471634	−	1.45154i	−0.0152378	−	0.0468971i
$959$	7.86006	−	24.1908i	0.253815	−	0.781161i
$960$	−13.8806			−0.447994
$961$		0			0
$962$	−0.0177828			−0.000573339
$963$	2.00081	−	6.15785i	0.0644751	−	0.198434i
$964$	−0.483356	−	1.48762i	−0.0155678	−	0.0479129i
$965$	−20.5697	−	14.9448i	−0.662164	−	0.481090i
$966$	−2.00352			−0.0644622
$967$	44.5447			1.43246			0.716230	−	0.697864i	$-0.245866\pi$
$967$	44.5447			1.43246			0.716230	+	0.697864i	$0.245866\pi$
$968$	8.29338	+	6.02550i	0.266559	+	0.193667i
$969$	25.3003	−	18.3817i	0.812762	−	0.590506i
$970$	0.418387	−	0.303976i	0.0134336	−	0.00976008i
$971$	1.96452	−	6.04617i	0.0630445	−	0.194031i	−0.914573	−	0.404420i	$-0.867473\pi$
$971$	1.96452	−	6.04617i	0.0630445	−	0.194031i	0.977618	+	0.210390i	$0.0674732\pi$
$972$	−13.1336	−	9.54216i	−0.421262	−	0.306065i
$973$	−11.0012	+	33.8581i	−0.352681	+	1.08544i
$974$	0.580443	+	1.78642i	0.0185986	+	0.0572406i
$975$	−0.0562152	+	0.0408427i	−0.00180033	+	0.00130801i
$976$	−4.47943	−	13.7863i	−0.143383	−	0.441287i
$977$	−4.15101	−	12.7755i	−0.132803	−	0.408724i	0.862439	−	0.506161i	$-0.168936\pi$
$977$	−4.15101	−	12.7755i	−0.132803	−	0.408724i	−0.995242	+	0.0974365i	$0.968936\pi$
$978$	−1.06941	+	0.776975i	−0.0341961	+	0.0248449i
$979$	−15.3227	−	47.1583i	−0.489714	−	1.50719i
$980$	0.0852243	−	0.262293i	0.00272239	−	0.00837866i
$981$	4.13695	+	3.00567i	0.132083	+	0.0959636i
$982$	1.17165	−	3.60598i	0.0373889	−	0.115071i
$983$	−34.1224	+	24.7914i	−1.08834	+	0.790723i	−0.979118	−	0.203294i	$-0.934835\pi$
$983$	−34.1224	+	24.7914i	−1.08834	+	0.790723i	−0.109219	+	0.994018i	$0.534835\pi$
$984$	4.23060	−	3.07371i	0.134866	−	0.0979862i
$985$	−0.749249	−	0.544361i	−0.0238731	−	0.0173448i
$986$	−1.30512			−0.0415635
$987$	38.7036			1.23195
$988$	−0.128935	−	0.0936771i	−0.00410198	−	0.00298026i
$989$	4.01331	+	12.3517i	0.127616	+	0.392761i
$990$	0.215692	−	0.663833i	0.00685515	−	0.0210980i
$991$	40.1209			1.27448			0.637241	−	0.770665i	$-0.280076\pi$
$991$	40.1209			1.27448			0.637241	+	0.770665i	$0.280076\pi$
$992$		0			0
$993$	−3.70907			−0.117704
$994$	0.384969	−	1.18481i	0.0122105	−	0.0375800i
$995$	−3.75764	−	11.5648i	−0.119125	−	0.366630i
$996$	4.91687	+	3.57232i	0.155797	+	0.113193i
$997$	−40.6053			−1.28598			−0.642991	−	0.765874i	$-0.722307\pi$
$997$	−40.6053			−1.28598			−0.642991	+	0.765874i	$0.722307\pi$
$998$	3.57960			0.113310
$999$	48.5153	+	35.2484i	1.53496	+	1.11521i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.s.628.11		64
31.2	even	5		961.2.a.l.1.11	✓	16
31.3	odd	30		961.2.g.w.816.5		128
31.4	even	5	inner	961.2.d.s.531.11		64
31.5	even	3		961.2.g.w.448.11		128
31.6	odd	6		961.2.g.w.846.11		128
31.7	even	15		961.2.g.w.547.11		128
31.8	even	5	inner	961.2.d.s.388.6		64
31.9	even	15		961.2.g.w.338.6		128
31.10	even	15		961.2.c.l.521.12		32
31.11	odd	30		961.2.g.w.844.11		128
31.12	odd	30		961.2.c.l.439.11		32
31.13	odd	30		961.2.g.w.732.6		128
31.14	even	15		961.2.g.w.235.5		128
31.15	odd	10	inner	961.2.d.s.374.5		64
31.16	even	5	inner	961.2.d.s.374.6		64
31.17	odd	30		961.2.g.w.235.6		128
31.18	even	15		961.2.g.w.732.5		128
31.19	even	15		961.2.c.l.439.12		32
31.20	even	15		961.2.g.w.844.12		128
31.21	odd	30		961.2.c.l.521.11		32
31.22	odd	30		961.2.g.w.338.5		128
31.23	odd	10	inner	961.2.d.s.388.5		64
31.24	odd	30		961.2.g.w.547.12		128
31.25	even	3		961.2.g.w.846.12		128
31.26	odd	6		961.2.g.w.448.12		128
31.27	odd	10	inner	961.2.d.s.531.12		64
31.28	even	15		961.2.g.w.816.6		128
31.29	odd	10		961.2.a.l.1.12	yes	16
31.30	odd	2	inner	961.2.d.s.628.12		64
93.2	odd	10		8649.2.a.bs.1.5		16
93.29	even	10		8649.2.a.bs.1.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.l.1.11	✓	16	31.2	even	5
961.2.a.l.1.12	yes	16	31.29	odd	10
961.2.c.l.439.11		32	31.12	odd	30
961.2.c.l.439.12		32	31.19	even	15
961.2.c.l.521.11		32	31.21	odd	30
961.2.c.l.521.12		32	31.10	even	15
961.2.d.s.374.5		64	31.15	odd	10	inner
961.2.d.s.374.6		64	31.16	even	5	inner
961.2.d.s.388.5		64	31.23	odd	10	inner
961.2.d.s.388.6		64	31.8	even	5	inner
961.2.d.s.531.11		64	31.4	even	5	inner
961.2.d.s.531.12		64	31.27	odd	10	inner
961.2.d.s.628.11		64	1.1	even	1	trivial
961.2.d.s.628.12		64	31.30	odd	2	inner
961.2.g.w.235.5		128	31.14	even	15
961.2.g.w.235.6		128	31.17	odd	30
961.2.g.w.338.5		128	31.22	odd	30
961.2.g.w.338.6		128	31.9	even	15
961.2.g.w.448.11		128	31.5	even	3
961.2.g.w.448.12		128	31.26	odd	6
961.2.g.w.547.11		128	31.7	even	15
961.2.g.w.547.12		128	31.24	odd	30
961.2.g.w.732.5		128	31.18	even	15
961.2.g.w.732.6		128	31.13	odd	30
961.2.g.w.816.5		128	31.3	odd	30
961.2.g.w.816.6		128	31.28	even	15
961.2.g.w.844.11		128	31.11	odd	30
961.2.g.w.844.12		128	31.20	even	15
961.2.g.w.846.11		128	31.6	odd	6
961.2.g.w.846.12		128	31.25	even	3
8649.2.a.bs.1.5		16	93.2	odd	10
8649.2.a.bs.1.6		16	93.29	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0383721 - 0.118097i) q^{2} +(-0.457114 - 1.40685i) q^{3} +(1.60556 + 1.16651i) q^{4} -1.22944 q^{5} -0.183686 q^{6} +(-2.15767 - 1.56764i) q^{7} +(0.400289 - 0.290827i) q^{8} +(0.656767 - 0.477169i) q^{9} +(-0.0471763 + 0.145194i) q^{10} +(-4.55632 - 3.31036i) q^{11} +(0.907181 - 2.79201i) q^{12} +(0.00416104 + 0.0128063i) q^{13} +(-0.267928 + 0.194661i) q^{14} +(0.561997 + 1.72965i) q^{15} +(1.20755 + 3.71646i) q^{16} +(2.86784 - 2.08361i) q^{17} +(-0.0311508 - 0.0958723i) q^{18} +(-1.84293 + 5.67196i) q^{19} +(-1.97395 - 1.43416i) q^{20} +(-1.21914 + 3.75212i) q^{21} +(-0.565779 + 0.411063i) q^{22} +(-3.30863 + 2.40386i) q^{23} +(-0.592128 - 0.430206i) q^{24} -3.48847 q^{25} +0.00167206 q^{26} +(-4.56175 - 3.31430i) q^{27} +(-1.63561 - 5.03388i) q^{28} +(0.916226 - 2.81985i) q^{29} +0.225832 q^{30} +1.47481 q^{32} +(-2.57443 + 7.92329i) q^{33} +(-0.136023 - 0.418637i) q^{34} +(2.65274 + 1.92733i) q^{35} +1.61110 q^{36} -10.6352 q^{37} +(0.599125 + 0.435290i) q^{38} +(0.0161146 - 0.0117079i) q^{39} +(-0.492133 + 0.357555i) q^{40} +(-2.20784 + 6.79504i) q^{41} +(0.396333 + 0.287953i) q^{42} +(0.981323 - 3.02020i) q^{43} +(-3.45388 - 10.6300i) q^{44} +(-0.807459 + 0.586654i) q^{45} +(0.156930 + 0.482981i) q^{46} +(-3.03154 - 9.33014i) q^{47} +(4.67653 - 3.39770i) q^{48} +(0.0349290 + 0.107500i) q^{49} +(-0.133860 + 0.411978i) q^{50} +(-4.24227 - 3.08219i) q^{51} +(-0.00825791 + 0.0254152i) q^{52} +(6.39793 - 4.64837i) q^{53} +(-0.566454 + 0.411553i) q^{54} +(5.60174 + 4.06990i) q^{55} -1.31960 q^{56} +8.82205 q^{57} +(-0.297859 - 0.216407i) q^{58} +(-3.21097 - 9.88236i) q^{59} +(-1.11533 + 3.43263i) q^{60} -3.70951 q^{61} -2.16512 q^{63} +(-2.35851 + 7.25876i) q^{64} +(-0.00511576 - 0.0157447i) q^{65} +(0.836931 + 0.608066i) q^{66} +3.56973 q^{67} +7.03504 q^{68} +(4.89430 + 3.55592i) q^{69} +(0.329403 - 0.239325i) q^{70} +(-3.04327 + 2.21107i) q^{71} +(0.124123 - 0.382011i) q^{72} +(-2.87218 - 2.08676i) q^{73} +(-0.408096 + 1.25599i) q^{74} +(1.59463 + 4.90776i) q^{75} +(-9.57532 + 6.95688i) q^{76} +(4.64158 + 14.2853i) q^{77} +(-0.000764323 - 0.00235234i) q^{78} +(-2.63729 + 1.91611i) q^{79} +(-1.48462 - 4.56919i) q^{80} +(-1.82491 + 5.61650i) q^{81} +(0.717755 + 0.521480i) q^{82} +(-0.639738 + 1.96891i) q^{83} +(-6.33427 + 4.60211i) q^{84} +(-3.52586 + 2.56168i) q^{85} +(-0.319022 - 0.231783i) q^{86} -4.38594 q^{87} -2.78658 q^{88} +(7.12284 + 5.17504i) q^{89} +(0.0382982 + 0.117870i) q^{90} +(0.0110976 - 0.0341549i) q^{91} -8.11632 q^{92} -1.21819 q^{94} +(2.26578 - 6.97336i) q^{95} +(-0.674156 - 2.07484i) q^{96} +(-2.74054 - 1.99112i) q^{97} +0.0140358 q^{98} -4.57204 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{2} - 8 q^{4} - 64 q^{5} + 16 q^{7} - 8 q^{10} + 8 q^{14} + 8 q^{16} + 24 q^{18} + 32 q^{19} + 24 q^{20} + 8 q^{28} - 32 q^{32} + 32 q^{33} + 16 q^{35} - 160 q^{36} + 24 q^{38} + 32 q^{39} + 32 q^{41}+ \cdots + 64 q^{98}+O(q^{100}) \) 64 * q + 8 * q^2 - 8 * q^4 - 64 * q^5 + 16 * q^7 - 8 * q^10 + 8 * q^14 + 8 * q^16 + 24 * q^18 + 32 * q^19 + 24 * q^20 + 8 * q^28 - 32 * q^32 + 32 * q^33 + 16 * q^35 - 160 * q^36 + 24 * q^38 + 32 * q^39 + 32 * q^41 + 16 * q^45 + 32 * q^47 + 16 * q^49 + 32 * q^50 + 32 * q^51 - 192 * q^56 + 64 * q^59 - 64 * q^63 + 16 * q^64 + 64 * q^67 + 32 * q^69 - 88 * q^70 + 48 * q^71 - 48 * q^72 - 40 * q^76 - 32 * q^78 + 40 * q^80 + 16 * q^81 - 88 * q^82 - 128 * q^87 - 40 * q^90 - 128 * q^94 + 48 * q^95 + 64 * q^98

Introduction

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