LMFDB - Embedded newform 234.2.z.a.41.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(41,234)] 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("234.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			41.13
Character	$\chi$	$=$	234.41
Dual form			234.2.z.a.137.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 - 0.258819i) q^{2} +(1.10250 - 1.33585i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.00707659 + 0.00189617i) q^{5} +(0.719190 - 1.57568i) q^{6} +(-2.39172 - 2.39172i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.568989 - 2.94555i) q^{9} +(-0.00634470 + 0.00366311i) q^{10} +(1.12016 + 4.18051i) q^{11} +(0.286868 - 1.70813i) q^{12} +(-0.448036 + 3.57761i) q^{13} +(-2.92924 - 1.69120i) q^{14} +(-0.00526894 + 0.0115438i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.69940 - 2.94345i) q^{17} +(-1.31196 - 2.69792i) q^{18} +(1.98018 + 7.39012i) q^{19} +(-0.00518042 + 0.00518042i) q^{20} +(-5.83184 + 0.558107i) q^{21} +(2.16399 + 3.74814i) q^{22} +8.84301 q^{23} +(-0.165003 - 1.72417i) q^{24} +(-4.33008 + 2.49997i) q^{25} +(0.493183 + 3.57166i) q^{26} +(-4.56212 - 2.48738i) q^{27} +(-3.26715 - 0.875429i) q^{28} +(-6.23056 - 3.59721i) q^{29} +(-0.00210166 + 0.0125141i) q^{30} +(-1.62808 - 6.07609i) q^{31} +(0.258819 - 0.965926i) q^{32} +(6.81951 + 3.11264i) q^{33} +(0.879676 - 3.28299i) q^{34} +(0.0214603 + 0.0123901i) q^{35} +(-1.96553 - 2.26642i) q^{36} +(-0.558952 + 2.08604i) q^{37} +(3.82541 + 6.62580i) q^{38} +(4.28518 + 4.54282i) q^{39} +(-0.00366311 + 0.00634470i) q^{40} +(1.01757 + 1.01757i) q^{41} +(-5.48868 + 2.04848i) q^{42} +5.84706i q^{43} +(3.06034 + 3.06034i) q^{44} +(0.00961175 + 0.0197655i) q^{45} +(8.54170 - 2.28874i) q^{46} +(0.667387 + 0.178826i) q^{47} +(-0.605630 - 1.62272i) q^{48} +4.44062i q^{49} +(-3.53550 + 3.53550i) q^{50} +(-2.05842 - 5.51530i) q^{51} +(1.40079 + 3.32232i) q^{52} -1.59509i q^{53} +(-5.05045 - 1.22186i) q^{54} +(-0.0158539 - 0.0274597i) q^{55} -3.38240 q^{56} +(12.0552 + 5.50239i) q^{57} +(-6.94928 - 1.86206i) q^{58} +(1.43000 + 0.383168i) q^{59} +(0.00120885 + 0.0126317i) q^{60} -14.7526 q^{61} +(-3.14521 - 5.44767i) q^{62} +(-5.68406 + 8.40578i) q^{63} -1.00000i q^{64} +(-0.00361317 - 0.0261668i) q^{65} +(7.39275 + 1.24156i) q^{66} +(-3.40387 + 3.40387i) q^{67} -3.39881i q^{68} +(9.74942 - 11.8129i) q^{69} +(0.0239359 + 0.00641359i) q^{70} +(4.18049 - 1.12016i) q^{71} +(-2.48515 - 1.68048i) q^{72} +(-6.17624 - 6.17624i) q^{73} +2.15962i q^{74} +(-1.43432 + 8.54056i) q^{75} +(5.40994 + 5.40994i) q^{76} +(7.31947 - 12.6777i) q^{77} +(5.31494 + 3.27894i) q^{78} +(-4.25708 - 7.37348i) q^{79} +(-0.00189617 + 0.00707659i) q^{80} +(-8.35250 + 3.35197i) q^{81} +(1.24627 + 0.719534i) q^{82} +(-2.52103 + 9.40860i) q^{83} +(-4.77147 + 3.39926i) q^{84} +(-0.00644470 + 0.0240520i) q^{85} +(1.51333 + 5.64783i) q^{86} +(-11.6745 + 4.35716i) q^{87} +(3.74814 + 2.16399i) q^{88} +(-6.15029 - 1.64797i) q^{89} +(0.0143999 + 0.0166043i) q^{90} +(9.62820 - 7.48505i) q^{91} +(7.65827 - 4.42151i) q^{92} +(-9.91170 - 4.52401i) q^{93} +0.690930 q^{94} +(-0.0280258 - 0.0485421i) q^{95} +(-1.00498 - 1.41068i) q^{96} +(1.80444 - 1.80444i) q^{97} +(1.14932 + 4.28931i) q^{98} +(11.6765 - 5.67816i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	1.10250	−	1.33585i	0.636528	−	0.771253i
$3$	1.10250	−	1.33585i	0.636528	−	0.771253i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−0.00707659	+	0.00189617i	−0.00316475	+	0.000847992i	−0.260401	−	0.965501i	$-0.583855\pi$
$5$	−0.00707659	+	0.00189617i	−0.00316475	+	0.000847992i	0.257236	+	0.966349i	$0.417188\pi$
$6$	0.719190	−	1.57568i	0.293608	−	0.643269i
$7$	−2.39172	−	2.39172i	−0.903984	−	0.903984i	0.0917939	−	0.995778i	$-0.470740\pi$
$7$	−2.39172	−	2.39172i	−0.903984	−	0.903984i	−0.995778	+	0.0917939i	$0.970740\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.568989	−	2.94555i	−0.189663	−	0.981849i
$10$	−0.00634470	+	0.00366311i	−0.00200637	+	0.00115838i
$11$	1.12016	+	4.18051i	0.337742	+	1.26047i	0.900866	+	0.434098i	$0.142933\pi$
$11$	1.12016	+	4.18051i	0.337742	+	1.26047i	−0.563124	+	0.826372i	$0.690401\pi$
$12$	0.286868	−	1.70813i	0.0828116	−	0.493095i
$13$	−0.448036	+	3.57761i	−0.124263	+	0.992249i
$13$	−0.448036	+	3.57761i	−0.124263	+	0.992249i
$14$	−2.92924	−	1.69120i	−0.782873	−	0.451992i
$15$	−0.00526894	+	0.0115438i	−0.00136044	+	0.00298059i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.69940	−	2.94345i	0.412166	−	0.713892i	−0.582961	−	0.812500i	$-0.698106\pi$
$17$	1.69940	−	2.94345i	0.412166	−	0.713892i	0.995126	+	0.0986085i	$0.0314391\pi$
$18$	−1.31196	−	2.69792i	−0.309233	−	0.635905i
$19$	1.98018	+	7.39012i	0.454284	+	1.69541i	0.690185	+	0.723633i	$0.257529\pi$
$19$	1.98018	+	7.39012i	0.454284	+	1.69541i	−0.235902	+	0.971777i	$0.575804\pi$
$20$	−0.00518042	+	0.00518042i	−0.00115838	+	0.00115838i
$21$	−5.83184	+	0.558107i	−1.27261	+	0.121789i
$22$	2.16399	+	3.74814i	0.461364	+	0.799106i
$23$	8.84301			1.84390			0.921948	−	0.387314i	$-0.126597\pi$
$23$	8.84301			1.84390			0.921948	+	0.387314i	$0.126597\pi$
$24$	−0.165003	−	1.72417i	−0.0336812	−	0.351945i
$25$	−4.33008	+	2.49997i	−0.866016	+	0.499995i
$26$	0.493183	+	3.57166i	0.0967211	+	0.700461i
$27$	−4.56212	−	2.48738i	−0.877980	−	0.478697i
$28$	−3.26715	−	0.875429i	−0.617433	−	0.165441i
$29$	−6.23056	−	3.59721i	−1.15699	−	0.667986i	−0.206406	−	0.978466i	$-0.566177\pi$
$29$	−6.23056	−	3.59721i	−1.15699	−	0.667986i	−0.950580	+	0.310481i	$0.899510\pi$
$30$	−0.00210166	+	0.0125141i	−0.000383709	+	0.00228476i
$31$	−1.62808	−	6.07609i	−0.292412	−	1.09130i	−0.943251	−	0.332081i	$-0.892249\pi$
$31$	−1.62808	−	6.07609i	−0.292412	−	1.09130i	0.650839	−	0.759216i	$-0.274417\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	6.81951	+	3.11264i	1.18712	+	0.541841i
$34$	0.879676	−	3.28299i	0.150863	−	0.563029i
$35$	0.0214603	+	0.0123901i	0.00362745	+	0.00209431i
$36$	−1.96553	−	2.26642i	−0.327589	−	0.377737i
$37$	−0.558952	+	2.08604i	−0.0918911	+	0.342942i	−0.996530	−	0.0832371i	$-0.973474\pi$
$37$	−0.558952	+	2.08604i	−0.0918911	+	0.342942i	0.904639	+	0.426179i	$0.140141\pi$
$38$	3.82541	+	6.62580i	0.620563	+	1.07485i
$39$	4.28518	+	4.54282i	0.686179	+	0.727433i
$40$	−0.00366311	+	0.00634470i	−0.000579189	+	0.00100318i
$41$	1.01757	+	1.01757i	0.158918	+	0.158918i	0.782087	−	0.623169i	$-0.214155\pi$
$41$	1.01757	+	1.01757i	0.158918	+	0.158918i	−0.623169	+	0.782087i	$0.714155\pi$
$42$	−5.48868	+	2.04848i	−0.846921	+	0.316088i
$43$			5.84706i			0.891669i	0.895115	+	0.445834i	$0.147093\pi$
$43$			5.84706i			0.891669i	−0.895115	+	0.445834i	$0.852907\pi$
$44$	3.06034	+	3.06034i	0.461364	+	0.461364i
$45$	0.00961175	+	0.0197655i	0.00143284	+	0.00294647i
$46$	8.54170	−	2.28874i	1.25940	−	0.337456i
$47$	0.667387	+	0.178826i	0.0973484	+	0.0260844i	0.307164	−	0.951656i	$-0.400620\pi$
$47$	0.667387	+	0.178826i	0.0973484	+	0.0260844i	−0.209816	+	0.977741i	$0.567287\pi$
$48$	−0.605630	−	1.62272i	−0.0874152	−	0.234219i
$49$			4.44062i			0.634375i
$50$	−3.53550	+	3.53550i	−0.499995	+	0.499995i
$51$	−2.05842	−	5.51530i	−0.288236	−	0.772297i
$52$	1.40079	+	3.32232i	0.194255	+	0.460722i
$53$		−	1.59509i		−	0.219103i	−0.993981	−	0.109551i	$-0.965059\pi$
$53$		−	1.59509i		−	0.219103i	0.993981	−	0.109551i	$-0.0349414\pi$
$54$	−5.05045	−	1.22186i	−0.687279	−	0.166274i
$55$	−0.0158539	−	0.0274597i	−0.00213774	−	0.00370267i
$56$	−3.38240			−0.451992
$57$	12.0552	+	5.50239i	1.59675	+	0.728809i
$58$	−6.94928	−	1.86206i	−0.912486	−	0.244500i
$59$	1.43000	+	0.383168i	0.186171	+	0.0498843i	0.350700	−	0.936488i	$-0.385944\pi$
$59$	1.43000	+	0.383168i	0.186171	+	0.0498843i	−0.164529	+	0.986372i	$0.552610\pi$
$60$	0.00120885	+	0.0126317i	0.000156062	+	0.00163074i
$61$	−14.7526			−1.88888			−0.944441	−	0.328680i	$-0.893396\pi$
$61$	−14.7526			−1.88888			−0.944441	+	0.328680i	$0.893396\pi$
$62$	−3.14521	−	5.44767i	−0.399443	−	0.691855i
$63$	−5.68406	+	8.40578i	−0.716124	+	1.05903i
$64$		−	1.00000i		−	0.125000i
$65$	−0.00361317	−	0.0261668i	−0.000448158	−	0.00324559i
$66$	7.39275	+	1.24156i	0.909984	+	0.152825i
$67$	−3.40387	+	3.40387i	−0.415849	+	0.415849i	−0.883770	−	0.467921i	$-0.845003\pi$
$67$	−3.40387	+	3.40387i	−0.415849	+	0.415849i	0.467921	+	0.883770i	$0.345003\pi$
$68$		−	3.39881i		−	0.412166i
$69$	9.74942	−	11.8129i	1.17369	−	1.42211i
$70$	0.0239359	+	0.00641359i	0.00286088	+	0.000766571i
$71$	4.18049	−	1.12016i	0.496133	−	0.132939i	−0.00207155	−	0.999998i	$-0.500659\pi$
$71$	4.18049	−	1.12016i	0.496133	−	0.132939i	0.498205	+	0.867059i	$0.333993\pi$
$72$	−2.48515	−	1.68048i	−0.292878	−	0.198047i
$73$	−6.17624	−	6.17624i	−0.722874	−	0.722874i	0.246316	−	0.969190i	$-0.420780\pi$
$73$	−6.17624	−	6.17624i	−0.722874	−	0.722874i	−0.969190	+	0.246316i	$0.920780\pi$
$74$			2.15962i			0.251051i
$75$	−1.43432	+	8.54056i	−0.165621	+	0.986179i
$76$	5.40994	+	5.40994i	0.620563	+	0.620563i
$77$	7.31947	−	12.6777i	0.834132	−	1.44476i
$78$	5.31494	+	3.27894i	0.601798	+	0.371267i
$79$	−4.25708	−	7.37348i	−0.478959	−	0.829581i	0.520750	−	0.853709i	$-0.325652\pi$
$79$	−4.25708	−	7.37348i	−0.478959	−	0.829581i	−0.999709	+	0.0241282i	$0.992319\pi$
$80$	−0.00189617	+	0.00707659i	−0.000211998	+	0.000791187i
$81$	−8.35250	+	3.35197i	−0.928056	+	0.372441i
$82$	1.24627	+	0.719534i	0.137627	+	0.0794592i
$83$	−2.52103	+	9.40860i	−0.276719	+	1.03273i	0.677962	+	0.735097i	$0.262863\pi$
$83$	−2.52103	+	9.40860i	−0.276719	+	1.03273i	−0.954681	+	0.297631i	$0.903803\pi$
$84$	−4.77147	+	3.39926i	−0.520610	+	0.370889i
$85$	−0.00644470	+	0.0240520i	−0.000699026	+	0.00260880i
$86$	1.51333	+	5.64783i	0.163187	+	0.609021i
$87$	−11.6745	+	4.35716i	−1.25164	+	0.467137i
$88$	3.74814	+	2.16399i	0.399553	+	0.230682i
$89$	−6.15029	−	1.64797i	−0.651930	−	0.174684i	−0.0823284	−	0.996605i	$-0.526236\pi$
$89$	−6.15029	−	1.64797i	−0.651930	−	0.174684i	−0.569601	+	0.821921i	$0.692902\pi$
$90$	0.0143999	+	0.0166043i	0.00151789	+	0.00175025i
$91$	9.62820	−	7.48505i	1.00931	−	0.784646i
$92$	7.65827	−	4.42151i	0.798430	−	0.460974i
$93$	−9.91170	−	4.52401i	−1.02780	−	0.469118i
$94$	0.690930			0.0712640
$95$	−0.0280258	−	0.0485421i	−0.00287539	−	0.00498031i
$96$	−1.00498	−	1.41068i	−0.102571	−	0.143977i
$97$	1.80444	−	1.80444i	0.183213	−	0.183213i	−0.609541	−	0.792754i	$-0.708646\pi$
$97$	1.80444	−	1.80444i	0.183213	−	0.183213i	0.792754	+	0.609541i	$0.208646\pi$
$98$	1.14932	+	4.28931i	0.116099	+	0.433286i
$99$	11.6765	−	5.67816i	1.17353	−	0.570676i
$100$	−2.49997	+	4.33008i	−0.249997	+	0.433008i
$101$	4.43730	−	7.68564i	0.441528	−	0.764749i	−0.556275	−	0.830998i	$-0.687770\pi$
$101$	4.43730	−	7.68564i	0.441528	−	0.764749i	0.997803	+	0.0662490i	$0.0211032\pi$
$102$	−3.41574	−	4.79461i	−0.338209	−	0.474738i
$103$	1.63615	+	0.944630i	0.161214	+	0.0930772i	0.578437	−	0.815727i	$-0.303663\pi$
$103$	1.63615	+	0.944630i	0.161214	+	0.0930772i	−0.417222	+	0.908804i	$0.636996\pi$
$104$	2.21294	+	2.84656i	0.216997	+	0.279128i
$105$	0.0402113	−	0.0150076i	0.00392422	−	0.00146460i
$106$	−0.412841	−	1.54074i	−0.0400986	−	0.149650i
$107$	7.61187	−	4.39471i	0.735867	−	0.424853i	−0.0846978	−	0.996407i	$-0.526992\pi$
$107$	7.61187	−	4.39471i	0.735867	−	0.424853i	0.820565	+	0.571554i	$0.193659\pi$
$108$	−5.19460	+	0.126924i	−0.499851	+	0.0122132i
$109$	4.81846	−	4.81846i	0.461524	−	0.461524i	−0.437631	−	0.899155i	$-0.644182\pi$
$109$	4.81846	−	4.81846i	0.461524	−	0.461524i	0.899155	+	0.437631i	$0.144182\pi$
$110$	−0.0224208	−	0.0224208i	−0.00213774	−	0.00213774i
$111$	2.17039	+	3.04653i	0.206004	+	0.289164i
$112$	−3.26715	+	0.875429i	−0.308716	+	0.0827203i
$113$	6.88106	−	3.97278i	0.647315	−	0.373728i	−0.140112	−	0.990136i	$-0.544746\pi$
$113$	6.88106	−	3.97278i	0.647315	−	0.373728i	0.787427	+	0.616408i	$0.211413\pi$
$114$	13.0686	+	2.19477i	1.22398	+	0.205559i
$115$	−0.0625784	+	0.0167678i	−0.00583546	+	0.00156361i
$116$	−7.19443			−0.667986
$117$	10.7929	−	0.715906i	0.997807	−	0.0661855i
$118$	1.48045			0.136286
$119$	−11.1044	+	2.97541i	−1.01794	+	0.272756i
$120$	0.00443698	+	0.0118884i	0.000405039	+	0.00108526i
$121$	−6.69559	+	3.86570i	−0.608690	+	0.351427i
$122$	−14.2500	+	3.81827i	−1.29013	+	0.345690i
$123$	2.48120	−	0.237451i	0.223723	−	0.0214102i
$124$	−4.44800	−	4.44800i	−0.399443	−	0.399443i
$125$	0.0518040	−	0.0518040i	0.00463349	−	0.00463349i
$126$	−3.31480	+	9.59050i	−0.295306	+	0.854390i
$127$	9.81401	−	5.66612i	0.870853	−	0.502787i	0.00322112	−	0.999995i	$-0.498975\pi$
$127$	9.81401	−	5.66612i	0.870853	−	0.502787i	0.867631	+	0.497208i	$0.165641\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	7.81080	+	6.44639i	0.687702	+	0.567573i
$130$	−0.0102625	−	0.0243400i	−0.000900082	−	0.00213476i
$131$	−12.0036	−	6.93030i	−1.04876	−	0.605504i	−0.126460	−	0.991972i	$-0.540362\pi$
$131$	−12.0036	−	6.93030i	−1.04876	−	0.605504i	−0.922303	+	0.386468i	$0.873695\pi$
$132$	7.46218	−	0.714131i	0.649500	−	0.0621571i
$133$	12.9391	−	22.4111i	1.12196	−	1.94329i
$134$	−2.40690	+	4.16888i	−0.207925	+	0.360136i
$135$	0.0370007	+	0.00895164i	0.00318452	+	0.000770435i
$136$	−0.879676	−	3.28299i	−0.0754316	−	0.281514i
$137$	11.0783	−	11.0783i	0.946483	−	0.946483i	−0.0521564	−	0.998639i	$-0.516609\pi$
$137$	11.0783	−	11.0783i	0.946483	−	0.946483i	0.998639	+	0.0521564i	$0.0166094\pi$
$138$	6.35980	−	13.9338i	0.541382	−	1.18612i
$139$	5.62781	+	9.74766i	0.477345	+	0.826786i	0.999663	−	0.0259652i	$-0.00826592\pi$
$139$	5.62781	+	9.74766i	0.477345	+	0.826786i	−0.522318	+	0.852751i	$0.674933\pi$
$140$	0.0247802			0.00209431
$141$	0.974678	−	0.694373i	0.0820827	−	0.0584768i
$142$	3.74813	−	2.16398i	0.314536	−	0.181597i
$143$	−15.4581	+	2.13448i	−1.29267	+	0.178495i
$144$	−2.83541	−	0.980015i	−0.236284	−	0.0816679i
$145$	0.0509120	+	0.0136418i	0.00422801	+	0.00113289i
$146$	−7.56431	−	4.36726i	−0.626027	−	0.361437i
$147$	5.93200	+	4.89578i	0.489263	+	0.403797i
$148$	0.558952	+	2.08604i	0.0459456	+	0.171471i
$149$	−4.63061	+	17.2817i	−0.379354	+	1.41577i	0.467523	+	0.883981i	$0.345146\pi$
$149$	−4.63061	+	17.2817i	−0.379354	+	1.41577i	−0.846877	+	0.531788i	$0.821520\pi$
$150$	0.825008	+	8.62077i	0.0673616	+	0.703883i
$151$	−0.0484351	+	0.180762i	−0.00394159	+	0.0147102i	−0.967869	−	0.251456i	$-0.919090\pi$
$151$	−0.0484351	+	0.180762i	−0.00394159	+	0.0147102i	0.963927	+	0.266167i	$0.0857571\pi$
$152$	6.62580	+	3.82541i	0.537423	+	0.310281i
$153$	−9.63702	−	3.33088i	−0.779107	−	0.269286i
$154$	3.78884	−	14.1401i	0.305313	−	1.13944i
$155$	0.0230425	+	0.0399109i	0.00185082	+	0.00320572i
$156$	5.98249	+	1.79160i	0.478982	+	0.143443i
$157$	2.79848	−	4.84712i	0.223343	−	0.386842i	−0.732478	−	0.680791i	$-0.761636\pi$
$157$	2.79848	−	4.84712i	0.223343	−	0.386842i	0.955821	+	0.293949i	$0.0949696\pi$
$158$	−6.02042	−	6.02042i	−0.478959	−	0.478959i
$159$	−2.13080	−	1.75859i	−0.168984	−	0.139465i
$160$			0.00732623i			0.000579189i
$161$	−21.1500	−	21.1500i	−1.66685	−	1.66685i
$162$	−7.20035	+	5.39954i	−0.565713	+	0.424228i
$163$	1.99197	−	0.533748i	0.156024	−	0.0418064i	−0.179962	−	0.983674i	$-0.557597\pi$
$163$	1.99197	−	0.533748i	0.156024	−	0.0418064i	0.335985	+	0.941867i	$0.390931\pi$
$164$	1.39003	+	0.372458i	0.108543	+	0.0290841i
$165$	−0.0541609	−	0.00909593i	−0.00421642	−	0.000708117i
$166$			9.74049i			0.756009i
$167$	−10.9349	+	10.9349i	−0.846169	+	0.846169i	−0.989653	−	0.143484i	$-0.954170\pi$
$167$	−10.9349	+	10.9349i	−0.846169	+	0.846169i	0.143484	+	0.989653i	$0.454170\pi$
$168$	−3.72909	+	4.51838i	−0.287706	+	0.348600i
$169$	−12.5985	−	3.20579i	−0.969117	−	0.246600i
$170$			0.0249004i			0.00190977i
$171$	20.6413	−	10.0376i	1.57848	−	0.767594i
$172$	2.92353	+	5.06371i	0.222917	+	0.386104i
$173$	−2.32584			−0.176830			−0.0884152	−	0.996084i	$-0.528180\pi$
$173$	−2.32584			−0.176830			−0.0884152	+	0.996084i	$0.528180\pi$
$174$	−10.1490	+	7.23028i	−0.769394	+	0.548126i
$175$	16.3356	+	4.37710i	1.23485	+	0.330878i
$176$	4.18051	+	1.12016i	0.315117	+	0.0844355i
$177$	2.08843	−	1.48783i	0.156976	−	0.111832i
$178$	−6.36725			−0.477246
$179$	10.4906	+	18.1702i	0.784102	+	1.35811i	0.929534	+	0.368737i	$0.120210\pi$
$179$	10.4906	+	18.1702i	0.784102	+	1.35811i	−0.145431	+	0.989368i	$0.546457\pi$
$180$	0.0182068	+	0.0123116i	0.00135705	+	0.000917651i
$181$		−	15.9164i		−	1.18306i	−0.806284	−	0.591529i	$-0.798524\pi$
$181$		−	15.9164i		−	1.18306i	0.806284	−	0.591529i	$-0.201476\pi$
$182$	7.36285	−	9.72196i	0.545771	−	0.720640i
$183$	−16.2648	+	19.7073i	−1.20233	+	1.45681i
$184$	6.25295	−	6.25295i	0.460974	−	0.460974i
$185$		−	0.0158219i		−	0.00116325i
$186$	−10.7449	−	1.80452i	−0.787852	−	0.132314i
$187$	14.2087	+	3.80722i	1.03904	+	0.278411i
$188$	0.667387	−	0.178826i	0.0486742	−	0.0130422i
$189$	4.96219	+	16.8604i	0.360946	+	1.22641i
$190$	−0.0396345	−	0.0396345i	−0.00287539	−	0.00287539i
$191$		−	17.3134i		−	1.25275i	−0.779520	−	0.626377i	$-0.784537\pi$
$191$		−	17.3134i		−	1.25275i	0.779520	−	0.626377i	$-0.215463\pi$
$192$	−1.33585	−	1.10250i	−0.0964066	−	0.0795661i
$193$	5.54889	+	5.54889i	0.399418	+	0.399418i	0.878028	−	0.478610i	$-0.158859\pi$
$193$	5.54889	+	5.54889i	0.399418	+	0.399418i	−0.478610	+	0.878028i	$0.658859\pi$
$194$	1.27593	−	2.20997i	0.0916064	−	0.158667i
$195$	−0.0389384	−	0.0240222i	−0.00278844	−	0.00172027i
$196$	2.22031	+	3.84569i	0.158594	+	0.274692i
$197$	−0.388990	+	1.45173i	−0.0277144	+	0.103431i	−0.978398	−	0.206732i	$-0.933717\pi$
$197$	−0.388990	+	1.45173i	−0.0277144	+	0.103431i	0.950683	+	0.310164i	$0.100384\pi$
$198$	9.80904	−	8.50678i	0.697098	−	0.604551i
$199$	−0.807763	−	0.466362i	−0.0572608	−	0.0330595i	0.471096	−	0.882082i	$-0.343858\pi$
$199$	−0.807763	−	0.466362i	−0.0572608	−	0.0330595i	−0.528357	+	0.849022i	$0.677192\pi$
$200$	−1.29408	+	4.82958i	−0.0915054	+	0.341503i
$201$	0.794294	+	8.29983i	0.0560252	+	0.585425i
$202$	2.29692	−	8.57221i	0.161611	−	0.603139i
$203$	6.29821	+	23.5052i	0.442048	+	1.64975i
$204$	−4.54029	−	3.74718i	−0.317884	−	0.262355i
$205$	−0.00913045	−	0.00527147i	−0.000637698	−	0.000368175i
$206$	1.82489	+	0.488977i	0.127146	+	0.0340686i
$207$	−5.03158	−	26.0475i	−0.349719	−	1.81043i
$208$	2.87428	+	2.17681i	0.199295	+	0.150935i
$209$	−28.6763	+	16.5563i	−1.98358	+	1.14522i
$210$	0.0349569	−	0.0249037i	0.00241225	−	0.00171852i
$211$	−8.73833			−0.601572			−0.300786	−	0.953692i	$-0.597249\pi$
$211$	−8.73833			−0.601572			−0.300786	+	0.953692i	$0.597249\pi$
$212$	−0.797547	−	1.38139i	−0.0547757	−	0.0948743i
$213$	3.11263	−	6.81949i	0.213274	−	0.467264i
$214$	6.21506	−	6.21506i	0.424853	−	0.424853i
$215$	−0.0110870	−	0.0413773i	−0.000756128	−	0.00282191i
$216$	−4.98475	+	1.46706i	−0.339169	+	0.0998209i
$217$	−10.6384	+	18.4262i	−0.722179	+	1.25085i
$218$	3.40716	−	5.90138i	0.230762	−	0.399692i
$219$	−15.0598	+	1.44122i	−1.01765	+	0.0973889i
$220$	−0.0274597	−	0.0158539i	−0.00185133	−	0.00106887i
$221$	9.76912	+	7.39857i	0.657142	+	0.497681i
$222$	2.88493	+	2.38099i	0.193624	+	0.159801i
$223$	1.90659	+	7.11551i	0.127675	+	0.476490i	0.999921	−	0.0125779i	$-0.00400378\pi$
$223$	1.90659	+	7.11551i	0.127675	+	0.476490i	−0.872246	+	0.489068i	$0.837337\pi$
$224$	−2.92924	+	1.69120i	−0.195718	+	0.112998i
$225$	9.82756	+	11.3320i	0.655171	+	0.755467i
$226$	5.61836	−	5.61836i	0.373728	−	0.373728i
$227$	−3.91405	−	3.91405i	−0.259784	−	0.259784i	0.565182	−	0.824966i	$-0.308806\pi$
$227$	−3.91405	−	3.91405i	−0.259784	−	0.259784i	−0.824966	+	0.565182i	$0.808806\pi$
$228$	13.1913	−	1.26241i	0.873617	−	0.0836052i
$229$	−9.86987	+	2.64462i	−0.652219	+	0.174762i	−0.569732	−	0.821830i	$-0.692953\pi$
$229$	−9.86987	+	2.64462i	−0.652219	+	0.174762i	−0.0824872	+	0.996592i	$0.526286\pi$
$230$	−0.0561062	+	0.0323930i	−0.00369954	+	0.00213593i
$231$	−8.86579	−	23.7549i	−0.583326	−	1.56296i
$232$	−6.94928	+	1.86206i	−0.456243	+	0.122250i
$233$	−2.21636			−0.145199			−0.0725993	−	0.997361i	$-0.523129\pi$
$233$	−2.21636			−0.145199			−0.0725993	+	0.997361i	$0.523129\pi$
$234$	10.2399	−	3.48493i	0.669402	−	0.227817i
$235$	−0.00506191			−0.000330202
$236$	1.43000	−	0.383168i	0.0930853	−	0.0249421i
$237$	−14.5433	−	2.44244i	−0.944688	−	0.158653i
$238$	−9.95593	+	5.74806i	−0.645347	+	0.372591i
$239$	4.39817	−	1.17848i	0.284494	−	0.0762299i	−0.113750	−	0.993509i	$-0.536286\pi$
$239$	4.39817	−	1.17848i	0.284494	−	0.0762299i	0.398244	+	0.917280i	$0.369620\pi$
$240$	0.00736274	+	0.0103349i	0.000475263	+	0.000667117i
$241$	15.3246	+	15.3246i	0.987143	+	0.987143i	0.999918	−	0.0127755i	$-0.00406668\pi$
$241$	15.3246	+	15.3246i	0.987143	+	0.987143i	−0.0127755	+	0.999918i	$0.504067\pi$
$242$	−5.46692	+	5.46692i	−0.351427	+	0.351427i
$243$	−4.73091	+	14.8532i	−0.303488	+	0.952835i
$244$	−12.7762	+	7.37632i	−0.817910	+	0.472221i
$245$	−0.00842016	−	0.0314245i	−0.000537944	−	0.00200764i
$246$	2.33520	−	0.871543i	0.148887	−	0.0555675i
$247$	−27.3261	+	3.77325i	−1.73872	+	0.240086i
$248$	−5.44767	−	3.14521i	−0.345927	−	0.199721i
$249$	9.78904	+	13.7407i	0.620355	+	0.870781i
$250$	0.0366309	−	0.0634466i	0.00231674	−	0.00401272i
$251$	−3.11506	+	5.39544i	−0.196621	+	0.340557i	−0.947431	−	0.319961i	$-0.896330\pi$
$251$	−3.11506	+	5.39544i	−0.196621	+	0.340557i	0.750810	+	0.660519i	$0.229663\pi$
$252$	−0.719649	+	10.1216i	−0.0453336	+	0.637604i
$253$	9.90562	+	36.9683i	0.622761	+	2.32418i
$254$	8.01311	−	8.01311i	0.502787	−	0.502787i
$255$	0.0250245	+	0.0351264i	0.00156710	+	0.00219970i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.13741			−0.0709499			−0.0354750	−	0.999371i	$-0.511294\pi$
$257$	−1.13741			−0.0709499			−0.0354750	+	0.999371i	$0.511294\pi$
$258$	9.21310	+	4.20515i	0.573582	+	0.261801i
$259$	6.32607	−	3.65236i	0.393083	−	0.226946i
$260$	−0.0162125	−	0.0208545i	−0.00100546	−	0.00129334i
$261$	−7.05065	+	20.3992i	−0.436424	+	1.26268i
$262$	−13.3883	−	3.58739i	−0.827133	−	0.221630i
$263$	23.0993	+	13.3364i	1.42436	+	0.822356i	0.996668	−	0.0815669i	$-0.0259924\pi$
$263$	23.0993	+	13.3364i	1.42436	+	0.822356i	0.427695	+	0.903923i	$0.359326\pi$
$264$	7.02309	−	2.62115i	0.432241	−	0.161321i
$265$	0.00302456	+	0.0112878i	0.000185797	+	0.000693405i
$266$	6.69775	−	24.9963i	0.410665	−	1.53262i
$267$	−8.98213	+	6.39898i	−0.549697	+	0.391611i
$268$	−1.24590	+	4.64978i	−0.0761057	+	0.284030i
$269$	4.17266	+	2.40909i	0.254411	+	0.146885i	0.621783	−	0.783190i	$-0.286409\pi$
$269$	4.17266	+	2.40909i	0.254411	+	0.146885i	−0.367371	+	0.930074i	$0.619742\pi$
$270$	0.0380568		0.000929872i	0.00231606		5.65902e-5i
$271$	5.35788	−	19.9959i	0.325468	−	1.21466i	−0.588372	−	0.808590i	$-0.700231\pi$
$271$	5.35788	−	19.9959i	0.325468	−	1.21466i	0.913841	−	0.406073i	$-0.133102\pi$
$272$	−1.69940	−	2.94345i	−0.103041	−	0.178473i
$273$	0.616189	−	21.1141i	0.0372935	−	1.27788i
$274$	7.83354	−	13.5681i	0.473241	−	0.819678i
$275$	−15.3015	−	15.3015i	−0.922718	−	0.922718i
$276$	2.53678	−	15.1050i	0.152696	−	0.909215i
$277$			6.27648i			0.377117i	0.982062	+	0.188558i	$0.0603815\pi$
$277$			6.27648i			0.377117i	−0.982062	+	0.188558i	$0.939619\pi$
$278$	7.95893	+	7.95893i	0.477345	+	0.477345i
$279$	−16.9710	+	8.25282i	−1.01603	+	0.494083i
$280$	0.0239359	−	0.00641359i	0.00143044	−	0.000383285i
$281$	14.5112	+	3.88826i	0.865664	+	0.231954i	0.664212	−	0.747544i	$-0.268767\pi$
$281$	14.5112	+	3.88826i	0.865664	+	0.231954i	0.201452	+	0.979498i	$0.435434\pi$
$282$	0.761750	−	0.922978i	0.0453615	−	0.0549626i
$283$		−	13.6282i		−	0.810112i	−0.914292	−	0.405056i	$-0.867252\pi$
$283$		−	13.6282i		−	0.810112i	0.914292	−	0.405056i	$-0.132748\pi$
$284$	3.06033	−	3.06033i	0.181597	−	0.181597i
$285$	−0.0957434	−	0.0160794i	−0.00567135	−	0.000952461i
$286$	−14.3789	+	6.06260i	−0.850243	+	0.358489i
$287$		−	4.86750i		−	0.287320i
$288$	−2.99245	−	0.212763i	−0.176332	−	0.0125372i
$289$	2.72406	+	4.71821i	0.160239	+	0.277542i
$290$	0.0527080			0.00309512
$291$	−0.421065	−	4.39985i	−0.0246833	−	0.257924i
$292$	−8.43689	−	2.26066i	−0.493732	−	0.132295i
$293$	−7.19654	−	1.92831i	−0.420427	−	0.112653i	0.0424023	−	0.999101i	$-0.486499\pi$
$293$	−7.19654	−	1.92831i	−0.420427	−	0.112653i	−0.462829	+	0.886448i	$0.653166\pi$
$294$	6.99700	+	3.19365i	0.408073	+	0.186257i
$295$	−0.0108461			−0.000631485
$296$	1.07981	+	1.87029i	0.0627628	+	0.108708i
$297$	5.28820	−	21.8582i	0.306852	−	1.26834i
$298$			17.8913i			1.03641i
$299$	−3.96199	+	31.6368i	−0.229128	+	1.82960i
$300$	3.02812	+	8.11350i	0.174828	+	0.468433i
$301$	13.9845	−	13.9845i	0.806054	−	0.806054i
$302$			0.187139i			0.0107686i
$303$	−5.37473	−	14.4010i	−0.308770	−	0.827315i
$304$	7.39012	+	1.98018i	0.423852	+	0.113571i
$305$	0.104398	−	0.0279735i	0.00597784	−	0.00160176i
$306$	−10.1707	−	0.723139i	−0.581423	−	0.0413391i
$307$	−18.2096	−	18.2096i	−1.03928	−	1.03928i	−0.999196	−	0.0400805i	$-0.987239\pi$
$307$	−18.2096	−	18.2096i	−1.03928	−	1.03928i	−0.0400805	−	0.999196i	$-0.512761\pi$
$308$		−	14.6389i		−	0.834132i
$309$	3.06574	−	1.14419i	0.174404	−	0.0650909i
$310$	0.0325871	+	0.0325871i	0.00185082	+	0.00185082i
$311$	−5.59249	+	9.68648i	−0.317121	+	0.549270i	−0.979886	−	0.199558i	$-0.936050\pi$
$311$	−5.59249	+	9.68648i	−0.317121	+	0.549270i	0.662765	+	0.748827i	$0.269383\pi$
$312$	6.24234	+	0.182175i	0.353403	+	0.0103136i
$313$	5.98363	+	10.3640i	0.338215	+	0.585806i	0.984097	−	0.177632i	$-0.0568436\pi$
$313$	5.98363	+	10.3640i	0.338215	+	0.585806i	−0.645882	+	0.763437i	$0.723510\pi$
$314$	1.44860	−	5.40625i	0.0817493	−	0.305093i
$315$	0.0242850	−	0.0702622i	0.00136830	−	0.00395882i
$316$	−7.37348	−	4.25708i	−0.414791	−	0.239479i
$317$	−1.37318	+	5.12478i	−0.0771255	+	0.287836i	−0.993707	−	0.112012i	$-0.964271\pi$
$317$	−1.37318	+	5.12478i	−0.0771255	+	0.287836i	0.916581	+	0.399848i	$0.130937\pi$
$318$	−2.51336	−	1.14717i	−0.140942	−	0.0643303i
$319$	8.05893	−	30.0763i	0.451214	−	1.68395i
$320$	0.00189617	+	0.00707659i	0.000105999	+	0.000395593i
$321$	2.52140	−	15.0135i	0.140731	−	0.837971i
$322$	−25.9033	−	14.9553i	−1.44354	−	0.833426i
$323$	25.1176	+	6.73023i	1.39758	+	0.374480i
$324$	−5.55750	+	7.07914i	−0.308750	+	0.393286i
$325$	−7.00389	−	16.6114i	−0.388506	−	0.921435i
$326$	1.78596	−	1.03112i	0.0989149	−	0.0571086i
$327$	−1.12439	−	11.7491i	−0.0621787	−	0.649726i
$328$	1.43907			0.0794592
$329$	−1.16850	−	2.02390i	−0.0644215	−	0.111581i
$330$	−0.0546697	+	0.00523189i	−0.00300947	+	0.000288006i
$331$	−0.572232	+	0.572232i	−0.0314527	+	0.0314527i	−0.722658	−	0.691206i	$-0.757080\pi$
$331$	−0.572232	+	0.572232i	−0.0314527	+	0.0314527i	0.691206	+	0.722658i	$0.257080\pi$
$332$	2.52103	+	9.40860i	0.138359	+	0.516364i
$333$	6.46256	+	0.459488i	0.354146	+	0.0251798i
$334$	−7.73215	+	13.3925i	−0.423084	+	0.732804i
$335$	0.0176335	−	0.0305421i	0.000963421	−	0.00166869i
$336$	−2.43259	+	5.32958i	−0.132708	+	0.290752i
$337$	10.6165	+	6.12944i	0.578318	+	0.333892i	0.760465	−	0.649379i	$-0.224971\pi$
$337$	10.6165	+	6.12944i	0.578318	+	0.333892i	−0.182147	+	0.983271i	$0.558305\pi$
$338$	−12.9990	+	0.164179i	−0.707050	+	0.00893015i
$339$	2.27933	−	13.5720i	0.123796	−	0.737132i
$340$	0.00644470	+	0.0240520i	0.000349513	+	0.00130440i
$341$	23.5774	−	13.6124i	1.27679	−	0.737154i
$342$	17.3400	−	15.0379i	0.937640	−	0.813158i
$343$	−6.12131	+	6.12131i	−0.330520	+	0.330520i
$344$	4.13450	+	4.13450i	0.222917	+	0.222917i
$345$	−0.0465934	+	0.102082i	−0.00250850	+	0.00549590i
$346$	−2.24659	+	0.601972i	−0.120777	+	0.0323622i
$347$	26.1827	−	15.1166i	1.40556	−	0.811501i	0.410605	−	0.911813i	$-0.365318\pi$
$347$	26.1827	−	15.1166i	1.40556	−	0.811501i	0.994956	+	0.100312i	$0.0319842\pi$
$348$	−7.93185	+	9.61067i	−0.425192	+	0.515186i
$349$	−13.9019	+	3.72500i	−0.744151	+	0.199395i	−0.610922	−	0.791690i	$-0.709201\pi$
$349$	−13.9019	+	3.72500i	−0.744151	+	0.199395i	−0.133229	+	0.991085i	$0.542535\pi$
$350$	16.9118			0.903974
$351$	10.9429	−	15.2070i	0.584087	−	0.811691i
$352$	4.32798			0.230682
$353$	10.6271	−	2.84752i	0.565624	−	0.151558i	0.0353350	−	0.999376i	$-0.488750\pi$
$353$	10.6271	−	2.84752i	0.565624	−	0.151558i	0.530289	+	0.847817i	$0.322084\pi$
$354$	1.63219	−	1.97766i	0.0867502	−	0.105111i
$355$	−0.0274596	+	0.0158538i	−0.00145741	+	0.000841434i
$356$	−6.15029	+	1.64797i	−0.325965	+	0.0873420i
$357$	−8.26789	+	18.1142i	−0.437583	+	0.958705i
$358$	14.8359	+	14.8359i	0.784102	+	0.784102i
$359$	7.93090	−	7.93090i	0.418577	−	0.418577i	−0.466136	−	0.884713i	$-0.654354\pi$
$359$	7.93090	−	7.93090i	0.418577	−	0.418577i	0.884713	+	0.466136i	$0.154354\pi$
$360$	0.0207729	+	0.00717981i	0.00109483	+	0.000378409i
$361$	−34.2383	+	19.7675i	−1.80201	+	1.04039i
$362$	−4.11947	−	15.3741i	−0.216515	−	0.808044i
$363$	−2.21789	+	13.2062i	−0.116409	+	0.693147i
$364$	4.59574	−	11.2963i	0.240882	−	0.592089i
$365$	0.0554179	+	0.0319955i	0.00290070	+	0.00167472i
$366$	−10.6100	+	23.2454i	−0.554591	+	1.21506i
$367$	−2.52409	+	4.37185i	−0.131756	+	0.228209i	−0.924354	−	0.381537i	$-0.875395\pi$
$367$	−2.52409	+	4.37185i	−0.131756	+	0.228209i	0.792597	+	0.609745i	$0.208728\pi$
$368$	4.42151	−	7.65827i	0.230487	−	0.399215i
$369$	2.41833	−	3.57630i	0.125893	−	0.186175i
$370$	−0.00409501	−	0.0152828i	−0.000212889	−	0.000794514i
$371$	−3.81501	+	3.81501i	−0.198066	+	0.198066i
$372$	−10.8458	+	1.03794i	−0.562328	+	0.0538148i
$373$	10.2036	+	17.6731i	0.528321	+	0.915078i	0.999455	+	0.0330165i	$0.0105114\pi$
$373$	10.2036	+	17.6731i	0.528321	+	0.915078i	−0.471134	+	0.882062i	$0.656155\pi$
$374$	14.7100			0.760634
$375$	−0.0120885	−	0.126316i	−0.000624245	−	0.00652294i
$376$	0.598363	−	0.345465i	0.0308582	−	0.0178160i
$377$	15.6609	−	20.6788i	0.806579	−	1.06501i
$378$	9.15690	+	15.0016i	0.470980	+	0.771599i
$379$	33.4698	+	8.96819i	1.71923	+	0.460665i	0.977656	−	0.210211i	$-0.0674150\pi$
$379$	33.4698	+	8.96819i	1.71923	+	0.460665i	0.741570	+	0.670876i	$0.234082\pi$
$380$	−0.0485421	−	0.0280258i	−0.00249016	−	0.00143769i
$381$	3.25086	−	19.3569i	0.166546	−	0.991686i
$382$	−4.48104	−	16.7235i	−0.229270	−	0.855647i
$383$	6.22250	−	23.2227i	0.317955	−	1.18662i	−0.603252	−	0.797550i	$-0.706129\pi$
$383$	6.22250	−	23.2227i	0.317955	−	1.18662i	0.921207	−	0.389073i	$-0.127205\pi$
$384$	−1.57568	−	0.719190i	−0.0804086	−	0.0367010i
$385$	−0.0277579	+	0.103594i	−0.00141467	+	0.00527963i
$386$	6.79597	+	3.92365i	0.345906	+	0.199709i
$387$	17.2228	−	3.32691i	0.875484	−	0.169117i
$388$	0.660470	−	2.46491i	0.0335303	−	0.125137i
$389$	−12.9561	−	22.4406i	−0.656898	−	1.13778i	−0.981414	−	0.191901i	$-0.938535\pi$
$389$	−12.9561	−	22.4406i	−0.656898	−	1.13778i	0.324516	−	0.945880i	$-0.394799\pi$
$390$	−0.0438291	−	0.0131257i	−0.00221937	−	0.000664646i
$391$	15.0278	−	26.0290i	0.759991	−	1.31634i
$392$	3.13999	+	3.13999i	0.158594	+	0.158594i
$393$	−22.4919	+	8.39440i	−1.13456	+	0.423441i
$394$			1.50294i			0.0757171i
$395$	0.0441069	+	0.0441069i	0.00221926	+	0.00221926i
$396$	7.27308	−	10.7557i	0.365486	−	0.540494i
$397$	−27.4735	+	7.36149i	−1.37885	+	0.369463i	−0.870705	−	0.491806i	$-0.836337\pi$
$397$	−27.4735	+	7.36149i	−1.37885	+	0.369463i	−0.508149	+	0.861269i	$0.669670\pi$
$398$	−0.900942	−	0.241407i	−0.0451602	−	0.0121006i
$399$	−15.6726	−	41.9929i	−0.784609	−	2.10227i
$400$			4.99995i			0.249997i
$401$	−0.285836	+	0.285836i	−0.0142740	+	0.0142740i	−0.714208	−	0.699934i	$-0.753213\pi$
$401$	−0.285836	+	0.285836i	−0.0142740	+	0.0142740i	0.699934	+	0.714208i	$0.253213\pi$
$402$	2.91538	+	7.81144i	0.145406	+	0.389599i
$403$	22.4673	−	3.10233i	1.11918	−	0.154538i
$404$		−	8.87461i		−	0.441528i
$405$	0.0527514	−	0.0395582i	0.00262124	−	0.00196566i
$406$	12.1672	+	21.0742i	0.603849	+	1.04590i
$407$	−9.34681			−0.463304
$408$	−5.35543	−	2.44439i	−0.265133	−	0.121015i
$409$	−21.4506	−	5.74766i	−1.06066	−	0.284204i	−0.314011	−	0.949419i	$-0.601673\pi$
$409$	−21.4506	−	5.74766i	−1.06066	−	0.284204i	−0.746651	+	0.665216i	$0.768340\pi$
$410$	−0.0101837	−	0.00272871i	−0.000502937	−	0.000134762i
$411$	−2.58512	−	27.0128i	−0.127515	−	1.33244i
$412$	1.88926			0.0930772
$413$	−2.50373	−	4.33660i	−0.123201	−	0.213390i
$414$	−11.6017	−	23.8577i	−0.570194	−	1.17254i
$415$		−	0.0713611i		−	0.00350298i
$416$	3.33974	+	1.35872i	0.163744	+	0.0666168i
$417$	19.2261	+	3.22888i	0.941505	+	0.158119i
$418$	−23.4141	+	23.4141i	−1.14522	+	1.14522i
$419$		−	38.4264i		−	1.87725i	−0.344935	−	0.938627i	$-0.612099\pi$
$419$		−	38.4264i		−	1.87725i	0.344935	−	0.938627i	$-0.387901\pi$
$420$	0.0273202	−	0.0331026i	0.00133309	−	0.00161524i
$421$	−2.57281	−	0.689382i	−0.125391	−	0.0335984i	0.195578	−	0.980688i	$-0.437342\pi$
$421$	−2.57281	−	0.689382i	−0.125391	−	0.0335984i	−0.320969	+	0.947090i	$0.604008\pi$
$422$	−8.44058	+	2.26165i	−0.410881	+	0.110095i
$423$	0.147004	−	2.06757i	0.00714759	−	0.100529i
$424$	−1.12790	−	1.12790i	−0.0547757	−	0.0547757i
$425$			16.9938i			0.824323i
$426$	1.24155	−	7.39273i	0.0601535	−	0.358179i
$427$	35.2842	+	35.2842i	1.70752	+	1.70752i
$428$	4.39471	−	7.61187i	0.212426	−	0.367933i
$429$	−14.1912	+	23.0029i	−0.685156	+	1.11059i
$430$	−0.0214185	−	0.0370978i	−0.00103289	−	0.00178902i
$431$	−8.33838	+	31.1192i	−0.401646	+	1.49896i	0.408514	+	0.912752i	$0.366047\pi$
$431$	−8.33838	+	31.1192i	−0.401646	+	1.49896i	−0.810160	+	0.586209i	$0.800620\pi$
$432$	−4.43520	+	2.70722i	−0.213388	+	0.130251i
$433$	2.57896	+	1.48896i	0.123937	+	0.0715550i	0.560687	−	0.828028i	$-0.310537\pi$
$433$	2.57896	+	1.48896i	0.123937	+	0.0715550i	−0.436750	+	0.899583i	$0.643871\pi$
$434$	−5.50682	+	20.5517i	−0.264336	+	0.986515i
$435$	0.0743539	−	0.0529707i	0.00356500	−	0.00253975i
$436$	1.76368	−	6.58213i	0.0844648	−	0.315227i
$437$	17.5107	+	65.3509i	0.837652	+	3.12616i
$438$	−14.1737	+	5.28988i	−0.677243	+	0.252760i
$439$	5.06772	+	2.92585i	0.241869	+	0.139643i	0.616036	−	0.787718i	$-0.288738\pi$
$439$	5.06772	+	2.92585i	0.241869	+	0.139643i	−0.374166	+	0.927362i	$0.622071\pi$
$440$	−0.0306273	−	0.00820657i	−0.00146010	−	0.000391233i
$441$	13.0801	−	2.52666i	0.622860	−	0.120317i
$442$	11.3511	+	4.61803i	0.539918	+	0.219657i
$443$	−3.42857	+	1.97949i	−0.162896	+	0.0940483i	−0.579232	−	0.815163i	$-0.696647\pi$
$443$	−3.42857	+	1.97949i	−0.162896	+	0.0940483i	0.416336	+	0.909211i	$0.363314\pi$
$444$	3.40288	+	1.55318i	0.161493	+	0.0737106i
$445$	0.0466479			0.00221132
$446$	3.68326	+	6.37959i	0.174407	+	0.302082i
$447$	17.9805	+	25.2388i	0.850447	+	1.19376i
$448$	−2.39172	+	2.39172i	−0.112998	+	0.112998i
$449$	−1.69373	−	6.32109i	−0.0799322	−	0.298311i	0.914374	−	0.404870i	$-0.132683\pi$
$449$	−1.69373	−	6.32109i	−0.0799322	−	0.298311i	−0.994306	+	0.106559i	$0.966017\pi$
$450$	12.4256	+	8.40231i	0.585750	+	0.396089i
$451$	−3.11413	+	5.39383i	−0.146639	+	0.253985i
$452$	3.97278	−	6.88106i	0.186864	−	0.323658i
$453$	0.188071	+	0.263992i	0.00883637	+	0.0124034i
$454$	−4.79371	−	2.76765i	−0.224980	−	0.129892i
$455$	−0.0539419	+	0.0712253i	−0.00252884	+	0.00333909i
$456$	12.4151	−	4.63356i	0.581391	−	0.216986i
$457$	−4.35685	−	16.2600i	−0.203805	−	0.760609i	−0.989811	−	0.142390i	$-0.954521\pi$
$457$	−4.35685	−	16.2600i	−0.203805	−	0.760609i	0.786006	−	0.618219i	$-0.212146\pi$
$458$	−8.84908	+	5.10902i	−0.413490	+	0.238729i
$459$	−15.0744	+	9.20131i	−0.703611	+	0.429481i
$460$	−0.0458106	+	0.0458106i	−0.00213593	+	0.00213593i
$461$	−0.680194	−	0.680194i	−0.0316798	−	0.0316798i	0.691089	−	0.722769i	$-0.257131\pi$
$461$	−0.680194	−	0.680194i	−0.0316798	−	0.0316798i	−0.722769	+	0.691089i	$0.757131\pi$
$462$	−14.7119	−	20.6508i	−0.684460	−	0.960763i
$463$	−37.9000	+	10.1553i	−1.76136	+	0.471955i	−0.986991	−	0.160777i	$-0.948600\pi$
$463$	−37.9000	+	10.1553i	−1.76136	+	0.471955i	−0.774371	+	0.632732i	$0.781933\pi$
$464$	−6.23056	+	3.59721i	−0.289246	+	0.166996i
$465$	0.0787193	+	0.0132203i	0.00365052	+	0.000613078i
$466$	−2.14084	+	0.573636i	−0.0991725	+	0.0265732i
$467$	−21.0464			−0.973910			−0.486955	−	0.873427i	$-0.661892\pi$
$467$	−21.0464			−0.973910			−0.486955	+	0.873427i	$0.661892\pi$
$468$	8.98900	−	6.01646i	0.415517	−	0.278111i
$469$	16.2822			0.751842
$470$	−0.00488943	+	0.00131012i	−0.000225532	+	6.04312e-5i
$471$	−3.38969	−	9.08230i	−0.156189	−	0.418490i
$472$	1.28211	−	0.740225i	0.0590137	−	0.0340716i
$473$	−24.4437	+	6.54966i	−1.12392	+	0.301154i
$474$	−14.6799	+	1.40486i	−0.674269	+	0.0645276i
$475$	−27.0494	−	27.0494i	−1.24111	−	1.24111i
$476$	−8.12898	+	8.12898i	−0.372591	+	0.372591i
$477$	−4.69842	+	0.907590i	−0.215126	+	0.0415557i
$478$	3.94329	−	2.27666i	0.180362	−	0.104132i
$479$	6.30328	+	23.5242i	0.288004	+	1.07485i	0.946616	+	0.322364i	$0.104477\pi$
$479$	6.30328	+	23.5242i	0.288004	+	1.07485i	−0.658612	+	0.752483i	$0.728856\pi$
$480$	0.00978674	+	0.00807716i	0.000446701	+	0.000368670i
$481$	−7.21259	−	2.93433i	−0.328866	−	0.133794i
$482$	18.7687	+	10.8361i	0.854891	+	0.493571i
$483$	−51.5711	+	4.93535i	−2.34656	+	0.224566i
$484$	−3.86570	+	6.69559i	−0.175714	+	0.304345i
$485$	−0.00934774	+	0.0161908i	−0.000424459	+	0.000735185i
$486$	−0.725405	+	15.5716i	−0.0329051	+	0.706341i
$487$	−2.62593	−	9.80011i	−0.118992	−	0.444085i	0.880562	−	0.473931i	$-0.157165\pi$
$487$	−2.62593	−	9.80011i	−0.118992	−	0.444085i	−0.999555	+	0.0298452i	$0.990499\pi$
$488$	−10.4317	+	10.4317i	−0.472221	+	0.472221i
$489$	1.48314	−	3.24944i	0.0670701	−	0.146945i
$490$	−0.0162665	−	0.0281744i	−0.000734845	−	0.00127279i
$491$	−2.22679			−0.100494			−0.0502468	−	0.998737i	$-0.516001\pi$
$491$	−2.22679			−0.100494			−0.0502468	+	0.998737i	$0.516001\pi$
$492$	2.03006	−	1.44624i	0.0915221	−	0.0652015i
$493$	−21.1765	+	12.2262i	−0.953739	+	0.550642i
$494$	−25.4184	+	10.7172i	−1.14363	+	0.482190i
$495$	−0.0718632	+	0.0623226i	−0.00323001	+	0.00280119i
$496$	−6.07609	−	1.62808i	−0.272824	−	0.0731031i
$497$	−12.6777	−	7.31945i	−0.568671	−	0.328322i
$498$	13.0118	+	10.7389i	0.583074	+	0.481221i
$499$	−7.78525	−	29.0549i	−0.348516	−	1.30068i	−0.888451	−	0.458971i	$-0.848218\pi$
$499$	−7.78525	−	29.0549i	−0.348516	−	1.30068i	0.539936	−	0.841706i	$-0.318449\pi$
$500$	0.0189616	−	0.0707655i	0.000847987	−	0.00316473i
$501$	2.55166	+	26.6631i	0.114000	+	1.19122i
$502$	−1.61247	+	6.01784i	−0.0719683	+	0.268589i
$503$	13.5496	+	7.82284i	0.604145	+	0.348803i	0.770670	−	0.637234i	$-0.219922\pi$
$503$	13.5496	+	7.82284i	0.604145	+	0.348803i	−0.166526	+	0.986037i	$0.553255\pi$
$504$	1.92455	+	9.96302i	0.0857262	+	0.443788i
$505$	−0.0168277	+	0.0628020i	−0.000748824	+	0.00279465i
$506$	19.1362	+	33.1448i	0.850707	+	1.47347i
$507$	−18.1723	+	13.2954i	−0.807062	+	0.590467i
$508$	5.66612	−	9.81401i	0.251393	−	0.435426i
$509$	−1.42351	−	1.42351i	−0.0630958	−	0.0630958i	0.674855	−	0.737951i	$-0.264206\pi$
$509$	−1.42351	−	1.42351i	−0.0630958	−	0.0630958i	−0.737951	+	0.674855i	$0.764206\pi$
$510$	0.0332632	+	0.0274527i	0.00147292	+	0.00121563i
$511$			29.5436i			1.30693i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	9.34825	−	38.6401i	0.412735	−	1.70600i
$514$	−1.09866	+	0.294384i	−0.0484597	+	0.0129847i
$515$	−0.0133695	−	0.00358235i	−0.000589132	−	0.000157857i
$516$	9.98754	+	1.67733i	0.439677	+	0.0738405i
$517$			2.99033i			0.131515i
$518$	5.16521	−	5.16521i	0.226946	−	0.226946i
$519$	−2.56424	+	3.10698i	−0.112558	+	0.136381i
$520$	−0.0210576	−	0.0159478i	−0.000923438	−	0.000699359i
$521$		−	34.1838i		−	1.49762i	−0.662784	−	0.748811i	$-0.730625\pi$
$521$		−	34.1838i		−	1.49762i	0.662784	−	0.748811i	$-0.269375\pi$
$522$	−1.53071	+	21.5289i	−0.0669972	+	0.942296i
$523$	6.14607	+	10.6453i	0.268749	+	0.465486i	0.968539	−	0.248862i	$-0.0800566\pi$
$523$	6.14607	+	10.6453i	0.268749	+	0.465486i	−0.699790	+	0.714348i	$0.746723\pi$
$524$	−13.8606			−0.605504
$525$	23.8571	−	16.9961i	1.04121	−	0.741771i
$526$	25.7639	+	6.90342i	1.12336	+	0.301003i
$527$	−20.6514	−	5.53354i	−0.899591	−	0.241045i
$528$	6.10538	−	4.34955i	0.265702	−	0.189290i
$529$	55.1989			2.39995
$530$	0.00584301	+	0.0101204i	0.000253804	+	0.000439601i
$531$	0.314984	−	4.43016i	0.0136692	−	0.192253i
$532$		−	25.8781i		−	1.12196i
$533$	−4.09639	+	3.18457i	−0.177434	+	0.137939i
$534$	−7.01989	+	8.50569i	−0.303780	+	0.368077i
$535$	−0.0455330	+	0.0455330i	−0.00196856	+	0.00196856i
$536$			4.81380i			0.207925i
$537$	35.8385	+	6.01882i	1.54655	+	0.259731i
$538$	4.65400	+	1.24703i	0.200648	+	0.0537635i
$539$	−18.5640	+	4.97422i	−0.799610	+	0.214255i
$540$	0.0365194	−	0.0107480i	0.00157154	−	0.000462521i
$541$	−6.69233	−	6.69233i	−0.287726	−	0.287726i	0.548455	−	0.836180i	$-0.315216\pi$
$541$	−6.69233	−	6.69233i	−0.287726	−	0.287726i	−0.836180	+	0.548455i	$0.815216\pi$
$542$		−	20.7013i		−	0.889195i
$543$	−21.2619	−	17.5478i	−0.912437	−	0.753050i
$544$	−2.40332	−	2.40332i	−0.103041	−	0.103041i
$545$	−0.0249616	+	0.0432348i	−0.00106924	+	0.00185198i
$546$	−4.86953	−	20.5541i	−0.208397	−	0.879635i
$547$	17.8148	+	30.8561i	0.761705	+	1.31931i	0.941971	+	0.335694i	$0.108971\pi$
$547$	17.8148	+	30.8561i	0.761705	+	1.31931i	−0.180266	+	0.983618i	$0.557696\pi$
$548$	4.05494	−	15.1332i	0.173218	−	0.646460i
$549$	8.39409	+	43.4546i	0.358251	+	1.85460i
$550$	−18.7405	−	10.8198i	−0.799097	−	0.461359i
$551$	14.2462	−	53.1677i	0.606910	−	2.26502i
$552$	−1.45913	−	15.2469i	−0.0621046	−	0.648951i
$553$	−7.45354	+	27.8170i	−0.316957	+	1.18290i
$554$	1.62447	+	6.06261i	0.0690172	+	0.257576i
$555$	−0.0211357	−	0.0174436i	−0.000897160	−	0.000740441i
$556$	9.74766	+	5.62781i	0.413393	+	0.238672i
$557$	−5.79876	−	1.55377i	−0.245701	−	0.0658355i	0.133867	−	0.990999i	$-0.457261\pi$
$557$	−5.79876	−	1.55377i	−0.245701	−	0.0658355i	−0.379568	+	0.925164i	$0.623927\pi$
$558$	−14.2568	+	12.3640i	−0.603538	+	0.523412i
$559$	−20.9185	−	2.61970i	−0.884758	−	0.110801i
$560$	0.0214603	−	0.0123901i	0.000906863	−	0.000523578i
$561$	20.7510	−	14.7833i	0.876107	−	0.624150i
$562$	15.0231			0.633710
$563$	18.6698	+	32.3370i	0.786838	+	1.36284i	0.927895	+	0.372842i	$0.121617\pi$
$563$	18.6698	+	32.3370i	0.786838	+	1.36284i	−0.141057	+	0.990001i	$0.545050\pi$
$564$	0.496910	−	1.08868i	0.0209237	−	0.0458419i
$565$	−0.0411614	+	0.0411614i	−0.00173167	+	0.00173167i
$566$	−3.52724	−	13.1638i	−0.148261	−	0.553317i
$567$	27.9938	+	11.9599i	1.17563	+	0.502267i
$568$	2.16398	−	3.74813i	0.0907987	−	0.157268i
$569$	−10.9706	+	19.0016i	−0.459910	+	0.796587i	−0.998956	−	0.0456892i	$-0.985452\pi$
$569$	−10.9706	+	19.0016i	−0.459910	+	0.796587i	0.539046	+	0.842276i	$0.318785\pi$
$570$	−0.0966427	+	0.00924870i	−0.00404792	+	0.000387386i
$571$	6.83716	+	3.94743i	0.286126	+	0.165195i	0.636194	−	0.771530i	$-0.280508\pi$
$571$	6.83716	+	3.94743i	0.286126	+	0.165195i	−0.350067	+	0.936725i	$0.613841\pi$
$572$	−12.3198	+	9.57756i	−0.515119	+	0.400458i
$573$	−23.1281	−	19.0880i	−0.966191	−	0.797414i
$574$	−1.25980	−	4.70165i	−0.0525831	−	0.196243i
$575$	−38.2910	+	22.1073i	−1.59684	+	0.921938i
$576$	−2.94555	+	0.568989i	−0.122731	+	0.0237079i
$577$	−6.22708	+	6.22708i	−0.259237	+	0.259237i	−0.824744	−	0.565507i	$-0.808681\pi$
$577$	−6.22708	+	6.22708i	−0.259237	+	0.259237i	0.565507	+	0.824744i	$0.308681\pi$
$578$	3.85240	+	3.85240i	0.160239	+	0.160239i
$579$	13.5301	−	1.29483i	0.562293	−	0.0538114i
$580$	0.0509120	−	0.0136418i	0.00211401	−	0.000566446i
$581$	28.5323	−	16.4731i	1.18372	−	0.683420i
$582$	−1.54548	−	4.14095i	−0.0640623	−	0.171648i
$583$	6.66830	−	1.78676i	0.276173	−	0.0740002i
$584$	−8.73452			−0.361437
$585$	−0.0750197	+	0.0255314i	−0.00310168	+	0.00105559i
$586$	−7.45041			−0.307774
$587$	30.9580	−	8.29518i	1.27777	−	0.342379i	0.444770	−	0.895645i	$-0.353286\pi$
$587$	30.9580	−	8.29518i	1.27777	−	0.342379i	0.833004	+	0.553266i	$0.186619\pi$
$588$	7.58516	+	1.27387i	0.312807	+	0.0525336i
$589$	41.6791	−	24.0634i	1.71736	−	0.991517i
$590$	−0.0104765	+	0.00280718i	−0.000431312	+	0.000115570i
$591$	1.51043	+	2.12016i	0.0621308	+	0.0872119i
$592$	1.52709	+	1.52709i	0.0627628	+	0.0627628i
$593$	−19.2789	+	19.2789i	−0.791691	+	0.791691i	−0.981769	−	0.190078i	$-0.939126\pi$
$593$	−19.2789	+	19.2789i	−0.791691	+	0.791691i	0.190078	+	0.981769i	$0.439126\pi$
$594$	−0.549323	−	22.4821i	−0.0225390	−	0.922453i
$595$	0.0729394	−	0.0421116i	0.00299022	−	0.00172641i
$596$	4.63061	+	17.2817i	0.189677	+	0.707884i
$597$	−1.51355	+	0.564886i	−0.0619454	+	0.0231192i
$598$	4.36122	+	31.5843i	0.178344	+	1.29158i
$599$	−14.8845	−	8.59354i	−0.608162	−	0.351123i	0.164084	−	0.986446i	$-0.447533\pi$
$599$	−14.8845	−	8.59354i	−0.608162	−	0.351123i	−0.772246	+	0.635324i	$0.780867\pi$
$600$	5.02487	+	7.05331i	0.205139	+	0.287950i
$601$	5.48390	−	9.49839i	0.223693	−	0.387447i	−0.732234	−	0.681054i	$-0.761522\pi$
$601$	5.48390	−	9.49839i	0.223693	−	0.387447i	0.955926	+	0.293606i	$0.0948554\pi$
$602$	9.88855	−	17.1275i	0.403027	−	0.698064i
$603$	11.9630	+	8.08950i	0.487172	+	0.329430i
$604$	0.0484351	+	0.180762i	0.00197080	+	0.00735511i
$605$	0.0400519	−	0.0400519i	0.00162834	−	0.00162834i
$606$	−8.91884	−	12.5192i	−0.362303	−	0.508558i
$607$	−18.3450	−	31.7745i	−0.744602	−	1.28969i	−0.950380	−	0.311090i	$-0.899306\pi$
$607$	−18.3450	−	31.7745i	−0.744602	−	1.28969i	0.205778	−	0.978599i	$-0.434028\pi$
$608$	7.65081			0.310281
$609$	38.3433	+	17.5011i	1.55375	+	0.709179i
$610$	0.0936011	−	0.0540406i	0.00378980	−	0.00218804i
$611$	−0.938782	+	2.30753i	−0.0379790	+	0.0933526i
$612$	−10.0113	+	1.93388i	−0.404685	+	0.0781726i
$613$	28.7680	+	7.70835i	1.16193	+	0.311337i	0.787735	−	0.616014i	$-0.211254\pi$
$613$	28.7680	+	7.70835i	1.16193	+	0.311337i	0.374192	+	0.927351i	$0.377920\pi$
$614$	−22.3021	−	12.8761i	−0.900040	−	0.519639i
$615$	−0.0171082	+	0.00638512i	−0.000689870	+	0.000257473i
$616$	−3.78884	−	14.1401i	−0.152657	−	0.569722i
$617$	10.5432	−	39.3478i	0.424454	−	1.58408i	−0.340659	−	0.940187i	$-0.610650\pi$
$617$	10.5432	−	39.3478i	0.424454	−	1.58408i	0.765113	−	0.643896i	$-0.222683\pi$
$618$	2.66514	−	1.89868i	0.107207	−	0.0763760i
$619$	10.6369	−	39.6974i	0.427533	−	1.59557i	−0.330797	−	0.943702i	$-0.607317\pi$
$619$	10.6369	−	39.6974i	0.427533	−	1.59557i	0.758329	−	0.651871i	$-0.226016\pi$
$620$	0.0399109	+	0.0230425i	0.00160286	+	0.000925411i
$621$	−40.3429	−	21.9960i	−1.61890	−	0.882667i
$622$	−2.89489	+	10.8039i	−0.116074	+	0.433195i
$623$	10.7683	+	18.6512i	0.431422	+	0.747246i
$624$	6.07679	−	1.43967i	0.243266	−	0.0576329i
$625$	12.4996	−	21.6499i	0.499984	−	0.865998i
$626$	8.46214	+	8.46214i	0.338215	+	0.338215i
$627$	−9.49893	+	56.5605i	−0.379351	+	2.25881i
$628$		−	5.59697i		−	0.223343i
$629$	5.19027	+	5.19027i	0.206949	+	0.206949i
$630$	0.00527231	−	0.0741535i	0.000210054	−	0.00295434i
$631$	15.2740	−	4.09266i	0.608048	−	0.162926i	0.0583596	−	0.998296i	$-0.481413\pi$
$631$	15.2740	−	4.09266i	0.608048	−	0.162926i	0.549689	+	0.835370i	$0.314746\pi$
$632$	−8.22405	−	2.20363i	−0.327135	−	0.0876555i
$633$	−9.63401	+	11.6731i	−0.382917	+	0.463964i
$634$			5.30556i			0.210711i
$635$	−0.0587058	+	0.0587058i	−0.00232967	+	0.00232967i
$636$	−2.72463	−	0.457581i	−0.108038	−	0.0181443i
$637$	−15.8868	−	1.98956i	−0.629458	−	0.0788292i
$638$		−	31.1373i		−	1.23274i
$639$	−5.67814	−	11.6765i	−0.224624	−	0.461915i
$640$	0.00366311	+	0.00634470i	0.000144797	+	0.000250796i
$641$	16.0814			0.635179			0.317589	−	0.948228i	$-0.397127\pi$
$641$	16.0814			0.635179			0.317589	+	0.948228i	$0.397127\pi$
$642$	−1.45029	−	15.1545i	−0.0572382	−	0.598100i
$643$	10.8844	+	2.91647i	0.429240	+	0.115014i	0.466969	−	0.884274i	$-0.345346\pi$
$643$	10.8844	+	2.91647i	0.429240	+	0.115014i	−0.0377296	+	0.999288i	$0.512013\pi$
$644$	−28.8914	−	7.74143i	−1.13848	−	0.305055i
$645$	−0.0674972	−	0.0308079i	−0.00265770	−	0.00121306i
$646$	26.0036			1.02310
$647$	3.89939	+	6.75395i	0.153301	+	0.265525i	0.932439	−	0.361327i	$-0.117676\pi$
$647$	3.89939	+	6.75395i	0.153301	+	0.265525i	−0.779138	+	0.626852i	$0.784343\pi$
$648$	−3.53591	+	8.27631i	−0.138904	+	0.325124i
$649$			6.40735i			0.251511i
$650$	−11.0646	−	14.2326i	−0.433989	−	0.558250i
$651$	12.8858	+	34.5261i	0.505035	+	1.35319i
$652$	1.45823	−	1.45823i	0.0571086	−	0.0571086i
$653$			47.8391i			1.87209i	0.351883	+	0.936044i	$0.385542\pi$
$653$			47.8391i			1.87209i	−0.351883	+	0.936044i	$0.614458\pi$
$654$	−4.12696	−	11.0577i	−0.161377	−	0.432391i
$655$	0.0980859	+	0.0262820i	0.00383253	+	0.00102692i
$656$	1.39003	−	0.372458i	0.0542717	−	0.0145421i
$657$	−14.6782	+	21.7066i	−0.572651	+	0.846855i
$658$	−1.65251	−	1.65251i	−0.0644215	−	0.0644215i
$659$		−	35.2603i		−	1.37355i	−0.726872	−	0.686773i	$-0.759027\pi$
$659$		−	35.2603i		−	1.37355i	0.726872	−	0.686773i	$-0.240973\pi$
$660$	−0.0514527	+	0.0192032i	−0.00200279	+	0.000747482i
$661$	−23.4103	−	23.4103i	−0.910554	−	0.910554i	0.0857619	−	0.996316i	$-0.472668\pi$
$661$	−23.4103	−	23.4103i	−0.910554	−	0.910554i	−0.996316	+	0.0857619i	$0.972668\pi$
$662$	−0.404629	+	0.700838i	−0.0157263	+	0.0272388i
$663$	20.6538	−	4.89315i	0.802128	−	0.190034i
$664$	4.87025	+	8.43552i	0.189002	+	0.327362i
$665$	−0.0490692	+	0.183129i	−0.00190282	+	0.00710143i
$666$	6.36128	−	1.22880i	0.246495	−	0.0476151i
$667$	−55.0969	−	31.8102i	−2.13336	−	1.23170i
$668$	−4.00246	+	14.9374i	−0.154860	+	0.577944i
$669$	11.6073	+	5.29792i	0.448763	+	0.204829i
$670$	0.00912777	−	0.0340653i	0.000352637	−	0.00131606i
$671$	−16.5254	−	61.6735i	−0.637955	−	2.38088i
$672$	−0.970302	+	5.77758i	−0.0374302	+	0.222875i
$673$	17.0006	+	9.81529i	0.655324	+	0.378351i	0.790493	−	0.612471i	$-0.209824\pi$
$673$	17.0006	+	9.81529i	0.655324	+	0.378351i	−0.135169	+	0.990823i	$0.543158\pi$
$674$	11.8412	+	3.17283i	0.456105	+	0.122213i
$675$	25.9727	−	0.634612i	0.999691	−	0.0244262i
$676$	−12.5135	+	3.52296i	−0.481290	+	0.135499i
$677$	−18.0882	+	10.4433i	−0.695188	+	0.401367i	−0.805552	−	0.592524i	$-0.798131\pi$
$677$	−18.0882	+	10.4433i	−0.695188	+	0.401367i	0.110365	+	0.993891i	$0.464798\pi$
$678$	−1.31104	−	13.6995i	−0.0503503	−	0.526127i
$679$	−8.63140			−0.331243
$680$	0.0124502	+	0.0215644i	0.000477444	+	0.000826957i
$681$	−9.54382	+	0.913343i	−0.365720	+	0.0349994i
$682$	19.2509	−	19.2509i	0.737154	−	0.737154i
$683$	−1.73590	−	6.47848i	−0.0664225	−	0.247892i	0.924729	−	0.380625i	$-0.124291\pi$
$683$	−1.73590	−	6.47848i	−0.0664225	−	0.247892i	−0.991152	+	0.132733i	$0.957625\pi$
$684$	12.8570	−	19.0134i	0.491601	−	0.726997i
$685$	−0.0573903	+	0.0994028i	−0.00219277	+	0.00379799i
$686$	−4.32842	+	7.49704i	−0.165260	+	0.286238i
$687$	−7.34871	+	16.1004i	−0.280371	+	0.614267i
$688$	5.06371	+	2.92353i	0.193052	+	0.111459i
$689$	5.70661	+	0.714660i	0.217405	+	0.0272264i
$690$	−0.0185850	+	0.110663i	−0.000707519	+	0.00421286i
$691$	6.78423	+	25.3191i	0.258084	+	0.963183i	0.966349	+	0.257236i	$0.0828117\pi$
$691$	6.78423	+	25.3191i	0.258084	+	0.963183i	−0.708265	+	0.705947i	$0.750522\pi$
$692$	−2.01424	+	1.16292i	−0.0765699	+	0.0442076i
$693$	−41.5075	−	14.3464i	−1.57674	−	0.544974i
$694$	21.3781	−	21.3781i	0.811501	−	0.811501i
$695$	−0.0583089	−	0.0583089i	−0.00221178	−	0.00221178i
$696$	−5.17416	+	11.3361i	−0.196126	+	0.429694i
$697$	4.72445	−	1.26591i	0.178951	−	0.0479499i
$698$	−12.4641	+	7.19615i	−0.471773	+	0.272378i
$699$	−2.44354	+	2.96072i	−0.0924230	+	0.111985i
$700$	16.3356	−	4.37710i	0.617426	−	0.165439i
$701$	−13.5585			−0.512096			−0.256048	−	0.966664i	$-0.582421\pi$
$701$	−13.5585			−0.512096			−0.256048	+	0.966664i	$0.582421\pi$
$702$	6.63413	−	17.5211i	0.250389	−	0.661291i
$703$	−16.5229			−0.623173
$704$	4.18051	−	1.12016i	0.157559	−	0.0422177i
$705$	−0.00558075	+	0.00676195i	−0.000210183	+	0.000254670i
$706$	9.52800	−	5.50099i	0.358591	−	0.207033i
$707$	−28.9946	+	7.76909i	−1.09046	+	0.292187i
$708$	1.06472	−	2.33271i	0.0400148	−	0.0876687i
$709$	−15.5433	−	15.5433i	−0.583740	−	0.583740i	0.352189	−	0.935929i	$-0.385437\pi$
$709$	−15.5433	−	15.5433i	−0.583740	−	0.583740i	−0.935929	+	0.352189i	$0.885437\pi$
$710$	−0.0224207	+	0.0224207i	−0.000841434	+	0.000841434i
$711$	−19.2967	+	16.7349i	−0.723683	+	0.627606i
$712$	−5.51420	+	3.18363i	−0.206653	+	0.119311i
$713$	−14.3972	−	53.7309i	−0.539178	−	2.01224i
$714$	−3.29787	+	19.6369i	−0.123420	+	0.734891i
$715$	0.105343	−	0.0444160i	0.00393961	−	0.00166106i
$716$	18.1702	+	10.4906i	0.679053	+	0.392051i
$717$	3.27470	−	7.17457i	0.122296	−	0.267939i
$718$	5.60800	−	9.71333i	0.209289	−	0.362498i
$719$	−9.35852	+	16.2094i	−0.349014	+	0.604510i	−0.986075	−	0.166304i	$-0.946817\pi$
$719$	−9.35852	+	16.2094i	−0.349014	+	0.604510i	0.637061	+	0.770814i	$0.280150\pi$
$720$	0.0219233	+	0.00155875i	0.000817034	+	5.80911e-5i
$721$	−1.65391	−	6.17249i	−0.0615950	−	0.229876i
$722$	−27.9554	+	27.9554i	−1.04039	+	1.04039i
$723$	37.3667	−	3.57599i	1.38968	−	0.132993i
$724$	−7.95821	−	13.7840i	−0.295765	−	0.512279i
$725$	35.9718			1.33596
$726$	1.27571	+	13.3303i	0.0473459	+	0.494733i
$727$	−8.84788	+	5.10832i	−0.328150	+	0.189457i	−0.655019	−	0.755612i	$-0.727340\pi$
$727$	−8.84788	+	5.10832i	−0.328150	+	0.189457i	0.326870	+	0.945069i	$0.394006\pi$
$728$	1.51544	−	12.1009i	0.0561659	−	0.448489i
$729$	14.6259	+	22.6955i	0.541699	+	0.840573i
$730$	0.0618106	+	0.0165621i	0.00228771	+	0.000612991i
$731$	17.2105	+	9.93651i	0.636555	+	0.367515i
$732$	−4.23206	+	25.1994i	−0.156421	+	0.931398i
$733$	−9.59101	−	35.7942i	−0.354252	−	1.32209i	−0.881423	−	0.472328i	$-0.843414\pi$
$733$	−9.59101	−	35.7942i	−0.354252	−	1.32209i	0.527171	−	0.849759i	$-0.323253\pi$
$734$	−1.30656	+	4.87616i	−0.0482261	+	0.179982i
$735$	−0.0512616	−	0.0233974i	−0.00189081	−	0.000863026i
$736$	2.28874	−	8.54170i	0.0843641	−	0.314851i
$737$	−18.0428	−	10.4170i	−0.664615	−	0.383716i
$738$	1.41031	−	4.08035i	0.0519142	−	0.150200i
$739$	−1.21696	+	4.54175i	−0.0447665	+	0.167071i	−0.984690	−	0.174314i	$-0.944229\pi$
$739$	−1.21696	+	4.54175i	−0.0447665	+	0.167071i	0.939924	+	0.341385i	$0.110896\pi$
$740$	−0.00791095	−	0.0137022i	−0.000290812	−	0.000503702i
$741$	−25.0865	+	40.6636i	−0.921577	+	1.49381i
$742$	−2.69762	+	4.67242i	−0.0990328	+	0.171530i
$743$	5.42021	+	5.42021i	0.198848	+	0.198848i	0.799506	−	0.600658i	$-0.205095\pi$
$743$	5.42021	+	5.42021i	0.198848	+	0.198848i	−0.600658	+	0.799506i	$0.705095\pi$
$744$	−10.2076	+	3.80967i	−0.374228	+	0.139669i
$745$		−	0.131076i		−	0.00480224i
$746$	14.4300	+	14.4300i	0.528321	+	0.528321i
$747$	29.1479	+	2.07241i	1.06647	+	0.0758257i
$748$	14.2087	−	3.80722i	0.519522	−	0.139206i
$749$	−28.7163	−	7.69452i	−1.04927	−	0.281152i
$750$	−0.0443696	−	0.118883i	−0.00162015	−	0.00434100i
$751$			50.7215i			1.85085i	0.378927	+	0.925426i	$0.376293\pi$
$751$			50.7215i			1.85085i	−0.378927	+	0.925426i	$0.623707\pi$
$752$	0.488561	−	0.488561i	0.0178160	−	0.0178160i
$753$	3.77315	+	10.1097i	0.137501	+	0.368419i
$754$	9.77523	−	24.0275i	0.355993	−	0.875031i
$755$		−	0.00137102i		−	4.98966e-5i
$756$	12.7276	+	12.1205i	0.462898	+	0.440817i
$757$	0.927481	+	1.60644i	0.0337099	+	0.0583872i	0.882388	−	0.470522i	$-0.155934\pi$
$757$	0.927481	+	1.60644i	0.0337099	+	0.0583872i	−0.848678	+	0.528909i	$0.822601\pi$
$758$	34.6504			1.25856
$759$	60.3050	+	27.5251i	2.18893	+	0.999097i
$760$	−0.0541417	−	0.0145072i	−0.00196393	−	0.000526232i
$761$	−50.0164	−	13.4018i	−1.81309	−	0.485817i	−0.817199	−	0.576355i	$-0.804475\pi$
$761$	−50.0164	−	13.4018i	−1.81309	−	0.485817i	−0.995893	+	0.0905383i	$0.971141\pi$
$762$	−1.86986	−	19.5388i	−0.0677378	−	0.707814i
$763$	−23.0488			−0.834421
$764$	−8.65671	−	14.9939i	−0.313189	−	0.542459i
$765$	0.0745131	+	0.00529788i	0.00269403	+	0.000191545i
$766$		−	24.0419i		−	0.868669i
$767$	−2.01152	+	4.94432i	−0.0726317	+	0.178529i
$768$	−1.70813	−	0.286868i	−0.0616368	−	0.0103515i
$769$	−32.2731	+	32.2731i	−1.16380	+	1.16380i	−0.180161	+	0.983637i	$0.557662\pi$
$769$	−32.2731	+	32.2731i	−1.16380	+	1.16380i	−0.983637	+	0.180161i	$0.942338\pi$
$770$			0.107248i			0.00386496i
$771$	−1.25400	+	1.51941i	−0.0451616	+	0.0547204i
$772$	7.57992	+	2.03103i	0.272807	+	0.0730985i
$773$	35.8207	−	9.59812i	1.28838	−	0.345220i	0.451335	−	0.892354i	$-0.350948\pi$
$773$	35.8207	−	9.59812i	1.28838	−	0.345220i	0.837045	+	0.547134i	$0.184281\pi$
$774$	15.7749	−	7.67114i	0.567016	−	0.275733i
$775$	22.2398	+	22.2398i	0.798877	+	0.798877i
$776$		−	2.55186i		−	0.0916064i
$777$	2.09549	−	12.4774i	0.0751752	−	0.447624i
$778$	−18.3226	−	18.3226i	−0.656898	−	0.656898i
$779$	−5.50502	+	9.53498i	−0.197238	+	0.341626i
$780$	−0.0457328	−	0.00133466i	−0.00163750	−	4.77884e-5i
$781$	9.36567	+	16.2218i	0.335130	+	0.580462i
$782$	7.77898	−	29.0316i	0.278176	−	1.03817i
$783$	19.4769	+	31.9087i	0.696048	+	1.14032i
$784$	3.84569	+	2.22031i	0.137346	+	0.0792968i
$785$	−0.0106128	+	0.0396074i	−0.000378786	+	0.00141365i
$786$	−19.5528	+	13.9297i	−0.697426	+	0.496856i
$787$	1.49348	−	5.57374i	0.0532368	−	0.198682i	−0.934185	−	0.356788i	$-0.883872\pi$
$787$	1.49348	−	5.57374i	0.0532368	−	0.198682i	0.987422	+	0.158105i	$0.0505386\pi$
$788$	0.388990	+	1.45173i	0.0138572	+	0.0517157i
$789$	43.2823	−	16.1538i	1.54089	−	0.575091i
$790$	0.0540198	+	0.0311883i	0.00192194	+	0.00110963i
$791$	−25.9593	−	6.95577i	−0.923007	−	0.247319i
$792$	4.24148	−	12.2716i	0.150715	−	0.436053i
$793$	6.60972	−	52.7792i	0.234718	−	1.87424i
$794$	−24.6320	+	14.2213i	−0.874158	+	0.504695i
$795$	0.0184134	+	0.00840446i	0.000653056	+	0.000298075i
$796$	−0.932724			−0.0330595
$797$	11.1291	+	19.2762i	0.394213	+	0.682797i	0.993000	−	0.118111i	$-0.0376839\pi$
$797$	11.1291	+	19.2762i	0.394213	+	0.682797i	−0.598787	+	0.800908i	$0.704351\pi$
$798$	−26.0071	−	36.5056i	−0.920641	−	1.29229i
$799$	1.66052	−	1.66052i	0.0587451	−	0.0587451i
$800$	1.29408	+	4.82958i	0.0457527	+	0.170751i
$801$	−1.35471	+	19.0537i	−0.0478665	+	0.673228i
$802$	−0.202117	+	0.350076i	−0.00713698	+	0.0123616i
$803$	18.9014	−	32.7382i	0.667016	−	1.15531i
$804$	4.83779	+	6.79072i	0.170616	+	0.239490i
$805$	0.189774	+	0.109566i	0.00668864	+	0.00386169i
$806$	20.8988	−	8.81158i	0.736128	−	0.310375i
$807$	7.81853	−	2.91803i	0.275225	−	0.102719i
$808$	−2.29692	−	8.57221i	−0.0808053	−	0.301569i
$809$	37.1990	−	21.4768i	1.30785	−	0.755086i	0.326110	−	0.945332i	$-0.394262\pi$
$809$	37.1990	−	21.4768i	1.30785	−	0.755086i	0.981736	+	0.190246i	$0.0609286\pi$
$810$	0.0407155	−	0.0518634i	0.00143060	−	0.00182229i
$811$	−14.3552	+	14.3552i	−0.504078	+	0.504078i	−0.912703	−	0.408625i	$-0.866009\pi$
$811$	−14.3552	+	14.3552i	−0.504078	+	0.504078i	0.408625	+	0.912703i	$0.366009\pi$
$812$	17.2070	+	17.2070i	0.603849	+	0.603849i
$813$	−20.8044	−	29.2028i	−0.729643	−	1.02419i
$814$	−9.02832	+	2.41913i	−0.316443	+	0.0847905i
$815$	−0.0130843	+	0.00755423i	−0.000458324	+	0.000264613i
$816$	−5.80560	−	0.975008i	−0.203237	−	0.0341321i
$817$	−43.2105	+	11.5782i	−1.51174	+	0.405071i
$818$	−22.2073			−0.776458
$819$	−27.5259	−	24.1014i	−0.961833	−	0.842171i
$820$	−0.0105429			−0.000368175
$821$	−16.1565	+	4.32912i	−0.563866	+	0.151087i	−0.529482	−	0.848321i	$-0.677614\pi$
$821$	−16.1565	+	4.32912i	−0.563866	+	0.151087i	−0.0343839	+	0.999409i	$0.510947\pi$
$822$	−9.48845	−	25.4232i	−0.330948	−	0.886737i
$823$	5.52322	−	3.18883i	0.192527	−	0.111156i	−0.400638	−	0.916237i	$-0.631211\pi$
$823$	5.52322	−	3.18883i	0.192527	−	0.111156i	0.593165	+	0.805081i	$0.297878\pi$
$824$	1.82489	−	0.488977i	0.0635729	−	0.0170343i
$825$	−37.3105	+	3.57062i	−1.29899	+	0.124313i
$826$	−3.54082	−	3.54082i	−0.123201	−	0.123201i
$827$	24.0234	−	24.0234i	0.835376	−	0.835376i	−0.152870	−	0.988246i	$-0.548852\pi$
$827$	24.0234	−	24.0234i	0.835376	−	0.835376i	0.988246	+	0.152870i	$0.0488516\pi$
$828$	−17.3812	−	20.0420i	−0.604040	−	0.696508i
$829$	42.2827	−	24.4119i	1.46854	−	0.847860i	0.469159	−	0.883114i	$-0.344557\pi$
$829$	42.2827	−	24.4119i	1.46854	−	0.847860i	0.999378	+	0.0352535i	$0.0112239\pi$
$830$	−0.0184696	−	0.0689295i	−0.000641089	−	0.00239258i
$831$	8.38443	+	6.91981i	0.290853	+	0.240046i
$832$	3.57761	+	0.448036i	0.124031	+	0.0155329i
$833$	13.0708	+	7.54640i	0.452875	+	0.261467i
$834$	19.4067	−	1.85722i	0.671997	−	0.0643101i
$835$	0.0566475	−	0.0981163i	0.00196037	−	0.00339546i
$836$	−16.5563	+	28.6763i	−0.572611	+	0.991791i
$837$	−7.68604	+	31.7695i	−0.265668	+	1.09811i
$838$	−9.94549	−	37.1171i	−0.343561	−	1.28219i
$839$	12.7534	−	12.7534i	0.440297	−	0.440297i	−0.451815	−	0.892112i	$-0.649223\pi$
$839$	12.7534	−	12.7534i	0.440297	−	0.440297i	0.892112	+	0.451815i	$0.149223\pi$
$840$	0.0178217	−	0.0390457i	0.000614906	−	0.00134720i
$841$	11.3799	+	19.7106i	0.392410	+	0.679675i
$842$	−2.66357			−0.0917926
$843$	21.1927	−	15.0979i	0.729915	−	0.520001i
$844$	−7.56762	+	4.36917i	−0.260488	+	0.150393i
$845$	0.0952333	−	0.00120281i	0.00327613	−	4.13780e-5i
$846$	−0.393131	−	2.03517i	−0.0135161	−	0.0699705i
$847$	25.2596	+	6.76829i	0.867930	+	0.232561i
$848$	−1.38139	−	0.797547i	−0.0474372	−	0.0273879i
$849$	−18.2052	−	15.0251i	−0.624802	−	0.515660i
$850$	4.39833	+	16.4148i	0.150861	+	0.563023i
$851$	−4.94282	+	18.4469i	−0.169438	+	0.632350i
$852$	−0.714129	−	7.46216i	−0.0244657	−	0.255650i
$853$	0.228323	−	0.852113i	0.00781763	−	0.0291758i	−0.961907	−	0.273377i	$-0.911859\pi$
$853$	0.228323	−	0.852113i	0.00781763	−	0.0291758i	0.969724	+	0.244202i	$0.0785259\pi$
$854$	43.2141	+	24.9497i	1.47876	+	0.853760i
$855$	−0.127037	+	0.110171i	−0.00434456	+	0.00376778i
$856$	2.27487	−	8.48993i	0.0777535	−	0.290180i
$857$	9.08509	+	15.7358i	0.310341	+	0.537526i	0.978436	−	0.206550i	$-0.0662235\pi$
$857$	9.08509	+	15.7358i	0.310341	+	0.537526i	−0.668095	+	0.744076i	$0.732890\pi$
$858$	−7.75402	+	25.8921i	−0.264718	+	0.883941i
$859$	1.17203	−	2.03002i	0.0399893	−	0.0692634i	−0.845338	−	0.534232i	$-0.820601\pi$
$859$	1.17203	−	2.03002i	0.0399893	−	0.0692634i	0.885327	+	0.464968i	$0.153934\pi$
$860$	−0.0302903	−	0.0302903i	−0.00103289	−	0.00103289i
$861$	−6.50225	−	5.36642i	−0.221596	−	0.182887i
$862$			32.2170i			1.09732i
$863$	4.76972	+	4.76972i	0.162363	+	0.162363i	0.783613	−	0.621250i	$-0.213375\pi$
$863$	4.76972	+	4.76972i	0.162363	+	0.162363i	−0.621250	+	0.783613i	$0.713375\pi$
$864$	−3.58339	+	3.76289i	−0.121909	+	0.128016i
$865$	0.0164590	−	0.00441018i	0.000559624	−	0.000149951i
$866$	2.87646	+	0.770744i	0.0977460	+	0.0261910i
$867$	9.30610	+	1.56289i	0.316052	+	0.0530786i
$868$			21.2767i			0.722179i
$869$	26.0562	−	26.0562i	0.883897	−	0.883897i
$870$	0.0581106	−	0.0704100i	0.00197013	−	0.00238712i
$871$	−10.6527	−	13.7028i	−0.360951	−	0.464301i
$872$		−	6.81433i		−	0.230762i
$873$	−6.34176	−	4.28835i	−0.214636	−	0.145139i
$874$	33.8281	+	58.5920i	1.14425	+	1.98191i
$875$	−0.247801			−0.00837720
$876$	−12.3216	+	8.77805i	−0.416307	+	0.296583i
$877$	8.54024	+	2.28835i	0.288383	+	0.0772721i	0.400111	−	0.916467i	$-0.368972\pi$
$877$	8.54024	+	2.28835i	0.288383	+	0.0772721i	−0.111727	+	0.993739i	$0.535638\pi$
$878$	5.65231	+	1.51453i	0.190756	+	0.0511130i
$879$	−10.5101	+	7.48754i	−0.354497	+	0.252548i
$880$	−0.0317077			−0.00106887
$881$	17.1506	+	29.7057i	0.577818	+	1.00081i	0.995729	+	0.0923225i	$0.0294291\pi$
$881$	17.1506	+	29.7057i	0.577818	+	1.00081i	−0.417911	+	0.908488i	$0.637238\pi$
$882$	11.9804	−	5.82594i	0.403402	−	0.196170i
$883$			46.9973i			1.58159i	0.612084	+	0.790793i	$0.290331\pi$
$883$			46.9973i			1.58159i	−0.612084	+	0.790793i	$0.709669\pi$
$884$	12.1596	+	1.52279i	0.408971	+	0.0512169i
$885$	−0.0119578	+	0.0144888i	−0.000401958	+	0.000487034i
$886$	−2.79942	+	2.79942i	−0.0940483	+	0.0940483i
$887$		−	18.4455i		−	0.619339i	−0.950844	−	0.309669i	$-0.899782\pi$
$887$		−	18.4455i		−	0.619339i	0.950844	−	0.309669i	$-0.100218\pi$
$888$	3.68892	+	0.619527i	0.123792	+	0.0207900i
$889$	−37.0241	−	9.92058i	−1.24175	−	0.332725i
$890$	0.0450584	−	0.0120734i	0.00151036	−	0.000404700i
$891$	−23.3691	−	31.1629i	−0.782894	−	1.04400i
$892$	5.20891	+	5.20891i	0.174407	+	0.174407i
$893$			5.28618i			0.176895i
$894$	23.9001	+	19.7251i	0.799338	+	0.659708i
$895$	−0.108691	−	0.108691i	−0.00363315	−	0.00363315i
$896$	−1.69120	+	2.92924i	−0.0564990	+	0.0978591i
$897$	37.8939	+	40.1722i	1.26524	+	1.34131i
$898$	−3.27204	−	5.66734i	−0.109189	−	0.189122i
$899$	−11.7131	+	43.7140i	−0.390654	+	1.45794i
$900$	14.1769	+	4.90002i	0.472564	+	0.163334i
$901$	−4.69508	−	2.71071i	−0.156416	−	0.0903067i
$902$	−1.61199	+	6.01603i	−0.0536734	+	0.200312i
$903$	−3.26329	−	34.0991i	−0.108595	−	1.13475i
$904$	2.05646	−	7.67482i	0.0683969	−	0.255261i
$905$	0.0301802	+	0.112634i	0.00100322	+	0.00374408i
$906$	0.249989	+	0.206320i	0.00830534	+	0.00685454i
$907$	−22.6840	−	13.0966i	−0.753209	−	0.434865i	0.0736432	−	0.997285i	$-0.476537\pi$
$907$	−22.6840	−	13.0966i	−0.753209	−	0.434865i	−0.826852	+	0.562419i	$0.809871\pi$
$908$	−5.34669	−	1.43264i	−0.177436	−	0.0475439i
$909$	−25.1632	−	8.69725i	−0.834610	−	0.288470i
$910$	−0.0336694	+	0.0827595i	−0.00111613	+	0.00274345i
$911$	26.5380	−	15.3217i	0.879244	−	0.507632i	0.00883508	−	0.999961i	$-0.497188\pi$
$911$	26.5380	−	15.3217i	0.879244	−	0.507632i	0.870409	+	0.492329i	$0.163854\pi$
$912$	10.7928	−	7.68894i	0.357386	−	0.254606i
$913$	−42.1567			−1.39518
$914$	−8.41678	−	14.5783i	−0.278402	−	0.482207i
$915$	0.0777309	−	0.170301i	0.00256970	−	0.00562999i
$916$	−7.22525	+	7.22525i	−0.238729	+	0.238729i
$917$	12.1340	+	45.2846i	0.400699	+	1.49543i
$918$	−12.1792	+	12.7893i	−0.401975	+	0.422110i
$919$	−20.9265	+	36.2458i	−0.690302	+	1.19564i	0.281437	+	0.959580i	$0.409189\pi$
$919$	−20.9265	+	36.2458i	−0.690302	+	1.19564i	−0.971739	+	0.236058i	$0.924144\pi$
$920$	−0.0323930	+	0.0561062i	−0.00106796	+	0.00184977i
$921$	−44.4014	+	4.24921i	−1.46308	+	0.140016i
$922$	−0.833065	−	0.480970i	−0.0274355	−	0.0158399i
$923$	2.13448	+	15.4580i	0.0702572	+	0.508807i
$924$	−19.5554	−	16.1394i	−0.643327	−	0.530948i
$925$	−2.79473	−	10.4301i	−0.0918902	−	0.342939i
$926$	−33.9802	+	19.6185i	−1.11666	+	0.644703i
$927$	1.85150	−	5.35684i	0.0608114	−	0.175942i
$928$	−5.08723	+	5.08723i	−0.166996	+	0.166996i
$929$	−35.4704	−	35.4704i	−1.16374	−	1.16374i	−0.983649	−	0.180095i	$-0.942359\pi$
$929$	−35.4704	−	35.4704i	−1.16374	−	1.16374i	−0.180095	−	0.983649i	$-0.557641\pi$
$930$	0.0794587	−	0.00760420i	0.00260555	−	0.000249351i
$931$	−32.8167	+	8.79321i	−1.07552	+	0.288186i
$932$	−1.91942	+	1.10818i	−0.0628728	+	0.0362996i
$933$	6.77396	+	18.1501i	0.221770	+	0.594207i
$934$	−20.3292	+	5.44720i	−0.665193	+	0.178238i
$935$	−0.107768			−0.00352441
$936$	7.12554	−	8.13798i	0.232905	−	0.265998i
$937$	2.41475			0.0788863			0.0394432	−	0.999222i	$-0.487442\pi$
$937$	2.41475			0.0788863			0.0394432	+	0.999222i	$0.487442\pi$
$938$	15.7274	−	4.21414i	0.513518	−	0.137597i
$939$	20.4416	+	3.43302i	0.667088	+	0.112033i
$940$	−0.00438374	+	0.00253095i	−0.000142982	+	8.25506e-5i
$941$	14.8084	−	3.96789i	0.482740	−	0.129350i	−0.00923843	−	0.999957i	$-0.502941\pi$
$941$	14.8084	−	3.96789i	0.482740	−	0.129350i	0.491978	+	0.870608i	$0.336274\pi$
$942$	−5.62486	−	7.89551i	−0.183268	−	0.257250i
$943$	8.99843	+	8.99843i	0.293029	+	0.293029i
$944$	1.04684	−	1.04684i	0.0340716	−	0.0340716i
$945$	−0.0670855	−	0.109905i	−0.00218229	−	0.00357521i
$946$	−21.9156	+	12.6530i	−0.712538	+	0.411384i
$947$	−3.42756	−	12.7918i	−0.111381	−	0.415679i	0.887610	−	0.460596i	$-0.152364\pi$
$947$	−3.42756	−	12.7918i	−0.111381	−	0.415679i	−0.998991	+	0.0449170i	$0.985698\pi$
$948$	−13.8161	+	5.15643i	−0.448725	+	0.167473i
$949$	24.8633	−	19.3290i	0.807097	−	0.627445i
$950$	−33.1286	−	19.1268i	−1.07484	−	0.620556i
$951$	5.33201	+	7.48443i	0.172902	+	0.242699i
$952$	−5.74806	+	9.95593i	−0.186296	+	0.322673i
$953$	4.42175	−	7.65870i	0.143235	−	0.248090i	−0.785478	−	0.618889i	$-0.787583\pi$
$953$	4.42175	−	7.65870i	0.143235	−	0.248090i	0.928713	+	0.370800i	$0.120916\pi$
$954$	−4.30343	+	2.09271i	−0.139329	+	0.0677539i
$955$	0.0328291	+	0.122520i	0.00106233	+	0.00396465i
$956$	3.21968	−	3.21968i	0.104132	−	0.104132i
$957$	−31.2925	−	43.9247i	−1.01154	−	1.41988i
$958$	12.1770	+	21.0912i	0.393421	+	0.681426i
$959$	−52.9923			−1.71121
$960$	0.0115438	+	0.00526894i	0.000372574	+	0.000170054i
$961$	−7.42139	+	4.28474i	−0.239400	+	0.138217i
$962$	−7.72629	−	0.967590i	−0.249105	−	0.0311964i
$963$	−17.2759	−	19.9206i	−0.556708	−	0.641931i
$964$	20.9338	+	5.60919i	0.674231	+	0.180660i
$965$	−0.0497888	−	0.0287456i	−0.00160276	−	0.000925353i
$966$	−48.5365	+	18.1148i	−1.56163	+	0.582833i
$967$	13.2489	+	49.4457i	0.426057	+	1.59007i	0.761604	+	0.648043i	$0.224412\pi$
$967$	13.2489	+	49.4457i	0.426057	+	1.59007i	−0.335547	+	0.942023i	$0.608921\pi$
$968$	−2.00103	+	7.46796i	−0.0643156	+	0.240029i
$969$	36.6827	−	26.1332i	1.17842	−	0.839520i
$970$	−0.00483875	+	0.0180585i	−0.000155363	+	0.000579822i
$971$	9.96190	+	5.75150i	0.319693	+	0.184575i	0.651256	−	0.758859i	$-0.274243\pi$
$971$	9.96190	+	5.75150i	0.319693	+	0.184575i	−0.331563	+	0.943433i	$0.607576\pi$
$972$	3.32953	+	15.2287i	0.106795	+	0.488462i
$973$	9.85350	−	36.7738i	0.315889	−	1.17891i
$974$	−5.07291	−	8.78654i	−0.162547	−	0.281539i
$975$	−29.9121	−	8.95793i	−0.957954	−	0.286883i
$976$	−7.37632	+	12.7762i	−0.236110	+	0.408955i
$977$	−20.9948	−	20.9948i	−0.671684	−	0.671684i	0.286420	−	0.958104i	$-0.407535\pi$
$977$	−20.9948	−	20.9948i	−0.671684	−	0.671684i	−0.958104	+	0.286420i	$0.907535\pi$
$978$	0.591592	−	3.52258i	0.0189170	−	0.112640i
$979$		−	27.5573i		−	0.880736i
$980$	−0.0230043	−	0.0230043i	−0.000734845	−	0.000734845i
$981$	−16.9346	−	11.4513i	−0.540681	−	0.365613i
$982$	−2.15091	+	0.576335i	−0.0686384	+	0.0183916i
$983$	36.4245	+	9.75991i	1.16176	+	0.311293i	0.787669	−	0.616099i	$-0.211288\pi$
$983$	36.4245	+	9.75991i	1.16176	+	0.311293i	0.374092	+	0.927392i	$0.377955\pi$
$984$	1.58657	−	1.92238i	0.0505781	−	0.0612832i
$985$		−	0.0110109i		−	0.000350836i
$986$	−17.2905	+	17.2905i	−0.550642	+	0.550642i
$987$	−3.99190	−	0.670410i	−0.127064	−	0.0213394i
$988$	−21.7785	+	16.9308i	−0.692866	+	0.538640i
$989$			51.7057i			1.64414i
$990$	−0.0532843	+	0.0787986i	−0.00169348	+	0.00250438i
$991$	14.2275	+	24.6428i	0.451953	+	0.782805i	0.998507	−	0.0546184i	$-0.0173942\pi$
$991$	14.2275	+	24.6428i	0.451953	+	0.782805i	−0.546555	+	0.837423i	$0.684061\pi$
$992$	−6.29043			−0.199721
$993$	0.133530	+	1.39530i	0.00423746	+	0.0442785i
$994$	−14.1401	−	3.78883i	−0.448497	−	0.120174i
$995$	0.00660051	+	0.00176860i	0.000209250	+	5.60684e-5i
$996$	15.3479	+	7.00526i	0.486317	+	0.221970i
$997$	45.2562			1.43328			0.716639	−	0.697444i	$-0.245679\pi$
$997$	45.2562			1.43328			0.716639	+	0.697444i	$0.245679\pi$
$998$	−15.0399	−	26.0499i	−0.476081	−	0.824597i
$999$	7.73878	−	8.12642i	0.244844	−	0.257109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.z.a.41.13	yes	56
3.2	odd	2		702.2.bc.a.665.4		56
9.2	odd	6		234.2.y.a.119.8	yes	56
9.7	even	3		702.2.bb.a.197.4		56
13.7	odd	12		234.2.y.a.59.8	✓	56
39.20	even	12		702.2.bb.a.449.4		56
117.7	odd	12		702.2.bc.a.683.4		56
117.20	even	12	inner	234.2.z.a.137.13	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.8	✓	56	13.7	odd	12
234.2.y.a.119.8	yes	56	9.2	odd	6
234.2.z.a.41.13	yes	56	1.1	even	1	trivial
234.2.z.a.137.13	yes	56	117.20	even	12	inner
702.2.bb.a.197.4		56	9.7	even	3
702.2.bb.a.449.4		56	39.20	even	12
702.2.bc.a.665.4		56	3.2	odd	2
702.2.bc.a.683.4		56	117.7	odd	12

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(1.10250 - 1.33585i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.00707659 + 0.00189617i) q^{5} +(0.719190 - 1.57568i) q^{6} +(-2.39172 - 2.39172i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.568989 - 2.94555i) q^{9} +(-0.00634470 + 0.00366311i) q^{10} +(1.12016 + 4.18051i) q^{11} +(0.286868 - 1.70813i) q^{12} +(-0.448036 + 3.57761i) q^{13} +(-2.92924 - 1.69120i) q^{14} +(-0.00526894 + 0.0115438i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.69940 - 2.94345i) q^{17} +(-1.31196 - 2.69792i) q^{18} +(1.98018 + 7.39012i) q^{19} +(-0.00518042 + 0.00518042i) q^{20} +(-5.83184 + 0.558107i) q^{21} +(2.16399 + 3.74814i) q^{22} +8.84301 q^{23} +(-0.165003 - 1.72417i) q^{24} +(-4.33008 + 2.49997i) q^{25} +(0.493183 + 3.57166i) q^{26} +(-4.56212 - 2.48738i) q^{27} +(-3.26715 - 0.875429i) q^{28} +(-6.23056 - 3.59721i) q^{29} +(-0.00210166 + 0.0125141i) q^{30} +(-1.62808 - 6.07609i) q^{31} +(0.258819 - 0.965926i) q^{32} +(6.81951 + 3.11264i) q^{33} +(0.879676 - 3.28299i) q^{34} +(0.0214603 + 0.0123901i) q^{35} +(-1.96553 - 2.26642i) q^{36} +(-0.558952 + 2.08604i) q^{37} +(3.82541 + 6.62580i) q^{38} +(4.28518 + 4.54282i) q^{39} +(-0.00366311 + 0.00634470i) q^{40} +(1.01757 + 1.01757i) q^{41} +(-5.48868 + 2.04848i) q^{42} +5.84706i q^{43} +(3.06034 + 3.06034i) q^{44} +(0.00961175 + 0.0197655i) q^{45} +(8.54170 - 2.28874i) q^{46} +(0.667387 + 0.178826i) q^{47} +(-0.605630 - 1.62272i) q^{48} +4.44062i q^{49} +(-3.53550 + 3.53550i) q^{50} +(-2.05842 - 5.51530i) q^{51} +(1.40079 + 3.32232i) q^{52} -1.59509i q^{53} +(-5.05045 - 1.22186i) q^{54} +(-0.0158539 - 0.0274597i) q^{55} -3.38240 q^{56} +(12.0552 + 5.50239i) q^{57} +(-6.94928 - 1.86206i) q^{58} +(1.43000 + 0.383168i) q^{59} +(0.00120885 + 0.0126317i) q^{60} -14.7526 q^{61} +(-3.14521 - 5.44767i) q^{62} +(-5.68406 + 8.40578i) q^{63} -1.00000i q^{64} +(-0.00361317 - 0.0261668i) q^{65} +(7.39275 + 1.24156i) q^{66} +(-3.40387 + 3.40387i) q^{67} -3.39881i q^{68} +(9.74942 - 11.8129i) q^{69} +(0.0239359 + 0.00641359i) q^{70} +(4.18049 - 1.12016i) q^{71} +(-2.48515 - 1.68048i) q^{72} +(-6.17624 - 6.17624i) q^{73} +2.15962i q^{74} +(-1.43432 + 8.54056i) q^{75} +(5.40994 + 5.40994i) q^{76} +(7.31947 - 12.6777i) q^{77} +(5.31494 + 3.27894i) q^{78} +(-4.25708 - 7.37348i) q^{79} +(-0.00189617 + 0.00707659i) q^{80} +(-8.35250 + 3.35197i) q^{81} +(1.24627 + 0.719534i) q^{82} +(-2.52103 + 9.40860i) q^{83} +(-4.77147 + 3.39926i) q^{84} +(-0.00644470 + 0.0240520i) q^{85} +(1.51333 + 5.64783i) q^{86} +(-11.6745 + 4.35716i) q^{87} +(3.74814 + 2.16399i) q^{88} +(-6.15029 - 1.64797i) q^{89} +(0.0143999 + 0.0166043i) q^{90} +(9.62820 - 7.48505i) q^{91} +(7.65827 - 4.42151i) q^{92} +(-9.91170 - 4.52401i) q^{93} +0.690930 q^{94} +(-0.0280258 - 0.0485421i) q^{95} +(-1.00498 - 1.41068i) q^{96} +(1.80444 - 1.80444i) q^{97} +(1.14932 + 4.28931i) q^{98} +(11.6765 - 5.67816i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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