LMFDB - Embedded newform 820.2.k.c.83.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(83,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.83"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [108] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			83.12
Character	$\chi$	$=$	820.83
Dual form			820.2.k.c.247.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.958818 - 1.03955i) q^{2} +(-1.58218 + 1.58218i) q^{3} +(-0.161335 + 1.99348i) q^{4} +(-2.15223 + 0.606551i) q^{5} +(3.16177 + 0.127734i) q^{6} +(-0.113172 - 0.113172i) q^{7} +(2.22702 - 1.74367i) q^{8} -2.00656i q^{9} +(2.69414 + 1.65578i) q^{10} -5.63904i q^{11} +(-2.89878 - 3.40930i) q^{12} +(4.27017 + 4.27017i) q^{13} +(-0.00913672 + 0.226159i) q^{14} +(2.44554 - 4.36488i) q^{15} +(-3.94794 - 0.643236i) q^{16} +(3.58910 - 3.58910i) q^{17} +(-2.08593 + 1.92393i) q^{18} +4.35561 q^{19} +(-0.861918 - 4.38829i) q^{20} +0.358115 q^{21} +(-5.86208 + 5.40682i) q^{22} +(-3.77965 + 3.77965i) q^{23} +(-0.764740 + 6.28233i) q^{24} +(4.26419 - 2.61087i) q^{25} +(0.344744 - 8.53338i) q^{26} +(-1.57179 - 1.57179i) q^{27} +(0.243864 - 0.207347i) q^{28} +1.86012i q^{29} +(-6.88234 + 1.64286i) q^{30} +3.14069i q^{31} +(3.11668 + 4.72084i) q^{32} +(8.92196 + 8.92196i) q^{33} +(-7.17235 - 0.289759i) q^{34} +(0.312216 + 0.174927i) q^{35} +(4.00005 + 0.323729i) q^{36} +(-6.54344 + 6.54344i) q^{37} +(-4.17624 - 4.52788i) q^{38} -13.5123 q^{39} +(-3.73543 + 5.10358i) q^{40} +1.00000 q^{41} +(-0.343368 - 0.372279i) q^{42} +(-4.48850 + 4.48850i) q^{43} +(11.2413 + 0.909774i) q^{44} +(1.21708 + 4.31859i) q^{45} +(7.55313 + 0.305143i) q^{46} +(2.95761 + 2.95761i) q^{47} +(7.26405 - 5.22863i) q^{48} -6.97438i q^{49} +(-6.80272 - 1.92949i) q^{50} +11.3572i q^{51} +(-9.20143 + 7.82358i) q^{52} +(5.55347 + 5.55347i) q^{53} +(-0.126896 + 3.14102i) q^{54} +(3.42036 + 12.1365i) q^{55} +(-0.449370 - 0.0547012i) q^{56} +(-6.89135 + 6.89135i) q^{57} +(1.93369 - 1.78351i) q^{58} -4.84179 q^{59} +(8.30676 + 5.57934i) q^{60} -10.2919 q^{61} +(3.26491 - 3.01135i) q^{62} +(-0.227086 + 0.227086i) q^{63} +(1.91922 - 7.76638i) q^{64} +(-11.7805 - 6.60032i) q^{65} +(0.720298 - 17.8294i) q^{66} +(10.3783 + 10.3783i) q^{67} +(6.57576 + 7.73385i) q^{68} -11.9601i q^{69} +(-0.117513 - 0.492288i) q^{70} -4.04058i q^{71} +(-3.49879 - 4.46866i) q^{72} +(3.04551 + 3.04551i) q^{73} +(13.0762 + 0.528273i) q^{74} +(-2.61584 + 10.8776i) q^{75} +(-0.702711 + 8.68283i) q^{76} +(-0.638180 + 0.638180i) q^{77} +(12.9559 + 14.0468i) q^{78} +8.95774 q^{79} +(8.88704 - 1.01023i) q^{80} +10.9934 q^{81} +(-0.958818 - 1.03955i) q^{82} +(-7.57058 + 7.57058i) q^{83} +(-0.0577765 + 0.713897i) q^{84} +(-5.54760 + 9.90154i) q^{85} +(8.96967 + 0.362370i) q^{86} +(-2.94303 - 2.94303i) q^{87} +(-9.83264 - 12.5583i) q^{88} +0.237988i q^{89} +(3.32243 - 5.40596i) q^{90} -0.966525i q^{91} +(-6.92487 - 8.14445i) q^{92} +(-4.96912 - 4.96912i) q^{93} +(0.238778 - 5.91041i) q^{94} +(-9.37428 + 2.64190i) q^{95} +(-12.4003 - 2.53805i) q^{96} +(6.67189 - 6.67189i) q^{97} +(-7.25023 + 6.68717i) q^{98} -11.3151 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) $ 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.958818	−	1.03955i	−0.677987	−	0.735074i
$2$	−0.958818	−	1.03955i	−0.677987	−	0.735074i
$3$	−1.58218	+	1.58218i	−0.913470	+	0.913470i	−0.996543	−	0.0830734i	$-0.973526\pi$
$3$	−1.58218	+	1.58218i	−0.913470	+	0.913470i	0.0830734	+	0.996543i	$0.473526\pi$
$4$	−0.161335	+	1.99348i	−0.0806674	+	0.996741i
$5$	−2.15223	+	0.606551i	−0.962507	+	0.271258i
$5$	−2.15223	+	0.606551i	−0.962507	+	0.271258i
$6$	3.16177	+	0.127734i	1.29079	+	0.0521472i
$7$	−0.113172	−	0.113172i	−0.0427749	−	0.0427749i	0.685396	−	0.728171i	$-0.259629\pi$
$7$	−0.113172	−	0.113172i	−0.0427749	−	0.0427749i	−0.728171	+	0.685396i	$0.759629\pi$
$8$	2.22702	−	1.74367i	0.787370	−	0.616481i
$9$		−	2.00656i		−	0.668855i
$10$	2.69414	+	1.65578i	0.851961	+	0.523604i
$11$		−	5.63904i		−	1.70024i	−0.526593	−	0.850118i	$-0.676531\pi$
$11$		−	5.63904i		−	1.70024i	0.526593	−	0.850118i	$-0.323469\pi$
$12$	−2.89878	−	3.40930i	−0.836806	−	0.984180i
$13$	4.27017	+	4.27017i	1.18433	+	1.18433i	0.978611	+	0.205721i	$0.0659540\pi$
$13$	4.27017	+	4.27017i	1.18433	+	1.18433i	0.205721	+	0.978611i	$0.434046\pi$
$14$	−0.00913672	+	0.226159i	−0.00244189	+	0.0604435i
$15$	2.44554	−	4.36488i	0.631435	−	1.12701i
$16$	−3.94794	−	0.643236i	−0.986986	−	0.160809i
$17$	3.58910	−	3.58910i	0.870484	−	0.870484i	−0.122041	−	0.992525i	$-0.538944\pi$
$17$	3.58910	−	3.58910i	0.870484	−	0.870484i	0.992525	+	0.122041i	$0.0389439\pi$
$18$	−2.08593	+	1.92393i	−0.491658	+	0.453475i
$19$	4.35561			0.999246			0.499623	−	0.866243i	$-0.333472\pi$
$19$	4.35561			0.999246			0.499623	+	0.866243i	$0.333472\pi$
$20$	−0.861918	−	4.38829i	−0.192731	−	0.981252i
$21$	0.358115			0.0781472
$22$	−5.86208	+	5.40682i	−1.24980	+	1.15274i
$23$	−3.77965	+	3.77965i	−0.788111	+	0.788111i	−0.981184	−	0.193073i	$-0.938154\pi$
$23$	−3.77965	+	3.77965i	−0.788111	+	0.788111i	0.193073	+	0.981184i	$0.438154\pi$
$24$	−0.764740	+	6.28233i	−0.156102	+	1.28238i
$25$	4.26419	−	2.61087i	0.852839	−	0.522175i
$26$	0.344744	−	8.53338i	0.0676099	−	1.67353i
$27$	−1.57179	−	1.57179i	−0.302491	−	0.302491i
$28$	0.243864	−	0.207347i	0.0460860	−	0.0391850i
$29$			1.86012i			0.345415i	0.984973	+	0.172707i	$0.0552515\pi$
$29$			1.86012i			0.345415i	−0.984973	+	0.172707i	$0.944748\pi$
$30$	−6.88234	+	1.64286i	−1.25654	+	0.299944i
$31$			3.14069i			0.564084i	0.959402	+	0.282042i	$0.0910118\pi$
$31$			3.14069i			0.564084i	−0.959402	+	0.282042i	$0.908988\pi$
$32$	3.11668	+	4.72084i	0.550957	+	0.834534i
$33$	8.92196	+	8.92196i	1.55311	+	1.55311i
$34$	−7.17235	−	0.289759i	−1.23005	−	0.0496933i
$35$	0.312216	+	0.174927i	0.0527742	+	0.0295681i
$36$	4.00005	+	0.323729i	0.666675	+	0.0539548i
$37$	−6.54344	+	6.54344i	−1.07573	+	1.07573i	−0.0788484	+	0.996887i	$0.525124\pi$
$37$	−6.54344	+	6.54344i	−1.07573	+	1.07573i	−0.996887	+	0.0788484i	$0.974876\pi$
$38$	−4.17624	−	4.52788i	−0.677476	−	0.734519i
$39$	−13.5123			−2.16370
$40$	−3.73543	+	5.10358i	−0.590624	+	0.806947i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	−0.343368	−	0.372279i	−0.0529828	−	0.0574440i
$43$	−4.48850	+	4.48850i	−0.684489	+	0.684489i	−0.961008	−	0.276519i	$-0.910819\pi$
$43$	−4.48850	+	4.48850i	−0.684489	+	0.684489i	0.276519	+	0.961008i	$0.410819\pi$
$44$	11.2413	+	0.909774i	1.69469	+	0.137154i
$45$	1.21708	+	4.31859i	0.181432	+	0.643777i
$46$	7.55313	+	0.305143i	1.11365	+	0.0449909i
$47$	2.95761	+	2.95761i	0.431412	+	0.431412i	0.889109	−	0.457696i	$-0.151325\pi$
$47$	2.95761	+	2.95761i	0.431412	+	0.431412i	−0.457696	+	0.889109i	$0.651325\pi$
$48$	7.26405	−	5.22863i	1.04848	−	0.754687i
$49$		−	6.97438i		−	0.996341i
$50$	−6.80272	−	1.92949i	−0.962050	−	0.272872i
$51$			11.3572i			1.59032i
$52$	−9.20143	+	7.82358i	−1.27601	+	1.08494i
$53$	5.55347	+	5.55347i	0.762828	+	0.762828i	0.976833	−	0.214004i	$-0.0686507\pi$
$53$	5.55347	+	5.55347i	0.762828	+	0.762828i	−0.214004	+	0.976833i	$0.568651\pi$
$54$	−0.126896	+	3.14102i	−0.0172683	+	0.427438i
$55$	3.42036	+	12.1365i	0.461202	+	1.63649i
$56$	−0.449370	−	0.0547012i	−0.0600496	−	0.00730975i
$57$	−6.89135	+	6.89135i	−0.912781	+	0.912781i
$58$	1.93369	−	1.78351i	0.253905	−	0.234187i
$59$	−4.84179			−0.630348			−0.315174	−	0.949034i	$-0.602063\pi$
$59$	−4.84179			−0.630348			−0.315174	+	0.949034i	$0.602063\pi$
$60$	8.30676	+	5.57934i	1.07240	+	0.720290i
$61$	−10.2919			−1.31774			−0.658869	−	0.752257i	$-0.728965\pi$
$61$	−10.2919			−1.31774			−0.658869	+	0.752257i	$0.728965\pi$
$62$	3.26491	−	3.01135i	0.414644	−	0.382442i
$63$	−0.227086	+	0.227086i	−0.0286102	+	0.0286102i
$64$	1.91922	−	7.76638i	0.239902	−	0.970797i
$65$	−11.7805	−	6.60032i	−1.46119	−	0.818668i
$66$	0.720298	−	17.8294i	0.0886626	−	2.19464i
$67$	10.3783	+	10.3783i	1.26791	+	1.26791i	0.947164	+	0.320750i	$0.103935\pi$
$67$	10.3783	+	10.3783i	1.26791	+	1.26791i	0.320750	+	0.947164i	$0.396065\pi$
$68$	6.57576	+	7.73385i	0.797428	+	0.937867i
$69$		−	11.9601i		−	1.43983i
$70$	−0.117513	−	0.492288i	−0.0140454	−	0.0588397i
$71$		−	4.04058i		−	0.479529i	−0.970831	−	0.239765i	$-0.922930\pi$
$71$		−	4.04058i		−	0.479529i	0.970831	−	0.239765i	$-0.0770703\pi$
$72$	−3.49879	−	4.46866i	−0.412336	−	0.526636i
$73$	3.04551	+	3.04551i	0.356450	+	0.356450i	0.862502	−	0.506053i	$-0.168896\pi$
$73$	3.04551	+	3.04551i	0.356450	+	0.356450i	−0.506053	+	0.862502i	$0.668896\pi$
$74$	13.0762	+	0.528273i	1.52008	+	0.0614105i
$75$	−2.61584	+	10.8776i	−0.302052	+	1.25603i
$76$	−0.702711	+	8.68283i	−0.0806065	+	0.995989i
$77$	−0.638180	+	0.638180i	−0.0727274	+	0.0727274i
$78$	12.9559	+	14.0468i	1.46696	+	1.59048i
$79$	8.95774			1.00782			0.503912	−	0.863755i	$-0.331893\pi$
$79$	8.95774			1.00782			0.503912	+	0.863755i	$0.331893\pi$
$80$	8.88704	−	1.01023i	0.993601	−	0.112948i
$81$	10.9934			1.22149
$82$	−0.958818	−	1.03955i	−0.105884	−	0.114799i
$83$	−7.57058	+	7.57058i	−0.830979	+	0.830979i	−0.987651	−	0.156672i	$-0.949923\pi$
$83$	−7.57058	+	7.57058i	−0.830979	+	0.830979i	0.156672	+	0.987651i	$0.449923\pi$
$84$	−0.0577765	+	0.713897i	−0.00630393	+	0.0778925i
$85$	−5.54760	+	9.90154i	−0.601721	+	1.07397i
$86$	8.96967	+	0.362370i	0.967225	+	0.0390754i
$87$	−2.94303	−	2.94303i	−0.315526	−	0.315526i
$88$	−9.83264	−	12.5583i	−1.04816	−	1.33871i
$89$			0.237988i			0.0252267i	0.999920	+	0.0126134i	$0.00401506\pi$
$89$			0.237988i			0.0252267i	−0.999920	+	0.0126134i	$0.995985\pi$
$90$	3.32243	−	5.40596i	0.350215	−	0.569839i
$91$		−	0.966525i		−	0.101319i
$92$	−6.92487	−	8.14445i	−0.721968	−	0.849117i
$93$	−4.96912	−	4.96912i	−0.515274	−	0.515274i
$94$	0.238778	−	5.91041i	0.0246280	−	0.609612i
$95$	−9.37428	+	2.64190i	−0.961781	+	0.271053i
$96$	−12.4003	−	2.53805i	−1.26560	−	0.259039i
$97$	6.67189	−	6.67189i	0.677428	−	0.677428i	−0.281989	−	0.959418i	$-0.590994\pi$
$97$	6.67189	−	6.67189i	0.677428	−	0.677428i	0.959418	+	0.281989i	$0.0909943\pi$
$98$	−7.25023	+	6.68717i	−0.732384	+	0.675506i
$99$	−11.3151			−1.13721
$100$	4.51677	+	8.92182i	0.451677	+	0.892182i
$101$	11.7452			1.16869			0.584346	−	0.811505i	$-0.301351\pi$
$101$	11.7452			1.16869			0.584346	+	0.811505i	$0.301351\pi$
$102$	11.8064	−	10.8895i	1.16900	−	1.07822i
$103$	1.64966	−	1.64966i	0.162545	−	0.162545i	−0.621148	−	0.783693i	$-0.713333\pi$
$103$	1.64966	−	1.64966i	0.162545	−	0.162545i	0.783693	+	0.621148i	$0.213333\pi$
$104$	16.9555	+	2.06397i	1.66263	+	0.202389i
$105$	−0.770747	+	0.217215i	−0.0752172	+	0.0211980i
$106$	0.448350	−	11.0979i	0.0435476	−	1.07792i
$107$	−0.336992	−	0.336992i	−0.0325782	−	0.0325782i	0.690630	−	0.723208i	$-0.257333\pi$
$107$	−0.336992	−	0.336992i	−0.0325782	−	0.0325782i	−0.723208	+	0.690630i	$0.757333\pi$
$108$	3.38692	−	2.87975i	0.325907	−	0.277104i
$109$		−	5.33238i		−	0.510749i	−0.966842	−	0.255375i	$-0.917801\pi$
$109$		−	5.33238i		−	0.510749i	0.966842	−	0.255375i	$-0.0821988\pi$
$110$	9.33703	−	15.1924i	0.890251	−	1.44854i
$111$		−	20.7058i		−	1.96530i
$112$	0.373999	+	0.519592i	0.0353396	+	0.0490968i
$113$	1.53165	+	1.53165i	0.144085	+	0.144085i	0.775470	−	0.631385i	$-0.217513\pi$
$113$	1.53165	+	1.53165i	0.144085	+	0.144085i	−0.631385	+	0.775470i	$0.717513\pi$
$114$	13.7715	+	0.556360i	1.28982	+	0.0521079i
$115$	5.84213	−	10.4272i	0.544781	−	0.972343i
$116$	−3.70811	−	0.300101i	−0.344289	−	0.0278637i
$117$	8.56837	−	8.56837i	0.792146	−	0.792146i
$118$	4.64240	+	5.03329i	0.427368	+	0.463352i
$119$	−0.812369			−0.0744697
$120$	−2.16466	−	13.9849i	−0.197605	−	1.27664i
$121$	−20.7988			−1.89080
$122$	9.86803	+	10.6989i	0.893410	+	0.968635i
$123$	−1.58218	+	1.58218i	−0.142660	+	0.142660i
$124$	−6.26091	−	0.506702i	−0.562246	−	0.0455032i
$125$	−7.59390	+	8.20565i	−0.679219	+	0.733936i
$126$	0.453803	+	0.0183334i	0.0404280	+	0.00163327i
$127$	5.00022	+	5.00022i	0.443698	+	0.443698i	0.893253	−	0.449555i	$-0.148417\pi$
$127$	5.00022	+	5.00022i	0.443698	+	0.443698i	−0.449555	+	0.893253i	$0.648417\pi$
$128$	−9.91373	+	5.45142i	−0.876258	+	0.481842i
$129$		−	14.2032i		−	1.25052i
$130$	4.43396	+	18.5749i	0.388884	+	1.62913i
$131$			10.5951i			0.925695i	0.886438	+	0.462847i	$0.153172\pi$
$131$			10.5951i			0.925695i	−0.886438	+	0.462847i	$0.846828\pi$
$132$	−19.2252	+	16.3463i	−1.67334	+	1.42277i
$133$	−0.492932	−	0.492932i	−0.0427426	−	0.0427426i
$134$	0.837875	−	20.7397i	0.0723814	−	1.79164i
$135$	4.33623	+	2.42948i	0.373203	+	0.209097i
$136$	1.73478	−	14.2512i	0.148756	−	1.22203i
$137$	−4.50916	+	4.50916i	−0.385243	+	0.385243i	−0.872987	−	0.487744i	$-0.837820\pi$
$137$	−4.50916	+	4.50916i	−0.385243	+	0.385243i	0.487744	+	0.872987i	$0.337820\pi$
$138$	−12.4332	+	11.4676i	−1.05838	+	0.976187i
$139$	2.23216			0.189330			0.0946649	−	0.995509i	$-0.469822\pi$
$139$	2.23216			0.189330			0.0946649	+	0.995509i	$0.469822\pi$
$140$	−0.399086	+	0.594175i	−0.0337289	+	0.0502170i
$141$	−9.35894			−0.788165
$142$	−4.20040	+	3.87419i	−0.352489	+	0.325115i
$143$	24.0797	−	24.0797i	2.01364	−	2.01364i
$144$	−1.29069	+	7.92180i	−0.107558	+	0.660150i
$145$	−1.12825	−	4.00340i	−0.0936964	−	0.332464i
$146$	0.245873	−	6.08605i	0.0203486	−	0.503685i
$147$	11.0347	+	11.0347i	0.910127	+	0.910127i
$148$	−11.9885	−	14.0999i	−0.985453	−	1.15901i
$149$			21.4719i			1.75904i	0.475857	+	0.879522i	$0.342138\pi$
$149$			21.4719i			1.75904i	−0.475857	+	0.879522i	$0.657862\pi$
$150$	13.8159	−	7.71031i	1.12806	−	0.629544i
$151$			15.6064i			1.27003i	0.772501	+	0.635014i	$0.219005\pi$
$151$			15.6064i			1.27003i	−0.772501	+	0.635014i	$0.780995\pi$
$152$	9.70002	−	7.59475i	0.786776	−	0.616016i
$153$	−7.20176	−	7.20176i	−0.582228	−	0.582228i
$154$	1.27532	+	0.0515223i	0.102768	+	0.00415179i
$155$	−1.90499	−	6.75948i	−0.153012	−	0.542935i
$156$	2.18001	−	26.9366i	0.174540	−	2.15665i
$157$	−1.89980	+	1.89980i	−0.151620	+	0.151620i	−0.778841	−	0.627221i	$-0.784192\pi$
$157$	−1.89980	+	1.89980i	−0.151620	+	0.151620i	0.627221	+	0.778841i	$0.284192\pi$
$158$	−8.58885	−	9.31203i	−0.683292	−	0.740826i
$159$	−17.5732			−1.39364
$160$	−9.57125	−	8.26990i	−0.756673	−	0.653793i
$161$	0.855499			0.0674227
$162$	−10.5407	−	11.4282i	−0.828153	−	0.897884i
$163$	−16.5799	+	16.5799i	−1.29864	+	1.29864i	−0.369352	+	0.929290i	$0.620420\pi$
$163$	−16.5799	+	16.5799i	−1.29864	+	1.29864i	−0.929290	+	0.369352i	$0.879580\pi$
$164$	−0.161335	+	1.99348i	−0.0125981	+	0.155665i
$165$	−24.6137	−	13.7905i	−1.91618	−	1.07359i
$166$	15.1288	+	0.611197i	1.17422	+	0.0474381i
$167$	−5.54783	−	5.54783i	−0.429304	−	0.429304i	0.459087	−	0.888391i	$-0.348176\pi$
$167$	−5.54783	−	5.54783i	−0.429304	−	0.429304i	−0.888391	+	0.459087i	$0.848176\pi$
$168$	0.797529	−	0.624436i	0.0615307	−	0.0481762i
$169$			23.4687i			1.80528i
$170$	15.6123	−	3.72676i	1.19741	−	0.285830i
$171$		−	8.73981i		−	0.668350i
$172$	−8.22358	−	9.67188i	−0.627042	−	0.737474i
$173$	10.4134	+	10.4134i	0.791713	+	0.791713i	0.981773	−	0.190060i	$-0.0608682\pi$
$173$	10.4134	+	10.4134i	0.791713	+	0.791713i	−0.190060	+	0.981773i	$0.560868\pi$
$174$	−0.237600	+	5.88127i	−0.0180124	+	0.445858i
$175$	−0.778063	−	0.187109i	−0.0588161	−	0.0141441i
$176$	−3.62723	+	22.2626i	−0.273413	+	1.67811i
$177$	7.66057	−	7.66057i	0.575804	−	0.575804i
$178$	0.247401	−	0.228188i	0.0185435	−	0.0171034i
$179$	9.47187			0.707961			0.353980	−	0.935253i	$-0.384828\pi$
$179$	9.47187			0.707961			0.353980	+	0.935253i	$0.384828\pi$
$180$	−8.80539	+	1.72949i	−0.656315	+	0.128909i
$181$	20.8741			1.55156			0.775779	−	0.631005i	$-0.217357\pi$
$181$	20.8741			1.55156			0.775779	+	0.631005i	$0.217357\pi$
$182$	−1.00475	+	0.926722i	−0.0744772	+	0.0686932i
$183$	16.2835	−	16.2835i	1.20371	−	1.20371i
$184$	−1.82688	+	15.0078i	−0.134679	+	1.10639i
$185$	10.1141	−	18.0519i	0.743601	−	1.32720i
$186$	−0.401173	+	9.93014i	−0.0294154	+	0.728114i
$187$	−20.2391	−	20.2391i	−1.48003	−	1.48003i
$188$	−6.37312	+	5.41879i	−0.464807	+	0.395206i
$189$			0.355765i			0.0258781i
$190$	11.7346	+	7.21195i	0.851319	+	0.523210i
$191$			11.8936i			0.860593i	0.902688	+	0.430297i	$0.141591\pi$
$191$			11.8936i			0.860593i	−0.902688	+	0.430297i	$0.858409\pi$
$192$	9.25123	+	15.3243i	0.667650	+	1.10594i
$193$	−11.8636	−	11.8636i	−0.853960	−	0.853960i	0.136658	−	0.990618i	$-0.456364\pi$
$193$	−11.8636	−	11.8636i	−0.853960	−	0.853960i	−0.990618	+	0.136658i	$0.956364\pi$
$194$	−13.3329	−	0.538643i	−0.957247	−	0.0386723i
$195$	29.0816	−	8.19591i	2.08258	−	0.586921i
$196$	13.9033	+	1.12521i	0.993094	+	0.0803722i
$197$	6.62733	−	6.62733i	0.472177	−	0.472177i	−0.430441	−	0.902619i	$-0.641642\pi$
$197$	6.62733	−	6.62733i	0.472177	−	0.472177i	0.902619	+	0.430441i	$0.141642\pi$
$198$	10.8491	+	11.7626i	0.771014	+	0.835934i
$199$	−13.5645			−0.961560			−0.480780	−	0.876841i	$-0.659646\pi$
$199$	−13.5645			−0.961560			−0.480780	+	0.876841i	$0.659646\pi$
$200$	4.94393	−	13.2498i	0.349589	−	0.936903i
$201$	−32.8407			−2.31640
$202$	−11.2615	−	12.2097i	−0.792358	−	0.859075i
$203$	0.210513	−	0.210513i	0.0147751	−	0.0147751i
$204$	−22.6403	−	1.83231i	−1.58514	−	0.128287i
$205$	−2.15223	+	0.606551i	−0.150318	+	0.0423633i
$206$	−3.29662	−	0.133182i	−0.229687	−	0.00927923i
$207$	7.58411	+	7.58411i	0.527132	+	0.527132i
$208$	−14.1117	−	19.6051i	−0.978467	−	1.35937i
$209$		−	24.5615i		−	1.69895i
$210$	0.964812	+	0.592961i	0.0665784	+	0.0409182i
$211$			11.0246i			0.758965i	0.925199	+	0.379483i	$0.123898\pi$
$211$			11.0246i			0.758965i	−0.925199	+	0.379483i	$0.876102\pi$
$212$	−11.9667	+	10.1748i	−0.821878	+	0.698807i
$213$	6.39292	+	6.39292i	0.438035	+	0.438035i
$214$	−0.0272064	+	0.673434i	−0.00185979	+	0.0460350i
$215$	6.93778	−	12.3828i	0.473152	−	0.844498i
$216$	−6.24109	−	0.759720i	−0.424652	−	0.0516924i
$217$	0.355437	−	0.355437i	0.0241286	−	0.0241286i
$218$	−5.54328	+	5.11278i	−0.375438	+	0.346281i
$219$	−9.63706			−0.651212
$220$	−24.7458	+	4.86039i	−1.66836	+	0.327688i
$221$	30.6521			2.06188
$222$	−21.5247	+	19.8531i	−1.44464	+	1.33245i
$223$	2.02947	−	2.02947i	0.135903	−	0.135903i	−0.635883	−	0.771786i	$-0.719364\pi$
$223$	2.02947	−	2.02947i	0.135903	−	0.135903i	0.771786	+	0.635883i	$0.219364\pi$
$224$	0.181545	−	0.886986i	0.0121300	−	0.0592642i
$225$	−5.23889	−	8.55638i	−0.349259	−	0.570425i
$226$	0.123655	−	3.06080i	0.00822540	−	0.203601i
$227$	−7.00027	−	7.00027i	−0.464625	−	0.464625i	0.435543	−	0.900168i	$-0.356556\pi$
$227$	−7.00027	−	7.00027i	−0.464625	−	0.464625i	−0.900168	+	0.435543i	$0.856556\pi$
$228$	−12.6260	−	14.8496i	−0.836175	−	0.983438i
$229$			18.0219i			1.19092i	0.803385	+	0.595461i	$0.203030\pi$
$229$			18.0219i			1.19092i	−0.803385	+	0.595461i	$0.796970\pi$
$230$	−16.4412	+	3.92462i	−1.08410	+	0.258782i
$231$		−	2.01943i		−	0.132869i
$232$	3.24343	+	4.14251i	0.212942	+	0.271969i
$233$	−13.8638	−	13.8638i	−0.908247	−	0.908247i	0.0878840	−	0.996131i	$-0.471990\pi$
$233$	−13.8638	−	13.8638i	−0.908247	−	0.908247i	−0.996131	+	0.0878840i	$0.971990\pi$
$234$	−17.1228	−	0.691752i	−1.11935	−	0.0452212i
$235$	−8.15941	−	4.57153i	−0.532261	−	0.298213i
$236$	0.781149	−	9.65203i	0.0508485	−	0.628294i
$237$	−14.1727	+	14.1727i	−0.920618	+	0.920618i
$238$	0.778914	+	0.844499i	0.0504895	+	0.0547408i
$239$	−23.7522			−1.53640			−0.768202	−	0.640207i	$-0.778848\pi$
$239$	−23.7522			−1.53640			−0.768202	+	0.640207i	$0.778848\pi$
$240$	−12.4625	+	15.6592i	−0.804450	+	1.01080i
$241$	4.74279			0.305510			0.152755	−	0.988264i	$-0.451186\pi$
$241$	4.74279			0.305510			0.152755	+	0.988264i	$0.451186\pi$
$242$	19.9423	+	21.6214i	1.28194	+	1.38988i
$243$	−12.6781	+	12.6781i	−0.813301	+	0.813301i
$244$	1.66044	−	20.5167i	0.106299	−	1.31344i
$245$	4.23032	+	15.0105i	0.270265	+	0.958985i
$246$	3.16177	+	0.127734i	0.201587	+	0.00814403i
$247$	18.5992	+	18.5992i	1.18344	+	1.18344i
$248$	5.47633	+	6.99437i	0.347747	+	0.444143i
$249$		−	23.9560i		−	1.51815i
$250$	15.8114	+	0.0265222i	0.999999	+	0.00167741i
$251$			18.0804i			1.14122i	0.821220	+	0.570612i	$0.193294\pi$
$251$			18.0804i			1.14122i	−0.821220	+	0.570612i	$0.806706\pi$
$252$	−0.416056	−	0.489330i	−0.0262091	−	0.0308249i
$253$	21.3136	+	21.3136i	1.33997	+	1.33997i
$254$	0.403684	−	9.99229i	0.0253294	−	0.626972i
$255$	−6.88870	−	24.4433i	−0.431387	−	1.53070i
$256$	15.1725	+	5.07892i	0.948281	+	0.317432i
$257$	−4.79166	+	4.79166i	−0.298895	+	0.298895i	−0.840581	−	0.541686i	$-0.817786\pi$
$257$	−4.79166	+	4.79166i	−0.298895	+	0.298895i	0.541686	+	0.840581i	$0.317786\pi$
$258$	−14.7649	+	13.6183i	−0.919225	+	0.847837i
$259$	1.48107			0.0920289
$260$	15.0582	−	22.4193i	0.933871	−	1.39038i
$261$	3.73244			0.231032
$262$	11.0141	−	10.1587i	0.680454	−	0.627609i
$263$	14.2028	−	14.2028i	0.875783	−	0.875783i	−0.117312	−	0.993095i	$-0.537428\pi$
$263$	14.2028	−	14.2028i	0.875783	−	0.875783i	0.993095	+	0.117312i	$0.0374277\pi$
$264$	35.4263	+	4.31240i	2.18034	+	0.265410i
$265$	−15.3208	−	8.58389i	−0.941151	−	0.527304i
$266$	−0.0397960	+	0.985061i	−0.00244005	+	0.0603979i
$267$	−0.376540	−	0.376540i	−0.0230438	−	0.0230438i
$268$	−22.3634	+	19.0146i	−1.36606	+	1.16150i
$269$		−	17.9740i		−	1.09590i	−0.836513	−	0.547948i	$-0.815409\pi$
$269$		−	17.9740i		−	1.09590i	0.836513	−	0.547948i	$-0.184591\pi$
$270$	−1.63208	−	6.83716i	−0.0993251	−	0.416097i
$271$		−	0.0331829i		−	0.00201571i	−0.999999	−	0.00100786i	$-0.999679\pi$
$271$		−	0.0331829i		−	0.00201571i	0.999999	−	0.00100786i	$-0.000320811\pi$
$272$	−16.4782	+	11.8609i	−0.999137	+	0.719174i
$273$	1.52921	+	1.52921i	0.0925522	+	0.0925522i
$274$	9.01097	+	0.364039i	0.544372	+	0.0219924i
$275$	−14.7228	−	24.0460i	−0.887820	−	1.45003i
$276$	23.8423	+	1.92959i	1.43514	+	0.116147i
$277$	10.2808	−	10.2808i	0.617714	−	0.617714i	−0.327230	−	0.944945i	$-0.606115\pi$
$277$	10.2808	−	10.2808i	0.617714	−	0.617714i	0.944945	+	0.327230i	$0.106115\pi$
$278$	−2.14024	−	2.32045i	−0.128363	−	0.139171i
$279$	6.30199			0.377290
$280$	1.00033	−	0.154836i	0.0597810	−	0.00925322i
$281$	28.3956			1.69394			0.846969	−	0.531642i	$-0.178425\pi$
$281$	28.3956			1.69394			0.846969	+	0.531642i	$0.178425\pi$
$282$	8.97352	+	9.72910i	0.534365	+	0.579359i
$283$	9.36534	−	9.36534i	0.556712	−	0.556712i	−0.371658	−	0.928370i	$-0.621211\pi$
$283$	9.36534	−	9.36534i	0.556712	−	0.556712i	0.928370	+	0.371658i	$0.121211\pi$
$284$	8.05483	+	0.651887i	0.477966	+	0.0386824i
$285$	10.6518	−	19.0117i	0.630959	−	1.12616i
$286$	−48.1201	−	1.94403i	−2.84540	−	0.114953i
$287$	−0.113172	−	0.113172i	−0.00668032	−	0.00668032i
$288$	9.47266	−	6.25382i	0.558182	−	0.368510i
$289$		−	8.76325i		−	0.515485i
$290$	−3.07995	+	5.01141i	−0.180861	+	0.294280i
$291$			21.1122i			1.23762i
$292$	−6.56251	+	5.57982i	−0.384042	+	0.326534i
$293$	−15.2919	−	15.2919i	−0.893360	−	0.893360i	0.101478	−	0.994838i	$-0.467643\pi$
$293$	−15.2919	−	15.2919i	−0.893360	−	0.893360i	−0.994838	+	0.101478i	$0.967643\pi$
$294$	0.890867	−	22.0514i	0.0519564	−	1.28607i
$295$	10.4207	−	2.93679i	0.606714	−	0.170987i
$296$	−3.16275	+	25.9820i	−0.183831	+	1.51017i
$297$	−8.86339	+	8.86339i	−0.514306	+	0.514306i
$298$	22.3211	−	20.5876i	1.29303	−	1.19261i
$299$	−32.2795			−1.86677
$300$	−21.2622	−	6.96957i	−1.22757	−	0.402388i
$301$	1.01594			0.0585579
$302$	16.2236	−	14.9637i	0.933564	−	0.861062i
$303$	−18.5830	+	18.5830i	−1.06757	+	1.06757i
$304$	−17.1957	−	2.80169i	−0.986241	−	0.160688i
$305$	22.1505	−	6.24254i	1.26833	−	0.357447i
$306$	−0.581421	+	14.3918i	−0.0332376	+	0.822723i
$307$	−0.404493	−	0.404493i	−0.0230856	−	0.0230856i	0.695470	−	0.718555i	$-0.255196\pi$
$307$	−0.404493	−	0.404493i	−0.0230856	−	0.0230856i	−0.718555	+	0.695470i	$0.755196\pi$
$308$	−1.16924	−	1.37516i	−0.0666237	−	0.0783571i
$309$			5.22009i			0.296961i
$310$	−5.20030	+	8.46145i	−0.295357	+	0.480578i
$311$		−	17.8602i		−	1.01276i	−0.862310	−	0.506380i	$-0.830983\pi$
$311$		−	17.8602i		−	1.01276i	0.862310	−	0.506380i	$-0.169017\pi$
$312$	−30.0922	+	23.5611i	−1.70363	+	1.33388i
$313$	14.5002	+	14.5002i	0.819601	+	0.819601i	0.986050	−	0.166449i	$-0.0532303\pi$
$313$	14.5002	+	14.5002i	0.819601	+	0.819601i	−0.166449	+	0.986050i	$0.553230\pi$
$314$	3.79649	+	0.153377i	0.214249	+	0.00865554i
$315$	0.351003	−	0.626482i	0.0197768	−	0.0352982i
$316$	−1.44519	+	17.8571i	−0.0812986	+	1.00454i
$317$	−10.3615	+	10.3615i	−0.581962	+	0.581962i	−0.935442	−	0.353480i	$-0.884998\pi$
$317$	−10.3615	+	10.3615i	−0.581962	+	0.581962i	0.353480	+	0.935442i	$0.384998\pi$
$318$	16.8495	+	18.2682i	0.944871	+	1.02443i
$319$	10.4893			0.587287
$320$	0.580097	+	17.8791i	0.0324284	+	0.999474i
$321$	1.06636			0.0595185
$322$	−0.820268	−	0.889335i	−0.0457117	−	0.0495607i
$323$	15.6327	−	15.6327i	0.869828	−	0.869828i
$324$	−1.77362	+	21.9151i	−0.0985342	+	1.21751i
$325$	29.3577	+	7.05995i	1.62847	+	0.391616i
$326$	33.1329	+	1.33855i	1.83506	+	0.0741355i
$327$	8.43676	+	8.43676i	0.466554	+	0.466554i
$328$	2.22702	−	1.74367i	0.122967	−	0.0962782i
$329$		−	0.669437i		−	0.0369073i
$330$	9.26417	+	38.8098i	0.509976	+	2.13641i
$331$			2.49526i			0.137152i	0.997646	+	0.0685759i	$0.0218455\pi$
$331$			2.49526i			0.137152i	−0.997646	+	0.0685759i	$0.978154\pi$
$332$	−13.8704	−	16.3132i	−0.761238	−	0.895303i
$333$	13.1298	+	13.1298i	0.719511	+	0.719511i
$334$	−0.447894	+	11.0866i	−0.0245077	+	0.606632i
$335$	−28.6315	−	16.0416i	−1.56431	−	0.876445i
$336$	−1.41382	−	0.230353i	−0.0771301	−	0.0125668i
$337$	−16.4339	+	16.4339i	−0.895209	+	0.895209i	−0.995008	−	0.0997987i	$-0.968180\pi$
$337$	−16.4339	+	16.4339i	−0.895209	+	0.895209i	0.0997987	+	0.995008i	$0.468180\pi$
$338$	24.3969	−	22.5022i	1.32702	−	1.22396i
$339$	−4.84668			−0.263235
$340$	−18.8435	−	12.6565i	−1.02193	−	0.686395i
$341$	17.7105			0.959076
$342$	−9.08549	+	8.37989i	−0.491287	+	0.453133i
$343$	−1.58151	+	1.58151i	−0.0853933	+	0.0853933i
$344$	−2.16950	+	17.8224i	−0.116972	+	0.960921i
$345$	7.25443	+	25.7410i	0.390565	+	1.38585i
$346$	0.840703	−	20.8097i	0.0451965	−	1.11874i
$347$	16.3083	+	16.3083i	0.875477	+	0.875477i	0.993063	−	0.117586i	$-0.0375155\pi$
$347$	16.3083	+	16.3083i	0.875477	+	0.875477i	−0.117586	+	0.993063i	$0.537516\pi$
$348$	6.34169	−	5.39207i	0.339951	−	0.289045i
$349$		−	5.98917i		−	0.320593i	−0.987069	−	0.160296i	$-0.948755\pi$
$349$		−	5.98917i		−	0.320593i	0.987069	−	0.160296i	$-0.0512450\pi$
$350$	0.551512	+	0.988240i	0.0294795	+	0.0528237i
$351$		−	13.4236i		−	0.716500i
$352$	26.6210	−	17.5751i	1.41890	−	0.936756i
$353$	16.2905	+	16.2905i	0.867053	+	0.867053i	0.992145	−	0.125092i	$-0.0399226\pi$
$353$	16.2905	+	16.2905i	0.867053	+	0.867053i	−0.125092	+	0.992145i	$0.539923\pi$
$354$	−15.3087	−	0.618462i	−0.813646	−	0.0328709i
$355$	2.45082	+	8.69627i	0.130076	+	0.461550i
$356$	−0.474425	−	0.0383958i	−0.0251445	−	0.00203497i
$357$	1.28531	−	1.28531i	0.0680259	−	0.0680259i
$358$	−9.08180	−	9.84649i	−0.479988	−	0.520403i
$359$	15.8268			0.835307			0.417653	−	0.908606i	$-0.362853\pi$
$359$	15.8268			0.835307			0.417653	+	0.908606i	$0.362853\pi$
$360$	10.2407	+	7.49538i	0.539731	+	0.395041i
$361$	−0.0286525			−0.00150802
$362$	−20.0144	−	21.6997i	−1.05194	−	1.14051i
$363$	32.9074	−	32.9074i	1.72719	−	1.72719i
$364$	1.92675	+	0.155934i	0.100989	+	0.00817317i
$365$	−8.40189	−	4.70738i	−0.439775	−	0.246395i
$366$	−32.5406	−	1.31462i	−1.70092	−	0.0687164i
$367$	22.0237	+	22.0237i	1.14963	+	1.14963i	0.986626	+	0.163003i	$0.0521181\pi$
$367$	22.0237	+	22.0237i	1.14963	+	1.14963i	0.163003	+	0.986626i	$0.447882\pi$
$368$	17.3530	−	12.4906i	0.904589	−	0.651119i
$369$		−	2.00656i		−	0.104458i
$370$	−28.4635	+	6.79442i	−1.47974	+	0.353225i
$371$		−	1.25699i		−	0.0652598i
$372$	10.7075	−	9.10417i	0.555161	−	0.472029i
$373$	−8.15183	−	8.15183i	−0.422086	−	0.422086i	0.463836	−	0.885921i	$-0.346473\pi$
$373$	−8.15183	−	8.15183i	−0.422086	−	0.422086i	−0.885921	+	0.463836i	$0.846473\pi$
$374$	−1.63397	+	40.4452i	−0.0844903	+	2.09137i
$375$	−0.967897	−	24.9977i	−0.0499820	−	1.29087i
$376$	11.7438	+	1.42955i	0.605639	+	0.0737236i
$377$	−7.94301	+	7.94301i	−0.409086	+	0.409086i
$378$	0.369836	−	0.341114i	0.0190223	−	0.0175450i
$379$	8.10446			0.416298			0.208149	−	0.978097i	$-0.433256\pi$
$379$	8.10446			0.416298			0.208149	+	0.978097i	$0.433256\pi$
$380$	−3.75418	−	19.1137i	−0.192585	−	0.980512i
$381$	−15.8225			−0.810610
$382$	12.3640	−	11.4038i	0.632600	−	0.583471i
$383$	21.4226	−	21.4226i	1.09464	−	1.09464i	0.0996181	−	0.995026i	$-0.468238\pi$
$383$	21.4226	−	21.4226i	1.09464	−	1.09464i	0.995026	−	0.0996181i	$-0.0317621\pi$
$384$	7.06017	−	24.3104i	0.360288	−	1.24058i
$385$	0.986423	−	1.76060i	0.0502728	−	0.0897285i
$386$	−0.957785	+	23.7078i	−0.0487500	+	1.20670i
$387$	9.00645	+	9.00645i	0.457824	+	0.457824i
$388$	12.2239	+	14.3767i	0.620574	+	0.729867i
$389$			1.13288i			0.0574392i	0.999588	+	0.0287196i	$0.00914299\pi$
$389$			1.13288i			0.0574392i	−0.999588	+	0.0287196i	$0.990857\pi$
$390$	−36.4041	−	22.3735i	−1.84339	−	1.13292i
$391$			27.1310i			1.37208i
$392$	−12.1610	−	15.5321i	−0.614225	−	0.784489i
$393$	−16.7633	−	16.7633i	−0.845594	−	0.845594i
$394$	−13.2438	−	0.535045i	−0.667215	−	0.0269552i
$395$	−19.2791	+	5.43332i	−0.970038	+	0.273380i
$396$	1.82552	−	22.5565i	0.0917358	−	1.13350i
$397$	−2.35432	+	2.35432i	−0.118160	+	0.118160i	−0.763714	−	0.645554i	$-0.776626\pi$
$397$	−2.35432	+	2.35432i	−0.118160	+	0.118160i	0.645554	+	0.763714i	$0.276626\pi$
$398$	13.0059	+	14.1010i	0.651925	+	0.706818i
$399$	1.55981			0.0780882
$400$	−18.5142	+	7.56469i	−0.925710	+	0.378235i
$401$	32.3420			1.61508			0.807542	−	0.589810i	$-0.200797\pi$
$401$	32.3420			1.61508			0.807542	+	0.589810i	$0.200797\pi$
$402$	31.4882	+	34.1396i	1.57049	+	1.70273i
$403$	−13.4113	+	13.4113i	−0.668063	+	0.668063i
$404$	−1.89491	+	23.4139i	−0.0942753	+	1.16488i
$405$	−23.6603	+	6.66805i	−1.17569	+	0.331338i
$406$	−0.420682	−	0.0169954i	−0.0208781	−	0.000843465i
$407$	36.8987	+	36.8987i	1.82900	+	1.82900i
$408$	19.8032	+	25.2926i	0.980403	+	1.25217i
$409$			4.38354i			0.216752i	0.994110	+	0.108376i	$0.0345651\pi$
$409$			4.38354i			0.216752i	−0.994110	+	0.108376i	$0.965435\pi$
$410$	2.69414	+	1.65578i	0.133054	+	0.0817733i
$411$		−	14.2686i		−	0.703817i
$412$	3.02241	+	3.55471i	0.148904	+	0.175128i
$413$	0.547954	+	0.547954i	0.0269631	+	0.0269631i
$414$	0.612289	−	15.1558i	0.0300924	−	0.744869i
$415$	11.7017	−	20.8856i	0.574413	−	1.02523i
$416$	−6.85001	+	33.4675i	−0.335849	+	1.64088i
$417$	−3.53168	+	3.53168i	−0.172947	+	0.172947i
$418$	−25.5329	+	23.5500i	−1.24886	+	1.15187i
$419$	34.1706			1.66934			0.834671	−	0.550748i	$-0.185658\pi$
$419$	34.1706			1.66934			0.834671	+	0.550748i	$0.185658\pi$
$420$	−0.308666	−	1.57151i	−0.0150614	−	0.0766820i
$421$	−7.63548			−0.372130			−0.186065	−	0.982537i	$-0.559574\pi$
$421$	−7.63548			−0.372130			−0.186065	+	0.982537i	$0.559574\pi$
$422$	11.4607	−	10.5706i	0.557896	−	0.514569i
$423$	5.93465	−	5.93465i	0.288552	−	0.288552i
$424$	22.0511	+	2.68425i	1.07090	+	0.130359i
$425$	5.93393	−	24.6753i	0.287838	−	1.19693i
$426$	0.516121	−	12.7754i	0.0250061	−	0.618971i
$427$	1.16475	+	1.16475i	0.0563661	+	0.0563661i
$428$	0.726156	−	0.617419i	0.0351001	−	0.0298441i
$429$			76.1966i			3.67880i
$430$	−19.5246	+	4.66066i	−0.941560	+	0.224757i
$431$		−	23.4641i		−	1.13022i	−0.825014	−	0.565112i	$-0.808833\pi$
$431$		−	23.4641i		−	1.13022i	0.825014	−	0.565112i	$-0.191167\pi$
$432$	5.19431	+	7.21637i	0.249911	+	0.347198i
$433$	−1.52405	−	1.52405i	−0.0732411	−	0.0732411i	0.669537	−	0.742778i	$-0.266492\pi$
$433$	−1.52405	−	1.52405i	−0.0732411	−	0.0732411i	−0.742778	+	0.669537i	$0.766492\pi$
$434$	−0.710295	−	0.0286956i	−0.0340952	−	0.00137743i
$435$	8.11918	+	4.54899i	0.389285	+	0.218107i
$436$	10.6300	+	0.860298i	0.509085	+	0.0412008i
$437$	−16.4627	+	16.4627i	−0.787516	+	0.787516i
$438$	9.24019	+	10.0182i	0.441513	+	0.478689i
$439$	16.7825			0.800984			0.400492	−	0.916300i	$-0.368839\pi$
$439$	16.7825			0.800984			0.400492	+	0.916300i	$0.368839\pi$
$440$	28.7793	+	21.0643i	1.37200	+	1.00420i
$441$	−13.9946			−0.666407
$442$	−29.3898	−	31.8645i	−1.39793	−	1.51564i
$443$	7.98569	−	7.98569i	0.379411	−	0.379411i	−0.491478	−	0.870890i	$-0.663543\pi$
$443$	7.98569	−	7.98569i	0.379411	−	0.379411i	0.870890	+	0.491478i	$0.163543\pi$
$444$	41.2766	+	3.34056i	1.95890	+	0.158536i
$445$	−0.144352	−	0.512206i	−0.00684294	−	0.0242809i
$446$	−4.05562	−	0.163845i	−0.192039	−	0.00775830i
$447$	−33.9723	−	33.9723i	−1.60683	−	1.60683i
$448$	−1.09614	+	0.661733i	−0.0517875	+	0.0312639i
$449$			15.4276i			0.728075i	0.931384	+	0.364038i	$0.118602\pi$
$449$			15.4276i			0.728075i	−0.931384	+	0.364038i	$0.881398\pi$
$450$	−3.87166	+	13.6501i	−0.182512	+	0.643472i
$451$		−	5.63904i		−	0.265532i
$452$	−3.30042	+	2.80621i	−0.155239	+	0.131993i
$453$	−24.6920	−	24.6920i	−1.16013	−	1.16013i
$454$	−0.565154	+	13.9891i	−0.0265240	+	0.656543i
$455$	0.586246	+	2.08018i	0.0274837	+	0.0975206i
$456$	−3.33091	+	27.3634i	−0.155984	+	1.28141i
$457$	7.65966	−	7.65966i	0.358304	−	0.358304i	−0.504884	−	0.863187i	$-0.668465\pi$
$457$	7.65966	−	7.65966i	0.358304	−	0.358304i	0.863187	+	0.504884i	$0.168465\pi$
$458$	18.7347	−	17.2797i	0.875415	−	0.807429i
$459$	−11.2826			−0.526628
$460$	19.8439	+	13.3284i	0.925228	+	0.621442i
$461$	−40.8172			−1.90105			−0.950524	−	0.310651i	$-0.899453\pi$
$461$	−40.8172			−1.90105			−0.950524	+	0.310651i	$0.899453\pi$
$462$	−2.09930	+	1.93626i	−0.0976682	+	0.0900832i
$463$	21.6957	−	21.6957i	1.00829	−	1.00829i	0.00832053	−	0.999965i	$-0.497351\pi$
$463$	21.6957	−	21.6957i	1.00829	−	1.00829i	0.999965	−	0.00832053i	$-0.00264854\pi$
$464$	1.19649	−	7.34363i	0.0555458	−	0.340920i
$465$	13.7087	+	7.68067i	0.635727	+	0.356183i
$466$	−1.11927	+	27.7050i	−0.0518491	+	1.28341i
$467$	−19.2984	−	19.2984i	−0.893024	−	0.893024i	0.101783	−	0.994807i	$-0.467545\pi$
$467$	−19.2984	−	19.2984i	−0.893024	−	0.893024i	−0.994807	+	0.101783i	$0.967545\pi$
$468$	15.6985	+	18.4633i	0.725664	+	0.853465i
$469$		−	2.34907i		−	0.108470i
$470$	3.07106	+	12.8654i	0.141657	+	0.593436i
$471$		−	6.01162i		−	0.277001i
$472$	−10.7828	+	8.44250i	−0.496317	+	0.388597i
$473$	25.3108	+	25.3108i	1.16379	+	1.16379i
$474$	28.3224	+	1.14421i	1.30089	+	0.0525553i
$475$	18.5732	−	11.3719i	0.852195	−	0.521781i
$476$	0.131063	−	1.61944i	0.00600728	−	0.0742271i
$477$	11.1434	−	11.1434i	0.510221	−	0.510221i
$478$	22.7741	+	24.6917i	1.04166	+	1.12937i
$479$	−21.3501			−0.975510			−0.487755	−	0.872981i	$-0.662184\pi$
$479$	−21.3501			−0.975510			−0.487755	+	0.872981i	$0.662184\pi$
$480$	28.2278	−	2.05896i	1.28842	−	0.0939780i
$481$	−55.8832			−2.54805
$482$	−4.54747	−	4.93037i	−0.207132	−	0.224572i
$483$	−1.35355	+	1.35355i	−0.0615886	+	0.0615886i
$484$	3.35557	−	41.4620i	0.152526	−	1.88464i
$485$	−10.3126	+	18.4063i	−0.468272	+	0.835787i
$486$	25.3356	+	1.02354i	1.14924	+	0.0464289i
$487$	4.27729	+	4.27729i	0.193822	+	0.193822i	0.797346	−	0.603523i	$-0.206237\pi$
$487$	4.27729	+	4.27729i	0.193822	+	0.193822i	−0.603523	+	0.797346i	$0.706237\pi$
$488$	−22.9202	+	17.9456i	−1.03755	+	0.812361i
$489$		−	52.4648i		−	2.37254i
$490$	11.5481	−	18.7900i	0.521688	−	0.848844i
$491$			19.6170i			0.885303i	0.896694	+	0.442651i	$0.145962\pi$
$491$			19.6170i			0.885303i	−0.896694	+	0.442651i	$0.854038\pi$
$492$	−2.89878	−	3.40930i	−0.130687	−	0.153703i
$493$	6.67614	+	6.67614i	0.300678	+	0.300678i
$494$	1.50157	−	37.1681i	0.0675589	−	1.67227i
$495$	24.3527	−	6.86318i	1.09457	−	0.308477i
$496$	2.02020	−	12.3993i	0.0907098	−	0.556743i
$497$	−0.457280	+	0.457280i	−0.0205118	+	0.0205118i
$498$	−24.9035	+	22.9694i	−1.11595	+	1.02928i
$499$	10.1337			0.453646			0.226823	−	0.973936i	$-0.427166\pi$
$499$	10.1337			0.453646			0.226823	+	0.973936i	$0.427166\pi$
$500$	−15.1327	−	16.4622i	−0.676753	−	0.736210i
$501$	17.5553			0.784312
$502$	18.7955	−	17.3358i	0.838884	−	0.773735i
$503$	−1.56443	+	1.56443i	−0.0697543	+	0.0697543i	−0.741123	−	0.671369i	$-0.765707\pi$
$503$	−1.56443	+	1.56443i	−0.0697543	+	0.0697543i	0.671369	+	0.741123i	$0.265707\pi$
$504$	−0.109761	+	0.901690i	−0.00488916	+	0.0401644i
$505$	−25.2784	+	7.12406i	−1.12487	+	0.317017i
$506$	1.72071	−	42.5924i	0.0764951	−	1.89346i
$507$	−37.1316	−	37.1316i	−1.64907	−	1.64907i
$508$	−10.7746	+	9.16115i	−0.478044	+	0.406460i
$509$		−	16.7604i		−	0.742892i	−0.928455	−	0.371446i	$-0.878862\pi$
$509$		−	16.7604i		−	0.742892i	0.928455	−	0.371446i	$-0.121138\pi$
$510$	−18.8050	+	30.5978i	−0.832700	+	1.35489i
$511$		−	0.689331i		−	0.0304942i
$512$	−9.26787	−	20.6423i	−0.409586	−	0.912272i
$513$	−6.84611	−	6.84611i	−0.302263	−	0.302263i
$514$	9.57551	+	0.386846i	0.422358	+	0.0170630i
$515$	−2.54984	+	4.55104i	−0.112359	+	0.200543i
$516$	28.3138	+	2.29147i	1.24645	+	0.100876i
$517$	16.6781	−	16.6781i	0.733503	−	0.733503i
$518$	−1.42007	−	1.53964i	−0.0623944	−	0.0676481i
$519$	−32.9515			−1.44641
$520$	−37.7441	+	5.84223i	−1.65519	+	0.256199i
$521$	0.744530			0.0326184			0.0163092	−	0.999867i	$-0.494808\pi$
$521$	0.744530			0.0326184			0.0163092	+	0.999867i	$0.494808\pi$
$522$	−3.57873	−	3.88007i	−0.156637	−	0.169826i
$523$	3.34017	−	3.34017i	0.146056	−	0.146056i	−0.630298	−	0.776353i	$-0.717067\pi$
$523$	3.34017	−	3.34017i	0.146056	−	0.146056i	0.776353	+	0.630298i	$0.217067\pi$
$524$	−21.1211	−	1.70935i	−0.922678	−	0.0746734i
$525$	1.52707	−	0.934994i	0.0666469	−	0.0408065i
$526$	−28.3825	−	1.14664i	−1.23754	−	0.0499958i
$527$	11.2722	+	11.2722i	0.491026	+	0.491026i
$528$	−29.4845	−	40.9623i	−1.28315	−	1.78266i
$529$		−	5.57147i		−	0.242238i
$530$	5.76648	+	24.1572i	0.250480	+	1.04932i
$531$			9.71537i			0.421611i
$532$	1.06218	−	0.903124i	0.0460513	−	0.0391554i
$533$	4.27017	+	4.27017i	0.184962	+	0.184962i
$534$	−0.0303992	+	0.752465i	−0.00131550	+	0.0325624i
$535$	0.929686	+	0.520881i	0.0401939	+	0.0225197i
$536$	41.2091	+	5.01633i	1.77996	+	0.216672i
$537$	−14.9862	+	14.9862i	−0.646701	+	0.646701i
$538$	−18.6849	+	17.2338i	−0.805564	+	0.743003i
$539$	−39.3289			−1.69401
$540$	−5.54272	+	8.25223i	−0.238521	+	0.355119i
$541$	−6.78106			−0.291541			−0.145770	−	0.989318i	$-0.546566\pi$
$541$	−6.78106			−0.291541			−0.145770	+	0.989318i	$0.546566\pi$
$542$	−0.0344953	+	0.0318163i	−0.00148170	+	0.00136663i
$543$	−33.0265	+	33.0265i	−1.41730	+	1.41730i
$544$	28.1296	+	5.75746i	1.20605	+	0.246849i
$545$	3.23436	+	11.4765i	0.138545	+	0.491600i
$546$	0.123458	−	3.05593i	0.00528353	−	0.130782i
$547$	−24.1468	−	24.1468i	−1.03244	−	1.03244i	−0.999456	−	0.0329854i	$-0.989499\pi$
$547$	−24.1468	−	24.1468i	−1.03244	−	1.03244i	−0.0329854	−	0.999456i	$-0.510501\pi$
$548$	−8.26144	−	9.71641i	−0.352911	−	0.415065i
$549$			20.6513i			0.881376i
$550$	−10.8805	+	38.3608i	−0.463946	+	1.63571i
$551$			8.10194i			0.345154i
$552$	−20.8546	−	26.6354i	−0.887629	−	1.13368i
$553$	−1.01376	−	1.01376i	−0.0431096	−	0.0431096i
$554$	−20.5449	−	0.830003i	−0.872868	−	0.0352635i
$555$	12.5591	+	44.5636i	0.533104	+	1.89162i
$556$	−0.360126	+	4.44978i	−0.0152727	+	0.188713i
$557$	−4.01614	+	4.01614i	−0.170169	+	0.170169i	−0.787054	−	0.616885i	$-0.788395\pi$
$557$	−4.01614	+	4.01614i	−0.170169	+	0.170169i	0.616885	+	0.787054i	$0.288395\pi$
$558$	−6.04247	−	6.55125i	−0.255798	−	0.277336i
$559$	−38.3333			−1.62132
$560$	−1.12009	−	0.891432i	−0.0473325	−	0.0376699i
$561$	64.0436			2.70392
$562$	−27.2262	−	29.5187i	−1.14847	−	1.24517i
$563$	−13.8094	+	13.8094i	−0.581997	+	0.581997i	−0.935452	−	0.353454i	$-0.885007\pi$
$563$	−13.8094	+	13.8094i	−0.581997	+	0.581997i	0.353454	+	0.935452i	$0.385007\pi$
$564$	1.50992	−	18.6569i	0.0635792	−	0.785596i
$565$	−4.22548	−	2.36744i	−0.177767	−	0.0995989i
$566$	−18.7154	−	0.756094i	−0.786667	−	0.0317810i
$567$	−1.24414	−	1.24414i	−0.0522490	−	0.0522490i
$568$	−7.04545	−	8.99845i	−0.295621	−	0.377567i
$569$		−	15.9326i		−	0.667930i	−0.942585	−	0.333965i	$-0.891613\pi$
$569$		−	15.9326i		−	0.667930i	0.942585	−	0.333965i	$-0.108387\pi$
$570$	−29.9768	+	7.15567i	−1.25559	+	0.299718i
$571$		−	25.6813i		−	1.07473i	−0.843350	−	0.537365i	$-0.819420\pi$
$571$		−	25.6813i		−	1.07473i	0.843350	−	0.537365i	$-0.180580\pi$
$572$	44.1175	+	51.8873i	1.84465	+	2.16952i
$573$	−18.8178	−	18.8178i	−0.786126	−	0.786126i
$574$	−0.00913672	+	0.226159i	−0.000381359	+	0.00943970i
$575$	−6.24896	+	25.9853i	−0.260600	+	1.08366i
$576$	−15.5837	−	3.85104i	−0.649322	−	0.160460i
$577$	−13.4819	+	13.4819i	−0.561258	+	0.561258i	−0.929665	−	0.368407i	$-0.879903\pi$
$577$	−13.4819	+	13.4819i	−0.561258	+	0.561258i	0.368407	+	0.929665i	$0.379903\pi$
$578$	−9.10985	+	8.40237i	−0.378920	+	0.349492i
$579$	37.5406			1.56013
$580$	8.16273	−	1.60327i	0.338939	−	0.0665721i
$581$	1.71355			0.0710901
$582$	21.9472	−	20.2428i	0.909742	−	0.839090i
$583$	31.3163	−	31.3163i	1.29699	−	1.29699i
$584$	12.0928	+	1.47204i	0.500402	+	0.0609133i
$585$	−13.2440	+	23.6383i	−0.547570	+	0.977322i
$586$	−1.23456	+	30.5588i	−0.0509992	+	1.26237i
$587$	−6.37771	−	6.37771i	−0.263236	−	0.263236i	0.563131	−	0.826368i	$-0.309597\pi$
$587$	−6.37771	−	6.37771i	−0.263236	−	0.263236i	−0.826368	+	0.563131i	$0.809597\pi$
$588$	−23.7778	+	20.2172i	−0.980579	+	0.833744i
$589$			13.6796i			0.563659i
$590$	−13.0445	−	8.01696i	−0.537032	−	0.330053i
$591$			20.9712i			0.862640i
$592$	30.0421	−	21.6241i	1.23472	−	0.888747i
$593$	−26.8501	−	26.8501i	−1.10260	−	1.10260i	−0.994096	−	0.108505i	$-0.965394\pi$
$593$	−26.8501	−	26.8501i	−1.10260	−	1.10260i	−0.108505	−	0.994096i	$-0.534606\pi$
$594$	17.7123	+	0.715570i	0.726746	+	0.0293602i
$595$	1.74841	−	0.492743i	0.0716776	−	0.0202005i
$596$	−42.8038	−	3.46416i	−1.75331	−	0.141898i
$597$	21.4614	−	21.4614i	0.878356	−	0.878356i
$598$	30.9501	+	33.5562i	1.26565	+	1.37221i
$599$	−11.9882			−0.489826			−0.244913	−	0.969545i	$-0.578759\pi$
$599$	−11.9882			−0.489826			−0.244913	+	0.969545i	$0.578759\pi$
$600$	13.1414	+	28.7857i	0.536494	+	1.17517i
$601$	1.06705			0.0435259			0.0217629	−	0.999763i	$-0.493072\pi$
$601$	1.06705			0.0435259			0.0217629	+	0.999763i	$0.493072\pi$
$602$	−0.974104	−	1.05612i	−0.0397015	−	0.0430444i
$603$	20.8248	−	20.8248i	0.848050	−	0.848050i
$604$	−31.1110	−	2.51785i	−1.26589	−	0.102450i
$605$	44.7638	−	12.6155i	1.81991	−	0.512894i
$606$	37.1357	+	1.50026i	1.50853	+	0.0609441i
$607$	3.85391	+	3.85391i	0.156425	+	0.156425i	0.780981	−	0.624555i	$-0.214720\pi$
$607$	3.85391	+	3.85391i	0.156425	+	0.156425i	−0.624555	+	0.780981i	$0.714720\pi$
$608$	13.5751	+	20.5621i	0.550541	+	0.833904i
$609$			0.666136i			0.0269932i
$610$	−27.7277	−	17.0411i	−1.12266	−	0.689974i
$611$			25.2590i			1.02187i
$612$	15.5185	−	13.1947i	0.627297	−	0.533363i
$613$	4.12963	+	4.12963i	0.166794	+	0.166794i	0.785569	−	0.618775i	$-0.212371\pi$
$613$	4.12963	+	4.12963i	0.166794	+	0.166794i	−0.618775	+	0.785569i	$0.712371\pi$
$614$	−0.0326560	+	0.808327i	−0.00131789	+	0.0326214i
$615$	2.44554	−	4.36488i	0.0986136	−	0.176009i
$616$	−0.308462	+	2.53402i	−0.0124283	+	0.102098i
$617$	−24.5220	+	24.5220i	−0.987220	+	0.987220i	−0.999919	−	0.0126989i	$-0.995958\pi$
$617$	−24.5220	+	24.5220i	−0.987220	+	0.987220i	0.0126989	+	0.999919i	$0.495958\pi$
$618$	5.42656	−	5.00512i	0.218288	−	0.201336i
$619$	17.5609			0.705833			0.352916	−	0.935655i	$-0.385190\pi$
$619$	17.5609			0.705833			0.352916	+	0.935655i	$0.385190\pi$
$620$	13.7823	−	2.70702i	0.553509	−	0.108716i
$621$	11.8816			0.476793
$622$	−18.5666	+	17.1247i	−0.744454	+	0.686638i
$623$	0.0269336	−	0.0269336i	0.00107907	−	0.00107907i
$624$	53.3459	+	8.69161i	2.13554	+	0.347943i
$625$	11.3667	−	22.2665i	0.454667	−	0.890661i
$626$	1.17065	−	28.9768i	0.0467885	−	1.15815i
$627$	38.8606	+	38.8606i	1.55194	+	1.55194i
$628$	−3.48071	−	4.09371i	−0.138895	−	0.163357i
$629$			46.9701i			1.87282i
$630$	−0.987808	+	0.235797i	−0.0393552	+	0.00939436i
$631$			21.3955i			0.851740i	0.904784	+	0.425870i	$0.140032\pi$
$631$			21.3955i			0.851740i	−0.904784	+	0.425870i	$0.859968\pi$
$632$	19.9491	−	15.6194i	0.793531	−	0.621305i
$633$	−17.4429	−	17.4429i	−0.693292	−	0.693292i
$634$	20.7062	+	0.836520i	0.822348	+	0.0332225i
$635$	−13.7945	−	7.72874i	−0.547419	−	0.306706i
$636$	2.83516	−	35.0318i	0.112421	−	1.38910i
$637$	29.7818	−	29.7818i	1.18000	−	1.18000i
$638$	−10.0573	−	10.9041i	−0.398173	−	0.431699i
$639$	−8.10769			−0.320735
$640$	18.0301	−	17.7459i	0.712701	−	0.701468i
$641$	−11.2688			−0.445091			−0.222546	−	0.974922i	$-0.571437\pi$
$641$	−11.2688			−0.445091			−0.222546	+	0.974922i	$0.571437\pi$
$642$	−1.02245	−	1.10854i	−0.0403527	−	0.0437505i
$643$	25.3210	−	25.3210i	0.998562	−	0.998562i	−0.00143730	−	0.999999i	$-0.500458\pi$
$643$	25.3210	−	25.3210i	0.998562	−	0.998562i	0.999999	+	0.00143730i	$0.000457506\pi$
$644$	−0.138022	+	1.70542i	−0.00543881	+	0.0672030i
$645$	8.61495	+	30.5685i	0.339213	+	1.20363i
$646$	−31.2399	−	1.26208i	−1.22912	−	0.0496558i
$647$	−7.60476	−	7.60476i	−0.298974	−	0.298974i	0.541638	−	0.840612i	$-0.317804\pi$
$647$	−7.60476	−	7.60476i	−0.298974	−	0.298974i	−0.840612	+	0.541638i	$0.817804\pi$
$648$	24.4825	−	19.1689i	0.961763	−	0.753024i
$649$			27.3031i			1.07174i
$650$	−20.8095	−	37.2881i	−0.816216	−	1.46256i
$651$			1.12473i			0.0440816i
$652$	−30.3769	−	35.7267i	−1.18965	−	1.39917i
$653$	−8.65155	−	8.65155i	−0.338561	−	0.338561i	0.517264	−	0.855826i	$-0.326950\pi$
$653$	−8.65155	−	8.65155i	−0.338561	−	0.338561i	−0.855826	+	0.517264i	$0.826950\pi$
$654$	0.681127	−	16.8598i	0.0266342	−	0.659269i
$655$	−6.42644	−	22.8030i	−0.251102	−	0.890988i
$656$	−3.94794	−	0.643236i	−0.154141	−	0.0251141i
$657$	6.11100	−	6.11100i	0.238413	−	0.238413i
$658$	−0.695914	+	0.641868i	−0.0271296	+	0.0250226i
$659$	14.4577			0.563194			0.281597	−	0.959533i	$-0.409136\pi$
$659$	14.4577			0.563194			0.281597	+	0.959533i	$0.409136\pi$
$660$	31.4622	−	46.8422i	1.22466	−	1.82333i
$661$	−15.6956			−0.610489			−0.305245	−	0.952274i	$-0.598738\pi$
$661$	−15.6956			−0.610489			−0.305245	+	0.952274i	$0.598738\pi$
$662$	2.59395	−	2.39250i	0.100817	−	0.0929871i
$663$	−48.4971	+	48.4971i	−1.88347	+	1.88347i
$664$	−3.65921	+	30.0604i	−0.142005	+	1.16657i
$665$	1.35989	+	0.761915i	0.0527343	+	0.0295458i
$666$	1.06001	−	26.2383i	0.0410747	−	1.01671i
$667$	−7.03058	−	7.03058i	−0.272225	−	0.272225i
$668$	11.9546	−	10.1644i	0.462536	−	0.393274i
$669$			6.42195i			0.248287i
$670$	10.7764	+	45.1449i	0.416328	+	1.74410i
$671$			58.0363i			2.24047i
$672$	1.11613	+	1.69060i	0.0430557	+	0.0652165i
$673$	25.2232	+	25.2232i	0.972284	+	0.972284i	0.999626	−	0.0273417i	$-0.00870422\pi$
$673$	25.2232	+	25.2232i	0.972284	+	0.972284i	−0.0273417	+	0.999626i	$0.508704\pi$
$674$	32.8409	+	1.32676i	1.26498	+	0.0511048i
$675$	−10.8062	−	2.59867i	−0.415929	−	0.100023i
$676$	−46.7844	−	3.78632i	−1.79940	−	0.145628i
$677$	−25.2312	+	25.2312i	−0.969713	+	0.969713i	−0.999555	−	0.0298412i	$-0.990500\pi$
$677$	−25.2312	+	25.2312i	−0.969713	+	0.969713i	0.0298412	+	0.999555i	$0.490500\pi$
$678$	4.64708	+	5.03837i	0.178470	+	0.193497i
$679$	−1.51014			−0.0579538
$680$	4.91043	+	31.7241i	0.188306	+	1.21656i
$681$	22.1513			0.848841
$682$	−16.9811	−	18.4110i	−0.650241	−	0.704992i
$683$	−29.6852	+	29.6852i	−1.13587	+	1.13587i	−0.146691	+	0.989182i	$0.546862\pi$
$683$	−29.6852	+	29.6852i	−1.13587	+	1.13587i	−0.989182	+	0.146691i	$0.953138\pi$
$684$	17.4227	+	1.41004i	0.666172	+	0.0539141i
$685$	6.96972	−	12.4398i	0.266299	−	0.475300i
$686$	3.16043	+	0.127680i	0.120666	+	0.00487484i
$687$	−28.5138	−	28.5138i	−1.08787	−	1.08787i
$688$	20.6075	−	14.8332i	0.785653	−	0.565509i
$689$			47.4286i			1.80688i
$690$	19.8034	−	32.2223i	0.753902	−	1.22668i
$691$		−	52.1621i		−	1.98434i	−0.124895	−	0.992170i	$-0.539859\pi$
$691$		−	52.1621i		−	1.98434i	0.124895	−	0.992170i	$-0.460141\pi$
$692$	−22.4389	+	19.0788i	−0.852998	+	0.725267i
$693$	1.28055	+	1.28055i	0.0486441	+	0.0486441i
$694$	1.31662	−	32.5901i	0.0499783	−	1.23710i
$695$	−4.80413	+	1.35392i	−0.182231	+	0.0513571i
$696$	−11.6859	−	1.42250i	−0.442952	−	0.0539199i
$697$	3.58910	−	3.58910i	0.135947	−	0.135947i
$698$	−6.22605	+	5.74252i	−0.235659	+	0.217358i
$699$	43.8699			1.65931
$700$	0.498527	−	1.52087i	0.0188426	−	0.0574834i
$701$	−36.6831			−1.38550			−0.692751	−	0.721177i	$-0.743602\pi$
$701$	−36.6831			−1.38550			−0.692751	+	0.721177i	$0.743602\pi$
$702$	−13.9545	+	12.8708i	−0.526680	+	0.485778i
$703$	−28.5007	+	28.5007i	−1.07492	+	1.07492i
$704$	−43.7949	−	10.8226i	−1.65058	−	0.407891i
$705$	20.1426	−	5.67667i	0.758614	−	0.213796i
$706$	1.31518	−	32.5543i	0.0494975	−	1.22520i
$707$	−1.32923	−	1.32923i	−0.0499907	−	0.0499907i
$708$	14.0353	+	16.5071i	0.527479	+	0.620376i
$709$		−	36.4867i		−	1.37029i	−0.728407	−	0.685144i	$-0.759739\pi$
$709$		−	36.4867i		−	1.37029i	0.728407	−	0.685144i	$-0.240261\pi$
$710$	6.69033	−	10.8859i	0.251084	−	0.408540i
$711$		−	17.9743i		−	0.674088i
$712$	0.414973	+	0.530004i	0.0155518	+	0.0198628i
$713$	−11.8707	−	11.8707i	−0.444561	−	0.444561i
$714$	−2.56853	−	0.103767i	−0.0961247	−	0.00388339i
$715$	−37.2195	+	66.4305i	−1.39193	+	2.48436i
$716$	−1.52814	+	18.8820i	−0.0571093	+	0.705653i
$717$	37.5802	−	37.5802i	1.40346	−	1.40346i
$718$	−15.1750	−	16.4528i	−0.566327	−	0.614012i
$719$	−36.7994			−1.37239			−0.686194	−	0.727419i	$-0.740720\pi$
$719$	−36.7994			−1.37239			−0.686194	+	0.727419i	$0.740720\pi$
$720$	−2.02710	−	17.8324i	−0.0755456	−	0.664575i
$721$	−0.373389			−0.0139057
$722$	0.0274725	+	0.0297857i	0.00102242	+	0.00110851i
$723$	−7.50392	+	7.50392i	−0.279074	+	0.279074i
$724$	−3.36771	+	41.6121i	−0.125160	+	1.54650i
$725$	4.85653	+	7.93189i	0.180367	+	0.294583i
$726$	−65.7611	−	2.65672i	−2.44062	−	0.0986000i
$727$	10.4192	+	10.4192i	0.386426	+	0.386426i	0.873411	−	0.486984i	$-0.161903\pi$
$727$	10.4192	+	10.4192i	0.386426	+	0.386426i	−0.486984	+	0.873411i	$0.661903\pi$
$728$	−1.68530	−	2.15247i	−0.0624615	−	0.0797758i
$729$		−	7.13785i		−	0.264365i
$730$	3.16232	+	13.2477i	0.117043	+	0.490320i
$731$			32.2193i			1.19167i
$732$	29.8339	+	35.0881i	1.10269	+	1.29689i
$733$	−26.2550	−	26.2550i	−0.969750	−	0.969750i	0.0298057	−	0.999556i	$-0.490511\pi$
$733$	−26.2550	−	26.2550i	−0.969750	−	0.969750i	−0.999556	+	0.0298057i	$0.990511\pi$
$734$	1.77804	−	44.0115i	0.0656288	−	1.62450i
$735$	−30.4423	−	17.0561i	−1.12288	−	0.629125i
$736$	−29.6231	−	6.06313i	−1.09192	−	0.223490i
$737$	58.5238	−	58.5238i	2.15575	−	2.15575i
$738$	−2.08593	+	1.92393i	−0.0767840	+	0.0708209i
$739$	35.3598			1.30073			0.650365	−	0.759622i	$-0.274616\pi$
$739$	35.3598			1.30073			0.650365	+	0.759622i	$0.274616\pi$
$740$	34.3544	+	23.0746i	1.26289	+	0.848240i
$741$	−58.8544			−2.16207
$742$	−1.30671	+	1.20523i	−0.0479708	+	0.0442453i
$743$	−3.54738	+	3.54738i	−0.130141	+	0.130141i	−0.769177	−	0.639036i	$-0.779333\pi$
$743$	−3.54738	+	3.54738i	−0.130141	+	0.130141i	0.639036	+	0.769177i	$0.279333\pi$
$744$	−19.7308	−	2.40181i	−0.723368	−	0.0880546i
$745$	−13.0238	−	46.2124i	−0.477154	−	1.69309i
$746$	−0.658123	+	16.2904i	−0.0240956	+	0.596433i
$747$	15.1908	+	15.1908i	0.555804	+	0.555804i
$748$	43.6115	−	37.0810i	1.59459	−	1.35581i
$749$			0.0762759i			0.00278706i
$750$	−25.0583	+	24.9744i	−0.915001	+	0.911936i
$751$			21.5611i			0.786777i	0.919372	+	0.393388i	$0.128697\pi$
$751$			21.5611i			0.786777i	−0.919372	+	0.393388i	$0.871303\pi$
$752$	−9.77405	−	13.5789i	−0.356423	−	0.495173i
$753$	−28.6064	−	28.6064i	−1.04247	−	1.04247i
$754$	15.8731	+	0.641265i	0.578063	+	0.0233535i
$755$	−9.46604	−	33.5885i	−0.344505	−	1.22241i
$756$	−0.709210	−	0.0573972i	−0.0257937	−	0.00208752i
$757$	−1.39795	+	1.39795i	−0.0508092	+	0.0508092i	−0.732055	−	0.681246i	$-0.761439\pi$
$757$	−1.39795	+	1.39795i	−0.0508092	+	0.0508092i	0.681246	+	0.732055i	$0.261439\pi$
$758$	−7.77071	−	8.42501i	−0.282245	−	0.306010i
$759$	−67.4437			−2.44805
$760$	−16.2701	+	22.2292i	−0.590178	+	0.806339i
$761$	2.53272			0.0918111			0.0459055	−	0.998946i	$-0.485383\pi$
$761$	2.53272			0.0918111			0.0459055	+	0.998946i	$0.485383\pi$
$762$	15.1709	+	16.4483i	0.549583	+	0.595858i
$763$	−0.603475	+	0.603475i	−0.0218472	+	0.0218472i
$764$	−23.7098	−	1.91886i	−0.857789	−	0.0694218i
$765$	19.8681	+	11.1316i	0.718332	+	0.402464i
$766$	−42.8103	−	1.72951i	−1.54680	−	0.0624899i
$767$	−20.6753	−	20.6753i	−0.746541	−	0.746541i
$768$	−32.0413	+	15.9698i	−1.15619	+	0.576261i
$769$		−	20.9037i		−	0.753807i	−0.926252	−	0.376904i	$-0.876989\pi$
$769$		−	20.9037i		−	0.753807i	0.926252	−	0.376904i	$-0.123011\pi$
$770$	−2.77603	+	0.662658i	−0.100041	+	0.0238805i
$771$		−	15.1625i		−	0.546064i
$772$	25.5639	−	21.7358i	0.920064	−	0.782290i
$773$	1.22905	+	1.22905i	0.0442059	+	0.0442059i	0.728864	−	0.684658i	$-0.240049\pi$
$773$	1.22905	+	1.22905i	0.0442059	+	0.0442059i	−0.684658	+	0.728864i	$0.740049\pi$
$774$	0.727120	−	17.9982i	0.0261358	−	0.646933i
$775$	8.19994	+	13.3925i	0.294550	+	0.481073i
$776$	3.22484	−	26.4920i	0.115765	−	0.951008i
$777$	−2.34331	+	2.34331i	−0.0840657	+	0.0840657i
$778$	1.17768	−	1.08622i	0.0422220	−	0.0389430i
$779$	4.35561			0.156056
$780$	11.6465	+	59.2960i	0.417012	+	2.12314i
$781$	−22.7850			−0.815312
$782$	28.2041	−	26.0137i	1.00858	−	0.930250i
$783$	2.92371	−	2.92371i	0.104485	−	0.104485i
$784$	−4.48617	+	27.5345i	−0.160221	+	0.983374i
$785$	2.93648	−	5.24112i	0.104807	−	0.187064i
$786$	−1.35335	+	33.4992i	−0.0482724	+	1.19488i
$787$	−15.0630	−	15.0630i	−0.536939	−	0.536939i	0.385690	−	0.922628i	$-0.373963\pi$
$787$	−15.0630	−	15.0630i	−0.536939	−	0.536939i	−0.922628	+	0.385690i	$0.873963\pi$
$788$	12.1422	+	14.2807i	0.432549	+	0.508728i
$789$			44.9427i			1.60000i
$790$	24.1334	+	14.8321i	0.858628	+	0.527701i
$791$		−	0.346679i		−	0.0123265i
$792$	−25.1989	+	19.7298i	−0.895405	+	0.701069i
$793$	−43.9480	−	43.9480i	−1.56064	−	1.56064i
$794$	4.70480	+	0.190072i	0.166967	+	0.00674540i
$795$	37.8215	−	10.6590i	1.34139	−	0.378036i
$796$	2.18842	−	27.0405i	0.0775665	−	0.958426i
$797$	35.5471	−	35.5471i	1.25914	−	1.25914i	0.307641	−	0.951503i	$-0.400461\pi$
$797$	35.5471	−	35.5471i	1.25914	−	1.25914i	0.951503	−	0.307641i	$-0.0995395\pi$
$798$	−1.49558	−	1.62150i	−0.0529428	−	0.0574006i
$799$	21.2303			0.751075
$800$	25.6156	+	11.9933i	0.905650	+	0.424027i
$801$	0.477539			0.0168730
$802$	−31.0101	−	33.6212i	−1.09501	−	1.18721i
$803$	17.1737	−	17.1737i	0.606048	−	0.606048i
$804$	5.29834	−	65.4673i	0.186858	−	2.30885i
$805$	−1.84123	+	0.518903i	−0.0648948	+	0.0182889i
$806$	26.8007	+	1.08273i	0.944014	+	0.0381377i
$807$	28.4381	+	28.4381i	1.00107	+	1.00107i
$808$	26.1568	−	20.4798i	0.920193	−	0.720476i
$809$			3.45243i			0.121381i	0.998157	+	0.0606904i	$0.0193302\pi$
$809$			3.45243i			0.121381i	−0.998157	+	0.0606904i	$0.980670\pi$
$810$	29.6177	+	18.2027i	1.04066	+	0.639577i
$811$		−	8.52365i		−	0.299306i	−0.988739	−	0.149653i	$-0.952184\pi$
$811$		−	8.52365i		−	0.299306i	0.988739	−	0.149653i	$-0.0478156\pi$
$812$	0.385690	+	0.453616i	0.0135351	+	0.0159188i
$813$	0.0525011	+	0.0525011i	0.00184129	+	0.00184129i
$814$	2.97895	−	73.7373i	0.104412	−	2.58449i
$815$	25.6273	−	45.7404i	0.897685	−	1.60222i
$816$	7.30534	−	44.8375i	0.255738	−	1.56963i
$817$	−19.5501	+	19.5501i	−0.683973	+	0.683973i
$818$	4.55692	−	4.20302i	0.159329	−	0.146955i
$819$	−1.93939			−0.0677679
$820$	−0.861918	−	4.38829i	−0.0300995	−	0.153246i
$821$	44.6016			1.55661			0.778304	−	0.627888i	$-0.216080\pi$
$821$	44.6016			1.55661			0.778304	+	0.627888i	$0.216080\pi$
$822$	−14.8329	+	13.6810i	−0.517357	+	0.477179i
$823$	27.2956	−	27.2956i	0.951465	−	0.951465i	−0.0474105	−	0.998875i	$-0.515097\pi$
$823$	27.2956	−	27.2956i	0.951465	−	0.951465i	0.998875	+	0.0474105i	$0.0150969\pi$
$824$	0.797356	−	6.55027i	0.0277772	−	0.228190i
$825$	61.3391	+	14.7509i	2.13555	+	0.513559i
$826$	0.0442381	−	1.09502i	0.00153924	−	0.0381005i
$827$	18.4367	+	18.4367i	0.641109	+	0.641109i	0.950828	−	0.309719i	$-0.100235\pi$
$827$	18.4367	+	18.4367i	0.641109	+	0.641109i	−0.309719	+	0.950828i	$0.600235\pi$
$828$	−16.3424	+	13.8952i	−0.567936	+	0.482892i
$829$		−	2.47882i		−	0.0860930i	−0.999073	−	0.0430465i	$-0.986294\pi$
$829$		−	2.47882i		−	0.0860930i	0.999073	−	0.0430465i	$-0.0137064\pi$
$830$	−32.9314	+	7.86095i	−1.14307	+	0.272858i
$831$			32.5321i			1.12853i
$832$	41.3591	−	24.9683i	1.43387	−	0.865622i
$833$	−25.0317	−	25.0317i	−0.867299	−	0.867299i
$834$	7.05760	+	0.285124i	0.244385	+	0.00987302i
$835$	15.3052	+	8.57517i	0.529660	+	0.296756i
$836$	48.9629	+	3.96262i	1.69342	+	0.137050i
$837$	4.93650	−	4.93650i	0.170631	−	0.170631i
$838$	−32.7634	−	35.5221i	−1.13179	−	1.22709i
$839$	7.88972			0.272383			0.136192	−	0.990683i	$-0.456514\pi$
$839$	7.88972			0.272383			0.136192	+	0.990683i	$0.456514\pi$
$840$	−1.33772	+	1.82767i	−0.0461556	+	0.0630606i
$841$	25.5400			0.880689
$842$	7.32104	+	7.93747i	0.252300	+	0.273543i
$843$	−44.9268	+	44.9268i	−1.54736	+	1.54736i
$844$	−21.9774	−	1.77865i	−0.756492	−	0.0612238i
$845$	−14.2350	−	50.5100i	−0.489697	−	1.73760i
$846$	−11.8596	−	0.479123i	−0.407742	−	0.0164726i
$847$	2.35384	+	2.35384i	0.0808788	+	0.0808788i
$848$	−18.3526	−	25.4970i	−0.630231	−	0.875570i
$849$			29.6352i			1.01708i
$850$	−31.3408	+	17.4905i	−1.07498	+	0.599919i
$851$		−	49.4638i		−	1.69560i
$852$	−13.7756	+	11.7128i	−0.471943	+	0.401273i
$853$	2.72427	+	2.72427i	0.0932773	+	0.0932773i	0.752206	−	0.658928i	$-0.228990\pi$
$853$	2.72427	+	2.72427i	0.0932773	+	0.0932773i	−0.658928	+	0.752206i	$0.728990\pi$
$854$	0.0940339	−	2.32760i	0.00321777	−	0.0796488i
$855$	5.30114	+	18.8101i	0.181295	+	0.643292i
$856$	−1.33809	−	0.162884i	−0.0457350	−	0.00556725i
$857$	−28.0952	+	28.0952i	−0.959714	+	0.959714i	−0.999219	−	0.0395057i	$-0.987422\pi$
$857$	−28.0952	+	28.0952i	−0.959714	+	0.959714i	0.0395057	+	0.999219i	$0.487422\pi$
$858$	79.2103	−	73.0587i	2.70419	−	2.49418i
$859$	4.10140			0.139938			0.0699690	−	0.997549i	$-0.477710\pi$
$859$	4.10140			0.139938			0.0699690	+	0.997549i	$0.477710\pi$
$860$	23.5655	+	15.8281i	0.803578	+	0.539734i
$861$	0.358115			0.0122045
$862$	−24.3921	+	22.4978i	−0.830798	+	0.766277i
$863$	−18.5268	+	18.5268i	−0.630659	+	0.630659i	−0.948233	−	0.317575i	$-0.897132\pi$
$863$	−18.5268	+	18.5268i	−0.630659	+	0.630659i	0.317575	+	0.948233i	$0.397132\pi$
$864$	2.52139	−	12.3189i	0.0857795	−	0.419099i
$865$	−28.7282	−	16.0957i	−0.976787	−	0.547271i
$866$	−0.123041	+	3.04561i	−0.00418112	+	0.103494i
$867$	13.8650	+	13.8650i	0.470880	+	0.470880i
$868$	0.651213	+	0.765902i	0.0221036	+	0.0259964i
$869$		−	50.5131i		−	1.71354i
$870$	−3.05591	−	12.8020i	−0.103605	−	0.434027i
$871$			88.6344i			3.00326i
$872$	−9.29792	−	11.8753i	−0.314867	−	0.402148i
$873$	−13.3876	−	13.3876i	−0.453101	−	0.453101i
$874$	32.8985	+	1.32908i	1.11281	+	0.0449569i
$875$	1.78806	−	0.0692329i	0.0604476	−	0.00234050i
$876$	1.55479	−	19.2113i	0.0525316	−	0.649090i
$877$	−31.8902	+	31.8902i	−1.07685	+	1.07685i	−0.0800650	+	0.996790i	$0.525513\pi$
$877$	−31.8902	+	31.8902i	−1.07685	+	1.07685i	−0.996790	+	0.0800650i	$0.974487\pi$
$878$	−16.0913	−	17.4462i	−0.543056	−	0.588782i
$879$	48.3888			1.63211
$880$	−5.69676	−	50.1144i	−0.192038	−	1.68936i
$881$	17.2879			0.582445			0.291223	−	0.956655i	$-0.405938\pi$
$881$	17.2879			0.582445			0.291223	+	0.956655i	$0.405938\pi$
$882$	13.4182	+	14.5481i	0.451815	+	0.489859i
$883$	0.801784	−	0.801784i	0.0269822	−	0.0269822i	−0.693487	−	0.720469i	$-0.743927\pi$
$883$	0.801784	−	0.801784i	0.0269822	−	0.0269822i	0.720469	+	0.693487i	$0.243927\pi$
$884$	−4.94525	+	61.1044i	−0.166327	+	2.05516i
$885$	−11.8408	+	21.1338i	−0.398024	+	0.710406i
$886$	−15.9584	−	0.644710i	−0.536131	−	0.0216595i
$887$	−9.82563	−	9.82563i	−0.329912	−	0.329912i	0.522641	−	0.852553i	$-0.324947\pi$
$887$	−9.82563	−	9.82563i	−0.329912	−	0.329912i	−0.852553	+	0.522641i	$0.824947\pi$
$888$	−36.1040	−	46.1121i	−1.21157	−	1.54742i
$889$		−	1.13177i		−	0.0379583i
$890$	−0.394057	+	0.641174i	−0.0132088	+	0.0214922i
$891$		−	61.9922i		−	2.07682i
$892$	3.71828	+	4.37313i	0.124497	+	0.146423i
$893$	12.8822	+	12.8822i	0.431087	+	0.431087i
$894$	−2.74269	+	67.8892i	−0.0917293	+	2.27056i
$895$	−20.3856	+	5.74517i	−0.681417	+	0.192040i
$896$	1.73890	+	0.505008i	0.0580926	+	0.0168711i
$897$	51.0718	−	51.0718i	1.70524	−	1.70524i
$898$	16.0378	−	14.7923i	0.535189	−	0.493626i
$899$	−5.84204			−0.194843
$900$	17.9022	−	9.06318i	0.596740	−	0.302106i
$901$	39.8639			1.32806
$902$	−5.86208	+	5.40682i	−0.195186	+	0.180027i
$903$	−1.60740	+	1.60740i	−0.0534909	+	0.0534909i
$904$	6.08170	+	0.740317i	0.202274	+	0.0246226i
$905$	−44.9258	+	12.6612i	−1.49338	+	0.420872i
$906$	−1.99346	+	49.3438i	−0.0662284	+	1.63934i
$907$	11.9119	+	11.9119i	0.395529	+	0.395529i	0.876653	−	0.481124i	$-0.159771\pi$
$907$	11.9119	+	11.9119i	0.395529	+	0.395529i	−0.481124	+	0.876653i	$0.659771\pi$
$908$	15.0843	−	12.8255i	0.500590	−	0.425630i
$909$		−	23.5675i		−	0.781685i
$910$	1.60036	−	2.60395i	0.0530513	−	0.0863202i
$911$			12.9898i			0.430370i	0.976573	+	0.215185i	$0.0690354\pi$
$911$			12.9898i			0.430370i	−0.976573	+	0.215185i	$0.930965\pi$
$912$	31.6394	−	22.7739i	1.04768	−	0.754118i
$913$	42.6908	+	42.6908i	1.41286	+	1.41286i
$914$	−15.3068	−	0.618388i	−0.506305	−	0.0204545i
$915$	−25.1692	+	44.9227i	−0.832067	+	1.48510i
$916$	−35.9263	−	2.90756i	−1.18704	−	0.0960685i
$917$	1.19906	−	1.19906i	0.0395965	−	0.0395965i
$918$	10.8180	+	11.7289i	0.357047	+	0.387110i
$919$	18.4665			0.609153			0.304576	−	0.952488i	$-0.401485\pi$
$919$	18.4665			0.609153			0.304576	+	0.952488i	$0.401485\pi$
$920$	−5.17113	−	33.4084i	−0.170487	−	1.10144i
$921$	1.27996			0.0421761
$922$	39.1363	+	42.4316i	1.28889	+	1.39741i
$923$	17.2540	−	17.2540i	0.567922	−	0.567922i
$924$	4.02569	+	0.325804i	0.132436	+	0.0107182i
$925$	−10.8184	+	44.9866i	−0.355707	+	1.47915i
$926$	−43.3561	−	1.75156i	−1.42477	−	0.0575600i
$927$	−3.31014	−	3.31014i	−0.108719	−	0.108719i
$928$	−8.78130	+	5.79739i	−0.288260	+	0.190309i
$929$			2.35965i			0.0774178i	0.999251	+	0.0387089i	$0.0123245\pi$
$929$			2.35965i			0.0774178i	−0.999251	+	0.0387089i	$0.987676\pi$
$930$	−5.15972	−	21.6153i	−0.169194	−	0.708793i
$931$		−	30.3777i		−	0.995589i
$932$	29.8739	−	25.4005i	0.978553	−	0.832021i
$933$	28.2580	+	28.2580i	0.925126	+	0.925126i
$934$	−1.55802	+	38.5654i	−0.0509800	+	1.26190i
$935$	55.8352	+	31.2831i	1.82601	+	1.02307i
$936$	4.14149	−	34.0223i	0.135369	−	1.11205i
$937$	34.5039	−	34.5039i	1.12719	−	1.12719i	0.136562	−	0.990632i	$-0.456395\pi$
$937$	34.5039	−	34.5039i	1.12719	−	1.12719i	0.990632	−	0.136562i	$-0.0436053\pi$
$938$	−2.44198	+	2.25233i	−0.0797333	+	0.0735411i
$939$	−45.8838			−1.49736
$940$	10.4297	−	15.5281i	0.340178	−	0.506471i
$941$	23.7020			0.772664			0.386332	−	0.922360i	$-0.373742\pi$
$941$	23.7020			0.772664			0.386332	+	0.922360i	$0.373742\pi$
$942$	−6.24939	+	5.76405i	−0.203616	+	0.187803i
$943$	−3.77965	+	3.77965i	−0.123082	+	0.123082i
$944$	19.1151	+	3.11442i	0.622144	+	0.101366i
$945$	−0.215789	−	0.765687i	−0.00701962	−	0.0249078i
$946$	2.04342	−	50.5804i	0.0664374	−	1.64451i
$947$	−33.5807	−	33.5807i	−1.09123	−	1.09123i	−0.995398	−	0.0958294i	$-0.969450\pi$
$947$	−33.5807	−	33.5807i	−1.09123	−	1.09123i	−0.0958294	−	0.995398i	$-0.530550\pi$
$948$	−25.9665	−	30.5396i	−0.843354	−	0.991881i
$949$			26.0097i			0.844309i
$950$	−29.6300	−	8.40413i	−0.961325	−	0.272666i
$951$		−	32.7876i		−	1.06321i
$952$	−1.80916	+	1.41650i	−0.0586352	+	0.0459092i
$953$	−23.3981	−	23.3981i	−0.757938	−	0.757938i	0.218009	−	0.975947i	$-0.430044\pi$
$953$	−23.3981	−	23.3981i	−0.757938	−	0.757938i	−0.975947	+	0.218009i	$0.930044\pi$
$954$	−22.2686	−	0.899642i	−0.720974	−	0.0291270i
$955$	−7.21409	−	25.5979i	−0.233443	−	0.828327i
$956$	3.83206	−	47.3497i	0.123938	−	1.53140i
$957$	−16.5959	+	16.5959i	−0.536469	+	0.536469i
$958$	20.4708	+	22.1945i	0.661383	+	0.717072i
$959$	1.02062			0.0329575
$960$	−29.2058	−	27.3701i	−0.942612	−	0.883367i
$961$	21.1361			0.681809
$962$	53.5818	+	58.0935i	1.72755	+	1.87301i
$963$	−0.676196	+	0.676196i	−0.0217901	+	0.0217901i
$964$	−0.765176	+	9.45466i	−0.0246447	+	0.304514i
$965$	32.7290	+	18.3373i	1.05359	+	0.590299i
$966$	2.70489	+	0.109276i	0.0870285	+	0.00351591i
$967$	16.0179	+	16.0179i	0.515102	+	0.515102i	0.916085	−	0.400983i	$-0.131331\pi$
$967$	16.0179	+	16.0179i	0.515102	+	0.515102i	−0.400983	+	0.916085i	$0.631331\pi$
$968$	−46.3193	+	36.2663i	−1.48876	+	1.16564i
$969$			49.4674i			1.58912i
$970$	29.0222	−	6.92780i	0.931847	−	0.222438i
$971$			28.9072i			0.927677i	0.885920	+	0.463839i	$0.153528\pi$
$971$			28.9072i			0.927677i	−0.885920	+	0.463839i	$0.846472\pi$
$972$	−23.2282	−	27.3190i	−0.745044	−	0.876258i
$973$	−0.252618	−	0.252618i	−0.00809856	−	0.00809856i
$974$	0.345319	−	8.54761i	0.0110647	−	0.273883i
$975$	−57.6192	+	35.2790i	−1.84529	+	1.12983i
$976$	40.6317	+	6.62010i	1.30059	+	0.211904i
$977$	21.8231	−	21.8231i	0.698184	−	0.698184i	−0.265835	−	0.964019i	$-0.585647\pi$
$977$	21.8231	−	21.8231i	0.698184	−	0.698184i	0.964019	+	0.265835i	$0.0856475\pi$
$978$	−54.5399	+	50.3042i	−1.74399	+	1.60855i
$979$	1.34203			0.0428913
$980$	−30.6056	+	6.01135i	−0.977661	+	0.192025i
$981$	−10.6998			−0.341617
$982$	20.3929	−	18.8091i	0.650763	−	0.600224i
$983$	−3.02980	+	3.02980i	−0.0966355	+	0.0966355i	−0.753772	−	0.657136i	$-0.771768\pi$
$983$	−3.02980	+	3.02980i	−0.0966355	+	0.0966355i	0.657136	+	0.753772i	$0.271768\pi$
$984$	−0.764740	+	6.28233i	−0.0243790	+	0.200273i
$985$	−10.2437	+	18.2833i	−0.326392	+	0.582556i
$986$	0.538986	−	13.3414i	0.0171648	−	0.424877i
$987$	1.05917	+	1.05917i	0.0337137	+	0.0337137i
$988$	−40.0779	+	34.0765i	−1.27505	+	1.08412i
$989$		−	33.9299i		−	1.07891i
$990$	−30.4845	−	18.7354i	−0.968860	−	0.595449i
$991$			15.4786i			0.491695i	0.969308	+	0.245848i	$0.0790663\pi$
$991$			15.4786i			0.491695i	−0.969308	+	0.245848i	$0.920934\pi$
$992$	−14.8267	+	9.78853i	−0.470747	+	0.310786i
$993$	−3.94794	−	3.94794i	−0.125284	−	0.125284i
$994$	0.913815	+	0.0369177i	0.0289844	+	0.00117096i
$995$	29.1939	−	8.22754i	0.925508	−	0.260830i
$996$	47.7558	+	3.86493i	1.51320	+	0.122465i
$997$	−39.8960	+	39.8960i	−1.26352	+	1.26352i	−0.314141	+	0.949376i	$0.601717\pi$
$997$	−39.8960	+	39.8960i	−1.26352	+	1.26352i	−0.949376	+	0.314141i	$0.898283\pi$
$998$	−9.71636	−	10.5345i	−0.307566	−	0.333463i
$999$	20.5698			0.650801

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.k.c.83.12	✓	108
4.3	odd	2	inner	820.2.k.c.83.39	yes	108
5.2	odd	4	inner	820.2.k.c.247.39	yes	108
20.7	even	4	inner	820.2.k.c.247.12	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.12	✓	108	1.1	even	1	trivial
820.2.k.c.83.39	yes	108	4.3	odd	2	inner
820.2.k.c.247.12	yes	108	20.7	even	4	inner
820.2.k.c.247.39	yes	108	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.958818 - 1.03955i) q^{2} +(-1.58218 + 1.58218i) q^{3} +(-0.161335 + 1.99348i) q^{4} +(-2.15223 + 0.606551i) q^{5} +(3.16177 + 0.127734i) q^{6} +(-0.113172 - 0.113172i) q^{7} +(2.22702 - 1.74367i) q^{8} -2.00656i q^{9} +(2.69414 + 1.65578i) q^{10} -5.63904i q^{11} +(-2.89878 - 3.40930i) q^{12} +(4.27017 + 4.27017i) q^{13} +(-0.00913672 + 0.226159i) q^{14} +(2.44554 - 4.36488i) q^{15} +(-3.94794 - 0.643236i) q^{16} +(3.58910 - 3.58910i) q^{17} +(-2.08593 + 1.92393i) q^{18} +4.35561 q^{19} +(-0.861918 - 4.38829i) q^{20} +0.358115 q^{21} +(-5.86208 + 5.40682i) q^{22} +(-3.77965 + 3.77965i) q^{23} +(-0.764740 + 6.28233i) q^{24} +(4.26419 - 2.61087i) q^{25} +(0.344744 - 8.53338i) q^{26} +(-1.57179 - 1.57179i) q^{27} +(0.243864 - 0.207347i) q^{28} +1.86012i q^{29} +(-6.88234 + 1.64286i) q^{30} +3.14069i q^{31} +(3.11668 + 4.72084i) q^{32} +(8.92196 + 8.92196i) q^{33} +(-7.17235 - 0.289759i) q^{34} +(0.312216 + 0.174927i) q^{35} +(4.00005 + 0.323729i) q^{36} +(-6.54344 + 6.54344i) q^{37} +(-4.17624 - 4.52788i) q^{38} -13.5123 q^{39} +(-3.73543 + 5.10358i) q^{40} +1.00000 q^{41} +(-0.343368 - 0.372279i) q^{42} +(-4.48850 + 4.48850i) q^{43} +(11.2413 + 0.909774i) q^{44} +(1.21708 + 4.31859i) q^{45} +(7.55313 + 0.305143i) q^{46} +(2.95761 + 2.95761i) q^{47} +(7.26405 - 5.22863i) q^{48} -6.97438i q^{49} +(-6.80272 - 1.92949i) q^{50} +11.3572i q^{51} +(-9.20143 + 7.82358i) q^{52} +(5.55347 + 5.55347i) q^{53} +(-0.126896 + 3.14102i) q^{54} +(3.42036 + 12.1365i) q^{55} +(-0.449370 - 0.0547012i) q^{56} +(-6.89135 + 6.89135i) q^{57} +(1.93369 - 1.78351i) q^{58} -4.84179 q^{59} +(8.30676 + 5.57934i) q^{60} -10.2919 q^{61} +(3.26491 - 3.01135i) q^{62} +(-0.227086 + 0.227086i) q^{63} +(1.91922 - 7.76638i) q^{64} +(-11.7805 - 6.60032i) q^{65} +(0.720298 - 17.8294i) q^{66} +(10.3783 + 10.3783i) q^{67} +(6.57576 + 7.73385i) q^{68} -11.9601i q^{69} +(-0.117513 - 0.492288i) q^{70} -4.04058i q^{71} +(-3.49879 - 4.46866i) q^{72} +(3.04551 + 3.04551i) q^{73} +(13.0762 + 0.528273i) q^{74} +(-2.61584 + 10.8776i) q^{75} +(-0.702711 + 8.68283i) q^{76} +(-0.638180 + 0.638180i) q^{77} +(12.9559 + 14.0468i) q^{78} +8.95774 q^{79} +(8.88704 - 1.01023i) q^{80} +10.9934 q^{81} +(-0.958818 - 1.03955i) q^{82} +(-7.57058 + 7.57058i) q^{83} +(-0.0577765 + 0.713897i) q^{84} +(-5.54760 + 9.90154i) q^{85} +(8.96967 + 0.362370i) q^{86} +(-2.94303 - 2.94303i) q^{87} +(-9.83264 - 12.5583i) q^{88} +0.237988i q^{89} +(3.32243 - 5.40596i) q^{90} -0.966525i q^{91} +(-6.92487 - 8.14445i) q^{92} +(-4.96912 - 4.96912i) q^{93} +(0.238778 - 5.91041i) q^{94} +(-9.37428 + 2.64190i) q^{95} +(-12.4003 - 2.53805i) q^{96} +(6.67189 - 6.67189i) q^{97} +(-7.25023 + 6.68717i) q^{98} -11.3151 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) \) 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Introduction

L-functions

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