LMFDB - Embedded newform 510.2.bi.b.97.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [510,2,Mod(37,510)] 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("510.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(510, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 4, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.bi (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [80] 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:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			97.9
Character	$\chi$	$=$	510.97
Dual form			510.2.bi.b.163.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.382683 + 0.923880i) q^{2} +(0.195090 - 0.980785i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(1.38580 + 1.75487i) q^{5} +(0.831470 + 0.555570i) q^{6} +(1.76005 + 1.17603i) q^{7} +(0.923880 - 0.382683i) q^{8} +(-0.923880 - 0.382683i) q^{9} +(-2.15161 + 0.608751i) q^{10} +(-2.97442 + 4.45154i) q^{11} +(-0.831470 + 0.555570i) q^{12} -3.35117 q^{13} +(-1.76005 + 1.17603i) q^{14} +(1.99151 - 1.01681i) q^{15} +1.00000i q^{16} +(3.50857 + 2.16563i) q^{17} +(0.707107 - 0.707107i) q^{18} +(5.76589 - 2.38831i) q^{19} +(0.260973 - 2.22079i) q^{20} +(1.49680 - 1.49680i) q^{21} +(-2.97442 - 4.45154i) q^{22} +(0.766268 - 0.152420i) q^{23} +(-0.195090 - 0.980785i) q^{24} +(-1.15913 + 4.86379i) q^{25} +(1.28244 - 3.09608i) q^{26} +(-0.555570 + 0.831470i) q^{27} +(-0.412966 - 2.07612i) q^{28} +(2.32922 + 0.463311i) q^{29} +(0.177296 + 2.22903i) q^{30} +(0.946809 + 1.41700i) q^{31} +(-0.923880 - 0.382683i) q^{32} +(3.78572 + 3.78572i) q^{33} +(-3.34345 + 2.41274i) q^{34} +(0.375298 + 4.71839i) q^{35} +(0.382683 + 0.923880i) q^{36} +(-7.43946 - 1.47980i) q^{37} +6.24096i q^{38} +(-0.653782 + 3.28678i) q^{39} +(1.95187 + 1.09097i) q^{40} +(-2.56016 + 0.509247i) q^{41} +(0.810061 + 1.95566i) q^{42} +(2.28262 + 5.51072i) q^{43} +(5.25095 - 1.04448i) q^{44} +(-0.608751 - 2.15161i) q^{45} +(-0.152420 + 0.766268i) q^{46} +11.8907i q^{47} +(0.980785 + 0.195090i) q^{48} +(-0.964053 - 2.32743i) q^{49} +(-4.04997 - 2.93219i) q^{50} +(2.80851 - 3.01866i) q^{51} +(2.36964 + 2.36964i) q^{52} +(12.4297 + 5.14854i) q^{53} +(-0.555570 - 0.831470i) q^{54} +(-11.9338 + 0.949208i) q^{55} +(2.07612 + 0.412966i) q^{56} +(-1.21755 - 6.12104i) q^{57} +(-1.31940 + 1.97462i) q^{58} +(2.11444 - 5.10470i) q^{59} +(-2.12720 - 0.689212i) q^{60} +(-2.81641 - 14.1590i) q^{61} +(-1.67147 + 0.332475i) q^{62} +(-1.17603 - 1.76005i) q^{63} +(0.707107 - 0.707107i) q^{64} +(-4.64405 - 5.88087i) q^{65} +(-4.94628 + 2.04882i) q^{66} +(10.3713 - 10.3713i) q^{67} +(-0.949597 - 4.01226i) q^{68} -0.781280i q^{69} +(-4.50284 - 1.45892i) q^{70} +(8.18231 - 5.46724i) q^{71} -1.00000 q^{72} +(-13.1042 + 8.75594i) q^{73} +(4.21411 - 6.30687i) q^{74} +(4.54419 + 2.08574i) q^{75} +(-5.76589 - 2.38831i) q^{76} +(-10.4703 + 4.33692i) q^{77} +(-2.78640 - 1.86181i) q^{78} +(3.08664 + 2.06242i) q^{79} +(-1.75487 + 1.38580i) q^{80} +(0.707107 + 0.707107i) q^{81} +(0.509247 - 2.56016i) q^{82} +(1.13814 - 2.74772i) q^{83} -2.11679 q^{84} +(1.06176 + 9.15820i) q^{85} -5.96476 q^{86} +(0.908816 - 2.19408i) q^{87} +(-1.04448 + 5.25095i) q^{88} +(-2.36962 - 2.36962i) q^{89} +(2.22079 + 0.260973i) q^{90} +(-5.89823 - 3.94107i) q^{91} +(-0.649610 - 0.434056i) q^{92} +(1.57449 - 0.652174i) q^{93} +(-10.9856 - 4.55039i) q^{94} +(12.1815 + 6.80867i) q^{95} +(-0.555570 + 0.831470i) q^{96} +(-3.08350 + 2.06033i) q^{97} +2.51919 q^{98} +(4.45154 - 2.97442i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 48 q^{25} + 16 q^{28} + 32 q^{29} + 16 q^{30} + 16 q^{31} - 16 q^{33} - 32 q^{34} - 32 q^{35} + 48 q^{37} + 32 q^{41} + 32 q^{43} + 16 q^{44} - 64 q^{49} + 48 q^{50} - 32 q^{51} + 16 q^{52} - 32 q^{53}+ \cdots - 144 q^{98}+O(q^{100}) $ 80 * q + 48 * q^25 + 16 * q^28 + 32 * q^29 + 16 * q^30 + 16 * q^31 - 16 * q^33 - 32 * q^34 - 32 * q^35 + 48 * q^37 + 32 * q^41 + 32 * q^43 + 16 * q^44 - 64 * q^49 + 48 * q^50 - 32 * q^51 + 16 * q^52 - 32 * q^53 + 16 * q^55 - 16 * q^56 + 32 * q^57 + 32 * q^58 - 16 * q^60 + 48 * q^61 + 32 * q^62 - 32 * q^65 - 16 * q^67 - 16 * q^70 - 80 * q^72 - 80 * q^73 - 32 * q^74 - 48 * q^77 - 32 * q^78 - 64 * q^79 - 16 * q^80 - 32 * q^82 - 32 * q^83 - 32 * q^85 - 48 * q^87 - 16 * q^88 - 32 * q^89 - 32 * q^92 - 48 * q^93 - 16 * q^94 - 96 * q^95 + 80 * q^97 - 144 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.382683	+	0.923880i	−0.270598	+	0.653281i
$2$	−0.382683	+	0.923880i	−0.270598	+	0.653281i
$3$	0.195090	−	0.980785i	0.112635	−	0.566257i
$3$	0.195090	−	0.980785i	0.112635	−	0.566257i
$4$	−0.707107	−	0.707107i	−0.353553	−	0.353553i
$5$	1.38580	+	1.75487i	0.619747	+	0.784801i
$5$	1.38580	+	1.75487i	0.619747	+	0.784801i
$6$	0.831470	+	0.555570i	0.339446	+	0.226811i
$7$	1.76005	+	1.17603i	0.665236	+	0.444496i	0.841798	−	0.539793i	$-0.181498\pi$
$7$	1.76005	+	1.17603i	0.665236	+	0.444496i	−0.176562	+	0.984290i	$0.556498\pi$
$8$	0.923880	−	0.382683i	0.326641	−	0.135299i
$9$	−0.923880	−	0.382683i	−0.307960	−	0.127561i
$10$	−2.15161	+	0.608751i	−0.680399	+	0.192504i
$11$	−2.97442	+	4.45154i	−0.896822	+	1.34219i	0.0424799	+	0.999097i	$0.486474\pi$
$11$	−2.97442	+	4.45154i	−0.896822	+	1.34219i	−0.939302	+	0.343092i	$0.888526\pi$
$12$	−0.831470	+	0.555570i	−0.240025	+	0.160379i
$13$	−3.35117			−0.929449			−0.464724	−	0.885455i	$-0.653847\pi$
$13$	−3.35117			−0.929449			−0.464724	+	0.885455i	$0.653847\pi$
$14$	−1.76005	+	1.17603i	−0.470393	+	0.314306i
$15$	1.99151	−	1.01681i	0.514204	−	0.262540i
$16$			1.00000i			0.250000i
$17$	3.50857	+	2.16563i	0.850952	+	0.525243i
$17$	3.50857	+	2.16563i	0.850952	+	0.525243i
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	5.76589	−	2.38831i	1.32279	−	0.547916i	0.394198	−	0.919026i	$-0.371023\pi$
$19$	5.76589	−	2.38831i	1.32279	−	0.547916i	0.928589	+	0.371110i	$0.121023\pi$
$20$	0.260973	−	2.22079i	0.0583553	−	0.496583i
$21$	1.49680	−	1.49680i	0.326628	−	0.326628i
$22$	−2.97442	−	4.45154i	−0.634149	−	0.949071i
$23$	0.766268	−	0.152420i	0.159778	−	0.0317818i	−0.114553	−	0.993417i	$-0.536544\pi$
$23$	0.766268	−	0.152420i	0.159778	−	0.0317818i	0.274331	+	0.961635i	$0.411544\pi$
$24$	−0.195090	−	0.980785i	−0.0398226	−	0.200202i
$25$	−1.15913	+	4.86379i	−0.231826	+	0.972757i
$26$	1.28244	−	3.09608i	0.251507	−	0.607192i
$27$	−0.555570	+	0.831470i	−0.106920	+	0.160016i
$28$	−0.412966	−	2.07612i	−0.0780432	−	0.392349i
$29$	2.32922	+	0.463311i	0.432525	+	0.0860346i	0.406551	−	0.913628i	$-0.366731\pi$
$29$	2.32922	+	0.463311i	0.432525	+	0.0860346i	0.0259740	+	0.999663i	$0.491731\pi$
$30$	0.177296	+	2.22903i	0.0323696	+	0.406963i
$31$	0.946809	+	1.41700i	0.170052	+	0.254501i	0.906701	−	0.421775i	$-0.138593\pi$
$31$	0.946809	+	1.41700i	0.170052	+	0.254501i	−0.736649	+	0.676276i	$0.763593\pi$
$32$	−0.923880	−	0.382683i	−0.163320	−	0.0676495i
$33$	3.78572	+	3.78572i	0.659009	+	0.659009i
$34$	−3.34345	+	2.41274i	−0.573398	+	0.413782i
$35$	0.375298	+	4.71839i	0.0634369	+	0.797553i
$36$	0.382683	+	0.923880i	0.0637806	+	0.153980i
$37$	−7.43946	−	1.47980i	−1.22304	−	0.243278i	−0.458993	−	0.888440i	$-0.651790\pi$
$37$	−7.43946	−	1.47980i	−1.22304	−	0.243278i	−0.764046	+	0.645162i	$0.776790\pi$
$38$			6.24096i			1.01242i
$39$	−0.653782	+	3.28678i	−0.104689	+	0.526306i
$40$	1.95187	+	1.09097i	0.308618	+	0.172497i
$41$	−2.56016	+	0.509247i	−0.399830	+	0.0795311i	−0.390909	−	0.920429i	$-0.627839\pi$
$41$	−2.56016	+	0.509247i	−0.399830	+	0.0795311i	−0.00892028	+	0.999960i	$0.502839\pi$
$42$	0.810061	+	1.95566i	0.124995	+	0.301765i
$43$	2.28262	+	5.51072i	0.348096	+	0.840377i	0.996845	+	0.0793751i	$0.0252925\pi$
$43$	2.28262	+	5.51072i	0.348096	+	0.840377i	−0.648749	+	0.761002i	$0.724708\pi$
$44$	5.25095	−	1.04448i	0.791610	−	0.157461i
$45$	−0.608751	−	2.15161i	−0.0907472	−	0.320743i
$46$	−0.152420	+	0.766268i	−0.0224731	+	0.112980i
$47$			11.8907i			1.73444i	0.497923	+	0.867221i	$0.334096\pi$
$47$			11.8907i			1.73444i	−0.497923	+	0.867221i	$0.665904\pi$
$48$	0.980785	+	0.195090i	0.141564	+	0.0281589i
$49$	−0.964053	−	2.32743i	−0.137722	−	0.332490i
$50$	−4.04997	−	2.93219i	−0.572753	−	0.414674i
$51$	2.80851	−	3.01866i	0.393270	−	0.422696i
$52$	2.36964	+	2.36964i	0.328610	+	0.328610i
$53$	12.4297	+	5.14854i	1.70735	+	0.707207i	1.00000		0.000340662i	$0.000108436\pi$
$53$	12.4297	+	5.14854i	1.70735	+	0.707207i	0.707348	+	0.706866i	$0.249892\pi$
$54$	−0.555570	−	0.831470i	−0.0756035	−	0.113149i
$55$	−11.9338	+	0.949208i	−1.60915	+	0.127991i
$56$	2.07612	+	0.412966i	0.277433	+	0.0551848i
$57$	−1.21755	−	6.12104i	−0.161269	−	0.810752i
$58$	−1.31940	+	1.97462i	−0.173245	+	0.259280i
$59$	2.11444	−	5.10470i	0.275276	−	0.664576i	−0.724416	−	0.689363i	$-0.757891\pi$
$59$	2.11444	−	5.10470i	0.275276	−	0.664576i	0.999693	+	0.0247868i	$0.00789068\pi$
$60$	−2.12720	−	0.689212i	−0.274621	−	0.0889769i
$61$	−2.81641	−	14.1590i	−0.360604	−	1.81288i	−0.554878	−	0.831932i	$-0.687235\pi$
$61$	−2.81641	−	14.1590i	−0.360604	−	1.81288i	0.194274	−	0.980947i	$-0.437765\pi$
$62$	−1.67147	+	0.332475i	−0.212276	+	0.0422244i
$63$	−1.17603	−	1.76005i	−0.148165	−	0.221745i
$64$	0.707107	−	0.707107i	0.0883883	−	0.0883883i
$65$	−4.64405	−	5.88087i	−0.576023	−	0.729432i
$66$	−4.94628	+	2.04882i	−0.608845	+	0.252192i
$67$	10.3713	−	10.3713i	1.26705	−	1.26705i	0.319447	−	0.947604i	$-0.396503\pi$
$67$	10.3713	−	10.3713i	1.26705	−	1.26705i	0.947604	−	0.319447i	$-0.103497\pi$
$68$	−0.949597	−	4.01226i	−0.115156	−	0.486559i
$69$		−	0.781280i		−	0.0940550i
$70$	−4.50284	−	1.45892i	−0.538193	−	0.174374i
$71$	8.18231	−	5.46724i	0.971061	−	0.648842i	0.0345217	−	0.999404i	$-0.489009\pi$
$71$	8.18231	−	5.46724i	0.971061	−	0.648842i	0.936540	+	0.350561i	$0.114009\pi$
$72$	−1.00000			−0.117851
$73$	−13.1042	+	8.75594i	−1.53373	+	1.02481i	−0.552151	+	0.833744i	$0.686193\pi$
$73$	−13.1042	+	8.75594i	−1.53373	+	1.02481i	−0.981578	+	0.191061i	$0.938807\pi$
$74$	4.21411	−	6.30687i	0.489881	−	0.733158i
$75$	4.54419	+	2.08574i	0.524718	+	0.240840i
$76$	−5.76589	−	2.38831i	−0.661393	−	0.273958i
$77$	−10.4703	+	4.33692i	−1.19320	+	0.494238i
$78$	−2.78640	−	1.86181i	−0.315498	−	0.210809i
$79$	3.08664	+	2.06242i	0.347274	+	0.232041i	0.716958	−	0.697117i	$-0.245534\pi$
$79$	3.08664	+	2.06242i	0.347274	+	0.232041i	−0.369684	+	0.929158i	$0.620534\pi$
$80$	−1.75487	+	1.38580i	−0.196200	+	0.154937i
$81$	0.707107	+	0.707107i	0.0785674	+	0.0785674i
$82$	0.509247	−	2.56016i	0.0562370	−	0.282722i
$83$	1.13814	−	2.74772i	0.124928	−	0.301602i	−0.849025	−	0.528352i	$-0.822810\pi$
$83$	1.13814	−	2.74772i	0.124928	−	0.301602i	0.973953	+	0.226750i	$0.0728101\pi$
$84$	−2.11679			−0.230961
$85$	1.06176	+	9.15820i	0.115164	+	0.993346i
$86$	−5.96476			−0.643197
$87$	0.908816	−	2.19408i	0.0974353	−	0.235230i
$88$	−1.04448	+	5.25095i	−0.111342	+	0.559753i
$89$	−2.36962	−	2.36962i	−0.251180	−	0.251180i	0.570275	−	0.821454i	$-0.306837\pi$
$89$	−2.36962	−	2.36962i	−0.251180	−	0.251180i	−0.821454	+	0.570275i	$0.806837\pi$
$90$	2.22079	+	0.260973i	0.234091	+	0.0275090i
$91$	−5.89823	−	3.94107i	−0.618302	−	0.413136i
$92$	−0.649610	−	0.434056i	−0.0677266	−	0.0452534i
$93$	1.57449	−	0.652174i	0.163267	−	0.0676272i
$94$	−10.9856	−	4.55039i	−1.13308	−	0.469337i
$95$	12.1815	+	6.80867i	1.24980	+	0.698555i
$96$	−0.555570	+	0.831470i	−0.0567026	+	0.0848615i
$97$	−3.08350	+	2.06033i	−0.313082	+	0.209195i	−0.702176	−	0.712003i	$-0.747788\pi$
$97$	−3.08350	+	2.06033i	−0.313082	+	0.209195i	0.389094	+	0.921198i	$0.372788\pi$
$98$	2.51919			0.254477
$99$	4.45154	−	2.97442i	0.447396	−	0.298941i
$100$	4.25885	−	2.61959i	0.425885	−	0.261959i
$101$		−	15.7203i		−	1.56423i	−0.623136	−	0.782114i	$-0.714142\pi$
$101$		−	15.7203i		−	1.56423i	0.623136	−	0.782114i	$-0.285858\pi$
$102$	1.71410	+	3.74991i	0.169722	+	0.371297i
$103$	1.27906	−	1.27906i	0.126029	−	0.126029i	−0.641279	−	0.767308i	$-0.721596\pi$
$103$	1.27906	−	1.27906i	0.126029	−	0.126029i	0.767308	+	0.641279i	$0.221596\pi$
$104$	−3.09608	+	1.28244i	−0.303596	+	0.125753i
$105$	4.70094	+	0.552425i	0.458765	+	0.0539112i
$106$	−9.51326	+	9.51326i	−0.924010	+	0.924010i
$107$	−3.12141	−	4.67152i	−0.301758	−	0.451613i	0.649342	−	0.760497i	$-0.275045\pi$
$107$	−3.12141	−	4.67152i	−0.301758	−	0.451613i	−0.951100	+	0.308884i	$0.900045\pi$
$108$	0.980785	−	0.195090i	0.0943761	−	0.0187726i
$109$	−1.86101	−	9.35595i	−0.178253	−	0.896137i	−0.961579	−	0.274527i	$-0.911479\pi$
$109$	−1.86101	−	9.35595i	−0.178253	−	0.896137i	0.783327	−	0.621610i	$-0.213521\pi$
$110$	3.68992	−	11.3887i	0.351820	−	1.08587i
$111$	−2.90273	+	7.00782i	−0.275515	+	0.665152i
$112$	−1.17603	+	1.76005i	−0.111124	+	0.166309i
$113$	−2.17030	−	10.9108i	−0.204165	−	1.02641i	−0.937883	−	0.346952i	$-0.887217\pi$
$113$	−2.17030	−	10.9108i	−0.204165	−	1.02641i	0.733718	−	0.679454i	$-0.237783\pi$
$114$	6.12104	+	1.21755i	0.573288	+	0.114034i
$115$	1.32937	+	1.13348i	0.123964	+	0.105697i
$116$	−1.31940	−	1.97462i	−0.122503	−	0.183339i
$117$	3.09608	+	1.28244i	0.286233	+	0.118562i
$118$	3.90697	+	3.90697i	0.359666	+	0.359666i
$119$	3.62840	+	7.93778i	0.332615	+	0.727656i
$120$	1.45079	−	1.70153i	0.132439	−	0.155328i
$121$	−6.75948	−	16.3188i	−0.614498	−	1.48353i
$122$	14.1590	+	2.81641i	1.28190	+	0.254986i
$123$			2.61032i			0.235364i
$124$	0.332475	−	1.67147i	0.0298572	−	0.150102i
$125$	−10.1416	+	4.70610i	−0.907095	+	0.420926i
$126$	2.07612	−	0.412966i	0.184955	−	0.0367899i
$127$	−3.62211	−	8.74456i	−0.321411	−	0.775954i	−0.999173	−	0.0406725i	$-0.987050\pi$
$127$	−3.62211	−	8.74456i	−0.321411	−	0.775954i	0.677762	−	0.735281i	$-0.262950\pi$
$128$	0.382683	+	0.923880i	0.0338248	+	0.0816602i
$129$	5.85015	−	1.16367i	0.515077	−	0.102455i
$130$	7.21042	−	2.04003i	0.632396	−	0.178922i
$131$	−0.783020	+	3.93651i	−0.0684128	+	0.343934i	−0.999798	−	0.0201010i	$-0.993601\pi$
$131$	−0.783020	+	3.93651i	−0.0684128	+	0.343934i	0.931385	+	0.364035i	$0.118601\pi$
$132$		−	5.35382i		−	0.465990i
$133$	12.9570	+	2.57730i	1.12351	+	0.223480i
$134$	5.61289	+	13.5507i	0.484880	+	1.17060i
$135$	−2.22903	+	0.177296i	−0.191844	+	0.0152592i
$136$	4.07024	+	0.658114i	0.349021	+	0.0564328i
$137$	−8.59271	−	8.59271i	−0.734125	−	0.734125i	0.237309	−	0.971434i	$-0.423735\pi$
$137$	−8.59271	−	8.59271i	−0.734125	−	0.734125i	−0.971434	+	0.237309i	$0.923735\pi$
$138$	0.721808	+	0.298983i	0.0614444	+	0.0254511i
$139$	−0.0654831	−	0.0980024i	−0.00555420	−	0.00831246i	0.828682	−	0.559720i	$-0.189091\pi$
$139$	−0.0654831	−	0.0980024i	−0.00555420	−	0.00831246i	−0.834236	+	0.551407i	$0.814091\pi$
$140$	3.07103	−	3.60178i	0.259549	−	0.304406i
$141$	11.6623	+	2.31977i	0.982139	+	0.195360i
$142$	1.91984	+	9.65169i	0.161109	+	0.809952i
$143$	9.96781	−	14.9179i	0.833550	−	1.24750i
$144$	0.382683	−	0.923880i	0.0318903	−	0.0769900i
$145$	2.41478	+	4.72953i	0.200536	+	0.392766i
$146$	−3.07468	−	15.4574i	−0.254462	−	1.27927i
$147$	−2.47079	+	0.491470i	−0.203787	+	0.0405358i
$148$	4.21411	+	6.30687i	0.346398	+	0.518421i
$149$	2.41133	−	2.41133i	0.197544	−	0.197544i	−0.601402	−	0.798946i	$-0.705391\pi$
$149$	2.41133	−	2.41133i	0.197544	−	0.197544i	0.798946	+	0.601402i	$0.205391\pi$
$150$	−3.66596	+	3.40011i	−0.299324	+	0.277618i
$151$	4.43641	−	1.83762i	0.361030	−	0.149544i	−0.194793	−	0.980844i	$-0.562403\pi$
$151$	4.43641	−	1.83762i	0.361030	−	0.149544i	0.555823	+	0.831301i	$0.312403\pi$
$152$	4.41302	−	4.41302i	0.357944	−	0.357944i
$153$	−2.41274	−	3.34345i	−0.195058	−	0.270302i
$154$		−	11.3329i		−	0.913233i
$155$	−1.17456	+	3.62520i	−0.0943432	+	0.291183i
$156$	2.78640	−	1.86181i	0.223091	−	0.149064i
$157$	12.8424			1.02494			0.512468	−	0.858707i	$-0.328731\pi$
$157$	12.8424			1.02494			0.512468	+	0.858707i	$0.328731\pi$
$158$	−3.08664	+	2.06242i	−0.245560	+	0.164078i
$159$	7.47452	−	11.1864i	0.592768	−	0.887140i
$160$	−0.608751	−	2.15161i	−0.0481260	−	0.170100i
$161$	1.52792	+	0.632884i	0.120417	+	0.0498783i
$162$	−0.923880	+	0.382683i	−0.0725868	+	0.0300665i
$163$	−4.95818	−	3.31295i	−0.388355	−	0.259490i	0.346031	−	0.938223i	$-0.387529\pi$
$163$	−4.95818	−	3.31295i	−0.388355	−	0.259490i	−0.734385	+	0.678733i	$0.762529\pi$
$164$	2.17040	+	1.45021i	0.169480	+	0.113243i
$165$	−1.39720	+	11.8897i	−0.108772	+	0.925611i
$166$	2.10302	+	2.10302i	0.163226	+	0.163226i
$167$	−3.75625	+	18.8839i	−0.290667	+	1.46128i	0.508962	+	0.860789i	$0.330029\pi$
$167$	−3.75625	+	18.8839i	−0.290667	+	1.46128i	−0.799629	+	0.600494i	$0.794971\pi$
$168$	0.810061	−	1.95566i	0.0624976	−	0.150882i
$169$	−1.76963			−0.136125
$170$	−8.86739	−	2.52375i	−0.680098	−	0.193563i
$171$	−6.24096			−0.477258
$172$	2.28262	−	5.51072i	0.174048	−	0.420189i
$173$	−1.76712	+	8.88393i	−0.134352	+	0.675432i	0.853632	+	0.520876i	$0.174395\pi$
$173$	−1.76712	+	8.88393i	−0.134352	+	0.675432i	−0.987984	+	0.154556i	$0.950605\pi$
$174$	1.67927	+	1.67927i	0.127305	+	0.127305i
$175$	−7.76007	+	7.19733i	−0.586606	+	0.544067i
$176$	−4.45154	−	2.97442i	−0.335547	−	0.224205i
$177$	−4.59411	−	3.06969i	−0.345315	−	0.230732i
$178$	3.09606	−	1.28243i	0.232060	−	0.0961222i
$179$	−8.38860	−	3.47467i	−0.626993	−	0.259709i	0.0464817	−	0.998919i	$-0.485199\pi$
$179$	−8.38860	−	3.47467i	−0.626993	−	0.259709i	−0.673475	+	0.739210i	$0.735199\pi$
$180$	−1.09097	+	1.95187i	−0.0813158	+	0.145484i
$181$	10.1041	−	15.1219i	0.751033	−	1.12400i	−0.237262	−	0.971446i	$-0.576250\pi$
$181$	10.1041	−	15.1219i	0.751033	−	1.12400i	0.988295	−	0.152555i	$-0.0487501\pi$
$182$	5.89823	−	3.94107i	0.437206	−	0.292132i
$183$	−14.4364			−1.06717
$184$	0.649610	−	0.434056i	0.0478899	−	0.0319990i
$185$	−7.71273	−	15.1060i	−0.567051	−	1.11061i
$186$			1.70421i			0.124959i
$187$	−20.0764	+	9.17701i	−1.46813	+	0.671089i
$188$	8.40802	−	8.40802i	0.613218	−	0.613218i
$189$	−1.95566	+	0.810061i	−0.142253	+	0.0589233i
$190$	−10.9521	+	8.64870i	−0.794546	+	0.627443i
$191$	−9.24033	+	9.24033i	−0.668607	+	0.668607i	−0.957393	−	0.288787i	$-0.906748\pi$
$191$	−9.24033	+	9.24033i	−0.668607	+	0.668607i	0.288787	+	0.957393i	$0.406748\pi$
$192$	−0.555570	−	0.831470i	−0.0400948	−	0.0600062i
$193$	9.91920	−	1.97305i	0.714000	−	0.142023i	0.175292	−	0.984516i	$-0.443913\pi$
$193$	9.91920	−	1.97305i	0.714000	−	0.142023i	0.538707	+	0.842493i	$0.318913\pi$
$194$	−0.723491	−	3.63724i	−0.0519436	−	0.261138i
$195$	−6.67388	+	3.40751i	−0.477927	+	0.244017i
$196$	−0.964053	+	2.32743i	−0.0688609	+	0.166245i
$197$	−7.37323	+	11.0348i	−0.525321	+	0.786198i	−0.995337	−	0.0964598i	$-0.969248\pi$
$197$	−7.37323	+	11.0348i	−0.525321	+	0.786198i	0.470016	+	0.882658i	$0.344248\pi$
$198$	1.04448	+	5.25095i	0.0742278	+	0.373168i
$199$	17.8180	+	3.54422i	1.26308	+	0.251243i	0.780805	−	0.624775i	$-0.214809\pi$
$199$	17.8180	+	3.54422i	1.26308	+	0.251243i	0.482279	+	0.876018i	$0.339809\pi$
$200$	0.790393	+	4.93713i	0.0558893	+	0.349108i
$201$	−8.14865	−	12.1953i	−0.574761	−	0.860191i
$202$	14.5237	+	6.01589i	1.02188	+	0.423277i
$203$	3.55467	+	3.55467i	0.249489	+	0.249489i
$204$	−4.12043	+	0.148597i	−0.288488	+	0.0104039i
$205$	−4.44153	−	3.78703i	−0.310210	−	0.264498i
$206$	0.692222	+	1.67117i	0.0482294	+	0.116436i
$207$	−0.766268	−	0.152420i	−0.0532593	−	0.0105939i
$208$		−	3.35117i		−	0.232362i
$209$	−6.51854	+	32.7709i	−0.450897	+	2.26681i
$210$	−2.30935	+	4.13170i	−0.159360	+	0.285114i
$211$	11.3680	−	2.26124i	0.782606	−	0.155670i	0.212412	−	0.977180i	$-0.431868\pi$
$211$	11.3680	−	2.26124i	0.782606	−	0.155670i	0.570194	+	0.821510i	$0.306868\pi$
$212$	−5.14854	−	12.4297i	−0.353603	−	0.853674i
$213$	−3.76590	−	9.09169i	−0.258035	−	0.622953i
$214$	5.51044	−	1.09609i	0.376686	−	0.0749274i
$215$	−6.50735	+	11.6424i	−0.443798	+	0.794008i
$216$	−0.195090	+	0.980785i	−0.0132742	+	0.0667340i
$217$			3.60746i			0.244890i
$218$	9.35595	+	1.86101i	0.633665	+	0.126044i
$219$	6.03119	+	14.5606i	0.407550	+	0.983914i
$220$	9.10967	+	7.76729i	0.614174	+	0.523670i
$221$	−11.7578	−	7.25741i	−0.790916	−	0.488186i
$222$	−5.36355	−	5.36355i	−0.359978	−	0.359978i
$223$	2.36655	+	0.980257i	0.158476	+	0.0656429i	0.460511	−	0.887654i	$-0.347666\pi$
$223$	2.36655	+	0.980257i	0.158476	+	0.0656429i	−0.302035	+	0.953297i	$0.597666\pi$
$224$	−1.17603	−	1.76005i	−0.0785766	−	0.117598i
$225$	2.93219	−	4.04997i	0.195479	−	0.269998i
$226$	10.9108	+	2.17030i	0.725779	+	0.144366i
$227$	3.24538	+	16.3156i	0.215404	+	1.08291i	0.925484	+	0.378786i	$0.123658\pi$
$227$	3.24538	+	16.3156i	0.215404	+	1.08291i	−0.710081	+	0.704120i	$0.751342\pi$
$228$	−3.46729	+	5.18917i	−0.229627	+	0.343661i
$229$	9.70634	−	23.4332i	0.641413	−	1.54851i	−0.183361	−	0.983046i	$-0.558698\pi$
$229$	9.70634	−	23.4332i	0.641413	−	1.54851i	0.824774	−	0.565463i	$-0.191302\pi$
$230$	−1.55592	+	0.794415i	−0.102595	+	0.0523821i
$231$	2.21094	+	11.1152i	0.145469	+	0.731324i
$232$	2.32922	−	0.463311i	0.152921	−	0.0304178i
$233$	−7.08276	−	10.6001i	−0.464007	−	0.694435i	0.523497	−	0.852027i	$-0.324627\pi$
$233$	−7.08276	−	10.6001i	−0.464007	−	0.694435i	−0.987504	+	0.157592i	$0.949627\pi$
$234$	−2.36964	+	2.36964i	−0.154908	+	0.154908i
$235$	−20.8667	+	16.4782i	−1.36119	+	1.07492i
$236$	−5.10470	+	2.11444i	−0.332288	+	0.137638i
$237$	2.62497	−	2.62497i	0.170510	−	0.170510i
$238$	−8.72209	+	0.314549i	−0.565369	+	0.0203892i
$239$		−	0.745232i		−	0.0482050i	−0.999709	−	0.0241025i	$-0.992327\pi$
$239$		−	0.745232i		−	0.0482050i	0.999709	−	0.0241025i	$-0.00767281\pi$
$240$	1.01681	+	1.99151i	0.0656349	+	0.128551i
$241$	1.90948	−	1.27587i	0.123000	−	0.0821861i	−0.492548	−	0.870285i	$-0.663935\pi$
$241$	1.90948	−	1.27587i	0.123000	−	0.0821861i	0.615549	+	0.788099i	$0.288935\pi$
$242$	17.6634			1.13544
$243$	0.831470	−	0.555570i	0.0533388	−	0.0356398i
$244$	−8.02045	+	12.0035i	−0.513457	+	0.768442i
$245$	2.74835	−	4.91713i	0.175586	−	0.314144i
$246$	−2.41162	−	0.998925i	−0.153759	−	0.0636891i
$247$	−19.3225	+	8.00365i	−1.22946	+	0.509260i
$248$	1.41700	+	0.946809i	0.0899796	+	0.0601224i
$249$	−2.47289	−	1.65233i	−0.156713	−	0.104712i
$250$	−0.466837	−	11.1706i	−0.0295254	−	0.706490i
$251$	−7.00423	−	7.00423i	−0.442103	−	0.442103i	0.450615	−	0.892718i	$-0.351205\pi$
$251$	−7.00423	−	7.00423i	−0.442103	−	0.442103i	−0.892718	+	0.450615i	$0.851205\pi$
$252$	−0.412966	+	2.07612i	−0.0260144	+	0.130783i
$253$	−1.60070	+	3.86443i	−0.100635	+	0.242955i
$254$	9.46504			0.593889
$255$	9.18937	+	0.745318i	0.575461	+	0.0466736i
$256$	−1.00000			−0.0625000
$257$	−3.13438	+	7.56705i	−0.195517	+	0.472020i	−0.990985	−	0.133976i	$-0.957225\pi$
$257$	−3.13438	+	7.56705i	−0.195517	+	0.472020i	0.795468	+	0.605996i	$0.207225\pi$
$258$	−1.16367	+	5.85015i	−0.0724468	+	0.364215i
$259$	−11.3535	−	11.3535i	−0.705473	−	0.705473i
$260$	−0.874566	+	7.44224i	−0.0542383	+	0.461548i
$261$	−1.97462	−	1.31940i	−0.122226	−	0.0816686i
$262$	−3.33721	−	2.22985i	−0.206174	−	0.137761i
$263$	18.1225	−	7.50661i	1.11748	−	0.462877i	0.253975	−	0.967211i	$-0.418262\pi$
$263$	18.1225	−	7.50661i	1.11748	−	0.462877i	0.863509	+	0.504334i	$0.168262\pi$
$264$	4.94628	+	2.04882i	0.304423	+	0.126096i
$265$	8.19000	+	28.9473i	0.503108	+	1.77822i
$266$	−7.33953	+	10.9844i	−0.450016	+	0.673496i
$267$	−2.78638	+	1.86180i	−0.170524	+	0.113940i
$268$	−14.6672			−0.895940
$269$	−15.7742	+	10.5400i	−0.961767	+	0.642632i	−0.934110	−	0.356985i	$-0.883805\pi$
$269$	−15.7742	+	10.5400i	−0.961767	+	0.642632i	−0.0276573	+	0.999617i	$0.508805\pi$
$270$	0.689212	−	2.12720i	0.0419441	−	0.129457i
$271$			17.5410i			1.06554i	0.846260	+	0.532770i	$0.178849\pi$
$271$			17.5410i			1.06554i	−0.846260	+	0.532770i	$0.821151\pi$
$272$	−2.16563	+	3.50857i	−0.131311	+	0.212738i
$273$	−5.01603	+	5.01603i	−0.303584	+	0.303584i
$274$	11.2269	−	4.65034i	0.678243	−	0.280937i
$275$	−18.2036	−	19.6269i	−1.09772	−	1.18354i
$276$	−0.552448	+	0.552448i	−0.0332535	+	0.0332535i
$277$	8.46760	+	12.6727i	0.508769	+	0.761426i	0.993573	−	0.113197i	$-0.0361090\pi$
$277$	8.46760	+	12.6727i	0.508769	+	0.761426i	−0.484804	+	0.874623i	$0.661109\pi$
$278$	0.115602	−	0.0229946i	0.00693333	−	0.00137913i
$279$	−0.332475	−	1.67147i	−0.0199048	−	0.100068i
$280$	2.15238	+	4.21560i	0.128629	+	0.251930i
$281$	1.01047	−	2.43950i	0.0602799	−	0.145528i	−0.890870	−	0.454259i	$-0.849904\pi$
$281$	1.01047	−	2.43950i	0.0602799	−	0.145528i	0.951150	+	0.308730i	$0.0999041\pi$
$282$	−6.60614	+	9.88678i	−0.393390	+	0.588749i
$283$	−2.32406	−	11.6838i	−0.138151	−	0.694532i	−0.986325	−	0.164814i	$-0.947298\pi$
$283$	−2.32406	−	11.6838i	−0.138151	−	0.694532i	0.848174	−	0.529718i	$-0.177702\pi$
$284$	−9.65169	−	1.91984i	−0.572723	−	0.113922i
$285$	9.05434	−	10.6192i	0.536333	−	0.629025i
$286$	9.96781	+	14.9179i	0.589409	+	0.882113i
$287$	−5.10489	−	2.11452i	−0.301332	−	0.124816i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$	7.62007	+	15.1965i	0.448239	+	0.893914i
$290$	−5.29361	+	0.421051i	−0.310852	+	0.0247249i
$291$	1.41918	+	3.42620i	0.0831938	+	0.200847i
$292$	15.4574	+	3.07468i	0.904578	+	0.179932i
$293$		−	3.30725i		−	0.193211i	−0.995323	−	0.0966057i	$-0.969201\pi$
$293$		−	3.30725i		−	0.193211i	0.995323	−	0.0966057i	$-0.0307986\pi$
$294$	0.491470	−	2.47079i	0.0286631	−	0.144099i
$295$	11.8883	−	3.36353i	0.692162	−	0.195832i
$296$	−7.43946	+	1.47980i	−0.432410	+	0.0860116i
$297$	−2.04882	−	4.94628i	−0.118884	−	0.287012i
$298$	1.30500	+	3.15055i	0.0755968	+	0.182507i
$299$	−2.56790	+	0.510786i	−0.148505	+	0.0295395i
$300$	−1.73839	−	4.68807i	−0.100366	−	0.270666i
$301$	−2.46324	+	12.3836i	−0.141979	+	0.713776i
$302$			4.80194i			0.276320i
$303$	−15.4182	−	3.06688i	−0.885754	−	0.176187i
$304$	2.38831	+	5.76589i	0.136979	+	0.330697i
$305$	20.9443	−	24.5640i	1.19927	−	1.40653i
$306$	4.01226	−	0.949597i	0.229366	−	0.0542848i
$307$	10.4048	+	10.4048i	0.593833	+	0.593833i	0.938665	−	0.344831i	$-0.112064\pi$
$307$	10.4048	+	10.4048i	0.593833	+	0.593833i	−0.344831	+	0.938665i	$0.612064\pi$
$308$	10.4703	+	4.33692i	0.596598	+	0.247119i
$309$	−1.00495	−	1.50401i	−0.0571696	−	0.0855604i
$310$	−2.89976	−	2.47246i	−0.164695	−	0.140426i
$311$	−7.01351	−	1.39507i	−0.397700	−	0.0791074i	−0.00781127	−	0.999969i	$-0.502486\pi$
$311$	−7.01351	−	1.39507i	−0.397700	−	0.0791074i	−0.389888	+	0.920862i	$0.627486\pi$
$312$	0.653782	+	3.28678i	0.0370131	+	0.186077i
$313$	4.81308	−	7.20328i	0.272051	−	0.407153i	−0.670137	−	0.742237i	$-0.733765\pi$
$313$	4.81308	−	7.20328i	0.272051	−	0.407153i	0.942188	+	0.335084i	$0.108765\pi$
$314$	−4.91457	+	11.8648i	−0.277345	+	0.669571i
$315$	1.45892	−	4.50284i	0.0822008	−	0.253706i
$316$	−0.724227	−	3.64094i	−0.0407410	−	0.204819i
$317$	5.96353	−	1.18622i	0.334945	−	0.0666247i	−0.0247527	−	0.999694i	$-0.507880\pi$
$317$	5.96353	−	1.18622i	0.334945	−	0.0666247i	0.359698	+	0.933069i	$0.382880\pi$
$318$	7.47452	+	11.1864i	0.419150	+	0.627303i
$319$	−8.99053	+	8.99053i	−0.503373	+	0.503373i
$320$	2.22079	+	0.260973i	0.124146	+	0.0145888i
$321$	−5.19072	+	2.15007i	−0.289718	+	0.120005i
$322$	−1.16942	+	1.16942i	−0.0651691	+	0.0651691i
$323$	25.4022	+	4.10726i	1.41342	+	0.228534i
$324$		−	1.00000i		−	0.0555556i
$325$	3.88445	−	16.2994i	0.215470	−	0.904128i
$326$	4.95818	−	3.31295i	0.274608	−	0.183487i
$327$	−9.53924			−0.527521
$328$	−2.17040	+	1.45021i	−0.119840	+	0.0800747i
$329$	−13.9838	+	20.9283i	−0.770953	+	1.15381i
$330$	−10.4500	−	5.84083i	−0.575251	−	0.321527i
$331$	12.6117	+	5.22392i	0.693199	+	0.287133i	0.701332	−	0.712834i	$-0.252589\pi$
$331$	12.6117	+	5.22392i	0.693199	+	0.287133i	−0.00813306	+	0.999967i	$0.502589\pi$
$332$	−2.74772	+	1.13814i	−0.150801	+	0.0624638i
$333$	6.30687	+	4.21411i	0.345614	+	0.230932i
$334$	−16.0090	−	10.6969i	−0.875975	−	0.585308i
$335$	32.5727	+	3.82774i	1.77964	+	0.209132i
$336$	1.49680	+	1.49680i	0.0816570	+	0.0816570i
$337$	−4.01296	+	20.1745i	−0.218600	+	1.09898i	0.703106	+	0.711085i	$0.251796\pi$
$337$	−4.01296	+	20.1745i	−0.218600	+	1.09898i	−0.921706	+	0.387890i	$0.873204\pi$
$338$	0.677208	−	1.63492i	0.0368352	−	0.0889282i
$339$	−11.1246			−0.604206
$340$	5.72505	−	7.22660i	0.310484	−	0.391918i
$341$	−9.12404			−0.494094
$342$	2.38831	−	5.76589i	0.129145	−	0.311784i
$343$	3.93110	−	19.7630i	0.212259	−	1.06710i
$344$	4.21773	+	4.21773i	0.227405	+	0.227405i
$345$	1.37104	−	1.08270i	0.0738145	−	0.0582904i
$346$	−7.53143	−	5.03234i	−0.404892	−	0.270540i
$347$	−6.34624	−	4.24043i	−0.340684	−	0.227638i	0.373444	−	0.927653i	$-0.378177\pi$
$347$	−6.34624	−	4.24043i	−0.340684	−	0.227638i	−0.714128	+	0.700015i	$0.753177\pi$
$348$	−2.19408	+	0.908816i	−0.117615	+	0.0487177i
$349$	−2.02827	−	0.840138i	−0.108571	−	0.0449715i	0.327737	−	0.944769i	$-0.393714\pi$
$349$	−2.02827	−	0.840138i	−0.108571	−	0.0449715i	−0.436308	+	0.899798i	$0.643714\pi$
$350$	−3.67982	−	9.92367i	−0.196694	−	0.530442i
$351$	1.86181	−	2.78640i	0.0993762	−	0.148727i
$352$	4.45154	−	2.97442i	0.237268	−	0.158537i
$353$	14.5444			0.774121			0.387060	−	0.922054i	$-0.373491\pi$
$353$	14.5444			0.774121			0.387060	+	0.922054i	$0.373491\pi$
$354$	4.59411	−	3.06969i	0.244174	−	0.163152i
$355$	20.9333	+	6.78239i	1.11103	+	0.359972i
$356$			3.35115i			0.177611i
$357$	8.49313	−	2.01010i	0.449504	−	0.106386i
$358$	6.42036	−	6.42036i	0.339326	−	0.339326i
$359$	23.9664	−	9.92720i	1.26490	−	0.523938i	0.353488	−	0.935439i	$-0.384995\pi$
$359$	23.9664	−	9.92720i	1.26490	−	0.523938i	0.911409	+	0.411501i	$0.134995\pi$
$360$	−1.38580	−	1.75487i	−0.0730379	−	0.0924897i
$361$	14.1065	−	14.1065i	0.742446	−	0.742446i
$362$	10.1041	+	15.1219i	0.531061	+	0.794788i
$363$	−17.3240	+	3.44595i	−0.909273	+	0.180866i
$364$	1.38392	+	6.95743i	0.0725371	+	0.364669i
$365$	−33.5253	−	10.8622i	−1.75479	−	0.568552i
$366$	5.52458	−	13.3375i	0.288775	−	0.697164i
$367$	3.85880	−	5.77511i	0.201428	−	0.301458i	−0.716979	−	0.697094i	$-0.754476\pi$
$367$	3.85880	−	5.77511i	0.201428	−	0.301458i	0.918407	+	0.395636i	$0.129476\pi$
$368$	0.152420	+	0.766268i	0.00794545	+	0.0399445i
$369$	2.56016	+	0.509247i	0.133277	+	0.0265104i
$370$	16.9076	−	1.34482i	0.878986	−	0.0699140i
$371$	15.8220	+	23.6793i	0.821438	+	1.22937i
$372$	−1.57449	−	0.652174i	−0.0816333	−	0.0338136i
$373$	−4.56654	−	4.56654i	−0.236447	−	0.236447i	0.578930	−	0.815377i	$-0.303470\pi$
$373$	−4.56654	−	4.56654i	−0.236447	−	0.236447i	−0.815377	+	0.578930i	$0.803470\pi$
$374$	−0.795560	−	22.0600i	−0.0411374	−	1.14070i
$375$	2.63714	+	10.8649i	0.136181	+	0.561060i
$376$	4.55039	+	10.9856i	0.234668	+	0.566539i
$377$	−7.80562	−	1.55263i	−0.402010	−	0.0799647i
$378$		−	2.11679i		−	0.108876i
$379$	−5.34890	+	26.8907i	−0.274754	+	1.38128i	0.559009	+	0.829162i	$0.311182\pi$
$379$	−5.34890	+	26.8907i	−0.274754	+	1.38128i	−0.833763	+	0.552122i	$0.813818\pi$
$380$	−3.79919	−	13.4281i	−0.194894	−	0.688847i
$381$	−9.28317	+	1.84654i	−0.475591	+	0.0946010i
$382$	−5.00083	−	12.0731i	−0.255865	−	0.617712i
$383$	−9.17604	−	22.1529i	−0.468874	−	1.13196i	−0.964655	−	0.263514i	$-0.915118\pi$
$383$	−9.17604	−	22.1529i	−0.468874	−	1.13196i	0.495782	−	0.868447i	$-0.334882\pi$
$384$	0.980785	−	0.195090i	0.0500505	−	0.00995566i
$385$	−22.1204	−	12.3638i	−1.12736	−	0.630119i
$386$	−1.97305	+	9.91920i	−0.100426	+	0.504874i
$387$		−	5.96476i		−	0.303206i
$388$	3.63724	+	0.723491i	0.184653	+	0.0367297i
$389$	3.37888	+	8.15735i	0.171316	+	0.413594i	0.986096	−	0.166177i	$-0.0531422\pi$
$389$	3.37888	+	8.15735i	0.171316	+	0.413594i	−0.814780	+	0.579771i	$0.803142\pi$
$390$	−0.594148	−	7.46986i	−0.0300859	−	0.378251i
$391$	3.01859	+	1.12468i	0.152656	+	0.0568774i
$392$	−1.78134	−	1.78134i	−0.0899712	−	0.0899712i
$393$	3.70811	+	1.53595i	0.187049	+	0.0774784i
$394$	−7.37323	−	11.0348i	−0.371458	−	0.555926i
$395$	0.658168	+	8.27474i	0.0331160	+	0.416348i
$396$	−5.25095	−	1.04448i	−0.263870	−	0.0524870i
$397$	−6.46022	−	32.4777i	−0.324229	−	1.63001i	−0.707740	−	0.706473i	$-0.750285\pi$
$397$	−6.46022	−	32.4777i	−0.324229	−	1.63001i	0.383511	−	0.923536i	$-0.374715\pi$
$398$	−10.0931	+	15.1054i	−0.505920	+	0.757163i
$399$	5.05556	−	12.2052i	0.253094	−	0.611024i
$400$	−4.86379	−	1.15913i	−0.243189	−	0.0579565i
$401$	−0.116570	−	0.586039i	−0.00582124	−	0.0292654i	0.977765	−	0.209701i	$-0.0672492\pi$
$401$	−0.116570	−	0.586039i	−0.00582124	−	0.0292654i	−0.983587	+	0.180436i	$0.942249\pi$
$402$	14.3854	−	2.86142i	0.717476	−	0.142715i
$403$	−3.17292	−	4.74861i	−0.158055	−	0.236545i
$404$	−11.1159	+	11.1159i	−0.553038	+	0.553038i
$405$	−0.260973	+	2.22079i	−0.0129679	+	0.110352i
$406$	−4.64440	+	1.92377i	−0.230498	+	0.0954753i
$407$	28.7155	−	28.7155i	1.42337	−	1.42337i
$408$	1.43953	−	3.86364i	0.0712675	−	0.191279i
$409$		−	22.7763i		−	1.12622i	−0.826383	−	0.563108i	$-0.809606\pi$
$409$		−	22.7763i		−	1.12622i	0.826383	−	0.563108i	$-0.190394\pi$
$410$	5.19846	−	2.65420i	0.256734	−	0.131082i
$411$	−10.1040	+	6.75125i	−0.498392	+	0.333015i
$412$	−1.80886			−0.0891162
$413$	9.72478	−	6.49789i	0.478525	−	0.319740i
$414$	0.434056	−	0.649610i	0.0213327	−	0.0319266i
$415$	6.39913	−	1.81049i	0.314121	−	0.0888737i
$416$	3.09608	+	1.28244i	0.151798	+	0.0628767i
$417$	−0.108894	+	0.0451056i	−0.00533258	+	0.00220883i
$418$	−27.7819	−	18.5632i	−1.35886	−	0.907958i
$419$	−22.0028	−	14.7018i	−1.07491	−	0.718229i	−0.113548	−	0.993533i	$-0.536222\pi$
$419$	−22.0028	−	14.7018i	−1.07491	−	0.718229i	−0.961357	+	0.275304i	$0.911222\pi$
$420$	−2.93344	−	3.71469i	−0.143137	−	0.181258i
$421$	21.0741	+	21.0741i	1.02709	+	1.02709i	0.999623	+	0.0274648i	$0.00874342\pi$
$421$	21.0741	+	21.0741i	1.02709	+	1.02709i	0.0274648	+	0.999623i	$0.491257\pi$
$422$	−2.26124	+	11.3680i	−0.110075	+	0.553386i
$423$	4.55039	−	10.9856i	0.221247	−	0.534138i
$424$	13.4538			0.653374
$425$	−14.6001	+	14.5547i	−0.708207	+	0.706005i
$426$	9.84078			0.476787
$427$	11.6944	−	28.2328i	0.565931	−	1.36628i
$428$	−1.09609	+	5.51044i	−0.0529817	+	0.266357i
$429$	−12.6866	−	12.6866i	−0.612515	−	0.612515i
$430$	−8.26596	−	10.4674i	−0.398620	−	0.504782i
$431$	14.4627	+	9.66368i	0.696645	+	0.465483i	0.852792	−	0.522251i	$-0.174907\pi$
$431$	14.4627	+	9.66368i	0.696645	+	0.465483i	−0.156147	+	0.987734i	$0.549907\pi$
$432$	−0.831470	−	0.555570i	−0.0400041	−	0.0267299i
$433$	−15.6756	+	6.49306i	−0.753323	+	0.312037i	−0.726097	−	0.687593i	$-0.758667\pi$
$433$	−15.6756	+	6.49306i	−0.753323	+	0.312037i	−0.0272263	+	0.999629i	$0.508667\pi$
$434$	−3.33286	−	1.38052i	−0.159982	−	0.0662669i
$435$	5.10975	−	1.44569i	0.244994	−	0.0693156i
$436$	−5.29972	+	7.93159i	−0.253811	+	0.379854i
$437$	4.05419	−	2.70892i	0.193938	−	0.129585i
$438$	−15.7603			−0.753055
$439$	9.94751	−	6.64671i	0.474769	−	0.317230i	−0.295062	−	0.955478i	$-0.595340\pi$
$439$	9.94751	−	6.64671i	0.474769	−	0.317230i	0.769831	+	0.638248i	$0.220340\pi$
$440$	−10.6622	+	5.44383i	−0.508298	+	0.259524i
$441$			2.51919i			0.119962i
$442$	11.2045	−	8.08551i	0.532944	−	0.384589i
$443$	−23.1203	+	23.1203i	−1.09848	+	1.09848i	−0.103892	+	0.994589i	$0.533130\pi$
$443$	−23.1203	+	23.1203i	−1.09848	+	1.09848i	−0.994589	+	0.103892i	$0.966870\pi$
$444$	7.00782	−	2.90273i	0.332576	−	0.137758i
$445$	0.874560	−	7.44219i	0.0414581	−	0.352794i
$446$	−1.81128	+	1.81128i	−0.0857665	+	0.0857665i
$447$	−1.89457	−	2.83542i	−0.0896101	−	0.134111i
$448$	2.07612	−	0.412966i	0.0980874	−	0.0195108i
$449$	6.63438	+	33.3533i	0.313096	+	1.57404i	0.741817	+	0.670602i	$0.233964\pi$
$449$	6.63438	+	33.3533i	0.313096	+	1.57404i	−0.428722	+	0.903437i	$0.641036\pi$
$450$	2.61959	+	4.25885i	0.123489	+	0.200764i
$451$	5.34806	−	12.9114i	0.251830	−	0.607972i
$452$	−6.18050	+	9.24977i	−0.290706	+	0.435073i
$453$	−0.936812	−	4.70967i	−0.0440153	−	0.221280i
$454$	−16.3156	−	3.24538i	−0.765731	−	0.152313i
$455$	−1.25769	−	15.8121i	−0.0589613	−	0.741285i
$456$	−3.46729	−	5.18917i	−0.162371	−	0.243005i
$457$	22.4060	+	9.28087i	1.04811	+	0.434141i	0.839216	−	0.543798i	$-0.183014\pi$
$457$	22.4060	+	9.28087i	1.04811	+	0.434141i	0.208893	+	0.977939i	$0.433014\pi$
$458$	17.9350	+	17.9350i	0.838047	+	0.838047i
$459$	−3.74991	+	1.71410i	−0.175031	+	0.0800076i
$460$	−0.138517	−	1.74149i	−0.00645841	−	0.0811976i
$461$	−4.06726	−	9.81925i	−0.189431	−	0.457328i	0.800419	−	0.599441i	$-0.204610\pi$
$461$	−4.06726	−	9.81925i	−0.189431	−	0.457328i	−0.989850	+	0.142113i	$0.954610\pi$
$462$	−11.1152	−	2.21094i	−0.517124	−	0.102862i
$463$			23.8145i			1.10675i	0.832931	+	0.553376i	$0.186661\pi$
$463$			23.8145i			1.10675i	−0.832931	+	0.553376i	$0.813339\pi$
$464$	−0.463311	+	2.32922i	−0.0215087	+	0.108131i
$465$	3.32640	+	1.85924i	0.154258	+	0.0862200i
$466$	12.5037	−	2.48713i	0.579221	−	0.115214i
$467$	−14.9342	−	36.0544i	−0.691073	−	1.66840i	−0.742608	−	0.669726i	$-0.766411\pi$
$467$	−14.9342	−	36.0544i	−0.691073	−	1.66840i	0.0515351	−	0.998671i	$-0.483589\pi$
$468$	−1.28244	−	3.09608i	−0.0592808	−	0.143116i
$469$	30.4508	−	6.05704i	1.40609	−	0.279688i
$470$	−7.23849	−	25.5842i	−0.333887	−	1.18011i
$471$	2.50543	−	12.5956i	0.115444	−	0.580376i
$472$		−	5.52529i		−	0.254322i
$473$	−31.3207	−	6.23007i	−1.44013	−	0.286459i
$474$	1.42062	+	3.42969i	0.0652513	+	0.157531i
$475$	4.93281	+	30.8124i	0.226333	+	1.41377i
$476$	3.04719	−	8.17853i	0.139668	−	0.374862i
$477$	−9.51326	−	9.51326i	−0.435582	−	0.435582i
$478$	0.688505	+	0.285188i	0.0314915	+	0.0130442i
$479$	19.6859	+	29.4621i	0.899474	+	1.34616i	0.937903	+	0.346897i	$0.112765\pi$
$479$	19.6859	+	29.4621i	0.899474	+	1.34616i	−0.0384294	+	0.999261i	$0.512235\pi$
$480$	−2.22903	+	0.177296i	−0.101741	+	0.00809240i
$481$	24.9309	+	4.95907i	1.13675	+	0.226114i
$482$	0.448027	+	2.25238i	0.0204071	+	0.102593i
$483$	0.918806	−	1.37509i	0.0418071	−	0.0625688i
$484$	−6.75948	+	16.3188i	−0.307249	+	0.741765i
$485$	−7.88871	−	2.55594i	−0.358208	−	0.116059i
$486$	0.195090	+	0.980785i	0.00884948	+	0.0444893i
$487$	−6.22717	+	1.23866i	−0.282180	+	0.0561291i	−0.334151	−	0.942520i	$-0.608450\pi$
$487$	−6.22717	+	1.23866i	−0.282180	+	0.0561291i	0.0519712	+	0.998649i	$0.483450\pi$
$488$	−8.02045	−	12.0035i	−0.363069	−	0.543371i
$489$	−4.21658	+	4.21658i	−0.190681	+	0.190681i
$490$	3.49109	+	4.42085i	0.157711	+	0.199714i
$491$	−26.8485	+	11.1210i	−1.21166	+	0.501884i	−0.894748	−	0.446572i	$-0.852645\pi$
$491$	−26.8485	+	11.1210i	−1.21166	+	0.501884i	−0.316908	+	0.948456i	$0.602645\pi$
$492$	1.84577	−	1.84577i	0.0832138	−	0.0832138i
$493$	7.16886	+	6.66979i	0.322869	+	0.300392i
$494$		−	20.9145i		−	0.940990i
$495$	11.3887	+	3.68992i	0.511882	+	0.165849i
$496$	−1.41700	+	0.946809i	−0.0636252	+	0.0425130i
$497$	20.8309			0.934393
$498$	2.47289	−	1.65233i	0.110813	−	0.0740427i
$499$	−1.57783	+	2.36139i	−0.0706333	+	0.105710i	−0.865105	−	0.501591i	$-0.832748\pi$
$499$	−1.57783	+	2.36139i	−0.0706333	+	0.105710i	0.794471	+	0.607302i	$0.207748\pi$
$500$	10.4989	+	3.84350i	0.469526	+	0.171886i
$501$	17.7883	+	7.36815i	0.794722	+	0.329185i
$502$	9.15147	−	3.79066i	0.408450	−	0.169186i
$503$	−2.55545	−	1.70750i	−0.113942	−	0.0761336i	0.497294	−	0.867582i	$-0.334327\pi$
$503$	−2.55545	−	1.70750i	−0.113942	−	0.0761336i	−0.611236	+	0.791449i	$0.709327\pi$
$504$	−1.76005	−	1.17603i	−0.0783988	−	0.0523844i
$505$	27.5871	−	21.7851i	1.22761	−	0.969426i
$506$	−2.95771	−	2.95771i	−0.131486	−	0.131486i
$507$	−0.345238	+	1.73563i	−0.0153325	+	0.0770819i
$508$	−3.62211	+	8.74456i	−0.160705	+	0.387977i
$509$	2.07510			0.0919771			0.0459886	−	0.998942i	$-0.485356\pi$
$509$	2.07510			0.0919771			0.0459886	+	0.998942i	$0.485356\pi$
$510$	−4.20520	+	8.20465i	−0.186210	+	0.363308i
$511$	−33.3612			−1.47581
$512$	0.382683	−	0.923880i	0.0169124	−	0.0408301i
$513$	−1.21755	+	6.12104i	−0.0537562	+	0.270251i
$514$	−5.79157	−	5.79157i	−0.255455	−	0.255455i
$515$	4.01710	+	0.472064i	0.177014	+	0.0208016i
$516$	−4.95952	−	3.31385i	−0.218331	−	0.145884i
$517$	−52.9320	−	35.3681i	−2.32795	−	1.55549i
$518$	14.8341	−	6.14448i	0.651772	−	0.269973i
$519$	8.36848	+	3.46634i	0.367335	+	0.152155i
$520$	−6.54105	−	3.65602i	−0.286844	−	0.160327i
$521$	−15.8418	+	23.7089i	−0.694040	+	1.03870i	0.302299	+	0.953213i	$0.402246\pi$
$521$	−15.8418	+	23.7089i	−0.694040	+	1.03870i	−0.996339	+	0.0854914i	$0.972754\pi$
$522$	1.97462	−	1.31940i	0.0864266	−	0.0577484i
$523$	27.3366			1.19534			0.597672	−	0.801741i	$-0.296092\pi$
$523$	27.3366			1.19534			0.597672	+	0.801741i	$0.296092\pi$
$524$	3.33721	−	2.22985i	0.145787	−	0.0974116i
$525$	5.54512	+	9.01509i	0.242009	+	0.393451i
$526$			19.6157i			0.855285i
$527$	0.253240	+	7.02208i	0.0110313	+	0.305887i
$528$	−3.78572	+	3.78572i	−0.164752	+	0.164752i
$529$	−20.6853	+	8.56813i	−0.899361	+	0.372527i
$530$	−29.8780	−	3.51107i	−1.29782	−	0.152511i
$531$	−3.90697	+	3.90697i	−0.169548	+	0.169548i
$532$	−7.33953	−	10.9844i	−0.318209	−	0.476234i
$533$	8.57954	−	1.70658i	0.371621	−	0.0739201i
$534$	−0.653777	−	3.28676i	−0.0282917	−	0.142232i
$535$	3.87227	−	11.9515i	0.167413	−	0.516706i
$536$	5.61289	−	13.5507i	0.242440	−	0.585301i
$537$	−5.04444	+	7.54954i	−0.217684	+	0.325787i
$538$	−3.70114	−	18.6069i	−0.159567	−	0.802200i
$539$	13.2281	+	2.63124i	0.569776	+	0.113336i
$540$	1.70153	+	1.45079i	0.0732221	+	0.0624322i
$541$	−4.03996	−	6.04622i	−0.173691	−	0.259947i	0.734402	−	0.678714i	$-0.237462\pi$
$541$	−4.03996	−	6.04622i	−0.173691	−	0.259947i	−0.908094	+	0.418767i	$0.862462\pi$
$542$	−16.2058	−	6.71265i	−0.696097	−	0.288333i
$543$	−12.8601	−	12.8601i	−0.551880	−	0.551880i
$544$	−2.41274	−	3.34345i	−0.103445	−	0.143349i
$545$	13.8395	−	16.2313i	0.592818	−	0.695272i
$546$	−2.71466	−	6.55376i	−0.116177	−	0.280475i
$547$	20.9007	+	4.15741i	0.893649	+	0.177758i	0.620493	−	0.784212i	$-0.286932\pi$
$547$	20.9007	+	4.15741i	0.893649	+	0.177758i	0.273156	+	0.961970i	$0.411932\pi$
$548$			12.1519i			0.519105i
$549$	−2.81641	+	14.1590i	−0.120201	+	0.604293i
$550$	25.0991	−	9.30704i	1.07023	−	0.396854i
$551$	14.5366	−	2.89150i	0.619278	−	0.123182i
$552$	−0.298983	−	0.721808i	−0.0127256	−	0.0307222i
$553$	3.00716	+	7.25993i	0.127878	+	0.308724i
$554$	−14.9484	+	2.97343i	−0.635098	+	0.126329i
$555$	−16.3204	+	4.61750i	−0.692762	+	0.196002i
$556$	−0.0229946	+	0.115602i	−0.000975189	+	0.00490260i
$557$		−	25.5629i		−	1.08313i	−0.840657	−	0.541567i	$-0.817831\pi$
$557$		−	25.5629i		−	1.08313i	0.840657	−	0.541567i	$-0.182169\pi$
$558$	1.67147	+	0.332475i	0.0707588	+	0.0140748i
$559$	−7.64945	−	18.4674i	−0.323537	−	0.781088i
$560$	−4.71839	+	0.375298i	−0.199388	+	0.0158592i
$561$	5.08397	+	21.4809i	0.214645	+	0.906926i
$562$	1.86711	+	1.86711i	0.0787594	+	0.0787594i
$563$	8.02543	+	3.32424i	0.338232	+	0.140100i	0.545333	−	0.838219i	$-0.316403\pi$
$563$	8.02543	+	3.32424i	0.338232	+	0.140100i	−0.207102	+	0.978319i	$0.566403\pi$
$564$	−6.60614	−	9.88678i	−0.278169	−	0.416309i
$565$	16.1395	−	18.9288i	0.678994	−	0.796342i
$566$	11.6838	+	2.32406i	0.491108	+	0.0976875i
$567$	0.412966	+	2.07612i	0.0173429	+	0.0871888i
$568$	5.46724	−	8.18231i	0.229400	−	0.343322i
$569$	−0.589730	+	1.42373i	−0.0247228	+	0.0596860i	−0.935759	−	0.352641i	$-0.885284\pi$
$569$	−0.589730	+	1.42373i	−0.0247228	+	0.0596860i	0.911036	+	0.412327i	$0.135284\pi$
$570$	6.34588	+	12.4289i	0.265800	+	0.520589i
$571$	1.75257	+	8.81075i	0.0733427	+	0.368718i	0.999974	−	0.00725355i	$-0.00230890\pi$
$571$	1.75257	+	8.81075i	0.0733427	+	0.368718i	−0.926631	+	0.375972i	$0.877309\pi$
$572$	−17.5968	+	3.50023i	−0.735761	+	0.146352i
$573$	7.26008	+	10.8655i	0.303294	+	0.453912i
$574$	3.90712	−	3.90712i	0.163080	−	0.163080i
$575$	−0.146865	+	3.90364i	−0.00612471	+	0.162793i
$576$	−0.923880	+	0.382683i	−0.0384950	+	0.0159451i
$577$	−31.3726	+	31.3726i	−1.30606	+	1.30606i	−0.381821	+	0.924236i	$0.624703\pi$
$577$	−31.3726	+	31.3726i	−1.30606	+	1.30606i	−0.924236	+	0.381821i	$0.875297\pi$
$578$	−16.9558	+	1.22456i	−0.705270	+	0.0509352i
$579$		−	10.1135i		−	0.420304i
$580$	1.63678	−	5.05179i	0.0679635	−	0.209764i
$581$	5.23459	−	3.49764i	0.217167	−	0.145106i
$582$	−3.70849			−0.153722
$583$	−59.8900	+	40.0172i	−2.48039	+	1.65734i
$584$	−8.75594	+	13.1042i	−0.362323	+	0.542255i
$585$	2.04003	+	7.21042i	0.0843448	+	0.298114i
$586$	3.05550	+	1.26563i	0.126221	+	0.0522826i
$587$	33.6406	−	13.9344i	1.38850	−	0.575135i	0.441758	−	0.897134i	$-0.354355\pi$
$587$	33.6406	−	13.9344i	1.38850	−	0.575135i	0.946740	+	0.322000i	$0.104355\pi$
$588$	2.09463	+	1.39959i	0.0863812	+	0.0577181i
$589$	8.84344	+	5.90900i	0.364388	+	0.243476i
$590$	−1.44195	+	12.2705i	−0.0593642	+	0.505168i
$591$	9.38434	+	9.38434i	0.386020	+	0.386020i
$592$	1.47980	−	7.43946i	0.0608194	−	0.305760i
$593$	−15.4296	+	37.2503i	−0.633616	+	1.52969i	0.201428	+	0.979503i	$0.435442\pi$
$593$	−15.4296	+	37.2503i	−0.633616	+	1.52969i	−0.835045	+	0.550182i	$0.814558\pi$
$594$	5.35382			0.219670
$595$	−8.90154	+	17.3675i	−0.364928	+	0.711999i
$596$	−3.41014			−0.139685
$597$	6.95223	−	16.7842i	0.284536	−	0.686931i
$598$	0.510786	−	2.56790i	0.0208876	−	0.105009i
$599$	−25.3004	−	25.3004i	−1.03375	−	1.03375i	−0.999410	−	0.0343358i	$-0.989068\pi$
$599$	−25.3004	−	25.3004i	−1.03375	−	1.03375i	−0.0343358	−	0.999410i	$-0.510932\pi$
$600$	4.99647	+	0.187981i	0.203980	+	0.00767428i
$601$	−31.1460	−	20.8111i	−1.27047	−	0.848901i	−0.276767	−	0.960937i	$-0.589263\pi$
$601$	−31.1460	−	20.8111i	−1.27047	−	0.848901i	−0.993704	+	0.112036i	$0.964263\pi$
$602$	−10.4983	−	7.01472i	−0.427878	−	0.285899i
$603$	−13.5507	+	5.61289i	−0.551827	+	0.228574i
$604$	−4.43641	−	1.83762i	−0.180515	−	0.0747718i
$605$	19.2701	−	34.4766i	0.783442	−	1.40167i
$606$	8.73373	−	13.0709i	0.354783	−	0.530971i
$607$	2.25237	−	1.50499i	0.0914210	−	0.0610855i	−0.509020	−	0.860755i	$-0.669992\pi$
$607$	2.25237	−	1.50499i	0.0914210	−	0.0610855i	0.600441	+	0.799669i	$0.294992\pi$
$608$	−6.24096			−0.253104
$609$	4.17985	−	2.79289i	0.169376	−	0.113174i
$610$	14.6791	+	28.7502i	0.594341	+	1.16406i
$611$		−	39.8479i		−	1.61207i
$612$	−0.658114	+	4.07024i	−0.0266027	+	0.164530i
$613$	−5.92478	+	5.92478i	−0.239300	+	0.239300i	−0.816560	−	0.577260i	$-0.804122\pi$
$613$	−5.92478	+	5.92478i	−0.239300	+	0.239300i	0.577260	+	0.816560i	$0.304122\pi$
$614$	−13.5945	+	5.63104i	−0.548631	+	0.227250i
$615$	−4.58076	+	3.61737i	−0.184714	+	0.145866i
$616$	−8.01358	+	8.01358i	−0.322876	+	0.322876i
$617$	21.1548	+	31.6604i	0.851659	+	1.27460i	0.959863	+	0.280470i	$0.0904902\pi$
$617$	21.1548	+	31.6604i	0.851659	+	1.27460i	−0.108203	+	0.994129i	$0.534510\pi$
$618$	1.77411	−	0.352891i	0.0713650	−	0.0141954i
$619$	0.909343	+	4.57158i	0.0365496	+	0.183747i	0.994748	−	0.102359i	$-0.0326390\pi$
$619$	0.909343	+	4.57158i	0.0365496	+	0.183747i	−0.958198	+	0.286106i	$0.907639\pi$
$620$	3.39395	−	1.73286i	0.136304	−	0.0695934i
$621$	−0.298983	+	0.721808i	−0.0119978	+	0.0289652i
$622$	3.97283	−	5.94577i	0.159296	−	0.238404i
$623$	−1.38391	−	6.95739i	−0.0554452	−	0.278742i
$624$	−3.28678	−	0.653782i	−0.131577	−	0.0261722i
$625$	−22.3128	−	11.2755i	−0.892513	−	0.451021i
$626$	4.81308	+	7.20328i	0.192369	+	0.287901i
$627$	30.8695	+	12.7866i	1.23281	+	0.510647i
$628$	−9.08095	−	9.08095i	−0.362369	−	0.362369i
$629$	−22.8971	−	21.3031i	−0.912968	−	0.849411i
$630$	3.60178	+	3.07103i	0.143498	+	0.122353i
$631$	−11.8980	−	28.7244i	−0.473654	−	1.14350i	−0.962537	−	0.271152i	$-0.912595\pi$
$631$	−11.8980	−	28.7244i	−0.473654	−	1.14350i	0.488883	−	0.872349i	$-0.337405\pi$
$632$	3.64094	+	0.724227i	0.144829	+	0.0288082i
$633$		−	11.5907i		−	0.460690i
$634$	−1.18622	+	5.96353i	−0.0471108	+	0.236842i
$635$	10.3260	−	18.4745i	0.409776	−	0.733139i
$636$	−13.1953	+	2.62470i	−0.523227	+	0.104076i
$637$	3.23071	+	7.79963i	0.128005	+	0.309032i
$638$	−4.86564	−	11.7467i	−0.192632	−	0.465056i
$639$	−9.65169	+	1.91984i	−0.381815	+	0.0759477i
$640$	−1.09097	+	1.95187i	−0.0431242	+	0.0771544i
$641$	−3.52685	+	17.7307i	−0.139302	+	0.700319i	0.846497	+	0.532393i	$0.178707\pi$
$641$	−3.52685	+	17.7307i	−0.139302	+	0.700319i	−0.985800	+	0.167926i	$0.946293\pi$
$642$		−	5.61839i		−	0.221740i
$643$	−15.4753	−	3.07824i	−0.610288	−	0.121394i	−0.119736	−	0.992806i	$-0.538205\pi$
$643$	−15.4753	−	3.07824i	−0.610288	−	0.121394i	−0.490552	+	0.871412i	$0.663205\pi$
$644$	−0.632884	−	1.52792i	−0.0249391	−	0.0602084i
$645$	10.1492	+	8.65364i	0.399625	+	0.340737i
$646$	−13.5156	+	21.8968i	−0.531765	+	0.861519i
$647$	8.10652	+	8.10652i	0.318700	+	0.318700i	0.848268	−	0.529568i	$-0.177646\pi$
$647$	8.10652	+	8.10652i	0.318700	+	0.318700i	−0.529568	+	0.848268i	$0.677646\pi$
$648$	0.923880	+	0.382683i	0.0362934	+	0.0150332i
$649$	16.4346	+	24.5960i	0.645113	+	0.965479i
$650$	13.5722	+	9.82627i	0.532344	+	0.385418i
$651$	3.53814	+	0.703781i	0.138671	+	0.0275833i
$652$	1.16335	+	5.84857i	0.0455604	+	0.229048i
$653$	20.0422	−	29.9953i	0.784312	−	1.17381i	−0.196815	−	0.980441i	$-0.563060\pi$
$653$	20.0422	−	29.9953i	0.784312	−	1.17381i	0.981127	−	0.193365i	$-0.0619403\pi$
$654$	3.65051	−	8.81311i	0.142746	−	0.344620i
$655$	−7.99316	+	4.08111i	−0.312319	+	0.159462i
$656$	−0.509247	−	2.56016i	−0.0198828	−	0.0999574i
$657$	15.4574	−	3.07468i	0.603052	−	0.119955i
$658$	−13.9838	−	20.9283i	−0.545146	−	0.815869i
$659$	29.5809	−	29.5809i	1.15231	−	1.15231i	0.166218	−	0.986089i	$-0.446845\pi$
$659$	29.5809	−	29.5809i	1.15231	−	1.15231i	0.986089	−	0.166218i	$-0.0531555\pi$
$660$	9.39525	−	7.41931i	0.365710	−	0.288796i
$661$	18.2679	−	7.56681i	0.710539	−	0.294315i	0.00201146	−	0.999998i	$-0.499360\pi$
$661$	18.2679	−	7.56681i	0.710539	−	0.294315i	0.708528	+	0.705683i	$0.249360\pi$
$662$	−9.65254	+	9.65254i	−0.375157	+	0.375157i
$663$	−9.41180	+	10.1160i	−0.365524	+	0.392875i
$664$		−	2.97412i		−	0.115418i
$665$	13.4329	+	26.3094i	0.520906	+	1.02023i
$666$	−6.30687	+	4.21411i	−0.244386	+	0.163294i
$667$	1.85542			0.0718423
$668$	16.0090	−	10.6969i	0.619408	−	0.413875i
$669$	1.42311	−	2.12984i	0.0550207	−	0.0823443i
$670$	−16.0014	+	28.6284i	−0.618188	+	1.10601i
$671$	71.4067	+	29.5776i	2.75662	+	1.14183i
$672$	−1.95566	+	0.810061i	−0.0754412	+	0.0312488i
$673$	18.9165	+	12.6396i	0.729176	+	0.487220i	0.863900	−	0.503663i	$-0.168015\pi$
$673$	18.9165	+	12.6396i	0.729176	+	0.487220i	−0.134724	+	0.990883i	$0.543015\pi$
$674$	−17.1031	−	11.4279i	−0.658787	−	0.440188i
$675$	−3.40011	−	3.66596i	−0.130870	−	0.141103i
$676$	1.25132	+	1.25132i	0.0481276	+	0.0481276i
$677$	1.23039	−	6.18559i	0.0472877	−	0.237731i	−0.949912	−	0.312518i	$-0.898828\pi$
$677$	1.23039	−	6.18559i	0.0472877	−	0.237731i	0.997200	+	0.0747866i	$0.0238276\pi$
$678$	4.25720	−	10.2778i	0.163497	−	0.394716i
$679$	−7.85011			−0.301260
$680$	4.48563	+	8.05476i	0.172016	+	0.308886i
$681$	16.6353			0.637465
$682$	3.49162	−	8.42951i	0.133701	−	0.322783i
$683$	−2.23842	+	11.2533i	−0.0856506	+	0.430595i	0.914038	+	0.405629i	$0.132948\pi$
$683$	−2.23842	+	11.2533i	−0.0856506	+	0.430595i	−0.999688	+	0.0249655i	$0.992052\pi$
$684$	4.41302	+	4.41302i	0.168736	+	0.168736i
$685$	3.17133	−	26.9868i	0.121170	−	1.03111i
$686$	16.7542	+	11.1948i	0.639680	+	0.427420i
$687$	−21.0893	−	14.0914i	−0.804607	−	0.537621i
$688$	−5.51072	+	2.28262i	−0.210094	+	0.0870239i
$689$	−41.6540	−	17.2537i	−1.58689	−	0.657312i
$690$	0.475605	+	1.68101i	0.0181060	+	0.0639949i
$691$	−7.19175	+	10.7632i	−0.273587	+	0.409452i	−0.942665	−	0.333740i	$-0.891689\pi$
$691$	−7.19175	+	10.7632i	−0.273587	+	0.409452i	0.669078	+	0.743192i	$0.266689\pi$
$692$	7.53143	−	5.03234i	0.286302	−	0.191301i
$693$	11.3329			0.430502
$694$	6.34624	−	4.24043i	0.240900	−	0.160964i
$695$	0.0812350	−	0.250726i	0.00308142	−	0.00951057i
$696$		−	2.37485i		−	0.0900185i
$697$	−10.0853	−	3.75764i	−0.382009	−	0.142331i
$698$	1.55237	−	1.55237i	0.0587581	−	0.0587581i
$699$	−11.7782	+	4.87869i	−0.445492	+	0.184529i
$700$	10.5765	+	0.397916i	0.399753	+	0.0150398i
$701$	2.35217	−	2.35217i	0.0888403	−	0.0888403i	−0.661290	−	0.750130i	$-0.729991\pi$
$701$	2.35217	−	2.35217i	0.0888403	−	0.0888403i	0.750130	+	0.661290i	$0.229991\pi$
$702$	1.86181	+	2.78640i	0.0702696	+	0.105166i
$703$	−46.4293	+	9.23537i	−1.75112	+	0.348319i
$704$	1.04448	+	5.25095i	0.0393653	+	0.197902i
$705$	12.0906	+	23.6805i	0.455360	+	0.891858i
$706$	−5.56590	+	13.4373i	−0.209476	+	0.505719i
$707$	18.4875	−	27.6685i	0.695293	−	1.04058i
$708$	1.07793	+	5.41912i	0.0405111	+	0.203663i
$709$	2.49975	+	0.497231i	0.0938801	+	0.0186739i	0.241807	−	0.970324i	$-0.422260\pi$
$709$	2.49975	+	0.497231i	0.0938801	+	0.0186739i	−0.147927	+	0.988998i	$0.547260\pi$
$710$	−14.2769	+	16.7444i	−0.535804	+	0.628405i
$711$	−2.06242	−	3.08664i	−0.0773469	−	0.115758i
$712$	−3.09606	−	1.28243i	−0.116030	−	0.0480611i
$713$	0.941489	+	0.941489i	0.0352590	+	0.0352590i
$714$	−1.39309	+	8.61586i	−0.0521351	+	0.322440i
$715$	39.9923	−	3.18096i	1.49563	−	0.118961i
$716$	3.47467	+	8.38860i	0.129855	+	0.313497i
$717$	−0.730913	−	0.145388i	−0.0272964	−	0.00542960i
$718$			25.9410i			0.968111i
$719$	4.16357	−	20.9317i	0.155275	−	0.780620i	−0.822139	−	0.569287i	$-0.807219\pi$
$719$	4.16357	−	20.9317i	0.155275	−	0.780620i	0.977414	−	0.211333i	$-0.0677806\pi$
$720$	2.15161	−	0.608751i	0.0801857	−	0.0226868i
$721$	3.75541	−	0.746998i	0.139859	−	0.0278197i
$722$	7.63437	+	18.4310i	0.284122	+	0.685930i
$723$	−0.878836	−	2.12170i	−0.0326843	−	0.0789068i
$724$	−17.8375	+	3.54809i	−0.662925	+	0.131864i
$725$	−4.95331	+	10.7918i	−0.183961	+	0.400797i
$726$	3.44595	−	17.3240i	0.127891	−	0.642953i
$727$		−	20.1350i		−	0.746767i	−0.927677	−	0.373383i	$-0.878198\pi$
$727$		−	20.1350i		−	0.746767i	0.927677	−	0.373383i	$-0.121802\pi$
$728$	−6.95743	−	1.38392i	−0.257860	−	0.0512915i
$729$	−0.382683	−	0.923880i	−0.0141735	−	0.0342178i
$730$	22.8649	−	26.8165i	0.846268	−	0.992525i
$731$	−3.92549	+	24.2780i	−0.145190	+	0.897956i
$732$	10.2081	+	10.2081i	0.377302	+	0.377302i
$733$	26.7559	+	11.0827i	0.988253	+	0.409348i	0.817476	−	0.575962i	$-0.195372\pi$
$733$	26.7559	+	11.0827i	0.988253	+	0.409348i	0.170777	+	0.985310i	$0.445372\pi$
$734$	3.85880	+	5.77511i	0.142431	+	0.213163i
$735$	−4.28648	−	3.65483i	−0.158109	−	0.134810i
$736$	−0.766268	−	0.152420i	−0.0282450	−	0.00561828i
$737$	15.3195	+	77.0166i	0.564303	+	2.83694i
$738$	−1.45021	+	2.17040i	−0.0533831	+	0.0798935i
$739$	−5.64544	+	13.6293i	−0.207671	+	0.501362i	−0.993056	−	0.117646i	$-0.962465\pi$
$739$	−5.64544	+	13.6293i	−0.207671	+	0.501362i	0.785385	+	0.619008i	$0.212465\pi$
$740$	−5.22782	+	16.1353i	−0.192178	+	0.593144i
$741$	4.08022	+	20.5127i	0.149891	+	0.753552i
$742$	−27.9317	+	5.55595i	−1.02540	+	0.203965i
$743$	−12.8954	−	19.2994i	−0.473088	−	0.708026i	0.515797	−	0.856711i	$-0.327496\pi$
$743$	−12.8954	−	19.2994i	−0.473088	−	0.708026i	−0.988885	+	0.148685i	$0.952496\pi$
$744$	1.20506	−	1.20506i	0.0441796	−	0.0441796i
$745$	7.57318	+	0.889953i	0.277460	+	0.0326054i
$746$	5.96648	−	2.47140i	0.218448	−	0.0904842i
$747$	−2.10302	+	2.10302i	−0.0769454	+	0.0769454i
$748$	20.6852	+	7.70700i	0.756328	+	0.281796i
$749$		−	11.8930i		−	0.434560i
$750$	−11.0470	−	1.72141i	−0.403380	−	0.0628569i
$751$	7.59891	−	5.07743i	0.277288	−	0.185278i	−0.409148	−	0.912468i	$-0.634174\pi$
$751$	7.59891	−	5.07743i	0.277288	−	0.185278i	0.686436	+	0.727190i	$0.259174\pi$
$752$	−11.8907			−0.433610
$753$	−8.23610	+	5.50319i	−0.300140	+	0.200547i
$754$	4.42153	−	6.61729i	0.161023	−	0.240987i
$755$	9.37276	+	5.23875i	0.341110	+	0.190658i
$756$	1.95566	+	0.810061i	0.0711267	+	0.0294616i
$757$	−50.0807	+	20.7441i	−1.82021	+	0.753958i	−0.844278	+	0.535906i	$0.819970\pi$
$757$	−50.0807	+	20.7441i	−1.82021	+	0.753958i	−0.975937	+	0.218052i	$0.930030\pi$
$758$	−22.7969	−	15.2324i	−0.828019	−	0.553265i
$759$	3.47790	+	2.32386i	0.126240	+	0.0843506i
$760$	13.8598	+	1.62872i	0.502749	+	0.0590799i
$761$	26.2101	+	26.2101i	0.950114	+	0.950114i	0.998813	−	0.0486999i	$-0.0155078\pi$
$761$	26.2101	+	26.2101i	0.950114	+	0.950114i	−0.0486999	+	0.998813i	$0.515508\pi$
$762$	1.84654	−	9.28317i	0.0668930	−	0.336294i
$763$	7.72737	−	18.6555i	0.279750	−	0.675375i
$764$	13.0678			0.472776
$765$	2.52375	−	8.86739i	0.0912465	−	0.320601i
$766$	23.9782			0.866366
$767$	−7.08585	+	17.1068i	−0.255855	+	0.617689i
$768$	−0.195090	+	0.980785i	−0.00703972	+	0.0353910i
$769$	−13.9783	−	13.9783i	−0.504071	−	0.504071i	0.408630	−	0.912700i	$-0.366007\pi$
$769$	−13.9783	−	13.9783i	−0.504071	−	0.504071i	−0.912700	+	0.408630i	$0.866007\pi$
$770$	19.8878	−	15.7051i	0.716706	−	0.565974i
$771$	6.81017	+	4.55041i	0.245262	+	0.163879i
$772$	−8.40909	−	5.61877i	−0.302650	−	0.202224i
$773$	2.97492	−	1.23225i	0.107000	−	0.0443210i	−0.328541	−	0.944490i	$-0.606557\pi$
$773$	2.97492	−	1.23225i	0.107000	−	0.0443210i	0.435541	+	0.900169i	$0.356557\pi$
$774$	5.51072	+	2.28262i	0.198079	+	0.0820470i
$775$	−7.98946	+	2.96259i	−0.286990	+	0.106419i
$776$	−2.06033	+	3.08350i	−0.0739615	+	0.110691i
$777$	−13.3503	+	8.92040i	−0.478940	+	0.320018i
$778$	−8.82945			−0.316551
$779$	−13.5454	+	9.05072i	−0.485313	+	0.324276i
$780$	7.12862	+	2.30967i	0.255246	+	0.0826995i
$781$			52.6857i			1.88524i
$782$	−2.19423	+	2.35841i	−0.0784655	+	0.0843367i
$783$	−1.67927	+	1.67927i	−0.0600123	+	0.0600123i
$784$	2.32743	−	0.964053i	0.0831225	−	0.0344305i
$785$	17.7970	+	22.5367i	0.635201	+	0.804370i
$786$	−2.83806	+	2.83806i	−0.101230	+	0.101230i
$787$	8.62176	+	12.9034i	0.307332	+	0.459955i	0.952698	−	0.303918i	$-0.0982950\pi$
$787$	8.62176	+	12.9034i	0.307332	+	0.459955i	−0.645366	+	0.763874i	$0.723295\pi$
$788$	13.0165	−	2.58913i	0.463692	−	0.0922340i
$789$	−3.82683	−	19.2388i	−0.136239	−	0.684919i
$790$	−7.89674	−	2.55854i	−0.280953	−	0.0910287i
$791$	9.01161	−	21.7560i	0.320416	−	0.773553i
$792$	2.97442	−	4.45154i	0.105691	−	0.158178i
$793$	9.43828	+	47.4494i	0.335163	+	1.68498i
$794$	32.4777	+	6.46022i	1.15259	+	0.229265i
$795$	29.9889	−	2.38530i	1.06360	−	0.0845977i
$796$	−10.0931	−	15.1054i	−0.357740	−	0.535395i
$797$	−26.3667	−	10.9215i	−0.933957	−	0.386858i	−0.136779	−	0.990602i	$-0.543675\pi$
$797$	−26.3667	−	10.9215i	−0.933957	−	0.386858i	−0.797178	+	0.603744i	$0.793675\pi$
$798$	9.34145	+	9.34145i	0.330684	+	0.330684i
$799$	−25.7510	+	41.7194i	−0.911004	+	1.47593i
$800$	2.93219	−	4.04997i	0.103668	−	0.143188i
$801$	1.28243	+	3.09606i	0.0453125	+	0.109394i
$802$	0.586039	+	0.116570i	0.0206937	+	0.00411624i
$803$		−	84.3776i		−	2.97762i
$804$	−2.86142	+	14.3854i	−0.100915	+	0.507332i
$805$	1.00676	+	3.55835i	0.0354835	+	0.125415i
$806$	5.60137	−	1.11418i	0.197300	−	0.0392454i
$807$	7.26005	+	17.5273i	0.255566	+	0.616990i
$808$	−6.01589	−	14.5237i	−0.211638	−	0.510940i
$809$	39.3513	−	7.82746i	1.38352	−	0.275199i	0.553460	−	0.832876i	$-0.313307\pi$
$809$	39.3513	−	7.82746i	1.38352	−	0.275199i	0.830058	+	0.557677i	$0.188307\pi$
$810$	−1.95187	−	1.09097i	−0.0685817	−	0.0383326i
$811$	6.95087	−	34.9444i	0.244078	−	1.22706i	−0.643153	−	0.765738i	$-0.722374\pi$
$811$	6.95087	−	34.9444i	0.244078	−	1.22706i	0.887231	−	0.461325i	$-0.152626\pi$
$812$		−	5.02707i		−	0.176415i
$813$	17.2039	+	3.42208i	0.603369	+	0.120017i
$814$	15.5407	+	37.5186i	0.544701	+	1.31503i
$815$	−1.05724	−	13.2920i	−0.0370335	−	0.465600i
$816$	3.01866	+	2.80851i	0.105674	+	0.0983174i
$817$	26.3226	+	26.3226i	0.920913	+	0.920913i
$818$	21.0426	+	8.71611i	0.735736	+	0.304752i
$819$	3.94107	+	5.89823i	0.137712	+	0.206101i
$820$	0.462797	+	5.81847i	0.0161616	+	0.203190i
$821$	−33.8337	−	6.72994i	−1.18080	−	0.234877i	−0.434619	−	0.900615i	$-0.643117\pi$
$821$	−33.8337	−	6.72994i	−1.18080	−	0.234877i	−0.746186	+	0.665738i	$0.768117\pi$
$822$	−2.37072	−	11.9184i	−0.0826885	−	0.415703i
$823$	8.15660	−	12.2072i	0.284321	−	0.425517i	−0.661628	−	0.749832i	$-0.730134\pi$
$823$	8.15660	−	12.2072i	0.284321	−	0.425517i	0.945949	+	0.324316i	$0.105134\pi$
$824$	0.692222	−	1.67117i	0.0241147	−	0.0582180i
$825$	−22.8011	+	14.0248i	−0.793832	+	0.488281i
$826$	2.28176	+	11.4712i	0.0793924	+	0.399133i
$827$	20.4219	−	4.06218i	0.710141	−	0.141256i	0.173213	−	0.984884i	$-0.444585\pi$
$827$	20.4219	−	4.06218i	0.710141	−	0.141256i	0.536927	+	0.843629i	$0.319585\pi$
$828$	0.434056	+	0.649610i	0.0150845	+	0.0225755i
$829$	−4.58169	+	4.58169i	−0.159129	+	0.159129i	−0.782180	−	0.623052i	$-0.785893\pi$
$829$	−4.58169	+	4.58169i	−0.159129	+	0.159129i	0.623052	+	0.782180i	$0.285893\pi$
$830$	−0.776164	+	6.60487i	−0.0269410	+	0.229259i
$831$	14.0811	−	5.83258i	0.488468	−	0.202330i
$832$	−2.36964	+	2.36964i	−0.0821524	+	0.0821524i
$833$	1.65792	−	10.2537i	0.0574434	−	0.355271i
$834$		−	0.117866i		−	0.00408138i
$835$	−38.3442	+	19.5776i	−1.32696	+	0.677510i
$836$	27.7819	−	18.5632i	0.960856	−	0.642023i
$837$	−1.70421			−0.0589062
$838$	22.0028	−	14.7018i	0.760073	−	0.507864i
$839$	−23.7562	+	35.5537i	−0.820156	+	1.22745i	0.150888	+	0.988551i	$0.451787\pi$
$839$	−23.7562	+	35.5537i	−0.820156	+	1.22745i	−0.971044	+	0.238900i	$0.923213\pi$
$840$	4.55451	−	1.28860i	0.157145	−	0.0444609i
$841$	−21.5819	−	8.93952i	−0.744203	−	0.308259i
$842$	−27.5346	+	11.4052i	−0.948905	+	0.393049i
$843$	−2.19549	−	1.46698i	−0.0756168	−	0.0505255i
$844$	−9.63733	−	6.43946i	−0.331731	−	0.221655i
$845$	−2.45235	−	3.10547i	−0.0843633	−	0.106831i
$846$	8.40802	+	8.40802i	0.289074	+	0.289074i
$847$	7.29436	−	36.6712i	0.250637	−	1.26004i
$848$	−5.14854	+	12.4297i	−0.176802	+	0.426837i
$849$	−11.9127			−0.408844
$850$	−7.85955	−	19.0585i	−0.269580	−	0.653702i
$851$	−5.92617			−0.203146
$852$	−3.76590	+	9.09169i	−0.129018	+	0.311476i
$853$	4.33736	−	21.8054i	0.148509	−	0.746603i	−0.832711	−	0.553708i	$-0.813212\pi$
$853$	4.33736	−	21.8054i	0.148509	−	0.746603i	0.981219	−	0.192895i	$-0.0617876\pi$
$854$	21.6084	+	21.6084i	0.739425	+	0.739425i
$855$	−8.64870	−	10.9521i	−0.295779	−	0.374553i
$856$	−4.67152	−	3.12141i	−0.159669	−	0.106688i
$857$	−7.69019	−	5.13842i	−0.262692	−	0.175525i	0.417249	−	0.908792i	$-0.362994\pi$
$857$	−7.69019	−	5.13842i	−0.262692	−	0.175525i	−0.679940	+	0.733267i	$0.737994\pi$
$858$	16.5759	−	6.86595i	0.565890	−	0.234400i
$859$	2.54654	+	1.05481i	0.0868869	+	0.0359897i	0.425704	−	0.904863i	$-0.360027\pi$
$859$	2.54654	+	1.05481i	0.0868869	+	0.0359897i	−0.338817	+	0.940852i	$0.610027\pi$
$860$	12.8338	−	3.63105i	0.437630	−	0.123818i
$861$	−3.06980	+	4.59428i	−0.104619	+	0.156573i
$862$	−14.4627	+	9.66368i	−0.492602	+	0.329146i
$863$	−37.2658			−1.26854			−0.634271	−	0.773110i	$-0.718700\pi$
$863$	−37.2658			−1.26854			−0.634271	+	0.773110i	$0.718700\pi$
$864$	0.831470	−	0.555570i	0.0282872	−	0.0189009i
$865$	−18.0390	+	9.21025i	−0.613344	+	0.313158i
$866$		−	16.9672i		−	0.576568i
$867$	16.3911	−	4.50895i	0.556672	−	0.153132i
$868$	2.55086	−	2.55086i	0.0865818	−	0.0865818i
$869$	−18.3619	+	7.60575i	−0.622885	+	0.258008i
$870$	−0.619772	+	5.27404i	−0.0210122	+	0.178807i
$871$	−34.7559	+	34.7559i	−1.17766	+	1.17766i
$872$	−5.29972	−	7.93159i	−0.179471	−	0.268598i
$873$	3.63724	−	0.723491i	0.123102	−	0.0244865i
$874$	0.951248	+	4.78224i	0.0321764	+	0.161762i
$875$	−23.3843	−	3.64386i	−0.790532	−	0.123185i
$876$	6.03119	−	14.5606i	0.203775	−	0.491957i
$877$	−15.9294	+	23.8400i	−0.537897	+	0.805020i	−0.996497	−	0.0836229i	$-0.973351\pi$
$877$	−15.9294	+	23.8400i	−0.537897	+	0.805020i	0.458601	+	0.888643i	$0.348351\pi$
$878$	2.33401	+	11.7339i	0.0787692	+	0.395999i
$879$	−3.24370	−	0.645212i	−0.109407	−	0.0217625i
$880$	−0.949208	−	11.9338i	−0.0319978	−	0.402289i
$881$	−26.0151	−	38.9343i	−0.876470	−	1.31173i	−0.949295	−	0.314386i	$-0.898202\pi$
$881$	−26.0151	−	38.9343i	−0.876470	−	1.31173i	0.0728253	−	0.997345i	$-0.476798\pi$
$882$	−2.32743	−	0.964053i	−0.0783687	−	0.0324614i
$883$	−16.8951	−	16.8951i	−0.568564	−	0.568564i	0.363162	−	0.931726i	$-0.381697\pi$
$883$	−16.8951	−	16.8951i	−0.568564	−	0.568564i	−0.931726	+	0.363162i	$0.881697\pi$
$884$	3.18227	+	13.4458i	0.107031	+	0.452231i
$885$	−0.979610	−	12.3160i	−0.0329292	−	0.413999i
$886$	−12.5126	−	30.2082i	−0.420370	−	1.01486i
$887$	−27.1938	−	5.40918i	−0.913077	−	0.181622i	−0.283873	−	0.958862i	$-0.591619\pi$
$887$	−27.1938	−	5.40918i	−0.913077	−	0.181622i	−0.629205	+	0.777240i	$0.716619\pi$
$888$			7.58521i			0.254543i
$889$	3.90874	−	19.6505i	0.131095	−	0.659058i
$890$	6.54101	+	3.65599i	0.219255	+	0.122549i
$891$	−5.25095	+	1.04448i	−0.175913	+	0.0349913i
$892$	−0.980257	−	2.36655i	−0.0328214	−	0.0792380i
$893$	28.3988	+	68.5607i	0.950329	+	2.29430i
$894$	3.34461	−	0.665284i	0.111861	−	0.0222504i
$895$	−5.52731	−	19.5361i	−0.184757	−	0.653019i
$896$	−0.412966	+	2.07612i	−0.0137962	+	0.0693582i
$897$			2.61820i			0.0874193i
$898$	−33.3533	−	6.63438i	−1.11301	−	0.221392i
$899$	1.54882	+	3.73917i	0.0516559	+	0.124708i
$900$	−4.93713	+	0.790393i	−0.164571	+	0.0263464i
$901$	32.4605	+	44.9821i	1.08142	+	1.49857i
$902$	9.88193	+	9.88193i	0.329032	+	0.329032i
$903$	11.6651	+	4.83182i	0.388189	+	0.160793i
$904$	−6.18050	−	9.24977i	−0.205560	−	0.307643i
$905$	40.5392	−	3.22446i	1.34757	−	0.107185i
$906$	4.70967	+	0.936812i	0.156468	+	0.0311235i
$907$	−7.54873	−	37.9500i	−0.250651	−	1.26011i	−0.876971	−	0.480543i	$-0.840439\pi$
$907$	−7.54873	−	37.9500i	−0.250651	−	1.26011i	0.626320	−	0.779566i	$-0.284561\pi$
$908$	9.24206	−	13.8317i	0.306709	−	0.459022i
$909$	−6.01589	+	14.5237i	−0.199535	+	0.481719i
$910$	15.0898	+	4.88909i	0.500222	+	0.162072i
$911$	−4.36839	−	21.9614i	−0.144731	−	0.727613i	−0.983181	−	0.182634i	$-0.941538\pi$
$911$	−4.36839	−	21.9614i	−0.144731	−	0.727613i	0.838450	−	0.544979i	$-0.183462\pi$
$912$	6.12104	−	1.21755i	0.202688	−	0.0403171i
$913$	8.84627	+	13.2394i	0.292769	+	0.438160i
$914$	−17.1488	+	17.1488i	−0.567233	+	0.567233i
$915$	−20.0060	−	25.3340i	−0.661377	−	0.837518i
$916$	−23.4332	+	9.70634i	−0.774254	+	0.320707i
$917$	−6.00759	+	6.00759i	−0.198388	+	0.198388i
$918$	−0.148597	−	4.12043i	−0.00490443	−	0.135994i
$919$			29.6128i			0.976836i	0.872610	+	0.488418i	$0.162426\pi$
$919$			29.6128i			0.976836i	−0.872610	+	0.488418i	$0.837574\pi$
$920$	1.66194	+	0.538468i	0.0547925	+	0.0177528i
$921$	12.2348	−	8.17500i	0.403149	−	0.269375i
$922$	10.6283			0.350024
$923$	−27.4203	+	18.3217i	−0.902552	+	0.603066i
$924$	6.29623	−	9.42298i	0.207131	−	0.309993i
$925$	15.8207	−	34.4686i	0.520183	−	1.13332i
$926$	−22.0017	−	9.11341i	−0.723021	−	0.299485i
$927$	−1.67117	+	0.692222i	−0.0548884	+	0.0227355i
$928$	−1.97462	−	1.31940i	−0.0648200	−	0.0433113i
$929$	−43.1304	−	28.8188i	−1.41506	−	0.945516i	−0.999351	−	0.0360198i	$-0.988532\pi$
$929$	−43.1304	−	28.8188i	−1.41506	−	0.945516i	−0.415713	−	0.909496i	$-0.636468\pi$
$930$	−2.99067	+	2.36169i	−0.0980679	+	0.0774429i
$931$	−11.1173	−	11.1173i	−0.364353	−	0.364353i
$932$	−2.48713	+	12.5037i	−0.0814688	+	0.409571i
$933$	−2.73654	+	6.60658i	−0.0895902	+	0.216290i
$934$	39.0250			1.27694
$935$	−43.9262	−	22.5139i	−1.43654	−	0.736283i
$936$	3.35117			0.109537
$937$	−15.3037	+	36.9464i	−0.499950	+	1.20699i	0.449560	+	0.893250i	$0.351581\pi$
$937$	−15.3037	+	36.9464i	−0.499950	+	1.20699i	−0.949510	+	0.313736i	$0.898419\pi$
$938$	−6.05704	+	30.4508i	−0.197769	+	0.994254i
$939$	−6.12588	−	6.12588i	−0.199911	−	0.199911i
$940$	26.4068	+	3.10316i	0.861294	+	0.101214i
$941$	2.43942	+	1.62997i	0.0795228	+	0.0531354i	0.594696	−	0.803951i	$-0.297272\pi$
$941$	2.43942	+	1.62997i	0.0795228	+	0.0531354i	−0.515173	+	0.857086i	$0.672272\pi$
$942$	10.6781	+	7.13486i	0.347910	+	0.232466i
$943$	−1.88415	+	0.780440i	−0.0613563	+	0.0254146i
$944$	5.10470	+	2.11444i	0.166144	+	0.0688191i
$945$	−4.13170	−	2.30935i	−0.134404	−	0.0751231i
$946$	17.7417	−	26.5524i	0.576833	−	0.863292i
$947$	−37.6254	+	25.1405i	−1.22266	+	0.816957i	−0.987899	−	0.155096i	$-0.950431\pi$
$947$	−37.6254	+	25.1405i	−1.22266	+	0.816957i	−0.234763	+	0.972053i	$0.575431\pi$
$948$	−3.71227			−0.120569
$949$	43.9144	−	29.3427i	1.42552	−	0.952504i
$950$	−30.3547	−	7.23409i	−0.984836	−	0.234705i
$951$		−	6.08036i		−	0.197169i
$952$	6.38987	+	5.94503i	0.207097	+	0.192679i
$953$	−25.6740	+	25.6740i	−0.831662	+	0.831662i	−0.987744	−	0.156082i	$-0.950113\pi$
$953$	−25.6740	+	25.6740i	−0.831662	+	0.831662i	0.156082	+	0.987744i	$0.450113\pi$
$954$	12.4297	−	5.14854i	0.402426	−	0.166690i
$955$	−29.0208	−	3.41034i	−0.939091	−	0.110356i
$956$	−0.526959	+	0.526959i	−0.0170431	+	0.0170431i
$957$	7.06381	+	10.5717i	0.228341	+	0.341736i
$958$	−34.7529	+	6.91279i	−1.12282	+	0.223342i
$959$	−5.01833	−	25.2288i	−0.162050	−	0.814682i
$960$	0.689212	−	2.12720i	0.0222442	−	0.0686551i
$961$	10.7517	−	25.9570i	0.346830	−	0.837323i
$962$	−14.1222	+	21.1354i	−0.455319	+	0.681433i
$963$	1.09609	+	5.51044i	0.0353211	+	0.177571i
$964$	−2.25238	−	0.448027i	−0.0725443	−	0.0144300i
$965$	17.2084	+	14.6726i	0.553960	+	0.472329i
$966$	0.918806	+	1.37509i	0.0295621	+	0.0442428i
$967$	−31.7545	−	13.1531i	−1.02116	−	0.422977i	−0.191644	−	0.981465i	$-0.561382\pi$
$967$	−31.7545	−	13.1531i	−1.02116	−	0.422977i	−0.829513	+	0.558488i	$0.811382\pi$
$968$	−12.4899	−	12.4899i	−0.401440	−	0.401440i
$969$	8.98407	−	24.1128i	0.288610	−	0.774616i
$970$	5.38026	−	6.31010i	0.172750	−	0.202605i
$971$	−4.32094	−	10.4317i	−0.138666	−	0.334769i	0.839257	−	0.543735i	$-0.182990\pi$
$971$	−4.32094	−	10.4317i	−0.138666	−	0.334769i	−0.977923	+	0.208966i	$0.932990\pi$
$972$	−0.980785	−	0.195090i	−0.0314587	−	0.00625752i
$973$		−	0.249499i		−	0.00799856i
$974$	1.23866	−	6.22717i	0.0396893	−	0.199531i
$975$	−15.2284	−	6.98966i	−0.487699	−	0.223848i
$976$	14.1590	−	2.81641i	0.453220	−	0.0901510i
$977$	−12.5092	−	30.1999i	−0.400205	−	0.966181i	−0.987616	−	0.156892i	$-0.949853\pi$
$977$	−12.5092	−	30.1999i	−0.400205	−	0.966181i	0.587411	−	0.809289i	$-0.300147\pi$
$978$	−2.28200	−	5.50923i	−0.0729703	−	0.176166i
$979$	17.5967	−	3.50021i	0.562394	−	0.111867i
$980$	−5.42032	+	1.53356i	−0.173146	+	0.0489878i
$981$	−1.86101	+	9.35595i	−0.0594176	+	0.298712i
$982$		−	29.0606i		−	0.927362i
$983$	36.6506	+	7.29025i	1.16897	+	0.232523i	0.741149	−	0.671340i	$-0.234281\pi$
$983$	36.6506	+	7.29025i	1.16897	+	0.232523i	0.427822	+	0.903863i	$0.359281\pi$
$984$	0.998925	+	2.41162i	0.0318446	+	0.0768796i
$985$	−29.5825	+	2.35297i	−0.942575	+	0.0749719i
$986$	−8.90549	+	4.07074i	−0.283608	+	0.129639i
$987$	17.7980	+	17.7980i	0.566517	+	0.566517i
$988$	19.3225	+	8.00365i	0.614731	+	0.254630i
$989$	2.58904	+	3.87477i	0.0823267	+	0.123211i
$990$	−7.76729	+	9.10967i	−0.246861	+	0.289524i
$991$	−37.3452	−	7.42841i	−1.18631	−	0.235971i	−0.437785	−	0.899080i	$-0.644237\pi$
$991$	−37.3452	−	7.42841i	−1.18631	−	0.235971i	−0.748523	+	0.663109i	$0.769237\pi$
$992$	−0.332475	−	1.67147i	−0.0105561	−	0.0530691i
$993$	7.58396	−	11.3502i	0.240670	−	0.360187i
$994$	−7.97163	+	19.2452i	−0.252845	+	0.610421i
$995$	18.4725	+	36.1798i	0.585617	+	1.14698i
$996$	0.580221	+	2.91697i	0.0183850	+	0.0924277i
$997$	41.6908	−	8.29283i	1.32036	−	0.262636i	0.515904	−	0.856646i	$-0.327456\pi$
$997$	41.6908	−	8.29283i	1.32036	−	0.262636i	0.804458	+	0.594010i	$0.202456\pi$
$998$	−1.57783	−	2.36139i	−0.0499453	−	0.0747484i
$999$	5.36355	−	5.36355i	0.169695	−	0.169695i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.bi.b.97.9	yes	80
5.3	odd	4		510.2.bd.b.403.10	yes	80
17.10	odd	16		510.2.bd.b.367.10	✓	80
85.78	even	16	inner	510.2.bi.b.163.9	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.bd.b.367.10	✓	80	17.10	odd	16
510.2.bd.b.403.10	yes	80	5.3	odd	4
510.2.bi.b.97.9	yes	80	1.1	even	1	trivial
510.2.bi.b.163.9	yes	80	85.78	even	16	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:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.bi (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.382683 + 0.923880i) q^{2} +(0.195090 - 0.980785i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(1.38580 + 1.75487i) q^{5} +(0.831470 + 0.555570i) q^{6} +(1.76005 + 1.17603i) q^{7} +(0.923880 - 0.382683i) q^{8} +(-0.923880 - 0.382683i) q^{9} +(-2.15161 + 0.608751i) q^{10} +(-2.97442 + 4.45154i) q^{11} +(-0.831470 + 0.555570i) q^{12} -3.35117 q^{13} +(-1.76005 + 1.17603i) q^{14} +(1.99151 - 1.01681i) q^{15} +1.00000i q^{16} +(3.50857 + 2.16563i) q^{17} +(0.707107 - 0.707107i) q^{18} +(5.76589 - 2.38831i) q^{19} +(0.260973 - 2.22079i) q^{20} +(1.49680 - 1.49680i) q^{21} +(-2.97442 - 4.45154i) q^{22} +(0.766268 - 0.152420i) q^{23} +(-0.195090 - 0.980785i) q^{24} +(-1.15913 + 4.86379i) q^{25} +(1.28244 - 3.09608i) q^{26} +(-0.555570 + 0.831470i) q^{27} +(-0.412966 - 2.07612i) q^{28} +(2.32922 + 0.463311i) q^{29} +(0.177296 + 2.22903i) q^{30} +(0.946809 + 1.41700i) q^{31} +(-0.923880 - 0.382683i) q^{32} +(3.78572 + 3.78572i) q^{33} +(-3.34345 + 2.41274i) q^{34} +(0.375298 + 4.71839i) q^{35} +(0.382683 + 0.923880i) q^{36} +(-7.43946 - 1.47980i) q^{37} +6.24096i q^{38} +(-0.653782 + 3.28678i) q^{39} +(1.95187 + 1.09097i) q^{40} +(-2.56016 + 0.509247i) q^{41} +(0.810061 + 1.95566i) q^{42} +(2.28262 + 5.51072i) q^{43} +(5.25095 - 1.04448i) q^{44} +(-0.608751 - 2.15161i) q^{45} +(-0.152420 + 0.766268i) q^{46} +11.8907i q^{47} +(0.980785 + 0.195090i) q^{48} +(-0.964053 - 2.32743i) q^{49} +(-4.04997 - 2.93219i) q^{50} +(2.80851 - 3.01866i) q^{51} +(2.36964 + 2.36964i) q^{52} +(12.4297 + 5.14854i) q^{53} +(-0.555570 - 0.831470i) q^{54} +(-11.9338 + 0.949208i) q^{55} +(2.07612 + 0.412966i) q^{56} +(-1.21755 - 6.12104i) q^{57} +(-1.31940 + 1.97462i) q^{58} +(2.11444 - 5.10470i) q^{59} +(-2.12720 - 0.689212i) q^{60} +(-2.81641 - 14.1590i) q^{61} +(-1.67147 + 0.332475i) q^{62} +(-1.17603 - 1.76005i) q^{63} +(0.707107 - 0.707107i) q^{64} +(-4.64405 - 5.88087i) q^{65} +(-4.94628 + 2.04882i) q^{66} +(10.3713 - 10.3713i) q^{67} +(-0.949597 - 4.01226i) q^{68} -0.781280i q^{69} +(-4.50284 - 1.45892i) q^{70} +(8.18231 - 5.46724i) q^{71} -1.00000 q^{72} +(-13.1042 + 8.75594i) q^{73} +(4.21411 - 6.30687i) q^{74} +(4.54419 + 2.08574i) q^{75} +(-5.76589 - 2.38831i) q^{76} +(-10.4703 + 4.33692i) q^{77} +(-2.78640 - 1.86181i) q^{78} +(3.08664 + 2.06242i) q^{79} +(-1.75487 + 1.38580i) q^{80} +(0.707107 + 0.707107i) q^{81} +(0.509247 - 2.56016i) q^{82} +(1.13814 - 2.74772i) q^{83} -2.11679 q^{84} +(1.06176 + 9.15820i) q^{85} -5.96476 q^{86} +(0.908816 - 2.19408i) q^{87} +(-1.04448 + 5.25095i) q^{88} +(-2.36962 - 2.36962i) q^{89} +(2.22079 + 0.260973i) q^{90} +(-5.89823 - 3.94107i) q^{91} +(-0.649610 - 0.434056i) q^{92} +(1.57449 - 0.652174i) q^{93} +(-10.9856 - 4.55039i) q^{94} +(12.1815 + 6.80867i) q^{95} +(-0.555570 + 0.831470i) q^{96} +(-3.08350 + 2.06033i) q^{97} +2.51919 q^{98} +(4.45154 - 2.97442i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 48 q^{25} + 16 q^{28} + 32 q^{29} + 16 q^{30} + 16 q^{31} - 16 q^{33} - 32 q^{34} - 32 q^{35} + 48 q^{37} + 32 q^{41} + 32 q^{43} + 16 q^{44} - 64 q^{49} + 48 q^{50} - 32 q^{51} + 16 q^{52} - 32 q^{53}+ \cdots - 144 q^{98}+O(q^{100}) \) 80 * q + 48 * q^25 + 16 * q^28 + 32 * q^29 + 16 * q^30 + 16 * q^31 - 16 * q^33 - 32 * q^34 - 32 * q^35 + 48 * q^37 + 32 * q^41 + 32 * q^43 + 16 * q^44 - 64 * q^49 + 48 * q^50 - 32 * q^51 + 16 * q^52 - 32 * q^53 + 16 * q^55 - 16 * q^56 + 32 * q^57 + 32 * q^58 - 16 * q^60 + 48 * q^61 + 32 * q^62 - 32 * q^65 - 16 * q^67 - 16 * q^70 - 80 * q^72 - 80 * q^73 - 32 * q^74 - 48 * q^77 - 32 * q^78 - 64 * q^79 - 16 * q^80 - 32 * q^82 - 32 * q^83 - 32 * q^85 - 48 * q^87 - 16 * q^88 - 32 * q^89 - 32 * q^92 - 48 * q^93 - 16 * q^94 - 96 * q^95 + 80 * q^97 - 144 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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