LMFDB - Embedded newform 168.2.ba.c.5.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [168,2,Mod(5,168)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(168, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("168.5"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.10
Character	$\chi$	$=$	168.5
Dual form			168.2.ba.c.101.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.368276 + 1.36542i) q^{2} +(-1.26610 - 1.18195i) q^{3} +(-1.72875 - 1.00570i) q^{4} +(1.54900 + 0.894317i) q^{5} +(2.08013 - 1.29347i) q^{6} +(2.63573 + 0.230049i) q^{7} +(2.00986 - 1.99009i) q^{8} +(0.206000 + 2.99292i) q^{9} +(-1.79158 + 1.78568i) q^{10} +(0.501346 + 0.868358i) q^{11} +(1.00007 + 3.31660i) q^{12} +2.47302 q^{13} +(-1.28479 + 3.51416i) q^{14} +(-0.904151 - 2.96313i) q^{15} +(1.97713 + 3.47721i) q^{16} +(3.32963 + 5.76708i) q^{17} +(-4.16246 - 0.820942i) q^{18} +(1.85941 - 3.22059i) q^{19} +(-1.77842 - 3.10388i) q^{20} +(-3.06518 - 3.40656i) q^{21} +(-1.37031 + 0.364754i) q^{22} +(-6.85244 - 3.95626i) q^{23} +(-4.89686 + 0.144094i) q^{24} +(-0.900394 - 1.55953i) q^{25} +(-0.910752 + 3.37671i) q^{26} +(3.27666 - 4.03281i) q^{27} +(-4.32515 - 3.04846i) q^{28} +0.748403 q^{29} +(4.37890 - 0.143297i) q^{30} +(2.87254 - 1.65846i) q^{31} +(-5.47598 + 1.41904i) q^{32} +(0.391600 - 1.69199i) q^{33} +(-9.10071 + 2.42246i) q^{34} +(3.87702 + 2.71353i) q^{35} +(2.65386 - 5.38117i) q^{36} +(-3.22429 - 1.86155i) q^{37} +(3.71268 + 3.72494i) q^{38} +(-3.13108 - 2.92298i) q^{39} +(4.89305 - 1.28520i) q^{40} -2.01044 q^{41} +(5.78022 - 2.93071i) q^{42} +9.19651i q^{43} +(0.00660852 - 2.00538i) q^{44} +(-2.35752 + 4.82027i) q^{45} +(7.92554 - 7.89946i) q^{46} +(-1.19840 + 2.07569i) q^{47} +(1.60665 - 6.73934i) q^{48} +(6.89415 + 1.21270i) q^{49} +(2.46101 - 0.655080i) q^{50} +(2.60076 - 11.2371i) q^{51} +(-4.27522 - 2.48712i) q^{52} +(-6.33884 - 10.9792i) q^{53} +(4.29976 + 5.95920i) q^{54} +1.79345i q^{55} +(5.75527 - 4.78297i) q^{56} +(-6.16075 + 1.87985i) q^{57} +(-0.275619 + 1.02188i) q^{58} +(-7.34922 + 4.24308i) q^{59} +(-1.41698 + 6.03181i) q^{60} +(-2.02442 + 3.50640i) q^{61} +(1.20661 + 4.53300i) q^{62} +(-0.145558 + 7.93592i) q^{63} +(0.0790881 - 7.99961i) q^{64} +(3.83071 + 2.21166i) q^{65} +(2.16606 + 1.15782i) q^{66} +(-6.89843 + 3.98281i) q^{67} +(0.0438896 - 13.3184i) q^{68} +(3.99976 + 13.1082i) q^{69} +(-5.13292 + 4.29443i) q^{70} -5.46843i q^{71} +(6.37021 + 5.60539i) q^{72} +(-5.68546 + 3.28250i) q^{73} +(3.72922 - 3.71695i) q^{74} +(-0.703295 + 3.03873i) q^{75} +(-6.45340 + 3.69757i) q^{76} +(1.12165 + 2.40409i) q^{77} +(5.14419 - 3.19878i) q^{78} +(2.53988 - 4.39920i) q^{79} +(-0.0471537 + 7.15438i) q^{80} +(-8.91513 + 1.23308i) q^{81} +(0.740396 - 2.74510i) q^{82} +5.65457i q^{83} +(1.87294 + 8.97174i) q^{84} +11.9110i q^{85} +(-12.5571 - 3.38685i) q^{86} +(-0.947550 - 0.884573i) q^{87} +(2.73575 + 0.747554i) q^{88} +(7.39495 - 12.8084i) q^{89} +(-5.71347 - 4.99420i) q^{90} +(6.51821 + 0.568916i) q^{91} +(7.86731 + 13.7309i) q^{92} +(-5.59713 - 1.29542i) q^{93} +(-2.39285 - 2.40075i) q^{94} +(5.76045 - 3.32580i) q^{95} +(8.61034 + 4.67568i) q^{96} +1.75577i q^{97} +(-4.19479 + 8.96681i) q^{98} +(-2.49565 + 1.67937i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42}+ \cdots + 90 q^{96}+O(q^{100}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	−0.368276	+	1.36542i	−0.260410	+	0.965498i
$2$	−0.368276	+	1.36542i	−0.260410	+	0.965498i
$3$	−1.26610	−	1.18195i	−0.730981	−	0.682398i
$3$	−1.26610	−	1.18195i	−0.730981	−	0.682398i
$4$	−1.72875	−	1.00570i	−0.864373	−	0.502851i
$5$	1.54900	+	0.894317i	0.692735	+	0.399951i	0.804636	−	0.593769i	$-0.202361\pi$
$5$	1.54900	+	0.894317i	0.692735	+	0.399951i	−0.111901	+	0.993719i	$0.535694\pi$
$6$	2.08013	−	1.29347i	0.849209	−	0.528057i
$7$	2.63573	+	0.230049i	0.996213	+	0.0869505i
$7$	2.63573	+	0.230049i	0.996213	+	0.0869505i
$8$	2.00986	−	1.99009i	0.710593	−	0.703603i
$9$	0.206000	+	2.99292i	0.0686667	+	0.997640i
$10$	−1.79158	+	1.78568i	−0.566547	+	0.564683i
$11$	0.501346	+	0.868358i	0.151162	+	0.261820i	0.931655	−	0.363345i	$-0.118365\pi$
$11$	0.501346	+	0.868358i	0.151162	+	0.261820i	−0.780493	+	0.625164i	$0.785032\pi$
$12$	1.00007	+	3.31660i	0.288696	+	0.957421i
$13$	2.47302			0.685891			0.342946	−	0.939355i	$-0.388575\pi$
$13$	2.47302			0.685891			0.342946	+	0.939355i	$0.388575\pi$
$14$	−1.28479	+	3.51416i	−0.343375	+	0.939199i
$15$	−0.904151	−	2.96313i	−0.233451	−	0.765077i
$16$	1.97713	+	3.47721i	0.494281	+	0.869302i
$17$	3.32963	+	5.76708i	0.807553	+	1.39872i	0.914554	+	0.404464i	$0.132542\pi$
$17$	3.32963	+	5.76708i	0.807553	+	1.39872i	−0.107001	+	0.994259i	$0.534125\pi$
$18$	−4.16246	−	0.820942i	−0.981101	−	0.193498i
$19$	1.85941	−	3.22059i	0.426577	−	0.738854i	−0.569989	−	0.821652i	$-0.693053\pi$
$19$	1.85941	−	3.22059i	0.426577	−	0.738854i	0.996566	+	0.0827988i	$0.0263859\pi$
$20$	−1.77842	−	3.10388i	−0.397666	−	0.694049i
$21$	−3.06518	−	3.40656i	−0.668878	−	0.743372i
$22$	−1.37031	+	0.364754i	−0.292150	+	0.0777658i
$23$	−6.85244	−	3.95626i	−1.42883	−	0.824936i	−0.431803	−	0.901968i	$-0.642123\pi$
$23$	−6.85244	−	3.95626i	−1.42883	−	0.824936i	−0.997029	+	0.0770314i	$0.975456\pi$
$24$	−4.89686	+	0.144094i	−0.999567	+	0.0294131i
$25$	−0.900394	−	1.55953i	−0.180079	−	0.311906i
$26$	−0.910752	+	3.37671i	−0.178613	+	0.662227i
$27$	3.27666	−	4.03281i	0.630593	−	0.776114i
$28$	−4.32515	−	3.04846i	−0.817376	−	0.576104i
$29$	0.748403			0.138975			0.0694875	−	0.997583i	$-0.477864\pi$
$29$	0.748403			0.138975			0.0694875	+	0.997583i	$0.477864\pi$
$30$	4.37890	−	0.143297i	0.799474	−	0.0261623i
$31$	2.87254	−	1.65846i	0.515924	−	0.297869i	−0.219341	−	0.975648i	$-0.570391\pi$
$31$	2.87254	−	1.65846i	0.515924	−	0.297869i	0.735265	+	0.677779i	$0.237058\pi$
$32$	−5.47598	+	1.41904i	−0.968025	+	0.250853i
$33$	0.391600	−	1.69199i	0.0681688	−	0.294538i
$34$	−9.10071	+	2.42246i	−1.56076	+	0.415449i
$35$	3.87702	+	2.71353i	0.655335	+	0.458670i
$36$	2.65386	−	5.38117i	0.442311	−	0.896862i
$37$	−3.22429	−	1.86155i	−0.530071	−	0.306036i	0.210975	−	0.977492i	$-0.432336\pi$
$37$	−3.22429	−	1.86155i	−0.530071	−	0.306036i	−0.741045	+	0.671455i	$0.765670\pi$
$38$	3.71268	+	3.72494i	0.602277	+	0.604265i
$39$	−3.13108	−	2.92298i	−0.501374	−	0.468051i
$40$	4.89305	−	1.28520i	0.773659	−	0.203208i
$41$	−2.01044			−0.313978			−0.156989	−	0.987600i	$-0.550179\pi$
$41$	−2.01044			−0.313978			−0.156989	+	0.987600i	$0.550179\pi$
$42$	5.78022	−	2.93071i	0.891907	−	0.452218i
$43$			9.19651i			1.40245i	0.712938	+	0.701227i	$0.247364\pi$
$43$			9.19651i			1.40245i	−0.712938	+	0.701227i	$0.752636\pi$
$44$	0.00660852	−	2.00538i	0.000996272	−	0.302322i
$45$	−2.35752	+	4.82027i	−0.351439	+	0.718563i
$46$	7.92554	−	7.89946i	1.16856	−	1.16471i
$47$	−1.19840	+	2.07569i	−0.174805	+	0.302771i	−0.940094	−	0.340916i	$-0.889263\pi$
$47$	−1.19840	+	2.07569i	−0.174805	+	0.302771i	0.765289	+	0.643687i	$0.222596\pi$
$48$	1.60665	−	6.73934i	0.231899	−	0.972740i
$49$	6.89415	+	1.21270i	0.984879	+	0.173242i
$50$	2.46101	−	0.655080i	0.348039	−	0.0926423i
$51$	2.60076	−	11.2371i	0.364179	−	1.57351i
$52$	−4.27522	−	2.48712i	−0.592866	−	0.344901i
$53$	−6.33884	−	10.9792i	−0.870707	−	1.50811i	−0.861267	−	0.508153i	$-0.830329\pi$
$53$	−6.33884	−	10.9792i	−0.870707	−	1.50811i	−0.00943963	−	0.999955i	$-0.503005\pi$
$54$	4.29976	+	5.95920i	0.585123	+	0.810944i
$55$			1.79345i			0.241829i
$56$	5.75527	−	4.78297i	0.769081	−	0.639152i
$57$	−6.16075	+	1.87985i	−0.816012	+	0.248993i
$58$	−0.275619	+	1.02188i	−0.0361905	+	0.134180i
$59$	−7.34922	+	4.24308i	−0.956787	+	0.552401i	−0.895183	−	0.445699i	$-0.852955\pi$
$59$	−7.34922	+	4.24308i	−0.956787	+	0.552401i	−0.0616046	+	0.998101i	$0.519622\pi$
$60$	−1.41698	+	6.03181i	−0.182931	+	0.778703i
$61$	−2.02442	+	3.50640i	−0.259200	+	0.448948i	−0.966028	−	0.258438i	$-0.916792\pi$
$61$	−2.02442	+	3.50640i	−0.259200	+	0.448948i	0.706828	+	0.707386i	$0.250126\pi$
$62$	1.20661	+	4.53300i	0.153240	+	0.575692i
$63$	−0.145558	+	7.93592i	−0.0183386	+	0.999832i
$64$	0.0790881	−	7.99961i	0.00988602	−	0.999951i
$65$	3.83071	+	2.21166i	0.475141	+	0.274323i
$66$	2.16606	+	1.15782i	0.266624	+	0.142517i
$67$	−6.89843	+	3.98281i	−0.842777	+	0.486577i	−0.858207	−	0.513303i	$-0.828422\pi$
$67$	−6.89843	+	3.98281i	−0.842777	+	0.486577i	0.0154303	+	0.999881i	$0.495088\pi$
$68$	0.0438896	−	13.3184i	0.00532240	−	1.61510i
$69$	3.99976	+	13.1082i	0.481514	+	1.57804i
$70$	−5.13292	+	4.29443i	−0.613501	+	0.513283i
$71$		−	5.46843i		−	0.648984i	−0.945889	−	0.324492i	$-0.894807\pi$
$71$		−	5.46843i		−	0.648984i	0.945889	−	0.324492i	$-0.105193\pi$
$72$	6.37021	+	5.60539i	0.750736	+	0.660602i
$73$	−5.68546	+	3.28250i	−0.665433	+	0.384188i	−0.794344	−	0.607468i	$-0.792185\pi$
$73$	−5.68546	+	3.28250i	−0.665433	+	0.384188i	0.128911	+	0.991656i	$0.458852\pi$
$74$	3.72922	−	3.71695i	0.433513	−	0.432087i
$75$	−0.703295	+	3.03873i	−0.0812095	+	0.350883i
$76$	−6.45340	+	3.69757i	−0.740255	+	0.424140i
$77$	1.12165	+	2.40409i	0.127824	+	0.273972i
$78$	5.14419	−	3.19878i	0.582465	−	0.362190i
$79$	2.53988	−	4.39920i	0.285759	−	0.494949i	−0.687034	−	0.726625i	$-0.741088\pi$
$79$	2.53988	−	4.39920i	0.285759	−	0.494949i	0.972793	+	0.231676i	$0.0744210\pi$
$80$	−0.0471537	+	7.15438i	−0.00527194	+	0.799884i
$81$	−8.91513	+	1.23308i	−0.990570	+	0.137009i
$82$	0.740396	−	2.74510i	0.0817631	−	0.303145i
$83$			5.65457i			0.620669i	0.950627	+	0.310335i	$0.100441\pi$
$83$			5.65457i			0.620669i	−0.950627	+	0.310335i	$0.899559\pi$
$84$	1.87294	+	8.97174i	0.204354	+	0.978897i
$85$			11.9110i			1.29193i
$86$	−12.5571	−	3.38685i	−1.35407	−	0.365213i
$87$	−0.947550	−	0.884573i	−0.101588	−	0.0948362i
$88$	2.73575	+	0.747554i	0.291632	+	0.0796896i
$89$	7.39495	−	12.8084i	0.783863	−	1.35769i	−0.145812	−	0.989312i	$-0.546580\pi$
$89$	7.39495	−	12.8084i	0.783863	−	1.35769i	0.929676	−	0.368379i	$-0.120087\pi$
$90$	−5.71347	−	4.99420i	−0.602253	−	0.526435i
$91$	6.51821	+	0.568916i	0.683294	+	0.0596386i
$92$	7.86731	+	13.7309i	0.820223	+	1.43154i
$93$	−5.59713	−	1.29542i	−0.580396	−	0.134329i
$94$	−2.39285	−	2.40075i	−0.246804	−	0.247619i
$95$	5.76045	−	3.32580i	0.591010	−	0.341220i
$96$	8.61034	+	4.67568i	0.878789	+	0.477210i
$97$			1.75577i			0.178271i	0.996019	+	0.0891356i	$0.0284105\pi$
$97$			1.75577i			0.178271i	−0.996019	+	0.0891356i	$0.971590\pi$
$98$	−4.19479	+	8.96681i	−0.423738	+	0.905785i
$99$	−2.49565	+	1.67937i	−0.250822	+	0.168783i
$100$	−0.0118686	+	3.60156i	−0.00118686	+	0.360156i
$101$	12.6803	−	7.32100i	1.26174	−	0.728467i	0.288330	−	0.957531i	$-0.406900\pi$
$101$	12.6803	−	7.32100i	1.26174	−	0.728467i	0.973411	+	0.229064i	$0.0735667\pi$
$102$	14.3856	+	7.68949i	1.42439	+	0.761373i
$103$	−8.54056	−	4.93089i	−0.841526	−	0.485855i	0.0162566	−	0.999868i	$-0.494825\pi$
$103$	−8.54056	−	4.93089i	−0.841526	−	0.485855i	−0.857783	+	0.514013i	$0.828158\pi$
$104$	4.97042	−	4.92152i	0.487390	−	0.482595i
$105$	−1.70143	−	8.01802i	−0.166043	−	0.782478i
$106$	17.3257	−	4.61181i	1.68282	−	0.447939i
$107$	−3.48110	+	6.02945i	−0.336531	+	0.582889i	−0.983778	−	0.179392i	$-0.942587\pi$
$107$	−3.48110	+	6.02945i	−0.336531	+	0.582889i	0.647247	+	0.762281i	$0.275920\pi$
$108$	−9.72031	+	3.67635i	−0.935337	+	0.353757i
$109$	2.36373	−	1.36470i	0.226404	−	0.130715i	−0.382508	−	0.923952i	$-0.624939\pi$
$109$	2.36373	−	1.36470i	0.226404	−	0.130715i	0.608912	+	0.793238i	$0.291606\pi$
$110$	−2.44881	−	0.660484i	−0.233485	−	0.0629747i
$111$	1.88202	+	6.16785i	0.178633	+	0.585426i
$112$	4.41124	+	9.61982i	0.416823	+	0.908988i
$113$			0.531154i			0.0499667i	0.999688	+	0.0249834i	$0.00795328\pi$
$113$			0.531154i			0.0499667i	−0.999688	+	0.0249834i	$0.992047\pi$
$114$	−0.297933	−	9.10432i	−0.0279040	−	0.852698i
$115$	−7.07629	−	12.2565i	−0.659868	−	1.14292i
$116$	−1.29380	−	0.752671i	−0.120126	−	0.0698837i
$117$	0.509442	+	7.40154i	0.0470979	+	0.684272i
$118$	−3.08704	−	11.5974i	−0.284185	−	1.06763i
$119$	7.44929	+	15.9665i	0.682875	+	1.46364i
$120$	−7.71411	−	4.15614i	−0.704199	−	0.379402i
$121$	4.99730	−	8.65558i	0.454300	−	0.786871i
$122$	−4.04216	−	4.05550i	−0.365960	−	0.367168i
$123$	2.54541	+	2.37623i	0.229512	+	0.214258i
$124$	−6.63382	−	0.0218611i	−0.595734	−	0.00196319i
$125$		−	12.1641i		−	1.08799i
$126$	−10.7823	−	3.12135i	−0.960560	−	0.278072i
$127$	−4.52393			−0.401434			−0.200717	−	0.979649i	$-0.564327\pi$
$127$	−4.52393			−0.401434			−0.200717	+	0.979649i	$0.564327\pi$
$128$	10.8937	+	3.05405i	0.962876	+	0.269942i
$129$	10.8698	−	11.6437i	0.957031	−	1.02517i
$130$	−4.43060	+	4.41603i	−0.388590	+	0.387311i
$131$	−13.3927	−	7.73228i	−1.17013	−	0.675573i	−0.216416	−	0.976301i	$-0.569437\pi$
$131$	−13.3927	−	7.73228i	−1.17013	−	0.675573i	−0.953710	+	0.300729i	$0.902770\pi$
$132$	−2.37862	+	2.53119i	−0.207032	+	0.220312i
$133$	5.64179	−	8.06085i	0.489205	−	0.698964i
$134$	−2.89768	−	10.8860i	−0.250322	−	0.940409i
$135$	8.68216	−	3.31646i	0.747241	−	0.285435i
$136$	18.1691	+	4.96478i	1.55799	+	0.425727i
$137$	−9.71195	+	5.60719i	−0.829748	+	0.479055i	−0.853766	−	0.520657i	$-0.825687\pi$
$137$	−9.71195	+	5.60719i	−0.829748	+	0.479055i	0.0240187	+	0.999712i	$0.492354\pi$
$138$	−19.3712	+	0.633912i	−1.64899	+	0.0539622i
$139$	17.9824			1.52525			0.762625	−	0.646840i	$-0.223910\pi$
$139$	17.9824			1.52525			0.762625	+	0.646840i	$0.223910\pi$
$140$	−3.97338	−	8.59012i	−0.335812	−	0.725998i
$141$	3.97066	−	1.21158i	0.334390	−	0.102033i
$142$	7.46671	+	2.01389i	0.626592	+	0.169002i
$143$	1.23984	+	2.14746i	0.103680	+	0.179580i
$144$	−9.99971	+	6.63368i	−0.833309	+	0.552807i
$145$	1.15928	+	0.669310i	0.0962728	+	0.0555831i
$146$	−2.38818	−	8.97191i	−0.197647	−	0.742520i
$147$	−7.29532	−	9.68392i	−0.601708	−	0.798716i
$148$	3.70182	+	6.46082i	0.304288	+	0.531076i
$149$	−0.462495	+	0.801066i	−0.0378891	+	0.0656258i	−0.884348	−	0.466828i	$-0.845397\pi$
$149$	−0.462495	+	0.801066i	−0.0378891	+	0.0656258i	0.846459	+	0.532454i	$0.178730\pi$
$150$	−3.89014	−	2.07938i	−0.317629	−	0.169781i
$151$	9.56720	+	16.5709i	0.778568	+	1.34852i	0.932767	+	0.360479i	$0.117387\pi$
$151$	9.56720	+	16.5709i	0.778568	+	1.34852i	−0.154200	+	0.988040i	$0.549280\pi$
$152$	−2.67211	−	10.1733i	−0.216736	−	0.825165i
$153$	−16.5745	+	11.1533i	−1.33997	+	0.901693i
$154$	−3.69567	+	0.646154i	−0.297806	+	0.0520686i
$155$	5.93277			0.476531
$156$	2.47319	+	8.20201i	0.198014	+	0.656687i
$157$	−5.46873	−	9.47212i	−0.436452	−	0.755957i	0.560961	−	0.827842i	$-0.310432\pi$
$157$	−5.46873	−	9.47212i	−0.436452	−	0.755957i	−0.997413	+	0.0718851i	$0.977099\pi$
$158$	5.07139	+	5.08813i	0.403458	+	0.404790i
$159$	−4.95125	+	21.3929i	−0.392659	+	1.69657i
$160$	−9.75137	−	2.69917i	−0.770914	−	0.213388i
$161$	−17.1510	−	12.0040i	−1.35169	−	0.946050i
$162$	1.59955	−	12.6270i	0.125672	−	0.992072i
$163$	−9.21188	−	5.31848i	−0.721530	−	0.416576i	0.0937855	−	0.995592i	$-0.470103\pi$
$163$	−9.21188	−	5.31848i	−0.721530	−	0.416576i	−0.815316	+	0.579017i	$0.803437\pi$
$164$	3.47554	+	2.02190i	0.271394	+	0.157884i
$165$	2.11976	−	2.27068i	0.165023	−	0.176772i
$166$	−7.72086	−	2.08244i	−0.599255	−	0.161629i
$167$	7.93040			0.613673			0.306836	−	0.951762i	$-0.400730\pi$
$167$	7.93040			0.613673			0.306836	+	0.951762i	$0.400730\pi$
$168$	−12.9400	−	0.746727i	−0.998339	−	0.0576112i
$169$	−6.88419			−0.529553
$170$	−16.2635	−	4.38652i	−1.24735	−	0.336431i
$171$	10.0220	+	4.90161i	0.766401	+	0.374836i
$172$	9.24895	−	15.8984i	0.705226	−	1.21224i
$173$	3.69882	+	2.13552i	0.281216	+	0.162360i	0.633974	−	0.773354i	$-0.281423\pi$
$173$	3.69882	+	2.13552i	0.281216	+	0.162360i	−0.352758	+	0.935715i	$0.614756\pi$
$174$	1.55677	−	0.968038i	0.118019	−	0.0733868i
$175$	−2.01443	−	4.31763i	−0.152276	−	0.326382i
$176$	−2.02823	+	3.46014i	−0.152884	+	0.260818i
$177$	14.3199	+	3.31425i	1.07635	+	0.249115i
$178$	14.7655	+	14.8143i	1.10672	+	1.11038i
$179$	3.77825	+	6.54412i	0.282399	+	0.489130i	0.971975	−	0.235083i	$-0.0755363\pi$
$179$	3.77825	+	6.54412i	0.282399	+	0.489130i	−0.689576	+	0.724214i	$0.742203\pi$
$180$	8.92331	−	5.96205i	0.665105	−	0.444385i
$181$	5.00239			0.371824			0.185912	−	0.982566i	$-0.440476\pi$
$181$	5.00239			0.371824			0.185912	+	0.982566i	$0.440476\pi$
$182$	−3.17731	+	8.69057i	−0.235518	+	0.644188i
$183$	6.70749	−	2.04668i	0.495832	−	0.151295i
$184$	−21.6458	+	5.68543i	−1.59575	+	0.419136i
$185$	−3.32963	−	5.76708i	−0.244799	−	0.424004i
$186$	3.83008	−	7.16537i	0.280835	−	0.525390i
$187$	−3.33859	+	5.78261i	−0.244142	+	0.422867i
$188$	4.15927	−	2.38311i	0.303346	−	0.173806i
$189$	9.56413	−	9.87560i	0.695688	−	0.718344i
$190$	2.41968	+	9.09025i	0.175542	+	0.659476i
$191$	−10.4891	−	6.05587i	−0.758963	−	0.438188i	0.0699601	−	0.997550i	$-0.477713\pi$
$191$	−10.4891	−	6.05587i	−0.758963	−	0.438188i	−0.828923	+	0.559362i	$0.811046\pi$
$192$	−9.55525	+	10.0348i	−0.689591	+	0.724199i
$193$	0.592437	+	1.02613i	0.0426445	+	0.0738625i	0.886560	−	0.462614i	$-0.153088\pi$
$193$	0.592437	+	1.02613i	0.0426445	+	0.0738625i	−0.843915	+	0.536476i	$0.819755\pi$
$194$	−2.39736	−	0.646607i	−0.172121	−	0.0464237i
$195$	−2.23598	−	7.32787i	−0.160122	−	0.524760i
$196$	−10.6986	−	9.02991i	−0.764188	−	0.644994i
$197$	−19.5111			−1.39011			−0.695054	−	0.718957i	$-0.744620\pi$
$197$	−19.5111			−1.39011			−0.695054	+	0.718957i	$0.744620\pi$
$198$	−1.37396	−	4.02608i	−0.0976432	−	0.286121i
$199$	−12.7632	+	7.36884i	−0.904760	+	0.522363i	−0.878741	−	0.477298i	$-0.841616\pi$
$199$	−12.7632	+	7.36884i	−0.904760	+	0.522363i	−0.0260186	+	0.999661i	$0.508283\pi$
$200$	−4.91327	−	1.34257i	−0.347421	−	0.0949341i
$201$	13.4415	+	3.11096i	0.948093	+	0.219430i
$202$	5.32638	+	20.0101i	0.374763	+	1.40791i
$203$	1.97259	+	0.172170i	0.138449	+	0.0120839i
$204$	−15.7973	+	16.8105i	−1.10603	+	1.17697i
$205$	−3.11418	−	1.79797i	−0.217503	−	0.125576i
$206$	9.87802	−	9.84552i	0.688234	−	0.685970i
$207$	10.4292	−	21.3238i	0.724876	−	1.48211i
$208$	4.88946	+	8.59919i	0.339023	+	0.596247i
$209$	3.72883			0.257929
$210$	11.5746	+	0.629671i	0.798720	+	0.0434514i
$211$		−	14.9240i		−	1.02741i	−0.857967	−	0.513704i	$-0.828273\pi$
$211$		−	14.9240i		−	1.02741i	0.857967	−	0.513704i	$-0.171727\pi$
$212$	−0.0835557	+	25.3552i	−0.00573863	+	1.74140i
$213$	−6.46340	+	6.92356i	−0.442865	+	0.474395i
$214$	−6.95073	−	6.97367i	−0.475142	−	0.476710i
$215$	−8.22459	+	14.2454i	−0.560913	+	0.971529i
$216$	−1.44002	−	14.6262i	−0.0979807	−	0.995188i
$217$	7.95278	−	3.71044i	0.539870	−	0.251881i
$218$	0.992886	+	3.73007i	0.0672467	+	0.252633i
$219$	11.0781	+	2.56395i	0.748587	+	0.173256i
$220$	1.80368	−	3.10042i	0.121604	−	0.209030i
$221$	8.23422	+	14.2621i	0.553894	+	0.959372i
$222$	−9.11480	+	0.298276i	−0.611746	+	0.0200190i
$223$			7.62187i			0.510398i	0.966889	+	0.255199i	$0.0821410\pi$
$223$			7.62187i			0.510398i	−0.966889	+	0.255199i	$0.917859\pi$
$224$	−14.7597	+	2.48045i	−0.986171	+	0.165732i
$225$	4.48206	−	3.01607i	0.298804	−	0.201071i
$226$	−0.725248	−	0.195611i	−0.0482428	−	0.0130118i
$227$	13.6531	−	7.88264i	0.906190	−	0.523189i	0.0269870	−	0.999636i	$-0.491409\pi$
$227$	13.6531	−	7.88264i	0.906190	−	0.523189i	0.879203	+	0.476446i	$0.158075\pi$
$228$	12.5410	+	2.94610i	0.830545	+	0.195110i
$229$	8.82193	−	15.2800i	0.582970	−	1.00973i	−0.412155	−	0.911114i	$-0.635224\pi$
$229$	8.82193	−	15.2800i	0.582970	−	1.00973i	0.995125	−	0.0986198i	$-0.0314428\pi$
$230$	19.3413	−	5.14835i	1.27533	−	0.339472i
$231$	1.42139	−	4.36954i	0.0935208	−	0.287495i
$232$	1.50419	−	1.48939i	0.0987547	−	0.0977832i
$233$	15.7079	+	9.06896i	1.02906	+	0.594127i	0.916715	−	0.399542i	$-0.130831\pi$
$233$	15.7079	+	9.06896i	1.02906	+	0.594127i	0.112344	+	0.993669i	$0.464164\pi$
$234$	−10.2938	−	2.03020i	−0.672928	−	0.132719i
$235$	−3.71266	+	2.14350i	−0.242187	+	0.139827i
$236$	16.9722	+	0.0559303i	1.10480	+	0.00364075i
$237$	−8.41536	+	2.56781i	−0.546637	+	0.166797i
$238$	−24.5443	+	4.29135i	−1.59097	+	0.278167i
$239$			5.41040i			0.349970i	0.984571	+	0.174985i	$0.0559877\pi$
$239$			5.41040i			0.349970i	−0.984571	+	0.174985i	$0.944012\pi$
$240$	8.51580	−	9.00240i	0.549693	−	0.581103i
$241$	−18.6025	+	10.7401i	−1.19829	+	0.691834i	−0.960174	−	0.279403i	$-0.909863\pi$
$241$	−18.6025	+	10.7401i	−1.19829	+	0.691834i	−0.238117	+	0.971236i	$0.576530\pi$
$242$	9.97813	+	10.0111i	0.641418	+	0.643535i
$243$	12.7449	+	8.97601i	0.817583	+	0.575811i
$244$	7.02610	−	4.02571i	0.449800	−	0.257719i
$245$	9.59453	+	8.04403i	0.612972	+	0.513914i
$246$	−4.18197	+	2.60045i	−0.266633	+	0.165798i
$247$	4.59834	−	7.96457i	0.292586	−	0.506773i
$248$	2.47292	−	9.04990i	0.157031	−	0.574669i
$249$	6.68340	−	7.15923i	0.423543	−	0.453698i
$250$	16.6091	+	4.47975i	1.05045	+	0.283324i
$251$			19.8553i			1.25325i	0.779319	+	0.626627i	$0.215565\pi$
$251$			19.8553i			1.25325i	−0.779319	+	0.626627i	$0.784435\pi$
$252$	8.23281	−	13.5728i	0.518618	−	0.855006i
$253$		−	7.93382i		−	0.498795i
$254$	1.66605	−	6.17707i	0.104538	−	0.387584i
$255$	14.0781	−	15.0804i	0.881607	−	0.944373i
$256$	−8.18195	+	13.7498i	−0.511372	+	0.859360i
$257$	4.36616	−	7.56240i	0.272353	−	0.471730i	−0.697111	−	0.716964i	$-0.745531\pi$
$257$	4.36616	−	7.56240i	0.272353	−	0.471730i	0.969464	+	0.245234i	$0.0788647\pi$
$258$	11.8954	+	19.1299i	0.740576	+	1.19098i
$259$	−8.07012	−	5.64828i	−0.501453	−	0.350967i
$260$	−4.39805	−	7.67595i	−0.272755	−	0.476042i
$261$	0.154171	+	2.23991i	0.00954295	+	0.138647i
$262$	15.4900	−	15.4391i	0.956977	−	0.953828i
$263$	17.1429	−	9.89747i	1.05708	−	0.610304i	0.132455	−	0.991189i	$-0.457714\pi$
$263$	17.1429	−	9.89747i	1.05708	−	0.610304i	0.924623	+	0.380885i	$0.124381\pi$
$264$	−2.58015	−	4.17998i	−0.158797	−	0.257260i
$265$		−	22.6757i		−	1.39296i
$266$	8.92871	+	10.6720i	0.547454	+	0.654344i
$267$	−24.5016	+	7.47627i	−1.49947	+	0.457540i
$268$	15.9311	+	0.0524996i	0.973150	+	0.00320692i
$269$	−0.805574	+	0.465098i	−0.0491167	+	0.0283575i	−0.524357	−	0.851498i	$-0.675694\pi$
$269$	−0.805574	+	0.465098i	−0.0491167	+	0.0283575i	0.475241	+	0.879856i	$0.342361\pi$
$270$	1.33093	+	13.0762i	0.0809977	+	0.795790i
$271$	−7.45646	−	4.30499i	−0.452948	−	0.261509i	0.256127	−	0.966643i	$-0.417554\pi$
$271$	−7.45646	−	4.30499i	−0.452948	−	0.261509i	−0.709074	+	0.705134i	$0.750887\pi$
$272$	−13.4703	+	22.9801i	−0.816754	+	1.39337i
$273$	−7.58025	−	8.42448i	−0.458777	−	0.509873i
$274$	−4.07950	−	15.3259i	−0.246452	−	0.925870i
$275$	0.902819	−	1.56373i	0.0544420	−	0.0942964i
$276$	6.26840	−	26.6834i	0.377314	−	1.60615i
$277$	−25.5583	+	14.7561i	−1.53565	+	0.886607i	−0.536562	+	0.843861i	$0.680277\pi$
$277$	−25.5583	+	14.7561i	−1.53565	+	0.886607i	−0.999086	+	0.0427456i	$0.986390\pi$
$278$	−6.62250	+	24.5536i	−0.397191	+	1.47263i
$279$	5.55539	+	8.25565i	0.332593	+	0.494253i
$280$	13.1924	−	2.26180i	0.788398	−	0.135168i
$281$			21.3260i			1.27220i	0.771605	+	0.636102i	$0.219454\pi$
$281$			21.3260i			1.27220i	−0.771605	+	0.636102i	$0.780546\pi$
$282$	0.192020	+	5.86781i	0.0114346	+	0.349423i
$283$	10.4247	+	18.0561i	0.619684	+	1.07332i	0.989543	+	0.144236i	$0.0460724\pi$
$283$	10.4247	+	18.0561i	0.619684	+	1.07332i	−0.369860	+	0.929088i	$0.620594\pi$
$284$	−5.49962	+	9.45353i	−0.326342	+	0.560964i
$285$	−11.2242	−	2.59777i	−0.664865	−	0.153879i
$286$	−3.38879	+	0.902042i	−0.200383	+	0.0533389i
$287$	−5.29898	−	0.462500i	−0.312789	−	0.0273005i
$288$	−5.37511	−	16.0968i	−0.316732	−	0.948515i
$289$	−13.6728	+	23.6820i	−0.804284	+	1.39306i
$290$	−1.34082	+	1.33641i	−0.0787358	+	0.0784768i
$291$	2.07523	−	2.22297i	0.121652	−	0.130313i
$292$	13.1299	+	0.0432684i	0.768371	+	0.00253209i
$293$		−	13.1058i		−	0.765652i	−0.923821	−	0.382826i	$-0.874951\pi$
$293$		−	13.1058i		−	0.765652i	0.923821	−	0.382826i	$-0.125049\pi$
$294$	15.9093	−	6.39483i	0.927850	−	0.372954i
$295$	−15.1786			−0.883733
$296$	−10.1850	+	2.67518i	−0.591993	+	0.155492i
$297$	5.14466	+	0.823477i	0.298523	+	0.0477830i
$298$	−0.923465	−	0.926514i	−0.0534949	−	0.0536715i
$299$	−16.9462	−	9.78389i	−0.980023	−	0.565817i
$300$	4.27188	−	4.54589i	0.246637	−	0.262457i
$301$	−2.11565	+	24.2395i	−0.121944	+	1.39714i
$302$	−26.1496	+	6.96060i	−1.50474	+	0.400537i
$303$	−24.7076	−	5.71841i	−1.41941	−	0.328514i
$304$	14.8749	+	0.0980389i	0.853136	+	0.00562292i
$305$	−6.27166	+	3.62094i	−0.359114	+	0.207335i
$306$	−9.12499	−	26.7387i	−0.521641	−	1.52855i
$307$	−18.6425			−1.06398			−0.531992	−	0.846750i	$-0.678556\pi$
$307$	−18.6425			−1.06398			−0.531992	+	0.846750i	$0.678556\pi$
$308$	0.478754	−	5.28411i	0.0272795	−	0.301090i
$309$	4.98511	+	16.3375i	0.283593	+	0.929406i
$310$	−2.18489	+	8.10072i	−0.124094	+	0.460090i
$311$	−9.92896	−	17.1975i	−0.563020	−	0.975179i	−0.997231	−	0.0743677i	$-0.976306\pi$
$311$	−9.92896	−	17.1975i	−0.563020	−	0.975179i	0.434211	−	0.900811i	$-0.357027\pi$
$312$	−12.1100	+	0.356347i	−0.685595	+	0.0201742i
$313$	2.33108	+	1.34585i	0.131760	+	0.0760718i	0.564431	−	0.825480i	$-0.309096\pi$
$313$	2.33108	+	1.34585i	0.131760	+	0.0760718i	−0.432671	+	0.901552i	$0.642429\pi$
$314$	14.9474	−	3.97876i	0.843532	−	0.224535i
$315$	−7.32270	+	12.1626i	−0.412587	+	0.685284i
$316$	−8.81510	+	5.05074i	−0.495888	+	0.284126i
$317$	−5.35288	+	9.27147i	−0.300648	+	0.520737i	−0.976283	−	0.216499i	$-0.930536\pi$
$317$	−5.35288	+	9.27147i	−0.300648	+	0.520737i	0.675635	+	0.737236i	$0.263870\pi$
$318$	−27.3869	−	14.6390i	−1.53578	−	0.820915i
$319$	0.375209	+	0.649881i	0.0210077	+	0.0363864i
$320$	7.27669	−	12.3207i	0.406780	−	0.688747i
$321$	11.5339	−	3.51938i	0.643760	−	0.196433i
$322$	22.7069	−	18.9976i	1.26540	−	1.05869i
$323$	24.7645			1.37794
$324$	16.6521	+	6.83428i	0.925117	+	0.379682i
$325$	−2.22669	−	3.85674i	−0.123514	−	0.213933i
$326$	10.6545	−	10.6194i	0.590097	−	0.588155i
$327$	−4.60572	−	1.06596i	−0.254697	−	0.0589479i
$328$	−4.04071	+	4.00095i	−0.223111	+	0.220916i
$329$	−3.63618	+	5.19528i	−0.200469	+	0.286425i
$330$	2.31978	+	3.73061i	0.127700	+	0.205363i
$331$	18.8525	+	10.8845i	1.03623	+	0.598266i	0.918762	−	0.394811i	$-0.129190\pi$
$331$	18.8525	+	10.8845i	1.03623	+	0.598266i	0.117465	+	0.993077i	$0.462523\pi$
$332$	5.68681	−	9.77531i	0.312104	−	0.536490i
$333$	4.90725	−	10.0335i	0.268916	−	0.549834i
$334$	−2.92057	+	10.8283i	−0.159807	+	0.592500i
$335$	−14.2476			−0.778428
$336$	5.78507	−	17.3935i	0.315601	−	0.948892i
$337$	−11.3104			−0.616116			−0.308058	−	0.951368i	$-0.599679\pi$
$337$	−11.3104			−0.616116			−0.308058	+	0.951368i	$0.599679\pi$
$338$	2.53528	−	9.39982i	0.137901	−	0.511283i
$339$	0.627796	−	0.672492i	0.0340972	−	0.0365247i
$340$	11.9789	−	20.5910i	0.649646	−	1.11671i
$341$	2.88028	+	1.66293i	0.155976	+	0.0900527i
$342$	−10.3836	+	11.8791i	−0.561482	+	0.642348i
$343$	17.8922	+	4.78234i	0.966086	+	0.258222i
$344$	18.3019	+	18.4837i	0.986771	+	0.996575i
$345$	−5.52727	+	23.8817i	−0.297578	+	1.28575i
$346$	−4.27806	+	4.26399i	−0.229990	+	0.229233i
$347$	−9.94032	−	17.2171i	−0.533624	−	0.924265i	−0.999229	−	0.0392715i	$-0.987496\pi$
$347$	−9.94032	−	17.2171i	−0.533624	−	0.924265i	0.465604	−	0.884993i	$-0.345837\pi$
$348$	0.748457	+	2.48216i	0.0401215	+	0.133058i
$349$	9.45348			0.506033			0.253017	−	0.967462i	$-0.418577\pi$
$349$	9.45348			0.506033			0.253017	+	0.967462i	$0.418577\pi$
$350$	6.63725	−	1.16046i	0.354776	−	0.0620293i
$351$	8.10323	−	9.97319i	0.432518	−	0.532330i
$352$	−3.97759	−	4.04368i	−0.212006	−	0.215529i
$353$	8.48135	+	14.6901i	0.451417	+	0.781877i	0.998474	−	0.0552182i	$-0.0175854\pi$
$353$	8.48135	+	14.6901i	0.451417	+	0.781877i	−0.547057	+	0.837095i	$0.684252\pi$
$354$	−9.79903	+	18.3322i	−0.520812	+	0.974343i
$355$	4.89051	−	8.47062i	0.259561	−	0.449574i
$356$	−25.6655	+	14.7054i	−1.36027	+	0.779385i
$357$	9.44000	−	29.0197i	0.499618	−	1.53589i
$358$	−10.3269	+	2.74886i	−0.545794	+	0.145282i
$359$	−18.2162	−	10.5171i	−0.961413	−	0.555072i	−0.0648056	−	0.997898i	$-0.520643\pi$
$359$	−18.2162	−	10.5171i	−0.961413	−	0.555072i	−0.896608	+	0.442826i	$0.853976\pi$
$360$	4.85447	+	14.3798i	0.255853	+	0.757880i
$361$	2.58521	+	4.47771i	0.136064	+	0.235669i
$362$	−1.84226	+	6.83036i	−0.0968269	+	0.358996i
$363$	−16.5575	+	5.05225i	−0.869044	+	0.265174i
$364$	−10.6962	−	7.53889i	−0.560631	−	0.395145i
$365$	−11.7424			−0.614625
$366$	0.324373	+	9.91228i	0.0169553	+	0.518123i
$367$	1.24875	−	0.720966i	0.0651842	−	0.0376341i	−0.467054	−	0.884229i	$-0.654685\pi$
$367$	1.24875	−	0.720966i	0.0651842	−	0.0376341i	0.532238	+	0.846595i	$0.321351\pi$
$368$	0.208597	−	31.6494i	0.0108739	−	1.64984i
$369$	−0.414151	−	6.01708i	−0.0215598	−	0.313237i
$370$	9.10071	−	2.42246i	0.473124	−	0.125938i
$371$	−14.1817	−	30.3964i	−0.736278	−	1.57810i
$372$	8.37321	+	7.86850i	0.434131	+	0.407963i
$373$	18.8362	+	10.8751i	0.975302	+	0.563091i	0.900848	−	0.434134i	$-0.142945\pi$
$373$	18.8362	+	10.8751i	0.975302	+	0.563091i	0.0744535	+	0.997224i	$0.476279\pi$
$374$	−6.66618	−	6.68818i	−0.344700	−	0.345838i
$375$	−14.3774	+	15.4010i	−0.742443	+	0.795302i
$376$	1.72219	+	6.55679i	0.0888154	+	0.338141i
$377$	1.85081			0.0953217
$378$	9.96210	+	16.6960i	0.512395	+	0.858750i
$379$			1.82298i			0.0936402i	0.998903	+	0.0468201i	$0.0149087\pi$
$379$			1.82298i			0.0936402i	−0.998903	+	0.0468201i	$0.985091\pi$
$380$	−13.3031	−	0.0438392i	−0.682436	−	0.00224890i
$381$	5.72774	+	5.34705i	0.293441	+	0.273938i
$382$	12.1317	−	12.0918i	0.620711	−	0.618669i
$383$	4.81069	−	8.33236i	0.245815	−	0.425763i	−0.716546	−	0.697540i	$-0.754278\pi$
$383$	4.81069	−	8.33236i	0.245815	−	0.425763i	0.962360	+	0.271777i	$0.0876112\pi$
$384$	−10.1828	−	16.7425i	−0.519636	−	0.854388i
$385$	−0.412582	+	4.72705i	−0.0210271	+	0.240913i
$386$	−1.61928	+	0.431026i	−0.0824192	+	0.0219387i
$387$	−27.5244	+	1.89448i	−1.39914	+	0.0963019i
$388$	1.76578	−	3.03528i	0.0896439	−	0.154093i
$389$	14.0629	+	24.3576i	0.713017	+	1.23498i	0.963719	+	0.266917i	$0.0860050\pi$
$389$	14.0629	+	24.3576i	0.713017	+	1.23498i	−0.250703	+	0.968064i	$0.580662\pi$
$390$	10.8291	−	0.354375i	0.548352	−	0.0179445i
$391$		−	52.6914i		−	2.66472i
$392$	16.2697	−	11.2826i	0.821743	−	0.569859i
$393$	7.81730	+	25.6193i	0.394331	+	1.29232i
$394$	7.18546	−	26.6409i	0.361998	−	1.34215i
$395$	7.86857	−	4.54292i	0.395911	−	0.228579i
$396$	6.00329	−	0.393329i	0.301676	−	0.0197655i
$397$	−9.42646	+	16.3271i	−0.473101	+	0.819434i	−0.999526	−	0.0307871i	$-0.990199\pi$
$397$	−9.42646	+	16.3271i	−0.473101	+	0.819434i	0.526425	+	0.850221i	$0.323532\pi$
$398$	−5.36119	−	20.1409i	−0.268732	−	1.00957i
$399$	−16.6706	+	3.53751i	−0.834571	+	0.177097i
$400$	3.64261	−	6.21424i	0.182131	−	0.310712i
$401$	5.22718	+	3.01791i	0.261033	+	0.150707i	0.624806	−	0.780780i	$-0.285178\pi$
$401$	5.22718	+	3.01791i	0.261033	+	0.150707i	−0.363773	+	0.931488i	$0.618512\pi$
$402$	−9.19796	+	17.2077i	−0.458753	+	0.858240i
$403$	7.10385	−	4.10141i	0.353868	−	0.204306i
$404$	−29.2838	−	0.0965021i	−1.45693	−	0.00480116i
$405$	−14.9123	−	6.06290i	−0.740999	−	0.301268i
$406$	−0.961541	+	2.63001i	−0.0477205	+	0.130525i
$407$		−	3.73312i		−	0.185044i
$408$	−17.1357	−	27.7608i	−0.848344	−	1.37437i
$409$	22.6629	−	13.0844i	1.12061	−	0.646984i	0.179052	−	0.983840i	$-0.442697\pi$
$409$	22.6629	−	13.0844i	1.12061	−	0.646984i	0.941556	+	0.336856i	$0.109364\pi$
$410$	3.60186	−	3.59001i	0.177883	−	0.177298i
$411$	18.9237	+	4.37976i	0.933436	+	0.216038i
$412$	9.80544	+	17.1135i	0.483080	+	0.843123i
$413$	−20.3467	+	9.49292i	−1.00120	+	0.467116i
$414$	25.2751	+	22.0932i	1.24220	+	1.08582i
$415$	−5.05698	+	8.75894i	−0.248237	+	0.429959i
$416$	−13.5422	+	3.50930i	−0.663960	+	0.172058i
$417$	−22.7675	−	21.2543i	−1.11493	−	1.04083i
$418$	−1.37324	+	5.09142i	−0.0671672	+	0.249029i
$419$		−	2.51866i		−	0.123045i	−0.998106	−	0.0615223i	$-0.980404\pi$
$419$		−	2.51866i		−	0.123045i	0.998106	−	0.0615223i	$-0.0195955\pi$
$420$	−5.12239	+	15.5722i	−0.249947	+	0.759848i
$421$		−	33.4873i		−	1.63207i	−0.578003	−	0.816034i	$-0.696168\pi$
$421$		−	33.4873i		−	1.63207i	0.578003	−	0.816034i	$-0.303832\pi$
$422$	20.3775	+	5.49614i	0.991961	+	0.267548i
$423$	−6.45926	−	3.15913i	−0.314060	−	0.153602i
$424$	−34.5898	−	9.45180i	−1.67983	−	0.459020i
$425$	5.99595	−	10.3853i	0.290846	−	0.503761i
$426$	−7.07326	−	11.3750i	−0.342701	−	0.551123i
$427$	−6.14247	+	8.77620i	−0.297255	+	0.424710i
$428$	12.0818	−	6.92243i	0.583995	−	0.334608i
$429$	0.968433	−	4.18432i	0.0467564	−	0.202021i
$430$	−16.4221	−	16.4763i	−0.791942	−	0.794556i
$431$	12.0003	−	6.92836i	0.578033	−	0.333727i	−0.182319	−	0.983240i	$-0.558360\pi$
$431$	12.0003	−	6.92836i	0.578033	−	0.333727i	0.760351	+	0.649512i	$0.225027\pi$
$432$	20.5013	+	3.42026i	0.986368	+	0.164557i
$433$			9.79368i			0.470654i	0.971916	+	0.235327i	$0.0756161\pi$
$433$			9.79368i			0.470654i	−0.971916	+	0.235327i	$0.924384\pi$
$434$	2.13749	+	12.2254i	0.102603	+	0.586836i
$435$	−0.676669	−	2.21762i	−0.0324438	−	0.106327i
$436$	−5.45878	−	0.0179889i	−0.261428	−	0.000861511i
$437$	−25.4829	+	14.7126i	−1.21901	+	0.703798i
$438$	−7.58066	+	14.1820i	−0.362218	+	0.677642i
$439$	6.99463	+	4.03835i	0.333835	+	0.192740i	0.657543	−	0.753417i	$-0.271596\pi$
$439$	6.99463	+	4.03835i	0.333835	+	0.192740i	−0.323707	+	0.946157i	$0.604929\pi$
$440$	3.56913	+	3.60459i	0.170151	+	0.171842i
$441$	−2.20931	+	20.8835i	−0.105205	+	0.994451i
$442$	−22.5062	+	5.99079i	−1.07051	+	0.284953i
$443$	8.84884	−	15.3266i	0.420421	−	0.728191i	−0.575559	−	0.817760i	$-0.695216\pi$
$443$	8.84884	−	15.3266i	0.420421	−	0.728191i	0.995981	+	0.0895692i	$0.0285490\pi$
$444$	2.94949	−	12.5554i	0.139977	−	0.595852i
$445$	22.9096	−	13.2269i	1.08602	−	0.627014i
$446$	−10.4071	−	2.80695i	−0.492788	−	0.132913i
$447$	1.53238	−	0.467581i	0.0724791	−	0.0221158i
$448$	2.04876	−	21.0666i	0.0967948	−	0.995304i
$449$		−	19.4650i		−	0.918609i	−0.888279	−	0.459305i	$-0.848099\pi$
$449$		−	19.4650i		−	0.918609i	0.888279	−	0.459305i	$-0.151901\pi$
$450$	2.46757	+	7.23064i	0.116322	+	0.340856i
$451$	−1.00793	−	1.74578i	−0.0474614	−	0.0822056i
$452$	0.534182	−	0.918230i	0.0251258	−	0.0431899i
$453$	7.47291	−	32.2882i	0.351108	−	1.51703i
$454$	5.73500	+	21.5453i	0.269157	+	1.01117i
$455$	9.58793	+	6.71059i	0.449489	+	0.314597i
$456$	−8.64119	+	16.0387i	−0.404661	+	0.751081i
$457$	7.75626	−	13.4342i	0.362823	−	0.628427i	−0.625601	−	0.780143i	$-0.715146\pi$
$457$	7.75626	−	13.4342i	0.362823	−	0.628427i	0.988424	+	0.151715i	$0.0484797\pi$
$458$	17.6148	+	17.6729i	0.823084	+	0.825801i
$459$	34.1676	+	5.46902i	1.59481	+	0.255272i
$460$	−0.0932765	+	28.3050i	−0.00434904	+	1.31973i
$461$			0.857290i			0.0399280i	0.999801	+	0.0199640i	$0.00635516\pi$
$461$			0.857290i			0.0399280i	−0.999801	+	0.0199640i	$0.993645\pi$
$462$	5.44280	+	3.55000i	0.253222	+	0.165161i
$463$	37.5731			1.74617			0.873086	−	0.487566i	$-0.162115\pi$
$463$	37.5731			1.74617			0.873086	+	0.487566i	$0.162115\pi$
$464$	1.47969	+	2.60235i	0.0686927	+	0.120811i
$465$	−7.51146	−	7.01222i	−0.348335	−	0.325184i
$466$	−18.1678	+	18.1080i	−0.841606	+	0.838837i
$467$	8.69155	+	5.01807i	0.402197	+	0.232208i	0.687431	−	0.726249i	$-0.258738\pi$
$467$	8.69155	+	5.01807i	0.402197	+	0.232208i	−0.285235	+	0.958458i	$0.592072\pi$
$468$	6.56305	−	13.3077i	0.303377	−	0.615150i
$469$	−19.0986	+	8.91063i	−0.881893	+	0.411455i
$470$	−1.55950	−	5.85874i	−0.0719345	−	0.270244i
$471$	−4.27161	+	18.4564i	−0.196825	+	0.850424i
$472$	−6.32682	+	23.1536i	−0.291216	+	1.06573i
$473$	−7.98586	+	4.61064i	−0.367190	+	0.211997i
$474$	−0.406966	−	12.4362i	−0.0186926	−	0.571212i
$475$	−6.69680			−0.307270
$476$	3.17958	−	35.0937i	0.145736	−	1.60852i
$477$	31.5540	−	21.2333i	1.44476	−	0.972208i
$478$	−7.38747	−	1.99252i	−0.337895	−	0.0911357i
$479$	11.0594	+	19.1555i	0.505318	+	0.875237i	0.999981	+	0.00615194i	$0.00195824\pi$
$479$	11.0594	+	19.1555i	0.505318	+	0.875237i	−0.494663	+	0.869085i	$0.664708\pi$
$480$	9.15590	+	14.9430i	0.417908	+	0.682052i
$481$	−7.97373	−	4.60364i	−0.363571	−	0.209908i
$482$	−7.81397	−	29.3555i	−0.355917	−	1.33711i
$483$	7.52675	+	35.4699i	0.342479	+	1.61394i
$484$	−17.3440	+	9.93751i	−0.788364	+	0.451705i
$485$	−1.57021	+	2.71969i	−0.0712997	+	0.123495i
$486$	−16.9496	+	14.0964i	−0.768852	+	0.639427i
$487$	11.2659	+	19.5131i	0.510506	+	0.884223i	0.999926	+	0.0121746i	$0.00387541\pi$
$487$	11.2659	+	19.5131i	0.510506	+	0.884223i	−0.489419	+	0.872049i	$0.662791\pi$
$488$	2.90924	+	11.0761i	0.131695	+	0.501394i
$489$	5.37696	+	17.6217i	0.243155	+	0.796879i
$490$	−14.5169	+	10.1381i	−0.655807	+	0.457995i
$491$	25.1085			1.13313			0.566565	−	0.824017i	$-0.308272\pi$
$491$	25.1085			1.13313			0.566565	+	0.824017i	$0.308272\pi$
$492$	−2.01058	−	6.66783i	−0.0906441	−	0.300609i
$493$	2.49190	+	4.31610i	0.112230	+	0.194387i
$494$	9.18152	+	9.21183i	0.413096	+	0.414460i
$495$	−5.36765	+	0.369451i	−0.241258	+	0.0166056i
$496$	11.4462	+	6.70944i	0.513950	+	0.301263i
$497$	1.25801	−	14.4133i	0.0564295	−	0.646526i
$498$	7.31402	+	11.7622i	0.327749	+	0.527078i
$499$	9.19695	+	5.30986i	0.411712	+	0.237702i	0.691525	−	0.722353i	$-0.256939\pi$
$499$	9.19695	+	5.30986i	0.411712	+	0.237702i	−0.279813	+	0.960054i	$0.590273\pi$
$500$	−12.2335	+	21.0287i	−0.547098	+	0.940431i
$501$	−10.0407	−	9.37332i	−0.448583	−	0.418769i
$502$	−27.1108	−	7.31222i	−1.21001	−	0.326360i
$503$	13.3046			0.593223			0.296612	−	0.954998i	$-0.404143\pi$
$503$	13.3046			0.593223			0.296612	+	0.954998i	$0.404143\pi$
$504$	15.5006	+	16.2398i	0.690453	+	0.723377i
$505$	26.1892			1.16540
$506$	10.8330	+	2.92183i	0.481586	+	0.129891i
$507$	8.71605	+	8.13675i	0.387093	+	0.361366i
$508$	7.82073	+	4.54973i	0.346989	+	0.201862i
$509$	20.2595	+	11.6968i	0.897985	+	0.518452i	0.876546	−	0.481318i	$-0.159842\pi$
$509$	20.2595	+	11.6968i	0.897985	+	0.518452i	0.0214392	+	0.999770i	$0.493175\pi$
$510$	15.4065	+	24.7763i	0.682211	+	1.09711i
$511$	−15.7405	+	7.34385i	−0.696318	+	0.324873i
$512$	−15.7610	−	16.2355i	−0.696544	−	0.717515i
$513$	−6.89536	−	18.0514i	−0.304438	−	0.796988i
$514$	8.71791	+	8.74669i	0.384531	+	0.385800i
$515$	−8.81956	−	15.2759i	−0.388636	−	0.673138i
$516$	−30.5012	+	9.19717i	−1.34274	+	0.404883i
$517$	−2.40326			−0.105695
$518$	10.6843	−	8.93899i	0.469442	−	0.392757i
$519$	−2.15900	−	7.07558i	−0.0947695	−	0.310584i
$520$	12.1006	−	3.17832i	0.530646	−	0.139379i
$521$	−0.735700	−	1.27427i	−0.0322316	−	0.0558267i	0.849460	−	0.527654i	$-0.176928\pi$
$521$	−0.735700	−	1.27427i	−0.0322316	−	0.0558267i	−0.881691	+	0.471827i	$0.843595\pi$
$522$	−3.11520	−	0.614396i	−0.136348	−	0.0268914i
$523$	5.30372	−	9.18631i	0.231915	−	0.401689i	−0.726456	−	0.687213i	$-0.758834\pi$
$523$	5.30372	−	9.18631i	0.231915	−	0.401689i	0.958372	+	0.285523i	$0.0921674\pi$
$524$	15.3762	+	26.8362i	0.671713	+	1.17235i
$525$	−2.55275	+	7.84749i	−0.111411	+	0.342492i
$526$	7.20089	+	27.0523i	0.313974	+	1.17954i
$527$	19.1290	+	11.0441i	0.833272	+	0.481090i
$528$	6.65764	−	1.98360i	0.289737	−	0.0863252i
$529$	19.8039	+	34.3014i	0.861040	+	1.49137i
$530$	30.9619	+	8.35092i	1.34490	+	0.362741i
$531$	−14.2131	−	21.1216i	−0.616797	−	0.916597i
$532$	−17.8600	+	8.26119i	−0.774331	+	0.358168i
$533$	−4.97185			−0.215355
$534$	−1.18490	−	36.2083i	−0.0512754	−	1.56689i
$535$	−10.7845	+	6.22642i	−0.466254	+	0.269192i
$536$	−5.93874	+	21.7334i	−0.256514	+	0.938739i
$537$	2.95118	−	12.7512i	0.127353	−	0.550254i
$538$	−0.338381	−	1.27123i	−0.0145887	−	0.0548067i
$539$	2.40331	+	6.59457i	0.103518	+	0.284048i
$540$	−18.3446	−	2.99836i	−0.789426	−	0.129029i
$541$	−14.0009	−	8.08343i	−0.601946	−	0.347534i	0.167861	−	0.985811i	$-0.446314\pi$
$541$	−14.0009	−	8.08343i	−0.601946	−	0.347534i	−0.769807	+	0.638277i	$0.779647\pi$
$542$	8.62415	−	8.59578i	0.370439	−	0.369220i
$543$	−6.33350	−	5.91256i	−0.271797	−	0.253732i
$544$	−26.4167	−	26.8556i	−1.13261	−	1.15142i
$545$	4.88190			0.209118
$546$	14.2946	−	7.24769i	0.611751	−	0.310173i
$547$		−	12.4170i		−	0.530914i	−0.964123	−	0.265457i	$-0.914477\pi$
$547$		−	12.4170i		−	0.530914i	0.964123	−	0.265457i	$-0.0855228\pi$
$548$	22.4287	+	0.0739115i	0.958105	+	0.00315734i
$549$	−10.9114	−	5.33660i	−0.465687	−	0.227761i
$550$	1.80266	+	1.80861i	0.0768657	+	0.0771194i
$551$	1.39159	−	2.41030i	0.0592836	−	0.102682i
$552$	34.1255	+	18.3858i	1.45248	+	0.782553i
$553$	7.70648	−	11.0108i	0.327713	−	0.468228i
$554$	−10.7358	−	40.3321i	−0.456119	−	1.71355i
$555$	−2.60076	+	11.2371i	−0.110396	+	0.476989i
$556$	−31.0871	−	18.0850i	−1.31839	−	0.766974i
$557$	−10.7167	−	18.5619i	−0.454081	−	0.786492i	0.544554	−	0.838726i	$-0.316699\pi$
$557$	−10.7167	−	18.5619i	−0.454081	−	0.786492i	−0.998635	+	0.0522341i	$0.983366\pi$
$558$	−13.3183	+	4.54509i	−0.563810	+	0.192409i
$559$			22.7431i			0.961931i
$560$	−1.77015	+	18.8462i	−0.0748023	+	0.796396i
$561$	11.0617	−	3.37530i	0.467026	−	0.142505i
$562$	−29.1190	−	7.85385i	−1.22831	−	0.331295i
$563$	−17.9430	+	10.3594i	−0.756205	+	0.436595i	−0.827932	−	0.560829i	$-0.810483\pi$
$563$	−17.9430	+	10.3594i	−0.756205	+	0.436595i	0.0717262	+	0.997424i	$0.477149\pi$
$564$	−8.08274	−	1.89878i	−0.340345	−	0.0799532i
$565$	−0.475020	+	0.822758i	−0.0199842	+	0.0346137i
$566$	−28.4933	+	7.58447i	−1.19766	+	0.318799i
$567$	−23.7815	+	1.19916i	−0.998731	+	0.0503598i
$568$	−10.8827	−	10.9908i	−0.456627	−	0.461164i
$569$	−23.8691	−	13.7808i	−1.00064	−	0.577722i	−0.0922056	−	0.995740i	$-0.529392\pi$
$569$	−23.8691	−	13.7808i	−1.00064	−	0.577722i	−0.908439	+	0.418018i	$0.862725\pi$
$570$	7.68065	−	14.3691i	0.321707	−	0.601854i
$571$	−0.339940	+	0.196264i	−0.0142260	+	0.00821340i	−0.507096	−	0.861889i	$-0.669281\pi$
$571$	−0.339940	+	0.196264i	−0.0142260	+	0.00821340i	0.492870	+	0.870103i	$0.335948\pi$
$572$	0.0163430	−	4.95933i	0.000683334	−	0.207360i
$573$	6.12246	+	20.0649i	0.255770	+	0.838222i
$574$	2.58299	−	7.06500i	0.107812	−	0.294888i
$575$			14.2488i			0.594214i
$576$	23.9585	−	1.41122i	0.998270	−	0.0588007i
$577$	−12.7927	+	7.38589i	−0.532569	+	0.307479i	−0.742062	−	0.670331i	$-0.766152\pi$
$577$	−12.7927	+	7.38589i	−0.532569	+	0.307479i	0.209493	+	0.977810i	$0.432819\pi$
$578$	−27.3006	−	27.3907i	−1.13555	−	1.13930i
$579$	0.462751	−	1.99941i	0.0192313	−	0.0830926i
$580$	−1.33097	−	2.32296i	−0.0552656	−	0.0964555i
$581$	−1.30083	+	14.9039i	−0.0539675	+	0.618319i
$582$	2.27104	+	3.65222i	0.0941375	+	0.151389i
$583$	6.35591	−	11.0088i	0.263235	−	0.455936i
$584$	−4.89452	+	17.9119i	−0.202536	+	0.741202i
$585$	−5.83019	+	11.9206i	−0.241049	+	0.492856i
$586$	17.8950	+	4.82656i	0.739235	+	0.199384i
$587$		−	3.51421i		−	0.145047i	−0.997367	−	0.0725236i	$-0.976895\pi$
$587$		−	3.51421i		−	0.145047i	0.997367	−	0.0725236i	$-0.0231052\pi$
$588$	2.87262	+	24.0780i	0.118465	+	0.992958i
$589$		−	12.3350i		−	0.508256i
$590$	5.58992	−	20.7252i	0.230133	−	0.853243i
$591$	24.7029	+	23.0611i	1.01614	+	0.948607i
$592$	0.0981518	−	14.8921i	0.00403401	−	0.612060i
$593$	−17.8824	+	30.9732i	−0.734342	+	1.27192i	0.220670	+	0.975349i	$0.429176\pi$
$593$	−17.8824	+	30.9732i	−0.734342	+	1.27192i	−0.955012	+	0.296568i	$0.904158\pi$
$594$	−3.01905	+	6.72135i	−0.123873	+	0.275781i
$595$	−2.74011	+	31.3941i	−0.112334	+	1.28703i
$596$	1.60517	−	0.919706i	0.0657504	−	0.0376726i
$597$	24.8690	+	5.75578i	1.01782	+	0.235568i
$598$	19.6000	−	19.5355i	0.801503	−	0.798866i
$599$	−35.4819	+	20.4855i	−1.44975	+	0.837014i	−0.998466	−	0.0553669i	$-0.982367\pi$
$599$	−35.4819	+	20.4855i	−1.44975	+	0.837014i	−0.451284	+	0.892380i	$0.649034\pi$
$600$	4.63382	+	7.50705i	0.189175	+	0.306474i
$601$		−	36.1540i		−	1.47475i	−0.675482	−	0.737377i	$-0.736064\pi$
$601$		−	36.1540i		−	1.47475i	0.675482	−	0.737377i	$-0.263936\pi$
$602$	−32.3180	−	11.8156i	−1.31718	−	0.481567i
$603$	−13.3413	−	19.8260i	−0.543300	−	0.807376i
$604$	0.126110	−	38.2686i	0.00513136	−	1.55713i
$605$	15.4817	−	8.93835i	0.629419	−	0.363395i
$606$	16.9072	−	31.6303i	0.686809	−	1.28489i
$607$	9.04038	+	5.21946i	0.366938	+	0.211851i	0.672120	−	0.740443i	$-0.265384\pi$
$607$	9.04038	+	5.21946i	0.366938	+	0.211851i	−0.305182	+	0.952294i	$0.598717\pi$
$608$	−5.61194	+	20.2744i	−0.227594	+	0.822237i
$609$	−2.29399	−	2.54948i	−0.0929573	−	0.103310i
$610$	−2.63441	−	9.89696i	−0.106664	−	0.400716i
$611$	−2.96367	+	5.13323i	−0.119897	+	0.207668i
$612$	39.8700	−	2.61224i	1.61165	−	0.105594i
$613$	−5.37925	+	3.10571i	−0.217266	+	0.125439i	−0.604684	−	0.796466i	$-0.706700\pi$
$613$	−5.37925	+	3.10571i	−0.217266	+	0.125439i	0.387418	+	0.921904i	$0.373367\pi$
$614$	6.86558	−	25.4548i	0.277072	−	1.02727i
$615$	1.81774	+	5.95720i	0.0732984	+	0.240217i
$616$	7.03872	+	2.59971i	0.283598	+	0.104745i
$617$		−	22.4963i		−	0.905669i	−0.891595	−	0.452834i	$-0.850413\pi$
$617$		−	22.4963i		−	0.905669i	0.891595	−	0.452834i	$-0.149587\pi$
$618$	−24.1434	+	0.790078i	−0.971191	+	0.0317816i
$619$	−14.1624	−	24.5300i	−0.569235	−	0.985943i	−0.996642	−	0.0818842i	$-0.973906\pi$
$619$	−14.1624	−	24.5300i	−0.569235	−	0.985943i	0.427407	−	0.904059i	$-0.359427\pi$
$620$	−10.2563	−	5.96660i	−0.411901	−	0.239624i
$621$	−38.4079	+	14.6712i	−1.54126	+	0.588737i
$622$	27.1384	−	7.22380i	1.08815	−	0.289648i
$623$	22.4377	−	32.0584i	0.898947	−	1.28439i
$624$	3.97326	−	16.6665i	0.159058	−	0.667194i
$625$	6.37661	−	11.0446i	0.255064	−	0.441785i
$626$	−2.69613	+	2.68726i	−0.107759	+	0.107404i
$627$	−4.72106	−	4.40728i	−0.188541	−	0.176010i
$628$	−0.0720863	+	21.8748i	−0.00287656	+	0.872899i
$629$		−	24.7930i		−	0.988563i
$630$	−13.9103	−	14.4777i	−0.554198	−	0.576807i
$631$	8.51542			0.338993			0.169497	−	0.985531i	$-0.445786\pi$
$631$	8.51542			0.338993			0.169497	+	0.985531i	$0.445786\pi$
$632$	−3.65000	−	13.8964i	−0.145189	−	0.552768i
$633$	−17.6393	+	18.8952i	−0.701101	+	0.751016i
$634$	−10.6881	−	10.7234i	−0.424479	−	0.425880i
$635$	−7.00758	−	4.04583i	−0.278087	−	0.160554i
$636$	30.0743	−	32.0034i	1.19252	−	1.26902i
$637$	17.0494	+	2.99902i	0.675520	+	0.118825i
$638$	−1.02554	+	0.272983i	−0.0406016	+	0.0108075i
$639$	16.3666	−	1.12650i	0.647452	−	0.0445636i
$640$	14.1431	+	14.4732i	0.559055	+	0.572102i
$641$	−0.0793494	+	0.0458124i	−0.00313411	+	0.00180948i	−0.501566	−	0.865119i	$-0.667243\pi$
$641$	−0.0793494	+	0.0458124i	−0.00313411	+	0.00180948i	0.498432	+	0.866929i	$0.333909\pi$
$642$	0.557778	+	17.0447i	0.0220138	+	0.672702i
$643$	5.89351			0.232417			0.116209	−	0.993225i	$-0.462926\pi$
$643$	5.89351			0.232417			0.116209	+	0.993225i	$0.462926\pi$
$644$	17.5773	+	38.0008i	0.692644	+	1.49744i
$645$	27.2505	−	8.31503i	1.07299	−	0.327404i
$646$	−9.12017	+	33.8140i	−0.358828	+	1.33039i
$647$	4.05903	+	7.03045i	0.159577	+	0.276396i	0.934716	−	0.355395i	$-0.115654\pi$
$647$	4.05903	+	7.03045i	0.159577	+	0.276396i	−0.775139	+	0.631791i	$0.782320\pi$
$648$	−15.4642	+	20.2202i	−0.607492	+	0.794326i
$649$	−7.36901	−	4.25450i	−0.289259	−	0.167004i
$650$	6.08611	−	1.62002i	0.238717	−	0.0635426i
$651$	−14.4545	−	4.70200i	−0.566518	−	0.184286i
$652$	10.5762	+	18.4587i	0.414196	+	0.722899i
$653$	16.7312	−	28.9792i	0.654741	−	1.13404i	−0.327218	−	0.944949i	$-0.606111\pi$
$653$	16.7312	−	28.9792i	0.654741	−	1.13404i	0.981959	−	0.189095i	$-0.0605555\pi$
$654$	3.15166	−	5.89617i	0.123240	−	0.230559i
$655$	−13.8302	−	23.9547i	−0.540392	−	0.935986i
$656$	−3.97489	−	6.99072i	−0.155193	−	0.272942i
$657$	−10.9955	−	16.3399i	−0.428974	−	0.637481i
$658$	−5.75463	−	6.87821i	−0.224339	−	0.268141i
$659$	−15.5448			−0.605540			−0.302770	−	0.953064i	$-0.597911\pi$
$659$	−15.5448			−0.605540			−0.302770	+	0.953064i	$0.597911\pi$
$660$	−5.94816	+	1.79358i	−0.231532	+	0.0698150i
$661$	15.4190	+	26.7065i	0.599731	+	1.03876i	0.992861	+	0.119281i	$0.0380590\pi$
$661$	15.4190	+	26.7065i	0.599731	+	1.03876i	−0.393130	+	0.919483i	$0.628608\pi$
$662$	−21.8048	+	21.7331i	−0.847469	+	0.844681i
$663$	6.43172	−	27.7896i	0.249787	−	1.07926i
$664$	11.2531	+	11.3649i	0.436705	+	0.441044i
$665$	15.9481	−	7.44072i	0.618441	−	0.288539i
$666$	11.8928	+	10.3956i	0.460835	+	0.402820i
$667$	−5.12838	−	2.96087i	−0.198572	−	0.114646i
$668$	−13.7096	−	7.97562i	−0.530442	−	0.308586i
$669$	9.00865	−	9.65002i	0.348294	−	0.373091i
$670$	5.24703	−	19.4539i	0.202711	−	0.751571i
$671$	−4.05974			−0.156725
$672$	21.6189	+	14.3046i	0.833967	+	0.551814i
$673$	3.84855			0.148351			0.0741753	−	0.997245i	$-0.476368\pi$
$673$	3.84855			0.148351			0.0741753	+	0.997245i	$0.476368\pi$
$674$	4.16534	−	15.4434i	0.160443	−	0.594858i
$675$	−9.23956	−	1.47893i	−0.355631	−	0.0569239i
$676$	11.9010	+	6.92345i	0.457731	+	0.266286i
$677$	32.5497	+	18.7926i	1.25099	+	0.722257i	0.971305	−	0.237836i	$-0.0764382\pi$
$677$	32.5497	+	18.7926i	1.25099	+	0.722257i	0.279680	+	0.960093i	$0.409772\pi$
$678$	0.687032	+	1.10487i	0.0263853	+	0.0424322i
$679$	−0.403913	+	4.62773i	−0.0155008	+	0.177596i
$680$	23.7039	+	23.9394i	0.909003	+	0.918034i
$681$	−26.6031	−	6.15711i	−1.01943	−	0.235941i
$682$	−3.33134	+	3.32038i	−0.127563	+	0.127144i
$683$	1.02051	+	1.76757i	0.0390487	+	0.0676343i	0.884889	−	0.465802i	$-0.154234\pi$
$683$	1.02051	+	1.76757i	0.0390487	+	0.0676343i	−0.845841	+	0.533436i	$0.820901\pi$
$684$	−12.3959	−	18.5528i	−0.473970	−	0.709384i
$685$	−20.0584			−0.766394
$686$	−13.1191	+	22.6691i	−0.500891	+	0.865510i
$687$	−29.2296	+	8.91894i	−1.11518	+	0.340279i
$688$	−31.9782	+	18.1826i	−1.21916	+	0.693207i
$689$	−15.6761	−	27.1517i	−0.597210	−	1.03440i
$690$	−30.5730	−	16.3421i	−1.16390	−	0.622133i
$691$	−11.7334	+	20.3229i	−0.446360	+	0.773119i	−0.998146	−	0.0608673i	$-0.980613\pi$
$691$	−11.7334	+	20.3229i	−0.446360	+	0.773119i	0.551786	+	0.833986i	$0.313947\pi$
$692$	−4.24663	−	7.41168i	−0.161433	−	0.281750i
$693$	−6.96419	+	3.85225i	−0.264548	+	0.146335i
$694$	27.1694	−	7.23206i	1.03134	−	0.274525i
$695$	27.8548	+	16.0820i	1.05659	+	0.610025i
$696$	−3.66482	+	0.107840i	−0.138915	+	0.00408768i
$697$	−6.69401	−	11.5944i	−0.253554	−	0.439168i
$698$	−3.48149	+	12.9080i	−0.131776	+	0.488574i
$699$	−9.16868	−	30.0481i	−0.346791	−	1.13652i
$700$	−0.859818	+	9.49000i	−0.0324981	+	0.358688i
$701$	−15.4603			−0.583926			−0.291963	−	0.956430i	$-0.594308\pi$
$701$	−15.4603			−0.583926			−0.291963	+	0.956430i	$0.594308\pi$
$702$	10.6334	+	14.7372i	0.401331	+	0.556220i
$703$	−11.9906	+	6.92275i	−0.452232	+	0.261096i
$704$	6.98617	−	3.94190i	0.263301	−	0.148566i
$705$	7.23409	+	1.67428i	0.272452	+	0.0630572i
$706$	−23.1817	+	6.17059i	−0.872454	+	0.232233i
$707$	35.1062	−	16.3791i	1.32030	−	0.615999i
$708$	−21.4223	−	20.1311i	−0.805101	−	0.756572i
$709$	41.7153	+	24.0843i	1.56665	+	0.904505i	0.996556	+	0.0829254i	$0.0264263\pi$
$709$	41.7153	+	24.0843i	1.56665	+	0.904505i	0.570093	+	0.821580i	$0.306907\pi$
$710$	9.76490	+	9.79713i	0.366470	+	0.367680i
$711$	13.6897	+	6.69542i	0.513403	+	0.251098i
$712$	−10.6271	−	40.4598i	−0.398267	−	1.51630i
$713$	−26.2452			−0.982891
$714$	36.1476	+	23.5768i	1.35279	+	0.882341i
$715$			4.43523i			0.165868i
$716$	0.0498031	−	15.1129i	0.00186123	−	0.564796i
$717$	6.39481	−	6.85009i	0.238819	−	0.255821i
$718$	21.0689	−	20.9995i	0.786283	−	0.783696i
$719$	−6.49021	+	11.2414i	−0.242044	+	0.419232i	−0.961296	−	0.275517i	$-0.911151\pi$
$719$	−6.49021	+	11.2414i	−0.242044	+	0.419232i	0.719252	+	0.694749i	$0.244484\pi$
$720$	−21.4222	+	1.33268i	−0.798358	+	0.0496659i
$721$	−21.3763	−	14.9613i	−0.796094	−	0.557186i
$722$	−7.06603	+	1.88086i	−0.262970	+	0.0699985i
$723$	36.2468	+	8.38909i	1.34803	+	0.311994i
$724$	−8.64786	−	5.03091i	−0.321395	−	0.186972i
$725$	−0.673858	−	1.16716i	−0.0250264	−	0.0433471i
$726$	−0.800719	−	24.4686i	−0.0297175	−	0.908115i
$727$		−	12.0095i		−	0.445406i	−0.974886	−	0.222703i	$-0.928512\pi$
$727$		−	12.0095i		−	0.445406i	0.974886	−	0.222703i	$-0.0714880\pi$
$728$	14.2329	−	11.8284i	0.527506	−	0.438389i
$729$	−5.52704	−	26.4282i	−0.204705	−	0.978824i
$730$	4.32444	−	16.0333i	0.160055	−	0.593419i
$731$	−53.0370	+	30.6209i	−1.96164	+	1.13256i
$732$	−13.6539	−	3.20755i	−0.504662	−	0.118554i
$733$	−4.29808	+	7.44449i	−0.158753	+	0.274968i	−0.934419	−	0.356175i	$-0.884081\pi$
$733$	−4.29808	+	7.44449i	−0.158753	+	0.274968i	0.775666	+	0.631143i	$0.217414\pi$
$734$	0.524538	+	1.97058i	0.0193610	+	0.0727355i
$735$	−2.63998	−	21.5247i	−0.0973770	−	0.793952i
$736$	43.1379	+	11.9405i	1.59008	+	0.440133i
$737$	−6.91700	−	3.99353i	−0.254791	−	0.147104i
$738$	8.36837	+	1.65046i	0.308044	+	0.0607541i
$739$	2.25350	−	1.30106i	0.0828963	−	0.0478602i	−0.457979	−	0.888963i	$-0.651426\pi$
$739$	2.25350	−	1.30106i	0.0828963	−	0.0478602i	0.540875	+	0.841103i	$0.318093\pi$
$740$	−0.0438896	+	13.3184i	−0.00161342	+	0.489595i
$741$	−15.2356	+	4.64891i	−0.559695	+	0.170782i
$742$	46.7267	−	8.16974i	1.71539	−	0.299921i
$743$			13.4061i			0.491823i	0.969292	+	0.245911i	$0.0790872\pi$
$743$			13.4061i			0.491823i	−0.969292	+	0.245911i	$0.920913\pi$
$744$	−13.8275	+	8.53518i	−0.506940	+	0.312915i
$745$	−1.43281	+	0.827235i	−0.0524942	+	0.0303075i
$746$	−21.7860	+	21.7143i	−0.797642	+	0.795018i
$747$	−16.9237	+	1.16484i	−0.619204	+	0.0426193i
$748$	11.5872	−	6.63904i	0.423669	−	0.242747i
$749$	−10.5623	+	15.0912i	−0.385939	+	0.551420i
$750$	−15.7339	−	25.3029i	−0.574522	−	0.923932i
$751$	−7.86182	+	13.6171i	−0.286882	+	0.496894i	−0.973064	−	0.230536i	$-0.925952\pi$
$751$	−7.86182	+	13.6171i	−0.286882	+	0.496894i	0.686182	+	0.727430i	$0.259285\pi$
$752$	−9.58701	−	0.0631869i	−0.349602	−	0.00230419i
$753$	23.4679	−	25.1387i	0.855218	−	0.916105i
$754$	−0.681609	+	2.52714i	−0.0248228	+	0.0920329i
$755$			34.2244i			1.24555i
$756$	−26.4659	+	7.45373i	−0.962554	+	0.271090i
$757$			48.7626i			1.77231i	0.463391	+	0.886154i	$0.346633\pi$
$757$			48.7626i			1.77231i	−0.463391	+	0.886154i	$0.653367\pi$
$758$	−2.48913	−	0.671359i	−0.0904094	−	0.0243849i
$759$	−9.37736	+	10.0450i	−0.340377	+	0.364610i
$760$	4.95908	−	18.1482i	0.179885	−	0.658305i
$761$	−21.7170	+	37.6149i	−0.787240	+	1.36354i	0.140411	+	0.990093i	$0.455158\pi$
$761$	−21.7170	+	37.6149i	−0.787240	+	1.36354i	−0.927652	+	0.373447i	$0.878176\pi$
$762$	−9.41036	+	5.85158i	−0.340901	+	0.211980i
$763$	6.54411	−	3.05321i	0.236913	−	0.110534i
$764$	12.0426	+	21.0180i	0.435684	+	0.760403i
$765$	−35.6486	+	2.45366i	−1.28888	+	0.0887123i
$766$	9.60551	+	9.63722i	0.347061	+	0.348207i
$767$	−18.1747	+	10.4932i	−0.656252	+	0.378887i
$768$	26.6106	−	7.73788i	0.960228	−	0.279217i
$769$			23.9226i			0.862670i	0.902192	+	0.431335i	$0.141957\pi$
$769$			23.9226i			0.862670i	−0.902192	+	0.431335i	$0.858043\pi$
$770$	−6.30247	−	2.30421i	−0.227125	−	0.0830379i
$771$	−14.4663	+	4.41417i	−0.520993	+	0.158972i
$772$	0.00780924	−	2.36974i	0.000281061	−	0.0852886i
$773$	14.3402	−	8.27930i	0.515780	−	0.297786i	−0.219427	−	0.975629i	$-0.570419\pi$
$773$	14.3402	−	8.27930i	0.515780	−	0.297786i	0.735206	+	0.677843i	$0.237085\pi$
$774$	7.54980	−	38.2801i	0.271372	−	1.37595i
$775$	−5.17284	−	2.98654i	−0.185814	−	0.107280i
$776$	3.49414	+	3.52885i	0.125432	+	0.126678i
$777$	3.54158	+	16.6897i	0.127053	+	0.598741i
$778$	−38.4374	+	10.2314i	−1.37805	+	0.366815i
$779$	−3.73823	+	6.47480i	−0.133936	+	0.231984i
$780$	−3.50422	+	14.9168i	−0.125471	+	0.534106i
$781$	4.74856	−	2.74158i	0.169917	−	0.0981014i
$782$	71.9460	+	19.4050i	2.57278	+	0.693920i
$783$	2.45226	−	3.01816i	0.0876366	−	0.107860i
$784$	9.41381	+	26.3701i	0.336208	+	0.941788i
$785$		−	19.5631i		−	0.698237i
$786$	−37.8600	+	1.23895i	−1.35042	+	0.0441917i
$787$	5.81161	+	10.0660i	0.207162	+	0.358814i	0.950819	−	0.309746i	$-0.100244\pi$
$787$	5.81161	+	10.0660i	0.207162	+	0.358814i	−0.743658	+	0.668561i	$0.766911\pi$
$788$	33.7297	+	19.6224i	1.20157	+	0.699018i
$789$	−33.4029	−	7.73088i	−1.18917	−	0.275227i
$790$	3.30519	+	12.4169i	0.117593	+	0.441775i
$791$	−0.122192	+	1.39998i	−0.00434463	+	0.0497775i
$792$	−1.67381	+	8.34186i	−0.0594761	+	0.296415i
$793$	−5.00642	+	8.67137i	−0.177783	+	0.307930i
$794$	−18.8218	−	18.8840i	−0.667962	−	0.670167i
$795$	−26.8015	+	28.7097i	−0.950552	+	1.01823i
$796$	29.4752	+	0.0971328i	1.04472	+	0.00344278i
$797$		−	2.35681i		−	0.0834824i	−0.999128	−	0.0417412i	$-0.986709\pi$
$797$		−	2.35681i		−	0.0834824i	0.999128	−	0.0417412i	$-0.0132905\pi$
$798$	1.30917	−	24.0651i	0.0463442	−	0.851895i
$799$	−15.9609			−0.564657
$800$	7.14357	+	7.26225i	0.252563	+	0.256759i
$801$	39.8580	+	19.4940i	1.40831	+	0.688785i
$802$	−6.04577	+	6.02587i	−0.213483	+	0.212781i
$803$	−5.70077	−	3.29134i	−0.201176	−	0.116149i
$804$	−20.1083	−	18.8962i	−0.709166	−	0.666419i
$805$	−15.8316	−	33.9327i	−0.557991	−	1.19597i
$806$	2.98397	+	11.2102i	0.105106	+	0.394862i
$807$	1.56966	+	0.363287i	0.0552545	+	0.0127883i
$808$	10.9163	−	39.9492i	0.384034	−	1.40541i
$809$	39.6070	−	22.8671i	1.39251	−	0.803964i	0.398914	−	0.916988i	$-0.369387\pi$
$809$	39.6070	−	22.8671i	1.39251	−	0.803964i	0.993592	+	0.113024i	$0.0360538\pi$
$810$	13.7703	−	18.1288i	0.483837	−	0.636980i
$811$	−0.844573			−0.0296570			−0.0148285	−	0.999890i	$-0.504720\pi$
$811$	−0.844573			−0.0296570			−0.0148285	+	0.999890i	$0.504720\pi$
$812$	−3.23695	−	2.28148i	−0.113595	−	0.0800641i
$813$	4.35233	+	14.2637i	0.152643	+	0.500249i
$814$	5.09728	+	1.37482i	0.178660	+	0.0481873i
$815$	−9.51282	−	16.4767i	−0.333219	−	0.577153i
$816$	44.2159	−	13.1738i	1.54786	−	0.461176i
$817$	29.6182	+	17.1000i	1.03621	+	0.598255i
$818$	9.51956	+	35.7631i	0.332844	+	1.25043i
$819$	−0.359968	+	19.6257i	−0.0125783	+	0.685776i
$820$	3.57540	+	6.24017i	0.124858	+	0.217916i
$821$	−18.4890	+	32.0239i	−0.645272	+	1.11764i	0.338967	+	0.940798i	$0.389922\pi$
$821$	−18.4890	+	32.0239i	−0.645272	+	1.11764i	−0.984239	+	0.176845i	$0.943411\pi$
$822$	−12.9493	+	24.2258i	−0.451660	+	0.844972i
$823$	−3.62518	−	6.27899i	−0.126366	−	0.218872i	0.795900	−	0.605428i	$-0.206998\pi$
$823$	−3.62518	−	6.27899i	−0.126366	−	0.218872i	−0.922266	+	0.386556i	$0.873665\pi$
$824$	−26.9783	+	7.08606i	−0.939832	+	0.246855i
$825$	−2.99130	+	0.912746i	−0.104144	+	0.0317777i
$826$	−5.46864	−	31.2778i	−0.190278	−	1.08829i
$827$	43.4014			1.50921			0.754607	−	0.656176i	$-0.227827\pi$
$827$	43.4014			1.50921			0.754607	+	0.656176i	$0.227827\pi$
$828$	−39.4747	+	26.3748i	−1.37184	+	0.916587i
$829$	−12.7789	−	22.1338i	−0.443830	−	0.768737i	0.554139	−	0.832424i	$-0.313047\pi$
$829$	−12.7789	−	22.1338i	−0.443830	−	0.768737i	−0.997970	+	0.0636869i	$0.979714\pi$
$830$	−10.0973	−	10.1306i	−0.350481	−	0.351638i
$831$	49.8001	+	11.5259i	1.72755	+	0.399830i
$832$	0.195586	−	19.7832i	0.00678073	−	0.685858i
$833$	15.9612	+	43.7970i	0.553024	+	1.51748i
$834$	37.4058	−	23.2598i	1.29526	−	0.805420i
$835$	12.2842	+	7.09229i	0.425113	+	0.245439i
$836$	−6.44620	−	3.75009i	−0.222946	−	0.129700i
$837$	2.72408	−	17.0186i	0.0941579	−	0.588250i
$838$	3.43903	+	0.927561i	0.118799	+	0.0320421i
$839$	−19.2288			−0.663854			−0.331927	−	0.943305i	$-0.607699\pi$
$839$	−19.2288			−0.663854			−0.331927	+	0.943305i	$0.607699\pi$
$840$	−19.3762	−	12.7291i	−0.668543	−	0.439196i
$841$	−28.4399			−0.980686
$842$	45.7242	+	12.3325i	1.57576	+	0.425007i
$843$	25.2062	−	27.0008i	0.868149	−	0.929956i
$844$	−15.0091	+	25.7998i	−0.516634	+	0.888064i
$845$	−10.6636	−	6.15665i	−0.366840	−	0.211795i
$846$	6.69233	−	7.65617i	0.230087	−	0.263225i
$847$	15.1628	−	21.6642i	0.520999	−	0.744389i
$848$	25.6443	−	43.7487i	0.880627	−	1.50234i
$849$	8.14269	−	35.1822i	0.279457	−	1.20745i
$850$	11.9721	+	12.0116i	0.410641	+	0.411996i
$851$	14.7295	+	25.5123i	0.504921	+	0.874549i
$852$	18.1366	−	5.46883i	0.621350	−	0.187359i
$853$	−43.5472			−1.49103			−0.745514	−	0.666489i	$-0.767796\pi$
$853$	−43.5472			−1.49103			−0.745514	+	0.666489i	$0.767796\pi$
$854$	−9.72108	−	11.6191i	−0.332649	−	0.397598i
$855$	11.1405	+	16.5555i	0.380997	+	0.566185i
$856$	5.00261	+	19.0461i	0.170986	+	0.650981i
$857$	4.41603	+	7.64878i	0.150849	+	0.261277i	0.931540	−	0.363640i	$-0.118466\pi$
$857$	4.41603	+	7.64878i	0.150849	+	0.261277i	−0.780691	+	0.624917i	$0.785133\pi$
$858$	5.35670	+	2.86330i	0.182875	+	0.0977515i
$859$	2.94564	−	5.10200i	0.100504	−	0.174078i	−0.811388	−	0.584507i	$-0.801288\pi$
$859$	2.94564	−	5.10200i	0.100504	−	0.174078i	0.911892	+	0.410429i	$0.134621\pi$
$860$	28.5449	−	16.3552i	0.973372	−	0.557708i
$861$	6.16237	+	6.84868i	0.210013	+	0.233403i
$862$	5.04071	+	18.9370i	0.171687	+	0.644995i
$863$	2.80835	+	1.62140i	0.0955974	+	0.0551932i	0.547037	−	0.837109i	$-0.315756\pi$
$863$	2.80835	+	1.62140i	0.0955974	+	0.0551932i	−0.451439	+	0.892302i	$0.649089\pi$
$864$	−12.2202	+	26.7332i	−0.415740	+	0.909484i
$865$	3.81966	+	6.61584i	0.129872	+	0.224945i
$866$	−13.3725	−	3.60677i	−0.454416	−	0.122563i
$867$	45.3020	−	13.8232i	1.53854	−	0.469460i
$868$	−17.4799	−	1.58373i	−0.593307	−	0.0537552i
$869$	5.09344			0.172783
$870$	3.27718	−	0.107244i	0.111107	−	0.00363590i
$871$	−17.0599	+	9.84955i	−0.578053	+	0.333739i
$872$	2.03490	−	7.44690i	0.0689103	−	0.252184i
$873$	−5.25487	+	0.361689i	−0.177850	+	0.0122413i
$874$	−10.7041	−	40.2132i	−0.362072	−	1.36023i
$875$	2.79835	−	32.0614i	0.0946015	−	1.08387i
$876$	−16.5726	−	15.5737i	−0.559937	−	0.526186i
$877$	−39.1526	−	22.6048i	−1.32209	−	0.763309i	−0.338028	−	0.941136i	$-0.609760\pi$
$877$	−39.1526	−	22.6048i	−1.32209	−	0.763309i	−0.984062	+	0.177828i	$0.943093\pi$
$878$	−8.09000	+	8.06338i	−0.273024	+	0.272126i
$879$	−15.4904	+	16.5933i	−0.522479	+	0.559677i
$880$	−6.23620	+	3.54588i	−0.210222	+	0.119532i
$881$	28.1014			0.946759			0.473380	−	0.880859i	$-0.343034\pi$
$881$	28.1014			0.946759			0.473380	+	0.880859i	$0.343034\pi$
$882$	−27.7011	−	10.7075i	−0.932744	−	0.360540i
$883$			5.45102i			0.183442i	0.995785	+	0.0917208i	$0.0292367\pi$
$883$			5.45102i			0.183442i	−0.995785	+	0.0917208i	$0.970763\pi$
$884$	0.108540	−	32.9367i	0.00365059	−	1.10778i
$885$	19.2176	+	17.9403i	0.645992	+	0.603058i
$886$	17.6685	+	17.7268i	0.593585	+	0.595544i
$887$	25.3783	−	43.9566i	0.852122	−	1.47592i	−0.0271684	−	0.999631i	$-0.508649\pi$
$887$	25.3783	−	43.9566i	0.852122	−	1.47592i	0.879290	−	0.476287i	$-0.158018\pi$
$888$	16.0572	+	8.65113i	0.538843	+	0.290313i
$889$	−11.9239	−	1.04073i	−0.399914	−	0.0349049i
$890$	9.62318	+	36.1524i	0.322570	+	1.21183i
$891$	−5.54033	−	7.12332i	−0.185608	−	0.238640i
$892$	7.66533	−	13.1763i	0.256654	−	0.441174i
$893$	4.45664	+	7.71912i	0.149136	+	0.258311i
$894$	0.0741058	+	2.26454i	0.00247847	+	0.0757377i
$895$			13.5158i			0.451783i
$896$	28.0103	+	10.5557i	0.935758	+	0.352643i
$897$	9.89147	+	32.4168i	0.330266	+	1.08237i
$898$	26.5779	+	7.16848i	0.886915	+	0.239215i
$899$	2.14982	−	1.24120i	0.0717005	−	0.0413963i
$900$	−10.7816	+	0.706400i	−0.359387	+	0.0235467i
$901$	42.2119	−	73.1132i	1.40628	−	2.43575i
$902$	2.75492	−	0.733315i	0.0917288	−	0.0244167i
$903$	31.3285	−	28.1890i	1.04255	−	0.938070i
$904$	1.05704	+	1.06755i	0.0351567	+	0.0355060i
$905$	7.74871	+	4.47372i	0.257576	+	0.148711i
$906$	41.3349	+	22.0946i	1.37326	+	0.734045i
$907$	−8.66652	+	5.00362i	−0.287767	+	0.166142i	−0.636934	−	0.770918i	$-0.719798\pi$
$907$	−8.66652	+	5.00362i	−0.287767	+	0.166142i	0.349167	+	0.937060i	$0.386464\pi$
$908$	−31.5304	−	0.103905i	−1.04637	−	0.00344822i
$909$	24.5233	+	36.4431i	0.813387	+	1.20874i
$910$	−12.6938	+	10.6202i	−0.420795	+	0.352056i
$911$		−	14.5940i		−	0.483521i	−0.970336	−	0.241761i	$-0.922275\pi$
$911$		−	14.5940i		−	0.483521i	0.970336	−	0.241761i	$-0.0777249\pi$
$912$	−18.7172	−	17.7055i	−0.619789	−	0.586288i
$913$	−4.91019	+	2.83490i	−0.162503	+	0.0938214i
$914$	15.4869	+	15.5381i	0.512263	+	0.513954i
$915$	12.2203	+	2.82831i	0.403990	+	0.0935010i
$916$	−30.6181	+	17.5431i	−1.01165	+	0.579639i
$917$	−33.5208	−	23.4612i	−1.10695	−	0.774757i
$918$	−20.0506	+	44.6390i	−0.661768	+	1.47331i
$919$	−1.14316	+	1.98001i	−0.0377093	+	0.0653145i	−0.884264	−	0.466987i	$-0.845339\pi$
$919$	−1.14316	+	1.98001i	−0.0377093	+	0.0653145i	0.846555	+	0.532302i	$0.178673\pi$
$920$	−38.6139	−	10.5514i	−1.27306	−	0.347870i
$921$	23.6032	+	22.0344i	0.777751	+	0.726060i
$922$	−1.17056	−	0.315719i	−0.0385504	−	0.0103977i
$923$		−	13.5235i		−	0.445132i
$924$	−6.85169	+	6.12433i	−0.225404	+	0.201476i
$925$			6.70450i			0.220443i
$926$	−13.8373	+	51.3031i	−0.454721	+	1.68593i
$927$	12.9984	−	26.5770i	0.426924	−	0.872902i
$928$	−4.09824	+	1.06201i	−0.134531	+	0.0348622i
$929$	−9.71753	+	16.8313i	−0.318822	+	0.552216i	−0.980242	−	0.197799i	$-0.936621\pi$
$929$	−9.71753	+	16.8313i	−0.318822	+	0.552216i	0.661421	+	0.750015i	$0.269954\pi$
$930$	12.3409	−	7.67387i	0.404675	−	0.251636i
$931$	16.7246	−	19.9483i	0.548128	−	0.653780i
$932$	−18.0343	−	31.4754i	−0.590733	−	1.03101i
$933$	−7.75548	+	33.5092i	−0.253903	+	1.09704i
$934$	−10.0527	+	10.0196i	−0.328933	+	0.327851i
$935$	−10.3430	+	5.97152i	−0.338252	+	0.195290i
$936$	15.7536	+	13.8622i	0.514923	+	0.453101i
$937$			21.6552i			0.707445i	0.935350	+	0.353723i	$0.115084\pi$
$937$			21.6552i			0.707445i	−0.935350	+	0.353723i	$0.884916\pi$
$938$	−5.13319	−	29.3592i	−0.167605	−	0.958613i
$939$	−1.36065	−	4.45918i	−0.0444030	−	0.145520i
$940$	8.57397	+	0.0282547i	0.279652	+	0.000921567i
$941$	5.82024	−	3.36032i	0.189735	−	0.109543i	−0.402124	−	0.915585i	$-0.631728\pi$
$941$	5.82024	−	3.36032i	0.189735	−	0.109543i	0.591858	+	0.806042i	$0.298395\pi$
$942$	−23.6276	−	12.6296i	−0.769828	−	0.411494i
$943$	13.7764	+	7.95381i	0.448622	+	0.259012i
$944$	−29.2844	−	17.1657i	−0.953126	−	0.558695i
$945$	23.6468	−	6.74396i	0.769230	−	0.219381i
$946$	−3.35446	−	12.6020i	−0.109063	−	0.409728i
$947$	−10.5673	+	18.3031i	−0.343392	+	0.594772i	−0.985060	−	0.172210i	$-0.944909\pi$
$947$	−10.5673	+	18.3031i	−0.343392	+	0.594772i	0.641668	+	0.766982i	$0.278243\pi$
$948$	17.1305	+	4.02426i	0.556372	+	0.130702i
$949$	−14.0602	+	8.11768i	−0.456414	+	0.263511i
$950$	2.46627	−	9.14394i	0.0800163	−	0.296669i
$951$	17.7357	−	5.41174i	0.575118	−	0.175488i
$952$	46.7467	+	17.2656i	1.51507	+	0.559582i
$953$			2.18327i			0.0707230i	0.999375	+	0.0353615i	$0.0112583\pi$
$953$			2.18327i			0.0707230i	−0.999375	+	0.0353615i	$0.988742\pi$
$954$	17.3719	+	50.9042i	0.562435	+	1.64809i
$955$	−10.8317	−	18.7611i	−0.350507	−	0.607096i
$956$	5.44125	−	9.35321i	0.175983	−	0.302504i
$957$	0.293075	−	1.26629i	0.00947376	−	0.0409333i
$958$	−30.2282	+	8.04627i	−0.976630	+	0.259963i
$959$	−26.8880	+	12.5448i	−0.868259	+	0.405094i
$960$	−23.7754	+	6.99850i	−0.767348	+	0.225876i
$961$	−9.99900	+	17.3188i	−0.322548	+	0.558670i
$962$	9.22243	−	9.19209i	0.297343	−	0.296365i
$963$	−18.7628	−	9.17660i	−0.604622	−	0.295712i
$964$	42.9603	+	0.141572i	1.38366	+	0.00455972i
$965$			2.11931i			0.0682229i
$966$	−51.2032	−	2.78552i	−1.64744	−	0.0896227i
$967$	−25.1413			−0.808490			−0.404245	−	0.914651i	$-0.632466\pi$
$967$	−25.1413			−0.808490			−0.404245	+	0.914651i	$0.632466\pi$
$968$	−7.18150	−	27.3416i	−0.230822	−	0.878793i
$969$	−31.3543	−	29.2704i	−1.00724	−	0.940300i
$970$	−3.13525	−	3.14560i	−0.100667	−	0.100999i
$971$	30.0100	+	17.3263i	0.963065	+	0.556026i	0.897115	−	0.441797i	$-0.145659\pi$
$971$	30.0100	+	17.3263i	0.963065	+	0.556026i	0.0659503	+	0.997823i	$0.478992\pi$
$972$	−13.0054	−	28.3348i	−0.417149	−	0.908838i
$973$	47.3969	+	4.13685i	1.51947	+	0.132621i
$974$	−30.7925	+	8.19648i	−0.986657	+	0.262632i
$975$	−1.73926	+	7.51483i	−0.0557009	+	0.240667i
$976$	−16.1950	−	0.106739i	−0.518389	−	0.00341664i
$977$	−3.22538	+	1.86218i	−0.103189	+	0.0595763i	−0.550706	−	0.834699i	$-0.685642\pi$
$977$	−3.22538	+	1.86218i	−0.103189	+	0.0595763i	0.447517	+	0.894275i	$0.352308\pi$
$978$	−26.0412	+	0.852182i	−0.832705	+	0.0272498i
$979$	14.8297			0.473960
$980$	−8.49660	−	23.5553i	−0.271414	−	0.752447i
$981$	4.57137	+	6.79333i	0.145953	+	0.216894i
$982$	−9.24685	+	34.2837i	−0.295079	+	1.09404i
$983$	−27.3018	−	47.2881i	−0.870792	−	1.50826i	−0.861179	−	0.508302i	$-0.830273\pi$
$983$	−27.3018	−	47.2881i	−0.870792	−	1.50826i	−0.00961355	−	0.999954i	$-0.503060\pi$
$984$	9.84484	−	0.289692i	0.313842	−	0.00923505i
$985$	−30.2227	−	17.4491i	−0.962977	−	0.555975i
$986$	−6.81100	+	1.81298i	−0.216906	+	0.0577370i
$987$	10.7443	−	2.27995i	0.341995	−	0.0725717i
$988$	−15.9594	+	9.14415i	−0.507735	+	0.290914i
$989$	36.3837	−	63.0185i	1.15694	−	2.00387i
$990$	1.47232	−	7.46516i	0.0467934	−	0.237258i
$991$	−25.1790	−	43.6114i	−0.799839	−	1.38536i	−0.919721	−	0.392573i	$-0.871585\pi$
$991$	−25.1790	−	43.6114i	−0.799839	−	1.38536i	0.119882	−	0.992788i	$-0.461748\pi$
$992$	−13.3766	+	13.1580i	−0.424706	+	0.417765i
$993$	−11.0042	−	36.0635i	−0.349207	−	1.14444i
$994$	19.2169	+	7.02579i	0.609525	+	0.222844i
$995$	−26.3603			−0.835679
$996$	−18.7540	+	5.65497i	−0.594242	+	0.179185i
$997$	−12.7609	−	22.1025i	−0.404141	−	0.699993i	0.590080	−	0.807345i	$-0.299096\pi$
$997$	−12.7609	−	22.1025i	−0.404141	−	0.699993i	−0.994221	+	0.107352i	$0.965763\pi$
$998$	−10.6372	+	10.6022i	−0.336715	+	0.335607i
$999$	−18.0722	+	6.90330i	−0.571778	+	0.218411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.ba.c.5.10	yes	48
3.2	odd	2	inner	168.2.ba.c.5.15	yes	48
4.3	odd	2		672.2.bi.c.593.20		48
7.3	odd	6	inner	168.2.ba.c.101.7	yes	48
8.3	odd	2		672.2.bi.c.593.5		48
8.5	even	2	inner	168.2.ba.c.5.18	yes	48
12.11	even	2		672.2.bi.c.593.14		48
21.17	even	6	inner	168.2.ba.c.101.18	yes	48
24.5	odd	2	inner	168.2.ba.c.5.7	✓	48
24.11	even	2		672.2.bi.c.593.11		48
28.3	even	6		672.2.bi.c.17.11		48
56.3	even	6		672.2.bi.c.17.14		48
56.45	odd	6	inner	168.2.ba.c.101.15	yes	48
84.59	odd	6		672.2.bi.c.17.5		48
168.59	odd	6		672.2.bi.c.17.20		48
168.101	even	6	inner	168.2.ba.c.101.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.7	✓	48	24.5	odd	2	inner
168.2.ba.c.5.10	yes	48	1.1	even	1	trivial
168.2.ba.c.5.15	yes	48	3.2	odd	2	inner
168.2.ba.c.5.18	yes	48	8.5	even	2	inner
168.2.ba.c.101.7	yes	48	7.3	odd	6	inner
168.2.ba.c.101.10	yes	48	168.101	even	6	inner
168.2.ba.c.101.15	yes	48	56.45	odd	6	inner
168.2.ba.c.101.18	yes	48	21.17	even	6	inner
672.2.bi.c.17.5		48	84.59	odd	6
672.2.bi.c.17.11		48	28.3	even	6
672.2.bi.c.17.14		48	56.3	even	6
672.2.bi.c.17.20		48	168.59	odd	6
672.2.bi.c.593.5		48	8.3	odd	2
672.2.bi.c.593.11		48	24.11	even	2
672.2.bi.c.593.14		48	12.11	even	2
672.2.bi.c.593.20		48	4.3	odd	2

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.368276 + 1.36542i) q^{2} +(-1.26610 - 1.18195i) q^{3} +(-1.72875 - 1.00570i) q^{4} +(1.54900 + 0.894317i) q^{5} +(2.08013 - 1.29347i) q^{6} +(2.63573 + 0.230049i) q^{7} +(2.00986 - 1.99009i) q^{8} +(0.206000 + 2.99292i) q^{9} +(-1.79158 + 1.78568i) q^{10} +(0.501346 + 0.868358i) q^{11} +(1.00007 + 3.31660i) q^{12} +2.47302 q^{13} +(-1.28479 + 3.51416i) q^{14} +(-0.904151 - 2.96313i) q^{15} +(1.97713 + 3.47721i) q^{16} +(3.32963 + 5.76708i) q^{17} +(-4.16246 - 0.820942i) q^{18} +(1.85941 - 3.22059i) q^{19} +(-1.77842 - 3.10388i) q^{20} +(-3.06518 - 3.40656i) q^{21} +(-1.37031 + 0.364754i) q^{22} +(-6.85244 - 3.95626i) q^{23} +(-4.89686 + 0.144094i) q^{24} +(-0.900394 - 1.55953i) q^{25} +(-0.910752 + 3.37671i) q^{26} +(3.27666 - 4.03281i) q^{27} +(-4.32515 - 3.04846i) q^{28} +0.748403 q^{29} +(4.37890 - 0.143297i) q^{30} +(2.87254 - 1.65846i) q^{31} +(-5.47598 + 1.41904i) q^{32} +(0.391600 - 1.69199i) q^{33} +(-9.10071 + 2.42246i) q^{34} +(3.87702 + 2.71353i) q^{35} +(2.65386 - 5.38117i) q^{36} +(-3.22429 - 1.86155i) q^{37} +(3.71268 + 3.72494i) q^{38} +(-3.13108 - 2.92298i) q^{39} +(4.89305 - 1.28520i) q^{40} -2.01044 q^{41} +(5.78022 - 2.93071i) q^{42} +9.19651i q^{43} +(0.00660852 - 2.00538i) q^{44} +(-2.35752 + 4.82027i) q^{45} +(7.92554 - 7.89946i) q^{46} +(-1.19840 + 2.07569i) q^{47} +(1.60665 - 6.73934i) q^{48} +(6.89415 + 1.21270i) q^{49} +(2.46101 - 0.655080i) q^{50} +(2.60076 - 11.2371i) q^{51} +(-4.27522 - 2.48712i) q^{52} +(-6.33884 - 10.9792i) q^{53} +(4.29976 + 5.95920i) q^{54} +1.79345i q^{55} +(5.75527 - 4.78297i) q^{56} +(-6.16075 + 1.87985i) q^{57} +(-0.275619 + 1.02188i) q^{58} +(-7.34922 + 4.24308i) q^{59} +(-1.41698 + 6.03181i) q^{60} +(-2.02442 + 3.50640i) q^{61} +(1.20661 + 4.53300i) q^{62} +(-0.145558 + 7.93592i) q^{63} +(0.0790881 - 7.99961i) q^{64} +(3.83071 + 2.21166i) q^{65} +(2.16606 + 1.15782i) q^{66} +(-6.89843 + 3.98281i) q^{67} +(0.0438896 - 13.3184i) q^{68} +(3.99976 + 13.1082i) q^{69} +(-5.13292 + 4.29443i) q^{70} -5.46843i q^{71} +(6.37021 + 5.60539i) q^{72} +(-5.68546 + 3.28250i) q^{73} +(3.72922 - 3.71695i) q^{74} +(-0.703295 + 3.03873i) q^{75} +(-6.45340 + 3.69757i) q^{76} +(1.12165 + 2.40409i) q^{77} +(5.14419 - 3.19878i) q^{78} +(2.53988 - 4.39920i) q^{79} +(-0.0471537 + 7.15438i) q^{80} +(-8.91513 + 1.23308i) q^{81} +(0.740396 - 2.74510i) q^{82} +5.65457i q^{83} +(1.87294 + 8.97174i) q^{84} +11.9110i q^{85} +(-12.5571 - 3.38685i) q^{86} +(-0.947550 - 0.884573i) q^{87} +(2.73575 + 0.747554i) q^{88} +(7.39495 - 12.8084i) q^{89} +(-5.71347 - 4.99420i) q^{90} +(6.51821 + 0.568916i) q^{91} +(7.86731 + 13.7309i) q^{92} +(-5.59713 - 1.29542i) q^{93} +(-2.39285 - 2.40075i) q^{94} +(5.76045 - 3.32580i) q^{95} +(8.61034 + 4.67568i) q^{96} +1.75577i q^{97} +(-4.19479 + 8.96681i) q^{98} +(-2.49565 + 1.67937i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42}+ \cdots + 90 q^{96}+O(q^{100}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

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