LMFDB - Embedded newform 168.2.ba.c.101.10

Newspace parameters

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

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			101.10
Character	$\chi$	$=$	168.101
Dual form			168.2.ba.c.5.10

$q$-expansion

$f(q)$	$=$	$q+(-0.368276 - 1.36542i) q^{2} +(-1.26610 + 1.18195i) q^{3} +(-1.72875 + 1.00570i) q^{4} +(1.54900 - 0.894317i) q^{5} +(2.08013 + 1.29347i) q^{6} +(2.63573 - 0.230049i) q^{7} +(2.00986 + 1.99009i) q^{8} +(0.206000 - 2.99292i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.111901	−	0.993719i	$-0.535694\pi$
$5$	1.54900	−	0.894317i	0.692735	−	0.399951i	0.804636	+	0.593769i	$0.202361\pi$
$6$	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	−0.780493	−	0.625164i	$-0.785032\pi$
$11$	0.501346	−	0.868358i	0.151162	−	0.261820i	0.931655	+	0.363345i	$0.118365\pi$
$12$	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	−0.107001	−	0.994259i	$-0.534125\pi$
$17$	3.32963	−	5.76708i	0.807553	−	1.39872i	0.914554	−	0.404464i	$-0.132542\pi$
$18$	−4.16246	+	0.820942i	−0.981101	+	0.193498i
$19$	1.85941	+	3.22059i	0.426577	+	0.738854i	0.996566	−	0.0827988i	$-0.0263859\pi$
$19$	1.85941	+	3.22059i	0.426577	+	0.738854i	−0.569989	+	0.821652i	$0.693053\pi$
$20$	−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	−0.997029	−	0.0770314i	$-0.975456\pi$
$23$	−6.85244	+	3.95626i	−1.42883	+	0.824936i	−0.431803	+	0.901968i	$0.642123\pi$
$24$	−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	0.735265	−	0.677779i	$-0.237058\pi$
$31$	2.87254	+	1.65846i	0.515924	+	0.297869i	−0.219341	+	0.975648i	$0.570391\pi$
$32$	−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	−0.741045	−	0.671455i	$-0.765670\pi$
$37$	−3.22429	+	1.86155i	−0.530071	+	0.306036i	0.210975	+	0.977492i	$0.432336\pi$
$38$	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	$-0.752636\pi$
$43$		−	9.19651i		−	1.40245i	0.712938	−	0.701227i	$-0.247364\pi$
$44$	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	0.765289	−	0.643687i	$-0.222596\pi$
$47$	−1.19840	−	2.07569i	−0.174805	−	0.302771i	−0.940094	+	0.340916i	$0.889263\pi$
$48$	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	−0.00943963	+	0.999955i	$0.503005\pi$
$53$	−6.33884	+	10.9792i	−0.870707	+	1.50811i	−0.861267	+	0.508153i	$0.830329\pi$
$54$	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	−0.0616046	−	0.998101i	$-0.519622\pi$
$59$	−7.34922	−	4.24308i	−0.956787	−	0.552401i	−0.895183	+	0.445699i	$0.852955\pi$
$60$	−1.41698	−	6.03181i	−0.182931	−	0.778703i
$61$	−2.02442	−	3.50640i	−0.259200	−	0.448948i	0.706828	−	0.707386i	$-0.250126\pi$
$61$	−2.02442	−	3.50640i	−0.259200	−	0.448948i	−0.966028	+	0.258438i	$0.916792\pi$
$62$	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	0.0154303	−	0.999881i	$-0.495088\pi$
$67$	−6.89843	−	3.98281i	−0.842777	−	0.486577i	−0.858207	+	0.513303i	$0.828422\pi$
$68$	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	$0.105193\pi$
$71$			5.46843i			0.648984i	−0.945889	+	0.324492i	$0.894807\pi$
$72$	6.37021	−	5.60539i	0.750736	−	0.660602i
$73$	−5.68546	−	3.28250i	−0.665433	−	0.384188i	0.128911	−	0.991656i	$-0.458852\pi$
$73$	−5.68546	−	3.28250i	−0.665433	−	0.384188i	−0.794344	+	0.607468i	$0.792185\pi$
$74$	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	0.972793	−	0.231676i	$-0.0744210\pi$
$79$	2.53988	+	4.39920i	0.285759	+	0.494949i	−0.687034	+	0.726625i	$0.741088\pi$
$80$	−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	$-0.899559\pi$
$83$		−	5.65457i		−	0.620669i	0.950627	−	0.310335i	$-0.100441\pi$
$84$	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	0.929676	+	0.368379i	$0.120087\pi$
$89$	7.39495	+	12.8084i	0.783863	+	1.35769i	−0.145812	+	0.989312i	$0.546580\pi$
$90$	−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	$-0.971590\pi$
$97$		−	1.75577i		−	0.178271i	0.996019	−	0.0891356i	$-0.0284105\pi$
$98$	−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	0.973411	−	0.229064i	$-0.0735667\pi$
$101$	12.6803	+	7.32100i	1.26174	+	0.728467i	0.288330	+	0.957531i	$0.406900\pi$
$102$	14.3856	−	7.68949i	1.42439	−	0.761373i
$103$	−8.54056	+	4.93089i	−0.841526	+	0.485855i	−0.857783	−	0.514013i	$-0.828158\pi$
$103$	−8.54056	+	4.93089i	−0.841526	+	0.485855i	0.0162566	+	0.999868i	$0.494825\pi$
$104$	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	0.647247	−	0.762281i	$-0.275920\pi$
$107$	−3.48110	−	6.02945i	−0.336531	−	0.582889i	−0.983778	+	0.179392i	$0.942587\pi$
$108$	−9.72031	−	3.67635i	−0.935337	−	0.353757i
$109$	2.36373	+	1.36470i	0.226404	+	0.130715i	0.608912	−	0.793238i	$-0.291606\pi$
$109$	2.36373	+	1.36470i	0.226404	+	0.130715i	−0.382508	+	0.923952i	$0.624939\pi$
$110$	−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	$-0.992047\pi$
$113$		−	0.531154i		−	0.0499667i	0.999688	−	0.0249834i	$-0.00795328\pi$
$114$	−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	−0.953710	−	0.300729i	$-0.902770\pi$
$131$	−13.3927	+	7.73228i	−1.17013	+	0.675573i	−0.216416	+	0.976301i	$0.569437\pi$
$132$	−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	0.0240187	−	0.999712i	$-0.492354\pi$
$137$	−9.71195	−	5.60719i	−0.829748	−	0.479055i	−0.853766	+	0.520657i	$0.825687\pi$
$138$	−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	0.846459	−	0.532454i	$-0.178730\pi$
$149$	−0.462495	−	0.801066i	−0.0378891	−	0.0656258i	−0.884348	+	0.466828i	$0.845397\pi$
$150$	−3.89014	+	2.07938i	−0.317629	+	0.169781i
$151$	9.56720	−	16.5709i	0.778568	−	1.34852i	−0.154200	−	0.988040i	$-0.549280\pi$
$151$	9.56720	−	16.5709i	0.778568	−	1.34852i	0.932767	−	0.360479i	$-0.117387\pi$
$152$	−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	−0.997413	−	0.0718851i	$-0.977099\pi$
$157$	−5.46873	+	9.47212i	−0.436452	+	0.755957i	0.560961	+	0.827842i	$0.310432\pi$
$158$	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	−0.815316	−	0.579017i	$-0.803437\pi$
$163$	−9.21188	+	5.31848i	−0.721530	+	0.416576i	0.0937855	+	0.995592i	$0.470103\pi$
$164$	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	−0.352758	−	0.935715i	$-0.614756\pi$
$173$	3.69882	−	2.13552i	0.281216	−	0.162360i	0.633974	+	0.773354i	$0.281423\pi$
$174$	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	−0.689576	−	0.724214i	$-0.742203\pi$
$179$	3.77825	−	6.54412i	0.282399	−	0.489130i	0.971975	+	0.235083i	$0.0755363\pi$
$180$	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	−0.828923	−	0.559362i	$-0.811046\pi$
$191$	−10.4891	+	6.05587i	−0.758963	+	0.438188i	0.0699601	+	0.997550i	$0.477713\pi$
$192$	−9.55525	−	10.0348i	−0.689591	−	0.724199i
$193$	0.592437	−	1.02613i	0.0426445	−	0.0738625i	−0.843915	−	0.536476i	$-0.819755\pi$
$193$	0.592437	−	1.02613i	0.0426445	−	0.0738625i	0.886560	+	0.462614i	$0.153088\pi$
$194$	−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	−0.0260186	−	0.999661i	$-0.508283\pi$
$199$	−12.7632	−	7.36884i	−0.904760	−	0.522363i	−0.878741	+	0.477298i	$0.841616\pi$
$200$	−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	$0.171727\pi$
$211$			14.9240i			1.02741i	−0.857967	+	0.513704i	$0.828273\pi$
$212$	−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	$-0.917859\pi$
$223$		−	7.62187i		−	0.510398i	0.966889	−	0.255199i	$-0.0821410\pi$
$224$	−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	0.879203	−	0.476446i	$-0.158075\pi$
$227$	13.6531	+	7.88264i	0.906190	+	0.523189i	0.0269870	+	0.999636i	$0.491409\pi$
$228$	12.5410	−	2.94610i	0.830545	−	0.195110i
$229$	8.82193	+	15.2800i	0.582970	+	1.00973i	0.995125	+	0.0986198i	$0.0314428\pi$
$229$	8.82193	+	15.2800i	0.582970	+	1.00973i	−0.412155	+	0.911114i	$0.635224\pi$
$230$	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	0.112344	−	0.993669i	$-0.464164\pi$
$233$	15.7079	−	9.06896i	1.02906	−	0.594127i	0.916715	+	0.399542i	$0.130831\pi$
$234$	−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	$-0.944012\pi$
$239$		−	5.41040i		−	0.349970i	0.984571	−	0.174985i	$-0.0559877\pi$
$240$	8.51580	+	9.00240i	0.549693	+	0.581103i
$241$	−18.6025	−	10.7401i	−1.19829	−	0.691834i	−0.238117	−	0.971236i	$-0.576530\pi$
$241$	−18.6025	−	10.7401i	−1.19829	−	0.691834i	−0.960174	+	0.279403i	$0.909863\pi$
$242$	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	$-0.784435\pi$
$251$		−	19.8553i		−	1.25325i	0.779319	−	0.626627i	$-0.215565\pi$
$252$	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	0.969464	−	0.245234i	$-0.0788647\pi$
$257$	4.36616	+	7.56240i	0.272353	+	0.471730i	−0.697111	+	0.716964i	$0.745531\pi$
$258$	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	0.924623	−	0.380885i	$-0.124381\pi$
$263$	17.1429	+	9.89747i	1.05708	+	0.610304i	0.132455	+	0.991189i	$0.457714\pi$
$264$	−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	0.475241	−	0.879856i	$-0.342361\pi$
$269$	−0.805574	−	0.465098i	−0.0491167	−	0.0283575i	−0.524357	+	0.851498i	$0.675694\pi$
$270$	1.33093	−	13.0762i	0.0809977	−	0.795790i
$271$	−7.45646	+	4.30499i	−0.452948	+	0.261509i	−0.709074	−	0.705134i	$-0.750887\pi$
$271$	−7.45646	+	4.30499i	−0.452948	+	0.261509i	0.256127	+	0.966643i	$0.417554\pi$
$272$	−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	−0.999086	−	0.0427456i	$-0.986390\pi$
$277$	−25.5583	−	14.7561i	−1.53565	−	0.886607i	−0.536562	−	0.843861i	$-0.680277\pi$
$278$	−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	$-0.780546\pi$
$281$		−	21.3260i		−	1.27220i	0.771605	−	0.636102i	$-0.219454\pi$
$282$	0.192020	−	5.86781i	0.0114346	−	0.349423i
$283$	10.4247	−	18.0561i	0.619684	−	1.07332i	−0.369860	−	0.929088i	$-0.620594\pi$
$283$	10.4247	−	18.0561i	0.619684	−	1.07332i	0.989543	−	0.144236i	$-0.0460724\pi$
$284$	−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	$0.125049\pi$
$293$			13.1058i			0.765652i	−0.923821	+	0.382826i	$0.874951\pi$
$294$	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	0.434211	+	0.900811i	$0.357027\pi$
$311$	−9.92896	+	17.1975i	−0.563020	+	0.975179i	−0.997231	+	0.0743677i	$0.976306\pi$
$312$	−12.1100	−	0.356347i	−0.685595	−	0.0201742i
$313$	2.33108	−	1.34585i	0.131760	−	0.0760718i	−0.432671	−	0.901552i	$-0.642429\pi$
$313$	2.33108	−	1.34585i	0.131760	−	0.0760718i	0.564431	+	0.825480i	$0.309096\pi$
$314$	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	0.675635	−	0.737236i	$-0.263870\pi$
$317$	−5.35288	−	9.27147i	−0.300648	−	0.520737i	−0.976283	+	0.216499i	$0.930536\pi$
$318$	−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	0.117465	−	0.993077i	$-0.462523\pi$
$331$	18.8525	−	10.8845i	1.03623	−	0.598266i	0.918762	+	0.394811i	$0.129190\pi$
$332$	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	0.465604	+	0.884993i	$0.345837\pi$
$347$	−9.94032	+	17.2171i	−0.533624	+	0.924265i	−0.999229	+	0.0392715i	$0.987496\pi$
$348$	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	−0.547057	−	0.837095i	$-0.684252\pi$
$353$	8.48135	−	14.6901i	0.451417	−	0.781877i	0.998474	+	0.0552182i	$0.0175854\pi$
$354$	−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	−0.896608	−	0.442826i	$-0.853976\pi$
$359$	−18.2162	+	10.5171i	−0.961413	+	0.555072i	−0.0648056	+	0.997898i	$0.520643\pi$
$360$	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	0.532238	−	0.846595i	$-0.321351\pi$
$367$	1.24875	+	0.720966i	0.0651842	+	0.0376341i	−0.467054	+	0.884229i	$0.654685\pi$
$368$	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	0.0744535	−	0.997224i	$-0.476279\pi$
$373$	18.8362	−	10.8751i	0.975302	−	0.563091i	0.900848	+	0.434134i	$0.142945\pi$
$374$	−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	$-0.985091\pi$
$379$		−	1.82298i		−	0.0936402i	0.998903	−	0.0468201i	$-0.0149087\pi$
$380$	−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	0.962360	−	0.271777i	$-0.0876112\pi$
$383$	4.81069	+	8.33236i	0.245815	+	0.425763i	−0.716546	+	0.697540i	$0.754278\pi$
$384$	−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	−0.250703	−	0.968064i	$-0.580662\pi$
$389$	14.0629	−	24.3576i	0.713017	−	1.23498i	0.963719	−	0.266917i	$-0.0860050\pi$
$390$	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	0.526425	−	0.850221i	$-0.323532\pi$
$397$	−9.42646	−	16.3271i	−0.473101	−	0.819434i	−0.999526	+	0.0307871i	$0.990199\pi$
$398$	−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	−0.363773	−	0.931488i	$-0.618512\pi$
$401$	5.22718	−	3.01791i	0.261033	−	0.150707i	0.624806	+	0.780780i	$0.285178\pi$
$402$	−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	0.941556	−	0.336856i	$-0.109364\pi$
$409$	22.6629	+	13.0844i	1.12061	+	0.646984i	0.179052	+	0.983840i	$0.442697\pi$
$410$	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	$0.0195955\pi$
$419$			2.51866i			0.123045i	−0.998106	+	0.0615223i	$0.980404\pi$
$420$	−5.12239	−	15.5722i	−0.249947	−	0.759848i
$421$			33.4873i			1.63207i	0.578003	+	0.816034i	$0.303832\pi$
$421$			33.4873i			1.63207i	−0.578003	+	0.816034i	$0.696168\pi$
$422$	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	0.760351	−	0.649512i	$-0.225027\pi$
$431$	12.0003	+	6.92836i	0.578033	+	0.333727i	−0.182319	+	0.983240i	$0.558360\pi$
$432$	20.5013	−	3.42026i	0.986368	−	0.164557i
$433$		−	9.79368i		−	0.470654i	−0.971916	−	0.235327i	$-0.924384\pi$
$433$		−	9.79368i		−	0.470654i	0.971916	−	0.235327i	$-0.0756161\pi$
$434$	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	−0.323707	−	0.946157i	$-0.604929\pi$
$439$	6.99463	−	4.03835i	0.333835	−	0.192740i	0.657543	+	0.753417i	$0.271596\pi$
$440$	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	0.995981	−	0.0895692i	$-0.0285490\pi$
$443$	8.84884	+	15.3266i	0.420421	+	0.728191i	−0.575559	+	0.817760i	$0.695216\pi$
$444$	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	$0.151901\pi$
$449$			19.4650i			0.918609i	−0.888279	+	0.459305i	$0.848099\pi$
$450$	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	0.988424	−	0.151715i	$-0.0484797\pi$
$457$	7.75626	+	13.4342i	0.362823	+	0.628427i	−0.625601	+	0.780143i	$0.715146\pi$
$458$	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	$-0.993645\pi$
$461$		−	0.857290i		−	0.0399280i	0.999801	−	0.0199640i	$-0.00635516\pi$
$462$	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	−0.285235	−	0.958458i	$-0.592072\pi$
$467$	8.69155	−	5.01807i	0.402197	−	0.232208i	0.687431	+	0.726249i	$0.258738\pi$
$468$	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	−0.494663	−	0.869085i	$-0.664708\pi$
$479$	11.0594	−	19.1555i	0.505318	−	0.875237i	0.999981	−	0.00615194i	$-0.00195824\pi$
$480$	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	−0.489419	−	0.872049i	$-0.662791\pi$
$487$	11.2659	−	19.5131i	0.510506	−	0.884223i	0.999926	−	0.0121746i	$-0.00387541\pi$
$488$	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	−0.279813	−	0.960054i	$-0.590273\pi$
$499$	9.19695	−	5.30986i	0.411712	−	0.237702i	0.691525	+	0.722353i	$0.256939\pi$
$500$	−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	0.0214392	−	0.999770i	$-0.493175\pi$
$509$	20.2595	−	11.6968i	0.897985	−	0.518452i	0.876546	+	0.481318i	$0.159842\pi$
$510$	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	−0.881691	−	0.471827i	$-0.843595\pi$
$521$	−0.735700	+	1.27427i	−0.0322316	+	0.0558267i	0.849460	+	0.527654i	$0.176928\pi$
$522$	−3.11520	+	0.614396i	−0.136348	+	0.0268914i
$523$	5.30372	+	9.18631i	0.231915	+	0.401689i	0.958372	−	0.285523i	$-0.0921674\pi$
$523$	5.30372	+	9.18631i	0.231915	+	0.401689i	−0.726456	+	0.687213i	$0.758834\pi$
$524$	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	−0.769807	−	0.638277i	$-0.779647\pi$
$541$	−14.0009	+	8.08343i	−0.601946	+	0.347534i	0.167861	+	0.985811i	$0.446314\pi$
$542$	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	$0.0855228\pi$
$547$			12.4170i			0.530914i	−0.964123	+	0.265457i	$0.914477\pi$
$548$	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	−0.998635	−	0.0522341i	$-0.983366\pi$
$557$	−10.7167	+	18.5619i	−0.454081	+	0.786492i	0.544554	+	0.838726i	$0.316699\pi$
$558$	−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	0.0717262	−	0.997424i	$-0.477149\pi$
$563$	−17.9430	−	10.3594i	−0.756205	−	0.436595i	−0.827932	+	0.560829i	$0.810483\pi$
$564$	−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	−0.908439	−	0.418018i	$-0.862725\pi$
$569$	−23.8691	+	13.7808i	−1.00064	+	0.577722i	−0.0922056	+	0.995740i	$0.529392\pi$
$570$	7.68065	+	14.3691i	0.321707	+	0.601854i
$571$	−0.339940	−	0.196264i	−0.0142260	−	0.00821340i	0.492870	−	0.870103i	$-0.335948\pi$
$571$	−0.339940	−	0.196264i	−0.0142260	−	0.00821340i	−0.507096	+	0.861889i	$0.669281\pi$
$572$	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	0.209493	−	0.977810i	$-0.432819\pi$
$577$	−12.7927	−	7.38589i	−0.532569	−	0.307479i	−0.742062	+	0.670331i	$0.766152\pi$
$578$	−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	$0.0231052\pi$
$587$			3.51421i			0.145047i	−0.997367	+	0.0725236i	$0.976895\pi$
$588$	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	−0.955012	−	0.296568i	$-0.904158\pi$
$593$	−17.8824	−	30.9732i	−0.734342	−	1.27192i	0.220670	−	0.975349i	$-0.429176\pi$
$594$	−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	−0.451284	−	0.892380i	$-0.649034\pi$
$599$	−35.4819	−	20.4855i	−1.44975	−	0.837014i	−0.998466	+	0.0553669i	$0.982367\pi$
$600$	4.63382	−	7.50705i	0.189175	−	0.306474i
$601$			36.1540i			1.47475i	0.675482	+	0.737377i	$0.263936\pi$
$601$			36.1540i			1.47475i	−0.675482	+	0.737377i	$0.736064\pi$
$602$	−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	−0.305182	−	0.952294i	$-0.598717\pi$
$607$	9.04038	−	5.21946i	0.366938	−	0.211851i	0.672120	+	0.740443i	$0.265384\pi$
$608$	−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	0.387418	−	0.921904i	$-0.373367\pi$
$613$	−5.37925	−	3.10571i	−0.217266	−	0.125439i	−0.604684	+	0.796466i	$0.706700\pi$
$614$	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	$0.149587\pi$
$617$			22.4963i			0.905669i	−0.891595	+	0.452834i	$0.850413\pi$
$618$	−24.1434	−	0.790078i	−0.971191	−	0.0317816i
$619$	−14.1624	+	24.5300i	−0.569235	+	0.985943i	0.427407	+	0.904059i	$0.359427\pi$
$619$	−14.1624	+	24.5300i	−0.569235	+	0.985943i	−0.996642	+	0.0818842i	$0.973906\pi$
$620$	−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	0.498432	−	0.866929i	$-0.333909\pi$
$641$	−0.0793494	−	0.0458124i	−0.00313411	−	0.00180948i	−0.501566	+	0.865119i	$0.667243\pi$
$642$	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	−0.775139	−	0.631791i	$-0.782320\pi$
$647$	4.05903	−	7.03045i	0.159577	−	0.276396i	0.934716	+	0.355395i	$0.115654\pi$
$648$	−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	0.981959	+	0.189095i	$0.0605555\pi$
$653$	16.7312	+	28.9792i	0.654741	+	1.13404i	−0.327218	+	0.944949i	$0.606111\pi$
$654$	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	−0.393130	−	0.919483i	$-0.628608\pi$
$661$	15.4190	−	26.7065i	0.599731	−	1.03876i	0.992861	−	0.119281i	$-0.0380590\pi$
$662$	−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	0.279680	−	0.960093i	$-0.409772\pi$
$677$	32.5497	−	18.7926i	1.25099	−	0.722257i	0.971305	+	0.237836i	$0.0764382\pi$
$678$	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	−0.845841	−	0.533436i	$-0.820901\pi$
$683$	1.02051	−	1.76757i	0.0390487	−	0.0676343i	0.884889	+	0.465802i	$0.154234\pi$
$684$	−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	0.551786	−	0.833986i	$-0.313947\pi$
$691$	−11.7334	−	20.3229i	−0.446360	−	0.773119i	−0.998146	+	0.0608673i	$0.980613\pi$
$692$	−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	0.570093	−	0.821580i	$-0.306907\pi$
$709$	41.7153	−	24.0843i	1.56665	−	0.904505i	0.996556	−	0.0829254i	$-0.0264263\pi$
$710$	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	0.719252	−	0.694749i	$-0.244484\pi$
$719$	−6.49021	−	11.2414i	−0.242044	−	0.419232i	−0.961296	+	0.275517i	$0.911151\pi$
$720$	−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	$0.0714880\pi$
$727$			12.0095i			0.445406i	−0.974886	+	0.222703i	$0.928512\pi$
$728$	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	0.775666	−	0.631143i	$-0.217414\pi$
$733$	−4.29808	−	7.44449i	−0.158753	−	0.274968i	−0.934419	+	0.356175i	$0.884081\pi$
$734$	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	0.540875	−	0.841103i	$-0.318093\pi$
$739$	2.25350	+	1.30106i	0.0828963	+	0.0478602i	−0.457979	+	0.888963i	$0.651426\pi$
$740$	−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	$-0.920913\pi$
$743$		−	13.4061i		−	0.491823i	0.969292	−	0.245911i	$-0.0790872\pi$
$744$	−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	0.686182	−	0.727430i	$-0.259285\pi$
$751$	−7.86182	−	13.6171i	−0.286882	−	0.496894i	−0.973064	+	0.230536i	$0.925952\pi$
$752$	−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	$-0.653367\pi$
$757$		−	48.7626i		−	1.77231i	0.463391	−	0.886154i	$-0.346633\pi$
$758$	−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	−0.927652	−	0.373447i	$-0.878176\pi$
$761$	−21.7170	−	37.6149i	−0.787240	−	1.36354i	0.140411	−	0.990093i	$-0.455158\pi$
$762$	−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	$-0.858043\pi$
$769$		−	23.9226i		−	0.862670i	0.902192	−	0.431335i	$-0.141957\pi$
$770$	−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

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.368276 - 1.36542i) q^{2} +(-1.26610 + 1.18195i) q^{3} +(-1.72875 + 1.00570i) q^{4} +(1.54900 - 0.894317i) q^{5} +(2.08013 + 1.29347i) q^{6} +(2.63573 - 0.230049i) q^{7} +(2.00986 + 1.99009i) q^{8} +(0.206000 - 2.99292i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) \) 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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