LMFDB - Embedded newform 74.2.h.a.3.2

Newspace parameters

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.h (of order $18$, degree $6$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.2
Root			$0.642788 - 0.766044i$ of defining polynomial
Character	$\chi$	$=$	74.3
Dual form			74.2.h.a.25.2

$q$-expansion

$f(q)$	$=$	$q+(0.642788 - 0.766044i) q^{2} +(1.43969 - 1.20805i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.45842 + 4.00698i) q^{5} -1.87939i q^{6} +(-3.39364 - 1.23518i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.0923963 - 0.524005i) q^{9} +O(q^{10})$	\(q+(0.642788 - 0.766044i) q^{2} +(1.43969 - 1.20805i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.45842 + 4.00698i) q^{5} -1.87939i q^{6} +(-3.39364 - 1.23518i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.0923963 - 0.524005i) q^{9} +(2.13207 + 3.69285i) q^{10} +(1.05840 - 1.83321i) q^{11} +(-1.43969 - 1.20805i) q^{12} +(2.84019 - 0.500802i) q^{13} +(-3.12760 + 1.80572i) q^{14} +(2.74094 + 7.53066i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(0.0263137 + 0.00463982i) q^{17} +(-0.342020 - 0.407604i) q^{18} +(-2.07522 - 2.47315i) q^{19} +(4.19936 + 0.740460i) q^{20} +(-6.37796 + 2.32139i) q^{21} +(-0.723990 - 1.98915i) q^{22} +(2.57421 - 1.48622i) q^{23} +(-1.85083 + 0.326352i) q^{24} +(-10.0987 - 8.47380i) q^{25} +(1.44200 - 2.49762i) q^{26} +(2.31908 + 4.01676i) q^{27} +(-0.627119 + 3.55657i) q^{28} +(4.96493 + 2.86650i) q^{29} +(7.53066 + 2.74094i) q^{30} +6.76932i q^{31} +(-0.342020 + 0.939693i) q^{32} +(-0.690823 - 3.91785i) q^{33} +(0.0204685 - 0.0171751i) q^{34} +(9.89872 - 11.7968i) q^{35} -0.532089 q^{36} +(-4.49375 - 4.09954i) q^{37} -3.22847 q^{38} +(3.48401 - 4.15208i) q^{39} +(3.26652 - 2.74094i) q^{40} +(0.259000 + 1.46886i) q^{41} +(-2.32139 + 6.37796i) q^{42} -5.53737i q^{43} +(-1.98915 - 0.723990i) q^{44} +(1.96493 + 1.13445i) q^{45} +(0.516159 - 2.92728i) q^{46} +(-1.30654 - 2.26300i) q^{47} +(-0.939693 + 1.62760i) q^{48} +(4.62880 + 3.88403i) q^{49} +(-12.9826 + 2.28918i) q^{50} +(0.0434888 - 0.0251083i) q^{51} +(-0.986387 - 2.71008i) q^{52} +(-1.79389 + 0.652924i) q^{53} +(4.56769 + 0.805407i) q^{54} +(5.80203 + 6.91459i) q^{55} +(2.32139 + 2.76652i) q^{56} +(-5.97536 - 1.05362i) q^{57} +(5.38726 - 1.96080i) q^{58} +(1.92380 + 5.28560i) q^{59} +(6.94029 - 4.00698i) q^{60} +(-5.65366 + 0.996892i) q^{61} +(5.18560 + 4.35124i) q^{62} +(-0.960802 + 1.66416i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-2.13549 + 12.1110i) q^{65} +(-3.44530 - 1.98915i) q^{66} +(-6.50406 - 2.36728i) q^{67} -0.0267197i q^{68} +(1.91065 - 5.24947i) q^{69} +(-2.67412 - 15.1657i) q^{70} +(-7.10830 + 5.96457i) q^{71} +(-0.342020 + 0.407604i) q^{72} +16.2707 q^{73} +(-6.02896 + 0.807274i) q^{74} -24.7757 q^{75} +(-2.07522 + 2.47315i) q^{76} +(-5.85619 + 4.91392i) q^{77} +(-0.941199 - 5.33781i) q^{78} +(-0.484006 + 1.32980i) q^{79} -4.26414i q^{80} +(9.69119 + 3.52730i) q^{81} +(1.29170 + 0.745761i) q^{82} +(-0.294580 + 1.67065i) q^{83} +(3.39364 + 5.87796i) q^{84} +(-0.0569682 + 0.0986718i) q^{85} +(-4.24187 - 3.55935i) q^{86} +(10.6108 - 1.87098i) q^{87} +(-1.83321 + 1.05840i) q^{88} +(2.82882 + 7.77213i) q^{89} +(2.13207 - 0.776010i) q^{90} +(-10.2572 - 1.80861i) q^{91} +(-1.91065 - 2.27702i) q^{92} +(8.17765 + 9.74574i) q^{93} +(-2.57339 - 0.453757i) q^{94} +(12.9364 - 4.70847i) q^{95} +(0.642788 + 1.76604i) q^{96} +(5.65105 - 3.26264i) q^{97} +(5.95067 - 1.04926i) q^{98} +(-0.862818 - 0.723990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} - 12 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 - 12 * q^7 - 6 * q^9	$ 12 q + 6 q^{3} - 12 q^{7} - 6 q^{9} + 6 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{13} - 18 q^{14} - 18 q^{19} - 6 q^{21} - 18 q^{25} + 12 q^{26} - 6 q^{27} - 6 q^{28} + 18 q^{29} + 24 q^{30} - 6 q^{33} + 12 q^{34} + 18 q^{35} + 12 q^{36} + 30 q^{37} - 24 q^{38} + 30 q^{39} + 12 q^{40} + 24 q^{41} + 6 q^{44} - 18 q^{45} + 30 q^{46} + 6 q^{47} + 12 q^{49} - 36 q^{50} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 36 q^{57} + 6 q^{58} - 36 q^{61} - 6 q^{63} + 6 q^{64} + 36 q^{65} - 30 q^{67} - 18 q^{69} - 12 q^{70} + 12 q^{71} - 48 q^{74} - 36 q^{75} - 18 q^{76} + 12 q^{77} - 6 q^{78} + 6 q^{79} + 24 q^{81} - 48 q^{83} + 12 q^{84} + 18 q^{85} - 36 q^{86} + 36 q^{87} - 36 q^{88} - 18 q^{89} + 6 q^{90} - 6 q^{91} + 18 q^{92} - 12 q^{93} + 36 q^{97} + 36 q^{98} + 30 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 - 12 * q^7 - 6 * q^9 + 6 * q^10 - 6 * q^11 - 6 * q^12 + 6 * q^13 - 18 * q^14 - 18 * q^19 - 6 * q^21 - 18 * q^25 + 12 * q^26 - 6 * q^27 - 6 * q^28 + 18 * q^29 + 24 * q^30 - 6 * q^33 + 12 * q^34 + 18 * q^35 + 12 * q^36 + 30 * q^37 - 24 * q^38 + 30 * q^39 + 12 * q^40 + 24 * q^41 + 6 * q^44 - 18 * q^45 + 30 * q^46 + 6 * q^47 + 12 * q^49 - 36 * q^50 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 36 * q^57 + 6 * q^58 - 36 * q^61 - 6 * q^63 + 6 * q^64 + 36 * q^65 - 30 * q^67 - 18 * q^69 - 12 * q^70 + 12 * q^71 - 48 * q^74 - 36 * q^75 - 18 * q^76 + 12 * q^77 - 6 * q^78 + 6 * q^79 + 24 * q^81 - 48 * q^83 + 12 * q^84 + 18 * q^85 - 36 * q^86 + 36 * q^87 - 36 * q^88 - 18 * q^89 + 6 * q^90 - 6 * q^91 + 18 * q^92 - 12 * q^93 + 36 * q^97 + 36 * q^98 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$3$	1.43969	−	1.20805i	0.831207	−	0.697465i	−0.124361	−	0.992237i	$-0.539688\pi$
$3$	1.43969	−	1.20805i	0.831207	−	0.697465i	0.955568	+	0.294772i	$0.0952436\pi$
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$	−1.45842	+	4.00698i	−0.652226	+	1.79198i	−0.0428683	+	0.999081i	$0.513650\pi$
$5$	−1.45842	+	4.00698i	−0.652226	+	1.79198i	−0.609358	+	0.792895i	$0.708573\pi$
$6$		−	1.87939i		−	0.767256i
$7$	−3.39364	−	1.23518i	−1.28268	−	0.466856i	−0.391359	−	0.920238i	$-0.627995\pi$
$7$	−3.39364	−	1.23518i	−1.28268	−	0.466856i	−0.891316	+	0.453382i	$0.850217\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	0.0923963	−	0.524005i	0.0307988	−	0.174668i
$10$	2.13207	+	3.69285i	0.674220	+	1.16778i
$11$	1.05840	−	1.83321i	0.319120	−	0.552733i	−0.661184	−	0.750223i	$-0.729946\pi$
$11$	1.05840	−	1.83321i	0.319120	−	0.552733i	0.980305	+	0.197491i	$0.0632792\pi$
$12$	−1.43969	−	1.20805i	−0.415603	−	0.348733i
$13$	2.84019	−	0.500802i	0.787726	−	0.138897i	0.234707	−	0.972066i	$-0.424587\pi$
$13$	2.84019	−	0.500802i	0.787726	−	0.138897i	0.553019	+	0.833169i	$0.313476\pi$
$14$	−3.12760	+	1.80572i	−0.835885	+	0.482598i
$15$	2.74094	+	7.53066i	0.707707	+	1.94441i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	0.0263137	+	0.00463982i	0.00638202	+	0.00112532i	0.176838	−	0.984240i	$-0.443413\pi$
$17$	0.0263137	+	0.00463982i	0.00638202	+	0.00112532i	−0.170456	+	0.985365i	$0.554524\pi$
$18$	−0.342020	−	0.407604i	−0.0806149	−	0.0960731i
$19$	−2.07522	−	2.47315i	−0.476088	−	0.567380i	0.473534	−	0.880775i	$-0.342978\pi$
$19$	−2.07522	−	2.47315i	−0.476088	−	0.567380i	−0.949623	+	0.313395i	$0.898534\pi$
$20$	4.19936	+	0.740460i	0.939005	+	0.165572i
$21$	−6.37796	+	2.32139i	−1.39178	+	0.506568i
$22$	−0.723990	−	1.98915i	−0.154355	−	0.424087i
$23$	2.57421	−	1.48622i	0.536760	−	0.309899i	−0.207005	−	0.978340i	$-0.566372\pi$
$23$	2.57421	−	1.48622i	0.536760	−	0.309899i	0.743765	+	0.668441i	$0.233038\pi$
$24$	−1.85083	+	0.326352i	−0.377800	+	0.0666163i
$25$	−10.0987	−	8.47380i	−2.01974	−	1.69476i
$26$	1.44200	−	2.49762i	0.282800	−	0.489823i
$27$	2.31908	+	4.01676i	0.446307	+	0.773026i
$28$	−0.627119	+	3.55657i	−0.118514	+	0.672129i
$29$	4.96493	+	2.86650i	0.921964	+	0.532296i	0.884261	−	0.466993i	$-0.154663\pi$
$29$	4.96493	+	2.86650i	0.921964	+	0.532296i	0.0377027	+	0.999289i	$0.487996\pi$
$30$	7.53066	+	2.74094i	1.37490	+	0.500424i
$31$			6.76932i			1.21581i	0.794011	+	0.607903i	$0.207989\pi$
$31$			6.76932i			1.21581i	−0.794011	+	0.607903i	$0.792011\pi$
$32$	−0.342020	+	0.939693i	−0.0604612	+	0.166116i
$33$	−0.690823	−	3.91785i	−0.120257	−	0.682011i
$34$	0.0204685	−	0.0171751i	0.00351031	−	0.00294550i
$35$	9.89872	−	11.7968i	1.67319	−	1.99403i
$36$	−0.532089			−0.0886815
$37$	−4.49375	−	4.09954i	−0.738767	−	0.673961i
$37$	−4.49375	−	4.09954i	−0.738767	−	0.673961i
$38$	−3.22847			−0.523727
$39$	3.48401	−	4.15208i	0.557887	−	0.664864i
$40$	3.26652	−	2.74094i	0.516482	−	0.433380i
$41$	0.259000	+	1.46886i	0.0404490	+	0.229398i	0.998330	−	0.0577674i	$-0.0183982\pi$
$41$	0.259000	+	1.46886i	0.0404490	+	0.229398i	−0.957881	+	0.287165i	$0.907287\pi$
$42$	−2.32139	+	6.37796i	−0.358198	+	0.984140i
$43$		−	5.53737i		−	0.844441i	−0.906493	−	0.422221i	$-0.861251\pi$
$43$		−	5.53737i		−	0.844441i	0.906493	−	0.422221i	$-0.138749\pi$
$44$	−1.98915	−	0.723990i	−0.299875	−	0.109146i
$45$	1.96493	+	1.13445i	0.292914	+	0.169114i
$46$	0.516159	−	2.92728i	0.0761035	−	0.431605i
$47$	−1.30654	−	2.26300i	−0.190579	−	0.330092i	0.754863	−	0.655882i	$-0.227703\pi$
$47$	−1.30654	−	2.26300i	−0.190579	−	0.330092i	−0.945442	+	0.325790i	$0.894370\pi$
$48$	−0.939693	+	1.62760i	−0.135633	+	0.234923i
$49$	4.62880	+	3.88403i	0.661257	+	0.554861i
$50$	−12.9826	+	2.28918i	−1.83602	+	0.323740i
$51$	0.0434888	−	0.0251083i	0.00608965	−	0.00351586i
$52$	−0.986387	−	2.71008i	−0.136787	−	0.375820i
$53$	−1.79389	+	0.652924i	−0.246410	+	0.0896860i	−0.462273	−	0.886738i	$-0.652966\pi$
$53$	−1.79389	+	0.652924i	−0.246410	+	0.0896860i	0.215862	+	0.976424i	$0.430744\pi$
$54$	4.56769	+	0.805407i	0.621584	+	0.109602i
$55$	5.80203	+	6.91459i	0.782345	+	0.932363i
$56$	2.32139	+	2.76652i	0.310208	+	0.369692i
$57$	−5.97536	−	1.05362i	−0.791456	−	0.139555i
$58$	5.38726	−	1.96080i	0.707382	−	0.257466i
$59$	1.92380	+	5.28560i	0.250457	+	0.688126i	0.999667	+	0.0257935i	$0.00821124\pi$
$59$	1.92380	+	5.28560i	0.250457	+	0.688126i	−0.749210	+	0.662333i	$0.769567\pi$
$60$	6.94029	−	4.00698i	0.895988	−	0.517299i
$61$	−5.65366	+	0.996892i	−0.723876	+	0.127639i	−0.523434	−	0.852066i	$-0.675349\pi$
$61$	−5.65366	+	0.996892i	−0.723876	+	0.127639i	−0.200443	+	0.979705i	$0.564238\pi$
$62$	5.18560	+	4.35124i	0.658572	+	0.552608i
$63$	−0.960802	+	1.66416i	−0.121050	+	0.209664i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−2.13549	+	12.1110i	−0.264875	+	1.50218i
$66$	−3.44530	−	1.98915i	−0.424087	−	0.244847i
$67$	−6.50406	−	2.36728i	−0.794597	−	0.289210i	−0.0873516	−	0.996178i	$-0.527840\pi$
$67$	−6.50406	−	2.36728i	−0.794597	−	0.289210i	−0.707246	+	0.706968i	$0.750063\pi$
$68$		−	0.0267197i		−	0.00324024i
$69$	1.91065	−	5.24947i	0.230015	−	0.631962i
$70$	−2.67412	−	15.1657i	−0.319619	−	1.81265i
$71$	−7.10830	+	5.96457i	−0.843600	+	0.707865i	−0.958371	−	0.285527i	$-0.907831\pi$
$71$	−7.10830	+	5.96457i	−0.843600	+	0.707865i	0.114770	+	0.993392i	$0.463387\pi$
$72$	−0.342020	+	0.407604i	−0.0403075	+	0.0480366i
$73$	16.2707			1.90434			0.952169	−	0.305571i	$-0.0988473\pi$
$73$	16.2707			1.90434			0.952169	+	0.305571i	$0.0988473\pi$
$74$	−6.02896	+	0.807274i	−0.700852	+	0.0938437i
$75$	−24.7757			−2.86085
$76$	−2.07522	+	2.47315i	−0.238044	+	0.283690i
$77$	−5.85619	+	4.91392i	−0.667374	+	0.559993i
$78$	−0.941199	−	5.33781i	−0.106570	−	0.604388i
$79$	−0.484006	+	1.32980i	−0.0544549	+	0.149614i	−0.963938	−	0.266128i	$-0.914256\pi$
$79$	−0.484006	+	1.32980i	−0.0544549	+	0.149614i	0.909483	+	0.415742i	$0.136478\pi$
$80$		−	4.26414i		−	0.476745i
$81$	9.69119	+	3.52730i	1.07680	+	0.391923i
$82$	1.29170	+	0.745761i	0.142644	+	0.0823556i
$83$	−0.294580	+	1.67065i	−0.0323343	+	0.183377i	−0.996697	−	0.0812054i	$-0.974123\pi$
$83$	−0.294580	+	1.67065i	−0.0323343	+	0.183377i	0.964363	+	0.264583i	$0.0852342\pi$
$84$	3.39364	+	5.87796i	0.370276	+	0.641338i
$85$	−0.0569682	+	0.0986718i	−0.00617907	+	0.0107025i
$86$	−4.24187	−	3.55935i	−0.457413	−	0.383815i
$87$	10.6108	−	1.87098i	1.13760	−	0.200590i
$88$	−1.83321	+	1.05840i	−0.195421	+	0.112826i
$89$	2.82882	+	7.77213i	0.299855	+	0.823844i	0.994523	+	0.104514i	$0.0333288\pi$
$89$	2.82882	+	7.77213i	0.299855	+	0.823844i	−0.694669	+	0.719330i	$0.744449\pi$
$90$	2.13207	−	0.776010i	0.224740	−	0.0817986i
$91$	−10.2572	−	1.80861i	−1.07524	−	0.189594i
$92$	−1.91065	−	2.27702i	−0.199199	−	0.237396i
$93$	8.17765	+	9.74574i	0.847983	+	1.01059i
$94$	−2.57339	−	0.453757i	−0.265425	−	0.0468015i
$95$	12.9364	−	4.70847i	1.32725	−	0.483079i
$96$	0.642788	+	1.76604i	0.0656042	+	0.180246i
$97$	5.65105	−	3.26264i	0.573777	−	0.331270i	−0.184879	−	0.982761i	$-0.559189\pi$
$97$	5.65105	−	3.26264i	0.573777	−	0.331270i	0.758657	+	0.651491i	$0.225856\pi$
$98$	5.95067	−	1.04926i	0.601109	−	0.105992i
$99$	−0.862818	−	0.723990i	−0.0867164	−	0.0727637i
$100$	−6.59144	+	11.4167i	−0.659144	+	1.14167i
$101$	−8.29974	−	14.3756i	−0.825855	−	1.43042i	−0.901264	−	0.433271i	$-0.857359\pi$
$101$	−8.29974	−	14.3756i	−0.825855	−	1.43042i	0.0754083	−	0.997153i	$-0.475974\pi$
$102$	0.00872001	−	0.0494537i	0.000863410	−	0.00489664i
$103$	1.64095	+	0.947403i	0.161688	+	0.0933504i	0.578660	−	0.815569i	$-0.303576\pi$
$103$	1.64095	+	0.947403i	0.161688	+	0.0933504i	−0.416973	+	0.908919i	$0.636909\pi$
$104$	−2.71008	−	0.986387i	−0.265745	−	0.0967232i
$105$		−	28.9419i		−	2.82444i
$106$	−0.652924	+	1.79389i	−0.0634176	+	0.174238i
$107$	0.0663781	+	0.376449i	0.00641702	+	0.0363927i	0.987848	−	0.155422i	$-0.0496738\pi$
$107$	0.0663781	+	0.376449i	0.00641702	+	0.0363927i	−0.981431	+	0.191815i	$0.938563\pi$
$108$	3.55303	−	2.98135i	0.341891	−	0.286880i
$109$	−0.620666	+	0.739681i	−0.0594490	+	0.0708485i	−0.794949	−	0.606676i	$-0.792503\pi$
$109$	−0.620666	+	0.739681i	−0.0594490	+	0.0708485i	0.735500	+	0.677524i	$0.236947\pi$
$110$	9.02635			0.860629
$111$	−11.4220	−	0.473431i	−1.08413	−	0.0449361i
$112$	3.61144			0.341249
$113$	1.21535	−	1.44839i	0.114330	−	0.136254i	−0.705844	−	0.708367i	$-0.749432\pi$
$113$	1.21535	−	1.44839i	0.114330	−	0.136254i	0.820174	+	0.572114i	$0.193876\pi$
$114$	−4.64801	+	3.90014i	−0.435326	+	0.365282i
$115$	2.20098	+	12.4824i	0.205242	+	1.16399i
$116$	1.96080	−	5.38726i	0.182056	−	0.500195i
$117$		−	1.53455i		−	0.141869i
$118$	5.28560	+	1.92380i	0.486579	+	0.177100i
$119$	−0.0835683	−	0.0482482i	−0.00766070	−	0.00442291i
$120$	1.39161	−	7.89221i	0.127036	−	0.720457i
$121$	3.25957	+	5.64574i	0.296324	+	0.513249i
$122$	−2.87044	+	4.97174i	−0.259877	+	0.450120i
$123$	2.14733	+	1.80183i	0.193619	+	0.162465i
$124$	6.66648	−	1.17548i	0.598668	−	0.105561i
$125$	30.2182	−	17.4465i	2.70280	−	1.56046i
$126$	0.657228	+	1.80572i	0.0585505	+	0.160866i
$127$	15.1426	−	5.51145i	1.34369	−	0.489062i	0.432715	−	0.901531i	$-0.357556\pi$
$127$	15.1426	−	5.51145i	1.34369	−	0.489062i	0.910972	+	0.412469i	$0.135334\pi$
$128$	0.984808	+	0.173648i	0.0870455	+	0.0153485i
$129$	−6.68940	−	7.97212i	−0.588969	−	0.701906i
$130$	7.90487	+	9.42065i	0.693303	+	0.826246i
$131$	−0.810446	−	0.142903i	−0.0708090	−	0.0124855i	0.138131	−	0.990414i	$-0.455890\pi$
$131$	−0.810446	−	0.142903i	−0.0708090	−	0.0124855i	−0.208940	+	0.977928i	$0.567001\pi$
$132$	−3.73837	+	1.36066i	−0.325384	+	0.118430i
$133$	3.98776	+	10.9563i	0.345782	+	0.950029i
$134$	−5.99417	+	3.46074i	−0.517818	+	0.298962i
$135$	−19.4773	+	3.43437i	−1.67634	+	0.295583i
$136$	−0.0204685	−	0.0171751i	−0.00175516	−	0.00147275i
$137$	−8.67847	+	15.0316i	−0.741452	+	1.28423i	0.210382	+	0.977619i	$0.432529\pi$
$137$	−8.67847	+	15.0316i	−0.741452	+	1.28423i	−0.951834	+	0.306613i	$0.900804\pi$
$138$	−2.79318	−	4.83793i	−0.237772	−	0.411832i
$139$	1.60198	−	9.08528i	0.135878	−	0.770604i	−0.838366	−	0.545108i	$-0.816489\pi$
$139$	1.60198	−	9.08528i	0.135878	−	0.770604i	0.974244	−	0.225496i	$-0.0724002\pi$
$140$	−13.3365	−	7.69983i	−1.12714	−	0.650755i
$141$	−4.61482	−	1.67966i	−0.388638	−	0.141453i
$142$			9.27923i			0.778696i
$143$	2.08799	−	5.73670i	0.174606	−	0.479727i
$144$	0.0923963	+	0.524005i	0.00769969	+	0.0436671i
$145$	−18.7270	+	15.7138i	−1.55519	+	1.30496i
$146$	10.4586	−	12.4641i	0.865559	−	1.03153i
$147$	11.3561			0.936638
$148$	−3.25693	+	5.13735i	−0.267718	+	0.422288i
$149$	−7.73776			−0.633902			−0.316951	−	0.948442i	$-0.602659\pi$
$149$	−7.73776			−0.633902			−0.316951	+	0.948442i	$0.602659\pi$
$150$	−15.9255	+	18.9793i	−1.30031	+	1.54965i
$151$	−9.68000	+	8.12248i	−0.787747	+	0.660998i	−0.945187	−	0.326530i	$-0.894120\pi$
$151$	−9.68000	+	8.12248i	−0.787747	+	0.660998i	0.157440	+	0.987529i	$0.449676\pi$
$152$	0.560618	+	3.17942i	0.0454721	+	0.257885i
$153$	0.00486258	−	0.0133598i	0.000393117	−	0.00108008i
$154$			7.64471i			0.616028i
$155$	−27.1245	−	9.87253i	−2.17870	−	0.792980i
$156$	−4.69399	−	2.71008i	−0.375820	−	0.216980i
$157$	2.26554	−	12.8485i	0.180810	−	1.02542i	−0.750412	−	0.660971i	$-0.770145\pi$
$157$	2.26554	−	12.8485i	0.180810	−	1.02542i	0.931222	−	0.364453i	$-0.118744\pi$
$158$	0.707569	+	1.22555i	0.0562912	+	0.0974992i
$159$	−1.79389	+	3.10712i	−0.142265	+	0.246410i
$160$	−3.26652	−	2.74094i	−0.258241	−	0.216690i
$161$	−10.5717	+	1.86408i	−0.833167	+	0.146910i
$162$	8.93145	−	5.15657i	0.701721	−	0.405139i
$163$	−8.63820	−	23.7332i	−0.676596	−	1.85893i	−0.476558	−	0.879143i	$-0.658116\pi$
$163$	−8.63820	−	23.7332i	−0.676596	−	1.85893i	−0.200038	−	0.979788i	$-0.564107\pi$
$164$	1.40157	−	0.510131i	0.109444	−	0.0398345i
$165$	16.7063	+	2.94577i	1.30058	+	0.229328i
$166$	1.09044	+	1.29953i	0.0846343	+	0.100863i
$167$	−6.60851	−	7.87572i	−0.511382	−	0.609441i	0.447139	−	0.894465i	$-0.352443\pi$
$167$	−6.60851	−	7.87572i	−0.511382	−	0.609441i	−0.958521	+	0.285023i	$0.907999\pi$
$168$	6.68417	+	1.17860i	0.515695	+	0.0909309i
$169$	−4.40014	+	1.60152i	−0.338472	+	0.123194i
$170$	0.0389686	+	0.107065i	0.00298875	+	0.00821153i
$171$	−1.48769	+	0.858917i	−0.113766	+	0.0656830i
$172$	−5.45325	+	0.961555i	−0.415806	+	0.0733179i
$173$	18.1222	+	15.2064i	1.37781	+	1.15612i	0.970016	+	0.243043i	$0.0781456\pi$
$173$	18.1222	+	15.2064i	1.37781	+	1.15612i	0.407792	+	0.913075i	$0.366299\pi$
$174$	5.38726	−	9.33101i	0.408407	−	0.707382i
$175$	23.8046	+	41.2307i	1.79946	+	3.11675i
$176$	−0.367579	+	2.08465i	−0.0277073	+	0.157136i
$177$	9.15492	+	5.28560i	0.688126	+	0.397290i
$178$	7.77213	+	2.82882i	0.582546	+	0.212029i
$179$			5.05746i			0.378013i	0.981976	+	0.189006i	$0.0605267\pi$
$179$			5.05746i			0.378013i	−0.981976	+	0.189006i	$0.939473\pi$
$180$	0.776010	−	2.13207i	0.0578404	−	0.158915i
$181$	−0.181540	−	1.02956i	−0.0134938	−	0.0765269i	0.977317	−	0.211781i	$-0.0679262\pi$
$181$	−0.181540	−	1.02956i	−0.0134938	−	0.0765269i	−0.990811	+	0.135254i	$0.956815\pi$
$182$	−7.97865	+	6.69488i	−0.591417	+	0.496258i
$183$	−6.93524	+	8.26509i	−0.512667	+	0.610973i
$184$	−2.97244			−0.219131
$185$	22.9806	−	12.0275i	1.68956	−	0.884279i
$186$	12.7222			0.932834
$187$	0.0363563	−	0.0433277i	0.00265864	−	0.00316844i
$188$	−2.00174	+	1.67966i	−0.145992	+	0.122502i
$189$	−2.90868	−	16.4959i	−0.211575	−	1.19990i
$190$	4.70847	−	12.9364i	0.341588	−	0.938507i
$191$		−	13.4633i		−	0.974173i	−0.873354	−	0.487087i	$-0.838060\pi$
$191$		−	13.4633i		−	0.974173i	0.873354	−	0.487087i	$-0.161940\pi$
$192$	1.76604	+	0.642788i	0.127453	+	0.0463892i
$193$	3.91641	+	2.26114i	0.281909	+	0.162760i	0.634288	−	0.773097i	$-0.281294\pi$
$193$	3.91641	+	2.26114i	0.281909	+	0.162760i	−0.352378	+	0.935858i	$0.614627\pi$
$194$	1.13310	−	6.42614i	0.0813519	−	0.461370i
$195$	11.5561	+	20.0158i	0.827552	+	1.43336i
$196$	3.02124	−	5.23293i	0.215803	−	0.373781i
$197$	−9.47751	−	7.95257i	−0.675245	−	0.566597i	0.239368	−	0.970929i	$-0.423060\pi$
$197$	−9.47751	−	7.95257i	−0.675245	−	0.566597i	−0.914613	+	0.404331i	$0.867504\pi$
$198$	−1.10922	+	0.195585i	−0.0788286	+	0.0138996i
$199$	−3.90547	+	2.25483i	−0.276852	+	0.159840i	−0.631997	−	0.774971i	$-0.717765\pi$
$199$	−3.90547	+	2.25483i	−0.276852	+	0.159840i	0.355146	+	0.934811i	$0.384431\pi$
$200$	4.50881	+	12.3879i	0.318821	+	0.875954i
$201$	−12.2236	+	4.44904i	−0.862189	+	0.313811i
$202$	−16.3473	−	2.88247i	−1.15019	−	0.202810i
$203$	−13.3085	−	15.8605i	−0.934075	−	1.11319i
$204$	−0.0322786	−	0.0384681i	−0.00225995	−	0.00269331i
$205$	−6.26344	−	1.10441i	−0.437457	−	0.0771356i
$206$	1.78053	−	0.648062i	0.124056	−	0.0451526i
$207$	−0.540940	−	1.48622i	−0.0375980	−	0.103300i
$208$	−2.49762	+	1.44200i	−0.173179	+	0.0999848i
$209$	−6.73022	+	1.18672i	−0.465539	+	0.0820871i
$210$	−22.1708	−	18.6035i	−1.52993	−	1.28376i
$211$	8.12299	−	14.0694i	0.559209	−	0.968579i	−0.438353	−	0.898803i	$-0.644438\pi$
$211$	8.12299	−	14.0694i	0.559209	−	0.968579i	0.997563	−	0.0697764i	$-0.0222286\pi$
$212$	0.954511	+	1.65326i	0.0655561	+	0.113546i
$213$	−3.02829	+	17.1743i	−0.207495	+	1.17676i
$214$	0.331044	+	0.191128i	0.0226297	+	0.0130653i
$215$	22.1881	+	8.07582i	1.51322	+	0.550767i
$216$		−	4.63816i		−	0.315587i
$217$	8.36136	−	22.9726i	0.567606	−	1.55948i
$218$	0.167672	+	0.950915i	0.0113562	+	0.0644041i
$219$	23.4248	−	19.6557i	1.58290	−	1.32821i
$220$	5.80203	−	6.91459i	0.391173	−	0.466181i
$221$	0.0770596			0.00518359
$222$	−7.70462	+	8.44548i	−0.517100	+	0.566824i
$223$	−0.847777			−0.0567713			−0.0283857	−	0.999597i	$-0.509037\pi$
$223$	−0.847777			−0.0567713			−0.0283857	+	0.999597i	$0.509037\pi$
$224$	2.32139	−	2.76652i	0.155104	−	0.184846i
$225$	−5.37339	+	4.50881i	−0.358226	+	0.300588i
$226$	−0.328324	−	1.86202i	−0.0218398	−	0.123860i
$227$	−4.14827	+	11.3973i	−0.275331	+	0.756464i	0.722546	+	0.691323i	$0.242972\pi$
$227$	−4.14827	+	11.3973i	−0.275331	+	0.756464i	−0.997876	+	0.0651411i	$0.979250\pi$
$228$			6.06754i			0.401833i
$229$	−12.4674	−	4.53775i	−0.823867	−	0.299863i	−0.104528	−	0.994522i	$-0.533333\pi$
$229$	−12.4674	−	4.53775i	−0.823867	−	0.299863i	−0.719339	+	0.694659i	$0.755555\pi$
$230$	10.9768	+	6.33746i	0.723788	+	0.417879i
$231$	−2.49486	+	14.1491i	−0.164150	+	0.930941i
$232$	−2.86650	−	4.96493i	−0.188195	−	0.325963i
$233$	−2.15328	+	3.72960i	−0.141066	+	0.244334i	−0.927898	−	0.372833i	$-0.878386\pi$
$233$	−2.15328	+	3.72960i	−0.141066	+	0.244334i	0.786832	+	0.617167i	$0.211720\pi$
$234$	−1.17553	−	0.986387i	−0.0768468	−	0.0644821i
$235$	10.9733	−	1.93489i	0.715818	−	0.126218i
$236$	4.87123	−	2.81241i	0.317090	−	0.183072i
$237$	0.909634	+	2.49920i	0.0590871	+	0.162340i
$238$	−0.0906770	+	0.0330037i	−0.00587771	+	0.00213931i
$239$	−14.0259	−	2.47315i	−0.907262	−	0.159975i	−0.299502	−	0.954096i	$-0.596821\pi$
$239$	−14.0259	−	2.47315i	−0.907262	−	0.159975i	−0.607760	+	0.794121i	$0.707932\pi$
$240$	−5.15127	−	6.13905i	−0.332513	−	0.396274i
$241$	9.16681	+	10.9246i	0.590486	+	0.703714i	0.975699	−	0.219114i	$-0.0703166\pi$
$241$	9.16681	+	10.9246i	0.590486	+	0.703714i	−0.385213	+	0.922828i	$0.625872\pi$
$242$	6.42010	+	1.13204i	0.412699	+	0.0727700i
$243$	5.13816	−	1.87014i	0.329613	−	0.119969i
$244$	1.96349	+	5.39466i	0.125700	+	0.345357i
$245$	−22.3140	+	12.8830i	−1.42559	+	0.823063i
$246$	2.76056	−	0.486761i	0.176007	−	0.0310348i
$247$	−7.13258	−	5.98494i	−0.453835	−	0.380813i
$248$	3.38466	−	5.86241i	0.214926	−	0.372263i
$249$	1.59411	+	2.76108i	0.101023	+	0.174976i
$250$	6.05910	−	34.3629i	0.383211	−	2.17330i
$251$	21.3974	+	12.3538i	1.35059	+	0.779764i	0.988332	−	0.152314i	$-0.0486725\pi$
$251$	21.3974	+	12.3538i	1.35059	+	0.779764i	0.362258	+	0.932078i	$0.382006\pi$
$252$	1.80572	+	0.657228i	0.113750	+	0.0414014i
$253$		−	6.29208i		−	0.395580i
$254$	5.51145	−	15.1426i	0.345819	−	0.950130i
$255$	0.0371834	+	0.210877i	0.00232851	+	0.0132057i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−10.5496	+	12.5726i	−0.658068	+	0.784255i	−0.987107	−	0.160062i	$-0.948831\pi$
$257$	−10.5496	+	12.5726i	−0.658068	+	0.784255i	0.329039	+	0.944316i	$0.393275\pi$
$258$	−10.4069			−0.647903
$259$	10.1865	+	19.4630i	0.632956	+	1.20937i
$260$	12.2978			0.762676
$261$	1.96080	−	2.33679i	0.121371	−	0.144644i
$262$	−0.630415	+	0.528981i	−0.0389472	+	0.0326806i
$263$	−4.88671	−	27.7139i	−0.301327	−	1.70891i	−0.640308	−	0.768118i	$-0.721193\pi$
$263$	−4.88671	−	27.7139i	−0.301327	−	1.70891i	0.338980	−	0.940793i	$-0.389918\pi$
$264$	−1.36066	+	3.73837i	−0.0837426	+	0.230081i
$265$		−	8.14034i		−	0.500057i
$266$	10.9563	+	3.98776i	0.671772	+	0.244505i
$267$	13.4617	+	7.77213i	0.823844	+	0.475647i
$268$	−1.20190	+	6.81632i	−0.0734178	+	0.416373i
$269$	−11.5852	−	20.0661i	−0.706359	−	1.22345i	−0.966199	−	0.257798i	$-0.917003\pi$
$269$	−11.5852	−	20.0661i	−0.706359	−	1.22345i	0.259840	−	0.965652i	$-0.416330\pi$
$270$	−9.88887	+	17.1280i	−0.601818	+	1.04238i
$271$	8.12679	+	6.81919i	0.493667	+	0.414236i	0.855338	−	0.518070i	$-0.173349\pi$
$271$	8.12679	+	6.81919i	0.493667	+	0.414236i	−0.361671	+	0.932306i	$0.617794\pi$
$272$	−0.0263137	+	0.00463982i	−0.00159551	+	0.000281331i
$273$	−16.9520	+	9.78726i	−1.02598	+	0.592352i
$274$	5.93642	+	16.3102i	0.358632	+	0.985335i
$275$	−26.2227	+	9.54428i	−1.58129	+	0.575542i
$276$	−5.50150	−	0.970062i	−0.331151	−	0.0583909i
$277$	15.4537	+	18.4170i	0.928521	+	1.10657i	0.994073	+	0.108719i	$0.0346748\pi$
$277$	15.4537	+	18.4170i	0.928521	+	1.10657i	−0.0655519	+	0.997849i	$0.520881\pi$
$278$	−5.93000	−	7.06710i	−0.355658	−	0.423856i
$279$	3.54716	+	0.625460i	0.212363	+	0.0374453i
$280$	−14.4710	+	5.26700i	−0.864805	+	0.314763i
$281$	4.35215	+	11.9574i	0.259628	+	0.713321i	0.999190	+	0.0402335i	$0.0128102\pi$
$281$	4.35215	+	11.9574i	0.259628	+	0.713321i	−0.739563	+	0.673088i	$0.764968\pi$
$282$	−4.25305	+	2.45550i	−0.253265	+	0.146223i
$283$	−0.253793	+	0.0447506i	−0.0150864	+	0.00266015i	−0.181186	−	0.983449i	$-0.557994\pi$
$283$	−0.253793	+	0.0447506i	−0.0150864	+	0.00266015i	0.166100	+	0.986109i	$0.446883\pi$
$284$	7.10830	+	5.96457i	0.421800	+	0.353932i
$285$	12.9364	−	22.4065i	0.766287	−	1.32725i
$286$	−3.05244	−	5.28697i	−0.180494	−	0.312625i
$287$	0.935363	−	5.30471i	0.0552127	−	0.313127i
$288$	0.460802	+	0.266044i	0.0271530	+	0.0156768i
$289$	−15.9741	−	5.81410i	−0.939653	−	0.342006i
$290$			24.4463i			1.43554i
$291$	4.19436	−	11.5239i	0.245878	−	0.675544i
$292$	−2.82537	−	16.0235i	−0.165342	−	0.937704i
$293$	−6.87967	+	5.77273i	−0.401914	+	0.337246i	−0.821233	−	0.570593i	$-0.806713\pi$
$293$	−6.87967	+	5.77273i	−0.401914	+	0.337246i	0.419319	+	0.907839i	$0.362269\pi$
$294$	7.29958	−	8.69930i	0.425720	−	0.507353i
$295$	−23.9850			−1.39646
$296$	1.84193	+	5.79718i	0.107060	+	0.336954i
$297$	9.81807			0.569702
$298$	−4.97374	+	5.92747i	−0.288121	+	0.343369i
$299$	6.56694	−	5.51032i	0.379776	−	0.318670i
$300$	4.30226	+	24.3993i	0.248391	+	1.40870i
$301$	−6.83967	+	18.7918i	−0.394232	+	1.08314i
$302$			12.6363i			0.727140i
$303$	−29.3154	−	10.6699i	−1.68413	−	0.612972i
$304$	2.79594	+	1.61424i	0.160358	+	0.0925828i
$305$	4.25089	−	24.1080i	0.243405	−	1.38042i
$306$	−0.00710862	−	0.0123125i	−0.000406373	−	0.000703858i
$307$	7.39912	−	12.8157i	0.422290	−	0.731428i	−0.573873	−	0.818944i	$-0.694560\pi$
$307$	7.39912	−	12.8157i	0.422290	−	0.731428i	0.996163	+	0.0875163i	$0.0278930\pi$
$308$	5.85619	+	4.91392i	0.333687	+	0.279997i
$309$	3.50697	−	0.618373i	0.199504	−	0.0351780i
$310$	−24.9981	+	14.4327i	−1.41980	+	0.819721i
$311$	9.13738	+	25.1047i	0.518133	+	1.42356i	0.872574	+	0.488481i	$0.162449\pi$
$311$	9.13738	+	25.1047i	0.518133	+	1.42356i	−0.354441	+	0.935078i	$0.615329\pi$
$312$	−5.09328	+	1.85380i	−0.288350	+	0.104951i
$313$	9.37905	+	1.65378i	0.530135	+	0.0934772i	0.432308	−	0.901726i	$-0.357699\pi$
$313$	9.37905	+	1.65378i	0.530135	+	0.0934772i	0.0978278	+	0.995203i	$0.468811\pi$
$314$	−8.38628	−	9.99438i	−0.473265	−	0.564016i
$315$	−5.26700	−	6.27696i	−0.296762	−	0.353667i
$316$	1.39364	+	0.245736i	0.0783984	+	0.0138237i
$317$	14.2417	−	5.18354i	0.799891	−	0.291137i	0.0904498	−	0.995901i	$-0.471170\pi$
$317$	14.2417	−	5.18354i	0.799891	−	0.291137i	0.709441	+	0.704764i	$0.248947\pi$
$318$	1.22710	+	3.37142i	0.0688121	+	0.189060i
$319$	10.5098	−	6.06783i	0.588435	−	0.339733i
$320$	−4.19936	+	0.740460i	−0.234751	+	0.0413930i
$321$	0.550332	+	0.461783i	0.0307165	+	0.0257742i
$322$	−5.36739	+	9.29660i	−0.299113	+	0.518079i
$323$	−0.0431318	−	0.0747066i	−0.00239992	−	0.00415678i
$324$	1.79086	−	10.1565i	0.0994922	−	0.564248i
$325$	−32.9258	−	19.0097i	−1.82640	−	1.05447i
$326$	−23.7332	−	8.63820i	−1.31446	−	0.478425i
$327$			1.81470i			0.100353i
$328$	0.510131	−	1.40157i	0.0281673	−	0.0773889i
$329$	1.63872	+	9.29362i	0.0903453	+	0.512374i
$330$	12.9952	−	10.9042i	0.715361	−	0.600259i
$331$	1.32812	−	1.58279i	0.0729998	−	0.0869978i	−0.728309	−	0.685249i	$-0.759693\pi$
$331$	1.32812	−	1.58279i	0.0729998	−	0.0869978i	0.801308	+	0.598252i	$0.204138\pi$
$332$	1.69642			0.0931030
$333$	−2.56339	+	1.97596i	−0.140473	+	0.108282i
$334$	−10.2810			−0.562552
$335$	18.9713	−	22.6091i	1.03651	−	1.23527i
$336$	5.19936	−	4.36278i	0.283648	−	0.238009i
$337$	−2.41835	−	13.7152i	−0.131736	−	0.747112i	−0.977077	−	0.212885i	$-0.931714\pi$
$337$	−2.41835	−	13.7152i	−0.131736	−	0.747112i	0.845341	−	0.534227i	$-0.179397\pi$
$338$	−1.60152	+	4.40014i	−0.0871112	+	0.239336i
$339$		−	3.55344i		−	0.192996i
$340$	0.107065	+	0.0389686i	0.00580643	+	0.00211337i
$341$	12.4096	+	7.16467i	0.672016	+	0.387989i
$342$	−0.298299	+	1.69174i	−0.0161301	+	0.0914786i
$343$	1.72903	+	2.99477i	0.0933588	+	0.161702i
$344$	−2.76869	+	4.79551i	−0.149278	+	0.258556i
$345$	18.2480	+	15.3119i	0.982438	+	0.824363i
$346$	23.2975	−	4.10798i	1.25248	−	0.220846i
$347$	−17.5037	+	10.1058i	−0.939647	+	0.542505i	−0.889850	−	0.456254i	$-0.849191\pi$
$347$	−17.5037	+	10.1058i	−0.939647	+	0.542505i	−0.0497972	+	0.998759i	$0.515857\pi$
$348$	−3.68510	−	10.1247i	−0.197542	−	0.542743i
$349$	−10.3271	+	3.75877i	−0.552799	+	0.201202i	−0.603290	−	0.797522i	$-0.706144\pi$
$349$	−10.3271	+	3.75877i	−0.552799	+	0.201202i	0.0504906	+	0.998725i	$0.483922\pi$
$350$	46.8859	+	8.26724i	2.50615	+	0.441903i
$351$	8.59822	+	10.2470i	0.458939	+	0.546942i
$352$	1.36066	+	1.62157i	0.0725232	+	0.0864298i
$353$	−4.29024	−	0.756485i	−0.228346	−	0.0402636i	0.0583041	−	0.998299i	$-0.481431\pi$
$353$	−4.29024	−	0.756485i	−0.228346	−	0.0402636i	−0.286650	+	0.958035i	$0.592542\pi$
$354$	9.93368	−	3.61556i	0.527969	−	0.192165i
$355$	−13.5330	−	37.1817i	−0.718259	−	1.97340i
$356$	7.16283	−	4.13546i	0.379629	−	0.219179i
$357$	−0.178599	+	0.0314918i	−0.00945245	+	0.00166672i
$358$	3.87424	+	3.25088i	0.204760	+	0.171814i
$359$	−3.84332	+	6.65683i	−0.202843	+	0.351334i	−0.949443	−	0.313939i	$-0.898351\pi$
$359$	−3.84332	+	6.65683i	−0.202843	+	0.351334i	0.746600	+	0.665273i	$0.231685\pi$
$360$	−1.13445	−	1.96493i	−0.0597908	−	0.103561i
$361$	1.48938	−	8.44667i	0.0783882	−	0.444562i
$362$	−0.905384	−	0.522724i	−0.0475859	−	0.0274737i
$363$	11.5131	+	4.19042i	0.604280	+	0.219940i
$364$			10.4154i			0.545915i
$365$	−23.7295	+	65.1963i	−1.24206	+	3.41253i
$366$	1.87354	+	10.6254i	0.0979317	+	0.555398i
$367$	15.8706	−	13.3170i	0.828440	−	0.695143i	−0.126492	−	0.991968i	$-0.540372\pi$
$367$	15.8706	−	13.3170i	0.828440	−	0.695143i	0.954932	+	0.296824i	$0.0959275\pi$
$368$	−1.91065	+	2.27702i	−0.0995995	+	0.118698i
$369$	0.793623			0.0413143
$370$	5.55803	−	25.3353i	0.288948	−	1.31712i
$371$	6.89431			0.357935
$372$	8.17765	−	9.74574i	0.423991	−	0.505293i
$373$	11.9553	−	10.0317i	0.619023	−	0.519422i	−0.278473	−	0.960444i	$-0.589828\pi$
$373$	11.9553	−	10.0317i	0.619023	−	0.519422i	0.897496	+	0.441022i	$0.145384\pi$
$374$	−0.00982160	−	0.0557011i	−0.000507863	−	0.00288023i
$375$	22.4288	−	61.6225i	1.15822	−	3.18217i
$376$			2.61309i			0.134760i
$377$	15.5369	+	5.65496i	0.800190	+	0.291245i
$378$	−14.5063	−	8.37520i	−0.746122	−	0.430774i
$379$	−4.37193	+	24.7944i	−0.224571	+	1.27360i	0.638933	+	0.769262i	$0.279376\pi$
$379$	−4.37193	+	24.7944i	−0.224571	+	1.27360i	−0.863504	+	0.504342i	$0.831735\pi$
$380$	−6.88333	−	11.9223i	−0.353107	−	0.611600i
$381$	15.1426	−	26.2277i	0.775778	−	1.34369i
$382$	−10.3135	−	8.65407i	−0.527685	−	0.442781i
$383$	−29.7545	+	5.24652i	−1.52038	+	0.268085i	−0.870584	−	0.492020i	$-0.836259\pi$
$383$	−29.7545	+	5.24652i	−1.52038	+	0.268085i	−0.649801	+	0.760105i	$0.725148\pi$
$384$	1.62760	−	0.939693i	0.0830579	−	0.0479535i
$385$	−11.1492	−	30.6322i	−0.568216	−	1.56116i
$386$	4.24956	−	1.54671i	0.216297	−	0.0787255i
$387$	−2.90161	−	0.511633i	−0.147497	−	0.0260077i
$388$	−4.19436	−	4.99865i	−0.212937	−	0.253768i
$389$	16.0701	+	19.1516i	0.814786	+	0.971024i	0.999932	−	0.0116872i	$-0.00372024\pi$
$389$	16.0701	+	19.1516i	0.814786	+	0.971024i	−0.185146	+	0.982711i	$0.559276\pi$
$390$	22.7612	+	4.01341i	1.15256	+	0.203227i
$391$	0.0746329	−	0.0271642i	0.00377435	−	0.00137375i
$392$	−2.06665	−	5.67806i	−0.104381	−	0.286786i
$393$	−1.33943	+	0.773318i	−0.0675651	+	0.0390088i
$394$	−12.1841	+	2.14838i	−0.613824	+	0.108234i
$395$	−4.62258	−	3.87881i	−0.232587	−	0.195164i
$396$	−0.563164	+	0.975429i	−0.0283001	+	0.0490172i
$397$	−6.83681	−	11.8417i	−0.343130	−	0.594318i	0.641882	−	0.766803i	$-0.278154\pi$
$397$	−6.83681	−	11.8417i	−0.343130	−	0.594318i	−0.985012	+	0.172485i	$0.944820\pi$
$398$	−0.783093	+	4.44114i	−0.0392529	+	0.222614i
$399$	18.9768	+	10.9563i	0.950029	+	0.548499i
$400$	12.3879	+	4.50881i	0.619393	+	0.225441i
$401$		−	1.62020i		−	0.0809089i	−0.999181	−	0.0404544i	$-0.987119\pi$
$401$		−	1.62020i		−	0.0809089i	0.999181	−	0.0404544i	$-0.0128806\pi$
$402$	−4.44904	+	12.2236i	−0.221898	+	0.609659i
$403$	3.39009	+	19.2261i	0.168872	+	0.957723i
$404$	−12.7159	+	10.6699i	−0.632642	+	0.530850i
$405$	−28.2677	+	33.6881i	−1.40463	+	1.67398i
$406$	−20.7044			−1.02754
$407$	−12.2715	+	3.89900i	−0.608276	+	0.193266i
$408$	−0.0502166			−0.00248609
$409$	−5.86780	+	6.99297i	−0.290144	+	0.345780i	−0.891351	−	0.453313i	$-0.850242\pi$
$409$	−5.86780	+	6.99297i	−0.290144	+	0.345780i	0.601208	+	0.799093i	$0.294686\pi$
$410$	−4.87209	+	4.08817i	−0.240615	+	0.201900i
$411$	5.66447	+	32.1248i	0.279408	+	1.58460i
$412$	0.648062	−	1.78053i	0.0319277	−	0.0877206i
$413$		−	20.3137i		−	0.999570i
$414$	−1.48622	−	0.540940i	−0.0730438	−	0.0265858i
$415$	−6.26462	−	3.61688i	−0.307518	−	0.177546i
$416$	−0.500802	+	2.84019i	−0.0245538	+	0.139252i
$417$	−8.66908	−	15.0153i	−0.424526	−	0.735301i
$418$	−3.41702	+	5.91846i	−0.167132	+	0.289481i
$419$	10.9146	+	9.15844i	0.533213	+	0.447419i	0.869209	−	0.494444i	$-0.164628\pi$
$419$	10.9146	+	9.15844i	0.533213	+	0.447419i	−0.335996	+	0.941863i	$0.609073\pi$
$420$	−28.5022	+	5.02571i	−1.39077	+	0.245230i
$421$	29.2667	−	16.8971i	1.42637	−	0.823516i	0.429539	−	0.903048i	$-0.358676\pi$
$421$	29.2667	−	16.8971i	1.42637	−	0.823516i	0.996832	+	0.0795325i	$0.0253427\pi$
$422$	−5.55645	−	15.2662i	−0.270484	−	0.743148i
$423$	−1.30654	+	0.475543i	−0.0635263	+	0.0231217i
$424$	1.88002	+	0.331498i	0.0913018	+	0.0160990i
$425$	−0.226417	−	0.269833i	−0.0109828	−	0.0130888i
$426$	11.2097	+	13.3592i	0.543113	+	0.647257i
$427$	20.4178	+	3.60021i	0.988087	+	0.174226i
$428$	0.359204	−	0.130739i	0.0173628	−	0.00631953i
$429$	−3.92414	−	10.7815i	−0.189459	−	0.520534i
$430$	20.4487	−	11.8061i	0.986124	−	0.569339i
$431$	38.2487	−	6.74428i	1.84238	−	0.324861i	0.859787	−	0.510652i	$-0.170596\pi$
$431$	38.2487	−	6.74428i	1.84238	−	0.324861i	0.982589	+	0.185791i	$0.0594849\pi$
$432$	−3.55303	−	2.98135i	−0.170945	−	0.143440i
$433$	−9.05610	+	15.6856i	−0.435208	+	0.753803i	−0.997313	−	0.0732633i	$-0.976659\pi$
$433$	−9.05610	+	15.6856i	−0.435208	+	0.753803i	0.562104	+	0.827066i	$0.309992\pi$
$434$	−12.2235	−	21.1717i	−0.586746	−	1.01627i
$435$	−7.97810	+	45.2461i	−0.382521	+	2.16938i
$436$	0.836221	+	0.482792i	0.0400477	+	0.0231216i
$437$	−9.01771	−	3.28218i	−0.431376	−	0.157008i
$438$		−	30.5789i		−	1.46111i
$439$	−4.90855	+	13.4861i	−0.234273	+	0.643659i	0.765727	+	0.643165i	$0.222379\pi$
$439$	−4.90855	+	13.4861i	−0.234273	+	0.643659i	−1.00000		0.000493184i	$0.999843\pi$
$440$	−1.56741	−	8.88922i	−0.0747233	−	0.423777i
$441$	2.46293	−	2.06665i	0.117283	−	0.0984117i
$442$	0.0495330	−	0.0590311i	0.00235604	−	0.00280782i
$443$	5.43539			0.258243			0.129121	−	0.991629i	$-0.458784\pi$
$443$	5.43539			0.258243			0.129121	+	0.991629i	$0.458784\pi$
$444$	1.51718	+	11.3307i	0.0720021	+	0.537733i
$445$	−35.2684			−1.67188
$446$	−0.544940	+	0.649435i	−0.0258037	+	0.0307516i
$447$	−11.1400	+	9.34757i	−0.526904	+	0.442125i
$448$	−0.627119	−	3.55657i	−0.0296286	−	0.168032i
$449$	−0.0445442	+	0.122384i	−0.00210217	+	0.00577566i	−0.940739	−	0.339131i	$-0.889867\pi$
$449$	−0.0445442	+	0.122384i	−0.00210217	+	0.00577566i	0.938637	+	0.344906i	$0.112089\pi$
$450$			7.01447i			0.330665i
$451$	2.96686	+	1.07985i	0.139704	+	0.0508480i
$452$	−1.63743	−	0.945373i	−0.0770184	−	0.0444666i
$453$	−4.12389	+	23.3878i	−0.193757	+	1.09885i
$454$	6.06437	+	10.5038i	0.284615	+	0.492968i
$455$	22.2063	−	38.4625i	1.04105	−	1.80315i
$456$	4.64801	+	3.90014i	0.217663	+	0.182641i
$457$	27.8381	−	4.90861i	1.30221	−	0.229615i	0.520825	−	0.853663i	$-0.325624\pi$
$457$	27.8381	−	4.90861i	1.30221	−	0.229615i	0.781386	+	0.624048i	$0.214513\pi$
$458$	−11.4900	+	6.63375i	−0.536892	+	0.309975i
$459$	0.0423866	+	0.116456i	0.00197844	+	0.00543571i
$460$	11.9105	−	4.33508i	0.555331	−	0.202124i
$461$	−7.89127	−	1.39144i	−0.367533	−	0.0648060i	−0.0131684	−	0.999913i	$-0.504192\pi$
$461$	−7.89127	−	1.39144i	−0.367533	−	0.0648060i	−0.354365	+	0.935107i	$0.615303\pi$
$462$	9.23515	+	11.0060i	0.429658	+	0.512047i
$463$	−22.0020	−	26.2210i	−1.02252	−	1.21859i	−0.975568	−	0.219697i	$-0.929493\pi$
$463$	−22.0020	−	26.2210i	−1.02252	−	1.21859i	−0.0469535	−	0.998897i	$-0.514951\pi$
$464$	−5.64591	−	0.995526i	−0.262105	−	0.0462161i
$465$	−50.9775	+	18.5543i	−2.36402	+	0.860434i
$466$	1.47293	+	4.04685i	0.0682323	+	0.187467i
$467$	−17.7860	+	10.2688i	−0.823040	+	0.475182i	−0.851464	−	0.524414i	$-0.824285\pi$
$467$	−17.7860	+	10.2688i	−0.823040	+	0.475182i	0.0284236	+	0.999596i	$0.490951\pi$
$468$	−1.51123	+	0.266471i	−0.0698567	+	0.0123176i
$469$	19.1484	+	16.0674i	0.884191	+	0.741925i
$470$	5.57128	−	9.64974i	0.256984	−	0.445109i
$471$	−12.2599	−	21.2348i	−0.564907	−	0.978448i
$472$	0.976739	−	5.53936i	0.0449581	−	0.254970i
$473$	−10.1512	−	5.86077i	−0.466750	−	0.269479i
$474$	2.49920	+	0.909634i	0.114792	+	0.0417809i
$475$			42.5606i			1.95281i
$476$	−0.0330037	+	0.0906770i	−0.00151272	+	0.00415617i
$477$	0.176387	+	1.00034i	0.00807619	+	0.0458023i
$478$	−10.9102	+	9.15478i	−0.499023	+	0.418730i
$479$	−4.04948	+	4.82598i	−0.185025	+	0.220505i	−0.850582	−	0.525843i	$-0.823750\pi$
$479$	−4.04948	+	4.82598i	−0.185025	+	0.220505i	0.665556	+	0.746348i	$0.268194\pi$
$480$	−8.01396			−0.365786
$481$	−14.8161	−	9.39299i	−0.675558	−	0.428284i
$482$	14.2610			0.649572
$483$	−12.9681	+	15.4548i	−0.590070	+	0.703218i
$484$	4.99395	−	4.19042i	0.226998	−	0.190474i
$485$	4.83170	+	27.4019i	0.219396	+	1.24426i
$486$	1.87014	−	5.13816i	0.0848311	−	0.233071i
$487$			27.5903i			1.25024i	0.780530	+	0.625118i	$0.214949\pi$
$487$			27.5903i			1.25024i	−0.780530	+	0.625118i	$0.785051\pi$
$488$	5.39466	+	1.96349i	0.244205	+	0.0888832i
$489$	−41.1072	−	23.7332i	−1.85893	−	1.07325i
$490$	−4.47421	+	25.3745i	−0.202124	+	1.14630i
$491$	−16.5100	−	28.5962i	−0.745088	−	1.29053i	−0.950154	−	0.311781i	$-0.899074\pi$
$491$	−16.5100	−	28.5962i	−0.745088	−	1.29053i	0.205066	−	0.978748i	$-0.434259\pi$
$492$	1.40157	−	2.42760i	0.0631878	−	0.109444i
$493$	0.117346	+	0.0984648i	0.00528499	+	0.00443463i
$494$	−9.16946	+	1.61682i	−0.412554	+	0.0727443i
$495$	4.15937	−	2.40141i	0.186950	−	0.107935i
$496$	−2.31524	−	6.36108i	−0.103958	−	0.285621i
$497$	31.4904	−	11.4616i	1.41254	−	0.514121i
$498$	3.13979	+	0.553629i	0.140697	+	0.0248087i
$499$	13.5539	+	16.1529i	0.606756	+	0.723103i	0.978733	−	0.205139i	$-0.0657645\pi$
$499$	13.5539	+	16.1529i	0.606756	+	0.723103i	−0.371977	+	0.928242i	$0.621320\pi$
$500$	−22.4288	−	26.7296i	−1.00305	−	1.19538i
$501$	−19.0284	−	3.35523i	−0.850128	−	0.149901i
$502$	23.2175	−	8.45048i	1.03625	−	0.377164i
$503$	6.03817	+	16.5897i	0.269229	+	0.739700i	0.998462	+	0.0554349i	$0.0176545\pi$
$503$	6.03817	+	16.5897i	0.269229	+	0.739700i	−0.729234	+	0.684265i	$0.760123\pi$
$504$	1.66416	−	0.960802i	0.0741275	−	0.0427975i
$505$	69.7072	−	12.2913i	3.10193	−	0.546954i
$506$	−4.82002	−	4.04447i	−0.214276	−	0.179799i
$507$	−4.40014	+	7.62127i	−0.195417	+	0.338472i
$508$	−8.05720	−	13.9555i	−0.357480	−	0.619174i
$509$	7.26094	−	41.1788i	0.321835	−	1.82522i	−0.209203	−	0.977872i	$-0.567087\pi$
$509$	7.26094	−	41.1788i	0.321835	−	1.82522i	0.531039	−	0.847347i	$-0.321802\pi$
$510$	0.185442	+	0.107065i	0.00821153	+	0.00474093i
$511$	−55.2168	−	20.0973i	−2.44265	−	0.889051i
$512$		−	1.00000i		−	0.0441942i
$513$	5.12146	−	14.0711i	0.226118	−	0.621254i
$514$	2.84997	+	16.1630i	0.125707	+	0.712918i
$515$	−6.18942	+	5.19354i	−0.272738	+	0.228855i
$516$	−6.68940	+	7.97212i	−0.294484	+	0.350953i
$517$	−5.53139			−0.243270
$518$	21.4572	+	4.70727i	0.942777	+	0.206826i
$519$	44.4604			1.95160
$520$	7.90487	−	9.42065i	0.346651	−	0.413123i
$521$	27.5629	−	23.1280i	1.20755	−	1.01326i	0.208170	−	0.978093i	$-0.433249\pi$
$521$	27.5629	−	23.1280i	1.20755	−	1.01326i	0.999382	−	0.0351633i	$-0.0111951\pi$
$522$	−0.529708	−	3.00412i	−0.0231847	−	0.131487i
$523$	−11.2216	+	30.8312i	−0.490688	+	1.34815i	0.409363	+	0.912371i	$0.365751\pi$
$523$	−11.2216	+	30.8312i	−0.490688	+	1.34815i	−0.900052	+	0.435783i	$0.856471\pi$
$524$			0.822948i			0.0359507i
$525$	84.0799	+	30.6026i	3.66955	+	1.33561i
$526$	−24.3712	−	14.0707i	−1.06263	−	0.613512i
$527$	−0.0314085	+	0.178126i	−0.00136817	+	0.00775930i
$528$	1.98915	+	3.44530i	0.0865665	+	0.149938i
$529$	−7.08229	+	12.2669i	−0.307926	+	0.533343i
$530$	−6.23586	−	5.23251i	−0.270868	−	0.227286i
$531$	2.94743	−	0.519712i	0.127908	−	0.0225536i
$532$	10.0974	−	5.82971i	0.437776	−	0.252750i
$533$	1.47122	+	4.04214i	0.0637255	+	0.175085i
$534$	14.6068	−	5.31645i	0.632099	−	0.230065i
$535$	−1.60523	−	0.283046i	−0.0694002	−	0.0122371i
$536$	4.44904	+	5.30216i	0.192169	+	0.229018i
$537$	6.10965	+	7.28119i	0.263651	+	0.314207i
$538$	−22.8183	−	4.02348i	−0.983766	−	0.173465i
$539$	12.0194	−	4.37469i	0.517710	−	0.188431i
$540$	6.76439	+	18.5850i	0.291093	+	0.799771i
$541$	32.4941	−	18.7605i	1.39703	−	0.806576i	0.402950	−	0.915222i	$-0.367985\pi$
$541$	32.4941	−	18.7605i	1.39703	−	0.806576i	0.994080	+	0.108646i	$0.0346516\pi$
$542$	10.4476	−	1.84219i	0.448763	−	0.0791290i
$543$	−1.50512	−	1.26295i	−0.0645910	−	0.0541983i
$544$	−0.0133598	+	0.0231399i	−0.000572798	+	0.000992116i
$545$	−2.05869	−	3.56576i	−0.0881847	−	0.152740i
$546$	−3.39908	+	19.2771i	−0.145467	+	0.824986i
$547$	−22.5841	−	13.0389i	−0.965627	−	0.557505i	−0.0677265	−	0.997704i	$-0.521575\pi$
$547$	−22.5841	−	13.0389i	−0.965627	−	0.557505i	−0.897900	+	0.440199i	$0.854908\pi$
$548$	16.3102	+	5.93642i	0.696737	+	0.253591i
$549$			3.05465i			0.130369i
$550$	−9.54428	+	26.2227i	−0.406969	+	1.11814i
$551$	−3.21403	−	18.2276i	−0.136922	−	0.776524i
$552$	−4.27940	+	3.59085i	−0.182144	+	0.152837i
$553$	3.28508	−	3.91501i	0.139696	−	0.166483i
$554$	24.0416			1.02143
$555$	18.5552	−	45.0775i	0.787624	−	1.91343i
$556$	−9.22544			−0.391246
$557$	−4.18253	+	4.98455i	−0.177220	+	0.211202i	−0.847341	−	0.531050i	$-0.821798\pi$
$557$	−4.18253	+	4.98455i	−0.177220	+	0.211202i	0.670121	+	0.742252i	$0.266242\pi$
$558$	2.75920	−	2.31524i	0.116806	−	0.0980121i
$559$	−2.77313	−	15.7272i	−0.117291	−	0.665189i
$560$	−5.26700	+	14.4710i	−0.222571	+	0.611509i
$561$		−	0.106299i		−	0.00448793i
$562$	11.9574	+	4.35215i	0.504394	+	0.183585i
$563$	−33.5577	−	19.3746i	−1.41429	−	0.816540i	−0.418500	−	0.908217i	$-0.637444\pi$
$563$	−33.5577	−	19.3746i	−1.41429	−	0.816540i	−0.995789	+	0.0916766i	$0.970777\pi$
$564$	−0.852785	+	4.83638i	−0.0359087	+	0.203649i
$565$	4.03120	+	6.98224i	0.169594	+	0.293745i
$566$	−0.128854	+	0.223182i	−0.00541615	+	0.00938104i
$567$	−28.5315	−	23.9408i	−1.19821	−	1.00542i
$568$	9.13826	−	1.61132i	0.383433	−	0.0676095i
$569$	11.1846	−	6.45744i	0.468883	−	0.270710i	−0.246889	−	0.969044i	$-0.579408\pi$
$569$	11.1846	−	6.45744i	0.468883	−	0.270710i	0.715772	+	0.698334i	$0.246075\pi$
$570$	−8.84903	−	24.3125i	−0.370645	−	1.01834i
$571$	−2.81875	+	1.02594i	−0.117961	+	0.0429343i	−0.400326	−	0.916373i	$-0.631103\pi$
$571$	−2.81875	+	1.02594i	−0.117961	+	0.0429343i	0.282365	+	0.959307i	$0.408881\pi$
$572$	−6.01212	−	1.06010i	−0.251380	−	0.0443250i
$573$	−16.2643	−	19.3831i	−0.679452	−	0.809739i
$574$	−3.46240	−	4.12633i	−0.144518	−	0.172230i
$575$	−38.5901	−	6.80447i	−1.60932	−	0.283766i
$576$	0.500000	−	0.181985i	0.0208333	−	0.00758271i
$577$	9.86791	+	27.1119i	0.410806	+	1.12868i	0.956763	+	0.290868i	$0.0939440\pi$
$577$	9.86791	+	27.1119i	0.410806	+	1.12868i	−0.545957	+	0.837813i	$0.683834\pi$
$578$	−14.7218	+	8.49964i	−0.612347	+	0.353539i
$579$	8.36999	−	1.47586i	0.347845	−	0.0613344i
$580$	18.7270	+	15.7138i	0.777595	+	0.652480i
$581$	3.06325	−	5.30571i	0.127085	−	0.220118i
$582$	−6.13175	−	10.6205i	−0.254169	−	0.440234i
$583$	−0.701717	+	3.97964i	−0.0290622	+	0.164820i
$584$	−14.0908	−	8.13534i	−0.583082	−	0.336643i
$585$	6.14889	+	2.23801i	0.254225	+	0.0925305i
$586$			8.98077i			0.370992i
$587$	8.30296	−	22.8122i	0.342700	−	0.941560i	−0.641908	−	0.766782i	$-0.721857\pi$
$587$	8.30296	−	22.8122i	0.342700	−	0.941560i	0.984608	−	0.174778i	$-0.0559208\pi$
$588$	−1.97197	−	11.1836i	−0.0813227	−	0.461204i
$589$	16.7416	−	14.0478i	0.689824	−	0.578831i
$590$	−15.4173	+	18.3736i	−0.634719	+	0.756428i
$591$	−23.2518			−0.956450
$592$	5.62487	+	2.31536i	0.231181	+	0.0951606i
$593$	12.0052			0.492995			0.246497	−	0.969143i	$-0.420720\pi$
$593$	12.0052			0.492995			0.246497	+	0.969143i	$0.420720\pi$
$594$	6.31094	−	7.52108i	0.258941	−	0.308594i
$595$	0.315207	−	0.264490i	0.0129222	−	0.0108431i
$596$	1.34365	+	7.62021i	0.0550380	+	0.312136i
$597$	−2.89875	+	7.96425i	−0.118638	+	0.325955i
$598$		−	8.57253i		−	0.350557i
$599$	17.9026	+	6.51602i	0.731481	+	0.266237i	0.680792	−	0.732477i	$-0.261636\pi$
$599$	17.9026	+	6.51602i	0.731481	+	0.266237i	0.0506895	+	0.998714i	$0.483858\pi$
$600$	21.4564	+	12.3879i	0.875954	+	0.505732i
$601$	−3.95300	+	22.4186i	−0.161246	+	0.914472i	0.791605	+	0.611033i	$0.209246\pi$
$601$	−3.95300	+	22.4186i	−0.161246	+	0.914472i	−0.952851	+	0.303439i	$0.901865\pi$
$602$	9.99893	+	17.3187i	0.407526	+	0.705856i
$603$	−1.84142	+	3.18943i	−0.0749884	+	0.129884i
$604$	9.68000	+	8.12248i	0.393874	+	0.330499i
$605$	−27.3762	+	4.82716i	−1.11300	+	0.196252i
$606$	−27.0173	+	15.5984i	−1.09750	+	0.633642i
$607$	−6.70527	−	18.4226i	−0.272159	−	0.747750i	−0.998193	−	0.0600911i	$-0.980861\pi$
$607$	−6.70527	−	18.4226i	−0.272159	−	0.747750i	0.726034	−	0.687658i	$-0.241361\pi$
$608$	3.03377	−	1.10420i	0.123036	−	0.0447813i
$609$	−38.3203	−	6.75691i	−1.55282	−	0.273804i
$610$	−15.7354	−	18.7527i	−0.637106	−	0.759274i
$611$	−4.84414	−	5.77302i	−0.195973	−	0.233551i
$612$	−0.0140013	−	0.00246880i	−0.000565967	−	9.97953e-5i
$613$	2.38568	−	0.868317i	0.0963568	−	0.0350710i	−0.293392	−	0.955992i	$-0.594784\pi$
$613$	2.38568	−	0.868317i	0.0963568	−	0.0350710i	0.389749	+	0.920921i	$0.372562\pi$
$614$	−5.06130	−	13.9058i	−0.204257	−	0.561192i
$615$	−10.3516	+	5.97650i	−0.417417	+	0.240996i
$616$	7.52857	−	1.32749i	0.303335	−	0.0534861i
$617$	−14.5342	−	12.1956i	−0.585124	−	0.490977i	0.301502	−	0.953466i	$-0.402512\pi$
$617$	−14.5342	−	12.1956i	−0.585124	−	0.490977i	−0.886625	+	0.462489i	$0.846957\pi$
$618$	1.78053	−	3.08398i	0.0716236	−	0.124056i
$619$	−1.25679	−	2.17683i	−0.0505147	−	0.0874940i	0.839662	−	0.543109i	$-0.182753\pi$
$619$	−1.25679	−	2.17683i	−0.0505147	−	0.0874940i	−0.890177	+	0.455615i	$0.849420\pi$
$620$	−5.01241	+	28.4268i	−0.201303	+	1.14165i
$621$	11.9396	+	6.89333i	0.479119	+	0.276620i
$622$	25.1047	+	9.13738i	1.00661	+	0.366376i
$623$		−	29.8699i		−	1.19671i
$624$	−1.85380	+	5.09328i	−0.0742114	+	0.203894i
$625$	14.3909	+	81.6150i	0.575637	+	3.26460i
$626$	7.29561	−	6.12174i	0.291591	−	0.244674i
$627$	−8.25584	+	9.83892i	−0.329706	+	0.392929i
$628$	−13.0467			−0.520621
$629$	−0.0992261	−	0.128724i	−0.00395640	−	0.00513258i
$630$	−8.19399			−0.326456
$631$	−4.27007	+	5.08887i	−0.169989	+	0.202585i	−0.844313	−	0.535851i	$-0.819991\pi$
$631$	−4.27007	+	5.08887i	−0.169989	+	0.202585i	0.674324	+	0.738436i	$0.264435\pi$
$632$	1.08406	−	0.909634i	0.0431216	−	0.0361833i
$633$	−5.30190	−	30.0686i	−0.210732	−	1.19512i
$634$	5.18354	−	14.2417i	0.205865	−	0.565609i
$635$			68.7140i			2.72683i
$636$	3.37142	+	1.22710i	0.133685	+	0.0486575i
$637$	15.0918	+	8.71325i	0.597958	+	0.345231i
$638$	2.10733	−	11.9513i	0.0834301	−	0.473156i
$639$	2.46869	+	4.27589i	0.0976598	+	0.169152i
$640$	−2.13207	+	3.69285i	−0.0842775	+	0.145973i
$641$	6.30793	+	5.29298i	0.249148	+	0.209060i	0.758805	−	0.651317i	$-0.225783\pi$
$641$	6.30793	+	5.29298i	0.249148	+	0.209060i	−0.509657	+	0.860378i	$0.670228\pi$
$642$	0.707493	−	0.124750i	0.0279225	−	0.00492349i
$643$	−12.3142	+	7.10959i	−0.485623	+	0.280375i	−0.722757	−	0.691102i	$-0.757125\pi$
$643$	−12.3142	+	7.10959i	−0.485623	+	0.280375i	0.237134	+	0.971477i	$0.423792\pi$
$644$	3.67151	+	10.0874i	0.144678	+	0.397499i
$645$	41.7001	−	15.1776i	1.64194	−	0.597617i
$646$	−0.0849532	−	0.0149795i	−0.00334244	−	0.000589362i
$647$	25.6313	+	30.5462i	1.00767	+	1.20089i	0.979532	+	0.201291i	$0.0645136\pi$
$647$	25.6313	+	30.5462i	1.00767	+	1.20089i	0.0281389	+	0.999604i	$0.491042\pi$
$648$	−6.62916	−	7.90033i	−0.260418	−	0.310354i
$649$	11.7258	+	2.06757i	0.460276	+	0.0811591i
$650$	−35.7266	+	13.0034i	−1.40131	+	0.510036i
$651$	−15.7142	−	43.1744i	−0.615889	−	1.69214i
$652$	−21.8727	+	12.6282i	−0.856600	+	0.494558i
$653$	7.99174	−	1.40916i	0.312741	−	0.0551447i	−0.0150747	−	0.999886i	$-0.504799\pi$
$653$	7.99174	−	1.40916i	0.312741	−	0.0551447i	0.327816	+	0.944742i	$0.393687\pi$
$654$	1.39014	+	1.16647i	0.0543590	+	0.0456126i
$655$	1.75458	−	3.03903i	0.0685572	−	0.118745i
$656$	−0.745761	−	1.29170i	−0.0291171	−	0.0504323i
$657$	1.50335	−	8.52592i	0.0586513	−	0.332628i
$658$	8.17267	+	4.71850i	0.318604	+	0.183946i
$659$	26.3535	+	9.59188i	1.02659	+	0.373647i	0.799780	−	0.600293i	$-0.204950\pi$
$659$	26.3535	+	9.59188i	1.02659	+	0.373647i	0.226806	+	0.973940i	$0.427172\pi$
$660$		−	16.9640i		−	0.660323i
$661$	−1.54764	+	4.25209i	−0.0601961	+	0.165387i	−0.966145	−	0.258000i	$-0.916937\pi$
$661$	−1.54764	+	4.25209i	−0.0601961	+	0.165387i	0.905949	+	0.423387i	$0.139159\pi$
$662$	−0.358788	−	2.03479i	−0.0139447	−	0.0790844i
$663$	0.110942	−	0.0930915i	0.00430864	−	0.00361537i
$664$	1.09044	−	1.29953i	0.0423171	−	0.0504316i
$665$	−49.7174			−1.92796
$666$	−0.134037	+	3.23379i	−0.00519383	+	0.125307i
$667$	17.0410			0.659831
$668$	−6.60851	+	7.87572i	−0.255691	+	0.304721i
$669$	−1.22054	+	1.02415i	−0.0471887	+	0.0395960i
$670$	−5.12508	−	29.0658i	−0.197999	−	1.12291i
$671$	−4.15633	+	11.4194i	−0.160454	+	0.440842i
$672$		−	6.78728i		−	0.261825i
$673$	−9.85346	−	3.58637i	−0.379823	−	0.138244i	0.145051	−	0.989424i	$-0.453665\pi$
$673$	−9.85346	−	3.58637i	−0.379823	−	0.138244i	−0.524874	+	0.851180i	$0.675888\pi$
$674$	−12.0609	−	6.96337i	−0.464569	−	0.268219i
$675$	10.6176	−	60.2154i	0.408671	−	2.31769i
$676$	2.34127	+	4.05519i	0.0900487	+	0.155969i
$677$	−13.4277	+	23.2574i	−0.516067	+	0.893853i	0.483760	+	0.875201i	$0.339271\pi$
$677$	−13.4277	+	23.2574i	−0.516067	+	0.893853i	−0.999826	+	0.0186525i	$0.994062\pi$
$678$	−2.72209	−	2.28411i	−0.104541	−	0.0877206i
$679$	−23.2076	+	4.09212i	−0.890625	+	0.157041i
$680$	0.0986718	−	0.0569682i	0.00378389	−	0.00218463i
$681$	7.79620	+	21.4199i	0.298751	+	0.820812i
$682$	13.4652	−	4.90092i	0.515608	−	0.187666i
$683$	17.6006	+	3.10346i	0.673469	+	0.118751i	0.499916	−	0.866074i	$-0.333364\pi$
$683$	17.6006	+	3.10346i	0.673469	+	0.118751i	0.173553	+	0.984825i	$0.444475\pi$
$684$	1.10420	+	1.31594i	0.0422202	+	0.0503161i
$685$	−47.5743	−	56.6968i	−1.81772	−	2.16627i
$686$	3.40552	+	0.600485i	0.130023	+	0.0229266i
$687$	−23.4310	+	8.52819i	−0.893948	+	0.325371i
$688$	1.89389	+	5.20343i	0.0722040	+	0.198379i
$689$	−4.76801	+	2.75281i	−0.181647	+	0.104874i
$690$	23.4591	−	4.13648i	0.893074	−	0.157473i
$691$	16.1699	+	13.5682i	0.615133	+	0.516158i	0.896269	−	0.443510i	$-0.146267\pi$
$691$	16.1699	+	13.5682i	0.615133	+	0.516158i	−0.281137	+	0.959668i	$0.590711\pi$
$692$	11.8284	−	20.4875i	0.449650	−	0.778817i
$693$	2.03383	+	3.52270i	0.0772589	+	0.133816i
$694$	−3.50969	+	19.9044i	−0.133226	+	0.755563i
$695$	34.0682	+	19.6693i	1.29228	+	0.746098i
$696$	−10.1247	−	3.68510i	−0.383777	−	0.139683i
$697$			0.0398530i			0.00150954i
$698$	−3.75877	+	10.3271i	−0.142272	+	0.390888i
$699$	1.40546	+	7.97074i	0.0531593	+	0.301481i
$700$	36.4707	−	30.6026i	1.37846	−	1.15667i
$701$	2.94056	−	3.50442i	0.111063	−	0.132360i	−0.707649	−	0.706564i	$-0.750244\pi$
$701$	2.94056	−	3.50442i	0.111063	−	0.132360i	0.818712	+	0.574204i	$0.194688\pi$
$702$	13.3765			0.504862
$703$	−0.813275	+	19.6212i	−0.0306733	+	0.740027i
$704$	2.11681			0.0797801
$705$	13.4607	−	16.0419i	0.506960	−	0.604171i
$706$	−3.33721	+	2.80025i	−0.125598	+	0.105389i
$707$	10.4099	+	59.0372i	0.391503	+	2.22032i
$708$	3.61556	−	9.93368i	0.135881	−	0.373330i
$709$			4.67695i			0.175647i	0.996136	+	0.0878233i	$0.0279911\pi$
$709$			4.67695i			0.175647i	−0.996136	+	0.0878233i	$0.972009\pi$
$710$	−37.1817	−	13.5330i	−1.39540	−	0.507886i
$711$	0.652100	+	0.376490i	0.0244556	+	0.0141195i
$712$	1.43623	−	8.14527i	0.0538251	−	0.305257i
$713$	10.0607	+	17.4257i	0.376777	+	0.652596i
$714$	−0.0906770	+	0.157057i	−0.00339350	+	0.00587771i
$715$	19.9417	+	16.7331i	0.745777	+	0.625781i
$716$	4.98063	−	0.878219i	0.186135	−	0.0328206i
$717$	−23.1807	+	13.3834i	−0.865699	+	0.499812i
$718$	2.62899	+	7.22308i	0.0981129	+	0.269563i
$719$	−43.2845	+	15.7543i	−1.61424	+	0.587535i	−0.982272	−	0.187460i	$-0.939974\pi$
$719$	−43.2845	+	15.7543i	−1.61424	+	0.587535i	−0.631967	+	0.774995i	$0.717752\pi$
$720$	−2.23443	−	0.393991i	−0.0832724	−	0.0146832i
$721$	−4.39857	−	5.24202i	−0.163811	−	0.195223i
$722$	−5.51317	−	6.57034i	−0.205179	−	0.244523i
$723$	26.3948	+	4.65411i	0.981632	+	0.173088i
$724$	−0.982399	+	0.357564i	−0.0365106	+	0.0132888i
$725$	−25.8490	−	71.0196i	−0.960009	−	2.63760i
$726$	10.6105	−	6.12598i	0.393793	−	0.227357i
$727$	−42.9014	+	7.56467i	−1.59112	+	0.280558i	−0.897912	−	0.440175i	$-0.854916\pi$
$727$	−42.9014	+	7.56467i	−1.59112	+	0.280558i	−0.693213	+	0.720733i	$0.743805\pi$
$728$	7.97865	+	6.69488i	0.295708	+	0.248129i
$729$	−10.3316	+	17.8948i	−0.382651	+	0.662770i
$730$	34.6902	+	60.0852i	1.28394	+	2.22385i
$731$	0.0256924	−	0.145709i	0.000950269	−	0.00538924i
$732$	9.34382	+	5.39466i	0.345357	+	0.199392i
$733$	26.1238	+	9.50828i	0.964904	+	0.351196i	0.775953	−	0.630790i	$-0.217269\pi$
$733$	26.1238	+	9.50828i	0.964904	+	0.351196i	0.188950	+	0.981987i	$0.439491\pi$
$734$		−	20.7176i		−	0.764702i
$735$	−16.5620	+	45.5038i	−0.610900	+	1.67843i
$736$	0.516159	+	2.92728i	0.0190259	+	0.107901i
$737$	−11.2236	+	9.41775i	−0.413428	+	0.346907i
$738$	0.510131	−	0.607950i	0.0187782	−	0.0223790i
$739$	26.4463			0.972843			0.486421	−	0.873724i	$-0.338302\pi$
$739$	26.4463			0.972843			0.486421	+	0.873724i	$0.338302\pi$
$740$	−15.8353	−	20.5429i	−0.582117	−	0.755171i
$741$	−17.4988			−0.642835
$742$	4.43158	−	5.28135i	0.162688	−	0.193884i
$743$	31.0557	−	26.0589i	1.13932	−	0.956007i	0.139908	−	0.990165i	$-0.455319\pi$
$743$	31.0557	−	26.0589i	1.13932	−	0.956007i	0.999416	+	0.0341578i	$0.0108749\pi$
$744$	−2.20918	−	12.5289i	−0.0809925	−	0.459331i
$745$	11.2849	−	31.0051i	0.413447	−	1.13594i
$746$		−	15.6066i		−	0.571397i
$747$	0.848209	+	0.308723i	0.0310343	+	0.0112956i
$748$	−0.0489827	−	0.0282802i	−0.00179098	−	0.00103403i
$749$	0.239720	−	1.35952i	0.00875919	−	0.0496759i
$750$	−32.7887	−	56.7916i	−1.19727	−	2.07374i
$751$	−5.14164	+	8.90559i	−0.187621	+	0.324969i	−0.944457	−	0.328636i	$-0.893411\pi$
$751$	−5.14164	+	8.90559i	−0.187621	+	0.324969i	0.756835	+	0.653605i	$0.226744\pi$
$752$	2.00174	+	1.67966i	0.0729959	+	0.0612509i
$753$	45.7296	−	8.06336i	1.66648	−	0.293845i
$754$	14.3189	−	8.26700i	0.521462	−	0.301066i
$755$	−18.4291	−	50.6336i	−0.670704	−	1.84274i
$756$	−15.7402	+	5.72898i	−0.572467	+	0.208361i
$757$	−34.9139	−	6.15626i	−1.26897	−	0.223753i	−0.501678	−	0.865054i	$-0.667284\pi$
$757$	−34.9139	−	6.15626i	−1.26897	−	0.223753i	−0.767289	+	0.641301i	$0.778395\pi$
$758$	16.1834	+	19.2866i	0.587808	+	0.700522i
$759$	−7.60112	−	9.05867i	−0.275903	−	0.328809i
$760$	−13.5575	−	2.39055i	−0.491782	−	0.0867145i
$761$	−4.68947	+	1.70683i	−0.169993	+	0.0618725i	−0.425615	−	0.904904i	$-0.639942\pi$
$761$	−4.68947	+	1.70683i	−0.169993	+	0.0618725i	0.255622	+	0.966777i	$0.417720\pi$
$762$	−10.3581	−	28.4587i	−0.375236	−	1.03095i
$763$	3.01996	−	1.74357i	0.109330	−	0.0631216i
$764$	−13.2588	+	2.33788i	−0.479687	+	0.0845817i
$765$	0.0464409	+	0.0389686i	0.00167907	+	0.00140891i
$766$	−15.1068	+	26.1657i	−0.545829	+	0.945404i
$767$	8.11099	+	14.0486i	0.292871	+	0.507267i
$768$	0.326352	−	1.85083i	0.0117762	−	0.0667862i
$769$	−30.5000	−	17.6092i	−1.09986	−	0.635004i	−0.163675	−	0.986514i	$-0.552335\pi$
$769$	−30.5000	−	17.6092i	−1.09986	−	0.635004i	−0.936184	+	0.351511i	$0.885668\pi$
$770$	−30.6322	−	11.1492i	−1.10391	−	0.401789i

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	74.h (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 - 0.766044i) q^{2} +(1.43969 - 1.20805i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.45842 + 4.00698i) q^{5} -1.87939i q^{6} +(-3.39364 - 1.23518i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.0923963 - 0.524005i) q^{9} +O(q^{10})\)	\(q+(0.642788 - 0.766044i) q^{2} +(1.43969 - 1.20805i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.45842 + 4.00698i) q^{5} -1.87939i q^{6} +(-3.39364 - 1.23518i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.0923963 - 0.524005i) q^{9} +(2.13207 + 3.69285i) q^{10} +(1.05840 - 1.83321i) q^{11} +(-1.43969 - 1.20805i) q^{12} +(2.84019 - 0.500802i) q^{13} +(-3.12760 + 1.80572i) q^{14} +(2.74094 + 7.53066i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(0.0263137 + 0.00463982i) q^{17} +(-0.342020 - 0.407604i) q^{18} +(-2.07522 - 2.47315i) q^{19} +(4.19936 + 0.740460i) q^{20} +(-6.37796 + 2.32139i) q^{21} +(-0.723990 - 1.98915i) q^{22} +(2.57421 - 1.48622i) q^{23} +(-1.85083 + 0.326352i) q^{24} +(-10.0987 - 8.47380i) q^{25} +(1.44200 - 2.49762i) q^{26} +(2.31908 + 4.01676i) q^{27} +(-0.627119 + 3.55657i) q^{28} +(4.96493 + 2.86650i) q^{29} +(7.53066 + 2.74094i) q^{30} +6.76932i q^{31} +(-0.342020 + 0.939693i) q^{32} +(-0.690823 - 3.91785i) q^{33} +(0.0204685 - 0.0171751i) q^{34} +(9.89872 - 11.7968i) q^{35} -0.532089 q^{36} +(-4.49375 - 4.09954i) q^{37} -3.22847 q^{38} +(3.48401 - 4.15208i) q^{39} +(3.26652 - 2.74094i) q^{40} +(0.259000 + 1.46886i) q^{41} +(-2.32139 + 6.37796i) q^{42} -5.53737i q^{43} +(-1.98915 - 0.723990i) q^{44} +(1.96493 + 1.13445i) q^{45} +(0.516159 - 2.92728i) q^{46} +(-1.30654 - 2.26300i) q^{47} +(-0.939693 + 1.62760i) q^{48} +(4.62880 + 3.88403i) q^{49} +(-12.9826 + 2.28918i) q^{50} +(0.0434888 - 0.0251083i) q^{51} +(-0.986387 - 2.71008i) q^{52} +(-1.79389 + 0.652924i) q^{53} +(4.56769 + 0.805407i) q^{54} +(5.80203 + 6.91459i) q^{55} +(2.32139 + 2.76652i) q^{56} +(-5.97536 - 1.05362i) q^{57} +(5.38726 - 1.96080i) q^{58} +(1.92380 + 5.28560i) q^{59} +(6.94029 - 4.00698i) q^{60} +(-5.65366 + 0.996892i) q^{61} +(5.18560 + 4.35124i) q^{62} +(-0.960802 + 1.66416i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-2.13549 + 12.1110i) q^{65} +(-3.44530 - 1.98915i) q^{66} +(-6.50406 - 2.36728i) q^{67} -0.0267197i q^{68} +(1.91065 - 5.24947i) q^{69} +(-2.67412 - 15.1657i) q^{70} +(-7.10830 + 5.96457i) q^{71} +(-0.342020 + 0.407604i) q^{72} +16.2707 q^{73} +(-6.02896 + 0.807274i) q^{74} -24.7757 q^{75} +(-2.07522 + 2.47315i) q^{76} +(-5.85619 + 4.91392i) q^{77} +(-0.941199 - 5.33781i) q^{78} +(-0.484006 + 1.32980i) q^{79} -4.26414i q^{80} +(9.69119 + 3.52730i) q^{81} +(1.29170 + 0.745761i) q^{82} +(-0.294580 + 1.67065i) q^{83} +(3.39364 + 5.87796i) q^{84} +(-0.0569682 + 0.0986718i) q^{85} +(-4.24187 - 3.55935i) q^{86} +(10.6108 - 1.87098i) q^{87} +(-1.83321 + 1.05840i) q^{88} +(2.82882 + 7.77213i) q^{89} +(2.13207 - 0.776010i) q^{90} +(-10.2572 - 1.80861i) q^{91} +(-1.91065 - 2.27702i) q^{92} +(8.17765 + 9.74574i) q^{93} +(-2.57339 - 0.453757i) q^{94} +(12.9364 - 4.70847i) q^{95} +(0.642788 + 1.76604i) q^{96} +(5.65105 - 3.26264i) q^{97} +(5.95067 - 1.04926i) q^{98} +(-0.862818 - 0.723990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} - 12 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 - 12 * q^7 - 6 * q^9	\( 12 q + 6 q^{3} - 12 q^{7} - 6 q^{9} + 6 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{13} - 18 q^{14} - 18 q^{19} - 6 q^{21} - 18 q^{25} + 12 q^{26} - 6 q^{27} - 6 q^{28} + 18 q^{29} + 24 q^{30} - 6 q^{33} + 12 q^{34} + 18 q^{35} + 12 q^{36} + 30 q^{37} - 24 q^{38} + 30 q^{39} + 12 q^{40} + 24 q^{41} + 6 q^{44} - 18 q^{45} + 30 q^{46} + 6 q^{47} + 12 q^{49} - 36 q^{50} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 36 q^{57} + 6 q^{58} - 36 q^{61} - 6 q^{63} + 6 q^{64} + 36 q^{65} - 30 q^{67} - 18 q^{69} - 12 q^{70} + 12 q^{71} - 48 q^{74} - 36 q^{75} - 18 q^{76} + 12 q^{77} - 6 q^{78} + 6 q^{79} + 24 q^{81} - 48 q^{83} + 12 q^{84} + 18 q^{85} - 36 q^{86} + 36 q^{87} - 36 q^{88} - 18 q^{89} + 6 q^{90} - 6 q^{91} + 18 q^{92} - 12 q^{93} + 36 q^{97} + 36 q^{98} + 30 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 - 12 * q^7 - 6 * q^9 + 6 * q^10 - 6 * q^11 - 6 * q^12 + 6 * q^13 - 18 * q^14 - 18 * q^19 - 6 * q^21 - 18 * q^25 + 12 * q^26 - 6 * q^27 - 6 * q^28 + 18 * q^29 + 24 * q^30 - 6 * q^33 + 12 * q^34 + 18 * q^35 + 12 * q^36 + 30 * q^37 - 24 * q^38 + 30 * q^39 + 12 * q^40 + 24 * q^41 + 6 * q^44 - 18 * q^45 + 30 * q^46 + 6 * q^47 + 12 * q^49 - 36 * q^50 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 36 * q^57 + 6 * q^58 - 36 * q^61 - 6 * q^63 + 6 * q^64 + 36 * q^65 - 30 * q^67 - 18 * q^69 - 12 * q^70 + 12 * q^71 - 48 * q^74 - 36 * q^75 - 18 * q^76 + 12 * q^77 - 6 * q^78 + 6 * q^79 + 24 * q^81 - 48 * q^83 + 12 * q^84 + 18 * q^85 - 36 * q^86 + 36 * q^87 - 36 * q^88 - 18 * q^89 + 6 * q^90 - 6 * q^91 + 18 * q^92 - 12 * q^93 + 36 * q^97 + 36 * q^98 + 30 * q^99

Introduction

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