LMFDB - Embedded newform 74.2.f.b.53.2

Newspace parameters

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	74.f (of order $9$, degree $6$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$0.590892974957$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
Defining polynomial:	$ x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 $ x^12 - 24x^10 + 264x^8 - 1687x^6 + 6600x^4 - 15000*x^2 + 15625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			53.2
Root			$-2.00752 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	74.53
Dual form			74.2.f.b.7.2

$q$-expansion

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(1.72328 - 0.627223i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.326352 + 1.85083i) q^{5} -1.83388 q^{6} +(0.598489 - 3.39420i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.278152 - 0.233397i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(1.72328 - 0.627223i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.326352 + 1.85083i) q^{5} -1.83388 q^{6} +(0.598489 - 3.39420i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.278152 - 0.233397i) q^{9} +(0.939693 - 1.62760i) q^{10} +(1.40483 + 2.43324i) q^{11} +(1.72328 + 0.627223i) q^{12} +(-2.65877 - 2.23097i) q^{13} +(-1.72328 + 2.98481i) q^{14} +(0.598489 + 3.39420i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.37417 + 1.99217i) q^{17} +(-0.341204 + 0.124188i) q^{18} +(-6.99748 + 2.54687i) q^{19} +(-1.43969 + 1.20805i) q^{20} +(-1.09755 - 6.22454i) q^{21} +(-0.487893 - 2.76698i) q^{22} +(0.321769 - 0.557320i) q^{23} +(-1.40483 - 1.17879i) q^{24} +(1.37939 + 0.502055i) q^{25} +(1.73539 + 3.00578i) q^{26} +(-2.41787 + 4.18788i) q^{27} +(2.64022 - 2.21541i) q^{28} +(-1.08449 - 1.87840i) q^{29} +(0.598489 - 3.39420i) q^{30} +9.90716 q^{31} +(0.173648 - 0.984808i) q^{32} +(3.94710 + 3.31201i) q^{33} +(2.91235 - 1.06001i) q^{34} +(6.08678 + 2.21541i) q^{35} +0.363102 q^{36} +(-2.56368 - 5.51612i) q^{37} +7.44656 q^{38} +(-5.98112 - 2.17695i) q^{39} +(1.76604 - 0.642788i) q^{40} +(-8.13803 - 6.82862i) q^{41} +(-1.09755 + 6.22454i) q^{42} +8.30465 q^{43} +(-0.487893 + 2.76698i) q^{44} +(0.341204 + 0.590982i) q^{45} +(-0.492978 + 0.413658i) q^{46} +(3.92821 - 6.80387i) q^{47} +(0.916938 + 1.58818i) q^{48} +(-4.58455 - 1.66864i) q^{49} +(-1.12449 - 0.943555i) q^{50} +(-2.84183 + 4.92220i) q^{51} +(-0.602694 - 3.41805i) q^{52} +(0.839394 + 4.76044i) q^{53} +(3.70440 - 3.10836i) q^{54} +(-4.96199 + 1.80602i) q^{55} +(-3.23871 + 1.17879i) q^{56} +(-10.4612 + 8.77795i) q^{57} +(0.376641 + 2.13604i) q^{58} +(0.0961039 + 0.545032i) q^{59} +(-1.72328 + 2.98481i) q^{60} +(5.37102 + 4.50682i) q^{61} +(-9.30969 - 3.38845i) q^{62} +(-0.625726 - 1.08379i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(4.99685 - 4.19285i) q^{65} +(-2.57629 - 4.46226i) q^{66} +(0.0366435 - 0.207815i) q^{67} -3.09926 q^{68} +(0.204934 - 1.16224i) q^{69} +(-4.96199 - 4.16360i) q^{70} +(-4.75197 + 1.72957i) q^{71} +(-0.341204 - 0.124188i) q^{72} +10.2297 q^{73} +(0.522449 + 6.06028i) q^{74} +2.69197 q^{75} +(-6.99748 - 2.54687i) q^{76} +(9.09967 - 3.31201i) q^{77} +(4.87585 + 4.09132i) q^{78} +(-0.330775 + 1.87592i) q^{79} -1.87939 q^{80} +(-1.72910 + 9.80619i) q^{81} +(5.31172 + 9.20017i) q^{82} +(5.21650 - 4.37717i) q^{83} +(3.16028 - 5.47377i) q^{84} +(-2.91235 - 5.04435i) q^{85} +(-7.80382 - 2.84036i) q^{86} +(-3.04706 - 2.55679i) q^{87} +(1.40483 - 2.43324i) q^{88} +(-1.68226 - 9.54055i) q^{89} +(-0.118499 - 0.672040i) q^{90} +(-9.16360 + 7.68917i) q^{91} +(0.604727 - 0.220103i) q^{92} +(17.0728 - 6.21400i) q^{93} +(-6.01837 + 5.05001i) q^{94} +(-2.43020 - 13.7823i) q^{95} +(-0.318449 - 1.80602i) q^{96} +(-8.52990 + 14.7742i) q^{97} +(3.73736 + 3.13602i) q^{98} +(0.958667 + 0.348926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9	$ 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{14} + 6 q^{15} - 3 q^{17} + 6 q^{18} - 3 q^{19} - 6 q^{20} - 33 q^{21} - 3 q^{22} - 21 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{27} - 3 q^{28} + 6 q^{29} + 6 q^{30} + 42 q^{31} + 57 q^{33} - 3 q^{34} - 9 q^{35} + 24 q^{36} - 3 q^{37} + 42 q^{38} - 24 q^{39} + 12 q^{40} - 21 q^{41} - 33 q^{42} + 36 q^{43} - 3 q^{44} - 6 q^{45} + 3 q^{46} + 9 q^{47} - 12 q^{49} + 12 q^{50} + 3 q^{52} - 6 q^{53} - 27 q^{54} - 3 q^{56} - 36 q^{57} - 3 q^{58} - 6 q^{59} + 3 q^{60} - 18 q^{61} - 33 q^{62} + 36 q^{63} - 6 q^{64} + 3 q^{65} + 3 q^{66} - 27 q^{67} + 6 q^{68} - 12 q^{69} - 18 q^{71} + 6 q^{72} + 54 q^{73} + 3 q^{74} - 6 q^{75} - 3 q^{76} + 51 q^{77} - 33 q^{78} - 12 q^{79} - 36 q^{81} - 18 q^{82} - 6 q^{83} - 6 q^{84} + 3 q^{85} + 39 q^{87} + 3 q^{88} - 15 q^{89} - 15 q^{90} - 51 q^{91} - 6 q^{92} + 45 q^{93} - 12 q^{94} - 15 q^{95} + 6 q^{96} - 42 q^{97} + 51 q^{98} - 33 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^14 + 6 * q^15 - 3 * q^17 + 6 * q^18 - 3 * q^19 - 6 * q^20 - 33 * q^21 - 3 * q^22 - 21 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^27 - 3 * q^28 + 6 * q^29 + 6 * q^30 + 42 * q^31 + 57 * q^33 - 3 * q^34 - 9 * q^35 + 24 * q^36 - 3 * q^37 + 42 * q^38 - 24 * q^39 + 12 * q^40 - 21 * q^41 - 33 * q^42 + 36 * q^43 - 3 * q^44 - 6 * q^45 + 3 * q^46 + 9 * q^47 - 12 * q^49 + 12 * q^50 + 3 * q^52 - 6 * q^53 - 27 * q^54 - 3 * q^56 - 36 * q^57 - 3 * q^58 - 6 * q^59 + 3 * q^60 - 18 * q^61 - 33 * q^62 + 36 * q^63 - 6 * q^64 + 3 * q^65 + 3 * q^66 - 27 * q^67 + 6 * q^68 - 12 * q^69 - 18 * q^71 + 6 * q^72 + 54 * q^73 + 3 * q^74 - 6 * q^75 - 3 * q^76 + 51 * q^77 - 33 * q^78 - 12 * q^79 - 36 * q^81 - 18 * q^82 - 6 * q^83 - 6 * q^84 + 3 * q^85 + 39 * q^87 + 3 * q^88 - 15 * q^89 - 15 * q^90 - 51 * q^91 - 6 * q^92 + 45 * q^93 - 12 * q^94 - 15 * q^95 + 6 * q^96 - 42 * q^97 + 51 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	1.72328	−	0.627223i	0.994936	−	0.362127i	0.207306	−	0.978276i	$-0.433530\pi$
$3$	1.72328	−	0.627223i	0.994936	−	0.362127i	0.787630	+	0.616149i	$0.211308\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−0.326352	+	1.85083i	−0.145949	+	0.827718i	0.820651	+	0.571429i	$0.193611\pi$
$5$	−0.326352	+	1.85083i	−0.145949	+	0.827718i	−0.966600	+	0.256289i	$0.917500\pi$
$6$	−1.83388			−0.748677
$7$	0.598489	−	3.39420i	0.226208	−	1.28289i	−0.634156	−	0.773205i	$-0.718652\pi$
$7$	0.598489	−	3.39420i	0.226208	−	1.28289i	0.860363	−	0.509681i	$-0.170237\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	0.278152	−	0.233397i	0.0927173	−	0.0777991i
$10$	0.939693	−	1.62760i	0.297157	−	0.514691i
$11$	1.40483	+	2.43324i	0.423572	+	0.733649i	0.996286	−	0.0861067i	$-0.0274426\pi$
$11$	1.40483	+	2.43324i	0.423572	+	0.733649i	−0.572714	+	0.819756i	$0.694109\pi$
$12$	1.72328	+	0.627223i	0.497468	+	0.181064i
$13$	−2.65877	−	2.23097i	−0.737409	−	0.618760i	0.194731	−	0.980857i	$-0.437617\pi$
$13$	−2.65877	−	2.23097i	−0.737409	−	0.618760i	−0.932141	+	0.362097i	$0.882061\pi$
$14$	−1.72328	+	2.98481i	−0.460566	+	0.797724i
$15$	0.598489	+	3.39420i	0.154529	+	0.876378i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−2.37417	+	1.99217i	−0.575822	+	0.483172i	−0.883572	−	0.468295i	$-0.844868\pi$
$17$	−2.37417	+	1.99217i	−0.575822	+	0.483172i	0.307750	+	0.951467i	$0.400424\pi$
$18$	−0.341204	+	0.124188i	−0.0804225	+	0.0292714i
$19$	−6.99748	+	2.54687i	−1.60533	+	0.584293i	−0.980509	−	0.196474i	$-0.937051\pi$
$19$	−6.99748	+	2.54687i	−1.60533	+	0.584293i	−0.624822	+	0.780767i	$0.714829\pi$
$20$	−1.43969	+	1.20805i	−0.321925	+	0.270127i
$21$	−1.09755	−	6.22454i	−0.239506	−	1.35831i
$22$	−0.487893	−	2.76698i	−0.104019	−	0.589921i
$23$	0.321769	−	0.557320i	0.0670934	−	0.116209i	−0.830527	−	0.556978i	$-0.811961\pi$
$23$	0.321769	−	0.557320i	0.0670934	−	0.116209i	0.897621	+	0.440769i	$0.145294\pi$
$24$	−1.40483	−	1.17879i	−0.286760	−	0.240620i
$25$	1.37939	+	0.502055i	0.275877	+	0.100411i
$26$	1.73539	+	3.00578i	0.340337	+	0.589482i
$27$	−2.41787	+	4.18788i	−0.465320	+	0.805958i
$28$	2.64022	−	2.21541i	0.498954	−	0.418672i
$29$	−1.08449	−	1.87840i	−0.201385	−	0.348810i	0.747590	−	0.664161i	$-0.231211\pi$
$29$	−1.08449	−	1.87840i	−0.201385	−	0.348810i	−0.948975	+	0.315351i	$0.897878\pi$
$30$	0.598489	−	3.39420i	0.109269	−	0.619693i
$31$	9.90716			1.77938			0.889690	−	0.456566i	$-0.150921\pi$
$31$	9.90716			1.77938			0.889690	+	0.456566i	$0.150921\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	3.94710	+	3.31201i	0.687102	+	0.576547i
$34$	2.91235	−	1.06001i	0.499465	−	0.181790i
$35$	6.08678	+	2.21541i	1.02885	+	0.374472i
$36$	0.363102			0.0605169
$37$	−2.56368	−	5.51612i	−0.421466	−	0.906844i
$37$	−2.56368	−	5.51612i	−0.421466	−	0.906844i
$38$	7.44656			1.20799
$39$	−5.98112	−	2.17695i	−0.957745	−	0.348591i
$40$	1.76604	−	0.642788i	0.279236	−	0.101634i
$41$	−8.13803	−	6.82862i	−1.27095	−	1.06645i	−0.994425	−	0.105443i	$-0.966374\pi$
$41$	−8.13803	−	6.82862i	−1.27095	−	1.06645i	−0.276521	−	0.961008i	$-0.589182\pi$
$42$	−1.09755	+	6.22454i	−0.169356	+	0.960467i
$43$	8.30465			1.26645			0.633224	−	0.773969i	$-0.281731\pi$
$43$	8.30465			1.26645			0.633224	+	0.773969i	$0.281731\pi$
$44$	−0.487893	+	2.76698i	−0.0735526	+	0.417137i
$45$	0.341204	+	0.590982i	0.0508637	+	0.0880984i
$46$	−0.492978	+	0.413658i	−0.0726857	+	0.0609905i
$47$	3.92821	−	6.80387i	0.572989	−	0.992446i	−0.423268	−	0.906004i	$-0.639117\pi$
$47$	3.92821	−	6.80387i	0.572989	−	0.992446i	0.996257	−	0.0864413i	$-0.0275495\pi$
$48$	0.916938	+	1.58818i	0.132349	+	0.229235i
$49$	−4.58455	−	1.66864i	−0.654935	−	0.238377i
$50$	−1.12449	−	0.943555i	−0.159026	−	0.133439i
$51$	−2.84183	+	4.92220i	−0.397936	+	0.689246i
$52$	−0.602694	−	3.41805i	−0.0835786	−	0.473998i
$53$	0.839394	+	4.76044i	0.115300	+	0.653897i	0.986601	+	0.163149i	$0.0521651\pi$
$53$	0.839394	+	4.76044i	0.115300	+	0.653897i	−0.871302	+	0.490748i	$0.836724\pi$
$54$	3.70440	−	3.10836i	0.504104	−	0.422994i
$55$	−4.96199	+	1.80602i	−0.669074	+	0.243523i
$56$	−3.23871	+	1.17879i	−0.432790	+	0.157523i
$57$	−10.4612	+	8.77795i	−1.38561	+	1.16267i
$58$	0.376641	+	2.13604i	0.0494553	+	0.280475i
$59$	0.0961039	+	0.545032i	0.0125117	+	0.0709572i	0.990424	−	0.138057i	$-0.0440857\pi$
$59$	0.0961039	+	0.545032i	0.0125117	+	0.0709572i	−0.977913	+	0.209014i	$0.932975\pi$
$60$	−1.72328	+	2.98481i	−0.222474	+	0.385337i
$61$	5.37102	+	4.50682i	0.687689	+	0.577039i	0.918242	−	0.396020i	$-0.129609\pi$
$61$	5.37102	+	4.50682i	0.687689	+	0.577039i	−0.230553	+	0.973060i	$0.574053\pi$
$62$	−9.30969	−	3.38845i	−1.18233	−	0.430333i
$63$	−0.625726	−	1.08379i	−0.0788340	−	0.136545i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	4.99685	−	4.19285i	0.619783	−	0.520060i
$66$	−2.57629	−	4.46226i	−0.317119	−	0.549266i
$67$	0.0366435	−	0.207815i	0.00447671	−	0.0253887i	−0.982488	−	0.186328i	$-0.940341\pi$
$67$	0.0366435	−	0.207815i	0.00447671	−	0.0253887i	0.986964	+	0.160939i	$0.0514524\pi$
$68$	−3.09926			−0.375841
$69$	0.204934	−	1.16224i	0.0246711	−	0.139917i
$70$	−4.96199	−	4.16360i	−0.593071	−	0.497646i
$71$	−4.75197	+	1.72957i	−0.563955	+	0.205263i	−0.608236	−	0.793756i	$-0.708123\pi$
$71$	−4.75197	+	1.72957i	−0.563955	+	0.205263i	0.0442811	+	0.999019i	$0.485900\pi$
$72$	−0.341204	−	0.124188i	−0.0402113	−	0.0146357i
$73$	10.2297			1.19730			0.598648	−	0.801012i	$-0.295705\pi$
$73$	10.2297			1.19730			0.598648	+	0.801012i	$0.295705\pi$
$74$	0.522449	+	6.06028i	0.0607334	+	0.704494i
$75$	2.69197			0.310842
$76$	−6.99748	−	2.54687i	−0.802666	−	0.292146i
$77$	9.09967	−	3.31201i	1.03700	−	0.377438i
$78$	4.87585	+	4.09132i	0.552081	+	0.463251i
$79$	−0.330775	+	1.87592i	−0.0372151	+	0.211057i	−0.997745	−	0.0671197i	$-0.978619\pi$
$79$	−0.330775	+	1.87592i	−0.0372151	+	0.211057i	0.960530	+	0.278177i	$0.0897302\pi$
$80$	−1.87939			−0.210122
$81$	−1.72910	+	9.80619i	−0.192122	+	1.08958i
$82$	5.31172	+	9.20017i	0.586582	+	1.01599i
$83$	5.21650	−	4.37717i	0.572586	−	0.480456i	−0.309917	−	0.950764i	$-0.600301\pi$
$83$	5.21650	−	4.37717i	0.572586	−	0.480456i	0.882503	+	0.470307i	$0.155857\pi$
$84$	3.16028	−	5.47377i	0.344815	−	0.597237i
$85$	−2.91235	−	5.04435i	−0.315889	−	0.547136i
$86$	−7.80382	−	2.84036i	−0.841507	−	0.306284i
$87$	−3.04706	−	2.55679i	−0.326679	−	0.274116i
$88$	1.40483	−	2.43324i	0.149755	−	0.259384i
$89$	−1.68226	−	9.54055i	−0.178319	−	1.01130i	−0.934243	−	0.356637i	$-0.883923\pi$
$89$	−1.68226	−	9.54055i	−0.178319	−	1.01130i	0.755924	−	0.654659i	$-0.227188\pi$
$90$	−0.118499	−	0.672040i	−0.0124909	−	0.0708393i
$91$	−9.16360	+	7.68917i	−0.960606	+	0.806044i
$92$	0.604727	−	0.220103i	0.0630472	−	0.0229473i
$93$	17.0728	−	6.21400i	1.77037	−	0.644361i
$94$	−6.01837	+	5.05001i	−0.620748	+	0.520869i
$95$	−2.43020	−	13.7823i	−0.249333	−	1.41404i
$96$	−0.318449	−	1.80602i	−0.0325016	−	0.184326i
$97$	−8.52990	+	14.7742i	−0.866080	+	1.50009i	−0.000109562		1.00000i	$0.500035\pi$
$97$	−8.52990	+	14.7742i	−0.866080	+	1.50009i	−0.865971	+	0.500095i	$0.833298\pi$
$98$	3.73736	+	3.13602i	0.377530	+	0.316785i
$99$	0.958667	+	0.348926i	0.0963497	+	0.0350684i
$100$	0.733956	+	1.27125i	0.0733956	+	0.127125i
$101$	−5.98911	+	10.3734i	−0.595938	+	1.03220i	0.397475	+	0.917613i	$0.369886\pi$
$101$	−5.98911	+	10.3734i	−0.595938	+	1.03220i	−0.993414	+	0.114583i	$0.963447\pi$
$102$	4.35394	−	3.65339i	0.431104	−	0.361739i
$103$	−6.47233	−	11.2104i	−0.637737	−	1.10459i	−0.985928	−	0.167170i	$-0.946537\pi$
$103$	−6.47233	−	11.2104i	−0.637737	−	1.10459i	0.348191	−	0.937424i	$-0.386796\pi$
$104$	−0.602694	+	3.41805i	−0.0590990	+	0.335167i
$105$	11.8788			1.15925
$106$	0.839394	−	4.76044i	0.0815291	−	0.462375i
$107$	11.9706	+	10.0445i	1.15724	+	0.971037i	0.999864	−	0.0165017i	$-0.00525290\pi$
$107$	11.9706	+	10.0445i	1.15724	+	0.971037i	0.157374	+	0.987539i	$0.449697\pi$
$108$	−4.54411	+	1.65392i	−0.437258	+	0.159149i
$109$	−1.45663	−	0.530170i	−0.139520	−	0.0507810i	0.271317	−	0.962490i	$-0.412541\pi$
$109$	−1.45663	−	0.530170i	−0.139520	−	0.0507810i	−0.410836	+	0.911709i	$0.634763\pi$
$110$	5.28044			0.503470
$111$	−7.87777	−	7.89781i	−0.747725	−	0.749627i
$112$	3.44656			0.325669
$113$	4.80629	+	1.74935i	0.452138	+	0.164565i	0.558044	−	0.829811i	$-0.311552\pi$
$113$	4.80629	+	1.74935i	0.452138	+	0.164565i	−0.105906	+	0.994376i	$0.533774\pi$
$114$	12.8325	−	4.67065i	1.20187	−	0.437446i
$115$	0.926496	+	0.777422i	0.0863962	+	0.0724950i
$116$	0.376641	−	2.13604i	0.0349702	−	0.198326i
$117$	−1.26024			−0.116510
$118$	0.0961039	−	0.545032i	0.00884708	−	0.0501743i
$119$	5.34090	+	9.25071i	0.489599	+	0.848011i
$120$	2.64022	−	2.21541i	0.241018	−	0.202238i
$121$	1.55290	−	2.68971i	0.141173	−	0.244519i
$122$	−3.50569	−	6.07203i	−0.317390	−	0.549735i
$123$	−18.3072	−	6.66326i	−1.65070	−	0.600806i
$124$	7.58933	+	6.36820i	0.681542	+	0.571881i
$125$	−6.07785	+	10.5271i	−0.543619	+	0.941576i
$126$	0.217312	+	1.23244i	0.0193597	+	0.109794i
$127$	−1.23207	−	6.98740i	−0.109328	−	0.620032i	−0.989403	−	0.145196i	$-0.953619\pi$
$127$	−1.23207	−	6.98740i	−0.109328	−	0.620032i	0.880075	−	0.474836i	$-0.157492\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	14.3112	−	5.20886i	1.26003	−	0.458615i
$130$	−6.12954	+	2.23097i	−0.537596	+	0.195669i
$131$	13.3781	−	11.2256i	1.16885	−	0.980781i	0.168861	−	0.985640i	$-0.445991\pi$
$131$	13.3781	−	11.2256i	1.16885	−	0.980781i	0.999988	+	0.00485874i	$0.00154659\pi$
$132$	0.894734	+	5.07429i	0.0778766	+	0.441660i
$133$	4.45668	+	25.2751i	0.386443	+	2.19163i
$134$	−0.105511	+	0.182750i	−0.00911473	+	0.0157872i
$135$	−6.96199	−	5.84180i	−0.599192	−	0.502782i
$136$	2.91235	+	1.06001i	0.249732	+	0.0908951i
$137$	−4.92852	−	8.53645i	−0.421072	−	0.729318i	0.574973	−	0.818173i	$-0.305013\pi$
$137$	−4.92852	−	8.53645i	−0.421072	−	0.729318i	−0.996045	+	0.0888546i	$0.971679\pi$
$138$	−0.590084	+	1.02206i	−0.0502313	+	0.0870031i
$139$	−6.89049	+	5.78181i	−0.584444	+	0.490407i	−0.886403	−	0.462914i	$-0.846804\pi$
$139$	−6.89049	+	5.78181i	−0.584444	+	0.490407i	0.301959	+	0.953321i	$0.402359\pi$
$140$	3.23871	+	5.60960i	0.273721	+	0.474098i
$141$	2.50187	−	14.1888i	0.210696	−	1.19491i
$142$	5.05694			0.424369
$143$	1.69337	−	9.60355i	0.141606	−	0.803089i
$144$	0.278152	+	0.233397i	0.0231793	+	0.0194498i
$145$	3.83053	−	1.39420i	0.318108	−	0.115782i
$146$	−9.61277	−	3.49876i	−0.795559	−	0.289560i
$147$	−8.94707			−0.737942
$148$	1.58180	−	5.87349i	0.130023	−	0.482798i
$149$	−9.97301			−0.817021			−0.408511	−	0.912754i	$-0.633952\pi$
$149$	−9.97301			−0.817021			−0.408511	+	0.912754i	$0.633952\pi$
$150$	−2.52962	−	0.920707i	−0.206543	−	0.0751754i
$151$	−9.07997	+	3.30484i	−0.738918	+	0.268944i	−0.683935	−	0.729543i	$-0.739733\pi$
$151$	−9.07997	+	3.30484i	−0.738918	+	0.268944i	−0.0549831	+	0.998487i	$0.517510\pi$
$152$	5.70440	+	4.78656i	0.462688	+	0.388241i
$153$	−0.195414	+	1.10825i	−0.0157983	+	0.0895968i
$154$	−9.68366			−0.780332
$155$	−3.23322	+	18.3365i	−0.259699	+	1.47282i
$156$	−3.18249	−	5.51223i	−0.254803	−	0.441331i
$157$	−6.73320	+	5.64982i	−0.537368	+	0.450905i	−0.870637	−	0.491927i	$-0.836293\pi$
$157$	−6.73320	+	5.64982i	−0.537368	+	0.450905i	0.333269	+	0.942832i	$0.391848\pi$
$158$	0.952429	−	1.64965i	0.0757712	−	0.131239i
$159$	4.43236	+	7.67708i	0.351509	+	0.608832i
$160$	1.76604	+	0.642788i	0.139618	+	0.0508168i
$161$	−1.69908	−	1.42570i	−0.133906	−	0.112361i
$162$	4.97873	−	8.62341i	0.391166	−	0.677519i
$163$	−0.331175	−	1.87819i	−0.0259397	−	0.147111i	0.969087	−	0.246719i	$-0.0793524\pi$
$163$	−0.331175	−	1.87819i	−0.0259397	−	0.147111i	−0.995027	+	0.0996076i	$0.968241\pi$
$164$	−1.84474	−	10.4620i	−0.144050	−	0.816949i
$165$	−7.41812	+	6.22454i	−0.577500	+	0.484580i
$166$	−6.39899	+	2.32904i	−0.496658	+	0.180769i
$167$	−6.22793	+	2.26678i	−0.481932	+	0.175409i	−0.571550	−	0.820567i	$-0.693658\pi$
$167$	−6.22793	+	2.26678i	−0.481932	+	0.175409i	0.0896181	+	0.995976i	$0.471435\pi$
$168$	−4.84183	+	4.06278i	−0.373555	+	0.313450i
$169$	−0.165612	−	0.939235i	−0.0127394	−	0.0722488i
$170$	1.01145	+	5.73622i	0.0775747	+	0.439948i
$171$	−1.35193	+	2.34161i	−0.103385	+	0.179067i
$172$	6.36173	+	5.33813i	0.485077	+	0.407028i
$173$	−23.8769	−	8.69049i	−1.81533	−	0.660725i	−0.996198	−	0.0871179i	$-0.972234\pi$
$173$	−23.8769	−	8.69049i	−1.81533	−	0.660725i	−0.819130	−	0.573608i	$-0.805543\pi$
$174$	1.98883	+	3.44475i	0.150773	+	0.261146i
$175$	2.52962	−	4.38143i	0.191221	−	0.331205i
$176$	−2.15233	+	1.80602i	−0.162238	+	0.136134i
$177$	0.507471	+	0.878965i	0.0381438	+	0.0660670i
$178$	−1.68226	+	9.54055i	−0.126090	+	0.715095i
$179$	8.12492			0.607285			0.303643	−	0.952786i	$-0.401797\pi$
$179$	8.12492			0.607285			0.303643	+	0.952786i	$0.401797\pi$
$180$	−0.118499	+	0.672040i	−0.00883238	+	0.0500909i
$181$	9.12118	+	7.65358i	0.677972	+	0.568886i	0.915413	−	0.402516i	$-0.131864\pi$
$181$	9.12118	+	7.65358i	0.677972	+	0.568886i	−0.237441	+	0.971402i	$0.576309\pi$
$182$	11.2408	−	4.09132i	0.833225	−	0.303269i
$183$	12.0826	+	4.39769i	0.893168	+	0.325087i
$184$	−0.643537			−0.0474422
$185$	11.0461	−	2.94475i	0.812123	−	0.216502i
$186$	−18.1685			−1.33218
$187$	−8.18273	−	2.97827i	−0.598381	−	0.217793i
$188$	7.38263	−	2.68706i	0.538433	−	0.195974i
$189$	12.7674	+	10.7131i	0.928693	+	0.779266i
$190$	−2.43020	+	13.7823i	−0.176305	+	0.999876i
$191$	0.266722			0.0192993			0.00964965	−	0.999953i	$-0.496928\pi$
$191$	0.266722			0.0192993			0.00964965	+	0.999953i	$0.496928\pi$
$192$	−0.318449	+	1.80602i	−0.0229821	+	0.130338i
$193$	−3.96417	−	6.86615i	−0.285348	−	0.494236i	0.687346	−	0.726330i	$-0.258776\pi$
$193$	−3.96417	−	6.86615i	−0.285348	−	0.494236i	−0.972693	+	0.232094i	$0.925442\pi$
$194$	13.0686	−	10.9658i	0.938268	−	0.787301i
$195$	5.98112	−	10.3596i	0.428317	−	0.741866i
$196$	−2.43939	−	4.22514i	−0.174242	−	0.301796i
$197$	0.386805	+	0.140786i	0.0275587	+	0.0100306i	0.355763	−	0.934576i	$-0.384221\pi$
$197$	0.386805	+	0.140786i	0.0275587	+	0.0100306i	−0.328204	+	0.944607i	$0.606443\pi$
$198$	−0.781513	−	0.655767i	−0.0555397	−	0.0466033i
$199$	1.01751	−	1.76239i	0.0721297	−	0.124932i	−0.827705	−	0.561164i	$-0.810354\pi$
$199$	1.01751	−	1.76239i	0.0721297	−	0.124932i	0.899834	+	0.436232i	$0.143687\pi$
$200$	−0.254900	−	1.44561i	−0.0180242	−	0.102220i
$201$	−0.0671996	−	0.381108i	−0.00473989	−	0.0268813i
$202$	9.17584	−	7.69945i	0.645610	−	0.541731i
$203$	−7.02471	+	2.55679i	−0.493038	+	0.179451i
$204$	−5.34090	+	1.94393i	−0.373938	+	0.136102i
$205$	15.2945	−	12.8336i	1.06821	−	0.896338i
$206$	2.24782	+	12.7480i	0.156613	+	0.888195i
$207$	−0.0405763	−	0.230119i	−0.00282024	−	0.0159944i
$208$	1.73539	−	3.00578i	0.120327	−	0.208413i
$209$	−16.0274	−	13.4486i	−1.10864	−	0.930259i
$210$	−11.1624	−	4.06278i	−0.770278	−	0.280358i
$211$	7.87052	+	13.6321i	0.541829	+	0.938475i	0.998799	+	0.0489932i	$0.0156013\pi$
$211$	7.87052	+	13.6321i	0.541829	+	0.938475i	−0.456970	+	0.889482i	$0.651065\pi$
$212$	−2.41694	+	4.18626i	−0.165996	+	0.287513i
$213$	−7.10414	+	5.96108i	−0.486768	+	0.408447i
$214$	−7.81323	−	13.5329i	−0.534101	−	0.925090i
$215$	−2.71024	+	15.3705i	−0.184837	+	1.04826i
$216$	4.83575			0.329031
$217$	5.92933	−	33.6269i	0.402509	−	2.28274i
$218$	1.18745	+	0.996393i	0.0804246	+	0.0674842i
$219$	17.6286	−	6.41630i	1.19123	−	0.433573i
$220$	−4.96199	−	1.80602i	−0.334537	−	0.121762i
$221$	10.7568			0.723584
$222$	4.70147	+	10.1159i	0.315542	+	0.678933i
$223$	−3.43531			−0.230045			−0.115023	−	0.993363i	$-0.536694\pi$
$223$	−3.43531			−0.230045			−0.115023	+	0.993363i	$0.536694\pi$
$224$	−3.23871	−	1.17879i	−0.216395	−	0.0787614i
$225$	0.500857	−	0.182297i	0.0333905	−	0.0121531i
$226$	−3.91812	−	3.28770i	−0.260630	−	0.218694i
$227$	−0.401614	+	2.27767i	−0.0266561	+	0.151174i	−0.995231	−	0.0975489i	$-0.968900\pi$
$227$	−0.401614	+	2.27767i	−0.0266561	+	0.151174i	0.968575	+	0.248723i	$0.0800109\pi$
$228$	−13.6561			−0.904395
$229$	−1.02642	+	5.82114i	−0.0678280	+	0.384672i	0.931929	+	0.362640i	$0.118125\pi$
$229$	−1.02642	+	5.82114i	−0.0678280	+	0.384672i	−0.999757	+	0.0220316i	$0.992987\pi$
$230$	−0.604727	−	1.04742i	−0.0398745	−	0.0690647i
$231$	13.6039	−	11.4150i	0.895071	−	0.751054i
$232$	−1.08449	+	1.87840i	−0.0712005	+	0.123323i
$233$	14.1679	+	24.5395i	0.928168	+	1.60763i	0.786386	+	0.617736i	$0.211950\pi$
$233$	14.1679	+	24.5395i	0.928168	+	1.60763i	0.141782	+	0.989898i	$0.454717\pi$
$234$	1.18424	+	0.431029i	0.0774163	+	0.0281772i
$235$	11.3108	+	9.49092i	0.737838	+	0.619120i
$236$	−0.276720	+	0.479293i	−0.0180129	+	0.0311993i
$237$	0.606600	+	3.44020i	0.0394029	+	0.223465i
$238$	−1.85487	−	10.5195i	−0.120234	−	0.681879i
$239$	18.5674	−	15.5799i	1.20103	−	1.00778i	0.201427	−	0.979504i	$-0.435442\pi$
$239$	18.5674	−	15.5799i	1.20103	−	1.00778i	0.999600	−	0.0282780i	$-0.00900236\pi$
$240$	−3.23871	+	1.17879i	−0.209058	+	0.0760907i
$241$	−8.31692	+	3.02711i	−0.535740	+	0.194993i	−0.595700	−	0.803207i	$-0.703125\pi$
$241$	−8.31692	+	3.02711i	−0.535740	+	0.194993i	0.0599594	+	0.998201i	$0.480903\pi$
$242$	−2.37918	+	1.99637i	−0.152940	+	0.128332i
$243$	0.651791	+	3.69649i	0.0418124	+	0.237130i
$244$	1.21751	+	6.90485i	0.0779432	+	0.442038i
$245$	4.58455	−	7.94067i	0.292896	−	0.507311i
$246$	14.9241	+	12.5228i	0.951528	+	0.798427i
$247$	24.2867	+	8.83962i	1.54532	+	0.562452i
$248$	−4.95358	−	8.57985i	−0.314553	−	0.544821i
$249$	6.24404	−	10.8150i	0.395700	−	0.685372i
$250$	9.31180	−	7.81353i	0.588930	−	0.494171i
$251$	−3.29525	−	5.70754i	−0.207994	−	0.360257i	0.743088	−	0.669193i	$-0.233360\pi$
$251$	−3.29525	−	5.70754i	−0.207994	−	0.360257i	−0.951083	+	0.308937i	$0.900027\pi$
$252$	0.217312	−	1.23244i	0.0136894	−	0.0776363i
$253$	1.80812			0.113676
$254$	−1.23207	+	6.98740i	−0.0773068	+	0.438429i
$255$	−8.18273	−	6.86613i	−0.512422	−	0.429973i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−9.04522	−	3.29219i	−0.564225	−	0.205361i	0.0441304	−	0.999026i	$-0.485948\pi$
$257$	−9.04522	−	3.29219i	−0.564225	−	0.205361i	−0.608356	+	0.793665i	$0.708171\pi$
$258$	−15.2297			−0.948160
$259$	−20.2571	+	5.40031i	−1.25872	+	0.335559i
$260$	6.52292			0.404534
$261$	−0.740067	−	0.269362i	−0.0458090	−	0.0166731i
$262$	−16.4107	+	5.97299i	−1.01385	+	0.369013i
$263$	−1.21898	−	1.02284i	−0.0751654	−	0.0630712i	0.604431	−	0.796658i	$-0.293401\pi$
$263$	−1.21898	−	1.02284i	−0.0751654	−	0.0630712i	−0.679596	+	0.733586i	$0.737845\pi$
$264$	0.894734	−	5.07429i	0.0550671	−	0.312301i
$265$	−9.08472			−0.558070
$266$	4.45668	−	25.2751i	0.273257	−	1.54972i
$267$	−8.88305	−	15.3859i	−0.543634	−	0.941601i
$268$	0.161652	−	0.135642i	0.00987445	−	0.00828565i
$269$	−11.5599	+	20.0223i	−0.704819	+	1.22078i	0.261938	+	0.965085i	$0.415638\pi$
$269$	−11.5599	+	20.0223i	−0.704819	+	1.22078i	−0.966757	+	0.255697i	$0.917695\pi$
$270$	4.54411	+	7.87064i	0.276546	+	0.478992i
$271$	−0.172362	−	0.0627348i	−0.0104703	−	0.00381087i	0.336780	−	0.941583i	$-0.390662\pi$
$271$	−0.172362	−	0.0627348i	−0.0104703	−	0.00381087i	−0.347250	+	0.937773i	$0.612884\pi$
$272$	−2.37417	−	1.99217i	−0.143955	−	0.120793i
$273$	−10.9686	+	18.9982i	−0.663851	+	1.14982i
$274$	1.71166	+	9.70729i	0.103405	+	0.586439i
$275$	0.716183	+	4.06167i	0.0431875	+	0.244928i
$276$	0.904061	−	0.758597i	0.0544181	−	0.0456622i
$277$	11.9260	−	4.34070i	0.716562	−	0.260807i	0.0420965	−	0.999114i	$-0.486596\pi$
$277$	11.9260	−	4.34070i	0.716562	−	0.260807i	0.674466	+	0.738306i	$0.264374\pi$
$278$	8.45244	−	3.07644i	0.506944	−	0.184512i
$279$	2.75570	−	2.31230i	0.164979	−	0.138434i
$280$	−1.12479	−	6.37901i	−0.0672191	−	0.381219i
$281$	3.02774	+	17.1712i	0.180620	+	1.02435i	0.931455	+	0.363857i	$0.118540\pi$
$281$	3.02774	+	17.1712i	0.180620	+	1.02435i	−0.750835	+	0.660490i	$0.770349\pi$
$282$	−7.20386	+	12.4774i	−0.428983	+	0.743021i
$283$	−10.0612	−	8.44232i	−0.598074	−	0.501844i	0.292752	−	0.956188i	$-0.405429\pi$
$283$	−10.0612	−	8.44232i	−0.598074	−	0.501844i	−0.890826	+	0.454345i	$0.849873\pi$
$284$	−4.75197	−	1.72957i	−0.281977	−	0.102631i
$285$	−12.8325	−	22.2266i	−0.760132	−	1.31659i
$286$	−4.87585	+	8.44522i	−0.288315	+	0.499376i
$287$	−28.0482	+	23.5352i	−1.65563	+	1.38924i
$288$	−0.181551	−	0.314455i	−0.0106980	−	0.0185294i
$289$	−1.28405	+	7.28223i	−0.0755325	+	0.428366i
$290$	−4.07636			−0.239372
$291$	−5.43268	+	30.8103i	−0.318469	+	1.80613i
$292$	7.83641	+	6.57552i	0.458591	+	0.384803i
$293$	−6.37791	+	2.32137i	−0.372602	+	0.135616i	−0.521532	−	0.853232i	$-0.674639\pi$
$293$	−6.37791	+	2.32137i	−0.372602	+	0.135616i	0.148930	+	0.988848i	$0.452417\pi$
$294$	8.40749	+	3.06008i	0.490335	+	0.178467i
$295$	−1.04013			−0.0605586
$296$	−3.49526	+	4.97827i	−0.203158	+	0.289356i
$297$	−13.5868			−0.788386
$298$	9.37157	+	3.41097i	0.542880	+	0.197592i
$299$	−2.09887	+	0.763927i	−0.121381	+	0.0441790i
$300$	2.06217	+	1.73036i	0.119059	+	0.0999026i
$301$	4.97024	−	28.1876i	0.286480	−	1.62471i
$302$	9.66271			0.556026
$303$	−3.81445	+	21.6328i	−0.219135	+	1.24277i
$304$	−3.72328	−	6.44891i	−0.213545	−	0.369870i
$305$	−10.0942	+	8.47006i	−0.577993	+	0.484994i
$306$	0.562674	−	0.974579i	0.0321659	−	0.0557130i
$307$	−4.10242	−	7.10560i	−0.234138	−	0.405538i	0.724884	−	0.688871i	$-0.241893\pi$
$307$	−4.10242	−	7.10560i	−0.234138	−	0.405538i	−0.959022	+	0.283333i	$0.908560\pi$
$308$	9.09967	+	3.31201i	0.518502	+	0.188719i
$309$	−18.1850	−	15.2591i	−1.03451	−	0.868058i
$310$	9.30969	−	16.1249i	0.528755	−	0.915830i
$311$	−1.88461	−	10.6882i	−0.106867	−	0.606070i	−0.990458	−	0.137812i	$-0.955993\pi$
$311$	−1.88461	−	10.6882i	−0.106867	−	0.606070i	0.883592	−	0.468258i	$-0.155118\pi$
$312$	1.10527	+	6.26827i	0.0625733	+	0.354871i
$313$	−6.63058	+	5.56372i	−0.374783	+	0.314480i	−0.810650	−	0.585531i	$-0.800886\pi$
$313$	−6.63058	+	5.56372i	−0.374783	+	0.314480i	0.435867	+	0.900011i	$0.356442\pi$
$314$	8.25949	−	3.00621i	0.466110	−	0.169650i
$315$	2.21012	−	0.804417i	0.124526	−	0.0453238i
$316$	−1.45921	+	1.22442i	−0.0820867	+	0.0688789i
$317$	−4.41505	−	25.0390i	−0.247974	−	1.40633i	−0.813484	−	0.581587i	$-0.802432\pi$
$317$	−4.41505	−	25.0390i	−0.247974	−	1.40633i	0.565510	−	0.824741i	$-0.308679\pi$
$318$	−1.53934	−	8.73005i	−0.0863221	−	0.489557i
$319$	3.04706	−	5.27766i	0.170603	−	0.295492i
$320$	−1.43969	−	1.20805i	−0.0804813	−	0.0675318i
$321$	26.9287	+	9.80126i	1.50302	+	0.547053i
$322$	1.10899	+	1.92084i	0.0618019	+	0.107044i
$323$	11.5394	−	19.9869i	0.642071	−	1.11210i
$324$	−7.62786	+	6.40053i	−0.423770	+	0.355585i
$325$	−2.54739	−	4.41222i	−0.141304	−	0.244746i
$326$	−0.331175	+	1.87819i	−0.0183421	+	0.104023i
$327$	−2.84271			−0.157202
$328$	−1.84474	+	10.4620i	−0.101859	+	0.577670i
$329$	−20.7427	−	17.4052i	−1.14358	−	0.959578i
$330$	9.09967	−	3.31201i	0.500920	−	0.182320i
$331$	19.5470	+	7.11454i	1.07440	+	0.391050i	0.817821	−	0.575473i	$-0.195182\pi$
$331$	19.5470	+	7.11454i	1.07440	+	0.391050i	0.256581	+	0.966523i	$0.417404\pi$
$332$	6.80966			0.373729
$333$	−2.00054	−	0.935963i	−0.109629	−	0.0512904i
$334$	6.62762			0.362647
$335$	0.372673	+	0.135642i	0.0203613	+	0.00741091i
$336$	5.93939	−	2.16176i	0.324020	−	0.117934i
$337$	−1.89385	−	1.58913i	−0.103165	−	0.0865653i	0.589746	−	0.807588i	$-0.299228\pi$
$337$	−1.89385	−	1.58913i	−0.103165	−	0.0865653i	−0.692911	+	0.721023i	$0.743672\pi$
$338$	−0.165612	+	0.939235i	−0.00900813	+	0.0510876i
$339$	9.37981			0.509442
$340$	1.01145	−	5.73622i	0.0548536	−	0.311090i
$341$	13.9179	+	24.1065i	0.753696	+	1.30544i
$342$	2.07127	−	1.73801i	0.112002	−	0.0939806i
$343$	3.65547	−	6.33145i	0.197377	−	0.341866i
$344$	−4.15233	−	7.19204i	−0.223878	−	0.387769i
$345$	2.08423	+	0.758597i	0.112211	+	0.0408415i
$346$	19.4646	+	16.3328i	1.04643	+	0.878055i
$347$	2.92690	−	5.06953i	0.157124	−	0.272147i	−0.776706	−	0.629863i	$-0.783111\pi$
$347$	2.92690	−	5.06953i	0.157124	−	0.272147i	0.933830	+	0.357716i	$0.116444\pi$
$348$	−0.690712	−	3.91722i	−0.0370261	−	0.209985i
$349$	0.545283	+	3.09246i	0.0291883	+	0.165535i	0.995918	−	0.0902661i	$-0.0287718\pi$
$349$	0.545283	+	3.09246i	0.0291883	+	0.165535i	−0.966729	+	0.255801i	$0.917661\pi$
$350$	−3.87561	+	3.25202i	−0.207160	+	0.173828i
$351$	15.7716	−	5.74039i	0.841825	−	0.306399i
$352$	2.64022	−	0.960961i	0.140724	−	0.0512194i
$353$	−8.61667	+	7.23024i	−0.458619	+	0.384827i	−0.842623	−	0.538505i	$-0.818989\pi$
$353$	−8.61667	+	7.23024i	−0.458619	+	0.384827i	0.384004	+	0.923332i	$0.374545\pi$
$354$	−0.176243	−	0.999522i	−0.00936719	−	0.0531240i
$355$	−1.65034	−	9.35955i	−0.0875910	−	0.496753i
$356$	4.84387	−	8.38982i	0.256724	−	0.444660i
$357$	15.0061	+	12.5916i	0.794208	+	0.666419i
$358$	−7.63493	−	2.77889i	−0.403518	−	0.146869i
$359$	11.5467	+	19.9994i	0.609410	+	1.05553i	0.991338	+	0.131337i	$0.0419271\pi$
$359$	11.5467	+	19.9994i	0.609410	+	1.05553i	−0.381927	+	0.924192i	$0.624740\pi$
$360$	0.341204	−	0.590982i	0.0179830	−	0.0311475i
$361$	27.9233	−	23.4304i	1.46965	−	1.23318i
$362$	−5.95343	−	10.3116i	−0.312905	−	0.541968i
$363$	0.989041	−	5.60913i	0.0519112	−	0.294403i
$364$	−11.9622			−0.626991
$365$	−3.33848	+	18.9335i	−0.174744	+	0.991023i
$366$	−9.84979	−	8.26495i	−0.514857	−	0.432016i
$367$	−1.47673	+	0.537487i	−0.0770848	+	0.0280566i	−0.380275	−	0.924874i	$-0.624171\pi$
$367$	−1.47673	+	0.537487i	−0.0770848	+	0.0280566i	0.303190	+	0.952930i	$0.401948\pi$
$368$	0.604727	+	0.220103i	0.0315236	+	0.0114736i
$369$	−3.85739			−0.200808
$370$	−11.3871	−	1.01082i	−0.591986	−	0.0525500i
$371$	16.6602			0.864957
$372$	17.0728	+	6.21400i	0.885184	+	0.322181i
$373$	−6.28835	+	2.28877i	−0.325599	+	0.118508i	−0.499647	−	0.866229i	$-0.666537\pi$
$373$	−6.28835	+	2.28877i	−0.325599	+	0.118508i	0.174049	+	0.984737i	$0.444315\pi$
$374$	6.67062	+	5.59732i	0.344930	+	0.289430i
$375$	−3.87097	+	21.9534i	−0.199896	+	1.13367i
$376$	−7.85643			−0.405164
$377$	−1.30723	+	7.41370i	−0.0673260	+	0.381825i
$378$	−8.33334	−	14.4338i	−0.428621	−	0.742393i
$379$	−8.40501	+	7.05264i	−0.431737	+	0.362270i	−0.832606	−	0.553865i	$-0.813152\pi$
$379$	−8.40501	+	7.05264i	−0.431737	+	0.362270i	0.400870	+	0.916135i	$0.368708\pi$
$380$	6.99748	−	12.1200i	0.358963	−	0.621742i
$381$	−6.50586	−	11.2685i	−0.333305	−	0.577301i
$382$	−0.250636	−	0.0912241i	−0.0128237	−	0.00466743i
$383$	−19.3480	−	16.2349i	−0.988638	−	0.829566i	−0.00326840	−	0.999995i	$-0.501040\pi$
$383$	−19.3480	−	16.2349i	−0.988638	−	0.829566i	−0.985370	+	0.170429i	$0.945485\pi$
$384$	0.916938	−	1.58818i	0.0467923	−	0.0810466i
$385$	3.16028	+	17.9228i	0.161063	+	0.913433i
$386$	1.37674	+	7.80790i	0.0700744	+	0.397412i
$387$	2.30995	−	1.93828i	0.117422	−	0.0985284i
$388$	−16.0310	+	5.83480i	−0.813849	+	0.296217i
$389$	10.1599	−	3.69792i	0.515130	−	0.187492i	−0.0713568	−	0.997451i	$-0.522733\pi$
$389$	10.1599	−	3.69792i	0.515130	−	0.187492i	0.586487	+	0.809959i	$0.300511\pi$
$390$	−9.16360	+	7.68917i	−0.464017	+	0.389356i
$391$	0.346340	+	1.96419i	0.0175152	+	0.0993334i
$392$	0.847190	+	4.80465i	0.0427896	+	0.242672i
$393$	16.0133	−	27.7358i	0.807763	−	1.39909i
$394$	−0.315326	−	0.264590i	−0.0158859	−	0.0133299i
$395$	−3.36406	−	1.22442i	−0.169264	−	0.0616072i
$396$	0.510096	+	0.883512i	0.0256333	+	0.0443982i
$397$	5.40570	−	9.36295i	0.271304	−	0.469913i	−0.697892	−	0.716203i	$-0.745878\pi$
$397$	5.40570	−	9.36295i	0.271304	−	0.469913i	0.969196	+	0.246290i	$0.0792117\pi$
$398$	−1.55892	+	1.30809i	−0.0781417	+	0.0655687i
$399$	23.5332	+	40.7607i	1.17813	+	2.04059i
$400$	−0.254900	+	1.44561i	−0.0127450	+	0.0722805i
$401$	−34.6974			−1.73271			−0.866353	−	0.499432i	$-0.833542\pi$
$401$	−34.6974			−1.73271			−0.866353	+	0.499432i	$0.833542\pi$
$402$	−0.0671996	+	0.381108i	−0.00335161	+	0.0190079i
$403$	−26.3408	−	22.1026i	−1.31213	−	1.10101i
$404$	−11.2558	+	4.09679i	−0.559999	+	0.203823i
$405$	−17.5853	−	6.40053i	−0.873822	−	0.318045i
$406$	7.47554			0.371005
$407$	9.82049	−	13.9873i	0.486783	−	0.693322i
$408$	5.68366			0.281383
$409$	−1.77330	−	0.645428i	−0.0876840	−	0.0319144i	0.297806	−	0.954627i	$-0.403745\pi$
$409$	−1.77330	−	0.645428i	−0.0876840	−	0.0319144i	−0.385490	+	0.922712i	$0.625967\pi$
$410$	−18.7615	+	6.82862i	−0.926563	+	0.337241i
$411$	−13.8475	−	11.6194i	−0.683046	−	0.573143i
$412$	2.24782	−	12.7480i	0.110742	−	0.628049i
$413$	1.90747			0.0938602
$414$	−0.0405763	+	0.230119i	−0.00199421	+	0.0113098i
$415$	6.39899	+	11.0834i	0.314114	+	0.544061i
$416$	−2.65877	+	2.23097i	−0.130357	+	0.109382i
$417$	−8.24777	+	14.2856i	−0.403895	+	0.699566i
$418$	10.4612	+	18.1193i	0.511672	+	0.886242i
$419$	16.3766	+	5.96059i	0.800048	+	0.291194i	0.709507	−	0.704699i	$-0.248918\pi$
$419$	16.3766	+	5.96059i	0.800048	+	0.291194i	0.0905419	+	0.995893i	$0.471140\pi$
$420$	9.09967	+	7.63553i	0.444018	+	0.372576i
$421$	9.07719	−	15.7222i	0.442395	−	0.766251i	−0.555471	−	0.831536i	$-0.687462\pi$
$421$	9.07719	−	15.7222i	0.442395	−	0.766251i	0.997867	+	0.0652845i	$0.0207955\pi$
$422$	−2.73340	−	15.5019i	−0.133060	−	0.754621i
$423$	−0.495363	−	2.80934i	−0.0240854	−	0.136595i
$424$	3.70296	−	3.10716i	0.179832	−	0.150897i
$425$	−4.27508	+	1.55600i	−0.207372	+	0.0754771i
$426$	8.71452	−	3.17183i	0.422220	−	0.153675i
$427$	18.5115	−	15.5330i	0.895837	−	0.751696i
$428$	2.71350	+	15.3891i	0.131162	+	0.743858i
$429$	−3.10542	−	17.6117i	−0.149931	−	0.850302i
$430$	7.80382	−	13.5166i	0.376334	−	0.651829i
$431$	21.7480	+	18.2487i	1.04756	+	0.879011i	0.992835	−	0.119491i	$-0.0381262\pi$
$431$	21.7480	+	18.2487i	1.04756	+	0.879011i	0.0547286	+	0.998501i	$0.482571\pi$
$432$	−4.54411	−	1.65392i	−0.218629	−	0.0795744i
$433$	3.73468	+	6.46865i	0.179477	+	0.310864i	0.941702	−	0.336449i	$-0.109226\pi$
$433$	3.73468	+	6.46865i	0.179477	+	0.310864i	−0.762224	+	0.647313i	$0.775893\pi$
$434$	−17.0728	+	29.5710i	−0.819521	+	1.41945i
$435$	5.72660	−	4.80519i	0.274569	−	0.230391i
$436$	−0.775056	−	1.34244i	−0.0371185	−	0.0642910i
$437$	−0.832146	+	4.71934i	−0.0398069	+	0.225756i
$438$	−18.7600			−0.896388
$439$	−5.99873	+	34.0205i	−0.286304	+	1.62371i	0.414287	+	0.910146i	$0.364031\pi$
$439$	−5.99873	+	34.0205i	−0.286304	+	1.62371i	−0.700590	+	0.713564i	$0.747080\pi$
$440$	4.04505	+	3.39420i	0.192840	+	0.161812i
$441$	−1.66466	+	0.605885i	−0.0792693	+	0.0288517i
$442$	−10.1081	−	3.67906i	−0.480795	−	0.174995i
$443$	−2.89849			−0.137712			−0.0688558	−	0.997627i	$-0.521935\pi$
$443$	−2.89849			−0.137712			−0.0688558	+	0.997627i	$0.521935\pi$
$444$	−0.958106	−	11.1138i	−0.0454697	−	0.527438i
$445$	18.2070			0.863094
$446$	3.22814	+	1.17495i	0.152857	+	0.0556353i
$447$	−17.1863	+	6.25530i	−0.812884	+	0.295866i
$448$	2.64022	+	2.21541i	0.124739	+	0.104668i
$449$	4.84053	−	27.4520i	0.228439	−	1.29554i	−0.627563	−	0.778566i	$-0.715948\pi$
$449$	4.84053	−	27.4520i	0.228439	−	1.29554i	0.856002	−	0.516973i	$-0.172941\pi$
$450$	−0.533001			−0.0251259
$451$	5.18310	−	29.3948i	0.244063	−	1.38415i
$452$	2.55737	+	4.42950i	0.120289	+	0.208346i
$453$	−13.5745	+	11.3903i	−0.637784	+	0.535164i
$454$	1.15640	−	2.00295i	0.0542726	−	0.0940029i
$455$	−11.2408	−	19.4697i	−0.526978	−	0.912752i
$456$	12.8325	+	4.67065i	0.600937	+	0.218723i
$457$	7.48390	+	6.27974i	0.350082	+	0.293754i	0.800823	−	0.598901i	$-0.204396\pi$
$457$	7.48390	+	6.27974i	0.350082	+	0.293754i	−0.450741	+	0.892655i	$0.648840\pi$
$458$	2.95547	−	5.11902i	0.138100	−	0.239196i
$459$	−2.60251	−	14.7596i	−0.121475	−	0.688917i
$460$	0.210020	+	1.19108i	0.00979221	+	0.0555344i
$461$	11.8337	−	9.92965i	0.551150	−	0.462470i	−0.324180	−	0.945995i	$-0.605088\pi$
$461$	11.8337	−	9.92965i	0.551150	−	0.462470i	0.875330	+	0.483525i	$0.160644\pi$
$462$	−16.6877	+	6.07381i	−0.776380	+	0.282579i
$463$	−17.2009	+	6.26063i	−0.799395	+	0.290956i	−0.709236	−	0.704971i	$-0.750960\pi$
$463$	−17.2009	+	6.26063i	−0.799395	+	0.290956i	−0.0901595	+	0.995927i	$0.528738\pi$
$464$	1.66154	−	1.39420i	0.0771351	−	0.0647240i
$465$	5.92933	+	33.6269i	0.274966	+	1.55941i
$466$	−4.92045	−	27.9053i	−0.227935	−	1.29269i
$467$	−11.8035	+	20.4443i	−0.546201	+	0.946048i	0.452329	+	0.891851i	$0.350593\pi$
$467$	−11.8035	+	20.4443i	−0.546201	+	0.946048i	−0.998530	+	0.0541966i	$0.982740\pi$
$468$	−0.965403	−	0.810069i	−0.0446257	−	0.0374454i
$469$	−0.683436	−	0.248750i	−0.0315581	−	0.0114862i
$470$	−7.38263	−	12.7871i	−0.340535	−	0.589824i
$471$	−8.05949	+	13.9594i	−0.371362	+	0.643217i
$472$	0.423960	−	0.355745i	0.0195143	−	0.0163745i
$473$	11.6666	+	20.2072i	0.536432	+	0.929128i
$474$	0.606600	−	3.44020i	0.0278621	−	0.158014i
$475$	−10.9309			−0.501544
$476$	−1.85487	+	10.5195i	−0.0850180	+	0.482161i
$477$	1.34455	+	1.12821i	0.0615628	+	0.0516573i
$478$	−22.7763	+	8.28990i	−1.04176	+	0.379171i
$479$	8.16238	+	2.97086i	0.372949	+	0.135742i	0.521693	−	0.853134i	$-0.325301\pi$
$479$	8.16238	+	2.97086i	0.372949	+	0.135742i	−0.148744	+	0.988876i	$0.547523\pi$
$480$	3.44656			0.157313
$481$	−5.49006	+	20.3856i	−0.250325	+	0.929502i
$482$	8.85069			0.403138
$483$	−3.82222	−	1.39117i	−0.173917	−	0.0633006i
$484$	2.91850	−	1.06225i	0.132659	−	0.0482840i
$485$	−24.5609	−	20.6090i	−1.11525	−	0.935807i
$486$	0.651791	−	3.69649i	0.0295658	−	0.167676i
$487$	20.9350			0.948654			0.474327	−	0.880349i	$-0.342691\pi$
$487$	20.9350			0.948654			0.474327	+	0.880349i	$0.342691\pi$
$488$	1.21751	−	6.90485i	0.0551142	−	0.312568i
$489$	−1.74875	−	3.02892i	−0.0790812	−	0.136973i
$490$	−7.02393	+	5.89378i	−0.317309	+	0.266254i
$491$	−21.6055	+	37.4219i	−0.975044	+	1.68883i	−0.295253	+	0.955419i	$0.595404\pi$
$491$	−21.6055	+	37.4219i	−0.975044	+	1.68883i	−0.679791	+	0.733406i	$0.737930\pi$
$492$	−9.74104	−	16.8720i	−0.439160	−	0.760647i
$493$	6.31686	+	2.29915i	0.284497	+	0.103548i
$494$	−19.7987	−	16.6131i	−0.890784	−	0.747457i
$495$	−0.958667	+	1.66046i	−0.0430889	+	0.0746321i
$496$	1.72036	+	9.75665i	0.0772465	+	0.438087i
$497$	3.02652	+	17.1643i	0.135758	+	0.769922i
$498$	−9.56642	+	8.02718i	−0.428682	+	0.359707i
$499$	6.35892	−	2.31446i	0.284664	−	0.103609i	−0.195742	−	0.980655i	$-0.562711\pi$
$499$	6.35892	−	2.31446i	0.284664	−	0.103609i	0.480406	+	0.877046i	$0.340489\pi$
$500$	−11.4226	+	4.15749i	−0.510835	+	0.185929i
$501$	−9.31069	+	7.81260i	−0.415971	+	0.349041i
$502$	1.14443	+	6.49037i	0.0510783	+	0.289679i
$503$	−4.76565	−	27.0274i	−0.212490	−	1.20509i	−0.885209	−	0.465193i	$-0.845985\pi$
$503$	−4.76565	−	27.0274i	−0.212490	−	1.20509i	0.672719	−	0.739898i	$-0.265126\pi$
$504$	−0.625726	+	1.08379i	−0.0278720	+	0.0482758i
$505$	−17.2449	−	14.4702i	−0.767390	−	0.643917i
$506$	−1.69908	−	0.618414i	−0.0755333	−	0.0274919i
$507$	−0.874506	−	1.51469i	−0.0388382	−	0.0672697i
$508$	3.54760	−	6.14462i	0.157399	−	0.272623i
$509$	16.0780	−	13.4910i	0.712643	−	0.597978i	−0.212696	−	0.977118i	$-0.568225\pi$
$509$	16.0780	−	13.4910i	0.712643	−	0.597978i	0.925339	+	0.379140i	$0.123780\pi$
$510$	5.34090	+	9.25071i	0.236499	+	0.409628i
$511$	6.12236	−	34.7216i	0.270837	−	1.53599i
$512$	1.00000			0.0441942
$513$	6.25301	−	35.4626i	0.276077	−	1.56571i
$514$	7.37373	+	6.18729i	0.325241	+	0.272910i
$515$	22.8608	−	8.32066i	1.00737	−	0.366652i
$516$	14.3112	+	5.20886i	0.630017	+	0.229307i
$517$	22.0739			0.970809
$518$	20.8825	+	1.85372i	0.917524	+	0.0814477i
$519$	−46.5975			−2.04540
$520$	−6.12954	−	2.23097i	−0.268798	−	0.0978345i
$521$	35.3011	−	12.8486i	1.54657	−	0.562906i	0.578961	−	0.815355i	$-0.303458\pi$
$521$	35.3011	−	12.8486i	1.54657	−	0.562906i	0.967610	+	0.252449i	$0.0812361\pi$
$522$	0.603308	+	0.506235i	0.0264061	+	0.0221573i
$523$	3.28508	−	18.6306i	0.143647	−	0.814660i	−0.824797	−	0.565428i	$-0.808711\pi$
$523$	3.28508	−	18.6306i	0.143647	−	0.814660i	0.968444	−	0.249232i	$-0.0801781\pi$
$524$	17.4639			0.762912
$525$	1.61111	−	9.13707i	0.0703147	−	0.398774i
$526$	0.795631	+	1.37807i	0.0346912	+	0.0600869i
$527$	−23.5213	+	19.7367i	−1.02460	+	0.859746i
$528$	−2.57629	+	4.46226i	−0.112118	+	0.194195i
$529$	11.2929	+	19.5599i	0.490997	+	0.850432i
$530$	8.53684	+	3.10716i	0.370817	+	0.134966i
$531$	0.153940	+	0.129171i	0.00668045	+	0.00560556i
$532$	−12.8325	+	22.2266i	−0.556360	+	0.963643i
$533$	6.40268	+	36.3114i	0.277331	+	1.57282i
$534$	3.08505	+	17.4962i	0.133503	+	0.757134i
$535$	−22.4973	+	18.8775i	−0.972643	+	0.816144i
$536$	−0.198295	+	0.0721735i	−0.00856505	+	0.00311742i
$537$	14.0015	−	5.09613i	0.604210	−	0.219914i
$538$	17.7108	−	14.8611i	0.763566	−	0.640708i
$539$	−2.38032	−	13.4994i	−0.102528	−	0.581462i
$540$	−1.57815	−	8.95016i	−0.0679129	−	0.385153i
$541$	−8.23739	+	14.2676i	−0.354153	+	0.613411i	−0.986973	−	0.160888i	$-0.948564\pi$
$541$	−8.23739	+	14.2676i	−0.354153	+	0.613411i	0.632820	+	0.774299i	$0.281897\pi$
$542$	0.140511	+	0.117903i	0.00603547	+	0.00506436i
$543$	20.5188	+	7.46825i	0.880548	+	0.320493i
$544$	1.54963	+	2.68404i	0.0664399	+	0.115077i
$545$	1.45663	−	2.52296i	0.0623951	−	0.108072i
$546$	16.8049	−	14.1010i	0.719184	−	0.603467i
$547$	6.00067	+	10.3935i	0.256570	+	0.444392i	0.965321	−	0.261067i	$-0.0840742\pi$
$547$	6.00067	+	10.3935i	0.256570	+	0.444392i	−0.708751	+	0.705459i	$0.750741\pi$
$548$	1.71166	−	9.70729i	0.0731184	−	0.414675i
$549$	2.54584			0.108654
$550$	0.716183	−	4.06167i	0.0305381	−	0.173190i
$551$	12.3728	+	10.3820i	0.527097	+	0.442287i
$552$	−1.10899	+	0.403641i	−0.0472020	+	0.0171801i
$553$	6.16927	+	2.24543i	0.262344	+	0.0954855i
$554$	−12.6914			−0.539204
$555$	17.1885	−	12.0030i	0.729610	−	0.509498i
$556$	−8.99490			−0.381469
$557$	40.2026	+	14.6325i	1.70344	+	0.620001i	0.996210	−	0.0869842i	$-0.0277230\pi$
$557$	40.2026	+	14.6325i	1.70344	+	0.620001i	0.707229	+	0.706985i	$0.249945\pi$
$558$	−3.38036	+	1.23035i	−0.143102	+	0.0520849i
$559$	−22.0801	−	18.5274i	−0.933890	−	0.783627i
$560$	−1.12479	+	6.37901i	−0.0475311	+	0.269562i
$561$	−15.9692			−0.674219
$562$	3.02774	−	17.1712i	0.127718	−	0.724323i
$563$	−11.8738	−	20.5660i	−0.500421	−	0.866754i	−1.00000		0.000486132i	$-0.999845\pi$
$563$	−11.8738	−	20.5660i	−0.500421	−	0.866754i	0.499579	−	0.866268i	$-0.333488\pi$
$564$	11.0369	−	9.26110i	0.464739	−	0.389963i
$565$	−4.80629	+	8.32474i	−0.202202	+	0.350224i
$566$	6.56696	+	11.3743i	0.276030	+	0.478098i
$567$	32.2493	+	11.7378i	1.35434	+	0.492941i
$568$	3.87384	+	3.25054i	0.162543	+	0.136389i
$569$	2.64332	−	4.57837i	0.110814	−	0.191935i	−0.805285	−	0.592888i	$-0.797988\pi$
$569$	2.64332	−	4.57837i	0.110814	−	0.191935i	0.916099	+	0.400953i	$0.131321\pi$
$570$	4.45668	+	25.2751i	0.186670	+	1.05866i
$571$	−4.21057	−	23.8793i	−0.176207	−	0.999318i	−0.936742	−	0.350021i	$-0.886174\pi$
$571$	−4.21057	−	23.8793i	−0.176207	−	0.999318i	0.760535	−	0.649297i	$-0.224937\pi$
$572$	7.47024	−	6.26827i	0.312346	−	0.262090i
$573$	0.459636	−	0.167294i	0.0192016	−	0.00698880i
$574$	34.4062	−	12.5228i	1.43609	−	0.522693i
$575$	0.723648	−	0.607213i	0.0301782	−	0.0253225i
$576$	0.0630519	+	0.357585i	0.00262716	+	0.0148994i
$577$	−0.296836	−	1.68344i	−0.0123574	−	0.0700825i	0.978005	−	0.208579i	$-0.0668840\pi$
$577$	−0.296836	−	1.68344i	−0.0123574	−	0.0700825i	−0.990363	+	0.138497i	$0.955773\pi$
$578$	3.69728	−	6.40388i	0.153787	−	0.266366i
$579$	−11.1380	−	9.34588i	−0.462879	−	0.388402i
$580$	3.83053	+	1.39420i	0.159054	+	0.0578909i
$581$	−11.7350	−	20.3255i	−0.486848	−	0.843245i
$582$	15.6428	−	27.0941i	0.648414	−	1.12309i
$583$	−10.4041	+	8.73005i	−0.430893	+	0.361562i
$584$	−5.11485	−	8.85918i	−0.211654	−	0.366595i
$585$	0.411283	−	2.33250i	0.0170044	−	0.0964370i
$586$	6.78723			0.280378
$587$	4.51530	−	25.6076i	0.186366	−	1.05694i	−0.737821	−	0.674997i	$-0.764145\pi$
$587$	4.51530	−	25.6076i	0.186366	−	1.05694i	0.924187	−	0.381940i	$-0.124744\pi$
$588$	−6.85385	−	5.75106i	−0.282648	−	0.237170i
$589$	−69.3251	+	25.2323i	−2.85649	+	1.03968i
$590$	0.977400	+	0.355745i	0.0402389	+	0.0146458i
$591$	0.754877			0.0310515
$592$	4.98714	−	3.48260i	0.204970	−	0.143134i
$593$	19.5933			0.804601			0.402300	−	0.915508i	$-0.368211\pi$
$593$	19.5933			0.804601			0.402300	+	0.915508i	$0.368211\pi$
$594$	12.7674	+	4.64696i	0.523854	+	0.190667i
$595$	−18.8645	+	6.86613i	−0.773370	+	0.281484i
$596$	−7.63977	−	6.41053i	−0.312937	−	0.262586i
$597$	0.648053	−	3.67529i	0.0265231	−	0.150420i
$598$	2.23357			0.0913376
$599$	6.43804	−	36.5119i	0.263051	−	1.49184i	−0.511477	−	0.859297i	$-0.670901\pi$
$599$	6.43804	−	36.5119i	0.263051	−	1.49184i	0.774528	−	0.632540i	$-0.217988\pi$
$600$	−1.34598	−	2.33131i	−0.0549495	−	0.0951754i
$601$	−14.1667	+	11.8873i	−0.577871	+	0.484892i	−0.884247	−	0.467019i	$-0.845328\pi$
$601$	−14.1667	+	11.8873i	−0.577871	+	0.484892i	0.306376	+	0.951911i	$0.400884\pi$
$602$	−14.3112	+	24.7878i	−0.583282	+	1.01027i
$603$	−0.0383111	−	0.0663567i	−0.00156015	−	0.00270226i
$604$	−9.07997	−	3.30484i	−0.369459	−	0.134472i
$605$	4.47140	+	3.75195i	0.181788	+	0.152539i
$606$	10.9833	−	19.0236i	0.446165	−	0.772781i
$607$	0.923385	+	5.23678i	0.0374791	+	0.212554i	0.997796	−	0.0663569i	$-0.0211376\pi$
$607$	0.923385	+	5.23678i	0.0374791	+	0.212554i	−0.960317	+	0.278911i	$0.910026\pi$
$608$	1.29308	+	7.33343i	0.0524414	+	0.297410i
$609$	−10.5019	+	8.81212i	−0.425557	+	0.357085i
$610$	12.3824	−	4.50682i	0.501348	−	0.182476i
$611$	−25.6234	+	9.32617i	−1.03661	+	0.377296i
$612$	−0.862066	+	0.723359i	−0.0348470	+	0.0292401i
$613$	7.01848	+	39.8038i	0.283474	+	1.60766i	0.710687	+	0.703508i	$0.248384\pi$
$613$	7.01848	+	39.8038i	0.283474	+	1.60766i	−0.427213	+	0.904151i	$0.640505\pi$
$614$	1.42476	+	8.08020i	0.0574985	+	0.326090i
$615$	18.3072	−	31.7089i	0.738216	−	1.27863i
$616$	−7.41812	−	6.22454i	−0.298884	−	0.250794i
$617$	30.8191	+	11.2172i	1.24073	+	0.451589i	0.877259	−	0.480017i	$-0.159370\pi$
$617$	30.8191	+	11.2172i	1.24073	+	0.451589i	0.363470	+	0.931606i	$0.381592\pi$
$618$	11.8694	+	20.5585i	0.477459	+	0.826984i
$619$	2.07537	−	3.59465i	0.0834163	−	0.144481i	−0.821299	−	0.570498i	$-0.806750\pi$
$619$	2.07537	−	3.59465i	0.0834163	−	0.144481i	0.904715	+	0.426017i	$0.140084\pi$
$620$	−14.2633	+	11.9683i	−0.572827	+	0.480659i
$621$	1.55599	+	2.69506i	0.0624398	+	0.108149i
$622$	−1.88461	+	10.6882i	−0.0755660	+	0.428556i
$623$	−33.3893			−1.33772
$624$	1.10527	−	6.26827i	0.0442460	−	0.250932i
$625$	−11.8780	−	9.96686i	−0.475122	−	0.398674i
$626$	8.13361	−	2.96039i	0.325085	−	0.118321i
$627$	−36.0550	−	13.1229i	−1.43990	−	0.524080i
$628$	−8.78957			−0.350742
$629$	17.0757	+	7.98893i	0.680851	+	0.318540i
$630$	−2.35196			−0.0937043
$631$	−28.1162	−	10.2335i	−1.11929	−	0.407387i	−0.284896	−	0.958559i	$-0.591959\pi$
$631$	−28.1162	−	10.2335i	−1.11929	−	0.407387i	−0.834392	+	0.551171i	$0.814181\pi$
$632$	1.78998	−	0.651500i	0.0712016	−	0.0259153i
$633$	22.1135	+	18.5554i	0.878932	+	0.737512i
$634$	−4.41505	+	25.0390i	−0.175344	+	0.994425i
$635$	13.3346			0.529168
$636$	−1.53934	+	8.73005i	−0.0610390	+	0.346169i
$637$	8.46656	+	14.6645i	0.335457	+	0.581029i
$638$	−4.66837	+	3.91722i	−0.184822	+	0.155084i
$639$	−0.918091	+	1.59018i	−0.0363191	+	0.0629065i
$640$	0.939693	+	1.62760i	0.0371446	+	0.0643364i
$641$	−6.42331	−	2.33789i	−0.253705	−	0.0923412i	0.212037	−	0.977262i	$-0.431990\pi$
$641$	−6.42331	−	2.33789i	−0.253705	−	0.0923412i	−0.465742	+	0.884920i	$0.654213\pi$
$642$	−21.9525	−	18.4203i	−0.866397	−	0.726993i
$643$	−18.7592	+	32.4920i	−0.739792	+	1.28136i	0.212796	+	0.977097i	$0.431743\pi$
$643$	−18.7592	+	32.4920i	−0.739792	+	1.28136i	−0.952589	+	0.304262i	$0.901590\pi$
$644$	−0.385150	−	2.18429i	−0.0151770	−	0.0860732i
$645$	4.97024	+	28.1876i	0.195703	+	1.10989i
$646$	−17.6794	+	14.8348i	−0.695588	+	0.583667i
$647$	−2.48480	+	0.904395i	−0.0976877	+	0.0355554i	−0.390402	−	0.920645i	$-0.627664\pi$
$647$	−2.48480	+	0.904395i	−0.0976877	+	0.0355554i	0.292714	+	0.956200i	$0.405442\pi$
$648$	9.35695	−	3.40565i	0.367576	−	0.133787i
$649$	−1.19118	+	0.999522i	−0.0467580	+	0.0392347i
$650$	0.884701	+	5.01739i	0.0347008	+	0.196798i
$651$	−10.8736	−	61.6675i	−0.426172	−	2.41694i
$652$	0.953582	−	1.65165i	0.0373451	−	0.0646837i
$653$	−34.2792	−	28.7636i	−1.34145	−	1.12561i	−0.981251	−	0.192732i	$-0.938265\pi$
$653$	−34.2792	−	28.7636i	−1.34145	−	1.12561i	−0.360197	−	0.932876i	$-0.617290\pi$
$654$	2.67128	+	0.972265i	0.104455	+	0.0380186i
$655$	16.4107	+	28.4241i	0.641218	+	1.11062i
$656$	5.31172	−	9.20017i	0.207388	−	0.359206i
$657$	2.84541	−	2.38758i	0.111010	−	0.0931485i
$658$	13.5388	+	23.4499i	0.527798	+	0.914173i
$659$	−0.790306	+	4.48205i	−0.0307859	+	0.174596i	−0.996324	−	0.0856667i	$-0.972698\pi$
$659$	−0.790306	+	4.48205i	−0.0307859	+	0.174596i	0.965538	+	0.260262i	$0.0838091\pi$
$660$	−9.68366			−0.376936
$661$	−7.56467	+	42.9014i	−0.294231	+	1.66867i	0.376078	+	0.926588i	$0.377272\pi$
$661$	−7.56467	+	42.9014i	−0.294231	+	1.66867i	−0.670310	+	0.742082i	$0.733839\pi$
$662$	−15.9349	−	13.3710i	−0.619327	−	0.519677i
$663$	18.5371	−	6.74694i	0.719919	−	0.262029i
$664$	−6.39899	−	2.32904i	−0.248329	−	0.0903843i
$665$	−48.2344			−1.87045
$666$	1.55977	+	1.56374i	0.0604400	+	0.0605938i
$667$	−1.39582			−0.0540465
$668$	−6.22793	−	2.26678i	−0.240966	−	0.0877044i
$669$	−5.92000	+	2.15470i	−0.228880	+	0.0833057i
$670$	−0.303806	−	0.254923i	−0.0117370	−	0.00984855i
$671$	−3.42080	+	19.4003i	−0.132058	+	0.748940i
$672$	−6.32056			−0.243821
$673$	6.60813	−	37.4766i	0.254725	−	1.44462i	−0.542053	−	0.840344i	$-0.682353\pi$
$673$	6.60813	−	37.4766i	0.254725	−	1.44462i	0.796778	−	0.604272i	$-0.206536\pi$
$674$	1.23612	+	2.14103i	0.0476136	+	0.0824693i
$675$	−5.43772	+	4.56279i	−0.209298	+	0.175622i
$676$	0.476862	−	0.825949i	0.0183408	−	0.0317673i
$677$	−22.0131	−	38.1278i	−0.846032	−	1.46537i	−0.884722	−	0.466120i	$-0.845652\pi$
$677$	−22.0131	−	38.1278i	−0.846032	−	1.46537i	0.0386894	−	0.999251i	$-0.487682\pi$
$678$	−8.81414	−	3.20809i	−0.338505	−	0.123206i
$679$	45.0416	+	37.7944i	1.72854	+	1.45042i
$680$	−2.91235	+	5.04435i	−0.111684	+	0.193442i
$681$	0.736510	+	4.17696i	0.0282231	+	0.160061i
$682$	−4.83363	−	27.4129i	−0.185089	−	1.04969i
$683$	14.4021	−	12.0848i	0.551081	−	0.462412i	−0.324226	−	0.945980i	$-0.605104\pi$
$683$	14.4021	−	12.0848i	0.551081	−	0.462412i	0.875307	+	0.483568i	$0.160659\pi$
$684$	−2.54079	+	0.924774i	−0.0971497	+	0.0353596i
$685$	17.4080	−	6.33598i	0.665125	−	0.242086i
$686$	−5.60050	+	4.69938i	−0.213828	+	0.179423i
$687$	1.88233	+	10.6752i	0.0718155	+	0.407286i
$688$	1.44209	+	8.17848i	0.0549791	+	0.311802i
$689$	8.38865	−	14.5296i	0.319582	−	0.553532i
$690$	−1.69908	−	1.42570i	−0.0646828	−	0.0542753i
$691$	−25.3128	−	9.21310i	−0.962944	−	0.350483i	−0.187757	−	0.982215i	$-0.560122\pi$
$691$	−25.3128	−	9.21310i	−0.962944	−	0.350483i	−0.775186	+	0.631733i	$0.782344\pi$
$692$	−12.7046	−	22.0051i	−0.482958	−	0.836508i
$693$	1.75808	−	3.04508i	0.0667838	−	0.115673i
$694$	−4.48427	+	3.76275i	−0.170220	+	0.142832i
$695$	−8.45244	−	14.6401i	−0.320619	−	0.555329i
$696$	−0.690712	+	3.91722i	−0.0261814	+	0.148482i
$697$	32.9248			1.24712
$698$	0.545283	−	3.09246i	0.0206393	−	0.117051i
$699$	39.8069	+	33.4020i	1.50564	+	1.26338i
$700$	4.75413	−	1.73036i	0.179689	−	0.0654016i
$701$	−6.98332	−	2.54172i	−0.263756	−	0.0959995i	0.206757	−	0.978392i	$-0.433709\pi$
$701$	−6.98332	−	2.54172i	−0.263756	−	0.0959995i	−0.470513	+	0.882393i	$0.655931\pi$
$702$	−16.7838			−0.633463
$703$	31.9881	+	32.0695i	1.20646	+	1.20953i
$704$	−2.80966			−0.105893
$705$	25.4447	+	9.26110i	0.958302	+	0.348793i
$706$	10.5699	−	3.84713i	0.397804	−	0.144789i
$707$	31.6251	+	26.5366i	1.18938	+	0.998012i
$708$	−0.176243	+	0.999522i	−0.00662360	+	0.0375643i
$709$	0.834473			0.0313393			0.0156697	−	0.999877i	$-0.495012\pi$
$709$	0.834473			0.0313393			0.0156697	+	0.999877i	$0.495012\pi$
$710$	−1.65034	+	9.35955i	−0.0619362	+	0.351258i
$711$	0.345828	+	0.598992i	0.0129696	+	0.0224640i
$712$	−7.42123	+	6.22715i	−0.278122	+	0.233372i
$713$	3.18781	−	5.52146i	0.119385	−	0.206780i
$714$	−9.79455	−	16.9646i	−0.366552	−	0.634886i
$715$	17.2219	+	6.26827i	0.644064	+	0.234420i
$716$	6.22405	+	5.22260i	0.232604	+	0.195178i
$717$	22.2248	−	38.4945i	0.830000	−	1.43760i
$718$	−4.01012	−	22.7425i	−0.149656	−	0.848743i
$719$	−0.874879	−	4.96169i	−0.0326275	−	0.185040i	0.964138	−	0.265400i	$-0.0855040\pi$
$719$	−0.874879	−	4.96169i	−0.0326275	−	0.185040i	−0.996766	+	0.0803603i	$0.974393\pi$
$720$	−0.522755	+	0.438643i	−0.0194819	+	0.0163473i
$721$	−41.9239	+	15.2591i	−1.56133	+	0.568277i
$722$	−34.2530	+	12.4671i	−1.27476	+	0.463976i
$723$	−12.4337	+	10.4331i	−0.462415	+	0.388012i
$724$	2.06760	+	11.7260i	0.0768419	+	0.435792i
$725$	−0.552875	−	3.13551i	−0.0205333	−	0.116450i
$726$	−2.84783	+	4.93259i	−0.105693	+	0.183065i
$727$	14.2591	+	11.9648i	0.528842	+	0.443751i	0.867701	−	0.497086i	$-0.165597\pi$
$727$	14.2591	+	11.9648i	0.528842	+	0.443751i	−0.338860	+	0.940837i	$0.610041\pi$
$728$	11.2408	+	4.09132i	0.416613	+	0.151635i
$729$	−11.4945	−	19.9090i	−0.425720	−	0.737369i
$730$	9.61277	−	16.6498i	0.355785	−	0.616237i
$731$	−19.7167	+	16.5443i	−0.729248	+	0.611912i
$732$	6.42899	+	11.1353i	0.237622	+	0.411574i
$733$	0.797139	−	4.52080i	0.0294430	−	0.166980i	−0.966541	−	0.256513i	$-0.917426\pi$
$733$	0.797139	−	4.52080i	0.0294430	−	0.166980i	0.995984	+	0.0895332i	$0.0285375\pi$
$734$	1.57151			0.0580054
$735$	2.91989	−	16.5595i	0.107702	−	0.610807i
$736$	−0.492978	−	0.413658i	−0.0181714	−	0.0152476i
$737$	0.557142	−	0.202783i	0.0205226	−	0.00746961i
$738$	3.62476	+	1.31930i	0.133429	+	0.0485643i
$739$	−46.9098			−1.72560			−0.862802	−	0.505542i	$-0.831292\pi$
$739$	−46.9098			−1.72560			−0.862802	+	0.505542i	$0.831292\pi$
$740$	10.3546	+	4.84447i	0.380644	+	0.178086i
$741$	47.3971			1.74118
$742$	−15.6555	−	5.69814i	−0.574732	−	0.209185i
$743$	−4.69037	+	1.70716i	−0.172073	+	0.0626295i	−0.426620	−	0.904431i	$-0.640296\pi$
$743$	−4.69037	+	1.70716i	−0.172073	+	0.0626295i	0.254547	+	0.967060i	$0.418074\pi$
$744$	−13.9179	−	11.6785i	−0.510254	−	0.428154i
$745$	3.25471	−	18.4584i	0.119243	−	0.676263i
$746$	6.69192			0.245009
$747$	0.429362	−	2.43503i	0.0157095	−	0.0890932i
$748$	−4.35394	−	7.54125i	−0.159196	−	0.275735i
$749$	41.2572	−	34.6189i	1.50751	−	1.26495i
$750$	11.1460	−	19.3055i	0.406995	−	0.704936i
$751$	−9.41422	−	16.3059i	−0.343530	−	0.595011i	0.641556	−	0.767077i	$-0.278289\pi$
$751$	−9.41422	−	16.3059i	−0.343530	−	0.595011i	−0.985086	+	0.172065i	$0.944956\pi$
$752$	7.38263	+	2.68706i	0.269217	+	0.0979869i
$753$	−9.25853	−	7.76883i	−0.337400	−	0.283112i
$754$	3.76403	−	6.51950i	0.137078	−	0.237426i
$755$	−3.15344	−	17.8841i	−0.114766	−	0.650867i
$756$	2.89414	+	16.4135i	0.105259	+	0.596952i
$757$	0.598778	−	0.502435i	0.0217630	−	0.0182613i	−0.631841	−	0.775098i	$-0.717701\pi$
$757$	0.598778	−	0.502435i	0.0217630	−	0.0182613i	0.653604	+	0.756837i	$0.273256\pi$
$758$	10.3103	−	3.75263i	0.374486	−	0.136302i
$759$	3.11590	−	1.13409i	0.113100	−	0.0411650i
$760$	−10.7208	+	8.99578i	−0.388883	+	0.326311i
$761$	−5.27399	−	29.9103i	−0.191182	−	1.08425i	−0.917752	−	0.397154i	$-0.869998\pi$
$761$	−5.27399	−	29.9103i	−0.191182	−	1.08425i	0.726570	−	0.687092i	$-0.241113\pi$
$762$	2.25946	+	12.8140i	0.0818516	+	0.464203i
$763$	−2.67128	+	4.62679i	−0.0967067	+	0.167501i
$764$	0.204321	+	0.171445i	0.00739206	+	0.00620267i
$765$	−1.98741	−	0.723359i	−0.0718551	−	0.0261531i
$766$	12.6285	+	21.8733i	0.456287	+	0.790313i
$767$	0.960433	−	1.66352i	0.0346792	−	0.0600662i
$768$	−1.40483	+	1.17879i	−0.0506925	+	0.0425360i
$769$	7.98228	+	13.8257i	0.287848	+	0.498568i	0.973296	−	0.229554i	$-0.0737268\pi$
$769$	7.98228	+	13.8257i	0.287848	+	0.498568i

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.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(1.72328 - 0.627223i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.326352 + 1.85083i) q^{5} -1.83388 q^{6} +(0.598489 - 3.39420i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.278152 - 0.233397i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(1.72328 - 0.627223i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.326352 + 1.85083i) q^{5} -1.83388 q^{6} +(0.598489 - 3.39420i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.278152 - 0.233397i) q^{9} +(0.939693 - 1.62760i) q^{10} +(1.40483 + 2.43324i) q^{11} +(1.72328 + 0.627223i) q^{12} +(-2.65877 - 2.23097i) q^{13} +(-1.72328 + 2.98481i) q^{14} +(0.598489 + 3.39420i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.37417 + 1.99217i) q^{17} +(-0.341204 + 0.124188i) q^{18} +(-6.99748 + 2.54687i) q^{19} +(-1.43969 + 1.20805i) q^{20} +(-1.09755 - 6.22454i) q^{21} +(-0.487893 - 2.76698i) q^{22} +(0.321769 - 0.557320i) q^{23} +(-1.40483 - 1.17879i) q^{24} +(1.37939 + 0.502055i) q^{25} +(1.73539 + 3.00578i) q^{26} +(-2.41787 + 4.18788i) q^{27} +(2.64022 - 2.21541i) q^{28} +(-1.08449 - 1.87840i) q^{29} +(0.598489 - 3.39420i) q^{30} +9.90716 q^{31} +(0.173648 - 0.984808i) q^{32} +(3.94710 + 3.31201i) q^{33} +(2.91235 - 1.06001i) q^{34} +(6.08678 + 2.21541i) q^{35} +0.363102 q^{36} +(-2.56368 - 5.51612i) q^{37} +7.44656 q^{38} +(-5.98112 - 2.17695i) q^{39} +(1.76604 - 0.642788i) q^{40} +(-8.13803 - 6.82862i) q^{41} +(-1.09755 + 6.22454i) q^{42} +8.30465 q^{43} +(-0.487893 + 2.76698i) q^{44} +(0.341204 + 0.590982i) q^{45} +(-0.492978 + 0.413658i) q^{46} +(3.92821 - 6.80387i) q^{47} +(0.916938 + 1.58818i) q^{48} +(-4.58455 - 1.66864i) q^{49} +(-1.12449 - 0.943555i) q^{50} +(-2.84183 + 4.92220i) q^{51} +(-0.602694 - 3.41805i) q^{52} +(0.839394 + 4.76044i) q^{53} +(3.70440 - 3.10836i) q^{54} +(-4.96199 + 1.80602i) q^{55} +(-3.23871 + 1.17879i) q^{56} +(-10.4612 + 8.77795i) q^{57} +(0.376641 + 2.13604i) q^{58} +(0.0961039 + 0.545032i) q^{59} +(-1.72328 + 2.98481i) q^{60} +(5.37102 + 4.50682i) q^{61} +(-9.30969 - 3.38845i) q^{62} +(-0.625726 - 1.08379i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(4.99685 - 4.19285i) q^{65} +(-2.57629 - 4.46226i) q^{66} +(0.0366435 - 0.207815i) q^{67} -3.09926 q^{68} +(0.204934 - 1.16224i) q^{69} +(-4.96199 - 4.16360i) q^{70} +(-4.75197 + 1.72957i) q^{71} +(-0.341204 - 0.124188i) q^{72} +10.2297 q^{73} +(0.522449 + 6.06028i) q^{74} +2.69197 q^{75} +(-6.99748 - 2.54687i) q^{76} +(9.09967 - 3.31201i) q^{77} +(4.87585 + 4.09132i) q^{78} +(-0.330775 + 1.87592i) q^{79} -1.87939 q^{80} +(-1.72910 + 9.80619i) q^{81} +(5.31172 + 9.20017i) q^{82} +(5.21650 - 4.37717i) q^{83} +(3.16028 - 5.47377i) q^{84} +(-2.91235 - 5.04435i) q^{85} +(-7.80382 - 2.84036i) q^{86} +(-3.04706 - 2.55679i) q^{87} +(1.40483 - 2.43324i) q^{88} +(-1.68226 - 9.54055i) q^{89} +(-0.118499 - 0.672040i) q^{90} +(-9.16360 + 7.68917i) q^{91} +(0.604727 - 0.220103i) q^{92} +(17.0728 - 6.21400i) q^{93} +(-6.01837 + 5.05001i) q^{94} +(-2.43020 - 13.7823i) q^{95} +(-0.318449 - 1.80602i) q^{96} +(-8.52990 + 14.7742i) q^{97} +(3.73736 + 3.13602i) q^{98} +(0.958667 + 0.348926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9	\( 12 q - 3 q^{3} - 6 q^{5} + 6 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{14} + 6 q^{15} - 3 q^{17} + 6 q^{18} - 3 q^{19} - 6 q^{20} - 33 q^{21} - 3 q^{22} - 21 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{27} - 3 q^{28} + 6 q^{29} + 6 q^{30} + 42 q^{31} + 57 q^{33} - 3 q^{34} - 9 q^{35} + 24 q^{36} - 3 q^{37} + 42 q^{38} - 24 q^{39} + 12 q^{40} - 21 q^{41} - 33 q^{42} + 36 q^{43} - 3 q^{44} - 6 q^{45} + 3 q^{46} + 9 q^{47} - 12 q^{49} + 12 q^{50} + 3 q^{52} - 6 q^{53} - 27 q^{54} - 3 q^{56} - 36 q^{57} - 3 q^{58} - 6 q^{59} + 3 q^{60} - 18 q^{61} - 33 q^{62} + 36 q^{63} - 6 q^{64} + 3 q^{65} + 3 q^{66} - 27 q^{67} + 6 q^{68} - 12 q^{69} - 18 q^{71} + 6 q^{72} + 54 q^{73} + 3 q^{74} - 6 q^{75} - 3 q^{76} + 51 q^{77} - 33 q^{78} - 12 q^{79} - 36 q^{81} - 18 q^{82} - 6 q^{83} - 6 q^{84} + 3 q^{85} + 39 q^{87} + 3 q^{88} - 15 q^{89} - 15 q^{90} - 51 q^{91} - 6 q^{92} + 45 q^{93} - 12 q^{94} - 15 q^{95} + 6 q^{96} - 42 q^{97} + 51 q^{98} - 33 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - 6 * q^5 + 6 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^11 - 3 * q^12 - 6 * q^13 + 3 * q^14 + 6 * q^15 - 3 * q^17 + 6 * q^18 - 3 * q^19 - 6 * q^20 - 33 * q^21 - 3 * q^22 - 21 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^27 - 3 * q^28 + 6 * q^29 + 6 * q^30 + 42 * q^31 + 57 * q^33 - 3 * q^34 - 9 * q^35 + 24 * q^36 - 3 * q^37 + 42 * q^38 - 24 * q^39 + 12 * q^40 - 21 * q^41 - 33 * q^42 + 36 * q^43 - 3 * q^44 - 6 * q^45 + 3 * q^46 + 9 * q^47 - 12 * q^49 + 12 * q^50 + 3 * q^52 - 6 * q^53 - 27 * q^54 - 3 * q^56 - 36 * q^57 - 3 * q^58 - 6 * q^59 + 3 * q^60 - 18 * q^61 - 33 * q^62 + 36 * q^63 - 6 * q^64 + 3 * q^65 + 3 * q^66 - 27 * q^67 + 6 * q^68 - 12 * q^69 - 18 * q^71 + 6 * q^72 + 54 * q^73 + 3 * q^74 - 6 * q^75 - 3 * q^76 + 51 * q^77 - 33 * q^78 - 12 * q^79 - 36 * q^81 - 18 * q^82 - 6 * q^83 - 6 * q^84 + 3 * q^85 + 39 * q^87 + 3 * q^88 - 15 * q^89 - 15 * q^90 - 51 * q^91 - 6 * q^92 + 45 * q^93 - 12 * q^94 - 15 * q^95 + 6 * q^96 - 42 * q^97 + 51 * q^98 - 33 * q^99

Introduction

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