LMFDB - Embedded newform 690.2.h.a.689.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(689,690)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("690.689");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			689.7
Character	$\chi$	$=$	690.689
Dual form			690.2.h.a.689.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.29400 + 1.15133i) q^{3} +1.00000 q^{4} +(-2.22484 + 0.223804i) q^{5} +(1.29400 - 1.15133i) q^{6} +0.666856 q^{7} -1.00000 q^{8} +(0.348885 - 2.97964i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.29400 + 1.15133i) q^{3} +1.00000 q^{4} +(-2.22484 + 0.223804i) q^{5} +(1.29400 - 1.15133i) q^{6} +0.666856 q^{7} -1.00000 q^{8} +(0.348885 - 2.97964i) q^{9} +(2.22484 - 0.223804i) q^{10} +4.92726 q^{11} +(-1.29400 + 1.15133i) q^{12} +3.71145i q^{13} -0.666856 q^{14} +(2.62128 - 2.85112i) q^{15} +1.00000 q^{16} -0.810614i q^{17} +(-0.348885 + 2.97964i) q^{18} -4.16671i q^{19} +(-2.22484 + 0.223804i) q^{20} +(-0.862914 + 0.767771i) q^{21} -4.92726 q^{22} +(-1.14656 + 4.65676i) q^{23} +(1.29400 - 1.15133i) q^{24} +(4.89982 - 0.995856i) q^{25} -3.71145i q^{26} +(2.97909 + 4.25735i) q^{27} +0.666856 q^{28} +9.02232i q^{29} +(-2.62128 + 2.85112i) q^{30} -6.13458 q^{31} -1.00000 q^{32} +(-6.37589 + 5.67289i) q^{33} +0.810614i q^{34} +(-1.48365 + 0.149245i) q^{35} +(0.348885 - 2.97964i) q^{36} +2.21928 q^{37} +4.16671i q^{38} +(-4.27309 - 4.80262i) q^{39} +(2.22484 - 0.223804i) q^{40} +2.54295i q^{41} +(0.862914 - 0.767771i) q^{42} -3.56526 q^{43} +4.92726 q^{44} +(-0.109357 + 6.70731i) q^{45} +(1.14656 - 4.65676i) q^{46} -10.0928 q^{47} +(-1.29400 + 1.15133i) q^{48} -6.55530 q^{49} +(-4.89982 + 0.995856i) q^{50} +(0.933283 + 1.04894i) q^{51} +3.71145i q^{52} -10.6281i q^{53} +(-2.97909 - 4.25735i) q^{54} +(-10.9624 + 1.10274i) q^{55} -0.666856 q^{56} +(4.79725 + 5.39173i) q^{57} -9.02232i q^{58} +6.81080i q^{59} +(2.62128 - 2.85112i) q^{60} +9.21371i q^{61} +6.13458 q^{62} +(0.232656 - 1.98699i) q^{63} +1.00000 q^{64} +(-0.830637 - 8.25737i) q^{65} +(6.37589 - 5.67289i) q^{66} +7.95053 q^{67} -0.810614i q^{68} +(-3.87781 - 7.34592i) q^{69} +(1.48365 - 0.149245i) q^{70} +14.5288i q^{71} +(-0.348885 + 2.97964i) q^{72} +4.84561i q^{73} -2.21928 q^{74} +(-5.19383 + 6.92995i) q^{75} -4.16671i q^{76} +3.28577 q^{77} +(4.27309 + 4.80262i) q^{78} +11.5161i q^{79} +(-2.22484 + 0.223804i) q^{80} +(-8.75656 - 2.07911i) q^{81} -2.54295i q^{82} +13.5358i q^{83} +(-0.862914 + 0.767771i) q^{84} +(0.181419 + 1.80349i) q^{85} +3.56526 q^{86} +(-10.3877 - 11.6749i) q^{87} -4.92726 q^{88} +12.5342 q^{89} +(0.109357 - 6.70731i) q^{90} +2.47500i q^{91} +(-1.14656 + 4.65676i) q^{92} +(7.93816 - 7.06292i) q^{93} +10.0928 q^{94} +(0.932526 + 9.27026i) q^{95} +(1.29400 - 1.15133i) q^{96} -1.04670 q^{97} +6.55530 q^{98} +(1.71905 - 14.6815i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 2 q^{3} + 24 q^{4} - 2 q^{6} - 24 q^{8} + 6 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 2 * q^3 + 24 * q^4 - 2 * q^6 - 24 * q^8 + 6 * q^9	$ 24 q - 24 q^{2} + 2 q^{3} + 24 q^{4} - 2 q^{6} - 24 q^{8} + 6 q^{9} + 2 q^{12} + 24 q^{16} - 6 q^{18} - 4 q^{23} - 2 q^{24} + 12 q^{25} + 2 q^{27} - 28 q^{31} - 24 q^{32} + 8 q^{35} + 6 q^{36} + 4 q^{46} + 16 q^{47} + 2 q^{48} - 4 q^{49} - 12 q^{50} - 2 q^{54} + 4 q^{55} + 28 q^{62} + 24 q^{64} - 8 q^{69} - 8 q^{70} - 6 q^{72} + 14 q^{75} + 8 q^{77} + 14 q^{81} - 44 q^{85} + 28 q^{87} - 4 q^{92} - 4 q^{93} - 16 q^{94} + 4 q^{95} - 2 q^{96} + 4 q^{98}+O(q^{100}) $ 24 * q - 24 * q^2 + 2 * q^3 + 24 * q^4 - 2 * q^6 - 24 * q^8 + 6 * q^9 + 2 * q^12 + 24 * q^16 - 6 * q^18 - 4 * q^23 - 2 * q^24 + 12 * q^25 + 2 * q^27 - 28 * q^31 - 24 * q^32 + 8 * q^35 + 6 * q^36 + 4 * q^46 + 16 * q^47 + 2 * q^48 - 4 * q^49 - 12 * q^50 - 2 * q^54 + 4 * q^55 + 28 * q^62 + 24 * q^64 - 8 * q^69 - 8 * q^70 - 6 * q^72 + 14 * q^75 + 8 * q^77 + 14 * q^81 - 44 * q^85 + 28 * q^87 - 4 * q^92 - 4 * q^93 - 16 * q^94 + 4 * q^95 - 2 * q^96 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.29400	+	1.15133i	−0.747093	+	0.664720i
$3$	−1.29400	+	1.15133i	−0.747093	+	0.664720i
$4$	1.00000			0.500000
$5$	−2.22484	+	0.223804i	−0.994979	+	0.100088i
$5$	−2.22484	+	0.223804i	−0.994979	+	0.100088i
$6$	1.29400	−	1.15133i	0.528274	−	0.470028i
$7$	0.666856			0.252048			0.126024	−	0.992027i	$-0.459778\pi$
$7$	0.666856			0.252048			0.126024	+	0.992027i	$0.459778\pi$
$8$	−1.00000			−0.353553
$9$	0.348885	−	2.97964i	0.116295	−	0.993215i
$10$	2.22484	−	0.223804i	0.703556	−	0.0707731i
$11$	4.92726			1.48562			0.742812	−	0.669500i	$-0.233491\pi$
$11$	4.92726			1.48562			0.742812	+	0.669500i	$0.233491\pi$
$12$	−1.29400	+	1.15133i	−0.373546	+	0.332360i
$13$			3.71145i			1.02937i	0.857379	+	0.514685i	$0.172091\pi$
$13$			3.71145i			1.02937i	−0.857379	+	0.514685i	$0.827909\pi$
$14$	−0.666856			−0.178225
$15$	2.62128	−	2.85112i	0.676811	−	0.736157i
$16$	1.00000			0.250000
$17$		−	0.810614i		−	0.196603i	−0.995157	−	0.0983013i	$-0.968659\pi$
$17$		−	0.810614i		−	0.196603i	0.995157	−	0.0983013i	$-0.0313409\pi$
$18$	−0.348885	+	2.97964i	−0.0822330	+	0.702309i
$19$		−	4.16671i		−	0.955908i	−0.878385	−	0.477954i	$-0.841379\pi$
$19$		−	4.16671i		−	0.955908i	0.878385	−	0.477954i	$-0.158621\pi$
$20$	−2.22484	+	0.223804i	−0.497489	+	0.0500441i
$21$	−0.862914	+	0.767771i	−0.188303	+	0.167541i
$22$	−4.92726			−1.05050
$23$	−1.14656	+	4.65676i	−0.239074	+	0.971001i
$23$	−1.14656	+	4.65676i	−0.239074	+	0.971001i
$24$	1.29400	−	1.15133i	0.264137	−	0.235014i
$25$	4.89982	−	0.995856i	0.979965	−	0.199171i
$26$		−	3.71145i		−	0.727874i
$27$	2.97909	+	4.25735i	0.573326	+	0.819327i
$28$	0.666856			0.126024
$29$			9.02232i			1.67540i	0.546129	+	0.837701i	$0.316101\pi$
$29$			9.02232i			1.67540i	−0.546129	+	0.837701i	$0.683899\pi$
$30$	−2.62128	+	2.85112i	−0.478577	+	0.520542i
$31$	−6.13458			−1.10180			−0.550902	−	0.834570i	$-0.685716\pi$
$31$	−6.13458			−1.10180			−0.550902	+	0.834570i	$0.685716\pi$
$32$	−1.00000			−0.176777
$33$	−6.37589	+	5.67289i	−1.10990	+	0.987524i
$34$			0.810614i			0.139019i
$35$	−1.48365	+	0.149245i	−0.250782	+	0.0252270i
$36$	0.348885	−	2.97964i	0.0581475	−	0.496607i
$37$	2.21928			0.364848			0.182424	−	0.983220i	$-0.441606\pi$
$37$	2.21928			0.364848			0.182424	+	0.983220i	$0.441606\pi$
$38$			4.16671i			0.675929i
$39$	−4.27309	−	4.80262i	−0.684243	−	0.769035i
$40$	2.22484	−	0.223804i	0.351778	−	0.0353865i
$41$			2.54295i			0.397143i	0.980086	+	0.198571i	$0.0636302\pi$
$41$			2.54295i			0.397143i	−0.980086	+	0.198571i	$0.936370\pi$
$42$	0.862914	−	0.767771i	0.133151	−	0.118470i
$43$	−3.56526			−0.543698			−0.271849	−	0.962340i	$-0.587635\pi$
$43$	−3.56526			−0.543698			−0.271849	+	0.962340i	$0.587635\pi$
$44$	4.92726			0.742812
$45$	−0.109357	+	6.70731i	−0.0163019	+	0.999867i
$46$	1.14656	−	4.65676i	0.169051	−	0.686602i
$47$	−10.0928			−1.47218			−0.736090	−	0.676883i	$-0.763330\pi$
$47$	−10.0928			−1.47218			−0.736090	+	0.676883i	$0.763330\pi$
$48$	−1.29400	+	1.15133i	−0.186773	+	0.166180i
$49$	−6.55530			−0.936472
$50$	−4.89982	+	0.995856i	−0.692940	+	0.140835i
$51$	0.933283	+	1.04894i	0.130686	+	0.146880i
$52$			3.71145i			0.514685i
$53$		−	10.6281i		−	1.45988i	−0.683511	−	0.729940i	$-0.739548\pi$
$53$		−	10.6281i		−	1.45988i	0.683511	−	0.729940i	$-0.260452\pi$
$54$	−2.97909	−	4.25735i	−0.405403	−	0.579352i
$55$	−10.9624	+	1.10274i	−1.47816	+	0.148694i
$56$	−0.666856			−0.0891124
$57$	4.79725	+	5.39173i	0.635411	+	0.714152i
$58$		−	9.02232i		−	1.18469i
$59$			6.81080i			0.886690i	0.896351	+	0.443345i	$0.146208\pi$
$59$			6.81080i			0.886690i	−0.896351	+	0.443345i	$0.853792\pi$
$60$	2.62128	−	2.85112i	0.338405	−	0.368079i
$61$			9.21371i			1.17969i	0.807515	+	0.589847i	$0.200812\pi$
$61$			9.21371i			1.17969i	−0.807515	+	0.589847i	$0.799188\pi$
$62$	6.13458			0.779092
$63$	0.232656	−	1.98699i	0.0293119	−	0.250338i
$64$	1.00000			0.125000
$65$	−0.830637	−	8.25737i	−0.103028	−	1.02420i
$66$	6.37589	−	5.67289i	0.784817	−	0.698285i
$67$	7.95053			0.971312			0.485656	−	0.874150i	$-0.338581\pi$
$67$	7.95053			0.971312			0.485656	+	0.874150i	$0.338581\pi$
$68$		−	0.810614i		−	0.0983013i
$69$	−3.87781	−	7.34592i	−0.466834	−	0.884345i
$70$	1.48365	−	0.149245i	0.177330	−	0.0178382i
$71$			14.5288i			1.72425i	0.506695	+	0.862126i	$0.330867\pi$
$71$			14.5288i			1.72425i	−0.506695	+	0.862126i	$0.669133\pi$
$72$	−0.348885	+	2.97964i	−0.0411165	+	0.351154i
$73$			4.84561i			0.567136i	0.958952	+	0.283568i	$0.0915181\pi$
$73$			4.84561i			0.567136i	−0.958952	+	0.283568i	$0.908482\pi$
$74$	−2.21928			−0.257986
$75$	−5.19383	+	6.92995i	−0.599731	+	0.800201i
$76$		−	4.16671i		−	0.477954i
$77$	3.28577			0.374449
$78$	4.27309	+	4.80262i	0.483833	+	0.543790i
$79$			11.5161i			1.29566i	0.761785	+	0.647830i	$0.224323\pi$
$79$			11.5161i			1.29566i	−0.761785	+	0.647830i	$0.775677\pi$
$80$	−2.22484	+	0.223804i	−0.248745	+	0.0250221i
$81$	−8.75656	−	2.07911i	−0.972951	−	0.231012i
$82$		−	2.54295i		−	0.280822i
$83$			13.5358i			1.48575i	0.669433	+	0.742873i	$0.266537\pi$
$83$			13.5358i			1.48575i	−0.669433	+	0.742873i	$0.733463\pi$
$84$	−0.862914	+	0.767771i	−0.0941516	+	0.0837707i
$85$	0.181419	+	1.80349i	0.0196776	+	0.195615i
$86$	3.56526			0.384452
$87$	−10.3877	−	11.6749i	−1.11367	−	1.25168i
$88$	−4.92726			−0.525248
$89$	12.5342			1.32862			0.664312	−	0.747455i	$-0.268725\pi$
$89$	12.5342			1.32862			0.664312	+	0.747455i	$0.268725\pi$
$90$	0.109357	−	6.70731i	0.0115272	−	0.707013i
$91$			2.47500i			0.259451i
$92$	−1.14656	+	4.65676i	−0.119537	+	0.485501i
$93$	7.93816	−	7.06292i	0.823149	−	0.732390i
$94$	10.0928			1.04099
$95$	0.932526	+	9.27026i	0.0956752	+	0.951108i
$96$	1.29400	−	1.15133i	0.132069	−	0.117507i
$97$	−1.04670			−0.106277			−0.0531383	−	0.998587i	$-0.516922\pi$
$97$	−1.04670			−0.106277			−0.0531383	+	0.998587i	$0.516922\pi$
$98$	6.55530			0.662186
$99$	1.71905	−	14.6815i	0.172771	−	1.47554i
$100$	4.89982	−	0.995856i	0.489982	−	0.0995856i
$101$		−	11.5777i		−	1.15203i	−0.817440	−	0.576013i	$-0.804608\pi$
$101$		−	11.5777i		−	1.15203i	0.817440	−	0.576013i	$-0.195392\pi$
$102$	−0.933283	−	1.04894i	−0.0924087	−	0.103860i
$103$	−14.2870			−1.40774			−0.703871	−	0.710327i	$-0.748547\pi$
$103$	−14.2870			−1.40774			−0.703871	+	0.710327i	$0.748547\pi$
$104$		−	3.71145i		−	0.363937i
$105$	1.74801	−	1.90129i	0.170589	−	0.185547i
$106$			10.6281i			1.03229i
$107$		−	10.4647i		−	1.01166i	−0.862633	−	0.505830i	$-0.831186\pi$
$107$		−	10.4647i		−	1.01166i	0.862633	−	0.505830i	$-0.168814\pi$
$108$	2.97909	+	4.25735i	0.286663	+	0.409664i
$109$		−	7.00879i		−	0.671321i	−0.941983	−	0.335660i	$-0.891041\pi$
$109$		−	7.00879i		−	0.671321i	0.941983	−	0.335660i	$-0.108959\pi$
$110$	10.9624	−	1.10274i	1.04522	−	0.105142i
$111$	−2.87176	+	2.55512i	−0.272575	+	0.242522i
$112$	0.666856			0.0630120
$113$			14.6901i			1.38193i	0.722888	+	0.690965i	$0.242814\pi$
$113$			14.6901i			1.38193i	−0.722888	+	0.690965i	$0.757186\pi$
$114$	−4.79725	−	5.39173i	−0.449304	−	0.504982i
$115$	1.50871	−	10.6171i	0.140688	−	0.990054i
$116$			9.02232i			0.837701i
$117$	11.0588	+	1.29487i	1.02239	+	0.119711i
$118$		−	6.81080i		−	0.626985i
$119$		−	0.540563i		−	0.0495533i
$120$	−2.62128	+	2.85112i	−0.239289	+	0.260271i
$121$	13.2779			1.20708
$122$		−	9.21371i		−	0.834170i
$123$	−2.92778	−	3.29059i	−0.263989	−	0.296702i
$124$	−6.13458			−0.550902
$125$	−10.6784	+	3.31222i	−0.955109	+	0.296254i
$126$	−0.232656	+	1.98699i	−0.0207267	+	0.177016i
$127$			1.83972i			0.163249i	0.996663	+	0.0816245i	$0.0260108\pi$
$127$			1.83972i			0.163249i	−0.996663	+	0.0816245i	$0.973989\pi$
$128$	−1.00000			−0.0883883
$129$	4.61346	−	4.10479i	0.406192	−	0.361407i
$130$	0.830637	+	8.25737i	0.0728517	+	0.724219i
$131$			6.59703i			0.576385i	0.957573	+	0.288192i	$0.0930543\pi$
$131$			6.59703i			0.576385i	−0.957573	+	0.288192i	$0.906946\pi$
$132$	−6.37589	+	5.67289i	−0.554950	+	0.493762i
$133$		−	2.77860i		−	0.240935i
$134$	−7.95053			−0.686821
$135$	−7.58081	−	8.80518i	−0.652452	−	0.757830i
$136$			0.810614i			0.0695095i
$137$		−	16.5441i		−	1.41346i	−0.707485	−	0.706728i	$-0.750170\pi$
$137$		−	16.5441i		−	1.41346i	0.707485	−	0.706728i	$-0.249830\pi$
$138$	3.87781	+	7.34592i	0.330101	+	0.625326i
$139$	5.46913			0.463885			0.231943	−	0.972729i	$-0.425492\pi$
$139$	5.46913			0.463885			0.231943	+	0.972729i	$0.425492\pi$
$140$	−1.48365	+	0.149245i	−0.125391	+	0.0126135i
$141$	13.0601	−	11.6201i	1.09986	−	0.978588i
$142$		−	14.5288i		−	1.21923i
$143$			18.2873i			1.52926i
$144$	0.348885	−	2.97964i	0.0290737	−	0.248304i
$145$	−2.01923	−	20.0732i	−0.167688	−	1.66699i
$146$		−	4.84561i		−	0.401026i
$147$	8.48258	−	7.54731i	0.699631	−	0.622491i
$148$	2.21928			0.182424
$149$	2.91067			0.238452			0.119226	−	0.992867i	$-0.461959\pi$
$149$	2.91067			0.238452			0.119226	+	0.992867i	$0.461959\pi$
$150$	5.19383	−	6.92995i	0.424074	−	0.565828i
$151$	5.50476			0.447971			0.223985	−	0.974592i	$-0.428093\pi$
$151$	5.50476			0.447971			0.223985	+	0.974592i	$0.428093\pi$
$152$			4.16671i			0.337965i
$153$	−2.41534	−	0.282811i	−0.195269	−	0.0228639i
$154$	−3.28577			−0.264775
$155$	13.6485	−	1.37294i	1.09627	−	0.110278i
$156$	−4.27309	−	4.80262i	−0.342121	−	0.384517i
$157$	8.36290			0.667432			0.333716	−	0.942674i	$-0.391697\pi$
$157$	8.36290			0.667432			0.333716	+	0.942674i	$0.391697\pi$
$158$		−	11.5161i		−	0.916170i
$159$	12.2364	+	13.7528i	0.970412	+	1.09067i
$160$	2.22484	−	0.223804i	0.175889	−	0.0176933i
$161$	−0.764590	+	3.10539i	−0.0602581	+	0.244739i
$162$	8.75656	+	2.07911i	0.687980	+	0.163350i
$163$			12.1701i			0.953233i	0.879111	+	0.476617i	$0.158137\pi$
$163$			12.1701i			0.953233i	−0.879111	+	0.476617i	$0.841863\pi$
$164$			2.54295i			0.198571i
$165$	12.9157	−	14.0482i	1.00549	−	1.09365i
$166$		−	13.5358i		−	1.05058i
$167$	14.3712			1.11208			0.556038	−	0.831157i	$-0.312321\pi$
$167$	14.3712			1.11208			0.556038	+	0.831157i	$0.312321\pi$
$168$	0.862914	−	0.767771i	0.0665753	−	0.0592348i
$169$	−0.774832			−0.0596025
$170$	−0.181419	−	1.80349i	−0.0139142	−	0.138321i
$171$	−12.4153	−	1.45370i	−0.949422	−	0.111167i
$172$	−3.56526			−0.271849
$173$	18.2848			1.39017			0.695085	−	0.718927i	$-0.255367\pi$
$173$	18.2848			1.39017			0.695085	+	0.718927i	$0.255367\pi$
$174$	10.3877	+	11.6749i	0.787486	+	0.885072i
$175$	3.26748	−	0.664093i	0.246998	−	0.0502007i
$176$	4.92726			0.371406
$177$	−7.84146	−	8.81319i	−0.589401	−	0.662440i
$178$	−12.5342			−0.939479
$179$		−	5.02306i		−	0.375441i	−0.982222	−	0.187721i	$-0.939890\pi$
$179$		−	5.02306i		−	0.375441i	0.982222	−	0.187721i	$-0.0601099\pi$
$180$	−0.109357	+	6.70731i	−0.00815096	+	0.499934i
$181$			0.342921i			0.0254891i	0.999919	+	0.0127445i	$0.00405682\pi$
$181$			0.342921i			0.0254891i	−0.999919	+	0.0127445i	$0.995943\pi$
$182$		−	2.47500i		−	0.183459i
$183$	−10.6080	−	11.9226i	−0.784166	−	0.881341i
$184$	1.14656	−	4.65676i	0.0845254	−	0.343301i
$185$	−4.93755	+	0.496684i	−0.363016	+	0.0365170i
$186$	−7.93816	+	7.06292i	−0.582054	+	0.517878i
$187$		−	3.99410i		−	0.292078i
$188$	−10.0928			−0.736090
$189$	1.98663	+	2.83904i	0.144506	+	0.206510i
$190$	−0.932526	−	9.27026i	−0.0676525	−	0.672535i
$191$	−26.5716			−1.92265			−0.961325	−	0.275416i	$-0.911184\pi$
$191$	−26.5716			−1.92265			−0.961325	+	0.275416i	$0.911184\pi$
$192$	−1.29400	+	1.15133i	−0.0933866	+	0.0830900i
$193$			0.121042i			0.00871281i	0.999991	+	0.00435640i	$0.00138669\pi$
$193$			0.121042i			0.00871281i	−0.999991	+	0.00435640i	$0.998613\pi$
$194$	1.04670			0.0751489
$195$	10.5818	+	9.72873i	0.757778	+	0.696688i
$196$	−6.55530			−0.468236
$197$	−4.06795			−0.289829			−0.144915	−	0.989444i	$-0.546291\pi$
$197$	−4.06795			−0.289829			−0.144915	+	0.989444i	$0.546291\pi$
$198$	−1.71905	+	14.6815i	−0.122167	+	1.04337i
$199$		−	3.82379i		−	0.271061i	−0.990773	−	0.135531i	$-0.956726\pi$
$199$		−	3.82379i		−	0.271061i	0.990773	−	0.135531i	$-0.0432739\pi$
$200$	−4.89982	+	0.995856i	−0.346470	+	0.0704177i
$201$	−10.2880	+	9.15367i	−0.725660	+	0.645650i
$202$			11.5777i			0.814606i
$203$			6.01659i			0.422282i
$204$	0.933283	+	1.04894i	0.0653429	+	0.0734402i
$205$	−0.569123	−	5.65766i	−0.0397493	−	0.395148i
$206$	14.2870			0.995425
$207$	13.4755	+	5.04101i	0.936610	+	0.350374i
$208$			3.71145i			0.257342i
$209$		−	20.5304i		−	1.42012i
$210$	−1.74801	+	1.90129i	−0.120624	+	0.131202i
$211$	−10.9491			−0.753765			−0.376882	−	0.926261i	$-0.623004\pi$
$211$	−10.9491			−0.753765			−0.376882	+	0.926261i	$0.623004\pi$
$212$		−	10.6281i		−	0.729940i
$213$	−16.7274	−	18.8003i	−1.14614	−	1.28818i
$214$			10.4647i			0.715352i
$215$	7.93214	−	0.797920i	0.540967	−	0.0544177i
$216$	−2.97909	−	4.25735i	−0.202702	−	0.289676i
$217$	−4.09088			−0.277707
$218$			7.00879i			0.474695i
$219$	−5.57889	−	6.27023i	−0.376986	−	0.423703i
$220$	−10.9624	+	1.10274i	−0.739082	+	0.0743468i
$221$	3.00855			0.202377
$222$	2.87176	−	2.55512i	0.192740	−	0.171489i
$223$		−	3.05235i		−	0.204401i	−0.994764	−	0.102200i	$-0.967412\pi$
$223$		−	3.05235i		−	0.204401i	0.994764	−	0.102200i	$-0.0325883\pi$
$224$	−0.666856			−0.0445562
$225$	−1.25782	−	14.9472i	−0.0838549	−	0.996478i
$226$		−	14.6901i		−	0.977172i
$227$		−	16.8065i		−	1.11549i	−0.830014	−	0.557743i	$-0.811668\pi$
$227$		−	16.8065i		−	1.11549i	0.830014	−	0.557743i	$-0.188332\pi$
$228$	4.79725	+	5.39173i	0.317706	+	0.357076i
$229$			10.0750i			0.665775i	0.942966	+	0.332888i	$0.108023\pi$
$229$			10.0750i			0.665775i	−0.942966	+	0.332888i	$0.891977\pi$
$230$	−1.50871	+	10.6171i	−0.0994811	+	0.700074i
$231$	−4.25180	+	3.78301i	−0.279748	+	0.248904i
$232$		−	9.02232i		−	0.592344i
$233$	13.0601			0.855593			0.427796	−	0.903875i	$-0.359290\pi$
$233$	13.0601			0.855593			0.427796	+	0.903875i	$0.359290\pi$
$234$	−11.0588	−	1.29487i	−0.722936	−	0.0846481i
$235$	22.4548	−	2.25880i	1.46479	−	0.147348i
$236$			6.81080i			0.443345i
$237$	−13.2588	−	14.9018i	−0.861251	−	0.967978i
$238$			0.540563i			0.0350395i
$239$			14.5163i			0.938984i	0.882937	+	0.469492i	$0.155563\pi$
$239$			14.5163i			0.938984i	−0.882937	+	0.469492i	$0.844437\pi$
$240$	2.62128	−	2.85112i	0.169203	−	0.184039i
$241$			7.90101i			0.508949i	0.967079	+	0.254475i	$0.0819025\pi$
$241$			7.90101i			0.508949i	−0.967079	+	0.254475i	$0.918098\pi$
$242$	−13.2779			−0.853535
$243$	13.7247	−	7.39131i	0.880443	−	0.474153i
$244$			9.21371i			0.589847i
$245$	14.5845	−	1.46710i	0.931769	−	0.0937298i
$246$	2.92778	+	3.29059i	0.186668	+	0.209800i
$247$	15.4645			0.983983
$248$	6.13458			0.389546
$249$	−15.5841	−	17.5153i	−0.987604	−	1.10999i
$250$	10.6784	−	3.31222i	0.675364	−	0.209483i
$251$	−6.40105			−0.404031			−0.202015	−	0.979382i	$-0.564749\pi$
$251$	−6.40105			−0.404031			−0.202015	+	0.979382i	$0.564749\pi$
$252$	0.232656	−	1.98699i	0.0146560	−	0.125169i
$253$	−5.64939	+	22.9451i	−0.355174	+	1.44254i
$254$		−	1.83972i		−	0.115434i
$255$	−2.31116	−	2.12484i	−0.144730	−	0.133063i
$256$	1.00000			0.0625000
$257$	−14.7993			−0.923153			−0.461576	−	0.887101i	$-0.652716\pi$
$257$	−14.7993			−0.923153			−0.461576	+	0.887101i	$0.652716\pi$
$258$	−4.61346	+	4.10479i	−0.287221	+	0.255553i
$259$	1.47994			0.0919592
$260$	−0.830637	−	8.25737i	−0.0515139	−	0.512101i
$261$	26.8833	+	3.14775i	1.66403	+	0.194841i
$262$		−	6.59703i		−	0.407566i
$263$			1.33588i			0.0823737i	0.999151	+	0.0411868i	$0.0131139\pi$
$263$			1.33588i			0.0823737i	−0.999151	+	0.0411868i	$0.986886\pi$
$264$	6.37589	−	5.67289i	0.392409	−	0.349143i
$265$	2.37861	+	23.6458i	0.146117	+	1.45255i
$266$			2.77860i			0.170367i
$267$	−16.2193	+	14.4310i	−0.992605	+	0.883163i
$268$	7.95053			0.485656
$269$		−	12.2843i		−	0.748989i	−0.927229	−	0.374495i	$-0.877816\pi$
$269$		−	12.2843i		−	0.748989i	0.927229	−	0.374495i	$-0.122184\pi$
$270$	7.58081	+	8.80518i	0.461354	+	0.535866i
$271$	−19.5706			−1.18883			−0.594415	−	0.804158i	$-0.702616\pi$
$271$	−19.5706			−1.18883			−0.594415	+	0.804158i	$0.702616\pi$
$272$		−	0.810614i		−	0.0491507i
$273$	−2.84954	−	3.20266i	−0.172462	−	0.193834i
$274$			16.5441i			0.999464i
$275$	24.1427	−	4.90684i	1.45586	−	0.295894i
$276$	−3.87781	−	7.34592i	−0.233417	−	0.442173i
$277$			13.9776i			0.839830i	0.907563	+	0.419915i	$0.137940\pi$
$277$			13.9776i			0.839830i	−0.907563	+	0.419915i	$0.862060\pi$
$278$	−5.46913			−0.328016
$279$	−2.14026	+	18.2789i	−0.128134	+	1.09433i
$280$	1.48365	−	0.149245i	0.0886650	−	0.00891911i
$281$	−9.12634			−0.544432			−0.272216	−	0.962236i	$-0.587756\pi$
$281$	−9.12634			−0.544432			−0.272216	+	0.962236i	$0.587756\pi$
$282$	−13.0601	+	11.6201i	−0.777715	+	0.691966i
$283$	−30.4398			−1.80946			−0.904730	−	0.425984i	$-0.859928\pi$
$283$	−30.4398			−1.80946			−0.904730	+	0.425984i	$0.859928\pi$
$284$			14.5288i			0.862126i
$285$	−11.8798	−	10.9221i	−0.703699	−	0.646969i
$286$		−	18.2873i		−	1.08135i
$287$			1.69579i			0.100099i
$288$	−0.348885	+	2.97964i	−0.0205582	+	0.175577i
$289$	16.3429			0.961347
$290$	2.01923	+	20.0732i	0.118573	+	1.17874i
$291$	1.35444	−	1.20510i	0.0793985	−	0.0706442i
$292$			4.84561i			0.283568i
$293$			27.1711i			1.58735i	0.608341	+	0.793676i	$0.291835\pi$
$293$			27.1711i			1.58735i	−0.608341	+	0.793676i	$0.708165\pi$
$294$	−8.48258	+	7.54731i	−0.494714	+	0.440168i
$295$	−1.52428	−	15.1529i	−0.0887472	−	0.882238i
$296$	−2.21928			−0.128993
$297$	14.6788	+	20.9771i	0.851748	+	1.21721i
$298$	−2.91067			−0.168611
$299$	−17.2833	−	4.25539i	−0.999520	−	0.246095i
$300$	−5.19383	+	6.92995i	−0.299866	+	0.400101i
$301$	−2.37752			−0.137038
$302$	−5.50476			−0.316763
$303$	13.3298	+	14.9816i	0.765775	+	0.860671i
$304$		−	4.16671i		−	0.238977i
$305$	−2.06207	−	20.4990i	−0.118074	−	1.17377i
$306$	2.41534	+	0.282811i	0.138076	+	0.0161672i
$307$			8.27262i			0.472144i	0.971736	+	0.236072i	$0.0758601\pi$
$307$			8.27262i			0.472144i	−0.971736	+	0.236072i	$0.924140\pi$
$308$	3.28577			0.187224
$309$	18.4875	−	16.4491i	1.05171	−	0.935755i
$310$	−13.6485	+	1.37294i	−0.775180	+	0.0779780i
$311$			0.256130i			0.0145238i	0.999974	+	0.00726189i	$0.00231155\pi$
$311$			0.256130i			0.0145238i	−0.999974	+	0.00726189i	$0.997688\pi$
$312$	4.27309	+	4.80262i	0.241916	+	0.271895i
$313$	7.18955			0.406377			0.203189	−	0.979140i	$-0.434870\pi$
$313$	7.18955			0.406377			0.203189	+	0.979140i	$0.434870\pi$
$314$	−8.36290			−0.471946
$315$	−0.0729252	+	4.47281i	−0.00410887	+	0.252015i
$316$			11.5161i			0.647830i
$317$	16.3815			0.920075			0.460037	−	0.887900i	$-0.347836\pi$
$317$	16.3815			0.920075			0.460037	+	0.887900i	$0.347836\pi$
$318$	−12.2364	−	13.7528i	−0.686185	−	0.771218i
$319$			44.4553i			2.48902i
$320$	−2.22484	+	0.223804i	−0.124372	+	0.0125110i
$321$	12.0483	+	13.5413i	0.672471	+	0.755804i
$322$	0.764590	−	3.10539i	0.0426089	−	0.173057i
$323$	−3.37759			−0.187934
$324$	−8.75656	−	2.07911i	−0.486475	−	0.115506i
$325$	3.69607	+	18.1854i	0.205021	+	1.00875i
$326$		−	12.1701i		−	0.674038i
$327$	8.06943	+	9.06940i	0.446240	+	0.501539i
$328$		−	2.54295i		−	0.140411i
$329$	−6.73042			−0.371060
$330$	−12.9157	+	14.0482i	−0.710986	+	0.773330i
$331$	22.0597			1.21251			0.606255	−	0.795271i	$-0.292671\pi$
$331$	22.0597			1.21251			0.606255	+	0.795271i	$0.292671\pi$
$332$			13.5358i			0.742873i
$333$	0.774274	−	6.61267i	0.0424300	−	0.362372i
$334$	−14.3712			−0.786357
$335$	−17.6887	+	1.77936i	−0.966434	+	0.0972169i
$336$	−0.862914	+	0.767771i	−0.0470758	+	0.0418853i
$337$	11.1835			0.609203			0.304601	−	0.952480i	$-0.401477\pi$
$337$	11.1835			0.609203			0.304601	+	0.952480i	$0.401477\pi$
$338$	0.774832			0.0421453
$339$	−16.9131	−	19.0090i	−0.918596	−	1.03243i
$340$	0.181419	+	1.80349i	0.00983881	+	0.0978077i
$341$	−30.2267			−1.63687
$342$	12.4153	+	1.45370i	0.671343	+	0.0786072i
$343$	−9.03944			−0.488084
$344$	3.56526			0.192226
$345$	10.2716	+	15.4756i	0.553002	+	0.833180i
$346$	−18.2848			−0.982999
$347$	−13.1611			−0.706525			−0.353262	−	0.935524i	$-0.614928\pi$
$347$	−13.1611			−0.706525			−0.353262	+	0.935524i	$0.614928\pi$
$348$	−10.3877	−	11.6749i	−0.556837	−	0.625840i
$349$	7.16860			0.383726			0.191863	−	0.981422i	$-0.438547\pi$
$349$	7.16860			0.383726			0.191863	+	0.981422i	$0.438547\pi$
$350$	−3.26748	+	0.664093i	−0.174654	+	0.0354973i
$351$	−15.8009	+	11.0567i	−0.843391	+	0.590165i
$352$	−4.92726			−0.262624
$353$	−29.9100			−1.59195			−0.795976	−	0.605329i	$-0.793042\pi$
$353$	−29.9100			−1.59195			−0.795976	+	0.605329i	$0.793042\pi$
$354$	7.84146	+	8.81319i	0.416769	+	0.468416i
$355$	−3.25160	−	32.3243i	−0.172577	−	1.71559i
$356$	12.5342			0.664312
$357$	0.622366	+	0.699490i	0.0329391	+	0.0370209i
$358$			5.02306i			0.265477i
$359$	13.4801			0.711452			0.355726	−	0.934590i	$-0.384234\pi$
$359$	13.4801			0.711452			0.355726	+	0.934590i	$0.384234\pi$
$360$	0.109357	−	6.70731i	0.00576360	−	0.353506i
$361$	1.63855			0.0862395
$362$		−	0.342921i		−	0.0180235i
$363$	−17.1816	+	15.2872i	−0.901801	+	0.802370i
$364$			2.47500i			0.129725i
$365$	−1.08447	−	10.7807i	−0.0567636	−	0.564288i
$366$	10.6080	+	11.9226i	0.554489	+	0.623202i
$367$	−11.3468			−0.592297			−0.296148	−	0.955142i	$-0.595702\pi$
$367$	−11.3468			−0.592297			−0.296148	+	0.955142i	$0.595702\pi$
$368$	−1.14656	+	4.65676i	−0.0597685	+	0.242750i
$369$	7.57710	+	0.887198i	0.394448	+	0.0461857i
$370$	4.93755	−	0.496684i	0.256691	−	0.0258214i
$371$		−	7.08741i		−	0.367960i
$372$	7.93816	−	7.06292i	0.411574	−	0.366195i
$373$	25.0799			1.29859			0.649295	−	0.760537i	$-0.275064\pi$
$373$	25.0799			1.29859			0.649295	+	0.760537i	$0.275064\pi$
$374$			3.99410i			0.206530i
$375$	10.0045	−	16.5804i	0.516629	−	0.856209i
$376$	10.0928			0.520494
$377$	−33.4858			−1.72461
$378$	−1.98663	−	2.83904i	−0.102181	−	0.146024i
$379$			19.4678i			0.999992i	0.866028	+	0.499996i	$0.166665\pi$
$379$			19.4678i			0.999992i	−0.866028	+	0.499996i	$0.833335\pi$
$380$	0.932526	+	9.27026i	0.0478376	+	0.475554i
$381$	−2.11812	−	2.38060i	−0.108515	−	0.121962i
$382$	26.5716			1.35952
$383$		−	26.1779i		−	1.33763i	−0.743429	−	0.668815i	$-0.766802\pi$
$383$		−	26.1779i		−	1.33763i	0.743429	−	0.668815i	$-0.233198\pi$
$384$	1.29400	−	1.15133i	0.0660343	−	0.0587535i
$385$	−7.31032	+	0.735370i	−0.372569	+	0.0374779i
$386$		−	0.121042i		−	0.00616089i
$387$	−1.24387	+	10.6232i	−0.0632293	+	0.540008i
$388$	−1.04670			−0.0531383
$389$	22.4773			1.13965			0.569823	−	0.821768i	$-0.307012\pi$
$389$	22.4773			1.13965			0.569823	+	0.821768i	$0.307012\pi$
$390$	−10.5818	−	9.72873i	−0.535830	−	0.492633i
$391$	3.77483	+	0.929415i	0.190901	+	0.0470026i
$392$	6.55530			0.331093
$393$	−7.59535	−	8.53657i	−0.383135	−	0.430613i
$394$	4.06795			0.204940
$395$	−2.57734	−	25.6214i	−0.129680	−	1.28915i
$396$	1.71905	−	14.6815i	0.0863853	−	0.737772i
$397$			11.5042i			0.577380i	0.957423	+	0.288690i	$0.0932197\pi$
$397$			11.5042i			0.577380i	−0.957423	+	0.288690i	$0.906780\pi$
$398$			3.82379i			0.191669i
$399$	3.19908	+	3.59551i	0.160154	+	0.180001i
$400$	4.89982	−	0.995856i	0.244991	−	0.0497928i
$401$	−9.84524			−0.491648			−0.245824	−	0.969315i	$-0.579058\pi$
$401$	−9.84524			−0.491648			−0.245824	+	0.969315i	$0.579058\pi$
$402$	10.2880	−	9.15367i	0.513119	−	0.456544i
$403$		−	22.7682i		−	1.13416i
$404$		−	11.5777i		−	0.576013i
$405$	19.9473	+	2.66592i	0.991187	+	0.132471i
$406$		−	6.01659i		−	0.298598i
$407$	10.9350			0.542027
$408$	−0.933283	−	1.04894i	−0.0462044	−	0.0519301i
$409$	18.8120			0.930195			0.465098	−	0.885259i	$-0.346019\pi$
$409$	18.8120			0.930195			0.465098	+	0.885259i	$0.346019\pi$
$410$	0.569123	+	5.65766i	0.0281070	+	0.279412i
$411$	19.0477	+	21.4081i	0.939552	+	1.05598i
$412$	−14.2870			−0.703871
$413$			4.54182i			0.223489i
$414$	−13.4755	−	5.04101i	−0.662283	−	0.247752i
$415$	−3.02936	−	30.1149i	−0.148706	−	1.47828i
$416$		−	3.71145i		−	0.181969i
$417$	−7.07706	+	6.29676i	−0.346565	+	0.308354i
$418$			20.5304i			1.00418i
$419$	−8.48762			−0.414647			−0.207324	−	0.978272i	$-0.566475\pi$
$419$	−8.48762			−0.414647			−0.207324	+	0.978272i	$0.566475\pi$
$420$	1.74801	−	1.90129i	0.0852944	−	0.0927735i
$421$		−	30.8277i		−	1.50245i	−0.660045	−	0.751226i	$-0.729463\pi$
$421$		−	30.8277i		−	1.50245i	0.660045	−	0.751226i	$-0.270537\pi$
$422$	10.9491			0.532992
$423$	−3.52121	+	30.0728i	−0.171207	+	1.46219i
$424$			10.6281i			0.516146i
$425$	−0.807255	−	3.97186i	−0.0391576	−	0.192664i
$426$	16.7274	+	18.8003i	0.810446	+	0.910878i
$427$			6.14422i			0.297340i
$428$		−	10.4647i		−	0.505830i
$429$	−21.0546	−	23.6638i	−1.01653	−	1.14250i
$430$	−7.93214	+	0.797920i	−0.382522	+	0.0384791i
$431$	27.9563			1.34661			0.673303	−	0.739367i	$-0.264875\pi$
$431$	27.9563			1.34661			0.673303	+	0.739367i	$0.264875\pi$
$432$	2.97909	+	4.25735i	0.143332	+	0.204832i
$433$	37.3143			1.79321			0.896606	−	0.442829i	$-0.146025\pi$
$433$	37.3143			1.79321			0.896606	+	0.442829i	$0.146025\pi$
$434$	4.09088			0.196369
$435$	25.7238	+	23.6500i	1.23336	+	1.13393i
$436$		−	7.00879i		−	0.335660i
$437$	19.4034	+	4.77737i	0.928188	+	0.228533i
$438$	5.57889	+	6.27023i	0.266570	+	0.299603i
$439$	−24.1100			−1.15071			−0.575354	−	0.817904i	$-0.695136\pi$
$439$	−24.1100			−1.15071			−0.575354	+	0.817904i	$0.695136\pi$
$440$	10.9624	−	1.10274i	0.522610	−	0.0525711i
$441$	−2.28705	+	19.5325i	−0.108907	+	0.930118i
$442$	−3.00855			−0.143102
$443$	14.5534			0.691451			0.345726	−	0.938336i	$-0.387633\pi$
$443$	14.5534			0.691451			0.345726	+	0.938336i	$0.387633\pi$
$444$	−2.87176	+	2.55512i	−0.136288	+	0.121261i
$445$	−27.8866	+	2.80521i	−1.32195	+	0.132980i
$446$			3.05235i			0.144533i
$447$	−3.76642	+	3.35114i	−0.178146	+	0.158504i
$448$	0.666856			0.0315060
$449$		−	25.8545i		−	1.22015i	−0.792344	−	0.610075i	$-0.791139\pi$
$449$		−	25.8545i		−	1.22015i	0.792344	−	0.610075i	$-0.208861\pi$
$450$	1.25782	+	14.9472i	0.0592943	+	0.704616i
$451$			12.5298i			0.590005i
$452$			14.6901i			0.690965i
$453$	−7.12317	+	6.33778i	−0.334676	+	0.297775i
$454$			16.8065i			0.788767i
$455$	−0.553915	−	5.50648i	−0.0259680	−	0.258148i
$456$	−4.79725	−	5.39173i	−0.224652	−	0.252491i
$457$	−23.6100			−1.10443			−0.552214	−	0.833702i	$-0.686217\pi$
$457$	−23.6100			−1.10443			−0.552214	+	0.833702i	$0.686217\pi$
$458$		−	10.0750i		−	0.470774i
$459$	3.45106	−	2.41489i	0.161082	−	0.112718i
$460$	1.50871	−	10.6171i	0.0703438	−	0.495027i
$461$		−	38.3275i		−	1.78509i	−0.450959	−	0.892545i	$-0.648918\pi$
$461$		−	38.3275i		−	1.78509i	0.450959	−	0.892545i	$-0.351082\pi$
$462$	4.25180	−	3.78301i	0.197812	−	0.176001i
$463$			1.86463i			0.0866567i	0.999061	+	0.0433284i	$0.0137962\pi$
$463$			1.86463i			0.0866567i	−0.999061	+	0.0433284i	$0.986204\pi$
$464$			9.02232i			0.418851i
$465$	−16.0804	+	17.4905i	−0.745712	+	0.811100i
$466$	−13.0601			−0.604996
$467$		−	22.7789i		−	1.05408i	−0.849840	−	0.527040i	$-0.823302\pi$
$467$		−	22.7789i		−	1.05408i	0.849840	−	0.527040i	$-0.176698\pi$
$468$	11.0588	+	1.29487i	0.511193	+	0.0598553i
$469$	5.30186			0.244817
$470$	−22.4548	+	2.25880i	−1.03576	+	0.104191i
$471$	−10.8216	+	9.62845i	−0.498634	+	0.443655i
$472$		−	6.81080i		−	0.313492i
$473$	−17.5670			−0.807731
$474$	13.2588	+	14.9018i	0.608996	+	0.684464i
$475$	−4.14944	−	20.4161i	−0.190389	−	0.936756i
$476$		−	0.540563i		−	0.0247767i
$477$	−31.6679	−	3.70798i	−1.44998	−	0.169777i
$478$		−	14.5163i		−	0.663962i
$479$	−22.7286			−1.03849			−0.519247	−	0.854624i	$-0.673788\pi$
$479$	−22.7286			−1.03849			−0.519247	+	0.854624i	$0.673788\pi$
$480$	−2.62128	+	2.85112i	−0.119644	+	0.130135i
$481$			8.23675i			0.375563i
$482$		−	7.90101i		−	0.359881i
$483$	−2.58594	−	4.89868i	−0.117664	−	0.222897i
$484$	13.2779			0.603540
$485$	2.32875	−	0.234257i	0.105743	−	0.0106370i
$486$	−13.7247	+	7.39131i	−0.622567	+	0.335277i
$487$			9.28752i			0.420858i	0.977609	+	0.210429i	$0.0674860\pi$
$487$			9.28752i			0.420858i	−0.977609	+	0.210429i	$0.932514\pi$
$488$		−	9.21371i		−	0.417085i
$489$	−14.0117	−	15.7481i	−0.633633	−	0.712154i
$490$	−14.5845	+	1.46710i	−0.658860	+	0.0662770i
$491$		−	16.4543i		−	0.742571i	−0.928519	−	0.371286i	$-0.878917\pi$
$491$		−	16.4543i		−	0.742571i	0.928519	−	0.371286i	$-0.121083\pi$
$492$	−2.92778	−	3.29059i	−0.131994	−	0.148351i
$493$	7.31361			0.329389
$494$	−15.4645			−0.695781
$495$	−0.538828	+	33.0487i	−0.0242185	+	1.48543i
$496$	−6.13458			−0.275451
$497$			9.68862i			0.434594i
$498$	15.5841	+	17.5153i	0.698342	+	0.784881i
$499$	14.8139			0.663163			0.331582	−	0.943427i	$-0.392418\pi$
$499$	14.8139			0.663163			0.331582	+	0.943427i	$0.392418\pi$
$500$	−10.6784	+	3.31222i	−0.477555	+	0.148127i
$501$	−18.5964	+	16.5460i	−0.830824	+	0.739219i
$502$	6.40105			0.285693
$503$			6.33019i			0.282249i	0.989992	+	0.141125i	$0.0450718\pi$
$503$			6.33019i			0.282249i	−0.989992	+	0.141125i	$0.954928\pi$
$504$	−0.232656	+	1.98699i	−0.0103633	+	0.0885078i
$505$	2.59114	+	25.7586i	0.115304	+	1.14624i
$506$	5.64939	−	22.9451i	0.251146	−	1.02003i
$507$	1.00263	−	0.892086i	0.0445286	−	0.0396190i
$508$			1.83972i			0.0816245i
$509$		−	3.11552i		−	0.138093i	−0.997613	−	0.0690465i	$-0.978004\pi$
$509$		−	3.11552i		−	0.138093i	0.997613	−	0.0690465i	$-0.0219957\pi$
$510$	2.31116	+	2.12484i	0.102340	+	0.0940896i
$511$			3.23133i			0.142945i
$512$	−1.00000			−0.0441942
$513$	17.7391	−	12.4130i	0.783201	−	0.548047i
$514$	14.7993			0.652767
$515$	31.7864	−	3.19750i	1.40067	−	0.140898i
$516$	4.61346	−	4.10479i	0.203096	−	0.180703i
$517$	−49.7297			−2.18711
$518$	−1.47994			−0.0650250
$519$	−23.6606	+	21.0519i	−1.03859	+	0.924074i
$520$	0.830637	+	8.25737i	0.0364258	+	0.362110i
$521$	−4.59001			−0.201092			−0.100546	−	0.994932i	$-0.532059\pi$
$521$	−4.59001			−0.201092			−0.100546	+	0.994932i	$0.532059\pi$
$522$	−26.8833	−	3.14775i	−1.17665	−	0.137773i
$523$	25.4462			1.11269			0.556343	−	0.830953i	$-0.312204\pi$
$523$	25.4462			1.11269			0.556343	+	0.830953i	$0.312204\pi$
$524$			6.59703i			0.288192i
$525$	−3.46354	+	4.62128i	−0.151161	+	0.201689i
$526$		−	1.33588i		−	0.0582470i
$527$			4.97277i			0.216617i
$528$	−6.37589	+	5.67289i	−0.277475	+	0.246881i
$529$	−20.3708	−	10.6785i	−0.885687	−	0.464282i
$530$	−2.37861	−	23.6458i	−0.103320	−	1.02711i
$531$	20.2937	+	2.37618i	0.880674	+	0.103118i
$532$		−	2.77860i		−	0.120467i
$533$	−9.43804			−0.408807
$534$	16.2193	−	14.4310i	0.701878	−	0.624490i
$535$	2.34204	+	23.2823i	0.101255	+	1.00658i
$536$	−7.95053			−0.343411
$537$	5.78319	+	6.49985i	0.249563	+	0.280489i
$538$			12.2843i			0.529615i
$539$	−32.2997			−1.39125
$540$	−7.58081	−	8.80518i	−0.326226	−	0.378915i
$541$	21.7426			0.934787			0.467394	−	0.884049i	$-0.345193\pi$
$541$	21.7426			0.934787			0.467394	+	0.884049i	$0.345193\pi$
$542$	19.5706			0.840630
$543$	−0.394814	−	0.443740i	−0.0169431	−	0.0190427i
$544$			0.810614i			0.0347548i
$545$	1.56860	+	15.5934i	0.0671913	+	0.667950i
$546$	2.84954	+	3.20266i	0.121949	+	0.137061i
$547$		−	23.9240i		−	1.02292i	−0.859308	−	0.511459i	$-0.829105\pi$
$547$		−	23.9240i		−	1.02292i	0.859308	−	0.511459i	$-0.170895\pi$
$548$		−	16.5441i		−	0.706728i
$549$	27.4536	+	3.21452i	1.17169	+	0.137193i
$550$	−24.1427	+	4.90684i	−1.02945	+	0.209228i
$551$	37.5934			1.60153
$552$	3.87781	+	7.34592i	0.165051	+	0.312663i
$553$			7.67957i			0.326569i
$554$		−	13.9776i		−	0.593850i
$555$	5.81735	−	6.32745i	0.246933	−	0.268585i
$556$	5.46913			0.231943
$557$			25.3753i			1.07519i	0.843204	+	0.537593i	$0.180666\pi$
$557$			25.3753i			1.07519i	−0.843204	+	0.537593i	$0.819334\pi$
$558$	2.14026	−	18.2789i	0.0906045	−	0.773806i
$559$		−	13.2323i		−	0.559666i
$560$	−1.48365	+	0.149245i	−0.0626956	+	0.00630676i
$561$	4.59853	+	5.16838i	0.194150	+	0.218209i
$562$	9.12634			0.384971
$563$		−	10.1241i		−	0.426681i	−0.976978	−	0.213340i	$-0.931566\pi$
$563$		−	10.1241i		−	0.426681i	0.976978	−	0.213340i	$-0.0684343\pi$
$564$	13.0601	−	11.6201i	0.549928	−	0.489294i
$565$	−3.28771	−	32.6831i	−0.138315	−	1.37499i
$566$	30.4398			1.27948
$567$	−5.83937	−	1.38647i	−0.245230	−	0.0582261i
$568$		−	14.5288i		−	0.609615i
$569$	−5.98029			−0.250707			−0.125353	−	0.992112i	$-0.540006\pi$
$569$	−5.98029			−0.250707			−0.125353	+	0.992112i	$0.540006\pi$
$570$	11.8798	+	10.9221i	0.497590	+	0.457476i
$571$		−	15.5442i		−	0.650504i	−0.945627	−	0.325252i	$-0.894551\pi$
$571$		−	15.5442i		−	0.650504i	0.945627	−	0.325252i	$-0.105449\pi$
$572$			18.2873i			0.764629i
$573$	34.3837	−	30.5926i	1.43640	−	1.27802i
$574$		−	1.69579i		−	0.0707807i
$575$	−0.980468	+	23.9591i	−0.0408883	+	0.999164i
$576$	0.348885	−	2.97964i	0.0145369	−	0.124152i
$577$		−	2.43133i		−	0.101218i	−0.998719	−	0.0506088i	$-0.983884\pi$
$577$		−	2.43133i		−	0.101218i	0.998719	−	0.0506088i	$-0.0161162\pi$
$578$	−16.3429			−0.679775
$579$	−0.139359	−	0.156629i	−0.00579158	−	0.00650928i
$580$	−2.01923	−	20.0732i	−0.0838440	−	0.833495i
$581$			9.02642i			0.374479i
$582$	−1.35444	+	1.20510i	−0.0561432	+	0.0499530i
$583$		−	52.3674i		−	2.16884i
$584$		−	4.84561i		−	0.200513i
$585$	−24.8938	−	0.405871i	−1.02923	−	0.0167807i
$586$		−	27.1711i		−	1.12243i
$587$	−25.0136			−1.03242			−0.516211	−	0.856461i	$-0.672658\pi$
$587$	−25.0136			−1.03242			−0.516211	+	0.856461i	$0.672658\pi$
$588$	8.48258	−	7.54731i	0.349816	−	0.311246i
$589$			25.5610i			1.05322i
$590$	1.52428	+	15.1529i	0.0627538	+	0.623836i
$591$	5.26393	−	4.68354i	0.216529	−	0.192655i
$592$	2.21928			0.0912120
$593$	12.0918			0.496551			0.248276	−	0.968689i	$-0.420136\pi$
$593$	12.0918			0.496551			0.248276	+	0.968689i	$0.420136\pi$
$594$	−14.6788	−	20.9771i	−0.602277	−	0.860699i
$595$	0.120980	+	1.20267i	0.00495970	+	0.0493045i
$596$	2.91067			0.119226
$597$	4.40244	+	4.94799i	0.180180	+	0.202508i
$598$	17.2833	+	4.25539i	0.706767	+	0.174016i
$599$			44.0064i			1.79805i	0.437892	+	0.899027i	$0.355725\pi$
$599$			44.0064i			1.79805i	−0.437892	+	0.899027i	$0.644275\pi$
$600$	5.19383	−	6.92995i	0.212037	−	0.282914i
$601$	−17.6495			−0.719937			−0.359968	−	0.932964i	$-0.617213\pi$
$601$	−17.6495			−0.719937			−0.359968	+	0.932964i	$0.617213\pi$
$602$	2.37752			0.0969004
$603$	2.77382	−	23.6897i	0.112959	−	0.964721i
$604$	5.50476			0.223985
$605$	−29.5412	+	2.97165i	−1.20102	+	0.120815i
$606$	−13.3298	−	14.9816i	−0.541485	−	0.608586i
$607$		−	16.4500i		−	0.667686i	−0.942629	−	0.333843i	$-0.891654\pi$
$607$		−	16.4500i		−	0.667686i	0.942629	−	0.333843i	$-0.108346\pi$
$608$			4.16671i			0.168982i
$609$	−6.92707	−	7.78548i	−0.280699	−	0.315484i
$610$	2.06207	+	20.4990i	0.0834906	+	0.829981i
$611$		−	37.4587i		−	1.51542i
$612$	−2.41534	−	0.282811i	−0.0976343	−	0.0114320i
$613$	−21.9260			−0.885583			−0.442792	−	0.896625i	$-0.646012\pi$
$613$	−21.9260			−0.885583			−0.442792	+	0.896625i	$0.646012\pi$
$614$		−	8.27262i		−	0.333856i
$615$	7.25028	+	6.66578i	0.292359	+	0.268790i
$616$	−3.28577			−0.132388
$617$		−	3.85770i		−	0.155305i	−0.996980	−	0.0776526i	$-0.975257\pi$
$617$		−	3.85770i		−	0.155305i	0.996980	−	0.0776526i	$-0.0247425\pi$
$618$	−18.4875	+	16.4491i	−0.743674	+	0.661678i
$619$			35.4506i			1.42488i	0.701732	+	0.712441i	$0.252410\pi$
$619$			35.4506i			1.42488i	−0.701732	+	0.712441i	$0.747590\pi$
$620$	13.6485	−	1.37294i	0.548135	−	0.0551388i
$621$	−23.2411	+	8.99162i	−0.932635	+	0.360821i
$622$		−	0.256130i		−	0.0102699i
$623$	8.35852			0.334877
$624$	−4.27309	−	4.80262i	−0.171061	−	0.192259i
$625$	23.0165	−	9.75904i	0.920662	−	0.390362i
$626$	−7.18955			−0.287352
$627$	23.6373	+	26.5665i	0.943983	+	1.06096i
$628$	8.36290			0.333716
$629$		−	1.79898i		−	0.0717301i
$630$	0.0729252	−	4.47281i	0.00290541	−	0.178201i
$631$		−	28.1979i		−	1.12254i	−0.827632	−	0.561271i	$-0.810312\pi$
$631$		−	28.1979i		−	1.12254i	0.827632	−	0.561271i	$-0.189688\pi$
$632$		−	11.5161i		−	0.458085i
$633$	14.1681	−	12.6060i	0.563132	−	0.501043i
$634$	−16.3815			−0.650591
$635$	−0.411737	−	4.09309i	−0.0163393	−	0.162429i
$636$	12.2364	+	13.7528i	0.485206	+	0.545333i
$637$		−	24.3297i		−	0.963976i
$638$		−	44.4553i		−	1.76000i
$639$	43.2907	+	5.06888i	1.71255	+	0.200522i
$640$	2.22484	−	0.223804i	0.0879445	−	0.00884663i
$641$	−10.3529			−0.408915			−0.204457	−	0.978875i	$-0.565543\pi$
$641$	−10.3529			−0.408915			−0.204457	+	0.978875i	$0.565543\pi$
$642$	−12.0483	−	13.5413i	−0.475509	−	0.534434i
$643$	0.851752			0.0335898			0.0167949	−	0.999859i	$-0.494654\pi$
$643$	0.851752			0.0335898			0.0167949	+	0.999859i	$0.494654\pi$
$644$	−0.764590	+	3.10539i	−0.0301290	+	0.122370i
$645$	−9.34554	+	10.1650i	−0.367980	+	0.400247i
$646$	3.37759			0.132889
$647$	44.6917			1.75701			0.878505	−	0.477732i	$-0.158541\pi$
$647$	44.6917			1.75701			0.878505	+	0.477732i	$0.158541\pi$
$648$	8.75656	+	2.07911i	0.343990	+	0.0816750i
$649$			33.5586i			1.31729i
$650$	−3.69607	−	18.1854i	−0.144972	−	0.713291i
$651$	5.29361	−	4.70995i	0.207473	−	0.184598i
$652$			12.1701i			0.476617i
$653$	27.2860			1.06779			0.533893	−	0.845552i	$-0.320729\pi$
$653$	27.2860			1.06779			0.533893	+	0.845552i	$0.320729\pi$
$654$	−8.06943	−	9.06940i	−0.315539	−	0.354642i
$655$	−1.47644	−	14.6773i	−0.0576893	−	0.573491i
$656$			2.54295i			0.0992857i
$657$	14.4382	+	1.69056i	0.563288	+	0.0659551i
$658$	6.73042			0.262379
$659$	8.99528			0.350406			0.175203	−	0.984532i	$-0.443942\pi$
$659$	8.99528			0.350406			0.175203	+	0.984532i	$0.443942\pi$
$660$	12.9157	−	14.0482i	0.502743	−	0.546827i
$661$		−	19.4246i		−	0.755530i	−0.925902	−	0.377765i	$-0.876693\pi$
$661$		−	19.4246i		−	0.755530i	0.925902	−	0.377765i	$-0.123307\pi$
$662$	−22.0597			−0.857374
$663$	−3.89307	+	3.46383i	−0.151194	+	0.134524i
$664$		−	13.5358i		−	0.525290i
$665$	0.621861	+	6.18193i	0.0241147	+	0.239725i
$666$	−0.774274	+	6.61267i	−0.0300025	+	0.256236i
$667$	−42.0148	−	10.3446i	−1.62682	−	0.400545i
$668$	14.3712			0.556038
$669$	3.51426	+	3.94975i	0.135869	+	0.152706i
$670$	17.6887	−	1.77936i	0.683372	−	0.0687427i
$671$			45.3983i			1.75258i
$672$	0.862914	−	0.767771i	0.0332876	−	0.0296174i
$673$		−	43.1690i		−	1.66404i	−0.554744	−	0.832021i	$-0.687184\pi$
$673$		−	43.1690i		−	1.66404i	0.554744	−	0.832021i	$-0.312816\pi$
$674$	−11.1835			−0.430771
$675$	18.8367	+	17.8935i	0.725026	+	0.688721i
$676$	−0.774832			−0.0298012
$677$		−	27.0862i		−	1.04101i	−0.853859	−	0.520504i	$-0.825744\pi$
$677$		−	27.0862i		−	1.04101i	0.853859	−	0.520504i	$-0.174256\pi$
$678$	16.9131	+	19.0090i	0.649546	+	0.730038i
$679$	−0.698001			−0.0267868
$680$	−0.181419	−	1.80349i	−0.00695709	−	0.0691605i
$681$	19.3498	+	21.7476i	0.741485	+	0.833371i
$682$	30.2267			1.15744
$683$	25.8177			0.987886			0.493943	−	0.869494i	$-0.335555\pi$
$683$	25.8177			0.987886			0.493943	+	0.869494i	$0.335555\pi$
$684$	−12.4153	−	1.45370i	−0.474711	−	0.0555837i
$685$	3.70263	+	36.8079i	0.141470	+	1.40636i
$686$	9.03944			0.345127
$687$	−11.5996	−	13.0371i	−0.442554	−	0.497396i
$688$	−3.56526			−0.135924
$689$	39.4456			1.50276
$690$	−10.2716	−	15.4756i	−0.391031	−	0.589147i
$691$	−7.66316			−0.291520			−0.145760	−	0.989320i	$-0.546563\pi$
$691$	−7.66316			−0.291520			−0.145760	+	0.989320i	$0.546563\pi$
$692$	18.2848			0.695085
$693$	1.14636	−	9.79044i	0.0435465	−	0.371908i
$694$	13.1611			0.499588
$695$	−12.1679	+	1.22401i	−0.461556	+	0.0464294i
$696$	10.3877	+	11.6749i	0.393743	+	0.442536i
$697$	2.06135			0.0780793
$698$	−7.16860			−0.271335
$699$	−16.8998	+	15.0364i	−0.639207	+	0.568730i
$700$	3.26748	−	0.664093i	0.123499	−	0.0251004i
$701$	19.8123			0.748301			0.374150	−	0.927368i	$-0.377934\pi$
$701$	19.8123			0.748301			0.374150	+	0.927368i	$0.377934\pi$
$702$	15.8009	−	11.0567i	0.596367	−	0.417310i
$703$		−	9.24710i		−	0.348761i
$704$	4.92726			0.185703
$705$	−26.4559	+	28.7757i	−0.996388	+	1.08376i
$706$	29.9100			1.12568
$707$		−	7.72068i		−	0.290366i
$708$	−7.84146	−	8.81319i	−0.294700	−	0.331220i
$709$		−	32.3675i		−	1.21559i	−0.794096	−	0.607793i	$-0.792055\pi$
$709$		−	32.3675i		−	1.21559i	0.794096	−	0.607793i	$-0.207945\pi$
$710$	3.25160	+	32.3243i	0.122031	+	1.21311i
$711$	34.3138	+	4.01779i	1.28687	+	0.150679i
$712$	−12.5342			−0.469739
$713$	7.03365	−	28.5673i	0.263412	−	1.06985i
$714$	−0.622366	−	0.699490i	−0.0232914	−	0.0261777i
$715$	−4.09276	−	40.6862i	−0.153061	−	1.52158i
$716$		−	5.02306i		−	0.187721i
$717$	−16.7131	−	18.7842i	−0.624162	−	0.701508i
$718$	−13.4801			−0.503073
$719$		−	3.18213i		−	0.118673i	−0.998238	−	0.0593367i	$-0.981101\pi$
$719$		−	3.18213i		−	0.118673i	0.998238	−	0.0593367i	$-0.0188986\pi$
$720$	−0.109357	+	6.70731i	−0.00407548	+	0.249967i
$721$	−9.52740			−0.354819
$722$	−1.63855			−0.0609805
$723$	−9.09666	−	10.2239i	−0.338309	−	0.380232i
$724$			0.342921i			0.0127445i
$725$	8.98493	+	44.2078i	0.333692	+	1.64184i
$726$	17.1816	−	15.2872i	0.637670	−	0.567362i
$727$	11.1704			0.414288			0.207144	−	0.978310i	$-0.433583\pi$
$727$	11.1704			0.414288			0.207144	+	0.978310i	$0.433583\pi$
$728$		−	2.47500i		−	0.0917297i
$729$	−9.25003	+	25.3661i	−0.342594	+	0.939484i
$730$	1.08447	+	10.7807i	0.0401379	+	0.399012i
$731$			2.89005i			0.106892i
$732$	−10.6080	−	11.9226i	−0.392083	−	0.440671i
$733$	50.0167			1.84741			0.923704	−	0.383107i	$-0.125146\pi$
$733$	50.0167			1.84741			0.923704	+	0.383107i	$0.125146\pi$
$734$	11.3468			0.418817
$735$	−17.1833	+	18.6900i	−0.633814	+	0.689390i
$736$	1.14656	−	4.65676i	0.0422627	−	0.171650i
$737$	39.1743			1.44300
$738$	−7.57710	−	0.887198i	−0.278917	−	0.0326582i
$739$	−15.4765			−0.569314			−0.284657	−	0.958629i	$-0.591880\pi$
$739$	−15.4765			−0.569314			−0.284657	+	0.958629i	$0.591880\pi$
$740$	−4.93755	+	0.496684i	−0.181508	+	0.0182585i
$741$	−20.0111	+	17.8047i	−0.735127	+	0.654073i
$742$			7.08741i			0.260187i
$743$		−	13.3519i		−	0.489833i	−0.969544	−	0.244917i	$-0.921239\pi$
$743$		−	13.3519i		−	0.489833i	0.969544	−	0.244917i	$-0.0787606\pi$
$744$	−7.93816	+	7.06292i	−0.291027	+	0.258939i
$745$	−6.47578	+	0.651421i	−0.237254	+	0.0238662i
$746$	−25.0799			−0.918242
$747$	40.3318	+	4.72243i	1.47566	+	0.172785i
$748$		−	3.99410i		−	0.146039i
$749$		−	6.97845i		−	0.254987i
$750$	−10.0045	+	16.5804i	−0.365312	+	0.605431i
$751$		−	46.8490i		−	1.70955i	−0.519002	−	0.854773i	$-0.673696\pi$
$751$		−	46.8490i		−	1.70955i	0.519002	−	0.854773i	$-0.326304\pi$
$752$	−10.0928			−0.368045
$753$	8.28298	−	7.36972i	0.301849	−	0.268567i
$754$	33.4858			1.21948
$755$	−12.2472	+	1.23199i	−0.445721	+	0.0448366i
$756$	1.98663	+	2.83904i	0.0722529	+	0.103255i
$757$	23.6532			0.859692			0.429846	−	0.902902i	$-0.358568\pi$
$757$	23.6532			0.859692			0.429846	+	0.902902i	$0.358568\pi$
$758$		−	19.4678i		−	0.707101i
$759$	−19.1070	−	36.1953i	−0.693540	−	1.31381i
$760$	−0.932526	−	9.27026i	−0.0338263	−	0.336268i
$761$			42.4465i			1.53869i	0.638836	+	0.769343i	$0.279416\pi$
$761$			42.4465i			1.53869i	−0.638836	+	0.769343i	$0.720584\pi$
$762$	2.11812	+	2.38060i	0.0767316	+	0.0862402i
$763$		−	4.67386i		−	0.169205i
$764$	−26.5716			−0.961325
$765$	5.43704	+	0.0886460i	0.196577	+	0.00320500i
$766$			26.1779i			0.945848i
$767$	−25.2779			−0.912732
$768$	−1.29400	+	1.15133i	−0.0466933	+	0.0415450i
$769$		−	30.3882i		−	1.09582i	−0.836536	−	0.547912i	$-0.815423\pi$
$769$		−	30.3882i		−	1.09582i	0.836536	−	0.547912i	$-0.184577\pi$
$770$	7.31032	−	0.735370i	0.263446	−	0.0265009i
$771$	19.1503	−	17.0388i	0.689680	−	0.613638i
$772$			0.121042i			0.00435640i
$773$		−	35.3747i		−	1.27234i	−0.771550	−	0.636169i	$-0.780518\pi$
$773$		−	35.3747i		−	1.27234i	0.771550	−	0.636169i	$-0.219482\pi$
$774$	1.24387	−	10.6232i	0.0447099	−	0.381844i
$775$	−30.0584	+	6.10916i	−1.07973	+	0.219448i
$776$	1.04670			0.0375745
$777$	−1.91505	+	1.70390i	−0.0687020	+	0.0611271i
$778$	−22.4773			−0.805851
$779$	10.5957			0.379632
$780$	10.5818	+	9.72873i	0.378889	+	0.348344i
$781$			71.5872i			2.56159i
$782$	−3.77483	−	0.929415i	−0.134988	−	0.0332358i
$783$	−38.4111	+	26.8783i	−1.37270	+	0.960552i
$784$	−6.55530			−0.234118
$785$	−18.6061	+	1.87165i	−0.664081	+	0.0668021i
$786$	7.59535	+	8.53657i	0.270917	+	0.304489i
$787$	−2.58816			−0.0922578			−0.0461289	−	0.998935i	$-0.514688\pi$
$787$	−2.58816			−0.0922578			−0.0461289	+	0.998935i	$0.514688\pi$
$788$	−4.06795			−0.144915
$789$	−1.53803	−	1.72863i	−0.0547554	−	0.0615408i
$790$	2.57734	+	25.6214i	0.0916978	+	0.911569i
$791$			9.79620i			0.348313i
$792$	−1.71905	+	14.6815i	−0.0610837	+	0.521684i
$793$	−34.1962			−1.21434
$794$		−	11.5042i		−	0.408269i
$795$	−30.3020	−	27.8592i	−1.07470	−	0.988063i
$796$		−	3.82379i		−	0.135531i
$797$			41.0402i			1.45372i	0.686786	+	0.726859i	$0.259021\pi$
$797$			41.0402i			1.45372i	−0.686786	+	0.726859i	$0.740979\pi$
$798$	−3.19908	−	3.59551i	−0.113246	−	0.127280i
$799$			8.18133i			0.289435i
$800$	−4.89982	+	0.995856i	−0.173235	+	0.0352088i
$801$	4.37300	−	37.3475i	0.154512	−	1.31961i
$802$	9.84524			0.347647
$803$			23.8756i			0.842551i
$804$	−10.2880	+	9.15367i	−0.362830	+	0.322825i
$805$	1.00609	−	7.08011i	0.0354600	−	0.249541i
$806$			22.7682i			0.801974i
$807$	14.1433	+	15.8960i	0.497868	+	0.559564i
$808$			11.5777i			0.407303i
$809$			6.18091i			0.217309i	0.994080	+	0.108655i	$0.0346542\pi$
$809$			6.18091i			0.217309i	−0.994080	+	0.108655i	$0.965346\pi$
$810$	−19.9473	−	2.66592i	−0.700875	−	0.0936710i
$811$	−2.55486			−0.0897134			−0.0448567	−	0.998993i	$-0.514283\pi$
$811$	−2.55486			−0.0897134			−0.0448567	+	0.998993i	$0.514283\pi$
$812$			6.01659i			0.211141i
$813$	25.3244	−	22.5322i	0.888166	−	0.790239i
$814$	−10.9350			−0.383271
$815$	−2.72371	−	27.0765i	−0.0954074	−	0.948447i
$816$	0.933283	+	1.04894i	0.0326714	+	0.0367201i
$817$			14.8554i			0.519725i
$818$	−18.8120			−0.657747
$819$	7.37462	+	0.863491i	0.257690	+	0.0301728i
$820$	−0.569123	−	5.65766i	−0.0198747	−	0.197574i
$821$			8.36428i			0.291915i	0.989291	+	0.145958i	$0.0466263\pi$
$821$			8.36428i			0.291915i	−0.989291	+	0.145958i	$0.953374\pi$
$822$	−19.0477	−	21.4081i	−0.664364	−	0.746692i
$823$		−	22.8495i		−	0.796484i	−0.917280	−	0.398242i	$-0.869620\pi$
$823$		−	22.8495i		−	0.796484i	0.917280	−	0.398242i	$-0.130380\pi$
$824$	14.2870			0.497712
$825$	−25.5913	+	34.1457i	−0.890976	+	1.18880i
$826$		−	4.54182i		−	0.158030i
$827$			49.9487i			1.73689i	0.495789	+	0.868443i	$0.334879\pi$
$827$			49.9487i			1.73689i	−0.495789	+	0.868443i	$0.665121\pi$
$828$	13.4755	+	5.04101i	0.468305	+	0.175187i
$829$	−5.29100			−0.183764			−0.0918820	−	0.995770i	$-0.529288\pi$
$829$	−5.29100			−0.183764			−0.0918820	+	0.995770i	$0.529288\pi$
$830$	3.02936	+	30.1149i	0.105151	+	1.04530i
$831$	−16.0928	−	18.0870i	−0.558252	−	0.627431i
$832$			3.71145i			0.128671i
$833$			5.31382i			0.184113i
$834$	7.07706	−	6.29676i	0.245059	−	0.218039i
$835$	−31.9736	+	3.21633i	−1.10649	+	0.111306i
$836$		−	20.5304i		−	0.710060i
$837$	−18.2755	−	26.1170i	−0.631693	−	0.902737i
$838$	8.48762			0.293200
$839$	32.3193			1.11579			0.557893	−	0.829913i	$-0.311610\pi$
$839$	32.3193			1.11579			0.557893	+	0.829913i	$0.311610\pi$
$840$	−1.74801	+	1.90129i	−0.0603122	+	0.0656008i
$841$	−52.4022			−1.80697
$842$			30.8277i			1.06239i
$843$	11.8095	−	10.5074i	0.406741	−	0.361894i
$844$	−10.9491			−0.376882
$845$	1.72388	−	0.173411i	0.0593032	−	0.00596551i
$846$	3.52121	−	30.0728i	0.121062	−	1.03393i
$847$	8.85444			0.304242
$848$		−	10.6281i		−	0.364970i
$849$	39.3892	−	35.0463i	1.35184	−	1.20278i
$850$	0.807255	+	3.97186i	0.0276886	+	0.136234i
$851$	−2.54454	+	10.3347i	−0.0872256	+	0.354268i
$852$	−16.7274	−	18.8003i	−0.573072	−	0.644088i
$853$			26.1818i			0.896448i	0.893921	+	0.448224i	$0.147943\pi$
$853$			26.1818i			0.896448i	−0.893921	+	0.448224i	$0.852057\pi$
$854$		−	6.14422i		−	0.210251i
$855$	27.9474	+	0.455657i	0.955781	+	0.0155831i
$856$			10.4647i			0.357676i
$857$	−4.33206			−0.147980			−0.0739902	−	0.997259i	$-0.523573\pi$
$857$	−4.33206			−0.147980			−0.0739902	+	0.997259i	$0.523573\pi$
$858$	21.0546	+	23.6638i	0.718794	+	0.807867i
$859$	16.2823			0.555545			0.277772	−	0.960647i	$-0.410404\pi$
$859$	16.2823			0.555545			0.277772	+	0.960647i	$0.410404\pi$
$860$	7.93214	−	0.797920i	0.270484	−	0.0272089i
$861$	−1.95241	−	2.19435i	−0.0665378	−	0.0747833i
$862$	−27.9563			−0.952194
$863$	−47.3991			−1.61348			−0.806742	−	0.590903i	$-0.798771\pi$
$863$	−47.3991			−1.61348			−0.806742	+	0.590903i	$0.798771\pi$
$864$	−2.97909	−	4.25735i	−0.101351	−	0.144838i
$865$	−40.6808	+	4.09222i	−1.38319	+	0.139140i
$866$	−37.3143			−1.26799
$867$	−21.1478	+	18.8161i	−0.718216	+	0.639027i
$868$	−4.09088			−0.138854
$869$			56.7427i			1.92486i
$870$	−25.7238	−	23.6500i	−0.872117	−	0.801810i
$871$			29.5080i			0.999839i
$872$			7.00879i			0.237348i
$873$	−0.365179	+	3.11880i	−0.0123594	+	0.105556i
$874$	−19.4034	−	4.77737i	−0.656328	−	0.161597i
$875$	−7.12099	+	2.20878i	−0.240733	+	0.0746703i
$876$	−5.57889	−	6.27023i	−0.188493	−	0.211852i
$877$		−	6.13247i		−	0.207079i	−0.994625	−	0.103539i	$-0.966983\pi$
$877$		−	6.13247i		−	0.207079i	0.994625	−	0.103539i	$-0.0330168\pi$
$878$	24.1100			0.813674
$879$	−31.2829	−	35.1595i	−1.05514	−	1.18590i
$880$	−10.9624	+	1.10274i	−0.369541	+	0.0371734i
$881$	−16.6943			−0.562445			−0.281222	−	0.959643i	$-0.590740\pi$
$881$	−16.6943			−0.562445			−0.281222	+	0.959643i	$0.590740\pi$
$882$	2.28705	−	19.5325i	0.0770089	−	0.657692i
$883$			43.1929i			1.45356i	0.686873	+	0.726778i	$0.258983\pi$
$883$			43.1929i			1.45356i	−0.686873	+	0.726778i	$0.741017\pi$
$884$	3.00855			0.101188
$885$	19.4184	+	17.8530i	0.652743	+	0.600121i
$886$	−14.5534			−0.488930
$887$	−18.4339			−0.618951			−0.309475	−	0.950907i	$-0.600153\pi$
$887$	−18.4339			−0.618951			−0.309475	+	0.950907i	$0.600153\pi$
$888$	2.87176	−	2.55512i	0.0963699	−	0.0857443i
$889$			1.22683i			0.0411466i
$890$	27.8866	−	2.80521i	0.934761	−	0.0940308i
$891$	−43.1458	−	10.2443i	−1.44544	−	0.343197i
$892$		−	3.05235i		−	0.102200i
$893$			42.0536i			1.40727i
$894$	3.76642	−	3.35114i	0.125968	−	0.112079i
$895$	1.12418	+	11.1755i	0.0375772	+	0.373556i
$896$	−0.666856			−0.0222781
$897$	27.2640	−	14.3923i	0.910318	−	0.480544i
$898$			25.8545i			0.862776i
$899$		−	55.3481i		−	1.84596i
$900$	−1.25782	−	14.9472i	−0.0419274	−	0.498239i
$901$	−8.61528			−0.287017
$902$		−	12.5298i		−	0.417197i
$903$	3.07652	−	2.73731i	0.102380	−	0.0910918i
$904$		−	14.6901i		−	0.488586i
$905$	−0.0767470	−	0.762943i	−0.00255116	−	0.0253611i
$906$	7.12317	−	6.33778i	0.236651	−	0.210559i
$907$	33.2776			1.10496			0.552482	−	0.833525i	$-0.313681\pi$
$907$	33.2776			1.10496			0.552482	+	0.833525i	$0.313681\pi$
$908$		−	16.8065i		−	0.557743i
$909$	−34.4975	−	4.03929i	−1.14421	−	0.133975i
$910$	0.553915	+	5.50648i	0.0183621	+	0.182538i
$911$	38.3776			1.27151			0.635753	−	0.771892i	$-0.280690\pi$
$911$	38.3776			1.27151			0.635753	+	0.771892i	$0.280690\pi$
$912$	4.79725	+	5.39173i	0.158853	+	0.178538i
$913$			66.6943i			2.20726i
$914$	23.6100			0.780949
$915$	26.2694	+	24.1517i	0.868441	+	0.798430i
$916$			10.0750i			0.332888i
$917$			4.39927i			0.145277i
$918$	−3.45106	+	2.41489i	−0.113902	+	0.0797033i
$919$			42.5549i			1.40376i	0.712297	+	0.701878i	$0.247655\pi$
$919$			42.5549i			1.40376i	−0.712297	+	0.701878i	$0.752345\pi$
$920$	−1.50871	+	10.6171i	−0.0497406	+	0.350037i
$921$	−9.52451	−	10.7048i	−0.313843	−	0.352735i
$922$			38.3275i			1.26225i
$923$	−53.9229			−1.77489
$924$	−4.25180	+	3.78301i	−0.139874	+	0.124452i
$925$	10.8741	−	2.21009i	0.357538	−	0.0726672i
$926$		−	1.86463i		−	0.0612756i
$927$	−4.98453	+	42.5703i	−0.163713	+	1.39819i
$928$		−	9.02232i		−	0.296172i
$929$			14.6150i			0.479501i	0.970834	+	0.239751i	$0.0770657\pi$
$929$			14.6150i			0.479501i	−0.970834	+	0.239751i	$0.922934\pi$
$930$	16.0804	−	17.4905i	0.527298	−	0.573534i
$931$			27.3140i			0.895181i
$932$	13.0601			0.427796
$933$	−0.294889	−	0.331432i	−0.00965424	−	0.0108506i
$934$			22.7789i			0.745348i
$935$	0.893897	+	8.88624i	0.0292335	+	0.290611i
$936$	−11.0588	−	1.29487i	−0.361468	−	0.0423241i
$937$	43.2537			1.41304			0.706519	−	0.707694i	$-0.250265\pi$
$937$	43.2537			1.41304			0.706519	+	0.707694i	$0.250265\pi$
$938$	−5.30186			−0.173112
$939$	−9.30329	+	8.27753i	−0.303601	+	0.270127i
$940$	22.4548	−	2.25880i	0.732394	−	0.0736740i
$941$	9.65494			0.314742			0.157371	−	0.987540i	$-0.449698\pi$
$941$	9.65494			0.314742			0.157371	+	0.987540i	$0.449698\pi$
$942$	10.8216	−	9.62845i	0.352587	−	0.313712i
$943$	−11.8419	−	2.91564i	−0.385626	−	0.0949464i
$944$			6.81080i			0.221673i
$945$	−5.05531	−	5.87179i	−0.164449	−	0.191009i
$946$	17.5670			0.571152
$947$	1.54817			0.0503088			0.0251544	−	0.999684i	$-0.491992\pi$
$947$	1.54817			0.0503088			0.0251544	+	0.999684i	$0.491992\pi$
$948$	−13.2588	−	14.9018i	−0.430625	−	0.483989i
$949$	−17.9842			−0.583793
$950$	4.14944	+	20.4161i	0.134626	+	0.662387i
$951$	−21.1977	+	18.8605i	−0.687381	+	0.611592i
$952$			0.540563i			0.0175197i
$953$		−	50.4280i		−	1.63352i	−0.576976	−	0.816761i	$-0.695767\pi$
$953$		−	50.4280i		−	1.63352i	0.576976	−	0.816761i	$-0.304233\pi$
$954$	31.6679	+	3.70798i	1.02529	+	0.120050i
$955$	59.1175	−	5.94682i	1.91300	−	0.192435i
$956$			14.5163i			0.469492i
$957$	−51.1827	−	57.5253i	−1.65450	−	1.85953i
$958$	22.7286			0.734326
$959$		−	11.0325i		−	0.356259i
$960$	2.62128	−	2.85112i	0.0846013	−	0.0920197i
$961$	6.63307			0.213970
$962$		−	8.23675i		−	0.265563i
$963$	−31.1811	−	3.65098i	−1.00480	−	0.117651i
$964$			7.90101i			0.254475i
$965$	−0.0270897	−	0.269299i	−0.000872049	−	0.00866906i
$966$	2.58594	+	4.89868i	0.0832014	+	0.157612i
$967$		−	39.1313i		−	1.25838i	−0.777252	−	0.629189i	$-0.783387\pi$
$967$		−	39.1313i		−	1.25838i	0.777252	−	0.629189i	$-0.216613\pi$
$968$	−13.2779			−0.426767
$969$	4.37061	−	3.88872i	0.140404	−	0.124924i
$970$	−2.32875	+	0.234257i	−0.0747716	+	0.00752152i
$971$	−31.3611			−1.00643			−0.503214	−	0.864162i	$-0.667849\pi$
$971$	−31.3611			−1.00643			−0.503214	+	0.864162i	$0.667849\pi$
$972$	13.7247	−	7.39131i	0.440221	−	0.237076i
$973$	3.64712			0.116921
$974$		−	9.28752i		−	0.297591i
$975$	−25.7201	−	19.2766i	−0.823703	−	0.617345i
$976$			9.21371i			0.294924i
$977$		−	10.1353i		−	0.324256i	−0.986770	−	0.162128i	$-0.948164\pi$
$977$		−	10.1353i		−	0.324256i	0.986770	−	0.162128i	$-0.0518357\pi$
$978$	14.0117	+	15.7481i	0.448046	+	0.503569i
$979$	61.7593			1.97384
$980$	14.5845	−	1.46710i	0.465885	−	0.0468649i
$981$	−20.8837	−	2.44526i	−0.666766	−	0.0780712i
$982$			16.4543i			0.525077i
$983$			8.84663i			0.282164i	0.989998	+	0.141082i	$0.0450581\pi$
$983$			8.84663i			0.282164i	−0.989998	+	0.141082i	$0.954942\pi$
$984$	2.92778	+	3.29059i	0.0933341	+	0.104900i
$985$	9.05053	−	0.910423i	0.288374	−	0.0290085i
$986$	−7.31361			−0.232913
$987$	8.70919	−	7.74893i	0.277216	−	0.246651i
$988$	15.4645			0.491992
$989$	4.08778	−	16.6026i	0.129984	−	0.527931i
$990$	0.538828	−	33.0487i	0.0171251	−	1.05036i
$991$	12.7133			0.403850			0.201925	−	0.979401i	$-0.435280\pi$
$991$	12.7133			0.403850			0.201925	+	0.979401i	$0.435280\pi$
$992$	6.13458			0.194773
$993$	−28.5453	+	25.3979i	−0.905857	+	0.805979i
$994$		−	9.68862i		−	0.307304i
$995$	0.855779	+	8.50731i	0.0271300	+	0.269700i
$996$	−15.5841	−	17.5153i	−0.493802	−	0.554995i
$997$			36.9919i			1.17154i	0.810476	+	0.585772i	$0.199209\pi$
$997$			36.9919i			1.17154i	−0.810476	+	0.585772i	$0.800791\pi$
$998$	−14.8139			−0.468927
$999$	6.61145	+	9.44826i	0.209177	+	0.298930i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.h.a.689.7	yes	24
3.2	odd	2		690.2.h.b.689.20	yes	24
5.4	even	2		690.2.h.b.689.17	yes	24
15.14	odd	2	inner	690.2.h.a.689.6	yes	24
23.22	odd	2	inner	690.2.h.a.689.8	yes	24
69.68	even	2		690.2.h.b.689.19	yes	24
115.114	odd	2		690.2.h.b.689.18	yes	24
345.344	even	2	inner	690.2.h.a.689.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.h.a.689.5	✓	24	345.344	even	2	inner
690.2.h.a.689.6	yes	24	15.14	odd	2	inner
690.2.h.a.689.7	yes	24	1.1	even	1	trivial
690.2.h.a.689.8	yes	24	23.22	odd	2	inner
690.2.h.b.689.17	yes	24	5.4	even	2
690.2.h.b.689.18	yes	24	115.114	odd	2
690.2.h.b.689.19	yes	24	69.68	even	2
690.2.h.b.689.20	yes	24	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.29400 + 1.15133i) q^{3} +1.00000 q^{4} +(-2.22484 + 0.223804i) q^{5} +(1.29400 - 1.15133i) q^{6} +0.666856 q^{7} -1.00000 q^{8} +(0.348885 - 2.97964i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.29400 + 1.15133i) q^{3} +1.00000 q^{4} +(-2.22484 + 0.223804i) q^{5} +(1.29400 - 1.15133i) q^{6} +0.666856 q^{7} -1.00000 q^{8} +(0.348885 - 2.97964i) q^{9} +(2.22484 - 0.223804i) q^{10} +4.92726 q^{11} +(-1.29400 + 1.15133i) q^{12} +3.71145i q^{13} -0.666856 q^{14} +(2.62128 - 2.85112i) q^{15} +1.00000 q^{16} -0.810614i q^{17} +(-0.348885 + 2.97964i) q^{18} -4.16671i q^{19} +(-2.22484 + 0.223804i) q^{20} +(-0.862914 + 0.767771i) q^{21} -4.92726 q^{22} +(-1.14656 + 4.65676i) q^{23} +(1.29400 - 1.15133i) q^{24} +(4.89982 - 0.995856i) q^{25} -3.71145i q^{26} +(2.97909 + 4.25735i) q^{27} +0.666856 q^{28} +9.02232i q^{29} +(-2.62128 + 2.85112i) q^{30} -6.13458 q^{31} -1.00000 q^{32} +(-6.37589 + 5.67289i) q^{33} +0.810614i q^{34} +(-1.48365 + 0.149245i) q^{35} +(0.348885 - 2.97964i) q^{36} +2.21928 q^{37} +4.16671i q^{38} +(-4.27309 - 4.80262i) q^{39} +(2.22484 - 0.223804i) q^{40} +2.54295i q^{41} +(0.862914 - 0.767771i) q^{42} -3.56526 q^{43} +4.92726 q^{44} +(-0.109357 + 6.70731i) q^{45} +(1.14656 - 4.65676i) q^{46} -10.0928 q^{47} +(-1.29400 + 1.15133i) q^{48} -6.55530 q^{49} +(-4.89982 + 0.995856i) q^{50} +(0.933283 + 1.04894i) q^{51} +3.71145i q^{52} -10.6281i q^{53} +(-2.97909 - 4.25735i) q^{54} +(-10.9624 + 1.10274i) q^{55} -0.666856 q^{56} +(4.79725 + 5.39173i) q^{57} -9.02232i q^{58} +6.81080i q^{59} +(2.62128 - 2.85112i) q^{60} +9.21371i q^{61} +6.13458 q^{62} +(0.232656 - 1.98699i) q^{63} +1.00000 q^{64} +(-0.830637 - 8.25737i) q^{65} +(6.37589 - 5.67289i) q^{66} +7.95053 q^{67} -0.810614i q^{68} +(-3.87781 - 7.34592i) q^{69} +(1.48365 - 0.149245i) q^{70} +14.5288i q^{71} +(-0.348885 + 2.97964i) q^{72} +4.84561i q^{73} -2.21928 q^{74} +(-5.19383 + 6.92995i) q^{75} -4.16671i q^{76} +3.28577 q^{77} +(4.27309 + 4.80262i) q^{78} +11.5161i q^{79} +(-2.22484 + 0.223804i) q^{80} +(-8.75656 - 2.07911i) q^{81} -2.54295i q^{82} +13.5358i q^{83} +(-0.862914 + 0.767771i) q^{84} +(0.181419 + 1.80349i) q^{85} +3.56526 q^{86} +(-10.3877 - 11.6749i) q^{87} -4.92726 q^{88} +12.5342 q^{89} +(0.109357 - 6.70731i) q^{90} +2.47500i q^{91} +(-1.14656 + 4.65676i) q^{92} +(7.93816 - 7.06292i) q^{93} +10.0928 q^{94} +(0.932526 + 9.27026i) q^{95} +(1.29400 - 1.15133i) q^{96} -1.04670 q^{97} +6.55530 q^{98} +(1.71905 - 14.6815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 2 q^{3} + 24 q^{4} - 2 q^{6} - 24 q^{8} + 6 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 2 * q^3 + 24 * q^4 - 2 * q^6 - 24 * q^8 + 6 * q^9	\( 24 q - 24 q^{2} + 2 q^{3} + 24 q^{4} - 2 q^{6} - 24 q^{8} + 6 q^{9} + 2 q^{12} + 24 q^{16} - 6 q^{18} - 4 q^{23} - 2 q^{24} + 12 q^{25} + 2 q^{27} - 28 q^{31} - 24 q^{32} + 8 q^{35} + 6 q^{36} + 4 q^{46} + 16 q^{47} + 2 q^{48} - 4 q^{49} - 12 q^{50} - 2 q^{54} + 4 q^{55} + 28 q^{62} + 24 q^{64} - 8 q^{69} - 8 q^{70} - 6 q^{72} + 14 q^{75} + 8 q^{77} + 14 q^{81} - 44 q^{85} + 28 q^{87} - 4 q^{92} - 4 q^{93} - 16 q^{94} + 4 q^{95} - 2 q^{96} + 4 q^{98}+O(q^{100}) \) 24 * q - 24 * q^2 + 2 * q^3 + 24 * q^4 - 2 * q^6 - 24 * q^8 + 6 * q^9 + 2 * q^12 + 24 * q^16 - 6 * q^18 - 4 * q^23 - 2 * q^24 + 12 * q^25 + 2 * q^27 - 28 * q^31 - 24 * q^32 + 8 * q^35 + 6 * q^36 + 4 * q^46 + 16 * q^47 + 2 * q^48 - 4 * q^49 - 12 * q^50 - 2 * q^54 + 4 * q^55 + 28 * q^62 + 24 * q^64 - 8 * q^69 - 8 * q^70 - 6 * q^72 + 14 * q^75 + 8 * q^77 + 14 * q^81 - 44 * q^85 + 28 * q^87 - 4 * q^92 - 4 * q^93 - 16 * q^94 + 4 * q^95 - 2 * q^96 + 4 * q^98

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