LMFDB - Embedded newform 690.2.h.a.689.6

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			689.6
Character	$\chi$	$=$	690.689
Dual form			690.2.h.a.689.8

$q$-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} +(6.84511 - 4.70579i) 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	$-0.540222\pi$
$7$	−0.666856			−0.252048			−0.126024	+	0.992027i	$0.540222\pi$
$8$	−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	$-0.766509\pi$
$11$	−4.92726			−1.48562			−0.742812	+	0.669500i	$0.766509\pi$
$12$	−1.29400	−	1.15133i	−0.373546	−	0.332360i
$13$		−	3.71145i		−	1.02937i	−0.857379	−	0.514685i	$-0.827909\pi$
$13$		−	3.71145i		−	1.02937i	0.857379	−	0.514685i	$-0.172091\pi$
$14$	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	$-0.683899\pi$
$29$		−	9.02232i		−	1.67540i	0.546129	−	0.837701i	$-0.316101\pi$
$30$	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	$-0.558394\pi$
$37$	−2.21928			−0.364848			−0.182424	+	0.983220i	$0.558394\pi$
$38$			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	$-0.936370\pi$
$41$		−	2.54295i		−	0.397143i	0.980086	−	0.198571i	$-0.0636302\pi$
$42$	−0.862914	−	0.767771i	−0.133151	−	0.118470i
$43$	3.56526			0.543698			0.271849	−	0.962340i	$-0.412365\pi$
$43$	3.56526			0.543698			0.271849	+	0.962340i	$0.412365\pi$
$44$	−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	$-0.853792\pi$
$59$		−	6.81080i		−	0.886690i	0.896351	−	0.443345i	$-0.146208\pi$
$60$	−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	$-0.661419\pi$
$67$	−7.95053			−0.971312			−0.485656	+	0.874150i	$0.661419\pi$
$68$		−	0.810614i		−	0.0983013i
$69$	6.84511	−	4.70579i	0.824054	−	0.566511i
$70$	1.48365	+	0.149245i	0.177330	+	0.0178382i
$71$		−	14.5288i		−	1.72425i	−0.506695	−	0.862126i	$-0.669133\pi$
$71$		−	14.5288i		−	1.72425i	0.506695	−	0.862126i	$-0.330867\pi$
$72$	−0.348885	−	2.97964i	−0.0411165	−	0.351154i
$73$		−	4.84561i		−	0.567136i	−0.958952	−	0.283568i	$-0.908482\pi$
$73$		−	4.84561i		−	0.567136i	0.958952	−	0.283568i	$-0.0915181\pi$
$74$	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	$-0.731275\pi$
$89$	−12.5342			−1.32862			−0.664312	+	0.747455i	$0.731275\pi$
$90$	−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	$-0.483078\pi$
$97$	1.04670			0.106277			0.0531383	+	0.998587i	$0.483078\pi$
$98$	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	$0.195392\pi$
$101$			11.5777i			1.15203i	−0.817440	+	0.576013i	$0.804608\pi$
$102$	0.933283	−	1.04894i	0.0924087	−	0.103860i
$103$	14.2870			1.40774			0.703871	−	0.710327i	$-0.251453\pi$
$103$	14.2870			1.40774			0.703871	+	0.710327i	$0.251453\pi$
$104$			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
$115$	−3.59311	+	10.1039i	−0.335059	+	0.942197i
$116$		−	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	$-0.973989\pi$
$127$		−	1.83972i		−	0.163249i	0.996663	−	0.0816245i	$-0.0260108\pi$
$128$	−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	$-0.906946\pi$
$131$		−	6.59703i		−	0.576385i	0.957573	−	0.288192i	$-0.0930543\pi$
$132$	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	$-0.249830\pi$
$138$	−6.84511	+	4.70579i	−0.582694	+	0.400584i
$139$	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	$-0.538041\pi$
$149$	−2.91067			−0.238452			−0.119226	+	0.992867i	$0.538041\pi$
$150$	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	$-0.608303\pi$
$157$	−8.36290			−0.667432			−0.333716	+	0.942674i	$0.608303\pi$
$158$		−	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	$-0.841863\pi$
$163$		−	12.1701i		−	0.953233i	0.879111	−	0.476617i	$-0.158137\pi$
$164$		−	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	$0.0601099\pi$
$179$			5.02306i			0.375441i	−0.982222	+	0.187721i	$0.939890\pi$
$180$	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	$-0.0888155\pi$
$191$	26.5716			1.92265			0.961325	+	0.275416i	$0.0888155\pi$
$192$	−1.29400	−	1.15133i	−0.0933866	−	0.0830900i
$193$		−	0.121042i		−	0.00871281i	−0.999991	−	0.00435640i	$-0.998613\pi$
$193$		−	0.121042i		−	0.00871281i	0.999991	−	0.00435640i	$-0.00138669\pi$
$194$	−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
$207$	−14.2755	−	1.79166i	−0.992216	−	0.124529i
$208$		−	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	$0.0325883\pi$
$223$			3.05235i			0.204401i	−0.994764	+	0.102200i	$0.967412\pi$
$224$	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	$0.891977\pi$
$230$	3.59311	−	10.1039i	0.236923	−	0.666234i
$231$	−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	$-0.844437\pi$
$239$		−	14.5163i		−	0.938984i	0.882937	−	0.469492i	$-0.155563\pi$
$240$	−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	$-0.435251\pi$
$251$	6.40105			0.404031			0.202015	+	0.979382i	$0.435251\pi$
$252$	−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	$0.122184\pi$
$269$			12.2843i			0.748989i	−0.927229	+	0.374495i	$0.877816\pi$
$270$	−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
$276$	6.84511	−	4.70579i	0.412027	−	0.283255i
$277$		−	13.9776i		−	0.839830i	−0.907563	−	0.419915i	$-0.862060\pi$
$277$		−	13.9776i		−	0.839830i	0.907563	−	0.419915i	$-0.137940\pi$
$278$	−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	$-0.412244\pi$
$281$	9.12634			0.544432			0.272216	+	0.962236i	$0.412244\pi$
$282$	−13.0601	−	11.6201i	−0.777715	−	0.691966i
$283$	30.4398			1.80946			0.904730	−	0.425984i	$-0.140072\pi$
$283$	30.4398			1.80946			0.904730	+	0.425984i	$0.140072\pi$
$284$		−	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	$-0.924140\pi$
$307$		−	8.27262i		−	0.472144i	0.971736	−	0.236072i	$-0.0758601\pi$
$308$	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	$-0.997688\pi$
$311$		−	0.256130i		−	0.0145238i	0.999974	−	0.00726189i	$-0.00231155\pi$
$312$	4.27309	−	4.80262i	0.241916	−	0.271895i
$313$	−7.18955			−0.406377			−0.203189	−	0.979140i	$-0.565130\pi$
$313$	−7.18955			−0.406377			−0.203189	+	0.979140i	$0.565130\pi$
$314$	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	$-0.598523\pi$
$337$	−11.1835			−0.609203			−0.304601	+	0.952480i	$0.598523\pi$
$338$	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
$345$	16.2824	−	8.93767i	0.876617	−	0.481188i
$346$	−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	$-0.615766\pi$
$359$	−13.4801			−0.711452			−0.355726	+	0.934590i	$0.615766\pi$
$360$	−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	$-0.404298\pi$
$367$	11.3468			0.592297			0.296148	+	0.955142i	$0.404298\pi$
$368$	−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	$-0.724936\pi$
$373$	−25.0799			−1.29859			−0.649295	+	0.760537i	$0.724936\pi$
$374$		−	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	$-0.692988\pi$
$389$	−22.4773			−1.13965			−0.569823	+	0.821768i	$0.692988\pi$
$390$	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	$-0.906780\pi$
$397$		−	11.5042i		−	0.577380i	0.957423	−	0.288690i	$-0.0932197\pi$
$398$			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	$-0.420942\pi$
$401$	9.84524			0.491648			0.245824	+	0.969315i	$0.420942\pi$
$402$	−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
$414$	14.2755	+	1.79166i	0.701603	+	0.0880553i
$415$	−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	$-0.433525\pi$
$419$	8.48762			0.414647			0.207324	+	0.978272i	$0.433525\pi$
$420$	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	$-0.735125\pi$
$431$	−27.9563			−1.34661			−0.673303	+	0.739367i	$0.735125\pi$
$432$	2.97909	−	4.25735i	0.143332	−	0.204832i
$433$	−37.3143			−1.79321			−0.896606	−	0.442829i	$-0.853975\pi$
$433$	−37.3143			−1.79321			−0.896606	+	0.442829i	$0.853975\pi$
$434$	−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	$0.208861\pi$
$449$			25.8545i			1.22015i	−0.792344	+	0.610075i	$0.791139\pi$
$450$	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	$-0.313783\pi$
$457$	23.6100			1.10443			0.552214	+	0.833702i	$0.313783\pi$
$458$		−	10.0750i		−	0.470774i
$459$	−3.45106	−	2.41489i	−0.161082	−	0.112718i
$460$	−3.59311	+	10.1039i	−0.167530	+	0.471099i
$461$			38.3275i			1.78509i	0.450959	+	0.892545i	$0.351082\pi$
$461$			38.3275i			1.78509i	−0.450959	+	0.892545i	$0.648918\pi$
$462$	4.25180	+	3.78301i	0.197812	+	0.176001i
$463$		−	1.86463i		−	0.0866567i	−0.999061	−	0.0433284i	$-0.986204\pi$
$463$		−	1.86463i		−	0.0866567i	0.999061	−	0.0433284i	$-0.0137962\pi$
$464$		−	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	$-0.326212\pi$
$479$	22.7286			1.03849			0.519247	+	0.854624i	$0.326212\pi$
$480$	2.62128	+	2.85112i	0.119644	+	0.130135i
$481$			8.23675i			0.375563i
$482$		−	7.90101i		−	0.359881i
$483$	−4.56470	+	3.13809i	−0.207701	+	0.142788i
$484$	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	$-0.932514\pi$
$487$		−	9.28752i		−	0.420858i	0.977609	−	0.210429i	$-0.0674860\pi$
$488$		−	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	$0.121083\pi$
$491$			16.4543i			0.742571i	−0.928519	+	0.371286i	$0.878917\pi$
$492$	−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	$0.0219957\pi$
$509$			3.11552i			0.138093i	−0.997613	+	0.0690465i	$0.978004\pi$
$510$	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	$-0.467941\pi$
$521$	4.59001			0.201092			0.100546	+	0.994932i	$0.467941\pi$
$522$	−26.8833	+	3.14775i	−1.17665	+	0.137773i
$523$	−25.4462			−1.11269			−0.556343	−	0.830953i	$-0.687796\pi$
$523$	−25.4462			−1.11269			−0.556343	+	0.830953i	$0.687796\pi$
$524$		−	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	$0.170895\pi$
$547$			23.9240i			1.02292i	−0.859308	+	0.511459i	$0.829105\pi$
$548$		−	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
$552$	−6.84511	+	4.70579i	−0.291347	+	0.200292i
$553$		−	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	$-0.459994\pi$
$569$	5.98029			0.250707			0.125353	+	0.992112i	$0.459994\pi$
$570$	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
$575$	−10.2554	+	21.6755i	−0.427679	+	0.903930i
$576$	0.348885	+	2.97964i	0.0145369	+	0.124152i
$577$			2.43133i			0.101218i	0.998719	+	0.0506088i	$0.0161162\pi$
$577$			2.43133i			0.101218i	−0.998719	+	0.0506088i	$0.983884\pi$
$578$	−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	$-0.644275\pi$
$599$		−	44.0064i		−	1.79805i	0.437892	−	0.899027i	$-0.355725\pi$
$600$	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	$0.108346\pi$
$607$			16.4500i			0.667686i	−0.942629	+	0.333843i	$0.891654\pi$
$608$			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	$-0.353988\pi$
$613$	21.9260			0.885583			0.442792	+	0.896625i	$0.353988\pi$
$614$			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
$621$	16.4097	+	18.7542i	0.658500	+	0.752580i
$622$			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	$-0.434457\pi$
$641$	10.3529			0.408915			0.204457	+	0.978875i	$0.434457\pi$
$642$	12.0483	−	13.5413i	0.475509	−	0.534434i
$643$	−0.851752			−0.0335898			−0.0167949	−	0.999859i	$-0.505346\pi$
$643$	−0.851752			−0.0335898			−0.0167949	+	0.999859i	$0.505346\pi$
$644$	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	$-0.556058\pi$
$659$	−8.99528			−0.350406			−0.175203	+	0.984532i	$0.556058\pi$
$660$	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	$0.312816\pi$
$673$			43.1690i			1.66404i	−0.554744	+	0.832021i	$0.687184\pi$
$674$	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
$690$	−16.2824	+	8.93767i	−0.619862	+	0.340251i
$691$	−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	$-0.622066\pi$
$701$	−19.8123			−0.748301			−0.374150	+	0.927368i	$0.622066\pi$
$702$	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	$0.0188986\pi$
$719$			3.18213i			0.118673i	−0.998238	+	0.0593367i	$0.981101\pi$
$720$	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	$-0.566417\pi$
$727$	−11.1704			−0.414288			−0.207144	+	0.978310i	$0.566417\pi$
$728$		−	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	$-0.874854\pi$
$733$	−50.0167			−1.84741			−0.923704	+	0.383107i	$0.874854\pi$
$734$	−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	$-0.641432\pi$
$757$	−23.6532			−0.859692			−0.429846	+	0.902902i	$0.641432\pi$
$758$		−	19.4678i		−	0.707101i
$759$	−33.7276	+	23.1867i	−1.22424	+	0.841623i
$760$	−0.932526	+	9.27026i	−0.0338263	+	0.336268i
$761$		−	42.4465i		−	1.53869i	−0.638836	−	0.769343i	$-0.720584\pi$
$761$		−	42.4465i		−	1.53869i	0.638836	−	0.769343i	$-0.279416\pi$
$762$	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	$-0.485312\pi$
$787$	2.58816			0.0922578			0.0461289	+	0.998935i	$0.485312\pi$
$788$	−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
$805$	2.39609	−	6.73788i	0.0844510	−	0.237479i
$806$		−	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	$-0.965346\pi$
$809$		−	6.18091i		−	0.217309i	0.994080	−	0.108655i	$-0.0346542\pi$
$810$	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	$-0.953374\pi$
$821$		−	8.36428i		−	0.291915i	0.989291	−	0.145958i	$-0.0466263\pi$
$822$	19.0477	−	21.4081i	0.664364	−	0.746692i
$823$			22.8495i			0.796484i	0.917280	+	0.398242i	$0.130380\pi$
$823$			22.8495i			0.796484i	−0.917280	+	0.398242i	$0.869620\pi$
$824$	−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	$0.665121\pi$
$828$	−14.2755	−	1.79166i	−0.496108	−	0.0622645i
$829$	−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	$-0.688390\pi$
$839$	−32.3193			−1.11579			−0.557893	+	0.829913i	$0.688390\pi$
$840$	−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	$-0.852057\pi$
$853$		−	26.1818i		−	0.896448i	0.893921	−	0.448224i	$-0.147943\pi$
$854$			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	$0.0330168\pi$
$877$			6.13247i			0.207079i	−0.994625	+	0.103539i	$0.966983\pi$
$878$	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	$-0.409260\pi$
$881$	16.6943			0.562445			0.281222	+	0.959643i	$0.409260\pi$
$882$	2.28705	+	19.5325i	0.0770089	+	0.657692i
$883$		−	43.1929i		−	1.45356i	−0.686873	−	0.726778i	$-0.741017\pi$
$883$		−	43.1929i		−	1.45356i	0.686873	−	0.726778i	$-0.258983\pi$
$884$	−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
$897$	−17.4653	−	25.4053i	−0.583149	−	0.848257i
$898$		−	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	$-0.686319\pi$
$907$	−33.2776			−1.10496			−0.552482	+	0.833525i	$0.686319\pi$
$908$		−	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	$-0.719310\pi$
$911$	−38.3776			−1.27151			−0.635753	+	0.771892i	$0.719310\pi$
$912$	−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	$0.752345\pi$
$920$	3.59311	−	10.1039i	0.118461	−	0.333117i
$921$	−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	$-0.922934\pi$
$929$		−	14.6150i		−	0.479501i	0.970834	−	0.239751i	$-0.0770657\pi$
$930$	−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	$-0.749735\pi$
$937$	−43.2537			−1.41304			−0.706519	+	0.707694i	$0.749735\pi$
$938$	−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	$-0.550302\pi$
$941$	−9.65494			−0.314742			−0.157371	+	0.987540i	$0.550302\pi$
$942$	−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
$966$	4.56470	−	3.13809i	0.146867	−	0.100966i
$967$			39.1313i			1.25838i	0.777252	+	0.629189i	$0.216613\pi$
$967$			39.1313i			1.25838i	−0.777252	+	0.629189i	$0.783387\pi$
$968$	−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	$-0.332151\pi$
$971$	31.3611			1.00643			0.503214	+	0.864162i	$0.332151\pi$
$972$	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	$-0.800791\pi$
$997$		−	36.9919i		−	1.17154i	0.810476	−	0.585772i	$-0.199209\pi$
$998$	−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.689.6	yes	24
3.2	odd	2		690.2.h.b.689.17	yes	24
5.4	even	2		690.2.h.b.689.20	yes	24
15.14	odd	2	inner	690.2.h.a.689.7	yes	24
23.22	odd	2	inner	690.2.h.a.689.5	✓	24
69.68	even	2		690.2.h.b.689.18	yes	24
115.114	odd	2		690.2.h.b.689.19	yes	24
345.344	even	2	inner	690.2.h.a.689.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.h.a.689.5	✓	24	23.22	odd	2	inner
690.2.h.a.689.6	yes	24	1.1	even	1	trivial
690.2.h.a.689.7	yes	24	15.14	odd	2	inner
690.2.h.a.689.8	yes	24	345.344	even	2	inner
690.2.h.b.689.17	yes	24	3.2	odd	2
690.2.h.b.689.18	yes	24	69.68	even	2
690.2.h.b.689.19	yes	24	115.114	odd	2
690.2.h.b.689.20	yes	24	5.4	even	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} +(6.84511 - 4.70579i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more