LMFDB - Embedded newform 546.2.e.g.545.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(545,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, 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("546.545");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.e (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.303595776.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			545.8
Root			$1.26217 + 1.18614i$ of defining polynomial
Character	$\chi$	$=$	546.545
Dual form			546.2.e.g.545.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.26217 + 1.18614i) q^{3} +1.00000 q^{4} -3.37228i q^{5} +(1.26217 + 1.18614i) q^{6} +(2.52434 - 0.792287i) q^{7} +1.00000 q^{8} +(0.186141 + 2.99422i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.26217 + 1.18614i) q^{3} +1.00000 q^{4} -3.37228i q^{5} +(1.26217 + 1.18614i) q^{6} +(2.52434 - 0.792287i) q^{7} +1.00000 q^{8} +(0.186141 + 2.99422i) q^{9} -3.37228i q^{10} -5.74456 q^{11} +(1.26217 + 1.18614i) q^{12} +(3.46410 - 1.00000i) q^{13} +(2.52434 - 0.792287i) q^{14} +(4.00000 - 4.25639i) q^{15} +1.00000 q^{16} -0.792287 q^{17} +(0.186141 + 2.99422i) q^{18} +2.37686 q^{19} -3.37228i q^{20} +(4.12590 + 1.99422i) q^{21} -5.74456 q^{22} +0.147477i q^{23} +(1.26217 + 1.18614i) q^{24} -6.37228 q^{25} +(3.46410 - 1.00000i) q^{26} +(-3.31662 + 4.00000i) q^{27} +(2.52434 - 0.792287i) q^{28} +2.37686i q^{29} +(4.00000 - 4.25639i) q^{30} -4.10891 q^{31} +1.00000 q^{32} +(-7.25061 - 6.81386i) q^{33} -0.792287 q^{34} +(-2.67181 - 8.51278i) q^{35} +(0.186141 + 2.99422i) q^{36} +8.36530i q^{37} +2.37686 q^{38} +(5.55842 + 2.84674i) q^{39} -3.37228i q^{40} +8.37228i q^{41} +(4.12590 + 1.99422i) q^{42} -2.62772 q^{43} -5.74456 q^{44} +(10.0974 - 0.627719i) q^{45} +0.147477i q^{46} -10.3723i q^{47} +(1.26217 + 1.18614i) q^{48} +(5.74456 - 4.00000i) q^{49} -6.37228 q^{50} +(-1.00000 - 0.939764i) q^{51} +(3.46410 - 1.00000i) q^{52} +10.0974i q^{53} +(-3.31662 + 4.00000i) q^{54} +19.3723i q^{55} +(2.52434 - 0.792287i) q^{56} +(3.00000 + 2.81929i) q^{57} +2.37686i q^{58} -2.74456i q^{59} +(4.00000 - 4.25639i) q^{60} +7.74456i q^{61} -4.10891 q^{62} +(2.84216 + 7.41095i) q^{63} +1.00000 q^{64} +(-3.37228 - 11.6819i) q^{65} +(-7.25061 - 6.81386i) q^{66} -5.98844i q^{67} -0.792287 q^{68} +(-0.174928 + 0.186141i) q^{69} +(-2.67181 - 8.51278i) q^{70} -2.00000 q^{71} +(0.186141 + 2.99422i) q^{72} -10.2448 q^{73} +8.36530i q^{74} +(-8.04290 - 7.55842i) q^{75} +2.37686 q^{76} +(-14.5012 + 4.55134i) q^{77} +(5.55842 + 2.84674i) q^{78} -3.62772 q^{79} -3.37228i q^{80} +(-8.93070 + 1.11469i) q^{81} +8.37228i q^{82} -6.74456i q^{83} +(4.12590 + 1.99422i) q^{84} +2.67181i q^{85} -2.62772 q^{86} +(-2.81929 + 3.00000i) q^{87} -5.74456 q^{88} +10.0000i q^{89} +(10.0974 - 0.627719i) q^{90} +(7.95228 - 5.26890i) q^{91} +0.147477i q^{92} +(-5.18614 - 4.87375i) q^{93} -10.3723i q^{94} -8.01544i q^{95} +(1.26217 + 1.18614i) q^{96} -9.15759 q^{97} +(5.74456 - 4.00000i) q^{98} +(-1.06930 - 17.2005i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 10 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 - 10 * q^9	$ 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 10 q^{9} + 32 q^{15} + 8 q^{16} - 10 q^{18} + 14 q^{21} - 28 q^{25} + 32 q^{30} + 8 q^{32} - 10 q^{36} + 10 q^{39} + 14 q^{42} - 44 q^{43} - 28 q^{50} - 8 q^{51} + 24 q^{57} + 32 q^{60} - 4 q^{63} + 8 q^{64} - 4 q^{65} - 16 q^{71} - 10 q^{72} + 10 q^{78} - 52 q^{79} - 14 q^{81} + 14 q^{84} - 44 q^{86} + 24 q^{91} - 30 q^{93} - 66 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 - 10 * q^9 + 32 * q^15 + 8 * q^16 - 10 * q^18 + 14 * q^21 - 28 * q^25 + 32 * q^30 + 8 * q^32 - 10 * q^36 + 10 * q^39 + 14 * q^42 - 44 * q^43 - 28 * q^50 - 8 * q^51 + 24 * q^57 + 32 * q^60 - 4 * q^63 + 8 * q^64 - 4 * q^65 - 16 * q^71 - 10 * q^72 + 10 * q^78 - 52 * q^79 - 14 * q^81 + 14 * q^84 - 44 * q^86 + 24 * q^91 - 30 * q^93 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$-1$

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
$3$	1.26217	+	1.18614i	0.728714	+	0.684819i
$3$	1.26217	+	1.18614i	0.728714	+	0.684819i
$4$	1.00000			0.500000
$5$		−	3.37228i		−	1.50813i	−0.656800	−	0.754065i	$-0.728090\pi$
$5$		−	3.37228i		−	1.50813i	0.656800	−	0.754065i	$-0.271910\pi$
$6$	1.26217	+	1.18614i	0.515278	+	0.484240i
$7$	2.52434	−	0.792287i	0.954110	−	0.299456i
$7$	2.52434	−	0.792287i	0.954110	−	0.299456i
$8$	1.00000			0.353553
$9$	0.186141	+	2.99422i	0.0620469	+	0.998073i
$10$		−	3.37228i		−	1.06641i
$11$	−5.74456			−1.73205			−0.866025	−	0.500000i	$-0.833333\pi$
$11$	−5.74456			−1.73205			−0.866025	+	0.500000i	$0.833333\pi$
$12$	1.26217	+	1.18614i	0.364357	+	0.342409i
$13$	3.46410	−	1.00000i	0.960769	−	0.277350i
$13$	3.46410	−	1.00000i	0.960769	−	0.277350i
$14$	2.52434	−	0.792287i	0.674658	−	0.211748i
$15$	4.00000	−	4.25639i	1.03280	−	1.09899i
$16$	1.00000			0.250000
$17$	−0.792287			−0.192158			−0.0960789	−	0.995374i	$-0.530630\pi$
$17$	−0.792287			−0.192158			−0.0960789	+	0.995374i	$0.530630\pi$
$18$	0.186141	+	2.99422i	0.0438738	+	0.705744i
$19$	2.37686			0.545289			0.272645	−	0.962115i	$-0.412102\pi$
$19$	2.37686			0.545289			0.272645	+	0.962115i	$0.412102\pi$
$20$		−	3.37228i		−	0.754065i
$21$	4.12590	+	1.99422i	0.900346	+	0.435174i
$22$	−5.74456			−1.22474
$23$			0.147477i			0.0307510i	0.999882	+	0.0153755i	$0.00489437\pi$
$23$			0.147477i			0.0307510i	−0.999882	+	0.0153755i	$0.995106\pi$
$24$	1.26217	+	1.18614i	0.257639	+	0.242120i
$25$	−6.37228			−1.27446
$26$	3.46410	−	1.00000i	0.679366	−	0.196116i
$27$	−3.31662	+	4.00000i	−0.638285	+	0.769800i
$28$	2.52434	−	0.792287i	0.477055	−	0.149728i
$29$			2.37686i			0.441372i	0.975345	+	0.220686i	$0.0708296\pi$
$29$			2.37686i			0.441372i	−0.975345	+	0.220686i	$0.929170\pi$
$30$	4.00000	−	4.25639i	0.730297	−	0.777107i
$31$	−4.10891			−0.737982			−0.368991	−	0.929433i	$-0.620297\pi$
$31$	−4.10891			−0.737982			−0.368991	+	0.929433i	$0.620297\pi$
$32$	1.00000			0.176777
$33$	−7.25061	−	6.81386i	−1.26217	−	1.18614i
$34$	−0.792287			−0.135876
$35$	−2.67181	−	8.51278i	−0.451619	−	1.43892i
$36$	0.186141	+	2.99422i	0.0310234	+	0.499037i
$37$			8.36530i			1.37525i	0.726067	+	0.687623i	$0.241346\pi$
$37$			8.36530i			1.37525i	−0.726067	+	0.687623i	$0.758654\pi$
$38$	2.37686			0.385578
$39$	5.55842	+	2.84674i	0.890060	+	0.455844i
$40$		−	3.37228i		−	0.533204i
$41$			8.37228i			1.30753i	0.756697	+	0.653765i	$0.226812\pi$
$41$			8.37228i			1.30753i	−0.756697	+	0.653765i	$0.773188\pi$
$42$	4.12590	+	1.99422i	0.636641	+	0.307715i
$43$	−2.62772			−0.400723			−0.200362	−	0.979722i	$-0.564212\pi$
$43$	−2.62772			−0.400723			−0.200362	+	0.979722i	$0.564212\pi$
$44$	−5.74456			−0.866025
$45$	10.0974	−	0.627719i	1.50522	−	0.0935748i
$46$			0.147477i			0.0217443i
$47$		−	10.3723i		−	1.51295i	−0.654021	−	0.756476i	$-0.726919\pi$
$47$		−	10.3723i		−	1.51295i	0.654021	−	0.756476i	$-0.273081\pi$
$48$	1.26217	+	1.18614i	0.182178	+	0.171205i
$49$	5.74456	−	4.00000i	0.820652	−	0.571429i
$50$	−6.37228			−0.901177
$51$	−1.00000	−	0.939764i	−0.140028	−	0.131593i
$52$	3.46410	−	1.00000i	0.480384	−	0.138675i
$53$			10.0974i			1.38698i	0.720467	+	0.693489i	$0.243927\pi$
$53$			10.0974i			1.38698i	−0.720467	+	0.693489i	$0.756073\pi$
$54$	−3.31662	+	4.00000i	−0.451335	+	0.544331i
$55$			19.3723i			2.61216i
$56$	2.52434	−	0.792287i	0.337329	−	0.105874i
$57$	3.00000	+	2.81929i	0.397360	+	0.373424i
$58$			2.37686i			0.312097i
$59$		−	2.74456i		−	0.357312i	−0.983912	−	0.178656i	$-0.942825\pi$
$59$		−	2.74456i		−	0.357312i	0.983912	−	0.178656i	$-0.0571749\pi$
$60$	4.00000	−	4.25639i	0.516398	−	0.549497i
$61$			7.74456i			0.991590i	0.868440	+	0.495795i	$0.165123\pi$
$61$			7.74456i			0.991590i	−0.868440	+	0.495795i	$0.834877\pi$
$62$	−4.10891			−0.521832
$63$	2.84216	+	7.41095i	0.358079	+	0.933691i
$64$	1.00000			0.125000
$65$	−3.37228	−	11.6819i	−0.418280	−	1.44896i
$66$	−7.25061	−	6.81386i	−0.892488	−	0.838728i
$67$		−	5.98844i		−	0.731604i	−0.930693	−	0.365802i	$-0.880795\pi$
$67$		−	5.98844i		−	0.731604i	0.930693	−	0.365802i	$-0.119205\pi$
$68$	−0.792287			−0.0960789
$69$	−0.174928	+	0.186141i	−0.0210589	+	0.0224087i
$70$	−2.67181	−	8.51278i	−0.319343	−	1.01747i
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$	0.186141	+	2.99422i	0.0219369	+	0.352872i
$73$	−10.2448			−1.19907			−0.599533	−	0.800350i	$-0.704647\pi$
$73$	−10.2448			−1.19907			−0.599533	+	0.800350i	$0.704647\pi$
$74$			8.36530i			0.972446i
$75$	−8.04290	−	7.55842i	−0.928714	−	0.872771i
$76$	2.37686			0.272645
$77$	−14.5012	+	4.55134i	−1.65257	+	0.518674i
$78$	5.55842	+	2.84674i	0.629367	+	0.322330i
$79$	−3.62772			−0.408150			−0.204075	−	0.978955i	$-0.565419\pi$
$79$	−3.62772			−0.408150			−0.204075	+	0.978955i	$0.565419\pi$
$80$		−	3.37228i		−	0.377033i
$81$	−8.93070	+	1.11469i	−0.992300	+	0.123855i
$82$			8.37228i			0.924564i
$83$		−	6.74456i		−	0.740312i	−0.928970	−	0.370156i	$-0.879304\pi$
$83$		−	6.74456i		−	0.740312i	0.928970	−	0.370156i	$-0.120696\pi$
$84$	4.12590	+	1.99422i	0.450173	+	0.217587i
$85$			2.67181i			0.289799i
$86$	−2.62772			−0.283354
$87$	−2.81929	+	3.00000i	−0.302260	+	0.321634i
$88$	−5.74456			−0.612372
$89$			10.0000i			1.06000i	0.847998	+	0.529999i	$0.177808\pi$
$89$			10.0000i			1.06000i	−0.847998	+	0.529999i	$0.822192\pi$
$90$	10.0974	−	0.627719i	1.06435	−	0.0661674i
$91$	7.95228	−	5.26890i	0.833625	−	0.552331i
$92$			0.147477i			0.0153755i
$93$	−5.18614	−	4.87375i	−0.537778	−	0.505384i
$94$		−	10.3723i		−	1.06982i
$95$		−	8.01544i		−	0.822367i
$96$	1.26217	+	1.18614i	0.128820	+	0.121060i
$97$	−9.15759			−0.929812			−0.464906	−	0.885360i	$-0.653912\pi$
$97$	−9.15759			−0.929812			−0.464906	+	0.885360i	$0.653912\pi$
$98$	5.74456	−	4.00000i	0.580288	−	0.404061i
$99$	−1.06930	−	17.2005i	−0.107468	−	1.72871i
$100$	−6.37228			−0.637228
$101$	17.6704			1.75827			0.879133	−	0.476576i	$-0.158122\pi$
$101$	17.6704			1.75827			0.879133	+	0.476576i	$0.158122\pi$
$102$	−1.00000	−	0.939764i	−0.0990148	−	0.0930505i
$103$		−	7.37228i		−	0.726412i	−0.931709	−	0.363206i	$-0.881682\pi$
$103$		−	7.37228i		−	0.726412i	0.931709	−	0.363206i	$-0.118318\pi$
$104$	3.46410	−	1.00000i	0.339683	−	0.0980581i
$105$	6.72507	−	13.9137i	0.656300	−	1.35784i
$106$			10.0974i			0.980741i
$107$		−	17.0256i		−	1.64592i	−0.568098	−	0.822961i	$-0.692320\pi$
$107$		−	17.0256i		−	1.64592i	0.568098	−	0.822961i	$-0.307680\pi$
$108$	−3.31662	+	4.00000i	−0.319142	+	0.384900i
$109$		−	19.6974i		−	1.88667i	−0.331848	−	0.943333i	$-0.607672\pi$
$109$		−	19.6974i		−	1.88667i	0.331848	−	0.943333i	$-0.392328\pi$
$110$			19.3723i			1.84707i
$111$	−9.92242	+	10.5584i	−0.941795	+	1.00216i
$112$	2.52434	−	0.792287i	0.238528	−	0.0748641i
$113$			5.69349i			0.535598i	0.963475	+	0.267799i	$0.0862963\pi$
$113$			5.69349i			0.535598i	−0.963475	+	0.267799i	$0.913704\pi$
$114$	3.00000	+	2.81929i	0.280976	+	0.264051i
$115$	0.497333			0.0463766
$116$			2.37686i			0.220686i
$117$	3.63903	+	10.1861i	0.336428	+	0.941709i
$118$		−	2.74456i		−	0.252657i
$119$	−2.00000	+	0.627719i	−0.183340	+	0.0575429i
$120$	4.00000	−	4.25639i	0.365148	−	0.388553i
$121$	22.0000			2.00000
$122$			7.74456i			0.701160i
$123$	−9.93070	+	10.5672i	−0.895421	+	0.952815i
$124$	−4.10891			−0.368991
$125$			4.62772i			0.413916i
$126$	2.84216	+	7.41095i	0.253200	+	0.660219i
$127$	−10.3723			−0.920391			−0.460196	−	0.887818i	$-0.652221\pi$
$127$	−10.3723			−0.920391			−0.460196	+	0.887818i	$0.652221\pi$
$128$	1.00000			0.0883883
$129$	−3.31662	−	3.11684i	−0.292013	−	0.274423i
$130$	−3.37228	−	11.6819i	−0.295769	−	1.02457i
$131$	3.96143			0.346112			0.173056	−	0.984912i	$-0.444636\pi$
$131$	3.96143			0.346112			0.173056	+	0.984912i	$0.444636\pi$
$132$	−7.25061	−	6.81386i	−0.631084	−	0.593070i
$133$	6.00000	−	1.88316i	0.520266	−	0.163290i
$134$		−	5.98844i		−	0.517322i
$135$	13.4891	+	11.1846i	1.16096	+	0.962616i
$136$	−0.792287			−0.0679380
$137$	−18.1168			−1.54783			−0.773913	−	0.633292i	$-0.781703\pi$
$137$	−18.1168			−1.54783			−0.773913	+	0.633292i	$0.781703\pi$
$138$	−0.174928	+	0.186141i	−0.0148909	+	0.0158453i
$139$		−	5.25544i		−	0.445760i	−0.974846	−	0.222880i	$-0.928454\pi$
$139$		−	5.25544i		−	0.445760i	0.974846	−	0.222880i	$-0.0715459\pi$
$140$	−2.67181	−	8.51278i	−0.225810	−	0.719461i
$141$	12.3030	−	13.0916i	1.03610	−	1.10251i
$142$	−2.00000			−0.167836
$143$	−19.8997	+	5.74456i	−1.66410	+	0.480384i
$144$	0.186141	+	2.99422i	0.0155117	+	0.249518i
$145$	8.01544			0.665646
$146$	−10.2448			−0.847868
$147$	11.9952	+	1.76518i	0.989345	+	0.145590i
$148$			8.36530i			0.687623i
$149$	−7.62772			−0.624887			−0.312444	−	0.949936i	$-0.601148\pi$
$149$	−7.62772			−0.624887			−0.312444	+	0.949936i	$0.601148\pi$
$150$	−8.04290	−	7.55842i	−0.656700	−	0.617143i
$151$			17.8178i			1.45000i	0.688751	+	0.724998i	$0.258159\pi$
$151$			17.8178i			1.45000i	−0.688751	+	0.724998i	$0.741841\pi$
$152$	2.37686			0.192789
$153$	−0.147477	−	2.37228i	−0.0119228	−	0.191788i
$154$	−14.5012	+	4.55134i	−1.16854	+	0.366758i
$155$			13.8564i			1.11297i
$156$	5.55842	+	2.84674i	0.445030	+	0.227922i
$157$		−	8.25544i		−	0.658856i	−0.944181	−	0.329428i	$-0.893144\pi$
$157$		−	8.25544i		−	0.658856i	0.944181	−	0.329428i	$-0.106856\pi$
$158$	−3.62772			−0.288606
$159$	−11.9769	+	12.7446i	−0.949828	+	1.01071i
$160$		−	3.37228i		−	0.266602i
$161$	0.116844	+	0.372281i	0.00920859	+	0.0293399i
$162$	−8.93070	+	1.11469i	−0.701662	+	0.0875785i
$163$			8.21782i			0.643670i	0.946796	+	0.321835i	$0.104300\pi$
$163$			8.21782i			0.643670i	−0.946796	+	0.321835i	$0.895700\pi$
$164$			8.37228i			0.653765i
$165$	−22.9783	+	24.4511i	−1.78885	+	1.90351i
$166$		−	6.74456i		−	0.523480i
$167$		−	12.6277i		−	0.977162i	−0.872518	−	0.488581i	$-0.837515\pi$
$167$		−	12.6277i		−	0.977162i	0.872518	−	0.488581i	$-0.162485\pi$
$168$	4.12590	+	1.99422i	0.318320	+	0.153857i
$169$	11.0000	−	6.92820i	0.846154	−	0.532939i
$170$			2.67181i			0.204919i
$171$	0.442430	+	7.11684i	0.0338335	+	0.544239i
$172$	−2.62772			−0.200362
$173$	10.6873			0.812537			0.406269	−	0.913754i	$-0.366830\pi$
$173$	10.6873			0.812537			0.406269	+	0.913754i	$0.366830\pi$
$174$	−2.81929	+	3.00000i	−0.213730	+	0.227429i
$175$	−16.0858	+	5.04868i	−1.21597	+	0.381644i
$176$	−5.74456			−0.433013
$177$	3.25544	−	3.46410i	0.244694	−	0.260378i
$178$			10.0000i			0.749532i
$179$			20.1947i			1.50942i	0.656057	+	0.754711i	$0.272223\pi$
$179$			20.1947i			1.50942i	−0.656057	+	0.754711i	$0.727777\pi$
$180$	10.0974	−	0.627719i	0.752612	−	0.0467874i
$181$		−	20.3723i		−	1.51426i	−0.653264	−	0.757130i	$-0.726601\pi$
$181$		−	20.3723i		−	1.51426i	0.653264	−	0.757130i	$-0.273399\pi$
$182$	7.95228	−	5.26890i	0.589462	−	0.390557i
$183$	−9.18614	+	9.77495i	−0.679059	+	0.722585i
$184$			0.147477i			0.0108721i
$185$	28.2101			2.07405
$186$	−5.18614	−	4.87375i	−0.380266	−	0.357360i
$187$	4.55134			0.332827
$188$		−	10.3723i		−	0.756476i
$189$	−5.20313	+	12.7251i	−0.378472	+	0.925613i
$190$		−	8.01544i		−	0.581501i
$191$			2.96677i			0.214668i	0.994223	+	0.107334i	$0.0342314\pi$
$191$			2.96677i			0.214668i	−0.994223	+	0.107334i	$0.965769\pi$
$192$	1.26217	+	1.18614i	0.0910892	+	0.0856023i
$193$			20.7846i			1.49611i	0.663637	+	0.748054i	$0.269012\pi$
$193$			20.7846i			1.49611i	−0.663637	+	0.748054i	$0.730988\pi$
$194$	−9.15759			−0.657476
$195$	9.60002	−	18.7446i	0.687472	−	1.34233i
$196$	5.74456	−	4.00000i	0.410326	−	0.285714i
$197$	21.1168			1.50451			0.752256	−	0.658870i	$-0.228965\pi$
$197$	21.1168			1.50451			0.752256	+	0.658870i	$0.228965\pi$
$198$	−1.06930	−	17.2005i	−0.0759916	−	1.22239i
$199$			12.1168i			0.858940i	0.903081	+	0.429470i	$0.141300\pi$
$199$			12.1168i			0.858940i	−0.903081	+	0.429470i	$0.858700\pi$
$200$	−6.37228			−0.450588
$201$	7.10313	−	7.55842i	0.501016	−	0.533130i
$202$	17.6704			1.24328
$203$	1.88316	+	6.00000i	0.132172	+	0.421117i
$204$	−1.00000	−	0.939764i	−0.0700140	−	0.0657966i
$205$	28.2337			1.97193
$206$		−	7.37228i		−	0.513651i
$207$	−0.441578	+	0.0274514i	−0.0306918	+	0.00190801i
$208$	3.46410	−	1.00000i	0.240192	−	0.0693375i
$209$	−13.6540			−0.944469
$210$	6.72507	−	13.9137i	0.464074	−	0.960137i
$211$	17.3723			1.19596			0.597979	−	0.801512i	$-0.295971\pi$
$211$	17.3723			1.19596			0.597979	+	0.801512i	$0.295971\pi$
$212$			10.0974i			0.693489i
$213$	−2.52434	−	2.37228i	−0.172965	−	0.162546i
$214$		−	17.0256i		−	1.16384i
$215$			8.86141i			0.604343i
$216$	−3.31662	+	4.00000i	−0.225668	+	0.272166i
$217$	−10.3723	+	3.25544i	−0.704116	+	0.220993i
$218$		−	19.6974i		−	1.33407i
$219$	−12.9307	−	12.1518i	−0.873776	−	0.821143i
$220$			19.3723i			1.30608i
$221$	−2.74456	+	0.792287i	−0.184619	+	0.0532950i
$222$	−9.92242	+	10.5584i	−0.665949	+	0.708635i
$223$	−0.644810			−0.0431797			−0.0215898	−	0.999767i	$-0.506873\pi$
$223$	−0.644810			−0.0431797			−0.0215898	+	0.999767i	$0.506873\pi$
$224$	2.52434	−	0.792287i	0.168664	−	0.0529369i
$225$	−1.18614	−	19.0800i	−0.0790760	−	1.27200i
$226$			5.69349i			0.378725i
$227$		−	11.4891i		−	0.762560i	−0.924460	−	0.381280i	$-0.875483\pi$
$227$		−	11.4891i		−	0.762560i	0.924460	−	0.381280i	$-0.124517\pi$
$228$	3.00000	+	2.81929i	0.198680	+	0.186712i
$229$	5.04868			0.333626			0.166813	−	0.985989i	$-0.446652\pi$
$229$	5.04868			0.333626			0.166813	+	0.985989i	$0.446652\pi$
$230$	0.497333			0.0327932
$231$	−23.7015	−	11.4559i	−1.55945	−	0.753744i
$232$			2.37686i			0.156049i
$233$		−	10.7422i		−	0.703742i	−0.936048	−	0.351871i	$-0.885546\pi$
$233$		−	10.7422i		−	0.703742i	0.936048	−	0.351871i	$-0.114454\pi$
$234$	3.63903	+	10.1861i	0.237891	+	0.665889i
$235$	−34.9783			−2.28173
$236$		−	2.74456i		−	0.178656i
$237$	−4.57879	−	4.30298i	−0.297425	−	0.279509i
$238$	−2.00000	+	0.627719i	−0.129641	+	0.0406890i
$239$	18.0000			1.16432			0.582162	−	0.813073i	$-0.302207\pi$
$239$	18.0000			1.16432			0.582162	+	0.813073i	$0.302207\pi$
$240$	4.00000	−	4.25639i	0.258199	−	0.274749i
$241$	16.4356			1.05871			0.529357	−	0.848399i	$-0.322433\pi$
$241$	16.4356			1.05871			0.529357	+	0.848399i	$0.322433\pi$
$242$	22.0000			1.41421
$243$	−12.5942	−	9.18614i	−0.807921	−	0.589291i
$244$			7.74456i			0.495795i
$245$	−13.4891	−	19.3723i	−0.861789	−	1.23765i
$246$	−9.93070	+	10.5672i	−0.633159	+	0.673742i
$247$	8.23369	−	2.37686i	0.523897	−	0.151236i
$248$	−4.10891			−0.260916
$249$	8.00000	−	8.51278i	0.506979	−	0.539475i
$250$			4.62772i			0.292683i
$251$	6.78073			0.427996			0.213998	−	0.976834i	$-0.431351\pi$
$251$	6.78073			0.427996			0.213998	+	0.976834i	$0.431351\pi$
$252$	2.84216	+	7.41095i	0.179039	+	0.466846i
$253$		−	0.847190i		−	0.0532624i
$254$	−10.3723			−0.650815
$255$	−3.16915	+	3.37228i	−0.198460	+	0.211180i
$256$	1.00000			0.0625000
$257$	18.9051			1.17927			0.589633	−	0.807671i	$-0.299272\pi$
$257$	18.9051			1.17927			0.589633	+	0.807671i	$0.299272\pi$
$258$	−3.31662	−	3.11684i	−0.206484	−	0.194046i
$259$	6.62772	+	21.1168i	0.411826	+	1.31214i
$260$	−3.37228	−	11.6819i	−0.209140	−	0.724482i
$261$	−7.11684	+	0.442430i	−0.440522	+	0.0273858i
$262$	3.96143			0.244738
$263$		−	7.22316i		−	0.445399i	−0.974887	−	0.222699i	$-0.928513\pi$
$263$		−	7.22316i		−	0.445399i	0.974887	−	0.222699i	$-0.0714869\pi$
$264$	−7.25061	−	6.81386i	−0.446244	−	0.419364i
$265$	34.0511			2.09174
$266$	6.00000	−	1.88316i	0.367884	−	0.115464i
$267$	−11.8614	+	12.6217i	−0.725906	+	0.772435i
$268$		−	5.98844i		−	0.365802i
$269$	−14.5012			−0.884155			−0.442077	−	0.896977i	$-0.645758\pi$
$269$	−14.5012			−0.884155			−0.442077	+	0.896977i	$0.645758\pi$
$270$	13.4891	+	11.1846i	0.820922	+	0.680673i
$271$	−11.3321			−0.688374			−0.344187	−	0.938901i	$-0.611845\pi$
$271$	−11.3321			−0.688374			−0.344187	+	0.938901i	$0.611845\pi$
$272$	−0.792287			−0.0480395
$273$	16.2868	+	2.78228i	0.985720	+	0.168391i
$274$	−18.1168			−1.09448
$275$	36.6060			2.20742
$276$	−0.174928	+	0.186141i	−0.0105294	+	0.0112044i
$277$	17.4891			1.05082			0.525410	−	0.850849i	$-0.323912\pi$
$277$	17.4891			1.05082			0.525410	+	0.850849i	$0.323912\pi$
$278$		−	5.25544i		−	0.315200i
$279$	−0.764836	−	12.3030i	−0.0457895	−	0.736560i
$280$	−2.67181	−	8.51278i	−0.159671	−	0.508736i
$281$	−14.0000			−0.835170			−0.417585	−	0.908638i	$-0.637123\pi$
$281$	−14.0000			−0.835170			−0.417585	+	0.908638i	$0.637123\pi$
$282$	12.3030	−	13.0916i	0.732632	−	0.779592i
$283$		−	0.372281i		−	0.0221298i	−0.999939	−	0.0110649i	$-0.996478\pi$
$283$		−	0.372281i		−	0.0221298i	0.999939	−	0.0110649i	$-0.00352214\pi$
$284$	−2.00000			−0.118678
$285$	9.50744	−	10.1168i	0.563172	−	0.599270i
$286$	−19.8997	+	5.74456i	−1.17670	+	0.339683i
$287$	6.63325	+	21.1345i	0.391548	+	1.24753i
$288$	0.186141	+	2.99422i	0.0109684	+	0.176436i
$289$	−16.3723			−0.963075
$290$	8.01544			0.470683
$291$	−11.5584	−	10.8622i	−0.677567	−	0.636753i
$292$	−10.2448			−0.599533
$293$			11.4891i			0.671202i	0.942004	+	0.335601i	$0.108939\pi$
$293$			11.4891i			0.671202i	−0.942004	+	0.335601i	$0.891061\pi$
$294$	11.9952	+	1.76518i	0.699573	+	0.102948i
$295$	−9.25544			−0.538872
$296$			8.36530i			0.486223i
$297$	19.0526	−	22.9783i	1.10554	−	1.33333i
$298$	−7.62772			−0.441862
$299$	0.147477	+	0.510875i	0.00852880	+	0.0295446i
$300$	−8.04290	−	7.55842i	−0.464357	−	0.436386i
$301$	−6.63325	+	2.08191i	−0.382334	+	0.119999i
$302$			17.8178i			1.02530i
$303$	22.3030	+	20.9595i	1.28127	+	1.20409i
$304$	2.37686			0.136322
$305$	26.1168			1.49545
$306$	−0.147477	−	2.37228i	−0.00843069	−	0.135614i
$307$	31.8766			1.81930			0.909648	−	0.415381i	$-0.136352\pi$
$307$	31.8766			1.81930			0.909648	+	0.415381i	$0.136352\pi$
$308$	−14.5012	+	4.55134i	−0.826284	+	0.259337i
$309$	8.74456	−	9.30506i	0.497461	−	0.529347i
$310$			13.8564i			0.786991i
$311$	−10.3923			−0.589294			−0.294647	−	0.955606i	$-0.595202\pi$
$311$	−10.3923			−0.589294			−0.294647	+	0.955606i	$0.595202\pi$
$312$	5.55842	+	2.84674i	0.314684	+	0.161165i
$313$			2.74456i			0.155132i	0.996987	+	0.0775659i	$0.0247148\pi$
$313$			2.74456i			0.155132i	−0.996987	+	0.0775659i	$0.975285\pi$
$314$		−	8.25544i		−	0.465881i
$315$	24.9918	−	9.58457i	1.40813	−	0.540030i
$316$	−3.62772			−0.204075
$317$	−3.86141			−0.216878			−0.108439	−	0.994103i	$-0.534585\pi$
$317$	−3.86141			−0.216878			−0.108439	+	0.994103i	$0.534585\pi$
$318$	−11.9769	+	12.7446i	−0.671630	+	0.714680i
$319$		−	13.6540i		−	0.764479i
$320$		−	3.37228i		−	0.188516i
$321$	20.1947	−	21.4891i	1.12716	−	1.19941i
$322$	0.116844	+	0.372281i	0.00651146	+	0.0207464i
$323$	−1.88316			−0.104782
$324$	−8.93070	+	1.11469i	−0.496150	+	0.0619273i
$325$	−22.0742	+	6.37228i	−1.22446	+	0.353471i
$326$			8.21782i			0.455143i
$327$	23.3639	−	24.8614i	1.29202	−	1.37484i
$328$			8.37228i			0.462282i
$329$	−8.21782	−	26.1831i	−0.453063	−	1.44352i
$330$	−22.9783	+	24.4511i	−1.26491	+	1.34599i
$331$		−	17.0805i		−	0.938827i	−0.882979	−	0.469413i	$-0.844465\pi$
$331$		−	17.0805i		−	0.938827i	0.882979	−	0.469413i	$-0.155535\pi$
$332$		−	6.74456i		−	0.370156i
$333$	−25.0475	+	1.55712i	−1.37260	+	0.0853298i
$334$		−	12.6277i		−	0.690958i
$335$	−20.1947			−1.10335
$336$	4.12590	+	1.99422i	0.225087	+	0.108794i
$337$	5.00000			0.272367			0.136184	−	0.990684i	$-0.456516\pi$
$337$	5.00000			0.272367			0.136184	+	0.990684i	$0.456516\pi$
$338$	11.0000	−	6.92820i	0.598321	−	0.376845i
$339$	−6.75327	+	7.18614i	−0.366788	+	0.390298i
$340$			2.67181i			0.144899i
$341$	23.6039			1.27822
$342$	0.442430	+	7.11684i	0.0239239	+	0.384835i
$343$	11.3321	−	14.6487i	0.611874	−	0.790955i
$344$	−2.62772			−0.141677
$345$	0.627719	+	0.589907i	0.0337952	+	0.0317595i
$346$	10.6873			0.574551
$347$			19.2000i			1.03071i	0.856976	+	0.515356i	$0.172340\pi$
$347$			19.2000i			1.03071i	−0.856976	+	0.515356i	$0.827660\pi$
$348$	−2.81929	+	3.00000i	−0.151130	+	0.160817i
$349$	−16.4356			−0.879780			−0.439890	−	0.898052i	$-0.644983\pi$
$349$	−16.4356			−0.879780			−0.439890	+	0.898052i	$0.644983\pi$
$350$	−16.0858	+	5.04868i	−0.859822	+	0.269863i
$351$	−7.48913	+	17.1730i	−0.399740	+	0.916629i
$352$	−5.74456			−0.306186
$353$			11.1168i			0.591690i	0.955236	+	0.295845i	$0.0956012\pi$
$353$			11.1168i			0.591690i	−0.955236	+	0.295845i	$0.904399\pi$
$354$	3.25544	−	3.46410i	0.173025	−	0.184115i
$355$			6.74456i			0.357964i
$356$			10.0000i			0.529999i
$357$	−3.26890	−	1.57999i	−0.173009	−	0.0836222i
$358$			20.1947i			1.06732i
$359$	6.23369			0.329001			0.164501	−	0.986377i	$-0.447399\pi$
$359$	6.23369			0.329001			0.164501	+	0.986377i	$0.447399\pi$
$360$	10.0974	−	0.627719i	0.532177	−	0.0330837i
$361$	−13.3505			−0.702660
$362$		−	20.3723i		−	1.07074i
$363$	27.7677	+	26.0951i	1.45743	+	1.36964i
$364$	7.95228	−	5.26890i	0.416812	−	0.276165i
$365$			34.5484i			1.80835i
$366$	−9.18614	+	9.77495i	−0.480167	+	0.510945i
$367$		−	4.74456i		−	0.247664i	−0.992303	−	0.123832i	$-0.960482\pi$
$367$		−	4.74456i		−	0.247664i	0.992303	−	0.123832i	$-0.0395184\pi$
$368$			0.147477i			0.00768776i
$369$	−25.0684	+	1.55842i	−1.30501	+	0.0811282i
$370$	28.2101			1.46658
$371$	8.00000	+	25.4891i	0.415339	+	1.32333i
$372$	−5.18614	−	4.87375i	−0.268889	−	0.252692i
$373$	−12.2337			−0.633436			−0.316718	−	0.948520i	$-0.602581\pi$
$373$	−12.2337			−0.633436			−0.316718	+	0.948520i	$0.602581\pi$
$374$	4.55134			0.235344
$375$	−5.48913	+	5.84096i	−0.283457	+	0.301626i
$376$		−	10.3723i		−	0.534910i
$377$	2.37686	+	8.23369i	0.122415	+	0.424057i
$378$	−5.20313	+	12.7251i	−0.267620	+	0.654507i
$379$		−	18.3152i		−	0.940787i	−0.882457	−	0.470394i	$-0.844112\pi$
$379$		−	18.3152i		−	0.940787i	0.882457	−	0.470394i	$-0.155888\pi$
$380$		−	8.01544i		−	0.411184i
$381$	−13.0916	−	12.3030i	−0.670701	−	0.630301i
$382$			2.96677i			0.151793i
$383$		−	3.51087i		−	0.179397i	−0.995969	−	0.0896987i	$-0.971410\pi$
$383$		−	3.51087i		−	0.179397i	0.995969	−	0.0896987i	$-0.0285904\pi$
$384$	1.26217	+	1.18614i	0.0644098	+	0.0605300i
$385$	15.3484	+	48.9022i	0.782227	+	2.49229i
$386$			20.7846i			1.05791i
$387$	−0.489125	−	7.86797i	−0.0248636	−	0.399951i
$388$	−9.15759			−0.464906
$389$		−	25.2434i		−	1.27989i	−0.768421	−	0.639945i	$-0.778957\pi$
$389$		−	25.2434i		−	1.27989i	0.768421	−	0.639945i	$-0.221043\pi$
$390$	9.60002	−	18.7446i	0.486116	−	0.949168i
$391$		−	0.116844i		−	0.00590905i
$392$	5.74456	−	4.00000i	0.290144	−	0.202031i
$393$	5.00000	+	4.69882i	0.252217	+	0.237024i
$394$	21.1168			1.06385
$395$			12.2337i			0.615544i
$396$	−1.06930	−	17.2005i	−0.0537342	−	0.864357i
$397$	−6.63325			−0.332913			−0.166457	−	0.986049i	$-0.553233\pi$
$397$	−6.63325			−0.332913			−0.166457	+	0.986049i	$0.553233\pi$
$398$			12.1168i			0.607363i
$399$	9.80670	+	4.73998i	0.490949	+	0.237296i
$400$	−6.37228			−0.318614
$401$	28.9783			1.44710			0.723552	−	0.690269i	$-0.242508\pi$
$401$	28.9783			1.44710			0.723552	+	0.690269i	$0.242508\pi$
$402$	7.10313	−	7.55842i	0.354272	−	0.376980i
$403$	−14.2337	+	4.10891i	−0.709030	+	0.204679i
$404$	17.6704			0.879133
$405$	3.75906	+	30.1168i	0.186789	+	1.49652i
$406$	1.88316	+	6.00000i	0.0934595	+	0.297775i
$407$		−	48.0550i		−	2.38200i
$408$	−1.00000	−	0.939764i	−0.0495074	−	0.0465252i
$409$	−29.7947			−1.47325			−0.736627	−	0.676299i	$-0.763583\pi$
$409$	−29.7947			−1.47325			−0.736627	+	0.676299i	$0.763583\pi$
$410$	28.2337			1.39436
$411$	−22.8665	−	21.4891i	−1.12792	−	1.05998i
$412$		−	7.37228i		−	0.363206i
$413$	−2.17448	−	6.92820i	−0.106999	−	0.340915i
$414$	−0.441578	+	0.0274514i	−0.0217024	+	0.00134916i
$415$	−22.7446			−1.11649
$416$	3.46410	−	1.00000i	0.169842	−	0.0490290i
$417$	6.23369	−	6.63325i	0.305265	−	0.324832i
$418$	−13.6540			−0.667840
$419$	−4.90120			−0.239439			−0.119720	−	0.992808i	$-0.538200\pi$
$419$	−4.90120			−0.239439			−0.119720	+	0.992808i	$0.538200\pi$
$420$	6.72507	−	13.9137i	0.328150	−	0.678920i
$421$			23.0140i			1.12163i	0.827940	+	0.560817i	$0.189513\pi$
$421$			23.0140i			1.12163i	−0.827940	+	0.560817i	$0.810487\pi$
$422$	17.3723			0.845669
$423$	31.0569	−	1.93070i	1.51004	−	0.0938740i
$424$			10.0974i			0.490371i
$425$	5.04868			0.244897
$426$	−2.52434	−	2.37228i	−0.122305	−	0.114937i
$427$	6.13592	+	19.5499i	0.296938	+	0.946086i
$428$		−	17.0256i		−	0.822961i
$429$	−31.9307	−	16.3533i	−1.54163	−	0.789544i
$430$			8.86141i			0.427335i
$431$	−28.2337			−1.35997			−0.679984	−	0.733227i	$-0.738013\pi$
$431$	−28.2337			−1.35997			−0.679984	+	0.733227i	$0.738013\pi$
$432$	−3.31662	+	4.00000i	−0.159571	+	0.192450i
$433$		−	30.4674i		−	1.46417i	−0.681214	−	0.732084i	$-0.738548\pi$
$433$		−	30.4674i		−	1.46417i	0.681214	−	0.732084i	$-0.261452\pi$
$434$	−10.3723	+	3.25544i	−0.497885	+	0.156266i
$435$	10.1168	+	9.50744i	0.485066	+	0.455847i
$436$		−	19.6974i		−	0.943333i
$437$			0.350532i			0.0167682i
$438$	−12.9307	−	12.1518i	−0.617853	−	0.580636i
$439$		−	5.60597i		−	0.267558i	−0.991011	−	0.133779i	$-0.957289\pi$
$439$		−	5.60597i		−	0.267558i	0.991011	−	0.133779i	$-0.0427113\pi$
$440$			19.3723i			0.923537i
$441$	13.0462	+	16.4559i	0.621246	+	0.783615i
$442$	−2.74456	+	0.792287i	−0.130546	+	0.0376852i
$443$			16.7306i			0.794895i	0.917625	+	0.397447i	$0.130104\pi$
$443$			16.7306i			0.794895i	−0.917625	+	0.397447i	$0.869896\pi$
$444$	−9.92242	+	10.5584i	−0.470897	+	0.501081i
$445$	33.7228			1.59861
$446$	−0.644810			−0.0305326
$447$	−9.62747	−	9.04755i	−0.455364	−	0.427934i
$448$	2.52434	−	0.792287i	0.119264	−	0.0374320i
$449$	14.1168			0.666215			0.333108	−	0.942889i	$-0.391903\pi$
$449$	14.1168			0.666215			0.333108	+	0.942889i	$0.391903\pi$
$450$	−1.18614	−	19.0800i	−0.0559152	−	0.899440i
$451$		−	48.0951i		−	2.26471i
$452$			5.69349i			0.267799i
$453$	−21.1345	+	22.4891i	−0.992984	+	1.05663i
$454$		−	11.4891i		−	0.539211i
$455$	−17.7682	−	26.8173i	−0.832987	−	1.25721i
$456$	3.00000	+	2.81929i	0.140488	+	0.132025i
$457$		−	23.6588i		−	1.10671i	−0.832945	−	0.553356i	$-0.813347\pi$
$457$		−	23.6588i		−	1.10671i	0.832945	−	0.553356i	$-0.186653\pi$
$458$	5.04868			0.235909
$459$	2.62772	−	3.16915i	0.122651	−	0.147923i
$460$	0.497333			0.0231883
$461$		−	21.6060i		−	1.00629i	−0.864202	−	0.503145i	$-0.832176\pi$
$461$		−	21.6060i		−	1.00629i	0.864202	−	0.503145i	$-0.167824\pi$
$462$	−23.7015	−	11.4559i	−1.10269	−	0.532978i
$463$		−	31.6742i		−	1.47203i	−0.676967	−	0.736014i	$-0.736706\pi$
$463$		−	31.6742i		−	1.47203i	0.676967	−	0.736014i	$-0.263294\pi$
$464$			2.37686i			0.110343i
$465$	−16.4356	+	17.4891i	−0.762185	+	0.811039i
$466$		−	10.7422i		−	0.497621i
$467$	21.5769			0.998460			0.499230	−	0.866470i	$-0.333616\pi$
$467$	21.5769			0.998460			0.499230	+	0.866470i	$0.333616\pi$
$468$	3.63903	+	10.1861i	0.168214	+	0.470855i
$469$	−4.74456	−	15.1168i	−0.219084	−	0.698031i
$470$	−34.9783			−1.61343
$471$	9.79211	−	10.4198i	0.451197	−	0.480117i
$472$		−	2.74456i		−	0.126329i
$473$	15.0951			0.694073
$474$	−4.57879	−	4.30298i	−0.210311	−	0.197643i
$475$	−15.1460			−0.694947
$476$	−2.00000	+	0.627719i	−0.0916698	+	0.0287714i
$477$	−30.2337	+	1.87953i	−1.38431	+	0.0860577i
$478$	18.0000			0.823301
$479$			28.6277i			1.30803i	0.756480	+	0.654017i	$0.226918\pi$
$479$			28.6277i			1.30803i	−0.756480	+	0.654017i	$0.773082\pi$
$480$	4.00000	−	4.25639i	0.182574	−	0.194277i
$481$	8.36530	+	28.9783i	0.381425	+	1.32129i
$482$	16.4356			0.748623
$483$	−0.294101	+	0.608475i	−0.0133821	+	0.0276866i
$484$	22.0000			1.00000
$485$			30.8820i			1.40228i
$486$	−12.5942	−	9.18614i	−0.571286	−	0.416692i
$487$			37.5152i			1.69998i	0.526802	+	0.849988i	$0.323391\pi$
$487$			37.5152i			1.69998i	−0.526802	+	0.849988i	$0.676609\pi$
$488$			7.74456i			0.350580i
$489$	−9.74749	+	10.3723i	−0.440797	+	0.469051i
$490$	−13.4891	−	19.3723i	−0.609377	−	0.875150i
$491$			11.6819i			0.527198i	0.964632	+	0.263599i	$0.0849095\pi$
$491$			11.6819i			0.527198i	−0.964632	+	0.263599i	$0.915090\pi$
$492$	−9.93070	+	10.5672i	−0.447711	+	0.476408i
$493$		−	1.88316i		−	0.0848131i
$494$	8.23369	−	2.37686i	0.370451	−	0.106940i
$495$	−58.0049	+	3.60597i	−2.60712	+	0.162076i
$496$	−4.10891			−0.184496
$497$	−5.04868	+	1.58457i	−0.226464	+	0.0710779i
$498$	8.00000	−	8.51278i	0.358489	−	0.381467i
$499$		−	10.4472i		−	0.467681i	−0.972275	−	0.233841i	$-0.924871\pi$
$499$		−	10.4472i		−	0.467681i	0.972275	−	0.233841i	$-0.0751294\pi$
$500$			4.62772i			0.206958i
$501$	14.9783	−	15.9383i	0.669179	−	0.712071i
$502$	6.78073			0.302639
$503$	−27.4179			−1.22250			−0.611251	−	0.791437i	$-0.709333\pi$
$503$	−27.4179			−1.22250			−0.611251	+	0.791437i	$0.709333\pi$
$504$	2.84216	+	7.41095i	0.126600	+	0.330110i
$505$		−	59.5894i		−	2.65170i
$506$		−	0.847190i		−	0.0376622i
$507$	22.1017	+	4.30298i	0.981570	+	0.191102i
$508$	−10.3723			−0.460196
$509$			22.1168i			0.980312i	0.871635	+	0.490156i	$0.163060\pi$
$509$			22.1168i			0.980312i	−0.871635	+	0.490156i	$0.836940\pi$
$510$	−3.16915	+	3.37228i	−0.140332	+	0.149327i
$511$	−25.8614	+	8.11684i	−1.14404	+	0.359068i
$512$	1.00000			0.0441942
$513$	−7.88316	+	9.50744i	−0.348050	+	0.419764i
$514$	18.9051			0.833867
$515$	−24.8614			−1.09552
$516$	−3.31662	−	3.11684i	−0.146006	−	0.137211i
$517$			59.5842i			2.62051i
$518$	6.62772	+	21.1168i	0.291205	+	0.927821i
$519$	13.4891	+	12.6766i	0.592107	+	0.556441i
$520$	−3.37228	−	11.6819i	−0.147884	−	0.512286i
$521$	20.3971			0.893612			0.446806	−	0.894631i	$-0.352561\pi$
$521$	20.3971			0.893612			0.446806	+	0.894631i	$0.352561\pi$
$522$	−7.11684	+	0.442430i	−0.311496	+	0.0193647i
$523$		−	37.3505i		−	1.63322i	−0.577186	−	0.816612i	$-0.695849\pi$
$523$		−	37.3505i		−	1.63322i	0.577186	−	0.816612i	$-0.304151\pi$
$524$	3.96143			0.173056
$525$	−26.2914	−	12.7077i	−1.14745	−	0.554611i
$526$		−	7.22316i		−	0.314945i
$527$	3.25544			0.141809
$528$	−7.25061	−	6.81386i	−0.315542	−	0.296535i
$529$	22.9783			0.999054
$530$	34.0511			1.47909
$531$	8.21782	−	0.510875i	0.356623	−	0.0221701i
$532$	6.00000	−	1.88316i	0.260133	−	0.0816452i
$533$	8.37228	+	29.0024i	0.362644	+	1.25623i
$534$	−11.8614	+	12.6217i	−0.513293	+	0.546194i
$535$	−57.4150			−2.48227
$536$		−	5.98844i		−	0.258661i
$537$	−23.9538	+	25.4891i	−1.03368	+	1.09994i
$538$	−14.5012			−0.625192
$539$	−33.0000	+	22.9783i	−1.42141	+	0.989743i
$540$	13.4891	+	11.1846i	0.580480	+	0.481308i
$541$			24.4511i			1.05123i	0.850721	+	0.525617i	$0.176166\pi$
$541$			24.4511i			1.05123i	−0.850721	+	0.525617i	$0.823834\pi$
$542$	−11.3321			−0.486754
$543$	24.1644	−	25.7133i	1.03699	−	1.10346i
$544$	−0.792287			−0.0339690
$545$	−66.4251			−2.84534
$546$	16.2868	+	2.78228i	0.697009	+	0.119070i
$547$	−5.48913			−0.234698			−0.117349	−	0.993091i	$-0.537440\pi$
$547$	−5.48913			−0.234698			−0.117349	+	0.993091i	$0.537440\pi$
$548$	−18.1168			−0.773913
$549$	−23.1889	+	1.44158i	−0.989679	+	0.0615251i
$550$	36.6060			1.56088
$551$			5.64947i			0.240675i
$552$	−0.174928	+	0.186141i	−0.00744544	+	0.00792267i
$553$	−9.15759	+	2.87419i	−0.389420	+	0.122223i
$554$	17.4891			0.743042
$555$	35.6060	+	33.4612i	1.51139	+	1.42035i
$556$		−	5.25544i		−	0.222880i
$557$	30.3723			1.28691			0.643457	−	0.765482i	$-0.277499\pi$
$557$	30.3723			1.28691			0.643457	+	0.765482i	$0.277499\pi$
$558$	−0.764836	−	12.3030i	−0.0323781	−	0.520827i
$559$	−9.10268	+	2.62772i	−0.385003	+	0.111141i
$560$	−2.67181	−	8.51278i	−0.112905	−	0.359730i
$561$	5.74456	+	5.39853i	0.242536	+	0.227926i
$562$	−14.0000			−0.590554
$563$	9.25016			0.389848			0.194924	−	0.980818i	$-0.437554\pi$
$563$	9.25016			0.389848			0.194924	+	0.980818i	$0.437554\pi$
$564$	12.3030	−	13.0916i	0.518049	−	0.551255i
$565$	19.2000			0.807752
$566$		−	0.372281i		−	0.0156482i
$567$	−21.6610	+	9.88954i	−0.909675	+	0.415322i
$568$	−2.00000			−0.0839181
$569$			10.1523i			0.425605i	0.977095	+	0.212802i	$0.0682590\pi$
$569$			10.1523i			0.425605i	−0.977095	+	0.212802i	$0.931741\pi$
$570$	9.50744	−	10.1168i	0.398223	−	0.423748i
$571$	−20.0000			−0.836974			−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000			−0.836974			−0.418487	+	0.908223i	$0.637439\pi$
$572$	−19.8997	+	5.74456i	−0.832050	+	0.240192i
$573$	−3.51900	+	3.74456i	−0.147009	+	0.156431i
$574$	6.63325	+	21.1345i	0.276866	+	0.882136i
$575$		−	0.939764i		−	0.0391909i
$576$	0.186141	+	2.99422i	0.00775586	+	0.124759i
$577$	−6.92820			−0.288425			−0.144212	−	0.989547i	$-0.546065\pi$
$577$	−6.92820			−0.288425			−0.144212	+	0.989547i	$0.546065\pi$
$578$	−16.3723			−0.680997
$579$	−24.6535	+	26.2337i	−1.02456	+	1.09023i
$580$	8.01544			0.332823
$581$	−5.34363	−	17.0256i	−0.221691	−	0.706339i
$582$	−11.5584	−	10.8622i	−0.479112	−	0.450252i
$583$		−	58.0049i		−	2.40232i
$584$	−10.2448			−0.423934
$585$	34.3505	−	12.2718i	1.42022	−	0.507378i
$586$			11.4891i			0.474611i
$587$		−	16.7446i		−	0.691122i	−0.938396	−	0.345561i	$-0.887689\pi$
$587$		−	16.7446i		−	0.691122i	0.938396	−	0.345561i	$-0.112311\pi$
$588$	11.9952	+	1.76518i	0.494673	+	0.0727950i
$589$	−9.76631			−0.402414
$590$	−9.25544			−0.381040
$591$	26.6530	+	25.0475i	1.09636	+	1.03032i
$592$			8.36530i			0.343812i
$593$			19.2554i			0.790726i	0.918525	+	0.395363i	$0.129381\pi$
$593$			19.2554i			0.790726i	−0.918525	+	0.395363i	$0.870619\pi$
$594$	19.0526	−	22.9783i	0.781736	−	0.942809i
$595$	2.11684	+	6.74456i	0.0867821	+	0.276500i
$596$	−7.62772			−0.312444
$597$	−14.3723	+	15.2935i	−0.588218	+	0.625921i
$598$	0.147477	+	0.510875i	0.00603078	+	0.0208912i
$599$		−	11.8294i		−	0.483336i	−0.970359	−	0.241668i	$-0.922305\pi$
$599$		−	11.8294i		−	0.483336i	0.970359	−	0.241668i	$-0.0776945\pi$
$600$	−8.04290	−	7.55842i	−0.328350	−	0.308571i
$601$		−	26.0000i		−	1.06056i	−0.847822	−	0.530281i	$-0.822086\pi$
$601$		−	26.0000i		−	1.06056i	0.847822	−	0.530281i	$-0.177914\pi$
$602$	−6.63325	+	2.08191i	−0.270351	+	0.0848522i
$603$	17.9307	−	1.11469i	0.730195	−	0.0453938i
$604$			17.8178i			0.724998i
$605$		−	74.1902i		−	3.01626i
$606$	22.3030	+	20.9595i	0.905997	+	0.851423i
$607$			18.1168i			0.735340i	0.929956	+	0.367670i	$0.119844\pi$
$607$			18.1168i			0.735340i	−0.929956	+	0.367670i	$0.880156\pi$
$608$	2.37686			0.0963944
$609$	−4.73998	+	9.80670i	−0.192074	+	0.397388i
$610$	26.1168			1.05744
$611$	−10.3723	−	35.9306i	−0.419618	−	1.45360i
$612$	−0.147477	−	2.37228i	−0.00596140	−	0.0958938i
$613$			16.8781i			0.681699i	0.940118	+	0.340850i	$0.110715\pi$
$613$			16.8781i			0.681699i	−0.940118	+	0.340850i	$0.889285\pi$
$614$	31.8766			1.28644
$615$	35.6357	+	33.4891i	1.43697	+	1.35041i
$616$	−14.5012	+	4.55134i	−0.584271	+	0.183379i
$617$	−17.6060			−0.708790			−0.354395	−	0.935096i	$-0.615313\pi$
$617$	−17.6060			−0.708790			−0.354395	+	0.935096i	$0.615313\pi$
$618$	8.74456	−	9.30506i	0.351758	−	0.374305i
$619$	−13.0641			−0.525091			−0.262546	−	0.964920i	$-0.584562\pi$
$619$	−13.0641			−0.525091			−0.262546	+	0.964920i	$0.584562\pi$
$620$			13.8564i			0.556487i
$621$	−0.589907	−	0.489125i	−0.0236722	−	0.0196279i
$622$	−10.3923			−0.416693
$623$	7.92287	+	25.2434i	0.317423	+	1.01135i
$624$	5.55842	+	2.84674i	0.222515	+	0.113961i
$625$	−16.2554			−0.650217
$626$			2.74456i			0.109695i
$627$	−17.2337	−	16.1956i	−0.688247	−	0.646790i
$628$		−	8.25544i		−	0.329428i
$629$		−	6.62772i		−	0.264264i
$630$	24.9918	−	9.58457i	0.995697	−	0.381859i
$631$		−	12.1793i		−	0.484849i	−0.970170	−	0.242424i	$-0.922057\pi$
$631$		−	12.1793i		−	0.484849i	0.970170	−	0.242424i	$-0.0779426\pi$
$632$	−3.62772			−0.144303
$633$	21.9268	+	20.6060i	0.871510	+	0.819014i
$634$	−3.86141			−0.153356
$635$			34.9783i			1.38807i
$636$	−11.9769	+	12.7446i	−0.474914	+	0.505355i
$637$	15.8997	−	19.6010i	0.629971	−	0.776619i
$638$		−	13.6540i		−	0.540568i
$639$	−0.372281	−	5.98844i	−0.0147272	−	0.236899i
$640$		−	3.37228i		−	0.133301i
$641$		−	8.86263i		−	0.350053i	−0.984564	−	0.175026i	$-0.943999\pi$
$641$		−	8.86263i		−	0.350053i	0.984564	−	0.175026i	$-0.0560011\pi$
$642$	20.1947	−	21.4891i	0.797021	−	0.848108i
$643$	−18.4077			−0.725931			−0.362965	−	0.931803i	$-0.618236\pi$
$643$	−18.4077			−0.725931			−0.362965	+	0.931803i	$0.618236\pi$
$644$	0.116844	+	0.372281i	0.00460430	+	0.0146699i
$645$	−10.5109	+	11.1846i	−0.413865	+	0.440393i
$646$	−1.88316			−0.0740918
$647$	−26.1282			−1.02721			−0.513604	−	0.858028i	$-0.671690\pi$
$647$	−26.1282			−1.02721			−0.513604	+	0.858028i	$0.671690\pi$
$648$	−8.93070	+	1.11469i	−0.350831	+	0.0437892i
$649$			15.7663i			0.618882i
$650$	−22.0742	+	6.37228i	−0.865823	+	0.249941i
$651$	−16.9530	−	8.19407i	−0.664440	−	0.321151i
$652$			8.21782i			0.321835i
$653$		−	14.6487i		−	0.573248i	−0.958043	−	0.286624i	$-0.907467\pi$
$653$		−	14.6487i		−	0.573248i	0.958043	−	0.286624i	$-0.0925330\pi$
$654$	23.3639	−	24.8614i	0.913599	−	0.972158i
$655$		−	13.3591i		−	0.521982i
$656$			8.37228i			0.326883i
$657$	−1.90698	−	30.6753i	−0.0743983	−	1.19676i
$658$	−8.21782	−	26.1831i	−0.320364	−	1.02073i
$659$		−	37.9200i		−	1.47715i	−0.674170	−	0.738576i	$-0.735499\pi$
$659$		−	37.9200i		−	1.47715i	0.674170	−	0.738576i	$-0.264501\pi$
$660$	−22.9783	+	24.4511i	−0.894427	+	0.951757i
$661$	42.2689			1.64407			0.822035	−	0.569436i	$-0.192838\pi$
$661$	42.2689			1.64407			0.822035	+	0.569436i	$0.192838\pi$
$662$		−	17.0805i		−	0.663851i
$663$	−4.40387	−	2.25544i	−0.171032	−	0.0875939i
$664$		−	6.74456i		−	0.261740i
$665$	−6.35053	−	20.2337i	−0.246263	−	0.784629i
$666$	−25.0475	+	1.55712i	−0.970573	+	0.0603373i
$667$	−0.350532			−0.0135726
$668$		−	12.6277i		−	0.488581i
$669$	−0.813859	−	0.764836i	−0.0314656	−	0.0295703i
$670$	−20.1947			−0.780189
$671$		−	44.4891i		−	1.71748i
$672$	4.12590	+	1.99422i	0.159160	+	0.0769287i
$673$	−45.2337			−1.74363			−0.871815	−	0.489835i	$-0.837057\pi$
$673$	−45.2337			−1.74363			−0.871815	+	0.489835i	$0.837057\pi$
$674$	5.00000			0.192593
$675$	21.1345	−	25.4891i	0.813466	−	0.981077i
$676$	11.0000	−	6.92820i	0.423077	−	0.266469i
$677$	−20.5446			−0.789592			−0.394796	−	0.918769i	$-0.629185\pi$
$677$	−20.5446			−0.789592			−0.394796	+	0.918769i	$0.629185\pi$
$678$	−6.75327	+	7.18614i	−0.259358	+	0.275982i
$679$	−23.1168	+	7.25544i	−0.887143	+	0.278438i
$680$			2.67181i			0.102459i
$681$	13.6277	−	14.5012i	0.522215	−	0.555688i
$682$	23.6039			0.903840
$683$	−19.0000			−0.727015			−0.363507	−	0.931591i	$-0.618421\pi$
$683$	−19.0000			−0.727015			−0.363507	+	0.931591i	$0.618421\pi$
$684$	0.442430	+	7.11684i	0.0169168	+	0.272119i
$685$			61.0951i			2.33432i
$686$	11.3321	−	14.6487i	0.432660	−	0.559290i
$687$	6.37228	+	5.98844i	0.243118	+	0.228473i
$688$	−2.62772			−0.100181
$689$	10.0974	+	34.9783i	0.384678	+	1.33257i
$690$	0.627719	+	0.589907i	0.0238968	+	0.0224574i
$691$	31.1769			1.18603			0.593013	−	0.805193i	$-0.297938\pi$
$691$	31.1769			1.18603			0.593013	+	0.805193i	$0.297938\pi$
$692$	10.6873			0.406269
$693$	−16.3270	−	42.5726i	−0.620211	−	1.61720i
$694$			19.2000i			0.728823i
$695$	−17.7228			−0.672265
$696$	−2.81929	+	3.00000i	−0.106865	+	0.113715i
$697$		−	6.63325i		−	0.251252i
$698$	−16.4356			−0.622098
$699$	12.7417	−	13.5584i	0.481936	−	0.512827i
$700$	−16.0858	+	5.04868i	−0.607986	+	0.190822i
$701$		−	13.2665i		−	0.501069i	−0.968108	−	0.250534i	$-0.919394\pi$
$701$		−	13.2665i		−	0.501069i	0.968108	−	0.250534i	$-0.0806063\pi$
$702$	−7.48913	+	17.1730i	−0.282659	+	0.648154i
$703$			19.8832i			0.749907i
$704$	−5.74456			−0.216506
$705$	−44.1485	−	41.4891i	−1.66273	−	1.56257i
$706$			11.1168i			0.418388i
$707$	44.6060	−	14.0000i	1.67758	−	0.526524i
$708$	3.25544	−	3.46410i	0.122347	−	0.130189i
$709$			33.7013i			1.26568i	0.774284	+	0.632839i	$0.218110\pi$
$709$			33.7013i			1.26568i	−0.774284	+	0.632839i	$0.781890\pi$
$710$			6.74456i			0.253119i
$711$	−0.675266	−	10.8622i	−0.0253245	−	0.407364i
$712$			10.0000i			0.374766i
$713$		−	0.605969i		−	0.0226937i
$714$	−3.26890	−	1.57999i	−0.122336	−	0.0591298i
$715$	19.3723	+	67.1076i	0.724482	+	2.50968i
$716$			20.1947i			0.754711i
$717$	22.7190	+	21.3505i	0.848458	+	0.797350i
$718$	6.23369			0.232639
$719$	−16.4356			−0.612946			−0.306473	−	0.951879i	$-0.599149\pi$
$719$	−16.4356			−0.612946			−0.306473	+	0.951879i	$0.599149\pi$
$720$	10.0974	−	0.627719i	0.376306	−	0.0233937i
$721$	−5.84096	−	18.6101i	−0.217529	−	0.693077i
$722$	−13.3505			−0.496855
$723$	20.7446	+	19.4950i	0.771499	+	0.725026i
$724$		−	20.3723i		−	0.757130i
$725$		−	15.1460i		−	0.562509i
$726$	27.7677	+	26.0951i	1.03056	+	0.968480i
$727$			1.13859i			0.0422281i	0.999777	+	0.0211140i	$0.00672131\pi$
$727$			1.13859i			0.0422281i	−0.999777	+	0.0211140i	$0.993279\pi$
$728$	7.95228	−	5.26890i	0.294731	−	0.195278i
$729$	−5.00000	−	26.5330i	−0.185185	−	0.982704i
$730$			34.5484i			1.27870i
$731$	2.08191			0.0770021
$732$	−9.18614	+	9.77495i	−0.339530	+	0.361292i
$733$	18.6101			0.687381			0.343690	−	0.939083i	$-0.388323\pi$
$733$	18.6101			0.687381			0.343690	+	0.939083i	$0.388323\pi$
$734$		−	4.74456i		−	0.175125i
$735$	5.95270	−	40.4511i	0.219569	−	1.49206i
$736$			0.147477i			0.00543607i
$737$			34.4010i			1.26718i
$738$	−25.0684	+	1.55842i	−0.922782	+	0.0573663i
$739$			44.8482i			1.64977i	0.565303	+	0.824883i	$0.308759\pi$
$739$			44.8482i			1.64977i	−0.565303	+	0.824883i	$0.691241\pi$
$740$	28.2101			1.03703
$741$	13.2116	+	6.76631i	0.485340	+	0.248567i
$742$	8.00000	+	25.4891i	0.293689	+	0.935735i
$743$	0.978251			0.0358885			0.0179443	−	0.999839i	$-0.494288\pi$
$743$	0.978251			0.0358885			0.0179443	+	0.999839i	$0.494288\pi$
$744$	−5.18614	−	4.87375i	−0.190133	−	0.178680i
$745$			25.7228i			0.942411i
$746$	−12.2337			−0.447907
$747$	20.1947	−	1.25544i	0.738886	−	0.0459341i
$748$	4.55134			0.166414
$749$	−13.4891	−	42.9783i	−0.492882	−	1.57039i
$750$	−5.48913	+	5.84096i	−0.200435	+	0.213282i
$751$	18.6060			0.678941			0.339471	−	0.940617i	$-0.389752\pi$
$751$	18.6060			0.678941			0.339471	+	0.940617i	$0.389752\pi$
$752$		−	10.3723i		−	0.378238i
$753$	8.55842	+	8.04290i	0.311886	+	0.293099i
$754$	2.37686	+	8.23369i	0.0865602	+	0.299853i
$755$	60.0868			2.18678
$756$	−5.20313	+	12.7251i	−0.189236	+	0.462806i
$757$	50.4674			1.83427			0.917134	−	0.398579i	$-0.130497\pi$
$757$	50.4674			1.83427			0.917134	+	0.398579i	$0.130497\pi$
$758$		−	18.3152i		−	0.665237i
$759$	1.00489	−	1.06930i	0.0364751	−	0.0388130i
$760$		−	8.01544i		−	0.290751i
$761$		−	2.13859i		−	0.0775239i	−0.999248	−	0.0387620i	$-0.987659\pi$
$761$		−	2.13859i		−	0.0775239i	0.999248	−	0.0387620i	$-0.0123414\pi$
$762$	−13.0916	−	12.3030i	−0.474258	−	0.445690i
$763$	−15.6060	−	49.7228i	−0.564974	−	1.80009i
$764$			2.96677i			0.107334i
$765$	−8.00000	+	0.497333i	−0.289241	+	0.0179811i
$766$		−	3.51087i		−	0.126853i
$767$	−2.74456	−	9.50744i	−0.0991004	−	0.343294i
$768$	1.26217	+	1.18614i	0.0455446	+	0.0428012i
$769$	−34.1986			−1.23323			−0.616616	−	0.787264i	$-0.711497\pi$
$769$	−34.1986			−1.23323			−0.616616	+	0.787264i	$0.711497\pi$
$770$	15.3484	+	48.9022i	0.553118	+	1.76231i
$771$	23.8614	+	22.4241i	0.859348	+	0.807584i
$772$			20.7846i			0.748054i
$773$		−	18.8614i		−	0.678398i	−0.940715	−	0.339199i	$-0.889844\pi$
$773$		−	18.8614i		−	0.678398i	0.940715	−	0.339199i	$-0.110156\pi$
$774$	−0.489125	−	7.86797i	−0.0175812	−	0.282808i
$775$	26.1831			0.940526
$776$	−9.15759			−0.328738
$777$	−16.6822	+	34.5144i	−0.598472	+	1.23820i
$778$		−	25.2434i		−	0.905019i
$779$			19.8997i			0.712982i
$780$	9.60002	−	18.7446i	0.343736	−	0.671163i
$781$	11.4891			0.411113
$782$		−	0.116844i		−	0.00417833i
$783$	−9.50744	−	7.88316i	−0.339768	−	0.281721i
$784$	5.74456	−	4.00000i	0.205163	−	0.142857i
$785$	−27.8397			−0.993640
$786$	5.00000	+	4.69882i	0.178344	+	0.167601i
$787$	36.7229			1.30903			0.654515	−	0.756049i	$-0.272873\pi$
$787$	36.7229			1.30903			0.654515	+	0.756049i	$0.272873\pi$
$788$	21.1168			0.752256
$789$	8.56768	−	9.11684i	0.305017	−	0.324568i
$790$			12.2337i			0.435255i
$791$	4.51087	+	14.3723i	0.160388	+	0.511019i
$792$	−1.06930	−	17.2005i	−0.0379958	−	0.611193i
$793$	7.74456	+	26.8280i	0.275017	+	0.952689i
$794$	−6.63325			−0.235405
$795$	42.9783	+	40.3894i	1.52428	+	1.43246i
$796$			12.1168i			0.429470i
$797$	14.2063			0.503212			0.251606	−	0.967830i	$-0.419041\pi$
$797$	14.2063			0.503212			0.251606	+	0.967830i	$0.419041\pi$
$798$	9.80670	+	4.73998i	0.347153	+	0.167794i
$799$			8.21782i			0.290726i
$800$	−6.37228			−0.225294
$801$	−29.9422	+	1.86141i	−1.05796	+	0.0657696i
$802$	28.9783			1.02326
$803$	58.8521			2.07684
$804$	7.10313	−	7.55842i	0.250508	−	0.266565i
$805$	1.25544	−	0.394031i	0.0442484	−	0.0138878i
$806$	−14.2337	+	4.10891i	−0.501360	+	0.144730i
$807$	−18.3030	−	17.2005i	−0.644296	−	0.605486i
$808$	17.6704			0.621641
$809$			1.58457i			0.0557107i	0.999612	+	0.0278553i	$0.00886777\pi$
$809$			1.58457i			0.0557107i	−0.999612	+	0.0278553i	$0.991132\pi$
$810$	3.75906	+	30.1168i	0.132080	+	1.05820i
$811$	−9.60002			−0.337102			−0.168551	−	0.985693i	$-0.553909\pi$
$811$	−9.60002			−0.337102			−0.168551	+	0.985693i	$0.553909\pi$
$812$	1.88316	+	6.00000i	0.0660858	+	0.210559i
$813$	−14.3030	−	13.4414i	−0.501628	−	0.471411i
$814$		−	48.0550i		−	1.68433i
$815$	27.7128			0.970737
$816$	−1.00000	−	0.939764i	−0.0350070	−	0.0328983i
$817$	−6.24572			−0.218510
$818$	−29.7947			−1.04175
$819$	17.2565	+	22.8301i	0.602990	+	0.797748i
$820$	28.2337			0.985963
$821$	−43.7228			−1.52594			−0.762968	−	0.646436i	$-0.776259\pi$
$821$	−43.7228			−1.52594			−0.762968	+	0.646436i	$0.776259\pi$
$822$	−22.8665	−	21.4891i	−0.797561	−	0.749519i
$823$	35.8614			1.25005			0.625025	−	0.780605i	$-0.285089\pi$
$823$	35.8614			1.25005			0.625025	+	0.780605i	$0.285089\pi$
$824$		−	7.37228i		−	0.256826i
$825$	46.2029	+	43.4198i	1.60858	+	1.51168i
$826$	−2.17448	−	6.92820i	−0.0756599	−	0.241063i
$827$	22.1168			0.769078			0.384539	−	0.923109i	$-0.374360\pi$
$827$	22.1168			0.769078			0.384539	+	0.923109i	$0.374360\pi$
$828$	−0.441578	+	0.0274514i	−0.0153459	+	0.000954003i
$829$		−	33.6060i		−	1.16718i	−0.812047	−	0.583592i	$-0.801647\pi$
$829$		−	33.6060i		−	1.16718i	0.812047	−	0.583592i	$-0.198353\pi$
$830$	−22.7446			−0.789475
$831$	22.0742	+	20.7446i	0.765747	+	0.719621i
$832$	3.46410	−	1.00000i	0.120096	−	0.0346688i
$833$	−4.55134	+	3.16915i	−0.157695	+	0.109804i
$834$	6.23369	−	6.63325i	0.215855	−	0.229691i
$835$	−42.5842			−1.47369
$836$	−13.6540			−0.472234
$837$	13.6277	−	16.4356i	0.471043	−	0.568099i
$838$	−4.90120			−0.169309
$839$			5.62772i			0.194290i	0.995270	+	0.0971452i	$0.0309711\pi$
$839$			5.62772i			0.194290i	−0.995270	+	0.0971452i	$0.969029\pi$
$840$	6.72507	−	13.9137i	0.232037	−	0.480069i
$841$	23.3505			0.805191
$842$			23.0140i			0.793115i
$843$	−17.6704	−	16.6060i	−0.608600	−	0.571940i
$844$	17.3723			0.597979
$845$	−23.3639	−	37.0951i	−0.803741	−	1.27611i
$846$	31.0569	−	1.93070i	1.06776	−	0.0663789i
$847$	55.5354	−	17.4303i	1.90822	−	0.598913i
$848$			10.0974i			0.346744i
$849$	0.441578	−	0.469882i	0.0151549	−	0.0161263i
$850$	5.04868			0.173168
$851$	−1.23369			−0.0422903
$852$	−2.52434	−	2.37228i	−0.0864824	−	0.0812730i
$853$	−56.7152			−1.94189			−0.970947	−	0.239297i	$-0.923083\pi$
$853$	−56.7152			−1.94189			−0.970947	+	0.239297i	$0.923083\pi$
$854$	6.13592	+	19.5499i	0.209967	+	0.668984i
$855$	24.0000	−	1.49200i	0.820783	−	0.0510253i
$856$		−	17.0256i		−	0.581921i
$857$	−24.6535			−0.842147			−0.421073	−	0.907027i	$-0.638346\pi$
$857$	−24.6535			−0.842147			−0.421073	+	0.907027i	$0.638346\pi$
$858$	−31.9307	−	16.3533i	−1.09010	−	0.558292i
$859$			10.0951i			0.344440i	0.985058	+	0.172220i	$0.0550940\pi$
$859$			10.0951i			0.344440i	−0.985058	+	0.172220i	$0.944906\pi$
$860$			8.86141i			0.302171i
$861$	−16.6962	+	34.5432i	−0.569004	+	1.17723i
$862$	−28.2337			−0.961643
$863$	11.4891			0.391094			0.195547	−	0.980694i	$-0.437352\pi$
$863$	11.4891			0.391094			0.195547	+	0.980694i	$0.437352\pi$
$864$	−3.31662	+	4.00000i	−0.112834	+	0.136083i
$865$		−	36.0404i		−	1.22541i
$866$		−	30.4674i		−	1.03532i
$867$	−20.6646	−	19.4198i	−0.701806	−	0.659532i
$868$	−10.3723	+	3.25544i	−0.352058	+	0.110497i
$869$	20.8397			0.706937
$870$	10.1168	+	9.50744i	0.342993	+	0.322333i
$871$	−5.98844	−	20.7446i	−0.202911	−	0.702903i
$872$		−	19.6974i		−	0.667037i
$873$	−1.70460	−	27.4198i	−0.0576919	−	0.928021i
$874$			0.350532i			0.0118569i
$875$	3.66648	+	11.6819i	0.123950	+	0.394921i
$876$	−12.9307	−	12.1518i	−0.436888	−	0.410572i
$877$		−	13.5065i		−	0.456084i	−0.973651	−	0.228042i	$-0.926768\pi$
$877$		−	13.5065i		−	0.456084i	0.973651	−	0.228042i	$-0.0732323\pi$
$878$		−	5.60597i		−	0.189192i
$879$	−13.6277	+	14.5012i	−0.459652	+	0.489114i
$880$			19.3723i			0.653039i
$881$	−15.9383			−0.536975			−0.268488	−	0.963283i	$-0.586524\pi$
$881$	−15.9383			−0.536975			−0.268488	+	0.963283i	$0.586524\pi$
$882$	13.0462	+	16.4559i	0.439288	+	0.554100i
$883$	−9.09509			−0.306074			−0.153037	−	0.988220i	$-0.548905\pi$
$883$	−9.09509			−0.306074			−0.153037	+	0.988220i	$0.548905\pi$
$884$	−2.74456	+	0.792287i	−0.0923096	+	0.0266475i
$885$	−11.6819	−	10.9783i	−0.392684	−	0.369030i
$886$			16.7306i			0.562076i
$887$	48.6072			1.63207			0.816035	−	0.578002i	$-0.196167\pi$
$887$	48.6072			1.63207			0.816035	+	0.578002i	$0.196167\pi$
$888$	−9.92242	+	10.5584i	−0.332975	+	0.354317i
$889$	−26.1831	+	8.21782i	−0.878154	+	0.275617i
$890$	33.7228			1.13039
$891$	51.3030	−	6.40342i	1.71871	−	0.214523i
$892$	−0.644810			−0.0215898
$893$		−	24.6535i		−	0.824997i
$894$	−9.62747	−	9.04755i	−0.321991	−	0.302595i
$895$	68.1022			2.27641
$896$	2.52434	−	0.792287i	0.0843322	−	0.0264685i
$897$	−0.419829	+	0.819738i	−0.0140177	+	0.0273703i
$898$	14.1168			0.471085
$899$		−	9.76631i		−	0.325725i
$900$	−1.18614	−	19.0800i	−0.0395380	−	0.636000i
$901$		−	8.00000i		−	0.266519i
$902$		−	48.0951i		−	1.60139i
$903$	−10.8417	−	5.24025i	−0.360790	−	0.174385i
$904$			5.69349i			0.189363i
$905$	−68.7011			−2.28370
$906$	−21.1345	+	22.4891i	−0.702146	+	0.747151i
$907$	20.0000			0.664089			0.332045	−	0.943264i	$-0.392262\pi$
$907$	20.0000			0.664089			0.332045	+	0.943264i	$0.392262\pi$
$908$		−	11.4891i		−	0.381280i
$909$	3.28917	+	52.9090i	0.109095	+	1.75488i
$910$	−17.7682	−	26.8173i	−0.589011	−	0.888985i
$911$		−	24.1561i		−	0.800329i	−0.916443	−	0.400164i	$-0.868953\pi$
$911$		−	24.1561i		−	0.800329i	0.916443	−	0.400164i	$-0.131047\pi$
$912$	3.00000	+	2.81929i	0.0993399	+	0.0933561i
$913$			38.7446i			1.28226i
$914$		−	23.6588i		−	0.782564i
$915$	32.9639	+	30.9783i	1.08975	+	1.02411i
$916$	5.04868			0.166813
$917$	10.0000	−	3.13859i	0.330229	−	0.103645i
$918$	2.62772	−	3.16915i	0.0867276	−	0.104597i
$919$	−45.5842			−1.50368			−0.751842	−	0.659343i	$-0.770835\pi$
$919$	−45.5842			−1.50368			−0.751842	+	0.659343i	$0.770835\pi$
$920$	0.497333			0.0163966
$921$	40.2337	+	37.8102i	1.32575	+	1.24589i
$922$		−	21.6060i		−	0.711555i
$923$	−6.92820	+	2.00000i	−0.228045	+	0.0658308i
$924$	−23.7015	−	11.4559i	−0.779723	−	0.376872i
$925$		−	53.3060i		−	1.75269i
$926$		−	31.6742i		−	1.04088i
$927$	22.0742	−	1.37228i	0.725013	−	0.0450716i
$928$			2.37686i			0.0780243i
$929$			24.6060i			0.807296i	0.914914	+	0.403648i	$0.132258\pi$
$929$			24.6060i			0.807296i	−0.914914	+	0.403648i	$0.867742\pi$
$930$	−16.4356	+	17.4891i	−0.538946	+	0.573491i
$931$	13.6540	−	9.50744i	0.447493	−	0.311594i
$932$		−	10.7422i		−	0.351871i
$933$	−13.1168	−	12.3267i	−0.429426	−	0.403559i
$934$	21.5769			0.706018
$935$		−	15.3484i		−	0.501947i
$936$	3.63903	+	10.1861i	0.118945	+	0.332944i
$937$		−	43.4891i		−	1.42073i	−0.703835	−	0.710364i	$-0.748530\pi$
$937$		−	43.4891i		−	1.42073i	0.703835	−	0.710364i	$-0.251470\pi$
$938$	−4.74456	−	15.1168i	−0.154915	−	0.493582i
$939$	−3.25544	+	3.46410i	−0.106237	+	0.113047i
$940$	−34.9783			−1.14086
$941$			51.4891i			1.67850i	0.543748	+	0.839249i	$0.317005\pi$
$941$			51.4891i			1.67850i	−0.543748	+	0.839249i	$0.682995\pi$
$942$	9.79211	−	10.4198i	0.319044	−	0.339494i
$943$	−1.23472			−0.0402079
$944$		−	2.74456i		−	0.0893279i
$945$	42.9125	+	17.5464i	1.39594	+	0.570785i
$946$	15.0951			0.490784
$947$	−22.1168			−0.718701			−0.359350	−	0.933203i	$-0.617002\pi$
$947$	−22.1168			−0.718701			−0.359350	+	0.933203i	$0.617002\pi$
$948$	−4.57879	−	4.30298i	−0.148712	−	0.139754i
$949$	−35.4891	+	10.2448i	−1.15203	+	0.332561i
$950$	−15.1460			−0.491402
$951$	−4.87375	−	4.58017i	−0.158042	−	0.148522i
$952$	−2.00000	+	0.627719i	−0.0648204	+	0.0203445i
$953$			19.7899i			0.641059i	0.947239	+	0.320530i	$0.103861\pi$
$953$			19.7899i			0.641059i	−0.947239	+	0.320530i	$0.896139\pi$
$954$	−30.2337	+	1.87953i	−0.978852	+	0.0608520i
$955$	10.0048			0.323747
$956$	18.0000			0.582162
$957$	16.1956	−	17.2337i	0.523529	−	0.557086i
$958$			28.6277i			0.924920i
$959$	−45.7330	+	14.3537i	−1.47680	+	0.463506i
$960$	4.00000	−	4.25639i	0.129099	−	0.137374i
$961$	−14.1168			−0.455382
$962$	8.36530	+	28.9783i	0.269708	+	0.934296i
$963$	50.9783	−	3.16915i	1.64275	−	0.102124i
$964$	16.4356			0.529357
$965$	70.0916			2.25633
$966$	−0.294101	+	0.608475i	−0.00946255	+	0.0195774i
$967$			29.2048i			0.939163i	0.882889	+	0.469582i	$0.155595\pi$
$967$			29.2048i			0.939163i	−0.882889	+	0.469582i	$0.844405\pi$
$968$	22.0000			0.707107
$969$	−2.37686	−	2.23369i	−0.0763558	−	0.0717564i
$970$			30.8820i			0.991560i
$971$	−3.22405			−0.103465			−0.0517324	−	0.998661i	$-0.516474\pi$
$971$	−3.22405			−0.103465			−0.0517324	+	0.998661i	$0.516474\pi$
$972$	−12.5942	−	9.18614i	−0.403960	−	0.294646i
$973$	−4.16381	−	13.2665i	−0.133486	−	0.425304i
$974$			37.5152i			1.20206i
$975$	−35.4198	−	18.1402i	−1.13434	−	0.580953i
$976$			7.74456i			0.247897i
$977$	40.3505			1.29093			0.645464	−	0.763791i	$-0.276664\pi$
$977$	40.3505			1.29093			0.645464	+	0.763791i	$0.276664\pi$
$978$	−9.74749	+	10.3723i	−0.311691	+	0.331669i
$979$		−	57.4456i		−	1.83597i
$980$	−13.4891	−	19.3723i	−0.430894	−	0.618825i
$981$	58.9783	−	3.66648i	1.88303	−	0.117062i
$982$			11.6819i			0.372785i
$983$			54.1168i			1.72606i	0.505153	+	0.863030i	$0.331436\pi$
$983$			54.1168i			1.72606i	−0.505153	+	0.863030i	$0.668564\pi$
$984$	−9.93070	+	10.5672i	−0.316579	+	0.336871i
$985$		−	71.2119i		−	2.26900i
$986$		−	1.88316i		−	0.0599719i
$987$	20.6846	−	42.7950i	0.658398	−	1.36218i
$988$	8.23369	−	2.37686i	0.261949	−	0.0756180i
$989$		−	0.387528i		−	0.0123227i
$990$	−58.0049	+	3.60597i	−1.84352	+	0.114605i
$991$	−15.1168			−0.480202			−0.240101	−	0.970748i	$-0.577181\pi$
$991$	−15.1168			−0.480202			−0.240101	+	0.970748i	$0.577181\pi$
$992$	−4.10891			−0.130458
$993$	20.2598	−	21.5584i	0.642926	−	0.684136i
$994$	−5.04868	+	1.58457i	−0.160134	+	0.0502596i
$995$	40.8614			1.29539
$996$	8.00000	−	8.51278i	0.253490	−	0.269738i
$997$		−	8.37228i		−	0.265153i	−0.991173	−	0.132576i	$-0.957675\pi$
$997$		−	8.37228i		−	0.265153i	0.991173	−	0.132576i	$-0.0423250\pi$
$998$		−	10.4472i		−	0.330701i
$999$	−33.4612	−	27.7446i	−1.05867	−	0.877799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.e.g.545.8	yes	8
3.2	odd	2		546.2.e.e.545.2	yes	8
7.6	odd	2	inner	546.2.e.g.545.1	yes	8
13.12	even	2		546.2.e.e.545.8	yes	8
21.20	even	2		546.2.e.e.545.7	yes	8
39.38	odd	2	inner	546.2.e.g.545.2	yes	8
91.90	odd	2		546.2.e.e.545.1	✓	8
273.272	even	2	inner	546.2.e.g.545.7	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.e.e.545.1	✓	8	91.90	odd	2
546.2.e.e.545.2	yes	8	3.2	odd	2
546.2.e.e.545.7	yes	8	21.20	even	2
546.2.e.e.545.8	yes	8	13.12	even	2
546.2.e.g.545.1	yes	8	7.6	odd	2	inner
546.2.e.g.545.2	yes	8	39.38	odd	2	inner
546.2.e.g.545.7	yes	8	273.272	even	2	inner
546.2.e.g.545.8	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.26217 + 1.18614i) q^{3} +1.00000 q^{4} -3.37228i q^{5} +(1.26217 + 1.18614i) q^{6} +(2.52434 - 0.792287i) q^{7} +1.00000 q^{8} +(0.186141 + 2.99422i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.26217 + 1.18614i) q^{3} +1.00000 q^{4} -3.37228i q^{5} +(1.26217 + 1.18614i) q^{6} +(2.52434 - 0.792287i) q^{7} +1.00000 q^{8} +(0.186141 + 2.99422i) q^{9} -3.37228i q^{10} -5.74456 q^{11} +(1.26217 + 1.18614i) q^{12} +(3.46410 - 1.00000i) q^{13} +(2.52434 - 0.792287i) q^{14} +(4.00000 - 4.25639i) q^{15} +1.00000 q^{16} -0.792287 q^{17} +(0.186141 + 2.99422i) q^{18} +2.37686 q^{19} -3.37228i q^{20} +(4.12590 + 1.99422i) q^{21} -5.74456 q^{22} +0.147477i q^{23} +(1.26217 + 1.18614i) q^{24} -6.37228 q^{25} +(3.46410 - 1.00000i) q^{26} +(-3.31662 + 4.00000i) q^{27} +(2.52434 - 0.792287i) q^{28} +2.37686i q^{29} +(4.00000 - 4.25639i) q^{30} -4.10891 q^{31} +1.00000 q^{32} +(-7.25061 - 6.81386i) q^{33} -0.792287 q^{34} +(-2.67181 - 8.51278i) q^{35} +(0.186141 + 2.99422i) q^{36} +8.36530i q^{37} +2.37686 q^{38} +(5.55842 + 2.84674i) q^{39} -3.37228i q^{40} +8.37228i q^{41} +(4.12590 + 1.99422i) q^{42} -2.62772 q^{43} -5.74456 q^{44} +(10.0974 - 0.627719i) q^{45} +0.147477i q^{46} -10.3723i q^{47} +(1.26217 + 1.18614i) q^{48} +(5.74456 - 4.00000i) q^{49} -6.37228 q^{50} +(-1.00000 - 0.939764i) q^{51} +(3.46410 - 1.00000i) q^{52} +10.0974i q^{53} +(-3.31662 + 4.00000i) q^{54} +19.3723i q^{55} +(2.52434 - 0.792287i) q^{56} +(3.00000 + 2.81929i) q^{57} +2.37686i q^{58} -2.74456i q^{59} +(4.00000 - 4.25639i) q^{60} +7.74456i q^{61} -4.10891 q^{62} +(2.84216 + 7.41095i) q^{63} +1.00000 q^{64} +(-3.37228 - 11.6819i) q^{65} +(-7.25061 - 6.81386i) q^{66} -5.98844i q^{67} -0.792287 q^{68} +(-0.174928 + 0.186141i) q^{69} +(-2.67181 - 8.51278i) q^{70} -2.00000 q^{71} +(0.186141 + 2.99422i) q^{72} -10.2448 q^{73} +8.36530i q^{74} +(-8.04290 - 7.55842i) q^{75} +2.37686 q^{76} +(-14.5012 + 4.55134i) q^{77} +(5.55842 + 2.84674i) q^{78} -3.62772 q^{79} -3.37228i q^{80} +(-8.93070 + 1.11469i) q^{81} +8.37228i q^{82} -6.74456i q^{83} +(4.12590 + 1.99422i) q^{84} +2.67181i q^{85} -2.62772 q^{86} +(-2.81929 + 3.00000i) q^{87} -5.74456 q^{88} +10.0000i q^{89} +(10.0974 - 0.627719i) q^{90} +(7.95228 - 5.26890i) q^{91} +0.147477i q^{92} +(-5.18614 - 4.87375i) q^{93} -10.3723i q^{94} -8.01544i q^{95} +(1.26217 + 1.18614i) q^{96} -9.15759 q^{97} +(5.74456 - 4.00000i) q^{98} +(-1.06930 - 17.2005i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 10 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 - 10 * q^9	\( 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} - 10 q^{9} + 32 q^{15} + 8 q^{16} - 10 q^{18} + 14 q^{21} - 28 q^{25} + 32 q^{30} + 8 q^{32} - 10 q^{36} + 10 q^{39} + 14 q^{42} - 44 q^{43} - 28 q^{50} - 8 q^{51} + 24 q^{57} + 32 q^{60} - 4 q^{63} + 8 q^{64} - 4 q^{65} - 16 q^{71} - 10 q^{72} + 10 q^{78} - 52 q^{79} - 14 q^{81} + 14 q^{84} - 44 q^{86} + 24 q^{91} - 30 q^{93} - 66 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 - 10 * q^9 + 32 * q^15 + 8 * q^16 - 10 * q^18 + 14 * q^21 - 28 * q^25 + 32 * q^30 + 8 * q^32 - 10 * q^36 + 10 * q^39 + 14 * q^42 - 44 * q^43 - 28 * q^50 - 8 * q^51 + 24 * q^57 + 32 * q^60 - 4 * q^63 + 8 * q^64 - 4 * q^65 - 16 * q^71 - 10 * q^72 + 10 * q^78 - 52 * q^79 - 14 * q^81 + 14 * q^84 - 44 * q^86 + 24 * q^91 - 30 * q^93 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more