LMFDB - Embedded newform 819.2.fn.f.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(73,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("819.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fn (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.2
Character	$\chi$	$=$	819.73
Dual form			819.2.fn.f.460.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.542736 + 2.02552i) q^{2} +(-2.07611 - 1.19864i) q^{4} +(-0.821926 - 0.220234i) q^{5} +(2.59841 - 0.498246i) q^{7} +(0.589092 - 0.589092i) q^{8} +O(q^{10})$	\(q+(-0.542736 + 2.02552i) q^{2} +(-2.07611 - 1.19864i) q^{4} +(-0.821926 - 0.220234i) q^{5} +(2.59841 - 0.498246i) q^{7} +(0.589092 - 0.589092i) q^{8} +(0.892178 - 1.54530i) q^{10} +(-0.803294 - 2.99793i) q^{11} +(-3.60505 - 0.0598320i) q^{13} +(-0.401046 + 5.53355i) q^{14} +(-1.52379 - 2.63929i) q^{16} +(0.206711 - 0.358033i) q^{17} +(-7.98261 - 2.13893i) q^{19} +(1.44243 + 1.44243i) q^{20} +6.50834 q^{22} +(-0.426092 + 0.246004i) q^{23} +(-3.70307 - 2.13797i) q^{25} +(2.07778 - 7.26963i) q^{26} +(-5.99182 - 2.08016i) q^{28} -9.90597 q^{29} +(1.12127 + 4.18465i) q^{31} +(7.78237 - 2.08528i) q^{32} +(0.613014 + 0.613014i) q^{34} +(-2.24543 - 0.162739i) q^{35} +(-1.17753 - 0.315519i) q^{37} +(8.66490 - 15.0080i) q^{38} +(-0.613928 + 0.354452i) q^{40} +(2.61146 - 2.61146i) q^{41} +4.14927i q^{43} +(-1.92573 + 7.18691i) q^{44} +(-0.267031 - 0.996572i) q^{46} +(1.45255 - 5.42098i) q^{47} +(6.50350 - 2.58930i) q^{49} +(6.34028 - 6.34028i) q^{50} +(7.41278 + 4.44540i) q^{52} +(3.68892 - 6.38940i) q^{53} +2.64099i q^{55} +(1.23719 - 1.82422i) q^{56} +(5.37633 - 20.0647i) q^{58} +(-3.37641 + 0.904707i) q^{59} +(2.20104 - 1.27077i) q^{61} -9.08463 q^{62} +10.7999i q^{64} +(2.94991 + 0.843135i) q^{65} +(13.7298 - 3.67889i) q^{67} +(-0.858309 + 0.495545i) q^{68} +(1.54831 - 4.45984i) q^{70} +(6.37812 + 6.37812i) q^{71} +(-13.5232 + 3.62354i) q^{73} +(1.27818 - 2.21387i) q^{74} +(14.0090 + 14.0090i) q^{76} +(-3.58100 - 7.38963i) q^{77} +(-4.27606 - 7.40636i) q^{79} +(0.671183 + 2.50489i) q^{80} +(3.87223 + 6.70690i) q^{82} +(-8.63202 + 8.63202i) q^{83} +(-0.248752 + 0.248752i) q^{85} +(-8.40443 - 2.25196i) q^{86} +(-2.23927 - 1.29284i) q^{88} +(-1.74928 + 6.52842i) q^{89} +(-9.39723 + 1.64074i) q^{91} +1.17949 q^{92} +(10.1919 + 5.88432i) q^{94} +(6.09005 + 3.51609i) q^{95} +(-4.47968 + 4.47968i) q^{97} +(1.71499 + 14.5783i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{7}+O(q^{10}) $ 36 * q - 6 * q^7	$ 36 q - 6 q^{7} - 4 q^{11} + 36 q^{14} + 12 q^{16} - 4 q^{17} - 18 q^{19} - 44 q^{20} - 8 q^{22} + 12 q^{23} - 48 q^{25} + 32 q^{26} + 4 q^{28} + 16 q^{29} - 6 q^{31} - 76 q^{32} - 48 q^{34} - 8 q^{35} - 8 q^{37} - 16 q^{38} + 60 q^{40} + 32 q^{41} - 4 q^{44} + 28 q^{46} - 14 q^{47} + 6 q^{49} + 68 q^{50} - 62 q^{52} + 8 q^{53} + 8 q^{56} + 36 q^{58} - 26 q^{59} + 36 q^{61} - 48 q^{62} + 8 q^{65} - 40 q^{67} - 36 q^{68} - 64 q^{70} + 36 q^{71} - 8 q^{73} - 40 q^{74} - 60 q^{76} - 60 q^{77} - 26 q^{80} - 24 q^{83} + 44 q^{85} - 48 q^{86} + 168 q^{88} - 10 q^{89} + 4 q^{91} + 40 q^{92} + 36 q^{97} - 38 q^{98}+O(q^{100}) $ 36 * q - 6 * q^7 - 4 * q^11 + 36 * q^14 + 12 * q^16 - 4 * q^17 - 18 * q^19 - 44 * q^20 - 8 * q^22 + 12 * q^23 - 48 * q^25 + 32 * q^26 + 4 * q^28 + 16 * q^29 - 6 * q^31 - 76 * q^32 - 48 * q^34 - 8 * q^35 - 8 * q^37 - 16 * q^38 + 60 * q^40 + 32 * q^41 - 4 * q^44 + 28 * q^46 - 14 * q^47 + 6 * q^49 + 68 * q^50 - 62 * q^52 + 8 * q^53 + 8 * q^56 + 36 * q^58 - 26 * q^59 + 36 * q^61 - 48 * q^62 + 8 * q^65 - 40 * q^67 - 36 * q^68 - 64 * q^70 + 36 * q^71 - 8 * q^73 - 40 * q^74 - 60 * q^76 - 60 * q^77 - 26 * q^80 - 24 * q^83 + 44 * q^85 - 48 * q^86 + 168 * q^88 - 10 * q^89 + 4 * q^91 + 40 * q^92 + 36 * q^97 - 38 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.542736	+	2.02552i	−0.383772	+	1.43226i	0.456321	+	0.889815i	$0.349167\pi$
$2$	−0.542736	+	2.02552i	−0.383772	+	1.43226i	−0.840093	+	0.542443i	$0.817500\pi$
$3$		0			0
$3$		0			0
$4$	−2.07611	−	1.19864i	−1.03806	−	0.599322i
$5$	−0.821926	−	0.220234i	−0.367576	−	0.0984918i	0.0703026	−	0.997526i	$-0.477604\pi$
$5$	−0.821926	−	0.220234i	−0.367576	−	0.0984918i	−0.437879	+	0.899034i	$0.644270\pi$
$6$		0			0
$7$	2.59841	−	0.498246i	0.982108	−	0.188319i
$7$	2.59841	−	0.498246i	0.982108	−	0.188319i
$8$	0.589092	−	0.589092i	0.208275	−	0.208275i
$9$		0			0
$10$	0.892178	−	1.54530i	0.282131	−	0.488666i
$11$	−0.803294	−	2.99793i	−0.242202	−	0.903911i	−0.974769	−	0.223216i	$-0.928345\pi$
$11$	−0.803294	−	2.99793i	−0.242202	−	0.903911i	0.732567	−	0.680695i	$-0.238322\pi$
$12$		0			0
$13$	−3.60505	−	0.0598320i	−0.999862	−	0.0165944i
$13$	−3.60505	−	0.0598320i	−0.999862	−	0.0165944i
$14$	−0.401046	+	5.53355i	−0.107184	+	1.47890i
$15$		0			0
$16$	−1.52379	−	2.63929i	−0.380948	−	0.659822i
$17$	0.206711	−	0.358033i	0.0501347	−	0.0868358i	−0.839869	−	0.542789i	$-0.817368\pi$
$17$	0.206711	−	0.358033i	0.0501347	−	0.0868358i	0.890004	+	0.455953i	$0.150702\pi$
$18$		0			0
$19$	−7.98261	−	2.13893i	−1.83134	−	0.490705i	−0.833270	−	0.552867i	$-0.813534\pi$
$19$	−7.98261	−	2.13893i	−1.83134	−	0.490705i	−0.998066	+	0.0621617i	$0.980201\pi$
$20$	1.44243	+	1.44243i	0.322537	+	0.322537i
$21$		0			0
$22$	6.50834			1.38758
$23$	−0.426092	+	0.246004i	−0.0888463	+	0.0512954i	−0.543765	−	0.839238i	$-0.683002\pi$
$23$	−0.426092	+	0.246004i	−0.0888463	+	0.0512954i	0.454919	+	0.890533i	$0.349668\pi$
$24$		0			0
$25$	−3.70307	−	2.13797i	−0.740614	−	0.427593i
$26$	2.07778	−	7.26963i	0.407487	−	1.42569i
$27$		0			0
$28$	−5.99182	−	2.08016i	−1.13235	−	0.393113i
$29$	−9.90597			−1.83949			−0.919746	−	0.392513i	$-0.871606\pi$
$29$	−9.90597			−1.83949			−0.919746	+	0.392513i	$0.871606\pi$
$30$		0			0
$31$	1.12127	+	4.18465i	0.201386	+	0.751584i	0.990521	+	0.137364i	$0.0438629\pi$
$31$	1.12127	+	4.18465i	0.201386	+	0.751584i	−0.789134	+	0.614221i	$0.789470\pi$
$32$	7.78237	−	2.08528i	1.37574	−	0.368629i
$33$		0			0
$34$	0.613014	+	0.613014i	0.105131	+	0.105131i
$35$	−2.24543	−	0.162739i	−0.379548	−	0.0275078i
$36$		0			0
$37$	−1.17753	−	0.315519i	−0.193585	−	0.0518710i	0.160724	−	0.986999i	$-0.448617\pi$
$37$	−1.17753	−	0.315519i	−0.193585	−	0.0518710i	−0.354309	+	0.935128i	$0.615284\pi$
$38$	8.66490	−	15.0080i	1.40563	−	2.43463i
$39$		0			0
$40$	−0.613928	+	0.354452i	−0.0970706	+	0.0560437i
$41$	2.61146	−	2.61146i	0.407842	−	0.407842i	−0.473143	−	0.880985i	$-0.656881\pi$
$41$	2.61146	−	2.61146i	0.407842	−	0.407842i	0.880985	+	0.473143i	$0.156881\pi$
$42$		0			0
$43$			4.14927i			0.632758i	0.948633	+	0.316379i	$0.102467\pi$
$43$			4.14927i			0.632758i	−0.948633	+	0.316379i	$0.897533\pi$
$44$	−1.92573	+	7.18691i	−0.290314	+	1.08347i
$45$		0			0
$46$	−0.267031	−	0.996572i	−0.0393715	−	0.146937i
$47$	1.45255	−	5.42098i	0.211876	−	0.790731i	−0.775367	−	0.631510i	$-0.782435\pi$
$47$	1.45255	−	5.42098i	0.211876	−	0.790731i	0.987243	−	0.159220i	$-0.0508980\pi$
$48$		0			0
$49$	6.50350	−	2.58930i	0.929072	−	0.369900i
$50$	6.34028	−	6.34028i	0.896651	−	0.896651i
$51$		0			0
$52$	7.41278	+	4.44540i	1.02797	+	0.616465i
$53$	3.68892	−	6.38940i	0.506713	−	0.877652i	−0.493257	−	0.869884i	$-0.664194\pi$
$53$	3.68892	−	6.38940i	0.506713	−	0.877652i	0.999970	−	0.00776859i	$-0.00247284\pi$
$54$		0			0
$55$			2.64099i			0.356111i
$56$	1.23719	−	1.82422i	0.165327	−	0.243771i
$57$		0			0
$58$	5.37633	−	20.0647i	0.705946	−	2.63463i
$59$	−3.37641	+	0.904707i	−0.439572	+	0.117783i	−0.471816	−	0.881697i	$-0.656401\pi$
$59$	−3.37641	+	0.904707i	−0.439572	+	0.117783i	0.0322441	+	0.999480i	$0.489735\pi$
$60$		0			0
$61$	2.20104	−	1.27077i	0.281814	−	0.162705i	−0.352430	−	0.935838i	$-0.614645\pi$
$61$	2.20104	−	1.27077i	0.281814	−	0.162705i	0.634244	+	0.773133i	$0.281311\pi$
$62$	−9.08463			−1.15375
$63$		0			0
$64$			10.7999i			1.34999i
$65$	2.94991	+	0.843135i	0.365891	+	0.104578i
$66$		0			0
$67$	13.7298	−	3.67889i	1.67736	−	0.449448i	0.710282	−	0.703917i	$-0.248567\pi$
$67$	13.7298	−	3.67889i	1.67736	−	0.449448i	0.967081	+	0.254469i	$0.0819005\pi$
$68$	−0.858309	+	0.495545i	−0.104085	+	0.0600937i
$69$		0			0
$70$	1.54831	−	4.45984i	0.185058	−	0.533053i
$71$	6.37812	+	6.37812i	0.756943	+	0.756943i	0.975765	−	0.218822i	$-0.0702212\pi$
$71$	6.37812	+	6.37812i	0.756943	+	0.756943i	−0.218822	+	0.975765i	$0.570221\pi$
$72$		0			0
$73$	−13.5232	+	3.62354i	−1.58277	+	0.424103i	−0.939783	−	0.341771i	$-0.888973\pi$
$73$	−13.5232	+	3.62354i	−1.58277	+	0.424103i	−0.642991	+	0.765874i	$0.722307\pi$
$74$	1.27818	−	2.21387i	0.148585	−	0.257357i
$75$		0			0
$76$	14.0090	+	14.0090i	1.60694	+	1.60694i
$77$	−3.58100	−	7.38963i	−0.408092	−	0.842126i
$78$		0			0
$79$	−4.27606	−	7.40636i	−0.481095	−	0.833280i	0.518670	−	0.854974i	$-0.326427\pi$
$79$	−4.27606	−	7.40636i	−0.481095	−	0.833280i	−0.999765	+	0.0216943i	$0.993094\pi$
$80$	0.671183	+	2.50489i	0.0750406	+	0.280055i
$81$		0			0
$82$	3.87223	+	6.70690i	0.427617	+	0.740654i
$83$	−8.63202	+	8.63202i	−0.947487	+	0.947487i	−0.998688	−	0.0512011i	$-0.983695\pi$
$83$	−8.63202	+	8.63202i	−0.947487	+	0.947487i	0.0512011	+	0.998688i	$0.483695\pi$
$84$		0			0
$85$	−0.248752	+	0.248752i	−0.0269810	+	0.0269810i
$86$	−8.40443	−	2.25196i	−0.906273	−	0.242835i
$87$		0			0
$88$	−2.23927	−	1.29284i	−0.238707	−	0.137818i
$89$	−1.74928	+	6.52842i	−0.185424	+	0.692011i	0.809116	+	0.587649i	$0.199947\pi$
$89$	−1.74928	+	6.52842i	−0.185424	+	0.692011i	−0.994539	+	0.104361i	$0.966720\pi$
$90$		0			0
$91$	−9.39723	+	1.64074i	−0.985098	+	0.171996i
$92$	1.17949			0.122970
$93$		0			0
$94$	10.1919	+	5.88432i	1.05122	+	0.606921i
$95$	6.09005	+	3.51609i	0.624825	+	0.360743i
$96$		0			0
$97$	−4.47968	+	4.47968i	−0.454843	+	0.454843i	−0.896958	−	0.442115i	$-0.854228\pi$
$97$	−4.47968	+	4.47968i	−0.454843	+	0.454843i	0.442115	+	0.896958i	$0.354228\pi$
$98$	1.71499	+	14.5783i	0.173240	+	1.47263i
$99$		0			0
$100$	5.12532	+	8.87732i	0.512532	+	0.887732i
$101$	4.31959	−	7.48175i	0.429815	−	0.744462i	−0.567041	−	0.823689i	$-0.691912\pi$
$101$	4.31959	−	7.48175i	0.429815	−	0.744462i	0.996857	+	0.0792273i	$0.0252453\pi$
$102$		0			0
$103$	4.65197	+	8.05745i	0.458372	+	0.793924i	0.998875	−	0.0474182i	$-0.0150994\pi$
$103$	4.65197	+	8.05745i	0.458372	+	0.793924i	−0.540503	+	0.841342i	$0.681766\pi$
$104$	−2.15896	+	2.08846i	−0.211703	+	0.204791i
$105$		0			0
$106$	10.9397	+	10.9397i	1.06256	+	1.06256i
$107$	−4.62055	−	8.00303i	−0.446686	−	0.773683i	0.551482	−	0.834187i	$-0.314062\pi$
$107$	−4.62055	−	8.00303i	−0.446686	−	0.773683i	−0.998168	+	0.0605042i	$0.980729\pi$
$108$		0			0
$109$	−2.49896	+	0.669594i	−0.239357	+	0.0641355i	−0.376503	−	0.926415i	$-0.622874\pi$
$109$	−2.49896	+	0.669594i	−0.239357	+	0.0641355i	0.137146	+	0.990551i	$0.456207\pi$
$110$	−5.34938	−	1.43336i	−0.510043	−	0.136666i
$111$		0			0
$112$	−5.27446	−	6.09873i	−0.498389	−	0.576276i
$113$	9.92126			0.933314			0.466657	−	0.884438i	$-0.345458\pi$
$113$	9.92126			0.933314			0.466657	+	0.884438i	$0.345458\pi$
$114$		0			0
$115$	0.404395	−	0.108357i	0.0377100	−	0.0101044i
$116$	20.5659	+	11.8737i	1.90950	+	1.10245i
$117$		0			0
$118$		−	7.33001i		−	0.674782i
$119$	0.358731	−	1.03331i	0.0328848	−	0.0947235i
$120$		0			0
$121$	1.18396	−	0.683560i	0.107633	−	0.0621418i
$122$	1.37939	+	5.14794i	0.124884	+	0.466072i
$123$		0			0
$124$	2.68801	−	10.0318i	0.241391	−	0.900882i
$125$	5.58125	+	5.58125i	0.499202	+	0.499202i
$126$		0			0
$127$		−	17.6691i		−	1.56788i	−0.620838	−	0.783939i	$-0.713207\pi$
$127$		−	17.6691i		−	1.56788i	0.620838	−	0.783939i	$-0.286793\pi$
$128$	−6.31070	−	1.69095i	−0.557793	−	0.149460i
$129$		0			0
$130$	−3.30881	+	5.51750i	−0.290202	+	0.483917i
$131$	−16.3849	+	9.45984i	−1.43156	+	0.826510i	−0.997240	−	0.0742495i	$-0.976344\pi$
$131$	−16.3849	+	9.45984i	−1.43156	+	0.826510i	−0.434318	+	0.900760i	$0.643011\pi$
$132$		0			0
$133$	−21.8078	−	1.58053i	−1.89098	−	0.137049i
$134$			29.8067i			2.57490i
$135$		0			0
$136$	−0.0891430	−	0.332686i	−0.00764395	−	0.0285276i
$137$	2.90106	+	10.8269i	0.247854	+	0.925003i	0.971928	+	0.235281i	$0.0756009\pi$
$137$	2.90106	+	10.8269i	0.247854	+	0.925003i	−0.724074	+	0.689723i	$0.757732\pi$
$138$		0			0
$139$		−	2.52712i		−	0.214347i	−0.994240	−	0.107174i	$-0.965820\pi$
$139$		−	2.52712i		−	0.214347i	0.994240	−	0.107174i	$-0.0341801\pi$
$140$	4.46671	+	3.02934i	0.377506	+	0.256026i
$141$		0			0
$142$	−16.3806	+	9.45736i	−1.37463	+	0.793644i
$143$	2.71655	+	10.8558i	0.227169	+	0.907805i
$144$		0			0
$145$	8.14197	+	2.18164i	0.676154	+	0.181175i
$146$		−	29.3582i		−	2.42970i
$147$		0			0
$148$	2.06650	+	2.06650i	0.169865	+	0.169865i
$149$	−2.11309	+	7.88614i	−0.173111	+	0.646058i	0.823755	+	0.566946i	$0.191875\pi$
$149$	−2.11309	+	7.88614i	−0.173111	+	0.646058i	−0.996866	+	0.0791120i	$0.974792\pi$
$150$		0			0
$151$	0.754224	+	2.81480i	0.0613779	+	0.229065i	0.989800	−	0.142460i	$-0.0455014\pi$
$151$	0.754224	+	2.81480i	0.0613779	+	0.229065i	−0.928423	+	0.371526i	$0.878835\pi$
$152$	−5.96252	+	3.44246i	−0.483624	+	0.279221i
$153$		0			0
$154$	16.9114	−	3.24276i	1.36276	−	0.261309i
$155$		−	3.68641i		−	0.296100i
$156$		0			0
$157$	−9.56036	−	5.51968i	−0.763000	−	0.440518i	0.0673717	−	0.997728i	$-0.478539\pi$
$157$	−9.56036	−	5.51968i	−0.763000	−	0.440518i	−0.830372	+	0.557210i	$0.811872\pi$
$158$	17.3225	−	4.64155i	1.37810	−	0.369262i
$159$		0			0
$160$	−6.85578			−0.541997
$161$	−0.984592	+	0.851519i	−0.0775967	+	0.0671091i
$162$		0			0
$163$	−2.19035	−	0.586902i	−0.171561	−	0.0459697i	0.172016	−	0.985094i	$-0.444972\pi$
$163$	−2.19035	−	0.586902i	−0.171561	−	0.0459697i	−0.343577	+	0.939124i	$0.611639\pi$
$164$	−8.55191	+	2.29148i	−0.667792	+	0.178934i
$165$		0			0
$166$	−12.7994	−	22.1692i	−0.993427	−	1.72067i
$167$	8.26961	+	8.26961i	0.639922	+	0.639922i	0.950536	−	0.310614i	$-0.100535\pi$
$167$	8.26961	+	8.26961i	0.639922	+	0.639922i	−0.310614	+	0.950536i	$0.600535\pi$
$168$		0			0
$169$	12.9928	+	0.431396i	0.999449	+	0.0331843i
$170$	−0.368845	−	0.638859i	−0.0282891	−	0.0489982i
$171$		0			0
$172$	4.97350	−	8.61436i	0.379226	−	0.656839i
$173$	−9.65446	−	16.7220i	−0.734015	−	1.27135i	−0.955154	−	0.296109i	$-0.904311\pi$
$173$	−9.65446	−	16.7220i	−0.734015	−	1.27135i	0.221139	−	0.975242i	$-0.429023\pi$
$174$		0			0
$175$	−10.6873	−	3.71028i	−0.807887	−	0.280471i
$176$	−6.68835	+	6.68835i	−0.504153	+	0.504153i
$177$		0			0
$178$	−12.2740	−	7.08641i	−0.919977	−	0.531149i
$179$	−11.5367	−	6.66069i	−0.862290	−	0.497843i	0.00248848	−	0.999997i	$-0.499208\pi$
$179$	−11.5367	−	6.66069i	−0.862290	−	0.497843i	−0.864778	+	0.502154i	$0.832541\pi$
$180$		0			0
$181$	−0.758135			−0.0563517			−0.0281759	−	0.999603i	$-0.508970\pi$
$181$	−0.758135			−0.0563517			−0.0281759	+	0.999603i	$0.508970\pi$
$182$	1.77688	−	19.9248i	0.131711	−	1.47692i
$183$		0			0
$184$	−0.106088	+	0.395926i	−0.00782092	+	0.0291881i
$185$	0.898357	+	0.518667i	0.0660485	+	0.0381331i
$186$		0			0
$187$	−1.23941	−	0.332099i	−0.0906346	−	0.0242855i
$188$	−9.51347	+	9.51347i	−0.693841	+	0.693841i
$189$		0			0
$190$	−10.4272	+	10.4272i	−0.756468	+	0.756468i
$191$	−11.4856	−	19.8936i	−0.831068	−	1.43945i	−0.897192	−	0.441641i	$-0.854396\pi$
$191$	−11.4856	−	19.8936i	−0.831068	−	1.43945i	0.0661232	−	0.997811i	$-0.478937\pi$
$192$		0			0
$193$	−1.66408	−	6.21044i	−0.119783	−	0.447037i	0.879817	−	0.475313i	$-0.157665\pi$
$193$	−1.66408	−	6.21044i	−0.119783	−	0.447037i	−0.999600	+	0.0282756i	$0.990998\pi$
$194$	−6.64240	−	11.5050i	−0.476896	−	0.826009i
$195$		0			0
$196$	−16.6056	−	2.41971i	−1.18612	−	0.172836i
$197$	0.897366	+	0.897366i	0.0639347	+	0.0639347i	0.738351	−	0.674416i	$-0.235605\pi$
$197$	0.897366	+	0.897366i	0.0639347	+	0.0639347i	−0.674416	+	0.738351i	$0.735605\pi$
$198$		0			0
$199$	−2.13922	+	3.70523i	−0.151645	+	0.262657i	−0.931832	−	0.362889i	$-0.881790\pi$
$199$	−2.13922	+	3.70523i	−0.151645	+	0.262657i	0.780187	+	0.625546i	$0.215124\pi$
$200$	−3.44091	+	0.921988i	−0.243309	+	0.0651944i
$201$		0			0
$202$	12.8100	+	12.8100i	0.901311	+	0.901311i
$203$	−25.7398	+	4.93561i	−1.80658	+	0.346412i
$204$		0			0
$205$	−2.72156	+	1.57130i	−0.190082	+	0.109744i
$206$	−18.8453	+	5.04958i	−1.31301	+	0.351821i
$207$		0			0
$208$	5.33544	+	9.60594i	0.369946	+	0.666052i
$209$			25.6495i			1.77421i
$210$		0			0
$211$	14.4403			0.994110			0.497055	−	0.867719i	$-0.334415\pi$
$211$	14.4403			0.994110			0.497055	+	0.867719i	$0.334415\pi$
$212$	−15.3172	+	8.84341i	−1.05199	+	0.607368i
$213$		0			0
$214$	18.7180	−	5.01548i	1.27954	−	0.342851i
$215$	0.913813	−	3.41040i	0.0623215	−	0.232587i
$216$		0			0
$217$	4.99851	+	10.3148i	0.339321	+	0.700212i
$218$		−	5.42510i		−	0.367434i
$219$		0			0
$220$	3.16561	−	5.48300i	0.213425	−	0.369663i
$221$	−0.766625	+	1.27836i	−0.0515688	+	0.0859919i
$222$		0			0
$223$	−0.913313	+	0.913313i	−0.0611599	+	0.0611599i	−0.737025	−	0.675865i	$-0.763770\pi$
$223$	−0.913313	+	0.913313i	−0.0611599	+	0.0611599i	0.675865	+	0.737025i	$0.263770\pi$
$224$	19.1828	−	9.29596i	1.28171	−	0.621112i
$225$		0			0
$226$	−5.38463	+	20.0957i	−0.358180	+	1.33675i
$227$	−1.88405	−	7.03137i	−0.125049	−	0.466688i	0.874793	−	0.484498i	$-0.160998\pi$
$227$	−1.88405	−	7.03137i	−0.125049	−	0.466688i	−0.999841	+	0.0178091i	$0.994331\pi$
$228$		0			0
$229$	−2.54196	+	9.48673i	−0.167977	+	0.626901i	0.829664	+	0.558263i	$0.188532\pi$
$229$	−2.54196	+	9.48673i	−0.167977	+	0.626901i	−0.997642	+	0.0686377i	$0.978135\pi$
$230$			0.877918i			0.0578882i
$231$		0			0
$232$	−5.83553	+	5.83553i	−0.383121	+	0.383121i
$233$	−0.958246	+	0.553244i	−0.0627768	+	0.0362442i	−0.531060	−	0.847334i	$-0.678206\pi$
$233$	−0.958246	+	0.553244i	−0.0627768	+	0.0362442i	0.468283	+	0.883578i	$0.344873\pi$
$234$		0			0
$235$	−2.38777	+	4.13574i	−0.155761	+	0.269786i
$236$	8.09424	+	2.16884i	0.526890	+	0.141180i
$237$		0			0
$238$	1.89830	+	1.28743i	0.123048	+	0.0834518i
$239$	8.91696	+	8.91696i	0.576790	+	0.576790i	0.934018	−	0.357227i	$-0.116278\pi$
$239$	8.91696	+	8.91696i	0.576790	+	0.576790i	−0.357227	+	0.934018i	$0.616278\pi$
$240$		0			0
$241$	−16.7789	+	4.49590i	−1.08082	+	0.289606i	−0.754934	−	0.655801i	$-0.772331\pi$
$241$	−16.7789	+	4.49590i	−1.08082	+	0.289606i	−0.325891	+	0.945407i	$0.605664\pi$
$242$	0.741985	+	2.76913i	0.0476966	+	0.178006i
$243$		0			0
$244$	−6.09281			−0.390052
$245$	−5.91565	+	0.695917i	−0.377937	+	0.0444605i
$246$		0			0
$247$	28.6498	+	8.18859i	1.82294	+	0.521027i
$248$	3.12567	+	1.80461i	0.198480	+	0.114593i
$249$		0			0
$250$	−14.3341	+	8.27578i	−0.906567	+	0.523406i
$251$	−13.4051			−0.846120			−0.423060	−	0.906102i	$-0.639044\pi$
$251$	−13.4051			−0.846120			−0.423060	+	0.906102i	$0.639044\pi$
$252$		0			0
$253$	1.07978	+	1.07978i	0.0678853	+	0.0678853i
$254$	35.7891	+	9.58965i	2.24561	+	0.601708i
$255$		0			0
$256$	−3.94983	+	6.84131i	−0.246864	+	0.427582i
$257$	−5.41754	−	9.38346i	−0.337937	−	0.585324i	0.646107	−	0.763246i	$-0.276396\pi$
$257$	−5.41754	−	9.38346i	−0.337937	−	0.585324i	−0.984045	+	0.177922i	$0.943062\pi$
$258$		0			0
$259$	−3.21692	−	0.233148i	−0.199890	−	0.0144871i
$260$	−5.11373	−	5.28634i	−0.317140	−	0.327845i
$261$		0			0
$262$	−10.2684	−	38.3222i	−0.634384	−	2.36755i
$263$	−11.4819	+	19.8873i	−0.708007	+	1.22630i	0.257589	+	0.966255i	$0.417072\pi$
$263$	−11.4819	+	19.8873i	−0.708007	+	1.22630i	−0.965595	+	0.260049i	$0.916261\pi$
$264$		0			0
$265$	−4.43919	+	4.43919i	−0.272697	+	0.272697i
$266$	15.0373	−	43.3144i	0.921995	−	2.65577i
$267$		0			0
$268$	−32.9143	−	8.81936i	−2.01056	−	0.538728i
$269$	2.45827	+	1.41928i	0.149883	+	0.0865353i	0.573066	−	0.819509i	$-0.305754\pi$
$269$	2.45827	+	1.41928i	0.149883	+	0.0865353i	−0.423183	+	0.906044i	$0.639087\pi$
$270$		0			0
$271$	7.46876	−	27.8738i	0.453695	−	1.69321i	−0.238203	−	0.971215i	$-0.576558\pi$
$271$	7.46876	−	27.8738i	0.453695	−	1.69321i	0.691897	−	0.721996i	$-0.256775\pi$
$272$	−1.25994			−0.0763949
$273$		0			0
$274$	−23.5046			−1.41996
$275$	−3.43483	+	12.8190i	−0.207128	+	0.773013i
$276$		0			0
$277$	−1.07397	−	0.620055i	−0.0645284	−	0.0372555i	0.467389	−	0.884052i	$-0.345195\pi$
$277$	−1.07397	−	0.620055i	−0.0645284	−	0.0372555i	−0.531917	+	0.846796i	$0.678528\pi$
$278$	5.11872	+	1.37156i	0.307001	+	0.0822606i
$279$		0			0
$280$	−1.41864	+	1.22690i	−0.0847797	+	0.0733213i
$281$	8.85289	−	8.85289i	0.528119	−	0.528119i	−0.391892	−	0.920011i	$-0.628179\pi$
$281$	8.85289	−	8.85289i	0.528119	−	0.528119i	0.920011	+	0.391892i	$0.128179\pi$
$282$		0			0
$283$	−1.47438	+	2.55370i	−0.0876428	+	0.151802i	−0.906514	−	0.422175i	$-0.861267\pi$
$283$	−1.47438	+	2.55370i	−0.0876428	+	0.151802i	0.818871	+	0.573977i	$0.194600\pi$
$284$	−5.59660	−	20.8868i	−0.332097	−	1.23940i
$285$		0			0
$286$	−23.4629	−	0.389408i	−1.38739	−	0.0230262i
$287$	5.48451	−	8.08681i	0.323740	−	0.477349i
$288$		0			0
$289$	8.41454	+	14.5744i	0.494973	+	0.857318i
$290$	−8.83789	+	15.3077i	−0.518979	+	0.898897i
$291$		0			0
$292$	32.4191	+	8.68667i	1.89718	+	0.508349i
$293$	19.9885	+	19.9885i	1.16774	+	1.16774i	0.982739	+	0.184999i	$0.0592283\pi$
$293$	19.9885	+	19.9885i	1.16774	+	1.16774i	0.184999	+	0.982739i	$0.440772\pi$
$294$		0			0
$295$	2.97441			0.173177
$296$	−0.879545	+	0.507806i	−0.0511225	+	0.0295156i
$297$		0			0
$298$	−14.8267	−	8.56019i	−0.858886	−	0.495878i
$299$	1.55080	−	0.861365i	0.0896853	−	0.0498140i
$300$		0			0
$301$	2.06736	+	10.7815i	0.119161	+	0.621437i
$302$	−6.11078			−0.351636
$303$		0			0
$304$	6.51858	+	24.3277i	0.373866	+	1.39529i
$305$	−2.08896	+	0.559735i	−0.119613	+	0.0320503i
$306$		0			0
$307$	−16.9481	−	16.9481i	−0.967282	−	0.967282i	0.0321997	−	0.999481i	$-0.489749\pi$
$307$	−16.9481	−	16.9481i	−0.967282	−	0.967282i	−0.999481	+	0.0321997i	$0.989749\pi$
$308$	−1.42298	+	19.6340i	−0.0810820	+	1.11875i
$309$		0			0
$310$	7.46689	+	2.00075i	0.424091	+	0.113635i
$311$	−14.2289	+	24.6452i	−0.806847	+	1.39750i	0.108190	+	0.994130i	$0.465495\pi$
$311$	−14.2289	+	24.6452i	−0.806847	+	1.39750i	−0.915037	+	0.403370i	$0.867839\pi$
$312$		0			0
$313$	8.98398	−	5.18691i	0.507805	−	0.293181i	−0.224126	−	0.974560i	$-0.571953\pi$
$313$	8.98398	−	5.18691i	0.507805	−	0.293181i	0.731931	+	0.681379i	$0.238619\pi$
$314$	16.3690	−	16.3690i	0.923754	−	0.923754i
$315$		0			0
$316$			20.5019i			1.15332i
$317$	1.43655	−	5.36127i	0.0806845	−	0.301119i	−0.913778	−	0.406215i	$-0.866848\pi$
$317$	1.43655	−	5.36127i	0.0806845	−	0.301119i	0.994462	+	0.105096i	$0.0335151\pi$
$318$		0			0
$319$	7.95740	+	29.6974i	0.445529	+	1.66274i
$320$	2.37851	−	8.87674i	0.132963	−	0.496225i
$321$		0			0
$322$	−1.19039	−	2.45646i	−0.0663381	−	0.136893i
$323$	−2.41590	+	2.41590i	−0.134424	+	0.134424i
$324$		0			0
$325$	13.2218	+	7.92905i	0.733416	+	0.439825i
$326$	2.37756	−	4.11806i	0.131681	−	0.228078i
$327$		0			0
$328$		−	3.07678i		−	0.169887i
$329$	1.07333	−	14.8097i	0.0591749	−	0.816483i
$330$		0			0
$331$	−0.464548	+	1.73372i	−0.0255339	+	0.0952937i	−0.977517	−	0.210857i	$-0.932375\pi$
$331$	−0.464548	+	1.73372i	−0.0255339	+	0.0952937i	0.951983	+	0.306151i	$0.0990412\pi$
$332$	28.2678	−	7.57432i	1.55140	−	0.415695i
$333$		0			0
$334$	−21.2385	+	12.2620i	−1.16212	+	0.670949i
$335$	−12.0951			−0.660826
$336$		0			0
$337$		−	34.8975i		−	1.90099i	−0.310741	−	0.950495i	$-0.600577\pi$
$337$		−	34.8975i		−	1.90099i	0.310741	−	0.950495i	$-0.399423\pi$
$338$	−7.92548	+	26.0831i	−0.431089	+	1.41873i
$339$		0			0
$340$	0.814603	−	0.218272i	0.0441780	−	0.0118375i
$341$	11.6446	−	6.72300i	0.630589	−	0.364071i
$342$		0			0
$343$	15.6087	−	9.96841i	0.842789	−	0.538244i
$344$	2.44430	+	2.44430i	0.131788	+	0.131788i
$345$		0			0
$346$	39.1106	−	10.4796i	2.10260	−	0.563389i
$347$	−8.36008	+	14.4801i	−0.448793	+	0.777332i	−0.998308	−	0.0581520i	$-0.981479\pi$
$347$	−8.36008	+	14.4801i	−0.448793	+	0.777332i	0.549515	+	0.835484i	$0.314813\pi$
$348$		0			0
$349$	20.0733	+	20.0733i	1.07450	+	1.07450i	0.996992	+	0.0775094i	$0.0246968\pi$
$349$	20.0733	+	20.0733i	1.07450	+	1.07450i	0.0775094	+	0.996992i	$0.475303\pi$
$350$	13.3156	−	19.6337i	0.711751	−	1.04946i
$351$		0			0
$352$	−12.5031	−	21.6559i	−0.666415	−	1.15427i
$353$	−4.12415	−	15.3915i	−0.219506	−	0.819209i	−0.984531	−	0.175208i	$-0.943940\pi$
$353$	−4.12415	−	15.3915i	−0.219506	−	0.819209i	0.765025	−	0.644000i	$-0.222727\pi$
$354$		0			0
$355$	−3.83766	−	6.64702i	−0.203682	−	0.352787i
$356$	11.4570	−	11.4570i	0.607217	−	0.607217i
$357$		0			0
$358$	19.7527	−	19.7527i	1.04396	−	1.04396i
$359$	−23.9724	−	6.42338i	−1.26521	−	0.339013i	−0.437019	−	0.899452i	$-0.643966\pi$
$359$	−23.9724	−	6.42338i	−1.26521	−	0.339013i	−0.828196	+	0.560439i	$0.810632\pi$
$360$		0			0
$361$	42.6925	+	24.6485i	2.24697	+	1.29729i
$362$	0.411467	−	1.53562i	0.0216262	−	0.0807102i
$363$		0			0
$364$	21.4764	+	7.85758i	1.12567	+	0.411849i
$365$	11.9131			0.623561
$366$		0			0
$367$	−27.5277	−	15.8931i	−1.43693	−	0.829615i	−0.439299	−	0.898341i	$-0.644773\pi$
$367$	−27.5277	−	15.8931i	−1.43693	−	0.829615i	−0.997636	+	0.0687263i	$0.978106\pi$
$368$	1.29855	+	0.749719i	0.0676917	+	0.0390818i
$369$		0			0
$370$	−1.53814	+	1.53814i	−0.0799641	+	0.0799641i
$371$	6.40185	−	18.4403i	0.332368	−	0.957373i
$372$		0			0
$373$	1.03118	+	1.78606i	0.0533925	+	0.0924784i	0.891486	−	0.453048i	$-0.149663\pi$
$373$	1.03118	+	1.78606i	0.0533925	+	0.0924784i	−0.838094	+	0.545526i	$0.816330\pi$
$374$	1.34534	−	2.33020i	0.0695661	−	0.120492i
$375$		0			0
$376$	−2.33777	−	4.04914i	−0.120561	−	0.208818i
$377$	35.7116	+	0.592694i	1.83924	+	0.0305253i
$378$		0			0
$379$	16.5343	+	16.5343i	0.849312	+	0.849312i	0.990047	−	0.140735i	$-0.0449466\pi$
$379$	16.5343	+	16.5343i	0.849312	+	0.849312i	−0.140735	+	0.990047i	$0.544947\pi$
$380$	−8.42908	−	14.5996i	−0.432403	−	0.748943i
$381$		0			0
$382$	46.5286	−	12.4673i	2.38061	−	0.637882i
$383$	−15.8461	−	4.24594i	−0.809695	−	0.216957i	−0.169859	−	0.985468i	$-0.554331\pi$
$383$	−15.8461	−	4.24594i	−0.809695	−	0.216957i	−0.639836	+	0.768511i	$0.720998\pi$
$384$		0			0
$385$	1.31586	+	6.86239i	0.0670626	+	0.349740i
$386$	13.4825			0.686242
$387$		0			0
$388$	14.6699	−	3.93078i	0.744750	−	0.199555i
$389$	27.5754	+	15.9207i	1.39813	+	0.807210i	0.994196	−	0.107579i	$-0.0343100\pi$
$389$	27.5754	+	15.9207i	1.39813	+	0.807210i	0.403932	+	0.914789i	$0.367643\pi$
$390$		0			0
$391$			0.203407i			0.0102867i
$392$	2.30583	−	5.35650i	0.116462	−	0.270544i
$393$		0			0
$394$	−2.30466	+	1.33060i	−0.116107	+	0.0670346i
$395$	1.88347	+	7.02921i	0.0947677	+	0.353678i
$396$		0			0
$397$	0.667382	−	2.49070i	0.0334949	−	0.125005i	−0.947154	−	0.320779i	$-0.896055\pi$
$397$	0.667382	−	2.49070i	0.0334949	−	0.125005i	0.980649	+	0.195774i	$0.0627220\pi$
$398$	−6.34398	−	6.34398i	−0.317995	−	0.317995i
$399$		0			0
$400$			13.0313i			0.651564i
$401$	27.3463	+	7.32742i	1.36561	+	0.365914i	0.865873	−	0.500264i	$-0.166764\pi$
$401$	27.3463	+	7.32742i	1.36561	+	0.365914i	0.499736	+	0.866178i	$0.333430\pi$
$402$		0			0
$403$	−3.79187	−	15.1530i	−0.188887	−	0.754823i
$404$	−17.9359	+	10.3553i	−0.892345	+	0.515196i
$405$		0			0
$406$	3.97275	−	54.8152i	0.197164	−	2.72043i
$407$			3.78362i			0.187547i
$408$		0			0
$409$	0.0165610	+	0.0618067i	0.000818891	+	0.00305614i	0.966334	−	0.257291i	$-0.0828298\pi$
$409$	0.0165610	+	0.0618067i	0.000818891	+	0.00305614i	−0.965515	+	0.260347i	$0.916163\pi$
$410$	−1.70560	−	6.36538i	−0.0842334	−	0.314364i
$411$		0			0
$412$		−	22.3042i		−	1.09885i
$413$	−8.32255	+	4.03309i	−0.409526	+	0.198455i
$414$		0			0
$415$	8.99595	−	5.19381i	0.441594	−	0.254954i
$416$	−28.1806	+	7.05191i	−1.38167	+	0.345749i
$417$		0			0
$418$	−51.9536	−	13.9209i	−2.54113	−	0.680894i
$419$		−	4.23556i		−	0.206921i	−0.994634	−	0.103460i	$-0.967009\pi$
$419$		−	4.23556i		−	0.206921i	0.994634	−	0.103460i	$-0.0329915\pi$
$420$		0			0
$421$	−13.3618	−	13.3618i	−0.651216	−	0.651216i	0.302070	−	0.953286i	$-0.402322\pi$
$421$	−13.3618	−	13.3618i	−0.651216	−	0.651216i	−0.953286	+	0.302070i	$0.902322\pi$
$422$	−7.83726	+	29.2491i	−0.381512	+	1.42382i
$423$		0			0
$424$	−1.59083	−	5.93706i	−0.0772576	−	0.288329i
$425$	−1.53093	+	0.883881i	−0.0742609	+	0.0428745i
$426$		0			0
$427$	5.08605	−	4.39865i	0.246131	−	0.212865i
$428$			22.1536i			1.07083i
$429$		0			0
$430$	6.41186	+	3.70189i	0.309207	+	0.178521i
$431$	14.5600	−	3.90135i	0.701332	−	0.187921i	0.109505	−	0.993986i	$-0.465073\pi$
$431$	14.5600	−	3.90135i	0.701332	−	0.187921i	0.591827	+	0.806065i	$0.298407\pi$
$432$		0			0
$433$	8.45509			0.406326			0.203163	−	0.979145i	$-0.434878\pi$
$433$	8.45509			0.406326			0.203163	+	0.979145i	$0.434878\pi$
$434$	−23.6056	+	4.52638i	−1.13311	+	0.217273i
$435$		0			0
$436$	5.99072	+	1.60521i	0.286904	+	0.0768756i
$437$	3.92751	−	1.05237i	0.187878	−	0.0503418i
$438$		0			0
$439$	−9.90274	−	17.1520i	−0.472632	−	0.818623i	0.526877	−	0.849941i	$-0.323363\pi$
$439$	−9.90274	−	17.1520i	−0.472632	−	0.818623i	−0.999509	+	0.0313187i	$0.990029\pi$
$440$	1.55579	+	1.55579i	0.0741692	+	0.0741692i
$441$		0			0
$442$	−2.17327	−	2.24663i	−0.103372	−	0.106861i
$443$	−1.30200	−	2.25514i	−0.0618601	−	0.107145i	0.833437	−	0.552615i	$-0.186370\pi$
$443$	−1.30200	−	2.25514i	−0.0618601	−	0.107145i	−0.895297	+	0.445470i	$0.853037\pi$
$444$		0			0
$445$	2.87556	−	4.98062i	0.136315	−	0.236104i
$446$	−1.35424	−	2.34562i	−0.0641253	−	0.111068i
$447$		0			0
$448$	5.38102	+	28.0627i	0.254229	+	1.32584i
$449$	20.6509	−	20.6509i	0.974578	−	0.974578i	−0.0251065	−	0.999685i	$-0.507992\pi$
$449$	20.6509	−	20.6509i	0.974578	−	0.974578i	0.999685	+	0.0251065i	$0.00799250\pi$
$450$		0			0
$451$	−9.92676	−	5.73122i	−0.467433	−	0.269873i
$452$	−20.5977	−	11.8921i	−0.968832	−	0.559356i
$453$		0			0
$454$	15.2647			0.716409
$455$	8.08518	+	0.721030i	0.379039	+	0.0338024i
$456$		0			0
$457$	5.39726	−	20.1428i	0.252473	−	0.942243i	−0.717006	−	0.697067i	$-0.754488\pi$
$457$	5.39726	−	20.1428i	0.252473	−	0.942243i	0.969479	−	0.245175i	$-0.0788455\pi$
$458$	−17.8359	−	10.2976i	−0.833418	−	0.481174i
$459$		0			0
$460$	−0.969450	−	0.259763i	−0.0452009	−	0.0121115i
$461$	25.6893	−	25.6893i	1.19647	−	1.19647i	0.221256	−	0.975216i	$-0.428985\pi$
$461$	25.6893	−	25.6893i	1.19647	−	1.19647i	0.975216	−	0.221256i	$-0.0710155\pi$
$462$		0			0
$463$	−16.4838	+	16.4838i	−0.766066	+	0.766066i	−0.977411	−	0.211345i	$-0.932216\pi$
$463$	−16.4838	+	16.4838i	−0.766066	+	0.766066i	0.211345	+	0.977411i	$0.432216\pi$
$464$	15.0946	+	26.1447i	0.700751	+	1.21374i
$465$		0			0
$466$	−0.600531	−	2.24121i	−0.0278190	−	0.103822i
$467$	7.45050	+	12.9047i	0.344768	+	0.597156i	0.985312	−	0.170766i	$-0.0546242\pi$
$467$	7.45050	+	12.9047i	0.344768	+	0.597156i	−0.640543	+	0.767922i	$0.721291\pi$
$468$		0			0
$469$	33.8427	−	16.4001i	1.56271	−	0.757287i
$470$	−7.08109	−	7.08109i	−0.326626	−	0.326626i
$471$		0			0
$472$	−1.45606	+	2.52197i	−0.0670207	+	0.116083i
$473$	12.4392	−	3.33308i	0.571957	−	0.153255i
$474$		0			0
$475$	24.9872	+	24.9872i	1.14649	+	1.14649i
$476$	−1.98334	+	1.71528i	−0.0909062	+	0.0786197i
$477$		0			0
$478$	−22.9010	+	13.2219i	−1.04747	+	0.604756i
$479$	−14.0492	+	3.76447i	−0.641924	+	0.172003i	−0.565075	−	0.825040i	$-0.691153\pi$
$479$	−14.0492	+	3.76447i	−0.641924	+	0.172003i	−0.0768490	+	0.997043i	$0.524486\pi$
$480$		0			0
$481$	4.22619	+	1.20792i	0.192698	+	0.0550763i
$482$		−	36.4261i		−	1.65916i
$483$		0			0
$484$	−3.27738			−0.148972
$485$	4.66855	−	2.69539i	0.211988	−	0.122391i
$486$		0			0
$487$	−28.4242	+	7.61625i	−1.28802	+	0.345125i	−0.836910	−	0.547341i	$-0.815640\pi$
$487$	−28.4242	+	7.61625i	−1.28802	+	0.345125i	−0.451115	+	0.892466i	$0.648973\pi$
$488$	0.548014	−	2.04522i	0.0248074	−	0.0925826i
$489$		0			0
$490$	1.80104	−	12.3600i	0.0813629	−	0.558366i
$491$		−	25.7337i		−	1.16135i	−0.814137	−	0.580673i	$-0.802790\pi$
$491$		−	25.7337i		−	1.16135i	0.814137	−	0.580673i	$-0.197210\pi$
$492$		0			0
$493$	−2.04767	+	3.54667i	−0.0922224	+	0.159734i
$494$	−32.1354	+	53.5864i	−1.44584	+	2.41097i
$495$		0			0
$496$	9.33589	−	9.33589i	0.419194	−	0.419194i
$497$	19.7509	+	13.3951i	0.885947	+	0.600853i
$498$		0			0
$499$	−9.17150	+	34.2285i	−0.410573	+	1.53228i	0.382968	+	0.923762i	$0.374902\pi$
$499$	−9.17150	+	34.2285i	−0.410573	+	1.53228i	−0.793541	+	0.608517i	$0.791765\pi$
$500$	−4.89737	−	18.2772i	−0.219017	−	0.817383i
$501$		0			0
$502$	7.27541	−	27.1522i	0.324717	−	1.21186i
$503$		−	29.3220i		−	1.30740i	−0.756753	−	0.653701i	$-0.773215\pi$
$503$		−	29.3220i		−	1.30740i	0.756753	−	0.653701i	$-0.226785\pi$
$504$		0			0
$505$	−5.19812	+	5.19812i	−0.231313	+	0.231313i
$506$	−2.77315	+	1.60108i	−0.123282	+	0.0711767i
$507$		0			0
$508$	−21.1789	+	36.6830i	−0.939664	+	1.62755i
$509$	−28.3119	−	7.58614i	−1.25490	−	0.336250i	−0.430674	−	0.902508i	$-0.641724\pi$
$509$	−28.3119	−	7.58614i	−1.25490	−	0.336250i	−0.824228	+	0.566258i	$0.808391\pi$
$510$		0			0
$511$	−33.3335	+	16.1533i	−1.47459	+	0.714582i
$512$	−20.9530	−	20.9530i	−0.926000	−	0.926000i
$513$		0			0
$514$	21.9467	−	5.88059i	0.968026	−	0.259382i
$515$	−2.04905	−	7.64715i	−0.0902918	−	0.336974i
$516$		0			0
$517$	−17.4185			−0.766066
$518$	2.21819	−	6.38940i	0.0974615	−	0.280734i
$519$		0			0
$520$	2.23445	−	1.24109i	0.0979872	−	0.0544252i
$521$	8.32208	+	4.80476i	0.364597	+	0.210500i	0.671095	−	0.741371i	$-0.265824\pi$
$521$	8.32208	+	4.80476i	0.364597	+	0.210500i	−0.306498	+	0.951871i	$0.599157\pi$
$522$		0			0
$523$	4.36673	−	2.52113i	0.190944	−	0.110241i	−0.401481	−	0.915868i	$-0.631504\pi$
$523$	4.36673	−	2.52113i	0.190944	−	0.110241i	0.592424	+	0.805626i	$0.298171\pi$
$524$	45.3559			1.98138
$525$		0			0
$526$	−34.0504	−	34.0504i	−1.48467	−	1.48467i
$527$	1.73002	+	0.463558i	0.0753609	+	0.0201929i
$528$		0			0
$529$	−11.3790	+	19.7089i	−0.494738	+	0.856911i
$530$	−6.58235	−	11.4010i	−0.285919	−	0.495226i
$531$		0			0
$532$	43.3810	+	29.4212i	1.88081	+	1.27557i
$533$	−9.57072	+	9.25822i	−0.414554	+	0.401018i
$534$		0			0
$535$	2.03521	+	7.59551i	0.0879898	+	0.328382i
$536$	5.92092	−	10.2553i	0.255745	−	0.442963i
$537$		0			0
$538$	−4.20898	+	4.20898i	−0.181462	+	0.181462i
$539$	−12.9868	−	17.4171i	−0.559380	−	0.750207i
$540$		0			0
$541$	13.9049	+	3.72582i	0.597820	+	0.160185i	0.545025	−	0.838420i	$-0.316520\pi$
$541$	13.9049	+	3.72582i	0.597820	+	0.160185i	0.0527954	+	0.998605i	$0.483187\pi$
$542$	52.4053	+	30.2562i	2.25100	+	1.29962i
$543$		0			0
$544$	0.862099	−	3.21740i	0.0369622	−	0.137945i
$545$	2.20143			0.0942987
$546$		0			0
$547$	18.1309			0.775223			0.387612	−	0.921823i	$-0.373300\pi$
$547$	18.1309			0.775223			0.387612	+	0.921823i	$0.373300\pi$
$548$	6.95467	−	25.9552i	0.297089	−	1.10875i
$549$		0			0
$550$	−24.1008	−	13.9146i	−1.02766	−	0.593322i
$551$	79.0755	+	21.1882i	3.36873	+	0.902648i
$552$		0			0
$553$	−14.8012	−	17.1142i	−0.629409	−	0.727772i
$554$	1.83881	−	1.83881i	0.0781237	−	0.0781237i
$555$		0			0
$556$	−3.02911	+	5.24658i	−0.128463	+	0.222505i
$557$	−8.14011	−	30.3793i	−0.344907	−	1.28721i	−0.892720	−	0.450611i	$-0.851206\pi$
$557$	−8.14011	−	30.3793i	−0.344907	−	1.28721i	0.547813	−	0.836601i	$-0.315461\pi$
$558$		0			0
$559$	0.248259	−	14.9584i	0.0105003	−	0.632671i
$560$	2.99206	+	6.17432i	0.126438	+	0.260913i
$561$		0			0
$562$	13.1269	+	22.7365i	0.553725	+	0.959080i
$563$	15.3955	−	26.6658i	0.648844	−	1.12383i	−0.334555	−	0.942376i	$-0.608586\pi$
$563$	15.3955	−	26.6658i	0.648844	−	1.12383i	0.983399	−	0.181455i	$-0.0580806\pi$
$564$		0			0
$565$	−8.15454	−	2.18500i	−0.343064	−	0.0919238i
$566$	−4.37237	−	4.37237i	−0.183784	−	0.183784i
$567$		0			0
$568$	7.51460			0.315306
$569$	−15.6802	+	9.05299i	−0.657350	+	0.379521i	−0.791266	−	0.611471i	$-0.790578\pi$
$569$	−15.6802	+	9.05299i	−0.657350	+	0.379521i	0.133917	+	0.990993i	$0.457245\pi$
$570$		0			0
$571$	4.25643	+	2.45745i	0.178126	+	0.102841i	0.586412	−	0.810013i	$-0.300540\pi$
$571$	4.25643	+	2.45745i	0.178126	+	0.102841i	−0.408286	+	0.912854i	$0.633873\pi$
$572$	7.37236	−	25.7940i	0.308254	−	1.07850i
$573$		0			0
$574$	13.4033	+	15.4980i	0.559445	+	0.646873i
$575$	2.10380			0.0877344
$576$		0			0
$577$	5.80630	+	21.6694i	0.241719	+	0.902109i	0.975004	+	0.222187i	$0.0713197\pi$
$577$	5.80630	+	21.6694i	0.241719	+	0.902109i	−0.733285	+	0.679922i	$0.762014\pi$
$578$	−34.0876	+	9.13375i	−1.41786	+	0.379914i
$579$		0			0
$580$	−14.2887	−	14.2887i	−0.593304	−	0.593304i
$581$	−18.1287	+	26.7304i	−0.752104	+	1.10896i
$582$		0			0
$583$	−22.1183	−	5.92658i	−0.916046	−	0.245454i
$584$	−5.83183	+	10.1010i	−0.241323	+	0.417983i
$585$		0			0
$586$	−51.3354	+	29.6385i	−2.12065	+	1.22436i
$587$	−22.0551	+	22.0551i	−0.910312	+	0.910312i	−0.996296	−	0.0859844i	$-0.972596\pi$
$587$	−22.0551	+	22.0551i	−0.910312	+	0.910312i	0.0859844	+	0.996296i	$0.472596\pi$
$588$		0			0
$589$		−	35.8027i		−	1.47522i
$590$	−1.61432	+	6.02472i	−0.0664605	+	0.248034i
$591$		0			0
$592$	0.961571	+	3.58863i	0.0395203	+	0.147492i
$593$	−0.998325	+	3.72580i	−0.0409963	+	0.153000i	−0.983390	−	0.181506i	$-0.941903\pi$
$593$	−0.998325	+	3.72580i	−0.0409963	+	0.153000i	0.942394	+	0.334506i	$0.108570\pi$
$594$		0			0
$595$	−0.522421	+	0.770301i	−0.0214172	+	0.0315792i
$596$	13.8397	−	13.8397i	0.566895	−	0.566895i
$597$		0			0
$598$	0.903034	+	3.60868i	0.0369278	+	0.147570i
$599$	5.92981	−	10.2707i	0.242285	−	0.419651i	−0.719080	−	0.694928i	$-0.755436\pi$
$599$	5.92981	−	10.2707i	0.242285	−	0.419651i	0.961365	+	0.275277i	$0.0887696\pi$
$600$		0			0
$601$		−	4.00550i		−	0.163388i	−0.996657	−	0.0816939i	$-0.973967\pi$
$601$		−	4.00550i		−	0.163388i	0.996657	−	0.0816939i	$-0.0260330\pi$
$602$	−22.9602	−	1.66405i	−0.935788	−	0.0678216i
$603$		0			0
$604$	1.80809	−	6.74789i	0.0735702	−	0.274568i
$605$	−1.12367	+	0.301087i	−0.0456837	+	0.0122409i
$606$		0			0
$607$	−21.2877	+	12.2904i	−0.864040	+	0.498854i	−0.865363	−	0.501145i	$-0.832912\pi$
$607$	−21.2877	+	12.2904i	−0.864040	+	0.498854i	0.00132321	+	0.999999i	$0.499579\pi$
$608$	−66.5839			−2.70033
$609$		0			0
$610$		−	4.53501i		−	0.183617i
$611$	−5.56086	+	19.4560i	−0.224968	+	0.787106i
$612$		0			0
$613$	−17.8464	+	4.78193i	−0.720809	+	0.193140i	−0.600533	−	0.799600i	$-0.705045\pi$
$613$	−17.8464	+	4.78193i	−0.720809	+	0.193140i	−0.120277	+	0.992740i	$0.538378\pi$
$614$	43.5272	−	25.1304i	1.75661	−	1.01418i
$615$		0			0
$616$	−6.46271	−	2.24364i	−0.260390	−	0.0903986i
$617$	21.0606	+	21.0606i	0.847867	+	0.847867i	0.989867	−	0.142000i	$-0.0453533\pi$
$617$	21.0606	+	21.0606i	0.847867	+	0.847867i	−0.142000	+	0.989867i	$0.545353\pi$
$618$		0			0
$619$	13.2380	−	3.54712i	0.532082	−	0.142571i	0.0172324	−	0.999852i	$-0.494514\pi$
$619$	13.2380	−	3.54712i	0.532082	−	0.142571i	0.514849	+	0.857281i	$0.327848\pi$
$620$	−4.41870	+	7.65340i	−0.177459	+	0.307368i
$621$		0			0
$622$	−42.1967	−	42.1967i	−1.69194	−	1.69194i
$623$	−1.29260	+	17.8351i	−0.0517871	+	0.714548i
$624$		0			0
$625$	7.33164	+	12.6988i	0.293266	+	0.507951i
$626$	5.63024	+	21.0123i	0.225030	+	0.839822i
$627$		0			0
$628$	13.2323	+	22.9190i	0.528025	+	0.914566i
$629$	−0.356375	+	0.356375i	−0.0142096	+	0.0142096i
$630$		0			0
$631$	−32.1535	+	32.1535i	−1.28001	+	1.28001i	−0.339350	+	0.940660i	$0.610207\pi$
$631$	−32.1535	+	32.1535i	−1.28001	+	1.28001i	−0.940660	+	0.339350i	$0.889793\pi$
$632$	−6.88202	−	1.84403i	−0.273752	−	0.0733516i
$633$		0			0
$634$	10.0797	+	5.81951i	0.400315	+	0.231122i
$635$	−3.89134	+	14.5227i	−0.154423	+	0.576315i
$636$		0			0
$637$	−23.6004	+	8.94545i	−0.935082	+	0.354431i
$638$	−64.4715			−2.55245
$639$		0			0
$640$	4.81453	+	2.77967i	0.190311	+	0.109876i
$641$	−25.6992	−	14.8374i	−1.01506	−	0.586044i	−0.102389	−	0.994744i	$-0.532649\pi$
$641$	−25.6992	−	14.8374i	−1.01506	−	0.586044i	−0.912669	+	0.408700i	$0.865982\pi$
$642$		0			0
$643$	24.1967	−	24.1967i	0.954225	−	0.954225i	−0.0447727	−	0.998997i	$-0.514256\pi$
$643$	24.1967	−	24.1967i	0.954225	−	0.954225i	0.998997	+	0.0447727i	$0.0142563\pi$
$644$	3.06479	−	0.587674i	0.120770	−	0.0231576i
$645$		0			0
$646$	−3.58225	−	6.20465i	−0.140942	−	0.244119i
$647$	2.61599	−	4.53103i	0.102845	−	0.178133i	−0.810011	−	0.586415i	$-0.800539\pi$
$647$	2.61599	−	4.53103i	0.102845	−	0.178133i	0.912856	+	0.408282i	$0.133872\pi$
$648$		0			0
$649$	5.42450	+	9.39552i	0.212930	+	0.368806i
$650$	−23.2364	+	22.4777i	−0.911407	+	0.881648i
$651$		0			0
$652$	3.84392	+	3.84392i	0.150540	+	0.150540i
$653$	−9.75711	−	16.8998i	−0.381825	−	0.661341i	0.609498	−	0.792788i	$-0.291371\pi$
$653$	−9.75711	−	16.8998i	−0.381825	−	0.661341i	−0.991323	+	0.131447i	$0.958038\pi$
$654$		0			0
$655$	15.5506	−	4.16676i	0.607611	−	0.162809i
$656$	−10.8717	−	2.91307i	−0.424470	−	0.113736i
$657$		0			0
$658$	29.4147	+	10.2118i	1.14670	+	0.398097i
$659$	−32.6455			−1.27169			−0.635844	−	0.771817i	$-0.719348\pi$
$659$	−32.6455			−1.27169			−0.635844	+	0.771817i	$0.719348\pi$
$660$		0			0
$661$	−32.1921	+	8.62585i	−1.25213	+	0.335506i	−0.823158	−	0.567813i	$-0.807790\pi$
$661$	−32.1921	+	8.62585i	−1.25213	+	0.335506i	−0.428969	+	0.903319i	$0.641123\pi$
$662$	−3.25955	−	1.88190i	−0.126686	−	0.0731422i
$663$		0			0
$664$			10.1701i			0.394677i
$665$	17.5763	+	6.10191i	0.681581	+	0.236622i
$666$		0			0
$667$	4.22085	−	2.43691i	0.163432	−	0.0943576i
$668$	−7.25633	−	27.0810i	−0.280756	−	1.04779i
$669$		0			0
$670$	6.56445	−	24.4989i	0.253607	−	0.946474i
$671$	−5.57777	−	5.57777i	−0.215327	−	0.215327i
$672$		0			0
$673$		−	34.9465i		−	1.34709i	−0.739147	−	0.673544i	$-0.764771\pi$
$673$		−	34.9465i		−	1.34709i	0.739147	−	0.673544i	$-0.235229\pi$
$674$	70.6856	+	18.9401i	2.72271	+	0.729547i
$675$		0			0
$676$	−26.4575	−	16.4694i	−1.01760	−	0.633439i
$677$	−3.10994	+	1.79552i	−0.119525	+	0.0690075i	−0.558570	−	0.829457i	$-0.688650\pi$
$677$	−3.10994	+	1.79552i	−0.119525	+	0.0690075i	0.439046	+	0.898465i	$0.355317\pi$
$678$		0			0
$679$	−9.40809	+	13.8721i	−0.361049	+	0.532361i
$680$			0.293076i			0.0112389i
$681$		0			0
$682$	7.29763	+	27.2351i	0.279441	+	1.04289i
$683$	−7.74595	−	28.9083i	−0.296390	−	1.10614i	−0.940107	−	0.340880i	$-0.889275\pi$
$683$	−7.74595	−	28.9083i	−0.296390	−	1.10614i	0.643716	−	0.765264i	$-0.277392\pi$
$684$		0			0
$685$		−	9.53781i		−	0.364421i
$686$	11.7198	+	37.0259i	0.447465	+	1.41365i
$687$		0			0
$688$	10.9511	−	6.32263i	0.417508	−	0.241048i
$689$	−13.6811	+	22.8134i	−0.521207	+	0.869123i
$690$		0			0
$691$	4.66531	+	1.25007i	0.177477	+	0.0475547i	0.346463	−	0.938064i	$-0.387383\pi$
$691$	4.66531	+	1.25007i	0.177477	+	0.0475547i	−0.168986	+	0.985618i	$0.554049\pi$
$692$			46.2890i			1.75965i
$693$		0			0
$694$	−24.7924	−	24.7924i	−0.941105	−	0.941105i
$695$	−0.556558	+	2.07710i	−0.0211115	+	0.0787890i
$696$		0			0
$697$	−0.395174	−	1.47481i	−0.0149683	−	0.0558623i
$698$	−51.5534	+	29.7644i	−1.95133	+	1.12660i
$699$		0			0
$700$	17.7408	+	20.5133i	0.670539	+	0.775329i
$701$		−	37.4256i		−	1.41355i	−0.707440	−	0.706773i	$-0.750150\pi$
$701$		−	37.4256i		−	1.41355i	0.707440	−	0.706773i	$-0.249850\pi$
$702$		0			0
$703$	8.72491	+	5.03733i	0.329066	+	0.189986i
$704$	32.3774	−	8.67551i	1.22027	−	0.326971i
$705$		0			0
$706$	33.4142			1.25756
$707$	7.49633	−	21.5929i	0.281928	−	0.812085i
$708$		0			0
$709$	1.77718	+	0.476195i	0.0667435	+	0.0178839i	0.292036	−	0.956407i	$-0.405667\pi$
$709$	1.77718	+	0.476195i	0.0667435	+	0.0178839i	−0.225293	+	0.974291i	$0.572334\pi$
$710$	15.5465	−	4.16567i	0.583450	−	0.156335i
$711$		0			0
$712$	2.81535	+	4.87633i	0.105510	+	0.182748i
$713$	−1.50721	−	1.50721i	−0.0564453	−	0.0564453i
$714$		0			0
$715$	0.158016	−	9.52092i	0.00590946	−	0.356062i
$716$	15.9676	+	27.6567i	0.596737	+	1.03358i
$717$		0			0
$718$	26.0214	−	45.0703i	0.971109	−	1.68201i
$719$	−15.2707	−	26.4497i	−0.569502	−	0.986407i	−0.996615	−	0.0822086i	$-0.973803\pi$
$719$	−15.2707	−	26.4497i	−0.569502	−	0.986407i	0.427113	−	0.904198i	$-0.359531\pi$
$720$		0			0
$721$	16.1023	+	18.6188i	0.599682	+	0.693399i
$722$	−73.0968	+	73.0968i	−2.72038	+	2.72038i
$723$		0			0
$724$	1.57397	+	0.908734i	0.0584963	+	0.0337728i
$725$	36.6825	+	21.1786i	1.36235	+	0.786555i
$726$		0			0
$727$	−13.0799			−0.485108			−0.242554	−	0.970138i	$-0.577985\pi$
$727$	−13.0799			−0.485108			−0.242554	+	0.970138i	$0.577985\pi$
$728$	−4.56929	+	6.50238i	−0.169349	+	0.240994i
$729$		0			0
$730$	−6.46568	+	24.1302i	−0.239306	+	0.893101i
$731$	1.48558	+	0.857699i	0.0549461	+	0.0317231i
$732$		0			0
$733$	12.0109	+	3.21831i	0.443632	+	0.118871i	0.473718	−	0.880676i	$-0.342911\pi$
$733$	12.0109	+	3.21831i	0.443632	+	0.118871i	−0.0300861	+	0.999547i	$0.509578\pi$
$734$	47.1321	−	47.1321i	1.73968	−	1.73968i
$735$		0			0
$736$	−2.80302	+	2.80302i	−0.103321	+	0.103321i
$737$	−22.0581	−	38.2058i	−0.812522	−	1.40733i
$738$		0			0
$739$	−5.07533	−	18.9414i	−0.186699	−	0.696770i	−0.994260	−	0.106987i	$-0.965880\pi$
$739$	−5.07533	−	18.9414i	−0.186699	−	0.696770i	0.807561	−	0.589784i	$-0.200787\pi$
$740$	−1.24339	−	2.15362i	−0.0457080	−	0.0791687i
$741$		0			0
$742$	33.8767	+	22.9753i	1.24365	+	0.843449i
$743$	−15.1899	−	15.1899i	−0.557264	−	0.557264i	0.371263	−	0.928528i	$-0.378925\pi$
$743$	−15.1899	−	15.1899i	−0.557264	−	0.557264i	−0.928528	+	0.371263i	$0.878925\pi$
$744$		0			0
$745$	3.47360	−	6.01645i	0.127263	−	0.220426i
$746$	−4.17735	+	1.11932i	−0.152944	+	0.0409811i
$747$		0			0
$748$	2.17508	+	2.17508i	0.0795290	+	0.0795290i
$749$	−15.9936	−	18.4930i	−0.584393	−	0.675720i
$750$		0			0
$751$	−20.2091	+	11.6677i	−0.737442	+	0.425762i	−0.821138	−	0.570729i	$-0.806661\pi$
$751$	−20.2091	+	11.6677i	−0.737442	+	0.425762i	0.0836967	+	0.996491i	$0.473327\pi$
$752$	−16.5209	+	4.42676i	−0.602455	+	0.161427i
$753$		0			0
$754$	−20.5825	+	72.0128i	−0.749569	+	2.62255i
$755$		−	2.47967i		−	0.0902443i
$756$		0			0
$757$	−31.8412			−1.15729			−0.578644	−	0.815580i	$-0.696418\pi$
$757$	−31.8412			−1.15729			−0.578644	+	0.815580i	$0.696418\pi$
$758$	−42.4644	+	24.5168i	−1.54238	+	0.890492i
$759$		0			0
$760$	5.65890	−	1.51630i	0.205270	−	0.0550019i
$761$	−11.7636	+	43.9024i	−0.426430	+	1.59146i	0.334349	+	0.942449i	$0.391484\pi$
$761$	−11.7636	+	43.9024i	−0.426430	+	1.59146i	−0.760779	+	0.649011i	$0.775183\pi$
$762$		0			0
$763$	−6.15970	+	2.98498i	−0.222996	+	0.108063i
$764$			55.0686i			1.99231i
$765$		0			0
$766$	17.2004	−	29.7921i	0.621478	−	1.07643i
$767$	12.2263	−	3.05950i	0.441466	−	0.110472i
$768$		0			0
$769$	24.5113	−	24.5113i	0.883898	−	0.883898i	−0.110030	−	0.993928i	$-0.535095\pi$
$769$	24.5113	−	24.5113i	0.883898	−	0.883898i	0.993928	+	0.110030i	$0.0350947\pi$
$770$	−14.6141	−	1.05916i	−0.526654	−	0.0381694i
$771$		0			0
$772$	−3.98928	+	14.8882i	−0.143577	+	0.535838i
$773$	5.87810	+	21.9374i	0.211421	+	0.789033i	0.987396	+	0.158269i	$0.0505914\pi$
$773$	5.87810	+	21.9374i	0.211421	+	0.789033i	−0.775975	+	0.630763i	$0.782742\pi$
$774$		0			0
$775$	4.79449	−	17.8933i	0.172223	−	0.642745i
$776$			5.27789i			0.189465i
$777$		0			0
$778$	−47.2138	+	47.2138i	−1.69270	+	1.69270i
$779$	−26.4320	+	15.2605i	−0.947026	+	0.546766i
$780$		0			0
$781$	13.9977	−	24.2447i	0.500876	−	0.867543i
$782$	−0.412004	−	0.110396i	−0.0147332	−	0.00394776i
$783$		0			0
$784$	−16.7439	−	13.2191i	−0.597996	−	0.472109i
$785$	6.64229	+	6.64229i	0.237073	+	0.237073i
$786$		0			0
$787$	−17.0663	+	4.57290i	−0.608348	+	0.163006i	−0.549825	−	0.835280i	$-0.685306\pi$
$787$	−17.0663	+	4.57290i	−0.608348	+	0.163006i	−0.0585226	+	0.998286i	$0.518639\pi$
$788$	−0.787410	−	2.93866i	−0.0280503	−	0.104685i
$789$		0			0
$790$	−15.2600			−0.542927
$791$	25.7795	−	4.94323i	0.916615	−	0.175761i
$792$		0			0
$793$	−8.01090	+	4.44950i	−0.284475	+	0.158007i
$794$	4.68275	+	2.70359i	0.166185	+	0.0959467i
$795$		0			0
$796$	8.88250	−	5.12832i	0.314832	−	0.181768i
$797$	22.9818			0.814058			0.407029	−	0.913415i	$-0.366565\pi$
$797$	22.9818			0.814058			0.407029	+	0.913415i	$0.366565\pi$
$798$		0			0
$799$	−1.64063	−	1.64063i	−0.0580414	−	0.0580414i
$800$	−33.2769	−	8.91652i	−1.17652	−	0.315247i
$801$		0			0
$802$	−29.6837	+	51.4136i	−1.04817	+	1.81548i
$803$	21.7262	+	37.6310i	0.766703	+	1.32797i
$804$		0			0
$805$	0.996796	−	0.483045i	0.0351324	−	0.0170251i
$806$	32.7506	+	0.543552i	1.15359	+	0.0191458i
$807$		0			0
$808$	−1.86280	−	6.95208i	−0.0655332	−	0.244573i
$809$	20.7877	−	36.0053i	0.730856	−	1.26588i	−0.225661	−	0.974206i	$-0.572454\pi$
$809$	20.7877	−	36.0053i	0.730856	−	1.26588i	0.956518	−	0.291674i	$-0.0942124\pi$
$810$		0			0
$811$	16.0291	−	16.0291i	0.562859	−	0.562859i	−0.367259	−	0.930119i	$-0.619704\pi$
$811$	16.0291	−	16.0291i	0.562859	−	0.562859i	0.930119	+	0.367259i	$0.119704\pi$
$812$	59.3548	+	20.6060i	2.08294	+	0.723128i
$813$		0			0
$814$	−7.66379	−	2.05351i	−0.268616	−	0.0719754i
$815$	1.67105	+	0.964780i	0.0585342	+	0.0337948i
$816$		0			0
$817$	8.87502	−	33.1220i	0.310498	−	1.15879i
$818$	−0.134179			−0.00469145
$819$		0			0
$820$	7.53370			0.263088
$821$	14.5451	−	54.2832i	0.507629	−	1.89450i	0.0647853	−	0.997899i	$-0.479364\pi$
$821$	14.5451	−	54.2832i	0.507629	−	1.89450i	0.442844	−	0.896599i	$-0.353970\pi$
$822$		0			0
$823$	−7.43047	−	4.28998i	−0.259010	−	0.149539i	0.364873	−	0.931057i	$-0.381112\pi$
$823$	−7.43047	−	4.28998i	−0.259010	−	0.149539i	−0.623883	+	0.781518i	$0.714446\pi$
$824$	7.48702	+	2.00614i	0.260823	+	0.0698872i
$825$		0			0
$826$	−3.65215	−	19.0464i	−0.127074	−	0.662709i
$827$	12.1796	−	12.1796i	0.423527	−	0.423527i	−0.462889	−	0.886416i	$-0.653187\pi$
$827$	12.1796	−	12.1796i	0.423527	−	0.423527i	0.886416	+	0.462889i	$0.153187\pi$
$828$		0			0
$829$	10.1278	−	17.5419i	0.351754	−	0.609255i	−0.634803	−	0.772674i	$-0.718919\pi$
$829$	10.1278	−	17.5419i	0.351754	−	0.609255i	0.986557	+	0.163419i	$0.0522522\pi$
$830$	5.63774	+	21.0403i	0.195689	+	0.730321i
$831$		0			0
$832$	0.646181	−	38.9343i	0.0224023	−	1.34980i
$833$	0.417288	−	2.86371i	0.0144582	−	0.0992215i
$834$		0			0
$835$	−4.97576	−	8.61826i	−0.172193	−	0.298247i
$836$	30.7446	−	53.2513i	1.06333	−	1.84173i
$837$		0			0
$838$	8.57921	+	2.29879i	0.296364	+	0.0794105i
$839$	6.54394	+	6.54394i	0.225922	+	0.225922i	0.810987	−	0.585065i	$-0.198931\pi$
$839$	6.54394	+	6.54394i	0.225922	+	0.225922i	−0.585065	+	0.810987i	$0.698931\pi$
$840$		0			0
$841$	69.1283			2.38373
$842$	34.3166	−	19.8127i	1.18263	−	0.682791i
$843$		0			0
$844$	−29.9796	−	17.3088i	−1.03194	−	0.595792i
$845$	−10.5841	−	3.21605i	−0.364106	−	0.110635i
$846$		0			0
$847$	2.73584	−	2.36607i	0.0940045	−	0.0812993i
$848$	−22.4846			−0.772125
$849$		0			0
$850$	−0.959428	−	3.58064i	−0.0329081	−	0.122815i
$851$	0.579356	−	0.155238i	0.0198601	−	0.00532149i
$852$		0			0
$853$	26.9552	+	26.9552i	0.922928	+	0.922928i	0.997235	−	0.0743069i	$-0.0236745\pi$
$853$	26.9552	+	26.9552i	0.922928	+	0.922928i	−0.0743069	+	0.997235i	$0.523674\pi$
$854$	6.14916	+	12.6892i	0.210420	+	0.434215i
$855$		0			0
$856$	−7.43646	−	1.99259i	−0.254173	−	0.0681054i
$857$	−27.5423	+	47.7047i	−0.940828	+	1.62956i	−0.176932	+	0.984223i	$0.556617\pi$
$857$	−27.5423	+	47.7047i	−0.940828	+	1.62956i	−0.763896	+	0.645339i	$0.776716\pi$
$858$		0			0
$859$	40.4711	−	23.3660i	1.38086	−	0.797237i	0.388595	−	0.921409i	$-0.372961\pi$
$859$	40.4711	−	23.3660i	1.38086	−	0.797237i	0.992261	+	0.124172i	$0.0396273\pi$
$860$	−5.98503	+	5.98503i	−0.204088	+	0.204088i
$861$		0			0
$862$			31.6090i			1.07661i
$863$	8.70817	−	32.4993i	0.296430	−	1.10629i	−0.643646	−	0.765324i	$-0.722579\pi$
$863$	8.70817	−	32.4993i	0.296430	−	1.10629i	0.940075	−	0.340967i	$-0.110754\pi$
$864$		0			0
$865$	4.25249	+	15.8705i	0.144589	+	0.539613i
$866$	−4.58888	+	17.1259i	−0.155937	+	0.581963i
$867$		0			0
$868$	1.98626	−	27.4061i	0.0674181	−	0.930222i
$869$	−18.7688	+	18.7688i	−0.636689	+	0.636689i
$870$		0			0
$871$	−49.7168	+	12.4411i	−1.68459	+	0.421551i
$872$	−1.07766	+	1.86657i	−0.0364943	+	0.0632100i
$873$		0			0
$874$			8.52641i			0.288410i
$875$	17.2832	+	11.7216i	0.584280	+	0.396261i
$876$		0			0
$877$	12.2814	−	45.8348i	0.414713	−	1.54773i	−0.370696	−	0.928754i	$-0.620881\pi$
$877$	12.2814	−	45.8348i	0.414713	−	1.54773i	0.785409	−	0.618977i	$-0.212452\pi$
$878$	40.1164	−	10.7491i	1.35386	−	0.362766i
$879$		0			0
$880$	6.97033	−	4.02432i	0.234970	−	0.135660i
$881$	−38.1764			−1.28620			−0.643099	−	0.765783i	$-0.722351\pi$
$881$	−38.1764			−1.28620			−0.643099	+	0.765783i	$0.722351\pi$
$882$		0			0
$883$			40.9343i			1.37755i	0.724976	+	0.688775i	$0.241851\pi$
$883$			40.9343i			1.37755i	−0.724976	+	0.688775i	$0.758149\pi$
$884$	3.12390	−	1.73511i	0.105068	−	0.0583582i
$885$		0			0
$886$	5.27447	−	1.41329i	0.177199	−	0.0474804i
$887$	−6.85775	+	3.95932i	−0.230261	+	0.132941i	−0.610692	−	0.791868i	$-0.709109\pi$
$887$	−6.85775	+	3.95932i	−0.230261	+	0.132941i	0.380432	+	0.924809i	$0.375775\pi$
$888$		0			0
$889$	−8.80356	−	45.9116i	−0.295262	−	1.53983i
$890$	8.52767	+	8.52767i	0.285848	+	0.285848i
$891$		0			0
$892$	2.99088	−	0.801403i	0.100142	−	0.0268330i
$893$	−23.1902	+	40.1666i	−0.776031	+	1.34412i
$894$		0			0
$895$	8.01536	+	8.01536i	0.267924	+	0.267924i
$896$	−17.2403	−	1.24950i	−0.575959	−	0.0417428i
$897$		0			0
$898$	30.6209	+	53.0369i	1.02183	+	1.76986i
$899$	−11.1073	−	41.4530i	−0.370449	−	1.38253i
$900$		0			0
$901$	−1.52508	−	2.64152i	−0.0508078	−	0.0880017i
$902$	16.9963	−	16.9963i	0.565915	−	0.565915i
$903$		0			0
$904$	5.84454	−	5.84454i	0.194386	−	0.194386i
$905$	0.623131	+	0.166967i	0.0207136	+	0.00555018i
$906$		0			0
$907$	−5.92117	−	3.41859i	−0.196609	−	0.113512i	0.398464	−	0.917184i	$-0.369543\pi$
$907$	−5.92117	−	3.41859i	−0.196609	−	0.113512i	−0.595073	+	0.803672i	$0.702877\pi$
$908$	−4.51661	+	16.8562i	−0.149889	+	0.559393i
$909$		0			0
$910$	−5.84858	+	15.9853i	−0.193878	+	0.529909i
$911$	59.0374			1.95600			0.977998	−	0.208613i	$-0.0668949\pi$
$911$	59.0374			1.95600			0.977998	+	0.208613i	$0.0668949\pi$
$912$		0			0
$913$	32.8123	+	18.9442i	1.08593	+	0.626960i
$914$	37.8704	+	21.8645i	1.25264	+	0.723213i
$915$		0			0
$916$	16.6486	−	16.6486i	0.550085	−	0.550085i
$917$	−37.8615	+	32.7443i	−1.25030	+	1.08131i
$918$		0			0
$919$	0.228793	+	0.396282i	0.00754720	+	0.0130721i	0.869774	−	0.493450i	$-0.164264\pi$
$919$	0.228793	+	0.396282i	0.00754720	+	0.0130721i	−0.862227	+	0.506522i	$0.830931\pi$
$920$	0.174393	−	0.302058i	0.00574958	−	0.00995856i
$921$		0			0
$922$	38.0917	+	65.9767i	1.25448	+	2.17283i
$923$	−22.6119	−	23.3751i	−0.744278	−	0.769400i
$924$		0			0
$925$	3.68592	+	3.68592i	0.121192	+	0.121192i
$926$	−24.4419	−	42.3345i	−0.803209	−	1.39120i
$927$		0			0
$928$	−77.0919	+	20.6567i	−2.53067	+	0.678090i
$929$	15.4655	+	4.14397i	0.507407	+	0.135959i	0.503435	−	0.864033i	$-0.332069\pi$
$929$	15.4655	+	4.14397i	0.507407	+	0.135959i	0.00397147	+	0.999992i	$0.498736\pi$
$930$		0			0
$931$	−57.4532	+	6.75880i	−1.88295	+	0.221511i
$932$	2.65257			0.0868878
$933$		0			0
$934$	−30.1823	+	8.08731i	−0.987594	+	0.264625i
$935$	0.945563	+	0.545921i	0.0309232	+	0.0178535i
$936$		0			0
$937$			21.9493i			0.717052i	0.933520	+	0.358526i	$0.116721\pi$
$937$			21.9493i			0.717052i	−0.933520	+	0.358526i	$0.883279\pi$
$938$	14.8511	+	77.4500i	0.484904	+	2.52883i
$939$		0			0
$940$	9.91456	−	5.72417i	0.323377	−	0.186702i
$941$	1.65891	+	6.19114i	0.0540789	+	0.201825i	0.987680	−	0.156490i	$-0.0500179\pi$
$941$	1.65891	+	6.19114i	0.0540789	+	0.201825i	−0.933601	+	0.358315i	$0.883351\pi$
$942$		0			0
$943$	−0.470292	+	1.75515i	−0.0153148	+	0.0571557i
$944$	7.53274	+	7.53274i	0.245170	+	0.245170i
$945$		0			0
$946$			27.0049i			0.878005i
$947$	15.5883	+	4.17686i	0.506551	+	0.135730i	0.503039	−	0.864264i	$-0.332215\pi$
$947$	15.5883	+	4.17686i	0.506551	+	0.135730i	0.00351220	+	0.999994i	$0.498882\pi$
$948$		0			0
$949$	48.9688	−	12.2539i	1.58959	−	0.397779i
$950$	−64.1734	+	37.0505i	−2.08206	+	1.20208i
$951$		0			0
$952$	−0.397390	−	0.820041i	−0.0128795	−	0.0265777i
$953$		−	29.0712i		−	0.941710i	−0.882211	−	0.470855i	$-0.843946\pi$
$953$		−	29.0712i		−	0.941710i	0.882211	−	0.470855i	$-0.156054\pi$
$954$		0			0
$955$	5.05905	+	18.8806i	0.163707	+	0.610962i
$956$	−7.82435	−	29.2009i	−0.253058	−	0.944424i
$957$		0			0
$958$		−	30.5000i		−	0.985410i
$959$	12.9326	+	26.6873i	0.417615	+	0.861777i
$960$		0			0
$961$	10.5928	−	6.11575i	0.341703	−	0.197282i
$962$	−4.74037	+	7.90465i	−0.152836	+	0.254856i
$963$		0			0
$964$	40.2239	+	10.7780i	1.29552	+	0.347135i
$965$			5.47101i			0.176118i
$966$		0			0
$967$	−13.9005	−	13.9005i	−0.447009	−	0.447009i	0.447350	−	0.894359i	$-0.352368\pi$
$967$	−13.9005	−	13.9005i	−0.447009	−	0.447009i	−0.894359	+	0.447350i	$0.852368\pi$
$968$	0.294782	−	1.10014i	0.00947465	−	0.0353599i
$969$		0			0
$970$	2.92577	+	10.9191i	0.0939408	+	0.350592i
$971$	13.3914	−	7.73151i	0.429750	−	0.248116i	−0.269490	−	0.963003i	$-0.586855\pi$
$971$	13.3914	−	7.73151i	0.429750	−	0.248116i	0.699240	+	0.714887i	$0.253522\pi$
$972$		0			0
$973$	−1.25913	−	6.56649i	−0.0403657	−	0.210512i
$974$		−	61.7074i		−	1.97723i
$975$		0			0
$976$	−6.70786	−	3.87278i	−0.214713	−	0.123965i
$977$	38.3637	−	10.2795i	1.22736	−	0.328871i	0.413811	−	0.910363i	$-0.364198\pi$
$977$	38.3637	−	10.2795i	1.22736	−	0.328871i	0.813552	+	0.581492i	$0.197531\pi$
$978$		0			0
$979$	20.9769			0.670426
$980$	13.1157	+	5.64596i	0.418966	+	0.180353i
$981$		0			0
$982$	52.1241	+	13.9666i	1.66335	+	0.445692i
$983$	16.4852	−	4.41721i	0.525798	−	0.140887i	0.0138507	−	0.999904i	$-0.495591\pi$
$983$	16.4852	−	4.41721i	0.525798	−	0.140887i	0.511947	+	0.859017i	$0.328924\pi$
$984$		0			0
$985$	−0.539938	−	0.935199i	−0.0172038	−	0.0297979i
$986$	−6.07250	−	6.07250i	−0.193388	−	0.193388i
$987$		0			0
$988$	−49.6649	−	51.3413i	−1.58005	−	1.63338i
$989$	−1.02074	−	1.76797i	−0.0324576	−	0.0562182i
$990$		0			0
$991$	0.801895	−	1.38892i	0.0254730	−	0.0441206i	−0.853008	−	0.521898i	$-0.825224\pi$
$991$	0.801895	−	1.38892i	0.0254730	−	0.0441206i	0.878481	+	0.477777i	$0.158557\pi$
$992$	17.4523	+	30.2283i	0.554112	+	0.959749i
$993$		0			0
$994$	−37.8516	+	32.7357i	−1.20058	+	1.03831i
$995$	2.57430	−	2.57430i	0.0816107	−	0.0816107i
$996$		0			0
$997$	−3.73168	−	2.15449i	−0.118184	−	0.0682333i	0.439743	−	0.898124i	$-0.355070\pi$
$997$	−3.73168	−	2.15449i	−0.118184	−	0.0682333i	−0.557926	+	0.829890i	$0.688403\pi$
$998$	−64.3528	−	37.1541i	−2.03705	−	1.17609i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fn.f.73.2		36
3.2	odd	2		273.2.bz.a.73.8	✓	36
7.5	odd	6		819.2.fn.g.775.8		36
13.5	odd	4		819.2.fn.g.577.8		36
21.5	even	6		273.2.bz.b.229.2	yes	36
39.5	even	4		273.2.bz.b.31.2	yes	36
91.5	even	12	inner	819.2.fn.f.460.2		36
273.5	odd	12		273.2.bz.a.187.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bz.a.73.8	✓	36	3.2	odd	2
273.2.bz.a.187.8	yes	36	273.5	odd	12
273.2.bz.b.31.2	yes	36	39.5	even	4
273.2.bz.b.229.2	yes	36	21.5	even	6
819.2.fn.f.73.2		36	1.1	even	1	trivial
819.2.fn.f.460.2		36	91.5	even	12	inner
819.2.fn.g.577.8		36	13.5	odd	4
819.2.fn.g.775.8		36	7.5	odd	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.542736 + 2.02552i) q^{2} +(-2.07611 - 1.19864i) q^{4} +(-0.821926 - 0.220234i) q^{5} +(2.59841 - 0.498246i) q^{7} +(0.589092 - 0.589092i) q^{8} +O(q^{10})\)	\(q+(-0.542736 + 2.02552i) q^{2} +(-2.07611 - 1.19864i) q^{4} +(-0.821926 - 0.220234i) q^{5} +(2.59841 - 0.498246i) q^{7} +(0.589092 - 0.589092i) q^{8} +(0.892178 - 1.54530i) q^{10} +(-0.803294 - 2.99793i) q^{11} +(-3.60505 - 0.0598320i) q^{13} +(-0.401046 + 5.53355i) q^{14} +(-1.52379 - 2.63929i) q^{16} +(0.206711 - 0.358033i) q^{17} +(-7.98261 - 2.13893i) q^{19} +(1.44243 + 1.44243i) q^{20} +6.50834 q^{22} +(-0.426092 + 0.246004i) q^{23} +(-3.70307 - 2.13797i) q^{25} +(2.07778 - 7.26963i) q^{26} +(-5.99182 - 2.08016i) q^{28} -9.90597 q^{29} +(1.12127 + 4.18465i) q^{31} +(7.78237 - 2.08528i) q^{32} +(0.613014 + 0.613014i) q^{34} +(-2.24543 - 0.162739i) q^{35} +(-1.17753 - 0.315519i) q^{37} +(8.66490 - 15.0080i) q^{38} +(-0.613928 + 0.354452i) q^{40} +(2.61146 - 2.61146i) q^{41} +4.14927i q^{43} +(-1.92573 + 7.18691i) q^{44} +(-0.267031 - 0.996572i) q^{46} +(1.45255 - 5.42098i) q^{47} +(6.50350 - 2.58930i) q^{49} +(6.34028 - 6.34028i) q^{50} +(7.41278 + 4.44540i) q^{52} +(3.68892 - 6.38940i) q^{53} +2.64099i q^{55} +(1.23719 - 1.82422i) q^{56} +(5.37633 - 20.0647i) q^{58} +(-3.37641 + 0.904707i) q^{59} +(2.20104 - 1.27077i) q^{61} -9.08463 q^{62} +10.7999i q^{64} +(2.94991 + 0.843135i) q^{65} +(13.7298 - 3.67889i) q^{67} +(-0.858309 + 0.495545i) q^{68} +(1.54831 - 4.45984i) q^{70} +(6.37812 + 6.37812i) q^{71} +(-13.5232 + 3.62354i) q^{73} +(1.27818 - 2.21387i) q^{74} +(14.0090 + 14.0090i) q^{76} +(-3.58100 - 7.38963i) q^{77} +(-4.27606 - 7.40636i) q^{79} +(0.671183 + 2.50489i) q^{80} +(3.87223 + 6.70690i) q^{82} +(-8.63202 + 8.63202i) q^{83} +(-0.248752 + 0.248752i) q^{85} +(-8.40443 - 2.25196i) q^{86} +(-2.23927 - 1.29284i) q^{88} +(-1.74928 + 6.52842i) q^{89} +(-9.39723 + 1.64074i) q^{91} +1.17949 q^{92} +(10.1919 + 5.88432i) q^{94} +(6.09005 + 3.51609i) q^{95} +(-4.47968 + 4.47968i) q^{97} +(1.71499 + 14.5783i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{7}+O(q^{10}) \) 36 * q - 6 * q^7	\( 36 q - 6 q^{7} - 4 q^{11} + 36 q^{14} + 12 q^{16} - 4 q^{17} - 18 q^{19} - 44 q^{20} - 8 q^{22} + 12 q^{23} - 48 q^{25} + 32 q^{26} + 4 q^{28} + 16 q^{29} - 6 q^{31} - 76 q^{32} - 48 q^{34} - 8 q^{35} - 8 q^{37} - 16 q^{38} + 60 q^{40} + 32 q^{41} - 4 q^{44} + 28 q^{46} - 14 q^{47} + 6 q^{49} + 68 q^{50} - 62 q^{52} + 8 q^{53} + 8 q^{56} + 36 q^{58} - 26 q^{59} + 36 q^{61} - 48 q^{62} + 8 q^{65} - 40 q^{67} - 36 q^{68} - 64 q^{70} + 36 q^{71} - 8 q^{73} - 40 q^{74} - 60 q^{76} - 60 q^{77} - 26 q^{80} - 24 q^{83} + 44 q^{85} - 48 q^{86} + 168 q^{88} - 10 q^{89} + 4 q^{91} + 40 q^{92} + 36 q^{97} - 38 q^{98}+O(q^{100}) \) 36 * q - 6 * q^7 - 4 * q^11 + 36 * q^14 + 12 * q^16 - 4 * q^17 - 18 * q^19 - 44 * q^20 - 8 * q^22 + 12 * q^23 - 48 * q^25 + 32 * q^26 + 4 * q^28 + 16 * q^29 - 6 * q^31 - 76 * q^32 - 48 * q^34 - 8 * q^35 - 8 * q^37 - 16 * q^38 + 60 * q^40 + 32 * q^41 - 4 * q^44 + 28 * q^46 - 14 * q^47 + 6 * q^49 + 68 * q^50 - 62 * q^52 + 8 * q^53 + 8 * q^56 + 36 * q^58 - 26 * q^59 + 36 * q^61 - 48 * q^62 + 8 * q^65 - 40 * q^67 - 36 * q^68 - 64 * q^70 + 36 * q^71 - 8 * q^73 - 40 * q^74 - 60 * q^76 - 60 * q^77 - 26 * q^80 - 24 * q^83 + 44 * q^85 - 48 * q^86 + 168 * q^88 - 10 * q^89 + 4 * q^91 + 40 * q^92 + 36 * q^97 - 38 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more