LMFDB - Embedded newform 1380.2.p.b.91.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(91,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))

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

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

chi := DirichletCharacter("1380.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.p (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:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.12
Character	$\chi$	$=$	1380.91
Dual form			1380.2.p.b.91.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17369 + 0.788958i) q^{2} -1.00000i q^{3} +(0.755090 - 1.85198i) q^{4} +1.00000i q^{5} +(0.788958 + 1.17369i) q^{6} +0.567108 q^{7} +(0.574895 + 2.76939i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.17369 + 0.788958i) q^{2} -1.00000i q^{3} +(0.755090 - 1.85198i) q^{4} +1.00000i q^{5} +(0.788958 + 1.17369i) q^{6} +0.567108 q^{7} +(0.574895 + 2.76939i) q^{8} -1.00000 q^{9} +(-0.788958 - 1.17369i) q^{10} -2.37156 q^{11} +(-1.85198 - 0.755090i) q^{12} -2.37596 q^{13} +(-0.665608 + 0.447424i) q^{14} +1.00000 q^{15} +(-2.85968 - 2.79683i) q^{16} +1.13985i q^{17} +(1.17369 - 0.788958i) q^{18} +1.96847 q^{19} +(1.85198 + 0.755090i) q^{20} -0.567108i q^{21} +(2.78347 - 1.87106i) q^{22} +(3.57265 - 3.19940i) q^{23} +(2.76939 - 0.574895i) q^{24} -1.00000 q^{25} +(2.78863 - 1.87453i) q^{26} +1.00000i q^{27} +(0.428218 - 1.05027i) q^{28} +2.90432 q^{29} +(-1.17369 + 0.788958i) q^{30} -10.3746i q^{31} +(5.56295 + 1.02644i) q^{32} +2.37156i q^{33} +(-0.899295 - 1.33783i) q^{34} +0.567108i q^{35} +(-0.755090 + 1.85198i) q^{36} -8.93030i q^{37} +(-2.31037 + 1.55304i) q^{38} +2.37596i q^{39} +(-2.76939 + 0.574895i) q^{40} -0.300821 q^{41} +(0.447424 + 0.665608i) q^{42} +3.96710 q^{43} +(-1.79074 + 4.39209i) q^{44} -1.00000i q^{45} +(-1.66899 + 6.57377i) q^{46} +0.733164i q^{47} +(-2.79683 + 2.85968i) q^{48} -6.67839 q^{49} +(1.17369 - 0.788958i) q^{50} +1.13985 q^{51} +(-1.79406 + 4.40023i) q^{52} +10.4803i q^{53} +(-0.788958 - 1.17369i) q^{54} -2.37156i q^{55} +(0.326028 + 1.57054i) q^{56} -1.96847i q^{57} +(-3.40877 + 2.29139i) q^{58} -5.02848i q^{59} +(0.755090 - 1.85198i) q^{60} -9.36387i q^{61} +(8.18514 + 12.1766i) q^{62} -0.567108 q^{63} +(-7.33899 + 3.18421i) q^{64} -2.37596i q^{65} +(-1.87106 - 2.78347i) q^{66} +13.7930 q^{67} +(2.11098 + 0.860691i) q^{68} +(-3.19940 - 3.57265i) q^{69} +(-0.447424 - 0.665608i) q^{70} -5.30639i q^{71} +(-0.574895 - 2.76939i) q^{72} -11.7495 q^{73} +(7.04563 + 10.4814i) q^{74} +1.00000i q^{75} +(1.48637 - 3.64556i) q^{76} -1.34493 q^{77} +(-1.87453 - 2.78863i) q^{78} -3.71293 q^{79} +(2.79683 - 2.85968i) q^{80} +1.00000 q^{81} +(0.353070 - 0.237335i) q^{82} -7.56680 q^{83} +(-1.05027 - 0.428218i) q^{84} -1.13985 q^{85} +(-4.65614 + 3.12988i) q^{86} -2.90432i q^{87} +(-1.36340 - 6.56776i) q^{88} -14.2021i q^{89} +(0.788958 + 1.17369i) q^{90} -1.34742 q^{91} +(-3.22755 - 9.03232i) q^{92} -10.3746 q^{93} +(-0.578436 - 0.860507i) q^{94} +1.96847i q^{95} +(1.02644 - 5.56295i) q^{96} -14.4809i q^{97} +(7.83835 - 5.26897i) q^{98} +2.37156 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) $ 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9	$ 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} + 2 q^{10} - 20 q^{14} + 48 q^{15} - 6 q^{16} + 4 q^{18} - 16 q^{19} - 28 q^{22} - 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} - 4 q^{30} + 16 q^{32} + 28 q^{34} + 2 q^{36} - 2 q^{40} - 8 q^{41} + 26 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 16 q^{51} - 16 q^{52} + 2 q^{54} - 40 q^{56} - 8 q^{58} - 2 q^{60} + 24 q^{62} - 26 q^{64} + 48 q^{67} + 44 q^{68} - 8 q^{69} + 4 q^{72} - 20 q^{74} + 64 q^{76} + 32 q^{77} + 64 q^{79} - 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} + 40 q^{86} - 2 q^{90} - 28 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) $ 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9 + 2 * q^10 - 20 * q^14 + 48 * q^15 - 6 * q^16 + 4 * q^18 - 16 * q^19 - 28 * q^22 - 4 * q^23 + 2 * q^24 - 48 * q^25 - 20 * q^26 + 32 * q^29 - 4 * q^30 + 16 * q^32 + 28 * q^34 + 2 * q^36 - 2 * q^40 - 8 * q^41 + 26 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 - 16 * q^51 - 16 * q^52 + 2 * q^54 - 40 * q^56 - 8 * q^58 - 2 * q^60 + 24 * q^62 - 26 * q^64 + 48 * q^67 + 44 * q^68 - 8 * q^69 + 4 * q^72 - 20 * q^74 + 64 * q^76 + 32 * q^77 + 64 * q^79 - 16 * q^80 + 48 * q^81 - 20 * q^82 + 16 * q^85 + 40 * q^86 - 2 * q^90 - 28 * q^92 - 32 * q^94 - 2 * q^96 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$1$	$1$	$-1$	$-1$

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 $

$2$	−1.17369	+	0.788958i	−0.829923	+	0.557878i
$2$	−1.17369	+	0.788958i	−0.829923	+	0.557878i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.755090	−	1.85198i	0.377545	−	0.925991i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.788958	+	1.17369i	0.322091	+	0.479156i
$7$	0.567108			0.214347			0.107173	−	0.994240i	$-0.465820\pi$
$7$	0.567108			0.214347			0.107173	+	0.994240i	$0.465820\pi$
$8$	0.574895	+	2.76939i	0.203256	+	0.979126i
$9$	−1.00000			−0.333333
$10$	−0.788958	−	1.17369i	−0.249490	−	0.371153i
$11$	−2.37156			−0.715052			−0.357526	−	0.933903i	$-0.616380\pi$
$11$	−2.37156			−0.715052			−0.357526	+	0.933903i	$0.616380\pi$
$12$	−1.85198	−	0.755090i	−0.534621	−	0.217976i
$13$	−2.37596			−0.658972			−0.329486	−	0.944160i	$-0.606875\pi$
$13$	−2.37596			−0.658972			−0.329486	+	0.944160i	$0.606875\pi$
$14$	−0.665608	+	0.447424i	−0.177891	+	0.119579i
$15$	1.00000			0.258199
$16$	−2.85968	−	2.79683i	−0.714919	−	0.699207i
$17$			1.13985i			0.276454i	0.990401	+	0.138227i	$0.0441404\pi$
$17$			1.13985i			0.276454i	−0.990401	+	0.138227i	$0.955860\pi$
$18$	1.17369	−	0.788958i	0.276641	−	0.185959i
$19$	1.96847			0.451597			0.225799	−	0.974174i	$-0.427501\pi$
$19$	1.96847			0.451597			0.225799	+	0.974174i	$0.427501\pi$
$20$	1.85198	+	0.755090i	0.414116	+	0.168843i
$21$		−	0.567108i		−	0.123753i
$22$	2.78347	−	1.87106i	0.593438	−	0.398912i
$23$	3.57265	−	3.19940i	0.744950	−	0.667121i
$23$	3.57265	−	3.19940i	0.744950	−	0.667121i
$24$	2.76939	−	0.574895i	0.565298	−	0.117350i
$25$	−1.00000			−0.200000
$26$	2.78863	−	1.87453i	0.546896	−	0.367626i
$27$			1.00000i			0.192450i
$28$	0.428218	−	1.05027i	0.0809255	−	0.198483i
$29$	2.90432			0.539319			0.269660	−	0.962956i	$-0.413089\pi$
$29$	2.90432			0.539319			0.269660	+	0.962956i	$0.413089\pi$
$30$	−1.17369	+	0.788958i	−0.214285	+	0.144043i
$31$		−	10.3746i		−	1.86334i	−0.363310	−	0.931668i	$-0.618354\pi$
$31$		−	10.3746i		−	1.86334i	0.363310	−	0.931668i	$-0.381646\pi$
$32$	5.56295	+	1.02644i	0.983400	+	0.181451i
$33$			2.37156i			0.412836i
$34$	−0.899295	−	1.33783i	−0.154228	−	0.229436i
$35$			0.567108i			0.0958587i
$36$	−0.755090	+	1.85198i	−0.125848	+	0.308664i
$37$		−	8.93030i		−	1.46813i	−0.679078	−	0.734066i	$-0.737620\pi$
$37$		−	8.93030i		−	1.46813i	0.679078	−	0.734066i	$-0.262380\pi$
$38$	−2.31037	+	1.55304i	−0.374791	+	0.251936i
$39$			2.37596i			0.380458i
$40$	−2.76939	+	0.574895i	−0.437878	+	0.0908989i
$41$	−0.300821			−0.0469804			−0.0234902	−	0.999724i	$-0.507478\pi$
$41$	−0.300821			−0.0469804			−0.0234902	+	0.999724i	$0.507478\pi$
$42$	0.447424	+	0.665608i	0.0690391	+	0.102706i
$43$	3.96710			0.604977			0.302489	−	0.953153i	$-0.402183\pi$
$43$	3.96710			0.604977			0.302489	+	0.953153i	$0.402183\pi$
$44$	−1.79074	+	4.39209i	−0.269964	+	0.662132i
$45$		−	1.00000i		−	0.149071i
$46$	−1.66899	+	6.57377i	−0.246079	+	0.969250i
$47$			0.733164i			0.106943i	0.998569	+	0.0534715i	$0.0170286\pi$
$47$			0.733164i			0.106943i	−0.998569	+	0.0534715i	$0.982971\pi$
$48$	−2.79683	+	2.85968i	−0.403687	+	0.412759i
$49$	−6.67839			−0.954056
$50$	1.17369	−	0.788958i	0.165985	−	0.111576i
$51$	1.13985			0.159611
$52$	−1.79406	+	4.40023i	−0.248792	+	0.610202i
$53$			10.4803i			1.43959i	0.694189	+	0.719793i	$0.255763\pi$
$53$			10.4803i			1.43959i	−0.694189	+	0.719793i	$0.744237\pi$
$54$	−0.788958	−	1.17369i	−0.107364	−	0.159719i
$55$		−	2.37156i		−	0.319781i
$56$	0.326028	+	1.57054i	0.0435673	+	0.209872i
$57$		−	1.96847i		−	0.260730i
$58$	−3.40877	+	2.29139i	−0.447593	+	0.300874i
$59$		−	5.02848i		−	0.654653i	−0.944911	−	0.327326i	$-0.893852\pi$
$59$		−	5.02848i		−	0.654653i	0.944911	−	0.327326i	$-0.106148\pi$
$60$	0.755090	−	1.85198i	0.0974818	−	0.239090i
$61$		−	9.36387i		−	1.19892i	−0.800404	−	0.599461i	$-0.795382\pi$
$61$		−	9.36387i		−	1.19892i	0.800404	−	0.599461i	$-0.204618\pi$
$62$	8.18514	+	12.1766i	1.03951	+	1.54643i
$63$	−0.567108			−0.0714489
$64$	−7.33899	+	3.18421i	−0.917374	+	0.398027i
$65$		−	2.37596i		−	0.294701i
$66$	−1.87106	−	2.78347i	−0.230312	−	0.342622i
$67$	13.7930			1.68509			0.842543	−	0.538629i	$-0.181058\pi$
$67$	13.7930			1.68509			0.842543	+	0.538629i	$0.181058\pi$
$68$	2.11098	+	0.860691i	0.255994	+	0.104374i
$69$	−3.19940	−	3.57265i	−0.385162	−	0.430097i
$70$	−0.447424	−	0.665608i	−0.0534774	−	0.0795554i
$71$		−	5.30639i		−	0.629752i	−0.949133	−	0.314876i	$-0.898037\pi$
$71$		−	5.30639i		−	0.629752i	0.949133	−	0.314876i	$-0.101963\pi$
$72$	−0.574895	−	2.76939i	−0.0677520	−	0.326375i
$73$	−11.7495			−1.37517			−0.687586	−	0.726103i	$-0.741329\pi$
$73$	−11.7495			−1.37517			−0.687586	+	0.726103i	$0.741329\pi$
$74$	7.04563	+	10.4814i	0.819038	+	1.21844i
$75$			1.00000i			0.115470i
$76$	1.48637	−	3.64556i	0.170498	−	0.418175i
$77$	−1.34493			−0.153269
$78$	−1.87453	−	2.78863i	−0.212249	−	0.315751i
$79$	−3.71293			−0.417737			−0.208868	−	0.977944i	$-0.566978\pi$
$79$	−3.71293			−0.417737			−0.208868	+	0.977944i	$0.566978\pi$
$80$	2.79683	−	2.85968i	0.312695	−	0.319722i
$81$	1.00000			0.111111
$82$	0.353070	−	0.237335i	0.0389901	−	0.0262093i
$83$	−7.56680			−0.830564			−0.415282	−	0.909693i	$-0.636317\pi$
$83$	−7.56680			−0.830564			−0.415282	+	0.909693i	$0.636317\pi$
$84$	−1.05027	−	0.428218i	−0.114594	−	0.0467224i
$85$	−1.13985			−0.123634
$86$	−4.65614	+	3.12988i	−0.502085	+	0.337503i
$87$		−	2.90432i		−	0.311376i
$88$	−1.36340	−	6.56776i	−0.145339	−	0.700126i
$89$		−	14.2021i		−	1.50542i	−0.658350	−	0.752712i	$-0.728745\pi$
$89$		−	14.2021i		−	1.50542i	0.658350	−	0.752712i	$-0.271255\pi$
$90$	0.788958	+	1.17369i	0.0831635	+	0.123718i
$91$	−1.34742			−0.141248
$92$	−3.22755	−	9.03232i	−0.336496	−	0.941685i
$93$	−10.3746			−1.07580
$94$	−0.578436	−	0.860507i	−0.0596611	−	0.0887545i
$95$			1.96847i			0.201960i
$96$	1.02644	−	5.56295i	0.104761	−	0.567766i
$97$		−	14.4809i		−	1.47031i	−0.677897	−	0.735157i	$-0.737109\pi$
$97$		−	14.4809i		−	1.47031i	0.677897	−	0.735157i	$-0.262891\pi$
$98$	7.83835	−	5.26897i	0.791793	−	0.532246i
$99$	2.37156			0.238351
$100$	−0.755090	+	1.85198i	−0.0755090	+	0.185198i
$101$	−2.94125			−0.292665			−0.146333	−	0.989235i	$-0.546747\pi$
$101$	−2.94125			−0.292665			−0.146333	+	0.989235i	$0.546747\pi$
$102$	−1.33783	+	0.899295i	−0.132465	+	0.0890434i
$103$	10.4335			1.02804			0.514020	−	0.857778i	$-0.328156\pi$
$103$	10.4335			1.02804			0.514020	+	0.857778i	$0.328156\pi$
$104$	−1.36593	−	6.57994i	−0.133940	−	0.645216i
$105$	0.567108			0.0553441
$106$	−8.26855	−	12.3007i	−0.803113	−	1.19475i
$107$	18.2868			1.76785			0.883926	−	0.467627i	$-0.154891\pi$
$107$	18.2868			1.76785			0.883926	+	0.467627i	$0.154891\pi$
$108$	1.85198	+	0.755090i	0.178207	+	0.0726586i
$109$			7.20450i			0.690066i	0.938591	+	0.345033i	$0.112132\pi$
$109$			7.20450i			0.690066i	−0.938591	+	0.345033i	$0.887868\pi$
$110$	1.87106	+	2.78347i	0.178399	+	0.265394i
$111$	−8.93030			−0.847627
$112$	−1.62175	−	1.58610i	−0.153240	−	0.149873i
$113$		−	10.7506i		−	1.01134i	−0.862728	−	0.505668i	$-0.831246\pi$
$113$		−	10.7506i		−	1.01134i	0.862728	−	0.505668i	$-0.168754\pi$
$114$	1.55304	+	2.31037i	0.145455	+	0.216386i
$115$	3.19940	+	3.57265i	0.298346	+	0.333152i
$116$	2.19303	−	5.37875i	0.203617	−	0.499405i
$117$	2.37596			0.219657
$118$	3.96726	+	5.90187i	0.365216	+	0.543311i
$119$			0.646418i			0.0592571i
$120$	0.574895	+	2.76939i	0.0524805	+	0.252809i
$121$	−5.37571			−0.488701
$122$	7.38770	+	10.9903i	0.668851	+	0.995013i
$123$			0.300821i			0.0271241i
$124$	−19.2136	−	7.83377i	−1.72543	−	0.703494i
$125$		−	1.00000i		−	0.0894427i
$126$	0.665608	−	0.447424i	0.0592971	−	0.0398597i
$127$		−	8.72999i		−	0.774661i	−0.921941	−	0.387331i	$-0.873397\pi$
$127$		−	8.72999i		−	0.774661i	0.921941	−	0.387331i	$-0.126603\pi$
$128$	6.10148	−	9.52743i	0.539300	−	0.842114i
$129$		−	3.96710i		−	0.349284i
$130$	1.87453	+	2.78863i	0.164407	+	0.244579i
$131$		−	19.7035i		−	1.72151i	−0.509022	−	0.860753i	$-0.669993\pi$
$131$		−	19.7035i		−	1.72151i	0.509022	−	0.860753i	$-0.330007\pi$
$132$	4.39209	+	1.79074i	0.382282	+	0.155864i
$133$	1.11633			0.0967983
$134$	−16.1887	+	10.8821i	−1.39849	+	0.940071i
$135$	−1.00000			−0.0860663
$136$	−3.15669	+	0.655295i	−0.270684	+	0.0561911i
$137$			8.43368i			0.720538i	0.932848	+	0.360269i	$0.117315\pi$
$137$			8.43368i			0.720538i	−0.932848	+	0.360269i	$0.882685\pi$
$138$	6.57377	+	1.66899i	0.559597	+	0.142074i
$139$		−	4.36147i		−	0.369935i	−0.982745	−	0.184968i	$-0.940782\pi$
$139$		−	4.36147i		−	0.369935i	0.982745	−	0.184968i	$-0.0592180\pi$
$140$	1.05027	+	0.428218i	0.0887643	+	0.0361910i
$141$	0.733164			0.0617436
$142$	4.18652	+	6.22805i	0.351325	+	0.522646i
$143$	5.63472			0.471199
$144$	2.85968	+	2.79683i	0.238306	+	0.233069i
$145$			2.90432i			0.241191i
$146$	13.7902	−	9.26984i	1.14129	−	0.767177i
$147$			6.67839i			0.550824i
$148$	−16.5388	−	6.74319i	−1.35948	−	0.554287i
$149$			6.27281i			0.513889i	0.966426	+	0.256944i	$0.0827157\pi$
$149$			6.27281i			0.513889i	−0.966426	+	0.256944i	$0.917284\pi$
$150$	−0.788958	−	1.17369i	−0.0644182	−	0.0958313i
$151$		−	3.53863i		−	0.287970i	−0.989580	−	0.143985i	$-0.954008\pi$
$151$		−	3.53863i		−	0.287970i	0.989580	−	0.143985i	$-0.0459917\pi$
$152$	1.13166	+	5.45144i	0.0917899	+	0.442170i
$153$		−	1.13985i		−	0.0921515i
$154$	1.57853	−	1.06109i	0.127201	−	0.0855053i
$155$	10.3746			0.833309
$156$	4.40023	+	1.79406i	0.352300	+	0.143640i
$157$			11.1028i			0.886099i	0.896497	+	0.443049i	$0.146103\pi$
$157$			11.1028i			0.886099i	−0.896497	+	0.443049i	$0.853897\pi$
$158$	4.35782	−	2.92934i	0.346690	−	0.233046i
$159$	10.4803			0.831145
$160$	−1.02644	+	5.56295i	−0.0811473	+	0.439790i
$161$	2.02608	−	1.81440i	0.159677	−	0.142995i
$162$	−1.17369	+	0.788958i	−0.0922137	+	0.0619864i
$163$		−	10.7661i		−	0.843265i	−0.906767	−	0.421633i	$-0.861457\pi$
$163$		−	10.7661i		−	0.843265i	0.906767	−	0.421633i	$-0.138543\pi$
$164$	−0.227147	+	0.557115i	−0.0177372	+	0.0435034i
$165$	−2.37156			−0.184626
$166$	8.88107	−	5.96989i	0.689305	−	0.463353i
$167$			20.5663i			1.59147i	0.605645	+	0.795735i	$0.292915\pi$
$167$			20.5663i			1.59147i	−0.605645	+	0.795735i	$0.707085\pi$
$168$	1.57054	−	0.326028i	0.121170	−	0.0251536i
$169$	−7.35483			−0.565756
$170$	1.33783	−	0.899295i	0.102607	−	0.0689728i
$171$	−1.96847			−0.150532
$172$	2.99552	−	7.34700i	0.228406	−	0.560203i
$173$	−3.88535			−0.295397			−0.147699	−	0.989032i	$-0.547187\pi$
$173$	−3.88535			−0.295397			−0.147699	+	0.989032i	$0.547187\pi$
$174$	2.29139	+	3.40877i	0.173710	+	0.258418i
$175$	−0.567108			−0.0428693
$176$	6.78189	+	6.63284i	0.511204	+	0.499969i
$177$	−5.02848			−0.377964
$178$	11.2049	+	16.6689i	0.839843	+	1.24939i
$179$		−	5.49382i		−	0.410627i	−0.978696	−	0.205314i	$-0.934179\pi$
$179$		−	5.49382i		−	0.410627i	0.978696	−	0.205314i	$-0.0658215\pi$
$180$	−1.85198	−	0.755090i	−0.138039	−	0.0562811i
$181$		−	1.42676i		−	0.106050i	−0.998593	−	0.0530251i	$-0.983114\pi$
$181$		−	1.42676i		−	0.106050i	0.998593	−	0.0530251i	$-0.0168863\pi$
$182$	1.58146	−	1.06306i	0.117225	−	0.0787993i
$183$	−9.36387			−0.692198
$184$	10.9143	+	8.05473i	0.804611	+	0.593803i
$185$	8.93030			0.656569
$186$	12.1766	−	8.18514i	0.892830	−	0.600163i
$187$		−	2.70322i		−	0.197679i
$188$	1.35781	+	0.553605i	0.0990283	+	0.0403758i
$189$			0.567108i			0.0412510i
$190$	−1.55304	−	2.31037i	−0.112669	−	0.167612i
$191$	−23.8995			−1.72931			−0.864654	−	0.502368i	$-0.832462\pi$
$191$	−23.8995			−1.72931			−0.864654	+	0.502368i	$0.832462\pi$
$192$	3.18421	+	7.33899i	0.229801	+	0.529646i
$193$	13.0675			0.940617			0.470308	−	0.882502i	$-0.344143\pi$
$193$	13.0675			0.940617			0.470308	+	0.882502i	$0.344143\pi$
$194$	11.4248	+	16.9961i	0.820255	+	1.22025i
$195$	−2.37596			−0.170146
$196$	−5.04279	+	12.3683i	−0.360199	+	0.883447i
$197$	16.2222			1.15579			0.577893	−	0.816112i	$-0.303875\pi$
$197$	16.2222			1.15579			0.577893	+	0.816112i	$0.303875\pi$
$198$	−2.78347	+	1.87106i	−0.197813	+	0.132971i
$199$	11.9953			0.850323			0.425161	−	0.905118i	$-0.360217\pi$
$199$	11.9953			0.850323			0.425161	+	0.905118i	$0.360217\pi$
$200$	−0.574895	−	2.76939i	−0.0406512	−	0.195825i
$201$		−	13.7930i		−	0.972885i
$202$	3.45211	−	2.32052i	0.242890	−	0.163271i
$203$	1.64706			0.115601
$204$	0.860691	−	2.11098i	0.0602604	−	0.147798i
$205$		−	0.300821i		−	0.0210103i
$206$	−12.2456	+	8.23157i	−0.853195	+	0.573521i
$207$	−3.57265	+	3.19940i	−0.248317	+	0.222374i
$208$	6.79447	+	6.64514i	0.471112	+	0.460758i
$209$	−4.66833			−0.322915
$210$	−0.665608	+	0.447424i	−0.0459313	+	0.0308752i
$211$		−	13.9664i		−	0.961487i	−0.876861	−	0.480744i	$-0.840367\pi$
$211$		−	13.9664i		−	0.961487i	0.876861	−	0.480744i	$-0.159633\pi$
$212$	19.4094	+	7.91361i	1.33304	+	0.543509i
$213$	−5.30639			−0.363588
$214$	−21.4630	+	14.4275i	−1.46718	+	0.986245i
$215$			3.96710i			0.270554i
$216$	−2.76939	+	0.574895i	−0.188433	+	0.0391167i
$217$		−	5.88353i		−	0.399400i
$218$	−5.68405	−	8.45584i	−0.384972	−	0.572702i
$219$			11.7495i			0.793956i
$220$	−4.39209	−	1.79074i	−0.296114	−	0.120732i
$221$		−	2.70824i		−	0.182176i
$222$	10.4814	−	7.04563i	0.703465	−	0.472872i
$223$			3.35640i			0.224761i	0.993665	+	0.112381i	$0.0358476\pi$
$223$			3.35640i			0.224761i	−0.993665	+	0.112381i	$0.964152\pi$
$224$	3.15479	+	0.582103i	0.210788	+	0.0388934i
$225$	1.00000			0.0666667
$226$	8.48181	+	12.6179i	0.564202	+	0.839331i
$227$	15.9943			1.06158			0.530789	−	0.847504i	$-0.321896\pi$
$227$	15.9943			1.06158			0.530789	+	0.847504i	$0.321896\pi$
$228$	−3.64556	−	1.48637i	−0.241433	−	0.0984373i
$229$		−	8.36724i		−	0.552923i	−0.961025	−	0.276461i	$-0.910838\pi$
$229$		−	8.36724i		−	0.552923i	0.961025	−	0.276461i	$-0.0891618\pi$
$230$	−6.57377	−	1.66899i	−0.433462	−	0.110050i
$231$			1.34493i			0.0884899i
$232$	1.66968	+	8.04319i	0.109620	+	0.528061i
$233$	0.542805			0.0355603			0.0177802	−	0.999842i	$-0.494340\pi$
$233$	0.542805			0.0355603			0.0177802	+	0.999842i	$0.494340\pi$
$234$	−2.78863	+	1.87453i	−0.182299	+	0.122542i
$235$	−0.733164			−0.0478264
$236$	−9.31266	−	3.79696i	−0.606202	−	0.247161i
$237$			3.71293i			0.241181i
$238$	−0.509997	−	0.758694i	−0.0330582	−	0.0491788i
$239$		−	5.53626i		−	0.358111i	−0.983839	−	0.179056i	$-0.942696\pi$
$239$		−	5.53626i		−	0.358111i	0.983839	−	0.179056i	$-0.0573042\pi$
$240$	−2.85968	−	2.79683i	−0.184591	−	0.180534i
$241$			16.4133i			1.05728i	0.848848	+	0.528638i	$0.177297\pi$
$241$			16.4133i			1.05728i	−0.848848	+	0.528638i	$0.822703\pi$
$242$	6.30941	−	4.24121i	0.405584	−	0.272635i
$243$		−	1.00000i		−	0.0641500i
$244$	−17.3417	−	7.07057i	−1.11019	−	0.452647i
$245$		−	6.67839i		−	0.426667i
$246$	−0.237335	−	0.353070i	−0.0151319	−	0.0225109i
$247$	−4.67699			−0.297590
$248$	28.7313	−	5.96432i	1.82444	−	0.378735i
$249$			7.56680i			0.479527i
$250$	0.788958	+	1.17369i	0.0498981	+	0.0742306i
$251$	−3.85732			−0.243472			−0.121736	−	0.992563i	$-0.538846\pi$
$251$	−3.85732			−0.243472			−0.121736	+	0.992563i	$0.538846\pi$
$252$	−0.428218	+	1.05027i	−0.0269752	+	0.0661610i
$253$	−8.47276	+	7.58757i	−0.532678	+	0.477026i
$254$	6.88760	+	10.2463i	0.432166	+	0.642910i
$255$			1.13985i			0.0713802i
$256$	0.355504	+	15.9961i	0.0222190	+	0.999753i
$257$	−19.2784			−1.20255			−0.601276	−	0.799041i	$-0.705341\pi$
$257$	−19.2784			−1.20255			−0.601276	+	0.799041i	$0.705341\pi$
$258$	3.12988	+	4.65614i	0.194858	+	0.289879i
$259$		−	5.06444i		−	0.314689i
$260$	−4.40023	−	1.79406i	−0.272891	−	0.111263i
$261$	−2.90432			−0.179773
$262$	15.5453	+	23.1258i	0.960390	+	1.42872i
$263$	−16.5776			−1.02222			−0.511109	−	0.859516i	$-0.670765\pi$
$263$	−16.5776			−1.02222			−0.511109	+	0.859516i	$0.670765\pi$
$264$	−6.56776	+	1.36340i	−0.404218	+	0.0839114i
$265$	−10.4803			−0.643802
$266$	−1.31023	+	0.880740i	−0.0803352	+	0.0540016i
$267$	−14.2021			−0.869157
$268$	10.4150	−	25.5444i	0.636196	−	1.56037i
$269$	9.52323			0.580641			0.290321	−	0.956929i	$-0.406238\pi$
$269$	9.52323			0.580641			0.290321	+	0.956929i	$0.406238\pi$
$270$	1.17369	−	0.788958i	0.0714284	−	0.0480145i
$271$			17.5307i			1.06492i	0.846456	+	0.532458i	$0.178732\pi$
$271$			17.5307i			1.06492i	−0.846456	+	0.532458i	$0.821268\pi$
$272$	3.18797	−	3.25961i	0.193299	−	0.197643i
$273$			1.34742i			0.0815498i
$274$	−6.65382	−	9.89852i	−0.401972	−	0.597991i
$275$	2.37156			0.143010
$276$	−9.03232	+	3.22755i	−0.543682	+	0.194276i
$277$	6.49323			0.390140			0.195070	−	0.980789i	$-0.437507\pi$
$277$	6.49323			0.390140			0.195070	+	0.980789i	$0.437507\pi$
$278$	3.44102	+	5.11901i	0.206379	+	0.307018i
$279$			10.3746i			0.621112i
$280$	−1.57054	+	0.326028i	−0.0938577	+	0.0194839i
$281$			1.60948i			0.0960137i	0.998847	+	0.0480068i	$0.0152869\pi$
$281$			1.60948i			0.0960137i	−0.998847	+	0.0480068i	$0.984713\pi$
$282$	−0.860507	+	0.578436i	−0.0512424	+	0.0344454i
$283$	−17.0934			−1.01609			−0.508047	−	0.861329i	$-0.669633\pi$
$283$	−17.0934			−1.01609			−0.508047	+	0.861329i	$0.669633\pi$
$284$	−9.82733	−	4.00680i	−0.583145	−	0.237760i
$285$	1.96847			0.116602
$286$	−6.61341	+	4.44556i	−0.391059	+	0.262872i
$287$	−0.170598			−0.0100701
$288$	−5.56295	−	1.02644i	−0.327800	−	0.0604836i
$289$	15.7007			0.923573
$290$	−2.29139	−	3.40877i	−0.134555	−	0.200170i
$291$	−14.4809			−0.848886
$292$	−8.87191	+	21.7598i	−0.519189	+	1.27340i
$293$			8.95831i			0.523350i	0.965156	+	0.261675i	$0.0842749\pi$
$293$			8.95831i			0.523350i	−0.965156	+	0.261675i	$0.915725\pi$
$294$	−5.26897	−	7.83835i	−0.307292	−	0.457142i
$295$	5.02848			0.292770
$296$	24.7315	−	5.13399i	1.43749	−	0.298407i
$297$		−	2.37156i		−	0.137612i
$298$	−4.94898	−	7.36233i	−0.286687	−	0.426488i
$299$	−8.48847	+	7.60164i	−0.490901	+	0.439614i
$300$	1.85198	+	0.755090i	0.106924	+	0.0435952i
$301$	2.24977			0.129675
$302$	2.79183	+	4.15325i	0.160652	+	0.238993i
$303$			2.94125i			0.168970i
$304$	−5.62918	−	5.50546i	−0.322855	−	0.315760i
$305$	9.36387			0.536174
$306$	0.899295	+	1.33783i	0.0514093	+	0.0764787i
$307$			14.4304i			0.823587i	0.911277	+	0.411793i	$0.135097\pi$
$307$			14.4304i			0.823587i	−0.911277	+	0.411793i	$0.864903\pi$
$308$	−1.01554	+	2.49079i	−0.0578660	+	0.141926i
$309$		−	10.4335i		−	0.593539i
$310$	−12.1766	+	8.18514i	−0.691583	+	0.464885i
$311$			4.98628i			0.282746i	0.989956	+	0.141373i	$0.0451517\pi$
$311$			4.98628i			0.282746i	−0.989956	+	0.141373i	$0.954848\pi$
$312$	−6.57994	+	1.36593i	−0.372516	+	0.0773304i
$313$		−	17.5039i		−	0.989379i	−0.869070	−	0.494690i	$-0.835282\pi$
$313$		−	17.5039i		−	0.989379i	0.869070	−	0.494690i	$-0.164718\pi$
$314$	−8.75963	−	13.0312i	−0.494335	−	0.735394i
$315$		−	0.567108i		−	0.0319529i
$316$	−2.80360	+	6.87628i	−0.157715	+	0.386821i
$317$	−21.7513			−1.22168			−0.610838	−	0.791755i	$-0.709167\pi$
$317$	−21.7513			−1.22168			−0.610838	+	0.791755i	$0.709167\pi$
$318$	−12.3007	+	8.26855i	−0.689787	+	0.463677i
$319$	−6.88777			−0.385641
$320$	−3.18421	−	7.33899i	−0.178003	−	0.410262i
$321$		−	18.2868i		−	1.02067i
$322$	−0.946497	+	3.72804i	−0.0527462	+	0.207755i
$323$			2.24376i			0.124846i
$324$	0.755090	−	1.85198i	0.0419495	−	0.102888i
$325$	2.37596			0.131794
$326$	8.49399	+	12.6360i	0.470439	+	0.699845i
$327$	7.20450			0.398410
$328$	−0.172941	−	0.833090i	−0.00954905	−	0.0459997i
$329$			0.415783i			0.0229229i
$330$	2.78347	−	1.87106i	0.153225	−	0.102999i
$331$			3.00106i			0.164953i	0.996593	+	0.0824767i	$0.0262830\pi$
$331$			3.00106i			0.164953i	−0.996593	+	0.0824767i	$0.973717\pi$
$332$	−5.71362	+	14.0136i	−0.313576	+	0.769095i
$333$			8.93030i			0.489378i
$334$	−16.2260	−	24.1385i	−0.887846	−	1.32080i
$335$			13.7930i			0.753593i
$336$	−1.58610	+	1.62175i	−0.0865290	+	0.0884734i
$337$			4.87667i			0.265649i	0.991140	+	0.132824i	$0.0424047\pi$
$337$			4.87667i			0.265649i	−0.991140	+	0.132824i	$0.957595\pi$
$338$	8.63228	−	5.80265i	0.469534	−	0.315623i
$339$	−10.7506			−0.583895
$340$	−0.860691	+	2.11098i	−0.0466775	+	0.114484i
$341$			24.6040i			1.33238i
$342$	2.31037	−	1.55304i	0.124930	−	0.0839786i
$343$	−7.75712			−0.418845
$344$	2.28067	+	10.9864i	0.122965	+	0.592349i
$345$	3.57265	−	3.19940i	0.192345	−	0.172250i
$346$	4.56019	−	3.06538i	0.245157	−	0.164796i
$347$			22.1760i			1.19047i	0.803551	+	0.595235i	$0.202941\pi$
$347$			22.1760i			1.19047i	−0.803551	+	0.595235i	$0.797059\pi$
$348$	−5.37875	−	2.19303i	−0.288331	−	0.117559i
$349$	24.5202			1.31253			0.656267	−	0.754528i	$-0.272134\pi$
$349$	24.5202			1.31253			0.656267	+	0.754528i	$0.272134\pi$
$350$	0.665608	−	0.447424i	0.0355782	−	0.0239158i
$351$		−	2.37596i		−	0.126819i
$352$	−13.1929	−	2.43427i	−0.703182	−	0.129747i
$353$	−9.01541			−0.479842			−0.239921	−	0.970792i	$-0.577122\pi$
$353$	−9.01541			−0.479842			−0.239921	+	0.970792i	$0.577122\pi$
$354$	5.90187	−	3.96726i	0.313681	−	0.210858i
$355$	5.30639			0.281634
$356$	−26.3021	−	10.7239i	−1.39401	−	0.568366i
$357$	0.646418			0.0342121
$358$	4.33439	+	6.44804i	0.229080	+	0.340789i
$359$	−19.7357			−1.04161			−0.520805	−	0.853675i	$-0.674368\pi$
$359$	−19.7357			−1.04161			−0.520805	+	0.853675i	$0.674368\pi$
$360$	2.76939	−	0.574895i	0.145959	−	0.0302996i
$361$	−15.1251			−0.796060
$362$	1.12565	+	1.67457i	0.0591630	+	0.0880135i
$363$			5.37571i			0.282151i
$364$	−1.01743	+	2.49541i	−0.0533277	+	0.130795i
$365$		−	11.7495i		−	0.614995i
$366$	10.9903	−	7.38770i	0.574471	−	0.386161i
$367$	8.41757			0.439394			0.219697	−	0.975568i	$-0.429493\pi$
$367$	8.41757			0.439394			0.219697	+	0.975568i	$0.429493\pi$
$368$	−19.1648	−	0.842847i	−0.999034	−	0.0439365i
$369$	0.300821			0.0156601
$370$	−10.4814	+	7.04563i	−0.544902	+	0.366285i
$371$			5.94349i			0.308570i
$372$	−7.83377	+	19.2136i	−0.406162	+	0.996179i
$373$			35.4286i			1.83442i	0.398401	+	0.917212i	$0.369565\pi$
$373$			35.4286i			1.83442i	−0.398401	+	0.917212i	$0.630435\pi$
$374$	2.13273	+	3.17274i	0.110281	+	0.164059i
$375$	−1.00000			−0.0516398
$376$	−2.03041	+	0.421493i	−0.104711	+	0.0217368i
$377$	−6.90055			−0.355396
$378$	−0.447424	−	0.665608i	−0.0230130	−	0.0342352i
$379$	−2.19365			−0.112680			−0.0563400	−	0.998412i	$-0.517943\pi$
$379$	−2.19365			−0.112680			−0.0563400	+	0.998412i	$0.517943\pi$
$380$	3.64556	+	1.48637i	0.187014	+	0.0762492i
$381$	−8.72999			−0.447251
$382$	28.0506	−	18.8557i	1.43519	−	0.964742i
$383$	−0.577081			−0.0294875			−0.0147437	−	0.999891i	$-0.504693\pi$
$383$	−0.577081			−0.0294875			−0.0147437	+	0.999891i	$0.504693\pi$
$384$	−9.52743	−	6.10148i	−0.486195	−	0.311365i
$385$		−	1.34493i		−	0.0685440i
$386$	−15.3371	+	10.3097i	−0.780640	+	0.524749i
$387$	−3.96710			−0.201659
$388$	−26.8184	−	10.9344i	−1.36150	−	0.555110i
$389$		−	10.5240i		−	0.533590i	−0.963753	−	0.266795i	$-0.914035\pi$
$389$		−	10.5240i		−	0.533590i	0.963753	−	0.266795i	$-0.0859647\pi$
$390$	2.78863	−	1.87453i	0.141208	−	0.0949205i
$391$	3.64684	+	4.07229i	0.184429	+	0.205945i
$392$	−3.83937	−	18.4950i	−0.193918	−	0.934140i
$393$	−19.7035			−0.993912
$394$	−19.0399	+	12.7987i	−0.959214	+	0.644787i
$395$		−	3.71293i		−	0.186818i
$396$	1.79074	−	4.39209i	0.0899882	−	0.220711i
$397$	29.0607			1.45851			0.729256	−	0.684241i	$-0.239866\pi$
$397$	29.0607			1.45851			0.729256	+	0.684241i	$0.239866\pi$
$398$	−14.0787	+	9.46377i	−0.705703	+	0.474376i
$399$		−	1.11633i		−	0.0558865i
$400$	2.85968	+	2.79683i	0.142984	+	0.139841i
$401$			21.4333i			1.07033i	0.844748	+	0.535165i	$0.179751\pi$
$401$			21.4333i			1.07033i	−0.844748	+	0.535165i	$0.820249\pi$
$402$	10.8821	+	16.1887i	0.542751	+	0.807420i
$403$			24.6496i			1.22789i
$404$	−2.22091	+	5.44714i	−0.110494	+	0.271005i
$405$			1.00000i			0.0496904i
$406$	−1.93314	+	1.29946i	−0.0959401	+	0.0644913i
$407$			21.1787i			1.04979i
$408$	0.655295	+	3.15669i	0.0324419	+	0.156279i
$409$	22.4387			1.10952			0.554762	−	0.832009i	$-0.312809\pi$
$409$	22.4387			1.10952			0.554762	+	0.832009i	$0.312809\pi$
$410$	0.237335	+	0.353070i	0.0117212	+	0.0174369i
$411$	8.43368			0.416003
$412$	7.87822	−	19.3226i	0.388132	−	0.951956i
$413$		−	2.85169i		−	0.140323i
$414$	1.66899	−	6.57377i	0.0820264	−	0.323083i
$415$		−	7.56680i		−	0.371440i
$416$	−13.2173	−	2.43878i	−0.648033	−	0.119571i
$417$	−4.36147			−0.213582
$418$	5.47917	−	3.68312i	0.267995	−	0.180147i
$419$	−6.70351			−0.327488			−0.163744	−	0.986503i	$-0.552357\pi$
$419$	−6.70351			−0.327488			−0.163744	+	0.986503i	$0.552357\pi$
$420$	0.428218	−	1.05027i	0.0208949	−	0.0512481i
$421$			17.3586i			0.846009i	0.906128	+	0.423004i	$0.139024\pi$
$421$			17.3586i			0.846009i	−0.906128	+	0.423004i	$0.860976\pi$
$422$	11.0189	+	16.3922i	0.536392	+	0.797961i
$423$		−	0.733164i		−	0.0356477i
$424$	−29.0241	+	6.02510i	−1.40954	+	0.292605i
$425$		−	1.13985i		−	0.0552909i
$426$	6.22805	−	4.18652i	0.301750	−	0.202837i
$427$		−	5.31033i		−	0.256985i
$428$	13.8082	−	33.8668i	0.667444	−	1.63702i
$429$		−	5.63472i		−	0.272047i
$430$	−3.12988	−	4.65614i	−0.150936	−	0.224539i
$431$	−10.7963			−0.520041			−0.260021	−	0.965603i	$-0.583729\pi$
$431$	−10.7963			−0.520041			−0.260021	+	0.965603i	$0.583729\pi$
$432$	2.79683	−	2.85968i	0.134562	−	0.137586i
$433$			37.1847i			1.78698i	0.449078	+	0.893492i	$0.351752\pi$
$433$			37.1847i			1.78698i	−0.449078	+	0.893492i	$0.648248\pi$
$434$	4.64186	+	6.90543i	0.222816	+	0.331471i
$435$	2.90432			0.139252
$436$	13.3426	+	5.44005i	0.638995	+	0.260531i
$437$	7.03265	−	6.29791i	0.336417	−	0.301270i
$438$	−9.26984	−	13.7902i	−0.442930	−	0.658922i
$439$		−	11.8041i		−	0.563378i	−0.959506	−	0.281689i	$-0.909105\pi$
$439$		−	11.8041i		−	0.563378i	0.959506	−	0.281689i	$-0.0908947\pi$
$440$	6.56776	−	1.36340i	0.313106	−	0.0649975i
$441$	6.67839			0.318019
$442$	2.13669	+	3.17863i	0.101632	+	0.151192i
$443$		−	19.9704i		−	0.948821i	−0.880304	−	0.474411i	$-0.842661\pi$
$443$		−	19.9704i		−	0.948821i	0.880304	−	0.474411i	$-0.157339\pi$
$444$	−6.74319	+	16.5388i	−0.320017	+	0.784895i
$445$	14.2021			0.673246
$446$	−2.64806	−	3.93937i	−0.125389	−	0.186535i
$447$	6.27281			0.296694
$448$	−4.16200	+	1.80579i	−0.196636	+	0.0853156i
$449$	18.6765			0.881399			0.440699	−	0.897655i	$-0.354731\pi$
$449$	18.6765			0.881399			0.440699	+	0.897655i	$0.354731\pi$
$450$	−1.17369	+	0.788958i	−0.0553282	+	0.0371918i
$451$	0.713415			0.0335934
$452$	−19.9100	−	8.11771i	−0.936488	−	0.381825i
$453$	−3.53863			−0.166259
$454$	−18.7723	+	12.6188i	−0.881028	+	0.592230i
$455$		−	1.34742i		−	0.0631682i
$456$	5.45144	−	1.13166i	0.255287	−	0.0529949i
$457$		−	16.9284i		−	0.791879i	−0.918277	−	0.395940i	$-0.870419\pi$
$457$		−	16.9284i		−	0.791879i	0.918277	−	0.395940i	$-0.129581\pi$
$458$	6.60140	+	9.82054i	0.308463	+	0.458884i
$459$	−1.13985			−0.0532037
$460$	9.03232	−	3.22755i	0.421134	−	0.150486i
$461$	−13.4938			−0.628471			−0.314236	−	0.949345i	$-0.601748\pi$
$461$	−13.4938			−0.628471			−0.314236	+	0.949345i	$0.601748\pi$
$462$	−1.06109	−	1.57853i	−0.0493665	−	0.0734398i
$463$		−	39.9756i		−	1.85782i	−0.370303	−	0.928911i	$-0.620746\pi$
$463$		−	39.9756i		−	1.85782i	0.370303	−	0.928911i	$-0.379254\pi$
$464$	−8.30542	−	8.12289i	−0.385570	−	0.377096i
$465$		−	10.3746i		−	0.481111i
$466$	−0.637084	+	0.428250i	−0.0295123	+	0.0198383i
$467$	−9.49804			−0.439517			−0.219758	−	0.975554i	$-0.570527\pi$
$467$	−9.49804			−0.439517			−0.219758	+	0.975554i	$0.570527\pi$
$468$	1.79406	−	4.40023i	0.0829306	−	0.203401i
$469$	7.82213			0.361192
$470$	0.860507	−	0.578436i	0.0396922	−	0.0266813i
$471$	11.1028			0.511589
$472$	13.9258	−	2.89085i	0.640987	−	0.133062i
$473$	−9.40821			−0.432590
$474$	−2.92934	−	4.35782i	−0.134549	−	0.200161i
$475$	−1.96847			−0.0903194
$476$	1.19716	+	0.488104i	0.0548715	+	0.0223722i
$477$		−	10.4803i		−	0.479862i
$478$	4.36788	+	6.49785i	0.199782	+	0.297205i
$479$	24.3925			1.11452			0.557260	−	0.830338i	$-0.311853\pi$
$479$	24.3925			1.11452			0.557260	+	0.830338i	$0.311853\pi$
$480$	5.56295	+	1.02644i	0.253913	+	0.0468504i
$481$			21.2180i			0.967458i
$482$	−12.9494	−	19.2641i	−0.589830	−	0.877457i
$483$	−1.81440	−	2.02608i	−0.0825582	−	0.0921898i
$484$	−4.05914	+	9.95571i	−0.184507	+	0.452532i
$485$	14.4809			0.657544
$486$	0.788958	+	1.17369i	0.0357879	+	0.0532396i
$487$			25.9365i			1.17529i	0.809117	+	0.587647i	$0.199946\pi$
$487$			25.9365i			1.17529i	−0.809117	+	0.587647i	$0.800054\pi$
$488$	25.9322	−	5.38325i	1.17389	−	0.243688i
$489$	−10.7661			−0.486859
$490$	5.26897	+	7.83835i	0.238028	+	0.354101i
$491$			10.7679i			0.485947i	0.970033	+	0.242974i	$0.0781229\pi$
$491$			10.7679i			0.485947i	−0.970033	+	0.242974i	$0.921877\pi$
$492$	0.557115	+	0.227147i	0.0251167	+	0.0102406i
$493$			3.31049i			0.149097i
$494$	5.48933	−	3.68995i	0.246977	−	0.166019i
$495$			2.37156i			0.106594i
$496$	−29.0160	+	29.6681i	−1.30286	+	1.33213i
$497$		−	3.00929i		−	0.134985i
$498$	−5.96989	−	8.88107i	−0.267517	−	0.397970i
$499$		−	3.70379i		−	0.165805i	−0.996558	−	0.0829023i	$-0.973581\pi$
$499$		−	3.70379i		−	0.165805i	0.996558	−	0.0829023i	$-0.0264189\pi$
$500$	−1.85198	−	0.755090i	−0.0828232	−	0.0337687i
$501$	20.5663			0.918836
$502$	4.52730	−	3.04327i	0.202063	−	0.135828i
$503$	−8.07455			−0.360026			−0.180013	−	0.983664i	$-0.557614\pi$
$503$	−8.07455			−0.360026			−0.180013	+	0.983664i	$0.557614\pi$
$504$	−0.326028	−	1.57054i	−0.0145224	−	0.0699574i
$505$		−	2.94125i		−	0.130884i
$506$	3.95811	−	15.5901i	0.175959	−	0.693064i
$507$			7.35483i			0.326639i
$508$	−16.1678	−	6.59193i	−0.717330	−	0.292470i
$509$	7.05419			0.312672			0.156336	−	0.987704i	$-0.450032\pi$
$509$	7.05419			0.312672			0.156336	+	0.987704i	$0.450032\pi$
$510$	−0.899295	−	1.33783i	−0.0398214	−	0.0592401i
$511$	−6.66322			−0.294763
$512$	−13.0375	−	18.4939i	−0.576180	−	0.817323i
$513$			1.96847i			0.0869099i
$514$	22.6268	−	15.2098i	0.998026	−	0.670877i
$515$			10.4335i			0.459754i
$516$	−7.34700	−	2.99552i	−0.323434	−	0.131870i
$517$		−	1.73874i		−	0.0764698i
$518$	3.99563	+	5.94408i	0.175558	+	0.261168i
$519$			3.88535i			0.170548i
$520$	6.57994	−	1.36593i	0.288550	−	0.0598998i
$521$		−	0.958111i		−	0.0419756i	−0.999780	−	0.0209878i	$-0.993319\pi$
$521$		−	0.958111i		−	0.0419756i	0.999780	−	0.0209878i	$-0.00668111\pi$
$522$	3.40877	−	2.29139i	0.149198	−	0.100291i
$523$	−27.9145			−1.22062			−0.610308	−	0.792164i	$-0.708954\pi$
$523$	−27.9145			−1.22062			−0.610308	+	0.792164i	$0.708954\pi$
$524$	−36.4906	−	14.8780i	−1.59410	−	0.649947i
$525$			0.567108i			0.0247506i
$526$	19.4569	−	13.0790i	0.848363	−	0.570273i
$527$	11.8255			0.515128
$528$	6.63284	−	6.78189i	0.288658	−	0.295144i
$529$	2.52769	−	22.8607i	0.109900	−	0.993943i
$530$	12.3007	−	8.26855i	0.534307	−	0.359163i
$531$			5.02848i			0.218218i
$532$	0.842932	−	2.06743i	0.0365457	−	0.0896344i
$533$	0.714738			0.0309587
$534$	16.6689	−	11.2049i	0.721334	−	0.484883i
$535$			18.2868i			0.790607i
$536$	7.92954	+	38.1982i	0.342504	+	1.64991i
$537$	−5.49382			−0.237076
$538$	−11.1773	+	7.51343i	−0.481888	+	0.323927i
$539$	15.8382			0.682199
$540$	−0.755090	+	1.85198i	−0.0324939	+	0.0796966i
$541$	20.0435			0.861735			0.430868	−	0.902415i	$-0.358208\pi$
$541$	20.0435			0.861735			0.430868	+	0.902415i	$0.358208\pi$
$542$	−13.8310	−	20.5756i	−0.594093	−	0.883799i
$543$	−1.42676			−0.0612281
$544$	−1.16999	+	6.34094i	−0.0501629	+	0.271865i
$545$	−7.20450			−0.308607
$546$	−1.06306	−	1.58146i	−0.0454948	−	0.0676801i
$547$		−	38.9217i		−	1.66417i	−0.554648	−	0.832085i	$-0.687147\pi$
$547$		−	38.9217i		−	1.66417i	0.554648	−	0.832085i	$-0.312853\pi$
$548$	15.6190	+	6.36819i	0.667212	+	0.272036i
$549$			9.36387i			0.399640i
$550$	−2.78347	+	1.87106i	−0.118688	+	0.0797823i
$551$	5.71706			0.243555
$552$	8.05473	−	10.9143i	0.342832	−	0.464542i
$553$	−2.10563			−0.0895405
$554$	−7.62103	+	5.12289i	−0.323787	+	0.217651i
$555$		−	8.93030i		−	0.379070i
$556$	−8.07737	−	3.29331i	−0.342557	−	0.139667i
$557$			39.1883i			1.66046i	0.557421	+	0.830230i	$0.311791\pi$
$557$			39.1883i			1.66046i	−0.557421	+	0.830230i	$0.688209\pi$
$558$	−8.18514	−	12.1766i	−0.346505	−	0.515475i
$559$	−9.42566			−0.398663
$560$	1.58610	−	1.62175i	0.0670251	−	0.0685312i
$561$	−2.70322			−0.114130
$562$	−1.26981	−	1.88903i	−0.0535639	−	0.0796840i
$563$	−25.3286			−1.06747			−0.533737	−	0.845650i	$-0.679213\pi$
$563$	−25.3286			−1.06747			−0.533737	+	0.845650i	$0.679213\pi$
$564$	0.553605	−	1.35781i	0.0233110	−	0.0571740i
$565$	10.7506			0.452283
$566$	20.0623	−	13.4859i	0.843281	−	0.566856i
$567$	0.567108			0.0238163
$568$	14.6954	−	3.05062i	0.616607	−	0.128001i
$569$		−	24.0241i		−	1.00714i	−0.863953	−	0.503572i	$-0.832019\pi$
$569$		−	24.0241i		−	1.00714i	0.863953	−	0.503572i	$-0.167981\pi$
$570$	−2.31037	+	1.55304i	−0.0967706	+	0.0650496i
$571$	40.2537			1.68456			0.842282	−	0.539037i	$-0.181212\pi$
$571$	40.2537			1.68456			0.842282	+	0.539037i	$0.181212\pi$
$572$	4.25473	−	10.4354i	0.177899	−	0.436326i
$573$			23.8995i			0.998416i
$574$	0.200229	−	0.134595i	0.00835740	−	0.00561787i
$575$	−3.57265	+	3.19940i	−0.148990	+	0.133424i
$576$	7.33899	−	3.18421i	0.305791	−	0.132676i
$577$	46.2140			1.92391			0.961957	−	0.273199i	$-0.0880819\pi$
$577$	46.2140			1.92391			0.961957	+	0.273199i	$0.0880819\pi$
$578$	−18.4278	+	12.3872i	−0.766495	+	0.515241i
$579$		−	13.0675i		−	0.543065i
$580$	5.37875	+	2.19303i	0.223341	+	0.0910604i
$581$	−4.29119			−0.178029
$582$	16.9961	−	11.4248i	0.704510	−	0.473574i
$583$		−	24.8548i		−	1.02938i
$584$	−6.75471	−	32.5388i	−0.279512	−	1.34647i
$585$			2.37596i			0.0982337i
$586$	−7.06773	−	10.5143i	−0.291965	−	0.434340i
$587$		−	38.1819i		−	1.57593i	−0.615717	−	0.787967i	$-0.711134\pi$
$587$		−	38.1819i		−	1.57593i	0.615717	−	0.787967i	$-0.288866\pi$
$588$	12.3683	+	5.04279i	0.510058	+	0.207961i
$589$		−	20.4221i		−	0.841477i
$590$	−5.90187	+	3.96726i	−0.242976	+	0.163330i
$591$		−	16.2222i		−	0.667294i
$592$	−24.9765	+	25.5378i	−1.02653	+	1.04960i
$593$	34.0163			1.39688			0.698441	−	0.715667i	$-0.253877\pi$
$593$	34.0163			1.39688			0.698441	+	0.715667i	$0.253877\pi$
$594$	1.87106	+	2.78347i	0.0767706	+	0.114207i
$595$	−0.646418			−0.0265006
$596$	11.6171	+	4.73654i	0.475856	+	0.194016i
$597$		−	11.9953i		−	0.490934i
$598$	3.96545	−	15.6190i	0.162159	−	0.638708i
$599$			38.2444i			1.56262i	0.624141	+	0.781311i	$0.285449\pi$
$599$			38.2444i			1.56262i	−0.624141	+	0.781311i	$0.714551\pi$
$600$	−2.76939	+	0.574895i	−0.113060	+	0.0234700i
$601$	−8.37118			−0.341468			−0.170734	−	0.985317i	$-0.554614\pi$
$601$	−8.37118			−0.341468			−0.170734	+	0.985317i	$0.554614\pi$
$602$	−2.64053	+	1.77498i	−0.107620	+	0.0723427i
$603$	−13.7930			−0.561695
$604$	−6.55348	−	2.67199i	−0.266657	−	0.108722i
$605$		−	5.37571i		−	0.218554i
$606$	−2.32052	−	3.45211i	−0.0942648	−	0.140232i
$607$		−	10.0636i		−	0.408469i	−0.978922	−	0.204234i	$-0.934530\pi$
$607$		−	10.0636i		−	0.408469i	0.978922	−	0.204234i	$-0.0654705\pi$
$608$	10.9505	+	2.02051i	0.444101	+	0.0819427i
$609$		−	1.64706i		−	0.0667424i
$610$	−10.9903	+	7.38770i	−0.444983	+	0.299119i
$611$		−	1.74197i		−	0.0704724i
$612$	−2.11098	−	0.860691i	−0.0853315	−	0.0347914i
$613$			34.5466i			1.39533i	0.716426	+	0.697663i	$0.245777\pi$
$613$			34.5466i			1.39533i	−0.716426	+	0.697663i	$0.754223\pi$
$614$	−11.3850	−	16.9368i	−0.459461	−	0.683514i
$615$	−0.300821			−0.0121303
$616$	−0.773194	−	3.72463i	−0.0311529	−	0.150070i
$617$			47.0181i			1.89288i	0.322885	+	0.946438i	$0.395347\pi$
$617$			47.0181i			1.89288i	−0.322885	+	0.946438i	$0.604653\pi$
$618$	8.23157	+	12.2456i	0.331122	+	0.492592i
$619$	28.9512			1.16365			0.581824	−	0.813315i	$-0.302339\pi$
$619$	28.9512			1.16365			0.581824	+	0.813315i	$0.302339\pi$
$620$	7.83377	−	19.2136i	0.314612	−	0.771637i
$621$	3.19940	+	3.57265i	0.128387	+	0.143366i
$622$	−3.93396	−	5.85234i	−0.157738	−	0.234657i
$623$		−	8.05415i		−	0.322683i
$624$	6.64514	−	6.79447i	0.266019	−	0.271996i
$625$	1.00000			0.0400000
$626$	13.8098	+	20.5441i	0.551953	+	0.821109i
$627$			4.66833i			0.186435i
$628$	20.5622	+	8.38361i	0.820520	+	0.334542i
$629$	10.1792			0.405872
$630$	0.447424	+	0.665608i	0.0178258	+	0.0265185i
$631$	28.9310			1.15173			0.575863	−	0.817546i	$-0.304666\pi$
$631$	28.9310			1.15173			0.575863	+	0.817546i	$0.304666\pi$
$632$	−2.13454	−	10.2825i	−0.0849076	−	0.409017i
$633$	−13.9664			−0.555115
$634$	25.5293	−	17.1609i	1.01390	−	0.681546i
$635$	8.72999			0.346439
$636$	7.91361	−	19.4094i	0.313795	−	0.769633i
$637$	15.8676			0.628696
$638$	8.08410	−	5.43416i	0.320053	−	0.215141i
$639$			5.30639i			0.209917i
$640$	9.52743	+	6.10148i	0.376605	+	0.241182i
$641$		−	41.8520i		−	1.65305i	−0.562898	−	0.826527i	$-0.690313\pi$
$641$		−	41.8520i		−	1.65305i	0.562898	−	0.826527i	$-0.309687\pi$
$642$	14.4275	+	21.4630i	0.569409	+	0.847078i
$643$	47.4233			1.87019			0.935096	−	0.354395i	$-0.115313\pi$
$643$	47.4233			1.87019			0.935096	+	0.354395i	$0.115313\pi$
$644$	−1.83037	−	5.12230i	−0.0721267	−	0.201847i
$645$	3.96710			0.156204
$646$	−1.77023	−	2.63347i	−0.0696488	−	0.103613i
$647$			3.93052i			0.154525i	0.997011	+	0.0772623i	$0.0246179\pi$
$647$			3.93052i			0.154525i	−0.997011	+	0.0772623i	$0.975382\pi$
$648$	0.574895	+	2.76939i	0.0225840	+	0.108792i
$649$			11.9253i			0.468111i
$650$	−2.78863	+	1.87453i	−0.109379	+	0.0735251i
$651$	−5.88353			−0.230594
$652$	−19.9386	−	8.12937i	−0.780856	−	0.318371i
$653$	17.0706			0.668024			0.334012	−	0.942569i	$-0.391597\pi$
$653$	17.0706			0.668024			0.334012	+	0.942569i	$0.391597\pi$
$654$	−8.45584	+	5.68405i	−0.330650	+	0.222264i
$655$	19.7035			0.769881
$656$	0.860251	+	0.841345i	0.0335872	+	0.0328490i
$657$	11.7495			0.458391
$658$	−0.328035	−	0.488000i	−0.0127882	−	0.0190242i
$659$	−19.0337			−0.741447			−0.370723	−	0.928743i	$-0.620890\pi$
$659$	−19.0337			−0.741447			−0.370723	+	0.928743i	$0.620890\pi$
$660$	−1.79074	+	4.39209i	−0.0697045	+	0.170962i
$661$			45.0893i			1.75377i	0.480699	+	0.876886i	$0.340383\pi$
$661$			45.0893i			1.75377i	−0.480699	+	0.876886i	$0.659617\pi$
$662$	−2.36771	−	3.52231i	−0.0920238	−	0.136899i
$663$	−2.70824			−0.105179
$664$	−4.35012	−	20.9554i	−0.168817	−	0.813227i
$665$			1.11633i			0.0432895i
$666$	−7.04563	−	10.4814i	−0.273013	−	0.406146i
$667$	10.3761	−	9.29209i	0.401766	−	0.359791i
$668$	38.0885	+	15.5294i	1.47369	+	0.600852i
$669$	3.35640			0.129766
$670$	−10.8821	−	16.1887i	−0.420413	−	0.625425i
$671$			22.2070i			0.857291i
$672$	0.582103	−	3.15479i	0.0224551	−	0.121699i
$673$	−20.8003			−0.801791			−0.400895	−	0.916124i	$-0.631301\pi$
$673$	−20.8003			−0.801791			−0.400895	+	0.916124i	$0.631301\pi$
$674$	−3.84748	−	5.72369i	−0.148200	−	0.220468i
$675$		−	1.00000i		−	0.0384900i
$676$	−5.55356	+	13.6210i	−0.213598	+	0.523885i
$677$			10.2255i			0.393000i	0.980504	+	0.196500i	$0.0629575\pi$
$677$			10.2255i			0.393000i	−0.980504	+	0.196500i	$0.937042\pi$
$678$	12.6179	−	8.48181i	0.484588	−	0.325742i
$679$		−	8.21224i		−	0.315157i
$680$	−0.655295	−	3.15669i	−0.0251294	−	0.121053i
$681$		−	15.9943i		−	0.612902i
$682$	−19.4115	−	28.8775i	−0.743306	−	1.10578i
$683$		−	15.2275i		−	0.582666i	−0.956622	−	0.291333i	$-0.905901\pi$
$683$		−	15.2275i		−	0.582666i	0.956622	−	0.291333i	$-0.0940987\pi$
$684$	−1.48637	+	3.64556i	−0.0568328	+	0.139392i
$685$	−8.43368			−0.322234
$686$	9.10445	−	6.12004i	0.347609	−	0.233664i
$687$	−8.36724			−0.319230
$688$	−11.3446	−	11.0953i	−0.432510	−	0.423004i
$689$		−	24.9009i		−	0.948647i
$690$	−1.66899	+	6.57377i	−0.0635374	+	0.250259i
$691$		−	19.7988i		−	0.753184i	−0.926379	−	0.376592i	$-0.877096\pi$
$691$		−	19.7988i		−	0.753184i	0.926379	−	0.376592i	$-0.122904\pi$
$692$	−2.93379	+	7.19559i	−0.111526	+	0.273535i
$693$	1.34493			0.0510897
$694$	−17.4959	−	26.0277i	−0.664137	−	0.987999i
$695$	4.36147			0.165440
$696$	8.04319	−	1.66968i	0.304876	−	0.0632891i
$697$		−	0.342891i		−	0.0129879i
$698$	−28.7790	+	19.3454i	−1.08930	+	0.732234i
$699$		−	0.542805i		−	0.0205308i
$700$	−0.428218	+	1.05027i	−0.0161851	+	0.0396966i
$701$			17.5015i			0.661024i	0.943802	+	0.330512i	$0.107221\pi$
$701$			17.5015i			0.661024i	−0.943802	+	0.330512i	$0.892779\pi$
$702$	1.87453	+	2.78863i	0.0707496	+	0.105250i
$703$		−	17.5790i		−	0.663005i
$704$	17.4049	−	7.55155i	0.655970	−	0.284610i
$705$			0.733164i			0.0276126i
$706$	10.5813	−	7.11278i	0.398232	−	0.267693i
$707$	−1.66801			−0.0627318
$708$	−3.79696	+	9.31266i	−0.142698	+	0.349991i
$709$			24.2885i			0.912173i	0.889936	+	0.456086i	$0.150749\pi$
$709$			24.2885i			0.912173i	−0.889936	+	0.456086i	$0.849251\pi$
$710$	−6.22805	+	4.18652i	−0.233734	+	0.157117i
$711$	3.71293			0.139246
$712$	39.3312	−	8.16475i	1.47400	−	0.305987i
$713$	−33.1925	−	37.0649i	−1.24307	−	1.38809i
$714$	−0.758694	+	0.509997i	−0.0283934	+	0.0190862i
$715$			5.63472i			0.210727i
$716$	−10.1745	−	4.14833i	−0.380237	−	0.155030i
$717$	−5.53626			−0.206756
$718$	23.1636	−	15.5706i	0.864457	−	0.581091i
$719$		−	13.8278i		−	0.515691i	−0.966186	−	0.257846i	$-0.916987\pi$
$719$		−	13.8278i		−	0.515691i	0.966186	−	0.257846i	$-0.0830126\pi$
$720$	−2.79683	+	2.85968i	−0.104232	+	0.106574i
$721$	5.91690			0.220357
$722$	17.7522	−	11.9331i	0.660669	−	0.444104i
$723$	16.4133			0.610418
$724$	−2.64233	−	1.07733i	−0.0982016	−	0.0400387i
$725$	−2.90432			−0.107864
$726$	−4.24121	−	6.30941i	−0.157406	−	0.234164i
$727$	−29.3700			−1.08927			−0.544637	−	0.838672i	$-0.683333\pi$
$727$	−29.3700			−1.08927			−0.544637	+	0.838672i	$0.683333\pi$
$728$	−0.774628	−	3.73154i	−0.0287096	−	0.138300i
$729$	−1.00000			−0.0370370
$730$	9.26984	+	13.7902i	0.343092	+	0.510399i
$731$			4.52190i			0.167249i
$732$	−7.07057	+	17.3417i	−0.261336	+	0.640969i
$733$		−	21.3518i		−	0.788648i	−0.918971	−	0.394324i	$-0.870979\pi$
$733$		−	21.3518i		−	0.788648i	0.918971	−	0.394324i	$-0.129021\pi$
$734$	−9.87961	+	6.64111i	−0.364663	+	0.245128i
$735$	−6.67839			−0.246336
$736$	23.1585	−	14.1310i	0.853633	−	0.520875i
$737$	−32.7110			−1.20492
$738$	−0.353070	+	0.237335i	−0.0129967	+	0.00873643i
$739$			15.2385i			0.560558i	0.959919	+	0.280279i	$0.0904270\pi$
$739$			15.2385i			0.560558i	−0.959919	+	0.280279i	$0.909573\pi$
$740$	6.74319	−	16.5388i	0.247884	−	0.607977i
$741$			4.67699i			0.171814i
$742$	−4.68916	−	6.97580i	−0.172144	−	0.256090i
$743$	−38.8478			−1.42519			−0.712594	−	0.701577i	$-0.752480\pi$
$743$	−38.8478			−1.42519			−0.712594	+	0.701577i	$0.752480\pi$
$744$	−5.96432	−	28.7313i	−0.218662	−	1.05334i
$745$	−6.27281			−0.229818
$746$	−27.9517	−	41.5821i	−1.02338	−	1.52243i
$747$	7.56680			0.276855
$748$	−5.00632	−	2.04118i	−0.183049	−	0.0746329i
$749$	10.3706			0.378933
$750$	1.17369	−	0.788958i	0.0428571	−	0.0288087i
$751$	1.76691			0.0644756			0.0322378	−	0.999480i	$-0.489737\pi$
$751$	1.76691			0.0644756			0.0322378	+	0.999480i	$0.489737\pi$
$752$	2.05053	−	2.09661i	0.0747753	−	0.0764556i
$753$			3.85732i			0.140569i
$754$	8.09909	−	5.44424i	0.294952	−	0.198268i
$755$	3.53863			0.128784
$756$	1.05027	+	0.428218i	0.0381981	+	0.0155741i
$757$		−	11.7925i		−	0.428605i	−0.976767	−	0.214302i	$-0.931252\pi$
$757$		−	11.7925i		−	0.428605i	0.976767	−	0.214302i	$-0.0687478\pi$
$758$	2.57466	−	1.73069i	0.0935158	−	0.0628617i
$759$	7.58757	+	8.47276i	0.275411	+	0.307542i
$760$	−5.45144	+	1.13166i	−0.197745	+	0.0410497i
$761$	−37.4484			−1.35750			−0.678752	−	0.734367i	$-0.737479\pi$
$761$	−37.4484			−1.35750			−0.678752	+	0.734367i	$0.737479\pi$
$762$	10.2463	−	6.88760i	0.371184	−	0.249511i
$763$			4.08573i			0.147913i
$764$	−18.0463	+	44.2615i	−0.652892	+	1.60132i
$765$	1.13985			0.0412114
$766$	0.677313	−	0.455293i	0.0244723	−	0.0164504i
$767$			11.9475i			0.431398i
$768$	15.9961	−	0.355504i	0.577208	−	0.0128281i
$769$		−	12.9769i		−	0.467958i	−0.972242	−	0.233979i	$-0.924825\pi$
$769$		−	12.9769i		−	0.467958i	0.972242	−	0.233979i	$-0.0751747\pi$
$770$	1.06109	+	1.57853i	0.0382391	+	0.0568862i
$771$			19.2784i			0.694294i
$772$	9.86712	−	24.2007i	0.355125	−	0.871003i
$773$			3.72681i			0.134044i	0.997751	+	0.0670221i	$0.0213498\pi$
$773$			3.72681i			0.134044i	−0.997751	+	0.0670221i	$0.978650\pi$
$774$	4.65614	−	3.12988i	0.167362	−	0.112501i
$775$			10.3746i			0.372667i
$776$	40.1032	−	8.32501i	1.43962	−	0.298850i
$777$	−5.06444			−0.181686
$778$	8.30303	+	12.3520i	0.297678	+	0.442839i
$779$	−0.592156			−0.0212162
$780$	−1.79406	+	4.40023i	−0.0642377	+	0.157554i
$781$			12.5844i			0.450306i
$782$	−7.49312	−	1.90240i	−0.267953	−	0.0680297i
$783$			2.90432i			0.103792i
$784$	19.0980	+	18.6783i	0.682073	+	0.667082i
$785$	−11.1028			−0.396275
$786$	23.1258	−	15.5453i	0.824871	−	0.554481i
$787$	−13.1959			−0.470384			−0.235192	−	0.971949i	$-0.575572\pi$
$787$	−13.1959			−0.470384			−0.235192	+	0.971949i	$0.575572\pi$
$788$	12.2493	−	30.0433i	0.436362	−	1.07025i
$789$			16.5776i			0.590178i
$790$	2.92934	+	4.35782i	0.104221	+	0.155044i
$791$		−	6.09678i		−	0.216776i
$792$	1.36340	+	6.56776i	0.0484462	+	0.233375i
$793$			22.2482i			0.790056i
$794$	−34.1082	+	22.9276i	−1.21045	+	0.813671i
$795$			10.4803i			0.371700i
$796$	9.05752	−	22.2150i	0.321035	−	0.787392i
$797$		−	47.3244i		−	1.67632i	−0.545427	−	0.838158i	$-0.683632\pi$
$797$		−	47.3244i		−	1.67632i	0.545427	−	0.838158i	$-0.316368\pi$
$798$	0.880740	+	1.31023i	0.0311778	+	0.0463815i
$799$	−0.835698			−0.0295649
$800$	−5.56295	−	1.02644i	−0.196680	−	0.0362902i
$801$			14.2021i			0.501808i
$802$	−16.9100	−	25.1561i	−0.597113	−	0.888292i
$803$	27.8646			0.983319
$804$	−25.5444	−	10.4150i	−0.900883	−	0.367308i
$805$	1.81440	+	2.02608i	0.0639493	+	0.0714099i
$806$	−19.4475	−	28.9310i	−0.685010	−	1.01905i
$807$		−	9.52323i		−	0.335234i
$808$	−1.69091	−	8.14545i	−0.0594860	−	0.286556i
$809$	17.0043			0.597840			0.298920	−	0.954278i	$-0.403374\pi$
$809$	17.0043			0.597840			0.298920	+	0.954278i	$0.403374\pi$
$810$	−0.788958	−	1.17369i	−0.0277212	−	0.0412392i
$811$			22.5072i			0.790335i	0.918609	+	0.395168i	$0.129313\pi$
$811$			22.5072i			0.790335i	−0.918609	+	0.395168i	$0.870687\pi$
$812$	1.24368	−	3.05033i	0.0436447	−	0.107046i
$813$	17.5307			0.614830
$814$	−16.7091	−	24.8573i	−0.585655	−	0.871246i
$815$	10.7661			0.377120
$816$	−3.25961	−	3.18797i	−0.114109	−	0.111601i
$817$	7.80910			0.273206
$818$	−26.3361	+	17.7032i	−0.920819	+	0.618978i
$819$	1.34742			0.0470828
$820$	−0.557115	−	0.227147i	−0.0194553	−	0.00793232i
$821$	32.5967			1.13763			0.568817	−	0.822464i	$-0.307401\pi$
$821$	32.5967			1.13763			0.568817	+	0.822464i	$0.307401\pi$
$822$	−9.89852	+	6.65382i	−0.345250	+	0.232079i
$823$			4.97289i			0.173344i	0.996237	+	0.0866720i	$0.0276232\pi$
$823$			4.97289i			0.173344i	−0.996237	+	0.0866720i	$0.972377\pi$
$824$	5.99815	+	28.8943i	0.208956	+	1.00658i
$825$		−	2.37156i		−	0.0825671i
$826$	2.24986	+	3.34700i	0.0782828	+	0.116457i
$827$	2.59097			0.0900970			0.0450485	−	0.998985i	$-0.485656\pi$
$827$	2.59097			0.0900970			0.0450485	+	0.998985i	$0.485656\pi$
$828$	3.22755	+	9.03232i	0.112165	+	0.313895i
$829$	−15.2773			−0.530602			−0.265301	−	0.964166i	$-0.585471\pi$
$829$	−15.2773			−0.530602			−0.265301	+	0.964166i	$0.585471\pi$
$830$	5.96989	+	8.88107i	0.207218	+	0.308266i
$831$		−	6.49323i		−	0.225248i
$832$	17.4371	−	7.56555i	0.604524	−	0.262288i
$833$		−	7.61237i		−	0.263753i
$834$	5.11901	−	3.44102i	0.177257	−	0.119153i
$835$	−20.5663			−0.711727
$836$	−3.52502	+	8.64567i	−0.121915	+	0.299017i
$837$	10.3746			0.358599
$838$	7.86783	−	5.28878i	0.271790	−	0.182698i
$839$	−17.2972			−0.597165			−0.298583	−	0.954384i	$-0.596514\pi$
$839$	−17.2972			−0.597165			−0.298583	+	0.954384i	$0.596514\pi$
$840$	0.326028	+	1.57054i	0.0112490	+	0.0541888i
$841$	−20.5649			−0.709135
$842$	−13.6952	−	20.3736i	−0.471969	−	0.702122i
$843$	1.60948			0.0554335
$844$	−25.8655	−	10.5459i	−0.890329	−	0.363005i
$845$		−	7.35483i		−	0.253014i
$846$	0.578436	+	0.860507i	0.0198870	+	0.0295848i
$847$	−3.04860			−0.104751
$848$	29.3117	−	29.9704i	1.00657	−	1.02919i
$849$			17.0934i			0.586643i
$850$	0.899295	+	1.33783i	0.0308456	+	0.0458872i
$851$	−28.5716	−	31.9049i	−0.979422	−	1.09368i
$852$	−4.00680	+	9.82733i	−0.137271	+	0.336679i
$853$	−31.6110			−1.08234			−0.541170	−	0.840913i	$-0.682018\pi$
$853$	−31.6110			−1.08234			−0.541170	+	0.840913i	$0.682018\pi$
$854$	4.18962	+	6.23267i	0.143366	+	0.213278i
$855$		−	1.96847i		−	0.0673201i
$856$	10.5130	+	50.6432i	0.359327	+	1.73095i
$857$	−57.5884			−1.96718			−0.983591	−	0.180412i	$-0.942257\pi$
$857$	−57.5884			−1.96718			−0.983591	+	0.180412i	$0.942257\pi$
$858$	4.44556	+	6.61341i	0.151769	+	0.225778i
$859$			17.9733i			0.613240i	0.951832	+	0.306620i	$0.0991982\pi$
$859$			17.9733i			0.613240i	−0.951832	+	0.306620i	$0.900802\pi$
$860$	7.34700	+	2.99552i	0.250531	+	0.102146i
$861$			0.170598i			0.00581396i
$862$	12.6715	−	8.51785i	0.431594	−	0.290119i
$863$			28.9066i			0.983991i	0.870598	+	0.491995i	$0.163732\pi$
$863$			28.9066i			0.983991i	−0.870598	+	0.491995i	$0.836268\pi$
$864$	−1.02644	+	5.56295i	−0.0349202	+	0.189255i
$865$		−	3.88535i		−	0.132106i
$866$	−29.3372	−	43.6433i	−0.996919	−	1.48306i
$867$		−	15.7007i		−	0.533225i
$868$	−10.8962	−	4.44259i	−0.369841	−	0.150791i
$869$	8.80543			0.298704
$870$	−3.40877	+	2.29139i	−0.115568	+	0.0776853i
$871$	−32.7716			−1.11042
$872$	−19.9520	+	4.14183i	−0.675662	+	0.140260i
$873$			14.4809i			0.490105i
$874$	−3.28535	+	12.9402i	−0.111129	+	0.437710i
$875$		−	0.567108i		−	0.0191717i
$876$	21.7598	+	8.87191i	0.735196	+	0.299754i
$877$	45.1521			1.52468			0.762339	−	0.647178i	$-0.224051\pi$
$877$	45.1521			1.52468			0.762339	+	0.647178i	$0.224051\pi$
$878$	9.31293	+	13.8543i	0.314296	+	0.467561i
$879$	8.95831			0.302156
$880$	−6.63284	+	6.78189i	−0.223593	+	0.228618i
$881$			10.2567i			0.345558i	0.984961	+	0.172779i	$0.0552747\pi$
$881$			10.2567i			0.345558i	−0.984961	+	0.172779i	$0.944725\pi$
$882$	−7.83835	+	5.26897i	−0.263931	+	0.177415i
$883$		−	3.20280i		−	0.107783i	−0.998547	−	0.0538914i	$-0.982838\pi$
$883$		−	3.20280i		−	0.107783i	0.998547	−	0.0538914i	$-0.0171625\pi$
$884$	−5.01561	−	2.04496i	−0.168693	−	0.0687796i
$885$		−	5.02848i		−	0.169031i
$886$	15.7558	+	23.4390i	0.529326	+	0.787449i
$887$		−	20.9192i		−	0.702399i	−0.936301	−	0.351199i	$-0.885774\pi$
$887$		−	20.9192i		−	0.702399i	0.936301	−	0.351199i	$-0.114226\pi$
$888$	−5.13399	−	24.7315i	−0.172285	−	0.829933i
$889$		−	4.95085i		−	0.166046i
$890$	−16.6689	+	11.2049i	−0.558743	+	0.375589i
$891$	−2.37156			−0.0794502
$892$	6.21600	+	2.53439i	0.208127	+	0.0848576i
$893$			1.44321i			0.0482952i
$894$	−7.36233	+	4.94898i	−0.246233	+	0.165519i
$895$	5.49382			0.183638
$896$	3.46020	−	5.40308i	0.115597	−	0.180504i
$897$	7.60164	+	8.48847i	0.253811	+	0.283422i
$898$	−21.9204	+	14.7350i	−0.731493	+	0.491713i
$899$		−	30.1312i		−	1.00493i
$900$	0.755090	−	1.85198i	0.0251697	−	0.0617327i
$901$	−11.9460			−0.397980
$902$	−0.837327	+	0.562855i	−0.0278800	+	0.0187410i
$903$		−	2.24977i		−	0.0748678i
$904$	29.7727	−	6.18050i	0.990225	−	0.205560i
$905$	1.42676			0.0474271
$906$	4.15325	−	2.79183i	0.137983	−	0.0927524i
$907$	−26.4810			−0.879288			−0.439644	−	0.898172i	$-0.644895\pi$
$907$	−26.4810			−0.879288			−0.439644	+	0.898172i	$0.644895\pi$
$908$	12.0771	−	29.6211i	0.400794	−	0.983012i
$909$	2.94125			0.0975551
$910$	1.06306	+	1.58146i	0.0352401	+	0.0524248i
$911$	−1.08817			−0.0360527			−0.0180263	−	0.999838i	$-0.505738\pi$
$911$	−1.08817			−0.0360527			−0.0180263	+	0.999838i	$0.505738\pi$
$912$	−5.50546	+	5.62918i	−0.182304	+	0.186401i
$913$	17.9451			0.593897
$914$	13.3558	+	19.8687i	0.441772	+	0.657199i
$915$		−	9.36387i		−	0.309560i
$916$	−15.4960	−	6.31802i	−0.512002	−	0.208753i
$917$		−	11.1740i		−	0.368999i
$918$	1.33783	−	0.899295i	0.0441550	−	0.0296811i
$919$	44.6411			1.47257			0.736287	−	0.676669i	$-0.236577\pi$
$919$	44.6411			1.47257			0.736287	+	0.676669i	$0.236577\pi$
$920$	−8.05473	+	10.9143i	−0.265557	+	0.359833i
$921$	14.4304			0.475498
$922$	15.8376	−	10.6461i	0.521583	−	0.350610i
$923$			12.6077i			0.414989i
$924$	2.49079	+	1.01554i	0.0819409	+	0.0334089i
$925$			8.93030i			0.293627i
$926$	31.5390	+	46.9189i	1.03644	+	1.54185i
$927$	−10.4335			−0.342680
$928$	16.1566	+	2.98111i	0.530366	+	0.0978599i
$929$	−45.9592			−1.50787			−0.753936	−	0.656948i	$-0.771847\pi$
$929$	−45.9592			−1.50787			−0.753936	+	0.656948i	$0.771847\pi$
$930$	8.18514	+	12.1766i	0.268401	+	0.399286i
$931$	−13.1462			−0.430849
$932$	0.409867	−	1.00526i	0.0134256	−	0.0329285i
$933$	4.98628			0.163243
$934$	11.1477	−	7.49355i	0.364765	−	0.245197i
$935$	2.70322			0.0884049
$936$	1.36593	+	6.57994i	0.0446467	+	0.215072i
$937$		−	31.6991i		−	1.03556i	−0.855513	−	0.517782i	$-0.826758\pi$
$937$		−	31.6991i		−	1.03556i	0.855513	−	0.517782i	$-0.173242\pi$
$938$	−9.18074	+	6.17133i	−0.299762	+	0.201501i
$939$	−17.5039			−0.571218
$940$	−0.553605	+	1.35781i	−0.0180566	+	0.0442868i
$941$		−	29.9327i		−	0.975778i	−0.872906	−	0.487889i	$-0.837767\pi$
$941$		−	29.9327i		−	0.975778i	0.872906	−	0.487889i	$-0.162233\pi$
$942$	−13.0312	+	8.75963i	−0.424580	+	0.285404i
$943$	−1.07473	+	0.962447i	−0.0349980	+	0.0313416i
$944$	−14.0638	+	14.3798i	−0.457738	+	0.468024i
$945$	−0.567108			−0.0184480
$946$	11.0423	−	7.42269i	0.359017	−	0.241332i
$947$			14.3482i			0.466253i	0.972446	+	0.233127i	$0.0748956\pi$
$947$			14.3482i			0.466253i	−0.972446	+	0.233127i	$0.925104\pi$
$948$	6.87628	+	2.80360i	0.223331	+	0.0910566i
$949$	27.9162			0.906200
$950$	2.31037	−	1.55304i	0.0749582	−	0.0503872i
$951$			21.7513i			0.705335i
$952$	−1.79018	+	0.371623i	−0.0580201	+	0.0120444i
$953$			43.0276i			1.39380i	0.717168	+	0.696901i	$0.245438\pi$
$953$			43.0276i			1.39380i	−0.717168	+	0.696901i	$0.754562\pi$
$954$	8.26855	+	12.3007i	0.267704	+	0.398249i
$955$		−	23.8995i		−	0.773370i
$956$	−10.2531	−	4.18038i	−0.331608	−	0.135203i
$957$			6.88777i			0.222650i
$958$	−28.6292	+	19.2446i	−0.924966	+	0.621766i
$959$			4.78281i			0.154445i
$960$	−7.33899	+	3.18421i	−0.236865	+	0.102770i
$961$	−76.6327			−2.47202
$962$	−16.7401	−	24.9034i	−0.539723	−	0.802916i
$963$	−18.2868			−0.589284
$964$	30.3972	+	12.3935i	0.979028	+	0.399169i
$965$			13.0675i			0.420657i
$966$	3.72804	+	0.946497i	0.119948	+	0.0304531i
$967$		−	33.7541i		−	1.08546i	−0.839908	−	0.542729i	$-0.817391\pi$
$967$		−	33.7541i		−	1.08546i	0.839908	−	0.542729i	$-0.182609\pi$
$968$	−3.09047	−	14.8874i	−0.0993314	−	0.478499i
$969$	2.24376			0.0720799
$970$	−16.9961	+	11.4248i	−0.545711	+	0.366829i
$971$	19.6385			0.630231			0.315115	−	0.949053i	$-0.397957\pi$
$971$	19.6385			0.630231			0.315115	+	0.949053i	$0.397957\pi$
$972$	−1.85198	−	0.755090i	−0.0594024	−	0.0242195i
$973$		−	2.47343i		−	0.0792944i
$974$	−20.4628	−	30.4413i	−0.655670	−	0.975404i
$975$		−	2.37596i		−	0.0760915i
$976$	−26.1891	+	26.7777i	−0.838294	+	0.857132i
$977$			10.1901i			0.326009i	0.986625	+	0.163005i	$0.0521185\pi$
$977$			10.1901i			0.326009i	−0.986625	+	0.163005i	$0.947881\pi$
$978$	12.6360	−	8.49399i	0.404056	−	0.271608i
$979$			33.6812i			1.07646i
$980$	−12.3683	−	5.04279i	−0.395090	−	0.161086i
$981$		−	7.20450i		−	0.230022i
$982$	−8.49540	−	12.6381i	−0.271099	−	0.403299i
$983$	9.75225			0.311049			0.155524	−	0.987832i	$-0.450293\pi$
$983$	9.75225			0.311049			0.155524	+	0.987832i	$0.450293\pi$
$984$	−0.833090	+	0.172941i	−0.0265579	+	0.00551315i
$985$			16.2222i			0.516884i
$986$	−2.61184	−	3.88549i	−0.0831780	−	0.123739i
$987$	0.415783			0.0132345
$988$	−3.53155	+	8.66171i	−0.112354	+	0.275566i
$989$	14.1731	−	12.6923i	0.450677	−	0.403593i
$990$	−1.87106	−	2.78347i	−0.0594662	−	0.0884646i
$991$			6.04837i			0.192133i	0.995375	+	0.0960665i	$0.0306261\pi$
$991$			6.04837i			0.192133i	−0.995375	+	0.0960665i	$0.969374\pi$
$992$	10.6489	−	57.7135i	0.338104	−	1.83240i
$993$	3.00106			0.0952359
$994$	2.37421	+	3.53197i	0.0753052	+	0.112027i
$995$			11.9953i			0.380276i
$996$	14.0136	+	5.71362i	0.444037	+	0.181043i
$997$	−13.2385			−0.419269			−0.209634	−	0.977780i	$-0.567227\pi$
$997$	−13.2385			−0.419269			−0.209634	+	0.977780i	$0.567227\pi$
$998$	2.92214	+	4.34710i	0.0924987	+	0.137605i
$999$	8.93030			0.282542

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.p.b.91.12	yes	48
4.3	odd	2		1380.2.p.a.91.11	✓	48
23.22	odd	2		1380.2.p.a.91.12	yes	48
92.91	even	2	inner	1380.2.p.b.91.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.p.a.91.11	✓	48	4.3	odd	2
1380.2.p.a.91.12	yes	48	23.22	odd	2
1380.2.p.b.91.11	yes	48	92.91	even	2	inner
1380.2.p.b.91.12	yes	48	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:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.p (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17369 + 0.788958i) q^{2} -1.00000i q^{3} +(0.755090 - 1.85198i) q^{4} +1.00000i q^{5} +(0.788958 + 1.17369i) q^{6} +0.567108 q^{7} +(0.574895 + 2.76939i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.17369 + 0.788958i) q^{2} -1.00000i q^{3} +(0.755090 - 1.85198i) q^{4} +1.00000i q^{5} +(0.788958 + 1.17369i) q^{6} +0.567108 q^{7} +(0.574895 + 2.76939i) q^{8} -1.00000 q^{9} +(-0.788958 - 1.17369i) q^{10} -2.37156 q^{11} +(-1.85198 - 0.755090i) q^{12} -2.37596 q^{13} +(-0.665608 + 0.447424i) q^{14} +1.00000 q^{15} +(-2.85968 - 2.79683i) q^{16} +1.13985i q^{17} +(1.17369 - 0.788958i) q^{18} +1.96847 q^{19} +(1.85198 + 0.755090i) q^{20} -0.567108i q^{21} +(2.78347 - 1.87106i) q^{22} +(3.57265 - 3.19940i) q^{23} +(2.76939 - 0.574895i) q^{24} -1.00000 q^{25} +(2.78863 - 1.87453i) q^{26} +1.00000i q^{27} +(0.428218 - 1.05027i) q^{28} +2.90432 q^{29} +(-1.17369 + 0.788958i) q^{30} -10.3746i q^{31} +(5.56295 + 1.02644i) q^{32} +2.37156i q^{33} +(-0.899295 - 1.33783i) q^{34} +0.567108i q^{35} +(-0.755090 + 1.85198i) q^{36} -8.93030i q^{37} +(-2.31037 + 1.55304i) q^{38} +2.37596i q^{39} +(-2.76939 + 0.574895i) q^{40} -0.300821 q^{41} +(0.447424 + 0.665608i) q^{42} +3.96710 q^{43} +(-1.79074 + 4.39209i) q^{44} -1.00000i q^{45} +(-1.66899 + 6.57377i) q^{46} +0.733164i q^{47} +(-2.79683 + 2.85968i) q^{48} -6.67839 q^{49} +(1.17369 - 0.788958i) q^{50} +1.13985 q^{51} +(-1.79406 + 4.40023i) q^{52} +10.4803i q^{53} +(-0.788958 - 1.17369i) q^{54} -2.37156i q^{55} +(0.326028 + 1.57054i) q^{56} -1.96847i q^{57} +(-3.40877 + 2.29139i) q^{58} -5.02848i q^{59} +(0.755090 - 1.85198i) q^{60} -9.36387i q^{61} +(8.18514 + 12.1766i) q^{62} -0.567108 q^{63} +(-7.33899 + 3.18421i) q^{64} -2.37596i q^{65} +(-1.87106 - 2.78347i) q^{66} +13.7930 q^{67} +(2.11098 + 0.860691i) q^{68} +(-3.19940 - 3.57265i) q^{69} +(-0.447424 - 0.665608i) q^{70} -5.30639i q^{71} +(-0.574895 - 2.76939i) q^{72} -11.7495 q^{73} +(7.04563 + 10.4814i) q^{74} +1.00000i q^{75} +(1.48637 - 3.64556i) q^{76} -1.34493 q^{77} +(-1.87453 - 2.78863i) q^{78} -3.71293 q^{79} +(2.79683 - 2.85968i) q^{80} +1.00000 q^{81} +(0.353070 - 0.237335i) q^{82} -7.56680 q^{83} +(-1.05027 - 0.428218i) q^{84} -1.13985 q^{85} +(-4.65614 + 3.12988i) q^{86} -2.90432i q^{87} +(-1.36340 - 6.56776i) q^{88} -14.2021i q^{89} +(0.788958 + 1.17369i) q^{90} -1.34742 q^{91} +(-3.22755 - 9.03232i) q^{92} -10.3746 q^{93} +(-0.578436 - 0.860507i) q^{94} +1.96847i q^{95} +(1.02644 - 5.56295i) q^{96} -14.4809i q^{97} +(7.83835 - 5.26897i) q^{98} +2.37156 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9}+O(q^{10}) \) 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9	\( 48 q - 4 q^{2} - 2 q^{4} - 2 q^{6} - 4 q^{8} - 48 q^{9} + 2 q^{10} - 20 q^{14} + 48 q^{15} - 6 q^{16} + 4 q^{18} - 16 q^{19} - 28 q^{22} - 4 q^{23} + 2 q^{24} - 48 q^{25} - 20 q^{26} + 32 q^{29} - 4 q^{30} + 16 q^{32} + 28 q^{34} + 2 q^{36} - 2 q^{40} - 8 q^{41} + 26 q^{46} + 16 q^{48} + 40 q^{49} + 4 q^{50} - 16 q^{51} - 16 q^{52} + 2 q^{54} - 40 q^{56} - 8 q^{58} - 2 q^{60} + 24 q^{62} - 26 q^{64} + 48 q^{67} + 44 q^{68} - 8 q^{69} + 4 q^{72} - 20 q^{74} + 64 q^{76} + 32 q^{77} + 64 q^{79} - 16 q^{80} + 48 q^{81} - 20 q^{82} + 16 q^{85} + 40 q^{86} - 2 q^{90} - 28 q^{92} - 32 q^{94} - 2 q^{96} + 24 q^{98}+O(q^{100}) \) 48 * q - 4 * q^2 - 2 * q^4 - 2 * q^6 - 4 * q^8 - 48 * q^9 + 2 * q^10 - 20 * q^14 + 48 * q^15 - 6 * q^16 + 4 * q^18 - 16 * q^19 - 28 * q^22 - 4 * q^23 + 2 * q^24 - 48 * q^25 - 20 * q^26 + 32 * q^29 - 4 * q^30 + 16 * q^32 + 28 * q^34 + 2 * q^36 - 2 * q^40 - 8 * q^41 + 26 * q^46 + 16 * q^48 + 40 * q^49 + 4 * q^50 - 16 * q^51 - 16 * q^52 + 2 * q^54 - 40 * q^56 - 8 * q^58 - 2 * q^60 + 24 * q^62 - 26 * q^64 + 48 * q^67 + 44 * q^68 - 8 * q^69 + 4 * q^72 - 20 * q^74 + 64 * q^76 + 32 * q^77 + 64 * q^79 - 16 * q^80 + 48 * q^81 - 20 * q^82 + 16 * q^85 + 40 * q^86 - 2 * q^90 - 28 * q^92 - 32 * q^94 - 2 * q^96 + 24 * q^98

Introduction

L-functions

Modular forms

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Database

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