LMFDB - Embedded newform 525.2.r.g.424.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(424,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("525.424");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			424.3
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	525.424
Dual form			525.2.r.g.499.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.41421 q^{6} +(2.09077 + 1.62132i) q^{7} +2.82843i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.41421 q^{6} +(2.09077 + 1.62132i) q^{7} +2.82843i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.70711 + 2.95680i) q^{11} +1.58579i q^{13} +(3.70711 + 0.507306i) q^{14} +(2.00000 + 3.46410i) q^{16} +(5.40629 + 3.12132i) q^{17} +(1.22474 + 0.707107i) q^{18} +(-3.32843 - 5.76500i) q^{19} +(-1.00000 - 2.44949i) q^{21} +4.82843i q^{22} +(5.40629 - 3.12132i) q^{23} +(1.41421 - 2.44949i) q^{24} +(1.12132 + 1.94218i) q^{26} -1.00000i q^{27} +0.242641 q^{29} +(0.0857864 - 0.148586i) q^{31} +(2.95680 - 1.70711i) q^{33} +8.82843 q^{34} +(-4.83743 + 2.79289i) q^{37} +(-8.15295 - 4.70711i) q^{38} +(0.792893 - 1.37333i) q^{39} +2.24264 q^{41} +(-2.95680 - 2.29289i) q^{42} +10.4142i q^{43} +(4.41421 - 7.64564i) q^{46} +(8.06591 - 4.65685i) q^{47} -4.00000i q^{48} +(1.74264 + 6.77962i) q^{49} +(-3.12132 - 5.40629i) q^{51} +(1.01461 + 0.585786i) q^{53} +(-0.707107 - 1.22474i) q^{54} +(-4.58579 + 5.91359i) q^{56} +6.65685i q^{57} +(0.297173 - 0.171573i) q^{58} +(0.707107 - 1.22474i) q^{59} +(-6.24264 - 10.8126i) q^{61} -0.242641i q^{62} +(-0.358719 + 2.62132i) q^{63} -8.00000 q^{64} +(2.41421 - 4.18154i) q^{66} +(-10.1567 - 5.86396i) q^{67} -6.24264 q^{69} -3.41421 q^{71} +(-2.44949 + 1.41421i) q^{72} +(1.79360 + 1.03553i) q^{73} +(-3.94975 + 6.84116i) q^{74} +(-8.36308 + 3.41421i) q^{77} -2.24264i q^{78} +(-2.32843 - 4.03295i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.74666 - 1.58579i) q^{82} -5.41421i q^{83} +(7.36396 + 12.7548i) q^{86} +(-0.210133 - 0.121320i) q^{87} +(-8.36308 - 4.82843i) q^{88} +(-1.87868 - 3.25397i) q^{89} +(-2.57107 + 3.31552i) q^{91} +(-0.148586 + 0.0857864i) q^{93} +(6.58579 - 11.4069i) q^{94} -10.8284i q^{97} +(6.92820 + 7.07107i) q^{98} -3.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^9	$ 8 q + 4 q^{9} - 8 q^{11} + 24 q^{14} + 16 q^{16} - 4 q^{19} - 8 q^{21} - 8 q^{26} - 32 q^{29} + 12 q^{31} + 48 q^{34} + 12 q^{39} - 16 q^{41} + 24 q^{46} - 20 q^{49} - 8 q^{51} - 48 q^{56} - 16 q^{61} - 64 q^{64} + 8 q^{66} - 16 q^{69} - 16 q^{71} + 8 q^{74} + 4 q^{79} - 4 q^{81} + 8 q^{86} - 32 q^{89} + 36 q^{91} + 64 q^{94} - 16 q^{99}+O(q^{100}) $ 8 * q + 4 * q^9 - 8 * q^11 + 24 * q^14 + 16 * q^16 - 4 * q^19 - 8 * q^21 - 8 * q^26 - 32 * q^29 + 12 * q^31 + 48 * q^34 + 12 * q^39 - 16 * q^41 + 24 * q^46 - 20 * q^49 - 8 * q^51 - 48 * q^56 - 16 * q^61 - 64 * q^64 + 8 * q^66 - 16 * q^69 - 16 * q^71 + 8 * q^74 + 4 * q^79 - 4 * q^81 + 8 * q^86 - 32 * q^89 + 36 * q^91 + 64 * q^94 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.22474	−	0.707107i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$2$	1.22474	−	0.707107i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		0			0
$5$		0			0
$5$		0			0
$6$	−1.41421			−0.577350
$7$	2.09077	+	1.62132i	0.790237	+	0.612801i
$7$	2.09077	+	1.62132i	0.790237	+	0.612801i
$8$			2.82843i			1.00000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−1.70711	+	2.95680i	−0.514712	+	0.891507i	0.485142	+	0.874435i	$0.338768\pi$
$11$	−1.70711	+	2.95680i	−0.514712	+	0.891507i	−0.999854	+	0.0170722i	$0.994565\pi$
$12$		0			0
$13$			1.58579i			0.439818i	0.975520	+	0.219909i	$0.0705760\pi$
$13$			1.58579i			0.439818i	−0.975520	+	0.219909i	$0.929424\pi$
$14$	3.70711	+	0.507306i	0.990766	+	0.135583i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	5.40629	+	3.12132i	1.31122	+	0.757031i	0.982298	−	0.187327i	$-0.0599823\pi$
$17$	5.40629	+	3.12132i	1.31122	+	0.757031i	0.328919	+	0.944358i	$0.393316\pi$
$18$	1.22474	+	0.707107i	0.288675	+	0.166667i
$19$	−3.32843	−	5.76500i	−0.763594	−	1.32258i	−0.940987	−	0.338443i	$-0.890100\pi$
$19$	−3.32843	−	5.76500i	−0.763594	−	1.32258i	0.177393	−	0.984140i	$-0.443233\pi$
$20$		0			0
$21$	−1.00000	−	2.44949i	−0.218218	−	0.534522i
$22$			4.82843i			1.02942i
$23$	5.40629	−	3.12132i	1.12729	−	0.650840i	0.184037	−	0.982919i	$-0.441083\pi$
$23$	5.40629	−	3.12132i	1.12729	−	0.650840i	0.943252	+	0.332079i	$0.107750\pi$
$24$	1.41421	−	2.44949i	0.288675	−	0.500000i
$25$		0			0
$26$	1.12132	+	1.94218i	0.219909	+	0.380894i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	0.242641			0.0450572			0.0225286	−	0.999746i	$-0.492828\pi$
$29$	0.242641			0.0450572			0.0225286	+	0.999746i	$0.492828\pi$
$30$		0			0
$31$	0.0857864	−	0.148586i	0.0154077	−	0.0266869i	−0.858219	−	0.513284i	$-0.828429\pi$
$31$	0.0857864	−	0.148586i	0.0154077	−	0.0266869i	0.873626	+	0.486597i	$0.161762\pi$
$32$		0			0
$33$	2.95680	−	1.70711i	0.514712	−	0.297169i
$34$	8.82843			1.51406
$35$		0			0
$36$		0			0
$37$	−4.83743	+	2.79289i	−0.795269	+	0.459149i	−0.841814	−	0.539767i	$-0.818512\pi$
$37$	−4.83743	+	2.79289i	−0.795269	+	0.459149i	0.0465451	+	0.998916i	$0.485179\pi$
$38$	−8.15295	−	4.70711i	−1.32258	−	0.763594i
$39$	0.792893	−	1.37333i	0.126965	−	0.219909i
$40$		0			0
$41$	2.24264			0.350242			0.175121	−	0.984547i	$-0.443968\pi$
$41$	2.24264			0.350242			0.175121	+	0.984547i	$0.443968\pi$
$42$	−2.95680	−	2.29289i	−0.456243	−	0.353801i
$43$			10.4142i			1.58815i	0.607818	+	0.794076i	$0.292045\pi$
$43$			10.4142i			1.58815i	−0.607818	+	0.794076i	$0.707955\pi$
$44$		0			0
$45$		0			0
$46$	4.41421	−	7.64564i	0.650840	−	1.12729i
$47$	8.06591	−	4.65685i	1.17653	−	0.679272i	0.221324	−	0.975200i	$-0.428962\pi$
$47$	8.06591	−	4.65685i	1.17653	−	0.679272i	0.955210	+	0.295928i	$0.0956290\pi$
$48$		−	4.00000i		−	0.577350i
$49$	1.74264	+	6.77962i	0.248949	+	0.968517i
$50$		0			0
$51$	−3.12132	−	5.40629i	−0.437072	−	0.757031i
$52$		0			0
$53$	1.01461	+	0.585786i	0.139368	+	0.0804640i	0.568063	−	0.822985i	$-0.307693\pi$
$53$	1.01461	+	0.585786i	0.139368	+	0.0804640i	−0.428695	+	0.903449i	$0.641026\pi$
$54$	−0.707107	−	1.22474i	−0.0962250	−	0.166667i
$55$		0			0
$56$	−4.58579	+	5.91359i	−0.612801	+	0.790237i
$57$			6.65685i			0.881722i
$58$	0.297173	−	0.171573i	0.0390207	−	0.0225286i
$59$	0.707107	−	1.22474i	0.0920575	−	0.159448i	−0.816319	−	0.577601i	$-0.803989\pi$
$59$	0.707107	−	1.22474i	0.0920575	−	0.159448i	0.908377	+	0.418153i	$0.137322\pi$
$60$		0			0
$61$	−6.24264	−	10.8126i	−0.799288	−	1.38441i	−0.920080	−	0.391730i	$-0.871877\pi$
$61$	−6.24264	−	10.8126i	−0.799288	−	1.38441i	0.120792	−	0.992678i	$-0.461457\pi$
$62$		−	0.242641i		−	0.0308154i
$63$	−0.358719	+	2.62132i	−0.0451944	+	0.330255i
$64$	−8.00000			−1.00000
$65$		0			0
$66$	2.41421	−	4.18154i	0.297169	−	0.514712i
$67$	−10.1567	−	5.86396i	−1.24084	−	0.716397i	−0.271571	−	0.962418i	$-0.587543\pi$
$67$	−10.1567	−	5.86396i	−1.24084	−	0.716397i	−0.969264	+	0.246021i	$0.920877\pi$
$68$		0			0
$69$	−6.24264			−0.751526
$70$		0			0
$71$	−3.41421			−0.405193			−0.202596	−	0.979262i	$-0.564938\pi$
$71$	−3.41421			−0.405193			−0.202596	+	0.979262i	$0.564938\pi$
$72$	−2.44949	+	1.41421i	−0.288675	+	0.166667i
$73$	1.79360	+	1.03553i	0.209925	+	0.121200i	0.601276	−	0.799041i	$-0.294659\pi$
$73$	1.79360	+	1.03553i	0.209925	+	0.121200i	−0.391352	+	0.920241i	$0.627992\pi$
$74$	−3.94975	+	6.84116i	−0.459149	+	0.795269i
$75$		0			0
$76$		0			0
$77$	−8.36308	+	3.41421i	−0.953062	+	0.389086i
$78$		−	2.24264i		−	0.253929i
$79$	−2.32843	−	4.03295i	−0.261969	−	0.453743i	0.704796	−	0.709410i	$-0.251038\pi$
$79$	−2.32843	−	4.03295i	−0.261969	−	0.453743i	−0.966765	+	0.255667i	$0.917705\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.74666	−	1.58579i	0.303318	−	0.175121i
$83$		−	5.41421i		−	0.594287i	−0.954833	−	0.297144i	$-0.903966\pi$
$83$		−	5.41421i		−	0.594287i	0.954833	−	0.297144i	$-0.0960340\pi$
$84$		0			0
$85$		0			0
$86$	7.36396	+	12.7548i	0.794076	+	1.37538i
$87$	−0.210133	−	0.121320i	−0.0225286	−	0.0130069i
$88$	−8.36308	−	4.82843i	−0.891507	−	0.514712i
$89$	−1.87868	−	3.25397i	−0.199140	−	0.344920i	0.749110	−	0.662446i	$-0.230481\pi$
$89$	−1.87868	−	3.25397i	−0.199140	−	0.344920i	−0.948250	+	0.317526i	$0.897148\pi$
$90$		0			0
$91$	−2.57107	+	3.31552i	−0.269521	+	0.347560i
$92$		0			0
$93$	−0.148586	+	0.0857864i	−0.0154077	+	0.00889564i
$94$	6.58579	−	11.4069i	0.679272	−	1.17653i
$95$		0			0
$96$		0			0
$97$		−	10.8284i		−	1.09946i	−0.835342	−	0.549730i	$-0.814731\pi$
$97$		−	10.8284i		−	1.09946i	0.835342	−	0.549730i	$-0.185269\pi$
$98$	6.92820	+	7.07107i	0.699854	+	0.714286i
$99$	−3.41421			−0.343141
$100$		0			0
$101$	3.12132	−	5.40629i	0.310583	−	0.537946i	−0.667906	−	0.744246i	$-0.732809\pi$
$101$	3.12132	−	5.40629i	0.310583	−	0.537946i	0.978489	+	0.206300i	$0.0661424\pi$
$102$	−7.64564	−	4.41421i	−0.757031	−	0.437072i
$103$	1.07616	−	0.621320i	0.106037	−	0.0612205i	−0.446044	−	0.895011i	$-0.647167\pi$
$103$	1.07616	−	0.621320i	0.106037	−	0.0612205i	0.552081	+	0.833791i	$0.313834\pi$
$104$	−4.48528			−0.439818
$105$		0			0
$106$	1.65685			0.160928
$107$	13.3491	−	7.70711i	1.29051	−	0.745074i	0.311762	−	0.950160i	$-0.399081\pi$
$107$	13.3491	−	7.70711i	1.29051	−	0.745074i	0.978744	+	0.205086i	$0.0657474\pi$
$108$		0			0
$109$	−6.74264	+	11.6786i	−0.645828	+	1.11861i	0.338282	+	0.941045i	$0.390154\pi$
$109$	−6.74264	+	11.6786i	−0.645828	+	1.11861i	−0.984110	+	0.177562i	$0.943179\pi$
$110$		0			0
$111$	5.58579			0.530179
$112$	−1.43488	+	10.4853i	−0.135583	+	0.990766i
$113$			4.34315i			0.408569i	0.978912	+	0.204284i	$0.0654867\pi$
$113$			4.34315i			0.408569i	−0.978912	+	0.204284i	$0.934513\pi$
$114$	4.70711	+	8.15295i	0.440861	+	0.763594i
$115$		0			0
$116$		0			0
$117$	−1.37333	+	0.792893i	−0.126965	+	0.0733030i
$118$		−	2.00000i		−	0.184115i
$119$	6.24264	+	15.2913i	0.572262	+	1.40175i
$120$		0			0
$121$	−0.328427	−	0.568852i	−0.0298570	−	0.0517139i
$122$	−15.2913	−	8.82843i	−1.38441	−	0.799288i
$123$	−1.94218	−	1.12132i	−0.175121	−	0.101106i
$124$		0			0
$125$		0			0
$126$	1.41421	+	3.46410i	0.125988	+	0.308607i
$127$		−	18.0711i		−	1.60355i	−0.597627	−	0.801774i	$-0.703890\pi$
$127$		−	18.0711i		−	1.60355i	0.597627	−	0.801774i	$-0.296110\pi$
$128$	−9.79796	+	5.65685i	−0.866025	+	0.500000i
$129$	5.20711	−	9.01897i	0.458460	−	0.794076i
$130$		0			0
$131$	5.24264	+	9.08052i	0.458052	+	0.793369i	0.998858	−	0.0477784i	$-0.0152141\pi$
$131$	5.24264	+	9.08052i	0.458052	+	0.793369i	−0.540806	+	0.841147i	$0.681881\pi$
$132$		0			0
$133$	2.38794	−	17.4497i	0.207061	−	1.51308i
$134$	−16.5858			−1.43279
$135$		0			0
$136$	−8.82843	+	15.2913i	−0.757031	+	1.31122i
$137$	2.53653	+	1.46447i	0.216710	+	0.125118i	0.604426	−	0.796661i	$-0.293402\pi$
$137$	2.53653	+	1.46447i	0.216710	+	0.125118i	−0.387716	+	0.921779i	$0.626736\pi$
$138$	−7.64564	+	4.41421i	−0.650840	+	0.375763i
$139$	−11.4853			−0.974169			−0.487084	−	0.873355i	$-0.661940\pi$
$139$	−11.4853			−0.974169			−0.487084	+	0.873355i	$0.661940\pi$
$140$		0			0
$141$	−9.31371			−0.784356
$142$	−4.18154	+	2.41421i	−0.350907	+	0.202596i
$143$	−4.68885	−	2.70711i	−0.392101	−	0.226380i
$144$	−2.00000	+	3.46410i	−0.166667	+	0.288675i
$145$		0			0
$146$	2.92893			0.242400
$147$	1.88064	−	6.74264i	0.155112	−	0.556124i
$148$		0			0
$149$	8.82843	+	15.2913i	0.723253	+	1.25271i	0.959689	+	0.281064i	$0.0906873\pi$
$149$	8.82843	+	15.2913i	0.723253	+	1.25271i	−0.236436	+	0.971647i	$0.575979\pi$
$150$		0			0
$151$	3.24264	−	5.61642i	0.263882	−	0.457058i	−0.703388	−	0.710806i	$-0.748330\pi$
$151$	3.24264	−	5.61642i	0.263882	−	0.457058i	0.967270	+	0.253749i	$0.0816636\pi$
$152$	16.3059	−	9.41421i	1.32258	−	0.763594i
$153$			6.24264i			0.504688i
$154$	−7.82843	+	10.0951i	−0.630833	+	0.813489i
$155$		0			0
$156$		0			0
$157$	13.9795	+	8.07107i	1.11569	+	0.644141i	0.940296	−	0.340358i	$-0.110548\pi$
$157$	13.9795	+	8.07107i	1.11569	+	0.644141i	0.175390	+	0.984499i	$0.443882\pi$
$158$	−5.70346	−	3.29289i	−0.453743	−	0.261969i
$159$	−0.585786	−	1.01461i	−0.0464559	−	0.0804640i
$160$		0			0
$161$	16.3640	+	2.23936i	1.28966	+	0.176486i
$162$			1.41421i			0.111111i
$163$	16.7262	−	9.65685i	1.31009	−	0.756383i	0.327983	−	0.944684i	$-0.393631\pi$
$163$	16.7262	−	9.65685i	1.31009	−	0.756383i	0.982111	+	0.188301i	$0.0602979\pi$
$164$		0			0
$165$		0			0
$166$	−3.82843	−	6.63103i	−0.297144	−	0.514668i
$167$			11.7574i			0.909812i	0.890540	+	0.454906i	$0.150327\pi$
$167$			11.7574i			0.909812i	−0.890540	+	0.454906i	$0.849673\pi$
$168$	6.92820	−	2.82843i	0.534522	−	0.218218i
$169$	10.4853			0.806560
$170$		0			0
$171$	3.32843	−	5.76500i	0.254531	−	0.440861i
$172$		0			0
$173$	2.44949	−	1.41421i	0.186231	−	0.107521i	−0.403986	−	0.914765i	$-0.632375\pi$
$173$	2.44949	−	1.41421i	0.186231	−	0.107521i	0.590217	+	0.807245i	$0.299042\pi$
$174$	−0.343146			−0.0260138
$175$		0			0
$176$	−13.6569			−1.02942
$177$	−1.22474	+	0.707107i	−0.0920575	+	0.0531494i
$178$	−4.60181	−	2.65685i	−0.344920	−	0.199140i
$179$	9.82843	−	17.0233i	0.734611	−	1.27238i	−0.220283	−	0.975436i	$-0.570698\pi$
$179$	9.82843	−	17.0233i	0.734611	−	1.27238i	0.954894	−	0.296948i	$-0.0959687\pi$
$180$		0			0
$181$	0.656854			0.0488236			0.0244118	−	0.999702i	$-0.492229\pi$
$181$	0.656854			0.0488236			0.0244118	+	0.999702i	$0.492229\pi$
$182$	−0.804479	+	5.87868i	−0.0596319	+	0.435757i
$183$			12.4853i			0.922939i
$184$	8.82843	+	15.2913i	0.650840	+	1.12729i
$185$		0			0
$186$	−0.121320	+	0.210133i	−0.00889564	+	0.0154077i
$187$	−18.4582	+	10.6569i	−1.34980	+	0.779306i
$188$		0			0
$189$	1.62132	−	2.09077i	0.117934	−	0.152081i
$190$		0			0
$191$	−9.48528	−	16.4290i	−0.686331	−	1.18876i	−0.973017	−	0.230735i	$-0.925887\pi$
$191$	−9.48528	−	16.4290i	−0.686331	−	1.18876i	0.286686	−	0.958025i	$-0.407446\pi$
$192$	6.92820	+	4.00000i	0.500000	+	0.288675i
$193$	−5.85204	−	3.37868i	−0.421239	−	0.243203i	0.274368	−	0.961625i	$-0.411531\pi$
$193$	−5.85204	−	3.37868i	−0.421239	−	0.243203i	−0.695607	+	0.718422i	$0.744865\pi$
$194$	−7.65685	−	13.2621i	−0.549730	−	0.952160i
$195$		0			0
$196$		0			0
$197$			5.55635i			0.395873i	0.980215	+	0.197937i	$0.0634241\pi$
$197$			5.55635i			0.395873i	−0.980215	+	0.197937i	$0.936576\pi$
$198$	−4.18154	+	2.41421i	−0.297169	+	0.171571i
$199$	2.75736	−	4.77589i	0.195464	−	0.338554i	−0.751589	−	0.659632i	$-0.770712\pi$
$199$	2.75736	−	4.77589i	0.195464	−	0.338554i	0.947053	+	0.321079i	$0.104045\pi$
$200$		0			0
$201$	5.86396	+	10.1567i	0.413612	+	0.716397i
$202$		−	8.82843i		−	0.621166i
$203$	0.507306	+	0.393398i	0.0356059	+	0.0276111i
$204$		0			0
$205$		0			0
$206$	0.878680	−	1.52192i	0.0612205	−	0.106037i
$207$	5.40629	+	3.12132i	0.375763	+	0.216947i
$208$	−5.49333	+	3.17157i	−0.380894	+	0.219909i
$209$	22.7279			1.57212
$210$		0			0
$211$	0.142136			0.00978502			0.00489251	−	0.999988i	$-0.498443\pi$
$211$	0.142136			0.00978502			0.00489251	+	0.999988i	$0.498443\pi$
$212$		0			0
$213$	2.95680	+	1.70711i	0.202596	+	0.116969i
$214$	10.8995	−	18.8785i	0.745074	−	1.29051i
$215$		0			0
$216$	2.82843			0.192450
$217$	0.420266	−	0.171573i	0.0285295	−	0.0116471i
$218$			19.0711i			1.29166i
$219$	−1.03553	−	1.79360i	−0.0699749	−	0.121200i
$220$		0			0
$221$	−4.94975	+	8.57321i	−0.332956	+	0.576697i
$222$	6.84116	−	3.94975i	0.459149	−	0.265090i
$223$		−	17.1716i		−	1.14989i	−0.818191	−	0.574947i	$-0.805023\pi$
$223$		−	17.1716i		−	1.14989i	0.818191	−	0.574947i	$-0.194977\pi$
$224$		0			0
$225$		0			0
$226$	3.07107	+	5.31925i	0.204284	+	0.353831i
$227$	−19.9801	−	11.5355i	−1.32613	−	0.765640i	−0.341429	−	0.939907i	$-0.610911\pi$
$227$	−19.9801	−	11.5355i	−1.32613	−	0.765640i	−0.984698	+	0.174267i	$0.944244\pi$
$228$		0			0
$229$	−7.15685	−	12.3960i	−0.472938	−	0.819153i	0.526582	−	0.850124i	$-0.323473\pi$
$229$	−7.15685	−	12.3960i	−0.472938	−	0.819153i	−0.999520	+	0.0309713i	$0.990140\pi$
$230$		0			0
$231$	8.94975	+	1.22474i	0.588850	+	0.0805823i
$232$			0.686292i			0.0450572i
$233$	19.4728	−	11.2426i	1.27571	−	0.736530i	0.299651	−	0.954049i	$-0.403130\pi$
$233$	19.4728	−	11.2426i	1.27571	−	0.736530i	0.976056	+	0.217519i	$0.0697964\pi$
$234$	−1.12132	+	1.94218i	−0.0733030	+	0.126965i
$235$		0			0
$236$		0			0
$237$			4.65685i			0.302495i
$238$	18.4582	+	14.3137i	1.19647	+	0.927820i
$239$	−17.3137			−1.11993			−0.559965	−	0.828516i	$-0.689186\pi$
$239$	−17.3137			−1.11993			−0.559965	+	0.828516i	$0.689186\pi$
$240$		0			0
$241$	5.17157	−	8.95743i	0.333130	−	0.576999i	−0.649994	−	0.759940i	$-0.725228\pi$
$241$	5.17157	−	8.95743i	0.333130	−	0.576999i	0.983124	+	0.182941i	$0.0585618\pi$
$242$	−0.804479	−	0.464466i	−0.0517139	−	0.0298570i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		0			0
$245$		0			0
$246$	−3.17157			−0.202212
$247$	9.14207	−	5.27817i	0.581696	−	0.335842i
$248$	0.420266	+	0.242641i	0.0266869	+	0.0154077i
$249$	−2.70711	+	4.68885i	−0.171556	+	0.297144i
$250$		0			0
$251$	−5.41421			−0.341742			−0.170871	−	0.985293i	$-0.554658\pi$
$251$	−5.41421			−0.341742			−0.170871	+	0.985293i	$0.554658\pi$
$252$		0			0
$253$			21.3137i			1.33998i
$254$	−12.7782	−	22.1324i	−0.801774	−	1.38871i
$255$		0			0
$256$		0			0
$257$	−25.8937	+	14.9497i	−1.61521	+	0.932540i	−0.627069	+	0.778964i	$0.715746\pi$
$257$	−25.8937	+	14.9497i	−1.61521	+	0.932540i	−0.988137	+	0.153576i	$0.950921\pi$
$258$		−	14.7279i		−	0.916920i
$259$	−14.6421	−	2.00373i	−0.909818	−	0.124506i
$260$		0			0
$261$	0.121320	+	0.210133i	0.00750954	+	0.0130069i
$262$	12.8418	+	7.41421i	0.793369	+	0.458052i
$263$	1.01461	+	0.585786i	0.0625636	+	0.0361211i	0.530956	−	0.847400i	$-0.321833\pi$
$263$	1.01461	+	0.585786i	0.0625636	+	0.0361211i	−0.468392	+	0.883521i	$0.655166\pi$
$264$	4.82843	+	8.36308i	0.297169	+	0.514712i
$265$		0			0
$266$	−9.41421	−	23.0600i	−0.577222	−	1.41390i
$267$			3.75736i			0.229947i
$268$		0			0
$269$	4.07107	−	7.05130i	0.248217	−	0.429925i	−0.714814	−	0.699315i	$-0.753489\pi$
$269$	4.07107	−	7.05130i	0.248217	−	0.429925i	0.963031	+	0.269390i	$0.0868219\pi$
$270$		0			0
$271$	−10.0711	−	17.4436i	−0.611774	−	1.05962i	−0.990941	−	0.134295i	$-0.957123\pi$
$271$	−10.0711	−	17.4436i	−0.611774	−	1.05962i	0.379168	−	0.925328i	$-0.376210\pi$
$272$			24.9706i			1.51406i
$273$	3.88437	−	1.58579i	0.235093	−	0.0959762i
$274$	4.14214			0.250236
$275$		0			0
$276$		0			0
$277$	20.2518	+	11.6924i	1.21681	+	0.702528i	0.964235	−	0.265049i	$-0.0853881\pi$
$277$	20.2518	+	11.6924i	1.21681	+	0.702528i	0.252578	+	0.967576i	$0.418721\pi$
$278$	−14.0665	+	8.12132i	−0.843655	+	0.487084i
$279$	0.171573			0.0102718
$280$		0			0
$281$	9.65685			0.576080			0.288040	−	0.957618i	$-0.406996\pi$
$281$	9.65685			0.576080			0.288040	+	0.957618i	$0.406996\pi$
$282$	−11.4069	+	6.58579i	−0.679272	+	0.392178i
$283$	−11.4685	−	6.62132i	−0.681729	−	0.393597i	0.118777	−	0.992921i	$-0.462103\pi$
$283$	−11.4685	−	6.62132i	−0.681729	−	0.393597i	−0.800506	+	0.599324i	$0.795436\pi$
$284$		0			0
$285$		0			0
$286$	−7.65685			−0.452759
$287$	4.68885	+	3.63604i	0.276774	+	0.214629i
$288$		0			0
$289$	10.9853	+	19.0271i	0.646193	+	1.11924i
$290$		0			0
$291$	−5.41421	+	9.37769i	−0.317387	+	0.549730i
$292$		0			0
$293$			15.3137i			0.894636i	0.894375	+	0.447318i	$0.147621\pi$
$293$			15.3137i			0.894636i	−0.894375	+	0.447318i	$0.852379\pi$
$294$	−2.46447	−	9.58783i	−0.143731	−	0.559173i
$295$		0			0
$296$	−7.89949	−	13.6823i	−0.459149	−	0.795269i
$297$	2.95680	+	1.70711i	0.171571	+	0.0990564i
$298$	21.6251	+	12.4853i	1.25271	+	0.723253i
$299$	4.94975	+	8.57321i	0.286251	+	0.495802i
$300$		0			0
$301$	−16.8848	+	21.7737i	−0.973222	+	1.25502i
$302$		−	9.17157i		−	0.527765i
$303$	−5.40629	+	3.12132i	−0.310583	+	0.179315i
$304$	13.3137	−	23.0600i	0.763594	−	1.32258i
$305$		0			0
$306$	4.41421	+	7.64564i	0.252344	+	0.437072i
$307$			1.58579i			0.0905056i	0.998976	+	0.0452528i	$0.0144093\pi$
$307$			1.58579i			0.0905056i	−0.998976	+	0.0452528i	$0.985591\pi$
$308$		0			0
$309$	−1.24264			−0.0706914
$310$		0			0
$311$	8.53553	−	14.7840i	0.484006	−	0.838323i	−0.515826	−	0.856694i	$-0.672515\pi$
$311$	8.53553	−	14.7840i	0.484006	−	0.838323i	0.999831	+	0.0183712i	$0.00584805\pi$
$312$	3.88437	+	2.24264i	0.219909	+	0.126965i
$313$	−22.7013	+	13.1066i	−1.28315	+	0.740829i	−0.977424	−	0.211289i	$-0.932234\pi$
$313$	−22.7013	+	13.1066i	−1.28315	+	0.740829i	−0.305730	+	0.952118i	$0.598900\pi$
$314$	22.8284			1.28828
$315$		0			0
$316$		0			0
$317$	0.0870399	−	0.0502525i	0.00488865	−	0.00282246i	−0.497554	−	0.867433i	$-0.665768\pi$
$317$	0.0870399	−	0.0502525i	0.00488865	−	0.00282246i	0.502442	+	0.864611i	$0.332435\pi$
$318$	−1.43488	−	0.828427i	−0.0804640	−	0.0464559i
$319$	−0.414214	+	0.717439i	−0.0231915	+	0.0401689i
$320$		0			0
$321$	−15.4142			−0.860338
$322$	21.6251	−	8.82843i	1.20512	−	0.491989i
$323$		−	41.5563i		−	2.31226i
$324$		0			0
$325$		0			0
$326$	13.6569	−	23.6544i	0.756383	−	1.31009i
$327$	11.6786	−	6.74264i	0.645828	−	0.372869i
$328$			6.34315i			0.350242i
$329$	24.4142	+	3.34101i	1.34600	+	0.184196i
$330$		0			0
$331$	13.8137	+	23.9260i	0.759270	+	1.31509i	0.943223	+	0.332159i	$0.107777\pi$
$331$	13.8137	+	23.9260i	0.759270	+	1.31509i	−0.183953	+	0.982935i	$0.558889\pi$
$332$		0			0
$333$	−4.83743	−	2.79289i	−0.265090	−	0.153050i
$334$	8.31371	+	14.3998i	0.454906	+	0.787920i
$335$		0			0
$336$	6.48528	−	8.36308i	0.353801	−	0.456243i
$337$		−	0.899495i		−	0.0489986i	−0.999700	−	0.0244993i	$-0.992201\pi$
$337$		−	0.899495i		−	0.0489986i	0.999700	−	0.0244993i	$-0.00779915\pi$
$338$	12.8418	−	7.41421i	0.698502	−	0.403280i
$339$	2.17157	−	3.76127i	0.117944	−	0.204284i
$340$		0			0
$341$	0.292893	+	0.507306i	0.0158611	+	0.0274722i
$342$		−	9.41421i		−	0.509062i
$343$	−7.34847	+	17.0000i	−0.396780	+	0.917914i
$344$	−29.4558			−1.58815
$345$		0			0
$346$	2.00000	−	3.46410i	0.107521	−	0.186231i
$347$	21.6251	+	12.4853i	1.16090	+	0.670245i	0.951519	−	0.307589i	$-0.0995223\pi$
$347$	21.6251	+	12.4853i	1.16090	+	0.670245i	0.209379	+	0.977835i	$0.432856\pi$
$348$		0			0
$349$	16.6274			0.890045			0.445023	−	0.895519i	$-0.353196\pi$
$349$	16.6274			0.890045			0.445023	+	0.895519i	$0.353196\pi$
$350$		0			0
$351$	1.58579			0.0846430
$352$		0			0
$353$	5.10911	+	2.94975i	0.271931	+	0.156999i	0.629765	−	0.776786i	$-0.283151\pi$
$353$	5.10911	+	2.94975i	0.271931	+	0.156999i	−0.357834	+	0.933785i	$0.616485\pi$
$354$	−1.00000	+	1.73205i	−0.0531494	+	0.0920575i
$355$		0			0
$356$		0			0
$357$	2.23936	−	16.3640i	0.118519	−	0.866073i
$358$		−	27.7990i		−	1.46922i
$359$	−13.2929	−	23.0240i	−0.701572	−	1.21516i	−0.967914	−	0.251280i	$-0.919149\pi$
$359$	−13.2929	−	23.0240i	−0.701572	−	1.21516i	0.266342	−	0.963878i	$-0.414185\pi$
$360$		0			0
$361$	−12.6569	+	21.9223i	−0.666150	+	1.15381i
$362$	0.804479	−	0.464466i	0.0422825	−	0.0244118i
$363$			0.656854i			0.0344759i
$364$		0			0
$365$		0			0
$366$	8.82843	+	15.2913i	0.461469	+	0.799288i
$367$	16.9618	+	9.79289i	0.885398	+	0.511185i	0.872434	−	0.488731i	$-0.162540\pi$
$367$	16.9618	+	9.79289i	0.885398	+	0.511185i	0.0129637	+	0.999916i	$0.495873\pi$
$368$	21.6251	+	12.4853i	1.12729	+	0.650840i
$369$	1.12132	+	1.94218i	0.0583736	+	0.101106i
$370$		0			0
$371$	1.17157	+	2.86976i	0.0608250	+	0.148990i
$372$		0			0
$373$	−16.6646	+	9.62132i	−0.862861	+	0.498173i	−0.864969	−	0.501825i	$-0.832662\pi$
$373$	−16.6646	+	9.62132i	−0.862861	+	0.498173i	0.00210826	+	0.999998i	$0.499329\pi$
$374$	−15.0711	+	26.1039i	−0.779306	+	1.34980i
$375$		0			0
$376$	13.1716	+	22.8138i	0.679272	+	1.17653i
$377$			0.384776i			0.0198170i
$378$	0.507306	−	3.70711i	0.0260930	−	0.190673i
$379$	−14.7990			−0.760173			−0.380087	−	0.924951i	$-0.624106\pi$
$379$	−14.7990			−0.760173			−0.380087	+	0.924951i	$0.624106\pi$
$380$		0			0
$381$	−9.03553	+	15.6500i	−0.462904	+	0.801774i
$382$	−23.2341	−	13.4142i	−1.18876	−	0.686331i
$383$	−10.8126	+	6.24264i	−0.552497	+	0.318984i	−0.750128	−	0.661292i	$-0.770008\pi$
$383$	−10.8126	+	6.24264i	−0.552497	+	0.318984i	0.197632	+	0.980276i	$0.436675\pi$
$384$	11.3137			0.577350
$385$		0			0
$386$	−9.55635			−0.486405
$387$	−9.01897	+	5.20711i	−0.458460	+	0.264692i
$388$		0			0
$389$	8.43503	−	14.6099i	0.427673	−	0.740751i	−0.568993	−	0.822342i	$-0.692667\pi$
$389$	8.43503	−	14.6099i	0.427673	−	0.740751i	0.996666	+	0.0815911i	$0.0260002\pi$
$390$		0			0
$391$	38.9706			1.97083
$392$	−19.1757	+	4.92893i	−0.968517	+	0.248949i
$393$		−	10.4853i		−	0.528912i
$394$	3.92893	+	6.80511i	0.197937	+	0.342836i
$395$		0			0
$396$		0			0
$397$	−20.9692	+	12.1066i	−1.05242	+	0.607613i	−0.923325	−	0.384020i	$-0.874539\pi$
$397$	−20.9692	+	12.1066i	−1.05242	+	0.607613i	−0.129092	+	0.991633i	$0.541206\pi$
$398$		−	7.79899i		−	0.390928i
$399$	−10.7929	+	13.9180i	−0.540320	+	0.696769i
$400$		0			0
$401$	−0.242641	−	0.420266i	−0.0121169	−	0.0209871i	0.859903	−	0.510457i	$-0.170524\pi$
$401$	−0.242641	−	0.420266i	−0.0121169	−	0.0209871i	−0.872020	+	0.489470i	$0.837190\pi$
$402$	14.3637	+	8.29289i	0.716397	+	0.413612i
$403$	0.235626	+	0.136039i	0.0117374	+	0.00677658i
$404$		0			0
$405$		0			0
$406$	0.899495	+	0.123093i	0.0446412	+	0.00610901i
$407$		−	19.0711i		−	0.945318i
$408$	15.2913	−	8.82843i	0.757031	−	0.437072i
$409$	−13.1569	+	22.7883i	−0.650565	+	1.12681i	0.332422	+	0.943131i	$0.392134\pi$
$409$	−13.1569	+	22.7883i	−0.650565	+	1.12681i	−0.982986	+	0.183680i	$0.941199\pi$
$410$		0			0
$411$	−1.46447	−	2.53653i	−0.0722368	−	0.125118i
$412$		0			0
$413$	3.46410	−	1.41421i	0.170457	−	0.0695889i
$414$	8.82843			0.433894
$415$		0			0
$416$		0			0
$417$	9.94655	+	5.74264i	0.487084	+	0.281218i
$418$	27.8359	−	16.0711i	1.36150	−	0.786062i
$419$	3.17157			0.154941			0.0774707	−	0.996995i	$-0.475316\pi$
$419$	3.17157			0.154941			0.0774707	+	0.996995i	$0.475316\pi$
$420$		0			0
$421$	27.4853			1.33955			0.669775	−	0.742564i	$-0.266390\pi$
$421$	27.4853			1.33955			0.669775	+	0.742564i	$0.266390\pi$
$422$	0.174080	−	0.100505i	0.00847408	−	0.00489251i
$423$	8.06591	+	4.65685i	0.392178	+	0.226424i
$424$	−1.65685	+	2.86976i	−0.0804640	+	0.139368i
$425$		0			0
$426$	4.82843			0.233938
$427$	4.47871	−	32.7279i	0.216740	−	1.58382i
$428$		0			0
$429$	2.70711	+	4.68885i	0.130700	+	0.226380i
$430$		0			0
$431$	−18.4142	+	31.8944i	−0.886981	+	1.53630i	−0.0435558	+	0.999051i	$0.513869\pi$
$431$	−18.4142	+	31.8944i	−0.886981	+	1.53630i	−0.843426	+	0.537246i	$0.819465\pi$
$432$	3.46410	−	2.00000i	0.166667	−	0.0962250i
$433$			24.5563i			1.18010i	0.807366	+	0.590051i	$0.200893\pi$
$433$			24.5563i			1.18010i	−0.807366	+	0.590051i	$0.799107\pi$
$434$	0.393398	−	0.507306i	0.0188837	−	0.0243515i
$435$		0			0
$436$		0			0
$437$	−35.9889	−	20.7782i	−1.72158	−	0.993955i
$438$	−2.53653	−	1.46447i	−0.121200	−	0.0699749i
$439$	0.171573	+	0.297173i	0.00818873	+	0.0141833i	0.870091	−	0.492892i	$-0.164060\pi$
$439$	0.171573	+	0.297173i	0.00818873	+	0.0141833i	−0.861902	+	0.507075i	$0.830727\pi$
$440$		0			0
$441$	−5.00000	+	4.89898i	−0.238095	+	0.233285i
$442$			14.0000i			0.665912i
$443$	−0.420266	+	0.242641i	−0.0199674	+	0.0115282i	−0.509950	−	0.860204i	$-0.670336\pi$
$443$	−0.420266	+	0.242641i	−0.0199674	+	0.0115282i	0.489983	+	0.871732i	$0.337003\pi$
$444$		0			0
$445$		0			0
$446$	−12.1421	−	21.0308i	−0.574947	−	0.995837i
$447$		−	17.6569i		−	0.835141i
$448$	−16.7262	−	12.9706i	−0.790237	−	0.612801i
$449$	6.97056			0.328961			0.164481	−	0.986380i	$-0.447405\pi$
$449$	6.97056			0.328961			0.164481	+	0.986380i	$0.447405\pi$
$450$		0			0
$451$	−3.82843	+	6.63103i	−0.180274	+	0.312243i
$452$		0			0
$453$	−5.61642	+	3.24264i	−0.263882	+	0.152353i
$454$	−32.6274			−1.53128
$455$		0			0
$456$	−18.8284			−0.881722
$457$	−18.0995	+	10.4497i	−0.846659	+	0.488819i	−0.859522	−	0.511099i	$-0.829239\pi$
$457$	−18.0995	+	10.4497i	−0.846659	+	0.488819i	0.0128634	+	0.999917i	$0.495905\pi$
$458$	−17.5306	−	10.1213i	−0.819153	−	0.472938i
$459$	3.12132	−	5.40629i	0.145691	−	0.252344i
$460$		0			0
$461$	−27.0711			−1.26083			−0.630413	−	0.776260i	$-0.717114\pi$
$461$	−27.0711			−1.26083			−0.630413	+	0.776260i	$0.717114\pi$
$462$	11.8272	−	4.82843i	0.550250	−	0.224639i
$463$			10.4142i			0.483990i	0.970278	+	0.241995i	$0.0778017\pi$
$463$			10.4142i			0.483990i	−0.970278	+	0.241995i	$0.922198\pi$
$464$	0.485281	+	0.840532i	0.0225286	+	0.0390207i
$465$		0			0
$466$	15.8995	−	27.5387i	0.736530	−	1.27571i
$467$	5.79050	−	3.34315i	0.267952	−	0.154702i	−0.360004	−	0.932951i	$-0.617225\pi$
$467$	5.79050	−	3.34315i	0.267952	−	0.154702i	0.627957	+	0.778248i	$0.283891\pi$
$468$		0			0
$469$	−11.7279	−	28.7274i	−0.541545	−	1.32651i
$470$		0			0
$471$	−8.07107	−	13.9795i	−0.371895	−	0.644141i
$472$	3.46410	+	2.00000i	0.159448	+	0.0920575i
$473$	−30.7927	−	17.7782i	−1.41585	−	0.817441i
$474$	3.29289	+	5.70346i	0.151248	+	0.261969i
$475$		0			0
$476$		0			0
$477$			1.17157i			0.0536426i
$478$	−21.2049	+	12.2426i	−0.969888	+	0.559965i
$479$	−17.3137	+	29.9882i	−0.791084	+	1.37020i	0.134213	+	0.990953i	$0.457149\pi$
$479$	−17.3137	+	29.9882i	−0.791084	+	1.37020i	−0.925297	+	0.379244i	$0.876184\pi$
$480$		0			0
$481$	−4.42893	−	7.67114i	−0.201942	−	0.349774i
$482$		−	14.6274i		−	0.666261i
$483$	−13.0519	−	10.1213i	−0.593883	−	0.460536i
$484$		0			0
$485$		0			0
$486$	0.707107	−	1.22474i	0.0320750	−	0.0555556i
$487$	−0.778985	−	0.449747i	−0.0352992	−	0.0203800i	0.482247	−	0.876036i	$-0.339821\pi$
$487$	−0.778985	−	0.449747i	−0.0352992	−	0.0203800i	−0.517546	+	0.855656i	$0.673154\pi$
$488$	30.5826	−	17.6569i	1.38441	−	0.799288i
$489$	−19.3137			−0.873396
$490$		0			0
$491$	−10.1421			−0.457708			−0.228854	−	0.973461i	$-0.573498\pi$
$491$	−10.1421			−0.457708			−0.228854	+	0.973461i	$0.573498\pi$
$492$		0			0
$493$	1.31178	+	0.757359i	0.0590798	+	0.0341097i
$494$	7.46447	−	12.9288i	0.335842	−	0.581696i
$495$		0			0
$496$	0.686292			0.0308154
$497$	−7.13834	−	5.53553i	−0.320198	−	0.248303i
$498$			7.65685i			0.343112i
$499$	4.39949	+	7.62015i	0.196948	+	0.341125i	0.947538	−	0.319645i	$-0.103564\pi$
$499$	4.39949	+	7.62015i	0.196948	+	0.341125i	−0.750589	+	0.660769i	$0.770230\pi$
$500$		0			0
$501$	5.87868	−	10.1822i	0.262640	−	0.454906i
$502$	−6.63103	+	3.82843i	−0.295957	+	0.170871i
$503$			18.4853i			0.824218i	0.911135	+	0.412109i	$0.135208\pi$
$503$			18.4853i			0.824218i	−0.911135	+	0.412109i	$0.864792\pi$
$504$	−7.41421	−	1.01461i	−0.330255	−	0.0451944i
$505$		0			0
$506$	15.0711	+	26.1039i	0.669991	+	1.16046i
$507$	−9.08052	−	5.24264i	−0.403280	−	0.232834i
$508$		0			0
$509$	6.89949	+	11.9503i	0.305815	+	0.529687i	0.977442	−	0.211202i	$-0.0677378\pi$
$509$	6.89949	+	11.9503i	0.305815	+	0.529687i	−0.671628	+	0.740889i	$0.734405\pi$
$510$		0			0
$511$	2.07107	+	5.07306i	0.0916186	+	0.224419i
$512$		−	22.6274i		−	1.00000i
$513$	−5.76500	+	3.32843i	−0.254531	+	0.146954i
$514$	−21.1421	+	36.6193i	−0.932540	+	1.61521i
$515$		0			0
$516$		0			0
$517$			31.7990i			1.39852i
$518$	−19.3497	+	7.89949i	−0.850178	+	0.347084i
$519$	−2.82843			−0.124154
$520$		0			0
$521$	19.5563	−	33.8726i	0.856779	−	1.48399i	−0.0182053	−	0.999834i	$-0.505795\pi$
$521$	19.5563	−	33.8726i	0.856779	−	1.48399i	0.874985	−	0.484151i	$-0.160871\pi$
$522$	0.297173	+	0.171573i	0.0130069	+	0.00750954i
$523$	6.56948	−	3.79289i	0.287263	−	0.165852i	−0.349444	−	0.936957i	$-0.613629\pi$
$523$	6.56948	−	3.79289i	0.287263	−	0.165852i	0.636707	+	0.771106i	$0.280296\pi$
$524$		0			0
$525$		0			0
$526$	1.65685			0.0722423
$527$	0.927572	−	0.535534i	0.0404057	−	0.0233282i
$528$	11.8272	+	6.82843i	0.514712	+	0.297169i
$529$	7.98528	−	13.8309i	0.347186	−	0.601344i
$530$		0			0
$531$	1.41421			0.0613716
$532$		0			0
$533$			3.55635i			0.154043i
$534$	2.65685	+	4.60181i	0.114973	+	0.199140i
$535$		0			0
$536$	16.5858	−	28.7274i	0.716397	−	1.24084i
$537$	−17.0233	+	9.82843i	−0.734611	+	0.424128i
$538$		−	11.5147i		−	0.496435i
$539$	−23.0208	−	6.42090i	−0.991577	−	0.276568i
$540$		0			0
$541$	−16.1569	−	27.9845i	−0.694637	−	1.20315i	−0.970303	−	0.241894i	$-0.922231\pi$
$541$	−16.1569	−	27.9845i	−0.694637	−	1.20315i	0.275665	−	0.961254i	$-0.411102\pi$
$542$	−24.6690	−	14.2426i	−1.05962	−	0.611774i
$543$	−0.568852	−	0.328427i	−0.0244118	−	0.0140942i
$544$		0			0
$545$		0			0
$546$	3.63604	−	4.68885i	0.155608	−	0.200664i
$547$		−	31.7990i		−	1.35963i	−0.733385	−	0.679813i	$-0.762061\pi$
$547$		−	31.7990i		−	1.35963i	0.733385	−	0.679813i	$-0.237939\pi$
$548$		0			0
$549$	6.24264	−	10.8126i	0.266429	−	0.461469i
$550$		0			0
$551$	−0.807612	−	1.39882i	−0.0344054	−	0.0595919i
$552$		−	17.6569i		−	0.751526i
$553$	1.67050	−	12.2071i	0.0710371	−	0.519099i
$554$	33.0711			1.40506
$555$		0			0
$556$		0			0
$557$	7.22538	+	4.17157i	0.306149	+	0.176755i	0.645202	−	0.764012i	$-0.276773\pi$
$557$	7.22538	+	4.17157i	0.306149	+	0.176755i	−0.339053	+	0.940767i	$0.610107\pi$
$558$	0.210133	−	0.121320i	0.00889564	−	0.00513590i
$559$	−16.5147			−0.698498
$560$		0			0
$561$	21.3137			0.899865
$562$	11.8272	−	6.82843i	0.498900	−	0.288040i
$563$	−12.3705	−	7.14214i	−0.521356	−	0.301005i	0.216133	−	0.976364i	$-0.430655\pi$
$563$	−12.3705	−	7.14214i	−0.521356	−	0.301005i	−0.737489	+	0.675359i	$0.763989\pi$
$564$		0			0
$565$		0			0
$566$	−18.7279			−0.787193
$567$	−2.44949	+	1.00000i	−0.102869	+	0.0419961i
$568$		−	9.65685i		−	0.405193i
$569$	−18.4350	−	31.9304i	−0.772837	−	1.33859i	−0.936002	−	0.351994i	$-0.885504\pi$
$569$	−18.4350	−	31.9304i	−0.772837	−	1.33859i	0.163166	−	0.986599i	$-0.447829\pi$
$570$		0			0
$571$	−13.9853	+	24.2232i	−0.585266	+	1.01371i	0.409576	+	0.912276i	$0.365677\pi$
$571$	−13.9853	+	24.2232i	−0.585266	+	1.01371i	−0.994842	+	0.101434i	$0.967657\pi$
$572$		0			0
$573$			18.9706i			0.792507i
$574$	8.31371	+	1.13770i	0.347007	+	0.0474869i
$575$		0			0
$576$	−4.00000	−	6.92820i	−0.166667	−	0.288675i
$577$	−5.67796	−	3.27817i	−0.236377	−	0.136472i	0.377134	−	0.926159i	$-0.376910\pi$
$577$	−5.67796	−	3.27817i	−0.236377	−	0.136472i	−0.613510	+	0.789687i	$0.710243\pi$
$578$	26.9083	+	15.5355i	1.11924	+	0.646193i
$579$	3.37868	+	5.85204i	0.140413	+	0.243203i
$580$		0			0
$581$	8.77817	−	11.3199i	0.364180	−	0.469628i
$582$			15.3137i			0.634774i
$583$	−3.46410	+	2.00000i	−0.143468	+	0.0828315i
$584$	−2.92893	+	5.07306i	−0.121200	+	0.209925i
$585$		0			0
$586$	10.8284	+	18.7554i	0.447318	+	0.774778i
$587$			30.2426i			1.24825i	0.781326	+	0.624124i	$0.214544\pi$
$587$			30.2426i			1.24825i	−0.781326	+	0.624124i	$0.785456\pi$
$588$		0			0
$589$	−1.14214			−0.0470609
$590$		0			0
$591$	2.77817	−	4.81194i	0.114279	−	0.197937i
$592$	−19.3497	−	11.1716i	−0.795269	−	0.459149i
$593$	−11.6170	+	6.70711i	−0.477055	+	0.275428i	−0.719188	−	0.694815i	$-0.755486\pi$
$593$	−11.6170	+	6.70711i	−0.477055	+	0.275428i	0.242133	+	0.970243i	$0.422153\pi$
$594$	4.82843			0.198113
$595$		0			0
$596$		0			0
$597$	−4.77589	+	2.75736i	−0.195464	+	0.112851i
$598$	12.1244	+	7.00000i	0.495802	+	0.286251i
$599$	−21.0711	+	36.4962i	−0.860940	+	1.49119i	0.0100818	+	0.999949i	$0.496791\pi$
$599$	−21.0711	+	36.4962i	−0.860940	+	1.49119i	−0.871022	+	0.491243i	$0.836543\pi$
$600$		0			0
$601$	−24.1716			−0.985979			−0.492990	−	0.870035i	$-0.664096\pi$
$601$	−24.1716			−0.985979			−0.492990	+	0.870035i	$0.664096\pi$
$602$	−5.28319	+	38.6066i	−0.215327	+	1.57349i
$603$		−	11.7279i		−	0.477598i
$604$		0			0
$605$		0			0
$606$	−4.41421	+	7.64564i	−0.179315	+	0.310583i
$607$	−1.07616	+	0.621320i	−0.0436799	+	0.0252186i	−0.521681	−	0.853141i	$-0.674695\pi$
$607$	−1.07616	+	0.621320i	−0.0436799	+	0.0252186i	0.478001	+	0.878359i	$0.341362\pi$
$608$		0			0
$609$	−0.242641	−	0.594346i	−0.00983230	−	0.0240841i
$610$		0			0
$611$	7.38478	+	12.7908i	0.298756	+	0.517461i
$612$		0			0
$613$	8.78335	+	5.07107i	0.354756	+	0.204818i	0.666778	−	0.745256i	$-0.267673\pi$
$613$	8.78335	+	5.07107i	0.354756	+	0.204818i	−0.312022	+	0.950075i	$0.601006\pi$
$614$	1.12132	+	1.94218i	0.0452528	+	0.0783802i
$615$		0			0
$616$	−9.65685	−	23.6544i	−0.389086	−	0.953062i
$617$		−	8.82843i		−	0.355419i	−0.984083	−	0.177710i	$-0.943131\pi$
$617$		−	8.82843i		−	0.355419i	0.984083	−	0.177710i	$-0.0568688\pi$
$618$	−1.52192	+	0.878680i	−0.0612205	+	0.0353457i
$619$	19.9853	−	34.6155i	0.803276	−	1.39132i	−0.114172	−	0.993461i	$-0.536422\pi$
$619$	19.9853	−	34.6155i	0.803276	−	1.39132i	0.917449	−	0.397854i	$-0.130245\pi$
$620$		0			0
$621$	−3.12132	−	5.40629i	−0.125254	−	0.216947i
$622$		−	24.1421i		−	0.968011i
$623$	1.34784	−	9.84924i	0.0540000	−	0.394602i
$624$	6.34315			0.253929
$625$		0			0
$626$	−18.5355	+	32.1045i	−0.740829	+	1.28315i
$627$	−19.6830	−	11.3640i	−0.786062	−	0.453833i
$628$		0			0
$629$	−34.8701			−1.39036
$630$		0			0
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$	11.4069	−	6.58579i	0.453743	−	0.261969i
$633$	−0.123093	−	0.0710678i	−0.00489251	−	0.00282469i
$634$	0.0710678	−	0.123093i	0.00282246	−	0.00488865i
$635$		0			0
$636$		0			0
$637$	−10.7510	+	2.76346i	−0.425971	+	0.109492i
$638$			1.17157i			0.0463830i
$639$	−1.70711	−	2.95680i	−0.0675321	−	0.116969i
$640$		0			0
$641$	6.60660	−	11.4430i	0.260945	−	0.451970i	−0.705548	−	0.708662i	$-0.749299\pi$
$641$	6.60660	−	11.4430i	0.260945	−	0.451970i	0.966493	+	0.256692i	$0.0826325\pi$
$642$	−18.8785	+	10.8995i	−0.745074	+	0.430169i
$643$		−	24.5563i		−	0.968408i	−0.874955	−	0.484204i	$-0.839109\pi$
$643$		−	24.5563i		−	0.968408i	0.874955	−	0.484204i	$-0.160891\pi$
$644$		0			0
$645$		0			0
$646$	−29.3848	−	50.8959i	−1.15613	−	2.00247i
$647$	−8.32703	−	4.80761i	−0.327369	−	0.189007i	0.327303	−	0.944919i	$-0.393860\pi$
$647$	−8.32703	−	4.80761i	−0.327369	−	0.189007i	−0.654673	+	0.755913i	$0.727193\pi$
$648$	−2.44949	−	1.41421i	−0.0962250	−	0.0555556i
$649$	2.41421	+	4.18154i	0.0947662	+	0.164140i
$650$		0			0
$651$	−0.449747	−	0.0615465i	−0.0176270	−	0.00241220i
$652$		0			0
$653$	−6.71807	+	3.87868i	−0.262898	+	0.151784i	−0.625656	−	0.780099i	$-0.715169\pi$
$653$	−6.71807	+	3.87868i	−0.262898	+	0.151784i	0.362758	+	0.931884i	$0.381835\pi$
$654$	9.53553	−	16.5160i	0.372869	−	0.645828i
$655$		0			0
$656$	4.48528	+	7.76874i	0.175121	+	0.303318i
$657$			2.07107i			0.0808001i
$658$	32.2636	−	13.1716i	1.25777	−	0.513481i
$659$	27.3137			1.06399			0.531996	−	0.846747i	$-0.321442\pi$
$659$	27.3137			1.06399			0.531996	+	0.846747i	$0.321442\pi$
$660$		0			0
$661$	−16.1569	+	27.9845i	−0.628429	+	1.08847i	0.359438	+	0.933169i	$0.382968\pi$
$661$	−16.1569	+	27.9845i	−0.628429	+	1.08847i	−0.987867	+	0.155302i	$0.950365\pi$
$662$	33.8365	+	19.5355i	1.31509	+	0.759270i
$663$	8.57321	−	4.94975i	0.332956	−	0.192232i
$664$	15.3137			0.594287
$665$		0			0
$666$	−7.89949			−0.306099
$667$	1.31178	−	0.757359i	0.0507925	−	0.0293251i
$668$		0			0
$669$	−8.58579	+	14.8710i	−0.331946	+	0.574947i
$670$		0			0
$671$	42.6274			1.64561
$672$		0			0
$673$		−	2.27208i		−	0.0875822i	−0.999041	−	0.0437911i	$-0.986056\pi$
$673$		−	2.27208i		−	0.0875822i	0.999041	−	0.0437911i	$-0.0139436\pi$
$674$	−0.636039	−	1.10165i	−0.0244993	−	0.0424340i
$675$		0			0
$676$		0			0
$677$	3.37706	−	1.94975i	0.129791	−	0.0749349i	−0.433699	−	0.901058i	$-0.642792\pi$
$677$	3.37706	−	1.94975i	0.129791	−	0.0749349i	0.563490	+	0.826123i	$0.309458\pi$
$678$		−	6.14214i		−	0.235887i
$679$	17.5563	−	22.6398i	0.673751	−	0.868834i
$680$		0			0
$681$	11.5355	+	19.9801i	0.442043	+	0.765640i
$682$	0.717439	+	0.414214i	0.0274722	+	0.0158611i
$683$	17.8278	+	10.2929i	0.682162	+	0.393847i	0.800669	−	0.599107i	$-0.204477\pi$
$683$	17.8278	+	10.2929i	0.682162	+	0.393847i	−0.118507	+	0.992953i	$0.537811\pi$
$684$		0			0
$685$		0			0
$686$	3.02082	+	26.0168i	0.115335	+	0.993327i
$687$			14.3137i			0.546102i
$688$	−36.0759	+	20.8284i	−1.37538	+	0.794076i
$689$	−0.928932	+	1.60896i	−0.0353895	+	0.0612964i
$690$		0			0
$691$	−15.1569	−	26.2524i	−0.576594	−	0.998690i	−0.995866	−	0.0908295i	$-0.971048\pi$
$691$	−15.1569	−	26.2524i	−0.576594	−	0.998690i	0.419273	−	0.907860i	$-0.362285\pi$
$692$		0			0
$693$	−7.13834	−	5.53553i	−0.271163	−	0.210278i
$694$	35.3137			1.34049
$695$		0			0
$696$	0.343146	−	0.594346i	0.0130069	−	0.0225286i
$697$	12.1244	+	7.00000i	0.459243	+	0.265144i
$698$	20.3643	−	11.7574i	0.770802	−	0.445023i
$699$	−22.4853			−0.850471
$700$		0			0
$701$	41.2132			1.55660			0.778301	−	0.627892i	$-0.216082\pi$
$701$	41.2132			1.55660			0.778301	+	0.627892i	$0.216082\pi$
$702$	1.94218	−	1.12132i	0.0733030	−	0.0423215i
$703$	32.2021	+	18.5919i	1.21452	+	0.701206i
$704$	13.6569	−	23.6544i	0.514712	−	0.891507i
$705$		0			0
$706$	8.34315			0.313998
$707$	15.2913	−	6.24264i	0.575088	−	0.234779i
$708$		0			0
$709$	−5.55635	−	9.62388i	−0.208673	−	0.361432i	0.742624	−	0.669709i	$-0.233581\pi$
$709$	−5.55635	−	9.62388i	−0.208673	−	0.361432i	−0.951297	+	0.308277i	$0.900248\pi$
$710$		0			0
$711$	2.32843	−	4.03295i	0.0873228	−	0.151248i
$712$	9.20361	−	5.31371i	0.344920	−	0.199140i
$713$		−	1.07107i		−	0.0401118i
$714$	−8.82843	−	21.6251i	−0.330396	−	0.809301i
$715$		0			0
$716$		0			0
$717$	14.9941	+	8.65685i	0.559965	+	0.323296i
$718$	−32.5608	−	18.7990i	−1.21516	−	0.701572i
$719$	8.75736	+	15.1682i	0.326594	+	0.565678i	0.981834	−	0.189743i	$-0.0607656\pi$
$719$	8.75736	+	15.1682i	0.326594	+	0.565678i	−0.655239	+	0.755421i	$0.727432\pi$
$720$		0			0
$721$	3.25736	+	0.445759i	0.121310	+	0.0166009i
$722$			35.7990i			1.33230i
$723$	−8.95743	+	5.17157i	−0.333130	+	0.192333i
$724$		0			0
$725$		0			0
$726$	0.464466	+	0.804479i	0.0172380	+	0.0298570i
$727$			4.75736i			0.176441i	0.996101	+	0.0882203i	$0.0281180\pi$
$727$			4.75736i			0.176441i	−0.996101	+	0.0882203i	$0.971882\pi$
$728$	−9.37769	−	7.27208i	−0.347560	−	0.269521i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−32.5061	+	56.3022i	−1.20228	+	2.08241i
$732$		0			0
$733$	9.31615	−	5.37868i	0.344100	−	0.198666i	−0.317984	−	0.948096i	$-0.603006\pi$
$733$	9.31615	−	5.37868i	0.344100	−	0.198666i	0.662083	+	0.749430i	$0.269672\pi$
$734$	27.6985			1.02237
$735$		0			0
$736$		0			0
$737$	34.6771	−	20.0208i	1.27735	−	0.737476i
$738$	2.74666	+	1.58579i	0.101106	+	0.0583736i
$739$	−17.5711	+	30.4340i	−0.646362	+	1.11953i	0.337623	+	0.941281i	$0.390377\pi$
$739$	−17.5711	+	30.4340i	−0.646362	+	1.11953i	−0.983985	+	0.178251i	$0.942956\pi$
$740$		0			0
$741$	−10.5563			−0.387797
$742$	3.46410	+	2.68629i	0.127171	+	0.0986169i
$743$			4.72792i			0.173451i	0.996232	+	0.0867253i	$0.0276402\pi$
$743$			4.72792i			0.173451i	−0.996232	+	0.0867253i	$0.972360\pi$
$744$	−0.242641	−	0.420266i	−0.00889564	−	0.0154077i
$745$		0			0
$746$	−13.6066	+	23.5673i	−0.498173	+	0.862861i
$747$	4.68885	−	2.70711i	0.171556	−	0.0990479i
$748$		0			0
$749$	40.4056	+	5.52938i	1.47639	+	0.202039i
$750$		0			0
$751$	−9.81371	−	16.9978i	−0.358107	−	0.620260i	0.629537	−	0.776970i	$-0.283244\pi$
$751$	−9.81371	−	16.9978i	−0.358107	−	0.620260i	−0.987645	+	0.156710i	$0.949911\pi$
$752$	32.2636	+	18.6274i	1.17653	+	0.679272i
$753$	4.68885	+	2.70711i	0.170871	+	0.0986525i
$754$	0.272078	+	0.471253i	0.00990849	+	0.0171620i
$755$		0			0
$756$		0			0
$757$			41.5980i			1.51190i	0.654627	+	0.755952i	$0.272826\pi$
$757$			41.5980i			1.51190i	−0.654627	+	0.755952i	$0.727174\pi$
$758$	−18.1250	+	10.4645i	−0.658329	+	0.380087i
$759$	10.6569	−	18.4582i	0.386819	−	0.669991i
$760$		0			0
$761$	10.4645	+	18.1250i	0.379337	+	0.657030i	0.990966	−	0.134114i	$-0.0428189\pi$
$761$	10.4645	+	18.1250i	0.379337	+	0.657030i	−0.611629	+	0.791145i	$0.709486\pi$
$762$			25.5563i			0.925809i
$763$	−33.0321	+	13.4853i	−1.19584	+	0.488200i
$764$		0			0
$765$		0			0
$766$	−8.82843	+	15.2913i	−0.318984	+	0.552497i
$767$	1.94218	+	1.12132i	0.0701282	+	0.0404885i
$768$		0			0
$769$	15.9706			0.575913			0.287957	−	0.957643i	$-0.407024\pi$
$769$	15.9706			0.575913			0.287957	+	0.957643i	$0.407024\pi$
$770$		0			0
$771$	29.8995			1.07680
$772$		0			0
$773$	21.5891	+	12.4645i	0.776506	+	0.448316i	0.835190	−	0.549961i	$-0.185357\pi$
$773$	21.5891	+	12.4645i	0.776506	+	0.448316i	−0.0586849	+	0.998277i	$0.518691\pi$
$774$	−7.36396	+	12.7548i	−0.264692	+	0.458460i
$775$		0			0
$776$	30.6274			1.09946
$777$	11.6786	+	9.05635i	0.418967	+	0.324895i
$778$		−	23.8579i		−	0.855346i
$779$	−7.46447	−	12.9288i	−0.267442	−	0.463224i
$780$		0			0
$781$	5.82843	−	10.0951i	0.208558	−	0.361232i
$782$	47.7290	−	27.5563i	1.70679	−	0.985413i
$783$		−	0.242641i		−	0.00867127i
$784$	−20.0000	+	19.5959i	−0.714286	+	0.699854i
$785$		0			0
$786$	−7.41421	−	12.8418i	−0.264456	−	0.458052i
$787$	−11.4069	−	6.58579i	−0.406613	−	0.234758i	0.282721	−	0.959202i	$-0.408763\pi$
$787$	−11.4069	−	6.58579i	−0.406613	−	0.234758i	−0.689333	+	0.724444i	$0.742096\pi$
$788$		0			0
$789$	−0.585786	−	1.01461i	−0.0208545	−	0.0361211i
$790$		0			0
$791$	−7.04163	+	9.08052i	−0.250372	+	0.322866i
$792$		−	9.65685i		−	0.343141i
$793$	17.1464	−	9.89949i	0.608888	−	0.351541i
$794$	−17.1213	+	29.6550i	−0.607613	+	1.05242i
$795$		0			0
$796$		0			0
$797$			10.4437i			0.369933i	0.982745	+	0.184967i	$0.0592177\pi$
$797$			10.4437i			0.369933i	−0.982745	+	0.184967i	$0.940782\pi$
$798$	−3.37706	+	24.6777i	−0.119547	+	0.873580i
$799$	58.1421			2.05692
$800$		0			0
$801$	1.87868	−	3.25397i	0.0663799	−	0.114973i
$802$	−0.594346	−	0.343146i	−0.0209871	−	0.0121169i
$803$	−6.12372	+	3.53553i	−0.216102	+	0.124766i
$804$		0			0
$805$		0			0
$806$	0.384776			0.0135532
$807$	−7.05130	+	4.07107i	−0.248217	+	0.143308i
$808$	15.2913	+	8.82843i	0.537946	+	0.310583i
$809$	−2.31371	+	4.00746i	−0.0813457	+	0.140895i	−0.903828	−	0.427896i	$-0.859255\pi$
$809$	−2.31371	+	4.00746i	−0.0813457	+	0.140895i	0.822483	+	0.568790i	$0.192588\pi$
$810$		0			0
$811$	−22.9706			−0.806606			−0.403303	−	0.915067i	$-0.632138\pi$
$811$	−22.9706			−0.806606			−0.403303	+	0.915067i	$0.632138\pi$
$812$		0			0
$813$			20.1421i			0.706416i
$814$	−13.4853	−	23.3572i	−0.472659	−	0.818669i
$815$		0			0
$816$	12.4853	−	21.6251i	0.437072	−	0.757031i
$817$	60.0380	−	34.6630i	2.10046	−	1.21270i
$818$			37.2132i			1.30113i
$819$	−4.15685	−	0.568852i	−0.145252	−	0.0198773i
$820$		0			0
$821$	−6.77817	−	11.7401i	−0.236560	−	0.409734i	0.723165	−	0.690675i	$-0.242687\pi$
$821$	−6.77817	−	11.7401i	−0.236560	−	0.409734i	−0.959725	+	0.280942i	$0.909353\pi$
$822$	−3.58719	−	2.07107i	−0.125118	−	0.0722368i
$823$	19.2987	+	11.1421i	0.672712	+	0.388390i	0.797103	−	0.603843i	$-0.206365\pi$
$823$	19.2987	+	11.1421i	0.672712	+	0.388390i	−0.124391	+	0.992233i	$0.539698\pi$
$824$	1.75736	+	3.04384i	0.0612205	+	0.106037i
$825$		0			0
$826$	3.24264	−	4.18154i	0.112826	−	0.145494i
$827$			12.8284i			0.446088i	0.974808	+	0.223044i	$0.0715994\pi$
$827$			12.8284i			0.446088i	−0.974808	+	0.223044i	$0.928401\pi$
$828$		0			0
$829$	−9.32843	+	16.1573i	−0.323990	+	0.561167i	−0.981307	−	0.192447i	$-0.938358\pi$
$829$	−9.32843	+	16.1573i	−0.323990	+	0.561167i	0.657318	+	0.753614i	$0.271691\pi$
$830$		0			0
$831$	−11.6924	−	20.2518i	−0.405604	−	0.702528i
$832$		−	12.6863i		−	0.439818i
$833$	−11.7401	+	42.0919i	−0.406772	+	1.45840i
$834$	16.2426			0.562437
$835$		0			0
$836$		0			0
$837$	−0.148586	−	0.0857864i	−0.00513590	−	0.00296521i
$838$	3.88437	−	2.24264i	0.134183	−	0.0774707i
$839$	7.27208			0.251060			0.125530	−	0.992090i	$-0.459937\pi$
$839$	7.27208			0.251060			0.125530	+	0.992090i	$0.459937\pi$
$840$		0			0
$841$	−28.9411			−0.997970
$842$	33.6625	−	19.4350i	1.16008	−	0.669775i
$843$	−8.36308	−	4.82843i	−0.288040	−	0.166300i
$844$		0			0
$845$		0			0
$846$	13.1716			0.452848
$847$	0.235626	−	1.72183i	0.00809622	−	0.0591626i
$848$			4.68629i			0.160928i
$849$	6.62132	+	11.4685i	0.227243	+	0.393597i
$850$		0			0
$851$	−17.4350	+	30.1984i	−0.597665	+	1.03519i
$852$		0			0
$853$		−	38.0122i		−	1.30151i	−0.759287	−	0.650756i	$-0.774452\pi$
$853$		−	38.0122i		−	1.30151i	0.759287	−	0.650756i	$-0.225548\pi$
$854$	−17.6569	−	43.2503i	−0.604205	−	1.47999i
$855$		0			0
$856$	21.7990	+	37.7570i	0.745074	+	1.29051i
$857$	5.40629	+	3.12132i	0.184675	+	0.106622i	0.589487	−	0.807778i	$-0.299330\pi$
$857$	5.40629	+	3.12132i	0.184675	+	0.106622i	−0.404812	+	0.914400i	$0.632663\pi$
$858$	6.63103	+	3.82843i	0.226380	+	0.130700i
$859$	7.82843	+	13.5592i	0.267102	+	0.462635i	0.968112	−	0.250517i	$-0.0806004\pi$
$859$	7.82843	+	13.5592i	0.267102	+	0.462635i	−0.701010	+	0.713152i	$0.747267\pi$
$860$		0			0
$861$	−2.24264	−	5.49333i	−0.0764290	−	0.187212i
$862$			52.0833i			1.77396i
$863$	8.48617	−	4.89949i	0.288873	−	0.166781i	−0.348561	−	0.937286i	$-0.613329\pi$
$863$	8.48617	−	4.89949i	0.288873	−	0.166781i	0.637433	+	0.770505i	$0.279996\pi$
$864$		0			0
$865$		0			0
$866$	17.3640	+	30.0753i	0.590051	+	1.02200i
$867$		−	21.9706i		−	0.746159i
$868$		0			0
$869$	15.8995			0.539353
$870$		0			0
$871$	9.29899	−	16.1063i	0.315084	−	0.545742i
$872$	−33.0321	−	19.0711i	−1.11861	−	0.645828i
$873$	9.37769	−	5.41421i	0.317387	−	0.183243i
$874$	−58.7696			−1.98791
$875$		0			0
$876$		0			0
$877$	−15.5885	+	9.00000i	−0.526385	+	0.303908i	−0.739543	−	0.673109i	$-0.764958\pi$
$877$	−15.5885	+	9.00000i	−0.526385	+	0.303908i	0.213158	+	0.977018i	$0.431625\pi$
$878$	0.420266	+	0.242641i	0.0141833	+	0.00818873i
$879$	7.65685	−	13.2621i	0.258259	−	0.447318i
$880$		0			0
$881$	−21.6569			−0.729638			−0.364819	−	0.931078i	$-0.618869\pi$
$881$	−21.6569			−0.729638			−0.364819	+	0.931078i	$0.618869\pi$
$882$	−2.65962	+	9.53553i	−0.0895542	+	0.321078i
$883$		−	8.07107i		−	0.271613i	−0.990735	−	0.135807i	$-0.956637\pi$
$883$		−	8.07107i		−	0.271613i	0.990735	−	0.135807i	$-0.0433626\pi$
$884$		0			0
$885$		0			0
$886$	−0.343146	+	0.594346i	−0.0115282	+	0.0199674i
$887$	4.51477	−	2.60660i	0.151591	−	0.0875211i	−0.422286	−	0.906463i	$-0.638772\pi$
$887$	4.51477	−	2.60660i	0.151591	−	0.0875211i	0.573877	+	0.818942i	$0.305439\pi$
$888$			15.7990i			0.530179i
$889$	29.2990	−	37.7825i	0.982657	−	1.26718i
$890$		0			0
$891$	−1.70711	−	2.95680i	−0.0571902	−	0.0990564i
$892$		0			0
$893$	−53.6936	−	31.0000i	−1.79679	−	1.03738i
$894$	−12.4853	−	21.6251i	−0.417570	−	0.723253i
$895$		0			0
$896$	−29.6569	−	4.05845i	−0.990766	−	0.135583i
$897$		−	9.89949i		−	0.330535i
$898$	8.53716	−	4.92893i	0.284889	−	0.164481i
$899$	0.0208153	−	0.0360531i	0.000694228	−	0.00120244i
$900$		0			0
$901$	3.65685	+	6.33386i	0.121827	+	0.211011i
$902$			10.8284i			0.360547i
$903$	25.5095	−	10.4142i	0.848903	−	0.346563i
$904$	−12.2843			−0.408569
$905$		0			0
$906$	−4.58579	+	7.94282i	−0.152353	+	0.263882i
$907$	7.46100	+	4.30761i	0.247739	+	0.143032i	0.618728	−	0.785605i	$-0.287648\pi$
$907$	7.46100	+	4.30761i	0.247739	+	0.143032i	−0.370990	+	0.928637i	$0.620982\pi$
$908$		0			0
$909$	6.24264			0.207055
$910$		0			0
$911$	4.24264			0.140565			0.0702825	−	0.997527i	$-0.477610\pi$
$911$	4.24264			0.140565			0.0702825	+	0.997527i	$0.477610\pi$
$912$	−23.0600	+	13.3137i	−0.763594	+	0.440861i
$913$	16.0087	+	9.24264i	0.529811	+	0.305887i
$914$	−14.7782	+	25.5965i	−0.488819	+	0.846659i
$915$		0			0
$916$		0			0
$917$	−3.76127	+	27.4853i	−0.124208	+	0.907644i
$918$		−	8.82843i		−	0.291382i
$919$	−23.3284	−	40.4060i	−0.769534	−	1.33287i	−0.937816	−	0.347133i	$-0.887155\pi$
$919$	−23.3284	−	40.4060i	−0.769534	−	1.33287i	0.168282	−	0.985739i	$-0.446178\pi$
$920$		0			0
$921$	0.792893	−	1.37333i	0.0261267	−	0.0452528i
$922$	−33.1552	+	19.1421i	−1.09191	+	0.630413i
$923$		−	5.41421i		−	0.178211i
$924$		0			0
$925$		0			0
$926$	7.36396	+	12.7548i	0.241995	+	0.419147i
$927$	1.07616	+	0.621320i	0.0353457	+	0.0204068i
$928$		0			0
$929$	−25.5061	−	44.1779i	−0.836828	−	1.44943i	−0.892533	−	0.450981i	$-0.851074\pi$
$929$	−25.5061	−	44.1779i	−0.836828	−	1.44943i	0.0557056	−	0.998447i	$-0.482259\pi$
$930$		0			0
$931$	33.2843	−	32.6118i	1.09085	−	1.06881i
$932$		0			0
$933$	−14.7840	+	8.53553i	−0.484006	+	0.279441i
$934$	4.72792	−	8.18900i	0.154702	−	0.267952i
$935$		0			0
$936$	−2.24264	−	3.88437i	−0.0733030	−	0.126965i
$937$		−	7.92893i		−	0.259027i	−0.991578	−	0.129513i	$-0.958658\pi$
$937$		−	7.92893i		−	0.259027i	0.991578	−	0.129513i	$-0.0413415\pi$
$938$	−34.6771	−	26.8909i	−1.13225	−	0.878018i
$939$	26.2132			0.855436
$940$		0			0
$941$	5.63604	−	9.76191i	0.183730	−	0.318229i	−0.759418	−	0.650603i	$-0.774516\pi$
$941$	5.63604	−	9.76191i	0.183730	−	0.318229i	0.943148	+	0.332374i	$0.107850\pi$
$942$	−19.7700	−	11.4142i	−0.644141	−	0.371895i
$943$	12.1244	−	7.00000i	0.394823	−	0.227951i
$944$	5.65685			0.184115
$945$		0			0
$946$	−50.2843			−1.63488
$947$	−4.26858	+	2.46447i	−0.138710	+	0.0800844i	−0.567749	−	0.823202i	$-0.692186\pi$
$947$	−4.26858	+	2.46447i	−0.138710	+	0.0800844i	0.429039	+	0.903286i	$0.358852\pi$
$948$		0			0
$949$	−1.64214	+	2.84426i	−0.0533060	+	0.0923287i
$950$		0			0
$951$	−0.100505			−0.00325910
$952$	−43.2503	+	17.6569i	−1.40175	+	0.572262i
$953$		−	48.4853i		−	1.57059i	−0.619120	−	0.785296i	$-0.712511\pi$
$953$		−	48.4853i		−	1.57059i	0.619120	−	0.785296i	$-0.287489\pi$
$954$	0.828427	+	1.43488i	0.0268213	+	0.0464559i
$955$		0			0
$956$		0			0
$957$	0.717439	−	0.414214i	0.0231915	−	0.0133896i
$958$			48.9706i			1.58217i
$959$	2.92893	+	7.17439i	0.0945802	+	0.231673i
$960$		0			0
$961$	15.4853	+	26.8213i	0.499525	+	0.865203i
$962$	−10.8486	−	6.26346i	−0.349774	−	0.201942i
$963$	13.3491	+	7.70711i	0.430169	+	0.248358i
$964$		0			0
$965$		0			0
$966$	−23.1421	−	3.16693i	−0.744586	−	0.101894i
$967$			23.3848i			0.752004i	0.926619	+	0.376002i	$0.122701\pi$
$967$			23.3848i			0.752004i	−0.926619	+	0.376002i	$0.877299\pi$
$968$	1.60896	−	0.928932i	0.0517139	−	0.0298570i
$969$	−20.7782	+	35.9889i	−0.667491	+	1.15613i
$970$		0			0
$971$	−7.17157	−	12.4215i	−0.230147	−	0.398626i	0.727704	−	0.685891i	$-0.240587\pi$
$971$	−7.17157	−	12.4215i	−0.230147	−	0.398626i	−0.957851	+	0.287265i	$0.907254\pi$
$972$		0			0
$973$	−24.0131	−	18.6213i	−0.769824	−	0.596972i
$974$	−1.27208			−0.0407600
$975$		0			0
$976$	24.9706	−	43.2503i	0.799288	−	1.38441i
$977$	−11.8632	−	6.84924i	−0.379539	−	0.219127i	0.298079	−	0.954541i	$-0.403654\pi$
$977$	−11.8632	−	6.84924i	−0.379539	−	0.219127i	−0.677617	+	0.735415i	$0.736987\pi$
$978$	−23.6544	+	13.6569i	−0.756383	+	0.436698i
$979$	12.8284			0.409998
$980$		0			0
$981$	−13.4853			−0.430552
$982$	−12.4215	+	7.17157i	−0.396387	+	0.228854i
$983$	46.0330	+	26.5772i	1.46822	+	0.847680i	0.999366	−	0.0355935i	$-0.0113322\pi$
$983$	46.0330	+	26.5772i	1.46822	+	0.847680i	0.468858	+	0.883273i	$0.344665\pi$
$984$	3.17157	−	5.49333i	0.101106	−	0.175121i
$985$		0			0
$986$	2.14214			0.0682195
$987$	−19.4728	−	15.1005i	−0.619827	−	0.480654i
$988$		0			0
$989$	32.5061	+	56.3022i	1.03363	+	1.79031i
$990$		0			0
$991$	15.3284	−	26.5496i	0.486924	−	0.843376i	−0.512963	−	0.858410i	$-0.671452\pi$
$991$	15.3284	−	26.5496i	0.486924	−	0.843376i	0.999887	+	0.0150341i	$0.00478570\pi$
$992$		0			0
$993$		−	27.6274i		−	0.876730i
$994$	−12.6569	−	1.73205i	−0.401451	−	0.0549373i
$995$		0			0
$996$		0			0
$997$	−0.655892	−	0.378680i	−0.0207723	−	0.0119929i	0.489578	−	0.871960i	$-0.337151\pi$
$997$	−0.655892	−	0.378680i	−0.0207723	−	0.0119929i	−0.510350	+	0.859967i	$0.670484\pi$
$998$	10.7765	+	6.22183i	0.341125	+	0.196948i
$999$	2.79289	+	4.83743i	0.0883632	+	0.153050i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.r.g.424.3		8
5.2	odd	4		525.2.i.g.151.2		4
5.3	odd	4		105.2.i.c.46.1	yes	4
5.4	even	2	inner	525.2.r.g.424.2		8
7.2	even	3	inner	525.2.r.g.499.2		8
15.8	even	4		315.2.j.d.46.2		4
20.3	even	4		1680.2.bg.p.1201.1		4
35.2	odd	12		525.2.i.g.226.2		4
35.3	even	12		735.2.a.j.1.2		2
35.9	even	6	inner	525.2.r.g.499.3		8
35.13	even	4		735.2.i.j.361.1		4
35.17	even	12		3675.2.a.x.1.1		2
35.18	odd	12		735.2.a.i.1.2		2
35.23	odd	12		105.2.i.c.16.1	✓	4
35.32	odd	12		3675.2.a.z.1.1		2
35.33	even	12		735.2.i.j.226.1		4
105.23	even	12		315.2.j.d.226.2		4
105.38	odd	12		2205.2.a.s.1.1		2
105.53	even	12		2205.2.a.u.1.1		2
140.23	even	12		1680.2.bg.p.961.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.c.16.1	✓	4	35.23	odd	12
105.2.i.c.46.1	yes	4	5.3	odd	4
315.2.j.d.46.2		4	15.8	even	4
315.2.j.d.226.2		4	105.23	even	12
525.2.i.g.151.2		4	5.2	odd	4
525.2.i.g.226.2		4	35.2	odd	12
525.2.r.g.424.2		8	5.4	even	2	inner
525.2.r.g.424.3		8	1.1	even	1	trivial
525.2.r.g.499.2		8	7.2	even	3	inner
525.2.r.g.499.3		8	35.9	even	6	inner
735.2.a.i.1.2		2	35.18	odd	12
735.2.a.j.1.2		2	35.3	even	12
735.2.i.j.226.1		4	35.33	even	12
735.2.i.j.361.1		4	35.13	even	4
1680.2.bg.p.961.1		4	140.23	even	12
1680.2.bg.p.1201.1		4	20.3	even	4
2205.2.a.s.1.1		2	105.38	odd	12
2205.2.a.u.1.1		2	105.53	even	12
3675.2.a.x.1.1		2	35.17	even	12
3675.2.a.z.1.1		2	35.32	odd	12

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.41421 q^{6} +(2.09077 + 1.62132i) q^{7} +2.82843i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 - 0.500000i) q^{3} -1.41421 q^{6} +(2.09077 + 1.62132i) q^{7} +2.82843i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.70711 + 2.95680i) q^{11} +1.58579i q^{13} +(3.70711 + 0.507306i) q^{14} +(2.00000 + 3.46410i) q^{16} +(5.40629 + 3.12132i) q^{17} +(1.22474 + 0.707107i) q^{18} +(-3.32843 - 5.76500i) q^{19} +(-1.00000 - 2.44949i) q^{21} +4.82843i q^{22} +(5.40629 - 3.12132i) q^{23} +(1.41421 - 2.44949i) q^{24} +(1.12132 + 1.94218i) q^{26} -1.00000i q^{27} +0.242641 q^{29} +(0.0857864 - 0.148586i) q^{31} +(2.95680 - 1.70711i) q^{33} +8.82843 q^{34} +(-4.83743 + 2.79289i) q^{37} +(-8.15295 - 4.70711i) q^{38} +(0.792893 - 1.37333i) q^{39} +2.24264 q^{41} +(-2.95680 - 2.29289i) q^{42} +10.4142i q^{43} +(4.41421 - 7.64564i) q^{46} +(8.06591 - 4.65685i) q^{47} -4.00000i q^{48} +(1.74264 + 6.77962i) q^{49} +(-3.12132 - 5.40629i) q^{51} +(1.01461 + 0.585786i) q^{53} +(-0.707107 - 1.22474i) q^{54} +(-4.58579 + 5.91359i) q^{56} +6.65685i q^{57} +(0.297173 - 0.171573i) q^{58} +(0.707107 - 1.22474i) q^{59} +(-6.24264 - 10.8126i) q^{61} -0.242641i q^{62} +(-0.358719 + 2.62132i) q^{63} -8.00000 q^{64} +(2.41421 - 4.18154i) q^{66} +(-10.1567 - 5.86396i) q^{67} -6.24264 q^{69} -3.41421 q^{71} +(-2.44949 + 1.41421i) q^{72} +(1.79360 + 1.03553i) q^{73} +(-3.94975 + 6.84116i) q^{74} +(-8.36308 + 3.41421i) q^{77} -2.24264i q^{78} +(-2.32843 - 4.03295i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.74666 - 1.58579i) q^{82} -5.41421i q^{83} +(7.36396 + 12.7548i) q^{86} +(-0.210133 - 0.121320i) q^{87} +(-8.36308 - 4.82843i) q^{88} +(-1.87868 - 3.25397i) q^{89} +(-2.57107 + 3.31552i) q^{91} +(-0.148586 + 0.0857864i) q^{93} +(6.58579 - 11.4069i) q^{94} -10.8284i q^{97} +(6.92820 + 7.07107i) q^{98} -3.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^9	\( 8 q + 4 q^{9} - 8 q^{11} + 24 q^{14} + 16 q^{16} - 4 q^{19} - 8 q^{21} - 8 q^{26} - 32 q^{29} + 12 q^{31} + 48 q^{34} + 12 q^{39} - 16 q^{41} + 24 q^{46} - 20 q^{49} - 8 q^{51} - 48 q^{56} - 16 q^{61} - 64 q^{64} + 8 q^{66} - 16 q^{69} - 16 q^{71} + 8 q^{74} + 4 q^{79} - 4 q^{81} + 8 q^{86} - 32 q^{89} + 36 q^{91} + 64 q^{94} - 16 q^{99}+O(q^{100}) \) 8 * q + 4 * q^9 - 8 * q^11 + 24 * q^14 + 16 * q^16 - 4 * q^19 - 8 * q^21 - 8 * q^26 - 32 * q^29 + 12 * q^31 + 48 * q^34 + 12 * q^39 - 16 * q^41 + 24 * q^46 - 20 * q^49 - 8 * q^51 - 48 * q^56 - 16 * q^61 - 64 * q^64 + 8 * q^66 - 16 * q^69 - 16 * q^71 + 8 * q^74 + 4 * q^79 - 4 * q^81 + 8 * q^86 - 32 * q^89 + 36 * q^91 + 64 * q^94 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more