LMFDB - Embedded newform 525.2.i.g.226.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(151,525)]

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, 0, 4]))

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

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

chi := DirichletCharacter("525.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.i (of order $3$, degree $2$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	525.226
Dual form			525.2.i.g.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

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

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 $

$2$	0.707107	−	1.22474i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$2$	0.707107	−	1.22474i	0.500000	−	0.866025i	1.00000			$0$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$		0			0
$5$		0			0
$6$	−1.41421			−0.577350
$7$	−1.62132	−	2.09077i	−0.612801	−	0.790237i
$7$	−1.62132	−	2.09077i	−0.612801	−	0.790237i
$8$	2.82843			1.00000
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−1.70711	−	2.95680i	−0.514712	−	0.891507i	−0.999854	−	0.0170722i	$-0.994565\pi$
$11$	−1.70711	−	2.95680i	−0.514712	−	0.891507i	0.485142	−	0.874435i	$-0.338768\pi$
$12$		0			0
$13$	1.58579			0.439818			0.219909	−	0.975520i	$-0.429424\pi$
$13$	1.58579			0.439818			0.219909	+	0.975520i	$0.429424\pi$
$14$	−3.70711	+	0.507306i	−0.990766	+	0.135583i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−3.12132	−	5.40629i	−0.757031	−	1.31122i	−0.944358	−	0.328919i	$-0.893316\pi$
$17$	−3.12132	−	5.40629i	−0.757031	−	1.31122i	0.187327	−	0.982298i	$-0.440018\pi$
$18$	0.707107	+	1.22474i	0.166667	+	0.288675i
$19$	3.32843	−	5.76500i	0.763594	−	1.32258i	−0.177393	−	0.984140i	$-0.556767\pi$
$19$	3.32843	−	5.76500i	0.763594	−	1.32258i	0.940987	−	0.338443i	$-0.109900\pi$
$20$		0			0
$21$	−1.00000	+	2.44949i	−0.218218	+	0.534522i
$22$	−4.82843			−1.02942
$23$	−3.12132	+	5.40629i	−0.650840	+	1.12729i	0.332079	+	0.943252i	$0.392250\pi$
$23$	−3.12132	+	5.40629i	−0.650840	+	1.12729i	−0.982919	+	0.184037i	$0.941083\pi$
$24$	−1.41421	−	2.44949i	−0.288675	−	0.500000i
$25$		0			0
$26$	1.12132	−	1.94218i	0.219909	−	0.380894i
$27$	1.00000			0.192450
$28$		0			0
$29$	−0.242641			−0.0450572			−0.0225286	−	0.999746i	$-0.507172\pi$
$29$	−0.242641			−0.0450572			−0.0225286	+	0.999746i	$0.507172\pi$
$30$		0			0
$31$	0.0857864	+	0.148586i	0.0154077	+	0.0266869i	0.873626	−	0.486597i	$-0.161762\pi$
$31$	0.0857864	+	0.148586i	0.0154077	+	0.0266869i	−0.858219	+	0.513284i	$0.828429\pi$
$32$		0			0
$33$	−1.70711	+	2.95680i	−0.297169	+	0.514712i
$34$	−8.82843			−1.51406
$35$		0			0
$36$		0			0
$37$	−2.79289	+	4.83743i	−0.459149	+	0.795269i	−0.998916	−	0.0465451i	$-0.985179\pi$
$37$	−2.79289	+	4.83743i	−0.459149	+	0.795269i	0.539767	+	0.841814i	$0.318512\pi$
$38$	−4.70711	−	8.15295i	−0.763594	−	1.32258i
$39$	−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	$0.443968\pi$
$42$	2.29289	+	2.95680i	0.353801	+	0.456243i
$43$	10.4142			1.58815			0.794076	−	0.607818i	$-0.207955\pi$
$43$	10.4142			1.58815			0.794076	+	0.607818i	$0.207955\pi$
$44$		0			0
$45$		0			0
$46$	4.41421	+	7.64564i	0.650840	+	1.12729i
$47$	4.65685	−	8.06591i	0.679272	−	1.17653i	−0.295928	−	0.955210i	$-0.595629\pi$
$47$	4.65685	−	8.06591i	0.679272	−	1.17653i	0.975200	−	0.221324i	$-0.0710377\pi$
$48$	−4.00000			−0.577350
$49$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$50$		0			0
$51$	−3.12132	+	5.40629i	−0.437072	+	0.757031i
$52$		0			0
$53$	0.585786	+	1.01461i	0.0804640	+	0.139368i	0.903449	−	0.428695i	$-0.141026\pi$
$53$	0.585786	+	1.01461i	0.0804640	+	0.139368i	−0.822985	+	0.568063i	$0.807693\pi$
$54$	0.707107	−	1.22474i	0.0962250	−	0.166667i
$55$		0			0
$56$	−4.58579	−	5.91359i	−0.612801	−	0.790237i
$57$	−6.65685			−0.881722
$58$	−0.171573	+	0.297173i	−0.0225286	+	0.0390207i
$59$	−0.707107	−	1.22474i	−0.0920575	−	0.159448i	0.816319	−	0.577601i	$-0.196011\pi$
$59$	−0.707107	−	1.22474i	−0.0920575	−	0.159448i	−0.908377	+	0.418153i	$0.862678\pi$
$60$		0			0
$61$	−6.24264	+	10.8126i	−0.799288	+	1.38441i	0.120792	+	0.992678i	$0.461457\pi$
$61$	−6.24264	+	10.8126i	−0.799288	+	1.38441i	−0.920080	+	0.391730i	$0.871877\pi$
$62$	0.242641			0.0308154
$63$	2.62132	−	0.358719i	0.330255	−	0.0451944i
$64$	8.00000			1.00000
$65$		0			0
$66$	2.41421	+	4.18154i	0.297169	+	0.514712i
$67$	5.86396	+	10.1567i	0.716397	+	1.24084i	0.962418	+	0.271571i	$0.0875433\pi$
$67$	5.86396	+	10.1567i	0.716397	+	1.24084i	−0.246021	+	0.969264i	$0.579123\pi$
$68$		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	$0.564938\pi$
$72$	−1.41421	+	2.44949i	−0.166667	+	0.288675i
$73$	1.03553	+	1.79360i	0.121200	+	0.209925i	0.920241	−	0.391352i	$-0.127992\pi$
$73$	1.03553	+	1.79360i	0.121200	+	0.209925i	−0.799041	+	0.601276i	$0.794659\pi$
$74$	3.94975	+	6.84116i	0.459149	+	0.795269i
$75$		0			0
$76$		0			0
$77$	−3.41421	+	8.36308i	−0.389086	+	0.953062i
$78$	−2.24264			−0.253929
$79$	2.32843	−	4.03295i	0.261969	−	0.453743i	−0.704796	−	0.709410i	$-0.748962\pi$
$79$	2.32843	−	4.03295i	0.261969	−	0.453743i	0.966765	+	0.255667i	$0.0822950\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.58579	−	2.74666i	0.175121	−	0.303318i
$83$	−5.41421			−0.594287			−0.297144	−	0.954833i	$-0.596034\pi$
$83$	−5.41421			−0.594287			−0.297144	+	0.954833i	$0.596034\pi$
$84$		0			0
$85$		0			0
$86$	7.36396	−	12.7548i	0.794076	−	1.37538i
$87$	0.121320	+	0.210133i	0.0130069	+	0.0225286i
$88$	−4.82843	−	8.36308i	−0.514712	−	0.891507i
$89$	1.87868	−	3.25397i	0.199140	−	0.344920i	−0.749110	−	0.662446i	$-0.769519\pi$
$89$	1.87868	−	3.25397i	0.199140	−	0.344920i	0.948250	+	0.317526i	$0.102852\pi$
$90$		0			0
$91$	−2.57107	−	3.31552i	−0.269521	−	0.347560i
$92$		0			0
$93$	0.0857864	−	0.148586i	0.00889564	−	0.0154077i
$94$	−6.58579	−	11.4069i	−0.679272	−	1.17653i
$95$		0			0
$96$		0			0
$97$	10.8284			1.09946			0.549730	−	0.835342i	$-0.314731\pi$
$97$	10.8284			1.09946			0.549730	+	0.835342i	$0.314731\pi$
$98$	7.07107	+	6.92820i	0.714286	+	0.699854i
$99$	3.41421			0.343141
$100$		0			0
$101$	3.12132	+	5.40629i	0.310583	+	0.537946i	0.978489	−	0.206300i	$-0.0661424\pi$
$101$	3.12132	+	5.40629i	0.310583	+	0.537946i	−0.667906	+	0.744246i	$0.732809\pi$
$102$	4.41421	+	7.64564i	0.437072	+	0.757031i
$103$	−0.621320	+	1.07616i	−0.0612205	+	0.106037i	−0.895011	−	0.446044i	$-0.852833\pi$
$103$	−0.621320	+	1.07616i	−0.0612205	+	0.106037i	0.833791	+	0.552081i	$0.186166\pi$
$104$	4.48528			0.439818
$105$		0			0
$106$	1.65685			0.160928
$107$	7.70711	−	13.3491i	0.745074	−	1.29051i	−0.205086	−	0.978744i	$-0.565747\pi$
$107$	7.70711	−	13.3491i	0.745074	−	1.29051i	0.950160	−	0.311762i	$-0.100919\pi$
$108$		0			0
$109$	6.74264	+	11.6786i	0.645828	+	1.11861i	0.984110	+	0.177562i	$0.0568210\pi$
$109$	6.74264	+	11.6786i	0.645828	+	1.11861i	−0.338282	+	0.941045i	$0.609846\pi$
$110$		0			0
$111$	5.58579			0.530179
$112$	−10.4853	+	1.43488i	−0.990766	+	0.135583i
$113$	4.34315			0.408569			0.204284	−	0.978912i	$-0.434513\pi$
$113$	4.34315			0.408569			0.204284	+	0.978912i	$0.434513\pi$
$114$	−4.70711	+	8.15295i	−0.440861	+	0.763594i
$115$		0			0
$116$		0			0
$117$	−0.792893	+	1.37333i	−0.0733030	+	0.126965i
$118$	−2.00000			−0.184115
$119$	−6.24264	+	15.2913i	−0.572262	+	1.40175i
$120$		0			0
$121$	−0.328427	+	0.568852i	−0.0298570	+	0.0517139i
$122$	8.82843	+	15.2913i	0.799288	+	1.38441i
$123$	−1.12132	−	1.94218i	−0.101106	−	0.175121i
$124$		0			0
$125$		0			0
$126$	1.41421	−	3.46410i	0.125988	−	0.308607i
$127$	18.0711			1.60355			0.801774	−	0.597627i	$-0.203890\pi$
$127$	18.0711			1.60355			0.801774	+	0.597627i	$0.203890\pi$
$128$	5.65685	−	9.79796i	0.500000	−	0.866025i
$129$	−5.20711	−	9.01897i	−0.458460	−	0.794076i
$130$		0			0
$131$	5.24264	−	9.08052i	0.458052	−	0.793369i	−0.540806	−	0.841147i	$-0.681881\pi$
$131$	5.24264	−	9.08052i	0.458052	−	0.793369i	0.998858	+	0.0477784i	$0.0152141\pi$
$132$		0			0
$133$	−17.4497	+	2.38794i	−1.51308	+	0.207061i
$134$	16.5858			1.43279
$135$		0			0
$136$	−8.82843	−	15.2913i	−0.757031	−	1.31122i
$137$	−1.46447	−	2.53653i	−0.125118	−	0.216710i	0.796661	−	0.604426i	$-0.206598\pi$
$137$	−1.46447	−	2.53653i	−0.125118	−	0.216710i	−0.921779	+	0.387716i	$0.873264\pi$
$138$	4.41421	−	7.64564i	0.375763	−	0.650840i
$139$	11.4853			0.974169			0.487084	−	0.873355i	$-0.338060\pi$
$139$	11.4853			0.974169			0.487084	+	0.873355i	$0.338060\pi$
$140$		0			0
$141$	−9.31371			−0.784356
$142$	−2.41421	+	4.18154i	−0.202596	+	0.350907i
$143$	−2.70711	−	4.68885i	−0.226380	−	0.392101i
$144$	2.00000	+	3.46410i	0.166667	+	0.288675i
$145$		0			0
$146$	2.92893			0.242400
$147$	6.74264	−	1.88064i	0.556124	−	0.155112i
$148$		0			0
$149$	−8.82843	+	15.2913i	−0.723253	+	1.25271i	0.236436	+	0.971647i	$0.424021\pi$
$149$	−8.82843	+	15.2913i	−0.723253	+	1.25271i	−0.959689	+	0.281064i	$0.909313\pi$
$150$		0			0
$151$	3.24264	+	5.61642i	0.263882	+	0.457058i	0.967270	−	0.253749i	$-0.0816636\pi$
$151$	3.24264	+	5.61642i	0.263882	+	0.457058i	−0.703388	+	0.710806i	$0.748330\pi$
$152$	9.41421	−	16.3059i	0.763594	−	1.32258i
$153$	6.24264			0.504688
$154$	7.82843	+	10.0951i	0.630833	+	0.813489i
$155$		0			0
$156$		0			0
$157$	−8.07107	−	13.9795i	−0.644141	−	1.11569i	−0.984499	−	0.175390i	$-0.943882\pi$
$157$	−8.07107	−	13.9795i	−0.644141	−	1.11569i	0.340358	−	0.940296i	$-0.389452\pi$
$158$	−3.29289	−	5.70346i	−0.261969	−	0.453743i
$159$	0.585786	−	1.01461i	0.0464559	−	0.0804640i
$160$		0			0
$161$	16.3640	−	2.23936i	1.28966	−	0.176486i
$162$	−1.41421			−0.111111
$163$	−9.65685	+	16.7262i	−0.756383	+	1.31009i	0.188301	+	0.982111i	$0.439702\pi$
$163$	−9.65685	+	16.7262i	−0.756383	+	1.31009i	−0.944684	+	0.327983i	$0.893631\pi$
$164$		0			0
$165$		0			0
$166$	−3.82843	+	6.63103i	−0.297144	+	0.514668i
$167$	−11.7574			−0.909812			−0.454906	−	0.890540i	$-0.650327\pi$
$167$	−11.7574			−0.909812			−0.454906	+	0.890540i	$0.650327\pi$
$168$	−2.82843	+	6.92820i	−0.218218	+	0.534522i
$169$	−10.4853			−0.806560
$170$		0			0
$171$	3.32843	+	5.76500i	0.254531	+	0.440861i
$172$		0			0
$173$	−1.41421	+	2.44949i	−0.107521	+	0.186231i	−0.914765	−	0.403986i	$-0.867625\pi$
$173$	−1.41421	+	2.44949i	−0.107521	+	0.186231i	0.807245	+	0.590217i	$0.200958\pi$
$174$	0.343146			0.0260138
$175$		0			0
$176$	−13.6569			−1.02942
$177$	−0.707107	+	1.22474i	−0.0531494	+	0.0920575i
$178$	−2.65685	−	4.60181i	−0.199140	−	0.344920i
$179$	−9.82843	−	17.0233i	−0.734611	−	1.27238i	−0.954894	−	0.296948i	$-0.904031\pi$
$179$	−9.82843	−	17.0233i	−0.734611	−	1.27238i	0.220283	−	0.975436i	$-0.429302\pi$
$180$		0			0
$181$	0.656854			0.0488236			0.0244118	−	0.999702i	$-0.492229\pi$
$181$	0.656854			0.0488236			0.0244118	+	0.999702i	$0.492229\pi$
$182$	−5.87868	+	0.804479i	−0.435757	+	0.0596319i
$183$	12.4853			0.922939
$184$	−8.82843	+	15.2913i	−0.650840	+	1.12729i
$185$		0			0
$186$	−0.121320	−	0.210133i	−0.00889564	−	0.0154077i
$187$	−10.6569	+	18.4582i	−0.779306	+	1.34980i
$188$		0			0
$189$	−1.62132	−	2.09077i	−0.117934	−	0.152081i
$190$		0			0
$191$	−9.48528	+	16.4290i	−0.686331	+	1.18876i	0.286686	+	0.958025i	$0.407446\pi$
$191$	−9.48528	+	16.4290i	−0.686331	+	1.18876i	−0.973017	+	0.230735i	$0.925887\pi$
$192$	−4.00000	−	6.92820i	−0.288675	−	0.500000i
$193$	−3.37868	−	5.85204i	−0.243203	−	0.421239i	0.718422	−	0.695607i	$-0.244865\pi$
$193$	−3.37868	−	5.85204i	−0.243203	−	0.421239i	−0.961625	+	0.274368i	$0.911531\pi$
$194$	7.65685	−	13.2621i	0.549730	−	0.952160i
$195$		0			0
$196$		0			0
$197$	−5.55635			−0.395873			−0.197937	−	0.980215i	$-0.563424\pi$
$197$	−5.55635			−0.395873			−0.197937	+	0.980215i	$0.563424\pi$
$198$	2.41421	−	4.18154i	0.171571	−	0.297169i
$199$	−2.75736	−	4.77589i	−0.195464	−	0.338554i	0.751589	−	0.659632i	$-0.229288\pi$
$199$	−2.75736	−	4.77589i	−0.195464	−	0.338554i	−0.947053	+	0.321079i	$0.895955\pi$
$200$		0			0
$201$	5.86396	−	10.1567i	0.413612	−	0.716397i
$202$	8.82843			0.621166
$203$	0.393398	+	0.507306i	0.0276111	+	0.0356059i
$204$		0			0
$205$		0			0
$206$	0.878680	+	1.52192i	0.0612205	+	0.106037i
$207$	−3.12132	−	5.40629i	−0.216947	−	0.375763i
$208$	3.17157	−	5.49333i	0.219909	−	0.380894i
$209$	−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
$213$	1.70711	+	2.95680i	0.116969	+	0.202596i
$214$	−10.8995	−	18.8785i	−0.745074	−	1.29051i
$215$		0			0
$216$	2.82843			0.192450
$217$	0.171573	−	0.420266i	0.0116471	−	0.0285295i
$218$	19.0711			1.29166
$219$	1.03553	−	1.79360i	0.0699749	−	0.121200i
$220$		0			0
$221$	−4.94975	−	8.57321i	−0.332956	−	0.576697i
$222$	3.94975	−	6.84116i	0.265090	−	0.459149i
$223$	−17.1716			−1.14989			−0.574947	−	0.818191i	$-0.694977\pi$
$223$	−17.1716			−1.14989			−0.574947	+	0.818191i	$0.694977\pi$
$224$		0			0
$225$		0			0
$226$	3.07107	−	5.31925i	0.204284	−	0.353831i
$227$	11.5355	+	19.9801i	0.765640	+	1.32613i	0.939907	+	0.341429i	$0.110911\pi$
$227$	11.5355	+	19.9801i	0.765640	+	1.32613i	−0.174267	+	0.984698i	$0.555756\pi$
$228$		0			0
$229$	7.15685	−	12.3960i	0.472938	−	0.819153i	−0.526582	−	0.850124i	$-0.676527\pi$
$229$	7.15685	−	12.3960i	0.472938	−	0.819153i	0.999520	+	0.0309713i	$0.00986003\pi$
$230$		0			0
$231$	8.94975	−	1.22474i	0.588850	−	0.0805823i
$232$	−0.686292			−0.0450572
$233$	−11.2426	+	19.4728i	−0.736530	+	1.27571i	0.217519	+	0.976056i	$0.430204\pi$
$233$	−11.2426	+	19.4728i	−0.736530	+	1.27571i	−0.954049	+	0.299651i	$0.903130\pi$
$234$	1.12132	+	1.94218i	0.0733030	+	0.126965i
$235$		0			0
$236$		0			0
$237$	−4.65685			−0.302495
$238$	14.3137	+	18.4582i	0.927820	+	1.19647i
$239$	17.3137			1.11993			0.559965	−	0.828516i	$-0.310814\pi$
$239$	17.3137			1.11993			0.559965	+	0.828516i	$0.310814\pi$
$240$		0			0
$241$	5.17157	+	8.95743i	0.333130	+	0.576999i	0.983124	−	0.182941i	$-0.0585618\pi$
$241$	5.17157	+	8.95743i	0.333130	+	0.576999i	−0.649994	+	0.759940i	$0.725228\pi$
$242$	0.464466	+	0.804479i	0.0298570	+	0.0517139i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$		0			0
$246$	−3.17157			−0.202212
$247$	5.27817	−	9.14207i	0.335842	−	0.581696i
$248$	0.242641	+	0.420266i	0.0154077	+	0.0266869i
$249$	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
$253$	21.3137			1.33998
$254$	12.7782	−	22.1324i	0.801774	−	1.38871i
$255$		0			0
$256$		0			0
$257$	−14.9497	+	25.8937i	−0.932540	+	1.61521i	−0.153576	+	0.988137i	$0.549079\pi$
$257$	−14.9497	+	25.8937i	−0.932540	+	1.61521i	−0.778964	+	0.627069i	$0.784254\pi$
$258$	−14.7279			−0.916920
$259$	14.6421	−	2.00373i	0.909818	−	0.124506i
$260$		0			0
$261$	0.121320	−	0.210133i	0.00750954	−	0.0130069i
$262$	−7.41421	−	12.8418i	−0.458052	−	0.793369i
$263$	0.585786	+	1.01461i	0.0361211	+	0.0625636i	0.883521	−	0.468392i	$-0.155166\pi$
$263$	0.585786	+	1.01461i	0.0361211	+	0.0625636i	−0.847400	+	0.530956i	$0.821833\pi$
$264$	−4.82843	+	8.36308i	−0.297169	+	0.514712i
$265$		0			0
$266$	−9.41421	+	23.0600i	−0.577222	+	1.41390i
$267$	−3.75736			−0.229947
$268$		0			0
$269$	−4.07107	−	7.05130i	−0.248217	−	0.429925i	0.714814	−	0.699315i	$-0.246511\pi$
$269$	−4.07107	−	7.05130i	−0.248217	−	0.429925i	−0.963031	+	0.269390i	$0.913178\pi$
$270$		0			0
$271$	−10.0711	+	17.4436i	−0.611774	+	1.05962i	0.379168	+	0.925328i	$0.376210\pi$
$271$	−10.0711	+	17.4436i	−0.611774	+	1.05962i	−0.990941	+	0.134295i	$0.957123\pi$
$272$	−24.9706			−1.51406
$273$	−1.58579	+	3.88437i	−0.0959762	+	0.235093i
$274$	−4.14214			−0.250236
$275$		0			0
$276$		0			0
$277$	−11.6924	−	20.2518i	−0.702528	−	1.21681i	−0.967576	−	0.252578i	$-0.918721\pi$
$277$	−11.6924	−	20.2518i	−0.702528	−	1.21681i	0.265049	−	0.964235i	$-0.414612\pi$
$278$	8.12132	−	14.0665i	0.487084	−	0.843655i
$279$	−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	$0.406996\pi$
$282$	−6.58579	+	11.4069i	−0.392178	+	0.679272i
$283$	−6.62132	−	11.4685i	−0.393597	−	0.681729i	0.599324	−	0.800506i	$-0.295436\pi$
$283$	−6.62132	−	11.4685i	−0.393597	−	0.681729i	−0.992921	+	0.118777i	$0.962103\pi$
$284$		0			0
$285$		0			0
$286$	−7.65685			−0.452759
$287$	−3.63604	−	4.68885i	−0.214629	−	0.276774i
$288$		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
$293$	15.3137			0.894636			0.447318	−	0.894375i	$-0.352379\pi$
$293$	15.3137			0.894636			0.447318	+	0.894375i	$0.352379\pi$
$294$	2.46447	−	9.58783i	0.143731	−	0.559173i
$295$		0			0
$296$	−7.89949	+	13.6823i	−0.459149	+	0.795269i
$297$	−1.70711	−	2.95680i	−0.0990564	−	0.171571i
$298$	12.4853	+	21.6251i	0.723253	+	1.25271i
$299$	−4.94975	+	8.57321i	−0.286251	+	0.495802i
$300$		0			0
$301$	−16.8848	−	21.7737i	−0.973222	−	1.25502i
$302$	9.17157			0.527765
$303$	3.12132	−	5.40629i	0.179315	−	0.310583i
$304$	−13.3137	−	23.0600i	−0.763594	−	1.32258i
$305$		0			0
$306$	4.41421	−	7.64564i	0.252344	−	0.437072i
$307$	−1.58579			−0.0905056			−0.0452528	−	0.998976i	$-0.514409\pi$
$307$	−1.58579			−0.0905056			−0.0452528	+	0.998976i	$0.514409\pi$
$308$		0			0
$309$	1.24264			0.0706914
$310$		0			0
$311$	8.53553	+	14.7840i	0.484006	+	0.838323i	0.999831	−	0.0183712i	$-0.00584805\pi$
$311$	8.53553	+	14.7840i	0.484006	+	0.838323i	−0.515826	+	0.856694i	$0.672515\pi$
$312$	−2.24264	−	3.88437i	−0.126965	−	0.219909i
$313$	13.1066	−	22.7013i	0.740829	−	1.28315i	−0.211289	−	0.977424i	$-0.567766\pi$
$313$	13.1066	−	22.7013i	0.740829	−	1.28315i	0.952118	−	0.305730i	$-0.0989004\pi$
$314$	−22.8284			−1.28828
$315$		0			0
$316$		0			0
$317$	0.0502525	−	0.0870399i	0.00282246	−	0.00488865i	−0.864611	−	0.502442i	$-0.832435\pi$
$317$	0.0502525	−	0.0870399i	0.00282246	−	0.00488865i	0.867433	+	0.497554i	$0.165768\pi$
$318$	−0.828427	−	1.43488i	−0.0464559	−	0.0804640i
$319$	0.414214	+	0.717439i	0.0231915	+	0.0401689i
$320$		0			0
$321$	−15.4142			−0.860338
$322$	8.82843	−	21.6251i	0.491989	−	1.20512i
$323$	−41.5563			−2.31226
$324$		0			0
$325$		0			0
$326$	13.6569	+	23.6544i	0.756383	+	1.31009i
$327$	6.74264	−	11.6786i	0.372869	−	0.645828i
$328$	6.34315			0.350242
$329$	−24.4142	+	3.34101i	−1.34600	+	0.184196i
$330$		0			0
$331$	13.8137	−	23.9260i	0.759270	−	1.31509i	−0.183953	−	0.982935i	$-0.558889\pi$
$331$	13.8137	−	23.9260i	0.759270	−	1.31509i	0.943223	−	0.332159i	$-0.107777\pi$
$332$		0			0
$333$	−2.79289	−	4.83743i	−0.153050	−	0.265090i
$334$	−8.31371	+	14.3998i	−0.454906	+	0.787920i
$335$		0			0
$336$	6.48528	+	8.36308i	0.353801	+	0.456243i
$337$	0.899495			0.0489986			0.0244993	−	0.999700i	$-0.492201\pi$
$337$	0.899495			0.0489986			0.0244993	+	0.999700i	$0.492201\pi$
$338$	−7.41421	+	12.8418i	−0.403280	+	0.698502i
$339$	−2.17157	−	3.76127i	−0.117944	−	0.204284i
$340$		0			0
$341$	0.292893	−	0.507306i	0.0158611	−	0.0274722i
$342$	9.41421			0.509062
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$	29.4558			1.58815
$345$		0			0
$346$	2.00000	+	3.46410i	0.107521	+	0.186231i
$347$	−12.4853	−	21.6251i	−0.670245	−	1.16090i	−0.977835	−	0.209379i	$-0.932856\pi$
$347$	−12.4853	−	21.6251i	−0.670245	−	1.16090i	0.307589	−	0.951519i	$-0.400478\pi$
$348$		0			0
$349$	−16.6274			−0.890045			−0.445023	−	0.895519i	$-0.646804\pi$
$349$	−16.6274			−0.890045			−0.445023	+	0.895519i	$0.646804\pi$
$350$		0			0
$351$	1.58579			0.0846430
$352$		0			0
$353$	2.94975	+	5.10911i	0.156999	+	0.271931i	0.933785	−	0.357834i	$-0.116485\pi$
$353$	2.94975	+	5.10911i	0.156999	+	0.271931i	−0.776786	+	0.629765i	$0.783151\pi$
$354$	1.00000	+	1.73205i	0.0531494	+	0.0920575i
$355$		0			0
$356$		0			0
$357$	16.3640	−	2.23936i	0.866073	−	0.118519i
$358$	−27.7990			−1.46922
$359$	13.2929	−	23.0240i	0.701572	−	1.21516i	−0.266342	−	0.963878i	$-0.585815\pi$
$359$	13.2929	−	23.0240i	0.701572	−	1.21516i	0.967914	−	0.251280i	$-0.0808515\pi$
$360$		0			0
$361$	−12.6569	−	21.9223i	−0.666150	−	1.15381i
$362$	0.464466	−	0.804479i	0.0244118	−	0.0422825i
$363$	0.656854			0.0344759
$364$		0			0
$365$		0			0
$366$	8.82843	−	15.2913i	0.461469	−	0.799288i
$367$	−9.79289	−	16.9618i	−0.511185	−	0.885398i	−0.999916	−	0.0129637i	$-0.995873\pi$
$367$	−9.79289	−	16.9618i	−0.511185	−	0.885398i	0.488731	−	0.872434i	$-0.337460\pi$
$368$	12.4853	+	21.6251i	0.650840	+	1.12729i
$369$	−1.12132	+	1.94218i	−0.0583736	+	0.101106i
$370$		0			0
$371$	1.17157	−	2.86976i	0.0608250	−	0.148990i
$372$		0			0
$373$	9.62132	−	16.6646i	0.498173	−	0.862861i	−0.501825	−	0.864969i	$-0.667338\pi$
$373$	9.62132	−	16.6646i	0.498173	−	0.862861i	0.999998	+	0.00210826i	$0.000671080\pi$
$374$	15.0711	+	26.1039i	0.779306	+	1.34980i
$375$		0			0
$376$	13.1716	−	22.8138i	0.679272	−	1.17653i
$377$	−0.384776			−0.0198170
$378$	−3.70711	+	0.507306i	−0.190673	+	0.0260930i
$379$	14.7990			0.760173			0.380087	−	0.924951i	$-0.375894\pi$
$379$	14.7990			0.760173			0.380087	+	0.924951i	$0.375894\pi$
$380$		0			0
$381$	−9.03553	−	15.6500i	−0.462904	−	0.801774i
$382$	13.4142	+	23.2341i	0.686331	+	1.18876i
$383$	6.24264	−	10.8126i	0.318984	−	0.552497i	−0.661292	−	0.750128i	$-0.729992\pi$
$383$	6.24264	−	10.8126i	0.318984	−	0.552497i	0.980276	+	0.197632i	$0.0633250\pi$
$384$	−11.3137			−0.577350
$385$		0			0
$386$	−9.55635			−0.486405
$387$	−5.20711	+	9.01897i	−0.264692	+	0.458460i
$388$		0			0
$389$	−8.43503	−	14.6099i	−0.427673	−	0.740751i	0.568993	−	0.822342i	$-0.307333\pi$
$389$	−8.43503	−	14.6099i	−0.427673	−	0.740751i	−0.996666	+	0.0815911i	$0.974000\pi$
$390$		0			0
$391$	38.9706			1.97083
$392$	−4.92893	+	19.1757i	−0.248949	+	0.968517i
$393$	−10.4853			−0.528912
$394$	−3.92893	+	6.80511i	−0.197937	+	0.342836i
$395$		0			0
$396$		0			0
$397$	−12.1066	+	20.9692i	−0.607613	+	1.05242i	0.384020	+	0.923325i	$0.374539\pi$
$397$	−12.1066	+	20.9692i	−0.607613	+	1.05242i	−0.991633	+	0.129092i	$0.958794\pi$
$398$	−7.79899			−0.390928
$399$	10.7929	+	13.9180i	0.540320	+	0.696769i
$400$		0			0
$401$	−0.242641	+	0.420266i	−0.0121169	+	0.0209871i	−0.872020	−	0.489470i	$-0.837190\pi$
$401$	−0.242641	+	0.420266i	−0.0121169	+	0.0209871i	0.859903	+	0.510457i	$0.170524\pi$
$402$	−8.29289	−	14.3637i	−0.413612	−	0.716397i
$403$	0.136039	+	0.235626i	0.00677658	+	0.0117374i
$404$		0			0
$405$		0			0
$406$	0.899495	−	0.123093i	0.0446412	−	0.00610901i
$407$	19.0711			0.945318
$408$	−8.82843	+	15.2913i	−0.437072	+	0.757031i
$409$	13.1569	+	22.7883i	0.650565	+	1.12681i	0.982986	+	0.183680i	$0.0588010\pi$
$409$	13.1569	+	22.7883i	0.650565	+	1.12681i	−0.332422	+	0.943131i	$0.607866\pi$
$410$		0			0
$411$	−1.46447	+	2.53653i	−0.0722368	+	0.125118i
$412$		0			0
$413$	−1.41421	+	3.46410i	−0.0695889	+	0.170457i
$414$	−8.82843			−0.433894
$415$		0			0
$416$		0			0
$417$	−5.74264	−	9.94655i	−0.281218	−	0.487084i
$418$	−16.0711	+	27.8359i	−0.786062	+	1.36150i
$419$	−3.17157			−0.154941			−0.0774707	−	0.996995i	$-0.524684\pi$
$419$	−3.17157			−0.154941			−0.0774707	+	0.996995i	$0.524684\pi$
$420$		0			0
$421$	27.4853			1.33955			0.669775	−	0.742564i	$-0.266390\pi$
$421$	27.4853			1.33955			0.669775	+	0.742564i	$0.266390\pi$
$422$	0.100505	−	0.174080i	0.00489251	−	0.00847408i
$423$	4.65685	+	8.06591i	0.226424	+	0.392178i
$424$	1.65685	+	2.86976i	0.0804640	+	0.139368i
$425$		0			0
$426$	4.82843			0.233938
$427$	32.7279	−	4.47871i	1.58382	−	0.216740i
$428$		0			0
$429$	−2.70711	+	4.68885i	−0.130700	+	0.226380i
$430$		0			0
$431$	−18.4142	−	31.8944i	−0.886981	−	1.53630i	−0.843426	−	0.537246i	$-0.819465\pi$
$431$	−18.4142	−	31.8944i	−0.886981	−	1.53630i	−0.0435558	−	0.999051i	$-0.513869\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	24.5563			1.18010			0.590051	−	0.807366i	$-0.299107\pi$
$433$	24.5563			1.18010			0.590051	+	0.807366i	$0.299107\pi$
$434$	−0.393398	−	0.507306i	−0.0188837	−	0.0243515i
$435$		0			0
$436$		0			0
$437$	20.7782	+	35.9889i	0.993955	+	1.72158i
$438$	−1.46447	−	2.53653i	−0.0699749	−	0.121200i
$439$	−0.171573	+	0.297173i	−0.00818873	+	0.0141833i	−0.870091	−	0.492892i	$-0.835940\pi$
$439$	−0.171573	+	0.297173i	−0.00818873	+	0.0141833i	0.861902	+	0.507075i	$0.169273\pi$
$440$		0			0
$441$	−5.00000	−	4.89898i	−0.238095	−	0.233285i
$442$	−14.0000			−0.665912
$443$	0.242641	−	0.420266i	0.0115282	−	0.0199674i	−0.860204	−	0.509950i	$-0.829664\pi$
$443$	0.242641	−	0.420266i	0.0115282	−	0.0199674i	0.871732	+	0.489983i	$0.162997\pi$
$444$		0			0
$445$		0			0
$446$	−12.1421	+	21.0308i	−0.574947	+	0.995837i
$447$	17.6569			0.835141
$448$	−12.9706	−	16.7262i	−0.612801	−	0.790237i
$449$	−6.97056			−0.328961			−0.164481	−	0.986380i	$-0.552595\pi$
$449$	−6.97056			−0.328961			−0.164481	+	0.986380i	$0.552595\pi$
$450$		0			0
$451$	−3.82843	−	6.63103i	−0.180274	−	0.312243i
$452$		0			0
$453$	3.24264	−	5.61642i	0.152353	−	0.263882i
$454$	32.6274			1.53128
$455$		0			0
$456$	−18.8284			−0.881722
$457$	−10.4497	+	18.0995i	−0.488819	+	0.846659i	−0.999917	−	0.0128634i	$-0.995905\pi$
$457$	−10.4497	+	18.0995i	−0.488819	+	0.846659i	0.511099	+	0.859522i	$0.329239\pi$
$458$	−10.1213	−	17.5306i	−0.472938	−	0.819153i
$459$	−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	$0.717114\pi$
$462$	4.82843	−	11.8272i	0.224639	−	0.550250i
$463$	10.4142			0.483990			0.241995	−	0.970278i	$-0.422198\pi$
$463$	10.4142			0.483990			0.241995	+	0.970278i	$0.422198\pi$
$464$	−0.485281	+	0.840532i	−0.0225286	+	0.0390207i
$465$		0			0
$466$	15.8995	+	27.5387i	0.736530	+	1.27571i
$467$	3.34315	−	5.79050i	0.154702	−	0.267952i	−0.778248	−	0.627957i	$-0.783891\pi$
$467$	3.34315	−	5.79050i	0.154702	−	0.267952i	0.932951	+	0.360004i	$0.117225\pi$
$468$		0			0
$469$	11.7279	−	28.7274i	0.541545	−	1.32651i
$470$		0			0
$471$	−8.07107	+	13.9795i	−0.371895	+	0.644141i
$472$	−2.00000	−	3.46410i	−0.0920575	−	0.159448i
$473$	−17.7782	−	30.7927i	−0.817441	−	1.41585i
$474$	−3.29289	+	5.70346i	−0.151248	+	0.261969i
$475$		0			0
$476$		0			0
$477$	−1.17157			−0.0536426
$478$	12.2426	−	21.2049i	0.559965	−	0.969888i
$479$	17.3137	+	29.9882i	0.791084	+	1.37020i	0.925297	+	0.379244i	$0.123816\pi$
$479$	17.3137	+	29.9882i	0.791084	+	1.37020i	−0.134213	+	0.990953i	$0.542851\pi$
$480$		0			0
$481$	−4.42893	+	7.67114i	−0.201942	+	0.349774i
$482$	14.6274			0.666261
$483$	−10.1213	−	13.0519i	−0.460536	−	0.593883i
$484$		0			0
$485$		0			0
$486$	0.707107	+	1.22474i	0.0320750	+	0.0555556i
$487$	0.449747	+	0.778985i	0.0203800	+	0.0352992i	0.876036	−	0.482247i	$-0.160179\pi$
$487$	0.449747	+	0.778985i	0.0203800	+	0.0352992i	−0.855656	+	0.517546i	$0.826846\pi$
$488$	−17.6569	+	30.5826i	−0.799288	+	1.38441i
$489$	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
$493$	0.757359	+	1.31178i	0.0341097	+	0.0590798i
$494$	−7.46447	−	12.9288i	−0.335842	−	0.581696i
$495$		0			0
$496$	0.686292			0.0308154
$497$	5.53553	+	7.13834i	0.248303	+	0.320198i
$498$	7.65685			0.343112
$499$	−4.39949	+	7.62015i	−0.196948	+	0.341125i	−0.947538	−	0.319645i	$-0.896436\pi$
$499$	−4.39949	+	7.62015i	−0.196948	+	0.341125i	0.750589	+	0.660769i	$0.229770\pi$
$500$		0			0
$501$	5.87868	+	10.1822i	0.262640	+	0.454906i
$502$	−3.82843	+	6.63103i	−0.170871	+	0.295957i
$503$	18.4853			0.824218			0.412109	−	0.911135i	$-0.364792\pi$
$503$	18.4853			0.824218			0.412109	+	0.911135i	$0.364792\pi$
$504$	7.41421	−	1.01461i	0.330255	−	0.0451944i
$505$		0			0
$506$	15.0711	−	26.1039i	0.669991	−	1.16046i
$507$	5.24264	+	9.08052i	0.232834	+	0.403280i
$508$		0			0
$509$	−6.89949	+	11.9503i	−0.305815	+	0.529687i	−0.977442	−	0.211202i	$-0.932262\pi$
$509$	−6.89949	+	11.9503i	−0.305815	+	0.529687i	0.671628	+	0.740889i	$0.265595\pi$
$510$		0			0
$511$	2.07107	−	5.07306i	0.0916186	−	0.224419i
$512$	22.6274			1.00000
$513$	3.32843	−	5.76500i	0.146954	−	0.254531i
$514$	21.1421	+	36.6193i	0.932540	+	1.61521i
$515$		0			0
$516$		0			0
$517$	−31.7990			−1.39852
$518$	7.89949	−	19.3497i	0.347084	−	0.850178i
$519$	2.82843			0.124154
$520$		0			0
$521$	19.5563	+	33.8726i	0.856779	+	1.48399i	0.874985	+	0.484151i	$0.160871\pi$
$521$	19.5563	+	33.8726i	0.856779	+	1.48399i	−0.0182053	+	0.999834i	$0.505795\pi$
$522$	−0.171573	−	0.297173i	−0.00750954	−	0.0130069i
$523$	−3.79289	+	6.56948i	−0.165852	+	0.287263i	−0.936957	−	0.349444i	$-0.886371\pi$
$523$	−3.79289	+	6.56948i	−0.165852	+	0.287263i	0.771106	+	0.636707i	$0.219704\pi$
$524$		0			0
$525$		0			0
$526$	1.65685			0.0722423
$527$	0.535534	−	0.927572i	0.0233282	−	0.0404057i
$528$	6.82843	+	11.8272i	0.297169	+	0.514712i
$529$	−7.98528	−	13.8309i	−0.347186	−	0.601344i
$530$		0			0
$531$	1.41421			0.0613716
$532$		0			0
$533$	3.55635			0.154043
$534$	−2.65685	+	4.60181i	−0.114973	+	0.199140i
$535$		0			0
$536$	16.5858	+	28.7274i	0.716397	+	1.24084i
$537$	−9.82843	+	17.0233i	−0.424128	+	0.734611i
$538$	−11.5147			−0.496435
$539$	23.0208	−	6.42090i	0.991577	−	0.276568i
$540$		0			0
$541$	−16.1569	+	27.9845i	−0.694637	+	1.20315i	0.275665	+	0.961254i	$0.411102\pi$
$541$	−16.1569	+	27.9845i	−0.694637	+	1.20315i	−0.970303	+	0.241894i	$0.922231\pi$
$542$	14.2426	+	24.6690i	0.611774	+	1.05962i
$543$	−0.328427	−	0.568852i	−0.0140942	−	0.0244118i
$544$		0			0
$545$		0			0
$546$	3.63604	+	4.68885i	0.155608	+	0.200664i
$547$	31.7990			1.35963			0.679813	−	0.733385i	$-0.262061\pi$
$547$	31.7990			1.35963			0.679813	+	0.733385i	$0.262061\pi$
$548$		0			0
$549$	−6.24264	−	10.8126i	−0.266429	−	0.461469i
$550$		0			0
$551$	−0.807612	+	1.39882i	−0.0344054	+	0.0595919i
$552$	17.6569			0.751526
$553$	−12.2071	+	1.67050i	−0.519099	+	0.0710371i
$554$	−33.0711			−1.40506
$555$		0			0
$556$		0			0
$557$	−4.17157	−	7.22538i	−0.176755	−	0.306149i	0.764012	−	0.645202i	$-0.223227\pi$
$557$	−4.17157	−	7.22538i	−0.176755	−	0.306149i	−0.940767	+	0.339053i	$0.889893\pi$
$558$	−0.121320	+	0.210133i	−0.00513590	+	0.00889564i
$559$	16.5147			0.698498
$560$		0			0
$561$	21.3137			0.899865
$562$	6.82843	−	11.8272i	0.288040	−	0.498900i
$563$	−7.14214	−	12.3705i	−0.301005	−	0.521356i	0.675359	−	0.737489i	$-0.263989\pi$
$563$	−7.14214	−	12.3705i	−0.301005	−	0.521356i	−0.976364	+	0.216133i	$0.930655\pi$
$564$		0			0
$565$		0			0
$566$	−18.7279			−0.787193
$567$	−1.00000	+	2.44949i	−0.0419961	+	0.102869i
$568$	−9.65685			−0.405193
$569$	18.4350	−	31.9304i	0.772837	−	1.33859i	−0.163166	−	0.986599i	$-0.552171\pi$
$569$	18.4350	−	31.9304i	0.772837	−	1.33859i	0.936002	−	0.351994i	$-0.114496\pi$
$570$		0			0
$571$	−13.9853	−	24.2232i	−0.585266	−	1.01371i	−0.994842	−	0.101434i	$-0.967657\pi$
$571$	−13.9853	−	24.2232i	−0.585266	−	1.01371i	0.409576	−	0.912276i	$-0.365677\pi$
$572$		0			0
$573$	18.9706			0.792507
$574$	−8.31371	+	1.13770i	−0.347007	+	0.0474869i
$575$		0			0
$576$	−4.00000	+	6.92820i	−0.166667	+	0.288675i
$577$	3.27817	+	5.67796i	0.136472	+	0.236377i	0.926159	−	0.377134i	$-0.123090\pi$
$577$	3.27817	+	5.67796i	0.136472	+	0.236377i	−0.789687	+	0.613510i	$0.789757\pi$
$578$	15.5355	+	26.9083i	0.646193	+	1.11924i
$579$	−3.37868	+	5.85204i	−0.140413	+	0.243203i
$580$		0			0
$581$	8.77817	+	11.3199i	0.364180	+	0.469628i
$582$	−15.3137			−0.634774
$583$	2.00000	−	3.46410i	0.0828315	−	0.143468i
$584$	2.92893	+	5.07306i	0.121200	+	0.209925i
$585$		0			0
$586$	10.8284	−	18.7554i	0.447318	−	0.774778i
$587$	−30.2426			−1.24825			−0.624124	−	0.781326i	$-0.714544\pi$
$587$	−30.2426			−1.24825			−0.624124	+	0.781326i	$0.714544\pi$
$588$		0			0
$589$	1.14214			0.0470609
$590$		0			0
$591$	2.77817	+	4.81194i	0.114279	+	0.197937i
$592$	11.1716	+	19.3497i	0.459149	+	0.795269i
$593$	6.70711	−	11.6170i	0.275428	−	0.477055i	−0.694815	−	0.719188i	$-0.744514\pi$
$593$	6.70711	−	11.6170i	0.275428	−	0.477055i	0.970243	+	0.242133i	$0.0778471\pi$
$594$	−4.82843			−0.198113
$595$		0			0
$596$		0			0
$597$	−2.75736	+	4.77589i	−0.112851	+	0.195464i
$598$	7.00000	+	12.1244i	0.286251	+	0.495802i
$599$	21.0711	+	36.4962i	0.860940	+	1.49119i	0.871022	+	0.491243i	$0.163457\pi$
$599$	21.0711	+	36.4962i	0.860940	+	1.49119i	−0.0100818	+	0.999949i	$0.503209\pi$
$600$		0			0
$601$	−24.1716			−0.985979			−0.492990	−	0.870035i	$-0.664096\pi$
$601$	−24.1716			−0.985979			−0.492990	+	0.870035i	$0.664096\pi$
$602$	−38.6066	+	5.28319i	−1.57349	+	0.215327i
$603$	−11.7279			−0.477598
$604$		0			0
$605$		0			0
$606$	−4.41421	−	7.64564i	−0.179315	−	0.310583i
$607$	−0.621320	+	1.07616i	−0.0252186	+	0.0436799i	−0.878359	−	0.478001i	$-0.841362\pi$
$607$	−0.621320	+	1.07616i	−0.0252186	+	0.0436799i	0.853141	+	0.521681i	$0.174695\pi$
$608$		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
$613$	5.07107	+	8.78335i	0.204818	+	0.354756i	0.950075	−	0.312022i	$-0.101006\pi$
$613$	5.07107	+	8.78335i	0.204818	+	0.354756i	−0.745256	+	0.666778i	$0.767673\pi$
$614$	−1.12132	+	1.94218i	−0.0452528	+	0.0783802i
$615$		0			0
$616$	−9.65685	+	23.6544i	−0.389086	+	0.953062i
$617$	8.82843			0.355419			0.177710	−	0.984083i	$-0.443131\pi$
$617$	8.82843			0.355419			0.177710	+	0.984083i	$0.443131\pi$
$618$	0.878680	−	1.52192i	0.0353457	−	0.0612205i
$619$	−19.9853	−	34.6155i	−0.803276	−	1.39132i	−0.917449	−	0.397854i	$-0.869755\pi$
$619$	−19.9853	−	34.6155i	−0.803276	−	1.39132i	0.114172	−	0.993461i	$-0.463578\pi$
$620$		0			0
$621$	−3.12132	+	5.40629i	−0.125254	+	0.216947i
$622$	24.1421			0.968011
$623$	−9.84924	+	1.34784i	−0.394602	+	0.0540000i
$624$	−6.34315			−0.253929
$625$		0			0
$626$	−18.5355	−	32.1045i	−0.740829	−	1.28315i
$627$	11.3640	+	19.6830i	0.453833	+	0.786062i
$628$		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	$0.396829\pi$
$632$	6.58579	−	11.4069i	0.261969	−	0.453743i
$633$	−0.0710678	−	0.123093i	−0.00282469	−	0.00489251i
$634$	−0.0710678	−	0.123093i	−0.00282246	−	0.00488865i
$635$		0			0
$636$		0			0
$637$	−2.76346	+	10.7510i	−0.109492	+	0.425971i
$638$	1.17157			0.0463830
$639$	1.70711	−	2.95680i	0.0675321	−	0.116969i
$640$		0			0
$641$	6.60660	+	11.4430i	0.260945	+	0.451970i	0.966493	−	0.256692i	$-0.0826325\pi$
$641$	6.60660	+	11.4430i	0.260945	+	0.451970i	−0.705548	+	0.708662i	$0.749299\pi$
$642$	−10.8995	+	18.8785i	−0.430169	+	0.745074i
$643$	−24.5563			−0.968408			−0.484204	−	0.874955i	$-0.660891\pi$
$643$	−24.5563			−0.968408			−0.484204	+	0.874955i	$0.660891\pi$
$644$		0			0
$645$		0			0
$646$	−29.3848	+	50.8959i	−1.15613	+	2.00247i
$647$	4.80761	+	8.32703i	0.189007	+	0.327369i	0.944919	−	0.327303i	$-0.106140\pi$
$647$	4.80761	+	8.32703i	0.189007	+	0.327369i	−0.755913	+	0.654673i	$0.772807\pi$
$648$	−1.41421	−	2.44949i	−0.0555556	−	0.0962250i
$649$	−2.41421	+	4.18154i	−0.0947662	+	0.164140i
$650$		0			0
$651$	−0.449747	+	0.0615465i	−0.0176270	+	0.00241220i
$652$		0			0
$653$	3.87868	−	6.71807i	0.151784	−	0.262898i	−0.780099	−	0.625656i	$-0.784831\pi$
$653$	3.87868	−	6.71807i	0.151784	−	0.262898i	0.931884	+	0.362758i	$0.118165\pi$
$654$	−9.53553	−	16.5160i	−0.372869	−	0.645828i
$655$		0			0
$656$	4.48528	−	7.76874i	0.175121	−	0.303318i
$657$	−2.07107			−0.0808001
$658$	−13.1716	+	32.2636i	−0.513481	+	1.25777i
$659$	−27.3137			−1.06399			−0.531996	−	0.846747i	$-0.678558\pi$
$659$	−27.3137			−1.06399			−0.531996	+	0.846747i	$0.678558\pi$
$660$		0			0
$661$	−16.1569	−	27.9845i	−0.628429	−	1.08847i	−0.987867	−	0.155302i	$-0.950365\pi$
$661$	−16.1569	−	27.9845i	−0.628429	−	1.08847i	0.359438	−	0.933169i	$-0.382968\pi$
$662$	−19.5355	−	33.8365i	−0.759270	−	1.31509i
$663$	−4.94975	+	8.57321i	−0.192232	+	0.332956i
$664$	−15.3137			−0.594287
$665$		0			0
$666$	−7.89949			−0.306099
$667$	0.757359	−	1.31178i	0.0293251	−	0.0507925i
$668$		0			0
$669$	8.58579	+	14.8710i	0.331946	+	0.574947i
$670$		0			0
$671$	42.6274			1.64561
$672$		0			0
$673$	−2.27208			−0.0875822			−0.0437911	−	0.999041i	$-0.513944\pi$
$673$	−2.27208			−0.0875822			−0.0437911	+	0.999041i	$0.513944\pi$
$674$	0.636039	−	1.10165i	0.0244993	−	0.0424340i
$675$		0			0
$676$		0			0
$677$	1.94975	−	3.37706i	0.0749349	−	0.129791i	−0.826123	−	0.563490i	$-0.809458\pi$
$677$	1.94975	−	3.37706i	0.0749349	−	0.129791i	0.901058	+	0.433699i	$0.142792\pi$
$678$	−6.14214			−0.235887
$679$	−17.5563	−	22.6398i	−0.673751	−	0.868834i
$680$		0			0
$681$	11.5355	−	19.9801i	0.442043	−	0.765640i
$682$	−0.414214	−	0.717439i	−0.0158611	−	0.0274722i
$683$	10.2929	+	17.8278i	0.393847	+	0.682162i	0.992953	−	0.118507i	$-0.0378108\pi$
$683$	10.2929	+	17.8278i	0.393847	+	0.682162i	−0.599107	+	0.800669i	$0.704477\pi$
$684$		0			0
$685$		0			0
$686$	3.02082	−	26.0168i	0.115335	−	0.993327i
$687$	−14.3137			−0.546102
$688$	20.8284	−	36.0759i	0.794076	−	1.37538i
$689$	0.928932	+	1.60896i	0.0353895	+	0.0612964i
$690$		0			0
$691$	−15.1569	+	26.2524i	−0.576594	+	0.998690i	0.419273	+	0.907860i	$0.362285\pi$
$691$	−15.1569	+	26.2524i	−0.576594	+	0.998690i	−0.995866	+	0.0908295i	$0.971048\pi$
$692$		0			0
$693$	−5.53553	−	7.13834i	−0.210278	−	0.271163i
$694$	−35.3137			−1.34049
$695$		0			0
$696$	0.343146	+	0.594346i	0.0130069	+	0.0225286i
$697$	−7.00000	−	12.1244i	−0.265144	−	0.459243i
$698$	−11.7574	+	20.3643i	−0.445023	+	0.770802i
$699$	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	$0.216082\pi$
$702$	1.12132	−	1.94218i	0.0423215	−	0.0733030i
$703$	18.5919	+	32.2021i	0.701206	+	1.21452i
$704$	−13.6569	−	23.6544i	−0.514712	−	0.891507i
$705$		0			0
$706$	8.34315			0.313998
$707$	6.24264	−	15.2913i	0.234779	−	0.575088i
$708$		0			0
$709$	5.55635	−	9.62388i	0.208673	−	0.361432i	−0.742624	−	0.669709i	$-0.766419\pi$
$709$	5.55635	−	9.62388i	0.208673	−	0.361432i	0.951297	+	0.308277i	$0.0997522\pi$
$710$		0			0
$711$	2.32843	+	4.03295i	0.0873228	+	0.151248i
$712$	5.31371	−	9.20361i	0.199140	−	0.344920i
$713$	−1.07107			−0.0401118
$714$	8.82843	−	21.6251i	0.330396	−	0.809301i
$715$		0			0
$716$		0			0
$717$	−8.65685	−	14.9941i	−0.323296	−	0.559965i
$718$	−18.7990	−	32.5608i	−0.701572	−	1.21516i
$719$	−8.75736	+	15.1682i	−0.326594	+	0.565678i	−0.981834	−	0.189743i	$-0.939234\pi$
$719$	−8.75736	+	15.1682i	−0.326594	+	0.565678i	0.655239	+	0.755421i	$0.272568\pi$
$720$		0			0
$721$	3.25736	−	0.445759i	0.121310	−	0.0166009i
$722$	−35.7990			−1.33230
$723$	5.17157	−	8.95743i	0.192333	−	0.333130i
$724$		0			0
$725$		0			0
$726$	0.464466	−	0.804479i	0.0172380	−	0.0298570i
$727$	−4.75736			−0.176441			−0.0882203	−	0.996101i	$-0.528118\pi$
$727$	−4.75736			−0.176441			−0.0882203	+	0.996101i	$0.528118\pi$
$728$	−7.27208	−	9.37769i	−0.269521	−	0.347560i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−32.5061	−	56.3022i	−1.20228	−	2.08241i
$732$		0			0
$733$	−5.37868	+	9.31615i	−0.198666	+	0.344100i	−0.948096	−	0.317984i	$-0.896994\pi$
$733$	−5.37868	+	9.31615i	−0.198666	+	0.344100i	0.749430	+	0.662083i	$0.230328\pi$
$734$	−27.6985			−1.02237
$735$		0			0
$736$		0			0
$737$	20.0208	−	34.6771i	0.737476	−	1.27735i
$738$	1.58579	+	2.74666i	0.0583736	+	0.101106i
$739$	17.5711	+	30.4340i	0.646362	+	1.11953i	0.983985	+	0.178251i	$0.0570438\pi$
$739$	17.5711	+	30.4340i	0.646362	+	1.11953i	−0.337623	+	0.941281i	$0.609623\pi$
$740$		0			0
$741$	−10.5563			−0.387797
$742$	−2.68629	−	3.46410i	−0.0986169	−	0.127171i
$743$	4.72792			0.173451			0.0867253	−	0.996232i	$-0.472360\pi$
$743$	4.72792			0.173451			0.0867253	+	0.996232i	$0.472360\pi$
$744$	0.242641	−	0.420266i	0.00889564	−	0.0154077i
$745$		0			0
$746$	−13.6066	−	23.5673i	−0.498173	−	0.862861i
$747$	2.70711	−	4.68885i	0.0990479	−	0.171556i
$748$		0			0
$749$	−40.4056	+	5.52938i	−1.47639	+	0.202039i
$750$		0			0
$751$	−9.81371	+	16.9978i	−0.358107	+	0.620260i	−0.987645	−	0.156710i	$-0.949911\pi$
$751$	−9.81371	+	16.9978i	−0.358107	+	0.620260i	0.629537	+	0.776970i	$0.283244\pi$
$752$	−18.6274	−	32.2636i	−0.679272	−	1.17653i
$753$	2.70711	+	4.68885i	0.0986525	+	0.170871i
$754$	−0.272078	+	0.471253i	−0.00990849	+	0.0171620i
$755$		0			0
$756$		0			0
$757$	−41.5980			−1.51190			−0.755952	−	0.654627i	$-0.772826\pi$
$757$	−41.5980			−1.51190			−0.755952	+	0.654627i	$0.772826\pi$
$758$	10.4645	−	18.1250i	0.380087	−	0.658329i
$759$	−10.6569	−	18.4582i	−0.386819	−	0.669991i
$760$		0			0
$761$	10.4645	−	18.1250i	0.379337	−	0.657030i	−0.611629	−	0.791145i	$-0.709486\pi$
$761$	10.4645	−	18.1250i	0.379337	−	0.657030i	0.990966	+	0.134114i	$0.0428189\pi$
$762$	−25.5563			−0.925809
$763$	13.4853	−	33.0321i	0.488200	−	1.19584i
$764$		0			0
$765$		0			0
$766$	−8.82843	−	15.2913i	−0.318984	−	0.552497i
$767$	−1.12132	−	1.94218i	−0.0404885	−	0.0701282i
$768$		0			0
$769$	−15.9706			−0.575913			−0.287957	−	0.957643i	$-0.592976\pi$
$769$	−15.9706			−0.575913			−0.287957	+	0.957643i	$0.592976\pi$
$770$		0			0
$771$	29.8995			1.07680
$772$		0			0
$773$	12.4645	+	21.5891i	0.448316	+	0.776506i	0.998277	−	0.0586849i	$-0.0186907\pi$
$773$	12.4645	+	21.5891i	0.448316	+	0.776506i	−0.549961	+	0.835190i	$0.685357\pi$
$774$	7.36396	+	12.7548i	0.264692	+	0.458460i
$775$		0			0
$776$	30.6274			1.09946
$777$	−9.05635	−	11.6786i	−0.324895	−	0.418967i
$778$	−23.8579			−0.855346
$779$	7.46447	−	12.9288i	0.267442	−	0.463224i
$780$		0			0
$781$	5.82843	+	10.0951i	0.208558	+	0.361232i
$782$	27.5563	−	47.7290i	0.985413	−	1.70679i
$783$	−0.242641			−0.00867127
$784$	20.0000	+	19.5959i	0.714286	+	0.699854i
$785$		0			0
$786$	−7.41421	+	12.8418i	−0.264456	+	0.458052i
$787$	6.58579	+	11.4069i	0.234758	+	0.406613i	0.959202	−	0.282721i	$-0.0912369\pi$
$787$	6.58579	+	11.4069i	0.234758	+	0.406613i	−0.724444	+	0.689333i	$0.757904\pi$
$788$		0			0
$789$	0.585786	−	1.01461i	0.0208545	−	0.0361211i
$790$		0			0
$791$	−7.04163	−	9.08052i	−0.250372	−	0.322866i
$792$	9.65685			0.343141
$793$	−9.89949	+	17.1464i	−0.351541	+	0.608888i
$794$	17.1213	+	29.6550i	0.607613	+	1.05242i
$795$		0			0
$796$		0			0
$797$	−10.4437			−0.369933			−0.184967	−	0.982745i	$-0.559218\pi$
$797$	−10.4437			−0.369933			−0.184967	+	0.982745i	$0.559218\pi$
$798$	24.6777	−	3.37706i	0.873580	−	0.119547i
$799$	−58.1421			−2.05692
$800$		0			0
$801$	1.87868	+	3.25397i	0.0663799	+	0.114973i
$802$	0.343146	+	0.594346i	0.0121169	+	0.0209871i
$803$	3.53553	−	6.12372i	0.124766	−	0.216102i
$804$		0			0
$805$		0			0
$806$	0.384776			0.0135532
$807$	−4.07107	+	7.05130i	−0.143308	+	0.248217i
$808$	8.82843	+	15.2913i	0.310583	+	0.537946i
$809$	2.31371	+	4.00746i	0.0813457	+	0.140895i	0.903828	−	0.427896i	$-0.140745\pi$
$809$	2.31371	+	4.00746i	0.0813457	+	0.140895i	−0.822483	+	0.568790i	$0.807412\pi$
$810$		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
$813$	20.1421			0.706416
$814$	13.4853	−	23.3572i	0.472659	−	0.818669i
$815$		0			0
$816$	12.4853	+	21.6251i	0.437072	+	0.757031i
$817$	34.6630	−	60.0380i	1.21270	−	2.10046i
$818$	37.2132			1.30113
$819$	4.15685	−	0.568852i	0.145252	−	0.0198773i
$820$		0			0
$821$	−6.77817	+	11.7401i	−0.236560	+	0.409734i	−0.959725	−	0.280942i	$-0.909353\pi$
$821$	−6.77817	+	11.7401i	−0.236560	+	0.409734i	0.723165	+	0.690675i	$0.242687\pi$
$822$	2.07107	+	3.58719i	0.0722368	+	0.125118i
$823$	11.1421	+	19.2987i	0.388390	+	0.672712i	0.992233	−	0.124391i	$-0.0396979\pi$
$823$	11.1421	+	19.2987i	0.388390	+	0.672712i	−0.603843	+	0.797103i	$0.706365\pi$
$824$	−1.75736	+	3.04384i	−0.0612205	+	0.106037i
$825$		0			0
$826$	3.24264	+	4.18154i	0.112826	+	0.145494i
$827$	−12.8284			−0.446088			−0.223044	−	0.974808i	$-0.571599\pi$
$827$	−12.8284			−0.446088			−0.223044	+	0.974808i	$0.571599\pi$
$828$		0			0
$829$	9.32843	+	16.1573i	0.323990	+	0.561167i	0.981307	−	0.192447i	$-0.0616424\pi$
$829$	9.32843	+	16.1573i	0.323990	+	0.561167i	−0.657318	+	0.753614i	$0.728309\pi$
$830$		0			0
$831$	−11.6924	+	20.2518i	−0.405604	+	0.702528i
$832$	12.6863			0.439818
$833$	42.0919	−	11.7401i	1.45840	−	0.406772i
$834$	−16.2426			−0.562437
$835$		0			0
$836$		0			0
$837$	0.0857864	+	0.148586i	0.00296521	+	0.00513590i
$838$	−2.24264	+	3.88437i	−0.0774707	+	0.134183i
$839$	−7.27208			−0.251060			−0.125530	−	0.992090i	$-0.540063\pi$
$839$	−7.27208			−0.251060			−0.125530	+	0.992090i	$0.540063\pi$
$840$		0			0
$841$	−28.9411			−0.997970
$842$	19.4350	−	33.6625i	0.669775	−	1.16008i
$843$	−4.82843	−	8.36308i	−0.166300	−	0.288040i
$844$		0			0
$845$		0			0
$846$	13.1716			0.452848
$847$	1.72183	−	0.235626i	0.0591626	−	0.00809622i
$848$	4.68629			0.160928
$849$	−6.62132	+	11.4685i	−0.227243	+	0.393597i
$850$		0			0
$851$	−17.4350	−	30.1984i	−0.597665	−	1.03519i
$852$		0			0
$853$	−38.0122			−1.30151			−0.650756	−	0.759287i	$-0.725548\pi$
$853$	−38.0122			−1.30151			−0.650756	+	0.759287i	$0.725548\pi$
$854$	17.6569	−	43.2503i	0.604205	−	1.47999i
$855$		0			0
$856$	21.7990	−	37.7570i	0.745074	−	1.29051i
$857$	−3.12132	−	5.40629i	−0.106622	−	0.184675i	0.807778	−	0.589487i	$-0.200670\pi$
$857$	−3.12132	−	5.40629i	−0.106622	−	0.184675i	−0.914400	+	0.404812i	$0.867337\pi$
$858$	3.82843	+	6.63103i	0.130700	+	0.226380i
$859$	−7.82843	+	13.5592i	−0.267102	+	0.462635i	−0.968112	−	0.250517i	$-0.919400\pi$
$859$	−7.82843	+	13.5592i	−0.267102	+	0.462635i	0.701010	+	0.713152i	$0.252733\pi$
$860$		0			0
$861$	−2.24264	+	5.49333i	−0.0764290	+	0.187212i
$862$	−52.0833			−1.77396
$863$	−4.89949	+	8.48617i	−0.166781	+	0.288873i	−0.937286	−	0.348561i	$-0.886671\pi$
$863$	−4.89949	+	8.48617i	−0.166781	+	0.288873i	0.770505	+	0.637433i	$0.220004\pi$
$864$		0			0
$865$		0			0
$866$	17.3640	−	30.0753i	0.590051	−	1.02200i
$867$	21.9706			0.746159
$868$		0			0
$869$	−15.8995			−0.539353
$870$		0			0
$871$	9.29899	+	16.1063i	0.315084	+	0.545742i
$872$	19.0711	+	33.0321i	0.645828	+	1.11861i
$873$	−5.41421	+	9.37769i	−0.183243	+	0.317387i
$874$	58.7696			1.98791
$875$		0			0
$876$		0			0
$877$	−9.00000	+	15.5885i	−0.303908	+	0.526385i	−0.977018	−	0.213158i	$-0.931625\pi$
$877$	−9.00000	+	15.5885i	−0.303908	+	0.526385i	0.673109	+	0.739543i	$0.264958\pi$
$878$	0.242641	+	0.420266i	0.00818873	+	0.0141833i
$879$	−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	$0.618869\pi$
$882$	−9.53553	+	2.65962i	−0.321078	+	0.0895542i
$883$	−8.07107			−0.271613			−0.135807	−	0.990735i	$-0.543363\pi$
$883$	−8.07107			−0.271613			−0.135807	+	0.990735i	$0.543363\pi$
$884$		0			0
$885$		0			0
$886$	−0.343146	−	0.594346i	−0.0115282	−	0.0199674i
$887$	2.60660	−	4.51477i	0.0875211	−	0.151591i	−0.818942	−	0.573877i	$-0.805439\pi$
$887$	2.60660	−	4.51477i	0.0875211	−	0.151591i	0.906463	+	0.422286i	$0.138772\pi$
$888$	15.7990			0.530179
$889$	−29.2990	−	37.7825i	−0.982657	−	1.26718i
$890$		0			0
$891$	−1.70711	+	2.95680i	−0.0571902	+	0.0990564i
$892$		0			0
$893$	−31.0000	−	53.6936i	−1.03738	−	1.79679i
$894$	12.4853	−	21.6251i	0.417570	−	0.723253i
$895$		0			0
$896$	−29.6569	+	4.05845i	−0.990766	+	0.135583i
$897$	9.89949			0.330535
$898$	−4.92893	+	8.53716i	−0.164481	+	0.284889i
$899$	−0.0208153	−	0.0360531i	−0.000694228	−	0.00120244i
$900$		0			0
$901$	3.65685	−	6.33386i	0.121827	−	0.211011i
$902$	−10.8284			−0.360547
$903$	−10.4142	+	25.5095i	−0.346563	+	0.848903i
$904$	12.2843			0.408569
$905$		0			0
$906$	−4.58579	−	7.94282i	−0.152353	−	0.263882i
$907$	−4.30761	−	7.46100i	−0.143032	−	0.247739i	0.785605	−	0.618728i	$-0.212352\pi$
$907$	−4.30761	−	7.46100i	−0.143032	−	0.247739i	−0.928637	+	0.370990i	$0.879018\pi$
$908$		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	$0.477610\pi$
$912$	−13.3137	+	23.0600i	−0.440861	+	0.763594i
$913$	9.24264	+	16.0087i	0.305887	+	0.529811i
$914$	14.7782	+	25.5965i	0.488819	+	0.846659i
$915$		0			0
$916$		0			0
$917$	−27.4853	+	3.76127i	−0.907644	+	0.124208i
$918$	−8.82843			−0.291382
$919$	23.3284	−	40.4060i	0.769534	−	1.33287i	−0.168282	−	0.985739i	$-0.553822\pi$
$919$	23.3284	−	40.4060i	0.769534	−	1.33287i	0.937816	−	0.347133i	$-0.112845\pi$
$920$		0			0
$921$	0.792893	+	1.37333i	0.0261267	+	0.0452528i
$922$	−19.1421	+	33.1552i	−0.630413	+	1.09191i
$923$	−5.41421			−0.178211
$924$		0			0
$925$		0			0
$926$	7.36396	−	12.7548i	0.241995	−	0.419147i
$927$	−0.621320	−	1.07616i	−0.0204068	−	0.0353457i
$928$		0			0
$929$	25.5061	−	44.1779i	0.836828	−	1.44943i	−0.0557056	−	0.998447i	$-0.517741\pi$
$929$	25.5061	−	44.1779i	0.836828	−	1.44943i	0.892533	−	0.450981i	$-0.148926\pi$
$930$		0			0
$931$	33.2843	+	32.6118i	1.09085	+	1.06881i
$932$		0			0
$933$	8.53553	−	14.7840i	0.279441	−	0.484006i
$934$	−4.72792	−	8.18900i	−0.154702	−	0.267952i
$935$		0			0
$936$	−2.24264	+	3.88437i	−0.0733030	+	0.126965i
$937$	7.92893			0.259027			0.129513	−	0.991578i	$-0.458658\pi$
$937$	7.92893			0.259027			0.129513	+	0.991578i	$0.458658\pi$
$938$	−26.8909	−	34.6771i	−0.878018	−	1.13225i
$939$	−26.2132			−0.855436
$940$		0			0
$941$	5.63604	+	9.76191i	0.183730	+	0.318229i	0.943148	−	0.332374i	$-0.107850\pi$
$941$	5.63604	+	9.76191i	0.183730	+	0.318229i	−0.759418	+	0.650603i	$0.774516\pi$
$942$	11.4142	+	19.7700i	0.371895	+	0.644141i
$943$	−7.00000	+	12.1244i	−0.227951	+	0.394823i
$944$	−5.65685			−0.184115
$945$		0			0
$946$	−50.2843			−1.63488
$947$	−2.46447	+	4.26858i	−0.0800844	+	0.138710i	−0.903286	−	0.429039i	$-0.858852\pi$
$947$	−2.46447	+	4.26858i	−0.0800844	+	0.138710i	0.823202	+	0.567749i	$0.192186\pi$
$948$		0			0
$949$	1.64214	+	2.84426i	0.0533060	+	0.0923287i
$950$		0			0
$951$	−0.100505			−0.00325910
$952$	−17.6569	+	43.2503i	−0.572262	+	1.40175i
$953$	−48.4853			−1.57059			−0.785296	−	0.619120i	$-0.787489\pi$
$953$	−48.4853			−1.57059			−0.785296	+	0.619120i	$0.787489\pi$
$954$	−0.828427	+	1.43488i	−0.0268213	+	0.0464559i
$955$		0			0
$956$		0			0
$957$	0.414214	−	0.717439i	0.0133896	−	0.0231915i
$958$	48.9706			1.58217
$959$	−2.92893	+	7.17439i	−0.0945802	+	0.231673i
$960$		0			0
$961$	15.4853	−	26.8213i	0.499525	−	0.865203i
$962$	6.26346	+	10.8486i	0.201942	+	0.349774i
$963$	7.70711	+	13.3491i	0.248358	+	0.430169i
$964$		0			0
$965$		0			0
$966$	−23.1421	+	3.16693i	−0.744586	+	0.101894i
$967$	−23.3848			−0.752004			−0.376002	−	0.926619i	$-0.622701\pi$
$967$	−23.3848			−0.752004			−0.376002	+	0.926619i	$0.622701\pi$
$968$	−0.928932	+	1.60896i	−0.0298570	+	0.0517139i
$969$	20.7782	+	35.9889i	0.667491	+	1.15613i
$970$		0			0
$971$	−7.17157	+	12.4215i	−0.230147	+	0.398626i	−0.957851	−	0.287265i	$-0.907254\pi$
$971$	−7.17157	+	12.4215i	−0.230147	+	0.398626i	0.727704	+	0.685891i	$0.240587\pi$
$972$		0			0
$973$	−18.6213	−	24.0131i	−0.596972	−	0.769824i
$974$	1.27208			0.0407600
$975$		0			0
$976$	24.9706	+	43.2503i	0.799288	+	1.38441i
$977$	6.84924	+	11.8632i	0.219127	+	0.379539i	0.954541	−	0.298079i	$-0.0963459\pi$
$977$	6.84924	+	11.8632i	0.219127	+	0.379539i	−0.735415	+	0.677617i	$0.763013\pi$
$978$	13.6569	−	23.6544i	0.436698	−	0.756383i
$979$	−12.8284			−0.409998
$980$		0			0
$981$	−13.4853			−0.430552
$982$	−7.17157	+	12.4215i	−0.228854	+	0.396387i
$983$	26.5772	+	46.0330i	0.847680	+	1.46822i	0.883273	+	0.468858i	$0.155335\pi$
$983$	26.5772	+	46.0330i	0.847680	+	1.46822i	−0.0355935	+	0.999366i	$0.511332\pi$
$984$	−3.17157	−	5.49333i	−0.101106	−	0.175121i
$985$		0			0
$986$	2.14214			0.0682195
$987$	15.1005	+	19.4728i	0.480654	+	0.619827i
$988$		0			0
$989$	−32.5061	+	56.3022i	−1.03363	+	1.79031i
$990$		0			0
$991$	15.3284	+	26.5496i	0.486924	+	0.843376i	0.999887	−	0.0150341i	$-0.00478570\pi$
$991$	15.3284	+	26.5496i	0.486924	+	0.843376i	−0.512963	+	0.858410i	$0.671452\pi$
$992$		0			0
$993$	−27.6274			−0.876730
$994$	12.6569	−	1.73205i	0.401451	−	0.0549373i
$995$		0			0
$996$		0			0
$997$	0.378680	+	0.655892i	0.0119929	+	0.0207723i	0.871960	−	0.489578i	$-0.162849\pi$
$997$	0.378680	+	0.655892i	0.0119929	+	0.0207723i	−0.859967	+	0.510350i	$0.829516\pi$
$998$	6.22183	+	10.7765i	0.196948	+	0.341125i
$999$	−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.i.g.226.2		4
5.2	odd	4		525.2.r.g.499.3		8
5.3	odd	4		525.2.r.g.499.2		8
5.4	even	2		105.2.i.c.16.1	✓	4
7.2	even	3		3675.2.a.z.1.1		2
7.4	even	3	inner	525.2.i.g.151.2		4
7.5	odd	6		3675.2.a.x.1.1		2
15.14	odd	2		315.2.j.d.226.2		4
20.19	odd	2		1680.2.bg.p.961.1		4
35.4	even	6		105.2.i.c.46.1	yes	4
35.9	even	6		735.2.a.i.1.2		2
35.18	odd	12		525.2.r.g.424.3		8
35.19	odd	6		735.2.a.j.1.2		2
35.24	odd	6		735.2.i.j.361.1		4
35.32	odd	12		525.2.r.g.424.2		8
35.34	odd	2		735.2.i.j.226.1		4
105.44	odd	6		2205.2.a.u.1.1		2
105.74	odd	6		315.2.j.d.46.2		4
105.89	even	6		2205.2.a.s.1.1		2
140.39	odd	6		1680.2.bg.p.1201.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.c.16.1	✓	4	5.4	even	2
105.2.i.c.46.1	yes	4	35.4	even	6
315.2.j.d.46.2		4	105.74	odd	6
315.2.j.d.226.2		4	15.14	odd	2
525.2.i.g.151.2		4	7.4	even	3	inner
525.2.i.g.226.2		4	1.1	even	1	trivial
525.2.r.g.424.2		8	35.32	odd	12
525.2.r.g.424.3		8	35.18	odd	12
525.2.r.g.499.2		8	5.3	odd	4
525.2.r.g.499.3		8	5.2	odd	4
735.2.a.i.1.2		2	35.9	even	6
735.2.a.j.1.2		2	35.19	odd	6
735.2.i.j.226.1		4	35.34	odd	2
735.2.i.j.361.1		4	35.24	odd	6
1680.2.bg.p.961.1		4	20.19	odd	2
1680.2.bg.p.1201.1		4	140.39	odd	6
2205.2.a.s.1.1		2	105.89	even	6
2205.2.a.u.1.1		2	105.44	odd	6
3675.2.a.x.1.1		2	7.5	odd	6
3675.2.a.z.1.1		2	7.2	even	3

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.i (of order \(3\), degree \(2\), minimal)

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

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