LMFDB - Embedded newform 315.2.j.d.46.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(46,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, 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("315.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.j (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:	$2.51528766367$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	315.46
Dual form			315.2.j.d.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-0.500000 - 0.866025i) q^{5} +(1.62132 - 2.09077i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(-0.500000 - 0.866025i) q^{5} +(1.62132 - 2.09077i) q^{7} +2.82843 q^{8} +(0.707107 - 1.22474i) q^{10} +(1.70711 - 2.95680i) q^{11} -1.58579 q^{13} +(3.70711 + 0.507306i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-3.12132 + 5.40629i) q^{17} +(3.32843 + 5.76500i) q^{19} +4.82843 q^{22} +(-3.12132 - 5.40629i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-1.12132 - 1.94218i) q^{26} +0.242641 q^{29} +(0.0857864 - 0.148586i) q^{31} -8.82843 q^{34} +(-2.62132 - 0.358719i) q^{35} +(2.79289 + 4.83743i) q^{37} +(-4.70711 + 8.15295i) q^{38} +(-1.41421 - 2.44949i) q^{40} -2.24264 q^{41} -10.4142 q^{43} +(4.41421 - 7.64564i) q^{46} +(4.65685 + 8.06591i) q^{47} +(-1.74264 - 6.77962i) q^{49} -1.41421 q^{50} +(0.585786 - 1.01461i) q^{53} -3.41421 q^{55} +(4.58579 - 5.91359i) q^{56} +(0.171573 + 0.297173i) q^{58} +(0.707107 - 1.22474i) q^{59} +(-6.24264 - 10.8126i) q^{61} +0.242641 q^{62} +8.00000 q^{64} +(0.792893 + 1.37333i) q^{65} +(-5.86396 + 10.1567i) q^{67} +(-1.41421 - 3.46410i) q^{70} +3.41421 q^{71} +(-1.03553 + 1.79360i) q^{73} +(-3.94975 + 6.84116i) q^{74} +(-3.41421 - 8.36308i) q^{77} +(2.32843 + 4.03295i) q^{79} +(2.00000 - 3.46410i) q^{80} +(-1.58579 - 2.74666i) q^{82} -5.41421 q^{83} +6.24264 q^{85} +(-7.36396 - 12.7548i) q^{86} +(4.82843 - 8.36308i) q^{88} +(-1.87868 - 3.25397i) q^{89} +(-2.57107 + 3.31552i) q^{91} +(-6.58579 + 11.4069i) q^{94} +(3.32843 - 5.76500i) q^{95} -10.8284 q^{97} +(7.07107 - 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{5} - 2 q^{7}+O(q^{10}) $ 4 * q - 2 * q^5 - 2 * q^7	$ 4 q - 2 q^{5} - 2 q^{7} + 4 q^{11} - 12 q^{13} + 12 q^{14} + 8 q^{16} - 4 q^{17} + 2 q^{19} + 8 q^{22} - 4 q^{23} - 2 q^{25} + 4 q^{26} - 16 q^{29} + 6 q^{31} - 24 q^{34} - 2 q^{35} + 14 q^{37} - 16 q^{38} + 8 q^{41} - 36 q^{43} + 12 q^{46} - 4 q^{47} + 10 q^{49} + 8 q^{53} - 8 q^{55} + 24 q^{56} + 12 q^{58} - 8 q^{61} - 16 q^{62} + 32 q^{64} + 6 q^{65} + 2 q^{67} + 8 q^{71} + 10 q^{73} + 4 q^{74} - 8 q^{77} - 2 q^{79} + 8 q^{80} - 12 q^{82} - 16 q^{83} + 8 q^{85} - 4 q^{86} + 8 q^{88} - 16 q^{89} + 18 q^{91} - 32 q^{94} + 2 q^{95} - 32 q^{97}+O(q^{100}) $ 4 * q - 2 * q^5 - 2 * q^7 + 4 * q^11 - 12 * q^13 + 12 * q^14 + 8 * q^16 - 4 * q^17 + 2 * q^19 + 8 * q^22 - 4 * q^23 - 2 * q^25 + 4 * q^26 - 16 * q^29 + 6 * q^31 - 24 * q^34 - 2 * q^35 + 14 * q^37 - 16 * q^38 + 8 * q^41 - 36 * q^43 + 12 * q^46 - 4 * q^47 + 10 * q^49 + 8 * q^53 - 8 * q^55 + 24 * q^56 + 12 * q^58 - 8 * q^61 - 16 * q^62 + 32 * q^64 + 6 * q^65 + 2 * q^67 + 8 * q^71 + 10 * q^73 + 4 * q^74 - 8 * q^77 - 2 * q^79 + 8 * q^80 - 12 * q^82 - 16 * q^83 + 8 * q^85 - 4 * q^86 + 8 * q^88 - 16 * q^89 + 18 * q^91 - 32 * q^94 + 2 * q^95 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.707107	+	1.22474i	0.500000	+	0.866025i	1.00000			$0$
$2$	0.707107	+	1.22474i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	1.62132	−	2.09077i	0.612801	−	0.790237i
$7$	1.62132	−	2.09077i	0.612801	−	0.790237i
$8$	2.82843			1.00000
$9$		0			0
$10$	0.707107	−	1.22474i	0.223607	−	0.387298i
$11$	1.70711	−	2.95680i	0.514712	−	0.891507i	−0.485142	−	0.874435i	$-0.661232\pi$
$11$	1.70711	−	2.95680i	0.514712	−	0.891507i	0.999854	−	0.0170722i	$-0.00543450\pi$
$12$		0			0
$13$	−1.58579			−0.439818			−0.219909	−	0.975520i	$-0.570576\pi$
$13$	−1.58579			−0.439818			−0.219909	+	0.975520i	$0.570576\pi$
$14$	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	0.187327	+	0.982298i	$0.440018\pi$
$17$	−3.12132	+	5.40629i	−0.757031	+	1.31122i	−0.944358	+	0.328919i	$0.893316\pi$
$18$		0			0
$19$	3.32843	+	5.76500i	0.763594	+	1.32258i	0.940987	+	0.338443i	$0.109900\pi$
$19$	3.32843	+	5.76500i	0.763594	+	1.32258i	−0.177393	+	0.984140i	$0.556767\pi$
$20$		0			0
$21$		0			0
$22$	4.82843			1.02942
$23$	−3.12132	−	5.40629i	−0.650840	−	1.12729i	−0.982919	−	0.184037i	$-0.941083\pi$
$23$	−3.12132	−	5.40629i	−0.650840	−	1.12729i	0.332079	−	0.943252i	$-0.392250\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.12132	−	1.94218i	−0.219909	−	0.380894i
$27$		0			0
$28$		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
$33$		0			0
$34$	−8.82843			−1.51406
$35$	−2.62132	−	0.358719i	−0.443084	−	0.0606347i
$36$		0			0
$37$	2.79289	+	4.83743i	0.459149	+	0.795269i	0.998916	−	0.0465451i	$-0.0148211\pi$
$37$	2.79289	+	4.83743i	0.459149	+	0.795269i	−0.539767	+	0.841814i	$0.681488\pi$
$38$	−4.70711	+	8.15295i	−0.763594	+	1.32258i
$39$		0			0
$40$	−1.41421	−	2.44949i	−0.223607	−	0.387298i
$41$	−2.24264			−0.350242			−0.175121	−	0.984547i	$-0.556032\pi$
$41$	−2.24264			−0.350242			−0.175121	+	0.984547i	$0.556032\pi$
$42$		0			0
$43$	−10.4142			−1.58815			−0.794076	−	0.607818i	$-0.792045\pi$
$43$	−10.4142			−1.58815			−0.794076	+	0.607818i	$0.792045\pi$
$44$		0			0
$45$		0			0
$46$	4.41421	−	7.64564i	0.650840	−	1.12729i
$47$	4.65685	+	8.06591i	0.679272	+	1.17653i	0.975200	+	0.221324i	$0.0710377\pi$
$47$	4.65685	+	8.06591i	0.679272	+	1.17653i	−0.295928	+	0.955210i	$0.595629\pi$
$48$		0			0
$49$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$50$	−1.41421			−0.200000
$51$		0			0
$52$		0			0
$53$	0.585786	−	1.01461i	0.0804640	−	0.139368i	−0.822985	−	0.568063i	$-0.807693\pi$
$53$	0.585786	−	1.01461i	0.0804640	−	0.139368i	0.903449	+	0.428695i	$0.141026\pi$
$54$		0			0
$55$	−3.41421			−0.460372
$56$	4.58579	−	5.91359i	0.612801	−	0.790237i
$57$		0			0
$58$	0.171573	+	0.297173i	0.0225286	+	0.0390207i
$59$	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	$-0.461457\pi$
$62$	0.242641			0.0308154
$63$		0			0
$64$	8.00000			1.00000
$65$	0.792893	+	1.37333i	0.0983463	+	0.170341i
$66$		0			0
$67$	−5.86396	+	10.1567i	−0.716397	+	1.24084i	0.246021	+	0.969264i	$0.420877\pi$
$67$	−5.86396	+	10.1567i	−0.716397	+	1.24084i	−0.962418	+	0.271571i	$0.912457\pi$
$68$		0			0
$69$		0			0
$70$	−1.41421	−	3.46410i	−0.169031	−	0.414039i
$71$	3.41421			0.405193			0.202596	−	0.979262i	$-0.435062\pi$
$71$	3.41421			0.405193			0.202596	+	0.979262i	$0.435062\pi$
$72$		0			0
$73$	−1.03553	+	1.79360i	−0.121200	+	0.209925i	−0.920241	−	0.391352i	$-0.872008\pi$
$73$	−1.03553	+	1.79360i	−0.121200	+	0.209925i	0.799041	+	0.601276i	$0.205341\pi$
$74$	−3.94975	+	6.84116i	−0.459149	+	0.795269i
$75$		0			0
$76$		0			0
$77$	−3.41421	−	8.36308i	−0.389086	−	0.953062i
$78$		0			0
$79$	2.32843	+	4.03295i	0.261969	+	0.453743i	0.966765	−	0.255667i	$-0.0822950\pi$
$79$	2.32843	+	4.03295i	0.261969	+	0.453743i	−0.704796	+	0.709410i	$0.748962\pi$
$80$	2.00000	−	3.46410i	0.223607	−	0.387298i
$81$		0			0
$82$	−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
$85$	6.24264			0.677109
$86$	−7.36396	−	12.7548i	−0.794076	−	1.37538i
$87$		0			0
$88$	4.82843	−	8.36308i	0.514712	−	0.891507i
$89$	−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			0
$94$	−6.58579	+	11.4069i	−0.679272	+	1.17653i
$95$	3.32843	−	5.76500i	0.341489	−	0.591477i
$96$		0			0
$97$	−10.8284			−1.09946			−0.549730	−	0.835342i	$-0.685269\pi$
$97$	−10.8284			−1.09946			−0.549730	+	0.835342i	$0.685269\pi$
$98$	7.07107	−	6.92820i	0.714286	−	0.699854i
$99$		0			0
$100$		0			0
$101$	−3.12132	+	5.40629i	−0.310583	+	0.537946i	−0.978489	−	0.206300i	$-0.933858\pi$
$101$	−3.12132	+	5.40629i	−0.310583	+	0.537946i	0.667906	+	0.744246i	$0.267191\pi$
$102$		0			0
$103$	0.621320	+	1.07616i	0.0612205	+	0.106037i	0.895011	−	0.446044i	$-0.147167\pi$
$103$	0.621320	+	1.07616i	0.0612205	+	0.106037i	−0.833791	+	0.552081i	$0.813834\pi$
$104$	−4.48528			−0.439818
$105$		0			0
$106$	1.65685			0.160928
$107$	7.70711	+	13.3491i	0.745074	+	1.29051i	0.950160	+	0.311762i	$0.100919\pi$
$107$	7.70711	+	13.3491i	0.745074	+	1.29051i	−0.205086	+	0.978744i	$0.565747\pi$
$108$		0			0
$109$	6.74264	−	11.6786i	0.645828	−	1.11861i	−0.338282	−	0.941045i	$-0.609846\pi$
$109$	6.74264	−	11.6786i	0.645828	−	1.11861i	0.984110	−	0.177562i	$-0.0568210\pi$
$110$	−2.41421	−	4.18154i	−0.230186	−	0.398694i
$111$		0			0
$112$	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	$0.434513\pi$
$114$		0			0
$115$	−3.12132	+	5.40629i	−0.291065	+	0.504139i
$116$		0			0
$117$		0			0
$118$	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
$123$		0			0
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−18.0711			−1.60355			−0.801774	−	0.597627i	$-0.796110\pi$
$127$	−18.0711			−1.60355			−0.801774	+	0.597627i	$0.796110\pi$
$128$	5.65685	+	9.79796i	0.500000	+	0.866025i
$129$		0			0
$130$	−1.12132	+	1.94218i	−0.0983463	+	0.170341i
$131$	−5.24264	−	9.08052i	−0.458052	−	0.793369i	0.540806	−	0.841147i	$-0.318119\pi$
$131$	−5.24264	−	9.08052i	−0.458052	−	0.793369i	−0.998858	+	0.0477784i	$0.984786\pi$
$132$		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	−0.921779	−	0.387716i	$-0.873264\pi$
$137$	−1.46447	+	2.53653i	−0.125118	+	0.216710i	0.796661	+	0.604426i	$0.206598\pi$
$138$		0			0
$139$	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
$141$		0			0
$142$	2.41421	+	4.18154i	0.202596	+	0.350907i
$143$	−2.70711	+	4.68885i	−0.226380	+	0.392101i
$144$		0			0
$145$	−0.121320	−	0.210133i	−0.0100751	−	0.0174506i
$146$	−2.92893			−0.242400
$147$		0			0
$148$		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	$0.0816636\pi$
$152$	9.41421	+	16.3059i	0.763594	+	1.32258i
$153$		0			0
$154$	7.82843	−	10.0951i	0.630833	−	0.813489i
$155$	−0.171573			−0.0137811
$156$		0			0
$157$	8.07107	−	13.9795i	0.644141	−	1.11569i	−0.340358	−	0.940296i	$-0.610548\pi$
$157$	8.07107	−	13.9795i	0.644141	−	1.11569i	0.984499	−	0.175390i	$-0.0561185\pi$
$158$	−3.29289	+	5.70346i	−0.261969	+	0.453743i
$159$		0			0
$160$		0			0
$161$	−16.3640	−	2.23936i	−1.28966	−	0.176486i
$162$		0			0
$163$	9.65685	+	16.7262i	0.756383	+	1.31009i	0.944684	+	0.327983i	$0.106369\pi$
$163$	9.65685	+	16.7262i	0.756383	+	1.31009i	−0.188301	+	0.982111i	$0.560298\pi$
$164$		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	$0.650327\pi$
$168$		0			0
$169$	−10.4853			−0.806560
$170$	4.41421	+	7.64564i	0.338555	+	0.586394i
$171$		0			0
$172$		0			0
$173$	−1.41421	−	2.44949i	−0.107521	−	0.186231i	0.807245	−	0.590217i	$-0.200958\pi$
$173$	−1.41421	−	2.44949i	−0.107521	−	0.186231i	−0.914765	+	0.403986i	$0.867625\pi$
$174$		0			0
$175$	1.00000	+	2.44949i	0.0755929	+	0.185164i
$176$	13.6569			1.02942
$177$		0			0
$178$	2.65685	−	4.60181i	0.199140	−	0.344920i
$179$	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	$0.492229\pi$
$182$	−5.87868	−	0.804479i	−0.435757	−	0.0596319i
$183$		0			0
$184$	−8.82843	−	15.2913i	−0.650840	−	1.12729i
$185$	2.79289	−	4.83743i	0.205338	−	0.355655i
$186$		0			0
$187$	10.6569	+	18.4582i	0.779306	+	1.34980i
$188$		0			0
$189$		0			0
$190$	9.41421			0.682979
$191$	9.48528	+	16.4290i	0.686331	+	1.18876i	0.973017	+	0.230735i	$0.0741131\pi$
$191$	9.48528	+	16.4290i	0.686331	+	1.18876i	−0.286686	+	0.958025i	$0.592554\pi$
$192$		0			0
$193$	3.37868	−	5.85204i	0.243203	−	0.421239i	−0.718422	−	0.695607i	$-0.755135\pi$
$193$	3.37868	−	5.85204i	0.243203	−	0.421239i	0.961625	+	0.274368i	$0.0884687\pi$
$194$	−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	$0.563424\pi$
$198$		0			0
$199$	−2.75736	+	4.77589i	−0.195464	+	0.338554i	−0.947053	−	0.321079i	$-0.895955\pi$
$199$	−2.75736	+	4.77589i	−0.195464	+	0.338554i	0.751589	+	0.659632i	$0.229288\pi$
$200$	−1.41421	+	2.44949i	−0.100000	+	0.173205i
$201$		0			0
$202$	−8.82843			−0.621166
$203$	0.393398	−	0.507306i	0.0276111	−	0.0356059i
$204$		0			0
$205$	1.12132	+	1.94218i	0.0783164	+	0.135648i
$206$	−0.878680	+	1.52192i	−0.0612205	+	0.106037i
$207$		0			0
$208$	−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
$213$		0			0
$214$	−10.8995	+	18.8785i	−0.745074	+	1.29051i
$215$	5.20711	+	9.01897i	0.355122	+	0.615089i
$216$		0			0
$217$	−0.171573	−	0.420266i	−0.0116471	−	0.0285295i
$218$	19.0711			1.29166
$219$		0			0
$220$		0			0
$221$	4.94975	−	8.57321i	0.332956	−	0.576697i
$222$		0			0
$223$	17.1716			1.14989			0.574947	−	0.818191i	$-0.305023\pi$
$223$	17.1716			1.14989			0.574947	+	0.818191i	$0.305023\pi$
$224$		0			0
$225$		0			0
$226$	3.07107	+	5.31925i	0.204284	+	0.353831i
$227$	11.5355	−	19.9801i	0.765640	−	1.32613i	−0.174267	−	0.984698i	$-0.555756\pi$
$227$	11.5355	−	19.9801i	0.765640	−	1.32613i	0.939907	−	0.341429i	$-0.110911\pi$
$228$		0			0
$229$	7.15685	+	12.3960i	0.472938	+	0.819153i	0.999520	−	0.0309713i	$-0.00986003\pi$
$229$	7.15685	+	12.3960i	0.472938	+	0.819153i	−0.526582	+	0.850124i	$0.676527\pi$
$230$	−8.82843			−0.582129
$231$		0			0
$232$	0.686292			0.0450572
$233$	−11.2426	−	19.4728i	−0.736530	−	1.27571i	−0.954049	−	0.299651i	$-0.903130\pi$
$233$	−11.2426	−	19.4728i	−0.736530	−	1.27571i	0.217519	−	0.976056i	$-0.430204\pi$
$234$		0			0
$235$	4.65685	−	8.06591i	0.303780	−	0.526162i
$236$		0			0
$237$		0			0
$238$	−14.3137	+	18.4582i	−0.927820	+	1.19647i
$239$	−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	$0.0585618\pi$
$242$	0.464466	−	0.804479i	0.0298570	−	0.0517139i
$243$		0			0
$244$		0			0
$245$	−5.00000	+	4.89898i	−0.319438	+	0.312984i
$246$		0			0
$247$	−5.27817	−	9.14207i	−0.335842	−	0.581696i
$248$	0.242641	−	0.420266i	0.0154077	−	0.0266869i
$249$		0			0
$250$	0.707107	+	1.22474i	0.0447214	+	0.0774597i
$251$	5.41421			0.341742			0.170871	−	0.985293i	$-0.445342\pi$
$251$	5.41421			0.341742			0.170871	+	0.985293i	$0.445342\pi$
$252$		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	−0.778964	−	0.627069i	$-0.784254\pi$
$257$	−14.9497	−	25.8937i	−0.932540	−	1.61521i	−0.153576	−	0.988137i	$-0.549079\pi$
$258$		0			0
$259$	14.6421	+	2.00373i	0.909818	+	0.124506i
$260$		0			0
$261$		0			0
$262$	7.41421	−	12.8418i	0.458052	−	0.793369i
$263$	0.585786	−	1.01461i	0.0361211	−	0.0625636i	−0.847400	−	0.530956i	$-0.821833\pi$
$263$	0.585786	−	1.01461i	0.0361211	−	0.0625636i	0.883521	+	0.468392i	$0.155166\pi$
$264$		0			0
$265$	−1.17157			−0.0719691
$266$	9.41421	+	23.0600i	0.577222	+	1.41390i
$267$		0			0
$268$		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	$-0.376210\pi$
$272$	−24.9706			−1.51406
$273$		0			0
$274$	−4.14214			−0.250236
$275$	1.70711	+	2.95680i	0.102942	+	0.178301i
$276$		0			0
$277$	11.6924	−	20.2518i	0.702528	−	1.21681i	−0.265049	−	0.964235i	$-0.585388\pi$
$277$	11.6924	−	20.2518i	0.702528	−	1.21681i	0.967576	−	0.252578i	$-0.0812786\pi$
$278$	8.12132	+	14.0665i	0.487084	+	0.843655i
$279$		0			0
$280$	−7.41421	−	1.01461i	−0.443084	−	0.0606347i
$281$	−9.65685			−0.576080			−0.288040	−	0.957618i	$-0.593004\pi$
$281$	−9.65685			−0.576080			−0.288040	+	0.957618i	$0.593004\pi$
$282$		0			0
$283$	6.62132	−	11.4685i	0.393597	−	0.681729i	−0.599324	−	0.800506i	$-0.704564\pi$
$283$	6.62132	−	11.4685i	0.393597	−	0.681729i	0.992921	+	0.118777i	$0.0378973\pi$
$284$		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
$290$	0.171573	−	0.297173i	0.0100751	−	0.0174506i
$291$		0			0
$292$		0			0
$293$	15.3137			0.894636			0.447318	−	0.894375i	$-0.352379\pi$
$293$	15.3137			0.894636			0.447318	+	0.894375i	$0.352379\pi$
$294$		0			0
$295$	−1.41421			−0.0823387
$296$	7.89949	+	13.6823i	0.459149	+	0.795269i
$297$		0			0
$298$	−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
$303$		0			0
$304$	−13.3137	+	23.0600i	−0.763594	+	1.32258i
$305$	−6.24264	+	10.8126i	−0.357453	+	0.619126i
$306$		0			0
$307$	1.58579			0.0905056			0.0452528	−	0.998976i	$-0.485591\pi$
$307$	1.58579			0.0905056			0.0452528	+	0.998976i	$0.485591\pi$
$308$		0			0
$309$		0			0
$310$	−0.121320	−	0.210133i	−0.00689053	−	0.0119348i
$311$	−8.53553	+	14.7840i	−0.484006	+	0.838323i	−0.999831	−	0.0183712i	$-0.994152\pi$
$311$	−8.53553	+	14.7840i	−0.484006	+	0.838323i	0.515826	+	0.856694i	$0.327485\pi$
$312$		0			0
$313$	−13.1066	−	22.7013i	−0.740829	−	1.28315i	−0.952118	−	0.305730i	$-0.901100\pi$
$313$	−13.1066	−	22.7013i	−0.740829	−	1.28315i	0.211289	−	0.977424i	$-0.432234\pi$
$314$	22.8284			1.28828
$315$		0			0
$316$		0			0
$317$	0.0502525	+	0.0870399i	0.00282246	+	0.00488865i	0.867433	−	0.497554i	$-0.165768\pi$
$317$	0.0502525	+	0.0870399i	0.00282246	+	0.00488865i	−0.864611	+	0.502442i	$0.832435\pi$
$318$		0			0
$319$	0.414214	−	0.717439i	0.0231915	−	0.0401689i
$320$	−4.00000	−	6.92820i	−0.223607	−	0.387298i
$321$		0			0
$322$	−8.82843	−	21.6251i	−0.491989	−	1.20512i
$323$	−41.5563			−2.31226
$324$		0			0
$325$	0.792893	−	1.37333i	0.0439818	−	0.0761787i
$326$	−13.6569	+	23.6544i	−0.756383	+	1.31009i
$327$		0			0
$328$	−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	0.943223	+	0.332159i	$0.107777\pi$
$331$	13.8137	+	23.9260i	0.759270	+	1.31509i	−0.183953	+	0.982935i	$0.558889\pi$
$332$		0			0
$333$		0			0
$334$	−8.31371	−	14.3998i	−0.454906	−	0.787920i
$335$	11.7279			0.640765
$336$		0			0
$337$	−0.899495			−0.0489986			−0.0244993	−	0.999700i	$-0.507799\pi$
$337$	−0.899495			−0.0489986			−0.0244993	+	0.999700i	$0.507799\pi$
$338$	−7.41421	−	12.8418i	−0.403280	−	0.698502i
$339$		0			0
$340$		0			0
$341$	−0.292893	−	0.507306i	−0.0158611	−	0.0274722i
$342$		0			0
$343$	−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	0.307589	+	0.951519i	$0.400478\pi$
$347$	−12.4853	+	21.6251i	−0.670245	+	1.16090i	−0.977835	+	0.209379i	$0.932856\pi$
$348$		0			0
$349$	−16.6274			−0.890045			−0.445023	−	0.895519i	$-0.646804\pi$
$349$	−16.6274			−0.890045			−0.445023	+	0.895519i	$0.646804\pi$
$350$	−2.29289	+	2.95680i	−0.122560	+	0.158047i
$351$		0			0
$352$		0			0
$353$	2.94975	−	5.10911i	0.156999	−	0.271931i	−0.776786	−	0.629765i	$-0.783151\pi$
$353$	2.94975	−	5.10911i	0.156999	−	0.271931i	0.933785	+	0.357834i	$0.116485\pi$
$354$		0			0
$355$	−1.70711	−	2.95680i	−0.0906038	−	0.156930i
$356$		0			0
$357$		0			0
$358$	27.7990			1.46922
$359$	−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
$362$	0.464466	+	0.804479i	0.0244118	+	0.0422825i
$363$		0			0
$364$		0			0
$365$	2.07107			0.108405
$366$		0			0
$367$	9.79289	−	16.9618i	0.511185	−	0.885398i	−0.488731	−	0.872434i	$-0.662540\pi$
$367$	9.79289	−	16.9618i	0.511185	−	0.885398i	0.999916	−	0.0129637i	$-0.00412658\pi$
$368$	12.4853	−	21.6251i	0.650840	−	1.12729i
$369$		0			0
$370$	7.89949			0.410675
$371$	−1.17157	−	2.86976i	−0.0608250	−	0.148990i
$372$		0			0
$373$	−9.62132	−	16.6646i	−0.498173	−	0.862861i	0.501825	−	0.864969i	$-0.332662\pi$
$373$	−9.62132	−	16.6646i	−0.498173	−	0.862861i	−0.999998	+	0.00210826i	$0.999329\pi$
$374$	−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
$378$		0			0
$379$	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
$381$		0			0
$382$	−13.4142	+	23.2341i	−0.686331	+	1.18876i
$383$	6.24264	+	10.8126i	0.318984	+	0.552497i	0.980276	−	0.197632i	$-0.0633250\pi$
$383$	6.24264	+	10.8126i	0.318984	+	0.552497i	−0.661292	+	0.750128i	$0.729992\pi$
$384$		0			0
$385$	−5.53553	+	7.13834i	−0.282117	+	0.363803i
$386$	9.55635			0.486405
$387$		0			0
$388$		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
$392$	−4.92893	−	19.1757i	−0.248949	−	0.968517i
$393$		0			0
$394$	−3.92893	−	6.80511i	−0.197937	−	0.342836i
$395$	2.32843	−	4.03295i	0.117156	−	0.202920i
$396$		0			0
$397$	12.1066	+	20.9692i	0.607613	+	1.05242i	0.991633	+	0.129092i	$0.0412061\pi$
$397$	12.1066	+	20.9692i	0.607613	+	1.05242i	−0.384020	+	0.923325i	$0.625461\pi$
$398$	−7.79899			−0.390928
$399$		0			0
$400$	−4.00000			−0.200000
$401$	0.242641	+	0.420266i	0.0121169	+	0.0209871i	0.872020	−	0.489470i	$-0.162810\pi$
$401$	0.242641	+	0.420266i	0.0121169	+	0.0209871i	−0.859903	+	0.510457i	$0.829476\pi$
$402$		0			0
$403$	−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
$408$		0			0
$409$	13.1569	−	22.7883i	0.650565	−	1.12681i	−0.332422	−	0.943131i	$-0.607866\pi$
$409$	13.1569	−	22.7883i	0.650565	−	1.12681i	0.982986	−	0.183680i	$-0.0588010\pi$
$410$	−1.58579	+	2.74666i	−0.0783164	+	0.135648i
$411$		0			0
$412$		0			0
$413$	−1.41421	−	3.46410i	−0.0695889	−	0.170457i
$414$		0			0
$415$	2.70711	+	4.68885i	0.132887	+	0.230166i
$416$		0			0
$417$		0			0
$418$	16.0711	+	27.8359i	0.786062	+	1.36150i
$419$	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	$0.266390\pi$
$422$	0.100505	+	0.174080i	0.00489251	+	0.00847408i
$423$		0			0
$424$	1.65685	−	2.86976i	0.0804640	−	0.139368i
$425$	−3.12132	−	5.40629i	−0.151406	−	0.262243i
$426$		0			0
$427$	−32.7279	−	4.47871i	−1.58382	−	0.216740i
$428$		0			0
$429$		0			0
$430$	−7.36396	+	12.7548i	−0.355122	+	0.615089i
$431$	18.4142	−	31.8944i	0.886981	−	1.53630i	0.0435558	−	0.999051i	$-0.486131\pi$
$431$	18.4142	−	31.8944i	0.886981	−	1.53630i	0.843426	−	0.537246i	$-0.180535\pi$
$432$		0			0
$433$	−24.5563			−1.18010			−0.590051	−	0.807366i	$-0.700893\pi$
$433$	−24.5563			−1.18010			−0.590051	+	0.807366i	$0.700893\pi$
$434$	0.393398	−	0.507306i	0.0188837	−	0.0243515i
$435$		0			0
$436$		0			0
$437$	20.7782	−	35.9889i	0.993955	−	1.72158i
$438$		0			0
$439$	−0.171573	−	0.297173i	−0.00818873	−	0.0141833i	0.861902	−	0.507075i	$-0.169273\pi$
$439$	−0.171573	−	0.297173i	−0.00818873	−	0.0141833i	−0.870091	+	0.492892i	$0.835940\pi$
$440$	−9.65685			−0.460372
$441$		0			0
$442$	14.0000			0.665912
$443$	0.242641	+	0.420266i	0.0115282	+	0.0199674i	0.871732	−	0.489983i	$-0.162997\pi$
$443$	0.242641	+	0.420266i	0.0115282	+	0.0199674i	−0.860204	+	0.509950i	$0.829664\pi$
$444$		0			0
$445$	−1.87868	+	3.25397i	−0.0890580	+	0.154253i
$446$	12.1421	+	21.0308i	0.574947	+	0.995837i
$447$		0			0
$448$	12.9706	−	16.7262i	0.612801	−	0.790237i
$449$	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
$453$		0			0
$454$	32.6274			1.53128
$455$	4.15685	+	0.568852i	0.194876	+	0.0266682i
$456$		0			0
$457$	10.4497	+	18.0995i	0.488819	+	0.846659i	0.999917	−	0.0128634i	$-0.00409467\pi$
$457$	10.4497	+	18.0995i	0.488819	+	0.846659i	−0.511099	+	0.859522i	$0.670761\pi$
$458$	−10.1213	+	17.5306i	−0.472938	+	0.819153i
$459$		0			0
$460$		0			0
$461$	27.0711			1.26083			0.630413	−	0.776260i	$-0.282886\pi$
$461$	27.0711			1.26083			0.630413	+	0.776260i	$0.282886\pi$
$462$		0			0
$463$	−10.4142			−0.483990			−0.241995	−	0.970278i	$-0.577802\pi$
$463$	−10.4142			−0.483990			−0.241995	+	0.970278i	$0.577802\pi$
$464$	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	0.932951	−	0.360004i	$-0.117225\pi$
$467$	3.34315	+	5.79050i	0.154702	+	0.267952i	−0.778248	+	0.627957i	$0.783891\pi$
$468$		0			0
$469$	11.7279	+	28.7274i	0.541545	+	1.32651i
$470$	13.1716			0.607559
$471$		0			0
$472$	2.00000	−	3.46410i	0.0920575	−	0.159448i
$473$	−17.7782	+	30.7927i	−0.817441	+	1.41585i
$474$		0			0
$475$	−6.65685			−0.305437
$476$		0			0
$477$		0			0
$478$	−12.2426	−	21.2049i	−0.559965	−	0.969888i
$479$	−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
$482$	14.6274			0.666261
$483$		0			0
$484$		0			0
$485$	5.41421	+	9.37769i	0.245847	+	0.425819i
$486$		0			0
$487$	−0.449747	+	0.778985i	−0.0203800	+	0.0352992i	−0.876036	−	0.482247i	$-0.839821\pi$
$487$	−0.449747	+	0.778985i	−0.0203800	+	0.0352992i	0.855656	+	0.517546i	$0.173154\pi$
$488$	−17.6569	−	30.5826i	−0.799288	−	1.38441i
$489$		0			0
$490$	−9.53553	−	2.65962i	−0.430772	−	0.120150i
$491$	10.1421			0.457708			0.228854	−	0.973461i	$-0.426502\pi$
$491$	10.1421			0.457708			0.228854	+	0.973461i	$0.426502\pi$
$492$		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
$498$		0			0
$499$	−4.39949	−	7.62015i	−0.196948	−	0.341125i	0.750589	−	0.660769i	$-0.229770\pi$
$499$	−4.39949	−	7.62015i	−0.196948	−	0.341125i	−0.947538	+	0.319645i	$0.896436\pi$
$500$		0			0
$501$		0			0
$502$	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	$0.364792\pi$
$504$		0			0
$505$	6.24264			0.277794
$506$	−15.0711	−	26.1039i	−0.669991	−	1.16046i
$507$		0			0
$508$		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
$512$	22.6274			1.00000
$513$		0			0
$514$	21.1421	−	36.6193i	0.932540	−	1.61521i
$515$	0.621320	−	1.07616i	0.0273786	−	0.0474212i
$516$		0			0
$517$	31.7990			1.39852
$518$	7.89949	+	19.3497i	0.347084	+	0.850178i
$519$		0			0
$520$	2.24264	+	3.88437i	0.0983463	+	0.170341i
$521$	−19.5563	+	33.8726i	−0.856779	+	1.48399i	0.0182053	+	0.999834i	$0.494205\pi$
$521$	−19.5563	+	33.8726i	−0.856779	+	1.48399i	−0.874985	+	0.484151i	$0.839129\pi$
$522$		0			0
$523$	3.79289	+	6.56948i	0.165852	+	0.287263i	0.936957	−	0.349444i	$-0.113629\pi$
$523$	3.79289	+	6.56948i	0.165852	+	0.287263i	−0.771106	+	0.636707i	$0.780296\pi$
$524$		0			0
$525$		0			0
$526$	1.65685			0.0722423
$527$	0.535534	+	0.927572i	0.0233282	+	0.0404057i
$528$		0			0
$529$	−7.98528	+	13.8309i	−0.347186	+	0.601344i
$530$	−0.828427	−	1.43488i	−0.0359846	−	0.0623271i
$531$		0			0
$532$		0			0
$533$	3.55635			0.154043
$534$		0			0
$535$	7.70711	−	13.3491i	0.333207	−	0.577132i
$536$	−16.5858	+	28.7274i	−0.716397	+	1.24084i
$537$		0			0
$538$	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	−0.970303	−	0.241894i	$-0.922231\pi$
$541$	−16.1569	−	27.9845i	−0.694637	−	1.20315i	0.275665	−	0.961254i	$-0.411102\pi$
$542$	14.2426	−	24.6690i	0.611774	−	1.05962i
$543$		0			0
$544$		0			0
$545$	−13.4853			−0.577646
$546$		0			0
$547$	−31.7990			−1.35963			−0.679813	−	0.733385i	$-0.737939\pi$
$547$	−31.7990			−1.35963			−0.679813	+	0.733385i	$0.737939\pi$
$548$		0			0
$549$		0			0
$550$	−2.41421	+	4.18154i	−0.102942	+	0.178301i
$551$	0.807612	+	1.39882i	0.0344054	+	0.0595919i
$552$		0			0
$553$	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	−0.940767	−	0.339053i	$-0.889893\pi$
$557$	−4.17157	+	7.22538i	−0.176755	+	0.306149i	0.764012	+	0.645202i	$0.223227\pi$
$558$		0			0
$559$	16.5147			0.698498
$560$	−4.00000	−	9.79796i	−0.169031	−	0.414039i
$561$		0			0
$562$	−6.82843	−	11.8272i	−0.288040	−	0.498900i
$563$	−7.14214	+	12.3705i	−0.301005	+	0.521356i	−0.976364	−	0.216133i	$-0.930655\pi$
$563$	−7.14214	+	12.3705i	−0.301005	+	0.521356i	0.675359	+	0.737489i	$0.263989\pi$
$564$		0			0
$565$	−2.17157	−	3.76127i	−0.0913588	−	0.158238i
$566$	18.7279			0.787193
$567$		0			0
$568$	9.65685			0.405193
$569$	−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
$573$		0			0
$574$	−8.31371	−	1.13770i	−0.347007	−	0.0474869i
$575$	6.24264			0.260336
$576$		0			0
$577$	−3.27817	+	5.67796i	−0.136472	+	0.236377i	−0.926159	−	0.377134i	$-0.876910\pi$
$577$	−3.27817	+	5.67796i	−0.136472	+	0.236377i	0.789687	+	0.613510i	$0.210243\pi$
$578$	15.5355	−	26.9083i	0.646193	−	1.11924i
$579$		0			0
$580$		0			0
$581$	−8.77817	+	11.3199i	−0.364180	+	0.469628i
$582$		0			0
$583$	−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
$590$	−1.00000	−	1.73205i	−0.0411693	−	0.0713074i
$591$		0			0
$592$	−11.1716	+	19.3497i	−0.459149	+	0.795269i
$593$	6.70711	+	11.6170i	0.275428	+	0.477055i	0.970243	−	0.242133i	$-0.0778471\pi$
$593$	6.70711	+	11.6170i	0.275428	+	0.477055i	−0.694815	+	0.719188i	$0.744514\pi$
$594$		0			0
$595$	10.1213	−	13.0519i	0.414934	−	0.535077i
$596$		0			0
$597$		0			0
$598$	−7.00000	+	12.1244i	−0.286251	+	0.495802i
$599$	−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	$0.664096\pi$
$602$	−38.6066	−	5.28319i	−1.57349	−	0.215327i
$603$		0			0
$604$		0			0
$605$	−0.328427	+	0.568852i	−0.0133525	+	0.0231271i
$606$		0			0
$607$	0.621320	+	1.07616i	0.0252186	+	0.0436799i	0.878359	−	0.478001i	$-0.158638\pi$
$607$	0.621320	+	1.07616i	0.0252186	+	0.0436799i	−0.853141	+	0.521681i	$0.825305\pi$
$608$		0			0
$609$		0			0
$610$	−17.6569			−0.714905
$611$	−7.38478	−	12.7908i	−0.298756	−	0.517461i
$612$		0			0
$613$	−5.07107	+	8.78335i	−0.204818	+	0.354756i	−0.950075	−	0.312022i	$-0.898994\pi$
$613$	−5.07107	+	8.78335i	−0.204818	+	0.354756i	0.745256	+	0.666778i	$0.232327\pi$
$614$	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			0
$619$	−19.9853	+	34.6155i	−0.803276	+	1.39132i	0.114172	+	0.993461i	$0.463578\pi$
$619$	−19.9853	+	34.6155i	−0.803276	+	1.39132i	−0.917449	+	0.397854i	$0.869755\pi$
$620$		0			0
$621$		0			0
$622$	−24.1421			−0.968011
$623$	−9.84924	−	1.34784i	−0.394602	−	0.0540000i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	18.5355	−	32.1045i	0.740829	−	1.28315i
$627$		0			0
$628$		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			0
$634$	−0.0710678	+	0.123093i	−0.00282246	+	0.00488865i
$635$	9.03553	+	15.6500i	0.358564	+	0.621051i
$636$		0			0
$637$	2.76346	+	10.7510i	0.109492	+	0.425971i
$638$	1.17157			0.0463830
$639$		0			0
$640$	5.65685	−	9.79796i	0.223607	−	0.387298i
$641$	−6.60660	+	11.4430i	−0.260945	+	0.451970i	−0.966493	−	0.256692i	$-0.917367\pi$
$641$	−6.60660	+	11.4430i	−0.260945	+	0.451970i	0.705548	+	0.708662i	$0.250701\pi$
$642$		0			0
$643$	24.5563			0.968408			0.484204	−	0.874955i	$-0.339109\pi$
$643$	24.5563			0.968408			0.484204	+	0.874955i	$0.339109\pi$
$644$		0			0
$645$		0			0
$646$	−29.3848	−	50.8959i	−1.15613	−	2.00247i
$647$	4.80761	−	8.32703i	0.189007	−	0.327369i	−0.755913	−	0.654673i	$-0.772807\pi$
$647$	4.80761	−	8.32703i	0.189007	−	0.327369i	0.944919	+	0.327303i	$0.106140\pi$
$648$		0			0
$649$	−2.41421	−	4.18154i	−0.0947662	−	0.164140i
$650$	2.24264			0.0879636
$651$		0			0
$652$		0			0
$653$	3.87868	+	6.71807i	0.151784	+	0.262898i	0.931884	−	0.362758i	$-0.118165\pi$
$653$	3.87868	+	6.71807i	0.151784	+	0.262898i	−0.780099	+	0.625656i	$0.784831\pi$
$654$		0			0
$655$	−5.24264	+	9.08052i	−0.204847	+	0.354805i
$656$	−4.48528	−	7.76874i	−0.175121	−	0.303318i
$657$		0			0
$658$	13.1716	+	32.2636i	0.513481	+	1.25777i
$659$	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	$0.950365\pi$
$662$	−19.5355	+	33.8365i	−0.759270	+	1.31509i
$663$		0			0
$664$	−15.3137			−0.594287
$665$	−6.65685	−	16.3059i	−0.258142	−	0.632316i
$666$		0			0
$667$	−0.757359	−	1.31178i	−0.0293251	−	0.0507925i
$668$		0			0
$669$		0			0
$670$	8.29289	+	14.3637i	0.320382	+	0.554919i
$671$	−42.6274			−1.64561
$672$		0			0
$673$	2.27208			0.0875822			0.0437911	−	0.999041i	$-0.486056\pi$
$673$	2.27208			0.0875822			0.0437911	+	0.999041i	$0.486056\pi$
$674$	−0.636039	−	1.10165i	−0.0244993	−	0.0424340i
$675$		0			0
$676$		0			0
$677$	1.94975	+	3.37706i	0.0749349	+	0.129791i	0.901058	−	0.433699i	$-0.142792\pi$
$677$	1.94975	+	3.37706i	0.0749349	+	0.129791i	−0.826123	+	0.563490i	$0.809458\pi$
$678$		0			0
$679$	−17.5563	+	22.6398i	−0.673751	+	0.868834i
$680$	17.6569			0.677109
$681$		0			0
$682$	0.414214	−	0.717439i	0.0158611	−	0.0274722i
$683$	10.2929	−	17.8278i	0.393847	−	0.682162i	−0.599107	−	0.800669i	$-0.704477\pi$
$683$	10.2929	−	17.8278i	0.393847	−	0.682162i	0.992953	+	0.118507i	$0.0378108\pi$
$684$		0			0
$685$	2.92893			0.111909
$686$	−3.02082	−	26.0168i	−0.115335	−	0.993327i
$687$		0			0
$688$	−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	−0.995866	−	0.0908295i	$-0.971048\pi$
$691$	−15.1569	−	26.2524i	−0.576594	−	0.998690i	0.419273	−	0.907860i	$-0.362285\pi$
$692$		0			0
$693$		0			0
$694$	−35.3137			−1.34049
$695$	−5.74264	−	9.94655i	−0.217831	−	0.377294i
$696$		0			0
$697$	7.00000	−	12.1244i	0.265144	−	0.459243i
$698$	−11.7574	−	20.3643i	−0.445023	−	0.770802i
$699$		0			0
$700$		0			0
$701$	−41.2132			−1.55660			−0.778301	−	0.627892i	$-0.783918\pi$
$701$	−41.2132			−1.55660			−0.778301	+	0.627892i	$0.783918\pi$
$702$		0			0
$703$	−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	0.951297	−	0.308277i	$-0.0997522\pi$
$709$	5.55635	+	9.62388i	0.208673	+	0.361432i	−0.742624	+	0.669709i	$0.766419\pi$
$710$	2.41421	−	4.18154i	0.0906038	−	0.156930i
$711$		0			0
$712$	−5.31371	−	9.20361i	−0.199140	−	0.344920i
$713$	−1.07107			−0.0401118
$714$		0			0
$715$	5.41421			0.202480
$716$		0			0
$717$		0			0
$718$	18.7990	−	32.5608i	0.701572	−	1.21516i
$719$	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
$722$	−35.7990			−1.33230
$723$		0			0
$724$		0			0
$725$	−0.121320	+	0.210133i	−0.00450572	+	0.00780414i
$726$		0			0
$727$	4.75736			0.176441			0.0882203	−	0.996101i	$-0.471882\pi$
$727$	4.75736			0.176441			0.0882203	+	0.996101i	$0.471882\pi$
$728$	−7.27208	+	9.37769i	−0.269521	+	0.347560i
$729$		0			0
$730$	1.46447	+	2.53653i	0.0542023	+	0.0938812i
$731$	32.5061	−	56.3022i	1.20228	−	2.08241i
$732$		0			0
$733$	5.37868	+	9.31615i	0.198666	+	0.344100i	0.948096	−	0.317984i	$-0.103006\pi$
$733$	5.37868	+	9.31615i	0.198666	+	0.344100i	−0.749430	+	0.662083i	$0.769672\pi$
$734$	27.6985			1.02237
$735$		0			0
$736$		0			0
$737$	20.0208	+	34.6771i	0.737476	+	1.27735i
$738$		0			0
$739$	17.5711	−	30.4340i	0.646362	−	1.11953i	−0.337623	−	0.941281i	$-0.609623\pi$
$739$	17.5711	−	30.4340i	0.646362	−	1.11953i	0.983985	−	0.178251i	$-0.0570438\pi$
$740$		0			0
$741$		0			0
$742$	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			0
$745$	8.82843	−	15.2913i	0.323449	−	0.560229i
$746$	13.6066	−	23.5673i	0.498173	−	0.862861i
$747$		0			0
$748$		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	$0.949911\pi$
$752$	−18.6274	+	32.2636i	−0.679272	+	1.17653i
$753$		0			0
$754$	−0.272078	−	0.471253i	−0.00990849	−	0.0171620i
$755$	−6.48528			−0.236024
$756$		0			0
$757$	41.5980			1.51190			0.755952	−	0.654627i	$-0.227174\pi$
$757$	41.5980			1.51190			0.755952	+	0.654627i	$0.227174\pi$
$758$	10.4645	+	18.1250i	0.380087	+	0.658329i
$759$		0			0
$760$	9.41421	−	16.3059i	0.341489	−	0.591477i
$761$	−10.4645	−	18.1250i	−0.379337	−	0.657030i	0.611629	−	0.791145i	$-0.290514\pi$
$761$	−10.4645	−	18.1250i	−0.379337	−	0.657030i	−0.990966	+	0.134114i	$0.957181\pi$
$762$		0			0
$763$	−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	$0.592976\pi$
$770$	−12.6569	−	1.73205i	−0.456121	−	0.0624188i
$771$		0			0
$772$		0			0
$773$	12.4645	−	21.5891i	0.448316	−	0.776506i	−0.549961	−	0.835190i	$-0.685357\pi$
$773$	12.4645	−	21.5891i	0.448316	−	0.776506i	0.998277	+	0.0586849i	$0.0186907\pi$
$774$		0			0
$775$	0.0857864	+	0.148586i	0.00308154	+	0.00533738i
$776$	−30.6274			−1.09946
$777$		0			0
$778$	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			0
$784$	20.0000	−	19.5959i	0.714286	−	0.699854i
$785$	−16.1421			−0.576138
$786$		0			0
$787$	−6.58579	+	11.4069i	−0.234758	+	0.406613i	−0.959202	−	0.282721i	$-0.908763\pi$
$787$	−6.58579	+	11.4069i	−0.234758	+	0.406613i	0.724444	+	0.689333i	$0.242096\pi$
$788$		0			0
$789$		0			0
$790$	6.58579			0.234312
$791$	7.04163	−	9.08052i	0.250372	−	0.322866i
$792$		0			0
$793$	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	$0.559218\pi$
$798$		0			0
$799$	−58.1421			−2.05692
$800$		0			0
$801$		0			0
$802$	−0.343146	+	0.594346i	−0.0121169	+	0.0209871i
$803$	3.53553	+	6.12372i	0.124766	+	0.216102i
$804$		0			0
$805$	6.24264	+	15.2913i	0.220024	+	0.538947i
$806$	−0.384776			−0.0135532
$807$		0			0
$808$	−8.82843	+	15.2913i	−0.310583	+	0.537946i
$809$	−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
$813$		0			0
$814$	13.4853	+	23.3572i	0.472659	+	0.818669i
$815$	9.65685	−	16.7262i	0.338265	−	0.585892i
$816$		0			0
$817$	−34.6630	−	60.0380i	−1.21270	−	2.10046i
$818$	37.2132			1.30113
$819$		0			0
$820$		0			0
$821$	6.77817	+	11.7401i	0.236560	+	0.409734i	0.959725	−	0.280942i	$-0.0906467\pi$
$821$	6.77817	+	11.7401i	0.236560	+	0.409734i	−0.723165	+	0.690675i	$0.757313\pi$
$822$		0			0
$823$	−11.1421	+	19.2987i	−0.388390	+	0.672712i	−0.992233	−	0.124391i	$-0.960302\pi$
$823$	−11.1421	+	19.2987i	−0.388390	+	0.672712i	0.603843	+	0.797103i	$0.293635\pi$
$824$	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	−0.657318	−	0.753614i	$-0.728309\pi$
$829$	9.32843	−	16.1573i	0.323990	−	0.561167i	0.981307	+	0.192447i	$0.0616424\pi$
$830$	−3.82843	+	6.63103i	−0.132887	+	0.230166i
$831$		0			0
$832$	−12.6863			−0.439818
$833$	42.0919	+	11.7401i	1.45840	+	0.406772i
$834$		0			0
$835$	5.87868	+	10.1822i	0.203440	+	0.352369i
$836$		0			0
$837$		0			0
$838$	2.24264	+	3.88437i	0.0774707	+	0.134183i
$839$	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
$842$	19.4350	+	33.6625i	0.669775	+	1.16008i
$843$		0			0
$844$		0			0
$845$	5.24264	+	9.08052i	0.180352	+	0.312379i
$846$		0			0
$847$	−1.72183	−	0.235626i	−0.0591626	−	0.00809622i
$848$	4.68629			0.160928
$849$		0			0
$850$	4.41421	−	7.64564i	0.151406	−	0.262243i
$851$	17.4350	−	30.1984i	0.597665	−	1.03519i
$852$		0			0
$853$	38.0122			1.30151			0.650756	−	0.759287i	$-0.274452\pi$
$853$	38.0122			1.30151			0.650756	+	0.759287i	$0.274452\pi$
$854$	−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	−0.914400	−	0.404812i	$-0.867337\pi$
$857$	−3.12132	+	5.40629i	−0.106622	+	0.184675i	0.807778	+	0.589487i	$0.200670\pi$
$858$		0			0
$859$	−7.82843	−	13.5592i	−0.267102	−	0.462635i	0.701010	−	0.713152i	$-0.252733\pi$
$859$	−7.82843	−	13.5592i	−0.267102	−	0.462635i	−0.968112	+	0.250517i	$0.919400\pi$
$860$		0			0
$861$		0			0
$862$	52.0833			1.77396
$863$	−4.89949	−	8.48617i	−0.166781	−	0.288873i	0.770505	−	0.637433i	$-0.220004\pi$
$863$	−4.89949	−	8.48617i	−0.166781	−	0.288873i	−0.937286	+	0.348561i	$0.886671\pi$
$864$		0			0
$865$	−1.41421	+	2.44949i	−0.0480847	+	0.0832851i
$866$	−17.3640	−	30.0753i	−0.590051	−	1.02200i
$867$		0			0
$868$		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
$873$		0			0
$874$	58.7696			1.98791
$875$	1.62132	−	2.09077i	0.0548106	−	0.0706809i
$876$		0			0
$877$	9.00000	+	15.5885i	0.303908	+	0.526385i	0.977018	−	0.213158i	$-0.0683750\pi$
$877$	9.00000	+	15.5885i	0.303908	+	0.526385i	−0.673109	+	0.739543i	$0.735042\pi$
$878$	0.242641	−	0.420266i	0.00818873	−	0.0141833i
$879$		0			0
$880$	−6.82843	−	11.8272i	−0.230186	−	0.398694i
$881$	21.6569			0.729638			0.364819	−	0.931078i	$-0.381131\pi$
$881$	21.6569			0.729638			0.364819	+	0.931078i	$0.381131\pi$
$882$		0			0
$883$	8.07107			0.271613			0.135807	−	0.990735i	$-0.456637\pi$
$883$	8.07107			0.271613			0.135807	+	0.990735i	$0.456637\pi$
$884$		0			0
$885$		0			0
$886$	−0.343146	+	0.594346i	−0.0115282	+	0.0199674i
$887$	2.60660	+	4.51477i	0.0875211	+	0.151591i	0.906463	−	0.422286i	$-0.138772\pi$
$887$	2.60660	+	4.51477i	0.0875211	+	0.151591i	−0.818942	+	0.573877i	$0.805439\pi$
$888$		0			0
$889$	−29.2990	+	37.7825i	−0.982657	+	1.26718i
$890$	−5.31371			−0.178116
$891$		0			0
$892$		0			0
$893$	−31.0000	+	53.6936i	−1.03738	+	1.79679i
$894$		0			0
$895$	−19.6569			−0.657056
$896$	29.6569	+	4.05845i	0.990766	+	0.135583i
$897$		0			0
$898$	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
$903$		0			0
$904$	12.2843			0.408569
$905$	−0.328427	−	0.568852i	−0.0109173	−	0.0189093i
$906$		0			0
$907$	4.30761	−	7.46100i	0.143032	−	0.247739i	−0.785605	−	0.618728i	$-0.787648\pi$
$907$	4.30761	−	7.46100i	0.143032	−	0.247739i	0.928637	+	0.370990i	$0.120982\pi$
$908$		0			0
$909$		0			0
$910$	2.24264	+	5.49333i	0.0743428	+	0.182102i
$911$	−4.24264			−0.140565			−0.0702825	−	0.997527i	$-0.522390\pi$
$911$	−4.24264			−0.140565			−0.0702825	+	0.997527i	$0.522390\pi$
$912$		0			0
$913$	−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
$918$		0			0
$919$	23.3284	+	40.4060i	0.769534	+	1.33287i	0.937816	+	0.347133i	$0.112845\pi$
$919$	23.3284	+	40.4060i	0.769534	+	1.33287i	−0.168282	+	0.985739i	$0.553822\pi$
$920$	−8.82843	+	15.2913i	−0.291065	+	0.504139i
$921$		0			0
$922$	19.1421	+	33.1552i	0.630413	+	1.09191i
$923$	−5.41421			−0.178211
$924$		0			0
$925$	−5.58579			−0.183660
$926$	−7.36396	−	12.7548i	−0.241995	−	0.419147i
$927$		0			0
$928$		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
$933$		0			0
$934$	−4.72792	+	8.18900i	−0.154702	+	0.267952i
$935$	10.6569	−	18.4582i	0.348516	−	0.603648i
$936$		0			0
$937$	−7.92893			−0.259027			−0.129513	−	0.991578i	$-0.541342\pi$
$937$	−7.92893			−0.259027			−0.129513	+	0.991578i	$0.541342\pi$
$938$	−26.8909	+	34.6771i	−0.878018	+	1.13225i
$939$		0			0
$940$		0			0
$941$	−5.63604	+	9.76191i	−0.183730	+	0.318229i	−0.943148	−	0.332374i	$-0.892150\pi$
$941$	−5.63604	+	9.76191i	−0.183730	+	0.318229i	0.759418	+	0.650603i	$0.225484\pi$
$942$		0			0
$943$	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	0.823202	−	0.567749i	$-0.192186\pi$
$947$	−2.46447	−	4.26858i	−0.0800844	−	0.138710i	−0.903286	+	0.429039i	$0.858852\pi$
$948$		0			0
$949$	1.64214	−	2.84426i	0.0533060	−	0.0923287i
$950$	−4.70711	−	8.15295i	−0.152719	−	0.264517i
$951$		0			0
$952$	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			0
$955$	9.48528	−	16.4290i	0.306936	−	0.531630i
$956$		0			0
$957$		0			0
$958$	−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
$963$		0			0
$964$		0			0
$965$	−6.75736			−0.217527
$966$		0			0
$967$	23.3848			0.752004			0.376002	−	0.926619i	$-0.377299\pi$
$967$	23.3848			0.752004			0.376002	+	0.926619i	$0.377299\pi$
$968$	−0.928932	−	1.60896i	−0.0298570	−	0.0517139i
$969$		0			0
$970$	−7.65685	+	13.2621i	−0.245847	+	0.425819i
$971$	7.17157	+	12.4215i	0.230147	+	0.398626i	0.957851	−	0.287265i	$-0.0927461\pi$
$971$	7.17157	+	12.4215i	0.230147	+	0.398626i	−0.727704	+	0.685891i	$0.759413\pi$
$972$		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	−0.735415	−	0.677617i	$-0.763013\pi$
$977$	6.84924	−	11.8632i	0.219127	−	0.379539i	0.954541	+	0.298079i	$0.0963459\pi$
$978$		0			0
$979$	−12.8284			−0.409998
$980$		0			0
$981$		0			0
$982$	7.17157	+	12.4215i	0.228854	+	0.396387i
$983$	26.5772	−	46.0330i	0.847680	−	1.46822i	−0.0355935	−	0.999366i	$-0.511332\pi$
$983$	26.5772	−	46.0330i	0.847680	−	1.46822i	0.883273	−	0.468858i	$-0.155335\pi$
$984$		0			0
$985$	2.77817	+	4.81194i	0.0885200	+	0.153321i
$986$	−2.14214			−0.0682195
$987$		0			0
$988$		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
$993$		0			0
$994$	12.6569	+	1.73205i	0.401451	+	0.0549373i
$995$	5.51472			0.174828
$996$		0			0
$997$	−0.378680	+	0.655892i	−0.0119929	+	0.0207723i	−0.871960	−	0.489578i	$-0.837151\pi$
$997$	−0.378680	+	0.655892i	−0.0119929	+	0.0207723i	0.859967	+	0.510350i	$0.170484\pi$
$998$	6.22183	−	10.7765i	0.196948	−	0.341125i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.j.d.46.2		4
3.2	odd	2		105.2.i.c.46.1	yes	4
7.2	even	3	inner	315.2.j.d.226.2		4
7.3	odd	6		2205.2.a.s.1.1		2
7.4	even	3		2205.2.a.u.1.1		2
12.11	even	2		1680.2.bg.p.1201.1		4
15.2	even	4		525.2.r.g.424.3		8
15.8	even	4		525.2.r.g.424.2		8
15.14	odd	2		525.2.i.g.151.2		4
21.2	odd	6		105.2.i.c.16.1	✓	4
21.5	even	6		735.2.i.j.226.1		4
21.11	odd	6		735.2.a.i.1.2		2
21.17	even	6		735.2.a.j.1.2		2
21.20	even	2		735.2.i.j.361.1		4
84.23	even	6		1680.2.bg.p.961.1		4
105.2	even	12		525.2.r.g.499.2		8
105.23	even	12		525.2.r.g.499.3		8
105.44	odd	6		525.2.i.g.226.2		4
105.59	even	6		3675.2.a.x.1.1		2
105.74	odd	6		3675.2.a.z.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.c.16.1	✓	4	21.2	odd	6
105.2.i.c.46.1	yes	4	3.2	odd	2
315.2.j.d.46.2		4	1.1	even	1	trivial
315.2.j.d.226.2		4	7.2	even	3	inner
525.2.i.g.151.2		4	15.14	odd	2
525.2.i.g.226.2		4	105.44	odd	6
525.2.r.g.424.2		8	15.8	even	4
525.2.r.g.424.3		8	15.2	even	4
525.2.r.g.499.2		8	105.2	even	12
525.2.r.g.499.3		8	105.23	even	12
735.2.a.i.1.2		2	21.11	odd	6
735.2.a.j.1.2		2	21.17	even	6
735.2.i.j.226.1		4	21.5	even	6
735.2.i.j.361.1		4	21.20	even	2
1680.2.bg.p.961.1		4	84.23	even	6
1680.2.bg.p.1201.1		4	12.11	even	2
2205.2.a.s.1.1		2	7.3	odd	6
2205.2.a.u.1.1		2	7.4	even	3
3675.2.a.x.1.1		2	105.59	even	6
3675.2.a.z.1.1		2	105.74	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-0.500000 - 0.866025i) q^{5} +(1.62132 - 2.09077i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(-0.500000 - 0.866025i) q^{5} +(1.62132 - 2.09077i) q^{7} +2.82843 q^{8} +(0.707107 - 1.22474i) q^{10} +(1.70711 - 2.95680i) q^{11} -1.58579 q^{13} +(3.70711 + 0.507306i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-3.12132 + 5.40629i) q^{17} +(3.32843 + 5.76500i) q^{19} +4.82843 q^{22} +(-3.12132 - 5.40629i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-1.12132 - 1.94218i) q^{26} +0.242641 q^{29} +(0.0857864 - 0.148586i) q^{31} -8.82843 q^{34} +(-2.62132 - 0.358719i) q^{35} +(2.79289 + 4.83743i) q^{37} +(-4.70711 + 8.15295i) q^{38} +(-1.41421 - 2.44949i) q^{40} -2.24264 q^{41} -10.4142 q^{43} +(4.41421 - 7.64564i) q^{46} +(4.65685 + 8.06591i) q^{47} +(-1.74264 - 6.77962i) q^{49} -1.41421 q^{50} +(0.585786 - 1.01461i) q^{53} -3.41421 q^{55} +(4.58579 - 5.91359i) q^{56} +(0.171573 + 0.297173i) q^{58} +(0.707107 - 1.22474i) q^{59} +(-6.24264 - 10.8126i) q^{61} +0.242641 q^{62} +8.00000 q^{64} +(0.792893 + 1.37333i) q^{65} +(-5.86396 + 10.1567i) q^{67} +(-1.41421 - 3.46410i) q^{70} +3.41421 q^{71} +(-1.03553 + 1.79360i) q^{73} +(-3.94975 + 6.84116i) q^{74} +(-3.41421 - 8.36308i) q^{77} +(2.32843 + 4.03295i) q^{79} +(2.00000 - 3.46410i) q^{80} +(-1.58579 - 2.74666i) q^{82} -5.41421 q^{83} +6.24264 q^{85} +(-7.36396 - 12.7548i) q^{86} +(4.82843 - 8.36308i) q^{88} +(-1.87868 - 3.25397i) q^{89} +(-2.57107 + 3.31552i) q^{91} +(-6.58579 + 11.4069i) q^{94} +(3.32843 - 5.76500i) q^{95} -10.8284 q^{97} +(7.07107 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{5} - 2 q^{7}+O(q^{10}) \) 4 * q - 2 * q^5 - 2 * q^7	\( 4 q - 2 q^{5} - 2 q^{7} + 4 q^{11} - 12 q^{13} + 12 q^{14} + 8 q^{16} - 4 q^{17} + 2 q^{19} + 8 q^{22} - 4 q^{23} - 2 q^{25} + 4 q^{26} - 16 q^{29} + 6 q^{31} - 24 q^{34} - 2 q^{35} + 14 q^{37} - 16 q^{38} + 8 q^{41} - 36 q^{43} + 12 q^{46} - 4 q^{47} + 10 q^{49} + 8 q^{53} - 8 q^{55} + 24 q^{56} + 12 q^{58} - 8 q^{61} - 16 q^{62} + 32 q^{64} + 6 q^{65} + 2 q^{67} + 8 q^{71} + 10 q^{73} + 4 q^{74} - 8 q^{77} - 2 q^{79} + 8 q^{80} - 12 q^{82} - 16 q^{83} + 8 q^{85} - 4 q^{86} + 8 q^{88} - 16 q^{89} + 18 q^{91} - 32 q^{94} + 2 q^{95} - 32 q^{97}+O(q^{100}) \) 4 * q - 2 * q^5 - 2 * q^7 + 4 * q^11 - 12 * q^13 + 12 * q^14 + 8 * q^16 - 4 * q^17 + 2 * q^19 + 8 * q^22 - 4 * q^23 - 2 * q^25 + 4 * q^26 - 16 * q^29 + 6 * q^31 - 24 * q^34 - 2 * q^35 + 14 * q^37 - 16 * q^38 + 8 * q^41 - 36 * q^43 + 12 * q^46 - 4 * q^47 + 10 * q^49 + 8 * q^53 - 8 * q^55 + 24 * q^56 + 12 * q^58 - 8 * q^61 - 16 * q^62 + 32 * q^64 + 6 * q^65 + 2 * q^67 + 8 * q^71 + 10 * q^73 + 4 * q^74 - 8 * q^77 - 2 * q^79 + 8 * q^80 - 12 * q^82 - 16 * q^83 + 8 * q^85 - 4 * q^86 + 8 * q^88 - 16 * q^89 + 18 * q^91 - 32 * q^94 + 2 * q^95 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more