LMFDB - Embedded newform 370.2.c.a.369.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(369,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("370.369");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 19x^{8} + 103x^{6} + 210x^{4} + 140x^{2} + 16 $ x^10 + 19x^8 + 103x^6 + 210x^4 + 140x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			369.2
Root			$-1.78647i$ of defining polynomial
Character	$\chi$	$=$	370.369
Dual form			370.2.c.a.369.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.78647i q^{3} +1.00000 q^{4} +(2.21736 + 0.288618i) q^{5} +1.78647i q^{6} -3.14934i q^{7} -1.00000 q^{8} -0.191472 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.78647i q^{3} +1.00000 q^{4} +(2.21736 + 0.288618i) q^{5} +1.78647i q^{6} -3.14934i q^{7} -1.00000 q^{8} -0.191472 q^{9} +(-2.21736 - 0.288618i) q^{10} -0.908956 q^{11} -1.78647i q^{12} +2.22269 q^{13} +3.14934i q^{14} +(0.515607 - 3.96125i) q^{15} +1.00000 q^{16} +2.10043 q^{17} +0.191472 q^{18} +4.16694i q^{19} +(2.21736 + 0.288618i) q^{20} -5.62620 q^{21} +0.908956 q^{22} -7.66680 q^{23} +1.78647i q^{24} +(4.83340 + 1.27994i) q^{25} -2.22269 q^{26} -5.01735i q^{27} -3.14934i q^{28} -2.69676i q^{29} +(-0.515607 + 3.96125i) q^{30} -5.96563i q^{31} -1.00000 q^{32} +1.62382i q^{33} -2.10043 q^{34} +(0.908956 - 6.98323i) q^{35} -0.191472 q^{36} +(-1.10043 - 5.98240i) q^{37} -4.16694i q^{38} -3.97076i q^{39} +(-2.21736 - 0.288618i) q^{40} +2.32312 q^{41} +5.62620 q^{42} -5.72663 q^{43} -0.908956 q^{44} +(-0.424564 - 0.0552624i) q^{45} +7.66680 q^{46} +8.89435i q^{47} -1.78647i q^{48} -2.91834 q^{49} +(-4.83340 - 1.27994i) q^{50} -3.75235i q^{51} +2.22269 q^{52} +9.37592i q^{53} +5.01735i q^{54} +(-2.01549 - 0.262341i) q^{55} +3.14934i q^{56} +7.44411 q^{57} +2.69676i q^{58} +5.55880i q^{59} +(0.515607 - 3.96125i) q^{60} -3.16611i q^{61} +5.96563i q^{62} +0.603011i q^{63} +1.00000 q^{64} +(4.92850 + 0.641508i) q^{65} -1.62382i q^{66} -7.64933i q^{67} +2.10043 q^{68} +13.6965i q^{69} +(-0.908956 + 6.98323i) q^{70} +13.5157 q^{71} +0.191472 q^{72} +2.14851i q^{73} +(1.10043 + 5.98240i) q^{74} +(2.28658 - 8.63472i) q^{75} +4.16694i q^{76} +2.86261i q^{77} +3.97076i q^{78} +3.35774i q^{79} +(2.21736 + 0.288618i) q^{80} -9.53776 q^{81} -2.32312 q^{82} +16.2776i q^{83} -5.62620 q^{84} +(4.65741 + 0.606222i) q^{85} +5.72663 q^{86} -4.81767 q^{87} +0.908956 q^{88} +8.35832i q^{89} +(0.424564 + 0.0552624i) q^{90} -7.00000i q^{91} -7.66680 q^{92} -10.6574 q^{93} -8.89435i q^{94} +(-1.20265 + 9.23962i) q^{95} +1.78647i q^{96} -5.14283 q^{97} +2.91834 q^{98} +0.174040 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} - 8 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 - 8 * q^9	$ 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} - 8 q^{9} + 3 q^{10} - 2 q^{13} - 10 q^{15} + 10 q^{16} + 18 q^{17} + 8 q^{18} - 3 q^{20} - 12 q^{21} + 10 q^{23} + 5 q^{25} + 2 q^{26} + 10 q^{30} - 10 q^{32} - 18 q^{34} - 8 q^{36} - 8 q^{37} + 3 q^{40} - 4 q^{41} + 12 q^{42} - 10 q^{43} + 20 q^{45} - 10 q^{46} - 8 q^{49} - 5 q^{50} - 2 q^{52} + 5 q^{55} + 12 q^{57} - 10 q^{60} + 10 q^{64} + 2 q^{65} + 18 q^{68} - 20 q^{71} + 8 q^{72} + 8 q^{74} + 25 q^{75} - 3 q^{80} + 58 q^{81} + 4 q^{82} - 12 q^{84} - 28 q^{85} + 10 q^{86} - 10 q^{87} - 20 q^{90} + 10 q^{92} - 32 q^{93} + 2 q^{95} + 2 q^{97} + 8 q^{98} - 82 q^{99}+O(q^{100}) $ 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 - 8 * q^9 + 3 * q^10 - 2 * q^13 - 10 * q^15 + 10 * q^16 + 18 * q^17 + 8 * q^18 - 3 * q^20 - 12 * q^21 + 10 * q^23 + 5 * q^25 + 2 * q^26 + 10 * q^30 - 10 * q^32 - 18 * q^34 - 8 * q^36 - 8 * q^37 + 3 * q^40 - 4 * q^41 + 12 * q^42 - 10 * q^43 + 20 * q^45 - 10 * q^46 - 8 * q^49 - 5 * q^50 - 2 * q^52 + 5 * q^55 + 12 * q^57 - 10 * q^60 + 10 * q^64 + 2 * q^65 + 18 * q^68 - 20 * q^71 + 8 * q^72 + 8 * q^74 + 25 * q^75 - 3 * q^80 + 58 * q^81 + 4 * q^82 - 12 * q^84 - 28 * q^85 + 10 * q^86 - 10 * q^87 - 20 * q^90 + 10 * q^92 - 32 * q^93 + 2 * q^95 + 2 * q^97 + 8 * q^98 - 82 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		−	1.78647i		−	1.03142i	−0.856764	−	0.515709i	$-0.827528\pi$
$3$		−	1.78647i		−	1.03142i	0.856764	−	0.515709i	$-0.172472\pi$
$4$	1.00000			0.500000
$5$	2.21736	+	0.288618i	0.991635	+	0.129074i
$5$	2.21736	+	0.288618i	0.991635	+	0.129074i
$6$			1.78647i			0.729323i
$7$		−	3.14934i		−	1.19034i	−0.803600	−	0.595169i	$-0.797085\pi$
$7$		−	3.14934i		−	1.19034i	0.803600	−	0.595169i	$-0.202915\pi$
$8$	−1.00000			−0.353553
$9$	−0.191472			−0.0638241
$10$	−2.21736	−	0.288618i	−0.701192	−	0.0912690i
$11$	−0.908956			−0.274061			−0.137030	−	0.990567i	$-0.543756\pi$
$11$	−0.908956			−0.274061			−0.137030	+	0.990567i	$0.543756\pi$
$12$		−	1.78647i		−	0.515709i
$13$	2.22269			0.616462			0.308231	−	0.951311i	$-0.400263\pi$
$13$	2.22269			0.616462			0.308231	+	0.951311i	$0.400263\pi$
$14$			3.14934i			0.841696i
$15$	0.515607	−	3.96125i	0.133129	−	1.02279i
$16$	1.00000			0.250000
$17$	2.10043			0.509429			0.254714	−	0.967016i	$-0.418019\pi$
$17$	2.10043			0.509429			0.254714	+	0.967016i	$0.418019\pi$
$18$	0.191472			0.0451305
$19$			4.16694i			0.955962i	0.878370	+	0.477981i	$0.158631\pi$
$19$			4.16694i			0.955962i	−0.878370	+	0.477981i	$0.841369\pi$
$20$	2.21736	+	0.288618i	0.495817	+	0.0645370i
$21$	−5.62620			−1.22774
$22$	0.908956			0.193790
$23$	−7.66680			−1.59864			−0.799319	−	0.600907i	$-0.794806\pi$
$23$	−7.66680			−1.59864			−0.799319	+	0.600907i	$0.794806\pi$
$24$			1.78647i			0.364662i
$25$	4.83340	+	1.27994i	0.966680	+	0.255988i
$26$	−2.22269			−0.435905
$27$		−	5.01735i		−	0.965589i
$28$		−	3.14934i		−	0.595169i
$29$		−	2.69676i		−	0.500775i	−0.968146	−	0.250387i	$-0.919442\pi$
$29$		−	2.69676i		−	0.500775i	0.968146	−	0.250387i	$-0.0805580\pi$
$30$	−0.515607	+	3.96125i	−0.0941366	+	0.723222i
$31$		−	5.96563i		−	1.07146i	−0.844390	−	0.535729i	$-0.820037\pi$
$31$		−	5.96563i		−	1.07146i	0.844390	−	0.535729i	$-0.179963\pi$
$32$	−1.00000			−0.176777
$33$			1.62382i			0.282671i
$34$	−2.10043			−0.360221
$35$	0.908956	−	6.98323i	0.153642	−	1.18038i
$36$	−0.191472			−0.0319121
$37$	−1.10043	−	5.98240i	−0.180909	−	0.983500i
$37$	−1.10043	−	5.98240i	−0.180909	−	0.983500i
$38$		−	4.16694i		−	0.675967i
$39$		−	3.97076i		−	0.635831i
$40$	−2.21736	−	0.288618i	−0.350596	−	0.0456345i
$41$	2.32312			0.362810			0.181405	−	0.983409i	$-0.441936\pi$
$41$	2.32312			0.362810			0.181405	+	0.983409i	$0.441936\pi$
$42$	5.62620			0.868141
$43$	−5.72663			−0.873302			−0.436651	−	0.899631i	$-0.643836\pi$
$43$	−5.72663			−0.873302			−0.436651	+	0.899631i	$0.643836\pi$
$44$	−0.908956			−0.137030
$45$	−0.424564	−	0.0552624i	−0.0632902	−	0.00823803i
$46$	7.66680			1.13041
$47$			8.89435i			1.29737i	0.761055	+	0.648687i	$0.224682\pi$
$47$			8.89435i			1.29737i	−0.761055	+	0.648687i	$0.775318\pi$
$48$		−	1.78647i		−	0.257855i
$49$	−2.91834			−0.416906
$50$	−4.83340	−	1.27994i	−0.683546	−	0.181011i
$51$		−	3.75235i		−	0.525434i
$52$	2.22269			0.308231
$53$			9.37592i			1.28788i	0.765075	+	0.643941i	$0.222702\pi$
$53$			9.37592i			1.28788i	−0.765075	+	0.643941i	$0.777298\pi$
$54$			5.01735i			0.682775i
$55$	−2.01549	−	0.262341i	−0.271768	−	0.0353741i
$56$			3.14934i			0.420848i
$57$	7.44411			0.985997
$58$			2.69676i			0.354101i
$59$			5.55880i			0.723694i	0.932238	+	0.361847i	$0.117854\pi$
$59$			5.55880i			0.723694i	−0.932238	+	0.361847i	$0.882146\pi$
$60$	0.515607	−	3.96125i	0.0665646	−	0.511395i
$61$		−	3.16611i		−	0.405378i	−0.979243	−	0.202689i	$-0.935032\pi$
$61$		−	3.16611i		−	0.405378i	0.979243	−	0.202689i	$-0.0649681\pi$
$62$			5.96563i			0.757636i
$63$			0.603011i			0.0759723i
$64$	1.00000			0.125000
$65$	4.92850	+	0.641508i	0.611306	+	0.0795692i
$66$		−	1.62382i		−	0.199879i
$67$		−	7.64933i		−	0.934515i	−0.884121	−	0.467257i	$-0.845242\pi$
$67$		−	7.64933i		−	0.934515i	0.884121	−	0.467257i	$-0.154758\pi$
$68$	2.10043			0.254714
$69$			13.6965i			1.64886i
$70$	−0.908956	+	6.98323i	−0.108641	+	0.834656i
$71$	13.5157			1.60402			0.802008	−	0.597313i	$-0.203765\pi$
$71$	13.5157			1.60402			0.802008	+	0.597313i	$0.203765\pi$
$72$	0.191472			0.0225652
$73$			2.14851i			0.251464i	0.992064	+	0.125732i	$0.0401279\pi$
$73$			2.14851i			0.251464i	−0.992064	+	0.125732i	$0.959872\pi$
$74$	1.10043	+	5.98240i	0.127922	+	0.695439i
$75$	2.28658	−	8.63472i	0.264031	−	0.997051i
$76$			4.16694i			0.477981i
$77$			2.86261i			0.326225i
$78$			3.97076i			0.449600i
$79$			3.35774i			0.377775i	0.981999	+	0.188888i	$0.0604882\pi$
$79$			3.35774i			0.377775i	−0.981999	+	0.188888i	$0.939512\pi$
$80$	2.21736	+	0.288618i	0.247909	+	0.0322685i
$81$	−9.53776			−1.05975
$82$	−2.32312			−0.256545
$83$			16.2776i			1.78670i	0.449361	+	0.893350i	$0.351652\pi$
$83$			16.2776i			1.78670i	−0.449361	+	0.893350i	$0.648348\pi$
$84$	−5.62620			−0.613869
$85$	4.65741	+	0.606222i	0.505167	+	0.0657540i
$86$	5.72663			0.617518
$87$	−4.81767			−0.516509
$88$	0.908956			0.0968951
$89$			8.35832i			0.885980i	0.896527	+	0.442990i	$0.146082\pi$
$89$			8.35832i			0.885980i	−0.896527	+	0.442990i	$0.853918\pi$
$90$	0.424564	+	0.0552624i	0.0447529	+	0.00582517i
$91$		−	7.00000i		−	0.733799i
$92$	−7.66680			−0.799319
$93$	−10.6574			−1.10512
$94$		−	8.89435i		−	0.917382i
$95$	−1.20265	+	9.23962i	−0.123390	+	0.947965i
$96$			1.78647i			0.182331i
$97$	−5.14283			−0.522175			−0.261087	−	0.965315i	$-0.584081\pi$
$97$	−5.14283			−0.522175			−0.261087	+	0.965315i	$0.584081\pi$
$98$	2.91834			0.294797
$99$	0.174040			0.0174917
$100$	4.83340	+	1.27994i	0.483340	+	0.127994i
$101$	−3.20212			−0.318623			−0.159311	−	0.987228i	$-0.550927\pi$
$101$	−3.20212			−0.318623			−0.159311	+	0.987228i	$0.550927\pi$
$102$			3.75235i			0.371538i
$103$	17.6871			1.74276			0.871382	−	0.490605i	$-0.163224\pi$
$103$	17.6871			1.74276			0.871382	+	0.490605i	$0.163224\pi$
$104$	−2.22269			−0.217952
$105$	−12.4753	−	1.62382i	−1.21747	−	0.158469i
$106$		−	9.37592i		−	0.910670i
$107$			6.75126i			0.652669i	0.945254	+	0.326335i	$0.105814\pi$
$107$			6.75126i			0.652669i	−0.945254	+	0.326335i	$0.894186\pi$
$108$		−	5.01735i		−	0.482795i
$109$			10.5304i			1.00863i	0.863520	+	0.504314i	$0.168255\pi$
$109$			10.5304i			1.00863i	−0.863520	+	0.504314i	$0.831745\pi$
$110$	2.01549	+	0.262341i	0.192169	+	0.0250133i
$111$	−10.6874	+	1.96588i	−1.01440	+	0.186593i
$112$		−	3.14934i		−	0.297585i
$113$	6.32365			0.594879			0.297439	−	0.954741i	$-0.403867\pi$
$113$	6.32365			0.594879			0.297439	+	0.954741i	$0.403867\pi$
$114$	−7.44411			−0.697205
$115$	−17.0001	−	2.21278i	−1.58527	−	0.206342i
$116$		−	2.69676i		−	0.250387i
$117$	−0.425583			−0.0393452
$118$		−	5.55880i		−	0.511729i
$119$		−	6.61496i		−	0.606393i
$120$	−0.515607	+	3.96125i	−0.0470683	+	0.361611i
$121$	−10.1738			−0.924891
$122$			3.16611i			0.286646i
$123$		−	4.15017i		−	0.374209i
$124$		−	5.96563i		−	0.535729i
$125$	10.3480	+	4.23310i	0.925552	+	0.378620i
$126$		−	0.603011i		−	0.0537205i
$127$			15.0472i			1.33522i	0.744512	+	0.667609i	$0.232682\pi$
$127$			15.0472i			1.33522i	−0.744512	+	0.667609i	$0.767318\pi$
$128$	−1.00000			−0.0883883
$129$			10.2304i			0.900740i
$130$	−4.92850	−	0.641508i	−0.432258	−	0.0562639i
$131$		−	3.31974i		−	0.290047i	−0.989428	−	0.145024i	$-0.953674\pi$
$131$		−	3.31974i		−	0.290047i	0.989428	−	0.145024i	$-0.0463258\pi$
$132$			1.62382i			0.141336i
$133$	13.1231			1.13792
$134$			7.64933i			0.660802i
$135$	1.44810	−	11.1253i	0.124632	−	0.957512i
$136$	−2.10043			−0.180110
$137$		−	17.9355i		−	1.53234i	−0.642640	−	0.766168i	$-0.722161\pi$
$137$		−	17.9355i		−	1.53234i	0.642640	−	0.766168i	$-0.277839\pi$
$138$		−	13.6965i		−	1.16592i
$139$	12.7472			1.08120			0.540601	−	0.841279i	$-0.318197\pi$
$139$	12.7472			1.08120			0.540601	+	0.841279i	$0.318197\pi$
$140$	0.908956	−	6.98323i	0.0768208	−	0.590191i
$141$	15.8895			1.33814
$142$	−13.5157			−1.13421
$143$	−2.02033			−0.168948
$144$	−0.191472			−0.0159560
$145$	0.778332	−	5.97969i	0.0646370	−	0.496586i
$146$		−	2.14851i		−	0.177812i
$147$			5.21353i			0.430004i
$148$	−1.10043	−	5.98240i	−0.0904547	−	0.491750i
$149$	−6.83795			−0.560186			−0.280093	−	0.959973i	$-0.590365\pi$
$149$	−6.83795			−0.560186			−0.280093	+	0.959973i	$0.590365\pi$
$150$	−2.28658	+	8.63472i	−0.186698	+	0.705022i
$151$	−2.80702			−0.228432			−0.114216	−	0.993456i	$-0.536436\pi$
$151$	−2.80702			−0.228432			−0.114216	+	0.993456i	$0.536436\pi$
$152$		−	4.16694i		−	0.337984i
$153$	−0.402174			−0.0325138
$154$		−	2.86261i		−	0.230676i
$155$	1.72179	−	13.2280i	0.138297	−	1.06250i
$156$		−	3.97076i		−	0.317915i
$157$		−	7.28275i		−	0.581227i	−0.956841	−	0.290613i	$-0.906141\pi$
$157$		−	7.28275i		−	0.581227i	0.956841	−	0.290613i	$-0.0938593\pi$
$158$		−	3.35774i		−	0.267127i
$159$	16.7498			1.32835
$160$	−2.21736	−	0.288618i	−0.175298	−	0.0228173i
$161$			24.1454i			1.90292i
$162$	9.53776			0.749357
$163$	22.2319			1.74134			0.870669	−	0.491870i	$-0.163686\pi$
$163$	22.2319			1.74134			0.870669	+	0.491870i	$0.163686\pi$
$164$	2.32312			0.181405
$165$	−0.468665	+	3.60060i	−0.0364855	+	0.280307i
$166$		−	16.2776i		−	1.26339i
$167$	−11.5050			−0.890286			−0.445143	−	0.895459i	$-0.646847\pi$
$167$	−11.5050			−0.890286			−0.445143	+	0.895459i	$0.646847\pi$
$168$	5.62620			0.434071
$169$	−8.05966			−0.619974
$170$	−4.65741	−	0.606222i	−0.357207	−	0.0464951i
$171$		−	0.797854i		−	0.0610134i
$172$	−5.72663			−0.436651
$173$			15.7081i			1.19427i	0.802142	+	0.597134i	$0.203694\pi$
$173$			15.7081i			1.19427i	−0.802142	+	0.597134i	$0.796306\pi$
$174$	4.81767			0.365227
$175$	4.03097	−	15.2220i	0.304713	−	1.15068i
$176$	−0.908956			−0.0685152
$177$	9.93062			0.746431
$178$		−	8.35832i		−	0.626483i
$179$			11.3128i			0.845560i	0.906232	+	0.422780i	$0.138946\pi$
$179$			11.3128i			0.845560i	−0.906232	+	0.422780i	$0.861054\pi$
$180$	−0.424564	−	0.0552624i	−0.0316451	−	0.00411901i
$181$	18.3136			1.36124			0.680618	−	0.732638i	$-0.261711\pi$
$181$	18.3136			1.36124			0.680618	+	0.732638i	$0.261711\pi$
$182$			7.00000i			0.518874i
$183$	−5.65615			−0.418115
$184$	7.66680			0.565204
$185$	−0.713423	−	13.5827i	−0.0524519	−	0.998623i
$186$	10.6574			0.781439
$187$	−1.90920			−0.139614
$188$			8.89435i			0.648687i
$189$	−15.8013			−1.14938
$190$	1.20265	−	9.23962i	0.0872497	−	0.670313i
$191$		−	7.66002i		−	0.554260i	−0.960832	−	0.277130i	$-0.910617\pi$
$191$		−	7.66002i		−	0.554260i	0.960832	−	0.277130i	$-0.0893832\pi$
$192$		−	1.78647i		−	0.128927i
$193$	−19.3148			−1.39031			−0.695156	−	0.718859i	$-0.744665\pi$
$193$	−19.3148			−1.39031			−0.695156	+	0.718859i	$0.744665\pi$
$194$	5.14283			0.369233
$195$	1.14603	−	8.80462i	0.0820692	−	0.630512i
$196$	−2.91834			−0.208453
$197$		−	13.1193i		−	0.934709i	−0.884070	−	0.467354i	$-0.845207\pi$
$197$		−	13.1193i		−	0.934709i	0.884070	−	0.467354i	$-0.154793\pi$
$198$	−0.174040			−0.0123685
$199$		−	6.04548i		−	0.428553i	−0.976773	−	0.214277i	$-0.931261\pi$
$199$		−	6.04548i		−	0.428553i	0.976773	−	0.214277i	$-0.0687394\pi$
$200$	−4.83340	−	1.27994i	−0.341773	−	0.0905056i
$201$	−13.6653			−0.963876
$202$	3.20212			0.225300
$203$	−8.49300			−0.596092
$204$		−	3.75235i		−	0.262717i
$205$	5.15119	+	0.670493i	0.359775	+	0.0468293i
$206$	−17.6871			−1.23232
$207$	1.46798			0.102032
$208$	2.22269			0.154116
$209$		−	3.78757i		−	0.261992i
$210$	12.4753	+	1.62382i	0.860879	+	0.112054i
$211$	3.06975			0.211330			0.105665	−	0.994402i	$-0.466303\pi$
$211$	3.06975			0.211330			0.105665	+	0.994402i	$0.466303\pi$
$212$			9.37592i			0.643941i
$213$		−	24.1454i		−	1.65441i
$214$		−	6.75126i		−	0.461507i
$215$	−12.6980	−	1.65281i	−0.865997	−	0.112721i
$216$			5.01735i			0.341387i
$217$	−18.7878			−1.27540
$218$		−	10.5304i		−	0.713208i
$219$	3.83824			0.259364
$220$	−2.01549	−	0.262341i	−0.135884	−	0.0176870i
$221$	4.66860			0.314044
$222$	10.6874	−	1.96588i	0.717289	−	0.131941i
$223$		−	13.9960i		−	0.937243i	−0.883399	−	0.468621i	$-0.844751\pi$
$223$		−	13.9960i		−	0.937243i	0.883399	−	0.468621i	$-0.155249\pi$
$224$			3.14934i			0.210424i
$225$	−0.925462	−	0.245074i	−0.0616975	−	0.0163382i
$226$	−6.32365			−0.420643
$227$	11.9087			0.790409			0.395205	−	0.918593i	$-0.370674\pi$
$227$	11.9087			0.790409			0.395205	+	0.918593i	$0.370674\pi$
$228$	7.44411			0.492998
$229$	−7.43448			−0.491285			−0.245642	−	0.969361i	$-0.578999\pi$
$229$	−7.43448			−0.491285			−0.245642	+	0.969361i	$0.578999\pi$
$230$	17.0001	+	2.21278i	1.12095	+	0.145906i
$231$	5.11397			0.336474
$232$			2.69676i			0.177051i
$233$			15.2152i			0.996782i	0.866952	+	0.498391i	$0.166076\pi$
$233$			15.2152i			0.996782i	−0.866952	+	0.498391i	$0.833924\pi$
$234$	0.425583			0.0278212
$235$	−2.56707	+	19.7220i	−0.167457	+	1.28652i
$236$			5.55880i			0.361847i
$237$	5.99850			0.389644
$238$			6.61496i			0.428784i
$239$		−	29.1359i		−	1.88465i	−0.334705	−	0.942323i	$-0.608637\pi$
$239$		−	29.1359i		−	1.88465i	0.334705	−	0.942323i	$-0.391363\pi$
$240$	0.515607	−	3.96125i	0.0332823	−	0.255698i
$241$			7.08791i			0.456572i	0.973594	+	0.228286i	$0.0733121\pi$
$241$			7.08791i			0.456572i	−0.973594	+	0.228286i	$0.926688\pi$
$242$	10.1738			0.653997
$243$			1.98686i			0.127457i
$244$		−	3.16611i		−	0.202689i
$245$	−6.47102	−	0.842286i	−0.413418	−	0.0538117i
$246$			4.15017i			0.264605i
$247$			9.26180i			0.589315i
$248$			5.96563i			0.378818i
$249$	29.0795			1.84284
$250$	−10.3480	−	4.23310i	−0.654464	−	0.267725i
$251$			17.3622i			1.09589i	0.836514	+	0.547946i	$0.184590\pi$
$251$			17.3622i			1.09589i	−0.836514	+	0.547946i	$0.815410\pi$
$252$			0.603011i			0.0379861i
$253$	6.96879			0.438124
$254$		−	15.0472i		−	0.944142i
$255$	1.08300	−	8.32033i	0.0678199	−	0.521039i
$256$	1.00000			0.0625000
$257$	−13.9118			−0.867797			−0.433899	−	0.900962i	$-0.642862\pi$
$257$	−13.9118			−0.867797			−0.433899	+	0.900962i	$0.642862\pi$
$258$		−	10.2304i		−	0.636920i
$259$	−18.8406	+	3.46562i	−1.17070	+	0.215343i
$260$	4.92850	+	0.641508i	0.305653	+	0.0397846i
$261$			0.516354i			0.0319615i
$262$			3.31974i			0.205094i
$263$		−	0.302157i		−	0.0186318i	−0.999957	−	0.00931590i	$-0.997035\pi$
$263$		−	0.302157i		−	0.0186318i	0.999957	−	0.00931590i	$-0.00296538\pi$
$264$		−	1.62382i		−	0.0999394i
$265$	−2.70606	+	20.7898i	−0.166232	+	1.27711i
$266$	−13.1231			−0.804630
$267$	14.9319			0.913816
$268$		−	7.64933i		−	0.467257i
$269$	−28.8001			−1.75597			−0.877986	−	0.478687i	$-0.841113\pi$
$269$	−28.8001			−1.75597			−0.877986	+	0.478687i	$0.841113\pi$
$270$	−1.44810	+	11.1253i	−0.0881284	+	0.677063i
$271$	1.57340			0.0955770			0.0477885	−	0.998857i	$-0.484783\pi$
$271$	1.57340			0.0955770			0.0477885	+	0.998857i	$0.484783\pi$
$272$	2.10043			0.127357
$273$	−12.5053			−0.756854
$274$			17.9355i			1.08353i
$275$	−4.39335	−	1.16341i	−0.264929	−	0.0701564i
$276$			13.6965i			0.824432i
$277$	26.3430			1.58280			0.791398	−	0.611301i	$-0.209354\pi$
$277$	26.3430			1.58280			0.791398	+	0.611301i	$0.209354\pi$
$278$	−12.7472			−0.764526
$279$			1.14225i			0.0683849i
$280$	−0.908956	+	6.98323i	−0.0543205	+	0.417328i
$281$		−	9.45482i		−	0.564027i	−0.959410	−	0.282014i	$-0.908998\pi$
$281$		−	9.45482i		−	0.564027i	0.959410	−	0.282014i	$-0.0910024\pi$
$282$	−15.8895			−0.946205
$283$	−21.7389			−1.29224			−0.646122	−	0.763234i	$-0.723610\pi$
$283$	−21.7389			−1.29224			−0.646122	+	0.763234i	$0.723610\pi$
$284$	13.5157			0.802008
$285$	16.5063	+	2.14851i	0.977749	+	0.127266i
$286$	2.02033			0.119464
$287$		−	7.31628i		−	0.431866i
$288$	0.191472			0.0112826
$289$	−12.5882			−0.740482
$290$	−0.778332	+	5.97969i	−0.0457053	+	0.351139i
$291$			9.18750i			0.538581i
$292$			2.14851i			0.125732i
$293$			11.1283i			0.650121i	0.945693	+	0.325061i	$0.105385\pi$
$293$			11.1283i			0.650121i	−0.945693	+	0.325061i	$0.894615\pi$
$294$		−	5.21353i		−	0.304059i
$295$	−1.60437	+	12.3259i	−0.0934100	+	0.717640i
$296$	1.10043	+	5.98240i	0.0639611	+	0.347720i
$297$			4.56055i			0.264630i
$298$	6.83795			0.396112
$299$	−17.0409			−0.985500
$300$	2.28658	−	8.63472i	0.132016	−	0.498526i
$301$			18.0351i			1.03953i
$302$	2.80702			0.161526
$303$			5.72049i			0.328633i
$304$			4.16694i			0.238990i
$305$	0.913795	−	7.02041i	0.0523238	−	0.401987i
$306$	0.402174			0.0229908
$307$			15.9903i			0.912615i	0.889822	+	0.456308i	$0.150828\pi$
$307$			15.9903i			0.912615i	−0.889822	+	0.456308i	$0.849172\pi$
$308$			2.86261i			0.163112i
$309$		−	31.5975i		−	1.79752i
$310$	−1.72179	+	13.2280i	−0.0977910	+	0.751298i
$311$		−	29.6416i		−	1.68082i	−0.541949	−	0.840411i	$-0.682313\pi$
$311$		−	29.6416i		−	1.68082i	0.541949	−	0.840411i	$-0.317687\pi$
$312$			3.97076i			0.224800i
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$			7.28275i			0.410989i
$315$	−0.174040	+	1.33710i	−0.00980604	+	0.0753368i
$316$			3.35774i			0.188888i
$317$			21.1397i			1.18732i	0.804715	+	0.593662i	$0.202318\pi$
$317$			21.1397i			1.18732i	−0.804715	+	0.593662i	$0.797682\pi$
$318$	−16.7498			−0.939282
$319$			2.45123i			0.137243i
$320$	2.21736	+	0.288618i	0.123954	+	0.0161342i
$321$	12.0609			0.673175
$322$		−	24.1454i		−	1.34557i
$323$			8.75236i			0.486994i
$324$	−9.53776			−0.529875
$325$	10.7431	+	2.84491i	0.595922	+	0.157807i
$326$	−22.2319			−1.23131
$327$	18.8122			1.04032
$328$	−2.32312			−0.128273
$329$	28.0113			1.54431
$330$	0.468665	−	3.60060i	0.0257991	−	0.198207i
$331$			18.7324i			1.02963i	0.857302	+	0.514814i	$0.172139\pi$
$331$			18.7324i			1.02963i	−0.857302	+	0.514814i	$0.827861\pi$
$332$			16.2776i			0.893350i
$333$	0.210702	+	1.14546i	0.0115464	+	0.0627710i
$334$	11.5050			0.629528
$335$	2.20774	−	16.9613i	0.120621	−	0.926697i
$336$	−5.62620			−0.306934
$337$			13.9123i			0.757850i	0.925427	+	0.378925i	$0.123706\pi$
$337$			13.9123i			0.757850i	−0.925427	+	0.378925i	$0.876294\pi$
$338$	8.05966			0.438388
$339$		−	11.2970i		−	0.613569i
$340$	4.65741	+	0.606222i	0.252584	+	0.0328770i
$341$			5.42250i			0.293645i
$342$			0.797854i			0.0431430i
$343$		−	12.8545i		−	0.694079i
$344$	5.72663			0.308759
$345$	−3.95306	+	30.3701i	−0.212825	+	1.63507i
$346$		−	15.7081i		−	0.844474i
$347$	−24.5885			−1.31998			−0.659990	−	0.751274i	$-0.729440\pi$
$347$	−24.5885			−1.31998			−0.659990	+	0.751274i	$0.729440\pi$
$348$	−4.81767			−0.258254
$349$	−10.2324			−0.547726			−0.273863	−	0.961769i	$-0.588301\pi$
$349$	−10.2324			−0.547726			−0.273863	+	0.961769i	$0.588301\pi$
$350$	−4.03097	+	15.2220i	−0.215465	+	0.813651i
$351$		−	11.1520i		−	0.595249i
$352$	0.908956			0.0484475
$353$	−1.74540			−0.0928981			−0.0464491	−	0.998921i	$-0.514791\pi$
$353$	−1.74540			−0.0928981			−0.0464491	+	0.998921i	$0.514791\pi$
$354$	−9.93062			−0.527806
$355$	29.9692	+	3.90087i	1.59060	+	0.207037i
$356$			8.35832i			0.442990i
$357$	−11.8174			−0.625445
$358$		−	11.3128i		−	0.597901i
$359$	21.1922			1.11848			0.559240	−	0.829006i	$-0.311093\pi$
$359$	21.1922			1.11848			0.559240	+	0.829006i	$0.311093\pi$
$360$	0.424564	+	0.0552624i	0.0223765	+	0.00291258i
$361$	1.63660			0.0861371
$362$	−18.3136			−0.962540
$363$			18.1752i			0.953949i
$364$		−	7.00000i		−	0.366900i
$365$	−0.620097	+	4.76402i	−0.0324574	+	0.249360i
$366$	5.65615			0.295652
$367$		−	9.69901i		−	0.506284i	−0.967429	−	0.253142i	$-0.918536\pi$
$367$		−	9.69901i		−	0.506284i	0.967429	−	0.253142i	$-0.0814640\pi$
$368$	−7.66680			−0.399659
$369$	−0.444812			−0.0231560
$370$	0.713423	+	13.5827i	0.0370891	+	0.706133i
$371$	29.5280			1.53302
$372$	−10.6574			−0.552561
$373$			36.8658i			1.90884i	0.298466	+	0.954420i	$0.403525\pi$
$373$			36.8658i			1.90884i	−0.298466	+	0.954420i	$0.596475\pi$
$374$	1.90920			0.0987223
$375$	7.56231	−	18.4864i	0.390516	−	0.954632i
$376$		−	8.89435i		−	0.458691i
$377$		−	5.99404i		−	0.308709i
$378$	15.8013			0.812733
$379$	31.7074			1.62870			0.814351	−	0.580372i	$-0.197093\pi$
$379$	31.7074			1.62870			0.814351	+	0.580372i	$0.197093\pi$
$380$	−1.20265	+	9.23962i	−0.0616949	+	0.473983i
$381$	26.8813			1.37717
$382$			7.66002i			0.391921i
$383$	−3.45325			−0.176453			−0.0882265	−	0.996100i	$-0.528120\pi$
$383$	−3.45325			−0.176453			−0.0882265	+	0.996100i	$0.528120\pi$
$384$			1.78647i			0.0911654i
$385$	−0.826202	+	6.34745i	−0.0421071	+	0.323496i
$386$	19.3148			0.983099
$387$	1.09649			0.0557378
$388$	−5.14283			−0.261087
$389$		−	39.2237i		−	1.98872i	−0.106056	−	0.994360i	$-0.533822\pi$
$389$		−	39.2237i		−	1.98872i	0.106056	−	0.994360i	$-0.466178\pi$
$390$	−1.14603	+	8.80462i	−0.0580317	+	0.445839i
$391$	−16.1036			−0.814392
$392$	2.91834			0.147399
$393$	−5.93062			−0.299160
$394$			13.1193i			0.660939i
$395$	−0.969104	+	7.44533i	−0.0487609	+	0.374615i
$396$	0.174040			0.00874584
$397$		−	5.75234i		−	0.288702i	−0.989527	−	0.144351i	$-0.953891\pi$
$397$		−	5.75234i		−	0.288702i	0.989527	−	0.144351i	$-0.0461094\pi$
$398$			6.04548i			0.303033i
$399$		−	23.4440i		−	1.17367i
$400$	4.83340	+	1.27994i	0.241670	+	0.0639971i
$401$		−	24.6273i		−	1.22983i	−0.788594	−	0.614914i	$-0.789191\pi$
$401$		−	24.6273i		−	1.22983i	0.788594	−	0.614914i	$-0.210809\pi$
$402$	13.6653			0.681563
$403$		−	13.2597i		−	0.660514i
$404$	−3.20212			−0.159311
$405$	−21.1487	−	2.75277i	−1.05089	−	0.136786i
$406$	8.49300			0.421501
$407$	1.00024	+	5.43774i	0.0495801	+	0.269539i
$408$			3.75235i			0.185769i
$409$		−	25.1947i		−	1.24580i	−0.782302	−	0.622899i	$-0.785955\pi$
$409$		−	25.1947i		−	1.24580i	0.782302	−	0.622899i	$-0.214045\pi$
$410$	−5.15119	−	0.670493i	−0.254399	−	0.0331133i
$411$	−32.0413			−1.58048
$412$	17.6871			0.871382
$413$	17.5065			0.861441
$414$	−1.46798			−0.0721473
$415$	−4.69801	+	36.0934i	−0.230616	+	1.77175i
$416$	−2.22269			−0.108976
$417$		−	22.7725i		−	1.11517i
$418$			3.78757i			0.185256i
$419$	7.19906			0.351697			0.175849	−	0.984417i	$-0.443733\pi$
$419$	7.19906			0.351697			0.175849	+	0.984417i	$0.443733\pi$
$420$	−12.4753	−	1.62382i	−0.608734	−	0.0792344i
$421$		−	34.0902i		−	1.66145i	−0.556680	−	0.830727i	$-0.687925\pi$
$421$		−	34.0902i		−	1.66145i	0.556680	−	0.830727i	$-0.312075\pi$
$422$	−3.06975			−0.149433
$423$		−	1.70302i		−	0.0828038i
$424$		−	9.37592i		−	0.455335i
$425$	10.1522	+	2.68843i	0.492455	+	0.130408i
$426$			24.1454i			1.16985i
$427$	−9.97114			−0.482537
$428$			6.75126i			0.326335i
$429$			3.60925i			0.174256i
$430$	12.6980	+	1.65281i	0.612353	+	0.0797055i
$431$			25.2123i			1.21443i	0.794536	+	0.607217i	$0.207714\pi$
$431$			25.2123i			1.21443i	−0.794536	+	0.607217i	$0.792286\pi$
$432$		−	5.01735i		−	0.241397i
$433$		−	21.8683i		−	1.05092i	−0.850817	−	0.525462i	$-0.823893\pi$
$433$		−	21.8683i		−	1.05092i	0.850817	−	0.525462i	$-0.176107\pi$
$434$	18.7878			0.901843
$435$	−10.6825	−	1.39047i	−0.512188	−	0.0666678i
$436$			10.5304i			0.504314i
$437$		−	31.9471i		−	1.52824i
$438$	−3.83824			−0.183398
$439$			9.00956i			0.430003i	0.976614	+	0.215001i	$0.0689756\pi$
$439$			9.00956i			0.430003i	−0.976614	+	0.215001i	$0.931024\pi$
$440$	2.01549	+	0.262341i	0.0960845	+	0.0125066i
$441$	0.558782			0.0266086
$442$	−4.66860			−0.222062
$443$		−	2.89007i		−	0.137311i	−0.997640	−	0.0686557i	$-0.978129\pi$
$443$		−	2.89007i		−	0.137311i	0.997640	−	0.0686557i	$-0.0218710\pi$
$444$	−10.6874	+	1.96588i	−0.507200	+	0.0932966i
$445$	−2.41236	+	18.5334i	−0.114357	+	0.878569i
$446$			13.9960i			0.662731i
$447$			12.2158i			0.577787i
$448$		−	3.14934i		−	0.148792i
$449$			18.1539i			0.856738i	0.903604	+	0.428369i	$0.140912\pi$
$449$			18.1539i			0.856738i	−0.903604	+	0.428369i	$0.859088\pi$
$450$	0.925462	+	0.245074i	0.0436267	+	0.0115529i
$451$	−2.11161			−0.0994319
$452$	6.32365			0.297439
$453$			5.01466i			0.235609i
$454$	−11.9087			−0.558904
$455$	2.02033	−	15.5215i	0.0947143	−	0.727661i
$456$	−7.44411			−0.348602
$457$	−10.4140			−0.487146			−0.243573	−	0.969883i	$-0.578320\pi$
$457$	−10.4140			−0.487146			−0.243573	+	0.969883i	$0.578320\pi$
$458$	7.43448			0.347391
$459$		−	10.5386i		−	0.491899i
$460$	−17.0001	−	2.21278i	−0.792633	−	0.103171i
$461$			17.7433i			0.826390i	0.910643	+	0.413195i	$0.135587\pi$
$461$			17.7433i			0.826390i	−0.910643	+	0.413195i	$0.864413\pi$
$462$	−5.11397			−0.237923
$463$	−11.6293			−0.540457			−0.270229	−	0.962796i	$-0.587099\pi$
$463$	−11.6293			−0.540457			−0.270229	+	0.962796i	$0.587099\pi$
$464$		−	2.69676i		−	0.125194i
$465$	−23.6314	−	3.07592i	−1.09588	−	0.142642i
$466$		−	15.2152i		−	0.704831i
$467$	−6.25208			−0.289312			−0.144656	−	0.989482i	$-0.546207\pi$
$467$	−6.25208			−0.289312			−0.144656	+	0.989482i	$0.546207\pi$
$468$	−0.425583			−0.0196726
$469$	−24.0903			−1.11239
$470$	2.56707	−	19.7220i	0.118410	−	0.909708i
$471$	−13.0104			−0.599488
$472$		−	5.55880i		−	0.255864i
$473$	5.20525			0.239338
$474$	−5.99850			−0.275520
$475$	−5.33344	+	20.1405i	−0.244715	+	0.924109i
$476$		−	6.61496i		−	0.303196i
$477$		−	1.79523i		−	0.0821979i
$478$			29.1359i			1.33265i
$479$		−	16.4452i		−	0.751398i	−0.926742	−	0.375699i	$-0.877403\pi$
$479$		−	16.4452i		−	0.751398i	0.926742	−	0.375699i	$-0.122597\pi$
$480$	−0.515607	+	3.96125i	−0.0235341	+	0.180806i
$481$	−2.44591	−	13.2970i	−0.111524	−	0.606291i
$482$		−	7.08791i		−	0.322845i
$483$	43.1349			1.96271
$484$	−10.1738			−0.462445
$485$	−11.4035	−	1.48431i	−0.517807	−	0.0673992i
$486$		−	1.98686i		−	0.0901259i
$487$	−13.7966			−0.625184			−0.312592	−	0.949887i	$-0.601197\pi$
$487$	−13.7966			−0.625184			−0.312592	+	0.949887i	$0.601197\pi$
$488$			3.16611i			0.143323i
$489$		−	39.7166i		−	1.79605i
$490$	6.47102	+	0.842286i	0.292331	+	0.0380506i
$491$	−39.0410			−1.76190			−0.880949	−	0.473211i	$-0.843095\pi$
$491$	−39.0410			−1.76190			−0.880949	+	0.473211i	$0.843095\pi$
$492$		−	4.15017i		−	0.187104i
$493$		−	5.66434i		−	0.255109i
$494$		−	9.26180i		−	0.416708i
$495$	0.385910	+	0.0502311i	0.0173454	+	0.00225772i
$496$		−	5.96563i		−	0.267865i
$497$		−	42.5655i		−	1.90932i
$498$	−29.0795			−1.30308
$499$			40.0886i			1.79461i	0.441410	+	0.897306i	$0.354479\pi$
$499$			40.0886i			1.79461i	−0.441410	+	0.897306i	$0.645521\pi$
$500$	10.3480	+	4.23310i	0.462776	+	0.189310i
$501$			20.5534i			0.918258i
$502$		−	17.3622i		−	0.774913i
$503$	−12.0731			−0.538312			−0.269156	−	0.963097i	$-0.586745\pi$
$503$	−12.0731			−0.538312			−0.269156	+	0.963097i	$0.586745\pi$
$504$		−	0.603011i		−	0.0268603i
$505$	−7.10026	−	0.924190i	−0.315958	−	0.0411259i
$506$	−6.96879			−0.309800
$507$			14.3983i			0.639453i
$508$			15.0472i			0.667609i
$509$	4.36466			0.193460			0.0967300	−	0.995311i	$-0.469162\pi$
$509$	4.36466			0.193460			0.0967300	+	0.995311i	$0.469162\pi$
$510$	−1.08300	+	8.32033i	−0.0479559	+	0.368430i
$511$	6.76637			0.299327
$512$	−1.00000			−0.0441942
$513$	20.9070			0.923066
$514$	13.9118			0.613625
$515$	39.2188	+	5.10482i	1.72819	+	0.224945i
$516$			10.2304i			0.450370i
$517$		−	8.08458i		−	0.355559i
$518$	18.8406	−	3.46562i	0.827808	−	0.152271i
$519$	28.0621			1.23179
$520$	−4.92850	−	0.641508i	−0.216129	−	0.0281320i
$521$	−16.7088			−0.732025			−0.366013	−	0.930610i	$-0.619277\pi$
$521$	−16.7088			−0.732025			−0.366013	+	0.930610i	$0.619277\pi$
$522$		−	0.516354i		−	0.0226002i
$523$	−32.5266			−1.42229			−0.711144	−	0.703047i	$-0.751823\pi$
$523$	−32.5266			−1.42229			−0.711144	+	0.703047i	$0.751823\pi$
$524$		−	3.31974i		−	0.145024i
$525$	−27.1937	−	7.20121i	−1.18683	−	0.314287i
$526$			0.302157i			0.0131747i
$527$		−	12.5304i		−	0.545832i
$528$			1.62382i			0.0706678i
$529$	35.7798			1.55564
$530$	2.70606	−	20.7898i	0.117544	−	0.903052i
$531$		−	1.06436i		−	0.0461891i
$532$	13.1231			0.568959
$533$	5.16356			0.223659
$534$	−14.9319			−0.646166
$535$	−1.94854	+	14.9700i	−0.0842426	+	0.647210i
$536$			7.64933i			0.330401i
$537$	20.2100			0.872126
$538$	28.8001			1.24166
$539$	2.65265			0.114258
$540$	1.44810	−	11.1253i	0.0623162	−	0.478756i
$541$		−	19.2331i		−	0.826894i	−0.910528	−	0.413447i	$-0.864325\pi$
$541$		−	19.2331i		−	0.826894i	0.910528	−	0.413447i	$-0.135675\pi$
$542$	−1.57340			−0.0675832
$543$		−	32.7166i		−	1.40400i
$544$	−2.10043			−0.0900551
$545$	−3.03926	+	23.3497i	−0.130188	+	1.00019i
$546$	12.5053			0.535177
$547$	8.88173			0.379755			0.189878	−	0.981808i	$-0.439191\pi$
$547$	8.88173			0.379755			0.189878	+	0.981808i	$0.439191\pi$
$548$		−	17.9355i		−	0.766168i
$549$			0.606222i			0.0258729i
$550$	4.39335	+	1.16341i	0.187333	+	0.0496080i
$551$	11.2372			0.478722
$552$		−	13.6965i		−	0.582962i
$553$	10.5747			0.449680
$554$	−26.3430			−1.11921
$555$	−24.2652	+	1.27451i	−1.03000	+	0.0540998i
$556$	12.7472			0.540601
$557$	44.3010			1.87709			0.938547	−	0.345150i	$-0.112172\pi$
$557$	44.3010			1.87709			0.938547	+	0.345150i	$0.112172\pi$
$558$		−	1.14225i		−	0.0483554i
$559$	−12.7285			−0.538358
$560$	0.908956	−	6.98323i	0.0384104	−	0.295095i
$561$			3.41072i			0.144001i
$562$			9.45482i			0.398828i
$563$	19.8885			0.838202			0.419101	−	0.907940i	$-0.362345\pi$
$563$	19.8885			0.838202			0.419101	+	0.907940i	$0.362345\pi$
$564$	15.8895			0.669068
$565$	14.0218	+	1.82512i	0.589903	+	0.0767834i
$566$	21.7389			0.913754
$567$			30.0376i			1.26146i
$568$	−13.5157			−0.567106
$569$			3.13170i			0.131288i	0.997843	+	0.0656439i	$0.0209101\pi$
$569$			3.13170i			0.131288i	−0.997843	+	0.0656439i	$0.979090\pi$
$570$	−16.5063	−	2.14851i	−0.691373	−	0.0899910i
$571$	−19.2774			−0.806732			−0.403366	−	0.915039i	$-0.632160\pi$
$571$	−19.2774			−0.806732			−0.403366	+	0.915039i	$0.632160\pi$
$572$	−2.02033			−0.0844741
$573$	−13.6844			−0.571674
$574$			7.31628i			0.305376i
$575$	−37.0567	−	9.81306i	−1.54537	−	0.409233i
$576$	−0.191472			−0.00797801
$577$	24.8001			1.03244			0.516220	−	0.856456i	$-0.327339\pi$
$577$	24.8001			1.03244			0.516220	+	0.856456i	$0.327339\pi$
$578$	12.5882			0.523600
$579$			34.5053i			1.43399i
$580$	0.778332	−	5.97969i	0.0323185	−	0.248293i
$581$	51.2637			2.12678
$582$		−	9.18750i		−	0.380834i
$583$		−	8.52230i		−	0.352958i
$584$		−	2.14851i		−	0.0889058i
$585$	−0.943672	−	0.122831i	−0.0390160	−	0.00507843i
$586$		−	11.1283i		−	0.459705i
$587$	−16.1319			−0.665836			−0.332918	−	0.942956i	$-0.608033\pi$
$587$	−16.1319			−0.665836			−0.332918	+	0.942956i	$0.608033\pi$
$588$			5.21353i			0.215002i
$589$	24.8584			1.02427
$590$	1.60437	−	12.3259i	0.0660508	−	0.507448i
$591$	−23.4372			−0.964076
$592$	−1.10043	−	5.98240i	−0.0452273	−	0.245875i
$593$		−	28.2040i		−	1.15820i	−0.815256	−	0.579100i	$-0.803404\pi$
$593$		−	28.2040i		−	1.15820i	0.815256	−	0.579100i	$-0.196596\pi$
$594$		−	4.56055i		−	0.187122i
$595$	1.90920	−	14.6678i	0.0782695	−	0.601320i
$596$	−6.83795			−0.280093
$597$	−10.8001			−0.442018
$598$	17.0409			0.696854
$599$	−24.8280			−1.01444			−0.507222	−	0.861815i	$-0.669328\pi$
$599$	−24.8280			−1.01444			−0.507222	+	0.861815i	$0.669328\pi$
$600$	−2.28658	+	8.63472i	−0.0933491	+	0.352511i
$601$	−2.87745			−0.117374			−0.0586868	−	0.998276i	$-0.518691\pi$
$601$	−2.87745			−0.117374			−0.0586868	+	0.998276i	$0.518691\pi$
$602$		−	18.0351i		−	0.735056i
$603$			1.46464i			0.0596446i
$604$	−2.80702			−0.114216
$605$	−22.5590	−	2.93634i	−0.917154	−	0.119379i
$606$		−	5.72049i		−	0.232379i
$607$	−25.7881			−1.04671			−0.523353	−	0.852116i	$-0.675319\pi$
$607$	−25.7881			−1.04671			−0.523353	+	0.852116i	$0.675319\pi$
$608$		−	4.16694i		−	0.168992i
$609$			15.1725i			0.614820i
$610$	−0.913795	+	7.02041i	−0.0369985	+	0.284248i
$611$			19.7694i			0.799783i
$612$	−0.402174			−0.0162569
$613$		−	32.4248i		−	1.30962i	−0.755792	−	0.654812i	$-0.772748\pi$
$613$		−	32.4248i		−	1.30962i	0.755792	−	0.654812i	$-0.227252\pi$
$614$		−	15.9903i		−	0.645317i
$615$	1.19782	−	9.20244i	0.0483006	−	0.371078i
$616$		−	2.86261i		−	0.115338i
$617$		−	5.69333i		−	0.229205i	−0.993411	−	0.114602i	$-0.963441\pi$
$617$		−	5.69333i		−	0.229205i	0.993411	−	0.114602i	$-0.0365594\pi$
$618$			31.5975i			1.27104i
$619$	−4.76393			−0.191478			−0.0957392	−	0.995406i	$-0.530521\pi$
$619$	−4.76393			−0.191478			−0.0957392	+	0.995406i	$0.530521\pi$
$620$	1.72179	−	13.2280i	0.0691487	−	0.531248i
$621$			38.4670i			1.54363i
$622$			29.6416i			1.18852i
$623$	26.3232			1.05462
$624$		−	3.97076i		−	0.158958i
$625$	21.7235	+	12.3729i	0.868940	+	0.494918i
$626$	10.0000			0.399680
$627$	−6.76637			−0.270223
$628$		−	7.28275i		−	0.290613i
$629$	−2.31137	−	12.5656i	−0.0921604	−	0.501023i
$630$	0.174040	−	1.33710i	0.00693392	−	0.0532712i
$631$			8.72673i			0.347405i	0.984798	+	0.173703i	$0.0555732\pi$
$631$			8.72673i			0.347405i	−0.984798	+	0.173703i	$0.944427\pi$
$632$		−	3.35774i		−	0.133564i
$633$		−	5.48401i		−	0.217970i
$634$		−	21.1397i		−	0.839564i
$635$	−4.34288	+	33.3650i	−0.172342	+	1.32405i
$636$	16.7498			0.664173
$637$	−6.48656			−0.257007
$638$		−	2.45123i		−	0.0970453i
$639$	−2.58788			−0.102375
$640$	−2.21736	−	0.288618i	−0.0876490	−	0.0114086i
$641$	−41.1790			−1.62647			−0.813237	−	0.581933i	$-0.802297\pi$
$641$	−41.1790			−1.62647			−0.813237	+	0.581933i	$0.802297\pi$
$642$	−12.0609			−0.476007
$643$	6.12834			0.241678			0.120839	−	0.992672i	$-0.461441\pi$
$643$	6.12834			0.241678			0.120839	+	0.992672i	$0.461441\pi$
$644$			24.1454i			0.951460i
$645$	−2.95269	+	22.6846i	−0.116262	+	0.893206i
$646$		−	8.75236i		−	0.344357i
$647$	31.3270			1.23159			0.615796	−	0.787905i	$-0.288834\pi$
$647$	31.3270			1.23159			0.615796	+	0.787905i	$0.288834\pi$
$648$	9.53776			0.374678
$649$		−	5.05270i		−	0.198336i
$650$	−10.7431	−	2.84491i	−0.421380	−	0.111587i
$651$			33.5638i			1.31547i
$652$	22.2319			0.870669
$653$	−0.716146			−0.0280250			−0.0140125	−	0.999902i	$-0.504460\pi$
$653$	−0.716146			−0.0280250			−0.0140125	+	0.999902i	$0.504460\pi$
$654$	−18.8122			−0.735616
$655$	0.958138	−	7.36108i	0.0374375	−	0.287621i
$656$	2.32312			0.0907024
$657$		−	0.411379i		−	0.0160494i
$658$	−28.0113			−1.09200
$659$	−10.8796			−0.423810			−0.211905	−	0.977290i	$-0.567967\pi$
$659$	−10.8796			−0.423810			−0.211905	+	0.977290i	$0.567967\pi$
$660$	−0.468665	+	3.60060i	−0.0182427	+	0.140153i
$661$		−	37.4927i		−	1.45830i	−0.684355	−	0.729149i	$-0.739916\pi$
$661$		−	37.4927i		−	1.45830i	0.684355	−	0.729149i	$-0.260084\pi$
$662$		−	18.7324i		−	0.728057i
$663$		−	8.34030i		−	0.323910i
$664$		−	16.2776i		−	0.631694i
$665$	29.0987	+	3.78757i	1.12840	+	0.146876i
$666$	−0.210702	−	1.14546i	−0.00816452	−	0.0443858i
$667$			20.6755i			0.800558i
$668$	−11.5050			−0.445143
$669$	−25.0035			−0.966689
$670$	−2.20774	+	16.9613i	−0.0852922	+	0.655274i
$671$			2.87785i			0.111098i
$672$	5.62620			0.217035
$673$			38.2532i			1.47455i	0.675591	+	0.737277i	$0.263889\pi$
$673$			38.2532i			1.47455i	−0.675591	+	0.737277i	$0.736111\pi$
$674$		−	13.9123i		−	0.535881i
$675$	6.42192	−	24.2508i	0.247180	−	0.933416i
$676$	−8.05966			−0.309987
$677$		−	45.0250i		−	1.73045i	−0.501381	−	0.865227i	$-0.667175\pi$
$677$		−	45.0250i		−	1.73045i	0.501381	−	0.865227i	$-0.332825\pi$
$678$			11.2970i			0.433859i
$679$			16.1965i			0.621565i
$680$	−4.65741	−	0.606222i	−0.178604	−	0.0232475i
$681$		−	21.2746i		−	0.815243i
$682$		−	5.42250i		−	0.207638i
$683$	−34.7787			−1.33077			−0.665384	−	0.746501i	$-0.731732\pi$
$683$	−34.7787			−1.33077			−0.665384	+	0.746501i	$0.731732\pi$
$684$		−	0.797854i		−	0.0305067i
$685$	5.17652	−	39.7696i	0.197785	−	1.51952i
$686$			12.8545i			0.490788i
$687$			13.2815i			0.506720i
$688$	−5.72663			−0.218326
$689$			20.8397i			0.793931i
$690$	3.95306	−	30.3701i	0.150490	−	1.15617i
$691$	38.8781			1.47899			0.739497	−	0.673160i	$-0.235063\pi$
$691$	38.8781			1.47899			0.739497	+	0.673160i	$0.235063\pi$
$692$			15.7081i			0.597134i
$693$		−	0.548111i		−	0.0208210i
$694$	24.5885			0.933367
$695$	28.2652	+	3.67907i	1.07216	+	0.139555i
$696$	4.81767			0.182613
$697$	4.87954			0.184826
$698$	10.2324			0.387301
$699$	27.1815			1.02810
$700$	4.03097	−	15.2220i	0.152356	−	0.575338i
$701$			41.6474i			1.57300i	0.617589	+	0.786501i	$0.288110\pi$
$701$			41.6474i			1.57300i	−0.617589	+	0.786501i	$0.711890\pi$
$702$			11.1520i			0.420905i
$703$	24.9283	−	4.58542i	0.940188	−	0.172942i
$704$	−0.908956			−0.0342576
$705$	35.2328	+	4.58599i	1.32694	+	0.172718i
$706$	1.74540			0.0656889
$707$			10.0846i			0.379269i
$708$	9.93062			0.373216
$709$			3.86911i			0.145307i	0.997357	+	0.0726537i	$0.0231468\pi$
$709$			3.86911i			0.145307i	−0.997357	+	0.0726537i	$0.976853\pi$
$710$	−29.9692	−	3.90087i	−1.12472	−	0.146397i
$711$		−	0.642914i		−	0.0241112i
$712$		−	8.35832i		−	0.313241i
$713$			45.7373i			1.71287i
$714$	11.8174			0.442256
$715$	−4.47980	−	0.583102i	−0.167535	−	0.0218068i
$716$			11.3128i			0.422780i
$717$	−52.0504			−1.94386
$718$	−21.1922			−0.790884
$719$	−26.4440			−0.986194			−0.493097	−	0.869974i	$-0.664135\pi$
$719$	−26.4440			−0.986194			−0.493097	+	0.869974i	$0.664135\pi$
$720$	−0.424564	−	0.0552624i	−0.0158226	−	0.00205951i
$721$		−	55.7028i		−	2.07448i
$722$	−1.63660			−0.0609081
$723$	12.6623			0.470917
$724$	18.3136			0.680618
$725$	3.45169	−	13.0345i	0.128193	−	0.484089i
$726$		−	18.1752i		−	0.674544i
$727$	−28.3958			−1.05314			−0.526571	−	0.850131i	$-0.676522\pi$
$727$	−28.3958			−1.05314			−0.526571	+	0.850131i	$0.676522\pi$
$728$			7.00000i			0.259437i
$729$	−25.0638			−0.928289
$730$	0.620097	−	4.76402i	0.0229508	−	0.176324i
$731$	−12.0284			−0.444885
$732$	−5.65615			−0.209057
$733$			19.8801i			0.734289i	0.930164	+	0.367144i	$0.119664\pi$
$733$			19.8801i			0.734289i	−0.930164	+	0.367144i	$0.880336\pi$
$734$			9.69901i			0.357997i
$735$	−1.50472	+	11.5603i	−0.0555024	+	0.426407i
$736$	7.66680			0.282602
$737$			6.95291i			0.256114i
$738$	0.444812			0.0163738
$739$	−42.1224			−1.54950			−0.774749	−	0.632269i	$-0.782124\pi$
$739$	−42.1224			−1.54950			−0.774749	+	0.632269i	$0.782124\pi$
$740$	−0.713423	−	13.5827i	−0.0262259	−	0.499312i
$741$	16.5459			0.607830
$742$	−29.5280			−1.08401
$743$		−	23.5575i		−	0.864242i	−0.901816	−	0.432121i	$-0.857765\pi$
$743$		−	23.5575i		−	0.864242i	0.901816	−	0.432121i	$-0.142235\pi$
$744$	10.6574			0.390720
$745$	−15.1622	−	1.97355i	−0.555500	−	0.0723054i
$746$		−	36.8658i		−	1.34975i
$747$		−	3.11671i		−	0.114035i
$748$	−1.90920			−0.0698072
$749$	21.2620			0.776897
$750$	−7.56231	+	18.4864i	−0.276136	+	0.675026i
$751$	32.6454			1.19125			0.595624	−	0.803263i	$-0.296905\pi$
$751$	32.6454			1.19125			0.595624	+	0.803263i	$0.296905\pi$
$752$			8.89435i			0.324344i
$753$	31.0170			1.13032
$754$			5.99404i			0.218290i
$755$	−6.22419	−	0.810158i	−0.226522	−	0.0294847i
$756$	−15.8013			−0.574689
$757$	30.3562			1.10331			0.551657	−	0.834071i	$-0.313996\pi$
$757$	30.3562			1.10331			0.551657	+	0.834071i	$0.313996\pi$
$758$	−31.7074			−1.15167
$759$		−	12.4495i		−	0.451889i
$760$	1.20265	−	9.23962i	0.0436249	−	0.335156i
$761$	−38.6682			−1.40172			−0.700860	−	0.713299i	$-0.747200\pi$
$761$	−38.6682			−1.40172			−0.700860	+	0.713299i	$0.747200\pi$
$762$	−26.8813			−0.973806
$763$	33.1638			1.20061
$764$		−	7.66002i		−	0.277130i
$765$	−0.891766	−	0.116075i	−0.0322419	−	0.00419669i
$766$	3.45325			0.124771
$767$			12.3555i			0.446130i
$768$		−	1.78647i		−	0.0644637i
$769$		−	23.8517i		−	0.860114i	−0.902802	−	0.430057i	$-0.858494\pi$
$769$		−	23.8517i		−	0.860114i	0.902802	−	0.430057i	$-0.141506\pi$
$770$	0.826202	−	6.34745i	0.0297742	−	0.228746i
$771$			24.8531i			0.895062i
$772$	−19.3148			−0.695156
$773$		−	38.4580i		−	1.38324i	−0.722262	−	0.691620i	$-0.756897\pi$
$773$		−	38.4580i		−	1.38324i	0.722262	−	0.691620i	$-0.243103\pi$
$774$	−1.09649			−0.0394125
$775$	7.63566	−	28.8343i	0.274281	−	1.03576i
$776$	5.14283			0.184617
$777$	6.19123	+	33.6581i	0.222109	+	1.20748i
$778$			39.2237i			1.40624i
$779$			9.68029i			0.346832i
$780$	1.14603	−	8.80462i	0.0410346	−	0.315256i
$781$	−12.2852			−0.439598
$782$	16.1036			0.575862
$783$	−13.5306			−0.483543
$784$	−2.91834			−0.104226
$785$	2.10193	−	16.1485i	0.0750212	−	0.576365i
$786$	5.93062			0.211538
$787$			39.3808i			1.40378i	0.712288	+	0.701888i	$0.247659\pi$
$787$			39.3808i			1.40378i	−0.712288	+	0.701888i	$0.752341\pi$
$788$		−	13.1193i		−	0.467354i
$789$	−0.539794			−0.0192172
$790$	0.969104	−	7.44533i	0.0344792	−	0.264893i
$791$		−	19.9153i		−	0.708107i
$792$	−0.174040			−0.00618424
$793$		−	7.03726i		−	0.249901i
$794$			5.75234i			0.204143i
$795$	37.1404	+	4.83429i	1.31723	+	0.171455i
$796$		−	6.04548i		−	0.214277i
$797$	−28.0428			−0.993327			−0.496663	−	0.867943i	$-0.665442\pi$
$797$	−28.0428			−0.993327			−0.496663	+	0.867943i	$0.665442\pi$
$798$			23.4440i			0.829910i
$799$			18.6820i			0.660920i
$800$	−4.83340	−	1.27994i	−0.170886	−	0.0452528i
$801$		−	1.60039i		−	0.0565469i
$802$			24.6273i			0.869620i
$803$		−	1.95290i		−	0.0689163i
$804$	−13.6653			−0.481938
$805$	−6.96879	+	53.5390i	−0.245617	+	1.88700i
$806$			13.2597i			0.467054i
$807$			51.4504i			1.81114i
$808$	3.20212			0.112650
$809$			6.86304i			0.241292i	0.992696	+	0.120646i	$0.0384965\pi$
$809$			6.86304i			0.241292i	−0.992696	+	0.120646i	$0.961503\pi$
$810$	21.1487	+	2.75277i	0.743088	+	0.0967224i
$811$	−13.4852			−0.473529			−0.236765	−	0.971567i	$-0.576087\pi$
$811$	−13.4852			−0.473529			−0.236765	+	0.971567i	$0.576087\pi$
$812$	−8.49300			−0.298046
$813$		−	2.81082i		−	0.0985799i
$814$	−1.00024	−	5.43774i	−0.0350585	−	0.190593i
$815$	49.2962	+	6.41653i	1.72677	+	0.224761i
$816$		−	3.75235i		−	0.131359i
$817$		−	23.8625i		−	0.834844i
$818$			25.1947i			0.880913i
$819$			1.34031i			0.0468341i
$820$	5.15119	+	0.670493i	0.179887	+	0.0234146i
$821$	−20.0198			−0.698697			−0.349349	−	0.936993i	$-0.613597\pi$
$821$	−20.0198			−0.698697			−0.349349	+	0.936993i	$0.613597\pi$
$822$	32.0413			1.11757
$823$			6.23551i			0.217356i	0.994077	+	0.108678i	$0.0346618\pi$
$823$			6.23551i			0.217356i	−0.994077	+	0.108678i	$0.965338\pi$
$824$	−17.6871			−0.616160
$825$	−2.07840	+	7.84858i	−0.0723606	+	0.273253i
$826$	−17.5065			−0.609130
$827$	33.7887			1.17495			0.587475	−	0.809243i	$-0.300122\pi$
$827$	33.7887			1.17495			0.587475	+	0.809243i	$0.300122\pi$
$828$	1.46798			0.0510158
$829$			31.8041i			1.10460i	0.833645	+	0.552301i	$0.186250\pi$
$829$			31.8041i			1.10460i	−0.833645	+	0.552301i	$0.813750\pi$
$830$	4.69801	−	36.0934i	0.163070	−	1.25282i
$831$		−	47.0609i		−	1.63253i
$832$	2.22269			0.0770578
$833$	−6.12977			−0.212384
$834$			22.7725i			0.788546i
$835$	−25.5108	−	3.32056i	−0.882839	−	0.114913i
$836$		−	3.78757i		−	0.130996i
$837$	−29.9316			−1.03459
$838$	−7.19906			−0.248687
$839$	1.55322			0.0536233			0.0268116	−	0.999641i	$-0.491465\pi$
$839$	1.55322			0.0536233			0.0268116	+	0.999641i	$0.491465\pi$
$840$	12.4753	+	1.62382i	0.430440	+	0.0560272i
$841$	21.7275			0.749224
$842$			34.0902i			1.17483i
$843$	−16.8907			−0.581748
$844$	3.06975			0.105665
$845$	−17.8712	−	2.32616i	−0.614788	−	0.0800225i
$846$			1.70302i			0.0585511i
$847$			32.0407i			1.10093i
$848$			9.37592i			0.321970i
$849$			38.8359i			1.33284i
$850$	−10.1522	−	2.68843i	−0.348218	−	0.0922123i
$851$	8.43677	+	45.8658i	0.289209	+	1.57226i
$852$		−	24.1454i		−	0.827206i
$853$	−37.4272			−1.28148			−0.640741	−	0.767757i	$-0.721373\pi$
$853$	−37.4272			−1.28148			−0.640741	+	0.767757i	$0.721373\pi$
$854$	9.97114			0.341206
$855$	0.230275	−	1.76913i	0.00787524	−	0.0605030i
$856$		−	6.75126i		−	0.230753i
$857$	−21.2048			−0.724341			−0.362171	−	0.932112i	$-0.617964\pi$
$857$	−21.2048			−0.724341			−0.362171	+	0.932112i	$0.617964\pi$
$858$		−	3.60925i		−	0.123218i
$859$			41.1942i			1.40553i	0.711424	+	0.702764i	$0.248051\pi$
$859$			41.1942i			1.40553i	−0.711424	+	0.702764i	$0.751949\pi$
$860$	−12.6980	−	1.65281i	−0.432999	−	0.0563603i
$861$	−13.0703			−0.445435
$862$		−	25.2123i		−	0.858734i
$863$		−	42.7716i		−	1.45596i	−0.685597	−	0.727982i	$-0.740459\pi$
$863$		−	42.7716i		−	1.45596i	0.685597	−	0.727982i	$-0.259541\pi$
$864$			5.01735i			0.170694i
$865$	−4.53365	+	34.8306i	−0.154149	+	1.18428i
$866$			21.8683i			0.743115i
$867$			22.4884i			0.763747i
$868$	−18.7878			−0.637699
$869$		−	3.05204i		−	0.103533i
$870$	10.6825	+	1.39047i	0.362172	+	0.0471412i
$871$		−	17.0021i		−	0.576093i
$872$		−	10.5304i		−	0.356604i
$873$	0.984709			0.0333273
$874$			31.9471i			1.08063i
$875$	13.3315	−	32.5893i	0.450686	−	1.10172i
$876$	3.83824			0.129682
$877$			50.8976i			1.71869i	0.511397	+	0.859345i	$0.329128\pi$
$877$			50.8976i			1.71869i	−0.511397	+	0.859345i	$0.670872\pi$
$878$		−	9.00956i		−	0.304058i
$879$	19.8803			0.670547
$880$	−2.01549	−	0.262341i	−0.0679420	−	0.00884352i
$881$	−44.1155			−1.48629			−0.743144	−	0.669132i	$-0.766666\pi$
$881$	−44.1155			−1.48629			−0.743144	+	0.669132i	$0.766666\pi$
$882$	−0.558782			−0.0188152
$883$	−46.0708			−1.55041			−0.775203	−	0.631713i	$-0.782352\pi$
$883$	−46.0708			−1.55041			−0.775203	+	0.631713i	$0.782352\pi$
$884$	4.66860			0.157022
$885$	22.0198	+	2.86616i	0.740187	+	0.0963448i
$886$			2.89007i			0.0970939i
$887$		−	41.8693i		−	1.40583i	−0.711272	−	0.702916i	$-0.751881\pi$
$887$		−	41.8693i		−	1.40583i	0.711272	−	0.702916i	$-0.248119\pi$
$888$	10.6874	−	1.96588i	0.358645	−	0.0659707i
$889$	47.3886			1.58936
$890$	2.41236	−	18.5334i	0.0808626	−	0.621242i
$891$	8.66940			0.290436
$892$		−	13.9960i		−	0.468621i
$893$	−37.0622			−1.24024
$894$		−	12.2158i		−	0.408557i
$895$	−3.26508	+	25.0846i	−0.109140	+	0.838487i
$896$			3.14934i			0.105212i
$897$			30.4430i			1.01646i
$898$		−	18.1539i		−	0.605805i
$899$	−16.0878			−0.536560
$900$	−0.925462	−	0.245074i	−0.0308487	−	0.00816912i
$901$			19.6935i			0.656084i
$902$	2.11161			0.0703089
$903$	32.2191			1.07219
$904$	−6.32365			−0.210321
$905$	40.6078	+	5.28563i	1.34985	+	0.175700i
$906$		−	5.01466i		−	0.166601i
$907$	30.2279			1.00370			0.501851	−	0.864954i	$-0.332653\pi$
$907$	30.2279			1.00370			0.501851	+	0.864954i	$0.332653\pi$
$908$	11.9087			0.395205
$909$	0.613117			0.0203358
$910$	−2.02033	+	15.5215i	−0.0669731	+	0.514534i
$911$			8.01080i			0.265409i	0.991156	+	0.132705i	$0.0423662\pi$
$911$			8.01080i			0.265409i	−0.991156	+	0.132705i	$0.957634\pi$
$912$	7.44411			0.246499
$913$		−	14.7956i		−	0.489664i
$914$	10.4140			0.344464
$915$	−12.5417	−	1.63247i	−0.414617	−	0.0539677i
$916$	−7.43448			−0.245642
$917$	−10.4550			−0.345255
$918$			10.5386i			0.347825i
$919$			27.1395i			0.895249i	0.894222	+	0.447624i	$0.147730\pi$
$919$			27.1395i			0.895249i	−0.894222	+	0.447624i	$0.852270\pi$
$920$	17.0001	+	2.21278i	0.560476	+	0.0729531i
$921$	28.5662			0.941288
$922$		−	17.7433i		−	0.584346i
$923$	30.0411			0.988816
$924$	5.11397			0.168237
$925$	2.33831	−	30.3238i	0.0768831	−	0.997040i
$926$	11.6293			0.382161
$927$	−3.38659			−0.111230
$928$			2.69676i			0.0885253i
$929$	47.1557			1.54713			0.773564	−	0.633719i	$-0.218472\pi$
$929$	47.1557			1.54713			0.773564	+	0.633719i	$0.218472\pi$
$930$	23.6314	+	3.07592i	0.774903	+	0.100863i
$931$		−	12.1606i		−	0.398546i
$932$			15.2152i			0.498391i
$933$	−52.9539			−1.73363
$934$	6.25208			0.204574
$935$	−4.23339	−	0.551029i	−0.138447	−	0.0180206i
$936$	0.425583			0.0139106
$937$		−	22.2885i		−	0.728133i	−0.931373	−	0.364066i	$-0.881388\pi$
$937$		−	22.2885i		−	0.728133i	0.931373	−	0.364066i	$-0.118612\pi$
$938$	24.0903			0.786578
$939$			17.8647i			0.582992i
$940$	−2.56707	+	19.7220i	−0.0837286	+	0.643261i
$941$	43.0380			1.40300			0.701499	−	0.712670i	$-0.252514\pi$
$941$	43.0380			1.40300			0.701499	+	0.712670i	$0.252514\pi$
$942$	13.0104			0.423902
$943$	−17.8109			−0.580001
$944$			5.55880i			0.180923i
$945$	−35.0373	−	4.56055i	−1.13976	−	0.148355i
$946$	−5.20525			−0.169237
$947$	16.4353			0.534075			0.267038	−	0.963686i	$-0.413955\pi$
$947$	16.4353			0.534075			0.267038	+	0.963686i	$0.413955\pi$
$948$	5.99850			0.194822
$949$			4.77545i			0.155018i
$950$	5.33344	−	20.1405i	0.173040	−	0.653444i
$951$	37.7654			1.22463
$952$			6.61496i			0.214392i
$953$			48.5182i			1.57166i	0.618443	+	0.785830i	$0.287764\pi$
$953$			48.5182i			1.57166i	−0.618443	+	0.785830i	$0.712236\pi$
$954$			1.79523i			0.0581227i
$955$	2.21082	−	16.9851i	0.0715405	−	0.549623i
$956$		−	29.1359i		−	0.942323i
$957$	4.37905			0.141555
$958$			16.4452i			0.531319i
$959$	−56.4851			−1.82400
$960$	0.515607	−	3.96125i	0.0166412	−	0.127849i
$961$	−4.58873			−0.148024
$962$	2.44591	+	13.2970i	0.0788593	+	0.428712i
$963$		−	1.29268i		−	0.0416560i
$964$			7.08791i			0.228286i
$965$	−42.8280	−	5.57461i	−1.37868	−	0.179453i
$966$	−43.1349			−1.38784
$967$	21.0002			0.675322			0.337661	−	0.941268i	$-0.390364\pi$
$967$	21.0002			0.675322			0.337661	+	0.941268i	$0.390364\pi$
$968$	10.1738			0.326998
$969$	15.6358			0.502295
$970$	11.4035	+	1.48431i	0.366145	+	0.0476584i
$971$	11.8732			0.381028			0.190514	−	0.981684i	$-0.438984\pi$
$971$	11.8732			0.381028			0.190514	+	0.981684i	$0.438984\pi$
$972$			1.98686i			0.0637286i
$973$		−	40.1452i		−	1.28700i
$974$	13.7966			0.442072
$975$	5.08235	−	19.1923i	0.162765	−	0.614645i
$976$		−	3.16611i		−	0.101345i
$977$	31.2226			0.998900			0.499450	−	0.866343i	$-0.333535\pi$
$977$	31.2226			0.998900			0.499450	+	0.866343i	$0.333535\pi$
$978$			39.7166i			1.27000i
$979$		−	7.59735i		−	0.242812i
$980$	−6.47102	−	0.842286i	−0.206709	−	0.0269058i
$981$		−	2.01628i		−	0.0643748i
$982$	39.0410			1.24585
$983$		−	57.5637i		−	1.83600i	−0.396583	−	0.917999i	$-0.629804\pi$
$983$		−	57.5637i		−	1.83600i	0.396583	−	0.917999i	$-0.370196\pi$
$984$			4.15017i			0.132303i
$985$	3.78646	−	29.0902i	0.120647	−	0.926890i
$986$			5.66434i			0.180389i
$987$		−	50.0414i		−	1.59283i
$988$			9.26180i			0.294657i
$989$	43.9049			1.39609
$990$	−0.385910	−	0.0502311i	−0.0122650	−	0.00159645i
$991$		−	14.9985i		−	0.476442i	−0.971211	−	0.238221i	$-0.923436\pi$
$991$		−	14.9985i		−	0.476442i	0.971211	−	0.238221i	$-0.0765642\pi$
$992$			5.96563i			0.189409i
$993$	33.4649			1.06198
$994$			42.5655i			1.35010i
$995$	1.74484	−	13.4050i	0.0553150	−	0.424968i
$996$	29.0795			0.921418
$997$	1.43497			0.0454459			0.0227229	−	0.999742i	$-0.492766\pi$
$997$	1.43497			0.0454459			0.0227229	+	0.999742i	$0.492766\pi$
$998$		−	40.0886i		−	1.26898i
$999$	−30.0158	+	5.52123i	−0.949657	+	0.174684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.c.a.369.2	✓	10
3.2	odd	2		3330.2.e.d.739.1		10
5.2	odd	4		1850.2.d.i.1701.2		20
5.3	odd	4		1850.2.d.i.1701.19		20
5.4	even	2		370.2.c.b.369.9	yes	10
15.14	odd	2		3330.2.e.c.739.9		10
37.36	even	2		370.2.c.b.369.2	yes	10
111.110	odd	2		3330.2.e.c.739.10		10
185.73	odd	4		1850.2.d.i.1701.9		20
185.147	odd	4		1850.2.d.i.1701.12		20
185.184	even	2	inner	370.2.c.a.369.9	yes	10
555.554	odd	2		3330.2.e.d.739.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.c.a.369.2	✓	10	1.1	even	1	trivial
370.2.c.a.369.9	yes	10	185.184	even	2	inner
370.2.c.b.369.2	yes	10	37.36	even	2
370.2.c.b.369.9	yes	10	5.4	even	2
1850.2.d.i.1701.2		20	5.2	odd	4
1850.2.d.i.1701.9		20	185.73	odd	4
1850.2.d.i.1701.12		20	185.147	odd	4
1850.2.d.i.1701.19		20	5.3	odd	4
3330.2.e.c.739.9		10	15.14	odd	2
3330.2.e.c.739.10		10	111.110	odd	2
3330.2.e.d.739.1		10	3.2	odd	2
3330.2.e.d.739.2		10	555.554	odd	2

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.78647i q^{3} +1.00000 q^{4} +(2.21736 + 0.288618i) q^{5} +1.78647i q^{6} -3.14934i q^{7} -1.00000 q^{8} -0.191472 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.78647i q^{3} +1.00000 q^{4} +(2.21736 + 0.288618i) q^{5} +1.78647i q^{6} -3.14934i q^{7} -1.00000 q^{8} -0.191472 q^{9} +(-2.21736 - 0.288618i) q^{10} -0.908956 q^{11} -1.78647i q^{12} +2.22269 q^{13} +3.14934i q^{14} +(0.515607 - 3.96125i) q^{15} +1.00000 q^{16} +2.10043 q^{17} +0.191472 q^{18} +4.16694i q^{19} +(2.21736 + 0.288618i) q^{20} -5.62620 q^{21} +0.908956 q^{22} -7.66680 q^{23} +1.78647i q^{24} +(4.83340 + 1.27994i) q^{25} -2.22269 q^{26} -5.01735i q^{27} -3.14934i q^{28} -2.69676i q^{29} +(-0.515607 + 3.96125i) q^{30} -5.96563i q^{31} -1.00000 q^{32} +1.62382i q^{33} -2.10043 q^{34} +(0.908956 - 6.98323i) q^{35} -0.191472 q^{36} +(-1.10043 - 5.98240i) q^{37} -4.16694i q^{38} -3.97076i q^{39} +(-2.21736 - 0.288618i) q^{40} +2.32312 q^{41} +5.62620 q^{42} -5.72663 q^{43} -0.908956 q^{44} +(-0.424564 - 0.0552624i) q^{45} +7.66680 q^{46} +8.89435i q^{47} -1.78647i q^{48} -2.91834 q^{49} +(-4.83340 - 1.27994i) q^{50} -3.75235i q^{51} +2.22269 q^{52} +9.37592i q^{53} +5.01735i q^{54} +(-2.01549 - 0.262341i) q^{55} +3.14934i q^{56} +7.44411 q^{57} +2.69676i q^{58} +5.55880i q^{59} +(0.515607 - 3.96125i) q^{60} -3.16611i q^{61} +5.96563i q^{62} +0.603011i q^{63} +1.00000 q^{64} +(4.92850 + 0.641508i) q^{65} -1.62382i q^{66} -7.64933i q^{67} +2.10043 q^{68} +13.6965i q^{69} +(-0.908956 + 6.98323i) q^{70} +13.5157 q^{71} +0.191472 q^{72} +2.14851i q^{73} +(1.10043 + 5.98240i) q^{74} +(2.28658 - 8.63472i) q^{75} +4.16694i q^{76} +2.86261i q^{77} +3.97076i q^{78} +3.35774i q^{79} +(2.21736 + 0.288618i) q^{80} -9.53776 q^{81} -2.32312 q^{82} +16.2776i q^{83} -5.62620 q^{84} +(4.65741 + 0.606222i) q^{85} +5.72663 q^{86} -4.81767 q^{87} +0.908956 q^{88} +8.35832i q^{89} +(0.424564 + 0.0552624i) q^{90} -7.00000i q^{91} -7.66680 q^{92} -10.6574 q^{93} -8.89435i q^{94} +(-1.20265 + 9.23962i) q^{95} +1.78647i q^{96} -5.14283 q^{97} +2.91834 q^{98} +0.174040 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} - 8 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 - 8 * q^9	\( 10 q - 10 q^{2} + 10 q^{4} - 3 q^{5} - 10 q^{8} - 8 q^{9} + 3 q^{10} - 2 q^{13} - 10 q^{15} + 10 q^{16} + 18 q^{17} + 8 q^{18} - 3 q^{20} - 12 q^{21} + 10 q^{23} + 5 q^{25} + 2 q^{26} + 10 q^{30} - 10 q^{32} - 18 q^{34} - 8 q^{36} - 8 q^{37} + 3 q^{40} - 4 q^{41} + 12 q^{42} - 10 q^{43} + 20 q^{45} - 10 q^{46} - 8 q^{49} - 5 q^{50} - 2 q^{52} + 5 q^{55} + 12 q^{57} - 10 q^{60} + 10 q^{64} + 2 q^{65} + 18 q^{68} - 20 q^{71} + 8 q^{72} + 8 q^{74} + 25 q^{75} - 3 q^{80} + 58 q^{81} + 4 q^{82} - 12 q^{84} - 28 q^{85} + 10 q^{86} - 10 q^{87} - 20 q^{90} + 10 q^{92} - 32 q^{93} + 2 q^{95} + 2 q^{97} + 8 q^{98} - 82 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^4 - 3 * q^5 - 10 * q^8 - 8 * q^9 + 3 * q^10 - 2 * q^13 - 10 * q^15 + 10 * q^16 + 18 * q^17 + 8 * q^18 - 3 * q^20 - 12 * q^21 + 10 * q^23 + 5 * q^25 + 2 * q^26 + 10 * q^30 - 10 * q^32 - 18 * q^34 - 8 * q^36 - 8 * q^37 + 3 * q^40 - 4 * q^41 + 12 * q^42 - 10 * q^43 + 20 * q^45 - 10 * q^46 - 8 * q^49 - 5 * q^50 - 2 * q^52 + 5 * q^55 + 12 * q^57 - 10 * q^60 + 10 * q^64 + 2 * q^65 + 18 * q^68 - 20 * q^71 + 8 * q^72 + 8 * q^74 + 25 * q^75 - 3 * q^80 + 58 * q^81 + 4 * q^82 - 12 * q^84 - 28 * q^85 + 10 * q^86 - 10 * q^87 - 20 * q^90 + 10 * q^92 - 32 * q^93 + 2 * q^95 + 2 * q^97 + 8 * q^98 - 82 * q^99

Introduction

L-functions

Modular forms

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