LMFDB - Embedded newform 756.2.b.f.55.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(55,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("756.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.b (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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} - 4x^{10} - 4x^{8} - 16x^{6} - 16x^{4} + 256 $ x^16 - x^12 - 4x^10 - 4x^8 - 16x^6 - 16x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.8
Root			$0.304958 + 1.38094i$ of defining polynomial
Character	$\chi$	$=$	756.55
Dual form			756.2.b.f.55.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.304958 + 1.38094i) q^{2} +(-1.81400 - 0.842259i) q^{4} +0.556957i q^{5} +(-1.25214 + 2.33070i) q^{7} +(1.71630 - 2.24818i) q^{8} +O(q^{10})$	\(q+(-0.304958 + 1.38094i) q^{2} +(-1.81400 - 0.842259i) q^{4} +0.556957i q^{5} +(-1.25214 + 2.33070i) q^{7} +(1.71630 - 2.24818i) q^{8} +(-0.769125 - 0.169848i) q^{10} +0.384447i q^{11} +4.88080i q^{13} +(-2.83671 - 2.43989i) q^{14} +(2.58120 + 3.05572i) q^{16} -5.55448i q^{17} -5.79490 q^{19} +(0.469102 - 1.01032i) q^{20} +(-0.530898 - 0.117240i) q^{22} +2.42219i q^{23} +4.68980 q^{25} +(-6.74010 - 1.48844i) q^{26} +(4.23443 - 3.17327i) q^{28} -6.72323 q^{29} -8.00767 q^{31} +(-5.00692 + 2.63262i) q^{32} +(7.67041 + 1.69388i) q^{34} +(-1.29810 - 0.697386i) q^{35} -4.16240 q^{37} +(1.76720 - 8.00241i) q^{38} +(1.25214 + 0.955907i) q^{40} -7.47347i q^{41} +7.80960i q^{43} +(0.323803 - 0.697386i) q^{44} +(-3.34490 - 0.738665i) q^{46} -11.4184 q^{47} +(-3.86430 - 5.83671i) q^{49} +(-1.43019 + 6.47634i) q^{50} +(4.11090 - 8.85378i) q^{52} +3.43261 q^{53} -0.214120 q^{55} +(3.09077 + 6.81521i) q^{56} +(2.05030 - 9.28439i) q^{58} +1.47260 q^{59} -3.06515i q^{61} +(2.44200 - 11.0581i) q^{62} +(-2.10860 - 7.71711i) q^{64} -2.71839 q^{65} +1.91900i q^{67} +(-4.67831 + 10.0758i) q^{68} +(1.35892 - 1.57992i) q^{70} +3.10158i q^{71} +4.89789i q^{73} +(1.26936 - 5.74804i) q^{74} +(10.5119 + 4.88080i) q^{76} +(-0.896029 - 0.481380i) q^{77} +6.35956i q^{79} +(-1.70190 + 1.43762i) q^{80} +(10.3204 + 2.27910i) q^{82} +12.9458 q^{83} +3.09360 q^{85} +(-10.7846 - 2.38160i) q^{86} +(0.864304 + 0.659827i) q^{88} +7.07419i q^{89} +(-11.3757 - 6.11143i) q^{91} +(2.04011 - 4.39385i) q^{92} +(3.48213 - 15.7682i) q^{94} -3.22751i q^{95} +9.28765i q^{97} +(9.23860 - 3.55643i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + q^{14} + 4 q^{16} + 26 q^{20} + 10 q^{22} - 20 q^{25} + 6 q^{26} - 11 q^{28} + 6 q^{35} + 8 q^{37} + 20 q^{38} - 6 q^{46} + 8 q^{47} - 14 q^{49} - 21 q^{56} + 14 q^{58} + 44 q^{59} - 48 q^{62} + 24 q^{64} + 2 q^{68} - 27 q^{70} - 54 q^{80} - 4 q^{83} + 8 q^{85} - 34 q^{88} + 47 q^{98}+O(q^{100}) $ 16 * q + q^14 + 4 * q^16 + 26 * q^20 + 10 * q^22 - 20 * q^25 + 6 * q^26 - 11 * q^28 + 6 * q^35 + 8 * q^37 + 20 * q^38 - 6 * q^46 + 8 * q^47 - 14 * q^49 - 21 * q^56 + 14 * q^58 + 44 * q^59 - 48 * q^62 + 24 * q^64 + 2 * q^68 - 27 * q^70 - 54 * q^80 - 4 * q^83 + 8 * q^85 - 34 * q^88 + 47 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.304958	+	1.38094i	−0.215638	+	0.976473i
$2$	−0.304958	+	1.38094i	−0.215638	+	0.976473i
$3$		0			0
$3$		0			0
$4$	−1.81400	−	0.842259i	−0.907001	−	0.421129i
$5$			0.556957i			0.249079i	0.992215	+	0.124539i	$0.0397453\pi$
$5$			0.556957i			0.249079i	−0.992215	+	0.124539i	$0.960255\pi$
$6$		0			0
$7$	−1.25214	+	2.33070i	−0.473263	+	0.880921i
$7$	−1.25214	+	2.33070i	−0.473263	+	0.880921i
$8$	1.71630	−	2.24818i	0.606805	−	0.794851i
$9$		0			0
$10$	−0.769125	−	0.169848i	−0.243219	−	0.0537108i
$11$			0.384447i			0.115915i	0.998319	+	0.0579575i	$0.0184588\pi$
$11$			0.384447i			0.115915i	−0.998319	+	0.0579575i	$0.981541\pi$
$12$		0			0
$13$			4.88080i			1.35369i	0.736125	+	0.676845i	$0.236653\pi$
$13$			4.88080i			1.35369i	−0.736125	+	0.676845i	$0.763347\pi$
$14$	−2.83671	−	2.43989i	−0.758142	−	0.652089i
$15$		0			0
$16$	2.58120	+	3.05572i	0.645300	+	0.763929i
$17$		−	5.55448i		−	1.34716i	−0.739115	−	0.673579i	$-0.764756\pi$
$17$		−	5.55448i		−	1.34716i	0.739115	−	0.673579i	$-0.235244\pi$
$18$		0			0
$19$	−5.79490			−1.32944			−0.664720	−	0.747093i	$-0.731449\pi$
$19$	−5.79490			−1.32944			−0.664720	+	0.747093i	$0.731449\pi$
$20$	0.469102	−	1.01032i	0.104894	−	0.225914i
$21$		0			0
$22$	−0.530898	−	0.117240i	−0.113188	−	0.0249957i
$23$			2.42219i			0.505061i	0.967589	+	0.252530i	$0.0812628\pi$
$23$			2.42219i			0.505061i	−0.967589	+	0.252530i	$0.918737\pi$
$24$		0			0
$25$	4.68980			0.937960
$26$	−6.74010	−	1.48844i	−1.32184	−	0.291907i
$27$		0			0
$28$	4.23443	−	3.17327i	0.800232	−	0.599691i
$29$	−6.72323			−1.24847			−0.624236	−	0.781236i	$-0.714590\pi$
$29$	−6.72323			−1.24847			−0.624236	+	0.781236i	$0.714590\pi$
$30$		0			0
$31$	−8.00767			−1.43822			−0.719110	−	0.694896i	$-0.755450\pi$
$31$	−8.00767			−1.43822			−0.719110	+	0.694896i	$0.755450\pi$
$32$	−5.00692	+	2.63262i	−0.885108	+	0.465386i
$33$		0			0
$34$	7.67041	+	1.69388i	1.31546	+	0.290498i
$35$	−1.29810	−	0.697386i	−0.219419	−	0.117880i
$36$		0			0
$37$	−4.16240			−0.684295			−0.342147	−	0.939646i	$-0.611154\pi$
$37$	−4.16240			−0.684295			−0.342147	+	0.939646i	$0.611154\pi$
$38$	1.76720	−	8.00241i	0.286678	−	1.29816i
$39$		0			0
$40$	1.25214	+	0.955907i	0.197980	+	0.151142i
$41$		−	7.47347i		−	1.16716i	−0.812056	−	0.583580i	$-0.801651\pi$
$41$		−	7.47347i		−	1.16716i	0.812056	−	0.583580i	$-0.198349\pi$
$42$		0			0
$43$			7.80960i			1.19095i	0.803373	+	0.595476i	$0.203037\pi$
$43$			7.80960i			1.19095i	−0.803373	+	0.595476i	$0.796963\pi$
$44$	0.323803	−	0.697386i	0.0488152	−	0.105135i
$45$		0			0
$46$	−3.34490	−	0.738665i	−0.493179	−	0.108910i
$47$	−11.4184			−1.66555			−0.832773	−	0.553615i	$-0.813248\pi$
$47$	−11.4184			−1.66555			−0.832773	+	0.553615i	$0.813248\pi$
$48$		0			0
$49$	−3.86430	−	5.83671i	−0.552043	−	0.833815i
$50$	−1.43019	+	6.47634i	−0.202260	+	0.915893i
$51$		0			0
$52$	4.11090	−	8.85378i	0.570079	−	1.22780i
$53$	3.43261			0.471505			0.235753	−	0.971813i	$-0.424245\pi$
$53$	3.43261			0.471505			0.235753	+	0.971813i	$0.424245\pi$
$54$		0			0
$55$	−0.214120			−0.0288720
$56$	3.09077	+	6.81521i	0.413022	+	0.910721i
$57$		0			0
$58$	2.05030	−	9.28439i	0.269218	−	1.21910i
$59$	1.47260			0.191717			0.0958583	−	0.995395i	$-0.469440\pi$
$59$	1.47260			0.191717			0.0958583	+	0.995395i	$0.469440\pi$
$60$		0			0
$61$		−	3.06515i		−	0.392453i	−0.980559	−	0.196226i	$-0.937131\pi$
$61$		−	3.06515i		−	0.392453i	0.980559	−	0.196226i	$-0.0628688\pi$
$62$	2.44200	−	11.0581i	0.310135	−	1.40438i
$63$		0			0
$64$	−2.10860	−	7.71711i	−0.263575	−	0.964639i
$65$	−2.71839			−0.337175
$66$		0			0
$67$			1.91900i			0.234443i	0.993106	+	0.117221i	$0.0373987\pi$
$67$			1.91900i			0.234443i	−0.993106	+	0.117221i	$0.962601\pi$
$68$	−4.67831	+	10.0758i	−0.567328	+	1.22187i
$69$		0			0
$70$	1.35892	−	1.57992i	0.162421	−	0.188837i
$71$			3.10158i			0.368090i	0.982918	+	0.184045i	$0.0589192\pi$
$71$			3.10158i			0.368090i	−0.982918	+	0.184045i	$0.941081\pi$
$72$		0			0
$73$			4.89789i			0.573254i	0.958042	+	0.286627i	$0.0925341\pi$
$73$			4.89789i			0.573254i	−0.958042	+	0.286627i	$0.907466\pi$
$74$	1.26936	−	5.74804i	0.147560	−	0.668196i
$75$		0			0
$76$	10.5119	+	4.88080i	1.20580	+	0.559866i
$77$	−0.896029	−	0.481380i	−0.102112	−	0.0548583i
$78$		0			0
$79$			6.35956i			0.715506i	0.933816	+	0.357753i	$0.116457\pi$
$79$			6.35956i			0.715506i	−0.933816	+	0.357753i	$0.883543\pi$
$80$	−1.70190	+	1.43762i	−0.190278	+	0.160731i
$81$		0			0
$82$	10.3204	+	2.27910i	1.13970	+	0.251684i
$83$	12.9458			1.42099			0.710493	−	0.703704i	$-0.248472\pi$
$83$	12.9458			1.42099			0.710493	+	0.703704i	$0.248472\pi$
$84$		0			0
$85$	3.09360			0.335548
$86$	−10.7846	−	2.38160i	−1.16293	−	0.256814i
$87$		0			0
$88$	0.864304	+	0.659827i	0.0921351	+	0.0703378i
$89$			7.07419i			0.749863i	0.927053	+	0.374931i	$0.122334\pi$
$89$			7.07419i			0.749863i	−0.927053	+	0.374931i	$0.877666\pi$
$90$		0			0
$91$	−11.3757	−	6.11143i	−1.19249	−	0.640652i
$92$	2.04011	−	4.39385i	0.212696	−	0.458091i
$93$		0			0
$94$	3.48213	−	15.7682i	0.359155	−	1.62636i
$95$		−	3.22751i		−	0.331135i
$96$		0			0
$97$			9.28765i			0.943018i	0.881861	+	0.471509i	$0.156291\pi$
$97$			9.28765i			0.943018i	−0.881861	+	0.471509i	$0.843709\pi$
$98$	9.23860	−	3.55643i	0.933240	−	0.359254i
$99$		0			0
$100$	−8.50730	−	3.95002i	−0.850730	−	0.395002i
$101$			6.91652i			0.688219i	0.938930	+	0.344110i	$0.111819\pi$
$101$			6.91652i			0.688219i	−0.938930	+	0.344110i	$0.888181\pi$
$102$		0			0
$103$	−0.291498			−0.0287222			−0.0143611	−	0.999897i	$-0.504571\pi$
$103$	−0.291498			−0.0287222			−0.0143611	+	0.999897i	$0.504571\pi$
$104$	10.9729	+	8.37694i	1.07598	+	0.821426i
$105$		0			0
$106$	−1.04680	+	4.74023i	−0.101674	+	0.460412i
$107$		−	13.1217i		−	1.26852i	−0.773119	−	0.634261i	$-0.781304\pi$
$107$		−	13.1217i		−	1.26852i	0.773119	−	0.634261i	$-0.218696\pi$
$108$		0			0
$109$	−4.16240			−0.398686			−0.199343	−	0.979930i	$-0.563881\pi$
$109$	−4.16240			−0.398686			−0.199343	+	0.979930i	$0.563881\pi$
$110$	0.0652976	−	0.295687i	0.00622589	−	0.0281927i
$111$		0			0
$112$	−10.3540	+	2.18982i	−0.978358	+	0.206919i
$113$	14.9450			1.40591			0.702955	−	0.711235i	$-0.251864\pi$
$113$	14.9450			1.40591			0.702955	+	0.711235i	$0.251864\pi$
$114$		0			0
$115$	−1.34905			−0.125800
$116$	12.1959	+	5.66270i	1.13237	+	0.525768i
$117$		0			0
$118$	−0.449082	+	2.03358i	−0.0413413	+	0.187206i
$119$	12.9458	+	6.95497i	1.18674	+	0.637561i
$120$		0			0
$121$	10.8522			0.986564
$122$	4.23280	+	0.934743i	0.383220	+	0.0846277i
$123$		0			0
$124$	14.5259	+	6.74453i	1.30447	+	0.605677i
$125$			5.39680i			0.482704i
$126$		0			0
$127$		−	10.5520i		−	0.936338i	−0.883639	−	0.468169i	$-0.844914\pi$
$127$		−	10.5520i		−	0.936338i	0.883639	−	0.468169i	$-0.155086\pi$
$128$	11.2999	−	0.558457i	0.998781	−	0.0493611i
$129$		0			0
$130$	0.828996	−	3.75395i	0.0727078	−	0.329243i
$131$	−13.3496			−1.16636			−0.583180	−	0.812343i	$-0.698192\pi$
$131$	−13.3496			−1.16636			−0.583180	+	0.812343i	$0.698192\pi$
$132$		0			0
$133$	7.25600	−	13.5061i	0.629175	−	1.17113i
$134$	−2.65002	−	0.585214i	−0.228927	−	0.0505548i
$135$		0			0
$136$	−12.4874	−	9.53317i	−1.07079	−	0.817463i
$137$	−16.4488			−1.40532			−0.702659	−	0.711527i	$-0.748004\pi$
$137$	−16.4488			−1.40532			−0.702659	+	0.711527i	$0.748004\pi$
$138$		0			0
$139$	2.29015			0.194248			0.0971242	−	0.995272i	$-0.469036\pi$
$139$	2.29015			0.194248			0.0971242	+	0.995272i	$0.469036\pi$
$140$	1.76737	+	2.35839i	0.149370	+	0.199321i
$141$		0			0
$142$	−4.28310	−	0.945852i	−0.359430	−	0.0793741i
$143$	−1.87641			−0.156913
$144$		0			0
$145$		−	3.74455i		−	0.310968i
$146$	−6.76370	−	1.49365i	−0.559768	−	0.123615i
$147$		0			0
$148$	7.55060	+	3.50582i	0.620656	+	0.288177i
$149$	22.0371			1.80535			0.902676	−	0.430321i	$-0.141600\pi$
$149$	22.0371			1.80535			0.902676	+	0.430321i	$0.141600\pi$
$150$		0			0
$151$			7.18296i			0.584541i	0.956336	+	0.292271i	$0.0944108\pi$
$151$			7.18296i			0.584541i	−0.956336	+	0.292271i	$0.905589\pi$
$152$	−9.94580	+	13.0279i	−0.806711	+	1.05671i
$153$		0			0
$154$	0.938009	−	1.09056i	0.0755869	−	0.0878801i
$155$		−	4.45993i		−	0.358230i
$156$		0			0
$157$			11.6905i			0.933004i	0.884520	+	0.466502i	$0.154486\pi$
$157$			11.6905i			0.933004i	−0.884520	+	0.466502i	$0.845514\pi$
$158$	−8.78218	−	1.93940i	−0.698673	−	0.154290i
$159$		0			0
$160$	−1.46626	−	2.78864i	−0.115918	−	0.220461i
$161$	−5.64539	−	3.03291i	−0.444919	−	0.239027i
$162$		0			0
$163$			7.78230i			0.609557i	0.952423	+	0.304779i	$0.0985824\pi$
$163$			7.78230i			0.609557i	−0.952423	+	0.304779i	$0.901418\pi$
$164$	−6.29460	+	13.5569i	−0.491525	+	1.05862i
$165$		0			0
$166$	−3.94793	+	17.8774i	−0.306419	+	1.38756i
$167$	7.29481			0.564490			0.282245	−	0.959342i	$-0.408921\pi$
$167$	7.29481			0.564490			0.282245	+	0.959342i	$0.408921\pi$
$168$		0			0
$169$	−10.8222			−0.832478
$170$	−0.943419	+	4.27209i	−0.0723569	+	0.327654i
$171$		0			0
$172$	6.57770	−	14.1666i	0.501545	−	1.08019i
$173$			22.9774i			1.74694i	0.486880	+	0.873469i	$0.338135\pi$
$173$			22.9774i			1.74694i	−0.486880	+	0.873469i	$0.661865\pi$
$174$		0			0
$175$	−5.87227	+	10.9305i	−0.443902	+	0.826268i
$176$	−1.17476	+	0.992334i	−0.0885508	+	0.0748000i
$177$		0			0
$178$	−9.76905	−	2.15733i	−0.732221	−	0.161699i
$179$			12.8461i			0.960162i	0.877224	+	0.480081i	$0.159393\pi$
$179$			12.8461i			0.960162i	−0.877224	+	0.480081i	$0.840607\pi$
$180$		0			0
$181$			17.0282i			1.26569i	0.774277	+	0.632847i	$0.218114\pi$
$181$			17.0282i			1.26569i	−0.774277	+	0.632847i	$0.781886\pi$
$182$	11.9086	−	13.8454i	0.882727	−	1.02629i
$183$		0			0
$184$	5.44550	+	4.15721i	0.401448	+	0.306474i
$185$		−	2.31828i		−	0.170443i
$186$		0			0
$187$	2.13540			0.156156
$188$	20.7130	+	9.61725i	1.51065	+	0.701410i
$189$		0			0
$190$	4.45700	+	0.984254i	0.323345	+	0.0714053i
$191$			18.7543i			1.35701i	0.734594	+	0.678507i	$0.237373\pi$
$191$			18.7543i			1.35701i	−0.734594	+	0.678507i	$0.762627\pi$
$192$		0			0
$193$	−15.6356			−1.12548			−0.562738	−	0.826636i	$-0.690252\pi$
$193$	−15.6356			−1.12548			−0.562738	+	0.826636i	$0.690252\pi$
$194$	−12.8257	−	2.83234i	−0.920832	−	0.203350i
$195$		0			0
$196$	2.09383	+	13.8425i	0.149560	+	0.988753i
$197$	−0.850956			−0.0606281			−0.0303141	−	0.999540i	$-0.509651\pi$
$197$	−0.850956			−0.0606281			−0.0303141	+	0.999540i	$0.509651\pi$
$198$		0			0
$199$	−1.62978			−0.115532			−0.0577660	−	0.998330i	$-0.518398\pi$
$199$	−1.62978			−0.115532			−0.0577660	+	0.998330i	$0.518398\pi$
$200$	8.04912	−	10.5435i	0.569159	−	0.745538i
$201$		0			0
$202$	−9.55131	−	2.10925i	−0.672028	−	0.148406i
$203$	8.41841	−	15.6698i	0.590856	−	1.09981i
$204$		0			0
$205$	4.16240			0.290715
$206$	0.0888947	−	0.402542i	0.00619358	−	0.0280464i
$207$		0			0
$208$	−14.9143	+	12.5983i	−1.03412	+	0.873537i
$209$		−	2.22783i		−	0.154102i
$210$		0			0
$211$			0.665725i			0.0458304i	0.999737	+	0.0229152i	$0.00729477\pi$
$211$			0.665725i			0.0458304i	−0.999737	+	0.0229152i	$0.992705\pi$
$212$	−6.22676	−	2.89114i	−0.427655	−	0.198565i
$213$		0			0
$214$	18.1203	+	4.00157i	1.23868	+	0.273542i
$215$	−4.34961			−0.296641
$216$		0			0
$217$	10.0267	−	18.6635i	0.680657	−	1.26696i
$218$	1.26936	−	5.74804i	0.0859718	−	0.389306i
$219$		0			0
$220$	0.388414	+	0.180345i	0.0261869	+	0.0121588i
$221$	27.1103			1.82364
$222$		0			0
$223$	7.72694			0.517434			0.258717	−	0.965953i	$-0.416700\pi$
$223$	7.72694			0.517434			0.258717	+	0.965953i	$0.416700\pi$
$224$	0.133508	−	14.9660i	0.00892040	−	0.999960i
$225$		0			0
$226$	−4.55760	+	20.6382i	−0.303167	+	1.37283i
$227$	−6.89101			−0.457372			−0.228686	−	0.973500i	$-0.573443\pi$
$227$	−6.89101			−0.457372			−0.228686	+	0.973500i	$0.573443\pi$
$228$		0			0
$229$		−	16.5713i		−	1.09506i	−0.836785	−	0.547531i	$-0.815568\pi$
$229$		−	16.5713i		−	1.09506i	0.836785	−	0.547531i	$-0.184432\pi$
$230$	0.411405	−	1.86296i	0.0271272	−	0.122840i
$231$		0			0
$232$	−11.5391	+	15.1150i	−0.757580	+	0.992349i
$233$	−21.3282			−1.39725			−0.698627	−	0.715486i	$-0.746205\pi$
$233$	−21.3282			−1.39725			−0.698627	+	0.715486i	$0.746205\pi$
$234$		0			0
$235$		−	6.35956i		−	0.414852i
$236$	−2.67130	−	1.24031i	−0.173887	−	0.0807375i
$237$		0			0
$238$	−13.5523	+	15.7564i	−0.878467	+	1.02134i
$239$		−	14.2750i		−	0.923376i	−0.887042	−	0.461688i	$-0.847244\pi$
$239$		−	14.2750i		−	0.923376i	0.887042	−	0.461688i	$-0.152756\pi$
$240$		0			0
$241$			18.9571i			1.22113i	0.791965	+	0.610566i	$0.209058\pi$
$241$			18.9571i			1.22113i	−0.791965	+	0.610566i	$0.790942\pi$
$242$	−3.30947	+	14.9863i	−0.212741	+	0.963353i
$243$		0			0
$244$	−2.58165	+	5.56019i	−0.165273	+	0.355955i
$245$	3.25079	−	2.15225i	0.207686	−	0.137502i
$246$		0			0
$247$		−	28.2837i		−	1.79965i
$248$	−13.7436	+	18.0027i	−0.872720	+	1.14317i
$249$		0			0
$250$	−7.45267	−	1.64580i	−0.471348	−	0.104089i
$251$	10.3496			0.653261			0.326631	−	0.945152i	$-0.394087\pi$
$251$	10.3496			0.653261			0.326631	+	0.945152i	$0.394087\pi$
$252$		0			0
$253$	−0.931201			−0.0585441
$254$	14.5717	+	3.21792i	0.914309	+	0.201910i
$255$		0			0
$256$	−2.67480	+	15.7748i	−0.167175	+	0.985927i
$257$		−	15.9488i		−	0.994858i	−0.867505	−	0.497429i	$-0.834277\pi$
$257$		−	15.9488i		−	0.994858i	0.867505	−	0.497429i	$-0.165723\pi$
$258$		0			0
$259$	5.21190	−	9.70130i	0.323852	−	0.602809i
$260$	4.93117	+	2.28959i	0.305818	+	0.141994i
$261$		0			0
$262$	4.07107	−	18.4350i	0.251512	−	1.13892i
$263$		−	26.9417i		−	1.66130i	−0.556798	−	0.830648i	$-0.687970\pi$
$263$		−	26.9417i		−	1.66130i	0.556798	−	0.830648i	$-0.312030\pi$
$264$		0			0
$265$			1.91181i			0.117442i
$266$	16.4384	+	14.1389i	1.00790	+	0.866913i
$267$		0			0
$268$	1.61629	−	3.48106i	0.0987307	−	0.212640i
$269$			26.7640i			1.63183i	0.578172	+	0.815915i	$0.303766\pi$
$269$			26.7640i			1.63183i	−0.578172	+	0.815915i	$0.696234\pi$
$270$		0			0
$271$	10.1431			0.616148			0.308074	−	0.951362i	$-0.400316\pi$
$271$	10.1431			0.616148			0.308074	+	0.951362i	$0.400316\pi$
$272$	16.9729	−	14.3372i	1.02913	−	0.869322i
$273$		0			0
$274$	5.01620	−	22.7149i	0.303040	−	1.37226i
$275$			1.80298i			0.108724i
$276$		0			0
$277$	9.29481			0.558471			0.279236	−	0.960223i	$-0.409919\pi$
$277$	9.29481			0.558471			0.279236	+	0.960223i	$0.409919\pi$
$278$	−0.698401	+	3.16257i	−0.0418873	+	0.189678i
$279$		0			0
$280$	−3.79578	+	1.72143i	−0.226841	+	0.102875i
$281$	−20.3871			−1.21619			−0.608095	−	0.793864i	$-0.708066\pi$
$281$	−20.3871			−1.21619			−0.608095	+	0.793864i	$0.708066\pi$
$282$		0			0
$283$	26.0527			1.54867			0.774337	−	0.632773i	$-0.218084\pi$
$283$	26.0527			1.54867			0.774337	+	0.632773i	$0.218084\pi$
$284$	2.61233	−	5.62627i	0.155013	−	0.333858i
$285$		0			0
$286$	0.572225	−	2.59121i	0.0338364	−	0.153221i
$287$	17.4184	+	9.35782i	1.02818	+	0.552374i
$288$		0			0
$289$	−13.8522			−0.814835
$290$	5.17100	+	1.14193i	0.303652	+	0.0670564i
$291$		0			0
$292$	4.12529	−	8.88477i	0.241414	−	0.519942i
$293$		−	1.51972i		−	0.0887828i	−0.999014	−	0.0443914i	$-0.985865\pi$
$293$		−	1.51972i		−	0.0887828i	0.999014	−	0.0443914i	$-0.0141349\pi$
$294$		0			0
$295$			0.820176i			0.0477525i
$296$	−7.14395	+	9.35782i	−0.415234	+	0.543912i
$297$		0			0
$298$	−6.72040	+	30.4320i	−0.389302	+	1.76288i
$299$	−11.8222			−0.683696
$300$		0			0
$301$	−18.2018	−	9.77869i	−1.04913	−	0.563634i
$302$	−9.91925	−	2.19050i	−0.570789	−	0.126049i
$303$		0			0
$304$	−14.9578	−	17.7076i	−0.857888	−	1.01560i
$305$	1.70716			0.0977516
$306$		0			0
$307$	26.2561			1.49851			0.749257	−	0.662280i	$-0.230411\pi$
$307$	26.2561			1.49851			0.749257	+	0.662280i	$0.230411\pi$
$308$	1.21995	+	1.62791i	0.0695131	+	0.0927589i
$309$		0			0
$310$	6.15890	+	1.36009i	0.349802	+	0.0772480i
$311$	−21.5420			−1.22153			−0.610767	−	0.791810i	$-0.709139\pi$
$311$	−21.5420			−1.22153			−0.610767	+	0.791810i	$0.709139\pi$
$312$		0			0
$313$		−	24.4211i		−	1.38036i	−0.723637	−	0.690181i	$-0.757531\pi$
$313$		−	24.4211i		−	1.38036i	0.723637	−	0.690181i	$-0.242469\pi$
$314$	−16.1439	−	3.56511i	−0.911053	−	0.201191i
$315$		0			0
$316$	5.35639	−	11.5362i	0.301321	−	0.648965i
$317$	2.15142			0.120836			0.0604178	−	0.998173i	$-0.480757\pi$
$317$	2.15142			0.120836			0.0604178	+	0.998173i	$0.480757\pi$
$318$		0			0
$319$		−	2.58472i		−	0.144717i
$320$	4.29810	−	1.17440i	0.240271	−	0.0656509i
$321$		0			0
$322$	5.90988	−	6.87104i	0.329345	−	0.382908i
$323$			32.1876i			1.79097i
$324$		0			0
$325$			22.8900i			1.26971i
$326$	−10.7469	−	2.37328i	−0.595216	−	0.131444i
$327$		0			0
$328$	−16.8017	−	12.8268i	−0.927718	−	0.708239i
$329$	14.2974	−	26.6129i	0.788242	−	1.46721i
$330$		0			0
$331$		−	13.7906i		−	0.758002i	−0.925396	−	0.379001i	$-0.876268\pi$
$331$		−	13.7906i		−	0.758002i	0.925396	−	0.379001i	$-0.123732\pi$
$332$	−23.4837	−	10.9037i	−1.28884	−	0.598419i
$333$		0			0
$334$	−2.22461	+	10.0737i	−0.121725	+	0.551209i
$335$	−1.06880			−0.0583947
$336$		0			0
$337$	24.4966			1.33442			0.667208	−	0.744871i	$-0.267489\pi$
$337$	24.4966			1.33442			0.667208	+	0.744871i	$0.267489\pi$
$338$	3.30032	−	14.9448i	0.179514	−	0.812892i
$339$		0			0
$340$	−5.61180	−	2.60561i	−0.304343	−	0.141309i
$341$		−	3.07852i		−	0.166711i
$342$		0			0
$343$	18.4422	−	1.69816i	0.995787	−	0.0916922i
$344$	17.5574	+	13.4036i	0.946629	+	0.722676i
$345$		0			0
$346$	−31.7304	−	7.00713i	−1.70584	−	0.376706i
$347$			21.9625i			1.17901i	0.807766	+	0.589504i	$0.200677\pi$
$347$			21.9625i			1.17901i	−0.807766	+	0.589504i	$0.799323\pi$
$348$		0			0
$349$		−	7.91178i		−	0.423508i	−0.977323	−	0.211754i	$-0.932082\pi$
$349$		−	7.91178i		−	0.423508i	0.977323	−	0.211754i	$-0.0679175\pi$
$350$	−13.3036	−	11.4426i	−0.711107	−	0.611633i
$351$		0			0
$352$	−1.01210	−	1.92489i	−0.0539453	−	0.102597i
$353$			0.714633i			0.0380361i	0.999819	+	0.0190180i	$0.00605399\pi$
$353$			0.714633i			0.0380361i	−0.999819	+	0.0190180i	$0.993946\pi$
$354$		0			0
$355$	−1.72745			−0.0916833
$356$	5.95830	−	12.8326i	0.315789	−	0.680126i
$357$		0			0
$358$	−17.7397	−	3.91752i	−0.937573	−	0.207047i
$359$		−	32.0617i		−	1.69215i	−0.533063	−	0.846075i	$-0.678959\pi$
$359$		−	32.0617i		−	1.69215i	0.533063	−	0.846075i	$-0.321041\pi$
$360$		0			0
$361$	14.5808			0.767411
$362$	−23.5149	−	5.19287i	−1.23592	−	0.272931i
$363$		0			0
$364$	15.4881	+	20.6674i	0.811796	+	1.08327i
$365$	−2.72791			−0.142785
$366$		0			0
$367$	33.6322			1.75558			0.877792	−	0.479041i	$-0.159016\pi$
$367$	33.6322			1.75558			0.877792	+	0.479041i	$0.159016\pi$
$368$	−7.40152	+	6.25215i	−0.385831	+	0.325916i
$369$		0			0
$370$	3.20141	+	0.706977i	0.166433	+	0.0367540i
$371$	−4.29810	+	8.00037i	−0.223146	+	0.415359i
$372$		0			0
$373$	−1.96119			−0.101547			−0.0507733	−	0.998710i	$-0.516169\pi$
$373$	−1.96119			−0.101547			−0.0507733	+	0.998710i	$0.516169\pi$
$374$	−0.651207	+	2.94886i	−0.0336731	+	0.152482i
$375$		0			0
$376$	−19.5975	+	25.6706i	−1.01066	+	1.32386i
$377$		−	32.8147i		−	1.69004i
$378$		0			0
$379$			5.91789i			0.303982i	0.988382	+	0.151991i	$0.0485684\pi$
$379$			5.91789i			0.303982i	−0.988382	+	0.151991i	$0.951432\pi$
$380$	−2.71839	+	5.85470i	−0.139451	+	0.300340i
$381$		0			0
$382$	−25.8986	−	5.71928i	−1.32509	−	0.292624i
$383$	−8.47320			−0.432960			−0.216480	−	0.976287i	$-0.569458\pi$
$383$	−8.47320			−0.432960			−0.216480	+	0.976287i	$0.569458\pi$
$384$		0			0
$385$	0.268108	−	0.499049i	0.0136640	−	0.0254339i
$386$	4.76820	−	21.5919i	0.242695	−	1.09900i
$387$		0			0
$388$	7.82261	−	16.8478i	0.397133	−	0.855318i
$389$	−29.2477			−1.48292			−0.741458	−	0.670999i	$-0.765865\pi$
$389$	−29.2477			−1.48292			−0.741458	+	0.670999i	$0.765865\pi$
$390$		0			0
$391$	13.4540			0.680397
$392$	−19.7543	−	1.32993i	−0.997741	−	0.0671716i
$393$		0			0
$394$	0.259506	−	1.17512i	0.0130737	−	0.0592017i
$395$	−3.54200			−0.178217
$396$		0			0
$397$		−	36.0945i		−	1.81153i	−0.423779	−	0.905766i	$-0.639297\pi$
$397$		−	36.0945i		−	1.81153i	0.423779	−	0.905766i	$-0.360703\pi$
$398$	0.497015	−	2.25063i	0.0249131	−	0.112814i
$399$		0			0
$400$	12.1053	+	14.3307i	0.605266	+	0.716535i
$401$	−16.6522			−0.831570			−0.415785	−	0.909463i	$-0.636493\pi$
$401$	−16.6522			−0.831570			−0.415785	+	0.909463i	$0.636493\pi$
$402$		0			0
$403$		−	39.0838i		−	1.94691i
$404$	5.82550	−	12.5466i	0.289829	−	0.624215i
$405$		0			0
$406$	19.0718	+	16.4040i	0.946520	+	0.814115i
$407$		−	1.60022i		−	0.0793200i
$408$		0			0
$409$			31.2308i			1.54426i	0.635463	+	0.772132i	$0.280809\pi$
$409$			31.2308i			1.54426i	−0.635463	+	0.772132i	$0.719191\pi$
$410$	−1.26936	+	5.74804i	−0.0626891	+	0.283875i
$411$		0			0
$412$	0.528778	+	0.245517i	0.0260510	+	0.0120957i
$413$	−1.84390	+	3.43219i	−0.0907324	+	0.168887i
$414$		0			0
$415$			7.21025i			0.353937i
$416$	−12.8493	−	24.4378i	−0.629989	−	1.19816i
$417$		0			0
$418$	3.07650	+	0.679394i	0.150477	+	0.0332302i
$419$	5.59620			0.273392			0.136696	−	0.990613i	$-0.456352\pi$
$419$	5.59620			0.273392			0.136696	+	0.990613i	$0.456352\pi$
$420$		0			0
$421$	−29.1476			−1.42057			−0.710284	−	0.703915i	$-0.751433\pi$
$421$	−29.1476			−1.42057			−0.710284	+	0.703915i	$0.751433\pi$
$422$	−0.919327	−	0.203018i	−0.0447521	−	0.00988277i
$423$		0			0
$424$	5.89140	−	7.71711i	0.286112	−	0.374776i
$425$		−	26.0494i		−	1.26358i
$426$		0			0
$427$	7.14395	+	3.83799i	0.345720	+	0.185734i
$428$	−11.0519	+	23.8028i	−0.534212	+	1.15055i
$429$		0			0
$430$	1.32645	−	6.00656i	0.0639670	−	0.289662i
$431$		−	0.768893i		−	0.0370363i	−0.999829	−	0.0185181i	$-0.994105\pi$
$431$		−	0.768893i		−	0.0370363i	0.999829	−	0.0185181i	$-0.00589484\pi$
$432$		0			0
$433$		−	21.3559i		−	1.02630i	−0.858299	−	0.513150i	$-0.828478\pi$
$433$		−	21.3559i		−	1.02630i	0.858299	−	0.513150i	$-0.171522\pi$
$434$	22.7154	+	19.5379i	1.09038	+	0.937848i
$435$		0			0
$436$	7.55060	+	3.50582i	0.361608	+	0.167898i
$437$		−	14.0363i		−	0.671448i
$438$		0			0
$439$	−15.5300			−0.741207			−0.370604	−	0.928791i	$-0.620849\pi$
$439$	−15.5300			−0.741207			−0.370604	+	0.928791i	$0.620849\pi$
$440$	−0.367495	+	0.481380i	−0.0175197	+	0.0229489i
$441$		0			0
$442$	−8.26750	+	37.4377i	−0.393245	+	1.78073i
$443$			18.4234i			0.875321i	0.899140	+	0.437660i	$0.144193\pi$
$443$			18.4234i			0.875321i	−0.899140	+	0.437660i	$0.855807\pi$
$444$		0			0
$445$	−3.94002			−0.186775
$446$	−2.35639	+	10.6705i	−0.111578	+	0.505261i
$447$		0			0
$448$	20.6265	+	4.74838i	0.974511	+	0.224340i
$449$	8.74217			0.412569			0.206284	−	0.978492i	$-0.433863\pi$
$449$	8.74217			0.412569			0.206284	+	0.978492i	$0.433863\pi$
$450$		0			0
$451$	2.87315			0.135291
$452$	−27.1103	−	12.5876i	−1.27516	−	0.592070i
$453$		0			0
$454$	2.10147	−	9.51608i	0.0986268	−	0.446612i
$455$	3.40380	−	6.33576i	0.159573	−	0.297025i
$456$		0			0
$457$	−27.0540			−1.26553			−0.632767	−	0.774343i	$-0.718081\pi$
$457$	−27.0540			−1.26553			−0.632767	+	0.774343i	$0.718081\pi$
$458$	22.8840	+	5.05355i	1.06930	+	0.236137i
$459$		0			0
$460$	2.44718	+	1.13625i	0.114101	+	0.0529780i
$461$			15.8062i			0.736169i	0.929792	+	0.368084i	$0.119986\pi$
$461$			15.8062i			0.736169i	−0.929792	+	0.368084i	$0.880014\pi$
$462$		0			0
$463$		−	30.4508i		−	1.41517i	−0.706628	−	0.707585i	$-0.749784\pi$
$463$		−	30.4508i		−	1.41517i	0.706628	−	0.707585i	$-0.250216\pi$
$464$	−17.3540	−	20.5443i	−0.805639	−	0.953744i
$465$		0			0
$466$	6.50419	−	29.4529i	0.301301	−	1.36438i
$467$	−37.4330			−1.73219			−0.866097	−	0.499877i	$-0.833379\pi$
$467$	−37.4330			−1.73219			−0.866097	+	0.499877i	$0.833379\pi$
$468$		0			0
$469$	−4.47260	−	2.40285i	−0.206526	−	0.110953i
$470$	8.78218	+	1.93940i	0.405092	+	0.0894578i
$471$		0			0
$472$	2.52743	−	3.31067i	0.116335	−	0.152386i
$473$	−3.00237			−0.138049
$474$		0			0
$475$	−27.1769			−1.24696
$476$	−17.6258	−	23.5200i	−0.807878	−	1.07804i
$477$		0			0
$478$	19.7130	+	4.35329i	0.901652	+	0.199115i
$479$	−0.581593			−0.0265737			−0.0132868	−	0.999912i	$-0.504229\pi$
$479$	−0.581593			−0.0265737			−0.0132868	+	0.999912i	$0.504229\pi$
$480$		0			0
$481$		−	20.3159i		−	0.926323i
$482$	−26.1786	−	5.78111i	−1.19240	−	0.263322i
$483$		0			0
$484$	−19.6859	−	9.14036i	−0.894814	−	0.415471i
$485$	−5.17282			−0.234886
$486$		0			0
$487$			18.2039i			0.824898i	0.910981	+	0.412449i	$0.135327\pi$
$487$			18.2039i			0.824898i	−0.910981	+	0.412449i	$0.864673\pi$
$488$	−6.89101	−	5.26074i	−0.311941	−	0.238142i
$489$		0			0
$490$	1.98078	+	5.14550i	0.0894824	+	0.232450i
$491$		−	26.6279i		−	1.20170i	−0.799363	−	0.600849i	$-0.794829\pi$
$491$		−	26.6279i		−	1.20170i	0.799363	−	0.600849i	$-0.205171\pi$
$492$		0			0
$493$			37.3440i			1.68189i
$494$	39.0582	+	8.62535i	1.75731	+	0.388073i
$495$		0			0
$496$	−20.6694	−	24.4692i	−0.928084	−	1.09870i
$497$	−7.22885	−	3.88361i	−0.324258	−	0.174204i
$498$		0			0
$499$			40.5697i			1.81615i	0.418806	+	0.908076i	$0.362449\pi$
$499$			40.5697i			1.81615i	−0.418806	+	0.908076i	$0.637551\pi$
$500$	4.54550	−	9.78980i	0.203281	−	0.437813i
$501$		0			0
$502$	−3.15620	+	14.2922i	−0.140868	+	0.637892i
$503$	9.54200			0.425457			0.212728	−	0.977111i	$-0.431765\pi$
$503$	9.54200			0.425457			0.212728	+	0.977111i	$0.431765\pi$
$504$		0			0
$505$	−3.85220			−0.171421
$506$	0.283977	−	1.28594i	0.0126243	−	0.0571668i
$507$		0			0
$508$	−8.88751	+	19.1413i	−0.394319	+	0.849259i
$509$			43.6756i			1.93589i	0.251171	+	0.967943i	$0.419184\pi$
$509$			43.6756i			1.93589i	−0.251171	+	0.967943i	$0.580816\pi$
$510$		0			0
$511$	−11.4155	−	6.13283i	−0.504992	−	0.271300i
$512$	−20.9684	−	8.50441i	−0.926682	−	0.375845i
$513$		0			0
$514$	22.0244	+	4.86371i	0.971453	+	0.214529i
$515$		−	0.162352i		−	0.00715408i
$516$		0			0
$517$		−	4.38977i		−	0.193062i
$518$	11.8075	+	10.1558i	0.518793	+	0.446221i
$519$		0			0
$520$	−4.66559	+	6.11143i	−0.204600	+	0.268004i
$521$		−	33.0266i		−	1.44692i	−0.690366	−	0.723461i	$-0.742550\pi$
$521$		−	33.0266i		−	1.44692i	0.690366	−	0.723461i	$-0.257450\pi$
$522$		0			0
$523$	11.7931			0.515678			0.257839	−	0.966188i	$-0.416990\pi$
$523$	11.7931			0.515678			0.257839	+	0.966188i	$0.416990\pi$
$524$	24.2162	+	11.2438i	1.05789	+	0.491189i
$525$		0			0
$526$	37.2049	+	8.21609i	1.62221	+	0.358238i
$527$			44.4784i			1.93751i
$528$		0			0
$529$	17.1330			0.744913
$530$	−2.64011	−	0.583023i	−0.114679	−	0.0253249i
$531$		0			0
$532$	−24.5381	+	18.3887i	−1.06386	+	0.797253i
$533$	36.4765			1.57997
$534$		0			0
$535$	7.30822			0.315962
$536$	4.31425	+	3.29358i	0.186347	+	0.142261i
$537$		0			0
$538$	−36.9595	−	8.16190i	−1.59344	−	0.351884i
$539$	2.24390	−	1.48562i	0.0966517	−	0.0639901i
$540$		0			0
$541$	24.6108			1.05810			0.529050	−	0.848590i	$-0.322548\pi$
$541$	24.6108			1.05810			0.529050	+	0.848590i	$0.322548\pi$
$542$	−3.09321	+	14.0070i	−0.132865	+	0.601652i
$543$		0			0
$544$	14.6228	+	27.8108i	0.626949	+	1.19238i
$545$		−	2.31828i		−	0.0993041i
$546$		0			0
$547$		−	11.5017i		−	0.491778i	−0.969298	−	0.245889i	$-0.920920\pi$
$547$		−	11.5017i		−	0.491778i	0.969298	−	0.245889i	$-0.0790798\pi$
$548$	29.8382	+	13.8542i	1.27462	+	0.591821i
$549$		0			0
$550$	−2.48981	−	0.549832i	−0.106166	−	0.0234449i
$551$	38.9604			1.65977
$552$		0			0
$553$	−14.8222	−	7.96304i	−0.630305	−	0.338623i
$554$	−2.83453	+	12.8356i	−0.120428	+	0.545332i
$555$		0			0
$556$	−4.15434	−	1.92890i	−0.176183	−	0.0818037i
$557$	16.0186			0.678730			0.339365	−	0.940655i	$-0.389788\pi$
$557$	16.0186			0.678730			0.339365	+	0.940655i	$0.389788\pi$
$558$		0			0
$559$	−38.1171			−1.61218
$560$	−1.21964	−	5.76671i	−0.0515390	−	0.243688i
$561$		0			0
$562$	6.21720	−	28.1533i	0.262257	−	1.18758i
$563$	28.6656			1.20811			0.604055	−	0.796942i	$-0.293551\pi$
$563$	28.6656			1.20811			0.604055	+	0.796942i	$0.293551\pi$
$564$		0			0
$565$			8.32373i			0.350182i
$566$	−7.94499	+	35.9773i	−0.333953	+	1.51224i
$567$		0			0
$568$	6.97290	+	5.32326i	0.292576	+	0.223359i
$569$	18.8079			0.788467			0.394233	−	0.919010i	$-0.371010\pi$
$569$	18.8079			0.788467			0.394233	+	0.919010i	$0.371010\pi$
$570$		0			0
$571$			36.0660i			1.50932i	0.656118	+	0.754658i	$0.272197\pi$
$571$			36.0660i			1.50932i	−0.656118	+	0.754658i	$0.727803\pi$
$572$	3.40380	+	1.58042i	0.142320	+	0.0660807i
$573$		0			0
$574$	−18.2345	+	21.2001i	−0.761093	+	0.884874i
$575$			11.3596i			0.473727i
$576$		0			0
$577$			43.5494i			1.81299i	0.422221	+	0.906493i	$0.361251\pi$
$577$			43.5494i			1.81299i	−0.422221	+	0.906493i	$0.638749\pi$
$578$	4.22434	−	19.1291i	0.175709	−	0.795665i
$579$		0			0
$580$	−3.15388	+	6.79262i	−0.130958	+	0.282048i
$581$	−16.2099	+	30.1728i	−0.672501	+	1.25178i
$582$		0			0
$583$			1.31965i			0.0546545i
$584$	11.0113	+	8.40627i	0.455652	+	0.347854i
$585$		0			0
$586$	2.09864	+	0.463450i	0.0866940	+	0.0191449i
$587$	−11.4732			−0.473550			−0.236775	−	0.971565i	$-0.576090\pi$
$587$	−11.4732			−0.473550			−0.236775	+	0.971565i	$0.576090\pi$
$588$		0			0
$589$	46.4036			1.91203
$590$	−1.13262	−	0.250119i	−0.0466290	−	0.0102972i
$591$		0			0
$592$	−10.7440	−	12.7191i	−0.441575	−	0.522753i
$593$			10.7031i			0.439526i	0.975553	+	0.219763i	$0.0705283\pi$
$593$			10.7031i			0.439526i	−0.975553	+	0.219763i	$0.929472\pi$
$594$		0			0
$595$	−3.87362	+	7.21025i	−0.158803	+	0.295592i
$596$	−39.9754	−	18.5610i	−1.63746	−	0.760287i
$597$		0			0
$598$	3.60528	−	16.3258i	0.147431	−	0.667611i
$599$			1.80523i			0.0737596i	0.999320	+	0.0368798i	$0.0117419\pi$
$599$			1.80523i			0.0737596i	−0.999320	+	0.0368798i	$0.988258\pi$
$600$		0			0
$601$			17.0452i			0.695290i	0.937626	+	0.347645i	$0.113019\pi$
$601$			17.0452i			0.695290i	−0.937626	+	0.347645i	$0.886981\pi$
$602$	19.0546	−	22.1536i	0.776607	−	0.902911i
$603$		0			0
$604$	6.04991	−	13.0299i	0.246167	−	0.530179i
$605$			6.04421i			0.245732i
$606$		0			0
$607$	−12.5988			−0.511368			−0.255684	−	0.966760i	$-0.582301\pi$
$607$	−12.5988			−0.511368			−0.255684	+	0.966760i	$0.582301\pi$
$608$	29.0146	−	15.2558i	1.17670	−	0.618703i
$609$		0			0
$610$	−0.520612	+	2.35749i	−0.0210790	+	0.0954519i
$611$		−	55.7310i		−	2.25463i
$612$		0			0
$613$	2.00000			0.0807792			0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000			0.0807792			0.0403896	+	0.999184i	$0.487140\pi$
$614$	−8.00700	+	36.2581i	−0.323136	+	1.46326i
$615$		0			0
$616$	−2.62009	+	1.18824i	−0.105566	+	0.0478754i
$617$	−37.5684			−1.51245			−0.756223	−	0.654314i	$-0.772958\pi$
$617$	−37.5684			−1.51245			−0.756223	+	0.654314i	$0.772958\pi$
$618$		0			0
$619$	−26.6640			−1.07172			−0.535859	−	0.844308i	$-0.680012\pi$
$619$	−26.6640			−1.07172			−0.535859	+	0.844308i	$0.680012\pi$
$620$	−3.75641	+	8.09031i	−0.150861	+	0.324915i
$621$		0			0
$622$	6.56941	−	29.7483i	0.263409	−	1.19280i
$623$	−16.4878	−	8.85786i	−0.660570	−	0.354883i
$624$		0			0
$625$	20.4432			0.817728
$626$	33.7241	+	7.44741i	1.34789	+	0.297658i
$627$		0			0
$628$	9.84643	−	21.2066i	0.392915	−	0.846235i
$629$			23.1200i			0.921853i
$630$		0			0
$631$			42.1775i			1.67906i	0.543315	+	0.839529i	$0.317169\pi$
$631$			42.1775i			1.67906i	−0.543315	+	0.839529i	$0.682831\pi$
$632$	14.2974	+	10.9149i	0.568721	+	0.434173i
$633$		0			0
$634$	−0.656092	+	2.97098i	−0.0260567	+	0.117993i
$635$	5.87701			0.233222
$636$		0			0
$637$	28.4878	−	18.8609i	1.12873	−	0.747296i
$638$	3.56935	+	0.788232i	0.141312	+	0.0312064i
$639$		0			0
$640$	0.311036	+	6.29357i	0.0122948	+	0.248775i
$641$	6.85997			0.270953			0.135476	−	0.990781i	$-0.456744\pi$
$641$	6.85997			0.270953			0.135476	+	0.990781i	$0.456744\pi$
$642$		0			0
$643$	−28.7496			−1.13377			−0.566886	−	0.823796i	$-0.691852\pi$
$643$	−28.7496			−1.13377			−0.566886	+	0.823796i	$0.691852\pi$
$644$	7.68624	+	10.2566i	0.302880	+	0.404166i
$645$		0			0
$646$	−44.4492	−	9.81587i	−1.74883	−	0.386200i
$647$	−13.1784			−0.518096			−0.259048	−	0.965864i	$-0.583409\pi$
$647$	−13.1784			−0.518096			−0.259048	+	0.965864i	$0.583409\pi$
$648$		0			0
$649$			0.566137i			0.0222228i
$650$	−31.6097	−	6.98048i	−1.23984	−	0.273797i
$651$		0			0
$652$	6.55471	−	14.1171i	0.256702	−	0.552869i
$653$	8.10859			0.317314			0.158657	−	0.987334i	$-0.449284\pi$
$653$	8.10859			0.317314			0.158657	+	0.987334i	$0.449284\pi$
$654$		0			0
$655$		−	7.43516i		−	0.290516i
$656$	22.8368	−	19.2905i	0.891628	−	0.753169i
$657$		0			0
$658$	32.3907	+	27.8597i	1.26272	+	1.08608i
$659$		−	9.74226i		−	0.379505i	−0.981832	−	0.189752i	$-0.939231\pi$
$659$		−	9.74226i		−	0.379505i	0.981832	−	0.189752i	$-0.0607685\pi$
$660$		0			0
$661$			20.9611i			0.815291i	0.913140	+	0.407646i	$0.133650\pi$
$661$			20.9611i			0.815291i	−0.913140	+	0.407646i	$0.866350\pi$
$662$	19.0441	+	4.20557i	0.740169	+	0.163454i
$663$		0			0
$664$	22.2189	−	29.1045i	0.862262	−	1.12947i
$665$	7.52234	+	4.04128i	0.291704	+	0.156714i
$666$		0			0
$667$		−	16.2849i		−	0.630555i
$668$	−13.2328	−	6.14412i	−0.511992	−	0.237723i
$669$		0			0
$670$	0.325939	−	1.47595i	0.0125921	−	0.0570209i
$671$	1.17839			0.0454912
$672$		0			0
$673$	−27.0540			−1.04286			−0.521428	−	0.853295i	$-0.674600\pi$
$673$	−27.0540			−1.04286			−0.521428	+	0.853295i	$0.674600\pi$
$674$	−7.47044	+	33.8284i	−0.287751	+	1.30302i
$675$		0			0
$676$	19.6315	+	9.11510i	0.755058	+	0.350581i
$677$			4.34359i			0.166938i	0.996510	+	0.0834688i	$0.0265999\pi$
$677$			4.34359i			0.166938i	−0.996510	+	0.0834688i	$0.973400\pi$
$678$		0			0
$679$	−21.6467	−	11.6294i	−0.830725	−	0.446296i
$680$	5.30956	−	6.95497i	0.203613	−	0.266711i
$681$		0			0
$682$	4.25126	+	0.938820i	0.162789	+	0.0359493i
$683$		−	9.96436i		−	0.381276i	−0.981660	−	0.190638i	$-0.938944\pi$
$683$		−	9.96436i		−	0.381276i	0.981660	−	0.190638i	$-0.0610556\pi$
$684$		0			0
$685$		−	9.16129i		−	0.350035i
$686$	−3.27904	+	25.9855i	−0.125194	+	0.992132i
$687$		0			0
$688$	−23.8639	+	20.1581i	−0.909803	+	0.768522i
$689$			16.7539i			0.638272i
$690$		0			0
$691$	−16.3950			−0.623695			−0.311847	−	0.950132i	$-0.600948\pi$
$691$	−16.3950			−0.623695			−0.311847	+	0.950132i	$0.600948\pi$
$692$	19.3529	−	41.6810i	0.735687	−	1.58447i
$693$		0			0
$694$	−30.3289	−	6.69763i	−1.15127	−	0.254239i
$695$			1.27552i			0.0483831i
$696$		0			0
$697$	−41.5112			−1.57235
$698$	10.9257	+	2.41276i	0.413544	+	0.0913243i
$699$		0			0
$700$	19.8586	−	14.8820i	0.750585	−	0.562486i
$701$	43.5073			1.64325			0.821624	−	0.570031i	$-0.193069\pi$
$701$	43.5073			1.64325			0.821624	+	0.570031i	$0.193069\pi$
$702$		0			0
$703$	24.1207			0.909729
$704$	2.96682	−	0.810643i	0.111816	−	0.0305523i
$705$		0			0
$706$	−0.986867	−	0.217933i	−0.0371412	−	0.00820202i
$707$	−16.1203	−	8.66043i	−0.606267	−	0.325709i
$708$		0			0
$709$	−2.98401			−0.112067			−0.0560335	−	0.998429i	$-0.517845\pi$
$709$	−2.98401			−0.112067			−0.0560335	+	0.998429i	$0.517845\pi$
$710$	0.526799	−	2.38550i	0.0197704	−	0.0895263i
$711$		0			0
$712$	15.9040	+	12.1415i	0.596029	+	0.455021i
$713$		−	19.3961i		−	0.726389i
$714$		0			0
$715$		−	1.04508i		−	0.0390837i
$716$	10.8197	−	23.3028i	0.404352	−	0.870868i
$717$		0			0
$718$	44.2753	+	9.77747i	1.65234	+	0.364892i
$719$	14.4732			0.539759			0.269880	−	0.962894i	$-0.413016\pi$
$719$	14.4732			0.539759			0.269880	+	0.962894i	$0.413016\pi$
$720$		0			0
$721$	0.364996	−	0.679394i	0.0135931	−	0.0253019i
$722$	−4.44653	+	20.1352i	−0.165483	+	0.749356i
$723$		0			0
$724$	14.3421	−	30.8891i	0.533021	−	1.14798i
$725$	−31.5306			−1.17102
$726$		0			0
$727$	0.0773779			0.00286979			0.00143489	−	0.999999i	$-0.499543\pi$
$727$	0.0773779			0.00286979			0.00143489	+	0.999999i	$0.499543\pi$
$728$	−33.2637	+	15.0854i	−1.23283	+	0.559104i
$729$		0			0
$730$	0.831899	−	3.76709i	0.0307899	−	0.139426i
$731$	43.3782			1.60440
$732$		0			0
$733$		−	1.13625i		−	0.0419684i	−0.999780	−	0.0209842i	$-0.993320\pi$
$733$		−	1.13625i		−	0.0419684i	0.999780	−	0.0209842i	$-0.00667997\pi$
$734$	−10.2564	+	46.4441i	−0.378571	+	1.71428i
$735$		0			0
$736$	−6.37671	−	12.1277i	−0.235049	−	0.447033i
$737$	−0.737752			−0.0271754
$738$		0			0
$739$			0.496254i			0.0182550i	0.999958	+	0.00912749i	$0.00290541\pi$
$739$			0.496254i			0.0182550i	−0.999958	+	0.00912749i	$0.997095\pi$
$740$	−1.95259	+	4.20536i	−0.0717786	+	0.154592i
$741$		0			0
$742$	−9.73731	−	8.37520i	−0.357468	−	0.307463i
$743$		−	8.82810i		−	0.323872i	−0.986801	−	0.161936i	$-0.948226\pi$
$743$		−	8.82810i		−	0.323872i	0.986801	−	0.161936i	$-0.0517738\pi$
$744$		0			0
$745$			12.2737i			0.449675i
$746$	0.598081	−	2.70829i	0.0218973	−	0.0991576i
$747$		0			0
$748$	−3.87362	−	1.79856i	−0.141633	−	0.0657618i
$749$	30.5827	+	16.4302i	1.11747	+	0.600346i
$750$		0			0
$751$		−	5.07577i		−	0.185217i	−0.995703	−	0.0926087i	$-0.970479\pi$
$751$		−	5.07577i		−	0.185217i	0.995703	−	0.0926087i	$-0.0295206\pi$
$752$	−29.4732	−	34.8914i	−1.07478	−	1.27236i
$753$		0			0
$754$	45.3152	+	10.0071i	1.65028	+	0.364438i
$755$	−4.00060			−0.145597
$756$		0			0
$757$	−13.1076			−0.476404			−0.238202	−	0.971216i	$-0.576558\pi$
$757$	−13.1076			−0.476404			−0.238202	+	0.971216i	$0.576558\pi$
$758$	−8.17227	−	1.80471i	−0.296830	−	0.0655500i
$759$		0			0
$760$	−7.25600	−	5.53938i	−0.263203	−	0.200935i
$761$		−	18.6880i		−	0.677438i	−0.940888	−	0.338719i	$-0.890006\pi$
$761$		−	18.6880i		−	0.677438i	0.940888	−	0.338719i	$-0.109994\pi$
$762$		0			0
$763$	5.21190	−	9.70130i	0.188683	−	0.351211i
$764$	15.7960	−	34.0203i	0.571478	−	1.23081i
$765$		0			0
$766$	2.58397	−	11.7010i	0.0933627	−	0.422774i
$767$			7.18748i			0.259525i
$768$		0			0
$769$		−	1.23242i		−	0.0444422i	−0.999753	−	0.0222211i	$-0.992926\pi$
$769$		−	1.23242i		−	0.0444422i	0.999753	−	0.0222211i	$-0.00707378\pi$
$770$	0.607396	+	0.522430i	0.0218890	+	0.0188271i
$771$		0			0
$772$	28.3630	+	13.1692i	1.02081	+	0.473971i
$773$			19.8996i			0.715740i	0.933771	+	0.357870i	$0.116497\pi$
$773$			19.8996i			0.715740i	−0.933771	+	0.357870i	$0.883503\pi$
$774$		0			0
$775$	−37.5544			−1.34899
$776$	20.8803	+	15.9404i	0.749559	+	0.572229i
$777$		0			0
$778$	8.91931	−	40.3893i	0.319773	−	1.44803i
$779$			43.3080i			1.55167i
$780$		0			0
$781$	−1.19239			−0.0426671
$782$	−4.10290	+	18.5792i	−0.146719	+	0.664390i
$783$		0			0
$784$	7.86078	−	26.8739i	0.280742	−	0.959783i
$785$	−6.51111			−0.232391
$786$		0			0
$787$	−4.49443			−0.160209			−0.0801047	−	0.996786i	$-0.525525\pi$
$787$	−4.49443			−0.160209			−0.0801047	+	0.996786i	$0.525525\pi$
$788$	1.54364	+	0.716725i	0.0549897	+	0.0255323i
$789$		0			0
$790$	1.08016	−	4.89130i	0.0384304	−	0.174025i
$791$	−18.7132	+	34.8323i	−0.665366	+	1.23849i
$792$		0			0
$793$	14.9604			0.531260
$794$	49.8444	+	11.0073i	1.76891	+	0.390635i
$795$		0			0
$796$	2.95642	+	1.37270i	0.104788	+	0.0486540i
$797$			20.5463i			0.727786i	0.931441	+	0.363893i	$0.118553\pi$
$797$			20.5463i			0.727786i	−0.931441	+	0.363893i	$0.881447\pi$
$798$		0			0
$799$			63.4233i			2.24375i
$800$	−23.4815	+	12.3465i	−0.830195	+	0.436514i
$801$		0			0
$802$	5.07822	−	22.9957i	0.179318	−	0.812006i
$803$	−1.88298			−0.0664488
$804$		0			0
$805$	1.68920	−	3.14424i	0.0595365	−	0.110820i
$806$	53.9725	+	11.9189i	1.90110	+	0.419826i
$807$		0			0
$808$	15.5496	+	11.8708i	0.547031	+	0.417615i
$809$	3.85760			0.135626			0.0678130	−	0.997698i	$-0.478398\pi$
$809$	3.85760			0.135626			0.0678130	+	0.997698i	$0.478398\pi$
$810$		0			0
$811$	−3.63921			−0.127790			−0.0638949	−	0.997957i	$-0.520352\pi$
$811$	−3.63921			−0.127790			−0.0638949	+	0.997957i	$0.520352\pi$
$812$	−28.4690	+	21.3346i	−0.999067	+	0.748697i
$813$		0			0
$814$	2.20981	+	0.488000i	0.0774539	+	0.0171044i
$815$	−4.33441			−0.151828
$816$		0			0
$817$		−	45.2558i		−	1.58330i
$818$	−43.1279	−	9.52408i	−1.50793	−	0.333002i
$819$		0			0
$820$	−7.55060	−	3.50582i	−0.263678	−	0.122428i
$821$	5.22467			0.182342			0.0911711	−	0.995835i	$-0.470939\pi$
$821$	5.22467			0.182342			0.0911711	+	0.995835i	$0.470939\pi$
$822$		0			0
$823$		−	10.6510i		−	0.371271i	−0.982619	−	0.185636i	$-0.940566\pi$
$823$		−	10.6510i		−	0.371271i	0.982619	−	0.185636i	$-0.0594344\pi$
$824$	−0.500299	+	0.655339i	−0.0174288	+	0.0228298i
$825$		0			0
$826$	−4.17735	−	3.59299i	−0.145348	−	0.125016i
$827$			20.9224i			0.727543i	0.931488	+	0.363771i	$0.118511\pi$
$827$			20.9224i			0.727543i	−0.931488	+	0.363771i	$0.881489\pi$
$828$		0			0
$829$			8.35791i			0.290282i	0.989411	+	0.145141i	$0.0463636\pi$
$829$			8.35791i			0.290282i	−0.989411	+	0.145141i	$0.953636\pi$
$830$	−9.95694	−	2.19882i	−0.345610	−	0.0763223i
$831$		0			0
$832$	37.6657	−	10.2916i	1.30582	−	0.356799i
$833$	−32.4199	+	21.4642i	−1.12328	+	0.743690i
$834$		0			0
$835$			4.06290i			0.140602i
$836$	−1.87641	+	4.04128i	−0.0648969	+	0.139771i
$837$		0			0
$838$	−1.70660	+	7.72802i	−0.0589537	+	0.266960i
$839$	−21.2808			−0.734695			−0.367348	−	0.930084i	$-0.619734\pi$
$839$	−21.2808			−0.734695			−0.367348	+	0.930084i	$0.619734\pi$
$840$		0			0
$841$	16.2018			0.558683
$842$	8.88880	−	40.2512i	0.306328	−	1.38715i
$843$		0			0
$844$	0.560712	−	1.20763i	0.0193005	−	0.0415682i
$845$		−	6.02750i		−	0.207352i
$846$		0			0
$847$	−13.5884	+	25.2932i	−0.466905	+	0.869085i
$848$	8.86025	+	10.4891i	0.304262	+	0.360196i
$849$		0			0
$850$	35.9727	+	7.94397i	1.23385	+	0.272476i
$851$		−	10.0821i		−	0.345610i
$852$		0			0
$853$		−	20.6936i		−	0.708536i	−0.935144	−	0.354268i	$-0.884730\pi$
$853$		−	20.6936i		−	0.708536i	0.935144	−	0.354268i	$-0.115270\pi$
$854$	−7.47865	+	8.69495i	−0.255914	+	0.297535i
$855$		0			0
$856$	−29.4999	−	22.5208i	−1.00829	−	0.769746i
$857$		−	36.9465i		−	1.26207i	−0.775755	−	0.631034i	$-0.782631\pi$
$857$		−	36.9465i		−	1.26207i	0.775755	−	0.631034i	$-0.217369\pi$
$858$		0			0
$859$	−7.00948			−0.239160			−0.119580	−	0.992825i	$-0.538155\pi$
$859$	−7.00948			−0.239160			−0.119580	+	0.992825i	$0.538155\pi$
$860$	7.89019	+	3.66349i	0.269053	+	0.124924i
$861$		0			0
$862$	1.06180	+	0.234480i	0.0361649	+	0.00798642i
$863$		−	41.1956i		−	1.40231i	−0.713007	−	0.701157i	$-0.752667\pi$
$863$		−	41.1956i		−	1.40231i	0.713007	−	0.701157i	$-0.247333\pi$
$864$		0			0
$865$	−12.7974			−0.435125
$866$	29.4913	+	6.51266i	1.00216	+	0.221309i
$867$		0			0
$868$	−33.9079	+	25.4105i	−1.15091	+	0.862487i
$869$	−2.44491			−0.0829379
$870$		0			0
$871$	−9.36624			−0.317363
$872$	−7.14395	+	9.35782i	−0.241925	+	0.316896i
$873$		0			0
$874$	19.3833	+	4.28049i	0.655651	+	0.144790i
$875$	−12.5783	−	6.75753i	−0.425224	−	0.228446i
$876$		0			0
$877$	−34.8120			−1.17552			−0.587759	−	0.809036i	$-0.699990\pi$
$877$	−34.8120			−1.17552			−0.587759	+	0.809036i	$0.699990\pi$
$878$	4.73600	−	21.4460i	0.159832	−	0.723769i
$879$		0			0
$880$	−0.552687	−	0.654290i	−0.0186311	−	0.0220561i
$881$			29.5032i			0.993987i	0.867754	+	0.496994i	$0.165563\pi$
$881$			29.5032i			0.993987i	−0.867754	+	0.496994i	$0.834437\pi$
$882$		0			0
$883$		−	16.2218i		−	0.545906i	−0.962027	−	0.272953i	$-0.912000\pi$
$883$		−	16.2218i		−	0.545906i	0.962027	−	0.272953i	$-0.0880003\pi$
$884$	−49.1781	−	22.8339i	−1.65404	−	0.767986i
$885$		0			0
$886$	−25.4416	−	5.61836i	−0.854728	−	0.188752i
$887$	30.3356			1.01857			0.509285	−	0.860598i	$-0.329910\pi$
$887$	30.3356			1.01857			0.509285	+	0.860598i	$0.329910\pi$
$888$		0			0
$889$	24.5935	+	13.2125i	0.824840	+	0.443135i
$890$	1.20154	−	5.44094i	0.0402757	−	0.182381i
$891$		0			0
$892$	−14.0167	−	6.50809i	−0.469313	−	0.217907i
$893$	66.1685			2.21424
$894$		0			0
$895$	−7.15472			−0.239156
$896$	−12.8475	+	27.0360i	−0.429203	+	0.903208i
$897$		0			0
$898$	−2.66600	+	12.0724i	−0.0889654	+	0.402862i
$899$	53.8374			1.79558
$900$		0			0
$901$		−	19.0663i		−	0.635192i
$902$	−0.876190	+	3.96765i	−0.0291739	+	0.132108i
$903$		0			0
$904$	25.6502	−	33.5991i	0.853113	−	1.11749i
$905$	−9.48395			−0.315257
$906$		0			0
$907$			39.2175i			1.30219i	0.758994	+	0.651097i	$0.225691\pi$
$907$			39.2175i			1.30219i	−0.758994	+	0.651097i	$0.774309\pi$
$908$	12.5003	+	5.80401i	0.414837	+	0.192613i
$909$		0			0
$910$	7.71130	+	6.63260i	0.255627	+	0.219868i
$911$		−	5.44469i		−	0.180391i	−0.995924	−	0.0901953i	$-0.971251\pi$
$911$		−	5.44469i		−	0.180391i	0.995924	−	0.0901953i	$-0.0287491\pi$
$912$		0			0
$913$			4.97697i			0.164714i
$914$	8.25034	−	37.3600i	0.272897	−	1.23576i
$915$		0			0
$916$	−13.9573	+	30.0604i	−0.461163	+	0.993222i
$917$	16.7155	−	31.1139i	0.551996	−	1.02747i
$918$		0			0
$919$		−	12.9558i		−	0.427373i	−0.976902	−	0.213686i	$-0.931453\pi$
$919$		−	12.9558i		−	0.427373i	0.976902	−	0.213686i	$-0.0685471\pi$
$920$	−2.31539	+	3.03291i	−0.0763360	+	0.0999921i
$921$		0			0
$922$	−21.8275	−	4.82023i	−0.718849	−	0.158746i
$923$	−15.1382			−0.498280
$924$		0			0
$925$	−19.5208			−0.641841
$926$	42.0509	+	9.28623i	1.38188	+	0.305164i
$927$		0			0
$928$	33.6627	−	17.6997i	1.10503	−	0.581022i
$929$			7.36141i			0.241520i	0.992682	+	0.120760i	$0.0385331\pi$
$929$			7.36141i			0.241520i	−0.992682	+	0.120760i	$0.961467\pi$
$930$		0			0
$931$	22.3932	+	33.8231i	0.733909	+	1.10851i
$932$	38.6893	+	17.9638i	1.26731	+	0.588425i
$933$		0			0
$934$	11.4155	−	51.6928i	0.373526	−	1.69144i
$935$			1.18932i			0.0388951i
$936$		0			0
$937$			17.7246i			0.579039i	0.957172	+	0.289519i	$0.0934955\pi$
$937$			17.7246i			0.579039i	−0.957172	+	0.289519i	$0.906505\pi$
$938$	4.68215	−	5.44364i	0.152878	−	0.177741i
$939$		0			0
$940$	−5.35639	+	11.5362i	−0.174706	+	0.376271i
$941$			23.0678i			0.751990i	0.926622	+	0.375995i	$0.122699\pi$
$941$			23.0678i			0.751990i	−0.926622	+	0.375995i	$0.877301\pi$
$942$		0			0
$943$	18.1021			0.589487
$944$	3.80108	+	4.49986i	0.123715	+	0.146458i
$945$		0			0
$946$	0.915597	−	4.14610i	0.0297686	−	0.134801i
$947$		−	15.1257i		−	0.491519i	−0.969331	−	0.245760i	$-0.920963\pi$
$947$		−	15.1257i		−	0.491519i	0.969331	−	0.245760i	$-0.0790374\pi$
$948$		0			0
$949$	−23.9056			−0.776009
$950$	8.28781	−	37.5297i	0.268892	−	1.21762i
$951$		0			0
$952$	37.8549	−	17.1676i	1.22689	−	0.556406i
$953$	−49.2659			−1.59588			−0.797939	−	0.602738i	$-0.794076\pi$
$953$	−49.2659			−1.59588			−0.797939	+	0.602738i	$0.794076\pi$
$954$		0			0
$955$	−10.4453			−0.338003
$956$	−12.0233	+	25.8949i	−0.388861	+	0.837502i
$957$		0			0
$958$	0.177362	−	0.803147i	0.00573029	−	0.0259485i
$959$	20.5962	−	38.3373i	0.665086	−	1.23797i
$960$		0			0
$961$	33.1228			1.06848
$962$	28.0550	+	6.19548i	0.904530	+	0.199750i
$963$		0			0
$964$	15.9668	−	34.3881i	0.514254	−	1.10757i
$965$		−	8.70836i		−	0.280332i
$966$		0			0
$967$		−	33.4687i		−	1.07628i	−0.842856	−	0.538140i	$-0.819127\pi$
$967$		−	33.4687i		−	1.07628i	0.842856	−	0.538140i	$-0.180873\pi$
$968$	18.6257	−	24.3977i	0.598652	−	0.784171i
$969$		0			0
$970$	1.57749	−	7.14337i	0.0506503	−	0.229360i
$971$	43.7424			1.40376			0.701881	−	0.712295i	$-0.252344\pi$
$971$	43.7424			1.40376			0.701881	+	0.712295i	$0.252344\pi$
$972$		0			0
$973$	−2.86759	+	5.33766i	−0.0919307	+	0.171117i
$974$	−25.1385	−	5.55143i	−0.805491	−	0.177879i
$975$		0			0
$976$	9.36624	−	7.91178i	0.299806	−	0.253250i
$977$	−11.9426			−0.382079			−0.191040	−	0.981582i	$-0.561186\pi$
$977$	−11.9426			−0.382079			−0.191040	+	0.981582i	$0.561186\pi$
$978$		0			0
$979$	−2.71965			−0.0869203
$980$	−7.70970	+	1.16618i	−0.246277	+	0.0372521i
$981$		0			0
$982$	36.7715	+	8.12038i	1.17343	+	0.259132i
$983$	−58.2552			−1.85805			−0.929026	−	0.370013i	$-0.879353\pi$
$983$	−58.2552			−1.85805			−0.929026	+	0.370013i	$0.879353\pi$
$984$		0			0
$985$		−	0.473946i		−	0.0151012i
$986$	−51.5699	−	11.3884i	−1.64232	−	0.362679i
$987$		0			0
$988$	−23.8222	+	51.3067i	−0.757885	+	1.63228i
$989$	−18.9163			−0.601503
$990$		0			0
$991$		−	44.8168i		−	1.42365i	−0.702356	−	0.711826i	$-0.747869\pi$
$991$		−	44.8168i		−	1.42365i	0.702356	−	0.711826i	$-0.252131\pi$
$992$	40.0938	−	21.0812i	1.27298	−	0.669328i
$993$		0			0
$994$	7.56753	−	8.79828i	0.240027	−	0.279065i
$995$		−	0.907718i		−	0.0287766i
$996$		0			0
$997$			13.0151i			0.412193i	0.978532	+	0.206096i	$0.0660761\pi$
$997$			13.0151i			0.412193i	−0.978532	+	0.206096i	$0.933924\pi$
$998$	−56.0245	−	12.3721i	−1.77342	−	0.391631i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.b.f.55.8	yes	16
3.2	odd	2		756.2.b.e.55.9	yes	16
4.3	odd	2		756.2.b.e.55.7	✓	16
7.6	odd	2		756.2.b.e.55.8	yes	16
12.11	even	2	inner	756.2.b.f.55.10	yes	16
21.20	even	2	inner	756.2.b.f.55.9	yes	16
28.27	even	2	inner	756.2.b.f.55.7	yes	16
84.83	odd	2		756.2.b.e.55.10	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.b.e.55.7	✓	16	4.3	odd	2
756.2.b.e.55.8	yes	16	7.6	odd	2
756.2.b.e.55.9	yes	16	3.2	odd	2
756.2.b.e.55.10	yes	16	84.83	odd	2
756.2.b.f.55.7	yes	16	28.27	even	2	inner
756.2.b.f.55.8	yes	16	1.1	even	1	trivial
756.2.b.f.55.9	yes	16	21.20	even	2	inner
756.2.b.f.55.10	yes	16	12.11	even	2	inner

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.304958 + 1.38094i) q^{2} +(-1.81400 - 0.842259i) q^{4} +0.556957i q^{5} +(-1.25214 + 2.33070i) q^{7} +(1.71630 - 2.24818i) q^{8} +O(q^{10})\)	\(q+(-0.304958 + 1.38094i) q^{2} +(-1.81400 - 0.842259i) q^{4} +0.556957i q^{5} +(-1.25214 + 2.33070i) q^{7} +(1.71630 - 2.24818i) q^{8} +(-0.769125 - 0.169848i) q^{10} +0.384447i q^{11} +4.88080i q^{13} +(-2.83671 - 2.43989i) q^{14} +(2.58120 + 3.05572i) q^{16} -5.55448i q^{17} -5.79490 q^{19} +(0.469102 - 1.01032i) q^{20} +(-0.530898 - 0.117240i) q^{22} +2.42219i q^{23} +4.68980 q^{25} +(-6.74010 - 1.48844i) q^{26} +(4.23443 - 3.17327i) q^{28} -6.72323 q^{29} -8.00767 q^{31} +(-5.00692 + 2.63262i) q^{32} +(7.67041 + 1.69388i) q^{34} +(-1.29810 - 0.697386i) q^{35} -4.16240 q^{37} +(1.76720 - 8.00241i) q^{38} +(1.25214 + 0.955907i) q^{40} -7.47347i q^{41} +7.80960i q^{43} +(0.323803 - 0.697386i) q^{44} +(-3.34490 - 0.738665i) q^{46} -11.4184 q^{47} +(-3.86430 - 5.83671i) q^{49} +(-1.43019 + 6.47634i) q^{50} +(4.11090 - 8.85378i) q^{52} +3.43261 q^{53} -0.214120 q^{55} +(3.09077 + 6.81521i) q^{56} +(2.05030 - 9.28439i) q^{58} +1.47260 q^{59} -3.06515i q^{61} +(2.44200 - 11.0581i) q^{62} +(-2.10860 - 7.71711i) q^{64} -2.71839 q^{65} +1.91900i q^{67} +(-4.67831 + 10.0758i) q^{68} +(1.35892 - 1.57992i) q^{70} +3.10158i q^{71} +4.89789i q^{73} +(1.26936 - 5.74804i) q^{74} +(10.5119 + 4.88080i) q^{76} +(-0.896029 - 0.481380i) q^{77} +6.35956i q^{79} +(-1.70190 + 1.43762i) q^{80} +(10.3204 + 2.27910i) q^{82} +12.9458 q^{83} +3.09360 q^{85} +(-10.7846 - 2.38160i) q^{86} +(0.864304 + 0.659827i) q^{88} +7.07419i q^{89} +(-11.3757 - 6.11143i) q^{91} +(2.04011 - 4.39385i) q^{92} +(3.48213 - 15.7682i) q^{94} -3.22751i q^{95} +9.28765i q^{97} +(9.23860 - 3.55643i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + q^{14} + 4 q^{16} + 26 q^{20} + 10 q^{22} - 20 q^{25} + 6 q^{26} - 11 q^{28} + 6 q^{35} + 8 q^{37} + 20 q^{38} - 6 q^{46} + 8 q^{47} - 14 q^{49} - 21 q^{56} + 14 q^{58} + 44 q^{59} - 48 q^{62} + 24 q^{64} + 2 q^{68} - 27 q^{70} - 54 q^{80} - 4 q^{83} + 8 q^{85} - 34 q^{88} + 47 q^{98}+O(q^{100}) \) 16 * q + q^14 + 4 * q^16 + 26 * q^20 + 10 * q^22 - 20 * q^25 + 6 * q^26 - 11 * q^28 + 6 * q^35 + 8 * q^37 + 20 * q^38 - 6 * q^46 + 8 * q^47 - 14 * q^49 - 21 * q^56 + 14 * q^58 + 44 * q^59 - 48 * q^62 + 24 * q^64 + 2 * q^68 - 27 * q^70 - 54 * q^80 - 4 * q^83 + 8 * q^85 - 34 * q^88 + 47 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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