LMFDB - Embedded newform 756.2.b.f.55.9

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			55.9
Root			$-0.304958 - 1.38094i$ of defining polynomial
Character	$\chi$	$=$	756.55
Dual form			756.2.b.f.55.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.304958 - 1.38094i) q^{2} +(-1.81400 - 0.842259i) q^{4} +0.556957i q^{5} +(1.25214 + 2.33070i) q^{7} +(-1.71630 + 2.24818i) q^{8} +O(q^{10})$	\(q+(0.304958 - 1.38094i) q^{2} +(-1.81400 - 0.842259i) q^{4} +0.556957i q^{5} +(1.25214 + 2.33070i) q^{7} +(-1.71630 + 2.24818i) q^{8} +(0.769125 + 0.169848i) q^{10} -0.384447i q^{11} -4.88080i q^{13} +(3.60041 - 1.01836i) q^{14} +(2.58120 + 3.05572i) q^{16} -5.55448i q^{17} +5.79490 q^{19} +(0.469102 - 1.01032i) q^{20} +(-0.530898 - 0.117240i) q^{22} -2.42219i q^{23} +4.68980 q^{25} +(-6.74010 - 1.48844i) q^{26} +(-0.308329 - 5.28251i) q^{28} +6.72323 q^{29} +8.00767 q^{31} +(5.00692 - 2.63262i) q^{32} +(-7.67041 - 1.69388i) q^{34} +(-1.29810 + 0.697386i) q^{35} -4.16240 q^{37} +(1.76720 - 8.00241i) q^{38} +(-1.25214 - 0.955907i) q^{40} -7.47347i q^{41} +7.80960i q^{43} +(-0.323803 + 0.697386i) q^{44} +(-3.34490 - 0.738665i) q^{46} -11.4184 q^{47} +(-3.86430 + 5.83671i) q^{49} +(1.43019 - 6.47634i) q^{50} +(-4.11090 + 8.85378i) q^{52} -3.43261 q^{53} +0.214120 q^{55} +(-7.38887 - 1.18516i) q^{56} +(2.05030 - 9.28439i) q^{58} +1.47260 q^{59} +3.06515i q^{61} +(2.44200 - 11.0581i) q^{62} +(-2.10860 - 7.71711i) q^{64} +2.71839 q^{65} +1.91900i q^{67} +(-4.67831 + 10.0758i) q^{68} +(0.567185 + 2.00527i) q^{70} -3.10158i q^{71} -4.89789i q^{73} +(-1.26936 + 5.74804i) q^{74} +(-10.5119 - 4.88080i) q^{76} +(0.896029 - 0.481380i) q^{77} +6.35956i q^{79} +(-1.70190 + 1.43762i) q^{80} +(-10.3204 - 2.27910i) q^{82} +12.9458 q^{83} +3.09360 q^{85} +(10.7846 + 2.38160i) q^{86} +(0.864304 + 0.659827i) q^{88} +7.07419i q^{89} +(11.3757 - 6.11143i) q^{91} +(-2.04011 + 4.39385i) q^{92} +(-3.48213 + 15.7682i) q^{94} +3.22751i q^{95} -9.28765i q^{97} +(6.88170 + 7.11633i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.981541\pi$
$11$		−	0.384447i		−	0.115915i	0.998319	−	0.0579575i	$-0.0184588\pi$
$12$		0			0
$13$		−	4.88080i		−	1.35369i	−0.736125	−	0.676845i	$-0.763347\pi$
$13$		−	4.88080i		−	1.35369i	0.736125	−	0.676845i	$-0.236653\pi$
$14$	3.60041	−	1.01836i	0.962249	−	0.272169i
$15$		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	$-0.268551\pi$
$19$	5.79490			1.32944			0.664720	+	0.747093i	$0.268551\pi$
$20$	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	$-0.918737\pi$
$23$		−	2.42219i		−	0.505061i	0.967589	−	0.252530i	$-0.0812628\pi$
$24$		0			0
$25$	4.68980			0.937960
$26$	−6.74010	−	1.48844i	−1.32184	−	0.291907i
$27$		0			0
$28$	−0.308329	−	5.28251i	−0.0582686	−	0.998301i
$29$	6.72323			1.24847			0.624236	−	0.781236i	$-0.285410\pi$
$29$	6.72323			1.24847			0.624236	+	0.781236i	$0.285410\pi$
$30$		0			0
$31$	8.00767			1.43822			0.719110	−	0.694896i	$-0.244550\pi$
$31$	8.00767			1.43822			0.719110	+	0.694896i	$0.244550\pi$
$32$	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	$-0.575755\pi$
$53$	−3.43261			−0.471505			−0.235753	+	0.971813i	$0.575755\pi$
$54$		0			0
$55$	0.214120			0.0288720
$56$	−7.38887	−	1.18516i	−0.987379	−	0.158374i
$57$		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	$0.0628688\pi$
$61$			3.06515i			0.392453i	−0.980559	+	0.196226i	$0.937131\pi$
$62$	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
$70$	0.567185	+	2.00527i	0.0677916	+	0.239676i
$71$		−	3.10158i		−	0.368090i	−0.982918	−	0.184045i	$-0.941081\pi$
$71$		−	3.10158i		−	0.368090i	0.982918	−	0.184045i	$-0.0589192\pi$
$72$		0			0
$73$		−	4.89789i		−	0.573254i	−0.958042	−	0.286627i	$-0.907466\pi$
$73$		−	4.89789i		−	0.573254i	0.958042	−	0.286627i	$-0.0925341\pi$
$74$	−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	$-0.843709\pi$
$97$		−	9.28765i		−	0.943018i	0.881861	−	0.471509i	$-0.156291\pi$
$98$	6.88170	+	7.11633i	0.695157	+	0.718858i
$99$		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	$-0.495429\pi$
$103$	0.291498			0.0287222			0.0143611	+	0.999897i	$0.495429\pi$
$104$	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	$0.218696\pi$
$107$			13.1217i			1.26852i	−0.773119	+	0.634261i	$0.781304\pi$
$108$		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
$112$	−3.88993	+	9.84218i	−0.367564	+	0.929998i
$113$	−14.9450			−1.40591			−0.702955	−	0.711235i	$-0.748136\pi$
$113$	−14.9450			−1.40591			−0.702955	+	0.711235i	$0.748136\pi$
$114$		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	$-0.251996\pi$
$137$	16.4488			1.40532			0.702659	+	0.711527i	$0.251996\pi$
$138$		0			0
$139$	−2.29015			−0.194248			−0.0971242	−	0.995272i	$-0.530964\pi$
$139$	−2.29015			−0.194248			−0.0971242	+	0.995272i	$0.530964\pi$
$140$	2.94213	−	0.171726i	0.248655	−	0.0145135i
$141$		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	$-0.858400\pi$
$149$	−22.0371			−1.80535			−0.902676	+	0.430321i	$0.858400\pi$
$150$		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
$154$	−0.391507	−	1.38416i	−0.0315485	−	0.111539i
$155$			4.45993i			0.358230i
$156$		0			0
$157$		−	11.6905i		−	0.933004i	−0.884520	−	0.466502i	$-0.845514\pi$
$157$		−	11.6905i		−	0.933004i	0.884520	−	0.466502i	$-0.154486\pi$
$158$	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	$-0.840607\pi$
$179$		−	12.8461i		−	0.960162i	0.877224	−	0.480081i	$-0.159393\pi$
$180$		0			0
$181$		−	17.0282i		−	1.26569i	−0.774277	−	0.632847i	$-0.781886\pi$
$181$		−	17.0282i		−	1.26569i	0.774277	−	0.632847i	$-0.218114\pi$
$182$	−4.97043	−	17.5729i	−0.368433	−	1.30259i
$183$		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	$-0.762627\pi$
$191$		−	18.7543i		−	1.35701i	0.734594	−	0.678507i	$-0.237373\pi$
$192$		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
$196$	11.9259	−	7.33305i	0.851848	−	0.523789i
$197$	0.850956			0.0606281			0.0303141	−	0.999540i	$-0.490349\pi$
$197$	0.850956			0.0606281			0.0303141	+	0.999540i	$0.490349\pi$
$198$		0			0
$199$	1.62978			0.115532			0.0577660	−	0.998330i	$-0.481602\pi$
$199$	1.62978			0.115532			0.0577660	+	0.998330i	$0.481602\pi$
$200$	−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	$-0.583300\pi$
$223$	−7.72694			−0.517434			−0.258717	+	0.965953i	$0.583300\pi$
$224$	12.4052	+	8.37322i	0.828858	+	0.559459i
$225$		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	$0.184432\pi$
$229$			16.5713i			1.09506i	−0.836785	+	0.547531i	$0.815568\pi$
$230$	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	$-0.253795\pi$
$233$	21.3282			1.39725			0.698627	+	0.715486i	$0.253795\pi$
$234$		0			0
$235$		−	6.35956i		−	0.414852i
$236$	−2.67130	−	1.24031i	−0.173887	−	0.0807375i
$237$		0			0
$238$	−5.65648	−	19.9984i	−0.366655	−	1.29630i
$239$			14.2750i			0.923376i	0.887042	+	0.461688i	$0.152756\pi$
$239$			14.2750i			0.923376i	−0.887042	+	0.461688i	$0.847244\pi$
$240$		0			0
$241$		−	18.9571i		−	1.22113i	−0.791965	−	0.610566i	$-0.790942\pi$
$241$		−	18.9571i		−	1.22113i	0.791965	−	0.610566i	$-0.209058\pi$
$242$	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	$0.312030\pi$
$263$			26.9417i			1.66130i	−0.556798	+	0.830648i	$0.687970\pi$
$264$		0			0
$265$		−	1.91181i		−	0.117442i
$266$	20.8640	−	5.90131i	1.27925	−	0.361833i
$267$		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	$-0.599684\pi$
$271$	−10.1431			−0.616148			−0.308074	+	0.951362i	$0.599684\pi$
$272$	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
$280$	0.660083	−	4.11528i	0.0394475	−	0.245935i
$281$	20.3871			1.21619			0.608095	−	0.793864i	$-0.291934\pi$
$281$	20.3871			1.21619			0.608095	+	0.793864i	$0.291934\pi$
$282$		0			0
$283$	−26.0527			−1.54867			−0.774337	−	0.632773i	$-0.781916\pi$
$283$	−26.0527			−1.54867			−0.774337	+	0.632773i	$0.781916\pi$
$284$	−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	$-0.769589\pi$
$307$	−26.2561			−1.49851			−0.749257	+	0.662280i	$0.769589\pi$
$308$	−2.03084	+	0.118536i	−0.115718	+	0.00675421i
$309$		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	$0.242469\pi$
$313$			24.4211i			1.38036i	−0.723637	+	0.690181i	$0.757531\pi$
$314$	−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	$-0.519243\pi$
$317$	−2.15142			−0.120836			−0.0604178	+	0.998173i	$0.519243\pi$
$318$		0			0
$319$		−	2.58472i		−	0.144717i
$320$	4.29810	−	1.17440i	0.240271	−	0.0656509i
$321$		0			0
$322$	−2.46667	−	8.72086i	−0.137462	−	0.485995i
$323$		−	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	$-0.799323\pi$
$347$		−	21.9625i		−	1.17901i	0.807766	−	0.589504i	$-0.200677\pi$
$348$		0			0
$349$			7.91178i			0.423508i	0.977323	+	0.211754i	$0.0679175\pi$
$349$			7.91178i			0.423508i	−0.977323	+	0.211754i	$0.932082\pi$
$350$	16.8852	−	4.77592i	0.902551	−	0.255284i
$351$		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	$0.321041\pi$
$359$			32.0617i			1.69215i	−0.533063	+	0.846075i	$0.678959\pi$
$360$		0			0
$361$	14.5808			0.767411
$362$	−23.5149	−	5.19287i	−1.23592	−	0.272931i
$363$		0			0
$364$	−25.7829	+	1.50489i	−1.35139	+	0.0788777i
$365$	2.72791			0.142785
$366$		0			0
$367$	−33.6322			−1.75558			−0.877792	−	0.479041i	$-0.840984\pi$
$367$	−33.6322			−1.75558			−0.877792	+	0.479041i	$0.840984\pi$
$368$	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	$-0.234135\pi$
$389$	29.2477			1.48292			0.741458	+	0.670999i	$0.234135\pi$
$390$		0			0
$391$	−13.4540			−0.680397
$392$	−6.48963	−	18.7052i	−0.327776	−	0.944756i
$393$		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	$0.360703\pi$
$397$			36.0945i			1.81153i	−0.423779	+	0.905766i	$0.639297\pi$
$398$	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	$-0.363507\pi$
$401$	16.6522			0.831570			0.415785	+	0.909463i	$0.363507\pi$
$402$		0			0
$403$		−	39.0838i		−	1.94691i
$404$	5.82550	−	12.5466i	0.289829	−	0.624215i
$405$		0			0
$406$	24.2064	−	6.84670i	1.20134	−	0.339796i
$407$			1.60022i			0.0793200i
$408$		0			0
$409$		−	31.2308i		−	1.54426i	−0.635463	−	0.772132i	$-0.719191\pi$
$409$		−	31.2308i		−	1.54426i	0.635463	−	0.772132i	$-0.280809\pi$
$410$	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	$0.00589484\pi$
$431$			0.768893i			0.0370363i	−0.999829	+	0.0185181i	$0.994105\pi$
$432$		0			0
$433$			21.3559i			1.02630i	0.858299	+	0.513150i	$0.171522\pi$
$433$			21.3559i			1.02630i	−0.858299	+	0.513150i	$0.828478\pi$
$434$	28.8309	−	8.15473i	1.38393	−	0.391439i
$435$		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	$-0.379151\pi$
$439$	15.5300			0.741207			0.370604	+	0.928791i	$0.379151\pi$
$440$	−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	$-0.855807\pi$
$443$		−	18.4234i		−	0.875321i	0.899140	−	0.437660i	$-0.144193\pi$
$444$		0			0
$445$	−3.94002			−0.186775
$446$	−2.35639	+	10.6705i	−0.111578	+	0.505261i
$447$		0			0
$448$	15.3460	−	14.5774i	0.725030	−	0.688717i
$449$	−8.74217			−0.412569			−0.206284	−	0.978492i	$-0.566137\pi$
$449$	−8.74217			−0.412569			−0.206284	+	0.978492i	$0.566137\pi$
$450$		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
$476$	−29.3416	+	1.71260i	−1.34487	+	0.0784971i
$477$		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
$490$	−3.96349	+	3.83281i	−0.179052	+	0.173149i
$491$			26.6279i			1.20170i	0.799363	+	0.600849i	$0.205171\pi$
$491$			26.6279i			1.20170i	−0.799363	+	0.600849i	$0.794829\pi$
$492$		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
$518$	−14.9863	+	4.23884i	−0.658462	+	0.186244i
$519$		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	$-0.583010\pi$
$523$	−11.7931			−0.515678			−0.257839	+	0.966188i	$0.583010\pi$
$524$	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
$532$	−1.78673	−	30.6116i	−0.0774646	−	1.32718i
$533$	−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	$-0.610212\pi$
$557$	−16.0186			−0.678730			−0.339365	+	0.940655i	$0.610212\pi$
$558$		0			0
$559$	38.1171			1.61218
$560$	−5.48167	−	2.16652i	−0.231643	−	0.0915524i
$561$		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	$-0.628990\pi$
$569$	−18.8079			−0.788467			−0.394233	+	0.919010i	$0.628990\pi$
$570$		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
$574$	−7.61072	−	26.9075i	−0.317665	−	1.12310i
$575$		−	11.3596i		−	0.473727i
$576$		0			0
$577$		−	43.5494i		−	1.81299i	−0.422221	−	0.906493i	$-0.638749\pi$
$577$		−	43.5494i		−	1.81299i	0.422221	−	0.906493i	$-0.361251\pi$
$578$	−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	$-0.988258\pi$
$599$		−	1.80523i		−	0.0737596i	0.999320	−	0.0368798i	$-0.0117419\pi$
$600$		0			0
$601$		−	17.0452i		−	0.695290i	−0.937626	−	0.347645i	$-0.886981\pi$
$601$		−	17.0452i		−	0.695290i	0.937626	−	0.347645i	$-0.113019\pi$
$602$	7.95301	+	28.1177i	0.324141	+	1.14599i
$603$		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	$-0.417699\pi$
$607$	12.5988			0.511368			0.255684	+	0.966760i	$0.417699\pi$
$608$	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
$616$	−0.455631	+	2.84063i	−0.0183579	+	0.114452i
$617$	37.5684			1.51245			0.756223	−	0.654314i	$-0.227042\pi$
$617$	37.5684			1.51245			0.756223	+	0.654314i	$0.227042\pi$
$618$		0			0
$619$	26.6640			1.07172			0.535859	−	0.844308i	$-0.319988\pi$
$619$	26.6640			1.07172			0.535859	+	0.844308i	$0.319988\pi$
$620$	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	$-0.543256\pi$
$641$	−6.85997			−0.270953			−0.135476	+	0.990781i	$0.543256\pi$
$642$		0			0
$643$	28.7496			1.13377			0.566886	−	0.823796i	$-0.308148\pi$
$643$	28.7496			1.13377			0.566886	+	0.823796i	$0.308148\pi$
$644$	−12.7952	+	0.746829i	−0.504203	+	0.0294292i
$645$		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	$-0.550716\pi$
$653$	−8.10859			−0.317314			−0.158657	+	0.987334i	$0.550716\pi$
$654$		0			0
$655$		−	7.43516i		−	0.290516i
$656$	22.8368	−	19.2905i	0.891628	−	0.753169i
$657$		0			0
$658$	−41.1109	+	11.6281i	−1.60267	+	0.453310i
$659$			9.74226i			0.379505i	0.981832	+	0.189752i	$0.0607685\pi$
$659$			9.74226i			0.379505i	−0.981832	+	0.189752i	$0.939231\pi$
$660$		0			0
$661$		−	20.9611i		−	0.815291i	−0.913140	−	0.407646i	$-0.866350\pi$
$661$		−	20.9611i		−	0.815291i	0.913140	−	0.407646i	$-0.133650\pi$
$662$	−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	$0.0610556\pi$
$683$			9.96436i			0.381276i	−0.981660	+	0.190638i	$0.938944\pi$
$684$		0			0
$685$			9.16129i			0.350035i
$686$	−7.96917	+	24.9498i	−0.304265	+	0.952588i
$687$		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	$-0.399052\pi$
$691$	16.3950			0.623695			0.311847	+	0.950132i	$0.399052\pi$
$692$	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
$700$	−1.44600	−	24.7739i	−0.0546536	−	0.936366i
$701$	−43.5073			−1.64325			−0.821624	−	0.570031i	$-0.806931\pi$
$701$	−43.5073			−1.64325			−0.821624	+	0.570031i	$0.806931\pi$
$702$		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	$-0.500457\pi$
$727$	−0.0773779			−0.00286979			−0.00143489	+	0.999999i	$0.500457\pi$
$728$	−5.78453	+	36.0636i	−0.214389	+	1.33661i
$729$		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	$0.00667997\pi$
$733$			1.13625i			0.0419684i	−0.999780	+	0.0209842i	$0.993320\pi$
$734$	−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
$742$	−12.3588	+	3.49565i	−0.453705	+	0.128329i
$743$			8.82810i			0.323872i	0.986801	+	0.161936i	$0.0517738\pi$
$743$			8.82810i			0.323872i	−0.986801	+	0.161936i	$0.948226\pi$
$744$		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	$0.00707378\pi$
$769$			1.23242i			0.0444422i	−0.999753	+	0.0222211i	$0.992926\pi$
$770$	0.770920	−	0.218052i	0.0277820	−	0.00785806i
$771$		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
$784$	−27.8099	+	3.25750i	−0.993210	+	0.116339i
$785$	6.51111			0.232391
$786$		0			0
$787$	4.49443			0.160209			0.0801047	−	0.996786i	$-0.474475\pi$
$787$	4.49443			0.160209			0.0801047	+	0.996786i	$0.474475\pi$
$788$	−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	$-0.521602\pi$
$809$	−3.85760			−0.135626			−0.0678130	+	0.997698i	$0.521602\pi$
$810$		0			0
$811$	3.63921			0.127790			0.0638949	−	0.997957i	$-0.479648\pi$
$811$	3.63921			0.127790			0.0638949	+	0.997957i	$0.479648\pi$
$812$	−2.07296	−	35.5155i	−0.0727468	−	1.24635i
$813$		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	$-0.529061\pi$
$821$	−5.22467			−0.182342			−0.0911711	+	0.995835i	$0.529061\pi$
$822$		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
$826$	5.30197	−	1.49965i	0.184479	−	0.0521793i
$827$		−	20.9224i		−	0.727543i	−0.931488	−	0.363771i	$-0.881489\pi$
$827$		−	20.9224i		−	0.727543i	0.931488	−	0.363771i	$-0.118511\pi$
$828$		0			0
$829$		−	8.35791i		−	0.290282i	−0.989411	−	0.145141i	$-0.953636\pi$
$829$		−	8.35791i		−	0.290282i	0.989411	−	0.145141i	$-0.0463636\pi$
$830$	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	$0.115270\pi$
$853$			20.6936i			0.708536i	−0.935144	+	0.354268i	$0.884730\pi$
$854$	3.12144	+	11.0358i	0.106814	+	0.377637i
$855$		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	$-0.461845\pi$
$859$	7.00948			0.239160			0.119580	+	0.992825i	$0.461845\pi$
$860$	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	$0.247333\pi$
$863$			41.1956i			1.40231i	−0.713007	+	0.701157i	$0.752667\pi$
$864$		0			0
$865$	−12.7974			−0.435125
$866$	29.4913	+	6.51266i	1.00216	+	0.221309i
$867$		0			0
$868$	−2.46899	−	42.3006i	−0.0838031	−	1.43578i
$869$	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
$896$	−15.4506	−	25.6374i	−0.516170	−	0.856486i
$897$		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
$910$	9.78733	−	2.76832i	0.324447	−	0.0917688i
$911$			5.44469i			0.180391i	0.995924	+	0.0901953i	$0.0287491\pi$
$911$			5.44469i			0.180391i	−0.995924	+	0.0901953i	$0.971251\pi$
$912$		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	$-0.906505\pi$
$937$		−	17.7246i		−	0.579039i	0.957172	−	0.289519i	$-0.0934955\pi$
$938$	1.95424	+	6.90917i	0.0638081	+	0.225592i
$939$		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	$0.0790374\pi$
$947$			15.1257i			0.491519i	−0.969331	+	0.245760i	$0.920963\pi$
$948$		0			0
$949$	−23.9056			−0.776009
$950$	8.28781	−	37.5297i	0.268892	−	1.21762i
$951$		0			0
$952$	−6.58295	+	41.0413i	−0.213354	+	1.33016i
$953$	49.2659			1.59588			0.797939	−	0.602738i	$-0.205924\pi$
$953$	49.2659			1.59588			0.797939	+	0.602738i	$0.205924\pi$
$954$		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	$-0.438814\pi$
$977$	11.9426			0.382079			0.191040	+	0.981582i	$0.438814\pi$
$978$		0			0
$979$	2.71965			0.0869203
$980$	4.08419	+	6.64219i	0.130465	+	0.212177i
$981$		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
$994$	−3.15854	−	11.1670i	−0.100183	−	0.354194i
$995$			0.907718i			0.0287766i
$996$		0			0
$997$		−	13.0151i		−	0.412193i	−0.978532	−	0.206096i	$-0.933924\pi$
$997$		−	13.0151i		−	0.412193i	0.978532	−	0.206096i	$-0.0660761\pi$
$998$	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.55.9	yes	16
3.2	odd	2		756.2.b.e.55.8	yes	16
4.3	odd	2		756.2.b.e.55.10	yes	16
7.6	odd	2		756.2.b.e.55.9	yes	16
12.11	even	2	inner	756.2.b.f.55.7	yes	16
21.20	even	2	inner	756.2.b.f.55.8	yes	16
28.27	even	2	inner	756.2.b.f.55.10	yes	16
84.83	odd	2		756.2.b.e.55.7	✓	16

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

\(f(q)\)	\(=\)	\(q+(0.304958 - 1.38094i) q^{2} +(-1.81400 - 0.842259i) q^{4} +0.556957i q^{5} +(1.25214 + 2.33070i) q^{7} +(-1.71630 + 2.24818i) q^{8} +O(q^{10})\)	\(q+(0.304958 - 1.38094i) q^{2} +(-1.81400 - 0.842259i) q^{4} +0.556957i q^{5} +(1.25214 + 2.33070i) q^{7} +(-1.71630 + 2.24818i) q^{8} +(0.769125 + 0.169848i) q^{10} -0.384447i q^{11} -4.88080i q^{13} +(3.60041 - 1.01836i) q^{14} +(2.58120 + 3.05572i) q^{16} -5.55448i q^{17} +5.79490 q^{19} +(0.469102 - 1.01032i) q^{20} +(-0.530898 - 0.117240i) q^{22} -2.42219i q^{23} +4.68980 q^{25} +(-6.74010 - 1.48844i) q^{26} +(-0.308329 - 5.28251i) q^{28} +6.72323 q^{29} +8.00767 q^{31} +(5.00692 - 2.63262i) q^{32} +(-7.67041 - 1.69388i) q^{34} +(-1.29810 + 0.697386i) q^{35} -4.16240 q^{37} +(1.76720 - 8.00241i) q^{38} +(-1.25214 - 0.955907i) q^{40} -7.47347i q^{41} +7.80960i q^{43} +(-0.323803 + 0.697386i) q^{44} +(-3.34490 - 0.738665i) q^{46} -11.4184 q^{47} +(-3.86430 + 5.83671i) q^{49} +(1.43019 - 6.47634i) q^{50} +(-4.11090 + 8.85378i) q^{52} -3.43261 q^{53} +0.214120 q^{55} +(-7.38887 - 1.18516i) q^{56} +(2.05030 - 9.28439i) q^{58} +1.47260 q^{59} +3.06515i q^{61} +(2.44200 - 11.0581i) q^{62} +(-2.10860 - 7.71711i) q^{64} +2.71839 q^{65} +1.91900i q^{67} +(-4.67831 + 10.0758i) q^{68} +(0.567185 + 2.00527i) q^{70} -3.10158i q^{71} -4.89789i q^{73} +(-1.26936 + 5.74804i) q^{74} +(-10.5119 - 4.88080i) q^{76} +(0.896029 - 0.481380i) q^{77} +6.35956i q^{79} +(-1.70190 + 1.43762i) q^{80} +(-10.3204 - 2.27910i) q^{82} +12.9458 q^{83} +3.09360 q^{85} +(10.7846 + 2.38160i) q^{86} +(0.864304 + 0.659827i) q^{88} +7.07419i q^{89} +(11.3757 - 6.11143i) q^{91} +(-2.04011 + 4.39385i) q^{92} +(-3.48213 + 15.7682i) q^{94} +3.22751i q^{95} -9.28765i q^{97} +(6.88170 + 7.11633i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 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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