LMFDB - Embedded newform 756.2.b.f.55.2

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			55.2
Root			$1.41109 + 0.0939769i$ of defining polynomial
Character	$\chi$	$=$	756.55
Dual form			756.2.b.f.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41109 + 0.0939769i) q^{2} +(1.98234 - 0.265219i) q^{4} +2.91758i q^{5} +(1.63542 + 2.07976i) q^{7} +(-2.77233 + 0.560541i) q^{8} +O(q^{10})$	\(q+(-1.41109 + 0.0939769i) q^{2} +(1.98234 - 0.265219i) q^{4} +2.91758i q^{5} +(1.63542 + 2.07976i) q^{7} +(-2.77233 + 0.560541i) q^{8} +(-0.274185 - 4.11696i) q^{10} +2.40700i q^{11} +1.28591i q^{13} +(-2.50318 - 2.78103i) q^{14} +(3.85932 - 1.05151i) q^{16} +5.02059i q^{17} -4.84850 q^{19} +(0.773798 + 5.78362i) q^{20} +(-0.226202 - 3.39648i) q^{22} -8.04597i q^{23} -3.51227 q^{25} +(-0.120846 - 1.81454i) q^{26} +(3.79355 + 3.68903i) q^{28} -2.57469 q^{29} +6.34051 q^{31} +(-5.34702 + 1.84646i) q^{32} +(-0.471820 - 7.08450i) q^{34} +(-6.06786 + 4.77148i) q^{35} -6.71864 q^{37} +(6.84165 - 0.455647i) q^{38} +(-1.63542 - 8.08848i) q^{40} -2.30281i q^{41} -9.79488i q^{43} +(0.638382 + 4.77148i) q^{44} +(0.756135 + 11.3536i) q^{46} +1.21071 q^{47} +(-1.65078 + 6.80257i) q^{49} +(4.95612 - 0.330072i) q^{50} +(0.341049 + 2.54912i) q^{52} -5.54465 q^{53} -7.02260 q^{55} +(-5.69972 - 4.84904i) q^{56} +(3.63312 - 0.241961i) q^{58} +12.2309 q^{59} +8.95597i q^{61} +(-8.94701 + 0.595861i) q^{62} +(7.37159 - 3.10801i) q^{64} -3.75176 q^{65} +7.32341i q^{67} +(1.33156 + 9.95251i) q^{68} +(8.11387 - 7.30321i) q^{70} +8.42187i q^{71} +14.7329i q^{73} +(9.48058 - 0.631396i) q^{74} +(-9.61135 + 1.28591i) q^{76} +(-5.00597 + 3.93646i) q^{77} -3.53235i q^{79} +(3.06786 + 11.2599i) q^{80} +(0.216411 + 3.24947i) q^{82} -10.4416 q^{83} -14.6480 q^{85} +(0.920492 + 13.8214i) q^{86} +(-1.34922 - 6.67298i) q^{88} -9.97593i q^{89} +(-2.67439 + 2.10301i) q^{91} +(-2.13394 - 15.9498i) q^{92} +(-1.70842 + 0.113779i) q^{94} -14.1459i q^{95} +11.8187i q^{97} +(1.69011 - 9.75415i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.41109	+	0.0939769i	−0.997790	+	0.0664517i
$2$	−1.41109	+	0.0939769i	−0.997790	+	0.0664517i
$3$		0			0
$3$		0			0
$4$	1.98234	−	0.265219i	0.991168	−	0.132610i
$5$			2.91758i			1.30478i	0.757883	+	0.652391i	$0.226234\pi$
$5$			2.91758i			1.30478i	−0.757883	+	0.652391i	$0.773766\pi$
$6$		0			0
$7$	1.63542	+	2.07976i	0.618132	+	0.786074i
$7$	1.63542	+	2.07976i	0.618132	+	0.786074i
$8$	−2.77233	+	0.560541i	−0.980165	+	0.198181i
$9$		0			0
$10$	−0.274185	−	4.11696i	−0.0867049	−	1.30190i
$11$			2.40700i			0.725737i	0.931840	+	0.362868i	$0.118203\pi$
$11$			2.40700i			0.725737i	−0.931840	+	0.362868i	$0.881797\pi$
$12$		0			0
$13$			1.28591i			0.356648i	0.983972	+	0.178324i	$0.0570676\pi$
$13$			1.28591i			0.356648i	−0.983972	+	0.178324i	$0.942932\pi$
$14$	−2.50318	−	2.78103i	−0.669002	−	0.743261i
$15$		0			0
$16$	3.85932	−	1.05151i	0.964829	−	0.262877i
$17$			5.02059i			1.21767i	0.793296	+	0.608836i	$0.208363\pi$
$17$			5.02059i			1.21767i	−0.793296	+	0.608836i	$0.791637\pi$
$18$		0			0
$19$	−4.84850			−1.11232			−0.556161	−	0.831075i	$-0.687726\pi$
$19$	−4.84850			−1.11232			−0.556161	+	0.831075i	$0.687726\pi$
$20$	0.773798	+	5.78362i	0.173026	+	1.29326i
$21$		0			0
$22$	−0.226202	−	3.39648i	−0.0482264	−	0.724133i
$23$		−	8.04597i		−	1.67770i	−0.544363	−	0.838850i	$-0.683228\pi$
$23$		−	8.04597i		−	1.67770i	0.544363	−	0.838850i	$-0.316772\pi$
$24$		0			0
$25$	−3.51227			−0.702454
$26$	−0.120846	−	1.81454i	−0.0236999	−	0.355860i
$27$		0			0
$28$	3.79355	+	3.68903i	0.716914	+	0.697162i
$29$	−2.57469			−0.478108			−0.239054	−	0.971006i	$-0.576837\pi$
$29$	−2.57469			−0.478108			−0.239054	+	0.971006i	$0.576837\pi$
$30$		0			0
$31$	6.34051			1.13879			0.569394	−	0.822065i	$-0.307178\pi$
$31$	6.34051			1.13879			0.569394	+	0.822065i	$0.307178\pi$
$32$	−5.34702	+	1.84646i	−0.945228	+	0.326410i
$33$		0			0
$34$	−0.471820	−	7.08450i	−0.0809164	−	1.21498i
$35$	−6.06786	+	4.77148i	−1.02565	+	0.806527i
$36$		0			0
$37$	−6.71864			−1.10454			−0.552268	−	0.833666i	$-0.686238\pi$
$37$	−6.71864			−1.10454			−0.552268	+	0.833666i	$0.686238\pi$
$38$	6.84165	−	0.455647i	1.10986	−	0.0739156i
$39$		0			0
$40$	−1.63542	−	8.08848i	−0.258583	−	1.27890i
$41$		−	2.30281i		−	0.359639i	−0.983700	−	0.179819i	$-0.942449\pi$
$41$		−	2.30281i		−	0.359639i	0.983700	−	0.179819i	$-0.0575513\pi$
$42$		0			0
$43$		−	9.79488i		−	1.49370i	−0.664990	−	0.746852i	$-0.731564\pi$
$43$		−	9.79488i		−	1.49370i	0.664990	−	0.746852i	$-0.268436\pi$
$44$	0.638382	+	4.77148i	0.0962397	+	0.719327i
$45$		0			0
$46$	0.756135	+	11.3536i	0.111486	+	1.67399i
$47$	1.21071			0.176600			0.0883002	−	0.996094i	$-0.471857\pi$
$47$	1.21071			0.176600			0.0883002	+	0.996094i	$0.471857\pi$
$48$		0			0
$49$	−1.65078	+	6.80257i	−0.235826	+	0.971795i
$50$	4.95612	−	0.330072i	0.700901	−	0.0466792i
$51$		0			0
$52$	0.341049	+	2.54912i	0.0472950	+	0.353499i
$53$	−5.54465			−0.761617			−0.380808	−	0.924654i	$-0.624354\pi$
$53$	−5.54465			−0.761617			−0.380808	+	0.924654i	$0.624354\pi$
$54$		0			0
$55$	−7.02260			−0.946928
$56$	−5.69972	−	4.84904i	−0.761657	−	0.647981i
$57$		0			0
$58$	3.63312	−	0.241961i	0.477051	−	0.0317711i
$59$	12.2309			1.59233			0.796164	−	0.605081i	$-0.206859\pi$
$59$	12.2309			1.59233			0.796164	+	0.605081i	$0.206859\pi$
$60$		0			0
$61$			8.95597i			1.14669i	0.819312	+	0.573347i	$0.194355\pi$
$61$			8.95597i			1.14669i	−0.819312	+	0.573347i	$0.805645\pi$
$62$	−8.94701	+	0.595861i	−1.13627	+	0.0756744i
$63$		0			0
$64$	7.37159	−	3.10801i	0.921448	−	0.388501i
$65$	−3.75176			−0.465348
$66$		0			0
$67$			7.32341i			0.894696i	0.894360	+	0.447348i	$0.147632\pi$
$67$			7.32341i			0.894696i	−0.894360	+	0.447348i	$0.852368\pi$
$68$	1.33156	+	9.95251i	0.161475	+	1.20692i
$69$		0			0
$70$	8.11387	−	7.30321i	0.969793	−	0.872901i
$71$			8.42187i			0.999493i	0.866172	+	0.499746i	$0.166573\pi$
$71$			8.42187i			0.999493i	−0.866172	+	0.499746i	$0.833427\pi$
$72$		0			0
$73$			14.7329i			1.72435i	0.506610	+	0.862175i	$0.330898\pi$
$73$			14.7329i			1.72435i	−0.506610	+	0.862175i	$0.669102\pi$
$74$	9.48058	−	0.631396i	1.10210	−	0.0733983i
$75$		0			0
$76$	−9.61135	+	1.28591i	−1.10250	+	0.147504i
$77$	−5.00597	+	3.93646i	−0.570483	+	0.448601i
$78$		0			0
$79$		−	3.53235i		−	0.397420i	−0.980058	−	0.198710i	$-0.936325\pi$
$79$		−	3.53235i		−	0.397420i	0.980058	−	0.198710i	$-0.0636752\pi$
$80$	3.06786	+	11.2599i	0.342997	+	1.25889i
$81$		0			0
$82$	0.216411	+	3.24947i	0.0238986	+	0.358844i
$83$	−10.4416			−1.14612			−0.573058	−	0.819515i	$-0.694243\pi$
$83$	−10.4416			−1.14612			−0.573058	+	0.819515i	$0.694243\pi$
$84$		0			0
$85$	−14.6480			−1.58880
$86$	0.920492	+	13.8214i	0.0992592	+	1.49040i
$87$		0			0
$88$	−1.34922	−	6.67298i	−0.143827	−	0.711342i
$89$		−	9.97593i		−	1.05745i	−0.848794	−	0.528723i	$-0.822671\pi$
$89$		−	9.97593i		−	1.05745i	0.848794	−	0.528723i	$-0.177329\pi$
$90$		0			0
$91$	−2.67439	+	2.10301i	−0.280352	+	0.220456i
$92$	−2.13394	−	15.9498i	−0.222479	−	1.66288i
$93$		0			0
$94$	−1.70842	+	0.113779i	−0.176210	+	0.0117354i
$95$		−	14.1459i		−	1.45134i
$96$		0			0
$97$			11.8187i			1.20001i	0.799998	+	0.600003i	$0.204834\pi$
$97$			11.8187i			1.20001i	−0.799998	+	0.600003i	$0.795166\pi$
$98$	1.69011	−	9.75415i	0.170727	−	0.985318i
$99$		0			0
$100$	−6.96250	+	0.931521i	−0.696250	+	0.0931521i
$101$		−	0.614768i		−	0.0611717i	−0.999532	−	0.0305858i	$-0.990263\pi$
$101$		−	0.614768i		−	0.0611717i	0.999532	−	0.0305858i	$-0.00973730\pi$
$102$		0			0
$103$	−7.91816			−0.780199			−0.390100	−	0.920773i	$-0.627559\pi$
$103$	−7.91816			−0.780199			−0.390100	+	0.920773i	$0.627559\pi$
$104$	−0.720808	−	3.56497i	−0.0706810	−	0.349574i
$105$		0			0
$106$	7.82399	−	0.521069i	0.759933	−	0.0506107i
$107$		−	7.67670i		−	0.742135i	−0.928606	−	0.371067i	$-0.878992\pi$
$107$		−	7.67670i		−	0.742135i	0.928606	−	0.371067i	$-0.121008\pi$
$108$		0			0
$109$	−6.71864			−0.643529			−0.321764	−	0.946820i	$-0.604276\pi$
$109$	−6.71864			−0.643529			−0.321764	+	0.946820i	$0.604276\pi$
$110$	9.90951	−	0.659962i	0.944835	−	0.0629249i
$111$		0			0
$112$	8.49850	+	6.30678i	0.803033	+	0.595935i
$113$	3.25679			0.306373			0.153187	−	0.988197i	$-0.451046\pi$
$113$	3.25679			0.306373			0.153187	+	0.988197i	$0.451046\pi$
$114$		0			0
$115$	23.4747			2.18903
$116$	−5.10391	+	0.682858i	−0.473886	+	0.0634017i
$117$		0			0
$118$	−17.2589	+	1.14942i	−1.58881	+	0.105813i
$119$	−10.4416	+	8.21080i	−0.957181	+	0.752683i
$120$		0			0
$121$	5.20637			0.473306
$122$	−0.841654	−	12.6377i	−0.0761998	−	1.14416i
$123$		0			0
$124$	12.5690	−	1.68162i	1.12873	−	0.151014i
$125$			4.34057i			0.388233i
$126$		0			0
$127$			12.9588i			1.14990i	0.818187	+	0.574952i	$0.194979\pi$
$127$			12.9588i			1.14990i	−0.818187	+	0.574952i	$0.805021\pi$
$128$	−10.1099	+	5.07843i	−0.893595	+	0.448874i
$129$		0			0
$130$	5.29406	−	0.352578i	0.464320	−	0.0309232i
$131$	19.5773			1.71048			0.855240	−	0.518233i	$-0.173410\pi$
$131$	19.5773			1.71048			0.855240	+	0.518233i	$0.173410\pi$
$132$		0			0
$133$	−7.92935	−	10.0837i	−0.687562	−	0.874367i
$134$	−0.688231	−	10.3340i	−0.0594541	−	0.892719i
$135$		0			0
$136$	−2.81425	−	13.9187i	−0.241320	−	1.19352i
$137$	18.4269			1.57431			0.787156	−	0.616754i	$-0.211553\pi$
$137$	18.4269			1.57431			0.787156	+	0.616754i	$0.211553\pi$
$138$		0			0
$139$	−10.2935			−0.873079			−0.436540	−	0.899685i	$-0.643796\pi$
$139$	−10.2935			−0.873079			−0.436540	+	0.899685i	$0.643796\pi$
$140$	−10.7630	+	11.0680i	−0.909643	+	0.935416i
$141$		0			0
$142$	−0.791461	−	11.8840i	−0.0664180	−	0.997283i
$143$	−3.09519			−0.258833
$144$		0			0
$145$		−	7.51187i		−	0.623827i
$146$	−1.38455	−	20.7894i	−0.114586	−	1.72054i
$147$		0			0
$148$	−13.3186	+	1.78191i	−1.09478	+	0.146472i
$149$	14.6452			1.19978			0.599890	−	0.800082i	$-0.295211\pi$
$149$	14.6452			1.19978			0.599890	+	0.800082i	$0.295211\pi$
$150$		0			0
$151$		−	14.0196i		−	1.14090i	−0.821331	−	0.570451i	$-0.806768\pi$
$151$		−	14.0196i		−	1.14090i	0.821331	−	0.570451i	$-0.193232\pi$
$152$	13.4416	−	2.71778i	1.09026	−	0.220441i
$153$		0			0
$154$	6.69392	−	6.02513i	0.539412	−	0.485519i
$155$			18.4989i			1.48587i
$156$		0			0
$157$		−	0.158192i		−	0.0126251i	−0.999980	−	0.00631255i	$-0.997991\pi$
$157$		−	0.158192i		−	0.0126251i	0.999980	−	0.00631255i	$-0.00200936\pi$
$158$	0.331959	+	4.98445i	0.0264092	+	0.396542i
$159$		0			0
$160$	−5.38718	−	15.6003i	−0.425894	−	1.23332i
$161$	16.7337	−	13.1586i	1.31880	−	1.03704i
$162$		0			0
$163$			6.64972i			0.520847i	0.965495	+	0.260423i	$0.0838621\pi$
$163$			6.64972i			0.520847i	−0.965495	+	0.260423i	$0.916138\pi$
$164$	−0.610750	−	4.56495i	−0.0476915	−	0.356463i
$165$		0			0
$166$	14.7340	−	0.981270i	1.14358	−	0.0761613i
$167$	−4.11552			−0.318468			−0.159234	−	0.987241i	$-0.550903\pi$
$167$	−4.11552			−0.318468			−0.159234	+	0.987241i	$0.550903\pi$
$168$		0			0
$169$	11.3464			0.872802
$170$	20.6696	−	1.37657i	1.58528	−	0.105578i
$171$		0			0
$172$	−2.59779	−	19.4167i	−0.198080	−	1.48051i
$173$			9.82601i			0.747058i	0.927619	+	0.373529i	$0.121852\pi$
$173$			9.82601i			0.747058i	−0.927619	+	0.373529i	$0.878148\pi$
$174$		0			0
$175$	−5.74405	−	7.30467i	−0.434209	−	0.552181i
$176$	2.53098	+	9.28937i	0.190779	+	0.700212i
$177$		0			0
$178$	0.937507	+	14.0769i	0.0702691	+	1.05511i
$179$		−	2.45324i		−	0.183364i	−0.995788	−	0.0916819i	$-0.970776\pi$
$179$		−	2.45324i		−	0.183364i	0.995788	−	0.0916819i	$-0.0292243\pi$
$180$		0			0
$181$		−	21.5661i		−	1.60299i	−0.597999	−	0.801497i	$-0.704037\pi$
$181$		−	21.5661i		−	1.60299i	0.597999	−	0.801497i	$-0.295963\pi$
$182$	3.57616	−	3.21887i	0.265083	−	0.238598i
$183$		0			0
$184$	4.51010	+	22.3060i	0.332489	+	1.64442i
$185$		−	19.6022i		−	1.44118i
$186$		0			0
$187$	−12.0846			−0.883710
$188$	2.40004	−	0.321104i	0.175041	−	0.0234189i
$189$		0			0
$190$	1.32938	+	19.9611i	0.0964437	+	1.44813i
$191$			0.329664i			0.0238536i	0.999929	+	0.0119268i	$0.00379651\pi$
$191$			0.329664i			0.0238536i	−0.999929	+	0.0119268i	$0.996203\pi$
$192$		0			0
$193$	15.9539			1.14839			0.574193	−	0.818720i	$-0.305316\pi$
$193$	15.9539			1.14839			0.574193	+	0.818720i	$0.305316\pi$
$194$	−1.11068	−	16.6772i	−0.0797423	−	1.19735i
$195$		0			0
$196$	−1.46823	+	13.9228i	−0.104873	+	0.994486i
$197$	3.16936			0.225807			0.112904	−	0.993606i	$-0.463985\pi$
$197$	3.16936			0.225807			0.112904	+	0.993606i	$0.463985\pi$
$198$		0			0
$199$	27.0253			1.91577			0.957887	−	0.287146i	$-0.0927064\pi$
$199$	27.0253			1.91577			0.957887	+	0.287146i	$0.0927064\pi$
$200$	9.73716	−	1.96877i	0.688521	−	0.139213i
$201$		0			0
$202$	0.0577740	+	0.867491i	0.00406496	+	0.0610365i
$203$	−4.21071	−	5.35473i	−0.295534	−	0.375829i
$204$		0			0
$205$	6.71864			0.469250
$206$	11.1732	−	0.744123i	0.778475	−	0.0518455i
$207$		0			0
$208$	1.35215	+	4.96275i	0.0937546	+	0.344105i
$209$		−	11.6703i		−	0.807253i
$210$		0			0
$211$		−	1.12613i		−	0.0775260i	−0.999248	−	0.0387630i	$-0.987658\pi$
$211$		−	1.12613i		−	0.0775260i	0.999248	−	0.0387630i	$-0.0123417\pi$
$212$	−10.9914	+	1.47055i	−0.754890	+	0.100998i
$213$		0			0
$214$	0.721432	+	10.8325i	0.0493161	+	0.740494i
$215$	28.5773			1.94896
$216$		0			0
$217$	10.3694	+	13.1867i	0.703922	+	0.895172i
$218$	9.48058	−	0.631396i	0.642106	−	0.0427635i
$219$		0			0
$220$	−13.9212	+	1.86253i	−0.938565	+	0.125572i
$221$	−6.45605			−0.434281
$222$		0			0
$223$	−2.78994			−0.186828			−0.0934140	−	0.995627i	$-0.529778\pi$
$223$	−2.78994			−0.186828			−0.0934140	+	0.995627i	$0.529778\pi$
$224$	−12.5848	−	8.10076i	−0.840859	−	0.541255i
$225$		0			0
$226$	−4.59562	+	0.306063i	−0.305696	+	0.0203590i
$227$	−5.02019			−0.333202			−0.166601	−	0.986024i	$-0.553279\pi$
$227$	−5.02019			−0.333202			−0.166601	+	0.986024i	$0.553279\pi$
$228$		0			0
$229$		−	1.12772i		−	0.0745220i	−0.999306	−	0.0372610i	$-0.988137\pi$
$229$		−	1.12772i		−	0.0745220i	0.999306	−	0.0372610i	$-0.0118633\pi$
$230$	−33.1249	+	2.20608i	−2.18419	+	0.145465i
$231$		0			0
$232$	7.13789	−	1.44322i	0.468625	−	0.0947521i
$233$	−4.15055			−0.271911			−0.135956	−	0.990715i	$-0.543410\pi$
$233$	−4.15055			−0.271911			−0.135956	+	0.990715i	$0.543410\pi$
$234$		0			0
$235$			3.53235i			0.230425i
$236$	24.2458	−	3.24387i	1.57827	−	0.211158i
$237$		0			0
$238$	13.9624	−	12.5674i	0.905049	−	0.814625i
$239$		−	14.8977i		−	0.963651i	−0.876267	−	0.481826i	$-0.839974\pi$
$239$		−	14.8977i		−	0.963651i	0.876267	−	0.481826i	$-0.160026\pi$
$240$		0			0
$241$		−	24.2961i		−	1.56505i	−0.622620	−	0.782524i	$-0.713932\pi$
$241$		−	24.2961i		−	1.56505i	0.622620	−	0.782524i	$-0.286068\pi$
$242$	−7.34664	+	0.489278i	−0.472260	+	0.0314520i
$243$		0			0
$244$	2.37530	+	17.7538i	0.152063	+	1.13657i
$245$	−19.8470	−	4.81628i	−1.26798	−	0.307701i
$246$		0			0
$247$		−	6.23475i		−	0.396708i
$248$	−17.5780	+	3.55412i	−1.11620	+	0.225687i
$249$		0			0
$250$	−0.407913	−	6.12493i	−0.0257987	−	0.387374i
$251$	−22.5773			−1.42507			−0.712534	−	0.701637i	$-0.752453\pi$
$251$	−22.5773			−1.42507			−0.712534	+	0.701637i	$0.752453\pi$
$252$		0			0
$253$	19.3666			1.21757
$254$	−1.21782	−	18.2860i	−0.0764131	−	1.14736i
$255$		0			0
$256$	13.7887	−	8.11620i	0.861792	−	0.507263i
$257$			8.61820i			0.537588i	0.963198	+	0.268794i	$0.0866251\pi$
$257$			8.61820i			0.537588i	−0.963198	+	0.268794i	$0.913375\pi$
$258$		0			0
$259$	−10.9878	−	13.9731i	−0.682750	−	0.868248i
$260$	−7.43725	+	0.995038i	−0.461238	+	0.0617096i
$261$		0			0
$262$	−27.6253	+	1.83982i	−1.70670	+	0.113664i
$263$			24.1043i			1.48634i	0.669104	+	0.743169i	$0.266678\pi$
$263$			24.1043i			1.48634i	−0.669104	+	0.743169i	$0.733322\pi$
$264$		0			0
$265$		−	16.1770i		−	0.993743i
$266$	12.1366	+	13.4838i	0.744145	+	0.826745i
$267$		0			0
$268$	1.94231	+	14.5175i	0.118645	+	0.886795i
$269$			11.1901i			0.682272i	0.940014	+	0.341136i	$0.110812\pi$
$269$			11.1901i			0.682272i	−0.940014	+	0.341136i	$0.889188\pi$
$270$		0			0
$271$	−18.4251			−1.11924			−0.559621	−	0.828748i	$-0.689053\pi$
$271$	−18.4251			−1.11924			−0.559621	+	0.828748i	$0.689053\pi$
$272$	5.27919	+	19.3761i	0.320098	+	1.17485i
$273$		0			0
$274$	−26.0019	+	1.73170i	−1.57083	+	0.104616i
$275$		−	8.45402i		−	0.509797i
$276$		0			0
$277$	−2.11552			−0.127109			−0.0635546	−	0.997978i	$-0.520244\pi$
$277$	−2.11552			−0.127109			−0.0635546	+	0.997978i	$0.520244\pi$
$278$	14.5250	−	0.967346i	0.871149	−	0.0580176i
$279$		0			0
$280$	14.1475	−	16.6294i	0.845473	−	0.993795i
$281$	9.03075			0.538729			0.269365	−	0.963038i	$-0.413186\pi$
$281$	9.03075			0.538729			0.269365	+	0.963038i	$0.413186\pi$
$282$		0			0
$283$	24.9368			1.48234			0.741171	−	0.671316i	$-0.234271\pi$
$283$	24.9368			1.48234			0.741171	+	0.671316i	$0.234271\pi$
$284$	2.23364	+	16.6950i	0.132542	+	0.990665i
$285$		0			0
$286$	4.36759	−	0.290876i	0.258261	−	0.0171999i
$287$	4.78929	−	3.76607i	0.282703	−	0.222304i
$288$		0			0
$289$	−8.20637			−0.482727
$290$	0.705942	+	10.5999i	0.0414543	+	0.622448i
$291$		0			0
$292$	3.90744	+	29.2055i	0.228665	+	1.70912i
$293$			4.95534i			0.289494i	0.989469	+	0.144747i	$0.0462368\pi$
$293$			4.95534i			0.289494i	−0.989469	+	0.144747i	$0.953763\pi$
$294$		0			0
$295$			35.6846i			2.07764i
$296$	18.6262	−	3.76607i	1.08263	−	0.218899i
$297$		0			0
$298$	−20.6656	+	1.37631i	−1.19713	+	0.0797274i
$299$	10.3464			0.598349
$300$		0			0
$301$	20.3710	−	16.0188i	1.17416	−	0.923307i
$302$	1.31752	+	19.7829i	0.0758149	+	1.13838i
$303$		0			0
$304$	−18.7119	+	5.09823i	−1.07320	+	0.292404i
$305$	−26.1298			−1.49619
$306$		0			0
$307$	20.4907			1.16947			0.584734	−	0.811225i	$-0.301199\pi$
$307$	20.4907			1.16947			0.584734	+	0.811225i	$0.301199\pi$
$308$	−8.87949	+	9.13107i	−0.505956	+	0.520291i
$309$		0			0
$310$	−1.73847	−	26.1036i	−0.0987385	−	1.48259i
$311$	−7.69410			−0.436292			−0.218146	−	0.975916i	$-0.570001\pi$
$311$	−7.69410			−0.436292			−0.218146	+	0.975916i	$0.570001\pi$
$312$		0			0
$313$		−	19.8765i		−	1.12349i	−0.827311	−	0.561744i	$-0.810131\pi$
$313$		−	19.8765i		−	1.12349i	0.827311	−	0.561744i	$-0.189869\pi$
$314$	0.0148664	+	0.223223i	0.000838959	+	0.0125972i
$315$		0			0
$316$	−0.936846	−	7.00230i	−0.0527017	−	0.393910i
$317$	−20.4069			−1.14616			−0.573082	−	0.819498i	$-0.694252\pi$
$317$	−20.4069			−1.14616			−0.573082	+	0.819498i	$0.694252\pi$
$318$		0			0
$319$		−	6.19727i		−	0.346981i
$320$	9.06786	+	21.5072i	0.506909	+	1.20229i
$321$		0			0
$322$	−22.3761	+	20.1405i	−1.24697	+	1.12238i
$323$		−	24.3423i		−	1.35444i
$324$		0			0
$325$		−	4.51648i		−	0.250529i
$326$	−0.624920	−	9.38334i	−0.0346111	−	0.519695i
$327$		0			0
$328$	1.29082	+	6.38414i	0.0712737	+	0.352505i
$329$	1.98003	+	2.51799i	0.109162	+	0.138821i
$330$		0			0
$331$			18.9813i			1.04331i	0.853157	+	0.521654i	$0.174685\pi$
$331$			18.9813i			1.04331i	−0.853157	+	0.521654i	$0.825315\pi$
$332$	−20.6988	+	2.76932i	−1.13599	+	0.151986i
$333$		0			0
$334$	5.80736	−	0.386764i	0.317765	−	0.0211628i
$335$	−21.3666			−1.16738
$336$		0			0
$337$	−25.4865			−1.38834			−0.694169	−	0.719812i	$-0.744228\pi$
$337$	−25.4865			−1.38834			−0.694169	+	0.719812i	$0.744228\pi$
$338$	−16.0108	+	1.06630i	−0.870873	+	0.0579991i
$339$		0			0
$340$	−29.0372	+	3.88493i	−1.57477	+	0.210690i
$341$			15.2616i			0.826461i
$342$		0			0
$343$	−16.8474	+	7.69186i	−0.909675	+	0.415321i
$344$	5.49043	+	27.1546i	0.296024	+	1.46408i
$345$		0			0
$346$	−0.923418	−	13.8654i	−0.0496433	−	0.745407i
$347$			10.5446i			0.566066i	0.959110	+	0.283033i	$0.0913405\pi$
$347$			10.5446i			0.566066i	−0.959110	+	0.283033i	$0.908659\pi$
$348$		0			0
$349$			34.5639i			1.85017i	0.379765	+	0.925083i	$0.376005\pi$
$349$			34.5639i			1.85017i	−0.379765	+	0.925083i	$0.623995\pi$
$350$	8.79183	+	9.76772i	0.469943	+	0.522106i
$351$		0			0
$352$	−4.44441	−	12.8703i	−0.236888	−	0.685987i
$353$		−	6.44359i		−	0.342958i	−0.985188	−	0.171479i	$-0.945146\pi$
$353$		−	6.44359i		−	0.342958i	0.985188	−	0.171479i	$-0.0548545\pi$
$354$		0			0
$355$	−24.5715			−1.30412
$356$	−2.64581	−	19.7757i	−0.140228	−	1.04811i
$357$		0			0
$358$	0.230548	+	3.46174i	0.0121848	+	0.182959i
$359$			30.0663i			1.58684i	0.608674	+	0.793420i	$0.291702\pi$
$359$			30.0663i			1.58684i	−0.608674	+	0.793420i	$0.708298\pi$
$360$		0			0
$361$	4.50792			0.237259
$362$	2.02671	+	30.4316i	0.106522	+	1.59945i
$363$		0			0
$364$	−4.74378	+	4.87818i	−0.248642	+	0.255686i
$365$	−42.9843			−2.24990
$366$		0			0
$367$	4.55113			0.237567			0.118784	−	0.992920i	$-0.462101\pi$
$367$	4.55113			0.237567			0.118784	+	0.992920i	$0.462101\pi$
$368$	−8.46039	−	31.0519i	−0.441028	−	1.61869i
$369$		0			0
$370$	1.84215	+	27.6604i	0.0957687	+	1.43799i
$371$	−9.06786	−	11.5315i	−0.470780	−	0.598687i
$372$		0			0
$373$	1.81383			0.0939164			0.0469582	−	0.998897i	$-0.485047\pi$
$373$	1.81383			0.0939164			0.0469582	+	0.998897i	$0.485047\pi$
$374$	17.0524	−	1.13567i	0.881757	−	0.0587240i
$375$		0			0
$376$	−3.35649	+	0.678654i	−0.173098	+	0.0349989i
$377$		−	3.31083i		−	0.170517i
$378$		0			0
$379$		−	33.5629i		−	1.72401i	−0.506900	−	0.862005i	$-0.669209\pi$
$379$		−	33.5629i		−	1.72401i	0.506900	−	0.862005i	$-0.330791\pi$
$380$	−3.75176	−	28.0419i	−0.192461	−	1.43852i
$381$		0			0
$382$	−0.0309808	−	0.465184i	−0.00158511	−	0.0238009i
$383$	25.6725			1.31180			0.655902	−	0.754846i	$-0.272288\pi$
$383$	25.6725			1.31180			0.655902	+	0.754846i	$0.272288\pi$
$384$		0			0
$385$	−11.4849	−	14.6053i	−0.585326	−	0.744356i
$386$	−22.5123	+	1.49930i	−1.14585	+	0.0763122i
$387$		0			0
$388$	3.13454	+	23.4286i	0.159132	+	1.18941i
$389$	14.5542			0.737929			0.368964	−	0.929443i	$-0.379712\pi$
$389$	14.5542			0.737929			0.368964	+	0.929443i	$0.379712\pi$
$390$		0			0
$391$	40.3955			2.04289
$392$	0.763378	−	19.7843i	0.0385564	−	0.999256i
$393$		0			0
$394$	−4.47224	+	0.297846i	−0.225308	+	0.0150053i
$395$	10.3059			0.518546
$396$		0			0
$397$		−	6.27138i		−	0.314752i	−0.987539	−	0.157376i	$-0.949697\pi$
$397$		−	6.27138i		−	0.314752i	0.987539	−	0.157376i	$-0.0503034\pi$
$398$	−38.1351	+	2.53975i	−1.91154	+	0.127306i
$399$		0			0
$400$	−13.5550	+	3.69318i	−0.677748	+	0.184659i
$401$	22.8730			1.14222			0.571111	−	0.820873i	$-0.306513\pi$
$401$	22.8730			1.14222			0.571111	+	0.820873i	$0.306513\pi$
$402$		0			0
$403$			8.15335i			0.406147i
$404$	−0.163048	−	1.21868i	−0.00811195	−	0.0606314i
$405$		0			0
$406$	6.44490	+	7.16029i	0.319855	+	0.355359i
$407$		−	16.1717i		−	0.801603i
$408$		0			0
$409$			18.4324i			0.911424i	0.890127	+	0.455712i	$0.150615\pi$
$409$			18.4324i			0.911424i	−0.890127	+	0.455712i	$0.849385\pi$
$410$	−9.48058	+	0.631396i	−0.468213	+	0.0311824i
$411$		0			0
$412$	−15.6965	+	2.10005i	−0.773309	+	0.103462i
$413$	20.0027	+	25.4373i	0.984269	+	1.25169i
$414$		0			0
$415$		−	30.4642i		−	1.49543i
$416$	−2.37438	−	6.87581i	−0.116414	−	0.337114i
$417$		0			0
$418$	1.09674	+	16.4678i	0.0536433	+	0.805468i
$419$	15.1357			0.739428			0.369714	−	0.929146i	$-0.379456\pi$
$419$	15.1357			0.739428			0.369714	+	0.929146i	$0.379456\pi$
$420$		0			0
$421$	32.8126			1.59919			0.799594	−	0.600541i	$-0.205048\pi$
$421$	32.8126			1.59919			0.799594	+	0.600541i	$0.205048\pi$
$422$	0.105830	+	1.58907i	0.00515174	+	0.0773547i
$423$		0			0
$424$	15.3716	−	3.10801i	0.746510	−	0.150938i
$425$		−	17.6337i		−	0.855359i
$426$		0			0
$427$	−18.6262	+	14.6468i	−0.901387	+	0.708809i
$428$	−2.03601	−	15.2178i	−0.0984141	−	0.735580i
$429$		0			0
$430$	−40.3251	+	2.68561i	−1.94465	+	0.129512i
$431$		−	4.81399i		−	0.231882i	−0.993256	−	0.115941i	$-0.963012\pi$
$431$		−	4.81399i		−	0.231882i	0.993256	−	0.115941i	$-0.0369883\pi$
$432$		0			0
$433$		−	28.8325i		−	1.38560i	−0.721129	−	0.692801i	$-0.756377\pi$
$433$		−	28.8325i		−	1.38560i	0.721129	−	0.692801i	$-0.243623\pi$
$434$	−15.8714	−	17.6331i	−0.761851	−	0.846417i
$435$		0			0
$436$	−13.3186	+	1.78191i	−0.637845	+	0.0853381i
$437$			39.0108i			1.86614i
$438$		0			0
$439$	−23.0795			−1.10152			−0.550762	−	0.834663i	$-0.685663\pi$
$439$	−23.0795			−1.10152			−0.550762	+	0.834663i	$0.685663\pi$
$440$	19.4690	−	3.93646i	0.928146	−	0.187663i
$441$		0			0
$442$	9.11006	−	0.606720i	0.433321	−	0.0288587i
$443$			28.7475i			1.36583i	0.730496	+	0.682916i	$0.239289\pi$
$443$			28.7475i			1.36583i	−0.730496	+	0.682916i	$0.760711\pi$
$444$		0			0
$445$	29.1056			1.37974
$446$	3.93685	−	0.262190i	0.186415	−	0.0124150i
$447$		0			0
$448$	18.5196	+	10.2482i	0.874967	+	0.484182i
$449$	35.0643			1.65479			0.827394	−	0.561622i	$-0.189822\pi$
$449$	35.0643			1.65479			0.827394	+	0.561622i	$0.189822\pi$
$450$		0			0
$451$	5.54286			0.261003
$452$	6.45605	−	0.863763i	0.303667	−	0.0406280i
$453$		0			0
$454$	7.08393	−	0.471782i	0.332465	−	0.0221418i
$455$	−6.13571	−	7.80274i	−0.287647	−	0.365798i
$456$		0			0
$457$	17.1646			0.802926			0.401463	−	0.915875i	$-0.368502\pi$
$457$	17.1646			0.802926			0.401463	+	0.915875i	$0.368502\pi$
$458$	0.105980	+	1.59132i	0.00495211	+	0.0743573i
$459$		0			0
$460$	46.5349	−	6.22595i	2.16970	−	0.290287i
$461$			34.9394i			1.62729i	0.581363	+	0.813644i	$0.302520\pi$
$461$			34.9394i			1.62729i	−0.581363	+	0.813644i	$0.697480\pi$
$462$		0			0
$463$		−	12.1288i		−	0.563674i	−0.959462	−	0.281837i	$-0.909056\pi$
$463$		−	12.1288i		−	0.563674i	0.959462	−	0.281837i	$-0.0909438\pi$
$464$	−9.93655	+	2.70731i	−0.461293	+	0.125684i
$465$		0			0
$466$	5.85679	−	0.390056i	0.271310	−	0.0180690i
$467$	−21.7143			−1.00482			−0.502409	−	0.864630i	$-0.667553\pi$
$467$	−21.7143			−1.00482			−0.502409	+	0.864630i	$0.667553\pi$
$468$		0			0
$469$	−15.2309	+	11.9769i	−0.703298	+	0.553041i
$470$	−0.331959	−	4.98445i	−0.0153121	−	0.229916i
$471$		0			0
$472$	−33.9081	+	6.85593i	−1.56074	+	0.315570i
$473$	23.5762			1.08404
$474$		0			0
$475$	17.0292			0.781355
$476$	−18.5211	+	19.0459i	−0.848915	+	0.872967i
$477$		0			0
$478$	1.40004	+	21.0219i	0.0640363	+	0.961521i
$479$	−13.2107			−0.603613			−0.301806	−	0.953369i	$-0.597590\pi$
$479$	−13.2107			−0.603613			−0.301806	+	0.953369i	$0.597590\pi$
$480$		0			0
$481$		−	8.63959i		−	0.393931i
$482$	2.28327	+	34.2839i	0.104000	+	1.56159i
$483$		0			0
$484$	10.3208	−	1.38083i	0.469126	−	0.0627649i
$485$	−34.4819			−1.56574
$486$		0			0
$487$		−	13.3925i		−	0.606871i	−0.952852	−	0.303436i	$-0.901866\pi$
$487$		−	13.3925i		−	0.606871i	0.952852	−	0.303436i	$-0.0981337\pi$
$488$	−5.02019	−	24.8289i	−0.227253	−	1.12395i
$489$		0			0
$490$	28.4585	+	4.93103i	1.28562	+	0.222761i
$491$		−	17.7604i		−	0.801515i	−0.916184	−	0.400758i	$-0.868747\pi$
$491$		−	17.7604i		−	0.801515i	0.916184	−	0.400758i	$-0.131253\pi$
$492$		0			0
$493$		−	12.9265i		−	0.582179i
$494$	0.585922	+	8.79778i	0.0263619	+	0.395831i
$495$		0			0
$496$	24.4700	−	6.66709i	1.09874	−	0.299361i
$497$	−17.5155	+	13.7733i	−0.785675	+	0.617818i
$498$		0			0
$499$			26.4052i			1.18206i	0.806651	+	0.591029i	$0.201278\pi$
$499$			26.4052i			1.18206i	−0.806651	+	0.591029i	$0.798722\pi$
$500$	1.15120	+	8.60448i	0.0514834	+	0.384804i
$501$		0			0
$502$	31.8586	−	2.12175i	1.42192	−	0.0946982i
$503$	−4.30590			−0.191991			−0.0959954	−	0.995382i	$-0.530603\pi$
$503$	−4.30590			−0.191991			−0.0959954	+	0.995382i	$0.530603\pi$
$504$		0			0
$505$	1.79363			0.0798157
$506$	−27.3280	+	1.82001i	−1.21488	+	0.0809095i
$507$		0			0
$508$	3.43691	+	25.6886i	0.152488	+	1.13975i
$509$		−	5.30102i		−	0.234964i	−0.993075	−	0.117482i	$-0.962518\pi$
$509$		−	5.30102i		−	0.234964i	0.993075	−	0.117482i	$-0.0374822\pi$
$510$		0			0
$511$	−30.6408	+	24.0945i	−1.35547	+	1.06588i
$512$	−18.6943	+	12.7485i	−0.826178	+	0.563409i
$513$		0			0
$514$	−0.809911	−	12.1610i	−0.0357236	−	0.536400i
$515$		−	23.1018i		−	1.01799i
$516$		0			0
$517$			2.91418i			0.128165i
$518$	16.8179	+	18.6847i	0.738937	+	0.820959i
$519$		0			0
$520$	10.4011	−	2.10301i	0.456118	−	0.0922233i
$521$		−	22.7952i		−	0.998674i	−0.866408	−	0.499337i	$-0.833577\pi$
$521$		−	22.7952i		−	0.998674i	0.866408	−	0.499337i	$-0.166423\pi$
$522$		0			0
$523$	5.25087			0.229605			0.114802	−	0.993388i	$-0.463377\pi$
$523$	5.25087			0.229605			0.114802	+	0.993388i	$0.463377\pi$
$524$	38.8089	−	5.19228i	1.69537	−	0.226826i
$525$		0			0
$526$	−2.26525	−	34.0133i	−0.0987696	−	1.48305i
$527$			31.8331i			1.38667i
$528$		0			0
$529$	−41.7376			−1.81468
$530$	1.52026	+	22.8271i	0.0660359	+	0.991546i
$531$		0			0
$532$	−18.3930	−	17.8863i	−0.797439	−	0.775468i
$533$	2.96122			0.128265
$534$		0			0
$535$	22.3974			0.968323
$536$	−4.10507	−	20.3029i	−0.177312	−	0.876950i
$537$		0			0
$538$	−1.05161	−	15.7902i	−0.0453381	−	0.680764i
$539$	−16.3738	−	3.97342i	−0.705268	−	0.171147i
$540$		0			0
$541$	31.0607			1.33540			0.667702	−	0.744428i	$-0.267278\pi$
$541$	31.0607			1.33540			0.667702	+	0.744428i	$0.267278\pi$
$542$	25.9994	−	1.73153i	1.11677	−	0.0743756i
$543$		0			0
$544$	−9.27030	−	26.8452i	−0.397461	−	1.15098i
$545$		−	19.6022i		−	0.839664i
$546$		0			0
$547$		−	25.3068i		−	1.08204i	−0.841009	−	0.541020i	$-0.818038\pi$
$547$		−	25.3068i		−	1.08204i	0.841009	−	0.541020i	$-0.181962\pi$
$548$	36.5282	−	4.88715i	1.56041	−	0.208769i
$549$		0			0
$550$	0.794482	+	11.9294i	0.0338768	+	0.508670i
$551$	12.4834			0.531810
$552$		0			0
$553$	7.34642	−	5.77688i	0.312402	−	0.245658i
$554$	2.98518	−	0.198810i	0.126828	−	0.00844662i
$555$		0			0
$556$	−20.4051	+	2.73002i	−0.865368	+	0.115779i
$557$	−36.4584			−1.54479			−0.772397	−	0.635140i	$-0.780942\pi$
$557$	−36.4584			−1.54479			−0.772397	+	0.635140i	$0.780942\pi$
$558$		0			0
$559$	12.5954			0.532727
$560$	−18.4005	+	24.7950i	−0.777565	+	1.04778i
$561$		0			0
$562$	−12.7432	+	0.848681i	−0.537538	+	0.0357995i
$563$	13.5989			0.573125			0.286563	−	0.958061i	$-0.407487\pi$
$563$	13.5989			0.573125			0.286563	+	0.958061i	$0.407487\pi$
$564$		0			0
$565$			9.50194i			0.399750i
$566$	−35.1881	+	2.34349i	−1.47907	+	0.0985041i
$567$		0			0
$568$	−4.72081	−	23.3482i	−0.198081	−	0.979668i
$569$	15.7437			0.660011			0.330006	−	0.943979i	$-0.392949\pi$
$569$	15.7437			0.660011			0.330006	+	0.943979i	$0.392949\pi$
$570$		0			0
$571$			12.8845i			0.539199i	0.962973	+	0.269599i	$0.0868912\pi$
$571$			12.8845i			0.539199i	−0.962973	+	0.269599i	$0.913109\pi$
$572$	−6.13571	+	0.820904i	−0.256547	+	0.0343237i
$573$		0			0
$574$	−6.40418	+	5.76434i	−0.267305	+	0.240599i
$575$			28.2596i			1.17851i
$576$		0			0
$577$		−	5.59877i		−	0.233080i	−0.993186	−	0.116540i	$-0.962820\pi$
$577$		−	5.59877i		−	0.233080i	0.993186	−	0.116540i	$-0.0371803\pi$
$578$	11.5799	−	0.771208i	0.481660	−	0.0320780i
$579$		0			0
$580$	−1.99229	−	14.8911i	−0.0827254	−	0.618317i
$581$	−17.0765	−	21.7160i	−0.708451	−	0.900933i
$582$		0			0
$583$		−	13.3460i		−	0.552733i
$584$	−8.25838	−	40.8443i	−0.341734	−	1.69015i
$585$		0			0
$586$	−0.465687	−	6.99242i	−0.0192374	−	0.288854i
$587$	22.6725			0.935795			0.467898	−	0.883783i	$-0.345012\pi$
$587$	22.6725			0.935795			0.467898	+	0.883783i	$0.345012\pi$
$588$		0			0
$589$	−30.7419			−1.26670
$590$	−3.35353	−	50.3541i	−0.138063	−	2.07305i
$591$		0			0
$592$	−25.9293	+	7.06469i	−1.06569	+	0.290357i
$593$			0.749311i			0.0307705i	0.999882	+	0.0153852i	$0.00489747\pi$
$593$			0.749311i			0.0307705i	−0.999882	+	0.0153852i	$0.995103\pi$
$594$		0			0
$595$	−23.9557	−	30.4642i	−0.982086	−	1.24891i
$596$	29.0317	−	3.88418i	1.18918	−	0.159102i
$597$		0			0
$598$	−14.5997	+	0.972324i	−0.597027	+	0.0397613i
$599$		−	17.9701i		−	0.734237i	−0.930174	−	0.367118i	$-0.880344\pi$
$599$		−	17.9701i		−	0.734237i	0.930174	−	0.367118i	$-0.119656\pi$
$600$		0			0
$601$		−	8.11913i		−	0.331186i	−0.986194	−	0.165593i	$-0.947046\pi$
$601$		−	8.11913i		−	0.331186i	0.986194	−	0.165593i	$-0.0529538\pi$
$602$	−27.2398	+	24.5183i	−1.11021	+	0.999291i
$603$		0			0
$604$	−3.71828	−	27.7917i	−0.151295	−	1.13083i
$605$			15.1900i			0.617561i
$606$		0			0
$607$	15.4587			0.627449			0.313724	−	0.949514i	$-0.398423\pi$
$607$	15.4587			0.627449			0.313724	+	0.949514i	$0.398423\pi$
$608$	25.9250	−	8.95253i	1.05140	−	0.363073i
$609$		0			0
$610$	36.8714	−	2.45559i	1.49288	−	0.0994241i
$611$			1.55687i			0.0629843i
$612$		0			0
$613$	2.00000			0.0807792			0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000			0.0807792			0.0403896	+	0.999184i	$0.487140\pi$
$614$	−28.9142	+	1.92565i	−1.16688	+	0.0777131i
$615$		0			0
$616$	11.6716	−	13.7192i	0.470263	−	0.552762i
$617$	−9.96087			−0.401009			−0.200505	−	0.979693i	$-0.564258\pi$
$617$	−9.96087			−0.401009			−0.200505	+	0.979693i	$0.564258\pi$
$618$		0			0
$619$	16.1653			0.649739			0.324869	−	0.945759i	$-0.394680\pi$
$619$	16.1653			0.649739			0.324869	+	0.945759i	$0.394680\pi$
$620$	4.90627	+	36.6711i	0.197041	+	1.47275i
$621$		0			0
$622$	10.8570	−	0.723067i	0.435328	−	0.0289923i
$623$	20.7475	−	16.3149i	0.831232	−	0.653642i
$624$		0			0
$625$	−30.2253			−1.20901
$626$	1.86793	+	28.0475i	0.0746576	+	1.12100i
$627$		0			0
$628$	−0.0419556	−	0.313590i	−0.00167421	−	0.0125136i
$629$		−	33.7315i		−	1.34496i
$630$		0			0
$631$			10.7815i			0.429203i	0.976702	+	0.214602i	$0.0688453\pi$
$631$			10.7815i			0.429203i	−0.976702	+	0.214602i	$0.931155\pi$
$632$	1.98003	+	9.79282i	0.0787612	+	0.389537i
$633$		0			0
$634$	28.7959	−	1.91777i	1.14363	−	0.0761646i
$635$	−37.8082			−1.50037
$636$		0			0
$637$	−8.74752	−	2.12276i	−0.346589	−	0.0841068i
$638$	0.582400	+	8.74490i	0.0230575	+	0.346214i
$639$		0			0
$640$	−14.8167	−	29.4964i	−0.585682	−	1.16595i
$641$	8.70174			0.343698			0.171849	−	0.985123i	$-0.445026\pi$
$641$	8.70174			0.343698			0.171849	+	0.985123i	$0.445026\pi$
$642$		0			0
$643$	−5.75116			−0.226803			−0.113402	−	0.993549i	$-0.536175\pi$
$643$	−5.75116			−0.226803			−0.113402	+	0.993549i	$0.536175\pi$
$644$	29.6818	−	30.5228i	1.16963	−	1.20277i
$645$		0			0
$646$	2.28762	+	34.3492i	0.0900051	+	1.35145i
$647$	9.55700			0.375724			0.187862	−	0.982195i	$-0.439844\pi$
$647$	9.55700			0.375724			0.187862	+	0.982195i	$0.439844\pi$
$648$		0			0
$649$			29.4397i			1.15561i
$650$	0.424444	+	6.37315i	0.0166481	+	0.249975i
$651$		0			0
$652$	1.76363	+	13.1820i	0.0690692	+	0.516247i
$653$	21.4789			0.840533			0.420267	−	0.907401i	$-0.361937\pi$
$653$	21.4789			0.840533			0.420267	+	0.907401i	$0.361937\pi$
$654$		0			0
$655$			57.1184i			2.23180i
$656$	−2.42142	−	8.88728i	−0.0945407	−	0.346990i
$657$		0			0
$658$	−3.03062	−	3.36702i	−0.118146	−	0.131260i
$659$			1.35908i			0.0529421i	0.999650	+	0.0264710i	$0.00842698\pi$
$659$			1.35908i			0.0529421i	−0.999650	+	0.0264710i	$0.991573\pi$
$660$		0			0
$661$		−	1.78646i		−	0.0694851i	−0.999396	−	0.0347426i	$-0.988939\pi$
$661$		−	1.78646i		−	0.0694851i	0.999396	−	0.0347426i	$-0.0110611\pi$
$662$	−1.78381	−	26.7843i	−0.0693296	−	1.04100i
$663$		0			0
$664$	28.9476	−	5.85296i	1.12338	−	0.227139i
$665$	29.4200	−	23.1345i	1.14086	−	0.897117i
$666$		0			0
$667$			20.7159i			0.802122i
$668$	−8.15835	+	1.09151i	−0.315656	+	0.0422320i
$669$		0			0
$670$	30.1502	−	2.00797i	1.16480	−	0.0775746i
$671$	−21.5570			−0.832199
$672$		0			0
$673$	17.1646			0.661647			0.330823	−	0.943693i	$-0.392674\pi$
$673$	17.1646			0.661647			0.330823	+	0.943693i	$0.392674\pi$
$674$	35.9637	−	2.39514i	1.38527	−	0.0922573i
$675$		0			0
$676$	22.4924	−	3.00929i	0.865094	−	0.115742i
$677$			4.28166i			0.164557i	0.996609	+	0.0822787i	$0.0262198\pi$
$677$			4.28166i			0.164557i	−0.996609	+	0.0822787i	$0.973780\pi$
$678$		0			0
$679$	−24.5800	+	19.3285i	−0.943293	+	0.741762i
$680$	40.6090	−	8.21080i	1.55728	−	0.314870i
$681$		0			0
$682$	−1.43424	−	21.5354i	−0.0549197	−	0.824634i
$683$			22.0539i			0.843870i	0.906626	+	0.421935i	$0.138649\pi$
$683$			22.0539i			0.843870i	−0.906626	+	0.421935i	$0.861351\pi$
$684$		0			0
$685$			53.7618i			2.05413i
$686$	23.0503	−	12.4372i	0.880065	−	0.474853i
$687$		0			0
$688$	−10.2994	−	37.8015i	−0.392660	−	1.44117i
$689$		−	7.12995i		−	0.271629i
$690$		0			0
$691$	−7.60142			−0.289172			−0.144586	−	0.989492i	$-0.546185\pi$
$691$	−7.60142			−0.289172			−0.144586	+	0.989492i	$0.546185\pi$
$692$	2.60605	+	19.4785i	0.0990671	+	0.740460i
$693$		0			0
$694$	−0.990952	−	14.8794i	−0.0376160	−	0.564814i
$695$		−	30.0320i		−	1.13918i
$696$		0			0
$697$	11.5615			0.437922
$698$	−3.24821	−	48.7728i	−0.122947	−	1.84608i
$699$		0			0
$700$	−13.3240	−	12.9569i	−0.503599	−	0.489724i
$701$	5.13174			0.193823			0.0969116	−	0.995293i	$-0.469104\pi$
$701$	5.13174			0.193823			0.0969116	+	0.995293i	$0.469104\pi$
$702$		0			0
$703$	32.5753			1.22860
$704$	7.48096	+	17.7434i	0.281949	+	0.668729i
$705$		0			0
$706$	0.605548	+	9.09247i	0.0227901	+	0.342199i
$707$	1.27857	−	1.00541i	0.0480855	−	0.0378122i
$708$		0			0
$709$	−28.2756			−1.06191			−0.530957	−	0.847399i	$-0.678167\pi$
$709$	−28.2756			−1.06191			−0.530957	+	0.847399i	$0.678167\pi$
$710$	34.6725	−	2.30915i	1.30124	−	0.0866609i
$711$		0			0
$712$	5.59192	+	27.6565i	0.209566	+	1.03647i
$713$		−	51.0155i		−	1.91055i
$714$		0			0
$715$		−	9.03047i		−	0.337720i
$716$	−0.650646	−	4.86315i	−0.0243158	−	0.181744i
$717$		0			0
$718$	−2.82554	−	42.4262i	−0.105448	−	1.58333i
$719$	−19.6725			−0.733661			−0.366831	−	0.930288i	$-0.619557\pi$
$719$	−19.6725			−0.733661			−0.366831	+	0.930288i	$0.619557\pi$
$720$		0			0
$721$	−12.9495	−	16.4678i	−0.482266	−	0.613294i
$722$	−6.36108	+	0.423640i	−0.236735	+	0.0157663i
$723$		0			0
$724$	−5.71974	−	42.7512i	−0.212572	−	1.58884i
$725$	9.04301			0.335849
$726$		0			0
$727$	0.895551			0.0332142			0.0166071	−	0.999862i	$-0.494714\pi$
$727$	0.895551			0.0332142			0.0166071	+	0.999862i	$0.494714\pi$
$728$	6.23545	−	7.32935i	0.231101	−	0.271644i
$729$		0			0
$730$	60.6546	−	4.03953i	2.24493	−	0.149510i
$731$	49.1761			1.81884
$732$		0			0
$733$			6.22595i			0.229961i	0.993368	+	0.114980i	$0.0366805\pi$
$733$			6.22595i			0.229961i	−0.993368	+	0.114980i	$0.963319\pi$
$734$	−6.42205	+	0.427701i	−0.237042	+	0.0157867i
$735$		0			0
$736$	14.8565	+	43.0219i	0.547619	+	1.58581i
$737$	−17.6274			−0.649314
$738$		0			0
$739$		−	2.85866i		−	0.105158i	−0.998617	−	0.0525788i	$-0.983256\pi$
$739$		−	2.85866i		−	0.105158i	0.998617	−	0.0525788i	$-0.0167441\pi$
$740$	−5.19887	−	38.8581i	−0.191114	−	1.42845i
$741$		0			0
$742$	13.8792	+	15.4198i	0.509523	+	0.566080i
$743$			15.8280i			0.580672i	0.956925	+	0.290336i	$0.0937671\pi$
$743$			15.8280i			0.580672i	−0.956925	+	0.290336i	$0.906233\pi$
$744$		0			0
$745$			42.7285i			1.56545i
$746$	−2.55947	+	0.170458i	−0.0937088	+	0.00624090i
$747$		0			0
$748$	−23.9557	+	3.20506i	−0.875906	+	0.117188i
$749$	15.9657	−	12.5547i	0.583373	−	0.458737i
$750$		0			0
$751$		−	50.6346i		−	1.84768i	−0.382773	−	0.923842i	$-0.625031\pi$
$751$		−	50.6346i		−	1.84768i	0.382773	−	0.923842i	$-0.374969\pi$
$752$	4.67252	−	1.27307i	0.170389	−	0.0464242i
$753$		0			0
$754$	0.311142	+	4.67188i	0.0113311	+	0.170140i
$755$	40.9034			1.48863
$756$		0			0
$757$	−37.1804			−1.35135			−0.675673	−	0.737201i	$-0.736147\pi$
$757$	−37.1804			−1.35135			−0.675673	+	0.737201i	$0.736147\pi$
$758$	3.15413	+	47.3602i	0.114563	+	1.72020i
$759$		0			0
$760$	7.92935	+	39.2170i	0.287628	+	1.42255i
$761$		−	34.3898i		−	1.24663i	−0.781970	−	0.623315i	$-0.785785\pi$
$761$		−	34.3898i		−	1.24663i	0.781970	−	0.623315i	$-0.214215\pi$
$762$		0			0
$763$	−10.9878	−	13.9731i	−0.397786	−	0.505861i
$764$	0.0874331	+	0.653504i	0.00316322	+	0.0236430i
$765$		0			0
$766$	−36.2262	+	2.41262i	−1.30890	+	0.0871716i
$767$			15.7279i			0.567901i
$768$		0			0
$769$			32.6448i			1.17720i	0.808424	+	0.588601i	$0.200321\pi$
$769$			32.6448i			1.17720i	−0.808424	+	0.588601i	$0.799679\pi$
$770$	17.5788	+	19.5301i	0.633496	+	0.703814i
$771$		0			0
$772$	31.6260	−	4.23128i	1.13824	−	0.152287i
$773$		−	39.6845i		−	1.42735i	−0.700475	−	0.713677i	$-0.747029\pi$
$773$		−	39.6845i		−	1.42735i	0.700475	−	0.713677i	$-0.252971\pi$
$774$		0			0
$775$	−22.2696			−0.799946
$776$	−6.62486	−	32.7652i	−0.237819	−	1.17620i
$777$		0			0
$778$	−20.5373	+	1.36776i	−0.736298	+	0.0490366i
$779$			11.1652i			0.400034i
$780$		0			0
$781$	−20.2714			−0.725369
$782$	−57.0016	+	3.79625i	−2.03837	+	0.135753i
$783$		0			0
$784$	0.782071	+	27.9891i	0.0279311	+	0.999610i
$785$	0.461538			0.0164730
$786$		0			0
$787$	−22.0860			−0.787282			−0.393641	−	0.919264i	$-0.628785\pi$
$787$	−22.0860			−0.787282			−0.393641	+	0.919264i	$0.628785\pi$
$788$	6.28273	−	0.840574i	0.223813	−	0.0299442i
$789$		0			0
$790$	−14.5425	+	0.968516i	−0.517400	+	0.0344583i
$791$	5.32623	+	6.77333i	0.189379	+	0.240832i
$792$		0			0
$793$	−11.5166			−0.408967
$794$	0.589365	+	8.84947i	0.0209158	+	0.314056i
$795$		0			0
$796$	53.5733	−	7.16763i	1.89885	−	0.254050i
$797$			35.9370i			1.27295i	0.771296	+	0.636477i	$0.219609\pi$
$797$			35.9370i			1.27295i	−0.771296	+	0.636477i	$0.780391\pi$
$798$		0			0
$799$			6.07849i			0.215042i
$800$	18.7802	−	6.48525i	0.663979	−	0.229288i
$801$		0			0
$802$	−32.2758	+	2.14953i	−1.13970	+	0.0759026i
$803$	−35.4619			−1.25142
$804$		0			0
$805$	38.3912	+	48.8218i	1.35311	+	1.72074i
$806$	−0.766226	−	11.5051i	−0.0269892	−	0.405249i
$807$		0			0
$808$	0.344603	+	1.70434i	0.0121231	+	0.0599584i
$809$	32.2780			1.13483			0.567417	−	0.823431i	$-0.307943\pi$
$809$	32.2780			1.13483			0.567417	+	0.823431i	$0.307943\pi$
$810$		0			0
$811$	33.7682			1.18576			0.592881	−	0.805290i	$-0.297990\pi$
$811$	33.7682			1.18576			0.592881	+	0.805290i	$0.297990\pi$
$812$	−9.76723	−	9.49812i	−0.342762	−	0.333319i
$813$		0			0
$814$	1.51977	+	22.8197i	0.0532679	+	0.799831i
$815$	−19.4011			−0.679591
$816$		0			0
$817$			47.4904i			1.66148i
$818$	−1.73222	−	26.0097i	−0.0605656	−	0.909409i
$819$		0			0
$820$	13.3186	−	1.78191i	0.465106	−	0.0622270i
$821$	4.46728			0.155909			0.0779547	−	0.996957i	$-0.475161\pi$
$821$	4.46728			0.155909			0.0779547	+	0.996957i	$0.475161\pi$
$822$		0			0
$823$		−	52.2387i		−	1.82093i	−0.413590	−	0.910463i	$-0.635725\pi$
$823$		−	52.2387i		−	1.82093i	0.413590	−	0.910463i	$-0.364275\pi$
$824$	21.9517	−	4.43845i	0.764724	−	0.154621i
$825$		0			0
$826$	−30.6161	−	34.0145i	−1.06527	−	1.18352i
$827$		−	9.64827i		−	0.335503i	−0.985829	−	0.167752i	$-0.946349\pi$
$827$		−	9.64827i		−	0.335503i	0.985829	−	0.167752i	$-0.0536506\pi$
$828$		0			0
$829$			36.3958i			1.26408i	0.774936	+	0.632040i	$0.217782\pi$
$829$			36.3958i			1.26408i	−0.774936	+	0.632040i	$0.782218\pi$
$830$	2.86293	+	42.9877i	0.0993739	+	1.49213i
$831$		0			0
$832$	3.99663	+	9.47923i	0.138558	+	0.328633i
$833$	−34.1529	−	8.28789i	−1.18333	−	0.287158i
$834$		0			0
$835$		−	12.0074i		−	0.415532i
$836$	−3.09519	−	23.1345i	−0.107049	−	0.800123i
$837$		0			0
$838$	−21.3578	+	1.42241i	−0.737794	+	0.0491362i
$839$	31.9439			1.10283			0.551414	−	0.834232i	$-0.314089\pi$
$839$	31.9439			1.10283			0.551414	+	0.834232i	$0.314089\pi$
$840$		0			0
$841$	−22.3710			−0.771413
$842$	−46.3014	+	3.08362i	−1.59565	+	0.106269i
$843$		0			0
$844$	−0.298671	−	2.23237i	−0.0102807	−	0.0768414i
$845$			33.1041i			1.13882i
$846$		0			0
$847$	8.51461	+	10.8280i	0.292566	+	0.372054i
$848$	−21.3986	+	5.83024i	−0.734830	+	0.200211i
$849$		0			0
$850$	1.65716	+	24.8827i	0.0568400	+	0.853468i
$851$			54.0579i			1.85308i
$852$		0			0
$853$		−	25.8116i		−	0.883772i	−0.897071	−	0.441886i	$-0.854310\pi$
$853$		−	25.8116i		−	0.883772i	0.897071	−	0.441886i	$-0.145690\pi$
$854$	24.9068	−	22.4184i	0.852293	−	0.767141i
$855$		0			0
$856$	4.30311	+	21.2823i	0.147077	+	0.727415i
$857$			11.8918i			0.406217i	0.979156	+	0.203109i	$0.0651045\pi$
$857$			11.8918i			0.406217i	−0.979156	+	0.203109i	$0.934896\pi$
$858$		0			0
$859$	−30.2839			−1.03327			−0.516637	−	0.856205i	$-0.672816\pi$
$859$	−30.2839			−1.03327			−0.516637	+	0.856205i	$0.672816\pi$
$860$	56.6499	−	7.57926i	1.93175	−	0.258450i
$861$		0			0
$862$	0.452404	+	6.79297i	0.0154089	+	0.231369i
$863$		−	56.2350i		−	1.91426i	−0.289658	−	0.957130i	$-0.593541\pi$
$863$		−	56.2350i		−	1.91426i	0.289658	−	0.957130i	$-0.406459\pi$
$864$		0			0
$865$	−28.6682			−0.974747
$866$	2.70959	+	40.6852i	0.0920755	+	1.38254i
$867$		0			0
$868$	24.0530	+	23.3903i	0.816413	+	0.793920i
$869$	8.50235			0.288422
$870$		0			0
$871$	−9.41727			−0.319092
$872$	18.6262	−	3.76607i	0.630764	−	0.127535i
$873$		0			0
$874$	−3.66612	−	55.0477i	−0.124008	−	1.86202i
$875$	−9.02734	+	7.09867i	−0.305180	+	0.239979i
$876$		0			0
$877$	−47.5932			−1.60711			−0.803554	−	0.595232i	$-0.797060\pi$
$877$	−47.5932			−1.60711			−0.803554	+	0.595232i	$0.797060\pi$
$878$	32.5672	−	2.16894i	1.09909	−	0.0731981i
$879$		0			0
$880$	−27.1025	+	7.38432i	−0.913624	+	0.248925i
$881$			54.1981i			1.82598i	0.407980	+	0.912991i	$0.366233\pi$
$881$			54.1981i			1.82598i	−0.407980	+	0.912991i	$0.633767\pi$
$882$		0			0
$883$			45.0923i			1.51748i	0.651395	+	0.758739i	$0.274184\pi$
$883$			45.0923i			1.51748i	−0.651395	+	0.758739i	$0.725816\pi$
$884$	−12.7981	+	1.71227i	−0.430446	+	0.0575899i
$885$		0			0
$886$	−2.70160	−	40.5652i	−0.0907619	−	1.36281i
$887$	−44.4058			−1.49100			−0.745500	−	0.666506i	$-0.767789\pi$
$887$	−44.4058			−1.49100			−0.745500	+	0.666506i	$0.767789\pi$
$888$		0			0
$889$	−26.9511	+	21.1931i	−0.903911	+	0.710793i
$890$	−41.0705	+	2.73525i	−1.37669	+	0.0916858i
$891$		0			0
$892$	−5.53060	+	0.739945i	−0.185178	+	0.0247752i
$893$	−5.87013			−0.196436
$894$		0			0
$895$	7.15752			0.239250
$896$	−27.0958	−	12.7207i	−0.905208	−	0.424969i
$897$		0			0
$898$	−49.4788	+	3.29524i	−1.65113	+	0.109963i
$899$	−16.3248			−0.544464
$900$		0			0
$901$		−	27.8375i		−	0.927400i
$902$	−7.82146	+	0.520901i	−0.260426	+	0.0173441i
$903$		0			0
$904$	−9.02888	+	1.82557i	−0.300296	+	0.0607174i
$905$	62.9207			2.09156
$906$		0			0
$907$		−	47.2418i		−	1.56864i	−0.620357	−	0.784320i	$-0.713012\pi$
$907$		−	47.2418i		−	1.56864i	0.620357	−	0.784320i	$-0.286988\pi$
$908$	−9.95171	+	1.33145i	−0.330259	+	0.0441858i
$909$		0			0
$910$	9.39131	+	10.4337i	0.311319	+	0.345875i
$911$		−	40.2417i		−	1.33327i	−0.745386	−	0.666634i	$-0.767735\pi$
$911$		−	40.2417i		−	1.33327i	0.745386	−	0.666634i	$-0.232265\pi$
$912$		0			0
$913$		−	25.1329i		−	0.831779i
$914$	−24.2208	+	1.61307i	−0.801151	+	0.0533558i
$915$		0			0
$916$	−0.299094	−	2.23553i	−0.00988233	−	0.0738638i
$917$	32.0172	+	40.7161i	1.05730	+	1.34456i
$918$		0			0
$919$			22.6252i			0.746335i	0.927764	+	0.373168i	$0.121728\pi$
$919$			22.6252i			0.746335i	−0.927764	+	0.373168i	$0.878272\pi$
$920$	−65.0797	+	13.1586i	−2.14561	+	0.433825i
$921$		0			0
$922$	−3.28349	−	49.3025i	−0.108136	−	1.62369i
$923$	−10.8298			−0.356468
$924$		0			0
$925$	23.5977			0.775886
$926$	1.13983	+	17.1148i	0.0374571	+	0.562428i
$927$		0			0
$928$	13.7669	−	4.75405i	0.451921	−	0.156059i
$929$		−	16.7562i		−	0.549752i	−0.961480	−	0.274876i	$-0.911363\pi$
$929$		−	16.7562i		−	0.549752i	0.961480	−	0.274876i	$-0.0886368\pi$
$930$		0			0
$931$	8.00380	−	32.9822i	0.262314	−	1.08095i
$932$	−8.22778	+	1.10081i	−0.269510	+	0.0360581i
$933$		0			0
$934$	30.6408	−	2.04064i	1.00260	−	0.0667718i
$935$		−	35.2576i		−	1.15305i
$936$		0			0
$937$			8.34871i			0.272741i	0.990658	+	0.136370i	$0.0435437\pi$
$937$			8.34871i			0.272741i	−0.990658	+	0.136370i	$0.956456\pi$
$938$	20.3666	−	18.3318i	0.664993	−	0.598553i
$939$		0			0
$940$	0.936846	+	7.00230i	0.0305566	+	0.228390i
$941$			17.7578i			0.578889i	0.957195	+	0.289445i	$0.0934706\pi$
$941$			17.7578i			0.578889i	−0.957195	+	0.289445i	$0.906529\pi$
$942$		0			0
$943$	−18.5283			−0.603366
$944$	47.2029	−	12.8609i	1.53632	−	0.418586i
$945$		0			0
$946$	−33.2681	+	2.21562i	−1.08164	+	0.0720360i
$947$		−	30.1863i		−	0.980924i	−0.871463	−	0.490462i	$-0.836828\pi$
$947$		−	30.1863i		−	0.980924i	0.871463	−	0.490462i	$-0.163172\pi$
$948$		0			0
$949$	−18.9452			−0.614987
$950$	−24.0297	+	1.60035i	−0.779627	+	0.0519223i
$951$		0			0
$952$	24.3451	−	28.6160i	0.789028	−	0.927449i
$953$	32.3987			1.04950			0.524748	−	0.851257i	$-0.324159\pi$
$953$	32.3987			1.04950			0.524748	+	0.851257i	$0.324159\pi$
$954$		0			0
$955$	−0.961820			−0.0311238
$956$	−3.95115	−	29.5322i	−0.127789	−	0.955141i
$957$		0			0
$958$	18.6415	−	1.24150i	0.602279	−	0.0401111i
$959$	30.1357	+	38.3234i	0.973133	+	1.23753i
$960$		0			0
$961$	9.20202			0.296839
$962$	0.811921	+	12.1912i	0.0261774	+	0.393061i
$963$		0			0
$964$	−6.44379	−	48.1630i	−0.207540	−	1.55123i
$965$			46.5467i			1.49839i
$966$		0			0
$967$			8.90900i			0.286494i	0.989687	+	0.143247i	$0.0457543\pi$
$967$			8.90900i			0.286494i	−0.989687	+	0.143247i	$0.954246\pi$
$968$	−14.4337	+	2.91838i	−0.463918	+	0.0938004i
$969$		0			0
$970$	48.6570	−	3.24050i	1.56228	−	0.104046i
$971$	13.5238			0.433998			0.216999	−	0.976172i	$-0.430373\pi$
$971$	13.5238			0.433998			0.216999	+	0.976172i	$0.430373\pi$
$972$		0			0
$973$	−16.8342	−	21.4079i	−0.539678	−	0.686305i
$974$	1.25858	+	18.8980i	0.0403276	+	0.605530i
$975$		0			0
$976$	9.41727	+	34.5639i	0.301440	+	1.10636i
$977$	−26.8330			−0.858465			−0.429232	−	0.903194i	$-0.641216\pi$
$977$	−26.8330			−0.858465			−0.429232	+	0.903194i	$0.641216\pi$
$978$		0			0
$979$	24.0120			0.767428
$980$	−40.6209	−	4.28367i	−1.29759	−	0.136837i
$981$		0			0
$982$	1.66907	+	25.0615i	0.0532620	+	0.799744i
$983$	−20.3679			−0.649634			−0.324817	−	0.945777i	$-0.605303\pi$
$983$	−20.3679			−0.649634			−0.324817	+	0.945777i	$0.605303\pi$
$984$		0			0
$985$			9.24685i			0.294629i
$986$	1.21479	+	18.2404i	0.0386868	+	0.580893i
$987$		0			0
$988$	−1.65358	−	12.3594i	−0.0526073	−	0.393204i
$989$	−78.8092			−2.50599
$990$		0			0
$991$			15.9105i			0.505413i	0.967543	+	0.252706i	$0.0813206\pi$
$991$			15.9105i			0.505413i	−0.967543	+	0.252706i	$0.918679\pi$
$992$	−33.9028	+	11.7075i	−1.07642	+	0.371712i
$993$		0			0
$994$	23.4215	−	21.0814i	0.742884	−	0.668662i
$995$			78.8485i			2.49967i
$996$		0			0
$997$			5.88360i			0.186336i	0.995650	+	0.0931678i	$0.0296993\pi$
$997$			5.88360i			0.186336i	−0.995650	+	0.0931678i	$0.970301\pi$
$998$	−2.48147	−	37.2600i	−0.0785497	−	1.17944i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.b.f.55.2	yes	16
3.2	odd	2		756.2.b.e.55.15	yes	16
4.3	odd	2		756.2.b.e.55.1	✓	16
7.6	odd	2		756.2.b.e.55.2	yes	16
12.11	even	2	inner	756.2.b.f.55.16	yes	16
21.20	even	2	inner	756.2.b.f.55.15	yes	16
28.27	even	2	inner	756.2.b.f.55.1	yes	16
84.83	odd	2		756.2.b.e.55.16	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.b.e.55.1	✓	16	4.3	odd	2
756.2.b.e.55.2	yes	16	7.6	odd	2
756.2.b.e.55.15	yes	16	3.2	odd	2
756.2.b.e.55.16	yes	16	84.83	odd	2
756.2.b.f.55.1	yes	16	28.27	even	2	inner
756.2.b.f.55.2	yes	16	1.1	even	1	trivial
756.2.b.f.55.15	yes	16	21.20	even	2	inner
756.2.b.f.55.16	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)

\(f(q)\)	\(=\)	\(q+(-1.41109 + 0.0939769i) q^{2} +(1.98234 - 0.265219i) q^{4} +2.91758i q^{5} +(1.63542 + 2.07976i) q^{7} +(-2.77233 + 0.560541i) q^{8} +O(q^{10})\)	\(q+(-1.41109 + 0.0939769i) q^{2} +(1.98234 - 0.265219i) q^{4} +2.91758i q^{5} +(1.63542 + 2.07976i) q^{7} +(-2.77233 + 0.560541i) q^{8} +(-0.274185 - 4.11696i) q^{10} +2.40700i q^{11} +1.28591i q^{13} +(-2.50318 - 2.78103i) q^{14} +(3.85932 - 1.05151i) q^{16} +5.02059i q^{17} -4.84850 q^{19} +(0.773798 + 5.78362i) q^{20} +(-0.226202 - 3.39648i) q^{22} -8.04597i q^{23} -3.51227 q^{25} +(-0.120846 - 1.81454i) q^{26} +(3.79355 + 3.68903i) q^{28} -2.57469 q^{29} +6.34051 q^{31} +(-5.34702 + 1.84646i) q^{32} +(-0.471820 - 7.08450i) q^{34} +(-6.06786 + 4.77148i) q^{35} -6.71864 q^{37} +(6.84165 - 0.455647i) q^{38} +(-1.63542 - 8.08848i) q^{40} -2.30281i q^{41} -9.79488i q^{43} +(0.638382 + 4.77148i) q^{44} +(0.756135 + 11.3536i) q^{46} +1.21071 q^{47} +(-1.65078 + 6.80257i) q^{49} +(4.95612 - 0.330072i) q^{50} +(0.341049 + 2.54912i) q^{52} -5.54465 q^{53} -7.02260 q^{55} +(-5.69972 - 4.84904i) q^{56} +(3.63312 - 0.241961i) q^{58} +12.2309 q^{59} +8.95597i q^{61} +(-8.94701 + 0.595861i) q^{62} +(7.37159 - 3.10801i) q^{64} -3.75176 q^{65} +7.32341i q^{67} +(1.33156 + 9.95251i) q^{68} +(8.11387 - 7.30321i) q^{70} +8.42187i q^{71} +14.7329i q^{73} +(9.48058 - 0.631396i) q^{74} +(-9.61135 + 1.28591i) q^{76} +(-5.00597 + 3.93646i) q^{77} -3.53235i q^{79} +(3.06786 + 11.2599i) q^{80} +(0.216411 + 3.24947i) q^{82} -10.4416 q^{83} -14.6480 q^{85} +(0.920492 + 13.8214i) q^{86} +(-1.34922 - 6.67298i) q^{88} -9.97593i q^{89} +(-2.67439 + 2.10301i) q^{91} +(-2.13394 - 15.9498i) q^{92} +(-1.70842 + 0.113779i) q^{94} -14.1459i q^{95} +11.8187i q^{97} +(1.69011 - 9.75415i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 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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