LMFDB - Embedded newform 448.2.m.d.113.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(113,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("448.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.m (of order $4$, degree $2$, not 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:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.20138089353117696.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{10} - 2x^{9} + 2x^{8} + 4x^{7} + 2x^{6} + 8x^{5} + 8x^{4} - 16x^{3} - 48x^{2} + 64 $ x^12 - 3x^10 - 2x^9 + 2x^8 + 4x^7 + 2x^6 + 8x^5 + 8x^4 - 16x^3 - 48*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			113.5
Root			$1.37925 + 0.312504i$ of defining polynomial
Character	$\chi$	$=$	448.113
Dual form			448.2.m.d.337.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.599978 - 0.599978i) q^{3} +(0.974969 + 0.974969i) q^{5} -1.00000i q^{7} +2.28005i q^{9} +O(q^{10})$	\(q+(0.599978 - 0.599978i) q^{3} +(0.974969 + 0.974969i) q^{5} -1.00000i q^{7} +2.28005i q^{9} +(1.72409 + 1.72409i) q^{11} +(1.90592 - 1.90592i) q^{13} +1.16992 q^{15} +6.71697 q^{17} +(-2.94908 + 2.94908i) q^{19} +(-0.599978 - 0.599978i) q^{21} -5.29883i q^{23} -3.09887i q^{25} +(3.16792 + 3.16792i) q^{27} +(-3.03004 + 3.03004i) q^{29} -1.19996 q^{31} +2.06883 q^{33} +(0.974969 - 0.974969i) q^{35} +(-2.25002 - 2.25002i) q^{37} -2.28702i q^{39} -3.94994i q^{41} +(7.02292 + 7.02292i) q^{43} +(-2.22298 + 2.22298i) q^{45} +3.06186 q^{47} -1.00000 q^{49} +(4.03004 - 4.03004i) q^{51} +(-3.01877 - 3.01877i) q^{53} +3.36187i q^{55} +3.53876i q^{57} +(-4.96785 - 4.96785i) q^{59} +(-9.69194 + 9.69194i) q^{61} +2.28005 q^{63} +3.71643 q^{65} +(-3.55596 + 3.55596i) q^{67} +(-3.17918 - 3.17918i) q^{69} -11.5771i q^{71} -10.3271i q^{73} +(-1.85925 - 1.85925i) q^{75} +(1.72409 - 1.72409i) q^{77} -4.06883 q^{79} -3.03880 q^{81} +(-9.17886 + 9.17886i) q^{83} +(6.54884 + 6.54884i) q^{85} +3.63591i q^{87} +16.9287i q^{89} +(-1.90592 - 1.90592i) q^{91} +(-0.719947 + 0.719947i) q^{93} -5.75052 q^{95} -2.51522 q^{97} +(-3.93102 + 3.93102i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} + 4 q^{5}+O(q^{10}) $ 12 * q - 4 * q^3 + 4 * q^5	$ 12 q - 4 q^{3} + 4 q^{5} + 24 q^{15} - 8 q^{17} + 4 q^{21} - 4 q^{27} - 4 q^{29} + 8 q^{31} + 4 q^{35} - 20 q^{37} - 16 q^{43} + 40 q^{45} - 16 q^{47} - 12 q^{49} + 16 q^{51} + 4 q^{53} + 16 q^{59} - 20 q^{61} - 12 q^{63} + 32 q^{65} - 24 q^{67} - 4 q^{69} + 40 q^{75} - 24 q^{79} - 44 q^{81} + 20 q^{83} - 8 q^{85} - 48 q^{93} + 48 q^{97} - 32 q^{99}+O(q^{100}) $ 12 * q - 4 * q^3 + 4 * q^5 + 24 * q^15 - 8 * q^17 + 4 * q^21 - 4 * q^27 - 4 * q^29 + 8 * q^31 + 4 * q^35 - 20 * q^37 - 16 * q^43 + 40 * q^45 - 16 * q^47 - 12 * q^49 + 16 * q^51 + 4 * q^53 + 16 * q^59 - 20 * q^61 - 12 * q^63 + 32 * q^65 - 24 * q^67 - 4 * q^69 + 40 * q^75 - 24 * q^79 - 44 * q^81 + 20 * q^83 - 8 * q^85 - 48 * q^93 + 48 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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			0
$2$		0			0
$3$	0.599978	−	0.599978i	0.346397	−	0.346397i	−0.512368	−	0.858766i	$-0.671232\pi$
$3$	0.599978	−	0.599978i	0.346397	−	0.346397i	0.858766	+	0.512368i	$0.171232\pi$
$4$		0			0
$5$	0.974969	+	0.974969i	0.436020	+	0.436020i	0.890670	−	0.454650i	$-0.150236\pi$
$5$	0.974969	+	0.974969i	0.436020	+	0.436020i	−0.454650	+	0.890670i	$0.650236\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		0			0
$9$			2.28005i			0.760018i
$10$		0			0
$11$	1.72409	+	1.72409i	0.519833	+	0.519833i	0.917521	−	0.397688i	$-0.130187\pi$
$11$	1.72409	+	1.72409i	0.519833	+	0.519833i	−0.397688	+	0.917521i	$0.630187\pi$
$12$		0			0
$13$	1.90592	−	1.90592i	0.528608	−	0.528608i	−0.391549	−	0.920157i	$-0.628061\pi$
$13$	1.90592	−	1.90592i	0.528608	−	0.528608i	0.920157	+	0.391549i	$0.128061\pi$
$14$		0			0
$15$	1.16992			0.302072
$16$		0			0
$17$	6.71697			1.62910			0.814552	−	0.580090i	$-0.196983\pi$
$17$	6.71697			1.62910			0.814552	+	0.580090i	$0.196983\pi$
$18$		0			0
$19$	−2.94908	+	2.94908i	−0.676565	+	0.676565i	−0.959221	−	0.282656i	$-0.908784\pi$
$19$	−2.94908	+	2.94908i	−0.676565	+	0.676565i	0.282656	+	0.959221i	$0.408784\pi$
$20$		0			0
$21$	−0.599978	−	0.599978i	−0.130926	−	0.130926i
$22$		0			0
$23$		−	5.29883i		−	1.10488i	−0.833552	−	0.552441i	$-0.813697\pi$
$23$		−	5.29883i		−	1.10488i	0.833552	−	0.552441i	$-0.186303\pi$
$24$		0			0
$25$		−	3.09887i		−	0.619774i
$26$		0			0
$27$	3.16792	+	3.16792i	0.609666	+	0.609666i
$28$		0			0
$29$	−3.03004	+	3.03004i	−0.562663	+	0.562663i	−0.930063	−	0.367400i	$-0.880248\pi$
$29$	−3.03004	+	3.03004i	−0.562663	+	0.562663i	0.367400	+	0.930063i	$0.380248\pi$
$30$		0			0
$31$	−1.19996			−0.215518			−0.107759	−	0.994177i	$-0.534368\pi$
$31$	−1.19996			−0.215518			−0.107759	+	0.994177i	$0.534368\pi$
$32$		0			0
$33$	2.06883			0.360138
$34$		0			0
$35$	0.974969	−	0.974969i	0.164800	−	0.164800i
$36$		0			0
$37$	−2.25002	−	2.25002i	−0.369901	−	0.369901i	0.497540	−	0.867441i	$-0.334237\pi$
$37$	−2.25002	−	2.25002i	−0.369901	−	0.369901i	−0.867441	+	0.497540i	$0.834237\pi$
$38$		0			0
$39$		−	2.28702i		−	0.366217i
$40$		0			0
$41$		−	3.94994i		−	0.616877i	−0.951244	−	0.308438i	$-0.900194\pi$
$41$		−	3.94994i		−	0.616877i	0.951244	−	0.308438i	$-0.0998064\pi$
$42$		0			0
$43$	7.02292	+	7.02292i	1.07098	+	1.07098i	0.997280	+	0.0737045i	$0.0234822\pi$
$43$	7.02292	+	7.02292i	1.07098	+	1.07098i	0.0737045	+	0.997280i	$0.476518\pi$
$44$		0			0
$45$	−2.22298	+	2.22298i	−0.331383	+	0.331383i
$46$		0			0
$47$	3.06186			0.446619			0.223309	−	0.974748i	$-0.428314\pi$
$47$	3.06186			0.446619			0.223309	+	0.974748i	$0.428314\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	4.03004	−	4.03004i	0.564318	−	0.564318i
$52$		0			0
$53$	−3.01877	−	3.01877i	−0.414660	−	0.414660i	0.468698	−	0.883358i	$-0.344723\pi$
$53$	−3.01877	−	3.01877i	−0.414660	−	0.414660i	−0.883358	+	0.468698i	$0.844723\pi$
$54$		0			0
$55$			3.36187i			0.453315i
$56$		0			0
$57$			3.53876i			0.468721i
$58$		0			0
$59$	−4.96785	−	4.96785i	−0.646759	−	0.646759i	0.305449	−	0.952208i	$-0.401193\pi$
$59$	−4.96785	−	4.96785i	−0.646759	−	0.646759i	−0.952208	+	0.305449i	$0.901193\pi$
$60$		0			0
$61$	−9.69194	+	9.69194i	−1.24093	+	1.24093i	−0.281308	+	0.959617i	$0.590768\pi$
$61$	−9.69194	+	9.69194i	−1.24093	+	1.24093i	−0.959617	+	0.281308i	$0.909232\pi$
$62$		0			0
$63$	2.28005			0.287260
$64$		0			0
$65$	3.71643			0.460967
$66$		0			0
$67$	−3.55596	+	3.55596i	−0.434430	+	0.434430i	−0.890132	−	0.455702i	$-0.849388\pi$
$67$	−3.55596	+	3.55596i	−0.434430	+	0.434430i	0.455702	+	0.890132i	$0.349388\pi$
$68$		0			0
$69$	−3.17918	−	3.17918i	−0.382728	−	0.382728i
$70$		0			0
$71$		−	11.5771i		−	1.37395i	−0.726682	−	0.686974i	$-0.758939\pi$
$71$		−	11.5771i		−	1.37395i	0.726682	−	0.686974i	$-0.241061\pi$
$72$		0			0
$73$		−	10.3271i		−	1.20869i	−0.796722	−	0.604346i	$-0.793434\pi$
$73$		−	10.3271i		−	1.20869i	0.796722	−	0.604346i	$-0.206566\pi$
$74$		0			0
$75$	−1.85925	−	1.85925i	−0.214688	−	0.214688i
$76$		0			0
$77$	1.72409	−	1.72409i	0.196478	−	0.196478i
$78$		0			0
$79$	−4.06883			−0.457780			−0.228890	−	0.973452i	$-0.573510\pi$
$79$	−4.06883			−0.457780			−0.228890	+	0.973452i	$0.573510\pi$
$80$		0			0
$81$	−3.03880			−0.337644
$82$		0			0
$83$	−9.17886	+	9.17886i	−1.00751	+	1.00751i	−0.00753873	+	0.999972i	$0.502400\pi$
$83$	−9.17886	+	9.17886i	−1.00751	+	1.00751i	−0.999972	+	0.00753873i	$0.997600\pi$
$84$		0			0
$85$	6.54884	+	6.54884i	0.710322	+	0.710322i
$86$		0			0
$87$			3.63591i			0.389810i
$88$		0			0
$89$			16.9287i			1.79444i	0.441582	+	0.897221i	$0.354417\pi$
$89$			16.9287i			1.79444i	−0.441582	+	0.897221i	$0.645583\pi$
$90$		0			0
$91$	−1.90592	−	1.90592i	−0.199795	−	0.199795i
$92$		0			0
$93$	−0.719947	+	0.719947i	−0.0746551	+	0.0746551i
$94$		0			0
$95$	−5.75052			−0.589991
$96$		0			0
$97$	−2.51522			−0.255382			−0.127691	−	0.991814i	$-0.540757\pi$
$97$	−2.51522			−0.255382			−0.127691	+	0.991814i	$0.540757\pi$
$98$		0			0
$99$	−3.93102	+	3.93102i	−0.395082	+	0.395082i
$100$		0			0
$101$	−8.56282	−	8.56282i	−0.852033	−	0.852033i	0.138351	−	0.990383i	$-0.455820\pi$
$101$	−8.56282	−	8.56282i	−0.852033	−	0.852033i	−0.990383	+	0.138351i	$0.955820\pi$
$102$		0			0
$103$			17.8356i			1.75739i	0.477382	+	0.878696i	$0.341586\pi$
$103$			17.8356i			1.75739i	−0.477382	+	0.878696i	$0.658414\pi$
$104$		0			0
$105$		−	1.16992i		−	0.114173i
$106$		0			0
$107$	−8.49285	−	8.49285i	−0.821034	−	0.821034i	0.165222	−	0.986256i	$-0.447166\pi$
$107$	−8.49285	−	8.49285i	−0.821034	−	0.821034i	−0.986256	+	0.165222i	$0.947166\pi$
$108$		0			0
$109$	7.26700	−	7.26700i	0.696052	−	0.696052i	−0.267504	−	0.963557i	$-0.586199\pi$
$109$	7.26700	−	7.26700i	0.696052	−	0.696052i	0.963557	+	0.267504i	$0.0861990\pi$
$110$		0			0
$111$	−2.69992			−0.256265
$112$		0			0
$113$	−13.8351			−1.30150			−0.650749	−	0.759293i	$-0.725545\pi$
$113$	−13.8351			−1.30150			−0.650749	+	0.759293i	$0.725545\pi$
$114$		0			0
$115$	5.16619	−	5.16619i	0.481750	−	0.481750i
$116$		0			0
$117$	4.34560	+	4.34560i	0.401751	+	0.401751i
$118$		0			0
$119$		−	6.71697i		−	0.615744i
$120$		0			0
$121$		−	5.05502i		−	0.459547i
$122$		0			0
$123$	−2.36988	−	2.36988i	−0.213685	−	0.213685i
$124$		0			0
$125$	7.89615	−	7.89615i	0.706253	−	0.706253i
$126$		0			0
$127$	−14.1434			−1.25502			−0.627512	−	0.778607i	$-0.715927\pi$
$127$	−14.1434			−1.25502			−0.627512	+	0.778607i	$0.715927\pi$
$128$		0			0
$129$	8.42719			0.741973
$130$		0			0
$131$	3.04995	−	3.04995i	0.266475	−	0.266475i	−0.561203	−	0.827678i	$-0.689661\pi$
$131$	3.04995	−	3.04995i	0.266475	−	0.266475i	0.827678	+	0.561203i	$0.189661\pi$
$132$		0			0
$133$	2.94908	+	2.94908i	0.255717	+	0.255717i
$134$		0			0
$135$			6.17724i			0.531652i
$136$		0			0
$137$		−	11.5811i		−	0.989440i	−0.869052	−	0.494720i	$-0.835271\pi$
$137$		−	11.5811i		−	0.989440i	0.869052	−	0.494720i	$-0.164729\pi$
$138$		0			0
$139$	2.25088	+	2.25088i	0.190917	+	0.190917i	0.796092	−	0.605175i	$-0.206897\pi$
$139$	2.25088	+	2.25088i	0.190917	+	0.190917i	−0.605175	+	0.796092i	$0.706897\pi$
$140$		0			0
$141$	1.83705	−	1.83705i	0.154708	−	0.154708i
$142$		0			0
$143$	6.57197			0.549576
$144$		0			0
$145$	−5.90838			−0.490665
$146$		0			0
$147$	−0.599978	+	0.599978i	−0.0494854	+	0.0494854i
$148$		0			0
$149$	−2.29883	−	2.29883i	−0.188327	−	0.188327i	0.606645	−	0.794973i	$-0.292515\pi$
$149$	−2.29883	−	2.29883i	−0.188327	−	0.188327i	−0.794973	+	0.606645i	$0.792515\pi$
$150$		0			0
$151$		−	18.1587i		−	1.47774i	−0.673850	−	0.738868i	$-0.735361\pi$
$151$		−	18.1587i		−	1.47774i	0.673850	−	0.738868i	$-0.264639\pi$
$152$		0			0
$153$			15.3150i			1.23815i
$154$		0			0
$155$	−1.16992	−	1.16992i	−0.0939703	−	0.0939703i
$156$		0			0
$157$	−10.8110	+	10.8110i	−0.862816	+	0.862816i	−0.991664	−	0.128849i	$-0.958872\pi$
$157$	−10.8110	+	10.8110i	−0.862816	+	0.862816i	0.128849	+	0.991664i	$0.458872\pi$
$158$		0			0
$159$	−3.62239			−0.287275
$160$		0			0
$161$	−5.29883			−0.417606
$162$		0			0
$163$	6.43105	−	6.43105i	0.503719	−	0.503719i	−0.408873	−	0.912591i	$-0.634078\pi$
$163$	6.43105	−	6.43105i	0.503719	−	0.503719i	0.912591	+	0.408873i	$0.134078\pi$
$164$		0			0
$165$	2.01705	+	2.01705i	0.157027	+	0.157027i
$166$		0			0
$167$		−	0.661950i		−	0.0512232i	−0.999672	−	0.0256116i	$-0.991847\pi$
$167$		−	0.661950i		−	0.0512232i	0.999672	−	0.0256116i	$-0.00815332\pi$
$168$		0			0
$169$			5.73492i			0.441148i
$170$		0			0
$171$	−6.72405	−	6.72405i	−0.514201	−	0.514201i
$172$		0			0
$173$	6.35590	−	6.35590i	0.483230	−	0.483230i	−0.422932	−	0.906162i	$-0.638999\pi$
$173$	6.35590	−	6.35590i	0.483230	−	0.483230i	0.906162	+	0.422932i	$0.138999\pi$
$174$		0			0
$175$	−3.09887			−0.234252
$176$		0			0
$177$	−5.96120			−0.448071
$178$		0			0
$179$	7.61603	−	7.61603i	0.569249	−	0.569249i	−0.362669	−	0.931918i	$-0.618134\pi$
$179$	7.61603	−	7.61603i	0.569249	−	0.569249i	0.931918	+	0.362669i	$0.118134\pi$
$180$		0			0
$181$	13.9902	+	13.9902i	1.03989	+	1.03989i	0.999171	+	0.0407146i	$0.0129634\pi$
$181$	13.9902	+	13.9902i	1.03989	+	1.03989i	0.0407146	+	0.999171i	$0.487037\pi$
$182$		0			0
$183$			11.6299i			0.859707i
$184$		0			0
$185$		−	4.38740i		−	0.322568i
$186$		0			0
$187$	11.5807	+	11.5807i	0.846862	+	0.846862i
$188$		0			0
$189$	3.16792	−	3.16792i	0.230432	−	0.230432i
$190$		0			0
$191$	22.4422			1.62386			0.811929	−	0.583756i	$-0.198418\pi$
$191$	22.4422			1.62386			0.811929	+	0.583756i	$0.198418\pi$
$192$		0			0
$193$	−6.31408			−0.454498			−0.227249	−	0.973837i	$-0.572973\pi$
$193$	−6.31408			−0.454498			−0.227249	+	0.973837i	$0.572973\pi$
$194$		0			0
$195$	2.22978	−	2.22978i	0.159678	−	0.159678i
$196$		0			0
$197$	3.81709	+	3.81709i	0.271957	+	0.271957i	0.829887	−	0.557931i	$-0.188405\pi$
$197$	3.81709	+	3.81709i	0.271957	+	0.271957i	−0.557931	+	0.829887i	$0.688405\pi$
$198$		0			0
$199$			25.6304i			1.81689i	0.418005	+	0.908445i	$0.362730\pi$
$199$			25.6304i			1.81689i	−0.418005	+	0.908445i	$0.637270\pi$
$200$		0			0
$201$			4.26700i			0.300971i
$202$		0			0
$203$	3.03004	+	3.03004i	0.212667	+	0.212667i
$204$		0			0
$205$	3.85107	−	3.85107i	0.268970	−	0.268970i
$206$		0			0
$207$	12.0816			0.839729
$208$		0			0
$209$	−10.1690			−0.703401
$210$		0			0
$211$	−0.737145	+	0.737145i	−0.0507472	+	0.0507472i	−0.732025	−	0.681278i	$-0.761425\pi$
$211$	−0.737145	+	0.737145i	−0.0507472	+	0.0507472i	0.681278	+	0.732025i	$0.261425\pi$
$212$		0			0
$213$	−6.94600	−	6.94600i	−0.475932	−	0.475932i
$214$		0			0
$215$			13.6943i			0.933941i
$216$		0			0
$217$			1.19996i			0.0814583i
$218$		0			0
$219$	−6.19601	−	6.19601i	−0.418688	−	0.418688i
$220$		0			0
$221$	12.8020	−	12.8020i	0.861158	−	0.861158i
$222$		0			0
$223$	5.76178			0.385838			0.192919	−	0.981215i	$-0.438205\pi$
$223$	5.76178			0.385838			0.192919	+	0.981215i	$0.438205\pi$
$224$		0			0
$225$	7.06558			0.471039
$226$		0			0
$227$	18.2179	−	18.2179i	1.20916	−	1.20916i	0.237864	−	0.971299i	$-0.423553\pi$
$227$	18.2179	−	18.2179i	1.20916	−	1.20916i	0.971299	−	0.237864i	$-0.0764472\pi$
$228$		0			0
$229$	0.512762	+	0.512762i	0.0338843	+	0.0338843i	0.723846	−	0.689962i	$-0.242373\pi$
$229$	0.512762	+	0.512762i	0.0338843	+	0.0338843i	−0.689962	+	0.723846i	$0.742373\pi$
$230$		0			0
$231$		−	2.06883i		−	0.136119i
$232$		0			0
$233$		−	14.4425i		−	0.946160i	−0.881019	−	0.473080i	$-0.843142\pi$
$233$		−	14.4425i		−	0.946160i	0.881019	−	0.473080i	$-0.156858\pi$
$234$		0			0
$235$	2.98522	+	2.98522i	0.194734	+	0.194734i
$236$		0			0
$237$	−2.44121	+	2.44121i	−0.158574	+	0.158574i
$238$		0			0
$239$	7.34716			0.475248			0.237624	−	0.971357i	$-0.423631\pi$
$239$	7.34716			0.475248			0.237624	+	0.971357i	$0.423631\pi$
$240$		0			0
$241$	3.25347			0.209575			0.104787	−	0.994495i	$-0.466584\pi$
$241$	3.25347			0.209575			0.104787	+	0.994495i	$0.466584\pi$
$242$		0			0
$243$	−11.3270	+	11.3270i	−0.726625	+	0.726625i
$244$		0			0
$245$	−0.974969	−	0.974969i	−0.0622885	−	0.0622885i
$246$		0			0
$247$			11.2414i			0.715275i
$248$		0			0
$249$			11.0142i			0.697998i
$250$		0			0
$251$	−2.08074	−	2.08074i	−0.131335	−	0.131335i	0.638383	−	0.769719i	$-0.279604\pi$
$251$	−2.08074	−	2.08074i	−0.131335	−	0.131335i	−0.769719	+	0.638383i	$0.779604\pi$
$252$		0			0
$253$	9.13566	−	9.13566i	0.574354	−	0.574354i
$254$		0			0
$255$	7.85832			0.492107
$256$		0			0
$257$	10.9620			0.683788			0.341894	−	0.939738i	$-0.388932\pi$
$257$	10.9620			0.683788			0.341894	+	0.939738i	$0.388932\pi$
$258$		0			0
$259$	−2.25002	+	2.25002i	−0.139809	+	0.139809i
$260$		0			0
$261$	−6.90864	−	6.90864i	−0.427634	−	0.427634i
$262$		0			0
$263$		−	10.1931i		−	0.628534i	−0.949335	−	0.314267i	$-0.898241\pi$
$263$		−	10.1931i		−	0.628534i	0.949335	−	0.314267i	$-0.101759\pi$
$264$		0			0
$265$		−	5.88642i		−	0.361600i
$266$		0			0
$267$	10.1569	+	10.1569i	0.621590	+	0.621590i
$268$		0			0
$269$	1.75782	−	1.75782i	0.107176	−	0.107176i	−0.651485	−	0.758661i	$-0.725854\pi$
$269$	1.75782	−	1.75782i	0.107176	−	0.107176i	0.758661	+	0.651485i	$0.225854\pi$
$270$		0			0
$271$	5.66166			0.343921			0.171961	−	0.985104i	$-0.444990\pi$
$271$	5.66166			0.343921			0.171961	+	0.985104i	$0.444990\pi$
$272$		0			0
$273$	−2.28702			−0.138417
$274$		0			0
$275$	5.34273	−	5.34273i	0.322179	−	0.322179i
$276$		0			0
$277$	21.3329	+	21.3329i	1.28177	+	1.28177i	0.939662	+	0.342106i	$0.111140\pi$
$277$	21.3329	+	21.3329i	1.28177	+	1.28177i	0.342106	+	0.939662i	$0.388860\pi$
$278$		0			0
$279$		−	2.73596i		−	0.163798i
$280$		0			0
$281$			1.60009i			0.0954532i	0.998860	+	0.0477266i	$0.0151976\pi$
$281$			1.60009i			0.0954532i	−0.998860	+	0.0477266i	$0.984802\pi$
$282$		0			0
$283$	−14.3940	−	14.3940i	−0.855635	−	0.855635i	0.135186	−	0.990820i	$-0.456837\pi$
$283$	−14.3940	−	14.3940i	−0.855635	−	0.855635i	−0.990820	+	0.135186i	$0.956837\pi$
$284$		0			0
$285$	−3.45019	+	3.45019i	−0.204371	+	0.204371i
$286$		0			0
$287$	−3.94994			−0.233158
$288$		0			0
$289$	28.1177			1.65398
$290$		0			0
$291$	−1.50908	+	1.50908i	−0.0884638	+	0.0884638i
$292$		0			0
$293$	0.267863	+	0.267863i	0.0156487	+	0.0156487i	0.714888	−	0.699239i	$-0.246478\pi$
$293$	0.267863	+	0.267863i	0.0156487	+	0.0156487i	−0.699239	+	0.714888i	$0.746478\pi$
$294$		0			0
$295$		−	9.68700i		−	0.563999i
$296$		0			0
$297$			10.9235i			0.633849i
$298$		0			0
$299$	−10.0992	−	10.0992i	−0.584049	−	0.584049i
$300$		0			0
$301$	7.02292	−	7.02292i	0.404794	−	0.404794i
$302$		0			0
$303$	−10.2750			−0.590284
$304$		0			0
$305$	−18.8987			−1.08214
$306$		0			0
$307$	12.3805	−	12.3805i	0.706594	−	0.706594i	−0.259223	−	0.965817i	$-0.583466\pi$
$307$	12.3805	−	12.3805i	0.706594	−	0.706594i	0.965817	+	0.259223i	$0.0834665\pi$
$308$		0			0
$309$	10.7010	+	10.7010i	0.608756	+	0.608756i
$310$		0			0
$311$			3.69468i			0.209506i	0.994498	+	0.104753i	$0.0334053\pi$
$311$			3.69468i			0.209506i	−0.994498	+	0.104753i	$0.966595\pi$
$312$		0			0
$313$		−	10.4700i		−	0.591799i	−0.955219	−	0.295900i	$-0.904381\pi$
$313$		−	10.4700i		−	0.591799i	0.955219	−	0.295900i	$-0.0956194\pi$
$314$		0			0
$315$	2.22298	+	2.22298i	0.125251	+	0.125251i
$316$		0			0
$317$	−15.7941	+	15.7941i	−0.887085	+	0.887085i	−0.994242	−	0.107157i	$-0.965825\pi$
$317$	−15.7941	+	15.7941i	−0.887085	+	0.887085i	0.107157	+	0.994242i	$0.465825\pi$
$318$		0			0
$319$	−10.4481			−0.584982
$320$		0			0
$321$	−10.1910			−0.568809
$322$		0			0
$323$	−19.8089	+	19.8089i	−1.10219	+	1.10219i
$324$		0			0
$325$	−5.90620	−	5.90620i	−0.327617	−	0.327617i
$326$		0			0
$327$		−	8.72008i		−	0.482221i
$328$		0			0
$329$		−	3.06186i		−	0.168806i
$330$		0			0
$331$	−6.76260	−	6.76260i	−0.371706	−	0.371706i	0.496392	−	0.868098i	$-0.334658\pi$
$331$	−6.76260	−	6.76260i	−0.371706	−	0.371706i	−0.868098	+	0.496392i	$0.834658\pi$
$332$		0			0
$333$	5.13016	−	5.13016i	0.281131	−	0.281131i
$334$		0			0
$335$	−6.93391			−0.378840
$336$		0			0
$337$	−27.1949			−1.48140			−0.740700	−	0.671836i	$-0.765506\pi$
$337$	−27.1949			−1.48140			−0.740700	+	0.671836i	$0.765506\pi$
$338$		0			0
$339$	−8.30076	+	8.30076i	−0.450835	+	0.450835i
$340$		0			0
$341$	−2.06883	−	2.06883i	−0.112034	−	0.112034i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$		−	6.19920i		−	0.333754i
$346$		0			0
$347$	4.18157	+	4.18157i	0.224479	+	0.224479i	0.810381	−	0.585903i	$-0.199260\pi$
$347$	4.18157	+	4.18157i	0.224479	+	0.224479i	−0.585903	+	0.810381i	$0.699260\pi$
$348$		0			0
$349$	−24.5827	+	24.5827i	−1.31588	+	1.31588i	−0.398877	+	0.917004i	$0.630600\pi$
$349$	−24.5827	+	24.5827i	−1.31588	+	1.31588i	−0.917004	+	0.398877i	$0.869400\pi$
$350$		0			0
$351$	12.0756			0.644548
$352$		0			0
$353$	33.3458			1.77482			0.887409	−	0.460982i	$-0.152503\pi$
$353$	33.3458			1.77482			0.887409	+	0.460982i	$0.152503\pi$
$354$		0			0
$355$	11.2873	−	11.2873i	0.599068	−	0.599068i
$356$		0			0
$357$	−4.03004	−	4.03004i	−0.213292	−	0.213292i
$358$		0			0
$359$			7.89898i			0.416892i	0.978034	+	0.208446i	$0.0668406\pi$
$359$			7.89898i			0.416892i	−0.978034	+	0.208446i	$0.933159\pi$
$360$		0			0
$361$			1.60588i			0.0845202i
$362$		0			0
$363$	−3.03290	−	3.03290i	−0.159186	−	0.159186i
$364$		0			0
$365$	10.0686	−	10.0686i	0.527013	−	0.527013i
$366$		0			0
$367$	−29.5941			−1.54480			−0.772401	−	0.635136i	$-0.780944\pi$
$367$	−29.5941			−1.54480			−0.772401	+	0.635136i	$0.780944\pi$
$368$		0			0
$369$	9.00607			0.468837
$370$		0			0
$371$	−3.01877	+	3.01877i	−0.156727	+	0.156727i
$372$		0			0
$373$	−4.31630	−	4.31630i	−0.223490	−	0.223490i	0.586477	−	0.809966i	$-0.300515\pi$
$373$	−4.31630	−	4.31630i	−0.223490	−	0.223490i	−0.809966	+	0.586477i	$0.800515\pi$
$374$		0			0
$375$		−	9.47503i		−	0.489289i
$376$		0			0
$377$			11.5500i			0.594857i
$378$		0			0
$379$	15.1468	+	15.1468i	0.778037	+	0.778037i	0.979497	−	0.201460i	$-0.0645684\pi$
$379$	15.1468	+	15.1468i	0.778037	+	0.778037i	−0.201460	+	0.979497i	$0.564568\pi$
$380$		0			0
$381$	−8.48573	+	8.48573i	−0.434737	+	0.434737i
$382$		0			0
$383$	−6.62147			−0.338341			−0.169171	−	0.985587i	$-0.554109\pi$
$383$	−6.62147			−0.338341			−0.169171	+	0.985587i	$0.554109\pi$
$384$		0			0
$385$	3.36187			0.171337
$386$		0			0
$387$	−16.0126	+	16.0126i	−0.813967	+	0.813967i
$388$		0			0
$389$	−25.6610	−	25.6610i	−1.30106	−	1.30106i	−0.927676	−	0.373386i	$-0.878197\pi$
$389$	−25.6610	−	25.6610i	−1.30106	−	1.30106i	−0.373386	−	0.927676i	$-0.621803\pi$
$390$		0			0
$391$		−	35.5921i		−	1.79997i
$392$		0			0
$393$		−	3.65981i		−	0.184613i
$394$		0			0
$395$	−3.96699	−	3.96699i	−0.199601	−	0.199601i
$396$		0			0
$397$	−9.47099	+	9.47099i	−0.475336	+	0.475336i	−0.903636	−	0.428301i	$-0.859112\pi$
$397$	−9.47099	+	9.47099i	−0.475336	+	0.475336i	0.428301	+	0.903636i	$0.359112\pi$
$398$		0			0
$399$	3.53876			0.177160
$400$		0			0
$401$	17.5138			0.874598			0.437299	−	0.899316i	$-0.355935\pi$
$401$	17.5138			0.874598			0.437299	+	0.899316i	$0.355935\pi$
$402$		0			0
$403$	−2.28702	+	2.28702i	−0.113925	+	0.113925i
$404$		0			0
$405$	−2.96274	−	2.96274i	−0.147220	−	0.147220i
$406$		0			0
$407$		−	7.75847i		−	0.384573i
$408$		0			0
$409$			10.3755i			0.513037i	0.966539	+	0.256519i	$0.0825755\pi$
$409$			10.3755i			0.513037i	−0.966539	+	0.256519i	$0.917425\pi$
$410$		0			0
$411$	−6.94840	−	6.94840i	−0.342739	−	0.342739i
$412$		0			0
$413$	−4.96785	+	4.96785i	−0.244452	+	0.244452i
$414$		0			0
$415$	−17.8982			−0.878589
$416$		0			0
$417$	2.70096			0.132266
$418$		0			0
$419$	−12.6045	+	12.6045i	−0.615771	+	0.615771i	−0.944444	−	0.328673i	$-0.893399\pi$
$419$	−12.6045	+	12.6045i	−0.615771	+	0.615771i	0.328673	+	0.944444i	$0.393399\pi$
$420$		0			0
$421$	−17.6588	−	17.6588i	−0.860635	−	0.860635i	0.130777	−	0.991412i	$-0.458253\pi$
$421$	−17.6588	−	17.6588i	−0.860635	−	0.860635i	−0.991412	+	0.130777i	$0.958253\pi$
$422$		0			0
$423$			6.98121i			0.339438i
$424$		0			0
$425$		−	20.8150i		−	1.00968i
$426$		0			0
$427$	9.69194	+	9.69194i	0.469026	+	0.469026i
$428$		0			0
$429$	3.94304	−	3.94304i	0.190372	−	0.190372i
$430$		0			0
$431$	−9.58438			−0.461663			−0.230832	−	0.972994i	$-0.574145\pi$
$431$	−9.58438			−0.461663			−0.230832	+	0.972994i	$0.574145\pi$
$432$		0			0
$433$	−0.958633			−0.0460690			−0.0230345	−	0.999735i	$-0.507333\pi$
$433$	−0.958633			−0.0460690			−0.0230345	+	0.999735i	$0.507333\pi$
$434$		0			0
$435$	−3.54490	+	3.54490i	−0.169965	+	0.169965i
$436$		0			0
$437$	15.6266	+	15.6266i	0.747524	+	0.747524i
$438$		0			0
$439$		−	9.97389i		−	0.476028i	−0.971262	−	0.238014i	$-0.923504\pi$
$439$		−	9.97389i		−	0.476028i	0.971262	−	0.238014i	$-0.0764964\pi$
$440$		0			0
$441$		−	2.28005i		−	0.108574i
$442$		0			0
$443$	15.4846	+	15.4846i	0.735697	+	0.735697i	0.971742	−	0.236045i	$-0.0758514\pi$
$443$	15.4846	+	15.4846i	0.735697	+	0.735697i	−0.236045	+	0.971742i	$0.575851\pi$
$444$		0			0
$445$	−16.5050	+	16.5050i	−0.782412	+	0.782412i
$446$		0			0
$447$	−2.75849			−0.130472
$448$		0			0
$449$	−8.77877			−0.414296			−0.207148	−	0.978310i	$-0.566418\pi$
$449$	−8.77877			−0.414296			−0.207148	+	0.978310i	$0.566418\pi$
$450$		0			0
$451$	6.81005	−	6.81005i	0.320673	−	0.320673i
$452$		0			0
$453$	−10.8948	−	10.8948i	−0.511884	−	0.511884i
$454$		0			0
$455$		−	3.71643i		−	0.174229i
$456$		0			0
$457$		−	1.87158i		−	0.0875486i	−0.999041	−	0.0437743i	$-0.986062\pi$
$457$		−	1.87158i		−	0.0875486i	0.999041	−	0.0437743i	$-0.0139383\pi$
$458$		0			0
$459$	21.2788	+	21.2788i	0.993209	+	0.993209i
$460$		0			0
$461$	13.2713	−	13.2713i	0.618107	−	0.618107i	−0.326939	−	0.945046i	$-0.606017\pi$
$461$	13.2713	−	13.2713i	0.618107	−	0.618107i	0.945046	+	0.326939i	$0.106017\pi$
$462$		0			0
$463$	1.89824			0.0882189			0.0441095	−	0.999027i	$-0.485955\pi$
$463$	1.89824			0.0882189			0.0441095	+	0.999027i	$0.485955\pi$
$464$		0			0
$465$	−1.40385			−0.0651021
$466$		0			0
$467$	−1.08393	+	1.08393i	−0.0501585	+	0.0501585i	−0.731741	−	0.681583i	$-0.761292\pi$
$467$	−1.08393	+	1.08393i	−0.0501585	+	0.0501585i	0.681583	+	0.731741i	$0.261292\pi$
$468$		0			0
$469$	3.55596	+	3.55596i	0.164199	+	0.164199i
$470$		0			0
$471$			12.9728i			0.597754i
$472$		0			0
$473$			24.2163i			1.11347i
$474$		0			0
$475$	9.13880	+	9.13880i	0.419317	+	0.419317i
$476$		0			0
$477$	6.88296	−	6.88296i	0.315149	−	0.315149i
$478$		0			0
$479$	28.2972			1.29293			0.646466	−	0.762942i	$-0.276246\pi$
$479$	28.2972			1.29293			0.646466	+	0.762942i	$0.276246\pi$
$480$		0			0
$481$	−8.57672			−0.391065
$482$		0			0
$483$	−3.17918	+	3.17918i	−0.144658	+	0.144658i
$484$		0			0
$485$	−2.45227	−	2.45227i	−0.111352	−	0.111352i
$486$		0			0
$487$			6.19712i			0.280818i	0.990094	+	0.140409i	$0.0448418\pi$
$487$			6.19712i			0.280818i	−0.990094	+	0.140409i	$0.955158\pi$
$488$		0			0
$489$		−	7.71698i		−	0.348974i
$490$		0			0
$491$	−21.5658	−	21.5658i	−0.973249	−	0.973249i	0.0264026	−	0.999651i	$-0.491595\pi$
$491$	−21.5658	−	21.5658i	−0.973249	−	0.973249i	−0.999651	+	0.0264026i	$0.991595\pi$
$492$		0			0
$493$	−20.3527	+	20.3527i	−0.916638	+	0.916638i
$494$		0			0
$495$	−7.66525			−0.344527
$496$		0			0
$497$	−11.5771			−0.519303
$498$		0			0
$499$	−2.45487	+	2.45487i	−0.109895	+	0.109895i	−0.759916	−	0.650021i	$-0.774760\pi$
$499$	−2.45487	+	2.45487i	−0.109895	+	0.109895i	0.650021	+	0.759916i	$0.274760\pi$
$500$		0			0
$501$	−0.397156	−	0.397156i	−0.0177436	−	0.0177436i
$502$		0			0
$503$		−	13.1803i		−	0.587680i	−0.955855	−	0.293840i	$-0.905067\pi$
$503$		−	13.1803i		−	0.587680i	0.955855	−	0.293840i	$-0.0949332\pi$
$504$		0			0
$505$		−	16.6970i		−	0.743006i
$506$		0			0
$507$	3.44082	+	3.44082i	0.152812	+	0.152812i
$508$		0			0
$509$	−1.53507	+	1.53507i	−0.0680410	+	0.0680410i	−0.740308	−	0.672267i	$-0.765321\pi$
$509$	−1.53507	+	1.53507i	−0.0680410	+	0.0680410i	0.672267	+	0.740308i	$0.265321\pi$
$510$		0			0
$511$	−10.3271			−0.456843
$512$		0			0
$513$	−18.6849			−0.824957
$514$		0			0
$515$	−17.3891	+	17.3891i	−0.766257	+	0.766257i
$516$		0			0
$517$	5.27893	+	5.27893i	0.232167	+	0.232167i
$518$		0			0
$519$		−	7.62680i		−	0.334779i
$520$		0			0
$521$		−	10.0170i		−	0.438854i	−0.975629	−	0.219427i	$-0.929581\pi$
$521$		−	10.0170i		−	0.438854i	0.975629	−	0.219427i	$-0.0704189\pi$
$522$		0			0
$523$	16.3284	+	16.3284i	0.713992	+	0.713992i	0.967368	−	0.253376i	$-0.0815409\pi$
$523$	16.3284	+	16.3284i	0.713992	+	0.713992i	−0.253376	+	0.967368i	$0.581541\pi$
$524$		0			0
$525$	−1.85925	+	1.85925i	−0.0811445	+	0.0811445i
$526$		0			0
$527$	−8.06007			−0.351102
$528$		0			0
$529$	−5.07755			−0.220763
$530$		0			0
$531$	11.3270	−	11.3270i	0.491548	−	0.491548i
$532$		0			0
$533$	−7.52828	−	7.52828i	−0.326086	−	0.326086i
$534$		0			0
$535$		−	16.5605i		−	0.715974i
$536$		0			0
$537$		−	9.13891i		−	0.394373i
$538$		0			0
$539$	−1.72409	−	1.72409i	−0.0742619	−	0.0742619i
$540$		0			0
$541$	−6.69916	+	6.69916i	−0.288020	+	0.288020i	−0.836297	−	0.548277i	$-0.815284\pi$
$541$	−6.69916	+	6.69916i	−0.288020	+	0.288020i	0.548277	+	0.836297i	$0.315284\pi$
$542$		0			0
$543$	16.7877			0.720427
$544$		0			0
$545$	14.1702			0.606985
$546$		0			0
$547$	21.2058	−	21.2058i	0.906695	−	0.906695i	−0.0893091	−	0.996004i	$-0.528466\pi$
$547$	21.2058	−	21.2058i	0.906695	−	0.906695i	0.996004	+	0.0893091i	$0.0284659\pi$
$548$		0			0
$549$	−22.0981	−	22.0981i	−0.943125	−	0.943125i
$550$		0			0
$551$		−	17.8716i		−	0.761357i
$552$		0			0
$553$			4.06883i			0.173024i
$554$		0			0
$555$	−2.63234	−	2.63234i	−0.111737	−	0.111737i
$556$		0			0
$557$	−16.9582	+	16.9582i	−0.718543	+	0.718543i	−0.968307	−	0.249764i	$-0.919647\pi$
$557$	−16.9582	+	16.9582i	−0.718543	+	0.718543i	0.249764	+	0.968307i	$0.419647\pi$
$558$		0			0
$559$	26.7703			1.13226
$560$		0			0
$561$	13.8963			0.586702
$562$		0			0
$563$	−7.49559	+	7.49559i	−0.315901	+	0.315901i	−0.847191	−	0.531289i	$-0.821708\pi$
$563$	−7.49559	+	7.49559i	−0.315901	+	0.315901i	0.531289	+	0.847191i	$0.321708\pi$
$564$		0			0
$565$	−13.4888	−	13.4888i	−0.567478	−	0.567478i
$566$		0			0
$567$			3.03880i			0.127618i
$568$		0			0
$569$			44.0529i			1.84679i	0.383848	+	0.923396i	$0.374599\pi$
$569$			44.0529i			1.84679i	−0.383848	+	0.923396i	$0.625401\pi$
$570$		0			0
$571$	−9.43664	−	9.43664i	−0.394911	−	0.394911i	0.481523	−	0.876434i	$-0.340084\pi$
$571$	−9.43664	−	9.43664i	−0.394911	−	0.394911i	−0.876434	+	0.481523i	$0.840084\pi$
$572$		0			0
$573$	13.4648	−	13.4648i	0.562500	−	0.562500i
$574$		0			0
$575$	−16.4204			−0.684777
$576$		0			0
$577$	16.4631			0.685369			0.342685	−	0.939450i	$-0.388664\pi$
$577$	16.4631			0.685369			0.342685	+	0.939450i	$0.388664\pi$
$578$		0			0
$579$	−3.78831	+	3.78831i	−0.157437	+	0.157437i
$580$		0			0
$581$	9.17886	+	9.17886i	0.380803	+	0.380803i
$582$		0			0
$583$		−	10.4093i		−	0.431108i
$584$		0			0
$585$			8.47366i			0.350343i
$586$		0			0
$587$	21.5452	+	21.5452i	0.889267	+	0.889267i	0.994453	−	0.105186i	$-0.0335438\pi$
$587$	21.5452	+	21.5452i	0.889267	+	0.889267i	−0.105186	+	0.994453i	$0.533544\pi$
$588$		0			0
$589$	3.53876	−	3.53876i	0.145812	−	0.145812i
$590$		0			0
$591$	4.58034			0.188410
$592$		0			0
$593$	26.2918			1.07967			0.539837	−	0.841770i	$-0.318486\pi$
$593$	26.2918			1.07967			0.539837	+	0.841770i	$0.318486\pi$
$594$		0			0
$595$	6.54884	−	6.54884i	0.268476	−	0.268476i
$596$		0			0
$597$	15.3777	+	15.3777i	0.629366	+	0.629366i
$598$		0			0
$599$			27.8214i			1.13675i	0.822769	+	0.568376i	$0.192428\pi$
$599$			27.8214i			1.13675i	−0.822769	+	0.568376i	$0.807572\pi$
$600$		0			0
$601$		−	18.3631i		−	0.749047i	−0.927217	−	0.374523i	$-0.877806\pi$
$601$		−	18.3631i		−	0.749047i	0.927217	−	0.374523i	$-0.122194\pi$
$602$		0			0
$603$	−8.10778	−	8.10778i	−0.330174	−	0.330174i
$604$		0			0
$605$	4.92849	−	4.92849i	0.200372	−	0.200372i
$606$		0			0
$607$	−9.91188			−0.402311			−0.201155	−	0.979559i	$-0.564470\pi$
$607$	−9.91188			−0.402311			−0.201155	+	0.979559i	$0.564470\pi$
$608$		0			0
$609$	3.63591			0.147334
$610$		0			0
$611$	5.83567	−	5.83567i	0.236086	−	0.236086i
$612$		0			0
$613$	30.5010	+	30.5010i	1.23193	+	1.23193i	0.963223	+	0.268702i	$0.0865948\pi$
$613$	30.5010	+	30.5010i	1.23193	+	1.23193i	0.268702	+	0.963223i	$0.413405\pi$
$614$		0			0
$615$		−	4.62112i		−	0.186341i
$616$		0			0
$617$			7.78309i			0.313336i	0.987651	+	0.156668i	$0.0500752\pi$
$617$			7.78309i			0.313336i	−0.987651	+	0.156668i	$0.949925\pi$
$618$		0			0
$619$	−27.6514	−	27.6514i	−1.11140	−	1.11140i	−0.992961	−	0.118441i	$-0.962210\pi$
$619$	−27.6514	−	27.6514i	−1.11140	−	1.11140i	−0.118441	−	0.992961i	$-0.537790\pi$
$620$		0			0
$621$	16.7862	−	16.7862i	0.673608	−	0.673608i
$622$		0			0
$623$	16.9287			0.678235
$624$		0			0
$625$	−0.0973335			−0.00389334
$626$		0			0
$627$	−6.10115	+	6.10115i	−0.243656	+	0.243656i
$628$		0			0
$629$	−15.1133	−	15.1133i	−0.602607	−	0.602607i
$630$		0			0
$631$		−	6.10120i		−	0.242885i	−0.992598	−	0.121442i	$-0.961248\pi$
$631$		−	6.10120i		−	0.242885i	0.992598	−	0.121442i	$-0.0387520\pi$
$632$		0			0
$633$			0.884542i			0.0351574i
$634$		0			0
$635$	−13.7894	−	13.7894i	−0.547215	−	0.547215i
$636$		0			0
$637$	−1.90592	+	1.90592i	−0.0755154	+	0.0755154i
$638$		0			0
$639$	26.3964			1.04422
$640$		0			0
$641$	8.80169			0.347646			0.173823	−	0.984777i	$-0.444388\pi$
$641$	8.80169			0.347646			0.173823	+	0.984777i	$0.444388\pi$
$642$		0			0
$643$	−20.3898	+	20.3898i	−0.804095	+	0.804095i	−0.983733	−	0.179638i	$-0.942507\pi$
$643$	−20.3898	+	20.3898i	−0.804095	+	0.804095i	0.179638	+	0.983733i	$0.442507\pi$
$644$		0			0
$645$	8.21625	+	8.21625i	0.323515	+	0.323515i
$646$		0			0
$647$			50.8466i			1.99898i	0.0318632	+	0.999492i	$0.489856\pi$
$647$			50.8466i			1.99898i	−0.0318632	+	0.999492i	$0.510144\pi$
$648$		0			0
$649$		−	17.1300i		−	0.672413i
$650$		0			0
$651$	0.719947	+	0.719947i	0.0282170	+	0.0282170i
$652$		0			0
$653$	−1.69069	+	1.69069i	−0.0661618	+	0.0661618i	−0.739413	−	0.673252i	$-0.764897\pi$
$653$	−1.69069	+	1.69069i	−0.0661618	+	0.0661618i	0.673252	+	0.739413i	$0.264897\pi$
$654$		0			0
$655$	5.94722			0.232377
$656$		0			0
$657$	23.5463			0.918627
$658$		0			0
$659$	3.01195	−	3.01195i	0.117329	−	0.117329i	−0.646005	−	0.763334i	$-0.723561\pi$
$659$	3.01195	−	3.01195i	0.117329	−	0.117329i	0.763334	+	0.646005i	$0.223561\pi$
$660$		0			0
$661$	1.93721	+	1.93721i	0.0753488	+	0.0753488i	0.743777	−	0.668428i	$-0.233033\pi$
$661$	1.93721	+	1.93721i	0.0753488	+	0.0753488i	−0.668428	+	0.743777i	$0.733033\pi$
$662$		0			0
$663$		−	15.3619i		−	0.596606i
$664$		0			0
$665$			5.75052i			0.222996i
$666$		0			0
$667$	16.0556	+	16.0556i	0.621676	+	0.621676i
$668$		0			0
$669$	3.45694	−	3.45694i	0.133653	−	0.133653i
$670$		0			0
$671$	−33.4196			−1.29015
$672$		0			0
$673$	17.6937			0.682041			0.341021	−	0.940056i	$-0.389227\pi$
$673$	17.6937			0.682041			0.341021	+	0.940056i	$0.389227\pi$
$674$		0			0
$675$	9.81696	−	9.81696i	0.377855	−	0.377855i
$676$		0			0
$677$	11.2232	+	11.2232i	0.431342	+	0.431342i	0.889085	−	0.457742i	$-0.151342\pi$
$677$	11.2232	+	11.2232i	0.431342	+	0.431342i	−0.457742	+	0.889085i	$0.651342\pi$
$678$		0			0
$679$			2.51522i			0.0965254i
$680$		0			0
$681$		−	21.8606i		−	0.837702i
$682$		0			0
$683$	−6.78769	−	6.78769i	−0.259724	−	0.259724i	0.565218	−	0.824942i	$-0.308792\pi$
$683$	−6.78769	−	6.78769i	−0.259724	−	0.259724i	−0.824942	+	0.565218i	$0.808792\pi$
$684$		0			0
$685$	11.2912	−	11.2912i	0.431415	−	0.431415i
$686$		0			0
$687$	0.615292			0.0234749
$688$		0			0
$689$	−11.5071			−0.438385
$690$		0			0
$691$	34.3472	−	34.3472i	1.30663	−	1.30663i	0.382795	−	0.923833i	$-0.374962\pi$
$691$	34.3472	−	34.3472i	1.30663	−	1.30663i	0.923833	−	0.382795i	$-0.125038\pi$
$692$		0			0
$693$	3.93102	+	3.93102i	0.149327	+	0.149327i
$694$		0			0
$695$			4.38908i			0.166487i
$696$		0			0
$697$		−	26.5316i		−	1.00496i
$698$		0			0
$699$	−8.66519	−	8.66519i	−0.327747	−	0.327747i
$700$		0			0
$701$	4.68514	−	4.68514i	0.176955	−	0.176955i	−0.613072	−	0.790027i	$-0.710066\pi$
$701$	4.68514	−	4.68514i	0.176955	−	0.176955i	0.790027	+	0.613072i	$0.210066\pi$
$702$		0			0
$703$	13.2709			0.500523
$704$		0			0
$705$	3.58214			0.134911
$706$		0			0
$707$	−8.56282	+	8.56282i	−0.322038	+	0.322038i
$708$		0			0
$709$	17.0134	+	17.0134i	0.638951	+	0.638951i	0.950297	−	0.311346i	$-0.100780\pi$
$709$	17.0134	+	17.0134i	0.638951	+	0.638951i	−0.311346	+	0.950297i	$0.600780\pi$
$710$		0			0
$711$		−	9.27715i		−	0.347920i
$712$		0			0
$713$			6.35836i			0.238122i
$714$		0			0
$715$	6.40747	+	6.40747i	0.239626	+	0.239626i
$716$		0			0
$717$	4.40814	−	4.40814i	0.164625	−	0.164625i
$718$		0			0
$719$	24.5042			0.913853			0.456927	−	0.889504i	$-0.348950\pi$
$719$	24.5042			0.913853			0.456927	+	0.889504i	$0.348950\pi$
$720$		0			0
$721$	17.8356			0.664232
$722$		0			0
$723$	1.95201	−	1.95201i	0.0725961	−	0.0725961i
$724$		0			0
$725$	9.38968	+	9.38968i	0.348724	+	0.348724i
$726$		0			0
$727$			41.6544i			1.54488i	0.635090	+	0.772438i	$0.280963\pi$
$727$			41.6544i			1.54488i	−0.635090	+	0.772438i	$0.719037\pi$
$728$		0			0
$729$			4.47546i			0.165758i
$730$		0			0
$731$	47.1727	+	47.1727i	1.74475	+	1.74475i
$732$		0			0
$733$	18.5348	−	18.5348i	0.684598	−	0.684598i	−0.276434	−	0.961033i	$-0.589153\pi$
$733$	18.5348	−	18.5348i	0.684598	−	0.684598i	0.961033	+	0.276434i	$0.0891529\pi$
$734$		0			0
$735$	−1.16992			−0.0431532
$736$		0			0
$737$	−12.2616			−0.451662
$738$		0			0
$739$	−4.93924	+	4.93924i	−0.181693	+	0.181693i	−0.792093	−	0.610400i	$-0.791009\pi$
$739$	−4.93924	+	4.93924i	−0.181693	+	0.181693i	0.610400	+	0.792093i	$0.291009\pi$
$740$		0			0
$741$	6.74461	+	6.74461i	0.247769	+	0.247769i
$742$		0			0
$743$		−	17.8484i		−	0.654796i	−0.944887	−	0.327398i	$-0.893828\pi$
$743$		−	17.8484i		−	0.654796i	0.944887	−	0.327398i	$-0.106172\pi$
$744$		0			0
$745$		−	4.48257i		−	0.164229i
$746$		0			0
$747$	−20.9283	−	20.9283i	−0.765726	−	0.765726i
$748$		0			0
$749$	−8.49285	+	8.49285i	−0.310322	+	0.310322i
$750$		0			0
$751$	−18.3471			−0.669495			−0.334747	−	0.942308i	$-0.608651\pi$
$751$	−18.3471			−0.669495			−0.334747	+	0.942308i	$0.608651\pi$
$752$		0			0
$753$	−2.49680			−0.0909885
$754$		0			0
$755$	17.7042	−	17.7042i	0.644322	−	0.644322i
$756$		0			0
$757$	4.90437	+	4.90437i	0.178252	+	0.178252i	0.790594	−	0.612341i	$-0.209772\pi$
$757$	4.90437	+	4.90437i	0.178252	+	0.178252i	−0.612341	+	0.790594i	$0.709772\pi$
$758$		0			0
$759$		−	10.9624i		−	0.397909i
$760$		0			0
$761$			3.48443i			0.126311i	0.998004	+	0.0631553i	$0.0201163\pi$
$761$			3.48443i			0.126311i	−0.998004	+	0.0631553i	$0.979884\pi$
$762$		0			0
$763$	−7.26700	−	7.26700i	−0.263083	−	0.263083i
$764$		0			0
$765$	−14.9317	+	14.9317i	−0.539857	+	0.539857i
$766$		0			0
$767$	−18.9367			−0.683764
$768$		0			0
$769$	−13.5559			−0.488837			−0.244418	−	0.969670i	$-0.578597\pi$
$769$	−13.5559			−0.488837			−0.244418	+	0.969670i	$0.578597\pi$
$770$		0			0
$771$	6.57694	−	6.57694i	0.236863	−	0.236863i
$772$		0			0
$773$	20.3801	+	20.3801i	0.733022	+	0.733022i	0.971217	−	0.238195i	$-0.0765557\pi$
$773$	20.3801	+	20.3801i	0.733022	+	0.733022i	−0.238195	+	0.971217i	$0.576556\pi$
$774$		0			0
$775$			3.71851i			0.133573i
$776$		0			0
$777$			2.69992i			0.0968592i
$778$		0			0
$779$	11.6487	+	11.6487i	0.417357	+	0.417357i
$780$		0			0
$781$	19.9599	−	19.9599i	0.714223	−	0.714223i
$782$		0			0
$783$	−19.1978			−0.686073
$784$		0			0
$785$	−21.0809			−0.752409
$786$		0			0
$787$	−27.7178	+	27.7178i	−0.988034	+	0.988034i	−0.999929	−	0.0118952i	$-0.996214\pi$
$787$	−27.7178	+	27.7178i	−0.988034	+	0.988034i	0.0118952	+	0.999929i	$0.496214\pi$
$788$		0			0
$789$	−6.11565	−	6.11565i	−0.217723	−	0.217723i
$790$		0			0
$791$			13.8351i			0.491920i
$792$		0			0
$793$			36.9442i			1.31193i
$794$		0			0
$795$	−3.53172	−	3.53172i	−0.125257	−	0.125257i
$796$		0			0
$797$	−2.87837	+	2.87837i	−0.101957	+	0.101957i	−0.756245	−	0.654288i	$-0.772968\pi$
$797$	−2.87837	+	2.87837i	−0.101957	+	0.101957i	0.654288	+	0.756245i	$0.272968\pi$
$798$		0			0
$799$	20.5664			0.727588
$800$		0			0
$801$	−38.5984			−1.36381
$802$		0			0
$803$	17.8048	−	17.8048i	0.628318	−	0.628318i
$804$		0			0
$805$	−5.16619	−	5.16619i	−0.182084	−	0.182084i
$806$		0			0
$807$		−	2.10931i		−	0.0742511i
$808$		0			0
$809$			21.5478i			0.757581i	0.925482	+	0.378791i	$0.123660\pi$
$809$			21.5478i			0.757581i	−0.925482	+	0.378791i	$0.876340\pi$
$810$		0			0
$811$	−20.4977	−	20.4977i	−0.719772	−	0.719772i	0.248787	−	0.968558i	$-0.419968\pi$
$811$	−20.4977	−	20.4977i	−0.719772	−	0.719772i	−0.968558	+	0.248787i	$0.919968\pi$
$812$		0			0
$813$	3.39687	−	3.39687i	0.119134	−	0.119134i
$814$		0			0
$815$	12.5402			0.439263
$816$		0			0
$817$	−41.4222			−1.44918
$818$		0			0
$819$	4.34560	−	4.34560i	0.151848	−	0.151848i
$820$		0			0
$821$	−9.10771	−	9.10771i	−0.317861	−	0.317861i	0.530084	−	0.847945i	$-0.322160\pi$
$821$	−9.10771	−	9.10771i	−0.317861	−	0.317861i	−0.847945	+	0.530084i	$0.822160\pi$
$822$		0			0
$823$			41.4587i			1.44516i	0.691287	+	0.722580i	$0.257044\pi$
$823$			41.4587i			1.44516i	−0.691287	+	0.722580i	$0.742956\pi$
$824$		0			0
$825$		−	6.41104i		−	0.223204i
$826$		0			0
$827$	−14.8134	−	14.8134i	−0.515111	−	0.515111i	0.400977	−	0.916088i	$-0.368671\pi$
$827$	−14.8134	−	14.8134i	−0.515111	−	0.515111i	−0.916088	+	0.400977i	$0.868671\pi$
$828$		0			0
$829$	17.2948	−	17.2948i	0.600675	−	0.600675i	−0.339817	−	0.940492i	$-0.610365\pi$
$829$	17.2948	−	17.2948i	0.600675	−	0.600675i	0.940492	+	0.339817i	$0.110365\pi$
$830$		0			0
$831$	25.5985			0.888002
$832$		0			0
$833$	−6.71697			−0.232729
$834$		0			0
$835$	0.645381	−	0.645381i	0.0223343	−	0.0223343i
$836$		0			0
$837$	−3.80136	−	3.80136i	−0.131394	−	0.131394i
$838$		0			0
$839$			26.6645i			0.920562i	0.887773	+	0.460281i	$0.152251\pi$
$839$			26.6645i			0.920562i	−0.887773	+	0.460281i	$0.847749\pi$
$840$		0			0
$841$			10.6378i			0.366820i
$842$		0			0
$843$	0.960018	+	0.960018i	0.0330648	+	0.0330648i
$844$		0			0
$845$	−5.59137	+	5.59137i	−0.192349	+	0.192349i
$846$		0			0
$847$	−5.05502			−0.173693
$848$		0			0
$849$	−17.2722			−0.592779
$850$		0			0
$851$	−11.9224	+	11.9224i	−0.408696	+	0.408696i
$852$		0			0
$853$	−12.4072	−	12.4072i	−0.424815	−	0.424815i	0.462043	−	0.886858i	$-0.347117\pi$
$853$	−12.4072	−	12.4072i	−0.424815	−	0.424815i	−0.886858	+	0.462043i	$0.847117\pi$
$854$		0			0
$855$		−	13.1115i		−	0.448404i
$856$		0			0
$857$		−	2.47165i		−	0.0844298i	−0.999109	−	0.0422149i	$-0.986559\pi$
$857$		−	2.47165i		−	0.0844298i	0.999109	−	0.0422149i	$-0.0134414\pi$
$858$		0			0
$859$	−18.9839	−	18.9839i	−0.647723	−	0.647723i	0.304719	−	0.952442i	$-0.401437\pi$
$859$	−18.9839	−	18.9839i	−0.647723	−	0.647723i	−0.952442	+	0.304719i	$0.901437\pi$
$860$		0			0
$861$	−2.36988	+	2.36988i	−0.0807652	+	0.0807652i
$862$		0			0
$863$	35.3848			1.20451			0.602255	−	0.798303i	$-0.294269\pi$
$863$	35.3848			1.20451			0.602255	+	0.798303i	$0.294269\pi$
$864$		0			0
$865$	12.3936			0.421395
$866$		0			0
$867$	16.8700	−	16.8700i	0.572935	−	0.572935i
$868$		0			0
$869$	−7.01504	−	7.01504i	−0.237969	−	0.237969i
$870$		0			0
$871$			13.5548i			0.459286i
$872$		0			0
$873$		−	5.73484i		−	0.194095i
$874$		0			0
$875$	−7.89615	−	7.89615i	−0.266939	−	0.266939i
$876$		0			0
$877$	4.32355	−	4.32355i	0.145996	−	0.145996i	−0.630331	−	0.776327i	$-0.717081\pi$
$877$	4.32355	−	4.32355i	0.145996	−	0.145996i	0.776327	+	0.630331i	$0.217081\pi$
$878$		0			0
$879$	0.321424			0.0108414
$880$		0			0
$881$	−26.3944			−0.889249			−0.444625	−	0.895717i	$-0.646663\pi$
$881$	−26.3944			−0.889249			−0.444625	+	0.895717i	$0.646663\pi$
$882$		0			0
$883$	29.3078	−	29.3078i	0.986286	−	0.986286i	−0.0136216	−	0.999907i	$-0.504336\pi$
$883$	29.3078	−	29.3078i	0.986286	−	0.986286i	0.999907	+	0.0136216i	$0.00433601\pi$
$884$		0			0
$885$	−5.81199	−	5.81199i	−0.195368	−	0.195368i
$886$		0			0
$887$		−	18.2241i		−	0.611904i	−0.952047	−	0.305952i	$-0.901025\pi$
$887$		−	18.2241i		−	0.611904i	0.952047	−	0.305952i	$-0.0989747\pi$
$888$		0			0
$889$			14.1434i			0.474355i
$890$		0			0
$891$	−5.23916	−	5.23916i	−0.175519	−	0.175519i
$892$		0			0
$893$	−9.02967	+	9.02967i	−0.302166	+	0.302166i
$894$		0			0
$895$	14.8508			0.496407
$896$		0			0
$897$	−12.1185			−0.404626
$898$		0			0
$899$	3.63591	−	3.63591i	0.121264	−	0.121264i
$900$		0			0
$901$	−20.2770	−	20.2770i	−0.675525	−	0.675525i
$902$		0			0
$903$		−	8.42719i		−	0.280439i
$904$		0			0
$905$			27.2801i			0.906821i
$906$		0			0
$907$	13.0697	+	13.0697i	0.433974	+	0.433974i	0.889978	−	0.456004i	$-0.150720\pi$
$907$	13.0697	+	13.0697i	0.433974	+	0.433974i	−0.456004	+	0.889978i	$0.650720\pi$
$908$		0			0
$909$	19.5237	−	19.5237i	0.647560	−	0.647560i
$910$		0			0
$911$	−21.3908			−0.708708			−0.354354	−	0.935111i	$-0.615299\pi$
$911$	−21.3908			−0.708708			−0.354354	+	0.935111i	$0.615299\pi$
$912$		0			0
$913$	−31.6504			−1.04747
$914$		0			0
$915$	−11.3388	+	11.3388i	−0.374849	+	0.374849i
$916$		0			0
$917$	−3.04995	−	3.04995i	−0.100718	−	0.100718i
$918$		0			0
$919$		−	10.5692i		−	0.348645i	−0.984689	−	0.174322i	$-0.944227\pi$
$919$		−	10.5692i		−	0.348645i	0.984689	−	0.174322i	$-0.0557735\pi$
$920$		0			0
$921$		−	14.8561i		−	0.489525i
$922$		0			0
$923$	−22.0650	−	22.0650i	−0.726279	−	0.726279i
$924$		0			0
$925$	−6.97251	+	6.97251i	−0.229255	+	0.229255i
$926$		0			0
$927$	−40.6661			−1.33565
$928$		0			0
$929$	−17.5372			−0.575378			−0.287689	−	0.957724i	$-0.592887\pi$
$929$	−17.5372			−0.575378			−0.287689	+	0.957724i	$0.592887\pi$
$930$		0			0
$931$	2.94908	−	2.94908i	0.0966521	−	0.0966521i
$932$		0			0
$933$	2.21673	+	2.21673i	0.0725725	+	0.0725725i
$934$		0			0
$935$			22.5816i			0.738497i
$936$		0			0
$937$		−	43.7391i		−	1.42890i	−0.699689	−	0.714448i	$-0.746678\pi$
$937$		−	43.7391i		−	1.42890i	0.699689	−	0.714448i	$-0.253322\pi$
$938$		0			0
$939$	−6.28177	−	6.28177i	−0.204998	−	0.204998i
$940$		0			0
$941$	7.61563	−	7.61563i	0.248262	−	0.248262i	−0.571995	−	0.820257i	$-0.693830\pi$
$941$	7.61563	−	7.61563i	0.248262	−	0.248262i	0.820257	+	0.571995i	$0.193830\pi$
$942$		0			0
$943$	−20.9300			−0.681576
$944$		0			0
$945$	6.17724			0.200946
$946$		0			0
$947$	−9.69441	+	9.69441i	−0.315026	+	0.315026i	−0.846853	−	0.531827i	$-0.821506\pi$
$947$	−9.69441	+	9.69441i	−0.315026	+	0.315026i	0.531827	+	0.846853i	$0.321506\pi$
$948$		0			0
$949$	−19.6826	−	19.6826i	−0.638924	−	0.638924i
$950$		0			0
$951$			18.9522i			0.614568i
$952$		0			0
$953$		−	3.19629i		−	0.103538i	−0.998659	−	0.0517690i	$-0.983514\pi$
$953$		−	3.19629i		−	0.103538i	0.998659	−	0.0517690i	$-0.0164860\pi$
$954$		0			0
$955$	21.8804	+	21.8804i	0.708034	+	0.708034i
$956$		0			0
$957$	−6.26864	+	6.26864i	−0.202636	+	0.202636i
$958$		0			0
$959$	−11.5811			−0.373973
$960$		0			0
$961$	−29.5601			−0.953552
$962$		0			0
$963$	19.3641	−	19.3641i	0.624001	−	0.624001i
$964$		0			0
$965$	−6.15604	−	6.15604i	−0.198170	−	0.198170i
$966$		0			0
$967$			25.7940i			0.829479i	0.909940	+	0.414739i	$0.136127\pi$
$967$			25.7940i			0.829479i	−0.909940	+	0.414739i	$0.863873\pi$
$968$		0			0
$969$			23.7698i			0.763595i
$970$		0			0
$971$	11.9004	+	11.9004i	0.381901	+	0.381901i	0.871787	−	0.489885i	$-0.162961\pi$
$971$	11.9004	+	11.9004i	0.381901	+	0.381901i	−0.489885	+	0.871787i	$0.662961\pi$
$972$		0			0
$973$	2.25088	−	2.25088i	0.0721599	−	0.0721599i
$974$		0			0
$975$	−7.08719			−0.226972
$976$		0			0
$977$	2.74136			0.0877038			0.0438519	−	0.999038i	$-0.486037\pi$
$977$	2.74136			0.0877038			0.0438519	+	0.999038i	$0.486037\pi$
$978$		0			0
$979$	−29.1867	+	29.1867i	−0.932810	+	0.932810i
$980$		0			0
$981$	16.5691	+	16.5691i	0.529012	+	0.529012i
$982$		0			0
$983$		−	44.6295i		−	1.42346i	−0.702454	−	0.711729i	$-0.747912\pi$
$983$		−	44.6295i		−	1.42346i	0.702454	−	0.711729i	$-0.252088\pi$
$984$		0			0
$985$			7.44310i			0.237157i
$986$		0			0
$987$	−1.83705	−	1.83705i	−0.0584740	−	0.0584740i
$988$		0			0
$989$	37.2132	−	37.2132i	1.18331	−	1.18331i
$990$		0			0
$991$	−1.08451			−0.0344508			−0.0172254	−	0.999852i	$-0.505483\pi$
$991$	−1.08451			−0.0344508			−0.0172254	+	0.999852i	$0.505483\pi$
$992$		0			0
$993$	−8.11482			−0.257516
$994$		0			0
$995$	−24.9888	+	24.9888i	−0.792200	+	0.792200i
$996$		0			0
$997$	29.3910	+	29.3910i	0.930823	+	0.930823i	0.997757	−	0.0669342i	$-0.0213217\pi$
$997$	29.3910	+	29.3910i	0.930823	+	0.930823i	−0.0669342	+	0.997757i	$0.521322\pi$
$998$		0			0
$999$		−	14.2557i		−	0.451031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.m.d.113.5		12
4.3	odd	2		112.2.m.d.85.4	yes	12
8.3	odd	2		896.2.m.g.225.5		12
8.5	even	2		896.2.m.h.225.2		12
16.3	odd	4		112.2.m.d.29.4	✓	12
16.5	even	4		896.2.m.h.673.2		12
16.11	odd	4		896.2.m.g.673.5		12
16.13	even	4	inner	448.2.m.d.337.5		12
28.3	even	6		784.2.x.m.373.1		24
28.11	odd	6		784.2.x.l.373.1		24
28.19	even	6		784.2.x.m.165.5		24
28.23	odd	6		784.2.x.l.165.5		24
28.27	even	2		784.2.m.h.197.4		12
32.3	odd	8		7168.2.a.bj.1.5		12
32.13	even	8		7168.2.a.bi.1.5		12
32.19	odd	8		7168.2.a.bj.1.8		12
32.29	even	8		7168.2.a.bi.1.8		12
112.3	even	12		784.2.x.m.765.5		24
112.19	even	12		784.2.x.m.557.1		24
112.51	odd	12		784.2.x.l.557.1		24
112.67	odd	12		784.2.x.l.765.5		24
112.83	even	4		784.2.m.h.589.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.4	✓	12	16.3	odd	4
112.2.m.d.85.4	yes	12	4.3	odd	2
448.2.m.d.113.5		12	1.1	even	1	trivial
448.2.m.d.337.5		12	16.13	even	4	inner
784.2.m.h.197.4		12	28.27	even	2
784.2.m.h.589.4		12	112.83	even	4
784.2.x.l.165.5		24	28.23	odd	6
784.2.x.l.373.1		24	28.11	odd	6
784.2.x.l.557.1		24	112.51	odd	12
784.2.x.l.765.5		24	112.67	odd	12
784.2.x.m.165.5		24	28.19	even	6
784.2.x.m.373.1		24	28.3	even	6
784.2.x.m.557.1		24	112.19	even	12
784.2.x.m.765.5		24	112.3	even	12
896.2.m.g.225.5		12	8.3	odd	2
896.2.m.g.673.5		12	16.11	odd	4
896.2.m.h.225.2		12	8.5	even	2
896.2.m.h.673.2		12	16.5	even	4
7168.2.a.bi.1.5		12	32.13	even	8
7168.2.a.bi.1.8		12	32.29	even	8
7168.2.a.bj.1.5		12	32.3	odd	8
7168.2.a.bj.1.8		12	32.19	odd	8

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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.m (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.599978 - 0.599978i) q^{3} +(0.974969 + 0.974969i) q^{5} -1.00000i q^{7} +2.28005i q^{9} +O(q^{10})\)	\(q+(0.599978 - 0.599978i) q^{3} +(0.974969 + 0.974969i) q^{5} -1.00000i q^{7} +2.28005i q^{9} +(1.72409 + 1.72409i) q^{11} +(1.90592 - 1.90592i) q^{13} +1.16992 q^{15} +6.71697 q^{17} +(-2.94908 + 2.94908i) q^{19} +(-0.599978 - 0.599978i) q^{21} -5.29883i q^{23} -3.09887i q^{25} +(3.16792 + 3.16792i) q^{27} +(-3.03004 + 3.03004i) q^{29} -1.19996 q^{31} +2.06883 q^{33} +(0.974969 - 0.974969i) q^{35} +(-2.25002 - 2.25002i) q^{37} -2.28702i q^{39} -3.94994i q^{41} +(7.02292 + 7.02292i) q^{43} +(-2.22298 + 2.22298i) q^{45} +3.06186 q^{47} -1.00000 q^{49} +(4.03004 - 4.03004i) q^{51} +(-3.01877 - 3.01877i) q^{53} +3.36187i q^{55} +3.53876i q^{57} +(-4.96785 - 4.96785i) q^{59} +(-9.69194 + 9.69194i) q^{61} +2.28005 q^{63} +3.71643 q^{65} +(-3.55596 + 3.55596i) q^{67} +(-3.17918 - 3.17918i) q^{69} -11.5771i q^{71} -10.3271i q^{73} +(-1.85925 - 1.85925i) q^{75} +(1.72409 - 1.72409i) q^{77} -4.06883 q^{79} -3.03880 q^{81} +(-9.17886 + 9.17886i) q^{83} +(6.54884 + 6.54884i) q^{85} +3.63591i q^{87} +16.9287i q^{89} +(-1.90592 - 1.90592i) q^{91} +(-0.719947 + 0.719947i) q^{93} -5.75052 q^{95} -2.51522 q^{97} +(-3.93102 + 3.93102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} + 4 q^{5}+O(q^{10}) \) 12 * q - 4 * q^3 + 4 * q^5	\( 12 q - 4 q^{3} + 4 q^{5} + 24 q^{15} - 8 q^{17} + 4 q^{21} - 4 q^{27} - 4 q^{29} + 8 q^{31} + 4 q^{35} - 20 q^{37} - 16 q^{43} + 40 q^{45} - 16 q^{47} - 12 q^{49} + 16 q^{51} + 4 q^{53} + 16 q^{59} - 20 q^{61} - 12 q^{63} + 32 q^{65} - 24 q^{67} - 4 q^{69} + 40 q^{75} - 24 q^{79} - 44 q^{81} + 20 q^{83} - 8 q^{85} - 48 q^{93} + 48 q^{97} - 32 q^{99}+O(q^{100}) \) 12 * q - 4 * q^3 + 4 * q^5 + 24 * q^15 - 8 * q^17 + 4 * q^21 - 4 * q^27 - 4 * q^29 + 8 * q^31 + 4 * q^35 - 20 * q^37 - 16 * q^43 + 40 * q^45 - 16 * q^47 - 12 * q^49 + 16 * q^51 + 4 * q^53 + 16 * q^59 - 20 * q^61 - 12 * q^63 + 32 * q^65 - 24 * q^67 - 4 * q^69 + 40 * q^75 - 24 * q^79 - 44 * q^81 + 20 * q^83 - 8 * q^85 - 48 * q^93 + 48 * q^97 - 32 * q^99

Introduction

L-functions

Modular forms

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Database

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