LMFDB - Embedded newform 804.2.q.b.397.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(25,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("804.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.q (of order $11$, degree $10$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			397.3
Character	$\chi$	$=$	804.397
Dual form			804.2.q.b.241.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{3} +(-0.960253 + 0.281956i) q^{5} +(0.00738542 - 0.00852322i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{3} +(-0.960253 + 0.281956i) q^{5} +(0.00738542 - 0.00852322i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(-0.0286737 + 0.00841935i) q^{11} +(-0.796658 + 0.511981i) q^{13} +(0.655379 + 0.756348i) q^{15} +(1.11543 - 7.75799i) q^{17} +(-0.720395 - 0.831380i) q^{19} +(-0.0108210 - 0.00317734i) q^{21} +(-2.46117 - 5.38921i) q^{23} +(-3.36368 + 2.16171i) q^{25} +(0.959493 + 0.281733i) q^{27} +0.886974 q^{29} +(-7.56934 - 4.86452i) q^{31} +(0.0195700 + 0.0225850i) q^{33} +(-0.00468869 + 0.0102668i) q^{35} -6.19364 q^{37} +(0.796658 + 0.511981i) q^{39} +(-0.919259 + 6.39359i) q^{41} +(0.139722 - 0.971788i) q^{43} +(0.415744 - 0.910352i) q^{45} +(-2.18150 - 4.77681i) q^{47} +(0.996186 + 6.92862i) q^{49} +(-7.52028 + 2.20815i) q^{51} +(-0.980545 - 6.81984i) q^{53} +(0.0251601 - 0.0161694i) q^{55} +(-0.456987 + 1.00066i) q^{57} +(-8.10432 - 5.20833i) q^{59} +(6.93827 + 2.03726i) q^{61} +(0.00160500 + 0.0111630i) q^{63} +(0.620637 - 0.716253i) q^{65} +(7.38311 + 3.53408i) q^{67} +(-3.87979 + 4.47751i) q^{69} +(-1.67456 - 11.6468i) q^{71} +(-9.65633 - 2.83536i) q^{73} +(3.36368 + 2.16171i) q^{75} +(-0.000140007 + 0.000306573i) q^{77} +(5.45532 - 3.50592i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(7.98130 - 2.34352i) q^{83} +(1.11631 + 7.76413i) q^{85} +(-0.368462 - 0.806820i) q^{87} +(-4.02122 + 8.80524i) q^{89} +(-0.00151992 + 0.0105713i) q^{91} +(-1.28050 + 8.90611i) q^{93} +(0.926173 + 0.595215i) q^{95} -13.0928 q^{97} +(0.0124143 - 0.0271836i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	$ 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) $ 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$		0			0
$5$	−0.960253	+	0.281956i	−0.429438	+	0.126094i	−0.489307	−	0.872112i	$-0.662750\pi$
$5$	−0.960253	+	0.281956i	−0.429438	+	0.126094i	0.0598685	+	0.998206i	$0.480932\pi$
$6$		0			0
$7$	0.00738542	−	0.00852322i	0.00279142	−	0.00322148i	−0.754352	−	0.656470i	$-0.772049\pi$
$7$	0.00738542	−	0.00852322i	0.00279142	−	0.00322148i	0.757144	+	0.653249i	$0.226594\pi$
$8$		0			0
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$		0			0
$11$	−0.0286737	+	0.00841935i	−0.00864544	+	0.00253853i	−0.286052	−	0.958214i	$-0.592343\pi$
$11$	−0.0286737	+	0.00841935i	−0.00864544	+	0.00253853i	0.277407	+	0.960753i	$0.410525\pi$
$12$		0			0
$13$	−0.796658	+	0.511981i	−0.220953	+	0.141998i	−0.646435	−	0.762969i	$-0.723741\pi$
$13$	−0.796658	+	0.511981i	−0.220953	+	0.141998i	0.425482	+	0.904967i	$0.360105\pi$
$14$		0			0
$15$	0.655379	+	0.756348i	0.169218	+	0.195288i
$16$		0			0
$17$	1.11543	−	7.75799i	0.270532	−	1.88159i	−0.172390	−	0.985029i	$-0.555149\pi$
$17$	1.11543	−	7.75799i	0.270532	−	1.88159i	0.442921	−	0.896560i	$-0.353942\pi$
$18$		0			0
$19$	−0.720395	−	0.831380i	−0.165270	−	0.190732i	0.667074	−	0.744992i	$-0.267547\pi$
$19$	−0.720395	−	0.831380i	−0.165270	−	0.190732i	−0.832343	+	0.554260i	$0.813001\pi$
$20$		0			0
$21$	−0.0108210	−	0.00317734i	−0.00236134	−	0.000693351i
$22$		0			0
$23$	−2.46117	−	5.38921i	−0.513189	−	1.12373i	−0.971954	−	0.235170i	$-0.924435\pi$
$23$	−2.46117	−	5.38921i	−0.513189	−	1.12373i	0.458765	−	0.888557i	$-0.348292\pi$
$24$		0			0
$25$	−3.36368	+	2.16171i	−0.672736	+	0.432341i
$26$		0			0
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$		0			0
$29$	0.886974			0.164707			0.0823535	−	0.996603i	$-0.473756\pi$
$29$	0.886974			0.164707			0.0823535	+	0.996603i	$0.473756\pi$
$30$		0			0
$31$	−7.56934	−	4.86452i	−1.35949	−	0.873693i	−0.361223	−	0.932480i	$-0.617641\pi$
$31$	−7.56934	−	4.86452i	−1.35949	−	0.873693i	−0.998271	+	0.0587864i	$0.981277\pi$
$32$		0			0
$33$	0.0195700	+	0.0225850i	0.00340670	+	0.00393154i
$34$		0			0
$35$	−0.00468869	+	0.0102668i	−0.000792534	+	0.00173541i
$36$		0			0
$37$	−6.19364			−1.01823			−0.509114	−	0.860699i	$-0.670027\pi$
$37$	−6.19364			−1.01823			−0.509114	+	0.860699i	$0.670027\pi$
$38$		0			0
$39$	0.796658	+	0.511981i	0.127567	+	0.0819826i
$40$		0			0
$41$	−0.919259	+	6.39359i	−0.143564	+	0.998510i	0.782905	+	0.622141i	$0.213737\pi$
$41$	−0.919259	+	6.39359i	−0.143564	+	0.998510i	−0.926470	+	0.376370i	$0.877172\pi$
$42$		0			0
$43$	0.139722	−	0.971788i	0.0213074	−	0.148196i	−0.976390	−	0.216014i	$-0.930694\pi$
$43$	0.139722	−	0.971788i	0.0213074	−	0.148196i	0.997698	+	0.0678174i	$0.0216035\pi$
$44$		0			0
$45$	0.415744	−	0.910352i	0.0619754	−	0.135707i
$46$		0			0
$47$	−2.18150	−	4.77681i	−0.318204	−	0.696770i	0.681171	−	0.732125i	$-0.261471\pi$
$47$	−2.18150	−	4.77681i	−0.318204	−	0.696770i	−0.999375	+	0.0353548i	$0.988744\pi$
$48$		0			0
$49$	0.996186	+	6.92862i	0.142312	+	0.989803i
$50$		0			0
$51$	−7.52028	+	2.20815i	−1.05305	+	0.309203i
$52$		0			0
$53$	−0.980545	−	6.81984i	−0.134688	−	0.936777i	−0.939330	−	0.343016i	$-0.888551\pi$
$53$	−0.980545	−	6.81984i	−0.134688	−	0.936777i	0.804641	−	0.593761i	$-0.202358\pi$
$54$		0			0
$55$	0.0251601	−	0.0161694i	0.00339259	−	0.00218028i
$56$		0			0
$57$	−0.456987	+	1.00066i	−0.0605294	+	0.132541i
$58$		0			0
$59$	−8.10432	−	5.20833i	−1.05509	−	0.678067i	−0.106419	−	0.994321i	$-0.533938\pi$
$59$	−8.10432	−	5.20833i	−1.05509	−	0.678067i	−0.948674	+	0.316254i	$0.897575\pi$
$60$		0			0
$61$	6.93827	+	2.03726i	0.888355	+	0.260845i	0.693904	−	0.720068i	$-0.255889\pi$
$61$	6.93827	+	2.03726i	0.888355	+	0.260845i	0.194451	+	0.980912i	$0.437707\pi$
$62$		0			0
$63$	0.00160500	+	0.0111630i	0.000202212	+	0.00140641i
$64$		0			0
$65$	0.620637	−	0.716253i	0.0769805	−	0.0888403i
$66$		0			0
$67$	7.38311	+	3.53408i	0.901990	+	0.431756i
$67$	7.38311	+	3.53408i	0.901990	+	0.431756i
$68$		0			0
$69$	−3.87979	+	4.47751i	−0.467072	+	0.539029i
$70$		0			0
$71$	−1.67456	−	11.6468i	−0.198734	−	1.38222i	−0.807964	−	0.589231i	$-0.799431\pi$
$71$	−1.67456	−	11.6468i	−0.198734	−	1.38222i	0.609231	−	0.792993i	$-0.291478\pi$
$72$		0			0
$73$	−9.65633	−	2.83536i	−1.13019	−	0.331853i	−0.337407	−	0.941359i	$-0.609550\pi$
$73$	−9.65633	−	2.83536i	−1.13019	−	0.331853i	−0.792782	+	0.609506i	$0.791368\pi$
$74$		0			0
$75$	3.36368	+	2.16171i	0.388404	+	0.249612i
$76$		0			0
$77$	−0.000140007	0	0.000306573i	−1.59553e−5	0	3.49372e-5i
$78$		0			0
$79$	5.45532	−	3.50592i	0.613771	−	0.394447i	−0.196498	−	0.980504i	$-0.562957\pi$
$79$	5.45532	−	3.50592i	0.613771	−	0.394447i	0.810270	+	0.586057i	$0.199321\pi$
$80$		0			0
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$		0			0
$83$	7.98130	−	2.34352i	0.876062	−	0.257235i	0.187370	−	0.982289i	$-0.440004\pi$
$83$	7.98130	−	2.34352i	0.876062	−	0.257235i	0.688692	+	0.725054i	$0.258185\pi$
$84$		0			0
$85$	1.11631	+	7.76413i	0.121081	+	0.842139i
$86$		0			0
$87$	−0.368462	−	0.806820i	−0.0395033	−	0.0865002i
$88$		0			0
$89$	−4.02122	+	8.80524i	−0.426248	+	0.933354i	0.567672	+	0.823255i	$0.307844\pi$
$89$	−4.02122	+	8.80524i	−0.426248	+	0.933354i	−0.993921	+	0.110099i	$0.964883\pi$
$90$		0			0
$91$	−0.00151992	+	0.0105713i	−0.000159331	+	0.00110817i
$92$		0			0
$93$	−1.28050	+	8.90611i	−0.132782	+	0.923520i
$94$		0			0
$95$	0.926173	+	0.595215i	0.0950233	+	0.0610678i
$96$		0			0
$97$	−13.0928			−1.32937			−0.664687	−	0.747122i	$-0.731435\pi$
$97$	−13.0928			−1.32937			−0.664687	+	0.747122i	$0.731435\pi$
$98$		0			0
$99$	0.0124143	−	0.0271836i	0.00124769	−	0.00273206i
$100$		0			0
$101$	−2.54029	−	2.93165i	−0.252768	−	0.291710i	0.615157	−	0.788404i	$-0.289092\pi$
$101$	−2.54029	−	2.93165i	−0.252768	−	0.291710i	−0.867926	+	0.496694i	$0.834547\pi$
$102$		0			0
$103$	1.68237	+	1.08119i	0.165769	+	0.106533i	0.620895	−	0.783894i	$-0.286769\pi$
$103$	1.68237	+	1.08119i	0.165769	+	0.106533i	−0.455126	+	0.890427i	$0.650406\pi$
$104$		0			0
$105$	0.0112868			0.00110148
$106$		0			0
$107$	8.53327	+	2.50559i	0.824942	+	0.242225i	0.666843	−	0.745198i	$-0.267645\pi$
$107$	8.53327	+	2.50559i	0.824942	+	0.242225i	0.158099	+	0.987423i	$0.449463\pi$
$108$		0			0
$109$	11.6058	−	7.45861i	1.11164	−	0.714405i	0.149987	−	0.988688i	$-0.452077\pi$
$109$	11.6058	−	7.45861i	1.11164	−	0.714405i	0.961649	+	0.274283i	$0.0884404\pi$
$110$		0			0
$111$	2.57293	+	5.63393i	0.244212	+	0.534749i
$112$		0			0
$113$	16.7838	+	4.92817i	1.57889	+	0.463603i	0.949573	−	0.313546i	$-0.101517\pi$
$113$	16.7838	+	4.92817i	1.57889	+	0.463603i	0.629316	+	0.777150i	$0.283335\pi$
$114$		0			0
$115$	3.88286	+	4.48106i	0.362079	+	0.417861i
$116$		0			0
$117$	0.134771	−	0.937350i	0.0124595	−	0.0866581i
$118$		0			0
$119$	−0.0578852	−	0.0668031i	−0.00530633	−	0.00612383i
$120$		0			0
$121$	−9.25304	+	5.94657i	−0.841185	+	0.540597i
$122$		0			0
$123$	6.19768	−	1.81980i	0.558826	−	0.164086i
$124$		0			0
$125$	5.89737	−	6.80593i	0.527477	−	0.608741i
$126$		0			0
$127$	−2.41350	+	2.78532i	−0.214163	+	0.247158i	−0.852659	−	0.522468i	$-0.825012\pi$
$127$	−2.41350	+	2.78532i	−0.214163	+	0.247158i	0.638496	+	0.769625i	$0.279557\pi$
$128$		0			0
$129$	−0.942012	+	0.276600i	−0.0829395	+	0.0243532i
$130$		0			0
$131$	−6.78648	−	14.8603i	−0.592938	−	1.29835i	−0.933651	−	0.358185i	$-0.883396\pi$
$131$	−6.78648	−	14.8603i	−0.592938	−	1.29835i	0.340713	−	0.940167i	$-0.389332\pi$
$132$		0			0
$133$	−0.0124064			−0.00107578
$134$		0			0
$135$	−1.00079			−0.0861344
$136$		0			0
$137$	−1.73337	−	3.79556i	−0.148092	−	0.324277i	0.821019	−	0.570901i	$-0.193406\pi$
$137$	−1.73337	−	3.79556i	−0.148092	−	0.324277i	−0.969111	+	0.246624i	$0.920679\pi$
$138$		0			0
$139$	20.9716	−	6.15783i	1.77879	−	0.522300i	0.783689	−	0.621154i	$-0.213336\pi$
$139$	20.9716	−	6.15783i	1.77879	−	0.522300i	0.995102	+	0.0988538i	$0.0315176\pi$
$140$		0			0
$141$	−3.43892	+	3.96872i	−0.289609	+	0.334227i
$142$		0			0
$143$	0.0185326	−	0.0213877i	0.00154977	−	0.00178853i
$144$		0			0
$145$	−0.851719	+	0.250087i	−0.0707315	+	0.0207686i
$146$		0			0
$147$	5.88867	−	3.78442i	0.485689	−	0.312133i
$148$		0			0
$149$	3.32893	+	3.84179i	0.272717	+	0.314732i	0.875543	−	0.483141i	$-0.160504\pi$
$149$	3.32893	+	3.84179i	0.272717	+	0.314732i	−0.602826	+	0.797873i	$0.705959\pi$
$150$		0			0
$151$	−1.55503	+	10.8155i	−0.126547	+	0.880150i	0.823338	+	0.567551i	$0.192109\pi$
$151$	−1.55503	+	10.8155i	−0.126547	+	0.880150i	−0.949885	+	0.312600i	$0.898800\pi$
$152$		0			0
$153$	5.13265	+	5.92339i	0.414950	+	0.478878i
$154$		0			0
$155$	8.64005	+	2.53695i	0.693986	+	0.203773i
$156$		0			0
$157$	−1.14967	−	2.51742i	−0.0917534	−	0.200912i	0.858191	−	0.513330i	$-0.171588\pi$
$157$	−1.14967	−	2.51742i	−0.0917534	−	0.200912i	−0.949945	+	0.312418i	$0.898861\pi$
$158$		0			0
$159$	−5.79621	+	3.72500i	−0.459670	+	0.295412i
$160$		0			0
$161$	−0.0641102	−	0.0188244i	−0.00505259	−	0.00148357i
$162$		0			0
$163$	7.47422			0.585426			0.292713	−	0.956200i	$-0.405442\pi$
$163$	7.47422			0.585426			0.292713	+	0.956200i	$0.405442\pi$
$164$		0			0
$165$	−0.0251601	−	0.0161694i	−0.00195871	−	0.00125879i
$166$		0			0
$167$	−6.46153	−	7.45700i	−0.500008	−	0.577040i	0.448504	−	0.893781i	$-0.351957\pi$
$167$	−6.46153	−	7.45700i	−0.500008	−	0.577040i	−0.948512	+	0.316741i	$0.897412\pi$
$168$		0			0
$169$	−5.02786	+	11.0095i	−0.386758	+	0.846882i
$170$		0			0
$171$	1.10007			0.0841247
$172$		0			0
$173$	10.3702	+	6.66449i	0.788428	+	0.506692i	0.871821	−	0.489825i	$-0.162939\pi$
$173$	10.3702	+	6.66449i	0.788428	+	0.506692i	−0.0833928	+	0.996517i	$0.526576\pi$
$174$		0			0
$175$	−0.00641747	+	0.0446345i	−0.000485115	+	0.00337405i
$176$		0			0
$177$	−1.37101	+	9.53557i	−0.103051	+	0.716738i
$178$		0			0
$179$	7.15402	−	15.6651i	0.534716	−	1.17087i	−0.428845	−	0.903378i	$-0.641079\pi$
$179$	7.15402	−	15.6651i	0.534716	−	1.17087i	0.963561	−	0.267487i	$-0.0861934\pi$
$180$		0			0
$181$	4.31046	+	9.43859i	0.320394	+	0.701565i	0.999472	−	0.0325013i	$-0.0103473\pi$
$181$	4.31046	+	9.43859i	0.320394	+	0.701565i	−0.679078	+	0.734066i	$0.737620\pi$
$182$		0			0
$183$	−1.02911	−	7.15759i	−0.0760737	−	0.529104i
$184$		0			0
$185$	5.94746	−	1.74633i	0.437266	−	0.128393i
$186$		0			0
$187$	0.0333338	+	0.231841i	0.00243761	+	0.0169539i
$188$		0			0
$189$	0.00948752	−	0.00609726i	0.000690116	−	0.000443511i
$190$		0			0
$191$	−5.14173	+	11.2588i	−0.372042	+	0.814659i	0.627313	+	0.778767i	$0.284155\pi$
$191$	−5.14173	+	11.2588i	−0.372042	+	0.814659i	−0.999356	+	0.0358921i	$0.988573\pi$
$192$		0			0
$193$	13.6948	+	8.80109i	0.985770	+	0.633516i	0.931014	−	0.364984i	$-0.118925\pi$
$193$	13.6948	+	8.80109i	0.985770	+	0.633516i	0.0547564	+	0.998500i	$0.482562\pi$
$194$		0			0
$195$	−0.909349	−	0.267009i	−0.0651198	−	0.0191209i
$196$		0			0
$197$	0.582925	+	4.05433i	0.0415317	+	0.288859i	0.999993	+	0.00363791i	$0.00115799\pi$
$197$	0.582925	+	4.05433i	0.0415317	+	0.288859i	−0.958462	+	0.285221i	$0.907933\pi$
$198$		0			0
$199$	−0.892500	+	1.03000i	−0.0632677	+	0.0730148i	−0.786501	−	0.617589i	$-0.788110\pi$
$199$	−0.892500	+	1.03000i	−0.0632677	+	0.0730148i	0.723233	+	0.690604i	$0.242655\pi$
$200$		0			0
$201$	0.147655	−	8.18402i	0.0104148	−	0.577256i
$202$		0			0
$203$	0.00655067	−	0.00755988i	0.000459767	−	0.000530600i
$204$		0			0
$205$	−0.919987	−	6.39865i	−0.0642547	−	0.446901i
$206$		0			0
$207$	5.68461	+	1.66915i	0.395108	+	0.116014i
$208$		0			0
$209$	0.0276560	+	0.0177735i	0.00191301	+	0.00122942i
$210$		0			0
$211$	−3.96139	+	8.67423i	−0.272713	+	0.597158i	−0.995589	−	0.0938192i	$-0.970092\pi$
$211$	−3.96139	+	8.67423i	−0.272713	+	0.597158i	0.722876	+	0.690978i	$0.242820\pi$
$212$		0			0
$213$	−9.89869	+	6.36150i	−0.678247	+	0.435883i
$214$		0			0
$215$	0.139833	+	0.972557i	0.00953651	+	0.0663279i
$216$		0			0
$217$	−0.0973641	+	0.0285887i	−0.00660950	+	0.00194073i
$218$		0			0
$219$	1.43226	+	9.96156i	0.0967829	+	0.673140i
$220$		0			0
$221$	3.08333	+	6.75154i	0.207407	+	0.454158i
$222$		0			0
$223$	3.76060	−	8.23458i	0.251829	−	0.551428i	−0.740926	−	0.671587i	$-0.765613\pi$
$223$	3.76060	−	8.23458i	0.251829	−	0.551428i	0.992755	+	0.120159i	$0.0383404\pi$
$224$		0			0
$225$	0.569034	−	3.95772i	0.0379356	−	0.263848i
$226$		0			0
$227$	−0.0393316	+	0.273557i	−0.00261053	+	0.0181566i	−0.991085	−	0.133231i	$-0.957465\pi$
$227$	−0.0393316	+	0.273557i	−0.00261053	+	0.0181566i	0.988475	+	0.151387i	$0.0483740\pi$
$228$		0			0
$229$	−10.3283	−	6.63757i	−0.682511	−	0.438623i	0.152906	−	0.988241i	$-0.451137\pi$
$229$	−10.3283	−	6.63757i	−0.682511	−	0.438623i	−0.835416	+	0.549618i	$0.814773\pi$
$230$		0			0
$231$	0.000337029	0		2.21749e−5	0
$232$		0			0
$233$	−0.417140	+	0.913410i	−0.0273278	+	0.0598395i	−0.922804	−	0.385271i	$-0.874108\pi$
$233$	−0.417140	+	0.913410i	−0.0273278	+	0.0598395i	0.895476	+	0.445110i	$0.146835\pi$
$234$		0			0
$235$	3.44164	+	3.97186i	0.224508	+	0.259096i
$236$		0			0
$237$	−5.45532	−	3.50592i	−0.354361	−	0.227734i
$238$		0			0
$239$	2.24067			0.144937			0.0724684	−	0.997371i	$-0.476912\pi$
$239$	2.24067			0.144937			0.0724684	+	0.997371i	$0.476912\pi$
$240$		0			0
$241$	20.5581	+	6.03642i	1.32427	+	0.388840i	0.866031	−	0.499991i	$-0.166663\pi$
$241$	20.5581	+	6.03642i	1.32427	+	0.388840i	0.458236	+	0.888831i	$0.348481\pi$
$242$		0			0
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$		0			0
$245$	−2.91015	−	6.37235i	−0.185923	−	0.407114i
$246$		0			0
$247$	0.999559	+	0.293497i	0.0636004	+	0.0186748i
$248$		0			0
$249$	−5.44730	−	6.28652i	−0.345208	−	0.398392i
$250$		0			0
$251$	−2.21729	+	15.4216i	−0.139954	+	0.973401i	0.791922	+	0.610623i	$0.209081\pi$
$251$	−2.21729	+	15.4216i	−0.139954	+	0.973401i	−0.931876	+	0.362778i	$0.881828\pi$
$252$		0			0
$253$	0.115944	+	0.133807i	0.00728936	+	0.00841237i
$254$		0			0
$255$	6.59877	−	4.24077i	0.413231	−	0.265567i
$256$		0			0
$257$	18.7580	−	5.50786i	1.17010	−	0.343571i	0.361747	−	0.932276i	$-0.382180\pi$
$257$	18.7580	−	5.50786i	1.17010	−	0.343571i	0.808348	+	0.588705i	$0.200362\pi$
$258$		0			0
$259$	−0.0457426	+	0.0527898i	−0.00284231	+	0.00328020i
$260$		0			0
$261$	−0.580845	+	0.670330i	−0.0359534	+	0.0414924i
$262$		0			0
$263$	−9.64233	+	2.83124i	−0.594572	+	0.174582i	−0.565154	−	0.824985i	$-0.691183\pi$
$263$	−9.64233	+	2.83124i	−0.594572	+	0.174582i	−0.0294174	+	0.999567i	$0.509365\pi$
$264$		0			0
$265$	2.86446	+	6.27230i	0.175963	+	0.385304i
$266$		0			0
$267$	9.68000			0.592407
$268$		0			0
$269$	−14.1374			−0.861971			−0.430985	−	0.902359i	$-0.641834\pi$
$269$	−14.1374			−0.861971			−0.430985	+	0.902359i	$0.641834\pi$
$270$		0			0
$271$	−7.69386	−	16.8472i	−0.467369	−	1.02340i	−0.985746	−	0.168243i	$-0.946191\pi$
$271$	−7.69386	−	16.8472i	−0.467369	−	1.02340i	0.518377	−	0.855152i	$-0.326537\pi$
$272$		0			0
$273$	0.0102474	−	0.00300890i	0.000620200	−	0.000182107i
$274$		0			0
$275$	0.0782490	−	0.0903041i	0.00471859	−	0.00544554i
$276$		0			0
$277$	−20.8043	+	24.0094i	−1.25001	+	1.44259i	−0.399410	+	0.916772i	$0.630785\pi$
$277$	−20.8043	+	24.0094i	−1.25001	+	1.44259i	−0.850599	+	0.525815i	$0.823760\pi$
$278$		0			0
$279$	8.63322	−	2.53494i	0.516857	−	0.151763i
$280$		0			0
$281$	−18.5128	+	11.8975i	−1.10438	+	0.709744i	−0.960062	−	0.279787i	$-0.909736\pi$
$281$	−18.5128	+	11.8975i	−1.10438	+	0.709744i	−0.144321	+	0.989531i	$0.546100\pi$
$282$		0			0
$283$	10.6618	+	12.3044i	0.633780	+	0.731421i	0.978262	−	0.207372i	$-0.0664909\pi$
$283$	10.6618	+	12.3044i	0.633780	+	0.731421i	−0.344482	+	0.938793i	$0.611945\pi$
$284$		0			0
$285$	0.156681	−	1.08974i	0.00928096	−	0.0645505i
$286$		0			0
$287$	0.0477049	+	0.0550543i	0.00281593	+	0.00324975i
$288$		0			0
$289$	−42.6309	−	12.5176i	−2.50770	−	0.736327i
$290$		0			0
$291$	5.43895	+	11.9096i	0.318837	+	0.698156i
$292$		0			0
$293$	13.5477	−	8.70659i	0.791466	−	0.508644i	−0.0813548	−	0.996685i	$-0.525925\pi$
$293$	13.5477	−	8.70659i	0.791466	−	0.508644i	0.872821	+	0.488041i	$0.162288\pi$
$294$		0			0
$295$	9.25072	+	2.71626i	0.538598	+	0.158147i
$296$		0			0
$297$	−0.0298842			−0.00173406
$298$		0			0
$299$	4.71988	+	3.03328i	0.272958	+	0.175419i
$300$		0			0
$301$	−0.00725086	−	0.00836794i	−0.000417933	−	0.000482320i
$302$		0			0
$303$	−1.61145	+	3.52858i	−0.0925752	+	0.202711i
$304$		0			0
$305$	−7.23691			−0.414384
$306$		0			0
$307$	−8.35460	−	5.36917i	−0.476822	−	0.306435i	0.280065	−	0.959981i	$-0.409644\pi$
$307$	−8.35460	−	5.36917i	−0.476822	−	0.306435i	−0.756887	+	0.653546i	$0.773280\pi$
$308$		0			0
$309$	0.284606	−	1.97948i	0.0161907	−	0.112609i
$310$		0			0
$311$	0.373970	−	2.60102i	0.0212059	−	0.147490i	−0.976468	−	0.215664i	$-0.930808\pi$
$311$	0.373970	−	2.60102i	0.0212059	−	0.147490i	0.997673	+	0.0681743i	$0.0217174\pi$
$312$		0			0
$313$	−2.44696	+	5.35810i	−0.138311	+	0.302858i	−0.966094	−	0.258189i	$-0.916874\pi$
$313$	−2.44696	+	5.35810i	−0.138311	+	0.302858i	0.827784	+	0.561047i	$0.189601\pi$
$314$		0			0
$315$	−0.00468869	−	0.0102668i	−0.000264178	−	0.000578469i
$316$		0			0
$317$	−1.40646	−	9.78213i	−0.0789946	−	0.549419i	−0.990434	−	0.137986i	$-0.955937\pi$
$317$	−1.40646	−	9.78213i	−0.0789946	−	0.549419i	0.911440	−	0.411434i	$-0.134972\pi$
$318$		0			0
$319$	−0.0254328	+	0.00746775i	−0.00142396	+	0.000418114i
$320$		0			0
$321$	−1.26568	−	8.80300i	−0.0706434	−	0.491335i
$322$		0			0
$323$	−7.25339	+	4.66147i	−0.403589	+	0.259371i
$324$		0			0
$325$	1.57295	−	3.44428i	0.0872516	−	0.191054i
$326$		0			0
$327$	−11.6058	−	7.45861i	−0.641804	−	0.412462i
$328$		0			0
$329$	−0.0568251	−	0.0166854i	−0.00313287	−	0.000919894i
$330$		0			0
$331$	−2.25469	−	15.6817i	−0.123929	−	0.861947i	−0.953036	−	0.302857i	$-0.902060\pi$
$331$	−2.25469	−	15.6817i	−0.123929	−	0.861947i	0.829107	−	0.559090i	$-0.188849\pi$
$332$		0			0
$333$	4.05597	−	4.68084i	0.222266	−	0.256508i
$334$		0			0
$335$	−8.08610	−	1.31190i	−0.441791	−	0.0716766i
$336$		0			0
$337$	8.32107	−	9.60303i	0.453278	−	0.523110i	−0.482407	−	0.875947i	$-0.660237\pi$
$337$	8.32107	−	9.60303i	0.453278	−	0.523110i	0.935685	+	0.352837i	$0.114783\pi$
$338$		0			0
$339$	−2.48943	−	17.3143i	−0.135207	−	0.940385i
$340$		0			0
$341$	0.257997	+	0.0757547i	0.0139713	+	0.00410235i
$342$		0			0
$343$	0.132824	+	0.0853609i	0.00717183	+	0.00460905i
$344$		0			0
$345$	2.46312	−	5.39347i	0.132610	−	0.290375i
$346$		0			0
$347$	−4.77003	+	3.06551i	−0.256068	+	0.164565i	−0.662377	−	0.749171i	$-0.730452\pi$
$347$	−4.77003	+	3.06551i	−0.256068	+	0.164565i	0.406308	+	0.913736i	$0.366816\pi$
$348$		0			0
$349$	−2.01607	−	14.0221i	−0.107918	−	0.750585i	−0.969875	−	0.243603i	$-0.921670\pi$
$349$	−2.01607	−	14.0221i	−0.107918	−	0.750585i	0.861957	−	0.506981i	$-0.169239\pi$
$350$		0			0
$351$	−0.908629	+	0.266798i	−0.0484991	+	0.0142406i
$352$		0			0
$353$	0.442471	+	3.07746i	0.0235504	+	0.163796i	0.998203	−	0.0599286i	$-0.0190873\pi$
$353$	0.442471	+	3.07746i	0.0235504	+	0.163796i	−0.974652	+	0.223725i	$0.928178\pi$
$354$		0			0
$355$	4.89189	+	10.7117i	0.259635	+	0.568521i
$356$		0			0
$357$	−0.0367198	+	0.0804052i	−0.00194342	+	0.00425549i
$358$		0			0
$359$	−2.28215	+	15.8727i	−0.120447	+	0.837728i	0.836604	+	0.547808i	$0.184538\pi$
$359$	−2.28215	+	15.8727i	−0.120447	+	0.837728i	−0.957051	+	0.289920i	$0.906371\pi$
$360$		0			0
$361$	2.53176	−	17.6088i	0.133250	−	0.926777i
$362$		0			0
$363$	9.25304	+	5.94657i	0.485659	+	0.312114i
$364$		0			0
$365$	10.0720			0.527191
$366$		0			0
$367$	12.2314	−	26.7831i	0.638476	−	1.39807i	−0.262812	−	0.964847i	$-0.584650\pi$
$367$	12.2314	−	26.7831i	0.638476	−	1.39807i	0.901288	−	0.433221i	$-0.142623\pi$
$368$		0			0
$369$	−4.22996	−	4.88164i	−0.220203	−	0.254128i
$370$		0			0
$371$	−0.0653688	−	0.0420100i	−0.00339378	−	0.00218105i
$372$		0			0
$373$	19.0550			0.986628			0.493314	−	0.869851i	$-0.335785\pi$
$373$	19.0550			0.986628			0.493314	+	0.869851i	$0.335785\pi$
$374$		0			0
$375$	−8.64075	−	2.53715i	−0.446207	−	0.131018i
$376$		0			0
$377$	−0.706615	+	0.454114i	−0.0363925	+	0.0233881i
$378$		0			0
$379$	−10.6665	−	23.3564i	−0.547903	−	1.19974i	−0.957754	−	0.287588i	$-0.907147\pi$
$379$	−10.6665	−	23.3564i	−0.547903	−	1.19974i	0.409852	−	0.912152i	$-0.365580\pi$
$380$		0			0
$381$	3.53622	+	1.03833i	0.181166	+	0.0531952i
$382$		0			0
$383$	−23.5322	−	27.1576i	−1.20244	−	1.38769i	−0.900781	−	0.434273i	$-0.857005\pi$
$383$	−23.5322	−	27.1576i	−1.20244	−	1.38769i	−0.301659	−	0.953416i	$-0.597540\pi$
$384$		0			0
$385$	4.80023e−5	0	0.000333863i	2.44642e−6	0	1.70152e-5i
$386$		0			0
$387$	0.642930	+	0.741981i	0.0326820	+	0.0377170i
$388$		0			0
$389$	23.4324	−	15.0591i	1.18807	−	0.763526i	0.211217	−	0.977439i	$-0.432257\pi$
$389$	23.4324	−	15.0591i	1.18807	−	0.763526i	0.976853	+	0.213914i	$0.0686211\pi$
$390$		0			0
$391$	−44.5547	+	13.0824i	−2.25323	+	0.661607i
$392$		0			0
$393$	−10.6982	+	12.3464i	−0.539654	+	0.622794i
$394$		0			0
$395$	−4.24997	+	4.90473i	−0.213839	+	0.246784i
$396$		0			0
$397$	−7.12812	+	2.09300i	−0.357750	+	0.105045i	−0.455668	−	0.890150i	$-0.650600\pi$
$397$	−7.12812	+	2.09300i	−0.357750	+	0.105045i	0.0979185	+	0.995194i	$0.468782\pi$
$398$		0			0
$399$	0.00515382	+	0.0112853i	0.000258014	+	0.000564972i
$400$		0			0
$401$	−19.1740			−0.957503			−0.478752	−	0.877950i	$-0.658911\pi$
$401$	−19.1740			−0.957503			−0.478752	+	0.877950i	$0.658911\pi$
$402$		0			0
$403$	8.52071			0.424447
$404$		0			0
$405$	0.415744	+	0.910352i	0.0206585	+	0.0452358i
$406$		0			0
$407$	0.177594	−	0.0521464i	0.00880303	−	0.00258480i
$408$		0			0
$409$	7.99494	−	9.22665i	0.395324	−	0.456229i	−0.522838	−	0.852432i	$-0.675127\pi$
$409$	7.99494	−	9.22665i	0.395324	−	0.456229i	0.918163	+	0.396203i	$0.129672\pi$
$410$		0			0
$411$	−2.73249	+	3.15347i	−0.134784	+	0.155549i
$412$		0			0
$413$	−0.104246	+	0.0306093i	−0.00512959	+	0.00150618i
$414$		0			0
$415$	−7.00330	+	4.50075i	−0.343778	+	0.220933i
$416$		0			0
$417$	−14.3133	−	16.5184i	−0.700925	−	0.808910i
$418$		0			0
$419$	−2.71180	+	18.8610i	−0.132480	+	0.921421i	0.809826	+	0.586670i	$0.199561\pi$
$419$	−2.71180	+	18.8610i	−0.132480	+	0.921421i	−0.942307	+	0.334751i	$0.891348\pi$
$420$		0			0
$421$	−7.24193	−	8.35763i	−0.352950	−	0.407326i	0.551315	−	0.834297i	$-0.314126\pi$
$421$	−7.24193	−	8.35763i	−0.352950	−	0.407326i	−0.904265	+	0.426971i	$0.859581\pi$
$422$		0			0
$423$	5.03865	+	1.47948i	0.244988	+	0.0719349i
$424$		0			0
$425$	13.0185	+	28.5066i	0.631492	+	1.38278i
$426$		0			0
$427$	0.0686061	−	0.0440904i	0.00332008	−	0.00213369i
$428$		0			0
$429$	−0.0271537	−	0.00797304i	−0.00131099	−	0.000384942i
$430$		0			0
$431$	−31.2358			−1.50458			−0.752288	−	0.658835i	$-0.771050\pi$
$431$	−31.2358			−1.50458			−0.752288	+	0.658835i	$0.771050\pi$
$432$		0			0
$433$	−1.84774	−	1.18747i	−0.0887969	−	0.0570663i	0.495489	−	0.868614i	$-0.334989\pi$
$433$	−1.84774	−	1.18747i	−0.0887969	−	0.0570663i	−0.584286	+	0.811548i	$0.698625\pi$
$434$		0			0
$435$	0.581305	+	0.670861i	0.0278714	+	0.0321653i
$436$		0			0
$437$	−2.70746	+	5.92852i	−0.129516	+	0.283600i
$438$		0			0
$439$	8.00230			0.381929			0.190964	−	0.981597i	$-0.438838\pi$
$439$	8.00230			0.381929			0.190964	+	0.981597i	$0.438838\pi$
$440$		0			0
$441$	−5.88867	−	3.78442i	−0.280413	−	0.180210i
$442$		0			0
$443$	−2.76791	+	19.2512i	−0.131507	+	0.914653i	0.812084	+	0.583540i	$0.198333\pi$
$443$	−2.76791	+	19.2512i	−0.131507	+	0.914653i	−0.943591	+	0.331112i	$0.892576\pi$
$444$		0			0
$445$	1.37870	−	9.58906i	0.0653566	−	0.454565i
$446$		0			0
$447$	2.11173	−	4.62404i	0.0998814	−	0.218710i
$448$		0			0
$449$	7.65959	+	16.7722i	0.361478	+	0.791527i	0.999764	+	0.0217273i	$0.00691657\pi$
$449$	7.65959	+	16.7722i	0.361478	+	0.791527i	−0.638286	+	0.769800i	$0.720356\pi$
$450$		0			0
$451$	−0.0274713	−	0.191067i	−0.00129357	−	0.00899701i
$452$		0			0
$453$	10.4841	−	3.07840i	0.492585	−	0.144636i
$454$		0			0
$455$	−0.00152113	−	0.0105797i	−7.13114e−5	−	0.000495982i
$456$		0			0
$457$	12.8510	−	8.25885i	0.601146	−	0.386333i	−0.204382	−	0.978891i	$-0.565518\pi$
$457$	12.8510	−	8.25885i	0.601146	−	0.386333i	0.805528	+	0.592558i	$0.201882\pi$
$458$		0			0
$459$	3.25593	−	7.12949i	0.151974	−	0.332776i
$460$		0			0
$461$	−5.62452	−	3.61466i	−0.261960	−	0.168351i	0.403068	−	0.915170i	$-0.367944\pi$
$461$	−5.62452	−	3.61466i	−0.261960	−	0.168351i	−0.665028	+	0.746819i	$0.731580\pi$
$462$		0			0
$463$	13.5187	+	3.96945i	0.628268	+	0.184476i	0.580339	−	0.814375i	$-0.302920\pi$
$463$	13.5187	+	3.96945i	0.628268	+	0.184476i	0.0479282	+	0.998851i	$0.484738\pi$
$464$		0			0
$465$	−1.28152	−	8.91316i	−0.0594290	−	0.413338i
$466$		0			0
$467$	−6.54900	+	7.55795i	−0.303052	+	0.349740i	−0.886766	−	0.462219i	$-0.847053\pi$
$467$	−6.54900	+	7.55795i	−0.303052	+	0.349740i	0.583714	+	0.811959i	$0.301599\pi$
$468$		0			0
$469$	0.0846491	−	0.0368273i	0.00390873	−	0.00170053i
$470$		0			0
$471$	−1.81234	+	2.09155i	−0.0835080	+	0.0963734i
$472$		0			0
$473$	0.00417548	+	0.0290411i	0.000191989	+	0.00133531i
$474$		0			0
$475$	4.22038	+	1.23921i	0.193644	+	0.0568591i
$476$		0			0
$477$	5.79621	+	3.72500i	0.265390	+	0.170556i
$478$		0			0
$479$	8.60830	−	18.8495i	0.393323	−	0.861258i	−0.604581	−	0.796544i	$-0.706659\pi$
$479$	8.60830	−	18.8495i	0.393323	−	0.861258i	0.997904	−	0.0647137i	$-0.0206134\pi$
$480$		0			0
$481$	4.93421	−	3.17102i	0.224981	−	0.144586i
$482$		0			0
$483$	0.00950901	+	0.0661366i	0.000432675	+	0.00300932i
$484$		0			0
$485$	12.5724	−	3.69159i	0.570884	−	0.167627i
$486$		0			0
$487$	−4.92647	−	34.2643i	−0.223239	−	1.55266i	−0.725668	−	0.688046i	$-0.758469\pi$
$487$	−4.92647	−	34.2643i	−0.223239	−	1.55266i	0.502428	−	0.864619i	$-0.332440\pi$
$488$		0			0
$489$	−3.10491	−	6.79879i	−0.140409	−	0.307452i
$490$		0			0
$491$	−2.01649	+	4.41550i	−0.0910030	+	0.199269i	−0.949660	−	0.313281i	$-0.898572\pi$
$491$	−2.01649	+	4.41550i	−0.0910030	+	0.199269i	0.858657	+	0.512550i	$0.171299\pi$
$492$		0			0
$493$	0.989358	−	6.88114i	0.0445585	−	0.309911i
$494$		0			0
$495$	−0.00425633	+	0.0296035i	−0.000191308	+	0.00133058i
$496$		0			0
$497$	−0.111636	−	0.0717440i	−0.00500755	−	0.00321816i
$498$		0			0
$499$	10.6616			0.477278			0.238639	−	0.971108i	$-0.423299\pi$
$499$	10.6616			0.477278			0.238639	+	0.971108i	$0.423299\pi$
$500$		0			0
$501$	−4.09891	+	8.97536i	−0.183126	+	0.400990i
$502$		0			0
$503$	−23.7443	−	27.4024i	−1.05871	−	1.22181i	−0.974270	−	0.225386i	$-0.927636\pi$
$503$	−23.7443	−	27.4024i	−1.05871	−	1.22181i	−0.0844385	−	0.996429i	$-0.526910\pi$
$504$		0			0
$505$	3.26591	+	2.09887i	0.145331	+	0.0933987i
$506$		0			0
$507$	12.1032			0.537522
$508$		0			0
$509$	−12.2768	−	3.60480i	−0.544160	−	0.159780i	−0.00191189	−	0.999998i	$-0.500609\pi$
$509$	−12.2768	−	3.60480i	−0.544160	−	0.159780i	−0.542248	+	0.840218i	$0.682427\pi$
$510$		0			0
$511$	−0.0954824	+	0.0613628i	−0.00422389	+	0.00271453i
$512$		0			0
$513$	−0.456987	−	1.00066i	−0.0201765	−	0.0441803i
$514$		0			0
$515$	−1.92035	−	0.563865i	−0.0846207	−	0.0248469i
$516$		0			0
$517$	0.102769	+	0.118602i	0.00451979	+	0.00521611i
$518$		0			0
$519$	1.75432	−	12.2016i	0.0770060	−	0.535589i
$520$		0			0
$521$	6.77537	+	7.81920i	0.296835	+	0.342565i	0.884501	−	0.466538i	$-0.154499\pi$
$521$	6.77537	+	7.81920i	0.296835	+	0.342565i	−0.587667	+	0.809103i	$0.699953\pi$
$522$		0			0
$523$	14.9373	−	9.59960i	0.653161	−	0.419761i	−0.171659	−	0.985156i	$-0.554913\pi$
$523$	14.9373	−	9.59960i	0.653161	−	0.419761i	0.824820	+	0.565395i	$0.191276\pi$
$524$		0			0
$525$	0.0432669	−	0.0127043i	0.00188832	−	0.000554461i
$526$		0			0
$527$	−46.1820	+	53.2968i	−2.01172	+	2.32165i
$528$		0			0
$529$	−7.92440	+	9.14524i	−0.344539	+	0.397619i
$530$		0			0
$531$	9.24340	−	2.71411i	0.401129	−	0.117782i
$532$		0			0
$533$	−2.54106	−	5.56414i	−0.110066	−	0.241010i
$534$		0			0
$535$	−8.90056			−0.384805
$536$		0			0
$537$	−17.2214			−0.743157
$538$		0			0
$539$	−0.0868989	−	0.190282i	−0.00374300	−	0.00819602i
$540$		0			0
$541$	−41.3501	+	12.1415i	−1.77778	+	0.522003i	−0.994962	−	0.100251i	$-0.968036\pi$
$541$	−41.3501	+	12.1415i	−1.77778	+	0.522003i	−0.782816	+	0.622253i	$0.786217\pi$
$542$		0			0
$543$	6.79502	−	7.84187i	0.291602	−	0.336527i
$544$		0			0
$545$	−9.04153	+	10.4345i	−0.387296	+	0.446964i
$546$		0			0
$547$	−12.6909	+	3.72638i	−0.542623	+	0.159328i	−0.541546	−	0.840671i	$-0.682161\pi$
$547$	−12.6909	+	3.72638i	−0.542623	+	0.159328i	−0.00107671	+	0.999999i	$0.500343\pi$
$548$		0			0
$549$	−6.08326	+	3.90948i	−0.259627	+	0.166852i
$550$		0			0
$551$	−0.638971	−	0.737412i	−0.0272211	−	0.0314148i
$552$		0			0
$553$	0.0104081	−	0.0723896i	0.000442595	−	0.00307832i
$554$		0			0
$555$	−4.05918	−	4.68455i	−0.172303	−	0.198848i
$556$		0			0
$557$	−1.74596	−	0.512660i	−0.0739786	−	0.0217221i	0.244534	−	0.969641i	$-0.421365\pi$
$557$	−1.74596	−	0.512660i	−0.0739786	−	0.0217221i	−0.318512	+	0.947919i	$0.603183\pi$
$558$		0			0
$559$	0.386226	+	0.845718i	0.0163356	+	0.0357700i
$560$		0			0
$561$	0.197043	−	0.126632i	0.00831916	−	0.00534640i
$562$		0			0
$563$	31.3250	+	9.19785i	1.32019	+	0.387643i	0.864562	−	0.502527i	$-0.167596\pi$
$563$	31.3250	+	9.19785i	1.32019	+	0.387643i	0.455629	+	0.890170i	$0.349414\pi$
$564$		0			0
$565$	−17.5062			−0.736493
$566$		0			0
$567$	−0.00948752	−	0.00609726i	−0.000398439	−	0.000256061i
$568$		0			0
$569$	19.7860	+	22.8343i	0.829473	+	0.957263i	0.999603	−	0.0281584i	$-0.00896429\pi$
$569$	19.7860	+	22.8343i	0.829473	+	0.957263i	−0.170130	+	0.985422i	$0.554419\pi$
$570$		0			0
$571$	−14.6984	+	32.1851i	−0.615111	+	1.34690i	0.303912	+	0.952700i	$0.401707\pi$
$571$	−14.6984	+	32.1851i	−0.615111	+	1.34690i	−0.919023	+	0.394205i	$0.871020\pi$
$572$		0			0
$573$	12.3773			0.517070
$574$		0			0
$575$	19.9285	+	12.8072i	0.831075	+	0.534099i
$576$		0			0
$577$	5.54781	−	38.5859i	0.230958	−	1.60635i	−0.463016	−	0.886350i	$-0.653233\pi$
$577$	5.54781	−	38.5859i	0.230958	−	1.60635i	0.693974	−	0.720000i	$-0.255858\pi$
$578$		0			0
$579$	2.31674	−	16.1133i	0.0962805	−	0.669646i
$580$		0			0
$581$	0.0389709	−	0.0853343i	0.00161678	−	0.00354026i
$582$		0			0
$583$	0.0855345	+	0.187294i	0.00354248	+	0.00775694i
$584$		0			0
$585$	0.134877	+	0.938092i	0.00557649	+	0.0387853i
$586$		0			0
$587$	−4.97576	+	1.46102i	−0.205372	+	0.0603026i	−0.382800	−	0.923831i	$-0.625040\pi$
$587$	−4.97576	+	1.46102i	−0.205372	+	0.0603026i	0.177429	+	0.984134i	$0.443222\pi$
$588$		0			0
$589$	1.40865	+	9.79736i	0.0580423	+	0.403693i
$590$		0			0
$591$	3.44579	−	2.21448i	0.141741	−	0.0910914i
$592$		0			0
$593$	12.4797	−	27.3266i	0.512478	−	1.12217i	−0.459731	−	0.888058i	$-0.652054\pi$
$593$	12.4797	−	27.3266i	0.512478	−	1.12217i	0.972210	−	0.234112i	$-0.0752184\pi$
$594$		0			0
$595$	0.0744199	+	0.0478268i	0.00305092	+	0.00196071i
$596$		0			0
$597$	1.30768	+	0.383969i	0.0535197	+	0.0157148i
$598$		0			0
$599$	4.85638	+	33.7769i	0.198426	+	1.38009i	0.808852	+	0.588012i	$0.200089\pi$
$599$	4.85638	+	33.7769i	0.198426	+	1.38009i	−0.610425	+	0.792074i	$0.709002\pi$
$600$		0			0
$601$	9.82729	−	11.3413i	0.400864	−	0.462621i	−0.519049	−	0.854744i	$-0.673714\pi$
$601$	9.82729	−	11.3413i	0.400864	−	0.462621i	0.919913	+	0.392123i	$0.128259\pi$
$602$		0			0
$603$	−7.50579	+	3.26545i	−0.305659	+	0.132980i
$604$		0			0
$605$	7.20859	−	8.31915i	0.293071	−	0.338222i
$606$		0			0
$607$	4.90935	+	34.1453i	0.199265	+	1.38592i	0.806425	+	0.591336i	$0.201399\pi$
$607$	4.90935	+	34.1453i	0.199265	+	1.38592i	−0.607161	+	0.794579i	$0.707692\pi$
$608$		0			0
$609$	−0.00959796	−	0.00281821i	−0.000388929	−	0.000114200i
$610$		0			0
$611$	4.18355	+	2.68860i	0.169248	+	0.108769i
$612$		0			0
$613$	16.9415	−	37.0967i	0.684261	−	1.49832i	−0.173803	−	0.984780i	$-0.555606\pi$
$613$	16.9415	−	37.0967i	0.684261	−	1.49832i	0.858064	−	0.513542i	$-0.171667\pi$
$614$		0			0
$615$	−5.43824	+	3.49494i	−0.219291	+	0.140930i
$616$		0			0
$617$	1.50370	+	10.4585i	0.0605366	+	0.421042i	0.997443	+	0.0714620i	$0.0227665\pi$
$617$	1.50370	+	10.4585i	0.0605366	+	0.421042i	−0.936907	+	0.349580i	$0.886324\pi$
$618$		0			0
$619$	−25.0025	+	7.34141i	−1.00494	+	0.295076i	−0.742480	−	0.669868i	$-0.766351\pi$
$619$	−25.0025	+	7.34141i	−1.00494	+	0.295076i	−0.262457	+	0.964944i	$0.584533\pi$
$620$		0			0
$621$	−0.843159	−	5.86430i	−0.0338348	−	0.235326i
$622$		0			0
$623$	0.0453507	+	0.0993041i	0.00181694	+	0.00397854i
$624$		0			0
$625$	4.56101	−	9.98722i	0.182440	−	0.399489i
$626$		0			0
$627$	0.00467857	−	0.0325402i	0.000186844	−	0.00129953i
$628$		0			0
$629$	−6.90857	+	48.0502i	−0.275463	+	1.91589i
$630$		0			0
$631$	−34.3799	−	22.0946i	−1.36864	−	0.879573i	−0.369869	−	0.929084i	$-0.620597\pi$
$631$	−34.3799	−	22.0946i	−1.36864	−	0.879573i	−0.998774	+	0.0495107i	$0.984234\pi$
$632$		0			0
$633$	9.53597			0.379021
$634$		0			0
$635$	1.53223	−	3.35511i	0.0608047	−	0.133144i
$636$		0			0
$637$	−4.34094	−	5.00972i	−0.171994	−	0.198492i
$638$		0			0
$639$	9.89869	+	6.36150i	0.391586	+	0.251657i
$640$		0			0
$641$	−7.87182			−0.310918			−0.155459	−	0.987842i	$-0.549686\pi$
$641$	−7.87182			−0.310918			−0.155459	+	0.987842i	$0.549686\pi$
$642$		0			0
$643$	45.3101	+	13.3042i	1.78685	+	0.524668i	0.996161	−	0.0875443i	$-0.0279019\pi$
$643$	45.3101	+	13.3042i	1.78685	+	0.524668i	0.790694	+	0.612212i	$0.209720\pi$
$644$		0			0
$645$	0.826581	−	0.531211i	0.0325466	−	0.0209164i
$646$		0			0
$647$	−8.61308	−	18.8600i	−0.338615	−	0.741463i	0.661348	−	0.750079i	$-0.269985\pi$
$647$	−8.61308	−	18.8600i	−0.338615	−	0.741463i	−0.999963	+	0.00861598i	$0.997257\pi$
$648$		0			0
$649$	0.276232	+	0.0811089i	0.0108430	+	0.00318380i
$650$		0			0
$651$	0.0664517	+	0.0766893i	0.00260445	+	0.00300569i
$652$		0			0
$653$	2.90942	−	20.2355i	0.113855	−	0.791876i	−0.850255	−	0.526371i	$-0.823552\pi$
$653$	2.90942	−	20.2355i	0.113855	−	0.791876i	0.964110	−	0.265505i	$-0.0855386\pi$
$654$		0			0
$655$	10.7067	+	12.3562i	0.418345	+	0.482796i
$656$		0			0
$657$	8.46637	−	5.44101i	0.330305	−	0.212274i
$658$		0			0
$659$	−36.6412	+	10.7588i	−1.42734	+	0.419105i	−0.901981	−	0.431776i	$-0.857887\pi$
$659$	−36.6412	+	10.7588i	−1.42734	+	0.419105i	−0.525358	+	0.850881i	$0.676069\pi$
$660$		0			0
$661$	2.39916	−	2.76878i	0.0933165	−	0.107693i	−0.707171	−	0.707043i	$-0.750029\pi$
$661$	2.39916	−	2.76878i	0.0933165	−	0.107693i	0.800487	+	0.599350i	$0.204574\pi$
$662$		0			0
$663$	4.86056	−	5.60939i	0.188769	−	0.217851i
$664$		0			0
$665$	0.0119133	−	0.00349807i	0.000461979	−	0.000135649i
$666$		0			0
$667$	−2.18299	−	4.78009i	−0.0845258	−	0.185086i
$668$		0			0
$669$	−9.05264			−0.349995
$670$		0			0
$671$	−0.216098			−0.00834238
$672$		0			0
$673$	−4.02010	−	8.80280i	−0.154964	−	0.339323i	0.816188	−	0.577787i	$-0.196083\pi$
$673$	−4.02010	−	8.80280i	−0.154964	−	0.339323i	−0.971151	+	0.238464i	$0.923356\pi$
$674$		0			0
$675$	−3.83645	+	1.12648i	−0.147665	+	0.0433584i
$676$		0			0
$677$	19.7694	−	22.8152i	0.759802	−	0.876858i	−0.235678	−	0.971831i	$-0.575731\pi$
$677$	19.7694	−	22.8152i	0.759802	−	0.876858i	0.995480	+	0.0949734i	$0.0302766\pi$
$678$		0			0
$679$	−0.0966959	+	0.111593i	−0.00371085	+	0.00428255i
$680$		0			0
$681$	0.265175	−	0.0778625i	0.0101615	−	0.00298370i
$682$		0			0
$683$	29.5280	−	18.9765i	1.12986	−	0.726116i	0.164328	−	0.986406i	$-0.447454\pi$
$683$	29.5280	−	18.9765i	1.12986	−	0.726116i	0.965531	+	0.260290i	$0.0838181\pi$
$684$		0			0
$685$	2.73466	+	3.15596i	0.104486	+	0.120583i
$686$		0			0
$687$	−1.74723	+	12.1523i	−0.0666610	+	0.463638i
$688$		0			0
$689$	4.27279	+	4.93106i	0.162780	+	0.187858i
$690$		0			0
$691$	22.9955	+	6.75209i	0.874790	+	0.256862i	0.688151	−	0.725567i	$-0.258422\pi$
$691$	22.9955	+	6.75209i	0.874790	+	0.256862i	0.186639	+	0.982429i	$0.440241\pi$
$692$		0			0
$693$	−0.000140007	0	0.000306573i	−5.31843e−6	0	1.16457e-5i
$694$		0			0
$695$	−18.4018	+	11.8261i	−0.698021	+	0.448591i
$696$		0			0
$697$	48.5760	+	14.2632i	1.83995	+	0.540257i
$698$		0			0
$699$	1.00415			0.0379806
$700$		0			0
$701$	18.2215	+	11.7102i	0.688216	+	0.442289i	0.837451	−	0.546512i	$-0.184045\pi$
$701$	18.2215	+	11.7102i	0.688216	+	0.442289i	−0.149235	+	0.988802i	$0.547681\pi$
$702$		0			0
$703$	4.46186	+	5.14926i	0.168282	+	0.194208i
$704$		0			0
$705$	2.18322	−	4.78060i	0.0822250	−	0.180048i
$706$		0			0
$707$	−0.0437482			−0.00164532
$708$		0			0
$709$	27.0150	+	17.3615i	1.01457	+	0.652024i	0.938572	−	0.345085i	$-0.112150\pi$
$709$	27.0150	+	17.3615i	1.01457	+	0.652024i	0.0759968	+	0.997108i	$0.475786\pi$
$710$		0			0
$711$	−0.922876	+	6.41874i	−0.0346106	+	0.240722i
$712$		0			0
$713$	−7.58648	+	52.7651i	−0.284116	+	1.97607i
$714$		0			0
$715$	−0.0117656	+	0.0257630i	−0.000440007	+	0.000963481i
$716$		0			0
$717$	−0.930807	−	2.03818i	−0.0347616	−	0.0761173i
$718$		0			0
$719$	1.66081	+	11.5512i	0.0619378	+	0.430787i	0.997070	+	0.0764891i	$0.0243710\pi$
$719$	1.66081	+	11.5512i	0.0619378	+	0.430787i	−0.935133	+	0.354298i	$0.884720\pi$
$720$		0			0
$721$	0.0216403	−	0.00635415i	0.000805925	−	0.000236641i
$722$		0			0
$723$	−3.04925	−	21.2080i	−0.113403	−	0.788733i
$724$		0			0
$725$	−2.98350	+	1.91738i	−0.110804	+	0.0712096i
$726$		0			0
$727$	−7.82175	+	17.1273i	−0.290093	+	0.635215i	−0.997429	−	0.0716627i	$-0.977169\pi$
$727$	−7.82175	+	17.1273i	−0.290093	+	0.635215i	0.707336	+	0.706877i	$0.249897\pi$
$728$		0			0
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$		0			0
$731$	−7.38327	−	2.16792i	−0.273080	−	0.0801836i
$732$		0			0
$733$	2.43652	+	16.9464i	0.0899950	+	0.625929i	0.984039	+	0.177951i	$0.0569468\pi$
$733$	2.43652	+	16.9464i	0.0899950	+	0.625929i	−0.894044	+	0.447978i	$0.852144\pi$
$734$		0			0
$735$	−4.58757	+	5.29434i	−0.169215	+	0.195285i
$736$		0			0
$737$	−0.241456	−	0.0391740i	−0.00889413	−	0.00144299i
$738$		0			0
$739$	−4.71923	+	5.44629i	−0.173600	+	0.200345i	−0.835881	−	0.548910i	$-0.815043\pi$
$739$	−4.71923	+	5.44629i	−0.173600	+	0.200345i	0.662281	+	0.749255i	$0.269588\pi$
$740$		0			0
$741$	−0.148257	−	1.03115i	−0.00544637	−	0.0378804i
$742$		0			0
$743$	11.2729	+	3.31002i	0.413563	+	0.121433i	0.481894	−	0.876230i	$-0.339949\pi$
$743$	11.2729	+	3.31002i	0.413563	+	0.121433i	−0.0683309	+	0.997663i	$0.521767\pi$
$744$		0			0
$745$	−4.27983	−	2.75048i	−0.156801	−	0.100770i
$746$		0			0
$747$	−3.45553	+	7.56655i	−0.126431	+	0.276846i
$748$		0			0
$749$	0.0843775	−	0.0542261i	0.00308309	−	0.00198138i
$750$		0			0
$751$	3.02810	+	21.0609i	0.110497	+	0.768523i	0.967438	+	0.253109i	$0.0814530\pi$
$751$	3.02810	+	21.0609i	0.110497	+	0.768523i	−0.856941	+	0.515415i	$0.827638\pi$
$752$		0			0
$753$	14.9490	−	4.38944i	0.544773	−	0.159960i
$754$		0			0
$755$	−1.55626	−	10.8240i	−0.0566381	−	0.393927i
$756$		0			0
$757$	15.9434	+	34.9112i	0.579474	+	1.26887i	0.941597	+	0.336741i	$0.109325\pi$
$757$	15.9434	+	34.9112i	0.579474	+	1.26887i	−0.362123	+	0.932130i	$0.617948\pi$
$758$		0			0
$759$	0.0735501	−	0.161052i	0.00266970	−	0.00584582i
$760$		0			0
$761$	3.51530	−	24.4495i	0.127430	−	0.886292i	−0.821366	−	0.570402i	$-0.806788\pi$
$761$	3.51530	−	24.4495i	0.127430	−	0.886292i	0.948796	−	0.315891i	$-0.102303\pi$
$762$		0			0
$763$	0.0221424	−	0.154004i	0.000801610	−	0.00557532i
$764$		0			0
$765$	−6.59877	−	4.24077i	−0.238579	−	0.153325i
$766$		0			0
$767$	9.12294			0.329410
$768$		0			0
$769$	9.07294	−	19.8670i	0.327179	−	0.716421i	−0.672542	−	0.740059i	$-0.734798\pi$
$769$	9.07294	−	19.8670i	0.327179	−	0.716421i	0.999721	+	0.0236378i	$0.00752484\pi$
$770$		0			0
$771$	−12.8025	−	14.7749i	−0.461071	−	0.532104i
$772$		0			0
$773$	10.4607	+	6.72266i	0.376244	+	0.241797i	0.715072	−	0.699051i	$-0.246394\pi$
$773$	10.4607	+	6.72266i	0.376244	+	0.241797i	−0.338828	+	0.940848i	$0.610030\pi$
$774$		0			0
$775$	35.9765			1.29231
$776$		0			0
$777$	0.0670214	+	0.0196793i	0.00240438	+	0.000705990i
$778$		0			0
$779$	5.97773	−	3.84165i	0.214174	−	0.137641i
$780$		0			0
$781$	0.146075	+	0.319859i	0.00522696	+	0.0114454i
$782$		0			0
$783$	0.851046	+	0.249890i	0.0304139	+	0.00893032i
$784$		0			0
$785$	1.81377	+	2.09320i	0.0647362	+	0.0747096i
$786$		0			0
$787$	4.59829	−	31.9818i	0.163911	−	1.14003i	−0.727260	−	0.686362i	$-0.759206\pi$
$787$	4.59829	−	31.9818i	0.163911	−	1.14003i	0.891171	−	0.453667i	$-0.149884\pi$
$788$		0			0
$789$	6.58096	+	7.59483i	0.234288	+	0.270383i
$790$		0			0
$791$	0.165959	−	0.106656i	0.00590084	−	0.00379224i
$792$		0			0
$793$	−6.57047	+	1.92926i	−0.233324	+	0.0685102i
$794$		0			0
$795$	4.51554	−	5.21122i	0.160150	−	0.184823i
$796$		0			0
$797$	−11.3531	+	13.1022i	−0.402149	+	0.464104i	−0.920316	−	0.391175i	$-0.872069\pi$
$797$	−11.3531	+	13.1022i	−0.402149	+	0.464104i	0.518168	+	0.855279i	$0.326614\pi$
$798$		0			0
$799$	−39.4918	+	11.5958i	−1.39712	+	0.410231i
$800$		0			0
$801$	−4.02122	−	8.80524i	−0.142083	−	0.311118i
$802$		0			0
$803$	0.300755			0.0106134
$804$		0			0
$805$	0.0668696			0.00235684
$806$		0			0
$807$	5.87288	+	12.8598i	0.206735	+	0.452687i
$808$		0			0
$809$	52.4360	−	15.3966i	1.84355	−	0.541315i	0.843559	−	0.537036i	$-0.180456\pi$
$809$	52.4360	−	15.3966i	1.84355	−	0.541315i	0.999991	−	0.00427865i	$-0.00136194\pi$
$810$		0			0
$811$	27.7077	−	31.9764i	0.972949	−	1.12284i	−0.0194534	−	0.999811i	$-0.506193\pi$
$811$	27.7077	−	31.9764i	0.972949	−	1.12284i	0.992403	−	0.123033i	$-0.0392620\pi$
$812$		0			0
$813$	−12.1286	+	13.9972i	−0.425369	+	0.490902i
$814$		0			0
$815$	−7.17714	+	2.10740i	−0.251404	+	0.0738190i
$816$		0			0
$817$	−0.908580	+	0.583909i	−0.0317872	+	0.0204284i
$818$		0			0
$819$	−0.00699391	−	0.00807140i	−0.000244387	−	0.000282038i
$820$		0			0
$821$	3.58362	−	24.9247i	0.125069	−	0.869877i	−0.826608	−	0.562778i	$-0.809733\pi$
$821$	3.58362	−	24.9247i	0.125069	−	0.869877i	0.951678	−	0.307099i	$-0.0993582\pi$
$822$		0			0
$823$	3.11672	+	3.59688i	0.108642	+	0.125379i	0.807466	−	0.589914i	$-0.200838\pi$
$823$	3.11672	+	3.59688i	0.108642	+	0.125379i	−0.698824	+	0.715294i	$0.746293\pi$
$824$		0			0
$825$	−0.114649	−	0.0336641i	−0.00399158	−	0.00117203i
$826$		0			0
$827$	9.76818	+	21.3893i	0.339673	+	0.743780i	0.999974	−	0.00722092i	$-0.00229851\pi$
$827$	9.76818	+	21.3893i	0.339673	+	0.743780i	−0.660301	+	0.751001i	$0.729571\pi$
$828$		0			0
$829$	−3.06603	+	1.97042i	−0.106488	+	0.0684355i	−0.592801	−	0.805349i	$-0.701978\pi$
$829$	−3.06603	+	1.97042i	−0.106488	+	0.0684355i	0.486313	+	0.873785i	$0.338341\pi$
$830$		0			0
$831$	30.4822	+	8.95037i	1.05741	+	0.310485i
$832$		0			0
$833$	54.8634			1.90090
$834$		0			0
$835$	8.30724	+	5.33874i	0.287484	+	0.184755i
$836$		0			0
$837$	−5.89223	−	6.80000i	−0.203665	−	0.235042i
$838$		0			0
$839$	−3.44127	+	7.53534i	−0.118806	+	0.260149i	−0.959687	−	0.281071i	$-0.909310\pi$
$839$	−3.44127	+	7.53534i	−0.118806	+	0.260149i	0.840881	+	0.541220i	$0.182037\pi$
$840$		0			0
$841$	−28.2133			−0.972872
$842$		0			0
$843$	18.5128	+	11.8975i	0.637616	+	0.409771i
$844$		0			0
$845$	1.72383	−	11.9895i	0.0593016	−	0.412451i
$846$		0			0
$847$	−0.0176536	+	0.122784i	−0.000606585	+	0.00421889i
$848$		0			0
$849$	6.76340	−	14.8098i	0.232119	−	0.508270i
$850$		0			0
$851$	15.2436	+	33.3788i	0.522543	+	1.14421i
$852$		0			0
$853$	2.78424	+	19.3648i	0.0953305	+	0.663038i	0.980318	+	0.197424i	$0.0632576\pi$
$853$	2.78424	+	19.3648i	0.0953305	+	0.663038i	−0.884988	+	0.465614i	$0.845833\pi$
$854$		0			0
$855$	−1.05635	+	0.310172i	−0.0361263	+	0.0106076i
$856$		0			0
$857$	−5.41557	−	37.6661i	−0.184992	−	1.28665i	−0.844746	−	0.535168i	$-0.820248\pi$
$857$	−5.41557	−	37.6661i	−0.184992	−	1.28665i	0.659753	−	0.751482i	$-0.270661\pi$
$858$		0			0
$859$	16.6255	−	10.6846i	0.567255	−	0.364553i	−0.225359	−	0.974276i	$-0.572356\pi$
$859$	16.6255	−	10.6846i	0.567255	−	0.364553i	0.792615	+	0.609723i	$0.208719\pi$
$860$		0			0
$861$	0.0302619	−	0.0662643i	0.00103132	−	0.00225828i
$862$		0			0
$863$	22.9692	+	14.7614i	0.781879	+	0.502483i	0.869657	−	0.493657i	$-0.164340\pi$
$863$	22.9692	+	14.7614i	0.781879	+	0.502483i	−0.0877776	+	0.996140i	$0.527976\pi$
$864$		0			0
$865$	−11.8371	−	3.47567i	−0.402472	−	0.118176i
$866$		0			0
$867$	6.32314	+	43.9784i	0.214745	+	1.49358i
$868$		0			0
$869$	−0.126907	+	0.146458i	−0.00430501	+	0.00496824i
$870$		0			0
$871$	−7.69119	+	0.964561i	−0.260606	+	0.0326829i
$872$		0			0
$873$	8.57398	−	9.89489i	0.290185	−	0.334891i
$874$		0			0
$875$	−0.0144539	−	0.100529i	−0.000488632	−	0.00339851i
$876$		0			0
$877$	2.71173	+	0.796236i	0.0915687	+	0.0268870i	0.327196	−	0.944957i	$-0.393896\pi$
$877$	2.71173	+	0.796236i	0.0915687	+	0.0268870i	−0.235627	+	0.971843i	$0.575714\pi$
$878$		0			0
$879$	−13.5477	−	8.70659i	−0.456953	−	0.293666i
$880$		0			0
$881$	8.65909	−	18.9608i	0.291732	−	0.638804i	−0.705846	−	0.708366i	$-0.749433\pi$
$881$	8.65909	−	18.9608i	0.291732	−	0.638804i	0.997578	+	0.0695615i	$0.0221600\pi$
$882$		0			0
$883$	−18.7849	+	12.0723i	−0.632163	+	0.406267i	−0.817110	−	0.576482i	$-0.804425\pi$
$883$	−18.7849	+	12.0723i	−0.632163	+	0.406267i	0.184947	+	0.982749i	$0.440789\pi$
$884$		0			0
$885$	−1.37209	−	9.54312i	−0.0461224	−	0.320789i
$886$		0			0
$887$	−37.5164	+	11.0158i	−1.25968	+	0.369874i	−0.842374	−	0.538894i	$-0.818843\pi$
$887$	−37.5164	+	11.0158i	−1.25968	+	0.369874i	−0.417302	+	0.908768i	$0.637024\pi$
$888$		0			0
$889$	0.00591526	+	0.0411416i	0.000198392	+	0.00137984i
$890$		0			0
$891$	0.0124143	+	0.0271836i	0.000415896	+	0.000910686i
$892$		0			0
$893$	−2.39981	+	5.25484i	−0.0803065	+	0.175847i
$894$		0			0
$895$	−2.45280	+	17.0596i	−0.0819880	+	0.570239i
$896$		0			0
$897$	0.798462	−	5.55343i	0.0266599	−	0.185423i
$898$		0			0
$899$	−6.71381	−	4.31470i	−0.223918	−	0.143903i
$900$		0			0
$901$	−54.0020			−1.79907
$902$		0			0
$903$	−0.00459963	+	0.0100718i	−0.000153066	+	0.000335168i
$904$		0			0
$905$	−6.80040	−	7.84808i	−0.226053	−	0.260879i
$906$		0			0
$907$	25.0252	+	16.0827i	0.830949	+	0.534018i	0.885579	−	0.464488i	$-0.153762\pi$
$907$	25.0252	+	16.0827i	0.830949	+	0.534018i	−0.0546306	+	0.998507i	$0.517398\pi$
$908$		0			0
$909$	3.87913			0.128663
$910$		0			0
$911$	−7.46150	−	2.19090i	−0.247211	−	0.0725876i	0.155780	−	0.987792i	$-0.450211\pi$
$911$	−7.46150	−	2.19090i	−0.247211	−	0.0725876i	−0.402990	+	0.915204i	$0.632029\pi$
$912$		0			0
$913$	−0.209122	+	0.134395i	−0.00692094	+	0.00444782i
$914$		0			0
$915$	3.00632	+	6.58293i	0.0993860	+	0.217625i
$916$		0			0
$917$	−0.176779	−	0.0519070i	−0.00583775	−	0.00171412i
$918$		0			0
$919$	−1.69827	−	1.95990i	−0.0560206	−	0.0646512i	0.727048	−	0.686587i	$-0.240892\pi$
$919$	−1.69827	−	1.95990i	−0.0560206	−	0.0646512i	−0.783068	+	0.621936i	$0.786346\pi$
$920$		0			0
$921$	−1.41335	+	9.83004i	−0.0465714	+	0.323911i
$922$		0			0
$923$	7.29701	+	8.42120i	0.240184	+	0.277187i
$924$		0			0
$925$	20.8334	−	13.3888i	0.684999	−	0.440222i
$926$		0			0
$927$	−1.91883	+	0.563419i	−0.0630226	+	0.0185051i
$928$		0			0
$929$	−4.43668	+	5.12020i	−0.145563	+	0.167988i	−0.823849	−	0.566810i	$-0.808178\pi$
$929$	−4.43668	+	5.12020i	−0.145563	+	0.167988i	0.678286	+	0.734798i	$0.262723\pi$
$930$		0			0
$931$	5.04267	−	5.81955i	0.165267	−	0.190728i
$932$		0			0
$933$	−2.52132	+	0.740326i	−0.0825443	+	0.0242372i
$934$		0			0
$935$	−0.0973778	−	0.213228i	−0.00318460	−	0.00697329i
$936$		0			0
$937$	−41.9670			−1.37100			−0.685501	−	0.728071i	$-0.740417\pi$
$937$	−41.9670			−1.37100			−0.685501	+	0.728071i	$0.740417\pi$
$938$		0			0
$939$	5.89041			0.192226
$940$		0			0
$941$	−16.6529	−	36.4649i	−0.542870	−	1.18872i	−0.960033	−	0.279888i	$-0.909703\pi$
$941$	−16.6529	−	36.4649i	−0.542870	−	1.18872i	0.417162	−	0.908832i	$-0.363025\pi$
$942$		0			0
$943$	36.7188	−	10.7816i	1.19573	−	0.351098i
$944$		0			0
$945$	−0.00739126	+	0.00852997i	−0.000240438	+	0.000277480i
$946$		0			0
$947$	−17.8140	+	20.5584i	−0.578877	+	0.668059i	−0.967363	−	0.253395i	$-0.918453\pi$
$947$	−17.8140	+	20.5584i	−0.578877	+	0.668059i	0.388486	+	0.921455i	$0.372998\pi$
$948$		0			0
$949$	9.14444	−	2.68505i	0.296841	−	0.0871604i
$950$		0			0
$951$	−8.31388	+	5.34300i	−0.269596	+	0.173259i
$952$		0			0
$953$	1.65165	+	1.90611i	0.0535022	+	0.0617449i	0.781870	−	0.623442i	$-0.214266\pi$
$953$	1.65165	+	1.90611i	0.0535022	+	0.0617449i	−0.728368	+	0.685187i	$0.759721\pi$
$954$		0			0
$955$	1.76287	−	12.2610i	0.0570452	−	0.396758i
$956$		0			0
$957$	0.0173581	+	0.0200323i	0.000561107	+	0.000647552i
$958$		0			0
$959$	−0.0451521	−	0.0132579i	−0.00145804	−	0.000428118i
$960$		0			0
$961$	20.7535	+	45.4438i	0.669467	+	1.46593i
$962$		0			0
$963$	−7.48171	+	4.80820i	−0.241095	+	0.154942i
$964$		0			0
$965$	−15.6319	−	4.58995i	−0.503210	−	0.147756i
$966$		0			0
$967$	−17.4205			−0.560207			−0.280103	−	0.959970i	$-0.590369\pi$
$967$	−17.4205			−0.560207			−0.280103	+	0.959970i	$0.590369\pi$
$968$		0			0
$969$	7.25339	+	4.66147i	0.233012	+	0.149748i
$970$		0			0
$971$	−4.37506	−	5.04909i	−0.140402	−	0.162033i	0.681193	−	0.732104i	$-0.261461\pi$
$971$	−4.37506	−	5.04909i	−0.140402	−	0.162033i	−0.821596	+	0.570071i	$0.806916\pi$
$972$		0			0
$973$	0.102400	−	0.224224i	0.00328278	−	0.00718829i
$974$		0			0
$975$	−3.78646			−0.121264
$976$		0			0
$977$	−13.3951	−	8.60852i	−0.428548	−	0.275411i	0.308535	−	0.951213i	$-0.400161\pi$
$977$	−13.3951	−	8.60852i	−0.428548	−	0.275411i	−0.737083	+	0.675802i	$0.763798\pi$
$978$		0			0
$979$	0.0411687	−	0.286335i	0.00131576	−	0.00915130i
$980$		0			0
$981$	−1.96336	+	13.6554i	−0.0626852	+	0.435985i
$982$		0			0
$983$	6.54988	−	14.3422i	0.208909	−	0.457446i	−0.775953	−	0.630791i	$-0.782730\pi$
$983$	6.54988	−	14.3422i	0.208909	−	0.457446i	0.984861	+	0.173345i	$0.0554577\pi$
$984$		0			0
$985$	−1.70290	−	3.72882i	−0.0542588	−	0.118810i
$986$		0			0
$987$	0.00842847	+	0.0586213i	0.000268281	+	0.00186594i
$988$		0			0
$989$	−5.58105	+	1.63874i	−0.177467	+	0.0521090i
$990$		0			0
$991$	−7.83894	−	54.5210i	−0.249012	−	1.73192i	−0.603946	−	0.797025i	$-0.706406\pi$
$991$	−7.83894	−	54.5210i	−0.249012	−	1.73192i	0.354934	−	0.934891i	$-0.384503\pi$
$992$		0			0
$993$	−13.3280	+	8.56538i	−0.422951	+	0.271814i
$994$		0			0
$995$	0.566611	−	1.24071i	0.0179628	−	0.0393330i
$996$		0			0
$997$	−0.513496	−	0.330004i	−0.0162626	−	0.0104513i	0.532484	−	0.846440i	$-0.321259\pi$
$997$	−0.513496	−	0.330004i	−0.0162626	−	0.0104513i	−0.548747	+	0.835989i	$0.684895\pi$
$998$		0			0
$999$	−5.94275	−	1.74495i	−0.188020	−	0.0552078i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.q.b.397.3	yes	60
67.40	even	11	inner	804.2.q.b.241.3	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.b.241.3	✓	60	67.40	even	11	inner
804.2.q.b.397.3	yes	60	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{3} +(-0.960253 + 0.281956i) q^{5} +(0.00738542 - 0.00852322i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{3} +(-0.960253 + 0.281956i) q^{5} +(0.00738542 - 0.00852322i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(-0.0286737 + 0.00841935i) q^{11} +(-0.796658 + 0.511981i) q^{13} +(0.655379 + 0.756348i) q^{15} +(1.11543 - 7.75799i) q^{17} +(-0.720395 - 0.831380i) q^{19} +(-0.0108210 - 0.00317734i) q^{21} +(-2.46117 - 5.38921i) q^{23} +(-3.36368 + 2.16171i) q^{25} +(0.959493 + 0.281733i) q^{27} +0.886974 q^{29} +(-7.56934 - 4.86452i) q^{31} +(0.0195700 + 0.0225850i) q^{33} +(-0.00468869 + 0.0102668i) q^{35} -6.19364 q^{37} +(0.796658 + 0.511981i) q^{39} +(-0.919259 + 6.39359i) q^{41} +(0.139722 - 0.971788i) q^{43} +(0.415744 - 0.910352i) q^{45} +(-2.18150 - 4.77681i) q^{47} +(0.996186 + 6.92862i) q^{49} +(-7.52028 + 2.20815i) q^{51} +(-0.980545 - 6.81984i) q^{53} +(0.0251601 - 0.0161694i) q^{55} +(-0.456987 + 1.00066i) q^{57} +(-8.10432 - 5.20833i) q^{59} +(6.93827 + 2.03726i) q^{61} +(0.00160500 + 0.0111630i) q^{63} +(0.620637 - 0.716253i) q^{65} +(7.38311 + 3.53408i) q^{67} +(-3.87979 + 4.47751i) q^{69} +(-1.67456 - 11.6468i) q^{71} +(-9.65633 - 2.83536i) q^{73} +(3.36368 + 2.16171i) q^{75} +(-0.000140007 + 0.000306573i) q^{77} +(5.45532 - 3.50592i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(7.98130 - 2.34352i) q^{83} +(1.11631 + 7.76413i) q^{85} +(-0.368462 - 0.806820i) q^{87} +(-4.02122 + 8.80524i) q^{89} +(-0.00151992 + 0.0105713i) q^{91} +(-1.28050 + 8.90611i) q^{93} +(0.926173 + 0.595215i) q^{95} -13.0928 q^{97} +(0.0124143 - 0.0271836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) \) 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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