LMFDB - Embedded newform 504.2.q.d.121.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(25,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))

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

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

chi := DirichletCharacter("504.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.q (of order $3$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.6
Character	$\chi$	$=$	504.121
Dual form			504.2.q.d.25.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.273951 + 1.71025i) q^{3} +(-1.33401 - 2.31057i) q^{5} +(0.581213 + 2.58112i) q^{7} +(-2.84990 + 0.937047i) q^{9} +O(q^{10})$	\(q+(0.273951 + 1.71025i) q^{3} +(-1.33401 - 2.31057i) q^{5} +(0.581213 + 2.58112i) q^{7} +(-2.84990 + 0.937047i) q^{9} +(-0.682257 + 1.18170i) q^{11} +(-2.75597 + 4.77348i) q^{13} +(3.58620 - 2.91447i) q^{15} +(-1.23930 - 2.14654i) q^{17} +(-2.19600 + 3.80358i) q^{19} +(-4.25514 + 1.70112i) q^{21} +(2.34501 + 4.06167i) q^{23} +(-1.05916 + 1.83452i) q^{25} +(-2.38332 - 4.61734i) q^{27} +(2.94810 + 5.10625i) q^{29} +3.11678 q^{31} +(-2.20791 - 0.843100i) q^{33} +(5.18852 - 4.78617i) q^{35} +(-3.15627 + 5.46681i) q^{37} +(-8.91883 - 3.40569i) q^{39} +(1.38693 - 2.40224i) q^{41} +(-4.87889 - 8.45048i) q^{43} +(5.96691 + 5.33487i) q^{45} -10.0501 q^{47} +(-6.32438 + 3.00036i) q^{49} +(3.33160 - 2.70756i) q^{51} +(-1.47823 - 2.56037i) q^{53} +3.64055 q^{55} +(-7.10667 - 2.71371i) q^{57} +3.55617 q^{59} +1.32609 q^{61} +(-4.07503 - 6.81132i) q^{63} +14.7059 q^{65} +8.29874 q^{67} +(-6.30406 + 5.12325i) q^{69} +12.3069 q^{71} +(-1.11577 - 1.93257i) q^{73} +(-3.42764 - 1.30886i) q^{75} +(-3.44666 - 1.07417i) q^{77} +12.8307 q^{79} +(7.24388 - 5.34099i) q^{81} +(5.15934 + 8.93625i) q^{83} +(-3.30648 + 5.72700i) q^{85} +(-7.92533 + 6.44084i) q^{87} +(7.73159 - 13.3915i) q^{89} +(-13.9227 - 4.33908i) q^{91} +(0.853843 + 5.33046i) q^{93} +11.7179 q^{95} +(-2.55369 - 4.42311i) q^{97} +(0.837053 - 4.00705i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9}+O(q^{10}) $ 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9	$ 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9} - 3 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} + 2 q^{23} - 10 q^{25} - 4 q^{27} + 9 q^{29} + 8 q^{31} + 29 q^{33} + 14 q^{35} + 2 q^{37} - 16 q^{39} + 16 q^{41} + q^{45} - 10 q^{47} + 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} + 38 q^{59} + 26 q^{61} + 48 q^{63} - 26 q^{65} - 52 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 23 q^{75} + 17 q^{77} - 20 q^{79} - 38 q^{81} - 28 q^{83} - 20 q^{85} - 33 q^{87} + 6 q^{89} - 37 q^{91} + 19 q^{93} - 24 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9 - 3 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 + 2 * q^23 - 10 * q^25 - 4 * q^27 + 9 * q^29 + 8 * q^31 + 29 * q^33 + 14 * q^35 + 2 * q^37 - 16 * q^39 + 16 * q^41 + q^45 - 10 * q^47 + 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 + 38 * q^59 + 26 * q^61 + 48 * q^63 - 26 * q^65 - 52 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 23 * q^75 + 17 * q^77 - 20 * q^79 - 38 * q^81 - 28 * q^83 - 20 * q^85 - 33 * q^87 + 6 * q^89 - 37 * q^91 + 19 * q^93 - 24 * q^95 - 29 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	0.273951	+	1.71025i	0.158165	+	0.987413i
$3$	0.273951	+	1.71025i	0.158165	+	0.987413i
$4$		0			0
$5$	−1.33401	−	2.31057i	−0.596587	−	1.03332i	−0.993321	−	0.115385i	$-0.963190\pi$
$5$	−1.33401	−	2.31057i	−0.596587	−	1.03332i	0.396734	−	0.917934i	$-0.370144\pi$
$6$		0			0
$7$	0.581213	+	2.58112i	0.219678	+	0.975572i
$7$	0.581213	+	2.58112i	0.219678	+	0.975572i
$8$		0			0
$9$	−2.84990	+	0.937047i	−0.949967	+	0.312349i
$10$		0			0
$11$	−0.682257	+	1.18170i	−0.205708	+	0.356297i	−0.950358	−	0.311158i	$-0.899283\pi$
$11$	−0.682257	+	1.18170i	−0.205708	+	0.356297i	0.744650	+	0.667455i	$0.232616\pi$
$12$		0			0
$13$	−2.75597	+	4.77348i	−0.764368	+	1.32392i	0.176212	+	0.984352i	$0.443616\pi$
$13$	−2.75597	+	4.77348i	−0.764368	+	1.32392i	−0.940580	+	0.339572i	$0.889718\pi$
$14$		0			0
$15$	3.58620	−	2.91447i	0.925953	−	0.752513i
$16$		0			0
$17$	−1.23930	−	2.14654i	−0.300575	−	0.520611i	0.675691	−	0.737185i	$-0.263845\pi$
$17$	−1.23930	−	2.14654i	−0.300575	−	0.520611i	−0.976266	+	0.216573i	$0.930512\pi$
$18$		0			0
$19$	−2.19600	+	3.80358i	−0.503797	+	0.872601i	0.496194	+	0.868212i	$0.334731\pi$
$19$	−2.19600	+	3.80358i	−0.503797	+	0.872601i	−0.999990	+	0.00438950i	$0.998603\pi$
$20$		0			0
$21$	−4.25514	+	1.70112i	−0.928547	+	0.371215i
$22$		0			0
$23$	2.34501	+	4.06167i	0.488968	+	0.846918i	0.999919	−	0.0126921i	$-0.00404012\pi$
$23$	2.34501	+	4.06167i	0.488968	+	0.846918i	−0.510951	+	0.859610i	$0.670707\pi$
$24$		0			0
$25$	−1.05916	+	1.83452i	−0.211832	+	0.366904i
$26$		0			0
$27$	−2.38332	−	4.61734i	−0.458670	−	0.888607i
$28$		0			0
$29$	2.94810	+	5.10625i	0.547448	+	0.948207i	0.998448	+	0.0556837i	$0.0177338\pi$
$29$	2.94810	+	5.10625i	0.547448	+	0.948207i	−0.451001	+	0.892524i	$0.648933\pi$
$30$		0			0
$31$	3.11678			0.559789			0.279895	−	0.960031i	$-0.409700\pi$
$31$	3.11678			0.559789			0.279895	+	0.960031i	$0.409700\pi$
$32$		0			0
$33$	−2.20791	−	0.843100i	−0.384348	−	0.146765i
$34$		0			0
$35$	5.18852	−	4.78617i	0.877021	−	0.809011i
$36$		0			0
$37$	−3.15627	+	5.46681i	−0.518887	+	0.898739i	0.480872	+	0.876791i	$0.340320\pi$
$37$	−3.15627	+	5.46681i	−0.518887	+	0.898739i	−0.999759	+	0.0219479i	$0.993013\pi$
$38$		0			0
$39$	−8.91883	−	3.40569i	−1.42816	−	0.545348i
$40$		0			0
$41$	1.38693	−	2.40224i	0.216603	−	0.375167i	−0.737164	−	0.675713i	$-0.763836\pi$
$41$	1.38693	−	2.40224i	0.216603	−	0.375167i	0.953767	+	0.300546i	$0.0971690\pi$
$42$		0			0
$43$	−4.87889	−	8.45048i	−0.744023	−	1.28869i	−0.950650	−	0.310267i	$-0.899582\pi$
$43$	−4.87889	−	8.45048i	−0.744023	−	1.28869i	0.206626	−	0.978420i	$-0.433752\pi$
$44$		0			0
$45$	5.96691	+	5.33487i	0.889494	+	0.795276i
$46$		0			0
$47$	−10.0501			−1.46596			−0.732979	−	0.680252i	$-0.761871\pi$
$47$	−10.0501			−1.46596			−0.732979	+	0.680252i	$0.761871\pi$
$48$		0			0
$49$	−6.32438	+	3.00036i	−0.903483	+	0.428623i
$50$		0			0
$51$	3.33160	−	2.70756i	0.466518	−	0.379134i
$52$		0			0
$53$	−1.47823	−	2.56037i	−0.203050	−	0.351694i	0.746459	−	0.665431i	$-0.231752\pi$
$53$	−1.47823	−	2.56037i	−0.203050	−	0.351694i	−0.949510	+	0.313737i	$0.898419\pi$
$54$		0			0
$55$	3.64055			0.490891
$56$		0			0
$57$	−7.10667	−	2.71371i	−0.941301	−	0.359440i
$58$		0			0
$59$	3.55617			0.462974			0.231487	−	0.972838i	$-0.425641\pi$
$59$	3.55617			0.462974			0.231487	+	0.972838i	$0.425641\pi$
$60$		0			0
$61$	1.32609			0.169788			0.0848940	−	0.996390i	$-0.472945\pi$
$61$	1.32609			0.169788			0.0848940	+	0.996390i	$0.472945\pi$
$62$		0			0
$63$	−4.07503	−	6.81132i	−0.513406	−	0.858146i
$64$		0			0
$65$	14.7059			1.82405
$66$		0			0
$67$	8.29874			1.01385			0.506926	−	0.861990i	$-0.330782\pi$
$67$	8.29874			1.01385			0.506926	+	0.861990i	$0.330782\pi$
$68$		0			0
$69$	−6.30406	+	5.12325i	−0.758919	+	0.616766i
$70$		0			0
$71$	12.3069			1.46056			0.730279	−	0.683149i	$-0.239390\pi$
$71$	12.3069			1.46056			0.730279	+	0.683149i	$0.239390\pi$
$72$		0			0
$73$	−1.11577	−	1.93257i	−0.130591	−	0.226190i	0.793314	−	0.608813i	$-0.208354\pi$
$73$	−1.11577	−	1.93257i	−0.130591	−	0.226190i	−0.923905	+	0.382623i	$0.875021\pi$
$74$		0			0
$75$	−3.42764	−	1.30886i	−0.395790	−	0.151134i
$76$		0			0
$77$	−3.44666	−	1.07417i	−0.392783	−	0.122413i
$78$		0			0
$79$	12.8307			1.44357			0.721783	−	0.692119i	$-0.243323\pi$
$79$	12.8307			1.44357			0.721783	+	0.692119i	$0.243323\pi$
$80$		0			0
$81$	7.24388	−	5.34099i	0.804876	−	0.593443i
$82$		0			0
$83$	5.15934	+	8.93625i	0.566312	+	0.980881i	0.996926	+	0.0783447i	$0.0249635\pi$
$83$	5.15934	+	8.93625i	0.566312	+	0.980881i	−0.430615	+	0.902536i	$0.641703\pi$
$84$		0			0
$85$	−3.30648	+	5.72700i	−0.358638	+	0.621180i
$86$		0			0
$87$	−7.92533	+	6.44084i	−0.849684	+	0.690530i
$88$		0			0
$89$	7.73159	−	13.3915i	0.819547	−	1.41950i	−0.0864698	−	0.996254i	$-0.527559\pi$
$89$	7.73159	−	13.3915i	0.819547	−	1.41950i	0.906017	−	0.423242i	$-0.139108\pi$
$90$		0			0
$91$	−13.9227	−	4.33908i	−1.45950	−	0.454860i
$92$		0			0
$93$	0.853843	+	5.33046i	0.0885394	+	0.552743i
$94$		0			0
$95$	11.7179			1.20223
$96$		0			0
$97$	−2.55369	−	4.42311i	−0.259288	−	0.449099i	0.706764	−	0.707450i	$-0.250154\pi$
$97$	−2.55369	−	4.42311i	−0.259288	−	0.449099i	−0.966051	+	0.258351i	$0.916821\pi$
$98$		0			0
$99$	0.837053	−	4.00705i	0.0841270	−	0.402723i
$100$		0			0
$101$	1.34748	−	2.33391i	0.134079	−	0.232232i	−0.791166	−	0.611601i	$-0.790526\pi$
$101$	1.34748	−	2.33391i	0.134079	−	0.232232i	0.925245	+	0.379369i	$0.123859\pi$
$102$		0			0
$103$	6.51071	+	11.2769i	0.641519	+	1.11114i	0.985094	+	0.172019i	$0.0550290\pi$
$103$	6.51071	+	11.2769i	0.641519	+	1.11114i	−0.343574	+	0.939126i	$0.611638\pi$
$104$		0			0
$105$	9.60695	+	7.56249i	0.937542	+	0.738024i
$106$		0			0
$107$	−1.49753	+	2.59379i	−0.144771	+	0.250751i	−0.929288	−	0.369357i	$-0.879578\pi$
$107$	−1.49753	+	2.59379i	−0.144771	+	0.250751i	0.784516	+	0.620108i	$0.212911\pi$
$108$		0			0
$109$	10.0132	+	17.3434i	0.959093	+	1.66120i	0.724710	+	0.689054i	$0.241974\pi$
$109$	10.0132	+	17.3434i	0.959093	+	1.66120i	0.234383	+	0.972144i	$0.424693\pi$
$110$		0			0
$111$	−10.2143	−	3.90036i	−0.969496	−	0.370206i
$112$		0			0
$113$	−6.23211	+	10.7943i	−0.586267	+	1.01544i	0.408449	+	0.912781i	$0.366070\pi$
$113$	−6.23211	+	10.7943i	−0.586267	+	1.01544i	−0.994716	+	0.102664i	$0.967263\pi$
$114$		0			0
$115$	6.25652	−	10.8366i	0.583424	−	1.01052i
$116$		0			0
$117$	3.38127	−	16.1864i	0.312598	−	1.49643i
$118$		0			0
$119$	4.82017	−	4.44639i	0.441864	−	0.407600i
$120$		0			0
$121$	4.56905	+	7.91383i	0.415368	+	0.719439i
$122$		0			0
$123$	4.48838	+	1.71391i	0.404704	+	0.154538i
$124$		0			0
$125$	−7.68837			−0.687669
$126$		0			0
$127$	15.0734			1.33754			0.668772	−	0.743467i	$-0.266820\pi$
$127$	15.0734			1.33754			0.668772	+	0.743467i	$0.266820\pi$
$128$		0			0
$129$	13.1159	−	10.6591i	1.15479	−	0.938484i
$130$		0			0
$131$	−7.42032	−	12.8524i	−0.648316	−	1.12292i	−0.983525	−	0.180773i	$-0.942140\pi$
$131$	−7.42032	−	12.8524i	−0.648316	−	1.12292i	0.335208	−	0.942144i	$-0.391193\pi$
$132$		0			0
$133$	−11.0938	−	3.45745i	−0.961959	−	0.299799i
$134$		0			0
$135$	−7.48932	+	11.6664i	−0.644578	+	1.00408i
$136$		0			0
$137$	10.0779	−	17.4555i	0.861017	−	1.49132i	−0.00993230	−	0.999951i	$-0.503162\pi$
$137$	10.0779	−	17.4555i	0.861017	−	1.49132i	0.870949	−	0.491374i	$-0.163505\pi$
$138$		0			0
$139$	−9.91552	+	17.1742i	−0.841023	+	1.45669i	0.0480074	+	0.998847i	$0.484713\pi$
$139$	−9.91552	+	17.1742i	−0.841023	+	1.45669i	−0.889031	+	0.457848i	$0.848620\pi$
$140$		0			0
$141$	−2.75323	−	17.1882i	−0.231864	−	1.44750i
$142$		0			0
$143$	−3.76056	−	6.51347i	−0.314473	−	0.544684i
$144$		0			0
$145$	7.86557	−	13.6236i	0.653200	−	1.13138i
$146$		0			0
$147$	−6.86394	−	9.99432i	−0.566128	−	0.824317i
$148$		0			0
$149$	−8.65166	−	14.9851i	−0.708772	−	1.22763i	−0.965313	−	0.261096i	$-0.915916\pi$
$149$	−8.65166	−	14.9851i	−0.708772	−	1.22763i	0.256541	−	0.966533i	$-0.417417\pi$
$150$		0			0
$151$	1.99488	−	3.45523i	0.162341	−	0.281183i	−0.773367	−	0.633959i	$-0.781429\pi$
$151$	1.99488	−	3.45523i	0.162341	−	0.281183i	0.935708	+	0.352776i	$0.114762\pi$
$152$		0			0
$153$	5.54330	+	4.95613i	0.448149	+	0.400680i
$154$		0			0
$155$	−4.15781	−	7.20153i	−0.333963	−	0.578441i
$156$		0			0
$157$	−24.1988			−1.93127			−0.965637	−	0.259896i	$-0.916312\pi$
$157$	−24.1988			−1.93127			−0.965637	+	0.259896i	$0.916312\pi$
$158$		0			0
$159$	3.97391	−	3.22955i	0.315151	−	0.256120i
$160$		0			0
$161$	−9.12073	+	8.41345i	−0.718814	+	0.663073i
$162$		0			0
$163$	2.34498	−	4.06162i	0.183673	−	0.318131i	−0.759456	−	0.650559i	$-0.774535\pi$
$163$	2.34498	−	4.06162i	0.183673	−	0.318131i	0.943129	+	0.332428i	$0.107868\pi$
$164$		0			0
$165$	0.997330	+	6.22624i	0.0776420	+	0.484712i
$166$		0			0
$167$	−6.12627	+	10.6110i	−0.474065	+	0.821104i	−0.999559	−	0.0296928i	$-0.990547\pi$
$167$	−6.12627	+	10.6110i	−0.474065	+	0.821104i	0.525494	+	0.850797i	$0.323880\pi$
$168$		0			0
$169$	−8.69072	−	15.0528i	−0.668517	−	1.15791i
$170$		0			0
$171$	2.69424	−	12.8976i	0.206034	−	0.986303i
$172$		0			0
$173$	−8.11006			−0.616596			−0.308298	−	0.951290i	$-0.599759\pi$
$173$	−8.11006			−0.616596			−0.308298	+	0.951290i	$0.599759\pi$
$174$		0			0
$175$	−5.35072	−	1.66757i	−0.404476	−	0.126057i
$176$		0			0
$177$	0.974216	+	6.08194i	0.0732265	+	0.457147i
$178$		0			0
$179$	4.91636	+	8.51538i	0.367466	+	0.636469i	0.989169	−	0.146784i	$-0.0468922\pi$
$179$	4.91636	+	8.51538i	0.367466	+	0.636469i	−0.621703	+	0.783253i	$0.713559\pi$
$180$		0			0
$181$	15.8876			1.18092			0.590458	−	0.807068i	$-0.298947\pi$
$181$	15.8876			1.18092			0.590458	+	0.807068i	$0.298947\pi$
$182$		0			0
$183$	0.363282	+	2.26794i	0.0268546	+	0.167651i
$184$		0			0
$185$	16.8419			1.23824
$186$		0			0
$187$	3.38209			0.247323
$188$		0			0
$189$	10.5327	−	8.83529i	0.766141	−	0.642673i
$190$		0			0
$191$	−2.21898			−0.160560			−0.0802800	−	0.996772i	$-0.525581\pi$
$191$	−2.21898			−0.160560			−0.0802800	+	0.996772i	$0.525581\pi$
$192$		0			0
$193$	5.84168			0.420493			0.210247	−	0.977648i	$-0.432573\pi$
$193$	5.84168			0.420493			0.210247	+	0.977648i	$0.432573\pi$
$194$		0			0
$195$	4.02870	+	25.1508i	0.288501	+	1.80109i
$196$		0			0
$197$	1.93695			0.138002			0.0690010	−	0.997617i	$-0.478019\pi$
$197$	1.93695			0.138002			0.0690010	+	0.997617i	$0.478019\pi$
$198$		0			0
$199$	1.84540	+	3.19633i	0.130817	+	0.226582i	0.923992	−	0.382412i	$-0.124907\pi$
$199$	1.84540	+	3.19633i	0.130817	+	0.226582i	−0.793175	+	0.608994i	$0.791573\pi$
$200$		0			0
$201$	2.27344	+	14.1929i	0.160356	+	1.00109i
$202$		0			0
$203$	−11.4664	+	10.5772i	−0.804783	+	0.742375i
$204$		0			0
$205$	−7.40073			−0.516889
$206$		0			0
$207$	−10.4890	−	9.37799i	−0.729038	−	0.651815i
$208$		0			0
$209$	−2.99647	−	5.19004i	−0.207270	−	0.359002i
$210$		0			0
$211$	−5.67097	+	9.82241i	−0.390406	+	0.676202i	−0.992503	−	0.122220i	$-0.960999\pi$
$211$	−5.67097	+	9.82241i	−0.390406	+	0.676202i	0.602097	+	0.798423i	$0.294332\pi$
$212$		0			0
$213$	3.37148	+	21.0478i	0.231010	+	1.44217i
$214$		0			0
$215$	−13.0170	+	22.5460i	−0.887749	+	1.53763i
$216$		0			0
$217$	1.81151	+	8.04478i	0.122973	+	0.546115i
$218$		0			0
$219$	2.99951	−	2.43767i	0.202688	−	0.164723i
$220$		0			0
$221$	13.6619			0.919000
$222$		0			0
$223$	−0.965547	−	1.67238i	−0.0646578	−	0.111991i	0.831884	−	0.554949i	$-0.187262\pi$
$223$	−0.965547	−	1.67238i	−0.0646578	−	0.111991i	−0.896542	+	0.442958i	$0.853929\pi$
$224$		0			0
$225$	1.29947	−	6.22068i	0.0866314	−	0.414712i
$226$		0			0
$227$	−9.86413	+	17.0852i	−0.654705	+	1.13398i	0.327262	+	0.944934i	$0.393874\pi$
$227$	−9.86413	+	17.0852i	−0.654705	+	1.13398i	−0.981968	+	0.189049i	$0.939459\pi$
$228$		0			0
$229$	−13.2098	−	22.8801i	−0.872931	−	1.51196i	−0.858951	−	0.512058i	$-0.828883\pi$
$229$	−13.2098	−	22.8801i	−0.872931	−	1.51196i	−0.0139803	−	0.999902i	$-0.504450\pi$
$230$		0			0
$231$	0.892878	−	6.18891i	0.0587471	−	0.407200i
$232$		0			0
$233$	−4.24071	+	7.34513i	−0.277818	+	0.481196i	−0.970842	−	0.239719i	$-0.922945\pi$
$233$	−4.24071	+	7.34513i	−0.277818	+	0.481196i	0.693024	+	0.720915i	$0.256278\pi$
$234$		0			0
$235$	13.4069	+	23.2215i	0.874571	+	1.51480i
$236$		0			0
$237$	3.51498	+	21.9437i	0.228322	+	1.42540i
$238$		0			0
$239$	−8.08023	+	13.9954i	−0.522667	+	0.905286i	0.476985	+	0.878911i	$0.341730\pi$
$239$	−8.08023	+	13.9954i	−0.522667	+	0.905286i	−0.999652	+	0.0263743i	$0.991604\pi$
$240$		0			0
$241$	−5.48677	+	9.50336i	−0.353434	+	0.612165i	−0.986849	−	0.161647i	$-0.948319\pi$
$241$	−5.48677	+	9.50336i	−0.353434	+	0.612165i	0.633415	+	0.773812i	$0.281653\pi$
$242$		0			0
$243$	11.1189	+	10.9257i	0.713277	+	0.700883i
$244$		0			0
$245$	15.3693	+	10.6104i	0.981911	+	0.677875i
$246$		0			0
$247$	−12.1042	−	20.9651i	−0.770172	−	1.33398i
$248$		0			0
$249$	−13.8698	+	11.2719i	−0.878963	+	0.714325i
$250$		0			0
$251$	2.85873			0.180442			0.0902208	−	0.995922i	$-0.471243\pi$
$251$	2.85873			0.180442			0.0902208	+	0.995922i	$0.471243\pi$
$252$		0			0
$253$	−6.39959			−0.402339
$254$		0			0
$255$	−10.7004	−	4.08599i	−0.670085	−	0.255875i
$256$		0			0
$257$	−12.2938	−	21.2934i	−0.766864	−	1.32825i	−0.939256	−	0.343218i	$-0.888483\pi$
$257$	−12.2938	−	21.2934i	−0.766864	−	1.32825i	0.172392	−	0.985028i	$-0.444850\pi$
$258$		0			0
$259$	−15.9450	−	4.96933i	−0.990773	−	0.308779i
$260$		0			0
$261$	−13.1866	−	11.7898i	−0.816229	−	0.729771i
$262$		0			0
$263$	−0.478986	+	0.829628i	−0.0295355	+	0.0511570i	−0.880415	−	0.474203i	$-0.842736\pi$
$263$	−0.478986	+	0.829628i	−0.0295355	+	0.0511570i	0.850880	+	0.525360i	$0.176069\pi$
$264$		0			0
$265$	−3.94394	+	6.83111i	−0.242274	+	0.419632i
$266$		0			0
$267$	25.0209	+	9.55433i	1.53125	+	0.584715i
$268$		0			0
$269$	8.31005	+	14.3934i	0.506673	+	0.877583i	0.999970	+	0.00772245i	$0.00245816\pi$
$269$	8.31005	+	14.3934i	0.506673	+	0.877583i	−0.493297	+	0.869861i	$0.664209\pi$
$270$		0			0
$271$	7.21801	−	12.5020i	0.438463	−	0.759440i	−0.559108	−	0.829095i	$-0.688856\pi$
$271$	7.21801	−	12.5020i	0.438463	−	0.759440i	0.997571	+	0.0696545i	$0.0221897\pi$
$272$		0			0
$273$	3.60677	−	25.0000i	0.218292	−	1.51307i
$274$		0			0
$275$	−1.44524	−	2.50323i	−0.0871511	−	0.150950i
$276$		0			0
$277$	2.23321	−	3.86804i	0.134181	−	0.232408i	−0.791103	−	0.611682i	$-0.790493\pi$
$277$	2.23321	−	3.86804i	0.134181	−	0.232408i	0.925284	+	0.379275i	$0.123826\pi$
$278$		0			0
$279$	−8.88251	+	2.92057i	−0.531782	+	0.174850i
$280$		0			0
$281$	2.62617	+	4.54867i	0.156664	+	0.271351i	0.933664	−	0.358151i	$-0.116593\pi$
$281$	2.62617	+	4.54867i	0.156664	+	0.271351i	−0.776999	+	0.629501i	$0.783259\pi$
$282$		0			0
$283$	11.3150			0.672608			0.336304	−	0.941754i	$-0.390823\pi$
$283$	11.3150			0.672608			0.336304	+	0.941754i	$0.390823\pi$
$284$		0			0
$285$	3.21013	+	20.0406i	0.190152	+	1.18710i
$286$		0			0
$287$	7.00658	+	2.18363i	0.413585	+	0.128896i
$288$		0			0
$289$	5.42826	−	9.40201i	0.319309	−	0.553060i
$290$		0			0
$291$	6.86504	−	5.57915i	0.402436	−	0.327056i
$292$		0			0
$293$	−5.38422	+	9.32574i	−0.314549	+	0.544815i	−0.979342	−	0.202213i	$-0.935187\pi$
$293$	−5.38422	+	9.32574i	−0.314549	+	0.544815i	0.664792	+	0.747028i	$0.268520\pi$
$294$		0			0
$295$	−4.74397	−	8.21679i	−0.276204	−	0.478400i
$296$		0			0
$297$	7.08236	+	0.333836i	0.410960	+	0.0193711i
$298$		0			0
$299$	−25.8511			−1.49501
$300$		0			0
$301$	18.9761	−	17.5045i	1.09376	−	1.00894i
$302$		0			0
$303$	4.36070	+	1.66515i	0.250516	+	0.0956606i
$304$		0			0
$305$	−1.76901	−	3.06402i	−0.101293	−	0.175445i
$306$		0			0
$307$	9.42151			0.537714			0.268857	−	0.963180i	$-0.413354\pi$
$307$	9.42151			0.537714			0.268857	+	0.963180i	$0.413354\pi$
$308$		0			0
$309$	−17.5027	+	14.2242i	−0.995692	+	0.809189i
$310$		0			0
$311$	−11.3151			−0.641619			−0.320809	−	0.947144i	$-0.603955\pi$
$311$	−11.3151			−0.641619			−0.320809	+	0.947144i	$0.603955\pi$
$312$		0			0
$313$	21.6862			1.22578			0.612889	−	0.790169i	$-0.290007\pi$
$313$	21.6862			1.22578			0.612889	+	0.790169i	$0.290007\pi$
$314$		0			0
$315$	−10.3019	+	18.5020i	−0.580447	+	1.04247i
$316$		0			0
$317$	−25.2174			−1.41635			−0.708174	−	0.706038i	$-0.750481\pi$
$317$	−25.2174			−1.41635			−0.708174	+	0.706038i	$0.750481\pi$
$318$		0			0
$319$	−8.04543			−0.450458
$320$		0			0
$321$	−4.84628	−	1.85057i	−0.270493	−	0.103289i
$322$		0			0
$323$	10.8860			0.605715
$324$		0			0
$325$	−5.83802	−	10.1118i	−0.323835	−	0.560899i
$326$		0			0
$327$	−26.9184	+	21.8763i	−1.48859	+	1.20976i
$328$		0			0
$329$	−5.84125	−	25.9405i	−0.322038	−	1.43015i
$330$		0			0
$331$	−17.0245			−0.935753			−0.467876	−	0.883794i	$-0.654981\pi$
$331$	−17.0245			−0.935753			−0.467876	+	0.883794i	$0.654981\pi$
$332$		0			0
$333$	3.87239	−	18.5375i	0.212205	−	1.01585i
$334$		0			0
$335$	−11.0706	−	19.1748i	−0.604851	−	1.04763i
$336$		0			0
$337$	6.85166	−	11.8674i	0.373233	−	0.646459i	−0.616827	−	0.787098i	$-0.711582\pi$
$337$	6.85166	−	11.8674i	0.373233	−	0.646459i	0.990061	+	0.140639i	$0.0449157\pi$
$338$		0			0
$339$	−20.1683	−	7.70134i	−1.09539	−	0.418279i
$340$		0			0
$341$	−2.12644	+	3.68310i	−0.115153	+	0.199451i
$342$		0			0
$343$	−11.4201	−	14.5802i	−0.616628	−	0.787254i
$344$		0			0
$345$	20.2473	+	7.73152i	1.09008	+	0.416251i
$346$		0			0
$347$	24.4366			1.31182			0.655912	−	0.754837i	$-0.272284\pi$
$347$	24.4366			1.31182			0.655912	+	0.754837i	$0.272284\pi$
$348$		0			0
$349$	11.4881	+	19.8979i	0.614943	+	1.06511i	0.990394	+	0.138271i	$0.0441544\pi$
$349$	11.4881	+	19.8979i	0.614943	+	1.06511i	−0.375451	+	0.926842i	$0.622512\pi$
$350$		0			0
$351$	28.6091	+	1.34853i	1.52704	+	0.0719790i
$352$		0			0
$353$	−12.0152	+	20.8110i	−0.639507	+	1.10766i	0.346034	+	0.938222i	$0.387528\pi$
$353$	−12.0152	+	20.8110i	−0.639507	+	1.10766i	−0.985541	+	0.169437i	$0.945805\pi$
$354$		0			0
$355$	−16.4175	−	28.4359i	−0.871349	−	1.50922i
$356$		0			0
$357$	8.92492	+	7.02560i	0.472357	+	0.371834i
$358$		0			0
$359$	−9.84234	+	17.0474i	−0.519459	+	0.899729i	0.480285	+	0.877112i	$0.340533\pi$
$359$	−9.84234	+	17.0474i	−0.519459	+	0.899729i	−0.999744	+	0.0226169i	$0.992800\pi$
$360$		0			0
$361$	−0.144819	−	0.250833i	−0.00762204	−	0.0132018i
$362$		0			0
$363$	−12.2829	+	9.98221i	−0.644686	+	0.523930i
$364$		0			0
$365$	−2.97690	+	5.15613i	−0.155818	+	0.269884i
$366$		0			0
$367$	7.10028	−	12.2980i	0.370632	−	0.641953i	−0.619031	−	0.785366i	$-0.712475\pi$
$367$	7.10028	−	12.2980i	0.370632	−	0.641953i	0.989663	+	0.143414i	$0.0458079\pi$
$368$		0			0
$369$	−1.70161	+	8.14577i	−0.0885824	+	0.424052i
$370$		0			0
$371$	5.74946	−	5.30361i	0.298497	−	0.275350i
$372$		0			0
$373$	14.2335	+	24.6531i	0.736980	+	1.27649i	0.953849	+	0.300287i	$0.0970823\pi$
$373$	14.2335	+	24.6531i	0.736980	+	1.27649i	−0.216869	+	0.976201i	$0.569584\pi$
$374$		0			0
$375$	−2.10623	−	13.1490i	−0.108765	−	0.679013i
$376$		0			0
$377$	−32.4994			−1.67381
$378$		0			0
$379$	−4.25098			−0.218358			−0.109179	−	0.994022i	$-0.534822\pi$
$379$	−4.25098			−0.218358			−0.109179	+	0.994022i	$0.534822\pi$
$380$		0			0
$381$	4.12936	+	25.7792i	0.211553	+	1.32071i
$382$		0			0
$383$	17.9214	+	31.0407i	0.915740	+	1.58611i	0.805814	+	0.592168i	$0.201728\pi$
$383$	17.9214	+	31.0407i	0.915740	+	1.58611i	0.109926	+	0.993940i	$0.464939\pi$
$384$		0			0
$385$	2.11593	+	9.39669i	0.107838	+	0.478900i
$386$		0			0
$387$	21.8229	+	19.5113i	1.10932	+	0.991815i
$388$		0			0
$389$	15.8972	−	27.5348i	0.806020	−	1.39607i	−0.109580	−	0.993978i	$-0.534951\pi$
$389$	15.8972	−	27.5348i	0.806020	−	1.39607i	0.915600	−	0.402090i	$-0.131716\pi$
$390$		0			0
$391$	5.81235	−	10.0673i	0.293943	−	0.509125i
$392$		0			0
$393$	19.9480	−	16.2115i	1.00624	−	0.817762i
$394$		0			0
$395$	−17.1163	−	29.6462i	−0.861213	−	1.49166i
$396$		0			0
$397$	3.07669	−	5.32899i	0.154415	−	0.267454i	−0.778431	−	0.627730i	$-0.783984\pi$
$397$	3.07669	−	5.32899i	0.154415	−	0.267454i	0.932846	+	0.360276i	$0.117317\pi$
$398$		0			0
$399$	2.87393	−	19.9204i	0.143877	−	0.997268i
$400$		0			0
$401$	7.41146	+	12.8370i	0.370111	+	0.641051i	0.989582	−	0.143968i	$-0.0459864\pi$
$401$	7.41146	+	12.8370i	0.370111	+	0.641051i	−0.619471	+	0.785019i	$0.712653\pi$
$402$		0			0
$403$	−8.58974	+	14.8779i	−0.427885	+	0.741119i
$404$		0			0
$405$	−22.0041	−	9.61259i	−1.09339	−	0.477653i
$406$		0			0
$407$	−4.30677	−	7.45954i	−0.213479	−	0.369756i
$408$		0			0
$409$	21.4443			1.06035			0.530177	−	0.847887i	$-0.322125\pi$
$409$	21.4443			1.06035			0.530177	+	0.847887i	$0.322125\pi$
$410$		0			0
$411$	32.6141	+	12.4538i	1.60874	+	0.614303i
$412$		0			0
$413$	2.06689	+	9.17892i	0.101705	+	0.451665i
$414$		0			0
$415$	13.7652	−	23.8421i	0.675708	−	1.17036i
$416$		0			0
$417$	−32.0885	−	12.2531i	−1.57138	−	0.600038i
$418$		0			0
$419$	13.2332	−	22.9205i	0.646483	−	1.11974i	−0.337474	−	0.941335i	$-0.609572\pi$
$419$	13.2332	−	22.9205i	0.646483	−	1.11974i	0.983957	−	0.178406i	$-0.0570942\pi$
$420$		0			0
$421$	−8.54824	−	14.8060i	−0.416616	−	0.721600i	0.578981	−	0.815341i	$-0.303451\pi$
$421$	−8.54824	−	14.8060i	−0.416616	−	0.721600i	−0.995597	+	0.0937415i	$0.970117\pi$
$422$		0			0
$423$	28.6418	−	9.41742i	1.39261	−	0.457891i
$424$		0			0
$425$	5.25048			0.254686
$426$		0			0
$427$	0.770739	+	3.42279i	0.0372987	+	0.165640i
$428$		0			0
$429$	10.1095	−	8.21586i	0.488089	−	0.396665i
$430$		0			0
$431$	−12.0292	−	20.8352i	−0.579425	−	1.00359i	−0.995545	−	0.0942846i	$-0.969944\pi$
$431$	−12.0292	−	20.8352i	−0.579425	−	1.00359i	0.416120	−	0.909310i	$-0.363390\pi$
$432$		0			0
$433$	−6.58345			−0.316380			−0.158190	−	0.987409i	$-0.550566\pi$
$433$	−6.58345			−0.316380			−0.158190	+	0.987409i	$0.550566\pi$
$434$		0			0
$435$	25.4545	+	9.71990i	1.22045	+	0.466034i
$436$		0			0
$437$	−20.5985			−0.985362
$438$		0			0
$439$	21.2654			1.01494			0.507472	−	0.861668i	$-0.330580\pi$
$439$	21.2654			1.01494			0.507472	+	0.861668i	$0.330580\pi$
$440$		0			0
$441$	15.2124	−	14.4770i	0.724399	−	0.689380i
$442$		0			0
$443$	−0.943448			−0.0448246			−0.0224123	−	0.999749i	$-0.507135\pi$
$443$	−0.943448			−0.0448246			−0.0224123	+	0.999749i	$0.507135\pi$
$444$		0			0
$445$	−41.2560			−1.95572
$446$		0			0
$447$	23.2582	−	18.9017i	1.10007	−	0.894019i
$448$		0			0
$449$	−17.7959			−0.839842			−0.419921	−	0.907561i	$-0.637942\pi$
$449$	−17.7959			−0.839842			−0.419921	+	0.907561i	$0.637942\pi$
$450$		0			0
$451$	1.89249	+	3.27789i	0.0891139	+	0.154350i
$452$		0			0
$453$	6.45581	+	2.46518i	0.303320	+	0.115824i
$454$		0			0
$455$	8.54729	+	37.9578i	0.400703	+	1.77949i
$456$		0			0
$457$	−13.7770			−0.644462			−0.322231	−	0.946661i	$-0.604433\pi$
$457$	−13.7770			−0.644462			−0.322231	+	0.946661i	$0.604433\pi$
$458$		0			0
$459$	−6.95763	+	10.8382i	−0.324754	+	0.505882i
$460$		0			0
$461$	−2.97576	−	5.15417i	−0.138595	−	0.240054i	0.788370	−	0.615201i	$-0.210925\pi$
$461$	−2.97576	−	5.15417i	−0.138595	−	0.240054i	−0.926965	+	0.375148i	$0.877592\pi$
$462$		0			0
$463$	−17.7618	+	30.7644i	−0.825463	+	1.42974i	0.0761023	+	0.997100i	$0.475752\pi$
$463$	−17.7618	+	30.7644i	−0.825463	+	1.42974i	−0.901565	+	0.432643i	$0.857581\pi$
$464$		0			0
$465$	11.1774	−	9.08375i	0.518339	−	0.421249i
$466$		0			0
$467$	12.2574	−	21.2305i	0.567207	−	0.982431i	−0.429634	−	0.903003i	$-0.641357\pi$
$467$	12.2574	−	21.2305i	0.567207	−	0.982431i	0.996841	−	0.0794277i	$-0.0253093\pi$
$468$		0			0
$469$	4.82333	+	21.4200i	0.222721	+	0.989086i
$470$		0			0
$471$	−6.62927	−	41.3859i	−0.305461	−	1.90696i
$472$		0			0
$473$	13.3146			0.612207
$474$		0			0
$475$	−4.65183	−	8.05720i	−0.213440	−	0.369690i
$476$		0			0
$477$	6.61200	+	5.91163i	0.302743	+	0.270675i
$478$		0			0
$479$	−9.61760	+	16.6582i	−0.439439	+	0.761131i	−0.997646	−	0.0685707i	$-0.978156\pi$
$479$	−9.61760	+	16.6582i	−0.439439	+	0.761131i	0.558207	+	0.829702i	$0.311489\pi$
$480$		0			0
$481$	−17.3971	−	30.1327i	−0.793241	−	1.37393i
$482$		0			0
$483$	−16.8877	−	13.2938i	−0.768418	−	0.604891i
$484$		0			0
$485$	−6.81328	+	11.8009i	−0.309375	+	0.535853i
$486$		0			0
$487$	12.3089	+	21.3197i	0.557770	+	0.966086i	0.997682	+	0.0680455i	$0.0216763\pi$
$487$	12.3089	+	21.3197i	0.557770	+	0.966086i	−0.439912	+	0.898041i	$0.644990\pi$
$488$		0			0
$489$	7.58879	+	2.89781i	0.343177	+	0.131044i
$490$		0			0
$491$	9.73086	−	16.8543i	0.439147	−	0.760626i	−0.558476	−	0.829520i	$-0.688614\pi$
$491$	9.73086	−	16.8543i	0.439147	−	0.760626i	0.997624	+	0.0688947i	$0.0219472\pi$
$492$		0			0
$493$	7.30717	−	12.6564i	0.329098	−	0.570015i
$494$		0			0
$495$	−10.3752	+	3.41136i	−0.466331	+	0.153329i
$496$		0			0
$497$	7.15292	+	31.7655i	0.320852	+	1.42488i
$498$		0			0
$499$	3.58890	+	6.21617i	0.160661	+	0.278274i	0.935106	−	0.354368i	$-0.115304\pi$
$499$	3.58890	+	6.21617i	0.160661	+	0.278274i	−0.774445	+	0.632642i	$0.781971\pi$
$500$		0			0
$501$	−19.8258	−	7.57055i	−0.885749	−	0.338227i
$502$		0			0
$503$	22.1112			0.985889			0.492945	−	0.870061i	$-0.335921\pi$
$503$	22.1112			0.985889			0.492945	+	0.870061i	$0.335921\pi$
$504$		0			0
$505$	−7.19021			−0.319960
$506$		0			0
$507$	23.3632	−	18.9870i	1.03759	−	0.843243i
$508$		0			0
$509$	15.6787	+	27.1564i	0.694947	+	1.20368i	0.970198	+	0.242312i	$0.0779057\pi$
$509$	15.6787	+	27.1564i	0.694947	+	1.20368i	−0.275251	+	0.961372i	$0.588761\pi$
$510$		0			0
$511$	4.33970	−	4.00318i	0.191977	−	0.177090i
$512$		0			0
$513$	22.7962	+	1.07453i	1.00648	+	0.0474415i
$514$		0			0
$515$	17.3707	−	30.0869i	0.765444	−	1.32579i
$516$		0			0
$517$	6.85675	−	11.8762i	0.301559	−	0.522316i
$518$		0			0
$519$	−2.22176	−	13.8702i	−0.0975243	−	0.608835i
$520$		0			0
$521$	1.76588	+	3.05859i	0.0773645	+	0.133999i	0.902112	−	0.431502i	$-0.142016\pi$
$521$	1.76588	+	3.05859i	0.0773645	+	0.133999i	−0.824748	+	0.565501i	$0.808683\pi$
$522$		0			0
$523$	−7.03821	+	12.1905i	−0.307759	+	0.533055i	−0.977872	−	0.209205i	$-0.932912\pi$
$523$	−7.03821	+	12.1905i	−0.307759	+	0.533055i	0.670113	+	0.742259i	$0.266246\pi$
$524$		0			0
$525$	1.38614	−	9.60789i	0.0604960	−	0.419323i
$526$		0			0
$527$	−3.86263	−	6.69027i	−0.168259	−	0.291433i
$528$		0			0
$529$	0.501870	−	0.869264i	0.0218204	−	0.0377941i
$530$		0			0
$531$	−10.1347	+	3.33230i	−0.439810	+	0.144610i
$532$		0			0
$533$	7.64469	+	13.2410i	0.331128	+	0.573531i
$534$		0			0
$535$	7.99086			0.345475
$536$		0			0
$537$	−13.2166	+	10.7410i	−0.570337	+	0.463508i
$538$		0			0
$539$	0.769313	−	9.52056i	0.0331367	−	0.410080i
$540$		0			0
$541$	11.5799	−	20.0569i	0.497858	−	0.862315i	−0.502139	−	0.864787i	$-0.667454\pi$
$541$	11.5799	−	20.0569i	0.497858	−	0.862315i	0.999997	+	0.00247207i	$0.000786884\pi$
$542$		0			0
$543$	4.35242	+	27.1718i	0.186780	+	1.16605i
$544$		0			0
$545$	26.7155	−	46.2725i	1.14436	−	1.98210i
$546$		0			0
$547$	−5.76832	−	9.99102i	−0.246635	−	0.427185i	0.715955	−	0.698147i	$-0.245992\pi$
$547$	−5.76832	−	9.99102i	−0.246635	−	0.427185i	−0.962590	+	0.270962i	$0.912658\pi$
$548$		0			0
$549$	−3.77922	+	1.24261i	−0.161293	+	0.0530331i
$550$		0			0
$551$	−25.8961			−1.10321
$552$		0			0
$553$	7.45737	+	33.1176i	0.317120	+	1.40830i
$554$		0			0
$555$	4.61386	+	28.8039i	0.195848	+	1.22266i
$556$		0			0
$557$	−1.04108	−	1.80321i	−0.0441122	−	0.0764045i	0.843126	−	0.537716i	$-0.180713\pi$
$557$	−1.04108	−	1.80321i	−0.0441122	−	0.0764045i	−0.887238	+	0.461311i	$0.847379\pi$
$558$		0			0
$559$	53.7842			2.27483
$560$		0			0
$561$	0.926526	+	5.78422i	0.0391180	+	0.244210i
$562$		0			0
$563$	−6.70807			−0.282711			−0.141356	−	0.989959i	$-0.545146\pi$
$563$	−6.70807			−0.282711			−0.141356	+	0.989959i	$0.545146\pi$
$564$		0			0
$565$	33.2548			1.39904
$566$		0			0
$567$	17.9960	+	15.5931i	0.755760	+	0.654849i
$568$		0			0
$569$	−8.02223			−0.336309			−0.168155	−	0.985761i	$-0.553781\pi$
$569$	−8.02223			−0.336309			−0.168155	+	0.985761i	$0.553781\pi$
$570$		0			0
$571$	6.68430			0.279729			0.139865	−	0.990171i	$-0.455333\pi$
$571$	6.68430			0.279729			0.139865	+	0.990171i	$0.455333\pi$
$572$		0			0
$573$	−0.607892	−	3.79501i	−0.0253951	−	0.158539i
$574$		0			0
$575$	−9.93496			−0.414316
$576$		0			0
$577$	−14.0088	−	24.2639i	−0.583193	−	1.01012i	−0.995098	−	0.0988925i	$-0.968470\pi$
$577$	−14.0088	−	24.2639i	−0.583193	−	1.01012i	0.411906	−	0.911227i	$-0.364863\pi$
$578$		0			0
$579$	1.60033	+	9.99073i	0.0665075	+	0.415201i
$580$		0			0
$581$	−20.0669	+	18.5108i	−0.832514	+	0.767956i
$582$		0			0
$583$	4.03413			0.167076
$584$		0			0
$585$	−41.9105	+	13.7802i	−1.73279	+	0.569740i
$586$		0			0
$587$	−3.35952	−	5.81886i	−0.138662	−	0.240170i	0.788328	−	0.615255i	$-0.210947\pi$
$587$	−3.35952	−	5.81886i	−0.138662	−	0.240170i	−0.926990	+	0.375085i	$0.877614\pi$
$588$		0			0
$589$	−6.84443	+	11.8549i	−0.282020	+	0.488473i
$590$		0			0
$591$	0.530629	+	3.31267i	0.0218272	+	0.136265i
$592$		0			0
$593$	−3.19462	+	5.53325i	−0.131187	+	0.227223i	−0.924135	−	0.382067i	$-0.875212\pi$
$593$	−3.19462	+	5.53325i	−0.131187	+	0.227223i	0.792947	+	0.609290i	$0.208546\pi$
$594$		0			0
$595$	−16.7038	−	5.20583i	−0.684791	−	0.213418i
$596$		0			0
$597$	−4.96097	+	4.03173i	−0.203039	+	0.165008i
$598$		0			0
$599$	−5.92196			−0.241965			−0.120982	−	0.992655i	$-0.538604\pi$
$599$	−5.92196			−0.241965			−0.120982	+	0.992655i	$0.538604\pi$
$600$		0			0
$601$	−1.97104	−	3.41393i	−0.0804002	−	0.139257i	0.823022	−	0.568010i	$-0.192287\pi$
$601$	−1.97104	−	3.41393i	−0.0804002	−	0.139257i	−0.903422	+	0.428753i	$0.858953\pi$
$602$		0			0
$603$	−23.6506	+	7.77631i	−0.963126	+	0.316676i
$604$		0			0
$605$	12.1903	−	21.1142i	0.495607	−	0.858416i
$606$		0			0
$607$	3.54775	+	6.14489i	0.143999	+	0.249413i	0.928999	−	0.370082i	$-0.120670\pi$
$607$	3.54775	+	6.14489i	0.143999	+	0.249413i	−0.785000	+	0.619496i	$0.787337\pi$
$608$		0			0
$609$	−21.2309	−	16.7127i	−0.860319	−	0.677235i
$610$		0			0
$611$	27.6978	−	47.9739i	1.12053	−	1.94082i
$612$		0			0
$613$	6.87000	+	11.8992i	0.277477	+	0.480604i	0.970757	−	0.240064i	$-0.0771685\pi$
$613$	6.87000	+	11.8992i	0.277477	+	0.480604i	−0.693280	+	0.720668i	$0.743835\pi$
$614$		0			0
$615$	−2.02743	−	12.6571i	−0.0817541	−	0.510383i
$616$		0			0
$617$	−16.3605	+	28.3372i	−0.658649	+	1.14081i	0.322317	+	0.946632i	$0.395538\pi$
$617$	−16.3605	+	28.3372i	−0.658649	+	1.14081i	−0.980966	+	0.194182i	$0.937795\pi$
$618$		0			0
$619$	−11.3090	+	19.5878i	−0.454547	+	0.787299i	−0.998662	−	0.0517121i	$-0.983532\pi$
$619$	−11.3090	+	19.5878i	−0.454547	+	0.787299i	0.544115	+	0.839011i	$0.316866\pi$
$620$		0			0
$621$	13.1652	−	20.5080i	0.528302	−	0.822956i
$622$		0			0
$623$	39.0588	+	12.1729i	1.56486	+	0.487695i
$624$		0			0
$625$	15.5522	+	26.9371i	0.622086	+	1.07749i
$626$		0			0
$627$	8.05537	−	6.54652i	0.321700	−	0.261443i
$628$		0			0
$629$	15.6463			0.623858
$630$		0			0
$631$	−43.9355			−1.74905			−0.874523	−	0.484984i	$-0.838825\pi$
$631$	−43.9355			−1.74905			−0.874523	+	0.484984i	$0.838825\pi$
$632$		0			0
$633$	−18.3523	−	7.00792i	−0.729440	−	0.278540i
$634$		0			0
$635$	−20.1080	−	34.8281i	−0.797962	−	1.38211i
$636$		0			0
$637$	3.10763	−	38.4582i	0.123129	−	1.52377i
$638$		0			0
$639$	−35.0734	+	11.5321i	−1.38748	+	0.456204i
$640$		0			0
$641$	−19.9297	+	34.5193i	−0.787178	+	1.36343i	0.140512	+	0.990079i	$0.455125\pi$
$641$	−19.9297	+	34.5193i	−0.787178	+	1.36343i	−0.927689	+	0.373353i	$0.878208\pi$
$642$		0			0
$643$	9.24049	−	16.0050i	0.364410	−	0.631176i	−0.624272	−	0.781207i	$-0.714604\pi$
$643$	9.24049	−	16.0050i	0.364410	−	0.631176i	0.988681	+	0.150032i	$0.0479375\pi$
$644$		0			0
$645$	−42.1253	−	16.0857i	−1.65868	−	0.633375i
$646$		0			0
$647$	8.76068	+	15.1739i	0.344418	+	0.596549i	0.985248	−	0.171134i	$-0.0547430\pi$
$647$	8.76068	+	15.1739i	0.344418	+	0.596549i	−0.640830	+	0.767683i	$0.721410\pi$
$648$		0			0
$649$	−2.42622	+	4.20234i	−0.0952376	+	0.164956i
$650$		0			0
$651$	−13.2623	+	5.30201i	−0.519791	+	0.207802i
$652$		0			0
$653$	−13.7027	−	23.7338i	−0.536230	−	0.928777i	−0.999103	−	0.0423525i	$-0.986515\pi$
$653$	−13.7027	−	23.7338i	−0.536230	−	0.928777i	0.462873	−	0.886425i	$-0.346819\pi$
$654$		0			0
$655$	−19.7975	+	34.2904i	−0.773554	+	1.33984i
$656$		0			0
$657$	4.99075	+	4.46211i	0.194708	+	0.174083i
$658$		0			0
$659$	−16.2580	−	28.1597i	−0.633322	−	1.09695i	−0.986868	−	0.161529i	$-0.948358\pi$
$659$	−16.2580	−	28.1597i	−0.633322	−	1.09695i	0.353546	−	0.935417i	$-0.384976\pi$
$660$		0			0
$661$	38.8671			1.51176			0.755878	−	0.654712i	$-0.227210\pi$
$661$	38.8671			1.51176			0.755878	+	0.654712i	$0.227210\pi$
$662$		0			0
$663$	3.74269	+	23.3653i	0.145354	+	0.907433i
$664$		0			0
$665$	6.81061	+	30.2454i	0.264104	+	1.17287i
$666$		0			0
$667$	−13.8266	+	23.9484i	−0.535369	+	0.927286i
$668$		0			0
$669$	2.59567	−	2.10947i	0.100354	−	0.0815570i
$670$		0			0
$671$	−0.904731	+	1.56704i	−0.0349268	+	0.0604949i
$672$		0			0
$673$	−4.50978	−	7.81117i	−0.173839	−	0.301099i	0.765920	−	0.642936i	$-0.222284\pi$
$673$	−4.50978	−	7.81117i	−0.173839	−	0.301099i	−0.939759	+	0.341838i	$0.888951\pi$
$674$		0			0
$675$	10.9949	+	0.518259i	0.423194	+	0.0199478i
$676$		0			0
$677$	18.8287			0.723646			0.361823	−	0.932247i	$-0.382155\pi$
$677$	18.8287			0.723646			0.361823	+	0.932247i	$0.382155\pi$
$678$		0			0
$679$	9.93236	−	9.16215i	0.381169	−	0.351611i
$680$		0			0
$681$	−31.9222	−	12.1896i	−1.22326	−	0.467107i
$682$		0			0
$683$	5.35476	+	9.27471i	0.204894	+	0.354887i	0.950099	−	0.311949i	$-0.100982\pi$
$683$	5.35476	+	9.27471i	0.204894	+	0.354887i	−0.745205	+	0.666836i	$0.767648\pi$
$684$		0			0
$685$	−53.7763			−2.05468
$686$		0			0
$687$	35.5118	−	28.8601i	1.35486	−	1.10108i
$688$		0			0
$689$	16.2958			0.620821
$690$		0			0
$691$	5.04553			0.191941			0.0959705	−	0.995384i	$-0.469405\pi$
$691$	5.04553			0.191941			0.0959705	+	0.995384i	$0.469405\pi$
$692$		0			0
$693$	10.8292	−	0.168412i	0.411366	−	0.00639743i
$694$		0			0
$695$	52.9096			2.00697
$696$		0			0
$697$	−6.87533			−0.260422
$698$		0			0
$699$	−13.7238	−	5.24047i	−0.519080	−	0.198213i
$700$		0			0
$701$	44.9138			1.69637			0.848186	−	0.529698i	$-0.177695\pi$
$701$	44.9138			1.69637			0.848186	+	0.529698i	$0.177695\pi$
$702$		0			0
$703$	−13.8623	−	24.0102i	−0.522827	−	0.905563i
$704$		0			0
$705$	−36.0417	+	29.2907i	−1.35741	+	1.10315i
$706$		0			0
$707$	6.80727	+	2.12152i	0.256014	+	0.0797879i
$708$		0			0
$709$	7.45317			0.279910			0.139955	−	0.990158i	$-0.455304\pi$
$709$	7.45317			0.279910			0.139955	+	0.990158i	$0.455304\pi$
$710$		0			0
$711$	−36.5662	+	12.0230i	−1.37134	+	0.450897i
$712$		0			0
$713$	7.30887	+	12.6593i	0.273719	+	0.474096i
$714$		0			0
$715$	−10.0332	+	17.3781i	−0.375222	+	0.649903i
$716$		0			0
$717$	−26.1492	−	9.98517i	−0.976558	−	0.372903i
$718$		0			0
$719$	21.5574	−	37.3385i	0.803954	−	1.39249i	−0.113040	−	0.993590i	$-0.536059\pi$
$719$	21.5574	−	37.3385i	0.803954	−	1.39249i	0.916995	−	0.398899i	$-0.130608\pi$
$720$		0			0
$721$	−25.3229	+	23.3592i	−0.943074	+	0.869943i
$722$		0			0
$723$	−17.7562	−	6.78029i	−0.660361	−	0.252162i
$724$		0			0
$725$	−12.4900			−0.463868
$726$		0			0
$727$	−0.389926	−	0.675372i	−0.0144616	−	0.0250482i	0.858704	−	0.512472i	$-0.171270\pi$
$727$	−0.389926	−	0.675372i	−0.0144616	−	0.0250482i	−0.873166	+	0.487424i	$0.837937\pi$
$728$		0			0
$729$	−15.6396	+	22.0092i	−0.579245	+	0.815154i
$730$		0			0
$731$	−12.0928	+	20.9454i	−0.447270	+	0.774694i
$732$		0			0
$733$	7.83859	+	13.5768i	0.289525	+	0.501472i	0.973696	−	0.227849i	$-0.0731694\pi$
$733$	7.83859	+	13.5768i	0.289525	+	0.501472i	−0.684171	+	0.729321i	$0.739836\pi$
$734$		0			0
$735$	−13.9360	+	29.1921i	−0.514038	+	1.07677i
$736$		0			0
$737$	−5.66187	+	9.80664i	−0.208558	+	0.361232i
$738$		0			0
$739$	8.87450	+	15.3711i	0.326454	+	0.565434i	0.981805	−	0.189889i	$-0.0608129\pi$
$739$	8.87450	+	15.3711i	0.326454	+	0.565434i	−0.655352	+	0.755324i	$0.727480\pi$
$740$		0			0
$741$	32.5396	−	26.4446i	1.19537	−	0.971467i
$742$		0			0
$743$	−3.74308	+	6.48321i	−0.137320	+	0.237846i	−0.926481	−	0.376340i	$-0.877182\pi$
$743$	−3.74308	+	6.48321i	−0.137320	+	0.237846i	0.789161	+	0.614186i	$0.210516\pi$
$744$		0			0
$745$	−23.0828	+	39.9806i	−0.845688	+	1.46477i
$746$		0			0
$747$	−23.0773	−	20.6329i	−0.844355	−	0.754918i
$748$		0			0
$749$	−7.56528	−	2.35775i	−0.276429	−	0.0861505i
$750$		0			0
$751$	−11.6800	−	20.2303i	−0.426208	−	0.738213i	0.570325	−	0.821419i	$-0.306817\pi$
$751$	−11.6800	−	20.2303i	−0.426208	−	0.738213i	−0.996532	+	0.0832060i	$0.973484\pi$
$752$		0			0
$753$	0.783152	+	4.88915i	0.0285396	+	0.178170i
$754$		0			0
$755$	−10.6447			−0.387402
$756$		0			0
$757$	31.2350			1.13525			0.567627	−	0.823286i	$-0.307862\pi$
$757$	31.2350			1.13525			0.567627	+	0.823286i	$0.307862\pi$
$758$		0			0
$759$	−1.75317	−	10.9449i	−0.0636361	−	0.397274i
$760$		0			0
$761$	−8.30735	−	14.3887i	−0.301141	−	0.521592i	0.675254	−	0.737586i	$-0.264034\pi$
$761$	−8.30735	−	14.3887i	−0.301141	−	0.521592i	−0.976395	+	0.215994i	$0.930701\pi$
$762$		0			0
$763$	−38.9457	+	35.9256i	−1.40993	+	1.30059i
$764$		0			0
$765$	4.05669	−	19.4197i	0.146670	−	0.702121i
$766$		0			0
$767$	−9.80070	+	16.9753i	−0.353883	+	0.612943i
$768$		0			0
$769$	18.3794	−	31.8340i	0.662777	−	1.14796i	−0.317106	−	0.948390i	$-0.602711\pi$
$769$	18.3794	−	31.8340i	0.662777	−	1.14796i	0.979883	−	0.199573i	$-0.0639556\pi$
$770$		0			0
$771$	33.0492	−	26.8587i	1.19024	−	0.967294i
$772$		0			0
$773$	4.77690	+	8.27382i	0.171813	+	0.297589i	0.939054	−	0.343770i	$-0.111704\pi$
$773$	4.77690	+	8.27382i	0.171813	+	0.297589i	−0.767241	+	0.641359i	$0.778371\pi$
$774$		0			0
$775$	−3.30116	+	5.71778i	−0.118581	+	0.205389i
$776$		0			0
$777$	4.13065	−	28.6312i	0.148186	−	1.02714i
$778$		0			0
$779$	6.09141	+	10.5506i	0.218247	+	0.378016i
$780$		0			0
$781$	−8.39645	+	14.5431i	−0.300448	+	0.520392i
$782$		0			0
$783$	16.5510	−	25.7822i	0.591486	−	0.921380i
$784$		0			0
$785$	32.2814	+	55.9130i	1.15217	+	1.99562i
$786$		0			0
$787$	−20.2677			−0.722466			−0.361233	−	0.932476i	$-0.617644\pi$
$787$	−20.2677			−0.722466			−0.361233	+	0.932476i	$0.617644\pi$
$788$		0			0
$789$	−1.55009	−	0.591908i	−0.0551846	−	0.0210725i
$790$		0			0
$791$	−31.4837	−	9.81203i	−1.11943	−	0.348876i
$792$		0			0
$793$	−3.65465	+	6.33004i	−0.129780	+	0.224786i
$794$		0			0
$795$	−12.7633	−	4.87374i	−0.452669	−	0.172854i
$796$		0			0
$797$	21.4236	−	37.1068i	0.758863	−	1.31439i	−0.184567	−	0.982820i	$-0.559088\pi$
$797$	21.4236	−	37.1068i	0.758863	−	1.31439i	0.943431	−	0.331570i	$-0.107578\pi$
$798$		0			0
$799$	12.4551	+	21.5729i	0.440630	+	0.763194i
$800$		0			0
$801$	−9.48580	+	45.4093i	−0.335164	+	1.60446i
$802$		0			0
$803$	3.04497			0.107455
$804$		0			0
$805$	31.6070	+	9.85047i	1.11400	+	0.347183i
$806$		0			0
$807$	−22.3398	+	18.1554i	−0.786399	+	0.639099i
$808$		0			0
$809$	−10.4750	−	18.1432i	−0.368282	−	0.637883i	0.621015	−	0.783798i	$-0.286720\pi$
$809$	−10.4750	−	18.1432i	−0.368282	−	0.637883i	−0.989297	+	0.145916i	$0.953387\pi$
$810$		0			0
$811$	−19.0129			−0.667633			−0.333817	−	0.942638i	$-0.608337\pi$
$811$	−19.0129			−0.667633			−0.333817	+	0.942638i	$0.608337\pi$
$812$		0			0
$813$	23.3588	+	8.91968i	0.819231	+	0.312827i
$814$		0			0
$815$	−12.5129			−0.438307
$816$		0			0
$817$	42.8561			1.49935
$818$		0			0
$819$	43.7444	−	0.680297i	1.52855	−	0.0237715i
$820$		0			0
$821$	−33.3905			−1.16534			−0.582669	−	0.812710i	$-0.697992\pi$
$821$	−33.3905			−1.16534			−0.582669	+	0.812710i	$0.697992\pi$
$822$		0			0
$823$	−9.04079			−0.315142			−0.157571	−	0.987508i	$-0.550366\pi$
$823$	−9.04079			−0.315142			−0.157571	+	0.987508i	$0.550366\pi$
$824$		0			0
$825$	3.88521	−	3.15748i	0.135266	−	0.109929i
$826$		0			0
$827$	22.4071			0.779172			0.389586	−	0.920990i	$-0.372618\pi$
$827$	22.4071			0.779172			0.389586	+	0.920990i	$0.372618\pi$
$828$		0			0
$829$	−11.4090	−	19.7610i	−0.396252	−	0.686328i	0.597008	−	0.802235i	$-0.296356\pi$
$829$	−11.4090	−	19.7610i	−0.396252	−	0.686328i	−0.993260	+	0.115907i	$0.963023\pi$
$830$		0			0
$831$	7.22710	+	2.75970i	0.250705	+	0.0957328i
$832$		0			0
$833$	14.2782	+	9.85716i	0.494711	+	0.341530i
$834$		0			0
$835$	32.6900			1.13128
$836$		0			0
$837$	−7.42826	−	14.3912i	−0.256758	−	0.497433i
$838$		0			0
$839$	−8.05060	−	13.9441i	−0.277938	−	0.481402i	0.692934	−	0.721001i	$-0.256318\pi$
$839$	−8.05060	−	13.9441i	−0.277938	−	0.481402i	−0.970872	+	0.239598i	$0.922984\pi$
$840$		0			0
$841$	−2.88254	+	4.99271i	−0.0993980	+	0.172162i
$842$		0			0
$843$	−7.05991	+	5.73752i	−0.243156	+	0.197611i
$844$		0			0
$845$	−23.1870	+	40.1611i	−0.797657	+	1.38158i
$846$		0			0
$847$	−17.7710	+	16.3929i	−0.610618	+	0.563267i
$848$		0			0
$849$	3.09975	+	19.3515i	0.106383	+	0.664141i
$850$		0			0
$851$	−29.6059			−1.01488
$852$		0			0
$853$	12.7818	+	22.1387i	0.437639	+	0.758013i	0.997507	−	0.0705689i	$-0.0224815\pi$
$853$	12.7818	+	22.1387i	0.437639	+	0.758013i	−0.559868	+	0.828582i	$0.689148\pi$
$854$		0			0
$855$	−33.3949	+	10.9803i	−1.14208	+	0.375517i
$856$		0			0
$857$	26.3278	−	45.6011i	0.899340	−	1.55770i	0.0710001	−	0.997476i	$-0.477381\pi$
$857$	26.3278	−	45.6011i	0.899340	−	1.55770i	0.828340	−	0.560226i	$-0.189286\pi$
$858$		0			0
$859$	15.4431	+	26.7482i	0.526912	+	0.912638i	0.999508	+	0.0313592i	$0.00998358\pi$
$859$	15.4431	+	26.7482i	0.526912	+	0.912638i	−0.472596	+	0.881279i	$0.656683\pi$
$860$		0			0
$861$	−1.81510	+	12.5812i	−0.0618584	+	0.428766i
$862$		0			0
$863$	−0.929596	+	1.61011i	−0.0316438	+	0.0548087i	−0.881414	−	0.472345i	$-0.843408\pi$
$863$	−0.929596	+	1.61011i	−0.0316438	+	0.0548087i	0.849770	+	0.527154i	$0.176741\pi$
$864$		0			0
$865$	10.8189	+	18.7389i	0.367853	+	0.637141i
$866$		0			0
$867$	17.5669	+	6.70798i	0.596602	+	0.227815i
$868$		0			0
$869$	−8.75383	+	15.1621i	−0.296953	+	0.514338i
$870$		0			0
$871$	−22.8711	+	39.6138i	−0.774956	+	1.34226i
$872$		0			0
$873$	11.4224	+	10.2125i	0.386590	+	0.345641i
$874$		0			0
$875$	−4.46858	−	19.8446i	−0.151066	−	0.670871i
$876$		0			0
$877$	6.65184	+	11.5213i	0.224617	+	0.389048i	0.956204	−	0.292700i	$-0.0945536\pi$
$877$	6.65184	+	11.5213i	0.224617	+	0.389048i	−0.731588	+	0.681747i	$0.761220\pi$
$878$		0			0
$879$	−17.4243	−	6.65356i	−0.587709	−	0.224419i
$880$		0			0
$881$	21.2210			0.714954			0.357477	−	0.933922i	$-0.383637\pi$
$881$	21.2210			0.714954			0.357477	+	0.933922i	$0.383637\pi$
$882$		0			0
$883$	−49.8289			−1.67687			−0.838437	−	0.544998i	$-0.816530\pi$
$883$	−49.8289			−1.67687			−0.838437	+	0.544998i	$0.816530\pi$
$884$		0			0
$885$	12.7531	−	10.3644i	0.428692	−	0.348394i
$886$		0			0
$887$	0.886358	+	1.53522i	0.0297610	+	0.0515475i	0.880522	−	0.474005i	$-0.157192\pi$
$887$	0.886358	+	1.53522i	0.0297610	+	0.0515475i	−0.850761	+	0.525552i	$0.823859\pi$
$888$		0			0
$889$	8.76084	+	38.9062i	0.293829	+	1.30487i
$890$		0			0
$891$	1.36927	+	12.2040i	0.0458724	+	0.408851i
$892$		0			0
$893$	22.0700	−	38.2264i	0.738544	−	1.27920i
$894$		0			0
$895$	13.1169	−	22.7192i	0.438450	−	0.759419i
$896$		0			0
$897$	−7.08192	−	44.2118i	−0.236458	−	1.47619i
$898$		0			0
$899$	9.18855	+	15.9150i	0.306455	+	0.530796i
$900$		0			0
$901$	−3.66395	+	6.34615i	−0.122064	+	0.211421i
$902$		0			0
$903$	35.1356	+	27.6584i	1.16924	+	0.920414i
$904$		0			0
$905$	−21.1942	−	36.7094i	−0.704519	−	1.22026i
$906$		0			0
$907$	5.28748	−	9.15818i	0.175568	−	0.304092i	−0.764790	−	0.644280i	$-0.777157\pi$
$907$	5.28748	−	9.15818i	0.175568	−	0.304092i	0.940358	+	0.340188i	$0.110491\pi$
$908$		0			0
$909$	−1.65321	+	7.91406i	−0.0548335	+	0.262493i
$910$		0			0
$911$	15.2693	+	26.4473i	0.505896	+	0.876237i	0.999977	+	0.00682127i	$0.00217130\pi$
$911$	15.2693	+	26.4473i	0.505896	+	0.876237i	−0.494081	+	0.869416i	$0.664495\pi$
$912$		0			0
$913$	−14.0800			−0.465980
$914$		0			0
$915$	4.75561	−	3.86484i	0.157216	−	0.127768i
$916$		0			0
$917$	28.8608	−	26.6227i	0.953066	−	0.879160i
$918$		0			0
$919$	−0.552490	+	0.956940i	−0.0182249	+	0.0315665i	−0.874994	−	0.484134i	$-0.839135\pi$
$919$	−0.552490	+	0.956940i	−0.0182249	+	0.0315665i	0.856769	+	0.515700i	$0.172468\pi$
$920$		0			0
$921$	2.58103	+	16.1131i	0.0850478	+	0.530945i
$922$		0			0
$923$	−33.9174	+	58.7466i	−1.11640	+	1.93367i
$924$		0			0
$925$	−6.68598	−	11.5805i	−0.219834	−	0.380763i
$926$		0			0
$927$	−29.1219	−	26.0372i	−0.956488	−	0.855173i
$928$		0			0
$929$	−5.27458			−0.173053			−0.0865266	−	0.996250i	$-0.527577\pi$
$929$	−5.27458			−0.173053			−0.0865266	+	0.996250i	$0.527577\pi$
$930$		0			0
$931$	2.47621	−	30.6441i	0.0811545	−	1.00432i
$932$		0			0
$933$	−3.09977	−	19.3516i	−0.101482	−	0.633542i
$934$		0			0
$935$	−4.51174	−	7.81456i	−0.147550	−	0.255564i
$936$		0			0
$937$	17.7481			0.579806			0.289903	−	0.957056i	$-0.406377\pi$
$937$	17.7481			0.579806			0.289903	+	0.957056i	$0.406377\pi$
$938$		0			0
$939$	5.94096	+	37.0889i	0.193876	+	1.21035i
$940$		0			0
$941$	−27.7367			−0.904192			−0.452096	−	0.891969i	$-0.649323\pi$
$941$	−27.7367			−0.904192			−0.452096	+	0.891969i	$0.649323\pi$
$942$		0			0
$943$	13.0095			0.423647
$944$		0			0
$945$	−34.4653	−	12.5502i	−1.12116	−	0.408258i
$946$		0			0
$947$	15.2766			0.496422			0.248211	−	0.968706i	$-0.420157\pi$
$947$	15.2766			0.496422			0.248211	+	0.968706i	$0.420157\pi$
$948$		0			0
$949$	12.3001			0.399279
$950$		0			0
$951$	−6.90831	−	43.1280i	−0.224017	−	1.39852i
$952$		0			0
$953$	−25.3569			−0.821390			−0.410695	−	0.911773i	$-0.634714\pi$
$953$	−25.3569			−0.821390			−0.410695	+	0.911773i	$0.634714\pi$
$954$		0			0
$955$	2.96014	+	5.12712i	0.0957880	+	0.165910i
$956$		0			0
$957$	−2.20405	−	13.7597i	−0.0712469	−	0.444788i
$958$		0			0
$959$	50.9122	+	15.8670i	1.64404	+	0.512373i
$960$		0			0
$961$	−21.2857			−0.686636
$962$		0			0
$963$	1.83730	−	8.79531i	0.0592061	−	0.283425i
$964$		0			0
$965$	−7.79286	−	13.4976i	−0.250861	−	0.434504i
$966$		0			0
$967$	−13.5566	+	23.4808i	−0.435952	+	0.755090i	−0.997373	−	0.0724398i	$-0.976921\pi$
$967$	−13.5566	+	23.4808i	−0.435952	+	0.755090i	0.561421	+	0.827530i	$0.310255\pi$
$968$		0			0
$969$	2.98224	+	18.6178i	0.0958032	+	0.598091i
$970$		0			0
$971$	−21.1555	+	36.6423i	−0.678911	+	1.17591i	0.296398	+	0.955064i	$0.404214\pi$
$971$	−21.1555	+	36.6423i	−0.678911	+	1.17591i	−0.975309	+	0.220844i	$0.929119\pi$
$972$		0			0
$973$	−50.0917	−	15.6113i	−1.60587	−	0.500475i
$974$		0			0
$975$	15.6943	−	12.7546i	0.502619	−	0.408474i
$976$		0			0
$977$	2.37816			0.0760841			0.0380421	−	0.999276i	$-0.487888\pi$
$977$	2.37816			0.0760841			0.0380421	+	0.999276i	$0.487888\pi$
$978$		0			0
$979$	10.5499	+	18.2729i	0.337175	+	0.584004i
$980$		0			0
$981$	−44.7883	−	40.0442i	−1.42998	−	1.27851i
$982$		0			0
$983$	−1.64641	+	2.85167i	−0.0525124	+	0.0909542i	−0.891087	−	0.453833i	$-0.850056\pi$
$983$	−1.64641	+	2.85167i	−0.0525124	+	0.0909542i	0.838574	+	0.544787i	$0.183390\pi$
$984$		0			0
$985$	−2.58391	−	4.47547i	−0.0823303	−	0.142600i
$986$		0			0
$987$	42.7645	−	17.0964i	1.36121	−	0.544185i
$988$		0			0
$989$	22.8821	−	39.6329i	0.727607	−	1.26025i
$990$		0			0
$991$	−29.5482	−	51.1790i	−0.938630	−	1.62575i	−0.768030	−	0.640414i	$-0.778763\pi$
$991$	−29.5482	−	51.1790i	−0.938630	−	1.62575i	−0.170600	−	0.985340i	$-0.554571\pi$
$992$		0			0
$993$	−4.66388	−	29.1162i	−0.148004	−	0.923974i
$994$		0			0
$995$	4.92356	−	8.52786i	0.156087	−	0.270351i
$996$		0			0
$997$	8.48987	−	14.7049i	0.268877	−	0.465708i	−0.699695	−	0.714441i	$-0.746681\pi$
$997$	8.48987	−	14.7049i	0.268877	−	0.465708i	0.968572	+	0.248733i	$0.0800142\pi$
$998$		0			0
$999$	32.7645	+	1.54440i	1.03662	+	0.0488626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.q.d.121.6	yes	22
3.2	odd	2		1512.2.q.c.793.10		22
4.3	odd	2		1008.2.q.k.625.6		22
7.4	even	3		504.2.t.d.193.9	yes	22
9.2	odd	6		1512.2.t.d.289.2		22
9.7	even	3		504.2.t.d.457.9	yes	22
12.11	even	2		3024.2.q.k.2305.10		22
21.11	odd	6		1512.2.t.d.361.2		22
28.11	odd	6		1008.2.t.k.193.3		22
36.7	odd	6		1008.2.t.k.961.3		22
36.11	even	6		3024.2.t.l.289.2		22
63.11	odd	6		1512.2.q.c.1369.10		22
63.25	even	3	inner	504.2.q.d.25.6	✓	22
84.11	even	6		3024.2.t.l.1873.2		22
252.11	even	6		3024.2.q.k.2881.10		22
252.151	odd	6		1008.2.q.k.529.6		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.6	✓	22	63.25	even	3	inner
504.2.q.d.121.6	yes	22	1.1	even	1	trivial
504.2.t.d.193.9	yes	22	7.4	even	3
504.2.t.d.457.9	yes	22	9.7	even	3
1008.2.q.k.529.6		22	252.151	odd	6
1008.2.q.k.625.6		22	4.3	odd	2
1008.2.t.k.193.3		22	28.11	odd	6
1008.2.t.k.961.3		22	36.7	odd	6
1512.2.q.c.793.10		22	3.2	odd	2
1512.2.q.c.1369.10		22	63.11	odd	6
1512.2.t.d.289.2		22	9.2	odd	6
1512.2.t.d.361.2		22	21.11	odd	6
3024.2.q.k.2305.10		22	12.11	even	2
3024.2.q.k.2881.10		22	252.11	even	6
3024.2.t.l.289.2		22	36.11	even	6
3024.2.t.l.1873.2		22	84.11	even	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.273951 + 1.71025i) q^{3} +(-1.33401 - 2.31057i) q^{5} +(0.581213 + 2.58112i) q^{7} +(-2.84990 + 0.937047i) q^{9} +O(q^{10})\)	\(q+(0.273951 + 1.71025i) q^{3} +(-1.33401 - 2.31057i) q^{5} +(0.581213 + 2.58112i) q^{7} +(-2.84990 + 0.937047i) q^{9} +(-0.682257 + 1.18170i) q^{11} +(-2.75597 + 4.77348i) q^{13} +(3.58620 - 2.91447i) q^{15} +(-1.23930 - 2.14654i) q^{17} +(-2.19600 + 3.80358i) q^{19} +(-4.25514 + 1.70112i) q^{21} +(2.34501 + 4.06167i) q^{23} +(-1.05916 + 1.83452i) q^{25} +(-2.38332 - 4.61734i) q^{27} +(2.94810 + 5.10625i) q^{29} +3.11678 q^{31} +(-2.20791 - 0.843100i) q^{33} +(5.18852 - 4.78617i) q^{35} +(-3.15627 + 5.46681i) q^{37} +(-8.91883 - 3.40569i) q^{39} +(1.38693 - 2.40224i) q^{41} +(-4.87889 - 8.45048i) q^{43} +(5.96691 + 5.33487i) q^{45} -10.0501 q^{47} +(-6.32438 + 3.00036i) q^{49} +(3.33160 - 2.70756i) q^{51} +(-1.47823 - 2.56037i) q^{53} +3.64055 q^{55} +(-7.10667 - 2.71371i) q^{57} +3.55617 q^{59} +1.32609 q^{61} +(-4.07503 - 6.81132i) q^{63} +14.7059 q^{65} +8.29874 q^{67} +(-6.30406 + 5.12325i) q^{69} +12.3069 q^{71} +(-1.11577 - 1.93257i) q^{73} +(-3.42764 - 1.30886i) q^{75} +(-3.44666 - 1.07417i) q^{77} +12.8307 q^{79} +(7.24388 - 5.34099i) q^{81} +(5.15934 + 8.93625i) q^{83} +(-3.30648 + 5.72700i) q^{85} +(-7.92533 + 6.44084i) q^{87} +(7.73159 - 13.3915i) q^{89} +(-13.9227 - 4.33908i) q^{91} +(0.853843 + 5.33046i) q^{93} +11.7179 q^{95} +(-2.55369 - 4.42311i) q^{97} +(0.837053 - 4.00705i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9}+O(q^{10}) \) 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9	\( 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9} - 3 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} + 2 q^{23} - 10 q^{25} - 4 q^{27} + 9 q^{29} + 8 q^{31} + 29 q^{33} + 14 q^{35} + 2 q^{37} - 16 q^{39} + 16 q^{41} + q^{45} - 10 q^{47} + 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} + 38 q^{59} + 26 q^{61} + 48 q^{63} - 26 q^{65} - 52 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 23 q^{75} + 17 q^{77} - 20 q^{79} - 38 q^{81} - 28 q^{83} - 20 q^{85} - 33 q^{87} + 6 q^{89} - 37 q^{91} + 19 q^{93} - 24 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9 - 3 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 + 2 * q^23 - 10 * q^25 - 4 * q^27 + 9 * q^29 + 8 * q^31 + 29 * q^33 + 14 * q^35 + 2 * q^37 - 16 * q^39 + 16 * q^41 + q^45 - 10 * q^47 + 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 + 38 * q^59 + 26 * q^61 + 48 * q^63 - 26 * q^65 - 52 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 23 * q^75 + 17 * q^77 - 20 * q^79 - 38 * q^81 - 28 * q^83 - 20 * q^85 - 33 * q^87 + 6 * q^89 - 37 * q^91 + 19 * q^93 - 24 * q^95 - 29 * q^97 - 56 * q^99

Introduction

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