LMFDB - Embedded newform 252.4.bm.a.173.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(173,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.173");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.bm (of order $6$, 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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			173.19
Character	$\chi$	$=$	252.173
Dual form			252.4.bm.a.185.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.66543 + 3.68302i) q^{3} +6.67787 q^{5} +(-16.9163 - 7.53913i) q^{7} +(-0.129304 + 26.9997i) q^{9} +O(q^{10})$	\(q+(3.66543 + 3.68302i) q^{3} +6.67787 q^{5} +(-16.9163 - 7.53913i) q^{7} +(-0.129304 + 26.9997i) q^{9} +36.3014i q^{11} +(-39.1385 + 22.5966i) q^{13} +(24.4772 + 24.5947i) q^{15} +(39.7169 + 68.7917i) q^{17} +(80.2233 + 46.3169i) q^{19} +(-34.2387 - 89.9373i) q^{21} +14.1755i q^{23} -80.4061 q^{25} +(-99.9144 + 98.4891i) q^{27} +(9.72891 + 5.61699i) q^{29} +(107.492 + 62.0608i) q^{31} +(-133.699 + 133.060i) q^{33} +(-112.965 - 50.3453i) q^{35} +(92.0975 - 159.518i) q^{37} +(-226.683 - 61.3218i) q^{39} +(-117.681 - 203.830i) q^{41} +(-157.199 + 272.276i) q^{43} +(-0.863474 + 180.300i) q^{45} +(24.1574 + 41.8418i) q^{47} +(229.323 + 255.068i) q^{49} +(-107.782 + 398.429i) q^{51} +(5.19348 - 2.99846i) q^{53} +242.416i q^{55} +(123.466 + 465.235i) q^{57} +(30.3202 - 52.5161i) q^{59} +(330.422 - 190.769i) q^{61} +(205.741 - 455.760i) q^{63} +(-261.362 + 150.897i) q^{65} +(-348.337 + 603.337i) q^{67} +(-52.2086 + 51.9592i) q^{69} -831.889i q^{71} +(505.959 - 292.116i) q^{73} +(-294.722 - 296.137i) q^{75} +(273.681 - 614.086i) q^{77} +(257.347 + 445.737i) q^{79} +(-728.967 - 6.98232i) q^{81} +(-138.138 + 239.262i) q^{83} +(265.224 + 459.382i) q^{85} +(14.9731 + 56.4205i) q^{87} +(807.932 - 1399.38i) q^{89} +(832.439 - 87.1815i) q^{91} +(165.434 + 623.376i) q^{93} +(535.720 + 309.298i) q^{95} +(177.393 + 102.418i) q^{97} +(-980.127 - 4.69391i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 - 30 * q^9	$ 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	3.66543	+	3.68302i	0.705412	+	0.708798i
$3$	3.66543	+	3.68302i	0.705412	+	0.708798i
$4$		0			0
$5$	6.67787			0.597287			0.298643	−	0.954365i	$-0.403466\pi$
$5$	6.67787			0.597287			0.298643	+	0.954365i	$0.403466\pi$
$6$		0			0
$7$	−16.9163	−	7.53913i	−0.913395	−	0.407075i
$7$	−16.9163	−	7.53913i	−0.913395	−	0.407075i
$8$		0			0
$9$	−0.129304	+	26.9997i	−0.00478903	+	0.999989i
$10$		0			0
$11$			36.3014i			0.995026i	0.867457	+	0.497513i	$0.165753\pi$
$11$			36.3014i			0.995026i	−0.867457	+	0.497513i	$0.834247\pi$
$12$		0			0
$13$	−39.1385	+	22.5966i	−0.835006	+	0.482091i	−0.855564	−	0.517698i	$-0.826789\pi$
$13$	−39.1385	+	22.5966i	−0.835006	+	0.482091i	0.0205576	+	0.999789i	$0.493456\pi$
$14$		0			0
$15$	24.4772	+	24.5947i	0.421333	+	0.423356i
$16$		0			0
$17$	39.7169	+	68.7917i	0.566634	+	0.981438i	0.996896	+	0.0787341i	$0.0250878\pi$
$17$	39.7169	+	68.7917i	0.566634	+	0.981438i	−0.430262	+	0.902704i	$0.641579\pi$
$18$		0			0
$19$	80.2233	+	46.3169i	0.968657	+	0.559254i	0.898826	−	0.438305i	$-0.144421\pi$
$19$	80.2233	+	46.3169i	0.968657	+	0.559254i	0.0698303	+	0.997559i	$0.477754\pi$
$20$		0			0
$21$	−34.2387	−	89.9373i	−0.355786	−	0.934568i
$22$		0			0
$23$			14.1755i			0.128513i	0.997933	+	0.0642564i	$0.0204675\pi$
$23$			14.1755i			0.128513i	−0.997933	+	0.0642564i	$0.979532\pi$
$24$		0			0
$25$	−80.4061			−0.643248
$26$		0			0
$27$	−99.9144	+	98.4891i	−0.712168	+	0.702009i
$28$		0			0
$29$	9.72891	+	5.61699i	0.0622970	+	0.0359672i	0.530825	−	0.847481i	$-0.321882\pi$
$29$	9.72891	+	5.61699i	0.0622970	+	0.0359672i	−0.468528	+	0.883449i	$0.655215\pi$
$30$		0			0
$31$	107.492	+	62.0608i	0.622781	+	0.359563i	0.777951	−	0.628325i	$-0.216259\pi$
$31$	107.492	+	62.0608i	0.622781	+	0.359563i	−0.155170	+	0.987888i	$0.549592\pi$
$32$		0			0
$33$	−133.699	+	133.060i	−0.705272	+	0.701903i
$34$		0			0
$35$	−112.965	−	50.3453i	−0.545559	−	0.243140i
$36$		0			0
$37$	92.0975	−	159.518i	0.409209	−	0.708771i	−0.585592	−	0.810606i	$-0.699138\pi$
$37$	92.0975	−	159.518i	0.409209	−	0.708771i	0.994801	+	0.101835i	$0.0324713\pi$
$38$		0			0
$39$	−226.683	−	61.3218i	−0.930728	−	0.251778i
$40$		0			0
$41$	−117.681	−	203.830i	−0.448262	−	0.776413i	0.550011	−	0.835158i	$-0.314624\pi$
$41$	−117.681	−	203.830i	−0.448262	−	0.776413i	−0.998273	+	0.0587446i	$0.981290\pi$
$42$		0			0
$43$	−157.199	+	272.276i	−0.557502	+	0.965621i	0.440203	+	0.897898i	$0.354907\pi$
$43$	−157.199	+	272.276i	−0.557502	+	0.965621i	−0.997704	+	0.0677226i	$0.978427\pi$
$44$		0			0
$45$	−0.863474	+	180.300i	−0.00286042	+	0.597280i
$46$		0			0
$47$	24.1574	+	41.8418i	0.0749727	+	0.129856i	0.901074	−	0.433665i	$-0.142780\pi$
$47$	24.1574	+	41.8418i	0.0749727	+	0.129856i	−0.826102	+	0.563521i	$0.809446\pi$
$48$		0			0
$49$	229.323	+	255.068i	0.668581	+	0.743640i
$50$		0			0
$51$	−107.782	+	398.429i	−0.295931	+	1.09395i
$52$		0			0
$53$	5.19348	−	2.99846i	0.0134600	−	0.00777113i	−0.493255	−	0.869885i	$-0.664193\pi$
$53$	5.19348	−	2.99846i	0.0134600	−	0.00777113i	0.506715	+	0.862114i	$0.330860\pi$
$54$		0			0
$55$			242.416i			0.594316i
$56$		0			0
$57$	123.466	+	465.235i	0.286903	+	1.08109i
$58$		0			0
$59$	30.3202	−	52.5161i	0.0669042	−	0.115882i	−0.830633	−	0.556820i	$-0.812021\pi$
$59$	30.3202	−	52.5161i	0.0669042	−	0.115882i	0.897537	+	0.440939i	$0.145354\pi$
$60$		0			0
$61$	330.422	−	190.769i	0.693544	−	0.400418i	−0.111394	−	0.993776i	$-0.535532\pi$
$61$	330.422	−	190.769i	0.693544	−	0.400418i	0.804938	+	0.593358i	$0.202198\pi$
$62$		0			0
$63$	205.741	−	455.760i	0.411444	−	0.911435i
$64$		0			0
$65$	−261.362	+	150.897i	−0.498738	+	0.287947i
$66$		0			0
$67$	−348.337	+	603.337i	−0.635166	+	1.10014i	0.351314	+	0.936258i	$0.385735\pi$
$67$	−348.337	+	603.337i	−0.635166	+	1.10014i	−0.986480	+	0.163882i	$0.947598\pi$
$68$		0			0
$69$	−52.2086	+	51.9592i	−0.0910895	+	0.0906544i
$70$		0			0
$71$		−	831.889i		−	1.39052i	−0.718757	−	0.695261i	$-0.755289\pi$
$71$		−	831.889i		−	1.39052i	0.718757	−	0.695261i	$-0.244711\pi$
$72$		0			0
$73$	505.959	−	292.116i	0.811206	−	0.468350i	−0.0361685	−	0.999346i	$-0.511515\pi$
$73$	505.959	−	292.116i	0.811206	−	0.468350i	0.847375	+	0.530996i	$0.178182\pi$
$74$		0			0
$75$	−294.722	−	296.137i	−0.453755	−	0.455933i
$76$		0			0
$77$	273.681	−	614.086i	0.405050	−	0.908852i
$78$		0			0
$79$	257.347	+	445.737i	0.366503	+	0.634802i	0.989016	−	0.147807i	$-0.0472215\pi$
$79$	257.347	+	445.737i	0.366503	+	0.634802i	−0.622513	+	0.782610i	$0.713888\pi$
$80$		0			0
$81$	−728.967	−	6.98232i	−0.999954	−	0.00957795i
$82$		0			0
$83$	−138.138	+	239.262i	−0.182682	+	0.316415i	−0.942793	−	0.333379i	$-0.891811\pi$
$83$	−138.138	+	239.262i	−0.182682	+	0.316415i	0.760111	+	0.649793i	$0.225145\pi$
$84$		0			0
$85$	265.224	+	459.382i	0.338443	+	0.586200i
$86$		0			0
$87$	14.9731	+	56.4205i	0.0184516	+	0.0695277i
$88$		0			0
$89$	807.932	−	1399.38i	0.962254	−	1.66667i	0.245436	−	0.969413i	$-0.421069\pi$
$89$	807.932	−	1399.38i	0.962254	−	1.66667i	0.716818	−	0.697260i	$-0.245598\pi$
$90$		0			0
$91$	832.439	−	87.1815i	0.958937	−	0.100430i
$92$		0			0
$93$	165.434	+	623.376i	0.184460	+	0.695066i
$94$		0			0
$95$	535.720	+	309.298i	0.578566	+	0.334035i
$96$		0			0
$97$	177.393	+	102.418i	0.185686	+	0.107206i	0.589961	−	0.807431i	$-0.299143\pi$
$97$	177.393	+	102.418i	0.185686	+	0.107206i	−0.404275	+	0.914637i	$0.632476\pi$
$98$		0			0
$99$	−980.127	−	4.69391i	−0.995015	−	0.00476521i
$100$		0			0
$101$	−1919.85			−1.89141			−0.945704	−	0.325030i	$-0.894626\pi$
$101$	−1919.85			−1.89141			−0.945704	+	0.325030i	$0.894626\pi$
$102$		0			0
$103$		−	531.045i		−	0.508014i	−0.967202	−	0.254007i	$-0.918251\pi$
$103$		−	531.045i		−	0.508014i	0.967202	−	0.254007i	$-0.0817486\pi$
$104$		0			0
$105$	−228.642	−	600.589i	−0.212506	−	0.558205i
$106$		0			0
$107$	1102.16	+	636.334i	0.995795	+	0.574922i	0.907001	−	0.421128i	$-0.138366\pi$
$107$	1102.16	+	636.334i	0.995795	+	0.574922i	0.0887933	+	0.996050i	$0.471699\pi$
$108$		0			0
$109$	−523.741	−	907.146i	−0.460232	−	0.797145i	0.538740	−	0.842472i	$-0.318900\pi$
$109$	−523.741	−	907.146i	−0.460232	−	0.797145i	−0.998972	+	0.0453268i	$0.985567\pi$
$110$		0			0
$111$	925.084	−	245.503i	0.791036	−	0.209929i
$112$		0			0
$113$	923.526	−	533.198i	0.768832	−	0.443885i	−0.0636257	−	0.997974i	$-0.520266\pi$
$113$	923.526	−	533.198i	0.768832	−	0.443885i	0.832458	+	0.554088i	$0.186933\pi$
$114$		0			0
$115$			94.6620i			0.0767590i
$116$		0			0
$117$	−605.042	−	1059.65i	−0.478087	−	0.837305i
$118$		0			0
$119$	−153.234	−	1463.13i	−0.118042	−	1.12710i
$120$		0			0
$121$	13.2077			0.00992316
$122$		0			0
$123$	319.359	−	1180.55i	0.234111	−	0.865418i
$124$		0			0
$125$	−1371.67			−0.981491
$126$		0			0
$127$	2473.36			1.72815			0.864077	−	0.503359i	$-0.167903\pi$
$127$	2473.36			1.72815			0.864077	+	0.503359i	$0.167903\pi$
$128$		0			0
$129$	−1579.00	+	419.042i	−1.07770	+	0.286004i
$130$		0			0
$131$	1314.91			0.876977			0.438489	−	0.898737i	$-0.355514\pi$
$131$	1314.91			0.876977			0.438489	+	0.898737i	$0.355514\pi$
$132$		0			0
$133$	−1007.89	−	1388.32i	−0.657108	−	0.905136i
$134$		0			0
$135$	−667.215	+	657.698i	−0.425369	+	0.419301i
$136$		0			0
$137$		−	2388.22i		−	1.48934i	−0.667433	−	0.744670i	$-0.732607\pi$
$137$		−	2388.22i		−	1.48934i	0.667433	−	0.744670i	$-0.267393\pi$
$138$		0			0
$139$	138.794	−	80.1326i	0.0846931	−	0.0488976i	−0.457055	−	0.889438i	$-0.651096\pi$
$139$	138.794	−	80.1326i	0.0846931	−	0.0488976i	0.541748	+	0.840541i	$0.317763\pi$
$140$		0			0
$141$	−65.5572	+	242.340i	−0.0391554	+	0.144743i
$142$		0			0
$143$	−820.290	−	1420.78i	−0.479693	−	0.830853i
$144$		0			0
$145$	64.9684	+	37.5095i	0.0372092	+	0.0214827i
$146$		0			0
$147$	−98.8554	+	1779.54i	−0.0554657	+	0.998461i
$148$		0			0
$149$		−	3279.01i		−	1.80287i	−0.432917	−	0.901434i	$-0.642516\pi$
$149$		−	3279.01i		−	1.80287i	0.432917	−	0.901434i	$-0.357484\pi$
$150$		0			0
$151$	2279.21			1.22834			0.614169	−	0.789174i	$-0.289491\pi$
$151$	2279.21			1.22834			0.614169	+	0.789174i	$0.289491\pi$
$152$		0			0
$153$	−1862.49	+	1063.45i	−0.984140	+	0.561927i
$154$		0			0
$155$	717.821	+	414.434i	0.371979	+	0.214762i
$156$		0			0
$157$	1709.06	+	986.729i	0.868778	+	0.501589i	0.866942	−	0.498409i	$-0.166082\pi$
$157$	1709.06	+	986.729i	0.868778	+	0.501589i	0.00183629	+	0.999998i	$0.499415\pi$
$158$		0			0
$159$	30.0797	+	8.13708i	0.0150030	+	0.00405857i
$160$		0			0
$161$	106.871	−	239.797i	0.0523143	−	0.117383i
$162$		0			0
$163$	−553.358	+	958.445i	−0.265904	+	0.460559i	−0.967800	−	0.251720i	$-0.919004\pi$
$163$	−553.358	+	958.445i	−0.265904	+	0.460559i	0.701896	+	0.712279i	$0.252337\pi$
$164$		0			0
$165$	−892.824	+	888.558i	−0.421250	+	0.419237i
$166$		0			0
$167$	1788.76	+	3098.23i	0.828854	+	1.43562i	0.898938	+	0.438076i	$0.144340\pi$
$167$	1788.76	+	3098.23i	0.828854	+	1.43562i	−0.0700839	+	0.997541i	$0.522327\pi$
$168$		0			0
$169$	−77.2831	+	133.858i	−0.0351767	+	0.0609277i
$170$		0			0
$171$	−1260.92	+	2160.01i	−0.563887	+	0.965967i
$172$		0			0
$173$	−314.585	−	544.878i	−0.138251	−	0.239458i	0.788583	−	0.614928i	$-0.210815\pi$
$173$	−314.585	−	544.878i	−0.138251	−	0.239458i	−0.926835	+	0.375469i	$0.877482\pi$
$174$		0			0
$175$	1360.17	+	606.191i	0.587540	+	0.261850i
$176$		0			0
$177$	304.554	−	80.8239i	0.129332	−	0.0343226i
$178$		0			0
$179$	526.123	−	303.757i	0.219689	−	0.126837i	−0.386117	−	0.922450i	$-0.626184\pi$
$179$	526.123	−	303.757i	0.219689	−	0.126837i	0.605806	+	0.795612i	$0.292851\pi$
$180$		0			0
$181$			3208.45i			1.31758i	0.752326	+	0.658791i	$0.228932\pi$
$181$			3208.45i			1.31758i	−0.752326	+	0.658791i	$0.771068\pi$
$182$		0			0
$183$	1913.74	+	517.701i	0.773049	+	0.209123i
$184$		0			0
$185$	615.015	−	1065.24i	0.244415	−	0.423340i
$186$		0			0
$187$	−2497.24	+	1441.78i	−0.976556	+	0.563815i
$188$		0			0
$189$	2432.71	−	912.806i	0.936261	−	0.351306i
$190$		0			0
$191$	−2243.70	+	1295.40i	−0.849990	+	0.490742i	−0.860648	−	0.509201i	$-0.829941\pi$
$191$	−2243.70	+	1295.40i	−0.849990	+	0.490742i	0.0106572	+	0.999943i	$0.496608\pi$
$192$		0			0
$193$	−280.211	+	485.339i	−0.104508	+	0.181013i	−0.913537	−	0.406756i	$-0.866660\pi$
$193$	−280.211	+	485.339i	−0.104508	+	0.181013i	0.809029	+	0.587768i	$0.199993\pi$
$194$		0			0
$195$	−1513.76	−	409.499i	−0.555912	−	0.150384i
$196$		0			0
$197$			5115.86i			1.85020i	0.379722	+	0.925101i	$0.376020\pi$
$197$			5115.86i			1.85020i	−0.379722	+	0.925101i	$0.623980\pi$
$198$		0			0
$199$	19.8171	−	11.4414i	0.00705928	−	0.00407568i	−0.496466	−	0.868056i	$-0.665369\pi$
$199$	19.8171	−	11.4414i	0.00705928	−	0.00407568i	0.503525	+	0.863980i	$0.332036\pi$
$200$		0			0
$201$	−3498.91	+	928.555i	−1.22783	+	0.325847i
$202$		0			0
$203$	−122.230	−	168.366i	−0.0422605	−	0.0582118i
$204$		0			0
$205$	−785.861	−	1361.15i	−0.267741	−	0.463741i
$206$		0			0
$207$	−382.734	−	1.83294i	−0.128511	−	0.000615451i
$208$		0			0
$209$	−1681.37	+	2912.22i	−0.556473	+	0.963839i
$210$		0			0
$211$	2497.03	+	4324.99i	0.814705	+	1.41111i	0.909540	+	0.415617i	$0.136434\pi$
$211$	2497.03	+	4324.99i	0.814705	+	1.41111i	−0.0948347	+	0.995493i	$0.530232\pi$
$212$		0			0
$213$	3063.87	−	3049.23i	0.985599	−	0.980890i
$214$		0			0
$215$	−1049.75	+	1818.22i	−0.332988	+	0.576753i
$216$		0			0
$217$	−1350.49	−	1860.24i	−0.422476	−	0.581941i
$218$		0			0
$219$	2930.42	+	792.730i	0.904200	+	0.244602i
$220$		0			0
$221$	−3108.93	−	1794.94i	−0.946285	−	0.546338i
$222$		0			0
$223$	−2700.86	−	1559.34i	−0.811043	−	0.468256i	0.0362748	−	0.999342i	$-0.488451\pi$
$223$	−2700.86	−	1559.34i	−0.811043	−	0.468256i	−0.847318	+	0.531086i	$0.821784\pi$
$224$		0			0
$225$	10.3968	−	2170.94i	0.00308053	−	0.643241i
$226$		0			0
$227$	−4078.40			−1.19248			−0.596239	−	0.802807i	$-0.703339\pi$
$227$	−4078.40			−1.19248			−0.596239	+	0.802807i	$0.703339\pi$
$228$		0			0
$229$		−	2737.22i		−	0.789870i	−0.918709	−	0.394935i	$-0.870767\pi$
$229$		−	2737.22i		−	0.789870i	0.918709	−	0.394935i	$-0.129233\pi$
$230$		0			0
$231$	3264.85	−	1242.91i	0.929919	−	0.354016i
$232$		0			0
$233$	527.258	+	304.412i	0.148248	+	0.0855911i	0.572289	−	0.820052i	$-0.306055\pi$
$233$	527.258	+	304.412i	0.148248	+	0.0855911i	−0.424041	+	0.905643i	$0.639389\pi$
$234$		0			0
$235$	161.320	+	279.414i	0.0447802	+	0.0775615i
$236$		0			0
$237$	−698.376	+	2581.63i	−0.191411	+	0.707574i
$238$		0			0
$239$	4960.69	−	2864.06i	1.34260	−	0.775148i	0.355408	−	0.934711i	$-0.384342\pi$
$239$	4960.69	−	2864.06i	1.34260	−	0.775148i	0.987188	+	0.159563i	$0.0510085\pi$
$240$		0			0
$241$			1262.11i			0.337343i	0.985672	+	0.168672i	$0.0539478\pi$
$241$			1262.11i			0.337343i	−0.985672	+	0.168672i	$0.946052\pi$
$242$		0			0
$243$	−2646.26	−	2710.39i	−0.698590	−	0.715522i
$244$		0			0
$245$	1531.39	+	1703.31i	0.399334	+	0.444166i
$246$		0			0
$247$	−4186.43			−1.07845
$248$		0			0
$249$	−1387.54	+	368.232i	−0.353140	+	0.0937179i
$250$		0			0
$251$	4619.76			1.16174			0.580869	−	0.813997i	$-0.302713\pi$
$251$	4619.76			1.16174			0.580869	+	0.813997i	$0.302713\pi$
$252$		0			0
$253$	−514.590			−0.127874
$254$		0			0
$255$	−719.754	+	2660.66i	−0.176756	+	0.653400i
$256$		0			0
$257$	−6855.52			−1.66395			−0.831976	−	0.554811i	$-0.812791\pi$
$257$	−6855.52			−1.66395			−0.831976	+	0.554811i	$0.812791\pi$
$258$		0			0
$259$	−2760.57	+	2004.11i	−0.662292	+	0.480809i
$260$		0			0
$261$	−152.915	+	261.951i	−0.0362651	+	0.0621241i
$262$		0			0
$263$			1773.10i			0.415718i	0.978159	+	0.207859i	$0.0666495\pi$
$263$			1773.10i			0.415718i	−0.978159	+	0.207859i	$0.933350\pi$
$264$		0			0
$265$	34.6814	−	20.0233i	0.00803947	−	0.00464159i
$266$		0			0
$267$	8115.36	−	2153.69i	1.86012	−	0.493647i
$268$		0			0
$269$	3270.12	+	5664.01i	0.741200	+	1.28380i	0.951949	+	0.306255i	$0.0990761\pi$
$269$	3270.12	+	5664.01i	0.741200	+	1.28380i	−0.210750	+	0.977540i	$0.567591\pi$
$270$		0			0
$271$	−4730.17	−	2730.96i	−1.06028	−	0.612156i	−0.134774	−	0.990876i	$-0.543031\pi$
$271$	−4730.17	−	2730.96i	−1.06028	−	0.612156i	−0.925511	+	0.378721i	$0.876364\pi$
$272$		0			0
$273$	3372.33	+	2746.33i	0.747630	+	0.608848i
$274$		0			0
$275$		−	2918.85i		−	0.640049i
$276$		0			0
$277$	5901.59			1.28012			0.640058	−	0.768326i	$-0.278910\pi$
$277$	5901.59			1.28012			0.640058	+	0.768326i	$0.278910\pi$
$278$		0			0
$279$	−1689.52	+	2894.24i	−0.362541	+	0.621052i
$280$		0			0
$281$	1135.22	+	655.420i	0.241002	+	0.139143i	0.615637	−	0.788030i	$-0.288899\pi$
$281$	1135.22	+	655.420i	0.241002	+	0.139143i	−0.374635	+	0.927172i	$0.622232\pi$
$282$		0			0
$283$	−7791.33	−	4498.33i	−1.63656	−	0.944868i	−0.982005	−	0.188854i	$-0.939523\pi$
$283$	−7791.33	−	4498.33i	−1.63656	−	0.944868i	−0.654555	−	0.756015i	$-0.727144\pi$
$284$		0			0
$285$	824.491	+	3106.78i	0.171364	+	0.645719i
$286$		0			0
$287$	454.034	+	4335.27i	0.0933825	+	0.891648i
$288$		0			0
$289$	−698.369	+	1209.61i	−0.142147	+	0.246206i
$290$		0			0
$291$	273.014	+	1028.75i	0.0549978	+	0.207238i
$292$		0			0
$293$	−1661.49	−	2877.79i	−0.331281	−	0.573796i	0.651482	−	0.758664i	$-0.274148\pi$
$293$	−1661.49	−	2877.79i	−0.331281	−	0.573796i	−0.982763	+	0.184868i	$0.940814\pi$
$294$		0			0
$295$	202.474	−	350.695i	0.0399610	−	0.0692145i
$296$		0			0
$297$	−3575.29	−	3627.03i	−0.698517	−	0.708626i
$298$		0			0
$299$	−320.318	−	554.808i	−0.0619548	−	0.107309i
$300$		0			0
$301$	4711.94	−	3420.77i	0.902299	−	0.655049i
$302$		0			0
$303$	−7037.07	−	7070.85i	−1.33422	−	1.34063i
$304$		0			0
$305$	2206.51	−	1273.93i	0.414245	−	0.239164i
$306$		0			0
$307$			3761.71i			0.699323i	0.936876	+	0.349661i	$0.113703\pi$
$307$			3761.71i			0.699323i	−0.936876	+	0.349661i	$0.886297\pi$
$308$		0			0
$309$	1955.85	−	1946.51i	0.360079	−	0.358359i
$310$		0			0
$311$	−350.602	+	607.260i	−0.0639254	+	0.110722i	−0.896217	−	0.443616i	$-0.853695\pi$
$311$	−350.602	+	607.260i	−0.0639254	+	0.110722i	0.832291	+	0.554338i	$0.187029\pi$
$312$		0			0
$313$	2709.37	−	1564.25i	0.489273	−	0.282482i	−0.235000	−	0.971995i	$-0.575509\pi$
$313$	2709.37	−	1564.25i	0.489273	−	0.282482i	0.724273	+	0.689514i	$0.242176\pi$
$314$		0			0
$315$	1373.91	−	3043.51i	0.245750	−	0.544388i
$316$		0			0
$317$	2304.60	−	1330.56i	0.408326	−	0.235747i	−0.281744	−	0.959490i	$-0.590913\pi$
$317$	2304.60	−	1330.56i	0.408326	−	0.235747i	0.690070	+	0.723742i	$0.257580\pi$
$318$		0			0
$319$	−203.905	+	353.173i	−0.0357883	+	0.0619872i
$320$		0			0
$321$	1696.26	+	6391.72i	0.294941	+	1.11137i
$322$		0			0
$323$			7358.26i			1.26757i
$324$		0			0
$325$	3146.98	−	1816.91i	0.537116	−	0.310104i
$326$		0			0
$327$	1421.30	−	5254.03i	0.240362	−	0.888527i
$328$		0			0
$329$	−93.2031	−	889.934i	−0.0156184	−	0.149130i
$330$		0			0
$331$	1048.52	+	1816.09i	0.174114	+	0.301575i	0.939854	−	0.341575i	$-0.110960\pi$
$331$	1048.52	+	1816.09i	0.174114	+	0.301575i	−0.765740	+	0.643150i	$0.777627\pi$
$332$		0			0
$333$	4295.02	+	2507.23i	0.706803	+	0.412599i
$334$		0			0
$335$	−2326.15	+	4029.01i	−0.379376	+	0.657099i
$336$		0			0
$337$	−4125.58	−	7145.72i	−0.666869	−	1.15505i	−0.978775	−	0.204937i	$-0.934301\pi$
$337$	−4125.58	−	7145.72i	−0.666869	−	1.15505i	0.311907	−	0.950113i	$-0.399032\pi$
$338$		0			0
$339$	5348.90	+	1446.97i	0.856968	+	0.231825i
$340$		0			0
$341$	−2252.89	+	3902.13i	−0.357774	+	0.619683i
$342$		0			0
$343$	−1956.31	−	6043.71i	−0.307961	−	0.951399i
$344$		0			0
$345$	−348.642	+	346.977i	−0.0544066	+	0.0541467i
$346$		0			0
$347$	3257.15	+	1880.52i	0.503899	+	0.290926i	0.730322	−	0.683103i	$-0.239370\pi$
$347$	3257.15	+	1880.52i	0.503899	+	0.290926i	−0.226423	+	0.974029i	$0.572703\pi$
$348$		0			0
$349$	4993.70	+	2883.12i	0.765922	+	0.442205i	0.831418	−	0.555647i	$-0.187530\pi$
$349$	4993.70	+	2883.12i	0.765922	+	0.442205i	−0.0654958	+	0.997853i	$0.520863\pi$
$350$		0			0
$351$	1684.98	−	6112.45i	0.256232	−	0.929512i
$352$		0			0
$353$	−11093.9			−1.67272			−0.836360	−	0.548180i	$-0.815321\pi$
$353$	−11093.9			−1.67272			−0.836360	+	0.548180i	$0.815321\pi$
$354$		0			0
$355$		−	5555.25i		−	0.830540i
$356$		0			0
$357$	4827.08	−	5927.37i	0.715620	−	0.878739i
$358$		0			0
$359$	5406.80	+	3121.62i	0.794874	+	0.458921i	0.841676	−	0.539983i	$-0.181570\pi$
$359$	5406.80	+	3121.62i	0.794874	+	0.458921i	−0.0468016	+	0.998904i	$0.514903\pi$
$360$		0			0
$361$	861.015	+	1491.32i	0.125531	+	0.217425i
$362$		0			0
$363$	48.4120	+	48.6444i	0.00699991	+	0.00703352i
$364$		0			0
$365$	3378.73	−	1950.71i	0.484523	−	0.279739i
$366$		0			0
$367$		−	7500.23i		−	1.06678i	−0.845869	−	0.533391i	$-0.820918\pi$
$367$		−	7500.23i		−	1.06678i	0.845869	−	0.533391i	$-0.179082\pi$
$368$		0			0
$369$	5518.57	−	3151.01i	0.778551	−	0.444539i
$370$		0			0
$371$	−110.460	+	11.5685i	−0.0154577	+	0.00161889i
$372$		0			0
$373$	−436.698			−0.0606203			−0.0303102	−	0.999541i	$-0.509650\pi$
$373$	−436.698			−0.0606203			−0.0303102	+	0.999541i	$0.509650\pi$
$374$		0			0
$375$	−5027.77	−	5051.91i	−0.692355	−	0.695679i
$376$		0			0
$377$	−507.701			−0.0693578
$378$		0			0
$379$	−11102.0			−1.50467			−0.752335	−	0.658781i	$-0.771072\pi$
$379$	−11102.0			−1.50467			−0.752335	+	0.658781i	$0.771072\pi$
$380$		0			0
$381$	9065.93	+	9109.46i	1.21906	+	1.22491i
$382$		0			0
$383$	4304.86			0.574329			0.287164	−	0.957881i	$-0.407287\pi$
$383$	4304.86			0.574329			0.287164	+	0.957881i	$0.407287\pi$
$384$		0			0
$385$	1827.61	−	4100.79i	0.241931	−	0.542845i
$386$		0			0
$387$	−7331.04	−	4279.52i	−0.962940	−	0.562120i
$388$		0			0
$389$		−	13455.8i		−	1.75382i	−0.480652	−	0.876911i	$-0.659600\pi$
$389$		−	13455.8i		−	1.75382i	0.480652	−	0.876911i	$-0.340400\pi$
$390$		0			0
$391$	−975.156	+	563.007i	−0.126127	+	0.0728196i
$392$		0			0
$393$	4819.70	+	4842.83i	0.618630	+	0.621600i
$394$		0			0
$395$	1718.53	+	2976.58i	0.218908	+	0.379159i
$396$		0			0
$397$	−11464.4	−	6618.96i	−1.44932	−	0.836765i	−0.450879	−	0.892585i	$-0.648890\pi$
$397$	−11464.4	−	6618.96i	−1.44932	−	0.836765i	−0.998441	+	0.0558195i	$0.982223\pi$
$398$		0			0
$399$	1418.88	−	8800.89i	0.178027	−	1.10425i
$400$		0			0
$401$			5844.18i			0.727792i	0.931440	+	0.363896i	$0.118554\pi$
$401$			5844.18i			0.727792i	−0.931440	+	0.363896i	$0.881446\pi$
$402$		0			0
$403$	−5609.46			−0.693368
$404$		0			0
$405$	−4867.94	−	46.6270i	−0.597259	−	0.00572078i
$406$		0			0
$407$	5790.71	+	3343.27i	0.705246	+	0.407174i
$408$		0			0
$409$	−5915.13	−	3415.10i	−0.715121	−	0.412875i	0.0978335	−	0.995203i	$-0.468809\pi$
$409$	−5915.13	−	3415.10i	−0.715121	−	0.412875i	−0.812954	+	0.582328i	$0.802142\pi$
$410$		0			0
$411$	8795.87	−	8753.85i	1.05564	−	1.05060i
$412$		0			0
$413$	−908.831	+	659.791i	−0.108282	+	0.0786106i
$414$		0			0
$415$	−922.468	+	1597.76i	−0.109114	+	0.188990i
$416$		0			0
$417$	803.869	+	217.460i	0.0944020	+	0.0255374i
$418$		0			0
$419$	−4104.58	−	7109.34i	−0.478572	−	0.828912i	0.521126	−	0.853480i	$-0.325512\pi$
$419$	−4104.58	−	7109.34i	−0.478572	−	0.828912i	−0.999698	+	0.0245683i	$0.992179\pi$
$420$		0			0
$421$	1540.67	−	2668.52i	0.178356	−	0.308921i	−0.762962	−	0.646444i	$-0.776256\pi$
$421$	1540.67	−	2668.52i	0.178356	−	0.308921i	0.941317	+	0.337523i	$0.109589\pi$
$422$		0			0
$423$	−1132.84	+	646.831i	−0.130214	+	0.0743499i
$424$		0			0
$425$	−3193.48	−	5531.27i	−0.364486	−	0.631309i
$426$		0			0
$427$	−7027.75	+	736.019i	−0.796480	+	0.0834155i
$428$		0			0
$429$	2226.07	−	8228.93i	0.250526	−	0.926099i
$430$		0			0
$431$	1575.95	−	909.876i	0.176127	−	0.101687i	−0.409345	−	0.912380i	$-0.634243\pi$
$431$	1575.95	−	909.876i	0.176127	−	0.101687i	0.585472	+	0.810693i	$0.300909\pi$
$432$		0			0
$433$			14856.9i			1.64891i	0.565929	+	0.824454i	$0.308518\pi$
$433$			14856.9i			1.64891i	−0.565929	+	0.824454i	$0.691482\pi$
$434$		0			0
$435$	99.9885	+	376.768i	0.0110209	+	0.0415280i
$436$		0			0
$437$	−656.565	+	1137.20i	−0.0718713	+	0.124485i
$438$		0			0
$439$	−8005.53	+	4622.00i	−0.870349	+	0.502496i	−0.867464	−	0.497500i	$-0.834252\pi$
$439$	−8005.53	+	4622.00i	−0.870349	+	0.502496i	−0.00288478	+	0.999996i	$0.500918\pi$
$440$		0			0
$441$	−6916.42	+	6158.67i	−0.746833	+	0.665012i
$442$		0			0
$443$	−1061.19	+	612.681i	−0.113812	+	0.0657096i	−0.555826	−	0.831299i	$-0.687598\pi$
$443$	−1061.19	+	612.681i	−0.113812	+	0.0657096i	0.442013	+	0.897009i	$0.354264\pi$
$444$		0			0
$445$	5395.26	−	9344.87i	0.574742	−	0.995482i
$446$		0			0
$447$	12076.7	−	12019.0i	1.27787	−	1.27176i
$448$		0			0
$449$			12542.2i			1.31827i	0.752023	+	0.659136i	$0.229078\pi$
$449$			12542.2i			1.31827i	−0.752023	+	0.659136i	$0.770922\pi$
$450$		0			0
$451$	7399.32	−	4272.00i	0.772551	−	0.446033i
$452$		0			0
$453$	8354.26	+	8394.37i	0.866485	+	0.870644i
$454$		0			0
$455$	5558.92	−	582.187i	0.572761	−	0.0599854i
$456$		0			0
$457$	7667.25	+	13280.1i	0.784811	+	1.35933i	0.929112	+	0.369799i	$0.120573\pi$
$457$	7667.25	+	13280.1i	0.784811	+	1.35933i	−0.144301	+	0.989534i	$0.546093\pi$
$458$		0			0
$459$	−10743.5	−	2961.60i	−1.09252	−	0.301167i
$460$		0			0
$461$	−3411.92	+	5909.62i	−0.344705	+	0.597047i	−0.985300	−	0.170832i	$-0.945354\pi$
$461$	−3411.92	+	5909.62i	−0.344705	+	0.597047i	0.640595	+	0.767879i	$0.278688\pi$
$462$		0			0
$463$	5117.73	+	8864.16i	0.513695	+	0.889746i	0.999874	+	0.0158869i	$0.00505718\pi$
$463$	5117.73	+	8864.16i	0.513695	+	0.889746i	−0.486178	+	0.873860i	$0.661609\pi$
$464$		0			0
$465$	1104.75	+	4162.83i	0.110175	+	0.415154i
$466$		0			0
$467$	−2313.87	+	4007.75i	−0.229279	+	0.397123i	−0.957595	−	0.288119i	$-0.906970\pi$
$467$	−2313.87	+	4007.75i	−0.229279	+	0.397123i	0.728316	+	0.685242i	$0.240304\pi$
$468$		0			0
$469$	10441.2	−	7580.08i	1.02800	−	0.746302i
$470$		0			0
$471$	2630.31	+	9911.30i	0.257321	+	0.969615i
$472$		0			0
$473$	−9884.00	−	5706.53i	−0.960818	−	0.554729i
$474$		0			0
$475$	−6450.44	−	3724.16i	−0.623087	−	0.359739i
$476$		0			0
$477$	80.2859	+	140.610i	0.00770658	+	0.0134971i
$478$		0			0
$479$	−11495.0			−1.09649			−0.548245	−	0.836318i	$-0.684704\pi$
$479$	−11495.0			−1.09649			−0.548245	+	0.836318i	$0.684704\pi$
$480$		0			0
$481$			8324.38i			0.789104i
$482$		0			0
$483$	1274.90	−	485.350i	0.120104	−	0.0457230i
$484$		0			0
$485$	1184.61	+	683.934i	0.110908	+	0.0640327i
$486$		0			0
$487$	3438.48	+	5955.62i	0.319943	+	0.554158i	0.980476	−	0.196639i	$-0.0630028\pi$
$487$	3438.48	+	5955.62i	0.319943	+	0.554158i	−0.660533	+	0.750797i	$0.729669\pi$
$488$		0			0
$489$	−5558.27	+	1475.08i	−0.514015	+	0.136412i
$490$		0			0
$491$	11307.3	−	6528.30i	1.03929	−	0.600037i	0.119661	−	0.992815i	$-0.461819\pi$
$491$	11307.3	−	6528.30i	1.03929	−	0.600037i	0.919633	+	0.392778i	$0.128486\pi$
$492$		0			0
$493$			892.358i			0.0815209i
$494$		0			0
$495$	−6545.16	−	31.3453i	−0.594309	−	0.00284620i
$496$		0			0
$497$	−6271.71	+	14072.5i	−0.566046	+	1.27010i
$498$		0			0
$499$	6920.54			0.620854			0.310427	−	0.950597i	$-0.399528\pi$
$499$	6920.54			0.620854			0.310427	+	0.950597i	$0.399528\pi$
$500$		0			0
$501$	−4854.26	+	17944.4i	−0.432879	+	1.60019i
$502$		0			0
$503$	748.409			0.0663417			0.0331709	−	0.999450i	$-0.489439\pi$
$503$	748.409			0.0663417			0.0331709	+	0.999450i	$0.489439\pi$
$504$		0			0
$505$	−12820.5			−1.12971
$506$		0			0
$507$	−776.278	+	206.012i	−0.0679995	+	0.0180460i
$508$		0			0
$509$	4221.89			0.367646			0.183823	−	0.982959i	$-0.441153\pi$
$509$	4221.89			0.367646			0.183823	+	0.982959i	$0.441153\pi$
$510$		0			0
$511$	−10761.3	+	1127.03i	−0.931605	+	0.0975672i
$512$		0			0
$513$	−12577.2	+	3273.39i	−1.08245	+	0.281723i
$514$		0			0
$515$		−	3546.25i		−	0.303430i
$516$		0			0
$517$	−1518.92	+	876.947i	−0.129211	+	0.0745997i
$518$		0			0
$519$	853.708	−	3155.84i	0.0722035	−	0.266909i
$520$		0			0
$521$	−3978.11	−	6890.29i	−0.334519	−	0.579403i	0.648874	−	0.760896i	$-0.275240\pi$
$521$	−3978.11	−	6890.29i	−0.334519	−	0.579403i	−0.983392	+	0.181493i	$0.941907\pi$
$522$		0			0
$523$	17010.3	+	9820.92i	1.42220	+	0.821107i	0.996487	−	0.0837512i	$-0.0266901\pi$
$523$	17010.3	+	9820.92i	1.42220	+	0.821107i	0.425713	+	0.904858i	$0.360023\pi$
$524$		0			0
$525$	2753.00	+	7231.50i	0.228859	+	0.601159i
$526$		0			0
$527$			9859.46i			0.814962i
$528$		0			0
$529$	11966.1			0.983484
$530$		0			0
$531$	1414.00	+	825.426i	0.115560	+	0.0674584i
$532$		0			0
$533$	9211.76	+	5318.41i	0.748603	+	0.432206i
$534$		0			0
$535$	7360.09	+	4249.35i	0.594775	+	0.343394i
$536$		0			0
$537$	3047.21	+	824.323i	0.244873	+	0.0662424i
$538$		0			0
$539$	−9259.34	+	8324.75i	−0.739941	+	0.665255i
$540$		0			0
$541$	1172.15	−	2030.22i	0.0931510	−	0.161342i	−0.815684	−	0.578497i	$-0.803639\pi$
$541$	1172.15	−	2030.22i	0.0931510	−	0.161342i	0.908835	+	0.417155i	$0.136973\pi$
$542$		0			0
$543$	−11816.8	+	11760.3i	−0.933900	+	0.929438i
$544$		0			0
$545$	−3497.47	−	6057.80i	−0.274890	−	0.476124i
$546$		0			0
$547$	−5959.72	+	10322.5i	−0.465849	+	0.806873i	−0.999239	−	0.0389956i	$-0.987584\pi$
$547$	−5959.72	+	10322.5i	−0.465849	+	0.806873i	0.533391	+	0.845869i	$0.320918\pi$
$548$		0			0
$549$	5107.98	+	8945.96i	0.397092	+	0.695454i
$550$		0			0
$551$	520.323	+	901.227i	0.0402296	+	0.0696797i
$552$		0			0
$553$	−992.885	−	9480.40i	−0.0763504	−	0.729019i
$554$		0			0
$555$	6177.59	−	1639.44i	0.472476	−	0.125388i
$556$		0			0
$557$	3386.01	−	1954.91i	0.257576	−	0.148711i	−0.365652	−	0.930751i	$-0.619154\pi$
$557$	3386.01	−	1954.91i	0.257576	−	0.148711i	0.623228	+	0.782040i	$0.285821\pi$
$558$		0			0
$559$		−	14208.6i		−	1.07507i
$560$		0			0
$561$	−14463.5	−	3912.64i	−1.08851	−	0.294459i
$562$		0			0
$563$	3795.41	−	6573.84i	0.284116	−	0.492104i	−0.688278	−	0.725447i	$-0.741633\pi$
$563$	3795.41	−	6573.84i	0.284116	−	0.492104i	0.972394	+	0.233343i	$0.0749665\pi$
$564$		0			0
$565$	6167.19	−	3560.63i	0.459213	−	0.265127i
$566$		0			0
$567$	12278.8	+	5613.89i	0.909454	+	0.415804i
$568$		0			0
$569$	9443.07	−	5451.96i	0.695736	−	0.401684i	−0.110021	−	0.993929i	$-0.535092\pi$
$569$	9443.07	−	5451.96i	0.695736	−	0.401684i	0.805757	+	0.592246i	$0.201758\pi$
$570$		0			0
$571$	−12051.0	+	20872.9i	−0.883218	+	1.52978i	−0.0354761	+	0.999371i	$0.511295\pi$
$571$	−12051.0	+	20872.9i	−0.883218	+	1.52978i	−0.847742	+	0.530408i	$0.822039\pi$
$572$		0			0
$573$	−12995.1	−	3515.40i	−0.947430	−	0.256296i
$574$		0			0
$575$		−	1139.79i		−	0.0826656i
$576$		0			0
$577$	7098.95	−	4098.58i	0.512189	−	0.295712i	−0.221544	−	0.975150i	$-0.571110\pi$
$577$	7098.95	−	4098.58i	0.512189	−	0.295712i	0.733733	+	0.679438i	$0.237776\pi$
$578$		0			0
$579$	−2814.60	+	746.952i	−0.202022	+	0.0536136i
$580$		0			0
$581$	4140.61	−	3005.99i	0.295665	−	0.214646i
$582$		0			0
$583$	108.848	+	188.531i	0.00773248	+	0.0133930i
$584$		0			0
$585$	−4040.39	−	7076.21i	−0.285555	−	0.500111i
$586$		0			0
$587$	11153.4	−	19318.3i	0.784242	−	1.35835i	−0.145209	−	0.989401i	$-0.546385\pi$
$587$	11153.4	−	19318.3i	0.784242	−	1.35835i	0.929451	−	0.368946i	$-0.120281\pi$
$588$		0			0
$589$	5748.93	+	9957.44i	0.402174	+	0.696586i
$590$		0			0
$591$	−18841.8	+	18751.8i	−1.31142	+	1.30515i
$592$		0			0
$593$	5870.27	−	10167.6i	0.406514	−	0.704104i	−0.587982	−	0.808874i	$-0.700077\pi$
$593$	5870.27	−	10167.6i	0.406514	−	0.704104i	0.994496	+	0.104770i	$0.0334108\pi$
$594$		0			0
$595$	−1023.28	−	9770.61i	−0.0705048	−	0.673204i
$596$		0			0
$597$	114.777	+	31.0492i	0.00786853	+	0.00212857i
$598$		0			0
$599$	−11375.5	−	6567.65i	−0.775944	−	0.447991i	0.0590472	−	0.998255i	$-0.481194\pi$
$599$	−11375.5	−	6567.65i	−0.775944	−	0.447991i	−0.834991	+	0.550264i	$0.814527\pi$
$600$		0			0
$601$	−4.16380	−	2.40397i	−0.000282604	−	0.000163161i	0.499859	−	0.866107i	$-0.333385\pi$
$601$	−4.16380	−	2.40397i	−0.000282604	−	0.000163161i	−0.500141	+	0.865944i	$0.666719\pi$
$602$		0			0
$603$	−16244.9	−	9483.00i	−1.09708	−	0.640427i
$604$		0			0
$605$	88.1995			0.00592697
$606$		0			0
$607$			14169.8i			0.947501i	0.880659	+	0.473751i	$0.157100\pi$
$607$			14169.8i			0.947501i	−0.880659	+	0.473751i	$0.842900\pi$
$608$		0			0
$609$	172.071	−	1067.31i	0.0114494	−	0.0710174i
$610$		0			0
$611$	−1890.97	−	1091.75i	−0.125205	−	0.0722873i
$612$		0			0
$613$	12867.0	+	22286.3i	0.847785	+	1.46841i	0.883180	+	0.469034i	$0.155398\pi$
$613$	12867.0	+	22286.3i	0.847785	+	1.46841i	−0.0353949	+	0.999373i	$0.511269\pi$
$614$		0			0
$615$	2132.63	−	7883.54i	0.139831	−	0.516903i
$616$		0			0
$617$	−10203.5	+	5890.97i	−0.665763	+	0.384379i	−0.794469	−	0.607304i	$-0.792251\pi$
$617$	−10203.5	+	5890.97i	−0.665763	+	0.384379i	0.128706	+	0.991683i	$0.458918\pi$
$618$		0			0
$619$		−	23042.3i		−	1.49620i	−0.663585	−	0.748101i	$-0.730966\pi$
$619$		−	23042.3i		−	1.49620i	0.663585	−	0.748101i	$-0.269034\pi$
$620$		0			0
$621$	−1396.13	−	1416.34i	−0.0902171	−	0.0915227i
$622$		0			0
$623$	−24217.3	+	17581.2i	−1.55738	+	1.13062i
$624$		0			0
$625$	890.891			0.0570170
$626$		0			0
$627$	−16888.7	+	4482.00i	−1.07571	+	0.285476i
$628$		0			0
$629$	14631.3			0.927487
$630$		0			0
$631$	−9923.76			−0.626084			−0.313042	−	0.949739i	$-0.601348\pi$
$631$	−9923.76			−0.626084			−0.313042	+	0.949739i	$0.601348\pi$
$632$		0			0
$633$	−6776.33	+	25049.5i	−0.425490	+	1.57287i
$634$		0			0
$635$	16516.8			1.03220
$636$		0			0
$637$	−14739.1	−	4801.07i	−0.916771	−	0.298627i
$638$		0			0
$639$	22460.7	+	107.566i	1.39051	+	0.00665925i
$640$		0			0
$641$		−	17492.1i		−	1.07784i	−0.842357	−	0.538921i	$-0.818832\pi$
$641$		−	17492.1i		−	1.07784i	0.842357	−	0.538921i	$-0.181168\pi$
$642$		0			0
$643$	2937.02	−	1695.69i	0.180132	−	0.103999i	−0.407223	−	0.913329i	$-0.633503\pi$
$643$	2937.02	−	1695.69i	0.180132	−	0.103999i	0.587355	+	0.809330i	$0.300169\pi$
$644$		0			0
$645$	−10544.3	+	2798.31i	−0.643695	+	0.170827i
$646$		0			0
$647$	−11172.9	−	19352.0i	−0.678903	−	1.17589i	−0.975312	−	0.220834i	$-0.929122\pi$
$647$	−11172.9	−	19352.0i	−0.678903	−	1.17589i	0.296408	−	0.955061i	$-0.404211\pi$
$648$		0			0
$649$	1906.41	+	1100.66i	0.115305	+	0.0665715i
$650$		0			0
$651$	1901.17	−	11792.5i	0.114459	−	0.709958i
$652$		0			0
$653$		−	9778.05i		−	0.585980i	−0.956116	−	0.292990i	$-0.905350\pi$
$653$		−	9778.05i		−	0.585980i	0.956116	−	0.292990i	$-0.0946502\pi$
$654$		0			0
$655$	8780.78			0.523807
$656$		0			0
$657$	7821.61	+	13698.5i	0.464460	+	0.813440i
$658$		0			0
$659$	−14282.6	−	8246.08i	−0.844268	−	0.487438i	0.0144449	−	0.999896i	$-0.495402\pi$
$659$	−14282.6	−	8246.08i	−0.844268	−	0.487438i	−0.858713	+	0.512457i	$0.828735\pi$
$660$		0			0
$661$	22119.1	+	12770.5i	1.30157	+	0.751459i	0.980673	−	0.195656i	$-0.0626837\pi$
$661$	22119.1	+	12770.5i	1.30157	+	0.751459i	0.320893	+	0.947116i	$0.396017\pi$
$662$		0			0
$663$	−4784.74	−	18029.5i	−0.280277	−	1.05612i
$664$		0			0
$665$	−6730.58	−	9271.05i	−0.392482	−	0.540626i
$666$		0			0
$667$	−79.6235	+	137.912i	−0.00462224	+	0.00800596i
$668$		0			0
$669$	−4156.70	−	15663.0i	−0.240220	−	0.905179i
$670$		0			0
$671$	6925.19	+	11994.8i	0.398426	+	0.690095i
$672$		0			0
$673$	−6191.35	+	10723.7i	−0.354619	+	0.614219i	−0.987053	−	0.160396i	$-0.948723\pi$
$673$	−6191.35	+	10723.7i	−0.354619	+	0.614219i	0.632433	+	0.774615i	$0.282056\pi$
$674$		0			0
$675$	8033.72	−	7919.12i	0.458101	−	0.451566i
$676$		0			0
$677$	13097.6	+	22685.7i	0.743547	+	1.28786i	0.950871	+	0.309589i	$0.100191\pi$
$677$	13097.6	+	22685.7i	0.743547	+	1.28786i	−0.207323	+	0.978272i	$0.566475\pi$
$678$		0			0
$679$	−2228.70	−	3069.92i	−0.125964	−	0.173509i
$680$		0			0
$681$	−14949.1	−	15020.8i	−0.841188	−	0.845226i
$682$		0			0
$683$	19831.2	−	11449.6i	1.11101	−	0.641443i	0.171920	−	0.985111i	$-0.445003\pi$
$683$	19831.2	−	11449.6i	1.11101	−	0.641443i	0.939091	+	0.343668i	$0.111669\pi$
$684$		0			0
$685$		−	15948.2i		−	0.889563i
$686$		0			0
$687$	10081.2	−	10033.1i	0.559858	−	0.557184i
$688$		0			0
$689$	−135.510	+	234.710i	−0.00749278	+	0.0129779i
$690$		0			0
$691$	6872.89	−	3968.07i	0.378375	−	0.218455i	−0.298736	−	0.954336i	$-0.596565\pi$
$691$	6872.89	−	3968.07i	0.378375	−	0.218455i	0.677111	+	0.735881i	$0.263232\pi$
$692$		0			0
$693$	16544.7	+	7468.70i	0.906902	+	0.409398i
$694$		0			0
$695$	926.847	−	535.115i	0.0505861	−	0.0292059i
$696$		0			0
$697$	9347.89	−	16191.0i	0.508001	−	0.879883i
$698$		0			0
$699$	811.467	+	3057.70i	0.0439091	+	0.165455i
$700$		0			0
$701$		−	30331.5i		−	1.63424i	−0.576466	−	0.817121i	$-0.695569\pi$
$701$		−	30331.5i		−	1.63424i	0.576466	−	0.817121i	$-0.304431\pi$
$702$		0			0
$703$	14776.7	−	8531.35i	0.792767	−	0.457704i
$704$		0			0
$705$	−437.782	+	1618.32i	−0.0233870	+	0.0864529i
$706$		0			0
$707$	32476.8	+	14474.0i	1.72760	+	0.769944i
$708$		0			0
$709$	1072.65	+	1857.88i	0.0568181	+	0.0984119i	0.893035	−	0.449986i	$-0.148571\pi$
$709$	1072.65	+	1857.88i	0.0568181	+	0.0984119i	−0.836217	+	0.548398i	$0.815238\pi$
$710$		0			0
$711$	−12068.0	+	6890.64i	−0.636550	+	0.363459i
$712$		0			0
$713$	−879.742	+	1523.76i	−0.0462084	+	0.0800353i
$714$		0			0
$715$	−5477.79	−	9487.81i	−0.286514	−	0.496257i
$716$		0			0
$717$	28731.4	+	7772.35i	1.49651	+	0.404831i
$718$		0			0
$719$	4053.00	−	7020.00i	0.210224	−	0.364119i	−0.741560	−	0.670886i	$-0.765914\pi$
$719$	4053.00	−	7020.00i	0.210224	−	0.364119i	0.951785	+	0.306767i	$0.0992472\pi$
$720$		0			0
$721$	−4003.61	+	8983.32i	−0.206799	+	0.464017i
$722$		0			0
$723$	−4648.39	+	4626.18i	−0.239108	+	0.237966i
$724$		0			0
$725$	−782.263	−	451.640i	−0.0400725	−	0.0231358i
$726$		0			0
$727$	756.456	+	436.740i	0.0385906	+	0.0222803i	0.519171	−	0.854670i	$-0.326241\pi$
$727$	756.456	+	436.740i	0.0385906	+	0.0222803i	−0.480581	+	0.876951i	$0.659574\pi$
$728$		0			0
$729$	282.779	−	19681.0i	0.0143666	−	0.999897i
$730$		0			0
$731$	−24973.8			−1.26360
$732$		0			0
$733$			18354.5i			0.924885i	0.886649	+	0.462442i	$0.153027\pi$
$733$			18354.5i			0.924885i	−0.886649	+	0.462442i	$0.846973\pi$
$734$		0			0
$735$	−660.144	+	11883.5i	−0.0331289	+	0.596367i
$736$		0			0
$737$	−21902.0	−	12645.1i	−1.09467	−	0.632006i
$738$		0			0
$739$	16385.9	+	28381.3i	0.815651	+	1.41275i	0.908860	+	0.417102i	$0.136954\pi$
$739$	16385.9	+	28381.3i	0.815651	+	1.41275i	−0.0932087	+	0.995647i	$0.529712\pi$
$740$		0			0
$741$	−15345.0	−	15418.7i	−0.760748	−	0.764400i
$742$		0			0
$743$	2711.17	−	1565.29i	0.133867	−	0.0772880i	−0.431571	−	0.902079i	$-0.642041\pi$
$743$	2711.17	−	1565.29i	0.133867	−	0.0772880i	0.565438	+	0.824791i	$0.308707\pi$
$744$		0			0
$745$		−	21896.8i		−	1.07683i
$746$		0			0
$747$	−6442.14	−	3760.62i	−0.315536	−	0.184195i
$748$		0			0
$749$	−13847.1	−	19073.8i	−0.675518	−	0.930494i
$750$		0			0
$751$	−3024.28			−0.146947			−0.0734737	−	0.997297i	$-0.523409\pi$
$751$	−3024.28			−0.146947			−0.0734737	+	0.997297i	$0.523409\pi$
$752$		0			0
$753$	16933.4	+	17014.7i	0.819504	+	0.823438i
$754$		0			0
$755$	15220.2			0.733671
$756$		0			0
$757$	2011.02			0.0965547			0.0482773	−	0.998834i	$-0.484627\pi$
$757$	2011.02			0.0965547			0.0482773	+	0.998834i	$0.484627\pi$
$758$		0			0
$759$	−1886.19	−	1895.25i	−0.0902034	−	0.0906365i
$760$		0			0
$761$	−20366.3			−0.970142			−0.485071	−	0.874475i	$-0.661206\pi$
$761$	−20366.3			−0.970142			−0.485071	+	0.874475i	$0.661206\pi$
$762$		0			0
$763$	2020.68	+	19294.1i	0.0958761	+	0.915457i
$764$		0			0
$765$	−12437.5	+	7101.58i	−0.587814	+	0.335632i
$766$		0			0
$767$			2740.54i			0.129016i
$768$		0			0
$769$	22927.3	−	13237.1i	1.07514	−	0.620731i	0.145557	−	0.989350i	$-0.453502\pi$
$769$	22927.3	−	13237.1i	1.07514	−	0.620731i	0.929581	+	0.368619i	$0.120169\pi$
$770$		0			0
$771$	−25128.4	−	25249.0i	−1.17377	−	1.17941i
$772$		0			0
$773$	−5624.70	−	9742.27i	−0.261716	−	0.453305i	0.704982	−	0.709225i	$-0.250955\pi$
$773$	−5624.70	−	9742.27i	−0.261716	−	0.453305i	−0.966698	+	0.255920i	$0.917622\pi$
$774$		0			0
$775$	−8643.05	−	4990.06i	−0.400603	−	0.231288i
$776$		0			0
$777$	−17499.9	−	2821.32i	−0.807985	−	0.130263i
$778$		0			0
$779$		−	21802.6i		−	1.00277i
$780$		0			0
$781$	30198.7			1.38361
$782$		0			0
$783$	−1525.27	+	396.974i	−0.0696152	+	0.0181184i
$784$		0			0
$785$	11412.9	+	6589.25i	0.518910	+	0.299593i
$786$		0			0
$787$	16774.4	+	9684.72i	0.759776	+	0.438657i	0.829215	−	0.558929i	$-0.188788\pi$
$787$	16774.4	+	9684.72i	0.759776	+	0.438657i	−0.0694391	+	0.997586i	$0.522121\pi$
$788$		0			0
$789$	−6530.36	+	6499.16i	−0.294660	+	0.293252i
$790$		0			0
$791$	−19642.5	+	2057.16i	−0.882942	+	0.0924707i
$792$		0			0
$793$	−8621.49	+	14932.9i	−0.386076	+	0.668703i
$794$		0			0
$795$	200.868	+	54.3384i	0.00896109	+	0.00242413i
$796$		0			0
$797$	−14722.8	−	25500.7i	−0.654341	−	1.13335i	−0.982059	−	0.188576i	$-0.939613\pi$
$797$	−14722.8	−	25500.7i	−0.654341	−	1.13335i	0.327718	−	0.944776i	$-0.393720\pi$
$798$		0			0
$799$	−1918.91	+	3323.66i	−0.0849640	+	0.147162i
$800$		0			0
$801$	37678.3	+	21994.9i	1.66205	+	0.970225i
$802$		0			0
$803$	10604.2	+	18367.0i	0.466021	+	0.807171i
$804$		0			0
$805$	713.669	−	1601.33i	0.0312466	−	0.0701112i
$806$		0			0
$807$	−8874.30	+	32804.9i	−0.387101	+	1.43096i
$808$		0			0
$809$	29159.7	−	16835.4i	1.26725	−	0.731645i	0.292780	−	0.956180i	$-0.405420\pi$
$809$	29159.7	−	16835.4i	1.26725	−	0.731645i	0.974466	+	0.224535i	$0.0720863\pi$
$810$		0			0
$811$			10173.1i			0.440477i	0.975446	+	0.220239i	$0.0706836\pi$
$811$			10173.1i			0.440477i	−0.975446	+	0.220239i	$0.929316\pi$
$812$		0			0
$813$	−7279.88	−	27431.5i	−0.314043	−	1.18335i
$814$		0			0
$815$	−3695.25	+	6400.37i	−0.158821	+	0.275086i
$816$		0			0
$817$	−25222.0	+	14561.9i	−1.08006	+	0.623570i
$818$		0			0
$819$	2246.24	+	22486.9i	0.0958362	+	0.959407i
$820$		0			0
$821$	37272.1	−	21519.1i	1.58442	−	0.914763i	0.590213	−	0.807247i	$-0.299044\pi$
$821$	37272.1	−	21519.1i	1.58442	−	0.914763i	0.994203	−	0.107516i	$-0.0342897\pi$
$822$		0			0
$823$	−7880.46	+	13649.3i	−0.333773	+	0.578112i	−0.983248	−	0.182271i	$-0.941655\pi$
$823$	−7880.46	+	13649.3i	−0.333773	+	0.578112i	0.649475	+	0.760383i	$0.274989\pi$
$824$		0			0
$825$	10750.2	−	10698.8i	0.453665	−	0.451498i
$826$		0			0
$827$			638.310i			0.0268394i	0.999910	+	0.0134197i	$0.00427176\pi$
$827$			638.310i			0.0268394i	−0.999910	+	0.0134197i	$0.995728\pi$
$828$		0			0
$829$	37757.3	−	21799.2i	1.58186	−	0.913289i	0.587275	−	0.809388i	$-0.300201\pi$
$829$	37757.3	−	21799.2i	1.58186	−	0.913289i	0.994588	−	0.103901i	$-0.0331324\pi$
$830$		0			0
$831$	21631.9	+	21735.7i	0.903009	+	0.907344i
$832$		0			0
$833$	−8438.59	+	25906.1i	−0.350996	+	1.07754i
$834$		0			0
$835$	11945.1	+	20689.6i	0.495064	+	0.857475i
$836$		0			0
$837$	−16852.4	+	4386.07i	−0.695941	+	0.181129i
$838$		0			0
$839$	18758.8	−	32491.2i	0.771903	−	1.33698i	−0.164616	−	0.986358i	$-0.552638\pi$
$839$	18758.8	−	32491.2i	0.771903	−	1.33698i	0.936519	−	0.350618i	$-0.114028\pi$
$840$		0			0
$841$	−12131.4	−	21012.2i	−0.497413	−	0.861544i
$842$		0			0
$843$	1747.14	+	6583.44i	0.0713817	+	0.268975i
$844$		0			0
$845$	−516.086	+	893.888i	−0.0210105	+	0.0363913i
$846$		0			0
$847$	−223.426	−	99.5747i	−0.00906377	−	0.00403947i
$848$		0			0
$849$	−11991.1	−	45183.9i	−0.484728	−	1.82651i
$850$		0			0
$851$	2261.24	+	1305.53i	0.0910861	+	0.0525886i
$852$		0			0
$853$	1305.69	+	753.838i	0.0524101	+	0.0302590i	0.525976	−	0.850499i	$-0.323700\pi$
$853$	1305.69	+	753.838i	0.0524101	+	0.0302590i	−0.473566	+	0.880758i	$0.657033\pi$
$854$		0			0
$855$	−8420.23	+	14424.3i	−0.336802	+	0.576960i
$856$		0			0
$857$	−23766.2			−0.947302			−0.473651	−	0.880713i	$-0.657064\pi$
$857$	−23766.2			−0.947302			−0.473651	+	0.880713i	$0.657064\pi$
$858$		0			0
$859$		−	31917.6i		−	1.26777i	−0.773428	−	0.633884i	$-0.781459\pi$
$859$		−	31917.6i		−	1.26777i	0.773428	−	0.633884i	$-0.218541\pi$
$860$		0			0
$861$	−14302.7	+	17562.8i	−0.566125	+	0.695168i
$862$		0			0
$863$	3568.67	+	2060.37i	0.140763	+	0.0812698i	0.568728	−	0.822526i	$-0.307436\pi$
$863$	3568.67	+	2060.37i	0.140763	+	0.0812698i	−0.427964	+	0.903796i	$0.640769\pi$
$864$		0			0
$865$	−2100.76	−	3638.62i	−0.0825757	−	0.143025i
$866$		0			0
$867$	−7014.84	+	1861.63i	−0.274783	+	0.0729230i
$868$		0			0
$869$	−16180.9	+	9342.05i	−0.631645	+	0.364680i
$870$		0			0
$871$		−	31485.0i		−	1.22483i
$872$		0			0
$873$	−2788.19	+	4776.32i	−0.108094	+	0.185171i
$874$		0			0
$875$	23203.7	+	10341.2i	0.896489	+	0.399540i
$876$		0			0
$877$	−33585.4			−1.29316			−0.646578	−	0.762848i	$-0.723800\pi$
$877$	−33585.4			−1.29316			−0.646578	+	0.762848i	$0.723800\pi$
$878$		0			0
$879$	4508.88	−	16667.6i	0.173016	−	0.639574i
$880$		0			0
$881$	−37119.8			−1.41952			−0.709760	−	0.704444i	$-0.751197\pi$
$881$	−37119.8			−1.41952			−0.709760	+	0.704444i	$0.751197\pi$
$882$		0			0
$883$	−45189.5			−1.72225			−0.861125	−	0.508394i	$-0.830240\pi$
$883$	−45189.5			−1.72225			−0.861125	+	0.508394i	$0.830240\pi$
$884$		0			0
$885$	2033.77	−	539.732i	0.0772481	−	0.0205004i
$886$		0			0
$887$	−6924.22			−0.262111			−0.131055	−	0.991375i	$-0.541837\pi$
$887$	−6924.22			−0.262111			−0.131055	+	0.991375i	$0.541837\pi$
$888$		0			0
$889$	−41840.2	−	18647.0i	−1.57849	−	0.703488i
$890$		0			0
$891$	253.468	−	26462.5i	0.00953031	−	0.994980i
$892$		0			0
$893$			4475.58i			0.167715i
$894$		0			0
$895$	3513.38	−	2028.45i	0.131217	−	0.0757583i
$896$		0			0
$897$	869.266	−	3213.35i	0.0323567	−	0.119610i
$898$		0			0
$899$	697.190	+	1207.57i	0.0258649	+	0.0447994i
$900$		0			0
$901$	412.538	+	238.179i	0.0152538	+	0.00880676i
$902$		0			0
$903$	29870.0	+	4815.63i	1.10079	+	0.177469i
$904$		0			0
$905$			21425.6i			0.786974i
$906$		0			0
$907$	−5207.01			−0.190624			−0.0953119	−	0.995447i	$-0.530385\pi$
$907$	−5207.01			−0.190624			−0.0953119	+	0.995447i	$0.530385\pi$
$908$		0			0
$909$	248.244	−	51835.3i	0.00905800	−	1.89139i
$910$		0			0
$911$	21011.8	+	12131.1i	0.764161	+	0.441188i	0.830788	−	0.556590i	$-0.187890\pi$
$911$	21011.8	+	12131.1i	0.764161	+	0.441188i	−0.0666269	+	0.997778i	$0.521224\pi$
$912$		0			0
$913$	−8685.55	−	5014.60i	−0.314841	−	0.181773i
$914$		0			0
$915$	12779.7	+	3457.14i	0.461732	+	0.124907i
$916$		0			0
$917$	−22243.4	−	9913.25i	−0.801027	−	0.356995i
$918$		0			0
$919$	16380.1	−	28371.1i	0.587953	−	1.01837i	−0.406547	−	0.913630i	$-0.633267\pi$
$919$	16380.1	−	28371.1i	0.587953	−	1.01837i	0.994500	−	0.104735i	$-0.0333995\pi$
$920$		0			0
$921$	−13854.5	+	13788.3i	−0.495679	+	0.493310i
$922$		0			0
$923$	18797.9	+	32558.9i	0.670358	+	1.16109i
$924$		0			0
$925$	−7405.20	+	12826.2i	−0.263223	+	0.455916i
$926$		0			0
$927$	14338.1	+	68.6661i	0.508008	+	0.00243289i
$928$		0			0
$929$	22646.3	+	39224.6i	0.799786	+	1.38527i	0.919755	+	0.392493i	$0.128387\pi$
$929$	22646.3	+	39224.6i	0.799786	+	1.38527i	−0.119969	+	0.992778i	$0.538279\pi$
$930$		0			0
$931$	6583.07	+	31084.0i	0.231742	+	1.09424i
$932$		0			0
$933$	−3521.66	+	934.593i	−0.123573	+	0.0327944i
$934$		0			0
$935$	−16676.2	+	9628.02i	−0.583284	+	0.336759i
$936$		0			0
$937$		−	26759.6i		−	0.932975i	−0.884528	−	0.466488i	$-0.845519\pi$
$937$		−	26759.6i		−	0.932975i	0.884528	−	0.466488i	$-0.154481\pi$
$938$		0			0
$939$	15692.2	+	4245.00i	0.545361	+	0.147530i
$940$		0			0
$941$	−17255.3	+	29887.1i	−0.597776	+	1.03538i	0.395373	+	0.918521i	$0.370615\pi$
$941$	−17255.3	+	29887.1i	−0.597776	+	1.03538i	−0.993149	+	0.116857i	$0.962718\pi$
$942$		0			0
$943$	2889.39	−	1668.19i	0.0997789	−	0.0576074i
$944$		0			0
$945$	16245.3	−	6095.60i	0.559216	−	0.209830i
$946$		0			0
$947$	44869.1	−	25905.2i	1.53965	−	0.888919i	0.540793	−	0.841155i	$-0.318124\pi$
$947$	44869.1	−	25905.2i	1.53965	−	0.888919i	0.998859	−	0.0477631i	$-0.0152093\pi$
$948$		0			0
$949$	−13201.7	+	22866.0i	−0.451575	+	0.782150i
$950$		0			0
$951$	13347.8	+	3610.82i	0.455135	+	0.123122i
$952$		0			0
$953$			49557.5i			1.68450i	0.539091	+	0.842248i	$0.318768\pi$
$953$			49557.5i			1.68450i	−0.539091	+	0.842248i	$0.681232\pi$
$954$		0			0
$955$	−14983.1	+	8650.50i	−0.507688	+	0.293114i
$956$		0			0
$957$	−2048.14	+	543.545i	−0.0691819	+	0.0183598i
$958$		0			0
$959$	−18005.1	+	40399.9i	−0.606272	+	1.36036i
$960$		0			0
$961$	−7192.41	−	12457.6i	−0.241429	−	0.418167i
$962$		0			0
$963$	−17323.3	+	29675.8i	−0.579685	+	0.993030i
$964$		0			0
$965$	−1871.21	+	3241.03i	−0.0624211	+	0.108117i
$966$		0			0
$967$	−6281.58	−	10880.0i	−0.208895	−	0.361818i	0.742471	−	0.669878i	$-0.233654\pi$
$967$	−6281.58	−	10880.0i	−0.208895	−	0.361818i	−0.951367	+	0.308060i	$0.900320\pi$
$968$		0			0
$969$	−27100.6	+	26971.2i	−0.898450	+	0.894158i
$970$		0			0
$971$	−13678.2	+	23691.4i	−0.452065	+	0.782999i	−0.998514	−	0.0544932i	$-0.982646\pi$
$971$	−13678.2	+	23691.4i	−0.452065	+	0.782999i	0.546450	+	0.837492i	$0.315979\pi$
$972$		0			0
$973$	−2952.01	+	309.165i	−0.0972632	+	0.0101864i
$974$		0			0
$975$	18226.7	+	4930.64i	0.598689	+	0.161956i
$976$		0			0
$977$	11803.2	+	6814.59i	0.386508	+	0.223151i	0.680646	−	0.732612i	$-0.261699\pi$
$977$	11803.2	+	6814.59i	0.386508	+	0.223151i	−0.294138	+	0.955763i	$0.595033\pi$
$978$		0			0
$979$	50799.4	+	29329.1i	1.65838	+	0.957468i
$980$		0			0
$981$	24560.4	−	14023.5i	0.799340	−	0.456409i
$982$		0			0
$983$	−32007.8			−1.03854			−0.519272	−	0.854609i	$-0.673797\pi$
$983$	−32007.8			−1.03854			−0.519272	+	0.854609i	$0.673797\pi$
$984$		0			0
$985$			34163.0i			1.10510i
$986$		0			0
$987$	2936.02	−	3605.26i	0.0946854	−	0.116268i
$988$		0			0
$989$	−3859.64	−	2228.37i	−0.124095	−	0.0716460i
$990$		0			0
$991$	9974.68	+	17276.7i	0.319734	+	0.553795i	0.980432	−	0.196856i	$-0.0630731\pi$
$991$	9974.68	+	17276.7i	0.319734	+	0.553795i	−0.660699	+	0.750651i	$0.729740\pi$
$992$		0			0
$993$	−2845.43	+	10518.5i	−0.0909334	+	0.336147i
$994$		0			0
$995$	132.336	−	76.4042i	0.00421642	−	0.00243435i
$996$		0			0
$997$			2407.75i			0.0764838i	0.999269	+	0.0382419i	$0.0121757\pi$
$997$			2407.75i			0.0764838i	−0.999269	+	0.0382419i	$0.987824\pi$
$998$		0			0
$999$	6508.88	+	25008.7i	0.206138	+	0.792033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.bm.a.173.19	yes	48
3.2	odd	2		756.4.bm.a.89.9		48
7.3	odd	6		252.4.w.a.101.10	yes	48
9.4	even	3		756.4.w.a.341.9		48
9.5	odd	6		252.4.w.a.5.10	✓	48
21.17	even	6		756.4.w.a.521.9		48
63.31	odd	6		756.4.bm.a.17.9		48
63.59	even	6	inner	252.4.bm.a.185.19	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.10	✓	48	9.5	odd	6
252.4.w.a.101.10	yes	48	7.3	odd	6
252.4.bm.a.173.19	yes	48	1.1	even	1	trivial
252.4.bm.a.185.19	yes	48	63.59	even	6	inner
756.4.w.a.341.9		48	9.4	even	3
756.4.w.a.521.9		48	21.17	even	6
756.4.bm.a.17.9		48	63.31	odd	6
756.4.bm.a.89.9		48	3.2	odd	2

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.66543 + 3.68302i) q^{3} +6.67787 q^{5} +(-16.9163 - 7.53913i) q^{7} +(-0.129304 + 26.9997i) q^{9} +O(q^{10})\)	\(q+(3.66543 + 3.68302i) q^{3} +6.67787 q^{5} +(-16.9163 - 7.53913i) q^{7} +(-0.129304 + 26.9997i) q^{9} +36.3014i q^{11} +(-39.1385 + 22.5966i) q^{13} +(24.4772 + 24.5947i) q^{15} +(39.7169 + 68.7917i) q^{17} +(80.2233 + 46.3169i) q^{19} +(-34.2387 - 89.9373i) q^{21} +14.1755i q^{23} -80.4061 q^{25} +(-99.9144 + 98.4891i) q^{27} +(9.72891 + 5.61699i) q^{29} +(107.492 + 62.0608i) q^{31} +(-133.699 + 133.060i) q^{33} +(-112.965 - 50.3453i) q^{35} +(92.0975 - 159.518i) q^{37} +(-226.683 - 61.3218i) q^{39} +(-117.681 - 203.830i) q^{41} +(-157.199 + 272.276i) q^{43} +(-0.863474 + 180.300i) q^{45} +(24.1574 + 41.8418i) q^{47} +(229.323 + 255.068i) q^{49} +(-107.782 + 398.429i) q^{51} +(5.19348 - 2.99846i) q^{53} +242.416i q^{55} +(123.466 + 465.235i) q^{57} +(30.3202 - 52.5161i) q^{59} +(330.422 - 190.769i) q^{61} +(205.741 - 455.760i) q^{63} +(-261.362 + 150.897i) q^{65} +(-348.337 + 603.337i) q^{67} +(-52.2086 + 51.9592i) q^{69} -831.889i q^{71} +(505.959 - 292.116i) q^{73} +(-294.722 - 296.137i) q^{75} +(273.681 - 614.086i) q^{77} +(257.347 + 445.737i) q^{79} +(-728.967 - 6.98232i) q^{81} +(-138.138 + 239.262i) q^{83} +(265.224 + 459.382i) q^{85} +(14.9731 + 56.4205i) q^{87} +(807.932 - 1399.38i) q^{89} +(832.439 - 87.1815i) q^{91} +(165.434 + 623.376i) q^{93} +(535.720 + 309.298i) q^{95} +(177.393 + 102.418i) q^{97} +(-980.127 - 4.69391i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 - 30 * q^9	\( 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more