LMFDB - Embedded newform 252.4.w.a.5.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(5,252)]

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, 5, 5]))

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

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

chi := DirichletCharacter("252.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.w (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			5.10
Character	$\chi$	$=$	252.5
Dual form			252.4.w.a.101.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35688 - 5.01586i) q^{3} +(3.33893 + 5.78320i) q^{5} +(14.9872 - 10.8804i) q^{7} +(-23.3178 + 13.6118i) q^{9} +O(q^{10})$	\(q+(-1.35688 - 5.01586i) q^{3} +(3.33893 + 5.78320i) q^{5} +(14.9872 - 10.8804i) q^{7} +(-23.3178 + 13.6118i) q^{9} +(31.4379 + 18.1507i) q^{11} +(39.1385 + 22.5966i) q^{13} +(24.4772 - 24.5947i) q^{15} +(-39.7169 - 68.7917i) q^{17} +(80.2233 + 46.3169i) q^{19} +(-74.9104 - 60.4105i) q^{21} +(-12.2763 + 7.08774i) q^{23} +(40.2030 - 69.6337i) q^{25} +(99.9144 + 98.4891i) q^{27} +(9.72891 - 5.61699i) q^{29} -124.122i q^{31} +(48.3840 - 182.317i) q^{33} +(112.965 + 50.3453i) q^{35} +(92.0975 - 159.518i) q^{37} +(60.2355 - 226.974i) q^{39} +(117.681 - 203.830i) q^{41} +(-157.199 - 272.276i) q^{43} +(-156.576 - 89.4024i) q^{45} +48.3147 q^{47} +(106.234 - 326.134i) q^{49} +(-291.159 + 292.557i) q^{51} +(-5.19348 + 2.99846i) q^{53} +242.416i q^{55} +(123.466 - 465.235i) q^{57} +60.6403 q^{59} +381.538i q^{61} +(-201.367 + 457.710i) q^{63} +301.795i q^{65} +696.673 q^{67} +(52.2086 + 51.9592i) q^{69} +831.889i q^{71} +(505.959 - 292.116i) q^{73} +(-403.824 - 107.168i) q^{75} +(668.654 - 70.0284i) q^{77} -514.693 q^{79} +(358.436 - 634.795i) q^{81} +(138.138 + 239.262i) q^{83} +(265.224 - 459.382i) q^{85} +(-41.3750 - 41.1773i) q^{87} +(-807.932 + 1399.38i) q^{89} +(832.439 - 87.1815i) q^{91} +(-622.577 + 168.418i) q^{93} +618.597i q^{95} +(-177.393 + 102.418i) q^{97} +(-980.127 + 4.69391i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 12 * q^9	$ 48 q + 6 q^{7} + 12 q^{9} + 12 q^{11} - 36 q^{13} + 66 q^{15} - 72 q^{17} + 24 q^{21} + 30 q^{23} - 600 q^{25} - 396 q^{27} + 42 q^{29} + 390 q^{35} + 84 q^{37} - 840 q^{39} - 618 q^{41} - 42 q^{43} + 366 q^{45} + 396 q^{47} + 318 q^{49} - 738 q^{51} - 1620 q^{53} + 492 q^{57} + 1500 q^{59} + 672 q^{63} - 588 q^{67} - 924 q^{69} + 564 q^{75} - 2472 q^{77} + 1608 q^{79} + 2592 q^{81} - 360 q^{85} + 2640 q^{87} + 1722 q^{89} + 540 q^{91} + 660 q^{93} - 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 12 * q^9 + 12 * q^11 - 36 * q^13 + 66 * q^15 - 72 * q^17 + 24 * q^21 + 30 * q^23 - 600 * q^25 - 396 * q^27 + 42 * q^29 + 390 * q^35 + 84 * q^37 - 840 * q^39 - 618 * q^41 - 42 * q^43 + 366 * q^45 + 396 * q^47 + 318 * q^49 - 738 * q^51 - 1620 * q^53 + 492 * q^57 + 1500 * q^59 + 672 * q^63 - 588 * q^67 - 924 * q^69 + 564 * q^75 - 2472 * q^77 + 1608 * q^79 + 2592 * q^81 - 360 * q^85 + 2640 * q^87 + 1722 * q^89 + 540 * q^91 + 660 * q^93 - 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.35688	−	5.01586i	−0.261131	−	0.965303i
$3$	−1.35688	−	5.01586i	−0.261131	−	0.965303i
$4$		0			0
$5$	3.33893	+	5.78320i	0.298643	+	0.517266i	0.975826	−	0.218550i	$-0.0701325\pi$
$5$	3.33893	+	5.78320i	0.298643	+	0.517266i	−0.677182	+	0.735815i	$0.736799\pi$
$6$		0			0
$7$	14.9872	−	10.8804i	0.809234	−	0.587486i
$7$	14.9872	−	10.8804i	0.809234	−	0.587486i
$8$		0			0
$9$	−23.3178	+	13.6118i	−0.863621	+	0.504142i
$10$		0			0
$11$	31.4379	+	18.1507i	0.861718	+	0.497513i	0.864587	−	0.502483i	$-0.167580\pi$
$11$	31.4379	+	18.1507i	0.861718	+	0.497513i	−0.00286934	+	0.999996i	$0.500913\pi$
$12$		0			0
$13$	39.1385	+	22.5966i	0.835006	+	0.482091i	0.855564	−	0.517698i	$-0.173211\pi$
$13$	39.1385	+	22.5966i	0.835006	+	0.482091i	−0.0205576	+	0.999789i	$0.506544\pi$
$14$		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	$-0.974912\pi$
$17$	−39.7169	−	68.7917i	−0.566634	−	0.981438i	0.430262	−	0.902704i	$-0.358421\pi$
$18$		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
$21$	−74.9104	−	60.4105i	−0.778419	−	0.627746i
$22$		0			0
$23$	−12.2763	+	7.08774i	−0.111295	+	0.0642564i	−0.554614	−	0.832108i	$-0.687134\pi$
$23$	−12.2763	+	7.08774i	−0.111295	+	0.0642564i	0.443319	+	0.896364i	$0.353801\pi$
$24$		0			0
$25$	40.2030	−	69.6337i	0.321624	−	0.557070i
$26$		0			0
$27$	99.9144	+	98.4891i	0.712168	+	0.702009i
$28$		0			0
$29$	9.72891	−	5.61699i	0.0622970	−	0.0359672i	−0.468528	−	0.883449i	$-0.655215\pi$
$29$	9.72891	−	5.61699i	0.0622970	−	0.0359672i	0.530825	+	0.847481i	$0.321882\pi$
$30$		0			0
$31$		−	124.122i		−	0.719126i	−0.933121	−	0.359563i	$-0.882926\pi$
$31$		−	124.122i		−	0.719126i	0.933121	−	0.359563i	$-0.117074\pi$
$32$		0			0
$33$	48.3840	−	182.317i	0.255230	−	0.961735i
$34$		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
$39$	60.2355	−	226.974i	0.247318	−	0.931923i
$40$		0			0
$41$	117.681	−	203.830i	0.448262	−	0.776413i	−0.550011	−	0.835158i	$-0.685376\pi$
$41$	117.681	−	203.830i	0.448262	−	0.776413i	0.998273	+	0.0587446i	$0.0187098\pi$
$42$		0			0
$43$	−157.199	−	272.276i	−0.557502	−	0.965621i	−0.997704	−	0.0677226i	$-0.978427\pi$
$43$	−157.199	−	272.276i	−0.557502	−	0.965621i	0.440203	−	0.897898i	$-0.354907\pi$
$44$		0			0
$45$	−156.576	−	89.4024i	−0.518690	−	0.296163i
$46$		0			0
$47$	48.3147			0.149945			0.0749727	−	0.997186i	$-0.476113\pi$
$47$	48.3147			0.149945			0.0749727	+	0.997186i	$0.476113\pi$
$48$		0			0
$49$	106.234	−	326.134i	0.309720	−	0.950828i
$50$		0			0
$51$	−291.159	+	292.557i	−0.799420	+	0.803257i
$52$		0			0
$53$	−5.19348	+	2.99846i	−0.0134600	+	0.00777113i	−0.506715	−	0.862114i	$-0.669140\pi$
$53$	−5.19348	+	2.99846i	−0.0134600	+	0.00777113i	0.493255	+	0.869885i	$0.335807\pi$
$54$		0			0
$55$			242.416i			0.594316i
$56$		0			0
$57$	123.466	−	465.235i	0.286903	−	1.08109i
$58$		0			0
$59$	60.6403			0.133808			0.0669042	−	0.997759i	$-0.478688\pi$
$59$	60.6403			0.133808			0.0669042	+	0.997759i	$0.478688\pi$
$60$		0			0
$61$			381.538i			0.800836i	0.916333	+	0.400418i	$0.131135\pi$
$61$			381.538i			0.800836i	−0.916333	+	0.400418i	$0.868865\pi$
$62$		0			0
$63$	−201.367	+	457.710i	−0.402696	+	0.915334i
$64$		0			0
$65$			301.795i			0.575893i
$66$		0			0
$67$	696.673			1.27033			0.635166	−	0.772376i	$-0.280932\pi$
$67$	696.673			1.27033			0.635166	+	0.772376i	$0.280932\pi$
$68$		0			0
$69$	52.2086	+	51.9592i	0.0910895	+	0.0906544i
$70$		0			0
$71$			831.889i			1.39052i	0.718757	+	0.695261i	$0.244711\pi$
$71$			831.889i			1.39052i	−0.718757	+	0.695261i	$0.755289\pi$
$72$		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
$75$	−403.824	−	107.168i	−0.621727	−	0.164997i
$76$		0			0
$77$	668.654	−	70.0284i	0.989614	−	0.103643i
$78$		0			0
$79$	−514.693			−0.733007			−0.366503	−	0.930417i	$-0.619445\pi$
$79$	−514.693			−0.733007			−0.366503	+	0.930417i	$0.619445\pi$
$80$		0			0
$81$	358.436	−	634.795i	0.491682	−	0.870775i
$82$		0			0
$83$	138.138	+	239.262i	0.182682	+	0.316415i	0.942793	−	0.333379i	$-0.108189\pi$
$83$	138.138	+	239.262i	0.182682	+	0.316415i	−0.760111	+	0.649793i	$0.774855\pi$
$84$		0			0
$85$	265.224	−	459.382i	0.338443	−	0.586200i
$86$		0			0
$87$	−41.3750	−	41.1773i	−0.0509870	−	0.0507434i
$88$		0			0
$89$	−807.932	+	1399.38i	−0.962254	+	1.66667i	−0.245436	+	0.969413i	$0.578931\pi$
$89$	−807.932	+	1399.38i	−0.962254	+	1.66667i	−0.716818	+	0.697260i	$0.754402\pi$
$90$		0			0
$91$	832.439	−	87.1815i	0.958937	−	0.100430i
$92$		0			0
$93$	−622.577	+	168.418i	−0.694174	+	0.187786i
$94$		0			0
$95$			618.597i			0.668070i
$96$		0			0
$97$	−177.393	+	102.418i	−0.185686	+	0.107206i	−0.589961	−	0.807431i	$-0.700857\pi$
$97$	−177.393	+	102.418i	−0.185686	+	0.107206i	0.404275	+	0.914637i	$0.367524\pi$
$98$		0			0
$99$	−980.127	+	4.69391i	−0.995015	+	0.00476521i
$100$		0			0
$101$	−959.925	+	1662.64i	−0.945704	+	1.63801i	−0.191368	+	0.981518i	$0.561292\pi$
$101$	−959.925	+	1662.64i	−0.945704	+	1.63801i	−0.754336	+	0.656489i	$0.772041\pi$
$102$		0			0
$103$	−459.898	+	265.522i	−0.439953	+	0.254007i	−0.703578	−	0.710618i	$-0.748415\pi$
$103$	−459.898	+	265.522i	−0.439953	+	0.254007i	0.263625	+	0.964625i	$0.415082\pi$
$104$		0			0
$105$	99.2455	−	634.929i	0.0922417	−	0.590121i
$106$		0			0
$107$	−1102.16	−	636.334i	−0.995795	−	0.574922i	−0.0887933	−	0.996050i	$-0.528301\pi$
$107$	−1102.16	−	636.334i	−0.995795	−	0.574922i	−0.907001	+	0.421128i	$0.861634\pi$
$108$		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	0.832458	−	0.554088i	$-0.186933\pi$
$113$	923.526	+	533.198i	0.768832	+	0.443885i	−0.0636257	+	0.997974i	$0.520266\pi$
$114$		0			0
$115$	−81.9797	−	47.3310i	−0.0664752	−	0.0383795i
$116$		0			0
$117$	−1220.20	+	5.84366i	−0.964171	+	0.00461749i
$118$		0			0
$119$	−1343.73	−	598.862i	−1.03512	−	0.461324i
$120$		0			0
$121$	−6.60387	−	11.4382i	−0.00496158	−	0.00859371i
$122$		0			0
$123$	−1182.06	−	313.701i	−0.866529	−	0.229963i
$124$		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
$129$	−1152.40	+	1157.93i	−0.786536	+	0.790312i
$130$		0			0
$131$	657.454	+	1138.74i	0.438489	+	0.759485i	0.997573	−	0.0696261i	$-0.0221806\pi$
$131$	657.454	+	1138.74i	0.438489	+	0.759485i	−0.559085	+	0.829111i	$0.688847\pi$
$132$		0			0
$133$	1706.27	−	178.698i	1.11242	−	0.116505i
$134$		0			0
$135$	−235.975	+	906.674i	−0.150441	+	0.578030i
$136$		0			0
$137$	−2068.26	−	1194.11i	−1.28981	−	0.744670i	−0.311187	−	0.950349i	$-0.600726\pi$
$137$	−2068.26	−	1194.11i	−1.28981	−	0.744670i	−0.978620	+	0.205679i	$0.934060\pi$
$138$		0			0
$139$	−138.794	−	80.1326i	−0.0846931	−	0.0488976i	0.457055	−	0.889438i	$-0.348904\pi$
$139$	−138.794	−	80.1326i	−0.0846931	−	0.0488976i	−0.541748	+	0.840541i	$0.682237\pi$
$140$		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
$147$	−1779.99	−	90.3320i	−0.998715	−	0.0506834i
$148$		0			0
$149$	2839.71	−	1639.51i	1.56133	−	0.901434i	0.564207	−	0.825634i	$-0.309182\pi$
$149$	2839.71	−	1639.51i	1.56133	−	0.901434i	0.997123	−	0.0758003i	$-0.0241512\pi$
$150$		0			0
$151$	−1139.60	+	1973.85i	−0.614169	+	1.06377i	0.376360	+	0.926473i	$0.377176\pi$
$151$	−1139.60	+	1973.85i	−0.614169	+	1.06377i	−0.990530	+	0.137299i	$0.956158\pi$
$152$		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
$157$		−	1973.46i		−	1.00318i	−0.865106	−	0.501589i	$-0.832749\pi$
$157$		−	1973.46i		−	1.00318i	0.865106	−	0.501589i	$-0.167251\pi$
$158$		0			0
$159$	22.0868	+	21.9812i	0.0110163	+	0.0109637i
$160$		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
$165$	1215.93	−	328.929i	0.573695	−	0.155194i
$166$		0			0
$167$	−1788.76	+	3098.23i	−0.828854	+	1.43562i	0.0700839	+	0.997541i	$0.477673\pi$
$167$	−1788.76	+	3098.23i	−0.828854	+	1.43562i	−0.898938	+	0.438076i	$0.855660\pi$
$168$		0			0
$169$	−77.2831	−	133.858i	−0.0351767	−	0.0609277i
$170$		0			0
$171$	−2501.09	+	11.9779i	−1.11850	+	0.00535657i
$172$		0			0
$173$	−629.171			−0.276503			−0.138251	−	0.990397i	$-0.544148\pi$
$173$	−629.171			−0.276503			−0.138251	+	0.990397i	$0.544148\pi$
$174$		0			0
$175$	−155.110	−	1481.04i	−0.0670011	−	0.639750i
$176$		0			0
$177$	−82.2815	−	304.164i	−0.0349416	−	0.129166i
$178$		0			0
$179$	−526.123	+	303.757i	−0.219689	+	0.126837i	−0.605806	−	0.795612i	$-0.707149\pi$
$179$	−526.123	+	303.757i	−0.219689	+	0.126837i	0.386117	+	0.922450i	$0.373816\pi$
$180$		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
$185$	1230.03			0.488831
$186$		0			0
$187$		−	2883.56i		−	1.12763i
$188$		0			0
$189$	2569.04	+	388.971i	0.988731	+	0.149701i
$190$		0			0
$191$			2590.80i			0.981484i	0.871305	+	0.490742i	$0.163274\pi$
$191$			2590.80i			0.981484i	−0.871305	+	0.490742i	$0.836726\pi$
$192$		0			0
$193$	560.421			0.209015			0.104508	−	0.994524i	$-0.466673\pi$
$193$	560.421			0.209015			0.104508	+	0.994524i	$0.466673\pi$
$194$		0			0
$195$	1513.76	−	409.499i	0.555912	−	0.150384i
$196$		0			0
$197$		−	5115.86i		−	1.85020i	−0.379722	−	0.925101i	$-0.623980\pi$
$197$		−	5115.86i		−	1.85020i	0.379722	−	0.925101i	$-0.376020\pi$
$198$		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
$201$	−945.301	−	3494.42i	−0.331723	−	1.22626i
$202$		0			0
$203$	84.6944	−	190.038i	0.0292827	−	0.0657045i
$204$		0			0
$205$	1571.72			0.535482
$206$		0			0
$207$	189.779	−	332.374i	0.0637226	−	0.111602i
$208$		0			0
$209$	1681.37	+	2912.22i	0.556473	+	0.963839i
$210$		0			0
$211$	2497.03	−	4324.99i	0.814705	−	1.41111i	−0.0948347	−	0.995493i	$-0.530232\pi$
$211$	2497.03	−	4324.99i	0.814705	−	1.41111i	0.909540	−	0.415617i	$-0.136434\pi$
$212$		0			0
$213$	4172.64	−	1128.77i	1.34228	−	0.363109i
$214$		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
$219$	−2151.74	−	2141.46i	−0.663931	−	0.660759i
$220$		0			0
$221$		−	3589.88i		−	1.09268i
$222$		0			0
$223$	2700.86	−	1559.34i	0.811043	−	0.468256i	−0.0362748	−	0.999342i	$-0.511549\pi$
$223$	2700.86	−	1559.34i	0.811043	−	0.468256i	0.847318	+	0.531086i	$0.178216\pi$
$224$		0			0
$225$	10.3968	+	2170.94i	0.00308053	+	0.643241i
$226$		0			0
$227$	−2039.20	+	3531.99i	−0.596239	+	1.03272i	0.397131	+	0.917762i	$0.370006\pi$
$227$	−2039.20	+	3531.99i	−0.596239	+	1.03272i	−0.993371	+	0.114955i	$0.963328\pi$
$228$		0			0
$229$	−2370.50	+	1368.61i	−0.684048	+	0.394935i	−0.801378	−	0.598158i	$-0.795900\pi$
$229$	−2370.50	+	1368.61i	−0.684048	+	0.394935i	0.117331	+	0.993093i	$0.462566\pi$
$230$		0			0
$231$	−1258.53	−	3258.86i	−0.358465	−	0.928213i
$232$		0			0
$233$	−527.258	−	304.412i	−0.148248	−	0.0855911i	0.424041	−	0.905643i	$-0.360611\pi$
$233$	−527.258	−	304.412i	−0.148248	−	0.0855911i	−0.572289	+	0.820052i	$0.693945\pi$
$234$		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	0.987188	−	0.159563i	$-0.0510085\pi$
$239$	4960.69	+	2864.06i	1.34260	+	0.775148i	0.355408	+	0.934711i	$0.384342\pi$
$240$		0			0
$241$	−1093.02	−	631.056i	−0.292148	−	0.168672i	0.346762	−	0.937953i	$-0.387281\pi$
$241$	−1093.02	−	631.056i	−0.292148	−	0.168672i	−0.638910	+	0.769281i	$0.720614\pi$
$242$		0			0
$243$	−3670.40	−	936.529i	−0.968955	−	0.247236i
$244$		0			0
$245$	2240.81	−	474.566i	0.584326	−	0.123751i
$246$		0			0
$247$	2093.21	+	3625.55i	0.539223	+	0.933961i
$248$		0			0
$249$	1012.67	−	1017.53i	0.257732	−	0.258969i
$250$		0			0
$251$	−4619.76			−1.16174			−0.580869	−	0.813997i	$-0.697287\pi$
$251$	−4619.76			−1.16174			−0.580869	+	0.813997i	$0.697287\pi$
$252$		0			0
$253$	−514.590			−0.127874
$254$		0			0
$255$	−2664.08	−	707.004i	−0.654239	−	0.173625i
$256$		0			0
$257$	−3427.76	−	5937.06i	−0.831976	−	1.44103i	−0.896469	−	0.443107i	$-0.853876\pi$
$257$	−3427.76	−	5937.06i	−0.831976	−	1.44103i	0.0644924	−	0.997918i	$-0.479457\pi$
$258$		0			0
$259$	−355.327	−	3392.78i	−0.0852470	−	0.813967i
$260$		0			0
$261$	−150.399	+	263.404i	−0.0356684	+	0.0624686i
$262$		0			0
$263$	1535.55	+	886.549i	0.360022	+	0.207859i	0.669091	−	0.743181i	$-0.266684\pi$
$263$	1535.55	+	886.549i	0.360022	+	0.207859i	−0.309068	+	0.951040i	$0.600017\pi$
$264$		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	$-0.900924\pi$
$269$	−3270.12	−	5664.01i	−0.741200	−	1.28380i	0.210750	−	0.977540i	$-0.432409\pi$
$270$		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
$273$	−1566.81	−	4057.10i	−0.347354	−	0.899440i
$274$		0			0
$275$	2527.80	−	1459.43i	0.554299	−	0.320024i
$276$		0			0
$277$	−2950.80	+	5110.93i	−0.640058	+	1.10861i	0.345361	+	0.938470i	$0.387757\pi$
$277$	−2950.80	+	5110.93i	−0.640058	+	1.10861i	−0.985419	+	0.170144i	$0.945577\pi$
$278$		0			0
$279$	1689.52	+	2894.24i	0.362541	+	0.621052i
$280$		0			0
$281$	1135.22	−	655.420i	0.241002	−	0.139143i	−0.374635	−	0.927172i	$-0.622232\pi$
$281$	1135.22	−	655.420i	0.241002	−	0.139143i	0.615637	+	0.788030i	$0.288899\pi$
$282$		0			0
$283$			8996.65i			1.88974i	0.327451	+	0.944868i	$0.393811\pi$
$283$			8996.65i			1.88974i	−0.327451	+	0.944868i	$0.606189\pi$
$284$		0			0
$285$	3102.80	−	839.360i	0.644891	−	0.174454i
$286$		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
$291$	754.416	+	750.811i	0.151975	+	0.151249i
$292$		0			0
$293$	1661.49	−	2877.79i	0.331281	−	0.573796i	−0.651482	−	0.758664i	$-0.725852\pi$
$293$	1661.49	−	2877.79i	0.331281	−	0.573796i	0.982763	+	0.184868i	$0.0591858\pi$
$294$		0			0
$295$	202.474	+	350.695i	0.0399610	+	0.0692145i
$296$		0			0
$297$	1353.46	+	4909.81i	0.264429	+	0.959247i
$298$		0			0
$299$	−640.637			−0.123910
$300$		0			0
$301$	−5318.44	−	2370.28i	−1.01844	−	0.453889i
$302$		0			0
$303$	9642.07	+	2558.85i	1.82813	+	0.485156i
$304$		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
$311$	−701.204			−0.127851			−0.0639254	−	0.997955i	$-0.520362\pi$
$311$	−701.204			−0.127851			−0.0639254	+	0.997955i	$0.520362\pi$
$312$		0			0
$313$			3128.51i			0.564964i	0.959273	+	0.282482i	$0.0911577\pi$
$313$			3128.51i			0.564964i	−0.959273	+	0.282482i	$0.908842\pi$
$314$		0			0
$315$	−3319.38	+	363.719i	−0.593733	+	0.0650579i
$316$		0			0
$317$		−	2661.12i		−	0.471494i	−0.971814	−	0.235747i	$-0.924246\pi$
$317$		−	2661.12i		−	0.471494i	0.971814	−	0.235747i	$-0.0757537\pi$
$318$		0			0
$319$	407.809			0.0715766
$320$		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
$327$	−3839.47	+	3857.90i	−0.649306	+	0.652423i
$328$		0			0
$329$	724.104	−	525.683i	0.121341	−	0.0880908i
$330$		0			0
$331$	−2097.04			−0.348229			−0.174114	−	0.984725i	$-0.555706\pi$
$331$	−2097.04			−0.348229			−0.174114	+	0.984725i	$0.555706\pi$
$332$		0			0
$333$	23.8171	+	4973.21i	0.00391943	+	0.818409i
$334$		0			0
$335$	2326.15	+	4029.01i	0.379376	+	0.657099i
$336$		0			0
$337$	−4125.58	+	7145.72i	−0.666869	+	1.15505i	0.311907	+	0.950113i	$0.399032\pi$
$337$	−4125.58	+	7145.72i	−0.666869	+	1.15505i	−0.978775	+	0.204937i	$0.934301\pi$
$338$		0			0
$339$	1421.34	−	5355.76i	0.227718	−	0.858069i
$340$		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
$345$	−126.169	+	475.421i	−0.0196891	+	0.0741908i
$346$		0			0
$347$			3761.04i			0.581853i	0.956745	+	0.290926i	$0.0939635\pi$
$347$			3761.04i			0.581853i	−0.956745	+	0.290926i	$0.906036\pi$
$348$		0			0
$349$	−4993.70	+	2883.12i	−0.765922	+	0.442205i	−0.831418	−	0.555647i	$-0.812470\pi$
$349$	−4993.70	+	2883.12i	−0.765922	+	0.442205i	0.0654958	+	0.997853i	$0.479137\pi$
$350$		0			0
$351$	1684.98	+	6112.45i	0.256232	+	0.929512i
$352$		0			0
$353$	−5546.97	+	9607.63i	−0.836360	+	1.44862i	0.0565575	+	0.998399i	$0.481988\pi$
$353$	−5546.97	+	9607.63i	−0.836360	+	1.44862i	−0.892918	+	0.450219i	$0.851346\pi$
$354$		0			0
$355$	−4810.98	+	2777.62i	−0.719269	+	0.415270i
$356$		0			0
$357$	−1180.53	+	7552.54i	−0.175015	+	1.11967i
$358$		0			0
$359$	−5406.80	−	3121.62i	−0.794874	−	0.458921i	0.0468016	−	0.998904i	$-0.485097\pi$
$359$	−5406.80	−	3121.62i	−0.794874	−	0.458921i	−0.841676	+	0.539983i	$0.818430\pi$
$360$		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
$367$	6495.39	+	3750.11i	0.923860	+	0.533391i	0.884864	−	0.465849i	$-0.154251\pi$
$367$	6495.39	+	3750.11i	0.923860	+	0.533391i	0.0389954	+	0.999239i	$0.487584\pi$
$368$		0			0
$369$	30.4333	+	6354.72i	0.00429348	+	0.896514i
$370$		0			0
$371$	−45.2115	+	101.446i	−0.00632686	+	0.0141962i
$372$		0			0
$373$	218.349	+	378.192i	0.0303102	+	0.0524987i	0.880783	−	0.473521i	$-0.157017\pi$
$373$	218.349	+	378.192i	0.0303102	+	0.0524987i	−0.850472	+	0.526020i	$0.823684\pi$
$374$		0			0
$375$	−1861.20	−	6880.13i	−0.256298	−	0.947436i
$376$		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
$381$	−3356.05	−	12406.1i	−0.451275	−	1.66819i
$382$		0			0
$383$	2152.43	+	3728.12i	0.287164	+	0.497383i	0.973132	−	0.230249i	$-0.0739541\pi$
$383$	2152.43	+	3728.12i	0.287164	+	0.497383i	−0.685967	+	0.727632i	$0.740621\pi$
$384$		0			0
$385$	2637.58	+	3633.15i	0.349152	+	0.480941i
$386$		0			0
$387$	7371.69	+	4209.11i	0.968280	+	0.552871i
$388$		0			0
$389$	−11653.1	−	6727.91i	−1.51885	−	0.876911i	−0.999754	−	0.0221983i	$-0.992933\pi$
$389$	−11653.1	−	6727.91i	−1.51885	−	0.876911i	−0.519101	−	0.854713i	$-0.673733\pi$
$390$		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
$399$	−3211.53	−	8315.95i	−0.402951	−	1.04340i
$400$		0			0
$401$	−5061.21	+	2922.09i	−0.630286	+	0.363896i	−0.780863	−	0.624702i	$-0.785220\pi$
$401$	−5061.21	+	2922.09i	−0.630286	+	0.363896i	0.150577	+	0.988598i	$0.451887\pi$
$402$		0			0
$403$	2804.73	−	4857.94i	0.346684	−	0.600474i
$404$		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
$409$			6830.20i			0.825750i	0.910788	+	0.412875i	$0.135475\pi$
$409$			6830.20i			0.825750i	−0.910788	+	0.412875i	$0.864525\pi$
$410$		0			0
$411$	−3183.12	+	11994.4i	−0.382024	+	1.43951i
$412$		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
$417$	−213.608	+	804.901i	−0.0250850	+	0.0945232i
$418$		0			0
$419$	4104.58	−	7109.34i	0.478572	−	0.828912i	−0.521126	−	0.853480i	$-0.674488\pi$
$419$	4104.58	−	7109.34i	0.478572	−	0.828912i	0.999698	+	0.0245683i	$0.00782111\pi$
$420$		0			0
$421$	1540.67	+	2668.52i	0.178356	+	0.308921i	0.941317	−	0.337523i	$-0.109589\pi$
$421$	1540.67	+	2668.52i	0.178356	+	0.308921i	−0.762962	+	0.646444i	$0.776256\pi$
$422$		0			0
$423$	−1126.59	+	657.652i	−0.129496	+	0.0755937i
$424$		0			0
$425$	−6386.96			−0.728972
$426$		0			0
$427$	4151.29	+	5718.20i	0.470480	+	0.648064i
$428$		0			0
$429$	6013.43	−	6042.29i	0.676762	−	0.680011i
$430$		0			0
$431$	−1575.95	+	909.876i	−0.176127	+	0.101687i	−0.585472	−	0.810693i	$-0.699091\pi$
$431$	−1575.95	+	909.876i	−0.176127	+	0.101687i	0.409345	+	0.912380i	$0.365757\pi$
$432$		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
$437$	−1313.13			−0.143743
$438$		0			0
$439$		−	9243.99i		−	1.00499i	−0.864579	−	0.502496i	$-0.832415\pi$
$439$		−	9243.99i		−	1.00499i	0.864579	−	0.502496i	$-0.167585\pi$
$440$		0			0
$441$	1962.14	+	9050.75i	0.211871	+	0.977298i
$442$		0			0
$443$			1225.36i			0.131419i	0.997839	+	0.0657096i	$0.0209311\pi$
$443$			1225.36i			0.131419i	−0.997839	+	0.0657096i	$0.979069\pi$
$444$		0			0
$445$	−10790.5			−1.14948
$446$		0			0
$447$	−12076.7	−	12019.0i	−1.27787	−	1.27176i
$448$		0			0
$449$		−	12542.2i		−	1.31827i	−0.752023	−	0.659136i	$-0.770922\pi$
$449$		−	12542.2i		−	1.31827i	0.752023	−	0.659136i	$-0.229078\pi$
$450$		0			0
$451$	7399.32	−	4272.00i	0.772551	−	0.446033i
$452$		0			0
$453$	11446.9	+	3037.82i	1.18724	+	0.315076i
$454$		0			0
$455$	3283.65	+	4523.07i	0.338329	+	0.466033i
$456$		0			0
$457$	−15334.5			−1.56962			−0.784811	−	0.619735i	$-0.787240\pi$
$457$	−15334.5			−1.56962			−0.784811	+	0.619735i	$0.787240\pi$
$458$		0			0
$459$	2806.95	−	10785.0i	0.285440	−	1.09673i
$460$		0			0
$461$	3411.92	+	5909.62i	0.344705	+	0.597047i	0.985300	−	0.170832i	$-0.0546456\pi$
$461$	3411.92	+	5909.62i	0.344705	+	0.597047i	−0.640595	+	0.767879i	$0.721312\pi$
$462$		0			0
$463$	5117.73	−	8864.16i	0.513695	−	0.889746i	−0.486178	−	0.873860i	$-0.661609\pi$
$463$	5117.73	−	8864.16i	0.513695	−	0.889746i	0.999874	−	0.0158869i	$-0.00505718\pi$
$464$		0			0
$465$	−3052.74	−	3038.15i	−0.304446	−	0.302991i
$466$		0			0
$467$	2313.87	−	4007.75i	0.229279	−	0.397123i	−0.728316	−	0.685242i	$-0.759696\pi$
$467$	2313.87	−	4007.75i	0.229279	−	0.397123i	0.957595	+	0.288119i	$0.0930298\pi$
$468$		0			0
$469$	10441.2	−	7580.08i	1.02800	−	0.746302i
$470$		0			0
$471$	−9898.59	+	2677.74i	−0.968372	+	0.261961i
$472$		0			0
$473$		−	11413.1i		−	1.10946i
$474$		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
$479$	−5747.48	+	9954.93i	−0.548245	+	0.949588i	0.450150	+	0.892953i	$0.351370\pi$
$479$	−5747.48	+	9954.93i	−0.548245	+	0.949588i	−0.998395	+	0.0566348i	$0.981963\pi$
$480$		0			0
$481$	7209.13	−	4162.19i	0.683384	−	0.394552i
$482$		0			0
$483$	1347.80	+	210.674i	0.126971	+	0.0198468i
$484$		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	0.919633	−	0.392778i	$-0.128486\pi$
$491$	11307.3	+	6528.30i	1.03929	+	0.600037i	0.119661	+	0.992815i	$0.461819\pi$
$492$		0			0
$493$	−772.805	−	446.179i	−0.0705992	−	0.0407604i
$494$		0			0
$495$	−3299.73	−	5652.60i	−0.299619	−	0.513264i
$496$		0			0
$497$	9051.28	+	12467.7i	0.816912	+	1.12526i
$498$		0			0
$499$	−3460.27	−	5993.37i	−0.310427	−	0.537675i	0.668028	−	0.744136i	$-0.267139\pi$
$499$	−3460.27	−	5993.37i	−0.310427	−	0.537675i	−0.978455	+	0.206461i	$0.933805\pi$
$500$		0			0
$501$	17967.4	+	4768.27i	1.60225	+	0.425211i
$502$		0			0
$503$	−748.409			−0.0663417			−0.0331709	−	0.999450i	$-0.510561\pi$
$503$	−748.409			−0.0663417			−0.0331709	+	0.999450i	$0.510561\pi$
$504$		0			0
$505$	−12820.5			−1.12971
$506$		0			0
$507$	−566.551	+	569.271i	−0.0496280	+	0.0498663i
$508$		0			0
$509$	2110.94	+	3656.26i	0.183823	+	0.318391i	0.943179	−	0.332284i	$-0.107819\pi$
$509$	2110.94	+	3656.26i	0.183823	+	0.318391i	−0.759356	+	0.650675i	$0.774486\pi$
$510$		0			0
$511$	4404.59	−	9883.04i	0.381307	−	0.855577i
$512$		0			0
$513$	3453.75	+	12528.8i	0.297245	+	1.07829i
$514$		0			0
$515$	−3071.14	−	1773.12i	−0.262778	−	0.151715i
$516$		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	0.983392	−	0.181493i	$-0.0580929\pi$
$521$	3978.11	+	6890.29i	0.334519	+	0.579403i	−0.648874	+	0.760896i	$0.724760\pi$
$522$		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
$525$	−7218.23	+	2787.60i	−0.600056	+	0.231735i
$526$		0			0
$527$	−8538.54	+	4929.73i	−0.705777	+	0.407481i
$528$		0			0
$529$	−5983.03	+	10362.9i	−0.491742	+	0.851723i
$530$		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
$535$		−	8498.70i		−	0.686787i
$536$		0			0
$537$	2237.49	+	2226.80i	0.179804	+	0.178945i
$538$		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
$543$	16093.2	−	4353.48i	1.27187	−	0.344062i
$544$		0			0
$545$	3497.47	−	6057.80i	0.274890	−	0.476124i
$546$		0			0
$547$	−5959.72	−	10322.5i	−0.465849	−	0.806873i	0.533391	−	0.845869i	$-0.320918\pi$
$547$	−5959.72	−	10322.5i	−0.465849	−	0.806873i	−0.999239	+	0.0389956i	$0.987584\pi$
$548$		0			0
$549$	−5193.43	−	8896.62i	−0.403735	−	0.691619i
$550$		0			0
$551$	1040.65			0.0804592
$552$		0			0
$553$	−7713.83	+	5600.06i	−0.593174	+	0.430631i
$554$		0			0
$555$	−1669.00	−	6169.67i	−0.127649	−	0.471870i
$556$		0			0
$557$	−3386.01	+	1954.91i	−0.257576	+	0.148711i	−0.623228	−	0.782040i	$-0.714179\pi$
$557$	−3386.01	+	1954.91i	−0.257576	+	0.148711i	0.365652	+	0.930751i	$0.380846\pi$
$558$		0			0
$559$		−	14208.6i		−	1.07507i
$560$		0			0
$561$	−14463.5	+	3912.64i	−1.08851	+	0.294459i
$562$		0			0
$563$	7590.82			0.568233			0.284116	−	0.958790i	$-0.408300\pi$
$563$	7590.82			0.568233			0.284116	+	0.958790i	$0.408300\pi$
$564$		0			0
$565$			7121.25i			0.530254i
$566$		0			0
$567$	−1534.85	−	13413.7i	−0.113682	−	0.993517i
$568$		0			0
$569$		−	10903.9i		−	0.803367i	−0.915779	−	0.401684i	$-0.868425\pi$
$569$		−	10903.9i		−	0.803367i	0.915779	−	0.401684i	$-0.131575\pi$
$570$		0			0
$571$	24102.0			1.76644			0.883218	−	0.468962i	$-0.155372\pi$
$571$	24102.0			1.76644			0.883218	+	0.468962i	$0.155372\pi$
$572$		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
$579$	−760.423	−	2811.00i	−0.0545805	−	0.201763i
$580$		0			0
$581$	4673.57	+	2082.88i	0.333722	+	0.148730i
$582$		0			0
$583$	−217.696			−0.0154650
$584$		0			0
$585$	−4107.98	−	7037.18i	−0.290332	−	0.497353i
$586$		0			0
$587$	−11153.4	−	19318.3i	−0.784242	−	1.35835i	−0.929451	−	0.368946i	$-0.879719\pi$
$587$	−11153.4	−	19318.3i	−0.784242	−	1.35835i	0.145209	−	0.989401i	$-0.453615\pi$
$588$		0			0
$589$	5748.93	−	9957.44i	0.402174	−	0.696586i
$590$		0			0
$591$	−25660.4	+	6941.59i	−1.78601	+	0.483145i
$592$		0			0
$593$	−5870.27	+	10167.6i	−0.406514	+	0.704104i	−0.994496	−	0.104770i	$-0.966589\pi$
$593$	−5870.27	+	10167.6i	−0.406514	+	0.704104i	0.587982	+	0.808874i	$0.299923\pi$
$594$		0			0
$595$	−1023.28	−	9770.61i	−0.0705048	−	0.673204i
$596$		0			0
$597$	−84.2779	−	83.8753i	−0.00577766	−	0.00575006i
$598$		0			0
$599$		−	13135.3i		−	0.895982i	−0.894038	−	0.447991i	$-0.852140\pi$
$599$		−	13135.3i		−	0.895982i	0.894038	−	0.447991i	$-0.147860\pi$
$600$		0			0
$601$	4.16380	−	2.40397i	0.000282604	−	0.000163161i	−0.499859	−	0.866107i	$-0.666615\pi$
$601$	4.16380	−	2.40397i	0.000282604	−	0.000163161i	0.500141	+	0.865944i	$0.333281\pi$
$602$		0			0
$603$	−16244.9	+	9483.00i	−1.09708	+	0.640427i
$604$		0			0
$605$	44.0997	−	76.3830i	0.00296349	−	0.00513291i
$606$		0			0
$607$	12271.4	−	7084.89i	0.820560	−	0.473751i	−0.0300495	−	0.999548i	$-0.509566\pi$
$607$	12271.4	−	7084.89i	0.820560	−	0.473751i	0.850610	+	0.525798i	$0.176233\pi$
$608$		0			0
$609$	−1068.12	−	166.958i	−0.0710714	−	0.0111091i
$610$		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	0.128706	−	0.991683i	$-0.458918\pi$
$617$	−10203.5	−	5890.97i	−0.665763	−	0.384379i	−0.794469	+	0.607304i	$0.792251\pi$
$618$		0			0
$619$	19955.2	+	11521.2i	1.29575	+	0.748101i	0.979667	−	0.200631i	$-0.0642993\pi$
$619$	19955.2	+	11521.2i	1.29575	+	0.748101i	0.316082	+	0.948732i	$0.397633\pi$
$620$		0			0
$621$	−1924.65	−	500.918i	−0.124369	−	0.0323690i
$622$		0			0
$623$	3117.13	+	29763.4i	0.200458	+	1.91404i
$624$		0			0
$625$	−445.446	−	771.534i	−0.0285085	−	0.0493782i
$626$		0			0
$627$	12325.9	−	12385.0i	0.785084	−	0.788853i
$628$		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
$633$	−25081.7	−	6656.29i	−1.57489	−	0.417952i
$634$		0			0
$635$	8258.40	+	14304.0i	0.516102	+	0.893915i
$636$		0			0
$637$	11527.4	−	10363.9i	0.717004	−	0.644633i
$638$		0			0
$639$	−11323.5	−	19397.8i	−0.701020	−	1.20088i
$640$		0			0
$641$	−15148.6	−	8746.05i	−0.933438	−	0.538921i	−0.0455406	−	0.998962i	$-0.514501\pi$
$641$	−15148.6	−	8746.05i	−0.933438	−	0.538921i	−0.887897	+	0.460042i	$0.847834\pi$
$642$		0			0
$643$	−2937.02	−	1695.69i	−0.180132	−	0.103999i	0.407223	−	0.913329i	$-0.366497\pi$
$643$	−2937.02	−	1695.69i	−0.180132	−	0.103999i	−0.587355	+	0.809330i	$0.699831\pi$
$644$		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	$0.0708777\pi$
$647$	11172.9	+	19352.0i	0.678903	+	1.17589i	−0.296408	+	0.955061i	$0.595789\pi$
$648$		0			0
$649$	1906.41	+	1100.66i	0.115305	+	0.0665715i
$650$		0			0
$651$	−7498.25	+	9298.00i	−0.451428	+	0.559781i
$652$		0			0
$653$	8468.04	−	4889.02i	0.507473	−	0.292990i	−0.224321	−	0.974515i	$-0.572016\pi$
$653$	8468.04	−	4889.02i	0.507473	−	0.292990i	0.731794	+	0.681526i	$0.238683\pi$
$654$		0			0
$655$	−4390.39	+	7604.38i	−0.261903	+	0.453630i
$656$		0			0
$657$	−7821.61	+	13698.5i	−0.464460	+	0.813440i
$658$		0			0
$659$	−14282.6	+	8246.08i	−0.844268	+	0.487438i	−0.858713	−	0.512457i	$-0.828735\pi$
$659$	−14282.6	+	8246.08i	−0.844268	+	0.487438i	0.0144449	+	0.999896i	$0.495402\pi$
$660$		0			0
$661$		−	25541.0i		−	1.50292i	−0.659780	−	0.751459i	$-0.729350\pi$
$661$		−	25541.0i		−	1.50292i	0.659780	−	0.751459i	$-0.270650\pi$
$662$		0			0
$663$	−18006.3	+	4871.02i	−1.05476	+	0.285332i
$664$		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
$669$	−11486.2	−	11431.3i	−0.663798	−	0.660626i
$670$		0			0
$671$	−6925.19	+	11994.8i	−0.398426	+	0.690095i
$672$		0			0
$673$	−6191.35	−	10723.7i	−0.354619	−	0.614219i	0.632433	−	0.774615i	$-0.282056\pi$
$673$	−6191.35	−	10723.7i	−0.354619	−	0.614219i	−0.987053	+	0.160396i	$0.948723\pi$
$674$		0			0
$675$	10875.0	−	2997.85i	0.620118	−	0.170944i
$676$		0			0
$677$	26195.2			1.48709			0.743547	−	0.668684i	$-0.233142\pi$
$677$	26195.2			1.48709			0.743547	+	0.668684i	$0.233142\pi$
$678$		0			0
$679$	−1544.28	+	3465.07i	−0.0872816	+	0.195843i
$680$		0			0
$681$	20482.9	+	5435.85i	1.15258	+	0.305877i
$682$		0			0
$683$	−19831.2	+	11449.6i	−1.11101	+	0.641443i	−0.939091	−	0.343668i	$-0.888331\pi$
$683$	−19831.2	+	11449.6i	−1.11101	+	0.641443i	−0.171920	+	0.985111i	$0.554997\pi$
$684$		0			0
$685$		−	15948.2i		−	0.889563i
$686$		0			0
$687$	10081.2	+	10033.1i	0.559858	+	0.557184i
$688$		0			0
$689$	−271.020			−0.0149856
$690$		0			0
$691$			7936.14i			0.436910i	0.975847	+	0.218455i	$0.0701017\pi$
$691$			7936.14i			0.436910i	−0.975847	+	0.218455i	$0.929898\pi$
$692$		0			0
$693$	−14638.3	+	10734.5i	−0.802401	+	0.588413i
$694$		0			0
$695$		−	1070.23i		−	0.0584117i
$696$		0			0
$697$	−18695.8			−1.01600
$698$		0			0
$699$	−811.467	+	3057.70i	−0.0439091	+	0.165455i
$700$		0			0
$701$			30331.5i			1.63424i	0.576466	+	0.817121i	$0.304431\pi$
$701$			30331.5i			1.63424i	−0.576466	+	0.817121i	$0.695569\pi$
$702$		0			0
$703$	14776.7	−	8531.35i	0.792767	−	0.457704i
$704$		0			0
$705$	1182.61	−	1188.29i	0.0631769	−	0.0634802i
$706$		0			0
$707$	3703.55	+	35362.7i	0.197010	+	1.88112i
$708$		0			0
$709$	−2145.29			−0.113636			−0.0568181	−	0.998385i	$-0.518096\pi$
$709$	−2145.29			−0.113636			−0.0568181	+	0.998385i	$0.518096\pi$
$710$		0			0
$711$	12001.5	−	7005.91i	0.633040	−	0.369539i
$712$		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
$717$	7634.66	−	28768.3i	0.397659	−	1.49843i
$718$		0			0
$719$	−4053.00	+	7020.00i	−0.210224	+	0.364119i	−0.951785	−	0.306767i	$-0.900753\pi$
$719$	−4053.00	+	7020.00i	−0.210224	+	0.364119i	0.741560	+	0.670886i	$0.234086\pi$
$720$		0			0
$721$	−4003.61	+	8983.32i	−0.206799	+	0.464017i
$722$		0			0
$723$	−1682.19	+	6338.71i	−0.0865304	+	0.326057i
$724$		0			0
$725$		−	903.280i		−	0.0462717i
$726$		0			0
$727$	−756.456	+	436.740i	−0.0385906	+	0.0222803i	−0.519171	−	0.854670i	$-0.673759\pi$
$727$	−756.456	+	436.740i	−0.0385906	+	0.0222803i	0.480581	+	0.876951i	$0.340426\pi$
$728$		0			0
$729$	282.779	+	19681.0i	0.0143666	+	0.999897i
$730$		0			0
$731$	−12486.9	+	21627.9i	−0.631798	+	1.09431i
$732$		0			0
$733$	15895.5	−	9177.27i	0.800974	−	0.462442i	−0.0428379	−	0.999082i	$-0.513640\pi$
$733$	15895.5	−	9177.27i	0.800974	−	0.462442i	0.843811	+	0.536640i	$0.180307\pi$
$734$		0			0
$735$	−5420.86	−	10595.7i	−0.272043	−	0.531737i
$736$		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	0.565438	−	0.824791i	$-0.308707\pi$
$743$	2711.17	+	1565.29i	0.133867	+	0.0772880i	−0.431571	+	0.902079i	$0.642041\pi$
$744$		0			0
$745$	18963.2	+	10948.4i	0.932562	+	0.538415i
$746$		0			0
$747$	−6477.86	−	3698.75i	−0.317286	−	0.181165i
$748$		0			0
$749$	−23441.9	+	2455.08i	−1.14359	+	0.119768i
$750$		0			0
$751$	1512.14	+	2619.10i	0.0734737	+	0.127260i	0.900422	−	0.435018i	$-0.143258\pi$
$751$	1512.14	+	2619.10i	0.0734737	+	0.127260i	−0.826948	+	0.562279i	$0.809925\pi$
$752$		0			0
$753$	6268.45	+	23172.1i	0.303366	+	1.12143i
$754$		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
$759$	698.236	+	2581.11i	0.0333918	+	0.123437i
$760$		0			0
$761$	−10183.2	−	17637.7i	−0.485071	−	0.840167i	0.514782	−	0.857321i	$-0.327873\pi$
$761$	−10183.2	−	17637.7i	−0.485071	−	0.840167i	−0.999853	+	0.0171537i	$0.994540\pi$
$762$		0			0
$763$	−17719.5	−	7897.10i	−0.840747	−	0.374697i
$764$		0			0
$765$	68.5890	+	14322.0i	0.00324162	+	0.676878i
$766$		0			0
$767$	2373.37	+	1370.27i	0.111731	+	0.0645079i
$768$		0			0
$769$	−22927.3	−	13237.1i	−1.07514	−	0.620731i	−0.145557	−	0.989350i	$-0.546498\pi$
$769$	−22927.3	−	13237.1i	−1.07514	−	0.620731i	−0.929581	+	0.368619i	$0.879831\pi$
$770$		0			0
$771$	−25128.4	+	25249.0i	−1.17377	+	1.17941i
$772$		0			0
$773$	5624.70	+	9742.27i	0.261716	+	0.453305i	0.966698	−	0.255920i	$-0.0823783\pi$
$773$	5624.70	+	9742.27i	0.261716	+	0.453305i	−0.704982	+	0.709225i	$0.749045\pi$
$774$		0			0
$775$	−8643.05	−	4990.06i	−0.400603	−	0.231288i
$776$		0			0
$777$	−16535.6	+	6385.87i	−0.763464	+	0.294841i
$778$		0			0
$779$	18881.6	−	10901.3i	0.868424	−	0.501385i
$780$		0			0
$781$	−15099.4	+	26152.9i	−0.691803	+	1.19824i
$782$		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
$787$		−	19369.4i		−	0.877314i	−0.898655	−	0.438657i	$-0.855454\pi$
$787$		−	19369.4i		−	0.877314i	0.898655	−	0.438657i	$-0.144546\pi$
$788$		0			0
$789$	2363.26	−	8905.03i	0.106634	−	0.401809i
$790$		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
$795$	−53.3758	+	201.126i	−0.00238119	+	0.00897260i
$796$		0			0
$797$	14722.8	−	25500.7i	0.654341	−	1.13335i	−0.327718	−	0.944776i	$-0.606280\pi$
$797$	14722.8	−	25500.7i	0.654341	−	1.13335i	0.982059	−	0.188576i	$-0.0603871\pi$
$798$		0			0
$799$	−1918.91	−	3323.66i	−0.0849640	−	0.147162i
$800$		0			0
$801$	−208.937	−	43627.8i	−0.00921652	−	1.92449i
$802$		0			0
$803$	21208.4			0.932041
$804$		0			0
$805$	−1743.63	+	182.611i	−0.0763414	+	0.00799526i
$806$		0			0
$807$	−23972.8	+	24087.8i	−1.04570	+	1.05072i
$808$		0			0
$809$	−29159.7	+	16835.4i	−1.26725	+	0.731645i	−0.974466	−	0.224535i	$-0.927914\pi$
$809$	−29159.7	+	16835.4i	−1.26725	+	0.731645i	−0.292780	+	0.956180i	$0.594580\pi$
$810$		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
$815$	−7390.51			−0.317642
$816$		0			0
$817$		−	29123.8i		−	1.24714i
$818$		0			0
$819$	−18223.9	+	13363.9i	−0.777527	+	0.570173i
$820$		0			0
$821$		−	43038.1i		−	1.82953i	−0.403990	−	0.914763i	$-0.632377\pi$
$821$		−	43038.1i		−	1.82953i	0.403990	−	0.914763i	$-0.367623\pi$
$822$		0			0
$823$	15760.9			0.667547			0.333773	−	0.942653i	$-0.391678\pi$
$823$	15760.9			0.667547			0.333773	+	0.942653i	$0.391678\pi$
$824$		0			0
$825$	−10750.2	−	10698.8i	−0.453665	−	0.451498i
$826$		0			0
$827$		−	638.310i		−	0.0268394i	−0.999910	−	0.0134197i	$-0.995728\pi$
$827$		−	638.310i		−	0.0268394i	0.999910	−	0.0134197i	$-0.00427176\pi$
$828$		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
$831$	29639.6	+	7865.89i	1.23729	+	0.328357i
$832$		0			0
$833$	−26654.6	+	5645.01i	−1.10868	+	0.234799i
$834$		0			0
$835$	−23890.2			−0.990127
$836$		0			0
$837$	12224.6	−	12401.5i	0.504833	−	0.512138i
$838$		0			0
$839$	−18758.8	−	32491.2i	−0.771903	−	1.33698i	−0.936519	−	0.350618i	$-0.885972\pi$
$839$	−18758.8	−	32491.2i	−0.771903	−	1.33698i	0.164616	−	0.986358i	$-0.447362\pi$
$840$		0			0
$841$	−12131.4	+	21012.2i	−0.497413	+	0.861544i
$842$		0			0
$843$	−4827.85	−	4804.79i	−0.197248	−	0.196306i
$844$		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
$849$	45126.0	−	12207.4i	1.82417	−	0.493469i
$850$		0			0
$851$			2611.05i			0.105177i
$852$		0			0
$853$	−1305.69	+	753.838i	−0.0524101	+	0.0302590i	−0.525976	−	0.850499i	$-0.676300\pi$
$853$	−1305.69	+	753.838i	−0.0524101	+	0.0302590i	0.473566	+	0.880758i	$0.342967\pi$
$854$		0			0
$855$	−8420.23	−	14424.3i	−0.336802	−	0.576960i
$856$		0			0
$857$	−11883.1	+	20582.1i	−0.473651	+	0.820388i	−0.999545	−	0.0301623i	$-0.990398\pi$
$857$	−11883.1	+	20582.1i	−0.473651	+	0.820388i	0.525894	+	0.850550i	$0.323731\pi$
$858$		0			0
$859$	−27641.4	+	15958.8i	−1.09792	+	0.633884i	−0.935674	−	0.352866i	$-0.885207\pi$
$859$	−27641.4	+	15958.8i	−1.09792	+	0.633884i	−0.162246	+	0.986750i	$0.551874\pi$
$860$		0			0
$861$	−21129.1	+	8159.80i	−0.836325	+	0.322980i
$862$		0			0
$863$	−3568.67	−	2060.37i	−0.140763	−	0.0812698i	0.427964	−	0.903796i	$-0.359231\pi$
$863$	−3568.67	−	2060.37i	−0.140763	−	0.0812698i	−0.568728	+	0.822526i	$0.692564\pi$
$864$		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
$871$	27266.8	+	15742.5i	1.06073	+	0.612415i
$872$		0			0
$873$	2742.32	−	4802.80i	0.106315	−	0.186197i
$874$		0			0
$875$	20557.6	−	14924.4i	0.794256	−	0.576612i
$876$		0			0
$877$	16792.7	+	29085.8i	0.646578	+	1.11991i	0.983935	+	0.178529i	$0.0571337\pi$
$877$	16792.7	+	29085.8i	0.646578	+	1.11991i	−0.337357	+	0.941377i	$0.609533\pi$
$878$		0			0
$879$	−16689.0	−	4429.01i	−0.640395	−	0.169951i
$880$		0			0
$881$	37119.8			1.41952			0.709760	−	0.704444i	$-0.248803\pi$
$881$	37119.8			1.41952			0.709760	+	0.704444i	$0.248803\pi$
$882$		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
$885$	1484.31	−	1491.43i	0.0563779	−	0.0566486i
$886$		0			0
$887$	−3462.11	−	5996.55i	−0.131055	−	0.226995i	0.793028	−	0.609185i	$-0.208503\pi$
$887$	−3462.11	−	5996.55i	−0.131055	−	0.226995i	−0.924084	+	0.382190i	$0.875170\pi$
$888$		0			0
$889$	37068.9	−	26911.2i	1.39848	−	1.01527i
$890$		0			0
$891$	22790.5	−	13450.8i	0.856913	−	0.505744i
$892$		0			0
$893$	3875.97	+	2237.79i	0.145246	+	0.0838575i
$894$		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
$903$	−4672.53	+	29892.8i	−0.172195	+	1.10163i
$904$		0			0
$905$	−18555.1	+	10712.8i	−0.681540	+	0.393487i
$906$		0			0
$907$	2603.50	−	4509.40i	0.0953119	−	0.165085i	−0.814427	−	0.580266i	$-0.802948\pi$
$907$	2603.50	−	4509.40i	0.0953119	−	0.165085i	0.909739	+	0.415181i	$0.136282\pi$
$908$		0			0
$909$	−248.244	−	51835.3i	−0.00905800	−	1.89139i
$910$		0			0
$911$	21011.8	−	12131.1i	0.764161	−	0.441188i	−0.0666269	−	0.997778i	$-0.521224\pi$
$911$	21011.8	−	12131.1i	0.764161	−	0.441188i	0.830788	+	0.556590i	$0.187890\pi$
$912$		0			0
$913$			10029.2i			0.363547i
$914$		0			0
$915$	9383.84	+	9339.01i	0.339038	+	0.337419i
$916$		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
$921$	18868.2	−	5104.18i	0.675059	−	0.182615i
$922$		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
$927$	7109.56	−	12451.4i	0.251897	−	0.441164i
$928$		0			0
$929$	45292.6			1.59957			0.799786	−	0.600285i	$-0.204946\pi$
$929$	45292.6			1.59957			0.799786	+	0.600285i	$0.204946\pi$
$930$		0			0
$931$	23628.0	−	21243.1i	0.831767	−	0.747813i
$932$		0			0
$933$	951.448	+	3517.14i	0.0333859	+	0.123415i
$934$		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
$941$	−34510.6			−1.19555			−0.597776	−	0.801663i	$-0.703949\pi$
$941$	−34510.6			−1.19555			−0.597776	+	0.801663i	$0.703949\pi$
$942$		0			0
$943$			3336.38i			0.115215i
$944$		0			0
$945$	6328.36	+	16156.0i	0.217843	+	0.556144i
$946$		0			0
$947$		−	51810.4i		−	1.77784i	−0.458065	−	0.888919i	$-0.651457\pi$
$947$		−	51810.4i		−	1.77784i	0.458065	−	0.888919i	$-0.348543\pi$
$948$		0			0
$949$	26403.3			0.903149
$950$		0			0
$951$	−13347.8	+	3610.82i	−0.455135	+	0.123122i
$952$		0			0
$953$		−	49557.5i		−	1.68450i	−0.539091	−	0.842248i	$-0.681232\pi$
$953$		−	49557.5i		−	1.68450i	0.539091	−	0.842248i	$-0.318768\pi$
$954$		0			0
$955$	−14983.1	+	8650.50i	−0.507688	+	0.293114i
$956$		0			0
$957$	−553.347	−	2045.52i	−0.0186909	−	0.0690931i
$958$		0			0
$959$	−43989.9	+	4607.07i	−1.48124	+	0.155131i
$960$		0			0
$961$	14384.8			0.482858
$962$		0			0
$963$	34361.6	−	164.561i	1.14983	−	0.00550664i
$964$		0			0
$965$	1871.21	+	3241.03i	0.0624211	+	0.108117i
$966$		0			0
$967$	−6281.58	+	10880.0i	−0.208895	+	0.361818i	−0.951367	−	0.308060i	$-0.900320\pi$
$967$	−6281.58	+	10880.0i	−0.208895	+	0.361818i	0.742471	+	0.669878i	$0.233654\pi$
$968$		0			0
$969$	−36908.0	+	9984.26i	−1.22359	+	0.331002i
$970$		0			0
$971$	13678.2	−	23691.4i	0.452065	−	0.782999i	−0.546450	−	0.837492i	$-0.684021\pi$
$971$	13678.2	−	23691.4i	0.452065	−	0.782999i	0.998514	+	0.0544932i	$0.0173543\pi$
$972$		0			0
$973$	−2952.01	+	309.165i	−0.0972632	+	0.0101864i
$974$		0			0
$975$	−13383.4	−	13319.5i	−0.439603	−	0.437502i
$976$		0			0
$977$			13629.2i			0.446301i	0.974784	+	0.223151i	$0.0716342\pi$
$977$			13629.2i			0.446301i	−0.974784	+	0.223151i	$0.928366\pi$
$978$		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
$983$	−16003.9	+	27719.5i	−0.519272	+	0.899406i	0.480477	+	0.877007i	$0.340464\pi$
$983$	−16003.9	+	27719.5i	−0.519272	+	0.899406i	−0.999749	+	0.0223983i	$0.992870\pi$
$984$		0			0
$985$	29586.0	−	17081.5i	0.957045	−	0.552550i
$986$		0			0
$987$	−3619.28	−	2918.72i	−0.116720	−	0.0941275i
$988$		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
$997$	−2085.18	−	1203.88i	−0.0662369	−	0.0382419i	0.466516	−	0.884513i	$-0.345509\pi$
$997$	−2085.18	−	1203.88i	−0.0662369	−	0.0382419i	−0.532753	+	0.846271i	$0.678842\pi$
$998$		0			0
$999$	24912.6	−	6867.50i	0.788990	−	0.217496i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.10	✓	48	1.1	even	1	trivial
252.4.w.a.101.10	yes	48	63.38	even	6	inner
252.4.bm.a.173.19	yes	48	9.2	odd	6
252.4.bm.a.185.19	yes	48	7.3	odd	6
756.4.w.a.341.9		48	3.2	odd	2
756.4.w.a.521.9		48	63.52	odd	6
756.4.bm.a.17.9		48	21.17	even	6
756.4.bm.a.89.9		48	9.7	even	3

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.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35688 - 5.01586i) q^{3} +(3.33893 + 5.78320i) q^{5} +(14.9872 - 10.8804i) q^{7} +(-23.3178 + 13.6118i) q^{9} +O(q^{10})\)	\(q+(-1.35688 - 5.01586i) q^{3} +(3.33893 + 5.78320i) q^{5} +(14.9872 - 10.8804i) q^{7} +(-23.3178 + 13.6118i) q^{9} +(31.4379 + 18.1507i) q^{11} +(39.1385 + 22.5966i) q^{13} +(24.4772 - 24.5947i) q^{15} +(-39.7169 - 68.7917i) q^{17} +(80.2233 + 46.3169i) q^{19} +(-74.9104 - 60.4105i) q^{21} +(-12.2763 + 7.08774i) q^{23} +(40.2030 - 69.6337i) q^{25} +(99.9144 + 98.4891i) q^{27} +(9.72891 - 5.61699i) q^{29} -124.122i q^{31} +(48.3840 - 182.317i) q^{33} +(112.965 + 50.3453i) q^{35} +(92.0975 - 159.518i) q^{37} +(60.2355 - 226.974i) q^{39} +(117.681 - 203.830i) q^{41} +(-157.199 - 272.276i) q^{43} +(-156.576 - 89.4024i) q^{45} +48.3147 q^{47} +(106.234 - 326.134i) q^{49} +(-291.159 + 292.557i) q^{51} +(-5.19348 + 2.99846i) q^{53} +242.416i q^{55} +(123.466 - 465.235i) q^{57} +60.6403 q^{59} +381.538i q^{61} +(-201.367 + 457.710i) q^{63} +301.795i q^{65} +696.673 q^{67} +(52.2086 + 51.9592i) q^{69} +831.889i q^{71} +(505.959 - 292.116i) q^{73} +(-403.824 - 107.168i) q^{75} +(668.654 - 70.0284i) q^{77} -514.693 q^{79} +(358.436 - 634.795i) q^{81} +(138.138 + 239.262i) q^{83} +(265.224 - 459.382i) q^{85} +(-41.3750 - 41.1773i) q^{87} +(-807.932 + 1399.38i) q^{89} +(832.439 - 87.1815i) q^{91} +(-622.577 + 168.418i) q^{93} +618.597i q^{95} +(-177.393 + 102.418i) q^{97} +(-980.127 + 4.69391i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 12 * q^9	\( 48 q + 6 q^{7} + 12 q^{9} + 12 q^{11} - 36 q^{13} + 66 q^{15} - 72 q^{17} + 24 q^{21} + 30 q^{23} - 600 q^{25} - 396 q^{27} + 42 q^{29} + 390 q^{35} + 84 q^{37} - 840 q^{39} - 618 q^{41} - 42 q^{43} + 366 q^{45} + 396 q^{47} + 318 q^{49} - 738 q^{51} - 1620 q^{53} + 492 q^{57} + 1500 q^{59} + 672 q^{63} - 588 q^{67} - 924 q^{69} + 564 q^{75} - 2472 q^{77} + 1608 q^{79} + 2592 q^{81} - 360 q^{85} + 2640 q^{87} + 1722 q^{89} + 540 q^{91} + 660 q^{93} - 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 12 * q^9 + 12 * q^11 - 36 * q^13 + 66 * q^15 - 72 * q^17 + 24 * q^21 + 30 * q^23 - 600 * q^25 - 396 * q^27 + 42 * q^29 + 390 * q^35 + 84 * q^37 - 840 * q^39 - 618 * q^41 - 42 * q^43 + 366 * q^45 + 396 * q^47 + 318 * q^49 - 738 * q^51 - 1620 * q^53 + 492 * q^57 + 1500 * q^59 + 672 * q^63 - 588 * q^67 - 924 * q^69 + 564 * q^75 - 2472 * q^77 + 1608 * q^79 + 2592 * q^81 - 360 * q^85 + 2640 * q^87 + 1722 * q^89 + 540 * q^91 + 660 * q^93 - 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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