LMFDB - Embedded newform 252.4.j.b.85.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(85,252)]

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, 2, 0]))

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

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

chi := DirichletCharacter("252.85");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 7 x^{17} + 81 x^{16} - 470 x^{15} + 2687 x^{14} - 12243 x^{13} + 43732 x^{12} + \cdots + 5500612092612 $ x^18 - 7x^17 + 81x^16 - 470x^15 + 2687x^14 - 12243x^13 + 43732x^12 - 169303x^11 + 166449x^10 - 57172x^9 - 3758051x^8 + 73649097x^7 + 358194386x^6 + 3599409199x^5 + 26802380109x^4 + 114591208112x^3 + 655546044172x^2 + 1324018291596*x + 5500612092612
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			85.7
Root			$-2.16791 + 4.11878i$ of defining polynomial
Character	$\chi$	$=$	252.85
Dual form			252.4.j.b.169.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.16791 + 4.11878i) q^{3} +(8.76630 - 15.1837i) q^{5} +(-3.50000 - 6.06218i) q^{7} +(-6.92866 + 26.0959i) q^{9} +O(q^{10})$	\(q+(3.16791 + 4.11878i) q^{3} +(8.76630 - 15.1837i) q^{5} +(-3.50000 - 6.06218i) q^{7} +(-6.92866 + 26.0959i) q^{9} +(-26.5449 - 45.9771i) q^{11} +(45.5112 - 78.8276i) q^{13} +(90.3091 - 11.9941i) q^{15} -86.1853 q^{17} -22.5369 q^{19} +(13.8811 - 33.6202i) q^{21} +(-21.7741 + 37.7139i) q^{23} +(-91.1960 - 157.956i) q^{25} +(-129.432 + 54.1318i) q^{27} +(60.4638 + 104.726i) q^{29} +(16.0632 - 27.8222i) q^{31} +(105.278 - 254.984i) q^{33} -122.728 q^{35} +304.741 q^{37} +(468.849 - 62.2687i) q^{39} +(250.408 - 433.719i) q^{41} +(245.889 + 425.892i) q^{43} +(335.492 + 333.967i) q^{45} +(-147.328 - 255.180i) q^{47} +(-24.5000 + 42.4352i) q^{49} +(-273.028 - 354.978i) q^{51} +391.010 q^{53} -930.803 q^{55} +(-71.3948 - 92.8243i) q^{57} +(-105.915 + 183.451i) q^{59} +(122.354 + 211.924i) q^{61} +(182.448 - 49.3327i) q^{63} +(-797.929 - 1382.05i) q^{65} +(10.7731 - 18.6596i) q^{67} +(-224.314 + 29.7915i) q^{69} +87.0355 q^{71} +45.0771 q^{73} +(361.685 - 876.008i) q^{75} +(-185.814 + 321.840i) q^{77} +(411.776 + 713.217i) q^{79} +(-632.987 - 361.619i) q^{81} +(385.587 + 667.856i) q^{83} +(-755.527 + 1308.61i) q^{85} +(-239.801 + 580.801i) q^{87} +136.331 q^{89} -637.156 q^{91} +(165.480 - 21.9777i) q^{93} +(-197.565 + 342.192i) q^{95} +(731.763 + 1267.45i) q^{97} +(1383.73 - 374.152i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9}+O(q^{10}) $ 18 * q + 11 * q^3 - 6 * q^5 - 63 * q^7 - 109 * q^9	$ 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9} - 93 q^{11} - 18 q^{13} + 162 q^{15} - 54 q^{17} - 90 q^{19} - 49 q^{21} - 246 q^{23} - 315 q^{25} - 394 q^{27} - 318 q^{29} - 18 q^{31} + 33 q^{33} + 84 q^{35} - 72 q^{37} + 268 q^{39} - 57 q^{41} - 171 q^{43} - 318 q^{45} - 1056 q^{47} - 441 q^{49} + 705 q^{51} + 1512 q^{53} - 1800 q^{55} - 1271 q^{57} - 411 q^{59} - 198 q^{61} + 308 q^{63} - 1326 q^{65} - 441 q^{67} + 642 q^{69} + 3516 q^{71} + 54 q^{73} - 2497 q^{75} - 651 q^{77} + 72 q^{79} + 1163 q^{81} - 558 q^{83} - 1008 q^{85} + 2766 q^{87} + 2784 q^{89} + 252 q^{91} - 2618 q^{93} - 156 q^{95} + 909 q^{97} + 6318 q^{99}+O(q^{100}) $ 18 * q + 11 * q^3 - 6 * q^5 - 63 * q^7 - 109 * q^9 - 93 * q^11 - 18 * q^13 + 162 * q^15 - 54 * q^17 - 90 * q^19 - 49 * q^21 - 246 * q^23 - 315 * q^25 - 394 * q^27 - 318 * q^29 - 18 * q^31 + 33 * q^33 + 84 * q^35 - 72 * q^37 + 268 * q^39 - 57 * q^41 - 171 * q^43 - 318 * q^45 - 1056 * q^47 - 441 * q^49 + 705 * q^51 + 1512 * q^53 - 1800 * q^55 - 1271 * q^57 - 411 * q^59 - 198 * q^61 + 308 * q^63 - 1326 * q^65 - 441 * q^67 + 642 * q^69 + 3516 * q^71 + 54 * q^73 - 2497 * q^75 - 651 * q^77 + 72 * q^79 + 1163 * q^81 - 558 * q^83 - 1008 * q^85 + 2766 * q^87 + 2784 * q^89 + 252 * q^91 - 2618 * q^93 - 156 * q^95 + 909 * q^97 + 6318 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	3.16791	+	4.11878i	0.609665	+	0.792659i
$3$	3.16791	+	4.11878i	0.609665	+	0.792659i
$4$		0			0
$5$	8.76630	−	15.1837i	0.784082	−	1.35807i	−0.145464	−	0.989363i	$-0.546468\pi$
$5$	8.76630	−	15.1837i	0.784082	−	1.35807i	0.929546	−	0.368706i	$-0.120199\pi$
$6$		0			0
$7$	−3.50000	−	6.06218i	−0.188982	−	0.327327i
$7$	−3.50000	−	6.06218i	−0.188982	−	0.327327i
$8$		0			0
$9$	−6.92866	+	26.0959i	−0.256617	+	0.966513i
$10$		0			0
$11$	−26.5449	−	45.9771i	−0.727599	−	1.26024i	−0.957895	−	0.287118i	$-0.907303\pi$
$11$	−26.5449	−	45.9771i	−0.727599	−	1.26024i	0.230296	−	0.973121i	$-0.426031\pi$
$12$		0			0
$13$	45.5112	−	78.8276i	0.970963	−	1.68176i	0.278304	−	0.960493i	$-0.410228\pi$
$13$	45.5112	−	78.8276i	0.970963	−	1.68176i	0.692659	−	0.721265i	$-0.256439\pi$
$14$		0			0
$15$	90.3091	−	11.9941i	1.55451	−	0.206458i
$16$		0			0
$17$	−86.1853			−1.22959			−0.614795	−	0.788687i	$-0.710761\pi$
$17$	−86.1853			−1.22959			−0.614795	+	0.788687i	$0.710761\pi$
$18$		0			0
$19$	−22.5369			−0.272122			−0.136061	−	0.990700i	$-0.543444\pi$
$19$	−22.5369			−0.272122			−0.136061	+	0.990700i	$0.543444\pi$
$20$		0			0
$21$	13.8811	−	33.6202i	0.144243	−	0.349358i
$22$		0			0
$23$	−21.7741	+	37.7139i	−0.197401	+	0.341908i	−0.947685	−	0.319207i	$-0.896583\pi$
$23$	−21.7741	+	37.7139i	−0.197401	+	0.341908i	0.750284	+	0.661116i	$0.229917\pi$
$24$		0			0
$25$	−91.1960	−	157.956i	−0.729568	−	1.26365i
$26$		0			0
$27$	−129.432	+	54.1318i	−0.922566	+	0.385839i
$28$		0			0
$29$	60.4638	+	104.726i	0.387167	+	0.670593i	0.992067	−	0.125708i	$-0.0401203\pi$
$29$	60.4638	+	104.726i	0.387167	+	0.670593i	−0.604900	+	0.796301i	$0.706787\pi$
$30$		0			0
$31$	16.0632	−	27.8222i	0.0930654	−	0.161194i	−0.815734	−	0.578427i	$-0.803667\pi$
$31$	16.0632	−	27.8222i	0.0930654	−	0.161194i	0.908800	+	0.417233i	$0.137000\pi$
$32$		0			0
$33$	105.278	−	254.984i	0.555348	−	1.34506i
$34$		0			0
$35$	−122.728			−0.592710
$36$		0			0
$37$	304.741			1.35403			0.677014	−	0.735970i	$-0.263274\pi$
$37$	304.741			1.35403			0.677014	+	0.735970i	$0.263274\pi$
$38$		0			0
$39$	468.849	−	62.2687i	1.92502	−	0.255666i
$40$		0			0
$41$	250.408	−	433.719i	0.953832	−	1.65209i	0.216814	−	0.976213i	$-0.430434\pi$
$41$	250.408	−	433.719i	0.953832	−	1.65209i	0.737018	−	0.675873i	$-0.236233\pi$
$42$		0			0
$43$	245.889	+	425.892i	0.872039	+	1.51042i	0.859884	+	0.510489i	$0.170536\pi$
$43$	245.889	+	425.892i	0.872039	+	1.51042i	0.0121545	+	0.999926i	$0.496131\pi$
$44$		0			0
$45$	335.492	+	333.967i	1.11138	+	1.10633i
$46$		0			0
$47$	−147.328	−	255.180i	−0.457235	−	0.791954i	0.541579	−	0.840650i	$-0.317827\pi$
$47$	−147.328	−	255.180i	−0.457235	−	0.791954i	−0.998814	+	0.0486962i	$0.984493\pi$
$48$		0			0
$49$	−24.5000	+	42.4352i	−0.0714286	+	0.123718i
$50$		0			0
$51$	−273.028	−	354.978i	−0.749638	−	0.974645i
$52$		0			0
$53$	391.010			1.01338			0.506692	−	0.862127i	$-0.330868\pi$
$53$	391.010			1.01338			0.506692	+	0.862127i	$0.330868\pi$
$54$		0			0
$55$	−930.803			−2.28199
$56$		0			0
$57$	−71.3948	−	92.8243i	−0.165903	−	0.215700i
$58$		0			0
$59$	−105.915	+	183.451i	−0.233712	+	0.404801i	−0.958898	−	0.283753i	$-0.908421\pi$
$59$	−105.915	+	183.451i	−0.233712	+	0.404801i	0.725186	+	0.688553i	$0.241754\pi$
$60$		0			0
$61$	122.354	+	211.924i	0.256818	+	0.444821i	0.965388	−	0.260819i	$-0.0839927\pi$
$61$	122.354	+	211.924i	0.256818	+	0.444821i	−0.708570	+	0.705641i	$0.750659\pi$
$62$		0			0
$63$	182.448	−	49.3327i	0.364862	−	0.0986561i
$64$		0			0
$65$	−797.929	−	1382.05i	−1.52263	−	2.63727i
$66$		0			0
$67$	10.7731	−	18.6596i	0.0196440	−	0.0340244i	−0.856036	−	0.516916i	$-0.827080\pi$
$67$	10.7731	−	18.6596i	0.0196440	−	0.0340244i	0.875680	+	0.482891i	$0.160413\pi$
$68$		0			0
$69$	−224.314	+	29.7915i	−0.391365	+	0.0519779i
$70$		0			0
$71$	87.0355			0.145482			0.0727409	−	0.997351i	$-0.476825\pi$
$71$	87.0355			0.145482			0.0727409	+	0.997351i	$0.476825\pi$
$72$		0			0
$73$	45.0771			0.0722723			0.0361362	−	0.999347i	$-0.488495\pi$
$73$	45.0771			0.0722723			0.0361362	+	0.999347i	$0.488495\pi$
$74$		0			0
$75$	361.685	−	876.008i	0.556851	−	1.34870i
$76$		0			0
$77$	−185.814	+	321.840i	−0.275007	+	0.476326i
$78$		0			0
$79$	411.776	+	713.217i	0.586436	+	1.01574i	0.994695	+	0.102870i	$0.0328027\pi$
$79$	411.776	+	713.217i	0.586436	+	1.01574i	−0.408259	+	0.912866i	$0.633864\pi$
$80$		0			0
$81$	−632.987	−	361.619i	−0.868295	−	0.496048i
$82$		0			0
$83$	385.587	+	667.856i	0.509923	+	0.883213i	0.999934	+	0.0114965i	$0.00365953\pi$
$83$	385.587	+	667.856i	0.509923	+	0.883213i	−0.490011	+	0.871716i	$0.663007\pi$
$84$		0			0
$85$	−755.527	+	1308.61i	−0.964098	+	1.66987i
$86$		0			0
$87$	−239.801	+	580.801i	−0.295510	+	0.715729i
$88$		0			0
$89$	136.331			0.162371			0.0811855	−	0.996699i	$-0.474129\pi$
$89$	136.331			0.162371			0.0811855	+	0.996699i	$0.474129\pi$
$90$		0			0
$91$	−637.156			−0.733979
$92$		0			0
$93$	165.480	−	21.9777i	0.184511	−	0.0245052i
$94$		0			0
$95$	−197.565	+	342.192i	−0.213366	+	0.369560i
$96$		0			0
$97$	731.763	+	1267.45i	0.765972	+	1.32670i	0.939731	+	0.341915i	$0.111075\pi$
$97$	731.763	+	1267.45i	0.765972	+	1.32670i	−0.173759	+	0.984788i	$0.555591\pi$
$98$		0			0
$99$	1383.73	−	374.152i	1.40475	−	0.379835i
$100$		0			0
$101$	−686.424	−	1188.92i	−0.676254	−	1.17131i	−0.976101	−	0.217319i	$-0.930269\pi$
$101$	−686.424	−	1188.92i	−0.676254	−	1.17131i	0.299846	−	0.953988i	$-0.403065\pi$
$102$		0			0
$103$	546.234	−	946.105i	0.522544	−	0.905073i	−0.477112	−	0.878843i	$-0.658316\pi$
$103$	546.234	−	946.105i	0.522544	−	0.905073i	0.999656	−	0.0262303i	$-0.00835032\pi$
$104$		0			0
$105$	−388.792	−	505.490i	−0.361355	−	0.469817i
$106$		0			0
$107$	−396.626			−0.358348			−0.179174	−	0.983817i	$-0.557343\pi$
$107$	−396.626			−0.358348			−0.179174	+	0.983817i	$0.557343\pi$
$108$		0			0
$109$	−2078.82			−1.82674			−0.913370	−	0.407130i	$-0.866529\pi$
$109$	−2078.82			−1.82674			−0.913370	+	0.407130i	$0.866529\pi$
$110$		0			0
$111$	965.391	+	1255.16i	0.825504	+	1.07328i
$112$		0			0
$113$	−100.189	+	173.532i	−0.0834069	+	0.144465i	−0.904711	−	0.426025i	$-0.859913\pi$
$113$	−100.189	+	173.532i	−0.0834069	+	0.144465i	0.821304	+	0.570490i	$0.193247\pi$
$114$		0			0
$115$	381.757	+	661.223i	0.309557	+	0.536168i
$116$		0			0
$117$	1741.74	+	1733.82i	1.37628	+	1.37002i
$118$		0			0
$119$	301.649	+	522.471i	0.232371	+	0.402478i
$120$		0			0
$121$	−743.765	+	1288.24i	−0.558801	+	0.967872i
$122$		0			0
$123$	2579.66	−	342.610i	1.89106	−	0.251155i
$124$		0			0
$125$	−1006.23			−0.720001
$126$		0			0
$127$	−367.323			−0.256650			−0.128325	−	0.991732i	$-0.540960\pi$
$127$	−367.323			−0.256650			−0.128325	+	0.991732i	$0.540960\pi$
$128$		0			0
$129$	−975.199	+	2361.95i	−0.665593	+	1.61208i
$130$		0			0
$131$	−151.852	+	263.016i	−0.101278	+	0.175418i	−0.912211	−	0.409720i	$-0.865626\pi$
$131$	−151.852	+	263.016i	−0.101278	+	0.175418i	0.810934	+	0.585138i	$0.198960\pi$
$132$		0			0
$133$	78.8790	+	136.622i	0.0514262	+	0.0890727i
$134$		0			0
$135$	−312.724	+	2439.80i	−0.199371	+	1.55544i
$136$		0			0
$137$	−903.040	−	1564.11i	−0.563153	−	0.975409i	−0.997219	−	0.0745283i	$-0.976255\pi$
$137$	−903.040	−	1564.11i	−0.563153	−	0.975409i	0.434066	−	0.900881i	$-0.357078\pi$
$138$		0			0
$139$	−387.992	+	672.023i	−0.236756	+	0.410074i	−0.959782	−	0.280748i	$-0.909418\pi$
$139$	−387.992	+	672.023i	−0.236756	+	0.410074i	0.723026	+	0.690821i	$0.242751\pi$
$140$		0			0
$141$	584.307	−	1415.20i	0.348989	−	0.845258i
$142$		0			0
$143$	−4832.36			−2.82589
$144$		0			0
$145$	2120.18			1.21428
$146$		0			0
$147$	−252.395	+	33.5211i	−0.141614	+	0.0188080i
$148$		0			0
$149$	−320.519	+	555.155i	−0.176228	+	0.305235i	−0.940585	−	0.339557i	$-0.889723\pi$
$149$	−320.519	+	555.155i	−0.176228	+	0.305235i	0.764358	+	0.644792i	$0.223056\pi$
$150$		0			0
$151$	492.879	+	853.691i	0.265628	+	0.460082i	0.967728	−	0.251997i	$-0.0810872\pi$
$151$	492.879	+	853.691i	0.265628	+	0.460082i	−0.702100	+	0.712079i	$0.747754\pi$
$152$		0			0
$153$	597.149	−	2249.08i	0.315534	−	1.18841i
$154$		0			0
$155$	−281.629	−	487.795i	−0.145942	−	0.252779i
$156$		0			0
$157$	−45.5454	+	78.8870i	−0.0231524	+	0.0401011i	−0.877369	−	0.479815i	$-0.840704\pi$
$157$	−45.5454	+	78.8870i	−0.0231524	+	0.0401011i	0.854217	+	0.519917i	$0.174037\pi$
$158$		0			0
$159$	1238.69	+	1610.48i	0.617825	+	0.803268i
$160$		0			0
$161$	304.838			0.149221
$162$		0			0
$163$	1858.92			0.893265			0.446632	−	0.894718i	$-0.352623\pi$
$163$	1858.92			0.893265			0.446632	+	0.894718i	$0.352623\pi$
$164$		0			0
$165$	−2948.70	−	3833.77i	−1.39125	−	1.80884i
$166$		0			0
$167$	−937.157	+	1623.20i	−0.434248	+	0.752139i	−0.997234	−	0.0743273i	$-0.976319\pi$
$167$	−937.157	+	1623.20i	−0.434248	+	0.752139i	0.562986	+	0.826466i	$0.309652\pi$
$168$		0			0
$169$	−3044.03	−	5272.42i	−1.38554	−	2.39983i
$170$		0			0
$171$	156.150	−	588.119i	0.0698311	−	0.263009i
$172$		0			0
$173$	−992.606	−	1719.24i	−0.436222	−	0.755559i	0.561172	−	0.827699i	$-0.310350\pi$
$173$	−992.606	−	1719.24i	−0.436222	−	0.755559i	−0.997395	+	0.0721400i	$0.977017\pi$
$174$		0			0
$175$	−638.372	+	1105.69i	−0.275751	+	0.477615i
$176$		0			0
$177$	−1091.12	+	144.914i	−0.463355	+	0.0615390i
$178$		0			0
$179$	1404.92			0.586639			0.293320	−	0.956014i	$-0.405240\pi$
$179$	1404.92			0.586639			0.293320	+	0.956014i	$0.405240\pi$
$180$		0			0
$181$	1159.79			0.476280			0.238140	−	0.971231i	$-0.423462\pi$
$181$	1159.79			0.476280			0.238140	+	0.971231i	$0.423462\pi$
$182$		0			0
$183$	−485.260	+	1175.31i	−0.196019	+	0.474761i
$184$		0			0
$185$	2671.45	−	4627.08i	1.06167	−	1.83886i
$186$		0			0
$187$	2287.78	+	3962.56i	0.894648	+	1.54958i
$188$		0			0
$189$	781.170	+	595.181i	0.300644	+	0.229064i
$190$		0			0
$191$	−32.3424	−	56.0186i	−0.0122524	−	0.0212218i	0.859834	−	0.510573i	$-0.170567\pi$
$191$	−32.3424	−	56.0186i	−0.0122524	−	0.0212218i	−0.872087	+	0.489352i	$0.837233\pi$
$192$		0			0
$193$	−1884.74	+	3264.46i	−0.702935	+	1.21752i	0.264496	+	0.964387i	$0.414794\pi$
$193$	−1884.74	+	3264.46i	−0.702935	+	1.21752i	−0.967432	+	0.253133i	$0.918539\pi$
$194$		0			0
$195$	3164.60	−	7664.72i	1.16216	−	2.81478i
$196$		0			0
$197$	5056.77			1.82883			0.914416	−	0.404775i	$-0.132650\pi$
$197$	5056.77			1.82883			0.914416	+	0.404775i	$0.132650\pi$
$198$		0			0
$199$	3142.34			1.11937			0.559685	−	0.828705i	$-0.310922\pi$
$199$	3142.34			1.11937			0.559685	+	0.828705i	$0.310922\pi$
$200$		0			0
$201$	110.983	−	14.7399i	0.0389460	−	0.00517249i
$202$		0			0
$203$	423.247	−	733.085i	0.146335	−	0.253460i
$204$		0			0
$205$	−4390.30	−	7604.22i	−1.49576	−	2.59074i
$206$		0			0
$207$	−833.311	−	829.521i	−0.279802	−	0.278530i
$208$		0			0
$209$	598.239	+	1036.18i	0.197995	+	0.342938i
$210$		0			0
$211$	−2206.87	+	3822.41i	−0.720035	+	1.24714i	0.240951	+	0.970537i	$0.422541\pi$
$211$	−2206.87	+	3822.41i	−0.720035	+	1.24714i	−0.960985	+	0.276599i	$0.910793\pi$
$212$		0			0
$213$	275.721	+	358.480i	0.0886952	+	0.115318i
$214$		0			0
$215$	8622.13			2.73500
$216$		0			0
$217$	−224.884			−0.0703508
$218$		0			0
$219$	142.800	+	185.663i	0.0440619	+	0.0572873i
$220$		0			0
$221$	−3922.39	+	6793.79i	−1.19389	+	2.06787i
$222$		0			0
$223$	558.330	+	967.056i	0.167662	+	0.290399i	0.937597	−	0.347723i	$-0.113045\pi$
$223$	558.330	+	967.056i	0.167662	+	0.290399i	−0.769936	+	0.638122i	$0.779712\pi$
$224$		0			0
$225$	4753.87	−	1285.41i	1.40855	−	0.380863i
$226$		0			0
$227$	−2975.20	−	5153.20i	−0.869917	−	1.50674i	−0.862080	−	0.506772i	$-0.830839\pi$
$227$	−2975.20	−	5153.20i	−0.869917	−	1.50674i	−0.00783689	−	0.999969i	$-0.502495\pi$
$228$		0			0
$229$	2003.46	−	3470.10i	0.578134	−	1.00136i	−0.417559	−	0.908650i	$-0.637114\pi$
$229$	2003.46	−	3470.10i	0.578134	−	1.00136i	0.995693	−	0.0927078i	$-0.0295522\pi$
$230$		0			0
$231$	−1914.23	+	254.233i	−0.545226	+	0.0724125i
$232$		0			0
$233$	−1239.96			−0.348636			−0.174318	−	0.984689i	$-0.555772\pi$
$233$	−1239.96			−0.348636			−0.174318	+	0.984689i	$0.555772\pi$
$234$		0			0
$235$	−5166.09			−1.43404
$236$		0			0
$237$	−1633.11	+	3955.42i	−0.447603	+	1.08410i
$238$		0			0
$239$	2619.97	−	4537.92i	0.709087	−	1.22818i	−0.256109	−	0.966648i	$-0.582441\pi$
$239$	2619.97	−	4537.92i	0.709087	−	1.22818i	0.965196	−	0.261527i	$-0.0842262\pi$
$240$		0			0
$241$	1211.61	+	2098.56i	0.323844	+	0.560914i	0.981278	−	0.192598i	$-0.0616913\pi$
$241$	1211.61	+	2098.56i	0.323844	+	0.560914i	−0.657434	+	0.753512i	$0.728358\pi$
$242$		0			0
$243$	−515.821	−	3752.71i	−0.136173	−	0.990685i
$244$		0			0
$245$	429.549	+	744.000i	0.112012	+	0.194010i
$246$		0			0
$247$	−1025.68	+	1776.53i	−0.264220	+	0.457643i
$248$		0			0
$249$	−1529.24	+	3703.85i	−0.389204	+	0.942659i
$250$		0			0
$251$	3715.51			0.934347			0.467173	−	0.884166i	$-0.345272\pi$
$251$	3715.51			0.934347			0.467173	+	0.884166i	$0.345272\pi$
$252$		0			0
$253$	2311.97			0.574515
$254$		0			0
$255$	−7783.32	+	1033.72i	−1.91141	+	0.253858i
$256$		0			0
$257$	−299.202	+	518.233i	−0.0726214	+	0.125784i	−0.900049	−	0.435788i	$-0.856470\pi$
$257$	−299.202	+	518.233i	−0.0726214	+	0.125784i	0.827428	+	0.561572i	$0.189803\pi$
$258$		0			0
$259$	−1066.59	−	1847.39i	−0.255887	−	0.443210i
$260$		0			0
$261$	−3151.86	+	852.241i	−0.747491	+	0.202116i
$262$		0			0
$263$	−2859.19	−	4952.26i	−0.670362	−	1.16110i	−0.977802	−	0.209533i	$-0.932806\pi$
$263$	−2859.19	−	4952.26i	−0.670362	−	1.16110i	0.307440	−	0.951568i	$-0.400528\pi$
$264$		0			0
$265$	3427.71	−	5936.97i	0.794576	−	1.37625i
$266$		0			0
$267$	431.883	+	561.516i	0.0989919	+	0.128705i
$268$		0			0
$269$	3607.12			0.817583			0.408792	−	0.912628i	$-0.365950\pi$
$269$	3607.12			0.817583			0.408792	+	0.912628i	$0.365950\pi$
$270$		0			0
$271$	6390.74			1.43251			0.716254	−	0.697839i	$-0.245855\pi$
$271$	6390.74			1.43251			0.716254	+	0.697839i	$0.245855\pi$
$272$		0			0
$273$	−2018.45	−	2624.30i	−0.447482	−	0.581795i
$274$		0			0
$275$	−4841.58	+	8385.87i	−1.06167	+	1.83886i
$276$		0			0
$277$	176.773	+	306.180i	0.0383439	+	0.0664136i	0.884560	−	0.466426i	$-0.154458\pi$
$277$	176.773	+	306.180i	0.0383439	+	0.0664136i	−0.846217	+	0.532839i	$0.821125\pi$
$278$		0			0
$279$	614.748	+	611.952i	0.131914	+	0.131314i
$280$		0			0
$281$	2255.89	+	3907.32i	0.478916	+	0.829507i	0.999708	−	0.0241770i	$-0.00769652\pi$
$281$	2255.89	+	3907.32i	0.478916	+	0.829507i	−0.520792	+	0.853684i	$0.674363\pi$
$282$		0			0
$283$	4661.52	−	8073.99i	0.979148	−	1.69593i	0.313641	−	0.949542i	$-0.398451\pi$
$283$	4661.52	−	8073.99i	0.979148	−	1.69593i	0.665507	−	0.746392i	$-0.268215\pi$
$284$		0			0
$285$	−2035.28	+	270.310i	−0.423017	+	0.0561816i
$286$		0			0
$287$	−3505.71			−0.721029
$288$		0			0
$289$	2514.91			0.511890
$290$		0			0
$291$	−2902.19	+	7029.15i	−0.584637	+	1.41600i
$292$		0			0
$293$	−654.258	+	1133.21i	−0.130451	+	0.225948i	−0.923850	−	0.382754i	$-0.874976\pi$
$293$	−654.258	+	1133.21i	−0.130451	+	0.225948i	0.793400	+	0.608701i	$0.208309\pi$
$294$		0			0
$295$	1856.97	+	3216.37i	0.366498	+	0.634794i
$296$		0			0
$297$	5924.60	+	4514.01i	1.15751	+	0.881917i
$298$		0			0
$299$	1981.93	+	3432.81i	0.383338	+	0.663961i
$300$		0			0
$301$	1721.22	−	2981.24i	0.329600	−	0.570883i
$302$		0			0
$303$	2722.37	−	6593.62i	0.516159	−	1.25014i
$304$		0			0
$305$	4290.38			0.805464
$306$		0			0
$307$	417.504			0.0776163			0.0388081	−	0.999247i	$-0.487644\pi$
$307$	417.504			0.0776163			0.0388081	+	0.999247i	$0.487644\pi$
$308$		0			0
$309$	5627.22	−	747.361i	1.03599	−	0.137592i
$310$		0			0
$311$	−4520.53	+	7829.79i	−0.824231	+	1.42761i	0.0782741	+	0.996932i	$0.475059\pi$
$311$	−4520.53	+	7829.79i	−0.824231	+	1.42761i	−0.902505	+	0.430679i	$0.858274\pi$
$312$		0			0
$313$	−1786.58	−	3094.44i	−0.322630	−	0.558812i	0.658399	−	0.752669i	$-0.271234\pi$
$313$	−1786.58	−	3094.44i	−0.322630	−	0.558812i	−0.981030	+	0.193856i	$0.937900\pi$
$314$		0			0
$315$	850.342	−	3202.70i	0.152100	−	0.572862i
$316$		0			0
$317$	−1840.40	−	3187.66i	−0.326079	−	0.564785i	0.655651	−	0.755064i	$-0.272394\pi$
$317$	−1840.40	−	3187.66i	−0.326079	−	0.564785i	−0.981730	+	0.190279i	$0.939061\pi$
$318$		0			0
$319$	3210.01	−	5559.90i	0.563405	−	0.975846i
$320$		0			0
$321$	−1256.48	−	1633.61i	−0.218472	−	0.284048i
$322$		0			0
$323$	1942.35			0.334598
$324$		0			0
$325$	−16601.7			−2.83354
$326$		0			0
$327$	−6585.51	−	8562.19i	−1.11370	−	1.44798i
$328$		0			0
$329$	−1031.30	+	1786.26i	−0.172818	+	0.299330i
$330$		0			0
$331$	202.551	+	350.829i	0.0336351	+	0.0582577i	0.882353	−	0.470588i	$-0.155958\pi$
$331$	202.551	+	350.829i	0.0336351	+	0.0582577i	−0.848718	+	0.528846i	$0.822625\pi$
$332$		0			0
$333$	−2111.44	+	7952.47i	−0.347467	+	1.30869i
$334$		0			0
$335$	−188.881	−	327.152i	−0.0308050	−	0.0533558i
$336$		0			0
$337$	1538.30	−	2664.41i	0.248654	−	0.430682i	−0.714498	−	0.699637i	$-0.753345\pi$
$337$	1538.30	−	2664.41i	0.248654	−	0.430682i	0.963153	+	0.268955i	$0.0866784\pi$
$338$		0			0
$339$	−1032.13	+	137.079i	−0.165362	+	0.0219620i
$340$		0			0
$341$	−1705.58			−0.270857
$342$		0			0
$343$	343.000			0.0539949
$344$		0			0
$345$	−1514.06	+	3667.07i	−0.236273	+	0.572256i
$346$		0			0
$347$	−2403.08	+	4162.27i	−0.371770	+	0.643925i	−0.989838	−	0.142200i	$-0.954582\pi$
$347$	−2403.08	+	4162.27i	−0.371770	+	0.643925i	0.618068	+	0.786125i	$0.287916\pi$
$348$		0			0
$349$	−4139.79	−	7170.33i	−0.634952	−	1.09977i	−0.986525	−	0.163608i	$-0.947687\pi$
$349$	−4139.79	−	7170.33i	−0.634952	−	1.09977i	0.351574	−	0.936160i	$-0.385647\pi$
$350$		0			0
$351$	−1623.54	+	12666.5i	−0.246889	+	1.92617i
$352$		0			0
$353$	5041.42	+	8732.00i	0.760135	+	1.31659i	0.942781	+	0.333414i	$0.108201\pi$
$353$	5041.42	+	8732.00i	0.760135	+	1.31659i	−0.182645	+	0.983179i	$0.558466\pi$
$354$		0			0
$355$	762.979	−	1321.52i	0.114070	−	0.197574i
$356$		0			0
$357$	−1196.34	+	2897.57i	−0.177359	+	0.429567i
$358$		0			0
$359$	−6001.93			−0.882367			−0.441184	−	0.897417i	$-0.645441\pi$
$359$	−6001.93			−0.882367			−0.441184	+	0.897417i	$0.645441\pi$
$360$		0			0
$361$	−6351.09			−0.925950
$362$		0			0
$363$	−7662.15	+	1017.62i	−1.10787	+	0.147139i
$364$		0			0
$365$	395.160	−	684.437i	0.0566674	−	0.0981508i
$366$		0			0
$367$	643.899	+	1115.27i	0.0915838	+	0.158628i	0.908178	−	0.418585i	$-0.137474\pi$
$367$	643.899	+	1115.27i	0.0915838	+	0.158628i	−0.816594	+	0.577213i	$0.804140\pi$
$368$		0			0
$369$	9583.28	+	9539.70i	1.35199	+	1.34584i
$370$		0			0
$371$	−1368.53	−	2370.37i	−0.191512	−	0.331708i
$372$		0			0
$373$	−4400.21	+	7621.38i	−0.610815	+	1.05796i	0.380288	+	0.924868i	$0.375825\pi$
$373$	−4400.21	+	7621.38i	−0.610815	+	1.05796i	−0.991103	+	0.133095i	$0.957508\pi$
$374$		0			0
$375$	−3187.66	−	4144.45i	−0.438960	−	0.570716i
$376$		0			0
$377$	11007.1			1.50370
$378$		0			0
$379$	572.265			0.0775601			0.0387800	−	0.999248i	$-0.487653\pi$
$379$	572.265			0.0775601			0.0387800	+	0.999248i	$0.487653\pi$
$380$		0			0
$381$	−1163.65	−	1512.92i	−0.156471	−	0.203436i
$382$		0			0
$383$	−4368.43	+	7566.35i	−0.582811	+	1.00946i	0.412334	+	0.911033i	$0.364714\pi$
$383$	−4368.43	+	7566.35i	−0.582811	+	1.00946i	−0.995145	+	0.0984246i	$0.968620\pi$
$384$		0			0
$385$	3257.81	+	5642.69i	0.431255	+	0.746956i
$386$		0			0
$387$	−12817.7	+	3465.81i	−1.68362	+	0.455238i
$388$		0			0
$389$	2812.95	+	4872.17i	0.366638	+	0.635035i	0.989038	−	0.147664i	$-0.0471755\pi$
$389$	2812.95	+	4872.17i	0.366638	+	0.635035i	−0.622400	+	0.782700i	$0.713842\pi$
$390$		0			0
$391$	1876.61	−	3250.38i	0.242722	−	0.420407i
$392$		0			0
$393$	−1564.36	+	207.765i	−0.200792	+	0.0266676i
$394$		0			0
$395$	14439.0			1.83925
$396$		0			0
$397$	7771.31			0.982445			0.491223	−	0.871034i	$-0.336550\pi$
$397$	7771.31			0.982445			0.491223	+	0.871034i	$0.336550\pi$
$398$		0			0
$399$	−312.836	+	757.693i	−0.0392516	+	0.0950679i
$400$		0			0
$401$	2312.53	−	4005.42i	0.287986	−	0.498806i	−0.685343	−	0.728221i	$-0.740348\pi$
$401$	2312.53	−	4005.42i	0.287986	−	0.498806i	0.973329	+	0.229414i	$0.0736810\pi$
$402$		0			0
$403$	−1462.11	−	2532.44i	−0.180726	−	0.313027i
$404$		0			0
$405$	−11039.7	+	6441.02i	−1.35448	+	0.790263i
$406$		0			0
$407$	−8089.31	−	14011.1i	−0.985190	−	1.70640i
$408$		0			0
$409$	−4573.73	+	7921.93i	−0.552949	+	0.957737i	0.445110	+	0.895476i	$0.353164\pi$
$409$	−4573.73	+	7921.93i	−0.552949	+	0.957737i	−0.998060	+	0.0622609i	$0.980169\pi$
$410$		0			0
$411$	3581.48	−	8674.39i	0.429833	−	1.04106i
$412$		0			0
$413$	1482.81			0.176669
$414$		0			0
$415$	13520.7			1.59929
$416$		0			0
$417$	−3997.04	+	530.854i	−0.469390	+	0.0623406i
$418$		0			0
$419$	−1153.64	+	1998.16i	−0.134508	+	0.232975i	−0.925409	−	0.378969i	$-0.876279\pi$
$419$	−1153.64	+	1998.16i	−0.134508	+	0.232975i	0.790901	+	0.611944i	$0.209612\pi$
$420$		0			0
$421$	1535.97	+	2660.37i	0.177811	+	0.307978i	0.941130	−	0.338044i	$-0.109765\pi$
$421$	1535.97	+	2660.37i	0.177811	+	0.307978i	−0.763320	+	0.646021i	$0.776432\pi$
$422$		0			0
$423$	7679.93	−	2076.60i	0.882768	−	0.238694i
$424$		0			0
$425$	7859.76	+	13613.5i	0.897069	+	1.55377i
$426$		0			0
$427$	856.481	−	1483.47i	0.0970680	−	0.168127i
$428$		0			0
$429$	−15308.5	−	19903.4i	−1.72285	−	2.23997i
$430$		0			0
$431$	−8169.57			−0.913027			−0.456513	−	0.889717i	$-0.650902\pi$
$431$	−8169.57			−0.913027			−0.456513	+	0.889717i	$0.650902\pi$
$432$		0			0
$433$	16056.7			1.78207			0.891033	−	0.453939i	$-0.149981\pi$
$433$	16056.7			1.78207			0.891033	+	0.453939i	$0.149981\pi$
$434$		0			0
$435$	6716.53	+	8732.53i	0.740306	+	0.962512i
$436$		0			0
$437$	490.720	−	849.953i	0.0537170	−	0.0930406i
$438$		0			0
$439$	4984.72	+	8633.78i	0.541931	+	0.938651i	0.998793	+	0.0491139i	$0.0156397\pi$
$439$	4984.72	+	8633.78i	0.541931	+	0.938651i	−0.456863	+	0.889537i	$0.651027\pi$
$440$		0			0
$441$	−937.632	−	933.368i	−0.101245	−	0.100785i
$442$		0			0
$443$	8326.16	+	14421.3i	0.892974	+	1.54668i	0.836292	+	0.548285i	$0.184719\pi$
$443$	8326.16	+	14421.3i	0.892974	+	1.54668i	0.0566828	+	0.998392i	$0.481948\pi$
$444$		0			0
$445$	1195.12	−	2070.00i	0.127312	−	0.220511i
$446$		0			0
$447$	−3301.93	+	438.536i	−0.349387	+	0.0464028i
$448$		0			0
$449$	5548.18			0.583151			0.291576	−	0.956548i	$-0.405820\pi$
$449$	5548.18			0.583151			0.291576	+	0.956548i	$0.405820\pi$
$450$		0			0
$451$	−26588.2			−2.77603
$452$		0			0
$453$	−1954.77	+	4734.48i	−0.202744	+	0.491049i
$454$		0			0
$455$	−5585.50	+	9674.37i	−0.575500	+	0.996795i
$456$		0			0
$457$	−2406.96	−	4168.98i	−0.246374	−	0.426732i	0.716143	−	0.697954i	$-0.245906\pi$
$457$	−2406.96	−	4168.98i	−0.246374	−	0.426732i	−0.962517	+	0.271221i	$0.912573\pi$
$458$		0			0
$459$	11155.2	−	4665.36i	1.13438	−	0.474424i
$460$		0			0
$461$	−2148.39	−	3721.11i	−0.217051	−	0.375943i	0.736854	−	0.676052i	$-0.236310\pi$
$461$	−2148.39	−	3721.11i	−0.217051	−	0.375943i	−0.953905	+	0.300109i	$0.902977\pi$
$462$		0			0
$463$	344.777	−	597.172i	0.0346073	−	0.0599415i	−0.848203	−	0.529671i	$-0.822315\pi$
$463$	344.777	−	597.172i	0.0346073	−	0.0599415i	0.882810	+	0.469730i	$0.155649\pi$
$464$		0			0
$465$	1116.95	−	2705.26i	0.111392	−	0.269792i
$466$		0			0
$467$	1362.82			0.135040			0.0675202	−	0.997718i	$-0.478491\pi$
$467$	1362.82			0.135040			0.0675202	+	0.997718i	$0.478491\pi$
$468$		0			0
$469$	−150.824			−0.0148495
$470$		0			0
$471$	−469.202	+	62.3156i	−0.0459017	+	0.00609629i
$472$		0			0
$473$	13054.2	−	22610.5i	1.26899	−	2.19795i
$474$		0			0
$475$	2055.27	+	3559.84i	0.198531	+	0.343866i
$476$		0			0
$477$	−2709.18	+	10203.7i	−0.260052	+	0.979449i
$478$		0			0
$479$	−4620.25	−	8002.51i	−0.440720	−	0.763349i	0.557023	−	0.830497i	$-0.311943\pi$
$479$	−4620.25	−	8002.51i	−0.440720	−	0.763349i	−0.997743	+	0.0671481i	$0.978610\pi$
$480$		0			0
$481$	13869.1	−	24022.0i	1.31471	−	2.27715i
$482$		0			0
$483$	965.699	+	1255.56i	0.0909748	+	0.118281i
$484$		0			0
$485$	25659.4			2.40234
$486$		0			0
$487$	2894.08			0.269288			0.134644	−	0.990894i	$-0.457011\pi$
$487$	2894.08			0.269288			0.134644	+	0.990894i	$0.457011\pi$
$488$		0			0
$489$	5888.91	+	7656.50i	0.544592	+	0.708055i
$490$		0			0
$491$	3029.45	−	5247.17i	0.278447	−	0.482284i	−0.692552	−	0.721368i	$-0.743514\pi$
$491$	3029.45	−	5247.17i	0.278447	−	0.482284i	0.970999	+	0.239084i	$0.0768471\pi$
$492$		0			0
$493$	−5211.09	−	9025.88i	−0.476056	−	0.824554i
$494$		0			0
$495$	6449.22	−	24290.1i	0.585597	−	2.20557i
$496$		0			0
$497$	−304.624	−	527.625i	−0.0274935	−	0.0476201i
$498$		0			0
$499$	−5003.26	+	8665.90i	−0.448851	+	0.777433i	−0.998312	−	0.0580870i	$-0.981500\pi$
$499$	−5003.26	+	8665.90i	−0.448851	+	0.777433i	0.549461	+	0.835520i	$0.314833\pi$
$500$		0			0
$501$	−9654.44	+	1282.22i	−0.860935	+	0.114342i
$502$		0			0
$503$	−10942.0			−0.969939			−0.484969	−	0.874531i	$-0.661169\pi$
$503$	−10942.0			−0.969939			−0.484969	+	0.874531i	$0.661169\pi$
$504$		0			0
$505$	−24069.6			−2.12096
$506$		0			0
$507$	12072.7	−	29240.2i	1.05753	−	2.56135i
$508$		0			0
$509$	−1753.51	+	3037.17i	−0.152698	+	0.264480i	−0.932218	−	0.361896i	$-0.882129\pi$
$509$	−1753.51	+	3037.17i	−0.152698	+	0.264480i	0.779521	+	0.626377i	$0.215463\pi$
$510$		0			0
$511$	−157.770	−	273.266i	−0.0136582	−	0.0236567i
$512$		0			0
$513$	2917.00	−	1219.96i	0.251050	−	0.104995i
$514$		0			0
$515$	−9576.90	−	16587.7i	−0.819435	−	1.41930i
$516$		0			0
$517$	−7821.63	+	13547.5i	−0.665367	+	1.15245i
$518$		0			0
$519$	3936.70	−	9534.74i	0.332951	−	0.806413i
$520$		0			0
$521$	−3765.62			−0.316650			−0.158325	−	0.987387i	$-0.550609\pi$
$521$	−3765.62			−0.316650			−0.158325	+	0.987387i	$0.550609\pi$
$522$		0			0
$523$	−21229.9			−1.77499			−0.887494	−	0.460820i	$-0.847555\pi$
$523$	−21229.9			−1.77499			−0.887494	+	0.460820i	$0.847555\pi$
$524$		0			0
$525$	−6576.41	+	873.426i	−0.546701	+	0.0726084i
$526$		0			0
$527$	−1384.41	+	2397.87i	−0.114432	+	0.198202i
$528$		0			0
$529$	5135.28	+	8894.56i	0.422066	+	0.731039i
$530$		0			0
$531$	−4053.45	−	4035.02i	−0.331271	−	0.329764i
$532$		0			0
$533$	−22792.7	−	39478.1i	−1.85227	−	3.20823i
$534$		0			0
$535$	−3476.94	+	6022.24i	−0.280974	+	0.486662i
$536$		0			0
$537$	4450.65	+	5786.54i	0.357653	+	0.465005i
$538$		0			0
$539$	2601.40			0.207886
$540$		0			0
$541$	9167.82			0.728568			0.364284	−	0.931288i	$-0.381314\pi$
$541$	9167.82			0.728568			0.364284	+	0.931288i	$0.381314\pi$
$542$		0			0
$543$	3674.12	+	4776.93i	0.290371	+	0.377528i
$544$		0			0
$545$	−18223.5	+	31564.1i	−1.43231	+	2.48084i
$546$		0			0
$547$	−4906.09	−	8497.60i	−0.383491	−	0.664225i	0.608068	−	0.793885i	$-0.291945\pi$
$547$	−4906.09	−	8497.60i	−0.383491	−	0.664225i	−0.991559	+	0.129660i	$0.958612\pi$
$548$		0			0
$549$	−6378.09	+	1724.59i	−0.495829	+	0.134069i
$550$		0			0
$551$	−1362.66	−	2360.20i	−0.105357	−	0.182483i
$552$		0			0
$553$	2882.43	−	4992.52i	0.221652	−	0.383912i
$554$		0			0
$555$	27520.8	−	3655.09i	2.10485	−	0.279550i
$556$		0			0
$557$	−2135.71			−0.162465			−0.0812324	−	0.996695i	$-0.525886\pi$
$557$	−2135.71			−0.162465			−0.0812324	+	0.996695i	$0.525886\pi$
$558$		0			0
$559$	44762.7			3.38687
$560$		0			0
$561$	−9073.39	+	21975.9i	−0.682850	+	1.65387i
$562$		0			0
$563$	1170.24	−	2026.91i	0.0876016	−	0.151730i	−0.818895	−	0.573943i	$-0.805413\pi$
$563$	1170.24	−	2026.91i	0.0876016	−	0.151730i	0.906497	+	0.422213i	$0.138746\pi$
$564$		0			0
$565$	1756.57	+	3042.47i	0.130796	+	0.226545i
$566$		0			0
$567$	23.2585	+	5102.95i	0.00172269	+	0.377961i
$568$		0			0
$569$	−2873.99	−	4977.90i	−0.211747	−	0.366756i	0.740514	−	0.672040i	$-0.234582\pi$
$569$	−2873.99	−	4977.90i	−0.211747	−	0.366756i	−0.952261	+	0.305284i	$0.901249\pi$
$570$		0			0
$571$	11624.2	−	20133.6i	0.851937	−	1.47560i	−0.0275200	−	0.999621i	$-0.508761\pi$
$571$	11624.2	−	20133.6i	0.851937	−	1.47560i	0.879457	−	0.475978i	$-0.157906\pi$
$572$		0			0
$573$	128.270	−	310.673i	0.00935179	−	0.0226502i
$574$		0			0
$575$	7942.86			0.576070
$576$		0			0
$577$	4081.32			0.294467			0.147234	−	0.989102i	$-0.452963\pi$
$577$	4081.32			0.294467			0.147234	+	0.989102i	$0.452963\pi$
$578$		0			0
$579$	−19416.3	+	2578.71i	−1.39363	+	0.185091i
$580$		0			0
$581$	2699.11	−	4674.99i	0.192733	−	0.333823i
$582$		0			0
$583$	−10379.3	−	17977.5i	−0.737337	−	1.27711i
$584$		0			0
$585$	41594.4	−	11246.9i	2.93969	−	0.794872i
$586$		0			0
$587$	−1209.58	−	2095.06i	−0.0850507	−	0.147312i	0.820362	−	0.571844i	$-0.193772\pi$
$587$	−1209.58	−	2095.06i	−0.0850507	−	0.147312i	−0.905413	+	0.424532i	$0.860439\pi$
$588$		0			0
$589$	−362.013	+	627.025i	−0.0253251	+	0.0438644i
$590$		0			0
$591$	16019.4	+	20827.7i	1.11498	+	1.44964i
$592$		0			0
$593$	−8391.07			−0.581079			−0.290539	−	0.956863i	$-0.593835\pi$
$593$	−8391.07			−0.581079			−0.290539	+	0.956863i	$0.593835\pi$
$594$		0			0
$595$	10577.4			0.728790
$596$		0			0
$597$	9954.67	+	12942.6i	0.682441	+	0.887280i
$598$		0			0
$599$	939.336	−	1626.98i	0.0640738	−	0.110979i	−0.832209	−	0.554462i	$-0.812924\pi$
$599$	939.336	−	1626.98i	0.0640738	−	0.110979i	0.896283	+	0.443483i	$0.146257\pi$
$600$		0			0
$601$	2555.41	+	4426.11i	0.173440	+	0.300407i	0.939620	−	0.342219i	$-0.111178\pi$
$601$	2555.41	+	4426.11i	0.173440	+	0.300407i	−0.766180	+	0.642626i	$0.777845\pi$
$602$		0			0
$603$	412.295	+	410.420i	0.0278441	+	0.0277174i
$604$		0			0
$605$	13040.1	+	22586.2i	0.876292	+	1.51778i
$606$		0			0
$607$	−5699.39	+	9871.63i	−0.381105	+	0.660094i	−0.991221	−	0.132219i	$-0.957790\pi$
$607$	−5699.39	+	9871.63i	−0.381105	+	0.660094i	0.610115	+	0.792313i	$0.291123\pi$
$608$		0			0
$609$	4360.22	−	579.089i	0.290123	−	0.0385318i
$610$		0			0
$611$	−26820.3			−1.77583
$612$		0			0
$613$	7564.15			0.498390			0.249195	−	0.968453i	$-0.419834\pi$
$613$	7564.15			0.498390			0.249195	+	0.968453i	$0.419834\pi$
$614$		0			0
$615$	17412.0	−	42172.2i	1.14166	−	2.76512i
$616$		0			0
$617$	12265.8	−	21245.0i	0.800327	−	1.38621i	−0.119074	−	0.992885i	$-0.537993\pi$
$617$	12265.8	−	21245.0i	0.800327	−	1.38621i	0.919401	−	0.393321i	$-0.128674\pi$
$618$		0			0
$619$	8129.23	+	14080.2i	0.527854	+	0.914270i	0.999473	+	0.0324672i	$0.0103364\pi$
$619$	8129.23	+	14080.2i	0.527854	+	0.914270i	−0.471619	+	0.881802i	$0.656330\pi$
$620$		0			0
$621$	776.758	−	6060.07i	0.0501936	−	0.391598i
$622$		0			0
$623$	−477.157	−	826.461i	−0.0306852	−	0.0531484i
$624$		0			0
$625$	2578.57	−	4466.21i	0.165028	−	0.285838i
$626$		0			0
$627$	−2372.63	+	5746.54i	−0.151122	+	0.366020i
$628$		0			0
$629$	−26264.2			−1.66490
$630$		0			0
$631$	−17481.0			−1.10286			−0.551432	−	0.834220i	$-0.685918\pi$
$631$	−17481.0			−1.10286			−0.551432	+	0.834220i	$0.685918\pi$
$632$		0			0
$633$	−22734.8	+	3019.46i	−1.42753	+	0.189593i
$634$		0			0
$635$	−3220.06	+	5577.31i	−0.201235	+	0.348549i
$636$		0			0
$637$	2230.05	+	3862.55i	0.138709	+	0.240251i
$638$		0			0
$639$	−603.040	+	2271.27i	−0.0373331	+	0.140610i
$640$		0			0
$641$	1593.19	+	2759.48i	0.0981703	+	0.170036i	0.910927	−	0.412567i	$-0.135368\pi$
$641$	1593.19	+	2759.48i	0.0981703	+	0.170036i	−0.812757	+	0.582603i	$0.802034\pi$
$642$		0			0
$643$	−11750.5	+	20352.5i	−0.720676	+	1.24825i	0.240053	+	0.970760i	$0.422835\pi$
$643$	−11750.5	+	20352.5i	−0.720676	+	1.24825i	−0.960729	+	0.277488i	$0.910498\pi$
$644$		0			0
$645$	27314.2	+	35512.7i	1.66743	+	2.16792i
$646$		0			0
$647$	−3615.80			−0.219709			−0.109855	−	0.993948i	$-0.535039\pi$
$647$	−3615.80			−0.219709			−0.109855	+	0.993948i	$0.535039\pi$
$648$		0			0
$649$	11246.0			0.680194
$650$		0			0
$651$	−712.413	−	926.248i	−0.0428904	−	0.0557642i
$652$		0			0
$653$	−2920.81	+	5058.98i	−0.175038	+	0.303175i	−0.940174	−	0.340693i	$-0.889338\pi$
$653$	−2920.81	+	5058.98i	−0.175038	+	0.303175i	0.765136	+	0.643868i	$0.222672\pi$
$654$		0			0
$655$	2662.36	+	4611.35i	0.158820	+	0.275084i
$656$		0			0
$657$	−312.324	+	1176.33i	−0.0185463	+	0.0698521i
$658$		0			0
$659$	1058.45	+	1833.29i	0.0625665	+	0.108368i	0.895612	−	0.444836i	$-0.146738\pi$
$659$	1058.45	+	1833.29i	0.0625665	+	0.108368i	−0.833045	+	0.553205i	$0.813405\pi$
$660$		0			0
$661$	−11342.7	+	19646.1i	−0.667443	+	1.15605i	0.311174	+	0.950353i	$0.399278\pi$
$661$	−11342.7	+	19646.1i	−0.667443	+	1.15605i	−0.978617	+	0.205692i	$0.934055\pi$
$662$		0			0
$663$	−40407.9	+	5366.65i	−2.36699	+	0.314364i
$664$		0			0
$665$	2765.91			0.161289
$666$		0			0
$667$	−5266.19			−0.305708
$668$		0			0
$669$	−2214.35	+	5363.19i	−0.127970	+	0.309944i
$670$		0			0
$671$	6495.77	−	11251.0i	0.373721	−	0.647303i
$672$		0			0
$673$	−8609.95	−	14912.9i	−0.493149	−	0.854159i	0.506820	−	0.862052i	$-0.330821\pi$
$673$	−8609.95	−	14912.9i	−0.493149	−	0.854159i	−0.999969	+	0.00789288i	$0.997488\pi$
$674$		0			0
$675$	20354.2	+	15508.0i	1.16064	+	0.884304i
$676$		0			0
$677$	−2317.11	−	4013.36i	−0.131542	−	0.227838i	0.792729	−	0.609574i	$-0.208660\pi$
$677$	−2317.11	−	4013.36i	−0.131542	−	0.227838i	−0.924271	+	0.381737i	$0.875326\pi$
$678$		0			0
$679$	5122.34	−	8872.16i	0.289510	−	0.501447i
$680$		0			0
$681$	11799.7	−	28579.1i	0.663974	−	1.60816i
$682$		0			0
$683$	−11821.1			−0.662259			−0.331130	−	0.943585i	$-0.607430\pi$
$683$	−11821.1			−0.662259			−0.331130	+	0.943585i	$0.607430\pi$
$684$		0			0
$685$	−31665.3			−1.76623
$686$		0			0
$687$	20639.4	−	2741.16i	1.14620	−	0.152229i
$688$		0			0
$689$	17795.3	−	30822.4i	0.983959	−	1.70427i
$690$		0			0
$691$	10685.9	+	18508.6i	0.588295	+	1.01896i	0.994456	+	0.105155i	$0.0335340\pi$
$691$	10685.9	+	18508.6i	0.588295	+	1.01896i	−0.406161	+	0.913802i	$0.633133\pi$
$692$		0			0
$693$	−7111.24	−	7078.91i	−0.389803	−	0.388031i
$694$		0			0
$695$	6802.52	+	11782.3i	0.371272	+	0.643062i
$696$		0			0
$697$	−21581.5	+	37380.2i	−1.17282	+	2.03139i
$698$		0			0
$699$	−3928.07	−	5107.10i	−0.212551	−	0.276350i
$700$		0			0
$701$	6626.57			0.357036			0.178518	−	0.983937i	$-0.442870\pi$
$701$	6626.57			0.357036			0.178518	+	0.983937i	$0.442870\pi$
$702$		0			0
$703$	−6867.90			−0.368460
$704$		0			0
$705$	−16365.7	−	21278.0i	−0.874282	−	1.13670i
$706$		0			0
$707$	−4804.97	+	8322.44i	−0.255600	+	0.442712i
$708$		0			0
$709$	5919.65	+	10253.1i	0.313564	+	0.543110i	0.979131	−	0.203229i	$-0.0651435\pi$
$709$	5919.65	+	10253.1i	0.313564	+	0.543110i	−0.665567	+	0.746338i	$0.731810\pi$
$710$		0			0
$711$	−21465.1	+	5804.01i	−1.13221	+	0.306142i
$712$		0			0
$713$	699.522	+	1211.61i	0.0367424	+	0.0636397i
$714$		0			0
$715$	−42361.9	+	73373.0i	−2.21573	+	3.83775i
$716$		0			0
$717$	26990.5	−	3584.66i	1.40583	−	0.186711i
$718$		0			0
$719$	−8357.40			−0.433489			−0.216744	−	0.976228i	$-0.569544\pi$
$719$	−8357.40			−0.433489			−0.216744	+	0.976228i	$0.569544\pi$
$720$		0			0
$721$	−7647.28			−0.395006
$722$		0			0
$723$	−4805.25	+	11638.4i	−0.247178	+	0.598668i
$724$		0			0
$725$	11028.1	−	19101.3i	0.564930	−	0.978487i
$726$		0			0
$727$	−15466.2	−	26788.2i	−0.789009	−	1.36660i	−0.926575	−	0.376111i	$-0.877261\pi$
$727$	−15466.2	−	26788.2i	−0.789009	−	1.36660i	0.137566	−	0.990493i	$-0.456072\pi$
$728$		0			0
$729$	13822.5	−	14012.8i	0.702256	−	0.711925i
$730$		0			0
$731$	−21192.0	−	36705.6i	−1.07225	−	1.85719i
$732$		0			0
$733$	−7589.90	+	13146.1i	−0.382455	+	0.662431i	−0.991413	−	0.130771i	$-0.958255\pi$
$733$	−7589.90	+	13146.1i	−0.382455	+	0.662431i	0.608958	+	0.793203i	$0.291588\pi$
$734$		0			0
$735$	−1703.60	+	4126.14i	−0.0854941	+	0.207068i
$736$		0			0
$737$	−1143.89			−0.0571718
$738$		0			0
$739$	16843.9			0.838449			0.419225	−	0.907883i	$-0.362302\pi$
$739$	16843.9			0.838449			0.419225	+	0.907883i	$0.362302\pi$
$740$		0			0
$741$	−10566.4	+	1403.34i	−0.523840	+	0.0695722i
$742$		0			0
$743$	−8304.96	+	14384.6i	−0.410066	+	0.710256i	−0.994897	−	0.100900i	$-0.967828\pi$
$743$	−8304.96	+	14384.6i	−0.410066	+	0.710256i	0.584830	+	0.811156i	$0.301161\pi$
$744$		0			0
$745$	5619.53	+	9733.31i	0.276354	+	0.478659i
$746$		0			0
$747$	−20099.9	+	5434.87i	−0.984492	+	0.266200i
$748$		0			0
$749$	1388.19	+	2404.42i	0.0677215	+	0.117297i
$750$		0			0
$751$	7250.78	−	12558.7i	0.352310	−	0.610218i	−0.634344	−	0.773051i	$-0.718730\pi$
$751$	7250.78	−	12558.7i	0.352310	−	0.610218i	0.986654	+	0.162833i	$0.0520630\pi$
$752$		0			0
$753$	11770.4	+	15303.4i	0.569638	+	0.740618i
$754$		0			0
$755$	17282.9			0.833098
$756$		0			0
$757$	−21222.1			−1.01893			−0.509466	−	0.860491i	$-0.670157\pi$
$757$	−21222.1			−1.01893			−0.509466	+	0.860491i	$0.670157\pi$
$758$		0			0
$759$	7324.11	+	9522.49i	0.350262	+	0.455394i
$760$		0			0
$761$	−6102.12	+	10569.2i	−0.290672	+	0.503459i	−0.973969	−	0.226682i	$-0.927212\pi$
$761$	−6102.12	+	10569.2i	−0.290672	+	0.503459i	0.683297	+	0.730141i	$0.260546\pi$
$762$		0			0
$763$	7275.86	+	12602.2i	0.345221	+	0.597941i
$764$		0			0
$765$	−28914.5	−	28783.0i	−1.36654	−	1.36033i
$766$		0			0
$767$	9640.65	+	16698.1i	0.453851	+	0.786093i
$768$		0			0
$769$	12828.8	−	22220.2i	0.601585	−	1.04198i	−0.390996	−	0.920392i	$-0.627869\pi$
$769$	12828.8	−	22220.2i	0.601585	−	1.04198i	0.992581	−	0.121584i	$-0.0387973\pi$
$770$		0			0
$771$	−3082.33	+	409.370i	−0.143979	+	0.0191221i
$772$		0			0
$773$	827.023			0.0384812			0.0192406	−	0.999815i	$-0.493875\pi$
$773$	827.023			0.0384812			0.0192406	+	0.999815i	$0.493875\pi$
$774$		0			0
$775$	−5859.58			−0.271590
$776$		0			0
$777$	4230.13	−	10245.4i	0.195309	−	0.473041i
$778$		0			0
$779$	−5643.40	+	9774.66i	−0.259558	+	0.449568i
$780$		0			0
$781$	−2310.35	−	4001.64i	−0.105853	−	0.183342i
$782$		0			0
$783$	−13495.0	−	10282.0i	−0.615928	−	0.469282i
$784$		0			0
$785$	798.530	+	1383.09i	0.0363067	+	0.0628850i
$786$		0			0
$787$	9088.72	−	15742.1i	0.411662	−	0.713019i	−0.583410	−	0.812178i	$-0.698282\pi$
$787$	9088.72	−	15742.1i	0.411662	−	0.713019i	0.995072	+	0.0991586i	$0.0316151\pi$
$788$		0			0
$789$	11339.6	−	27464.7i	0.511661	−	1.23925i
$790$		0			0
$791$	1402.65			0.0630497
$792$		0			0
$793$	22274.0			0.997442
$794$		0			0
$795$	35311.7	−	4689.82i	1.57532	−	0.209221i
$796$		0			0
$797$	−15907.2	+	27552.1i	−0.706979	+	1.22452i	0.258994	+	0.965879i	$0.416609\pi$
$797$	−15907.2	+	27552.1i	−0.706979	+	1.22452i	−0.965973	+	0.258644i	$0.916724\pi$
$798$		0			0
$799$	12697.5	+	21992.8i	0.562211	+	0.973778i
$800$		0			0
$801$	−944.589	+	3557.66i	−0.0416672	+	0.156934i
$802$		0			0
$803$	−1196.57	−	2072.52i	−0.0525853	−	0.0910804i
$804$		0			0
$805$	2672.30	−	4628.56i	0.117001	−	0.202652i
$806$		0			0
$807$	11427.0	+	14856.9i	0.498452	+	0.648065i
$808$		0			0
$809$	21778.4			0.946461			0.473231	−	0.880939i	$-0.343088\pi$
$809$	21778.4			0.946461			0.473231	+	0.880939i	$0.343088\pi$
$810$		0			0
$811$	34001.7			1.47221			0.736105	−	0.676868i	$-0.236663\pi$
$811$	34001.7			1.47221			0.736105	+	0.676868i	$0.236663\pi$
$812$		0			0
$813$	20245.3	+	26322.0i	0.873351	+	1.13549i
$814$		0			0
$815$	16295.9	−	28225.3i	0.700393	−	1.21312i
$816$		0			0
$817$	−5541.56	−	9598.26i	−0.237301	−	0.411017i
$818$		0			0
$819$	4414.64	−	16627.1i	0.188352	−	0.709401i
$820$		0			0
$821$	16878.2	+	29233.9i	0.717482	+	1.24271i	0.961995	+	0.273069i	$0.0880386\pi$
$821$	16878.2	+	29233.9i	0.717482	+	1.24271i	−0.244513	+	0.969646i	$0.578628\pi$
$822$		0			0
$823$	−15918.0	+	27570.8i	−0.674201	+	1.16775i	0.302501	+	0.953149i	$0.402178\pi$
$823$	−15918.0	+	27570.8i	−0.674201	+	1.16775i	−0.976702	+	0.214601i	$0.931155\pi$
$824$		0			0
$825$	−49877.2	+	6624.29i	−2.10485	+	0.279549i
$826$		0			0
$827$	−317.710			−0.0133589			−0.00667947	−	0.999978i	$-0.502126\pi$
$827$	−317.710			−0.0133589			−0.00667947	+	0.999978i	$0.502126\pi$
$828$		0			0
$829$	28689.0			1.20194			0.600970	−	0.799271i	$-0.294781\pi$
$829$	28689.0			1.20194			0.600970	+	0.799271i	$0.294781\pi$
$830$		0			0
$831$	−701.085	+	1698.04i	−0.0292664	+	0.0708837i
$832$		0			0
$833$	2111.54	−	3657.30i	0.0878278	−	0.152122i
$834$		0			0
$835$	16430.8	+	28459.0i	0.680971	+	1.17948i
$836$		0			0
$837$	−573.028	+	4470.62i	−0.0236640	+	0.184620i
$838$		0			0
$839$	−33.8959	−	58.7094i	−0.00139478	−	0.00241582i	0.865327	−	0.501207i	$-0.167111\pi$
$839$	−33.8959	−	58.7094i	−0.00139478	−	0.00241582i	−0.866722	+	0.498792i	$0.833777\pi$
$840$		0			0
$841$	4882.76	−	8457.18i	0.200203	−	0.346762i
$842$		0			0
$843$	−8946.92	+	21669.6i	−0.365538	+	0.885338i
$844$		0			0
$845$	−106740.			−4.34551
$846$		0			0
$847$	10412.7			0.422414
$848$		0			0
$849$	48022.3	−	6377.93i	1.94125	−	0.257821i
$850$		0			0
$851$	−6635.46	+	11493.0i	−0.267286	+	0.462953i
$852$		0			0
$853$	−2509.42	−	4346.44i	−0.100728	−	0.174466i	0.811257	−	0.584690i	$-0.198784\pi$
$853$	−2509.42	−	4346.44i	−0.100728	−	0.174466i	−0.911985	+	0.410224i	$0.865450\pi$
$854$		0			0
$855$	−7560.94	−	7526.56i	−0.302431	−	0.301056i
$856$		0			0
$857$	−13060.5	−	22621.5i	−0.520582	−	0.901674i	−0.999714	−	0.0239313i	$-0.992382\pi$
$857$	−13060.5	−	22621.5i	−0.520582	−	0.901674i	0.479132	−	0.877743i	$-0.340952\pi$
$858$		0			0
$859$	8536.13	−	14785.0i	0.339056	−	0.587262i	−0.645200	−	0.764014i	$-0.723226\pi$
$859$	8536.13	−	14785.0i	0.339056	−	0.587262i	0.984255	+	0.176752i	$0.0565592\pi$
$860$		0			0
$861$	−11105.8	−	14439.2i	−0.439586	−	0.571530i
$862$		0			0
$863$	−12261.4			−0.483643			−0.241822	−	0.970321i	$-0.577745\pi$
$863$	−12261.4			−0.483643			−0.241822	+	0.970321i	$0.577745\pi$
$864$		0			0
$865$	−34805.9			−1.36814
$866$		0			0
$867$	7967.03	+	10358.4i	0.312081	+	0.405754i
$868$		0			0
$869$	21861.1	−	37864.6i	0.853380	−	1.47810i
$870$		0			0
$871$	−980.596	−	1698.44i	−0.0381472	−	0.0660729i
$872$		0			0
$873$	−38145.4	+	10314.3i	−1.47884	+	0.399868i
$874$		0			0
$875$	3521.81	+	6099.96i	0.136067	+	0.235676i
$876$		0			0
$877$	13115.4	−	22716.5i	0.504989	−	0.874666i	−0.494994	−	0.868896i	$-0.664830\pi$
$877$	13115.4	−	22716.5i	0.504989	−	0.874666i	0.999983	−	0.00577033i	$-0.00183676\pi$
$878$		0			0
$879$	−6740.06	+	895.160i	−0.258631	+	0.0343493i
$880$		0			0
$881$	27908.0			1.06725			0.533624	−	0.845722i	$-0.320830\pi$
$881$	27908.0			1.06725			0.533624	+	0.845722i	$0.320830\pi$
$882$		0			0
$883$	−36371.5			−1.38618			−0.693091	−	0.720850i	$-0.743752\pi$
$883$	−36371.5			−1.38618			−0.693091	+	0.720850i	$0.743752\pi$
$884$		0			0
$885$	−7364.78	+	17837.6i	−0.279734	+	0.677520i
$886$		0			0
$887$	−15699.5	+	27192.2i	−0.594291	+	1.02934i	0.399356	+	0.916796i	$0.369234\pi$
$887$	−15699.5	+	27192.2i	−0.594291	+	1.02934i	−0.993647	+	0.112546i	$0.964099\pi$
$888$		0			0
$889$	1285.63	+	2226.77i	0.0485024	+	0.0840086i
$890$		0			0
$891$	176.399	+	38702.1i	0.00663252	+	1.45518i
$892$		0			0
$893$	3320.32	+	5750.96i	0.124423	+	0.215508i
$894$		0			0
$895$	12315.9	−	21331.8i	0.459973	−	0.796697i
$896$		0			0
$897$	−7860.38	+	19038.0i	−0.292587	+	0.708650i
$898$		0			0
$899$	3884.96			0.144127
$900$		0			0
$901$	−33699.3			−1.24605
$902$		0			0
$903$	17731.7	−	2354.99i	0.653461	−	0.0867874i
$904$		0			0
$905$	10167.1	−	17609.9i	0.373443	−	0.646822i
$906$		0			0
$907$	−18314.1	−	31720.9i	−0.670462	−	1.16127i	−0.977773	−	0.209665i	$-0.932763\pi$
$907$	−18314.1	−	31720.9i	−0.670462	−	1.16127i	0.307312	−	0.951609i	$-0.400571\pi$
$908$		0			0
$909$	35781.9	−	9675.18i	1.30562	−	0.353031i
$910$		0			0
$911$	−2964.85	−	5135.28i	−0.107827	−	0.186761i	0.807063	−	0.590465i	$-0.201056\pi$
$911$	−2964.85	−	5135.28i	−0.107827	−	0.186761i	−0.914890	+	0.403704i	$0.867722\pi$
$912$		0			0
$913$	20470.7	−	35456.3i	0.742039	−	1.28525i
$914$		0			0
$915$	13591.6	+	17671.1i	0.491063	+	0.638459i
$916$		0			0
$917$	2125.93			0.0765588
$918$		0			0
$919$	43023.8			1.54431			0.772156	−	0.635433i	$-0.219178\pi$
$919$	43023.8			1.54431			0.772156	+	0.635433i	$0.219178\pi$
$920$		0			0
$921$	1322.62	+	1719.61i	0.0473199	+	0.0615233i
$922$		0			0
$923$	3961.09	−	6860.80i	0.141258	−	0.244665i
$924$		0			0
$925$	−27791.1	−	48135.7i	−0.987856	−	1.71102i
$926$		0			0
$927$	20904.8	+	20809.7i	0.740671	+	0.737303i
$928$		0			0
$929$	12680.8	+	21963.8i	0.447841	+	0.775683i	0.998245	−	0.0592150i	$-0.0188598\pi$
$929$	12680.8	+	21963.8i	0.447841	+	0.775683i	−0.550404	+	0.834898i	$0.685526\pi$
$930$		0			0
$931$	552.153	−	956.357i	0.0194373	−	0.0336663i
$932$		0			0
$933$	−46569.8	+	6185.03i	−1.63411	+	0.217030i
$934$		0			0
$935$	80221.5			2.80591
$936$		0			0
$937$	−38679.3			−1.34856			−0.674279	−	0.738477i	$-0.735546\pi$
$937$	−38679.3			−1.34856			−0.674279	+	0.738477i	$0.735546\pi$
$938$		0			0
$939$	7085.60	−	17161.4i	0.246251	−	0.596424i
$940$		0			0
$941$	14184.1	−	24567.6i	0.491381	−	0.851096i	−0.508570	−	0.861021i	$-0.669826\pi$
$941$	14184.1	−	24567.6i	0.491381	−	0.851096i	0.999951	+	0.00992428i	$0.00315905\pi$
$942$		0			0
$943$	10904.8	+	18887.7i	0.376574	+	0.652246i
$944$		0			0
$945$	15885.0	−	6643.49i	0.546814	−	0.228691i
$946$		0			0
$947$	−23084.9	−	39984.2i	−0.792142	−	1.37203i	−0.924638	−	0.380846i	$-0.875633\pi$
$947$	−23084.9	−	39984.2i	−0.792142	−	1.37203i	0.132497	−	0.991183i	$-0.457701\pi$
$948$		0			0
$949$	2051.51	−	3553.32i	0.0701738	−	0.121545i
$950$		0			0
$951$	7299.05	−	17678.4i	0.248883	−	0.602799i
$952$		0			0
$953$	−41217.2			−1.40100			−0.700501	−	0.713651i	$-0.747040\pi$
$953$	−41217.2			−1.40100			−0.700501	+	0.713651i	$0.747040\pi$
$954$		0			0
$955$	−1134.09			−0.0384276
$956$		0			0
$957$	33069.1	−	4391.96i	1.11700	−	0.148351i
$958$		0			0
$959$	−6321.28	+	10948.8i	−0.212852	+	0.368670i
$960$		0			0
$961$	14379.5	+	24905.9i	0.482678	+	0.836022i
$962$		0			0
$963$	2748.09	−	10350.3i	0.0919583	−	0.346348i
$964$		0			0
$965$	33044.4	+	57234.5i	1.10232	+	1.90927i
$966$		0			0
$967$	11401.8	−	19748.6i	0.379171	−	0.656744i	−0.611771	−	0.791035i	$-0.709542\pi$
$967$	11401.8	−	19748.6i	0.379171	−	0.656744i	0.990942	+	0.134291i	$0.0428758\pi$
$968$		0			0
$969$	6153.19	+	8000.10i	0.203993	+	0.265222i
$970$		0			0
$971$	5838.43			0.192960			0.0964801	−	0.995335i	$-0.469242\pi$
$971$	5838.43			0.192960			0.0964801	+	0.995335i	$0.469242\pi$
$972$		0			0
$973$	5431.89			0.178971
$974$		0			0
$975$	−52592.9	−	68378.9i	−1.72751	−	2.24603i
$976$		0			0
$977$	−8893.65	+	15404.2i	−0.291231	+	0.504427i	−0.974101	−	0.226113i	$-0.927398\pi$
$977$	−8893.65	+	15404.2i	−0.291231	+	0.504427i	0.682870	+	0.730540i	$0.260732\pi$
$978$		0			0
$979$	−3618.88	−	6268.09i	−0.118141	−	0.204626i
$980$		0			0
$981$	14403.4	−	54248.5i	0.468773	−	1.76557i
$982$		0			0
$983$	26955.4	+	46688.1i	0.874612	+	1.51487i	0.857175	+	0.515025i	$0.172217\pi$
$983$	26955.4	+	46688.1i	0.874612	+	1.51487i	0.0174371	+	0.999848i	$0.494449\pi$
$984$		0			0
$985$	44329.2	−	76780.4i	1.43395	−	2.48368i
$986$		0			0
$987$	−10624.3	+	1411.03i	−0.342628	+	0.0455051i
$988$		0			0
$989$	−21416.0			−0.688565
$990$		0			0
$991$	−21141.7			−0.677688			−0.338844	−	0.940843i	$-0.610036\pi$
$991$	−21141.7			−0.677688			−0.338844	+	0.940843i	$0.610036\pi$
$992$		0			0
$993$	−803.322	+	1945.66i	−0.0256724	+	0.0621788i
$994$		0			0
$995$	27546.7	−	47712.3i	0.877678	−	1.52018i
$996$		0			0
$997$	−16776.5	−	29057.7i	−0.532914	−	0.923035i	−0.999261	−	0.0384328i	$-0.987763\pi$
$997$	−16776.5	−	29057.7i	−0.532914	−	0.923035i	0.466347	−	0.884602i	$-0.345570\pi$
$998$		0			0
$999$	−39443.3	+	16496.1i	−1.24918	+	0.522437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.j.b.85.7	✓	18
3.2	odd	2		756.4.j.b.253.1		18
9.2	odd	6		756.4.j.b.505.1		18
9.4	even	3		2268.4.a.i.1.1		9
9.5	odd	6		2268.4.a.h.1.9		9
9.7	even	3	inner	252.4.j.b.169.7	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.j.b.85.7	✓	18	1.1	even	1	trivial
252.4.j.b.169.7	yes	18	9.7	even	3	inner
756.4.j.b.253.1		18	3.2	odd	2
756.4.j.b.505.1		18	9.2	odd	6
2268.4.a.h.1.9		9	9.5	odd	6
2268.4.a.i.1.1		9	9.4	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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.16791 + 4.11878i) q^{3} +(8.76630 - 15.1837i) q^{5} +(-3.50000 - 6.06218i) q^{7} +(-6.92866 + 26.0959i) q^{9} +O(q^{10})\)	\(q+(3.16791 + 4.11878i) q^{3} +(8.76630 - 15.1837i) q^{5} +(-3.50000 - 6.06218i) q^{7} +(-6.92866 + 26.0959i) q^{9} +(-26.5449 - 45.9771i) q^{11} +(45.5112 - 78.8276i) q^{13} +(90.3091 - 11.9941i) q^{15} -86.1853 q^{17} -22.5369 q^{19} +(13.8811 - 33.6202i) q^{21} +(-21.7741 + 37.7139i) q^{23} +(-91.1960 - 157.956i) q^{25} +(-129.432 + 54.1318i) q^{27} +(60.4638 + 104.726i) q^{29} +(16.0632 - 27.8222i) q^{31} +(105.278 - 254.984i) q^{33} -122.728 q^{35} +304.741 q^{37} +(468.849 - 62.2687i) q^{39} +(250.408 - 433.719i) q^{41} +(245.889 + 425.892i) q^{43} +(335.492 + 333.967i) q^{45} +(-147.328 - 255.180i) q^{47} +(-24.5000 + 42.4352i) q^{49} +(-273.028 - 354.978i) q^{51} +391.010 q^{53} -930.803 q^{55} +(-71.3948 - 92.8243i) q^{57} +(-105.915 + 183.451i) q^{59} +(122.354 + 211.924i) q^{61} +(182.448 - 49.3327i) q^{63} +(-797.929 - 1382.05i) q^{65} +(10.7731 - 18.6596i) q^{67} +(-224.314 + 29.7915i) q^{69} +87.0355 q^{71} +45.0771 q^{73} +(361.685 - 876.008i) q^{75} +(-185.814 + 321.840i) q^{77} +(411.776 + 713.217i) q^{79} +(-632.987 - 361.619i) q^{81} +(385.587 + 667.856i) q^{83} +(-755.527 + 1308.61i) q^{85} +(-239.801 + 580.801i) q^{87} +136.331 q^{89} -637.156 q^{91} +(165.480 - 21.9777i) q^{93} +(-197.565 + 342.192i) q^{95} +(731.763 + 1267.45i) q^{97} +(1383.73 - 374.152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9}+O(q^{10}) \) 18 * q + 11 * q^3 - 6 * q^5 - 63 * q^7 - 109 * q^9	\( 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9} - 93 q^{11} - 18 q^{13} + 162 q^{15} - 54 q^{17} - 90 q^{19} - 49 q^{21} - 246 q^{23} - 315 q^{25} - 394 q^{27} - 318 q^{29} - 18 q^{31} + 33 q^{33} + 84 q^{35} - 72 q^{37} + 268 q^{39} - 57 q^{41} - 171 q^{43} - 318 q^{45} - 1056 q^{47} - 441 q^{49} + 705 q^{51} + 1512 q^{53} - 1800 q^{55} - 1271 q^{57} - 411 q^{59} - 198 q^{61} + 308 q^{63} - 1326 q^{65} - 441 q^{67} + 642 q^{69} + 3516 q^{71} + 54 q^{73} - 2497 q^{75} - 651 q^{77} + 72 q^{79} + 1163 q^{81} - 558 q^{83} - 1008 q^{85} + 2766 q^{87} + 2784 q^{89} + 252 q^{91} - 2618 q^{93} - 156 q^{95} + 909 q^{97} + 6318 q^{99}+O(q^{100}) \) 18 * q + 11 * q^3 - 6 * q^5 - 63 * q^7 - 109 * q^9 - 93 * q^11 - 18 * q^13 + 162 * q^15 - 54 * q^17 - 90 * q^19 - 49 * q^21 - 246 * q^23 - 315 * q^25 - 394 * q^27 - 318 * q^29 - 18 * q^31 + 33 * q^33 + 84 * q^35 - 72 * q^37 + 268 * q^39 - 57 * q^41 - 171 * q^43 - 318 * q^45 - 1056 * q^47 - 441 * q^49 + 705 * q^51 + 1512 * q^53 - 1800 * q^55 - 1271 * q^57 - 411 * q^59 - 198 * q^61 + 308 * q^63 - 1326 * q^65 - 441 * q^67 + 642 * q^69 + 3516 * q^71 + 54 * q^73 - 2497 * q^75 - 651 * q^77 + 72 * q^79 + 1163 * q^81 - 558 * q^83 - 1008 * q^85 + 2766 * q^87 + 2784 * q^89 + 252 * q^91 - 2618 * q^93 - 156 * q^95 + 909 * q^97 + 6318 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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