LMFDB - Embedded newform 252.4.j.b.169.1

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			169.1
Root			$6.01410 - 1.36338i$ of defining polynomial
Character	$\chi$	$=$	252.169
Dual form			252.4.j.b.85.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.01410 - 1.36338i) q^{3} +(-0.333146 - 0.577025i) q^{5} +(-3.50000 + 6.06218i) q^{7} +(23.2824 + 13.6722i) q^{9} +O(q^{10})$	\(q+(-5.01410 - 1.36338i) q^{3} +(-0.333146 - 0.577025i) q^{5} +(-3.50000 + 6.06218i) q^{7} +(23.2824 + 13.6722i) q^{9} +(-6.42273 + 11.1245i) q^{11} +(-2.93360 - 5.08115i) q^{13} +(0.883722 + 3.34747i) q^{15} +10.4753 q^{17} +25.8933 q^{19} +(25.8144 - 25.6245i) q^{21} +(-32.0287 - 55.4753i) q^{23} +(62.2780 - 107.869i) q^{25} +(-98.0998 - 100.297i) q^{27} +(81.4630 - 141.098i) q^{29} +(-59.6865 - 103.380i) q^{31} +(47.3711 - 47.0227i) q^{33} +4.66404 q^{35} +292.816 q^{37} +(7.78184 + 29.4770i) q^{39} +(-196.421 - 340.212i) q^{41} +(70.7394 - 122.524i) q^{43} +(0.132792 - 17.9894i) q^{45} +(99.6313 - 172.566i) q^{47} +(-24.5000 - 42.4352i) q^{49} +(-52.5241 - 14.2818i) q^{51} +375.572 q^{53} +8.55882 q^{55} +(-129.832 - 35.3024i) q^{57} +(-226.870 - 392.950i) q^{59} +(126.869 - 219.744i) q^{61} +(-164.372 + 93.2892i) q^{63} +(-1.95463 + 3.38552i) q^{65} +(432.744 + 749.534i) q^{67} +(84.9611 + 321.826i) q^{69} -712.205 q^{71} +527.665 q^{73} +(-459.334 + 455.956i) q^{75} +(-44.9591 - 77.8714i) q^{77} +(-142.073 + 246.078i) q^{79} +(355.140 + 636.645i) q^{81} +(-29.5309 + 51.1489i) q^{83} +(-3.48979 - 6.04450i) q^{85} +(-600.834 + 596.415i) q^{87} -189.928 q^{89} +41.0704 q^{91} +(158.328 + 599.733i) q^{93} +(-8.62624 - 14.9411i) q^{95} +(143.777 - 249.030i) q^{97} +(-301.633 + 171.192i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−5.01410	−	1.36338i	−0.964964	−	0.262382i
$3$	−5.01410	−	1.36338i	−0.964964	−	0.262382i
$4$		0			0
$5$	−0.333146	−	0.577025i	−0.0297975	−	0.0516107i	0.850742	−	0.525583i	$-0.176153\pi$
$5$	−0.333146	−	0.577025i	−0.0297975	−	0.0516107i	−0.880540	+	0.473973i	$0.842820\pi$
$6$		0			0
$7$	−3.50000	+	6.06218i	−0.188982	+	0.327327i
$7$	−3.50000	+	6.06218i	−0.188982	+	0.327327i
$8$		0			0
$9$	23.2824	+	13.6722i	0.862311	+	0.506379i
$10$		0			0
$11$	−6.42273	+	11.1245i	−0.176048	+	0.304924i	−0.940523	−	0.339729i	$-0.889665\pi$
$11$	−6.42273	+	11.1245i	−0.176048	+	0.304924i	0.764476	+	0.644653i	$0.222998\pi$
$12$		0			0
$13$	−2.93360	−	5.08115i	−0.0625873	−	0.108404i	0.833034	−	0.553222i	$-0.186602\pi$
$13$	−2.93360	−	5.08115i	−0.0625873	−	0.108404i	−0.895621	+	0.444818i	$0.853269\pi$
$14$		0			0
$15$	0.883722	+	3.34747i	0.0152117	+	0.0576208i
$16$		0			0
$17$	10.4753			0.149449			0.0747243	−	0.997204i	$-0.476192\pi$
$17$	10.4753			0.149449			0.0747243	+	0.997204i	$0.476192\pi$
$18$		0			0
$19$	25.8933			0.312649			0.156324	−	0.987706i	$-0.450035\pi$
$19$	25.8933			0.312649			0.156324	+	0.987706i	$0.450035\pi$
$20$		0			0
$21$	25.8144	−	25.6245i	0.268246	−	0.266273i
$22$		0			0
$23$	−32.0287	−	55.4753i	−0.290367	−	0.502930i	0.683530	−	0.729923i	$-0.260444\pi$
$23$	−32.0287	−	55.4753i	−0.290367	−	0.502930i	−0.973896	+	0.226993i	$0.927111\pi$
$24$		0			0
$25$	62.2780	−	107.869i	0.498224	−	0.862950i
$26$		0			0
$27$	−98.0998	−	100.297i	−0.699234	−	0.714893i
$28$		0			0
$29$	81.4630	−	141.098i	0.521631	−	0.903491i	−0.478052	−	0.878331i	$-0.658657\pi$
$29$	81.4630	−	141.098i	0.521631	−	0.903491i	0.999683	−	0.0251601i	$-0.00800956\pi$
$30$		0			0
$31$	−59.6865	−	103.380i	−0.345807	−	0.598955i	0.639693	−	0.768630i	$-0.279061\pi$
$31$	−59.6865	−	103.380i	−0.345807	−	0.598955i	−0.985500	+	0.169675i	$0.945728\pi$
$32$		0			0
$33$	47.3711	−	47.0227i	0.249886	−	0.248049i
$34$		0			0
$35$	4.66404			0.0225248
$36$		0			0
$37$	292.816			1.30104			0.650522	−	0.759487i	$-0.274550\pi$
$37$	292.816			1.30104			0.650522	+	0.759487i	$0.274550\pi$
$38$		0			0
$39$	7.78184	+	29.4770i	0.0319511	+	0.121028i
$40$		0			0
$41$	−196.421	−	340.212i	−0.748191	−	1.29591i	−0.948689	−	0.316211i	$-0.897589\pi$
$41$	−196.421	−	340.212i	−0.748191	−	1.29591i	0.200497	−	0.979694i	$-0.435744\pi$
$42$		0			0
$43$	70.7394	−	122.524i	0.250876	−	0.434530i	−0.712891	−	0.701274i	$-0.752615\pi$
$43$	70.7394	−	122.524i	0.250876	−	0.434530i	0.963767	+	0.266745i	$0.0859481\pi$
$44$		0			0
$45$	0.132792	−	17.9894i	0.000439901	−	0.0595933i
$46$		0			0
$47$	99.6313	−	172.566i	0.309207	−	0.535562i	−0.668982	−	0.743278i	$-0.733270\pi$
$47$	99.6313	−	172.566i	0.309207	−	0.535562i	0.978189	+	0.207716i	$0.0666031\pi$
$48$		0			0
$49$	−24.5000	−	42.4352i	−0.0714286	−	0.123718i
$50$		0			0
$51$	−52.5241	−	14.2818i	−0.144213	−	0.0392127i
$52$		0			0
$53$	375.572			0.973374			0.486687	−	0.873576i	$-0.338205\pi$
$53$	375.572			0.973374			0.486687	+	0.873576i	$0.338205\pi$
$54$		0			0
$55$	8.55882			0.0209831
$56$		0			0
$57$	−129.832	−	35.3024i	−0.301695	−	0.0820336i
$58$		0			0
$59$	−226.870	−	392.950i	−0.500608	−	0.867079i	−1.00000		0.000702659i	$-0.999776\pi$
$59$	−226.870	−	392.950i	−0.500608	−	0.867079i	0.499391	−	0.866377i	$-0.333557\pi$
$60$		0			0
$61$	126.869	−	219.744i	0.266294	−	0.461234i	−0.701608	−	0.712563i	$-0.747534\pi$
$61$	126.869	−	219.744i	0.266294	−	0.461234i	0.967902	+	0.251329i	$0.0808675\pi$
$62$		0			0
$63$	−164.372	+	93.2892i	−0.328713	+	0.186561i
$64$		0			0
$65$	−1.95463	+	3.38552i	−0.00372988	+	0.00646035i
$66$		0			0
$67$	432.744	+	749.534i	0.789075	+	1.36672i	0.926534	+	0.376211i	$0.122773\pi$
$67$	432.744	+	749.534i	0.789075	+	1.36672i	−0.137458	+	0.990508i	$0.543893\pi$
$68$		0			0
$69$	84.9611	+	321.826i	0.148234	+	0.561497i
$70$		0			0
$71$	−712.205			−1.19047			−0.595234	−	0.803553i	$-0.702940\pi$
$71$	−712.205			−1.19047			−0.595234	+	0.803553i	$0.702940\pi$
$72$		0			0
$73$	527.665			0.846006			0.423003	−	0.906128i	$-0.360976\pi$
$73$	527.665			0.846006			0.423003	+	0.906128i	$0.360976\pi$
$74$		0			0
$75$	−459.334	+	455.956i	−0.707191	+	0.701990i
$76$		0			0
$77$	−44.9591	−	77.8714i	−0.0665398	−	0.115250i
$78$		0			0
$79$	−142.073	+	246.078i	−0.202335	+	0.350454i	−0.949280	−	0.314431i	$-0.898186\pi$
$79$	−142.073	+	246.078i	−0.202335	+	0.350454i	0.746945	+	0.664885i	$0.231520\pi$
$80$		0			0
$81$	355.140	+	636.645i	0.487161	+	0.873312i
$82$		0			0
$83$	−29.5309	+	51.1489i	−0.0390534	+	0.0676425i	−0.884891	−	0.465797i	$-0.845768\pi$
$83$	−29.5309	+	51.1489i	−0.0390534	+	0.0676425i	0.845838	+	0.533440i	$0.179101\pi$
$84$		0			0
$85$	−3.48979	−	6.04450i	−0.00445319	−	0.00771315i
$86$		0			0
$87$	−600.834	+	596.415i	−0.740415	+	0.734970i
$88$		0			0
$89$	−189.928			−0.226206			−0.113103	−	0.993583i	$-0.536079\pi$
$89$	−189.928			−0.226206			−0.113103	+	0.993583i	$0.536079\pi$
$90$		0			0
$91$	41.0704			0.0473115
$92$		0			0
$93$	158.328	+	599.733i	0.176536	+	0.668704i
$94$		0			0
$95$	−8.62624	−	14.9411i	−0.00931614	−	0.0161360i
$96$		0			0
$97$	143.777	−	249.030i	0.150499	−	0.260671i	−0.780912	−	0.624641i	$-0.785245\pi$
$97$	143.777	−	249.030i	0.150499	−	0.260671i	0.931411	+	0.363969i	$0.118579\pi$
$98$		0			0
$99$	−301.633	+	171.192i	−0.306215	+	0.173792i
$100$		0			0
$101$	−92.3450	+	159.946i	−0.0909770	+	0.157577i	−0.907922	−	0.419138i	$-0.862332\pi$
$101$	−92.3450	+	159.946i	−0.0909770	+	0.157577i	0.816946	+	0.576715i	$0.195666\pi$
$102$		0			0
$103$	58.2990	+	100.977i	0.0557706	+	0.0965976i	0.892563	−	0.450923i	$-0.148905\pi$
$103$	58.2990	+	100.977i	0.0557706	+	0.0965976i	−0.836792	+	0.547521i	$0.815572\pi$
$104$		0			0
$105$	−23.3860	−	6.35885i	−0.0217356	−	0.00591010i
$106$		0			0
$107$	31.0814			0.0280818			0.0140409	−	0.999901i	$-0.495530\pi$
$107$	31.0814			0.0280818			0.0140409	+	0.999901i	$0.495530\pi$
$108$		0			0
$109$	1531.46			1.34576			0.672879	−	0.739753i	$-0.265058\pi$
$109$	1531.46			1.34576			0.672879	+	0.739753i	$0.265058\pi$
$110$		0			0
$111$	−1468.21	−	399.219i	−1.25546	−	0.341371i
$112$		0			0
$113$	−702.471	−	1216.72i	−0.584804	−	1.01291i	−0.994900	−	0.100868i	$-0.967838\pi$
$113$	−702.471	−	1216.72i	−0.584804	−	1.01291i	0.410095	−	0.912043i	$-0.365495\pi$
$114$		0			0
$115$	−21.3404	+	36.9627i	−0.0173044	+	0.0299721i
$116$		0			0
$117$	1.16934	−	158.410i	0.000923978	−	0.125171i
$118$		0			0
$119$	−36.6634	+	63.5030i	−0.0282431	+	0.0489185i
$120$		0			0
$121$	582.997	+	1009.78i	0.438014	+	0.758663i
$122$		0			0
$123$	521.039	+	1973.65i	0.381955	+	1.44681i
$124$		0			0
$125$	−166.277			−0.118978
$126$		0			0
$127$	151.277			0.105698			0.0528489	−	0.998603i	$-0.483170\pi$
$127$	151.277			0.105698			0.0528489	+	0.998603i	$0.483170\pi$
$128$		0			0
$129$	−521.741	+	517.904i	−0.356099	+	0.353480i
$130$		0			0
$131$	−1020.83	−	1768.13i	−0.680841	−	1.17925i	−0.974725	−	0.223410i	$-0.928281\pi$
$131$	−1020.83	−	1768.13i	−0.680841	−	1.17925i	0.293884	−	0.955841i	$-0.405052\pi$
$132$		0			0
$133$	−90.6265	+	156.970i	−0.0590851	+	0.102338i
$134$		0			0
$135$	−25.1922	+	90.0195i	−0.0160607	+	0.0573900i
$136$		0			0
$137$	−281.424	+	487.441i	−0.175501	+	0.303977i	−0.940335	−	0.340251i	$-0.889488\pi$
$137$	−281.424	+	487.441i	−0.175501	+	0.303977i	0.764833	+	0.644228i	$0.222821\pi$
$138$		0			0
$139$	233.361	+	404.193i	0.142399	+	0.246642i	0.928399	−	0.371584i	$-0.121185\pi$
$139$	233.361	+	404.193i	0.142399	+	0.246642i	−0.786001	+	0.618226i	$0.787852\pi$
$140$		0			0
$141$	−734.835	+	729.431i	−0.438895	+	0.435668i
$142$		0			0
$143$	75.3669			0.0440734
$144$		0			0
$145$	−108.556			−0.0621731
$146$		0			0
$147$	64.9902	+	246.177i	0.0364646	+	0.138125i
$148$		0			0
$149$	375.931	+	651.132i	0.206695	+	0.358005i	0.950671	−	0.310200i	$-0.100396\pi$
$149$	375.931	+	651.132i	0.206695	+	0.358005i	−0.743977	+	0.668205i	$0.767063\pi$
$150$		0			0
$151$	−285.901	+	495.196i	−0.154082	+	0.266877i	−0.932724	−	0.360591i	$-0.882575\pi$
$151$	−285.901	+	495.196i	−0.154082	+	0.266877i	0.778643	+	0.627468i	$0.215909\pi$
$152$		0			0
$153$	243.889	+	143.220i	0.128871	+	0.0756776i
$154$		0			0
$155$	−39.7686	+	68.8812i	−0.0206083	+	0.0356947i
$156$		0			0
$157$	407.686	+	706.133i	0.207241	+	0.358952i	0.950845	−	0.309669i	$-0.100218\pi$
$157$	407.686	+	706.133i	0.207241	+	0.358952i	−0.743603	+	0.668621i	$0.766885\pi$
$158$		0			0
$159$	−1883.16	−	512.047i	−0.939271	−	0.255396i
$160$		0			0
$161$	448.401			0.219497
$162$		0			0
$163$	1926.66			0.925812			0.462906	−	0.886407i	$-0.346807\pi$
$163$	1926.66			0.925812			0.462906	+	0.886407i	$0.346807\pi$
$164$		0			0
$165$	−42.9148	−	11.6689i	−0.0202479	−	0.00550559i
$166$		0			0
$167$	−1344.59	−	2328.90i	−0.623040	−	1.07914i	−0.988916	−	0.148473i	$-0.952564\pi$
$167$	−1344.59	−	2328.90i	−0.623040	−	1.07914i	0.365877	−	0.930663i	$-0.380769\pi$
$168$		0			0
$169$	1081.29	−	1872.85i	0.492166	−	0.852456i
$170$		0			0
$171$	602.858	+	354.019i	0.269601	+	0.158319i
$172$		0			0
$173$	183.966	−	318.639i	0.0808479	−	0.140033i	−0.822766	−	0.568380i	$-0.807571\pi$
$173$	183.966	−	318.639i	0.0808479	−	0.140033i	0.903614	+	0.428347i	$0.140904\pi$
$174$		0			0
$175$	435.946	+	755.081i	0.188311	+	0.326164i
$176$		0			0
$177$	601.808	+	2279.60i	0.255563	+	0.968051i
$178$		0			0
$179$	894.591			0.373547			0.186773	−	0.982403i	$-0.440197\pi$
$179$	894.591			0.373547			0.186773	+	0.982403i	$0.440197\pi$
$180$		0			0
$181$	−1074.33			−0.441183			−0.220592	−	0.975366i	$-0.570799\pi$
$181$	−1074.33			−0.441183			−0.220592	+	0.975366i	$0.570799\pi$
$182$		0			0
$183$	−935.728	+	928.847i	−0.377984	+	0.375204i
$184$		0			0
$185$	−97.5504	−	168.962i	−0.0387678	−	0.0671479i
$186$		0			0
$187$	−67.2798	+	116.532i	−0.0263101	+	0.0455704i
$188$		0			0
$189$	951.366	−	243.660i	0.366146	−	0.0937761i
$190$		0			0
$191$	427.628	−	740.673i	0.162000	−	0.280593i	−0.773586	−	0.633692i	$-0.781539\pi$
$191$	427.628	−	740.673i	0.162000	−	0.280593i	0.935586	+	0.353099i	$0.114872\pi$
$192$		0			0
$193$	42.2904	+	73.2491i	0.0157727	+	0.0273191i	0.873804	−	0.486278i	$-0.161646\pi$
$193$	42.2904	+	73.2491i	0.0157727	+	0.0273191i	−0.858031	+	0.513597i	$0.828313\pi$
$194$		0			0
$195$	14.4165	−	14.3105i	0.00529428	−	0.00525535i
$196$		0			0
$197$	−132.433			−0.0478956			−0.0239478	−	0.999713i	$-0.507624\pi$
$197$	−132.433			−0.0478956			−0.0239478	+	0.999713i	$0.507624\pi$
$198$		0			0
$199$	964.275			0.343496			0.171748	−	0.985141i	$-0.445059\pi$
$199$	964.275			0.343496			0.171748	+	0.985141i	$0.445059\pi$
$200$		0			0
$201$	−1147.92	−	4348.23i	−0.402827	−	1.52587i
$202$		0			0
$203$	570.241	+	987.686i	0.197158	+	0.341488i
$204$		0			0
$205$	−130.874	+	226.680i	−0.0445884	+	0.0772294i
$206$		0			0
$207$	12.7667	−	1729.50i	0.00428669	−	0.580718i
$208$		0			0
$209$	−166.306	+	288.050i	−0.0550411	+	0.0953341i
$210$		0			0
$211$	−1039.03	−	1799.66i	−0.339004	−	0.587173i	0.645241	−	0.763979i	$-0.276757\pi$
$211$	−1039.03	−	1799.66i	−0.339004	−	0.587173i	−0.984246	+	0.176806i	$0.943423\pi$
$212$		0			0
$213$	3571.07	+	971.005i	1.14876	+	0.312357i
$214$		0			0
$215$	−94.2661			−0.0299018
$216$		0			0
$217$	835.611			0.261405
$218$		0			0
$219$	−2645.76	−	719.407i	−0.816366	−	0.221977i
$220$		0			0
$221$	−30.7303	−	53.2264i	−0.00935358	−	0.0162009i
$222$		0			0
$223$	323.227	−	559.845i	0.0970622	−	0.168117i	−0.813405	−	0.581697i	$-0.802389\pi$
$223$	323.227	−	559.845i	0.0970622	−	0.168117i	0.910467	+	0.413581i	$0.135722\pi$
$224$		0			0
$225$	2924.79	−	1659.96i	0.866604	−	0.491841i
$226$		0			0
$227$	−891.831	+	1544.70i	−0.260762	+	0.451653i	−0.966445	−	0.256875i	$-0.917307\pi$
$227$	−891.831	+	1544.70i	−0.260762	+	0.451653i	0.705683	+	0.708528i	$0.250640\pi$
$228$		0			0
$229$	−3364.13	−	5826.84i	−0.970777	−	1.68143i	−0.693220	−	0.720726i	$-0.743809\pi$
$229$	−3364.13	−	5826.84i	−0.970777	−	1.68143i	−0.277556	−	0.960709i	$-0.589525\pi$
$230$		0			0
$231$	119.261	+	451.751i	0.0339689	+	0.128671i
$232$		0			0
$233$	4058.14			1.14102			0.570509	−	0.821291i	$-0.306746\pi$
$233$	4058.14			1.14102			0.570509	+	0.821291i	$0.306746\pi$
$234$		0			0
$235$	−132.767			−0.0368543
$236$		0			0
$237$	1047.86	−	1040.16i	0.287199	−	0.285087i
$238$		0			0
$239$	−3028.96	−	5246.31i	−0.819779	−	1.41990i	−0.905845	−	0.423609i	$-0.860763\pi$
$239$	−3028.96	−	5246.31i	−0.819779	−	1.41990i	0.0860660	−	0.996289i	$-0.472570\pi$
$240$		0			0
$241$	1589.77	−	2753.55i	0.424920	−	0.735984i	−0.571493	−	0.820607i	$-0.693635\pi$
$241$	1589.77	−	2753.55i	0.424920	−	0.735984i	0.996413	+	0.0846236i	$0.0269688\pi$
$242$		0			0
$243$	−912.721	−	3676.39i	−0.240951	−	0.970537i
$244$		0			0
$245$	−16.3241	+	28.2742i	−0.00425678	+	0.00737296i
$246$		0			0
$247$	−75.9606	−	131.568i	−0.0195678	−	0.0338925i
$248$		0			0
$249$	217.806	−	216.204i	0.0554333	−	0.0550256i
$250$		0			0
$251$	5356.03			1.34689			0.673446	−	0.739237i	$-0.264813\pi$
$251$	5356.03			1.34689			0.673446	+	0.739237i	$0.264813\pi$
$252$		0			0
$253$	822.846			0.204474
$254$		0			0
$255$	9.25723	+	35.0656i	0.00227337	+	0.00861135i
$256$		0			0
$257$	−3133.65	−	5427.63i	−0.760589	−	1.31738i	−0.942547	−	0.334073i	$-0.891577\pi$
$257$	−3133.65	−	5427.63i	−0.760589	−	1.31738i	0.181958	−	0.983306i	$-0.441756\pi$
$258$		0			0
$259$	−1024.86	+	1775.10i	−0.245874	+	0.425867i
$260$		0			0
$261$	3825.78	−	2171.32i	0.907317	−	0.514948i
$262$		0			0
$263$	−1168.34	+	2023.63i	−0.273928	+	0.474458i	−0.969864	−	0.243646i	$-0.921656\pi$
$263$	−1168.34	+	2023.63i	−0.273928	+	0.474458i	0.695936	+	0.718104i	$0.254990\pi$
$264$		0			0
$265$	−125.120	−	216.715i	−0.0290041	−	0.0502365i
$266$		0			0
$267$	952.320	+	258.944i	0.218281	+	0.0593525i
$268$		0			0
$269$	2551.67			0.578358			0.289179	−	0.957275i	$-0.406618\pi$
$269$	2551.67			0.578358			0.289179	+	0.957275i	$0.406618\pi$
$270$		0			0
$271$	−7057.24			−1.58191			−0.790954	−	0.611876i	$-0.790415\pi$
$271$	−7057.24			−1.58191			−0.790954	+	0.611876i	$0.790415\pi$
$272$		0			0
$273$	−205.931	−	55.9945i	−0.0456539	−	0.0124137i
$274$		0			0
$275$	799.990	+	1385.62i	0.175422	+	0.303841i
$276$		0			0
$277$	547.265	−	947.890i	0.118707	−	0.205607i	−0.800548	−	0.599268i	$-0.795458\pi$
$277$	547.265	−	947.890i	0.118707	−	0.205607i	0.919256	+	0.393661i	$0.128792\pi$
$278$		0			0
$279$	23.7911	−	3222.98i	0.00510516	−	0.691595i
$280$		0			0
$281$	−3525.49	+	6106.34i	−0.748446	+	1.29635i	0.200121	+	0.979771i	$0.435866\pi$
$281$	−3525.49	+	6106.34i	−0.748446	+	1.29635i	−0.948567	+	0.316576i	$0.897467\pi$
$282$		0			0
$283$	2669.52	+	4623.75i	0.560730	+	0.971212i	0.997433	+	0.0716068i	$0.0228127\pi$
$283$	2669.52	+	4623.75i	0.560730	+	0.971212i	−0.436703	+	0.899606i	$0.643854\pi$
$284$		0			0
$285$	22.8825	+	86.6769i	0.00475593	+	0.0180151i
$286$		0			0
$287$	2749.90			0.565580
$288$		0			0
$289$	−4803.27			−0.977665
$290$		0			0
$291$	−1060.44	+	1052.64i	−0.213621	+	0.212050i
$292$		0			0
$293$	4031.27	+	6982.36i	0.803785	+	1.39220i	0.917108	+	0.398638i	$0.130517\pi$
$293$	4031.27	+	6982.36i	0.803785	+	1.39220i	−0.113323	+	0.993558i	$0.536150\pi$
$294$		0			0
$295$	−151.161	+	261.819i	−0.0298337	+	0.0516735i
$296$		0			0
$297$	1745.82	−	447.133i	0.341086	−	0.0873578i
$298$		0			0
$299$	−187.919	+	325.485i	−0.0363465	+	0.0629541i
$300$		0			0
$301$	495.176	+	857.670i	0.0948221	+	0.164237i
$302$		0			0
$303$	681.095	−	676.086i	0.129135	−	0.128185i
$304$		0			0
$305$	−169.064			−0.0317395
$306$		0			0
$307$	−2099.74			−0.390354			−0.195177	−	0.980768i	$-0.562528\pi$
$307$	−2099.74			−0.390354			−0.195177	+	0.980768i	$0.562528\pi$
$308$		0			0
$309$	−154.647	−	585.792i	−0.0284712	−	0.107846i
$310$		0			0
$311$	1546.53	+	2678.67i	0.281980	+	0.488403i	0.971872	−	0.235509i	$-0.0756756\pi$
$311$	1546.53	+	2678.67i	0.281980	+	0.488403i	−0.689893	+	0.723912i	$0.742342\pi$
$312$		0			0
$313$	−1263.36	+	2188.20i	−0.228144	+	0.395158i	−0.957258	−	0.289235i	$-0.906599\pi$
$313$	−1263.36	+	2188.20i	−0.228144	+	0.395158i	0.729114	+	0.684393i	$0.239933\pi$
$314$		0			0
$315$	108.590	+	63.7678i	0.0194234	+	0.0114061i
$316$		0			0
$317$	−4947.20	+	8568.79i	−0.876537	+	1.51821i	−0.0214203	+	0.999771i	$0.506819\pi$
$317$	−4947.20	+	8568.79i	−0.876537	+	1.51821i	−0.855117	+	0.518436i	$0.826515\pi$
$318$		0			0
$319$	1046.43	+	1812.47i	0.183664	+	0.318115i
$320$		0			0
$321$	−155.845	−	42.3757i	−0.0270979	−	0.00736817i
$322$		0			0
$323$	271.239			0.0467249
$324$		0			0
$325$	−730.796			−0.124730
$326$		0			0
$327$	−7678.91	−	2087.96i	−1.29861	−	0.353103i
$328$		0			0
$329$	697.419	+	1207.97i	0.116869	+	0.202423i
$330$		0			0
$331$	−2679.68	+	4641.34i	−0.444980	+	0.770728i	−0.998051	−	0.0624063i	$-0.980123\pi$
$331$	−2679.68	+	4641.34i	−0.444980	+	0.770728i	0.553071	+	0.833134i	$0.313456\pi$
$332$		0			0
$333$	6817.46	+	4003.45i	1.12191	+	0.658822i
$334$		0			0
$335$	288.333	−	499.408i	0.0470249	−	0.0814495i
$336$		0			0
$337$	−5067.01	−	8776.32i	−0.819044	−	1.41863i	−0.906388	−	0.422447i	$-0.861171\pi$
$337$	−5067.01	−	8776.32i	−0.819044	−	1.41863i	0.0873440	−	0.996178i	$-0.472162\pi$
$338$		0			0
$339$	1863.42	+	7058.47i	0.298545	+	1.13086i
$340$		0			0
$341$	1533.40			0.243514
$342$		0			0
$343$	343.000			0.0539949
$344$		0			0
$345$	157.397	−	156.240i	0.0245623	−	0.0243816i
$346$		0			0
$347$	319.080	+	552.663i	0.0493635	+	0.0855000i	0.889651	−	0.456640i	$-0.150947\pi$
$347$	319.080	+	552.663i	0.0493635	+	0.0855000i	−0.840288	+	0.542140i	$0.817614\pi$
$348$		0			0
$349$	−4694.26	+	8130.70i	−0.719995	+	1.24707i	0.241007	+	0.970524i	$0.422522\pi$
$349$	−4694.26	+	8130.70i	−0.719995	+	1.24707i	−0.961001	+	0.276544i	$0.910811\pi$
$350$		0			0
$351$	−221.836	+	792.690i	−0.0337343	+	0.120543i
$352$		0			0
$353$	−3799.82	+	6581.48i	−0.572929	+	0.992342i	0.423334	+	0.905974i	$0.360860\pi$
$353$	−3799.82	+	6581.48i	−0.572929	+	0.992342i	−0.996263	+	0.0863688i	$0.972474\pi$
$354$		0			0
$355$	237.268	+	410.960i	0.0354729	+	0.0614408i
$356$		0			0
$357$	270.413	−	268.424i	0.0400890	−	0.0397941i
$358$		0			0
$359$	9242.70			1.35881			0.679403	−	0.733766i	$-0.262239\pi$
$359$	9242.70			1.35881			0.679403	+	0.733766i	$0.262239\pi$
$360$		0			0
$361$	−6188.54			−0.902251
$362$		0			0
$363$	−1546.49	−	5857.99i	−0.223608	−	0.847010i
$364$		0			0
$365$	−175.789	−	304.476i	−0.0252088	−	0.0436630i
$366$		0			0
$367$	−1536.15	+	2660.69i	−0.218491	+	0.378438i	−0.954347	−	0.298700i	$-0.903447\pi$
$367$	−1536.15	+	2660.69i	−0.218491	+	0.378438i	0.735856	+	0.677138i	$0.236780\pi$
$368$		0			0
$369$	78.2939	−	10606.5i	0.0110456	−	1.49634i
$370$		0			0
$371$	−1314.50	+	2276.79i	−0.183950	+	0.318611i
$372$		0			0
$373$	3034.26	+	5255.49i	0.421201	+	0.729542i	0.996057	−	0.0887126i	$-0.0282753\pi$
$373$	3034.26	+	5255.49i	0.421201	+	0.729542i	−0.574856	+	0.818255i	$0.694942\pi$
$374$		0			0
$375$	833.730	+	226.699i	0.114810	+	0.0312178i
$376$		0			0
$377$	−955.920			−0.130590
$378$		0			0
$379$	2794.68			0.378768			0.189384	−	0.981903i	$-0.439351\pi$
$379$	2794.68			0.378768			0.189384	+	0.981903i	$0.439351\pi$
$380$		0			0
$381$	−758.516	−	206.247i	−0.101995	−	0.0277332i
$382$		0			0
$383$	2782.83	+	4820.00i	0.371269	+	0.643056i	0.989761	−	0.142735i	$-0.0455895\pi$
$383$	2782.83	+	4820.00i	0.371269	+	0.643056i	−0.618492	+	0.785791i	$0.712256\pi$
$384$		0			0
$385$	−29.9559	+	51.8851i	−0.00396543	+	0.00686833i
$386$		0			0
$387$	3322.16	−	1885.49i	0.436370	−	0.247661i
$388$		0			0
$389$	−4489.99	+	7776.90i	−0.585223	+	1.01364i	0.409625	+	0.912254i	$0.365660\pi$
$389$	−4489.99	+	7776.90i	−0.585223	+	1.01364i	−0.994848	+	0.101382i	$0.967674\pi$
$390$		0			0
$391$	−335.509	−	581.119i	−0.0433949	−	0.0751622i
$392$		0			0
$393$	2707.91	+	10257.3i	0.347572	+	1.31658i
$394$		0			0
$395$	189.324			0.0241163
$396$		0			0
$397$	−7081.82			−0.895280			−0.447640	−	0.894214i	$-0.647735\pi$
$397$	−7081.82			−0.895280			−0.447640	+	0.894214i	$0.647735\pi$
$398$		0			0
$399$	668.420	−	663.504i	0.0838668	−	0.0832500i
$400$		0			0
$401$	1004.78	+	1740.34i	0.125128	+	0.216729i	0.921783	−	0.387706i	$-0.126732\pi$
$401$	1004.78	+	1740.34i	0.125128	+	0.216729i	−0.796655	+	0.604435i	$0.793399\pi$
$402$		0			0
$403$	−350.193	+	606.552i	−0.0432862	+	0.0749739i
$404$		0			0
$405$	249.047	−	417.020i	0.0305561	−	0.0511652i
$406$		0			0
$407$	−1880.68	+	3257.43i	−0.229046	+	0.396719i
$408$		0			0
$409$	−7193.40	−	12459.3i	−0.869659	−	1.50629i	−0.862345	−	0.506321i	$-0.831005\pi$
$409$	−7193.40	−	12459.3i	−0.869659	−	1.50629i	−0.00731400	−	0.999973i	$-0.502328\pi$
$410$		0			0
$411$	2075.65	−	2060.39i	0.249111	−	0.247279i
$412$		0			0
$413$	3176.17			0.378424
$414$		0			0
$415$	39.3523			0.00465477
$416$		0			0
$417$	−619.027	−	2344.82i	−0.0726951	−	0.275363i
$418$		0			0
$419$	−5240.11	−	9076.13i	−0.610969	−	1.05823i	−0.991077	−	0.133287i	$-0.957447\pi$
$419$	−5240.11	−	9076.13i	−0.610969	−	1.05823i	0.380108	−	0.924942i	$-0.375887\pi$
$420$		0			0
$421$	6528.75	−	11308.1i	0.755800	−	1.30908i	−0.189176	−	0.981943i	$-0.560582\pi$
$421$	6528.75	−	11308.1i	0.755800	−	1.30908i	0.944976	−	0.327140i	$-0.106085\pi$
$422$		0			0
$423$	4679.03	−	2655.58i	0.537830	−	0.305245i
$424$		0			0
$425$	652.379	−	1129.95i	0.0744589	−	0.128967i
$426$		0			0
$427$	888.084	+	1538.21i	0.100650	+	0.174330i
$428$		0			0
$429$	−377.897	−	102.754i	−0.0425292	−	0.0115641i
$430$		0			0
$431$	11283.3			1.26101			0.630507	−	0.776184i	$-0.282847\pi$
$431$	11283.3			1.26101			0.630507	+	0.776184i	$0.282847\pi$
$432$		0			0
$433$	−8081.40			−0.896923			−0.448461	−	0.893802i	$-0.648028\pi$
$433$	−8081.40			−0.896923			−0.448461	+	0.893802i	$0.648028\pi$
$434$		0			0
$435$	544.312	+	148.003i	0.0599948	+	0.0163131i
$436$		0			0
$437$	−829.328	−	1436.44i	−0.0907829	−	0.157241i
$438$		0			0
$439$	−4058.00	+	7028.67i	−0.441180	+	0.764146i	−0.997777	−	0.0666366i	$-0.978773\pi$
$439$	−4058.00	+	7028.67i	−0.441180	+	0.764146i	0.556598	+	0.830782i	$0.312107\pi$
$440$		0			0
$441$	9.76574	−	1322.96i	0.00105450	−	0.142853i
$442$		0			0
$443$	1996.63	−	3458.26i	0.214137	−	0.370896i	−0.738868	−	0.673850i	$-0.764639\pi$
$443$	1996.63	−	3458.26i	0.214137	−	0.370896i	0.953005	+	0.302954i	$0.0979727\pi$
$444$		0			0
$445$	63.2738	+	109.593i	0.00674037	+	0.0116747i
$446$		0			0
$447$	−997.217	−	3777.38i	−0.105518	−	0.399695i
$448$		0			0
$449$	−18616.4			−1.95671			−0.978356	−	0.206928i	$-0.933653\pi$
$449$	−18616.4			−1.95671			−0.978356	+	0.206928i	$0.933653\pi$
$450$		0			0
$451$	5046.24			0.526870
$452$		0			0
$453$	2108.68	−	2093.17i	0.218707	−	0.217098i
$454$		0			0
$455$	−13.6824	−	23.6987i	−0.00140976	−	0.00244178i
$456$		0			0
$457$	−734.233	+	1271.73i	−0.0751553	+	0.130173i	−0.901154	−	0.433500i	$-0.857279\pi$
$457$	−734.233	+	1271.73i	−0.0751553	+	0.130173i	0.825999	+	0.563672i	$0.190612\pi$
$458$		0			0
$459$	−1027.62	−	1050.63i	−0.104500	−	0.106840i
$460$		0			0
$461$	−4674.37	+	8096.25i	−0.472250	+	0.817961i	−0.999496	−	0.0317519i	$-0.989891\pi$
$461$	−4674.37	+	8096.25i	−0.472250	+	0.817961i	0.527246	+	0.849713i	$0.323225\pi$
$462$		0			0
$463$	1461.07	+	2530.64i	0.146655	+	0.254015i	0.929989	−	0.367586i	$-0.119816\pi$
$463$	1461.07	+	2530.64i	0.146655	+	0.254015i	−0.783334	+	0.621601i	$0.786482\pi$
$464$		0			0
$465$	293.315	−	291.158i	0.0292519	−	0.0290368i
$466$		0			0
$467$	13329.0			1.32075			0.660376	−	0.750936i	$-0.270397\pi$
$467$	13329.0			1.32075			0.660376	+	0.750936i	$0.270397\pi$
$468$		0			0
$469$	−6058.41			−0.596485
$470$		0			0
$471$	−1081.45	−	4096.45i	−0.105798	−	0.400753i
$472$		0			0
$473$	908.680	+	1573.88i	0.0883322	+	0.152996i
$474$		0			0
$475$	1612.58	−	2793.08i	0.155769	−	0.269800i
$476$		0			0
$477$	8744.22	+	5134.91i	0.839351	+	0.492896i
$478$		0			0
$479$	3950.87	−	6843.11i	0.376868	−	0.652755i	−0.613736	−	0.789511i	$-0.710334\pi$
$479$	3950.87	−	6843.11i	0.376868	−	0.652755i	0.990605	+	0.136756i	$0.0436676\pi$
$480$		0			0
$481$	−859.006	−	1487.84i	−0.0814289	−	0.141039i
$482$		0			0
$483$	−2248.33	−	611.341i	−0.211806	−	0.0575921i
$484$		0			0
$485$	−191.595			−0.0179379
$486$		0			0
$487$	16390.6			1.52511			0.762555	−	0.646923i	$-0.223944\pi$
$487$	16390.6			1.52511			0.762555	+	0.646923i	$0.223944\pi$
$488$		0			0
$489$	−9660.45	−	2626.76i	−0.893376	−	0.242917i
$490$		0			0
$491$	−7105.46	−	12307.0i	−0.653085	−	1.13118i	−0.982370	−	0.186946i	$-0.940141\pi$
$491$	−7105.46	−	12307.0i	−0.653085	−	1.13118i	0.329285	−	0.944231i	$-0.393192\pi$
$492$		0			0
$493$	853.347	−	1478.04i	0.0779570	−	0.135026i
$494$		0			0
$495$	199.270	+	117.018i	0.0180940	+	0.0106254i
$496$		0			0
$497$	2492.72	−	4317.51i	0.224977	−	0.389672i
$498$		0			0
$499$	1833.28	+	3175.33i	0.164467	+	0.284865i	0.936466	−	0.350759i	$-0.114076\pi$
$499$	1833.28	+	3175.33i	0.164467	+	0.284865i	−0.771999	+	0.635624i	$0.780743\pi$
$500$		0			0
$501$	3566.74	+	13510.5i	0.318065	+	1.20480i
$502$		0			0
$503$	21619.5			1.91643			0.958215	−	0.286050i	$-0.0923423\pi$
$503$	21619.5			1.91643			0.958215	+	0.286050i	$0.0923423\pi$
$504$		0			0
$505$	123.057			0.0108435
$506$		0			0
$507$	−7975.08	+	7916.43i	−0.698592	+	0.693454i
$508$		0			0
$509$	3117.99	+	5400.52i	0.271518	+	0.470283i	0.969251	−	0.246075i	$-0.0791410\pi$
$509$	3117.99	+	5400.52i	0.271518	+	0.470283i	−0.697733	+	0.716358i	$0.745808\pi$
$510$		0			0
$511$	−1846.83	+	3198.80i	−0.159880	+	0.276921i
$512$		0			0
$513$	−2540.13	−	2597.01i	−0.218615	−	0.223510i
$514$		0			0
$515$	38.8441	−	67.2800i	0.00332365	−	0.00575672i
$516$		0			0
$517$	1279.81	+	2216.70i	0.108870	+	0.188569i
$518$		0			0
$519$	−1356.85	+	1346.87i	−0.114757	+	0.113913i
$520$		0			0
$521$	−18726.1			−1.57468			−0.787339	−	0.616520i	$-0.788542\pi$
$521$	−18726.1			−1.57468			−0.787339	+	0.616520i	$0.788542\pi$
$522$		0			0
$523$	7182.40			0.600506			0.300253	−	0.953860i	$-0.402929\pi$
$523$	7182.40			0.600506			0.300253	+	0.953860i	$0.402929\pi$
$524$		0			0
$525$	−1156.42	−	4380.41i	−0.0961336	−	0.364146i
$526$		0			0
$527$	−625.232	−	1082.93i	−0.0516803	−	0.0895130i
$528$		0			0
$529$	4031.83	−	6983.33i	0.331374	−	0.573957i
$530$		0			0
$531$	90.4306	−	12250.6i	0.00739049	−	1.00119i
$532$		0			0
$533$	−1152.44	+	1996.09i	−0.0936545	+	0.162214i
$534$		0			0
$535$	−10.3546	−	17.9348i	−0.000836767	−	0.00144932i
$536$		0			0
$537$	−4485.57	−	1219.67i	−0.360459	−	0.0980120i
$538$		0			0
$539$	629.427			0.0502994
$540$		0			0
$541$	2106.61			0.167412			0.0837061	−	0.996490i	$-0.473324\pi$
$541$	2106.61			0.167412			0.0837061	+	0.996490i	$0.473324\pi$
$542$		0			0
$543$	5386.79	+	1464.72i	0.425726	+	0.115759i
$544$		0			0
$545$	−510.200	−	883.693i	−0.0401001	−	0.0694555i
$546$		0			0
$547$	9802.22	−	16977.9i	0.766202	−	1.32710i	−0.173406	−	0.984850i	$-0.555477\pi$
$547$	9802.22	−	16977.9i	0.766202	−	1.32710i	0.939609	−	0.342251i	$-0.111189\pi$
$548$		0			0
$549$	5958.20	−	3381.58i	0.463188	−	0.262882i
$550$		0			0
$551$	2109.35	−	3653.49i	0.163087	−	0.282476i
$552$		0			0
$553$	−994.511	−	1722.54i	−0.0764754	−	0.132459i
$554$		0			0
$555$	258.768	+	980.192i	0.0197912	+	0.0749673i
$556$		0			0
$557$	−5686.70			−0.432591			−0.216296	−	0.976328i	$-0.569397\pi$
$557$	−5686.70			−0.432591			−0.216296	+	0.976328i	$0.569397\pi$
$558$		0			0
$559$	−830.085			−0.0628065
$560$		0			0
$561$	496.225	−	492.575i	0.0373452	−	0.0370705i
$562$		0			0
$563$	−7670.07	−	13284.9i	−0.574165	−	0.994482i	−0.996132	−	0.0878713i	$-0.971994\pi$
$563$	−7670.07	−	13284.9i	−0.574165	−	0.994482i	0.421967	−	0.906611i	$-0.361340\pi$
$564$		0			0
$565$	−468.050	+	810.687i	−0.0348514	+	0.0603643i
$566$		0			0
$567$	−5102.44	−	75.3337i	−0.377923	−	0.00557975i
$568$		0			0
$569$	7758.53	−	13438.2i	0.571625	−	0.990083i	−0.424775	−	0.905299i	$-0.639647\pi$
$569$	7758.53	−	13438.2i	0.571625	−	0.990083i	0.996399	−	0.0847838i	$-0.0270199\pi$
$570$		0			0
$571$	−1945.26	−	3369.29i	−0.142568	−	0.246936i	0.785895	−	0.618360i	$-0.212203\pi$
$571$	−1945.26	−	3369.29i	−0.142568	−	0.246936i	−0.928463	+	0.371425i	$0.878869\pi$
$572$		0			0
$573$	−3153.98	+	3130.79i	−0.229947	+	0.228256i
$574$		0			0
$575$	−7978.73			−0.578671
$576$		0			0
$577$	4707.77			0.339666			0.169833	−	0.985473i	$-0.445677\pi$
$577$	4707.77			0.339666			0.169833	+	0.985473i	$0.445677\pi$
$578$		0			0
$579$	−112.182	−	424.936i	−0.00805202	−	0.0305004i
$580$		0			0
$581$	−206.716	−	358.043i	−0.0147608	−	0.0255665i
$582$		0			0
$583$	−2412.20	+	4178.05i	−0.171360	+	0.296805i
$584$		0			0
$585$	−91.7962	+	52.0989i	−0.00648770	+	0.00368209i
$586$		0			0
$587$	7095.56	−	12289.9i	0.498918	−	0.864152i	−0.501081	−	0.865401i	$-0.667064\pi$
$587$	7095.56	−	12289.9i	0.498918	−	0.864152i	0.999999	+	0.00124845i	$0.000397393\pi$
$588$		0			0
$589$	−1545.48	−	2676.85i	−0.108116	−	0.187263i
$590$		0			0
$591$	664.031	+	180.556i	0.0462176	+	0.0125670i
$592$		0			0
$593$	11109.6			0.769338			0.384669	−	0.923054i	$-0.374316\pi$
$593$	11109.6			0.769338			0.384669	+	0.923054i	$0.374316\pi$
$594$		0			0
$595$	48.8571			0.00336629
$596$		0			0
$597$	−4834.97	−	1314.67i	−0.331461	−	0.0901272i
$598$		0			0
$599$	−9711.46	−	16820.7i	−0.662436	−	1.14737i	−0.979974	−	0.199128i	$-0.936189\pi$
$599$	−9711.46	−	16820.7i	−0.662436	−	1.14737i	0.317537	−	0.948246i	$-0.397144\pi$
$600$		0			0
$601$	−5722.99	+	9912.50i	−0.388428	+	0.672778i	−0.992238	−	0.124351i	$-0.960315\pi$
$601$	−5722.99	+	9912.50i	−0.388428	+	0.672778i	0.603810	+	0.797128i	$0.293649\pi$
$602$		0			0
$603$	−172.492	+	23367.5i	−0.0116491	+	1.57811i
$604$		0			0
$605$	388.446	−	672.808i	0.0261034	−	0.0452125i
$606$		0			0
$607$	13050.4	+	22604.0i	0.872651	+	1.51148i	0.859244	+	0.511566i	$0.170934\pi$
$607$	13050.4	+	22604.0i	0.872651	+	1.51148i	0.0134073	+	0.999910i	$0.495732\pi$
$608$		0			0
$609$	−1512.66	−	5729.81i	−0.100650	−	0.381254i
$610$		0			0
$611$	−1169.11			−0.0774097
$612$		0			0
$613$	10725.6			0.706690			0.353345	−	0.935493i	$-0.385044\pi$
$613$	10725.6			0.706690			0.353345	+	0.935493i	$0.385044\pi$
$614$		0			0
$615$	965.265	−	958.166i	0.0632898	−	0.0628244i
$616$		0			0
$617$	−8848.51	−	15326.1i	−0.577354	−	1.00001i	−0.995781	−	0.0917563i	$-0.970752\pi$
$617$	−8848.51	−	15326.1i	−0.577354	−	1.00001i	0.418427	−	0.908250i	$-0.362581\pi$
$618$		0			0
$619$	13563.1	−	23492.0i	0.880691	−	1.52540i	0.0301173	−	0.999546i	$-0.490412\pi$
$619$	13563.1	−	23492.0i	0.880691	−	1.52540i	0.850574	−	0.525856i	$-0.176255\pi$
$620$		0			0
$621$	−2421.98	+	8654.48i	−0.156507	+	0.559247i
$622$		0			0
$623$	664.749	−	1151.38i	0.0427490	−	0.0740434i
$624$		0			0
$625$	−7729.36	−	13387.6i	−0.494679	−	0.856809i
$626$		0			0
$627$	1226.59	−	1217.57i	0.0781267	−	0.0775521i
$628$		0			0
$629$	3067.33			0.194439
$630$		0			0
$631$	19730.4			1.24478			0.622389	−	0.782708i	$-0.286162\pi$
$631$	19730.4			1.24478			0.622389	+	0.782708i	$0.286162\pi$
$632$		0			0
$633$	2756.20	+	10440.2i	0.173063	+	0.655549i
$634$		0			0
$635$	−50.3971	−	87.2904i	−0.00314953	−	0.00545514i
$636$		0			0
$637$	−143.746	+	248.976i	−0.00894104	+	0.0154863i
$638$		0			0
$639$	−16581.8	−	9737.43i	−1.02655	−	0.602827i
$640$		0			0
$641$	943.282	−	1633.81i	0.0581239	−	0.100674i	−0.835499	−	0.549491i	$-0.814821\pi$
$641$	943.282	−	1633.81i	0.0581239	−	0.100674i	0.893623	+	0.448818i	$0.148155\pi$
$642$		0			0
$643$	5903.79	+	10225.7i	0.362088	+	0.627155i	0.988304	−	0.152494i	$-0.0487306\pi$
$643$	5903.79	+	10225.7i	0.362088	+	0.627155i	−0.626216	+	0.779650i	$0.715397\pi$
$644$		0			0
$645$	472.660	+	128.520i	0.0288542	+	0.00784571i
$646$		0			0
$647$	−19045.5			−1.15727			−0.578636	−	0.815586i	$-0.696415\pi$
$647$	−19045.5			−1.15727			−0.578636	+	0.815586i	$0.696415\pi$
$648$		0			0
$649$	5828.48			0.352524
$650$		0			0
$651$	−4189.84	−	1139.25i	−0.252247	−	0.0685881i
$652$		0			0
$653$	4517.88	+	7825.19i	0.270748	+	0.468949i	0.969053	−	0.246851i	$-0.0793958\pi$
$653$	4517.88	+	7825.19i	0.270748	+	0.468949i	−0.698306	+	0.715799i	$0.746062\pi$
$654$		0			0
$655$	−680.169	+	1178.09i	−0.0405747	+	0.0702774i
$656$		0			0
$657$	12285.3	+	7214.35i	0.729521	+	0.428400i
$658$		0			0
$659$	−11234.0	+	19457.8i	−0.664057	+	1.15018i	0.315483	+	0.948931i	$0.397833\pi$
$659$	−11234.0	+	19457.8i	−0.664057	+	1.15018i	−0.979540	+	0.201249i	$0.935500\pi$
$660$		0			0
$661$	1074.65	+	1861.35i	0.0632362	+	0.109528i	0.895910	−	0.444235i	$-0.146525\pi$
$661$	1074.65	+	1861.35i	0.0632362	+	0.109528i	−0.832674	+	0.553763i	$0.813191\pi$
$662$		0			0
$663$	81.5169	+	308.779i	0.00477505	+	0.0180875i
$664$		0			0
$665$	120.767			0.00704234
$666$		0			0
$667$	−10436.6			−0.605858
$668$		0			0
$669$	−2383.97	+	2366.44i	−0.137772	+	0.136759i
$670$		0			0
$671$	1629.69	+	2822.71i	0.0937609	+	0.162399i
$672$		0			0
$673$	11245.1	−	19477.1i	0.644083	−	1.11558i	−0.340430	−	0.940270i	$-0.610573\pi$
$673$	11245.1	−	19477.1i	0.644083	−	1.11558i	0.984513	−	0.175314i	$-0.0560941\pi$
$674$		0			0
$675$	−16928.3	+	4335.63i	−0.965292	+	0.247227i
$676$		0			0
$677$	3592.77	−	6222.86i	0.203961	−	0.353270i	−0.745840	−	0.666125i	$-0.767952\pi$
$677$	3592.77	−	6222.86i	0.203961	−	0.353270i	0.949801	+	0.312854i	$0.101285\pi$
$678$		0			0
$679$	1006.44	+	1743.21i	0.0568831	+	0.0985245i
$680$		0			0
$681$	6577.74	−	6529.36i	0.370131	−	0.367409i
$682$		0			0
$683$	−12056.1			−0.675421			−0.337711	−	0.941250i	$-0.609653\pi$
$683$	−12056.1			−0.675421			−0.337711	+	0.941250i	$0.609653\pi$
$684$		0			0
$685$	375.021			0.0209180
$686$		0			0
$687$	8923.89	+	33803.0i	0.495586	+	1.87724i
$688$		0			0
$689$	−1101.78	−	1908.34i	−0.0609208	−	0.105518i
$690$		0			0
$691$	−15029.9	+	26032.5i	−0.827443	+	1.43317i	0.0725947	+	0.997362i	$0.476872\pi$
$691$	−15029.9	+	26032.5i	−0.827443	+	1.43317i	−0.900038	+	0.435812i	$0.856461\pi$
$692$		0			0
$693$	17.9208	−	2427.72i	0.000982329	−	0.133076i
$694$		0			0
$695$	155.486	−	269.310i	0.00848623	−	0.0146986i
$696$		0			0
$697$	−2057.57	−	3563.81i	−0.111816	−	0.193671i
$698$		0			0
$699$	−20347.9	−	5532.78i	−1.10104	−	0.299383i
$700$		0			0
$701$	−5029.65			−0.270994			−0.135497	−	0.990778i	$-0.543263\pi$
$701$	−5029.65			−0.270994			−0.135497	+	0.990778i	$0.543263\pi$
$702$		0			0
$703$	7581.97			0.406770
$704$		0			0
$705$	665.707	+	181.012i	0.0355631	+	0.00966992i
$706$		0			0
$707$	−646.415	−	1119.62i	−0.0343861	−	0.0595584i
$708$		0			0
$709$	−732.843	+	1269.32i	−0.0388187	+	0.0672360i	−0.884782	−	0.466005i	$-0.845693\pi$
$709$	−732.843	+	1269.32i	−0.0388187	+	0.0672360i	0.845963	+	0.533241i	$0.179026\pi$
$710$		0			0
$711$	−6672.23	+	3786.82i	−0.351938	+	0.199742i
$712$		0			0
$713$	−3823.36	+	6622.25i	−0.200822	+	0.347833i
$714$		0			0
$715$	−25.1082	−	43.4886i	−0.00131328	−	0.00227466i
$716$		0			0
$717$	8034.80	+	30435.2i	0.418501	+	1.58525i
$718$		0			0
$719$	19500.5			1.01147			0.505735	−	0.862689i	$-0.331221\pi$
$719$	19500.5			1.01147			0.505735	+	0.862689i	$0.331221\pi$
$720$		0			0
$721$	−816.186			−0.0421586
$722$		0			0
$723$	−11725.4	+	11639.1i	−0.603142	+	0.598706i
$724$		0			0
$725$	−10146.7	−	17574.6i	−0.519778	−	0.900283i
$726$		0			0
$727$	−5587.94	+	9678.60i	−0.285069	+	0.493754i	−0.972626	−	0.232376i	$-0.925350\pi$
$727$	−5587.94	+	9678.60i	−0.285069	+	0.493754i	0.687557	+	0.726131i	$0.258683\pi$
$728$		0			0
$729$	−435.839	+	19678.2i	−0.0221429	+	0.999755i
$730$		0			0
$731$	741.014	−	1283.47i	0.0374930	−	0.0649398i
$732$		0			0
$733$	18392.5	+	31856.7i	0.926795	+	1.60526i	0.788648	+	0.614844i	$0.210781\pi$
$733$	18392.5	+	31856.7i	0.926795	+	1.60526i	0.138147	+	0.990412i	$0.455885\pi$
$734$		0			0
$735$	120.399	−	119.514i	0.00604217	−	0.00599774i
$736$		0			0
$737$	−11117.6			−0.555660
$738$		0			0
$739$	−20277.2			−1.00935			−0.504675	−	0.863309i	$-0.668388\pi$
$739$	−20277.2			−1.00935			−0.504675	+	0.863309i	$0.668388\pi$
$740$		0			0
$741$	201.498	+	763.256i	0.00998947	+	0.0378393i
$742$		0			0
$743$	−1326.46	−	2297.49i	−0.0654952	−	0.113441i	0.831418	−	0.555647i	$-0.187529\pi$
$743$	−1326.46	−	2297.49i	−0.0654952	−	0.113441i	−0.896914	+	0.442206i	$0.854196\pi$
$744$		0			0
$745$	250.480	−	433.844i	0.0123179	−	0.0213353i
$746$		0			0
$747$	−1386.87	+	787.117i	−0.0679289	+	0.0385530i
$748$		0			0
$749$	−108.785	+	188.421i	−0.00530696	+	0.00919193i
$750$		0			0
$751$	13048.0	+	22599.8i	0.633992	+	1.09811i	0.986728	+	0.162383i	$0.0519180\pi$
$751$	13048.0	+	22599.8i	0.633992	+	1.09811i	−0.352736	+	0.935723i	$0.614749\pi$
$752$		0			0
$753$	−26855.7	−	7302.30i	−1.29970	−	0.353400i
$754$		0			0
$755$	380.987			0.0183650
$756$		0			0
$757$	35450.1			1.70206			0.851028	−	0.525120i	$-0.175979\pi$
$757$	35450.1			1.70206			0.851028	+	0.525120i	$0.175979\pi$
$758$		0			0
$759$	−4125.83	−	1121.85i	−0.197310	−	0.0536503i
$760$		0			0
$761$	17487.1	+	30288.6i	0.832993	+	1.44279i	0.895654	+	0.444752i	$0.146708\pi$
$761$	17487.1	+	30288.6i	0.832993	+	1.44279i	−0.0626608	+	0.998035i	$0.519959\pi$
$762$		0			0
$763$	−5360.12	+	9284.00i	−0.254324	+	0.440502i
$764$		0			0
$765$	1.39104	−	188.444i	6.57425e−5	−	0.00890613i
$766$		0			0
$767$	−1331.09	+	2305.51i	−0.0626634	+	0.108536i
$768$		0			0
$769$	3406.79	+	5900.72i	0.159755	+	0.276704i	0.934780	−	0.355226i	$-0.115596\pi$
$769$	3406.79	+	5900.72i	0.159755	+	0.276704i	−0.775025	+	0.631930i	$0.782263\pi$
$770$		0			0
$771$	8312.49	+	31487.0i	0.388284	+	1.47079i
$772$		0			0
$773$	−15398.2			−0.716475			−0.358238	−	0.933630i	$-0.616622\pi$
$773$	−15398.2			−0.716475			−0.358238	+	0.933630i	$0.616622\pi$
$774$		0			0
$775$	−14868.6			−0.689157
$776$		0			0
$777$	7558.87	−	7503.28i	0.349000	−	0.346433i
$778$		0			0
$779$	−5085.99	−	8809.20i	−0.233921	−	0.405164i
$780$		0			0
$781$	4574.30	−	7922.92i	0.209579	−	0.363002i
$782$		0			0
$783$	−22143.2	+	5671.23i	−1.01064	+	0.258842i
$784$		0			0
$785$	271.638	−	470.490i	0.0123505	−	0.0213917i
$786$		0			0
$787$	−4472.23	−	7746.14i	−0.202564	−	0.350851i	0.746790	−	0.665060i	$-0.231594\pi$
$787$	−4472.23	−	7746.14i	−0.202564	−	0.350851i	−0.949354	+	0.314209i	$0.898261\pi$
$788$		0			0
$789$	8617.16	−	8553.79i	0.388820	−	0.385961i
$790$		0			0
$791$	9834.59			0.442071
$792$		0			0
$793$	−1488.73			−0.0666664
$794$		0			0
$795$	331.901	+	1257.22i	0.0148067	+	0.0560866i
$796$		0			0
$797$	18050.5	+	31264.3i	0.802233	+	1.38951i	0.918143	+	0.396249i	$0.129688\pi$
$797$	18050.5	+	31264.3i	0.802233	+	1.38951i	−0.115909	+	0.993260i	$0.536978\pi$
$798$		0			0
$799$	1043.66	−	1807.68i	0.0462105	−	0.0800390i
$800$		0			0
$801$	−4421.99	−	2596.74i	−0.195060	−	0.114546i
$802$		0			0
$803$	−3389.05	+	5870.00i	−0.148938	+	0.257967i
$804$		0			0
$805$	−149.383	−	258.739i	−0.00654045	−	0.0113284i
$806$		0			0
$807$	−12794.3	−	3478.90i	−0.558094	−	0.151751i
$808$		0			0
$809$	−33907.0			−1.47355			−0.736777	−	0.676135i	$-0.763653\pi$
$809$	−33907.0			−1.47355			−0.736777	+	0.676135i	$0.763653\pi$
$810$		0			0
$811$	22570.9			0.977276			0.488638	−	0.872487i	$-0.337494\pi$
$811$	22570.9			0.977276			0.488638	+	0.872487i	$0.337494\pi$
$812$		0			0
$813$	35385.7	+	9621.69i	1.52648	+	0.415065i
$814$		0			0
$815$	−641.857	−	1111.73i	−0.0275869	−	0.0477818i
$816$		0			0
$817$	1831.68	−	3172.56i	0.0784360	−	0.135855i
$818$		0			0
$819$	956.218	+	561.524i	0.0407973	+	0.0239576i
$820$		0			0
$821$	22320.7	−	38660.7i	0.948842	−	1.64344i	0.200972	−	0.979597i	$-0.435590\pi$
$821$	22320.7	−	38660.7i	0.948842	−	1.64344i	0.747870	−	0.663846i	$-0.231077\pi$
$822$		0			0
$823$	−16364.7	−	28344.5i	−0.693121	−	1.20052i	−0.970810	−	0.239849i	$-0.922902\pi$
$823$	−16364.7	−	28344.5i	−0.693121	−	1.20052i	0.277689	−	0.960671i	$-0.410431\pi$
$824$		0			0
$825$	−2122.10	−	8038.34i	−0.0895540	−	0.339223i
$826$		0			0
$827$	−33603.0			−1.41293			−0.706464	−	0.707749i	$-0.749711\pi$
$827$	−33603.0			−1.41293			−0.706464	+	0.707749i	$0.749711\pi$
$828$		0			0
$829$	5729.17			0.240027			0.120013	−	0.992772i	$-0.461706\pi$
$829$	5729.17			0.240027			0.120013	+	0.992772i	$0.461706\pi$
$830$		0			0
$831$	−4036.37	+	4006.69i	−0.168496	+	0.167257i
$832$		0			0
$833$	−256.644	−	444.521i	−0.0106749	−	0.0184895i
$834$		0			0
$835$	−895.890	+	1551.73i	−0.0371300	+	0.0643110i
$836$		0			0
$837$	−4513.44	+	16127.9i	−0.186389	+	0.666025i
$838$		0			0
$839$	17013.6	−	29468.3i	0.700087	−	1.21259i	−0.268348	−	0.963322i	$-0.586478\pi$
$839$	17013.6	−	29468.3i	0.700087	−	1.21259i	0.968435	−	0.249265i	$-0.0801889\pi$
$840$		0			0
$841$	−1077.94	−	1867.05i	−0.0441978	−	0.0765529i
$842$		0			0
$843$	26002.4	−	25811.2i	1.06236	−	1.05455i
$844$		0			0
$845$	−1440.91			−0.0586611
$846$		0			0
$847$	−8161.96			−0.331108
$848$		0			0
$849$	−7081.33	−	26823.5i	−0.286255	−	1.08431i
$850$		0			0
$851$	−9378.51	−	16244.1i	−0.377780	−	0.654335i
$852$		0			0
$853$	−19266.6	+	33370.7i	−0.773358	+	1.33950i	0.162355	+	0.986732i	$0.448091\pi$
$853$	−19266.6	+	33370.7i	−0.773358	+	1.33950i	−0.935713	+	0.352763i	$0.885242\pi$
$854$		0			0
$855$	3.43843	−	465.804i	0.000137534	−	0.0186318i
$856$		0			0
$857$	6348.27	−	10995.5i	0.253037	−	0.438273i	−0.711323	−	0.702865i	$-0.751904\pi$
$857$	6348.27	−	10995.5i	0.253037	−	0.438273i	0.964361	+	0.264592i	$0.0852372\pi$
$858$		0			0
$859$	−3887.48	−	6733.31i	−0.154411	−	0.267448i	0.778433	−	0.627727i	$-0.216015\pi$
$859$	−3887.48	−	6733.31i	−0.154411	−	0.267448i	−0.932844	+	0.360279i	$0.882681\pi$
$860$		0			0
$861$	−13788.3	−	3749.15i	−0.545764	−	0.148398i
$862$		0			0
$863$	3051.19			0.120352			0.0601759	−	0.998188i	$-0.480834\pi$
$863$	3051.19			0.120352			0.0601759	+	0.998188i	$0.480834\pi$
$864$		0			0
$865$	−245.150			−0.00963624
$866$		0			0
$867$	24084.1	+	6548.67i	0.943412	+	0.256522i
$868$		0			0
$869$	−1824.99	−	3160.98i	−0.0712412	−	0.123393i
$870$		0			0
$871$	2538.99	−	4397.67i	0.0987722	−	0.171078i
$872$		0			0
$873$	6752.27	−	3832.25i	0.261775	−	0.148570i
$874$		0			0
$875$	581.970	−	1008.00i	0.0224848	−	0.0389448i
$876$		0			0
$877$	−13335.6	−	23098.0i	−0.513469	−	0.889354i	−0.999878	−	0.0156231i	$-0.995027\pi$
$877$	−13335.6	−	23098.0i	−0.513469	−	0.889354i	0.486409	−	0.873731i	$-0.338307\pi$
$878$		0			0
$879$	−10693.6	−	40506.4i	−0.410336	−	1.55432i
$880$		0			0
$881$	31214.1			1.19368			0.596839	−	0.802361i	$-0.296423\pi$
$881$	31214.1			1.19368			0.596839	+	0.802361i	$0.296423\pi$
$882$		0			0
$883$	14463.8			0.551240			0.275620	−	0.961267i	$-0.411117\pi$
$883$	14463.8			0.551240			0.275620	+	0.961267i	$0.411117\pi$
$884$		0			0
$885$	1114.90	−	1106.70i	0.0423467	−	0.0420352i
$886$		0			0
$887$	18953.4	+	32828.3i	0.717467	+	1.24269i	0.962000	+	0.273049i	$0.0880320\pi$
$887$	18953.4	+	32828.3i	0.717467	+	1.24269i	−0.244533	+	0.969641i	$0.578635\pi$
$888$		0			0
$889$	−529.468	+	917.065i	−0.0199750	+	0.0345977i
$890$		0			0
$891$	−9363.32	−	138.242i	−0.352057	−	0.00519785i
$892$		0			0
$893$	2579.78	−	4468.32i	0.0966732	−	0.167443i
$894$		0			0
$895$	−298.029	−	516.201i	−0.0111307	−	0.0192790i
$896$		0			0
$897$	1386.00	−	1375.81i	0.0515911	−	0.0512117i
$898$		0			0
$899$	−19449.0			−0.721534
$900$		0			0
$901$	3934.22			0.145469
$902$		0			0
$903$	−1313.53	−	4975.55i	−0.0484071	−	0.183362i
$904$		0			0
$905$	357.908	+	619.914i	0.0131461	+	0.0227698i
$906$		0			0
$907$	19035.0	−	32969.6i	0.696853	−	1.20699i	−0.272698	−	0.962100i	$-0.587916\pi$
$907$	19035.0	−	32969.6i	0.696853	−	1.20699i	0.969552	−	0.244886i	$-0.0787506\pi$
$908$		0			0
$909$	−4336.84	+	2461.37i	−0.158244	+	0.0898113i
$910$		0			0
$911$	−12993.3	+	22505.1i	−0.472545	+	0.818472i	−0.999506	−	0.0314170i	$-0.989998\pi$
$911$	−12993.3	+	22505.1i	−0.472545	+	0.818472i	0.526961	+	0.849889i	$0.323331\pi$
$912$		0			0
$913$	−379.337	−	657.031i	−0.0137505	−	0.0238166i
$914$		0			0
$915$	847.702	+	230.498i	0.0306275	+	0.00832789i
$916$		0			0
$917$	14291.6			0.514667
$918$		0			0
$919$	−40516.5			−1.45432			−0.727158	−	0.686470i	$-0.759159\pi$
$919$	−40516.5			−1.45432			−0.727158	+	0.686470i	$0.759159\pi$
$920$		0			0
$921$	10528.3	+	2862.74i	0.376677	+	0.102422i
$922$		0			0
$923$	2089.32	+	3618.82i	0.0745081	+	0.129052i
$924$		0			0
$925$	18236.0	−	31585.7i	0.648212	−	1.12274i
$926$		0			0
$927$	−23.2381	+	3148.06i	−0.000823343	+	0.111538i
$928$		0			0
$929$	20238.2	−	35053.5i	0.714739	−	1.23796i	−0.248321	−	0.968678i	$-0.579879\pi$
$929$	20238.2	−	35053.5i	0.714739	−	1.23796i	0.963060	−	0.269287i	$-0.0867880\pi$
$930$		0			0
$931$	−634.386	−	1098.79i	−0.0223321	−	0.0386803i
$932$		0			0
$933$	−4102.42	−	15539.6i	−0.143952	−	0.545278i
$934$		0			0
$935$	89.6559			0.00313590
$936$		0			0
$937$	−17086.6			−0.595727			−0.297863	−	0.954609i	$-0.596274\pi$
$937$	−17086.6			−0.595727			−0.297863	+	0.954609i	$0.596274\pi$
$938$		0			0
$939$	9317.95	−	9249.42i	0.323834	−	0.321452i
$940$		0			0
$941$	19327.3	+	33475.9i	0.669557	+	1.15971i	0.978028	+	0.208473i	$0.0668493\pi$
$941$	19327.3	+	33475.9i	0.669557	+	1.15971i	−0.308471	+	0.951234i	$0.599817\pi$
$942$		0			0
$943$	−12582.2	+	21793.0i	−0.434500	+	0.752576i
$944$		0			0
$945$	−457.542	−	467.788i	−0.0157501	−	0.0161028i
$946$		0			0
$947$	−18207.0	+	31535.5i	−0.624761	+	1.08212i	0.363826	+	0.931467i	$0.381470\pi$
$947$	−18207.0	+	31535.5i	−0.624761	+	1.08212i	−0.988587	+	0.150651i	$0.951863\pi$
$948$		0			0
$949$	−1547.96	−	2681.14i	−0.0529492	−	0.0917108i
$950$		0			0
$951$	36488.2	−	36219.9i	1.24418	−	1.23503i
$952$		0			0
$953$	−17374.5			−0.590573			−0.295286	−	0.955409i	$-0.595415\pi$
$953$	−17374.5			−0.590573			−0.295286	+	0.955409i	$0.595415\pi$
$954$		0			0
$955$	−569.849			−0.0193088
$956$		0			0
$957$	−2775.82	−	10514.6i	−0.0937613	−	0.355160i
$958$		0			0
$959$	−1969.97	−	3412.08i	−0.0663333	−	0.114893i
$960$		0			0
$961$	7770.54	−	13459.0i	0.260835	−	0.451780i
$962$		0			0
$963$	723.650	+	424.952i	0.0242153	+	0.0142200i
$964$		0			0
$965$	28.1777	−	48.8052i	0.000939971	−	0.00162808i
$966$		0			0
$967$	−2257.27	−	3909.71i	−0.0750661	−	0.130018i	0.826049	−	0.563598i	$-0.190583\pi$
$967$	−2257.27	−	3909.71i	−0.0750661	−	0.130018i	−0.901115	+	0.433580i	$0.857250\pi$
$968$		0			0
$969$	−1360.02	−	369.802i	−0.0450879	−	0.0122598i
$970$		0			0
$971$	19368.2			0.640118			0.320059	−	0.947398i	$-0.396297\pi$
$971$	19368.2			0.640118			0.320059	+	0.947398i	$0.396297\pi$
$972$		0			0
$973$	−3267.05			−0.107643
$974$		0			0
$975$	3664.28	+	996.351i	0.120360	+	0.0327269i
$976$		0			0
$977$	−3259.56	−	5645.73i	−0.106738	−	0.184875i	0.807709	−	0.589581i	$-0.200707\pi$
$977$	−3259.56	−	5645.73i	−0.106738	−	0.184875i	−0.914447	+	0.404706i	$0.867374\pi$
$978$		0			0
$979$	1219.86	−	2112.86i	0.0398231	−	0.0689756i
$980$		0			0
$981$	35656.1	+	20938.5i	1.16046	+	0.681463i
$982$		0			0
$983$	13969.7	−	24196.2i	0.453269	−	0.785085i	−0.545318	−	0.838229i	$-0.683591\pi$
$983$	13969.7	−	24196.2i	0.453269	−	0.785085i	0.998587	+	0.0531443i	$0.0169243\pi$
$984$		0			0
$985$	44.1194	+	76.4170i	0.00142717	+	0.00247193i
$986$		0			0
$987$	−1850.02	−	7007.71i	−0.0596623	−	0.225996i
$988$		0			0
$989$	−9062.76			−0.291384
$990$		0			0
$991$	−25423.9			−0.814952			−0.407476	−	0.913216i	$-0.633591\pi$
$991$	−25423.9			−0.814952			−0.407476	+	0.913216i	$0.633591\pi$
$992$		0			0
$993$	19764.1	−	19618.7i	0.631615	−	0.626970i
$994$		0			0
$995$	−321.244	−	556.411i	−0.0102353	−	0.0177281i
$996$		0			0
$997$	12766.2	−	22111.7i	0.405526	−	0.702391i	−0.588857	−	0.808237i	$-0.700422\pi$
$997$	12766.2	−	22111.7i	0.405526	−	0.702391i	0.994382	+	0.105846i	$0.0337552\pi$
$998$		0			0
$999$	−28725.2	−	29368.5i	−0.909735	−	0.930107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.j.b.169.1	yes	18
3.2	odd	2		756.4.j.b.505.6		18
9.2	odd	6		2268.4.a.h.1.4		9
9.4	even	3	inner	252.4.j.b.85.1	✓	18
9.5	odd	6		756.4.j.b.253.6		18
9.7	even	3		2268.4.a.i.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.j.b.85.1	✓	18	9.4	even	3	inner
252.4.j.b.169.1	yes	18	1.1	even	1	trivial
756.4.j.b.253.6		18	9.5	odd	6
756.4.j.b.505.6		18	3.2	odd	2
2268.4.a.h.1.4		9	9.2	odd	6
2268.4.a.i.1.6		9	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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.01410 - 1.36338i) q^{3} +(-0.333146 - 0.577025i) q^{5} +(-3.50000 + 6.06218i) q^{7} +(23.2824 + 13.6722i) q^{9} +O(q^{10})\)	\(q+(-5.01410 - 1.36338i) q^{3} +(-0.333146 - 0.577025i) q^{5} +(-3.50000 + 6.06218i) q^{7} +(23.2824 + 13.6722i) q^{9} +(-6.42273 + 11.1245i) q^{11} +(-2.93360 - 5.08115i) q^{13} +(0.883722 + 3.34747i) q^{15} +10.4753 q^{17} +25.8933 q^{19} +(25.8144 - 25.6245i) q^{21} +(-32.0287 - 55.4753i) q^{23} +(62.2780 - 107.869i) q^{25} +(-98.0998 - 100.297i) q^{27} +(81.4630 - 141.098i) q^{29} +(-59.6865 - 103.380i) q^{31} +(47.3711 - 47.0227i) q^{33} +4.66404 q^{35} +292.816 q^{37} +(7.78184 + 29.4770i) q^{39} +(-196.421 - 340.212i) q^{41} +(70.7394 - 122.524i) q^{43} +(0.132792 - 17.9894i) q^{45} +(99.6313 - 172.566i) q^{47} +(-24.5000 - 42.4352i) q^{49} +(-52.5241 - 14.2818i) q^{51} +375.572 q^{53} +8.55882 q^{55} +(-129.832 - 35.3024i) q^{57} +(-226.870 - 392.950i) q^{59} +(126.869 - 219.744i) q^{61} +(-164.372 + 93.2892i) q^{63} +(-1.95463 + 3.38552i) q^{65} +(432.744 + 749.534i) q^{67} +(84.9611 + 321.826i) q^{69} -712.205 q^{71} +527.665 q^{73} +(-459.334 + 455.956i) q^{75} +(-44.9591 - 77.8714i) q^{77} +(-142.073 + 246.078i) q^{79} +(355.140 + 636.645i) q^{81} +(-29.5309 + 51.1489i) q^{83} +(-3.48979 - 6.04450i) q^{85} +(-600.834 + 596.415i) q^{87} -189.928 q^{89} +41.0704 q^{91} +(158.328 + 599.733i) q^{93} +(-8.62624 - 14.9411i) q^{95} +(143.777 - 249.030i) q^{97} +(-301.633 + 171.192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 11 q^{3} - 6 q^{5} - 63 q^{7} - 109 q^{9}+O(q^{10}) \) 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

Fields

Representations

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Database

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