LMFDB - Embedded newform 252.4.i.a.25.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(25,252)]

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, 4, 4]))

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

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

chi := DirichletCharacter("252.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.i (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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.11
Character	$\chi$	$=$	252.25
Dual form			252.4.i.a.121.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19189 + 5.05761i) q^{3} +(8.50761 - 14.7356i) q^{5} +(18.0631 + 4.08939i) q^{7} +(-24.1588 - 12.0562i) q^{9} +O(q^{10})$	\(q+(-1.19189 + 5.05761i) q^{3} +(8.50761 - 14.7356i) q^{5} +(18.0631 + 4.08939i) q^{7} +(-24.1588 - 12.0562i) q^{9} +(-0.550461 - 0.953427i) q^{11} +(-40.5966 - 70.3153i) q^{13} +(64.3868 + 60.5914i) q^{15} +(20.0390 - 34.7085i) q^{17} +(-57.4065 - 99.4310i) q^{19} +(-42.2119 + 86.4821i) q^{21} +(-87.2241 + 151.077i) q^{23} +(-82.2587 - 142.476i) q^{25} +(89.7704 - 107.816i) q^{27} +(101.824 - 176.364i) q^{29} +266.677 q^{31} +(5.47815 - 1.64763i) q^{33} +(213.934 - 231.380i) q^{35} +(12.7469 + 22.0782i) q^{37} +(404.014 - 121.513i) q^{39} +(78.6788 + 136.276i) q^{41} +(133.562 - 231.336i) q^{43} +(-383.190 + 253.425i) q^{45} +139.705 q^{47} +(309.554 + 147.734i) q^{49} +(151.658 + 142.718i) q^{51} +(89.4184 - 154.877i) q^{53} -18.7324 q^{55} +(571.305 - 171.829i) q^{57} -278.455 q^{59} -316.577 q^{61} +(-387.081 - 316.568i) q^{63} -1381.52 q^{65} +891.807 q^{67} +(-660.124 - 621.212i) q^{69} -930.534 q^{71} +(-66.6937 + 115.517i) q^{73} +(818.633 - 246.216i) q^{75} +(-6.04412 - 19.4729i) q^{77} -428.989 q^{79} +(438.294 + 582.529i) q^{81} +(-373.508 + 646.935i) q^{83} +(-340.967 - 590.572i) q^{85} +(770.615 + 725.190i) q^{87} +(312.943 + 542.034i) q^{89} +(-445.754 - 1436.13i) q^{91} +(-317.850 + 1348.75i) q^{93} -1953.57 q^{95} +(689.869 - 1194.89i) q^{97} +(1.80372 + 29.6701i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9}+O(q^{10}) $ 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9	$ 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9} + 4 q^{11} - 12 q^{13} - 26 q^{15} + 112 q^{17} + 60 q^{19} - 80 q^{21} + 10 q^{23} - 600 q^{25} + 194 q^{29} + 60 q^{31} - 472 q^{33} + 394 q^{35} - 84 q^{37} + 604 q^{39} + 210 q^{41} + 42 q^{43} + 254 q^{45} - 132 q^{47} - 78 q^{49} - 58 q^{51} - 468 q^{53} + 612 q^{55} + 1476 q^{57} - 916 q^{59} - 804 q^{61} - 444 q^{63} + 1656 q^{65} - 588 q^{67} - 28 q^{69} - 2228 q^{71} - 336 q^{73} - 668 q^{75} - 1216 q^{77} - 768 q^{79} - 104 q^{81} + 1024 q^{83} + 360 q^{85} + 2188 q^{87} + 2922 q^{89} - 120 q^{91} - 1292 q^{93} + 2428 q^{95} - 264 q^{97} - 2246 q^{99}+O(q^{100}) $ 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9 + 4 * q^11 - 12 * q^13 - 26 * q^15 + 112 * q^17 + 60 * q^19 - 80 * q^21 + 10 * q^23 - 600 * q^25 + 194 * q^29 + 60 * q^31 - 472 * q^33 + 394 * q^35 - 84 * q^37 + 604 * q^39 + 210 * q^41 + 42 * q^43 + 254 * q^45 - 132 * q^47 - 78 * q^49 - 58 * q^51 - 468 * q^53 + 612 * q^55 + 1476 * q^57 - 916 * q^59 - 804 * q^61 - 444 * q^63 + 1656 * q^65 - 588 * q^67 - 28 * q^69 - 2228 * q^71 - 336 * q^73 - 668 * q^75 - 1216 * q^77 - 768 * q^79 - 104 * q^81 + 1024 * q^83 + 360 * q^85 + 2188 * q^87 + 2922 * q^89 - 120 * q^91 - 1292 * q^93 + 2428 * q^95 - 264 * q^97 - 2246 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.19189	+	5.05761i	−0.229380	+	0.973337i
$3$	−1.19189	+	5.05761i	−0.229380	+	0.973337i
$4$		0			0
$5$	8.50761	−	14.7356i	0.760943	−	1.31799i	−0.181421	−	0.983405i	$-0.558070\pi$
$5$	8.50761	−	14.7356i	0.760943	−	1.31799i	0.942365	−	0.334587i	$-0.108597\pi$
$6$		0			0
$7$	18.0631	+	4.08939i	0.975318	+	0.220806i
$7$	18.0631	+	4.08939i	0.975318	+	0.220806i
$8$		0			0
$9$	−24.1588	−	12.0562i	−0.894770	−	0.446528i
$10$		0			0
$11$	−0.550461	−	0.953427i	−0.0150882	−	0.0261335i	0.858383	−	0.513010i	$-0.171470\pi$
$11$	−0.550461	−	0.953427i	−0.0150882	−	0.0261335i	−0.873471	+	0.486876i	$0.838136\pi$
$12$		0			0
$13$	−40.5966	−	70.3153i	−0.866112	−	1.50015i	−0.865938	−	0.500151i	$-0.833278\pi$
$13$	−40.5966	−	70.3153i	−0.866112	−	1.50015i	−0.000174170	−	1.00000i	$-0.500055\pi$
$14$		0			0
$15$	64.3868	+	60.5914i	1.10831	+	1.04298i
$16$		0			0
$17$	20.0390	−	34.7085i	0.285892	−	0.495179i	−0.686933	−	0.726720i	$-0.741044\pi$
$17$	20.0390	−	34.7085i	0.285892	−	0.495179i	0.972825	+	0.231541i	$0.0743769\pi$
$18$		0			0
$19$	−57.4065	−	99.4310i	−0.693156	−	1.20058i	−0.970798	−	0.239897i	$-0.922886\pi$
$19$	−57.4065	−	99.4310i	−0.693156	−	1.20058i	0.277643	−	0.960684i	$-0.410447\pi$
$20$		0			0
$21$	−42.2119	+	86.4821i	−0.438637	+	0.898664i
$22$		0			0
$23$	−87.2241	+	151.077i	−0.790760	+	1.36964i	0.134737	+	0.990881i	$0.456981\pi$
$23$	−87.2241	+	151.077i	−0.790760	+	1.36964i	−0.925497	+	0.378755i	$0.876352\pi$
$24$		0			0
$25$	−82.2587	−	142.476i	−0.658070	−	1.13981i
$26$		0			0
$27$	89.7704	−	107.816i	0.639864	−	0.768488i
$28$		0			0
$29$	101.824	−	176.364i	0.652005	−	1.12931i	−0.330630	−	0.943760i	$-0.607261\pi$
$29$	101.824	−	176.364i	0.652005	−	1.12931i	0.982636	−	0.185546i	$-0.0594054\pi$
$30$		0			0
$31$	266.677			1.54505			0.772525	−	0.634984i	$-0.218994\pi$
$31$	266.677			1.54505			0.772525	+	0.634984i	$0.218994\pi$
$32$		0			0
$33$	5.47815	−	1.64763i	0.0288977	−	0.00869141i
$34$		0			0
$35$	213.934	−	231.380i	1.03318	−	1.11744i
$36$		0			0
$37$	12.7469	+	22.0782i	0.0566371	+	0.0980983i	0.892954	−	0.450148i	$-0.148629\pi$
$37$	12.7469	+	22.0782i	0.0566371	+	0.0980983i	−0.836317	+	0.548247i	$0.815296\pi$
$38$		0			0
$39$	404.014	−	121.513i	1.65882	−	0.498915i
$40$		0			0
$41$	78.6788	+	136.276i	0.299697	+	0.519090i	0.976066	−	0.217472i	$-0.0697812\pi$
$41$	78.6788	+	136.276i	0.299697	+	0.519090i	−0.676370	+	0.736562i	$0.736448\pi$
$42$		0			0
$43$	133.562	−	231.336i	0.473675	−	0.820429i	−0.525871	−	0.850564i	$-0.676260\pi$
$43$	133.562	−	231.336i	0.473675	−	0.820429i	0.999546	+	0.0301352i	$0.00959378\pi$
$44$		0			0
$45$	−383.190	+	253.425i	−1.26939	+	0.839518i
$46$		0			0
$47$	139.705			0.433576			0.216788	−	0.976219i	$-0.430442\pi$
$47$	139.705			0.433576			0.216788	+	0.976219i	$0.430442\pi$
$48$		0			0
$49$	309.554	+	147.734i	0.902489	+	0.430713i
$50$		0			0
$51$	151.658	+	142.718i	0.416398	+	0.391853i
$52$		0			0
$53$	89.4184	−	154.877i	0.231747	−	0.401397i	−0.726576	−	0.687087i	$-0.758889\pi$
$53$	89.4184	−	154.877i	0.231747	−	0.401397i	0.958322	+	0.285690i	$0.0922227\pi$
$54$		0			0
$55$	−18.7324			−0.0459251
$56$		0			0
$57$	571.305	−	171.829i	1.32757	−	0.399285i
$58$		0			0
$59$	−278.455			−0.614437			−0.307219	−	0.951639i	$-0.599398\pi$
$59$	−278.455			−0.614437			−0.307219	+	0.951639i	$0.599398\pi$
$60$		0			0
$61$	−316.577			−0.664484			−0.332242	−	0.943194i	$-0.607805\pi$
$61$	−316.577			−0.664484			−0.332242	+	0.943194i	$0.607805\pi$
$62$		0			0
$63$	−387.081	−	316.568i	−0.774089	−	0.633077i
$64$		0			0
$65$	−1381.52			−2.63625
$66$		0			0
$67$	891.807			1.62614			0.813071	−	0.582164i	$-0.197794\pi$
$67$	891.807			1.62614			0.813071	+	0.582164i	$0.197794\pi$
$68$		0			0
$69$	−660.124	−	621.212i	−1.15173	−	1.08384i
$70$		0			0
$71$	−930.534			−1.55541			−0.777704	−	0.628630i	$-0.783616\pi$
$71$	−930.534			−1.55541			−0.777704	+	0.628630i	$0.783616\pi$
$72$		0			0
$73$	−66.6937	+	115.517i	−0.106930	+	0.185208i	−0.914525	−	0.404529i	$-0.867435\pi$
$73$	−66.6937	+	115.517i	−0.106930	+	0.185208i	0.807595	+	0.589738i	$0.200769\pi$
$74$		0			0
$75$	818.633	−	246.216i	1.26037	−	0.379074i
$76$		0			0
$77$	−6.04412	−	19.4729i	−0.00894534	−	0.0288201i
$78$		0			0
$79$	−428.989			−0.610950			−0.305475	−	0.952200i	$-0.598815\pi$
$79$	−428.989			−0.610950			−0.305475	+	0.952200i	$0.598815\pi$
$80$		0			0
$81$	438.294	+	582.529i	0.601226	+	0.799079i
$82$		0			0
$83$	−373.508	+	646.935i	−0.493950	+	0.855547i	−0.999976	−	0.00697172i	$-0.997781\pi$
$83$	−373.508	+	646.935i	−0.493950	+	0.855547i	0.506026	+	0.862518i	$0.331114\pi$
$84$		0			0
$85$	−340.967	−	590.572i	−0.435095	−	0.753607i
$86$		0			0
$87$	770.615	+	725.190i	0.949639	+	0.893661i
$88$		0			0
$89$	312.943	+	542.034i	0.372718	+	0.645567i	0.989983	−	0.141189i	$-0.0450925\pi$
$89$	312.943	+	542.034i	0.372718	+	0.645567i	−0.617265	+	0.786756i	$0.711759\pi$
$90$		0			0
$91$	−445.754	−	1436.13i	−0.513492	−	1.65437i
$92$		0			0
$93$	−317.850	+	1348.75i	−0.354403	+	1.50385i
$94$		0			0
$95$	−1953.57			−2.10981
$96$		0			0
$97$	689.869	−	1194.89i	0.722119	−	1.25075i	−0.238030	−	0.971258i	$-0.576502\pi$
$97$	689.869	−	1194.89i	0.722119	−	1.25075i	0.960149	−	0.279489i	$-0.0901652\pi$
$98$		0			0
$99$	1.80372	+	29.6701i	0.00183112	+	0.0301208i
$100$		0			0
$101$	136.037	+	235.623i	0.134022	+	0.232133i	0.925223	−	0.379423i	$-0.123877\pi$
$101$	136.037	+	235.623i	0.134022	+	0.232133i	−0.791201	+	0.611556i	$0.790544\pi$
$102$		0			0
$103$	380.406	−	658.882i	0.363908	−	0.630306i	−0.624693	−	0.780871i	$-0.714776\pi$
$103$	380.406	−	658.882i	0.363908	−	0.630306i	0.988600	+	0.150564i	$0.0481091\pi$
$104$		0			0
$105$	915.245	+	1357.77i	0.850655	+	1.26195i
$106$		0			0
$107$	−180.039	−	311.836i	−0.162663	−	0.281741i	0.773160	−	0.634211i	$-0.218675\pi$
$107$	−180.039	−	311.836i	−0.162663	−	0.281741i	−0.935823	+	0.352470i	$0.885342\pi$
$108$		0			0
$109$	−905.221	+	1567.89i	−0.795454	+	1.37777i	0.127097	+	0.991890i	$0.459434\pi$
$109$	−905.221	+	1567.89i	−0.795454	+	1.37777i	−0.922551	+	0.385876i	$0.873899\pi$
$110$		0			0
$111$	−126.856	+	38.1538i	−0.108474	+	0.0326252i
$112$		0			0
$113$	1137.91	+	1970.92i	0.947305	+	1.64078i	0.751068	+	0.660225i	$0.229539\pi$
$113$	1137.91	+	1970.92i	0.947305	+	1.64078i	0.196237	+	0.980556i	$0.437128\pi$
$114$		0			0
$115$	1484.14	+	2570.60i	1.20345	+	2.08443i
$116$		0			0
$117$	133.025	+	2188.17i	0.105112	+	1.72903i
$118$		0			0
$119$	503.903	−	544.997i	0.388174	−	0.419830i
$120$		0			0
$121$	664.894	−	1151.63i	0.499545	−	0.865237i
$122$		0			0
$123$	−783.005	+	235.500i	−0.573994	+	0.172637i
$124$		0			0
$125$	−672.398			−0.481129
$126$		0			0
$127$	−461.503			−0.322455			−0.161227	−	0.986917i	$-0.551545\pi$
$127$	−461.503			−0.322455			−0.161227	+	0.986917i	$0.551545\pi$
$128$		0			0
$129$	1010.82	+	951.233i	0.689903	+	0.649235i
$130$		0			0
$131$	−207.314	+	359.079i	−0.138268	+	0.239488i	−0.926841	−	0.375454i	$-0.877487\pi$
$131$	−207.314	+	359.079i	−0.138268	+	0.239488i	0.788573	+	0.614941i	$0.210820\pi$
$132$		0			0
$133$	−630.329	−	2030.79i	−0.410951	−	1.32400i
$134$		0			0
$135$	−825.001	−	2240.08i	−0.525961	−	1.42811i
$136$		0			0
$137$	−1123.69	−	1946.28i	−0.700753	−	1.21374i	−0.968202	−	0.250168i	$-0.919514\pi$
$137$	−1123.69	−	1946.28i	−0.700753	−	1.21374i	0.267450	−	0.963572i	$-0.413819\pi$
$138$		0			0
$139$	170.371	+	295.092i	0.103962	+	0.180067i	0.913314	−	0.407257i	$-0.133515\pi$
$139$	170.371	+	295.092i	0.103962	+	0.180067i	−0.809352	+	0.587324i	$0.800181\pi$
$140$		0			0
$141$	−166.514	+	706.574i	−0.0994537	+	0.422016i
$142$		0			0
$143$	−44.6937	+	77.4117i	−0.0261362	+	0.0452692i
$144$		0			0
$145$	−1732.55	−	3000.86i	−0.992278	−	1.71868i
$146$		0			0
$147$	−1116.14	+	1389.52i	−0.626241	+	0.779629i
$148$		0			0
$149$	−681.832	+	1180.97i	−0.374885	+	0.649319i	−0.990310	−	0.138876i	$-0.955651\pi$
$149$	−681.832	+	1180.97i	−0.374885	+	0.649319i	0.615425	+	0.788195i	$0.288984\pi$
$150$		0			0
$151$	14.6208	+	25.3240i	0.00787963	+	0.0136479i	0.869938	−	0.493161i	$-0.164158\pi$
$151$	14.6208	+	25.3240i	0.00787963	+	0.0136479i	−0.862059	+	0.506808i	$0.830825\pi$
$152$		0			0
$153$	−902.571	+	596.920i	−0.476918	+	0.315413i
$154$		0			0
$155$	2268.78	−	3929.64i	1.17570	−	2.03636i
$156$		0			0
$157$	−113.558			−0.0577255			−0.0288628	−	0.999583i	$-0.509189\pi$
$157$	−113.558			−0.0577255			−0.0288628	+	0.999583i	$0.509189\pi$
$158$		0			0
$159$	676.731	+	636.840i	0.337536	+	0.317640i
$160$		0			0
$161$	−2193.35	+	2372.22i	−1.07367	+	1.16123i
$162$		0			0
$163$	−366.541	−	634.867i	−0.176133	−	0.305071i	0.764420	−	0.644719i	$-0.223026\pi$
$163$	−366.541	−	634.867i	−0.176133	−	0.305071i	−0.940553	+	0.339648i	$0.889692\pi$
$164$		0			0
$165$	22.3270	−	94.7413i	0.0105343	−	0.0447006i
$166$		0			0
$167$	1979.21	+	3428.10i	0.917103	+	1.58847i	0.803792	+	0.594910i	$0.202812\pi$
$167$	1979.21	+	3428.10i	0.917103	+	1.58847i	0.113311	+	0.993560i	$0.463854\pi$
$168$		0			0
$169$	−2197.66	+	3806.46i	−1.00030	+	1.73257i
$170$		0			0
$171$	188.107	+	3094.24i	0.0841222	+	1.38376i
$172$		0			0
$173$	−1454.36			−0.639152			−0.319576	−	0.947561i	$-0.603540\pi$
$173$	−1454.36			−0.639152			−0.319576	+	0.947561i	$0.603540\pi$
$174$		0			0
$175$	−903.209	−	2909.96i	−0.390150	−	1.25698i
$176$		0			0
$177$	331.889	−	1408.32i	0.140940	−	0.598055i
$178$		0			0
$179$	667.557	−	1156.24i	0.278746	−	0.482803i	−0.692327	−	0.721584i	$-0.743415\pi$
$179$	667.557	−	1156.24i	0.278746	−	0.482803i	0.971073	+	0.238781i	$0.0767478\pi$
$180$		0			0
$181$	3949.91			1.62207			0.811035	−	0.584997i	$-0.198904\pi$
$181$	3949.91			1.62207			0.811035	+	0.584997i	$0.198904\pi$
$182$		0			0
$183$	377.326	−	1601.12i	0.152419	−	0.646767i
$184$		0			0
$185$	433.781			0.172390
$186$		0			0
$187$	−44.1227			−0.0172544
$188$		0			0
$189$	2062.44	−	1580.39i	0.793758	−	0.608234i
$190$		0			0
$191$	−2505.81			−0.949288			−0.474644	−	0.880178i	$-0.657423\pi$
$191$	−2505.81			−0.949288			−0.474644	+	0.880178i	$0.657423\pi$
$192$		0			0
$193$	−238.154			−0.0888223			−0.0444112	−	0.999013i	$-0.514141\pi$
$193$	−238.154			−0.0888223			−0.0444112	+	0.999013i	$0.514141\pi$
$194$		0			0
$195$	1646.62	−	6987.18i	0.604703	−	2.56596i
$196$		0			0
$197$	−2783.34			−1.00662			−0.503312	−	0.864105i	$-0.667885\pi$
$197$	−2783.34			−1.00662			−0.503312	+	0.864105i	$0.667885\pi$
$198$		0			0
$199$	1099.52	−	1904.42i	0.391672	−	0.678397i	−0.600998	−	0.799251i	$-0.705230\pi$
$199$	1099.52	−	1904.42i	0.391672	−	0.678397i	0.992670	+	0.120854i	$0.0385633\pi$
$200$		0			0
$201$	−1062.94	+	4510.41i	−0.373004	+	1.58278i
$202$		0			0
$203$	2560.47	−	2769.28i	0.885270	−	0.957466i
$204$		0			0
$205$	2677.47			0.912209
$206$		0			0
$207$	3928.64	−	2598.23i	1.31913	−	0.872413i
$208$		0			0
$209$	−63.2001	+	109.466i	−0.0209170	+	0.0362292i
$210$		0			0
$211$	814.638	+	1410.99i	0.265791	+	0.460364i	0.967771	−	0.251833i	$-0.0810334\pi$
$211$	814.638	+	1410.99i	0.265791	+	0.460364i	−0.701979	+	0.712197i	$0.747700\pi$
$212$		0			0
$213$	1109.10	−	4706.27i	0.356779	−	1.51394i
$214$		0			0
$215$	−2272.59	−	3936.24i	−0.720880	−	1.24860i
$216$		0			0
$217$	4817.02	+	1090.55i	1.50691	+	0.341157i
$218$		0			0
$219$	−504.747	−	474.994i	−0.155743	−	0.146562i
$220$		0			0
$221$	−3254.05			−0.990458
$222$		0			0
$223$	1094.87	−	1896.37i	0.328780	−	0.569463i	−0.653490	−	0.756935i	$-0.726696\pi$
$223$	1094.87	−	1896.37i	0.328780	−	0.569463i	0.982270	+	0.187472i	$0.0600293\pi$
$224$		0			0
$225$	269.541	+	4433.79i	0.0798641	+	1.31371i
$226$		0			0
$227$	2897.53	+	5018.68i	0.847208	+	1.46741i	0.883690	+	0.468073i	$0.155051\pi$
$227$	2897.53	+	5018.68i	0.847208	+	1.46741i	−0.0364824	+	0.999334i	$0.511615\pi$
$228$		0			0
$229$	−634.502	+	1098.99i	−0.183096	+	0.317132i	−0.942933	−	0.332981i	$-0.891945\pi$
$229$	−634.502	+	1098.99i	−0.183096	+	0.317132i	0.759837	+	0.650114i	$0.225279\pi$
$230$		0			0
$231$	105.690	−	7.35915i	0.0301035	−	0.00209609i
$232$		0			0
$233$	−2020.16	−	3499.01i	−0.568004	−	0.983812i	−0.996763	−	0.0803928i	$-0.974383\pi$
$233$	−2020.16	−	3499.01i	−0.568004	−	0.983812i	0.428759	−	0.903419i	$-0.358951\pi$
$234$		0			0
$235$	1188.56	−	2058.64i	0.329927	−	0.571451i
$236$		0			0
$237$	511.309	−	2169.66i	0.140140	−	0.594660i
$238$		0			0
$239$	1547.10	+	2679.66i	0.418718	+	0.725241i	0.995811	−	0.0914374i	$-0.0291462\pi$
$239$	1547.10	+	2679.66i	0.418718	+	0.725241i	−0.577093	+	0.816679i	$0.695813\pi$
$240$		0			0
$241$	219.155	+	379.587i	0.0585767	+	0.101458i	0.893827	−	0.448413i	$-0.148010\pi$
$241$	219.155	+	379.587i	0.0585767	+	0.101458i	−0.835250	+	0.549870i	$0.814677\pi$
$242$		0			0
$243$	−3468.60	+	1522.41i	−0.915682	+	0.401903i
$244$		0			0
$245$	4810.52	−	3304.60i	1.25442	−	0.861726i
$246$		0			0
$247$	−4661.02	+	8073.12i	−1.20070	+	2.07968i
$248$		0			0
$249$	−2826.76	−	2660.14i	−0.719433	−	0.677025i
$250$		0			0
$251$	6088.28			1.53103			0.765516	−	0.643417i	$-0.222484\pi$
$251$	6088.28			1.53103			0.765516	+	0.643417i	$0.222484\pi$
$252$		0			0
$253$	192.054			0.0477246
$254$		0			0
$255$	3393.28	−	1020.58i	0.833315	−	0.250632i
$256$		0			0
$257$	−752.620	+	1303.58i	−0.182674	+	0.316400i	−0.942790	−	0.333387i	$-0.891809\pi$
$257$	−752.620	+	1303.58i	−0.182674	+	0.316400i	0.760116	+	0.649787i	$0.225142\pi$
$258$		0			0
$259$	139.962	+	450.929i	0.0335784	+	0.108183i
$260$		0			0
$261$	−4586.22	+	3033.12i	−1.08766	+	0.719331i
$262$		0			0
$263$	−1834.75	−	3177.88i	−0.430173	−	0.745081i	0.566715	−	0.823914i	$-0.308214\pi$
$263$	−1834.75	−	3177.88i	−0.430173	−	0.745081i	−0.996888	+	0.0788329i	$0.974881\pi$
$264$		0			0
$265$	−1521.47	−	2635.27i	−0.352692	−	0.610881i
$266$		0			0
$267$	−3114.39	+	936.698i	−0.713848	+	0.214700i
$268$		0			0
$269$	1164.31	−	2016.64i	0.263900	−	0.457088i	−0.703375	−	0.710819i	$-0.748325\pi$
$269$	1164.31	−	2016.64i	0.263900	−	0.457088i	0.967275	+	0.253731i	$0.0816579\pi$
$270$		0			0
$271$	9.12979	+	15.8133i	0.00204648	+	0.00354460i	0.867047	−	0.498227i	$-0.166015\pi$
$271$	9.12979	+	15.8133i	0.00204648	+	0.00354460i	−0.865000	+	0.501771i	$0.832682\pi$
$272$		0			0
$273$	7794.68	−	542.738i	1.72804	−	0.120322i
$274$		0			0
$275$	−90.5605	+	156.855i	−0.0198582	+	0.0343954i
$276$		0			0
$277$	−1910.18	−	3308.53i	−0.414338	−	0.717655i	0.581021	−	0.813889i	$-0.302654\pi$
$277$	−1910.18	−	3308.53i	−0.414338	−	0.717655i	−0.995359	+	0.0962343i	$0.969320\pi$
$278$		0			0
$279$	−6442.58	−	3215.12i	−1.38246	−	0.689908i
$280$		0			0
$281$	−3064.34	+	5307.60i	−0.650546	+	1.12678i	0.332445	+	0.943123i	$0.392126\pi$
$281$	−3064.34	+	5307.60i	−0.650546	+	1.12678i	−0.982991	+	0.183655i	$0.941207\pi$
$282$		0			0
$283$	−55.4948			−0.0116566			−0.00582831	−	0.999983i	$-0.501855\pi$
$283$	−55.4948			−0.0116566			−0.00582831	+	0.999983i	$0.501855\pi$
$284$		0			0
$285$	2328.44	−	9880.38i	0.483948	−	2.05356i
$286$		0			0
$287$	863.901	+	2783.31i	0.177681	+	0.572452i
$288$		0			0
$289$	1653.38	+	2863.74i	0.336532	+	0.582890i
$290$		0			0
$291$	5221.02	+	4913.26i	1.05176	+	0.989762i
$292$		0			0
$293$	−1196.49	−	2072.38i	−0.238566	−	0.413208i	0.721737	−	0.692167i	$-0.243344\pi$
$293$	−1196.49	−	2072.38i	−0.238566	−	0.413208i	−0.960303	+	0.278959i	$0.910011\pi$
$294$		0			0
$295$	−2368.99	+	4103.21i	−0.467552	+	0.809824i
$296$		0			0
$297$	−152.210	−	26.2411i	−0.0297377	−	0.00512681i
$298$		0			0
$299$	14164.0			2.73955
$300$		0			0
$301$	3358.58	−	3632.47i	0.643140	−	0.695589i
$302$		0			0
$303$	−1353.83	+	407.185i	−0.256685	+	0.0772019i
$304$		0			0
$305$	−2693.31	+	4664.95i	−0.505635	+	0.875785i
$306$		0			0
$307$	−10315.0			−1.91762			−0.958809	−	0.284052i	$-0.908321\pi$
$307$	−10315.0			−1.91762			−0.958809	+	0.284052i	$0.908321\pi$
$308$		0			0
$309$	2878.96	+	2709.26i	0.530027	+	0.498784i
$310$		0			0
$311$	3982.06			0.726050			0.363025	−	0.931779i	$-0.381744\pi$
$311$	3982.06			0.726050			0.363025	+	0.931779i	$0.381744\pi$
$312$		0			0
$313$	−1042.40			−0.188242			−0.0941211	−	0.995561i	$-0.530004\pi$
$313$	−1042.40			−0.188242			−0.0941211	+	0.995561i	$0.530004\pi$
$314$		0			0
$315$	−7957.96	+	3010.63i	−1.42343	+	0.538507i
$316$		0			0
$317$	7910.14			1.40151			0.700753	−	0.713404i	$-0.252847\pi$
$317$	7910.14			1.40151			0.700753	+	0.713404i	$0.252847\pi$
$318$		0			0
$319$	−224.200			−0.0393504
$320$		0			0
$321$	1791.73	−	538.890i	0.311541	−	0.0937006i
$322$		0			0
$323$	−4601.47			−0.792670
$324$		0			0
$325$	−6678.85	+	11568.1i	−1.13993	+	1.97441i
$326$		0			0
$327$	−6850.84	−	6447.01i	−1.15857	−	1.09028i
$328$		0			0
$329$	2523.51	+	571.309i	0.422875	+	0.0957365i
$330$		0			0
$331$	−1325.51			−0.220110			−0.110055	−	0.993925i	$-0.535103\pi$
$331$	−1325.51			−0.220110			−0.110055	+	0.993925i	$0.535103\pi$
$332$		0			0
$333$	−41.7683	−	687.062i	−0.00687354	−	0.113065i
$334$		0			0
$335$	7587.14	−	13141.3i	1.23740	−	2.14324i
$336$		0			0
$337$	−3357.04	−	5814.56i	−0.542639	−	0.939879i	−0.998751	−	0.0499565i	$-0.984092\pi$
$337$	−3357.04	−	5814.56i	−0.542639	−	0.939879i	0.456112	−	0.889922i	$-0.349242\pi$
$338$		0			0
$339$	−11324.4	+	3405.98i	−1.81433	+	0.545685i
$340$		0			0
$341$	−146.795	−	254.257i	−0.0233120	−	0.0403776i
$342$		0			0
$343$	4987.37	+	3934.43i	0.785109	+	0.619357i
$344$		0			0
$345$	−14770.0	+	4442.30i	−2.30490	+	0.693233i
$346$		0			0
$347$	7271.23			1.12490			0.562450	−	0.826831i	$-0.309859\pi$
$347$	7271.23			1.12490			0.562450	+	0.826831i	$0.309859\pi$
$348$		0			0
$349$	1820.40	−	3153.03i	0.279209	−	0.483605i	−0.691979	−	0.721917i	$-0.743261\pi$
$349$	1820.40	−	3153.03i	0.279209	−	0.483605i	0.971188	+	0.238313i	$0.0765944\pi$
$350$		0			0
$351$	−11225.5	−	1935.28i	−1.70704	−	0.294295i
$352$		0			0
$353$	−1478.73	−	2561.23i	−0.222959	−	0.386177i	0.732746	−	0.680502i	$-0.238238\pi$
$353$	−1478.73	−	2561.23i	−0.222959	−	0.386177i	−0.955705	+	0.294325i	$0.904905\pi$
$354$		0			0
$355$	−7916.61	+	13712.0i	−1.18358	+	2.05002i
$356$		0			0
$357$	2155.78	+	3198.12i	0.319597	+	0.474125i
$358$		0			0
$359$	−2060.77	−	3569.36i	−0.302962	−	0.524745i	0.673844	−	0.738874i	$-0.264642\pi$
$359$	−2060.77	−	3569.36i	−0.302962	−	0.524745i	−0.976805	+	0.214129i	$0.931309\pi$
$360$		0			0
$361$	−3161.52	+	5475.91i	−0.460930	+	0.798354i
$362$		0			0
$363$	5032.01	+	4735.39i	0.727582	+	0.684693i
$364$		0			0
$365$	1134.81	+	1965.54i	0.162736	+	0.281866i
$366$		0			0
$367$	5504.36	+	9533.84i	0.782903	+	1.35603i	0.930244	+	0.366942i	$0.119595\pi$
$367$	5504.36	+	9533.84i	0.782903	+	1.35603i	−0.147340	+	0.989086i	$0.547071\pi$
$368$		0			0
$369$	−257.811	−	4240.82i	−0.0363715	−	0.598289i
$370$		0			0
$371$	2248.53	−	2431.90i	0.314658	−	0.340318i
$372$		0			0
$373$	−1036.04	+	1794.47i	−0.143818	+	0.249100i	−0.928931	−	0.370252i	$-0.879271\pi$
$373$	−1036.04	+	1794.47i	−0.143818	+	0.249100i	0.785113	+	0.619352i	$0.212605\pi$
$374$		0			0
$375$	801.427	−	3400.73i	0.110361	−	0.468301i
$376$		0			0
$377$	−16534.7			−2.25884
$378$		0			0
$379$	2446.71			0.331607			0.165803	−	0.986159i	$-0.446978\pi$
$379$	2446.71			0.331607			0.165803	+	0.986159i	$0.446978\pi$
$380$		0			0
$381$	550.062	−	2334.10i	0.0739646	−	0.313857i
$382$		0			0
$383$	−6807.85	+	11791.5i	−0.908263	+	1.57316i	−0.0917875	+	0.995779i	$0.529258\pi$
$383$	−6807.85	+	11791.5i	−0.908263	+	1.57316i	−0.816476	+	0.577380i	$0.804075\pi$
$384$		0			0
$385$	−338.366	−	76.6043i	−0.0447916	−	0.0101406i
$386$		0			0
$387$	−6015.75	+	3978.55i	−0.790175	+	0.522586i
$388$		0			0
$389$	6925.09	+	11994.6i	0.902612	+	1.56337i	0.824092	+	0.566457i	$0.191686\pi$
$389$	6925.09	+	11994.6i	0.902612	+	1.56337i	0.0785201	+	0.996913i	$0.474981\pi$
$390$		0			0
$391$	3495.76	+	6054.83i	0.452144	+	0.783136i
$392$		0			0
$393$	−1568.98	−	1476.50i	−0.201386	−	0.189515i
$394$		0			0
$395$	−3649.67	+	6321.41i	−0.464898	+	0.805228i
$396$		0			0
$397$	−1338.96	−	2319.15i	−0.169271	−	0.293186i	0.768893	−	0.639378i	$-0.220808\pi$
$397$	−1338.96	−	2319.15i	−0.169271	−	0.293186i	−0.938164	+	0.346192i	$0.887475\pi$
$398$		0			0
$399$	11022.2	−	767.471i	1.38296	−	0.0962948i
$400$		0			0
$401$	4489.33	−	7775.75i	0.559069	−	0.968335i	−0.438506	−	0.898728i	$-0.644492\pi$
$401$	4489.33	−	7775.75i	0.559069	−	0.968335i	0.997574	−	0.0696069i	$-0.0221745\pi$
$402$		0			0
$403$	−10826.2	−	18751.5i	−1.33819	−	2.31781i
$404$		0			0
$405$	12312.7	−	1502.60i	1.51068	−	0.184358i
$406$		0			0
$407$	14.0333	−	24.3064i	0.00170910	−	0.00296026i
$408$		0			0
$409$	4202.35			0.508051			0.254025	−	0.967198i	$-0.418245\pi$
$409$	4202.35			0.508051			0.254025	+	0.967198i	$0.418245\pi$
$410$		0			0
$411$	11182.9	−	3363.41i	1.34212	−	0.403661i
$412$		0			0
$413$	−5029.78	−	1138.71i	−0.599272	−	0.135672i
$414$		0			0
$415$	6355.32	+	11007.7i	0.751736	+	1.30205i
$416$		0			0
$417$	−1695.52	+	509.954i	−0.199113	+	0.0598862i
$418$		0			0
$419$	4537.80	+	7859.70i	0.529084	+	0.916400i	0.999425	+	0.0339153i	$0.0107976\pi$
$419$	4537.80	+	7859.70i	0.529084	+	0.916400i	−0.470341	+	0.882485i	$0.655869\pi$
$420$		0			0
$421$	3305.28	−	5724.91i	0.382635	−	0.662744i	−0.608803	−	0.793322i	$-0.708350\pi$
$421$	3305.28	−	5724.91i	0.382635	−	0.662744i	0.991438	+	0.130578i	$0.0416832\pi$
$422$		0			0
$423$	−3375.11	−	1684.32i	−0.387951	−	0.193604i
$424$		0			0
$425$	−6593.52			−0.752547
$426$		0			0
$427$	−5718.37	−	1294.61i	−0.648083	−	0.146722i
$428$		0			0
$429$	−338.248	−	318.310i	−0.0380671	−	0.0358231i
$430$		0			0
$431$	−2749.12	+	4761.62i	−0.307241	+	0.532156i	−0.977758	−	0.209738i	$-0.932739\pi$
$431$	−2749.12	+	4761.62i	−0.307241	+	0.532156i	0.670517	+	0.741894i	$0.266072\pi$
$432$		0			0
$433$	−8877.61			−0.985290			−0.492645	−	0.870230i	$-0.663970\pi$
$433$	−8877.61			−0.985290			−0.492645	+	0.870230i	$0.663970\pi$
$434$		0			0
$435$	17242.2	−	5185.85i	1.90046	−	0.571592i
$436$		0			0
$437$	20028.9			2.19248
$438$		0			0
$439$	2501.16			0.271922			0.135961	−	0.990714i	$-0.456588\pi$
$439$	2501.16			0.271922			0.135961	+	0.990714i	$0.456588\pi$
$440$		0			0
$441$	−5697.32	−	7301.14i	−0.615195	−	0.788375i
$442$		0			0
$443$	1978.50			0.212193			0.106097	−	0.994356i	$-0.466165\pi$
$443$	1978.50			0.212193			0.106097	+	0.994356i	$0.466165\pi$
$444$		0			0
$445$	10649.6			1.13447
$446$		0			0
$447$	−5160.20	−	4856.02i	−0.546016	−	0.513830i
$448$		0			0
$449$	2845.20			0.299050			0.149525	−	0.988758i	$-0.452226\pi$
$449$	2845.20			0.299050			0.149525	+	0.988758i	$0.452226\pi$
$450$		0			0
$451$	86.6192	−	150.029i	0.00904377	−	0.0156643i
$452$		0			0
$453$	−145.505	+	43.7628i	−0.0150914	+	0.00453898i
$454$		0			0
$455$	−24954.6	−	5649.57i	−2.57118	−	0.582101i
$456$		0			0
$457$	6029.14			0.617136			0.308568	−	0.951202i	$-0.400150\pi$
$457$	6029.14			0.617136			0.308568	+	0.951202i	$0.400150\pi$
$458$		0			0
$459$	−1943.22	−	5276.31i	−0.197607	−	0.536552i
$460$		0			0
$461$	4546.97	−	7875.58i	0.459378	−	0.795666i	−0.539550	−	0.841954i	$-0.681406\pi$
$461$	4546.97	−	7875.58i	0.459378	−	0.795666i	0.998928	+	0.0462873i	$0.0147390\pi$
$462$		0			0
$463$	5731.03	+	9926.44i	0.575256	+	0.996373i	0.996014	+	0.0892002i	$0.0284311\pi$
$463$	5731.03	+	9926.44i	0.575256	+	0.996373i	−0.420757	+	0.907173i	$0.638236\pi$
$464$		0			0
$465$	17170.4	+	16158.3i	1.71239	+	1.61145i
$466$		0			0
$467$	2470.34	+	4278.76i	0.244783	+	0.423977i	0.962071	−	0.272800i	$-0.0879499\pi$
$467$	2470.34	+	4278.76i	0.244783	+	0.423977i	−0.717287	+	0.696777i	$0.754617\pi$
$468$		0			0
$469$	16108.8	+	3646.95i	1.58601	+	0.359063i
$470$		0			0
$471$	135.349	−	574.331i	0.0132411	−	0.0561864i
$472$		0			0
$473$	−294.083			−0.0285876
$474$		0			0
$475$	−9444.38	+	16358.1i	−0.912290	+	1.58013i
$476$		0			0
$477$	−4027.48	+	2663.60i	−0.386595	+	0.255677i
$478$		0			0
$479$	6057.43	+	10491.8i	0.577810	+	1.00080i	0.995730	+	0.0923121i	$0.0294257\pi$
$479$	6057.43	+	10491.8i	0.577810	+	1.00080i	−0.417920	+	0.908484i	$0.637241\pi$
$480$		0			0
$481$	1034.96	−	1792.60i	0.0981082	−	0.169928i
$482$		0			0
$483$	−9383.53	−	13920.5i	−0.883987	−	1.31140i
$484$		0			0
$485$	−11738.3	−	20331.3i	−1.09898	−	1.90350i
$486$		0			0
$487$	825.979	−	1430.64i	0.0768556	−	0.133118i	−0.825036	−	0.565080i	$-0.808845\pi$
$487$	825.979	−	1430.64i	0.0768556	−	0.133118i	0.901892	+	0.431962i	$0.142179\pi$
$488$		0			0
$489$	3647.78	−	1097.13i	0.337338	−	0.101460i
$490$		0			0
$491$	814.415	+	1410.61i	0.0748555	+	0.129654i	0.901023	−	0.433770i	$-0.142817\pi$
$491$	814.415	+	1410.61i	0.0748555	+	0.129654i	−0.826168	+	0.563424i	$0.809484\pi$
$492$		0			0
$493$	−4080.87	−	7068.28i	−0.372806	−	0.645719i
$494$		0			0
$495$	452.553	+	225.843i	0.0410924	+	0.0205068i
$496$		0			0
$497$	−16808.4	−	3805.32i	−1.51702	−	0.343444i
$498$		0			0
$499$	3718.06	−	6439.86i	0.333553	−	0.577731i	−0.649653	−	0.760231i	$-0.725086\pi$
$499$	3718.06	−	6439.86i	0.333553	−	0.577731i	0.983206	+	0.182500i	$0.0584190\pi$
$500$		0			0
$501$	−19697.0	+	5924.16i	−1.75648	+	0.528288i
$502$		0			0
$503$	15492.0			1.37327			0.686636	−	0.727002i	$-0.259087\pi$
$503$	15492.0			1.37327			0.686636	+	0.727002i	$0.259087\pi$
$504$		0			0
$505$	4629.41			0.407932
$506$		0			0
$507$	−16632.2	−	15651.8i	−1.45693	−	1.37105i
$508$		0			0
$509$	4335.57	−	7509.42i	0.377546	−	0.653928i	−0.613159	−	0.789960i	$-0.710102\pi$
$509$	4335.57	−	7509.42i	0.377546	−	0.653928i	0.990705	+	0.136032i	$0.0434348\pi$
$510$		0			0
$511$	−1677.09	+	1813.86i	−0.145186	+	0.157026i
$512$		0			0
$513$	−15873.7	−	2736.63i	−1.36616	−	0.235527i
$514$		0			0
$515$	−6472.68	−	11211.0i	−0.553826	−	0.959255i
$516$		0			0
$517$	−76.9023	−	133.199i	−0.00654189	−	0.0113309i
$518$		0			0
$519$	1733.45	−	7355.60i	0.146609	−	0.622110i
$520$		0			0
$521$	4632.44	−	8023.62i	0.389541	−	0.674705i	−0.602847	−	0.797857i	$-0.705967\pi$
$521$	4632.44	−	8023.62i	0.389541	−	0.674705i	0.992388	+	0.123152i	$0.0393003\pi$
$522$		0			0
$523$	−5441.12	−	9424.30i	−0.454921	−	0.787946i	0.543763	−	0.839239i	$-0.316999\pi$
$523$	−5441.12	−	9424.30i	−0.454921	−	0.787946i	−0.998684	+	0.0512930i	$0.983666\pi$
$524$		0			0
$525$	15794.0	−	1099.72i	1.31296	−	0.0914206i
$526$		0			0
$527$	5343.92	−	9255.94i	0.441717	−	0.765076i
$528$		0			0
$529$	−9132.58	−	15818.1i	−0.750603	−	1.30008i
$530$		0			0
$531$	6727.14	+	3357.13i	0.549780	+	0.274363i
$532$		0			0
$533$	6388.18	−	11064.6i	0.519142	−	0.899180i
$534$		0			0
$535$	−6126.79			−0.495111
$536$		0			0
$537$	5052.17	+	4754.36i	0.405991	+	0.382059i
$538$		0			0
$539$	−29.5433	−	376.459i	−0.00236089	−	0.0300839i
$540$		0			0
$541$	−8656.15	−	14992.9i	−0.687906	−	1.19149i	−0.972514	−	0.232844i	$-0.925197\pi$
$541$	−8656.15	−	14992.9i	−0.687906	−	1.19149i	0.284608	−	0.958644i	$-0.408136\pi$
$542$		0			0
$543$	−4707.87	+	19977.1i	−0.372070	+	1.57882i
$544$		0			0
$545$	15402.5	+	26678.0i	1.21059	+	2.09681i
$546$		0			0
$547$	−3735.18	+	6469.53i	−0.291965	+	0.505698i	−0.974274	−	0.225365i	$-0.927642\pi$
$547$	−3735.18	+	6469.53i	−0.291965	+	0.505698i	0.682309	+	0.731064i	$0.260976\pi$
$548$		0			0
$549$	7648.12	+	3816.73i	0.594560	+	0.296711i
$550$		0			0
$551$	−23381.3			−1.80777
$552$		0			0
$553$	−7748.89	−	1754.30i	−0.595870	−	0.134902i
$554$		0			0
$555$	−517.021	+	2193.90i	−0.0395429	+	0.167794i
$556$		0			0
$557$	−7279.25	+	12608.0i	−0.553738	+	0.959102i	0.444263	+	0.895896i	$0.353466\pi$
$557$	−7279.25	+	12608.0i	−0.553738	+	0.959102i	−0.998001	+	0.0632053i	$0.979868\pi$
$558$		0			0
$559$	−21688.7			−1.64102
$560$		0			0
$561$	52.5895	−	223.155i	0.00395781	−	0.0167943i
$562$		0			0
$563$	−3480.92			−0.260574			−0.130287	−	0.991476i	$-0.541590\pi$
$563$	−3480.92			−0.260574			−0.130287	+	0.991476i	$0.541590\pi$
$564$		0			0
$565$	38723.5			2.88338
$566$		0			0
$567$	5534.77	+	12314.6i	0.409945	+	0.912110i
$568$		0			0
$569$	16065.2			1.18364			0.591818	−	0.806072i	$-0.298410\pi$
$569$	16065.2			1.18364			0.591818	+	0.806072i	$0.298410\pi$
$570$		0			0
$571$	18877.2			1.38351			0.691757	−	0.722130i	$-0.256837\pi$
$571$	18877.2			1.38351			0.691757	+	0.722130i	$0.256837\pi$
$572$		0			0
$573$	2986.65	−	12673.4i	0.217747	−	0.923977i
$574$		0			0
$575$	28699.8			2.08150
$576$		0			0
$577$	10526.4	−	18232.3i	0.759482	−	1.31546i	−0.183633	−	0.982995i	$-0.558786\pi$
$577$	10526.4	−	18232.3i	0.759482	−	1.31546i	0.943115	−	0.332467i	$-0.107881\pi$
$578$		0			0
$579$	283.854	−	1204.49i	0.0203741	−	0.0864541i
$580$		0			0
$581$	−9392.30	+	10158.3i	−0.670669	+	0.725363i
$582$		0			0
$583$	−196.886			−0.0139866
$584$		0			0
$585$	33375.8	+	16655.9i	2.35884	+	1.17716i
$586$		0			0
$587$	8673.11	−	15022.3i	0.609843	−	1.05628i	−0.381423	−	0.924400i	$-0.624566\pi$
$587$	8673.11	−	15022.3i	0.609843	−	1.05628i	0.991266	−	0.131878i	$-0.0421006\pi$
$588$		0			0
$589$	−15309.0	−	26515.9i	−1.07096	−	1.85496i
$590$		0			0
$591$	3317.45	−	14077.1i	0.230899	−	0.979785i
$592$		0			0
$593$	7255.54	+	12567.0i	0.502444	+	0.870259i	0.999996	+	0.00282454i	$0.000899081\pi$
$593$	7255.54	+	12567.0i	0.502444	+	0.870259i	−0.497552	+	0.867434i	$0.665768\pi$
$594$		0			0
$595$	−3743.85	−	12061.9i	−0.257955	−	0.831078i
$596$		0			0
$597$	8321.31	+	7830.80i	0.570467	+	0.536840i
$598$		0			0
$599$	−16778.7			−1.14451			−0.572254	−	0.820076i	$-0.693931\pi$
$599$	−16778.7			−1.14451			−0.572254	+	0.820076i	$0.693931\pi$
$600$		0			0
$601$	−12127.2	+	21005.0i	−0.823094	+	1.42564i	0.0802726	+	0.996773i	$0.474421\pi$
$601$	−12127.2	+	21005.0i	−0.823094	+	1.42564i	−0.903367	+	0.428868i	$0.858912\pi$
$602$		0			0
$603$	−21545.0	−	10751.8i	−1.45502	−	0.726118i
$604$		0			0
$605$	−11313.3	−	19595.2i	−0.760251	−	1.31679i
$606$		0			0
$607$	2809.48	−	4866.16i	0.187864	−	0.325389i	−0.756674	−	0.653792i	$-0.773177\pi$
$607$	2809.48	−	4866.16i	0.187864	−	0.325389i	0.944538	+	0.328403i	$0.106510\pi$
$608$		0			0
$609$	10954.1	+	16250.5i	0.728873	+	1.08129i
$610$		0			0
$611$	−5671.55	−	9823.41i	−0.375526	−	0.650430i
$612$		0			0
$613$	14025.8	−	24293.5i	0.924141	−	1.60066i	0.131203	−	0.991356i	$-0.458116\pi$
$613$	14025.8	−	24293.5i	0.924141	−	1.60066i	0.792938	−	0.609303i	$-0.208551\pi$
$614$		0			0
$615$	−3191.26	+	13541.6i	−0.209242	+	0.887886i
$616$		0			0
$617$	1260.90	+	2183.94i	0.0822720	+	0.142499i	0.904226	−	0.427055i	$-0.140449\pi$
$617$	1260.90	+	2183.94i	0.0822720	+	0.142499i	−0.821953	+	0.569555i	$0.807116\pi$
$618$		0			0
$619$	9537.81	+	16520.0i	0.619317	+	1.07269i	0.989611	+	0.143773i	$0.0459236\pi$
$619$	9537.81	+	16520.0i	0.619317	+	1.07269i	−0.370294	+	0.928915i	$0.620743\pi$
$620$		0			0
$621$	8458.31	+	22966.4i	0.546571	+	1.48407i
$622$		0			0
$623$	3436.15	+	11070.6i	0.220973	+	0.711931i
$624$		0			0
$625$	4561.84	−	7901.34i	0.291958	−	0.505686i
$626$		0			0
$627$	−478.308	−	450.113i	−0.0304653	−	0.0286695i
$628$		0			0
$629$	1021.74			0.0647683
$630$		0			0
$631$	19661.6			1.24044			0.620218	−	0.784430i	$-0.287044\pi$
$631$	19661.6			1.24044			0.620218	+	0.784430i	$0.287044\pi$
$632$		0			0
$633$	−8107.21	+	2438.36i	−0.509057	+	0.153106i
$634$		0			0
$635$	−3926.29	+	6800.53i	−0.245370	+	0.424993i
$636$		0			0
$637$	−2178.82	−	27763.9i	−0.135523	−	1.72692i
$638$		0			0
$639$	22480.6	+	11218.7i	1.39173	+	0.694533i
$640$		0			0
$641$	3180.98	+	5509.63i	0.196008	+	0.339496i	0.947231	−	0.320553i	$-0.103869\pi$
$641$	3180.98	+	5509.63i	0.196008	+	0.339496i	−0.751222	+	0.660049i	$0.770535\pi$
$642$		0			0
$643$	183.186	+	317.287i	0.0112350	+	0.0194597i	0.871588	−	0.490239i	$-0.163090\pi$
$643$	183.186	+	317.287i	0.0112350	+	0.0194597i	−0.860353	+	0.509698i	$0.829757\pi$
$644$		0			0
$645$	22616.6	−	6802.28i	1.38066	−	0.415255i
$646$		0			0
$647$	−3206.39	+	5553.63i	−0.194832	+	0.337458i	−0.946845	−	0.321689i	$-0.895749\pi$
$647$	−3206.39	+	5553.63i	−0.194832	+	0.337458i	0.752014	+	0.659148i	$0.229083\pi$
$648$		0			0
$649$	153.279	+	265.487i	0.00927076	+	0.0160574i
$650$		0			0
$651$	−11256.9	+	23062.8i	−0.677716	+	1.38848i
$652$		0			0
$653$	−5990.74	+	10376.3i	−0.359013	+	0.621829i	−0.987796	−	0.155752i	$-0.950220\pi$
$653$	−5990.74	+	10376.3i	−0.359013	+	0.621829i	0.628783	+	0.777581i	$0.283553\pi$
$654$		0			0
$655$	3527.50	+	6109.81i	0.210429	+	0.364473i
$656$		0			0
$657$	3003.94	−	1986.67i	0.178379	−	0.117972i
$658$		0			0
$659$	−12502.1	+	21654.3i	−0.739018	+	1.28002i	0.213920	+	0.976851i	$0.431377\pi$
$659$	−12502.1	+	21654.3i	−0.739018	+	1.28002i	−0.952938	+	0.303165i	$0.901957\pi$
$660$		0			0
$661$	−26159.4			−1.53931			−0.769654	−	0.638461i	$-0.779571\pi$
$661$	−26159.4			−1.53931			−0.769654	+	0.638461i	$0.779571\pi$
$662$		0			0
$663$	3878.48	−	16457.7i	0.227191	−	0.964049i
$664$		0			0
$665$	−35287.6	−	7988.91i	−2.05773	−	0.465860i
$666$		0			0
$667$	17762.9	+	30766.3i	1.03116	+	1.78602i
$668$		0			0
$669$	8286.13	+	7797.69i	0.478864	+	0.450637i
$670$		0			0
$671$	174.263	+	301.833i	0.0100259	+	0.0173653i
$672$		0			0
$673$	−9475.28	+	16411.7i	−0.542712	+	0.940005i	0.456035	+	0.889962i	$0.349269\pi$
$673$	−9475.28	+	16411.7i	−0.542712	+	0.940005i	−0.998747	+	0.0500428i	$0.984064\pi$
$674$		0			0
$675$	−22745.6	−	3921.36i	−1.29701	−	0.223605i
$676$		0			0
$677$	−16934.8			−0.961387			−0.480694	−	0.876889i	$-0.659615\pi$
$677$	−16934.8			−0.961387			−0.480694	+	0.876889i	$0.659615\pi$
$678$		0			0
$679$	17347.6	−	18762.3i	0.980469	−	1.06043i
$680$		0			0
$681$	−28836.1	+	8672.87i	−1.62261	+	0.488025i
$682$		0			0
$683$	10755.8	−	18629.6i	0.602576	−	1.04369i	−0.389853	−	0.920877i	$-0.627474\pi$
$683$	10755.8	−	18629.6i	0.602576	−	1.04369i	0.992430	−	0.122816i	$-0.0391924\pi$
$684$		0			0
$685$	−38239.6			−2.13293
$686$		0			0
$687$	−4802.00	−	4518.94i	−0.266678	−	0.250958i
$688$		0			0
$689$	−14520.3			−0.802874
$690$		0			0
$691$	−27164.0			−1.49546			−0.747732	−	0.664001i	$-0.768857\pi$
$691$	−27164.0			−1.49546			−0.747732	+	0.664001i	$0.768857\pi$
$692$		0			0
$693$	−88.7519	+	543.312i	−0.00486494	+	0.0297817i
$694$		0			0
$695$	5797.81			0.316437
$696$		0			0
$697$	6306.56			0.342723
$698$		0			0
$699$	20104.5	−	6046.71i	1.08787	−	0.327193i
$700$		0			0
$701$	−21986.3			−1.18461			−0.592306	−	0.805713i	$-0.701782\pi$
$701$	−21986.3			−1.18461			−0.592306	+	0.805713i	$0.701782\pi$
$702$		0			0
$703$	1463.51	−	2534.87i	0.0785166	−	0.135995i
$704$		0			0
$705$	8995.16	+	8464.93i	0.480535	+	0.452209i
$706$		0			0
$707$	1493.70	+	4812.41i	0.0794575	+	0.255996i
$708$		0			0
$709$	34051.5			1.80371			0.901856	−	0.432037i	$-0.142205\pi$
$709$	34051.5			1.80371			0.901856	+	0.432037i	$0.142205\pi$
$710$		0			0
$711$	10363.9	+	5172.00i	0.546660	+	0.272806i
$712$		0			0
$713$	−23260.6	+	40288.6i	−1.22176	+	2.11616i
$714$		0			0
$715$	760.472	+	1317.18i	0.0397763	+	0.0688946i
$716$		0			0
$717$	−15396.6	+	4630.77i	−0.801950	+	0.241198i
$718$		0			0
$719$	−4996.12	−	8653.54i	−0.259143	−	0.448849i	0.706869	−	0.707344i	$-0.250107\pi$
$719$	−4996.12	−	8653.54i	−0.259143	−	0.448849i	−0.966013	+	0.258495i	$0.916774\pi$
$720$		0			0
$721$	9565.74	−	10345.8i	0.494101	−	0.534396i
$722$		0			0
$723$	−2181.01	+	655.971i	−0.112189	+	0.0337425i
$724$		0			0
$725$	−33503.5			−1.71626
$726$		0			0
$727$	8636.12	−	14958.2i	0.440572	−	0.763093i	−0.557160	−	0.830405i	$-0.688109\pi$
$727$	8636.12	−	14958.2i	0.440572	−	0.763093i	0.997732	+	0.0673121i	$0.0214423\pi$
$728$		0			0
$729$	−3565.54	−	19357.4i	−0.181148	−	0.983456i
$730$		0			0
$731$	−5352.89	−	9271.48i	−0.270840	−	0.469108i
$732$		0			0
$733$	4255.39	−	7370.55i	0.214429	−	0.371402i	−0.738667	−	0.674071i	$-0.764544\pi$
$733$	4255.39	−	7370.55i	0.214429	−	0.371402i	0.953096	+	0.302669i	$0.0978777\pi$
$734$		0			0
$735$	10979.7	+	28268.4i	0.551011	+	1.41864i
$736$		0			0
$737$	−490.905	−	850.273i	−0.0245356	−	0.0424969i
$738$		0			0
$739$	−3046.44	+	5276.58i	−0.151644	+	0.262655i	−0.931832	−	0.362890i	$-0.881790\pi$
$739$	−3046.44	+	5276.58i	−0.151644	+	0.262655i	0.780188	+	0.625545i	$0.215123\pi$
$740$		0			0
$741$	−35275.2	−	33195.9i	−1.74881	−	1.64572i
$742$		0			0
$743$	−8461.62	−	14656.0i	−0.417802	−	0.723654i	0.577916	−	0.816096i	$-0.303866\pi$
$743$	−8461.62	−	14656.0i	−0.417802	−	0.723654i	−0.995718	+	0.0924420i	$0.970533\pi$
$744$		0			0
$745$	11601.5	+	20094.4i	0.570532	+	0.988191i
$746$		0			0
$747$	16823.1	−	11126.1i	0.823997	−	0.544955i
$748$		0			0
$749$	−1976.84	−	6368.98i	−0.0964382	−	0.310704i
$750$		0			0
$751$	−3844.48	+	6658.83i	−0.186800	+	0.323547i	−0.944182	−	0.329425i	$-0.893145\pi$
$751$	−3844.48	+	6658.83i	−0.186800	+	0.323547i	0.757382	+	0.652973i	$0.226478\pi$
$752$		0			0
$753$	−7256.58	+	30792.1i	−0.351188	+	1.49021i
$754$		0			0
$755$	497.552			0.0239838
$756$		0			0
$757$	−11687.6			−0.561154			−0.280577	−	0.959831i	$-0.590526\pi$
$757$	−11687.6			−0.561154			−0.280577	+	0.959831i	$0.590526\pi$
$758$		0			0
$759$	−228.908	+	971.333i	−0.0109471	+	0.0464521i
$760$		0			0
$761$	−547.154	+	947.698i	−0.0260635	+	0.0451433i	−0.878763	−	0.477259i	$-0.841631\pi$
$761$	−547.154	+	947.698i	−0.0260635	+	0.0451433i	0.852699	+	0.522402i	$0.174964\pi$
$762$		0			0
$763$	−22762.8	+	24619.2i	−1.08004	+	1.16812i
$764$		0			0
$765$	1117.26	+	18378.3i	0.0528036	+	0.868586i
$766$		0			0
$767$	11304.3	+	19579.7i	0.532172	+	0.921749i
$768$		0			0
$769$	5172.32	+	8958.72i	0.242547	+	0.420104i	0.961439	−	0.275018i	$-0.0886838\pi$
$769$	5172.32	+	8958.72i	0.242547	+	0.420104i	−0.718892	+	0.695122i	$0.755350\pi$
$770$		0			0
$771$	−5695.93	−	5360.18i	−0.266062	−	0.250379i
$772$		0			0
$773$	9445.03	−	16359.3i	0.439475	−	0.761193i	−0.558174	−	0.829724i	$-0.688498\pi$
$773$	9445.03	−	16359.3i	0.439475	−	0.761193i	0.997649	+	0.0685309i	$0.0218312\pi$
$774$		0			0
$775$	−21936.5	−	37995.1i	−1.01675	−	1.76106i
$776$		0			0
$777$	−2447.44	+	170.414i	−0.113001	+	0.00786815i
$778$		0			0
$779$	9033.35	−	15646.2i	0.415473	−	0.719620i
$780$		0			0
$781$	512.223	+	887.196i	0.0234683	+	0.0406483i
$782$		0			0
$783$	−9874.05	−	26810.4i	−0.450664	−	1.22366i
$784$		0			0
$785$	−966.106	+	1673.34i	−0.0439259	+	0.0760818i
$786$		0			0
$787$	2285.37			0.103513			0.0517565	−	0.998660i	$-0.483518\pi$
$787$	2285.37			0.103513			0.0517565	+	0.998660i	$0.483518\pi$
$788$		0			0
$789$	18259.3	−	5491.75i	0.823888	−	0.247796i
$790$		0			0
$791$	12494.4	+	40254.3i	0.561629	+	1.80945i
$792$		0			0
$793$	12851.9	+	22260.2i	0.575518	+	0.996826i
$794$		0			0
$795$	15141.6	−	4554.06i	0.675493	−	0.203165i
$796$		0			0
$797$	−4141.45	−	7173.20i	−0.184062	−	0.318805i	0.759198	−	0.650860i	$-0.225592\pi$
$797$	−4141.45	−	7173.20i	−0.184062	−	0.318805i	−0.943260	+	0.332055i	$0.892258\pi$
$798$		0			0
$799$	2799.54	−	4848.95i	0.123956	−	0.214698i
$800$		0			0
$801$	−1025.44	−	16867.8i	−0.0452335	−	0.744063i
$802$		0			0
$803$	146.849			0.00645354
$804$		0			0
$805$	16296.0	+	52502.3i	0.713487	+	2.29871i
$806$		0			0
$807$	8811.64	+	8292.22i	0.384367	+	0.361710i
$808$		0			0
$809$	−7926.89	+	13729.8i	−0.344493	+	0.596679i	−0.985261	−	0.171055i	$-0.945282\pi$
$809$	−7926.89	+	13729.8i	−0.344493	+	0.596679i	0.640769	+	0.767734i	$0.278616\pi$
$810$		0			0
$811$	12492.5			0.540901			0.270451	−	0.962734i	$-0.412827\pi$
$811$	12492.5			0.540901			0.270451	+	0.962734i	$0.412827\pi$
$812$		0			0
$813$	−90.8590	+	27.3272i	−0.00391951	+	0.00117885i
$814$		0			0
$815$	−12473.5			−0.536109
$816$		0			0
$817$	−30669.3			−1.31332
$818$		0			0
$819$	−6545.46	+	40069.3i	−0.279264	+	1.70957i
$820$		0			0
$821$	−13775.6			−0.585594			−0.292797	−	0.956175i	$-0.594586\pi$
$821$	−13775.6			−0.585594			−0.292797	+	0.956175i	$0.594586\pi$
$822$		0			0
$823$	−5854.79			−0.247977			−0.123989	−	0.992284i	$-0.539569\pi$
$823$	−5854.79			−0.247977			−0.123989	+	0.992284i	$0.539569\pi$
$824$		0			0
$825$	−685.375	−	644.974i	−0.0289233	−	0.0272183i
$826$		0			0
$827$	27389.0			1.15164			0.575822	−	0.817575i	$-0.304682\pi$
$827$	27389.0			1.15164			0.575822	+	0.817575i	$0.304682\pi$
$828$		0			0
$829$	−4362.29	+	7555.70i	−0.182761	+	0.316551i	−0.942820	−	0.333303i	$-0.891837\pi$
$829$	−4362.29	+	7555.70i	−0.182761	+	0.316551i	0.760059	+	0.649854i	$0.225170\pi$
$830$		0			0
$831$	19010.0	−	5717.53i	0.793560	−	0.238675i
$832$		0			0
$833$	11330.8	−	7783.70i	0.471294	−	0.323756i
$834$		0			0
$835$	67353.5			2.79146
$836$		0			0
$837$	23939.7	−	28752.0i	0.988622	−	1.18735i
$838$		0			0
$839$	−16964.1	+	29382.7i	−0.698052	+	1.20906i	0.271089	+	0.962554i	$0.412616\pi$
$839$	−16964.1	+	29382.7i	−0.698052	+	1.20906i	−0.969141	+	0.246507i	$0.920717\pi$
$840$		0			0
$841$	−8541.56	−	14794.4i	−0.350222	−	0.606602i
$842$		0			0
$843$	−23191.4	−	21824.3i	−0.947513	−	0.891660i
$844$		0			0
$845$	37393.7	+	64767.8i	1.52235	+	2.63678i
$846$		0			0
$847$	16719.5	−	18083.0i	0.678265	−	0.733578i
$848$		0			0
$849$	66.1439	−	280.671i	0.00267380	−	0.0113458i
$850$		0			0
$851$	−4447.33			−0.179145
$852$		0			0
$853$	−6479.36	+	11222.6i	−0.260081	+	0.450473i	−0.966263	−	0.257557i	$-0.917083\pi$
$853$	−6479.36	+	11222.6i	−0.260081	+	0.450473i	0.706182	+	0.708030i	$0.250416\pi$
$854$		0			0
$855$	47195.8	+	23552.7i	1.88779	+	0.942088i
$856$		0			0
$857$	−19273.8	−	33383.3i	−0.768240	−	1.33063i	−0.938517	−	0.345234i	$-0.887800\pi$
$857$	−19273.8	−	33383.3i	−0.768240	−	1.33063i	0.170277	−	0.985396i	$-0.445534\pi$
$858$		0			0
$859$	6912.59	−	11973.0i	0.274569	−	0.475567i	−0.695457	−	0.718567i	$-0.744798\pi$
$859$	6912.59	−	11973.0i	0.274569	−	0.475567i	0.970026	+	0.243000i	$0.0781316\pi$
$860$		0			0
$861$	−15106.6	+	1051.86i	−0.597945	+	0.0416345i
$862$		0			0
$863$	−13645.3	−	23634.3i	−0.538227	−	0.932236i	−0.999000	−	0.0447182i	$-0.985761\pi$
$863$	−13645.3	−	23634.3i	−0.538227	−	0.932236i	0.460773	−	0.887518i	$-0.347572\pi$
$864$		0			0
$865$	−12373.2	+	21430.9i	−0.486358	+	0.842398i
$866$		0			0
$867$	−16454.3	+	4948.88i	−0.644542	+	0.193856i
$868$		0			0
$869$	236.142	+	409.010i	0.00921814	+	0.0159663i
$870$		0			0
$871$	−36204.3	−	62707.7i	−1.40842	−	2.43946i
$872$		0			0
$873$	−31072.3	+	20549.8i	−1.20462	+	0.796685i
$874$		0			0
$875$	−12145.6	−	2749.70i	−0.469254	−	0.106236i
$876$		0			0
$877$	4258.02	−	7375.11i	0.163949	−	0.283968i	−0.772333	−	0.635218i	$-0.780910\pi$
$877$	4258.02	−	7375.11i	0.163949	−	0.283968i	0.936282	+	0.351250i	$0.114243\pi$
$878$		0			0
$879$	11907.4	−	3581.33i	0.456913	−	0.137423i
$880$		0			0
$881$	47675.0			1.82317			0.911584	−	0.411113i	$-0.134860\pi$
$881$	47675.0			1.82317			0.911584	+	0.411113i	$0.134860\pi$
$882$		0			0
$883$	−35837.8			−1.36584			−0.682920	−	0.730493i	$-0.739290\pi$
$883$	−35837.8			−1.36584			−0.682920	+	0.730493i	$0.739290\pi$
$884$		0			0
$885$	−17928.8	−	16872.0i	−0.680985	−	0.640843i
$886$		0			0
$887$	18093.4	−	31338.7i	0.684913	−	1.18630i	−0.288551	−	0.957464i	$-0.593174\pi$
$887$	18093.4	−	31338.7i	0.684913	−	1.18630i	0.973464	−	0.228839i	$-0.0734931\pi$
$888$		0			0
$889$	−8336.19	−	1887.27i	−0.314496	−	0.0712001i
$890$		0			0
$891$	314.135	−	738.541i	0.0118113	−	0.0277688i
$892$		0			0
$893$	−8019.99	−	13891.0i	−0.300536	−	0.520544i
$894$		0			0
$895$	−11358.6	−	19673.7i	−0.424220	−	0.734771i
$896$		0			0
$897$	−16882.0	+	71635.9i	−0.628397	+	2.66650i
$898$		0			0
$899$	27154.0	−	47032.0i	1.00738	−	1.74483i
$900$		0			0
$901$	−3583.70	−	6207.16i	−0.132509	−	0.229512i
$902$		0			0
$903$	14368.6	+	21315.9i	0.529519	+	0.785546i
$904$		0			0
$905$	33604.3	−	58204.4i	1.23430	−	2.13788i
$906$		0			0
$907$	−3873.58	−	6709.24i	−0.141808	−	0.245619i	0.786369	−	0.617757i	$-0.211958\pi$
$907$	−3873.58	−	6709.24i	−0.141808	−	0.245619i	−0.928178	+	0.372137i	$0.878625\pi$
$908$		0			0
$909$	−445.760	−	7332.47i	−0.0162651	−	0.267550i
$910$		0			0
$911$	6242.99	−	10813.2i	0.227047	−	0.393256i	−0.729885	−	0.683570i	$-0.760426\pi$
$911$	6242.99	−	10813.2i	0.227047	−	0.393256i	0.956932	+	0.290314i	$0.0937597\pi$
$912$		0			0
$913$	822.407			0.0298113
$914$		0			0
$915$	−20383.4	−	19181.8i	−0.736452	−	0.693041i
$916$		0			0
$917$	−5213.16	+	5638.31i	−0.187736	+	0.203046i
$918$		0			0
$919$	11230.8	+	19452.3i	0.403123	+	0.698230i	0.994101	−	0.108458i	$-0.0345913\pi$
$919$	11230.8	+	19452.3i	0.403123	+	0.698230i	−0.590978	+	0.806688i	$0.701258\pi$
$920$		0			0
$921$	12294.4	−	52169.3i	0.439863	−	1.86649i
$922$		0			0
$923$	37776.5	+	65430.8i	1.34716	+	2.33335i
$924$		0			0
$925$	2097.08	−	3632.25i	0.0745423	−	0.129111i
$926$		0			0
$927$	−17133.8	+	11331.5i	−0.607063	+	0.401484i
$928$		0			0
$929$	37313.5			1.31778			0.658889	−	0.752240i	$-0.271027\pi$
$929$	37313.5			1.31778			0.658889	+	0.752240i	$0.271027\pi$
$930$		0			0
$931$	−3081.01	−	39260.2i	−0.108460	−	1.38206i
$932$		0			0
$933$	−4746.18	+	20139.7i	−0.166541	+	0.706692i
$934$		0			0
$935$	−375.378	+	650.174i	−0.0131296	+	0.0227411i
$936$		0			0
$937$	46162.5			1.60946			0.804730	−	0.593641i	$-0.202310\pi$
$937$	46162.5			1.60946			0.804730	+	0.593641i	$0.202310\pi$
$938$		0			0
$939$	1242.43	−	5272.04i	0.0431790	−	0.183223i
$940$		0			0
$941$	27053.6			0.937218			0.468609	−	0.883406i	$-0.344755\pi$
$941$	27053.6			0.937218			0.468609	+	0.883406i	$0.344755\pi$
$942$		0			0
$943$	−27450.7			−0.947952
$944$		0			0
$945$	−5741.55	−	43836.6i	−0.197643	−	1.50900i
$946$		0			0
$947$	8405.31			0.288422			0.144211	−	0.989547i	$-0.453936\pi$
$947$	8405.31			0.288422			0.144211	+	0.989547i	$0.453936\pi$
$948$		0			0
$949$	10830.1			0.370454
$950$		0			0
$951$	−9428.03	+	40006.4i	−0.321477	+	1.36414i
$952$		0			0
$953$	−14865.2			−0.505279			−0.252640	−	0.967560i	$-0.581299\pi$
$953$	−14865.2			−0.505279			−0.252640	+	0.967560i	$0.581299\pi$
$954$		0			0
$955$	−21318.4	+	36924.6i	−0.722354	+	1.25115i
$956$		0			0
$957$	267.222	−	1133.91i	0.00902618	−	0.0383012i
$958$		0			0
$959$	−12338.2	−	39751.2i	−0.415455	−	1.33851i
$960$		0			0
$961$	41325.4			1.38718
$962$		0			0
$963$	589.942	+	9704.17i	0.0197410	+	0.324727i
$964$		0			0
$965$	−2026.12	+	3509.35i	−0.0675888	+	0.117067i
$966$		0			0
$967$	9875.43	+	17104.7i	0.328410	+	0.568823i	0.982197	−	0.187856i	$-0.0601539\pi$
$967$	9875.43	+	17104.7i	0.328410	+	0.568823i	−0.653787	+	0.756679i	$0.726821\pi$
$968$		0			0
$969$	5484.45	−	23272.4i	0.181823	−	0.771535i
$970$		0			0
$971$	−6166.55	−	10680.8i	−0.203804	−	0.352999i	0.745947	−	0.666006i	$-0.231997\pi$
$971$	−6166.55	−	10680.8i	−0.203804	−	0.352999i	−0.949751	+	0.313006i	$0.898664\pi$
$972$		0			0
$973$	1870.70	+	6027.00i	0.0616359	+	0.198578i
$974$		0			0
$975$	−50546.4	−	47566.9i	−1.66029	−	1.56242i
$976$		0			0
$977$	−51192.9			−1.67636			−0.838182	−	0.545391i	$-0.816381\pi$
$977$	−51192.9			−1.67636			−0.838182	+	0.545391i	$0.816381\pi$
$978$		0			0
$979$	344.526	−	596.737i	0.0112473	−	0.0194809i
$980$		0			0
$981$	40771.9	−	26964.7i	1.32696	−	0.877592i
$982$		0			0
$983$	12950.7	+	22431.4i	0.420208	+	0.727822i	0.995960	−	0.0898029i	$-0.0286237\pi$
$983$	12950.7	+	22431.4i	0.420208	+	0.727822i	−0.575751	+	0.817625i	$0.695290\pi$
$984$		0			0
$985$	−23679.6	+	41014.2i	−0.765984	+	1.32672i
$986$		0			0
$987$	−5897.21	+	12082.0i	−0.190183	+	0.389640i
$988$		0			0
$989$	23299.7	+	40356.2i	0.749127	+	1.29753i
$990$		0			0
$991$	9914.81	−	17173.0i	0.317815	−	0.550471i	−0.662217	−	0.749312i	$-0.730384\pi$
$991$	9914.81	−	17173.0i	0.317815	−	0.550471i	0.980032	+	0.198841i	$0.0637177\pi$
$992$		0			0
$993$	1579.86	−	6703.90i	0.0504889	−	0.214242i
$994$		0			0
$995$	−18708.5	−	32404.2i	−0.596081	−	1.03244i
$996$		0			0
$997$	−6268.14	−	10856.7i	−0.199111	−	0.344871i	0.749129	−	0.662424i	$-0.230472\pi$
$997$	−6268.14	−	10856.7i	−0.199111	−	0.344871i	−0.948240	+	0.317553i	$0.897139\pi$
$998$		0			0
$999$	3524.67	+	607.657i	0.111627	+	0.0192446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.i.a.25.11	✓	48
3.2	odd	2		756.4.i.a.613.3		48
7.2	even	3		252.4.l.a.205.6	yes	48
9.4	even	3		252.4.l.a.193.6	yes	48
9.5	odd	6		756.4.l.a.361.22		48
21.2	odd	6		756.4.l.a.289.22		48
63.23	odd	6		756.4.i.a.37.3		48
63.58	even	3	inner	252.4.i.a.121.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.i.a.25.11	✓	48	1.1	even	1	trivial
252.4.i.a.121.11	yes	48	63.58	even	3	inner
252.4.l.a.193.6	yes	48	9.4	even	3
252.4.l.a.205.6	yes	48	7.2	even	3
756.4.i.a.37.3		48	63.23	odd	6
756.4.i.a.613.3		48	3.2	odd	2
756.4.l.a.289.22		48	21.2	odd	6
756.4.l.a.361.22		48	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.19189 + 5.05761i) q^{3} +(8.50761 - 14.7356i) q^{5} +(18.0631 + 4.08939i) q^{7} +(-24.1588 - 12.0562i) q^{9} +O(q^{10})\)	\(q+(-1.19189 + 5.05761i) q^{3} +(8.50761 - 14.7356i) q^{5} +(18.0631 + 4.08939i) q^{7} +(-24.1588 - 12.0562i) q^{9} +(-0.550461 - 0.953427i) q^{11} +(-40.5966 - 70.3153i) q^{13} +(64.3868 + 60.5914i) q^{15} +(20.0390 - 34.7085i) q^{17} +(-57.4065 - 99.4310i) q^{19} +(-42.2119 + 86.4821i) q^{21} +(-87.2241 + 151.077i) q^{23} +(-82.2587 - 142.476i) q^{25} +(89.7704 - 107.816i) q^{27} +(101.824 - 176.364i) q^{29} +266.677 q^{31} +(5.47815 - 1.64763i) q^{33} +(213.934 - 231.380i) q^{35} +(12.7469 + 22.0782i) q^{37} +(404.014 - 121.513i) q^{39} +(78.6788 + 136.276i) q^{41} +(133.562 - 231.336i) q^{43} +(-383.190 + 253.425i) q^{45} +139.705 q^{47} +(309.554 + 147.734i) q^{49} +(151.658 + 142.718i) q^{51} +(89.4184 - 154.877i) q^{53} -18.7324 q^{55} +(571.305 - 171.829i) q^{57} -278.455 q^{59} -316.577 q^{61} +(-387.081 - 316.568i) q^{63} -1381.52 q^{65} +891.807 q^{67} +(-660.124 - 621.212i) q^{69} -930.534 q^{71} +(-66.6937 + 115.517i) q^{73} +(818.633 - 246.216i) q^{75} +(-6.04412 - 19.4729i) q^{77} -428.989 q^{79} +(438.294 + 582.529i) q^{81} +(-373.508 + 646.935i) q^{83} +(-340.967 - 590.572i) q^{85} +(770.615 + 725.190i) q^{87} +(312.943 + 542.034i) q^{89} +(-445.754 - 1436.13i) q^{91} +(-317.850 + 1348.75i) q^{93} -1953.57 q^{95} +(689.869 - 1194.89i) q^{97} +(1.80372 + 29.6701i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9}+O(q^{10}) \) 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9	\( 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9} + 4 q^{11} - 12 q^{13} - 26 q^{15} + 112 q^{17} + 60 q^{19} - 80 q^{21} + 10 q^{23} - 600 q^{25} + 194 q^{29} + 60 q^{31} - 472 q^{33} + 394 q^{35} - 84 q^{37} + 604 q^{39} + 210 q^{41} + 42 q^{43} + 254 q^{45} - 132 q^{47} - 78 q^{49} - 58 q^{51} - 468 q^{53} + 612 q^{55} + 1476 q^{57} - 916 q^{59} - 804 q^{61} - 444 q^{63} + 1656 q^{65} - 588 q^{67} - 28 q^{69} - 2228 q^{71} - 336 q^{73} - 668 q^{75} - 1216 q^{77} - 768 q^{79} - 104 q^{81} + 1024 q^{83} + 360 q^{85} + 2188 q^{87} + 2922 q^{89} - 120 q^{91} - 1292 q^{93} + 2428 q^{95} - 264 q^{97} - 2246 q^{99}+O(q^{100}) \) 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9 + 4 * q^11 - 12 * q^13 - 26 * q^15 + 112 * q^17 + 60 * q^19 - 80 * q^21 + 10 * q^23 - 600 * q^25 + 194 * q^29 + 60 * q^31 - 472 * q^33 + 394 * q^35 - 84 * q^37 + 604 * q^39 + 210 * q^41 + 42 * q^43 + 254 * q^45 - 132 * q^47 - 78 * q^49 - 58 * q^51 - 468 * q^53 + 612 * q^55 + 1476 * q^57 - 916 * q^59 - 804 * q^61 - 444 * q^63 + 1656 * q^65 - 588 * q^67 - 28 * q^69 - 2228 * q^71 - 336 * q^73 - 668 * q^75 - 1216 * q^77 - 768 * q^79 - 104 * q^81 + 1024 * q^83 + 360 * q^85 + 2188 * q^87 + 2922 * q^89 - 120 * q^91 - 1292 * q^93 + 2428 * q^95 - 264 * q^97 - 2246 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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