LMFDB - Embedded newform 108.4.b.b.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,4,Mod(107,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("108.107");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	108.b (of order $2$, degree $1$, 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:	$6.37220628062$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3 x^{10} - 12 x^{9} + 73 x^{8} - 12 x^{7} + 589 x^{6} + 84 x^{5} + 2452 x^{4} + 852 x^{3} + \cdots + 9496 $ x^12 + 3x^10 - 12x^9 + 73x^8 - 12x^7 + 589x^6 + 84x^5 + 2452x^4 + 852x^3 + 6854x^2 - 888x + 9496
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			107.1
Root			$2.61836 + 1.60260i$ of defining polynomial
Character	$\chi$	$=$	108.107
Dual form			108.4.b.b.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.72048 - 0.773954i) q^{2} +(6.80199 + 4.21105i) q^{4} +20.8488i q^{5} -13.9048i q^{7} +(-15.2455 - 16.7205i) q^{8} +O(q^{10})$	\(q+(-2.72048 - 0.773954i) q^{2} +(6.80199 + 4.21105i) q^{4} +20.8488i q^{5} -13.9048i q^{7} +(-15.2455 - 16.7205i) q^{8} +(16.1360 - 56.7186i) q^{10} -34.5116 q^{11} -31.3361 q^{13} +(-10.7617 + 37.8278i) q^{14} +(28.5341 + 57.2870i) q^{16} -34.4719i q^{17} +120.723i q^{19} +(-87.7953 + 141.813i) q^{20} +(93.8880 + 26.7104i) q^{22} -137.155 q^{23} -309.672 q^{25} +(85.2491 + 24.2527i) q^{26} +(58.5540 - 94.5806i) q^{28} +93.1005i q^{29} -111.365i q^{31} +(-33.2888 - 177.932i) q^{32} +(-26.6797 + 93.7799i) q^{34} +289.899 q^{35} -146.680 q^{37} +(93.4338 - 328.423i) q^{38} +(348.602 - 317.850i) q^{40} +8.44531i q^{41} +427.523i q^{43} +(-234.748 - 145.330i) q^{44} +(373.128 + 106.152i) q^{46} +318.826 q^{47} +149.655 q^{49} +(842.455 + 239.672i) q^{50} +(-213.148 - 131.958i) q^{52} -291.451i q^{53} -719.525i q^{55} +(-232.496 + 211.986i) q^{56} +(72.0555 - 253.278i) q^{58} -364.665 q^{59} -289.983 q^{61} +(-86.1914 + 302.966i) q^{62} +(-47.1499 + 509.824i) q^{64} -653.320i q^{65} +305.907i q^{67} +(145.163 - 234.477i) q^{68} +(-788.664 - 224.369i) q^{70} +102.802 q^{71} +442.688 q^{73} +(399.041 + 113.524i) q^{74} +(-508.369 + 821.154i) q^{76} +479.878i q^{77} +245.350i q^{79} +(-1194.37 + 594.901i) q^{80} +(6.53629 - 22.9753i) q^{82} +478.981 q^{83} +718.697 q^{85} +(330.884 - 1163.07i) q^{86} +(526.146 + 577.051i) q^{88} +1417.36i q^{89} +435.723i q^{91} +(-932.929 - 577.568i) q^{92} +(-867.360 - 246.757i) q^{94} -2516.92 q^{95} +1153.69 q^{97} +(-407.134 - 115.826i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4}+O(q^{10}) $ 12 * q + 6 * q^4	$ 12 q + 6 q^{4} + 42 q^{10} - 72 q^{13} + 114 q^{16} + 66 q^{22} - 384 q^{25} - 282 q^{28} - 324 q^{34} - 240 q^{37} + 774 q^{40} + 1752 q^{46} + 288 q^{49} + 924 q^{52} - 948 q^{58} + 144 q^{61} - 3066 q^{64} - 3558 q^{70} + 156 q^{73} + 576 q^{76} + 5832 q^{82} - 168 q^{85} + 5022 q^{88} - 3444 q^{94} + 516 q^{97}+O(q^{100}) $ 12 * q + 6 * q^4 + 42 * q^10 - 72 * q^13 + 114 * q^16 + 66 * q^22 - 384 * q^25 - 282 * q^28 - 324 * q^34 - 240 * q^37 + 774 * q^40 + 1752 * q^46 + 288 * q^49 + 924 * q^52 - 948 * q^58 + 144 * q^61 - 3066 * q^64 - 3558 * q^70 + 156 * q^73 + 576 * q^76 + 5832 * q^82 - 168 * q^85 + 5022 * q^88 - 3444 * q^94 + 516 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.72048	−	0.773954i	−0.961834	−	0.273634i
$2$	−2.72048	−	0.773954i	−0.961834	−	0.273634i
$3$		0			0
$3$		0			0
$4$	6.80199	+	4.21105i	0.850249	+	0.526381i
$5$			20.8488i			1.86477i	0.361464	+	0.932386i	$0.382277\pi$
$5$			20.8488i			1.86477i	−0.361464	+	0.932386i	$0.617723\pi$
$6$		0			0
$7$		−	13.9048i		−	0.750791i	−0.926865	−	0.375395i	$-0.877507\pi$
$7$		−	13.9048i		−	0.750791i	0.926865	−	0.375395i	$-0.122493\pi$
$8$	−15.2455	−	16.7205i	−0.673762	−	0.738948i
$9$		0			0
$10$	16.1360	−	56.7186i	0.510266	−	1.79360i
$11$	−34.5116			−0.945967			−0.472984	−	0.881071i	$-0.656823\pi$
$11$	−34.5116			−0.945967			−0.472984	+	0.881071i	$0.656823\pi$
$12$		0			0
$13$	−31.3361			−0.668544			−0.334272	−	0.942477i	$-0.608490\pi$
$13$	−31.3361			−0.668544			−0.334272	+	0.942477i	$0.608490\pi$
$14$	−10.7617	+	37.8278i	−0.205442	+	0.722136i
$15$		0			0
$16$	28.5341	+	57.2870i	0.445845	+	0.895110i
$17$		−	34.4719i		−	0.491803i	−0.969295	−	0.245902i	$-0.920916\pi$
$17$		−	34.4719i		−	0.491803i	0.969295	−	0.245902i	$-0.0790840\pi$
$18$		0			0
$19$			120.723i			1.45767i	0.684691	+	0.728833i	$0.259937\pi$
$19$			120.723i			1.45767i	−0.684691	+	0.728833i	$0.740063\pi$
$20$	−87.7953	+	141.813i	−0.981581	+	1.58552i
$21$		0			0
$22$	93.8880	+	26.7104i	0.909863	+	0.258849i
$23$	−137.155			−1.24343			−0.621714	−	0.783244i	$-0.713564\pi$
$23$	−137.155			−1.24343			−0.621714	+	0.783244i	$0.713564\pi$
$24$		0			0
$25$	−309.672			−2.47738
$26$	85.2491	+	24.2527i	0.643028	+	0.182936i
$27$		0			0
$28$	58.5540	−	94.5806i	0.395202	−	0.638359i
$29$			93.1005i			0.596149i	0.954543	+	0.298075i	$0.0963444\pi$
$29$			93.1005i			0.596149i	−0.954543	+	0.298075i	$0.903656\pi$
$30$		0			0
$31$		−	111.365i		−	0.645217i	−0.946532	−	0.322609i	$-0.895440\pi$
$31$		−	111.365i		−	0.645217i	0.946532	−	0.322609i	$-0.104560\pi$
$32$	−33.2888	−	177.932i	−0.183896	−	0.982946i
$33$		0			0
$34$	−26.6797	+	93.7799i	−0.134574	+	0.473033i
$35$	289.899			1.40005
$36$		0			0
$37$	−146.680			−0.651733			−0.325867	−	0.945416i	$-0.605656\pi$
$37$	−146.680			−0.651733			−0.325867	+	0.945416i	$0.605656\pi$
$38$	93.4338	−	328.423i	0.398867	−	1.40203i
$39$		0			0
$40$	348.602	−	317.850i	1.37797	−	1.25641i
$41$			8.44531i			0.0321692i	0.999871	+	0.0160846i	$0.00512011\pi$
$41$			8.44531i			0.0321692i	−0.999871	+	0.0160846i	$0.994880\pi$
$42$		0			0
$43$			427.523i			1.51620i	0.652137	+	0.758101i	$0.273873\pi$
$43$			427.523i			1.51620i	−0.652137	+	0.758101i	$0.726127\pi$
$44$	−234.748	−	145.330i	−0.804307	−	0.497939i
$45$		0			0
$46$	373.128	+	106.152i	1.19597	+	0.340245i
$47$	318.826			0.989481			0.494740	−	0.869041i	$-0.335263\pi$
$47$	318.826			0.989481			0.494740	+	0.869041i	$0.335263\pi$
$48$		0			0
$49$	149.655			0.436313
$50$	842.455	+	239.672i	2.38282	+	0.677895i
$51$		0			0
$52$	−213.148	−	131.958i	−0.568428	−	0.351909i
$53$		−	291.451i		−	0.755357i	−0.925937	−	0.377679i	$-0.876722\pi$
$53$		−	291.451i		−	0.755357i	0.925937	−	0.377679i	$-0.123278\pi$
$54$		0			0
$55$		−	719.525i		−	1.76401i
$56$	−232.496	+	211.986i	−0.554796	+	0.505854i
$57$		0			0
$58$	72.0555	−	253.278i	0.163127	−	0.573396i
$59$	−364.665			−0.804666			−0.402333	−	0.915493i	$-0.631801\pi$
$59$	−364.665			−0.804666			−0.402333	+	0.915493i	$0.631801\pi$
$60$		0			0
$61$	−289.983			−0.608664			−0.304332	−	0.952566i	$-0.598433\pi$
$61$	−289.983			−0.608664			−0.304332	+	0.952566i	$0.598433\pi$
$62$	−86.1914	+	302.966i	−0.176553	+	0.620592i
$63$		0			0
$64$	−47.1499	+	509.824i	−0.0920897	+	0.995751i
$65$		−	653.320i		−	1.24668i
$66$		0			0
$67$			305.907i			0.557797i	0.960321	+	0.278899i	$0.0899694\pi$
$67$			305.907i			0.557797i	−0.960321	+	0.278899i	$0.910031\pi$
$68$	145.163	−	234.477i	0.258876	−	0.418155i
$69$		0			0
$70$	−788.664	−	224.369i	−1.34662	−	0.383103i
$71$	102.802			0.171836			0.0859178	−	0.996302i	$-0.472618\pi$
$71$	102.802			0.171836			0.0859178	+	0.996302i	$0.472618\pi$
$72$		0			0
$73$	442.688			0.709764			0.354882	−	0.934911i	$-0.384521\pi$
$73$	442.688			0.709764			0.354882	+	0.934911i	$0.384521\pi$
$74$	399.041	+	113.524i	0.626859	+	0.178336i
$75$		0			0
$76$	−508.369	+	821.154i	−0.767288	+	1.23938i
$77$			479.878i			0.710224i
$78$		0			0
$79$			245.350i			0.349419i	0.984620	+	0.174709i	$0.0558986\pi$
$79$			245.350i			0.349419i	−0.984620	+	0.174709i	$0.944101\pi$
$80$	−1194.37	+	594.901i	−1.66918	+	0.831400i
$81$		0			0
$82$	6.53629	−	22.9753i	0.00880259	−	0.0309414i
$83$	478.981			0.633433			0.316717	−	0.948520i	$-0.397420\pi$
$83$	478.981			0.633433			0.316717	+	0.948520i	$0.397420\pi$
$84$		0			0
$85$	718.697			0.917101
$86$	330.884	−	1163.07i	0.414885	−	1.45833i
$87$		0			0
$88$	526.146	+	577.051i	0.637357	+	0.699021i
$89$			1417.36i			1.68809i	0.536273	+	0.844045i	$0.319832\pi$
$89$			1417.36i			1.68809i	−0.536273	+	0.844045i	$0.680168\pi$
$90$		0			0
$91$			435.723i			0.501937i
$92$	−932.929	−	577.568i	−1.05722	−	0.654518i
$93$		0			0
$94$	−867.360	−	246.757i	−0.951716	−	0.270756i
$95$	−2516.92			−2.71822
$96$		0			0
$97$	1153.69			1.20762			0.603811	−	0.797128i	$-0.293648\pi$
$97$	1153.69			1.20762			0.603811	+	0.797128i	$0.293648\pi$
$98$	−407.134	−	115.826i	−0.419661	−	0.119390i
$99$		0			0
$100$	−2106.39	−	1304.04i	−2.10639	−	1.30404i
$101$			767.096i			0.755732i	0.925860	+	0.377866i	$0.123342\pi$
$101$			767.096i			0.755732i	−0.925860	+	0.377866i	$0.876658\pi$
$102$		0			0
$103$		−	1202.04i		−	1.14991i	−0.818187	−	0.574953i	$-0.805021\pi$
$103$		−	1202.04i		−	1.14991i	0.818187	−	0.574953i	$-0.194979\pi$
$104$	477.734	+	523.955i	0.450439	+	0.494019i
$105$		0			0
$106$	−225.570	+	792.887i	−0.206692	+	0.726528i
$107$	1309.28			1.18292			0.591462	−	0.806333i	$-0.298551\pi$
$107$	1309.28			1.18292			0.591462	+	0.806333i	$0.298551\pi$
$108$		0			0
$109$	1102.04			0.968407			0.484204	−	0.874955i	$-0.339109\pi$
$109$	1102.04			0.968407			0.484204	+	0.874955i	$0.339109\pi$
$110$	−556.880	+	1957.45i	−0.482694	+	1.69669i
$111$		0			0
$112$	796.567	−	396.762i	0.672040	−	0.334737i
$113$			69.9098i			0.0581997i	0.999577	+	0.0290998i	$0.00926407\pi$
$113$			69.9098i			0.0581997i	−0.999577	+	0.0290998i	$0.990736\pi$
$114$		0			0
$115$		−	2859.52i		−	2.31871i
$116$	−392.051	+	633.268i	−0.313802	+	0.506875i
$117$		0			0
$118$	992.062	+	282.234i	0.773955	+	0.220184i
$119$	−479.326			−0.369241
$120$		0			0
$121$	−139.949			−0.105146
$122$	788.892	+	224.434i	0.585434	+	0.166551i
$123$		0			0
$124$	468.963	−	757.503i	0.339630	−	0.548595i
$125$		−	3850.19i		−	2.75497i
$126$		0			0
$127$			2558.29i			1.78749i	0.448574	+	0.893746i	$0.351932\pi$
$127$			2558.29i			1.78749i	−0.448574	+	0.893746i	$0.648068\pi$
$128$	522.851	−	1350.47i	0.361047	−	0.932548i
$129$		0			0
$130$	−505.640	+	1777.34i	−0.341135	+	1.19910i
$131$	86.6249			0.0577744			0.0288872	−	0.999583i	$-0.490804\pi$
$131$	86.6249			0.0577744			0.0288872	+	0.999583i	$0.490804\pi$
$132$		0			0
$133$	1678.63			1.09440
$134$	236.758	−	832.212i	0.152632	−	0.536508i
$135$		0			0
$136$	−576.387	+	525.540i	−0.363417	+	0.331358i
$137$		−	699.734i		−	0.436367i	−0.975908	−	0.218184i	$-0.929987\pi$
$137$		−	699.734i		−	0.436367i	0.975908	−	0.218184i	$-0.0700131\pi$
$138$		0			0
$139$			789.049i			0.481484i	0.970589	+	0.240742i	$0.0773908\pi$
$139$			789.049i			0.481484i	−0.970589	+	0.240742i	$0.922609\pi$
$140$	1971.89	+	1220.78i	1.19039	+	0.736962i
$141$		0			0
$142$	−279.670	−	79.5639i	−0.165277	−	0.0470201i
$143$	1081.46			0.632421
$144$		0			0
$145$	−1941.03			−1.11168
$146$	−1204.32	−	342.621i	−0.682675	−	0.194216i
$147$		0			0
$148$	−997.719	−	617.679i	−0.554135	−	0.343060i
$149$			1593.12i			0.875930i	0.898992	+	0.437965i	$0.144301\pi$
$149$			1593.12i			0.875930i	−0.898992	+	0.437965i	$0.855699\pi$
$150$		0			0
$151$			1502.12i			0.809544i	0.914418	+	0.404772i	$0.132649\pi$
$151$			1502.12i			0.809544i	−0.914418	+	0.404772i	$0.867351\pi$
$152$	2018.54	−	1840.48i	1.07714	−	0.982120i
$153$		0			0
$154$	371.404	−	1305.50i	0.194341	−	0.683117i
$155$	2321.82			1.20318
$156$		0			0
$157$	−3596.08			−1.82802			−0.914008	−	0.405696i	$-0.867029\pi$
$157$	−3596.08			−1.82802			−0.914008	+	0.405696i	$0.867029\pi$
$158$	189.890	−	667.470i	0.0956129	−	0.336083i
$159$		0			0
$160$	3709.67	−	694.031i	1.83297	−	0.342925i
$161$			1907.12i			0.933555i
$162$		0			0
$163$		−	3313.82i		−	1.59238i	−0.605044	−	0.796192i	$-0.706844\pi$
$163$		−	3313.82i		−	1.59238i	0.605044	−	0.796192i	$-0.293156\pi$
$164$	−35.5636	+	57.4449i	−0.0169333	+	0.0273518i
$165$		0			0
$166$	−1303.06	−	370.709i	−0.609257	−	0.173329i
$167$	−487.046			−0.225681			−0.112841	−	0.993613i	$-0.535995\pi$
$167$	−487.046			−0.225681			−0.112841	+	0.993613i	$0.535995\pi$
$168$		0			0
$169$	−1215.05			−0.553049
$170$	−1955.20	−	556.238i	−0.882099	−	0.250950i
$171$		0			0
$172$	−1800.32	+	2908.01i	−0.798101	+	1.28915i
$173$			1752.30i			0.770086i	0.922899	+	0.385043i	$0.125813\pi$
$173$			1752.30i			0.770086i	−0.922899	+	0.385043i	$0.874187\pi$
$174$		0			0
$175$			4305.94i			1.85999i
$176$	−984.758	−	1977.07i	−0.421755	−	0.846745i
$177$		0			0
$178$	1096.97	−	3855.90i	0.461919	−	1.62366i
$179$	2807.62			1.17236			0.586178	−	0.810182i	$-0.300632\pi$
$179$	2807.62			1.17236			0.586178	+	0.810182i	$0.300632\pi$
$180$		0			0
$181$	−2307.37			−0.947546			−0.473773	−	0.880647i	$-0.657108\pi$
$181$	−2307.37			−0.947546			−0.473773	+	0.880647i	$0.657108\pi$
$182$	337.230	−	1185.38i	0.137347	−	0.482780i
$183$		0			0
$184$	2091.00	+	2293.30i	0.837775	+	0.918830i
$185$		−	3058.11i		−	1.21533i
$186$		0			0
$187$			1189.68i			0.465230i
$188$	2168.65	+	1342.59i	0.841305	+	0.520844i
$189$		0			0
$190$	6847.22	+	1947.98i	2.61447	+	0.743797i
$191$	−3375.74			−1.27885			−0.639425	−	0.768854i	$-0.720827\pi$
$191$	−3375.74			−1.27885			−0.639425	+	0.768854i	$0.720827\pi$
$192$		0			0
$193$	561.917			0.209573			0.104787	−	0.994495i	$-0.466584\pi$
$193$	561.917			0.209573			0.104787	+	0.994495i	$0.466584\pi$
$194$	−3138.58	−	892.902i	−1.16153	−	0.330446i
$195$		0			0
$196$	1017.95	+	630.206i	0.370975	+	0.229667i
$197$			16.7420i			0.00605491i	0.999995	+	0.00302746i	$0.000963671\pi$
$197$			16.7420i			0.00605491i	−0.999995	+	0.00302746i	$0.999036\pi$
$198$		0			0
$199$		−	2760.01i		−	0.983176i	−0.870828	−	0.491588i	$-0.836417\pi$
$199$		−	2760.01i		−	0.983176i	0.870828	−	0.491588i	$-0.163583\pi$
$200$	4721.10	+	5177.87i	1.66916	+	1.83065i
$201$		0			0
$202$	593.697	−	2086.87i	0.206794	−	0.726888i
$203$	1294.55			0.447583
$204$		0			0
$205$	−176.075			−0.0599882
$206$	−930.322	+	3270.11i	−0.314653	+	1.10602i
$207$		0			0
$208$	−894.147	−	1795.15i	−0.298067	−	0.598420i
$209$		−	4166.33i		−	1.37890i
$210$		0			0
$211$		−	2766.47i		−	0.902615i	−0.892368	−	0.451308i	$-0.850958\pi$
$211$		−	2766.47i		−	0.902615i	0.892368	−	0.451308i	$-0.149042\pi$
$212$	1227.32	−	1982.45i	0.397606	−	0.642241i
$213$		0			0
$214$	−3561.86	−	1013.32i	−1.13778	−	0.323688i
$215$	−8913.34			−2.82737
$216$		0			0
$217$	−1548.51			−0.484423
$218$	−2998.08	−	852.930i	−0.931447	−	0.264989i
$219$		0			0
$220$	3029.96	−	4894.20i	0.928544	−	1.49985i
$221$			1080.21i			0.328792i
$222$		0			0
$223$			110.636i			0.0332231i	0.999862	+	0.0166115i	$0.00528786\pi$
$223$			110.636i			0.0332231i	−0.999862	+	0.0166115i	$0.994712\pi$
$224$	−2474.12	+	462.876i	−0.737987	+	0.138068i
$225$		0			0
$226$	54.1070	−	190.188i	0.0159254	−	0.0559784i
$227$	1800.57			0.526468			0.263234	−	0.964732i	$-0.415211\pi$
$227$	1800.57			0.526468			0.263234	+	0.964732i	$0.415211\pi$
$228$		0			0
$229$	−1491.95			−0.430528			−0.215264	−	0.976556i	$-0.569061\pi$
$229$	−1491.95			−0.430528			−0.215264	+	0.976556i	$0.569061\pi$
$230$	−2213.14	+	7779.26i	−0.634479	+	2.23022i
$231$		0			0
$232$	1556.69	−	1419.36i	0.440523	−	0.401663i
$233$			4545.75i			1.27812i	0.769157	+	0.639060i	$0.220676\pi$
$233$			4545.75i			1.27812i	−0.769157	+	0.639060i	$0.779324\pi$
$234$		0			0
$235$			6647.14i			1.84516i
$236$	−2480.45	−	1535.62i	−0.684166	−	0.423561i
$237$		0			0
$238$	1303.99	+	370.976i	0.355149	+	0.101037i
$239$	3305.97			0.894751			0.447376	−	0.894346i	$-0.352359\pi$
$239$	3305.97			0.894751			0.447376	+	0.894346i	$0.352359\pi$
$240$		0			0
$241$	−2337.95			−0.624898			−0.312449	−	0.949934i	$-0.601149\pi$
$241$	−2337.95			−0.624898			−0.312449	+	0.949934i	$0.601149\pi$
$242$	380.729	+	108.314i	0.101133	+	0.0287715i
$243$		0			0
$244$	−1972.46	−	1221.13i	−0.517516	−	0.320389i
$245$			3120.13i			0.813624i
$246$		0			0
$247$		−	3782.97i		−	0.974514i
$248$	−1862.08	+	1697.81i	−0.476782	+	0.434723i
$249$		0			0
$250$	−2979.87	+	10474.3i	−0.753854	+	2.64982i
$251$	−3625.36			−0.911675			−0.455838	−	0.890063i	$-0.650660\pi$
$251$	−3625.36			−0.911675			−0.455838	+	0.890063i	$0.650660\pi$
$252$		0			0
$253$	4733.45			1.17624
$254$	1980.00	−	6959.77i	0.489119	−	1.71927i
$255$		0			0
$256$	−2467.61	+	3269.27i	−0.602444	+	0.798161i
$257$			2124.02i			0.515537i	0.966207	+	0.257768i	$0.0829871\pi$
$257$			2124.02i			0.515537i	−0.966207	+	0.257768i	$0.917013\pi$
$258$		0			0
$259$			2039.57i			0.489315i
$260$	2751.16	−	4443.87i	0.656230	−	1.05999i
$261$		0			0
$262$	−235.661	−	67.0437i	−0.0555694	−	0.0158091i
$263$	−4785.87			−1.12209			−0.561044	−	0.827786i	$-0.689600\pi$
$263$	−4785.87			−1.12209			−0.561044	+	0.827786i	$0.689600\pi$
$264$		0			0
$265$	6076.41			1.40857
$266$	−4566.67	−	1299.18i	−1.05263	−	0.299466i
$267$		0			0
$268$	−1288.19	+	2080.77i	−0.293614	+	0.474267i
$269$			241.884i			0.0548249i	0.999624	+	0.0274125i	$0.00872675\pi$
$269$			241.884i			0.0548249i	−0.999624	+	0.0274125i	$0.991273\pi$
$270$		0			0
$271$			828.799i			0.185778i	0.995676	+	0.0928892i	$0.0296102\pi$
$271$			828.799i			0.185778i	−0.995676	+	0.0928892i	$0.970390\pi$
$272$	1974.79	−	983.624i	0.440218	−	0.219268i
$273$		0			0
$274$	−541.562	+	1903.61i	−0.119405	+	0.419713i
$275$	10687.3			2.34352
$276$		0			0
$277$	−5897.19			−1.27916			−0.639581	−	0.768724i	$-0.720892\pi$
$277$	−5897.19			−1.27916			−0.639581	+	0.768724i	$0.720892\pi$
$278$	610.688	−	2146.59i	0.131751	−	0.463108i
$279$		0			0
$280$	−4419.65	−	4847.26i	−0.943303	−	1.03457i
$281$			3055.95i			0.648763i	0.945926	+	0.324382i	$0.105156\pi$
$281$			3055.95i			0.648763i	−0.945926	+	0.324382i	$0.894844\pi$
$282$		0			0
$283$			196.045i			0.0411790i	0.999788	+	0.0205895i	$0.00655430\pi$
$283$			196.045i			0.0411790i	−0.999788	+	0.0205895i	$0.993446\pi$
$284$	699.257	+	432.904i	0.146103	+	0.0904511i
$285$		0			0
$286$	−2942.08	−	837.000i	−0.608283	−	0.173052i
$287$	117.431			0.0241523
$288$		0			0
$289$	3724.69			0.758130
$290$	5280.53	+	1502.27i	1.06925	+	0.304194i
$291$		0			0
$292$	3011.16	+	1864.18i	0.603476	+	0.373606i
$293$		−	8748.98i		−	1.74444i	−0.489114	−	0.872220i	$-0.662680\pi$
$293$		−	8748.98i		−	1.74444i	0.489114	−	0.872220i	$-0.337320\pi$
$294$		0			0
$295$		−	7602.82i		−	1.50052i
$296$	2236.22	+	2452.57i	0.439113	+	0.481597i
$297$		0			0
$298$	1233.00	−	4334.05i	0.239684	−	0.842499i
$299$	4297.91			0.831287
$300$		0			0
$301$	5944.65			1.13835
$302$	1162.58	−	4086.49i	0.221519	−	0.778646i
$303$		0			0
$304$	−6915.84	+	3444.71i	−1.30477	+	0.649894i
$305$		−	6045.79i		−	1.13502i
$306$		0			0
$307$		−	2095.99i		−	0.389656i	−0.980837	−	0.194828i	$-0.937585\pi$
$307$		−	2095.99i		−	0.389656i	0.980837	−	0.194828i	$-0.0624149\pi$
$308$	−2020.79	+	3264.13i	−0.373848	+	0.603867i
$309$		0			0
$310$	−6316.47	−	1796.99i	−1.15726	−	0.329232i
$311$	−3393.74			−0.618783			−0.309391	−	0.950935i	$-0.600125\pi$
$311$	−3393.74			−0.618783			−0.309391	+	0.950935i	$0.600125\pi$
$312$		0			0
$313$	3579.49			0.646405			0.323203	−	0.946330i	$-0.395240\pi$
$313$	3579.49			0.646405			0.323203	+	0.946330i	$0.395240\pi$
$314$	9783.05	+	2783.20i	1.75825	+	0.500208i
$315$		0			0
$316$	−1033.18	+	1668.87i	−0.183928	+	0.297093i
$317$		−	4356.56i		−	0.771889i	−0.922522	−	0.385945i	$-0.873876\pi$
$317$		−	4356.56i		−	0.771889i	0.922522	−	0.385945i	$-0.126124\pi$
$318$		0			0
$319$		−	3213.05i		−	0.563937i
$320$	−10629.2	−	983.019i	−1.85685	−	0.171726i
$321$		0			0
$322$	1476.03	−	5188.28i	0.255453	−	0.897925i
$323$	4161.53			0.716885
$324$		0			0
$325$	9703.91			1.65623
$326$	−2564.75	+	9015.18i	−0.435731	+	1.53161i
$327$		0			0
$328$	141.210	−	128.753i	0.0237714	−	0.0216744i
$329$		−	4433.23i		−	0.742893i
$330$		0			0
$331$			9191.99i			1.52640i	0.646164	+	0.763198i	$0.276372\pi$
$331$			9191.99i			1.52640i	−0.646164	+	0.763198i	$0.723628\pi$
$332$	3258.02	+	2017.01i	0.538576	+	0.333427i
$333$		0			0
$334$	1325.00	+	376.951i	0.217068	+	0.0617541i
$335$	−6377.78			−1.04017
$336$		0			0
$337$	1663.33			0.268865			0.134432	−	0.990923i	$-0.457079\pi$
$337$	1663.33			0.268865			0.134432	+	0.990923i	$0.457079\pi$
$338$	3305.51	+	940.393i	0.531941	+	0.151333i
$339$		0			0
$340$	4888.57	+	3026.47i	0.779764	+	0.482745i
$341$			3843.38i			0.610354i
$342$		0			0
$343$		−	6850.30i		−	1.07837i
$344$	7148.40	−	6517.80i	1.12040	−	1.02156i
$345$		0			0
$346$	1356.20	−	4767.09i	0.210722	−	0.740695i
$347$	9668.26			1.49573			0.747866	−	0.663850i	$-0.231078\pi$
$347$	9668.26			1.49573			0.747866	+	0.663850i	$0.231078\pi$
$348$		0			0
$349$	9928.24			1.52277			0.761384	−	0.648301i	$-0.224520\pi$
$349$	9928.24			1.52277			0.761384	+	0.648301i	$0.224520\pi$
$350$	3332.60	−	11714.2i	0.508957	−	1.78900i
$351$		0			0
$352$	1148.85	+	6140.72i	0.173960	+	0.929834i
$353$			4460.01i			0.672471i	0.941778	+	0.336236i	$0.109154\pi$
$353$			4460.01i			0.672471i	−0.941778	+	0.336236i	$0.890846\pi$
$354$		0			0
$355$			2143.29i			0.320434i
$356$	−5968.58	+	9640.88i	−0.888579	+	1.43530i
$357$		0			0
$358$	−7638.08	−	2172.97i	−1.12761	−	0.320797i
$359$	−2158.32			−0.317303			−0.158652	−	0.987335i	$-0.550715\pi$
$359$	−2158.32			−0.317303			−0.158652	+	0.987335i	$0.550715\pi$
$360$		0			0
$361$	−7714.95			−1.12479
$362$	6277.16	+	1785.80i	0.911382	+	0.259281i
$363$		0			0
$364$	−1834.85	+	2963.79i	−0.264210	+	0.426771i
$365$			9229.52i			1.32355i
$366$		0			0
$367$		−	1156.43i		−	0.164482i	−0.996612	−	0.0822411i	$-0.973792\pi$
$367$		−	1156.43i		−	0.164482i	0.996612	−	0.0822411i	$-0.0262078\pi$
$368$	−3913.60	−	7857.22i	−0.554377	−	1.11301i
$369$		0			0
$370$	−2366.84	+	8319.52i	−0.332557	+	1.16895i
$371$	−4052.59			−0.567115
$372$		0			0
$373$	−6286.39			−0.872647			−0.436323	−	0.899790i	$-0.643720\pi$
$373$	−6286.39			−0.872647			−0.436323	+	0.899790i	$0.643720\pi$
$374$	920.758	−	3236.49i	0.127303	−	0.447474i
$375$		0			0
$376$	−4860.66	−	5330.93i	−0.666674	−	0.731175i
$377$		−	2917.41i		−	0.398552i
$378$		0			0
$379$		−	6921.76i		−	0.938119i	−0.883167	−	0.469059i	$-0.844593\pi$
$379$		−	6921.76i		−	0.938119i	0.883167	−	0.469059i	$-0.155407\pi$
$380$	−17120.1	−	10598.9i	−2.31116	−	1.43082i
$381$		0			0
$382$	9183.63	+	2612.67i	1.23004	+	0.349937i
$383$	1802.67			0.240502			0.120251	−	0.992744i	$-0.461630\pi$
$383$	1802.67			0.240502			0.120251	+	0.992744i	$0.461630\pi$
$384$		0			0
$385$	−10004.9			−1.32441
$386$	−1528.68	−	434.898i	−0.201575	−	0.0573465i
$387$		0			0
$388$	7847.37	+	4858.24i	1.02678	+	0.635669i
$389$		−	4421.02i		−	0.576233i	−0.957595	−	0.288117i	$-0.906971\pi$
$389$		−	4421.02i		−	0.576233i	0.957595	−	0.288117i	$-0.0930291\pi$
$390$		0			0
$391$			4728.00i			0.611522i
$392$	−2281.57	−	2502.31i	−0.293971	−	0.322413i
$393$		0			0
$394$	12.9575	−	45.5462i	0.00165683	−	0.00582382i
$395$	−5115.26			−0.651586
$396$		0			0
$397$	−13769.8			−1.74077			−0.870383	−	0.492375i	$-0.836129\pi$
$397$	−13769.8			−1.74077			−0.870383	+	0.492375i	$0.836129\pi$
$398$	−2136.12	+	7508.54i	−0.269030	+	0.945651i
$399$		0			0
$400$	−8836.21	−	17740.2i	−1.10453	−	2.21752i
$401$			13534.1i			1.68544i	0.538350	+	0.842722i	$0.319048\pi$
$401$			13534.1i			1.68544i	−0.538350	+	0.842722i	$0.680952\pi$
$402$		0			0
$403$			3489.74i			0.431356i
$404$	−3230.28	+	5217.78i	−0.397803	+	0.642560i
$405$		0			0
$406$	−3521.79	−	1001.92i	−0.430501	−	0.122474i
$407$	5062.18			0.616518
$408$		0			0
$409$	7230.24			0.874114			0.437057	−	0.899434i	$-0.356021\pi$
$409$	7230.24			0.874114			0.437057	+	0.899434i	$0.356021\pi$
$410$	479.007	+	136.274i	0.0576987	+	0.0164148i
$411$		0			0
$412$	5061.84	−	8176.24i	0.605289	−	0.977705i
$413$			5070.61i			0.604136i
$414$		0			0
$415$			9986.16i			1.18121i
$416$	1043.14	+	5575.70i	0.122943	+	0.657142i
$417$		0			0
$418$	−3224.55	+	11334.4i	−0.377316	+	1.32628i
$419$	−9066.85			−1.05715			−0.528574	−	0.848887i	$-0.677273\pi$
$419$	−9066.85			−1.05715			−0.528574	+	0.848887i	$0.677273\pi$
$420$		0			0
$421$	6017.63			0.696630			0.348315	−	0.937378i	$-0.386754\pi$
$421$	6017.63			0.696630			0.348315	+	0.937378i	$0.386754\pi$
$422$	−2141.12	+	7526.12i	−0.246986	+	0.868166i
$423$		0			0
$424$	−4873.21	+	4443.32i	−0.558170	+	0.508931i
$425$			10675.0i			1.21838i
$426$		0			0
$427$			4032.17i			0.456979i
$428$	8905.70	+	5513.44i	1.00578	+	0.622669i
$429$		0			0
$430$	24248.5	+	6898.52i	2.71946	+	0.773666i
$431$	−10533.7			−1.17724			−0.588619	−	0.808410i	$-0.700328\pi$
$431$	−10533.7			−1.17724			−0.588619	+	0.808410i	$0.700328\pi$
$432$		0			0
$433$	−79.2056			−0.00879071			−0.00439536	−	0.999990i	$-0.501399\pi$
$433$	−79.2056			−0.00879071			−0.00439536	+	0.999990i	$0.501399\pi$
$434$	4212.69	+	1198.48i	0.465935	+	0.132555i
$435$		0			0
$436$	7496.07	+	4640.75i	0.823387	+	0.509751i
$437$		−	16557.7i		−	1.81250i
$438$		0			0
$439$			9484.31i			1.03112i	0.856854	+	0.515560i	$0.172416\pi$
$439$			9484.31i			1.03112i	−0.856854	+	0.515560i	$0.827584\pi$
$440$	−12030.8	+	10969.5i	−1.30352	+	1.18853i
$441$		0			0
$442$	836.036	−	2938.70i	0.0899687	−	0.316243i
$443$	−9734.58			−1.04403			−0.522013	−	0.852937i	$-0.674819\pi$
$443$	−9734.58			−1.04403			−0.522013	+	0.852937i	$0.674819\pi$
$444$		0			0
$445$	−29550.3			−3.14790
$446$	85.6273	−	300.983i	0.00909097	−	0.0319551i
$447$		0			0
$448$	7089.03	+	655.613i	0.747601	+	0.0691401i
$449$		−	9270.01i		−	0.974340i	−0.873307	−	0.487170i	$-0.838029\pi$
$449$		−	9270.01i		−	0.974340i	0.873307	−	0.487170i	$-0.161971\pi$
$450$		0			0
$451$		−	291.461i		−	0.0304310i
$452$	−294.394	+	475.526i	−0.0306352	+	0.0494842i
$453$		0			0
$454$	−4898.41	−	1393.56i	−0.506374	−	0.144060i
$455$	−9084.31			−0.935997
$456$		0			0
$457$	−2542.86			−0.260285			−0.130142	−	0.991495i	$-0.541543\pi$
$457$	−2542.86			−0.260285			−0.130142	+	0.991495i	$0.541543\pi$
$458$	4058.81	+	1154.70i	0.414096	+	0.117807i
$459$		0			0
$460$	12041.6	−	19450.4i	1.22053	−	1.97148i
$461$		−	10664.8i		−	1.07746i	−0.842479	−	0.538729i	$-0.818905\pi$
$461$		−	10664.8i		−	1.07746i	0.842479	−	0.538729i	$-0.181095\pi$
$462$		0			0
$463$		−	1963.48i		−	0.197086i	−0.995133	−	0.0985428i	$-0.968582\pi$
$463$		−	1963.48i		−	0.197086i	0.995133	−	0.0985428i	$-0.0314181\pi$
$464$	−5333.45	+	2656.54i	−0.533619	+	0.265790i
$465$		0			0
$466$	3518.20	−	12366.6i	0.349737	−	1.22934i
$467$	19778.8			1.95986			0.979928	−	0.199350i	$-0.0638829\pi$
$467$	19778.8			1.95986			0.979928	+	0.199350i	$0.0638829\pi$
$468$		0			0
$469$	4253.58			0.418789
$470$	5144.59	−	18083.4i	0.504898	−	1.77473i
$471$		0			0
$472$	5559.49	+	6097.38i	0.542154	+	0.594607i
$473$		−	14754.5i		−	1.43428i
$474$		0			0
$475$		−	37384.4i		−	3.61119i
$476$	−3260.37	−	2018.47i	−0.313947	−	0.194362i
$477$		0			0
$478$	−8993.82	−	2558.67i	−0.860602	−	0.244835i
$479$	16062.6			1.53219			0.766095	−	0.642728i	$-0.222197\pi$
$479$	16062.6			1.53219			0.766095	+	0.642728i	$0.222197\pi$
$480$		0			0
$481$	4596.39			0.435712
$482$	6360.33	+	1809.47i	0.601048	+	0.170994i
$483$		0			0
$484$	−951.933	−	589.333i	−0.0894002	−	0.0553469i
$485$			24053.0i			2.25194i
$486$		0			0
$487$			15907.5i			1.48016i	0.672519	+	0.740080i	$0.265212\pi$
$487$			15907.5i			1.48016i	−0.672519	+	0.740080i	$0.734788\pi$
$488$	4420.93	+	4848.66i	0.410095	+	0.449771i
$489$		0			0
$490$	2414.84	−	8488.25i	0.222635	−	0.782571i
$491$	−5924.49			−0.544538			−0.272269	−	0.962221i	$-0.587774\pi$
$491$	−5924.49			−0.544538			−0.272269	+	0.962221i	$0.587774\pi$
$492$		0			0
$493$	3209.35			0.293188
$494$	−2927.85	+	10291.5i	−0.266660	+	0.937320i
$495$		0			0
$496$	6379.77	−	3177.70i	0.577540	−	0.287667i
$497$		−	1429.44i		−	0.129013i
$498$		0			0
$499$		−	5331.33i		−	0.478283i	−0.970985	−	0.239142i	$-0.923134\pi$
$499$		−	5331.33i		−	0.478283i	0.970985	−	0.239142i	$-0.0768660\pi$
$500$	16213.3	−	26188.9i	1.45016	−	2.34241i
$501$		0			0
$502$	9862.70	+	2805.86i	0.876880	+	0.249466i
$503$	2144.13			0.190064			0.0950319	−	0.995474i	$-0.469705\pi$
$503$	2144.13			0.190064			0.0950319	+	0.995474i	$0.469705\pi$
$504$		0			0
$505$	−15993.0			−1.40927
$506$	−12877.2	−	3663.47i	−1.13135	−	0.321860i
$507$		0			0
$508$	−10773.1	+	17401.5i	−0.940902	+	1.51981i
$509$			14329.9i			1.24786i	0.781481	+	0.623929i	$0.214465\pi$
$509$			14329.9i			1.24786i	−0.781481	+	0.623929i	$0.785535\pi$
$510$		0			0
$511$		−	6155.51i		−	0.532884i
$512$	9243.34	−	6984.15i	0.797855	−	0.602849i
$513$		0			0
$514$	1643.90	−	5778.36i	0.141069	−	0.495861i
$515$	25061.0			2.14431
$516$		0			0
$517$	−11003.2			−0.936016
$518$	1578.53	−	5548.60i	0.133893	−	0.470640i
$519$		0			0
$520$	−10923.8	+	9960.18i	−0.921234	+	0.839967i
$521$		−	10822.8i		−	0.910087i	−0.890469	−	0.455043i	$-0.849624\pi$
$521$		−	10822.8i		−	0.910087i	0.890469	−	0.455043i	$-0.150376\pi$
$522$		0			0
$523$			12111.8i			1.01265i	0.862344	+	0.506323i	$0.168995\pi$
$523$			12111.8i			1.01265i	−0.862344	+	0.506323i	$0.831005\pi$
$524$	589.221	+	364.782i	0.0491226	+	0.0304114i
$525$		0			0
$526$	13019.8	+	3704.04i	1.07926	+	0.307042i
$527$	−3838.96			−0.317320
$528$		0			0
$529$	6644.58			0.546115
$530$	−16530.7	−	4702.86i	−1.35481	−	0.385433i
$531$		0			0
$532$	11418.0	+	7068.79i	0.930514	+	0.576073i
$533$		−	264.643i		−	0.0215065i
$534$		0			0
$535$			27296.9i			2.20588i
$536$	5114.91	−	4663.70i	0.412184	−	0.375823i
$537$		0			0
$538$	187.207	−	658.039i	0.0150020	−	0.0527324i
$539$	−5164.85			−0.412738
$540$		0			0
$541$	22063.1			1.75336			0.876681	−	0.481073i	$-0.159753\pi$
$541$	22063.1			1.75336			0.876681	+	0.481073i	$0.159753\pi$
$542$	641.453	−	2254.73i	0.0508353	−	0.178688i
$543$		0			0
$544$	−6133.65	+	1147.53i	−0.483416	+	0.0904409i
$545$			22976.2i			1.80586i
$546$		0			0
$547$			17842.7i			1.39470i	0.716731	+	0.697350i	$0.245637\pi$
$547$			17842.7i			1.39470i	−0.716731	+	0.697350i	$0.754363\pi$
$548$	2946.61	−	4759.58i	0.229695	−	0.371020i
$549$		0			0
$550$	−29074.5	−	8271.46i	−2.25407	−	0.641266i
$551$	−11239.3			−0.868987
$552$		0			0
$553$	3411.56			0.262340
$554$	16043.2	+	4564.15i	1.23034	+	0.350022i
$555$		0			0
$556$	−3322.73	+	5367.10i	−0.253444	+	0.409381i
$557$		−	10942.0i		−	0.832365i	−0.909281	−	0.416183i	$-0.863368\pi$
$557$		−	10942.0i		−	0.832365i	0.909281	−	0.416183i	$-0.136632\pi$
$558$		0			0
$559$		−	13396.9i		−	1.01365i
$560$	8272.01	+	16607.5i	0.624208	+	1.25320i
$561$		0			0
$562$	2365.16	−	8313.63i	0.177524	−	0.624002i
$563$	−1991.56			−0.149084			−0.0745418	−	0.997218i	$-0.523749\pi$
$563$	−1991.56			−0.149084			−0.0745418	+	0.997218i	$0.523749\pi$
$564$		0			0
$565$	−1457.53			−0.108529
$566$	151.730	−	533.335i	0.0112680	−	0.0396073i
$567$		0			0
$568$	−1567.26	−	1718.90i	−0.115776	−	0.126978i
$569$		−	12048.3i		−	0.887684i	−0.896105	−	0.443842i	$-0.853615\pi$
$569$		−	12048.3i		−	0.887684i	0.896105	−	0.443842i	$-0.146385\pi$
$570$		0			0
$571$		−	24916.7i		−	1.82615i	−0.407792	−	0.913075i	$-0.633701\pi$
$571$		−	24916.7i		−	1.82615i	0.407792	−	0.913075i	$-0.366299\pi$
$572$	7356.07	+	4554.08i	0.537715	+	0.332894i
$573$		0			0
$574$	−319.468	−	90.8861i	−0.0232305	−	0.00660890i
$575$	42473.2			3.08044
$576$		0			0
$577$	−17705.3			−1.27743			−0.638717	−	0.769441i	$-0.720535\pi$
$577$	−17705.3			−1.27743			−0.638717	+	0.769441i	$0.720535\pi$
$578$	−10132.9	−	2882.74i	−0.729195	−	0.207450i
$579$		0			0
$580$	−13202.9	−	8173.78i	−0.945206	−	0.585169i
$581$		−	6660.15i		−	0.475576i
$582$		0			0
$583$			10058.5i			0.714543i
$584$	−6749.00	−	7401.97i	−0.478212	−	0.524479i
$585$		0			0
$586$	−6771.31	+	23801.4i	−0.477339	+	1.67786i
$587$	−22453.6			−1.57880			−0.789402	−	0.613876i	$-0.789609\pi$
$587$	−22453.6			−1.57880			−0.789402	+	0.613876i	$0.789609\pi$
$588$		0			0
$589$	13444.3			0.940511
$590$	−5884.24	+	20683.3i	−0.410593	+	1.44325i
$591$		0			0
$592$	−4185.40	−	8402.89i	−0.290572	−	0.583373i
$593$		−	26839.1i		−	1.85860i	−0.369328	−	0.929299i	$-0.620412\pi$
$593$		−	26839.1i		−	1.85860i	0.369328	−	0.929299i	$-0.379588\pi$
$594$		0			0
$595$		−	9993.36i		−	0.688551i
$596$	−6708.71	+	10836.4i	−0.461073	+	0.744758i
$597$		0			0
$598$	−11692.4	−	3326.39i	−0.799560	−	0.227468i
$599$	−9254.44			−0.631262			−0.315631	−	0.948882i	$-0.602216\pi$
$599$	−9254.44			−0.631262			−0.315631	+	0.948882i	$0.602216\pi$
$600$		0			0
$601$	1102.45			0.0748250			0.0374125	−	0.999300i	$-0.488088\pi$
$601$	1102.45			0.0748250			0.0374125	+	0.999300i	$0.488088\pi$
$602$	−16172.3	−	4600.88i	−1.09490	−	0.311492i
$603$		0			0
$604$	−6325.52	+	10217.4i	−0.426129	+	0.688313i
$605$		−	2917.77i		−	0.196073i
$606$		0			0
$607$		−	21383.2i		−	1.42985i	−0.699202	−	0.714924i	$-0.746461\pi$
$607$		−	21383.2i		−	1.42985i	0.699202	−	0.714924i	$-0.253539\pi$
$608$	21480.4	−	4018.71i	1.43281	−	0.268060i
$609$		0			0
$610$	−4679.17	+	16447.4i	−0.310580	+	1.09170i
$611$	−9990.77			−0.661511
$612$		0			0
$613$	19769.0			1.30255			0.651274	−	0.758843i	$-0.274235\pi$
$613$	19769.0			1.30255			0.651274	+	0.758843i	$0.274235\pi$
$614$	−1622.20	+	5702.09i	−0.106623	+	0.374784i
$615$		0			0
$616$	8023.80	−	7315.98i	0.524819	−	0.478522i
$617$		−	2702.48i		−	0.176333i	−0.996106	−	0.0881667i	$-0.971899\pi$
$617$		−	2702.48i		−	0.176333i	0.996106	−	0.0881667i	$-0.0281008\pi$
$618$		0			0
$619$			6967.79i			0.452438i	0.974076	+	0.226219i	$0.0726365\pi$
$619$			6967.79i			0.452438i	−0.974076	+	0.226219i	$0.927364\pi$
$620$	15793.0	+	9777.32i	1.02300	+	0.633333i
$621$		0			0
$622$	9232.60	+	2626.60i	0.595166	+	0.169320i
$623$	19708.2			1.26740
$624$		0			0
$625$	41562.7			2.66001
$626$	−9737.92	−	2770.36i	−0.621734	−	0.176879i
$627$		0			0
$628$	−24460.5	−	15143.3i	−1.55427	−	0.962233i
$629$			5056.35i			0.320524i
$630$		0			0
$631$		−	19202.4i		−	1.21147i	−0.795667	−	0.605734i	$-0.792880\pi$
$631$		−	19202.4i		−	1.21147i	0.795667	−	0.605734i	$-0.207120\pi$
$632$	4102.38	−	3740.49i	0.258202	−	0.235425i
$633$		0			0
$634$	−3371.78	+	11851.9i	−0.211215	+	0.742429i
$635$	−53337.2			−3.33326
$636$		0			0
$637$	−4689.61			−0.291694
$638$	−2486.75	+	8741.02i	−0.154313	+	0.542414i
$639$		0			0
$640$	28155.7	+	10900.8i	1.73899	+	0.673270i
$641$			23580.8i			1.45302i	0.687155	+	0.726511i	$0.258860\pi$
$641$			23580.8i			1.45302i	−0.687155	+	0.726511i	$0.741140\pi$
$642$		0			0
$643$			25167.2i			1.54354i	0.635899	+	0.771772i	$0.280629\pi$
$643$			25167.2i			1.54354i	−0.635899	+	0.771772i	$0.719371\pi$
$644$	−8030.99	+	12972.2i	−0.491406	+	0.793754i
$645$		0			0
$646$	−11321.4	−	3220.84i	−0.689524	−	0.196164i
$647$	2247.67			0.136577			0.0682883	−	0.997666i	$-0.478246\pi$
$647$	2247.67			0.136577			0.0682883	+	0.997666i	$0.478246\pi$
$648$		0			0
$649$	12585.2			0.761188
$650$	−26399.3	−	7510.38i	−1.59302	−	0.453202i
$651$		0			0
$652$	13954.7	−	22540.6i	0.838202	−	1.35392i
$653$			11278.6i			0.675906i	0.941163	+	0.337953i	$0.109734\pi$
$653$			11278.6i			0.675906i	−0.941163	+	0.337953i	$0.890266\pi$
$654$		0			0
$655$			1806.02i			0.107736i
$656$	−483.807	+	240.979i	−0.0287950	+	0.0143425i
$657$		0			0
$658$	−3431.12	+	12060.5i	−0.203281	+	0.714540i
$659$	658.636			0.0389329			0.0194665	−	0.999811i	$-0.493803\pi$
$659$	658.636			0.0389329			0.0194665	+	0.999811i	$0.493803\pi$
$660$		0			0
$661$	1740.41			0.102412			0.0512060	−	0.998688i	$-0.483694\pi$
$661$	1740.41			0.102412			0.0512060	+	0.998688i	$0.483694\pi$
$662$	7114.18	−	25006.6i	0.417674	−	1.46814i
$663$		0			0
$664$	−7302.30	−	8008.79i	−0.426783	−	0.468074i
$665$			34997.4i			2.04081i
$666$		0			0
$667$		−	12769.2i		−	0.741269i
$668$	−3312.88	−	2050.97i	−0.191885	−	0.118794i
$669$		0			0
$670$	17350.6	+	4936.11i	1.00047	+	0.284625i
$671$	10007.8			0.575776
$672$		0			0
$673$	−273.146			−0.0156449			−0.00782243	−	0.999969i	$-0.502490\pi$
$673$	−273.146			−0.0156449			−0.00782243	+	0.999969i	$0.502490\pi$
$674$	−4525.05	−	1287.34i	−0.258603	−	0.0735706i
$675$		0			0
$676$	−8264.75	−	5116.63i	−0.470229	−	0.291115i
$677$			11373.1i			0.645649i	0.946459	+	0.322824i	$0.104632\pi$
$677$			11373.1i			0.645649i	−0.946459	+	0.322824i	$0.895368\pi$
$678$		0			0
$679$		−	16041.8i		−	0.906671i
$680$	−10956.9	−	12017.0i	−0.617908	−	0.677690i
$681$		0			0
$682$	2974.60	−	10455.8i	0.167014	−	0.587059i
$683$	1223.56			0.0685480			0.0342740	−	0.999412i	$-0.489088\pi$
$683$	1223.56			0.0685480			0.0342740	+	0.999412i	$0.489088\pi$
$684$		0			0
$685$	14588.6			0.813725
$686$	−5301.82	+	18636.1i	−0.295079	+	1.03721i
$687$		0			0
$688$	−24491.5	+	12199.0i	−1.35717	+	0.675992i
$689$			9132.95i			0.504989i
$690$		0			0
$691$			9247.55i			0.509108i	0.967059	+	0.254554i	$0.0819286\pi$
$691$			9247.55i			0.509108i	−0.967059	+	0.254554i	$0.918071\pi$
$692$	−7379.02	+	11919.1i	−0.405359	+	0.654764i
$693$		0			0
$694$	−26302.3	−	7482.79i	−1.43865	−	0.409284i
$695$	−16450.7			−0.897858
$696$		0			0
$697$	291.126			0.0158209
$698$	−27009.5	−	7684.00i	−1.46465	−	0.416682i
$699$		0			0
$700$	−18132.5	+	29289.0i	−0.979065	+	1.58145i
$701$		−	14448.0i		−	0.778447i	−0.921143	−	0.389224i	$-0.872743\pi$
$701$		−	14448.0i		−	0.778447i	0.921143	−	0.389224i	$-0.127257\pi$
$702$		0			0
$703$		−	17707.6i		−	0.950009i
$704$	1627.22	−	17594.9i	0.0871139	−	0.941948i
$705$		0			0
$706$	3451.84	−	12133.4i	0.184011	−	0.646806i
$707$	10666.4			0.567397
$708$		0			0
$709$	7819.28			0.414188			0.207094	−	0.978321i	$-0.433599\pi$
$709$	7819.28			0.414188			0.207094	+	0.978321i	$0.433599\pi$
$710$	1658.81	−	5830.78i	0.0876818	−	0.308205i
$711$		0			0
$712$	23699.0	−	21608.4i	1.24741	−	1.13737i
$713$			15274.3i			0.802281i
$714$		0			0
$715$			22547.1i			1.17932i
$716$	19097.4	+	11823.0i	0.996794	+	0.617106i
$717$		0			0
$718$	5871.67	+	1670.44i	0.305193	+	0.0868251i
$719$	7251.47			0.376126			0.188063	−	0.982157i	$-0.439779\pi$
$719$	7251.47			0.376126			0.188063	+	0.982157i	$0.439779\pi$
$720$		0			0
$721$	−16714.1			−0.863338
$722$	20988.3	+	5971.02i	1.08186	+	0.307781i
$723$		0			0
$724$	−15694.7	−	9716.47i	−0.805650	−	0.498771i
$725$		−	28830.6i		−	1.47689i
$726$		0			0
$727$			6605.59i			0.336985i	0.985703	+	0.168492i	$0.0538899\pi$
$727$			6605.59i			0.336985i	−0.985703	+	0.168492i	$0.946110\pi$
$728$	7285.51	−	6642.82i	0.370905	−	0.338186i
$729$		0			0
$730$	7143.23	−	25108.7i	0.362168	−	1.27303i
$731$	14737.5			0.745673
$732$		0			0
$733$	−37147.9			−1.87188			−0.935942	−	0.352155i	$-0.885449\pi$
$733$	−37147.9			−1.87188			−0.935942	+	0.352155i	$0.885449\pi$
$734$	−895.022	+	3146.03i	−0.0450080	+	0.158205i
$735$		0			0
$736$	4565.74	+	24404.3i	0.228662	+	1.22222i
$737$		−	10557.3i		−	0.527658i
$738$		0			0
$739$			34209.1i			1.70285i	0.524479	+	0.851423i	$0.324260\pi$
$739$			34209.1i			1.70285i	−0.524479	+	0.851423i	$0.675740\pi$
$740$	12877.9	−	20801.2i	0.639729	−	1.03334i
$741$		0			0
$742$	11025.0	+	3136.52i	0.545471	+	0.155182i
$743$	15746.4			0.777494			0.388747	−	0.921345i	$-0.372908\pi$
$743$	15746.4			0.777494			0.388747	+	0.921345i	$0.372908\pi$
$744$		0			0
$745$	−33214.6			−1.63341
$746$	17102.0	+	4865.38i	0.839341	+	0.238786i
$747$		0			0
$748$	−5009.80	+	8092.18i	−0.244888	+	0.395561i
$749$		−	18205.3i		−	0.888128i
$750$		0			0
$751$		−	27773.5i		−	1.34949i	−0.738049	−	0.674747i	$-0.764253\pi$
$751$		−	27773.5i		−	1.34949i	0.738049	−	0.674747i	$-0.235747\pi$
$752$	9097.42	+	18264.6i	0.441155	+	0.885694i
$753$		0			0
$754$	−2257.94	+	7936.73i	−0.109057	+	0.383341i
$755$	−31317.5			−1.50961
$756$		0			0
$757$	−12694.0			−0.609471			−0.304736	−	0.952437i	$-0.598568\pi$
$757$	−12694.0			−0.609471			−0.304736	+	0.952437i	$0.598568\pi$
$758$	−5357.13	+	18830.5i	−0.256701	+	0.902314i
$759$		0			0
$760$	38371.7	+	42084.1i	1.83143	+	2.00862i
$761$		−	18061.4i		−	0.860349i	−0.902746	−	0.430175i	$-0.858452\pi$
$761$		−	18061.4i		−	0.860349i	0.902746	−	0.430175i	$-0.141548\pi$
$762$		0			0
$763$		−	15323.7i		−	0.727071i
$764$	−22961.8	−	14215.4i	−1.08734	−	0.673162i
$765$		0			0
$766$	−4904.13	−	1395.19i	−0.231323	−	0.0658096i
$767$	11427.2			0.537955
$768$		0			0
$769$	32615.8			1.52946			0.764731	−	0.644350i	$-0.222872\pi$
$769$	32615.8			1.52946			0.764731	+	0.644350i	$0.222872\pi$
$770$	27218.1	+	7743.32i	1.27386	+	0.362403i
$771$		0			0
$772$	3822.15	+	2366.26i	0.178189	+	0.110316i
$773$		−	8518.40i		−	0.396359i	−0.980166	−	0.198179i	$-0.936497\pi$
$773$		−	8518.40i		−	0.396359i	0.980166	−	0.198179i	$-0.0635029\pi$
$774$		0			0
$775$			34486.6i			1.59844i
$776$	−17588.5	−	19290.2i	−0.813649	−	0.892370i
$777$		0			0
$778$	−3421.67	+	12027.3i	−0.157677	+	0.554241i
$779$	−1019.54			−0.0468919
$780$		0			0
$781$	−3547.86			−0.162551
$782$	3659.26	−	12862.4i	0.167333	−	0.588183i
$783$		0			0
$784$	4270.28	+	8573.31i	0.194528	+	0.390548i
$785$		−	74973.9i		−	3.40883i
$786$		0			0
$787$			12371.2i			0.560338i	0.959951	+	0.280169i	$0.0903906\pi$
$787$			12371.2i			0.560338i	−0.959951	+	0.280169i	$0.909609\pi$
$788$	−70.5014	+	113.879i	−0.00318719	+	0.00514818i
$789$		0			0
$790$	13915.9	+	3958.98i	0.626718	+	0.178296i
$791$	972.085			0.0436958
$792$		0			0
$793$	9086.93			0.406919
$794$	37460.3	+	10657.2i	1.67433	+	0.476333i
$795$		0			0
$796$	11622.5	−	18773.6i	0.517525	−	0.835944i
$797$			37675.0i			1.67443i	0.546877	+	0.837213i	$0.315816\pi$
$797$			37675.0i			1.67443i	−0.546877	+	0.837213i	$0.684184\pi$
$798$		0			0
$799$		−	10990.5i		−	0.486630i
$800$	10308.6	+	55100.6i	0.455581	+	2.43513i
$801$		0			0
$802$	10474.8	−	36819.3i	0.461195	−	1.62112i
$803$	−15277.9			−0.671413
$804$		0			0
$805$	−39761.2			−1.74087
$806$	2700.90	−	9493.76i	0.118034	−	0.414893i
$807$		0			0
$808$	12826.2	−	11694.8i	0.558447	−	0.509183i
$809$			41809.2i			1.81697i	0.417914	+	0.908487i	$0.362761\pi$
$809$			41809.2i			1.81697i	−0.417914	+	0.908487i	$0.637239\pi$
$810$		0			0
$811$			19357.2i			0.838129i	0.907956	+	0.419065i	$0.137642\pi$
$811$			19357.2i			0.838129i	−0.907956	+	0.419065i	$0.862358\pi$
$812$	8805.50	+	5451.40i	0.380557	+	0.235599i
$813$		0			0
$814$	−13771.5	−	3917.90i	−0.592988	−	0.168700i
$815$	69089.2			2.96943
$816$		0			0
$817$	−51611.7			−2.21012
$818$	−19669.7	−	5595.88i	−0.840752	−	0.239187i
$819$		0			0
$820$	−1197.66	−	741.459i	−0.0510049	−	0.0315767i
$821$			24774.0i			1.05313i	0.850135	+	0.526565i	$0.176520\pi$
$821$			24774.0i			1.05313i	−0.850135	+	0.526565i	$0.823480\pi$
$822$		0			0
$823$		−	10955.1i		−	0.463997i	−0.972716	−	0.231999i	$-0.925474\pi$
$823$		−	10955.1i		−	0.463997i	0.972716	−	0.231999i	$-0.0745265\pi$
$824$	−20098.7	+	18325.6i	−0.849721	+	0.774762i
$825$		0			0
$826$	3924.42	−	13794.5i	0.165312	−	0.581079i
$827$	−15446.2			−0.649475			−0.324738	−	0.945804i	$-0.605276\pi$
$827$	−15446.2			−0.649475			−0.324738	+	0.945804i	$0.605276\pi$
$828$		0			0
$829$	4599.69			0.192707			0.0963533	−	0.995347i	$-0.469282\pi$
$829$	4599.69			0.192707			0.0963533	+	0.995347i	$0.469282\pi$
$830$	7728.84	−	27167.1i	0.323219	−	1.13613i
$831$		0			0
$832$	1477.50	−	15975.9i	0.0615660	−	0.665703i
$833$		−	5158.90i		−	0.214580i
$834$		0			0
$835$		−	10154.3i		−	0.420844i
$836$	17544.6	−	28339.3i	0.725830	−	1.17241i
$837$		0			0
$838$	24666.2	+	7017.33i	1.01680	+	0.289272i
$839$	26299.3			1.08219			0.541093	−	0.840963i	$-0.318011\pi$
$839$	26299.3			1.08219			0.541093	+	0.840963i	$0.318011\pi$
$840$		0			0
$841$	15721.3			0.644606
$842$	−16370.8	−	4657.37i	−0.670042	−	0.190622i
$843$		0			0
$844$	11649.8	−	18817.5i	0.475120	−	0.767447i
$845$		−	25332.3i		−	1.03131i
$846$		0			0
$847$			1945.97i			0.0789426i
$848$	16696.4	−	8316.30i	0.676128	−	0.336772i
$849$		0			0
$850$	8261.94	−	29041.0i	0.333391	−	1.17188i
$851$	20118.0			0.810384
$852$		0			0
$853$	26223.5			1.05261			0.526305	−	0.850296i	$-0.323577\pi$
$853$	26223.5			1.05261			0.526305	+	0.850296i	$0.323577\pi$
$854$	3120.71	−	10969.4i	0.125045	−	0.439538i
$855$		0			0
$856$	−19960.6	−	21891.8i	−0.797009	−	0.874119i
$857$			13156.2i			0.524396i	0.965014	+	0.262198i	$0.0844473\pi$
$857$			13156.2i			0.524396i	−0.965014	+	0.262198i	$0.915553\pi$
$858$		0			0
$859$		−	33557.9i		−	1.33292i	−0.745539	−	0.666462i	$-0.767808\pi$
$859$		−	33557.9i		−	1.33292i	0.745539	−	0.666462i	$-0.232192\pi$
$860$	−60628.5	−	37534.5i	−2.40397	−	1.48828i
$861$		0			0
$862$	28656.7	+	8152.60i	1.13231	+	0.322133i
$863$	−16298.7			−0.642889			−0.321445	−	0.946928i	$-0.604168\pi$
$863$	−16298.7			−0.642889			−0.321445	+	0.946928i	$0.604168\pi$
$864$		0			0
$865$	−36533.3			−1.43603
$866$	215.477	+	61.3015i	0.00845520	+	0.00240544i
$867$		0			0
$868$	−10533.0	−	6520.86i	−0.411880	−	0.254991i
$869$		−	8467.44i		−	0.330539i
$870$		0			0
$871$		−	9585.92i		−	0.372912i
$872$	−16801.2	−	18426.7i	−0.652476	−	0.715603i
$873$		0			0
$874$	−12814.9	+	45045.0i	−0.495963	+	1.74333i
$875$	−53536.2			−2.06841
$876$		0			0
$877$	−28884.4			−1.11215			−0.556075	−	0.831132i	$-0.687693\pi$
$877$	−28884.4			−1.11215			−0.556075	+	0.831132i	$0.687693\pi$
$878$	7340.42	−	25801.8i	0.282149	−	0.991765i
$879$		0			0
$880$	41219.5	−	20531.0i	1.57899	−	0.786477i
$881$			47233.0i			1.80626i	0.429362	+	0.903132i	$0.358738\pi$
$881$			47233.0i			1.80626i	−0.429362	+	0.903132i	$0.641262\pi$
$882$		0			0
$883$		−	12998.5i		−	0.495394i	−0.968838	−	0.247697i	$-0.920326\pi$
$883$		−	12998.5i		−	0.495394i	0.968838	−	0.247697i	$-0.0796738\pi$
$884$	−4548.83	+	7347.60i	−0.173070	+	0.279555i
$885$		0			0
$886$	26482.7	+	7534.12i	1.00418	+	0.285682i
$887$	−16177.5			−0.612386			−0.306193	−	0.951970i	$-0.599055\pi$
$887$	−16177.5			−0.612386			−0.306193	+	0.951970i	$0.599055\pi$
$888$		0			0
$889$	35572.6			1.34203
$890$	80390.8	+	22870.6i	3.02776	+	0.861374i
$891$		0			0
$892$	−465.894	+	752.546i	−0.0174880	+	0.0282479i
$893$			38489.5i			1.44233i
$894$		0			0
$895$			58535.6i			2.18618i
$896$	−18778.1	−	7270.16i	−0.700148	−	0.271070i
$897$		0			0
$898$	−7174.56	+	25218.8i	−0.266613	+	0.937153i
$899$	10368.1			0.384646
$900$		0			0
$901$	−10046.9			−0.371487
$902$	−225.578	+	792.914i	−0.00832696	+	0.0292696i
$903$		0			0
$904$	1168.93	−	1065.81i	0.0430066	−	0.0392127i
$905$		−	48106.0i		−	1.76696i
$906$		0			0
$907$			41803.5i			1.53039i	0.643800	+	0.765194i	$0.277357\pi$
$907$			41803.5i			1.53039i	−0.643800	+	0.765194i	$0.722643\pi$
$908$	12247.5	+	7582.30i	0.447628	+	0.277123i
$909$		0			0
$910$	24713.6	+	7030.84i	0.900274	+	0.256121i
$911$	25834.2			0.939543			0.469772	−	0.882788i	$-0.344336\pi$
$911$	25834.2			0.939543			0.469772	+	0.882788i	$0.344336\pi$
$912$		0			0
$913$	−16530.4			−0.599207
$914$	6917.80	+	1968.06i	0.250351	+	0.0712228i
$915$		0			0
$916$	−10148.2	−	6282.68i	−0.366055	−	0.226622i
$917$		−	1204.51i		−	0.0433765i
$918$		0			0
$919$		−	18742.0i		−	0.672734i	−0.941731	−	0.336367i	$-0.890802\pi$
$919$		−	18742.0i		−	0.672734i	0.941731	−	0.336367i	$-0.109198\pi$
$920$	−47812.6	+	43594.8i	−1.71341	+	1.56226i
$921$		0			0
$922$	−8254.05	+	29013.3i	−0.294830	+	1.03634i
$923$	−3221.41			−0.114880
$924$		0			0
$925$	45422.8			1.61459
$926$	−1519.64	+	5341.60i	−0.0539293	+	0.189564i
$927$		0			0
$928$	16565.6	−	3099.20i	0.585982	−	0.109630i
$929$			9052.31i			0.319695i	0.987142	+	0.159847i	$0.0511002\pi$
$929$			9052.31i			0.319695i	−0.987142	+	0.159847i	$0.948900\pi$
$930$		0			0
$931$			18066.8i			0.635999i
$932$	−19142.4	+	30920.1i	−0.672778	+	1.08672i
$933$		0			0
$934$	−53807.7	−	15307.9i	−1.88506	−	0.536284i
$935$	−24803.4			−0.867547
$936$		0			0
$937$	−28189.2			−0.982819			−0.491409	−	0.870929i	$-0.663518\pi$
$937$	−28189.2			−0.982819			−0.491409	+	0.870929i	$0.663518\pi$
$938$	−11571.8	−	3292.08i	−0.402806	−	0.114595i
$939$		0			0
$940$	−27991.5	+	45213.8i	−0.971256	+	1.56884i
$941$		−	11490.8i		−	0.398074i	−0.979992	−	0.199037i	$-0.936219\pi$
$941$		−	11490.8i		−	0.398074i	0.979992	−	0.199037i	$-0.0637814\pi$
$942$		0			0
$943$		−	1158.32i		−	0.0400001i
$944$	−10405.4	−	20890.6i	−0.358757	−	0.720265i
$945$		0			0
$946$	−11419.3	+	40139.3i	−0.392468	+	1.37954i
$947$	−15309.8			−0.525344			−0.262672	−	0.964885i	$-0.584604\pi$
$947$	−15309.8			−0.525344			−0.262672	+	0.964885i	$0.584604\pi$
$948$		0			0
$949$	−13872.1			−0.474508
$950$	−28933.8	+	101703.i	−0.988144	+	3.47336i
$951$		0			0
$952$	7307.56	+	8014.57i	0.248781	+	0.272850i
$953$		−	9896.90i		−	0.336403i	−0.985753	−	0.168201i	$-0.946204\pi$
$953$		−	9896.90i		−	0.336403i	0.985753	−	0.168201i	$-0.0537959\pi$
$954$		0			0
$955$		−	70380.1i		−	2.38476i
$956$	22487.2	+	13921.6i	0.760761	+	0.470980i
$957$		0			0
$958$	−43697.9	−	12431.7i	−1.47371	−	0.419259i
$959$	−9729.69			−0.327620
$960$		0			0
$961$	17388.9			0.583695
$962$	−12504.4	−	3557.40i	−0.419083	−	0.119226i
$963$		0			0
$964$	−15902.7	−	9845.22i	−0.531319	−	0.328935i
$965$			11715.3i			0.390807i
$966$		0			0
$967$			16779.4i			0.558003i	0.960291	+	0.279001i	$0.0900034\pi$
$967$			16779.4i			0.558003i	−0.960291	+	0.279001i	$0.909997\pi$
$968$	2133.60	+	2340.02i	0.0708433	+	0.0776974i
$969$		0			0
$970$	18615.9	−	65435.6i	0.616207	−	2.16599i
$971$	−53400.1			−1.76487			−0.882437	−	0.470431i	$-0.844098\pi$
$971$	−53400.1			−1.76487			−0.882437	+	0.470431i	$0.844098\pi$
$972$		0			0
$973$	10971.6			0.361494
$974$	12311.7	−	43276.0i	0.405022	−	1.42367i
$975$		0			0
$976$	−8274.40	−	16612.3i	−0.271370	−	0.544821i
$977$			9474.13i			0.310240i	0.987896	+	0.155120i	$0.0495764\pi$
$977$			9474.13i			0.310240i	−0.987896	+	0.155120i	$0.950424\pi$
$978$		0			0
$979$		−	48915.4i		−	1.59688i
$980$	−13139.0	+	21223.1i	−0.428277	+	0.691783i
$981$		0			0
$982$	16117.4	+	4585.28i	0.523755	+	0.149004i
$983$	−56693.6			−1.83952			−0.919758	−	0.392485i	$-0.871615\pi$
$983$	−56693.6			−1.83952			−0.919758	+	0.392485i	$0.871615\pi$
$984$		0			0
$985$	−349.050			−0.0112910
$986$	−8730.95	−	2483.89i	−0.281998	−	0.0802263i
$987$		0			0
$988$	15930.3	−	25731.8i	0.512966	−	0.828579i
$989$		−	58637.1i		−	1.88529i
$990$		0			0
$991$			38944.6i			1.24835i	0.781285	+	0.624175i	$0.214565\pi$
$991$			38944.6i			1.24835i	−0.781285	+	0.624175i	$0.785435\pi$
$992$	−19815.4	+	3707.21i	−0.634213	+	0.118653i
$993$		0			0
$994$	−1106.32	+	3888.77i	−0.0353023	+	0.124089i
$995$	57542.9			1.83340
$996$		0			0
$997$	−33995.1			−1.07987			−0.539937	−	0.841705i	$-0.681552\pi$
$997$	−33995.1			−1.07987			−0.539937	+	0.841705i	$0.681552\pi$
$998$	−4126.21	+	14503.8i	−0.130875	+	0.460029i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.4.b.b.107.1	✓	12
3.2	odd	2	inner	108.4.b.b.107.12	yes	12
4.3	odd	2	inner	108.4.b.b.107.11	yes	12
8.3	odd	2		1728.4.c.j.1727.2		12
8.5	even	2		1728.4.c.j.1727.1		12
12.11	even	2	inner	108.4.b.b.107.2	yes	12
24.5	odd	2		1728.4.c.j.1727.11		12
24.11	even	2		1728.4.c.j.1727.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.b.b.107.1	✓	12	1.1	even	1	trivial
108.4.b.b.107.2	yes	12	12.11	even	2	inner
108.4.b.b.107.11	yes	12	4.3	odd	2	inner
108.4.b.b.107.12	yes	12	3.2	odd	2	inner
1728.4.c.j.1727.1		12	8.5	even	2
1728.4.c.j.1727.2		12	8.3	odd	2
1728.4.c.j.1727.11		12	24.5	odd	2
1728.4.c.j.1727.12		12	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	108.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.72048 - 0.773954i) q^{2} +(6.80199 + 4.21105i) q^{4} +20.8488i q^{5} -13.9048i q^{7} +(-15.2455 - 16.7205i) q^{8} +O(q^{10})\)	\(q+(-2.72048 - 0.773954i) q^{2} +(6.80199 + 4.21105i) q^{4} +20.8488i q^{5} -13.9048i q^{7} +(-15.2455 - 16.7205i) q^{8} +(16.1360 - 56.7186i) q^{10} -34.5116 q^{11} -31.3361 q^{13} +(-10.7617 + 37.8278i) q^{14} +(28.5341 + 57.2870i) q^{16} -34.4719i q^{17} +120.723i q^{19} +(-87.7953 + 141.813i) q^{20} +(93.8880 + 26.7104i) q^{22} -137.155 q^{23} -309.672 q^{25} +(85.2491 + 24.2527i) q^{26} +(58.5540 - 94.5806i) q^{28} +93.1005i q^{29} -111.365i q^{31} +(-33.2888 - 177.932i) q^{32} +(-26.6797 + 93.7799i) q^{34} +289.899 q^{35} -146.680 q^{37} +(93.4338 - 328.423i) q^{38} +(348.602 - 317.850i) q^{40} +8.44531i q^{41} +427.523i q^{43} +(-234.748 - 145.330i) q^{44} +(373.128 + 106.152i) q^{46} +318.826 q^{47} +149.655 q^{49} +(842.455 + 239.672i) q^{50} +(-213.148 - 131.958i) q^{52} -291.451i q^{53} -719.525i q^{55} +(-232.496 + 211.986i) q^{56} +(72.0555 - 253.278i) q^{58} -364.665 q^{59} -289.983 q^{61} +(-86.1914 + 302.966i) q^{62} +(-47.1499 + 509.824i) q^{64} -653.320i q^{65} +305.907i q^{67} +(145.163 - 234.477i) q^{68} +(-788.664 - 224.369i) q^{70} +102.802 q^{71} +442.688 q^{73} +(399.041 + 113.524i) q^{74} +(-508.369 + 821.154i) q^{76} +479.878i q^{77} +245.350i q^{79} +(-1194.37 + 594.901i) q^{80} +(6.53629 - 22.9753i) q^{82} +478.981 q^{83} +718.697 q^{85} +(330.884 - 1163.07i) q^{86} +(526.146 + 577.051i) q^{88} +1417.36i q^{89} +435.723i q^{91} +(-932.929 - 577.568i) q^{92} +(-867.360 - 246.757i) q^{94} -2516.92 q^{95} +1153.69 q^{97} +(-407.134 - 115.826i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4}+O(q^{10}) \) 12 * q + 6 * q^4	\( 12 q + 6 q^{4} + 42 q^{10} - 72 q^{13} + 114 q^{16} + 66 q^{22} - 384 q^{25} - 282 q^{28} - 324 q^{34} - 240 q^{37} + 774 q^{40} + 1752 q^{46} + 288 q^{49} + 924 q^{52} - 948 q^{58} + 144 q^{61} - 3066 q^{64} - 3558 q^{70} + 156 q^{73} + 576 q^{76} + 5832 q^{82} - 168 q^{85} + 5022 q^{88} - 3444 q^{94} + 516 q^{97}+O(q^{100}) \) 12 * q + 6 * q^4 + 42 * q^10 - 72 * q^13 + 114 * q^16 + 66 * q^22 - 384 * q^25 - 282 * q^28 - 324 * q^34 - 240 * q^37 + 774 * q^40 + 1752 * q^46 + 288 * q^49 + 924 * q^52 - 948 * q^58 + 144 * q^61 - 3066 * q^64 - 3558 * q^70 + 156 * q^73 + 576 * q^76 + 5832 * q^82 - 168 * q^85 + 5022 * q^88 - 3444 * q^94 + 516 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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