LMFDB - Embedded newform 65.4.b.a.14.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [65,4,Mod(14,65)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(65, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("65.14"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	65.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.83512415037$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			14.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	65.14
Dual form			65.4.b.a.14.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.00000i q^{2} +4.00000i q^{3} -1.00000 q^{4} +(2.00000 + 11.0000i) q^{5} +12.0000 q^{6} +28.0000i q^{7} -21.0000i q^{8} +11.0000 q^{9} +(33.0000 - 6.00000i) q^{10} +2.00000 q^{11} -4.00000i q^{12} -13.0000i q^{13} +84.0000 q^{14} +(-44.0000 + 8.00000i) q^{15} -71.0000 q^{16} -44.0000i q^{17} -33.0000i q^{18} +94.0000 q^{19} +(-2.00000 - 11.0000i) q^{20} -112.000 q^{21} -6.00000i q^{22} -18.0000i q^{23} +84.0000 q^{24} +(-117.000 + 44.0000i) q^{25} -39.0000 q^{26} +152.000i q^{27} -28.0000i q^{28} -118.000 q^{29} +(24.0000 + 132.000i) q^{30} -100.000 q^{31} +45.0000i q^{32} +8.00000i q^{33} -132.000 q^{34} +(-308.000 + 56.0000i) q^{35} -11.0000 q^{36} -126.000i q^{37} -282.000i q^{38} +52.0000 q^{39} +(231.000 - 42.0000i) q^{40} +474.000 q^{41} +336.000i q^{42} -200.000i q^{43} -2.00000 q^{44} +(22.0000 + 121.000i) q^{45} -54.0000 q^{46} -448.000i q^{47} -284.000i q^{48} -441.000 q^{49} +(132.000 + 351.000i) q^{50} +176.000 q^{51} +13.0000i q^{52} -754.000i q^{53} +456.000 q^{54} +(4.00000 + 22.0000i) q^{55} +588.000 q^{56} +376.000i q^{57} +354.000i q^{58} +446.000 q^{59} +(44.0000 - 8.00000i) q^{60} -638.000 q^{61} +300.000i q^{62} +308.000i q^{63} -433.000 q^{64} +(143.000 - 26.0000i) q^{65} +24.0000 q^{66} +868.000i q^{67} +44.0000i q^{68} +72.0000 q^{69} +(168.000 + 924.000i) q^{70} +536.000 q^{71} -231.000i q^{72} -58.0000i q^{73} -378.000 q^{74} +(-176.000 - 468.000i) q^{75} -94.0000 q^{76} +56.0000i q^{77} -156.000i q^{78} -232.000 q^{79} +(-142.000 - 781.000i) q^{80} -311.000 q^{81} -1422.00i q^{82} -108.000i q^{83} +112.000 q^{84} +(484.000 - 88.0000i) q^{85} -600.000 q^{86} -472.000i q^{87} -42.0000i q^{88} -1038.00 q^{89} +(363.000 - 66.0000i) q^{90} +364.000 q^{91} +18.0000i q^{92} -400.000i q^{93} -1344.00 q^{94} +(188.000 + 1034.00i) q^{95} -180.000 q^{96} +774.000i q^{97} +1323.00i q^{98} +22.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 4 q^{5} + 24 q^{6} + 22 q^{9} + 66 q^{10} + 4 q^{11} + 168 q^{14} - 88 q^{15} - 142 q^{16} + 188 q^{19} - 4 q^{20} - 224 q^{21} + 168 q^{24} - 234 q^{25} - 78 q^{26} - 236 q^{29} + 48 q^{30}+ \cdots + 44 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 + 4 * q^5 + 24 * q^6 + 22 * q^9 + 66 * q^10 + 4 * q^11 + 168 * q^14 - 88 * q^15 - 142 * q^16 + 188 * q^19 - 4 * q^20 - 224 * q^21 + 168 * q^24 - 234 * q^25 - 78 * q^26 - 236 * q^29 + 48 * q^30 - 200 * q^31 - 264 * q^34 - 616 * q^35 - 22 * q^36 + 104 * q^39 + 462 * q^40 + 948 * q^41 - 4 * q^44 + 44 * q^45 - 108 * q^46 - 882 * q^49 + 264 * q^50 + 352 * q^51 + 912 * q^54 + 8 * q^55 + 1176 * q^56 + 892 * q^59 + 88 * q^60 - 1276 * q^61 - 866 * q^64 + 286 * q^65 + 48 * q^66 + 144 * q^69 + 336 * q^70 + 1072 * q^71 - 756 * q^74 - 352 * q^75 - 188 * q^76 - 464 * q^79 - 284 * q^80 - 622 * q^81 + 224 * q^84 + 968 * q^85 - 1200 * q^86 - 2076 * q^89 + 726 * q^90 + 728 * q^91 - 2688 * q^94 + 376 * q^95 - 360 * q^96 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	3.00000i		−	1.06066i	−0.847791	−	0.530330i	$-0.822068\pi$
$2$		−	3.00000i		−	1.06066i	0.847791	−	0.530330i	$-0.177932\pi$
$3$			4.00000i			0.769800i	0.922958	+	0.384900i	$0.125764\pi$
$3$			4.00000i			0.769800i	−0.922958	+	0.384900i	$0.874236\pi$
$4$	−1.00000			−0.125000
$5$	2.00000	+	11.0000i	0.178885	+	0.983870i
$5$	2.00000	+	11.0000i	0.178885	+	0.983870i
$6$	12.0000			0.816497
$7$			28.0000i			1.51186i	0.654654	+	0.755929i	$0.272814\pi$
$7$			28.0000i			1.51186i	−0.654654	+	0.755929i	$0.727186\pi$
$8$		−	21.0000i		−	0.928078i
$9$	11.0000			0.407407
$10$	33.0000	−	6.00000i	1.04355	−	0.189737i
$11$	2.00000			0.0548202			0.0274101	−	0.999624i	$-0.491274\pi$
$11$	2.00000			0.0548202			0.0274101	+	0.999624i	$0.491274\pi$
$12$		−	4.00000i		−	0.0962250i
$13$		−	13.0000i		−	0.277350i
$13$		−	13.0000i		−	0.277350i
$14$	84.0000			1.60357
$15$	−44.0000	+	8.00000i	−0.757383	+	0.137706i
$16$	−71.0000			−1.10938
$17$		−	44.0000i		−	0.627739i	−0.949466	−	0.313870i	$-0.898375\pi$
$17$		−	44.0000i		−	0.627739i	0.949466	−	0.313870i	$-0.101625\pi$
$18$		−	33.0000i		−	0.432121i
$19$	94.0000			1.13500			0.567502	−	0.823372i	$-0.307910\pi$
$19$	94.0000			1.13500			0.567502	+	0.823372i	$0.307910\pi$
$20$	−2.00000	−	11.0000i	−0.0223607	−	0.122984i
$21$	−112.000			−1.16383
$22$		−	6.00000i		−	0.0581456i
$23$		−	18.0000i		−	0.163185i	−0.996666	−	0.0815926i	$-0.973999\pi$
$23$		−	18.0000i		−	0.163185i	0.996666	−	0.0815926i	$-0.0260006\pi$
$24$	84.0000			0.714435
$25$	−117.000	+	44.0000i	−0.936000	+	0.352000i
$26$	−39.0000			−0.294174
$27$			152.000i			1.08342i
$28$		−	28.0000i		−	0.188982i
$29$	−118.000			−0.755588			−0.377794	−	0.925890i	$-0.623317\pi$
$29$	−118.000			−0.755588			−0.377794	+	0.925890i	$0.623317\pi$
$30$	24.0000	+	132.000i	0.146059	+	0.803326i
$31$	−100.000			−0.579372			−0.289686	−	0.957122i	$-0.593551\pi$
$31$	−100.000			−0.579372			−0.289686	+	0.957122i	$0.593551\pi$
$32$			45.0000i			0.248592i
$33$			8.00000i			0.0422006i
$34$	−132.000			−0.665818
$35$	−308.000	+	56.0000i	−1.48747	+	0.270449i
$36$	−11.0000			−0.0509259
$37$		−	126.000i		−	0.559845i	−0.960023	−	0.279923i	$-0.909691\pi$
$37$		−	126.000i		−	0.559845i	0.960023	−	0.279923i	$-0.0903088\pi$
$38$		−	282.000i		−	1.20385i
$39$	52.0000			0.213504
$40$	231.000	−	42.0000i	0.913108	−	0.166020i
$41$	474.000			1.80552			0.902761	−	0.430144i	$-0.141537\pi$
$41$	474.000			1.80552			0.902761	+	0.430144i	$0.141537\pi$
$42$			336.000i			1.23443i
$43$		−	200.000i		−	0.709296i	−0.935000	−	0.354648i	$-0.884601\pi$
$43$		−	200.000i		−	0.709296i	0.935000	−	0.354648i	$-0.115399\pi$
$44$	−2.00000			−0.00685253
$45$	22.0000	+	121.000i	0.0728793	+	0.400836i
$46$	−54.0000			−0.173084
$47$		−	448.000i		−	1.39037i	−0.718830	−	0.695186i	$-0.755322\pi$
$47$		−	448.000i		−	1.39037i	0.718830	−	0.695186i	$-0.244678\pi$
$48$		−	284.000i		−	0.853997i
$49$	−441.000			−1.28571
$50$	132.000	+	351.000i	0.373352	+	0.992778i
$51$	176.000			0.483234
$52$			13.0000i			0.0346688i
$53$		−	754.000i		−	1.95415i	−0.212899	−	0.977074i	$-0.568291\pi$
$53$		−	754.000i		−	1.95415i	0.212899	−	0.977074i	$-0.431709\pi$
$54$	456.000			1.14914
$55$	4.00000	+	22.0000i	0.00980654	+	0.0539360i
$56$	588.000			1.40312
$57$			376.000i			0.873727i
$58$			354.000i			0.801422i
$59$	446.000			0.984140			0.492070	−	0.870556i	$-0.336240\pi$
$59$	446.000			0.984140			0.492070	+	0.870556i	$0.336240\pi$
$60$	44.0000	−	8.00000i	0.0946729	−	0.0172133i
$61$	−638.000			−1.33914			−0.669570	−	0.742749i	$-0.733522\pi$
$61$	−638.000			−1.33914			−0.669570	+	0.742749i	$0.733522\pi$
$62$			300.000i			0.614517i
$63$			308.000i			0.615942i
$64$	−433.000			−0.845703
$65$	143.000	−	26.0000i	0.272876	−	0.0496139i
$66$	24.0000			0.0447605
$67$			868.000i			1.58273i	0.611342	+	0.791366i	$0.290630\pi$
$67$			868.000i			1.58273i	−0.611342	+	0.791366i	$0.709370\pi$
$68$			44.0000i			0.0784674i
$69$	72.0000			0.125620
$70$	168.000	+	924.000i	0.286855	+	1.57770i
$71$	536.000			0.895937			0.447968	−	0.894049i	$-0.352148\pi$
$71$	536.000			0.895937			0.447968	+	0.894049i	$0.352148\pi$
$72$		−	231.000i		−	0.378106i
$73$		−	58.0000i		−	0.0929916i	−0.998918	−	0.0464958i	$-0.985195\pi$
$73$		−	58.0000i		−	0.0929916i	0.998918	−	0.0464958i	$-0.0148054\pi$
$74$	−378.000			−0.593806
$75$	−176.000	−	468.000i	−0.270970	−	0.720533i
$76$	−94.0000			−0.141876
$77$			56.0000i			0.0828804i
$78$		−	156.000i		−	0.226455i
$79$	−232.000			−0.330406			−0.165203	−	0.986260i	$-0.552828\pi$
$79$	−232.000			−0.330406			−0.165203	+	0.986260i	$0.552828\pi$
$80$	−142.000	−	781.000i	−0.198451	−	1.09148i
$81$	−311.000			−0.426612
$82$		−	1422.00i		−	1.91504i
$83$		−	108.000i		−	0.142826i	−0.997447	−	0.0714129i	$-0.977249\pi$
$83$		−	108.000i		−	0.142826i	0.997447	−	0.0714129i	$-0.0227508\pi$
$84$	112.000			0.145479
$85$	484.000	−	88.0000i	0.617614	−	0.112293i
$86$	−600.000			−0.752322
$87$		−	472.000i		−	0.581652i
$88$		−	42.0000i		−	0.0508774i
$89$	−1038.00			−1.23627			−0.618134	−	0.786073i	$-0.712111\pi$
$89$	−1038.00			−1.23627			−0.618134	+	0.786073i	$0.712111\pi$
$90$	363.000	−	66.0000i	0.425151	−	0.0773001i
$91$	364.000			0.419314
$92$			18.0000i			0.0203981i
$93$		−	400.000i		−	0.446001i
$94$	−1344.00			−1.47471
$95$	188.000	+	1034.00i	0.203036	+	1.11670i
$96$	−180.000			−0.191366
$97$			774.000i			0.810183i	0.914276	+	0.405092i	$0.132760\pi$
$97$			774.000i			0.810183i	−0.914276	+	0.405092i	$0.867240\pi$
$98$			1323.00i			1.36371i
$99$	22.0000			0.0223342
$100$	117.000	−	44.0000i	0.117000	−	0.0440000i
$101$	682.000			0.671896			0.335948	−	0.941880i	$-0.390943\pi$
$101$	682.000			0.671896			0.335948	+	0.941880i	$0.390943\pi$
$102$		−	528.000i		−	0.512547i
$103$		−	1134.00i		−	1.08482i	−0.840114	−	0.542409i	$-0.817512\pi$
$103$		−	1134.00i		−	1.08482i	0.840114	−	0.542409i	$-0.182488\pi$
$104$	−273.000			−0.257402
$105$	−224.000	−	1232.00i	−0.208192	−	1.14506i
$106$	−2262.00			−2.07269
$107$			1720.00i			1.55401i	0.629497	+	0.777003i	$0.283261\pi$
$107$			1720.00i			1.55401i	−0.629497	+	0.777003i	$0.716739\pi$
$108$		−	152.000i		−	0.135428i
$109$	420.000			0.369071			0.184535	−	0.982826i	$-0.440922\pi$
$109$	420.000			0.369071			0.184535	+	0.982826i	$0.440922\pi$
$110$	66.0000	−	12.0000i	0.0572078	−	0.0104014i
$111$	504.000			0.430969
$112$		−	1988.00i		−	1.67722i
$113$			828.000i			0.689307i	0.938730	+	0.344653i	$0.112004\pi$
$113$			828.000i			0.689307i	−0.938730	+	0.344653i	$0.887996\pi$
$114$	1128.00			0.926727
$115$	198.000	−	36.0000i	0.160553	−	0.0291915i
$116$	118.000			0.0944485
$117$		−	143.000i		−	0.112994i
$118$		−	1338.00i		−	1.04384i
$119$	1232.00			0.949053
$120$	168.000	+	924.000i	0.127802	+	0.702911i
$121$	−1327.00			−0.996995
$122$			1914.00i			1.42037i
$123$			1896.00i			1.38989i
$124$	100.000			0.0724215
$125$	−718.000	−	1199.00i	−0.513759	−	0.857935i
$126$	924.000			0.653305
$127$			294.000i			0.205420i	0.994711	+	0.102710i	$0.0327513\pi$
$127$			294.000i			0.205420i	−0.994711	+	0.102710i	$0.967249\pi$
$128$			1659.00i			1.14560i
$129$	800.000			0.546016
$130$	−78.0000	−	429.000i	−0.0526235	−	0.289429i
$131$	600.000			0.400170			0.200085	−	0.979779i	$-0.435878\pi$
$131$	600.000			0.400170			0.200085	+	0.979779i	$0.435878\pi$
$132$		−	8.00000i		−	0.00527508i
$133$			2632.00i			1.71596i
$134$	2604.00			1.67874
$135$	−1672.00	+	304.000i	−1.06595	+	0.193809i
$136$	−924.000			−0.582591
$137$		−	1246.00i		−	0.777029i	−0.921443	−	0.388514i	$-0.872988\pi$
$137$		−	1246.00i		−	0.777029i	0.921443	−	0.388514i	$-0.127012\pi$
$138$		−	216.000i		−	0.133240i
$139$	3080.00			1.87944			0.939720	−	0.341945i	$-0.111086\pi$
$139$	3080.00			1.87944			0.939720	+	0.341945i	$0.111086\pi$
$140$	308.000	−	56.0000i	0.185934	−	0.0338062i
$141$	1792.00			1.07031
$142$		−	1608.00i		−	0.950284i
$143$		−	26.0000i		−	0.0152044i
$144$	−781.000			−0.451968
$145$	−236.000	−	1298.00i	−0.135164	−	0.743400i
$146$	−174.000			−0.0986325
$147$		−	1764.00i		−	0.989743i
$148$			126.000i			0.0699807i
$149$	−3312.00			−1.82100			−0.910502	−	0.413505i	$-0.864305\pi$
$149$	−3312.00			−1.82100			−0.910502	+	0.413505i	$0.864305\pi$
$150$	−1404.00	+	528.000i	−0.764241	+	0.287407i
$151$	2360.00			1.27188			0.635941	−	0.771738i	$-0.280612\pi$
$151$	2360.00			1.27188			0.635941	+	0.771738i	$0.280612\pi$
$152$		−	1974.00i		−	1.05337i
$153$		−	484.000i		−	0.255746i
$154$	168.000			0.0879080
$155$	−200.000	−	1100.00i	−0.103641	−	0.570027i
$156$	−52.0000			−0.0266880
$157$			1742.00i			0.885521i	0.896640	+	0.442760i	$0.146001\pi$
$157$			1742.00i			0.885521i	−0.896640	+	0.442760i	$0.853999\pi$
$158$			696.000i			0.350448i
$159$	3016.00			1.50430
$160$	−495.000	+	90.0000i	−0.244582	+	0.0444695i
$161$	504.000			0.246713
$162$			933.000i			0.452490i
$163$			964.000i			0.463229i	0.972808	+	0.231614i	$0.0744008\pi$
$163$			964.000i			0.463229i	−0.972808	+	0.231614i	$0.925599\pi$
$164$	−474.000			−0.225690
$165$	−88.0000	+	16.0000i	−0.0415199	+	0.00754908i
$166$	−324.000			−0.151490
$167$			264.000i			0.122329i	0.998128	+	0.0611645i	$0.0194814\pi$
$167$			264.000i			0.122329i	−0.998128	+	0.0611645i	$0.980519\pi$
$168$			2352.00i			1.08012i
$169$	−169.000			−0.0769231
$170$	−264.000	−	1452.00i	−0.119105	−	0.655078i
$171$	1034.00			0.462409
$172$			200.000i			0.0886620i
$173$		−	2098.00i		−	0.922011i	−0.887397	−	0.461006i	$-0.847489\pi$
$173$		−	2098.00i		−	0.922011i	0.887397	−	0.461006i	$-0.152511\pi$
$174$	−1416.00			−0.616935
$175$	−1232.00	−	3276.00i	−0.532174	−	1.41510i
$176$	−142.000			−0.0608162
$177$			1784.00i			0.757591i
$178$			3114.00i			1.31126i
$179$	−2568.00			−1.07230			−0.536149	−	0.844123i	$-0.680121\pi$
$179$	−2568.00			−1.07230			−0.536149	+	0.844123i	$0.680121\pi$
$180$	−22.0000	−	121.000i	−0.00910991	−	0.0501045i
$181$	−3042.00			−1.24923			−0.624613	−	0.780934i	$-0.714743\pi$
$181$	−3042.00			−1.24923			−0.624613	+	0.780934i	$0.714743\pi$
$182$		−	1092.00i		−	0.444750i
$183$		−	2552.00i		−	1.03087i
$184$	−378.000			−0.151449
$185$	1386.00	−	252.000i	0.550815	−	0.100148i
$186$	−1200.00			−0.473055
$187$		−	88.0000i		−	0.0344128i
$188$			448.000i			0.173797i
$189$	−4256.00			−1.63798
$190$	3102.00	−	564.000i	1.18444	−	0.215352i
$191$	480.000			0.181841			0.0909204	−	0.995858i	$-0.471019\pi$
$191$	480.000			0.181841			0.0909204	+	0.995858i	$0.471019\pi$
$192$		−	1732.00i		−	0.651023i
$193$			1434.00i			0.534827i	0.963582	+	0.267413i	$0.0861689\pi$
$193$			1434.00i			0.534827i	−0.963582	+	0.267413i	$0.913831\pi$
$194$	2322.00			0.859329
$195$	104.000	+	572.000i	0.0381928	+	0.210060i
$196$	441.000			0.160714
$197$			2402.00i			0.868708i	0.900742	+	0.434354i	$0.143023\pi$
$197$			2402.00i			0.868708i	−0.900742	+	0.434354i	$0.856977\pi$
$198$		−	66.0000i		−	0.0236890i
$199$	−4296.00			−1.53033			−0.765164	−	0.643835i	$-0.777342\pi$
$199$	−4296.00			−1.53033			−0.765164	+	0.643835i	$0.777342\pi$
$200$	924.000	+	2457.00i	0.326683	+	0.868681i
$201$	−3472.00			−1.21839
$202$		−	2046.00i		−	0.712654i
$203$		−	3304.00i		−	1.14234i
$204$	−176.000			−0.0604042
$205$	948.000	+	5214.00i	0.322981	+	1.77640i
$206$	−3402.00			−1.15062
$207$		−	198.000i		−	0.0664829i
$208$			923.000i			0.307685i
$209$	188.000			0.0622212
$210$	−3696.00	+	672.000i	−1.21452	+	0.220821i
$211$	1052.00			0.343235			0.171618	−	0.985164i	$-0.445101\pi$
$211$	1052.00			0.343235			0.171618	+	0.985164i	$0.445101\pi$
$212$			754.000i			0.244269i
$213$			2144.00i			0.689692i
$214$	5160.00			1.64827
$215$	2200.00	−	400.000i	0.697855	−	0.126883i
$216$	3192.00			1.00550
$217$		−	2800.00i		−	0.875928i
$218$		−	1260.00i		−	0.391459i
$219$	232.000			0.0715850
$220$	−4.00000	−	22.0000i	−0.00122582	−	0.00674200i
$221$	−572.000			−0.174104
$222$		−	1512.00i		−	0.457112i
$223$		−	2408.00i		−	0.723101i	−0.932352	−	0.361551i	$-0.882247\pi$
$223$		−	2408.00i		−	0.723101i	0.932352	−	0.361551i	$-0.117753\pi$
$224$	−1260.00			−0.375836
$225$	−1287.00	+	484.000i	−0.381333	+	0.143407i
$226$	2484.00			0.731120
$227$			5532.00i			1.61750i	0.588155	+	0.808748i	$0.299855\pi$
$227$			5532.00i			1.61750i	−0.588155	+	0.808748i	$0.700145\pi$
$228$		−	376.000i		−	0.109216i
$229$	3088.00			0.891095			0.445548	−	0.895258i	$-0.353009\pi$
$229$	3088.00			0.891095			0.445548	+	0.895258i	$0.353009\pi$
$230$	−108.000	−	594.000i	−0.0309622	−	0.170292i
$231$	−224.000			−0.0638014
$232$			2478.00i			0.701244i
$233$		−	3500.00i		−	0.984089i	−0.870570	−	0.492044i	$-0.836250\pi$
$233$		−	3500.00i		−	0.984089i	0.870570	−	0.492044i	$-0.163750\pi$
$234$	−429.000			−0.119849
$235$	4928.00	−	896.000i	1.36795	−	0.248717i
$236$	−446.000			−0.123017
$237$		−	928.000i		−	0.254346i
$238$		−	3696.00i		−	1.00662i
$239$	−3636.00			−0.984072			−0.492036	−	0.870575i	$-0.663747\pi$
$239$	−3636.00			−0.984072			−0.492036	+	0.870575i	$0.663747\pi$
$240$	3124.00	−	568.000i	0.840222	−	0.152768i
$241$	−3870.00			−1.03439			−0.517196	−	0.855867i	$-0.673024\pi$
$241$	−3870.00			−1.03439			−0.517196	+	0.855867i	$0.673024\pi$
$242$			3981.00i			1.05747i
$243$			2860.00i			0.755017i
$244$	638.000			0.167392
$245$	−882.000	−	4851.00i	−0.229996	−	1.26498i
$246$	5688.00			1.47420
$247$		−	1222.00i		−	0.314794i
$248$			2100.00i			0.537702i
$249$	432.000			0.109947
$250$	−3597.00	+	2154.00i	−0.909977	+	0.544924i
$251$	1164.00			0.292713			0.146357	−	0.989232i	$-0.453245\pi$
$251$	1164.00			0.292713			0.146357	+	0.989232i	$0.453245\pi$
$252$		−	308.000i		−	0.0769928i
$253$		−	36.0000i		−	0.00894585i
$254$	882.000			0.217880
$255$	352.000	+	1936.00i	0.0864435	+	0.475439i
$256$	1513.00			0.369385
$257$		−	5244.00i		−	1.27281i	−0.771356	−	0.636404i	$-0.780421\pi$
$257$		−	5244.00i		−	1.27281i	0.771356	−	0.636404i	$-0.219579\pi$
$258$		−	2400.00i		−	0.579137i
$259$	3528.00			0.846406
$260$	−143.000	+	26.0000i	−0.0341096	+	0.00620174i
$261$	−1298.00			−0.307832
$262$		−	1800.00i		−	0.424444i
$263$			82.0000i			0.0192256i	0.999954	+	0.00961281i	$0.00305990\pi$
$263$			82.0000i			0.0192256i	−0.999954	+	0.00961281i	$0.996940\pi$
$264$	168.000			0.0391655
$265$	8294.00	−	1508.00i	1.92263	−	0.349569i
$266$	7896.00			1.82006
$267$		−	4152.00i		−	0.951679i
$268$		−	868.000i		−	0.197842i
$269$	−4954.00			−1.12287			−0.561433	−	0.827523i	$-0.689750\pi$
$269$	−4954.00			−1.12287			−0.561433	+	0.827523i	$0.689750\pi$
$270$	912.000	+	5016.00i	0.205565	+	1.13061i
$271$	−128.000			−0.0286917			−0.0143458	−	0.999897i	$-0.504567\pi$
$271$	−128.000			−0.0286917			−0.0143458	+	0.999897i	$0.504567\pi$
$272$			3124.00i			0.696398i
$273$			1456.00i			0.322788i
$274$	−3738.00			−0.824164
$275$	−234.000	+	88.0000i	−0.0513117	+	0.0192967i
$276$	−72.0000			−0.0157025
$277$			7418.00i			1.60904i	0.593925	+	0.804521i	$0.297578\pi$
$277$			7418.00i			1.60904i	−0.593925	+	0.804521i	$0.702422\pi$
$278$		−	9240.00i		−	1.99345i
$279$	−1100.00			−0.236040
$280$	1176.00	+	6468.00i	0.250998	+	1.38049i
$281$	−3906.00			−0.829226			−0.414613	−	0.909998i	$-0.636083\pi$
$281$	−3906.00			−0.829226			−0.414613	+	0.909998i	$0.636083\pi$
$282$		−	5376.00i		−	1.13523i
$283$		−	3164.00i		−	0.664595i	−0.943175	−	0.332297i	$-0.892176\pi$
$283$		−	3164.00i		−	0.664595i	0.943175	−	0.332297i	$-0.107824\pi$
$284$	−536.000			−0.111992
$285$	−4136.00	+	752.000i	−0.859633	+	0.156297i
$286$	−78.0000			−0.0161267
$287$			13272.0i			2.72969i
$288$			495.000i			0.101278i
$289$	2977.00			0.605943
$290$	−3894.00	+	708.000i	−0.788495	+	0.143363i
$291$	−3096.00			−0.623679
$292$			58.0000i			0.0116239i
$293$		−	154.000i		−	0.0307057i	−0.999882	−	0.0153529i	$-0.995113\pi$
$293$		−	154.000i		−	0.0307057i	0.999882	−	0.0153529i	$-0.00488716\pi$
$294$	−5292.00			−1.04978
$295$	892.000	+	4906.00i	0.176048	+	0.968266i
$296$	−2646.00			−0.519580
$297$			304.000i			0.0593935i
$298$			9936.00i			1.93147i
$299$	−234.000			−0.0452594
$300$	176.000	+	468.000i	0.0338712	+	0.0900666i
$301$	5600.00			1.07235
$302$		−	7080.00i		−	1.34903i
$303$			2728.00i			0.517226i
$304$	−6674.00			−1.25915
$305$	−1276.00	−	7018.00i	−0.239553	−	1.31754i
$306$	−1452.00			−0.271259
$307$			9484.00i			1.76313i	0.472064	+	0.881564i	$0.343509\pi$
$307$			9484.00i			1.76313i	−0.472064	+	0.881564i	$0.656491\pi$
$308$		−	56.0000i		−	0.0103601i
$309$	4536.00			0.835094
$310$	−3300.00	+	600.000i	−0.604605	+	0.109928i
$311$	−4264.00			−0.777457			−0.388729	−	0.921352i	$-0.627086\pi$
$311$	−4264.00			−0.777457			−0.388729	+	0.921352i	$0.627086\pi$
$312$		−	1092.00i		−	0.198148i
$313$		−	5096.00i		−	0.920265i	−0.887850	−	0.460133i	$-0.847802\pi$
$313$		−	5096.00i		−	0.920265i	0.887850	−	0.460133i	$-0.152198\pi$
$314$	5226.00			0.939236
$315$	−3388.00	+	616.000i	−0.606007	+	0.110183i
$316$	232.000			0.0413007
$317$		−	2214.00i		−	0.392273i	−0.980577	−	0.196137i	$-0.937160\pi$
$317$		−	2214.00i		−	0.392273i	0.980577	−	0.196137i	$-0.0628396\pi$
$318$		−	9048.00i		−	1.59556i
$319$	−236.000			−0.0414215
$320$	−866.000	−	4763.00i	−0.151284	−	0.832062i
$321$	−6880.00			−1.19627
$322$		−	1512.00i		−	0.261678i
$323$		−	4136.00i		−	0.712487i
$324$	311.000			0.0533265
$325$	572.000	+	1521.00i	0.0976272	+	0.259600i
$326$	2892.00			0.491328
$327$			1680.00i			0.284111i
$328$		−	9954.00i		−	1.67566i
$329$	12544.0			2.10205
$330$	48.0000	+	264.000i	0.00800701	+	0.0440386i
$331$	−4638.00			−0.770174			−0.385087	−	0.922880i	$-0.625829\pi$
$331$	−4638.00			−0.770174			−0.385087	+	0.922880i	$0.625829\pi$
$332$			108.000i			0.0178532i
$333$		−	1386.00i		−	0.228085i
$334$	792.000			0.129749
$335$	−9548.00	+	1736.00i	−1.55720	+	0.283128i
$336$	7952.00			1.29112
$337$		−	7712.00i		−	1.24659i	−0.781988	−	0.623293i	$-0.785794\pi$
$337$		−	7712.00i		−	1.24659i	0.781988	−	0.623293i	$-0.214206\pi$
$338$			507.000i			0.0815892i
$339$	−3312.00			−0.530629
$340$	−484.000	+	88.0000i	−0.0772017	+	0.0140367i
$341$	−200.000			−0.0317613
$342$		−	3102.00i		−	0.490459i
$343$		−	2744.00i		−	0.431959i
$344$	−4200.00			−0.658281
$345$	144.000	+	792.000i	0.0224716	+	0.123594i
$346$	−6294.00			−0.977941
$347$		−	2136.00i		−	0.330451i	−0.986256	−	0.165225i	$-0.947165\pi$
$347$		−	2136.00i		−	0.330451i	0.986256	−	0.165225i	$-0.0528352\pi$
$348$			472.000i			0.0727065i
$349$	8140.00			1.24849			0.624247	−	0.781227i	$-0.285406\pi$
$349$	8140.00			1.24849			0.624247	+	0.781227i	$0.285406\pi$
$350$	−9828.00	+	3696.00i	−1.50094	+	0.564456i
$351$	1976.00			0.300487
$352$			90.0000i			0.0136279i
$353$		−	406.000i		−	0.0612159i	−0.999531	−	0.0306079i	$-0.990256\pi$
$353$		−	406.000i		−	0.0612159i	0.999531	−	0.0306079i	$-0.00974433\pi$
$354$	5352.00			0.803547
$355$	1072.00	+	5896.00i	0.160270	+	0.881485i
$356$	1038.00			0.154533
$357$			4928.00i			0.730581i
$358$			7704.00i			1.13734i
$359$	−6740.00			−0.990874			−0.495437	−	0.868644i	$-0.664992\pi$
$359$	−6740.00			−0.990874			−0.495437	+	0.868644i	$0.664992\pi$
$360$	2541.00	−	462.000i	0.372007	−	0.0676376i
$361$	1977.00			0.288234
$362$			9126.00i			1.32501i
$363$		−	5308.00i		−	0.767487i
$364$	−364.000			−0.0524142
$365$	638.000	−	116.000i	0.0914916	−	0.0166348i
$366$	−7656.00			−1.09340
$367$		−	6002.00i		−	0.853684i	−0.904326	−	0.426842i	$-0.859626\pi$
$367$		−	6002.00i		−	0.853684i	0.904326	−	0.426842i	$-0.140374\pi$
$368$			1278.00i			0.181034i
$369$	5214.00			0.735583
$370$	−756.000	−	4158.00i	−0.106223	−	0.584227i
$371$	21112.0			2.95439
$372$			400.000i			0.0557501i
$373$			4442.00i			0.616617i	0.951286	+	0.308308i	$0.0997629\pi$
$373$			4442.00i			0.616617i	−0.951286	+	0.308308i	$0.900237\pi$
$374$	−264.000			−0.0365003
$375$	4796.00	−	2872.00i	0.660438	−	0.395492i
$376$	−9408.00			−1.29037
$377$			1534.00i			0.209562i
$378$			12768.0i			1.73734i
$379$	12070.0			1.63587			0.817934	−	0.575312i	$-0.195119\pi$
$379$	12070.0			1.63587			0.817934	+	0.575312i	$0.195119\pi$
$380$	−188.000	−	1034.00i	−0.0253795	−	0.139587i
$381$	−1176.00			−0.158132
$382$		−	1440.00i		−	0.192871i
$383$			1476.00i			0.196919i	0.995141	+	0.0984596i	$0.0313915\pi$
$383$			1476.00i			0.196919i	−0.995141	+	0.0984596i	$0.968608\pi$
$384$	−6636.00			−0.881880
$385$	−616.000	+	112.000i	−0.0815436	+	0.0148261i
$386$	4302.00			0.567270
$387$		−	2200.00i		−	0.288972i
$388$		−	774.000i		−	0.101273i
$389$	5330.00			0.694709			0.347354	−	0.937734i	$-0.387080\pi$
$389$	5330.00			0.694709			0.347354	+	0.937734i	$0.387080\pi$
$390$	1716.00	−	312.000i	0.222803	−	0.0405096i
$391$	−792.000			−0.102438
$392$			9261.00i			1.19324i
$393$			2400.00i			0.308051i
$394$	7206.00			0.921404
$395$	−464.000	−	2552.00i	−0.0591047	−	0.325076i
$396$	−22.0000			−0.00279177
$397$		−	13362.0i		−	1.68922i	−0.535384	−	0.844609i	$-0.679833\pi$
$397$		−	13362.0i		−	1.68922i	0.535384	−	0.844609i	$-0.320167\pi$
$398$			12888.0i			1.62316i
$399$	−10528.0			−1.32095
$400$	8307.00	−	3124.00i	1.03838	−	0.390500i
$401$	−5250.00			−0.653797			−0.326898	−	0.945060i	$-0.606003\pi$
$401$	−5250.00			−0.653797			−0.326898	+	0.945060i	$0.606003\pi$
$402$			10416.0i			1.29230i
$403$			1300.00i			0.160689i
$404$	−682.000			−0.0839870
$405$	−622.000	−	3421.00i	−0.0763146	−	0.419731i
$406$	−9912.00			−1.21164
$407$		−	252.000i		−	0.0306909i
$408$		−	3696.00i		−	0.448479i
$409$	2018.00			0.243970			0.121985	−	0.992532i	$-0.461074\pi$
$409$	2018.00			0.243970			0.121985	+	0.992532i	$0.461074\pi$
$410$	15642.0	−	2844.00i	1.88415	−	0.342574i
$411$	4984.00			0.598157
$412$			1134.00i			0.135602i
$413$			12488.0i			1.48788i
$414$	−594.000			−0.0705157
$415$	1188.00	−	216.000i	0.140522	−	0.0255495i
$416$	585.000			0.0689471
$417$			12320.0i			1.44679i
$418$		−	564.000i		−	0.0659956i
$419$	3080.00			0.359112			0.179556	−	0.983748i	$-0.442534\pi$
$419$	3080.00			0.359112			0.179556	+	0.983748i	$0.442534\pi$
$420$	224.000	+	1232.00i	0.0260240	+	0.143132i
$421$	13420.0			1.55356			0.776782	−	0.629769i	$-0.216850\pi$
$421$	13420.0			1.55356			0.776782	+	0.629769i	$0.216850\pi$
$422$		−	3156.00i		−	0.364056i
$423$		−	4928.00i		−	0.566448i
$424$	−15834.0			−1.81360
$425$	1936.00	+	5148.00i	0.220964	+	0.587564i
$426$	6432.00			0.731529
$427$		−	17864.0i		−	2.02459i
$428$		−	1720.00i		−	0.194251i
$429$	104.000			0.0117044
$430$	−1200.00	−	6600.00i	−0.134579	−	0.740187i
$431$	−17336.0			−1.93746			−0.968731	−	0.248115i	$-0.920189\pi$
$431$	−17336.0			−1.93746			−0.968731	+	0.248115i	$0.920189\pi$
$432$		−	10792.0i		−	1.20192i
$433$			14880.0i			1.65147i	0.564057	+	0.825736i	$0.309240\pi$
$433$			14880.0i			1.65147i	−0.564057	+	0.825736i	$0.690760\pi$
$434$	−8400.00			−0.929062
$435$	5192.00	−	944.000i	0.572270	−	0.104049i
$436$	−420.000			−0.0461338
$437$		−	1692.00i		−	0.185216i
$438$		−	696.000i		−	0.0759273i
$439$	−7040.00			−0.765378			−0.382689	−	0.923877i	$-0.625002\pi$
$439$	−7040.00			−0.765378			−0.382689	+	0.923877i	$0.625002\pi$
$440$	462.000	−	84.0000i	0.0500568	−	0.00910123i
$441$	−4851.00			−0.523810
$442$			1716.00i			0.184665i
$443$		−	10088.0i		−	1.08193i	−0.841045	−	0.540965i	$-0.818059\pi$
$443$		−	10088.0i		−	1.08193i	0.841045	−	0.540965i	$-0.181941\pi$
$444$	−504.000			−0.0538711
$445$	−2076.00	−	11418.0i	−0.221150	−	1.21633i
$446$	−7224.00			−0.766965
$447$		−	13248.0i		−	1.40181i
$448$		−	12124.0i		−	1.27858i
$449$	1434.00			0.150723			0.0753615	−	0.997156i	$-0.475989\pi$
$449$	1434.00			0.150723			0.0753615	+	0.997156i	$0.475989\pi$
$450$	1452.00	+	3861.00i	0.152107	+	0.404465i
$451$	948.000			0.0989791
$452$		−	828.000i		−	0.0861634i
$453$			9440.00i			0.979095i
$454$	16596.0			1.71561
$455$	728.000	+	4004.00i	0.0750092	+	0.412550i
$456$	7896.00			0.810886
$457$			4534.00i			0.464095i	0.972704	+	0.232048i	$0.0745425\pi$
$457$			4534.00i			0.464095i	−0.972704	+	0.232048i	$0.925457\pi$
$458$		−	9264.00i		−	0.945149i
$459$	6688.00			0.680107
$460$	−198.000	+	36.0000i	−0.0200691	+	0.00364893i
$461$	12860.0			1.29924			0.649620	−	0.760259i	$-0.274928\pi$
$461$	12860.0			1.29924			0.649620	+	0.760259i	$0.274928\pi$
$462$			672.000i			0.0676716i
$463$			4908.00i			0.492644i	0.969188	+	0.246322i	$0.0792220\pi$
$463$			4908.00i			0.492644i	−0.969188	+	0.246322i	$0.920778\pi$
$464$	8378.00			0.838230
$465$	4400.00	−	800.000i	0.438807	−	0.0797830i
$466$	−10500.0			−1.04378
$467$			8720.00i			0.864055i	0.901861	+	0.432027i	$0.142202\pi$
$467$			8720.00i			0.864055i	−0.901861	+	0.432027i	$0.857798\pi$
$468$			143.000i			0.0141243i
$469$	−24304.0			−2.39287
$470$	−2688.00	−	14784.0i	−0.263805	−	1.45093i
$471$	−6968.00			−0.681674
$472$		−	9366.00i		−	0.913358i
$473$		−	400.000i		−	0.0388838i
$474$	−2784.00			−0.269775
$475$	−10998.0	+	4136.00i	−1.06236	+	0.399521i
$476$	−1232.00			−0.118632
$477$		−	8294.00i		−	0.796135i
$478$			10908.0i			1.04377i
$479$	−12660.0			−1.20762			−0.603810	−	0.797128i	$-0.706352\pi$
$479$	−12660.0			−1.20762			−0.603810	+	0.797128i	$0.706352\pi$
$480$	−360.000	−	1980.00i	−0.0342327	−	0.188280i
$481$	−1638.00			−0.155273
$482$			11610.0i			1.09714i
$483$			2016.00i			0.189920i
$484$	1327.00			0.124624
$485$	−8514.00	+	1548.00i	−0.797115	+	0.144930i
$486$	8580.00			0.800816
$487$		−	2320.00i		−	0.215871i	−0.994158	−	0.107936i	$-0.965576\pi$
$487$		−	2320.00i		−	0.215871i	0.994158	−	0.107936i	$-0.0344240\pi$
$488$			13398.0i			1.24283i
$489$	−3856.00			−0.356594
$490$	−14553.0	+	2646.00i	−1.34171	+	0.243947i
$491$	−5584.00			−0.513243			−0.256622	−	0.966512i	$-0.582609\pi$
$491$	−5584.00			−0.513243			−0.256622	+	0.966512i	$0.582609\pi$
$492$		−	1896.00i		−	0.173736i
$493$			5192.00i			0.474312i
$494$	−3666.00			−0.333889
$495$	44.0000	+	242.000i	0.00399526	+	0.0219739i
$496$	7100.00			0.642741
$497$			15008.0i			1.35453i
$498$		−	1296.00i		−	0.116617i
$499$	−19470.0			−1.74669			−0.873344	−	0.487105i	$-0.838053\pi$
$499$	−19470.0			−1.74669			−0.873344	+	0.487105i	$0.838053\pi$
$500$	718.000	+	1199.00i	0.0642199	+	0.107242i
$501$	−1056.00			−0.0941689
$502$		−	3492.00i		−	0.310469i
$503$		−	4554.00i		−	0.403684i	−0.979418	−	0.201842i	$-0.935307\pi$
$503$		−	4554.00i		−	0.403684i	0.979418	−	0.201842i	$-0.0646927\pi$
$504$	6468.00			0.571642
$505$	1364.00	+	7502.00i	0.120192	+	0.661059i
$506$	−108.000			−0.00948851
$507$		−	676.000i		−	0.0592154i
$508$		−	294.000i		−	0.0256774i
$509$	9184.00			0.799752			0.399876	−	0.916569i	$-0.369053\pi$
$509$	9184.00			0.799752			0.399876	+	0.916569i	$0.369053\pi$
$510$	5808.00	−	1056.00i	0.504280	−	0.0916872i
$511$	1624.00			0.140590
$512$			8733.00i			0.753804i
$513$			14288.0i			1.22969i
$514$	−15732.0			−1.35002
$515$	12474.0	−	2268.00i	1.06732	−	0.194058i
$516$	−800.000			−0.0682520
$517$		−	896.000i		−	0.0762206i
$518$		−	10584.0i		−	0.897750i
$519$	8392.00			0.709765
$520$	−546.000	−	3003.00i	−0.0460455	−	0.253251i
$521$	2966.00			0.249410			0.124705	−	0.992194i	$-0.460201\pi$
$521$	2966.00			0.249410			0.124705	+	0.992194i	$0.460201\pi$
$522$			3894.00i			0.326505i
$523$			9208.00i			0.769862i	0.922945	+	0.384931i	$0.125775\pi$
$523$			9208.00i			0.769862i	−0.922945	+	0.384931i	$0.874225\pi$
$524$	−600.000			−0.0500212
$525$	13104.0	−	4928.00i	1.08934	−	0.409668i
$526$	246.000			0.0203918
$527$			4400.00i			0.363695i
$528$		−	568.000i		−	0.0468163i
$529$	11843.0			0.973371
$530$	−4524.00	−	24882.0i	−0.370774	−	2.03925i
$531$	4906.00			0.400946
$532$		−	2632.00i		−	0.214496i
$533$		−	6162.00i		−	0.500761i
$534$	−12456.0			−1.00941
$535$	−18920.0	+	3440.00i	−1.52894	+	0.277989i
$536$	18228.0			1.46890
$537$		−	10272.0i		−	0.825455i
$538$			14862.0i			1.19098i
$539$	−882.000			−0.0704832
$540$	1672.00	−	304.000i	0.133243	−	0.0242261i
$541$	14008.0			1.11322			0.556609	−	0.830775i	$-0.312102\pi$
$541$	14008.0			1.11322			0.556609	+	0.830775i	$0.312102\pi$
$542$			384.000i			0.0304321i
$543$		−	12168.0i		−	0.961655i
$544$	1980.00			0.156051
$545$	840.000	+	4620.00i	0.0660214	+	0.363118i
$546$	4368.00			0.342368
$547$		−	2548.00i		−	0.199167i	−0.995029	−	0.0995837i	$-0.968249\pi$
$547$		−	2548.00i		−	0.199167i	0.995029	−	0.0995837i	$-0.0317511\pi$
$548$			1246.00i			0.0971286i
$549$	−7018.00			−0.545575
$550$	264.000	+	702.000i	0.0204673	+	0.0544243i
$551$	−11092.0			−0.857595
$552$		−	1512.00i		−	0.116585i
$553$		−	6496.00i		−	0.499526i
$554$	22254.0			1.70665
$555$	1008.00	+	5544.00i	0.0770941	+	0.424017i
$556$	−3080.00			−0.234930
$557$		−	14218.0i		−	1.08157i	−0.841160	−	0.540786i	$-0.818127\pi$
$557$		−	14218.0i		−	1.08157i	0.841160	−	0.540786i	$-0.181873\pi$
$558$			3300.00i			0.250359i
$559$	−2600.00			−0.196723
$560$	21868.0	−	3976.00i	1.65016	−	0.300030i
$561$	352.000			0.0264910
$562$			11718.0i			0.879527i
$563$			11344.0i			0.849188i	0.905384	+	0.424594i	$0.139583\pi$
$563$			11344.0i			0.849188i	−0.905384	+	0.424594i	$0.860417\pi$
$564$	−1792.00			−0.133789
$565$	−9108.00	+	1656.00i	−0.678188	+	0.123307i
$566$	−9492.00			−0.704909
$567$		−	8708.00i		−	0.644976i
$568$		−	11256.0i		−	0.831499i
$569$	−12006.0			−0.884565			−0.442283	−	0.896876i	$-0.645831\pi$
$569$	−12006.0			−0.884565			−0.442283	+	0.896876i	$0.645831\pi$
$570$	2256.00	+	12408.0i	0.165778	+	0.911779i
$571$	6084.00			0.445898			0.222949	−	0.974830i	$-0.428432\pi$
$571$	6084.00			0.445898			0.222949	+	0.974830i	$0.428432\pi$
$572$			26.0000i			0.00190055i
$573$			1920.00i			0.139981i
$574$	39816.0			2.89527
$575$	792.000	+	2106.00i	0.0574412	+	0.152741i
$576$	−4763.00			−0.344546
$577$		−	16774.0i		−	1.21024i	−0.796133	−	0.605122i	$-0.793124\pi$
$577$		−	16774.0i		−	1.21024i	0.796133	−	0.605122i	$-0.206876\pi$
$578$		−	8931.00i		−	0.642700i
$579$	−5736.00			−0.411710
$580$	236.000	+	1298.00i	0.0168955	+	0.0929250i
$581$	3024.00			0.215932
$582$			9288.00i			0.661512i
$583$		−	1508.00i		−	0.107127i
$584$	−1218.00			−0.0863034
$585$	1573.00	−	286.000i	0.111172	−	0.0202131i
$586$	−462.000			−0.0325683
$587$			1908.00i			0.134159i	0.997748	+	0.0670797i	$0.0213682\pi$
$587$			1908.00i			0.134159i	−0.997748	+	0.0670797i	$0.978632\pi$
$588$			1764.00i			0.123718i
$589$	−9400.00			−0.657590
$590$	14718.0	−	2676.00i	1.02700	−	0.186727i
$591$	−9608.00			−0.668731
$592$			8946.00i			0.621078i
$593$			14242.0i			0.986254i	0.869957	+	0.493127i	$0.164146\pi$
$593$			14242.0i			0.986254i	−0.869957	+	0.493127i	$0.835854\pi$
$594$	912.000			0.0629963
$595$	2464.00	+	13552.0i	0.169772	+	0.933744i
$596$	3312.00			0.227626
$597$		−	17184.0i		−	1.17805i
$598$			702.000i			0.0480049i
$599$	16096.0			1.09794			0.548969	−	0.835843i	$-0.315021\pi$
$599$	16096.0			1.09794			0.548969	+	0.835843i	$0.315021\pi$
$600$	−9828.00	+	3696.00i	−0.668711	+	0.251481i
$601$	11270.0			0.764913			0.382457	−	0.923973i	$-0.375078\pi$
$601$	11270.0			0.764913			0.382457	+	0.923973i	$0.375078\pi$
$602$		−	16800.0i		−	1.13740i
$603$			9548.00i			0.644817i
$604$	−2360.00			−0.158985
$605$	−2654.00	−	14597.0i	−0.178348	−	0.980913i
$606$	8184.00			0.548601
$607$			22122.0i			1.47925i	0.673020	+	0.739625i	$0.264997\pi$
$607$			22122.0i			1.47925i	−0.673020	+	0.739625i	$0.735003\pi$
$608$			4230.00i			0.282153i
$609$	13216.0			0.879375
$610$	−21054.0	+	3828.00i	−1.39746	+	0.254084i
$611$	−5824.00			−0.385620
$612$			484.000i			0.0319682i
$613$		−	20738.0i		−	1.36639i	−0.730234	−	0.683197i	$-0.760589\pi$
$613$		−	20738.0i		−	1.36639i	0.730234	−	0.683197i	$-0.239411\pi$
$614$	28452.0			1.87008
$615$	−20856.0	+	3792.00i	−1.36747	+	0.248631i
$616$	1176.00			0.0769195
$617$			12734.0i			0.830878i	0.909621	+	0.415439i	$0.136372\pi$
$617$			12734.0i			0.830878i	−0.909621	+	0.415439i	$0.863628\pi$
$618$		−	13608.0i		−	0.885751i
$619$	1398.00			0.0907760			0.0453880	−	0.998969i	$-0.485548\pi$
$619$	1398.00			0.0907760			0.0453880	+	0.998969i	$0.485548\pi$
$620$	200.000	+	1100.00i	0.0129552	+	0.0712533i
$621$	2736.00			0.176799
$622$			12792.0i			0.824618i
$623$		−	29064.0i		−	1.86906i
$624$	−3692.00			−0.236856
$625$	11753.0	−	10296.0i	0.752192	−	0.658944i
$626$	−15288.0			−0.976088
$627$			752.000i			0.0478979i
$628$		−	1742.00i		−	0.110690i
$629$	−5544.00			−0.351437
$630$	1848.00	+	10164.0i	0.116867	+	0.642767i
$631$	−12944.0			−0.816628			−0.408314	−	0.912841i	$-0.633883\pi$
$631$	−12944.0			−0.816628			−0.408314	+	0.912841i	$0.633883\pi$
$632$			4872.00i			0.306642i
$633$			4208.00i			0.264223i
$634$	−6642.00			−0.416069
$635$	−3234.00	+	588.000i	−0.202106	+	0.0367466i
$636$	−3016.00			−0.188038
$637$			5733.00i			0.356593i
$638$			708.000i			0.0439342i
$639$	5896.00			0.365011
$640$	−18249.0	+	3318.00i	−1.12712	+	0.204930i
$641$	−14306.0			−0.881518			−0.440759	−	0.897625i	$-0.645291\pi$
$641$	−14306.0			−0.881518			−0.440759	+	0.897625i	$0.645291\pi$
$642$			20640.0i			1.26884i
$643$		−	10588.0i		−	0.649378i	−0.945821	−	0.324689i	$-0.894740\pi$
$643$		−	10588.0i		−	0.649378i	0.945821	−	0.324689i	$-0.105260\pi$
$644$	−504.000			−0.0308391
$645$	1600.00	+	8800.00i	0.0976743	+	0.537209i
$646$	−12408.0			−0.755706
$647$		−	8286.00i		−	0.503487i	−0.967794	−	0.251744i	$-0.918996\pi$
$647$		−	8286.00i		−	0.503487i	0.967794	−	0.251744i	$-0.0810040\pi$
$648$			6531.00i			0.395929i
$649$	892.000			0.0539508
$650$	4563.00	−	1716.00i	0.275347	−	0.103549i
$651$	11200.0			0.674290
$652$		−	964.000i		−	0.0579036i
$653$			2162.00i			0.129564i	0.997899	+	0.0647822i	$0.0206353\pi$
$653$			2162.00i			0.129564i	−0.997899	+	0.0647822i	$0.979365\pi$
$654$	5040.00			0.301345
$655$	1200.00	+	6600.00i	0.0715845	+	0.393715i
$656$	−33654.0			−2.00300
$657$		−	638.000i		−	0.0378855i
$658$		−	37632.0i		−	2.22956i
$659$	26480.0			1.56527			0.782636	−	0.622480i	$-0.213875\pi$
$659$	26480.0			1.56527			0.782636	+	0.622480i	$0.213875\pi$
$660$	88.0000	−	16.0000i	0.00518999	−	0.000943635i
$661$	24312.0			1.43060			0.715300	−	0.698817i	$-0.246290\pi$
$661$	24312.0			1.43060			0.715300	+	0.698817i	$0.246290\pi$
$662$			13914.0i			0.816893i
$663$		−	2288.00i		−	0.134025i
$664$	−2268.00			−0.132553
$665$	−28952.0	+	5264.00i	−1.68829	+	0.306961i
$666$	−4158.00			−0.241921
$667$			2124.00i			0.123301i
$668$		−	264.000i		−	0.0152911i
$669$	9632.00			0.556644
$670$	5208.00	+	28644.0i	0.300302	+	1.65166i
$671$	−1276.00			−0.0734120
$672$		−	5040.00i		−	0.289319i
$673$			1620.00i			0.0927881i	0.998923	+	0.0463941i	$0.0147730\pi$
$673$			1620.00i			0.0927881i	−0.998923	+	0.0463941i	$0.985227\pi$
$674$	−23136.0			−1.32220
$675$	−6688.00	−	17784.0i	−0.381365	−	1.01408i
$676$	169.000			0.00961538
$677$		−	12818.0i		−	0.727675i	−0.931463	−	0.363837i	$-0.881466\pi$
$677$		−	12818.0i		−	0.727675i	0.931463	−	0.363837i	$-0.118534\pi$
$678$			9936.00i			0.562817i
$679$	−21672.0			−1.22488
$680$	−1848.00	−	10164.0i	−0.104217	−	0.573194i
$681$	−22128.0			−1.24515
$682$			600.000i			0.0336880i
$683$		−	23580.0i		−	1.32103i	−0.750813	−	0.660515i	$-0.770338\pi$
$683$		−	23580.0i		−	1.32103i	0.750813	−	0.660515i	$-0.229662\pi$
$684$	−1034.00			−0.0578011
$685$	13706.0	−	2492.00i	0.764495	−	0.138999i
$686$	−8232.00			−0.458162
$687$			12352.0i			0.685965i
$688$			14200.0i			0.786875i
$689$	−9802.00			−0.541983
$690$	2376.00	−	432.000i	0.131091	−	0.0238347i
$691$	−5038.00			−0.277358			−0.138679	−	0.990337i	$-0.544286\pi$
$691$	−5038.00			−0.277358			−0.138679	+	0.990337i	$0.544286\pi$
$692$			2098.00i			0.115251i
$693$			616.000i			0.0337661i
$694$	−6408.00			−0.350496
$695$	6160.00	+	33880.0i	0.336204	+	1.84912i
$696$	−9912.00			−0.539818
$697$		−	20856.0i		−	1.13340i
$698$		−	24420.0i		−	1.32423i
$699$	14000.0			0.757552
$700$	1232.00	+	3276.00i	0.0665217	+	0.176887i
$701$	6474.00			0.348815			0.174408	−	0.984674i	$-0.444199\pi$
$701$	6474.00			0.348815			0.174408	+	0.984674i	$0.444199\pi$
$702$		−	5928.00i		−	0.318715i
$703$		−	11844.0i		−	0.635427i
$704$	−866.000			−0.0463617
$705$	3584.00	+	19712.0i	0.191463	+	1.05305i
$706$	−1218.00			−0.0649292
$707$			19096.0i			1.01581i
$708$		−	1784.00i		−	0.0946989i
$709$	−16480.0			−0.872947			−0.436473	−	0.899717i	$-0.643773\pi$
$709$	−16480.0			−0.872947			−0.436473	+	0.899717i	$0.643773\pi$
$710$	17688.0	−	3216.00i	0.934956	−	0.169992i
$711$	−2552.00			−0.134610
$712$			21798.0i			1.14735i
$713$			1800.00i			0.0945449i
$714$	14784.0			0.774898
$715$	286.000	−	52.0000i	0.0149592	−	0.00271985i
$716$	2568.00			0.134037
$717$		−	14544.0i		−	0.757539i
$718$			20220.0i			1.05098i
$719$	24408.0			1.26602			0.633008	−	0.774146i	$-0.281820\pi$
$719$	24408.0			1.26602			0.633008	+	0.774146i	$0.281820\pi$
$720$	−1562.00	−	8591.00i	−0.0808504	−	0.444677i
$721$	31752.0			1.64009
$722$		−	5931.00i		−	0.305719i
$723$		−	15480.0i		−	0.796276i
$724$	3042.00			0.156153
$725$	13806.0	−	5192.00i	0.707230	−	0.265967i
$726$	−15924.0			−0.814043
$727$		−	16474.0i		−	0.840422i	−0.907426	−	0.420211i	$-0.861956\pi$
$727$		−	16474.0i		−	0.840422i	0.907426	−	0.420211i	$-0.138044\pi$
$728$		−	7644.00i		−	0.389156i
$729$	−19837.0			−1.00782
$730$	−348.000	−	1914.00i	−0.0176439	−	0.0970415i
$731$	−8800.00			−0.445253
$732$			2552.00i			0.128859i
$733$			29402.0i			1.48157i	0.671745	+	0.740783i	$0.265545\pi$
$733$			29402.0i			1.48157i	−0.671745	+	0.740783i	$0.734455\pi$
$734$	−18006.0			−0.905468
$735$	19404.0	−	3528.00i	0.973779	−	0.177051i
$736$	810.000			0.0405666
$737$			1736.00i			0.0867658i
$738$		−	15642.0i		−	0.780203i
$739$	−11854.0			−0.590063			−0.295031	−	0.955488i	$-0.595330\pi$
$739$	−11854.0			−0.590063			−0.295031	+	0.955488i	$0.595330\pi$
$740$	−1386.00	+	252.000i	−0.0688519	+	0.0125185i
$741$	4888.00			0.242328
$742$		−	63336.0i		−	3.13361i
$743$			1804.00i			0.0890745i	0.999008	+	0.0445372i	$0.0141813\pi$
$743$			1804.00i			0.0890745i	−0.999008	+	0.0445372i	$0.985819\pi$
$744$	−8400.00			−0.413923
$745$	−6624.00	−	36432.0i	−0.325751	−	1.79163i
$746$	13326.0			0.654021
$747$		−	1188.00i		−	0.0581883i
$748$			88.0000i			0.00430160i
$749$	−48160.0			−2.34944
$750$	−8616.00	−	14388.0i	−0.419482	−	0.700501i
$751$	27072.0			1.31541			0.657704	−	0.753277i	$-0.271528\pi$
$751$	27072.0			1.31541			0.657704	+	0.753277i	$0.271528\pi$
$752$			31808.0i			1.54244i
$753$			4656.00i			0.225331i
$754$	4602.00			0.222274
$755$	4720.00	+	25960.0i	0.227521	+	1.25137i
$756$	4256.00			0.204748
$757$			27746.0i			1.33216i	0.745880	+	0.666080i	$0.232029\pi$
$757$			27746.0i			1.33216i	−0.745880	+	0.666080i	$0.767971\pi$
$758$		−	36210.0i		−	1.73510i
$759$	144.000			0.00688652
$760$	21714.0	−	3948.00i	1.03638	−	0.188433i
$761$	30398.0			1.44800			0.723999	−	0.689801i	$-0.242302\pi$
$761$	30398.0			1.44800			0.723999	+	0.689801i	$0.242302\pi$
$762$			3528.00i			0.167724i
$763$			11760.0i			0.557982i
$764$	−480.000			−0.0227301
$765$	5324.00	−	968.000i	0.251620	−	0.0457492i
$766$	4428.00			0.208864
$767$		−	5798.00i		−	0.272951i
$768$			6052.00i			0.284353i
$769$	2086.00			0.0978194			0.0489097	−	0.998803i	$-0.484425\pi$
$769$	2086.00			0.0978194			0.0489097	+	0.998803i	$0.484425\pi$
$770$	336.000	+	1848.00i	0.0157255	+	0.0864900i
$771$	20976.0			0.979808
$772$		−	1434.00i		−	0.0668534i
$773$			27034.0i			1.25789i	0.777452	+	0.628943i	$0.216512\pi$
$773$			27034.0i			1.25789i	−0.777452	+	0.628943i	$0.783488\pi$
$774$	−6600.00			−0.306501
$775$	11700.0	−	4400.00i	0.542292	−	0.203939i
$776$	16254.0			0.751913
$777$			14112.0i			0.651564i
$778$		−	15990.0i		−	0.736850i
$779$	44556.0			2.04927
$780$	−104.000	−	572.000i	−0.00477410	−	0.0262575i
$781$	1072.00			0.0491155
$782$			2376.00i			0.108652i
$783$		−	17936.0i		−	0.818621i
$784$	31311.0			1.42634
$785$	−19162.0	+	3484.00i	−0.871237	+	0.158407i
$786$	7200.00			0.326737
$787$			43604.0i			1.97499i	0.157660	+	0.987493i	$0.449605\pi$
$787$			43604.0i			1.97499i	−0.157660	+	0.987493i	$0.550395\pi$
$788$		−	2402.00i		−	0.108588i
$789$	−328.000			−0.0147999
$790$	−7656.00	+	1392.00i	−0.344795	+	0.0626900i
$791$	−23184.0			−1.04213
$792$		−	462.000i		−	0.0207278i
$793$			8294.00i			0.371411i
$794$	−40086.0			−1.79169
$795$	6032.00	+	33176.0i	0.269098	+	1.48004i
$796$	4296.00			0.191291
$797$			19066.0i			0.847368i	0.905810	+	0.423684i	$0.139263\pi$
$797$			19066.0i			0.847368i	−0.905810	+	0.423684i	$0.860737\pi$
$798$			31584.0i			1.40108i
$799$	−19712.0			−0.872792
$800$	−1980.00	−	5265.00i	−0.0875045	−	0.232682i
$801$	−11418.0			−0.503664
$802$			15750.0i			0.693456i
$803$		−	116.000i		−	0.00509782i
$804$	3472.00			0.152299
$805$	1008.00	+	5544.00i	0.0441333	+	0.242733i
$806$	3900.00			0.170436
$807$		−	19816.0i		−	0.864382i
$808$		−	14322.0i		−	0.623572i
$809$	20578.0			0.894294			0.447147	−	0.894460i	$-0.352440\pi$
$809$	20578.0			0.894294			0.447147	+	0.894460i	$0.352440\pi$
$810$	−10263.0	+	1866.00i	−0.445191	+	0.0809439i
$811$	34558.0			1.49630			0.748148	−	0.663532i	$-0.230943\pi$
$811$	34558.0			1.49630			0.748148	+	0.663532i	$0.230943\pi$
$812$			3304.00i			0.142793i
$813$		−	512.000i		−	0.0220869i
$814$	−756.000			−0.0325526
$815$	−10604.0	+	1928.00i	−0.455757	+	0.0828649i
$816$	−12496.0			−0.536088
$817$		−	18800.0i		−	0.805054i
$818$		−	6054.00i		−	0.258769i
$819$	4004.00			0.170832
$820$	−948.000	−	5214.00i	−0.0403727	−	0.222050i
$821$	2580.00			0.109674			0.0548372	−	0.998495i	$-0.482536\pi$
$821$	2580.00			0.109674			0.0548372	+	0.998495i	$0.482536\pi$
$822$		−	14952.0i		−	0.634441i
$823$			17662.0i			0.748066i	0.927415	+	0.374033i	$0.122025\pi$
$823$			17662.0i			0.748066i	−0.927415	+	0.374033i	$0.877975\pi$
$824$	−23814.0			−1.00680
$825$	−352.000	−	936.000i	−0.0148546	−	0.0394998i
$826$	37464.0			1.57813
$827$		−	3516.00i		−	0.147840i	−0.997264	−	0.0739198i	$-0.976449\pi$
$827$		−	3516.00i		−	0.147840i	0.997264	−	0.0739198i	$-0.0235509\pi$
$828$			198.000i			0.00831036i
$829$	2814.00			0.117894			0.0589471	−	0.998261i	$-0.481226\pi$
$829$	2814.00			0.117894			0.0589471	+	0.998261i	$0.481226\pi$
$830$	−648.000	−	3564.00i	−0.0270993	−	0.149046i
$831$	−29672.0			−1.23864
$832$			5629.00i			0.234556i
$833$			19404.0i			0.807093i
$834$	36960.0			1.53456
$835$	−2904.00	+	528.000i	−0.120356	+	0.0218829i
$836$	−188.000			−0.00777765
$837$		−	15200.0i		−	0.627705i
$838$		−	9240.00i		−	0.380896i
$839$	−8992.00			−0.370010			−0.185005	−	0.982738i	$-0.559230\pi$
$839$	−8992.00			−0.370010			−0.185005	+	0.982738i	$0.559230\pi$
$840$	−25872.0	+	4704.00i	−1.06270	+	0.193218i
$841$	−10465.0			−0.429087
$842$		−	40260.0i		−	1.64780i
$843$		−	15624.0i		−	0.638338i
$844$	−1052.00			−0.0429044
$845$	−338.000	−	1859.00i	−0.0137604	−	0.0756823i
$846$	−14784.0			−0.600809
$847$		−	37156.0i		−	1.50731i
$848$			53534.0i			2.16788i
$849$	12656.0			0.511605
$850$	15444.0	−	5808.00i	0.623206	−	0.234368i
$851$	−2268.00			−0.0913584
$852$		−	2144.00i		−	0.0862115i
$853$		−	7182.00i		−	0.288285i	−0.989557	−	0.144142i	$-0.953958\pi$
$853$		−	7182.00i		−	0.288285i	0.989557	−	0.144142i	$-0.0460423\pi$
$854$	−53592.0			−2.14740
$855$	2068.00	+	11374.0i	0.0827183	+	0.454950i
$856$	36120.0			1.44224
$857$		−	4696.00i		−	0.187179i	−0.995611	−	0.0935894i	$-0.970166\pi$
$857$		−	4696.00i		−	0.187179i	0.995611	−	0.0935894i	$-0.0298341\pi$
$858$		−	312.000i		−	0.0124143i
$859$	8140.00			0.323322			0.161661	−	0.986846i	$-0.448315\pi$
$859$	8140.00			0.323322			0.161661	+	0.986846i	$0.448315\pi$
$860$	−2200.00	+	400.000i	−0.0872318	+	0.0158603i
$861$	−53088.0			−2.10132
$862$			52008.0i			2.05499i
$863$		−	4944.00i		−	0.195012i	−0.995235	−	0.0975062i	$-0.968913\pi$
$863$		−	4944.00i		−	0.195012i	0.995235	−	0.0975062i	$-0.0310866\pi$
$864$	−6840.00			−0.269330
$865$	23078.0	−	4196.00i	0.907139	−	0.164934i
$866$	44640.0			1.75165
$867$			11908.0i			0.466455i
$868$			2800.00i			0.109491i
$869$	−464.000			−0.0181129
$870$	−2832.00	−	15576.0i	−0.110361	−	0.606984i
$871$	11284.0			0.438971
$872$		−	8820.00i		−	0.342526i
$873$			8514.00i			0.330075i
$874$	−5076.00			−0.196451
$875$	33572.0	−	20104.0i	1.29708	−	0.776731i
$876$	−232.000			−0.00894812
$877$		−	18726.0i		−	0.721017i	−0.932756	−	0.360509i	$-0.882603\pi$
$877$		−	18726.0i		−	0.721017i	0.932756	−	0.360509i	$-0.117397\pi$
$878$			21120.0i			0.811806i
$879$	616.000			0.0236373
$880$	−284.000	−	1562.00i	−0.0108791	−	0.0598352i
$881$	−15022.0			−0.574465			−0.287233	−	0.957861i	$-0.592735\pi$
$881$	−15022.0			−0.574465			−0.287233	+	0.957861i	$0.592735\pi$
$882$			14553.0i			0.555584i
$883$			2064.00i			0.0786627i	0.999226	+	0.0393313i	$0.0125228\pi$
$883$			2064.00i			0.0786627i	−0.999226	+	0.0393313i	$0.987477\pi$
$884$	572.000			0.0217629
$885$	−19624.0	+	3568.00i	−0.745371	+	0.135522i
$886$	−30264.0			−1.14756
$887$			12354.0i			0.467651i	0.972279	+	0.233826i	$0.0751245\pi$
$887$			12354.0i			0.467651i	−0.972279	+	0.233826i	$0.924876\pi$
$888$		−	10584.0i		−	0.399973i
$889$	−8232.00			−0.310565
$890$	−34254.0	+	6228.00i	−1.29011	+	0.234565i
$891$	−622.000			−0.0233870
$892$			2408.00i			0.0903877i
$893$		−	42112.0i		−	1.57808i
$894$	−39744.0			−1.48684
$895$	−5136.00	−	28248.0i	−0.191818	−	1.05500i
$896$	−46452.0			−1.73198
$897$		−	936.000i		−	0.0348407i
$898$		−	4302.00i		−	0.159866i
$899$	11800.0			0.437766
$900$	1287.00	−	484.000i	0.0476667	−	0.0179259i
$901$	−33176.0			−1.22670
$902$		−	2844.00i		−	0.104983i
$903$			22400.0i			0.825499i
$904$	17388.0			0.639730
$905$	−6084.00	−	33462.0i	−0.223469	−	1.22908i
$906$	28320.0			1.03849
$907$		−	512.000i		−	0.0187439i	−0.999956	−	0.00937193i	$-0.997017\pi$
$907$		−	512.000i		−	0.0187439i	0.999956	−	0.00937193i	$-0.00298322\pi$
$908$		−	5532.00i		−	0.202187i
$909$	7502.00			0.273736
$910$	12012.0	−	2184.00i	0.437576	−	0.0795592i
$911$	6112.00			0.222283			0.111141	−	0.993805i	$-0.464549\pi$
$911$	6112.00			0.222283			0.111141	+	0.993805i	$0.464549\pi$
$912$		−	26696.0i		−	0.969290i
$913$		−	216.000i		−	0.00782974i
$914$	13602.0			0.492247
$915$	28072.0	−	5104.00i	1.01424	−	0.184408i
$916$	−3088.00			−0.111387
$917$			16800.0i			0.605000i
$918$		−	20064.0i		−	0.721362i
$919$	−31032.0			−1.11388			−0.556938	−	0.830554i	$-0.688024\pi$
$919$	−31032.0			−1.11388			−0.556938	+	0.830554i	$0.688024\pi$
$920$	−756.000	−	4158.00i	−0.0270919	−	0.149006i
$921$	−37936.0			−1.35726
$922$		−	38580.0i		−	1.37805i
$923$		−	6968.00i		−	0.248488i
$924$	224.000			0.00797517
$925$	5544.00	+	14742.0i	0.197066	+	0.524015i
$926$	14724.0			0.522528
$927$		−	12474.0i		−	0.441963i
$928$		−	5310.00i		−	0.187833i
$929$	15122.0			0.534055			0.267027	−	0.963689i	$-0.413959\pi$
$929$	15122.0			0.534055			0.267027	+	0.963689i	$0.413959\pi$
$930$	−2400.00	−	13200.0i	−0.0846227	−	0.465425i
$931$	−41454.0			−1.45929
$932$			3500.00i			0.123011i
$933$		−	17056.0i		−	0.598487i
$934$	26160.0			0.916468
$935$	968.000	−	176.000i	0.0338577	−	0.00615595i
$936$	−3003.00			−0.104868
$937$		−	32240.0i		−	1.12405i	−0.827120	−	0.562025i	$-0.810022\pi$
$937$		−	32240.0i		−	1.12405i	0.827120	−	0.562025i	$-0.189978\pi$
$938$			72912.0i			2.53802i
$939$	20384.0			0.708420
$940$	−4928.00	+	896.000i	−0.170993	+	0.0310897i
$941$	21688.0			0.751338			0.375669	−	0.926754i	$-0.377413\pi$
$941$	21688.0			0.751338			0.375669	+	0.926754i	$0.377413\pi$
$942$			20904.0i			0.723025i
$943$		−	8532.00i		−	0.294634i
$944$	−31666.0			−1.09178
$945$	−8512.00	−	46816.0i	−0.293011	−	1.61156i
$946$	−1200.00			−0.0412425
$947$			3852.00i			0.132179i	0.997814	+	0.0660893i	$0.0210522\pi$
$947$			3852.00i			0.132179i	−0.997814	+	0.0660893i	$0.978948\pi$
$948$			928.000i			0.0317933i
$949$	−754.000			−0.0257912
$950$	12408.0	+	32994.0i	0.423757	+	1.12681i
$951$	8856.00			0.301972
$952$		−	25872.0i		−	0.880794i
$953$			6144.00i			0.208839i	0.994533	+	0.104420i	$0.0332985\pi$
$953$			6144.00i			0.208839i	−0.994533	+	0.104420i	$0.966702\pi$
$954$	−24882.0			−0.844428
$955$	960.000	+	5280.00i	0.0325287	+	0.178908i
$956$	3636.00			0.123009
$957$		−	944.000i		−	0.0318863i
$958$			37980.0i			1.28087i
$959$	34888.0			1.17476
$960$	19052.0	−	3464.00i	0.640522	−	0.116458i
$961$	−19791.0			−0.664328
$962$			4914.00i			0.164692i
$963$			18920.0i			0.633114i
$964$	3870.00			0.129299
$965$	−15774.0	+	2868.00i	−0.526200	+	0.0956727i
$966$	6048.00			0.201440
$967$			49916.0i			1.65997i	0.557786	+	0.829985i	$0.311651\pi$
$967$			49916.0i			1.65997i	−0.557786	+	0.829985i	$0.688349\pi$
$968$			27867.0i			0.925289i
$969$	16544.0			0.548472
$970$	4644.00	+	25542.0i	0.153721	+	0.845468i
$971$	−48868.0			−1.61509			−0.807543	−	0.589809i	$-0.799203\pi$
$971$	−48868.0			−1.61509			−0.807543	+	0.589809i	$0.799203\pi$
$972$		−	2860.00i		−	0.0943771i
$973$			86240.0i			2.84145i
$974$	−6960.00			−0.228966
$975$	−6084.00	+	2288.00i	−0.199840	+	0.0751535i
$976$	45298.0			1.48561
$977$		−	45126.0i		−	1.47770i	−0.673872	−	0.738848i	$-0.735370\pi$
$977$		−	45126.0i		−	1.47770i	0.673872	−	0.738848i	$-0.264630\pi$
$978$			11568.0i			0.378225i
$979$	−2076.00			−0.0677725
$980$	882.000	+	4851.00i	0.0287494	+	0.158122i
$981$	4620.00			0.150362
$982$			16752.0i			0.544377i
$983$			48068.0i			1.55965i	0.626001	+	0.779823i	$0.284691\pi$
$983$			48068.0i			1.55965i	−0.626001	+	0.779823i	$0.715309\pi$
$984$	39816.0			1.28993
$985$	−26422.0	+	4804.00i	−0.854695	+	0.155399i
$986$	15576.0			0.503084
$987$			50176.0i			1.61816i
$988$			1222.00i			0.0393492i
$989$	−3600.00			−0.115747
$990$	726.000	−	132.000i	0.0233069	−	0.00423761i
$991$	−34672.0			−1.11139			−0.555697	−	0.831385i	$-0.687549\pi$
$991$	−34672.0			−1.11139			−0.555697	+	0.831385i	$0.687549\pi$
$992$		−	4500.00i		−	0.144027i
$993$		−	18552.0i		−	0.592880i
$994$	45024.0			1.43669
$995$	−8592.00	−	47256.0i	−0.273753	−	1.50564i
$996$	−432.000			−0.0137434
$997$			24254.0i			0.770443i	0.922824	+	0.385222i	$0.125875\pi$
$997$			24254.0i			0.770443i	−0.922824	+	0.385222i	$0.874125\pi$
$998$			58410.0i			1.85264i
$999$	19152.0			0.606549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.4.b.a.14.1	✓	2
3.2	odd	2		585.4.c.b.469.2		2
5.2	odd	4		325.4.a.c.1.1		1
5.3	odd	4		325.4.a.b.1.1		1
5.4	even	2	inner	65.4.b.a.14.2	yes	2
15.14	odd	2		585.4.c.b.469.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.4.b.a.14.1	✓	2	1.1	even	1	trivial
65.4.b.a.14.2	yes	2	5.4	even	2	inner
325.4.a.b.1.1		1	5.3	odd	4
325.4.a.c.1.1		1	5.2	odd	4
585.4.c.b.469.1		2	15.14	odd	2
585.4.c.b.469.2		2	3.2	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	65.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.00000i q^{2} +4.00000i q^{3} -1.00000 q^{4} +(2.00000 + 11.0000i) q^{5} +12.0000 q^{6} +28.0000i q^{7} -21.0000i q^{8} +11.0000 q^{9} +(33.0000 - 6.00000i) q^{10} +2.00000 q^{11} -4.00000i q^{12} -13.0000i q^{13} +84.0000 q^{14} +(-44.0000 + 8.00000i) q^{15} -71.0000 q^{16} -44.0000i q^{17} -33.0000i q^{18} +94.0000 q^{19} +(-2.00000 - 11.0000i) q^{20} -112.000 q^{21} -6.00000i q^{22} -18.0000i q^{23} +84.0000 q^{24} +(-117.000 + 44.0000i) q^{25} -39.0000 q^{26} +152.000i q^{27} -28.0000i q^{28} -118.000 q^{29} +(24.0000 + 132.000i) q^{30} -100.000 q^{31} +45.0000i q^{32} +8.00000i q^{33} -132.000 q^{34} +(-308.000 + 56.0000i) q^{35} -11.0000 q^{36} -126.000i q^{37} -282.000i q^{38} +52.0000 q^{39} +(231.000 - 42.0000i) q^{40} +474.000 q^{41} +336.000i q^{42} -200.000i q^{43} -2.00000 q^{44} +(22.0000 + 121.000i) q^{45} -54.0000 q^{46} -448.000i q^{47} -284.000i q^{48} -441.000 q^{49} +(132.000 + 351.000i) q^{50} +176.000 q^{51} +13.0000i q^{52} -754.000i q^{53} +456.000 q^{54} +(4.00000 + 22.0000i) q^{55} +588.000 q^{56} +376.000i q^{57} +354.000i q^{58} +446.000 q^{59} +(44.0000 - 8.00000i) q^{60} -638.000 q^{61} +300.000i q^{62} +308.000i q^{63} -433.000 q^{64} +(143.000 - 26.0000i) q^{65} +24.0000 q^{66} +868.000i q^{67} +44.0000i q^{68} +72.0000 q^{69} +(168.000 + 924.000i) q^{70} +536.000 q^{71} -231.000i q^{72} -58.0000i q^{73} -378.000 q^{74} +(-176.000 - 468.000i) q^{75} -94.0000 q^{76} +56.0000i q^{77} -156.000i q^{78} -232.000 q^{79} +(-142.000 - 781.000i) q^{80} -311.000 q^{81} -1422.00i q^{82} -108.000i q^{83} +112.000 q^{84} +(484.000 - 88.0000i) q^{85} -600.000 q^{86} -472.000i q^{87} -42.0000i q^{88} -1038.00 q^{89} +(363.000 - 66.0000i) q^{90} +364.000 q^{91} +18.0000i q^{92} -400.000i q^{93} -1344.00 q^{94} +(188.000 + 1034.00i) q^{95} -180.000 q^{96} +774.000i q^{97} +1323.00i q^{98} +22.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 4 q^{5} + 24 q^{6} + 22 q^{9} + 66 q^{10} + 4 q^{11} + 168 q^{14} - 88 q^{15} - 142 q^{16} + 188 q^{19} - 4 q^{20} - 224 q^{21} + 168 q^{24} - 234 q^{25} - 78 q^{26} - 236 q^{29} + 48 q^{30}+ \cdots + 44 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 + 4 * q^5 + 24 * q^6 + 22 * q^9 + 66 * q^10 + 4 * q^11 + 168 * q^14 - 88 * q^15 - 142 * q^16 + 188 * q^19 - 4 * q^20 - 224 * q^21 + 168 * q^24 - 234 * q^25 - 78 * q^26 - 236 * q^29 + 48 * q^30 - 200 * q^31 - 264 * q^34 - 616 * q^35 - 22 * q^36 + 104 * q^39 + 462 * q^40 + 948 * q^41 - 4 * q^44 + 44 * q^45 - 108 * q^46 - 882 * q^49 + 264 * q^50 + 352 * q^51 + 912 * q^54 + 8 * q^55 + 1176 * q^56 + 892 * q^59 + 88 * q^60 - 1276 * q^61 - 866 * q^64 + 286 * q^65 + 48 * q^66 + 144 * q^69 + 336 * q^70 + 1072 * q^71 - 756 * q^74 - 352 * q^75 - 188 * q^76 - 464 * q^79 - 284 * q^80 - 622 * q^81 + 224 * q^84 + 968 * q^85 - 1200 * q^86 - 2076 * q^89 + 726 * q^90 + 728 * q^91 - 2688 * q^94 + 376 * q^95 - 360 * q^96 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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