LMFDB - Embedded newform 72.4.d.d.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,4,Mod(37,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("72.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	72.d (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:	$4.24813752041$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.8248384.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + x^{4} - 12x^{3} + 4x^{2} + 64 $ x^6 + x^4 - 12x^3 + 4x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 24)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			37.1
Root			$1.88322 - 0.673417i$ of defining polynomial
Character	$\chi$	$=$	72.37
Dual form			72.4.d.d.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.55664 - 1.20980i) q^{2} +(5.07277 + 6.18604i) q^{4} +0.612661i q^{5} -22.7441 q^{7} +(-5.48534 - 21.9525i) q^{8} +O(q^{10})$	\(q+(-2.55664 - 1.20980i) q^{2} +(5.07277 + 6.18604i) q^{4} +0.612661i q^{5} -22.7441 q^{7} +(-5.48534 - 21.9525i) q^{8} +(0.741198 - 1.56635i) q^{10} +60.2630i q^{11} +52.9062i q^{13} +(58.1485 + 27.5159i) q^{14} +(-12.5341 + 62.7606i) q^{16} -47.1643 q^{17} +29.1643i q^{19} +(-3.78994 + 3.10789i) q^{20} +(72.9062 - 154.070i) q^{22} -109.488 q^{23} +124.625 q^{25} +(64.0059 - 135.262i) q^{26} +(-115.376 - 140.696i) q^{28} +10.4250i q^{29} -220.881 q^{31} +(107.973 - 145.292i) q^{32} +(120.582 + 57.0593i) q^{34} -13.9345i q^{35} -408.348i q^{37} +(35.2829 - 74.5624i) q^{38} +(13.4494 - 3.36066i) q^{40} +360.742 q^{41} +236.414i q^{43} +(-372.789 + 305.700i) q^{44} +(279.922 + 132.459i) q^{46} -129.113 q^{47} +174.296 q^{49} +(-318.620 - 150.771i) q^{50} +(-327.279 + 268.381i) q^{52} +117.819i q^{53} -36.9208 q^{55} +(124.759 + 499.290i) q^{56} +(12.6122 - 26.6529i) q^{58} -262.854i q^{59} +273.465i q^{61} +(564.711 + 267.221i) q^{62} +(-451.822 + 240.834i) q^{64} -32.4135 q^{65} +89.4077i q^{67} +(-239.253 - 291.760i) q^{68} +(-16.8579 + 35.6253i) q^{70} +350.521 q^{71} +532.610 q^{73} +(-494.019 + 1044.00i) q^{74} +(-180.411 + 147.943i) q^{76} -1370.63i q^{77} -166.561 q^{79} +(-38.4510 - 7.67915i) q^{80} +(-922.286 - 436.426i) q^{82} +361.934i q^{83} -28.8957i q^{85} +(286.013 - 604.423i) q^{86} +(1322.92 - 330.563i) q^{88} -40.3285 q^{89} -1203.31i q^{91} +(-555.408 - 677.299i) q^{92} +(330.095 + 156.201i) q^{94} -17.8678 q^{95} -614.921 q^{97} +(-445.612 - 210.864i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 76 q^{8}+O(q^{10}) $ 6 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 76 * q^8	$ 6 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 76 q^{8} + 60 q^{10} + 100 q^{14} + 56 q^{16} - 52 q^{17} - 56 q^{20} + 224 q^{22} - 328 q^{23} - 106 q^{25} - 56 q^{26} - 352 q^{28} - 636 q^{31} + 248 q^{32} - 548 q^{34} + 776 q^{38} + 232 q^{40} - 236 q^{41} - 1152 q^{44} + 328 q^{46} + 408 q^{47} + 654 q^{49} - 1970 q^{50} - 368 q^{52} + 1024 q^{55} + 1864 q^{56} + 140 q^{58} + 2108 q^{62} + 832 q^{64} + 1744 q^{65} - 2976 q^{68} + 1352 q^{70} + 1704 q^{71} + 956 q^{73} - 1568 q^{74} - 1744 q^{76} - 44 q^{79} + 2112 q^{80} - 2236 q^{82} + 760 q^{86} + 1856 q^{88} + 220 q^{89} - 1728 q^{92} + 2088 q^{94} - 5104 q^{95} - 2444 q^{97} - 3354 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 76 * q^8 + 60 * q^10 + 100 * q^14 + 56 * q^16 - 52 * q^17 - 56 * q^20 + 224 * q^22 - 328 * q^23 - 106 * q^25 - 56 * q^26 - 352 * q^28 - 636 * q^31 + 248 * q^32 - 548 * q^34 + 776 * q^38 + 232 * q^40 - 236 * q^41 - 1152 * q^44 + 328 * q^46 + 408 * q^47 + 654 * q^49 - 1970 * q^50 - 368 * q^52 + 1024 * q^55 + 1864 * q^56 + 140 * q^58 + 2108 * q^62 + 832 * q^64 + 1744 * q^65 - 2976 * q^68 + 1352 * q^70 + 1704 * q^71 + 956 * q^73 - 1568 * q^74 - 1744 * q^76 - 44 * q^79 + 2112 * q^80 - 2236 * q^82 + 760 * q^86 + 1856 * q^88 + 220 * q^89 - 1728 * q^92 + 2088 * q^94 - 5104 * q^95 - 2444 * q^97 - 3354 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	−2.55664	−	1.20980i	−0.903907	−	0.427729i
$2$	−2.55664	−	1.20980i	−0.903907	−	0.427729i
$3$		0			0
$3$		0			0
$4$	5.07277	+	6.18604i	0.634096	+	0.773255i
$5$			0.612661i			0.0547981i	0.999625	+	0.0273990i	$0.00872248\pi$
$5$			0.612661i			0.0547981i	−0.999625	+	0.0273990i	$0.991278\pi$
$6$		0			0
$7$	−22.7441			−1.22807			−0.614034	−	0.789279i	$-0.710454\pi$
$7$	−22.7441			−1.22807			−0.614034	+	0.789279i	$0.710454\pi$
$8$	−5.48534	−	21.9525i	−0.242420	−	0.970171i
$9$		0			0
$10$	0.741198	−	1.56635i	0.0234387	−	0.0495324i
$11$			60.2630i			1.65182i	0.563805	+	0.825908i	$0.309337\pi$
$11$			60.2630i			1.65182i	−0.563805	+	0.825908i	$0.690663\pi$
$12$		0			0
$13$			52.9062i			1.12873i	0.825524	+	0.564367i	$0.190880\pi$
$13$			52.9062i			1.12873i	−0.825524	+	0.564367i	$0.809120\pi$
$14$	58.1485	+	27.5159i	1.11006	+	0.525281i
$15$		0			0
$16$	−12.5341	+	62.7606i	−0.195845	+	0.980635i
$17$	−47.1643			−0.672883			−0.336442	−	0.941704i	$-0.609223\pi$
$17$	−47.1643			−0.672883			−0.336442	+	0.941704i	$0.609223\pi$
$18$		0			0
$19$			29.1643i			0.352144i	0.984377	+	0.176072i	$0.0563392\pi$
$19$			29.1643i			0.352144i	−0.984377	+	0.176072i	$0.943661\pi$
$20$	−3.78994	+	3.10789i	−0.0423729	+	0.0347472i
$21$		0			0
$22$	72.9062	−	154.070i	0.706529	−	1.49309i
$23$	−109.488			−0.992604			−0.496302	−	0.868150i	$-0.665309\pi$
$23$	−109.488			−0.992604			−0.496302	+	0.868150i	$0.665309\pi$
$24$		0			0
$25$	124.625			0.996997
$26$	64.0059	−	135.262i	0.482792	−	1.02027i
$27$		0			0
$28$	−115.376	−	140.696i	−0.778713	−	0.949609i
$29$			10.4250i			0.0667542i	0.999443	+	0.0333771i	$0.0106262\pi$
$29$			10.4250i			0.0667542i	−0.999443	+	0.0333771i	$0.989374\pi$
$30$		0			0
$31$	−220.881			−1.27972			−0.639860	−	0.768492i	$-0.721008\pi$
$31$	−220.881			−1.27972			−0.639860	+	0.768492i	$0.721008\pi$
$32$	107.973	−	145.292i	0.596472	−	0.802634i
$33$		0			0
$34$	120.582	+	57.0593i	0.608224	+	0.287812i
$35$		−	13.9345i		−	0.0672958i
$36$		0			0
$37$		−	408.348i		−	1.81438i	−0.420725	−	0.907188i	$-0.638224\pi$
$37$		−	408.348i		−	1.81438i	0.420725	−	0.907188i	$-0.361776\pi$
$38$	35.2829	−	74.5624i	0.150622	−	0.318306i
$39$		0			0
$40$	13.4494	−	3.36066i	0.0531635	−	0.0132842i
$41$	360.742			1.37411			0.687054	−	0.726606i	$-0.258903\pi$
$41$	360.742			1.37411			0.687054	+	0.726606i	$0.258903\pi$
$42$		0			0
$43$			236.414i			0.838436i	0.907886	+	0.419218i	$0.137696\pi$
$43$			236.414i			0.838436i	−0.907886	+	0.419218i	$0.862304\pi$
$44$	−372.789	+	305.700i	−1.27727	+	1.04741i
$45$		0			0
$46$	279.922	+	132.459i	0.897222	+	0.424565i
$47$	−129.113			−0.400703			−0.200352	−	0.979724i	$-0.564208\pi$
$47$	−129.113			−0.400703			−0.200352	+	0.979724i	$0.564208\pi$
$48$		0			0
$49$	174.296			0.508152
$50$	−318.620	−	150.771i	−0.901193	−	0.426445i
$51$		0			0
$52$	−327.279	+	268.381i	−0.872798	+	0.715725i
$53$			117.819i			0.305353i	0.988276	+	0.152677i	$0.0487893\pi$
$53$			117.819i			0.305353i	−0.988276	+	0.152677i	$0.951211\pi$
$54$		0			0
$55$	−36.9208			−0.0905163
$56$	124.759	+	499.290i	0.297709	+	1.19144i
$57$		0			0
$58$	12.6122	−	26.6529i	0.0285527	−	0.0603396i
$59$		−	262.854i		−	0.580012i	−0.957025	−	0.290006i	$-0.906343\pi$
$59$		−	262.854i		−	0.580012i	0.957025	−	0.290006i	$-0.0936574\pi$
$60$		0			0
$61$			273.465i			0.573993i	0.957932	+	0.286996i	$0.0926568\pi$
$61$			273.465i			0.573993i	−0.957932	+	0.286996i	$0.907343\pi$
$62$	564.711	+	267.221i	1.15675	+	0.547373i
$63$		0			0
$64$	−451.822	+	240.834i	−0.882465	+	0.470378i
$65$	−32.4135			−0.0618524
$66$		0			0
$67$			89.4077i			0.163028i	0.996672	+	0.0815141i	$0.0259756\pi$
$67$			89.4077i			0.163028i	−0.996672	+	0.0815141i	$0.974024\pi$
$68$	−239.253	−	291.760i	−0.426672	−	0.520310i
$69$		0			0
$70$	−16.8579	+	35.6253i	−0.0287844	+	0.0608291i
$71$	350.521			0.585904			0.292952	−	0.956127i	$-0.405362\pi$
$71$	350.521			0.585904			0.292952	+	0.956127i	$0.405362\pi$
$72$		0			0
$73$	532.610			0.853936			0.426968	−	0.904267i	$-0.359582\pi$
$73$	532.610			0.853936			0.426968	+	0.904267i	$0.359582\pi$
$74$	−494.019	+	1044.00i	−0.776062	+	1.64003i
$75$		0			0
$76$	−180.411	+	147.943i	−0.272297	+	0.223293i
$77$		−	1370.63i		−	2.02854i
$78$		0			0
$79$	−166.561			−0.237210			−0.118605	−	0.992942i	$-0.537842\pi$
$79$	−166.561			−0.237210			−0.118605	+	0.992942i	$0.537842\pi$
$80$	−38.4510	−	7.67915i	−0.0537369	−	0.0107319i
$81$		0			0
$82$	−922.286	−	436.426i	−1.24207	−	0.587746i
$83$			361.934i			0.478644i	0.970940	+	0.239322i	$0.0769252\pi$
$83$			361.934i			0.478644i	−0.970940	+	0.239322i	$0.923075\pi$
$84$		0			0
$85$		−	28.8957i		−	0.0368727i
$86$	286.013	−	604.423i	0.358623	−	0.757868i
$87$		0			0
$88$	1322.92	−	330.563i	1.60254	−	0.400433i
$89$	−40.3285			−0.0480316			−0.0240158	−	0.999712i	$-0.507645\pi$
$89$	−40.3285			−0.0480316			−0.0240158	+	0.999712i	$0.507645\pi$
$90$		0			0
$91$		−	1203.31i		−	1.38616i
$92$	−555.408	−	677.299i	−0.629406	−	0.767535i
$93$		0			0
$94$	330.095	+	156.201i	0.362199	+	0.171392i
$95$	−17.8678			−0.0192968
$96$		0			0
$97$	−614.921			−0.643667			−0.321834	−	0.946796i	$-0.604299\pi$
$97$	−614.921			−0.643667			−0.321834	+	0.946796i	$0.604299\pi$
$98$	−445.612	−	210.864i	−0.459322	−	0.217351i
$99$		0			0
$100$	632.192	+	770.933i	0.632192	+	0.770933i
$101$			1664.99i			1.64033i	0.572130	+	0.820163i	$0.306117\pi$
$101$			1664.99i			1.64033i	−0.572130	+	0.820163i	$0.693883\pi$
$102$		0			0
$103$	396.858			0.379647			0.189823	−	0.981818i	$-0.439208\pi$
$103$	396.858			0.379647			0.189823	+	0.981818i	$0.439208\pi$
$104$	1161.42	−	290.208i	1.09506	−	0.273628i
$105$		0			0
$106$	142.538	−	301.221i	0.130608	−	0.276011i
$107$			350.630i			0.316791i	0.987376	+	0.158396i	$0.0506321\pi$
$107$			350.630i			0.316791i	−0.987376	+	0.158396i	$0.949368\pi$
$108$		0			0
$109$			597.009i			0.524615i	0.964984	+	0.262308i	$0.0844835\pi$
$109$			597.009i			0.524615i	−0.964984	+	0.262308i	$0.915516\pi$
$110$	94.3930	+	44.6668i	0.0818183	+	0.0387165i
$111$		0			0
$112$	285.077	−	1427.44i	0.240511	−	1.20429i
$113$	−496.422			−0.413270			−0.206635	−	0.978418i	$-0.566251\pi$
$113$	−496.422			−0.413270			−0.206635	+	0.978418i	$0.566251\pi$
$114$		0			0
$115$		−	67.0792i		−	0.0543928i
$116$	−64.4893	+	52.8835i	−0.0516180	+	0.0423285i
$117$		0			0
$118$	−318.001	+	672.023i	−0.248088	+	0.524277i
$119$	1072.71			0.826346
$120$		0			0
$121$	−2300.63			−1.72849
$122$	330.838	−	699.149i	0.245513	−	0.518836i
$123$		0			0
$124$	−1120.48	−	1366.37i	−0.811465	−	0.989549i
$125$			152.935i			0.109432i
$126$		0			0
$127$	1799.85			1.25756			0.628782	−	0.777581i	$-0.283554\pi$
$127$	1799.85			1.25756			0.628782	+	0.777581i	$0.283554\pi$
$128$	1446.50	−	69.1093i	0.998861	−	0.0477223i
$129$		0			0
$130$	82.8696	+	39.2139i	0.0559088	+	0.0264561i
$131$		−	1121.45i		−	0.747949i	−0.927439	−	0.373974i	$-0.877995\pi$
$131$		−	1121.45i		−	0.747949i	0.927439	−	0.373974i	$-0.122005\pi$
$132$		0			0
$133$		−	663.316i		−	0.432457i
$134$	108.166	−	228.583i	0.0697319	−	0.147362i
$135$		0			0
$136$	258.712	+	1035.37i	0.163120	+	0.652812i
$137$	−2449.55			−1.52759			−0.763793	−	0.645461i	$-0.776665\pi$
$137$	−2449.55			−1.52759			−0.763793	+	0.645461i	$0.776665\pi$
$138$		0			0
$139$			2457.56i			1.49962i	0.661652	+	0.749811i	$0.269856\pi$
$139$			2457.56i			1.49962i	−0.661652	+	0.749811i	$0.730144\pi$
$140$	86.1990	−	70.6862i	0.0520368	−	0.0426720i
$141$		0			0
$142$	−896.153	−	424.060i	−0.529602	−	0.250608i
$143$	−3188.28			−1.86446
$144$		0			0
$145$	−6.38698			−0.00365800
$146$	−1361.69	−	644.352i	−0.771878	−	0.365253i
$147$		0			0
$148$	2526.05	−	2071.45i	1.40297	−	1.15049i
$149$			2084.96i			1.14635i	0.819432	+	0.573177i	$0.194289\pi$
$149$			2084.96i			1.14635i	−0.819432	+	0.573177i	$0.805711\pi$
$150$		0			0
$151$	1057.80			0.570084			0.285042	−	0.958515i	$-0.407992\pi$
$151$	1057.80			0.570084			0.285042	+	0.958515i	$0.407992\pi$
$152$	640.228	−	159.976i	0.341640	−	0.0853669i
$153$		0			0
$154$	−1658.19	+	3504.20i	−0.867666	+	1.83361i
$155$		−	135.325i		−	0.0701262i
$156$		0			0
$157$			3193.01i			1.62312i	0.584270	+	0.811559i	$0.301381\pi$
$157$			3193.01i			1.62312i	−0.584270	+	0.811559i	$0.698619\pi$
$158$	425.836	+	201.506i	0.214416	+	0.101461i
$159$		0			0
$160$	89.0149	+	66.1508i	0.0439828	+	0.0326855i
$161$	2490.22			1.21899
$162$		0			0
$163$		−	846.854i		−	0.406937i	−0.979081	−	0.203469i	$-0.934779\pi$
$163$		−	846.854i		−	0.406937i	0.979081	−	0.203469i	$-0.0652215\pi$
$164$	1829.96	+	2231.56i	0.871316	+	1.06254i
$165$		0			0
$166$	437.868	−	925.334i	0.204730	−	0.432650i
$167$	2630.15			1.21873			0.609363	−	0.792892i	$-0.291425\pi$
$167$	2630.15			1.21873			0.609363	+	0.792892i	$0.291425\pi$
$168$		0			0
$169$	−602.062			−0.274038
$170$	−34.9580	+	73.8758i	−0.0157715	+	0.0333295i
$171$		0			0
$172$	−1462.46	+	1199.27i	−0.648324	+	0.531648i
$173$		−	429.843i		−	0.188904i	−0.995529	−	0.0944519i	$-0.969890\pi$
$173$		−	429.843i		−	0.188904i	0.995529	−	0.0944519i	$-0.0301099\pi$
$174$		0			0
$175$	−2834.48			−1.22438
$176$	−3782.14	−	755.341i	−1.61983	−	0.323500i
$177$		0			0
$178$	103.105	+	48.7895i	0.0434161	+	0.0205445i
$179$			1516.30i			0.633149i	0.948568	+	0.316574i	$0.102533\pi$
$179$			1516.30i			0.633149i	−0.948568	+	0.316574i	$0.897467\pi$
$180$		0			0
$181$		−	3380.20i		−	1.38811i	−0.719921	−	0.694056i	$-0.755822\pi$
$181$		−	3380.20i		−	1.38811i	0.719921	−	0.694056i	$-0.244178\pi$
$182$	−1455.76	+	3076.41i	−0.592901	+	1.25296i
$183$		0			0
$184$	600.581	+	2403.54i	0.240627	+	0.962996i
$185$	250.179			0.0994244
$186$		0			0
$187$		−	2842.26i		−	1.11148i
$188$	−654.960	−	798.697i	−0.254084	−	0.309846i
$189$		0			0
$190$	45.6815	+	21.6165i	0.0174425	+	0.00825381i
$191$	2799.71			1.06063			0.530314	−	0.847801i	$-0.322074\pi$
$191$	2799.71			1.06063			0.530314	+	0.847801i	$0.322074\pi$
$192$		0			0
$193$	624.106			0.232768			0.116384	−	0.993204i	$-0.462870\pi$
$193$	624.106			0.232768			0.116384	+	0.993204i	$0.462870\pi$
$194$	1572.13	+	743.931i	0.581816	+	0.275315i
$195$		0			0
$196$	884.164	+	1078.20i	0.322217	+	0.392931i
$197$		−	4779.25i		−	1.72846i	−0.503094	−	0.864232i	$-0.667805\pi$
$197$		−	4779.25i		−	1.72846i	0.503094	−	0.864232i	$-0.332195\pi$
$198$		0			0
$199$	2615.92			0.931846			0.465923	−	0.884825i	$-0.345722\pi$
$199$	2615.92			0.931846			0.465923	+	0.884825i	$0.345722\pi$
$200$	−683.609	−	2735.82i	−0.241692	−	0.967258i
$201$		0			0
$202$	2014.31	−	4256.78i	0.701615	−	1.48270i
$203$		−	237.107i		−	0.0819787i
$204$		0			0
$205$			221.013i			0.0752985i
$206$	−1014.62	−	480.119i	−0.343165	−	0.162386i
$207$		0			0
$208$	−3320.42	−	663.131i	−1.10687	−	0.221057i
$209$	−1757.52			−0.581677
$210$		0			0
$211$		−	1745.78i		−	0.569595i	−0.958588	−	0.284798i	$-0.908074\pi$
$211$		−	1745.78i		−	0.569595i	0.958588	−	0.284798i	$-0.0919264\pi$
$212$	−728.834	+	597.670i	−0.236116	+	0.193623i
$213$		0			0
$214$	424.192	−	896.432i	0.135501	−	0.286350i
$215$	−144.841			−0.0459447
$216$		0			0
$217$	5023.74			1.57158
$218$	722.261	−	1526.33i	0.224393	−	0.474203i
$219$		0			0
$220$	−187.290	−	228.393i	−0.0573960	−	0.0699921i
$221$		−	2495.28i		−	0.759505i
$222$		0			0
$223$	−3385.60			−1.01667			−0.508333	−	0.861161i	$-0.669738\pi$
$223$	−3385.60			−1.01667			−0.508333	+	0.861161i	$0.669738\pi$
$224$	−2455.75	+	3304.55i	−0.732508	+	0.985690i
$225$		0			0
$226$	1269.17	+	600.572i	0.373557	+	0.176767i
$227$		−	3847.72i		−	1.12503i	−0.826787	−	0.562515i	$-0.809834\pi$
$227$		−	3847.72i		−	1.12503i	0.826787	−	0.562515i	$-0.190166\pi$
$228$		0			0
$229$			1335.15i			0.385279i	0.981270	+	0.192640i	$0.0617049\pi$
$229$			1335.15i			0.385279i	−0.981270	+	0.192640i	$0.938295\pi$
$230$	−81.1525	+	171.497i	−0.0232654	+	0.0491660i
$231$		0			0
$232$	228.854	−	57.1846i	0.0647630	−	0.0161826i
$233$	5146.38			1.44700			0.723499	−	0.690325i	$-0.242532\pi$
$233$	5146.38			1.44700			0.723499	+	0.690325i	$0.242532\pi$
$234$		0			0
$235$		−	79.1025i		−	0.0219578i
$236$	1626.03	−	1333.40i	0.448497	−	0.367783i
$237$		0			0
$238$	−2742.53	−	1297.77i	−0.746940	−	0.353452i
$239$	−7085.07			−1.91755			−0.958777	−	0.284160i	$-0.908285\pi$
$239$	−7085.07			−1.91755			−0.958777	+	0.284160i	$0.908285\pi$
$240$		0			0
$241$	2538.40			0.678476			0.339238	−	0.940701i	$-0.389831\pi$
$241$	2538.40			0.678476			0.339238	+	0.940701i	$0.389831\pi$
$242$	5881.86	+	2783.30i	1.56240	+	0.739327i
$243$		0			0
$244$	−1691.66	+	1387.22i	−0.443843	+	0.363966i
$245$			106.784i			0.0278458i
$246$		0			0
$247$	−1542.97			−0.397477
$248$	1211.61	+	4848.87i	0.310230	+	1.24155i
$249$		0			0
$250$	185.021	−	391.000i	0.0468071	−	0.0989160i
$251$			1696.99i			0.426746i	0.976971	+	0.213373i	$0.0684449\pi$
$251$			1696.99i			0.426746i	−0.976971	+	0.213373i	$0.931555\pi$
$252$		0			0
$253$		−	6598.09i		−	1.63960i
$254$	−4601.56	−	2177.46i	−1.13672	−	0.537897i
$255$		0			0
$256$	−3781.79	−	1573.29i	−0.923289	−	0.384105i
$257$	382.902			0.0929369			0.0464685	−	0.998920i	$-0.485203\pi$
$257$	382.902			0.0929369			0.0464685	+	0.998920i	$0.485203\pi$
$258$		0			0
$259$			9287.52i			2.22818i
$260$	−164.426	−	200.511i	−0.0392203	−	0.0478276i
$261$		0			0
$262$	−1356.73	+	2867.13i	−0.319919	+	0.676076i
$263$	5002.02			1.17277			0.586383	−	0.810034i	$-0.300551\pi$
$263$	5002.02			1.17277			0.586383	+	0.810034i	$0.300551\pi$
$264$		0			0
$265$	−72.1833			−0.0167328
$266$	−802.480	+	1695.86i	−0.184974	+	0.390901i
$267$		0			0
$268$	−553.079	+	453.545i	−0.126062	+	0.103376i
$269$			6117.47i			1.38658i	0.720661	+	0.693288i	$0.243839\pi$
$269$			6117.47i			1.38658i	−0.720661	+	0.693288i	$0.756161\pi$
$270$		0			0
$271$	−3956.12			−0.886780			−0.443390	−	0.896329i	$-0.646224\pi$
$271$	−3956.12			−0.886780			−0.443390	+	0.896329i	$0.646224\pi$
$272$	591.161	−	2960.06i	0.131781	−	0.659853i
$273$		0			0
$274$	6262.61	+	2963.47i	1.38080	+	0.653393i
$275$			7510.25i			1.64686i
$276$		0			0
$277$			4842.17i			1.05032i	0.851004	+	0.525158i	$0.175994\pi$
$277$			4842.17i			1.05032i	−0.851004	+	0.525158i	$0.824006\pi$
$278$	2973.16	−	6283.09i	0.641432	−	1.35552i
$279$		0			0
$280$	−305.896	+	76.4353i	−0.0652884	+	0.0163139i
$281$	−1878.68			−0.398835			−0.199417	−	0.979915i	$-0.563905\pi$
$281$	−1878.68			−0.398835			−0.199417	+	0.979915i	$0.563905\pi$
$282$		0			0
$283$			5724.87i			1.20250i	0.799060	+	0.601251i	$0.205331\pi$
$283$			5724.87i			1.20250i	−0.799060	+	0.601251i	$0.794669\pi$
$284$	1778.11	+	2168.33i	0.371519	+	0.453053i
$285$		0			0
$286$	8151.27	+	3857.19i	1.68530	+	0.797483i
$287$	−8204.77			−1.68750
$288$		0			0
$289$	−2688.53			−0.547228
$290$	16.3292	+	7.72697i	0.00330649	+	0.00156463i
$291$		0			0
$292$	2701.81	+	3294.75i	0.541477	+	0.660310i
$293$			5088.75i			1.01464i	0.861759	+	0.507318i	$0.169363\pi$
$293$			5088.75i			1.01464i	−0.861759	+	0.507318i	$0.830637\pi$
$294$		0			0
$295$	161.041			0.0317836
$296$	−8964.24	+	2239.93i	−1.76026	+	0.439842i
$297$		0			0
$298$	2522.39	−	5330.49i	0.490329	−	1.03620i
$299$		−	5792.61i		−	1.12038i
$300$		0			0
$301$		−	5377.02i		−	1.02966i
$302$	−2704.41	−	1279.73i	−0.515303	−	0.243841i
$303$		0			0
$304$	−1830.37	−	365.547i	−0.345325	−	0.0689657i
$305$	−167.541			−0.0314537
$306$		0			0
$307$		−	7219.21i		−	1.34209i	−0.741416	−	0.671046i	$-0.765845\pi$
$307$		−	7219.21i		−	1.34209i	0.741416	−	0.671046i	$-0.234155\pi$
$308$	8478.76	−	6952.88i	1.56858	−	1.28629i
$309$		0			0
$310$	−163.716	+	345.976i	−0.0299950	+	0.0633875i
$311$	1537.06			0.280252			0.140126	−	0.990134i	$-0.455249\pi$
$311$	1537.06			0.280252			0.140126	+	0.990134i	$0.455249\pi$
$312$		0			0
$313$	−2200.93			−0.397456			−0.198728	−	0.980055i	$-0.563681\pi$
$313$	−2200.93			−0.397456			−0.198728	+	0.980055i	$0.563681\pi$
$314$	3862.90	−	8163.35i	0.694255	−	1.46715i
$315$		0			0
$316$	−844.925	−	1030.35i	−0.150414	−	0.183424i
$317$			2840.41i			0.503260i	0.967824	+	0.251630i	$0.0809665\pi$
$317$			2840.41i			0.503260i	−0.967824	+	0.251630i	$0.919033\pi$
$318$		0			0
$319$	−628.240			−0.110266
$320$	−147.549	−	276.814i	−0.0257758	−	0.0483574i
$321$		0			0
$322$	−6366.58	−	3012.67i	−1.10185	−	0.521395i
$323$		−	1375.51i		−	0.236952i
$324$		0			0
$325$			6593.41i			1.12534i
$326$	−1024.52	+	2165.10i	−0.174059	+	0.367833i
$327$		0			0
$328$	−1978.79	−	7919.18i	−0.333112	−	1.33312i
$329$	2936.56			0.492091
$330$		0			0
$331$		−	2118.52i		−	0.351795i	−0.984408	−	0.175898i	$-0.943717\pi$
$331$		−	2118.52i		−	0.351795i	0.984408	−	0.175898i	$-0.0562828\pi$
$332$	−2238.94	+	1836.01i	−0.370114	+	0.303506i
$333$		0			0
$334$	−6724.33	−	3181.96i	−1.10161	−	0.521284i
$335$	−54.7766			−0.00893364
$336$		0			0
$337$	−659.599			−0.106619			−0.0533096	−	0.998578i	$-0.516977\pi$
$337$	−659.599			−0.106619			−0.0533096	+	0.998578i	$0.516977\pi$
$338$	1539.25	+	728.375i	0.247705	+	0.117214i
$339$		0			0
$340$	178.750	−	146.581i	0.0285120	−	0.0233808i
$341$		−	13310.9i		−	2.11386i
$342$		0			0
$343$	3837.03			0.604023
$344$	5189.86	−	1296.81i	0.813426	−	0.203254i
$345$		0			0
$346$	−520.024	+	1098.95i	−0.0807996	+	0.170751i
$347$			8377.42i			1.29603i	0.761626	+	0.648017i	$0.224401\pi$
$347$			8377.42i			1.29603i	−0.761626	+	0.648017i	$0.775599\pi$
$348$		0			0
$349$		−	3254.18i		−	0.499119i	−0.968360	−	0.249559i	$-0.919714\pi$
$349$		−	3254.18i		−	0.499119i	0.968360	−	0.249559i	$-0.0802857\pi$
$350$	7246.73	+	3429.16i	1.10673	+	0.523703i
$351$		0			0
$352$	8755.74	+	6506.77i	1.32580	+	0.985261i
$353$	−11117.5			−1.67627			−0.838137	−	0.545459i	$-0.816355\pi$
$353$	−11117.5			−1.67627			−0.838137	+	0.545459i	$0.816355\pi$
$354$		0			0
$355$			214.750i			0.0321064i
$356$	−204.577	−	249.474i	−0.0304566	−	0.0371407i
$357$		0			0
$358$	1834.42	−	3876.63i	0.270816	−	0.572308i
$359$	4756.56			0.699281			0.349640	−	0.936884i	$-0.386304\pi$
$359$	4756.56			0.699281			0.349640	+	0.936884i	$0.386304\pi$
$360$		0			0
$361$	6008.45			0.875994
$362$	−4089.37	+	8641.94i	−0.593736	+	1.25472i
$363$		0			0
$364$	7443.69	−	6104.09i	1.07186	−	0.878959i
$365$			326.310i			0.0467940i
$366$		0			0
$367$	1837.40			0.261339			0.130670	−	0.991426i	$-0.458287\pi$
$367$	1837.40			0.261339			0.130670	+	0.991426i	$0.458287\pi$
$368$	1372.34	−	6871.55i	0.194397	−	0.973382i
$369$		0			0
$370$	−639.616	−	302.666i	−0.0898704	−	0.0425267i
$371$		−	2679.70i		−	0.374995i
$372$		0			0
$373$			5598.07i			0.777097i	0.921428	+	0.388549i	$0.127023\pi$
$373$			5598.07i			0.777097i	−0.921428	+	0.388549i	$0.872977\pi$
$374$	−3438.56	+	7266.62i	−0.475412	+	1.00467i
$375$		0			0
$376$	708.229	+	2834.35i	0.0971386	+	0.388751i
$377$	−551.546			−0.0753476
$378$		0			0
$379$		−	3460.18i		−	0.468965i	−0.972120	−	0.234482i	$-0.924661\pi$
$379$		−	3460.18i		−	0.468965i	0.972120	−	0.234482i	$-0.0753395\pi$
$380$	−90.6392	−	110.531i	−0.0122360	−	0.0149214i
$381$		0			0
$382$	−7157.84	−	3387.09i	−0.958709	−	0.453661i
$383$	−5059.63			−0.675027			−0.337513	−	0.941321i	$-0.609586\pi$
$383$	−5059.63			−0.675027			−0.337513	+	0.941321i	$0.609586\pi$
$384$		0			0
$385$	839.732			0.111160
$386$	−1595.61	−	755.044i	−0.210400	−	0.0995614i
$387$		0			0
$388$	−3119.35	−	3803.92i	−0.408147	−	0.497719i
$389$		−	2192.22i		−	0.285732i	−0.989742	−	0.142866i	$-0.954368\pi$
$389$		−	2192.22i		−	0.285732i	0.989742	−	0.142866i	$-0.0456318\pi$
$390$		0			0
$391$	5163.93			0.667906
$392$	−956.074	−	3826.23i	−0.123186	−	0.492995i
$393$		0			0
$394$	−5781.93	+	12218.8i	−0.739314	+	1.56237i
$395$		−	102.045i		−	0.0129986i
$396$		0			0
$397$			5519.94i			0.697828i	0.937155	+	0.348914i	$0.113449\pi$
$397$			5519.94i			0.697828i	−0.937155	+	0.348914i	$0.886551\pi$
$398$	−6687.94	−	3164.73i	−0.842302	−	0.398577i
$399$		0			0
$400$	−1562.06	+	7821.52i	−0.195257	+	0.977690i
$401$	7352.64			0.915645			0.457822	−	0.889044i	$-0.348630\pi$
$401$	7352.64			0.915645			0.457822	+	0.889044i	$0.348630\pi$
$402$		0			0
$403$		−	11685.9i		−	1.44446i
$404$	−10299.7	+	8446.12i	−1.26839	+	1.04012i
$405$		0			0
$406$	−286.853	+	606.197i	−0.0350647	+	0.0741011i
$407$	24608.2			2.99702
$408$		0			0
$409$	−11311.2			−1.36749			−0.683745	−	0.729721i	$-0.739650\pi$
$409$	−11311.2			−1.36749			−0.683745	+	0.729721i	$0.739650\pi$
$410$	267.381	−	565.049i	0.0322074	−	0.0680628i
$411$		0			0
$412$	2013.17	+	2454.98i	0.240732	+	0.293564i
$413$			5978.40i			0.712295i
$414$		0			0
$415$	−221.743			−0.0262288
$416$	7686.86	+	5712.43i	0.905960	+	0.673257i
$417$		0			0
$418$	4493.35	+	2126.25i	0.525782	+	0.248800i
$419$		−	13042.2i		−	1.52065i	−0.649543	−	0.760325i	$-0.725040\pi$
$419$		−	13042.2i		−	1.52065i	0.649543	−	0.760325i	$-0.274960\pi$
$420$		0			0
$421$		−	4544.38i		−	0.526080i	−0.964785	−	0.263040i	$-0.915275\pi$
$421$		−	4544.38i		−	0.526080i	0.964785	−	0.263040i	$-0.0847251\pi$
$422$	−2112.05	+	4463.33i	−0.243632	+	0.514861i
$423$		0			0
$424$	2586.42	−	646.279i	0.296245	−	0.0740238i
$425$	−5877.83			−0.670863
$426$		0			0
$427$		−	6219.72i		−	0.704903i
$428$	−2169.01	+	1778.66i	−0.244960	+	0.200876i
$429$		0			0
$430$	370.307	+	175.229i	0.0415297	+	0.0196519i
$431$	−7713.83			−0.862093			−0.431047	−	0.902330i	$-0.641856\pi$
$431$	−7713.83			−0.862093			−0.431047	+	0.902330i	$0.641856\pi$
$432$		0			0
$433$	−15068.3			−1.67237			−0.836183	−	0.548451i	$-0.815218\pi$
$433$	−15068.3			−1.67237			−0.836183	+	0.548451i	$0.815218\pi$
$434$	−12843.9	−	6077.72i	−1.42057	−	0.672212i
$435$		0			0
$436$	−3693.12	+	3028.49i	−0.405661	+	0.332656i
$437$		−	3193.14i		−	0.349540i
$438$		0			0
$439$	11004.7			1.19642			0.598208	−	0.801341i	$-0.295880\pi$
$439$	11004.7			1.19642			0.598208	+	0.801341i	$0.295880\pi$
$440$	202.523	+	810.502i	0.0219430	+	0.0878163i
$441$		0			0
$442$	−3018.79	+	6379.52i	−0.324862	+	0.686522i
$443$		−	2513.04i		−	0.269522i	−0.990878	−	0.134761i	$-0.956973\pi$
$443$		−	2513.04i		−	0.269522i	0.990878	−	0.134761i	$-0.0430266\pi$
$444$		0			0
$445$		−	24.7077i		−	0.00263204i
$446$	8655.74	+	4095.90i	0.918972	+	0.434858i
$447$		0			0
$448$	10276.3	−	5477.56i	1.08373	−	0.577657i
$449$	15752.7			1.65571			0.827855	−	0.560942i	$-0.189561\pi$
$449$	15752.7			1.65571			0.827855	+	0.560942i	$0.189561\pi$
$450$		0			0
$451$			21739.4i			2.26977i
$452$	−2518.23	−	3070.89i	−0.262053	−	0.319563i
$453$		0			0
$454$	−4654.97	+	9837.20i	−0.481208	+	1.01692i
$455$	737.218			0.0759590
$456$		0			0
$457$	−5257.06			−0.538107			−0.269053	−	0.963125i	$-0.586711\pi$
$457$	−5257.06			−0.538107			−0.269053	+	0.963125i	$0.586711\pi$
$458$	1615.26	−	3413.48i	0.164795	−	0.348257i
$459$		0			0
$460$	414.954	−	340.277i	0.0420595	−	0.0344902i
$461$			8066.31i			0.814936i	0.913220	+	0.407468i	$0.133588\pi$
$461$			8066.31i			0.814936i	−0.913220	+	0.407468i	$0.866412\pi$
$462$		0			0
$463$	5683.43			0.570478			0.285239	−	0.958456i	$-0.407927\pi$
$463$	5683.43			0.570478			0.285239	+	0.958456i	$0.407927\pi$
$464$	−654.279	−	130.668i	−0.0654615	−	0.0130735i
$465$		0			0
$466$	−13157.4	−	6226.09i	−1.30795	−	0.618923i
$467$			11139.3i			1.10378i	0.833916	+	0.551891i	$0.186094\pi$
$467$			11139.3i			1.10378i	−0.833916	+	0.551891i	$0.813906\pi$
$468$		0			0
$469$		−	2033.50i		−	0.200210i
$470$	−95.6982	+	202.236i	−0.00939198	+	0.0198478i
$471$		0			0
$472$	−5770.30	+	1441.85i	−0.562711	+	0.140607i
$473$	−14247.0			−1.38494
$474$		0			0
$475$			3634.59i			0.351087i
$476$	5441.61	+	6635.83i	0.523983	+	0.638976i
$477$		0			0
$478$	18114.0	+	8571.53i	1.73329	+	0.820193i
$479$	−3477.35			−0.331699			−0.165850	−	0.986151i	$-0.553037\pi$
$479$	−3477.35			−0.331699			−0.165850	+	0.986151i	$0.553037\pi$
$480$		0			0
$481$	21604.1			2.04795
$482$	−6489.76	−	3070.96i	−0.613279	−	0.290204i
$483$		0			0
$484$	−11670.5	−	14231.8i	−1.09603	−	1.33657i
$485$		−	376.738i		−	0.0352717i
$486$		0			0
$487$	−478.797			−0.0445510			−0.0222755	−	0.999752i	$-0.507091\pi$
$487$	−478.797			−0.0445510			−0.0222755	+	0.999752i	$0.507091\pi$
$488$	6003.23	−	1500.05i	0.556871	−	0.139147i
$489$		0			0
$490$	129.188	−	273.009i	0.0119104	−	0.0251700i
$491$		−	16601.8i		−	1.52592i	−0.646444	−	0.762961i	$-0.723745\pi$
$491$		−	16601.8i		−	1.52592i	0.646444	−	0.762961i	$-0.276255\pi$
$492$		0			0
$493$		−	491.687i		−	0.0449178i
$494$	3944.81	+	1866.68i	0.359282	+	0.170012i
$495$		0			0
$496$	2768.54	−	13862.6i	0.250627	−	1.25494i
$497$	−7972.29			−0.719530
$498$		0			0
$499$		−	9482.20i		−	0.850664i	−0.905037	−	0.425332i	$-0.860157\pi$
$499$		−	9482.20i		−	0.850664i	0.905037	−	0.425332i	$-0.139843\pi$
$500$	−946.063	+	775.805i	−0.0846185	+	0.0693901i
$501$		0			0
$502$	2053.02	−	4338.59i	0.182532	−	0.385738i
$503$	−16561.2			−1.46805			−0.734023	−	0.679124i	$-0.762360\pi$
$503$	−16561.2			−1.46805			−0.734023	+	0.679124i	$0.762360\pi$
$504$		0			0
$505$	−1020.08			−0.0898867
$506$	−7982.37	+	16868.9i	−0.701304	+	1.48204i
$507$		0			0
$508$	9130.21	+	11133.9i	0.797417	+	0.972418i
$509$		−	4197.35i		−	0.365509i	−0.983159	−	0.182755i	$-0.941499\pi$
$509$		−	4197.35i		−	0.365509i	0.983159	−	0.182755i	$-0.0585014\pi$
$510$		0			0
$511$	−12113.8			−1.04869
$512$	7765.29	+	8597.56i	0.670275	+	0.742113i
$513$		0			0
$514$	−978.941	−	463.235i	−0.0840063	−	0.0397518i
$515$			243.140i			0.0208039i
$516$		0			0
$517$		−	7780.73i		−	0.661888i
$518$	11236.0	−	23744.8i	0.953057	−	2.01407i
$519$		0			0
$520$	177.799	+	711.558i	0.0149943	+	0.0600074i
$521$	15755.5			1.32488			0.662440	−	0.749115i	$-0.269521\pi$
$521$	15755.5			1.32488			0.662440	+	0.749115i	$0.269521\pi$
$522$		0			0
$523$			11555.1i			0.966098i	0.875593	+	0.483049i	$0.160471\pi$
$523$			11555.1i			0.966098i	−0.875593	+	0.483049i	$0.839529\pi$
$524$	6937.31	−	5688.84i	0.578355	−	0.474271i
$525$		0			0
$526$	−12788.3	−	6051.44i	−1.06007	−	0.501626i
$527$	10417.7			0.861102
$528$		0			0
$529$	−179.314			−0.0147378
$530$	184.546	+	87.3274i	0.0151249	+	0.00715709i
$531$		0			0
$532$	4103.30	−	3364.85i	0.334399	−	0.274219i
$533$			19085.5i			1.55100i
$534$		0			0
$535$	−214.817			−0.0173595
$536$	1962.72	−	490.432i	0.158165	−	0.0395213i
$537$		0			0
$538$	7400.92	−	15640.1i	0.593079	−	1.25334i
$539$			10503.6i			0.839373i
$540$		0			0
$541$			7475.65i			0.594091i	0.954863	+	0.297045i	$0.0960013\pi$
$541$			7475.65i			0.594091i	−0.954863	+	0.297045i	$0.903999\pi$
$542$	10114.4	+	4786.12i	0.801566	+	0.379301i
$543$		0			0
$544$	−5092.46	+	6852.60i	−0.401356	+	0.540079i
$545$	−365.764			−0.0287479
$546$		0			0
$547$		−	6028.08i		−	0.471192i	−0.971851	−	0.235596i	$-0.924296\pi$
$547$		−	6028.08i		−	0.471192i	0.971851	−	0.235596i	$-0.0757043\pi$
$548$	−12426.0	−	15153.0i	−0.968636	−	1.18121i
$549$		0			0
$550$	9085.90	−	19201.0i	0.704408	−	1.48860i
$551$	−304.037			−0.0235071
$552$		0			0
$553$	3788.29			0.291310
$554$	5858.06	−	12379.7i	0.449251	−	0.949389i
$555$		0			0
$556$	−15202.6	+	12466.6i	−1.15959	+	0.950904i
$557$		−	19381.5i		−	1.47436i	−0.675696	−	0.737181i	$-0.736157\pi$
$557$		−	19381.5i		−	1.47436i	0.675696	−	0.737181i	$-0.263843\pi$
$558$		0			0
$559$	−12507.7			−0.946370
$560$	874.535	+	174.656i	0.0659926	+	0.0131796i
$561$		0			0
$562$	4803.10	+	2272.83i	0.360510	+	0.170593i
$563$			20565.0i			1.53946i	0.638372	+	0.769728i	$0.279608\pi$
$563$			20565.0i			1.53946i	−0.638372	+	0.769728i	$0.720392\pi$
$564$		0			0
$565$		−	304.139i		−	0.0226464i
$566$	6925.95	−	14636.4i	0.514345	−	1.08695i
$567$		0			0
$568$	−1922.73	−	7694.80i	−0.142035	−	0.568427i
$569$	−15252.9			−1.12379			−0.561895	−	0.827209i	$-0.689927\pi$
$569$	−15252.9			−1.12379			−0.561895	+	0.827209i	$0.689927\pi$
$570$		0			0
$571$		−	16492.8i		−	1.20876i	−0.796697	−	0.604379i	$-0.793421\pi$
$571$		−	16492.8i		−	1.20876i	0.796697	−	0.604379i	$-0.206579\pi$
$572$	−16173.4	−	19722.8i	−1.18225	−	1.44170i
$573$		0			0
$574$	20976.6	+	9926.13i	1.52534	+	0.721792i
$575$	−13644.9			−0.989623
$576$		0			0
$577$	−10298.2			−0.743016			−0.371508	−	0.928430i	$-0.621159\pi$
$577$	−10298.2			−0.743016			−0.371508	+	0.928430i	$0.621159\pi$
$578$	6873.60	+	3252.59i	0.494644	+	0.234065i
$579$		0			0
$580$	−32.3997	−	39.5101i	−0.00231952	−	0.00282857i
$581$		−	8231.89i		−	0.587808i
$582$		0			0
$583$	−7100.14			−0.504387
$584$	−2921.55	−	11692.1i	−0.207011	−	0.828464i
$585$		0			0
$586$	6156.38	−	13010.1i	0.433989	−	0.917136i
$587$			13104.8i			0.921453i	0.887542	+	0.460727i	$0.152411\pi$
$587$			13104.8i			0.921453i	−0.887542	+	0.460727i	$0.847589\pi$
$588$		0			0
$589$		−	6441.82i		−	0.450646i
$590$	−411.722	−	194.827i	−0.0287294	−	0.0135948i
$591$		0			0
$592$	25628.2	+	5118.27i	1.77924	+	0.355337i
$593$	−4163.34			−0.288310			−0.144155	−	0.989555i	$-0.546046\pi$
$593$	−4163.34			−0.288310			−0.144155	+	0.989555i	$0.546046\pi$
$594$		0			0
$595$			657.208i			0.0452822i
$596$	−12897.6	+	10576.5i	−0.886423	+	0.726898i
$597$		0			0
$598$	−7007.90	+	14809.6i	−0.479221	+	1.01272i
$599$	5718.60			0.390076			0.195038	−	0.980796i	$-0.437517\pi$
$599$	5718.60			0.390076			0.195038	+	0.980796i	$0.437517\pi$
$600$		0			0
$601$	17473.0			1.18592			0.592959	−	0.805233i	$-0.297960\pi$
$601$	17473.0			1.18592			0.592959	+	0.805233i	$0.297960\pi$
$602$	−6505.13	+	13747.1i	−0.440414	+	0.930713i
$603$		0			0
$604$	5365.98	+	6543.60i	0.361488	+	0.440820i
$605$		−	1409.50i		−	0.0947181i
$606$		0			0
$607$	−5647.60			−0.377643			−0.188821	−	0.982011i	$-0.560467\pi$
$607$	−5647.60			−0.377643			−0.188821	+	0.982011i	$0.560467\pi$
$608$	4237.34	+	3148.95i	0.282643	+	0.210044i
$609$		0			0
$610$	428.342	+	202.691i	0.0284312	+	0.0134537i
$611$		−	6830.87i		−	0.452287i
$612$		0			0
$613$			16023.6i			1.05577i	0.849317	+	0.527884i	$0.177014\pi$
$613$			16023.6i			1.05577i	−0.849317	+	0.527884i	$0.822986\pi$
$614$	−8733.81	+	18456.9i	−0.574052	+	1.21313i
$615$		0			0
$616$	−30088.7	+	7518.37i	−1.96803	+	0.491760i
$617$	21022.1			1.37167			0.685834	−	0.727758i	$-0.259438\pi$
$617$	21022.1			1.37167			0.685834	+	0.727758i	$0.259438\pi$
$618$		0			0
$619$			17824.2i			1.15737i	0.815550	+	0.578686i	$0.196434\pi$
$619$			17824.2i			1.15737i	−0.815550	+	0.578686i	$0.803566\pi$
$620$	837.125	−	686.472i	0.0542254	−	0.0444667i
$621$		0			0
$622$	−3929.69	−	1859.53i	−0.253322	−	0.119872i
$623$	917.238			0.0589861
$624$		0			0
$625$	15484.4			0.991001
$626$	5626.97	+	2662.68i	0.359263	+	0.170004i
$627$		0			0
$628$	−19752.0	+	16197.4i	−1.25508	+	1.02921i
$629$			19259.4i			1.22086i
$630$		0			0
$631$	−22339.0			−1.40935			−0.704677	−	0.709528i	$-0.748908\pi$
$631$	−22339.0			−1.40935			−0.704677	+	0.709528i	$0.748908\pi$
$632$	913.644	+	3656.42i	0.0575044	+	0.230134i
$633$		0			0
$634$	3436.33	−	7261.89i	0.215259	−	0.454900i
$635$			1102.70i			0.0689121i
$636$		0			0
$637$			9221.34i			0.573568i
$638$	1606.18	+	760.046i	0.0996698	+	0.0471638i
$639$		0			0
$640$	42.3406	+	886.217i	0.00261509	+	0.0547356i
$641$	5268.43			0.324634			0.162317	−	0.986739i	$-0.448103\pi$
$641$	5268.43			0.324634			0.162317	+	0.986739i	$0.448103\pi$
$642$		0			0
$643$			21965.8i			1.34719i	0.739099	+	0.673597i	$0.235252\pi$
$643$			21965.8i			1.34719i	−0.739099	+	0.673597i	$0.764748\pi$
$644$	12632.3	+	15404.6i	0.772953	+	0.942586i
$645$		0			0
$646$	−1664.09	+	3516.68i	−0.101351	+	0.214182i
$647$	−3165.40			−0.192341			−0.0961706	−	0.995365i	$-0.530659\pi$
$647$	−3165.40			−0.192341			−0.0961706	+	0.995365i	$0.530659\pi$
$648$		0			0
$649$	15840.4			0.958073
$650$	7976.71	−	16856.9i	0.481342	−	1.01721i
$651$		0			0
$652$	5238.67	−	4295.89i	0.314666	−	0.258037i
$653$		−	12094.7i		−	0.724814i	−0.932020	−	0.362407i	$-0.881955\pi$
$653$		−	12094.7i		−	0.724814i	0.932020	−	0.362407i	$-0.118045\pi$
$654$		0			0
$655$	687.067			0.0409861
$656$	−4521.57	+	22640.4i	−0.269112	+	1.34750i
$657$		0			0
$658$	−7507.72	−	3552.66i	−0.444805	−	0.210482i
$659$		−	7523.17i		−	0.444706i	−0.974966	−	0.222353i	$-0.928626\pi$
$659$		−	7523.17i		−	0.444706i	0.974966	−	0.222353i	$-0.0713737\pi$
$660$		0			0
$661$		−	24141.1i		−	1.42054i	−0.703928	−	0.710271i	$-0.748572\pi$
$661$		−	24141.1i		−	1.42054i	0.703928	−	0.710271i	$-0.251428\pi$
$662$	−2562.98	+	5416.28i	−0.150473	+	0.317990i
$663$		0			0
$664$	7945.36	−	1985.33i	0.464367	−	0.116033i
$665$	406.388			0.0236978
$666$		0			0
$667$		−	1141.41i		−	0.0662604i
$668$	13342.1	+	16270.2i	0.772789	+	0.942385i
$669$		0			0
$670$	140.044	+	66.2688i	0.00807518	+	0.00382118i
$671$	−16479.8			−0.948130
$672$		0			0
$673$	944.143			0.0540773			0.0270387	−	0.999634i	$-0.491392\pi$
$673$	944.143			0.0540773			0.0270387	+	0.999634i	$0.491392\pi$
$674$	1686.35	+	797.983i	0.0963738	+	0.0456041i
$675$		0			0
$676$	−3054.12	−	3724.38i	−0.173766	−	0.211901i
$677$			4450.51i			0.252654i	0.991989	+	0.126327i	$0.0403189\pi$
$677$			4450.51i			0.252654i	−0.991989	+	0.126327i	$0.959681\pi$
$678$		0			0
$679$	13985.8			0.790468
$680$	−634.332	+	158.503i	−0.0357728	+	0.00893869i
$681$		0			0
$682$	−16103.5	+	34031.2i	−0.904160	+	1.91073i
$683$		−	1726.40i		−	0.0967189i	−0.998830	−	0.0483594i	$-0.984601\pi$
$683$		−	1726.40i		−	0.0967189i	0.998830	−	0.0483594i	$-0.0153993\pi$
$684$		0			0
$685$		−	1500.75i		−	0.0837088i
$686$	−9809.87	−	4642.03i	−0.545981	−	0.258358i
$687$		0			0
$688$	−14837.5	−	2963.23i	−0.822199	−	0.164204i
$689$	−6233.37			−0.344662
$690$		0			0
$691$			683.143i			0.0376092i	0.999823	+	0.0188046i	$0.00598605\pi$
$691$			683.143i			0.0376092i	−0.999823	+	0.0188046i	$0.994014\pi$
$692$	2659.02	−	2180.49i	0.146071	−	0.119783i
$693$		0			0
$694$	10135.0	−	21418.0i	0.554351	−	1.17149i
$695$	−1505.65			−0.0821764
$696$		0			0
$697$	−17014.1			−0.924614
$698$	−3936.91	+	8319.76i	−0.213487	+	0.451157i
$699$		0			0
$700$	−14378.7	−	17534.2i	−0.776375	−	0.946758i
$701$		−	19533.2i		−	1.05244i	−0.850349	−	0.526220i	$-0.823609\pi$
$701$		−	19533.2i		−	1.05244i	0.850349	−	0.526220i	$-0.176391\pi$
$702$		0			0
$703$	11909.2			0.638922
$704$	−14513.4	−	27228.1i	−0.776978	−	1.45767i
$705$		0			0
$706$	28423.4	+	13450.0i	1.51520	+	0.716991i
$707$		−	37868.8i		−	2.01443i
$708$		0			0
$709$		−	26081.9i		−	1.38156i	−0.723066	−	0.690779i	$-0.757268\pi$
$709$		−	26081.9i		−	1.38156i	0.723066	−	0.690779i	$-0.242732\pi$
$710$	259.805	−	549.038i	0.0137328	−	0.0290212i
$711$		0			0
$712$	221.216	+	885.311i	0.0116438	+	0.0465989i
$713$	24183.8			1.27025
$714$		0			0
$715$		−	1953.34i		−	0.102169i
$716$	−9379.89	+	7691.84i	−0.489585	+	0.401477i
$717$		0			0
$718$	−12160.8	−	5754.49i	−0.632085	−	0.299103i
$719$	30077.3			1.56007			0.780036	−	0.625734i	$-0.215200\pi$
$719$	30077.3			1.56007			0.780036	+	0.625734i	$0.215200\pi$
$720$		0			0
$721$	−9026.21			−0.466232
$722$	−15361.4	−	7269.02i	−0.791818	−	0.374688i
$723$		0			0
$724$	20910.0	−	17147.0i	1.07336	−	0.880196i
$725$			1299.21i			0.0665537i
$726$		0			0
$727$	23049.9			1.17589			0.587946	−	0.808900i	$-0.299937\pi$
$727$	23049.9			1.17589			0.587946	+	0.808900i	$0.299937\pi$
$728$	−26415.5	+	6600.54i	−1.34481	+	0.336033i
$729$		0			0
$730$	394.769	−	834.254i	0.0200152	−	0.0422975i
$731$		−	11150.3i		−	0.564169i
$732$		0			0
$733$			4444.57i			0.223962i	0.993710	+	0.111981i	$0.0357195\pi$
$733$			4444.57i			0.223962i	−0.993710	+	0.111981i	$0.964280\pi$
$734$	−4697.56	−	2222.89i	−0.236226	−	0.111782i
$735$		0			0
$736$	−11821.8	+	15907.8i	−0.592060	+	0.796698i
$737$	−5387.98			−0.269293
$738$		0			0
$739$		−	28465.1i		−	1.41692i	−0.705749	−	0.708462i	$-0.749390\pi$
$739$		−	28465.1i		−	1.41692i	0.705749	−	0.708462i	$-0.250610\pi$
$740$	1269.10	+	1547.61i	0.0630446	+	0.0768803i
$741$		0			0
$742$	−3241.90	+	6851.01i	−0.160396	+	0.338960i
$743$	−4389.76			−0.216749			−0.108374	−	0.994110i	$-0.534565\pi$
$743$	−4389.76			−0.216749			−0.108374	+	0.994110i	$0.534565\pi$
$744$		0			0
$745$	−1277.38			−0.0628180
$746$	6772.55	−	14312.2i	0.332387	−	0.702423i
$747$		0			0
$748$	17582.3	−	14418.1i	0.859456	−	0.704784i
$749$		−	7974.77i		−	0.389041i
$750$		0			0
$751$	14121.9			0.686171			0.343085	−	0.939304i	$-0.388528\pi$
$751$	14121.9			0.686171			0.343085	+	0.939304i	$0.388528\pi$
$752$	1618.31	−	8103.21i	0.0784758	−	0.392944i
$753$		0			0
$754$	1410.10	+	667.260i	0.0681073	+	0.0322284i
$755$			648.074i			0.0312395i
$756$		0			0
$757$		−	17006.3i		−	0.816516i	−0.912866	−	0.408258i	$-0.866136\pi$
$757$		−	17006.3i		−	0.816516i	0.912866	−	0.408258i	$-0.133864\pi$
$758$	−4186.13	+	8846.42i	−0.200590	+	0.423900i
$759$		0			0
$760$	98.0110	+	392.243i	0.00467794	+	0.0187212i
$761$	4603.38			0.219280			0.109640	−	0.993971i	$-0.465030\pi$
$761$	4603.38			0.219280			0.109640	+	0.993971i	$0.465030\pi$
$762$		0			0
$763$		−	13578.5i		−	0.644264i
$764$	14202.3	+	17319.1i	0.672540	+	0.820136i
$765$		0			0
$766$	12935.6	+	6121.15i	0.610161	+	0.288728i
$767$	13906.6			0.654679
$768$		0			0
$769$	−12459.1			−0.584248			−0.292124	−	0.956380i	$-0.594362\pi$
$769$	−12459.1			−0.584248			−0.292124	+	0.956380i	$0.594362\pi$
$770$	−2146.89	−	1015.91i	−0.100478	−	0.0475465i
$771$		0			0
$772$	3165.94	+	3860.74i	0.147597	+	0.179989i
$773$			27068.1i			1.25947i	0.776808	+	0.629737i	$0.216837\pi$
$773$			27068.1i			1.25947i	−0.776808	+	0.629737i	$0.783163\pi$
$774$		0			0
$775$	−27527.2			−1.27588
$776$	3373.05	+	13499.0i	0.156038	+	0.624468i
$777$		0			0
$778$	−2652.15	+	5604.70i	−0.122216	+	0.258275i
$779$			10520.8i			0.483884i
$780$		0			0
$781$			21123.4i			0.967804i
$782$	−13202.3	−	6247.33i	−0.603725	−	0.285683i
$783$		0			0
$784$	−2184.64	+	10938.9i	−0.0995191	+	0.498312i
$785$	−1956.23			−0.0889438
$786$		0			0
$787$		−	6986.86i		−	0.316461i	−0.987402	−	0.158230i	$-0.949421\pi$
$787$		−	6986.86i		−	0.316461i	0.987402	−	0.158230i	$-0.0505789\pi$
$788$	29564.6	−	24244.0i	1.33654	−	1.09601i
$789$		0			0
$790$	−123.455	+	260.893i	−0.00555990	+	0.0117496i
$791$	11290.7			0.507523
$792$		0			0
$793$	−14468.0			−0.647885
$794$	6678.02	−	14112.5i	0.298481	−	0.630771i
$795$		0			0
$796$	13269.9	+	16182.1i	0.590879	+	0.720554i
$797$			27271.5i			1.21205i	0.795444	+	0.606027i	$0.207238\pi$
$797$			27271.5i			1.21205i	−0.795444	+	0.606027i	$0.792762\pi$
$798$		0			0
$799$	6089.52			0.269627
$800$	13456.1	−	18107.0i	0.594681	−	0.800224i
$801$		0			0
$802$	−18798.0	−	8895.23i	−0.827658	−	0.391648i
$803$			32096.7i			1.41054i
$804$		0			0
$805$			1525.66i			0.0667981i
$806$	−14137.7	+	29876.7i	−0.617838	+	1.30566i
$807$		0			0
$808$	36550.7	−	9133.06i	1.59140	−	0.397648i
$809$	−23785.9			−1.03371			−0.516853	−	0.856074i	$-0.672897\pi$
$809$	−23785.9			−1.03371			−0.516853	+	0.856074i	$0.672897\pi$
$810$		0			0
$811$			21703.5i			0.939718i	0.882741	+	0.469859i	$0.155695\pi$
$811$			21703.5i			0.939718i	−0.882741	+	0.469859i	$0.844305\pi$
$812$	1466.75	−	1202.79i	0.0633904	−	0.0519823i
$813$		0			0
$814$	−62914.3	−	29771.1i	−2.70902	−	1.28191i
$815$	518.835			0.0222994
$816$		0			0
$817$	−6894.83			−0.295250
$818$	28918.7	+	13684.3i	1.23608	+	0.584915i
$819$		0			0
$820$	−1367.19	+	1121.15i	−0.0582249	+	0.0477465i
$821$		−	33240.4i		−	1.41303i	−0.707698	−	0.706515i	$-0.750266\pi$
$821$		−	33240.4i		−	1.41303i	0.707698	−	0.706515i	$-0.249734\pi$
$822$		0			0
$823$	−17227.5			−0.729665			−0.364832	−	0.931073i	$-0.618874\pi$
$823$	−17227.5			−0.729665			−0.364832	+	0.931073i	$0.618874\pi$
$824$	−2176.90	−	8712.02i	−0.0920341	−	0.368322i
$825$		0			0
$826$	7232.67	−	15284.6i	0.304669	−	0.643848i
$827$		−	21678.4i		−	0.911528i	−0.890101	−	0.455764i	$-0.849366\pi$
$827$		−	21678.4i		−	0.911528i	0.890101	−	0.455764i	$-0.150634\pi$
$828$		0			0
$829$			34269.8i			1.43575i	0.696170	+	0.717877i	$0.254886\pi$
$829$			34269.8i			1.43575i	−0.696170	+	0.717877i	$0.745114\pi$
$830$	566.916	+	268.265i	0.0237084	+	0.0112188i
$831$		0			0
$832$	−12741.6	−	23904.2i	−0.530931	−	0.996067i
$833$	−8220.55			−0.341927
$834$		0			0
$835$			1611.39i			0.0667838i
$836$	−8915.51	−	10872.1i	−0.368839	−	0.449784i
$837$		0			0
$838$	−15778.4	+	33344.1i	−0.650426	+	1.37453i
$839$	−33444.1			−1.37618			−0.688092	−	0.725623i	$-0.741552\pi$
$839$	−33444.1			−1.37618			−0.688092	+	0.725623i	$0.741552\pi$
$840$		0			0
$841$	24280.3			0.995544
$842$	−5497.80	+	11618.3i	−0.225020	+	0.475527i
$843$		0			0
$844$	10799.5	−	8855.95i	0.440442	−	0.361178i
$845$		−	368.860i		−	0.0150168i
$846$		0			0
$847$	52325.8			2.12271
$848$	−7394.41	−	1476.76i	−0.299440	−	0.0598020i
$849$		0			0
$850$	15027.5	+	7111.00i	0.606397	+	0.286947i
$851$			44709.3i			1.80096i
$852$		0			0
$853$			37037.3i			1.48667i	0.668917	+	0.743337i	$0.266758\pi$
$853$			37037.3i			1.48667i	−0.668917	+	0.743337i	$0.733242\pi$
$854$	−7524.62	+	15901.6i	−0.301507	+	0.637166i
$855$		0			0
$856$	7697.19	−	1923.32i	0.307342	−	0.0767966i
$857$	−35794.2			−1.42673			−0.713365	−	0.700793i	$-0.752830\pi$
$857$	−35794.2			−1.42673			−0.713365	+	0.700793i	$0.752830\pi$
$858$		0			0
$859$		−	20582.1i		−	0.817522i	−0.912641	−	0.408761i	$-0.865961\pi$
$859$		−	20582.1i		−	0.817522i	0.912641	−	0.408761i	$-0.134039\pi$
$860$	−734.747	−	895.994i	−0.0291333	−	0.0355269i
$861$		0			0
$862$	19721.4	+	9332.19i	0.779252	+	0.368742i
$863$	25677.7			1.01284			0.506420	−	0.862287i	$-0.330969\pi$
$863$	25677.7			1.01284			0.506420	+	0.862287i	$0.330969\pi$
$864$		0			0
$865$	263.348			0.0103516
$866$	38524.0	+	18229.6i	1.51166	+	0.715319i
$867$		0			0
$868$	25484.2	+	31077.0i	0.996534	+	1.21523i
$869$		−	10037.5i		−	0.391827i
$870$		0			0
$871$	−4730.22			−0.184015
$872$	13105.8	−	3274.80i	0.508967	−	0.127177i
$873$		0			0
$874$	−3863.07	+	8163.71i	−0.149508	+	0.315951i
$875$		−	3478.38i		−	0.134389i
$876$		0			0
$877$			32783.0i			1.26226i	0.775676	+	0.631131i	$0.217409\pi$
$877$			32783.0i			1.26226i	−0.775676	+	0.631131i	$0.782591\pi$
$878$	−28135.0	−	13313.5i	−1.08145	−	0.511742i
$879$		0			0
$880$	462.768	−	2317.17i	0.0177272	−	0.0887634i
$881$	−26615.7			−1.01783			−0.508914	−	0.860818i	$-0.669953\pi$
$881$	−26615.7			−1.01783			−0.508914	+	0.860818i	$0.669953\pi$
$882$		0			0
$883$			19203.4i			0.731875i	0.930639	+	0.365937i	$0.119252\pi$
$883$			19203.4i			0.731875i	−0.930639	+	0.365937i	$0.880748\pi$
$884$	15435.9	−	12658.0i	0.587291	−	0.481599i
$885$		0			0
$886$	−3040.28	+	6424.93i	−0.115282	+	0.243623i
$887$	−23198.0			−0.878144			−0.439072	−	0.898452i	$-0.644693\pi$
$887$	−23198.0			−0.878144			−0.439072	+	0.898452i	$0.644693\pi$
$888$		0			0
$889$	−40936.0			−1.54438
$890$	−29.8914	+	63.1686i	−0.00112580	+	0.00237912i
$891$		0			0
$892$	−17174.4	−	20943.4i	−0.644664	−	0.786142i
$893$		−	3765.48i		−	0.141105i
$894$		0			0
$895$	−928.979			−0.0346953
$896$	−32899.5	+	1571.83i	−1.22667	+	0.0586063i
$897$		0			0
$898$	−40273.8	−	19057.6i	−1.49661	−	0.708195i
$899$		−	2302.68i		−	0.0854266i
$900$		0			0
$901$		−	5556.86i		−	0.205467i
$902$	26300.3	−	55579.7i	0.970848	−	2.05166i
$903$		0			0
$904$	2723.05	+	10897.7i	0.100185	+	0.400942i
$905$	2070.92			0.0760659
$906$		0			0
$907$		−	16151.3i		−	0.591285i	−0.955299	−	0.295643i	$-0.904466\pi$
$907$		−	16151.3i		−	0.591285i	0.955299	−	0.295643i	$-0.0955337\pi$
$908$	23802.1	−	19518.6i	0.869935	−	0.713377i
$909$		0			0
$910$	−1884.80	−	891.887i	−0.0686599	−	0.0324899i
$911$	3487.34			0.126829			0.0634143	−	0.997987i	$-0.479801\pi$
$911$	3487.34			0.126829			0.0634143	+	0.997987i	$0.479801\pi$
$912$		0			0
$913$	−21811.2			−0.790632
$914$	13440.4	+	6359.99i	0.486398	+	0.230164i
$915$		0			0
$916$	−8259.27	+	6772.89i	−0.297919	+	0.244304i
$917$			25506.3i			0.918532i
$918$		0			0
$919$	17055.5			0.612198			0.306099	−	0.952000i	$-0.400976\pi$
$919$	17055.5			0.612198			0.306099	+	0.952000i	$0.400976\pi$
$920$	−1472.55	+	367.953i	−0.0527703	+	0.0131859i
$921$		0			0
$922$	9758.62	−	20622.6i	0.348572	−	0.736626i
$923$			18544.7i			0.661329i
$924$		0			0
$925$		−	50890.2i		−	1.80893i
$926$	−14530.4	−	6875.81i	−0.515659	−	0.244010i
$927$		0			0
$928$	1514.67	+	1125.62i	0.0535792	+	0.0398170i
$929$	55339.3			1.95438			0.977192	−	0.212359i	$-0.0681146\pi$
$929$	55339.3			1.95438			0.977192	+	0.212359i	$0.0681146\pi$
$930$		0			0
$931$			5083.22i			0.178943i
$932$	26106.4	+	31835.7i	0.917536	+	1.11890i
$933$		0			0
$934$	13476.4	−	28479.2i	0.472120	−	0.997717i
$935$	1741.34			0.0609069
$936$		0			0
$937$	−20457.6			−0.713255			−0.356627	−	0.934247i	$-0.616073\pi$
$937$	−20457.6			−0.713255			−0.356627	+	0.934247i	$0.616073\pi$
$938$	−2460.13	+	5198.92i	−0.0856356	+	0.180971i
$939$		0			0
$940$	489.331	−	401.268i	0.0169789	−	0.0139233i
$941$			55891.0i			1.93623i	0.250502	+	0.968116i	$0.419404\pi$
$941$			55891.0i			1.93623i	−0.250502	+	0.968116i	$0.580596\pi$
$942$		0			0
$943$	−39497.0			−1.36395
$944$	16496.9	+	3294.64i	0.568780	+	0.113593i
$945$		0			0
$946$	36424.3	+	17236.0i	1.25186	+	0.592379i
$947$		−	54727.0i		−	1.87792i	−0.344027	−	0.938960i	$-0.611791\pi$
$947$		−	54727.0i		−	1.87792i	0.344027	−	0.938960i	$-0.388209\pi$
$948$		0			0
$949$			28178.4i			0.963865i
$950$	4397.12	−	9292.31i	0.150170	−	0.317350i
$951$		0			0
$952$	−5884.19	−	23548.7i	−0.200323	−	0.801698i
$953$	−29958.8			−1.01832			−0.509160	−	0.860672i	$-0.670044\pi$
$953$	−29958.8			−1.01832			−0.509160	+	0.860672i	$0.670044\pi$
$954$		0			0
$955$			1715.27i			0.0581204i
$956$	−35940.9	−	43828.5i	−1.21591	−	1.48276i
$957$		0			0
$958$	8890.31	+	4206.90i	0.299825	+	0.141877i
$959$	55713.0			1.87598
$960$		0			0
$961$	18997.2			0.637682
$962$	−55233.8	−	26136.7i	−1.85115	−	0.875966i
$963$		0			0
$964$	12876.7	+	15702.6i	0.430219	+	0.524634i
$965$			382.365i			0.0127552i
$966$		0			0
$967$	13498.5			0.448896			0.224448	−	0.974486i	$-0.427942\pi$
$967$	13498.5			0.448896			0.224448	+	0.974486i	$0.427942\pi$
$968$	12619.7	+	50504.4i	0.419022	+	1.67694i
$969$		0			0
$970$	−455.778	+	963.182i	−0.0150867	+	0.0318824i
$971$			9652.36i			0.319010i	0.987197	+	0.159505i	$0.0509899\pi$
$971$			9652.36i			0.319010i	−0.987197	+	0.159505i	$0.949010\pi$
$972$		0			0
$973$		−	55895.1i		−	1.84164i
$974$	1224.11	+	579.249i	0.0402700	+	0.0190558i
$975$		0			0
$976$	−17162.8	−	3427.63i	−0.562877	−	0.112414i
$977$	−12169.8			−0.398511			−0.199256	−	0.979948i	$-0.563852\pi$
$977$	−12169.8			−0.398511			−0.199256	+	0.979948i	$0.563852\pi$
$978$		0			0
$979$		−	2430.32i		−	0.0793394i
$980$	−660.573	+	541.693i	−0.0215319	+	0.0176569i
$981$		0			0
$982$	−20084.8	+	42444.7i	−0.652681	+	1.37929i
$983$	−47545.2			−1.54268			−0.771341	−	0.636423i	$-0.780413\pi$
$983$	−47545.2			−1.54268			−0.771341	+	0.636423i	$0.780413\pi$
$984$		0			0
$985$	2928.06			0.0947165
$986$	−594.843	+	1257.06i	−0.0192126	+	0.0406015i
$987$		0			0
$988$	−7827.12	−	9544.86i	−0.252038	−	0.307351i
$989$		−	25884.5i		−	0.832234i
$990$		0			0
$991$	−892.350			−0.0286039			−0.0143019	−	0.999898i	$-0.504553\pi$
$991$	−892.350			−0.0286039			−0.0143019	+	0.999898i	$0.504553\pi$
$992$	−23849.1	+	32092.2i	−0.763317	+	1.02715i
$993$		0			0
$994$	20382.2	+	9644.88i	0.650388	+	0.307764i
$995$			1602.67i			0.0510634i
$996$		0			0
$997$		−	4458.57i		−	0.141629i	−0.997489	−	0.0708146i	$-0.977440\pi$
$997$		−	4458.57i		−	0.141629i	0.997489	−	0.0708146i	$-0.0225599\pi$
$998$	−11471.6	+	24242.5i	−0.363854	+	0.768921i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.4.d.d.37.1		6
3.2	odd	2		24.4.d.a.13.6	yes	6
4.3	odd	2		288.4.d.d.145.4		6
8.3	odd	2		288.4.d.d.145.3		6
8.5	even	2	inner	72.4.d.d.37.2		6
12.11	even	2		96.4.d.a.49.5		6
16.3	odd	4		2304.4.a.bw.1.2		3
16.5	even	4		2304.4.a.bt.1.2		3
16.11	odd	4		2304.4.a.bu.1.2		3
16.13	even	4		2304.4.a.bv.1.2		3
24.5	odd	2		24.4.d.a.13.5	✓	6
24.11	even	2		96.4.d.a.49.2		6
48.5	odd	4		768.4.a.r.1.2		3
48.11	even	4		768.4.a.t.1.2		3
48.29	odd	4		768.4.a.s.1.2		3
48.35	even	4		768.4.a.q.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.4.d.a.13.5	✓	6	24.5	odd	2
24.4.d.a.13.6	yes	6	3.2	odd	2
72.4.d.d.37.1		6	1.1	even	1	trivial
72.4.d.d.37.2		6	8.5	even	2	inner
96.4.d.a.49.2		6	24.11	even	2
96.4.d.a.49.5		6	12.11	even	2
288.4.d.d.145.3		6	8.3	odd	2
288.4.d.d.145.4		6	4.3	odd	2
768.4.a.q.1.2		3	48.35	even	4
768.4.a.r.1.2		3	48.5	odd	4
768.4.a.s.1.2		3	48.29	odd	4
768.4.a.t.1.2		3	48.11	even	4
2304.4.a.bt.1.2		3	16.5	even	4
2304.4.a.bu.1.2		3	16.11	odd	4
2304.4.a.bv.1.2		3	16.13	even	4
2304.4.a.bw.1.2		3	16.3	odd	4

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	72.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.55664 - 1.20980i) q^{2} +(5.07277 + 6.18604i) q^{4} +0.612661i q^{5} -22.7441 q^{7} +(-5.48534 - 21.9525i) q^{8} +O(q^{10})\)	\(q+(-2.55664 - 1.20980i) q^{2} +(5.07277 + 6.18604i) q^{4} +0.612661i q^{5} -22.7441 q^{7} +(-5.48534 - 21.9525i) q^{8} +(0.741198 - 1.56635i) q^{10} +60.2630i q^{11} +52.9062i q^{13} +(58.1485 + 27.5159i) q^{14} +(-12.5341 + 62.7606i) q^{16} -47.1643 q^{17} +29.1643i q^{19} +(-3.78994 + 3.10789i) q^{20} +(72.9062 - 154.070i) q^{22} -109.488 q^{23} +124.625 q^{25} +(64.0059 - 135.262i) q^{26} +(-115.376 - 140.696i) q^{28} +10.4250i q^{29} -220.881 q^{31} +(107.973 - 145.292i) q^{32} +(120.582 + 57.0593i) q^{34} -13.9345i q^{35} -408.348i q^{37} +(35.2829 - 74.5624i) q^{38} +(13.4494 - 3.36066i) q^{40} +360.742 q^{41} +236.414i q^{43} +(-372.789 + 305.700i) q^{44} +(279.922 + 132.459i) q^{46} -129.113 q^{47} +174.296 q^{49} +(-318.620 - 150.771i) q^{50} +(-327.279 + 268.381i) q^{52} +117.819i q^{53} -36.9208 q^{55} +(124.759 + 499.290i) q^{56} +(12.6122 - 26.6529i) q^{58} -262.854i q^{59} +273.465i q^{61} +(564.711 + 267.221i) q^{62} +(-451.822 + 240.834i) q^{64} -32.4135 q^{65} +89.4077i q^{67} +(-239.253 - 291.760i) q^{68} +(-16.8579 + 35.6253i) q^{70} +350.521 q^{71} +532.610 q^{73} +(-494.019 + 1044.00i) q^{74} +(-180.411 + 147.943i) q^{76} -1370.63i q^{77} -166.561 q^{79} +(-38.4510 - 7.67915i) q^{80} +(-922.286 - 436.426i) q^{82} +361.934i q^{83} -28.8957i q^{85} +(286.013 - 604.423i) q^{86} +(1322.92 - 330.563i) q^{88} -40.3285 q^{89} -1203.31i q^{91} +(-555.408 - 677.299i) q^{92} +(330.095 + 156.201i) q^{94} -17.8678 q^{95} -614.921 q^{97} +(-445.612 - 210.864i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 76 q^{8}+O(q^{10}) \) 6 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 76 * q^8	\( 6 q - 2 q^{2} + 16 q^{4} + 28 q^{7} + 76 q^{8} + 60 q^{10} + 100 q^{14} + 56 q^{16} - 52 q^{17} - 56 q^{20} + 224 q^{22} - 328 q^{23} - 106 q^{25} - 56 q^{26} - 352 q^{28} - 636 q^{31} + 248 q^{32} - 548 q^{34} + 776 q^{38} + 232 q^{40} - 236 q^{41} - 1152 q^{44} + 328 q^{46} + 408 q^{47} + 654 q^{49} - 1970 q^{50} - 368 q^{52} + 1024 q^{55} + 1864 q^{56} + 140 q^{58} + 2108 q^{62} + 832 q^{64} + 1744 q^{65} - 2976 q^{68} + 1352 q^{70} + 1704 q^{71} + 956 q^{73} - 1568 q^{74} - 1744 q^{76} - 44 q^{79} + 2112 q^{80} - 2236 q^{82} + 760 q^{86} + 1856 q^{88} + 220 q^{89} - 1728 q^{92} + 2088 q^{94} - 5104 q^{95} - 2444 q^{97} - 3354 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 + 16 * q^4 + 28 * q^7 + 76 * q^8 + 60 * q^10 + 100 * q^14 + 56 * q^16 - 52 * q^17 - 56 * q^20 + 224 * q^22 - 328 * q^23 - 106 * q^25 - 56 * q^26 - 352 * q^28 - 636 * q^31 + 248 * q^32 - 548 * q^34 + 776 * q^38 + 232 * q^40 - 236 * q^41 - 1152 * q^44 + 328 * q^46 + 408 * q^47 + 654 * q^49 - 1970 * q^50 - 368 * q^52 + 1024 * q^55 + 1864 * q^56 + 140 * q^58 + 2108 * q^62 + 832 * q^64 + 1744 * q^65 - 2976 * q^68 + 1352 * q^70 + 1704 * q^71 + 956 * q^73 - 1568 * q^74 - 1744 * q^76 - 44 * q^79 + 2112 * q^80 - 2236 * q^82 + 760 * q^86 + 1856 * q^88 + 220 * q^89 - 1728 * q^92 + 2088 * q^94 - 5104 * q^95 - 2444 * q^97 - 3354 * q^98

Introduction

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