LMFDB - Embedded newform 243.4.e.c.28.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,4,Mod(28,243)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("243.28");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	243.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$14.3374641314$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			28.3
Character	$\chi$	$=$	243.28
Dual form			243.4.e.c.217.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.336951 - 1.91095i) q^{2} +(3.97937 - 1.44837i) q^{4} +(-2.07510 - 1.74122i) q^{5} +(11.1989 + 4.07607i) q^{7} +(-11.8703 - 20.5600i) q^{8} +O(q^{10})$	\(q+(-0.336951 - 1.91095i) q^{2} +(3.97937 - 1.44837i) q^{4} +(-2.07510 - 1.74122i) q^{5} +(11.1989 + 4.07607i) q^{7} +(-11.8703 - 20.5600i) q^{8} +(-2.62817 + 4.55212i) q^{10} +(-17.1606 + 14.3994i) q^{11} +(11.6626 - 66.1418i) q^{13} +(4.01566 - 22.7739i) q^{14} +(-9.33721 + 7.83485i) q^{16} +(44.8404 - 77.6659i) q^{17} +(39.1643 + 67.8345i) q^{19} +(-10.7795 - 3.92343i) q^{20} +(33.2988 + 27.9410i) q^{22} +(-93.6813 + 34.0972i) q^{23} +(-20.4318 - 115.875i) q^{25} -130.323 q^{26} +50.4682 q^{28} +(-18.9063 - 107.223i) q^{29} +(209.492 - 76.2489i) q^{31} +(-127.373 - 106.878i) q^{32} +(-163.524 - 59.5180i) q^{34} +(-16.1416 - 27.9580i) q^{35} +(-38.3904 + 66.4941i) q^{37} +(116.432 - 97.6977i) q^{38} +(-11.1673 + 63.3329i) q^{40} +(65.9957 - 374.280i) q^{41} +(-356.376 + 299.035i) q^{43} +(-47.4325 + 82.1555i) q^{44} +(96.7239 + 167.531i) q^{46} +(-355.160 - 129.268i) q^{47} +(-153.952 - 129.181i) q^{49} +(-214.545 + 78.0881i) q^{50} +(-49.3881 - 280.094i) q^{52} -0.995976 q^{53} +60.6826 q^{55} +(-49.1306 - 278.633i) q^{56} +(-198.527 + 72.2578i) q^{58} +(491.816 + 412.683i) q^{59} +(347.048 + 126.315i) q^{61} +(-216.296 - 374.636i) q^{62} +(-210.076 + 363.862i) q^{64} +(-139.368 + 116.944i) q^{65} +(74.2357 - 421.012i) q^{67} +(65.9474 - 374.007i) q^{68} +(-47.9873 + 40.2661i) q^{70} +(29.7664 - 51.5569i) q^{71} +(-157.281 - 272.418i) q^{73} +(140.002 + 50.9567i) q^{74} +(254.098 + 213.214i) q^{76} +(-250.873 + 91.3102i) q^{77} +(30.3749 + 172.265i) q^{79} +33.0179 q^{80} -737.467 q^{82} +(141.340 + 801.580i) q^{83} +(-228.282 + 83.0878i) q^{85} +(691.520 + 580.254i) q^{86} +(499.753 + 181.895i) q^{88} +(511.446 + 885.851i) q^{89} +(400.206 - 693.177i) q^{91} +(-323.407 + 271.371i) q^{92} +(-127.352 + 722.248i) q^{94} +(36.8448 - 208.957i) q^{95} +(618.233 - 518.759i) q^{97} +(-194.984 + 337.722i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 3 q^{2} + 3 q^{4} - 21 q^{5} + 3 q^{7} - 75 q^{8}+O(q^{10}) $ 48 * q + 3 * q^2 + 3 * q^4 - 21 * q^5 + 3 * q^7 - 75 * q^8	$ 48 q + 3 q^{2} + 3 q^{4} - 21 q^{5} + 3 q^{7} - 75 q^{8} - 3 q^{10} - 159 q^{11} + 3 q^{13} - 336 q^{14} - 45 q^{16} - 207 q^{17} - 3 q^{19} + 681 q^{20} + 111 q^{22} + 33 q^{23} + 435 q^{25} + 1914 q^{26} - 12 q^{28} - 51 q^{29} + 111 q^{31} + 1647 q^{32} - 513 q^{34} - 1257 q^{35} - 3 q^{37} - 525 q^{38} - 6 q^{40} + 447 q^{41} + 516 q^{43} - 2211 q^{44} - 3 q^{46} + 2109 q^{47} - 591 q^{49} - 4938 q^{50} - 1350 q^{52} + 2736 q^{53} - 12 q^{55} - 7773 q^{56} - 888 q^{58} + 3048 q^{59} + 57 q^{61} - 2118 q^{62} - 195 q^{64} + 3297 q^{65} + 2082 q^{67} + 3573 q^{68} + 1524 q^{70} - 3105 q^{71} - 219 q^{73} + 9006 q^{74} - 1425 q^{76} - 8985 q^{77} - 1401 q^{79} + 9870 q^{80} - 12 q^{82} - 8511 q^{83} - 1827 q^{85} + 12507 q^{86} - 3693 q^{88} - 5202 q^{89} + 267 q^{91} + 5118 q^{92} - 2211 q^{94} + 5178 q^{95} + 1569 q^{97} - 4392 q^{98}+O(q^{100}) $ 48 * q + 3 * q^2 + 3 * q^4 - 21 * q^5 + 3 * q^7 - 75 * q^8 - 3 * q^10 - 159 * q^11 + 3 * q^13 - 336 * q^14 - 45 * q^16 - 207 * q^17 - 3 * q^19 + 681 * q^20 + 111 * q^22 + 33 * q^23 + 435 * q^25 + 1914 * q^26 - 12 * q^28 - 51 * q^29 + 111 * q^31 + 1647 * q^32 - 513 * q^34 - 1257 * q^35 - 3 * q^37 - 525 * q^38 - 6 * q^40 + 447 * q^41 + 516 * q^43 - 2211 * q^44 - 3 * q^46 + 2109 * q^47 - 591 * q^49 - 4938 * q^50 - 1350 * q^52 + 2736 * q^53 - 12 * q^55 - 7773 * q^56 - 888 * q^58 + 3048 * q^59 + 57 * q^61 - 2118 * q^62 - 195 * q^64 + 3297 * q^65 + 2082 * q^67 + 3573 * q^68 + 1524 * q^70 - 3105 * q^71 - 219 * q^73 + 9006 * q^74 - 1425 * q^76 - 8985 * q^77 - 1401 * q^79 + 9870 * q^80 - 12 * q^82 - 8511 * q^83 - 1827 * q^85 + 12507 * q^86 - 3693 * q^88 - 5202 * q^89 + 267 * q^91 + 5118 * q^92 - 2211 * q^94 + 5178 * q^95 + 1569 * q^97 - 4392 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	−0.336951	−	1.91095i	−0.119130	−	0.675621i	−0.984622	−	0.174698i	$-0.944105\pi$
$2$	−0.336951	−	1.91095i	−0.119130	−	0.675621i	0.865492	−	0.500923i	$-0.167006\pi$
$3$		0			0
$3$		0			0
$4$	3.97937	−	1.44837i	0.497421	−	0.181046i
$5$	−2.07510	−	1.74122i	−0.185603	−	0.155739i	0.545252	−	0.838272i	$-0.316434\pi$
$5$	−2.07510	−	1.74122i	−0.185603	−	0.155739i	−0.730855	+	0.682533i	$0.760878\pi$
$6$		0			0
$7$	11.1989	+	4.07607i	0.604684	+	0.220087i	0.626175	−	0.779682i	$-0.284619\pi$
$7$	11.1989	+	4.07607i	0.604684	+	0.220087i	−0.0214918	+	0.999769i	$0.506842\pi$
$8$	−11.8703	−	20.5600i	−0.524598	−	0.908631i
$9$		0			0
$10$	−2.62817	+	4.55212i	−0.0831099	+	0.143951i
$11$	−17.1606	+	14.3994i	−0.470374	+	0.394690i	−0.846931	−	0.531703i	$-0.821552\pi$
$11$	−17.1606	+	14.3994i	−0.470374	+	0.394690i	0.376557	+	0.926393i	$0.377108\pi$
$12$		0			0
$13$	11.6626	−	66.1418i	0.248817	−	1.41111i	−0.562642	−	0.826700i	$-0.690215\pi$
$13$	11.6626	−	66.1418i	0.248817	−	1.41111i	0.811459	−	0.584409i	$-0.198674\pi$
$14$	4.01566	−	22.7739i	0.0766592	−	0.434756i
$15$		0			0
$16$	−9.33721	+	7.83485i	−0.145894	+	0.122419i
$17$	44.8404	−	77.6659i	0.639729	−	1.10804i	−0.345763	−	0.938322i	$-0.612380\pi$
$17$	44.8404	−	77.6659i	0.639729	−	1.10804i	0.985492	−	0.169722i	$-0.0542869\pi$
$18$		0			0
$19$	39.1643	+	67.8345i	0.472889	+	0.819068i	0.999519	−	0.0310268i	$-0.00987773\pi$
$19$	39.1643	+	67.8345i	0.472889	+	0.819068i	−0.526629	+	0.850095i	$0.676544\pi$
$20$	−10.7795	−	3.92343i	−0.120519	−	0.0438653i
$21$		0			0
$22$	33.2988	+	27.9410i	0.322697	+	0.270775i
$23$	−93.6813	+	34.0972i	−0.849300	+	0.309120i	−0.729755	−	0.683709i	$-0.760366\pi$
$23$	−93.6813	+	34.0972i	−0.849300	+	0.309120i	−0.119545	+	0.992829i	$0.538144\pi$
$24$		0			0
$25$	−20.4318	−	115.875i	−0.163454	−	0.926996i
$26$	−130.323			−0.983017
$27$		0			0
$28$	50.4682			0.340628
$29$	−18.9063	−	107.223i	−0.121062	−	0.686579i	−0.983569	−	0.180533i	$-0.942218\pi$
$29$	−18.9063	−	107.223i	−0.121062	−	0.686579i	0.862506	−	0.506046i	$-0.168893\pi$
$30$		0			0
$31$	209.492	−	76.2489i	1.21374	−	0.441765i	0.345740	−	0.938330i	$-0.387628\pi$
$31$	209.492	−	76.2489i	1.21374	−	0.441765i	0.867999	+	0.496566i	$0.165406\pi$
$32$	−127.373	−	106.878i	−0.703642	−	0.590426i
$33$		0			0
$34$	−163.524	−	59.5180i	−0.824829	−	0.300213i
$35$	−16.1416	−	27.9580i	−0.0779549	−	0.135022i
$36$		0			0
$37$	−38.3904	+	66.4941i	−0.170577	+	0.295448i	−0.938622	−	0.344948i	$-0.887896\pi$
$37$	−38.3904	+	66.4941i	−0.170577	+	0.295448i	0.768045	+	0.640396i	$0.221230\pi$
$38$	116.432	−	97.6977i	0.497044	−	0.417070i
$39$		0			0
$40$	−11.1673	+	63.3329i	−0.0441426	+	0.250345i
$41$	65.9957	−	374.280i	0.251385	−	1.42568i	−0.553798	−	0.832651i	$-0.686822\pi$
$41$	65.9957	−	374.280i	0.251385	−	1.42568i	0.805183	−	0.593026i	$-0.202067\pi$
$42$		0			0
$43$	−356.376	+	299.035i	−1.26388	+	1.06052i	−0.268621	+	0.963246i	$0.586568\pi$
$43$	−356.376	+	299.035i	−1.26388	+	1.06052i	−0.995258	+	0.0972737i	$0.968988\pi$
$44$	−47.4325	+	82.1555i	−0.162516	+	0.281486i
$45$		0			0
$46$	96.7239	+	167.531i	0.310025	+	0.536980i
$47$	−355.160	−	129.268i	−1.10224	−	0.401183i	−0.274100	−	0.961701i	$-0.588380\pi$
$47$	−355.160	−	129.268i	−1.10224	−	0.401183i	−0.828142	+	0.560518i	$0.810602\pi$
$48$		0			0
$49$	−153.952	−	129.181i	−0.448840	−	0.376622i
$50$	−214.545	+	78.0881i	−0.606826	+	0.220867i
$51$		0			0
$52$	−49.3881	−	280.094i	−0.131710	−	0.746962i
$53$	−0.995976			−0.00258128			−0.00129064	−	0.999999i	$-0.500411\pi$
$53$	−0.995976			−0.00258128			−0.00129064	+	0.999999i	$0.500411\pi$
$54$		0			0
$55$	60.6826			0.148772
$56$	−49.1306	−	278.633i	−0.117238	−	0.664892i
$57$		0			0
$58$	−198.527	+	72.2578i	−0.449445	+	0.163585i
$59$	491.816	+	412.683i	1.08524	+	0.910622i	0.996345	−	0.0854191i	$-0.0272229\pi$
$59$	491.816	+	412.683i	1.08524	+	0.910622i	0.0888921	+	0.996041i	$0.471667\pi$
$60$		0			0
$61$	347.048	+	126.315i	0.728442	+	0.265131i	0.679505	−	0.733671i	$-0.262195\pi$
$61$	347.048	+	126.315i	0.728442	+	0.265131i	0.0489366	+	0.998802i	$0.484417\pi$
$62$	−216.296	−	374.636i	−0.443059	−	0.767400i
$63$		0			0
$64$	−210.076	+	363.862i	−0.410304	+	0.710668i
$65$	−139.368	+	116.944i	−0.265946	+	0.223156i
$66$		0			0
$67$	74.2357	−	421.012i	0.135363	−	0.767683i	−0.839243	−	0.543757i	$-0.817001\pi$
$67$	74.2357	−	421.012i	0.135363	−	0.767683i	0.974606	−	0.223926i	$-0.0718875\pi$
$68$	65.9474	−	374.007i	0.117607	−	0.666985i
$69$		0			0
$70$	−47.9873	+	40.2661i	−0.0819368	+	0.0687532i
$71$	29.7664	−	51.5569i	0.0497552	−	0.0861786i	−0.840075	−	0.542470i	$-0.817489\pi$
$71$	29.7664	−	51.5569i	0.0497552	−	0.0861786i	0.889830	+	0.456291i	$0.150823\pi$
$72$		0			0
$73$	−157.281	−	272.418i	−0.252169	−	0.436769i	0.711954	−	0.702226i	$-0.247810\pi$
$73$	−157.281	−	272.418i	−0.252169	−	0.436769i	−0.964123	+	0.265457i	$0.914477\pi$
$74$	140.002	+	50.9567i	0.219932	+	0.0800485i
$75$		0			0
$76$	254.098	+	213.214i	0.383514	+	0.321807i
$77$	−250.873	+	91.3102i	−0.371293	+	0.135140i
$78$		0			0
$79$	30.3749	+	172.265i	0.0432588	+	0.245333i	0.998768	−	0.0496295i	$-0.0158040\pi$
$79$	30.3749	+	172.265i	0.0432588	+	0.245333i	−0.955509	+	0.294962i	$0.904693\pi$
$80$	33.0179			0.0461439
$81$		0			0
$82$	−737.467			−0.993166
$83$	141.340	+	801.580i	0.186917	+	1.06006i	0.923468	+	0.383676i	$0.125342\pi$
$83$	141.340	+	801.580i	0.186917	+	1.06006i	−0.736551	+	0.676382i	$0.763547\pi$
$84$		0			0
$85$	−228.282	+	83.0878i	−0.291302	+	0.106025i
$86$	691.520	+	580.254i	0.867076	+	0.727563i
$87$		0			0
$88$	499.753	+	181.895i	0.605385	+	0.220342i
$89$	511.446	+	885.851i	0.609137	+	1.05506i	0.991383	+	0.130996i	$0.0418174\pi$
$89$	511.446	+	885.851i	0.609137	+	1.05506i	−0.382246	+	0.924061i	$0.624849\pi$
$90$		0			0
$91$	400.206	−	693.177i	0.461022	−	0.798514i
$92$	−323.407	+	271.371i	−0.366494	+	0.307525i
$93$		0			0
$94$	−127.352	+	722.248i	−0.139738	+	0.792491i
$95$	36.8448	−	208.957i	0.0397915	−	0.225669i
$96$		0			0
$97$	618.233	−	518.759i	0.647134	−	0.543010i	−0.259066	−	0.965860i	$-0.583415\pi$
$97$	618.233	−	518.759i	0.647134	−	0.543010i	0.906200	+	0.422850i	$0.138970\pi$
$98$	−194.984	+	337.722i	−0.200983	+	0.348113i
$99$		0			0
$100$	−249.135	−	431.514i	−0.249135	−	0.431514i
$101$	1559.90	+	567.757i	1.53679	+	0.559346i	0.965273	−	0.261243i	$-0.0841325\pi$
$101$	1559.90	+	567.757i	1.53679	+	0.559346i	0.571518	+	0.820590i	$0.306355\pi$
$102$		0			0
$103$	−85.7238	−	71.9308i	−0.0820060	−	0.0688112i	0.600863	−	0.799352i	$-0.294824\pi$
$103$	−85.7238	−	71.9308i	−0.0820060	−	0.0688112i	−0.682869	+	0.730541i	$0.739268\pi$
$104$	−1498.31	+	545.341i	−1.41271	+	0.514183i
$105$		0			0
$106$	0.335595	+	1.90326i	0.000307509	+	0.00174397i
$107$	1525.97			1.37870			0.689351	−	0.724428i	$-0.257896\pi$
$107$	1525.97			1.37870			0.689351	+	0.724428i	$0.257896\pi$
$108$		0			0
$109$	1838.03			1.61515			0.807573	−	0.589767i	$-0.200781\pi$
$109$	1838.03			1.61515			0.807573	+	0.589767i	$0.200781\pi$
$110$	−20.4471	−	115.961i	−0.0177232	−	0.100513i
$111$		0			0
$112$	−136.502	+	49.6826i	−0.115163	+	0.0419157i
$113$	1171.25	+	982.798i	0.975064	+	0.818176i	0.983337	−	0.181790i	$-0.0581890\pi$
$113$	1171.25	+	982.798i	0.975064	+	0.818176i	−0.00827313	+	0.999966i	$0.502633\pi$
$114$		0			0
$115$	253.769	+	92.3645i	0.205775	+	0.0748959i
$116$	−230.534	−	399.296i	−0.184522	−	0.319601i
$117$		0			0
$118$	622.896	−	1078.89i	0.485951	−	0.841692i
$119$	818.735	−	687.000i	0.630700	−	0.529220i
$120$		0			0
$121$	−143.984	+	816.574i	−0.108177	+	0.613504i
$122$	124.443	−	705.752i	0.0923488	−	0.523736i
$123$		0			0
$124$	723.209	−	606.845i	0.523759	−	0.439486i
$125$	−328.668	+	569.270i	−0.235176	+	0.407337i
$126$		0			0
$127$	−307.885	−	533.273i	−0.215121	−	0.372601i	0.738189	−	0.674594i	$-0.235681\pi$
$127$	−307.885	−	533.273i	−0.215121	−	0.372601i	−0.953310	+	0.301993i	$0.902348\pi$
$128$	−483.861	−	176.111i	−0.334122	−	0.121611i
$129$		0			0
$130$	270.434	+	226.921i	0.182451	+	0.153095i
$131$	−699.893	+	254.740i	−0.466794	+	0.169899i	−0.564699	−	0.825297i	$-0.691008\pi$
$131$	−699.893	+	254.740i	−0.466794	+	0.169899i	0.0979057	+	0.995196i	$0.468786\pi$
$132$		0			0
$133$	162.099	+	919.307i	0.105682	+	0.599354i
$134$	−829.544			−0.534789
$135$		0			0
$136$	−2129.08			−1.34240
$137$	281.388	+	1595.83i	0.175479	+	0.995190i	0.937590	+	0.347744i	$0.113052\pi$
$137$	281.388	+	1595.83i	0.175479	+	0.995190i	−0.762111	+	0.647447i	$0.775837\pi$
$138$		0			0
$139$	−720.098	+	262.094i	−0.439410	+	0.159932i	−0.552245	−	0.833682i	$-0.686229\pi$
$139$	−720.098	+	262.094i	−0.439410	+	0.159932i	0.112836	+	0.993614i	$0.464007\pi$
$140$	−104.727	−	87.8761i	−0.0632216	−	0.0530492i
$141$		0			0
$142$	−108.552	−	39.5098i	−0.0641514	−	0.0233492i
$143$	752.268	+	1302.97i	0.439914	+	0.761954i
$144$		0			0
$145$	−147.466	+	255.419i	−0.0844579	+	0.146285i
$146$	−467.580	+	392.346i	−0.265049	+	0.222403i
$147$		0			0
$148$	−56.4613	+	320.208i	−0.0313587	+	0.177844i
$149$	190.413	−	1079.89i	0.104693	−	0.593743i	−0.886650	−	0.462442i	$-0.846973\pi$
$149$	190.413	−	1079.89i	0.104693	−	0.593743i	0.991343	−	0.131301i	$-0.0419154\pi$
$150$		0			0
$151$	−755.888	+	634.265i	−0.407373	+	0.341826i	−0.823335	−	0.567555i	$-0.807889\pi$
$151$	−755.888	+	634.265i	−0.407373	+	0.341826i	0.415962	+	0.909382i	$0.363445\pi$
$152$	929.783	−	1610.43i	0.496154	−	0.859364i
$153$		0			0
$154$	259.021	+	448.637i	0.135536	+	0.234754i
$155$	−567.484	−	206.547i	−0.294074	−	0.107034i
$156$		0			0
$157$	−1725.26	−	1447.66i	−0.877009	−	0.735898i	0.0885532	−	0.996071i	$-0.471776\pi$
$157$	−1725.26	−	1447.66i	−0.877009	−	0.735898i	−0.965562	+	0.260174i	$0.916220\pi$
$158$	318.954	−	116.090i	0.160599	−	0.0584531i
$159$		0			0
$160$	78.2130	+	443.568i	0.0386455	+	0.219170i
$161$	−1188.11			−0.581591
$162$		0			0
$163$	84.6969			0.0406992			0.0203496	−	0.999793i	$-0.493522\pi$
$163$	84.6969			0.0406992			0.0203496	+	0.999793i	$0.493522\pi$
$164$	−279.476	−	1584.98i	−0.133069	−	0.754674i
$165$		0			0
$166$	1484.15	−	540.187i	0.693931	−	0.252570i
$167$	2381.74	+	1998.52i	1.10362	+	0.926047i	0.997663	−	0.0683232i	$-0.0217649\pi$
$167$	2381.74	+	1998.52i	1.10362	+	0.926047i	0.105957	+	0.994371i	$0.466209\pi$
$168$		0			0
$169$	−2174.21	−	791.349i	−0.989628	−	0.360195i
$170$	235.696	+	408.238i	0.106336	+	0.184179i
$171$		0			0
$172$	−985.036	+	1706.13i	−0.436676	+	0.756345i
$173$	356.567	−	299.195i	0.156701	−	0.131488i	−0.561066	−	0.827771i	$-0.689609\pi$
$173$	356.567	−	299.195i	0.156701	−	0.131488i	0.717767	+	0.696283i	$0.245164\pi$
$174$		0			0
$175$	243.498	−	1380.95i	0.105181	−	0.596514i
$176$	47.4145	−	268.901i	0.0203068	−	0.115166i
$177$		0			0
$178$	1520.48	−	1275.83i	0.640252	−	0.537235i
$179$	−182.127	+	315.453i	−0.0760491	+	0.131721i	−0.901542	−	0.432692i	$-0.857564\pi$
$179$	−182.127	+	315.453i	−0.0760491	+	0.131721i	0.825493	+	0.564413i	$0.190897\pi$
$180$		0			0
$181$	566.151	+	980.602i	0.232495	+	0.402694i	0.958542	−	0.284952i	$-0.0919776\pi$
$181$	566.151	+	980.602i	0.232495	+	0.402694i	−0.726047	+	0.687646i	$0.758644\pi$
$182$	−1459.47	−	531.205i	−0.594414	−	0.216349i
$183$		0			0
$184$	1813.06	+	1521.34i	0.726418	+	0.609537i
$185$	195.445	−	71.1361i	0.0776724	−	0.0282704i
$186$		0			0
$187$	348.857	+	1978.47i	0.136422	+	0.773690i
$188$	−1600.54			−0.620911
$189$		0			0
$190$	−411.721			−0.157207
$191$	−148.209	−	840.537i	−0.0561469	−	0.318425i	0.943779	−	0.330576i	$-0.107243\pi$
$191$	−148.209	−	840.537i	−0.0561469	−	0.318425i	−0.999926	+	0.0121515i	$0.996132\pi$
$192$		0			0
$193$	−1153.15	+	419.714i	−0.430082	+	0.156537i	−0.547985	−	0.836488i	$-0.684605\pi$
$193$	−1153.15	+	419.714i	−0.430082	+	0.156537i	0.117903	+	0.993025i	$0.462383\pi$
$194$	−1199.63	−	1006.61i	−0.443962	−	0.372529i
$195$		0			0
$196$	−799.735	−	291.080i	−0.291448	−	0.106079i
$197$	−1699.66	−	2943.90i	−0.614700	−	1.06469i	−0.990437	−	0.137965i	$-0.955944\pi$
$197$	−1699.66	−	2943.90i	−0.614700	−	1.06469i	0.375737	−	0.926726i	$-0.377390\pi$
$198$		0			0
$199$	−1604.48	+	2779.04i	−0.571550	+	0.989954i	0.424857	+	0.905261i	$0.360324\pi$
$199$	−1604.48	+	2779.04i	−0.571550	+	0.989954i	−0.996407	+	0.0846936i	$0.973009\pi$
$200$	−2139.85	+	1795.54i	−0.756550	+	0.634821i
$201$		0			0
$202$	559.343	−	3172.19i	0.194828	−	1.10492i
$203$	225.318	−	1277.84i	0.0779026	−	0.441808i
$204$		0			0
$205$	−788.652	+	661.758i	−0.268692	+	0.225459i
$206$	−108.571	+	188.051i	−0.0367209	+	0.0636025i
$207$		0			0
$208$	409.315	+	708.954i	0.136447	+	0.236332i
$209$	−1648.86	−	600.136i	−0.545713	−	0.198623i
$210$		0			0
$211$	1041.92	+	874.279i	0.339948	+	0.285250i	0.796739	−	0.604324i	$-0.206557\pi$
$211$	1041.92	+	874.279i	0.339948	+	0.285250i	−0.456791	+	0.889574i	$0.651001\pi$
$212$	−3.96335	+	1.44254i	−0.00128398	+	0.000467331i
$213$		0			0
$214$	−514.177	−	2916.05i	−0.164245	−	0.931480i
$215$	1260.20			0.399744
$216$		0			0
$217$	2656.88			0.831155
$218$	−619.325	−	3512.37i	−0.192413	−	1.09123i
$219$		0			0
$220$	241.478	−	87.8908i	0.0740020	−	0.0269345i
$221$	−4614.00	−	3871.61i	−1.40440	−	1.17843i
$222$		0			0
$223$	−4146.44	−	1509.18i	−1.24514	−	0.453193i	−0.366382	−	0.930464i	$-0.619404\pi$
$223$	−4146.44	−	1509.18i	−1.24514	−	0.453193i	−0.878756	+	0.477271i	$0.841626\pi$
$224$	−990.791	−	1716.10i	−0.295536	−	0.511883i
$225$		0			0
$226$	1483.42	−	2569.36i	0.436617	−	0.756244i
$227$	3292.53	−	2762.76i	0.962700	−	0.807801i	−0.0186902	−	0.999825i	$-0.505950\pi$
$227$	3292.53	−	2762.76i	0.962700	−	0.807801i	0.981390	+	0.192024i	$0.0615052\pi$
$228$		0			0
$229$	−38.3484	+	217.485i	−0.0110661	+	0.0627589i	−0.989841	−	0.142181i	$-0.954589\pi$
$229$	−38.3484	+	217.485i	−0.0110661	+	0.0627589i	0.978775	+	0.204939i	$0.0656998\pi$
$230$	90.9956	−	516.061i	0.0260873	−	0.147948i
$231$		0			0
$232$	−1980.08	+	1661.48i	−0.560338	+	0.470180i
$233$	40.7671	−	70.6107i	0.0114624	−	0.0198535i	−0.860237	−	0.509894i	$-0.829685\pi$
$233$	40.7671	−	70.6107i	0.0114624	−	0.0198535i	0.871700	+	0.490040i	$0.163018\pi$
$234$		0			0
$235$	511.911	+	886.655i	0.142099	+	0.246123i
$236$	2554.83	+	929.883i	0.704684	+	0.256484i
$237$		0			0
$238$	−1588.69	−	1333.07i	−0.432688	−	0.363068i
$239$	−1491.33	+	542.798i	−0.403623	+	0.146907i	−0.535851	−	0.844313i	$-0.680009\pi$
$239$	−1491.33	+	542.798i	−0.403623	+	0.146907i	0.132228	+	0.991219i	$0.457787\pi$
$240$		0			0
$241$	−52.3619	−	296.959i	−0.0139955	−	0.0793727i	0.977010	−	0.213193i	$-0.0683865\pi$
$241$	−52.3619	−	296.959i	−0.0139955	−	0.0793727i	−0.991006	+	0.133821i	$0.957275\pi$
$242$	1608.94			0.427383
$243$		0			0
$244$	1563.98			0.410343
$245$	94.5341	+	536.129i	0.0246513	+	0.139804i
$246$		0			0
$247$	4943.45	−	1799.27i	1.27346	−	0.463501i
$248$	−4054.41	−	3402.06i	−1.03813	−	0.871092i
$249$		0			0
$250$	1198.59	+	436.251i	0.303222	+	0.110364i
$251$	−190.883	−	330.619i	−0.0480017	−	0.0831415i	0.841026	−	0.540994i	$-0.181952\pi$
$251$	−190.883	−	330.619i	−0.0480017	−	0.0831415i	−0.889028	+	0.457853i	$0.848619\pi$
$252$		0			0
$253$	1116.65	−	1934.09i	0.277482	−	0.480612i
$254$	−915.313	+	768.039i	−0.226110	+	0.189729i
$255$		0			0
$256$	−757.170	+	4294.12i	−0.184856	+	1.04837i
$257$	−829.944	+	4706.85i	−0.201442	+	1.14243i	0.701500	+	0.712669i	$0.252514\pi$
$257$	−829.944	+	4706.85i	−0.201442	+	1.14243i	−0.902942	+	0.429763i	$0.858597\pi$
$258$		0			0
$259$	−700.964	+	588.179i	−0.168169	+	0.141111i
$260$	−385.220	+	667.220i	−0.0918858	+	0.159151i
$261$		0			0
$262$	722.625	+	1251.62i	0.170397	+	0.295136i
$263$	552.506	+	201.096i	0.129540	+	0.0471486i	0.405977	−	0.913883i	$-0.366931\pi$
$263$	552.506	+	201.096i	0.129540	+	0.0471486i	−0.276437	+	0.961032i	$0.589154\pi$
$264$		0			0
$265$	2.06676	+	1.73421i	0.000479093	+	0.000402007i
$266$	1702.13	−	619.523i	0.392346	−	0.142802i
$267$		0			0
$268$	−314.370	−	1782.88i	−0.0716537	−	0.406368i
$269$	−3125.47			−0.708413			−0.354206	−	0.935167i	$-0.615249\pi$
$269$	−3125.47			−0.708413			−0.354206	+	0.935167i	$0.615249\pi$
$270$		0			0
$271$	153.883			0.0344935			0.0172467	−	0.999851i	$-0.494510\pi$
$271$	153.883			0.0344935			0.0172467	+	0.999851i	$0.494510\pi$
$272$	189.816	+	1076.50i	0.0423136	+	0.239972i
$273$		0			0
$274$	2954.73	−	1075.43i	0.651467	−	0.237114i
$275$	2019.15	+	1694.27i	0.442761	+	0.371521i
$276$		0			0
$277$	7396.30	+	2692.03i	1.60433	+	0.583930i	0.980308	−	0.197475i	$-0.0632740\pi$
$277$	7396.30	+	2692.03i	1.60433	+	0.583930i	0.624025	+	0.781404i	$0.285496\pi$
$278$	743.486	+	1287.76i	0.160400	+	0.277822i
$279$		0			0
$280$	−383.210	+	663.740i	−0.0817900	+	0.141664i
$281$	−395.654	+	331.993i	−0.0839955	+	0.0704806i	−0.683819	−	0.729652i	$-0.739682\pi$
$281$	−395.654	+	331.993i	−0.0839955	+	0.0704806i	0.599823	+	0.800133i	$0.295238\pi$
$282$		0			0
$283$	691.886	−	3923.88i	0.145330	−	0.824206i	−0.821772	−	0.569816i	$-0.807014\pi$
$283$	691.886	−	3923.88i	0.145330	−	0.824206i	0.967102	−	0.254390i	$-0.0818746\pi$
$284$	43.7779	−	248.277i	0.00914696	−	0.0518750i
$285$		0			0
$286$	2236.42	−	1876.58i	0.462385	−	0.387987i
$287$	2264.67	−	3922.53i	0.465782	−	0.806757i
$288$		0			0
$289$	−1564.83	−	2710.36i	−0.318508	−	0.551671i
$290$	537.780	+	195.736i	0.108895	+	0.0396345i
$291$		0			0
$292$	−1020.44	−	856.251i	−0.204509	−	0.171604i
$293$	6482.92	−	2359.59i	1.29262	−	0.470474i	0.398031	−	0.917372i	$-0.369694\pi$
$293$	6482.92	−	2359.59i	1.29262	−	0.470474i	0.894585	+	0.446898i	$0.147471\pi$
$294$		0			0
$295$	−301.999	−	1712.72i	−0.0596035	−	0.338028i
$296$	1822.82			0.357937
$297$		0			0
$298$	−2127.76			−0.413617
$299$	1162.68	+	6593.91i	0.224882	+	1.27537i
$300$		0			0
$301$	−5209.90	+	1896.25i	−0.997653	+	0.363116i
$302$	1466.74	+	1230.74i	0.279476	+	0.234508i
$303$		0			0
$304$	−897.158	−	326.539i	−0.169262	−	0.0616062i
$305$	−500.219	−	866.404i	−0.0939096	−	0.162656i
$306$		0			0
$307$	−2277.90	+	3945.44i	−0.423474	+	0.733479i	−0.996277	−	0.0862148i	$-0.972523\pi$
$307$	−2277.90	+	3945.44i	−0.423474	+	0.733479i	0.572802	+	0.819693i	$0.305856\pi$
$308$	−866.063	+	726.713i	−0.160222	+	0.134443i
$309$		0			0
$310$	−203.486	+	1154.03i	−0.0372814	+	0.211433i
$311$	−1723.45	+	9774.17i	−0.314238	+	1.78213i	0.262225	+	0.965007i	$0.415544\pi$
$311$	−1723.45	+	9774.17i	−0.314238	+	1.78213i	−0.576463	+	0.817123i	$0.695567\pi$
$312$		0			0
$313$	−246.104	+	206.506i	−0.0444430	+	0.0372921i	−0.664739	−	0.747076i	$-0.731457\pi$
$313$	−246.104	+	206.506i	−0.0444430	+	0.0372921i	0.620296	+	0.784368i	$0.287013\pi$
$314$	−2185.07	+	3784.66i	−0.392710	+	0.680193i
$315$		0			0
$316$	370.376	+	641.510i	0.0659344	+	0.114202i
$317$	−7315.09	−	2662.47i	−1.29608	−	0.471733i	−0.400360	−	0.916358i	$-0.631115\pi$
$317$	−7315.09	−	2662.47i	−1.29608	−	0.471733i	−0.895717	+	0.444625i	$0.853337\pi$
$318$		0			0
$319$	1868.39	+	1567.77i	0.327931	+	0.275167i
$320$	1069.49	−	389.264i	0.186833	−	0.0680016i
$321$		0			0
$322$	400.335	+	2270.41i	0.0692851	+	0.392935i
$323$	7024.57			1.21008
$324$		0			0
$325$	−7902.44			−1.34876
$326$	−28.5387	−	161.851i	−0.00484851	−	0.0274972i
$327$		0			0
$328$	−8478.59	+	3085.95i	−1.42729	+	0.519492i
$329$	−3450.50	−	2895.31i	−0.578213	−	0.485178i
$330$		0			0
$331$	6473.83	+	2356.28i	1.07503	+	0.391278i	0.818055	−	0.575141i	$-0.195053\pi$
$331$	6473.83	+	2356.28i	1.07503	+	0.391278i	0.256973	+	0.966419i	$0.417275\pi$
$332$	1723.43	+	2985.07i	0.284896	+	0.493455i
$333$		0			0
$334$	3016.53	−	5224.78i	0.494183	−	0.855950i
$335$	−887.121	+	744.383i	−0.144682	+	0.121403i
$336$		0			0
$337$	−770.185	+	4367.94i	−0.124495	+	0.706044i	0.857112	+	0.515130i	$0.172256\pi$
$337$	−770.185	+	4367.94i	−0.124495	+	0.706044i	−0.981607	+	0.190914i	$0.938855\pi$
$338$	−779.621	+	4421.45i	−0.125461	+	0.711524i
$339$		0			0
$340$	−788.075	+	661.274i	−0.125704	+	0.105478i
$341$	−2497.07	+	4325.04i	−0.396550	+	0.686845i
$342$		0			0
$343$	−3241.42	−	5614.30i	−0.510262	−	0.883800i
$344$	10378.4	+	3777.44i	1.62665	+	0.592052i
$345$		0			0
$346$	−691.892	−	580.566i	−0.107504	−	0.0902064i
$347$	11522.0	−	4193.67i	1.78252	−	0.648783i	0.782871	−	0.622184i	$-0.213755\pi$
$347$	11522.0	−	4193.67i	1.78252	−	0.648783i	0.999646	−	0.0265987i	$-0.00846763\pi$
$348$		0			0
$349$	−209.283	−	1186.91i	−0.0320994	−	0.182045i	0.964543	−	0.263927i	$-0.0850179\pi$
$349$	−209.283	−	1186.91i	−0.0320994	−	0.182045i	−0.996642	+	0.0818825i	$0.973907\pi$
$350$	−2720.96			−0.415548
$351$		0			0
$352$	3724.78			0.564010
$353$	−83.5507	−	473.839i	−0.0125976	−	0.0714445i	0.977861	−	0.209256i	$-0.0671043\pi$
$353$	−83.5507	−	473.839i	−0.0125976	−	0.0714445i	−0.990458	+	0.137812i	$0.955993\pi$
$354$		0			0
$355$	−151.540	+	55.1561i	−0.0226561	+	0.00824615i
$356$	3318.27	+	2784.36i	0.494011	+	0.414525i
$357$		0			0
$358$	664.181	+	241.742i	0.0980532	+	0.0356884i
$359$	2984.85	+	5169.92i	0.438815	+	0.760050i	0.997598	−	0.0692637i	$-0.0220650\pi$
$359$	2984.85	+	5169.92i	0.438815	+	0.760050i	−0.558783	+	0.829314i	$0.688732\pi$
$360$		0			0
$361$	361.822	−	626.695i	0.0527515	−	0.0913683i
$362$	1683.11	−	1412.30i	0.244371	−	0.205052i
$363$		0			0
$364$	588.589	−	3338.05i	0.0847539	−	0.480664i
$365$	−147.966	+	839.156i	−0.0212189	+	0.120338i
$366$		0			0
$367$	−3192.49	+	2678.82i	−0.454078	+	0.381017i	−0.840947	−	0.541118i	$-0.818001\pi$
$367$	−3192.49	+	2678.82i	−0.454078	+	0.381017i	0.386868	+	0.922135i	$0.373557\pi$
$368$	607.576	−	1052.35i	0.0860654	−	0.149070i
$369$		0			0
$370$	−201.793	−	349.515i	−0.0283532	−	0.0491093i
$371$	−11.1538	−	4.05966i	−0.00156086	−	0.000568106i
$372$		0			0
$373$	−1153.18	−	967.631i	−0.160078	−	0.134322i	0.559230	−	0.829012i	$-0.311097\pi$
$373$	−1153.18	−	967.631i	−0.160078	−	0.134322i	−0.719309	+	0.694691i	$0.755541\pi$
$374$	3663.20	−	1333.29i	0.506469	−	0.184340i
$375$		0			0
$376$	1558.12	+	8836.53i	0.213707	+	1.21199i
$377$	−7312.41			−0.998961
$378$		0			0
$379$	2159.41			0.292669			0.146334	−	0.989235i	$-0.453252\pi$
$379$	2159.41			0.292669			0.146334	+	0.989235i	$0.453252\pi$
$380$	−156.029	−	884.882i	−0.0210634	−	0.119457i
$381$		0			0
$382$	−1556.28	+	566.440i	−0.208446	+	0.0758680i
$383$	−5897.64	−	4948.70i	−0.786828	−	0.660227i	0.158130	−	0.987418i	$-0.449453\pi$
$383$	−5897.64	−	4948.70i	−0.786828	−	0.660227i	−0.944958	+	0.327191i	$0.893898\pi$
$384$		0			0
$385$	679.578	+	247.346i	0.0899597	+	0.0327427i
$386$	1190.61	+	2062.19i	0.156996	+	0.271924i
$387$		0			0
$388$	1708.82	−	2959.76i	0.223588	−	0.387266i
$389$	4641.74	−	3894.88i	0.605002	−	0.507657i	−0.288047	−	0.957616i	$-0.593006\pi$
$389$	4641.74	−	3894.88i	0.605002	−	0.507657i	0.893049	+	0.449959i	$0.148562\pi$
$390$		0			0
$391$	−1552.52	+	8804.78i	−0.200804	+	1.13882i
$392$	−828.503	+	4698.68i	−0.106749	+	0.605406i
$393$		0			0
$394$	−5052.93	+	4239.91i	−0.646099	+	0.542141i
$395$	236.919	−	410.357i	0.0301790	−	0.0522716i
$396$		0			0
$397$	−1243.55	−	2153.89i	−0.157209	−	0.272293i	0.776652	−	0.629929i	$-0.216916\pi$
$397$	−1243.55	−	2153.89i	−0.157209	−	0.272293i	−0.933861	+	0.357636i	$0.883583\pi$
$398$	5851.22	+	2129.67i	0.736923	+	0.268218i
$399$		0			0
$400$	1098.64	+	921.865i	0.137329	+	0.115233i
$401$	−11135.5	+	4052.99i	−1.38673	+	0.504729i	−0.924212	−	0.381880i	$-0.875277\pi$
$401$	−11135.5	+	4052.99i	−1.38673	+	0.504729i	−0.462520	+	0.886609i	$0.653055\pi$
$402$		0			0
$403$	−2600.02	−	14745.4i	−0.321380	−	1.82264i
$404$	7029.74			0.865699
$405$		0			0
$406$	−2517.81			−0.307775
$407$	−298.676	−	1693.88i	−0.0363755	−	0.206296i
$408$		0			0
$409$	−4125.48	+	1501.55i	−0.498757	+	0.181533i	−0.579135	−	0.815232i	$-0.696610\pi$
$409$	−4125.48	+	1501.55i	−0.498757	+	0.181533i	0.0803777	+	0.996764i	$0.474387\pi$
$410$	1530.32	+	1284.09i	0.184334	+	0.154675i
$411$		0			0
$412$	−445.309	−	162.079i	−0.0532495	−	0.0193812i
$413$	3825.68	+	6626.26i	0.455809	+	0.789485i
$414$		0			0
$415$	1102.43	−	1909.47i	0.130401	−	0.225860i
$416$	−8554.63	+	7178.18i	−1.00823	+	0.846008i
$417$		0			0
$418$	−591.241	+	3353.10i	−0.0691832	+	0.392357i
$419$	926.596	−	5254.99i	0.108036	−	0.612704i	−0.881928	−	0.471384i	$-0.843754\pi$
$419$	926.596	−	5254.99i	0.108036	−	0.612704i	0.989964	−	0.141319i	$-0.0451344\pi$
$420$		0			0
$421$	11532.1	−	9676.60i	1.33502	−	1.12021i	0.352138	−	0.935948i	$-0.385455\pi$
$421$	11532.1	−	9676.60i	1.33502	−	1.12021i	0.982877	−	0.184263i	$-0.0589898\pi$
$422$	1319.62	−	2285.65i	0.152223	−	0.263658i
$423$		0			0
$424$	11.8225	+	20.4773i	0.00135414	+	0.00234543i
$425$	−9915.67	−	3609.01i	−1.13172	−	0.411912i
$426$		0			0
$427$	3371.69	+	2829.18i	0.382125	+	0.320641i
$428$	6072.39	−	2210.17i	0.685795	−	0.249609i
$429$		0			0
$430$	−424.626	−	2408.18i	−0.0476216	−	0.270076i
$431$	−4779.82			−0.534190			−0.267095	−	0.963670i	$-0.586064\pi$
$431$	−4779.82			−0.534190			−0.267095	+	0.963670i	$0.586064\pi$
$432$		0			0
$433$	6331.13			0.702666			0.351333	−	0.936250i	$-0.385728\pi$
$433$	6331.13			0.702666			0.351333	+	0.936250i	$0.385728\pi$
$434$	−895.238	−	5077.15i	−0.0990157	−	0.561546i
$435$		0			0
$436$	7314.18	−	2662.14i	0.803407	−	0.292416i
$437$	−5981.93	−	5019.43i	−0.654815	−	0.549455i
$438$		0			0
$439$	−5697.21	−	2073.61i	−0.619392	−	0.225440i	0.0132159	−	0.999913i	$-0.495793\pi$
$439$	−5697.21	−	2073.61i	−0.619392	−	0.225440i	−0.632607	+	0.774473i	$0.718015\pi$
$440$	−720.321	−	1247.63i	−0.0780453	−	0.135178i
$441$		0			0
$442$	−5843.74	+	10121.7i	−0.628865	+	1.08923i
$443$	2145.65	−	1800.41i	0.230119	−	0.193093i	−0.520436	−	0.853901i	$-0.674231\pi$
$443$	2145.65	−	1800.41i	0.230119	−	0.193093i	0.750555	+	0.660808i	$0.229786\pi$
$444$		0			0
$445$	481.156	−	2728.77i	0.0512562	−	0.290688i
$446$	−1486.81	+	8432.13i	−0.157853	+	0.895231i
$447$		0			0
$448$	−3835.74	+	3218.57i	−0.404513	+	0.339427i
$449$	2667.38	−	4620.04i	0.280360	−	0.485598i	−0.691113	−	0.722746i	$-0.742880\pi$
$449$	2667.38	−	4620.04i	0.280360	−	0.485598i	0.971473	+	0.237149i	$0.0762128\pi$
$450$		0			0
$451$	4256.90	+	7373.17i	0.444456	+	0.769820i
$452$	6084.30	+	2214.50i	0.633145	+	0.230446i
$453$		0			0
$454$	−6388.91	−	5360.93i	−0.660454	−	0.554187i
$455$	−2037.44	+	741.569i	−0.209927	+	0.0764072i
$456$		0			0
$457$	2370.29	+	13442.6i	0.242620	+	1.37597i	0.825956	+	0.563735i	$0.190636\pi$
$457$	2370.29	+	13442.6i	0.242620	+	1.37597i	−0.583335	+	0.812231i	$0.698253\pi$
$458$	428.523			0.0437196
$459$		0			0
$460$	1143.62			0.115916
$461$	2362.15	+	13396.4i	0.238647	+	1.35344i	0.834795	+	0.550562i	$0.185586\pi$
$461$	2362.15	+	13396.4i	0.238647	+	1.35344i	−0.596147	+	0.802875i	$0.703303\pi$
$462$		0			0
$463$	15232.9	−	5544.32i	1.52901	−	0.556515i	0.565633	−	0.824657i	$-0.308632\pi$
$463$	15232.9	−	5544.32i	1.52901	−	0.556515i	0.963379	+	0.268143i	$0.0864098\pi$
$464$	1016.61	+	853.035i	0.101713	+	0.0853473i
$465$		0			0
$466$	−148.670	−	54.1113i	−0.0147789	−	0.00537910i
$467$	−8459.62	−	14652.5i	−0.838254	−	1.45190i	−0.891353	−	0.453310i	$-0.850243\pi$
$467$	−8459.62	−	14652.5i	−0.838254	−	1.45190i	0.0530989	−	0.998589i	$-0.483090\pi$
$468$		0			0
$469$	2547.43	−	4412.28i	0.250809	−	0.434414i
$470$	1521.86	−	1276.99i	0.149358	−	0.125326i
$471$		0			0
$472$	2646.74	−	15010.4i	0.258106	−	1.46379i
$473$	1809.68	−	10263.2i	0.175918	−	0.997681i
$474$		0			0
$475$	7060.09	−	5924.12i	0.681977	−	0.572247i
$476$	2263.01	−	3919.65i	0.217910	−	0.377431i
$477$		0			0
$478$	1539.76	+	2666.95i	0.147337	+	0.255195i
$479$	−953.110	−	346.904i	−0.0909159	−	0.0330907i	0.296162	−	0.955138i	$-0.404293\pi$
$479$	−953.110	−	346.904i	−0.0909159	−	0.0330907i	−0.387078	+	0.922047i	$0.626515\pi$
$480$		0			0
$481$	3950.31	+	3314.70i	0.374467	+	0.314215i
$482$	−549.829	+	200.121i	−0.0519586	+	0.0189114i
$483$		0			0
$484$	609.737	+	3457.99i	0.0572630	+	0.324755i
$485$	−2186.17			−0.204678
$486$		0			0
$487$	−4091.32			−0.380688			−0.190344	−	0.981717i	$-0.560960\pi$
$487$	−4091.32			−0.380688			−0.190344	+	0.981717i	$0.560960\pi$
$488$	−1522.53	−	8634.70i	−0.141233	−	0.800972i
$489$		0			0
$490$	992.660	−	361.299i	0.0915180	−	0.0333098i
$491$	75.1078	+	63.0230i	0.00690340	+	0.00579264i	0.646233	−	0.763140i	$-0.276344\pi$
$491$	75.1078	+	63.0230i	0.00690340	+	0.00579264i	−0.639329	+	0.768933i	$0.720788\pi$
$492$		0			0
$493$	−9175.33	−	3339.55i	−0.838207	−	0.305083i
$494$	−5104.00	−	8840.39i	−0.464858	−	0.805158i
$495$		0			0
$496$	−1358.67	+	2353.29i	−0.122996	+	0.213036i
$497$	543.500	−	456.051i	0.0490529	−	0.0411603i
$498$		0			0
$499$	1051.82	−	5965.16i	0.0943604	−	0.535145i	−0.900581	−	0.434688i	$-0.856859\pi$
$499$	1051.82	−	5965.16i	0.0943604	−	0.535145i	0.994941	−	0.100456i	$-0.0320303\pi$
$500$	−483.377	+	2741.37i	−0.0432346	+	0.245195i
$501$		0			0
$502$	−567.477	+	476.170i	−0.0504537	+	0.0423357i
$503$	−4856.15	+	8411.10i	−0.430467	+	0.745591i	−0.996914	−	0.0785074i	$-0.974985\pi$
$503$	−4856.15	+	8411.10i	−0.430467	+	0.745591i	0.566446	+	0.824099i	$0.308318\pi$
$504$		0			0
$505$	−2248.37	−	3894.28i	−0.198121	−	0.343155i
$506$	−4072.19	−	1482.16i	−0.357768	−	0.130217i
$507$		0			0
$508$	−1997.57	−	1676.16i	−0.174464	−	0.146393i
$509$	−9057.80	+	3296.77i	−0.788762	+	0.287086i	−0.704821	−	0.709385i	$-0.748973\pi$
$509$	−9057.80	+	3296.77i	−0.788762	+	0.287086i	−0.0839407	+	0.996471i	$0.526751\pi$
$510$		0			0
$511$	−650.976	−	3691.87i	−0.0563552	−	0.319606i
$512$	4341.65			0.374757
$513$		0			0
$514$	9274.18			0.795849
$515$	52.6385	+	298.528i	0.00450394	+	0.0255431i
$516$		0			0
$517$	7956.13	−	2895.79i	0.676809	−	0.246338i
$518$	1360.17	+	1141.32i	0.115371	+	0.0968081i
$519$		0			0
$520$	4058.71	+	1477.25i	0.342281	+	0.124580i
$521$	−8627.23	−	14942.8i	−0.725462	−	1.25654i	−0.958783	−	0.284138i	$-0.908293\pi$
$521$	−8627.23	−	14942.8i	−0.725462	−	1.25654i	0.233321	−	0.972400i	$-0.425041\pi$
$522$		0			0
$523$	−6426.55	+	11131.1i	−0.537311	+	0.930649i	0.461737	+	0.887017i	$0.347226\pi$
$523$	−6426.55	+	11131.1i	−0.537311	+	0.930649i	−0.999048	+	0.0436325i	$0.986107\pi$
$524$	−2416.17	+	2027.41i	−0.201433	+	0.169023i
$525$		0			0
$526$	198.115	−	1123.57i	0.0164225	−	0.0931367i
$527$	3471.78	−	19689.4i	0.286970	−	1.62749i
$528$		0			0
$529$	−1706.89	+	1432.25i	−0.140289	+	0.117716i
$530$	2.61759	−	4.53380i	0.000214530	−	0.000371577i
$531$		0			0
$532$	1976.55	+	3423.48i	0.161079	+	0.278998i
$533$	−23985.9	−	8730.15i	−1.94924	−	0.709465i
$534$		0			0
$535$	−3166.55	−	2657.05i	−0.255891	−	0.214718i
$536$	−9537.19	+	3471.25i	−0.768552	+	0.279730i
$537$		0			0
$538$	1053.13	+	5972.59i	0.0843934	+	0.478619i
$539$	4502.05			0.359772
$540$		0			0
$541$	−9727.92			−0.773080			−0.386540	−	0.922273i	$-0.626330\pi$
$541$	−9727.92			−0.773080			−0.386540	+	0.922273i	$0.626330\pi$
$542$	−51.8511	−	294.062i	−0.00410922	−	0.0233045i
$543$		0			0
$544$	−14012.3	+	5100.05i	−1.10436	+	0.401953i
$545$	−3814.10	−	3200.41i	−0.299776	−	0.251542i
$546$		0			0
$547$	−22854.0	−	8318.18i	−1.78641	−	0.650201i	−0.999449	−	0.0332016i	$-0.989430\pi$
$547$	−22854.0	−	8318.18i	−1.78641	−	0.650201i	−0.786964	−	0.616999i	$-0.788348\pi$
$548$	3431.10	+	5942.84i	0.267462	+	0.463258i
$549$		0			0
$550$	2557.30	−	4429.37i	0.198261	−	0.343398i
$551$	6532.96	−	5481.81i	0.505106	−	0.423834i
$552$		0			0
$553$	−361.997	+	2052.98i	−0.0278366	+	0.157869i
$554$	2652.13	−	15041.0i	0.203391	−	1.15349i
$555$		0			0
$556$	−2485.92	+	2085.94i	−0.189616	+	0.159107i
$557$	7540.43	−	13060.4i	0.573606	−	0.993514i	−0.422586	−	0.906323i	$-0.638878\pi$
$557$	7540.43	−	13060.4i	0.573606	−	0.993514i	0.996192	−	0.0871912i	$-0.0277891\pi$
$558$		0			0
$559$	15622.4	+	27058.8i	1.18204	+	2.04735i
$560$	369.764	+	134.583i	0.0279024	+	0.0101557i
$561$		0			0
$562$	767.737	+	644.208i	0.0576246	+	0.0483528i
$563$	2246.56	−	817.683i	0.168173	−	0.0612100i	−0.256562	−	0.966528i	$-0.582590\pi$
$563$	2246.56	−	817.683i	0.168173	−	0.0612100i	0.424735	+	0.905318i	$0.360367\pi$
$564$		0			0
$565$	−719.206	−	4078.82i	−0.0535526	−	0.303712i
$566$	−7731.45			−0.574164
$567$		0			0
$568$	−1413.34			−0.104406
$569$	−3723.92	−	21119.4i	−0.274367	−	1.55601i	−0.740964	−	0.671544i	$-0.765631\pi$
$569$	−3723.92	−	21119.4i	−0.274367	−	1.55601i	0.466597	−	0.884470i	$-0.345480\pi$
$570$		0			0
$571$	−10824.3	+	3939.71i	−0.793313	+	0.288742i	−0.706712	−	0.707501i	$-0.749823\pi$
$571$	−10824.3	+	3939.71i	−0.793313	+	0.288742i	−0.0866003	+	0.996243i	$0.527600\pi$
$572$	4880.72	+	4095.41i	0.356772	+	0.299367i
$573$		0			0
$574$	−8258.81	−	3005.96i	−0.600551	−	0.218583i
$575$	5865.08	+	10158.6i	0.425375	+	0.736771i
$576$		0			0
$577$	4116.78	−	7130.48i	0.297026	−	0.514464i	−0.678428	−	0.734667i	$-0.737339\pi$
$577$	4116.78	−	7130.48i	0.297026	−	0.514464i	0.975454	+	0.220203i	$0.0706719\pi$
$578$	−4652.08	+	3903.56i	−0.334777	+	0.280911i
$579$		0			0
$580$	−216.880	+	1229.99i	−0.0155267	+	0.0880562i
$581$	−1684.44	+	9552.93i	−0.120279	+	0.682138i
$582$		0			0
$583$	17.0915	−	14.3415i	0.00121417	−	0.00101881i
$584$	−3733.94	+	6467.37i	−0.264575	+	0.458257i
$585$		0			0
$586$	−6693.48	−	11593.4i	−0.471852	−	0.817271i
$587$	16390.4	+	5965.63i	1.15248	+	0.419469i	0.846406	−	0.532539i	$-0.178762\pi$
$587$	16390.4	+	5965.63i	1.15248	+	0.419469i	0.306075	+	0.952007i	$0.400984\pi$
$588$		0			0
$589$	13376.9	+	11224.6i	0.935800	+	0.785229i
$590$	−3171.15	+	1154.21i	−0.221279	+	0.0805388i
$591$		0			0
$592$	−162.512	−	921.652i	−0.0112824	−	0.0639859i
$593$	−14432.2			−0.999423			−0.499712	−	0.866192i	$-0.666561\pi$
$593$	−14432.2			−0.999423			−0.499712	+	0.866192i	$0.666561\pi$
$594$		0			0
$595$	−2895.18			−0.199480
$596$	−806.351	−	4573.05i	−0.0554185	−	0.314294i
$597$		0			0
$598$	12208.8	−	4443.65i	0.834877	−	0.303870i
$599$	14208.5	+	11922.4i	0.969191	+	0.813247i	0.982424	−	0.186665i	$-0.0597679\pi$
$599$	14208.5	+	11922.4i	0.969191	+	0.813247i	−0.0132330	+	0.999912i	$0.504212\pi$
$600$		0			0
$601$	20255.1	+	7372.25i	1.37475	+	0.500367i	0.920581	−	0.390551i	$-0.127715\pi$
$601$	20255.1	+	7372.25i	1.37475	+	0.500367i	0.454165	+	0.890918i	$0.349938\pi$
$602$	5379.11	+	9316.89i	0.364179	+	0.630777i
$603$		0			0
$604$	−2089.30	+	3618.78i	−0.140749	+	0.243785i
$605$	1720.62	−	1443.77i	0.115625	−	0.0970207i
$606$		0			0
$607$	1322.24	−	7498.81i	0.0884154	−	0.501429i	−0.908152	−	0.418641i	$-0.862507\pi$
$607$	1322.24	−	7498.81i	0.0884154	−	0.501429i	0.996567	−	0.0827877i	$-0.0263823\pi$
$608$	2261.58	−	12826.1i	0.150854	−	0.855537i
$609$		0			0
$610$	−1487.10	+	1247.83i	−0.0987065	+	0.0828246i
$611$	−12692.1	+	21983.3i	−0.840370	+	1.45556i
$612$		0			0
$613$	−13145.6	−	22768.8i	−0.866142	−	1.50020i	−0.865909	−	0.500201i	$-0.833259\pi$
$613$	−13145.6	−	22768.8i	−0.866142	−	1.50020i	−0.000232630	−	1.00000i	$-0.500074\pi$
$614$	8307.05	+	3023.52i	0.546002	+	0.198729i
$615$		0			0
$616$	4855.27	+	4074.05i	0.317572	+	0.266475i
$617$	−10358.3	+	3770.12i	−0.675867	+	0.245996i	−0.657072	−	0.753828i	$-0.728205\pi$
$617$	−10358.3	+	3770.12i	−0.675867	+	0.245996i	−0.0187953	+	0.999823i	$0.505983\pi$
$618$		0			0
$619$	815.202	+	4623.24i	0.0529334	+	0.300200i	0.999768	−	0.0215194i	$-0.00685036\pi$
$619$	815.202	+	4623.24i	0.0529334	+	0.300200i	−0.946835	+	0.321719i	$0.895739\pi$
$620$	−2557.38			−0.165656
$621$		0			0
$622$	19258.6			1.24148
$623$	2116.85	+	12005.2i	0.136131	+	0.772038i
$624$		0			0
$625$	−12147.5	+	4421.34i	−0.777442	+	0.282966i
$626$	477.547	+	400.710i	0.0304898	+	0.0255840i
$627$		0			0
$628$	−8962.17	−	3261.96i	−0.569474	−	0.207271i
$629$	3442.88	+	5963.25i	0.218246	+	0.378013i
$630$		0			0
$631$	1671.81	−	2895.66i	0.105473	−	0.182685i	−0.808458	−	0.588554i	$-0.799698\pi$
$631$	1671.81	−	2895.66i	0.105473	−	0.182685i	0.913932	+	0.405868i	$0.133031\pi$
$632$	3181.20	−	2669.34i	0.200224	−	0.168007i
$633$		0			0
$634$	−2623.01	+	14875.9i	−0.164311	+	0.931854i
$635$	−289.651	+	1642.69i	−0.0181015	+	0.102659i
$636$		0			0
$637$	−10339.8	+	8676.09i	−0.643134	+	0.539653i
$638$	2366.36	−	4098.66i	0.146842	−	0.254338i
$639$		0			0
$640$	697.414	+	1207.96i	0.0430745	+	0.0746073i
$641$	−6651.42	−	2420.92i	−0.409852	−	0.149174i	0.128862	−	0.991663i	$-0.458868\pi$
$641$	−6651.42	−	2420.92i	−0.409852	−	0.149174i	−0.538714	+	0.842489i	$0.681090\pi$
$642$		0			0
$643$	−14677.5	−	12315.9i	−0.900192	−	0.755351i	0.0700356	−	0.997544i	$-0.477689\pi$
$643$	−14677.5	−	12315.9i	−0.900192	−	0.755351i	−0.970228	+	0.242193i	$0.922133\pi$
$644$	−4727.92	+	1720.82i	−0.289295	+	0.105295i
$645$		0			0
$646$	−2366.94	−	13423.6i	−0.144158	−	0.817559i
$647$	26381.3			1.60302			0.801512	−	0.597978i	$-0.204029\pi$
$647$	26381.3			1.60302			0.801512	+	0.597978i	$0.204029\pi$
$648$		0			0
$649$	−14382.2			−0.869881
$650$	2662.74	+	15101.1i	0.160679	+	0.911253i
$651$		0			0
$652$	337.040	−	122.672i	0.0202446	−	0.00736844i
$653$	19612.3	+	16456.7i	1.17533	+	0.986216i	0.999999	+	0.00170587i	$0.000542995\pi$
$653$	19612.3	+	16456.7i	1.17533	+	0.986216i	0.175328	+	0.984510i	$0.443901\pi$
$654$		0			0
$655$	1895.91	+	690.055i	0.113098	+	0.0411644i
$656$	2316.21	+	4011.80i	0.137855	+	0.238772i
$657$		0			0
$658$	−4370.13	+	7569.29i	−0.258914	+	0.448452i
$659$	2105.07	−	1766.36i	0.124434	−	0.104412i	−0.578447	−	0.815720i	$-0.696341\pi$
$659$	2105.07	−	1766.36i	0.124434	−	0.104412i	0.702881	+	0.711308i	$0.251897\pi$
$660$		0			0
$661$	−4950.69	+	28076.8i	−0.291315	+	1.65213i	0.390496	+	0.920605i	$0.372303\pi$
$661$	−4950.69	+	28076.8i	−0.291315	+	1.65213i	−0.681812	+	0.731528i	$0.738808\pi$
$662$	2321.36	−	13165.1i	0.136287	−	0.772924i
$663$		0			0
$664$	14802.7	−	12421.0i	0.865146	−	0.725944i
$665$	1264.34	−	2189.91i	0.0737281	−	0.127701i
$666$		0			0
$667$	5427.17	+	9400.14i	0.315054	+	0.545689i
$668$	12372.4	+	4503.19i	0.716621	+	0.260829i
$669$		0			0
$670$	1721.39	+	1444.42i	0.0992584	+	0.0832877i
$671$	−7774.41	+	2829.65i	−0.447284	+	0.162798i
$672$		0			0
$673$	3922.79	+	22247.2i	0.224684	+	1.27425i	0.863288	+	0.504711i	$0.168401\pi$
$673$	3922.79	+	22247.2i	0.224684	+	1.27425i	−0.638604	+	0.769535i	$0.720488\pi$
$674$	8606.40			0.491849
$675$		0			0
$676$	−9798.16			−0.557474
$677$	−43.3014	−	245.574i	−0.00245821	−	0.0139412i	0.983554	−	0.180614i	$-0.0578086\pi$
$677$	−43.3014	−	245.574i	−0.00245821	−	0.0139412i	−0.986012	+	0.166673i	$0.946698\pi$
$678$		0			0
$679$	9038.02	−	3289.57i	0.510821	−	0.185924i
$680$	4418.06	+	3707.19i	0.249154	+	0.209065i
$681$		0			0
$682$	9106.31	+	3314.43i	0.511289	+	0.186094i
$683$	−3696.21	−	6402.03i	−0.207074	−	0.358663i	0.743717	−	0.668494i	$-0.233061\pi$
$683$	−3696.21	−	6402.03i	−0.207074	−	0.358663i	−0.950792	+	0.309831i	$0.899727\pi$
$684$		0			0
$685$	2194.78	−	3801.47i	0.122421	−	0.212039i
$686$	−9636.41	+	8085.91i	−0.536327	+	0.450031i
$687$		0			0
$688$	984.662	−	5584.30i	0.0545638	−	0.309447i
$689$	−11.6157	+	65.8756i	−0.000642266	+	0.00364247i
$690$		0			0
$691$	4316.61	−	3622.07i	0.237644	−	0.199407i	−0.516186	−	0.856476i	$-0.672649\pi$
$691$	4316.61	−	3622.07i	0.237644	−	0.199407i	0.753830	+	0.657070i	$0.228204\pi$
$692$	985.565	−	1707.05i	0.0541410	−	0.0937749i
$693$		0			0
$694$	−11896.2	−	20604.9i	−0.650683	−	1.12702i
$695$	1950.64	+	709.976i	0.106463	+	0.0387495i
$696$		0			0
$697$	−26109.5	−	21908.5i	−1.41889	−	1.19059i
$698$	−2197.59	+	799.858i	−0.119169	+	0.0433740i
$699$		0			0
$700$	−1031.16	−	5847.97i	−0.0556772	−	0.315761i
$701$	−3492.05			−0.188149			−0.0940747	−	0.995565i	$-0.529989\pi$
$701$	−3492.05			−0.188149			−0.0940747	+	0.995565i	$0.529989\pi$
$702$		0			0
$703$	−6014.12			−0.322656
$704$	−1634.39	−	9269.06i	−0.0874975	−	0.496223i
$705$		0			0
$706$	−877.329	+	319.321i	−0.0467687	+	0.0170224i
$707$	15154.9	+	12716.5i	0.806168	+	0.676455i
$708$		0			0
$709$	32327.1	+	11766.1i	1.71237	+	0.623252i	0.997136	−	0.0756335i	$-0.0240979\pi$
$709$	32327.1	+	11766.1i	1.71237	+	0.623252i	0.715234	+	0.698885i	$0.246320\pi$
$710$	156.462	+	271.000i	0.00827030	+	0.0143246i
$711$		0			0
$712$	12142.1	−	21030.6i	0.639105	−	1.10696i
$713$	−17025.6	+	14286.2i	−0.894270	+	0.750382i
$714$		0			0
$715$	707.715	−	4013.65i	0.0370169	−	0.209933i
$716$	−267.856	+	1519.09i	−0.0139808	+	0.0792891i
$717$		0			0
$718$	8873.68	−	7445.91i	0.461230	−	0.387018i
$719$	13224.9	−	22906.3i	0.685963	−	1.18812i	−0.287170	−	0.957880i	$-0.592715\pi$
$719$	13224.9	−	22906.3i	0.685963	−	1.18812i	0.973133	−	0.230243i	$-0.0739521\pi$
$720$		0			0
$721$	−666.817	−	1154.96i	−0.0344432	−	0.0596574i
$722$	−1319.50	−	480.257i	−0.0680146	−	0.0247553i
$723$		0			0
$724$	3673.20	+	3082.18i	0.188554	+	0.158216i
$725$	−12038.1	+	4381.52i	−0.616668	+	0.224449i
$726$		0			0
$727$	−2519.10	−	14286.5i	−0.128512	−	0.728828i	−0.979160	−	0.203092i	$-0.934901\pi$
$727$	−2519.10	−	14286.5i	−0.128512	−	0.728828i	0.850648	−	0.525736i	$-0.176210\pi$
$728$	−19002.3			−0.967406
$729$		0			0
$730$	1653.44			0.0838309
$731$	7244.76	+	41087.1i	0.366562	+	2.07888i
$732$		0			0
$733$	−9323.69	+	3393.54i	−0.469820	+	0.171001i	−0.566071	−	0.824357i	$-0.691537\pi$
$733$	−9323.69	+	3393.54i	−0.469820	+	0.171001i	0.0962507	+	0.995357i	$0.469315\pi$
$734$	6194.79	+	5198.04i	0.311517	+	0.261394i
$735$		0			0
$736$	15576.7	+	5669.46i	0.780116	+	0.283939i
$737$	4788.40	+	8293.76i	0.239326	+	0.414524i
$738$		0			0
$739$	−894.624	+	1549.53i	−0.0445322	+	0.0771320i	−0.887432	−	0.460938i	$-0.847513\pi$
$739$	−894.624	+	1549.53i	−0.0445322	+	0.0771320i	0.842900	+	0.538070i	$0.180846\pi$
$740$	674.715	−	566.153i	0.0335176	−	0.0281246i
$741$		0			0
$742$	−3.99950	+	22.6823i	−0.000197879	+	0.00112223i
$743$	−3071.97	+	17422.0i	−0.151682	+	0.860232i	0.810075	+	0.586327i	$0.199427\pi$
$743$	−3071.97	+	17422.0i	−0.151682	+	0.860232i	−0.961757	+	0.273905i	$0.911685\pi$
$744$		0			0
$745$	−2275.44	+	1909.32i	−0.111900	+	0.0938956i
$746$	−1460.52	+	2529.70i	−0.0716805	+	0.124154i
$747$		0			0
$748$	4253.79	+	7367.77i	0.207933	+	0.360150i
$749$	17089.2	+	6219.95i	0.833678	+	0.303434i
$750$		0			0
$751$	30830.2	+	25869.6i	1.49801	+	1.25698i	0.883818	+	0.467830i	$0.154964\pi$
$751$	30830.2	+	25869.6i	1.49801	+	1.25698i	0.614196	+	0.789153i	$0.289480\pi$
$752$	4328.99	−	1575.63i	0.209923	−	0.0764058i
$753$		0			0
$754$	2463.93	+	13973.6i	0.119006	+	0.674919i
$755$	2672.94			0.128845
$756$		0			0
$757$	28253.8			1.35654			0.678270	−	0.734813i	$-0.262730\pi$
$757$	28253.8			1.35654			0.678270	+	0.734813i	$0.262730\pi$
$758$	−727.615	−	4126.51i	−0.0348657	−	0.197733i
$759$		0			0
$760$	−4733.51	+	1722.86i	−0.225924	+	0.0822298i
$761$	2254.46	+	1891.72i	0.107390	+	0.0901112i	0.694902	−	0.719105i	$-0.255448\pi$
$761$	2254.46	+	1891.72i	0.107390	+	0.0901112i	−0.587511	+	0.809216i	$0.699892\pi$
$762$		0			0
$763$	20583.9	+	7491.91i	0.976653	+	0.355472i
$764$	−1807.19	−	3130.14i	−0.0855782	−	0.148226i
$765$		0			0
$766$	−7469.49	+	12937.5i	−0.352328	+	0.610251i
$767$	33031.4	−	27716.6i	1.55501	−	1.30481i
$768$		0			0
$769$	6532.18	−	37045.8i	0.306315	−	1.73720i	−0.310933	−	0.950432i	$-0.600642\pi$
$769$	6532.18	−	37045.8i	0.306315	−	1.73720i	0.617248	−	0.786768i	$-0.288247\pi$
$770$	243.680	−	1381.98i	0.0114047	−	0.0646793i
$771$		0			0
$772$	−3980.92	+	3340.39i	−0.185591	+	0.155730i
$773$	6917.54	−	11981.5i	0.321871	−	0.557497i	−0.659003	−	0.752140i	$-0.729022\pi$
$773$	6917.54	−	11981.5i	0.321871	−	0.557497i	0.980874	+	0.194643i	$0.0623549\pi$
$774$		0			0
$775$	−13115.6	−	22716.9i	−0.607905	−	1.05292i
$776$	−18004.3	−	6553.02i	−0.832881	−	0.303144i
$777$		0			0
$778$	−9006.95	−	7557.73i	−0.415058	−	0.348275i
$779$	27973.8	−	10181.6i	1.28660	−	0.468286i
$780$		0			0
$781$	231.582	+	1313.37i	0.0106103	+	0.0601740i
$782$	17348.6			0.793329
$783$		0			0
$784$	2449.60			0.111589
$785$	1059.39	+	6008.09i	0.0481672	+	0.273170i
$786$		0			0
$787$	−11218.6	+	4083.24i	−0.508133	+	0.184945i	−0.583348	−	0.812222i	$-0.698258\pi$
$787$	−11218.6	+	4083.24i	−0.508133	+	0.184945i	0.0752157	+	0.997167i	$0.476035\pi$
$788$	−11027.4	−	9253.12i	−0.498523	−	0.418310i
$789$		0			0
$790$	−863.999	−	314.470i	−0.0389110	−	0.0141625i
$791$	9110.80	+	15780.4i	0.409536	+	0.709336i
$792$		0			0
$793$	12402.2	−	21481.2i	0.555378	−	0.961942i
$794$	−3696.94	+	3102.10i	−0.165239	+	0.138652i
$795$		0			0
$796$	−2359.73	+	13382.7i	−0.105073	+	0.595901i
$797$	2469.10	−	14002.9i	0.109736	−	0.622346i	−0.879486	−	0.475925i	$-0.842114\pi$
$797$	2469.10	−	14002.9i	0.109736	−	0.622346i	0.989222	−	0.146421i	$-0.0467754\pi$
$798$		0			0
$799$	−25965.2	+	21787.4i	−1.14967	+	0.964684i
$800$	−9782.04	+	16943.0i	−0.432309	+	0.748781i
$801$		0			0
$802$	11497.1	+	19913.6i	0.506208	+	0.876777i
$803$	6621.70	+	2410.10i	0.291002	+	0.105916i
$804$		0			0
$805$	2465.45	+	2068.76i	0.107945	+	0.0905767i
$806$	−27301.7	+	9936.99i	−1.19313	+	0.434262i
$807$		0			0
$808$	−6843.42	−	38811.0i	−0.297959	−	1.68981i
$809$	−6797.07			−0.295392			−0.147696	−	0.989033i	$-0.547186\pi$
$809$	−6797.07			−0.295392			−0.147696	+	0.989033i	$0.547186\pi$
$810$		0			0
$811$	−9855.20			−0.426711			−0.213356	−	0.976975i	$-0.568439\pi$
$811$	−9855.20			−0.426711			−0.213356	+	0.976975i	$0.568439\pi$
$812$	−954.166	−	5411.34i	−0.0412373	−	0.233868i
$813$		0			0
$814$	−3136.27	+	1141.51i	−0.135044	+	0.0491521i
$815$	−175.755	−	147.476i	−0.00755389	−	0.00633847i
$816$		0			0
$817$	−34242.0	−	12463.1i	−1.46631	−	0.533694i
$818$	4259.47	+	7377.61i	0.182065	+	0.315345i
$819$		0			0
$820$	−2179.87	+	3775.64i	−0.0928344	+	0.160794i
$821$	−4978.94	+	4177.83i	−0.211652	+	0.177597i	−0.742450	−	0.669901i	$-0.766337\pi$
$821$	−4978.94	+	4177.83i	−0.211652	+	0.177597i	0.530799	+	0.847498i	$0.321892\pi$
$822$		0			0
$823$	−2804.02	+	15902.4i	−0.118763	+	0.673538i	0.866055	+	0.499949i	$0.166648\pi$
$823$	−2804.02	+	15902.4i	−0.118763	+	0.673538i	−0.984818	+	0.173590i	$0.944463\pi$
$824$	−461.328	+	2616.32i	−0.0195038	+	0.110611i
$825$		0			0
$826$	11373.4	−	9543.39i	0.479092	−	0.402006i
$827$	−9781.92	+	16942.8i	−0.411307	+	0.712404i	−0.995033	−	0.0995466i	$-0.968261\pi$
$827$	−9781.92	+	16942.8i	−0.411307	+	0.712404i	0.583726	+	0.811950i	$0.301594\pi$
$828$		0			0
$829$	3895.95	+	6747.99i	0.163223	+	0.282711i	0.936023	−	0.351939i	$-0.114478\pi$
$829$	3895.95	+	6747.99i	0.163223	+	0.282711i	−0.772800	+	0.634650i	$0.781144\pi$
$830$	−4020.35	−	1463.29i	−0.168131	−	0.0611946i
$831$		0			0
$832$	21616.5	+	18138.4i	0.900740	+	0.755811i
$833$	−16936.3	+	6164.30i	−0.704450	+	0.256399i
$834$		0			0
$835$	−1462.50	−	8294.26i	−0.0606132	−	0.343754i
$836$	−7430.63			−0.307409
$837$		0			0
$838$	−10354.2			−0.426826
$839$	−2103.97	−	11932.2i	−0.0865757	−	0.490995i	−0.997005	−	0.0773316i	$-0.975360\pi$
$839$	−2103.97	−	11932.2i	−0.0865757	−	0.490995i	0.910430	−	0.413664i	$-0.135751\pi$
$840$		0			0
$841$	11778.9	−	4287.15i	0.482958	−	0.175782i
$842$	−22377.2	−	18776.7i	−0.915879	−	0.768514i
$843$		0			0
$844$	5412.48	+	1969.98i	0.220741	+	0.0803431i
$845$	3133.81	+	5427.91i	0.127581	+	0.220977i
$846$		0			0
$847$	−4940.87	+	8557.84i	−0.200437	+	0.347167i
$848$	9.29964	−	7.80332i	0.000376593	−	0.000315999i
$849$		0			0
$850$	−3555.52	+	20164.4i	−0.143475	+	0.813685i
$851$	1329.20	−	7538.26i	0.0535421	−	0.303652i
$852$		0			0
$853$	−19883.6	+	16684.3i	−0.798125	+	0.669706i	−0.947742	−	0.319038i	$-0.896640\pi$
$853$	−19883.6	+	16684.3i	−0.798125	+	0.669706i	0.149617	+	0.988744i	$0.452196\pi$
$854$	4270.32	−	7396.40i	0.171109	−	0.296370i
$855$		0			0
$856$	−18113.7	−	31373.9i	−0.723265	−	1.25273i
$857$	12727.2	+	4632.31i	0.507294	+	0.184640i	0.582972	−	0.812492i	$-0.301890\pi$
$857$	12727.2	+	4632.31i	0.507294	+	0.184640i	−0.0756775	+	0.997132i	$0.524112\pi$
$858$		0			0
$859$	−16044.7	−	13463.1i	−0.637298	−	0.534756i	0.265889	−	0.964004i	$-0.414334\pi$
$859$	−16044.7	−	13463.1i	−0.637298	−	0.534756i	−0.903187	+	0.429247i	$0.858779\pi$
$860$	5014.80	−	1825.24i	0.198841	−	0.0723722i
$861$		0			0
$862$	1610.57	+	9133.97i	0.0636382	+	0.360910i
$863$	15861.7			0.625653			0.312826	−	0.949810i	$-0.398724\pi$
$863$	15861.7			0.625653			0.312826	+	0.949810i	$0.398724\pi$
$864$		0			0
$865$	−1260.88			−0.0495620
$866$	−2133.28	−	12098.4i	−0.0837088	−	0.474736i
$867$		0			0
$868$	10572.7	−	3848.14i	0.413434	−	0.150477i
$869$	−3001.77	−	2518.78i	−0.117178	−	0.0983242i
$870$		0			0
$871$	−26980.7	−	9820.16i	−1.04960	−	0.382025i
$872$	−21817.9	−	37789.8i	−0.847303	−	1.46757i
$873$		0			0
$874$	−7576.24	+	13122.4i	−0.293215	+	0.507864i
$875$	−6001.11	+	5035.53i	−0.231856	+	0.194551i
$876$		0			0
$877$	−172.042	+	975.699i	−0.00662423	+	0.0375679i	−0.987941	−	0.154833i	$-0.950516\pi$
$877$	−172.042	+	975.699i	−0.00662423	+	0.0375679i	0.981316	+	0.192401i	$0.0616273\pi$
$878$	−2042.88	+	11585.8i	−0.0785238	+	0.445331i
$879$		0			0
$880$	−566.606	+	475.439i	−0.0217049	+	0.0182125i
$881$	−20960.4	+	36304.6i	−0.801561	+	1.38834i	0.117027	+	0.993129i	$0.462664\pi$
$881$	−20960.4	+	36304.6i	−0.801561	+	1.38834i	−0.918588	+	0.395216i	$0.870670\pi$
$882$		0			0
$883$	24426.1	+	42307.3i	0.930922	+	1.61240i	0.781749	+	0.623594i	$0.214328\pi$
$883$	24426.1	+	42307.3i	0.930922	+	1.61240i	0.149174	+	0.988811i	$0.452339\pi$
$884$	−23968.3	−	8723.76i	−0.911926	−	0.331914i
$885$		0			0
$886$	−4163.46	−	3493.56i	−0.157872	−	0.132470i
$887$	26224.5	−	9544.92i	0.992707	−	0.361316i	0.205939	−	0.978565i	$-0.433975\pi$
$887$	26224.5	−	9544.92i	0.992707	−	0.361316i	0.786768	+	0.617249i	$0.211753\pi$
$888$		0			0
$889$	−1274.32	−	7227.03i	−0.0480757	−	0.272651i
$890$	−5376.66			−0.202501
$891$		0			0
$892$	−18686.0			−0.701407
$893$	−5140.77	−	29154.8i	−0.192642	−	1.09253i
$894$		0			0
$895$	927.205	−	337.475i	0.0346291	−	0.0126040i
$896$	−4700.87	−	3944.50i	−0.175273	−	0.147072i
$897$		0			0
$898$	−9727.43	−	3540.49i	−0.361479	−	0.131568i
$899$	−12136.4	−	21020.8i	−0.450245	−	0.779847i
$900$		0			0
$901$	−44.6600	+	77.3534i	−0.00165132	+	0.00286017i
$902$	12655.4	−	10619.1i	0.467159	−	0.391993i
$903$		0			0
$904$	6303.17	−	35747.1i	0.231903	−	1.31519i
$905$	532.621	−	3020.64i	0.0195634	−	0.110950i
$906$		0			0
$907$	11001.8	−	9231.59i	0.402765	−	0.337960i	−0.418796	−	0.908080i	$-0.637548\pi$
$907$	11001.8	−	9231.59i	0.402765	−	0.337960i	0.821561	+	0.570120i	$0.193103\pi$
$908$	9100.68	−	15762.8i	0.332617	−	0.576110i
$909$		0			0
$910$	2103.62	+	3643.57i	0.0766310	+	0.132729i
$911$	−12385.3	−	4507.89i	−0.450433	−	0.163944i	0.106835	−	0.994277i	$-0.465928\pi$
$911$	−12385.3	−	4507.89i	−0.450433	−	0.163944i	−0.557268	+	0.830333i	$0.688150\pi$
$912$		0			0
$913$	−13967.8	−	11720.4i	−0.506316	−	0.424849i
$914$	24889.3	−	9058.98i	0.900729	−	0.327838i
$915$		0			0
$916$	162.396	+	920.994i	0.00585777	+	0.0332211i
$917$	−8876.37			−0.319655
$918$		0			0
$919$	39299.4			1.41063			0.705314	−	0.708895i	$-0.250806\pi$
$919$	39299.4			1.41063			0.705314	+	0.708895i	$0.250806\pi$
$920$	−1113.31	−	6313.88i	−0.0398964	−	0.226264i
$921$		0			0
$922$	24803.9	−	9027.89i	0.885980	−	0.322471i
$923$	−3062.91	−	2570.09i	−0.109227	−	0.0916528i
$924$		0			0
$925$	8489.36	+	3089.87i	0.301760	+	0.109832i
$926$	−15727.6	−	27241.1i	−0.558145	−	0.966735i
$927$		0			0
$928$	−9051.68	+	15678.0i	−0.320189	+	0.554584i
$929$	−14288.8	+	11989.7i	−0.504628	+	0.423433i	−0.859234	−	0.511582i	$-0.829059\pi$
$929$	−14288.8	+	11989.7i	−0.504628	+	0.423433i	0.354606	+	0.935016i	$0.384615\pi$
$930$		0			0
$931$	2733.52	−	15502.6i	0.0962272	−	0.545731i
$932$	59.9567	−	340.031i	0.00210724	−	0.0119508i
$933$		0			0
$934$	−25149.6	+	21103.1i	−0.881072	+	0.739307i
$935$	2721.03	−	4712.97i	0.0951735	−	0.164845i
$936$		0			0
$937$	23914.1	+	41420.5i	0.833768	+	1.44413i	0.895029	+	0.446007i	$0.147155\pi$
$937$	23914.1	+	41420.5i	0.833768	+	1.44413i	−0.0612608	+	0.998122i	$0.519512\pi$
$938$	−9289.98	−	3381.28i	−0.323378	−	0.117700i
$939$		0			0
$940$	3321.28	+	2786.89i	0.115243	+	0.0967003i
$941$	7128.76	−	2594.66i	0.246962	−	0.0898867i	−0.215574	−	0.976488i	$-0.569162\pi$
$941$	7128.76	−	2594.66i	0.246962	−	0.0898867i	0.462535	+	0.886601i	$0.346940\pi$
$942$		0			0
$943$	6579.35	+	37313.4i	0.227204	+	1.28854i
$944$	−7825.49			−0.269807
$945$		0			0
$946$	−20222.2			−0.695012
$947$	−5302.62	−	30072.7i	−0.181956	−	1.03192i	−0.929805	−	0.368053i	$-0.880024\pi$
$947$	−5302.62	−	30072.7i	−0.181956	−	1.03192i	0.747849	−	0.663869i	$-0.231087\pi$
$948$		0			0
$949$	−19852.5	+	7225.73i	−0.679073	+	0.247162i
$950$	−13699.6	−	11495.3i	−0.467866	−	0.392586i
$951$		0			0
$952$	−23843.3	−	8678.26i	−0.811730	−	0.295446i
$953$	11433.4	+	19803.3i	0.388631	+	0.673128i	0.992266	−	0.124133i	$-0.0396149\pi$
$953$	11433.4	+	19803.3i	0.388631	+	0.673128i	−0.603635	+	0.797261i	$0.706282\pi$
$954$		0			0
$955$	−1156.01	+	2002.27i	−0.0391702	+	0.0678449i
$956$	−5148.36	+	4319.99i	−0.174173	+	0.146149i
$957$		0			0
$958$	−341.762	+	1938.23i	−0.0115259	+	0.0653668i
$959$	−3353.48	+	19018.5i	−0.112919	+	0.640396i
$960$		0			0
$961$	15251.8	−	12797.8i	0.511962	−	0.429587i
$962$	5003.15	−	8665.71i	0.167680	−	0.290430i
$963$		0			0
$964$	−638.474	−	1105.87i	−0.0213318	−	0.0369478i
$965$	3123.73	+	1136.94i	0.104204	+	0.0379270i
$966$		0			0
$967$	−8141.88	−	6831.85i	−0.270760	−	0.227195i	0.497290	−	0.867584i	$-0.334329\pi$
$967$	−8141.88	−	6831.85i	−0.270760	−	0.227195i	−0.768050	+	0.640389i	$0.778773\pi$
$968$	18497.9	−	6732.67i	0.614198	−	0.223550i
$969$		0			0
$970$	736.633	+	4177.65i	0.0243833	+	0.138285i
$971$	8417.86			0.278210			0.139105	−	0.990278i	$-0.455577\pi$
$971$	8417.86			0.278210			0.139105	+	0.990278i	$0.455577\pi$
$972$		0			0
$973$	−9132.62			−0.300903
$974$	1378.57	+	7818.28i	0.0453515	+	0.257201i
$975$		0			0
$976$	−4230.12	+	1539.64i	−0.138732	+	0.0504945i
$977$	−40297.1	−	33813.3i	−1.31957	−	1.10725i	−0.986396	−	0.164384i	$-0.947436\pi$
$977$	−40297.1	−	33813.3i	−1.31957	−	1.10725i	−0.333173	−	0.942866i	$-0.608119\pi$
$978$		0			0
$979$	−21532.5	−	7837.18i	−0.702942	−	0.255850i
$980$	1152.70	+	1996.53i	0.0375731	+	0.0650785i
$981$		0			0
$982$	95.1258	−	164.763i	0.00309123	−	0.00535416i
$983$	−7860.30	+	6595.57i	−0.255040	+	0.214004i	−0.761339	−	0.648354i	$-0.775458\pi$
$983$	−7860.30	+	6595.57i	−0.255040	+	0.214004i	0.506299	+	0.862358i	$0.331013\pi$
$984$		0			0
$985$	−1599.00	+	9068.38i	−0.0517243	+	0.293343i
$986$	−3290.05	+	18658.8i	−0.106264	+	0.602655i
$987$		0			0
$988$	17065.8	−	14319.9i	0.549529	−	0.461110i
$989$	23189.5	−	40165.4i	0.745584	−	1.29139i
$990$		0			0
$991$	−26864.7	−	46531.1i	−0.861137	−	1.49153i	−0.870832	−	0.491580i	$-0.836420\pi$
$991$	−26864.7	−	46531.1i	−0.861137	−	1.49153i	0.00969537	−	0.999953i	$-0.496914\pi$
$992$	−34833.0	−	12678.2i	−1.11487	−	0.405778i
$993$		0			0
$994$	−1054.62	−	884.932i	−0.0336525	−	0.0282378i
$995$	8168.38	−	2973.05i	0.260256	−	0.0947255i
$996$		0			0
$997$	−3180.40	−	18037.0i	−0.101027	−	0.572955i	−0.992733	−	0.120339i	$-0.961602\pi$
$997$	−3180.40	−	18037.0i	−0.101027	−	0.572955i	0.891705	−	0.452616i	$-0.149509\pi$
$998$	−11753.5			−0.372796
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.4.e.c.28.3		48
3.2	odd	2		243.4.e.b.28.6		48
9.2	odd	6		243.4.e.a.109.6		48
9.4	even	3		27.4.e.a.4.6	✓	48
9.5	odd	6		81.4.e.a.64.3		48
9.7	even	3		243.4.e.d.109.3		48
27.2	odd	18		243.4.e.b.217.6		48
27.5	odd	18		729.4.a.c.1.17		24
27.7	even	9		243.4.e.d.136.3		48
27.11	odd	18		81.4.e.a.19.3		48
27.16	even	9		27.4.e.a.7.6	yes	48
27.20	odd	18		243.4.e.a.136.6		48
27.22	even	9		729.4.a.d.1.8		24
27.25	even	9	inner	243.4.e.c.217.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.4.6	✓	48	9.4	even	3
27.4.e.a.7.6	yes	48	27.16	even	9
81.4.e.a.19.3		48	27.11	odd	18
81.4.e.a.64.3		48	9.5	odd	6
243.4.e.a.109.6		48	9.2	odd	6
243.4.e.a.136.6		48	27.20	odd	18
243.4.e.b.28.6		48	3.2	odd	2
243.4.e.b.217.6		48	27.2	odd	18
243.4.e.c.28.3		48	1.1	even	1	trivial
243.4.e.c.217.3		48	27.25	even	9	inner
243.4.e.d.109.3		48	9.7	even	3
243.4.e.d.136.3		48	27.7	even	9
729.4.a.c.1.17		24	27.5	odd	18
729.4.a.d.1.8		24	27.22	even	9

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	243.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.336951 - 1.91095i) q^{2} +(3.97937 - 1.44837i) q^{4} +(-2.07510 - 1.74122i) q^{5} +(11.1989 + 4.07607i) q^{7} +(-11.8703 - 20.5600i) q^{8} +O(q^{10})\)	\(q+(-0.336951 - 1.91095i) q^{2} +(3.97937 - 1.44837i) q^{4} +(-2.07510 - 1.74122i) q^{5} +(11.1989 + 4.07607i) q^{7} +(-11.8703 - 20.5600i) q^{8} +(-2.62817 + 4.55212i) q^{10} +(-17.1606 + 14.3994i) q^{11} +(11.6626 - 66.1418i) q^{13} +(4.01566 - 22.7739i) q^{14} +(-9.33721 + 7.83485i) q^{16} +(44.8404 - 77.6659i) q^{17} +(39.1643 + 67.8345i) q^{19} +(-10.7795 - 3.92343i) q^{20} +(33.2988 + 27.9410i) q^{22} +(-93.6813 + 34.0972i) q^{23} +(-20.4318 - 115.875i) q^{25} -130.323 q^{26} +50.4682 q^{28} +(-18.9063 - 107.223i) q^{29} +(209.492 - 76.2489i) q^{31} +(-127.373 - 106.878i) q^{32} +(-163.524 - 59.5180i) q^{34} +(-16.1416 - 27.9580i) q^{35} +(-38.3904 + 66.4941i) q^{37} +(116.432 - 97.6977i) q^{38} +(-11.1673 + 63.3329i) q^{40} +(65.9957 - 374.280i) q^{41} +(-356.376 + 299.035i) q^{43} +(-47.4325 + 82.1555i) q^{44} +(96.7239 + 167.531i) q^{46} +(-355.160 - 129.268i) q^{47} +(-153.952 - 129.181i) q^{49} +(-214.545 + 78.0881i) q^{50} +(-49.3881 - 280.094i) q^{52} -0.995976 q^{53} +60.6826 q^{55} +(-49.1306 - 278.633i) q^{56} +(-198.527 + 72.2578i) q^{58} +(491.816 + 412.683i) q^{59} +(347.048 + 126.315i) q^{61} +(-216.296 - 374.636i) q^{62} +(-210.076 + 363.862i) q^{64} +(-139.368 + 116.944i) q^{65} +(74.2357 - 421.012i) q^{67} +(65.9474 - 374.007i) q^{68} +(-47.9873 + 40.2661i) q^{70} +(29.7664 - 51.5569i) q^{71} +(-157.281 - 272.418i) q^{73} +(140.002 + 50.9567i) q^{74} +(254.098 + 213.214i) q^{76} +(-250.873 + 91.3102i) q^{77} +(30.3749 + 172.265i) q^{79} +33.0179 q^{80} -737.467 q^{82} +(141.340 + 801.580i) q^{83} +(-228.282 + 83.0878i) q^{85} +(691.520 + 580.254i) q^{86} +(499.753 + 181.895i) q^{88} +(511.446 + 885.851i) q^{89} +(400.206 - 693.177i) q^{91} +(-323.407 + 271.371i) q^{92} +(-127.352 + 722.248i) q^{94} +(36.8448 - 208.957i) q^{95} +(618.233 - 518.759i) q^{97} +(-194.984 + 337.722i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 3 q^{2} + 3 q^{4} - 21 q^{5} + 3 q^{7} - 75 q^{8}+O(q^{10}) \) 48 * q + 3 * q^2 + 3 * q^4 - 21 * q^5 + 3 * q^7 - 75 * q^8	\( 48 q + 3 q^{2} + 3 q^{4} - 21 q^{5} + 3 q^{7} - 75 q^{8} - 3 q^{10} - 159 q^{11} + 3 q^{13} - 336 q^{14} - 45 q^{16} - 207 q^{17} - 3 q^{19} + 681 q^{20} + 111 q^{22} + 33 q^{23} + 435 q^{25} + 1914 q^{26} - 12 q^{28} - 51 q^{29} + 111 q^{31} + 1647 q^{32} - 513 q^{34} - 1257 q^{35} - 3 q^{37} - 525 q^{38} - 6 q^{40} + 447 q^{41} + 516 q^{43} - 2211 q^{44} - 3 q^{46} + 2109 q^{47} - 591 q^{49} - 4938 q^{50} - 1350 q^{52} + 2736 q^{53} - 12 q^{55} - 7773 q^{56} - 888 q^{58} + 3048 q^{59} + 57 q^{61} - 2118 q^{62} - 195 q^{64} + 3297 q^{65} + 2082 q^{67} + 3573 q^{68} + 1524 q^{70} - 3105 q^{71} - 219 q^{73} + 9006 q^{74} - 1425 q^{76} - 8985 q^{77} - 1401 q^{79} + 9870 q^{80} - 12 q^{82} - 8511 q^{83} - 1827 q^{85} + 12507 q^{86} - 3693 q^{88} - 5202 q^{89} + 267 q^{91} + 5118 q^{92} - 2211 q^{94} + 5178 q^{95} + 1569 q^{97} - 4392 q^{98}+O(q^{100}) \) 48 * q + 3 * q^2 + 3 * q^4 - 21 * q^5 + 3 * q^7 - 75 * q^8 - 3 * q^10 - 159 * q^11 + 3 * q^13 - 336 * q^14 - 45 * q^16 - 207 * q^17 - 3 * q^19 + 681 * q^20 + 111 * q^22 + 33 * q^23 + 435 * q^25 + 1914 * q^26 - 12 * q^28 - 51 * q^29 + 111 * q^31 + 1647 * q^32 - 513 * q^34 - 1257 * q^35 - 3 * q^37 - 525 * q^38 - 6 * q^40 + 447 * q^41 + 516 * q^43 - 2211 * q^44 - 3 * q^46 + 2109 * q^47 - 591 * q^49 - 4938 * q^50 - 1350 * q^52 + 2736 * q^53 - 12 * q^55 - 7773 * q^56 - 888 * q^58 + 3048 * q^59 + 57 * q^61 - 2118 * q^62 - 195 * q^64 + 3297 * q^65 + 2082 * q^67 + 3573 * q^68 + 1524 * q^70 - 3105 * q^71 - 219 * q^73 + 9006 * q^74 - 1425 * q^76 - 8985 * q^77 - 1401 * q^79 + 9870 * q^80 - 12 * q^82 - 8511 * q^83 - 1827 * q^85 + 12507 * q^86 - 3693 * q^88 - 5202 * q^89 + 267 * q^91 + 5118 * q^92 - 2211 * q^94 + 5178 * q^95 + 1569 * q^97 - 4392 * q^98

Introduction

L-functions

Modular forms

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