LMFDB - Embedded newform 350.5.i.a.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,5,Mod(199,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("350.199");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	350.i (of order $6$, degree $2$, 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:	$36.1794870793$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.2
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	350.199
Dual form			350.5.i.a.299.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.44949 + 1.41421i) q^{2} +(7.49706 - 12.9853i) q^{3} +(4.00000 - 6.92820i) q^{4} +42.4098i q^{6} +(-48.4974 + 7.00000i) q^{7} +22.6274i q^{8} +(-71.9117 - 124.555i) q^{9} +O(q^{10})$	\(q+(-2.44949 + 1.41421i) q^{2} +(7.49706 - 12.9853i) q^{3} +(4.00000 - 6.92820i) q^{4} +42.4098i q^{6} +(-48.4974 + 7.00000i) q^{7} +22.6274i q^{8} +(-71.9117 - 124.555i) q^{9} +(-21.9853 + 38.0796i) q^{11} +(-59.9764 - 103.882i) q^{12} +162.507 q^{13} +(108.894 - 85.7321i) q^{14} +(-32.0000 - 55.4256i) q^{16} +(54.1182 - 93.7355i) q^{17} +(352.294 + 203.397i) q^{18} +(-389.338 + 224.784i) q^{19} +(-272.691 + 682.232i) q^{21} -124.368i q^{22} +(-377.433 + 217.911i) q^{23} +(293.823 + 169.639i) q^{24} +(-398.059 + 229.819i) q^{26} -941.981 q^{27} +(-145.492 + 364.000i) q^{28} -742.118 q^{29} +(-900.175 - 519.716i) q^{31} +(156.767 + 90.5097i) q^{32} +(329.650 + 570.970i) q^{33} +306.139i q^{34} -1150.59 q^{36} +(-854.486 + 493.338i) q^{37} +(635.786 - 1101.21i) q^{38} +(1218.32 - 2110.20i) q^{39} +1143.70i q^{41} +(-296.868 - 2056.76i) q^{42} +2418.82i q^{43} +(175.882 + 304.637i) q^{44} +(616.346 - 1067.54i) q^{46} +(672.714 + 1165.17i) q^{47} -959.623 q^{48} +(2303.00 - 678.964i) q^{49} +(-811.455 - 1405.48i) q^{51} +(650.027 - 1125.88i) q^{52} +(3088.42 + 1783.10i) q^{53} +(2307.37 - 1332.16i) q^{54} +(-158.392 - 1097.37i) q^{56} +6740.88i q^{57} +(1817.81 - 1049.51i) q^{58} +(-3710.93 - 2142.50i) q^{59} +(-1209.57 + 698.345i) q^{61} +2939.96 q^{62} +(4359.41 + 5537.20i) q^{63} -512.000 q^{64} +(-1614.95 - 932.390i) q^{66} +(6292.36 + 3632.89i) q^{67} +(-432.946 - 749.884i) q^{68} +6534.77i q^{69} +5987.76 q^{71} +(2818.35 - 1627.18i) q^{72} +(288.746 - 500.123i) q^{73} +(1395.37 - 2416.85i) q^{74} +3596.55i q^{76} +(799.672 - 2000.66i) q^{77} +6891.88i q^{78} +(-1573.12 - 2724.72i) q^{79} +(-1237.24 + 2142.95i) q^{81} +(-1617.43 - 2801.47i) q^{82} -4729.96 q^{83} +(3635.88 + 4618.19i) q^{84} +(-3420.73 - 5924.88i) q^{86} +(-5563.70 + 9636.61i) q^{87} +(-861.644 - 497.470i) q^{88} +(725.651 - 418.955i) q^{89} +(-7881.16 + 1137.55i) q^{91} +3486.58i q^{92} +(-13497.3 + 7792.69i) q^{93} +(-3295.61 - 1902.72i) q^{94} +(2350.59 - 1357.11i) q^{96} -5622.23 q^{97} +(-4680.97 + 4920.05i) q^{98} +6323.99 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 32 q^{4} - 168 q^{9}+O(q^{10}) $ 8 * q + 32 * q^4 - 168 * q^9	$ 8 q + 32 q^{4} - 168 q^{9} - 108 q^{11} - 256 q^{16} - 60 q^{19} - 756 q^{21} + 1536 q^{24} - 3456 q^{26} - 6480 q^{29} - 1092 q^{31} - 2688 q^{36} + 6624 q^{39} + 864 q^{44} + 7680 q^{46} + 18424 q^{49} + 636 q^{51} + 2880 q^{54} - 24732 q^{59} + 15372 q^{61} - 4096 q^{64} - 6912 q^{66} + 37584 q^{71} + 8640 q^{74} - 1588 q^{79} - 8676 q^{81} + 10080 q^{84} - 20736 q^{86} + 24948 q^{89} + 5376 q^{91} - 30336 q^{94} + 12288 q^{96} + 22896 q^{99}+O(q^{100}) $ 8 * q + 32 * q^4 - 168 * q^9 - 108 * q^11 - 256 * q^16 - 60 * q^19 - 756 * q^21 + 1536 * q^24 - 3456 * q^26 - 6480 * q^29 - 1092 * q^31 - 2688 * q^36 + 6624 * q^39 + 864 * q^44 + 7680 * q^46 + 18424 * q^49 + 636 * q^51 + 2880 * q^54 - 24732 * q^59 + 15372 * q^61 - 4096 * q^64 - 6912 * q^66 + 37584 * q^71 + 8640 * q^74 - 1588 * q^79 - 8676 * q^81 + 10080 * q^84 - 20736 * q^86 + 24948 * q^89 + 5376 * q^91 - 30336 * q^94 + 12288 * q^96 + 22896 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.44949	+	1.41421i	−0.612372	+	0.353553i
$2$	−2.44949	+	1.41421i	−0.612372	+	0.353553i
$3$	7.49706	−	12.9853i	0.833006	−	1.44281i	−0.0626373	−	0.998036i	$-0.519951\pi$
$3$	7.49706	−	12.9853i	0.833006	−	1.44281i	0.895643	−	0.444773i	$-0.146716\pi$
$4$	4.00000	−	6.92820i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$			42.4098i			1.17805i
$7$	−48.4974	+	7.00000i	−0.989743	+	0.142857i
$7$	−48.4974	+	7.00000i	−0.989743	+	0.142857i
$8$			22.6274i			0.353553i
$9$	−71.9117	−	124.555i	−0.887799	−	1.53771i
$10$		0			0
$11$	−21.9853	+	38.0796i	−0.181697	+	0.314708i	−0.942458	−	0.334324i	$-0.891492\pi$
$11$	−21.9853	+	38.0796i	−0.181697	+	0.314708i	0.760762	+	0.649031i	$0.224826\pi$
$12$	−59.9764	−	103.882i	−0.416503	−	0.721405i
$13$	162.507			0.961579			0.480790	−	0.876836i	$-0.340350\pi$
$13$	162.507			0.961579			0.480790	+	0.876836i	$0.340350\pi$
$14$	108.894	−	85.7321i	0.555584	−	0.437409i
$15$		0			0
$16$	−32.0000	−	55.4256i	−0.125000	−	0.216506i
$17$	54.1182	−	93.7355i	0.187260	−	0.324344i	−0.757076	−	0.653327i	$-0.773373\pi$
$17$	54.1182	−	93.7355i	0.187260	−	0.324344i	0.944336	+	0.328983i	$0.106706\pi$
$18$	352.294	+	203.397i	1.08733	+	0.627768i
$19$	−389.338	+	224.784i	−1.07850	+	0.622671i	−0.930491	−	0.366315i	$-0.880619\pi$
$19$	−389.338	+	224.784i	−1.07850	+	0.622671i	−0.148007	+	0.988986i	$0.547286\pi$
$20$		0			0
$21$	−272.691	+	682.232i	−0.618347	+	1.54701i
$22$		−	124.368i		−	0.256958i
$23$	−377.433	+	217.911i	−0.713485	+	0.411931i	−0.812350	−	0.583170i	$-0.801812\pi$
$23$	−377.433	+	217.911i	−0.713485	+	0.411931i	0.0988653	+	0.995101i	$0.468479\pi$
$24$	293.823	+	169.639i	0.510110	+	0.294512i
$25$		0			0
$26$	−398.059	+	229.819i	−0.588844	+	0.339970i
$27$	−941.981			−1.29215
$28$	−145.492	+	364.000i	−0.185577	+	0.464286i
$29$	−742.118			−0.882423			−0.441212	−	0.897403i	$-0.645451\pi$
$29$	−742.118			−0.882423			−0.441212	+	0.897403i	$0.645451\pi$
$30$		0			0
$31$	−900.175	−	519.716i	−0.936707	−	0.540808i	−0.0477804	−	0.998858i	$-0.515215\pi$
$31$	−900.175	−	519.716i	−0.936707	−	0.540808i	−0.888926	+	0.458050i	$0.848548\pi$
$32$	156.767	+	90.5097i	0.153093	+	0.0883883i
$33$	329.650	+	570.970i	0.302709	+	0.524307i
$34$			306.139i			0.264826i
$35$		0			0
$36$	−1150.59			−0.887799
$37$	−854.486	+	493.338i	−0.624168	+	0.360364i	−0.778490	−	0.627657i	$-0.784014\pi$
$37$	−854.486	+	493.338i	−0.624168	+	0.360364i	0.154322	+	0.988021i	$0.450681\pi$
$38$	635.786	−	1101.21i	0.440295	−	0.762613i
$39$	1218.32	−	2110.20i	0.801001	−	1.38737i
$40$		0			0
$41$			1143.70i			0.680366i	0.940359	+	0.340183i	$0.110489\pi$
$41$			1143.70i			0.680366i	−0.940359	+	0.340183i	$0.889511\pi$
$42$	−296.868	−	2056.76i	−0.168293	−	1.16597i
$43$			2418.82i			1.30818i	0.756418	+	0.654089i	$0.226948\pi$
$43$			2418.82i			1.30818i	−0.756418	+	0.654089i	$0.773052\pi$
$44$	175.882	+	304.637i	0.0908483	+	0.157354i
$45$		0			0
$46$	616.346	−	1067.54i	0.291279	−	0.504510i
$47$	672.714	+	1165.17i	0.304533	+	0.527467i	0.977157	−	0.212517i	$-0.0681662\pi$
$47$	672.714	+	1165.17i	0.304533	+	0.527467i	−0.672624	+	0.739984i	$0.734833\pi$
$48$	−959.623			−0.416503
$49$	2303.00	−	678.964i	0.959184	−	0.282784i
$50$		0			0
$51$	−811.455	−	1405.48i	−0.311978	−	0.540362i
$52$	650.027	−	1125.88i	0.240395	−	0.416376i
$53$	3088.42	+	1783.10i	1.09947	+	0.634782i	0.936083	−	0.351780i	$-0.114423\pi$
$53$	3088.42	+	1783.10i	1.09947	+	0.634782i	0.163391	+	0.986561i	$0.447757\pi$
$54$	2307.37	−	1332.16i	0.791280	−	0.456846i
$55$		0			0
$56$	−158.392	−	1097.37i	−0.0505076	−	0.349927i
$57$			6740.88i			2.07475i
$58$	1817.81	−	1049.51i	0.540372	−	0.311984i
$59$	−3710.93	−	2142.50i	−1.06605	−	0.615485i	−0.138952	−	0.990299i	$-0.544373\pi$
$59$	−3710.93	−	2142.50i	−1.06605	−	0.615485i	−0.927100	+	0.374814i	$0.877707\pi$
$60$		0			0
$61$	−1209.57	+	698.345i	−0.325066	+	0.187677i	−0.653648	−	0.756799i	$-0.726762\pi$
$61$	−1209.57	+	698.345i	−0.325066	+	0.187677i	0.328583	+	0.944475i	$0.393429\pi$
$62$	2939.96			0.764818
$63$	4359.41	+	5537.20i	1.09837	+	1.39511i
$64$	−512.000			−0.125000
$65$		0			0
$66$	−1614.95	−	932.390i	−0.370741	−	0.214047i
$67$	6292.36	+	3632.89i	1.40173	+	0.809288i	0.994570	−	0.104070i	$-0.0331866\pi$
$67$	6292.36	+	3632.89i	1.40173	+	0.809288i	0.407158	+	0.913358i	$0.366520\pi$
$68$	−432.946	−	749.884i	−0.0936301	−	0.162172i
$69$			6534.77i			1.37256i
$70$		0			0
$71$	5987.76			1.18781			0.593906	−	0.804534i	$-0.297585\pi$
$71$	5987.76			1.18781			0.593906	+	0.804534i	$0.297585\pi$
$72$	2818.35	−	1627.18i	0.543663	−	0.313884i
$73$	288.746	−	500.123i	0.0541840	−	0.0938494i	−0.837661	−	0.546190i	$-0.816078\pi$
$73$	288.746	−	500.123i	0.0541840	−	0.0938494i	0.891845	+	0.452341i	$0.149411\pi$
$74$	1395.37	−	2416.85i	0.254815	−	0.441353i
$75$		0			0
$76$			3596.55i			0.622671i
$77$	799.672	−	2000.66i	0.134875	−	0.337436i
$78$			6891.88i			1.13279i
$79$	−1573.12	−	2724.72i	−0.252061	−	0.436583i	0.712032	−	0.702147i	$-0.247775\pi$
$79$	−1573.12	−	2724.72i	−0.252061	−	0.436583i	−0.964093	+	0.265564i	$0.914442\pi$
$80$		0			0
$81$	−1237.24	+	2142.95i	−0.188574	+	0.326620i
$82$	−1617.43	−	2801.47i	−0.240546	−	0.416637i
$83$	−4729.96			−0.686596			−0.343298	−	0.939227i	$-0.611544\pi$
$83$	−4729.96			−0.686596			−0.343298	+	0.939227i	$0.611544\pi$
$84$	3635.88	+	4618.19i	0.515289	+	0.654505i
$85$		0			0
$86$	−3420.73	−	5924.88i	−0.462511	−	0.801092i
$87$	−5563.70	+	9636.61i	−0.735064	+	1.27317i
$88$	−861.644	−	497.470i	−0.111266	−	0.0642394i
$89$	725.651	−	418.955i	0.0916110	−	0.0528916i	−0.453495	−	0.891259i	$-0.649823\pi$
$89$	725.651	−	418.955i	0.0916110	−	0.0528916i	0.545106	+	0.838367i	$0.316490\pi$
$90$		0			0
$91$	−7881.16	+	1137.55i	−0.951716	+	0.137368i
$92$			3486.58i			0.411931i
$93$	−13497.3	+	7792.69i	−1.56057	+	0.900993i
$94$	−3295.61	−	1902.72i	−0.372975	−	0.215337i
$95$		0			0
$96$	2350.59	−	1357.11i	0.255055	−	0.147256i
$97$	−5622.23			−0.597537			−0.298769	−	0.954326i	$-0.596576\pi$
$97$	−5622.23			−0.597537			−0.298769	+	0.954326i	$0.596576\pi$
$98$	−4680.97	+	4920.05i	−0.487398	+	0.512292i
$99$	6323.99			0.645240
$100$		0			0
$101$	−5703.21	−	3292.75i	−0.559083	−	0.322787i	0.193694	−	0.981062i	$-0.437953\pi$
$101$	−5703.21	−	3292.75i	−0.559083	−	0.322787i	−0.752778	+	0.658275i	$0.771286\pi$
$102$	3975.30	+	2295.14i	0.382093	+	0.220602i
$103$	762.249	+	1320.25i	0.0718492	+	0.124447i	0.899712	−	0.436484i	$-0.143777\pi$
$103$	762.249	+	1320.25i	0.0718492	+	0.124447i	−0.827863	+	0.560931i	$0.810443\pi$
$104$			3677.11i			0.339970i
$105$		0			0
$106$	−10086.7			−0.897717
$107$	−9185.61	+	5303.31i	−0.802306	+	0.463212i	−0.844277	−	0.535907i	$-0.819970\pi$
$107$	−9185.61	+	5303.31i	−0.802306	+	0.463212i	0.0419706	+	0.999119i	$0.486636\pi$
$108$	−3767.92	+	6526.23i	−0.323039	+	0.559519i
$109$	−6976.13	+	12083.0i	−0.587167	+	1.01700i	0.407434	+	0.913235i	$0.366424\pi$
$109$	−6976.13	+	12083.0i	−0.587167	+	1.01700i	−0.994601	+	0.103769i	$0.966910\pi$
$110$		0			0
$111$			14794.3i			1.20074i
$112$	1939.90	+	2464.00i	0.154647	+	0.196429i
$113$		−	8811.30i		−	0.690054i	−0.938593	−	0.345027i	$-0.887870\pi$
$113$		−	8811.30i		−	0.690054i	0.938593	−	0.345027i	$-0.112130\pi$
$114$	−9533.04	−	16511.7i	−0.733537	−	1.27052i
$115$		0			0
$116$	−2968.47	+	5141.54i	−0.220606	+	0.382100i
$117$	−11686.1	−	20241.0i	−0.853689	−	1.47863i
$118$	12119.8			0.870427
$119$	−1968.45	+	4924.76i	−0.139005	+	0.347769i
$120$		0			0
$121$	6353.79	+	11005.1i	0.433973	+	0.751663i
$122$	1975.22	−	3421.18i	0.132707	−	0.229856i
$123$	14851.2	+	8574.35i	0.981638	+	0.566749i
$124$	−7201.40	+	4157.73i	−0.468353	+	0.270404i
$125$		0			0
$126$	−18509.1	−	7398.17i	−1.16586	−	0.465997i
$127$		−	3992.70i		−	0.247548i	−0.992310	−	0.123774i	$-0.960500\pi$
$127$		−	3992.70i		−	0.247548i	0.992310	−	0.123774i	$-0.0394998\pi$
$128$	1254.14	−	724.077i	0.0765466	−	0.0441942i
$129$	31409.1	+	18134.0i	1.88745	+	1.08972i
$130$		0			0
$131$	−17515.4	+	10112.5i	−1.02065	+	0.589272i	−0.914292	−	0.405056i	$-0.867252\pi$
$131$	−17515.4	+	10112.5i	−1.02065	+	0.589272i	−0.106357	+	0.994328i	$0.533919\pi$
$132$	5274.40			0.302709
$133$	17308.4	−	13626.8i	0.978483	−	0.770355i
$134$	−20550.7			−1.14451
$135$		0			0
$136$	2120.99	+	1224.56i	0.114673	+	0.0662065i
$137$	21700.6	+	12528.9i	1.15620	+	0.667530i	0.950389	−	0.311062i	$-0.100685\pi$
$137$	21700.6	+	12528.9i	1.15620	+	0.667530i	0.205807	+	0.978593i	$0.434018\pi$
$138$	−9241.56	−	16006.9i	−0.485274	−	0.840520i
$139$			20070.1i			1.03877i	0.854541	+	0.519385i	$0.173839\pi$
$139$			20070.1i			1.03877i	−0.854541	+	0.519385i	$0.826161\pi$
$140$		0			0
$141$	20173.5			1.01471
$142$	−14667.0	+	8467.98i	−0.727384	+	0.419955i
$143$	−3572.76	+	6188.20i	−0.174716	+	0.302616i
$144$	−4602.35	+	7971.50i	−0.221950	+	0.384428i
$145$		0			0
$146$			1633.40i			0.0766277i
$147$	8449.18	−	34995.3i	0.391003	−	1.61948i
$148$			7893.40i			0.360364i
$149$	−21353.9	−	36986.1i	−0.961846	−	1.66597i	−0.717860	−	0.696188i	$-0.754878\pi$
$149$	−21353.9	−	36986.1i	−0.961846	−	1.66597i	−0.243986	−	0.969779i	$-0.578455\pi$
$150$		0			0
$151$	−14803.7	+	25640.8i	−0.649258	+	1.12455i	0.334043	+	0.942558i	$0.391587\pi$
$151$	−14803.7	+	25640.8i	−0.649258	+	1.12455i	−0.983301	+	0.181989i	$0.941746\pi$
$152$	−5086.29	−	8809.71i	−0.220147	−	0.381307i
$153$	−15566.9			−0.664998
$154$	870.573	+	6031.50i	0.0367082	+	0.254322i
$155$		0			0
$156$	−9746.58	−	16881.6i	−0.400501	−	0.693687i
$157$	6118.53	−	10597.6i	0.248226	−	0.429940i	−0.714808	−	0.699321i	$-0.753486\pi$
$157$	6118.53	−	10597.6i	0.248226	−	0.429940i	0.963034	+	0.269381i	$0.0868191\pi$
$158$	7706.66	+	4449.44i	0.308711	+	0.178234i
$159$	46308.1	−	26736.0i	1.83174	−	1.05755i
$160$		0			0
$161$	16779.2	−	13210.2i	0.647319	−	0.509632i
$162$		−	6998.86i		−	0.266684i
$163$	18646.5	−	10765.6i	0.701814	−	0.405193i	−0.106209	−	0.994344i	$-0.533871\pi$
$163$	18646.5	−	10765.6i	0.701814	−	0.405193i	0.808023	+	0.589151i	$0.200538\pi$
$164$	7923.75	+	4574.78i	0.294607	+	0.170092i
$165$		0			0
$166$	11586.0	−	6689.17i	0.420452	−	0.242748i
$167$	−16578.9			−0.594461			−0.297230	−	0.954806i	$-0.596063\pi$
$167$	−16578.9			−0.594461			−0.297230	+	0.954806i	$0.596063\pi$
$168$	−15437.1	−	6170.29i	−0.546951	−	0.218619i
$169$	−2152.52			−0.0753658
$170$		0			0
$171$	55995.9	+	32329.2i	1.91498	+	1.10561i
$172$	16758.1	+	9675.28i	0.566458	+	0.327044i
$173$	−20191.5	−	34972.8i	−0.674648	−	1.16852i	−0.976572	−	0.215192i	$-0.930962\pi$
$173$	−20191.5	−	34972.8i	−0.674648	−	1.16852i	0.301924	−	0.953332i	$-0.402371\pi$
$174$		−	31473.0i		−	1.03954i
$175$		0			0
$176$	2814.12			0.0908483
$177$	−55642.0	+	32124.9i	−1.77606	+	1.02541i
$178$	−1184.98	+	2052.45i	−0.0374000	+	0.0647788i
$179$	−26747.2	+	46327.5i	−0.834780	+	1.44588i	0.0594290	+	0.998233i	$0.481072\pi$
$179$	−26747.2	+	46327.5i	−0.834780	+	1.44588i	−0.894209	+	0.447649i	$0.852261\pi$
$180$		0			0
$181$		−	54202.1i		−	1.65447i	−0.561857	−	0.827235i	$-0.689913\pi$
$181$		−	54202.1i		−	1.65447i	0.561857	−	0.827235i	$-0.310087\pi$
$182$	17696.1	−	13932.1i	0.534238	−	0.420603i
$183$			20942.1i			0.625343i
$184$	−4930.77	−	8540.34i	−0.145639	−	0.252255i
$185$		0			0
$186$	22041.0	−	38176.2i	0.637098	−	1.10349i
$187$	2379.61	+	4121.60i	0.0680491	+	0.117864i
$188$	10763.4			0.304533
$189$	45683.6	−	6593.86i	1.27890	−	0.184594i
$190$		0			0
$191$	601.936	+	1042.58i	0.0165000	+	0.0285788i	0.874158	−	0.485643i	$-0.161414\pi$
$191$	601.936	+	1042.58i	0.0165000	+	0.0285788i	−0.857658	+	0.514221i	$0.828081\pi$
$192$	−3838.49	+	6648.46i	−0.104126	+	0.180351i
$193$	−44438.3	−	25656.5i	−1.19301	−	0.688783i	−0.234019	−	0.972232i	$-0.575188\pi$
$193$	−44438.3	−	25656.5i	−1.19301	−	0.688783i	−0.958987	+	0.283449i	$0.908521\pi$
$194$	13771.6	−	7951.03i	0.365915	−	0.211261i
$195$		0			0
$196$	4508.00	−	18671.5i	0.117347	−	0.486035i
$197$			1456.28i			0.0375242i	0.999824	+	0.0187621i	$0.00597251\pi$
$197$			1456.28i			0.0375242i	−0.999824	+	0.0187621i	$0.994027\pi$
$198$	−15490.6	+	8943.48i	−0.395127	+	0.228127i
$199$	−59546.3	−	34379.1i	−1.50366	−	0.868137i	−0.999991	−	0.00423890i	$-0.998651\pi$
$199$	−59546.3	−	34379.1i	−1.50366	−	0.868137i	−0.503667	−	0.863898i	$-0.668016\pi$
$200$		0			0
$201$	94348.3	−	54472.0i	2.33530	−	1.34828i
$202$	18626.6			0.456490
$203$	35990.8	−	5194.82i	0.873372	−	0.126060i
$204$	−12983.3			−0.311978
$205$		0			0
$206$	−3734.24	−	2155.96i	−0.0879970	−	0.0508051i
$207$	54283.7	+	31340.7i	1.26686	+	0.731423i
$208$	−5200.22	−	9007.04i	−0.120197	−	0.208188i
$209$		−	19767.8i		−	0.452549i
$210$		0			0
$211$	−622.821			−0.0139894			−0.00699469	−	0.999976i	$-0.502226\pi$
$211$	−622.821			−0.0139894			−0.00699469	+	0.999976i	$0.502226\pi$
$212$	24707.4	−	14264.8i	0.549737	−	0.317391i
$213$	44890.6	−	77752.8i	0.989455	−	1.71379i
$214$	15000.0	−	25980.8i	0.327540	−	0.567316i
$215$		0			0
$216$		−	21314.6i		−	0.456846i
$217$	47294.2	+	18903.7i	1.00436	+	0.401446i
$218$		−	39463.0i		−	0.830380i
$219$	−4329.50	−	7498.91i	−0.0902712	−	0.156354i
$220$		0			0
$221$	8794.58	−	15232.7i	0.180066	−	0.311883i
$222$	−20922.3	−	36238.5i	−0.424526	−	0.735300i
$223$	11509.7			0.231449			0.115725	−	0.993281i	$-0.463081\pi$
$223$	11509.7			0.231449			0.115725	+	0.993281i	$0.463081\pi$
$224$	−8236.38	−	3292.11i	−0.164150	−	0.0656113i
$225$		0			0
$226$	12461.1	+	21583.2i	0.243971	+	0.422570i
$227$	−28183.6	+	48815.4i	−0.546946	+	0.947339i	0.451535	+	0.892253i	$0.350876\pi$
$227$	−28183.6	+	48815.4i	−0.546946	+	0.947339i	−0.998482	+	0.0550855i	$0.982457\pi$
$228$	46702.2	+	26963.5i	0.898395	+	0.518689i
$229$	36484.4	−	21064.3i	0.695722	−	0.401675i	−0.110030	−	0.993928i	$-0.535095\pi$
$229$	36484.4	−	21064.3i	0.695722	−	0.401675i	0.805752	+	0.592253i	$0.201761\pi$
$230$		0			0
$231$	−19984.0	−	25383.0i	−0.374505	−	0.475685i
$232$		−	16792.2i		−	0.311984i
$233$	−47719.6	+	27550.9i	−0.878992	+	0.507486i	−0.870326	−	0.492476i	$-0.836092\pi$
$233$	−47719.6	+	27550.9i	−0.878992	+	0.507486i	−0.00866633	+	0.999962i	$0.502759\pi$
$234$	57250.2	+	33053.4i	1.04555	+	0.603649i
$235$		0			0
$236$	−29687.4	+	17140.0i	−0.533026	+	0.307743i
$237$	−47174.9			−0.839875
$238$	−2142.97	−	14846.9i	−0.0378323	−	0.262110i
$239$	−23082.5			−0.404098			−0.202049	−	0.979375i	$-0.564760\pi$
$239$	−23082.5			−0.404098			−0.202049	+	0.979375i	$0.564760\pi$
$240$		0			0
$241$	70643.9	+	40786.3i	1.21630	+	0.702231i	0.964124	−	0.265451i	$-0.0855209\pi$
$241$	70643.9	+	40786.3i	1.21630	+	0.702231i	0.252175	+	0.967682i	$0.418854\pi$
$242$	−31127.1	−	17971.2i	−0.531506	−	0.306865i
$243$	−19599.0	−	33946.4i	−0.331910	−	0.574886i
$244$			11173.5i			0.187677i
$245$		0			0
$246$	−48503.8			−0.801504
$247$	−63270.0	+	36529.0i	−1.03706	+	0.598747i
$248$	11759.8	−	20368.6i	0.191204	−	0.331176i
$249$	−35460.8	+	61419.8i	−0.571939	+	0.990627i
$250$		0			0
$251$			27207.6i			0.431859i	0.976409	+	0.215930i	$0.0692782\pi$
$251$			27207.6i			0.431859i	−0.976409	+	0.215930i	$0.930722\pi$
$252$	55800.5	−	8054.11i	0.878693	−	0.126828i
$253$		−	19163.4i		−	0.299385i
$254$	5646.53	+	9780.08i	0.0875214	+	0.151592i
$255$		0			0
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	−53964.5	−	93469.3i	−0.817038	−	1.41515i	−0.907856	−	0.419283i	$-0.862281\pi$
$257$	−53964.5	−	93469.3i	−0.817038	−	1.41515i	0.0908179	−	0.995868i	$-0.471052\pi$
$258$	−102582.			−1.54110
$259$	37987.0	−	29907.0i	0.566286	−	0.445834i
$260$		0			0
$261$	53366.9	+	92434.3i	0.783414	+	1.35691i
$262$	28602.5	−	49540.9i	0.416678	−	0.721708i
$263$	34765.8	+	20072.0i	0.502621	+	0.290188i	0.729795	−	0.683666i	$-0.239615\pi$
$263$	34765.8	+	20072.0i	0.502621	+	0.290188i	−0.227174	+	0.973854i	$0.572949\pi$
$264$	−12919.6	+	7459.12i	−0.185370	+	0.107024i
$265$		0			0
$266$	−23125.5	+	57856.5i	−0.326834	+	0.817690i
$267$		−	12563.7i		−	0.176236i
$268$	50338.8	−	29063.1i	0.700864	−	0.404644i
$269$	−91239.0	−	52676.9i	−1.26089	−	0.727973i	−0.287641	−	0.957738i	$-0.592871\pi$
$269$	−91239.0	−	52676.9i	−1.26089	−	0.727973i	−0.973246	+	0.229765i	$0.926204\pi$
$270$		0			0
$271$	−13189.3	+	7614.84i	−0.179590	+	0.103687i	−0.587100	−	0.809514i	$-0.699731\pi$
$271$	−13189.3	+	7614.84i	−0.179590	+	0.103687i	0.407510	+	0.913201i	$0.366397\pi$
$272$	−6927.13			−0.0936301
$273$	−44314.1	+	110867.i	−0.594589	+	1.48757i
$274$	−70874.0			−0.944030
$275$		0			0
$276$	45274.2	+	26139.1i	0.594337	+	0.343141i
$277$	−8549.07	−	4935.81i	−0.111419	−	0.0643278i	0.443255	−	0.896396i	$-0.353824\pi$
$277$	−8549.07	−	4935.81i	−0.111419	−	0.0643278i	−0.554674	+	0.832068i	$0.687157\pi$
$278$	−28383.4	−	49161.4i	−0.367260	−	0.636114i
$279$			149495.i			1.92051i
$280$		0			0
$281$	−155117.			−1.96448			−0.982240	−	0.187631i	$-0.939919\pi$
$281$	−155117.			−1.96448			−0.982240	+	0.187631i	$0.939919\pi$
$282$	−49414.8	+	28529.6i	−0.621382	+	0.358755i
$283$	54831.0	−	94970.0i	0.684626	−	1.18581i	−0.288929	−	0.957351i	$-0.593299\pi$
$283$	54831.0	−	94970.0i	0.684626	−	1.18581i	0.973554	−	0.228456i	$-0.0733676\pi$
$284$	23951.1	−	41484.4i	0.296953	−	0.514338i
$285$		0			0
$286$		−	20210.6i		−	0.247085i
$287$	−8005.87	−	55466.3i	−0.0971952	−	0.673388i
$288$		−	26034.8i		−	0.313884i
$289$	35902.9	+	62185.7i	0.429867	+	0.744552i
$290$		0			0
$291$	−42150.2	+	73006.2i	−0.497752	+	0.862132i
$292$	−2309.97	−	4000.99i	−0.0270920	−	0.0469247i
$293$	−89912.4			−1.04733			−0.523666	−	0.851924i	$-0.675436\pi$
$293$	−89912.4			−1.04733			−0.523666	+	0.851924i	$0.675436\pi$
$294$	28794.7	+	97669.7i	0.333133	+	1.12997i
$295$		0			0
$296$	−11163.0	−	19334.8i	−0.127408	−	0.220677i
$297$	20709.7	−	35870.3i	0.234780	−	0.406651i
$298$	104613.	+	60398.1i	1.17802	+	0.680128i
$299$	−61335.5	+	35412.1i	−0.686072	+	0.396104i
$300$		0			0
$301$	−16931.7	−	117307.i	−0.186883	−	1.29476i
$302$		−	83742.5i		−	0.918189i
$303$	−85514.6	+	49371.9i	−0.931440	+	0.537767i
$304$	24917.6	+	14386.2i	0.269624	+	0.155668i
$305$		0			0
$306$	38131.0	−	22015.0i	0.407226	−	0.235112i
$307$	141681.			1.50327			0.751633	−	0.659582i	$-0.229267\pi$
$307$	141681.			1.50327			0.751633	+	0.659582i	$0.229267\pi$
$308$	−10662.3	−	13542.9i	−0.112396	−	0.142762i
$309$	22858.5			0.239403
$310$		0			0
$311$	−74171.3	−	42822.8i	−0.766858	−	0.442746i	0.0648948	−	0.997892i	$-0.479329\pi$
$311$	−74171.3	−	42822.8i	−0.766858	−	0.442746i	−0.831753	+	0.555147i	$0.812662\pi$
$312$	47748.3	+	27567.5i	0.490511	+	0.283197i
$313$	8915.78	+	15442.6i	0.0910061	+	0.157627i	0.907935	−	0.419112i	$-0.137658\pi$
$313$	8915.78	+	15442.6i	0.0910061	+	0.157627i	−0.816929	+	0.576739i	$0.804325\pi$
$314$			34611.6i			0.351045i
$315$		0			0
$316$	−25169.8			−0.252061
$317$	−69979.4	+	40402.6i	−0.696388	+	0.402060i	−0.806001	−	0.591914i	$-0.798372\pi$
$317$	−69979.4	+	40402.6i	−0.696388	+	0.402060i	0.109613	+	0.993974i	$0.465039\pi$
$318$	−75620.9	+	130979.i	−0.747804	+	1.29523i
$319$	16315.7	−	28259.6i	0.160333	−	0.277705i
$320$		0			0
$321$			159037.i			1.54343i
$322$	−22418.4	+	56087.5i	−0.216218	+	0.540946i
$323$			48659.7i			0.466406i
$324$	9897.88	+	17143.6i	0.0942871	+	0.163310i
$325$		0			0
$326$	−30449.6	+	52740.3i	−0.286514	+	0.496258i
$327$	104601.	+	181174.i	0.978228	+	1.69434i
$328$	−25878.9			−0.240546
$329$	−40781.1	−	51799.0i	−0.376762	−	0.478552i
$330$		0			0
$331$	−36402.1	−	63050.3i	−0.332254	−	0.575482i	0.650699	−	0.759336i	$-0.274476\pi$
$331$	−36402.1	−	63050.3i	−0.332254	−	0.575482i	−0.982954	+	0.183854i	$0.941143\pi$
$332$	−18919.8	+	32770.1i	−0.171649	+	0.297305i
$333$	122895.	+	70953.5i	1.10827	+	0.639860i
$334$	40609.9	−	23446.1i	0.364031	−	0.210174i
$335$		0			0
$336$	46539.2	−	6717.36i	0.412231	−	0.0595004i
$337$		−	126538.i		−	1.11419i	−0.830449	−	0.557095i	$-0.811916\pi$
$337$		−	126538.i		−	1.11419i	0.830449	−	0.557095i	$-0.188084\pi$
$338$	5272.58	−	3044.13i	0.0461519	−	0.0266458i
$339$	−114417.	−	66058.8i	−0.995616	−	0.574819i
$340$		0			0
$341$	39581.2	−	22852.2i	0.340393	−	0.196526i
$342$	−182882.			−1.56357
$343$	−106937.	+	49049.0i	−0.908948	+	0.416910i
$344$	−54731.7			−0.462511
$345$		0			0
$346$	98917.9	+	57110.3i	0.826271	+	0.477048i
$347$	−57979.8	−	33474.6i	−0.481524	−	0.278008i	0.239528	−	0.970890i	$-0.423007\pi$
$347$	−57979.8	−	33474.6i	−0.481524	−	0.278008i	−0.721051	+	0.692882i	$0.756341\pi$
$348$	44509.6	+	77092.9i	0.367532	+	0.636584i
$349$			25527.5i			0.209583i	0.994494	+	0.104792i	$0.0334176\pi$
$349$			25527.5i			0.209583i	−0.994494	+	0.104792i	$0.966582\pi$
$350$		0			0
$351$	−153078.			−1.24251
$352$	−6893.15	+	3979.76i	−0.0556330	+	0.0321197i
$353$	28287.8	−	48995.9i	0.227013	−	0.393197i	−0.729909	−	0.683545i	$-0.760437\pi$
$353$	28287.8	−	48995.9i	0.227013	−	0.393197i	0.956921	+	0.290347i	$0.0937708\pi$
$354$	90863.1	−	157379.i	0.725071	−	1.25586i
$355$		0			0
$356$		−	6703.27i		−	0.0528916i
$357$	49191.8	+	62482.0i	0.385973	+	0.490251i
$358$		−	151305.i		−	1.18056i
$359$	18902.4	+	32739.9i	0.146665	+	0.254032i	0.929993	−	0.367577i	$-0.119813\pi$
$359$	18902.4	+	32739.9i	0.146665	+	0.254032i	−0.783328	+	0.621609i	$0.786479\pi$
$360$		0			0
$361$	35895.4	−	62172.6i	0.275438	−	0.477073i
$362$	76653.3	+	132767.i	0.584943	+	1.01315i
$363$	190539.			1.44601
$364$	−23643.5	+	59152.5i	−0.178447	+	0.446447i
$365$		0			0
$366$	−29616.6	−	51297.5i	−0.221092	−	0.382943i
$367$	5408.20	−	9367.27i	0.0401532	−	0.0695474i	−0.845250	−	0.534370i	$-0.820549\pi$
$367$	5408.20	−	9367.27i	0.0401532	−	0.0695474i	0.885404	+	0.464823i	$0.153882\pi$
$368$	24155.7	+	13946.3i	0.178371	+	0.102983i
$369$	142453.	−	82245.1i	1.04621	−	0.604028i
$370$		0			0
$371$	−162262.	−	64856.9i	−1.17888	−	0.471203i
$372$			124683.i			0.900993i
$373$	−26867.0	+	15511.7i	−0.193109	+	0.111491i	−0.593437	−	0.804880i	$-0.702229\pi$
$373$	−26867.0	+	15511.7i	−0.193109	+	0.111491i	0.400328	+	0.916372i	$0.368896\pi$
$374$	−11657.7	−	6730.55i	−0.0833428	−	0.0481180i
$375$		0			0
$376$	−26364.9	+	15221.8i	−0.186488	+	0.107669i
$377$	−120599.			−0.848519
$378$	−102576.	+	80758.0i	−0.717900	+	0.565200i
$379$	98527.5			0.685929			0.342964	−	0.939348i	$-0.388569\pi$
$379$	98527.5			0.685929			0.342964	+	0.939348i	$0.388569\pi$
$380$		0			0
$381$	−51846.3	−	29933.5i	−0.357164	−	0.206209i
$382$	−2948.87	−	1702.53i	−0.0202083	−	0.0116673i
$383$	−2571.67	−	4454.26i	−0.0175314	−	0.0303653i	0.857127	−	0.515106i	$-0.172247\pi$
$383$	−2571.67	−	4454.26i	−0.0175314	−	0.0303653i	−0.874658	+	0.484741i	$0.838914\pi$
$384$		−	21713.8i		−	0.147256i
$385$		0			0
$386$	145135.			0.974086
$387$	301275.	−	173941.i	2.01160	−	1.16140i
$388$	−22488.9	+	38951.9i	−0.149384	+	0.258741i
$389$	43141.0	−	74722.4i	0.285096	−	0.493801i	−0.687537	−	0.726150i	$-0.741308\pi$
$389$	43141.0	−	74722.4i	0.285096	−	0.493801i	0.972632	+	0.232349i	$0.0746412\pi$
$390$		0			0
$391$			47171.9i			0.308553i
$392$	15363.2	+	52110.9i	0.0999792	+	0.339123i
$393$			303256.i			1.96347i
$394$	−2059.48	−	3567.13i	−0.0132668	−	0.0229788i
$395$		0			0
$396$	25296.0	−	43813.9i	0.161310	−	0.279397i
$397$	77963.1	+	135036.i	0.494661	+	0.856778i	0.999981	−	0.00615368i	$-0.00195879\pi$
$397$	77963.1	+	135036.i	0.494661	+	0.856778i	−0.505320	+	0.862932i	$0.668625\pi$
$398$	194478.			1.22773
$399$	−47186.2	−	326915.i	−0.296394	−	2.05347i
$400$		0			0
$401$	−17307.2	−	29977.0i	−0.107631	−	0.186423i	0.807179	−	0.590307i	$-0.200993\pi$
$401$	−17307.2	−	29977.0i	−0.107631	−	0.186423i	−0.914810	+	0.403884i	$0.867660\pi$
$402$	−154070.	+	266857.i	−0.953381	+	1.65130i
$403$	−146285.	−	84457.5i	−0.900718	−	0.520030i
$404$	−45625.7	+	26342.0i	−0.279542	+	0.161393i
$405$		0			0
$406$	−80812.5	+	63623.3i	−0.490260	+	0.385980i
$407$		−	43384.7i		−	0.261907i
$408$	31802.4	−	18361.1i	0.191047	−	0.110301i
$409$	271749.	+	156894.i	1.62450	+	0.937907i	0.985695	+	0.168542i	$0.0539058\pi$
$409$	271749.	+	156894.i	1.62450	+	0.937907i	0.638809	+	0.769366i	$0.279428\pi$
$410$		0			0
$411$	325382.	−	187859.i	1.92624	−	1.11211i
$412$	12196.0			0.0718492
$413$	194968.	+	77929.4i	1.14304	+	0.456879i
$414$	−177290.			−1.03439
$415$		0			0
$416$	25475.8	+	14708.4i	0.147211	+	0.0849924i
$417$	260615.	+	150466.i	1.49875	+	0.865301i
$418$	27955.9	+	48421.0i	0.160000	+	0.277128i
$419$		−	7324.74i		−	0.0417219i	−0.999782	−	0.0208609i	$-0.993359\pi$
$419$		−	7324.74i		−	0.0417219i	0.999782	−	0.0208609i	$-0.00664073\pi$
$420$		0			0
$421$	−25178.3			−0.142057			−0.0710285	−	0.997474i	$-0.522628\pi$
$421$	−25178.3			−0.142057			−0.0710285	+	0.997474i	$0.522628\pi$
$422$	1525.59	−	880.802i	0.00856671	−	0.00494599i
$423$	96752.0	−	167579.i	0.540728	−	0.936569i
$424$	−40347.0	+	69883.0i	−0.224429	+	0.388723i
$425$		0			0
$426$			253940.i			1.39930i
$427$	53772.6	−	42334.9i	0.294920	−	0.232190i
$428$			84853.0i			0.463212i
$429$	53570.3	+	92786.6i	0.291078	+	0.504162i
$430$		0			0
$431$	−6913.59	+	11974.7i	−0.0372176	+	0.0644629i	−0.884034	−	0.467422i	$-0.845183\pi$
$431$	−6913.59	+	11974.7i	−0.0372176	+	0.0644629i	0.846817	+	0.531885i	$0.178516\pi$
$432$	30143.4	+	52209.9i	0.161519	+	0.279760i
$433$	−47438.8			−0.253022			−0.126511	−	0.991965i	$-0.540378\pi$
$433$	−47438.8			−0.253022			−0.126511	+	0.991965i	$0.540378\pi$
$434$	−142580.	+	20579.7i	−0.756973	+	0.109260i
$435$		0			0
$436$	55809.1	+	96664.1i	0.293584	+	0.508502i
$437$	97966.0	−	169682.i	0.512994	−	0.888532i
$438$	21210.1	+	12245.7i	0.110559	+	0.0638314i
$439$	−95101.7	+	54907.0i	−0.493469	+	0.284904i	−0.726012	−	0.687682i	$-0.758628\pi$
$439$	−95101.7	+	54907.0i	−0.493469	+	0.284904i	0.232544	+	0.972586i	$0.425295\pi$
$440$		0			0
$441$	−250181.	−	238024.i	−1.28640	−	1.22389i
$442$			49749.7i			0.254651i
$443$	−71499.7	+	41280.4i	−0.364331	+	0.210347i	−0.670979	−	0.741476i	$-0.734126\pi$
$443$	−71499.7	+	41280.4i	−0.364331	+	0.210347i	0.306648	+	0.951823i	$0.400793\pi$
$444$	102498.	+	59177.3i	0.519936	+	0.300185i
$445$		0			0
$446$	−28193.0	+	16277.2i	−0.141733	+	0.0818297i
$447$	−640367.			−3.20490
$448$	24830.7	−	3584.00i	0.123718	−	0.0178571i
$449$	330438.			1.63907			0.819534	−	0.573030i	$-0.194232\pi$
$449$	330438.			1.63907			0.819534	+	0.573030i	$0.194232\pi$
$450$		0			0
$451$	−43551.5	−	25144.5i	−0.214116	−	0.123620i
$452$	−61046.4	−	35245.2i	−0.298802	−	0.172513i
$453$	221969.	+	384461.i	1.08167	+	1.87351i
$454$		−	159430.i		−	0.773499i
$455$		0			0
$456$	−152529.			−0.733537
$457$	323276.	−	186644.i	1.54789	−	0.893677i	0.549591	−	0.835434i	$-0.314783\pi$
$457$	323276.	−	186644.i	1.54789	−	0.893677i	0.998302	−	0.0582431i	$-0.0185499\pi$
$458$	−59578.7	+	103193.i	−0.284027	+	0.491950i
$459$	−50978.3	+	88297.0i	−0.241969	+	0.419103i
$460$		0			0
$461$			20355.2i			0.0957798i	0.998853	+	0.0478899i	$0.0152497\pi$
$461$			20355.2i			0.0957798i	−0.998853	+	0.0478899i	$0.984750\pi$
$462$	84847.5	+	33913.9i	0.397517	+	0.158889i
$463$		−	31552.7i		−	0.147189i	−0.997288	−	0.0735944i	$-0.976553\pi$
$463$		−	31552.7i		−	0.147189i	0.997288	−	0.0735944i	$-0.0234470\pi$
$464$	23747.8	+	41132.3i	0.110303	+	0.191050i
$465$		0			0
$466$	77925.8	−	134971.i	0.358847	−	0.621541i
$467$	120927.	+	209452.i	0.554486	+	0.960397i	0.997943	+	0.0641019i	$0.0204183\pi$
$467$	120927.	+	209452.i	0.554486	+	0.960397i	−0.443458	+	0.896295i	$0.646248\pi$
$468$	−186978.			−0.853689
$469$	−330593.	−	132139.i	−1.50296	−	0.600740i
$470$		0			0
$471$	−91741.9	−	158902.i	−0.413548	−	0.716286i
$472$	48479.3	−	83968.7i	0.217607	−	0.376906i
$473$	−92107.8	−	53178.5i	−0.411694	−	0.237691i
$474$	115555.	−	66715.4i	0.514316	−	0.296941i
$475$		0			0
$476$	26245.9	+	33336.8i	0.115837	+	0.147133i
$477$		−	512903.i		−	2.25423i
$478$	56540.3	−	32643.5i	0.247458	−	0.142870i
$479$	−235631.	−	136042.i	−1.02698	−	0.592926i	−0.110861	−	0.993836i	$-0.535361\pi$
$479$	−235631.	−	136042.i	−1.02698	−	0.592926i	−0.916117	+	0.400910i	$0.868694\pi$
$480$		0			0
$481$	−138860.	+	80170.8i	−0.600187	+	0.346518i
$482$	−230722.			−0.993104
$483$	−45743.4	−	316920.i	−0.196080	−	1.35848i
$484$	101661.			0.433973
$485$		0			0
$486$	96015.0	+	55434.3i	0.406506	+	0.234696i
$487$	−353119.	−	203873.i	−1.48889	−	0.859611i	−0.488971	−	0.872300i	$-0.662628\pi$
$487$	−353119.	−	203873.i	−1.48889	−	0.859611i	−0.999919	+	0.0126891i	$0.995961\pi$
$488$	−15801.7	−	27369.4i	−0.0663537	−	0.114928i
$489$		−	322840.i		−	1.35011i
$490$		0			0
$491$	−286772.			−1.18953			−0.594763	−	0.803901i	$-0.702754\pi$
$491$	−286772.			−1.18953			−0.594763	+	0.803901i	$0.702754\pi$
$492$	118810.	−	68594.8i	0.490819	−	0.283375i
$493$	−40162.1	+	69562.8i	−0.165243	+	0.286209i
$494$	103320.	−	178955.i	0.423378	−	0.733313i
$495$		0			0
$496$			66523.7i			0.270404i
$497$	−290391.	+	41914.3i	−1.17563	+	0.169687i
$498$		−	200596.i		−	0.808843i
$499$	175718.	+	304352.i	0.705690	+	1.22229i	0.966442	+	0.256886i	$0.0826964\pi$
$499$	175718.	+	304352.i	0.705690	+	1.22229i	−0.260751	+	0.965406i	$0.583970\pi$
$500$		0			0
$501$	−124293.	+	215282.i	−0.495189	+	0.857693i
$502$	−38477.3	−	66644.7i	−0.152685	−	0.264459i
$503$	−116045.			−0.458660			−0.229330	−	0.973349i	$-0.573653\pi$
$503$	−116045.			−0.458660			−0.229330	+	0.973349i	$0.573653\pi$
$504$	−125293.	+	98642.3i	−0.493247	+	0.388331i
$505$		0			0
$506$	27101.1	+	46940.5i	0.105849	+	0.183335i
$507$	−16137.6	+	27951.1i	−0.0627802	+	0.108738i
$508$	−27662.2	−	15970.8i	−0.107191	−	0.0618870i
$509$	−72030.7	+	41586.9i	−0.278024	+	0.160517i	−0.632528	−	0.774537i	$-0.717983\pi$
$509$	−72030.7	+	41586.9i	−0.278024	+	0.160517i	0.354505	+	0.935054i	$0.384649\pi$
$510$		0			0
$511$	−10502.6	+	26275.9i	−0.0402212	+	0.100627i
$512$		−	11585.2i		−	0.0441942i
$513$	366749.	−	211742.i	1.39359	−	0.804587i
$514$	264371.	+	152635.i	1.00066	+	0.577733i
$515$		0			0
$516$	251273.	−	145072.i	0.943725	−	0.544860i
$517$	−59159.2			−0.221330
$518$	−50753.9	+	126979.i	−0.189151	+	0.473229i
$519$	−605508.			−2.24794
$520$		0			0
$521$	174948.	+	101006.i	0.644517	+	0.372112i	0.786352	−	0.617778i	$-0.211967\pi$
$521$	174948.	+	101006.i	0.644517	+	0.372112i	−0.141835	+	0.989890i	$0.545300\pi$
$522$	−261444.	−	150945.i	−0.959482	−	0.553957i
$523$	−13933.8	−	24134.0i	−0.0509408	−	0.0882321i	0.839431	−	0.543467i	$-0.182889\pi$
$523$	−13933.8	−	24134.0i	−0.0509408	−	0.0882321i	−0.890371	+	0.455235i	$0.849555\pi$
$524$			161800.i			0.589272i
$525$		0			0
$526$	−113545.			−0.410389
$527$	−97431.8	+	56252.3i	−0.350816	+	0.202544i
$528$	21097.6	−	36542.1i	0.0756772	−	0.131077i
$529$	−44949.9	+	77855.5i	−0.160626	+	0.278213i
$530$		0			0
$531$			616284.i			2.18571i
$532$	−25175.8	−	174423.i	−0.0889530	−	0.616284i
$533$			185858.i			0.654226i
$534$	17767.8	+	30774.7i	0.0623089	+	0.107922i
$535$		0			0
$536$	−82203.0	+	142380.i	−0.286126	+	0.495586i
$537$	401050.	+	694640.i	1.39075	+	2.40886i
$538$	297985.			1.02951
$539$	−24777.4	+	102625.i	−0.0852861	+	0.353243i
$540$		0			0
$541$	18996.8	+	32903.4i	0.0649062	+	0.112421i	0.896652	−	0.442735i	$-0.145992\pi$
$541$	18996.8	+	32903.4i	0.0649062	+	0.112421i	−0.831746	+	0.555156i	$0.812659\pi$
$542$	21538.0	−	37305.0i	0.0733175	−	0.126990i
$543$	−703829.	−	406356.i	−2.38708	−	1.37818i
$544$	16967.9	−	9796.44i	0.0573365	−	0.0331032i
$545$		0			0
$546$	−48243.1	−	334238.i	−0.161827	−	1.12117i
$547$		−	360160.i		−	1.20371i	−0.798606	−	0.601854i	$-0.794429\pi$
$547$		−	360160.i		−	1.20371i	0.798606	−	0.601854i	$-0.205571\pi$
$548$	173605.	−	100231.i	0.578098	−	0.333765i
$549$	173964.	+	100438.i	0.577185	+	0.333238i
$550$		0			0
$551$	288934.	−	166816.i	0.951691	−	0.549459i
$552$	−147865.			−0.485274
$553$	95365.1	+	121130.i	0.311845	+	0.396097i
$554$	27921.1			0.0909732
$555$		0			0
$556$	139049.	+	80280.2i	0.449800	+	0.259692i
$557$	268938.	+	155272.i	0.866847	+	0.500474i	0.866299	−	0.499525i	$-0.166492\pi$
$557$	268938.	+	155272.i	0.866847	+	0.500474i	0.000547960		1.00000i	$0.499826\pi$
$558$	−211418.	−	366186.i	−0.679004	−	1.17607i
$559$			393075.i			1.25792i
$560$		0			0
$561$	71360.2			0.226741
$562$	379958.	−	219369.i	1.20299	−	0.694548i
$563$	−8344.68	+	14453.4i	−0.0263265	+	0.0455988i	−0.878888	−	0.477027i	$-0.841714\pi$
$563$	−8344.68	+	14453.4i	−0.0263265	+	0.0455988i	0.852562	+	0.522626i	$0.175048\pi$
$564$	80694.0	−	139766.i	0.253678	−	0.439383i
$565$		0			0
$566$			310171.i			0.968207i
$567$	45002.0	−	112588.i	0.139980	−	0.350209i
$568$			135488.i			0.419955i
$569$	−65131.1	−	112810.i	−0.201170	−	0.348437i	0.747736	−	0.663997i	$-0.231141\pi$
$569$	−65131.1	−	112810.i	−0.201170	−	0.348437i	−0.948906	+	0.315560i	$0.897808\pi$
$570$		0			0
$571$	249119.	−	431487.i	0.764073	−	1.32341i	−0.176662	−	0.984272i	$-0.556530\pi$
$571$	249119.	−	431487.i	0.764073	−	1.32341i	0.940735	−	0.339142i	$-0.110137\pi$
$572$	28582.1	+	49505.6i	0.0873578	+	0.151308i
$573$	18051.0			0.0549784
$574$	98051.5	+	124542.i	0.297598	+	0.378000i
$575$		0			0
$576$	36818.8	+	63772.0i	0.110975	+	0.192214i
$577$	−16858.1	+	29199.1i	−0.0506357	+	0.0877035i	−0.890232	−	0.455507i	$-0.849458\pi$
$577$	−16858.1	+	29199.1i	−0.0506357	+	0.0877035i	0.839597	+	0.543210i	$0.182791\pi$
$578$	−175888.	−	101549.i	−0.526478	−	0.303962i
$579$	−666313.	+	384696.i	−1.98756	+	1.14752i
$580$		0			0
$581$	229391.	−	33109.7i	0.679554	−	0.0980851i
$582$		−	238437.i		−	0.703928i
$583$	−135800.	+	78404.0i	−0.399541	+	0.230675i
$584$	11316.5	+	6533.58i	0.0331808	+	0.0191569i
$585$		0			0
$586$	220240.	−	127155.i	0.641357	−	0.370288i
$587$	356809.			1.03552			0.517762	−	0.855525i	$-0.326765\pi$
$587$	356809.			1.03552			0.517762	+	0.855525i	$0.326765\pi$
$588$	−208658.	−	198519.i	−0.603504	−	0.574179i
$589$	467296.			1.34698
$590$		0			0
$591$	18910.1	+	10917.8i	0.0541402	+	0.0312579i
$592$	54687.1	+	31573.6i	0.156042	+	0.0900909i
$593$	−16669.6	−	28872.6i	−0.0474041	−	0.0821063i	0.841350	−	0.540491i	$-0.181762\pi$
$593$	−16669.6	−	28872.6i	−0.0474041	−	0.0821063i	−0.888754	+	0.458385i	$0.848428\pi$
$594$			117152.i			0.332029i
$595$		0			0
$596$	−341663.			−0.961846
$597$	−892844.	+	515484.i	−2.50511	+	1.44633i
$598$	100160.	−	173483.i	0.280088	−	0.485126i
$599$	162165.	−	280878.i	0.451963	−	0.782824i	−0.546545	−	0.837430i	$-0.684057\pi$
$599$	162165.	−	280878.i	0.451963	−	0.782824i	0.998508	+	0.0546064i	$0.0173904\pi$
$600$		0			0
$601$			66322.0i			0.183615i	0.995777	+	0.0918076i	$0.0292645\pi$
$601$			66322.0i			0.183615i	−0.995777	+	0.0918076i	$0.970736\pi$
$602$	207371.	+	263396.i	0.572209	+	0.726803i
$603$		−	1.04499e6i		−	2.87394i
$604$	118430.	+	205126.i	0.324629	+	0.562274i
$605$		0			0
$606$	139645.	−	241872.i	0.380259	−	0.658628i
$607$	243828.	+	422322.i	0.661768	+	1.14622i	0.980151	+	0.198253i	$0.0635269\pi$
$607$	243828.	+	422322.i	0.661768	+	1.14622i	−0.318383	+	0.947962i	$0.603140\pi$
$608$	−81380.6			−0.220147
$609$	202369.	−	506297.i	0.545643	−	1.36512i
$610$		0			0
$611$	109321.	+	189349.i	0.292833	+	0.507201i
$612$	−62267.7	+	107851.i	−0.166249	+	0.287952i
$613$	295757.	+	170755.i	0.787070	+	0.454415i	0.838930	−	0.544239i	$-0.183182\pi$
$613$	295757.	+	170755.i	0.787070	+	0.454415i	−0.0518597	+	0.998654i	$0.516515\pi$
$614$	−347047.	+	200368.i	−0.920558	+	0.531484i
$615$		0			0
$616$	45269.8	+	18094.5i	0.119302	+	0.0476854i
$617$		−	240873.i		−	0.632728i	−0.948638	−	0.316364i	$-0.897538\pi$
$617$		−	240873.i		−	0.632728i	0.948638	−	0.316364i	$-0.102462\pi$
$618$	−55991.6	+	32326.8i	−0.146604	+	0.0846419i
$619$	133658.	+	77167.4i	0.348830	+	0.201397i	0.664170	−	0.747582i	$-0.268785\pi$
$619$	133658.	+	77167.4i	0.348830	+	0.201397i	−0.315340	+	0.948979i	$0.602119\pi$
$620$		0			0
$621$	355535.	−	205268.i	0.921932	−	0.532278i
$622$	242242.			0.626137
$623$	−32259.5	+	25397.8i	−0.0831154	+	0.0654364i
$624$	−155945.			−0.400501
$625$		0			0
$626$	−43678.2	−	25217.6i	−0.111459	−	0.0643510i
$627$	−256690.	−	148200.i	−0.652941	−	0.376976i
$628$	−48948.2	−	84780.8i	−0.124113	−	0.214970i
$629$			106794.i			0.269927i
$630$		0			0
$631$	220248.			0.553164			0.276582	−	0.960990i	$-0.410798\pi$
$631$	220248.			0.553164			0.276582	+	0.960990i	$0.410798\pi$
$632$	61653.3	−	35595.5i	0.154355	−	0.0891172i
$633$	−4669.32	+	8087.50i	−0.0116532	+	0.0201840i
$634$	114276.	−	197932.i	0.284299	−	0.492421i
$635$		0			0
$636$		−	427776.i		−	1.05755i
$637$	374253.	−	110336.i	0.922331	−	0.271919i
$638$			92295.4i			0.226745i
$639$	−430590.	−	745804.i	−1.05454	−	1.82651i
$640$		0			0
$641$	340604.	−	589943.i	0.828960	−	1.43580i	−0.0698947	−	0.997554i	$-0.522266\pi$
$641$	340604.	−	589943.i	0.828960	−	1.43580i	0.898855	−	0.438247i	$-0.144400\pi$
$642$	−224912.	−	389559.i	−0.545686	−	0.945156i
$643$	−572102.			−1.38373			−0.691865	−	0.722027i	$-0.743211\pi$
$643$	−572102.			−1.38373			−0.691865	+	0.722027i	$0.743211\pi$
$644$	−24406.1	−	169090.i	−0.0588472	−	0.407705i
$645$		0			0
$646$	−68815.2	−	119191.i	−0.164899	−	0.285614i
$647$	−303637.	+	525915.i	−0.725348	+	1.25634i	0.233482	+	0.972361i	$0.424988\pi$
$647$	−303637.	+	525915.i	−0.725348	+	1.25634i	−0.958830	+	0.283979i	$0.908345\pi$
$648$	−48489.5	−	27995.4i	−0.115478	−	0.0666710i
$649$	163171.	−	94207.1i	0.387396	−	0.223663i
$650$		0			0
$651$	600037.	−	472407.i	1.41585	−	1.11469i
$652$		−	172249.i		−	0.405193i
$653$	−419737.	+	242335.i	−0.984353	+	0.568316i	−0.903581	−	0.428416i	$-0.859072\pi$
$653$	−419737.	+	242335.i	−0.984353	+	0.568316i	−0.0807713	+	0.996733i	$0.525738\pi$
$654$	−512438.	−	295856.i	−1.19808	−	0.691711i
$655$		0			0
$656$	63390.0	−	36598.3i	0.147304	−	0.0850458i
$657$	−83057.0			−0.192418
$658$	173148.	+	69207.8i	0.399912	+	0.159847i
$659$	−329627.			−0.759017			−0.379509	−	0.925188i	$-0.623907\pi$
$659$	−329627.			−0.759017			−0.379509	+	0.925188i	$0.623907\pi$
$660$		0			0
$661$	−182392.	−	105304.i	−0.417449	−	0.241014i	0.276536	−	0.961003i	$-0.410813\pi$
$661$	−182392.	−	105304.i	−0.417449	−	0.241014i	−0.693985	+	0.719989i	$0.744147\pi$
$662$	178333.	+	102961.i	0.406927	+	0.234939i
$663$	−131867.	−	228400.i	−0.299991	−	0.519600i
$664$		−	107027.i		−	0.242748i
$665$		0			0
$666$	−401374.			−0.904899
$667$	280100.	−	161716.i	0.629595	−	0.363497i
$668$	−66315.7	+	114862.i	−0.148615	+	0.257409i
$669$	86289.2	−	149457.i	0.192799	−	0.333937i
$670$		0			0
$671$		−	61413.2i		−	0.136401i
$672$	−104498.	+	82270.5i	−0.231402	+	0.182182i
$673$			94709.8i			0.209105i	0.994519	+	0.104553i	$0.0333411\pi$
$673$			94709.8i			0.209105i	−0.994519	+	0.104553i	$0.966659\pi$
$674$	178951.	+	309952.i	0.393926	+	0.682300i
$675$		0			0
$676$	−8610.09	+	14913.1i	−0.0188414	+	0.0326343i
$677$	−269276.	−	466400.i	−0.587517	−	1.01761i	−0.994556	−	0.104199i	$-0.966772\pi$
$677$	−269276.	−	466400.i	−0.587517	−	1.01761i	0.407039	−	0.913411i	$-0.366561\pi$
$678$	373685.			0.812917
$679$	272664.	−	39355.6i	0.591408	−	0.0853625i
$680$		0			0
$681$	422588.	+	731944.i	0.911219	+	1.57828i
$682$	−64635.9	+	111953.i	−0.138965	+	0.240694i
$683$	111779.	+	64535.9i	0.239618	+	0.138344i	0.615001	−	0.788526i	$-0.289155\pi$
$683$	111779.	+	64535.9i	0.239618	+	0.138344i	−0.375383	+	0.926870i	$0.622489\pi$
$684$	447967.	−	258634.i	0.957489	−	0.552806i
$685$		0			0
$686$	192575.	−	271377.i	0.409215	−	0.576666i
$687$		−	631680.i		−	1.33839i
$688$	134065.	−	77402.3i	0.283229	−	0.163522i
$689$	501890.	+	289766.i	1.05723	+	0.610393i
$690$		0			0
$691$	113201.	−	65356.6i	0.237079	−	0.136878i	−0.376754	−	0.926313i	$-0.622960\pi$
$691$	113201.	−	65356.6i	0.237079	−	0.136878i	0.613834	+	0.789435i	$0.289627\pi$
$692$	−323064.			−0.674648
$693$	−306697.	+	44268.0i	−0.638622	+	0.0921771i
$694$	189361.			0.393162
$695$		0			0
$696$	−218052.	−	125892.i	−0.450133	−	0.259884i
$697$	107205.	+	61894.8i	0.220673	+	0.127406i
$698$	−36101.3	−	62529.3i	−0.0740989	−	0.128343i
$699$			826204.i			1.69096i
$700$		0			0
$701$	−182501.			−0.371389			−0.185694	−	0.982608i	$-0.559453\pi$
$701$	−182501.			−0.371389			−0.185694	+	0.982608i	$0.559453\pi$
$702$	374964.	−	216485.i	0.760878	−	0.439293i
$703$	221789.	−	384150.i	0.448776	−	0.777302i
$704$	11256.5	−	19496.8i	0.0227121	−	0.0393385i
$705$		0			0
$706$			160020.i			0.321044i
$707$	299640.	+	119767.i	0.599462	+	0.239607i
$708$			513999.i			1.02541i
$709$	406899.	+	704770.i	0.809458	+	1.40202i	0.913240	+	0.407422i	$0.133572\pi$
$709$	406899.	+	704770.i	0.809458	+	1.40202i	−0.103783	+	0.994600i	$0.533095\pi$
$710$		0			0
$711$	−226251.	+	391878.i	−0.447560	+	0.775196i
$712$	9479.86	+	16419.6i	0.0187000	+	0.0323894i
$713$	453008.			0.891101
$714$	−208858.	−	83481.3i	−0.409689	−	0.163754i
$715$		0			0
$716$	213978.	+	370620.i	0.417390	+	0.722941i
$717$	−173051.	+	299732.i	−0.336616	+	0.583036i
$718$	−92602.4	−	53464.0i	−0.179628	−	0.103708i
$719$	364222.	−	210283.i	0.704544	−	0.406769i	−0.104494	−	0.994526i	$-0.533322\pi$
$719$	364222.	−	210283.i	0.704544	−	0.406769i	0.809038	+	0.587757i	$0.199989\pi$
$720$		0			0
$721$	−46208.9	−	58693.1i	−0.0888904	−	0.112906i
$722$			203055.i			0.389528i
$723$	1.05924e6	−	611554.i	2.02637	−	1.16992i
$724$	−375523.	−	216808.i	−0.716406	−	0.413617i
$725$		0			0
$726$	−466723.	+	269463.i	−0.885495	+	0.511241i
$727$	172948.			0.327225			0.163613	−	0.986525i	$-0.447685\pi$
$727$	172948.			0.327225			0.163613	+	0.986525i	$0.447685\pi$
$728$	−25739.8	−	178330.i	−0.0485671	−	0.336483i
$729$	−788171.			−1.48308
$730$		0			0
$731$	226729.	+	130902.i	0.424300	+	0.244970i
$732$	145091.	+	83768.5i	0.270782	+	0.156336i
$733$	65780.9	+	113936.i	0.122431	+	0.212057i	0.920726	−	0.390210i	$-0.127598\pi$
$733$	65780.9	+	113936.i	0.122431	+	0.212057i	−0.798295	+	0.602267i	$0.794264\pi$
$734$			30593.4i			0.0567852i
$735$		0			0
$736$	−78892.3			−0.145639
$737$	−276678.	+	159740.i	−0.509378	+	0.294090i
$738$	−232624.	+	402917.i	−0.427112	+	0.739780i
$739$	−244884.	+	424151.i	−0.448406	+	0.776662i	−0.998282	−	0.0585842i	$-0.981341\pi$
$739$	−244884.	+	424151.i	−0.448406	+	0.776662i	0.549877	+	0.835246i	$0.314675\pi$
$740$		0			0
$741$			1.09544e6i			1.99504i
$742$	489181.	−	70607.2i	0.888509	−	0.128245i
$743$			580258.i			1.05110i	0.850763	+	0.525549i	$0.176140\pi$
$743$			580258.i			1.05110i	−0.850763	+	0.525549i	$0.823860\pi$
$744$	−176328.	−	305410.i	−0.318549	−	0.551743i
$745$		0			0
$746$	43873.7	−	75991.5i	0.0788364	−	0.136549i
$747$	340139.	+	589139.i	0.609559	+	1.05579i
$748$	38073.7			0.0680491
$749$	408355.	−	321496.i	0.727904	−	0.573076i
$750$		0			0
$751$	−218698.	−	378797.i	−0.387763	−	0.671624i	0.604386	−	0.796692i	$-0.293419\pi$
$751$	−218698.	−	378797.i	−0.387763	−	0.671624i	−0.992148	+	0.125067i	$0.960085\pi$
$752$	43053.7	−	74571.2i	0.0761333	−	0.131867i
$753$	353298.	+	203977.i	0.623091	+	0.359742i
$754$	295407.	−	170553.i	0.519610	−	0.299997i
$755$		0			0
$756$	137051.	−	342881.i	0.239794	−	0.599929i
$757$			24171.7i			0.0421809i	0.999778	+	0.0210905i	$0.00671380\pi$
$757$			24171.7i			0.0421809i	−0.999778	+	0.0210905i	$0.993286\pi$
$758$	−241342.	+	139339.i	−0.420044	+	0.242512i
$759$	−248842.	−	143669.i	−0.431956	−	0.249390i
$760$		0			0
$761$	−561376.	+	324111.i	−0.969359	+	0.559659i	−0.899041	−	0.437865i	$-0.855735\pi$
$761$	−561376.	+	324111.i	−0.969359	+	0.559659i	−0.0703180	+	0.997525i	$0.522401\pi$
$762$	169329.			0.291624
$763$	253743.	−	634828.i	0.435859	−	1.09045i
$764$	9630.98			0.0165000
$765$		0			0
$766$	12598.5	+	7273.77i	0.0214715	+	0.0123966i
$767$	−603051.	−	348172.i	−1.02509	−	0.591838i
$768$	30707.9	+	53187.7i	0.0520629	+	0.0901756i
$769$			179564.i			0.303646i	0.988408	+	0.151823i	$0.0485143\pi$
$769$			179564.i			0.303646i	−0.988408	+	0.151823i	$0.951486\pi$
$770$		0			0
$771$	−1.61830e6			−2.72239
$772$	−355506.	+	205252.i	−0.596503	+	0.344391i
$773$	−305457.	+	529068.i	−0.511201	+	0.885426i	0.488715	+	0.872444i	$0.337466\pi$
$773$	−305457.	+	529068.i	−0.511201	+	0.885426i	−0.999916	+	0.0129823i	$0.995867\pi$
$774$	−491981.	+	852136.i	−0.821233	+	1.42242i
$775$		0			0
$776$		−	127216.i		−	0.211261i
$777$	−103560.	−	717486.i	−0.171534	−	1.18842i
$778$			244042.i			0.403186i
$779$	−257085.	−	445284.i	−0.423644	−	0.733773i
$780$		0			0
$781$	−131643.	+	228012.i	−0.215821	+	0.373814i
$782$	−66711.1	−	115547.i	−0.109090	−	0.188949i
$783$	699061.			1.14023
$784$	−111328.	−	105918.i	−0.181122	−	0.172321i
$785$		0			0
$786$	−428868.	−	742822.i	−0.694191	−	1.20237i
$787$	595774.	−	1.03191e6i	0.961905	−	1.66607i	0.244195	−	0.969726i	$-0.421476\pi$
$787$	595774.	−	1.03191e6i	0.961905	−	1.66607i	0.717710	−	0.696342i	$-0.245190\pi$
$788$	10089.4	+	5825.10i	0.0162484	+	0.00938104i
$789$	521282.	−	300963.i	0.837373	−	0.483458i
$790$		0			0
$791$	61679.1	+	427325.i	0.0985791	+	0.682976i
$792$			143096.i			0.228127i
$793$	−196563.	+	113486.i	−0.312576	+	0.180466i
$794$	−381939.	−	220513.i	−0.605834	−	0.349778i
$795$		0			0
$796$	−476371.	+	275033.i	−0.751829	+	0.434069i
$797$	−900495.			−1.41764			−0.708818	−	0.705392i	$-0.750771\pi$
$797$	−900495.			−1.41764			−0.708818	+	0.705392i	$0.750771\pi$
$798$	577910.	+	734044.i	0.907516	+	1.15270i
$799$	145624.			0.228108
$800$		0			0
$801$	−104366.	−	60255.5i	−0.162664	−	0.0939142i
$802$	84787.8	+	48952.2i	0.131821	+	0.0761069i
$803$	12696.3	+	21990.7i	0.0196901	+	0.0341042i
$804$		−	871552.i		−	1.34828i
$805$		0			0
$806$	477764.			0.735433
$807$	−1.36805e6	+	789843.i	−2.10065	+	1.21281i
$808$	74506.4	−	129049.i	0.114122	−	0.197666i
$809$	277882.	−	481306.i	0.424584	−	0.735401i	−0.571798	−	0.820395i	$-0.693754\pi$
$809$	277882.	−	481306.i	0.424584	−	0.735401i	0.996381	+	0.0849939i	$0.0270871\pi$
$810$		0			0
$811$			70954.2i			0.107879i	0.998544	+	0.0539395i	$0.0171778\pi$
$811$			70954.2i			0.107879i	−0.998544	+	0.0539395i	$0.982822\pi$
$812$	107972.	−	270131.i	0.163757	−	0.409696i
$813$			228356.i			0.345486i
$814$	61355.2	+	106270.i	0.0925982	+	0.160385i
$815$		0			0
$816$	−51933.1	+	89950.8i	−0.0779945	+	0.135090i
$817$	−543713.	−	941738.i	−0.814564	−	1.41087i
$818$	−887527.			−1.32640
$819$	708435.	+	899833.i	1.05617	+	1.34151i
$820$		0			0
$821$	312356.	+	541016.i	0.463408	+	0.802646i	0.999128	−	0.0417495i	$-0.0132931\pi$
$821$	312356.	+	541016.i	0.463408	+	0.802646i	−0.535720	+	0.844396i	$0.679960\pi$
$822$	−531346.	+	920319.i	−0.786383	+	1.36206i
$823$	181916.	+	105029.i	0.268579	+	0.155064i	0.628242	−	0.778018i	$-0.283775\pi$
$823$	181916.	+	105029.i	0.268579	+	0.155064i	−0.359663	+	0.933082i	$0.617108\pi$
$824$	−29873.9	+	17247.7i	−0.0439985	+	0.0254025i
$825$		0			0
$826$	−587781.	+	84838.8i	−0.861500	+	0.124347i
$827$			880910.i			1.28801i	0.765020	+	0.644007i	$0.222729\pi$
$827$			880910.i			1.28801i	−0.765020	+	0.644007i	$0.777271\pi$
$828$	434270.	−	250726.i	0.633431	−	0.365711i
$829$	1.11951e6	+	646349.i	1.62899	+	0.940498i	0.984395	+	0.175974i	$0.0563075\pi$
$829$	1.11951e6	+	646349.i	1.62899	+	0.940498i	0.644595	+	0.764524i	$0.277026\pi$
$830$		0			0
$831$	−128186.	+	74008.1i	−0.185625	+	0.107171i
$832$	−83203.5			−0.120197
$833$	60991.2	−	252617.i	0.0878977	−	0.364060i
$834$	−851166.			−1.22372
$835$		0			0
$836$	−136955.	−	79071.1i	−0.195959	−	0.113137i
$837$	847948.	+	489563.i	1.21037	+	0.698808i
$838$	10358.7	+	17941.9i	0.0147509	+	0.0255493i
$839$		−	1.11586e6i		−	1.58520i	−0.609741	−	0.792601i	$-0.708726\pi$
$839$		−	1.11586e6i		−	1.58520i	0.609741	−	0.792601i	$-0.291274\pi$
$840$		0			0
$841$	−156542.			−0.221330
$842$	61674.1	−	35607.5i	0.0869918	−	0.0502247i
$843$	−1.16292e6	+	2.01424e6i	−1.63642	+	2.83437i
$844$	−2491.28	+	4315.03i	−0.00349734	+	0.00605758i
$845$		0			0
$846$			547312.i			0.764705i
$847$	−385178.	−	489242.i	−0.536902	−	0.681957i
$848$		−	228237.i		−	0.317391i
$849$	−822142.	−	1.42399e6i	−1.14059	−	1.97557i
$850$		0			0
$851$	215008.	−	372404.i	0.296889	−	0.514228i
$852$	−359125.	−	622022.i	−0.494728	−	0.856893i
$853$	1.28959e6			1.77236			0.886180	−	0.463341i	$-0.153350\pi$
$853$	1.28959e6			1.77236			0.886180	+	0.463341i	$0.153350\pi$
$854$	−71844.7	+	179745.i	−0.0985097	+	0.246457i
$855$		0			0
$856$	−120000.	−	207847.i	−0.163770	−	0.283658i
$857$	−327273.	+	566854.i	−0.445604	+	0.771809i	−0.998094	−	0.0617109i	$-0.980344\pi$
$857$	−327273.	+	566854.i	−0.445604	+	0.771809i	0.552490	+	0.833519i	$0.313678\pi$
$858$	−262440.	−	151520.i	−0.356497	−	0.205823i
$859$	−211796.	+	122281.i	−0.287033	+	0.165718i	−0.636603	−	0.771192i	$-0.719661\pi$
$859$	−211796.	+	122281.i	−0.287033	+	0.165718i	0.349570	+	0.936910i	$0.386328\pi$
$860$		0			0
$861$	−780266.	−	311875.i	−1.05253	−	0.420702i
$862$		−	39109.2i		−	0.0526337i
$863$	−402942.	+	232638.i	−0.541029	+	0.312363i	−0.745496	−	0.666510i	$-0.767787\pi$
$863$	−402942.	+	232638.i	−0.541029	+	0.312363i	0.204467	+	0.978873i	$0.434454\pi$
$864$	−147672.	−	85258.4i	−0.197820	−	0.114211i
$865$		0			0
$866$	116201.	−	67088.6i	0.154944	−	0.0894567i
$867$	1.07667e6			1.43233
$868$	320145.	−	252049.i	0.424921	−	0.334538i
$869$	138342.			0.183195
$870$		0			0
$871$	1.02255e6	+	590370.i	1.34787	+	0.778194i
$872$	−273407.	−	157852.i	−0.359565	−	0.207595i
$873$	404304.	+	700275.i	0.530493	+	0.918840i
$874$			554179.i			0.725484i
$875$		0			0
$876$	−69271.9			−0.0902712
$877$	−263420.	+	152086.i	−0.342492	+	0.197738i	−0.661373	−	0.750057i	$-0.730026\pi$
$877$	−263420.	+	152086.i	−0.342492	+	0.197738i	0.318882	+	0.947795i	$0.396693\pi$
$878$	155301.	−	268988.i	0.201458	−	0.348935i
$879$	−674078.	+	1.16754e6i	−0.872434	+	1.51110i
$880$		0			0
$881$		−	697876.i		−	0.899138i	−0.893246	−	0.449569i	$-0.851578\pi$
$881$		−	697876.i		−	0.899138i	0.893246	−	0.449569i	$-0.148422\pi$
$882$	949432.	+	229228.i	1.22047	+	0.294667i
$883$			891773.i			1.14375i	0.820339	+	0.571877i	$0.193785\pi$
$883$			891773.i			1.14375i	−0.820339	+	0.571877i	$0.806215\pi$
$884$	−70356.6	−	121861.i	−0.0900328	−	0.155941i
$885$		0			0
$886$	116758.	−	202232.i	0.148738	−	0.257621i
$887$	631278.	+	1.09340e6i	0.802367	+	1.38974i	0.918054	+	0.396455i	$0.129760\pi$
$887$	631278.	+	1.09340e6i	0.802367	+	1.38974i	−0.115687	+	0.993286i	$0.536907\pi$
$888$	−334757.			−0.424526
$889$	27948.9	+	193636.i	0.0353640	+	0.245009i
$890$		0			0
$891$	−54401.9	−	94226.9i	−0.0685265	−	0.118691i
$892$	46039.0	−	79741.8i	0.0578623	−	0.100220i
$893$	−523826.	−	302431.i	−0.656877	−	0.379248i
$894$	1.56857e6	−	905616.i	1.96259	−	1.13310i
$895$		0			0
$896$	−55754.0	+	43894.9i	−0.0694480	+	0.0546761i
$897$			1.06195e6i			1.31983i
$898$	−809404.	+	467310.i	−1.00372	+	0.579498i
$899$	668036.	+	385691.i	0.826572	+	0.477221i
$900$		0			0
$901$	334280.	−	192997.i	0.411776	−	0.237739i
$902$	142239.			0.174825
$903$	−1.65020e6	−	659590.i	−2.02377	−	0.808907i
$904$	199377.			0.243971
$905$		0			0
$906$	−1.08742e6	−	627822.i	−1.32477	−	0.764857i
$907$	824439.	+	475990.i	1.00218	+	0.578607i	0.908891	−	0.417033i	$-0.136930\pi$
$907$	824439.	+	475990.i	1.00218	+	0.578607i	0.0932848	+	0.995639i	$0.470263\pi$
$908$	225469.	+	390523.i	0.273473	+	0.473669i
$909$			947149.i			1.14628i
$910$		0			0
$911$	−743243.			−0.895559			−0.447779	−	0.894144i	$-0.647785\pi$
$911$	−743243.			−0.895559			−0.447779	+	0.894144i	$0.647785\pi$
$912$	373617.	−	215708.i	0.449198	−	0.259344i
$913$	103989.	−	180115.i	0.124752	−	0.216077i
$914$	−527908.	+	914363.i	−0.631925	+	1.09453i
$915$		0			0
$916$		−	337028.i		−	0.401675i
$917$	778662.	−	613038.i	0.925999	−	0.729035i
$918$		−	288377.i		−	0.342196i
$919$	−262150.	−	454057.i	−0.310398	−	0.537625i	0.668050	−	0.744116i	$-0.267129\pi$
$919$	−262150.	−	454057.i	−0.310398	−	0.537625i	−0.978449	+	0.206491i	$0.933796\pi$
$920$		0			0
$921$	1.06219e6	−	1.83977e6i	1.25223	−	2.16892i
$922$	−28786.6	−	49859.9i	−0.0338633	−	0.0586529i
$923$	973052.			1.14218
$924$	−255795.	+	36920.8i	−0.299604	+	0.0432441i
$925$		0			0
$926$	44622.3	+	77288.1i	0.0520391	+	0.0901344i
$927$	109629.	−	189883.i	0.127575	−	0.220967i
$928$	−116340.	−	67168.8i	−0.135093	−	0.0779959i
$929$	−848178.	+	489696.i	−0.982779	+	0.567408i	−0.903108	−	0.429414i	$-0.858720\pi$
$929$	−848178.	+	489696.i	−0.982779	+	0.567408i	−0.0796709	+	0.996821i	$0.525387\pi$
$930$		0			0
$931$	−744024.	+	782024.i	−0.858396	+	0.902237i
$932$			440815.i			0.507486i
$933$	−1.11213e6	+	642090.i	−1.27759	+	0.737620i
$934$	−592420.	−	342034.i	−0.679103	−	0.392081i
$935$		0			0
$936$	458001.	−	264427.i	0.522775	−	0.301824i
$937$	1.13988e6			1.29831			0.649155	−	0.760656i	$-0.275123\pi$
$937$	1.13988e6			1.29831			0.649155	+	0.760656i	$0.275123\pi$
$938$	996658.	−	143855.i	1.13277	−	0.163501i
$939$	267368.			0.303235
$940$		0			0
$941$	693791.	+	400561.i	0.783519	+	0.452365i	0.837676	−	0.546167i	$-0.183914\pi$
$941$	693791.	+	400561.i	0.783519	+	0.452365i	−0.0541569	+	0.998532i	$0.517247\pi$
$942$	449441.	+	259485.i	0.506491	+	0.292422i
$943$	−249224.	−	431669.i	−0.280264	−	0.485431i
$944$			274240.i			0.307743i
$945$		0			0
$946$	300823.			0.336146
$947$	−589145.	+	340143.i	−0.656935	+	0.379282i	−0.791108	−	0.611676i	$-0.790496\pi$
$947$	−589145.	+	340143.i	−0.656935	+	0.379282i	0.134173	+	0.990958i	$0.457162\pi$
$948$	−188700.	+	326838.i	−0.209969	+	0.363677i
$949$	46923.3	−	81273.5i	0.0521022	−	0.0902436i
$950$		0			0
$951$			1.21160e6i			1.33967i
$952$	−111435.	−	44540.8i	−0.122955	−	0.0491456i
$953$		−	394774.i		−	0.434673i	−0.976097	−	0.217337i	$-0.930263\pi$
$953$		−	394774.i		−	0.434673i	0.976097	−	0.217337i	$-0.0697369\pi$
$954$	725355.	+	1.25635e6i	0.796992	+	1.38043i
$955$		0			0
$956$	−92329.9	+	159920.i	−0.101024	+	0.174979i
$957$	−244639.	−	423727.i	−0.267117	−	0.462660i
$958$	769567.			0.838524
$959$	−1.14013e6	−	455714.i	−1.23970	−	0.495513i
$960$		0			0
$961$	78449.9	+	135879.i	0.0849465	+	0.147132i
$962$	226757.	−	392755.i	0.245025	−	0.424396i
$963$	1.32110e6	+	762740.i	1.42457	+	0.822478i
$964$	565151.	−	326290.i	0.608150	−	0.351115i
$965$		0			0
$966$	560240.	+	711600.i	0.600371	+	0.762574i
$967$			604328.i			0.646279i	0.946351	+	0.323140i	$0.104738\pi$
$967$			604328.i			0.646279i	−0.946351	+	0.323140i	$0.895262\pi$
$968$	−249017.	+	143770.i	−0.265753	+	0.153433i
$969$	631860.	+	364804.i	0.672935	+	0.388519i
$970$		0			0
$971$	657301.	−	379493.i	0.697149	−	0.402499i	−0.109136	−	0.994027i	$-0.534808\pi$
$971$	657301.	−	379493.i	0.697149	−	0.402499i	0.806285	+	0.591528i	$0.201475\pi$
$972$	−313584.			−0.331910
$973$	−140490.	−	973346.i	−0.148396	−	1.02811i
$974$	1.15328e6			1.21567
$975$		0			0
$976$	77412.4	+	44694.1i	0.0812664	+	0.0469192i
$977$	1.06104e6	+	612591.i	1.11158	+	0.641773i	0.939239	−	0.343263i	$-0.111532\pi$
$977$	1.06104e6	+	612591.i	1.11158	+	0.641773i	0.172345	+	0.985037i	$0.444866\pi$
$978$	456565.	+	790793.i	0.477337	+	0.826771i
$979$			36843.3i			0.0384409i
$980$		0			0
$981$	2.00666e6			2.08514
$982$	702446.	−	405557.i	0.728434	−	0.420561i
$983$	600236.	−	1.03964e6i	0.621177	−	1.07591i	−0.368090	−	0.929790i	$-0.619988\pi$
$983$	600236.	−	1.03964e6i	0.621177	−	1.07591i	0.989267	−	0.146120i	$-0.0466784\pi$
$984$	−194015.	+	336044.i	−0.200376	+	0.347062i
$985$		0			0
$986$		−	227191.i		−	0.233689i
$987$	−978362.	+	141214.i	−1.00430	+	0.144959i
$988$			584464.i			0.598747i
$989$	−527088.	−	912944.i	−0.538878	−	0.933365i
$990$		0			0
$991$	−904963.	+	1.56744e6i	−0.921475	+	1.59604i	−0.124340	+	0.992240i	$0.539682\pi$
$991$	−904963.	+	1.56744e6i	−0.921475	+	1.59604i	−0.797134	+	0.603802i	$0.793652\pi$
$992$	−94078.7	−	162949.i	−0.0956022	−	0.165588i
$993$	−1.09164e6			−1.10708
$994$	652034.	−	513344.i	0.659929	−	0.519560i
$995$		0			0
$996$	283686.	+	491359.i	0.285969	+	0.495313i
$997$	374644.	−	648903.i	0.376902	−	0.652814i	−0.613707	−	0.789534i	$-0.710323\pi$
$997$	374644.	−	648903.i	0.376902	−	0.652814i	0.990610	+	0.136719i	$0.0436559\pi$
$998$	−860837.	−	497004.i	−0.864291	−	0.498998i
$999$	804909.	−	464715.i	0.806521	−	0.465645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.5.i.a.199.2		8
5.2	odd	4		14.5.d.a.3.1	✓	4
5.3	odd	4		350.5.k.a.101.2		4
5.4	even	2	inner	350.5.i.a.199.3		8
7.5	odd	6	inner	350.5.i.a.299.3		8
15.2	even	4		126.5.n.a.73.2		4
20.7	even	4		112.5.s.b.17.2		4
35.2	odd	12		98.5.d.a.19.1		4
35.12	even	12		14.5.d.a.5.1	yes	4
35.17	even	12		98.5.b.b.97.3		4
35.19	odd	6	inner	350.5.i.a.299.2		8
35.27	even	4		98.5.d.a.31.1		4
35.32	odd	12		98.5.b.b.97.4		4
35.33	even	12		350.5.k.a.201.2		4
105.17	odd	12		882.5.c.b.685.2		4
105.32	even	12		882.5.c.b.685.1		4
105.47	odd	12		126.5.n.a.19.2		4
140.47	odd	12		112.5.s.b.33.2		4
140.67	even	12		784.5.c.b.97.1		4
140.87	odd	12		784.5.c.b.97.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.5.d.a.3.1	✓	4	5.2	odd	4
14.5.d.a.5.1	yes	4	35.12	even	12
98.5.b.b.97.3		4	35.17	even	12
98.5.b.b.97.4		4	35.32	odd	12
98.5.d.a.19.1		4	35.2	odd	12
98.5.d.a.31.1		4	35.27	even	4
112.5.s.b.17.2		4	20.7	even	4
112.5.s.b.33.2		4	140.47	odd	12
126.5.n.a.19.2		4	105.47	odd	12
126.5.n.a.73.2		4	15.2	even	4
350.5.i.a.199.2		8	1.1	even	1	trivial
350.5.i.a.199.3		8	5.4	even	2	inner
350.5.i.a.299.2		8	35.19	odd	6	inner
350.5.i.a.299.3		8	7.5	odd	6	inner
350.5.k.a.101.2		4	5.3	odd	4
350.5.k.a.201.2		4	35.33	even	12
784.5.c.b.97.1		4	140.67	even	12
784.5.c.b.97.4		4	140.87	odd	12
882.5.c.b.685.1		4	105.32	even	12
882.5.c.b.685.2		4	105.17	odd	12

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	350.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.44949 + 1.41421i) q^{2} +(7.49706 - 12.9853i) q^{3} +(4.00000 - 6.92820i) q^{4} +42.4098i q^{6} +(-48.4974 + 7.00000i) q^{7} +22.6274i q^{8} +(-71.9117 - 124.555i) q^{9} +O(q^{10})\)	\(q+(-2.44949 + 1.41421i) q^{2} +(7.49706 - 12.9853i) q^{3} +(4.00000 - 6.92820i) q^{4} +42.4098i q^{6} +(-48.4974 + 7.00000i) q^{7} +22.6274i q^{8} +(-71.9117 - 124.555i) q^{9} +(-21.9853 + 38.0796i) q^{11} +(-59.9764 - 103.882i) q^{12} +162.507 q^{13} +(108.894 - 85.7321i) q^{14} +(-32.0000 - 55.4256i) q^{16} +(54.1182 - 93.7355i) q^{17} +(352.294 + 203.397i) q^{18} +(-389.338 + 224.784i) q^{19} +(-272.691 + 682.232i) q^{21} -124.368i q^{22} +(-377.433 + 217.911i) q^{23} +(293.823 + 169.639i) q^{24} +(-398.059 + 229.819i) q^{26} -941.981 q^{27} +(-145.492 + 364.000i) q^{28} -742.118 q^{29} +(-900.175 - 519.716i) q^{31} +(156.767 + 90.5097i) q^{32} +(329.650 + 570.970i) q^{33} +306.139i q^{34} -1150.59 q^{36} +(-854.486 + 493.338i) q^{37} +(635.786 - 1101.21i) q^{38} +(1218.32 - 2110.20i) q^{39} +1143.70i q^{41} +(-296.868 - 2056.76i) q^{42} +2418.82i q^{43} +(175.882 + 304.637i) q^{44} +(616.346 - 1067.54i) q^{46} +(672.714 + 1165.17i) q^{47} -959.623 q^{48} +(2303.00 - 678.964i) q^{49} +(-811.455 - 1405.48i) q^{51} +(650.027 - 1125.88i) q^{52} +(3088.42 + 1783.10i) q^{53} +(2307.37 - 1332.16i) q^{54} +(-158.392 - 1097.37i) q^{56} +6740.88i q^{57} +(1817.81 - 1049.51i) q^{58} +(-3710.93 - 2142.50i) q^{59} +(-1209.57 + 698.345i) q^{61} +2939.96 q^{62} +(4359.41 + 5537.20i) q^{63} -512.000 q^{64} +(-1614.95 - 932.390i) q^{66} +(6292.36 + 3632.89i) q^{67} +(-432.946 - 749.884i) q^{68} +6534.77i q^{69} +5987.76 q^{71} +(2818.35 - 1627.18i) q^{72} +(288.746 - 500.123i) q^{73} +(1395.37 - 2416.85i) q^{74} +3596.55i q^{76} +(799.672 - 2000.66i) q^{77} +6891.88i q^{78} +(-1573.12 - 2724.72i) q^{79} +(-1237.24 + 2142.95i) q^{81} +(-1617.43 - 2801.47i) q^{82} -4729.96 q^{83} +(3635.88 + 4618.19i) q^{84} +(-3420.73 - 5924.88i) q^{86} +(-5563.70 + 9636.61i) q^{87} +(-861.644 - 497.470i) q^{88} +(725.651 - 418.955i) q^{89} +(-7881.16 + 1137.55i) q^{91} +3486.58i q^{92} +(-13497.3 + 7792.69i) q^{93} +(-3295.61 - 1902.72i) q^{94} +(2350.59 - 1357.11i) q^{96} -5622.23 q^{97} +(-4680.97 + 4920.05i) q^{98} +6323.99 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 32 q^{4} - 168 q^{9}+O(q^{10}) \) 8 * q + 32 * q^4 - 168 * q^9	\( 8 q + 32 q^{4} - 168 q^{9} - 108 q^{11} - 256 q^{16} - 60 q^{19} - 756 q^{21} + 1536 q^{24} - 3456 q^{26} - 6480 q^{29} - 1092 q^{31} - 2688 q^{36} + 6624 q^{39} + 864 q^{44} + 7680 q^{46} + 18424 q^{49} + 636 q^{51} + 2880 q^{54} - 24732 q^{59} + 15372 q^{61} - 4096 q^{64} - 6912 q^{66} + 37584 q^{71} + 8640 q^{74} - 1588 q^{79} - 8676 q^{81} + 10080 q^{84} - 20736 q^{86} + 24948 q^{89} + 5376 q^{91} - 30336 q^{94} + 12288 q^{96} + 22896 q^{99}+O(q^{100}) \) 8 * q + 32 * q^4 - 168 * q^9 - 108 * q^11 - 256 * q^16 - 60 * q^19 - 756 * q^21 + 1536 * q^24 - 3456 * q^26 - 6480 * q^29 - 1092 * q^31 - 2688 * q^36 + 6624 * q^39 + 864 * q^44 + 7680 * q^46 + 18424 * q^49 + 636 * q^51 + 2880 * q^54 - 24732 * q^59 + 15372 * q^61 - 4096 * q^64 - 6912 * q^66 + 37584 * q^71 + 8640 * q^74 - 1588 * q^79 - 8676 * q^81 + 10080 * q^84 - 20736 * q^86 + 24948 * q^89 + 5376 * q^91 - 30336 * q^94 + 12288 * q^96 + 22896 * q^99

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