LMFDB - Embedded newform 450.3.k.c.149.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,3,Mod(149,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("450.149");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	450.k (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:	$12.2616118962$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.14
Character	$\chi$	$=$	450.149
Dual form			450.3.k.c.299.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 1.22474i) q^{2} +(-2.99722 - 0.129213i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.96110 - 3.76219i) q^{6} +(5.74345 - 3.31598i) q^{7} -2.82843 q^{8} +(8.96661 + 0.774559i) q^{9} +(-18.2172 + 10.5177i) q^{11} +(3.22102 - 5.06212i) q^{12} +(8.47187 + 4.89124i) q^{13} +(8.12247 + 4.68951i) q^{14} +(-2.00000 - 3.46410i) q^{16} +12.9017 q^{17} +(5.39171 + 11.5295i) q^{18} -16.1821 q^{19} +(-17.6428 + 9.19659i) q^{21} +(-25.7630 - 14.8743i) q^{22} +(-8.46823 + 14.6674i) q^{23} +(8.47741 + 0.365470i) q^{24} +13.8345i q^{26} +(-26.7748 - 3.48012i) q^{27} +13.2639i q^{28} +(-43.3525 + 25.0296i) q^{29} +(5.03212 - 8.71588i) q^{31} +(2.82843 - 4.89898i) q^{32} +(55.9600 - 29.1700i) q^{33} +(9.12285 + 15.8012i) q^{34} +(-10.3082 + 14.7561i) q^{36} -2.54425i q^{37} +(-11.4425 - 19.8190i) q^{38} +(-24.7600 - 15.7548i) q^{39} +(-46.5617 - 26.8824i) q^{41} +(-23.7388 - 15.1050i) q^{42} +(-64.8089 + 37.4175i) q^{43} -42.0709i q^{44} -23.9518 q^{46} +(-23.6001 - 40.8766i) q^{47} +(5.54682 + 10.6411i) q^{48} +(-2.50850 + 4.34485i) q^{49} +(-38.6691 - 1.66706i) q^{51} +(-16.9437 + 9.78248i) q^{52} -1.08813 q^{53} +(-14.6704 - 35.2531i) q^{54} +(-16.2449 + 9.37902i) q^{56} +(48.5013 + 2.09094i) q^{57} +(-61.3097 - 35.3972i) q^{58} +(-8.34807 - 4.81976i) q^{59} +(22.4573 + 38.8971i) q^{61} +14.2330 q^{62} +(54.0677 - 25.2845i) q^{63} +8.00000 q^{64} +(75.2955 + 47.9104i) q^{66} +(-2.89369 - 1.67067i) q^{67} +(-12.9017 + 22.3463i) q^{68} +(27.2763 - 42.8672i) q^{69} +38.4670i q^{71} +(-25.3614 - 2.19078i) q^{72} -88.9201i q^{73} +(3.11606 - 1.79906i) q^{74} +(16.1821 - 28.0283i) q^{76} +(-69.7532 + 120.816i) q^{77} +(1.78760 - 41.4650i) q^{78} +(58.8235 + 101.885i) q^{79} +(79.8001 + 13.8903i) q^{81} -76.0349i q^{82} +(73.5614 + 127.412i) q^{83} +(1.71387 - 39.7549i) q^{84} +(-91.6537 - 52.9163i) q^{86} +(133.171 - 69.4173i) q^{87} +(51.5261 - 29.7486i) q^{88} +145.331i q^{89} +64.8771 q^{91} +(-16.9365 - 29.3348i) q^{92} +(-16.2086 + 25.4732i) q^{93} +(33.3756 - 57.8083i) q^{94} +(-9.11042 + 14.3178i) q^{96} +(40.7494 - 23.5267i) q^{97} -7.09511 q^{98} +(-171.493 + 80.1980i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} + 32 q^{6} + 8 q^{9} + 72 q^{14} - 64 q^{16} - 160 q^{19} - 88 q^{21} + 16 q^{24} + 144 q^{29} - 32 q^{31} + 96 q^{34} + 64 q^{36} + 16 q^{39} + 216 q^{41} + 48 q^{46} + 168 q^{49} + 336 q^{51}+ \cdots - 1632 q^{99}+O(q^{100}) $ 32 * q - 32 * q^4 + 32 * q^6 + 8 * q^9 + 72 * q^14 - 64 * q^16 - 160 * q^19 - 88 * q^21 + 16 * q^24 + 144 * q^29 - 32 * q^31 + 96 * q^34 + 64 * q^36 + 16 * q^39 + 216 * q^41 + 48 * q^46 + 168 * q^49 + 336 * q^51 - 296 * q^54 - 144 * q^56 - 288 * q^59 - 152 * q^61 + 256 * q^64 + 192 * q^66 + 144 * q^69 + 576 * q^74 + 160 * q^76 - 160 * q^79 + 640 * q^81 - 80 * q^84 - 432 * q^86 - 1312 * q^91 + 168 * q^94 - 160 * q^96 - 1632 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$	−2.99722	−	0.129213i	−0.999072	−	0.0430710i
$3$	−2.99722	−	0.129213i	−0.999072	−	0.0430710i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.96110	−	3.76219i	−0.326850	−	0.627032i
$7$	5.74345	−	3.31598i	0.820493	−	0.473712i	−0.0300933	−	0.999547i	$-0.509580\pi$
$7$	5.74345	−	3.31598i	0.820493	−	0.473712i	0.850587	+	0.525835i	$0.176247\pi$
$8$	−2.82843			−0.353553
$9$	8.96661	+	0.774559i	0.996290	+	0.0860621i
$10$		0			0
$11$	−18.2172	+	10.5177i	−1.65611	+	0.956156i	−0.681627	+	0.731699i	$0.738727\pi$
$11$	−18.2172	+	10.5177i	−1.65611	+	0.956156i	−0.974484	+	0.224457i	$0.927939\pi$
$12$	3.22102	−	5.06212i	0.268418	−	0.421843i
$13$	8.47187	+	4.89124i	0.651683	+	0.376249i	0.789101	−	0.614264i	$-0.210547\pi$
$13$	8.47187	+	4.89124i	0.651683	+	0.376249i	−0.137418	+	0.990513i	$0.543880\pi$
$14$	8.12247	+	4.68951i	0.580176	+	0.334965i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	12.9017			0.758921			0.379460	−	0.925208i	$-0.376110\pi$
$17$	12.9017			0.758921			0.379460	+	0.925208i	$0.376110\pi$
$18$	5.39171	+	11.5295i	0.299540	+	0.640528i
$19$	−16.1821			−0.851691			−0.425845	−	0.904796i	$-0.640023\pi$
$19$	−16.1821			−0.851691			−0.425845	+	0.904796i	$0.640023\pi$
$20$		0			0
$21$	−17.6428	+	9.19659i	−0.840135	+	0.437933i
$22$	−25.7630	−	14.8743i	−1.17105	−	0.676105i
$23$	−8.46823	+	14.6674i	−0.368184	+	0.637713i	−0.989282	−	0.146020i	$-0.953354\pi$
$23$	−8.46823	+	14.6674i	−0.368184	+	0.637713i	0.621098	+	0.783733i	$0.286687\pi$
$24$	8.47741	+	0.365470i	0.353225	+	0.0152279i
$25$		0			0
$26$			13.8345i			0.532097i
$27$	−26.7748	−	3.48012i	−0.991658	−	0.128893i
$28$			13.2639i			0.473712i
$29$	−43.3525	+	25.0296i	−1.49491	+	0.863089i	−0.999983	−	0.00584415i	$-0.998140\pi$
$29$	−43.3525	+	25.0296i	−1.49491	+	0.863089i	−0.494930	+	0.868933i	$0.664806\pi$
$30$		0			0
$31$	5.03212	−	8.71588i	0.162326	−	0.281158i	−0.773376	−	0.633947i	$-0.781434\pi$
$31$	5.03212	−	8.71588i	0.162326	−	0.281158i	0.935703	+	0.352790i	$0.114767\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$	55.9600	−	29.1700i	1.69576	−	0.883939i
$34$	9.12285	+	15.8012i	0.268319	+	0.464742i
$35$		0			0
$36$	−10.3082	+	14.7561i	−0.286338	+	0.409891i
$37$		−	2.54425i		−	0.0687635i	−0.999409	−	0.0343817i	$-0.989054\pi$
$37$		−	2.54425i		−	0.0687635i	0.999409	−	0.0343817i	$-0.0109462\pi$
$38$	−11.4425	−	19.8190i	−0.301118	−	0.521552i
$39$	−24.7600	−	15.7548i	−0.634872	−	0.403969i
$40$		0			0
$41$	−46.5617	−	26.8824i	−1.13565	−	0.655669i	−0.190301	−	0.981726i	$-0.560946\pi$
$41$	−46.5617	−	26.8824i	−1.13565	−	0.655669i	−0.945350	+	0.326057i	$0.894280\pi$
$42$	−23.7388	−	15.1050i	−0.565211	−	0.359643i
$43$	−64.8089	+	37.4175i	−1.50718	+	0.870173i	−0.507219	+	0.861817i	$0.669327\pi$
$43$	−64.8089	+	37.4175i	−1.50718	+	0.870173i	−0.999965	+	0.00835640i	$0.997340\pi$
$44$		−	42.0709i		−	0.956156i
$45$		0			0
$46$	−23.9518			−0.520690
$47$	−23.6001	−	40.8766i	−0.502131	−	0.869716i	−0.999997	−	0.00246200i	$-0.999216\pi$
$47$	−23.6001	−	40.8766i	−0.502131	−	0.869716i	0.497866	−	0.867254i	$-0.334117\pi$
$48$	5.54682	+	10.6411i	0.115559	+	0.221689i
$49$	−2.50850	+	4.34485i	−0.0511939	+	0.0886704i
$50$		0			0
$51$	−38.6691	−	1.66706i	−0.758217	−	0.0326875i
$52$	−16.9437	+	9.78248i	−0.325841	+	0.188125i
$53$	−1.08813			−0.0205307			−0.0102654	−	0.999947i	$-0.503268\pi$
$53$	−1.08813			−0.0205307			−0.0102654	+	0.999947i	$0.503268\pi$
$54$	−14.6704	−	35.2531i	−0.271673	−	0.652835i
$55$		0			0
$56$	−16.2449	+	9.37902i	−0.290088	+	0.167482i
$57$	48.5013	+	2.09094i	0.850900	+	0.0366832i
$58$	−61.3097	−	35.3972i	−1.05706	−	0.610296i
$59$	−8.34807	−	4.81976i	−0.141493	−	0.0816908i	0.427583	−	0.903976i	$-0.359365\pi$
$59$	−8.34807	−	4.81976i	−0.141493	−	0.0816908i	−0.569075	+	0.822285i	$0.692699\pi$
$60$		0			0
$61$	22.4573	+	38.8971i	0.368152	+	0.637657i	0.989277	−	0.146054i	$-0.0466574\pi$
$61$	22.4573	+	38.8971i	0.368152	+	0.637657i	−0.621125	+	0.783712i	$0.713324\pi$
$62$	14.2330			0.229564
$63$	54.0677	−	25.2845i	0.858218	−	0.401341i
$64$	8.00000			0.125000
$65$		0			0
$66$	75.2955	+	47.9104i	1.14084	+	0.725915i
$67$	−2.89369	−	1.67067i	−0.0431894	−	0.0249354i	0.478250	−	0.878224i	$-0.341271\pi$
$67$	−2.89369	−	1.67067i	−0.0431894	−	0.0249354i	−0.521439	+	0.853288i	$0.674605\pi$
$68$	−12.9017	+	22.3463i	−0.189730	+	0.328622i
$69$	27.2763	−	42.8672i	0.395309	−	0.621263i
$70$		0			0
$71$			38.4670i			0.541788i	0.962609	+	0.270894i	$0.0873193\pi$
$71$			38.4670i			0.541788i	−0.962609	+	0.270894i	$0.912681\pi$
$72$	−25.3614	−	2.19078i	−0.352242	−	0.0304276i
$73$		−	88.9201i		−	1.21808i	−0.793138	−	0.609042i	$-0.791554\pi$
$73$		−	88.9201i		−	1.21808i	0.793138	−	0.609042i	$-0.208446\pi$
$74$	3.11606	−	1.79906i	0.0421089	−	0.0243116i
$75$		0			0
$76$	16.1821	−	28.0283i	0.212923	−	0.368793i
$77$	−69.7532	+	120.816i	−0.905885	+	1.56904i
$78$	1.78760	−	41.4650i	0.0229180	−	0.531603i
$79$	58.8235	+	101.885i	0.744602	+	1.28969i	0.950381	+	0.311090i	$0.100694\pi$
$79$	58.8235	+	101.885i	0.744602	+	1.28969i	−0.205779	+	0.978599i	$0.565973\pi$
$80$		0			0
$81$	79.8001	+	13.8903i	0.985187	+	0.171486i
$82$		−	76.0349i		−	0.927255i
$83$	73.5614	+	127.412i	0.886282	+	1.53509i	0.844237	+	0.535970i	$0.180054\pi$
$83$	73.5614	+	127.412i	0.886282	+	1.53509i	0.0420449	+	0.999116i	$0.486613\pi$
$84$	1.71387	−	39.7549i	0.0204033	−	0.473272i
$85$		0			0
$86$	−91.6537	−	52.9163i	−1.06574	−	0.615305i
$87$	133.171	−	69.4173i	1.53070	−	0.797900i
$88$	51.5261	−	29.7486i	0.585524	−	0.338052i
$89$			145.331i			1.63293i	0.577396	+	0.816464i	$0.304069\pi$
$89$			145.331i			1.63293i	−0.577396	+	0.816464i	$0.695931\pi$
$90$		0			0
$91$	64.8771			0.712935
$92$	−16.9365	−	29.3348i	−0.184092	−	0.318856i
$93$	−16.2086	+	25.4732i	−0.174285	+	0.273905i
$94$	33.3756	−	57.8083i	0.355060	−	0.614982i
$95$		0			0
$96$	−9.11042	+	14.3178i	−0.0949002	+	0.149144i
$97$	40.7494	−	23.5267i	0.420097	−	0.242543i	−0.275022	−	0.961438i	$-0.588685\pi$
$97$	40.7494	−	23.5267i	0.420097	−	0.242543i	0.695119	+	0.718895i	$0.255352\pi$
$98$	−7.09511			−0.0723991
$99$	−171.493	+	80.1980i	−1.73226	+	0.810080i
$100$		0			0
$101$	−19.3600	+	11.1775i	−0.191683	+	0.110668i	−0.592770	−	0.805372i	$-0.701966\pi$
$101$	−19.3600	+	11.1775i	−0.191683	+	0.110668i	0.401087	+	0.916040i	$0.368632\pi$
$102$	−25.3014	−	48.5385i	−0.248053	−	0.475868i
$103$	−107.300	−	61.9495i	−1.04174	−	0.601452i	−0.121418	−	0.992601i	$-0.538744\pi$
$103$	−107.300	−	61.9495i	−1.04174	−	0.601452i	−0.920327	+	0.391150i	$0.872077\pi$
$104$	−23.9621	−	13.8345i	−0.230405	−	0.133024i
$105$		0			0
$106$	−0.769422	−	1.33268i	−0.00725870	−	0.0125724i
$107$	47.3690			0.442701			0.221351	−	0.975194i	$-0.428954\pi$
$107$	47.3690			0.442701			0.221351	+	0.975194i	$0.428954\pi$
$108$	32.8025	−	42.8952i	0.303727	−	0.397177i
$109$	26.8745			0.246555			0.123278	−	0.992372i	$-0.460659\pi$
$109$	26.8745			0.246555			0.123278	+	0.992372i	$0.460659\pi$
$110$		0			0
$111$	−0.328750	+	7.62567i	−0.00296171	+	0.0686997i
$112$	−22.9738	−	13.2639i	−0.205123	−	0.118428i
$113$	9.40495	−	16.2899i	0.0832297	−	0.144158i	−0.821406	−	0.570344i	$-0.806810\pi$
$113$	9.40495	−	16.2899i	0.0832297	−	0.144158i	0.904635	+	0.426186i	$0.140143\pi$
$114$	31.7347	+	60.8803i	0.278375	+	0.534037i
$115$		0			0
$116$		−	100.118i		−	0.863089i
$117$	72.1754	+	50.4198i	0.616884	+	0.430938i
$118$		−	13.6323i		−	0.115528i
$119$	74.1001	−	42.7817i	0.622690	−	0.359510i
$120$		0			0
$121$	160.745	−	278.418i	1.32847	−	2.30098i
$122$	−31.7593	+	55.0088i	−0.260323	+	0.450892i
$123$	136.082	+	86.5888i	1.10636	+	0.703974i
$124$	10.0642	+	17.4318i	0.0811632	+	0.140579i
$125$		0			0
$126$	69.1987	+	48.3403i	0.549196	+	0.383653i
$127$			128.820i			1.01433i	0.861849	+	0.507166i	$0.169307\pi$
$127$			128.820i			1.01433i	−0.861849	+	0.507166i	$0.830693\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$	199.081	−	103.774i	1.54327	−	0.804450i
$130$		0			0
$131$	−26.6836	−	15.4058i	−0.203692	−	0.117601i	0.394685	−	0.918817i	$-0.370854\pi$
$131$	−26.6836	−	15.4058i	−0.203692	−	0.117601i	−0.598376	+	0.801215i	$0.704187\pi$
$132$	−5.43611	+	126.096i	−0.0411826	+	0.955269i
$133$	−92.9413	+	53.6597i	−0.698806	+	0.403456i
$134$		−	4.72538i		−	0.0352640i
$135$		0			0
$136$	−36.4914			−0.268319
$137$	53.2723	+	92.2703i	0.388849	+	0.673506i	0.992295	−	0.123898i	$-0.0395395\pi$
$137$	53.2723	+	92.2703i	0.388849	+	0.673506i	−0.603446	+	0.797404i	$0.706206\pi$
$138$	71.7886	+	3.09488i	0.520207	+	0.0224267i
$139$	57.1183	−	98.9317i	0.410923	−	0.711739i	−0.584068	−	0.811705i	$-0.698540\pi$
$139$	57.1183	−	98.9317i	0.410923	−	0.711739i	0.994991	+	0.0999656i	$0.0318733\pi$
$140$		0			0
$141$	65.4529	+	125.566i	0.464205	+	0.890536i
$142$	−47.1122	+	27.2002i	−0.331776	+	0.191551i
$143$	−205.779			−1.43901
$144$	−15.2501	−	32.6104i	−0.105903	−	0.226461i
$145$		0			0
$146$	108.904	−	62.8760i	0.745921	−	0.430658i
$147$	8.07993	−	12.6983i	0.0549655	−	0.0863832i
$148$	4.40677	+	2.54425i	0.0297755	+	0.0171909i
$149$	−104.689	−	60.4419i	−0.702607	−	0.405651i	0.105710	−	0.994397i	$-0.466288\pi$
$149$	−104.689	−	60.4419i	−0.702607	−	0.405651i	−0.808318	+	0.588746i	$0.799622\pi$
$150$		0			0
$151$	−63.4938	−	109.975i	−0.420489	−	0.728308i	0.575498	−	0.817803i	$-0.304808\pi$
$151$	−63.4938	−	109.975i	−0.420489	−	0.728308i	−0.995987	+	0.0894947i	$0.971475\pi$
$152$	45.7700			0.301118
$153$	115.684	+	9.99310i	0.756105	+	0.0653144i
$154$	−197.292			−1.28112
$155$		0			0
$156$	52.0481	−	27.1308i	0.333642	−	0.173916i
$157$	90.2510	+	52.1064i	0.574847	+	0.331888i	0.759083	−	0.650994i	$-0.225648\pi$
$157$	90.2510	+	52.1064i	0.574847	+	0.331888i	−0.184236	+	0.982882i	$0.558981\pi$
$158$	−83.1891	+	144.088i	−0.526513	+	0.911947i
$159$	3.26135	+	0.140600i	0.0205117	+	0.000884279i
$160$		0			0
$161$			112.322i			0.697652i
$162$	39.4151	+	107.557i	0.243303	+	0.663930i
$163$		−	188.533i		−	1.15664i	−0.815809	−	0.578321i	$-0.803708\pi$
$163$		−	188.533i		−	1.15664i	0.815809	−	0.578321i	$-0.196292\pi$
$164$	93.1234	−	53.7648i	0.567826	−	0.327834i
$165$		0			0
$166$	−104.032	+	180.188i	−0.626696	+	1.08547i
$167$	−33.9581	+	58.8172i	−0.203342	+	0.352199i	−0.949603	−	0.313454i	$-0.898514\pi$
$167$	−33.9581	+	58.8172i	−0.203342	+	0.352199i	0.746261	+	0.665653i	$0.231847\pi$
$168$	49.9015	−	26.0119i	0.297033	−	0.154833i
$169$	−36.6516	−	63.4824i	−0.216873	−	0.375635i
$170$		0			0
$171$	−145.099	−	12.5340i	−0.848531	−	0.0732983i
$172$		−	149.670i		−	0.870173i
$173$	61.1963	+	105.995i	0.353736	+	0.612689i	0.986901	−	0.161328i	$-0.0515778\pi$
$173$	61.1963	+	105.995i	0.353736	+	0.612689i	−0.633165	+	0.774017i	$0.718244\pi$
$174$	179.185	+	114.015i	1.02980	+	0.655258i
$175$		0			0
$176$	72.8689	+	42.0709i	0.414028	+	0.239039i
$177$	24.3982	+	15.5245i	0.137843	+	0.0877093i
$178$	−177.993	+	102.764i	−0.999961	+	0.577328i
$179$		−	78.4259i		−	0.438134i	−0.975710	−	0.219067i	$-0.929699\pi$
$179$		−	78.4259i		−	0.438134i	0.975710	−	0.219067i	$-0.0703013\pi$
$180$		0			0
$181$	219.562			1.21305			0.606525	−	0.795064i	$-0.292563\pi$
$181$	219.562			1.21305			0.606525	+	0.795064i	$0.292563\pi$
$182$	45.8750	+	79.4579i	0.252061	+	0.436582i
$183$	−62.2832	−	119.485i	−0.340345	−	0.652922i
$184$	23.9518	−	41.4857i	0.130173	−	0.225466i
$185$		0			0
$186$	−42.6593	−	1.83909i	−0.229351	−	0.00988757i
$187$	−235.032	+	135.696i	−1.25686	+	0.725647i
$188$	94.4006			0.502131
$189$	−165.320	+	68.7968i	−0.874707	+	0.364004i
$190$		0			0
$191$	−279.710	+	161.491i	−1.46445	+	0.845501i	−0.999212	−	0.0396836i	$-0.987365\pi$
$191$	−279.710	+	161.491i	−1.46445	+	0.845501i	−0.465239	+	0.885185i	$0.654032\pi$
$192$	−23.9777	−	1.03370i	−0.124884	−	0.00538388i
$193$	149.635	+	86.3918i	0.775311	+	0.447626i	0.834766	−	0.550605i	$-0.185603\pi$
$193$	149.635	+	86.3918i	0.775311	+	0.447626i	−0.0594550	+	0.998231i	$0.518936\pi$
$194$	57.6284	+	33.2718i	0.297054	+	0.171504i
$195$		0			0
$196$	−5.01700	−	8.68970i	−0.0255970	−	0.0443352i
$197$	−71.7321			−0.364123			−0.182061	−	0.983287i	$-0.558277\pi$
$197$	−71.7321			−0.364123			−0.182061	+	0.983287i	$0.558277\pi$
$198$	−219.486	−	153.327i	−1.10852	−	0.774379i
$199$	−133.225			−0.669472			−0.334736	−	0.942312i	$-0.608647\pi$
$199$	−133.225			−0.669472			−0.334736	+	0.942312i	$0.608647\pi$
$200$		0			0
$201$	8.45714	+	5.38127i	0.0420753	+	0.0267725i
$202$	−27.3792	−	15.8074i	−0.135541	−	0.0782544i
$203$	−165.995	+	287.512i	−0.817711	+	1.41632i
$204$	41.5565	−	65.3097i	0.203708	−	0.320146i
$205$		0			0
$206$		−	175.220i		−	0.850581i
$207$	−87.2920	+	124.958i	−0.421701	+	0.603660i
$208$		−	39.1299i		−	0.188125i
$209$	294.793	−	170.199i	1.41049	−	0.814349i
$210$		0			0
$211$	188.164	−	325.909i	0.891771	−	1.54459i	0.0540209	−	0.998540i	$-0.482796\pi$
$211$	188.164	−	325.909i	0.891771	−	1.54459i	0.837750	−	0.546053i	$-0.183870\pi$
$212$	1.08813	−	1.88469i	0.00513268	−	0.00889006i
$213$	4.97043	−	115.294i	0.0233354	−	0.541285i
$214$	33.4949	+	58.0150i	0.156518	+	0.271098i
$215$		0			0
$216$	75.7305	+	9.84328i	0.350604	+	0.0455707i
$217$		−	66.7457i		−	0.307584i
$218$	19.0032	+	32.9144i	0.0871705	+	0.150984i
$219$	−11.4896	+	266.513i	−0.0524641	+	1.21695i
$220$		0			0
$221$	109.301	+	63.1051i	0.494576	+	0.285543i
$222$	−9.57196	+	4.98952i	−0.0431169	+	0.0224753i
$223$	51.2488	−	29.5885i	0.229815	−	0.132684i	−0.380672	−	0.924710i	$-0.624307\pi$
$223$	51.2488	−	29.5885i	0.229815	−	0.132684i	0.610487	+	0.792026i	$0.290974\pi$
$224$		−	37.5161i		−	0.167482i
$225$		0			0
$226$	26.6012			0.117705
$227$	−74.9193	−	129.764i	−0.330041	−	0.571647i	0.652479	−	0.757807i	$-0.273729\pi$
$227$	−74.9193	−	129.764i	−0.330041	−	0.571647i	−0.982520	+	0.186160i	$0.940396\pi$
$228$	−52.1229	+	81.9158i	−0.228609	+	0.359280i
$229$	−85.4319	+	147.972i	−0.373065	+	0.646167i	−0.990035	−	0.140819i	$-0.955026\pi$
$229$	−85.4319	+	147.972i	−0.373065	+	0.646167i	0.616970	+	0.786986i	$0.288360\pi$
$230$		0			0
$231$	224.676	−	353.099i	0.972625	−	1.52857i
$232$	122.619	−	70.7943i	0.528532	−	0.305148i
$233$	448.983			1.92697			0.963483	−	0.267770i	$-0.0862867\pi$
$233$	448.983			1.92697			0.963483	+	0.267770i	$0.0862867\pi$
$234$	−10.7156	+	124.049i	−0.0457934	+	0.530122i
$235$		0			0
$236$	16.6961	−	9.63952i	0.0707463	−	0.0408454i
$237$	−163.142	−	312.973i	−0.688363	−	1.32056i
$238$	104.793	+	60.5024i	0.440308	+	0.254212i
$239$	200.845	+	115.958i	0.840356	+	0.485180i	0.857385	−	0.514675i	$-0.172087\pi$
$239$	200.845	+	115.958i	0.840356	+	0.485180i	−0.0170289	+	0.999855i	$0.505421\pi$
$240$		0			0
$241$	198.671	+	344.108i	0.824359	+	1.42783i	0.902408	+	0.430882i	$0.141798\pi$
$241$	198.671	+	344.108i	0.824359	+	1.42783i	−0.0780488	+	0.996950i	$0.524869\pi$
$242$	454.655			1.87874
$243$	−237.383	−	51.9436i	−0.976886	−	0.213759i
$244$	−89.8290			−0.368152
$245$		0			0
$246$	−9.82471	+	227.893i	−0.0399378	+	0.926395i
$247$	−137.093	−	79.1506i	−0.555032	−	0.320448i
$248$	−14.2330	+	24.6522i	−0.0573910	+	0.0994042i
$249$	−204.016	−	391.387i	−0.819342	−	1.57183i
$250$		0			0
$251$		−	193.179i		−	0.769636i	−0.922992	−	0.384818i	$-0.874264\pi$
$251$		−	193.179i		−	0.769636i	0.922992	−	0.384818i	$-0.125736\pi$
$252$	−10.2737	+	118.933i	−0.0407687	+	0.471954i
$253$		−	356.266i		−	1.40816i
$254$	−157.772	+	91.0895i	−0.621148	+	0.358620i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	60.4331	−	104.673i	0.235148	−	0.407289i	−0.724167	−	0.689624i	$-0.757776\pi$
$257$	60.4331	−	104.673i	0.235148	−	0.407289i	0.959316	+	0.282335i	$0.0911091\pi$
$258$	267.868	+	170.444i	1.03825	+	0.660637i
$259$	−8.43669	−	14.6128i	−0.0325741	−	0.0564200i
$260$		0			0
$261$	−408.112	+	190.851i	−1.56365	+	0.731231i
$262$		−	43.5741i		−	0.166313i
$263$	−150.518	−	260.705i	−0.572312	−	0.991273i	−0.996328	−	0.0856183i	$-0.972713\pi$
$263$	−150.518	−	260.705i	−0.572312	−	0.991273i	0.424016	−	0.905655i	$-0.360620\pi$
$264$	−158.279	+	82.5051i	−0.599541	+	0.312519i
$265$		0			0
$266$	−131.439	−	75.8862i	−0.494131	−	0.285287i
$267$	18.7786	−	435.587i	0.0703319	−	1.63141i
$268$	5.78738	−	3.34135i	0.0215947	−	0.0124677i
$269$			128.065i			0.476077i	0.971256	+	0.238038i	$0.0765044\pi$
$269$			128.065i			0.476077i	−0.971256	+	0.238038i	$0.923496\pi$
$270$		0			0
$271$	−512.831			−1.89236			−0.946182	−	0.323635i	$-0.895095\pi$
$271$	−512.831			−1.89236			−0.946182	+	0.323635i	$0.895095\pi$
$272$	−25.8033	−	44.6927i	−0.0948651	−	0.164311i
$273$	−194.451	−	8.38297i	−0.712273	−	0.0307068i
$274$	−75.3384	+	130.490i	−0.274958	+	0.476240i
$275$		0			0
$276$	46.9718	+	90.1111i	0.170188	+	0.326490i
$277$	240.341	−	138.761i	0.867658	−	0.500942i	0.00108844	−	0.999999i	$-0.499654\pi$
$277$	240.341	−	138.761i	0.867658	−	0.500942i	0.866569	+	0.499057i	$0.166320\pi$
$278$	161.555			0.581133
$279$	51.8720	−	74.2542i	0.185921	−	0.266144i
$280$		0			0
$281$	−89.3698	+	51.5977i	−0.318042	+	0.183622i	−0.650519	−	0.759490i	$-0.725449\pi$
$281$	−89.3698	+	51.5977i	−0.318042	+	0.183622i	0.332478	+	0.943111i	$0.392115\pi$
$282$	−107.504	+	168.951i	−0.381218	+	0.599118i
$283$	142.087	+	82.0340i	0.502075	+	0.289873i	0.729570	−	0.683906i	$-0.239720\pi$
$283$	142.087	+	82.0340i	0.502075	+	0.289873i	−0.227495	+	0.973779i	$0.573054\pi$
$284$	−66.6267	−	38.4670i	−0.234601	−	0.135447i
$285$		0			0
$286$	−145.508	−	252.026i	−0.508768	−	0.881211i
$287$	−356.567			−1.24239
$288$	29.1559	−	41.7364i	0.101236	−	0.144918i
$289$	−122.547			−0.424039
$290$		0			0
$291$	−125.175	+	65.2492i	−0.430154	+	0.224224i
$292$	154.014	+	88.9201i	0.527446	+	0.304521i
$293$	146.494	−	253.735i	0.499979	−	0.865988i	−0.500021	−	0.866013i	$-0.666675\pi$
$293$	146.494	−	253.735i	0.499979	−	0.865988i	1.00000		2.47977e-5i	$7.89334e-6\pi$
$294$	21.2656	+	0.916781i	0.0723319	+	0.00311830i
$295$		0			0
$296$			7.19622i			0.0243116i
$297$	524.365	−	218.211i	1.76554	−	0.734719i
$298$		−	170.956i		−	0.573677i
$299$	−143.484	+	82.8402i	−0.479878	+	0.277058i
$300$		0			0
$301$	−248.151	+	429.811i	−0.824423	+	1.42794i
$302$	89.7938	−	155.527i	0.297331	−	0.514992i
$303$	59.4704	−	30.9998i	0.196272	−	0.102310i
$304$	32.3642	+	56.0565i	0.106461	+	0.184396i
$305$		0			0
$306$	69.5620	+	148.750i	0.227327	+	0.486110i
$307$			467.606i			1.52315i	0.648079	+	0.761573i	$0.275573\pi$
$307$			467.606i			1.52315i	−0.648079	+	0.761573i	$0.724427\pi$
$308$	−139.506	−	241.632i	−0.452943	−	0.784520i
$309$	313.596	+	199.541i	1.01487	+	0.645763i
$310$		0			0
$311$	465.753	+	268.902i	1.49760	+	0.864638i	0.999996	−	0.00276786i	$-0.000881040\pi$
$311$	465.753	+	268.902i	1.49760	+	0.864638i	0.497601	+	0.867406i	$0.334214\pi$
$312$	70.0319	+	44.5612i	0.224461	+	0.142824i
$313$	−230.586	+	133.129i	−0.736697	+	0.425332i	−0.820867	−	0.571119i	$-0.806509\pi$
$313$	−230.586	+	133.129i	−0.736697	+	0.425332i	0.0841703	+	0.996451i	$0.473176\pi$
$314$			147.379i			0.469361i
$315$		0			0
$316$	−235.294			−0.744602
$317$	−238.437	−	412.986i	−0.752168	−	1.30279i	−0.946770	−	0.321911i	$-0.895675\pi$
$317$	−238.437	−	412.986i	−0.752168	−	1.30279i	0.194602	−	0.980882i	$-0.437659\pi$
$318$	2.13393	+	4.09375i	0.00671046	+	0.0128734i
$319$	526.508	−	911.939i	1.65050	−	2.85874i
$320$		0			0
$321$	−141.975	−	6.12070i	−0.442290	−	0.0190676i
$322$	−137.566	+	79.4237i	−0.427223	+	0.246657i
$323$	−208.776			−0.646366
$324$	−103.859	+	124.328i	−0.320552	+	0.383727i
$325$		0			0
$326$	230.904	−	133.313i	0.708296	−	0.408935i
$327$	−80.5488	−	3.47254i	−0.246326	−	0.0106194i
$328$	131.696	+	76.0349i	0.401513	+	0.231814i
$329$	−271.093	−	156.515i	−0.823990	−	0.475731i
$330$		0			0
$331$	−17.6720	−	30.6088i	−0.0533898	−	0.0924738i	0.838095	−	0.545524i	$-0.183669\pi$
$331$	−17.6720	−	30.6088i	−0.0533898	−	0.0924738i	−0.891485	+	0.453050i	$0.850336\pi$
$332$	−294.246			−0.886282
$333$	1.97067	−	22.8133i	0.00591793	−	0.0685084i
$334$	−96.0482			−0.287569
$335$		0			0
$336$	67.1436	+	42.7234i	0.199832	+	0.127153i
$337$	−215.201	−	124.246i	−0.638579	−	0.368684i	0.145488	−	0.989360i	$-0.453525\pi$
$337$	−215.201	−	124.246i	−0.638579	−	0.368684i	−0.784067	+	0.620676i	$0.786858\pi$
$338$	51.8331	−	89.7776i	0.153352	−	0.265614i
$339$	−30.2935	+	47.6090i	−0.0893615	+	0.140439i
$340$		0			0
$341$			211.706i			0.620838i
$342$	−87.2493	−	186.572i	−0.255115	−	0.545532i
$343$			358.239i			1.04443i
$344$	183.307	−	105.833i	0.532870	−	0.307653i
$345$		0			0
$346$	−86.5447	+	149.900i	−0.250129	+	0.433237i
$347$	−1.34645	+	2.33212i	−0.00388026	+	0.00672082i	−0.867959	−	0.496636i	$-0.834568\pi$
$347$	−1.34645	+	2.33212i	−0.00388026	+	0.00672082i	0.864079	+	0.503357i	$0.167902\pi$
$348$	−12.9366	+	300.076i	−0.0371741	+	0.862288i
$349$	196.192	+	339.815i	0.562156	+	0.973682i	0.997308	+	0.0733253i	$0.0233611\pi$
$349$	196.192	+	339.815i	0.562156	+	0.973682i	−0.435152	+	0.900357i	$0.643306\pi$
$350$		0			0
$351$	−209.810	−	160.445i	−0.597751	−	0.457108i
$352$			118.994i			0.338052i
$353$	9.89124	+	17.1321i	0.0280205	+	0.0485329i	0.879696	−	0.475537i	$-0.157746\pi$
$353$	9.89124	+	17.1321i	0.0280205	+	0.0485329i	−0.851675	+	0.524070i	$0.824413\pi$
$354$	−1.76148	+	40.8591i	−0.00497592	+	0.115421i
$355$		0			0
$356$	−251.720	−	145.331i	−0.707079	−	0.408232i
$357$	−227.622	+	118.651i	−0.637596	+	0.332356i
$358$	96.0517	−	55.4555i	0.268301	−	0.154904i
$359$			415.325i			1.15689i	0.815720	+	0.578447i	$0.196341\pi$
$359$			415.325i			1.15689i	−0.815720	+	0.578447i	$0.803659\pi$
$360$		0			0
$361$	−99.1389			−0.274623
$362$	155.254	+	268.908i	0.428878	+	0.742839i
$363$	−517.762	+	813.709i	−1.42634	+	2.24162i
$364$	−64.8771	+	112.370i	−0.178234	+	0.308710i
$365$		0			0
$366$	102.297	−	160.770i	0.279501	−	0.439261i
$367$	461.927	−	266.694i	1.25866	−	0.726685i	0.285843	−	0.958276i	$-0.407726\pi$
$367$	461.927	−	266.694i	1.25866	−	0.726685i	0.972813	+	0.231591i	$0.0743931\pi$
$368$	67.7458			0.184092
$369$	−396.678	−	277.109i	−1.07501	−	0.750972i
$370$		0			0
$371$	−6.24961	+	3.60821i	−0.0168453	+	0.00972564i
$372$	−27.9123	−	53.5472i	−0.0750330	−	0.143944i
$373$	186.697	+	107.790i	0.500529	+	0.288981i	0.728932	−	0.684586i	$-0.240017\pi$
$373$	186.697	+	107.790i	0.500529	+	0.288981i	−0.228403	+	0.973567i	$0.573350\pi$
$374$	−332.386	−	191.903i	−0.888733	−	0.513110i
$375$		0			0
$376$	66.7513	+	115.617i	0.177530	+	0.307491i
$377$	−489.702			−1.29895
$378$	−201.157	−	153.828i	−0.532162	−	0.406952i
$379$	−176.846			−0.466612			−0.233306	−	0.972403i	$-0.574954\pi$
$379$	−176.846			−0.466612			−0.233306	+	0.972403i	$0.574954\pi$
$380$		0			0
$381$	16.6452	−	386.102i	0.0436883	−	1.01339i
$382$	−395.570	−	228.382i	−1.03552	−	0.597860i
$383$	−8.60134	+	14.8980i	−0.0224578	+	0.0388980i	−0.877036	−	0.480425i	$-0.840482\pi$
$383$	−8.60134	+	14.8980i	−0.0224578	+	0.0388980i	0.854578	+	0.519323i	$0.173816\pi$
$384$	−15.6888	−	30.0975i	−0.0408562	−	0.0783790i
$385$		0			0
$386$			244.353i			0.633039i
$387$	−610.098	+	285.309i	−1.57648	+	0.737233i
$388$			94.1068i			0.242543i
$389$	−298.375	+	172.267i	−0.767030	+	0.442845i	−0.831814	−	0.555055i	$-0.812697\pi$
$389$	−298.375	+	172.267i	−0.767030	+	0.442845i	0.0647844	+	0.997899i	$0.479364\pi$
$390$		0			0
$391$	−109.254	+	189.234i	−0.279422	+	0.483974i
$392$	7.09511	−	12.2891i	0.0180998	−	0.0313497i
$393$	77.9858	+	49.6223i	0.198437	+	0.126265i
$394$	−50.7223	−	87.8536i	−0.128737	−	0.222979i
$395$		0			0
$396$	32.5864	−	377.233i	0.0822888	−	0.952609i
$397$		−	68.9955i		−	0.173792i	−0.996217	−	0.0868960i	$-0.972305\pi$
$397$		−	68.9955i		−	0.173792i	0.996217	−	0.0868960i	$-0.0276948\pi$
$398$	−94.2042	−	163.167i	−0.236694	−	0.409966i
$399$	285.499	−	148.820i	0.715535	−	0.372983i
$400$		0			0
$401$	−154.315	−	89.0938i	−0.384825	−	0.222179i	0.295090	−	0.955469i	$-0.404650\pi$
$401$	−154.315	−	89.0938i	−0.384825	−	0.222179i	−0.679916	+	0.733290i	$0.737984\pi$
$402$	−0.610581	+	14.1630i	−0.00151886	+	0.0352313i
$403$	85.2629	−	49.2266i	0.211571	−	0.122150i
$404$		−	44.7100i		−	0.110668i
$405$		0			0
$406$	−469.506			−1.15642
$407$	26.7597	+	46.3492i	0.0657487	+	0.113880i
$408$	109.373	+	4.71517i	0.268070	+	0.0115568i
$409$	5.64530	−	9.77795i	0.0138027	−	0.0239070i	−0.859042	−	0.511906i	$-0.828940\pi$
$409$	5.64530	−	9.77795i	0.0138027	−	0.0239070i	0.872844	+	0.487999i	$0.162273\pi$
$410$		0			0
$411$	−147.746	−	283.437i	−0.359479	−	0.689629i
$412$	214.599	−	123.899i	0.520872	−	0.300726i
$413$	−63.9290			−0.154792
$414$	−214.766	−	18.5521i	−0.518759	−	0.0448117i
$415$		0			0
$416$	47.9242	−	27.6690i	0.115202	−	0.0665121i
$417$	−183.979	+	289.139i	−0.441197	+	0.693380i
$418$	416.901	+	240.698i	0.997370	+	0.575832i
$419$	56.3602	+	32.5396i	0.134511	+	0.0776601i	0.565746	−	0.824580i	$-0.308588\pi$
$419$	56.3602	+	32.5396i	0.134511	+	0.0776601i	−0.431234	+	0.902240i	$0.641922\pi$
$420$		0			0
$421$	115.044	+	199.262i	0.273263	+	0.473306i	0.969696	−	0.244317i	$-0.0785636\pi$
$421$	115.044	+	199.262i	0.273263	+	0.473306i	−0.696432	+	0.717623i	$0.745230\pi$
$422$	532.207			1.26116
$423$	−179.952	−	384.805i	−0.425418	−	0.909703i
$424$	3.07769			0.00725870
$425$		0			0
$426$	144.720	−	75.4375i	0.339719	−	0.177083i
$427$	257.964	+	148.936i	0.604132	+	0.348796i
$428$	−47.3690	+	82.0455i	−0.110675	+	0.191695i
$429$	616.763	+	26.5893i	1.43768	+	0.0619797i
$430$		0			0
$431$		−	67.4877i		−	0.156584i	−0.996930	−	0.0782920i	$-0.975053\pi$
$431$		−	67.4877i		−	0.156584i	0.996930	−	0.0782920i	$-0.0249467\pi$
$432$	41.4941	+	99.7108i	0.0960510	+	0.230812i
$433$			132.060i			0.304989i	0.988304	+	0.152495i	$0.0487307\pi$
$433$			132.060i			0.304989i	−0.988304	+	0.152495i	$0.951269\pi$
$434$	81.7464	−	47.1963i	0.188356	−	0.108747i
$435$		0			0
$436$	−26.8745	+	46.5480i	−0.0616388	+	0.106762i
$437$	137.034	−	237.350i	0.313579	−	0.543134i
$438$	−334.535	+	174.381i	−0.763778	+	0.398130i
$439$	344.511	+	596.711i	0.784764	+	1.35925i	0.929140	+	0.369728i	$0.120549\pi$
$439$	344.511	+	596.711i	0.784764	+	1.35925i	−0.144376	+	0.989523i	$0.546118\pi$
$440$		0			0
$441$	−25.8581	+	37.0156i	−0.0586351	+	0.0839356i
$442$			178.488i			0.403819i
$443$	34.0413	+	58.9612i	0.0768426	+	0.133095i	0.901886	−	0.431974i	$-0.142183\pi$
$443$	34.0413	+	58.9612i	0.0768426	+	0.133095i	−0.825043	+	0.565069i	$0.808849\pi$
$444$	−12.8793	−	8.19508i	−0.0290074	−	0.0184574i
$445$		0			0
$446$	72.4767	+	41.8444i	0.162504	+	0.0938216i
$447$	305.964	+	194.685i	0.684484	+	0.435536i
$448$	45.9476	−	26.5279i	0.102562	−	0.0592140i
$449$		−	685.554i		−	1.52685i	−0.645898	−	0.763423i	$-0.723517\pi$
$449$		−	685.554i		−	1.52685i	0.645898	−	0.763423i	$-0.276483\pi$
$450$		0			0
$451$	1130.97			2.50769
$452$	18.8099	+	32.5797i	0.0416148	+	0.0720790i
$453$	176.095	+	337.822i	0.388730	+	0.745743i
$454$	105.952	−	183.514i	0.233374	−	0.404216i
$455$		0			0
$456$	−137.182	−	5.91408i	−0.300839	−	0.0129695i
$457$	−449.810	+	259.698i	−0.984266	+	0.568266i	−0.903555	−	0.428471i	$-0.859052\pi$
$457$	−449.810	+	259.698i	−0.984266	+	0.568266i	−0.0807109	+	0.996738i	$0.525719\pi$
$458$	−241.638			−0.527593
$459$	−345.439	−	44.8994i	−0.752590	−	0.0978200i
$460$		0			0
$461$	77.5379	−	44.7665i	0.168195	−	0.0971074i	−0.413539	−	0.910486i	$-0.635708\pi$
$461$	77.5379	−	44.7665i	0.168195	−	0.0971074i	0.581734	+	0.813379i	$0.302374\pi$
$462$	591.326	+	25.4927i	1.27993	+	0.0551790i
$463$	441.640	+	254.981i	0.953865	+	0.550714i	0.894279	−	0.447509i	$-0.147689\pi$
$463$	441.640	+	254.981i	0.953865	+	0.550714i	0.0595857	+	0.998223i	$0.481022\pi$
$464$	173.410	+	100.118i	0.373728	+	0.215772i
$465$		0			0
$466$	317.479	+	549.890i	0.681285	+	1.18002i
$467$	539.803			1.15590			0.577948	−	0.816074i	$-0.303854\pi$
$467$	539.803			1.15590			0.577948	+	0.816074i	$0.303854\pi$
$468$	−159.505	+	74.5917i	−0.340823	+	0.159384i
$469$	−22.1597			−0.0472488
$470$		0			0
$471$	−263.769	−	167.836i	−0.560019	−	0.356339i
$472$	23.6119	+	13.6323i	0.0500252	+	0.0288821i
$473$	787.093	−	1363.28i	1.66404	−	2.88221i
$474$	267.954	−	421.113i	0.565303	−	0.888424i
$475$		0			0
$476$			171.127i			0.359510i
$477$	−9.75681	−	0.842819i	−0.0204545	−	0.00176692i
$478$			327.979i			0.686148i
$479$	−94.2261	+	54.4015i	−0.196714	+	0.113573i	−0.595122	−	0.803635i	$-0.702896\pi$
$479$	−94.2261	+	54.4015i	−0.196714	+	0.113573i	0.398408	+	0.917208i	$0.369563\pi$
$480$		0			0
$481$	12.4445	−	21.5546i	0.0258722	−	0.0448120i
$482$	−280.963	+	486.642i	−0.582910	+	1.00963i
$483$	14.5135	−	336.653i	0.0300486	−	0.697005i
$484$	321.490	+	556.837i	0.664235	+	1.15049i
$485$		0			0
$486$	−104.238	−	327.464i	−0.214481	−	0.673794i
$487$		−	342.524i		−	0.703334i	−0.936125	−	0.351667i	$-0.885615\pi$
$487$		−	342.524i		−	0.703334i	0.936125	−	0.351667i	$-0.114385\pi$
$488$	−63.5187	−	110.018i	−0.130161	−	0.225446i
$489$	−24.3609	+	565.073i	−0.0498178	+	1.15557i
$490$		0			0
$491$	430.657	+	248.640i	0.877102	+	0.506395i	0.869702	−	0.493577i	$-0.164311\pi$
$491$	430.657	+	248.640i	0.877102	+	0.506395i	0.00740027	+	0.999973i	$0.497644\pi$
$492$	−286.058	+	149.112i	−0.581419	+	0.303073i
$493$	−559.319	+	322.923i	−1.13452	+	0.655016i
$494$		−	223.872i		−	0.453182i
$495$		0			0
$496$	−40.2569			−0.0811632
$497$	127.556	+	220.933i	0.256652	+	0.444533i
$498$	335.088	−	526.620i	0.672867	−	1.05747i
$499$	77.5164	−	134.262i	0.155343	−	0.269063i	−0.777841	−	0.628462i	$-0.783685\pi$
$499$	77.5164	−	134.262i	0.155343	−	0.269063i	0.933184	+	0.359399i	$0.117018\pi$
$500$		0			0
$501$	109.380	−	171.900i	0.218323	−	0.343114i
$502$	236.595	−	136.598i	0.471304	−	0.272107i
$503$	−580.438			−1.15395			−0.576976	−	0.816761i	$-0.695767\pi$
$503$	−580.438			−1.15395			−0.576976	+	0.816761i	$0.695767\pi$
$504$	−152.927	+	71.5153i	−0.303426	+	0.141895i
$505$		0			0
$506$	436.335	−	251.918i	0.862321	−	0.497862i
$507$	101.650	+	195.006i	0.200493	+	0.384628i
$508$	−223.123	−	128.820i	−0.439218	−	0.253583i
$509$	−158.209	−	91.3419i	−0.310823	−	0.179454i	0.336472	−	0.941694i	$-0.390766\pi$
$509$	−158.209	−	91.3419i	−0.310823	−	0.179454i	−0.647295	+	0.762240i	$0.724100\pi$
$510$		0			0
$511$	−294.858	−	510.709i	−0.577021	−	0.999430i
$512$	−22.6274			−0.0441942
$513$	433.273	+	56.3158i	0.844586	+	0.109777i
$514$	170.931			0.332550
$515$		0			0
$516$	−19.3393	+	448.593i	−0.0374793	+	0.869366i
$517$	859.858	+	496.439i	1.66317	+	0.960231i
$518$	11.9313	−	20.6656i	0.0230334	−	0.0398950i
$519$	−169.723	−	325.598i	−0.327019	−	0.627356i
$520$		0			0
$521$			47.7611i			0.0916720i	0.998949	+	0.0458360i	$0.0145952\pi$
$521$			47.7611i			0.0916720i	−0.998949	+	0.0458360i	$0.985405\pi$
$522$	−522.323	−	364.880i	−1.00062	−	0.699005i
$523$			266.851i			0.510230i	0.966911	+	0.255115i	$0.0821134\pi$
$523$			266.851i			0.510230i	−0.966911	+	0.255115i	$0.917887\pi$
$524$	53.3672	−	30.8116i	0.101846	−	0.0588007i
$525$		0			0
$526$	212.865	−	368.692i	0.404685	−	0.700936i
$527$	64.9227	−	112.449i	0.123193	−	0.213376i
$528$	−212.968	−	135.511i	−0.403348	−	0.256650i
$529$	121.078	+	209.714i	0.228881	+	0.396434i
$530$		0			0
$531$	−71.1207	−	49.6830i	−0.133937	−	0.0935649i
$532$		−	214.639i		−	0.403456i
$533$	−262.977	−	455.489i	−0.493389	−	0.854576i
$534$	546.762	−	285.008i	1.02390	−	0.533722i
$535$		0			0
$536$	8.18459	+	4.72538i	0.0152698	+	0.00881600i
$537$	−10.1337	+	235.059i	−0.0188709	+	0.437727i
$538$	−156.847	+	90.5554i	−0.291536	+	0.168319i
$539$		−	105.535i		−	0.195798i
$540$		0			0
$541$	−707.266			−1.30733			−0.653666	−	0.756783i	$-0.726770\pi$
$541$	−707.266			−1.30733			−0.653666	+	0.756783i	$0.726770\pi$
$542$	−362.626	−	628.087i	−0.669052	−	1.15883i
$543$	−658.075	−	28.3703i	−1.21193	−	0.0522474i
$544$	36.4914	−	63.2050i	0.0670798	−	0.116186i
$545$		0			0
$546$	−127.230	−	244.080i	−0.233023	−	0.447033i
$547$	−178.686	+	103.164i	−0.326665	+	0.188600i	−0.654359	−	0.756184i	$-0.727062\pi$
$547$	−178.686	+	103.164i	−0.326665	+	0.188600i	0.327695	+	0.944784i	$0.393728\pi$
$548$	−213.089			−0.388849
$549$	171.237	+	366.170i	0.311908	+	0.666975i
$550$		0			0
$551$	701.535	−	405.032i	1.27320	−	0.735084i
$552$	−77.1491	+	121.247i	−0.139763	+	0.219650i
$553$	675.700	+	390.116i	1.22188	+	0.705454i
$554$	339.894	+	196.238i	0.613527	+	0.354220i
$555$		0			0
$556$	114.237	+	197.863i	0.205461	+	0.355870i
$557$	643.753			1.15575			0.577876	−	0.816125i	$-0.303882\pi$
$557$	643.753			1.15575			0.577876	+	0.816125i	$0.303882\pi$
$558$	127.622	+	11.0243i	0.228712	+	0.0197568i
$559$	−732.071			−1.30961
$560$		0			0
$561$	721.977	−	376.341i	1.28695	−	0.670840i
$562$	−126.388	−	72.9701i	−0.224890	−	0.129840i
$563$	361.822	−	626.694i	0.642668	−	1.11313i	−0.342167	−	0.939639i	$-0.611161\pi$
$563$	361.822	−	626.694i	0.642668	−	1.11313i	0.984835	−	0.173494i	$-0.0555058\pi$
$564$	−282.939	−	12.1978i	−0.501665	−	0.0216273i
$565$		0			0
$566$			232.027i			0.409942i
$567$	504.388	−	184.837i	0.889574	−	0.325992i
$568$		−	108.801i		−	0.191551i
$569$	−329.204	+	190.066i	−0.578566	+	0.334035i	−0.760563	−	0.649264i	$-0.775077\pi$
$569$	−329.204	+	190.066i	−0.578566	+	0.334035i	0.181997	+	0.983299i	$0.441744\pi$
$570$		0			0
$571$	−20.7292	+	35.9040i	−0.0363033	+	0.0628791i	−0.883606	−	0.468231i	$-0.844892\pi$
$571$	−20.7292	+	35.9040i	−0.0363033	+	0.0628791i	0.847303	+	0.531110i	$0.178225\pi$
$572$	205.779	−	356.419i	0.359753	−	0.623110i
$573$	859.219	−	447.881i	1.49951	−	0.781641i
$574$	−252.131	−	436.703i	−0.439252	−	0.760807i
$575$		0			0
$576$	71.7329	+	6.19647i	0.124536	+	0.0107578i
$577$			601.252i			1.04203i	0.853547	+	0.521016i	$0.174447\pi$
$577$			601.252i			1.04203i	−0.853547	+	0.521016i	$0.825553\pi$
$578$	−86.6540	−	150.089i	−0.149920	−	0.259670i
$579$	−437.325	−	278.270i	−0.755312	−	0.480604i
$580$		0			0
$581$	844.993	+	487.857i	1.45438	+	0.839685i
$582$	−168.426	−	107.169i	−0.289391	−	0.184139i
$583$	19.8227	−	11.4446i	0.0340011	−	0.0196306i
$584$			251.504i			0.430658i
$585$		0			0
$586$	414.347			0.707076
$587$	363.988	+	630.446i	0.620082	+	1.07401i	0.989470	+	0.144738i	$0.0462340\pi$
$587$	363.988	+	630.446i	0.620082	+	1.07401i	−0.369388	+	0.929275i	$0.620433\pi$
$588$	13.9142	+	26.6932i	0.0236636	+	0.0453966i
$589$	−81.4303	+	141.041i	−0.138252	+	0.239459i
$590$		0			0
$591$	214.997	+	9.26873i	0.363785	+	0.0156831i
$592$	−8.81354	+	5.08850i	−0.0148877	+	0.00859544i
$593$	−418.998			−0.706573			−0.353286	−	0.935515i	$-0.614936\pi$
$593$	−418.998			−0.706573			−0.353286	+	0.935515i	$0.614936\pi$
$594$	638.035	+	487.915i	1.07413	+	0.821405i
$595$		0			0
$596$	209.377	−	120.884i	0.351304	−	0.202825i
$597$	399.304	+	17.2144i	0.668851	+	0.0288348i
$598$	−202.916	−	117.154i	−0.339325	−	0.195909i
$599$	760.433	+	439.036i	1.26950	+	0.732948i	0.974894	−	0.222669i	$-0.0714771\pi$
$599$	760.433	+	439.036i	1.26950	+	0.732948i	0.294610	+	0.955618i	$0.404810\pi$
$600$		0			0
$601$	266.229	+	461.122i	0.442977	+	0.767259i	0.997909	−	0.0646372i	$-0.0205890\pi$
$601$	266.229	+	461.122i	0.442977	+	0.767259i	−0.554932	+	0.831896i	$0.687256\pi$
$602$	−701.878			−1.16591
$603$	−24.6526	−	17.2216i	−0.0408832	−	0.0285599i
$604$	253.975			0.420489
$605$		0			0
$606$	80.0188	+	50.9159i	0.132044	+	0.0840196i
$607$	81.8641	+	47.2643i	0.134867	+	0.0778653i	0.565915	−	0.824463i	$-0.308523\pi$
$607$	81.8641	+	47.2643i	0.134867	+	0.0778653i	−0.431049	+	0.902329i	$0.641856\pi$
$608$	−45.7700	+	79.2759i	−0.0752795	+	0.130388i
$609$	534.674	−	840.288i	0.877954	−	1.37978i
$610$		0			0
$611$		−	461.736i		−	0.755705i
$612$	−132.993	+	190.378i	−0.217308	+	0.311075i
$613$		−	816.657i		−	1.33223i	−0.745849	−	0.666115i	$-0.767956\pi$
$613$		−	816.657i		−	1.33223i	0.745849	−	0.666115i	$-0.232044\pi$
$614$	−572.698	+	330.647i	−0.932733	+	0.538513i
$615$		0			0
$616$	197.292	−	341.719i	0.320279	−	0.554739i
$617$	94.8195	−	164.232i	0.153678	−	0.266179i	−0.778899	−	0.627150i	$-0.784221\pi$
$617$	94.8195	−	164.232i	0.153678	−	0.266179i	0.932577	+	0.360971i	$0.117555\pi$
$618$	−22.6407	+	525.171i	−0.0366354	+	0.849792i
$619$	−47.7312	−	82.6728i	−0.0771101	−	0.133559i	0.824892	−	0.565291i	$-0.191236\pi$
$619$	−47.7312	−	82.6728i	−0.0771101	−	0.133559i	−0.902002	+	0.431732i	$0.857903\pi$
$620$		0			0
$621$	277.779	−	363.246i	0.447310	−	0.584937i
$622$			760.571i			1.22278i
$623$	481.914	+	834.700i	0.773538	+	1.33981i
$624$	−5.05610	+	117.281i	−0.00810272	+	0.187950i
$625$		0			0
$626$	−326.098	−	188.273i	−0.520923	−	0.300755i
$627$	−905.551	+	472.032i	−1.44426	+	0.752842i
$628$	−180.502	+	104.213i	−0.287423	+	0.165944i
$629$		−	32.8250i		−	0.0521861i
$630$		0			0
$631$	−192.912			−0.305724			−0.152862	−	0.988248i	$-0.548849\pi$
$631$	−192.912			−0.305724			−0.152862	+	0.988248i	$0.548849\pi$
$632$	−166.378	−	288.175i	−0.263257	−	0.455974i
$633$	−606.079	+	952.507i	−0.957471	+	1.50475i
$634$	337.201	−	584.050i	0.531863	−	0.921214i
$635$		0			0
$636$	−3.50488	+	5.50823i	−0.00551082	+	0.00866074i
$637$	−42.5034	+	24.5394i	−0.0667244	+	0.0385233i
$638$	1489.19			2.33415
$639$	−29.7949	+	344.918i	−0.0466274	+	0.539778i
$640$		0			0
$641$	−277.039	+	159.949i	−0.432198	+	0.249530i	−0.700283	−	0.713866i	$-0.746943\pi$
$641$	−277.039	+	159.949i	−0.432198	+	0.249530i	0.268084	+	0.963395i	$0.413609\pi$
$642$	−92.8953	−	178.211i	−0.144697	−	0.277588i
$643$	−131.937	−	76.1741i	−0.205190	−	0.118467i	0.393884	−	0.919160i	$-0.371131\pi$
$643$	−131.937	−	76.1741i	−0.205190	−	0.118467i	−0.599074	+	0.800693i	$0.704465\pi$
$644$	−194.547	−	112.322i	−0.302092	−	0.174413i
$645$		0			0
$646$	−147.627	−	255.698i	−0.228525	−	0.395817i
$647$	−632.862			−0.978148			−0.489074	−	0.872242i	$-0.662665\pi$
$647$	−632.862			−0.978148			−0.489074	+	0.872242i	$0.662665\pi$
$648$	−225.709	−	39.2878i	−0.348316	−	0.0606293i
$649$	202.772			0.312437
$650$		0			0
$651$	−8.62442	+	200.051i	−0.0132480	+	0.307298i
$652$	326.548	+	188.533i	0.500841	+	0.289160i
$653$	−408.937	+	708.299i	−0.626243	+	1.08468i	0.362056	+	0.932156i	$0.382075\pi$
$653$	−408.937	+	708.299i	−0.626243	+	1.08468i	−0.988299	+	0.152529i	$0.951258\pi$
$654$	−52.7036	−	101.107i	−0.0805865	−	0.154598i
$655$		0			0
$656$			215.059i			0.327834i
$657$	68.8739	−	797.312i	0.104831	−	1.21356i
$658$		−	442.692i		−	0.672785i
$659$	−368.474	+	212.738i	−0.559141	+	0.322820i	−0.752800	−	0.658249i	$-0.771297\pi$
$659$	−368.474	+	212.738i	−0.559141	+	0.322820i	0.193660	+	0.981069i	$0.437964\pi$
$660$		0			0
$661$	−142.986	+	247.659i	−0.216318	+	0.374673i	−0.953679	−	0.300825i	$-0.902738\pi$
$661$	−142.986	+	247.659i	−0.216318	+	0.374673i	0.737362	+	0.675498i	$0.236071\pi$
$662$	24.9920	−	43.2874i	0.0377523	−	0.0653889i
$663$	−319.445	−	203.263i	−0.481818	−	0.306580i
$664$	−208.063	−	360.376i	−0.313348	−	0.542735i
$665$		0			0
$666$	29.3339	−	13.7179i	0.0440449	−	0.0205974i
$667$		−	847.824i		−	1.27110i
$668$	−67.9163	−	117.634i	−0.101671	−	0.176100i
$669$	−157.427	+	82.0611i	−0.235317	+	0.122662i
$670$		0			0
$671$	−818.218	−	472.398i	−1.21940	−	0.704021i
$672$	−4.84757	+	112.444i	−0.00721364	+	0.167327i
$673$	1036.99	−	598.709i	1.54085	−	0.889612i	0.542068	−	0.840335i	$-0.317642\pi$
$673$	1036.99	−	598.709i	1.54085	−	0.889612i	0.998785	−	0.0492769i	$-0.0156917\pi$
$674$		−	351.422i		−	0.521398i
$675$		0			0
$676$	146.606			0.216873
$677$	452.777	+	784.232i	0.668799	+	1.15839i	0.978240	+	0.207475i	$0.0665245\pi$
$677$	452.777	+	784.232i	0.668799	+	1.15839i	−0.309442	+	0.950918i	$0.600142\pi$
$678$	−79.7296	−	3.43723i	−0.117595	−	0.00506966i
$679$	156.028	−	270.249i	0.229791	−	0.398010i
$680$		0			0
$681$	207.782	+	398.611i	0.305113	+	0.585332i
$682$	−259.285	+	149.698i	−0.380184	+	0.219499i
$683$	31.1970			0.0456764			0.0228382	−	0.999739i	$-0.492730\pi$
$683$	31.1970			0.0456764			0.0228382	+	0.999739i	$0.492730\pi$
$684$	166.808	−	238.784i	0.243872	−	0.349100i
$685$		0			0
$686$	−438.751	+	253.313i	−0.639579	+	0.369261i
$687$	275.178	−	432.466i	0.400550	−	0.629499i
$688$	259.236	+	149.670i	0.376796	+	0.217543i
$689$	−9.21848	−	5.32229i	−0.0133795	−	0.00772466i
$690$		0			0
$691$	101.532	+	175.858i	0.146935	+	0.254498i	0.930093	−	0.367324i	$-0.119726\pi$
$691$	101.532	+	175.858i	0.146935	+	0.254498i	−0.783158	+	0.621822i	$0.786393\pi$
$692$	−244.785			−0.353736
$693$	−719.029	+	1029.28i	−1.03756	+	1.48526i
$694$	−3.80834			−0.00548752
$695$		0			0
$696$	−376.664	+	196.342i	−0.541184	+	0.282100i
$697$	−600.723	−	346.828i	−0.861870	−	0.497601i
$698$	−277.458	+	480.571i	−0.397504	+	0.688497i
$699$	−1345.70	−	58.0145i	−1.92518	−	0.0829964i
$700$		0			0
$701$		−	633.699i		−	0.903993i	−0.892020	−	0.451997i	$-0.850712\pi$
$701$		−	633.699i		−	0.903993i	0.892020	−	0.451997i	$-0.149288\pi$
$702$	48.1458	−	370.416i	0.0685838	−	0.527658i
$703$			41.1714i			0.0585652i
$704$	−145.738	+	84.1418i	−0.207014	+	0.119520i
$705$		0			0
$706$	−13.9883	+	24.2285i	−0.0198135	+	0.0343180i
$707$	−74.1289	+	128.395i	−0.104850	+	0.181605i
$708$	−51.2875	+	26.7344i	−0.0724399	+	0.0377604i
$709$	−74.6901	−	129.367i	−0.105346	−	0.182464i	0.808534	−	0.588450i	$-0.200262\pi$
$709$	−74.6901	−	129.367i	−0.105346	−	0.182464i	−0.913879	+	0.405986i	$0.866928\pi$
$710$		0			0
$711$	448.531	+	959.128i	0.630846	+	1.34899i
$712$		−	411.057i		−	0.577328i
$713$	85.2262	+	147.616i	0.119532	+	0.207035i
$714$	−306.270	−	194.880i	−0.428950	−	0.272941i
$715$		0			0
$716$	135.838	+	78.4259i	0.189717	+	0.109533i
$717$	−586.993	−	373.503i	−0.818679	−	0.520925i
$718$	−508.667	+	293.679i	−0.708451	+	0.409024i
$719$		−	257.590i		−	0.358262i	−0.983825	−	0.179131i	$-0.942671\pi$
$719$		−	257.590i		−	0.358262i	0.983825	−	0.179131i	$-0.0573285\pi$
$720$		0			0
$721$	−821.694			−1.13966
$722$	−70.1018	−	121.420i	−0.0970939	−	0.168172i
$723$	−550.995	−	1057.04i	−0.762096	−	1.46201i
$724$	−219.562	+	380.293i	−0.303263	+	0.525266i
$725$		0			0
$726$	−1362.70	−	58.7474i	−1.87700	−	0.0809193i
$727$	−526.008	+	303.691i	−0.723532	+	0.417731i	−0.816051	−	0.577980i	$-0.803841\pi$
$727$	−526.008	+	303.691i	−0.723532	+	0.417731i	0.0925193	+	0.995711i	$0.470508\pi$
$728$	−183.500			−0.252061
$729$	704.777	+	186.359i	0.966773	+	0.255637i
$730$		0			0
$731$	−836.143	+	482.747i	−1.14383	+	0.660393i
$732$	269.237	+	11.6071i	0.367810	+	0.0158567i
$733$	−768.411	−	443.643i	−1.04831	−	0.605242i	−0.126134	−	0.992013i	$-0.540257\pi$
$733$	−768.411	−	443.643i	−1.04831	−	0.605242i	−0.922176	+	0.386771i	$0.873590\pi$
$734$	653.263	+	377.162i	0.890004	+	0.513844i
$735$		0			0
$736$	47.9035	+	82.9713i	0.0650863	+	0.112733i
$737$	70.2867			0.0953686
$738$	58.8936	−	681.775i	0.0798016	−	0.923815i
$739$	30.1955			0.0408599			0.0204300	−	0.999791i	$-0.493496\pi$
$739$	30.1955			0.0408599			0.0204300	+	0.999791i	$0.493496\pi$
$740$		0			0
$741$	400.670	+	254.946i	0.540715	+	0.344056i
$742$	−8.83828	−	5.10278i	−0.0119114	−	0.00687707i
$743$	−285.008	+	493.648i	−0.383591	+	0.664399i	−0.991573	−	0.129552i	$-0.958646\pi$
$743$	−285.008	+	493.648i	−0.383591	+	0.664399i	0.607982	+	0.793951i	$0.291979\pi$
$744$	45.8447	−	72.0490i	0.0616192	−	0.0968401i
$745$		0			0
$746$			304.876i			0.408680i
$747$	560.908	+	1199.43i	0.750881	+	1.60567i
$748$		−	542.784i		−	0.725647i
$749$	272.062	−	157.075i	0.363233	−	0.209713i
$750$		0			0
$751$	−213.747	+	370.221i	−0.284617	+	0.492970i	−0.972516	−	0.232836i	$-0.925200\pi$
$751$	−213.747	+	370.221i	−0.284617	+	0.492970i	0.687900	+	0.725806i	$0.258533\pi$
$752$	−94.4006	+	163.507i	−0.125533	+	0.217429i
$753$	−24.9612	+	578.998i	−0.0331490	+	0.768922i
$754$	−346.272	−	599.760i	−0.459247	−	0.795438i
$755$		0			0
$756$	46.1601	−	355.139i	0.0610584	−	0.469760i
$757$			587.791i			0.776474i	0.921560	+	0.388237i	$0.126916\pi$
$757$			587.791i			0.776474i	−0.921560	+	0.388237i	$0.873084\pi$
$758$	−125.049	−	216.591i	−0.164972	−	0.285740i
$759$	−46.0342	+	1067.81i	−0.0606511	+	1.40686i
$760$		0			0
$761$	−1135.73	−	655.716i	−1.49242	−	0.861651i	−0.492461	−	0.870335i	$-0.663903\pi$
$761$	−1135.73	−	655.716i	−1.49242	−	0.861651i	−0.999962	+	0.00868376i	$0.997236\pi$
$762$	484.646	−	252.629i	0.636018	−	0.331534i
$763$	154.353	−	89.1155i	0.202297	−	0.116796i
$764$		−	645.963i		−	0.845501i
$765$		0			0
$766$	−24.3283			−0.0317601
$767$	−47.1492	−	81.6648i	−0.0614722	−	0.106473i
$768$	25.7682	−	40.4969i	0.0335523	−	0.0527304i
$769$	−595.762	+	1031.89i	−0.774724	+	1.34186i	0.160226	+	0.987080i	$0.448778\pi$
$769$	−595.762	+	1031.89i	−0.774724	+	1.34186i	−0.934950	+	0.354780i	$0.884556\pi$
$770$		0			0
$771$	−194.656	+	305.920i	−0.252473	+	0.396783i
$772$	−299.270	+	172.784i	−0.387655	+	0.223813i
$773$	−204.848			−0.265003			−0.132502	−	0.991183i	$-0.542301\pi$
$773$	−204.848			−0.265003			−0.132502	+	0.991183i	$0.542301\pi$
$774$	−780.836	−	545.471i	−1.00883	−	0.704742i
$775$		0			0
$776$	−115.257	+	66.5435i	−0.148527	+	0.0857520i
$777$	23.3984	+	44.8878i	0.0301138	+	0.0577706i
$778$	−421.965	−	243.622i	−0.542372	−	0.313139i
$779$	753.467	+	435.014i	0.967223	+	0.558427i
$780$		0			0
$781$	−404.585	−	700.761i	−0.518034	−	0.897261i
$782$	−309.017			−0.395163
$783$	1247.86	−	519.289i	1.59369	−	0.663204i
$784$	20.0680			0.0255970
$785$		0			0
$786$	−5.63035	+	130.601i	−0.00716329	+	0.166159i
$787$	115.378	+	66.6137i	0.146605	+	0.0846426i	0.571508	−	0.820596i	$-0.306358\pi$
$787$	115.378	+	66.6137i	0.146605	+	0.0846426i	−0.424903	+	0.905239i	$0.639692\pi$
$788$	71.7321	−	124.244i	0.0910306	−	0.157670i
$789$	417.448	+	800.837i	0.529085	+	1.01500i
$790$		0			0
$791$		−	124.747i		−	0.157708i
$792$	485.056	−	226.834i	0.612445	−	0.286407i
$793$			439.375i			0.554067i
$794$	84.5018	−	48.7872i	0.106425	−	0.0614448i
$795$		0			0
$796$	133.225	−	230.752i	0.167368	−	0.289890i
$797$	304.460	−	527.341i	0.382008	−	0.661657i	−0.609341	−	0.792908i	$-0.708566\pi$
$797$	304.460	−	527.341i	0.382008	−	0.661657i	0.991349	+	0.131251i	$0.0418993\pi$
$798$	384.145	+	244.431i	0.481385	+	0.306304i
$799$	−304.481	−	527.376i	−0.381077	−	0.660046i
$800$		0			0
$801$	−112.567	+	1303.12i	−0.140533	+	1.62687i
$802$		−	251.995i		−	0.314208i
$803$	935.237	+	1619.88i	1.16468	+	2.01728i
$804$	−17.7778	+	9.26693i	−0.0221117	+	0.0115260i
$805$		0			0
$806$	120.580	+	69.6169i	0.149603	+	0.0863733i
$807$	16.5476	−	383.838i	0.0205051	−	0.475635i
$808$	54.7584	−	31.6148i	0.0677703	−	0.0391272i
$809$			164.342i			0.203142i	0.994828	+	0.101571i	$0.0323869\pi$
$809$			164.342i			0.203142i	−0.994828	+	0.101571i	$0.967613\pi$
$810$		0			0
$811$	−1026.77			−1.26606			−0.633028	−	0.774129i	$-0.718188\pi$
$811$	−1026.77			−1.26606			−0.633028	+	0.774129i	$0.718188\pi$
$812$	−331.991	−	575.025i	−0.408855	−	0.708158i
$813$	1537.06	+	66.2644i	1.89061	+	0.0815061i
$814$	−37.8439	+	65.5476i	−0.0464913	+	0.0805253i
$815$		0			0
$816$	71.5632	+	137.288i	0.0877000	+	0.168245i
$817$	1048.75	−	605.494i	1.28365	−	0.741118i
$818$	15.9673			0.0195200
$819$	581.727	+	50.2511i	0.710290	+	0.0613567i
$820$		0			0
$821$	262.140	−	151.347i	0.319293	−	0.184344i	−0.331784	−	0.943355i	$-0.607651\pi$
$821$	262.140	−	151.347i	0.319293	−	0.184344i	0.651078	+	0.759011i	$0.274317\pi$
$822$	242.666	−	381.372i	0.295215	−	0.463956i
$823$	603.723	+	348.559i	0.733563	+	0.423523i	0.819724	−	0.572758i	$-0.194127\pi$
$823$	603.723	+	348.559i	0.733563	+	0.423523i	−0.0861609	+	0.996281i	$0.527460\pi$
$824$	303.489	+	175.220i	0.368312	+	0.212645i
$825$		0			0
$826$	−45.2046	−	78.2967i	−0.0547271	−	0.0947902i
$827$	−454.516			−0.549596			−0.274798	−	0.961502i	$-0.588611\pi$
$827$	−454.516			−0.549596			−0.274798	+	0.961502i	$0.588611\pi$
$828$	−129.141	−	276.152i	−0.155967	−	0.333517i
$829$	−591.488			−0.713496			−0.356748	−	0.934201i	$-0.616115\pi$
$829$	−591.488			−0.713496			−0.356748	+	0.934201i	$0.616115\pi$
$830$		0			0
$831$	−738.284	+	384.842i	−0.888428	+	0.463107i
$832$	67.7750	+	39.1299i	0.0814603	+	0.0470311i
$833$	−32.3638	+	56.0558i	−0.0388521	+	0.0672939i
$834$	−484.215	−	20.8750i	−0.580593	−	0.0250300i
$835$		0			0
$836$			680.796i			0.814349i
$837$	−165.066	+	215.853i	−0.197212	+	0.257889i
$838$			92.0359i			0.109828i
$839$	1342.11	−	774.866i	1.59965	−	0.923559i	0.608097	−	0.793863i	$-0.291933\pi$
$839$	1342.11	−	774.866i	1.59965	−	0.923559i	0.991554	−	0.129696i	$-0.0414001\pi$
$840$		0			0
$841$	832.459	−	1441.86i	0.989844	−	1.71446i
$842$	−162.697	+	281.799i	−0.193226	+	0.334678i
$843$	274.528	−	143.102i	0.325655	−	0.169753i
$844$	376.327	+	651.818i	0.445886	+	0.772297i
$845$		0			0
$846$	344.042	−	492.493i	0.406669	−	0.582143i
$847$		−	2132.11i		−	2.51725i
$848$	2.17626	+	3.76938i	0.00256634	+	0.00444503i
$849$	−415.266	−	264.233i	−0.489124	−	0.311229i
$850$		0			0
$851$	37.3175	+	21.5453i	0.0438514	+	0.0253176i
$852$	194.724	+	123.903i	0.228550	+	0.145426i
$853$	−1421.62	+	820.773i	−1.66661	+	0.962219i	−0.697169	+	0.716907i	$0.745557\pi$
$853$	−1421.62	+	820.773i	−1.66661	+	0.962219i	−0.969444	+	0.245312i	$0.921110\pi$
$854$			421.254i			0.493272i
$855$		0			0
$856$	−133.980			−0.156518
$857$	−159.321	−	275.953i	−0.185906	−	0.321998i	0.757976	−	0.652283i	$-0.226189\pi$
$857$	−159.321	−	275.953i	−0.185906	−	0.321998i	−0.943881	+	0.330285i	$0.892855\pi$
$858$	403.552	+	774.179i	0.470341	+	0.902307i
$859$	−314.166	+	544.152i	−0.365735	+	0.633471i	−0.988894	−	0.148624i	$-0.952516\pi$
$859$	−314.166	+	544.152i	−0.365735	+	0.633471i	0.623159	+	0.782095i	$0.285849\pi$
$860$		0			0
$861$	1068.71	+	46.0731i	1.24124	+	0.0535111i
$862$	82.6552	−	47.7210i	0.0958878	−	0.0553608i
$863$	−183.620			−0.212770			−0.106385	−	0.994325i	$-0.533928\pi$
$863$	−183.620			−0.212770			−0.106385	+	0.994325i	$0.533928\pi$
$864$	−92.7796	+	121.326i	−0.107384	+	0.140423i
$865$		0			0
$866$	−161.740	+	93.3807i	−0.186767	+	0.107830i
$867$	367.301	+	15.8347i	0.423645	+	0.0182638i
$868$	115.607	+	66.7457i	0.133188	+	0.0768960i
$869$	−2143.20	−	1237.38i	−2.46629	−	1.42391i
$870$		0			0
$871$	−16.3433	−	28.3075i	−0.0187639	−	0.0325000i
$872$	−76.0126			−0.0871705
$873$	383.607	−	179.392i	0.439412	−	0.205489i
$874$	387.590			0.443467
$875$		0			0
$876$	−450.124	−	286.413i	−0.513840	−	0.326956i
$877$	−1251.66	−	722.647i	−1.42721	−	0.823999i	−0.430308	−	0.902682i	$-0.641595\pi$
$877$	−1251.66	−	722.647i	−1.42721	−	0.823999i	−0.996900	+	0.0786834i	$0.974928\pi$
$878$	−487.213	+	843.877i	−0.554912	+	0.961136i
$879$	−471.859	+	741.568i	−0.536814	+	0.843650i
$880$		0			0
$881$		−	608.977i		−	0.691234i	−0.938376	−	0.345617i	$-0.887670\pi$
$881$		−	608.977i		−	0.691234i	0.938376	−	0.345617i	$-0.112330\pi$
$882$	−63.6191	−	5.49558i	−0.0721305	−	0.00623082i
$883$		−	120.519i		−	0.136488i	−0.997669	−	0.0682440i	$-0.978260\pi$
$883$		−	120.519i		−	0.136488i	0.997669	−	0.0682440i	$-0.0217396\pi$
$884$	−218.602	+	126.210i	−0.247288	+	0.142772i
$885$		0			0
$886$	−48.1416	+	83.3837i	−0.0543359	+	0.0941126i
$887$	803.710	−	1392.07i	0.906100	−	1.56941i	0.0866653	−	0.996237i	$-0.472379\pi$
$887$	803.710	−	1392.07i	0.906100	−	1.56941i	0.819434	−	0.573173i	$-0.194288\pi$
$888$	0.929846	−	21.5686i	0.00104712	−	0.0242890i
$889$	427.165	+	739.872i	0.480501	+	0.832252i
$890$		0			0
$891$	−1599.83	+	586.272i	−1.79555	+	0.657993i
$892$			118.354i			0.132684i
$893$	381.900	+	661.471i	0.427660	+	0.740729i
$894$	−22.0897	+	512.391i	−0.0247088	+	0.573144i
$895$		0			0
$896$	64.9797	+	37.5161i	0.0725220	+	0.0418706i
$897$	440.755	−	229.750i	0.491366	−	0.256132i
$898$	839.629	−	484.760i	0.934999	−	0.539822i
$899$			503.807i			0.560408i
$900$		0			0
$901$	−14.0386			−0.0155812
$902$	799.714	+	1385.15i	0.886601	+	1.53564i
$903$	799.300	−	1256.17i	0.885161	−	1.39111i
$904$	−26.6012	+	46.0747i	−0.0294261	+	0.0509676i
$905$		0			0
$906$	−289.228	+	454.547i	−0.319236	+	0.501707i
$907$	−561.175	+	323.994i	−0.618715	+	0.357215i	−0.776369	−	0.630279i	$-0.782940\pi$
$907$	−561.175	+	323.994i	−0.618715	+	0.357215i	0.157653	+	0.987495i	$0.449607\pi$
$908$	299.677			0.330041
$909$	−182.251	+	85.2289i	−0.200496	+	0.0937611i
$910$		0			0
$911$	−173.671	+	100.269i	−0.190638	+	0.110065i	−0.592281	−	0.805731i	$-0.701773\pi$
$911$	−173.671	+	100.269i	−0.190638	+	0.110065i	0.401643	+	0.915796i	$0.368439\pi$
$912$	−89.7594	−	172.195i	−0.0984204	−	0.188811i
$913$	−2680.17	−	1547.40i	−2.93556	−	1.69485i
$914$	−636.127	−	367.268i	−0.695981	−	0.401825i
$915$		0			0
$916$	−170.864	−	295.945i	−0.186532	−	0.323084i
$917$	−204.341			−0.222837
$918$	−189.272	−	454.823i	−0.206179	−	0.495450i
$919$	619.581			0.674191			0.337095	−	0.941471i	$-0.390556\pi$
$919$	619.581			0.674191			0.337095	+	0.941471i	$0.390556\pi$
$920$		0			0
$921$	60.4208	−	1401.52i	0.0656035	−	1.52173i
$922$	109.655	+	63.3094i	0.118932	+	0.0686653i
$923$	−188.151	+	325.887i	−0.203847	+	0.353074i
$924$	386.909	+	742.250i	0.418732	+	0.803301i
$925$		0			0
$926$			721.194i			0.778828i
$927$	−914.131	−	638.587i	−0.986117	−	0.688875i
$928$			283.177i			0.305148i
$929$	615.591	−	355.411i	0.662638	−	0.382574i	−0.130643	−	0.991429i	$-0.541704\pi$
$929$	615.591	−	355.411i	0.662638	−	0.382574i	0.793281	+	0.608855i	$0.208371\pi$
$930$		0			0
$931$	40.5929	−	70.3089i	0.0436014	−	0.0755198i
$932$	−448.983	+	777.661i	−0.481741	+	0.834401i
$933$	−1361.22	−	866.140i	−1.45897	−	0.928339i
$934$	381.699	+	661.122i	0.408671	+	0.707839i
$935$		0			0
$936$	−204.143	−	142.609i	−0.218101	−	0.152360i
$937$		−	435.674i		−	0.464967i	−0.972600	−	0.232483i	$-0.925315\pi$
$937$		−	435.674i		−	0.464967i	0.972600	−	0.232483i	$-0.0746851\pi$
$938$	−15.6693	−	27.1400i	−0.0167050	−	0.0289339i
$939$	708.318	−	369.221i	0.754333	−	0.393207i
$940$		0			0
$941$	109.205	+	63.0496i	0.116052	+	0.0670027i	0.556902	−	0.830578i	$-0.311990\pi$
$941$	109.205	+	63.0496i	0.116052	+	0.0670027i	−0.440850	+	0.897581i	$0.645323\pi$
$942$	19.0433	−	441.727i	0.0202158	−	0.468925i
$943$	788.590	−	455.293i	0.836257	−	0.482813i
$944$			38.5581i			0.0408454i
$945$		0			0
$946$	2226.23			2.35331
$947$	283.686	+	491.359i	0.299563	+	0.518858i	0.976036	−	0.217609i	$-0.0698258\pi$
$947$	283.686	+	491.359i	0.299563	+	0.518858i	−0.676473	+	0.736467i	$0.736493\pi$
$948$	705.227	+	30.4031i	0.743911	+	0.0320708i
$949$	434.930	−	753.320i	0.458303	−	0.793804i
$950$		0			0
$951$	661.285	+	1268.62i	0.695358	+	1.33398i
$952$	−209.587	+	121.005i	−0.220154	+	0.127106i
$953$	−873.128			−0.916189			−0.458095	−	0.888903i	$-0.651468\pi$
$953$	−873.128			−0.916189			−0.458095	+	0.888903i	$0.651468\pi$
$954$	−5.86687	−	12.5456i	−0.00614976	−	0.0131505i
$955$		0			0
$956$	−401.690	+	231.916i	−0.420178	+	0.242590i
$957$	−1695.89	+	2665.25i	−1.77209	+	2.78500i
$958$	−133.256	−	76.9353i	−0.139098	−	0.0803082i
$959$	611.934	+	353.300i	0.638095	+	0.368405i
$960$		0			0
$961$	429.856	+	744.532i	0.447300	+	0.774747i
$962$	35.1985			0.0365888
$963$	424.739	+	36.6901i	0.441059	+	0.0380998i
$964$	−794.682			−0.824359
$965$		0			0
$966$	422.577	−	220.275i	0.437450	−	0.228027i
$967$	−728.109	−	420.374i	−0.752957	−	0.434720i	0.0738046	−	0.997273i	$-0.476486\pi$
$967$	−728.109	−	420.374i	−0.752957	−	0.434720i	−0.826761	+	0.562553i	$0.809819\pi$
$968$	−454.655	+	787.486i	−0.469685	+	0.813518i
$969$	625.747	+	26.9766i	0.645766	+	0.0278396i
$970$		0			0
$971$			258.099i			0.265807i	0.991129	+	0.132903i	$0.0424300\pi$
$971$			258.099i			0.265807i	−0.991129	+	0.132903i	$0.957570\pi$
$972$	327.352	−	359.217i	0.336782	−	0.369564i
$973$		−	757.613i		−	0.778636i
$974$	419.504	−	242.201i	0.430703	−	0.248666i
$975$		0			0
$976$	89.8290	−	155.588i	0.0920379	−	0.159414i
$977$	−575.995	+	997.653i	−0.589555	+	1.02114i	0.404736	+	0.914434i	$0.367364\pi$
$977$	−575.995	+	997.653i	−0.589555	+	1.02114i	−0.994291	+	0.106706i	$0.965970\pi$
$978$	−709.296	+	369.731i	−0.725251	+	0.378048i
$979$	−1528.55	−	2647.52i	−1.56134	−	2.70431i
$980$		0			0
$981$	240.973	+	20.8159i	0.245641	+	0.0212191i
$982$			703.260i			0.716151i
$983$	−319.689	−	553.718i	−0.325218	−	0.563294i	0.656338	−	0.754467i	$-0.272104\pi$
$983$	−319.689	−	553.718i	−0.325218	−	0.563294i	−0.981556	+	0.191172i	$0.938771\pi$
$984$	−384.898	−	244.910i	−0.391156	−	0.248892i
$985$		0			0
$986$	−790.996	−	456.682i	−0.802228	−	0.463166i
$987$	792.299	+	504.139i	0.802735	+	0.510779i
$988$	274.186	−	158.301i	0.277516	−	0.160224i
$989$		−	1267.44i		−	1.28153i
$990$		0			0
$991$	1875.09			1.89212			0.946060	−	0.323992i	$-0.105025\pi$
$991$	1875.09			1.89212			0.946060	+	0.323992i	$0.105025\pi$
$992$	−28.4660	−	49.3045i	−0.0286955	−	0.0497021i
$993$	49.0118	+	94.0248i	0.0493573	+	0.0946876i
$994$	−180.391	+	312.447i	−0.181480	+	0.314333i
$995$		0			0
$996$	881.918	+	38.0204i	0.885460	+	0.0381731i
$997$	818.736	−	472.697i	0.821199	−	0.474120i	−0.0296306	−	0.999561i	$-0.509433\pi$
$997$	818.736	−	472.697i	0.821199	−	0.474120i	0.850830	+	0.525441i	$0.176100\pi$
$998$	219.249			0.219689
$999$	−8.85430	+	68.1217i	−0.00886317	+	0.0681899i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.3.k.c.149.14		32
3.2	odd	2		1350.3.k.b.449.3		32
5.2	odd	4		90.3.h.a.41.3	yes	16
5.3	odd	4		450.3.i.g.401.6		16
5.4	even	2	inner	450.3.k.c.149.3		32
9.2	odd	6	inner	450.3.k.c.299.3		32
9.7	even	3		1350.3.k.b.899.14		32
15.2	even	4		270.3.h.a.71.6		16
15.8	even	4		1350.3.i.g.1151.2		16
15.14	odd	2		1350.3.k.b.449.14		32
20.7	even	4		720.3.bs.d.401.5		16
45.2	even	12		90.3.h.a.11.3	✓	16
45.7	odd	12		270.3.h.a.251.6		16
45.22	odd	12		810.3.d.c.161.1		16
45.29	odd	6	inner	450.3.k.c.299.14		32
45.32	even	12		810.3.d.c.161.13		16
45.34	even	6		1350.3.k.b.899.3		32
45.38	even	12		450.3.i.g.101.6		16
45.43	odd	12		1350.3.i.g.251.2		16
60.47	odd	4		2160.3.bs.d.881.1		16
180.7	even	12		2160.3.bs.d.1601.1		16
180.47	odd	12		720.3.bs.d.641.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.h.a.11.3	✓	16	45.2	even	12
90.3.h.a.41.3	yes	16	5.2	odd	4
270.3.h.a.71.6		16	15.2	even	4
270.3.h.a.251.6		16	45.7	odd	12
450.3.i.g.101.6		16	45.38	even	12
450.3.i.g.401.6		16	5.3	odd	4
450.3.k.c.149.3		32	5.4	even	2	inner
450.3.k.c.149.14		32	1.1	even	1	trivial
450.3.k.c.299.3		32	9.2	odd	6	inner
450.3.k.c.299.14		32	45.29	odd	6	inner
720.3.bs.d.401.5		16	20.7	even	4
720.3.bs.d.641.5		16	180.47	odd	12
810.3.d.c.161.1		16	45.22	odd	12
810.3.d.c.161.13		16	45.32	even	12
1350.3.i.g.251.2		16	45.43	odd	12
1350.3.i.g.1151.2		16	15.8	even	4
1350.3.k.b.449.3		32	3.2	odd	2
1350.3.k.b.449.14		32	15.14	odd	2
1350.3.k.b.899.3		32	45.34	even	6
1350.3.k.b.899.14		32	9.7	even	3
2160.3.bs.d.881.1		16	60.47	odd	4
2160.3.bs.d.1601.1		16	180.7	even	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:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	450.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-2.99722 - 0.129213i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.96110 - 3.76219i) q^{6} +(5.74345 - 3.31598i) q^{7} -2.82843 q^{8} +(8.96661 + 0.774559i) q^{9} +(-18.2172 + 10.5177i) q^{11} +(3.22102 - 5.06212i) q^{12} +(8.47187 + 4.89124i) q^{13} +(8.12247 + 4.68951i) q^{14} +(-2.00000 - 3.46410i) q^{16} +12.9017 q^{17} +(5.39171 + 11.5295i) q^{18} -16.1821 q^{19} +(-17.6428 + 9.19659i) q^{21} +(-25.7630 - 14.8743i) q^{22} +(-8.46823 + 14.6674i) q^{23} +(8.47741 + 0.365470i) q^{24} +13.8345i q^{26} +(-26.7748 - 3.48012i) q^{27} +13.2639i q^{28} +(-43.3525 + 25.0296i) q^{29} +(5.03212 - 8.71588i) q^{31} +(2.82843 - 4.89898i) q^{32} +(55.9600 - 29.1700i) q^{33} +(9.12285 + 15.8012i) q^{34} +(-10.3082 + 14.7561i) q^{36} -2.54425i q^{37} +(-11.4425 - 19.8190i) q^{38} +(-24.7600 - 15.7548i) q^{39} +(-46.5617 - 26.8824i) q^{41} +(-23.7388 - 15.1050i) q^{42} +(-64.8089 + 37.4175i) q^{43} -42.0709i q^{44} -23.9518 q^{46} +(-23.6001 - 40.8766i) q^{47} +(5.54682 + 10.6411i) q^{48} +(-2.50850 + 4.34485i) q^{49} +(-38.6691 - 1.66706i) q^{51} +(-16.9437 + 9.78248i) q^{52} -1.08813 q^{53} +(-14.6704 - 35.2531i) q^{54} +(-16.2449 + 9.37902i) q^{56} +(48.5013 + 2.09094i) q^{57} +(-61.3097 - 35.3972i) q^{58} +(-8.34807 - 4.81976i) q^{59} +(22.4573 + 38.8971i) q^{61} +14.2330 q^{62} +(54.0677 - 25.2845i) q^{63} +8.00000 q^{64} +(75.2955 + 47.9104i) q^{66} +(-2.89369 - 1.67067i) q^{67} +(-12.9017 + 22.3463i) q^{68} +(27.2763 - 42.8672i) q^{69} +38.4670i q^{71} +(-25.3614 - 2.19078i) q^{72} -88.9201i q^{73} +(3.11606 - 1.79906i) q^{74} +(16.1821 - 28.0283i) q^{76} +(-69.7532 + 120.816i) q^{77} +(1.78760 - 41.4650i) q^{78} +(58.8235 + 101.885i) q^{79} +(79.8001 + 13.8903i) q^{81} -76.0349i q^{82} +(73.5614 + 127.412i) q^{83} +(1.71387 - 39.7549i) q^{84} +(-91.6537 - 52.9163i) q^{86} +(133.171 - 69.4173i) q^{87} +(51.5261 - 29.7486i) q^{88} +145.331i q^{89} +64.8771 q^{91} +(-16.9365 - 29.3348i) q^{92} +(-16.2086 + 25.4732i) q^{93} +(33.3756 - 57.8083i) q^{94} +(-9.11042 + 14.3178i) q^{96} +(40.7494 - 23.5267i) q^{97} -7.09511 q^{98} +(-171.493 + 80.1980i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} + 32 q^{6} + 8 q^{9} + 72 q^{14} - 64 q^{16} - 160 q^{19} - 88 q^{21} + 16 q^{24} + 144 q^{29} - 32 q^{31} + 96 q^{34} + 64 q^{36} + 16 q^{39} + 216 q^{41} + 48 q^{46} + 168 q^{49} + 336 q^{51}+ \cdots - 1632 q^{99}+O(q^{100}) \) 32 * q - 32 * q^4 + 32 * q^6 + 8 * q^9 + 72 * q^14 - 64 * q^16 - 160 * q^19 - 88 * q^21 + 16 * q^24 + 144 * q^29 - 32 * q^31 + 96 * q^34 + 64 * q^36 + 16 * q^39 + 216 * q^41 + 48 * q^46 + 168 * q^49 + 336 * q^51 - 296 * q^54 - 144 * q^56 - 288 * q^59 - 152 * q^61 + 256 * q^64 + 192 * q^66 + 144 * q^69 + 576 * q^74 + 160 * q^76 - 160 * q^79 + 640 * q^81 - 80 * q^84 - 432 * q^86 - 1312 * q^91 + 168 * q^94 - 160 * q^96 - 1632 * q^99

Introduction

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