LMFDB - Embedded newform 925.2.o.c.824.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(174,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("925.174");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.o (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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			824.7
Character	$\chi$	$=$	925.824
Dual form			925.2.o.c.174.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.268684 - 0.155125i) q^{2} +(-1.78566 + 1.03095i) q^{3} +(-0.951873 - 1.64869i) q^{4} +0.639704 q^{6} +(-1.83659 + 1.06035i) q^{7} +1.21113i q^{8} +(0.625722 - 1.08378i) q^{9} +O(q^{10})$	\(q+(-0.268684 - 0.155125i) q^{2} +(-1.78566 + 1.03095i) q^{3} +(-0.951873 - 1.64869i) q^{4} +0.639704 q^{6} +(-1.83659 + 1.06035i) q^{7} +1.21113i q^{8} +(0.625722 - 1.08378i) q^{9} +5.48703 q^{11} +(3.39944 + 1.96267i) q^{12} +(-1.43093 + 0.826151i) q^{13} +0.657948 q^{14} +(-1.71587 + 2.97197i) q^{16} +(2.46379 + 1.42247i) q^{17} +(-0.336243 + 0.194130i) q^{18} +(-1.19568 - 2.07098i) q^{19} +(2.18635 - 3.78686i) q^{21} +(-1.47428 - 0.851174i) q^{22} -1.29182i q^{23} +(-1.24862 - 2.16267i) q^{24} +0.512625 q^{26} -3.60535i q^{27} +(3.49639 + 2.01864i) q^{28} +0.459480 q^{29} -7.00913 q^{31} +(3.01980 - 1.74348i) q^{32} +(-9.79798 + 5.65686i) q^{33} +(-0.441320 - 0.764389i) q^{34} -2.38243 q^{36} +(-5.58343 - 2.41356i) q^{37} +0.741917i q^{38} +(1.70344 - 2.95045i) q^{39} +(-3.63843 - 6.30194i) q^{41} +(-1.17487 + 0.678313i) q^{42} +4.39190i q^{43} +(-5.22296 - 9.04642i) q^{44} +(-0.200394 + 0.347092i) q^{46} -0.310249i q^{47} -7.07591i q^{48} +(-1.25130 + 2.16731i) q^{49} -5.86599 q^{51} +(2.72414 + 1.57278i) q^{52} +(-10.4052 - 6.00746i) q^{53} +(-0.559279 + 0.968700i) q^{54} +(-1.28423 - 2.22435i) q^{56} +(4.27015 + 2.46537i) q^{57} +(-0.123455 - 0.0712767i) q^{58} +(4.14947 - 7.18709i) q^{59} +(-5.10365 - 8.83978i) q^{61} +(1.88324 + 1.08729i) q^{62} +2.65395i q^{63} +5.78165 q^{64} +3.51008 q^{66} +(1.15098 - 0.664518i) q^{67} -5.41604i q^{68} +(1.33181 + 2.30676i) q^{69} +(-0.293650 - 0.508617i) q^{71} +(1.31261 + 0.757834i) q^{72} -10.8030i q^{73} +(1.12578 + 1.51461i) q^{74} +(-2.27627 + 3.94261i) q^{76} +(-10.0774 + 5.81820i) q^{77} +(-0.915375 + 0.528492i) q^{78} +(-1.41967 - 2.45893i) q^{79} +(5.59411 + 9.68928i) q^{81} +2.25764i q^{82} +(10.2381 + 5.91099i) q^{83} -8.32450 q^{84} +(0.681292 - 1.18003i) q^{86} +(-0.820476 + 0.473702i) q^{87} +6.64553i q^{88} +(-8.40980 + 14.5662i) q^{89} +(1.75202 - 3.03459i) q^{91} +(-2.12982 + 1.22965i) q^{92} +(12.5159 - 7.22607i) q^{93} +(-0.0481273 + 0.0833590i) q^{94} +(-3.59489 + 6.22653i) q^{96} -18.5979i q^{97} +(0.672407 - 0.388215i) q^{98} +(3.43336 - 5.94675i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 16 q^{4} + 8 q^{6} + 10 q^{9}+O(q^{10}) $ 28 * q + 16 * q^4 + 8 * q^6 + 10 * q^9	$ 28 q + 16 q^{4} + 8 q^{6} + 10 q^{9} - 20 q^{11} + 72 q^{14} - 28 q^{16} - 12 q^{19} + 26 q^{21} + 42 q^{24} + 4 q^{26} + 24 q^{29} - 16 q^{31} + 22 q^{34} - 16 q^{36} - 46 q^{39} - 6 q^{41} - 50 q^{44} + 20 q^{46} + 14 q^{49} - 28 q^{51} - 46 q^{54} + 38 q^{56} + 36 q^{59} - 40 q^{61} - 100 q^{64} - 84 q^{66} - 34 q^{69} - 22 q^{71} + 132 q^{74} + 80 q^{76} - 46 q^{79} + 58 q^{81} - 16 q^{84} - 6 q^{86} + 32 q^{89} + 24 q^{91} - 44 q^{94} - 134 q^{96} - 8 q^{99}+O(q^{100}) $ 28 * q + 16 * q^4 + 8 * q^6 + 10 * q^9 - 20 * q^11 + 72 * q^14 - 28 * q^16 - 12 * q^19 + 26 * q^21 + 42 * q^24 + 4 * q^26 + 24 * q^29 - 16 * q^31 + 22 * q^34 - 16 * q^36 - 46 * q^39 - 6 * q^41 - 50 * q^44 + 20 * q^46 + 14 * q^49 - 28 * q^51 - 46 * q^54 + 38 * q^56 + 36 * q^59 - 40 * q^61 - 100 * q^64 - 84 * q^66 - 34 * q^69 - 22 * q^71 + 132 * q^74 + 80 * q^76 - 46 * q^79 + 58 * q^81 - 16 * q^84 - 6 * q^86 + 32 * q^89 + 24 * q^91 - 44 * q^94 - 134 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.268684	−	0.155125i	−0.189988	−	0.109690i	0.401989	−	0.915645i	$-0.368319\pi$
$2$	−0.268684	−	0.155125i	−0.189988	−	0.109690i	−0.591977	+	0.805955i	$0.701652\pi$
$3$	−1.78566	+	1.03095i	−1.03095	+	0.595220i	−0.917257	−	0.398296i	$-0.869602\pi$
$3$	−1.78566	+	1.03095i	−1.03095	+	0.595220i	−0.113694	+	0.993516i	$0.536268\pi$
$4$	−0.951873	−	1.64869i	−0.475936	−	0.824346i
$5$		0			0
$5$		0			0
$6$	0.639704			0.261158
$7$	−1.83659	+	1.06035i	−0.694165	+	0.400776i	−0.805170	−	0.593044i	$-0.797926\pi$
$7$	−1.83659	+	1.06035i	−0.694165	+	0.400776i	0.111006	+	0.993820i	$0.464593\pi$
$8$			1.21113i			0.428201i
$9$	0.625722	−	1.08378i	0.208574	−	0.361261i
$10$		0			0
$11$	5.48703			1.65440			0.827201	−	0.561906i	$-0.189932\pi$
$11$	5.48703			1.65440			0.827201	+	0.561906i	$0.189932\pi$
$12$	3.39944	+	1.96267i	0.981335	+	0.566574i
$13$	−1.43093	+	0.826151i	−0.396870	+	0.229133i	−0.685133	−	0.728418i	$-0.740256\pi$
$13$	−1.43093	+	0.826151i	−0.396870	+	0.229133i	0.288263	+	0.957551i	$0.406922\pi$
$14$	0.657948			0.175844
$15$		0			0
$16$	−1.71587	+	2.97197i	−0.428967	+	0.742993i
$17$	2.46379	+	1.42247i	0.597557	+	0.345000i	0.768080	−	0.640354i	$-0.221212\pi$
$17$	2.46379	+	1.42247i	0.597557	+	0.345000i	−0.170523	+	0.985354i	$0.554546\pi$
$18$	−0.336243	+	0.194130i	−0.0792532	+	0.0457568i
$19$	−1.19568	−	2.07098i	−0.274308	−	0.475115i	0.695653	−	0.718378i	$-0.255115\pi$
$19$	−1.19568	−	2.07098i	−0.274308	−	0.475115i	−0.969960	+	0.243264i	$0.921782\pi$
$20$		0			0
$21$	2.18635	−	3.78686i	0.477100	−	0.826362i
$22$	−1.47428	−	0.851174i	−0.314317	−	0.181471i
$23$		−	1.29182i		−	0.269364i	−0.990889	−	0.134682i	$-0.956999\pi$
$23$		−	1.29182i		−	0.269364i	0.990889	−	0.134682i	$-0.0430013\pi$
$24$	−1.24862	−	2.16267i	−0.254874	−	0.441454i
$25$		0			0
$26$	0.512625			0.100534
$27$		−	3.60535i		−	0.693850i
$28$	3.49639	+	2.01864i	0.660756	+	0.381488i
$29$	0.459480			0.0853234			0.0426617	−	0.999090i	$-0.486416\pi$
$29$	0.459480			0.0853234			0.0426617	+	0.999090i	$0.486416\pi$
$30$		0			0
$31$	−7.00913			−1.25888			−0.629438	−	0.777051i	$-0.716715\pi$
$31$	−7.00913			−1.25888			−0.629438	+	0.777051i	$0.716715\pi$
$32$	3.01980	−	1.74348i	0.533830	−	0.308207i
$33$	−9.79798	+	5.65686i	−1.70561	+	0.984734i
$34$	−0.441320	−	0.764389i	−0.0756858	−	0.131092i
$35$		0			0
$36$	−2.38243			−0.397072
$37$	−5.58343	−	2.41356i	−0.917911	−	0.396786i
$37$	−5.58343	−	2.41356i	−0.917911	−	0.396786i
$38$			0.741917i			0.120355i
$39$	1.70344	−	2.95045i	0.272769	−	0.472450i
$40$		0			0
$41$	−3.63843	−	6.30194i	−0.568227	−	0.984198i	−0.996741	−	0.0806634i	$-0.974296\pi$
$41$	−3.63843	−	6.30194i	−0.568227	−	0.984198i	0.428514	−	0.903535i	$-0.359037\pi$
$42$	−1.17487	+	0.678313i	−0.181287	+	0.104666i
$43$			4.39190i			0.669758i	0.942261	+	0.334879i	$0.108696\pi$
$43$			4.39190i			0.669758i	−0.942261	+	0.334879i	$0.891304\pi$
$44$	−5.22296	−	9.04642i	−0.787390	−	1.36380i
$45$		0			0
$46$	−0.200394	+	0.347092i	−0.0295464	+	0.0511759i
$47$		−	0.310249i		−	0.0452545i	−0.999744	−	0.0226273i	$-0.992797\pi$
$47$		−	0.310249i		−	0.0452545i	0.999744	−	0.0226273i	$-0.00720309\pi$
$48$		−	7.07591i		−	1.02132i
$49$	−1.25130	+	2.16731i	−0.178757	+	0.309616i
$50$		0			0
$51$	−5.86599			−0.821403
$52$	2.72414	+	1.57278i	0.377770	+	0.218105i
$53$	−10.4052	−	6.00746i	−1.42927	−	0.825188i	−0.432204	−	0.901776i	$-0.642264\pi$
$53$	−10.4052	−	6.00746i	−1.42927	−	0.825188i	−0.997063	+	0.0765878i	$0.975597\pi$
$54$	−0.559279	+	0.968700i	−0.0761082	+	0.131823i
$55$		0			0
$56$	−1.28423	−	2.22435i	−0.171613	−	0.297242i
$57$	4.27015	+	2.46537i	0.565596	+	0.326547i
$58$	−0.123455	−	0.0712767i	−0.0162104	−	0.00935910i
$59$	4.14947	−	7.18709i	0.540215	−	0.935680i	−0.458676	−	0.888603i	$-0.651676\pi$
$59$	4.14947	−	7.18709i	0.540215	−	0.935680i	0.998891	−	0.0470765i	$-0.0149905\pi$
$60$		0			0
$61$	−5.10365	−	8.83978i	−0.653456	−	1.13182i	−0.982279	−	0.187427i	$-0.939985\pi$
$61$	−5.10365	−	8.83978i	−0.653456	−	1.13182i	0.328823	−	0.944392i	$-0.393348\pi$
$62$	1.88324	+	1.08729i	0.239172	+	0.138086i
$63$			2.65395i			0.334366i
$64$	5.78165			0.722706
$65$		0			0
$66$	3.51008			0.432061
$67$	1.15098	−	0.664518i	0.140614	−	0.0811838i	−0.428042	−	0.903759i	$-0.640797\pi$
$67$	1.15098	−	0.664518i	0.140614	−	0.0811838i	0.568657	+	0.822575i	$0.307463\pi$
$68$		−	5.41604i		−	0.656792i
$69$	1.33181	+	2.30676i	0.160331	+	0.277701i
$70$		0			0
$71$	−0.293650	−	0.508617i	−0.0348498	−	0.0603617i	0.848074	−	0.529877i	$-0.177762\pi$
$71$	−0.293650	−	0.508617i	−0.0348498	−	0.0603617i	−0.882924	+	0.469515i	$0.844429\pi$
$72$	1.31261	+	0.757834i	0.154692	+	0.0893115i
$73$		−	10.8030i		−	1.26439i	−0.774808	−	0.632197i	$-0.782153\pi$
$73$		−	10.8030i		−	1.26439i	0.774808	−	0.632197i	$-0.217847\pi$
$74$	1.12578	+	1.51461i	0.130869	+	0.176070i
$75$		0			0
$76$	−2.27627	+	3.94261i	−0.261106	+	0.452249i
$77$	−10.0774	+	5.81820i	−1.14843	+	0.663045i
$78$	−0.915375	+	0.528492i	−0.103646	+	0.0598399i
$79$	−1.41967	−	2.45893i	−0.159725	−	0.276652i	0.775045	−	0.631907i	$-0.217727\pi$
$79$	−1.41967	−	2.45893i	−0.159725	−	0.276652i	−0.934769	+	0.355255i	$0.884394\pi$
$80$		0			0
$81$	5.59411	+	9.68928i	0.621568	+	1.07659i
$82$			2.25764i			0.249315i
$83$	10.2381	+	5.91099i	1.12378	+	0.648815i	0.942363	−	0.334591i	$-0.108598\pi$
$83$	10.2381	+	5.91099i	1.12378	+	0.648815i	0.181417	+	0.983406i	$0.441932\pi$
$84$	−8.32450			−0.908277
$85$		0			0
$86$	0.681292	−	1.18003i	0.0734656	−	0.127246i
$87$	−0.820476	+	0.473702i	−0.0879643	+	0.0507862i
$88$			6.64553i			0.708416i
$89$	−8.40980	+	14.5662i	−0.891437	+	1.54401i	−0.0532843	+	0.998579i	$0.516969\pi$
$89$	−8.40980	+	14.5662i	−0.891437	+	1.54401i	−0.838153	+	0.545435i	$0.816364\pi$
$90$		0			0
$91$	1.75202	−	3.03459i	0.183662	−	0.318112i
$92$	−2.12982	+	1.22965i	−0.222049	+	0.128200i
$93$	12.5159	−	7.22607i	1.29784	−	0.749308i
$94$	−0.0481273	+	0.0833590i	−0.00496395	+	0.00859782i
$95$		0			0
$96$	−3.59489	+	6.22653i	−0.366902	+	0.635493i
$97$		−	18.5979i		−	1.88833i	−0.329472	−	0.944165i	$-0.606871\pi$
$97$		−	18.5979i		−	1.88833i	0.329472	−	0.944165i	$-0.393129\pi$
$98$	0.672407	−	0.388215i	0.0679234	−	0.0392156i
$99$	3.43336	−	5.94675i	0.345065	−	0.597671i
$100$		0			0
$101$	−8.79352			−0.874988			−0.437494	−	0.899221i	$-0.644134\pi$
$101$	−8.79352			−0.874988			−0.437494	+	0.899221i	$0.644134\pi$
$102$	1.57610	+	0.909960i	0.156057	+	0.0900994i
$103$		−	5.36532i		−	0.528660i	−0.964432	−	0.264330i	$-0.914849\pi$
$103$		−	5.36532i		−	0.528660i	0.964432	−	0.264330i	$-0.0851509\pi$
$104$	−1.00058	−	1.73305i	−0.0981149	−	0.169940i
$105$		0			0
$106$	1.86381	+	3.22821i	0.181029	+	0.313552i
$107$	−2.47158	+	1.42697i	−0.238937	+	0.137950i	−0.614688	−	0.788770i	$-0.710718\pi$
$107$	−2.47158	+	1.42697i	−0.238937	+	0.137950i	0.375751	+	0.926721i	$0.377385\pi$
$108$	−5.94412	+	3.43184i	−0.571973	+	0.330229i
$109$	4.37956	−	7.58562i	0.419486	−	0.726571i	−0.576402	−	0.817166i	$-0.695544\pi$
$109$	4.37956	−	7.58562i	0.419486	−	0.726571i	0.995888	+	0.0905956i	$0.0288771\pi$
$110$		0			0
$111$	12.4584	−	1.44646i	1.18250	−	0.137292i
$112$		−	7.27771i		−	0.687679i
$113$	−13.6527	−	7.88239i	−1.28434	−	0.741513i	−0.306699	−	0.951806i	$-0.599225\pi$
$113$	−13.6527	−	7.88239i	−1.28434	−	0.741513i	−0.977638	+	0.210294i	$0.932558\pi$
$114$	−0.764881	−	1.32481i	−0.0716376	−	0.124080i
$115$		0			0
$116$	−0.437367	−	0.757542i	−0.0406085	−	0.0703360i
$117$			2.06776i			0.191165i
$118$	−2.22979	+	1.28737i	−0.205269	+	0.118512i
$119$	−6.03329			−0.553071
$120$		0			0
$121$	19.1075			1.73705
$122$			3.16681i			0.286709i
$123$	12.9940	+	7.50209i	1.17163	+	0.676441i
$124$	6.67180	+	11.5559i	0.599145	+	1.03775i
$125$		0			0
$126$	0.411693	−	0.713073i	0.0366765	−	0.0635256i
$127$	−3.46973	−	2.00325i	−0.307889	−	0.177760i	0.338093	−	0.941113i	$-0.390218\pi$
$127$	−3.46973	−	2.00325i	−0.307889	−	0.177760i	−0.645981	+	0.763353i	$0.723552\pi$
$128$	−7.59303	−	4.38384i	−0.671135	−	0.387480i
$129$	−4.52784	−	7.84244i	−0.398654	−	0.690489i
$130$		0			0
$131$	10.2080	−	17.6807i	0.891873	−	1.54477i	0.0542464	−	0.998528i	$-0.482724\pi$
$131$	10.2080	−	17.6807i	0.891873	−	1.54477i	0.837627	−	0.546243i	$-0.183942\pi$
$132$	18.6529	+	10.7692i	1.62352	+	0.937341i
$133$	4.39194	+	2.53569i	0.380829	+	0.219872i
$134$	−0.412332			−0.0356201
$135$		0			0
$136$	−1.72280	+	2.98398i	−0.147729	+	0.255874i
$137$		−	5.52931i		−	0.472401i	−0.971704	−	0.236200i	$-0.924098\pi$
$137$		−	5.52931i		−	0.472401i	0.971704	−	0.236200i	$-0.0759022\pi$
$138$		−	0.826385i		−	0.0703465i
$139$	−10.4632	+	18.1228i	−0.887477	+	1.53716i	−0.0446295	+	0.999004i	$0.514211\pi$
$139$	−10.4632	+	18.1228i	−0.887477	+	1.53716i	−0.842848	+	0.538152i	$0.819123\pi$
$140$		0			0
$141$	0.319852	+	0.554000i	0.0269364	+	0.0466552i
$142$			0.182209i			0.0152907i
$143$	−7.85158	+	4.53311i	−0.656582	+	0.379078i
$144$	2.14731	+	3.71926i	0.178943	+	0.309938i
$145$		0			0
$146$	−1.67581	+	2.90259i	−0.138691	+	0.240220i
$147$		−	5.16011i		−	0.425599i
$148$	1.33551	+	11.5028i	0.109778	+	0.945521i
$149$	4.87785			0.399609			0.199804	−	0.979836i	$-0.435969\pi$
$149$	4.87785			0.399609			0.199804	+	0.979836i	$0.435969\pi$
$150$		0			0
$151$	11.8485	+	20.5222i	0.964216	+	1.67007i	0.711708	+	0.702475i	$0.247922\pi$
$151$	11.8485	+	20.5222i	0.964216	+	1.67007i	0.252507	+	0.967595i	$0.418745\pi$
$152$	2.50823	−	1.44813i	0.203444	−	0.117459i
$153$	3.08330	−	1.78014i	0.249270	−	0.143916i
$154$	3.61018			0.290917
$155$		0			0
$156$	−6.48584			−0.519283
$157$	−18.2533	−	10.5385i	−1.45677	−	0.841067i	−0.457920	−	0.888994i	$-0.651405\pi$
$157$	−18.2533	−	10.5385i	−1.45677	−	0.841067i	−0.998851	+	0.0479266i	$0.984739\pi$
$158$			0.880901i			0.0700807i
$159$	24.7736			1.96467
$160$		0			0
$161$	1.36979	+	2.37255i	0.107955	+	0.186983i
$162$		−	3.47114i		−	0.272718i
$163$	4.51313	+	2.60566i	0.353496	+	0.204091i	0.666224	−	0.745752i	$-0.267910\pi$
$163$	4.51313	+	2.60566i	0.353496	+	0.204091i	−0.312728	+	0.949843i	$0.601243\pi$
$164$	−6.92664	+	11.9973i	−0.540880	+	0.936832i
$165$		0			0
$166$	−1.83388	−	3.17637i	−0.142337	−	0.246534i
$167$	−9.15526	+	5.28579i	−0.708455	+	0.409027i	−0.810489	−	0.585754i	$-0.800798\pi$
$167$	−9.15526	+	5.28579i	−0.708455	+	0.409027i	0.102034	+	0.994781i	$0.467465\pi$
$168$	4.58640	+	2.64796i	0.353849	+	0.204295i
$169$	−5.13495	+	8.89400i	−0.394996	+	0.684153i
$170$		0			0
$171$	−2.99265			−0.228854
$172$	7.24089	−	4.18053i	0.552113	−	0.318762i
$173$	11.7250	+	6.76942i	0.891434	+	0.514670i	0.874411	−	0.485185i	$-0.161248\pi$
$173$	11.7250	+	6.76942i	0.891434	+	0.514670i	0.0170229	+	0.999855i	$0.494581\pi$
$174$	0.293931			0.0222829
$175$		0			0
$176$	−9.41503	+	16.3073i	−0.709684	+	1.22921i
$177$			17.1116i			1.28619i
$178$	4.51915	−	2.60914i	0.338725	−	0.195563i
$179$	14.8133			1.10720			0.553599	−	0.832783i	$-0.313254\pi$
$179$	14.8133			1.10720			0.553599	+	0.832783i	$0.313254\pi$
$180$		0			0
$181$	−2.30881	−	3.99897i	−0.171612	−	0.297241i	0.767371	−	0.641203i	$-0.221564\pi$
$181$	−2.30881	−	3.99897i	−0.171612	−	0.297241i	−0.938984	+	0.343962i	$0.888231\pi$
$182$	−0.941481	+	0.543564i	−0.0697872	+	0.0402917i
$183$	18.2268	+	10.5232i	1.34736	+	0.777900i
$184$	1.56457			0.115342
$185$		0			0
$186$	−4.48377			−0.328766
$187$	13.5189	+	7.80514i	0.988600	+	0.570768i
$188$	−0.511505	+	0.295318i	−0.0373054	+	0.0215383i
$189$	3.82295	+	6.62154i	0.278079	+	0.481646i
$190$		0			0
$191$	−11.6768			−0.844902			−0.422451	−	0.906386i	$-0.638830\pi$
$191$	−11.6768			−0.844902			−0.422451	+	0.906386i	$0.638830\pi$
$192$	−10.3241	+	5.96060i	−0.745075	+	0.430169i
$193$			15.2222i			1.09572i	0.836570	+	0.547859i	$0.184557\pi$
$193$			15.2222i			1.09572i	−0.836570	+	0.547859i	$0.815443\pi$
$194$	−2.88499	+	4.99695i	−0.207130	+	0.358760i
$195$		0			0
$196$	4.76431			0.340308
$197$	−9.25567	−	5.34376i	−0.659439	−	0.380727i	0.132624	−	0.991166i	$-0.457660\pi$
$197$	−9.25567	−	5.34376i	−0.659439	−	0.380727i	−0.792063	+	0.610439i	$0.790993\pi$
$198$	−1.84497	+	1.06520i	−0.131117	+	0.0757002i
$199$	3.95137			0.280105			0.140052	−	0.990144i	$-0.455273\pi$
$199$	3.95137			0.280105			0.140052	+	0.990144i	$0.455273\pi$
$200$		0			0
$201$	−1.37017	+	2.37321i	−0.0966444	+	0.167393i
$202$	2.36268	+	1.36409i	0.166237	+	0.0959771i
$203$	−0.843876	+	0.487212i	−0.0592285	+	0.0341956i
$204$	5.58368	+	9.67121i	0.390936	+	0.677120i
$205$		0			0
$206$	−0.832293	+	1.44157i	−0.0579886	+	0.100439i
$207$	−1.40006	−	0.808323i	−0.0973106	−	0.0561823i
$208$		−	5.67026i		−	0.393162i
$209$	−6.56073	−	11.3635i	−0.453815	−	0.786031i
$210$		0			0
$211$	8.40966			0.578945			0.289472	−	0.957186i	$-0.406520\pi$
$211$	8.40966			0.578945			0.289472	+	0.957186i	$0.406520\pi$
$212$			22.8733i			1.57095i
$213$	1.04872	+	0.605478i	0.0718570	+	0.0414867i
$214$	0.885432			0.0605269
$215$		0			0
$216$	4.36657			0.297107
$217$	12.8729	−	7.43216i	0.873867	−	0.504528i
$218$	−2.35343	+	1.35876i	−0.159395	+	0.0920265i
$219$	11.1374	+	19.2905i	0.752593	+	1.30353i
$220$		0			0
$221$	−4.70070			−0.316203
$222$	−3.57175	−	1.54396i	−0.239720	−	0.103624i
$223$		−	16.4686i		−	1.10282i	−0.834234	−	0.551411i	$-0.814090\pi$
$223$		−	16.4686i		−	1.10282i	0.834234	−	0.551411i	$-0.185910\pi$
$224$	−3.69741	+	6.40411i	−0.247044	+	0.427893i
$225$		0			0
$226$	2.44551	+	4.23574i	0.162673	+	0.281757i
$227$	−11.7627	+	6.79120i	−0.780719	+	0.450748i	−0.836685	−	0.547685i	$-0.815509\pi$
$227$	−11.7627	+	6.79120i	−0.780719	+	0.450748i	0.0559663	+	0.998433i	$0.482176\pi$
$228$		−	9.38689i		−	0.621662i
$229$	−10.9009	−	18.8809i	−0.720351	−	1.24768i	−0.960859	−	0.277037i	$-0.910648\pi$
$229$	−10.9009	−	18.8809i	−0.720351	−	1.24768i	0.240509	−	0.970647i	$-0.422686\pi$
$230$		0			0
$231$	11.9966	−	20.7786i	0.789316	−	1.36713i
$232$			0.556493i			0.0365355i
$233$		−	13.2237i		−	0.866313i	−0.901319	−	0.433156i	$-0.857400\pi$
$233$		−	13.2237i		−	0.866313i	0.901319	−	0.433156i	$-0.142600\pi$
$234$	0.320761	−	0.555574i	0.0209688	−	0.0363190i
$235$		0			0
$236$	−15.7991			−1.02843
$237$	5.07008	+	2.92721i	0.329337	+	0.190143i
$238$	1.62105	+	0.935912i	0.105077	+	0.0606661i
$239$	6.04811	−	10.4756i	0.391220	−	0.677613i	−0.601391	−	0.798955i	$-0.705387\pi$
$239$	6.04811	−	10.4756i	0.391220	−	0.677613i	0.992611	+	0.121342i	$0.0387199\pi$
$240$		0			0
$241$	7.34971	+	12.7301i	0.473436	+	0.820016i	0.999538	−	0.0304061i	$-0.00968004\pi$
$241$	7.34971	+	12.7301i	0.473436	+	0.820016i	−0.526101	+	0.850422i	$0.676347\pi$
$242$	−5.13388	−	2.96405i	−0.330018	−	0.190536i
$243$	−10.6114	−	6.12648i	−0.680720	−	0.393014i
$244$	−9.71605	+	16.8287i	−0.622007	+	1.07735i
$245$		0			0
$246$	−2.32752	−	4.03138i	−0.148397	−	0.257031i
$247$	3.42188	+	1.97562i	0.217729	+	0.125706i
$248$		−	8.48899i		−	0.539052i
$249$	−24.3758			−1.54475
$250$		0			0
$251$	−27.4854			−1.73486			−0.867430	−	0.497559i	$-0.834230\pi$
$251$	−27.4854			−1.73486			−0.867430	+	0.497559i	$0.834230\pi$
$252$	4.37554	−	2.52622i	0.275633	−	0.159137i
$253$		−	7.08828i		−	0.445636i
$254$	0.621507	+	1.07648i	0.0389968	+	0.0675445i
$255$		0			0
$256$	−4.42156	−	7.65837i	−0.276348	−	0.478648i
$257$	20.5056	+	11.8389i	1.27910	+	0.738491i	0.976684	−	0.214683i	$-0.0688719\pi$
$257$	20.5056	+	11.8389i	1.27910	+	0.738491i	0.302421	+	0.953174i	$0.402205\pi$
$258$			2.80952i			0.174913i
$259$	12.8137	−	1.48771i	0.796204	−	0.0924417i
$260$		0			0
$261$	0.287507	−	0.497977i	0.0177962	−	0.0308240i
$262$	−5.48543	+	3.16701i	−0.338891	+	0.195659i
$263$	16.2561	−	9.38548i	1.00240	−	0.578733i	0.0934393	−	0.995625i	$-0.470214\pi$
$263$	16.2561	−	9.38548i	1.00240	−	0.578733i	0.908956	+	0.416892i	$0.136881\pi$
$264$	−6.85122	−	11.8667i	−0.421664	−	0.730343i
$265$		0			0
$266$	−0.786695	−	1.36260i	−0.0482354	−	0.0835461i
$267$		−	34.6804i		−	2.12241i
$268$	−2.19117	−	1.26507i	−0.133847	−	0.0772766i
$269$	−2.86020			−0.174389			−0.0871947	−	0.996191i	$-0.527790\pi$
$269$	−2.86020			−0.174389			−0.0871947	+	0.996191i	$0.527790\pi$
$270$		0			0
$271$	11.3218	−	19.6099i	0.687750	−	1.19122i	−0.284814	−	0.958583i	$-0.591932\pi$
$271$	11.3218	−	19.6099i	0.687750	−	1.19122i	0.972564	−	0.232635i	$-0.0747349\pi$
$272$	−8.45508	+	4.88154i	−0.512665	+	0.295987i
$273$			7.22501i			0.437277i
$274$	−0.857732	+	1.48564i	−0.0518175	+	0.0897506i
$275$		0			0
$276$	2.53542	−	4.39148i	0.152615	−	0.264336i
$277$	0.142361	−	0.0821921i	0.00855364	−	0.00493844i	−0.495717	−	0.868484i	$-0.665095\pi$
$277$	0.142361	−	0.0821921i	0.00855364	−	0.00493844i	0.504271	+	0.863546i	$0.331761\pi$
$278$	5.62259	−	3.24620i	0.337220	−	0.194694i
$279$	−4.38577	+	7.59637i	−0.262569	+	0.454783i
$280$		0			0
$281$	−12.2966	+	21.2983i	−0.733554	+	1.27055i	0.221801	+	0.975092i	$0.428807\pi$
$281$	−12.2966	+	21.2983i	−0.733554	+	1.27055i	−0.955355	+	0.295461i	$0.904527\pi$
$282$		−	0.198468i		−	0.0118186i
$283$	18.0290	−	10.4090i	1.07171	−	0.618752i	0.143062	−	0.989714i	$-0.454305\pi$
$283$	18.0290	−	10.4090i	1.07171	−	0.618752i	0.928648	+	0.370962i	$0.120972\pi$
$284$	−0.559035	+	0.968277i	−0.0331726	+	0.0574567i
$285$		0			0
$286$	2.81279			0.166324
$287$	13.3646	+	7.71605i	0.788887	+	0.455464i
$288$		−	4.36374i		−	0.257136i
$289$	−4.45316	−	7.71309i	−0.261950	−	0.453711i
$290$		0			0
$291$	19.1735	+	33.2095i	1.12397	+	1.94678i
$292$	−17.8108	+	10.2831i	−1.04230	+	0.601771i
$293$	−10.1004	+	5.83149i	−0.590074	+	0.340679i	−0.765127	−	0.643880i	$-0.777324\pi$
$293$	−10.1004	+	5.83149i	−0.590074	+	0.340679i	0.175053	+	0.984559i	$0.443990\pi$
$294$	−0.800461	+	1.38644i	−0.0466838	+	0.0808587i
$295$		0			0
$296$	2.92314	−	6.76229i	0.169904	−	0.393050i
$297$		−	19.7827i		−	1.14791i
$298$	−1.31060	−	0.756674i	−0.0759209	−	0.0438330i
$299$	1.06724	+	1.84852i	0.0617201	+	0.106902i
$300$		0			0
$301$	−4.65697	−	8.06611i	−0.268423	−	0.464923i
$302$		−	7.35196i		−	0.423058i
$303$	15.7022	−	9.06569i	0.902070	−	0.520810i
$304$	8.20651			0.470676
$305$		0			0
$306$	−1.10458			−0.0631444
$307$		−	13.5798i		−	0.775039i	−0.921861	−	0.387520i	$-0.873332\pi$
$307$		−	13.5798i		−	0.775039i	0.921861	−	0.387520i	$-0.126668\pi$
$308$	19.1848	+	11.0764i	1.09316	+	0.631134i
$309$	5.53138	+	9.58063i	0.314669	+	0.545023i
$310$		0			0
$311$	1.32600	−	2.29670i	0.0751907	−	0.130234i	−0.825978	−	0.563702i	$-0.809377\pi$
$311$	1.32600	−	2.29670i	0.0751907	−	0.130234i	0.901169	+	0.433468i	$0.142710\pi$
$312$	3.57339	+	2.06310i	0.202303	+	0.116800i
$313$	−0.514255	−	0.296906i	−0.0290674	−	0.0167821i	0.485396	−	0.874294i	$-0.338675\pi$
$313$	−0.514255	−	0.296906i	−0.0290674	−	0.0167821i	−0.514463	+	0.857512i	$0.672009\pi$
$314$	3.26957	+	5.66307i	0.184513	+	0.319585i
$315$		0			0
$316$	−2.70268	+	4.68118i	−0.152038	+	0.263337i
$317$	5.86825	+	3.38803i	0.329594	+	0.190291i	0.655661	−	0.755056i	$-0.272390\pi$
$317$	5.86825	+	3.38803i	0.329594	+	0.190291i	−0.326067	+	0.945347i	$0.605724\pi$
$318$	−6.65626	−	3.84299i	−0.373265	−	0.215504i
$319$	2.52118			0.141159
$320$		0			0
$321$	2.94227	−	5.09616i	0.164221	−	0.284440i
$322$		−	0.849953i		−	0.0473660i
$323$		−	6.80327i		−	0.378544i
$324$	10.6498	−	18.4459i	0.591653	−	1.02477i
$325$		0			0
$326$	−0.808404	−	1.40020i	−0.0447733	−	0.0775497i
$327$			18.0605i			0.998746i
$328$	7.63250	−	4.40663i	0.421434	−	0.243315i
$329$	0.328974	+	0.569800i	0.0181369	+	0.0314141i
$330$		0			0
$331$	1.40790	−	2.43855i	0.0773850	−	0.134035i	−0.824736	−	0.565518i	$-0.808676\pi$
$331$	1.40790	−	2.43855i	0.0773850	−	0.134035i	0.902121	+	0.431483i	$0.142010\pi$
$332$		−	22.5060i		−	1.23518i
$333$	−6.10945	+	4.54101i	−0.334796	+	0.248846i
$334$	3.27983			0.179464
$335$		0			0
$336$	7.50297	+	12.9955i	0.409321	+	0.708964i
$337$	−21.3498	+	12.3263i	−1.16300	+	0.671457i	−0.952020	−	0.306035i	$-0.900998\pi$
$337$	−21.3498	+	12.3263i	−1.16300	+	0.671457i	−0.210976	+	0.977491i	$0.567664\pi$
$338$	2.75936	−	1.59311i	0.150089	−	0.0866540i
$339$	32.5054			1.76545
$340$		0			0
$341$	−38.4593			−2.08269
$342$	0.804077	+	0.464234i	0.0434795	+	0.0251029i
$343$		−	20.1522i		−	1.08812i
$344$	−5.31918			−0.286791
$345$		0			0
$346$	−2.10021	−	3.63767i	−0.112908	−	0.195562i
$347$			8.80294i			0.472566i	0.971684	+	0.236283i	$0.0759293\pi$
$347$			8.80294i			0.472566i	−0.971684	+	0.236283i	$0.924071\pi$
$348$	1.56198	+	0.901808i	0.0837308	+	0.0483420i
$349$	−1.42867	+	2.47454i	−0.0764752	+	0.132459i	−0.901727	−	0.432306i	$-0.857700\pi$
$349$	−1.42867	+	2.47454i	−0.0764752	+	0.132459i	0.825252	+	0.564765i	$0.191033\pi$
$350$		0			0
$351$	2.97856	+	5.15902i	0.158984	+	0.275368i
$352$	16.5697	−	9.56654i	0.883170	−	0.509898i
$353$	−10.7525	−	6.20795i	−0.572297	−	0.330416i	0.185769	−	0.982593i	$-0.440522\pi$
$353$	−10.7525	−	6.20795i	−0.572297	−	0.330416i	−0.758066	+	0.652177i	$0.773856\pi$
$354$	2.65443	−	4.59761i	0.141082	−	0.244360i
$355$		0			0
$356$	32.0202			1.69707
$357$	10.7734	−	6.22003i	0.570189	−	0.329199i
$358$	−3.98010	−	2.29791i	−0.210355	−	0.121448i
$359$	−21.7819			−1.14961			−0.574803	−	0.818292i	$-0.694921\pi$
$359$	−21.7819			−1.14961			−0.574803	+	0.818292i	$0.694921\pi$
$360$		0			0
$361$	6.64070	−	11.5020i	0.349511	−	0.605370i
$362$			1.43261i			0.0752964i
$363$	−34.1195	+	19.6989i	−1.79081	+	1.03393i
$364$	−6.67082			−0.349646
$365$		0			0
$366$	−3.26483	−	5.65484i	−0.170655	−	0.295583i
$367$	20.2050	−	11.6653i	1.05469	−	0.608926i	0.130732	−	0.991418i	$-0.458267\pi$
$367$	20.2050	−	11.6653i	1.05469	−	0.608926i	0.923959	+	0.382492i	$0.124934\pi$
$368$	3.83926	+	2.21660i	0.200135	+	0.115548i
$369$	−9.10658			−0.474070
$370$		0			0
$371$	25.4801			1.32286
$372$	−23.8271	−	13.7566i	−1.23538	−	0.713246i
$373$	−25.0981	+	14.4904i	−1.29953	+	0.750283i	−0.980323	−	0.197402i	$-0.936749\pi$
$373$	−25.0981	+	14.4904i	−1.29953	+	0.750283i	−0.319206	+	0.947685i	$0.603416\pi$
$374$	−2.42154	−	4.19423i	−0.125215	−	0.216878i
$375$		0			0
$376$	0.375754			0.0193780
$377$	−0.657487	+	0.379600i	−0.0338623	+	0.0195504i
$378$		−	2.37214i		−	0.122009i
$379$	−8.18583	+	14.1783i	−0.420478	+	0.728289i	−0.995986	−	0.0895072i	$-0.971471\pi$
$379$	−8.18583	+	14.1783i	−0.420478	+	0.728289i	0.575509	+	0.817796i	$0.304804\pi$
$380$		0			0
$381$	8.26102			0.423225
$382$	3.13736	+	1.81136i	0.160521	+	0.0926770i
$383$	3.47188	−	2.00449i	0.177405	−	0.102425i	−0.408668	−	0.912683i	$-0.634007\pi$
$383$	3.47188	−	2.00449i	0.177405	−	0.102425i	0.586073	+	0.810258i	$0.300673\pi$
$384$	18.0781			0.922544
$385$		0			0
$386$	2.36134	−	4.08996i	0.120189	−	0.208174i
$387$	4.75986	+	2.74811i	0.241958	+	0.139694i
$388$	−30.6622	+	17.7028i	−1.55664	+	0.898725i
$389$	−9.11602	−	15.7894i	−0.462200	−	0.800555i	0.536870	−	0.843665i	$-0.319607\pi$
$389$	−9.11602	−	15.7894i	−0.462200	−	0.800555i	−0.999070	+	0.0431105i	$0.986273\pi$
$390$		0			0
$391$	1.83758	−	3.18278i	0.0929305	−	0.160960i
$392$	−2.62491	−	1.51549i	−0.132578	−	0.0765438i
$393$			42.0956i			2.12344i
$394$	1.65790	+	2.87156i	0.0835237	+	0.144667i
$395$		0			0
$396$	−13.0725			−0.656917
$397$			25.9749i			1.30364i	0.758372	+	0.651822i	$0.225995\pi$
$397$			25.9749i			1.30364i	−0.758372	+	0.651822i	$0.774005\pi$
$398$	−1.06167	−	0.612954i	−0.0532166	−	0.0307246i
$399$	−10.4567			−0.523489
$400$		0			0
$401$	−16.7311			−0.835510			−0.417755	−	0.908560i	$-0.637183\pi$
$401$	−16.7311			−0.835510			−0.417755	+	0.908560i	$0.637183\pi$
$402$	0.736286	−	0.425095i	0.0367226	−	0.0212018i
$403$	10.0296	−	5.79059i	0.499610	−	0.288450i
$404$	8.37031	+	14.4978i	0.416439	+	0.721293i
$405$		0			0
$406$	0.302314			0.0150036
$407$	−30.6365	−	13.2433i	−1.51859	−	0.656444i
$408$		−	7.10450i		−	0.351725i
$409$	0.181239	−	0.313915i	0.00896170	−	0.0155221i	−0.861510	−	0.507741i	$-0.830481\pi$
$409$	0.181239	−	0.313915i	0.00896170	−	0.0155221i	0.870471	+	0.492219i	$0.163814\pi$
$410$		0			0
$411$	5.70045	+	9.87347i	0.281183	+	0.487022i
$412$	−8.84575	+	5.10710i	−0.435799	+	0.251609i
$413$			17.5996i			0.866021i
$414$	0.250782	+	0.434366i	0.0123252	+	0.0213479i
$415$		0			0
$416$	−2.88076	+	4.98962i	−0.141241	+	0.244636i
$417$		−	43.1482i		−	2.11298i
$418$			4.07092i			0.199115i
$419$	8.20109	−	14.2047i	0.400649	−	0.693945i	−0.593155	−	0.805088i	$-0.702118\pi$
$419$	8.20109	−	14.2047i	0.400649	−	0.693945i	0.993804	+	0.111143i	$0.0354512\pi$
$420$		0			0
$421$	−5.36363			−0.261407			−0.130704	−	0.991421i	$-0.541724\pi$
$421$	−5.36363			−0.261407			−0.130704	+	0.991421i	$0.541724\pi$
$422$	−2.25954	−	1.30455i	−0.109993	−	0.0635043i
$423$	−0.336243	−	0.194130i	−0.0163487	−	0.00943892i
$424$	7.27584	−	12.6021i	0.353346	−	0.612013i
$425$		0			0
$426$	−0.187849	−	0.325364i	−0.00910132	−	0.0157639i
$427$	18.7466	+	10.8234i	0.907212	+	0.523779i
$428$	4.70526	+	2.71658i	0.227437	+	0.131311i
$429$	9.34684	−	16.1892i	0.451270	−	0.781622i
$430$		0			0
$431$	−20.0498	−	34.7272i	−0.965763	−	1.67275i	−0.707551	−	0.706662i	$-0.750200\pi$
$431$	−20.0498	−	34.7272i	−0.965763	−	1.67275i	−0.258212	−	0.966088i	$-0.583133\pi$
$432$	10.7150	+	6.18631i	0.515526	+	0.297639i
$433$		−	8.94867i		−	0.430046i	−0.976609	−	0.215023i	$-0.931017\pi$
$433$		−	8.94867i		−	0.430046i	0.976609	−	0.215023i	$-0.0689826\pi$
$434$	−4.61164			−0.221366
$435$		0			0
$436$	−16.6751			−0.798594
$437$	−2.67534	+	1.54461i	−0.127979	+	0.0738885i
$438$		−	6.91071i		−	0.330207i
$439$	−11.9458	−	20.6906i	−0.570140	−	0.987511i	−0.996551	−	0.0829815i	$-0.973556\pi$
$439$	−11.9458	−	20.6906i	−0.570140	−	0.987511i	0.426411	−	0.904529i	$-0.359778\pi$
$440$		0			0
$441$	1.56593	+	2.71227i	0.0745681	+	0.129156i
$442$	1.26300	+	0.729194i	0.0600748	+	0.0346842i
$443$			40.0576i			1.90320i	0.307346	+	0.951598i	$0.400559\pi$
$443$			40.0576i			1.90320i	−0.307346	+	0.951598i	$0.599441\pi$
$444$	−14.2436	−	19.1632i	−0.675969	−	0.909445i
$445$		0			0
$446$	−2.55469	+	4.42486i	−0.120968	+	0.209523i
$447$	−8.71018	+	5.02882i	−0.411977	+	0.237855i
$448$	−10.6185	+	6.13059i	−0.501677	+	0.289643i
$449$	−3.83167	−	6.63665i	−0.180828	−	0.313203i	0.761335	−	0.648359i	$-0.224544\pi$
$449$	−3.83167	−	6.63665i	−0.180828	−	0.313203i	−0.942163	+	0.335156i	$0.891211\pi$
$450$		0			0
$451$	−19.9642	−	34.5790i	−0.940076	−	1.62826i
$452$			30.0121i			1.41165i
$453$	−42.3147	−	24.4304i	−1.98812	−	1.14784i
$454$	4.21393			0.197770
$455$		0			0
$456$	−2.98590	+	5.17173i	−0.139828	+	0.242188i
$457$	29.3676	−	16.9554i	1.37376	−	0.793141i	0.382361	−	0.924013i	$-0.375111\pi$
$457$	29.3676	−	16.9554i	1.37376	−	0.793141i	0.991399	+	0.130872i	$0.0417778\pi$
$458$			6.76398i			0.316060i
$459$	5.12851	−	8.88283i	0.239378	−	0.414615i
$460$		0			0
$461$	−7.29012	+	12.6269i	−0.339535	+	0.588091i	−0.984345	−	0.176251i	$-0.943603\pi$
$461$	−7.29012	+	12.6269i	−0.339535	+	0.588091i	0.644811	+	0.764342i	$0.276936\pi$
$462$	−6.44656	+	3.72192i	−0.299921	+	0.173160i
$463$	−3.45413	+	1.99424i	−0.160527	+	0.0926802i	−0.578111	−	0.815958i	$-0.696210\pi$
$463$	−3.45413	+	1.99424i	−0.160527	+	0.0926802i	0.417585	+	0.908638i	$0.362877\pi$
$464$	−0.788408	+	1.36556i	−0.0366009	+	0.0633947i
$465$		0			0
$466$	−2.05132	+	3.55299i	−0.0950256	+	0.164589i
$467$			14.7664i			0.683307i	0.939826	+	0.341653i	$0.110987\pi$
$467$			14.7664i			0.683307i	−0.939826	+	0.341653i	$0.889013\pi$
$468$	3.40910	−	1.96825i	0.157586	−	0.0909822i
$469$	−1.40925	+	2.44089i	−0.0650730	+	0.112710i
$470$		0			0
$471$	43.4589			2.00248
$472$	8.70454	+	5.02557i	0.400659	+	0.231320i
$473$			24.0985i			1.10805i
$474$	−0.908166	−	1.57299i	−0.0417134	−	0.0722498i
$475$		0			0
$476$	5.74292	+	9.94703i	0.263226	+	0.455922i
$477$	−13.0216	+	7.51800i	−0.596216	+	0.344226i
$478$	−3.25006	+	1.87642i	−0.148654	+	0.0858256i
$479$	7.80662	−	13.5215i	0.356693	−	0.617811i	−0.630713	−	0.776016i	$-0.717237\pi$
$479$	7.80662	−	13.5215i	0.356693	−	0.617811i	0.987406	+	0.158205i	$0.0505707\pi$
$480$		0			0
$481$	9.98349	−	1.15911i	0.455208	−	0.0528511i
$482$		−	4.56048i		−	0.207724i
$483$	−4.89196	−	2.82438i	−0.222592	−	0.128514i
$484$	−18.1879	−	31.5024i	−0.826724	−	1.43193i
$485$		0			0
$486$	1.90074	+	3.29217i	0.0862192	+	0.149336i
$487$			35.6982i			1.61764i	0.588056	+	0.808820i	$0.299893\pi$
$487$			35.6982i			1.61764i	−0.588056	+	0.808820i	$0.700107\pi$
$488$	10.7062	−	6.18121i	0.484645	−	0.279810i
$489$	−10.7452			−0.485916
$490$		0			0
$491$	−0.411627			−0.0185765			−0.00928823	−	0.999957i	$-0.502957\pi$
$491$	−0.411627			−0.0185765			−0.00928823	+	0.999957i	$0.502957\pi$
$492$		−	28.5641i		−	1.28777i
$493$	1.13206	+	0.653597i	0.0509856	+	0.0294365i
$494$	−0.612935	−	1.06163i	−0.0275773	−	0.0477652i
$495$		0			0
$496$	12.0267	−	20.8309i	0.540017	−	0.935336i
$497$	1.07863	+	0.622746i	0.0483831	+	0.0279340i
$498$	6.54937	+	3.78128i	0.293484	+	0.169443i
$499$	19.0374	+	32.9738i	0.852232	+	1.47611i	0.879190	+	0.476472i	$0.158085\pi$
$499$	19.0374	+	32.9738i	0.852232	+	1.47611i	−0.0269579	+	0.999637i	$0.508582\pi$
$500$		0			0
$501$	10.8988	−	18.8773i	0.486922	−	0.843374i
$502$	7.38487	+	4.26366i	0.329603	+	0.190296i
$503$	−13.4292	−	7.75338i	−0.598780	−	0.345706i	0.169781	−	0.985482i	$-0.445694\pi$
$503$	−13.4292	−	7.75338i	−0.598780	−	0.345706i	−0.768562	+	0.639776i	$0.779027\pi$
$504$	−3.21429			−0.143176
$505$		0			0
$506$	−1.09957	+	1.90451i	−0.0488817	+	0.0846656i
$507$		−	21.1755i		−	0.940439i
$508$			7.62736i			0.338409i
$509$	2.99718	−	5.19127i	0.132848	−	0.230099i	−0.791926	−	0.610618i	$-0.790921\pi$
$509$	2.99718	−	5.19127i	0.132848	−	0.230099i	0.924773	+	0.380519i	$0.124255\pi$
$510$		0			0
$511$	11.4550	+	19.8406i	0.506739	+	0.877698i
$512$			20.2789i			0.896210i
$513$	−7.46660	+	4.31084i	−0.329658	+	0.190328i
$514$	−3.67302	−	6.36185i	−0.162010	−	0.280609i
$515$		0			0
$516$	−8.61985	+	14.9300i	−0.379468	+	0.657257i
$517$		−	1.70235i		−	0.0748692i
$518$	−3.67361	−	1.58800i	−0.161409	−	0.0697725i
$519$	−27.9158			−1.22537
$520$		0			0
$521$	−8.46908	−	14.6689i	−0.371037	−	0.642655i	0.618688	−	0.785637i	$-0.287664\pi$
$521$	−8.46908	−	14.6689i	−0.371037	−	0.642655i	−0.989725	+	0.142982i	$0.954331\pi$
$522$	−0.154497	+	0.0891989i	−0.00676215	+	0.00390413i
$523$	2.97961	−	1.72028i	0.130289	−	0.0752226i	−0.433439	−	0.901183i	$-0.642700\pi$
$523$	2.97961	−	1.72028i	0.130289	−	0.0752226i	0.563728	+	0.825960i	$0.309367\pi$
$524$	−38.8667			−1.69790
$525$		0			0
$526$	−5.82368			−0.253924
$527$	−17.2690	−	9.97027i	−0.752250	−	0.434312i
$528$		−	38.8257i		−	1.68967i
$529$	21.3312			0.927443
$530$		0			0
$531$	−5.19283	−	8.99425i	−0.225350	−	0.390317i
$532$		−	9.65460i		−	0.418580i
$533$	10.4127	+	6.01178i	0.451025	+	0.260399i
$534$	−5.37978	+	9.31806i	−0.232806	+	0.403232i
$535$		0			0
$536$	0.804820	+	1.39399i	0.0347629	+	0.0602112i
$537$	−26.4515	+	15.2718i	−1.14147	+	0.659027i
$538$	0.768489	+	0.443687i	0.0331319	+	0.0191287i
$539$	−6.86592	+	11.8921i	−0.295736	+	0.512230i
$540$		0			0
$541$	26.7548			1.15028			0.575140	−	0.818055i	$-0.304948\pi$
$541$	26.7548			1.15028			0.575140	+	0.818055i	$0.304948\pi$
$542$	−6.08397	+	3.51258i	−0.261329	+	0.150878i
$543$	8.24549	+	4.76054i	0.353848	+	0.204294i
$544$	9.92020			0.425325
$545$		0			0
$546$	1.12078	−	1.94124i	0.0479648	−	0.0830775i
$547$			10.5797i			0.452357i	0.974086	+	0.226178i	$0.0726233\pi$
$547$			10.5797i			0.452357i	−0.974086	+	0.226178i	$0.927377\pi$
$548$	−9.11613	+	5.26320i	−0.389422	+	0.224833i
$549$	−12.7739			−0.545175
$550$		0			0
$551$	−0.549391	−	0.951573i	−0.0234048	−	0.0405384i
$552$	−2.79379	+	1.61300i	−0.118912	+	0.0686537i
$553$	5.21468	+	3.01070i	0.221751	+	0.128028i
$554$	−0.0510001			−0.00216679
$555$		0			0
$556$	39.8385			1.68953
$557$	36.3993	+	21.0151i	1.54229	+	0.890440i	0.998694	+	0.0510917i	$0.0162701\pi$
$557$	36.3993	+	21.0151i	1.54229	+	0.890440i	0.543594	+	0.839349i	$0.317063\pi$
$558$	2.35677	−	1.36068i	0.0997699	−	0.0576022i
$559$	−3.62837	−	6.28452i	−0.153464	−	0.265807i
$560$		0			0
$561$	−32.1869			−1.35893
$562$	6.60780	−	3.81501i	0.278733	−	0.160927i
$563$		−	15.1171i		−	0.637108i	−0.947905	−	0.318554i	$-0.896803\pi$
$563$		−	15.1171i		−	0.637108i	0.947905	−	0.318554i	$-0.103197\pi$
$564$	0.608917	−	1.05467i	0.0256400	−	0.0444098i
$565$		0			0
$566$	−6.45878			−0.271483
$567$	−20.5481	−	11.8635i	−0.862941	−	0.498219i
$568$	0.616003	−	0.355650i	0.0258469	−	0.0149227i
$569$	−29.9574			−1.25588			−0.627940	−	0.778262i	$-0.716102\pi$
$569$	−29.9574			−1.25588			−0.627940	+	0.778262i	$0.716102\pi$
$570$		0			0
$571$	−15.6228	+	27.0594i	−0.653792	+	1.13240i	0.328403	+	0.944538i	$0.393490\pi$
$571$	−15.6228	+	27.0594i	−0.653792	+	1.13240i	−0.982195	+	0.187863i	$0.939844\pi$
$572$	14.9474	+	8.62990i	0.624983	+	0.360834i
$573$	20.8507	−	12.0382i	0.871053	−	0.502902i
$574$	−2.39390	−	4.14635i	−0.0999194	−	0.173065i
$575$		0			0
$576$	3.61770	−	6.26605i	0.150738	−	0.261085i
$577$	−24.8994	−	14.3757i	−1.03658	−	0.598467i	−0.117714	−	0.993048i	$-0.537557\pi$
$577$	−24.8994	−	14.3757i	−1.03658	−	0.598467i	−0.918861	+	0.394581i	$0.870890\pi$
$578$			2.76318i			0.114933i
$579$	−15.6934	−	27.1817i	−0.652194	−	1.12963i
$580$		0			0
$581$	−25.0710			−1.04012
$582$		−	11.8971i		−	0.493153i
$583$	−57.0938	−	32.9631i	−2.36458	−	1.36519i
$584$	13.0839			0.541414
$585$		0			0
$586$	3.61843			0.149476
$587$	−12.2259	+	7.05861i	−0.504616	+	0.291340i	−0.730618	−	0.682787i	$-0.760768\pi$
$587$	−12.2259	+	7.05861i	−0.504616	+	0.291340i	0.226002	+	0.974127i	$0.427434\pi$
$588$	−8.50744	+	4.91177i	−0.350841	+	0.202558i
$589$	8.38066	+	14.5157i	0.345319	+	0.598110i
$590$		0			0
$591$	22.0366			0.906466
$592$	16.7535	−	12.4525i	0.688563	−	0.511793i
$593$			5.88296i			0.241584i	0.992678	+	0.120792i	$0.0385434\pi$
$593$			5.88296i			0.241584i	−0.992678	+	0.120792i	$0.961457\pi$
$594$	−3.06878	+	5.31529i	−0.125914	+	0.218089i
$595$		0			0
$596$	−4.64309	−	8.04207i	−0.190188	−	0.329416i
$597$	−7.05580	+	4.07367i	−0.288775	+	0.166724i
$598$		−	0.662221i		−	0.0270802i
$599$	7.85750	+	13.6096i	0.321049	+	0.556073i	0.980705	−	0.195495i	$-0.0626313\pi$
$599$	7.85750	+	13.6096i	0.321049	+	0.556073i	−0.659656	+	0.751568i	$0.729298\pi$
$600$		0			0
$601$	−7.77357	+	13.4642i	−0.317090	+	0.549217i	−0.979880	−	0.199589i	$-0.936039\pi$
$601$	−7.77357	+	13.4642i	−0.317090	+	0.549217i	0.662789	+	0.748806i	$0.269373\pi$
$602$			2.88964i			0.117773i
$603$		−	1.66321i		−	0.0677313i
$604$	22.5565	−	39.0690i	0.917810	−	1.58969i
$605$		0			0
$606$	−5.62525			−0.228510
$607$	−18.9989	−	10.9690i	−0.771141	−	0.445219i	0.0621402	−	0.998067i	$-0.480207\pi$
$607$	−18.9989	−	10.9690i	−0.771141	−	0.445219i	−0.833282	+	0.552849i	$0.813541\pi$
$608$	−7.22142	−	4.16929i	−0.292867	−	0.169087i
$609$	1.00458	−	1.73999i	0.0407078	−	0.0705080i
$610$		0			0
$611$	0.256313	+	0.443946i	0.0103693	+	0.0179602i
$612$	−5.86981	−	3.38894i	−0.237273	−	0.136990i
$613$	24.6605	+	14.2377i	0.996027	+	0.575057i	0.907070	−	0.420979i	$-0.138313\pi$
$613$	24.6605	+	14.2377i	0.996027	+	0.575057i	0.0889567	+	0.996035i	$0.471647\pi$
$614$	−2.10656	+	3.64867i	−0.0850138	+	0.147248i
$615$		0			0
$616$	−7.04662	−	12.2051i	−0.283916	−	0.491757i
$617$	30.8078	+	17.7869i	1.24027	+	0.716072i	0.969150	−	0.246472i	$-0.0792714\pi$
$617$	30.8078	+	17.7869i	1.24027	+	0.716072i	0.271124	+	0.962545i	$0.412605\pi$
$618$		−	3.43221i		−	0.138064i
$619$	9.30332			0.373932			0.186966	−	0.982366i	$-0.440135\pi$
$619$	9.30332			0.373932			0.186966	+	0.982366i	$0.440135\pi$
$620$		0			0
$621$	−4.65748			−0.186898
$622$	−0.712551	+	0.411391i	−0.0285707	+	0.0164953i
$623$		−	35.6695i		−	1.42907i
$624$	5.84577	+	10.1252i	0.234018	+	0.405331i
$625$		0			0
$626$	0.0921147	+	0.159547i	0.00368164	+	0.00637680i
$627$	23.4305	+	13.5276i	0.935723	+	0.540240i
$628$			40.1254i			1.60118i
$629$	−10.3232	−	13.8888i	−0.411613	−	0.553782i
$630$		0			0
$631$	−11.6294	+	20.1428i	−0.462961	+	0.801872i	−0.999107	−	0.0422534i	$-0.986546\pi$
$631$	−11.6294	+	20.1428i	−0.462961	+	0.801872i	0.536146	+	0.844125i	$0.319880\pi$
$632$	2.97810	−	1.71941i	0.118462	−	0.0683943i
$633$	−15.0168	+	8.66995i	−0.596864	+	0.344600i
$634$	−1.05114	−	1.82062i	−0.0417459	−	0.0723060i
$635$		0			0
$636$	−23.5813	−	40.8440i	−0.935060	−	1.61957i
$637$		−	4.13504i		−	0.163836i
$638$	−0.677401	−	0.391098i	−0.0268186	−	0.0154837i
$639$	−0.734973			−0.0290751
$640$		0			0
$641$	4.09344	−	7.09004i	0.161681	−	0.280040i	−0.773791	−	0.633441i	$-0.781642\pi$
$641$	4.09344	−	7.09004i	0.161681	−	0.280040i	0.935472	+	0.353402i	$0.114975\pi$
$642$	−1.58108	+	0.912837i	−0.0624003	+	0.0360268i
$643$		−	11.4564i		−	0.451796i	−0.974151	−	0.225898i	$-0.927468\pi$
$643$		−	11.4564i		−	0.451796i	0.974151	−	0.225898i	$-0.0725316\pi$
$644$	2.60773	−	4.51672i	0.102759	−	0.177984i
$645$		0			0
$646$	−1.05535	+	1.82793i	−0.0415224	+	0.0719189i
$647$	13.7897	−	7.96151i	0.542130	−	0.312999i	−0.203812	−	0.979010i	$-0.565333\pi$
$647$	13.7897	−	7.96151i	0.542130	−	0.312999i	0.745942	+	0.666011i	$0.232000\pi$
$648$	−11.7350	+	6.77522i	−0.460995	+	0.266156i
$649$	22.7683	−	39.4358i	0.893733	−	1.54799i
$650$		0			0
$651$	−15.3244	+	26.5426i	−0.600610	+	1.04029i
$652$		−	9.92102i		−	0.388537i
$653$	18.1677	−	10.4891i	0.710957	−	0.410471i	−0.100458	−	0.994941i	$-0.532031\pi$
$653$	18.1677	−	10.4891i	0.710957	−	0.410471i	0.811415	+	0.584470i	$0.198698\pi$
$654$	2.80162	−	4.85255i	0.109552	−	0.189750i
$655$		0			0
$656$	24.9723			0.975003
$657$	−11.7081	−	6.75967i	−0.456776	−	0.263720i
$658$		−	0.204128i		−	0.00795774i
$659$	−0.598998	−	1.03749i	−0.0233336	−	0.0404151i	0.854123	−	0.520071i	$-0.174095\pi$
$659$	−0.598998	−	1.03749i	−0.0233336	−	0.0404151i	−0.877456	+	0.479656i	$0.840761\pi$
$660$		0			0
$661$	16.1732	+	28.0129i	0.629066	+	1.08957i	0.987740	+	0.156111i	$0.0498958\pi$
$661$	16.1732	+	28.0129i	0.629066	+	1.08957i	−0.358674	+	0.933463i	$0.616771\pi$
$662$	−0.756558	+	0.436799i	−0.0294045	+	0.0169767i
$663$	8.39385	−	4.84619i	0.325990	−	0.188210i
$664$	−7.15900	+	12.3997i	−0.277823	+	0.481204i
$665$		0			0
$666$	2.34593	−	0.272370i	0.0909031	−	0.0105541i
$667$		−	0.593568i		−	0.0229830i
$668$	17.4293	+	10.0628i	0.674359	+	0.389341i
$669$	16.9784	+	29.4074i	0.656422	+	1.13696i
$670$		0			0
$671$	−28.0039	−	48.5042i	−1.08108	−	1.87248i
$672$		−	15.2474i		−	0.588182i
$673$	32.1264	−	18.5482i	1.23838	−	0.714981i	0.269620	−	0.962967i	$-0.413102\pi$
$673$	32.1264	−	18.5482i	1.23838	−	0.714981i	0.968764	+	0.247986i	$0.0797687\pi$
$674$	7.64845			0.294607
$675$		0			0
$676$	19.5513			0.751972
$677$			6.39266i			0.245690i	0.992426	+	0.122845i	$0.0392018\pi$
$677$			6.39266i			0.245690i	−0.992426	+	0.122845i	$0.960798\pi$
$678$	−8.73368	−	5.04239i	−0.335415	−	0.193652i
$679$	19.7204	+	34.1567i	0.756798	+	1.31081i
$680$		0			0
$681$	14.0028	−	24.2536i	0.536589	−	0.929399i
$682$	10.3334	+	5.96599i	0.395686	+	0.228449i
$683$	13.1246	+	7.57751i	0.502200	+	0.289945i	0.729622	−	0.683851i	$-0.239696\pi$
$683$	13.1246	+	7.57751i	0.502200	+	0.289945i	−0.227421	+	0.973796i	$0.573030\pi$
$684$	2.84862	+	4.93396i	0.108920	+	0.188655i
$685$		0			0
$686$	−3.12611	+	5.41458i	−0.119355	+	0.206730i
$687$	38.9306	+	22.4766i	1.48529	+	0.857534i
$688$	−13.0526	−	7.53592i	−0.497626	−	0.287304i
$689$	19.8523			0.756311
$690$		0			0
$691$	−19.1544	+	33.1764i	−0.728668	+	1.26209i	0.228779	+	0.973478i	$0.426527\pi$
$691$	−19.1544	+	33.1764i	−0.728668	+	1.26209i	−0.957447	+	0.288611i	$0.906807\pi$
$692$		−	25.7745i		−	0.979800i
$693$			14.5623i			0.553176i
$694$	1.36555	−	2.36521i	0.0518357	−	0.0897820i
$695$		0			0
$696$	−0.573717	−	0.993707i	−0.0217467	−	0.0376664i
$697$		−	20.7022i		−	0.784153i
$698$	0.767723	−	0.443245i	0.0290587	−	0.0167771i
$699$	13.6330	+	23.6130i	0.515647	+	0.893126i
$700$		0			0
$701$	−7.37527	+	12.7743i	−0.278560	+	0.482480i	−0.971027	−	0.238969i	$-0.923191\pi$
$701$	−7.37527	+	12.7743i	−0.278560	+	0.482480i	0.692467	+	0.721450i	$0.256524\pi$
$702$		−	1.84819i		−	0.0697556i
$703$	1.67757	+	14.4490i	0.0632709	+	0.544954i
$704$	31.7241			1.19565
$705$		0			0
$706$	1.92601	+	3.33595i	0.0724865	+	0.125550i
$707$	16.1501	−	9.32424i	0.607386	−	0.350674i
$708$	28.2118	−	16.2881i	1.06026	−	0.612143i
$709$	15.3282			0.575664			0.287832	−	0.957681i	$-0.407065\pi$
$709$	15.3282			0.575664			0.287832	+	0.957681i	$0.407065\pi$
$710$		0			0
$711$	−3.55327			−0.133258
$712$	−17.6416	−	10.1854i	−0.661148	−	0.381714i
$713$			9.05456i			0.339096i
$714$	−3.85952			−0.144439
$715$		0			0
$716$	−14.1004	−	24.4226i	−0.526956	−	0.912715i
$717$			24.9412i			0.931448i
$718$	5.85245	+	3.37891i	0.218411	+	0.126100i
$719$	−2.50682	+	4.34194i	−0.0934885	+	0.161927i	−0.908977	−	0.416847i	$-0.863135\pi$
$719$	−2.50682	+	4.34194i	−0.0934885	+	0.161927i	0.815488	+	0.578774i	$0.196469\pi$
$720$		0			0
$721$	5.68913	+	9.85387i	0.211874	+	0.366977i
$722$	−3.56850	+	2.06027i	−0.132806	+	0.0766755i
$723$	−26.2482	−	15.1544i	−0.976180	−	0.563598i
$724$	−4.39538	+	7.61302i	−0.163353	+	0.282936i
$725$		0			0
$726$	12.2232			0.453644
$727$	−26.4687	+	15.2817i	−0.981670	+	0.566767i	−0.902774	−	0.430115i	$-0.858473\pi$
$727$	−26.4687	+	15.2817i	−0.981670	+	0.566767i	−0.0788961	+	0.996883i	$0.525140\pi$
$728$	3.67530	+	2.12194i	0.136216	+	0.0786442i
$729$	−8.30023			−0.307416
$730$		0			0
$731$	−6.24735	+	10.8207i	−0.231066	+	0.400219i
$732$		−	40.0671i		−	1.48092i
$733$	0.111078	−	0.0641308i	0.00410275	−	0.00236872i	−0.497947	−	0.867207i	$-0.665913\pi$
$733$	0.111078	−	0.0641308i	0.00410275	−	0.00236872i	0.502050	+	0.864839i	$0.332579\pi$
$734$	−7.23833			−0.267172
$735$		0			0
$736$	−2.25227	−	3.90105i	−0.0830198	−	0.143794i
$737$	6.31546	−	3.64623i	0.232633	−	0.134311i
$738$	2.44679	+	1.41266i	0.0900676	+	0.0520006i
$739$	−3.03253			−0.111553			−0.0557767	−	0.998443i	$-0.517763\pi$
$739$	−3.03253			−0.111553			−0.0557767	+	0.998443i	$0.517763\pi$
$740$		0			0
$741$	−8.14708			−0.299290
$742$	−6.84610	−	3.95260i	−0.251328	−	0.145104i
$743$	−1.66788	+	0.962952i	−0.0611886	+	0.0353273i	−0.530282	−	0.847821i	$-0.677914\pi$
$743$	−1.66788	+	0.962952i	−0.0611886	+	0.0353273i	0.469094	+	0.883148i	$0.344581\pi$
$744$	8.75174	+	15.1585i	0.320854	+	0.555736i
$745$		0			0
$746$	8.99126			0.329193
$747$	12.8124	−	7.39727i	0.468783	−	0.270652i
$748$		−	29.7180i		−	1.08660i
$749$	3.02618	−	5.24150i	0.110574	−	0.191520i
$750$		0			0
$751$	11.6540			0.425261			0.212630	−	0.977133i	$-0.431797\pi$
$751$	11.6540			0.425261			0.212630	+	0.977133i	$0.431797\pi$
$752$	0.922052	+	0.532347i	0.0336238	+	0.0194127i
$753$	49.0795	−	28.3361i	1.78856	−	1.03262i
$754$	0.235541			0.00857791
$755$		0			0
$756$	7.27792	−	12.6057i	0.264696	−	0.458466i
$757$	−4.01870	−	2.32020i	−0.146062	−	0.0843290i	0.425188	−	0.905105i	$-0.360208\pi$
$757$	−4.01870	−	2.32020i	−0.146062	−	0.0843290i	−0.571250	+	0.820776i	$0.693541\pi$
$758$	4.39880	−	2.53965i	0.159771	−	0.0922441i
$759$	7.30767	+	12.6573i	0.265252	+	0.459429i
$760$		0			0
$761$	−6.38323	+	11.0561i	−0.231392	+	0.400782i	−0.958218	−	0.286039i	$-0.907661\pi$
$761$	−6.38323	+	11.0561i	−0.231392	+	0.400782i	0.726826	+	0.686822i	$0.240995\pi$
$762$	−2.21960	−	1.28149i	−0.0804077	−	0.0464234i
$763$			18.5755i			0.672480i
$764$	11.1148	+	19.2514i	0.402119	+	0.696491i
$765$		0			0
$766$	−1.24379			−0.0449398
$767$			13.7124i			0.495124i
$768$	15.7908	+	9.11684i	0.569802	+	0.328975i
$769$	−37.0113			−1.33466			−0.667330	−	0.744762i	$-0.732563\pi$
$769$	−37.0113			−1.33466			−0.667330	+	0.744762i	$0.732563\pi$
$770$		0			0
$771$	−48.8214			−1.75826
$772$	25.0967	−	14.4896i	0.903251	−	0.521492i
$773$	−37.9535	+	21.9124i	−1.36509	+	0.788136i	−0.990296	−	0.138972i	$-0.955620\pi$
$773$	−37.9535	+	21.9124i	−1.36509	+	0.788136i	−0.374795	+	0.927108i	$0.622287\pi$
$774$	−0.852599	−	1.47674i	−0.0306460	−	0.0530805i
$775$		0			0
$776$	22.5246			0.808584
$777$	−21.3471	+	15.8668i	−0.765824	+	0.569220i
$778$			5.65648i			0.202794i
$779$	−8.70079	+	15.0702i	−0.311738	+	0.539946i
$780$		0			0
$781$	−1.61127	−	2.79080i	−0.0576557	−	0.0998625i
$782$	−0.987456	+	0.570108i	−0.0353114	+	0.0203870i
$783$		−	1.65659i		−	0.0592017i
$784$	−4.29413	−	7.43765i	−0.153362	−	0.265630i
$785$		0			0
$786$	6.53007	−	11.3104i	0.232920	−	0.403429i
$787$		−	19.9883i		−	0.712506i	−0.934389	−	0.356253i	$-0.884054\pi$
$787$		−	19.9883i		−	0.712506i	0.934389	−	0.356253i	$-0.115946\pi$
$788$			20.3463i			0.724808i
$789$	−19.3519	+	33.5186i	−0.688947	+	1.19329i
$790$		0			0
$791$	33.4325			1.18872
$792$	7.20231	+	4.15826i	0.255923	+	0.147757i
$793$	14.6060	+	8.43277i	0.518674	+	0.299456i
$794$	4.02935	−	6.97904i	0.142996	−	0.247677i
$795$		0			0
$796$	−3.76120	−	6.51459i	−0.133312	−	0.230903i
$797$	−35.3441	−	20.4059i	−1.25195	−	0.722814i	−0.280454	−	0.959867i	$-0.590485\pi$
$797$	−35.3441	−	20.4059i	−1.25195	−	0.722814i	−0.971497	+	0.237053i	$0.923818\pi$
$798$	2.80954	+	1.62209i	0.0994566	+	0.0574213i
$799$	0.441320	−	0.764389i	0.0156128	−	0.0270421i
$800$		0			0
$801$	10.5244	+	18.2288i	0.371861	+	0.644083i
$802$	4.49537	+	2.59540i	0.158737	+	0.0916468i
$803$		−	59.2763i		−	2.09182i
$804$	5.21691			0.183986
$805$		0			0
$806$	−3.59305			−0.126560
$807$	5.10734	−	2.94873i	0.179787	−	0.103800i
$808$		−	10.6501i		−	0.374670i
$809$	1.45711	+	2.52378i	0.0512292	+	0.0887315i	0.890503	−	0.454978i	$-0.150353\pi$
$809$	1.45711	+	2.52378i	0.0512292	+	0.0887315i	−0.839274	+	0.543709i	$0.817019\pi$
$810$		0			0
$811$	13.8960	+	24.0686i	0.487956	+	0.845164i	0.999904	−	0.0138524i	$-0.00440949\pi$
$811$	13.8960	+	24.0686i	0.487956	+	0.845164i	−0.511949	+	0.859016i	$0.671076\pi$
$812$	1.60652	+	0.927528i	0.0563780	+	0.0325498i
$813$			46.6889i			1.63745i
$814$	6.17717	+	8.31072i	0.216510	+	0.291291i
$815$		0			0
$816$	10.0653	−	17.4336i	0.352355	−	0.610297i
$817$	9.09552	−	5.25130i	0.318212	−	0.183720i
$818$	−0.0973920	+	0.0562293i	−0.00340523	+	0.00196601i
$819$	−2.19256	−	3.79763i	−0.0766143	−	0.132700i
$820$		0			0
$821$	20.8119	+	36.0473i	0.726342	+	1.25806i	0.958419	+	0.285364i	$0.0921144\pi$
$821$	20.8119	+	36.0473i	0.726342	+	1.25806i	−0.232077	+	0.972697i	$0.574552\pi$
$822$		−	3.53712i		−	0.123371i
$823$	20.4659	+	11.8160i	0.713398	+	0.411880i	0.812318	−	0.583215i	$-0.198206\pi$
$823$	20.4659	+	11.8160i	0.713398	+	0.411880i	−0.0989202	+	0.995095i	$0.531539\pi$
$824$	6.49812			0.226373
$825$		0			0
$826$	2.73014	−	4.72874i	0.0949936	−	0.164534i
$827$	−10.5499	+	6.09101i	−0.366857	+	0.211805i	−0.672085	−	0.740474i	$-0.734601\pi$
$827$	−10.5499	+	6.09101i	−0.366857	+	0.211805i	0.305227	+	0.952279i	$0.401268\pi$
$828$			3.07768i			0.106957i
$829$	−3.01060	+	5.21452i	−0.104563	+	0.181108i	−0.913559	−	0.406705i	$-0.866678\pi$
$829$	−3.01060	+	5.21452i	−0.104563	+	0.181108i	0.808997	+	0.587813i	$0.200011\pi$
$830$		0			0
$831$	−0.169472	+	0.293534i	−0.00587892	+	0.0101826i
$832$	−8.27316	+	4.77651i	−0.286820	+	0.165596i
$833$	−6.16588	+	3.55987i	−0.213635	+	0.123342i
$834$	−6.69335	+	11.5932i	−0.231772	+	0.401441i
$835$		0			0
$836$	−12.4900	+	21.6332i	−0.431974	+	0.748201i
$837$			25.2704i			0.873472i
$838$	−4.40700	+	2.54438i	−0.152237	+	0.0878942i
$839$	−4.03238	+	6.98429i	−0.139213	+	0.241124i	−0.927199	−	0.374569i	$-0.877791\pi$
$839$	−4.03238	+	6.98429i	−0.139213	+	0.241124i	0.787986	+	0.615693i	$0.211124\pi$
$840$		0			0
$841$	−28.7889			−0.992720
$842$	1.44112	+	0.832031i	0.0496643	+	0.0286737i
$843$		−	50.7088i		−	1.74650i
$844$	−8.00493	−	13.8649i	−0.275541	−	0.477251i
$845$		0			0
$846$	0.0602287	+	0.104319i	0.00207070	+	0.00358656i
$847$	−35.0926	+	20.2607i	−1.20580	+	0.696167i
$848$	35.7080	−	20.6160i	1.22622	−	0.707957i
$849$	−21.4624	+	37.1740i	−0.736587	+	1.27581i
$850$		0			0
$851$	−3.11789	+	7.21281i	−0.106880	+	0.247252i
$852$		−	2.30535i		−	0.0789800i
$853$	37.3642	+	21.5722i	1.27933	+	0.738619i	0.976724	−	0.214498i	$-0.0688115\pi$
$853$	37.3642	+	21.5722i	1.27933	+	0.738619i	0.302602	+	0.953117i	$0.402145\pi$
$854$	−3.35794	−	5.81612i	−0.114906	−	0.199024i
$855$		0			0
$856$	−1.72825	−	2.99342i	−0.0590704	−	0.102313i
$857$		−	33.4524i		−	1.14271i	−0.820703	−	0.571356i	$-0.806418\pi$
$857$		−	33.4524i		−	1.14271i	0.820703	−	0.571356i	$-0.193582\pi$
$858$	−5.02269	+	2.89985i	−0.171472	+	0.0989993i
$859$	−7.52085			−0.256608			−0.128304	−	0.991735i	$-0.540953\pi$
$859$	−7.52085			−0.256608			−0.128304	+	0.991735i	$0.540953\pi$
$860$		0			0
$861$	−31.8195			−1.08441
$862$			12.4408i			0.423737i
$863$	−19.9370	−	11.5106i	−0.678664	−	0.391827i	0.120688	−	0.992691i	$-0.461490\pi$
$863$	−19.9370	−	11.5106i	−0.678664	−	0.391827i	−0.799351	+	0.600864i	$0.794823\pi$
$864$	−6.28586	−	10.8874i	−0.213849	−	0.370398i
$865$		0			0
$866$	−1.38816	+	2.40436i	−0.0471716	+	0.0817036i
$867$	15.9037	+	9.18198i	0.540116	+	0.311836i
$868$	−24.5067	−	14.1489i	−0.831810	−	0.480246i
$869$	−7.78975	−	13.4922i	−0.264249	−	0.457693i
$870$		0			0
$871$	−1.09798	+	1.90176i	−0.0372038	+	0.0644388i
$872$	9.18721	+	5.30424i	0.311118	+	0.179624i
$873$	−20.1561	−	11.6371i	−0.682180	−	0.393857i
$874$	0.958426			0.0324192
$875$		0			0
$876$	21.2027	−	36.7241i	0.716373	−	1.24079i
$877$			12.6479i			0.427089i	0.976933	+	0.213545i	$0.0685008\pi$
$877$			12.6479i			0.427089i	−0.976933	+	0.213545i	$0.931499\pi$
$878$			7.41232i			0.250154i
$879$	12.0240	−	20.8261i	0.405558	−	0.702448i
$880$		0			0
$881$	−2.42275	−	4.19633i	−0.0816247	−	0.141378i	0.822323	−	0.569021i	$-0.192678\pi$
$881$	−2.42275	−	4.19633i	−0.0816247	−	0.141378i	−0.903948	+	0.427643i	$0.859344\pi$
$882$		−	0.971658i		−	0.0327174i
$883$	−39.5494	+	22.8338i	−1.33094	+	0.768420i	−0.985444	−	0.169999i	$-0.945623\pi$
$883$	−39.5494	+	22.8338i	−1.33094	+	0.768420i	−0.345498	+	0.938419i	$0.612290\pi$
$884$	4.47447	+	7.75000i	0.150493	+	0.260661i
$885$		0			0
$886$	6.21393	−	10.7628i	0.208761	−	0.361585i
$887$			48.0641i			1.61383i	0.590665	+	0.806917i	$0.298866\pi$
$887$			48.0641i			1.61383i	−0.590665	+	0.806917i	$0.701134\pi$
$888$	1.75185	+	15.0888i	0.0587883	+	0.506346i
$889$	8.49662			0.284967
$890$		0			0
$891$	30.6951	+	53.1654i	1.02832	+	1.78111i
$892$	−27.1517	+	15.6761i	−0.909107	+	0.524873i
$893$	−0.642519	+	0.370959i	−0.0215011	+	0.0124137i
$894$	3.12038			0.104361
$895$		0			0
$896$	18.5937			0.621171
$897$	−3.81146	−	2.20055i	−0.127261	−	0.0734741i
$898$			2.37755i			0.0793398i
$899$	−3.22056			−0.107412
$900$		0			0
$901$	−17.0909	−	29.6022i	−0.569379	−	0.986194i
$902$			12.3877i			0.412467i
$903$	16.6315	+	9.60222i	0.553463	+	0.319542i
$904$	9.54663	−	16.5352i	0.317516	−	0.549954i
$905$		0			0
$906$	7.57952	+	13.1281i	0.251813	+	0.436152i
$907$	40.2719	−	23.2510i	1.33721	−	0.772036i	0.350813	−	0.936446i	$-0.385905\pi$
$907$	40.2719	−	23.2510i	1.33721	−	0.772036i	0.986392	+	0.164410i	$0.0525719\pi$
$908$	22.3932	+	12.9287i	0.743145	+	0.429055i
$909$	−5.50230	+	9.53026i	−0.182500	+	0.316099i
$910$		0			0
$911$	14.3173			0.474353			0.237177	−	0.971467i	$-0.423778\pi$
$911$	14.3173			0.474353			0.237177	+	0.971467i	$0.423778\pi$
$912$	−14.6540	+	8.46052i	−0.485244	+	0.280156i
$913$	56.1769	+	32.4338i	1.85919	+	1.07340i
$914$	−10.5208			−0.347997
$915$		0			0
$916$	−20.7525	+	35.9444i	−0.685682	+	1.18764i
$917$			43.2962i			1.42977i
$918$	−2.75589	+	1.59112i	−0.0909580	+	0.0525146i
$919$	43.3839			1.43110			0.715552	−	0.698559i	$-0.246175\pi$
$919$	43.3839			1.43110			0.715552	+	0.698559i	$0.246175\pi$
$920$		0			0
$921$	14.0001	+	24.2489i	0.461319	+	0.799028i
$922$	3.91747	−	2.26175i	0.129015	−	0.0744869i
$923$	0.840388	+	0.485198i	0.0276617	+	0.0159705i
$924$	−45.6768			−1.50266
$925$		0			0
$926$	1.23742			0.0406643
$927$	−5.81484	−	3.35720i	−0.190984	−	0.110265i
$928$	1.38754	−	0.801096i	0.0455482	−	0.0262973i
$929$	−14.8015	−	25.6370i	−0.485623	−	0.841124i	0.514240	−	0.857646i	$-0.328074\pi$
$929$	−14.8015	−	25.6370i	−0.485623	−	0.841124i	−0.999863	+	0.0165222i	$0.994741\pi$
$930$		0			0
$931$	5.98461			0.196138
$932$	−21.8018	+	12.5873i	−0.714141	+	0.412310i
$933$			5.46818i			0.179020i
$934$	2.29063	−	3.96749i	0.0749517	−	0.129820i
$935$		0			0
$936$	−2.50434			−0.0818569
$937$	−9.86973	−	5.69829i	−0.322430	−	0.186155i	0.330045	−	0.943965i	$-0.392936\pi$
$937$	−9.86973	−	5.69829i	−0.322430	−	0.186155i	−0.652475	+	0.757810i	$0.726269\pi$
$938$	0.757284	−	0.437218i	0.0247262	−	0.0142757i
$939$	1.22438			0.0399562
$940$		0			0
$941$	12.7126	−	22.0189i	0.414419	−	0.717795i	−0.580948	−	0.813940i	$-0.697318\pi$
$941$	12.7126	−	22.0189i	0.414419	−	0.717795i	0.995367	+	0.0961458i	$0.0306515\pi$
$942$	−11.6767	−	6.74154i	−0.380447	−	0.219651i
$943$	−8.14100	+	4.70021i	−0.265107	+	0.153060i
$944$	14.2399	+	24.6642i	0.463469	+	0.802752i
$945$		0			0
$946$	3.73827	−	6.47487i	0.121542	−	0.210516i
$947$	14.0192	+	8.09396i	0.455561	+	0.263018i	0.710176	−	0.704024i	$-0.248615\pi$
$947$	14.0192	+	8.09396i	0.455561	+	0.263018i	−0.254615	+	0.967043i	$0.581949\pi$
$948$		−	11.1453i		−	0.361984i
$949$	8.92489	+	15.4584i	0.289714	+	0.501800i
$950$		0			0
$951$	−13.9716			−0.453060
$952$		−	7.30712i		−	0.236825i
$953$	−16.8415	−	9.72346i	−0.545550	−	0.314974i	0.201775	−	0.979432i	$-0.435329\pi$
$953$	−16.8415	−	9.72346i	−0.545550	−	0.314974i	−0.747325	+	0.664458i	$0.768662\pi$
$954$	4.66491			0.151032
$955$		0			0
$956$	−23.0281			−0.744783
$957$	−4.50198	+	2.59922i	−0.145528	+	0.0840208i
$958$	−4.19502	+	2.42200i	−0.135535	+	0.0782512i
$959$	5.86303	+	10.1551i	0.189327	+	0.327924i
$960$		0			0
$961$	18.1278			0.584769
$962$	−2.86221	−	1.23725i	−0.0922813	−	0.0398906i
$963$			3.57154i			0.115091i
$964$	13.9920	−	24.2348i	0.450651	−	0.780551i
$965$		0			0
$966$	0.876260	+	1.51773i	0.0281932	+	0.0488321i
$967$	0.610774	−	0.352631i	0.0196412	−	0.0113398i	−0.490147	−	0.871640i	$-0.663057\pi$
$967$	0.610774	−	0.352631i	0.0196412	−	0.0113398i	0.509788	+	0.860300i	$0.329724\pi$
$968$			23.1418i			0.743805i
$969$	7.01384	+	12.1483i	0.225317	+	0.390261i
$970$		0			0
$971$	−5.02834	+	8.70933i	−0.161367	+	0.279496i	−0.935359	−	0.353699i	$-0.884924\pi$
$971$	−5.02834	+	8.70933i	−0.161367	+	0.279496i	0.773992	+	0.633195i	$0.218257\pi$
$972$			23.3265i			0.748199i
$973$		−	44.3788i		−	1.42272i
$974$	5.53767	−	9.59153i	0.177438	−	0.307332i
$975$		0			0
$976$	35.0288			1.12124
$977$	37.8923	+	21.8771i	1.21228	+	0.699911i	0.963256	−	0.268586i	$-0.0865564\pi$
$977$	37.8923	+	21.8771i	1.21228	+	0.699911i	0.249025	+	0.968497i	$0.419890\pi$
$978$	2.88707	+	1.66685i	0.0923183	+	0.0533000i
$979$	−46.1449	+	79.9252i	−1.47480	+	2.55442i
$980$		0			0
$981$	−5.48078	−	9.49298i	−0.174988	−	0.303088i
$982$	0.110597	+	0.0638534i	0.00352931	+	0.00203765i
$983$	10.4756	+	6.04809i	0.334119	+	0.192904i	0.657669	−	0.753307i	$-0.271543\pi$
$983$	10.4756	+	6.04809i	0.334119	+	0.192904i	−0.323549	+	0.946211i	$0.604876\pi$
$984$	−9.08604	+	15.7375i	−0.289652	+	0.501692i
$985$		0			0
$986$	−0.202778	−	0.351222i	−0.00645777	−	0.0111852i
$987$	−1.17487	−	0.678313i	−0.0373966	−	0.0215909i
$988$		−	7.52216i		−	0.239312i
$989$	5.67356			0.180409
$990$		0			0
$991$	−37.4383			−1.18927			−0.594633	−	0.803997i	$-0.702703\pi$
$991$	−37.4383			−1.18927			−0.594633	+	0.803997i	$0.702703\pi$
$992$	−21.1661	+	12.2203i	−0.672026	+	0.387994i
$993$			5.80589i			0.184244i
$994$	−0.193206	−	0.334643i	−0.00612814	−	0.0106142i
$995$		0			0
$996$	23.2026	+	40.1881i	0.735203	+	1.27341i
$997$	26.8024	+	15.4743i	0.848839	+	0.490078i	0.860259	−	0.509857i	$-0.170302\pi$
$997$	26.8024	+	15.4743i	0.848839	+	0.490078i	−0.0114198	+	0.999935i	$0.503635\pi$
$998$		−	11.8127i		−	0.373924i
$999$	−8.70173	+	20.1302i	−0.275310	+	0.636893i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.o.c.824.7		28
5.2	odd	4		925.2.e.b.676.5		14
5.3	odd	4		185.2.e.b.121.3	yes	14
5.4	even	2	inner	925.2.o.c.824.8		28
37.26	even	3	inner	925.2.o.c.174.8		28
185.63	odd	12		185.2.e.b.26.3	✓	14
185.137	odd	12		925.2.e.b.26.5		14
185.138	odd	12		6845.2.a.m.1.3		7
185.158	odd	12		6845.2.a.j.1.5		7
185.174	even	6	inner	925.2.o.c.174.7		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.e.b.26.3	✓	14	185.63	odd	12
185.2.e.b.121.3	yes	14	5.3	odd	4
925.2.e.b.26.5		14	185.137	odd	12
925.2.e.b.676.5		14	5.2	odd	4
925.2.o.c.174.7		28	185.174	even	6	inner
925.2.o.c.174.8		28	37.26	even	3	inner
925.2.o.c.824.7		28	1.1	even	1	trivial
925.2.o.c.824.8		28	5.4	even	2	inner
6845.2.a.j.1.5		7	185.158	odd	12
6845.2.a.m.1.3		7	185.138	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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.268684 - 0.155125i) q^{2} +(-1.78566 + 1.03095i) q^{3} +(-0.951873 - 1.64869i) q^{4} +0.639704 q^{6} +(-1.83659 + 1.06035i) q^{7} +1.21113i q^{8} +(0.625722 - 1.08378i) q^{9} +O(q^{10})\)	\(q+(-0.268684 - 0.155125i) q^{2} +(-1.78566 + 1.03095i) q^{3} +(-0.951873 - 1.64869i) q^{4} +0.639704 q^{6} +(-1.83659 + 1.06035i) q^{7} +1.21113i q^{8} +(0.625722 - 1.08378i) q^{9} +5.48703 q^{11} +(3.39944 + 1.96267i) q^{12} +(-1.43093 + 0.826151i) q^{13} +0.657948 q^{14} +(-1.71587 + 2.97197i) q^{16} +(2.46379 + 1.42247i) q^{17} +(-0.336243 + 0.194130i) q^{18} +(-1.19568 - 2.07098i) q^{19} +(2.18635 - 3.78686i) q^{21} +(-1.47428 - 0.851174i) q^{22} -1.29182i q^{23} +(-1.24862 - 2.16267i) q^{24} +0.512625 q^{26} -3.60535i q^{27} +(3.49639 + 2.01864i) q^{28} +0.459480 q^{29} -7.00913 q^{31} +(3.01980 - 1.74348i) q^{32} +(-9.79798 + 5.65686i) q^{33} +(-0.441320 - 0.764389i) q^{34} -2.38243 q^{36} +(-5.58343 - 2.41356i) q^{37} +0.741917i q^{38} +(1.70344 - 2.95045i) q^{39} +(-3.63843 - 6.30194i) q^{41} +(-1.17487 + 0.678313i) q^{42} +4.39190i q^{43} +(-5.22296 - 9.04642i) q^{44} +(-0.200394 + 0.347092i) q^{46} -0.310249i q^{47} -7.07591i q^{48} +(-1.25130 + 2.16731i) q^{49} -5.86599 q^{51} +(2.72414 + 1.57278i) q^{52} +(-10.4052 - 6.00746i) q^{53} +(-0.559279 + 0.968700i) q^{54} +(-1.28423 - 2.22435i) q^{56} +(4.27015 + 2.46537i) q^{57} +(-0.123455 - 0.0712767i) q^{58} +(4.14947 - 7.18709i) q^{59} +(-5.10365 - 8.83978i) q^{61} +(1.88324 + 1.08729i) q^{62} +2.65395i q^{63} +5.78165 q^{64} +3.51008 q^{66} +(1.15098 - 0.664518i) q^{67} -5.41604i q^{68} +(1.33181 + 2.30676i) q^{69} +(-0.293650 - 0.508617i) q^{71} +(1.31261 + 0.757834i) q^{72} -10.8030i q^{73} +(1.12578 + 1.51461i) q^{74} +(-2.27627 + 3.94261i) q^{76} +(-10.0774 + 5.81820i) q^{77} +(-0.915375 + 0.528492i) q^{78} +(-1.41967 - 2.45893i) q^{79} +(5.59411 + 9.68928i) q^{81} +2.25764i q^{82} +(10.2381 + 5.91099i) q^{83} -8.32450 q^{84} +(0.681292 - 1.18003i) q^{86} +(-0.820476 + 0.473702i) q^{87} +6.64553i q^{88} +(-8.40980 + 14.5662i) q^{89} +(1.75202 - 3.03459i) q^{91} +(-2.12982 + 1.22965i) q^{92} +(12.5159 - 7.22607i) q^{93} +(-0.0481273 + 0.0833590i) q^{94} +(-3.59489 + 6.22653i) q^{96} -18.5979i q^{97} +(0.672407 - 0.388215i) q^{98} +(3.43336 - 5.94675i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 16 q^{4} + 8 q^{6} + 10 q^{9}+O(q^{10}) \) 28 * q + 16 * q^4 + 8 * q^6 + 10 * q^9	\( 28 q + 16 q^{4} + 8 q^{6} + 10 q^{9} - 20 q^{11} + 72 q^{14} - 28 q^{16} - 12 q^{19} + 26 q^{21} + 42 q^{24} + 4 q^{26} + 24 q^{29} - 16 q^{31} + 22 q^{34} - 16 q^{36} - 46 q^{39} - 6 q^{41} - 50 q^{44} + 20 q^{46} + 14 q^{49} - 28 q^{51} - 46 q^{54} + 38 q^{56} + 36 q^{59} - 40 q^{61} - 100 q^{64} - 84 q^{66} - 34 q^{69} - 22 q^{71} + 132 q^{74} + 80 q^{76} - 46 q^{79} + 58 q^{81} - 16 q^{84} - 6 q^{86} + 32 q^{89} + 24 q^{91} - 44 q^{94} - 134 q^{96} - 8 q^{99}+O(q^{100}) \) 28 * q + 16 * q^4 + 8 * q^6 + 10 * q^9 - 20 * q^11 + 72 * q^14 - 28 * q^16 - 12 * q^19 + 26 * q^21 + 42 * q^24 + 4 * q^26 + 24 * q^29 - 16 * q^31 + 22 * q^34 - 16 * q^36 - 46 * q^39 - 6 * q^41 - 50 * q^44 + 20 * q^46 + 14 * q^49 - 28 * q^51 - 46 * q^54 + 38 * q^56 + 36 * q^59 - 40 * q^61 - 100 * q^64 - 84 * q^66 - 34 * q^69 - 22 * q^71 + 132 * q^74 + 80 * q^76 - 46 * q^79 + 58 * q^81 - 16 * q^84 - 6 * q^86 + 32 * q^89 + 24 * q^91 - 44 * q^94 - 134 * q^96 - 8 * q^99

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