LMFDB - Embedded newform 354.2.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(1,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("354.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.a (trivial)

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:	yes
Analytic conductor:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.34292$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.14637 q^{5} +1.00000 q^{6} +1.19656 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.14637 q^{5} +1.00000 q^{6} +1.19656 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.14637 q^{10} -6.17513 q^{11} +1.00000 q^{12} +2.34292 q^{13} +1.19656 q^{14} +1.14637 q^{15} +1.00000 q^{16} +1.48929 q^{17} +1.00000 q^{18} -4.97858 q^{19} +1.14637 q^{20} +1.19656 q^{21} -6.17513 q^{22} +0.685846 q^{23} +1.00000 q^{24} -3.68585 q^{25} +2.34292 q^{26} +1.00000 q^{27} +1.19656 q^{28} +1.83221 q^{29} +1.14637 q^{30} +3.83221 q^{31} +1.00000 q^{32} -6.17513 q^{33} +1.48929 q^{34} +1.37169 q^{35} +1.00000 q^{36} +6.92839 q^{37} -4.97858 q^{38} +2.34292 q^{39} +1.14637 q^{40} -10.8610 q^{41} +1.19656 q^{42} +4.17513 q^{43} -6.17513 q^{44} +1.14637 q^{45} +0.685846 q^{46} -11.6644 q^{47} +1.00000 q^{48} -5.56825 q^{49} -3.68585 q^{50} +1.48929 q^{51} +2.34292 q^{52} +2.51806 q^{53} +1.00000 q^{54} -7.07896 q^{55} +1.19656 q^{56} -4.97858 q^{57} +1.83221 q^{58} +1.00000 q^{59} +1.14637 q^{60} -6.41767 q^{61} +3.83221 q^{62} +1.19656 q^{63} +1.00000 q^{64} +2.68585 q^{65} -6.17513 q^{66} +11.6644 q^{67} +1.48929 q^{68} +0.685846 q^{69} +1.37169 q^{70} -9.02877 q^{71} +1.00000 q^{72} +13.7648 q^{73} +6.92839 q^{74} -3.68585 q^{75} -4.97858 q^{76} -7.38890 q^{77} +2.34292 q^{78} -9.78202 q^{79} +1.14637 q^{80} +1.00000 q^{81} -10.8610 q^{82} -5.78202 q^{83} +1.19656 q^{84} +1.70727 q^{85} +4.17513 q^{86} +1.83221 q^{87} -6.17513 q^{88} +2.87819 q^{89} +1.14637 q^{90} +2.80344 q^{91} +0.685846 q^{92} +3.83221 q^{93} -11.6644 q^{94} -5.70727 q^{95} +1.00000 q^{96} +5.31415 q^{97} -5.56825 q^{98} -6.17513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} + 3 q^{6} - q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 + 3 * q^6 - q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} + 3 q^{6} - q^{7} + 3 q^{8} + 3 q^{9} + 2 q^{10} + q^{11} + 3 q^{12} + q^{13} - q^{14} + 2 q^{15} + 3 q^{16} - 3 q^{17} + 3 q^{18} + 2 q^{20} - q^{21} + q^{22} - 10 q^{23} + 3 q^{24} + q^{25} + q^{26} + 3 q^{27} - q^{28} - 8 q^{29} + 2 q^{30} - 2 q^{31} + 3 q^{32} + q^{33} - 3 q^{34} - 20 q^{35} + 3 q^{36} + 9 q^{37} + q^{39} + 2 q^{40} - q^{41} - q^{42} - 7 q^{43} + q^{44} + 2 q^{45} - 10 q^{46} - 8 q^{47} + 3 q^{48} + 12 q^{49} + q^{50} - 3 q^{51} + q^{52} - 18 q^{53} + 3 q^{54} - q^{56} - 8 q^{58} + 3 q^{59} + 2 q^{60} - 2 q^{62} - q^{63} + 3 q^{64} - 4 q^{65} + q^{66} + 8 q^{67} - 3 q^{68} - 10 q^{69} - 20 q^{70} - 9 q^{71} + 3 q^{72} + 8 q^{73} + 9 q^{74} + q^{75} - 21 q^{77} + q^{78} - 19 q^{79} + 2 q^{80} + 3 q^{81} - q^{82} - 7 q^{83} - q^{84} + 8 q^{85} - 7 q^{86} - 8 q^{87} + q^{88} + 2 q^{90} + 13 q^{91} - 10 q^{92} - 2 q^{93} - 8 q^{94} - 20 q^{95} + 3 q^{96} + 28 q^{97} + 12 q^{98} + q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 + 3 * q^6 - q^7 + 3 * q^8 + 3 * q^9 + 2 * q^10 + q^11 + 3 * q^12 + q^13 - q^14 + 2 * q^15 + 3 * q^16 - 3 * q^17 + 3 * q^18 + 2 * q^20 - q^21 + q^22 - 10 * q^23 + 3 * q^24 + q^25 + q^26 + 3 * q^27 - q^28 - 8 * q^29 + 2 * q^30 - 2 * q^31 + 3 * q^32 + q^33 - 3 * q^34 - 20 * q^35 + 3 * q^36 + 9 * q^37 + q^39 + 2 * q^40 - q^41 - q^42 - 7 * q^43 + q^44 + 2 * q^45 - 10 * q^46 - 8 * q^47 + 3 * q^48 + 12 * q^49 + q^50 - 3 * q^51 + q^52 - 18 * q^53 + 3 * q^54 - q^56 - 8 * q^58 + 3 * q^59 + 2 * q^60 - 2 * q^62 - q^63 + 3 * q^64 - 4 * q^65 + q^66 + 8 * q^67 - 3 * q^68 - 10 * q^69 - 20 * q^70 - 9 * q^71 + 3 * q^72 + 8 * q^73 + 9 * q^74 + q^75 - 21 * q^77 + q^78 - 19 * q^79 + 2 * q^80 + 3 * q^81 - q^82 - 7 * q^83 - q^84 + 8 * q^85 - 7 * q^86 - 8 * q^87 + q^88 + 2 * q^90 + 13 * q^91 - 10 * q^92 - 2 * q^93 - 8 * q^94 - 20 * q^95 + 3 * q^96 + 28 * q^97 + 12 * q^98 + q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.14637	0.512670	0.256335	−	0.966588i	$-0.417485\pi$
$5$	1.14637	0.512670	0.256335	+	0.966588i	$0.417485\pi$
$6$	1.00000	0.408248
$7$	1.19656	0.452256	0.226128	−	0.974098i	$-0.427393\pi$
$7$	1.19656	0.452256	0.226128	+	0.974098i	$0.427393\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.14637	0.362513
$11$	−6.17513	−1.86187	−0.930937	−	0.365181i	$-0.881007\pi$
$11$	−6.17513	−1.86187	−0.930937	+	0.365181i	$0.881007\pi$
$12$	1.00000	0.288675
$13$	2.34292	0.649810	0.324905	−	0.945747i	$-0.394668\pi$
$13$	2.34292	0.649810	0.324905	+	0.945747i	$0.394668\pi$
$14$	1.19656	0.319793
$15$	1.14637	0.295990
$16$	1.00000	0.250000
$17$	1.48929	0.361206	0.180603	−	0.983556i	$-0.442195\pi$
$17$	1.48929	0.361206	0.180603	+	0.983556i	$0.442195\pi$
$18$	1.00000	0.235702
$19$	−4.97858	−1.14216	−0.571082	−	0.820893i	$-0.693476\pi$
$19$	−4.97858	−1.14216	−0.571082	+	0.820893i	$0.693476\pi$
$20$	1.14637	0.256335
$21$	1.19656	0.261110
$22$	−6.17513	−1.31654
$23$	0.685846	0.143009	0.0715044	−	0.997440i	$-0.477220\pi$
$23$	0.685846	0.143009	0.0715044	+	0.997440i	$0.477220\pi$
$24$	1.00000	0.204124
$25$	−3.68585	−0.737169
$26$	2.34292	0.459485
$27$	1.00000	0.192450
$28$	1.19656	0.226128
$29$	1.83221	0.340233	0.170117	−	0.985424i	$-0.445586\pi$
$29$	1.83221	0.340233	0.170117	+	0.985424i	$0.445586\pi$
$30$	1.14637	0.209297
$31$	3.83221	0.688286	0.344143	−	0.938917i	$-0.388170\pi$
$31$	3.83221	0.688286	0.344143	+	0.938917i	$0.388170\pi$
$32$	1.00000	0.176777
$33$	−6.17513	−1.07495
$34$	1.48929	0.255411
$35$	1.37169	0.231858
$36$	1.00000	0.166667
$37$	6.92839	1.13902	0.569510	−	0.821985i	$-0.307133\pi$
$37$	6.92839	1.13902	0.569510	+	0.821985i	$0.307133\pi$
$38$	−4.97858	−0.807632
$39$	2.34292	0.375168
$40$	1.14637	0.181256
$41$	−10.8610	−1.69620	−0.848100	−	0.529836i	$-0.822253\pi$
$41$	−10.8610	−1.69620	−0.848100	+	0.529836i	$0.822253\pi$
$42$	1.19656	0.184633
$43$	4.17513	0.636702	0.318351	−	0.947973i	$-0.396871\pi$
$43$	4.17513	0.636702	0.318351	+	0.947973i	$0.396871\pi$
$44$	−6.17513	−0.930937
$45$	1.14637	0.170890
$46$	0.685846	0.101123
$47$	−11.6644	−1.70143	−0.850716	−	0.525626i	$-0.823831\pi$
$47$	−11.6644	−1.70143	−0.850716	+	0.525626i	$0.823831\pi$
$48$	1.00000	0.144338
$49$	−5.56825	−0.795464
$50$	−3.68585	−0.521257
$51$	1.48929	0.208542
$52$	2.34292	0.324905
$53$	2.51806	0.345882	0.172941	−	0.984932i	$-0.444673\pi$
$53$	2.51806	0.345882	0.172941	+	0.984932i	$0.444673\pi$
$54$	1.00000	0.136083
$55$	−7.07896	−0.954527
$56$	1.19656	0.159897
$57$	−4.97858	−0.659429
$58$	1.83221	0.240581
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	1.14637	0.147995
$61$	−6.41767	−0.821699	−0.410849	−	0.911703i	$-0.634768\pi$
$61$	−6.41767	−0.821699	−0.410849	+	0.911703i	$0.634768\pi$
$62$	3.83221	0.486691
$63$	1.19656	0.150752
$64$	1.00000	0.125000
$65$	2.68585	0.333138
$66$	−6.17513	−0.760107
$67$	11.6644	1.42504	0.712518	−	0.701654i	$-0.247555\pi$
$67$	11.6644	1.42504	0.712518	+	0.701654i	$0.247555\pi$
$68$	1.48929	0.180603
$69$	0.685846	0.0825662
$70$	1.37169	0.163949
$71$	−9.02877	−1.07152	−0.535759	−	0.844371i	$-0.679974\pi$
$71$	−9.02877	−1.07152	−0.535759	+	0.844371i	$0.679974\pi$
$72$	1.00000	0.117851
$73$	13.7648	1.61105	0.805524	−	0.592563i	$-0.201884\pi$
$73$	13.7648	1.61105	0.805524	+	0.592563i	$0.201884\pi$
$74$	6.92839	0.805408
$75$	−3.68585	−0.425605
$76$	−4.97858	−0.571082
$77$	−7.38890	−0.842044
$78$	2.34292	0.265284
$79$	−9.78202	−1.10056	−0.550282	−	0.834979i	$-0.685480\pi$
$79$	−9.78202	−1.10056	−0.550282	+	0.834979i	$0.685480\pi$
$80$	1.14637	0.128168
$81$	1.00000	0.111111
$82$	−10.8610	−1.19939
$83$	−5.78202	−0.634659	−0.317330	−	0.948315i	$-0.602786\pi$
$83$	−5.78202	−0.634659	−0.317330	+	0.948315i	$0.602786\pi$
$84$	1.19656	0.130555
$85$	1.70727	0.185179
$86$	4.17513	0.450216
$87$	1.83221	0.196434
$88$	−6.17513	−0.658272
$89$	2.87819	0.305088	0.152544	−	0.988297i	$-0.451253\pi$
$89$	2.87819	0.305088	0.152544	+	0.988297i	$0.451253\pi$
$90$	1.14637	0.120838
$91$	2.80344	0.293881
$92$	0.685846	0.0715044
$93$	3.83221	0.397382
$94$	−11.6644	−1.20309
$95$	−5.70727	−0.585553
$96$	1.00000	0.102062
$97$	5.31415	0.539571	0.269785	−	0.962921i	$-0.413047\pi$
$97$	5.31415	0.539571	0.269785	+	0.962921i	$0.413047\pi$
$98$	−5.56825	−0.562478
$99$	−6.17513	−0.620624
$100$	−3.68585	−0.368585
$101$	2.51071	0.249825	0.124913	−	0.992168i	$-0.460135\pi$
$101$	2.51071	0.249825	0.124913	+	0.992168i	$0.460135\pi$
$102$	1.48929	0.147462
$103$	−3.24675	−0.319912	−0.159956	−	0.987124i	$-0.551135\pi$
$103$	−3.24675	−0.319912	−0.159956	+	0.987124i	$0.551135\pi$
$104$	2.34292	0.229743
$105$	1.37169	0.133863
$106$	2.51806	0.244575
$107$	−4.10038	−0.396399	−0.198200	−	0.980162i	$-0.563509\pi$
$107$	−4.10038	−0.396399	−0.198200	+	0.980162i	$0.563509\pi$
$108$	1.00000	0.0962250
$109$	2.75325	0.263714	0.131857	−	0.991269i	$-0.457906\pi$
$109$	2.75325	0.263714	0.131857	+	0.991269i	$0.457906\pi$
$110$	−7.07896	−0.674952
$111$	6.92839	0.657613
$112$	1.19656	0.113064
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	−4.97858	−0.466286
$115$	0.786230	0.0733164
$116$	1.83221	0.170117
$117$	2.34292	0.216603
$118$	1.00000	0.0920575
$119$	1.78202	0.163357
$120$	1.14637	0.104648
$121$	27.1323	2.46657
$122$	−6.41767	−0.581029
$123$	−10.8610	−0.979302
$124$	3.83221	0.344143
$125$	−9.95715	−0.890595
$126$	1.19656	0.106598
$127$	2.29273	0.203447	0.101723	−	0.994813i	$-0.467564\pi$
$127$	2.29273	0.203447	0.101723	+	0.994813i	$0.467564\pi$
$128$	1.00000	0.0883883
$129$	4.17513	0.367600
$130$	2.68585	0.235564
$131$	13.7648	1.20264	0.601318	−	0.799009i	$-0.294642\pi$
$131$	13.7648	1.20264	0.601318	+	0.799009i	$0.294642\pi$
$132$	−6.17513	−0.537476
$133$	−5.95715	−0.516551
$134$	11.6644	1.00765
$135$	1.14637	0.0986634
$136$	1.48929	0.127705
$137$	11.2969	0.965163	0.482581	−	0.875851i	$-0.339699\pi$
$137$	11.2969	0.965163	0.482581	+	0.875851i	$0.339699\pi$
$138$	0.685846	0.0583831
$139$	−0.978577	−0.0830018	−0.0415009	−	0.999138i	$-0.513214\pi$
$139$	−0.978577	−0.0830018	−0.0415009	+	0.999138i	$0.513214\pi$
$140$	1.37169	0.115929
$141$	−11.6644	−0.982322
$142$	−9.02877	−0.757677
$143$	−14.4679	−1.20986
$144$	1.00000	0.0833333
$145$	2.10038	0.174427
$146$	13.7648	1.13918
$147$	−5.56825	−0.459262
$148$	6.92839	0.569510
$149$	−9.15371	−0.749901	−0.374951	−	0.927045i	$-0.622340\pi$
$149$	−9.15371	−0.749901	−0.374951	+	0.927045i	$0.622340\pi$
$150$	−3.68585	−0.300948
$151$	2.02456	0.164756	0.0823781	−	0.996601i	$-0.473748\pi$
$151$	2.02456	0.164756	0.0823781	+	0.996601i	$0.473748\pi$
$152$	−4.97858	−0.403816
$153$	1.48929	0.120402
$154$	−7.38890	−0.595415
$155$	4.39312	0.352864
$156$	2.34292	0.187584
$157$	23.5395	1.87866	0.939328	−	0.343022i	$-0.111450\pi$
$157$	23.5395	1.87866	0.939328	+	0.343022i	$0.111450\pi$
$158$	−9.78202	−0.778216
$159$	2.51806	0.199695
$160$	1.14637	0.0906281
$161$	0.820654	0.0646766
$162$	1.00000	0.0785674
$163$	−13.3288	−1.04400	−0.521998	−	0.852947i	$-0.674813\pi$
$163$	−13.3288	−1.04400	−0.521998	+	0.852947i	$0.674813\pi$
$164$	−10.8610	−0.848100
$165$	−7.07896	−0.551096
$166$	−5.78202	−0.448772
$167$	14.1249	1.09302	0.546510	−	0.837452i	$-0.315956\pi$
$167$	14.1249	1.09302	0.546510	+	0.837452i	$0.315956\pi$
$168$	1.19656	0.0923164
$169$	−7.51071	−0.577747
$170$	1.70727	0.130942
$171$	−4.97858	−0.380721
$172$	4.17513	0.318351
$173$	25.4036	1.93140	0.965700	−	0.259661i	$-0.0836108\pi$
$173$	25.4036	1.93140	0.965700	+	0.259661i	$0.0836108\pi$
$174$	1.83221	0.138900
$175$	−4.41033	−0.333389
$176$	−6.17513	−0.465468
$177$	1.00000	0.0751646
$178$	2.87819	0.215730
$179$	10.5682	0.789908	0.394954	−	0.918701i	$-0.370761\pi$
$179$	10.5682	0.789908	0.394954	+	0.918701i	$0.370761\pi$
$180$	1.14637	0.0854450
$181$	19.3717	1.43989	0.719943	−	0.694033i	$-0.244168\pi$
$181$	19.3717	1.43989	0.719943	+	0.694033i	$0.244168\pi$
$182$	2.80344	0.207805
$183$	−6.41767	−0.474408
$184$	0.685846	0.0505613
$185$	7.94246	0.583941
$186$	3.83221	0.280991
$187$	−9.19656	−0.672519
$188$	−11.6644	−0.850716
$189$	1.19656	0.0870368
$190$	−5.70727	−0.414049
$191$	19.6644	1.42287	0.711434	−	0.702753i	$-0.248046\pi$
$191$	19.6644	1.42287	0.711434	+	0.702753i	$0.248046\pi$
$192$	1.00000	0.0721688
$193$	1.82487	0.131357	0.0656783	−	0.997841i	$-0.479079\pi$
$193$	1.82487	0.131357	0.0656783	+	0.997841i	$0.479079\pi$
$194$	5.31415	0.381534
$195$	2.68585	0.192337
$196$	−5.56825	−0.397732
$197$	−9.73183	−0.693364	−0.346682	−	0.937983i	$-0.612692\pi$
$197$	−9.73183	−0.693364	−0.346682	+	0.937983i	$0.612692\pi$
$198$	−6.17513	−0.438848
$199$	8.24989	0.584819	0.292409	−	0.956293i	$-0.405543\pi$
$199$	8.24989	0.584819	0.292409	+	0.956293i	$0.405543\pi$
$200$	−3.68585	−0.260629
$201$	11.6644	0.822745
$202$	2.51071	0.176653
$203$	2.19235	0.153873
$204$	1.48929	0.104271
$205$	−12.4507	−0.869591
$206$	−3.24675	−0.226212
$207$	0.685846	0.0476696
$208$	2.34292	0.162452
$209$	30.7434	2.12656
$210$	1.37169	0.0946558
$211$	2.31836	0.159603	0.0798014	−	0.996811i	$-0.474571\pi$
$211$	2.31836	0.159603	0.0798014	+	0.996811i	$0.474571\pi$
$212$	2.51806	0.172941
$213$	−9.02877	−0.618641
$214$	−4.10038	−0.280296
$215$	4.78623	0.326418
$216$	1.00000	0.0680414
$217$	4.58546	0.311281
$218$	2.75325	0.186474
$219$	13.7648	0.930139
$220$	−7.07896	−0.477263
$221$	3.48929	0.234715
$222$	6.92839	0.465003
$223$	−14.8034	−0.991312	−0.495656	−	0.868519i	$-0.665072\pi$
$223$	−14.8034	−0.991312	−0.495656	+	0.868519i	$0.665072\pi$
$224$	1.19656	0.0799484
$225$	−3.68585	−0.245723
$226$	−2.00000	−0.133038
$227$	25.5468	1.69560	0.847801	−	0.530314i	$-0.177926\pi$
$227$	25.5468	1.69560	0.847801	+	0.530314i	$0.177926\pi$
$228$	−4.97858	−0.329714
$229$	−0.0501921	−0.00331679	−0.00165839	−	0.999999i	$-0.500528\pi$
$229$	−0.0501921	−0.00331679	−0.00165839	+	0.999999i	$0.500528\pi$
$230$	0.786230	0.0518425
$231$	−7.38890	−0.486154
$232$	1.83221	0.120291
$233$	−22.4078	−1.46798	−0.733992	−	0.679158i	$-0.762345\pi$
$233$	−22.4078	−1.46798	−0.733992	+	0.679158i	$0.762345\pi$
$234$	2.34292	0.153162
$235$	−13.3717	−0.872273
$236$	1.00000	0.0650945
$237$	−9.78202	−0.635410
$238$	1.78202	0.115511
$239$	−26.8255	−1.73520	−0.867598	−	0.497266i	$-0.834337\pi$
$239$	−26.8255	−1.73520	−0.867598	+	0.497266i	$0.834337\pi$
$240$	1.14637	0.0739976
$241$	1.53213	0.0986934	0.0493467	−	0.998782i	$-0.484286\pi$
$241$	1.53213	0.0986934	0.0493467	+	0.998782i	$0.484286\pi$
$242$	27.1323	1.74413
$243$	1.00000	0.0641500
$244$	−6.41767	−0.410849
$245$	−6.38325	−0.407811
$246$	−10.8610	−0.692471
$247$	−11.6644	−0.742189
$248$	3.83221	0.243346
$249$	−5.78202	−0.366421
$250$	−9.95715	−0.629746
$251$	20.0000	1.26239	0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000	1.26239	0.631194	+	0.775625i	$0.282565\pi$
$252$	1.19656	0.0753760
$253$	−4.23519	−0.266264
$254$	2.29273	0.143859
$255$	1.70727	0.106913
$256$	1.00000	0.0625000
$257$	16.7178	1.04282	0.521412	−	0.853305i	$-0.325405\pi$
$257$	16.7178	1.04282	0.521412	+	0.853305i	$0.325405\pi$
$258$	4.17513	0.259933
$259$	8.29021	0.515129
$260$	2.68585	0.166569
$261$	1.83221	0.113411
$262$	13.7648	0.850393
$263$	−16.0073	−0.987055	−0.493528	−	0.869730i	$-0.664293\pi$
$263$	−16.0073	−0.987055	−0.493528	+	0.869730i	$0.664293\pi$
$264$	−6.17513	−0.380053
$265$	2.88661	0.177323
$266$	−5.95715	−0.365257
$267$	2.87819	0.176143
$268$	11.6644	0.712518
$269$	−18.7606	−1.14385	−0.571927	−	0.820305i	$-0.693804\pi$
$269$	−18.7606	−1.14385	−0.571927	+	0.820305i	$0.693804\pi$
$270$	1.14637	0.0697656
$271$	−22.5682	−1.37092	−0.685462	−	0.728109i	$-0.740400\pi$
$271$	−22.5682	−1.37092	−0.685462	+	0.728109i	$0.740400\pi$
$272$	1.48929	0.0903014
$273$	2.80344	0.169672
$274$	11.2969	0.682473
$275$	22.7606	1.37252
$276$	0.685846	0.0412831
$277$	20.2070	1.21412	0.607062	−	0.794655i	$-0.292348\pi$
$277$	20.2070	1.21412	0.607062	+	0.794655i	$0.292348\pi$
$278$	−0.978577	−0.0586912
$279$	3.83221	0.229429
$280$	1.37169	0.0819743
$281$	15.9828	0.953453	0.476727	−	0.879052i	$-0.341823\pi$
$281$	15.9828	0.953453	0.476727	+	0.879052i	$0.341823\pi$
$282$	−11.6644	−0.694606
$283$	−10.5682	−0.628217	−0.314109	−	0.949387i	$-0.601706\pi$
$283$	−10.5682	−0.628217	−0.314109	+	0.949387i	$0.601706\pi$
$284$	−9.02877	−0.535759
$285$	−5.70727	−0.338069
$286$	−14.4679	−0.855503
$287$	−12.9958	−0.767117
$288$	1.00000	0.0589256
$289$	−14.7820	−0.869531
$290$	2.10038	0.123339
$291$	5.31415	0.311521
$292$	13.7648	0.805524
$293$	10.5181	0.614471	0.307236	−	0.951633i	$-0.400596\pi$
$293$	10.5181	0.614471	0.307236	+	0.951633i	$0.400596\pi$
$294$	−5.56825	−0.324747
$295$	1.14637	0.0667440
$296$	6.92839	0.402704
$297$	−6.17513	−0.358318
$298$	−9.15371	−0.530260
$299$	1.60688	0.0929285
$300$	−3.68585	−0.212802
$301$	4.99579	0.287953
$302$	2.02456	0.116500
$303$	2.51071	0.144237
$304$	−4.97858	−0.285541
$305$	−7.35700	−0.421261
$306$	1.48929	0.0851370
$307$	−4.74338	−0.270719	−0.135360	−	0.990797i	$-0.543219\pi$
$307$	−4.74338	−0.270719	−0.135360	+	0.990797i	$0.543219\pi$
$308$	−7.38890	−0.421022
$309$	−3.24675	−0.184701
$310$	4.39312	0.249512
$311$	15.9070	0.902001	0.451001	−	0.892524i	$-0.351067\pi$
$311$	15.9070	0.902001	0.451001	+	0.892524i	$0.351067\pi$
$312$	2.34292	0.132642
$313$	6.24989	0.353264	0.176632	−	0.984277i	$-0.443480\pi$
$313$	6.24989	0.353264	0.176632	+	0.984277i	$0.443480\pi$
$314$	23.5395	1.32841
$315$	1.37169	0.0772861
$316$	−9.78202	−0.550282
$317$	−18.7679	−1.05411	−0.527056	−	0.849830i	$-0.676704\pi$
$317$	−18.7679	−1.05411	−0.527056	+	0.849830i	$0.676704\pi$
$318$	2.51806	0.141206
$319$	−11.3142	−0.633471
$320$	1.14637	0.0640838
$321$	−4.10038	−0.228861
$322$	0.820654	0.0457333
$323$	−7.41454	−0.412556
$324$	1.00000	0.0555556
$325$	−8.63565	−0.479020
$326$	−13.3288	−0.738217
$327$	2.75325	0.152255
$328$	−10.8610	−0.599697
$329$	−13.9572	−0.769483
$330$	−7.07896	−0.389684
$331$	−27.3717	−1.50448	−0.752242	−	0.658887i	$-0.771028\pi$
$331$	−27.3717	−1.50448	−0.752242	+	0.658887i	$0.771028\pi$
$332$	−5.78202	−0.317330
$333$	6.92839	0.379673
$334$	14.1249	0.772882
$335$	13.3717	0.730574
$336$	1.19656	0.0652776
$337$	−13.3288	−0.726069	−0.363034	−	0.931776i	$-0.618259\pi$
$337$	−13.3288	−0.726069	−0.363034	+	0.931776i	$0.618259\pi$
$338$	−7.51071	−0.408529
$339$	−2.00000	−0.108625
$340$	1.70727	0.0925897
$341$	−23.6644	−1.28150
$342$	−4.97858	−0.269211
$343$	−15.0386	−0.812010
$344$	4.17513	0.225108
$345$	0.786230	0.0423292
$346$	25.4036	1.36571
$347$	−28.3074	−1.51962	−0.759811	−	0.650144i	$-0.774709\pi$
$347$	−28.3074	−1.51962	−0.759811	+	0.650144i	$0.774709\pi$
$348$	1.83221	0.0982169
$349$	−32.4005	−1.73436	−0.867178	−	0.497997i	$-0.834069\pi$
$349$	−32.4005	−1.73436	−0.867178	+	0.497997i	$0.834069\pi$
$350$	−4.41033	−0.235742
$351$	2.34292	0.125056
$352$	−6.17513	−0.329136
$353$	−7.60688	−0.404874	−0.202437	−	0.979295i	$-0.564886\pi$
$353$	−7.60688	−0.404874	−0.202437	+	0.979295i	$0.564886\pi$
$354$	1.00000	0.0531494
$355$	−10.3503	−0.549335
$356$	2.87819	0.152544
$357$	1.78202	0.0943145
$358$	10.5682	0.558549
$359$	19.1867	1.01263	0.506317	−	0.862347i	$-0.331006\pi$
$359$	19.1867	1.01263	0.506317	+	0.862347i	$0.331006\pi$
$360$	1.14637	0.0604188
$361$	5.78623	0.304538
$362$	19.3717	1.01815
$363$	27.1323	1.42408
$364$	2.80344	0.146940
$365$	15.7795	0.825937
$366$	−6.41767	−0.335457
$367$	−34.2400	−1.78731	−0.893657	−	0.448750i	$-0.851869\pi$
$367$	−34.2400	−1.78731	−0.893657	+	0.448750i	$0.851869\pi$
$368$	0.685846	0.0357522
$369$	−10.8610	−0.565400
$370$	7.94246	0.412909
$371$	3.01300	0.156427
$372$	3.83221	0.198691
$373$	23.5212	1.21788	0.608941	−	0.793216i	$-0.291595\pi$
$373$	23.5212	1.21788	0.608941	+	0.793216i	$0.291595\pi$
$374$	−9.19656	−0.475543
$375$	−9.95715	−0.514185
$376$	−11.6644	−0.601547
$377$	4.29273	0.221087
$378$	1.19656	0.0615443
$379$	2.30742	0.118524	0.0592622	−	0.998242i	$-0.481125\pi$
$379$	2.30742	0.118524	0.0592622	+	0.998242i	$0.481125\pi$
$380$	−5.70727	−0.292777
$381$	2.29273	0.117460
$382$	19.6644	1.00612
$383$	4.35762	0.222664	0.111332	−	0.993783i	$-0.464488\pi$
$383$	4.35762	0.222664	0.111332	+	0.993783i	$0.464488\pi$
$384$	1.00000	0.0510310
$385$	−8.47038	−0.431691
$386$	1.82487	0.0928832
$387$	4.17513	0.212234
$388$	5.31415	0.269785
$389$	−26.4177	−1.33943	−0.669715	−	0.742619i	$-0.733584\pi$
$389$	−26.4177	−1.33943	−0.669715	+	0.742619i	$0.733584\pi$
$390$	2.68585	0.136003
$391$	1.02142	0.0516556
$392$	−5.56825	−0.281239
$393$	13.7648	0.694343
$394$	−9.73183	−0.490282
$395$	−11.2138	−0.564226
$396$	−6.17513	−0.310312
$397$	14.0330	0.704295	0.352148	−	0.935945i	$-0.385452\pi$
$397$	14.0330	0.704295	0.352148	+	0.935945i	$0.385452\pi$
$398$	8.24989	0.413529
$399$	−5.95715	−0.298231
$400$	−3.68585	−0.184292
$401$	31.7795	1.58699	0.793496	−	0.608575i	$-0.208259\pi$
$401$	31.7795	1.58699	0.793496	+	0.608575i	$0.208259\pi$
$402$	11.6644	0.581769
$403$	8.97858	0.447255
$404$	2.51071	0.124913
$405$	1.14637	0.0569634
$406$	2.19235	0.108804
$407$	−42.7837	−2.12071
$408$	1.48929	0.0737308
$409$	−20.4078	−1.00910	−0.504551	−	0.863382i	$-0.668342\pi$
$409$	−20.4078	−1.00910	−0.504551	+	0.863382i	$0.668342\pi$
$410$	−12.4507	−0.614894
$411$	11.2969	0.557237
$412$	−3.24675	−0.159956
$413$	1.19656	0.0588788
$414$	0.685846	0.0337075
$415$	−6.62831	−0.325371
$416$	2.34292	0.114871
$417$	−0.978577	−0.0479211
$418$	30.7434	1.50371
$419$	−7.50398	−0.366593	−0.183297	−	0.983058i	$-0.558677\pi$
$419$	−7.50398	−0.366593	−0.183297	+	0.983058i	$0.558677\pi$
$420$	1.37169	0.0669317
$421$	2.67850	0.130542	0.0652710	−	0.997868i	$-0.479209\pi$
$421$	2.67850	0.130542	0.0652710	+	0.997868i	$0.479209\pi$
$422$	2.31836	0.112856
$423$	−11.6644	−0.567144
$424$	2.51806	0.122288
$425$	−5.48929	−0.266270
$426$	−9.02877	−0.437445
$427$	−7.67912	−0.371618
$428$	−4.10038	−0.198200
$429$	−14.4679	−0.698515
$430$	4.78623	0.230813
$431$	−19.8139	−0.954403	−0.477202	−	0.878794i	$-0.658349\pi$
$431$	−19.8139	−0.954403	−0.477202	+	0.878794i	$0.658349\pi$
$432$	1.00000	0.0481125
$433$	−24.8610	−1.19474	−0.597371	−	0.801965i	$-0.703788\pi$
$433$	−24.8610	−1.19474	−0.597371	+	0.801965i	$0.703788\pi$
$434$	4.58546	0.220109
$435$	2.10038	0.100706
$436$	2.75325	0.131857
$437$	−3.41454	−0.163340
$438$	13.7648	0.657708
$439$	−7.48929	−0.357444	−0.178722	−	0.983900i	$-0.557196\pi$
$439$	−7.48929	−0.357444	−0.178722	+	0.983900i	$0.557196\pi$
$440$	−7.07896	−0.337476
$441$	−5.56825	−0.265155
$442$	3.48929	0.165969
$443$	−10.7178	−0.509216	−0.254608	−	0.967044i	$-0.581946\pi$
$443$	−10.7178	−0.509216	−0.254608	+	0.967044i	$0.581946\pi$
$444$	6.92839	0.328807
$445$	3.29946	0.156409
$446$	−14.8034	−0.700963
$447$	−9.15371	−0.432956
$448$	1.19656	0.0565320
$449$	0.0319048	0.00150568	0.000752841	−	1.00000i	$-0.499760\pi$
$449$	0.0319048	0.00150568	0.000752841		1.00000i	$0.499760\pi$
$450$	−3.68585	−0.173752
$451$	67.0680	3.15811
$452$	−2.00000	−0.0940721
$453$	2.02456	0.0951221
$454$	25.5468	1.19897
$455$	3.21377	0.150664
$456$	−4.97858	−0.233143
$457$	−9.89962	−0.463084	−0.231542	−	0.972825i	$-0.574377\pi$
$457$	−9.89962	−0.463084	−0.231542	+	0.972825i	$0.574377\pi$
$458$	−0.0501921	−0.00234532
$459$	1.48929	0.0695140
$460$	0.786230	0.0366582
$461$	−4.94560	−0.230339	−0.115170	−	0.993346i	$-0.536741\pi$
$461$	−4.94560	−0.230339	−0.115170	+	0.993346i	$0.536741\pi$
$462$	−7.38890	−0.343763
$463$	12.0821	0.561503	0.280751	−	0.959781i	$-0.409416\pi$
$463$	12.0821	0.561503	0.280751	+	0.959781i	$0.409416\pi$
$464$	1.83221	0.0850583
$465$	4.39312	0.203726
$466$	−22.4078	−1.03802
$467$	2.76060	0.127745	0.0638726	−	0.997958i	$-0.479655\pi$
$467$	2.76060	0.127745	0.0638726	+	0.997958i	$0.479655\pi$
$468$	2.34292	0.108302
$469$	13.9572	0.644482
$470$	−13.3717	−0.616790
$471$	23.5395	1.08464
$472$	1.00000	0.0460287
$473$	−25.7820	−1.18546
$474$	−9.78202	−0.449303
$475$	18.3503	0.841968
$476$	1.78202	0.0816787
$477$	2.51806	0.115294
$478$	−26.8255	−1.22697
$479$	28.0821	1.28310	0.641552	−	0.767080i	$-0.278291\pi$
$479$	28.0821	1.28310	0.641552	+	0.767080i	$0.278291\pi$
$480$	1.14637	0.0523242
$481$	16.2327	0.740146
$482$	1.53213	0.0697868
$483$	0.820654	0.0373411
$484$	27.1323	1.23329
$485$	6.09196	0.276622
$486$	1.00000	0.0453609
$487$	39.3692	1.78399	0.891994	−	0.452048i	$-0.149306\pi$
$487$	39.3692	1.78399	0.891994	+	0.452048i	$0.149306\pi$
$488$	−6.41767	−0.290514
$489$	−13.3288	−0.602751
$490$	−6.38325	−0.288366
$491$	24.1004	1.08764	0.543818	−	0.839203i	$-0.316978\pi$
$491$	24.1004	1.08764	0.543818	+	0.839203i	$0.316978\pi$
$492$	−10.8610	−0.489651
$493$	2.72869	0.122894
$494$	−11.6644	−0.524807
$495$	−7.07896	−0.318176
$496$	3.83221	0.172071
$497$	−10.8034	−0.484601
$498$	−5.78202	−0.259098
$499$	42.6577	1.90962	0.954810	−	0.297216i	$-0.0960581\pi$
$499$	42.6577	1.90962	0.954810	+	0.297216i	$0.0960581\pi$
$500$	−9.95715	−0.445297
$501$	14.1249	0.631056
$502$	20.0000	0.892644
$503$	−2.72869	−0.121666	−0.0608332	−	0.998148i	$-0.519376\pi$
$503$	−2.72869	−0.121666	−0.0608332	+	0.998148i	$0.519376\pi$
$504$	1.19656	0.0532989
$505$	2.87819	0.128078
$506$	−4.23519	−0.188277
$507$	−7.51071	−0.333562
$508$	2.29273	0.101723
$509$	−13.6644	−0.605665	−0.302832	−	0.953044i	$-0.597932\pi$
$509$	−13.6644	−0.605665	−0.302832	+	0.953044i	$0.597932\pi$
$510$	1.70727	0.0755991
$511$	16.4704	0.728607
$512$	1.00000	0.0441942
$513$	−4.97858	−0.219810
$514$	16.7178	0.737388
$515$	−3.72196	−0.164009
$516$	4.17513	0.183800
$517$	72.0294	3.16785
$518$	8.29021	0.364251
$519$	25.4036	1.11509
$520$	2.68585	0.117782
$521$	13.2797	0.581796	0.290898	−	0.956754i	$-0.406046\pi$
$521$	13.2797	0.581796	0.290898	+	0.956754i	$0.406046\pi$
$522$	1.83221	0.0801937
$523$	−39.9143	−1.74533	−0.872665	−	0.488319i	$-0.837610\pi$
$523$	−39.9143	−1.74533	−0.872665	+	0.488319i	$0.837610\pi$
$524$	13.7648	0.601318
$525$	−4.41033	−0.192482
$526$	−16.0073	−0.697953
$527$	5.70727	0.248613
$528$	−6.17513	−0.268738
$529$	−22.5296	−0.979548
$530$	2.88661	0.125387
$531$	1.00000	0.0433963
$532$	−5.95715	−0.258275
$533$	−25.4464	−1.10221
$534$	2.87819	0.124552
$535$	−4.70054	−0.203222
$536$	11.6644	0.503826
$537$	10.5682	0.456054
$538$	−18.7606	−0.808827
$539$	34.3847	1.48105
$540$	1.14637	0.0493317
$541$	−25.7722	−1.10803	−0.554016	−	0.832506i	$-0.686905\pi$
$541$	−25.7722	−1.10803	−0.554016	+	0.832506i	$0.686905\pi$
$542$	−22.5682	−0.969389
$543$	19.3717	0.831319
$544$	1.48929	0.0638527
$545$	3.15623	0.135198
$546$	2.80344	0.119976
$547$	15.9656	0.682639	0.341319	−	0.939947i	$-0.389126\pi$
$547$	15.9656	0.682639	0.341319	+	0.939947i	$0.389126\pi$
$548$	11.2969	0.482581
$549$	−6.41767	−0.273900
$550$	22.7606	0.970515
$551$	−9.12181	−0.388602
$552$	0.685846	0.0291916
$553$	−11.7047	−0.497737
$554$	20.2070	0.858515
$555$	7.94246	0.337139
$556$	−0.978577	−0.0415009
$557$	−4.11025	−0.174157	−0.0870784	−	0.996201i	$-0.527753\pi$
$557$	−4.11025	−0.174157	−0.0870784	+	0.996201i	$0.527753\pi$
$558$	3.83221	0.162230
$559$	9.78202	0.413735
$560$	1.37169	0.0579646
$561$	−9.19656	−0.388279
$562$	15.9828	0.674193
$563$	28.3931	1.19663	0.598314	−	0.801262i	$-0.295838\pi$
$563$	28.3931	1.19663	0.598314	+	0.801262i	$0.295838\pi$
$564$	−11.6644	−0.491161
$565$	−2.29273	−0.0964559
$566$	−10.5682	−0.444217
$567$	1.19656	0.0502507
$568$	−9.02877	−0.378839
$569$	−13.3288	−0.558774	−0.279387	−	0.960179i	$-0.590131\pi$
$569$	−13.3288	−0.558774	−0.279387	+	0.960179i	$0.590131\pi$
$570$	−5.70727	−0.239051
$571$	34.1579	1.42946	0.714732	−	0.699398i	$-0.246549\pi$
$571$	34.1579	1.42946	0.714732	+	0.699398i	$0.246549\pi$
$572$	−14.4679	−0.604932
$573$	19.6644	0.821493
$574$	−12.9958	−0.542434
$575$	−2.52792	−0.105422
$576$	1.00000	0.0416667
$577$	−19.6044	−0.816140	−0.408070	−	0.912951i	$-0.633798\pi$
$577$	−19.6044	−0.816140	−0.408070	+	0.912951i	$0.633798\pi$
$578$	−14.7820	−0.614851
$579$	1.82487	0.0758388
$580$	2.10038	0.0872137
$581$	−6.91852	−0.287029
$582$	5.31415	0.220279
$583$	−15.5493	−0.643988
$584$	13.7648	0.569592
$585$	2.68585	0.111046
$586$	10.5181	0.434497
$587$	40.6321	1.67706	0.838532	−	0.544852i	$-0.183414\pi$
$587$	40.6321	1.67706	0.838532	+	0.544852i	$0.183414\pi$
$588$	−5.56825	−0.229631
$589$	−19.0790	−0.786135
$590$	1.14637	0.0471951
$591$	−9.73183	−0.400314
$592$	6.92839	0.284755
$593$	−16.5426	−0.679324	−0.339662	−	0.940548i	$-0.610313\pi$
$593$	−16.5426	−0.679324	−0.339662	+	0.940548i	$0.610313\pi$
$594$	−6.17513	−0.253369
$595$	2.04285	0.0837485
$596$	−9.15371	−0.374951
$597$	8.24989	0.337645
$598$	1.60688	0.0657104
$599$	36.8940	1.50745	0.753723	−	0.657192i	$-0.228256\pi$
$599$	36.8940	1.50745	0.753723	+	0.657192i	$0.228256\pi$
$600$	−3.68585	−0.150474
$601$	16.1923	0.660500	0.330250	−	0.943894i	$-0.392867\pi$
$601$	16.1923	0.660500	0.330250	+	0.943894i	$0.392867\pi$
$602$	4.99579	0.203613
$603$	11.6644	0.475012
$604$	2.02456	0.0823781
$605$	31.1035	1.26454
$606$	2.51071	0.101991
$607$	−2.11760	−0.0859506	−0.0429753	−	0.999076i	$-0.513684\pi$
$607$	−2.11760	−0.0859506	−0.0429753	+	0.999076i	$0.513684\pi$
$608$	−4.97858	−0.201908
$609$	2.19235	0.0888384
$610$	−7.35700	−0.297876
$611$	−27.3288	−1.10561
$612$	1.48929	0.0602009
$613$	−34.2719	−1.38423	−0.692115	−	0.721787i	$-0.743321\pi$
$613$	−34.2719	−1.38423	−0.692115	+	0.721787i	$0.743321\pi$
$614$	−4.74338	−0.191427
$615$	−12.4507	−0.502059
$616$	−7.38890	−0.297707
$617$	−35.6963	−1.43708	−0.718540	−	0.695486i	$-0.755189\pi$
$617$	−35.6963	−1.43708	−0.718540	+	0.695486i	$0.755189\pi$
$618$	−3.24675	−0.130603
$619$	−2.15792	−0.0867342	−0.0433671	−	0.999059i	$-0.513809\pi$
$619$	−2.15792	−0.0867342	−0.0433671	+	0.999059i	$0.513809\pi$
$620$	4.39312	0.176432
$621$	0.685846	0.0275221
$622$	15.9070	0.637811
$623$	3.44392	0.137978
$624$	2.34292	0.0937920
$625$	7.01469	0.280588
$626$	6.24989	0.249796
$627$	30.7434	1.22777
$628$	23.5395	0.939328
$629$	10.3184	0.411420
$630$	1.37169	0.0546495
$631$	−47.7686	−1.90164	−0.950818	−	0.309750i	$-0.899755\pi$
$631$	−47.7686	−1.90164	−0.950818	+	0.309750i	$0.899755\pi$
$632$	−9.78202	−0.389108
$633$	2.31836	0.0921467
$634$	−18.7679	−0.745370
$635$	2.62831	0.104301
$636$	2.51806	0.0998475
$637$	−13.0460	−0.516901
$638$	−11.3142	−0.447932
$639$	−9.02877	−0.357173
$640$	1.14637	0.0453141
$641$	13.4637	0.531782	0.265891	−	0.964003i	$-0.414334\pi$
$641$	13.4637	0.531782	0.265891	+	0.964003i	$0.414334\pi$
$642$	−4.10038	−0.161829
$643$	28.4998	1.12392	0.561961	−	0.827164i	$-0.310047\pi$
$643$	28.4998	1.12392	0.561961	+	0.827164i	$0.310047\pi$
$644$	0.820654	0.0323383
$645$	4.78623	0.188458
$646$	−7.41454	−0.291721
$647$	23.7465	0.933572	0.466786	−	0.884370i	$-0.345412\pi$
$647$	23.7465	0.933572	0.466786	+	0.884370i	$0.345412\pi$
$648$	1.00000	0.0392837
$649$	−6.17513	−0.242395
$650$	−8.63565	−0.338718
$651$	4.58546	0.179718
$652$	−13.3288	−0.521998
$653$	−19.6399	−0.768567	−0.384284	−	0.923215i	$-0.625552\pi$
$653$	−19.6399	−0.768567	−0.384284	+	0.923215i	$0.625552\pi$
$654$	2.75325	0.107661
$655$	15.7795	0.616556
$656$	−10.8610	−0.424050
$657$	13.7648	0.537016
$658$	−13.9572	−0.544107
$659$	−16.5855	−0.646078	−0.323039	−	0.946386i	$-0.604704\pi$
$659$	−16.5855	−0.646078	−0.323039	+	0.946386i	$0.604704\pi$
$660$	−7.07896	−0.275548
$661$	50.3158	1.95706	0.978530	−	0.206105i	$-0.0660790\pi$
$661$	50.3158	1.95706	0.978530	+	0.206105i	$0.0660790\pi$
$662$	−27.3717	−1.06383
$663$	3.48929	0.135513
$664$	−5.78202	−0.224386
$665$	−6.82908	−0.264820
$666$	6.92839	0.268469
$667$	1.25662	0.0486563
$668$	14.1249	0.546510
$669$	−14.8034	−0.572334
$670$	13.3717	0.516594
$671$	39.6300	1.52990
$672$	1.19656	0.0461582
$673$	−8.96388	−0.345532	−0.172766	−	0.984963i	$-0.555270\pi$
$673$	−8.96388	−0.345532	−0.172766	+	0.984963i	$0.555270\pi$
$674$	−13.3288	−0.513408
$675$	−3.68585	−0.141868
$676$	−7.51071	−0.288874
$677$	−3.43910	−0.132175	−0.0660876	−	0.997814i	$-0.521052\pi$
$677$	−3.43910	−0.132175	−0.0660876	+	0.997814i	$0.521052\pi$
$678$	−2.00000	−0.0768095
$679$	6.35869	0.244024
$680$	1.70727	0.0654708
$681$	25.5468	0.978957
$682$	−23.6644	−0.906158
$683$	−5.44017	−0.208162	−0.104081	−	0.994569i	$-0.533190\pi$
$683$	−5.44017	−0.208162	−0.104081	+	0.994569i	$0.533190\pi$
$684$	−4.97858	−0.190361
$685$	12.9504	0.494810
$686$	−15.0386	−0.574178
$687$	−0.0501921	−0.00191495
$688$	4.17513	0.159176
$689$	5.89962	0.224757
$690$	0.786230	0.0299313
$691$	−4.42502	−0.168336	−0.0841678	−	0.996452i	$-0.526823\pi$
$691$	−4.42502	−0.168336	−0.0841678	+	0.996452i	$0.526823\pi$
$692$	25.4036	0.965700
$693$	−7.38890	−0.280681
$694$	−28.3074	−1.07454
$695$	−1.12181	−0.0425526
$696$	1.83221	0.0694498
$697$	−16.1751	−0.612677
$698$	−32.4005	−1.22638
$699$	−22.4078	−0.847541
$700$	−4.41033	−0.166695
$701$	−24.1176	−0.910909	−0.455455	−	0.890259i	$-0.650523\pi$
$701$	−24.1176	−0.910909	−0.455455	+	0.890259i	$0.650523\pi$
$702$	2.34292	0.0884279
$703$	−34.4935	−1.30095
$704$	−6.17513	−0.232734
$705$	−13.3717	−0.503607
$706$	−7.60688	−0.286289
$707$	3.00421	0.112985
$708$	1.00000	0.0375823
$709$	9.52962	0.357892	0.178946	−	0.983859i	$-0.442731\pi$
$709$	9.52962	0.357892	0.178946	+	0.983859i	$0.442731\pi$
$710$	−10.3503	−0.388439
$711$	−9.78202	−0.366854
$712$	2.87819	0.107865
$713$	2.62831	0.0984309
$714$	1.78202	0.0666904
$715$	−16.5855	−0.620261
$716$	10.5682	0.394954
$717$	−26.8255	−1.00182
$718$	19.1867	0.716041
$719$	−42.3221	−1.57835	−0.789174	−	0.614169i	$-0.789491\pi$
$719$	−42.3221	−1.57835	−0.789174	+	0.614169i	$0.789491\pi$
$720$	1.14637	0.0427225
$721$	−3.88492	−0.144682
$722$	5.78623	0.215341
$723$	1.53213	0.0569807
$724$	19.3717	0.719943
$725$	−6.75325	−0.250809
$726$	27.1323	1.00697
$727$	−29.9975	−1.11254	−0.556272	−	0.831000i	$-0.687769\pi$
$727$	−29.9975	−1.11254	−0.556272	+	0.831000i	$0.687769\pi$
$728$	2.80344	0.103902
$729$	1.00000	0.0370370
$730$	15.7795	0.584026
$731$	6.21798	0.229980
$732$	−6.41767	−0.237204
$733$	−10.5363	−0.389169	−0.194584	−	0.980886i	$-0.562336\pi$
$733$	−10.5363	−0.389169	−0.194584	+	0.980886i	$0.562336\pi$
$734$	−34.2400	−1.26382
$735$	−6.38325	−0.235450
$736$	0.685846	0.0252806
$737$	−72.0294	−2.65324
$738$	−10.8610	−0.399798
$739$	−50.4481	−1.85576	−0.927882	−	0.372873i	$-0.878373\pi$
$739$	−50.4481	−1.85576	−0.927882	+	0.372873i	$0.878373\pi$
$740$	7.94246	0.291971
$741$	−11.6644	−0.428503
$742$	3.01300	0.110611
$743$	−43.1611	−1.58343	−0.791713	−	0.610893i	$-0.790810\pi$
$743$	−43.1611	−1.58343	−0.791713	+	0.610893i	$0.790810\pi$
$744$	3.83221	0.140496
$745$	−10.4935	−0.384452
$746$	23.5212	0.861172
$747$	−5.78202	−0.211553
$748$	−9.19656	−0.336259
$749$	−4.90635	−0.179274
$750$	−9.95715	−0.363584
$751$	−2.13964	−0.0780764	−0.0390382	−	0.999238i	$-0.512429\pi$
$751$	−2.13964	−0.0780764	−0.0390382	+	0.999238i	$0.512429\pi$
$752$	−11.6644	−0.425358
$753$	20.0000	0.728841
$754$	4.29273	0.156332
$755$	2.32088	0.0844656
$756$	1.19656	0.0435184
$757$	32.3074	1.17423	0.587117	−	0.809502i	$-0.300263\pi$
$757$	32.3074	1.17423	0.587117	+	0.809502i	$0.300263\pi$
$758$	2.30742	0.0838094
$759$	−4.23519	−0.153728
$760$	−5.70727	−0.207024
$761$	20.7925	0.753728	0.376864	−	0.926269i	$-0.377002\pi$
$761$	20.7925	0.753728	0.376864	+	0.926269i	$0.377002\pi$
$762$	2.29273	0.0830569
$763$	3.29442	0.119266
$764$	19.6644	0.711434
$765$	1.70727	0.0617264
$766$	4.35762	0.157447
$767$	2.34292	0.0845980
$768$	1.00000	0.0360844
$769$	−1.75011	−0.0631108	−0.0315554	−	0.999502i	$-0.510046\pi$
$769$	−1.75011	−0.0631108	−0.0315554	+	0.999502i	$0.510046\pi$
$770$	−8.47038	−0.305251
$771$	16.7178	0.602075
$772$	1.82487	0.0656783
$773$	10.0491	0.361442	0.180721	−	0.983534i	$-0.442157\pi$
$773$	10.0491	0.361442	0.180721	+	0.983534i	$0.442157\pi$
$774$	4.17513	0.150072
$775$	−14.1249	−0.507383
$776$	5.31415	0.190767
$777$	8.29021	0.297410
$778$	−26.4177	−0.947119
$779$	54.0722	1.93734
$780$	2.68585	0.0961687
$781$	55.7539	1.99503
$782$	1.02142	0.0365260
$783$	1.83221	0.0654779
$784$	−5.56825	−0.198866
$785$	26.9848	0.963131
$786$	13.7648	0.490974
$787$	25.7135	0.916589	0.458294	−	0.888800i	$-0.348461\pi$
$787$	25.7135	0.916589	0.458294	+	0.888800i	$0.348461\pi$
$788$	−9.73183	−0.346682
$789$	−16.0073	−0.569877
$790$	−11.2138	−0.398968
$791$	−2.39312	−0.0850894
$792$	−6.17513	−0.219424
$793$	−15.0361	−0.533948
$794$	14.0330	0.498012
$795$	2.88661	0.102378
$796$	8.24989	0.292409
$797$	12.2180	0.432783	0.216392	−	0.976307i	$-0.430571\pi$
$797$	12.2180	0.432783	0.216392	+	0.976307i	$0.430571\pi$
$798$	−5.95715	−0.210881
$799$	−17.3717	−0.614566
$800$	−3.68585	−0.130314
$801$	2.87819	0.101696
$802$	31.7795	1.12217
$803$	−84.9995	−2.99957
$804$	11.6644	0.411372
$805$	0.940770	0.0331578
$806$	8.97858	0.316257
$807$	−18.7606	−0.660404
$808$	2.51071	0.0883265
$809$	52.9504	1.86164	0.930819	−	0.365481i	$-0.119095\pi$
$809$	52.9504	1.86164	0.930819	+	0.365481i	$0.119095\pi$
$810$	1.14637	0.0402792
$811$	0.425020	0.0149245	0.00746224	−	0.999972i	$-0.497625\pi$
$811$	0.425020	0.0149245	0.00746224	+	0.999972i	$0.497625\pi$
$812$	2.19235	0.0769363
$813$	−22.5682	−0.791503
$814$	−42.7837	−1.49957
$815$	−15.2797	−0.535226
$816$	1.48929	0.0521355
$817$	−20.7862	−0.727218
$818$	−20.4078	−0.713542
$819$	2.80344	0.0979602
$820$	−12.4507	−0.434796
$821$	−30.6749	−1.07056	−0.535281	−	0.844674i	$-0.679794\pi$
$821$	−30.6749	−1.07056	−0.535281	+	0.844674i	$0.679794\pi$
$822$	11.2969	0.394026
$823$	−43.6608	−1.52192	−0.760960	−	0.648798i	$-0.775272\pi$
$823$	−43.6608	−1.52192	−0.760960	+	0.648798i	$0.775272\pi$
$824$	−3.24675	−0.113106
$825$	22.7606	0.792422
$826$	1.19656	0.0416336
$827$	5.72196	0.198972	0.0994861	−	0.995039i	$-0.468280\pi$
$827$	5.72196	0.198972	0.0994861	+	0.995039i	$0.468280\pi$
$828$	0.685846	0.0238348
$829$	23.8077	0.826874	0.413437	−	0.910533i	$-0.364328\pi$
$829$	23.8077	0.826874	0.413437	+	0.910533i	$0.364328\pi$
$830$	−6.62831	−0.230072
$831$	20.2070	0.700974
$832$	2.34292	0.0812262
$833$	−8.29273	−0.287326
$834$	−0.978577	−0.0338854
$835$	16.1923	0.560359
$836$	30.7434	1.06328
$837$	3.83221	0.132461
$838$	−7.50398	−0.259221
$839$	31.8996	1.10130	0.550649	−	0.834737i	$-0.314380\pi$
$839$	31.8996	1.10130	0.550649	+	0.834737i	$0.314380\pi$
$840$	1.37169	0.0473279
$841$	−25.6430	−0.884241
$842$	2.67850	0.0923072
$843$	15.9828	0.550476
$844$	2.31836	0.0798014
$845$	−8.61002	−0.296194
$846$	−11.6644	−0.401031
$847$	32.4653	1.11552
$848$	2.51806	0.0864705
$849$	−10.5682	−0.362701
$850$	−5.48929	−0.188281
$851$	4.75181	0.162890
$852$	−9.02877	−0.309321
$853$	−15.1856	−0.519946	−0.259973	−	0.965616i	$-0.583714\pi$
$853$	−15.1856	−0.519946	−0.259973	+	0.965616i	$0.583714\pi$
$854$	−7.67912	−0.262774
$855$	−5.70727	−0.195184
$856$	−4.10038	−0.140148
$857$	3.51492	0.120067	0.0600337	−	0.998196i	$-0.480879\pi$
$857$	3.51492	0.120067	0.0600337	+	0.998196i	$0.480879\pi$
$858$	−14.4679	−0.493925
$859$	−22.7925	−0.777670	−0.388835	−	0.921307i	$-0.627122\pi$
$859$	−22.7925	−0.777670	−0.388835	+	0.921307i	$0.627122\pi$
$860$	4.78623	0.163209
$861$	−12.9958	−0.442895
$862$	−19.8139	−0.674865
$863$	15.0790	0.513294	0.256647	−	0.966505i	$-0.417382\pi$
$863$	15.0790	0.513294	0.256647	+	0.966505i	$0.417382\pi$
$864$	1.00000	0.0340207
$865$	29.1218	0.990171
$866$	−24.8610	−0.844811
$867$	−14.7820	−0.502024
$868$	4.58546	0.155641
$869$	60.4053	2.04911
$870$	2.10038	0.0712097
$871$	27.3288	0.926003
$872$	2.75325	0.0932368
$873$	5.31415	0.179857
$874$	−3.41454	−0.115498
$875$	−11.9143	−0.402777
$876$	13.7648	0.465070
$877$	−57.2285	−1.93247	−0.966234	−	0.257666i	$-0.917046\pi$
$877$	−57.2285	−1.93247	−0.966234	+	0.257666i	$0.917046\pi$
$878$	−7.48929	−0.252751
$879$	10.5181	0.354765
$880$	−7.07896	−0.238632
$881$	−17.9718	−0.605487	−0.302743	−	0.953072i	$-0.597903\pi$
$881$	−17.9718	−0.605487	−0.302743	+	0.953072i	$0.597903\pi$
$882$	−5.56825	−0.187493
$883$	−8.98700	−0.302437	−0.151218	−	0.988500i	$-0.548320\pi$
$883$	−8.98700	−0.302437	−0.151218	+	0.988500i	$0.548320\pi$
$884$	3.48929	0.117357
$885$	1.14637	0.0385347
$886$	−10.7178	−0.360070
$887$	0.820654	0.0275549	0.0137774	−	0.999905i	$-0.495614\pi$
$887$	0.820654	0.0275549	0.0137774	+	0.999905i	$0.495614\pi$
$888$	6.92839	0.232501
$889$	2.74338	0.0920102
$890$	3.29946	0.110598
$891$	−6.17513	−0.206875
$892$	−14.8034	−0.495656
$893$	58.0722	1.94331
$894$	−9.15371	−0.306146
$895$	12.1151	0.404962
$896$	1.19656	0.0399742
$897$	1.60688	0.0536523
$898$	0.0319048	0.00106468
$899$	7.02142	0.234178
$900$	−3.68585	−0.122862
$901$	3.75011	0.124934
$902$	67.0680	2.23312
$903$	4.99579	0.166249
$904$	−2.00000	−0.0665190
$905$	22.2070	0.738187
$906$	2.02456	0.0672614
$907$	58.2646	1.93464	0.967322	−	0.253552i	$-0.0815989\pi$
$907$	58.2646	1.93464	0.967322	+	0.253552i	$0.0815989\pi$
$908$	25.5468	0.847801
$909$	2.51071	0.0832750
$910$	3.21377	0.106535
$911$	−23.1867	−0.768209	−0.384105	−	0.923290i	$-0.625490\pi$
$911$	−23.1867	−0.768209	−0.384105	+	0.923290i	$0.625490\pi$
$912$	−4.97858	−0.164857
$913$	35.7047	1.18165
$914$	−9.89962	−0.327450
$915$	−7.35700	−0.243215
$916$	−0.0501921	−0.00165839
$917$	16.4704	0.543900
$918$	1.48929	0.0491538
$919$	34.0539	1.12334	0.561668	−	0.827363i	$-0.310160\pi$
$919$	34.0539	1.12334	0.561668	+	0.827363i	$0.310160\pi$
$920$	0.786230	0.0259212
$921$	−4.74338	−0.156300
$922$	−4.94560	−0.162875
$923$	−21.1537	−0.696283
$924$	−7.38890	−0.243077
$925$	−25.5370	−0.839650
$926$	12.0821	0.397042
$927$	−3.24675	−0.106637
$928$	1.83221	0.0601453
$929$	0.335577	0.0110099	0.00550496	−	0.999985i	$-0.498248\pi$
$929$	0.335577	0.0110099	0.00550496	+	0.999985i	$0.498248\pi$
$930$	4.39312	0.144056
$931$	27.7220	0.908551
$932$	−22.4078	−0.733992
$933$	15.9070	0.520771
$934$	2.76060	0.0903295
$935$	−10.5426	−0.344780
$936$	2.34292	0.0765808
$937$	−54.4141	−1.77763	−0.888815	−	0.458266i	$-0.848471\pi$
$937$	−54.4141	−1.77763	−0.888815	+	0.458266i	$0.848471\pi$
$938$	13.9572	0.455717
$939$	6.24989	0.203957
$940$	−13.3717	−0.436137
$941$	−18.4507	−0.601474	−0.300737	−	0.953707i	$-0.597233\pi$
$941$	−18.4507	−0.601474	−0.300737	+	0.953707i	$0.597233\pi$
$942$	23.5395	0.766958
$943$	−7.44896	−0.242572
$944$	1.00000	0.0325472
$945$	1.37169	0.0446212
$946$	−25.7820	−0.838246
$947$	39.6938	1.28988	0.644938	−	0.764235i	$-0.276883\pi$
$947$	39.6938	1.28988	0.644938	+	0.764235i	$0.276883\pi$
$948$	−9.78202	−0.317705
$949$	32.2499	1.04688
$950$	18.3503	0.595361
$951$	−18.7679	−0.608592
$952$	1.78202	0.0577556
$953$	21.1046	0.683645	0.341822	−	0.939765i	$-0.388956\pi$
$953$	21.1046	0.683645	0.341822	+	0.939765i	$0.388956\pi$
$954$	2.51806	0.0815251
$955$	22.5426	0.729462
$956$	−26.8255	−0.867598
$957$	−11.3142	−0.365735
$958$	28.0821	0.907291
$959$	13.5174	0.436501
$960$	1.14637	0.0369988
$961$	−16.3142	−0.526263
$962$	16.2327	0.523362
$963$	−4.10038	−0.132133
$964$	1.53213	0.0493467
$965$	2.09196	0.0673427
$966$	0.820654	0.0264041
$967$	2.12494	0.0683335	0.0341668	−	0.999416i	$-0.489122\pi$
$967$	2.12494	0.0683335	0.0341668	+	0.999416i	$0.489122\pi$
$968$	27.1323	0.872065
$969$	−7.41454	−0.238189
$970$	6.09196	0.195601
$971$	27.3435	0.877496	0.438748	−	0.898610i	$-0.355422\pi$
$971$	27.3435	0.877496	0.438748	+	0.898610i	$0.355422\pi$
$972$	1.00000	0.0320750
$973$	−1.17092	−0.0375381
$974$	39.3692	1.26147
$975$	−8.63565	−0.276562
$976$	−6.41767	−0.205425
$977$	−36.3074	−1.16158	−0.580789	−	0.814054i	$-0.697256\pi$
$977$	−36.3074	−1.16158	−0.580789	+	0.814054i	$0.697256\pi$
$978$	−13.3288	−0.426210
$979$	−17.7732	−0.568035
$980$	−6.38325	−0.203905
$981$	2.75325	0.0879045
$982$	24.1004	0.769074
$983$	2.14323	0.0683584	0.0341792	−	0.999416i	$-0.489118\pi$
$983$	2.14323	0.0683584	0.0341792	+	0.999416i	$0.489118\pi$
$984$	−10.8610	−0.346235
$985$	−11.1562	−0.355467
$986$	2.72869	0.0868993
$987$	−13.9572	−0.444261
$988$	−11.6644	−0.371095
$989$	2.86350	0.0910540
$990$	−7.07896	−0.224984
$991$	46.9603	1.49174	0.745871	−	0.666090i	$-0.232033\pi$
$991$	46.9603	1.49174	0.745871	+	0.666090i	$0.232033\pi$
$992$	3.83221	0.121673
$993$	−27.3717	−0.868614
$994$	−10.8034	−0.342664
$995$	9.45738	0.299819
$996$	−5.78202	−0.183210
$997$	16.1432	0.511261	0.255631	−	0.966775i	$-0.417717\pi$
$997$	16.1432	0.511261	0.255631	+	0.966775i	$0.417717\pi$
$998$	42.6577	1.35031
$999$	6.92839	0.219204

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.a.h.1.2	✓	3
3.2	odd	2		1062.2.a.n.1.2		3
4.3	odd	2		2832.2.a.r.1.2		3
5.4	even	2		8850.2.a.bu.1.2		3
12.11	even	2		8496.2.a.bi.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.a.h.1.2	✓	3	1.1	even	1	trivial
1062.2.a.n.1.2		3	3.2	odd	2
2832.2.a.r.1.2		3	4.3	odd	2
8496.2.a.bi.1.2		3	12.11	even	2
8850.2.a.bu.1.2		3	5.4	even	2

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.14637 q^{5} +1.00000 q^{6} +1.19656 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.14637 q^{5} +1.00000 q^{6} +1.19656 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.14637 q^{10} -6.17513 q^{11} +1.00000 q^{12} +2.34292 q^{13} +1.19656 q^{14} +1.14637 q^{15} +1.00000 q^{16} +1.48929 q^{17} +1.00000 q^{18} -4.97858 q^{19} +1.14637 q^{20} +1.19656 q^{21} -6.17513 q^{22} +0.685846 q^{23} +1.00000 q^{24} -3.68585 q^{25} +2.34292 q^{26} +1.00000 q^{27} +1.19656 q^{28} +1.83221 q^{29} +1.14637 q^{30} +3.83221 q^{31} +1.00000 q^{32} -6.17513 q^{33} +1.48929 q^{34} +1.37169 q^{35} +1.00000 q^{36} +6.92839 q^{37} -4.97858 q^{38} +2.34292 q^{39} +1.14637 q^{40} -10.8610 q^{41} +1.19656 q^{42} +4.17513 q^{43} -6.17513 q^{44} +1.14637 q^{45} +0.685846 q^{46} -11.6644 q^{47} +1.00000 q^{48} -5.56825 q^{49} -3.68585 q^{50} +1.48929 q^{51} +2.34292 q^{52} +2.51806 q^{53} +1.00000 q^{54} -7.07896 q^{55} +1.19656 q^{56} -4.97858 q^{57} +1.83221 q^{58} +1.00000 q^{59} +1.14637 q^{60} -6.41767 q^{61} +3.83221 q^{62} +1.19656 q^{63} +1.00000 q^{64} +2.68585 q^{65} -6.17513 q^{66} +11.6644 q^{67} +1.48929 q^{68} +0.685846 q^{69} +1.37169 q^{70} -9.02877 q^{71} +1.00000 q^{72} +13.7648 q^{73} +6.92839 q^{74} -3.68585 q^{75} -4.97858 q^{76} -7.38890 q^{77} +2.34292 q^{78} -9.78202 q^{79} +1.14637 q^{80} +1.00000 q^{81} -10.8610 q^{82} -5.78202 q^{83} +1.19656 q^{84} +1.70727 q^{85} +4.17513 q^{86} +1.83221 q^{87} -6.17513 q^{88} +2.87819 q^{89} +1.14637 q^{90} +2.80344 q^{91} +0.685846 q^{92} +3.83221 q^{93} -11.6644 q^{94} -5.70727 q^{95} +1.00000 q^{96} +5.31415 q^{97} -5.56825 q^{98} -6.17513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} + 3 q^{6} - q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 + 3 * q^6 - q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} + 3 q^{6} - q^{7} + 3 q^{8} + 3 q^{9} + 2 q^{10} + q^{11} + 3 q^{12} + q^{13} - q^{14} + 2 q^{15} + 3 q^{16} - 3 q^{17} + 3 q^{18} + 2 q^{20} - q^{21} + q^{22} - 10 q^{23} + 3 q^{24} + q^{25} + q^{26} + 3 q^{27} - q^{28} - 8 q^{29} + 2 q^{30} - 2 q^{31} + 3 q^{32} + q^{33} - 3 q^{34} - 20 q^{35} + 3 q^{36} + 9 q^{37} + q^{39} + 2 q^{40} - q^{41} - q^{42} - 7 q^{43} + q^{44} + 2 q^{45} - 10 q^{46} - 8 q^{47} + 3 q^{48} + 12 q^{49} + q^{50} - 3 q^{51} + q^{52} - 18 q^{53} + 3 q^{54} - q^{56} - 8 q^{58} + 3 q^{59} + 2 q^{60} - 2 q^{62} - q^{63} + 3 q^{64} - 4 q^{65} + q^{66} + 8 q^{67} - 3 q^{68} - 10 q^{69} - 20 q^{70} - 9 q^{71} + 3 q^{72} + 8 q^{73} + 9 q^{74} + q^{75} - 21 q^{77} + q^{78} - 19 q^{79} + 2 q^{80} + 3 q^{81} - q^{82} - 7 q^{83} - q^{84} + 8 q^{85} - 7 q^{86} - 8 q^{87} + q^{88} + 2 q^{90} + 13 q^{91} - 10 q^{92} - 2 q^{93} - 8 q^{94} - 20 q^{95} + 3 q^{96} + 28 q^{97} + 12 q^{98} + q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 + 3 * q^6 - q^7 + 3 * q^8 + 3 * q^9 + 2 * q^10 + q^11 + 3 * q^12 + q^13 - q^14 + 2 * q^15 + 3 * q^16 - 3 * q^17 + 3 * q^18 + 2 * q^20 - q^21 + q^22 - 10 * q^23 + 3 * q^24 + q^25 + q^26 + 3 * q^27 - q^28 - 8 * q^29 + 2 * q^30 - 2 * q^31 + 3 * q^32 + q^33 - 3 * q^34 - 20 * q^35 + 3 * q^36 + 9 * q^37 + q^39 + 2 * q^40 - q^41 - q^42 - 7 * q^43 + q^44 + 2 * q^45 - 10 * q^46 - 8 * q^47 + 3 * q^48 + 12 * q^49 + q^50 - 3 * q^51 + q^52 - 18 * q^53 + 3 * q^54 - q^56 - 8 * q^58 + 3 * q^59 + 2 * q^60 - 2 * q^62 - q^63 + 3 * q^64 - 4 * q^65 + q^66 + 8 * q^67 - 3 * q^68 - 10 * q^69 - 20 * q^70 - 9 * q^71 + 3 * q^72 + 8 * q^73 + 9 * q^74 + q^75 - 21 * q^77 + q^78 - 19 * q^79 + 2 * q^80 + 3 * q^81 - q^82 - 7 * q^83 - q^84 + 8 * q^85 - 7 * q^86 - 8 * q^87 + q^88 + 2 * q^90 + 13 * q^91 - 10 * q^92 - 2 * q^93 - 8 * q^94 - 20 * q^95 + 3 * q^96 + 28 * q^97 + 12 * q^98 + q^99

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