LMFDB - Embedded newform 946.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(1,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, 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("946.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.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:	$7.55384803121$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 1 $ x^4 - 5*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.18890$ of defining polynomial
Character	$\chi$	$=$	946.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.45685 q^{3} +1.00000 q^{4} +0.791288 q^{5} -1.45685 q^{6} -2.33444 q^{7} +1.00000 q^{8} -0.877587 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.45685 q^{3} +1.00000 q^{4} +0.791288 q^{5} -1.45685 q^{6} -2.33444 q^{7} +1.00000 q^{8} -0.877587 q^{9} +0.791288 q^{10} -1.00000 q^{11} -1.45685 q^{12} -0.354249 q^{13} -2.33444 q^{14} -1.15279 q^{15} +1.00000 q^{16} -7.65300 q^{17} -0.877587 q^{18} +5.56670 q^{19} +0.791288 q^{20} +3.40093 q^{21} -1.00000 q^{22} -2.85446 q^{23} -1.45685 q^{24} -4.37386 q^{25} -0.354249 q^{26} +5.64906 q^{27} -2.33444 q^{28} -7.22108 q^{29} -1.15279 q^{30} -8.21245 q^{31} +1.00000 q^{32} +1.45685 q^{33} -7.65300 q^{34} -1.84721 q^{35} -0.877587 q^{36} +5.13692 q^{37} +5.56670 q^{38} +0.516087 q^{39} +0.791288 q^{40} -3.25208 q^{41} +3.40093 q^{42} +1.00000 q^{43} -1.00000 q^{44} -0.694424 q^{45} -2.85446 q^{46} +7.03943 q^{47} -1.45685 q^{48} -1.55040 q^{49} -4.37386 q^{50} +11.1493 q^{51} -0.354249 q^{52} -1.79854 q^{53} +5.64906 q^{54} -0.791288 q^{55} -2.33444 q^{56} -8.10985 q^{57} -7.22108 q^{58} -8.19615 q^{59} -1.15279 q^{60} +1.84190 q^{61} -8.21245 q^{62} +2.04867 q^{63} +1.00000 q^{64} -0.280313 q^{65} +1.45685 q^{66} +6.17634 q^{67} -7.65300 q^{68} +4.15853 q^{69} -1.84721 q^{70} -6.23952 q^{71} -0.877587 q^{72} -14.9373 q^{73} +5.13692 q^{74} +6.37206 q^{75} +5.56670 q^{76} +2.33444 q^{77} +0.516087 q^{78} +1.01630 q^{79} +0.791288 q^{80} -5.59708 q^{81} -3.25208 q^{82} +10.5740 q^{83} +3.40093 q^{84} -6.05573 q^{85} +1.00000 q^{86} +10.5200 q^{87} -1.00000 q^{88} +2.90839 q^{89} -0.694424 q^{90} +0.826971 q^{91} -2.85446 q^{92} +11.9643 q^{93} +7.03943 q^{94} +4.40486 q^{95} -1.45685 q^{96} -13.6654 q^{97} -1.55040 q^{98} +0.877587 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 + 2 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 2 q^{9} - 6 q^{10} - 4 q^{11} - 4 q^{12} - 12 q^{13} - 2 q^{14} + 6 q^{15} + 4 q^{16} - 8 q^{17} + 2 q^{18} - 4 q^{19} - 6 q^{20} - 8 q^{21} - 4 q^{22} - 10 q^{23} - 4 q^{24} + 10 q^{25} - 12 q^{26} - 10 q^{27} - 2 q^{28} - 12 q^{29} + 6 q^{30} + 4 q^{31} + 4 q^{32} + 4 q^{33} - 8 q^{34} - 18 q^{35} + 2 q^{36} + 2 q^{37} - 4 q^{38} - 2 q^{39} - 6 q^{40} - 12 q^{41} - 8 q^{42} + 4 q^{43} - 4 q^{44} - 24 q^{45} - 10 q^{46} + 8 q^{47} - 4 q^{48} + 4 q^{49} + 10 q^{50} - 12 q^{52} + 14 q^{53} - 10 q^{54} + 6 q^{55} - 2 q^{56} - 8 q^{57} - 12 q^{58} - 12 q^{59} + 6 q^{60} - 24 q^{61} + 4 q^{62} + 40 q^{63} + 4 q^{64} + 18 q^{65} + 4 q^{66} - 14 q^{67} - 8 q^{68} + 24 q^{69} - 18 q^{70} + 6 q^{71} + 2 q^{72} - 28 q^{73} + 2 q^{74} - 10 q^{75} - 4 q^{76} + 2 q^{77} - 2 q^{78} - 12 q^{79} - 6 q^{80} + 20 q^{81} - 12 q^{82} + 4 q^{83} - 8 q^{84} + 12 q^{85} + 4 q^{86} + 48 q^{87} - 4 q^{88} - 34 q^{89} - 24 q^{90} + 20 q^{91} - 10 q^{92} + 22 q^{93} + 8 q^{94} + 6 q^{95} - 4 q^{96} - 6 q^{97} + 4 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 + 2 * q^9 - 6 * q^10 - 4 * q^11 - 4 * q^12 - 12 * q^13 - 2 * q^14 + 6 * q^15 + 4 * q^16 - 8 * q^17 + 2 * q^18 - 4 * q^19 - 6 * q^20 - 8 * q^21 - 4 * q^22 - 10 * q^23 - 4 * q^24 + 10 * q^25 - 12 * q^26 - 10 * q^27 - 2 * q^28 - 12 * q^29 + 6 * q^30 + 4 * q^31 + 4 * q^32 + 4 * q^33 - 8 * q^34 - 18 * q^35 + 2 * q^36 + 2 * q^37 - 4 * q^38 - 2 * q^39 - 6 * q^40 - 12 * q^41 - 8 * q^42 + 4 * q^43 - 4 * q^44 - 24 * q^45 - 10 * q^46 + 8 * q^47 - 4 * q^48 + 4 * q^49 + 10 * q^50 - 12 * q^52 + 14 * q^53 - 10 * q^54 + 6 * q^55 - 2 * q^56 - 8 * q^57 - 12 * q^58 - 12 * q^59 + 6 * q^60 - 24 * q^61 + 4 * q^62 + 40 * q^63 + 4 * q^64 + 18 * q^65 + 4 * q^66 - 14 * q^67 - 8 * q^68 + 24 * q^69 - 18 * q^70 + 6 * q^71 + 2 * q^72 - 28 * q^73 + 2 * q^74 - 10 * q^75 - 4 * q^76 + 2 * q^77 - 2 * q^78 - 12 * q^79 - 6 * q^80 + 20 * q^81 - 12 * q^82 + 4 * q^83 - 8 * q^84 + 12 * q^85 + 4 * q^86 + 48 * q^87 - 4 * q^88 - 34 * q^89 - 24 * q^90 + 20 * q^91 - 10 * q^92 + 22 * q^93 + 8 * q^94 + 6 * q^95 - 4 * q^96 - 6 * q^97 + 4 * q^98 - 2 * 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
$3$	−1.45685	−0.841113	−0.420556	−	0.907266i	$-0.638165\pi$
$3$	−1.45685	−0.841113	−0.420556	+	0.907266i	$0.638165\pi$
$4$	1.00000	0.500000
$5$	0.791288	0.353875	0.176937	−	0.984222i	$-0.443381\pi$
$5$	0.791288	0.353875	0.176937	+	0.984222i	$0.443381\pi$
$6$	−1.45685	−0.594757
$7$	−2.33444	−0.882334	−0.441167	−	0.897425i	$-0.645435\pi$
$7$	−2.33444	−0.882334	−0.441167	+	0.897425i	$0.645435\pi$
$8$	1.00000	0.353553
$9$	−0.877587	−0.292529
$10$	0.791288	0.250227
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.45685	−0.420556
$13$	−0.354249	−0.0982509	−0.0491255	−	0.998793i	$-0.515643\pi$
$13$	−0.354249	−0.0982509	−0.0491255	+	0.998793i	$0.515643\pi$
$14$	−2.33444	−0.623905
$15$	−1.15279	−0.297649
$16$	1.00000	0.250000
$17$	−7.65300	−1.85613	−0.928063	−	0.372424i	$-0.878527\pi$
$17$	−7.65300	−1.85613	−0.928063	+	0.372424i	$0.878527\pi$
$18$	−0.877587	−0.206849
$19$	5.56670	1.27709	0.638545	−	0.769585i	$-0.279537\pi$
$19$	5.56670	1.27709	0.638545	+	0.769585i	$0.279537\pi$
$20$	0.791288	0.176937
$21$	3.40093	0.742143
$22$	−1.00000	−0.213201
$23$	−2.85446	−0.595197	−0.297598	−	0.954691i	$-0.596186\pi$
$23$	−2.85446	−0.595197	−0.297598	+	0.954691i	$0.596186\pi$
$24$	−1.45685	−0.297378
$25$	−4.37386	−0.874773
$26$	−0.354249	−0.0694739
$27$	5.64906	1.08716
$28$	−2.33444	−0.441167
$29$	−7.22108	−1.34092	−0.670460	−	0.741946i	$-0.733903\pi$
$29$	−7.22108	−1.34092	−0.670460	+	0.741946i	$0.733903\pi$
$30$	−1.15279	−0.210469
$31$	−8.21245	−1.47500	−0.737500	−	0.675347i	$-0.763994\pi$
$31$	−8.21245	−1.47500	−0.737500	+	0.675347i	$0.763994\pi$
$32$	1.00000	0.176777
$33$	1.45685	0.253605
$34$	−7.65300	−1.31248
$35$	−1.84721	−0.312236
$36$	−0.877587	−0.146265
$37$	5.13692	0.844504	0.422252	−	0.906479i	$-0.361240\pi$
$37$	5.13692	0.844504	0.422252	+	0.906479i	$0.361240\pi$
$38$	5.56670	0.903039
$39$	0.516087	0.0826401
$40$	0.791288	0.125114
$41$	−3.25208	−0.507889	−0.253945	−	0.967219i	$-0.581728\pi$
$41$	−3.25208	−0.507889	−0.253945	+	0.967219i	$0.581728\pi$
$42$	3.40093	0.524774
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	−0.694424	−0.103519
$46$	−2.85446	−0.420868
$47$	7.03943	1.02681	0.513403	−	0.858148i	$-0.328385\pi$
$47$	7.03943	1.02681	0.513403	+	0.858148i	$0.328385\pi$
$48$	−1.45685	−0.210278
$49$	−1.55040	−0.221486
$50$	−4.37386	−0.618558
$51$	11.1493	1.56121
$52$	−0.354249	−0.0491255
$53$	−1.79854	−0.247048	−0.123524	−	0.992342i	$-0.539420\pi$
$53$	−1.79854	−0.247048	−0.123524	+	0.992342i	$0.539420\pi$
$54$	5.64906	0.768740
$55$	−0.791288	−0.106697
$56$	−2.33444	−0.311952
$57$	−8.10985	−1.07418
$58$	−7.22108	−0.948174
$59$	−8.19615	−1.06705	−0.533524	−	0.845785i	$-0.679133\pi$
$59$	−8.19615	−1.06705	−0.533524	+	0.845785i	$0.679133\pi$
$60$	−1.15279	−0.148824
$61$	1.84190	0.235832	0.117916	−	0.993024i	$-0.462379\pi$
$61$	1.84190	0.235832	0.117916	+	0.993024i	$0.462379\pi$
$62$	−8.21245	−1.04298
$63$	2.04867	0.258109
$64$	1.00000	0.125000
$65$	−0.280313	−0.0347685
$66$	1.45685	0.179326
$67$	6.17634	0.754560	0.377280	−	0.926099i	$-0.376859\pi$
$67$	6.17634	0.754560	0.377280	+	0.926099i	$0.376859\pi$
$68$	−7.65300	−0.928063
$69$	4.15853	0.500628
$70$	−1.84721	−0.220784
$71$	−6.23952	−0.740494	−0.370247	−	0.928933i	$-0.620727\pi$
$71$	−6.23952	−0.740494	−0.370247	+	0.928933i	$0.620727\pi$
$72$	−0.877587	−0.103425
$73$	−14.9373	−1.74827	−0.874137	−	0.485680i	$-0.838572\pi$
$73$	−14.9373	−1.74827	−0.874137	+	0.485680i	$0.838572\pi$
$74$	5.13692	0.597154
$75$	6.37206	0.735783
$76$	5.56670	0.638545
$77$	2.33444	0.266034
$78$	0.516087	0.0584354
$79$	1.01630	0.114343	0.0571715	−	0.998364i	$-0.481792\pi$
$79$	1.01630	0.114343	0.0571715	+	0.998364i	$0.481792\pi$
$80$	0.791288	0.0884687
$81$	−5.59708	−0.621898
$82$	−3.25208	−0.359132
$83$	10.5740	1.16064	0.580321	−	0.814388i	$-0.302927\pi$
$83$	10.5740	1.16064	0.580321	+	0.814388i	$0.302927\pi$
$84$	3.40093	0.371071
$85$	−6.05573	−0.656836
$86$	1.00000	0.107833
$87$	10.5200	1.12787
$88$	−1.00000	−0.106600
$89$	2.90839	0.308289	0.154144	−	0.988048i	$-0.450738\pi$
$89$	2.90839	0.308289	0.154144	+	0.988048i	$0.450738\pi$
$90$	−0.694424	−0.0731987
$91$	0.826971	0.0866902
$92$	−2.85446	−0.297598
$93$	11.9643	1.24064
$94$	7.03943	0.726061
$95$	4.40486	0.451930
$96$	−1.45685	−0.148689
$97$	−13.6654	−1.38751	−0.693754	−	0.720212i	$-0.744044\pi$
$97$	−13.6654	−1.38751	−0.693754	+	0.720212i	$0.744044\pi$
$98$	−1.55040	−0.156614
$99$	0.877587	0.0882008
$100$	−4.37386	−0.437386
$101$	−4.41742	−0.439550	−0.219775	−	0.975551i	$-0.570532\pi$
$101$	−4.41742	−0.439550	−0.219775	+	0.975551i	$0.570532\pi$
$102$	11.1493	1.10394
$103$	14.5238	1.43107	0.715535	−	0.698577i	$-0.246183\pi$
$103$	14.5238	1.43107	0.715535	+	0.698577i	$0.246183\pi$
$104$	−0.354249	−0.0347369
$105$	2.69111	0.262626
$106$	−1.79854	−0.174690
$107$	1.23364	0.119260	0.0596300	−	0.998221i	$-0.481008\pi$
$107$	1.23364	0.119260	0.0596300	+	0.998221i	$0.481008\pi$
$108$	5.64906	0.543581
$109$	−7.70362	−0.737873	−0.368936	−	0.929455i	$-0.620278\pi$
$109$	−7.70362	−0.737873	−0.368936	+	0.929455i	$0.620278\pi$
$110$	−0.791288	−0.0754463
$111$	−7.48372	−0.710323
$112$	−2.33444	−0.220584
$113$	14.7267	1.38538	0.692688	−	0.721238i	$-0.256426\pi$
$113$	14.7267	1.38538	0.692688	+	0.721238i	$0.256426\pi$
$114$	−8.10985	−0.759557
$115$	−2.25870	−0.210625
$116$	−7.22108	−0.670460
$117$	0.310884	0.0287413
$118$	−8.19615	−0.754517
$119$	17.8655	1.63772
$120$	−1.15279	−0.105235
$121$	1.00000	0.0909091
$122$	1.84190	0.166758
$123$	4.73779	0.427192
$124$	−8.21245	−0.737500
$125$	−7.41742	−0.663435
$126$	2.04867	0.182510
$127$	0.199661	0.0177171	0.00885854	−	0.999961i	$-0.497180\pi$
$127$	0.199661	0.0177171	0.00885854	+	0.999961i	$0.497180\pi$
$128$	1.00000	0.0883883
$129$	−1.45685	−0.128269
$130$	−0.280313	−0.0245850
$131$	−9.45154	−0.825785	−0.412893	−	0.910780i	$-0.635481\pi$
$131$	−9.45154	−0.825785	−0.412893	+	0.910780i	$0.635481\pi$
$132$	1.45685	0.126803
$133$	−12.9951	−1.12682
$134$	6.17634	0.533555
$135$	4.47004	0.384719
$136$	−7.65300	−0.656240
$137$	22.1169	1.88957	0.944787	−	0.327684i	$-0.106268\pi$
$137$	22.1169	1.88957	0.944787	+	0.327684i	$0.106268\pi$
$138$	4.15853	0.353997
$139$	4.19615	0.355913	0.177957	−	0.984038i	$-0.443051\pi$
$139$	4.19615	0.355913	0.177957	+	0.984038i	$0.443051\pi$
$140$	−1.84721	−0.156118
$141$	−10.2554	−0.863660
$142$	−6.23952	−0.523609
$143$	0.354249	0.0296238
$144$	−0.877587	−0.0731323
$145$	−5.71395	−0.474518
$146$	−14.9373	−1.23622
$147$	2.25870	0.186295
$148$	5.13692	0.422252
$149$	3.10260	0.254175	0.127088	−	0.991892i	$-0.459437\pi$
$149$	3.10260	0.254175	0.127088	+	0.991892i	$0.459437\pi$
$150$	6.37206	0.520277
$151$	8.72012	0.709633	0.354817	−	0.934936i	$-0.384543\pi$
$151$	8.72012	0.709633	0.354817	+	0.934936i	$0.384543\pi$
$152$	5.56670	0.451519
$153$	6.71618	0.542971
$154$	2.33444	0.188114
$155$	−6.49842	−0.521965
$156$	0.516087	0.0413201
$157$	10.8058	0.862396	0.431198	−	0.902257i	$-0.358091\pi$
$157$	10.8058	0.862396	0.431198	+	0.902257i	$0.358091\pi$
$158$	1.01630	0.0808527
$159$	2.62020	0.207796
$160$	0.791288	0.0625568
$161$	6.66357	0.525163
$162$	−5.59708	−0.439748
$163$	19.4296	1.52184	0.760922	−	0.648844i	$-0.224747\pi$
$163$	19.4296	1.52184	0.760922	+	0.648844i	$0.224747\pi$
$164$	−3.25208	−0.253945
$165$	1.15279	0.0897444
$166$	10.5740	0.820698
$167$	2.96783	0.229657	0.114829	−	0.993385i	$-0.463368\pi$
$167$	2.96783	0.229657	0.114829	+	0.993385i	$0.463368\pi$
$168$	3.40093	0.262387
$169$	−12.8745	−0.990347
$170$	−6.05573	−0.464453
$171$	−4.88527	−0.373586
$172$	1.00000	0.0762493
$173$	−8.51078	−0.647063	−0.323531	−	0.946217i	$-0.604870\pi$
$173$	−8.51078	−0.647063	−0.323531	+	0.946217i	$0.604870\pi$
$174$	10.5200	0.797521
$175$	10.2105	0.771842
$176$	−1.00000	−0.0753778
$177$	11.9406	0.897508
$178$	2.90839	0.217993
$179$	1.76029	0.131570	0.0657850	−	0.997834i	$-0.479045\pi$
$179$	1.76029	0.131570	0.0657850	+	0.997834i	$0.479045\pi$
$180$	−0.694424	−0.0517593
$181$	19.2783	1.43295	0.716473	−	0.697615i	$-0.245755\pi$
$181$	19.2783	1.43295	0.716473	+	0.697615i	$0.245755\pi$
$182$	0.826971	0.0612992
$183$	−2.68338	−0.198361
$184$	−2.85446	−0.210434
$185$	4.06478	0.298848
$186$	11.9643	0.877266
$187$	7.65300	0.559643
$188$	7.03943	0.513403
$189$	−13.1874	−0.959241
$190$	4.40486	0.319562
$191$	−10.4410	−0.755483	−0.377741	−	0.925911i	$-0.623299\pi$
$191$	−10.4410	−0.755483	−0.377741	+	0.925911i	$0.623299\pi$
$192$	−1.45685	−0.105139
$193$	7.33093	0.527692	0.263846	−	0.964565i	$-0.415009\pi$
$193$	7.33093	0.527692	0.263846	+	0.964565i	$0.415009\pi$
$194$	−13.6654	−0.981116
$195$	0.408374	0.0292442
$196$	−1.55040	−0.110743
$197$	17.3270	1.23450	0.617248	−	0.786768i	$-0.288247\pi$
$197$	17.3270	1.23450	0.617248	+	0.786768i	$0.288247\pi$
$198$	0.877587	0.0623674
$199$	−23.7362	−1.68262	−0.841308	−	0.540556i	$-0.818214\pi$
$199$	−23.7362	−1.68262	−0.841308	+	0.540556i	$0.818214\pi$
$200$	−4.37386	−0.309279
$201$	−8.99800	−0.634670
$202$	−4.41742	−0.310809
$203$	16.8572	1.18314
$204$	11.1493	0.780606
$205$	−2.57333	−0.179729
$206$	14.5238	1.01192
$207$	2.50504	0.174112
$208$	−0.354249	−0.0245627
$209$	−5.56670	−0.385057
$210$	2.69111	0.185704
$211$	8.12042	0.559033	0.279516	−	0.960141i	$-0.409826\pi$
$211$	8.12042	0.559033	0.279516	+	0.960141i	$0.409826\pi$
$212$	−1.79854	−0.123524
$213$	9.09004	0.622839
$214$	1.23364	0.0843296
$215$	0.791288	0.0539654
$216$	5.64906	0.384370
$217$	19.1715	1.30144
$218$	−7.70362	−0.521755
$219$	21.7613	1.47050
$220$	−0.791288	−0.0533486
$221$	2.71107	0.182366
$222$	−7.48372	−0.502274
$223$	11.5879	0.775982	0.387991	−	0.921663i	$-0.373169\pi$
$223$	11.5879	0.775982	0.387991	+	0.921663i	$0.373169\pi$
$224$	−2.33444	−0.155976
$225$	3.83845	0.255896
$226$	14.7267	0.979608
$227$	−15.7855	−1.04772	−0.523862	−	0.851803i	$-0.675509\pi$
$227$	−15.7855	−1.04772	−0.523862	+	0.851803i	$0.675509\pi$
$228$	−8.10985	−0.537088
$229$	7.91413	0.522980	0.261490	−	0.965206i	$-0.415786\pi$
$229$	7.91413	0.522980	0.261490	+	0.965206i	$0.415786\pi$
$230$	−2.25870	−0.148934
$231$	−3.40093	−0.223765
$232$	−7.22108	−0.474087
$233$	−15.8709	−1.03974	−0.519869	−	0.854246i	$-0.674019\pi$
$233$	−15.8709	−1.03974	−0.519869	+	0.854246i	$0.674019\pi$
$234$	0.310884	0.0203231
$235$	5.57021	0.363361
$236$	−8.19615	−0.533524
$237$	−1.48060	−0.0961753
$238$	17.8655	1.15805
$239$	−17.1493	−1.10929	−0.554647	−	0.832086i	$-0.687147\pi$
$239$	−17.1493	−1.10929	−0.554647	+	0.832086i	$0.687147\pi$
$240$	−1.15279	−0.0744121
$241$	17.9196	1.15430	0.577151	−	0.816638i	$-0.304164\pi$
$241$	17.9196	1.15430	0.577151	+	0.816638i	$0.304164\pi$
$242$	1.00000	0.0642824
$243$	−8.79309	−0.564077
$244$	1.84190	0.117916
$245$	−1.22681	−0.0783782
$246$	4.73779	0.302070
$247$	−1.97200	−0.125475
$248$	−8.21245	−0.521491
$249$	−15.4047	−0.976231
$250$	−7.41742	−0.469119
$251$	−18.4240	−1.16292	−0.581458	−	0.813577i	$-0.697517\pi$
$251$	−18.4240	−1.16292	−0.581458	+	0.813577i	$0.697517\pi$
$252$	2.04867	0.129054
$253$	2.85446	0.179459
$254$	0.199661	0.0125279
$255$	8.82229	0.552473
$256$	1.00000	0.0625000
$257$	−3.33112	−0.207790	−0.103895	−	0.994588i	$-0.533131\pi$
$257$	−3.33112	−0.207790	−0.103895	+	0.994588i	$0.533131\pi$
$258$	−1.45685	−0.0906995
$259$	−11.9918	−0.745135
$260$	−0.280313	−0.0173843
$261$	6.33712	0.392258
$262$	−9.45154	−0.583918
$263$	−1.55614	−0.0959556	−0.0479778	−	0.998848i	$-0.515278\pi$
$263$	−1.55614	−0.0959556	−0.0479778	+	0.998848i	$0.515278\pi$
$264$	1.45685	0.0896629
$265$	−1.42316	−0.0874242
$266$	−12.9951	−0.796782
$267$	−4.23709	−0.259306
$268$	6.17634	0.377280
$269$	−27.9417	−1.70364	−0.851819	−	0.523836i	$-0.824500\pi$
$269$	−27.9417	−1.70364	−0.851819	+	0.523836i	$0.824500\pi$
$270$	4.47004	0.272038
$271$	−15.8037	−0.960003	−0.480002	−	0.877268i	$-0.659364\pi$
$271$	−15.8037	−0.960003	−0.480002	+	0.877268i	$0.659364\pi$
$272$	−7.65300	−0.464031
$273$	−1.20477	−0.0729162
$274$	22.1169	1.33613
$275$	4.37386	0.263754
$276$	4.15853	0.250314
$277$	−6.15790	−0.369992	−0.184996	−	0.982739i	$-0.559227\pi$
$277$	−6.15790	−0.369992	−0.184996	+	0.982739i	$0.559227\pi$
$278$	4.19615	0.251668
$279$	7.20715	0.431481
$280$	−1.84721	−0.110392
$281$	18.1175	1.08080	0.540401	−	0.841408i	$-0.318273\pi$
$281$	18.1175	1.08080	0.540401	+	0.841408i	$0.318273\pi$
$282$	−10.2554	−0.610700
$283$	12.1313	0.721129	0.360564	−	0.932734i	$-0.382584\pi$
$283$	12.1313	0.721129	0.360564	+	0.932734i	$0.382584\pi$
$284$	−6.23952	−0.370247
$285$	−6.41723	−0.380124
$286$	0.354249	0.0209472
$287$	7.59177	0.448128
$288$	−0.877587	−0.0517123
$289$	41.5684	2.44520
$290$	−5.71395	−0.335535
$291$	19.9084	1.16705
$292$	−14.9373	−0.874137
$293$	−24.5885	−1.43647	−0.718237	−	0.695799i	$-0.755050\pi$
$293$	−24.5885	−1.43647	−0.718237	+	0.695799i	$0.755050\pi$
$294$	2.25870	0.131730
$295$	−6.48552	−0.377601
$296$	5.13692	0.298577
$297$	−5.64906	−0.327792
$298$	3.10260	0.179729
$299$	1.01119	0.0584786
$300$	6.37206	0.367891
$301$	−2.33444	−0.134555
$302$	8.72012	0.501786
$303$	6.43553	0.369711
$304$	5.56670	0.319272
$305$	1.45748	0.0834548
$306$	6.71618	0.383938
$307$	−30.0916	−1.71742	−0.858710	−	0.512461i	$-0.828734\pi$
$307$	−30.0916	−1.71742	−0.858710	+	0.512461i	$0.828734\pi$
$308$	2.33444	0.133017
$309$	−21.1590	−1.20369
$310$	−6.49842	−0.369085
$311$	27.9431	1.58451	0.792255	−	0.610190i	$-0.208907\pi$
$311$	27.9431	1.58451	0.792255	+	0.610190i	$0.208907\pi$
$312$	0.516087	0.0292177
$313$	−31.0227	−1.75351	−0.876754	−	0.480939i	$-0.840296\pi$
$313$	−31.0227	−1.75351	−0.876754	+	0.480939i	$0.840296\pi$
$314$	10.8058	0.609806
$315$	1.62109	0.0913381
$316$	1.01630	0.0571715
$317$	−32.5500	−1.82819	−0.914095	−	0.405499i	$-0.867098\pi$
$317$	−32.5500	−1.82819	−0.914095	+	0.405499i	$0.867098\pi$
$318$	2.62020	0.146934
$319$	7.22108	0.404303
$320$	0.791288	0.0442343
$321$	−1.79722	−0.100311
$322$	6.66357	0.371346
$323$	−42.6020	−2.37044
$324$	−5.59708	−0.310949
$325$	1.54944	0.0859472
$326$	19.4296	1.07611
$327$	11.2230	0.620634
$328$	−3.25208	−0.179566
$329$	−16.4331	−0.905986
$330$	1.15279	0.0634589
$331$	−25.2981	−1.39051	−0.695255	−	0.718763i	$-0.744709\pi$
$331$	−25.2981	−1.39051	−0.695255	+	0.718763i	$0.744709\pi$
$332$	10.5740	0.580321
$333$	−4.50809	−0.247042
$334$	2.96783	0.162392
$335$	4.88726	0.267020
$336$	3.40093	0.185536
$337$	−18.2179	−0.992393	−0.496196	−	0.868210i	$-0.665270\pi$
$337$	−18.2179	−0.992393	−0.496196	+	0.868210i	$0.665270\pi$
$338$	−12.8745	−0.700281
$339$	−21.4547	−1.16526
$340$	−6.05573	−0.328418
$341$	8.21245	0.444729
$342$	−4.88527	−0.264165
$343$	19.9604	1.07776
$344$	1.00000	0.0539164
$345$	3.29059	0.177159
$346$	−8.51078	−0.457542
$347$	−16.9912	−0.912134	−0.456067	−	0.889945i	$-0.650742\pi$
$347$	−16.9912	−0.912134	−0.456067	+	0.889945i	$0.650742\pi$
$348$	10.5200	0.563933
$349$	−34.4086	−1.84185	−0.920925	−	0.389739i	$-0.872565\pi$
$349$	−34.4086	−1.84185	−0.920925	+	0.389739i	$0.872565\pi$
$350$	10.2105	0.545775
$351$	−2.00117	−0.106815
$352$	−1.00000	−0.0533002
$353$	−20.7631	−1.10511	−0.552554	−	0.833477i	$-0.686347\pi$
$353$	−20.7631	−1.10511	−0.552554	+	0.833477i	$0.686347\pi$
$354$	11.9406	0.634634
$355$	−4.93725	−0.262042
$356$	2.90839	0.154144
$357$	−26.0273	−1.37751
$358$	1.76029	0.0930340
$359$	−21.7505	−1.14795	−0.573974	−	0.818874i	$-0.694599\pi$
$359$	−21.7505	−1.14795	−0.573974	+	0.818874i	$0.694599\pi$
$360$	−0.694424	−0.0365994
$361$	11.9882	0.630957
$362$	19.2783	1.01325
$363$	−1.45685	−0.0764648
$364$	0.826971	0.0433451
$365$	−11.8197	−0.618670
$366$	−2.68338	−0.140262
$367$	17.0790	0.891519	0.445760	−	0.895153i	$-0.352934\pi$
$367$	17.0790	0.891519	0.445760	+	0.895153i	$0.352934\pi$
$368$	−2.85446	−0.148799
$369$	2.85398	0.148572
$370$	4.06478	0.211318
$371$	4.19858	0.217979
$372$	11.9643	0.620321
$373$	12.2368	0.633595	0.316797	−	0.948493i	$-0.397392\pi$
$373$	12.2368	0.633595	0.316797	+	0.948493i	$0.397392\pi$
$374$	7.65300	0.395727
$375$	10.8061	0.558023
$376$	7.03943	0.363031
$377$	2.55806	0.131747
$378$	−13.1874	−0.678286
$379$	25.0079	1.28457	0.642285	−	0.766466i	$-0.277987\pi$
$379$	25.0079	1.28457	0.642285	+	0.766466i	$0.277987\pi$
$380$	4.40486	0.225965
$381$	−0.290877	−0.0149021
$382$	−10.4410	−0.534207
$383$	−26.4199	−1.34999	−0.674997	−	0.737820i	$-0.735855\pi$
$383$	−26.4199	−1.34999	−0.674997	+	0.737820i	$0.735855\pi$
$384$	−1.45685	−0.0743446
$385$	1.84721	0.0941426
$386$	7.33093	0.373134
$387$	−0.877587	−0.0446103
$388$	−13.6654	−0.693754
$389$	−7.29150	−0.369694	−0.184847	−	0.982767i	$-0.559179\pi$
$389$	−7.29150	−0.369694	−0.184847	+	0.982767i	$0.559179\pi$
$390$	0.408374	0.0206788
$391$	21.8452	1.10476
$392$	−1.55040	−0.0783071
$393$	13.7695	0.694578
$394$	17.3270	0.872921
$395$	0.804187	0.0404631
$396$	0.877587	0.0441004
$397$	8.30098	0.416614	0.208307	−	0.978063i	$-0.433205\pi$
$397$	8.30098	0.416614	0.208307	+	0.978063i	$0.433205\pi$
$398$	−23.7362	−1.18979
$399$	18.9319	0.947783
$400$	−4.37386	−0.218693
$401$	6.60102	0.329639	0.164820	−	0.986324i	$-0.447296\pi$
$401$	6.60102	0.329639	0.164820	+	0.986324i	$0.447296\pi$
$402$	−8.99800	−0.448780
$403$	2.90925	0.144920
$404$	−4.41742	−0.219775
$405$	−4.42890	−0.220074
$406$	16.8572	0.836606
$407$	−5.13692	−0.254627
$408$	11.1493	0.551972
$409$	−35.4480	−1.75279	−0.876396	−	0.481591i	$-0.840059\pi$
$409$	−35.4480	−1.75279	−0.876396	+	0.481591i	$0.840059\pi$
$410$	−2.57333	−0.127088
$411$	−32.2210	−1.58935
$412$	14.5238	0.715535
$413$	19.1334	0.941493
$414$	2.50504	0.123116
$415$	8.36704	0.410722
$416$	−0.354249	−0.0173685
$417$	−6.11317	−0.299363
$418$	−5.56670	−0.272276
$419$	13.8349	0.675878	0.337939	−	0.941168i	$-0.390270\pi$
$419$	13.8349	0.675878	0.337939	+	0.941168i	$0.390270\pi$
$420$	2.69111	0.131313
$421$	16.2158	0.790308	0.395154	−	0.918615i	$-0.370691\pi$
$421$	16.2158	0.790308	0.395154	+	0.918615i	$0.370691\pi$
$422$	8.12042	0.395296
$423$	−6.17771	−0.300371
$424$	−1.79854	−0.0873448
$425$	33.4732	1.62369
$426$	9.09004	0.440414
$427$	−4.29981	−0.208082
$428$	1.23364	0.0596300
$429$	−0.516087	−0.0249169
$430$	0.791288	0.0381593
$431$	17.3288	0.834698	0.417349	−	0.908746i	$-0.362959\pi$
$431$	17.3288	0.834698	0.417349	+	0.908746i	$0.362959\pi$
$432$	5.64906	0.271791
$433$	35.0806	1.68587	0.842933	−	0.538019i	$-0.180827\pi$
$433$	35.0806	1.68587	0.842933	+	0.538019i	$0.180827\pi$
$434$	19.1715	0.920260
$435$	8.32437	0.399123
$436$	−7.70362	−0.368936
$437$	−15.8900	−0.760119
$438$	21.7613	1.03980
$439$	1.56339	0.0746166	0.0373083	−	0.999304i	$-0.488122\pi$
$439$	1.56339	0.0746166	0.0373083	+	0.999304i	$0.488122\pi$
$440$	−0.791288	−0.0377232
$441$	1.36061	0.0647911
$442$	2.71107	0.128952
$443$	29.9605	1.42347	0.711734	−	0.702449i	$-0.247910\pi$
$443$	29.9605	1.42347	0.711734	+	0.702449i	$0.247910\pi$
$444$	−7.48372	−0.355161
$445$	2.30138	0.109096
$446$	11.5879	0.548702
$447$	−4.52003	−0.213790
$448$	−2.33444	−0.110292
$449$	−3.11804	−0.147150	−0.0735748	−	0.997290i	$-0.523441\pi$
$449$	−3.11804	−0.147150	−0.0735748	+	0.997290i	$0.523441\pi$
$450$	3.83845	0.180946
$451$	3.25208	0.153134
$452$	14.7267	0.692688
$453$	−12.7039	−0.596881
$454$	−15.7855	−0.740853
$455$	0.654372	0.0306775
$456$	−8.10985	−0.379779
$457$	−1.41699	−0.0662842	−0.0331421	−	0.999451i	$-0.510551\pi$
$457$	−1.41699	−0.0662842	−0.0331421	+	0.999451i	$0.510551\pi$
$458$	7.91413	0.369803
$459$	−43.2323	−2.01791
$460$	−2.25870	−0.105313
$461$	12.9096	0.601258	0.300629	−	0.953741i	$-0.402803\pi$
$461$	12.9096	0.601258	0.300629	+	0.953741i	$0.402803\pi$
$462$	−3.40093	−0.158225
$463$	21.1785	0.984247	0.492124	−	0.870525i	$-0.336221\pi$
$463$	21.1785	0.984247	0.492124	+	0.870525i	$0.336221\pi$
$464$	−7.22108	−0.335230
$465$	9.46722	0.439032
$466$	−15.8709	−0.735206
$467$	−19.0007	−0.879246	−0.439623	−	0.898182i	$-0.644888\pi$
$467$	−19.0007	−0.879246	−0.439623	+	0.898182i	$0.644888\pi$
$468$	0.310884	0.0143706
$469$	−14.4183	−0.665774
$470$	5.57021	0.256935
$471$	−15.7424	−0.725372
$472$	−8.19615	−0.377258
$473$	−1.00000	−0.0459800
$474$	−1.48060	−0.0680062
$475$	−24.3480	−1.11716
$476$	17.8655	0.818862
$477$	1.57838	0.0722688
$478$	−17.1493	−0.784390
$479$	−30.5659	−1.39659	−0.698295	−	0.715810i	$-0.746058\pi$
$479$	−30.5659	−1.39659	−0.698295	+	0.715810i	$0.746058\pi$
$480$	−1.15279	−0.0526173
$481$	−1.81975	−0.0829733
$482$	17.9196	0.816215
$483$	−9.70782	−0.441721
$484$	1.00000	0.0454545
$485$	−10.8132	−0.491004
$486$	−8.79309	−0.398863
$487$	−19.7360	−0.894325	−0.447162	−	0.894453i	$-0.647565\pi$
$487$	−19.7360	−0.894325	−0.447162	+	0.894453i	$0.647565\pi$
$488$	1.84190	0.0833791
$489$	−28.3060	−1.28004
$490$	−1.22681	−0.0554218
$491$	9.10966	0.411113	0.205557	−	0.978645i	$-0.434100\pi$
$491$	9.10966	0.411113	0.205557	+	0.978645i	$0.434100\pi$
$492$	4.73779	0.213596
$493$	55.2629	2.48892
$494$	−1.97200	−0.0887244
$495$	0.694424	0.0312120
$496$	−8.21245	−0.368750
$497$	14.5658	0.653364
$498$	−15.4047	−0.690300
$499$	−12.0870	−0.541087	−0.270543	−	0.962708i	$-0.587203\pi$
$499$	−12.0870	−0.541087	−0.270543	+	0.962708i	$0.587203\pi$
$500$	−7.41742	−0.331717
$501$	−4.32368	−0.193168
$502$	−18.4240	−0.822306
$503$	−0.0107604	−0.000479782 0	−0.000239891	−	1.00000i	$-0.500076\pi$
$503$	−0.0107604	−0.000479782 0	−0.000239891		1.00000i	$0.500076\pi$
$504$	2.04867	0.0912551
$505$	−3.49545	−0.155546
$506$	2.85446	0.126896
$507$	18.7562	0.832993
$508$	0.199661	0.00885854
$509$	−22.1983	−0.983924	−0.491962	−	0.870617i	$-0.663720\pi$
$509$	−22.1983	−0.983924	−0.491962	+	0.870617i	$0.663720\pi$
$510$	8.82229	0.390658
$511$	34.8701	1.54256
$512$	1.00000	0.0441942
$513$	31.4467	1.38840
$514$	−3.33112	−0.146930
$515$	11.4925	0.506419
$516$	−1.45685	−0.0641343
$517$	−7.03943	−0.309594
$518$	−11.9918	−0.526890
$519$	12.3989	0.544253
$520$	−0.280313	−0.0122925
$521$	−35.8719	−1.57158	−0.785789	−	0.618495i	$-0.787743\pi$
$521$	−35.8719	−1.57158	−0.785789	+	0.618495i	$0.787743\pi$
$522$	6.33712	0.277368
$523$	−10.8685	−0.475248	−0.237624	−	0.971357i	$-0.576369\pi$
$523$	−10.8685	−0.475248	−0.237624	+	0.971357i	$0.576369\pi$
$524$	−9.45154	−0.412893
$525$	−14.8752	−0.649206
$526$	−1.55614	−0.0678509
$527$	62.8499	2.73779
$528$	1.45685	0.0634013
$529$	−14.8520	−0.645741
$530$	−1.42316	−0.0618182
$531$	7.19284	0.312143
$532$	−12.9951	−0.563410
$533$	1.15204	0.0499006
$534$	−4.23709	−0.183357
$535$	0.976161	0.0422031
$536$	6.17634	0.266777
$537$	−2.56447	−0.110665
$538$	−27.9417	−1.20465
$539$	1.55040	0.0667805
$540$	4.47004	0.192360
$541$	41.3874	1.77938	0.889692	−	0.456561i	$-0.150919\pi$
$541$	41.3874	1.77938	0.889692	+	0.456561i	$0.150919\pi$
$542$	−15.8037	−0.678825
$543$	−28.0856	−1.20527
$544$	−7.65300	−0.328120
$545$	−6.09578	−0.261115
$546$	−1.20477	−0.0515595
$547$	−17.3494	−0.741805	−0.370903	−	0.928672i	$-0.620952\pi$
$547$	−17.3494	−0.741805	−0.370903	+	0.928672i	$0.620952\pi$
$548$	22.1169	0.944787
$549$	−1.61643	−0.0689876
$550$	4.37386	0.186502
$551$	−40.1976	−1.71247
$552$	4.15853	0.176999
$553$	−2.37249	−0.100889
$554$	−6.15790	−0.261624
$555$	−5.92177	−0.251365
$556$	4.19615	0.177957
$557$	8.20895	0.347824	0.173912	−	0.984761i	$-0.444359\pi$
$557$	8.20895	0.347824	0.173912	+	0.984761i	$0.444359\pi$
$558$	7.20715	0.305103
$559$	−0.354249	−0.0149831
$560$	−1.84721	−0.0780590
$561$	−11.1493	−0.470723
$562$	18.1175	0.764242
$563$	31.3494	1.32122	0.660609	−	0.750730i	$-0.270298\pi$
$563$	31.3494	1.32122	0.660609	+	0.750730i	$0.270298\pi$
$564$	−10.2554	−0.431830
$565$	11.6531	0.490249
$566$	12.1313	0.509915
$567$	13.0660	0.548722
$568$	−6.23952	−0.261804
$569$	−10.3672	−0.434615	−0.217308	−	0.976103i	$-0.569727\pi$
$569$	−10.3672	−0.434615	−0.217308	+	0.976103i	$0.569727\pi$
$570$	−6.41723	−0.268788
$571$	18.5084	0.774554	0.387277	−	0.921963i	$-0.373416\pi$
$571$	18.5084	0.774554	0.387277	+	0.921963i	$0.373416\pi$
$572$	0.354249	0.0148119
$573$	15.2109	0.635446
$574$	7.59177	0.316874
$575$	12.4850	0.520662
$576$	−0.877587	−0.0365661
$577$	−28.7858	−1.19837	−0.599184	−	0.800611i	$-0.704508\pi$
$577$	−28.7858	−1.19837	−0.599184	+	0.800611i	$0.704508\pi$
$578$	41.5684	1.72902
$579$	−10.6801	−0.443848
$580$	−5.71395	−0.237259
$581$	−24.6842	−1.02407
$582$	19.9084	0.825229
$583$	1.79854	0.0744879
$584$	−14.9373	−0.618108
$585$	0.245999	0.0101708
$586$	−24.5885	−1.01574
$587$	−23.3162	−0.962364	−0.481182	−	0.876621i	$-0.659792\pi$
$587$	−23.3162	−0.962364	−0.481182	+	0.876621i	$0.659792\pi$
$588$	2.25870	0.0931473
$589$	−45.7163	−1.88371
$590$	−6.48552	−0.267004
$591$	−25.2428	−1.03835
$592$	5.13692	0.211126
$593$	−9.81304	−0.402973	−0.201487	−	0.979491i	$-0.564577\pi$
$593$	−9.81304	−0.402973	−0.201487	+	0.979491i	$0.564577\pi$
$594$	−5.64906	−0.231784
$595$	14.1367	0.579549
$596$	3.10260	0.127088
$597$	34.5801	1.41527
$598$	1.01119	0.0413506
$599$	−5.59770	−0.228716	−0.114358	−	0.993440i	$-0.536481\pi$
$599$	−5.59770	−0.228716	−0.114358	+	0.993440i	$0.536481\pi$
$600$	6.37206	0.260138
$601$	−9.31911	−0.380135	−0.190067	−	0.981771i	$-0.560871\pi$
$601$	−9.31911	−0.380135	−0.190067	+	0.981771i	$0.560871\pi$
$602$	−2.33444	−0.0951446
$603$	−5.42028	−0.220731
$604$	8.72012	0.354817
$605$	0.791288	0.0321704
$606$	6.43553	0.261425
$607$	16.6689	0.676569	0.338284	−	0.941044i	$-0.390153\pi$
$607$	16.6689	0.676569	0.338284	+	0.941044i	$0.390153\pi$
$608$	5.56670	0.225760
$609$	−24.5583	−0.995154
$610$	1.45748	0.0590115
$611$	−2.49371	−0.100885
$612$	6.71618	0.271485
$613$	−13.2546	−0.535349	−0.267675	−	0.963509i	$-0.586255\pi$
$613$	−13.2546	−0.535349	−0.267675	+	0.963509i	$0.586255\pi$
$614$	−30.0916	−1.21440
$615$	3.74895	0.151172
$616$	2.33444	0.0940572
$617$	35.5354	1.43060	0.715301	−	0.698816i	$-0.246290\pi$
$617$	35.5354	1.43060	0.715301	+	0.698816i	$0.246290\pi$
$618$	−21.1590	−0.851138
$619$	21.6376	0.869687	0.434843	−	0.900506i	$-0.356804\pi$
$619$	21.6376	0.869687	0.434843	+	0.900506i	$0.356804\pi$
$620$	−6.49842	−0.260983
$621$	−16.1250	−0.647076
$622$	27.9431	1.12042
$623$	−6.78946	−0.272014
$624$	0.516087	0.0206600
$625$	16.0000	0.640000
$626$	−31.0227	−1.23992
$627$	8.10985	0.323876
$628$	10.8058	0.431198
$629$	−39.3128	−1.56751
$630$	1.62109	0.0645858
$631$	4.25559	0.169412	0.0847061	−	0.996406i	$-0.473005\pi$
$631$	4.25559	0.169412	0.0847061	+	0.996406i	$0.473005\pi$
$632$	1.01630	0.0404263
$633$	−11.8302	−0.470209
$634$	−32.5500	−1.29273
$635$	0.157990	0.00626963
$636$	2.62020	0.103898
$637$	0.549228	0.0217612
$638$	7.22108	0.285885
$639$	5.47572	0.216616
$640$	0.791288	0.0312784
$641$	−9.84736	−0.388947	−0.194474	−	0.980908i	$-0.562300\pi$
$641$	−9.84736	−0.388947	−0.194474	+	0.980908i	$0.562300\pi$
$642$	−1.79722	−0.0709307
$643$	−22.0707	−0.870382	−0.435191	−	0.900338i	$-0.643319\pi$
$643$	−22.0707	−0.870382	−0.435191	+	0.900338i	$0.643319\pi$
$644$	6.66357	0.262581
$645$	−1.15279	−0.0453910
$646$	−42.6020	−1.67615
$647$	−37.5875	−1.47772	−0.738858	−	0.673861i	$-0.764635\pi$
$647$	−37.5875	−1.47772	−0.738858	+	0.673861i	$0.764635\pi$
$648$	−5.59708	−0.219874
$649$	8.19615	0.321727
$650$	1.54944	0.0607739
$651$	−27.9299	−1.09466
$652$	19.4296	0.760922
$653$	17.8164	0.697211	0.348606	−	0.937269i	$-0.386655\pi$
$653$	17.8164	0.697211	0.348606	+	0.937269i	$0.386655\pi$
$654$	11.2230	0.438855
$655$	−7.47889	−0.292224
$656$	−3.25208	−0.126972
$657$	13.1087	0.511421
$658$	−16.4331	−0.640629
$659$	−27.0914	−1.05533	−0.527665	−	0.849453i	$-0.676932\pi$
$659$	−27.0914	−1.05533	−0.527665	+	0.849453i	$0.676932\pi$
$660$	1.15279	0.0448722
$661$	40.9819	1.59401	0.797006	−	0.603971i	$-0.206416\pi$
$661$	40.9819	1.59401	0.797006	+	0.603971i	$0.206416\pi$
$662$	−25.2981	−0.983240
$663$	−3.94962	−0.153390
$664$	10.5740	0.410349
$665$	−10.2829	−0.398753
$666$	−4.50809	−0.174685
$667$	20.6123	0.798111
$668$	2.96783	0.114829
$669$	−16.8818	−0.652689
$670$	4.88726	0.188811
$671$	−1.84190	−0.0711059
$672$	3.40093	0.131194
$673$	−45.7246	−1.76255	−0.881277	−	0.472600i	$-0.843315\pi$
$673$	−45.7246	−1.76255	−0.881277	+	0.472600i	$0.843315\pi$
$674$	−18.2179	−0.701728
$675$	−24.7082	−0.951020
$676$	−12.8745	−0.495173
$677$	−35.8880	−1.37929	−0.689643	−	0.724149i	$-0.742233\pi$
$677$	−35.8880	−1.37929	−0.689643	+	0.724149i	$0.742233\pi$
$678$	−21.4547	−0.823961
$679$	31.9009	1.22425
$680$	−6.05573	−0.232227
$681$	22.9972	0.881254
$682$	8.21245	0.314471
$683$	−0.538467	−0.0206039	−0.0103019	−	0.999947i	$-0.503279\pi$
$683$	−0.538467	−0.0206039	−0.0103019	+	0.999947i	$0.503279\pi$
$684$	−4.88527	−0.186793
$685$	17.5008	0.668673
$686$	19.9604	0.762091
$687$	−11.5297	−0.439886
$688$	1.00000	0.0381246
$689$	0.637130	0.0242727
$690$	3.29059	0.125271
$691$	21.6469	0.823488	0.411744	−	0.911300i	$-0.364920\pi$
$691$	21.6469	0.823488	0.411744	+	0.911300i	$0.364920\pi$
$692$	−8.51078	−0.323531
$693$	−2.04867	−0.0778226
$694$	−16.9912	−0.644976
$695$	3.32036	0.125949
$696$	10.5200	0.398761
$697$	24.8882	0.942706
$698$	−34.4086	−1.30238
$699$	23.1215	0.874537
$700$	10.2105	0.385921
$701$	11.9877	0.452768	0.226384	−	0.974038i	$-0.427310\pi$
$701$	11.9877	0.452768	0.226384	+	0.974038i	$0.427310\pi$
$702$	−2.00117	−0.0755294
$703$	28.5957	1.07851
$704$	−1.00000	−0.0376889
$705$	−8.11497	−0.305627
$706$	−20.7631	−0.781429
$707$	10.3122	0.387830
$708$	11.9406	0.448754
$709$	−21.3649	−0.802376	−0.401188	−	0.915996i	$-0.631403\pi$
$709$	−21.3649	−0.802376	−0.401188	+	0.915996i	$0.631403\pi$
$710$	−4.93725	−0.185292
$711$	−0.891894	−0.0334486
$712$	2.90839	0.108997
$713$	23.4422	0.877915
$714$	−26.0273	−0.974047
$715$	0.280313	0.0104831
$716$	1.76029	0.0657850
$717$	24.9839	0.933042
$718$	−21.7505	−0.811721
$719$	29.4537	1.09844	0.549219	−	0.835678i	$-0.314925\pi$
$719$	29.4537	1.09844	0.549219	+	0.835678i	$0.314925\pi$
$720$	−0.694424	−0.0258797
$721$	−33.9048	−1.26268
$722$	11.9882	0.446154
$723$	−26.1061	−0.970898
$724$	19.2783	0.716473
$725$	31.5840	1.17300
$726$	−1.45685	−0.0540688
$727$	47.6383	1.76681	0.883404	−	0.468612i	$-0.155246\pi$
$727$	47.6383	1.76681	0.883404	+	0.468612i	$0.155246\pi$
$728$	0.826971	0.0306496
$729$	29.6014	1.09635
$730$	−11.8197	−0.437466
$731$	−7.65300	−0.283057
$732$	−2.68338	−0.0991805
$733$	−4.36938	−0.161387	−0.0806933	−	0.996739i	$-0.525713\pi$
$733$	−4.36938	−0.161387	−0.0806933	+	0.996739i	$0.525713\pi$
$734$	17.0790	0.630399
$735$	1.78728	0.0659250
$736$	−2.85446	−0.105217
$737$	−6.17634	−0.227508
$738$	2.85398	0.105057
$739$	−4.26487	−0.156886	−0.0784429	−	0.996919i	$-0.524995\pi$
$739$	−4.26487	−0.156886	−0.0784429	+	0.996919i	$0.524995\pi$
$740$	4.06478	0.149424
$741$	2.87290	0.105539
$742$	4.19858	0.154135
$743$	−31.0190	−1.13798	−0.568988	−	0.822346i	$-0.692665\pi$
$743$	−31.0190	−1.13798	−0.568988	+	0.822346i	$0.692665\pi$
$744$	11.9643	0.438633
$745$	2.45505	0.0899461
$746$	12.2368	0.448019
$747$	−9.27957	−0.339522
$748$	7.65300	0.279821
$749$	−2.87984	−0.105227
$750$	10.8061	0.394582
$751$	−23.7755	−0.867579	−0.433789	−	0.901014i	$-0.642824\pi$
$751$	−23.7755	−0.867579	−0.433789	+	0.901014i	$0.642824\pi$
$752$	7.03943	0.256701
$753$	26.8411	0.978143
$754$	2.55806	0.0931589
$755$	6.90012	0.251121
$756$	−13.1874	−0.479621
$757$	44.6324	1.62219	0.811096	−	0.584914i	$-0.198872\pi$
$757$	44.6324	1.62219	0.811096	+	0.584914i	$0.198872\pi$
$758$	25.0079	0.908328
$759$	−4.15853	−0.150945
$760$	4.40486	0.159781
$761$	6.20948	0.225094	0.112547	−	0.993646i	$-0.464099\pi$
$761$	6.20948	0.225094	0.112547	+	0.993646i	$0.464099\pi$
$762$	−0.290877	−0.0105374
$763$	17.9836	0.651051
$764$	−10.4410	−0.377741
$765$	5.31443	0.192144
$766$	−26.4199	−0.954590
$767$	2.90348	0.104838
$768$	−1.45685	−0.0525696
$769$	−9.40030	−0.338983	−0.169492	−	0.985532i	$-0.554213\pi$
$769$	−9.40030	−0.338983	−0.169492	+	0.985532i	$0.554213\pi$
$770$	1.84721	0.0665689
$771$	4.85295	0.174775
$772$	7.33093	0.263846
$773$	15.4531	0.555810	0.277905	−	0.960609i	$-0.410360\pi$
$773$	15.4531	0.555810	0.277905	+	0.960609i	$0.410360\pi$
$774$	−0.877587	−0.0315442
$775$	35.9202	1.29029
$776$	−13.6654	−0.490558
$777$	17.4703	0.626742
$778$	−7.29150	−0.261413
$779$	−18.1033	−0.648620
$780$	0.408374	0.0146221
$781$	6.23952	0.223267
$782$	21.8452	0.781183
$783$	−40.7923	−1.45780
$784$	−1.55040	−0.0553715
$785$	8.55049	0.305180
$786$	13.7695	0.491141
$787$	−56.0889	−1.99935	−0.999677	−	0.0254233i	$-0.991907\pi$
$787$	−56.0889	−1.99935	−0.999677	+	0.0254233i	$0.991907\pi$
$788$	17.3270	0.617248
$789$	2.26706	0.0807095
$790$	0.804187	0.0286117
$791$	−34.3787	−1.22236
$792$	0.877587	0.0311837
$793$	−0.652492	−0.0231707
$794$	8.30098	0.294591
$795$	2.07333	0.0735336
$796$	−23.7362	−0.841308
$797$	−22.2312	−0.787471	−0.393736	−	0.919224i	$-0.628817\pi$
$797$	−22.2312	−0.787471	−0.393736	+	0.919224i	$0.628817\pi$
$798$	18.9319	0.670184
$799$	−53.8727	−1.90588
$800$	−4.37386	−0.154639
$801$	−2.55237	−0.0901835
$802$	6.60102	0.233090
$803$	14.9373	0.527124
$804$	−8.99800	−0.317335
$805$	5.27280	0.185842
$806$	2.90925	0.102474
$807$	40.7069	1.43295
$808$	−4.41742	−0.155404
$809$	−24.2929	−0.854092	−0.427046	−	0.904230i	$-0.640446\pi$
$809$	−24.2929	−0.854092	−0.427046	+	0.904230i	$0.640446\pi$
$810$	−4.42890	−0.155616
$811$	5.29715	0.186008	0.0930041	−	0.995666i	$-0.470353\pi$
$811$	5.29715	0.186008	0.0930041	+	0.995666i	$0.470353\pi$
$812$	16.8572	0.591570
$813$	23.0236	0.807471
$814$	−5.13692	−0.180049
$815$	15.3744	0.538542
$816$	11.1493	0.390303
$817$	5.56670	0.194754
$818$	−35.4480	−1.23941
$819$	−0.725740	−0.0253594
$820$	−2.57333	−0.0898645
$821$	4.30301	0.150176	0.0750880	−	0.997177i	$-0.476076\pi$
$821$	4.30301	0.150176	0.0750880	+	0.997177i	$0.476076\pi$
$822$	−32.2210	−1.12384
$823$	47.2421	1.64676	0.823378	−	0.567493i	$-0.192086\pi$
$823$	47.2421	1.64676	0.823378	+	0.567493i	$0.192086\pi$
$824$	14.5238	0.505959
$825$	−6.37206	−0.221847
$826$	19.1334	0.665736
$827$	−4.23781	−0.147363	−0.0736815	−	0.997282i	$-0.523475\pi$
$827$	−4.23781	−0.147363	−0.0736815	+	0.997282i	$0.523475\pi$
$828$	2.50504	0.0870562
$829$	25.7685	0.894978	0.447489	−	0.894290i	$-0.352318\pi$
$829$	25.7685	0.894978	0.447489	+	0.894290i	$0.352318\pi$
$830$	8.36704	0.290424
$831$	8.97114	0.311205
$832$	−0.354249	−0.0122814
$833$	11.8652	0.411106
$834$	−6.11317	−0.211682
$835$	2.34840	0.0812699
$836$	−5.56670	−0.192528
$837$	−46.3927	−1.60357
$838$	13.8349	0.477918
$839$	−9.88035	−0.341108	−0.170554	−	0.985348i	$-0.554556\pi$
$839$	−9.88035	−0.341108	−0.170554	+	0.985348i	$0.554556\pi$
$840$	2.69111	0.0928522
$841$	23.1439	0.798067
$842$	16.2158	0.558832
$843$	−26.3945	−0.909076
$844$	8.12042	0.279516
$845$	−10.1874	−0.350459
$846$	−6.17771	−0.212394
$847$	−2.33444	−0.0802122
$848$	−1.79854	−0.0617621
$849$	−17.6734	−0.606551
$850$	33.4732	1.14812
$851$	−14.6631	−0.502646
$852$	9.09004	0.311420
$853$	−25.7743	−0.882494	−0.441247	−	0.897386i	$-0.645464\pi$
$853$	−25.7743	−0.882494	−0.441247	+	0.897386i	$0.645464\pi$
$854$	−4.29981	−0.147136
$855$	−3.86565	−0.132203
$856$	1.23364	0.0421648
$857$	10.5823	0.361486	0.180743	−	0.983530i	$-0.442150\pi$
$857$	10.5823	0.361486	0.180743	+	0.983530i	$0.442150\pi$
$858$	−0.516087	−0.0176189
$859$	19.8479	0.677201	0.338600	−	0.940930i	$-0.390047\pi$
$859$	19.8479	0.677201	0.338600	+	0.940930i	$0.390047\pi$
$860$	0.791288	0.0269827
$861$	−11.0601	−0.376926
$862$	17.3288	0.590221
$863$	−32.3011	−1.09954	−0.549772	−	0.835315i	$-0.685285\pi$
$863$	−32.3011	−1.09954	−0.549772	+	0.835315i	$0.685285\pi$
$864$	5.64906	0.192185
$865$	−6.73448	−0.228979
$866$	35.0806	1.19209
$867$	−60.5590	−2.05669
$868$	19.1715	0.650722
$869$	−1.01630	−0.0344757
$870$	8.32437	0.282223
$871$	−2.18796	−0.0741362
$872$	−7.70362	−0.260877
$873$	11.9926	0.405886
$874$	−15.8900	−0.537486
$875$	17.3155	0.585371
$876$	21.7613	0.735248
$877$	−47.9363	−1.61869	−0.809346	−	0.587332i	$-0.800178\pi$
$877$	−47.9363	−1.61869	−0.809346	+	0.587332i	$0.800178\pi$
$878$	1.56339	0.0527619
$879$	35.8217	1.20824
$880$	−0.791288	−0.0266743
$881$	9.83839	0.331464	0.165732	−	0.986171i	$-0.447001\pi$
$881$	9.83839	0.331464	0.165732	+	0.986171i	$0.447001\pi$
$882$	1.36061	0.0458142
$883$	42.3779	1.42613	0.713066	−	0.701097i	$-0.247306\pi$
$883$	42.3779	1.42613	0.713066	+	0.701097i	$0.247306\pi$
$884$	2.71107	0.0911830
$885$	9.44843	0.317605
$886$	29.9605	1.00654
$887$	19.0332	0.639072	0.319536	−	0.947574i	$-0.396473\pi$
$887$	19.0332	0.639072	0.319536	+	0.947574i	$0.396473\pi$
$888$	−7.48372	−0.251137
$889$	−0.466097	−0.0156324
$890$	2.30138	0.0771423
$891$	5.59708	0.187509
$892$	11.5879	0.387991
$893$	39.1864	1.31132
$894$	−4.52003	−0.151172
$895$	1.39289	0.0465593
$896$	−2.33444	−0.0779881
$897$	−1.47315	−0.0491871
$898$	−3.11804	−0.104050
$899$	59.3028	1.97786
$900$	3.83845	0.127948
$901$	13.7642	0.458553
$902$	3.25208	0.108282
$903$	3.40093	0.113176
$904$	14.7267	0.489804
$905$	15.2547	0.507083
$906$	−12.7039	−0.422059
$907$	43.2476	1.43601	0.718007	−	0.696036i	$-0.245055\pi$
$907$	43.2476	1.43601	0.718007	+	0.696036i	$0.245055\pi$
$908$	−15.7855	−0.523862
$909$	3.87668	0.128581
$910$	0.654372	0.0216922
$911$	15.9740	0.529243	0.264621	−	0.964352i	$-0.414753\pi$
$911$	15.9740	0.529243	0.264621	+	0.964352i	$0.414753\pi$
$912$	−8.10985	−0.268544
$913$	−10.5740	−0.349947
$914$	−1.41699	−0.0468700
$915$	−2.12332	−0.0701949
$916$	7.91413	0.261490
$917$	22.0640	0.728619
$918$	−43.2323	−1.42688
$919$	−17.7673	−0.586091	−0.293045	−	0.956099i	$-0.594669\pi$
$919$	−17.7673	−0.586091	−0.293045	+	0.956099i	$0.594669\pi$
$920$	−2.25870	−0.0744672
$921$	43.8390	1.44454
$922$	12.9096	0.425154
$923$	2.21034	0.0727543
$924$	−3.40093	−0.111882
$925$	−22.4682	−0.738749
$926$	21.1785	0.695968
$927$	−12.7459	−0.418629
$928$	−7.22108	−0.237043
$929$	16.1205	0.528897	0.264448	−	0.964400i	$-0.414810\pi$
$929$	16.1205	0.528897	0.264448	+	0.964400i	$0.414810\pi$
$930$	9.46722	0.310442
$931$	−8.63062	−0.282857
$932$	−15.8709	−0.519869
$933$	−40.7090	−1.33275
$934$	−19.0007	−0.621721
$935$	6.05573	0.198043
$936$	0.310884	0.0101616
$937$	9.94096	0.324757	0.162378	−	0.986729i	$-0.448083\pi$
$937$	9.94096	0.324757	0.162378	+	0.986729i	$0.448083\pi$
$938$	−14.4183	−0.470774
$939$	45.1955	1.47490
$940$	5.57021	0.181680
$941$	−36.5233	−1.19062	−0.595312	−	0.803495i	$-0.702972\pi$
$941$	−36.5233	−1.19062	−0.595312	+	0.803495i	$0.702972\pi$
$942$	−15.7424	−0.512916
$943$	9.28293	0.302294
$944$	−8.19615	−0.266762
$945$	−10.4350	−0.339451
$946$	−1.00000	−0.0325128
$947$	13.3179	0.432775	0.216387	−	0.976308i	$-0.430573\pi$
$947$	13.3179	0.432775	0.216387	+	0.976308i	$0.430573\pi$
$948$	−1.48060	−0.0480876
$949$	5.29150	0.171769
$950$	−24.3480	−0.789953
$951$	47.4205	1.53771
$952$	17.8655	0.579023
$953$	−24.6936	−0.799904	−0.399952	−	0.916536i	$-0.630973\pi$
$953$	−24.6936	−0.799904	−0.399952	+	0.916536i	$0.630973\pi$
$954$	1.57838	0.0511018
$955$	−8.26182	−0.267346
$956$	−17.1493	−0.554647
$957$	−10.5200	−0.340064
$958$	−30.5659	−0.987539
$959$	−51.6305	−1.66724
$960$	−1.15279	−0.0372061
$961$	36.4444	1.17563
$962$	−1.81975	−0.0586710
$963$	−1.08262	−0.0348870
$964$	17.9196	0.577151
$965$	5.80087	0.186737
$966$	−9.70782	−0.312344
$967$	17.5803	0.565346	0.282673	−	0.959216i	$-0.408779\pi$
$967$	17.5803	0.565346	0.282673	+	0.959216i	$0.408779\pi$
$968$	1.00000	0.0321412
$969$	62.0647	1.99381
$970$	−10.8132	−0.347192
$971$	20.9456	0.672176	0.336088	−	0.941831i	$-0.390896\pi$
$971$	20.9456	0.672176	0.336088	+	0.941831i	$0.390896\pi$
$972$	−8.79309	−0.282038
$973$	−9.79566	−0.314034
$974$	−19.7360	−0.632383
$975$	−2.25730	−0.0722913
$976$	1.84190	0.0589579
$977$	44.0255	1.40850	0.704250	−	0.709952i	$-0.251283\pi$
$977$	44.0255	1.40850	0.704250	+	0.709952i	$0.251283\pi$
$978$	−28.3060	−0.905126
$979$	−2.90839	−0.0929526
$980$	−1.22681	−0.0391891
$981$	6.76060	0.215849
$982$	9.10966	0.290701
$983$	15.0358	0.479567	0.239783	−	0.970826i	$-0.422924\pi$
$983$	15.0358	0.479567	0.239783	+	0.970826i	$0.422924\pi$
$984$	4.73779	0.151035
$985$	13.7106	0.436857
$986$	55.2629	1.75993
$987$	23.9406	0.762037
$988$	−1.97200	−0.0627376
$989$	−2.85446	−0.0907667
$990$	0.694424	0.0220702
$991$	14.4848	0.460125	0.230062	−	0.973176i	$-0.426107\pi$
$991$	14.4848	0.460125	0.230062	+	0.973176i	$0.426107\pi$
$992$	−8.21245	−0.260746
$993$	36.8556	1.16958
$994$	14.5658	0.461998
$995$	−18.7822	−0.595435
$996$	−15.4047	−0.488116
$997$	−1.60464	−0.0508196	−0.0254098	−	0.999677i	$-0.508089\pi$
$997$	−1.60464	−0.0508196	−0.0254098	+	0.999677i	$0.508089\pi$
$998$	−12.0870	−0.382606
$999$	29.0188	0.918113

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.a.g.1.2	✓	4
3.2	odd	2		8514.2.a.bd.1.2		4
4.3	odd	2		7568.2.a.z.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.a.g.1.2	✓	4	1.1	even	1	trivial
7568.2.a.z.1.3		4	4.3	odd	2
8514.2.a.bd.1.2		4	3.2	odd	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:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.45685 q^{3} +1.00000 q^{4} +0.791288 q^{5} -1.45685 q^{6} -2.33444 q^{7} +1.00000 q^{8} -0.877587 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.45685 q^{3} +1.00000 q^{4} +0.791288 q^{5} -1.45685 q^{6} -2.33444 q^{7} +1.00000 q^{8} -0.877587 q^{9} +0.791288 q^{10} -1.00000 q^{11} -1.45685 q^{12} -0.354249 q^{13} -2.33444 q^{14} -1.15279 q^{15} +1.00000 q^{16} -7.65300 q^{17} -0.877587 q^{18} +5.56670 q^{19} +0.791288 q^{20} +3.40093 q^{21} -1.00000 q^{22} -2.85446 q^{23} -1.45685 q^{24} -4.37386 q^{25} -0.354249 q^{26} +5.64906 q^{27} -2.33444 q^{28} -7.22108 q^{29} -1.15279 q^{30} -8.21245 q^{31} +1.00000 q^{32} +1.45685 q^{33} -7.65300 q^{34} -1.84721 q^{35} -0.877587 q^{36} +5.13692 q^{37} +5.56670 q^{38} +0.516087 q^{39} +0.791288 q^{40} -3.25208 q^{41} +3.40093 q^{42} +1.00000 q^{43} -1.00000 q^{44} -0.694424 q^{45} -2.85446 q^{46} +7.03943 q^{47} -1.45685 q^{48} -1.55040 q^{49} -4.37386 q^{50} +11.1493 q^{51} -0.354249 q^{52} -1.79854 q^{53} +5.64906 q^{54} -0.791288 q^{55} -2.33444 q^{56} -8.10985 q^{57} -7.22108 q^{58} -8.19615 q^{59} -1.15279 q^{60} +1.84190 q^{61} -8.21245 q^{62} +2.04867 q^{63} +1.00000 q^{64} -0.280313 q^{65} +1.45685 q^{66} +6.17634 q^{67} -7.65300 q^{68} +4.15853 q^{69} -1.84721 q^{70} -6.23952 q^{71} -0.877587 q^{72} -14.9373 q^{73} +5.13692 q^{74} +6.37206 q^{75} +5.56670 q^{76} +2.33444 q^{77} +0.516087 q^{78} +1.01630 q^{79} +0.791288 q^{80} -5.59708 q^{81} -3.25208 q^{82} +10.5740 q^{83} +3.40093 q^{84} -6.05573 q^{85} +1.00000 q^{86} +10.5200 q^{87} -1.00000 q^{88} +2.90839 q^{89} -0.694424 q^{90} +0.826971 q^{91} -2.85446 q^{92} +11.9643 q^{93} +7.03943 q^{94} +4.40486 q^{95} -1.45685 q^{96} -13.6654 q^{97} -1.55040 q^{98} +0.877587 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 + 2 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} + 2 q^{9} - 6 q^{10} - 4 q^{11} - 4 q^{12} - 12 q^{13} - 2 q^{14} + 6 q^{15} + 4 q^{16} - 8 q^{17} + 2 q^{18} - 4 q^{19} - 6 q^{20} - 8 q^{21} - 4 q^{22} - 10 q^{23} - 4 q^{24} + 10 q^{25} - 12 q^{26} - 10 q^{27} - 2 q^{28} - 12 q^{29} + 6 q^{30} + 4 q^{31} + 4 q^{32} + 4 q^{33} - 8 q^{34} - 18 q^{35} + 2 q^{36} + 2 q^{37} - 4 q^{38} - 2 q^{39} - 6 q^{40} - 12 q^{41} - 8 q^{42} + 4 q^{43} - 4 q^{44} - 24 q^{45} - 10 q^{46} + 8 q^{47} - 4 q^{48} + 4 q^{49} + 10 q^{50} - 12 q^{52} + 14 q^{53} - 10 q^{54} + 6 q^{55} - 2 q^{56} - 8 q^{57} - 12 q^{58} - 12 q^{59} + 6 q^{60} - 24 q^{61} + 4 q^{62} + 40 q^{63} + 4 q^{64} + 18 q^{65} + 4 q^{66} - 14 q^{67} - 8 q^{68} + 24 q^{69} - 18 q^{70} + 6 q^{71} + 2 q^{72} - 28 q^{73} + 2 q^{74} - 10 q^{75} - 4 q^{76} + 2 q^{77} - 2 q^{78} - 12 q^{79} - 6 q^{80} + 20 q^{81} - 12 q^{82} + 4 q^{83} - 8 q^{84} + 12 q^{85} + 4 q^{86} + 48 q^{87} - 4 q^{88} - 34 q^{89} - 24 q^{90} + 20 q^{91} - 10 q^{92} + 22 q^{93} + 8 q^{94} + 6 q^{95} - 4 q^{96} - 6 q^{97} + 4 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^8 + 2 * q^9 - 6 * q^10 - 4 * q^11 - 4 * q^12 - 12 * q^13 - 2 * q^14 + 6 * q^15 + 4 * q^16 - 8 * q^17 + 2 * q^18 - 4 * q^19 - 6 * q^20 - 8 * q^21 - 4 * q^22 - 10 * q^23 - 4 * q^24 + 10 * q^25 - 12 * q^26 - 10 * q^27 - 2 * q^28 - 12 * q^29 + 6 * q^30 + 4 * q^31 + 4 * q^32 + 4 * q^33 - 8 * q^34 - 18 * q^35 + 2 * q^36 + 2 * q^37 - 4 * q^38 - 2 * q^39 - 6 * q^40 - 12 * q^41 - 8 * q^42 + 4 * q^43 - 4 * q^44 - 24 * q^45 - 10 * q^46 + 8 * q^47 - 4 * q^48 + 4 * q^49 + 10 * q^50 - 12 * q^52 + 14 * q^53 - 10 * q^54 + 6 * q^55 - 2 * q^56 - 8 * q^57 - 12 * q^58 - 12 * q^59 + 6 * q^60 - 24 * q^61 + 4 * q^62 + 40 * q^63 + 4 * q^64 + 18 * q^65 + 4 * q^66 - 14 * q^67 - 8 * q^68 + 24 * q^69 - 18 * q^70 + 6 * q^71 + 2 * q^72 - 28 * q^73 + 2 * q^74 - 10 * q^75 - 4 * q^76 + 2 * q^77 - 2 * q^78 - 12 * q^79 - 6 * q^80 + 20 * q^81 - 12 * q^82 + 4 * q^83 - 8 * q^84 + 12 * q^85 + 4 * q^86 + 48 * q^87 - 4 * q^88 - 34 * q^89 - 24 * q^90 + 20 * q^91 - 10 * q^92 + 22 * q^93 + 8 * q^94 + 6 * q^95 - 4 * q^96 - 6 * q^97 + 4 * q^98 - 2 * q^99

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