LMFDB - Embedded newform 1334.2.a.k.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, 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("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5x^{9} - 8x^{8} + 60x^{7} + 13x^{6} - 241x^{5} + 6x^{4} + 346x^{3} + 16x^{2} - 64x - 12 $ x^10 - 5x^9 - 8x^8 + 60x^7 + 13x^6 - 241x^5 + 6x^4 + 346x^3 + 16x^2 - 64*x - 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.521310$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.478690 q^{3} +1.00000 q^{4} -3.82976 q^{5} +0.478690 q^{6} +4.18279 q^{7} +1.00000 q^{8} -2.77086 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.478690 q^{3} +1.00000 q^{4} -3.82976 q^{5} +0.478690 q^{6} +4.18279 q^{7} +1.00000 q^{8} -2.77086 q^{9} -3.82976 q^{10} +0.506106 q^{11} +0.478690 q^{12} -0.446148 q^{13} +4.18279 q^{14} -1.83326 q^{15} +1.00000 q^{16} +2.81298 q^{17} -2.77086 q^{18} +6.82204 q^{19} -3.82976 q^{20} +2.00226 q^{21} +0.506106 q^{22} +1.00000 q^{23} +0.478690 q^{24} +9.66703 q^{25} -0.446148 q^{26} -2.76245 q^{27} +4.18279 q^{28} +1.00000 q^{29} -1.83326 q^{30} +8.63271 q^{31} +1.00000 q^{32} +0.242268 q^{33} +2.81298 q^{34} -16.0191 q^{35} -2.77086 q^{36} +6.56131 q^{37} +6.82204 q^{38} -0.213567 q^{39} -3.82976 q^{40} +7.95531 q^{41} +2.00226 q^{42} +0.372597 q^{43} +0.506106 q^{44} +10.6117 q^{45} +1.00000 q^{46} -12.2862 q^{47} +0.478690 q^{48} +10.4957 q^{49} +9.66703 q^{50} +1.34654 q^{51} -0.446148 q^{52} -3.90843 q^{53} -2.76245 q^{54} -1.93826 q^{55} +4.18279 q^{56} +3.26564 q^{57} +1.00000 q^{58} -10.5728 q^{59} -1.83326 q^{60} -6.55468 q^{61} +8.63271 q^{62} -11.5899 q^{63} +1.00000 q^{64} +1.70864 q^{65} +0.242268 q^{66} -16.1476 q^{67} +2.81298 q^{68} +0.478690 q^{69} -16.0191 q^{70} +12.6016 q^{71} -2.77086 q^{72} +7.47554 q^{73} +6.56131 q^{74} +4.62751 q^{75} +6.82204 q^{76} +2.11694 q^{77} -0.213567 q^{78} +5.65596 q^{79} -3.82976 q^{80} +6.99021 q^{81} +7.95531 q^{82} +18.0029 q^{83} +2.00226 q^{84} -10.7730 q^{85} +0.372597 q^{86} +0.478690 q^{87} +0.506106 q^{88} -6.85755 q^{89} +10.6117 q^{90} -1.86615 q^{91} +1.00000 q^{92} +4.13239 q^{93} -12.2862 q^{94} -26.1267 q^{95} +0.478690 q^{96} +5.41841 q^{97} +10.4957 q^{98} -1.40235 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9} - q^{10} + q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 10 q^{16} + 11 q^{18} + 20 q^{19} - q^{20} + 14 q^{21} + q^{22} + 10 q^{23} + 5 q^{24} + 23 q^{25} + 9 q^{26} + 23 q^{27} + 2 q^{28} + 10 q^{29} + 5 q^{30} + 21 q^{31} + 10 q^{32} + q^{33} + 2 q^{35} + 11 q^{36} - 8 q^{37} + 20 q^{38} + 23 q^{39} - q^{40} - 4 q^{41} + 14 q^{42} - 3 q^{43} + q^{44} - 18 q^{45} + 10 q^{46} - q^{47} + 5 q^{48} + 18 q^{49} + 23 q^{50} - 6 q^{51} + 9 q^{52} - 13 q^{53} + 23 q^{54} + 13 q^{55} + 2 q^{56} - 22 q^{57} + 10 q^{58} + 14 q^{59} + 5 q^{60} + 12 q^{61} + 21 q^{62} - 26 q^{63} + 10 q^{64} - 25 q^{65} + q^{66} + 6 q^{67} + 5 q^{69} + 2 q^{70} + 8 q^{71} + 11 q^{72} + 16 q^{73} - 8 q^{74} + 8 q^{75} + 20 q^{76} - 16 q^{77} + 23 q^{78} + 7 q^{79} - q^{80} - 2 q^{81} - 4 q^{82} + 18 q^{83} + 14 q^{84} + 8 q^{85} - 3 q^{86} + 5 q^{87} + q^{88} + 2 q^{89} - 18 q^{90} + 8 q^{91} + 10 q^{92} - 41 q^{93} - q^{94} - 16 q^{95} + 5 q^{96} + 6 q^{97} + 18 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9 - q^10 + q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 10 * q^16 + 11 * q^18 + 20 * q^19 - q^20 + 14 * q^21 + q^22 + 10 * q^23 + 5 * q^24 + 23 * q^25 + 9 * q^26 + 23 * q^27 + 2 * q^28 + 10 * q^29 + 5 * q^30 + 21 * q^31 + 10 * q^32 + q^33 + 2 * q^35 + 11 * q^36 - 8 * q^37 + 20 * q^38 + 23 * q^39 - q^40 - 4 * q^41 + 14 * q^42 - 3 * q^43 + q^44 - 18 * q^45 + 10 * q^46 - q^47 + 5 * q^48 + 18 * q^49 + 23 * q^50 - 6 * q^51 + 9 * q^52 - 13 * q^53 + 23 * q^54 + 13 * q^55 + 2 * q^56 - 22 * q^57 + 10 * q^58 + 14 * q^59 + 5 * q^60 + 12 * q^61 + 21 * q^62 - 26 * q^63 + 10 * q^64 - 25 * q^65 + q^66 + 6 * q^67 + 5 * q^69 + 2 * q^70 + 8 * q^71 + 11 * q^72 + 16 * q^73 - 8 * q^74 + 8 * q^75 + 20 * q^76 - 16 * q^77 + 23 * q^78 + 7 * q^79 - q^80 - 2 * q^81 - 4 * q^82 + 18 * q^83 + 14 * q^84 + 8 * q^85 - 3 * q^86 + 5 * q^87 + q^88 + 2 * q^89 - 18 * q^90 + 8 * q^91 + 10 * q^92 - 41 * q^93 - q^94 - 16 * q^95 + 5 * q^96 + 6 * q^97 + 18 * q^98 - 22 * 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
$3$	0.478690	0.276372	0.138186	−	0.990406i	$-0.455873\pi$
$3$	0.478690	0.276372	0.138186	+	0.990406i	$0.455873\pi$
$4$	1.00000	0.500000
$5$	−3.82976	−1.71272	−0.856360	−	0.516380i	$-0.827279\pi$
$5$	−3.82976	−1.71272	−0.856360	+	0.516380i	$0.827279\pi$
$6$	0.478690	0.195424
$7$	4.18279	1.58095	0.790473	−	0.612497i	$-0.209835\pi$
$7$	4.18279	1.58095	0.790473	+	0.612497i	$0.209835\pi$
$8$	1.00000	0.353553
$9$	−2.77086	−0.923619
$10$	−3.82976	−1.21108
$11$	0.506106	0.152597	0.0762984	−	0.997085i	$-0.475690\pi$
$11$	0.506106	0.152597	0.0762984	+	0.997085i	$0.475690\pi$
$12$	0.478690	0.138186
$13$	−0.446148	−0.123739	−0.0618696	−	0.998084i	$-0.519706\pi$
$13$	−0.446148	−0.123739	−0.0618696	+	0.998084i	$0.519706\pi$
$14$	4.18279	1.11790
$15$	−1.83326	−0.473347
$16$	1.00000	0.250000
$17$	2.81298	0.682247	0.341124	−	0.940018i	$-0.389192\pi$
$17$	2.81298	0.682247	0.341124	+	0.940018i	$0.389192\pi$
$18$	−2.77086	−0.653097
$19$	6.82204	1.56508	0.782542	−	0.622598i	$-0.213923\pi$
$19$	6.82204	1.56508	0.782542	+	0.622598i	$0.213923\pi$
$20$	−3.82976	−0.856360
$21$	2.00226	0.436929
$22$	0.506106	0.107902
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0.478690	0.0977121
$25$	9.66703	1.93341
$26$	−0.446148	−0.0874969
$27$	−2.76245	−0.531634
$28$	4.18279	0.790473
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−1.83326	−0.334707
$31$	8.63271	1.55048	0.775241	−	0.631666i	$-0.217629\pi$
$31$	8.63271	1.55048	0.775241	+	0.631666i	$0.217629\pi$
$32$	1.00000	0.176777
$33$	0.242268	0.0421734
$34$	2.81298	0.482422
$35$	−16.0191	−2.70772
$36$	−2.77086	−0.461809
$37$	6.56131	1.07867	0.539336	−	0.842091i	$-0.318675\pi$
$37$	6.56131	1.07867	0.539336	+	0.842091i	$0.318675\pi$
$38$	6.82204	1.10668
$39$	−0.213567	−0.0341980
$40$	−3.82976	−0.605538
$41$	7.95531	1.24241	0.621205	−	0.783648i	$-0.286643\pi$
$41$	7.95531	1.24241	0.621205	+	0.783648i	$0.286643\pi$
$42$	2.00226	0.308955
$43$	0.372597	0.0568205	0.0284102	−	0.999596i	$-0.490956\pi$
$43$	0.372597	0.0568205	0.0284102	+	0.999596i	$0.490956\pi$
$44$	0.506106	0.0762984
$45$	10.6117	1.58190
$46$	1.00000	0.147442
$47$	−12.2862	−1.79213	−0.896063	−	0.443927i	$-0.853585\pi$
$47$	−12.2862	−1.79213	−0.896063	+	0.443927i	$0.853585\pi$
$48$	0.478690	0.0690929
$49$	10.4957	1.49939
$50$	9.66703	1.36713
$51$	1.34654	0.188554
$52$	−0.446148	−0.0618696
$53$	−3.90843	−0.536864	−0.268432	−	0.963299i	$-0.586506\pi$
$53$	−3.90843	−0.536864	−0.268432	+	0.963299i	$0.586506\pi$
$54$	−2.76245	−0.375922
$55$	−1.93826	−0.261356
$56$	4.18279	0.558949
$57$	3.26564	0.432545
$58$	1.00000	0.131306
$59$	−10.5728	−1.37646	−0.688228	−	0.725495i	$-0.741611\pi$
$59$	−10.5728	−1.37646	−0.688228	+	0.725495i	$0.741611\pi$
$60$	−1.83326	−0.236673
$61$	−6.55468	−0.839240	−0.419620	−	0.907700i	$-0.637837\pi$
$61$	−6.55468	−0.839240	−0.419620	+	0.907700i	$0.637837\pi$
$62$	8.63271	1.09636
$63$	−11.5899	−1.46019
$64$	1.00000	0.125000
$65$	1.70864	0.211931
$66$	0.242268	0.0298211
$67$	−16.1476	−1.97274	−0.986369	−	0.164548i	$-0.947383\pi$
$67$	−16.1476	−1.97274	−0.986369	+	0.164548i	$0.947383\pi$
$68$	2.81298	0.341124
$69$	0.478690	0.0576275
$70$	−16.0191	−1.91465
$71$	12.6016	1.49553	0.747767	−	0.663961i	$-0.231126\pi$
$71$	12.6016	1.49553	0.747767	+	0.663961i	$0.231126\pi$
$72$	−2.77086	−0.326549
$73$	7.47554	0.874946	0.437473	−	0.899231i	$-0.355874\pi$
$73$	7.47554	0.874946	0.437473	+	0.899231i	$0.355874\pi$
$74$	6.56131	0.762737
$75$	4.62751	0.534339
$76$	6.82204	0.782542
$77$	2.11694	0.241247
$78$	−0.213567	−0.0241817
$79$	5.65596	0.636346	0.318173	−	0.948033i	$-0.396931\pi$
$79$	5.65596	0.636346	0.318173	+	0.948033i	$0.396931\pi$
$80$	−3.82976	−0.428180
$81$	6.99021	0.776690
$82$	7.95531	0.878517
$83$	18.0029	1.97607	0.988035	−	0.154228i	$-0.0492892\pi$
$83$	18.0029	1.97607	0.988035	+	0.154228i	$0.0492892\pi$
$84$	2.00226	0.218464
$85$	−10.7730	−1.16850
$86$	0.372597	0.0401782
$87$	0.478690	0.0513209
$88$	0.506106	0.0539511
$89$	−6.85755	−0.726899	−0.363449	−	0.931614i	$-0.618401\pi$
$89$	−6.85755	−0.726899	−0.363449	+	0.931614i	$0.618401\pi$
$90$	10.6117	1.11857
$91$	−1.86615	−0.195625
$92$	1.00000	0.104257
$93$	4.13239	0.428509
$94$	−12.2862	−1.26722
$95$	−26.1267	−2.68055
$96$	0.478690	0.0488561
$97$	5.41841	0.550156	0.275078	−	0.961422i	$-0.411296\pi$
$97$	5.41841	0.550156	0.275078	+	0.961422i	$0.411296\pi$
$98$	10.4957	1.06023
$99$	−1.40235	−0.140941
$100$	9.66703	0.966703
$101$	5.91256	0.588322	0.294161	−	0.955756i	$-0.404960\pi$
$101$	5.91256	0.588322	0.294161	+	0.955756i	$0.404960\pi$
$102$	1.34654	0.133328
$103$	−11.9150	−1.17402	−0.587008	−	0.809581i	$-0.699694\pi$
$103$	−11.9150	−1.17402	−0.587008	+	0.809581i	$0.699694\pi$
$104$	−0.446148	−0.0437484
$105$	−7.66816	−0.748336
$106$	−3.90843	−0.379620
$107$	−12.6211	−1.22012	−0.610062	−	0.792353i	$-0.708856\pi$
$107$	−12.6211	−1.22012	−0.610062	+	0.792353i	$0.708856\pi$
$108$	−2.76245	−0.265817
$109$	−6.80263	−0.651574	−0.325787	−	0.945443i	$-0.605629\pi$
$109$	−6.80263	−0.651574	−0.325787	+	0.945443i	$0.605629\pi$
$110$	−1.93826	−0.184806
$111$	3.14083	0.298114
$112$	4.18279	0.395237
$113$	15.0713	1.41779	0.708893	−	0.705316i	$-0.249195\pi$
$113$	15.0713	1.41779	0.708893	+	0.705316i	$0.249195\pi$
$114$	3.26564	0.305855
$115$	−3.82976	−0.357127
$116$	1.00000	0.0928477
$117$	1.23621	0.114288
$118$	−10.5728	−0.973301
$119$	11.7661	1.07860
$120$	−1.83326	−0.167353
$121$	−10.7439	−0.976714
$122$	−6.55468	−0.593432
$123$	3.80812	0.343367
$124$	8.63271	0.775241
$125$	−17.8736	−1.59866
$126$	−11.5899	−1.03251
$127$	19.3259	1.71490	0.857449	−	0.514569i	$-0.172048\pi$
$127$	19.3259	1.71490	0.857449	+	0.514569i	$0.172048\pi$
$128$	1.00000	0.0883883
$129$	0.178358	0.0157036
$130$	1.70864	0.149858
$131$	12.9988	1.13571	0.567855	−	0.823128i	$-0.307773\pi$
$131$	12.9988	1.13571	0.567855	+	0.823128i	$0.307773\pi$
$132$	0.242268	0.0210867
$133$	28.5352	2.47431
$134$	−16.1476	−1.39494
$135$	10.5795	0.910539
$136$	2.81298	0.241211
$137$	−16.6050	−1.41866	−0.709331	−	0.704875i	$-0.751003\pi$
$137$	−16.6050	−1.41866	−0.709331	+	0.704875i	$0.751003\pi$
$138$	0.478690	0.0407488
$139$	6.38859	0.541873	0.270936	−	0.962597i	$-0.412667\pi$
$139$	6.38859	0.541873	0.270936	+	0.962597i	$0.412667\pi$
$140$	−16.0191	−1.35386
$141$	−5.88127	−0.495293
$142$	12.6016	1.05750
$143$	−0.225799	−0.0188822
$144$	−2.77086	−0.230905
$145$	−3.82976	−0.318044
$146$	7.47554	0.618680
$147$	5.02420	0.414389
$148$	6.56131	0.539336
$149$	−19.1899	−1.57210	−0.786050	−	0.618162i	$-0.787877\pi$
$149$	−19.1899	−1.57210	−0.786050	+	0.618162i	$0.787877\pi$
$150$	4.62751	0.377835
$151$	−13.1005	−1.06611	−0.533053	−	0.846082i	$-0.678955\pi$
$151$	−13.1005	−1.06611	−0.533053	+	0.846082i	$0.678955\pi$
$152$	6.82204	0.553340
$153$	−7.79436	−0.630137
$154$	2.11694	0.170588
$155$	−33.0612	−2.65554
$156$	−0.213567	−0.0170990
$157$	−10.6301	−0.848376	−0.424188	−	0.905574i	$-0.639440\pi$
$157$	−10.6301	−0.848376	−0.424188	+	0.905574i	$0.639440\pi$
$158$	5.65596	0.449964
$159$	−1.87093	−0.148374
$160$	−3.82976	−0.302769
$161$	4.18279	0.329650
$162$	6.99021	0.549203
$163$	−8.85308	−0.693427	−0.346714	−	0.937971i	$-0.612702\pi$
$163$	−8.85308	−0.693427	−0.346714	+	0.937971i	$0.612702\pi$
$164$	7.95531	0.621205
$165$	−0.927827	−0.0722312
$166$	18.0029	1.39729
$167$	−14.5570	−1.12645	−0.563227	−	0.826302i	$-0.690440\pi$
$167$	−14.5570	−1.12645	−0.563227	+	0.826302i	$0.690440\pi$
$168$	2.00226	0.154478
$169$	−12.8010	−0.984689
$170$	−10.7730	−0.826253
$171$	−18.9029	−1.44554
$172$	0.372597	0.0284102
$173$	4.57770	0.348036	0.174018	−	0.984742i	$-0.444325\pi$
$173$	4.57770	0.348036	0.174018	+	0.984742i	$0.444325\pi$
$174$	0.478690	0.0362894
$175$	40.4352	3.05661
$176$	0.506106	0.0381492
$177$	−5.06107	−0.380413
$178$	−6.85755	−0.513995
$179$	−8.34733	−0.623909	−0.311955	−	0.950097i	$-0.600984\pi$
$179$	−8.34733	−0.623909	−0.311955	+	0.950097i	$0.600984\pi$
$180$	10.6117	0.790950
$181$	0.847782	0.0630151	0.0315076	−	0.999504i	$-0.489969\pi$
$181$	0.847782	0.0630151	0.0315076	+	0.999504i	$0.489969\pi$
$182$	−1.86615	−0.138328
$183$	−3.13765	−0.231942
$184$	1.00000	0.0737210
$185$	−25.1282	−1.84746
$186$	4.13239	0.303002
$187$	1.42367	0.104109
$188$	−12.2862	−0.896063
$189$	−11.5547	−0.840484
$190$	−26.1267	−1.89543
$191$	−5.41374	−0.391725	−0.195862	−	0.980631i	$-0.562751\pi$
$191$	−5.41374	−0.391725	−0.195862	+	0.980631i	$0.562751\pi$
$192$	0.478690	0.0345464
$193$	−7.23386	−0.520705	−0.260352	−	0.965514i	$-0.583839\pi$
$193$	−7.23386	−0.520705	−0.260352	+	0.965514i	$0.583839\pi$
$194$	5.41841	0.389019
$195$	0.817908	0.0585716
$196$	10.4957	0.749696
$197$	13.1707	0.938371	0.469186	−	0.883100i	$-0.344548\pi$
$197$	13.1707	0.938371	0.469186	+	0.883100i	$0.344548\pi$
$198$	−1.40235	−0.0996606
$199$	−24.5891	−1.74308	−0.871539	−	0.490327i	$-0.836877\pi$
$199$	−24.5891	−1.74308	−0.871539	+	0.490327i	$0.836877\pi$
$200$	9.66703	0.683563
$201$	−7.72967	−0.545209
$202$	5.91256	0.416006
$203$	4.18279	0.293574
$204$	1.34654	0.0942769
$205$	−30.4669	−2.12790
$206$	−11.9150	−0.830154
$207$	−2.77086	−0.192588
$208$	−0.446148	−0.0309348
$209$	3.45268	0.238827
$210$	−7.66816	−0.529154
$211$	15.8004	1.08774	0.543871	−	0.839169i	$-0.316958\pi$
$211$	15.8004	1.08774	0.543871	+	0.839169i	$0.316958\pi$
$212$	−3.90843	−0.268432
$213$	6.03225	0.413323
$214$	−12.6211	−0.862758
$215$	−1.42696	−0.0973175
$216$	−2.76245	−0.187961
$217$	36.1088	2.45123
$218$	−6.80263	−0.460732
$219$	3.57847	0.241810
$220$	−1.93826	−0.130678
$221$	−1.25501	−0.0844208
$222$	3.14083	0.210799
$223$	−7.49038	−0.501593	−0.250796	−	0.968040i	$-0.580692\pi$
$223$	−7.49038	−0.501593	−0.250796	+	0.968040i	$0.580692\pi$
$224$	4.18279	0.279474
$225$	−26.7860	−1.78573
$226$	15.0713	1.00253
$227$	−24.3784	−1.61805	−0.809024	−	0.587775i	$-0.800004\pi$
$227$	−24.3784	−1.61805	−0.809024	+	0.587775i	$0.800004\pi$
$228$	3.26564	0.216272
$229$	17.3549	1.14684	0.573422	−	0.819260i	$-0.305616\pi$
$229$	17.3549	1.14684	0.573422	+	0.819260i	$0.305616\pi$
$230$	−3.82976	−0.252527
$231$	1.01336	0.0666739
$232$	1.00000	0.0656532
$233$	23.3598	1.53035	0.765176	−	0.643822i	$-0.222652\pi$
$233$	23.3598	1.53035	0.765176	+	0.643822i	$0.222652\pi$
$234$	1.23621	0.0808138
$235$	47.0531	3.06941
$236$	−10.5728	−0.688228
$237$	2.70745	0.175868
$238$	11.7661	0.762683
$239$	−7.31368	−0.473082	−0.236541	−	0.971621i	$-0.576014\pi$
$239$	−7.31368	−0.473082	−0.236541	+	0.971621i	$0.576014\pi$
$240$	−1.83326	−0.118337
$241$	15.8753	1.02262	0.511309	−	0.859397i	$-0.329161\pi$
$241$	15.8753	1.02262	0.511309	+	0.859397i	$0.329161\pi$
$242$	−10.7439	−0.690641
$243$	11.6335	0.746289
$244$	−6.55468	−0.419620
$245$	−40.1961	−2.56804
$246$	3.80812	0.242797
$247$	−3.04364	−0.193662
$248$	8.63271	0.548178
$249$	8.61778	0.546130
$250$	−17.8736	−1.13043
$251$	9.24180	0.583337	0.291668	−	0.956519i	$-0.405790\pi$
$251$	9.24180	0.583337	0.291668	+	0.956519i	$0.405790\pi$
$252$	−11.5899	−0.730096
$253$	0.506106	0.0318186
$254$	19.3259	1.21262
$255$	−5.15693	−0.322940
$256$	1.00000	0.0625000
$257$	27.1563	1.69396	0.846981	−	0.531624i	$-0.178418\pi$
$257$	27.1563	1.69396	0.846981	+	0.531624i	$0.178418\pi$
$258$	0.178358	0.0111041
$259$	27.4446	1.70532
$260$	1.70864	0.105965
$261$	−2.77086	−0.171512
$262$	12.9988	0.803069
$263$	−15.0841	−0.930125	−0.465063	−	0.885278i	$-0.653968\pi$
$263$	−15.0841	−0.930125	−0.465063	+	0.885278i	$0.653968\pi$
$264$	0.242268	0.0149106
$265$	14.9683	0.919498
$266$	28.5352	1.74960
$267$	−3.28264	−0.200894
$268$	−16.1476	−0.986369
$269$	−18.0671	−1.10157	−0.550784	−	0.834648i	$-0.685671\pi$
$269$	−18.0671	−1.10157	−0.550784	+	0.834648i	$0.685671\pi$
$270$	10.5795	0.643848
$271$	−2.78913	−0.169428	−0.0847139	−	0.996405i	$-0.526998\pi$
$271$	−2.78913	−0.169428	−0.0847139	+	0.996405i	$0.526998\pi$
$272$	2.81298	0.170562
$273$	−0.893304	−0.0540652
$274$	−16.6050	−1.00315
$275$	4.89255	0.295032
$276$	0.478690	0.0288137
$277$	−13.4209	−0.806385	−0.403193	−	0.915115i	$-0.632100\pi$
$277$	−13.4209	−0.806385	−0.403193	+	0.915115i	$0.632100\pi$
$278$	6.38859	0.383162
$279$	−23.9200	−1.43205
$280$	−16.0191	−0.957323
$281$	3.62563	0.216287	0.108143	−	0.994135i	$-0.465509\pi$
$281$	3.62563	0.216287	0.108143	+	0.994135i	$0.465509\pi$
$282$	−5.88127	−0.350225
$283$	22.4416	1.33401	0.667007	−	0.745052i	$-0.267575\pi$
$283$	22.4416	1.33401	0.667007	+	0.745052i	$0.267575\pi$
$284$	12.6016	0.747767
$285$	−12.5066	−0.740827
$286$	−0.225799	−0.0133517
$287$	33.2754	1.96418
$288$	−2.77086	−0.163274
$289$	−9.08715	−0.534538
$290$	−3.82976	−0.224891
$291$	2.59374	0.152048
$292$	7.47554	0.437473
$293$	−14.1530	−0.826825	−0.413412	−	0.910544i	$-0.635663\pi$
$293$	−14.1530	−0.826825	−0.413412	+	0.910544i	$0.635663\pi$
$294$	5.02420	0.293017
$295$	40.4911	2.35748
$296$	6.56131	0.381368
$297$	−1.39809	−0.0811256
$298$	−19.1899	−1.11164
$299$	−0.446148	−0.0258014
$300$	4.62751	0.267169
$301$	1.55849	0.0898301
$302$	−13.1005	−0.753851
$303$	2.83028	0.162595
$304$	6.82204	0.391271
$305$	25.1028	1.43738
$306$	−7.79436	−0.445574
$307$	19.0709	1.08843	0.544217	−	0.838944i	$-0.316827\pi$
$307$	19.0709	1.08843	0.544217	+	0.838944i	$0.316827\pi$
$308$	2.11694	0.120624
$309$	−5.70357	−0.324465
$310$	−33.0612	−1.87775
$311$	−1.67587	−0.0950301	−0.0475150	−	0.998871i	$-0.515130\pi$
$311$	−1.67587	−0.0950301	−0.0475150	+	0.998871i	$0.515130\pi$
$312$	−0.213567	−0.0120908
$313$	−20.1344	−1.13806	−0.569031	−	0.822316i	$-0.692682\pi$
$313$	−20.1344	−1.13806	−0.569031	+	0.822316i	$0.692682\pi$
$314$	−10.6301	−0.599892
$315$	44.3865	2.50090
$316$	5.65596	0.318173
$317$	14.5574	0.817623	0.408811	−	0.912619i	$-0.365943\pi$
$317$	14.5574	0.817623	0.408811	+	0.912619i	$0.365943\pi$
$318$	−1.87093	−0.104916
$319$	0.506106	0.0283365
$320$	−3.82976	−0.214090
$321$	−6.04157	−0.337208
$322$	4.18279	0.233098
$323$	19.1902	1.06777
$324$	6.99021	0.388345
$325$	−4.31293	−0.239238
$326$	−8.85308	−0.490327
$327$	−3.25635	−0.180077
$328$	7.95531	0.439258
$329$	−51.3906	−2.83325
$330$	−0.927827	−0.0510752
$331$	−14.1881	−0.779849	−0.389925	−	0.920847i	$-0.627499\pi$
$331$	−14.1881	−0.779849	−0.389925	+	0.920847i	$0.627499\pi$
$332$	18.0029	0.988035
$333$	−18.1804	−0.996282
$334$	−14.5570	−0.796524
$335$	61.8412	3.37875
$336$	2.00226	0.109232
$337$	−23.6653	−1.28913	−0.644566	−	0.764549i	$-0.722962\pi$
$337$	−23.6653	−1.28913	−0.644566	+	0.764549i	$0.722962\pi$
$338$	−12.8010	−0.696280
$339$	7.21447	0.391836
$340$	−10.7730	−0.584249
$341$	4.36907	0.236599
$342$	−18.9029	−1.02215
$343$	14.6220	0.789511
$344$	0.372597	0.0200891
$345$	−1.83326	−0.0986996
$346$	4.57770	0.246099
$347$	−23.5487	−1.26416	−0.632080	−	0.774903i	$-0.717799\pi$
$347$	−23.5487	−1.26416	−0.632080	+	0.774903i	$0.717799\pi$
$348$	0.478690	0.0256605
$349$	10.7061	0.573082	0.286541	−	0.958068i	$-0.407495\pi$
$349$	10.7061	0.573082	0.286541	+	0.958068i	$0.407495\pi$
$350$	40.4352	2.16135
$351$	1.23246	0.0657840
$352$	0.506106	0.0269756
$353$	−0.960027	−0.0510971	−0.0255485	−	0.999674i	$-0.508133\pi$
$353$	−0.960027	−0.0510971	−0.0255485	+	0.999674i	$0.508133\pi$
$354$	−5.06107	−0.268993
$355$	−48.2610	−2.56143
$356$	−6.85755	−0.363449
$357$	5.63231	0.298093
$358$	−8.34733	−0.441170
$359$	−13.3927	−0.706840	−0.353420	−	0.935465i	$-0.614981\pi$
$359$	−13.3927	−0.706840	−0.353420	+	0.935465i	$0.614981\pi$
$360$	10.6117	0.559286
$361$	27.5402	1.44949
$362$	0.847782	0.0445584
$363$	−5.14297	−0.269936
$364$	−1.86615	−0.0978126
$365$	−28.6295	−1.49854
$366$	−3.13765	−0.164008
$367$	13.6159	0.710742	0.355371	−	0.934725i	$-0.384354\pi$
$367$	13.6159	0.710742	0.355371	+	0.934725i	$0.384354\pi$
$368$	1.00000	0.0521286
$369$	−22.0430	−1.14751
$370$	−25.1282	−1.30635
$371$	−16.3482	−0.848754
$372$	4.13239	0.214254
$373$	−1.56459	−0.0810114	−0.0405057	−	0.999179i	$-0.512897\pi$
$373$	−1.56459	−0.0810114	−0.0405057	+	0.999179i	$0.512897\pi$
$374$	1.42367	0.0736160
$375$	−8.55591	−0.441825
$376$	−12.2862	−0.633612
$377$	−0.446148	−0.0229778
$378$	−11.5547	−0.594312
$379$	−4.14487	−0.212908	−0.106454	−	0.994318i	$-0.533950\pi$
$379$	−4.14487	−0.212908	−0.106454	+	0.994318i	$0.533950\pi$
$380$	−26.1267	−1.34027
$381$	9.25112	0.473949
$382$	−5.41374	−0.276991
$383$	36.9274	1.88690	0.943452	−	0.331511i	$-0.107558\pi$
$383$	36.9274	1.88690	0.943452	+	0.331511i	$0.107558\pi$
$384$	0.478690	0.0244280
$385$	−8.10736	−0.413189
$386$	−7.23386	−0.368194
$387$	−1.03241	−0.0524805
$388$	5.41841	0.275078
$389$	11.7353	0.595002	0.297501	−	0.954722i	$-0.403847\pi$
$389$	11.7353	0.595002	0.297501	+	0.954722i	$0.403847\pi$
$390$	0.817908	0.0414164
$391$	2.81298	0.142258
$392$	10.4957	0.530115
$393$	6.22239	0.313878
$394$	13.1707	0.663529
$395$	−21.6610	−1.08988
$396$	−1.40235	−0.0704707
$397$	−12.5958	−0.632163	−0.316082	−	0.948732i	$-0.602367\pi$
$397$	−12.5958	−0.632163	−0.316082	+	0.948732i	$0.602367\pi$
$398$	−24.5891	−1.23254
$399$	13.6595	0.683830
$400$	9.66703	0.483352
$401$	−35.4101	−1.76830	−0.884149	−	0.467205i	$-0.845261\pi$
$401$	−35.4101	−1.76830	−0.884149	+	0.467205i	$0.845261\pi$
$402$	−7.72967	−0.385521
$403$	−3.85147	−0.191855
$404$	5.91256	0.294161
$405$	−26.7708	−1.33025
$406$	4.18279	0.207588
$407$	3.32072	0.164602
$408$	1.34654	0.0666638
$409$	15.8868	0.785549	0.392775	−	0.919635i	$-0.371515\pi$
$409$	15.8868	0.785549	0.392775	+	0.919635i	$0.371515\pi$
$410$	−30.4669	−1.50465
$411$	−7.94865	−0.392078
$412$	−11.9150	−0.587008
$413$	−44.2236	−2.17610
$414$	−2.77086	−0.136180
$415$	−68.9466	−3.38445
$416$	−0.446148	−0.0218742
$417$	3.05815	0.149758
$418$	3.45268	0.168876
$419$	−0.550302	−0.0268840	−0.0134420	−	0.999910i	$-0.504279\pi$
$419$	−0.550302	−0.0268840	−0.0134420	+	0.999910i	$0.504279\pi$
$420$	−7.66816	−0.374168
$421$	5.07669	0.247423	0.123711	−	0.992318i	$-0.460520\pi$
$421$	5.07669	0.247423	0.123711	+	0.992318i	$0.460520\pi$
$422$	15.8004	0.769150
$423$	34.0433	1.65524
$424$	−3.90843	−0.189810
$425$	27.1932	1.31906
$426$	6.03225	0.292264
$427$	−27.4168	−1.32679
$428$	−12.6211	−0.610062
$429$	−0.108087	−0.00521851
$430$	−1.42696	−0.0688139
$431$	−5.40319	−0.260262	−0.130131	−	0.991497i	$-0.541540\pi$
$431$	−5.40319	−0.260262	−0.130131	+	0.991497i	$0.541540\pi$
$432$	−2.76245	−0.132908
$433$	−8.05821	−0.387253	−0.193627	−	0.981075i	$-0.562025\pi$
$433$	−8.05821	−0.387253	−0.193627	+	0.981075i	$0.562025\pi$
$434$	36.1088	1.73328
$435$	−1.83326	−0.0878983
$436$	−6.80263	−0.325787
$437$	6.82204	0.326342
$438$	3.57847	0.170986
$439$	19.2279	0.917696	0.458848	−	0.888515i	$-0.348262\pi$
$439$	19.2279	0.917696	0.458848	+	0.888515i	$0.348262\pi$
$440$	−1.93826	−0.0924031
$441$	−29.0822	−1.38487
$442$	−1.25501	−0.0596945
$443$	17.6965	0.840788	0.420394	−	0.907342i	$-0.361892\pi$
$443$	17.6965	0.840788	0.420394	+	0.907342i	$0.361892\pi$
$444$	3.14083	0.149057
$445$	26.2627	1.24497
$446$	−7.49038	−0.354680
$447$	−9.18602	−0.434484
$448$	4.18279	0.197618
$449$	18.1011	0.854245	0.427123	−	0.904194i	$-0.359527\pi$
$449$	18.1011	0.854245	0.427123	+	0.904194i	$0.359527\pi$
$450$	−26.7860	−1.26270
$451$	4.02623	0.189588
$452$	15.0713	0.708893
$453$	−6.27109	−0.294641
$454$	−24.3784	−1.14413
$455$	7.14688	0.335051
$456$	3.26564	0.152928
$457$	14.0243	0.656029	0.328015	−	0.944673i	$-0.393620\pi$
$457$	14.0243	0.656029	0.328015	+	0.944673i	$0.393620\pi$
$458$	17.3549	0.810941
$459$	−7.77071	−0.362706
$460$	−3.82976	−0.178563
$461$	0.0740579	0.00344922	0.00172461	−	0.999999i	$-0.499451\pi$
$461$	0.0740579	0.00344922	0.00172461	+	0.999999i	$0.499451\pi$
$462$	1.01336	0.0471456
$463$	−16.5718	−0.770155	−0.385077	−	0.922884i	$-0.625825\pi$
$463$	−16.5718	−0.770155	−0.385077	+	0.922884i	$0.625825\pi$
$464$	1.00000	0.0464238
$465$	−15.8260	−0.733915
$466$	23.3598	1.08212
$467$	20.8926	0.966792	0.483396	−	0.875402i	$-0.339403\pi$
$467$	20.8926	0.966792	0.483396	+	0.875402i	$0.339403\pi$
$468$	1.23621	0.0571440
$469$	−67.5419	−3.11879
$470$	47.0531	2.17040
$471$	−5.08853	−0.234467
$472$	−10.5728	−0.486651
$473$	0.188574	0.00867063
$474$	2.70745	0.124357
$475$	65.9489	3.02594
$476$	11.7661	0.539298
$477$	10.8297	0.495858
$478$	−7.31368	−0.334520
$479$	8.60511	0.393178	0.196589	−	0.980486i	$-0.437014\pi$
$479$	8.60511	0.393178	0.196589	+	0.980486i	$0.437014\pi$
$480$	−1.83326	−0.0836767
$481$	−2.92732	−0.133474
$482$	15.8753	0.723100
$483$	2.00226	0.0911059
$484$	−10.7439	−0.488357
$485$	−20.7512	−0.942263
$486$	11.6335	0.527706
$487$	−6.73804	−0.305330	−0.152665	−	0.988278i	$-0.548785\pi$
$487$	−6.73804	−0.305330	−0.152665	+	0.988278i	$0.548785\pi$
$488$	−6.55468	−0.296716
$489$	−4.23788	−0.191644
$490$	−40.1961	−1.81588
$491$	9.15504	0.413161	0.206581	−	0.978430i	$-0.433766\pi$
$491$	9.15504	0.413161	0.206581	+	0.978430i	$0.433766\pi$
$492$	3.80812	0.171683
$493$	2.81298	0.126690
$494$	−3.04364	−0.136940
$495$	5.37065	0.241393
$496$	8.63271	0.387620
$497$	52.7098	2.36436
$498$	8.61778	0.386172
$499$	−20.0945	−0.899552	−0.449776	−	0.893141i	$-0.648496\pi$
$499$	−20.0945	−0.899552	−0.449776	+	0.893141i	$0.648496\pi$
$500$	−17.8736	−0.799332
$501$	−6.96829	−0.311320
$502$	9.24180	0.412482
$503$	6.08012	0.271099	0.135550	−	0.990771i	$-0.456720\pi$
$503$	6.08012	0.271099	0.135550	+	0.990771i	$0.456720\pi$
$504$	−11.5899	−0.516256
$505$	−22.6437	−1.00763
$506$	0.506106	0.0224992
$507$	−6.12768	−0.272140
$508$	19.3259	0.857449
$509$	−27.9362	−1.23825	−0.619125	−	0.785293i	$-0.712512\pi$
$509$	−27.9362	−1.23825	−0.619125	+	0.785293i	$0.712512\pi$
$510$	−5.15693	−0.228353
$511$	31.2686	1.38324
$512$	1.00000	0.0441942
$513$	−18.8455	−0.832051
$514$	27.1563	1.19781
$515$	45.6314	2.01076
$516$	0.178358	0.00785178
$517$	−6.21812	−0.273473
$518$	27.4446	1.20585
$519$	2.19130	0.0961873
$520$	1.70864	0.0749288
$521$	−11.4762	−0.502782	−0.251391	−	0.967886i	$-0.580888\pi$
$521$	−11.4762	−0.502782	−0.251391	+	0.967886i	$0.580888\pi$
$522$	−2.77086	−0.121277
$523$	−23.7968	−1.04056	−0.520280	−	0.853996i	$-0.674173\pi$
$523$	−23.7968	−1.04056	−0.520280	+	0.853996i	$0.674173\pi$
$524$	12.9988	0.567855
$525$	19.3559	0.844761
$526$	−15.0841	−0.657698
$527$	24.2836	1.05781
$528$	0.242268	0.0105434
$529$	1.00000	0.0434783
$530$	14.9683	0.650183
$531$	29.2956	1.27132
$532$	28.5352	1.23716
$533$	−3.54925	−0.153735
$534$	−3.28264	−0.142054
$535$	48.3356	2.08973
$536$	−16.1476	−0.697468
$537$	−3.99578	−0.172431
$538$	−18.0671	−0.778926
$539$	5.31196	0.228802
$540$	10.5795	0.455269
$541$	0.349567	0.0150291	0.00751453	−	0.999972i	$-0.497608\pi$
$541$	0.349567	0.0150291	0.00751453	+	0.999972i	$0.497608\pi$
$542$	−2.78913	−0.119804
$543$	0.405824	0.0174156
$544$	2.81298	0.120605
$545$	26.0524	1.11596
$546$	−0.893304	−0.0382299
$547$	−10.8044	−0.461965	−0.230982	−	0.972958i	$-0.574194\pi$
$547$	−10.8044	−0.461965	−0.230982	+	0.972958i	$0.574194\pi$
$548$	−16.6050	−0.709331
$549$	18.1621	0.775138
$550$	4.89255	0.208619
$551$	6.82204	0.290629
$552$	0.478690	0.0203744
$553$	23.6577	1.00603
$554$	−13.4209	−0.570200
$555$	−12.0286	−0.510586
$556$	6.38859	0.270936
$557$	−10.7861	−0.457022	−0.228511	−	0.973541i	$-0.573386\pi$
$557$	−10.7861	−0.457022	−0.228511	+	0.973541i	$0.573386\pi$
$558$	−23.9200	−1.01261
$559$	−0.166233	−0.00703093
$560$	−16.0191	−0.676929
$561$	0.681494	0.0287727
$562$	3.62563	0.152938
$563$	27.7022	1.16751	0.583754	−	0.811931i	$-0.301583\pi$
$563$	27.7022	1.16751	0.583754	+	0.811931i	$0.301583\pi$
$564$	−5.88127	−0.247646
$565$	−57.7193	−2.42827
$566$	22.4416	0.943290
$567$	29.2386	1.22791
$568$	12.6016	0.528751
$569$	23.9405	1.00364	0.501818	−	0.864973i	$-0.332665\pi$
$569$	23.9405	1.00364	0.501818	+	0.864973i	$0.332665\pi$
$570$	−12.5066	−0.523844
$571$	−25.9239	−1.08488	−0.542442	−	0.840093i	$-0.682500\pi$
$571$	−25.9239	−1.08488	−0.542442	+	0.840093i	$0.682500\pi$
$572$	−0.225799	−0.00944111
$573$	−2.59150	−0.108262
$574$	33.2754	1.38889
$575$	9.66703	0.403143
$576$	−2.77086	−0.115452
$577$	33.9244	1.41229	0.706146	−	0.708066i	$-0.250432\pi$
$577$	33.9244	1.41229	0.706146	+	0.708066i	$0.250432\pi$
$578$	−9.08715	−0.377976
$579$	−3.46277	−0.143908
$580$	−3.82976	−0.159022
$581$	75.3022	3.12406
$582$	2.59374	0.107514
$583$	−1.97808	−0.0819238
$584$	7.47554	0.309340
$585$	−4.73439	−0.195743
$586$	−14.1530	−0.584653
$587$	12.5211	0.516803	0.258402	−	0.966038i	$-0.416804\pi$
$587$	12.5211	0.516803	0.258402	+	0.966038i	$0.416804\pi$
$588$	5.02420	0.207195
$589$	58.8927	2.42663
$590$	40.4911	1.66699
$591$	6.30466	0.259339
$592$	6.56131	0.269668
$593$	8.71136	0.357733	0.178866	−	0.983873i	$-0.442757\pi$
$593$	8.71136	0.357733	0.178866	+	0.983873i	$0.442757\pi$
$594$	−1.39809	−0.0573645
$595$	−45.0613	−1.84733
$596$	−19.1899	−0.786050
$597$	−11.7706	−0.481737
$598$	−0.446148	−0.0182444
$599$	−7.50260	−0.306548	−0.153274	−	0.988184i	$-0.548982\pi$
$599$	−7.50260	−0.306548	−0.153274	+	0.988184i	$0.548982\pi$
$600$	4.62751	0.188917
$601$	23.9111	0.975353	0.487676	−	0.873025i	$-0.337845\pi$
$601$	23.9111	0.975353	0.487676	+	0.873025i	$0.337845\pi$
$602$	1.55849	0.0635195
$603$	44.7426	1.82206
$604$	−13.1005	−0.533053
$605$	41.1464	1.67284
$606$	2.83028	0.114972
$607$	9.49769	0.385499	0.192750	−	0.981248i	$-0.438259\pi$
$607$	9.49769	0.385499	0.192750	+	0.981248i	$0.438259\pi$
$608$	6.82204	0.276670
$609$	2.00226	0.0811356
$610$	25.1028	1.01638
$611$	5.48146	0.221756
$612$	−7.79436	−0.315068
$613$	8.77694	0.354497	0.177249	−	0.984166i	$-0.443280\pi$
$613$	8.77694	0.354497	0.177249	+	0.984166i	$0.443280\pi$
$614$	19.0709	0.769639
$615$	−14.5842	−0.588091
$616$	2.11694	0.0852938
$617$	−27.5829	−1.11045	−0.555223	−	0.831702i	$-0.687367\pi$
$617$	−27.5829	−1.11045	−0.555223	+	0.831702i	$0.687367\pi$
$618$	−5.70357	−0.229431
$619$	6.00307	0.241284	0.120642	−	0.992696i	$-0.461505\pi$
$619$	6.00307	0.241284	0.120642	+	0.992696i	$0.461505\pi$
$620$	−33.0612	−1.32777
$621$	−2.76245	−0.110853
$622$	−1.67587	−0.0671964
$623$	−28.6837	−1.14919
$624$	−0.213567	−0.00854951
$625$	20.1164	0.804655
$626$	−20.1344	−0.804731
$627$	1.65276	0.0660049
$628$	−10.6301	−0.424188
$629$	18.4568	0.735922
$630$	44.3865	1.76840
$631$	6.07271	0.241751	0.120875	−	0.992668i	$-0.461430\pi$
$631$	6.07271	0.241751	0.120875	+	0.992668i	$0.461430\pi$
$632$	5.65596	0.224982
$633$	7.56348	0.300621
$634$	14.5574	0.578146
$635$	−74.0135	−2.93714
$636$	−1.87093	−0.0741870
$637$	−4.68266	−0.185534
$638$	0.506106	0.0200369
$639$	−34.9172	−1.38130
$640$	−3.82976	−0.151384
$641$	21.9699	0.867758	0.433879	−	0.900971i	$-0.357144\pi$
$641$	21.9699	0.867758	0.433879	+	0.900971i	$0.357144\pi$
$642$	−6.04157	−0.238442
$643$	−29.2822	−1.15478	−0.577389	−	0.816469i	$-0.695928\pi$
$643$	−29.2822	−1.15478	−0.577389	+	0.816469i	$0.695928\pi$
$644$	4.18279	0.164825
$645$	−0.683069	−0.0268958
$646$	19.1902	0.755030
$647$	39.3449	1.54681	0.773404	−	0.633913i	$-0.218552\pi$
$647$	39.3449	1.54681	0.773404	+	0.633913i	$0.218552\pi$
$648$	6.99021	0.274602
$649$	−5.35094	−0.210043
$650$	−4.31293	−0.169167
$651$	17.2849	0.677450
$652$	−8.85308	−0.346714
$653$	−18.0438	−0.706109	−0.353054	−	0.935603i	$-0.614857\pi$
$653$	−18.0438	−0.706109	−0.353054	+	0.935603i	$0.614857\pi$
$654$	−3.25635	−0.127333
$655$	−49.7823	−1.94515
$656$	7.95531	0.310603
$657$	−20.7137	−0.808117
$658$	−51.3906	−2.00341
$659$	10.7012	0.416860	0.208430	−	0.978037i	$-0.433165\pi$
$659$	10.7012	0.416860	0.208430	+	0.978037i	$0.433165\pi$
$660$	−0.927827	−0.0361156
$661$	−45.6342	−1.77497	−0.887483	−	0.460840i	$-0.847548\pi$
$661$	−45.6342	−1.77497	−0.887483	+	0.460840i	$0.847548\pi$
$662$	−14.1881	−0.551437
$663$	−0.600758	−0.0233315
$664$	18.0029	0.698646
$665$	−109.283	−4.23780
$666$	−18.1804	−0.704478
$667$	1.00000	0.0387202
$668$	−14.5570	−0.563227
$669$	−3.58557	−0.138626
$670$	61.8412	2.38913
$671$	−3.31736	−0.128065
$672$	2.00226	0.0772388
$673$	20.7368	0.799346	0.399673	−	0.916658i	$-0.369124\pi$
$673$	20.7368	0.799346	0.399673	+	0.916658i	$0.369124\pi$
$674$	−23.6653	−0.911553
$675$	−26.7047	−1.02786
$676$	−12.8010	−0.492344
$677$	−39.7366	−1.52720	−0.763600	−	0.645689i	$-0.776570\pi$
$677$	−39.7366	−1.52720	−0.763600	+	0.645689i	$0.776570\pi$
$678$	7.21447	0.277070
$679$	22.6641	0.869768
$680$	−10.7730	−0.413127
$681$	−11.6697	−0.447183
$682$	4.36907	0.167300
$683$	−17.8654	−0.683602	−0.341801	−	0.939772i	$-0.611037\pi$
$683$	−17.8654	−0.683602	−0.341801	+	0.939772i	$0.611037\pi$
$684$	−18.9029	−0.722770
$685$	63.5932	2.42977
$686$	14.6220	0.558269
$687$	8.30761	0.316955
$688$	0.372597	0.0142051
$689$	1.74374	0.0664312
$690$	−1.83326	−0.0697912
$691$	23.7073	0.901867	0.450934	−	0.892557i	$-0.351091\pi$
$691$	23.7073	0.901867	0.450934	+	0.892557i	$0.351091\pi$
$692$	4.57770	0.174018
$693$	−5.86573	−0.222821
$694$	−23.5487	−0.893896
$695$	−24.4667	−0.928076
$696$	0.478690	0.0181447
$697$	22.3781	0.847631
$698$	10.7061	0.405230
$699$	11.1821	0.422946
$700$	40.4352	1.52831
$701$	−20.5536	−0.776300	−0.388150	−	0.921596i	$-0.626886\pi$
$701$	−20.5536	−0.776300	−0.388150	+	0.921596i	$0.626886\pi$
$702$	1.23246	0.0465163
$703$	44.7615	1.68821
$704$	0.506106	0.0190746
$705$	22.5238	0.848297
$706$	−0.960027	−0.0361311
$707$	24.7310	0.930105
$708$	−5.06107	−0.190207
$709$	43.9152	1.64927	0.824634	−	0.565666i	$-0.191381\pi$
$709$	43.9152	1.64927	0.824634	+	0.565666i	$0.191381\pi$
$710$	−48.2610	−1.81120
$711$	−15.6719	−0.587741
$712$	−6.85755	−0.256998
$713$	8.63271	0.323298
$714$	5.63231	0.210784
$715$	0.864753	0.0323399
$716$	−8.34733	−0.311955
$717$	−3.50098	−0.130747
$718$	−13.3927	−0.499811
$719$	8.58911	0.320320	0.160160	−	0.987091i	$-0.448799\pi$
$719$	8.58911	0.320320	0.160160	+	0.987091i	$0.448799\pi$
$720$	10.6117	0.395475
$721$	−49.8378	−1.85606
$722$	27.5402	1.02494
$723$	7.59935	0.282623
$724$	0.847782	0.0315076
$725$	9.66703	0.359025
$726$	−5.14297	−0.190874
$727$	34.5963	1.28311	0.641553	−	0.767079i	$-0.278290\pi$
$727$	34.5963	1.28311	0.641553	+	0.767079i	$0.278290\pi$
$728$	−1.86615	−0.0691639
$729$	−15.4018	−0.570437
$730$	−28.6295	−1.05963
$731$	1.04811	0.0387656
$732$	−3.13765	−0.115971
$733$	−37.9942	−1.40335	−0.701674	−	0.712498i	$-0.747564\pi$
$733$	−37.9942	−1.40335	−0.701674	+	0.712498i	$0.747564\pi$
$734$	13.6159	0.502571
$735$	−19.2415	−0.709732
$736$	1.00000	0.0368605
$737$	−8.17238	−0.301034
$738$	−22.0430	−0.811414
$739$	−15.5026	−0.570271	−0.285136	−	0.958487i	$-0.592039\pi$
$739$	−15.5026	−0.570271	−0.285136	+	0.958487i	$0.592039\pi$
$740$	−25.1282	−0.923731
$741$	−1.45696	−0.0535227
$742$	−16.3482	−0.600160
$743$	−40.7156	−1.49371	−0.746855	−	0.664987i	$-0.768437\pi$
$743$	−40.7156	−1.49371	−0.746855	+	0.664987i	$0.768437\pi$
$744$	4.13239	0.151501
$745$	73.4928	2.69257
$746$	−1.56459	−0.0572837
$747$	−49.8833	−1.82514
$748$	1.42367	0.0520544
$749$	−52.7913	−1.92895
$750$	−8.55591	−0.312418
$751$	6.60764	0.241116	0.120558	−	0.992706i	$-0.461532\pi$
$751$	6.60764	0.241116	0.120558	+	0.992706i	$0.461532\pi$
$752$	−12.2862	−0.448031
$753$	4.42395	0.161218
$754$	−0.446148	−0.0162478
$755$	50.1718	1.82594
$756$	−11.5547	−0.420242
$757$	−36.5851	−1.32971	−0.664853	−	0.746974i	$-0.731506\pi$
$757$	−36.5851	−1.32971	−0.664853	+	0.746974i	$0.731506\pi$
$758$	−4.14487	−0.150548
$759$	0.242268	0.00879377
$760$	−26.1267	−0.947717
$761$	19.0138	0.689251	0.344626	−	0.938740i	$-0.388006\pi$
$761$	19.0138	0.689251	0.344626	+	0.938740i	$0.388006\pi$
$762$	9.25112	0.335133
$763$	−28.4540	−1.03010
$764$	−5.41374	−0.195862
$765$	29.8505	1.07925
$766$	36.9274	1.33424
$767$	4.71702	0.170322
$768$	0.478690	0.0172732
$769$	22.2580	0.802643	0.401321	−	0.915937i	$-0.368551\pi$
$769$	22.2580	0.802643	0.401321	+	0.915937i	$0.368551\pi$
$770$	−8.10736	−0.292169
$771$	12.9994	0.468163
$772$	−7.23386	−0.260352
$773$	3.40838	0.122591	0.0612955	−	0.998120i	$-0.480477\pi$
$773$	3.40838	0.122591	0.0612955	+	0.998120i	$0.480477\pi$
$774$	−1.03241	−0.0371093
$775$	83.4527	2.99771
$776$	5.41841	0.194510
$777$	13.1374	0.471303
$778$	11.7353	0.420730
$779$	54.2714	1.94448
$780$	0.817908	0.0292858
$781$	6.37775	0.228214
$782$	2.81298	0.100592
$783$	−2.76245	−0.0987219
$784$	10.4957	0.374848
$785$	40.7108	1.45303
$786$	6.22239	0.221945
$787$	−23.1159	−0.823992	−0.411996	−	0.911186i	$-0.635168\pi$
$787$	−23.1159	−0.823992	−0.411996	+	0.911186i	$0.635168\pi$
$788$	13.1707	0.469186
$789$	−7.22060	−0.257060
$790$	−21.6610	−0.770662
$791$	63.0400	2.24144
$792$	−1.40235	−0.0498303
$793$	2.92436	0.103847
$794$	−12.5958	−0.447007
$795$	7.16519	0.254123
$796$	−24.5891	−0.871539
$797$	−19.5992	−0.694239	−0.347119	−	0.937821i	$-0.612840\pi$
$797$	−19.5992	−0.694239	−0.347119	+	0.937821i	$0.612840\pi$
$798$	13.6595	0.483541
$799$	−34.5608	−1.22267
$800$	9.66703	0.341781
$801$	19.0013	0.671377
$802$	−35.4101	−1.25038
$803$	3.78342	0.133514
$804$	−7.72967	−0.272604
$805$	−16.0191	−0.564598
$806$	−3.85147	−0.135662
$807$	−8.64852	−0.304442
$808$	5.91256	0.208003
$809$	−5.75509	−0.202338	−0.101169	−	0.994869i	$-0.532258\pi$
$809$	−5.75509	−0.202338	−0.101169	+	0.994869i	$0.532258\pi$
$810$	−26.7708	−0.940630
$811$	−18.2543	−0.640995	−0.320497	−	0.947249i	$-0.603850\pi$
$811$	−18.2543	−0.640995	−0.320497	+	0.947249i	$0.603850\pi$
$812$	4.18279	0.146787
$813$	−1.33513	−0.0468250
$814$	3.32072	0.116391
$815$	33.9052	1.18765
$816$	1.34654	0.0471385
$817$	2.54187	0.0889288
$818$	15.8868	0.555467
$819$	5.17082	0.180683
$820$	−30.4669	−1.06395
$821$	−28.3058	−0.987880	−0.493940	−	0.869496i	$-0.664444\pi$
$821$	−28.3058	−0.987880	−0.493940	+	0.869496i	$0.664444\pi$
$822$	−7.94865	−0.277241
$823$	−31.0281	−1.08157	−0.540786	−	0.841160i	$-0.681873\pi$
$823$	−31.0281	−1.08157	−0.540786	+	0.841160i	$0.681873\pi$
$824$	−11.9150	−0.415077
$825$	2.34201	0.0815384
$826$	−44.2236	−1.53874
$827$	−36.1781	−1.25804	−0.629019	−	0.777390i	$-0.716543\pi$
$827$	−36.1781	−1.25804	−0.629019	+	0.777390i	$0.716543\pi$
$828$	−2.77086	−0.0962939
$829$	−19.1176	−0.663983	−0.331991	−	0.943282i	$-0.607720\pi$
$829$	−19.1176	−0.663983	−0.331991	+	0.943282i	$0.607720\pi$
$830$	−68.9466	−2.39317
$831$	−6.42446	−0.222862
$832$	−0.446148	−0.0154674
$833$	29.5243	1.02296
$834$	3.05815	0.105895
$835$	55.7498	1.92930
$836$	3.45268	0.119413
$837$	−23.8474	−0.824288
$838$	−0.550302	−0.0190099
$839$	17.9385	0.619306	0.309653	−	0.950850i	$-0.399787\pi$
$839$	17.9385	0.619306	0.309653	+	0.950850i	$0.399787\pi$
$840$	−7.66816	−0.264577
$841$	1.00000	0.0344828
$842$	5.07669	0.174954
$843$	1.73555	0.0597756
$844$	15.8004	0.543871
$845$	49.0245	1.68649
$846$	34.0433	1.17043
$847$	−44.9393	−1.54413
$848$	−3.90843	−0.134216
$849$	10.7426	0.368683
$850$	27.1932	0.932718
$851$	6.56131	0.224919
$852$	6.03225	0.206662
$853$	28.6500	0.980956	0.490478	−	0.871454i	$-0.336822\pi$
$853$	28.6500	0.980956	0.490478	+	0.871454i	$0.336822\pi$
$854$	−27.4168	−0.938185
$855$	72.3935	2.47580
$856$	−12.6211	−0.431379
$857$	−17.6352	−0.602407	−0.301204	−	0.953560i	$-0.597388\pi$
$857$	−17.6352	−0.602407	−0.301204	+	0.953560i	$0.597388\pi$
$858$	−0.108087	−0.00369004
$859$	−34.8670	−1.18965	−0.594824	−	0.803856i	$-0.702778\pi$
$859$	−34.8670	−1.18965	−0.594824	+	0.803856i	$0.702778\pi$
$860$	−1.42696	−0.0486588
$861$	15.9286	0.542845
$862$	−5.40319	−0.184033
$863$	−9.59165	−0.326504	−0.163252	−	0.986584i	$-0.552198\pi$
$863$	−9.59165	−0.326504	−0.163252	+	0.986584i	$0.552198\pi$
$864$	−2.76245	−0.0939804
$865$	−17.5315	−0.596088
$866$	−8.05821	−0.273829
$867$	−4.34993	−0.147731
$868$	36.1088	1.22561
$869$	2.86252	0.0971043
$870$	−1.83326	−0.0621535
$871$	7.20421	0.244105
$872$	−6.80263	−0.230366
$873$	−15.0136	−0.508135
$874$	6.82204	0.230759
$875$	−74.7615	−2.52740
$876$	3.57847	0.120905
$877$	9.41126	0.317796	0.158898	−	0.987295i	$-0.449206\pi$
$877$	9.41126	0.317796	0.158898	+	0.987295i	$0.449206\pi$
$878$	19.2279	0.648909
$879$	−6.77488	−0.228511
$880$	−1.93826	−0.0653389
$881$	52.8080	1.77915	0.889573	−	0.456793i	$-0.151002\pi$
$881$	52.8080	1.77915	0.889573	+	0.456793i	$0.151002\pi$
$882$	−29.0822	−0.979248
$883$	14.7051	0.494865	0.247433	−	0.968905i	$-0.420413\pi$
$883$	14.7051	0.494865	0.247433	+	0.968905i	$0.420413\pi$
$884$	−1.25501	−0.0422104
$885$	19.3827	0.651541
$886$	17.6965	0.594527
$887$	−54.2699	−1.82220	−0.911102	−	0.412182i	$-0.864767\pi$
$887$	−54.2699	−1.82220	−0.911102	+	0.412182i	$0.864767\pi$
$888$	3.14083	0.105399
$889$	80.8363	2.71116
$890$	26.2627	0.880329
$891$	3.53779	0.118520
$892$	−7.49038	−0.250796
$893$	−83.8169	−2.80483
$894$	−9.18602	−0.307227
$895$	31.9683	1.06858
$896$	4.18279	0.139737
$897$	−0.213567	−0.00713078
$898$	18.1011	0.604043
$899$	8.63271	0.287917
$900$	−26.7860	−0.892865
$901$	−10.9943	−0.366274
$902$	4.02623	0.134059
$903$	0.746035	0.0248265
$904$	15.0713	0.501263
$905$	−3.24680	−0.107927
$906$	−6.27109	−0.208343
$907$	−9.91059	−0.329076	−0.164538	−	0.986371i	$-0.552613\pi$
$907$	−9.91059	−0.329076	−0.164538	+	0.986371i	$0.552613\pi$
$908$	−24.3784	−0.809024
$909$	−16.3829	−0.543385
$910$	7.14688	0.236917
$911$	19.8472	0.657568	0.328784	−	0.944405i	$-0.393361\pi$
$911$	19.8472	0.657568	0.328784	+	0.944405i	$0.393361\pi$
$912$	3.26564	0.108136
$913$	9.11136	0.301542
$914$	14.0243	0.463883
$915$	12.0165	0.397252
$916$	17.3549	0.573422
$917$	54.3713	1.79550
$918$	−7.77071	−0.256472
$919$	−48.7718	−1.60883	−0.804416	−	0.594067i	$-0.797522\pi$
$919$	−48.7718	−1.60883	−0.804416	+	0.594067i	$0.797522\pi$
$920$	−3.82976	−0.126263
$921$	9.12905	0.300812
$922$	0.0740579	0.00243897
$923$	−5.62218	−0.185056
$924$	1.01336	0.0333370
$925$	63.4284	2.08551
$926$	−16.5718	−0.544582
$927$	33.0146	1.08434
$928$	1.00000	0.0328266
$929$	51.5713	1.69200	0.846000	−	0.533183i	$-0.179004\pi$
$929$	51.5713	1.69200	0.846000	+	0.533183i	$0.179004\pi$
$930$	−15.8260	−0.518957
$931$	71.6024	2.34667
$932$	23.3598	0.765176
$933$	−0.802224	−0.0262636
$934$	20.8926	0.683625
$935$	−5.45230	−0.178309
$936$	1.23621	0.0404069
$937$	1.25525	0.0410071	0.0205036	−	0.999790i	$-0.493473\pi$
$937$	1.25525	0.0410071	0.0205036	+	0.999790i	$0.493473\pi$
$938$	−67.5419	−2.20532
$939$	−9.63811	−0.314528
$940$	47.0531	1.53470
$941$	−38.0683	−1.24099	−0.620496	−	0.784209i	$-0.713069\pi$
$941$	−38.0683	−1.24099	−0.620496	+	0.784209i	$0.713069\pi$
$942$	−5.08853	−0.165793
$943$	7.95531	0.259060
$944$	−10.5728	−0.344114
$945$	44.2519	1.43951
$946$	0.188574	0.00613106
$947$	−23.8437	−0.774815	−0.387407	−	0.921909i	$-0.626629\pi$
$947$	−23.8437	−0.774815	−0.387407	+	0.921909i	$0.626629\pi$
$948$	2.70745	0.0879339
$949$	−3.33520	−0.108265
$950$	65.9489	2.13966
$951$	6.96846	0.225968
$952$	11.7661	0.381341
$953$	−44.9400	−1.45575	−0.727874	−	0.685711i	$-0.759492\pi$
$953$	−44.9400	−1.45575	−0.727874	+	0.685711i	$0.759492\pi$
$954$	10.8297	0.350625
$955$	20.7333	0.670914
$956$	−7.31368	−0.236541
$957$	0.242268	0.00783141
$958$	8.60511	0.278019
$959$	−69.4553	−2.24283
$960$	−1.83326	−0.0591684
$961$	43.5237	1.40399
$962$	−2.92732	−0.0943805
$963$	34.9712	1.12693
$964$	15.8753	0.511309
$965$	27.7039	0.891821
$966$	2.00226	0.0644216
$967$	−12.3514	−0.397195	−0.198597	−	0.980081i	$-0.563639\pi$
$967$	−12.3514	−0.397195	−0.198597	+	0.980081i	$0.563639\pi$
$968$	−10.7439	−0.345321
$969$	9.18617	0.295102
$970$	−20.7512	−0.666281
$971$	14.9997	0.481364	0.240682	−	0.970604i	$-0.422629\pi$
$971$	14.9997	0.481364	0.240682	+	0.970604i	$0.422629\pi$
$972$	11.6335	0.373144
$973$	26.7221	0.856672
$974$	−6.73804	−0.215901
$975$	−2.06456	−0.0661187
$976$	−6.55468	−0.209810
$977$	0.846602	0.0270852	0.0135426	−	0.999908i	$-0.495689\pi$
$977$	0.846602	0.0270852	0.0135426	+	0.999908i	$0.495689\pi$
$978$	−4.23788	−0.135512
$979$	−3.47065	−0.110922
$980$	−40.1961	−1.28402
$981$	18.8491	0.601806
$982$	9.15504	0.292149
$983$	25.4437	0.811529	0.405764	−	0.913978i	$-0.367005\pi$
$983$	25.4437	0.811529	0.405764	+	0.913978i	$0.367005\pi$
$984$	3.80812	0.121399
$985$	−50.4404	−1.60717
$986$	2.81298	0.0895835
$987$	−24.6001	−0.783031
$988$	−3.04364	−0.0968311
$989$	0.372597	0.0118479
$990$	5.37065	0.170691
$991$	7.09507	0.225382	0.112691	−	0.993630i	$-0.464053\pi$
$991$	7.09507	0.225382	0.112691	+	0.993630i	$0.464053\pi$
$992$	8.63271	0.274089
$993$	−6.79170	−0.215528
$994$	52.7098	1.67185
$995$	94.1704	2.98540
$996$	8.61778	0.273065
$997$	29.7558	0.942377	0.471188	−	0.882033i	$-0.343825\pi$
$997$	29.7558	0.942377	0.471188	+	0.882033i	$0.343825\pi$
$998$	−20.0945	−0.636079
$999$	−18.1253	−0.573458

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.k.1.5	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.k.1.5	✓	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.478690 q^{3} +1.00000 q^{4} -3.82976 q^{5} +0.478690 q^{6} +4.18279 q^{7} +1.00000 q^{8} -2.77086 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.478690 q^{3} +1.00000 q^{4} -3.82976 q^{5} +0.478690 q^{6} +4.18279 q^{7} +1.00000 q^{8} -2.77086 q^{9} -3.82976 q^{10} +0.506106 q^{11} +0.478690 q^{12} -0.446148 q^{13} +4.18279 q^{14} -1.83326 q^{15} +1.00000 q^{16} +2.81298 q^{17} -2.77086 q^{18} +6.82204 q^{19} -3.82976 q^{20} +2.00226 q^{21} +0.506106 q^{22} +1.00000 q^{23} +0.478690 q^{24} +9.66703 q^{25} -0.446148 q^{26} -2.76245 q^{27} +4.18279 q^{28} +1.00000 q^{29} -1.83326 q^{30} +8.63271 q^{31} +1.00000 q^{32} +0.242268 q^{33} +2.81298 q^{34} -16.0191 q^{35} -2.77086 q^{36} +6.56131 q^{37} +6.82204 q^{38} -0.213567 q^{39} -3.82976 q^{40} +7.95531 q^{41} +2.00226 q^{42} +0.372597 q^{43} +0.506106 q^{44} +10.6117 q^{45} +1.00000 q^{46} -12.2862 q^{47} +0.478690 q^{48} +10.4957 q^{49} +9.66703 q^{50} +1.34654 q^{51} -0.446148 q^{52} -3.90843 q^{53} -2.76245 q^{54} -1.93826 q^{55} +4.18279 q^{56} +3.26564 q^{57} +1.00000 q^{58} -10.5728 q^{59} -1.83326 q^{60} -6.55468 q^{61} +8.63271 q^{62} -11.5899 q^{63} +1.00000 q^{64} +1.70864 q^{65} +0.242268 q^{66} -16.1476 q^{67} +2.81298 q^{68} +0.478690 q^{69} -16.0191 q^{70} +12.6016 q^{71} -2.77086 q^{72} +7.47554 q^{73} +6.56131 q^{74} +4.62751 q^{75} +6.82204 q^{76} +2.11694 q^{77} -0.213567 q^{78} +5.65596 q^{79} -3.82976 q^{80} +6.99021 q^{81} +7.95531 q^{82} +18.0029 q^{83} +2.00226 q^{84} -10.7730 q^{85} +0.372597 q^{86} +0.478690 q^{87} +0.506106 q^{88} -6.85755 q^{89} +10.6117 q^{90} -1.86615 q^{91} +1.00000 q^{92} +4.13239 q^{93} -12.2862 q^{94} -26.1267 q^{95} +0.478690 q^{96} +5.41841 q^{97} +10.4957 q^{98} -1.40235 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9} - q^{10} + q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 10 q^{16} + 11 q^{18} + 20 q^{19} - q^{20} + 14 q^{21} + q^{22} + 10 q^{23} + 5 q^{24} + 23 q^{25} + 9 q^{26} + 23 q^{27} + 2 q^{28} + 10 q^{29} + 5 q^{30} + 21 q^{31} + 10 q^{32} + q^{33} + 2 q^{35} + 11 q^{36} - 8 q^{37} + 20 q^{38} + 23 q^{39} - q^{40} - 4 q^{41} + 14 q^{42} - 3 q^{43} + q^{44} - 18 q^{45} + 10 q^{46} - q^{47} + 5 q^{48} + 18 q^{49} + 23 q^{50} - 6 q^{51} + 9 q^{52} - 13 q^{53} + 23 q^{54} + 13 q^{55} + 2 q^{56} - 22 q^{57} + 10 q^{58} + 14 q^{59} + 5 q^{60} + 12 q^{61} + 21 q^{62} - 26 q^{63} + 10 q^{64} - 25 q^{65} + q^{66} + 6 q^{67} + 5 q^{69} + 2 q^{70} + 8 q^{71} + 11 q^{72} + 16 q^{73} - 8 q^{74} + 8 q^{75} + 20 q^{76} - 16 q^{77} + 23 q^{78} + 7 q^{79} - q^{80} - 2 q^{81} - 4 q^{82} + 18 q^{83} + 14 q^{84} + 8 q^{85} - 3 q^{86} + 5 q^{87} + q^{88} + 2 q^{89} - 18 q^{90} + 8 q^{91} + 10 q^{92} - 41 q^{93} - q^{94} - 16 q^{95} + 5 q^{96} + 6 q^{97} + 18 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9 - q^10 + q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 10 * q^16 + 11 * q^18 + 20 * q^19 - q^20 + 14 * q^21 + q^22 + 10 * q^23 + 5 * q^24 + 23 * q^25 + 9 * q^26 + 23 * q^27 + 2 * q^28 + 10 * q^29 + 5 * q^30 + 21 * q^31 + 10 * q^32 + q^33 + 2 * q^35 + 11 * q^36 - 8 * q^37 + 20 * q^38 + 23 * q^39 - q^40 - 4 * q^41 + 14 * q^42 - 3 * q^43 + q^44 - 18 * q^45 + 10 * q^46 - q^47 + 5 * q^48 + 18 * q^49 + 23 * q^50 - 6 * q^51 + 9 * q^52 - 13 * q^53 + 23 * q^54 + 13 * q^55 + 2 * q^56 - 22 * q^57 + 10 * q^58 + 14 * q^59 + 5 * q^60 + 12 * q^61 + 21 * q^62 - 26 * q^63 + 10 * q^64 - 25 * q^65 + q^66 + 6 * q^67 + 5 * q^69 + 2 * q^70 + 8 * q^71 + 11 * q^72 + 16 * q^73 - 8 * q^74 + 8 * q^75 + 20 * q^76 - 16 * q^77 + 23 * q^78 + 7 * q^79 - q^80 - 2 * q^81 - 4 * q^82 + 18 * q^83 + 14 * q^84 + 8 * q^85 - 3 * q^86 + 5 * q^87 + q^88 + 2 * q^89 - 18 * q^90 + 8 * q^91 + 10 * q^92 - 41 * q^93 - q^94 - 16 * q^95 + 5 * q^96 + 6 * q^97 + 18 * q^98 - 22 * q^99

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