LMFDB - Embedded newform 1502.2.a.e.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4x^{10} - 9x^{9} + 58x^{8} - 40x^{7} - 146x^{6} + 237x^{5} - 47x^{4} - 89x^{3} + 39x^{2} - 1 $ x^11 - 4x^10 - 9x^9 + 58x^8 - 40x^7 - 146x^6 + 237x^5 - 47x^4 - 89x^3 + 39*x^2 - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$2.26367$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.04934 q^{3} +1.00000 q^{4} +2.15494 q^{5} -1.04934 q^{6} -0.540539 q^{7} -1.00000 q^{8} -1.89889 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.04934 q^{3} +1.00000 q^{4} +2.15494 q^{5} -1.04934 q^{6} -0.540539 q^{7} -1.00000 q^{8} -1.89889 q^{9} -2.15494 q^{10} -5.73469 q^{11} +1.04934 q^{12} -0.362290 q^{13} +0.540539 q^{14} +2.26126 q^{15} +1.00000 q^{16} +2.08724 q^{17} +1.89889 q^{18} -5.38631 q^{19} +2.15494 q^{20} -0.567208 q^{21} +5.73469 q^{22} +0.885870 q^{23} -1.04934 q^{24} -0.356227 q^{25} +0.362290 q^{26} -5.14059 q^{27} -0.540539 q^{28} -5.43569 q^{29} -2.26126 q^{30} -2.43075 q^{31} -1.00000 q^{32} -6.01762 q^{33} -2.08724 q^{34} -1.16483 q^{35} -1.89889 q^{36} -9.20088 q^{37} +5.38631 q^{38} -0.380164 q^{39} -2.15494 q^{40} -9.97313 q^{41} +0.567208 q^{42} +10.9478 q^{43} -5.73469 q^{44} -4.09200 q^{45} -0.885870 q^{46} +9.52323 q^{47} +1.04934 q^{48} -6.70782 q^{49} +0.356227 q^{50} +2.19022 q^{51} -0.362290 q^{52} -4.20045 q^{53} +5.14059 q^{54} -12.3579 q^{55} +0.540539 q^{56} -5.65205 q^{57} +5.43569 q^{58} +9.21368 q^{59} +2.26126 q^{60} -2.71974 q^{61} +2.43075 q^{62} +1.02642 q^{63} +1.00000 q^{64} -0.780714 q^{65} +6.01762 q^{66} +1.22588 q^{67} +2.08724 q^{68} +0.929577 q^{69} +1.16483 q^{70} +4.06325 q^{71} +1.89889 q^{72} +12.9646 q^{73} +9.20088 q^{74} -0.373803 q^{75} -5.38631 q^{76} +3.09982 q^{77} +0.380164 q^{78} +2.49119 q^{79} +2.15494 q^{80} +0.302460 q^{81} +9.97313 q^{82} +11.3436 q^{83} -0.567208 q^{84} +4.49788 q^{85} -10.9478 q^{86} -5.70387 q^{87} +5.73469 q^{88} -6.14683 q^{89} +4.09200 q^{90} +0.195832 q^{91} +0.885870 q^{92} -2.55068 q^{93} -9.52323 q^{94} -11.6072 q^{95} -1.04934 q^{96} -4.61580 q^{97} +6.70782 q^{98} +10.8895 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 19 q^{13} + 6 q^{14} + q^{15} + 11 q^{16} - 8 q^{17} - 3 q^{18} - 9 q^{19} + q^{20} - 6 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 2 q^{25} + 19 q^{26} - 16 q^{27} - 6 q^{28} + 13 q^{29} - q^{30} - 19 q^{31} - 11 q^{32} - 37 q^{33} + 8 q^{34} + 3 q^{35} + 3 q^{36} - 29 q^{37} + 9 q^{38} + 8 q^{39} - q^{40} - 23 q^{41} + 6 q^{42} - 13 q^{43} + 4 q^{44} - 6 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 5 q^{49} + 2 q^{50} + 33 q^{51} - 19 q^{52} - 25 q^{53} + 16 q^{54} - 14 q^{55} + 6 q^{56} + 4 q^{57} - 13 q^{58} + 6 q^{59} + q^{60} + 10 q^{61} + 19 q^{62} - 7 q^{63} + 11 q^{64} - 19 q^{65} + 37 q^{66} - 16 q^{67} - 8 q^{68} - 25 q^{69} - 3 q^{70} + 8 q^{71} - 3 q^{72} - 56 q^{73} + 29 q^{74} - 50 q^{75} - 9 q^{76} - 7 q^{77} - 8 q^{78} + 2 q^{79} + q^{80} - 5 q^{81} + 23 q^{82} + 21 q^{83} - 6 q^{84} - 55 q^{85} + 13 q^{86} - 11 q^{87} - 4 q^{88} - 24 q^{89} + 6 q^{90} - 43 q^{91} + 2 q^{92} + 10 q^{93} + 16 q^{94} + 25 q^{95} + 4 q^{96} - 84 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9 - q^10 + 4 * q^11 - 4 * q^12 - 19 * q^13 + 6 * q^14 + q^15 + 11 * q^16 - 8 * q^17 - 3 * q^18 - 9 * q^19 + q^20 - 6 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 2 * q^25 + 19 * q^26 - 16 * q^27 - 6 * q^28 + 13 * q^29 - q^30 - 19 * q^31 - 11 * q^32 - 37 * q^33 + 8 * q^34 + 3 * q^35 + 3 * q^36 - 29 * q^37 + 9 * q^38 + 8 * q^39 - q^40 - 23 * q^41 + 6 * q^42 - 13 * q^43 + 4 * q^44 - 6 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 5 * q^49 + 2 * q^50 + 33 * q^51 - 19 * q^52 - 25 * q^53 + 16 * q^54 - 14 * q^55 + 6 * q^56 + 4 * q^57 - 13 * q^58 + 6 * q^59 + q^60 + 10 * q^61 + 19 * q^62 - 7 * q^63 + 11 * q^64 - 19 * q^65 + 37 * q^66 - 16 * q^67 - 8 * q^68 - 25 * q^69 - 3 * q^70 + 8 * q^71 - 3 * q^72 - 56 * q^73 + 29 * q^74 - 50 * q^75 - 9 * q^76 - 7 * q^77 - 8 * q^78 + 2 * q^79 + q^80 - 5 * q^81 + 23 * q^82 + 21 * q^83 - 6 * q^84 - 55 * q^85 + 13 * q^86 - 11 * q^87 - 4 * q^88 - 24 * q^89 + 6 * q^90 - 43 * q^91 + 2 * q^92 + 10 * q^93 + 16 * q^94 + 25 * q^95 + 4 * q^96 - 84 * q^97 + 5 * q^98 + 14 * 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
$3$	1.04934	0.605835	0.302918	−	0.953017i	$-0.402039\pi$
$3$	1.04934	0.605835	0.302918	+	0.953017i	$0.402039\pi$
$4$	1.00000	0.500000
$5$	2.15494	0.963719	0.481860	−	0.876248i	$-0.339962\pi$
$5$	2.15494	0.963719	0.481860	+	0.876248i	$0.339962\pi$
$6$	−1.04934	−0.428390
$7$	−0.540539	−0.204305	−0.102152	−	0.994769i	$-0.532573\pi$
$7$	−0.540539	−0.204305	−0.102152	+	0.994769i	$0.532573\pi$
$8$	−1.00000	−0.353553
$9$	−1.89889	−0.632964
$10$	−2.15494	−0.681452
$11$	−5.73469	−1.72907	−0.864537	−	0.502569i	$-0.832388\pi$
$11$	−5.73469	−1.72907	−0.864537	+	0.502569i	$0.832388\pi$
$12$	1.04934	0.302918
$13$	−0.362290	−0.100481	−0.0502406	−	0.998737i	$-0.515999\pi$
$13$	−0.362290	−0.100481	−0.0502406	+	0.998737i	$0.515999\pi$
$14$	0.540539	0.144465
$15$	2.26126	0.583855
$16$	1.00000	0.250000
$17$	2.08724	0.506230	0.253115	−	0.967436i	$-0.418545\pi$
$17$	2.08724	0.506230	0.253115	+	0.967436i	$0.418545\pi$
$18$	1.89889	0.447573
$19$	−5.38631	−1.23570	−0.617852	−	0.786295i	$-0.711997\pi$
$19$	−5.38631	−1.23570	−0.617852	+	0.786295i	$0.711997\pi$
$20$	2.15494	0.481860
$21$	−0.567208	−0.123775
$22$	5.73469	1.22264
$23$	0.885870	0.184717	0.0923584	−	0.995726i	$-0.470559\pi$
$23$	0.885870	0.184717	0.0923584	+	0.995726i	$0.470559\pi$
$24$	−1.04934	−0.214195
$25$	−0.356227	−0.0712455
$26$	0.362290	0.0710509
$27$	−5.14059	−0.989307
$28$	−0.540539	−0.102152
$29$	−5.43569	−1.00938	−0.504691	−	0.863300i	$-0.668394\pi$
$29$	−5.43569	−1.00938	−0.504691	+	0.863300i	$0.668394\pi$
$30$	−2.26126	−0.412848
$31$	−2.43075	−0.436576	−0.218288	−	0.975884i	$-0.570047\pi$
$31$	−2.43075	−0.436576	−0.218288	+	0.975884i	$0.570047\pi$
$32$	−1.00000	−0.176777
$33$	−6.01762	−1.04753
$34$	−2.08724	−0.357958
$35$	−1.16483	−0.196892
$36$	−1.89889	−0.316482
$37$	−9.20088	−1.51262	−0.756308	−	0.654216i	$-0.772999\pi$
$37$	−9.20088	−1.51262	−0.756308	+	0.654216i	$0.772999\pi$
$38$	5.38631	0.873774
$39$	−0.380164	−0.0608750
$40$	−2.15494	−0.340726
$41$	−9.97313	−1.55754	−0.778771	−	0.627309i	$-0.784157\pi$
$41$	−9.97313	−1.55754	−0.778771	+	0.627309i	$0.784157\pi$
$42$	0.567208	0.0875221
$43$	10.9478	1.66952	0.834762	−	0.550611i	$-0.185605\pi$
$43$	10.9478	1.66952	0.834762	+	0.550611i	$0.185605\pi$
$44$	−5.73469	−0.864537
$45$	−4.09200	−0.609999
$46$	−0.885870	−0.130614
$47$	9.52323	1.38911	0.694553	−	0.719442i	$-0.255602\pi$
$47$	9.52323	1.38911	0.694553	+	0.719442i	$0.255602\pi$
$48$	1.04934	0.151459
$49$	−6.70782	−0.958260
$50$	0.356227	0.0503782
$51$	2.19022	0.306692
$52$	−0.362290	−0.0502406
$53$	−4.20045	−0.576977	−0.288488	−	0.957483i	$-0.593153\pi$
$53$	−4.20045	−0.576977	−0.288488	+	0.957483i	$0.593153\pi$
$54$	5.14059	0.699546
$55$	−12.3579	−1.66634
$56$	0.540539	0.0722326
$57$	−5.65205	−0.748633
$58$	5.43569	0.713741
$59$	9.21368	1.19952	0.599760	−	0.800180i	$-0.295263\pi$
$59$	9.21368	1.19952	0.599760	+	0.800180i	$0.295263\pi$
$60$	2.26126	0.291928
$61$	−2.71974	−0.348226	−0.174113	−	0.984726i	$-0.555706\pi$
$61$	−2.71974	−0.348226	−0.174113	+	0.984726i	$0.555706\pi$
$62$	2.43075	0.308706
$63$	1.02642	0.129317
$64$	1.00000	0.125000
$65$	−0.780714	−0.0968356
$66$	6.01762	0.740718
$67$	1.22588	0.149766	0.0748828	−	0.997192i	$-0.476142\pi$
$67$	1.22588	0.149766	0.0748828	+	0.997192i	$0.476142\pi$
$68$	2.08724	0.253115
$69$	0.929577	0.111908
$70$	1.16483	0.139224
$71$	4.06325	0.482219	0.241109	−	0.970498i	$-0.422489\pi$
$71$	4.06325	0.482219	0.241109	+	0.970498i	$0.422489\pi$
$72$	1.89889	0.223786
$73$	12.9646	1.51739	0.758696	−	0.651445i	$-0.225837\pi$
$73$	12.9646	1.51739	0.758696	+	0.651445i	$0.225837\pi$
$74$	9.20088	1.06958
$75$	−0.373803	−0.0431630
$76$	−5.38631	−0.617852
$77$	3.09982	0.353258
$78$	0.380164	0.0430451
$79$	2.49119	0.280281	0.140140	−	0.990132i	$-0.455245\pi$
$79$	2.49119	0.280281	0.140140	+	0.990132i	$0.455245\pi$
$80$	2.15494	0.240930
$81$	0.302460	0.0336066
$82$	9.97313	1.10135
$83$	11.3436	1.24512	0.622562	−	0.782571i	$-0.286092\pi$
$83$	11.3436	1.24512	0.622562	+	0.782571i	$0.286092\pi$
$84$	−0.567208	−0.0618874
$85$	4.49788	0.487863
$86$	−10.9478	−1.18053
$87$	−5.70387	−0.611519
$88$	5.73469	0.611320
$89$	−6.14683	−0.651563	−0.325781	−	0.945445i	$-0.605627\pi$
$89$	−6.14683	−0.651563	−0.325781	+	0.945445i	$0.605627\pi$
$90$	4.09200	0.431335
$91$	0.195832	0.0205288
$92$	0.885870	0.0923584
$93$	−2.55068	−0.264493
$94$	−9.52323	−0.982246
$95$	−11.6072	−1.19087
$96$	−1.04934	−0.107098
$97$	−4.61580	−0.468664	−0.234332	−	0.972157i	$-0.575290\pi$
$97$	−4.61580	−0.468664	−0.234332	+	0.972157i	$0.575290\pi$
$98$	6.70782	0.677592
$99$	10.8895	1.09444
$100$	−0.356227	−0.0356227
$101$	1.92354	0.191399	0.0956996	−	0.995410i	$-0.469491\pi$
$101$	1.92354	0.191399	0.0956996	+	0.995410i	$0.469491\pi$
$102$	−2.19022	−0.216864
$103$	−15.0179	−1.47976	−0.739880	−	0.672739i	$-0.765118\pi$
$103$	−15.0179	−1.47976	−0.739880	+	0.672739i	$0.765118\pi$
$104$	0.362290	0.0355255
$105$	−1.22230	−0.119284
$106$	4.20045	0.407984
$107$	11.0975	1.07284	0.536419	−	0.843952i	$-0.319777\pi$
$107$	11.0975	1.07284	0.536419	+	0.843952i	$0.319777\pi$
$108$	−5.14059	−0.494653
$109$	−13.0125	−1.24637	−0.623185	−	0.782074i	$-0.714162\pi$
$109$	−13.0125	−1.24637	−0.623185	+	0.782074i	$0.714162\pi$
$110$	12.3579	1.17828
$111$	−9.65483	−0.916396
$112$	−0.540539	−0.0510761
$113$	−18.3444	−1.72569	−0.862847	−	0.505465i	$-0.831321\pi$
$113$	−18.3444	−1.72569	−0.862847	+	0.505465i	$0.831321\pi$
$114$	5.65205	0.529363
$115$	1.90900	0.178015
$116$	−5.43569	−0.504691
$117$	0.687949	0.0636009
$118$	−9.21368	−0.848188
$119$	−1.12823	−0.103425
$120$	−2.26126	−0.206424
$121$	21.8867	1.98970
$122$	2.71974	0.246233
$123$	−10.4652	−0.943614
$124$	−2.43075	−0.218288
$125$	−11.5424	−1.03238
$126$	−1.02642	−0.0914412
$127$	−6.32302	−0.561078	−0.280539	−	0.959843i	$-0.590513\pi$
$127$	−6.32302	−0.561078	−0.280539	+	0.959843i	$0.590513\pi$
$128$	−1.00000	−0.0883883
$129$	11.4879	1.01146
$130$	0.780714	0.0684731
$131$	1.03834	0.0907201	0.0453600	−	0.998971i	$-0.485556\pi$
$131$	1.03834	0.0907201	0.0453600	+	0.998971i	$0.485556\pi$
$132$	−6.01762	−0.523767
$133$	2.91151	0.252460
$134$	−1.22588	−0.105900
$135$	−11.0777	−0.953414
$136$	−2.08724	−0.178979
$137$	22.5482	1.92642	0.963211	−	0.268745i	$-0.0866088\pi$
$137$	22.5482	1.92642	0.963211	+	0.268745i	$0.0866088\pi$
$138$	−0.929577	−0.0791308
$139$	−2.09392	−0.177604	−0.0888021	−	0.996049i	$-0.528304\pi$
$139$	−2.09392	−0.177604	−0.0888021	+	0.996049i	$0.528304\pi$
$140$	−1.16483	−0.0984461
$141$	9.99308	0.841569
$142$	−4.06325	−0.340980
$143$	2.07762	0.173739
$144$	−1.89889	−0.158241
$145$	−11.7136	−0.972761
$146$	−12.9646	−1.07296
$147$	−7.03876	−0.580547
$148$	−9.20088	−0.756308
$149$	−0.213433	−0.0174851	−0.00874254	−	0.999962i	$-0.502783\pi$
$149$	−0.213433	−0.0174851	−0.00874254	+	0.999962i	$0.502783\pi$
$150$	0.373803	0.0305209
$151$	−5.44763	−0.443322	−0.221661	−	0.975124i	$-0.571148\pi$
$151$	−5.44763	−0.443322	−0.221661	+	0.975124i	$0.571148\pi$
$152$	5.38631	0.436887
$153$	−3.96344	−0.320425
$154$	−3.09982	−0.249791
$155$	−5.23812	−0.420736
$156$	−0.380164	−0.0304375
$157$	−1.75511	−0.140073	−0.0700366	−	0.997544i	$-0.522312\pi$
$157$	−1.75511	−0.140073	−0.0700366	+	0.997544i	$0.522312\pi$
$158$	−2.49119	−0.198189
$159$	−4.40769	−0.349553
$160$	−2.15494	−0.170363
$161$	−0.478847	−0.0377385
$162$	−0.302460	−0.0237635
$163$	9.25080	0.724578	0.362289	−	0.932066i	$-0.381995\pi$
$163$	9.25080	0.724578	0.362289	+	0.932066i	$0.381995\pi$
$164$	−9.97313	−0.778771
$165$	−12.9676	−1.00953
$166$	−11.3436	−0.880435
$167$	−1.44142	−0.111540	−0.0557701	−	0.998444i	$-0.517761\pi$
$167$	−1.44142	−0.111540	−0.0557701	+	0.998444i	$0.517761\pi$
$168$	0.567208	0.0437610
$169$	−12.8687	−0.989904
$170$	−4.49788	−0.344971
$171$	10.2280	0.782155
$172$	10.9478	0.834762
$173$	20.9258	1.59096	0.795480	−	0.605979i	$-0.207219\pi$
$173$	20.9258	1.59096	0.795480	+	0.605979i	$0.207219\pi$
$174$	5.70387	0.432409
$175$	0.192555	0.0145558
$176$	−5.73469	−0.432268
$177$	9.66826	0.726711
$178$	6.14683	0.460724
$179$	−17.2046	−1.28593	−0.642964	−	0.765896i	$-0.722296\pi$
$179$	−17.2046	−1.28593	−0.642964	+	0.765896i	$0.722296\pi$
$180$	−4.09200	−0.305000
$181$	18.3130	1.36119	0.680596	−	0.732659i	$-0.261721\pi$
$181$	18.3130	1.36119	0.680596	+	0.732659i	$0.261721\pi$
$182$	−0.195832	−0.0145160
$183$	−2.85392	−0.210968
$184$	−0.885870	−0.0653072
$185$	−19.8274	−1.45774
$186$	2.55068	0.187025
$187$	−11.9697	−0.875309
$188$	9.52323	0.694553
$189$	2.77869	0.202120
$190$	11.6072	0.842073
$191$	−13.7212	−0.992833	−0.496417	−	0.868084i	$-0.665351\pi$
$191$	−13.7212	−0.992833	−0.496417	+	0.868084i	$0.665351\pi$
$192$	1.04934	0.0757294
$193$	−20.5941	−1.48239	−0.741197	−	0.671288i	$-0.765741\pi$
$193$	−20.5941	−1.48239	−0.741197	+	0.671288i	$0.765741\pi$
$194$	4.61580	0.331395
$195$	−0.819232	−0.0586664
$196$	−6.70782	−0.479130
$197$	−1.65605	−0.117988	−0.0589942	−	0.998258i	$-0.518789\pi$
$197$	−1.65605	−0.117988	−0.0589942	+	0.998258i	$0.518789\pi$
$198$	−10.8895	−0.773886
$199$	4.98022	0.353038	0.176519	−	0.984297i	$-0.443516\pi$
$199$	4.98022	0.353038	0.176519	+	0.984297i	$0.443516\pi$
$200$	0.356227	0.0251891
$201$	1.28637	0.0907333
$202$	−1.92354	−0.135340
$203$	2.93820	0.206221
$204$	2.19022	0.153346
$205$	−21.4915	−1.50103
$206$	15.0179	1.04635
$207$	−1.68217	−0.116919
$208$	−0.362290	−0.0251203
$209$	30.8888	2.13662
$210$	1.22230	0.0843467
$211$	18.0744	1.24430	0.622148	−	0.782900i	$-0.286260\pi$
$211$	18.0744	1.24430	0.622148	+	0.782900i	$0.286260\pi$
$212$	−4.20045	−0.288488
$213$	4.26372	0.292145
$214$	−11.0975	−0.758611
$215$	23.5919	1.60895
$216$	5.14059	0.349773
$217$	1.31392	0.0891944
$218$	13.0125	0.881317
$219$	13.6042	0.919290
$220$	−12.3579	−0.833171
$221$	−0.756186	−0.0508666
$222$	9.65483	0.647990
$223$	−22.2949	−1.49298	−0.746488	−	0.665399i	$-0.768261\pi$
$223$	−22.2949	−1.49298	−0.746488	+	0.665399i	$0.768261\pi$
$224$	0.540539	0.0361163
$225$	0.676437	0.0450958
$226$	18.3444	1.22025
$227$	−21.1309	−1.40251	−0.701253	−	0.712912i	$-0.747376\pi$
$227$	−21.1309	−1.40251	−0.701253	+	0.712912i	$0.747376\pi$
$228$	−5.65205	−0.374316
$229$	−13.8675	−0.916393	−0.458196	−	0.888851i	$-0.651504\pi$
$229$	−13.8675	−0.916393	−0.458196	+	0.888851i	$0.651504\pi$
$230$	−1.90900	−0.125876
$231$	3.25276	0.214016
$232$	5.43569	0.356870
$233$	14.8649	0.973835	0.486918	−	0.873448i	$-0.338121\pi$
$233$	14.8649	0.973835	0.486918	+	0.873448i	$0.338121\pi$
$234$	−0.687949	−0.0449726
$235$	20.5220	1.33871
$236$	9.21368	0.599760
$237$	2.61410	0.169804
$238$	1.12823	0.0731325
$239$	8.68547	0.561817	0.280908	−	0.959735i	$-0.409364\pi$
$239$	8.68547	0.561817	0.280908	+	0.959735i	$0.409364\pi$
$240$	2.26126	0.145964
$241$	−26.4084	−1.70111	−0.850556	−	0.525884i	$-0.823735\pi$
$241$	−26.4084	−1.70111	−0.850556	+	0.525884i	$0.823735\pi$
$242$	−21.8867	−1.40693
$243$	15.7392	1.00967
$244$	−2.71974	−0.174113
$245$	−14.4550	−0.923493
$246$	10.4652	0.667236
$247$	1.95140	0.124165
$248$	2.43075	0.154353
$249$	11.9033	0.754340
$250$	11.5424	0.730003
$251$	13.5671	0.856346	0.428173	−	0.903697i	$-0.359157\pi$
$251$	13.5671	0.856346	0.428173	+	0.903697i	$0.359157\pi$
$252$	1.02642	0.0646587
$253$	−5.08019	−0.319389
$254$	6.32302	0.396742
$255$	4.71979	0.295565
$256$	1.00000	0.0625000
$257$	−11.7072	−0.730275	−0.365138	−	0.930954i	$-0.618978\pi$
$257$	−11.7072	−0.730275	−0.365138	+	0.930954i	$0.618978\pi$
$258$	−11.4879	−0.715208
$259$	4.97343	0.309034
$260$	−0.780714	−0.0484178
$261$	10.3218	0.638902
$262$	−1.03834	−0.0641488
$263$	10.4844	0.646493	0.323247	−	0.946315i	$-0.395226\pi$
$263$	10.4844	0.646493	0.323247	+	0.946315i	$0.395226\pi$
$264$	6.01762	0.370359
$265$	−9.05173	−0.556044
$266$	−2.91151	−0.178516
$267$	−6.45010	−0.394740
$268$	1.22588	0.0748828
$269$	5.76384	0.351428	0.175714	−	0.984441i	$-0.443777\pi$
$269$	5.76384	0.351428	0.175714	+	0.984441i	$0.443777\pi$
$270$	11.0777	0.674166
$271$	14.7333	0.894987	0.447493	−	0.894287i	$-0.352317\pi$
$271$	14.7333	0.894987	0.447493	+	0.894287i	$0.352317\pi$
$272$	2.08724	0.126557
$273$	0.205494	0.0124370
$274$	−22.5482	−1.36219
$275$	2.04285	0.123189
$276$	0.929577	0.0559540
$277$	−0.287844	−0.0172949	−0.00864744	−	0.999963i	$-0.502753\pi$
$277$	−0.287844	−0.0172949	−0.00864744	+	0.999963i	$0.502753\pi$
$278$	2.09392	0.125585
$279$	4.61573	0.276336
$280$	1.16483	0.0696119
$281$	−17.8282	−1.06354	−0.531770	−	0.846889i	$-0.678473\pi$
$281$	−17.8282	−1.06354	−0.531770	+	0.846889i	$0.678473\pi$
$282$	−9.99308	−0.595079
$283$	8.91497	0.529940	0.264970	−	0.964257i	$-0.414638\pi$
$283$	8.91497	0.529940	0.264970	+	0.964257i	$0.414638\pi$
$284$	4.06325	0.241109
$285$	−12.1798	−0.721472
$286$	−2.07762	−0.122852
$287$	5.39087	0.318213
$288$	1.89889	0.111893
$289$	−12.6434	−0.743731
$290$	11.7136	0.687846
$291$	−4.84354	−0.283933
$292$	12.9646	0.758696
$293$	22.2467	1.29967	0.649835	−	0.760076i	$-0.274838\pi$
$293$	22.2467	1.29967	0.649835	+	0.760076i	$0.274838\pi$
$294$	7.03876	0.410509
$295$	19.8549	1.15600
$296$	9.20088	0.534790
$297$	29.4797	1.71058
$298$	0.213433	0.0123638
$299$	−0.320942	−0.0185606
$300$	−0.373803	−0.0215815
$301$	−5.91771	−0.341091
$302$	5.44763	0.313476
$303$	2.01844	0.115956
$304$	−5.38631	−0.308926
$305$	−5.86087	−0.335593
$306$	3.96344	0.226575
$307$	−28.0445	−1.60058	−0.800292	−	0.599611i	$-0.795322\pi$
$307$	−28.0445	−1.60058	−0.800292	+	0.599611i	$0.795322\pi$
$308$	3.09982	0.176629
$309$	−15.7589	−0.896490
$310$	5.23812	0.297505
$311$	−16.3521	−0.927245	−0.463622	−	0.886033i	$-0.653451\pi$
$311$	−16.3521	−0.927245	−0.463622	+	0.886033i	$0.653451\pi$
$312$	0.380164	0.0215226
$313$	−12.9326	−0.730992	−0.365496	−	0.930813i	$-0.619101\pi$
$313$	−12.9326	−0.730992	−0.365496	+	0.930813i	$0.619101\pi$
$314$	1.75511	0.0990466
$315$	2.21189	0.124626
$316$	2.49119	0.140140
$317$	−33.8898	−1.90344	−0.951720	−	0.306968i	$-0.900686\pi$
$317$	−33.8898	−1.90344	−0.951720	+	0.306968i	$0.900686\pi$
$318$	4.40769	0.247171
$319$	31.1720	1.74530
$320$	2.15494	0.120465
$321$	11.6450	0.649963
$322$	0.478847	0.0266851
$323$	−11.2425	−0.625550
$324$	0.302460	0.0168033
$325$	0.129058	0.00715883
$326$	−9.25080	−0.512354
$327$	−13.6545	−0.755095
$328$	9.97313	0.550674
$329$	−5.14768	−0.283801
$330$	12.9676	0.713844
$331$	−5.71187	−0.313953	−0.156976	−	0.987602i	$-0.550175\pi$
$331$	−5.71187	−0.313953	−0.156976	+	0.987602i	$0.550175\pi$
$332$	11.3436	0.622562
$333$	17.4715	0.957430
$334$	1.44142	0.0788708
$335$	2.64171	0.144332
$336$	−0.567208	−0.0309437
$337$	7.03784	0.383375	0.191688	−	0.981456i	$-0.438604\pi$
$337$	7.03784	0.383375	0.191688	+	0.981456i	$0.438604\pi$
$338$	12.8687	0.699968
$339$	−19.2495	−1.04549
$340$	4.49788	0.243932
$341$	13.9396	0.754871
$342$	−10.2280	−0.553067
$343$	7.40961	0.400081
$344$	−10.9478	−0.590266
$345$	2.00318	0.107848
$346$	−20.9258	−1.12498
$347$	−9.07481	−0.487162	−0.243581	−	0.969881i	$-0.578322\pi$
$347$	−9.07481	−0.487162	−0.243581	+	0.969881i	$0.578322\pi$
$348$	−5.70387	−0.305760
$349$	−22.5913	−1.20929	−0.604643	−	0.796497i	$-0.706684\pi$
$349$	−22.5913	−1.20929	−0.604643	+	0.796497i	$0.706684\pi$
$350$	−0.192555	−0.0102925
$351$	1.86238	0.0994067
$352$	5.73469	0.305660
$353$	26.8433	1.42872	0.714362	−	0.699776i	$-0.246717\pi$
$353$	26.8433	1.42872	0.714362	+	0.699776i	$0.246717\pi$
$354$	−9.66826	−0.513862
$355$	8.75606	0.464724
$356$	−6.14683	−0.325781
$357$	−1.18390	−0.0626585
$358$	17.2046	0.909289
$359$	32.4584	1.71309	0.856545	−	0.516072i	$-0.172606\pi$
$359$	32.4584	1.71309	0.856545	+	0.516072i	$0.172606\pi$
$360$	4.09200	0.215667
$361$	10.0123	0.526963
$362$	−18.3130	−0.962508
$363$	22.9665	1.20543
$364$	0.195832	0.0102644
$365$	27.9380	1.46234
$366$	2.85392	0.149177
$367$	3.35812	0.175292	0.0876461	−	0.996152i	$-0.472066\pi$
$367$	3.35812	0.175292	0.0876461	+	0.996152i	$0.472066\pi$
$368$	0.885870	0.0461792
$369$	18.9379	0.985867
$370$	19.8274	1.03078
$371$	2.27051	0.117879
$372$	−2.55068	−0.132246
$373$	7.60956	0.394008	0.197004	−	0.980403i	$-0.436879\pi$
$373$	7.60956	0.394008	0.197004	+	0.980403i	$0.436879\pi$
$374$	11.9697	0.618937
$375$	−12.1118	−0.625452
$376$	−9.52323	−0.491123
$377$	1.96930	0.101424
$378$	−2.77869	−0.142920
$379$	0.0680164	0.00349377	0.00174688	−	0.999998i	$-0.499444\pi$
$379$	0.0680164	0.00349377	0.00174688	+	0.999998i	$0.499444\pi$
$380$	−11.6072	−0.595435
$381$	−6.63499	−0.339921
$382$	13.7212	0.702039
$383$	−18.9420	−0.967890	−0.483945	−	0.875098i	$-0.660797\pi$
$383$	−18.9420	−0.967890	−0.483945	+	0.875098i	$0.660797\pi$
$384$	−1.04934	−0.0535488
$385$	6.67994	0.340441
$386$	20.5941	1.04821
$387$	−20.7887	−1.05675
$388$	−4.61580	−0.234332
$389$	28.4069	1.44029	0.720143	−	0.693825i	$-0.244076\pi$
$389$	28.4069	1.44029	0.720143	+	0.693825i	$0.244076\pi$
$390$	0.819232	0.0414834
$391$	1.84902	0.0935091
$392$	6.70782	0.338796
$393$	1.08957	0.0549614
$394$	1.65605	0.0834304
$395$	5.36837	0.270112
$396$	10.8895	0.547220
$397$	5.04847	0.253375	0.126688	−	0.991943i	$-0.459565\pi$
$397$	5.04847	0.253375	0.126688	+	0.991943i	$0.459565\pi$
$398$	−4.98022	−0.249636
$399$	3.05516	0.152949
$400$	−0.356227	−0.0178114
$401$	9.18004	0.458429	0.229215	−	0.973376i	$-0.426384\pi$
$401$	9.18004	0.458429	0.229215	+	0.973376i	$0.426384\pi$
$402$	−1.28637	−0.0641581
$403$	0.880636	0.0438676
$404$	1.92354	0.0956996
$405$	0.651783	0.0323873
$406$	−2.93820	−0.145821
$407$	52.7642	2.61542
$408$	−2.19022	−0.108432
$409$	29.2519	1.44641	0.723206	−	0.690632i	$-0.242668\pi$
$409$	29.2519	1.44641	0.723206	+	0.690632i	$0.242668\pi$
$410$	21.4915	1.06139
$411$	23.6607	1.16709
$412$	−15.0179	−0.739880
$413$	−4.98035	−0.245067
$414$	1.68217	0.0826742
$415$	24.4448	1.19995
$416$	0.362290	0.0177627
$417$	−2.19723	−0.107599
$418$	−30.8888	−1.51082
$419$	10.1683	0.496755	0.248377	−	0.968663i	$-0.420103\pi$
$419$	10.1683	0.496755	0.248377	+	0.968663i	$0.420103\pi$
$420$	−1.22230	−0.0596421
$421$	−18.3049	−0.892126	−0.446063	−	0.895001i	$-0.647174\pi$
$421$	−18.3049	−0.892126	−0.446063	+	0.895001i	$0.647174\pi$
$422$	−18.0744	−0.879850
$423$	−18.0836	−0.879253
$424$	4.20045	0.203992
$425$	−0.743532	−0.0360666
$426$	−4.26372	−0.206578
$427$	1.47012	0.0711443
$428$	11.0975	0.536419
$429$	2.18012	0.105257
$430$	−23.5919	−1.13770
$431$	−17.0446	−0.821010	−0.410505	−	0.911858i	$-0.634648\pi$
$431$	−17.0446	−0.821010	−0.410505	+	0.911858i	$0.634648\pi$
$432$	−5.14059	−0.247327
$433$	25.0017	1.20150	0.600752	−	0.799435i	$-0.294868\pi$
$433$	25.0017	1.20150	0.600752	+	0.799435i	$0.294868\pi$
$434$	−1.31392	−0.0630699
$435$	−12.2915	−0.589333
$436$	−13.0125	−0.623185
$437$	−4.77157	−0.228255
$438$	−13.6042	−0.650036
$439$	6.53281	0.311794	0.155897	−	0.987773i	$-0.450173\pi$
$439$	6.53281	0.311794	0.155897	+	0.987773i	$0.450173\pi$
$440$	12.3579	0.589141
$441$	12.7374	0.606544
$442$	0.756186	0.0359681
$443$	21.2773	1.01092	0.505458	−	0.862851i	$-0.331324\pi$
$443$	21.2773	1.01092	0.505458	+	0.862851i	$0.331324\pi$
$444$	−9.65483	−0.458198
$445$	−13.2461	−0.627924
$446$	22.2949	1.05569
$447$	−0.223963	−0.0105931
$448$	−0.540539	−0.0255381
$449$	−17.7042	−0.835511	−0.417756	−	0.908559i	$-0.637183\pi$
$449$	−17.7042	−0.835511	−0.417756	+	0.908559i	$0.637183\pi$
$450$	−0.676437	−0.0318876
$451$	57.1928	2.69310
$452$	−18.3444	−0.862847
$453$	−5.71640	−0.268580
$454$	21.1309	0.991722
$455$	0.422006	0.0197840
$456$	5.65205	0.264682
$457$	6.74358	0.315451	0.157726	−	0.987483i	$-0.449584\pi$
$457$	6.74358	0.315451	0.157726	+	0.987483i	$0.449584\pi$
$458$	13.8675	0.647988
$459$	−10.7296	−0.500817
$460$	1.90900	0.0890075
$461$	18.9430	0.882264	0.441132	−	0.897442i	$-0.354577\pi$
$461$	18.9430	0.882264	0.441132	+	0.897442i	$0.354577\pi$
$462$	−3.25276	−0.151332
$463$	−29.3365	−1.36338	−0.681692	−	0.731639i	$-0.738756\pi$
$463$	−29.3365	−1.36338	−0.681692	+	0.731639i	$0.738756\pi$
$464$	−5.43569	−0.252345
$465$	−5.49656	−0.254897
$466$	−14.8649	−0.688605
$467$	22.1448	1.02474	0.512370	−	0.858765i	$-0.328767\pi$
$467$	22.1448	1.02474	0.512370	+	0.858765i	$0.328767\pi$
$468$	0.687949	0.0318005
$469$	−0.662638	−0.0305978
$470$	−20.5220	−0.946609
$471$	−1.84170	−0.0848612
$472$	−9.21368	−0.424094
$473$	−62.7822	−2.88673
$474$	−2.61410	−0.120070
$475$	1.91875	0.0880383
$476$	−1.12823	−0.0517125
$477$	7.97621	0.365205
$478$	−8.68547	−0.397264
$479$	−2.23771	−0.102243	−0.0511217	−	0.998692i	$-0.516280\pi$
$479$	−2.23771	−0.102243	−0.0511217	+	0.998692i	$0.516280\pi$
$480$	−2.26126	−0.103212
$481$	3.33339	0.151989
$482$	26.4084	1.20287
$483$	−0.502473	−0.0228633
$484$	21.8867	0.994848
$485$	−9.94679	−0.451660
$486$	−15.7392	−0.713942
$487$	−35.3635	−1.60248	−0.801238	−	0.598346i	$-0.795825\pi$
$487$	−35.3635	−1.60248	−0.801238	+	0.598346i	$0.795825\pi$
$488$	2.71974	0.123117
$489$	9.70721	0.438975
$490$	14.4550	0.653008
$491$	−26.1657	−1.18084	−0.590422	−	0.807095i	$-0.701039\pi$
$491$	−26.1657	−1.18084	−0.590422	+	0.807095i	$0.701039\pi$
$492$	−10.4652	−0.471807
$493$	−11.3456	−0.510979
$494$	−1.95140	−0.0877979
$495$	23.4663	1.05473
$496$	−2.43075	−0.109144
$497$	−2.19634	−0.0985195
$498$	−11.9033	−0.533399
$499$	−16.0434	−0.718203	−0.359101	−	0.933299i	$-0.616917\pi$
$499$	−16.0434	−0.718203	−0.359101	+	0.933299i	$0.616917\pi$
$500$	−11.5424	−0.516190
$501$	−1.51253	−0.0675750
$502$	−13.5671	−0.605528
$503$	41.3662	1.84443	0.922214	−	0.386679i	$-0.126378\pi$
$503$	41.3662	1.84443	0.922214	+	0.386679i	$0.126378\pi$
$504$	−1.02642	−0.0457206
$505$	4.14511	0.184455
$506$	5.08019	0.225842
$507$	−13.5037	−0.599718
$508$	−6.32302	−0.280539
$509$	44.9153	1.99083	0.995417	−	0.0956271i	$-0.0304856\pi$
$509$	44.9153	1.99083	0.995417	+	0.0956271i	$0.0304856\pi$
$510$	−4.71979	−0.208996
$511$	−7.00787	−0.310010
$512$	−1.00000	−0.0441942
$513$	27.6888	1.22249
$514$	11.7072	0.516383
$515$	−32.3627	−1.42607
$516$	11.4879	0.505728
$517$	−54.6128	−2.40187
$518$	−4.97343	−0.218520
$519$	21.9582	0.963860
$520$	0.780714	0.0342366
$521$	30.2859	1.32685	0.663425	−	0.748243i	$-0.269102\pi$
$521$	30.2859	1.32685	0.663425	+	0.748243i	$0.269102\pi$
$522$	−10.3218	−0.451772
$523$	−11.8776	−0.519371	−0.259686	−	0.965693i	$-0.583619\pi$
$523$	−11.8776	−0.519371	−0.259686	+	0.965693i	$0.583619\pi$
$524$	1.03834	0.0453600
$525$	0.202055	0.00881840
$526$	−10.4844	−0.457140
$527$	−5.07355	−0.221008
$528$	−6.01762	−0.261883
$529$	−22.2152	−0.965880
$530$	9.05173	0.393182
$531$	−17.4958	−0.759252
$532$	2.91151	0.126230
$533$	3.61317	0.156504
$534$	6.45010	0.279123
$535$	23.9145	1.03391
$536$	−1.22588	−0.0529501
$537$	−18.0534	−0.779061
$538$	−5.76384	−0.248497
$539$	38.4672	1.65690
$540$	−11.0777	−0.476707
$541$	0.317287	0.0136412	0.00682061	−	0.999977i	$-0.497829\pi$
$541$	0.317287	0.0136412	0.00682061	+	0.999977i	$0.497829\pi$
$542$	−14.7333	−0.632851
$543$	19.2165	0.824658
$544$	−2.08724	−0.0894896
$545$	−28.0412	−1.20115
$546$	−0.205494	−0.00879432
$547$	−22.0443	−0.942544	−0.471272	−	0.881988i	$-0.656205\pi$
$547$	−22.0443	−0.942544	−0.471272	+	0.881988i	$0.656205\pi$
$548$	22.5482	0.963211
$549$	5.16448	0.220415
$550$	−2.04285	−0.0871076
$551$	29.2783	1.24730
$552$	−0.929577	−0.0395654
$553$	−1.34659	−0.0572627
$554$	0.287844	0.0122293
$555$	−20.8056	−0.883148
$556$	−2.09392	−0.0888021
$557$	11.5564	0.489659	0.244830	−	0.969566i	$-0.421268\pi$
$557$	11.5564	0.489659	0.244830	+	0.969566i	$0.421268\pi$
$558$	−4.61573	−0.195399
$559$	−3.96628	−0.167756
$560$	−1.16483	−0.0492230
$561$	−12.5602	−0.530293
$562$	17.8282	0.752037
$563$	−25.0069	−1.05391	−0.526957	−	0.849892i	$-0.676667\pi$
$563$	−25.0069	−1.05391	−0.526957	+	0.849892i	$0.676667\pi$
$564$	9.99308	0.420785
$565$	−39.5311	−1.66308
$566$	−8.91497	−0.374724
$567$	−0.163491	−0.00686599
$568$	−4.06325	−0.170490
$569$	21.9609	0.920648	0.460324	−	0.887751i	$-0.347733\pi$
$569$	21.9609	0.920648	0.460324	+	0.887751i	$0.347733\pi$
$570$	12.1798	0.510157
$571$	−27.3637	−1.14514	−0.572568	−	0.819857i	$-0.694053\pi$
$571$	−27.3637	−1.14514	−0.572568	+	0.819857i	$0.694053\pi$
$572$	2.07762	0.0868697
$573$	−14.3982	−0.601493
$574$	−5.39087	−0.225010
$575$	−0.315571	−0.0131602
$576$	−1.89889	−0.0791205
$577$	3.82187	0.159106	0.0795532	−	0.996831i	$-0.474651\pi$
$577$	3.82187	0.159106	0.0795532	+	0.996831i	$0.474651\pi$
$578$	12.6434	0.525898
$579$	−21.6101	−0.898086
$580$	−11.7136	−0.486380
$581$	−6.13167	−0.254384
$582$	4.84354	0.200771
$583$	24.0883	0.997635
$584$	−12.9646	−0.536479
$585$	1.48249	0.0612934
$586$	−22.2467	−0.919005
$587$	9.38197	0.387235	0.193618	−	0.981077i	$-0.437978\pi$
$587$	9.38197	0.387235	0.193618	+	0.981077i	$0.437978\pi$
$588$	−7.03876	−0.290274
$589$	13.0928	0.539478
$590$	−19.8549	−0.817415
$591$	−1.73775	−0.0714816
$592$	−9.20088	−0.378154
$593$	−1.11129	−0.0456351	−0.0228175	−	0.999740i	$-0.507264\pi$
$593$	−1.11129	−0.0456351	−0.0228175	+	0.999740i	$0.507264\pi$
$594$	−29.4797	−1.20957
$595$	−2.43128	−0.0996727
$596$	−0.213433	−0.00874254
$597$	5.22593	0.213883
$598$	0.320942	0.0131243
$599$	24.4011	0.997002	0.498501	−	0.866889i	$-0.333884\pi$
$599$	24.4011	0.997002	0.498501	+	0.866889i	$0.333884\pi$
$600$	0.373803	0.0152604
$601$	−8.13300	−0.331752	−0.165876	−	0.986147i	$-0.553045\pi$
$601$	−8.13300	−0.331752	−0.165876	+	0.986147i	$0.553045\pi$
$602$	5.91771	0.241188
$603$	−2.32782	−0.0947962
$604$	−5.44763	−0.221661
$605$	47.1645	1.91751
$606$	−2.01844	−0.0819936
$607$	20.9893	0.851930	0.425965	−	0.904740i	$-0.359935\pi$
$607$	20.9893	0.851930	0.425965	+	0.904740i	$0.359935\pi$
$608$	5.38631	0.218444
$609$	3.08317	0.124936
$610$	5.86087	0.237300
$611$	−3.45017	−0.139579
$612$	−3.96344	−0.160213
$613$	21.0369	0.849672	0.424836	−	0.905270i	$-0.360332\pi$
$613$	21.0369	0.849672	0.424836	+	0.905270i	$0.360332\pi$
$614$	28.0445	1.13178
$615$	−22.5519	−0.909379
$616$	−3.09982	−0.124895
$617$	−20.6491	−0.831302	−0.415651	−	0.909524i	$-0.636446\pi$
$617$	−20.6491	−0.831302	−0.415651	+	0.909524i	$0.636446\pi$
$618$	15.7589	0.633914
$619$	9.36007	0.376213	0.188107	−	0.982149i	$-0.439765\pi$
$619$	9.36007	0.376213	0.188107	+	0.982149i	$0.439765\pi$
$620$	−5.23812	−0.210368
$621$	−4.55390	−0.182742
$622$	16.3521	0.655661
$623$	3.32260	0.133117
$624$	−0.380164	−0.0152188
$625$	−23.0920	−0.923679
$626$	12.9326	0.516890
$627$	32.4128	1.29444
$628$	−1.75511	−0.0700366
$629$	−19.2044	−0.765731
$630$	−2.21189	−0.0881236
$631$	−7.20751	−0.286926	−0.143463	−	0.989656i	$-0.545824\pi$
$631$	−7.20751	−0.286926	−0.143463	+	0.989656i	$0.545824\pi$
$632$	−2.49119	−0.0990943
$633$	18.9662	0.753838
$634$	33.8898	1.34594
$635$	−13.6257	−0.540721
$636$	−4.40769	−0.174776
$637$	2.43018	0.0962870
$638$	−31.1720	−1.23411
$639$	−7.71567	−0.305227
$640$	−2.15494	−0.0851815
$641$	−33.4549	−1.32139	−0.660694	−	0.750656i	$-0.729738\pi$
$641$	−33.4549	−1.32139	−0.660694	+	0.750656i	$0.729738\pi$
$642$	−11.6450	−0.459593
$643$	4.51947	0.178231	0.0891153	−	0.996021i	$-0.471596\pi$
$643$	4.51947	0.178231	0.0891153	+	0.996021i	$0.471596\pi$
$644$	−0.478847	−0.0188692
$645$	24.7558	0.974760
$646$	11.2425	0.442331
$647$	8.28202	0.325600	0.162800	−	0.986659i	$-0.447948\pi$
$647$	8.28202	0.325600	0.162800	+	0.986659i	$0.447948\pi$
$648$	−0.302460	−0.0118817
$649$	−52.8376	−2.07406
$650$	−0.129058	−0.00506206
$651$	1.37874	0.0540371
$652$	9.25080	0.362289
$653$	−32.2952	−1.26381	−0.631904	−	0.775046i	$-0.717726\pi$
$653$	−32.2952	−1.26381	−0.631904	+	0.775046i	$0.717726\pi$
$654$	13.6545	0.533933
$655$	2.23756	0.0874287
$656$	−9.97313	−0.389385
$657$	−24.6184	−0.960454
$658$	5.14768	0.200677
$659$	21.3369	0.831169	0.415584	−	0.909555i	$-0.363577\pi$
$659$	21.3369	0.831169	0.415584	+	0.909555i	$0.363577\pi$
$660$	−12.9676	−0.504764
$661$	12.3854	0.481736	0.240868	−	0.970558i	$-0.422568\pi$
$661$	12.3854	0.481736	0.240868	+	0.970558i	$0.422568\pi$
$662$	5.71187	0.221998
$663$	−0.793494	−0.0308168
$664$	−11.3436	−0.440218
$665$	6.27413	0.243300
$666$	−17.4715	−0.677006
$667$	−4.81531	−0.186450
$668$	−1.44142	−0.0557701
$669$	−23.3948	−0.904497
$670$	−2.64171	−0.102058
$671$	15.5968	0.602109
$672$	0.567208	0.0218805
$673$	−9.63747	−0.371497	−0.185749	−	0.982597i	$-0.559471\pi$
$673$	−9.63747	−0.371497	−0.185749	+	0.982597i	$0.559471\pi$
$674$	−7.03784	−0.271087
$675$	1.83122	0.0704837
$676$	−12.8687	−0.494952
$677$	−44.0024	−1.69115	−0.845575	−	0.533856i	$-0.820742\pi$
$677$	−44.0024	−1.69115	−0.845575	+	0.533856i	$0.820742\pi$
$678$	19.2495	0.739271
$679$	2.49502	0.0957501
$680$	−4.49788	−0.172486
$681$	−22.1734	−0.849688
$682$	−13.9396	−0.533775
$683$	−40.9178	−1.56568	−0.782838	−	0.622225i	$-0.786229\pi$
$683$	−40.9178	−1.56568	−0.782838	+	0.622225i	$0.786229\pi$
$684$	10.2280	0.391078
$685$	48.5901	1.85653
$686$	−7.40961	−0.282900
$687$	−14.5517	−0.555183
$688$	10.9478	0.417381
$689$	1.52178	0.0579753
$690$	−2.00318	−0.0762599
$691$	−20.2714	−0.771162	−0.385581	−	0.922674i	$-0.625999\pi$
$691$	−20.2714	−0.771162	−0.385581	+	0.922674i	$0.625999\pi$
$692$	20.9258	0.795480
$693$	−5.88623	−0.223599
$694$	9.07481	0.344475
$695$	−4.51228	−0.171161
$696$	5.70387	0.216205
$697$	−20.8163	−0.788474
$698$	22.5913	0.855094
$699$	15.5983	0.589984
$700$	0.192555	0.00727789
$701$	−24.2072	−0.914295	−0.457147	−	0.889391i	$-0.651129\pi$
$701$	−24.2072	−0.914295	−0.457147	+	0.889391i	$0.651129\pi$
$702$	−1.86238	−0.0702912
$703$	49.5588	1.86914
$704$	−5.73469	−0.216134
$705$	21.5345	0.811036
$706$	−26.8433	−1.01026
$707$	−1.03975	−0.0391037
$708$	9.66826	0.363355
$709$	−28.6533	−1.07610	−0.538049	−	0.842914i	$-0.680838\pi$
$709$	−28.6533	−1.07610	−0.538049	+	0.842914i	$0.680838\pi$
$710$	−8.75606	−0.328609
$711$	−4.73050	−0.177408
$712$	6.14683	0.230362
$713$	−2.15333	−0.0806428
$714$	1.18390	0.0443063
$715$	4.47715	0.167436
$716$	−17.2046	−0.642964
$717$	9.11399	0.340368
$718$	−32.4584	−1.21134
$719$	29.3311	1.09387	0.546934	−	0.837176i	$-0.315795\pi$
$719$	29.3311	1.09387	0.546934	+	0.837176i	$0.315795\pi$
$720$	−4.09200	−0.152500
$721$	8.11777	0.302322
$722$	−10.0123	−0.372619
$723$	−27.7113	−1.03059
$724$	18.3130	0.680596
$725$	1.93634	0.0719139
$726$	−22.9665	−0.852366
$727$	−28.8755	−1.07093	−0.535467	−	0.844556i	$-0.679864\pi$
$727$	−28.8755	−1.07093	−0.535467	+	0.844556i	$0.679864\pi$
$728$	−0.195832	−0.00725801
$729$	15.6083	0.578085
$730$	−27.9380	−1.03403
$731$	22.8507	0.845163
$732$	−2.85392	−0.105484
$733$	0.763085	0.0281852	0.0140926	−	0.999901i	$-0.495514\pi$
$733$	0.763085	0.0281852	0.0140926	+	0.999901i	$0.495514\pi$
$734$	−3.35812	−0.123950
$735$	−15.1681	−0.559485
$736$	−0.885870	−0.0326536
$737$	−7.03006	−0.258956
$738$	−18.9379	−0.697113
$739$	8.83384	0.324958	0.162479	−	0.986712i	$-0.448051\pi$
$739$	8.83384	0.324958	0.162479	+	0.986712i	$0.448051\pi$
$740$	−19.8274	−0.728868
$741$	2.04768	0.0752235
$742$	−2.27051	−0.0833530
$743$	53.4465	1.96076	0.980381	−	0.197112i	$-0.0631562\pi$
$743$	53.4465	1.96076	0.980381	+	0.197112i	$0.0631562\pi$
$744$	2.55068	0.0935123
$745$	−0.459935	−0.0168507
$746$	−7.60956	−0.278606
$747$	−21.5403	−0.788118
$748$	−11.9697	−0.437654
$749$	−5.99865	−0.219186
$750$	12.1118	0.442261
$751$	−1.00000	−0.0364905
$751$	−1.00000	−0.0364905
$752$	9.52323	0.347276
$753$	14.2364	0.518805
$754$	−1.96930	−0.0717175
$755$	−11.7393	−0.427237
$756$	2.77869	0.101060
$757$	−40.6140	−1.47614	−0.738070	−	0.674724i	$-0.764263\pi$
$757$	−40.6140	−1.47614	−0.738070	+	0.674724i	$0.764263\pi$
$758$	−0.0680164	−0.00247047
$759$	−5.33083	−0.193497
$760$	11.6072	0.421036
$761$	48.1156	1.74419	0.872095	−	0.489336i	$-0.162761\pi$
$761$	48.1156	1.74419	0.872095	+	0.489336i	$0.162761\pi$
$762$	6.63499	0.240360
$763$	7.03376	0.254639
$764$	−13.7212	−0.496417
$765$	−8.54098	−0.308800
$766$	18.9420	0.684402
$767$	−3.33802	−0.120529
$768$	1.04934	0.0378647
$769$	−3.57513	−0.128922	−0.0644612	−	0.997920i	$-0.520533\pi$
$769$	−3.57513	−0.128922	−0.0644612	+	0.997920i	$0.520533\pi$
$770$	−6.67994	−0.240728
$771$	−12.2848	−0.442427
$772$	−20.5941	−0.741197
$773$	43.5402	1.56603	0.783016	−	0.622002i	$-0.213680\pi$
$773$	43.5402	1.56603	0.783016	+	0.622002i	$0.213680\pi$
$774$	20.7887	0.747234
$775$	0.865900	0.0311040
$776$	4.61580	0.165698
$777$	5.21881	0.187224
$778$	−28.4069	−1.01844
$779$	53.7183	1.92466
$780$	−0.819232	−0.0293332
$781$	−23.3015	−0.833792
$782$	−1.84902	−0.0661209
$783$	27.9426	0.998589
$784$	−6.70782	−0.239565
$785$	−3.78216	−0.134991
$786$	−1.08957	−0.0388636
$787$	−32.2631	−1.15005	−0.575027	−	0.818134i	$-0.695009\pi$
$787$	−32.2631	−1.15005	−0.575027	+	0.818134i	$0.695009\pi$
$788$	−1.65605	−0.0589942
$789$	11.0016	0.391668
$790$	−5.36837	−0.190998
$791$	9.91586	0.352567
$792$	−10.8895	−0.386943
$793$	0.985333	0.0349902
$794$	−5.04847	−0.179163
$795$	−9.49832	−0.336871
$796$	4.98022	0.176519
$797$	49.0542	1.73759	0.868794	−	0.495173i	$-0.164895\pi$
$797$	49.0542	1.73759	0.868794	+	0.495173i	$0.164895\pi$
$798$	−3.05516	−0.108151
$799$	19.8773	0.703207
$800$	0.356227	0.0125945
$801$	11.6722	0.412416
$802$	−9.18004	−0.324158
$803$	−74.3480	−2.62368
$804$	1.28637	0.0453666
$805$	−1.03189	−0.0363693
$806$	−0.880636	−0.0310191
$807$	6.04822	0.212907
$808$	−1.92354	−0.0676699
$809$	20.8377	0.732613	0.366307	−	0.930494i	$-0.380622\pi$
$809$	20.8377	0.732613	0.366307	+	0.930494i	$0.380622\pi$
$810$	−0.651783	−0.0229013
$811$	−10.4073	−0.365451	−0.182725	−	0.983164i	$-0.558492\pi$
$811$	−10.4073	−0.365451	−0.182725	+	0.983164i	$0.558492\pi$
$812$	2.93820	0.103111
$813$	15.4602	0.542214
$814$	−52.7642	−1.84938
$815$	19.9349	0.698290
$816$	2.19022	0.0766730
$817$	−58.9682	−2.06304
$818$	−29.2519	−1.02277
$819$	−0.371863	−0.0129940
$820$	−21.4915	−0.750516
$821$	−50.4421	−1.76044	−0.880221	−	0.474563i	$-0.842606\pi$
$821$	−50.4421	−1.76044	−0.880221	+	0.474563i	$0.842606\pi$
$822$	−23.6607	−0.825261
$823$	−45.3385	−1.58040	−0.790201	−	0.612848i	$-0.790024\pi$
$823$	−45.3385	−1.58040	−0.790201	+	0.612848i	$0.790024\pi$
$824$	15.0179	0.523174
$825$	2.14364	0.0746321
$826$	4.98035	0.173289
$827$	28.1105	0.977497	0.488748	−	0.872425i	$-0.337454\pi$
$827$	28.1105	0.977497	0.488748	+	0.872425i	$0.337454\pi$
$828$	−1.68217	−0.0584595
$829$	11.9969	0.416668	0.208334	−	0.978058i	$-0.433196\pi$
$829$	11.9969	0.416668	0.208334	+	0.978058i	$0.433196\pi$
$830$	−24.4448	−0.848492
$831$	−0.302046	−0.0104779
$832$	−0.362290	−0.0125601
$833$	−14.0008	−0.485100
$834$	2.19723	0.0760839
$835$	−3.10617	−0.107493
$836$	30.8888	1.06831
$837$	12.4955	0.431907
$838$	−10.1683	−0.351259
$839$	−20.4900	−0.707392	−0.353696	−	0.935360i	$-0.615075\pi$
$839$	−20.4900	−0.707392	−0.353696	+	0.935360i	$0.615075\pi$
$840$	1.22230	0.0421733
$841$	0.546707	0.0188520
$842$	18.3049	0.630829
$843$	−18.7078	−0.644330
$844$	18.0744	0.622148
$845$	−27.7314	−0.953989
$846$	18.0836	0.621726
$847$	−11.8306	−0.406504
$848$	−4.20045	−0.144244
$849$	9.35481	0.321056
$850$	0.743532	0.0255029
$851$	−8.15079	−0.279405
$852$	4.26372	0.146073
$853$	−11.3321	−0.388005	−0.194003	−	0.981001i	$-0.562147\pi$
$853$	−11.3321	−0.388005	−0.194003	+	0.981001i	$0.562147\pi$
$854$	−1.47012	−0.0503066
$855$	22.0408	0.753778
$856$	−11.0975	−0.379306
$857$	31.6709	1.08186	0.540929	−	0.841068i	$-0.318073\pi$
$857$	31.6709	1.08186	0.540929	+	0.841068i	$0.318073\pi$
$858$	−2.18012	−0.0744282
$859$	36.7021	1.25226	0.626130	−	0.779719i	$-0.284638\pi$
$859$	36.7021	1.25226	0.626130	+	0.779719i	$0.284638\pi$
$860$	23.5919	0.804476
$861$	5.65684	0.192785
$862$	17.0446	0.580542
$863$	−52.0874	−1.77308	−0.886538	−	0.462656i	$-0.846897\pi$
$863$	−52.0874	−1.77308	−0.886538	+	0.462656i	$0.846897\pi$
$864$	5.14059	0.174886
$865$	45.0939	1.53324
$866$	−25.0017	−0.849592
$867$	−13.2672	−0.450579
$868$	1.31392	0.0445972
$869$	−14.2862	−0.484626
$870$	12.2915	0.416721
$871$	−0.444126	−0.0150486
$872$	13.0125	0.440658
$873$	8.76491	0.296647
$874$	4.77157	0.161401
$875$	6.23909	0.210920
$876$	13.6042	0.459645
$877$	−21.7030	−0.732860	−0.366430	−	0.930446i	$-0.619420\pi$
$877$	−21.7030	−0.732860	−0.366430	+	0.930446i	$0.619420\pi$
$878$	−6.53281	−0.220472
$879$	23.3443	0.787385
$880$	−12.3579	−0.416585
$881$	−48.2594	−1.62590	−0.812950	−	0.582334i	$-0.802140\pi$
$881$	−48.2594	−1.62590	−0.812950	+	0.582334i	$0.802140\pi$
$882$	−12.7374	−0.428891
$883$	1.80256	0.0606609	0.0303305	−	0.999540i	$-0.490344\pi$
$883$	1.80256	0.0606609	0.0303305	+	0.999540i	$0.490344\pi$
$884$	−0.756186	−0.0254333
$885$	20.8345	0.700345
$886$	−21.2773	−0.714825
$887$	−30.2537	−1.01582	−0.507910	−	0.861410i	$-0.669582\pi$
$887$	−30.2537	−1.01582	−0.507910	+	0.861410i	$0.669582\pi$
$888$	9.65483	0.323995
$889$	3.41784	0.114631
$890$	13.2461	0.444009
$891$	−1.73451	−0.0581083
$892$	−22.2949	−0.746488
$893$	−51.2950	−1.71652
$894$	0.223963	0.00749044
$895$	−37.0748	−1.23927
$896$	0.540539	0.0180581
$897$	−0.336776	−0.0112446
$898$	17.7042	0.590796
$899$	13.2128	0.440671
$900$	0.676437	0.0225479
$901$	−8.76735	−0.292083
$902$	−57.1928	−1.90431
$903$	−6.20968	−0.206645
$904$	18.3444	0.610125
$905$	39.4634	1.31181
$906$	5.71640	0.189915
$907$	53.9951	1.79288	0.896439	−	0.443168i	$-0.146145\pi$
$907$	53.9951	1.79288	0.896439	+	0.443168i	$0.146145\pi$
$908$	−21.1309	−0.701253
$909$	−3.65259	−0.121149
$910$	−0.422006	−0.0139894
$911$	11.2187	0.371692	0.185846	−	0.982579i	$-0.440497\pi$
$911$	11.2187	0.371692	0.185846	+	0.982579i	$0.440497\pi$
$912$	−5.65205	−0.187158
$913$	−65.0521	−2.15291
$914$	−6.74358	−0.223058
$915$	−6.15003	−0.203314
$916$	−13.8675	−0.458196
$917$	−0.561263	−0.0185345
$918$	10.7296	0.354131
$919$	43.1946	1.42486	0.712429	−	0.701745i	$-0.247595\pi$
$919$	43.1946	1.42486	0.712429	+	0.701745i	$0.247595\pi$
$920$	−1.90900	−0.0629378
$921$	−29.4281	−0.969690
$922$	−18.9430	−0.623855
$923$	−1.47207	−0.0484539
$924$	3.25276	0.107008
$925$	3.27761	0.107767
$926$	29.3365	0.964058
$927$	28.5174	0.936634
$928$	5.43569	0.178435
$929$	−42.4911	−1.39409	−0.697045	−	0.717028i	$-0.745502\pi$
$929$	−42.4911	−1.39409	−0.697045	+	0.717028i	$0.745502\pi$
$930$	5.49656	0.180239
$931$	36.1304	1.18412
$932$	14.8649	0.486918
$933$	−17.1589	−0.561758
$934$	−22.1448	−0.724601
$935$	−25.7939	−0.843552
$936$	−0.687949	−0.0224863
$937$	−41.5779	−1.35829	−0.679146	−	0.734003i	$-0.737650\pi$
$937$	−41.5779	−1.35829	−0.679146	+	0.734003i	$0.737650\pi$
$938$	0.662638	0.0216359
$939$	−13.5706	−0.442861
$940$	20.5220	0.669354
$941$	47.1983	1.53862	0.769311	−	0.638874i	$-0.220600\pi$
$941$	47.1983	1.53862	0.769311	+	0.638874i	$0.220600\pi$
$942$	1.84170	0.0600060
$943$	−8.83490	−0.287704
$944$	9.21368	0.299880
$945$	5.98791	0.194787
$946$	62.7822	2.04123
$947$	11.2634	0.366010	0.183005	−	0.983112i	$-0.441417\pi$
$947$	11.2634	0.366010	0.183005	+	0.983112i	$0.441417\pi$
$948$	2.61410	0.0849021
$949$	−4.69695	−0.152469
$950$	−1.91875	−0.0622525
$951$	−35.5618	−1.15317
$952$	1.12823	0.0365663
$953$	−27.3578	−0.886207	−0.443104	−	0.896470i	$-0.646123\pi$
$953$	−27.3578	−0.886207	−0.443104	+	0.896470i	$0.646123\pi$
$954$	−7.97621	−0.258239
$955$	−29.5684	−0.956812
$956$	8.68547	0.280908
$957$	32.7099	1.05736
$958$	2.23771	0.0722971
$959$	−12.1882	−0.393577
$960$	2.26126	0.0729819
$961$	−25.0915	−0.809402
$962$	−3.33339	−0.107473
$963$	−21.0730	−0.679068
$964$	−26.4084	−0.850556
$965$	−44.3790	−1.42861
$966$	0.502473	0.0161668
$967$	−41.6012	−1.33780	−0.668902	−	0.743350i	$-0.733235\pi$
$967$	−41.6012	−1.33780	−0.668902	+	0.743350i	$0.733235\pi$
$968$	−21.8867	−0.703464
$969$	−11.7972	−0.378980
$970$	9.94679	0.319372
$971$	−18.8795	−0.605871	−0.302935	−	0.953011i	$-0.597967\pi$
$971$	−18.8795	−0.605871	−0.302935	+	0.953011i	$0.597967\pi$
$972$	15.7392	0.504834
$973$	1.13185	0.0362854
$974$	35.3635	1.13312
$975$	0.135425	0.00433707
$976$	−2.71974	−0.0870566
$977$	−24.2724	−0.776542	−0.388271	−	0.921545i	$-0.626927\pi$
$977$	−24.2724	−0.776542	−0.388271	+	0.921545i	$0.626927\pi$
$978$	−9.70721	−0.310402
$979$	35.2502	1.12660
$980$	−14.4550	−0.461747
$981$	24.7093	0.788907
$982$	26.1657	0.834983
$983$	−6.87247	−0.219198	−0.109599	−	0.993976i	$-0.534957\pi$
$983$	−6.87247	−0.219198	−0.109599	+	0.993976i	$0.534957\pi$
$984$	10.4652	0.333618
$985$	−3.56868	−0.113708
$986$	11.3456	0.361317
$987$	−5.40165	−0.171936
$988$	1.95140	0.0620825
$989$	9.69833	0.308389
$990$	−23.4663	−0.745809
$991$	49.5282	1.57331	0.786657	−	0.617390i	$-0.211810\pi$
$991$	49.5282	1.57331	0.786657	+	0.617390i	$0.211810\pi$
$992$	2.43075	0.0771764
$993$	−5.99368	−0.190204
$994$	2.19634	0.0696638
$995$	10.7321	0.340230
$996$	11.9033	0.377170
$997$	41.4609	1.31308	0.656541	−	0.754291i	$-0.272019\pi$
$997$	41.4609	1.31308	0.656541	+	0.754291i	$0.272019\pi$
$998$	16.0434	0.507846
$999$	47.2979	1.49644

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.e.1.9	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.e.1.9	✓	11	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:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.04934 q^{3} +1.00000 q^{4} +2.15494 q^{5} -1.04934 q^{6} -0.540539 q^{7} -1.00000 q^{8} -1.89889 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.04934 q^{3} +1.00000 q^{4} +2.15494 q^{5} -1.04934 q^{6} -0.540539 q^{7} -1.00000 q^{8} -1.89889 q^{9} -2.15494 q^{10} -5.73469 q^{11} +1.04934 q^{12} -0.362290 q^{13} +0.540539 q^{14} +2.26126 q^{15} +1.00000 q^{16} +2.08724 q^{17} +1.89889 q^{18} -5.38631 q^{19} +2.15494 q^{20} -0.567208 q^{21} +5.73469 q^{22} +0.885870 q^{23} -1.04934 q^{24} -0.356227 q^{25} +0.362290 q^{26} -5.14059 q^{27} -0.540539 q^{28} -5.43569 q^{29} -2.26126 q^{30} -2.43075 q^{31} -1.00000 q^{32} -6.01762 q^{33} -2.08724 q^{34} -1.16483 q^{35} -1.89889 q^{36} -9.20088 q^{37} +5.38631 q^{38} -0.380164 q^{39} -2.15494 q^{40} -9.97313 q^{41} +0.567208 q^{42} +10.9478 q^{43} -5.73469 q^{44} -4.09200 q^{45} -0.885870 q^{46} +9.52323 q^{47} +1.04934 q^{48} -6.70782 q^{49} +0.356227 q^{50} +2.19022 q^{51} -0.362290 q^{52} -4.20045 q^{53} +5.14059 q^{54} -12.3579 q^{55} +0.540539 q^{56} -5.65205 q^{57} +5.43569 q^{58} +9.21368 q^{59} +2.26126 q^{60} -2.71974 q^{61} +2.43075 q^{62} +1.02642 q^{63} +1.00000 q^{64} -0.780714 q^{65} +6.01762 q^{66} +1.22588 q^{67} +2.08724 q^{68} +0.929577 q^{69} +1.16483 q^{70} +4.06325 q^{71} +1.89889 q^{72} +12.9646 q^{73} +9.20088 q^{74} -0.373803 q^{75} -5.38631 q^{76} +3.09982 q^{77} +0.380164 q^{78} +2.49119 q^{79} +2.15494 q^{80} +0.302460 q^{81} +9.97313 q^{82} +11.3436 q^{83} -0.567208 q^{84} +4.49788 q^{85} -10.9478 q^{86} -5.70387 q^{87} +5.73469 q^{88} -6.14683 q^{89} +4.09200 q^{90} +0.195832 q^{91} +0.885870 q^{92} -2.55068 q^{93} -9.52323 q^{94} -11.6072 q^{95} -1.04934 q^{96} -4.61580 q^{97} +6.70782 q^{98} +10.8895 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 19 q^{13} + 6 q^{14} + q^{15} + 11 q^{16} - 8 q^{17} - 3 q^{18} - 9 q^{19} + q^{20} - 6 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 2 q^{25} + 19 q^{26} - 16 q^{27} - 6 q^{28} + 13 q^{29} - q^{30} - 19 q^{31} - 11 q^{32} - 37 q^{33} + 8 q^{34} + 3 q^{35} + 3 q^{36} - 29 q^{37} + 9 q^{38} + 8 q^{39} - q^{40} - 23 q^{41} + 6 q^{42} - 13 q^{43} + 4 q^{44} - 6 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 5 q^{49} + 2 q^{50} + 33 q^{51} - 19 q^{52} - 25 q^{53} + 16 q^{54} - 14 q^{55} + 6 q^{56} + 4 q^{57} - 13 q^{58} + 6 q^{59} + q^{60} + 10 q^{61} + 19 q^{62} - 7 q^{63} + 11 q^{64} - 19 q^{65} + 37 q^{66} - 16 q^{67} - 8 q^{68} - 25 q^{69} - 3 q^{70} + 8 q^{71} - 3 q^{72} - 56 q^{73} + 29 q^{74} - 50 q^{75} - 9 q^{76} - 7 q^{77} - 8 q^{78} + 2 q^{79} + q^{80} - 5 q^{81} + 23 q^{82} + 21 q^{83} - 6 q^{84} - 55 q^{85} + 13 q^{86} - 11 q^{87} - 4 q^{88} - 24 q^{89} + 6 q^{90} - 43 q^{91} + 2 q^{92} + 10 q^{93} + 16 q^{94} + 25 q^{95} + 4 q^{96} - 84 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9 - q^10 + 4 * q^11 - 4 * q^12 - 19 * q^13 + 6 * q^14 + q^15 + 11 * q^16 - 8 * q^17 - 3 * q^18 - 9 * q^19 + q^20 - 6 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 2 * q^25 + 19 * q^26 - 16 * q^27 - 6 * q^28 + 13 * q^29 - q^30 - 19 * q^31 - 11 * q^32 - 37 * q^33 + 8 * q^34 + 3 * q^35 + 3 * q^36 - 29 * q^37 + 9 * q^38 + 8 * q^39 - q^40 - 23 * q^41 + 6 * q^42 - 13 * q^43 + 4 * q^44 - 6 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 5 * q^49 + 2 * q^50 + 33 * q^51 - 19 * q^52 - 25 * q^53 + 16 * q^54 - 14 * q^55 + 6 * q^56 + 4 * q^57 - 13 * q^58 + 6 * q^59 + q^60 + 10 * q^61 + 19 * q^62 - 7 * q^63 + 11 * q^64 - 19 * q^65 + 37 * q^66 - 16 * q^67 - 8 * q^68 - 25 * q^69 - 3 * q^70 + 8 * q^71 - 3 * q^72 - 56 * q^73 + 29 * q^74 - 50 * q^75 - 9 * q^76 - 7 * q^77 - 8 * q^78 + 2 * q^79 + q^80 - 5 * q^81 + 23 * q^82 + 21 * q^83 - 6 * q^84 - 55 * q^85 + 13 * q^86 - 11 * q^87 - 4 * q^88 - 24 * q^89 + 6 * q^90 - 43 * q^91 + 2 * q^92 + 10 * q^93 + 16 * q^94 + 25 * q^95 + 4 * q^96 - 84 * q^97 + 5 * q^98 + 14 * q^99

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