LMFDB - Embedded newform 8034.2.a.o.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 4x^{5} + 14x^{4} + 3x^{3} - 12x^{2} - 3x + 1 $ x^7 - 3x^6 - 4x^5 + 14x^4 + 3x^3 - 12x^2 - 3x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.16681$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.61702 q^{5} +1.00000 q^{6} -0.977840 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.61702 q^{5} +1.00000 q^{6} -0.977840 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.61702 q^{10} -0.240785 q^{11} -1.00000 q^{12} +1.00000 q^{13} +0.977840 q^{14} +2.61702 q^{15} +1.00000 q^{16} -4.91508 q^{17} -1.00000 q^{18} -1.97784 q^{19} -2.61702 q^{20} +0.977840 q^{21} +0.240785 q^{22} -0.244868 q^{23} +1.00000 q^{24} +1.84882 q^{25} -1.00000 q^{26} -1.00000 q^{27} -0.977840 q^{28} +8.09791 q^{29} -2.61702 q^{30} -7.15427 q^{31} -1.00000 q^{32} +0.240785 q^{33} +4.91508 q^{34} +2.55903 q^{35} +1.00000 q^{36} +5.41686 q^{37} +1.97784 q^{38} -1.00000 q^{39} +2.61702 q^{40} +10.7554 q^{41} -0.977840 q^{42} -5.03820 q^{43} -0.240785 q^{44} -2.61702 q^{45} +0.244868 q^{46} +9.26343 q^{47} -1.00000 q^{48} -6.04383 q^{49} -1.84882 q^{50} +4.91508 q^{51} +1.00000 q^{52} +9.79000 q^{53} +1.00000 q^{54} +0.630140 q^{55} +0.977840 q^{56} +1.97784 q^{57} -8.09791 q^{58} -7.05375 q^{59} +2.61702 q^{60} +3.55737 q^{61} +7.15427 q^{62} -0.977840 q^{63} +1.00000 q^{64} -2.61702 q^{65} -0.240785 q^{66} -14.2272 q^{67} -4.91508 q^{68} +0.244868 q^{69} -2.55903 q^{70} +9.42409 q^{71} -1.00000 q^{72} +0.976521 q^{73} -5.41686 q^{74} -1.84882 q^{75} -1.97784 q^{76} +0.235449 q^{77} +1.00000 q^{78} -8.87366 q^{79} -2.61702 q^{80} +1.00000 q^{81} -10.7554 q^{82} +13.3970 q^{83} +0.977840 q^{84} +12.8629 q^{85} +5.03820 q^{86} -8.09791 q^{87} +0.240785 q^{88} -0.490697 q^{89} +2.61702 q^{90} -0.977840 q^{91} -0.244868 q^{92} +7.15427 q^{93} -9.26343 q^{94} +5.17606 q^{95} +1.00000 q^{96} +14.7754 q^{97} +6.04383 q^{98} -0.240785 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} - 7 q^{12} + 7 q^{13} + 9 q^{14} - 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 16 q^{19} + 2 q^{20} + 9 q^{21} + 6 q^{23} + 7 q^{24} + 15 q^{25} - 7 q^{26} - 7 q^{27} - 9 q^{28} - 5 q^{29} + 2 q^{30} - 16 q^{31} - 7 q^{32} - 3 q^{34} - 10 q^{35} + 7 q^{36} + 17 q^{37} + 16 q^{38} - 7 q^{39} - 2 q^{40} + 12 q^{41} - 9 q^{42} - 22 q^{43} + 2 q^{45} - 6 q^{46} - 7 q^{48} - 2 q^{49} - 15 q^{50} - 3 q^{51} + 7 q^{52} + 2 q^{53} + 7 q^{54} - 16 q^{55} + 9 q^{56} + 16 q^{57} + 5 q^{58} - 3 q^{59} - 2 q^{60} - 6 q^{61} + 16 q^{62} - 9 q^{63} + 7 q^{64} + 2 q^{65} + q^{67} + 3 q^{68} - 6 q^{69} + 10 q^{70} + 15 q^{71} - 7 q^{72} + 17 q^{73} - 17 q^{74} - 15 q^{75} - 16 q^{76} - 10 q^{77} + 7 q^{78} - 27 q^{79} + 2 q^{80} + 7 q^{81} - 12 q^{82} + 12 q^{83} + 9 q^{84} + 15 q^{85} + 22 q^{86} + 5 q^{87} - 9 q^{89} - 2 q^{90} - 9 q^{91} + 6 q^{92} + 16 q^{93} - 12 q^{95} + 7 q^{96} - 3 q^{97} + 2 q^{98}+O(q^{100}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 - 7 * q^12 + 7 * q^13 + 9 * q^14 - 2 * q^15 + 7 * q^16 + 3 * q^17 - 7 * q^18 - 16 * q^19 + 2 * q^20 + 9 * q^21 + 6 * q^23 + 7 * q^24 + 15 * q^25 - 7 * q^26 - 7 * q^27 - 9 * q^28 - 5 * q^29 + 2 * q^30 - 16 * q^31 - 7 * q^32 - 3 * q^34 - 10 * q^35 + 7 * q^36 + 17 * q^37 + 16 * q^38 - 7 * q^39 - 2 * q^40 + 12 * q^41 - 9 * q^42 - 22 * q^43 + 2 * q^45 - 6 * q^46 - 7 * q^48 - 2 * q^49 - 15 * q^50 - 3 * q^51 + 7 * q^52 + 2 * q^53 + 7 * q^54 - 16 * q^55 + 9 * q^56 + 16 * q^57 + 5 * q^58 - 3 * q^59 - 2 * q^60 - 6 * q^61 + 16 * q^62 - 9 * q^63 + 7 * q^64 + 2 * q^65 + q^67 + 3 * q^68 - 6 * q^69 + 10 * q^70 + 15 * q^71 - 7 * q^72 + 17 * q^73 - 17 * q^74 - 15 * q^75 - 16 * q^76 - 10 * q^77 + 7 * q^78 - 27 * q^79 + 2 * q^80 + 7 * q^81 - 12 * q^82 + 12 * q^83 + 9 * q^84 + 15 * q^85 + 22 * q^86 + 5 * q^87 - 9 * q^89 - 2 * q^90 - 9 * q^91 + 6 * q^92 + 16 * q^93 - 12 * q^95 + 7 * q^96 - 3 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−2.61702	−1.17037	−0.585184	−	0.810900i	$-0.698978\pi$
$5$	−2.61702	−1.17037	−0.585184	+	0.810900i	$0.698978\pi$
$6$	1.00000	0.408248
$7$	−0.977840	−0.369589	−0.184794	−	0.982777i	$-0.559162\pi$
$7$	−0.977840	−0.369589	−0.184794	+	0.982777i	$0.559162\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.61702	0.827576
$11$	−0.240785	−0.0725993	−0.0362997	−	0.999341i	$-0.511557\pi$
$11$	−0.240785	−0.0725993	−0.0362997	+	0.999341i	$0.511557\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.977840	0.261339
$15$	2.61702	0.675713
$16$	1.00000	0.250000
$17$	−4.91508	−1.19208	−0.596041	−	0.802954i	$-0.703261\pi$
$17$	−4.91508	−1.19208	−0.596041	+	0.802954i	$0.703261\pi$
$18$	−1.00000	−0.235702
$19$	−1.97784	−0.453748	−0.226874	−	0.973924i	$-0.572851\pi$
$19$	−1.97784	−0.453748	−0.226874	+	0.973924i	$0.572851\pi$
$20$	−2.61702	−0.585184
$21$	0.977840	0.213382
$22$	0.240785	0.0513355
$23$	−0.244868	−0.0510585	−0.0255292	−	0.999674i	$-0.508127\pi$
$23$	−0.244868	−0.0510585	−0.0255292	+	0.999674i	$0.508127\pi$
$24$	1.00000	0.204124
$25$	1.84882	0.369763
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	−0.977840	−0.184794
$29$	8.09791	1.50374	0.751872	−	0.659309i	$-0.229151\pi$
$29$	8.09791	1.50374	0.751872	+	0.659309i	$0.229151\pi$
$30$	−2.61702	−0.477801
$31$	−7.15427	−1.28494	−0.642472	−	0.766309i	$-0.722091\pi$
$31$	−7.15427	−1.28494	−0.642472	+	0.766309i	$0.722091\pi$
$32$	−1.00000	−0.176777
$33$	0.240785	0.0419152
$34$	4.91508	0.842930
$35$	2.55903	0.432555
$36$	1.00000	0.166667
$37$	5.41686	0.890526	0.445263	−	0.895400i	$-0.353110\pi$
$37$	5.41686	0.890526	0.445263	+	0.895400i	$0.353110\pi$
$38$	1.97784	0.320848
$39$	−1.00000	−0.160128
$40$	2.61702	0.413788
$41$	10.7554	1.67971	0.839855	−	0.542811i	$-0.182640\pi$
$41$	10.7554	1.67971	0.839855	+	0.542811i	$0.182640\pi$
$42$	−0.977840	−0.150884
$43$	−5.03820	−0.768318	−0.384159	−	0.923267i	$-0.625509\pi$
$43$	−5.03820	−0.768318	−0.384159	+	0.923267i	$0.625509\pi$
$44$	−0.240785	−0.0362997
$45$	−2.61702	−0.390123
$46$	0.244868	0.0361038
$47$	9.26343	1.35121	0.675605	−	0.737264i	$-0.263882\pi$
$47$	9.26343	1.35121	0.675605	+	0.737264i	$0.263882\pi$
$48$	−1.00000	−0.144338
$49$	−6.04383	−0.863404
$50$	−1.84882	−0.261462
$51$	4.91508	0.688249
$52$	1.00000	0.138675
$53$	9.79000	1.34476	0.672380	−	0.740206i	$-0.265272\pi$
$53$	9.79000	1.34476	0.672380	+	0.740206i	$0.265272\pi$
$54$	1.00000	0.136083
$55$	0.630140	0.0849680
$56$	0.977840	0.130669
$57$	1.97784	0.261971
$58$	−8.09791	−1.06331
$59$	−7.05375	−0.918320	−0.459160	−	0.888353i	$-0.651850\pi$
$59$	−7.05375	−0.918320	−0.459160	+	0.888353i	$0.651850\pi$
$60$	2.61702	0.337856
$61$	3.55737	0.455474	0.227737	−	0.973723i	$-0.426867\pi$
$61$	3.55737	0.455474	0.227737	+	0.973723i	$0.426867\pi$
$62$	7.15427	0.908593
$63$	−0.977840	−0.123196
$64$	1.00000	0.125000
$65$	−2.61702	−0.324602
$66$	−0.240785	−0.0296386
$67$	−14.2272	−1.73813	−0.869067	−	0.494694i	$-0.835280\pi$
$67$	−14.2272	−1.73813	−0.869067	+	0.494694i	$0.835280\pi$
$68$	−4.91508	−0.596041
$69$	0.244868	0.0294786
$70$	−2.55903	−0.305863
$71$	9.42409	1.11843	0.559217	−	0.829021i	$-0.311102\pi$
$71$	9.42409	1.11843	0.559217	+	0.829021i	$0.311102\pi$
$72$	−1.00000	−0.117851
$73$	0.976521	0.114293	0.0571466	−	0.998366i	$-0.481800\pi$
$73$	0.976521	0.114293	0.0571466	+	0.998366i	$0.481800\pi$
$74$	−5.41686	−0.629697
$75$	−1.84882	−0.213483
$76$	−1.97784	−0.226874
$77$	0.235449	0.0268319
$78$	1.00000	0.113228
$79$	−8.87366	−0.998365	−0.499182	−	0.866497i	$-0.666366\pi$
$79$	−8.87366	−0.998365	−0.499182	+	0.866497i	$0.666366\pi$
$80$	−2.61702	−0.292592
$81$	1.00000	0.111111
$82$	−10.7554	−1.18773
$83$	13.3970	1.47051	0.735253	−	0.677792i	$-0.237063\pi$
$83$	13.3970	1.47051	0.735253	+	0.677792i	$0.237063\pi$
$84$	0.977840	0.106691
$85$	12.8629	1.39518
$86$	5.03820	0.543283
$87$	−8.09791	−0.868187
$88$	0.240785	0.0256677
$89$	−0.490697	−0.0520138	−0.0260069	−	0.999662i	$-0.508279\pi$
$89$	−0.490697	−0.0520138	−0.0260069	+	0.999662i	$0.508279\pi$
$90$	2.61702	0.275859
$91$	−0.977840	−0.102506
$92$	−0.244868	−0.0255292
$93$	7.15427	0.741863
$94$	−9.26343	−0.955450
$95$	5.17606	0.531052
$96$	1.00000	0.102062
$97$	14.7754	1.50021	0.750107	−	0.661317i	$-0.230002\pi$
$97$	14.7754	1.50021	0.750107	+	0.661317i	$0.230002\pi$
$98$	6.04383	0.610519
$99$	−0.240785	−0.0241998
$100$	1.84882	0.184882
$101$	−10.7141	−1.06609	−0.533045	−	0.846087i	$-0.678953\pi$
$101$	−10.7141	−1.06609	−0.533045	+	0.846087i	$0.678953\pi$
$102$	−4.91508	−0.486666
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	−2.55903	−0.249736
$106$	−9.79000	−0.950889
$107$	−12.2317	−1.18248	−0.591241	−	0.806495i	$-0.701362\pi$
$107$	−12.2317	−1.18248	−0.591241	+	0.806495i	$0.701362\pi$
$108$	−1.00000	−0.0962250
$109$	−15.0495	−1.44148	−0.720740	−	0.693206i	$-0.756198\pi$
$109$	−15.0495	−1.44148	−0.720740	+	0.693206i	$0.756198\pi$
$110$	−0.630140	−0.0600814
$111$	−5.41686	−0.514145
$112$	−0.977840	−0.0923972
$113$	15.2767	1.43711	0.718557	−	0.695468i	$-0.244803\pi$
$113$	15.2767	1.43711	0.718557	+	0.695468i	$0.244803\pi$
$114$	−1.97784	−0.185242
$115$	0.640825	0.0597572
$116$	8.09791	0.751872
$117$	1.00000	0.0924500
$118$	7.05375	0.649351
$119$	4.80617	0.440581
$120$	−2.61702	−0.238901
$121$	−10.9420	−0.994729
$122$	−3.55737	−0.322069
$123$	−10.7554	−0.969781
$124$	−7.15427	−0.642472
$125$	8.24672	0.737609
$126$	0.977840	0.0871129
$127$	−5.61363	−0.498129	−0.249065	−	0.968487i	$-0.580123\pi$
$127$	−5.61363	−0.498129	−0.249065	+	0.968487i	$0.580123\pi$
$128$	−1.00000	−0.0883883
$129$	5.03820	0.443589
$130$	2.61702	0.229528
$131$	3.87103	0.338214	0.169107	−	0.985598i	$-0.445912\pi$
$131$	3.87103	0.338214	0.169107	+	0.985598i	$0.445912\pi$
$132$	0.240785	0.0209576
$133$	1.93401	0.167700
$134$	14.2272	1.22905
$135$	2.61702	0.225238
$136$	4.91508	0.421465
$137$	8.32317	0.711097	0.355548	−	0.934658i	$-0.384294\pi$
$137$	8.32317	0.711097	0.355548	+	0.934658i	$0.384294\pi$
$138$	−0.244868	−0.0208445
$139$	1.62532	0.137857	0.0689287	−	0.997622i	$-0.478042\pi$
$139$	1.62532	0.137857	0.0689287	+	0.997622i	$0.478042\pi$
$140$	2.55903	0.216278
$141$	−9.26343	−0.780122
$142$	−9.42409	−0.790852
$143$	−0.240785	−0.0201354
$144$	1.00000	0.0833333
$145$	−21.1924	−1.75994
$146$	−0.976521	−0.0808174
$147$	6.04383	0.498487
$148$	5.41686	0.445263
$149$	−6.63099	−0.543232	−0.271616	−	0.962406i	$-0.587558\pi$
$149$	−6.63099	−0.543232	−0.271616	+	0.962406i	$0.587558\pi$
$150$	1.84882	0.150955
$151$	7.91264	0.643922	0.321961	−	0.946753i	$-0.395658\pi$
$151$	7.91264	0.643922	0.321961	+	0.946753i	$0.395658\pi$
$152$	1.97784	0.160424
$153$	−4.91508	−0.397361
$154$	−0.235449	−0.0189730
$155$	18.7229	1.50386
$156$	−1.00000	−0.0800641
$157$	5.70092	0.454983	0.227492	−	0.973780i	$-0.426948\pi$
$157$	5.70092	0.454983	0.227492	+	0.973780i	$0.426948\pi$
$158$	8.87366	0.705950
$159$	−9.79000	−0.776398
$160$	2.61702	0.206894
$161$	0.239442	0.0188706
$162$	−1.00000	−0.0785674
$163$	11.8922	0.931469	0.465734	−	0.884925i	$-0.345790\pi$
$163$	11.8922	0.931469	0.465734	+	0.884925i	$0.345790\pi$
$164$	10.7554	0.839855
$165$	−0.630140	−0.0490563
$166$	−13.3970	−1.03981
$167$	7.73384	0.598462	0.299231	−	0.954181i	$-0.403270\pi$
$167$	7.73384	0.598462	0.299231	+	0.954181i	$0.403270\pi$
$168$	−0.977840	−0.0754420
$169$	1.00000	0.0769231
$170$	−12.8629	−0.986539
$171$	−1.97784	−0.151249
$172$	−5.03820	−0.384159
$173$	0.659015	0.0501040	0.0250520	−	0.999686i	$-0.492025\pi$
$173$	0.659015	0.0501040	0.0250520	+	0.999686i	$0.492025\pi$
$174$	8.09791	0.613901
$175$	−1.80785	−0.136660
$176$	−0.240785	−0.0181498
$177$	7.05375	0.530193
$178$	0.490697	0.0367793
$179$	20.3333	1.51978	0.759891	−	0.650051i	$-0.225253\pi$
$179$	20.3333	1.51978	0.759891	+	0.650051i	$0.225253\pi$
$180$	−2.61702	−0.195061
$181$	11.7556	0.873786	0.436893	−	0.899514i	$-0.356079\pi$
$181$	11.7556	0.873786	0.436893	+	0.899514i	$0.356079\pi$
$182$	0.977840	0.0724823
$183$	−3.55737	−0.262968
$184$	0.244868	0.0180519
$185$	−14.1760	−1.04224
$186$	−7.15427	−0.524576
$187$	1.18348	0.0865444
$188$	9.26343	0.675605
$189$	0.977840	0.0711274
$190$	−5.17606	−0.375511
$191$	6.63399	0.480019	0.240009	−	0.970771i	$-0.422849\pi$
$191$	6.63399	0.480019	0.240009	+	0.970771i	$0.422849\pi$
$192$	−1.00000	−0.0721688
$193$	7.61732	0.548306	0.274153	−	0.961686i	$-0.411602\pi$
$193$	7.61732	0.548306	0.274153	+	0.961686i	$0.411602\pi$
$194$	−14.7754	−1.06081
$195$	2.61702	0.187409
$196$	−6.04383	−0.431702
$197$	−5.85181	−0.416924	−0.208462	−	0.978030i	$-0.566846\pi$
$197$	−5.85181	−0.416924	−0.208462	+	0.978030i	$0.566846\pi$
$198$	0.240785	0.0171118
$199$	−1.15345	−0.0817656	−0.0408828	−	0.999164i	$-0.513017\pi$
$199$	−1.15345	−0.0817656	−0.0408828	+	0.999164i	$0.513017\pi$
$200$	−1.84882	−0.130731
$201$	14.2272	1.00351
$202$	10.7141	0.753840
$203$	−7.91847	−0.555767
$204$	4.91508	0.344125
$205$	−28.1471	−1.96588
$206$	−1.00000	−0.0696733
$207$	−0.244868	−0.0170195
$208$	1.00000	0.0693375
$209$	0.476234	0.0329418
$210$	2.55903	0.176590
$211$	0.706007	0.0486035	0.0243018	−	0.999705i	$-0.492264\pi$
$211$	0.706007	0.0486035	0.0243018	+	0.999705i	$0.492264\pi$
$212$	9.79000	0.672380
$213$	−9.42409	−0.645728
$214$	12.2317	0.836141
$215$	13.1851	0.899216
$216$	1.00000	0.0680414
$217$	6.99573	0.474901
$218$	15.0495	1.01928
$219$	−0.976521	−0.0659872
$220$	0.630140	0.0424840
$221$	−4.91508	−0.330624
$222$	5.41686	0.363556
$223$	14.3345	0.959906	0.479953	−	0.877294i	$-0.340654\pi$
$223$	14.3345	0.959906	0.479953	+	0.877294i	$0.340654\pi$
$224$	0.977840	0.0653347
$225$	1.84882	0.123254
$226$	−15.2767	−1.01619
$227$	12.2428	0.812586	0.406293	−	0.913743i	$-0.366821\pi$
$227$	12.2428	0.812586	0.406293	+	0.913743i	$0.366821\pi$
$228$	1.97784	0.130986
$229$	26.8538	1.77455	0.887274	−	0.461242i	$-0.152596\pi$
$229$	26.8538	1.77455	0.887274	+	0.461242i	$0.152596\pi$
$230$	−0.640825	−0.0422547
$231$	−0.235449	−0.0154914
$232$	−8.09791	−0.531654
$233$	−11.9179	−0.780769	−0.390384	−	0.920652i	$-0.627658\pi$
$233$	−11.9179	−0.780769	−0.390384	+	0.920652i	$0.627658\pi$
$234$	−1.00000	−0.0653720
$235$	−24.2426	−1.58141
$236$	−7.05375	−0.459160
$237$	8.87366	0.576406
$238$	−4.80617	−0.311538
$239$	−8.42147	−0.544739	−0.272370	−	0.962193i	$-0.587807\pi$
$239$	−8.42147	−0.544739	−0.272370	+	0.962193i	$0.587807\pi$
$240$	2.61702	0.168928
$241$	4.39928	0.283382	0.141691	−	0.989911i	$-0.454746\pi$
$241$	4.39928	0.283382	0.141691	+	0.989911i	$0.454746\pi$
$242$	10.9420	0.703380
$243$	−1.00000	−0.0641500
$244$	3.55737	0.227737
$245$	15.8168	1.01050
$246$	10.7554	0.685739
$247$	−1.97784	−0.125847
$248$	7.15427	0.454297
$249$	−13.3970	−0.848997
$250$	−8.24672	−0.521569
$251$	−22.7613	−1.43668	−0.718339	−	0.695693i	$-0.755097\pi$
$251$	−22.7613	−1.43668	−0.718339	+	0.695693i	$0.755097\pi$
$252$	−0.977840	−0.0615982
$253$	0.0589604	0.00370681
$254$	5.61363	0.352230
$255$	−12.8629	−0.805506
$256$	1.00000	0.0625000
$257$	−29.1047	−1.81550	−0.907752	−	0.419507i	$-0.862203\pi$
$257$	−29.1047	−1.81550	−0.907752	+	0.419507i	$0.862203\pi$
$258$	−5.03820	−0.313665
$259$	−5.29682	−0.329128
$260$	−2.61702	−0.162301
$261$	8.09791	0.501248
$262$	−3.87103	−0.239153
$263$	−6.72826	−0.414882	−0.207441	−	0.978247i	$-0.566514\pi$
$263$	−6.72826	−0.414882	−0.207441	+	0.978247i	$0.566514\pi$
$264$	−0.240785	−0.0148193
$265$	−25.6207	−1.57387
$266$	−1.93401	−0.118582
$267$	0.490697	0.0300302
$268$	−14.2272	−0.869067
$269$	−14.7972	−0.902204	−0.451102	−	0.892472i	$-0.648969\pi$
$269$	−14.7972	−0.902204	−0.451102	+	0.892472i	$0.648969\pi$
$270$	−2.61702	−0.159267
$271$	−1.96999	−0.119669	−0.0598343	−	0.998208i	$-0.519057\pi$
$271$	−1.96999	−0.119669	−0.0598343	+	0.998208i	$0.519057\pi$
$272$	−4.91508	−0.298021
$273$	0.977840	0.0591816
$274$	−8.32317	−0.502821
$275$	−0.445167	−0.0268446
$276$	0.244868	0.0147393
$277$	−16.6946	−1.00308	−0.501541	−	0.865134i	$-0.667233\pi$
$277$	−16.6946	−1.00308	−0.501541	+	0.865134i	$0.667233\pi$
$278$	−1.62532	−0.0974800
$279$	−7.15427	−0.428315
$280$	−2.55903	−0.152931
$281$	−27.9085	−1.66488	−0.832440	−	0.554115i	$-0.813057\pi$
$281$	−27.9085	−1.66488	−0.832440	+	0.554115i	$0.813057\pi$
$282$	9.26343	0.551629
$283$	−0.449681	−0.0267307	−0.0133654	−	0.999911i	$-0.504254\pi$
$283$	−0.449681	−0.0267307	−0.0133654	+	0.999911i	$0.504254\pi$
$284$	9.42409	0.559217
$285$	−5.17606	−0.306603
$286$	0.240785	0.0142379
$287$	−10.5171	−0.620802
$288$	−1.00000	−0.0589256
$289$	7.15805	0.421062
$290$	21.1924	1.24446
$291$	−14.7754	−0.866149
$292$	0.976521	0.0571466
$293$	2.83914	0.165864	0.0829322	−	0.996555i	$-0.473572\pi$
$293$	2.83914	0.165864	0.0829322	+	0.996555i	$0.473572\pi$
$294$	−6.04383	−0.352483
$295$	18.4598	1.07477
$296$	−5.41686	−0.314848
$297$	0.240785	0.0139717
$298$	6.63099	0.384123
$299$	−0.244868	−0.0141611
$300$	−1.84882	−0.106741
$301$	4.92655	0.283962
$302$	−7.91264	−0.455321
$303$	10.7141	0.615508
$304$	−1.97784	−0.113437
$305$	−9.30972	−0.533073
$306$	4.91508	0.280977
$307$	22.4489	1.28123	0.640614	−	0.767863i	$-0.278680\pi$
$307$	22.4489	1.28123	0.640614	+	0.767863i	$0.278680\pi$
$308$	0.235449	0.0134160
$309$	−1.00000	−0.0568880
$310$	−18.7229	−1.06339
$311$	−4.91789	−0.278868	−0.139434	−	0.990231i	$-0.544528\pi$
$311$	−4.91789	−0.278868	−0.139434	+	0.990231i	$0.544528\pi$
$312$	1.00000	0.0566139
$313$	14.2027	0.802781	0.401391	−	0.915907i	$-0.368527\pi$
$313$	14.2027	0.802781	0.401391	+	0.915907i	$0.368527\pi$
$314$	−5.70092	−0.321722
$315$	2.55903	0.144185
$316$	−8.87366	−0.499182
$317$	1.83459	0.103041	0.0515205	−	0.998672i	$-0.483593\pi$
$317$	1.83459	0.103041	0.0515205	+	0.998672i	$0.483593\pi$
$318$	9.79000	0.548996
$319$	−1.94985	−0.109171
$320$	−2.61702	−0.146296
$321$	12.2317	0.682706
$322$	−0.239442	−0.0133436
$323$	9.72125	0.540905
$324$	1.00000	0.0555556
$325$	1.84882	0.102554
$326$	−11.8922	−0.658648
$327$	15.0495	0.832239
$328$	−10.7554	−0.593867
$329$	−9.05816	−0.499392
$330$	0.630140	0.0346880
$331$	−22.7353	−1.24965	−0.624823	−	0.780767i	$-0.714829\pi$
$331$	−22.7353	−1.24965	−0.624823	+	0.780767i	$0.714829\pi$
$332$	13.3970	0.735253
$333$	5.41686	0.296842
$334$	−7.73384	−0.423177
$335$	37.2330	2.03426
$336$	0.977840	0.0533456
$337$	1.40532	0.0765528	0.0382764	−	0.999267i	$-0.487813\pi$
$337$	1.40532	0.0765528	0.0382764	+	0.999267i	$0.487813\pi$
$338$	−1.00000	−0.0543928
$339$	−15.2767	−0.829718
$340$	12.8629	0.697588
$341$	1.72264	0.0932861
$342$	1.97784	0.106949
$343$	12.7548	0.688693
$344$	5.03820	0.271641
$345$	−0.640825	−0.0345008
$346$	−0.659015	−0.0354289
$347$	−28.8724	−1.54995	−0.774977	−	0.631989i	$-0.782239\pi$
$347$	−28.8724	−1.54995	−0.774977	+	0.631989i	$0.782239\pi$
$348$	−8.09791	−0.434094
$349$	−22.1867	−1.18763	−0.593813	−	0.804603i	$-0.702378\pi$
$349$	−22.1867	−1.18763	−0.593813	+	0.804603i	$0.702378\pi$
$350$	1.80785	0.0966335
$351$	−1.00000	−0.0533761
$352$	0.240785	0.0128339
$353$	−5.73114	−0.305038	−0.152519	−	0.988301i	$-0.548738\pi$
$353$	−5.73114	−0.305038	−0.152519	+	0.988301i	$0.548738\pi$
$354$	−7.05375	−0.374903
$355$	−24.6631	−1.30898
$356$	−0.490697	−0.0260069
$357$	−4.80617	−0.254369
$358$	−20.3333	−1.07465
$359$	−16.9988	−0.897164	−0.448582	−	0.893742i	$-0.648071\pi$
$359$	−16.9988	−0.897164	−0.448582	+	0.893742i	$0.648071\pi$
$360$	2.61702	0.137929
$361$	−15.0881	−0.794113
$362$	−11.7556	−0.617860
$363$	10.9420	0.574307
$364$	−0.977840	−0.0512528
$365$	−2.55558	−0.133765
$366$	3.55737	0.185947
$367$	−8.06954	−0.421226	−0.210613	−	0.977569i	$-0.567546\pi$
$367$	−8.06954	−0.421226	−0.210613	+	0.977569i	$0.567546\pi$
$368$	−0.244868	−0.0127646
$369$	10.7554	0.559903
$370$	14.1760	0.736978
$371$	−9.57306	−0.497008
$372$	7.15427	0.370932
$373$	−9.23667	−0.478257	−0.239128	−	0.970988i	$-0.576862\pi$
$373$	−9.23667	−0.478257	−0.239128	+	0.970988i	$0.576862\pi$
$374$	−1.18348	−0.0611962
$375$	−8.24672	−0.425859
$376$	−9.26343	−0.477725
$377$	8.09791	0.417064
$378$	−0.977840	−0.0502947
$379$	−16.8755	−0.866834	−0.433417	−	0.901193i	$-0.642692\pi$
$379$	−16.8755	−0.866834	−0.433417	+	0.901193i	$0.642692\pi$
$380$	5.17606	0.265526
$381$	5.61363	0.287595
$382$	−6.63399	−0.339425
$383$	−10.8901	−0.556460	−0.278230	−	0.960514i	$-0.589748\pi$
$383$	−10.8901	−0.556460	−0.278230	+	0.960514i	$0.589748\pi$
$384$	1.00000	0.0510310
$385$	−0.616176	−0.0314032
$386$	−7.61732	−0.387711
$387$	−5.03820	−0.256106
$388$	14.7754	0.750107
$389$	23.2979	1.18125	0.590626	−	0.806945i	$-0.298881\pi$
$389$	23.2979	1.18125	0.590626	+	0.806945i	$0.298881\pi$
$390$	−2.61702	−0.132518
$391$	1.20355	0.0608659
$392$	6.04383	0.305259
$393$	−3.87103	−0.195268
$394$	5.85181	0.294810
$395$	23.2226	1.16845
$396$	−0.240785	−0.0120999
$397$	12.2264	0.613624	0.306812	−	0.951770i	$-0.400738\pi$
$397$	12.2264	0.613624	0.306812	+	0.951770i	$0.400738\pi$
$398$	1.15345	0.0578170
$399$	−1.93401	−0.0968217
$400$	1.84882	0.0924408
$401$	8.14554	0.406769	0.203385	−	0.979099i	$-0.434806\pi$
$401$	8.14554	0.406769	0.203385	+	0.979099i	$0.434806\pi$
$402$	−14.2272	−0.709590
$403$	−7.15427	−0.356380
$404$	−10.7141	−0.533045
$405$	−2.61702	−0.130041
$406$	7.91847	0.392987
$407$	−1.30430	−0.0646516
$408$	−4.91508	−0.243333
$409$	−23.0045	−1.13750	−0.568749	−	0.822511i	$-0.692572\pi$
$409$	−23.0045	−1.13750	−0.568749	+	0.822511i	$0.692572\pi$
$410$	28.1471	1.39009
$411$	−8.32317	−0.410552
$412$	1.00000	0.0492665
$413$	6.89744	0.339401
$414$	0.244868	0.0120346
$415$	−35.0602	−1.72104
$416$	−1.00000	−0.0490290
$417$	−1.62532	−0.0795921
$418$	−0.476234	−0.0232934
$419$	17.7485	0.867070	0.433535	−	0.901137i	$-0.357266\pi$
$419$	17.7485	0.867070	0.433535	+	0.901137i	$0.357266\pi$
$420$	−2.55903	−0.124868
$421$	9.92884	0.483902	0.241951	−	0.970288i	$-0.422213\pi$
$421$	9.92884	0.483902	0.241951	+	0.970288i	$0.422213\pi$
$422$	−0.706007	−0.0343679
$423$	9.26343	0.450403
$424$	−9.79000	−0.475445
$425$	−9.08709	−0.440788
$426$	9.42409	0.456599
$427$	−3.47854	−0.168338
$428$	−12.2317	−0.591241
$429$	0.240785	0.0116252
$430$	−13.1851	−0.635841
$431$	7.53987	0.363183	0.181591	−	0.983374i	$-0.441875\pi$
$431$	7.53987	0.363183	0.181591	+	0.983374i	$0.441875\pi$
$432$	−1.00000	−0.0481125
$433$	−9.84043	−0.472901	−0.236451	−	0.971644i	$-0.575984\pi$
$433$	−9.84043	−0.472901	−0.236451	+	0.971644i	$0.575984\pi$
$434$	−6.99573	−0.335806
$435$	21.1924	1.01610
$436$	−15.0495	−0.720740
$437$	0.484309	0.0231677
$438$	0.976521	0.0466600
$439$	−18.5120	−0.883528	−0.441764	−	0.897131i	$-0.645647\pi$
$439$	−18.5120	−0.883528	−0.441764	+	0.897131i	$0.645647\pi$
$440$	−0.630140	−0.0300407
$441$	−6.04383	−0.287801
$442$	4.91508	0.233787
$443$	−19.4535	−0.924264	−0.462132	−	0.886811i	$-0.652915\pi$
$443$	−19.4535	−0.924264	−0.462132	+	0.886811i	$0.652915\pi$
$444$	−5.41686	−0.257073
$445$	1.28417	0.0608753
$446$	−14.3345	−0.678756
$447$	6.63099	0.313635
$448$	−0.977840	−0.0461986
$449$	−42.1339	−1.98842	−0.994211	−	0.107445i	$-0.965733\pi$
$449$	−42.1339	−1.98842	−0.994211	+	0.107445i	$0.965733\pi$
$450$	−1.84882	−0.0871540
$451$	−2.58973	−0.121946
$452$	15.2767	0.718557
$453$	−7.91264	−0.371768
$454$	−12.2428	−0.574585
$455$	2.55903	0.119969
$456$	−1.97784	−0.0926209
$457$	22.9184	1.07208	0.536038	−	0.844194i	$-0.319920\pi$
$457$	22.9184	1.07208	0.536038	+	0.844194i	$0.319920\pi$
$458$	−26.8538	−1.25480
$459$	4.91508	0.229416
$460$	0.640825	0.0298786
$461$	−6.85452	−0.319247	−0.159623	−	0.987178i	$-0.551028\pi$
$461$	−6.85452	−0.319247	−0.159623	+	0.987178i	$0.551028\pi$
$462$	0.235449	0.0109541
$463$	−20.9881	−0.975399	−0.487699	−	0.873012i	$-0.662164\pi$
$463$	−20.9881	−0.975399	−0.487699	+	0.873012i	$0.662164\pi$
$464$	8.09791	0.375936
$465$	−18.7229	−0.868254
$466$	11.9179	0.552087
$467$	25.5979	1.18453	0.592264	−	0.805744i	$-0.298234\pi$
$467$	25.5979	1.18453	0.592264	+	0.805744i	$0.298234\pi$
$468$	1.00000	0.0462250
$469$	13.9120	0.642395
$470$	24.2426	1.11823
$471$	−5.70092	−0.262685
$472$	7.05375	0.324675
$473$	1.21312	0.0557794
$474$	−8.87366	−0.407581
$475$	−3.65666	−0.167779
$476$	4.80617	0.220290
$477$	9.79000	0.448253
$478$	8.42147	0.385189
$479$	−27.7457	−1.26773	−0.633867	−	0.773442i	$-0.718533\pi$
$479$	−27.7457	−1.26773	−0.633867	+	0.773442i	$0.718533\pi$
$480$	−2.61702	−0.119450
$481$	5.41686	0.246987
$482$	−4.39928	−0.200382
$483$	−0.239442	−0.0108950
$484$	−10.9420	−0.497365
$485$	−38.6676	−1.75580
$486$	1.00000	0.0453609
$487$	20.8544	0.945004	0.472502	−	0.881330i	$-0.343351\pi$
$487$	20.8544	0.945004	0.472502	+	0.881330i	$0.343351\pi$
$488$	−3.55737	−0.161034
$489$	−11.8922	−0.537784
$490$	−15.8168	−0.714532
$491$	−29.1552	−1.31576	−0.657879	−	0.753124i	$-0.728546\pi$
$491$	−29.1552	−1.31576	−0.657879	+	0.753124i	$0.728546\pi$
$492$	−10.7554	−0.484891
$493$	−39.8019	−1.79259
$494$	1.97784	0.0889872
$495$	0.630140	0.0283227
$496$	−7.15427	−0.321236
$497$	−9.21526	−0.413361
$498$	13.3970	0.600332
$499$	−22.6831	−1.01543	−0.507717	−	0.861524i	$-0.669511\pi$
$499$	−22.6831	−1.01543	−0.507717	+	0.861524i	$0.669511\pi$
$500$	8.24672	0.368805
$501$	−7.73384	−0.345522
$502$	22.7613	1.01588
$503$	−8.39406	−0.374272	−0.187136	−	0.982334i	$-0.559921\pi$
$503$	−8.39406	−0.374272	−0.187136	+	0.982334i	$0.559921\pi$
$504$	0.977840	0.0435565
$505$	28.0390	1.24772
$506$	−0.0589604	−0.00262111
$507$	−1.00000	−0.0444116
$508$	−5.61363	−0.249065
$509$	15.2631	0.676526	0.338263	−	0.941052i	$-0.390161\pi$
$509$	15.2631	0.676526	0.338263	+	0.941052i	$0.390161\pi$
$510$	12.8629	0.569579
$511$	−0.954881	−0.0422415
$512$	−1.00000	−0.0441942
$513$	1.97784	0.0873238
$514$	29.1047	1.28376
$515$	−2.61702	−0.115320
$516$	5.03820	0.221794
$517$	−2.23049	−0.0980970
$518$	5.29682	0.232729
$519$	−0.659015	−0.0289275
$520$	2.61702	0.114764
$521$	13.5364	0.593041	0.296521	−	0.955026i	$-0.404174\pi$
$521$	13.5364	0.593041	0.296521	+	0.955026i	$0.404174\pi$
$522$	−8.09791	−0.354436
$523$	−14.4599	−0.632288	−0.316144	−	0.948711i	$-0.602388\pi$
$523$	−14.4599	−0.632288	−0.316144	+	0.948711i	$0.602388\pi$
$524$	3.87103	0.169107
$525$	1.80785	0.0789009
$526$	6.72826	0.293366
$527$	35.1638	1.53176
$528$	0.240785	0.0104788
$529$	−22.9400	−0.997393
$530$	25.6207	1.11289
$531$	−7.05375	−0.306107
$532$	1.93401	0.0838501
$533$	10.7554	0.465868
$534$	−0.490697	−0.0212345
$535$	32.0106	1.38394
$536$	14.2272	0.614523
$537$	−20.3333	−0.877446
$538$	14.7972	0.637954
$539$	1.45526	0.0626826
$540$	2.61702	0.112619
$541$	−34.3574	−1.47714	−0.738571	−	0.674176i	$-0.764499\pi$
$541$	−34.3574	−1.47714	−0.738571	+	0.674176i	$0.764499\pi$
$542$	1.96999	0.0846185
$543$	−11.7556	−0.504480
$544$	4.91508	0.210732
$545$	39.3849	1.68706
$546$	−0.977840	−0.0418477
$547$	−7.44242	−0.318215	−0.159107	−	0.987261i	$-0.550862\pi$
$547$	−7.44242	−0.318215	−0.159107	+	0.987261i	$0.550862\pi$
$548$	8.32317	0.355548
$549$	3.55737	0.151825
$550$	0.445167	0.0189820
$551$	−16.0164	−0.682321
$552$	−0.244868	−0.0104223
$553$	8.67702	0.368984
$554$	16.6946	0.709286
$555$	14.1760	0.601740
$556$	1.62532	0.0689287
$557$	19.7550	0.837045	0.418522	−	0.908207i	$-0.362548\pi$
$557$	19.7550	0.837045	0.418522	+	0.908207i	$0.362548\pi$
$558$	7.15427	0.302864
$559$	−5.03820	−0.213093
$560$	2.55903	0.108139
$561$	−1.18348	−0.0499664
$562$	27.9085	1.17725
$563$	−12.0479	−0.507757	−0.253878	−	0.967236i	$-0.581706\pi$
$563$	−12.0479	−0.507757	−0.253878	+	0.967236i	$0.581706\pi$
$564$	−9.26343	−0.390061
$565$	−39.9796	−1.68195
$566$	0.449681	0.0189015
$567$	−0.977840	−0.0410654
$568$	−9.42409	−0.395426
$569$	−5.93297	−0.248723	−0.124362	−	0.992237i	$-0.539688\pi$
$569$	−5.93297	−0.248723	−0.124362	+	0.992237i	$0.539688\pi$
$570$	5.17606	0.216801
$571$	−5.79958	−0.242705	−0.121352	−	0.992609i	$-0.538723\pi$
$571$	−5.79958	−0.242705	−0.121352	+	0.992609i	$0.538723\pi$
$572$	−0.240785	−0.0100677
$573$	−6.63399	−0.277139
$574$	10.5171	0.438973
$575$	−0.452715	−0.0188795
$576$	1.00000	0.0416667
$577$	3.70002	0.154034	0.0770169	−	0.997030i	$-0.475460\pi$
$577$	3.70002	0.154034	0.0770169	+	0.997030i	$0.475460\pi$
$578$	−7.15805	−0.297736
$579$	−7.61732	−0.316565
$580$	−21.1924	−0.879968
$581$	−13.1001	−0.543483
$582$	14.7754	0.612460
$583$	−2.35728	−0.0976287
$584$	−0.976521	−0.0404087
$585$	−2.61702	−0.108201
$586$	−2.83914	−0.117284
$587$	18.7108	0.772278	0.386139	−	0.922441i	$-0.373808\pi$
$587$	18.7108	0.772278	0.386139	+	0.922441i	$0.373808\pi$
$588$	6.04383	0.249243
$589$	14.1500	0.583041
$590$	−18.4598	−0.759980
$591$	5.85181	0.240711
$592$	5.41686	0.222631
$593$	−23.9001	−0.981460	−0.490730	−	0.871312i	$-0.663270\pi$
$593$	−23.9001	−0.981460	−0.490730	+	0.871312i	$0.663270\pi$
$594$	−0.240785	−0.00987952
$595$	−12.5779	−0.515642
$596$	−6.63099	−0.271616
$597$	1.15345	0.0472074
$598$	0.244868	0.0100134
$599$	12.7785	0.522114	0.261057	−	0.965323i	$-0.415929\pi$
$599$	12.7785	0.522114	0.261057	+	0.965323i	$0.415929\pi$
$600$	1.84882	0.0754776
$601$	−2.45569	−0.100170	−0.0500848	−	0.998745i	$-0.515949\pi$
$601$	−2.45569	−0.100170	−0.0500848	+	0.998745i	$0.515949\pi$
$602$	−4.92655	−0.200791
$603$	−14.2272	−0.579378
$604$	7.91264	0.321961
$605$	28.6355	1.16420
$606$	−10.7141	−0.435230
$607$	37.5049	1.52228	0.761138	−	0.648590i	$-0.224641\pi$
$607$	37.5049	1.52228	0.761138	+	0.648590i	$0.224641\pi$
$608$	1.97784	0.0802120
$609$	7.91847	0.320872
$610$	9.30972	0.376939
$611$	9.26343	0.374758
$612$	−4.91508	−0.198680
$613$	21.6188	0.873176	0.436588	−	0.899662i	$-0.356187\pi$
$613$	21.6188	0.873176	0.436588	+	0.899662i	$0.356187\pi$
$614$	−22.4489	−0.905964
$615$	28.1471	1.13500
$616$	−0.235449	−0.00948651
$617$	−7.98471	−0.321452	−0.160726	−	0.986999i	$-0.551384\pi$
$617$	−7.98471	−0.321452	−0.160726	+	0.986999i	$0.551384\pi$
$618$	1.00000	0.0402259
$619$	−15.5740	−0.625972	−0.312986	−	0.949758i	$-0.601329\pi$
$619$	−15.5740	−0.625972	−0.312986	+	0.949758i	$0.601329\pi$
$620$	18.7229	0.751930
$621$	0.244868	0.00982620
$622$	4.91789	0.197189
$623$	0.479823	0.0192237
$624$	−1.00000	−0.0400320
$625$	−30.8260	−1.23304
$626$	−14.2027	−0.567652
$627$	−0.476234	−0.0190189
$628$	5.70092	0.227492
$629$	−26.6243	−1.06158
$630$	−2.55903	−0.101954
$631$	−19.6398	−0.781847	−0.390923	−	0.920423i	$-0.627844\pi$
$631$	−19.6398	−0.781847	−0.390923	+	0.920423i	$0.627844\pi$
$632$	8.87366	0.352975
$633$	−0.706007	−0.0280613
$634$	−1.83459	−0.0728609
$635$	14.6910	0.582995
$636$	−9.79000	−0.388199
$637$	−6.04383	−0.239465
$638$	1.94985	0.0771955
$639$	9.42409	0.372811
$640$	2.61702	0.103447
$641$	−1.62764	−0.0642879	−0.0321439	−	0.999483i	$-0.510233\pi$
$641$	−1.62764	−0.0642879	−0.0321439	+	0.999483i	$0.510233\pi$
$642$	−12.2317	−0.482746
$643$	−29.8776	−1.17826	−0.589128	−	0.808040i	$-0.700529\pi$
$643$	−29.8776	−1.17826	−0.589128	+	0.808040i	$0.700529\pi$
$644$	0.239442	0.00943532
$645$	−13.1851	−0.519162
$646$	−9.72125	−0.382478
$647$	−11.9039	−0.467989	−0.233995	−	0.972238i	$-0.575180\pi$
$647$	−11.9039	−0.467989	−0.233995	+	0.972238i	$0.575180\pi$
$648$	−1.00000	−0.0392837
$649$	1.69844	0.0666695
$650$	−1.84882	−0.0725165
$651$	−6.99573	−0.274184
$652$	11.8922	0.465734
$653$	13.2976	0.520374	0.260187	−	0.965558i	$-0.416216\pi$
$653$	13.2976	0.520374	0.260187	+	0.965558i	$0.416216\pi$
$654$	−15.0495	−0.588482
$655$	−10.1306	−0.395835
$656$	10.7554	0.419928
$657$	0.976521	0.0380977
$658$	9.05816	0.353124
$659$	0.0282496	0.00110045	0.000550223	−	1.00000i	$-0.499825\pi$
$659$	0.0282496	0.00110045	0.000550223		1.00000i	$0.499825\pi$
$660$	−0.630140	−0.0245281
$661$	11.7375	0.456536	0.228268	−	0.973598i	$-0.426694\pi$
$661$	11.7375	0.456536	0.228268	+	0.973598i	$0.426694\pi$
$662$	22.7353	0.883633
$663$	4.91508	0.190886
$664$	−13.3970	−0.519903
$665$	−5.06136	−0.196271
$666$	−5.41686	−0.209899
$667$	−1.98292	−0.0767789
$668$	7.73384	0.299231
$669$	−14.3345	−0.554202
$670$	−37.2330	−1.43844
$671$	−0.856560	−0.0330671
$672$	−0.977840	−0.0377210
$673$	−3.55254	−0.136940	−0.0684702	−	0.997653i	$-0.521812\pi$
$673$	−3.55254	−0.136940	−0.0684702	+	0.997653i	$0.521812\pi$
$674$	−1.40532	−0.0541310
$675$	−1.84882	−0.0711610
$676$	1.00000	0.0384615
$677$	−31.6198	−1.21525	−0.607623	−	0.794226i	$-0.707877\pi$
$677$	−31.6198	−1.21525	−0.607623	+	0.794226i	$0.707877\pi$
$678$	15.2767	0.586699
$679$	−14.4480	−0.554462
$680$	−12.8629	−0.493269
$681$	−12.2428	−0.469147
$682$	−1.72264	−0.0659633
$683$	10.8767	0.416184	0.208092	−	0.978109i	$-0.433275\pi$
$683$	10.8767	0.416184	0.208092	+	0.978109i	$0.433275\pi$
$684$	−1.97784	−0.0756246
$685$	−21.7819	−0.832245
$686$	−12.7548	−0.486980
$687$	−26.8538	−1.02454
$688$	−5.03820	−0.192080
$689$	9.79000	0.372969
$690$	0.640825	0.0243958
$691$	34.5054	1.31265	0.656324	−	0.754479i	$-0.272110\pi$
$691$	34.5054	1.31265	0.656324	+	0.754479i	$0.272110\pi$
$692$	0.659015	0.0250520
$693$	0.235449	0.00894397
$694$	28.8724	1.09598
$695$	−4.25349	−0.161344
$696$	8.09791	0.306951
$697$	−52.8637	−2.00235
$698$	22.1867	0.839778
$699$	11.9179	0.450777
$700$	−1.80785	−0.0683302
$701$	−7.94945	−0.300247	−0.150123	−	0.988667i	$-0.547967\pi$
$701$	−7.94945	−0.300247	−0.150123	+	0.988667i	$0.547967\pi$
$702$	1.00000	0.0377426
$703$	−10.7137	−0.404074
$704$	−0.240785	−0.00907492
$705$	24.2426	0.913030
$706$	5.73114	0.215694
$707$	10.4767	0.394015
$708$	7.05375	0.265096
$709$	−38.7513	−1.45534	−0.727668	−	0.685930i	$-0.759396\pi$
$709$	−38.7513	−1.45534	−0.727668	+	0.685930i	$0.759396\pi$
$710$	24.6631	0.925589
$711$	−8.87366	−0.332788
$712$	0.490697	0.0183896
$713$	1.75185	0.0656073
$714$	4.80617	0.179866
$715$	0.630140	0.0235659
$716$	20.3333	0.759891
$717$	8.42147	0.314505
$718$	16.9988	0.634391
$719$	11.9026	0.443894	0.221947	−	0.975059i	$-0.428759\pi$
$719$	11.9026	0.443894	0.221947	+	0.975059i	$0.428759\pi$
$720$	−2.61702	−0.0975307
$721$	−0.977840	−0.0364167
$722$	15.0881	0.561523
$723$	−4.39928	−0.163611
$724$	11.7556	0.436893
$725$	14.9716	0.556030
$726$	−10.9420	−0.406097
$727$	−20.3323	−0.754082	−0.377041	−	0.926197i	$-0.623058\pi$
$727$	−20.3323	−0.754082	−0.377041	+	0.926197i	$0.623058\pi$
$728$	0.977840	0.0362412
$729$	1.00000	0.0370370
$730$	2.55558	0.0945862
$731$	24.7632	0.915899
$732$	−3.55737	−0.131484
$733$	44.3842	1.63937	0.819684	−	0.572816i	$-0.194149\pi$
$733$	44.3842	1.63937	0.819684	+	0.572816i	$0.194149\pi$
$734$	8.06954	0.297852
$735$	−15.8168	−0.583413
$736$	0.244868	0.00902594
$737$	3.42570	0.126187
$738$	−10.7554	−0.395911
$739$	−47.1876	−1.73582	−0.867912	−	0.496718i	$-0.834538\pi$
$739$	−47.1876	−1.73582	−0.867912	+	0.496718i	$0.834538\pi$
$740$	−14.1760	−0.521122
$741$	1.97784	0.0726578
$742$	9.57306	0.351438
$743$	−21.0148	−0.770957	−0.385478	−	0.922717i	$-0.625964\pi$
$743$	−21.0148	−0.770957	−0.385478	+	0.922717i	$0.625964\pi$
$744$	−7.15427	−0.262288
$745$	17.3535	0.635782
$746$	9.23667	0.338179
$747$	13.3970	0.490169
$748$	1.18348	0.0432722
$749$	11.9606	0.437032
$750$	8.24672	0.301128
$751$	6.30191	0.229960	0.114980	−	0.993368i	$-0.463320\pi$
$751$	6.30191	0.229960	0.114980	+	0.993368i	$0.463320\pi$
$752$	9.26343	0.337803
$753$	22.7613	0.829467
$754$	−8.09791	−0.294909
$755$	−20.7076	−0.753626
$756$	0.977840	0.0355637
$757$	22.1721	0.805858	0.402929	−	0.915231i	$-0.367992\pi$
$757$	22.1721	0.805858	0.402929	+	0.915231i	$0.367992\pi$
$758$	16.8755	0.612945
$759$	−0.0589604	−0.00214013
$760$	−5.17606	−0.187755
$761$	11.4436	0.414830	0.207415	−	0.978253i	$-0.433495\pi$
$761$	11.4436	0.414830	0.207415	+	0.978253i	$0.433495\pi$
$762$	−5.61363	−0.203360
$763$	14.7160	0.532755
$764$	6.63399	0.240009
$765$	12.8629	0.465059
$766$	10.8901	0.393477
$767$	−7.05375	−0.254696
$768$	−1.00000	−0.0360844
$769$	11.7434	0.423479	0.211739	−	0.977326i	$-0.432087\pi$
$769$	11.7434	0.423479	0.211739	+	0.977326i	$0.432087\pi$
$770$	0.616176	0.0222054
$771$	29.1047	1.04818
$772$	7.61732	0.274153
$773$	−48.6889	−1.75122	−0.875608	−	0.483022i	$-0.839539\pi$
$773$	−48.6889	−1.75122	−0.875608	+	0.483022i	$0.839539\pi$
$774$	5.03820	0.181094
$775$	−13.2269	−0.475125
$776$	−14.7754	−0.530406
$777$	5.29682	0.190022
$778$	−23.2979	−0.835271
$779$	−21.2724	−0.762165
$780$	2.61702	0.0937045
$781$	−2.26918	−0.0811975
$782$	−1.20355	−0.0430387
$783$	−8.09791	−0.289396
$784$	−6.04383	−0.215851
$785$	−14.9195	−0.532498
$786$	3.87103	0.138075
$787$	46.3481	1.65213	0.826066	−	0.563574i	$-0.190574\pi$
$787$	46.3481	1.65213	0.826066	+	0.563574i	$0.190574\pi$
$788$	−5.85181	−0.208462
$789$	6.72826	0.239532
$790$	−23.2226	−0.826222
$791$	−14.9382	−0.531141
$792$	0.240785	0.00855591
$793$	3.55737	0.126326
$794$	−12.2264	−0.433898
$795$	25.6207	0.908672
$796$	−1.15345	−0.0408828
$797$	−16.4711	−0.583438	−0.291719	−	0.956504i	$-0.594227\pi$
$797$	−16.4711	−0.583438	−0.291719	+	0.956504i	$0.594227\pi$
$798$	1.93401	0.0684633
$799$	−45.5305	−1.61075
$800$	−1.84882	−0.0653655
$801$	−0.490697	−0.0173379
$802$	−8.14554	−0.287629
$803$	−0.235131	−0.00829760
$804$	14.2272	0.501756
$805$	−0.626624	−0.0220856
$806$	7.15427	0.251998
$807$	14.7972	0.520888
$808$	10.7141	0.376920
$809$	23.2860	0.818692	0.409346	−	0.912379i	$-0.365757\pi$
$809$	23.2860	0.818692	0.409346	+	0.912379i	$0.365757\pi$
$810$	2.61702	0.0919529
$811$	2.52046	0.0885053	0.0442527	−	0.999020i	$-0.485909\pi$
$811$	2.52046	0.0885053	0.0442527	+	0.999020i	$0.485909\pi$
$812$	−7.91847	−0.277884
$813$	1.96999	0.0690907
$814$	1.30430	0.0457156
$815$	−31.1222	−1.09016
$816$	4.91508	0.172062
$817$	9.96475	0.348623
$818$	23.0045	0.804333
$819$	−0.977840	−0.0341685
$820$	−28.1471	−0.982940
$821$	31.4193	1.09654	0.548270	−	0.836301i	$-0.315287\pi$
$821$	31.4193	1.09654	0.548270	+	0.836301i	$0.315287\pi$
$822$	8.32317	0.290304
$823$	−36.9734	−1.28881	−0.644405	−	0.764684i	$-0.722895\pi$
$823$	−36.9734	−1.28881	−0.644405	+	0.764684i	$0.722895\pi$
$824$	−1.00000	−0.0348367
$825$	0.445167	0.0154987
$826$	−6.89744	−0.239993
$827$	−21.9835	−0.764440	−0.382220	−	0.924071i	$-0.624840\pi$
$827$	−21.9835	−0.764440	−0.382220	+	0.924071i	$0.624840\pi$
$828$	−0.244868	−0.00850974
$829$	30.7938	1.06951	0.534757	−	0.845006i	$-0.320403\pi$
$829$	30.7938	1.06951	0.534757	+	0.845006i	$0.320403\pi$
$830$	35.0602	1.21696
$831$	16.6946	0.579130
$832$	1.00000	0.0346688
$833$	29.7059	1.02925
$834$	1.62532	0.0562801
$835$	−20.2396	−0.700422
$836$	0.476234	0.0164709
$837$	7.15427	0.247288
$838$	−17.7485	−0.613111
$839$	−44.1131	−1.52295	−0.761477	−	0.648191i	$-0.775526\pi$
$839$	−44.1131	−1.52295	−0.761477	+	0.648191i	$0.775526\pi$
$840$	2.55903	0.0882950
$841$	36.5762	1.26125
$842$	−9.92884	−0.342170
$843$	27.9085	0.961219
$844$	0.706007	0.0243018
$845$	−2.61702	−0.0900284
$846$	−9.26343	−0.318483
$847$	10.6996	0.367641
$848$	9.79000	0.336190
$849$	0.449681	0.0154330
$850$	9.08709	0.311685
$851$	−1.32641	−0.0454689
$852$	−9.42409	−0.322864
$853$	−14.4974	−0.496381	−0.248191	−	0.968711i	$-0.579836\pi$
$853$	−14.4974	−0.496381	−0.248191	+	0.968711i	$0.579836\pi$
$854$	3.47854	0.119033
$855$	5.17606	0.177017
$856$	12.2317	0.418071
$857$	4.24844	0.145124	0.0725620	−	0.997364i	$-0.476882\pi$
$857$	4.24844	0.145124	0.0725620	+	0.997364i	$0.476882\pi$
$858$	−0.240785	−0.00822026
$859$	−15.3950	−0.525271	−0.262636	−	0.964895i	$-0.584592\pi$
$859$	−15.3950	−0.525271	−0.262636	+	0.964895i	$0.584592\pi$
$860$	13.1851	0.449608
$861$	10.5171	0.358420
$862$	−7.53987	−0.256809
$863$	24.2821	0.826573	0.413287	−	0.910601i	$-0.364381\pi$
$863$	24.2821	0.826573	0.413287	+	0.910601i	$0.364381\pi$
$864$	1.00000	0.0340207
$865$	−1.72466	−0.0586401
$866$	9.84043	0.334392
$867$	−7.15805	−0.243100
$868$	6.99573	0.237451
$869$	2.13664	0.0724806
$870$	−21.1924	−0.718491
$871$	−14.2272	−0.482072
$872$	15.0495	0.509640
$873$	14.7754	0.500071
$874$	−0.484309	−0.0163820
$875$	−8.06398	−0.272612
$876$	−0.976521	−0.0329936
$877$	−1.83535	−0.0619752	−0.0309876	−	0.999520i	$-0.509865\pi$
$877$	−1.83535	−0.0619752	−0.0309876	+	0.999520i	$0.509865\pi$
$878$	18.5120	0.624749
$879$	−2.83914	−0.0957618
$880$	0.630140	0.0212420
$881$	−31.1530	−1.04957	−0.524785	−	0.851235i	$-0.675854\pi$
$881$	−31.1530	−1.04957	−0.524785	+	0.851235i	$0.675854\pi$
$882$	6.04383	0.203506
$883$	−21.5055	−0.723717	−0.361859	−	0.932233i	$-0.617858\pi$
$883$	−21.5055	−0.723717	−0.361859	+	0.932233i	$0.617858\pi$
$884$	−4.91508	−0.165312
$885$	−18.4598	−0.620521
$886$	19.4535	0.653553
$887$	−5.17151	−0.173642	−0.0868211	−	0.996224i	$-0.527671\pi$
$887$	−5.17151	−0.173642	−0.0868211	+	0.996224i	$0.527671\pi$
$888$	5.41686	0.181778
$889$	5.48923	0.184103
$890$	−1.28417	−0.0430453
$891$	−0.240785	−0.00806659
$892$	14.3345	0.479953
$893$	−18.3216	−0.613108
$894$	−6.63099	−0.221773
$895$	−53.2127	−1.77870
$896$	0.977840	0.0326674
$897$	0.244868	0.00817590
$898$	42.1339	1.40603
$899$	−57.9346	−1.93223
$900$	1.84882	0.0616272
$901$	−48.1187	−1.60307
$902$	2.58973	0.0862287
$903$	−4.92655	−0.163945
$904$	−15.2767	−0.508097
$905$	−30.7647	−1.02265
$906$	7.91264	0.262880
$907$	−44.7207	−1.48493	−0.742464	−	0.669886i	$-0.766343\pi$
$907$	−44.7207	−1.48493	−0.742464	+	0.669886i	$0.766343\pi$
$908$	12.2428	0.406293
$909$	−10.7141	−0.355364
$910$	−2.55903	−0.0848311
$911$	11.8184	0.391560	0.195780	−	0.980648i	$-0.437276\pi$
$911$	11.8184	0.391560	0.195780	+	0.980648i	$0.437276\pi$
$912$	1.97784	0.0654928
$913$	−3.22578	−0.106758
$914$	−22.9184	−0.758073
$915$	9.30972	0.307770
$916$	26.8538	0.887274
$917$	−3.78525	−0.125000
$918$	−4.91508	−0.162222
$919$	−5.92090	−0.195313	−0.0976563	−	0.995220i	$-0.531135\pi$
$919$	−5.92090	−0.195313	−0.0976563	+	0.995220i	$0.531135\pi$
$920$	−0.640825	−0.0211274
$921$	−22.4489	−0.739717
$922$	6.85452	0.225742
$923$	9.42409	0.310198
$924$	−0.235449	−0.00774570
$925$	10.0148	0.329284
$926$	20.9881	0.689711
$927$	1.00000	0.0328443
$928$	−8.09791	−0.265827
$929$	48.9683	1.60660	0.803299	−	0.595576i	$-0.203076\pi$
$929$	48.9683	1.60660	0.803299	+	0.595576i	$0.203076\pi$
$930$	18.7229	0.613948
$931$	11.9537	0.391768
$932$	−11.9179	−0.390384
$933$	4.91789	0.161004
$934$	−25.5979	−0.837588
$935$	−3.09719	−0.101289
$936$	−1.00000	−0.0326860
$937$	−2.99171	−0.0977350	−0.0488675	−	0.998805i	$-0.515561\pi$
$937$	−2.99171	−0.0977350	−0.0488675	+	0.998805i	$0.515561\pi$
$938$	−13.9120	−0.454242
$939$	−14.2027	−0.463486
$940$	−24.2426	−0.790707
$941$	53.2058	1.73446	0.867230	−	0.497908i	$-0.165898\pi$
$941$	53.2058	1.73446	0.867230	+	0.497908i	$0.165898\pi$
$942$	5.70092	0.185746
$943$	−2.63365	−0.0857634
$944$	−7.05375	−0.229580
$945$	−2.55903	−0.0832453
$946$	−1.21312	−0.0394420
$947$	−37.0349	−1.20347	−0.601737	−	0.798694i	$-0.705524\pi$
$947$	−37.0349	−1.20347	−0.601737	+	0.798694i	$0.705524\pi$
$948$	8.87366	0.288203
$949$	0.976521	0.0316992
$950$	3.65666	0.118638
$951$	−1.83459	−0.0594907
$952$	−4.80617	−0.155769
$953$	−6.97956	−0.226090	−0.113045	−	0.993590i	$-0.536060\pi$
$953$	−6.97956	−0.226090	−0.113045	+	0.993590i	$0.536060\pi$
$954$	−9.79000	−0.316963
$955$	−17.3613	−0.561799
$956$	−8.42147	−0.272370
$957$	1.94985	0.0630298
$958$	27.7457	0.896423
$959$	−8.13873	−0.262813
$960$	2.61702	0.0844641
$961$	20.1836	0.651083
$962$	−5.41686	−0.174646
$963$	−12.2317	−0.394161
$964$	4.39928	0.141691
$965$	−19.9347	−0.641721
$966$	0.239442	0.00770391
$967$	−22.8451	−0.734648	−0.367324	−	0.930093i	$-0.619726\pi$
$967$	−22.8451	−0.734648	−0.367324	+	0.930093i	$0.619726\pi$
$968$	10.9420	0.351690
$969$	−9.72125	−0.312292
$970$	38.6676	1.24154
$971$	−26.1693	−0.839812	−0.419906	−	0.907568i	$-0.637937\pi$
$971$	−26.1693	−0.839812	−0.419906	+	0.907568i	$0.637937\pi$
$972$	−1.00000	−0.0320750
$973$	−1.58930	−0.0509506
$974$	−20.8544	−0.668219
$975$	−1.84882	−0.0592095
$976$	3.55737	0.113869
$977$	−13.8230	−0.442235	−0.221118	−	0.975247i	$-0.570971\pi$
$977$	−13.8230	−0.442235	−0.221118	+	0.975247i	$0.570971\pi$
$978$	11.8922	0.380270
$979$	0.118152	0.00377617
$980$	15.8168	0.505251
$981$	−15.0495	−0.480493
$982$	29.1552	0.930381
$983$	−8.65886	−0.276175	−0.138087	−	0.990420i	$-0.544095\pi$
$983$	−8.65886	−0.276175	−0.138087	+	0.990420i	$0.544095\pi$
$984$	10.7554	0.342869
$985$	15.3143	0.487955
$986$	39.8019	1.26755
$987$	9.05816	0.288324
$988$	−1.97784	−0.0629235
$989$	1.23369	0.0392291
$990$	−0.630140	−0.0200271
$991$	4.05681	0.128869	0.0644344	−	0.997922i	$-0.479476\pi$
$991$	4.05681	0.128869	0.0644344	+	0.997922i	$0.479476\pi$
$992$	7.15427	0.227148
$993$	22.7353	0.721483
$994$	9.21526	0.292290
$995$	3.01859	0.0956959
$996$	−13.3970	−0.424499
$997$	−40.8563	−1.29393	−0.646966	−	0.762519i	$-0.723962\pi$
$997$	−40.8563	−1.29393	−0.646966	+	0.762519i	$0.723962\pi$
$998$	22.6831	0.718021
$999$	−5.41686	−0.171382

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.o.1.2	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.o.1.2	✓	7	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.61702 q^{5} +1.00000 q^{6} -0.977840 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.61702 q^{5} +1.00000 q^{6} -0.977840 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.61702 q^{10} -0.240785 q^{11} -1.00000 q^{12} +1.00000 q^{13} +0.977840 q^{14} +2.61702 q^{15} +1.00000 q^{16} -4.91508 q^{17} -1.00000 q^{18} -1.97784 q^{19} -2.61702 q^{20} +0.977840 q^{21} +0.240785 q^{22} -0.244868 q^{23} +1.00000 q^{24} +1.84882 q^{25} -1.00000 q^{26} -1.00000 q^{27} -0.977840 q^{28} +8.09791 q^{29} -2.61702 q^{30} -7.15427 q^{31} -1.00000 q^{32} +0.240785 q^{33} +4.91508 q^{34} +2.55903 q^{35} +1.00000 q^{36} +5.41686 q^{37} +1.97784 q^{38} -1.00000 q^{39} +2.61702 q^{40} +10.7554 q^{41} -0.977840 q^{42} -5.03820 q^{43} -0.240785 q^{44} -2.61702 q^{45} +0.244868 q^{46} +9.26343 q^{47} -1.00000 q^{48} -6.04383 q^{49} -1.84882 q^{50} +4.91508 q^{51} +1.00000 q^{52} +9.79000 q^{53} +1.00000 q^{54} +0.630140 q^{55} +0.977840 q^{56} +1.97784 q^{57} -8.09791 q^{58} -7.05375 q^{59} +2.61702 q^{60} +3.55737 q^{61} +7.15427 q^{62} -0.977840 q^{63} +1.00000 q^{64} -2.61702 q^{65} -0.240785 q^{66} -14.2272 q^{67} -4.91508 q^{68} +0.244868 q^{69} -2.55903 q^{70} +9.42409 q^{71} -1.00000 q^{72} +0.976521 q^{73} -5.41686 q^{74} -1.84882 q^{75} -1.97784 q^{76} +0.235449 q^{77} +1.00000 q^{78} -8.87366 q^{79} -2.61702 q^{80} +1.00000 q^{81} -10.7554 q^{82} +13.3970 q^{83} +0.977840 q^{84} +12.8629 q^{85} +5.03820 q^{86} -8.09791 q^{87} +0.240785 q^{88} -0.490697 q^{89} +2.61702 q^{90} -0.977840 q^{91} -0.244868 q^{92} +7.15427 q^{93} -9.26343 q^{94} +5.17606 q^{95} +1.00000 q^{96} +14.7754 q^{97} +6.04383 q^{98} -0.240785 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} - 7 q^{12} + 7 q^{13} + 9 q^{14} - 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 16 q^{19} + 2 q^{20} + 9 q^{21} + 6 q^{23} + 7 q^{24} + 15 q^{25} - 7 q^{26} - 7 q^{27} - 9 q^{28} - 5 q^{29} + 2 q^{30} - 16 q^{31} - 7 q^{32} - 3 q^{34} - 10 q^{35} + 7 q^{36} + 17 q^{37} + 16 q^{38} - 7 q^{39} - 2 q^{40} + 12 q^{41} - 9 q^{42} - 22 q^{43} + 2 q^{45} - 6 q^{46} - 7 q^{48} - 2 q^{49} - 15 q^{50} - 3 q^{51} + 7 q^{52} + 2 q^{53} + 7 q^{54} - 16 q^{55} + 9 q^{56} + 16 q^{57} + 5 q^{58} - 3 q^{59} - 2 q^{60} - 6 q^{61} + 16 q^{62} - 9 q^{63} + 7 q^{64} + 2 q^{65} + q^{67} + 3 q^{68} - 6 q^{69} + 10 q^{70} + 15 q^{71} - 7 q^{72} + 17 q^{73} - 17 q^{74} - 15 q^{75} - 16 q^{76} - 10 q^{77} + 7 q^{78} - 27 q^{79} + 2 q^{80} + 7 q^{81} - 12 q^{82} + 12 q^{83} + 9 q^{84} + 15 q^{85} + 22 q^{86} + 5 q^{87} - 9 q^{89} - 2 q^{90} - 9 q^{91} + 6 q^{92} + 16 q^{93} - 12 q^{95} + 7 q^{96} - 3 q^{97} + 2 q^{98}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 - 7 * q^12 + 7 * q^13 + 9 * q^14 - 2 * q^15 + 7 * q^16 + 3 * q^17 - 7 * q^18 - 16 * q^19 + 2 * q^20 + 9 * q^21 + 6 * q^23 + 7 * q^24 + 15 * q^25 - 7 * q^26 - 7 * q^27 - 9 * q^28 - 5 * q^29 + 2 * q^30 - 16 * q^31 - 7 * q^32 - 3 * q^34 - 10 * q^35 + 7 * q^36 + 17 * q^37 + 16 * q^38 - 7 * q^39 - 2 * q^40 + 12 * q^41 - 9 * q^42 - 22 * q^43 + 2 * q^45 - 6 * q^46 - 7 * q^48 - 2 * q^49 - 15 * q^50 - 3 * q^51 + 7 * q^52 + 2 * q^53 + 7 * q^54 - 16 * q^55 + 9 * q^56 + 16 * q^57 + 5 * q^58 - 3 * q^59 - 2 * q^60 - 6 * q^61 + 16 * q^62 - 9 * q^63 + 7 * q^64 + 2 * q^65 + q^67 + 3 * q^68 - 6 * q^69 + 10 * q^70 + 15 * q^71 - 7 * q^72 + 17 * q^73 - 17 * q^74 - 15 * q^75 - 16 * q^76 - 10 * q^77 + 7 * q^78 - 27 * q^79 + 2 * q^80 + 7 * q^81 - 12 * q^82 + 12 * q^83 + 9 * q^84 + 15 * q^85 + 22 * q^86 + 5 * q^87 - 9 * q^89 - 2 * q^90 - 9 * q^91 + 6 * q^92 + 16 * q^93 - 12 * q^95 + 7 * q^96 - 3 * q^97 + 2 * q^98

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