LMFDB - Embedded newform 8021.2.a.a.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$1$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.26323 q^{2} +2.87488 q^{3} +3.12222 q^{4} +0.727126 q^{5} -6.50652 q^{6} +0.231070 q^{7} -2.53984 q^{8} +5.26494 q^{9} +O(q^{10})$	\(q-2.26323 q^{2} +2.87488 q^{3} +3.12222 q^{4} +0.727126 q^{5} -6.50652 q^{6} +0.231070 q^{7} -2.53984 q^{8} +5.26494 q^{9} -1.64565 q^{10} -3.33792 q^{11} +8.97600 q^{12} +1.00000 q^{13} -0.522964 q^{14} +2.09040 q^{15} -0.496194 q^{16} -3.22094 q^{17} -11.9158 q^{18} +6.87412 q^{19} +2.27025 q^{20} +0.664297 q^{21} +7.55448 q^{22} +5.68451 q^{23} -7.30173 q^{24} -4.47129 q^{25} -2.26323 q^{26} +6.51144 q^{27} +0.721449 q^{28} -4.07676 q^{29} -4.73106 q^{30} -7.88925 q^{31} +6.20268 q^{32} -9.59611 q^{33} +7.28974 q^{34} +0.168017 q^{35} +16.4383 q^{36} -0.678172 q^{37} -15.5577 q^{38} +2.87488 q^{39} -1.84678 q^{40} -1.78071 q^{41} -1.50346 q^{42} -10.7329 q^{43} -10.4217 q^{44} +3.82828 q^{45} -12.8654 q^{46} -6.89821 q^{47} -1.42650 q^{48} -6.94661 q^{49} +10.1196 q^{50} -9.25983 q^{51} +3.12222 q^{52} -13.4534 q^{53} -14.7369 q^{54} -2.42709 q^{55} -0.586879 q^{56} +19.7623 q^{57} +9.22666 q^{58} +3.71415 q^{59} +6.52669 q^{60} -11.1669 q^{61} +17.8552 q^{62} +1.21657 q^{63} -13.0457 q^{64} +0.727126 q^{65} +21.7182 q^{66} -2.94515 q^{67} -10.0565 q^{68} +16.3423 q^{69} -0.380261 q^{70} +4.67416 q^{71} -13.3721 q^{72} -9.34443 q^{73} +1.53486 q^{74} -12.8544 q^{75} +21.4625 q^{76} -0.771291 q^{77} -6.50652 q^{78} -10.8175 q^{79} -0.360796 q^{80} +2.92479 q^{81} +4.03016 q^{82} +1.49211 q^{83} +2.07408 q^{84} -2.34203 q^{85} +24.2911 q^{86} -11.7202 q^{87} +8.47776 q^{88} -7.30224 q^{89} -8.66428 q^{90} +0.231070 q^{91} +17.7483 q^{92} -22.6807 q^{93} +15.6122 q^{94} +4.99835 q^{95} +17.8320 q^{96} +5.41826 q^{97} +15.7218 q^{98} -17.5739 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) $ 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * 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 $

$2$	−2.26323	−1.60035	−0.800173	−	0.599769i	$-0.795259\pi$
$2$	−2.26323	−1.60035	−0.800173	+	0.599769i	$0.795259\pi$
$3$	2.87488	1.65981	0.829907	−	0.557902i	$-0.188394\pi$
$3$	2.87488	1.65981	0.829907	+	0.557902i	$0.188394\pi$
$4$	3.12222	1.56111
$5$	0.727126	0.325181	0.162590	−	0.986694i	$-0.448015\pi$
$5$	0.727126	0.325181	0.162590	+	0.986694i	$0.448015\pi$
$6$	−6.50652	−2.65628
$7$	0.231070	0.0873361	0.0436680	−	0.999046i	$-0.486096\pi$
$7$	0.231070	0.0873361	0.0436680	+	0.999046i	$0.486096\pi$
$8$	−2.53984	−0.897968
$9$	5.26494	1.75498
$10$	−1.64565	−0.520402
$11$	−3.33792	−1.00642	−0.503210	−	0.864164i	$-0.667848\pi$
$11$	−3.33792	−1.00642	−0.503210	+	0.864164i	$0.667848\pi$
$12$	8.97600	2.59115
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.522964	−0.139768
$15$	2.09040	0.539739
$16$	−0.496194	−0.124049
$17$	−3.22094	−0.781194	−0.390597	−	0.920562i	$-0.627731\pi$
$17$	−3.22094	−0.781194	−0.390597	+	0.920562i	$0.627731\pi$
$18$	−11.9158	−2.80858
$19$	6.87412	1.57703	0.788516	−	0.615015i	$-0.210850\pi$
$19$	6.87412	1.57703	0.788516	+	0.615015i	$0.210850\pi$
$20$	2.27025	0.507642
$21$	0.664297	0.144962
$22$	7.55448	1.61062
$23$	5.68451	1.18530	0.592652	−	0.805459i	$-0.298081\pi$
$23$	5.68451	1.18530	0.592652	+	0.805459i	$0.298081\pi$
$24$	−7.30173	−1.49046
$25$	−4.47129	−0.894258
$26$	−2.26323	−0.443856
$27$	6.51144	1.25313
$28$	0.721449	0.136341
$29$	−4.07676	−0.757036	−0.378518	−	0.925594i	$-0.623566\pi$
$29$	−4.07676	−0.757036	−0.378518	+	0.925594i	$0.623566\pi$
$30$	−4.73106	−0.863770
$31$	−7.88925	−1.41695	−0.708476	−	0.705735i	$-0.750617\pi$
$31$	−7.88925	−1.41695	−0.708476	+	0.705735i	$0.750617\pi$
$32$	6.20268	1.09649
$33$	−9.59611	−1.67047
$34$	7.28974	1.25018
$35$	0.168017	0.0284000
$36$	16.4383	2.73972
$37$	−0.678172	−0.111491	−0.0557454	−	0.998445i	$-0.517754\pi$
$37$	−0.678172	−0.111491	−0.0557454	+	0.998445i	$0.517754\pi$
$38$	−15.5577	−2.52380
$39$	2.87488	0.460349
$40$	−1.84678	−0.292002
$41$	−1.78071	−0.278100	−0.139050	−	0.990285i	$-0.544405\pi$
$41$	−1.78071	−0.278100	−0.139050	+	0.990285i	$0.544405\pi$
$42$	−1.50346	−0.231989
$43$	−10.7329	−1.63676	−0.818379	−	0.574679i	$-0.805127\pi$
$43$	−10.7329	−1.63676	−0.818379	+	0.574679i	$0.805127\pi$
$44$	−10.4217	−1.57113
$45$	3.82828	0.570686
$46$	−12.8654	−1.89690
$47$	−6.89821	−1.00621	−0.503103	−	0.864226i	$-0.667809\pi$
$47$	−6.89821	−1.00621	−0.503103	+	0.864226i	$0.667809\pi$
$48$	−1.42650	−0.205898
$49$	−6.94661	−0.992372
$50$	10.1196	1.43112
$51$	−9.25983	−1.29664
$52$	3.12222	0.432974
$53$	−13.4534	−1.84796	−0.923981	−	0.382439i	$-0.875084\pi$
$53$	−13.4534	−1.84796	−0.923981	+	0.382439i	$0.875084\pi$
$54$	−14.7369	−2.00544
$55$	−2.42709	−0.327268
$56$	−0.586879	−0.0784250
$57$	19.7623	2.61758
$58$	9.22666	1.21152
$59$	3.71415	0.483541	0.241771	−	0.970333i	$-0.422272\pi$
$59$	3.71415	0.483541	0.241771	+	0.970333i	$0.422272\pi$
$60$	6.52669	0.842592
$61$	−11.1669	−1.42978	−0.714888	−	0.699239i	$-0.753522\pi$
$61$	−11.1669	−1.42978	−0.714888	+	0.699239i	$0.753522\pi$
$62$	17.8552	2.26761
$63$	1.21657	0.153273
$64$	−13.0457	−1.63071
$65$	0.727126	0.0901889
$66$	21.7182	2.67333
$67$	−2.94515	−0.359807	−0.179904	−	0.983684i	$-0.557579\pi$
$67$	−2.94515	−0.359807	−0.179904	+	0.983684i	$0.557579\pi$
$68$	−10.0565	−1.21953
$69$	16.3423	1.96738
$70$	−0.380261	−0.0454498
$71$	4.67416	0.554720	0.277360	−	0.960766i	$-0.410540\pi$
$71$	4.67416	0.554720	0.277360	+	0.960766i	$0.410540\pi$
$72$	−13.3721	−1.57592
$73$	−9.34443	−1.09368	−0.546841	−	0.837236i	$-0.684170\pi$
$73$	−9.34443	−1.09368	−0.546841	+	0.837236i	$0.684170\pi$
$74$	1.53486	0.178424
$75$	−12.8544	−1.48430
$76$	21.4625	2.46192
$77$	−0.771291	−0.0878967
$78$	−6.50652	−0.736719
$79$	−10.8175	−1.21707	−0.608534	−	0.793527i	$-0.708242\pi$
$79$	−10.8175	−1.21707	−0.608534	+	0.793527i	$0.708242\pi$
$80$	−0.360796	−0.0403382
$81$	2.92479	0.324977
$82$	4.03016	0.445057
$83$	1.49211	0.163780	0.0818902	−	0.996641i	$-0.473904\pi$
$83$	1.49211	0.163780	0.0818902	+	0.996641i	$0.473904\pi$
$84$	2.07408	0.226301
$85$	−2.34203	−0.254029
$86$	24.2911	2.61938
$87$	−11.7202	−1.25654
$88$	8.47776	0.903733
$89$	−7.30224	−0.774036	−0.387018	−	0.922072i	$-0.626495\pi$
$89$	−7.30224	−0.774036	−0.387018	+	0.922072i	$0.626495\pi$
$90$	−8.66428	−0.913295
$91$	0.231070	0.0242227
$92$	17.7483	1.85039
$93$	−22.6807	−2.35187
$94$	15.6122	1.61028
$95$	4.99835	0.512820
$96$	17.8320	1.81997
$97$	5.41826	0.550141	0.275070	−	0.961424i	$-0.411299\pi$
$97$	5.41826	0.550141	0.275070	+	0.961424i	$0.411299\pi$
$98$	15.7218	1.58814
$99$	−17.5739	−1.76625
$100$	−13.9603	−1.39603
$101$	10.0455	0.999565	0.499782	−	0.866151i	$-0.333413\pi$
$101$	10.0455	0.999565	0.499782	+	0.866151i	$0.333413\pi$
$102$	20.9571	2.07507
$103$	12.4191	1.22369	0.611844	−	0.790979i	$-0.290428\pi$
$103$	12.4191	1.22369	0.611844	+	0.790979i	$0.290428\pi$
$104$	−2.53984	−0.249052
$105$	0.483028	0.0471387
$106$	30.4481	2.95738
$107$	−14.9574	−1.44598	−0.722992	−	0.690857i	$-0.757234\pi$
$107$	−14.9574	−1.44598	−0.722992	+	0.690857i	$0.757234\pi$
$108$	20.3301	1.95627
$109$	−4.23403	−0.405546	−0.202773	−	0.979226i	$-0.564995\pi$
$109$	−4.23403	−0.405546	−0.202773	+	0.979226i	$0.564995\pi$
$110$	5.49306	0.523742
$111$	−1.94966	−0.185054
$112$	−0.114655	−0.0108339
$113$	15.7265	1.47943	0.739713	−	0.672922i	$-0.234961\pi$
$113$	15.7265	1.47943	0.739713	+	0.672922i	$0.234961\pi$
$114$	−44.7266	−4.18903
$115$	4.13336	0.385438
$116$	−12.7285	−1.18182
$117$	5.26494	0.486744
$118$	−8.40599	−0.773834
$119$	−0.744262	−0.0682264
$120$	−5.30928	−0.484669
$121$	0.141686	0.0128805
$122$	25.2733	2.28814
$123$	−5.11934	−0.461595
$124$	−24.6320	−2.21201
$125$	−6.88682	−0.615976
$126$	−2.75337	−0.245290
$127$	−17.2316	−1.52906	−0.764529	−	0.644589i	$-0.777028\pi$
$127$	−17.2316	−1.52906	−0.764529	+	0.644589i	$0.777028\pi$
$128$	17.1201	1.51322
$129$	−30.8559	−2.71671
$130$	−1.64565	−0.144333
$131$	21.0173	1.83629	0.918147	−	0.396240i	$-0.129685\pi$
$131$	21.0173	1.83629	0.918147	+	0.396240i	$0.129685\pi$
$132$	−29.9611	−2.60778
$133$	1.58840	0.137732
$134$	6.66556	0.575816
$135$	4.73464	0.407493
$136$	8.18067	0.701487
$137$	4.18841	0.357840	0.178920	−	0.983864i	$-0.442740\pi$
$137$	4.18841	0.357840	0.178920	+	0.983864i	$0.442740\pi$
$138$	−36.9864	−3.14849
$139$	−1.64264	−0.139327	−0.0696636	−	0.997571i	$-0.522193\pi$
$139$	−1.64264	−0.139327	−0.0696636	+	0.997571i	$0.522193\pi$
$140$	0.524585	0.0443355
$141$	−19.8315	−1.67012
$142$	−10.5787	−0.887745
$143$	−3.33792	−0.279131
$144$	−2.61243	−0.217703
$145$	−2.96432	−0.246173
$146$	21.1486	1.75027
$147$	−19.9707	−1.64715
$148$	−2.11740	−0.174049
$149$	0.782707	0.0641219	0.0320609	−	0.999486i	$-0.489793\pi$
$149$	0.782707	0.0641219	0.0320609	+	0.999486i	$0.489793\pi$
$150$	29.0925	2.37540
$151$	8.82419	0.718102	0.359051	−	0.933318i	$-0.383100\pi$
$151$	8.82419	0.718102	0.359051	+	0.933318i	$0.383100\pi$
$152$	−17.4591	−1.41612
$153$	−16.9581	−1.37098
$154$	1.74561	0.140665
$155$	−5.73648	−0.460765
$156$	8.97600	0.718655
$157$	−10.5723	−0.843763	−0.421882	−	0.906651i	$-0.638630\pi$
$157$	−10.5723	−0.843763	−0.421882	+	0.906651i	$0.638630\pi$
$158$	24.4826	1.94773
$159$	−38.6768	−3.06727
$160$	4.51013	0.356557
$161$	1.31352	0.103520
$162$	−6.61948	−0.520075
$163$	4.52550	0.354464	0.177232	−	0.984169i	$-0.443286\pi$
$163$	4.52550	0.354464	0.177232	+	0.984169i	$0.443286\pi$
$164$	−5.55977	−0.434145
$165$	−6.97758	−0.543204
$166$	−3.37699	−0.262105
$167$	23.7812	1.84024	0.920122	−	0.391632i	$-0.128089\pi$
$167$	23.7812	1.84024	0.920122	+	0.391632i	$0.128089\pi$
$168$	−1.68721	−0.130171
$169$	1.00000	0.0769231
$170$	5.30056	0.406535
$171$	36.1919	2.76766
$172$	−33.5106	−2.55516
$173$	8.48460	0.645072	0.322536	−	0.946557i	$-0.395465\pi$
$173$	8.48460	0.645072	0.322536	+	0.946557i	$0.395465\pi$
$174$	26.5255	2.01090
$175$	−1.03318	−0.0781009
$176$	1.65626	0.124845
$177$	10.6777	0.802589
$178$	16.5267	1.23873
$179$	−3.70508	−0.276931	−0.138465	−	0.990367i	$-0.544217\pi$
$179$	−3.70508	−0.276931	−0.138465	+	0.990367i	$0.544217\pi$
$180$	11.9527	0.890902
$181$	20.9145	1.55456	0.777281	−	0.629154i	$-0.216598\pi$
$181$	20.9145	1.55456	0.777281	+	0.629154i	$0.216598\pi$
$182$	−0.522964	−0.0387647
$183$	−32.1035	−2.37316
$184$	−14.4377	−1.06436
$185$	−0.493116	−0.0362546
$186$	51.3316	3.76381
$187$	10.7512	0.786209
$188$	−21.5377	−1.57080
$189$	1.50460	0.109443
$190$	−11.3124	−0.820690
$191$	−9.99153	−0.722962	−0.361481	−	0.932380i	$-0.617729\pi$
$191$	−9.99153	−0.722962	−0.361481	+	0.932380i	$0.617729\pi$
$192$	−37.5049	−2.70668
$193$	19.9574	1.43656	0.718282	−	0.695752i	$-0.244929\pi$
$193$	19.9574	1.43656	0.718282	+	0.695752i	$0.244929\pi$
$194$	−12.2628	−0.880416
$195$	2.09040	0.149697
$196$	−21.6888	−1.54920
$197$	11.2148	0.799023	0.399512	−	0.916728i	$-0.369180\pi$
$197$	11.2148	0.799023	0.399512	+	0.916728i	$0.369180\pi$
$198$	39.7739	2.82661
$199$	4.80276	0.340459	0.170229	−	0.985404i	$-0.445549\pi$
$199$	4.80276	0.340459	0.170229	+	0.985404i	$0.445549\pi$
$200$	11.3563	0.803015
$201$	−8.46696	−0.597213
$202$	−22.7353	−1.59965
$203$	−0.942016	−0.0661165
$204$	−28.9112	−2.02419
$205$	−1.29480	−0.0904329
$206$	−28.1072	−1.95832
$207$	29.9286	2.08018
$208$	−0.496194	−0.0344049
$209$	−22.9452	−1.58716
$210$	−1.09320	−0.0754383
$211$	−6.46430	−0.445021	−0.222510	−	0.974930i	$-0.571425\pi$
$211$	−6.46430	−0.445021	−0.222510	+	0.974930i	$0.571425\pi$
$212$	−42.0043	−2.88487
$213$	13.4376	0.920732
$214$	33.8520	2.31407
$215$	−7.80420	−0.532242
$216$	−16.5380	−1.12527
$217$	−1.82297	−0.123751
$218$	9.58258	0.649015
$219$	−26.8641	−1.81531
$220$	−7.57789	−0.510901
$221$	−3.22094	−0.216664
$222$	4.41254	0.296150
$223$	−1.79459	−0.120175	−0.0600874	−	0.998193i	$-0.519138\pi$
$223$	−1.79459	−0.120175	−0.0600874	+	0.998193i	$0.519138\pi$
$224$	1.43325	0.0957630
$225$	−23.5411	−1.56940
$226$	−35.5928	−2.36760
$227$	9.79583	0.650172	0.325086	−	0.945684i	$-0.394607\pi$
$227$	9.79583	0.650172	0.325086	+	0.945684i	$0.394607\pi$
$228$	61.7021	4.08632
$229$	−19.8591	−1.31232	−0.656162	−	0.754620i	$-0.727821\pi$
$229$	−19.8591	−1.31232	−0.656162	+	0.754620i	$0.727821\pi$
$230$	−9.35475	−0.616834
$231$	−2.21737	−0.145892
$232$	10.3543	0.679794
$233$	−21.0746	−1.38064	−0.690322	−	0.723502i	$-0.742531\pi$
$233$	−21.0746	−1.38064	−0.690322	+	0.723502i	$0.742531\pi$
$234$	−11.9158	−0.778959
$235$	−5.01587	−0.327199
$236$	11.5964	0.754861
$237$	−31.0992	−2.02011
$238$	1.68444	0.109186
$239$	29.6582	1.91843	0.959213	−	0.282684i	$-0.0912247\pi$
$239$	29.6582	1.91843	0.959213	+	0.282684i	$0.0912247\pi$
$240$	−1.03725	−0.0669539
$241$	5.26925	0.339422	0.169711	−	0.985494i	$-0.445717\pi$
$241$	5.26925	0.339422	0.169711	+	0.985494i	$0.445717\pi$
$242$	−0.320668	−0.0206133
$243$	−11.1259	−0.713727
$244$	−34.8655	−2.23203
$245$	−5.05106	−0.322700
$246$	11.5862	0.738712
$247$	6.87412	0.437390
$248$	20.0374	1.27238
$249$	4.28964	0.271845
$250$	15.5865	0.985775
$251$	6.16806	0.389324	0.194662	−	0.980870i	$-0.437639\pi$
$251$	6.16806	0.389324	0.194662	+	0.980870i	$0.437639\pi$
$252$	3.79839	0.239276
$253$	−18.9744	−1.19291
$254$	38.9991	2.44702
$255$	−6.73306	−0.421641
$256$	−12.6553	−0.790959
$257$	−3.02385	−0.188623	−0.0943113	−	0.995543i	$-0.530065\pi$
$257$	−3.02385	−0.188623	−0.0943113	+	0.995543i	$0.530065\pi$
$258$	69.8341	4.34768
$259$	−0.156705	−0.00973716
$260$	2.27025	0.140795
$261$	−21.4639	−1.32858
$262$	−47.5671	−2.93871
$263$	12.9573	0.798984	0.399492	−	0.916737i	$-0.369187\pi$
$263$	12.9573	0.798984	0.399492	+	0.916737i	$0.369187\pi$
$264$	24.3726	1.50003
$265$	−9.78229	−0.600921
$266$	−3.59492	−0.220419
$267$	−20.9931	−1.28476
$268$	−9.19540	−0.561698
$269$	−5.52691	−0.336982	−0.168491	−	0.985703i	$-0.553889\pi$
$269$	−5.52691	−0.336982	−0.168491	+	0.985703i	$0.553889\pi$
$270$	−10.7156	−0.652129
$271$	−4.95257	−0.300847	−0.150424	−	0.988622i	$-0.548064\pi$
$271$	−4.95257	−0.300847	−0.150424	+	0.988622i	$0.548064\pi$
$272$	1.59821	0.0969060
$273$	0.664297	0.0402051
$274$	−9.47935	−0.572668
$275$	14.9248	0.899998
$276$	51.0242	3.07130
$277$	−10.4964	−0.630670	−0.315335	−	0.948980i	$-0.602117\pi$
$277$	−10.4964	−0.630670	−0.315335	+	0.948980i	$0.602117\pi$
$278$	3.71768	0.222972
$279$	−41.5365	−2.48672
$280$	−0.426735	−0.0255023
$281$	10.4408	0.622846	0.311423	−	0.950271i	$-0.399194\pi$
$281$	10.4408	0.622846	0.311423	+	0.950271i	$0.399194\pi$
$282$	44.8833	2.67276
$283$	13.5942	0.808094	0.404047	−	0.914738i	$-0.367603\pi$
$283$	13.5942	0.808094	0.404047	+	0.914738i	$0.367603\pi$
$284$	14.5937	0.865979
$285$	14.3697	0.851186
$286$	7.55448	0.446706
$287$	−0.411468	−0.0242882
$288$	32.6567	1.92432
$289$	−6.62552	−0.389736
$290$	6.70894	0.393963
$291$	15.5769	0.913131
$292$	−29.1753	−1.70736
$293$	−17.8775	−1.04441	−0.522207	−	0.852818i	$-0.674891\pi$
$293$	−17.8775	−1.04441	−0.522207	+	0.852818i	$0.674891\pi$
$294$	45.1983	2.63602
$295$	2.70066	0.157238
$296$	1.72245	0.100115
$297$	−21.7346	−1.26117
$298$	−1.77145	−0.102617
$299$	5.68451	0.328744
$300$	−40.1343	−2.31715
$301$	−2.48005	−0.142948
$302$	−19.9712	−1.14921
$303$	28.8796	1.65909
$304$	−3.41090	−0.195629
$305$	−8.11974	−0.464935
$306$	38.3801	2.19404
$307$	−8.81980	−0.503372	−0.251686	−	0.967809i	$-0.580985\pi$
$307$	−8.81980	−0.503372	−0.251686	+	0.967809i	$0.580985\pi$
$308$	−2.40814	−0.137216
$309$	35.7033	2.03109
$310$	12.9830	0.737384
$311$	12.7692	0.724074	0.362037	−	0.932164i	$-0.382081\pi$
$311$	12.7692	0.724074	0.362037	+	0.932164i	$0.382081\pi$
$312$	−7.30173	−0.413379
$313$	−15.3799	−0.869323	−0.434662	−	0.900594i	$-0.643132\pi$
$313$	−15.3799	−0.869323	−0.434662	+	0.900594i	$0.643132\pi$
$314$	23.9276	1.35031
$315$	0.884598	0.0498415
$316$	−33.7747	−1.89998
$317$	−25.1672	−1.41353	−0.706764	−	0.707449i	$-0.749846\pi$
$317$	−25.1672	−1.41353	−0.706764	+	0.707449i	$0.749846\pi$
$318$	87.5346	4.90870
$319$	13.6079	0.761896
$320$	−9.48587	−0.530276
$321$	−43.0007	−2.40006
$322$	−2.97280	−0.165667
$323$	−22.1412	−1.23197
$324$	9.13183	0.507324
$325$	−4.47129	−0.248022
$326$	−10.2423	−0.567266
$327$	−12.1723	−0.673131
$328$	4.52272	0.249725
$329$	−1.59397	−0.0878782
$330$	15.7919	0.869315
$331$	−6.56601	−0.360901	−0.180450	−	0.983584i	$-0.557756\pi$
$331$	−6.56601	−0.360901	−0.180450	+	0.983584i	$0.557756\pi$
$332$	4.65869	0.255679
$333$	−3.57053	−0.195664
$334$	−53.8223	−2.94503
$335$	−2.14150	−0.117002
$336$	−0.329621	−0.0179823
$337$	−5.94918	−0.324072	−0.162036	−	0.986785i	$-0.551806\pi$
$337$	−5.94918	−0.324072	−0.162036	+	0.986785i	$0.551806\pi$
$338$	−2.26323	−0.123104
$339$	45.2119	2.45557
$340$	−7.31233	−0.396567
$341$	26.3337	1.42605
$342$	−81.9105	−4.42921
$343$	−3.22264	−0.174006
$344$	27.2599	1.46976
$345$	11.8829	0.639755
$346$	−19.2026	−1.03234
$347$	−10.7969	−0.579610	−0.289805	−	0.957086i	$-0.593590\pi$
$347$	−10.7969	−0.579610	−0.289805	+	0.957086i	$0.593590\pi$
$348$	−36.5930	−1.96159
$349$	6.09456	0.326234	0.163117	−	0.986607i	$-0.447845\pi$
$349$	6.09456	0.326234	0.163117	+	0.986607i	$0.447845\pi$
$350$	2.33832	0.124989
$351$	6.51144	0.347555
$352$	−20.7040	−1.10353
$353$	−14.3485	−0.763693	−0.381846	−	0.924226i	$-0.624712\pi$
$353$	−14.3485	−0.763693	−0.381846	+	0.924226i	$0.624712\pi$
$354$	−24.1662	−1.28442
$355$	3.39870	0.180384
$356$	−22.7992	−1.20835
$357$	−2.13967	−0.113243
$358$	8.38546	0.443185
$359$	−7.22186	−0.381155	−0.190578	−	0.981672i	$-0.561036\pi$
$359$	−7.22186	−0.381155	−0.190578	+	0.981672i	$0.561036\pi$
$360$	−9.72320	−0.512458
$361$	28.2535	1.48703
$362$	−47.3343	−2.48784
$363$	0.407330	0.0213793
$364$	0.721449	0.0378142
$365$	−6.79458	−0.355644
$366$	72.6577	3.79788
$367$	24.6065	1.28445	0.642224	−	0.766517i	$-0.278012\pi$
$367$	24.6065	1.28445	0.642224	+	0.766517i	$0.278012\pi$
$368$	−2.82062	−0.147035
$369$	−9.37535	−0.488061
$370$	1.11604	0.0580200
$371$	−3.10866	−0.161394
$372$	−70.8139	−3.67153
$373$	15.4082	0.797806	0.398903	−	0.916993i	$-0.369391\pi$
$373$	15.4082	0.797806	0.398903	+	0.916993i	$0.369391\pi$
$374$	−24.3326	−1.25821
$375$	−19.7988	−1.02241
$376$	17.5203	0.903542
$377$	−4.07676	−0.209964
$378$	−3.40525	−0.175147
$379$	16.8279	0.864391	0.432195	−	0.901780i	$-0.357739\pi$
$379$	16.8279	0.864391	0.432195	+	0.901780i	$0.357739\pi$
$380$	15.6059	0.800568
$381$	−49.5388	−2.53795
$382$	22.6131	1.15699
$383$	1.67797	0.0857405	0.0428702	−	0.999081i	$-0.486350\pi$
$383$	1.67797	0.0857405	0.0428702	+	0.999081i	$0.486350\pi$
$384$	49.2183	2.51166
$385$	−0.560826	−0.0285823
$386$	−45.1682	−2.29900
$387$	−56.5083	−2.87248
$388$	16.9170	0.858830
$389$	4.70040	0.238320	0.119160	−	0.992875i	$-0.461980\pi$
$389$	4.70040	0.238320	0.119160	+	0.992875i	$0.461980\pi$
$390$	−4.73106	−0.239567
$391$	−18.3095	−0.925951
$392$	17.6433	0.891119
$393$	60.4224	3.04791
$394$	−25.3818	−1.27871
$395$	−7.86572	−0.395767
$396$	−54.8696	−2.75730
$397$	−11.8147	−0.592965	−0.296482	−	0.955038i	$-0.595814\pi$
$397$	−11.8147	−0.592965	−0.296482	+	0.955038i	$0.595814\pi$
$398$	−10.8698	−0.544852
$399$	4.56646	0.228609
$400$	2.21863	0.110931
$401$	−28.4064	−1.41855	−0.709273	−	0.704934i	$-0.750977\pi$
$401$	−28.4064	−1.41855	−0.709273	+	0.704934i	$0.750977\pi$
$402$	19.1627	0.955748
$403$	−7.88925	−0.392992
$404$	31.3642	1.56043
$405$	2.12669	0.105676
$406$	2.13200	0.105809
$407$	2.26368	0.112206
$408$	23.5185	1.16434
$409$	−6.04617	−0.298964	−0.149482	−	0.988764i	$-0.547761\pi$
$409$	−6.04617	−0.298964	−0.149482	+	0.988764i	$0.547761\pi$
$410$	2.93044	0.144724
$411$	12.0412	0.593948
$412$	38.7750	1.91031
$413$	0.858227	0.0422306
$414$	−67.7354	−3.32902
$415$	1.08495	0.0532582
$416$	6.20268	0.304111
$417$	−4.72240	−0.231257
$418$	51.9304	2.54000
$419$	−29.6068	−1.44639	−0.723194	−	0.690644i	$-0.757327\pi$
$419$	−29.6068	−1.44639	−0.723194	+	0.690644i	$0.757327\pi$
$420$	1.50812	0.0735886
$421$	5.27427	0.257052	0.128526	−	0.991706i	$-0.458975\pi$
$421$	5.27427	0.257052	0.128526	+	0.991706i	$0.458975\pi$
$422$	14.6302	0.712188
$423$	−36.3187	−1.76587
$424$	34.1694	1.65941
$425$	14.4018	0.698588
$426$	−30.4125	−1.47349
$427$	−2.58033	−0.124871
$428$	−46.7002	−2.25734
$429$	−9.59611	−0.463305
$430$	17.6627	0.851771
$431$	2.20419	0.106172	0.0530859	−	0.998590i	$-0.483094\pi$
$431$	2.20419	0.106172	0.0530859	+	0.998590i	$0.483094\pi$
$432$	−3.23094	−0.155449
$433$	−30.8102	−1.48064	−0.740322	−	0.672252i	$-0.765327\pi$
$433$	−30.8102	−1.48064	−0.740322	+	0.672252i	$0.765327\pi$
$434$	4.12579	0.198044
$435$	−8.52207	−0.408602
$436$	−13.2196	−0.633102
$437$	39.0760	1.86926
$438$	60.7997	2.90512
$439$	−1.74225	−0.0831531	−0.0415766	−	0.999135i	$-0.513238\pi$
$439$	−1.74225	−0.0831531	−0.0415766	+	0.999135i	$0.513238\pi$
$440$	6.16440	0.293876
$441$	−36.5735	−1.74159
$442$	7.28974	0.346738
$443$	−7.07615	−0.336198	−0.168099	−	0.985770i	$-0.553763\pi$
$443$	−7.07615	−0.336198	−0.168099	+	0.985770i	$0.553763\pi$
$444$	−6.08727	−0.288889
$445$	−5.30965	−0.251702
$446$	4.06158	0.192321
$447$	2.25019	0.106430
$448$	−3.01447	−0.142420
$449$	3.08120	0.145411	0.0727054	−	0.997353i	$-0.476837\pi$
$449$	3.08120	0.145411	0.0727054	+	0.997353i	$0.476837\pi$
$450$	53.2789	2.51159
$451$	5.94387	0.279886
$452$	49.1016	2.30955
$453$	25.3685	1.19192
$454$	−22.1702	−1.04050
$455$	0.168017	0.00787674
$456$	−50.1930	−2.35050
$457$	29.2582	1.36864	0.684321	−	0.729181i	$-0.260099\pi$
$457$	29.2582	1.36864	0.684321	+	0.729181i	$0.260099\pi$
$458$	44.9457	2.10017
$459$	−20.9730	−0.978935
$460$	12.9052	0.601710
$461$	−21.4103	−0.997177	−0.498589	−	0.866839i	$-0.666148\pi$
$461$	−21.4103	−0.997177	−0.498589	+	0.866839i	$0.666148\pi$
$462$	5.01842	0.233478
$463$	−0.171564	−0.00797325	−0.00398662	−	0.999992i	$-0.501269\pi$
$463$	−0.171564	−0.00797325	−0.00398662	+	0.999992i	$0.501269\pi$
$464$	2.02287	0.0939092
$465$	−16.4917	−0.764784
$466$	47.6967	2.20951
$467$	0.438115	0.0202736	0.0101368	−	0.999949i	$-0.496773\pi$
$467$	0.438115	0.0202736	0.0101368	+	0.999949i	$0.496773\pi$
$468$	16.4383	0.759860
$469$	−0.680534	−0.0314242
$470$	11.3521	0.523632
$471$	−30.3942	−1.40049
$472$	−9.43334	−0.434205
$473$	35.8256	1.64726
$474$	70.3846	3.23287
$475$	−30.7362	−1.41027
$476$	−2.32375	−0.106509
$477$	−70.8312	−3.24314
$478$	−67.1233	−3.07015
$479$	22.0409	1.00707	0.503537	−	0.863973i	$-0.332032\pi$
$479$	22.0409	1.00707	0.503537	+	0.863973i	$0.332032\pi$
$480$	12.9661	0.591818
$481$	−0.678172	−0.0309220
$482$	−11.9255	−0.543193
$483$	3.77621	0.171823
$484$	0.442374	0.0201079
$485$	3.93976	0.178895
$486$	25.1805	1.14221
$487$	3.21183	0.145542	0.0727709	−	0.997349i	$-0.476816\pi$
$487$	3.21183	0.145542	0.0727709	+	0.997349i	$0.476816\pi$
$488$	28.3621	1.28389
$489$	13.0103	0.588345
$490$	11.4317	0.516432
$491$	39.8075	1.79649	0.898243	−	0.439500i	$-0.144844\pi$
$491$	39.8075	1.79649	0.898243	+	0.439500i	$0.144844\pi$
$492$	−15.9837	−0.720600
$493$	13.1310	0.591392
$494$	−15.5577	−0.699975
$495$	−12.7785	−0.574349
$496$	3.91460	0.175771
$497$	1.08006	0.0484471
$498$	−9.70845	−0.435046
$499$	−20.5000	−0.917708	−0.458854	−	0.888512i	$-0.651740\pi$
$499$	−20.5000	−0.917708	−0.458854	+	0.888512i	$0.651740\pi$
$500$	−21.5021	−0.961605
$501$	68.3681	3.05446
$502$	−13.9597	−0.623054
$503$	38.2808	1.70686	0.853429	−	0.521209i	$-0.174519\pi$
$503$	38.2808	1.70686	0.853429	+	0.521209i	$0.174519\pi$
$504$	−3.08988	−0.137634
$505$	7.30435	0.325039
$506$	42.9435	1.90907
$507$	2.87488	0.127678
$508$	−53.8008	−2.38703
$509$	9.77141	0.433110	0.216555	−	0.976270i	$-0.430518\pi$
$509$	9.77141	0.433110	0.216555	+	0.976270i	$0.430518\pi$
$510$	15.2385	0.674771
$511$	−2.15921	−0.0955179
$512$	−5.59824	−0.247410
$513$	44.7604	1.97622
$514$	6.84367	0.301862
$515$	9.03023	0.397919
$516$	−96.3389	−4.24108
$517$	23.0256	1.01267
$518$	0.354659	0.0155828
$519$	24.3922	1.07070
$520$	−1.84678	−0.0809867
$521$	7.79097	0.341328	0.170664	−	0.985329i	$-0.445409\pi$
$521$	7.79097	0.341328	0.170664	+	0.985329i	$0.445409\pi$
$522$	48.5778	2.12619
$523$	−10.7245	−0.468947	−0.234474	−	0.972122i	$-0.575337\pi$
$523$	−10.7245	−0.468947	−0.234474	+	0.972122i	$0.575337\pi$
$524$	65.6207	2.86665
$525$	−2.97027	−0.129633
$526$	−29.3255	−1.27865
$527$	25.4108	1.10691
$528$	4.76154	0.207219
$529$	9.31370	0.404943
$530$	22.1396	0.961682
$531$	19.5548	0.848606
$532$	4.95933	0.215014
$533$	−1.78071	−0.0771312
$534$	47.5122	2.05605
$535$	−10.8759	−0.470206
$536$	7.48020	0.323096
$537$	−10.6517	−0.459654
$538$	12.5087	0.539288
$539$	23.1872	0.998743
$540$	14.7826	0.636140
$541$	38.4437	1.65282	0.826411	−	0.563067i	$-0.190379\pi$
$541$	38.4437	1.65282	0.826411	+	0.563067i	$0.190379\pi$
$542$	11.2088	0.481460
$543$	60.1267	2.58028
$544$	−19.9785	−0.856570
$545$	−3.07867	−0.131876
$546$	−1.50346	−0.0643421
$547$	0.255008	0.0109034	0.00545168	−	0.999985i	$-0.498265\pi$
$547$	0.255008	0.0109034	0.00545168	+	0.999985i	$0.498265\pi$
$548$	13.0771	0.558627
$549$	−58.7931	−2.50923
$550$	−33.7782	−1.44031
$551$	−28.0242	−1.19387
$552$	−41.5068	−1.76665
$553$	−2.49961	−0.106294
$554$	23.7559	1.00929
$555$	−1.41765	−0.0601759
$556$	−5.12869	−0.217505
$557$	−3.93264	−0.166631	−0.0833157	−	0.996523i	$-0.526551\pi$
$557$	−3.93264	−0.166631	−0.0833157	+	0.996523i	$0.526551\pi$
$558$	94.0066	3.97962
$559$	−10.7329	−0.453955
$560$	−0.0833689	−0.00352298
$561$	30.9085	1.30496
$562$	−23.6300	−0.996770
$563$	−5.44011	−0.229274	−0.114637	−	0.993407i	$-0.536570\pi$
$563$	−5.44011	−0.229274	−0.114637	+	0.993407i	$0.536570\pi$
$564$	−61.9183	−2.60723
$565$	11.4352	0.481081
$566$	−30.7669	−1.29323
$567$	0.675830	0.0283822
$568$	−11.8716	−0.498121
$569$	13.0844	0.548528	0.274264	−	0.961654i	$-0.411566\pi$
$569$	13.0844	0.548528	0.274264	+	0.961654i	$0.411566\pi$
$570$	−32.5219	−1.36219
$571$	35.9286	1.50356	0.751782	−	0.659412i	$-0.229195\pi$
$571$	35.9286	1.50356	0.751782	+	0.659412i	$0.229195\pi$
$572$	−10.4217	−0.435753
$573$	−28.7245	−1.19998
$574$	0.931248	0.0388695
$575$	−25.4171	−1.05997
$576$	−68.6849	−2.86187
$577$	−34.1241	−1.42060	−0.710302	−	0.703897i	$-0.751441\pi$
$577$	−34.1241	−1.42060	−0.710302	+	0.703897i	$0.751441\pi$
$578$	14.9951	0.623713
$579$	57.3751	2.38443
$580$	−9.25525	−0.384303
$581$	0.344781	0.0143039
$582$	−35.2540	−1.46133
$583$	44.9062	1.85982
$584$	23.7333	0.982092
$585$	3.82828	0.158280
$586$	40.4609	1.67143
$587$	18.9242	0.781087	0.390543	−	0.920584i	$-0.372287\pi$
$587$	18.9242	0.781087	0.390543	+	0.920584i	$0.372287\pi$
$588$	−62.3528	−2.57138
$589$	−54.2317	−2.23458
$590$	−6.11221	−0.251636
$591$	32.2413	1.32623
$592$	0.336505	0.0138303
$593$	32.0440	1.31589	0.657944	−	0.753067i	$-0.271426\pi$
$593$	32.0440	1.31589	0.657944	+	0.753067i	$0.271426\pi$
$594$	49.1905	2.01831
$595$	−0.541172	−0.0221859
$596$	2.44378	0.100101
$597$	13.8074	0.565098
$598$	−12.8654	−0.526104
$599$	−43.6287	−1.78262	−0.891311	−	0.453393i	$-0.850213\pi$
$599$	−43.6287	−1.78262	−0.891311	+	0.453393i	$0.850213\pi$
$600$	32.6481	1.33285
$601$	21.5082	0.877339	0.438670	−	0.898648i	$-0.355450\pi$
$601$	21.5082	0.877339	0.438670	+	0.898648i	$0.355450\pi$
$602$	5.61294	0.228766
$603$	−15.5060	−0.631455
$604$	27.5510	1.12104
$605$	0.103024	0.00418850
$606$	−65.3613	−2.65512
$607$	−43.7596	−1.77615	−0.888073	−	0.459702i	$-0.847956\pi$
$607$	−43.7596	−1.77615	−0.888073	+	0.459702i	$0.847956\pi$
$608$	42.6380	1.72920
$609$	−2.70818	−0.109741
$610$	18.3769	0.744057
$611$	−6.89821	−0.279072
$612$	−52.9468	−2.14025
$613$	−40.7041	−1.64402	−0.822012	−	0.569471i	$-0.807148\pi$
$613$	−40.7041	−1.64402	−0.822012	+	0.569471i	$0.807148\pi$
$614$	19.9612	0.805570
$615$	−3.72240	−0.150102
$616$	1.95895	0.0789285
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	−80.8049	−3.25045
$619$	−11.0672	−0.444828	−0.222414	−	0.974952i	$-0.571394\pi$
$619$	−11.0672	−0.444828	−0.222414	+	0.974952i	$0.571394\pi$
$620$	−17.9105	−0.719304
$621$	37.0144	1.48534
$622$	−28.8996	−1.15877
$623$	−1.68733	−0.0676013
$624$	−1.42650	−0.0571057
$625$	17.3489	0.693954
$626$	34.8083	1.39122
$627$	−65.9648	−2.63438
$628$	−33.0091	−1.31721
$629$	2.18435	0.0870958
$630$	−2.00205	−0.0797636
$631$	42.4297	1.68910	0.844550	−	0.535477i	$-0.179868\pi$
$631$	42.4297	1.68910	0.844550	+	0.535477i	$0.179868\pi$
$632$	27.4748	1.09289
$633$	−18.5841	−0.738652
$634$	56.9591	2.26213
$635$	−12.5295	−0.497220
$636$	−120.757	−4.78834
$637$	−6.94661	−0.275235
$638$	−30.7978	−1.21930
$639$	24.6092	0.973523
$640$	12.4485	0.492069
$641$	30.2692	1.19556	0.597782	−	0.801659i	$-0.296049\pi$
$641$	30.2692	1.19556	0.597782	+	0.801659i	$0.296049\pi$
$642$	97.3205	3.84093
$643$	41.8938	1.65213	0.826065	−	0.563575i	$-0.190574\pi$
$643$	41.8938	1.65213	0.826065	+	0.563575i	$0.190574\pi$
$644$	4.10109	0.161606
$645$	−22.4361	−0.883422
$646$	50.1106	1.97157
$647$	22.0340	0.866246	0.433123	−	0.901335i	$-0.357412\pi$
$647$	22.0340	0.866246	0.433123	+	0.901335i	$0.357412\pi$
$648$	−7.42849	−0.291819
$649$	−12.3975	−0.486646
$650$	10.1196	0.396922
$651$	−5.24081	−0.205404
$652$	14.1296	0.553358
$653$	−40.6267	−1.58985	−0.794923	−	0.606710i	$-0.792489\pi$
$653$	−40.6267	−1.58985	−0.794923	+	0.606710i	$0.792489\pi$
$654$	27.5488	1.07724
$655$	15.2823	0.597127
$656$	0.883579	0.0344980
$657$	−49.1979	−1.91939
$658$	3.60751	0.140636
$659$	−29.4560	−1.14744	−0.573721	−	0.819051i	$-0.694501\pi$
$659$	−29.4560	−1.14744	−0.573721	+	0.819051i	$0.694501\pi$
$660$	−21.7855	−0.848001
$661$	−19.2038	−0.746940	−0.373470	−	0.927642i	$-0.621832\pi$
$661$	−19.2038	−0.746940	−0.373470	+	0.927642i	$0.621832\pi$
$662$	14.8604	0.577566
$663$	−9.25983	−0.359622
$664$	−3.78972	−0.147070
$665$	1.15497	0.0447877
$666$	8.08095	0.313130
$667$	−23.1744	−0.897317
$668$	74.2500	2.87282
$669$	−5.15924	−0.199468
$670$	4.84670	0.187244
$671$	37.2742	1.43895
$672$	4.12042	0.158949
$673$	24.0230	0.926018	0.463009	−	0.886353i	$-0.346770\pi$
$673$	24.0230	0.926018	0.463009	+	0.886353i	$0.346770\pi$
$674$	13.4644	0.518628
$675$	−29.1145	−1.12062
$676$	3.12222	0.120085
$677$	−31.2762	−1.20204	−0.601022	−	0.799233i	$-0.705240\pi$
$677$	−31.2762	−1.20204	−0.601022	+	0.799233i	$0.705240\pi$
$678$	−102.325	−3.92977
$679$	1.25199	0.0480471
$680$	5.94838	0.228110
$681$	28.1618	1.07916
$682$	−59.5992	−2.28217
$683$	27.7739	1.06274	0.531368	−	0.847141i	$-0.321678\pi$
$683$	27.7739	1.06274	0.531368	+	0.847141i	$0.321678\pi$
$684$	112.999	4.32062
$685$	3.04550	0.116363
$686$	7.29357	0.278470
$687$	−57.0925	−2.17821
$688$	5.32562	0.203037
$689$	−13.4534	−0.512532
$690$	−26.8938	−1.02383
$691$	17.4490	0.663791	0.331896	−	0.943316i	$-0.392312\pi$
$691$	17.4490	0.663791	0.331896	+	0.943316i	$0.392312\pi$
$692$	26.4908	1.00703
$693$	−4.06080	−0.154257
$694$	24.4360	0.927576
$695$	−1.19441	−0.0453065
$696$	29.7674	1.12833
$697$	5.73557	0.217250
$698$	−13.7934	−0.522088
$699$	−60.5870	−2.29161
$700$	−3.22581	−0.121924
$701$	34.0334	1.28542	0.642712	−	0.766108i	$-0.277809\pi$
$701$	34.0334	1.28542	0.642712	+	0.766108i	$0.277809\pi$
$702$	−14.7369	−0.556208
$703$	−4.66183	−0.175824
$704$	43.5455	1.64118
$705$	−14.4200	−0.543089
$706$	32.4740	1.22217
$707$	2.32121	0.0872981
$708$	33.3382	1.25293
$709$	−9.92587	−0.372774	−0.186387	−	0.982476i	$-0.559678\pi$
$709$	−9.92587	−0.372774	−0.186387	+	0.982476i	$0.559678\pi$
$710$	−7.69205	−0.288677
$711$	−56.9537	−2.13593
$712$	18.5465	0.695060
$713$	−44.8466	−1.67952
$714$	4.84256	0.181228
$715$	−2.42709	−0.0907679
$716$	−11.5681	−0.432319
$717$	85.2637	3.18423
$718$	16.3447	0.609980
$719$	−22.7950	−0.850110	−0.425055	−	0.905168i	$-0.639745\pi$
$719$	−22.7950	−0.850110	−0.425055	+	0.905168i	$0.639745\pi$
$720$	−1.89957	−0.0707928
$721$	2.86967	0.106872
$722$	−63.9443	−2.37976
$723$	15.1485	0.563377
$724$	65.2996	2.42684
$725$	18.2284	0.676985
$726$	−0.921883	−0.0342143
$727$	12.8379	0.476132	0.238066	−	0.971249i	$-0.423487\pi$
$727$	12.8379	0.476132	0.238066	+	0.971249i	$0.423487\pi$
$728$	−0.586879	−0.0217512
$729$	−40.7600	−1.50963
$730$	15.3777	0.569154
$731$	34.5702	1.27862
$732$	−100.234	−3.70476
$733$	31.0559	1.14708	0.573539	−	0.819178i	$-0.305570\pi$
$733$	31.0559	1.14708	0.573539	+	0.819178i	$0.305570\pi$
$734$	−55.6901	−2.05556
$735$	−14.5212	−0.535622
$736$	35.2592	1.29967
$737$	9.83066	0.362117
$738$	21.2186	0.781067
$739$	−19.5811	−0.720302	−0.360151	−	0.932894i	$-0.617275\pi$
$739$	−19.5811	−0.720302	−0.360151	+	0.932894i	$0.617275\pi$
$740$	−1.53962	−0.0565974
$741$	19.7623	0.725986
$742$	7.03562	0.258286
$743$	20.3408	0.746232	0.373116	−	0.927785i	$-0.378289\pi$
$743$	20.3408	0.746232	0.373116	+	0.927785i	$0.378289\pi$
$744$	57.6052	2.11191
$745$	0.569127	0.0208512
$746$	−34.8723	−1.27677
$747$	7.85588	0.287432
$748$	33.5677	1.22736
$749$	−3.45619	−0.126287
$750$	44.8092	1.63620
$751$	−25.8205	−0.942204	−0.471102	−	0.882079i	$-0.656144\pi$
$751$	−25.8205	−0.942204	−0.471102	+	0.882079i	$0.656144\pi$
$752$	3.42285	0.124819
$753$	17.7324	0.646206
$754$	9.22666	0.336015
$755$	6.41630	0.233513
$756$	4.69767	0.170853
$757$	38.1845	1.38784	0.693920	−	0.720052i	$-0.255882\pi$
$757$	38.1845	1.38784	0.693920	+	0.720052i	$0.255882\pi$
$758$	−38.0854	−1.38332
$759$	−54.5492	−1.98001
$760$	−12.6950	−0.460496
$761$	−18.3843	−0.666432	−0.333216	−	0.942851i	$-0.608134\pi$
$761$	−18.3843	−0.666432	−0.333216	+	0.942851i	$0.608134\pi$
$762$	112.118	4.06160
$763$	−0.978355	−0.0354188
$764$	−31.1957	−1.12862
$765$	−12.3307	−0.445816
$766$	−3.79764	−0.137214
$767$	3.71415	0.134110
$768$	−36.3826	−1.31284
$769$	−41.9478	−1.51268	−0.756339	−	0.654180i	$-0.773014\pi$
$769$	−41.9478	−1.51268	−0.756339	+	0.654180i	$0.773014\pi$
$770$	1.26928	0.0457416
$771$	−8.69321	−0.313078
$772$	62.3113	2.24263
$773$	−2.88745	−0.103854	−0.0519272	−	0.998651i	$-0.516536\pi$
$773$	−2.88745	−0.103854	−0.0519272	+	0.998651i	$0.516536\pi$
$774$	127.891	4.59696
$775$	35.2751	1.26712
$776$	−13.7615	−0.494009
$777$	−0.450508	−0.0161619
$778$	−10.6381	−0.381394
$779$	−12.2408	−0.438573
$780$	6.52669	0.233693
$781$	−15.6019	−0.558281
$782$	41.4386	1.48184
$783$	−26.5456	−0.948662
$784$	3.44687	0.123102
$785$	−7.68741	−0.274375
$786$	−136.750	−4.87770
$787$	−40.8556	−1.45634	−0.728172	−	0.685394i	$-0.759630\pi$
$787$	−40.8556	−1.45634	−0.728172	+	0.685394i	$0.759630\pi$
$788$	35.0151	1.24736
$789$	37.2508	1.32616
$790$	17.8019	0.633365
$791$	3.63392	0.129207
$792$	44.6349	1.58603
$793$	−11.1669	−0.396548
$794$	26.7395	0.948949
$795$	−28.1229	−0.997417
$796$	14.9953	0.531493
$797$	−2.94119	−0.104182	−0.0520911	−	0.998642i	$-0.516589\pi$
$797$	−2.94119	−0.104182	−0.0520911	+	0.998642i	$0.516589\pi$
$798$	−10.3350	−0.365854
$799$	22.2187	0.786043
$800$	−27.7340	−0.980543
$801$	−38.4459	−1.35842
$802$	64.2902	2.27017
$803$	31.1909	1.10070
$804$	−26.4357	−0.932314
$805$	0.955093	0.0336626
$806$	17.8552	0.628923
$807$	−15.8892	−0.559327
$808$	−25.5139	−0.897577
$809$	−36.1523	−1.27105	−0.635523	−	0.772082i	$-0.719215\pi$
$809$	−36.1523	−1.27105	−0.635523	+	0.772082i	$0.719215\pi$
$810$	−4.81319	−0.169118
$811$	15.1272	0.531187	0.265593	−	0.964085i	$-0.414432\pi$
$811$	15.1272	0.531187	0.265593	+	0.964085i	$0.414432\pi$
$812$	−2.94118	−0.103215
$813$	−14.2381	−0.499350
$814$	−5.12323	−0.179569
$815$	3.29061	0.115265
$816$	4.59468	0.160846
$817$	−73.7795	−2.58122
$818$	13.6839	0.478446
$819$	1.21657	0.0425103
$820$	−4.04265	−0.141176
$821$	−53.7149	−1.87466	−0.937331	−	0.348440i	$-0.886711\pi$
$821$	−53.7149	−1.87466	−0.937331	+	0.348440i	$0.886711\pi$
$822$	−27.2520	−0.950523
$823$	−16.5464	−0.576771	−0.288385	−	0.957514i	$-0.593118\pi$
$823$	−16.5464	−0.576771	−0.288385	+	0.957514i	$0.593118\pi$
$824$	−31.5424	−1.09883
$825$	42.9070	1.49383
$826$	−1.94237	−0.0675836
$827$	32.1477	1.11788	0.558942	−	0.829207i	$-0.311208\pi$
$827$	32.1477	1.11788	0.558942	+	0.829207i	$0.311208\pi$
$828$	93.4437	3.24739
$829$	36.6747	1.27376	0.636882	−	0.770961i	$-0.280224\pi$
$829$	36.6747	1.27376	0.636882	+	0.770961i	$0.280224\pi$
$830$	−2.45550	−0.0852316
$831$	−30.1760	−1.04679
$832$	−13.0457	−0.452278
$833$	22.3746	0.775235
$834$	10.6879	0.370091
$835$	17.2919	0.598412
$836$	−71.6400	−2.47772
$837$	−51.3704	−1.77562
$838$	67.0071	2.31472
$839$	−24.5399	−0.847212	−0.423606	−	0.905846i	$-0.639236\pi$
$839$	−24.5399	−0.847212	−0.423606	+	0.905846i	$0.639236\pi$
$840$	−1.22681	−0.0423291
$841$	−12.3800	−0.426897
$842$	−11.9369	−0.411372
$843$	30.0161	1.03381
$844$	−20.1830	−0.694726
$845$	0.727126	0.0250139
$846$	82.1975	2.82601
$847$	0.0327393	0.00112494
$848$	6.67548	0.229237
$849$	39.0818	1.34129
$850$	−32.5945	−1.11798
$851$	−3.85508	−0.132150
$852$	41.9552	1.43736
$853$	−47.5215	−1.62710	−0.813552	−	0.581492i	$-0.802469\pi$
$853$	−47.5215	−1.62710	−0.813552	+	0.581492i	$0.802469\pi$
$854$	5.83989	0.199837
$855$	26.3160	0.899989
$856$	37.9893	1.29845
$857$	56.4179	1.92720	0.963600	−	0.267349i	$-0.0861476\pi$
$857$	56.4179	1.92720	0.963600	+	0.267349i	$0.0861476\pi$
$858$	21.7182	0.741448
$859$	−31.8299	−1.08602	−0.543011	−	0.839726i	$-0.682716\pi$
$859$	−31.8299	−1.08602	−0.543011	+	0.839726i	$0.682716\pi$
$860$	−24.3664	−0.830887
$861$	−1.18292	−0.0403139
$862$	−4.98858	−0.169912
$863$	−20.4909	−0.697518	−0.348759	−	0.937212i	$-0.613397\pi$
$863$	−20.4909	−0.697518	−0.348759	+	0.937212i	$0.613397\pi$
$864$	40.3884	1.37404
$865$	6.16937	0.209765
$866$	69.7306	2.36954
$867$	−19.0476	−0.646890
$868$	−5.69169	−0.193189
$869$	36.1081	1.22488
$870$	19.2874	0.653905
$871$	−2.94515	−0.0997926
$872$	10.7537	0.364168
$873$	28.5268	0.965487
$874$	−88.4381	−2.99146
$875$	−1.59133	−0.0537969
$876$	−83.8756	−2.83389
$877$	−12.5402	−0.423452	−0.211726	−	0.977329i	$-0.567908\pi$
$877$	−12.5402	−0.423452	−0.211726	+	0.977329i	$0.567908\pi$
$878$	3.94312	0.133074
$879$	−51.3957	−1.73353
$880$	1.20431	0.0405972
$881$	−7.60706	−0.256288	−0.128144	−	0.991756i	$-0.540902\pi$
$881$	−7.60706	−0.256288	−0.128144	+	0.991756i	$0.540902\pi$
$882$	82.7743	2.78715
$883$	−38.5940	−1.29879	−0.649396	−	0.760450i	$-0.724978\pi$
$883$	−38.5940	−1.29879	−0.649396	+	0.760450i	$0.724978\pi$
$884$	−10.0565	−0.338236
$885$	7.76407	0.260986
$886$	16.0150	0.538034
$887$	−43.4524	−1.45899	−0.729495	−	0.683986i	$-0.760245\pi$
$887$	−43.4524	−1.45899	−0.729495	+	0.683986i	$0.760245\pi$
$888$	4.95183	0.166172
$889$	−3.98170	−0.133542
$890$	12.0170	0.402810
$891$	−9.76270	−0.327063
$892$	−5.60311	−0.187606
$893$	−47.4191	−1.58682
$894$	−5.09270	−0.170325
$895$	−2.69406	−0.0900526
$896$	3.95593	0.132158
$897$	16.3423	0.545654
$898$	−6.97347	−0.232708
$899$	32.1626	1.07268
$900$	−73.5003	−2.45001
$901$	43.3325	1.44362
$902$	−13.4523	−0.447914
$903$	−7.12986	−0.237267
$904$	−39.9428	−1.32848
$905$	15.2075	0.505514
$906$	−57.4148	−1.90748
$907$	−4.21894	−0.140088	−0.0700439	−	0.997544i	$-0.522314\pi$
$907$	−4.21894	−0.140088	−0.0700439	+	0.997544i	$0.522314\pi$
$908$	30.5847	1.01499
$909$	52.8890	1.75422
$910$	−0.380261	−0.0126055
$911$	−29.4628	−0.976147	−0.488073	−	0.872803i	$-0.662300\pi$
$911$	−29.4628	−0.976147	−0.488073	+	0.872803i	$0.662300\pi$
$912$	−9.80593	−0.324707
$913$	−4.98054	−0.164832
$914$	−66.2181	−2.19030
$915$	−23.3433	−0.771706
$916$	−62.0044	−2.04868
$917$	4.85647	0.160375
$918$	47.4667	1.56664
$919$	−23.8998	−0.788382	−0.394191	−	0.919029i	$-0.628975\pi$
$919$	−23.8998	−0.788382	−0.394191	+	0.919029i	$0.628975\pi$
$920$	−10.4981	−0.346111
$921$	−25.3559	−0.835504
$922$	48.4565	1.59583
$923$	4.67416	0.153852
$924$	−6.92311	−0.227754
$925$	3.03230	0.0997014
$926$	0.388289	0.0127600
$927$	65.3857	2.14755
$928$	−25.2868	−0.830081
$929$	45.3090	1.48654	0.743271	−	0.668991i	$-0.233274\pi$
$929$	45.3090	1.48654	0.743271	+	0.668991i	$0.233274\pi$
$930$	37.3245	1.22392
$931$	−47.7518	−1.56500
$932$	−65.7995	−2.15533
$933$	36.7099	1.20183
$934$	−0.991557	−0.0324447
$935$	7.81751	0.255660
$936$	−13.3721	−0.437081
$937$	−7.03101	−0.229693	−0.114847	−	0.993383i	$-0.536638\pi$
$937$	−7.03101	−0.229693	−0.114847	+	0.993383i	$0.536638\pi$
$938$	1.54021	0.0502895
$939$	−44.2154	−1.44291
$940$	−15.6606	−0.510793
$941$	45.0322	1.46801	0.734004	−	0.679146i	$-0.237650\pi$
$941$	45.0322	1.46801	0.734004	+	0.679146i	$0.237650\pi$
$942$	68.7890	2.24127
$943$	−10.1225	−0.329633
$944$	−1.84294	−0.0599826
$945$	1.09403	0.0355888
$946$	−81.0817	−2.63619
$947$	16.5944	0.539246	0.269623	−	0.962966i	$-0.413101\pi$
$947$	16.5944	0.539246	0.269623	+	0.962966i	$0.413101\pi$
$948$	−97.0983	−3.15361
$949$	−9.34443	−0.303333
$950$	69.5631	2.25692
$951$	−72.3526	−2.34619
$952$	1.89030	0.0612651
$953$	−6.82136	−0.220965	−0.110483	−	0.993878i	$-0.535240\pi$
$953$	−6.82136	−0.220965	−0.110483	+	0.993878i	$0.535240\pi$
$954$	160.307	5.19014
$955$	−7.26510	−0.235093
$956$	92.5992	2.99487
$957$	39.1211	1.26460
$958$	−49.8837	−1.61167
$959$	0.967815	0.0312524
$960$	−27.2708	−0.880160
$961$	31.2403	1.00775
$962$	1.53486	0.0494859
$963$	−78.7497	−2.53767
$964$	16.4517	0.529874
$965$	14.5115	0.467143
$966$	−8.54643	−0.274977
$967$	−11.8405	−0.380764	−0.190382	−	0.981710i	$-0.560973\pi$
$967$	−11.8405	−0.380764	−0.190382	+	0.981710i	$0.560973\pi$
$968$	−0.359859	−0.0115663
$969$	−63.6532	−2.04484
$970$	−8.91658	−0.286294
$971$	−21.0574	−0.675764	−0.337882	−	0.941189i	$-0.609710\pi$
$971$	−21.0574	−0.675764	−0.337882	+	0.941189i	$0.609710\pi$
$972$	−34.7375	−1.11420
$973$	−0.379565	−0.0121683
$974$	−7.26910	−0.232917
$975$	−12.8544	−0.411671
$976$	5.54095	0.177362
$977$	−26.8184	−0.857996	−0.428998	−	0.903305i	$-0.641133\pi$
$977$	−26.8184	−0.857996	−0.428998	+	0.903305i	$0.641133\pi$
$978$	−29.4453	−0.941556
$979$	24.3743	0.779005
$980$	−15.7705	−0.503770
$981$	−22.2919	−0.711726
$982$	−90.0935	−2.87500
$983$	−10.5295	−0.335839	−0.167920	−	0.985801i	$-0.553705\pi$
$983$	−10.5295	−0.335839	−0.167920	+	0.985801i	$0.553705\pi$
$984$	13.0023	0.414497
$985$	8.15459	0.259827
$986$	−29.7186	−0.946431
$987$	−4.58246	−0.145861
$988$	21.4625	0.682813
$989$	−61.0115	−1.94005
$990$	28.9206	0.919158
$991$	−1.12636	−0.0357799	−0.0178900	−	0.999840i	$-0.505695\pi$
$991$	−1.12636	−0.0357799	−0.0178900	+	0.999840i	$0.505695\pi$
$992$	−48.9345	−1.55367
$993$	−18.8765	−0.599028
$994$	−2.44441	−0.0775321
$995$	3.49222	0.110711
$996$	13.3932	0.424380
$997$	28.5834	0.905247	0.452623	−	0.891702i	$-0.350488\pi$
$997$	28.5834	0.905247	0.452623	+	0.891702i	$0.350488\pi$
$998$	46.3964	1.46865
$999$	−4.41587	−0.139712

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.a.1.15	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.a.1.15	✓	134	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.26323 q^{2} +2.87488 q^{3} +3.12222 q^{4} +0.727126 q^{5} -6.50652 q^{6} +0.231070 q^{7} -2.53984 q^{8} +5.26494 q^{9} +O(q^{10})\)	\(q-2.26323 q^{2} +2.87488 q^{3} +3.12222 q^{4} +0.727126 q^{5} -6.50652 q^{6} +0.231070 q^{7} -2.53984 q^{8} +5.26494 q^{9} -1.64565 q^{10} -3.33792 q^{11} +8.97600 q^{12} +1.00000 q^{13} -0.522964 q^{14} +2.09040 q^{15} -0.496194 q^{16} -3.22094 q^{17} -11.9158 q^{18} +6.87412 q^{19} +2.27025 q^{20} +0.664297 q^{21} +7.55448 q^{22} +5.68451 q^{23} -7.30173 q^{24} -4.47129 q^{25} -2.26323 q^{26} +6.51144 q^{27} +0.721449 q^{28} -4.07676 q^{29} -4.73106 q^{30} -7.88925 q^{31} +6.20268 q^{32} -9.59611 q^{33} +7.28974 q^{34} +0.168017 q^{35} +16.4383 q^{36} -0.678172 q^{37} -15.5577 q^{38} +2.87488 q^{39} -1.84678 q^{40} -1.78071 q^{41} -1.50346 q^{42} -10.7329 q^{43} -10.4217 q^{44} +3.82828 q^{45} -12.8654 q^{46} -6.89821 q^{47} -1.42650 q^{48} -6.94661 q^{49} +10.1196 q^{50} -9.25983 q^{51} +3.12222 q^{52} -13.4534 q^{53} -14.7369 q^{54} -2.42709 q^{55} -0.586879 q^{56} +19.7623 q^{57} +9.22666 q^{58} +3.71415 q^{59} +6.52669 q^{60} -11.1669 q^{61} +17.8552 q^{62} +1.21657 q^{63} -13.0457 q^{64} +0.727126 q^{65} +21.7182 q^{66} -2.94515 q^{67} -10.0565 q^{68} +16.3423 q^{69} -0.380261 q^{70} +4.67416 q^{71} -13.3721 q^{72} -9.34443 q^{73} +1.53486 q^{74} -12.8544 q^{75} +21.4625 q^{76} -0.771291 q^{77} -6.50652 q^{78} -10.8175 q^{79} -0.360796 q^{80} +2.92479 q^{81} +4.03016 q^{82} +1.49211 q^{83} +2.07408 q^{84} -2.34203 q^{85} +24.2911 q^{86} -11.7202 q^{87} +8.47776 q^{88} -7.30224 q^{89} -8.66428 q^{90} +0.231070 q^{91} +17.7483 q^{92} -22.6807 q^{93} +15.6122 q^{94} +4.99835 q^{95} +17.8320 q^{96} +5.41826 q^{97} +15.7218 q^{98} -17.5739 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * q^99

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