LMFDB - Embedded newform 6035.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, 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("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34625 q^{2} +1.66109 q^{3} +3.50491 q^{4} -1.00000 q^{5} -3.89733 q^{6} -1.01758 q^{7} -3.53091 q^{8} -0.240793 q^{9} +O(q^{10})$	\(q-2.34625 q^{2} +1.66109 q^{3} +3.50491 q^{4} -1.00000 q^{5} -3.89733 q^{6} -1.01758 q^{7} -3.53091 q^{8} -0.240793 q^{9} +2.34625 q^{10} +0.342582 q^{11} +5.82196 q^{12} +2.41384 q^{13} +2.38751 q^{14} -1.66109 q^{15} +1.27458 q^{16} -1.00000 q^{17} +0.564961 q^{18} -5.55646 q^{19} -3.50491 q^{20} -1.69030 q^{21} -0.803786 q^{22} +0.278087 q^{23} -5.86514 q^{24} +1.00000 q^{25} -5.66348 q^{26} -5.38324 q^{27} -3.56654 q^{28} +1.83484 q^{29} +3.89733 q^{30} +8.79367 q^{31} +4.07132 q^{32} +0.569059 q^{33} +2.34625 q^{34} +1.01758 q^{35} -0.843958 q^{36} +3.99848 q^{37} +13.0369 q^{38} +4.00959 q^{39} +3.53091 q^{40} +2.46978 q^{41} +3.96586 q^{42} -6.57818 q^{43} +1.20072 q^{44} +0.240793 q^{45} -0.652464 q^{46} +6.36834 q^{47} +2.11719 q^{48} -5.96452 q^{49} -2.34625 q^{50} -1.66109 q^{51} +8.46029 q^{52} +5.82214 q^{53} +12.6304 q^{54} -0.342582 q^{55} +3.59300 q^{56} -9.22977 q^{57} -4.30500 q^{58} -3.93844 q^{59} -5.82196 q^{60} +6.89457 q^{61} -20.6322 q^{62} +0.245027 q^{63} -12.1015 q^{64} -2.41384 q^{65} -1.33516 q^{66} -9.86463 q^{67} -3.50491 q^{68} +0.461927 q^{69} -2.38751 q^{70} -1.00000 q^{71} +0.850217 q^{72} -5.55609 q^{73} -9.38145 q^{74} +1.66109 q^{75} -19.4749 q^{76} -0.348607 q^{77} -9.40753 q^{78} +3.39968 q^{79} -1.27458 q^{80} -8.21964 q^{81} -5.79472 q^{82} -3.03118 q^{83} -5.92434 q^{84} +1.00000 q^{85} +15.4341 q^{86} +3.04783 q^{87} -1.20963 q^{88} -0.708567 q^{89} -0.564961 q^{90} -2.45629 q^{91} +0.974672 q^{92} +14.6070 q^{93} -14.9418 q^{94} +5.55646 q^{95} +6.76281 q^{96} +7.59597 q^{97} +13.9943 q^{98} -0.0824914 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4 q^{2} - 4 q^{3} + 38 q^{4} - 44 q^{5} - 2 q^{6} - 5 q^{7} - 12 q^{8} + 46 q^{9}+O(q^{10}) $ 44 * q - 4 * q^2 - 4 * q^3 + 38 * q^4 - 44 * q^5 - 2 * q^6 - 5 * q^7 - 12 * q^8 + 46 * q^9	\( 44 q - 4 q^{2} - 4 q^{3} + 38 q^{4} - 44 q^{5} - 2 q^{6} - 5 q^{7} - 12 q^{8} + 46 q^{9} + 4 q^{10} + 22 q^{11} - 28 q^{12} - 37 q^{13} + 4 q^{14} + 4 q^{15} + 22 q^{16} - 44 q^{17} - 27 q^{18} - 19 q^{19} - 38 q^{20} - 15 q^{21} - 31 q^{22} + 2 q^{23} + 9 q^{24} + 44 q^{25} - 2 q^{26} - 13 q^{27} - 16 q^{28} + 36 q^{29} + 2 q^{30} - 11 q^{31} - 33 q^{32} - 29 q^{33} + 4 q^{34} + 5 q^{35} + 68 q^{36} - 48 q^{37} - 13 q^{38} - 4 q^{39} + 12 q^{40} + 33 q^{41} - 16 q^{42} - 45 q^{43} + 49 q^{44} - 46 q^{45} + 2 q^{46} - 28 q^{47} - 54 q^{48} + 19 q^{49} - 4 q^{50} + 4 q^{51} - 95 q^{52} - 31 q^{53} - 20 q^{54} - 22 q^{55} - q^{56} - 26 q^{57} - 30 q^{58} + 28 q^{59} + 28 q^{60} - 57 q^{61} + 33 q^{62} - 40 q^{63} - 36 q^{64} + 37 q^{65} - 9 q^{66} - 27 q^{67} - 38 q^{68} - 89 q^{69} - 4 q^{70} - 44 q^{71} - 80 q^{72} - 37 q^{73} + 17 q^{74} - 4 q^{75} - 52 q^{76} - 103 q^{77} + 2 q^{78} - 21 q^{79} - 22 q^{80} + 36 q^{81} - 67 q^{82} - 50 q^{83} - 46 q^{84} + 44 q^{85} - 37 q^{86} - 80 q^{87} - 73 q^{88} + 27 q^{90} - 17 q^{91} - 56 q^{92} - 44 q^{93} - 28 q^{94} + 19 q^{95} + 73 q^{96} - 56 q^{97} - 8 q^{98} + 31 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 - 4 * q^3 + 38 * q^4 - 44 * q^5 - 2 * q^6 - 5 * q^7 - 12 * q^8 + 46 * q^9 + 4 * q^10 + 22 * q^11 - 28 * q^12 - 37 * q^13 + 4 * q^14 + 4 * q^15 + 22 * q^16 - 44 * q^17 - 27 * q^18 - 19 * q^19 - 38 * q^20 - 15 * q^21 - 31 * q^22 + 2 * q^23 + 9 * q^24 + 44 * q^25 - 2 * q^26 - 13 * q^27 - 16 * q^28 + 36 * q^29 + 2 * q^30 - 11 * q^31 - 33 * q^32 - 29 * q^33 + 4 * q^34 + 5 * q^35 + 68 * q^36 - 48 * q^37 - 13 * q^38 - 4 * q^39 + 12 * q^40 + 33 * q^41 - 16 * q^42 - 45 * q^43 + 49 * q^44 - 46 * q^45 + 2 * q^46 - 28 * q^47 - 54 * q^48 + 19 * q^49 - 4 * q^50 + 4 * q^51 - 95 * q^52 - 31 * q^53 - 20 * q^54 - 22 * q^55 - q^56 - 26 * q^57 - 30 * q^58 + 28 * q^59 + 28 * q^60 - 57 * q^61 + 33 * q^62 - 40 * q^63 - 36 * q^64 + 37 * q^65 - 9 * q^66 - 27 * q^67 - 38 * q^68 - 89 * q^69 - 4 * q^70 - 44 * q^71 - 80 * q^72 - 37 * q^73 + 17 * q^74 - 4 * q^75 - 52 * q^76 - 103 * q^77 + 2 * q^78 - 21 * q^79 - 22 * q^80 + 36 * q^81 - 67 * q^82 - 50 * q^83 - 46 * q^84 + 44 * q^85 - 37 * q^86 - 80 * q^87 - 73 * q^88 + 27 * q^90 - 17 * q^91 - 56 * q^92 - 44 * q^93 - 28 * q^94 + 19 * q^95 + 73 * q^96 - 56 * q^97 - 8 * q^98 + 31 * 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 $

$2$	−2.34625	−1.65905	−0.829526	−	0.558468i	$-0.811390\pi$
$2$	−2.34625	−1.65905	−0.829526	+	0.558468i	$0.811390\pi$
$3$	1.66109	0.959029	0.479514	−	0.877534i	$-0.340813\pi$
$3$	1.66109	0.959029	0.479514	+	0.877534i	$0.340813\pi$
$4$	3.50491	1.75246
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.89733	−1.59108
$7$	−1.01758	−0.384611	−0.192305	−	0.981335i	$-0.561596\pi$
$7$	−1.01758	−0.384611	−0.192305	+	0.981335i	$0.561596\pi$
$8$	−3.53091	−1.24836
$9$	−0.240793	−0.0802643
$10$	2.34625	0.741951
$11$	0.342582	0.103293	0.0516463	−	0.998665i	$-0.483553\pi$
$11$	0.342582	0.103293	0.0516463	+	0.998665i	$0.483553\pi$
$12$	5.82196	1.68066
$13$	2.41384	0.669479	0.334739	−	0.942311i	$-0.391352\pi$
$13$	2.41384	0.669479	0.334739	+	0.942311i	$0.391352\pi$
$14$	2.38751	0.638090
$15$	−1.66109	−0.428891
$16$	1.27458	0.318646
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.564961	0.133163
$19$	−5.55646	−1.27474	−0.637370	−	0.770558i	$-0.719978\pi$
$19$	−5.55646	−1.27474	−0.637370	+	0.770558i	$0.719978\pi$
$20$	−3.50491	−0.783722
$21$	−1.69030	−0.368853
$22$	−0.803786	−0.171368
$23$	0.278087	0.0579852	0.0289926	−	0.999580i	$-0.490770\pi$
$23$	0.278087	0.0579852	0.0289926	+	0.999580i	$0.490770\pi$
$24$	−5.86514	−1.19722
$25$	1.00000	0.200000
$26$	−5.66348	−1.11070
$27$	−5.38324	−1.03600
$28$	−3.56654	−0.674014
$29$	1.83484	0.340721	0.170361	−	0.985382i	$-0.445507\pi$
$29$	1.83484	0.340721	0.170361	+	0.985382i	$0.445507\pi$
$30$	3.89733	0.711552
$31$	8.79367	1.57939	0.789695	−	0.613500i	$-0.210239\pi$
$31$	8.79367	1.57939	0.789695	+	0.613500i	$0.210239\pi$
$32$	4.07132	0.719714
$33$	0.569059	0.0990605
$34$	2.34625	0.402379
$35$	1.01758	0.172003
$36$	−0.843958	−0.140660
$37$	3.99848	0.657346	0.328673	−	0.944444i	$-0.393399\pi$
$37$	3.99848	0.657346	0.328673	+	0.944444i	$0.393399\pi$
$38$	13.0369	2.11486
$39$	4.00959	0.642049
$40$	3.53091	0.558285
$41$	2.46978	0.385714	0.192857	−	0.981227i	$-0.438225\pi$
$41$	2.46978	0.385714	0.192857	+	0.981227i	$0.438225\pi$
$42$	3.96586	0.611946
$43$	−6.57818	−1.00316	−0.501581	−	0.865110i	$-0.667248\pi$
$43$	−6.57818	−1.00316	−0.501581	+	0.865110i	$0.667248\pi$
$44$	1.20072	0.181016
$45$	0.240793	0.0358953
$46$	−0.652464	−0.0962006
$47$	6.36834	0.928918	0.464459	−	0.885595i	$-0.346249\pi$
$47$	6.36834	0.928918	0.464459	+	0.885595i	$0.346249\pi$
$48$	2.11719	0.305591
$49$	−5.96452	−0.852074
$50$	−2.34625	−0.331811
$51$	−1.66109	−0.232599
$52$	8.46029	1.17323
$53$	5.82214	0.799732	0.399866	−	0.916574i	$-0.369057\pi$
$53$	5.82214	0.799732	0.399866	+	0.916574i	$0.369057\pi$
$54$	12.6304	1.71879
$55$	−0.342582	−0.0461938
$56$	3.59300	0.480134
$57$	−9.22977	−1.22251
$58$	−4.30500	−0.565275
$59$	−3.93844	−0.512741	−0.256371	−	0.966579i	$-0.582527\pi$
$59$	−3.93844	−0.512741	−0.256371	+	0.966579i	$0.582527\pi$
$60$	−5.82196	−0.751612
$61$	6.89457	0.882759	0.441380	−	0.897321i	$-0.354489\pi$
$61$	6.89457	0.882759	0.441380	+	0.897321i	$0.354489\pi$
$62$	−20.6322	−2.62029
$63$	0.245027	0.0308705
$64$	−12.1015	−1.51269
$65$	−2.41384	−0.299400
$66$	−1.33516	−0.164347
$67$	−9.86463	−1.20516	−0.602578	−	0.798060i	$-0.705860\pi$
$67$	−9.86463	−1.20516	−0.602578	+	0.798060i	$0.705860\pi$
$68$	−3.50491	−0.425033
$69$	0.461927	0.0556095
$70$	−2.38751	−0.285362
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	0.850217	0.100199
$73$	−5.55609	−0.650291	−0.325146	−	0.945664i	$-0.605413\pi$
$73$	−5.55609	−0.650291	−0.325146	+	0.945664i	$0.605413\pi$
$74$	−9.38145	−1.09057
$75$	1.66109	0.191806
$76$	−19.4749	−2.23393
$77$	−0.348607	−0.0397274
$78$	−9.40753	−1.06519
$79$	3.39968	0.382494	0.191247	−	0.981542i	$-0.438747\pi$
$79$	3.39968	0.382494	0.191247	+	0.981542i	$0.438747\pi$
$80$	−1.27458	−0.142503
$81$	−8.21964	−0.913293
$82$	−5.79472	−0.639920
$83$	−3.03118	−0.332715	−0.166358	−	0.986065i	$-0.553201\pi$
$83$	−3.03118	−0.332715	−0.166358	+	0.986065i	$0.553201\pi$
$84$	−5.92434	−0.646398
$85$	1.00000	0.108465
$86$	15.4341	1.66430
$87$	3.04783	0.326762
$88$	−1.20963	−0.128947
$89$	−0.708567	−0.0751080	−0.0375540	−	0.999295i	$-0.511957\pi$
$89$	−0.708567	−0.0751080	−0.0375540	+	0.999295i	$0.511957\pi$
$90$	−0.564961	−0.0595521
$91$	−2.45629	−0.257489
$92$	0.974672	0.101617
$93$	14.6070	1.51468
$94$	−14.9418	−1.54112
$95$	5.55646	0.570081
$96$	6.76281	0.690226
$97$	7.59597	0.771253	0.385627	−	0.922655i	$-0.373985\pi$
$97$	7.59597	0.771253	0.385627	+	0.922655i	$0.373985\pi$
$98$	13.9943	1.41364
$99$	−0.0824914	−0.00829070
$100$	3.50491	0.350491
$101$	13.7254	1.36573	0.682863	−	0.730546i	$-0.260734\pi$
$101$	13.7254	1.36573	0.682863	+	0.730546i	$0.260734\pi$
$102$	3.89733	0.385893
$103$	5.24530	0.516835	0.258418	−	0.966033i	$-0.416799\pi$
$103$	5.24530	0.516835	0.258418	+	0.966033i	$0.416799\pi$
$104$	−8.52304	−0.835753
$105$	1.69030	0.164956
$106$	−13.6602	−1.32680
$107$	9.93605	0.960554	0.480277	−	0.877117i	$-0.340536\pi$
$107$	9.93605	0.960554	0.480277	+	0.877117i	$0.340536\pi$
$108$	−18.8678	−1.81555
$109$	−16.5271	−1.58301	−0.791506	−	0.611161i	$-0.790703\pi$
$109$	−16.5271	−1.58301	−0.791506	+	0.611161i	$0.790703\pi$
$110$	0.803786	0.0766380
$111$	6.64182	0.630413
$112$	−1.29700	−0.122555
$113$	−14.9243	−1.40396	−0.701980	−	0.712197i	$-0.747700\pi$
$113$	−14.9243	−1.40396	−0.701980	+	0.712197i	$0.747700\pi$
$114$	21.6554	2.02821
$115$	−0.278087	−0.0259318
$116$	6.43096	0.597099
$117$	−0.581235	−0.0537352
$118$	9.24058	0.850665
$119$	1.01758	0.0932818
$120$	5.86514	0.535412
$121$	−10.8826	−0.989331
$122$	−16.1764	−1.46454
$123$	4.10251	0.369911
$124$	30.8210	2.76781
$125$	−1.00000	−0.0894427
$126$	−0.574896	−0.0512158
$127$	4.45573	0.395382	0.197691	−	0.980264i	$-0.436656\pi$
$127$	4.45573	0.395382	0.197691	+	0.980264i	$0.436656\pi$
$128$	20.2506	1.78992
$129$	−10.9269	−0.962062
$130$	5.66348	0.496720
$131$	7.66175	0.669410	0.334705	−	0.942323i	$-0.391363\pi$
$131$	7.66175	0.669410	0.334705	+	0.942323i	$0.391363\pi$
$132$	1.99450	0.173599
$133$	5.65417	0.490279
$134$	23.1449	1.99942
$135$	5.38324	0.463315
$136$	3.53091	0.302773
$137$	−18.9072	−1.61535	−0.807675	−	0.589629i	$-0.799274\pi$
$137$	−18.9072	−1.61535	−0.807675	+	0.589629i	$0.799274\pi$
$138$	−1.08380	−0.0922591
$139$	−10.7258	−0.909752	−0.454876	−	0.890555i	$-0.650316\pi$
$139$	−10.7258	−0.909752	−0.454876	+	0.890555i	$0.650316\pi$
$140$	3.56654	0.301428
$141$	10.5784	0.890859
$142$	2.34625	0.196893
$143$	0.826939	0.0691521
$144$	−0.306911	−0.0255759
$145$	−1.83484	−0.152375
$146$	13.0360	1.07887
$147$	−9.90758	−0.817164
$148$	14.0143	1.15197
$149$	1.99297	0.163270	0.0816351	−	0.996662i	$-0.473986\pi$
$149$	1.99297	0.163270	0.0816351	+	0.996662i	$0.473986\pi$
$150$	−3.89733	−0.318216
$151$	8.25396	0.671698	0.335849	−	0.941916i	$-0.390977\pi$
$151$	8.25396	0.671698	0.335849	+	0.941916i	$0.390977\pi$
$152$	19.6194	1.59134
$153$	0.240793	0.0194669
$154$	0.817920	0.0659099
$155$	−8.79367	−0.706324
$156$	14.0533	1.12516
$157$	−9.68288	−0.772778	−0.386389	−	0.922336i	$-0.626278\pi$
$157$	−9.68288	−0.772778	−0.386389	+	0.922336i	$0.626278\pi$
$158$	−7.97652	−0.634578
$159$	9.67107	0.766966
$160$	−4.07132	−0.321866
$161$	−0.282978	−0.0223018
$162$	19.2854	1.51520
$163$	−17.2670	−1.35246	−0.676228	−	0.736693i	$-0.736386\pi$
$163$	−17.2670	−1.35246	−0.676228	+	0.736693i	$0.736386\pi$
$164$	8.65635	0.675947
$165$	−0.569059	−0.0443012
$166$	7.11192	0.551992
$167$	−1.14365	−0.0884983	−0.0442491	−	0.999021i	$-0.514090\pi$
$167$	−1.14365	−0.0884983	−0.0442491	+	0.999021i	$0.514090\pi$
$168$	5.96828	0.460463
$169$	−7.17338	−0.551798
$170$	−2.34625	−0.179950
$171$	1.33796	0.102316
$172$	−23.0559	−1.75800
$173$	−19.2262	−1.46174	−0.730870	−	0.682517i	$-0.760885\pi$
$173$	−19.2262	−1.46174	−0.730870	+	0.682517i	$0.760885\pi$
$174$	−7.15098	−0.542115
$175$	−1.01758	−0.0769222
$176$	0.436650	0.0329137
$177$	−6.54209	−0.491733
$178$	1.66248	0.124608
$179$	0.158532	0.0118493	0.00592463	−	0.999982i	$-0.498114\pi$
$179$	0.158532	0.0118493	0.00592463	+	0.999982i	$0.498114\pi$
$180$	0.843958	0.0629049
$181$	16.8076	1.24930	0.624650	−	0.780904i	$-0.285241\pi$
$181$	16.8076	1.24930	0.624650	+	0.780904i	$0.285241\pi$
$182$	5.76307	0.427187
$183$	11.4525	0.846591
$184$	−0.981901	−0.0723867
$185$	−3.99848	−0.293974
$186$	−34.2718	−2.51293
$187$	−0.342582	−0.0250521
$188$	22.3205	1.62789
$189$	5.47790	0.398458
$190$	−13.0369	−0.945795
$191$	−18.7211	−1.35461	−0.677305	−	0.735703i	$-0.736852\pi$
$191$	−18.7211	−1.35461	−0.677305	+	0.735703i	$0.736852\pi$
$192$	−20.1017	−1.45071
$193$	−21.6812	−1.56065	−0.780325	−	0.625375i	$-0.784946\pi$
$193$	−21.6812	−1.56065	−0.780325	+	0.625375i	$0.784946\pi$
$194$	−17.8221	−1.27955
$195$	−4.00959	−0.287133
$196$	−20.9051	−1.49322
$197$	10.8792	0.775113	0.387557	−	0.921846i	$-0.373319\pi$
$197$	10.8792	0.775113	0.387557	+	0.921846i	$0.373319\pi$
$198$	0.193546	0.0137547
$199$	−25.9241	−1.83771	−0.918857	−	0.394591i	$-0.870886\pi$
$199$	−25.9241	−1.83771	−0.918857	+	0.394591i	$0.870886\pi$
$200$	−3.53091	−0.249673
$201$	−16.3860	−1.15578
$202$	−32.2032	−2.26581
$203$	−1.86711	−0.131045
$204$	−5.82196	−0.407619
$205$	−2.46978	−0.172497
$206$	−12.3068	−0.857457
$207$	−0.0669615	−0.00465414
$208$	3.07664	0.213327
$209$	−1.90355	−0.131671
$210$	−3.96586	−0.273671
$211$	9.99299	0.687946	0.343973	−	0.938980i	$-0.388227\pi$
$211$	9.99299	0.687946	0.343973	+	0.938980i	$0.388227\pi$
$212$	20.4061	1.40149
$213$	−1.66109	−0.113816
$214$	−23.3125	−1.59361
$215$	6.57818	0.448628
$216$	19.0077	1.29331
$217$	−8.94830	−0.607450
$218$	38.7769	2.62630
$219$	−9.22915	−0.623648
$220$	−1.20072	−0.0809526
$221$	−2.41384	−0.162372
$222$	−15.5834	−1.04589
$223$	−19.1633	−1.28327	−0.641636	−	0.767009i	$-0.721744\pi$
$223$	−19.1633	−1.28327	−0.641636	+	0.767009i	$0.721744\pi$
$224$	−4.14291	−0.276810
$225$	−0.240793	−0.0160529
$226$	35.0162	2.32924
$227$	−24.7119	−1.64019	−0.820093	−	0.572230i	$-0.806078\pi$
$227$	−24.7119	−1.64019	−0.820093	+	0.572230i	$0.806078\pi$
$228$	−32.3495	−2.14240
$229$	−3.14913	−0.208100	−0.104050	−	0.994572i	$-0.533180\pi$
$229$	−3.14913	−0.208100	−0.104050	+	0.994572i	$0.533180\pi$
$230$	0.652464	0.0430222
$231$	−0.579066	−0.0380997
$232$	−6.47865	−0.425344
$233$	11.3454	0.743263	0.371631	−	0.928380i	$-0.378798\pi$
$233$	11.3454	0.743263	0.371631	+	0.928380i	$0.378798\pi$
$234$	1.36373	0.0891495
$235$	−6.36834	−0.415425
$236$	−13.8039	−0.898556
$237$	5.64716	0.366823
$238$	−2.38751	−0.154759
$239$	13.5290	0.875115	0.437558	−	0.899190i	$-0.355844\pi$
$239$	13.5290	0.875115	0.437558	+	0.899190i	$0.355844\pi$
$240$	−2.11719	−0.136664
$241$	−1.06017	−0.0682915	−0.0341458	−	0.999417i	$-0.510871\pi$
$241$	−1.06017	−0.0682915	−0.0341458	+	0.999417i	$0.510871\pi$
$242$	25.5334	1.64135
$243$	2.49618	0.160130
$244$	24.1649	1.54700
$245$	5.96452	0.381059
$246$	−9.62554	−0.613702
$247$	−13.4124	−0.853411
$248$	−31.0496	−1.97165
$249$	−5.03505	−0.319084
$250$	2.34625	0.148390
$251$	29.1527	1.84010	0.920051	−	0.391798i	$-0.128147\pi$
$251$	29.1527	1.84010	0.920051	+	0.391798i	$0.128147\pi$
$252$	0.858798	0.0540992
$253$	0.0952679	0.00598944
$254$	−10.4543	−0.655960
$255$	1.66109	0.104021
$256$	−23.3100	−1.45688
$257$	9.00282	0.561580	0.280790	−	0.959769i	$-0.409404\pi$
$257$	9.00282	0.561580	0.280790	+	0.959769i	$0.409404\pi$
$258$	25.6373	1.59611
$259$	−4.06879	−0.252822
$260$	−8.46029	−0.524685
$261$	−0.441816	−0.0273478
$262$	−17.9764	−1.11059
$263$	7.67561	0.473298	0.236649	−	0.971595i	$-0.423951\pi$
$263$	7.67561	0.473298	0.236649	+	0.971595i	$0.423951\pi$
$264$	−2.00929	−0.123664
$265$	−5.82214	−0.357651
$266$	−13.2661	−0.813399
$267$	−1.17699	−0.0720307
$268$	−34.5747	−2.11198
$269$	−9.71997	−0.592637	−0.296319	−	0.955089i	$-0.595759\pi$
$269$	−9.71997	−0.592637	−0.296319	+	0.955089i	$0.595759\pi$
$270$	−12.6304	−0.768664
$271$	19.0365	1.15638	0.578192	−	0.815901i	$-0.303759\pi$
$271$	19.0365	1.15638	0.578192	+	0.815901i	$0.303759\pi$
$272$	−1.27458	−0.0772830
$273$	−4.08010	−0.246939
$274$	44.3611	2.67995
$275$	0.342582	0.0206585
$276$	1.61901	0.0974532
$277$	−28.5640	−1.71625	−0.858123	−	0.513444i	$-0.828369\pi$
$277$	−28.5640	−1.71625	−0.858123	+	0.513444i	$0.828369\pi$
$278$	25.1655	1.50933
$279$	−2.11745	−0.126769
$280$	−3.59300	−0.214723
$281$	−16.0124	−0.955218	−0.477609	−	0.878572i	$-0.658496\pi$
$281$	−16.0124	−0.955218	−0.477609	+	0.878572i	$0.658496\pi$
$282$	−24.8195	−1.47798
$283$	−27.1656	−1.61483	−0.807413	−	0.589987i	$-0.799133\pi$
$283$	−27.1656	−1.61483	−0.807413	+	0.589987i	$0.799133\pi$
$284$	−3.50491	−0.207978
$285$	9.22977	0.546724
$286$	−1.94021	−0.114727
$287$	−2.51321	−0.148350
$288$	−0.980343	−0.0577673
$289$	1.00000	0.0588235
$290$	4.30500	0.252799
$291$	12.6176	0.739654
$292$	−19.4736	−1.13961
$293$	23.4259	1.36855	0.684276	−	0.729223i	$-0.260118\pi$
$293$	23.4259	1.36855	0.684276	+	0.729223i	$0.260118\pi$
$294$	23.2457	1.35572
$295$	3.93844	0.229305
$296$	−14.1183	−0.820607
$297$	−1.84420	−0.107011
$298$	−4.67601	−0.270874
$299$	0.671259	0.0388199
$300$	5.82196	0.336131
$301$	6.69385	0.385827
$302$	−19.3659	−1.11438
$303$	22.7990	1.30977
$304$	−7.08218	−0.406191
$305$	−6.89457	−0.394782
$306$	−0.564961	−0.0322967
$307$	−0.558849	−0.0318952	−0.0159476	−	0.999873i	$-0.505076\pi$
$307$	−0.558849	−0.0318952	−0.0159476	+	0.999873i	$0.505076\pi$
$308$	−1.22184	−0.0696206
$309$	8.71290	0.495660
$310$	20.6322	1.17183
$311$	11.3624	0.644302	0.322151	−	0.946688i	$-0.395594\pi$
$311$	11.3624	0.644302	0.322151	+	0.946688i	$0.395594\pi$
$312$	−14.1575	−0.801511
$313$	−12.8138	−0.724280	−0.362140	−	0.932124i	$-0.617954\pi$
$313$	−12.8138	−0.724280	−0.362140	+	0.932124i	$0.617954\pi$
$314$	22.7185	1.28208
$315$	−0.245027	−0.0138057
$316$	11.9156	0.670304
$317$	−26.2135	−1.47230	−0.736148	−	0.676821i	$-0.763357\pi$
$317$	−26.2135	−1.47230	−0.736148	+	0.676821i	$0.763357\pi$
$318$	−22.6908	−1.27244
$319$	0.628584	0.0351940
$320$	12.1015	0.676495
$321$	16.5046	0.921199
$322$	0.663937	0.0369998
$323$	5.55646	0.309170
$324$	−28.8091	−1.60051
$325$	2.41384	0.133896
$326$	40.5128	2.24380
$327$	−27.4530	−1.51815
$328$	−8.72055	−0.481512
$329$	−6.48033	−0.357272
$330$	1.33516	0.0734980
$331$	27.4163	1.50693	0.753467	−	0.657485i	$-0.228380\pi$
$331$	27.4163	1.50693	0.753467	+	0.657485i	$0.228380\pi$
$332$	−10.6240	−0.583069
$333$	−0.962805	−0.0527614
$334$	2.68329	0.146823
$335$	9.86463	0.538962
$336$	−2.15442	−0.117533
$337$	−26.9224	−1.46656	−0.733278	−	0.679929i	$-0.762010\pi$
$337$	−26.9224	−1.46656	−0.733278	+	0.679929i	$0.762010\pi$
$338$	16.8306	0.915463
$339$	−24.7905	−1.34644
$340$	3.50491	0.190081
$341$	3.01256	0.163139
$342$	−3.13919	−0.169748
$343$	13.1925	0.712328
$344$	23.2269	1.25231
$345$	−0.461927	−0.0248693
$346$	45.1095	2.42510
$347$	−33.7521	−1.81191	−0.905953	−	0.423379i	$-0.860844\pi$
$347$	−33.7521	−1.81191	−0.905953	+	0.423379i	$0.860844\pi$
$348$	10.6824	0.572635
$349$	−17.0984	−0.915258	−0.457629	−	0.889143i	$-0.651301\pi$
$349$	−17.0984	−0.915258	−0.457629	+	0.889143i	$0.651301\pi$
$350$	2.38751	0.127618
$351$	−12.9943	−0.693583
$352$	1.39476	0.0743410
$353$	24.0092	1.27788	0.638940	−	0.769256i	$-0.279373\pi$
$353$	24.0092	1.27788	0.638940	+	0.769256i	$0.279373\pi$
$354$	15.3494	0.815812
$355$	1.00000	0.0530745
$356$	−2.48347	−0.131623
$357$	1.69030	0.0894599
$358$	−0.371957	−0.0196586
$359$	7.49014	0.395315	0.197657	−	0.980271i	$-0.436667\pi$
$359$	7.49014	0.395315	0.197657	+	0.980271i	$0.436667\pi$
$360$	−0.850217	−0.0448104
$361$	11.8743	0.624963
$362$	−39.4350	−2.07266
$363$	−18.0770	−0.948796
$364$	−8.60907	−0.451238
$365$	5.55609	0.290819
$366$	−26.8704	−1.40454
$367$	36.2844	1.89403	0.947016	−	0.321186i	$-0.104081\pi$
$367$	36.2844	1.89403	0.947016	+	0.321186i	$0.104081\pi$
$368$	0.354446	0.0184768
$369$	−0.594704	−0.0309591
$370$	9.38145	0.487718
$371$	−5.92452	−0.307586
$372$	51.1964	2.65441
$373$	−28.3231	−1.46652	−0.733258	−	0.679951i	$-0.762001\pi$
$373$	−28.3231	−1.46652	−0.733258	+	0.679951i	$0.762001\pi$
$374$	0.803786	0.0415628
$375$	−1.66109	−0.0857781
$376$	−22.4860	−1.15963
$377$	4.42901	0.228106
$378$	−12.8525	−0.661064
$379$	−9.96481	−0.511858	−0.255929	−	0.966696i	$-0.582381\pi$
$379$	−9.96481	−0.511858	−0.255929	+	0.966696i	$0.582381\pi$
$380$	19.4749	0.999042
$381$	7.40135	0.379183
$382$	43.9244	2.24737
$383$	−25.2669	−1.29108	−0.645539	−	0.763727i	$-0.723367\pi$
$383$	−25.2669	−1.29108	−0.645539	+	0.763727i	$0.723367\pi$
$384$	33.6380	1.71658
$385$	0.348607	0.0177666
$386$	50.8697	2.58920
$387$	1.58398	0.0805181
$388$	26.6232	1.35159
$389$	−23.6696	−1.20009	−0.600047	−	0.799964i	$-0.704852\pi$
$389$	−23.6696	−1.20009	−0.600047	+	0.799964i	$0.704852\pi$
$390$	9.40753	0.476369
$391$	−0.278087	−0.0140635
$392$	21.0602	1.06370
$393$	12.7268	0.641984
$394$	−25.5255	−1.28595
$395$	−3.39968	−0.171057
$396$	−0.289125	−0.0145291
$397$	23.2870	1.16874	0.584371	−	0.811486i	$-0.301341\pi$
$397$	23.2870	1.16874	0.584371	+	0.811486i	$0.301341\pi$
$398$	60.8246	3.04886
$399$	9.39207	0.470192
$400$	1.27458	0.0637292
$401$	27.5513	1.37584	0.687922	−	0.725785i	$-0.258523\pi$
$401$	27.5513	1.37584	0.687922	+	0.725785i	$0.258523\pi$
$402$	38.4457	1.91750
$403$	21.2265	1.05737
$404$	48.1063	2.39338
$405$	8.21964	0.408437
$406$	4.38071	0.217411
$407$	1.36981	0.0678989
$408$	5.86514	0.290368
$409$	17.0956	0.845321	0.422660	−	0.906288i	$-0.361096\pi$
$409$	17.0956	0.845321	0.422660	+	0.906288i	$0.361096\pi$
$410$	5.79472	0.286181
$411$	−31.4064	−1.54917
$412$	18.3843	0.905731
$413$	4.00770	0.197206
$414$	0.157109	0.00772147
$415$	3.03118	0.148795
$416$	9.82750	0.481833
$417$	−17.8165	−0.872478
$418$	4.46621	0.218449
$419$	−30.7404	−1.50177	−0.750883	−	0.660435i	$-0.770372\pi$
$419$	−30.7404	−1.50177	−0.750883	+	0.660435i	$0.770372\pi$
$420$	5.92434	0.289078
$421$	−39.3613	−1.91835	−0.959176	−	0.282808i	$-0.908734\pi$
$421$	−39.3613	−1.91835	−0.959176	+	0.282808i	$0.908734\pi$
$422$	−23.4461	−1.14134
$423$	−1.53345	−0.0745589
$424$	−20.5574	−0.998357
$425$	−1.00000	−0.0485071
$426$	3.89733	0.188826
$427$	−7.01581	−0.339519
$428$	34.8250	1.68333
$429$	1.37362	0.0663189
$430$	−15.4341	−0.744298
$431$	−4.86973	−0.234567	−0.117283	−	0.993098i	$-0.537419\pi$
$431$	−4.86973	−0.234567	−0.117283	+	0.993098i	$0.537419\pi$
$432$	−6.86139	−0.330119
$433$	2.51301	0.120767	0.0603837	−	0.998175i	$-0.480768\pi$
$433$	2.51301	0.120767	0.0603837	+	0.998175i	$0.480768\pi$
$434$	20.9950	1.00779
$435$	−3.04783	−0.146132
$436$	−57.9262	−2.77416
$437$	−1.54518	−0.0739161
$438$	21.6539	1.03466
$439$	32.6527	1.55843	0.779214	−	0.626757i	$-0.215618\pi$
$439$	32.6527	1.55843	0.779214	+	0.626757i	$0.215618\pi$
$440$	1.20963	0.0576667
$441$	1.43621	0.0683911
$442$	5.66348	0.269384
$443$	−20.9339	−0.994602	−0.497301	−	0.867578i	$-0.665676\pi$
$443$	−20.9339	−0.994602	−0.497301	+	0.867578i	$0.665676\pi$
$444$	23.2790	1.10477
$445$	0.708567	0.0335893
$446$	44.9621	2.12902
$447$	3.31049	0.156581
$448$	12.3143	0.581797
$449$	33.9979	1.60446	0.802231	−	0.597014i	$-0.203646\pi$
$449$	33.9979	1.60446	0.802231	+	0.597014i	$0.203646\pi$
$450$	0.564961	0.0266325
$451$	0.846102	0.0398414
$452$	−52.3083	−2.46038
$453$	13.7105	0.644177
$454$	57.9804	2.72116
$455$	2.45629	0.115152
$456$	32.5894	1.52614
$457$	−0.0145099	−0.000678743 0	−0.000339372	−	1.00000i	$-0.500108\pi$
$457$	−0.0145099	−0.000678743 0	−0.000339372		1.00000i	$0.500108\pi$
$458$	7.38866	0.345249
$459$	5.38324	0.251268
$460$	−0.974672	−0.0454443
$461$	30.2431	1.40856	0.704280	−	0.709922i	$-0.251270\pi$
$461$	30.2431	1.40856	0.704280	+	0.709922i	$0.251270\pi$
$462$	1.35864	0.0632095
$463$	−10.1299	−0.470778	−0.235389	−	0.971901i	$-0.575636\pi$
$463$	−10.1299	−0.470778	−0.235389	+	0.971901i	$0.575636\pi$
$464$	2.33866	0.108569
$465$	−14.6070	−0.677385
$466$	−26.6192	−1.23311
$467$	−2.02063	−0.0935038	−0.0467519	−	0.998907i	$-0.514887\pi$
$467$	−2.02063	−0.0935038	−0.0467519	+	0.998907i	$0.514887\pi$
$468$	−2.03718	−0.0941686
$469$	10.0381	0.463516
$470$	14.9418	0.689212
$471$	−16.0841	−0.741116
$472$	13.9063	0.640088
$473$	−2.25357	−0.103619
$474$	−13.2497	−0.608578
$475$	−5.55646	−0.254948
$476$	3.56654	0.163472
$477$	−1.40193	−0.0641899
$478$	−31.7424	−1.45186
$479$	−26.2492	−1.19936	−0.599679	−	0.800241i	$-0.704705\pi$
$479$	−26.2492	−1.19936	−0.599679	+	0.800241i	$0.704705\pi$
$480$	−6.76281	−0.308678
$481$	9.65168	0.440079
$482$	2.48743	0.113299
$483$	−0.470050	−0.0213880
$484$	−38.1427	−1.73376
$485$	−7.59597	−0.344915
$486$	−5.85667	−0.265664
$487$	−17.9845	−0.814955	−0.407478	−	0.913215i	$-0.633592\pi$
$487$	−17.9845	−0.814955	−0.407478	+	0.913215i	$0.633592\pi$
$488$	−24.3441	−1.10200
$489$	−28.6820	−1.29704
$490$	−13.9943	−0.632197
$491$	18.3878	0.829830	0.414915	−	0.909860i	$-0.363811\pi$
$491$	18.3878	0.829830	0.414915	+	0.909860i	$0.363811\pi$
$492$	14.3789	0.648253
$493$	−1.83484	−0.0826371
$494$	31.4689	1.41585
$495$	0.0824914	0.00370771
$496$	11.2083	0.503266
$497$	1.01758	0.0456449
$498$	11.8135	0.529376
$499$	32.4674	1.45344	0.726721	−	0.686933i	$-0.241043\pi$
$499$	32.4674	1.45344	0.726721	+	0.686933i	$0.241043\pi$
$500$	−3.50491	−0.156744
$501$	−1.89970	−0.0848724
$502$	−68.3997	−3.05283
$503$	−25.0003	−1.11471	−0.557353	−	0.830275i	$-0.688183\pi$
$503$	−25.0003	−1.11471	−0.557353	+	0.830275i	$0.688183\pi$
$504$	−0.865168	−0.0385376
$505$	−13.7254	−0.610771
$506$	−0.223523	−0.00993680
$507$	−11.9156	−0.529190
$508$	15.6169	0.692889
$509$	0.589677	0.0261370	0.0130685	−	0.999915i	$-0.495840\pi$
$509$	0.589677	0.0261370	0.0130685	+	0.999915i	$0.495840\pi$
$510$	−3.89733	−0.172577
$511$	5.65379	0.250109
$512$	14.1901	0.627120
$513$	29.9118	1.32064
$514$	−21.1229	−0.931691
$515$	−5.24530	−0.231136
$516$	−38.2979	−1.68597
$517$	2.18168	0.0959503
$518$	9.54642	0.419446
$519$	−31.9363	−1.40185
$520$	8.52304	0.373760
$521$	−23.7626	−1.04106	−0.520529	−	0.853844i	$-0.674265\pi$
$521$	−23.7626	−1.04106	−0.520529	+	0.853844i	$0.674265\pi$
$522$	1.03661	0.0453714
$523$	28.2609	1.23576	0.617880	−	0.786272i	$-0.287992\pi$
$523$	28.2609	1.23576	0.617880	+	0.786272i	$0.287992\pi$
$524$	26.8538	1.17311
$525$	−1.69030	−0.0737706
$526$	−18.0089	−0.785227
$527$	−8.79367	−0.383058
$528$	0.725313	0.0315652
$529$	−22.9227	−0.996638
$530$	13.6602	0.593362
$531$	0.948348	0.0411548
$532$	19.8174	0.859192
$533$	5.96164	0.258227
$534$	2.76152	0.119503
$535$	−9.93605	−0.429573
$536$	34.8311	1.50447
$537$	0.263336	0.0113638
$538$	22.8055	0.983216
$539$	−2.04334	−0.0880129
$540$	18.8678	0.811939
$541$	−14.5654	−0.626214	−0.313107	−	0.949718i	$-0.601370\pi$
$541$	−14.5654	−0.626214	−0.313107	+	0.949718i	$0.601370\pi$
$542$	−44.6644	−1.91850
$543$	27.9189	1.19812
$544$	−4.07132	−0.174556
$545$	16.5271	0.707945
$546$	9.57296	0.409685
$547$	−29.8760	−1.27741	−0.638704	−	0.769453i	$-0.720529\pi$
$547$	−29.8760	−1.27741	−0.638704	+	0.769453i	$0.720529\pi$
$548$	−66.2680	−2.83083
$549$	−1.66016	−0.0708540
$550$	−0.803786	−0.0342735
$551$	−10.1952	−0.434331
$552$	−1.63102	−0.0694209
$553$	−3.45946	−0.147111
$554$	67.0185	2.84734
$555$	−6.64182	−0.281929
$556$	−37.5931	−1.59430
$557$	20.9685	0.888464	0.444232	−	0.895912i	$-0.353477\pi$
$557$	20.9685	0.888464	0.444232	+	0.895912i	$0.353477\pi$
$558$	4.96808	0.210316
$559$	−15.8787	−0.671596
$560$	1.29700	0.0548081
$561$	−0.569059	−0.0240257
$562$	37.5691	1.58476
$563$	19.3652	0.816145	0.408072	−	0.912950i	$-0.366201\pi$
$563$	19.3652	0.816145	0.408072	+	0.912950i	$0.366201\pi$
$564$	37.0762	1.56119
$565$	14.9243	0.627870
$566$	63.7374	2.67908
$567$	8.36418	0.351263
$568$	3.53091	0.148154
$569$	12.4117	0.520325	0.260163	−	0.965565i	$-0.416224\pi$
$569$	12.4117	0.520325	0.260163	+	0.965565i	$0.416224\pi$
$570$	−21.6554	−0.907044
$571$	−39.3221	−1.64558	−0.822790	−	0.568346i	$-0.807584\pi$
$571$	−39.3221	−1.64558	−0.822790	+	0.568346i	$0.807584\pi$
$572$	2.89835	0.121186
$573$	−31.0973	−1.29911
$574$	5.89662	0.246120
$575$	0.278087	0.0115970
$576$	2.91396	0.121415
$577$	−14.0847	−0.586352	−0.293176	−	0.956058i	$-0.594712\pi$
$577$	−14.0847	−0.586352	−0.293176	+	0.956058i	$0.594712\pi$
$578$	−2.34625	−0.0975913
$579$	−36.0144	−1.49671
$580$	−6.43096	−0.267031
$581$	3.08448	0.127966
$582$	−29.6040	−1.22713
$583$	1.99456	0.0826063
$584$	19.6180	0.811800
$585$	0.581235	0.0240311
$586$	−54.9630	−2.27050
$587$	28.2890	1.16761	0.583807	−	0.811893i	$-0.301563\pi$
$587$	28.2890	1.16761	0.583807	+	0.811893i	$0.301563\pi$
$588$	−34.7252	−1.43204
$589$	−48.8617	−2.01331
$590$	−9.24058	−0.380429
$591$	18.0713	0.743356
$592$	5.09640	0.209461
$593$	−26.7416	−1.09815	−0.549074	−	0.835774i	$-0.685019\pi$
$593$	−26.7416	−1.09815	−0.549074	+	0.835774i	$0.685019\pi$
$594$	4.32697	0.177538
$595$	−1.01758	−0.0417169
$596$	6.98517	0.286124
$597$	−43.0622	−1.76242
$598$	−1.57494	−0.0644042
$599$	5.94652	0.242968	0.121484	−	0.992593i	$-0.461235\pi$
$599$	5.94652	0.242968	0.121484	+	0.992593i	$0.461235\pi$
$600$	−5.86514	−0.239443
$601$	16.9982	0.693372	0.346686	−	0.937981i	$-0.387307\pi$
$601$	16.9982	0.693372	0.346686	+	0.937981i	$0.387307\pi$
$602$	−15.7055	−0.640108
$603$	2.37533	0.0967310
$604$	28.9294	1.17712
$605$	10.8826	0.442442
$606$	−53.4924	−2.17298
$607$	34.0812	1.38331	0.691656	−	0.722227i	$-0.256881\pi$
$607$	34.0812	1.38331	0.691656	+	0.722227i	$0.256881\pi$
$608$	−22.6221	−0.917448
$609$	−3.10142	−0.125676
$610$	16.1764	0.654964
$611$	15.3722	0.621891
$612$	0.843958	0.0341150
$613$	25.5086	1.03028	0.515141	−	0.857105i	$-0.327740\pi$
$613$	25.5086	1.03028	0.515141	+	0.857105i	$0.327740\pi$
$614$	1.31120	0.0529158
$615$	−4.10251	−0.165429
$616$	1.23090	0.0495943
$617$	−8.83500	−0.355684	−0.177842	−	0.984059i	$-0.556912\pi$
$617$	−8.83500	−0.355684	−0.177842	+	0.984059i	$0.556912\pi$
$618$	−20.4427	−0.822326
$619$	−42.4867	−1.70768	−0.853842	−	0.520533i	$-0.825733\pi$
$619$	−42.4867	−1.70768	−0.853842	+	0.520533i	$0.825733\pi$
$620$	−30.8210	−1.23780
$621$	−1.49701	−0.0600730
$622$	−26.6591	−1.06893
$623$	0.721027	0.0288873
$624$	5.11056	0.204586
$625$	1.00000	0.0400000
$626$	30.0645	1.20162
$627$	−3.16196	−0.126276
$628$	−33.9376	−1.35426
$629$	−3.99848	−0.159430
$630$	0.574896	0.0229044
$631$	27.3030	1.08692	0.543458	−	0.839436i	$-0.317115\pi$
$631$	27.3030	1.08692	0.543458	+	0.839436i	$0.317115\pi$
$632$	−12.0040	−0.477492
$633$	16.5992	0.659759
$634$	61.5035	2.44262
$635$	−4.45573	−0.176820
$636$	33.8962	1.34407
$637$	−14.3974	−0.570446
$638$	−1.47482	−0.0583887
$639$	0.240793	0.00952562
$640$	−20.2506	−0.800475
$641$	−8.27291	−0.326760	−0.163380	−	0.986563i	$-0.552240\pi$
$641$	−8.27291	−0.326760	−0.163380	+	0.986563i	$0.552240\pi$
$642$	−38.7241	−1.52832
$643$	−2.93910	−0.115907	−0.0579535	−	0.998319i	$-0.518458\pi$
$643$	−2.93910	−0.115907	−0.0579535	+	0.998319i	$0.518458\pi$
$644$	−0.991811	−0.0390828
$645$	10.9269	0.430247
$646$	−13.0369	−0.512929
$647$	−3.59040	−0.141153	−0.0705766	−	0.997506i	$-0.522484\pi$
$647$	−3.59040	−0.141153	−0.0705766	+	0.997506i	$0.522484\pi$
$648$	29.0228	1.14012
$649$	−1.34924	−0.0529623
$650$	−5.66348	−0.222140
$651$	−14.8639	−0.582562
$652$	−60.5193	−2.37012
$653$	−6.51224	−0.254844	−0.127422	−	0.991849i	$-0.540670\pi$
$653$	−6.51224	−0.254844	−0.127422	+	0.991849i	$0.540670\pi$
$654$	64.4117	2.51870
$655$	−7.66175	−0.299369
$656$	3.14794	0.122906
$657$	1.33787	0.0521952
$658$	15.2045	0.592733
$659$	21.9299	0.854269	0.427134	−	0.904188i	$-0.359523\pi$
$659$	21.9299	0.854269	0.427134	+	0.904188i	$0.359523\pi$
$660$	−1.99450	−0.0776359
$661$	−33.4396	−1.30065	−0.650325	−	0.759656i	$-0.725367\pi$
$661$	−33.4396	−1.30065	−0.650325	+	0.759656i	$0.725367\pi$
$662$	−64.3256	−2.50008
$663$	−4.00959	−0.155720
$664$	10.7028	0.415350
$665$	−5.65417	−0.219259
$666$	2.25899	0.0875339
$667$	0.510246	0.0197568
$668$	−4.00839	−0.155089
$669$	−31.8320	−1.23069
$670$	−23.1449	−0.894167
$671$	2.36196	0.0911824
$672$	−6.88173	−0.265468
$673$	−44.2952	−1.70745	−0.853727	−	0.520720i	$-0.825663\pi$
$673$	−44.2952	−1.70745	−0.853727	+	0.520720i	$0.825663\pi$
$674$	63.1668	2.43309
$675$	−5.38324	−0.207201
$676$	−25.1421	−0.967002
$677$	−33.6107	−1.29176	−0.645882	−	0.763437i	$-0.723510\pi$
$677$	−33.6107	−1.29176	−0.645882	+	0.763437i	$0.723510\pi$
$678$	58.1649	2.23381
$679$	−7.72954	−0.296632
$680$	−3.53091	−0.135404
$681$	−41.0486	−1.57299
$682$	−7.06823	−0.270656
$683$	−8.29330	−0.317334	−0.158667	−	0.987332i	$-0.550720\pi$
$683$	−8.29330	−0.317334	−0.158667	+	0.987332i	$0.550720\pi$
$684$	4.68942	0.179304
$685$	18.9072	0.722406
$686$	−30.9530	−1.18179
$687$	−5.23097	−0.199574
$688$	−8.38444	−0.319654
$689$	14.0537	0.535403
$690$	1.08380	0.0412595
$691$	−35.5564	−1.35263	−0.676315	−	0.736612i	$-0.736424\pi$
$691$	−35.5564	−1.35263	−0.676315	+	0.736612i	$0.736424\pi$
$692$	−67.3861	−2.56163
$693$	0.0839420	0.00318869
$694$	79.1909	3.00605
$695$	10.7258	0.406854
$696$	−10.7616	−0.407917
$697$	−2.46978	−0.0935494
$698$	40.1173	1.51846
$699$	18.8457	0.712810
$700$	−3.56654	−0.134803
$701$	−21.8301	−0.824510	−0.412255	−	0.911068i	$-0.635259\pi$
$701$	−21.8301	−0.824510	−0.412255	+	0.911068i	$0.635259\pi$
$702$	30.4879	1.15069
$703$	−22.2174	−0.837945
$704$	−4.14577	−0.156249
$705$	−10.5784	−0.398404
$706$	−56.3317	−2.12007
$707$	−13.9667	−0.525273
$708$	−22.9294	−0.861741
$709$	−7.83518	−0.294256	−0.147128	−	0.989117i	$-0.547003\pi$
$709$	−7.83518	−0.294256	−0.147128	+	0.989117i	$0.547003\pi$
$710$	−2.34625	−0.0880534
$711$	−0.818619	−0.0307006
$712$	2.50188	0.0937621
$713$	2.44541	0.0915813
$714$	−3.96586	−0.148419
$715$	−0.826939	−0.0309258
$716$	0.555642	0.0207653
$717$	22.4728	0.839261
$718$	−17.5738	−0.655848
$719$	42.2714	1.57646	0.788229	−	0.615383i	$-0.210998\pi$
$719$	42.2714	1.57646	0.788229	+	0.615383i	$0.210998\pi$
$720$	0.306911	0.0114379
$721$	−5.33754	−0.198780
$722$	−27.8601	−1.03685
$723$	−1.76103	−0.0654935
$724$	58.9092	2.18934
$725$	1.83484	0.0681443
$726$	42.4132	1.57410
$727$	−38.5082	−1.42819	−0.714096	−	0.700048i	$-0.753162\pi$
$727$	−38.5082	−1.42819	−0.714096	+	0.700048i	$0.753162\pi$
$728$	8.67292	0.321440
$729$	28.8053	1.06686
$730$	−13.0360	−0.482484
$731$	6.57818	0.243303
$732$	40.1399	1.48361
$733$	−22.4889	−0.830646	−0.415323	−	0.909674i	$-0.636331\pi$
$733$	−22.4889	−0.830646	−0.415323	+	0.909674i	$0.636331\pi$
$734$	−85.1325	−3.14230
$735$	9.90758	0.365447
$736$	1.13218	0.0417328
$737$	−3.37945	−0.124484
$738$	1.39533	0.0513627
$739$	43.0486	1.58357	0.791784	−	0.610801i	$-0.209152\pi$
$739$	43.0486	1.58357	0.791784	+	0.610801i	$0.209152\pi$
$740$	−14.0143	−0.515176
$741$	−22.2792	−0.818446
$742$	13.9004	0.510301
$743$	5.54233	0.203329	0.101664	−	0.994819i	$-0.467583\pi$
$743$	5.54233	0.203329	0.101664	+	0.994819i	$0.467583\pi$
$744$	−51.5761	−1.89087
$745$	−1.99297	−0.0730166
$746$	66.4532	2.43303
$747$	0.729887	0.0267052
$748$	−1.20072	−0.0439027
$749$	−10.1108	−0.369439
$750$	3.89733	0.142310
$751$	−23.0443	−0.840900	−0.420450	−	0.907316i	$-0.638128\pi$
$751$	−23.0443	−0.840900	−0.420450	+	0.907316i	$0.638128\pi$
$752$	8.11699	0.295996
$753$	48.4252	1.76471
$754$	−10.3916	−0.378439
$755$	−8.25396	−0.300392
$756$	19.1996	0.698281
$757$	−51.1730	−1.85991	−0.929957	−	0.367669i	$-0.880156\pi$
$757$	−51.1730	−1.85991	−0.929957	+	0.367669i	$0.880156\pi$
$758$	23.3800	0.849200
$759$	0.158248	0.00574405
$760$	−19.6194	−0.711669
$761$	15.9642	0.578700	0.289350	−	0.957223i	$-0.406561\pi$
$761$	15.9642	0.578700	0.289350	+	0.957223i	$0.406561\pi$
$762$	−17.3655	−0.629084
$763$	16.8178	0.608844
$764$	−65.6157	−2.37389
$765$	−0.240793	−0.00870588
$766$	59.2826	2.14197
$767$	−9.50676	−0.343269
$768$	−38.7200	−1.39719
$769$	16.9204	0.610165	0.305082	−	0.952326i	$-0.401316\pi$
$769$	16.9204	0.610165	0.305082	+	0.952326i	$0.401316\pi$
$770$	−0.817920	−0.0294758
$771$	14.9545	0.538571
$772$	−75.9908	−2.73497
$773$	−1.84034	−0.0661926	−0.0330963	−	0.999452i	$-0.510537\pi$
$773$	−1.84034	−0.0661926	−0.0330963	+	0.999452i	$0.510537\pi$
$774$	−3.71642	−0.133584
$775$	8.79367	0.315878
$776$	−26.8206	−0.962805
$777$	−6.75861	−0.242464
$778$	55.5348	1.99102
$779$	−13.7232	−0.491685
$780$	−14.0533	−0.503188
$781$	−0.342582	−0.0122586
$782$	0.652464	0.0233321
$783$	−9.87738	−0.352989
$784$	−7.60228	−0.271510
$785$	9.68288	0.345597
$786$	−29.8604	−1.06508
$787$	4.01391	0.143081	0.0715403	−	0.997438i	$-0.477209\pi$
$787$	4.01391	0.143081	0.0715403	+	0.997438i	$0.477209\pi$
$788$	38.1308	1.35835
$789$	12.7498	0.453907
$790$	7.97652	0.283792
$791$	15.1867	0.539978
$792$	0.291269	0.0103498
$793$	16.6424	0.590988
$794$	−54.6373	−1.93901
$795$	−9.67107	−0.342997
$796$	−90.8618	−3.22051
$797$	23.0294	0.815744	0.407872	−	0.913039i	$-0.366271\pi$
$797$	23.0294	0.815744	0.407872	+	0.913039i	$0.366271\pi$
$798$	−22.0362	−0.780073
$799$	−6.36834	−0.225296
$800$	4.07132	0.143943
$801$	0.170618	0.00602849
$802$	−64.6423	−2.28260
$803$	−1.90342	−0.0671702
$804$	−57.4315	−2.02545
$805$	0.282978	0.00997365
$806$	−49.8028	−1.75423
$807$	−16.1457	−0.568356
$808$	−48.4630	−1.70492
$809$	−7.35368	−0.258542	−0.129271	−	0.991609i	$-0.541264\pi$
$809$	−7.35368	−0.258542	−0.129271	+	0.991609i	$0.541264\pi$
$810$	−19.2854	−0.677619
$811$	−6.55621	−0.230220	−0.115110	−	0.993353i	$-0.536722\pi$
$811$	−6.55621	−0.230220	−0.115110	+	0.993353i	$0.536722\pi$
$812$	−6.54404	−0.229651
$813$	31.6212	1.10900
$814$	−3.21392	−0.112648
$815$	17.2670	0.604837
$816$	−2.11719	−0.0741166
$817$	36.5514	1.27877
$818$	−40.1105	−1.40243
$819$	0.591456	0.0206671
$820$	−8.65635	−0.302293
$821$	11.7244	0.409184	0.204592	−	0.978847i	$-0.434413\pi$
$821$	11.7244	0.409184	0.204592	+	0.978847i	$0.434413\pi$
$822$	73.6875	2.57015
$823$	2.63326	0.0917898	0.0458949	−	0.998946i	$-0.485386\pi$
$823$	2.63326	0.0917898	0.0458949	+	0.998946i	$0.485386\pi$
$824$	−18.5207	−0.645199
$825$	0.569059	0.0198121
$826$	−9.40308	−0.327175
$827$	−41.2414	−1.43410	−0.717052	−	0.697020i	$-0.754509\pi$
$827$	−41.2414	−1.43410	−0.717052	+	0.697020i	$0.754509\pi$
$828$	−0.234694	−0.00815618
$829$	−3.45196	−0.119892	−0.0599458	−	0.998202i	$-0.519093\pi$
$829$	−3.45196	−0.119892	−0.0599458	+	0.998202i	$0.519093\pi$
$830$	−7.11192	−0.246859
$831$	−47.4473	−1.64593
$832$	−29.2111	−1.01271
$833$	5.96452	0.206658
$834$	41.8021	1.44749
$835$	1.14365	0.0395776
$836$	−6.67177	−0.230748
$837$	−47.3384	−1.63625
$838$	72.1248	2.49151
$839$	2.69454	0.0930257	0.0465129	−	0.998918i	$-0.485189\pi$
$839$	2.69454	0.0930257	0.0465129	+	0.998918i	$0.485189\pi$
$840$	−5.96828	−0.205925
$841$	−25.6334	−0.883909
$842$	92.3517	3.18265
$843$	−26.5979	−0.916081
$844$	35.0245	1.20559
$845$	7.17338	0.246772
$846$	3.59787	0.123697
$847$	11.0740	0.380507
$848$	7.42080	0.254831
$849$	−45.1244	−1.54866
$850$	2.34625	0.0804759
$851$	1.11193	0.0381164
$852$	−5.82196	−0.199457
$853$	−14.7704	−0.505728	−0.252864	−	0.967502i	$-0.581372\pi$
$853$	−14.7704	−0.505728	−0.252864	+	0.967502i	$0.581372\pi$
$854$	16.4609	0.563279
$855$	−1.33796	−0.0457572
$856$	−35.0833	−1.19912
$857$	22.4104	0.765524	0.382762	−	0.923847i	$-0.374973\pi$
$857$	22.4104	0.765524	0.382762	+	0.923847i	$0.374973\pi$
$858$	−3.22286	−0.110026
$859$	40.6977	1.38859	0.694294	−	0.719692i	$-0.255717\pi$
$859$	40.6977	1.38859	0.694294	+	0.719692i	$0.255717\pi$
$860$	23.0559	0.786201
$861$	−4.17465	−0.142272
$862$	11.4256	0.389158
$863$	−43.7114	−1.48795	−0.743977	−	0.668205i	$-0.767063\pi$
$863$	−43.7114	−1.48795	−0.743977	+	0.668205i	$0.767063\pi$
$864$	−21.9169	−0.745626
$865$	19.2262	0.653710
$866$	−5.89616	−0.200360
$867$	1.66109	0.0564134
$868$	−31.3630	−1.06453
$869$	1.16467	0.0395088
$870$	7.15098	0.242441
$871$	−23.8116	−0.806826
$872$	58.3558	1.97618
$873$	−1.82905	−0.0619041
$874$	3.62539	0.122631
$875$	1.01758	0.0344006
$876$	−32.3473	−1.09292
$877$	−19.1251	−0.645807	−0.322904	−	0.946432i	$-0.604659\pi$
$877$	−19.1251	−0.645807	−0.322904	+	0.946432i	$0.604659\pi$
$878$	−76.6116	−2.58552
$879$	38.9124	1.31248
$880$	−0.436650	−0.0147195
$881$	−57.9414	−1.95210	−0.976048	−	0.217555i	$-0.930192\pi$
$881$	−57.9414	−1.95210	−0.976048	+	0.217555i	$0.930192\pi$
$882$	−3.36972	−0.113465
$883$	−44.1399	−1.48542	−0.742712	−	0.669611i	$-0.766461\pi$
$883$	−44.1399	−1.48542	−0.742712	+	0.669611i	$0.766461\pi$
$884$	−8.46029	−0.284550
$885$	6.54209	0.219910
$886$	49.1164	1.65010
$887$	8.47799	0.284663	0.142332	−	0.989819i	$-0.454540\pi$
$887$	8.47799	0.284663	0.142332	+	0.989819i	$0.454540\pi$
$888$	−23.4516	−0.786985
$889$	−4.53408	−0.152068
$890$	−1.66248	−0.0557264
$891$	−2.81590	−0.0943364
$892$	−67.1658	−2.24888
$893$	−35.3855	−1.18413
$894$	−7.76725	−0.259776
$895$	−0.158532	−0.00529915
$896$	−20.6067	−0.688421
$897$	1.11502	0.0372294
$898$	−79.7678	−2.66189
$899$	16.1350	0.538132
$900$	−0.843958	−0.0281319
$901$	−5.82214	−0.193963
$902$	−1.98517	−0.0660990
$903$	11.1191	0.370019
$904$	52.6963	1.75265
$905$	−16.8076	−0.558704
$906$	−32.1684	−1.06872
$907$	−32.8730	−1.09153	−0.545765	−	0.837938i	$-0.683761\pi$
$907$	−32.8730	−1.09153	−0.545765	+	0.837938i	$0.683761\pi$
$908$	−86.6130	−2.87435
$909$	−3.30497	−0.109619
$910$	−5.76307	−0.191044
$911$	−40.2442	−1.33335	−0.666674	−	0.745349i	$-0.732283\pi$
$911$	−40.2442	−1.33335	−0.666674	+	0.745349i	$0.732283\pi$
$912$	−11.7641	−0.389549
$913$	−1.03843	−0.0343670
$914$	0.0340439	0.00112607
$915$	−11.4525	−0.378607
$916$	−11.0374	−0.364686
$917$	−7.79648	−0.257463
$918$	−12.6304	−0.416867
$919$	17.9859	0.593300	0.296650	−	0.954986i	$-0.404131\pi$
$919$	17.9859	0.593300	0.296650	+	0.954986i	$0.404131\pi$
$920$	0.981901	0.0323723
$921$	−0.928296	−0.0305884
$922$	−70.9579	−2.33688
$923$	−2.41384	−0.0794525
$924$	−2.02957	−0.0667681
$925$	3.99848	0.131469
$926$	23.7674	0.781046
$927$	−1.26303	−0.0414834
$928$	7.47022	0.245222
$929$	6.19306	0.203188	0.101594	−	0.994826i	$-0.467606\pi$
$929$	6.19306	0.203188	0.101594	+	0.994826i	$0.467606\pi$
$930$	34.2718	1.12382
$931$	33.1417	1.08617
$932$	39.7647	1.30254
$933$	18.8739	0.617904
$934$	4.74092	0.155128
$935$	0.342582	0.0112036
$936$	2.05229	0.0670811
$937$	31.9766	1.04463	0.522315	−	0.852753i	$-0.325069\pi$
$937$	31.9766	1.04463	0.522315	+	0.852753i	$0.325069\pi$
$938$	−23.5519	−0.768998
$939$	−21.2849	−0.694606
$940$	−22.3205	−0.728014
$941$	0.146067	0.00476166	0.00238083	−	0.999997i	$-0.499242\pi$
$941$	0.146067	0.00476166	0.00238083	+	0.999997i	$0.499242\pi$
$942$	37.7374	1.22955
$943$	0.686814	0.0223657
$944$	−5.01987	−0.163383
$945$	−5.47790	−0.178196
$946$	5.28745	0.171910
$947$	44.6735	1.45169	0.725847	−	0.687856i	$-0.241448\pi$
$947$	44.6735	1.45169	0.725847	+	0.687856i	$0.241448\pi$
$948$	19.7928	0.642841
$949$	−13.4115	−0.435356
$950$	13.0369	0.422972
$951$	−43.5428	−1.41197
$952$	−3.59300	−0.116450
$953$	−31.6231	−1.02437	−0.512187	−	0.858874i	$-0.671164\pi$
$953$	−31.6231	−1.02437	−0.512187	+	0.858874i	$0.671164\pi$
$954$	3.28928	0.106494
$955$	18.7211	0.605800
$956$	47.4178	1.53360
$957$	1.04413	0.0337520
$958$	61.5874	1.98980
$959$	19.2397	0.621281
$960$	20.1017	0.648778
$961$	46.3286	1.49447
$962$	−22.6453	−0.730114
$963$	−2.39253	−0.0770982
$964$	−3.71580	−0.119678
$965$	21.6812	0.697944
$966$	1.10286	0.0354839
$967$	24.2334	0.779295	0.389648	−	0.920964i	$-0.372597\pi$
$967$	24.2334	0.779295	0.389648	+	0.920964i	$0.372597\pi$
$968$	38.4256	1.23504
$969$	9.22977	0.296503
$970$	17.8221	0.572232
$971$	−18.1743	−0.583242	−0.291621	−	0.956534i	$-0.594195\pi$
$971$	−18.1743	−0.583242	−0.291621	+	0.956534i	$0.594195\pi$
$972$	8.74888	0.280621
$973$	10.9144	0.349901
$974$	42.1962	1.35205
$975$	4.00959	0.128410
$976$	8.78771	0.281288
$977$	24.2232	0.774967	0.387484	−	0.921877i	$-0.373344\pi$
$977$	24.2232	0.774967	0.387484	+	0.921877i	$0.373344\pi$
$978$	67.2952	2.15186
$979$	−0.242743	−0.00775809
$980$	20.9051	0.667790
$981$	3.97962	0.127059
$982$	−43.1425	−1.37673
$983$	37.4372	1.19406	0.597030	−	0.802219i	$-0.296347\pi$
$983$	37.4372	1.19406	0.597030	+	0.802219i	$0.296347\pi$
$984$	−14.4856	−0.461784
$985$	−10.8792	−0.346641
$986$	4.30500	0.137099
$987$	−10.7644	−0.342634
$988$	−47.0093	−1.49557
$989$	−1.82931	−0.0581686
$990$	−0.193546	−0.00615129
$991$	−13.6766	−0.434452	−0.217226	−	0.976121i	$-0.569701\pi$
$991$	−13.6766	−0.434452	−0.217226	+	0.976121i	$0.569701\pi$
$992$	35.8018	1.13671
$993$	45.5408	1.44519
$994$	−2.38751	−0.0757273
$995$	25.9241	0.821851
$996$	−17.6474	−0.559180
$997$	49.2537	1.55988	0.779941	−	0.625853i	$-0.215249\pi$
$997$	49.2537	1.55988	0.779941	+	0.625853i	$0.215249\pi$
$998$	−76.1768	−2.41134
$999$	−21.5248	−0.681013

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.c.1.5	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.c.1.5	✓	44	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.34625 q^{2} +1.66109 q^{3} +3.50491 q^{4} -1.00000 q^{5} -3.89733 q^{6} -1.01758 q^{7} -3.53091 q^{8} -0.240793 q^{9} +O(q^{10})\)	\(q-2.34625 q^{2} +1.66109 q^{3} +3.50491 q^{4} -1.00000 q^{5} -3.89733 q^{6} -1.01758 q^{7} -3.53091 q^{8} -0.240793 q^{9} +2.34625 q^{10} +0.342582 q^{11} +5.82196 q^{12} +2.41384 q^{13} +2.38751 q^{14} -1.66109 q^{15} +1.27458 q^{16} -1.00000 q^{17} +0.564961 q^{18} -5.55646 q^{19} -3.50491 q^{20} -1.69030 q^{21} -0.803786 q^{22} +0.278087 q^{23} -5.86514 q^{24} +1.00000 q^{25} -5.66348 q^{26} -5.38324 q^{27} -3.56654 q^{28} +1.83484 q^{29} +3.89733 q^{30} +8.79367 q^{31} +4.07132 q^{32} +0.569059 q^{33} +2.34625 q^{34} +1.01758 q^{35} -0.843958 q^{36} +3.99848 q^{37} +13.0369 q^{38} +4.00959 q^{39} +3.53091 q^{40} +2.46978 q^{41} +3.96586 q^{42} -6.57818 q^{43} +1.20072 q^{44} +0.240793 q^{45} -0.652464 q^{46} +6.36834 q^{47} +2.11719 q^{48} -5.96452 q^{49} -2.34625 q^{50} -1.66109 q^{51} +8.46029 q^{52} +5.82214 q^{53} +12.6304 q^{54} -0.342582 q^{55} +3.59300 q^{56} -9.22977 q^{57} -4.30500 q^{58} -3.93844 q^{59} -5.82196 q^{60} +6.89457 q^{61} -20.6322 q^{62} +0.245027 q^{63} -12.1015 q^{64} -2.41384 q^{65} -1.33516 q^{66} -9.86463 q^{67} -3.50491 q^{68} +0.461927 q^{69} -2.38751 q^{70} -1.00000 q^{71} +0.850217 q^{72} -5.55609 q^{73} -9.38145 q^{74} +1.66109 q^{75} -19.4749 q^{76} -0.348607 q^{77} -9.40753 q^{78} +3.39968 q^{79} -1.27458 q^{80} -8.21964 q^{81} -5.79472 q^{82} -3.03118 q^{83} -5.92434 q^{84} +1.00000 q^{85} +15.4341 q^{86} +3.04783 q^{87} -1.20963 q^{88} -0.708567 q^{89} -0.564961 q^{90} -2.45629 q^{91} +0.974672 q^{92} +14.6070 q^{93} -14.9418 q^{94} +5.55646 q^{95} +6.76281 q^{96} +7.59597 q^{97} +13.9943 q^{98} -0.0824914 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{2} - 4 q^{3} + 38 q^{4} - 44 q^{5} - 2 q^{6} - 5 q^{7} - 12 q^{8} + 46 q^{9}+O(q^{10}) \) 44 * q - 4 * q^2 - 4 * q^3 + 38 * q^4 - 44 * q^5 - 2 * q^6 - 5 * q^7 - 12 * q^8 + 46 * q^9	\( 44 q - 4 q^{2} - 4 q^{3} + 38 q^{4} - 44 q^{5} - 2 q^{6} - 5 q^{7} - 12 q^{8} + 46 q^{9} + 4 q^{10} + 22 q^{11} - 28 q^{12} - 37 q^{13} + 4 q^{14} + 4 q^{15} + 22 q^{16} - 44 q^{17} - 27 q^{18} - 19 q^{19} - 38 q^{20} - 15 q^{21} - 31 q^{22} + 2 q^{23} + 9 q^{24} + 44 q^{25} - 2 q^{26} - 13 q^{27} - 16 q^{28} + 36 q^{29} + 2 q^{30} - 11 q^{31} - 33 q^{32} - 29 q^{33} + 4 q^{34} + 5 q^{35} + 68 q^{36} - 48 q^{37} - 13 q^{38} - 4 q^{39} + 12 q^{40} + 33 q^{41} - 16 q^{42} - 45 q^{43} + 49 q^{44} - 46 q^{45} + 2 q^{46} - 28 q^{47} - 54 q^{48} + 19 q^{49} - 4 q^{50} + 4 q^{51} - 95 q^{52} - 31 q^{53} - 20 q^{54} - 22 q^{55} - q^{56} - 26 q^{57} - 30 q^{58} + 28 q^{59} + 28 q^{60} - 57 q^{61} + 33 q^{62} - 40 q^{63} - 36 q^{64} + 37 q^{65} - 9 q^{66} - 27 q^{67} - 38 q^{68} - 89 q^{69} - 4 q^{70} - 44 q^{71} - 80 q^{72} - 37 q^{73} + 17 q^{74} - 4 q^{75} - 52 q^{76} - 103 q^{77} + 2 q^{78} - 21 q^{79} - 22 q^{80} + 36 q^{81} - 67 q^{82} - 50 q^{83} - 46 q^{84} + 44 q^{85} - 37 q^{86} - 80 q^{87} - 73 q^{88} + 27 q^{90} - 17 q^{91} - 56 q^{92} - 44 q^{93} - 28 q^{94} + 19 q^{95} + 73 q^{96} - 56 q^{97} - 8 q^{98} + 31 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 - 4 * q^3 + 38 * q^4 - 44 * q^5 - 2 * q^6 - 5 * q^7 - 12 * q^8 + 46 * q^9 + 4 * q^10 + 22 * q^11 - 28 * q^12 - 37 * q^13 + 4 * q^14 + 4 * q^15 + 22 * q^16 - 44 * q^17 - 27 * q^18 - 19 * q^19 - 38 * q^20 - 15 * q^21 - 31 * q^22 + 2 * q^23 + 9 * q^24 + 44 * q^25 - 2 * q^26 - 13 * q^27 - 16 * q^28 + 36 * q^29 + 2 * q^30 - 11 * q^31 - 33 * q^32 - 29 * q^33 + 4 * q^34 + 5 * q^35 + 68 * q^36 - 48 * q^37 - 13 * q^38 - 4 * q^39 + 12 * q^40 + 33 * q^41 - 16 * q^42 - 45 * q^43 + 49 * q^44 - 46 * q^45 + 2 * q^46 - 28 * q^47 - 54 * q^48 + 19 * q^49 - 4 * q^50 + 4 * q^51 - 95 * q^52 - 31 * q^53 - 20 * q^54 - 22 * q^55 - q^56 - 26 * q^57 - 30 * q^58 + 28 * q^59 + 28 * q^60 - 57 * q^61 + 33 * q^62 - 40 * q^63 - 36 * q^64 + 37 * q^65 - 9 * q^66 - 27 * q^67 - 38 * q^68 - 89 * q^69 - 4 * q^70 - 44 * q^71 - 80 * q^72 - 37 * q^73 + 17 * q^74 - 4 * q^75 - 52 * q^76 - 103 * q^77 + 2 * q^78 - 21 * q^79 - 22 * q^80 + 36 * q^81 - 67 * q^82 - 50 * q^83 - 46 * q^84 + 44 * q^85 - 37 * q^86 - 80 * q^87 - 73 * q^88 + 27 * q^90 - 17 * q^91 - 56 * q^92 - 44 * q^93 - 28 * q^94 + 19 * q^95 + 73 * q^96 - 56 * q^97 - 8 * q^98 + 31 * q^99

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