LMFDB - Embedded newform 8035.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, 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("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$0$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68656 q^{2} -0.551136 q^{3} +5.21758 q^{4} +1.00000 q^{5} +1.48066 q^{6} -4.17471 q^{7} -8.64421 q^{8} -2.69625 q^{9} +O(q^{10})$	\(q-2.68656 q^{2} -0.551136 q^{3} +5.21758 q^{4} +1.00000 q^{5} +1.48066 q^{6} -4.17471 q^{7} -8.64421 q^{8} -2.69625 q^{9} -2.68656 q^{10} +2.50730 q^{11} -2.87560 q^{12} +5.38461 q^{13} +11.2156 q^{14} -0.551136 q^{15} +12.7880 q^{16} -0.137490 q^{17} +7.24362 q^{18} -5.14076 q^{19} +5.21758 q^{20} +2.30083 q^{21} -6.73601 q^{22} -4.07872 q^{23} +4.76414 q^{24} +1.00000 q^{25} -14.4661 q^{26} +3.13941 q^{27} -21.7819 q^{28} -3.45665 q^{29} +1.48066 q^{30} +1.69309 q^{31} -17.0672 q^{32} -1.38187 q^{33} +0.369374 q^{34} -4.17471 q^{35} -14.0679 q^{36} -4.56807 q^{37} +13.8110 q^{38} -2.96765 q^{39} -8.64421 q^{40} +9.05723 q^{41} -6.18132 q^{42} -5.50216 q^{43} +13.0821 q^{44} -2.69625 q^{45} +10.9577 q^{46} -7.93476 q^{47} -7.04792 q^{48} +10.4282 q^{49} -2.68656 q^{50} +0.0757755 q^{51} +28.0947 q^{52} -1.18174 q^{53} -8.43419 q^{54} +2.50730 q^{55} +36.0871 q^{56} +2.83326 q^{57} +9.28649 q^{58} +6.06653 q^{59} -2.87560 q^{60} +4.55268 q^{61} -4.54859 q^{62} +11.2561 q^{63} +20.2761 q^{64} +5.38461 q^{65} +3.71246 q^{66} +5.60322 q^{67} -0.717364 q^{68} +2.24793 q^{69} +11.2156 q^{70} +1.37739 q^{71} +23.3070 q^{72} -2.10680 q^{73} +12.2724 q^{74} -0.551136 q^{75} -26.8224 q^{76} -10.4673 q^{77} +7.97276 q^{78} -13.2753 q^{79} +12.7880 q^{80} +6.35851 q^{81} -24.3328 q^{82} -3.44693 q^{83} +12.0048 q^{84} -0.137490 q^{85} +14.7819 q^{86} +1.90508 q^{87} -21.6737 q^{88} +1.03400 q^{89} +7.24362 q^{90} -22.4792 q^{91} -21.2810 q^{92} -0.933125 q^{93} +21.3172 q^{94} -5.14076 q^{95} +9.40637 q^{96} -6.36595 q^{97} -28.0160 q^{98} -6.76032 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) $ 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * 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 $

$2$	−2.68656	−1.89968	−0.949841	−	0.312734i	$-0.898755\pi$
$2$	−2.68656	−1.89968	−0.949841	+	0.312734i	$0.898755\pi$
$3$	−0.551136	−0.318198	−0.159099	−	0.987263i	$-0.550859\pi$
$3$	−0.551136	−0.318198	−0.159099	+	0.987263i	$0.550859\pi$
$4$	5.21758	2.60879
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.48066	0.604476
$7$	−4.17471	−1.57789	−0.788947	−	0.614462i	$-0.789373\pi$
$7$	−4.17471	−1.57789	−0.788947	+	0.614462i	$0.789373\pi$
$8$	−8.64421	−3.05619
$9$	−2.69625	−0.898750
$10$	−2.68656	−0.849564
$11$	2.50730	0.755981	0.377990	−	0.925810i	$-0.376615\pi$
$11$	2.50730	0.755981	0.377990	+	0.925810i	$0.376615\pi$
$12$	−2.87560	−0.830113
$13$	5.38461	1.49342	0.746711	−	0.665148i	$-0.231632\pi$
$13$	5.38461	1.49342	0.746711	+	0.665148i	$0.231632\pi$
$14$	11.2156	2.99749
$15$	−0.551136	−0.142303
$16$	12.7880	3.19700
$17$	−0.137490	−0.0333461	−0.0166731	−	0.999861i	$-0.505307\pi$
$17$	−0.137490	−0.0333461	−0.0166731	+	0.999861i	$0.505307\pi$
$18$	7.24362	1.70734
$19$	−5.14076	−1.17937	−0.589686	−	0.807633i	$-0.700749\pi$
$19$	−5.14076	−1.17937	−0.589686	+	0.807633i	$0.700749\pi$
$20$	5.21758	1.16669
$21$	2.30083	0.502083
$22$	−6.73601	−1.43612
$23$	−4.07872	−0.850471	−0.425236	−	0.905083i	$-0.639809\pi$
$23$	−4.07872	−0.850471	−0.425236	+	0.905083i	$0.639809\pi$
$24$	4.76414	0.972475
$25$	1.00000	0.200000
$26$	−14.4661	−2.83703
$27$	3.13941	0.604179
$28$	−21.7819	−4.11639
$29$	−3.45665	−0.641884	−0.320942	−	0.947099i	$-0.603999\pi$
$29$	−3.45665	−0.641884	−0.320942	+	0.947099i	$0.603999\pi$
$30$	1.48066	0.270330
$31$	1.69309	0.304089	0.152044	−	0.988374i	$-0.451414\pi$
$31$	1.69309	0.304089	0.152044	+	0.988374i	$0.451414\pi$
$32$	−17.0672	−3.01709
$33$	−1.38187	−0.240552
$34$	0.369374	0.0633471
$35$	−4.17471	−0.705655
$36$	−14.0679	−2.34465
$37$	−4.56807	−0.750986	−0.375493	−	0.926825i	$-0.622527\pi$
$37$	−4.56807	−0.750986	−0.375493	+	0.926825i	$0.622527\pi$
$38$	13.8110	2.24043
$39$	−2.96765	−0.475205
$40$	−8.64421	−1.36677
$41$	9.05723	1.41450	0.707251	−	0.706962i	$-0.249935\pi$
$41$	9.05723	1.41450	0.707251	+	0.706962i	$0.249935\pi$
$42$	−6.18132	−0.953798
$43$	−5.50216	−0.839072	−0.419536	−	0.907739i	$-0.637807\pi$
$43$	−5.50216	−0.839072	−0.419536	+	0.907739i	$0.637807\pi$
$44$	13.0821	1.97220
$45$	−2.69625	−0.401933
$46$	10.9577	1.61562
$47$	−7.93476	−1.15740	−0.578702	−	0.815539i	$-0.696441\pi$
$47$	−7.93476	−1.15740	−0.578702	+	0.815539i	$0.696441\pi$
$48$	−7.04792	−1.01728
$49$	10.4282	1.48975
$50$	−2.68656	−0.379936
$51$	0.0757755	0.0106107
$52$	28.0947	3.89603
$53$	−1.18174	−0.162324	−0.0811620	−	0.996701i	$-0.525863\pi$
$53$	−1.18174	−0.162324	−0.0811620	+	0.996701i	$0.525863\pi$
$54$	−8.43419	−1.14775
$55$	2.50730	0.338085
$56$	36.0871	4.82234
$57$	2.83326	0.375274
$58$	9.28649	1.21938
$59$	6.06653	0.789795	0.394897	−	0.918725i	$-0.370780\pi$
$59$	6.06653	0.789795	0.394897	+	0.918725i	$0.370780\pi$
$60$	−2.87560	−0.371238
$61$	4.55268	0.582911	0.291456	−	0.956584i	$-0.405860\pi$
$61$	4.55268	0.582911	0.291456	+	0.956584i	$0.405860\pi$
$62$	−4.54859	−0.577672
$63$	11.2561	1.41813
$64$	20.2761	2.53451
$65$	5.38461	0.667879
$66$	3.71246	0.456972
$67$	5.60322	0.684542	0.342271	−	0.939601i	$-0.388804\pi$
$67$	5.60322	0.684542	0.342271	+	0.939601i	$0.388804\pi$
$68$	−0.717364	−0.0869931
$69$	2.24793	0.270619
$70$	11.2156	1.34052
$71$	1.37739	0.163466	0.0817328	−	0.996654i	$-0.473955\pi$
$71$	1.37739	0.163466	0.0817328	+	0.996654i	$0.473955\pi$
$72$	23.3070	2.74675
$73$	−2.10680	−0.246582	−0.123291	−	0.992371i	$-0.539345\pi$
$73$	−2.10680	−0.246582	−0.123291	+	0.992371i	$0.539345\pi$
$74$	12.2724	1.42664
$75$	−0.551136	−0.0636397
$76$	−26.8224	−3.07674
$77$	−10.4673	−1.19286
$78$	7.97276	0.902738
$79$	−13.2753	−1.49359	−0.746794	−	0.665055i	$-0.768408\pi$
$79$	−13.2753	−1.49359	−0.746794	+	0.665055i	$0.768408\pi$
$80$	12.7880	1.42974
$81$	6.35851	0.706501
$82$	−24.3328	−2.68710
$83$	−3.44693	−0.378350	−0.189175	−	0.981943i	$-0.560581\pi$
$83$	−3.44693	−0.378350	−0.189175	+	0.981943i	$0.560581\pi$
$84$	12.0048	1.30983
$85$	−0.137490	−0.0149128
$86$	14.7819	1.59397
$87$	1.90508	0.204246
$88$	−21.6737	−2.31042
$89$	1.03400	0.109604	0.0548018	−	0.998497i	$-0.482547\pi$
$89$	1.03400	0.109604	0.0548018	+	0.998497i	$0.482547\pi$
$90$	7.24362	0.763545
$91$	−22.4792	−2.35646
$92$	−21.2810	−2.21870
$93$	−0.933125	−0.0967606
$94$	21.3172	2.19870
$95$	−5.14076	−0.527431
$96$	9.40637	0.960033
$97$	−6.36595	−0.646365	−0.323182	−	0.946337i	$-0.604753\pi$
$97$	−6.36595	−0.646365	−0.323182	+	0.946337i	$0.604753\pi$
$98$	−28.0160	−2.83004
$99$	−6.76032	−0.679438
$100$	5.21758	0.521758
$101$	9.34813	0.930174	0.465087	−	0.885265i	$-0.346023\pi$
$101$	9.34813	0.930174	0.465087	+	0.885265i	$0.346023\pi$
$102$	−0.203575	−0.0201569
$103$	−10.2631	−1.01125	−0.505625	−	0.862753i	$-0.668738\pi$
$103$	−10.2631	−1.01125	−0.505625	+	0.862753i	$0.668738\pi$
$104$	−46.5457	−4.56419
$105$	2.30083	0.224538
$106$	3.17480	0.308364
$107$	−6.17808	−0.597257	−0.298629	−	0.954369i	$-0.596529\pi$
$107$	−6.17808	−0.597257	−0.298629	+	0.954369i	$0.596529\pi$
$108$	16.3801	1.57618
$109$	−2.26953	−0.217381	−0.108691	−	0.994076i	$-0.534666\pi$
$109$	−2.26953	−0.217381	−0.108691	+	0.994076i	$0.534666\pi$
$110$	−6.73601	−0.642254
$111$	2.51763	0.238963
$112$	−53.3862	−5.04452
$113$	−4.42636	−0.416397	−0.208198	−	0.978087i	$-0.566760\pi$
$113$	−4.42636	−0.416397	−0.208198	+	0.978087i	$0.566760\pi$
$114$	−7.61171	−0.712902
$115$	−4.07872	−0.380342
$116$	−18.0354	−1.67454
$117$	−14.5183	−1.34221
$118$	−16.2981	−1.50036
$119$	0.573980	0.0526167
$120$	4.76414	0.434904
$121$	−4.71342	−0.428493
$122$	−12.2310	−1.10735
$123$	−4.99177	−0.450092
$124$	8.83386	0.793304
$125$	1.00000	0.0894427
$126$	−30.2401	−2.69400
$127$	19.0217	1.68790	0.843950	−	0.536421i	$-0.180224\pi$
$127$	19.0217	1.68790	0.843950	+	0.536421i	$0.180224\pi$
$128$	−20.3384	−1.79768
$129$	3.03244	0.266991
$130$	−14.4661	−1.26876
$131$	−8.92416	−0.779708	−0.389854	−	0.920877i	$-0.627474\pi$
$131$	−8.92416	−0.779708	−0.389854	+	0.920877i	$0.627474\pi$
$132$	−7.21000	−0.627550
$133$	21.4612	1.86092
$134$	−15.0534	−1.30041
$135$	3.13941	0.270197
$136$	1.18849	0.101912
$137$	−14.1239	−1.20669	−0.603344	−	0.797481i	$-0.706165\pi$
$137$	−14.1239	−1.20669	−0.603344	+	0.797481i	$0.706165\pi$
$138$	−6.03918	−0.514089
$139$	9.55889	0.810774	0.405387	−	0.914145i	$-0.367137\pi$
$139$	9.55889	0.810774	0.405387	+	0.914145i	$0.367137\pi$
$140$	−21.7819	−1.84091
$141$	4.37313	0.368284
$142$	−3.70042	−0.310533
$143$	13.5009	1.12900
$144$	−34.4796	−2.87330
$145$	−3.45665	−0.287059
$146$	5.66003	0.468427
$147$	−5.74737	−0.474035
$148$	−23.8343	−1.95917
$149$	21.8435	1.78949	0.894745	−	0.446578i	$-0.147357\pi$
$149$	21.8435	1.78949	0.894745	+	0.446578i	$0.147357\pi$
$150$	1.48066	0.120895
$151$	7.11517	0.579024	0.289512	−	0.957174i	$-0.406507\pi$
$151$	7.11517	0.579024	0.289512	+	0.957174i	$0.406507\pi$
$152$	44.4379	3.60439
$153$	0.370706	0.0299698
$154$	28.1209	2.26605
$155$	1.69309	0.135993
$156$	−15.4840	−1.23971
$157$	−0.751237	−0.0599552	−0.0299776	−	0.999551i	$-0.509544\pi$
$157$	−0.751237	−0.0599552	−0.0299776	+	0.999551i	$0.509544\pi$
$158$	35.6648	2.83734
$159$	0.651298	0.0516513
$160$	−17.0672	−1.34928
$161$	17.0275	1.34195
$162$	−17.0825	−1.34213
$163$	−0.301965	−0.0236517	−0.0118258	−	0.999930i	$-0.503764\pi$
$163$	−0.301965	−0.0236517	−0.0118258	+	0.999930i	$0.503764\pi$
$164$	47.2569	3.69014
$165$	−1.38187	−0.107578
$166$	9.26038	0.718745
$167$	−15.3675	−1.18918	−0.594588	−	0.804030i	$-0.702685\pi$
$167$	−15.3675	−1.18918	−0.594588	+	0.804030i	$0.702685\pi$
$168$	−19.8889	−1.53446
$169$	15.9941	1.23031
$170$	0.369374	0.0283297
$171$	13.8608	1.05996
$172$	−28.7080	−2.18896
$173$	16.7019	1.26982	0.634912	−	0.772584i	$-0.281036\pi$
$173$	16.7019	1.26982	0.634912	+	0.772584i	$0.281036\pi$
$174$	−5.11812	−0.388003
$175$	−4.17471	−0.315579
$176$	32.0634	2.41687
$177$	−3.34348	−0.251311
$178$	−2.77789	−0.208212
$179$	−8.36947	−0.625563	−0.312782	−	0.949825i	$-0.601261\pi$
$179$	−8.36947	−0.625563	−0.312782	+	0.949825i	$0.601261\pi$
$180$	−14.0679	−1.04856
$181$	0.123471	0.00917756	0.00458878	−	0.999989i	$-0.498539\pi$
$181$	0.123471	0.00917756	0.00458878	+	0.999989i	$0.498539\pi$
$182$	60.3917	4.47653
$183$	−2.50915	−0.185481
$184$	35.2573	2.59920
$185$	−4.56807	−0.335851
$186$	2.50689	0.183814
$187$	−0.344729	−0.0252090
$188$	−41.4003	−3.01943
$189$	−13.1061	−0.953330
$190$	13.8110	1.00195
$191$	5.71354	0.413417	0.206709	−	0.978403i	$-0.433725\pi$
$191$	5.71354	0.413417	0.206709	+	0.978403i	$0.433725\pi$
$192$	−11.1749	−0.806478
$193$	−10.5684	−0.760732	−0.380366	−	0.924836i	$-0.624202\pi$
$193$	−10.5684	−0.760732	−0.380366	+	0.924836i	$0.624202\pi$
$194$	17.1025	1.22789
$195$	−2.96765	−0.212518
$196$	54.4101	3.88644
$197$	−10.1228	−0.721222	−0.360611	−	0.932716i	$-0.617432\pi$
$197$	−10.1228	−0.721222	−0.360611	+	0.932716i	$0.617432\pi$
$198$	18.1620	1.29072
$199$	−14.9223	−1.05782	−0.528908	−	0.848679i	$-0.677398\pi$
$199$	−14.9223	−1.05782	−0.528908	+	0.848679i	$0.677398\pi$
$200$	−8.64421	−0.611238
$201$	−3.08813	−0.217820
$202$	−25.1143	−1.76703
$203$	14.4305	1.01282
$204$	0.395365	0.0276811
$205$	9.05723	0.632585
$206$	27.5723	1.92105
$207$	10.9972	0.764361
$208$	68.8584	4.77447
$209$	−12.8895	−0.891583
$210$	−6.18132	−0.426551
$211$	−23.4320	−1.61313	−0.806564	−	0.591146i	$-0.798676\pi$
$211$	−23.4320	−1.61313	−0.806564	+	0.591146i	$0.798676\pi$
$212$	−6.16581	−0.423470
$213$	−0.759126	−0.0520145
$214$	16.5977	1.13460
$215$	−5.50216	−0.375245
$216$	−27.1377	−1.84649
$217$	−7.06818	−0.479820
$218$	6.09721	0.412955
$219$	1.16113	0.0784620
$220$	13.0821	0.881993
$221$	−0.740329	−0.0497999
$222$	−6.76375	−0.453953
$223$	−14.7466	−0.987505	−0.493752	−	0.869603i	$-0.664375\pi$
$223$	−14.7466	−0.987505	−0.493752	+	0.869603i	$0.664375\pi$
$224$	71.2508	4.76065
$225$	−2.69625	−0.179750
$226$	11.8917	0.791021
$227$	25.2136	1.67349	0.836743	−	0.547596i	$-0.184457\pi$
$227$	25.2136	1.67349	0.836743	+	0.547596i	$0.184457\pi$
$228$	14.7828	0.979012
$229$	4.51510	0.298366	0.149183	−	0.988810i	$-0.452336\pi$
$229$	4.51510	0.298366	0.149183	+	0.988810i	$0.452336\pi$
$230$	10.9577	0.722529
$231$	5.76889	0.379565
$232$	29.8800	1.96172
$233$	20.1643	1.32101	0.660503	−	0.750824i	$-0.270343\pi$
$233$	20.1643	1.32101	0.660503	+	0.750824i	$0.270343\pi$
$234$	39.0041	2.54978
$235$	−7.93476	−0.517607
$236$	31.6526	2.06041
$237$	7.31649	0.475257
$238$	−1.54203	−0.0999549
$239$	−22.5189	−1.45663	−0.728314	−	0.685243i	$-0.759696\pi$
$239$	−22.5189	−1.45663	−0.728314	+	0.685243i	$0.759696\pi$
$240$	−7.04792	−0.454941
$241$	0.214386	0.0138098	0.00690491	−	0.999976i	$-0.497802\pi$
$241$	0.214386	0.0138098	0.00690491	+	0.999976i	$0.497802\pi$
$242$	12.6629	0.814000
$243$	−12.9226	−0.828987
$244$	23.7540	1.52069
$245$	10.4282	0.666235
$246$	13.4107	0.855032
$247$	−27.6810	−1.76130
$248$	−14.6355	−0.929353
$249$	1.89973	0.120390
$250$	−2.68656	−0.169913
$251$	16.4492	1.03826	0.519131	−	0.854694i	$-0.326256\pi$
$251$	16.4492	1.03826	0.519131	+	0.854694i	$0.326256\pi$
$252$	58.7295	3.69961
$253$	−10.2266	−0.642940
$254$	−51.1028	−3.20647
$255$	0.0757755	0.00474524
$256$	14.0880	0.880502
$257$	−12.5060	−0.780101	−0.390050	−	0.920793i	$-0.627542\pi$
$257$	−12.5060	−0.780101	−0.390050	+	0.920793i	$0.627542\pi$
$258$	−8.14682	−0.507199
$259$	19.0704	1.18498
$260$	28.0947	1.74236
$261$	9.32000	0.576893
$262$	23.9753	1.48120
$263$	4.20507	0.259296	0.129648	−	0.991560i	$-0.458615\pi$
$263$	4.20507	0.259296	0.129648	+	0.991560i	$0.458615\pi$
$264$	11.9451	0.735173
$265$	−1.18174	−0.0725935
$266$	−57.6568	−3.53516
$267$	−0.569873	−0.0348757
$268$	29.2352	1.78583
$269$	7.18939	0.438345	0.219172	−	0.975686i	$-0.429664\pi$
$269$	7.18939	0.438345	0.219172	+	0.975686i	$0.429664\pi$
$270$	−8.43419	−0.513289
$271$	26.8734	1.63245	0.816223	−	0.577737i	$-0.196064\pi$
$271$	26.8734	1.63245	0.816223	+	0.577737i	$0.196064\pi$
$272$	−1.75822	−0.106608
$273$	12.3891	0.749822
$274$	37.9447	2.29232
$275$	2.50730	0.151196
$276$	11.7287	0.705987
$277$	−20.5493	−1.23469	−0.617343	−	0.786694i	$-0.711791\pi$
$277$	−20.5493	−1.23469	−0.617343	+	0.786694i	$0.711791\pi$
$278$	−25.6805	−1.54021
$279$	−4.56501	−0.273300
$280$	36.0871	2.15662
$281$	12.2280	0.729459	0.364730	−	0.931114i	$-0.381161\pi$
$281$	12.2280	0.729459	0.364730	+	0.931114i	$0.381161\pi$
$282$	−11.7487	−0.699623
$283$	16.4398	0.977247	0.488623	−	0.872495i	$-0.337499\pi$
$283$	16.4398	0.977247	0.488623	+	0.872495i	$0.337499\pi$
$284$	7.18662	0.426447
$285$	2.83326	0.167828
$286$	−36.2708	−2.14474
$287$	−37.8114	−2.23193
$288$	46.0175	2.71161
$289$	−16.9811	−0.998888
$290$	9.28649	0.545321
$291$	3.50851	0.205672
$292$	−10.9924	−0.643281
$293$	4.35771	0.254580	0.127290	−	0.991866i	$-0.459372\pi$
$293$	4.35771	0.254580	0.127290	+	0.991866i	$0.459372\pi$
$294$	15.4406	0.900516
$295$	6.06653	0.353207
$296$	39.4874	2.29516
$297$	7.87145	0.456748
$298$	−58.6838	−3.39946
$299$	−21.9623	−1.27011
$300$	−2.87560	−0.166023
$301$	22.9700	1.32397
$302$	−19.1153	−1.09996
$303$	−5.15209	−0.295980
$304$	−65.7401	−3.77045
$305$	4.55268	0.260686
$306$	−0.995924	−0.0569332
$307$	−5.57201	−0.318012	−0.159006	−	0.987278i	$-0.550829\pi$
$307$	−5.57201	−0.318012	−0.159006	+	0.987278i	$0.550829\pi$
$308$	−54.6139	−3.11191
$309$	5.65635	0.321778
$310$	−4.54859	−0.258343
$311$	8.45195	0.479266	0.239633	−	0.970864i	$-0.422973\pi$
$311$	8.45195	0.479266	0.239633	+	0.970864i	$0.422973\pi$
$312$	25.6530	1.45232
$313$	21.7270	1.22808	0.614041	−	0.789274i	$-0.289543\pi$
$313$	21.7270	1.22808	0.614041	+	0.789274i	$0.289543\pi$
$314$	2.01824	0.113896
$315$	11.2561	0.634208
$316$	−69.2650	−3.89646
$317$	6.21933	0.349312	0.174656	−	0.984629i	$-0.444119\pi$
$317$	6.21933	0.349312	0.174656	+	0.984629i	$0.444119\pi$
$318$	−1.74975	−0.0981210
$319$	−8.66688	−0.485252
$320$	20.2761	1.13347
$321$	3.40496	0.190046
$322$	−45.7452	−2.54928
$323$	0.706802	0.0393275
$324$	33.1760	1.84311
$325$	5.38461	0.298685
$326$	0.811245	0.0449307
$327$	1.25082	0.0691704
$328$	−78.2927	−4.32299
$329$	33.1254	1.82626
$330$	3.71246	0.204364
$331$	−1.60605	−0.0882764	−0.0441382	−	0.999025i	$-0.514054\pi$
$331$	−1.60605	−0.0882764	−0.0441382	+	0.999025i	$0.514054\pi$
$332$	−17.9847	−0.987036
$333$	12.3167	0.674949
$334$	41.2858	2.25906
$335$	5.60322	0.306136
$336$	29.4231	1.60516
$337$	19.7668	1.07676	0.538382	−	0.842701i	$-0.319036\pi$
$337$	19.7668	1.07676	0.538382	+	0.842701i	$0.319036\pi$
$338$	−42.9689	−2.33720
$339$	2.43952	0.132497
$340$	−0.717364	−0.0389045
$341$	4.24510	0.229885
$342$	−37.2378	−2.01359
$343$	−14.3119	−0.772768
$344$	47.5619	2.56437
$345$	2.24793	0.121024
$346$	−44.8707	−2.41226
$347$	28.4597	1.52780	0.763899	−	0.645336i	$-0.223283\pi$
$347$	28.4597	1.52780	0.763899	+	0.645336i	$0.223283\pi$
$348$	9.93993	0.532836
$349$	−9.69739	−0.519090	−0.259545	−	0.965731i	$-0.583573\pi$
$349$	−9.69739	−0.519090	−0.259545	+	0.965731i	$0.583573\pi$
$350$	11.2156	0.599499
$351$	16.9045	0.902295
$352$	−42.7928	−2.28086
$353$	−1.88103	−0.100117	−0.0500586	−	0.998746i	$-0.515941\pi$
$353$	−1.88103	−0.100117	−0.0500586	+	0.998746i	$0.515941\pi$
$354$	8.98245	0.477412
$355$	1.37739	0.0731040
$356$	5.39497	0.285933
$357$	−0.316341	−0.0167425
$358$	22.4850	1.18837
$359$	−14.2015	−0.749528	−0.374764	−	0.927120i	$-0.622276\pi$
$359$	−14.2015	−0.749528	−0.374764	+	0.927120i	$0.622276\pi$
$360$	23.3070	1.22838
$361$	7.42746	0.390919
$362$	−0.331713	−0.0174344
$363$	2.59774	0.136346
$364$	−117.287	−6.14752
$365$	−2.10680	−0.110275
$366$	6.74096	0.352356
$367$	26.2555	1.37053	0.685264	−	0.728295i	$-0.259687\pi$
$367$	26.2555	1.37053	0.685264	+	0.728295i	$0.259687\pi$
$368$	−52.1586	−2.71896
$369$	−24.4206	−1.27128
$370$	12.2724	0.638011
$371$	4.93341	0.256130
$372$	−4.86866	−0.252428
$373$	−20.6020	−1.06673	−0.533366	−	0.845884i	$-0.679073\pi$
$373$	−20.6020	−1.06673	−0.533366	+	0.845884i	$0.679073\pi$
$374$	0.926132	0.0478892
$375$	−0.551136	−0.0284605
$376$	68.5898	3.53725
$377$	−18.6127	−0.958604
$378$	35.2103	1.81102
$379$	−31.7907	−1.63298	−0.816489	−	0.577361i	$-0.804083\pi$
$379$	−31.7907	−1.63298	−0.816489	+	0.577361i	$0.804083\pi$
$380$	−26.8224	−1.37596
$381$	−10.4835	−0.537087
$382$	−15.3497	−0.785361
$383$	−18.7585	−0.958516	−0.479258	−	0.877674i	$-0.659094\pi$
$383$	−18.7585	−0.958516	−0.479258	+	0.877674i	$0.659094\pi$
$384$	11.2092	0.572018
$385$	−10.4673	−0.533462
$386$	28.3927	1.44515
$387$	14.8352	0.754116
$388$	−33.2149	−1.68623
$389$	15.3497	0.778259	0.389129	−	0.921183i	$-0.372776\pi$
$389$	15.3497	0.778259	0.389129	+	0.921183i	$0.372776\pi$
$390$	7.97276	0.403717
$391$	0.560781	0.0283599
$392$	−90.1438	−4.55295
$393$	4.91843	0.248102
$394$	27.1956	1.37009
$395$	−13.2753	−0.667953
$396$	−35.2725	−1.77251
$397$	6.77136	0.339845	0.169923	−	0.985457i	$-0.445648\pi$
$397$	6.77136	0.339845	0.169923	+	0.985457i	$0.445648\pi$
$398$	40.0897	2.00951
$399$	−11.8280	−0.592143
$400$	12.7880	0.639400
$401$	−1.40707	−0.0702657	−0.0351329	−	0.999383i	$-0.511185\pi$
$401$	−1.40707	−0.0702657	−0.0351329	+	0.999383i	$0.511185\pi$
$402$	8.29644	0.413789
$403$	9.11666	0.454133
$404$	48.7747	2.42663
$405$	6.35851	0.315957
$406$	−38.7684	−1.92404
$407$	−11.4535	−0.567731
$408$	−0.655019	−0.0324283
$409$	12.2604	0.606238	0.303119	−	0.952953i	$-0.401972\pi$
$409$	12.2604	0.606238	0.303119	+	0.952953i	$0.401972\pi$
$410$	−24.3328	−1.20171
$411$	7.78420	0.383966
$412$	−53.5484	−2.63814
$413$	−25.3260	−1.24621
$414$	−29.5447	−1.45204
$415$	−3.44693	−0.169203
$416$	−91.9005	−4.50579
$417$	−5.26825	−0.257987
$418$	34.6283	1.69372
$419$	−7.10863	−0.347279	−0.173640	−	0.984809i	$-0.555553\pi$
$419$	−7.10863	−0.347279	−0.173640	+	0.984809i	$0.555553\pi$
$420$	12.0048	0.585774
$421$	−13.0499	−0.636013	−0.318007	−	0.948088i	$-0.603013\pi$
$421$	−13.0499	−0.636013	−0.318007	+	0.948088i	$0.603013\pi$
$422$	62.9515	3.06443
$423$	21.3941	1.04022
$424$	10.2152	0.496093
$425$	−0.137490	−0.00666923
$426$	2.03943	0.0988109
$427$	−19.0061	−0.919772
$428$	−32.2346	−1.55812
$429$	−7.44081	−0.359246
$430$	14.7819	0.712845
$431$	7.98782	0.384760	0.192380	−	0.981321i	$-0.438379\pi$
$431$	7.98782	0.384760	0.192380	+	0.981321i	$0.438379\pi$
$432$	40.1467	1.93156
$433$	−23.3731	−1.12324	−0.561619	−	0.827396i	$-0.689821\pi$
$433$	−23.3731	−1.12324	−0.561619	+	0.827396i	$0.689821\pi$
$434$	18.9891	0.911505
$435$	1.90508	0.0913418
$436$	−11.8414	−0.567102
$437$	20.9677	1.00302
$438$	−3.11944	−0.149053
$439$	−35.4872	−1.69371	−0.846855	−	0.531824i	$-0.821507\pi$
$439$	−35.4872	−1.69371	−0.846855	+	0.531824i	$0.821507\pi$
$440$	−21.6737	−1.03325
$441$	−28.1171	−1.33891
$442$	1.98893	0.0946040
$443$	13.6082	0.646543	0.323272	−	0.946306i	$-0.395217\pi$
$443$	13.6082	0.646543	0.323272	+	0.946306i	$0.395217\pi$
$444$	13.1359	0.623404
$445$	1.03400	0.0490162
$446$	39.6175	1.87595
$447$	−12.0387	−0.569413
$448$	−84.6469	−3.99919
$449$	16.2595	0.767331	0.383666	−	0.923472i	$-0.374662\pi$
$449$	16.2595	0.767331	0.383666	+	0.923472i	$0.374662\pi$
$450$	7.24362	0.341468
$451$	22.7092	1.06934
$452$	−23.0949	−1.08629
$453$	−3.92142	−0.184244
$454$	−67.7377	−3.17909
$455$	−22.4792	−1.05384
$456$	−24.4913	−1.14691
$457$	−22.0888	−1.03327	−0.516636	−	0.856205i	$-0.672816\pi$
$457$	−22.0888	−1.03327	−0.516636	+	0.856205i	$0.672816\pi$
$458$	−12.1301	−0.566801
$459$	−0.431636	−0.0201470
$460$	−21.2810	−0.992233
$461$	21.2236	0.988484	0.494242	−	0.869324i	$-0.335446\pi$
$461$	21.2236	0.988484	0.494242	+	0.869324i	$0.335446\pi$
$462$	−15.4984	−0.721053
$463$	3.75121	0.174334	0.0871668	−	0.996194i	$-0.472219\pi$
$463$	3.75121	0.174334	0.0871668	+	0.996194i	$0.472219\pi$
$464$	−44.2037	−2.05210
$465$	−0.933125	−0.0432726
$466$	−54.1724	−2.50949
$467$	22.7424	1.05239	0.526196	−	0.850363i	$-0.323618\pi$
$467$	22.7424	1.05239	0.526196	+	0.850363i	$0.323618\pi$
$468$	−75.7502	−3.50155
$469$	−23.3918	−1.08013
$470$	21.3172	0.983288
$471$	0.414034	0.0190777
$472$	−52.4404	−2.41376
$473$	−13.7956	−0.634323
$474$	−19.6562	−0.902838
$475$	−5.14076	−0.235874
$476$	2.99479	0.137266
$477$	3.18626	0.145889
$478$	60.4984	2.76713
$479$	16.3008	0.744803	0.372401	−	0.928072i	$-0.378534\pi$
$479$	16.3008	0.744803	0.372401	+	0.928072i	$0.378534\pi$
$480$	9.40637	0.429340
$481$	−24.5973	−1.12154
$482$	−0.575960	−0.0262343
$483$	−9.38445	−0.427007
$484$	−24.5927	−1.11785
$485$	−6.36595	−0.289063
$486$	34.7173	1.57481
$487$	6.81584	0.308855	0.154428	−	0.988004i	$-0.450647\pi$
$487$	6.81584	0.308855	0.154428	+	0.988004i	$0.450647\pi$
$488$	−39.3544	−1.78149
$489$	0.166424	0.00752593
$490$	−28.0160	−1.26563
$491$	−7.37205	−0.332696	−0.166348	−	0.986067i	$-0.553197\pi$
$491$	−7.37205	−0.332696	−0.166348	+	0.986067i	$0.553197\pi$
$492$	−26.0449	−1.17420
$493$	0.475254	0.0214044
$494$	74.3666	3.34591
$495$	−6.76032	−0.303854
$496$	21.6513	0.972172
$497$	−5.75019	−0.257931
$498$	−5.10373	−0.228703
$499$	−19.3192	−0.864848	−0.432424	−	0.901670i	$-0.642342\pi$
$499$	−19.3192	−0.864848	−0.432424	+	0.901670i	$0.642342\pi$
$500$	5.21758	0.233337
$501$	8.46961	0.378394
$502$	−44.1916	−1.97237
$503$	38.1145	1.69944	0.849722	−	0.527231i	$-0.176770\pi$
$503$	38.1145	1.69944	0.849722	+	0.527231i	$0.176770\pi$
$504$	−97.2998	−4.33408
$505$	9.34813	0.415986
$506$	27.4743	1.22138
$507$	−8.81490	−0.391483
$508$	99.2472	4.40338
$509$	16.5328	0.732803	0.366401	−	0.930457i	$-0.380590\pi$
$509$	16.5328	0.732803	0.366401	+	0.930457i	$0.380590\pi$
$510$	−0.203575	−0.00901445
$511$	8.79527	0.389080
$512$	2.82850	0.125003
$513$	−16.1390	−0.712552
$514$	33.5980	1.48194
$515$	−10.2631	−0.452245
$516$	15.8220	0.696525
$517$	−19.8949	−0.874975
$518$	−51.2337	−2.25108
$519$	−9.20503	−0.404056
$520$	−46.5457	−2.04117
$521$	−9.38900	−0.411340	−0.205670	−	0.978621i	$-0.565937\pi$
$521$	−9.38900	−0.411340	−0.205670	+	0.978621i	$0.565937\pi$
$522$	−25.0387	−1.09591
$523$	44.8717	1.96210	0.981052	−	0.193744i	$-0.0620632\pi$
$523$	44.8717	1.96210	0.981052	+	0.193744i	$0.0620632\pi$
$524$	−46.5626	−2.03409
$525$	2.30083	0.100417
$526$	−11.2971	−0.492579
$527$	−0.232783	−0.0101402
$528$	−17.6713	−0.769044
$529$	−6.36408	−0.276699
$530$	3.17480	0.137905
$531$	−16.3569	−0.709828
$532$	111.976	4.85476
$533$	48.7697	2.11245
$534$	1.53100	0.0662527
$535$	−6.17808	−0.267101
$536$	−48.4354	−2.09209
$537$	4.61271	0.199053
$538$	−19.3147	−0.832716
$539$	26.1467	1.12622
$540$	16.3801	0.704888
$541$	35.1182	1.50985	0.754924	−	0.655812i	$-0.227674\pi$
$541$	35.1182	1.50985	0.754924	+	0.655812i	$0.227674\pi$
$542$	−72.1970	−3.10113
$543$	−0.0680496	−0.00292029
$544$	2.34657	0.100608
$545$	−2.26953	−0.0972159
$546$	−33.2840	−1.42442
$547$	−32.2773	−1.38008	−0.690038	−	0.723773i	$-0.742406\pi$
$547$	−32.2773	−1.38008	−0.690038	+	0.723773i	$0.742406\pi$
$548$	−73.6927	−3.14800
$549$	−12.2752	−0.523891
$550$	−6.73601	−0.287225
$551$	17.7698	0.757020
$552$	−19.4316	−0.827062
$553$	55.4206	2.35672
$554$	55.2068	2.34551
$555$	2.51763	0.106867
$556$	49.8743	2.11514
$557$	13.0377	0.552426	0.276213	−	0.961096i	$-0.410920\pi$
$557$	13.0377	0.552426	0.276213	+	0.961096i	$0.410920\pi$
$558$	12.2641	0.519183
$559$	−29.6270	−1.25309
$560$	−53.3862	−2.25598
$561$	0.189992	0.00802148
$562$	−32.8511	−1.38574
$563$	−42.3308	−1.78403	−0.892014	−	0.452007i	$-0.850708\pi$
$563$	−42.3308	−1.78403	−0.892014	+	0.452007i	$0.850708\pi$
$564$	22.8172	0.960776
$565$	−4.42636	−0.186218
$566$	−44.1665	−1.85646
$567$	−26.5449	−1.11478
$568$	−11.9064	−0.499582
$569$	41.0841	1.72234	0.861168	−	0.508320i	$-0.169733\pi$
$569$	41.0841	1.72234	0.861168	+	0.508320i	$0.169733\pi$
$570$	−7.61171	−0.318819
$571$	−26.1998	−1.09643	−0.548213	−	0.836339i	$-0.684692\pi$
$571$	−26.1998	−1.09643	−0.548213	+	0.836339i	$0.684692\pi$
$572$	70.4419	2.94532
$573$	−3.14893	−0.131549
$574$	101.582	4.23996
$575$	−4.07872	−0.170094
$576$	−54.6694	−2.27789
$577$	−13.4846	−0.561370	−0.280685	−	0.959800i	$-0.590562\pi$
$577$	−13.4846	−0.561370	−0.280685	+	0.959800i	$0.590562\pi$
$578$	45.6207	1.89757
$579$	5.82464	0.242064
$580$	−18.0354	−0.748878
$581$	14.3900	0.596996
$582$	−9.42580	−0.390712
$583$	−2.96298	−0.122714
$584$	18.2116	0.753602
$585$	−14.5183	−0.600256
$586$	−11.7072	−0.483621
$587$	−39.6361	−1.63596	−0.817979	−	0.575248i	$-0.804906\pi$
$587$	−39.6361	−1.63596	−0.817979	+	0.575248i	$0.804906\pi$
$588$	−29.9874	−1.23666
$589$	−8.70380	−0.358634
$590$	−16.2981	−0.670981
$591$	5.57906	0.229492
$592$	−58.4165	−2.40090
$593$	−17.9368	−0.736577	−0.368288	−	0.929712i	$-0.620056\pi$
$593$	−17.9368	−0.736577	−0.368288	+	0.929712i	$0.620056\pi$
$594$	−21.1471	−0.867676
$595$	0.573980	0.0235309
$596$	113.970	4.66840
$597$	8.22424	0.336596
$598$	59.0030	2.41281
$599$	−21.7227	−0.887565	−0.443782	−	0.896135i	$-0.646364\pi$
$599$	−21.7227	−0.887565	−0.443782	+	0.896135i	$0.646364\pi$
$600$	4.76414	0.194495
$601$	26.5987	1.08498	0.542491	−	0.840061i	$-0.317481\pi$
$601$	26.5987	1.08498	0.542491	+	0.840061i	$0.317481\pi$
$602$	−61.7101	−2.51511
$603$	−15.1077	−0.615232
$604$	37.1240	1.51055
$605$	−4.71342	−0.191628
$606$	13.8414	0.562268
$607$	17.9496	0.728553	0.364277	−	0.931291i	$-0.381316\pi$
$607$	17.9496	0.728553	0.364277	+	0.931291i	$0.381316\pi$
$608$	87.7387	3.55827
$609$	−7.95318	−0.322279
$610$	−12.2310	−0.495220
$611$	−42.7256	−1.72849
$612$	1.93419	0.0781851
$613$	−5.66539	−0.228823	−0.114412	−	0.993433i	$-0.536498\pi$
$613$	−5.66539	−0.228823	−0.114412	+	0.993433i	$0.536498\pi$
$614$	14.9695	0.604121
$615$	−4.99177	−0.201287
$616$	90.4814	3.64560
$617$	−10.5310	−0.423963	−0.211982	−	0.977274i	$-0.567992\pi$
$617$	−10.5310	−0.423963	−0.211982	+	0.977274i	$0.567992\pi$
$618$	−15.1961	−0.611276
$619$	22.2872	0.895799	0.447900	−	0.894084i	$-0.352172\pi$
$619$	22.2872	0.895799	0.447900	+	0.894084i	$0.352172\pi$
$620$	8.83386	0.354776
$621$	−12.8047	−0.513837
$622$	−22.7066	−0.910454
$623$	−4.31664	−0.172943
$624$	−37.9503	−1.51923
$625$	1.00000	0.0400000
$626$	−58.3708	−2.33296
$627$	7.10384	0.283700
$628$	−3.91964	−0.156411
$629$	0.628063	0.0250425
$630$	−30.2401	−1.20479
$631$	41.9274	1.66910	0.834552	−	0.550930i	$-0.185727\pi$
$631$	41.9274	1.66910	0.834552	+	0.550930i	$0.185727\pi$
$632$	114.755	4.56469
$633$	12.9142	0.513295
$634$	−16.7086	−0.663583
$635$	19.0217	0.754852
$636$	3.39820	0.134747
$637$	56.1520	2.22482
$638$	23.2841	0.921825
$639$	−3.71377	−0.146915
$640$	−20.3384	−0.803946
$641$	20.7974	0.821447	0.410723	−	0.911760i	$-0.365276\pi$
$641$	20.7974	0.821447	0.410723	+	0.911760i	$0.365276\pi$
$642$	−9.14761	−0.361027
$643$	43.7406	1.72496	0.862480	−	0.506091i	$-0.168910\pi$
$643$	43.7406	1.72496	0.862480	+	0.506091i	$0.168910\pi$
$644$	88.8422	3.50087
$645$	3.03244	0.119402
$646$	−1.89886	−0.0747098
$647$	49.3297	1.93935	0.969675	−	0.244397i	$-0.0785899\pi$
$647$	49.3297	1.93935	0.969675	+	0.244397i	$0.0785899\pi$
$648$	−54.9643	−2.15920
$649$	15.2106	0.597070
$650$	−14.4661	−0.567406
$651$	3.89553	0.152678
$652$	−1.57553	−0.0617023
$653$	7.98269	0.312387	0.156193	−	0.987727i	$-0.450078\pi$
$653$	7.98269	0.312387	0.156193	+	0.987727i	$0.450078\pi$
$654$	−3.36039	−0.131402
$655$	−8.92416	−0.348696
$656$	115.824	4.52216
$657$	5.68045	0.221615
$658$	−88.9931	−3.46931
$659$	42.2683	1.64654	0.823270	−	0.567649i	$-0.192147\pi$
$659$	42.2683	1.64654	0.823270	+	0.567649i	$0.192147\pi$
$660$	−7.21000	−0.280649
$661$	10.4675	0.407138	0.203569	−	0.979061i	$-0.434746\pi$
$661$	10.4675	0.407138	0.203569	+	0.979061i	$0.434746\pi$
$662$	4.31474	0.167697
$663$	0.408022	0.0158462
$664$	29.7960	1.15631
$665$	21.4612	0.832230
$666$	−33.0894	−1.28219
$667$	14.0987	0.545904
$668$	−80.1814	−3.10231
$669$	8.12737	0.314222
$670$	−15.0534	−0.581562
$671$	11.4150	0.440670
$672$	−39.2689	−1.51483
$673$	45.1154	1.73907	0.869536	−	0.493870i	$-0.164418\pi$
$673$	45.1154	1.73907	0.869536	+	0.493870i	$0.164418\pi$
$674$	−53.1046	−2.04551
$675$	3.13941	0.120836
$676$	83.4503	3.20963
$677$	4.12144	0.158400	0.0791999	−	0.996859i	$-0.474763\pi$
$677$	4.12144	0.158400	0.0791999	+	0.996859i	$0.474763\pi$
$678$	−6.55392	−0.251702
$679$	26.5760	1.01989
$680$	1.18849	0.0455765
$681$	−13.8961	−0.532500
$682$	−11.4047	−0.436709
$683$	10.8404	0.414797	0.207399	−	0.978257i	$-0.433500\pi$
$683$	10.8404	0.414797	0.207399	+	0.978257i	$0.433500\pi$
$684$	72.3198	2.76522
$685$	−14.1239	−0.539647
$686$	38.4496	1.46801
$687$	−2.48843	−0.0949397
$688$	−70.3617	−2.68251
$689$	−6.36320	−0.242418
$690$	−6.03918	−0.229908
$691$	−2.42507	−0.0922541	−0.0461270	−	0.998936i	$-0.514688\pi$
$691$	−2.42507	−0.0922541	−0.0461270	+	0.998936i	$0.514688\pi$
$692$	87.1437	3.31271
$693$	28.2224	1.07208
$694$	−76.4586	−2.90233
$695$	9.55889	0.362589
$696$	−16.4680	−0.624216
$697$	−1.24528	−0.0471682
$698$	26.0526	0.986105
$699$	−11.1132	−0.420342
$700$	−21.7819	−0.823279
$701$	4.92637	0.186066	0.0930332	−	0.995663i	$-0.470344\pi$
$701$	4.92637	0.186066	0.0930332	+	0.995663i	$0.470344\pi$
$702$	−45.4149	−1.71407
$703$	23.4834	0.885693
$704$	50.8384	1.91604
$705$	4.37313	0.164702
$706$	5.05350	0.190191
$707$	−39.0258	−1.46772
$708$	−17.4449	−0.655619
$709$	−17.3908	−0.653126	−0.326563	−	0.945175i	$-0.605891\pi$
$709$	−17.3908	−0.653126	−0.326563	+	0.945175i	$0.605891\pi$
$710$	−3.70042	−0.138874
$711$	35.7935	1.34236
$712$	−8.93810	−0.334969
$713$	−6.90565	−0.258619
$714$	0.849867	0.0318055
$715$	13.5009	0.504904
$716$	−43.6684	−1.63196
$717$	12.4110	0.463497
$718$	38.1532	1.42386
$719$	−25.8386	−0.963617	−0.481809	−	0.876277i	$-0.660020\pi$
$719$	−25.8386	−0.963617	−0.481809	+	0.876277i	$0.660020\pi$
$720$	−34.4796	−1.28498
$721$	42.8454	1.59565
$722$	−19.9543	−0.742621
$723$	−0.118156	−0.00439427
$724$	0.644223	0.0239423
$725$	−3.45665	−0.128377
$726$	−6.97896	−0.259014
$727$	14.0373	0.520614	0.260307	−	0.965526i	$-0.416176\pi$
$727$	14.0373	0.520614	0.260307	+	0.965526i	$0.416176\pi$
$728$	194.315	7.20180
$729$	−11.9534	−0.442719
$730$	5.66003	0.209487
$731$	0.756491	0.0279798
$732$	−13.0917	−0.483882
$733$	47.7566	1.76393	0.881966	−	0.471314i	$-0.156220\pi$
$733$	47.7566	1.76393	0.881966	+	0.471314i	$0.156220\pi$
$734$	−70.5370	−2.60357
$735$	−5.74737	−0.211995
$736$	69.6124	2.56595
$737$	14.0490	0.517500
$738$	65.6072	2.41503
$739$	−53.1000	−1.95331	−0.976657	−	0.214804i	$-0.931089\pi$
$739$	−53.1000	−1.95331	−0.976657	+	0.214804i	$0.931089\pi$
$740$	−23.8343	−0.876166
$741$	15.2560	0.560443
$742$	−13.2539	−0.486566
$743$	47.3435	1.73686	0.868432	−	0.495808i	$-0.165128\pi$
$743$	47.3435	1.73686	0.868432	+	0.495808i	$0.165128\pi$
$744$	8.06613	0.295719
$745$	21.8435	0.800284
$746$	55.3485	2.02645
$747$	9.29379	0.340042
$748$	−1.79865	−0.0657651
$749$	25.7917	0.942408
$750$	1.48066	0.0540659
$751$	−30.4409	−1.11081	−0.555403	−	0.831581i	$-0.687436\pi$
$751$	−30.4409	−1.11081	−0.555403	+	0.831581i	$0.687436\pi$
$752$	−101.470	−3.70022
$753$	−9.06573	−0.330374
$754$	50.0041	1.82104
$755$	7.11517	0.258947
$756$	−68.3823	−2.48704
$757$	−22.3310	−0.811633	−0.405817	−	0.913955i	$-0.633013\pi$
$757$	−22.3310	−0.811633	−0.405817	+	0.913955i	$0.633013\pi$
$758$	85.4075	3.10214
$759$	5.63624	0.204582
$760$	44.4379	1.61193
$761$	42.4805	1.53992	0.769959	−	0.638093i	$-0.220276\pi$
$761$	42.4805	1.53992	0.769959	+	0.638093i	$0.220276\pi$
$762$	28.1646	1.02029
$763$	9.47462	0.343004
$764$	29.8108	1.07852
$765$	0.370706	0.0134029
$766$	50.3959	1.82088
$767$	32.6659	1.17950
$768$	−7.76442	−0.280174
$769$	−51.5033	−1.85726	−0.928628	−	0.371012i	$-0.879011\pi$
$769$	−51.5033	−1.85726	−0.928628	+	0.371012i	$0.879011\pi$
$770$	28.1209	1.01341
$771$	6.89249	0.248227
$772$	−55.1416	−1.98459
$773$	−2.56997	−0.0924355	−0.0462177	−	0.998931i	$-0.514717\pi$
$773$	−2.56997	−0.0924355	−0.0462177	+	0.998931i	$0.514717\pi$
$774$	−39.8556	−1.43258
$775$	1.69309	0.0608178
$776$	55.0287	1.97541
$777$	−10.5104	−0.377058
$778$	−41.2377	−1.47844
$779$	−46.5611	−1.66822
$780$	−15.4840	−0.554415
$781$	3.45352	0.123577
$782$	−1.50657	−0.0538748
$783$	−10.8518	−0.387813
$784$	133.356	4.76272
$785$	−0.751237	−0.0268128
$786$	−13.2136	−0.471314
$787$	−17.4009	−0.620277	−0.310138	−	0.950691i	$-0.600375\pi$
$787$	−17.4009	−0.620277	−0.310138	+	0.950691i	$0.600375\pi$
$788$	−52.8167	−1.88152
$789$	−2.31756	−0.0825074
$790$	35.6648	1.26890
$791$	18.4788	0.657029
$792$	58.4376	2.07649
$793$	24.5144	0.870533
$794$	−18.1916	−0.645597
$795$	0.651298	0.0230991
$796$	−77.8585	−2.75962
$797$	44.9685	1.59287	0.796433	−	0.604727i	$-0.206718\pi$
$797$	44.9685	1.59287	0.796433	+	0.604727i	$0.206718\pi$
$798$	31.7767	1.12488
$799$	1.09095	0.0385950
$800$	−17.0672	−0.603418
$801$	−2.78792	−0.0985062
$802$	3.78017	0.133482
$803$	−5.28238	−0.186411
$804$	−16.1126	−0.568247
$805$	17.0275	0.600139
$806$	−24.4924	−0.862708
$807$	−3.96233	−0.139481
$808$	−80.8073	−2.84279
$809$	14.0536	0.494098	0.247049	−	0.969003i	$-0.420539\pi$
$809$	14.0536	0.494098	0.247049	+	0.969003i	$0.420539\pi$
$810$	−17.0825	−0.600217
$811$	−45.9069	−1.61201	−0.806005	−	0.591909i	$-0.798375\pi$
$811$	−45.9069	−1.61201	−0.806005	+	0.591909i	$0.798375\pi$
$812$	75.2925	2.64225
$813$	−14.8109	−0.519442
$814$	30.7706	1.07851
$815$	−0.301965	−0.0105774
$816$	0.969017	0.0339224
$817$	28.2853	0.989578
$818$	−32.9383	−1.15166
$819$	60.6096	2.11787
$820$	47.2569	1.65028
$821$	45.4069	1.58471	0.792357	−	0.610058i	$-0.208854\pi$
$821$	45.4069	1.58471	0.792357	+	0.610058i	$0.208854\pi$
$822$	−20.9127	−0.729414
$823$	39.5396	1.37826	0.689132	−	0.724635i	$-0.257992\pi$
$823$	39.5396	1.37826	0.689132	+	0.724635i	$0.257992\pi$
$824$	88.7162	3.09057
$825$	−1.38187	−0.0481104
$826$	68.0398	2.36741
$827$	42.7376	1.48613	0.743067	−	0.669218i	$-0.233371\pi$
$827$	42.7376	1.48613	0.743067	+	0.669218i	$0.233371\pi$
$828$	57.3790	1.99406
$829$	−21.3426	−0.741259	−0.370630	−	0.928781i	$-0.620858\pi$
$829$	−21.3426	−0.741259	−0.370630	+	0.928781i	$0.620858\pi$
$830$	9.26038	0.321432
$831$	11.3254	0.392875
$832$	109.179	3.78510
$833$	−1.43377	−0.0496773
$834$	14.1534	0.490093
$835$	−15.3675	−0.531816
$836$	−67.2518	−2.32595
$837$	5.31531	0.183724
$838$	19.0977	0.659720
$839$	17.2492	0.595509	0.297755	−	0.954642i	$-0.403762\pi$
$839$	17.2492	0.595509	0.297755	+	0.954642i	$0.403762\pi$
$840$	−19.8889	−0.686232
$841$	−17.0516	−0.587985
$842$	35.0593	1.20822
$843$	−6.73927	−0.232113
$844$	−122.259	−4.20832
$845$	15.9941	0.550212
$846$	−57.4764	−1.97608
$847$	19.6772	0.676116
$848$	−15.1121	−0.518950
$849$	−9.06058	−0.310958
$850$	0.369374	0.0126694
$851$	18.6319	0.638692
$852$	−3.96080	−0.135695
$853$	3.39166	0.116128	0.0580641	−	0.998313i	$-0.481507\pi$
$853$	3.39166	0.116128	0.0580641	+	0.998313i	$0.481507\pi$
$854$	51.0611	1.74727
$855$	13.8608	0.474029
$856$	53.4046	1.82533
$857$	−11.1756	−0.381750	−0.190875	−	0.981614i	$-0.561132\pi$
$857$	−11.1756	−0.381750	−0.190875	+	0.981614i	$0.561132\pi$
$858$	19.9902	0.682453
$859$	−34.0465	−1.16165	−0.580826	−	0.814027i	$-0.697271\pi$
$859$	−34.0465	−1.16165	−0.580826	+	0.814027i	$0.697271\pi$
$860$	−28.7080	−0.978935
$861$	20.8392	0.710198
$862$	−21.4597	−0.730921
$863$	−39.7923	−1.35455	−0.677273	−	0.735731i	$-0.736839\pi$
$863$	−39.7923	−1.35455	−0.677273	+	0.735731i	$0.736839\pi$
$864$	−53.5810	−1.82286
$865$	16.7019	0.567883
$866$	62.7931	2.13379
$867$	9.35889	0.317845
$868$	−36.8788	−1.25175
$869$	−33.2852	−1.12912
$870$	−5.11812	−0.173520
$871$	30.1711	1.02231
$872$	19.6183	0.664359
$873$	17.1642	0.580920
$874$	−56.3309	−1.90542
$875$	−4.17471	−0.141131
$876$	6.05830	0.204691
$877$	−20.2518	−0.683853	−0.341927	−	0.939727i	$-0.611079\pi$
$877$	−20.2518	−0.683853	−0.341927	+	0.939727i	$0.611079\pi$
$878$	95.3383	3.21751
$879$	−2.40169	−0.0810069
$880$	32.0634	1.08086
$881$	30.1657	1.01631	0.508154	−	0.861266i	$-0.330328\pi$
$881$	30.1657	1.01631	0.508154	+	0.861266i	$0.330328\pi$
$882$	75.5382	2.54350
$883$	45.4949	1.53103	0.765513	−	0.643421i	$-0.222485\pi$
$883$	45.4949	1.53103	0.765513	+	0.643421i	$0.222485\pi$
$884$	−3.86273	−0.129918
$885$	−3.34348	−0.112390
$886$	−36.5591	−1.22823
$887$	−3.27161	−0.109850	−0.0549250	−	0.998490i	$-0.517492\pi$
$887$	−3.27161	−0.109850	−0.0549250	+	0.998490i	$0.517492\pi$
$888$	−21.7629	−0.730316
$889$	−79.4100	−2.66333
$890$	−2.77789	−0.0931152
$891$	15.9427	0.534101
$892$	−76.9416	−2.57619
$893$	40.7907	1.36501
$894$	32.3427	1.08170
$895$	−8.36947	−0.279760
$896$	84.9070	2.83654
$897$	12.1042	0.404148
$898$	−43.6819	−1.45769
$899$	−5.85244	−0.195190
$900$	−14.0679	−0.468930
$901$	0.162477	0.00541288
$902$	−61.0097	−2.03140
$903$	−12.6596	−0.421284
$904$	38.2624	1.27259
$905$	0.123471	0.00410433
$906$	10.5351	0.350006
$907$	−27.2913	−0.906191	−0.453096	−	0.891462i	$-0.649680\pi$
$907$	−27.2913	−0.906191	−0.453096	+	0.891462i	$0.649680\pi$
$908$	131.554	4.36577
$909$	−25.2049	−0.835994
$910$	60.3917	2.00196
$911$	−27.6325	−0.915506	−0.457753	−	0.889079i	$-0.651346\pi$
$911$	−27.6325	−0.915506	−0.457753	+	0.889079i	$0.651346\pi$
$912$	36.2317	1.19975
$913$	−8.64251	−0.286025
$914$	59.3428	1.96289
$915$	−2.50915	−0.0829498
$916$	23.5579	0.778376
$917$	37.2558	1.23030
$918$	1.15961	0.0382730
$919$	35.1920	1.16088	0.580439	−	0.814304i	$-0.302881\pi$
$919$	35.1920	1.16088	0.580439	+	0.814304i	$0.302881\pi$
$920$	35.2573	1.16240
$921$	3.07094	0.101191
$922$	−57.0185	−1.87780
$923$	7.41669	0.244123
$924$	30.0997	0.990206
$925$	−4.56807	−0.150197
$926$	−10.0778	−0.331178
$927$	27.6718	0.908861
$928$	58.9955	1.93662
$929$	25.7186	0.843800	0.421900	−	0.906642i	$-0.361363\pi$
$929$	25.7186	0.843800	0.421900	+	0.906642i	$0.361363\pi$
$930$	2.50689	0.0822042
$931$	−53.6091	−1.75697
$932$	105.209	3.44623
$933$	−4.65817	−0.152502
$934$	−61.0987	−1.99921
$935$	−0.344729	−0.0112738
$936$	125.499	4.10206
$937$	3.14560	0.102762	0.0513811	−	0.998679i	$-0.483638\pi$
$937$	3.14560	0.102762	0.0513811	+	0.998679i	$0.483638\pi$
$938$	62.8434	2.05191
$939$	−11.9745	−0.390774
$940$	−41.4003	−1.35033
$941$	−31.3154	−1.02085	−0.510427	−	0.859921i	$-0.670513\pi$
$941$	−31.3154	−1.02085	−0.510427	+	0.859921i	$0.670513\pi$
$942$	−1.11232	−0.0362415
$943$	−36.9419	−1.20299
$944$	77.5788	2.52497
$945$	−13.1061	−0.426342
$946$	37.0627	1.20501
$947$	33.8579	1.10023	0.550117	−	0.835088i	$-0.314583\pi$
$947$	33.8579	1.10023	0.550117	+	0.835088i	$0.314583\pi$
$948$	38.1744	1.23985
$949$	−11.3443	−0.368251
$950$	13.8110	0.448086
$951$	−3.42770	−0.111151
$952$	−4.96161	−0.160807
$953$	23.4153	0.758496	0.379248	−	0.925295i	$-0.376183\pi$
$953$	23.4153	0.758496	0.379248	+	0.925295i	$0.376183\pi$
$954$	−8.56006	−0.277142
$955$	5.71354	0.184886
$956$	−117.494	−3.80004
$957$	4.77663	0.154406
$958$	−43.7930	−1.41489
$959$	58.9633	1.90403
$960$	−11.1749	−0.360668
$961$	−28.1334	−0.907530
$962$	66.0820	2.13057
$963$	16.6576	0.536785
$964$	1.11858	0.0360270
$965$	−10.5684	−0.340210
$966$	25.2118	0.811178
$967$	−2.38523	−0.0767040	−0.0383520	−	0.999264i	$-0.512211\pi$
$967$	−2.38523	−0.0767040	−0.0383520	+	0.999264i	$0.512211\pi$
$968$	40.7438	1.30956
$969$	−0.389544	−0.0125140
$970$	17.1025	0.549128
$971$	27.7365	0.890107	0.445053	−	0.895504i	$-0.353185\pi$
$971$	27.7365	0.890107	0.445053	+	0.895504i	$0.353185\pi$
$972$	−67.4248	−2.16265
$973$	−39.9056	−1.27932
$974$	−18.3111	−0.586727
$975$	−2.96765	−0.0950410
$976$	58.2197	1.86357
$977$	−5.82297	−0.186293	−0.0931467	−	0.995652i	$-0.529693\pi$
$977$	−5.82297	−0.186293	−0.0931467	+	0.995652i	$0.529693\pi$
$978$	−0.447106	−0.0142969
$979$	2.59255	0.0828582
$980$	54.4101	1.73807
$981$	6.11921	0.195371
$982$	19.8054	0.632016
$983$	57.7876	1.84314	0.921570	−	0.388213i	$-0.126908\pi$
$983$	57.7876	1.84314	0.921570	+	0.388213i	$0.126908\pi$
$984$	43.1499	1.37557
$985$	−10.1228	−0.322541
$986$	−1.27680	−0.0406615
$987$	−18.2566	−0.581113
$988$	−144.428	−4.59487
$989$	22.4418	0.713607
$990$	18.1620	0.577225
$991$	42.0597	1.33607	0.668035	−	0.744130i	$-0.267136\pi$
$991$	42.0597	1.33607	0.668035	+	0.744130i	$0.267136\pi$
$992$	−28.8965	−0.917463
$993$	0.885150	0.0280894
$994$	15.4482	0.489987
$995$	−14.9223	−0.473070
$996$	9.91199	0.314073
$997$	44.6992	1.41564	0.707819	−	0.706394i	$-0.249679\pi$
$997$	44.6992	1.41564	0.707819	+	0.706394i	$0.249679\pi$
$998$	51.9022	1.64294
$999$	−14.3410	−0.453730

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.e.1.4	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.4	✓	153	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68656 q^{2} -0.551136 q^{3} +5.21758 q^{4} +1.00000 q^{5} +1.48066 q^{6} -4.17471 q^{7} -8.64421 q^{8} -2.69625 q^{9} +O(q^{10})\)	\(q-2.68656 q^{2} -0.551136 q^{3} +5.21758 q^{4} +1.00000 q^{5} +1.48066 q^{6} -4.17471 q^{7} -8.64421 q^{8} -2.69625 q^{9} -2.68656 q^{10} +2.50730 q^{11} -2.87560 q^{12} +5.38461 q^{13} +11.2156 q^{14} -0.551136 q^{15} +12.7880 q^{16} -0.137490 q^{17} +7.24362 q^{18} -5.14076 q^{19} +5.21758 q^{20} +2.30083 q^{21} -6.73601 q^{22} -4.07872 q^{23} +4.76414 q^{24} +1.00000 q^{25} -14.4661 q^{26} +3.13941 q^{27} -21.7819 q^{28} -3.45665 q^{29} +1.48066 q^{30} +1.69309 q^{31} -17.0672 q^{32} -1.38187 q^{33} +0.369374 q^{34} -4.17471 q^{35} -14.0679 q^{36} -4.56807 q^{37} +13.8110 q^{38} -2.96765 q^{39} -8.64421 q^{40} +9.05723 q^{41} -6.18132 q^{42} -5.50216 q^{43} +13.0821 q^{44} -2.69625 q^{45} +10.9577 q^{46} -7.93476 q^{47} -7.04792 q^{48} +10.4282 q^{49} -2.68656 q^{50} +0.0757755 q^{51} +28.0947 q^{52} -1.18174 q^{53} -8.43419 q^{54} +2.50730 q^{55} +36.0871 q^{56} +2.83326 q^{57} +9.28649 q^{58} +6.06653 q^{59} -2.87560 q^{60} +4.55268 q^{61} -4.54859 q^{62} +11.2561 q^{63} +20.2761 q^{64} +5.38461 q^{65} +3.71246 q^{66} +5.60322 q^{67} -0.717364 q^{68} +2.24793 q^{69} +11.2156 q^{70} +1.37739 q^{71} +23.3070 q^{72} -2.10680 q^{73} +12.2724 q^{74} -0.551136 q^{75} -26.8224 q^{76} -10.4673 q^{77} +7.97276 q^{78} -13.2753 q^{79} +12.7880 q^{80} +6.35851 q^{81} -24.3328 q^{82} -3.44693 q^{83} +12.0048 q^{84} -0.137490 q^{85} +14.7819 q^{86} +1.90508 q^{87} -21.6737 q^{88} +1.03400 q^{89} +7.24362 q^{90} -22.4792 q^{91} -21.2810 q^{92} -0.933125 q^{93} +21.3172 q^{94} -5.14076 q^{95} +9.40637 q^{96} -6.36595 q^{97} -28.0160 q^{98} -6.76032 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * q^99

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