LMFDB - Embedded newform 5077.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5077,2,Mod(1,5077)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5077, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5077.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5077 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5077.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:	$40.5400491062$
Analytic rank:	$0$
Dimension:	$216$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	5077.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46105 q^{2} -2.68177 q^{3} +4.05676 q^{4} +2.96431 q^{5} +6.59997 q^{6} +0.509421 q^{7} -5.06178 q^{8} +4.19189 q^{9} +O(q^{10})$	\(q-2.46105 q^{2} -2.68177 q^{3} +4.05676 q^{4} +2.96431 q^{5} +6.59997 q^{6} +0.509421 q^{7} -5.06178 q^{8} +4.19189 q^{9} -7.29531 q^{10} +5.31673 q^{11} -10.8793 q^{12} +5.60467 q^{13} -1.25371 q^{14} -7.94959 q^{15} +4.34378 q^{16} +2.47085 q^{17} -10.3165 q^{18} -0.319690 q^{19} +12.0255 q^{20} -1.36615 q^{21} -13.0847 q^{22} +2.93671 q^{23} +13.5745 q^{24} +3.78712 q^{25} -13.7934 q^{26} -3.19639 q^{27} +2.06660 q^{28} -4.69144 q^{29} +19.5643 q^{30} +7.77911 q^{31} -0.566675 q^{32} -14.2582 q^{33} -6.08088 q^{34} +1.51008 q^{35} +17.0055 q^{36} +9.69240 q^{37} +0.786772 q^{38} -15.0304 q^{39} -15.0047 q^{40} -4.12169 q^{41} +3.36216 q^{42} +2.69266 q^{43} +21.5687 q^{44} +12.4261 q^{45} -7.22738 q^{46} +1.32018 q^{47} -11.6490 q^{48} -6.74049 q^{49} -9.32029 q^{50} -6.62625 q^{51} +22.7368 q^{52} +3.72208 q^{53} +7.86647 q^{54} +15.7604 q^{55} -2.57858 q^{56} +0.857334 q^{57} +11.5459 q^{58} +10.4400 q^{59} -32.2496 q^{60} -2.43738 q^{61} -19.1448 q^{62} +2.13544 q^{63} -7.29294 q^{64} +16.6140 q^{65} +35.0902 q^{66} +9.21258 q^{67} +10.0236 q^{68} -7.87557 q^{69} -3.71638 q^{70} +14.3692 q^{71} -21.2185 q^{72} -6.94100 q^{73} -23.8535 q^{74} -10.1562 q^{75} -1.29690 q^{76} +2.70845 q^{77} +36.9907 q^{78} -9.50471 q^{79} +12.8763 q^{80} -4.00370 q^{81} +10.1437 q^{82} +10.6751 q^{83} -5.54214 q^{84} +7.32436 q^{85} -6.62676 q^{86} +12.5814 q^{87} -26.9121 q^{88} +2.74486 q^{89} -30.5812 q^{90} +2.85513 q^{91} +11.9135 q^{92} -20.8618 q^{93} -3.24902 q^{94} -0.947658 q^{95} +1.51969 q^{96} +15.4084 q^{97} +16.5887 q^{98} +22.2872 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) $ 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9} + 24 q^{10} + 89 q^{11} + 114 q^{12} + 34 q^{13} + 53 q^{14} + 61 q^{15} + 229 q^{16} + 76 q^{17} + 57 q^{18} + 54 q^{19} + 118 q^{20} + 25 q^{21} + 26 q^{22} + 109 q^{23} + 65 q^{24} + 232 q^{25} + 58 q^{26} + 236 q^{27} + 57 q^{28} + 54 q^{29} + 6 q^{30} + 77 q^{31} + 155 q^{32} + 80 q^{33} + 28 q^{34} + 137 q^{35} + 257 q^{36} + 42 q^{37} + 104 q^{38} + 46 q^{39} + 47 q^{40} + 109 q^{41} + 27 q^{42} + 68 q^{43} + 145 q^{44} + 109 q^{45} - 7 q^{46} + 264 q^{47} + 198 q^{48} + 222 q^{49} + 86 q^{50} + 57 q^{51} + 68 q^{52} + 95 q^{53} + 79 q^{54} + 50 q^{55} + 108 q^{56} + 55 q^{57} + 38 q^{58} + 292 q^{59} + 91 q^{60} + 16 q^{61} + 91 q^{62} + 113 q^{63} + 231 q^{64} + 68 q^{65} - 15 q^{66} + 152 q^{67} + 199 q^{68} + 83 q^{69} + 24 q^{70} + 131 q^{71} + 162 q^{72} + 71 q^{73} + 10 q^{74} + 232 q^{75} + 60 q^{76} + 131 q^{77} + 102 q^{78} + 10 q^{79} + 236 q^{80} + 268 q^{81} + 54 q^{82} + 299 q^{83} - 9 q^{85} + 35 q^{86} + 103 q^{87} + 45 q^{88} + 134 q^{89} + 8 q^{90} + 79 q^{91} + 206 q^{92} + 95 q^{93} + 18 q^{94} + 119 q^{95} + 77 q^{96} + 129 q^{97} + 150 q^{98} + 221 q^{99}+O(q^{100}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9 + 24 * q^10 + 89 * q^11 + 114 * q^12 + 34 * q^13 + 53 * q^14 + 61 * q^15 + 229 * q^16 + 76 * q^17 + 57 * q^18 + 54 * q^19 + 118 * q^20 + 25 * q^21 + 26 * q^22 + 109 * q^23 + 65 * q^24 + 232 * q^25 + 58 * q^26 + 236 * q^27 + 57 * q^28 + 54 * q^29 + 6 * q^30 + 77 * q^31 + 155 * q^32 + 80 * q^33 + 28 * q^34 + 137 * q^35 + 257 * q^36 + 42 * q^37 + 104 * q^38 + 46 * q^39 + 47 * q^40 + 109 * q^41 + 27 * q^42 + 68 * q^43 + 145 * q^44 + 109 * q^45 - 7 * q^46 + 264 * q^47 + 198 * q^48 + 222 * q^49 + 86 * q^50 + 57 * q^51 + 68 * q^52 + 95 * q^53 + 79 * q^54 + 50 * q^55 + 108 * q^56 + 55 * q^57 + 38 * q^58 + 292 * q^59 + 91 * q^60 + 16 * q^61 + 91 * q^62 + 113 * q^63 + 231 * q^64 + 68 * q^65 - 15 * q^66 + 152 * q^67 + 199 * q^68 + 83 * q^69 + 24 * q^70 + 131 * q^71 + 162 * q^72 + 71 * q^73 + 10 * q^74 + 232 * q^75 + 60 * q^76 + 131 * q^77 + 102 * q^78 + 10 * q^79 + 236 * q^80 + 268 * q^81 + 54 * q^82 + 299 * q^83 - 9 * q^85 + 35 * q^86 + 103 * q^87 + 45 * q^88 + 134 * q^89 + 8 * q^90 + 79 * q^91 + 206 * q^92 + 95 * q^93 + 18 * q^94 + 119 * q^95 + 77 * q^96 + 129 * q^97 + 150 * q^98 + 221 * 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 $

$2$	−2.46105	−1.74022	−0.870112	−	0.492854i	$-0.835954\pi$
$2$	−2.46105	−1.74022	−0.870112	+	0.492854i	$0.835954\pi$
$3$	−2.68177	−1.54832	−0.774161	−	0.632989i	$-0.781828\pi$
$3$	−2.68177	−1.54832	−0.774161	+	0.632989i	$0.781828\pi$
$4$	4.05676	2.02838
$5$	2.96431	1.32568	0.662839	−	0.748762i	$-0.269351\pi$
$5$	2.96431	1.32568	0.662839	+	0.748762i	$0.269351\pi$
$6$	6.59997	2.69443
$7$	0.509421	0.192543	0.0962714	−	0.995355i	$-0.469308\pi$
$7$	0.509421	0.192543	0.0962714	+	0.995355i	$0.469308\pi$
$8$	−5.06178	−1.78961
$9$	4.19189	1.39730
$10$	−7.29531	−2.30698
$11$	5.31673	1.60305	0.801527	−	0.597959i	$-0.204021\pi$
$11$	5.31673	1.60305	0.801527	+	0.597959i	$0.204021\pi$
$12$	−10.8793	−3.14058
$13$	5.60467	1.55446	0.777228	−	0.629219i	$-0.216625\pi$
$13$	5.60467	1.55446	0.777228	+	0.629219i	$0.216625\pi$
$14$	−1.25371	−0.335068
$15$	−7.94959	−2.05258
$16$	4.34378	1.08594
$17$	2.47085	0.599269	0.299634	−	0.954054i	$-0.403135\pi$
$17$	2.47085	0.599269	0.299634	+	0.954054i	$0.403135\pi$
$18$	−10.3165	−2.43161
$19$	−0.319690	−0.0733418	−0.0366709	−	0.999327i	$-0.511675\pi$
$19$	−0.319690	−0.0733418	−0.0366709	+	0.999327i	$0.511675\pi$
$20$	12.0255	2.68898
$21$	−1.36615	−0.298118
$22$	−13.0847	−2.78967
$23$	2.93671	0.612346	0.306173	−	0.951976i	$-0.400951\pi$
$23$	2.93671	0.612346	0.306173	+	0.951976i	$0.400951\pi$
$24$	13.5745	2.77089
$25$	3.78712	0.757424
$26$	−13.7934	−2.70510
$27$	−3.19639	−0.615145
$28$	2.06660	0.390550
$29$	−4.69144	−0.871179	−0.435590	−	0.900145i	$-0.643460\pi$
$29$	−4.69144	−0.871179	−0.435590	+	0.900145i	$0.643460\pi$
$30$	19.5643	3.57194
$31$	7.77911	1.39717	0.698585	−	0.715527i	$-0.253813\pi$
$31$	7.77911	1.39717	0.698585	+	0.715527i	$0.253813\pi$
$32$	−0.566675	−0.100175
$33$	−14.2582	−2.48204
$34$	−6.08088	−1.04286
$35$	1.51008	0.255250
$36$	17.0055	2.83425
$37$	9.69240	1.59342	0.796710	−	0.604362i	$-0.206572\pi$
$37$	9.69240	1.59342	0.796710	+	0.604362i	$0.206572\pi$
$38$	0.786772	0.127631
$39$	−15.0304	−2.40680
$40$	−15.0047	−2.37245
$41$	−4.12169	−0.643700	−0.321850	−	0.946791i	$-0.604305\pi$
$41$	−4.12169	−0.643700	−0.321850	+	0.946791i	$0.604305\pi$
$42$	3.36216	0.518792
$43$	2.69266	0.410626	0.205313	−	0.978696i	$-0.434179\pi$
$43$	2.69266	0.410626	0.205313	+	0.978696i	$0.434179\pi$
$44$	21.5687	3.25160
$45$	12.4261	1.85237
$46$	−7.22738	−1.06562
$47$	1.32018	0.192567	0.0962837	−	0.995354i	$-0.469304\pi$
$47$	1.32018	0.192567	0.0962837	+	0.995354i	$0.469304\pi$
$48$	−11.6490	−1.68139
$49$	−6.74049	−0.962927
$50$	−9.32029	−1.31809
$51$	−6.62625	−0.927861
$52$	22.7368	3.15303
$53$	3.72208	0.511267	0.255634	−	0.966774i	$-0.417716\pi$
$53$	3.72208	0.511267	0.255634	+	0.966774i	$0.417716\pi$
$54$	7.86647	1.07049
$55$	15.7604	2.12513
$56$	−2.57858	−0.344577
$57$	0.857334	0.113557
$58$	11.5459	1.51605
$59$	10.4400	1.35917	0.679584	−	0.733597i	$-0.262160\pi$
$59$	10.4400	1.35917	0.679584	+	0.733597i	$0.262160\pi$
$60$	−32.2496	−4.16340
$61$	−2.43738	−0.312074	−0.156037	−	0.987751i	$-0.549872\pi$
$61$	−2.43738	−0.312074	−0.156037	+	0.987751i	$0.549872\pi$
$62$	−19.1448	−2.43139
$63$	2.13544	0.269040
$64$	−7.29294	−0.911617
$65$	16.6140	2.06071
$66$	35.0902	4.31931
$67$	9.21258	1.12550	0.562748	−	0.826628i	$-0.309744\pi$
$67$	9.21258	1.12550	0.562748	+	0.826628i	$0.309744\pi$
$68$	10.0236	1.21554
$69$	−7.87557	−0.948108
$70$	−3.71638	−0.444192
$71$	14.3692	1.70531	0.852656	−	0.522472i	$-0.174990\pi$
$71$	14.3692	1.70531	0.852656	+	0.522472i	$0.174990\pi$
$72$	−21.2185	−2.50062
$73$	−6.94100	−0.812383	−0.406191	−	0.913788i	$-0.633143\pi$
$73$	−6.94100	−0.812383	−0.406191	+	0.913788i	$0.633143\pi$
$74$	−23.8535	−2.77291
$75$	−10.1562	−1.17274
$76$	−1.29690	−0.148765
$77$	2.70845	0.308656
$78$	36.9907	4.18837
$79$	−9.50471	−1.06936	−0.534681	−	0.845054i	$-0.679568\pi$
$79$	−9.50471	−1.06936	−0.534681	+	0.845054i	$0.679568\pi$
$80$	12.8763	1.43961
$81$	−4.00370	−0.444856
$82$	10.1437	1.12018
$83$	10.6751	1.17175	0.585873	−	0.810403i	$-0.300752\pi$
$83$	10.6751	1.17175	0.585873	+	0.810403i	$0.300752\pi$
$84$	−5.54214	−0.604697
$85$	7.32436	0.794438
$86$	−6.62676	−0.714582
$87$	12.5814	1.34886
$88$	−26.9121	−2.86884
$89$	2.74486	0.290955	0.145477	−	0.989362i	$-0.453528\pi$
$89$	2.74486	0.290955	0.145477	+	0.989362i	$0.453528\pi$
$90$	−30.5812	−3.22354
$91$	2.85513	0.299299
$92$	11.9135	1.24207
$93$	−20.8618	−2.16327
$94$	−3.24902	−0.335111
$95$	−0.947658	−0.0972277
$96$	1.51969	0.155103
$97$	15.4084	1.56449	0.782243	−	0.622974i	$-0.214076\pi$
$97$	15.4084	1.56449	0.782243	+	0.622974i	$0.214076\pi$
$98$	16.5887	1.67571
$99$	22.2872	2.23994
$100$	15.3634	1.53634
$101$	−1.87792	−0.186860	−0.0934302	−	0.995626i	$-0.529783\pi$
$101$	−1.87792	−0.186860	−0.0934302	+	0.995626i	$0.529783\pi$
$102$	16.3075	1.61469
$103$	16.7256	1.64803	0.824014	−	0.566570i	$-0.191730\pi$
$103$	16.7256	1.64803	0.824014	+	0.566570i	$0.191730\pi$
$104$	−28.3696	−2.78187
$105$	−4.04969	−0.395209
$106$	−9.16023	−0.889720
$107$	−4.39282	−0.424670	−0.212335	−	0.977197i	$-0.568107\pi$
$107$	−4.39282	−0.424670	−0.212335	+	0.977197i	$0.568107\pi$
$108$	−12.9670	−1.24775
$109$	6.47424	0.620120	0.310060	−	0.950717i	$-0.399651\pi$
$109$	6.47424	0.620120	0.310060	+	0.950717i	$0.399651\pi$
$110$	−38.7871	−3.69821
$111$	−25.9928	−2.46713
$112$	2.21281	0.209091
$113$	11.6682	1.09765	0.548826	−	0.835937i	$-0.315075\pi$
$113$	11.6682	1.09765	0.548826	+	0.835937i	$0.315075\pi$
$114$	−2.10994	−0.197614
$115$	8.70530	0.811774
$116$	−19.0321	−1.76708
$117$	23.4942	2.17204
$118$	−25.6933	−2.36526
$119$	1.25870	0.115385
$120$	40.2391	3.67331
$121$	17.2676	1.56978
$122$	5.99850	0.543079
$123$	11.0534	0.996654
$124$	31.5580	2.83399
$125$	−3.59535	−0.321578
$126$	−5.25541	−0.468190
$127$	11.3220	1.00466	0.502330	−	0.864676i	$-0.332476\pi$
$127$	11.3220	1.00466	0.502330	+	0.864676i	$0.332476\pi$
$128$	19.0816	1.68659
$129$	−7.22109	−0.635781
$130$	−40.8878	−3.58610
$131$	4.01273	0.350594	0.175297	−	0.984516i	$-0.443911\pi$
$131$	4.01273	0.350594	0.175297	+	0.984516i	$0.443911\pi$
$132$	−57.8423	−5.03452
$133$	−0.162856	−0.0141214
$134$	−22.6726	−1.95862
$135$	−9.47508	−0.815485
$136$	−12.5069	−1.07246
$137$	−8.85706	−0.756710	−0.378355	−	0.925661i	$-0.623510\pi$
$137$	−8.85706	−0.756710	−0.378355	+	0.925661i	$0.623510\pi$
$138$	19.3822	1.64992
$139$	−22.2893	−1.89056	−0.945279	−	0.326263i	$-0.894210\pi$
$139$	−22.2893	−1.89056	−0.945279	+	0.326263i	$0.894210\pi$
$140$	6.12603	0.517744
$141$	−3.54041	−0.298156
$142$	−35.3633	−2.96763
$143$	29.7985	2.49188
$144$	18.2087	1.51739
$145$	−13.9069	−1.15490
$146$	17.0821	1.41373
$147$	18.0765	1.49092
$148$	39.3197	3.23206
$149$	−19.0041	−1.55688	−0.778439	−	0.627721i	$-0.783988\pi$
$149$	−19.0041	−1.55688	−0.778439	+	0.627721i	$0.783988\pi$
$150$	24.9949	2.04082
$151$	−15.2888	−1.24418	−0.622091	−	0.782945i	$-0.713717\pi$
$151$	−15.2888	−1.24418	−0.622091	+	0.782945i	$0.713717\pi$
$152$	1.61820	0.131253
$153$	10.3575	0.837358
$154$	−6.66563	−0.537131
$155$	23.0597	1.85220
$156$	−60.9749	−4.88190
$157$	−17.9218	−1.43032	−0.715158	−	0.698963i	$-0.753645\pi$
$157$	−17.9218	−1.43032	−0.715158	+	0.698963i	$0.753645\pi$
$158$	23.3915	1.86093
$159$	−9.98177	−0.791606
$160$	−1.67980	−0.132800
$161$	1.49602	0.117903
$162$	9.85331	0.774149
$163$	−8.45284	−0.662077	−0.331039	−	0.943617i	$-0.607399\pi$
$163$	−8.45284	−0.662077	−0.331039	+	0.943617i	$0.607399\pi$
$164$	−16.7207	−1.30567
$165$	−42.2658	−3.29039
$166$	−26.2720	−2.03910
$167$	−3.99197	−0.308908	−0.154454	−	0.988000i	$-0.549362\pi$
$167$	−3.99197	−0.308908	−0.154454	+	0.988000i	$0.549362\pi$
$168$	6.91515	0.533515
$169$	18.4123	1.41633
$170$	−18.0256	−1.38250
$171$	−1.34011	−0.102480
$172$	10.9235	0.832906
$173$	−24.4672	−1.86021	−0.930104	−	0.367295i	$-0.880284\pi$
$173$	−24.4672	−1.86021	−0.930104	+	0.367295i	$0.880284\pi$
$174$	−30.9634	−2.34733
$175$	1.92924	0.145837
$176$	23.0947	1.74083
$177$	−27.9976	−2.10443
$178$	−6.75523	−0.506326
$179$	−21.6767	−1.62019	−0.810097	−	0.586295i	$-0.800586\pi$
$179$	−21.6767	−1.62019	−0.810097	+	0.586295i	$0.800586\pi$
$180$	50.4096	3.75731
$181$	9.54699	0.709622	0.354811	−	0.934938i	$-0.384545\pi$
$181$	9.54699	0.709622	0.354811	+	0.934938i	$0.384545\pi$
$182$	−7.02662	−0.520848
$183$	6.53649	0.483191
$184$	−14.8650	−1.09586
$185$	28.7312	2.11236
$186$	51.3419	3.76457
$187$	13.1368	0.960660
$188$	5.35564	0.390600
$189$	−1.62831	−0.118442
$190$	2.33223	0.169198
$191$	15.2925	1.10652	0.553262	−	0.833007i	$-0.313383\pi$
$191$	15.2925	1.10652	0.553262	+	0.833007i	$0.313383\pi$
$192$	19.5580	1.41148
$193$	−18.8934	−1.35998	−0.679988	−	0.733223i	$-0.738015\pi$
$193$	−18.8934	−1.35998	−0.679988	+	0.733223i	$0.738015\pi$
$194$	−37.9208	−2.72256
$195$	−44.5549	−3.19064
$196$	−27.3445	−1.95318
$197$	−6.46157	−0.460368	−0.230184	−	0.973147i	$-0.573933\pi$
$197$	−6.46157	−0.460368	−0.230184	+	0.973147i	$0.573933\pi$
$198$	−54.8498	−3.89800
$199$	1.41100	0.100023	0.0500115	−	0.998749i	$-0.484074\pi$
$199$	1.41100	0.100023	0.0500115	+	0.998749i	$0.484074\pi$
$200$	−19.1696	−1.35549
$201$	−24.7060	−1.74263
$202$	4.62166	0.325179
$203$	−2.38992	−0.167739
$204$	−26.8811	−1.88205
$205$	−12.2180	−0.853340
$206$	−41.1626	−2.86794
$207$	12.3104	0.855629
$208$	24.3454	1.68805
$209$	−1.69970	−0.117571
$210$	9.96647	0.687752
$211$	−1.23071	−0.0847255	−0.0423628	−	0.999102i	$-0.513489\pi$
$211$	−1.23071	−0.0847255	−0.0423628	+	0.999102i	$0.513489\pi$
$212$	15.0996	1.03704
$213$	−38.5350	−2.64037
$214$	10.8109	0.739021
$215$	7.98186	0.544358
$216$	16.1794	1.10087
$217$	3.96284	0.269015
$218$	−15.9334	−1.07915
$219$	18.6142	1.25783
$220$	63.9362	4.31058
$221$	13.8483	0.931537
$222$	63.9695	4.29335
$223$	−26.0748	−1.74610	−0.873050	−	0.487631i	$-0.837861\pi$
$223$	−26.0748	−1.74610	−0.873050	+	0.487631i	$0.837861\pi$
$224$	−0.288676	−0.0192880
$225$	15.8752	1.05835
$226$	−28.7160	−1.91016
$227$	−0.882142	−0.0585498	−0.0292749	−	0.999571i	$-0.509320\pi$
$227$	−0.882142	−0.0585498	−0.0292749	+	0.999571i	$0.509320\pi$
$228$	3.47800	0.230336
$229$	−8.38820	−0.554308	−0.277154	−	0.960826i	$-0.589391\pi$
$229$	−8.38820	−0.554308	−0.277154	+	0.960826i	$0.589391\pi$
$230$	−21.4242	−1.41267
$231$	−7.26344	−0.477899
$232$	23.7471	1.55907
$233$	20.2085	1.32390	0.661950	−	0.749548i	$-0.269729\pi$
$233$	20.2085	1.32390	0.661950	+	0.749548i	$0.269729\pi$
$234$	−57.8203	−3.77983
$235$	3.91341	0.255283
$236$	42.3525	2.75691
$237$	25.4894	1.65572
$238$	−3.09772	−0.200796
$239$	−3.90841	−0.252814	−0.126407	−	0.991978i	$-0.540345\pi$
$239$	−3.90841	−0.252814	−0.126407	+	0.991978i	$0.540345\pi$
$240$	−34.5313	−2.22898
$241$	−10.4128	−0.670747	−0.335374	−	0.942085i	$-0.608863\pi$
$241$	−10.4128	−0.670747	−0.335374	+	0.942085i	$0.608863\pi$
$242$	−42.4964	−2.73177
$243$	20.3262	1.30392
$244$	−9.88785	−0.633005
$245$	−19.9809	−1.27653
$246$	−27.2030	−1.73440
$247$	−1.79176	−0.114007
$248$	−39.3762	−2.50039
$249$	−28.6282	−1.81424
$250$	8.84832	0.559617
$251$	1.63860	0.103428	0.0517138	−	0.998662i	$-0.483532\pi$
$251$	1.63860	0.103428	0.0517138	+	0.998662i	$0.483532\pi$
$252$	8.66295	0.545715
$253$	15.6137	0.981623
$254$	−27.8639	−1.74833
$255$	−19.6423	−1.23005
$256$	−32.3749	−2.02343
$257$	−4.13934	−0.258205	−0.129102	−	0.991631i	$-0.541210\pi$
$257$	−4.13934	−0.258205	−0.129102	+	0.991631i	$0.541210\pi$
$258$	17.7714	1.10640
$259$	4.93751	0.306802
$260$	67.3989	4.17990
$261$	−19.6660	−1.21730
$262$	−9.87552	−0.610111
$263$	−4.24519	−0.261770	−0.130885	−	0.991398i	$-0.541782\pi$
$263$	−4.24519	−0.261770	−0.130885	+	0.991398i	$0.541782\pi$
$264$	72.1721	4.44189
$265$	11.0334	0.677776
$266$	0.400798	0.0245745
$267$	−7.36108	−0.450491
$268$	37.3732	2.28293
$269$	−1.69124	−0.103117	−0.0515583	−	0.998670i	$-0.516419\pi$
$269$	−1.69124	−0.103117	−0.0515583	+	0.998670i	$0.516419\pi$
$270$	23.3186	1.41913
$271$	3.83364	0.232877	0.116439	−	0.993198i	$-0.462852\pi$
$271$	3.83364	0.232877	0.116439	+	0.993198i	$0.462852\pi$
$272$	10.7328	0.650773
$273$	−7.65682	−0.463412
$274$	21.7977	1.31684
$275$	20.1351	1.21419
$276$	−31.9493	−1.92312
$277$	−7.02152	−0.421882	−0.210941	−	0.977499i	$-0.567653\pi$
$277$	−7.02152	−0.421882	−0.210941	+	0.977499i	$0.567653\pi$
$278$	54.8552	3.28999
$279$	32.6092	1.95226
$280$	−7.64369	−0.456798
$281$	−23.5195	−1.40305	−0.701527	−	0.712642i	$-0.747498\pi$
$281$	−23.5195	−1.40305	−0.701527	+	0.712642i	$0.747498\pi$
$282$	8.71312	0.518859
$283$	−14.7623	−0.877529	−0.438764	−	0.898602i	$-0.644584\pi$
$283$	−14.7623	−0.877529	−0.438764	+	0.898602i	$0.644584\pi$
$284$	58.2925	3.45902
$285$	2.54140	0.150540
$286$	−73.3356	−4.33642
$287$	−2.09967	−0.123940
$288$	−2.37544	−0.139974
$289$	−10.8949	−0.640877
$290$	34.2255	2.00979
$291$	−41.3218	−2.42233
$292$	−28.1580	−1.64782
$293$	12.2059	0.713076	0.356538	−	0.934281i	$-0.383957\pi$
$293$	12.2059	0.713076	0.356538	+	0.934281i	$0.383957\pi$
$294$	−44.4870	−2.59454
$295$	30.9473	1.80182
$296$	−49.0608	−2.85160
$297$	−16.9943	−0.986111
$298$	46.7700	2.70932
$299$	16.4593	0.951864
$300$	−41.2012	−2.37875
$301$	1.37169	0.0790631
$302$	37.6264	2.16516
$303$	5.03616	0.289320
$304$	−1.38866	−0.0796451
$305$	−7.22513	−0.413710
$306$	−25.4904	−1.45719
$307$	−5.64330	−0.322080	−0.161040	−	0.986948i	$-0.551485\pi$
$307$	−5.64330	−0.322080	−0.161040	+	0.986948i	$0.551485\pi$
$308$	10.9875	0.626072
$309$	−44.8544	−2.55168
$310$	−56.7510	−3.22324
$311$	12.0814	0.685071	0.342536	−	0.939505i	$-0.388714\pi$
$311$	12.0814	0.685071	0.342536	+	0.939505i	$0.388714\pi$
$312$	76.0809	4.30723
$313$	−23.9734	−1.35505	−0.677527	−	0.735498i	$-0.736948\pi$
$313$	−23.9734	−1.35505	−0.677527	+	0.735498i	$0.736948\pi$
$314$	44.1064	2.48907
$315$	6.33009	0.356660
$316$	−38.5583	−2.16907
$317$	6.47460	0.363650	0.181825	−	0.983331i	$-0.441800\pi$
$317$	6.47460	0.363650	0.181825	+	0.983331i	$0.441800\pi$
$318$	24.5656	1.37757
$319$	−24.9431	−1.39655
$320$	−21.6185	−1.20851
$321$	11.7805	0.657526
$322$	−3.68177	−0.205177
$323$	−0.789905	−0.0439515
$324$	−16.2421	−0.902337
$325$	21.2256	1.17738
$326$	20.8028	1.15216
$327$	−17.3624	−0.960144
$328$	20.8631	1.15197
$329$	0.672525	0.0370775
$330$	104.018	5.72601
$331$	−18.2953	−1.00560	−0.502800	−	0.864403i	$-0.667697\pi$
$331$	−18.2953	−1.00560	−0.502800	+	0.864403i	$0.667697\pi$
$332$	43.3063	2.37674
$333$	40.6295	2.22648
$334$	9.82442	0.537568
$335$	27.3089	1.49205
$336$	−5.93425	−0.323740
$337$	−7.08664	−0.386034	−0.193017	−	0.981195i	$-0.561827\pi$
$337$	−7.08664	−0.386034	−0.193017	+	0.981195i	$0.561827\pi$
$338$	−45.3137	−2.46474
$339$	−31.2914	−1.69952
$340$	29.7132	1.61142
$341$	41.3594	2.23974
$342$	3.29806	0.178339
$343$	−6.99969	−0.377948
$344$	−13.6296	−0.734861
$345$	−23.3456	−1.25689
$346$	60.2150	3.23718
$347$	18.5704	0.996911	0.498456	−	0.866915i	$-0.333901\pi$
$347$	18.5704	0.996911	0.498456	+	0.866915i	$0.333901\pi$
$348$	51.0396	2.73601
$349$	−4.54374	−0.243221	−0.121610	−	0.992578i	$-0.538806\pi$
$349$	−4.54374	−0.243221	−0.121610	+	0.992578i	$0.538806\pi$
$350$	−4.74795	−0.253788
$351$	−17.9147	−0.956216
$352$	−3.01286	−0.160586
$353$	−20.2356	−1.07703	−0.538515	−	0.842616i	$-0.681015\pi$
$353$	−20.2356	−1.07703	−0.538515	+	0.842616i	$0.681015\pi$
$354$	68.9035	3.66218
$355$	42.5948	2.26070
$356$	11.1352	0.590166
$357$	−3.37555	−0.178653
$358$	53.3475	2.81950
$359$	26.4774	1.39743	0.698713	−	0.715402i	$-0.253756\pi$
$359$	26.4774	1.39743	0.698713	+	0.715402i	$0.253756\pi$
$360$	−62.8981	−3.31502
$361$	−18.8978	−0.994621
$362$	−23.4956	−1.23490
$363$	−46.3077	−2.43052
$364$	11.5826	0.607093
$365$	−20.5753	−1.07696
$366$	−16.0866	−0.840860
$367$	−14.0100	−0.731316	−0.365658	−	0.930749i	$-0.619156\pi$
$367$	−14.0100	−0.731316	−0.365658	+	0.930749i	$0.619156\pi$
$368$	12.7564	0.664973
$369$	−17.2777	−0.899441
$370$	−70.7090	−3.67599
$371$	1.89611	0.0984409
$372$	−84.6313	−4.38793
$373$	−34.7395	−1.79874	−0.899371	−	0.437186i	$-0.855975\pi$
$373$	−34.7395	−1.79874	−0.899371	+	0.437186i	$0.855975\pi$
$374$	−32.3304	−1.67176
$375$	9.64189	0.497905
$376$	−6.68245	−0.344621
$377$	−26.2940	−1.35421
$378$	4.00734	0.206115
$379$	−5.38103	−0.276405	−0.138202	−	0.990404i	$-0.544132\pi$
$379$	−5.38103	−0.276405	−0.138202	+	0.990404i	$0.544132\pi$
$380$	−3.84442	−0.197215
$381$	−30.3629	−1.55554
$382$	−37.6355	−1.92560
$383$	−19.2637	−0.984331	−0.492166	−	0.870502i	$-0.663795\pi$
$383$	−19.2637	−0.984331	−0.492166	+	0.870502i	$0.663795\pi$
$384$	−51.1725	−2.61139
$385$	8.02868	0.409179
$386$	46.4975	2.36666
$387$	11.2873	0.573767
$388$	62.5081	3.17337
$389$	31.2113	1.58248	0.791238	−	0.611509i	$-0.209437\pi$
$389$	31.2113	1.58248	0.791238	+	0.611509i	$0.209437\pi$
$390$	109.652	5.55243
$391$	7.25616	0.366960
$392$	34.1189	1.72326
$393$	−10.7612	−0.542831
$394$	15.9022	0.801143
$395$	−28.1749	−1.41763
$396$	90.4136	4.54346
$397$	21.0148	1.05470	0.527352	−	0.849647i	$-0.323185\pi$
$397$	21.0148	1.05470	0.527352	+	0.849647i	$0.323185\pi$
$398$	−3.47253	−0.174062
$399$	0.436744	0.0218645
$400$	16.4504	0.822520
$401$	−12.7336	−0.635883	−0.317942	−	0.948110i	$-0.602992\pi$
$401$	−12.7336	−0.635883	−0.317942	+	0.948110i	$0.602992\pi$
$402$	60.8028	3.03257
$403$	43.5994	2.17184
$404$	−7.61828	−0.379024
$405$	−11.8682	−0.589736
$406$	5.88170	0.291904
$407$	51.5318	2.55434
$408$	33.5407	1.66051
$409$	15.3529	0.759153	0.379576	−	0.925160i	$-0.376070\pi$
$409$	15.3529	0.759153	0.379576	+	0.925160i	$0.376070\pi$
$410$	30.0690	1.48500
$411$	23.7526	1.17163
$412$	67.8519	3.34282
$413$	5.31834	0.261698
$414$	−30.2964	−1.48899
$415$	31.6443	1.55336
$416$	−3.17603	−0.155718
$417$	59.7749	2.92719
$418$	4.18305	0.204600
$419$	−10.5882	−0.517267	−0.258634	−	0.965975i	$-0.583272\pi$
$419$	−10.5882	−0.517267	−0.258634	+	0.965975i	$0.583272\pi$
$420$	−16.4286	−0.801634
$421$	−19.4982	−0.950285	−0.475143	−	0.879909i	$-0.657604\pi$
$421$	−19.4982	−0.950285	−0.475143	+	0.879909i	$0.657604\pi$
$422$	3.02883	0.147441
$423$	5.53404	0.269074
$424$	−18.8404	−0.914970
$425$	9.35741	0.453901
$426$	94.8364	4.59484
$427$	−1.24165	−0.0600876
$428$	−17.8206	−0.861392
$429$	−79.9128	−3.85822
$430$	−19.6437	−0.947306
$431$	19.0229	0.916299	0.458149	−	0.888875i	$-0.348512\pi$
$431$	19.0229	0.916299	0.458149	+	0.888875i	$0.348512\pi$
$432$	−13.8844	−0.668013
$433$	16.0641	0.771993	0.385996	−	0.922500i	$-0.373858\pi$
$433$	16.0641	0.771993	0.385996	+	0.922500i	$0.373858\pi$
$434$	−9.75274	−0.468146
$435$	37.2951	1.78816
$436$	26.2644	1.25784
$437$	−0.938834	−0.0449105
$438$	−45.8104	−2.18890
$439$	−1.14929	−0.0548524	−0.0274262	−	0.999624i	$-0.508731\pi$
$439$	−1.14929	−0.0548524	−0.0274262	+	0.999624i	$0.508731\pi$
$440$	−79.7758	−3.80316
$441$	−28.2554	−1.34550
$442$	−34.0813	−1.62108
$443$	−37.8723	−1.79937	−0.899683	−	0.436544i	$-0.856202\pi$
$443$	−37.8723	−1.79937	−0.899683	+	0.436544i	$0.856202\pi$
$444$	−105.446	−5.00427
$445$	8.13661	0.385712
$446$	64.1714	3.03860
$447$	50.9647	2.41055
$448$	−3.71517	−0.175525
$449$	−2.93782	−0.138645	−0.0693223	−	0.997594i	$-0.522084\pi$
$449$	−2.93782	−0.138645	−0.0693223	+	0.997594i	$0.522084\pi$
$450$	−39.0697	−1.84176
$451$	−21.9139	−1.03189
$452$	47.3351	2.22646
$453$	41.0010	1.92639
$454$	2.17099	0.101890
$455$	8.46350	0.396775
$456$	−4.33964	−0.203222
$457$	−10.1951	−0.476909	−0.238454	−	0.971154i	$-0.576641\pi$
$457$	−10.1951	−0.476909	−0.238454	+	0.971154i	$0.576641\pi$
$458$	20.6438	0.964619
$459$	−7.89779	−0.368637
$460$	35.3153	1.64658
$461$	7.01973	0.326941	0.163471	−	0.986548i	$-0.447731\pi$
$461$	7.01973	0.326941	0.163471	+	0.986548i	$0.447731\pi$
$462$	17.8757	0.831652
$463$	23.9219	1.11175	0.555873	−	0.831267i	$-0.312384\pi$
$463$	23.9219	1.11175	0.555873	+	0.831267i	$0.312384\pi$
$464$	−20.3786	−0.946052
$465$	−61.8408	−2.86780
$466$	−49.7340	−2.30388
$467$	10.9429	0.506377	0.253188	−	0.967417i	$-0.418521\pi$
$467$	10.9429	0.506377	0.253188	+	0.967417i	$0.418521\pi$
$468$	95.3103	4.40572
$469$	4.69308	0.216706
$470$	−9.63109	−0.444249
$471$	48.0622	2.21459
$472$	−52.8449	−2.43238
$473$	14.3161	0.658256
$474$	−62.7308	−2.88132
$475$	−1.21070	−0.0555509
$476$	5.10625	0.234045
$477$	15.6026	0.714393
$478$	9.61879	0.439953
$479$	−16.1452	−0.737691	−0.368845	−	0.929491i	$-0.620247\pi$
$479$	−16.1452	−0.737691	−0.368845	+	0.929491i	$0.620247\pi$
$480$	4.50484	0.205617
$481$	54.3227	2.47690
$482$	25.6264	1.16725
$483$	−4.01198	−0.182551
$484$	70.0504	3.18411
$485$	45.6752	2.07401
$486$	−50.0237	−2.26912
$487$	1.95910	0.0887754	0.0443877	−	0.999014i	$-0.485866\pi$
$487$	1.95910	0.0887754	0.0443877	+	0.999014i	$0.485866\pi$
$488$	12.3375	0.558491
$489$	22.6686	1.02511
$490$	49.1739	2.22145
$491$	36.9414	1.66714	0.833571	−	0.552413i	$-0.186293\pi$
$491$	36.9414	1.66714	0.833571	+	0.552413i	$0.186293\pi$
$492$	44.8411	2.02159
$493$	−11.5918	−0.522071
$494$	4.40960	0.198397
$495$	66.0660	2.96945
$496$	33.7907	1.51725
$497$	7.31998	0.328346
$498$	70.4554	3.15718
$499$	−14.7958	−0.662351	−0.331176	−	0.943569i	$-0.607445\pi$
$499$	−14.7958	−0.662351	−0.331176	+	0.943569i	$0.607445\pi$
$500$	−14.5855	−0.652281
$501$	10.7055	0.478288
$502$	−4.03268	−0.179987
$503$	−4.57140	−0.203829	−0.101914	−	0.994793i	$-0.532497\pi$
$503$	−4.57140	−0.203829	−0.101914	+	0.994793i	$0.532497\pi$
$504$	−10.8091	−0.481477
$505$	−5.56674	−0.247717
$506$	−38.4260	−1.70824
$507$	−49.3777	−2.19294
$508$	45.9304	2.03783
$509$	−20.2486	−0.897502	−0.448751	−	0.893657i	$-0.648131\pi$
$509$	−20.2486	−0.897502	−0.448751	+	0.893657i	$0.648131\pi$
$510$	48.3405	2.14055
$511$	−3.53589	−0.156418
$512$	41.5130	1.83463
$513$	1.02185	0.0451159
$514$	10.1871	0.449334
$515$	49.5800	2.18475
$516$	−29.2942	−1.28961
$517$	7.01902	0.308696
$518$	−12.1514	−0.533904
$519$	65.6155	2.88020
$520$	−84.0963	−3.68787
$521$	26.8344	1.17563	0.587817	−	0.808994i	$-0.299987\pi$
$521$	26.8344	1.17563	0.587817	+	0.808994i	$0.299987\pi$
$522$	48.3991	2.11837
$523$	−5.53034	−0.241825	−0.120912	−	0.992663i	$-0.538582\pi$
$523$	−5.53034	−0.241825	−0.120912	+	0.992663i	$0.538582\pi$
$524$	16.2787	0.711137
$525$	−5.17377	−0.225802
$526$	10.4476	0.455538
$527$	19.2210	0.837281
$528$	−61.9346	−2.69536
$529$	−14.3758	−0.625033
$530$	−27.1537	−1.17948
$531$	43.7633	1.89916
$532$	−0.660669	−0.0286436
$533$	−23.1007	−1.00060
$534$	18.1160	0.783955
$535$	−13.0217	−0.562976
$536$	−46.6321	−2.01420
$537$	58.1320	2.50858
$538$	4.16222	0.179446
$539$	−35.8373	−1.54362
$540$	−38.4381	−1.65411
$541$	−15.0879	−0.648681	−0.324340	−	0.945940i	$-0.605142\pi$
$541$	−15.0879	−0.648681	−0.324340	+	0.945940i	$0.605142\pi$
$542$	−9.43478	−0.405259
$543$	−25.6028	−1.09872
$544$	−1.40017	−0.0600318
$545$	19.1916	0.822079
$546$	18.8438	0.806440
$547$	−18.5017	−0.791077	−0.395539	−	0.918449i	$-0.629442\pi$
$547$	−18.5017	−0.791077	−0.395539	+	0.918449i	$0.629442\pi$
$548$	−35.9310	−1.53490
$549$	−10.2172	−0.436061
$550$	−49.5534	−2.11297
$551$	1.49981	0.0638939
$552$	39.8644	1.69674
$553$	−4.84189	−0.205898
$554$	17.2803	0.734169
$555$	−77.0506	−3.27062
$556$	−90.4225	−3.83477
$557$	23.6808	1.00339	0.501694	−	0.865045i	$-0.332710\pi$
$557$	23.6808	1.00339	0.501694	+	0.865045i	$0.332710\pi$
$558$	−80.2529	−3.39737
$559$	15.0915	0.638300
$560$	6.55945	0.277187
$561$	−35.2300	−1.48741
$562$	57.8826	2.44163
$563$	34.5619	1.45661	0.728305	−	0.685254i	$-0.240309\pi$
$563$	34.5619	1.45661	0.728305	+	0.685254i	$0.240309\pi$
$564$	−14.3626	−0.604774
$565$	34.5881	1.45513
$566$	36.3308	1.52710
$567$	−2.03957	−0.0856538
$568$	−72.7339	−3.05185
$569$	27.7347	1.16270	0.581349	−	0.813654i	$-0.302525\pi$
$569$	27.7347	1.16270	0.581349	+	0.813654i	$0.302525\pi$
$570$	−6.25451	−0.261973
$571$	10.3937	0.434965	0.217482	−	0.976064i	$-0.430216\pi$
$571$	10.3937	0.434965	0.217482	+	0.976064i	$0.430216\pi$
$572$	120.885	5.05447
$573$	−41.0109	−1.71326
$574$	5.16740	0.215683
$575$	11.1217	0.463805
$576$	−30.5712	−1.27380
$577$	42.8693	1.78467	0.892337	−	0.451370i	$-0.149065\pi$
$577$	42.8693	1.78467	0.892337	+	0.451370i	$0.149065\pi$
$578$	26.8129	1.11527
$579$	50.6677	2.10568
$580$	−56.4169	−2.34258
$581$	5.43812	0.225611
$582$	101.695	4.21539
$583$	19.7893	0.819589
$584$	35.1338	1.45385
$585$	69.6440	2.87943
$586$	−30.0393	−1.24091
$587$	−34.8919	−1.44014	−0.720072	−	0.693900i	$-0.755891\pi$
$587$	−34.8919	−1.44014	−0.720072	+	0.693900i	$0.755891\pi$
$588$	73.3318	3.02415
$589$	−2.48690	−0.102471
$590$	−76.1628	−3.13557
$591$	17.3284	0.712797
$592$	42.1016	1.73037
$593$	−37.5188	−1.54071	−0.770357	−	0.637613i	$-0.779922\pi$
$593$	−37.5188	−1.54071	−0.770357	+	0.637613i	$0.779922\pi$
$594$	41.8239	1.71605
$595$	3.73118	0.152963
$596$	−77.0951	−3.15794
$597$	−3.78397	−0.154868
$598$	−40.5071	−1.65646
$599$	5.69171	0.232557	0.116278	−	0.993217i	$-0.462903\pi$
$599$	5.69171	0.232557	0.116278	+	0.993217i	$0.462903\pi$
$600$	51.4084	2.09874
$601$	−40.1689	−1.63852	−0.819262	−	0.573420i	$-0.805616\pi$
$601$	−40.1689	−1.63852	−0.819262	+	0.573420i	$0.805616\pi$
$602$	−3.37581	−0.137588
$603$	38.6182	1.57265
$604$	−62.0229	−2.52367
$605$	51.1864	2.08102
$606$	−12.3942	−0.503481
$607$	−37.9715	−1.54121	−0.770607	−	0.637311i	$-0.780047\pi$
$607$	−37.9715	−1.54121	−0.770607	+	0.637311i	$0.780047\pi$
$608$	0.181160	0.00734702
$609$	6.40921	0.259714
$610$	17.7814	0.719948
$611$	7.39915	0.299338
$612$	42.0180	1.69848
$613$	−17.9997	−0.727002	−0.363501	−	0.931594i	$-0.618419\pi$
$613$	−17.9997	−0.727002	−0.363501	+	0.931594i	$0.618419\pi$
$614$	13.8884	0.560491
$615$	32.7658	1.32124
$616$	−13.7096	−0.552375
$617$	−3.67067	−0.147775	−0.0738877	−	0.997267i	$-0.523541\pi$
$617$	−3.67067	−0.147775	−0.0738877	+	0.997267i	$0.523541\pi$
$618$	110.389	4.44049
$619$	−17.6426	−0.709116	−0.354558	−	0.935034i	$-0.615369\pi$
$619$	−17.6426	−0.709116	−0.354558	+	0.935034i	$0.615369\pi$
$620$	93.5476	3.75696
$621$	−9.38685	−0.376681
$622$	−29.7328	−1.19218
$623$	1.39829	0.0560212
$624$	−65.2889	−2.61365
$625$	−29.5933	−1.18373
$626$	58.9996	2.35810
$627$	4.55821	0.182037
$628$	−72.7044	−2.90122
$629$	23.9485	0.954887
$630$	−15.5787	−0.620669
$631$	−15.9504	−0.634974	−0.317487	−	0.948263i	$-0.602839\pi$
$631$	−15.9504	−0.634974	−0.317487	+	0.948263i	$0.602839\pi$
$632$	48.1108	1.91374
$633$	3.30048	0.131182
$634$	−15.9343	−0.632832
$635$	33.5618	1.33186
$636$	−40.4936	−1.60568
$637$	−37.7782	−1.49683
$638$	61.3862	2.43030
$639$	60.2343	2.38283
$640$	56.5638	2.23588
$641$	−14.4039	−0.568919	−0.284459	−	0.958688i	$-0.591814\pi$
$641$	−14.4039	−0.568919	−0.284459	+	0.958688i	$0.591814\pi$
$642$	−28.9925	−1.14424
$643$	−16.4388	−0.648284	−0.324142	−	0.946008i	$-0.605076\pi$
$643$	−16.4388	−0.648284	−0.324142	+	0.946008i	$0.605076\pi$
$644$	6.06899	0.239152
$645$	−21.4055	−0.842842
$646$	1.94399	0.0764854
$647$	27.2832	1.07261	0.536306	−	0.844023i	$-0.319819\pi$
$647$	27.2832	1.07261	0.536306	+	0.844023i	$0.319819\pi$
$648$	20.2659	0.796119
$649$	55.5065	2.17882
$650$	−52.2372	−2.04891
$651$	−10.6274	−0.416522
$652$	−34.2911	−1.34294
$653$	−10.4856	−0.410334	−0.205167	−	0.978727i	$-0.565774\pi$
$653$	−10.4856	−0.410334	−0.205167	+	0.978727i	$0.565774\pi$
$654$	42.7298	1.67087
$655$	11.8950	0.464775
$656$	−17.9037	−0.699022
$657$	−29.0959	−1.13514
$658$	−1.65512	−0.0645231
$659$	−10.8763	−0.423682	−0.211841	−	0.977304i	$-0.567946\pi$
$659$	−10.8763	−0.423682	−0.211841	+	0.977304i	$0.567946\pi$
$660$	−171.462	−6.67416
$661$	4.85508	0.188841	0.0944203	−	0.995532i	$-0.469900\pi$
$661$	4.85508	0.188841	0.0944203	+	0.995532i	$0.469900\pi$
$662$	45.0256	1.74997
$663$	−37.1380	−1.44232
$664$	−54.0351	−2.09697
$665$	−0.482757	−0.0187205
$666$	−99.9912	−3.87458
$667$	−13.7774	−0.533463
$668$	−16.1944	−0.626582
$669$	69.9267	2.70352
$670$	−67.2086	−2.59650
$671$	−12.9589	−0.500271
$672$	0.774163	0.0298640
$673$	1.59932	0.0616491	0.0308245	−	0.999525i	$-0.490187\pi$
$673$	1.59932	0.0616491	0.0308245	+	0.999525i	$0.490187\pi$
$674$	17.4406	0.671786
$675$	−12.1051	−0.465926
$676$	74.6944	2.87286
$677$	−10.6034	−0.407523	−0.203762	−	0.979021i	$-0.565317\pi$
$677$	−10.6034	−0.407523	−0.203762	+	0.979021i	$0.565317\pi$
$678$	77.0098	2.95754
$679$	7.84935	0.301231
$680$	−37.0743	−1.42174
$681$	2.36570	0.0906539
$682$	−101.788	−3.89765
$683$	47.4960	1.81739	0.908693	−	0.417466i	$-0.137082\pi$
$683$	47.4960	1.81739	0.908693	+	0.417466i	$0.137082\pi$
$684$	−5.43648	−0.207869
$685$	−26.2551	−1.00315
$686$	17.2266	0.657714
$687$	22.4952	0.858246
$688$	11.6963	0.445917
$689$	20.8611	0.794743
$690$	57.4547	2.18726
$691$	−37.7516	−1.43614	−0.718069	−	0.695972i	$-0.754974\pi$
$691$	−37.7516	−1.43614	−0.718069	+	0.695972i	$0.754974\pi$
$692$	−99.2577	−3.77321
$693$	11.3535	0.431285
$694$	−45.7026	−1.73485
$695$	−66.0725	−2.50627
$696$	−63.6842	−2.41394
$697$	−10.1841	−0.385750
$698$	11.1824	0.423259
$699$	−54.1945	−2.04982
$700$	7.82645	0.295812
$701$	−34.3860	−1.29874	−0.649371	−	0.760471i	$-0.724968\pi$
$701$	−34.3860	−1.29874	−0.649371	+	0.760471i	$0.724968\pi$
$702$	44.0890	1.66403
$703$	−3.09856	−0.116864
$704$	−38.7745	−1.46137
$705$	−10.4949	−0.395259
$706$	49.8007	1.87427
$707$	−0.956653	−0.0359786
$708$	−113.580	−4.26858
$709$	13.0658	0.490698	0.245349	−	0.969435i	$-0.421098\pi$
$709$	13.0658	0.490698	0.245349	+	0.969435i	$0.421098\pi$
$710$	−104.828	−3.93412
$711$	−39.8427	−1.49422
$712$	−13.8939	−0.520695
$713$	22.8450	0.855551
$714$	8.30739	0.310896
$715$	88.3319	3.30343
$716$	−87.9373	−3.28637
$717$	10.4815	0.391438
$718$	−65.1623	−2.43183
$719$	50.0741	1.86745	0.933725	−	0.357992i	$-0.116538\pi$
$719$	50.0741	1.86745	0.933725	+	0.357992i	$0.116538\pi$
$720$	53.9760	2.01157
$721$	8.52039	0.317316
$722$	46.5084	1.73086
$723$	27.9247	1.03853
$724$	38.7298	1.43938
$725$	−17.7671	−0.659852
$726$	113.965	4.22966
$727$	−27.2266	−1.00978	−0.504889	−	0.863184i	$-0.668467\pi$
$727$	−27.2266	−1.00978	−0.504889	+	0.863184i	$0.668467\pi$
$728$	−14.4521	−0.535629
$729$	−42.4990	−1.57404
$730$	50.6367	1.87415
$731$	6.65315	0.246076
$732$	26.5169	0.980095
$733$	−34.3850	−1.27004	−0.635020	−	0.772496i	$-0.719008\pi$
$733$	−34.3850	−1.27004	−0.635020	+	0.772496i	$0.719008\pi$
$734$	34.4793	1.27265
$735$	53.5842	1.97648
$736$	−1.66416	−0.0613417
$737$	48.9808	1.80423
$738$	42.5212	1.56523
$739$	3.27467	0.120461	0.0602303	−	0.998185i	$-0.480816\pi$
$739$	3.27467	0.120461	0.0602303	+	0.998185i	$0.480816\pi$
$740$	116.556	4.28467
$741$	4.80508	0.176519
$742$	−4.66641	−0.171309
$743$	−2.94932	−0.108200	−0.0541000	−	0.998536i	$-0.517229\pi$
$743$	−2.94932	−0.108200	−0.0541000	+	0.998536i	$0.517229\pi$
$744$	105.598	3.87141
$745$	−56.3340	−2.06392
$746$	85.4956	3.13021
$747$	44.7489	1.63728
$748$	53.2930	1.94858
$749$	−2.23779	−0.0817672
$750$	−23.7292	−0.866467
$751$	−23.8675	−0.870937	−0.435469	−	0.900204i	$-0.643417\pi$
$751$	−23.8675	−0.870937	−0.435469	+	0.900204i	$0.643417\pi$
$752$	5.73455	0.209117
$753$	−4.39436	−0.160139
$754$	64.7108	2.35663
$755$	−45.3206	−1.64939
$756$	−6.60564	−0.240245
$757$	−16.5062	−0.599930	−0.299965	−	0.953950i	$-0.596975\pi$
$757$	−16.5062	−0.599930	−0.299965	+	0.953950i	$0.596975\pi$
$758$	13.2430	0.481006
$759$	−41.8723	−1.51987
$760$	4.79684	0.174000
$761$	36.7709	1.33294	0.666472	−	0.745530i	$-0.267804\pi$
$761$	36.7709	1.33294	0.666472	+	0.745530i	$0.267804\pi$
$762$	74.7245	2.70698
$763$	3.29811	0.119400
$764$	62.0379	2.24445
$765$	30.7029	1.11007
$766$	47.4090	1.71296
$767$	58.5126	2.11277
$768$	86.8221	3.13292
$769$	−3.78764	−0.136586	−0.0682929	−	0.997665i	$-0.521755\pi$
$769$	−3.78764	−0.136586	−0.0682929	+	0.997665i	$0.521755\pi$
$770$	−19.7590	−0.712064
$771$	11.1007	0.399784
$772$	−76.6459	−2.75855
$773$	−4.39803	−0.158186	−0.0790931	−	0.996867i	$-0.525202\pi$
$773$	−4.39803	−0.158186	−0.0790931	+	0.996867i	$0.525202\pi$
$774$	−27.7787	−0.998484
$775$	29.4604	1.05825
$776$	−77.9940	−2.79982
$777$	−13.2413	−0.475028
$778$	−76.8125	−2.75386
$779$	1.31766	0.0472101
$780$	−180.748	−6.47183
$781$	76.3972	2.73371
$782$	−17.8578	−0.638592
$783$	14.9957	0.535902
$784$	−29.2792	−1.04569
$785$	−53.1258	−1.89614
$786$	26.4839	0.944648
$787$	13.1167	0.467559	0.233779	−	0.972290i	$-0.424891\pi$
$787$	13.1167	0.467559	0.233779	+	0.972290i	$0.424891\pi$
$788$	−26.2130	−0.933800
$789$	11.3846	0.405304
$790$	69.3397	2.46700
$791$	5.94402	0.211345
$792$	−112.813	−4.00863
$793$	−13.6607	−0.485106
$794$	−51.7185	−1.83542
$795$	−29.5891	−1.04942
$796$	5.72408	0.202885
$797$	−19.4415	−0.688655	−0.344327	−	0.938850i	$-0.611893\pi$
$797$	−19.4415	−0.688655	−0.344327	+	0.938850i	$0.611893\pi$
$798$	−1.07485	−0.0380492
$799$	3.26196	0.115400
$800$	−2.14607	−0.0758750
$801$	11.5062	0.406550
$802$	31.3379	1.10658
$803$	−36.9034	−1.30229
$804$	−100.226	−3.53471
$805$	4.43466	0.156301
$806$	−107.300	−3.77949
$807$	4.53551	0.159657
$808$	9.50564	0.334407
$809$	−14.4970	−0.509689	−0.254844	−	0.966982i	$-0.582024\pi$
$809$	−14.4970	−0.509689	−0.254844	+	0.966982i	$0.582024\pi$
$810$	29.2082	1.02627
$811$	2.15502	0.0756731	0.0378366	−	0.999284i	$-0.487953\pi$
$811$	2.15502	0.0756731	0.0378366	+	0.999284i	$0.487953\pi$
$812$	−9.69532	−0.340239
$813$	−10.2810	−0.360569
$814$	−126.822	−4.44512
$815$	−25.0568	−0.877702
$816$	−28.7830	−1.00760
$817$	−0.860814	−0.0301161
$818$	−37.7843	−1.32110
$819$	11.9684	0.418211
$820$	−49.5653	−1.73090
$821$	40.8637	1.42615	0.713076	−	0.701086i	$-0.247301\pi$
$821$	40.8637	1.42615	0.713076	+	0.701086i	$0.247301\pi$
$822$	−58.4563	−2.03890
$823$	7.54146	0.262879	0.131439	−	0.991324i	$-0.458040\pi$
$823$	7.54146	0.262879	0.131439	+	0.991324i	$0.458040\pi$
$824$	−84.6616	−2.94933
$825$	−53.9977	−1.87996
$826$	−13.0887	−0.455414
$827$	−44.6275	−1.55185	−0.775925	−	0.630825i	$-0.782717\pi$
$827$	−44.6275	−1.55185	−0.775925	+	0.630825i	$0.782717\pi$
$828$	49.9402	1.73554
$829$	−12.5652	−0.436408	−0.218204	−	0.975903i	$-0.570020\pi$
$829$	−12.5652	−0.436408	−0.218204	+	0.975903i	$0.570020\pi$
$830$	−77.8782	−2.70319
$831$	18.8301	0.653209
$832$	−40.8745	−1.41707
$833$	−16.6547	−0.577052
$834$	−147.109	−5.09397
$835$	−11.8334	−0.409512
$836$	−6.89528	−0.238478
$837$	−24.8651	−0.859462
$838$	26.0581	0.900161
$839$	−52.3631	−1.80778	−0.903888	−	0.427769i	$-0.859300\pi$
$839$	−52.3631	−1.80778	−0.903888	+	0.427769i	$0.859300\pi$
$840$	20.4986	0.707270
$841$	−6.99037	−0.241047
$842$	47.9861	1.65371
$843$	63.0739	2.17238
$844$	−4.99269	−0.171855
$845$	54.5799	1.87760
$846$	−13.6195	−0.468249
$847$	8.79646	0.302250
$848$	16.1679	0.555208
$849$	39.5892	1.35870
$850$	−23.0290	−0.789889
$851$	28.4637	0.975724
$852$	−156.327	−5.35568
$853$	−29.6640	−1.01568	−0.507838	−	0.861453i	$-0.669555\pi$
$853$	−29.6640	−1.01568	−0.507838	+	0.861453i	$0.669555\pi$
$854$	3.05576	0.104566
$855$	−3.97248	−0.135856
$856$	22.2355	0.759994
$857$	23.9074	0.816662	0.408331	−	0.912834i	$-0.366111\pi$
$857$	23.9074	0.816662	0.408331	+	0.912834i	$0.366111\pi$
$858$	196.669	6.71417
$859$	−57.0716	−1.94726	−0.973630	−	0.228135i	$-0.926737\pi$
$859$	−57.0716	−1.94726	−0.973630	+	0.228135i	$0.926737\pi$
$860$	32.3805	1.10417
$861$	5.63085	0.191899
$862$	−46.8162	−1.59457
$863$	10.2580	0.349188	0.174594	−	0.984641i	$-0.444139\pi$
$863$	10.2580	0.349188	0.174594	+	0.984641i	$0.444139\pi$
$864$	1.81131	0.0616222
$865$	−72.5284	−2.46604
$866$	−39.5346	−1.34344
$867$	29.2176	0.992283
$868$	16.0763	0.545665
$869$	−50.5339	−1.71425
$870$	−91.7850	−3.11180
$871$	51.6335	1.74953
$872$	−32.7712	−1.10977
$873$	64.5904	2.18605
$874$	2.31052	0.0781544
$875$	−1.83154	−0.0619175
$876$	75.5132	2.55135
$877$	16.1061	0.543865	0.271932	−	0.962316i	$-0.412337\pi$
$877$	16.1061	0.543865	0.271932	+	0.962316i	$0.412337\pi$
$878$	2.82845	0.0954555
$879$	−32.7334	−1.10407
$880$	68.4597	2.30778
$881$	28.6462	0.965115	0.482558	−	0.875864i	$-0.339708\pi$
$881$	28.6462	0.965115	0.482558	+	0.875864i	$0.339708\pi$
$882$	69.5380	2.34147
$883$	48.8402	1.64360	0.821801	−	0.569775i	$-0.192969\pi$
$883$	48.8402	1.64360	0.821801	+	0.569775i	$0.192969\pi$
$884$	56.1792	1.88951
$885$	−82.9936	−2.78980
$886$	93.2055	3.13130
$887$	29.9247	1.00477	0.502387	−	0.864643i	$-0.332455\pi$
$887$	29.9247	1.00477	0.502387	+	0.864643i	$0.332455\pi$
$888$	131.570	4.41520
$889$	5.76764	0.193440
$890$	−20.0246	−0.671226
$891$	−21.2866	−0.713128
$892$	−105.779	−3.54175
$893$	−0.422047	−0.0141232
$894$	−125.427	−4.19489
$895$	−64.2565	−2.14786
$896$	9.72057	0.324741
$897$	−44.1400	−1.47379
$898$	7.23013	0.241273
$899$	−36.4953	−1.21718
$900$	64.4019	2.14673
$901$	9.19671	0.306387
$902$	53.9312	1.79571
$903$	−3.67857	−0.122415
$904$	−59.0619	−1.96437
$905$	28.3002	0.940731
$906$	−100.905	−3.35236
$907$	19.2573	0.639428	0.319714	−	0.947514i	$-0.396413\pi$
$907$	19.2573	0.639428	0.319714	+	0.947514i	$0.396413\pi$
$908$	−3.57864	−0.118761
$909$	−7.87206	−0.261100
$910$	−20.8291	−0.690477
$911$	−41.9884	−1.39114	−0.695568	−	0.718460i	$-0.744847\pi$
$911$	−41.9884	−1.39114	−0.695568	+	0.718460i	$0.744847\pi$
$912$	3.72407	0.123316
$913$	56.7566	1.87837
$914$	25.0907	0.829928
$915$	19.3762	0.640556
$916$	−34.0289	−1.12435
$917$	2.04417	0.0675043
$918$	19.4369	0.641512
$919$	−24.7889	−0.817709	−0.408855	−	0.912600i	$-0.634072\pi$
$919$	−24.7889	−0.817709	−0.408855	+	0.912600i	$0.634072\pi$
$920$	−44.0644	−1.45276
$921$	15.1340	0.498683
$922$	−17.2759	−0.568951
$923$	80.5348	2.65083
$924$	−29.4660	−0.969361
$925$	36.7063	1.20690
$926$	−58.8730	−1.93469
$927$	70.1122	2.30279
$928$	2.65853	0.0872704
$929$	−6.21733	−0.203984	−0.101992	−	0.994785i	$-0.532522\pi$
$929$	−6.21733	−0.203984	−0.101992	+	0.994785i	$0.532522\pi$
$930$	152.193	4.99061
$931$	2.15486	0.0706228
$932$	81.9809	2.68537
$933$	−32.3994	−1.06071
$934$	−26.9310	−0.881209
$935$	38.9416	1.27353
$936$	−118.923	−3.88710
$937$	29.2969	0.957089	0.478545	−	0.878063i	$-0.341165\pi$
$937$	29.2969	0.957089	0.478545	+	0.878063i	$0.341165\pi$
$938$	−11.5499	−0.377117
$939$	64.2910	2.09806
$940$	15.8758	0.517810
$941$	23.8796	0.778451	0.389226	−	0.921142i	$-0.372743\pi$
$941$	23.8796	0.778451	0.389226	+	0.921142i	$0.372743\pi$
$942$	−118.283	−3.85388
$943$	−12.1042	−0.394167
$944$	45.3489	1.47598
$945$	−4.82680	−0.157016
$946$	−35.2327	−1.14551
$947$	20.8510	0.677566	0.338783	−	0.940865i	$-0.389985\pi$
$947$	20.8510	0.677566	0.338783	+	0.940865i	$0.389985\pi$
$948$	103.405	3.35842
$949$	−38.9020	−1.26281
$950$	2.97960	0.0966710
$951$	−17.3634	−0.563047
$952$	−6.37127	−0.206494
$953$	−26.0475	−0.843762	−0.421881	−	0.906651i	$-0.638630\pi$
$953$	−26.0475	−0.843762	−0.421881	+	0.906651i	$0.638630\pi$
$954$	−38.3987	−1.24320
$955$	45.3316	1.46690
$956$	−15.8555	−0.512803
$957$	66.8917	2.16230
$958$	39.7340	1.28375
$959$	−4.51197	−0.145699
$960$	57.9759	1.87116
$961$	29.5146	0.952083
$962$	−133.691	−4.31036
$963$	−18.4142	−0.593391
$964$	−42.2422	−1.36053
$965$	−56.0058	−1.80289
$966$	9.87367	0.317680
$967$	−11.7108	−0.376594	−0.188297	−	0.982112i	$-0.560297\pi$
$967$	−11.7108	−0.376594	−0.188297	+	0.982112i	$0.560297\pi$
$968$	−87.4048	−2.80930
$969$	2.11834	0.0680510
$970$	−112.409	−3.60923
$971$	51.0813	1.63928	0.819639	−	0.572881i	$-0.194174\pi$
$971$	51.0813	1.63928	0.819639	+	0.572881i	$0.194174\pi$
$972$	82.4584	2.64485
$973$	−11.3547	−0.364013
$974$	−4.82144	−0.154489
$975$	−56.9221	−1.82297
$976$	−10.5874	−0.338895
$977$	−56.4145	−1.80486	−0.902429	−	0.430838i	$-0.858218\pi$
$977$	−56.4145	−1.80486	−0.902429	+	0.430838i	$0.858218\pi$
$978$	−55.7885	−1.78392
$979$	14.5937	0.466416
$980$	−81.0577	−2.58929
$981$	27.1393	0.866492
$982$	−90.9145	−2.90120
$983$	−8.57607	−0.273534	−0.136767	−	0.990603i	$-0.543671\pi$
$983$	−8.57607	−0.273534	−0.136767	+	0.990603i	$0.543671\pi$
$984$	−55.9501	−1.78362
$985$	−19.1541	−0.610299
$986$	28.5281	0.908520
$987$	−1.80356	−0.0574079
$988$	−7.26872	−0.231249
$989$	7.90754	0.251445
$990$	−162.592	−5.16750
$991$	−60.0564	−1.90776	−0.953878	−	0.300195i	$-0.902948\pi$
$991$	−60.0564	−1.90776	−0.953878	+	0.300195i	$0.902948\pi$
$992$	−4.40823	−0.139961
$993$	49.0638	1.55699
$994$	−18.0148	−0.571395
$995$	4.18263	0.132598
$996$	−116.138	−3.67996
$997$	46.5701	1.47489	0.737445	−	0.675407i	$-0.236032\pi$
$997$	46.5701	1.47489	0.737445	+	0.675407i	$0.236032\pi$
$998$	36.4132	1.15264
$999$	−30.9807	−0.980185

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.c.1.15	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.c.1.15	✓	216	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:	\( N \)	\(=\)	\( 5077 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5077.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46105 q^{2} -2.68177 q^{3} +4.05676 q^{4} +2.96431 q^{5} +6.59997 q^{6} +0.509421 q^{7} -5.06178 q^{8} +4.19189 q^{9} +O(q^{10})\)	\(q-2.46105 q^{2} -2.68177 q^{3} +4.05676 q^{4} +2.96431 q^{5} +6.59997 q^{6} +0.509421 q^{7} -5.06178 q^{8} +4.19189 q^{9} -7.29531 q^{10} +5.31673 q^{11} -10.8793 q^{12} +5.60467 q^{13} -1.25371 q^{14} -7.94959 q^{15} +4.34378 q^{16} +2.47085 q^{17} -10.3165 q^{18} -0.319690 q^{19} +12.0255 q^{20} -1.36615 q^{21} -13.0847 q^{22} +2.93671 q^{23} +13.5745 q^{24} +3.78712 q^{25} -13.7934 q^{26} -3.19639 q^{27} +2.06660 q^{28} -4.69144 q^{29} +19.5643 q^{30} +7.77911 q^{31} -0.566675 q^{32} -14.2582 q^{33} -6.08088 q^{34} +1.51008 q^{35} +17.0055 q^{36} +9.69240 q^{37} +0.786772 q^{38} -15.0304 q^{39} -15.0047 q^{40} -4.12169 q^{41} +3.36216 q^{42} +2.69266 q^{43} +21.5687 q^{44} +12.4261 q^{45} -7.22738 q^{46} +1.32018 q^{47} -11.6490 q^{48} -6.74049 q^{49} -9.32029 q^{50} -6.62625 q^{51} +22.7368 q^{52} +3.72208 q^{53} +7.86647 q^{54} +15.7604 q^{55} -2.57858 q^{56} +0.857334 q^{57} +11.5459 q^{58} +10.4400 q^{59} -32.2496 q^{60} -2.43738 q^{61} -19.1448 q^{62} +2.13544 q^{63} -7.29294 q^{64} +16.6140 q^{65} +35.0902 q^{66} +9.21258 q^{67} +10.0236 q^{68} -7.87557 q^{69} -3.71638 q^{70} +14.3692 q^{71} -21.2185 q^{72} -6.94100 q^{73} -23.8535 q^{74} -10.1562 q^{75} -1.29690 q^{76} +2.70845 q^{77} +36.9907 q^{78} -9.50471 q^{79} +12.8763 q^{80} -4.00370 q^{81} +10.1437 q^{82} +10.6751 q^{83} -5.54214 q^{84} +7.32436 q^{85} -6.62676 q^{86} +12.5814 q^{87} -26.9121 q^{88} +2.74486 q^{89} -30.5812 q^{90} +2.85513 q^{91} +11.9135 q^{92} -20.8618 q^{93} -3.24902 q^{94} -0.947658 q^{95} +1.51969 q^{96} +15.4084 q^{97} +16.5887 q^{98} +22.2872 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9} + 24 q^{10} + 89 q^{11} + 114 q^{12} + 34 q^{13} + 53 q^{14} + 61 q^{15} + 229 q^{16} + 76 q^{17} + 57 q^{18} + 54 q^{19} + 118 q^{20} + 25 q^{21} + 26 q^{22} + 109 q^{23} + 65 q^{24} + 232 q^{25} + 58 q^{26} + 236 q^{27} + 57 q^{28} + 54 q^{29} + 6 q^{30} + 77 q^{31} + 155 q^{32} + 80 q^{33} + 28 q^{34} + 137 q^{35} + 257 q^{36} + 42 q^{37} + 104 q^{38} + 46 q^{39} + 47 q^{40} + 109 q^{41} + 27 q^{42} + 68 q^{43} + 145 q^{44} + 109 q^{45} - 7 q^{46} + 264 q^{47} + 198 q^{48} + 222 q^{49} + 86 q^{50} + 57 q^{51} + 68 q^{52} + 95 q^{53} + 79 q^{54} + 50 q^{55} + 108 q^{56} + 55 q^{57} + 38 q^{58} + 292 q^{59} + 91 q^{60} + 16 q^{61} + 91 q^{62} + 113 q^{63} + 231 q^{64} + 68 q^{65} - 15 q^{66} + 152 q^{67} + 199 q^{68} + 83 q^{69} + 24 q^{70} + 131 q^{71} + 162 q^{72} + 71 q^{73} + 10 q^{74} + 232 q^{75} + 60 q^{76} + 131 q^{77} + 102 q^{78} + 10 q^{79} + 236 q^{80} + 268 q^{81} + 54 q^{82} + 299 q^{83} - 9 q^{85} + 35 q^{86} + 103 q^{87} + 45 q^{88} + 134 q^{89} + 8 q^{90} + 79 q^{91} + 206 q^{92} + 95 q^{93} + 18 q^{94} + 119 q^{95} + 77 q^{96} + 129 q^{97} + 150 q^{98} + 221 q^{99}+O(q^{100}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9 + 24 * q^10 + 89 * q^11 + 114 * q^12 + 34 * q^13 + 53 * q^14 + 61 * q^15 + 229 * q^16 + 76 * q^17 + 57 * q^18 + 54 * q^19 + 118 * q^20 + 25 * q^21 + 26 * q^22 + 109 * q^23 + 65 * q^24 + 232 * q^25 + 58 * q^26 + 236 * q^27 + 57 * q^28 + 54 * q^29 + 6 * q^30 + 77 * q^31 + 155 * q^32 + 80 * q^33 + 28 * q^34 + 137 * q^35 + 257 * q^36 + 42 * q^37 + 104 * q^38 + 46 * q^39 + 47 * q^40 + 109 * q^41 + 27 * q^42 + 68 * q^43 + 145 * q^44 + 109 * q^45 - 7 * q^46 + 264 * q^47 + 198 * q^48 + 222 * q^49 + 86 * q^50 + 57 * q^51 + 68 * q^52 + 95 * q^53 + 79 * q^54 + 50 * q^55 + 108 * q^56 + 55 * q^57 + 38 * q^58 + 292 * q^59 + 91 * q^60 + 16 * q^61 + 91 * q^62 + 113 * q^63 + 231 * q^64 + 68 * q^65 - 15 * q^66 + 152 * q^67 + 199 * q^68 + 83 * q^69 + 24 * q^70 + 131 * q^71 + 162 * q^72 + 71 * q^73 + 10 * q^74 + 232 * q^75 + 60 * q^76 + 131 * q^77 + 102 * q^78 + 10 * q^79 + 236 * q^80 + 268 * q^81 + 54 * q^82 + 299 * q^83 - 9 * q^85 + 35 * q^86 + 103 * q^87 + 45 * q^88 + 134 * q^89 + 8 * q^90 + 79 * q^91 + 206 * q^92 + 95 * q^93 + 18 * q^94 + 119 * q^95 + 77 * q^96 + 129 * q^97 + 150 * q^98 + 221 * q^99

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