LMFDB - Embedded newform 4029.2.a.h.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.40291 q^{2} +1.00000 q^{3} -0.0318502 q^{4} +3.36351 q^{5} +1.40291 q^{6} -1.96099 q^{7} -2.85050 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.40291 q^{2} +1.00000 q^{3} -0.0318502 q^{4} +3.36351 q^{5} +1.40291 q^{6} -1.96099 q^{7} -2.85050 q^{8} +1.00000 q^{9} +4.71869 q^{10} -2.28030 q^{11} -0.0318502 q^{12} -6.98389 q^{13} -2.75109 q^{14} +3.36351 q^{15} -3.93529 q^{16} -1.00000 q^{17} +1.40291 q^{18} -1.80752 q^{19} -0.107129 q^{20} -1.96099 q^{21} -3.19905 q^{22} -3.31484 q^{23} -2.85050 q^{24} +6.31318 q^{25} -9.79775 q^{26} +1.00000 q^{27} +0.0624580 q^{28} +6.42884 q^{29} +4.71869 q^{30} -3.19472 q^{31} +0.180155 q^{32} -2.28030 q^{33} -1.40291 q^{34} -6.59580 q^{35} -0.0318502 q^{36} +3.10681 q^{37} -2.53579 q^{38} -6.98389 q^{39} -9.58767 q^{40} -6.30158 q^{41} -2.75109 q^{42} -7.54901 q^{43} +0.0726282 q^{44} +3.36351 q^{45} -4.65041 q^{46} +12.6702 q^{47} -3.93529 q^{48} -3.15452 q^{49} +8.85681 q^{50} -1.00000 q^{51} +0.222438 q^{52} -4.64105 q^{53} +1.40291 q^{54} -7.66981 q^{55} +5.58980 q^{56} -1.80752 q^{57} +9.01907 q^{58} -12.4726 q^{59} -0.107129 q^{60} -9.59575 q^{61} -4.48190 q^{62} -1.96099 q^{63} +8.12331 q^{64} -23.4904 q^{65} -3.19905 q^{66} -1.32184 q^{67} +0.0318502 q^{68} -3.31484 q^{69} -9.25331 q^{70} +4.41500 q^{71} -2.85050 q^{72} -7.95377 q^{73} +4.35857 q^{74} +6.31318 q^{75} +0.0575701 q^{76} +4.47165 q^{77} -9.79775 q^{78} +1.00000 q^{79} -13.2364 q^{80} +1.00000 q^{81} -8.84054 q^{82} -5.95566 q^{83} +0.0624580 q^{84} -3.36351 q^{85} -10.5906 q^{86} +6.42884 q^{87} +6.50000 q^{88} +7.57709 q^{89} +4.71869 q^{90} +13.6953 q^{91} +0.105578 q^{92} -3.19472 q^{93} +17.7751 q^{94} -6.07962 q^{95} +0.180155 q^{96} +14.9034 q^{97} -4.42550 q^{98} -2.28030 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9} - 9 q^{10} - 19 q^{11} + 21 q^{12} - 12 q^{13} - 15 q^{14} - 12 q^{15} + q^{16} - 25 q^{17} - 7 q^{18} - 35 q^{19} - 11 q^{20} - 4 q^{21} - 2 q^{22} - 16 q^{23} - 21 q^{24} + 19 q^{25} - 5 q^{26} + 25 q^{27} + 3 q^{28} - 37 q^{29} - 9 q^{30} - 28 q^{31} - 19 q^{32} - 19 q^{33} + 7 q^{34} - 42 q^{35} + 21 q^{36} + 8 q^{37} - 35 q^{38} - 12 q^{39} - 9 q^{40} - 34 q^{41} - 15 q^{42} - 19 q^{43} - 56 q^{44} - 12 q^{45} + q^{46} - 25 q^{47} + q^{48} + 25 q^{49} - 7 q^{50} - 25 q^{51} - 37 q^{52} - 44 q^{53} - 7 q^{54} - 11 q^{55} - 18 q^{56} - 35 q^{57} - 3 q^{58} - 47 q^{59} - 11 q^{60} - 28 q^{61} + 11 q^{62} - 4 q^{63} - 9 q^{64} - 63 q^{65} - 2 q^{66} - 28 q^{67} - 21 q^{68} - 16 q^{69} + 5 q^{70} - 27 q^{71} - 21 q^{72} - 21 q^{73} - 18 q^{74} + 19 q^{75} - 50 q^{76} - 58 q^{77} - 5 q^{78} + 25 q^{79} - 56 q^{80} + 25 q^{81} - 5 q^{82} - 61 q^{83} + 3 q^{84} + 12 q^{85} - 28 q^{86} - 37 q^{87} + 15 q^{88} - 34 q^{89} - 9 q^{90} - 30 q^{91} - 31 q^{92} - 28 q^{93} + q^{94} - 32 q^{95} - 19 q^{96} - 11 q^{97} - 66 q^{98} - 19 q^{99}+O(q^{100}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9 - 9 * q^10 - 19 * q^11 + 21 * q^12 - 12 * q^13 - 15 * q^14 - 12 * q^15 + q^16 - 25 * q^17 - 7 * q^18 - 35 * q^19 - 11 * q^20 - 4 * q^21 - 2 * q^22 - 16 * q^23 - 21 * q^24 + 19 * q^25 - 5 * q^26 + 25 * q^27 + 3 * q^28 - 37 * q^29 - 9 * q^30 - 28 * q^31 - 19 * q^32 - 19 * q^33 + 7 * q^34 - 42 * q^35 + 21 * q^36 + 8 * q^37 - 35 * q^38 - 12 * q^39 - 9 * q^40 - 34 * q^41 - 15 * q^42 - 19 * q^43 - 56 * q^44 - 12 * q^45 + q^46 - 25 * q^47 + q^48 + 25 * q^49 - 7 * q^50 - 25 * q^51 - 37 * q^52 - 44 * q^53 - 7 * q^54 - 11 * q^55 - 18 * q^56 - 35 * q^57 - 3 * q^58 - 47 * q^59 - 11 * q^60 - 28 * q^61 + 11 * q^62 - 4 * q^63 - 9 * q^64 - 63 * q^65 - 2 * q^66 - 28 * q^67 - 21 * q^68 - 16 * q^69 + 5 * q^70 - 27 * q^71 - 21 * q^72 - 21 * q^73 - 18 * q^74 + 19 * q^75 - 50 * q^76 - 58 * q^77 - 5 * q^78 + 25 * q^79 - 56 * q^80 + 25 * q^81 - 5 * q^82 - 61 * q^83 + 3 * q^84 + 12 * q^85 - 28 * q^86 - 37 * q^87 + 15 * q^88 - 34 * q^89 - 9 * q^90 - 30 * q^91 - 31 * q^92 - 28 * q^93 + q^94 - 32 * q^95 - 19 * q^96 - 11 * q^97 - 66 * q^98 - 19 * 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 $

$2$	1.40291	0.992005	0.496003	−	0.868321i	$-0.334801\pi$
$2$	1.40291	0.992005	0.496003	+	0.868321i	$0.334801\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.0318502	−0.0159251
$5$	3.36351	1.50421	0.752103	−	0.659045i	$-0.229039\pi$
$5$	3.36351	1.50421	0.752103	+	0.659045i	$0.229039\pi$
$6$	1.40291	0.572735
$7$	−1.96099	−0.741185	−0.370592	−	0.928796i	$-0.620845\pi$
$7$	−1.96099	−0.741185	−0.370592	+	0.928796i	$0.620845\pi$
$8$	−2.85050	−1.00780
$9$	1.00000	0.333333
$10$	4.71869	1.49218
$11$	−2.28030	−0.687537	−0.343768	−	0.939054i	$-0.611704\pi$
$11$	−2.28030	−0.687537	−0.343768	+	0.939054i	$0.611704\pi$
$12$	−0.0318502	−0.00919437
$13$	−6.98389	−1.93698	−0.968491	−	0.249049i	$-0.919882\pi$
$13$	−6.98389	−1.93698	−0.968491	+	0.249049i	$0.919882\pi$
$14$	−2.75109	−0.735259
$15$	3.36351	0.868454
$16$	−3.93529	−0.983821
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.40291	0.330668
$19$	−1.80752	−0.414675	−0.207337	−	0.978270i	$-0.566480\pi$
$19$	−1.80752	−0.414675	−0.207337	+	0.978270i	$0.566480\pi$
$20$	−0.107129	−0.0239547
$21$	−1.96099	−0.427923
$22$	−3.19905	−0.682040
$23$	−3.31484	−0.691191	−0.345596	−	0.938384i	$-0.612323\pi$
$23$	−3.31484	−0.691191	−0.345596	+	0.938384i	$0.612323\pi$
$24$	−2.85050	−0.581856
$25$	6.31318	1.26264
$26$	−9.79775	−1.92150
$27$	1.00000	0.192450
$28$	0.0624580	0.0118035
$29$	6.42884	1.19381	0.596903	−	0.802314i	$-0.296398\pi$
$29$	6.42884	1.19381	0.596903	+	0.802314i	$0.296398\pi$
$30$	4.71869	0.861511
$31$	−3.19472	−0.573789	−0.286894	−	0.957962i	$-0.592623\pi$
$31$	−3.19472	−0.573789	−0.286894	+	0.957962i	$0.592623\pi$
$32$	0.180155	0.0318472
$33$	−2.28030	−0.396950
$34$	−1.40291	−0.240597
$35$	−6.59580	−1.11489
$36$	−0.0318502	−0.00530837
$37$	3.10681	0.510756	0.255378	−	0.966841i	$-0.417800\pi$
$37$	3.10681	0.510756	0.255378	+	0.966841i	$0.417800\pi$
$38$	−2.53579	−0.411359
$39$	−6.98389	−1.11832
$40$	−9.58767	−1.51594
$41$	−6.30158	−0.984142	−0.492071	−	0.870555i	$-0.663760\pi$
$41$	−6.30158	−0.984142	−0.492071	+	0.870555i	$0.663760\pi$
$42$	−2.75109	−0.424502
$43$	−7.54901	−1.15121	−0.575607	−	0.817727i	$-0.695234\pi$
$43$	−7.54901	−1.15121	−0.575607	+	0.817727i	$0.695234\pi$
$44$	0.0726282	0.0109491
$45$	3.36351	0.501402
$46$	−4.65041	−0.685666
$47$	12.6702	1.84814	0.924069	−	0.382225i	$-0.124842\pi$
$47$	12.6702	1.84814	0.924069	+	0.382225i	$0.124842\pi$
$48$	−3.93529	−0.568009
$49$	−3.15452	−0.450645
$50$	8.85681	1.25254
$51$	−1.00000	−0.140028
$52$	0.222438	0.0308467
$53$	−4.64105	−0.637498	−0.318749	−	0.947839i	$-0.603263\pi$
$53$	−4.64105	−0.637498	−0.318749	+	0.947839i	$0.603263\pi$
$54$	1.40291	0.190912
$55$	−7.66981	−1.03420
$56$	5.58980	0.746968
$57$	−1.80752	−0.239412
$58$	9.01907	1.18426
$59$	−12.4726	−1.62379	−0.811895	−	0.583804i	$-0.801564\pi$
$59$	−12.4726	−1.62379	−0.811895	+	0.583804i	$0.801564\pi$
$60$	−0.107129	−0.0138302
$61$	−9.59575	−1.22861	−0.614305	−	0.789069i	$-0.710564\pi$
$61$	−9.59575	−1.22861	−0.614305	+	0.789069i	$0.710564\pi$
$62$	−4.48190	−0.569202
$63$	−1.96099	−0.247062
$64$	8.12331	1.01541
$65$	−23.4904	−2.91362
$66$	−3.19905	−0.393776
$67$	−1.32184	−0.161488	−0.0807440	−	0.996735i	$-0.525730\pi$
$67$	−1.32184	−0.161488	−0.0807440	+	0.996735i	$0.525730\pi$
$68$	0.0318502	0.00386241
$69$	−3.31484	−0.399060
$70$	−9.25331	−1.10598
$71$	4.41500	0.523964	0.261982	−	0.965073i	$-0.415624\pi$
$71$	4.41500	0.523964	0.261982	+	0.965073i	$0.415624\pi$
$72$	−2.85050	−0.335934
$73$	−7.95377	−0.930919	−0.465459	−	0.885069i	$-0.654111\pi$
$73$	−7.95377	−0.930919	−0.465459	+	0.885069i	$0.654111\pi$
$74$	4.35857	0.506673
$75$	6.31318	0.728984
$76$	0.0575701	0.00660374
$77$	4.47165	0.509592
$78$	−9.79775	−1.10938
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−13.2364	−1.47987
$81$	1.00000	0.111111
$82$	−8.84054	−0.976274
$83$	−5.95566	−0.653719	−0.326859	−	0.945073i	$-0.605990\pi$
$83$	−5.95566	−0.653719	−0.326859	+	0.945073i	$0.605990\pi$
$84$	0.0624580	0.00681473
$85$	−3.36351	−0.364824
$86$	−10.5906	−1.14201
$87$	6.42884	0.689244
$88$	6.50000	0.692902
$89$	7.57709	0.803170	0.401585	−	0.915822i	$-0.368460\pi$
$89$	7.57709	0.803170	0.401585	+	0.915822i	$0.368460\pi$
$90$	4.71869	0.497394
$91$	13.6953	1.43566
$92$	0.105578	0.0110073
$93$	−3.19472	−0.331277
$94$	17.7751	1.83336
$95$	−6.07962	−0.623756
$96$	0.180155	0.0183870
$97$	14.9034	1.51321	0.756603	−	0.653874i	$-0.226857\pi$
$97$	14.9034	1.51321	0.756603	+	0.653874i	$0.226857\pi$
$98$	−4.42550	−0.447043
$99$	−2.28030	−0.229179
$100$	−0.201076	−0.0201076
$101$	6.33045	0.629904	0.314952	−	0.949108i	$-0.398012\pi$
$101$	6.33045	0.629904	0.314952	+	0.949108i	$0.398012\pi$
$102$	−1.40291	−0.138909
$103$	−13.3162	−1.31209	−0.656043	−	0.754724i	$-0.727771\pi$
$103$	−13.3162	−1.31209	−0.656043	+	0.754724i	$0.727771\pi$
$104$	19.9076	1.95210
$105$	−6.59580	−0.643685
$106$	−6.51097	−0.632401
$107$	5.80141	0.560843	0.280422	−	0.959877i	$-0.409526\pi$
$107$	5.80141	0.560843	0.280422	+	0.959877i	$0.409526\pi$
$108$	−0.0318502	−0.00306479
$109$	−12.6355	−1.21026	−0.605129	−	0.796127i	$-0.706878\pi$
$109$	−12.6355	−1.21026	−0.605129	+	0.796127i	$0.706878\pi$
$110$	−10.7600	−1.02593
$111$	3.10681	0.294885
$112$	7.71705	0.729193
$113$	10.2271	0.962086	0.481043	−	0.876697i	$-0.340258\pi$
$113$	10.2271	0.962086	0.481043	+	0.876697i	$0.340258\pi$
$114$	−2.53579	−0.237498
$115$	−11.1495	−1.03969
$116$	−0.204760	−0.0190115
$117$	−6.98389	−0.645661
$118$	−17.4979	−1.61081
$119$	1.96099	0.179764
$120$	−9.58767	−0.875231
$121$	−5.80022	−0.527293
$122$	−13.4620	−1.21879
$123$	−6.30158	−0.568195
$124$	0.101753	0.00913766
$125$	4.41691	0.395060
$126$	−2.75109	−0.245086
$127$	9.23616	0.819576	0.409788	−	0.912181i	$-0.365603\pi$
$127$	9.23616	0.819576	0.409788	+	0.912181i	$0.365603\pi$
$128$	11.0359	0.975449
$129$	−7.54901	−0.664653
$130$	−32.9548	−2.89033
$131$	9.81989	0.857968	0.428984	−	0.903312i	$-0.358872\pi$
$131$	9.81989	0.857968	0.428984	+	0.903312i	$0.358872\pi$
$132$	0.0726282	0.00632147
$133$	3.54454	0.307350
$134$	−1.85441	−0.160197
$135$	3.36351	0.289485
$136$	2.85050	0.244428
$137$	19.0207	1.62505	0.812525	−	0.582927i	$-0.198092\pi$
$137$	19.0207	1.62505	0.812525	+	0.582927i	$0.198092\pi$
$138$	−4.65041	−0.395869
$139$	−21.9959	−1.86567	−0.932836	−	0.360301i	$-0.882674\pi$
$139$	−21.9959	−1.86567	−0.932836	+	0.360301i	$0.882674\pi$
$140$	0.210078	0.0177548
$141$	12.6702	1.06702
$142$	6.19383	0.519775
$143$	15.9254	1.33175
$144$	−3.93529	−0.327940
$145$	21.6235	1.79573
$146$	−11.1584	−0.923477
$147$	−3.15452	−0.260180
$148$	−0.0989526	−0.00813386
$149$	20.0686	1.64408	0.822042	−	0.569427i	$-0.192835\pi$
$149$	20.0686	1.64408	0.822042	+	0.569427i	$0.192835\pi$
$150$	8.85681	0.723156
$151$	8.29814	0.675293	0.337646	−	0.941273i	$-0.390369\pi$
$151$	8.29814	0.675293	0.337646	+	0.941273i	$0.390369\pi$
$152$	5.15234	0.417910
$153$	−1.00000	−0.0808452
$154$	6.27331	0.505518
$155$	−10.7455	−0.863097
$156$	0.222438	0.0178093
$157$	−19.0257	−1.51842	−0.759208	−	0.650848i	$-0.774414\pi$
$157$	−19.0257	−1.51842	−0.759208	+	0.650848i	$0.774414\pi$
$158$	1.40291	0.111609
$159$	−4.64105	−0.368059
$160$	0.605953	0.0479048
$161$	6.50036	0.512300
$162$	1.40291	0.110223
$163$	9.89318	0.774894	0.387447	−	0.921892i	$-0.373357\pi$
$163$	9.89318	0.774894	0.387447	+	0.921892i	$0.373357\pi$
$164$	0.200707	0.0156726
$165$	−7.66981	−0.597094
$166$	−8.35524	−0.648493
$167$	−12.1453	−0.939835	−0.469917	−	0.882710i	$-0.655716\pi$
$167$	−12.1453	−0.939835	−0.469917	+	0.882710i	$0.655716\pi$
$168$	5.58980	0.431262
$169$	35.7747	2.75190
$170$	−4.71869	−0.361907
$171$	−1.80752	−0.138225
$172$	0.240438	0.0183332
$173$	8.41631	0.639880	0.319940	−	0.947438i	$-0.396337\pi$
$173$	8.41631	0.639880	0.319940	+	0.947438i	$0.396337\pi$
$174$	9.01907	0.683734
$175$	−12.3801	−0.935847
$176$	8.97364	0.676413
$177$	−12.4726	−0.937495
$178$	10.6300	0.796749
$179$	15.0290	1.12332	0.561659	−	0.827369i	$-0.310163\pi$
$179$	15.0290	1.12332	0.561659	+	0.827369i	$0.310163\pi$
$180$	−0.107129	−0.00798489
$181$	10.8108	0.803561	0.401780	−	0.915736i	$-0.368392\pi$
$181$	10.8108	0.803561	0.401780	+	0.915736i	$0.368392\pi$
$182$	19.2133	1.42418
$183$	−9.59575	−0.709338
$184$	9.44894	0.696585
$185$	10.4498	0.768283
$186$	−4.48190	−0.328629
$187$	2.28030	0.166752
$188$	−0.403549	−0.0294318
$189$	−1.96099	−0.142641
$190$	−8.52915	−0.618769
$191$	−10.9087	−0.789324	−0.394662	−	0.918826i	$-0.629138\pi$
$191$	−10.9087	−0.789324	−0.394662	+	0.918826i	$0.629138\pi$
$192$	8.12331	0.586249
$193$	0.245857	0.0176972	0.00884859	−	0.999961i	$-0.497183\pi$
$193$	0.245857	0.0176972	0.00884859	+	0.999961i	$0.497183\pi$
$194$	20.9080	1.50111
$195$	−23.4904	−1.68218
$196$	0.100472	0.00717658
$197$	−23.8358	−1.69823	−0.849116	−	0.528206i	$-0.822865\pi$
$197$	−23.8358	−1.69823	−0.849116	+	0.528206i	$0.822865\pi$
$198$	−3.19905	−0.227347
$199$	−19.4767	−1.38066	−0.690332	−	0.723493i	$-0.742535\pi$
$199$	−19.4767	−1.38066	−0.690332	+	0.723493i	$0.742535\pi$
$200$	−17.9957	−1.27249
$201$	−1.32184	−0.0932352
$202$	8.88104	0.624868
$203$	−12.6069	−0.884830
$204$	0.0318502	0.00222996
$205$	−21.1954	−1.48035
$206$	−18.6814	−1.30160
$207$	−3.31484	−0.230397
$208$	27.4836	1.90564
$209$	4.12170	0.285104
$210$	−9.25331	−0.638539
$211$	−4.54170	−0.312664	−0.156332	−	0.987705i	$-0.549967\pi$
$211$	−4.54170	−0.312664	−0.156332	+	0.987705i	$0.549967\pi$
$212$	0.147819	0.0101522
$213$	4.41500	0.302510
$214$	8.13884	0.556360
$215$	−25.3912	−1.73166
$216$	−2.85050	−0.193952
$217$	6.26482	0.425283
$218$	−17.7264	−1.20058
$219$	−7.95377	−0.537466
$220$	0.244285	0.0164697
$221$	6.98389	0.469787
$222$	4.35857	0.292528
$223$	−18.3381	−1.22801	−0.614005	−	0.789302i	$-0.710442\pi$
$223$	−18.3381	−1.22801	−0.614005	+	0.789302i	$0.710442\pi$
$224$	−0.353282	−0.0236047
$225$	6.31318	0.420879
$226$	14.3477	0.954394
$227$	8.00484	0.531300	0.265650	−	0.964070i	$-0.414413\pi$
$227$	8.00484	0.531300	0.265650	+	0.964070i	$0.414413\pi$
$228$	0.0575701	0.00381267
$229$	−11.4571	−0.757109	−0.378554	−	0.925579i	$-0.623579\pi$
$229$	−11.4571	−0.757109	−0.378554	+	0.925579i	$0.623579\pi$
$230$	−15.6417	−1.03138
$231$	4.47165	0.294213
$232$	−18.3254	−1.20312
$233$	0.268934	0.0176185	0.00880923	−	0.999961i	$-0.497196\pi$
$233$	0.268934	0.0176185	0.00880923	+	0.999961i	$0.497196\pi$
$234$	−9.79775	−0.640499
$235$	42.6163	2.77998
$236$	0.397254	0.0258590
$237$	1.00000	0.0649570
$238$	2.75109	0.178327
$239$	3.72674	0.241063	0.120531	−	0.992710i	$-0.461540\pi$
$239$	3.72674	0.241063	0.120531	+	0.992710i	$0.461540\pi$
$240$	−13.2364	−0.854403
$241$	−16.4521	−1.05977	−0.529885	−	0.848069i	$-0.677765\pi$
$241$	−16.4521	−1.05977	−0.529885	+	0.848069i	$0.677765\pi$
$242$	−8.13718	−0.523078
$243$	1.00000	0.0641500
$244$	0.305627	0.0195658
$245$	−10.6102	−0.677864
$246$	−8.84054	−0.563652
$247$	12.6235	0.803217
$248$	9.10655	0.578266
$249$	−5.95566	−0.377425
$250$	6.19651	0.391902
$251$	5.51735	0.348252	0.174126	−	0.984723i	$-0.444290\pi$
$251$	5.51735	0.348252	0.174126	+	0.984723i	$0.444290\pi$
$252$	0.0624580	0.00393448
$253$	7.55883	0.475220
$254$	12.9575	0.813024
$255$	−3.36351	−0.210631
$256$	−0.764211	−0.0477632
$257$	23.5017	1.46600	0.732999	−	0.680230i	$-0.238120\pi$
$257$	23.5017	1.46600	0.732999	+	0.680230i	$0.238120\pi$
$258$	−10.5906	−0.659340
$259$	−6.09242	−0.378565
$260$	0.748174	0.0463998
$261$	6.42884	0.397935
$262$	13.7764	0.851109
$263$	1.48209	0.0913896	0.0456948	−	0.998955i	$-0.485450\pi$
$263$	1.48209	0.0913896	0.0456948	+	0.998955i	$0.485450\pi$
$264$	6.50000	0.400047
$265$	−15.6102	−0.958928
$266$	4.97266	0.304893
$267$	7.57709	0.463710
$268$	0.0421008	0.00257172
$269$	−9.76789	−0.595559	−0.297779	−	0.954635i	$-0.596246\pi$
$269$	−9.76789	−0.595559	−0.297779	+	0.954635i	$0.596246\pi$
$270$	4.71869	0.287170
$271$	−20.1727	−1.22541	−0.612703	−	0.790313i	$-0.709918\pi$
$271$	−20.1727	−1.22541	−0.612703	+	0.790313i	$0.709918\pi$
$272$	3.93529	0.238612
$273$	13.6953	0.828879
$274$	26.6843	1.61206
$275$	−14.3960	−0.868109
$276$	0.105578	0.00635507
$277$	16.5121	0.992115	0.496057	−	0.868290i	$-0.334781\pi$
$277$	16.5121	0.992115	0.496057	+	0.868290i	$0.334781\pi$
$278$	−30.8583	−1.85076
$279$	−3.19472	−0.191263
$280$	18.8013	1.12359
$281$	30.8611	1.84102	0.920509	−	0.390722i	$-0.127775\pi$
$281$	30.8611	1.84102	0.920509	+	0.390722i	$0.127775\pi$
$282$	17.7751	1.05849
$283$	−26.3827	−1.56829	−0.784143	−	0.620580i	$-0.786897\pi$
$283$	−26.3827	−1.56829	−0.784143	+	0.620580i	$0.786897\pi$
$284$	−0.140619	−0.00834418
$285$	−6.07962	−0.360126
$286$	22.3418	1.32110
$287$	12.3573	0.729431
$288$	0.180155	0.0106157
$289$	1.00000	0.0588235
$290$	30.3357	1.78137
$291$	14.9034	0.873650
$292$	0.253330	0.0148250
$293$	−19.8381	−1.15895	−0.579477	−	0.814989i	$-0.696743\pi$
$293$	−19.8381	−1.15895	−0.579477	+	0.814989i	$0.696743\pi$
$294$	−4.42550	−0.258100
$295$	−41.9516	−2.44251
$296$	−8.85595	−0.514742
$297$	−2.28030	−0.132317
$298$	28.1544	1.63094
$299$	23.1505	1.33883
$300$	−0.201076	−0.0116092
$301$	14.8035	0.853261
$302$	11.6415	0.669894
$303$	6.33045	0.363675
$304$	7.11312	0.407966
$305$	−32.2754	−1.84808
$306$	−1.40291	−0.0801989
$307$	−29.7080	−1.69552	−0.847762	−	0.530378i	$-0.822050\pi$
$307$	−29.7080	−1.69552	−0.847762	+	0.530378i	$0.822050\pi$
$308$	−0.142423	−0.00811531
$309$	−13.3162	−0.757533
$310$	−15.0749	−0.856197
$311$	24.9007	1.41199	0.705994	−	0.708218i	$-0.250500\pi$
$311$	24.9007	1.41199	0.705994	+	0.708218i	$0.250500\pi$
$312$	19.9076	1.12704
$313$	−28.3872	−1.60454	−0.802269	−	0.596962i	$-0.796374\pi$
$313$	−28.3872	−1.60454	−0.802269	+	0.596962i	$0.796374\pi$
$314$	−26.6913	−1.50628
$315$	−6.59580	−0.371632
$316$	−0.0318502	−0.00179172
$317$	−5.40756	−0.303719	−0.151859	−	0.988402i	$-0.548526\pi$
$317$	−5.40756	−0.303719	−0.151859	+	0.988402i	$0.548526\pi$
$318$	−6.51097	−0.365117
$319$	−14.6597	−0.820785
$320$	27.3228	1.52739
$321$	5.80141	0.323803
$322$	9.11941	0.508205
$323$	1.80752	0.100573
$324$	−0.0318502	−0.00176946
$325$	−44.0906	−2.44570
$326$	13.8792	0.768699
$327$	−12.6355	−0.698743
$328$	17.9627	0.991822
$329$	−24.8461	−1.36981
$330$	−10.7600	−0.592321
$331$	29.7942	1.63764	0.818819	−	0.574051i	$-0.194629\pi$
$331$	29.7942	1.63764	0.818819	+	0.574051i	$0.194629\pi$
$332$	0.189689	0.0104106
$333$	3.10681	0.170252
$334$	−17.0388	−0.932321
$335$	−4.44601	−0.242911
$336$	7.71705	0.421000
$337$	23.2952	1.26897	0.634486	−	0.772935i	$-0.281212\pi$
$337$	23.2952	1.26897	0.634486	+	0.772935i	$0.281212\pi$
$338$	50.1886	2.72990
$339$	10.2271	0.555460
$340$	0.107129	0.00580986
$341$	7.28493	0.394501
$342$	−2.53579	−0.137120
$343$	19.9129	1.07520
$344$	21.5184	1.16020
$345$	−11.1495	−0.600268
$346$	11.8073	0.634765
$347$	0.347109	0.0186338	0.00931689	−	0.999957i	$-0.497034\pi$
$347$	0.347109	0.0186338	0.00931689	+	0.999957i	$0.497034\pi$
$348$	−0.204760	−0.0109763
$349$	33.1028	1.77195	0.885977	−	0.463730i	$-0.153489\pi$
$349$	33.1028	1.77195	0.885977	+	0.463730i	$0.153489\pi$
$350$	−17.3681	−0.928365
$351$	−6.98389	−0.372772
$352$	−0.410808	−0.0218961
$353$	25.3497	1.34923	0.674615	−	0.738170i	$-0.264310\pi$
$353$	25.3497	1.34923	0.674615	+	0.738170i	$0.264310\pi$
$354$	−17.4979	−0.930000
$355$	14.8499	0.788149
$356$	−0.241332	−0.0127906
$357$	1.96099	0.103787
$358$	21.0843	1.11434
$359$	−16.9168	−0.892832	−0.446416	−	0.894826i	$-0.647300\pi$
$359$	−16.9168	−0.892832	−0.446416	+	0.894826i	$0.647300\pi$
$360$	−9.58767	−0.505315
$361$	−15.7329	−0.828045
$362$	15.1666	0.797137
$363$	−5.80022	−0.304433
$364$	−0.436200	−0.0228631
$365$	−26.7526	−1.40029
$366$	−13.4620	−0.703668
$367$	9.19437	0.479942	0.239971	−	0.970780i	$-0.422862\pi$
$367$	9.19437	0.479942	0.239971	+	0.970780i	$0.422862\pi$
$368$	13.0448	0.680009
$369$	−6.30158	−0.328047
$370$	14.6601	0.762141
$371$	9.10106	0.472503
$372$	0.101753	0.00527563
$373$	−22.1466	−1.14671	−0.573355	−	0.819307i	$-0.694358\pi$
$373$	−22.1466	−1.14671	−0.573355	+	0.819307i	$0.694358\pi$
$374$	3.19905	0.165419
$375$	4.41691	0.228088
$376$	−36.1164	−1.86256
$377$	−44.8983	−2.31238
$378$	−2.75109	−0.141501
$379$	0.0991218	0.00509154	0.00254577	−	0.999997i	$-0.499190\pi$
$379$	0.0991218	0.00509154	0.00254577	+	0.999997i	$0.499190\pi$
$380$	0.193637	0.00993339
$381$	9.23616	0.473183
$382$	−15.3039	−0.783014
$383$	−4.17857	−0.213515	−0.106757	−	0.994285i	$-0.534047\pi$
$383$	−4.17857	−0.213515	−0.106757	+	0.994285i	$0.534047\pi$
$384$	11.0359	0.563176
$385$	15.0404	0.766531
$386$	0.344915	0.0175557
$387$	−7.54901	−0.383738
$388$	−0.474676	−0.0240980
$389$	14.9580	0.758399	0.379199	−	0.925315i	$-0.376199\pi$
$389$	14.9580	0.758399	0.379199	+	0.925315i	$0.376199\pi$
$390$	−32.9548	−1.66873
$391$	3.31484	0.167639
$392$	8.99195	0.454162
$393$	9.81989	0.495348
$394$	−33.4395	−1.68466
$395$	3.36351	0.169236
$396$	0.0726282	0.00364970
$397$	−25.5448	−1.28206	−0.641029	−	0.767517i	$-0.721492\pi$
$397$	−25.5448	−1.28206	−0.641029	+	0.767517i	$0.721492\pi$
$398$	−27.3240	−1.36963
$399$	3.54454	0.177449
$400$	−24.8442	−1.24221
$401$	−21.6517	−1.08123	−0.540617	−	0.841269i	$-0.681809\pi$
$401$	−21.6517	−1.08123	−0.540617	+	0.841269i	$0.681809\pi$
$402$	−1.85441	−0.0924898
$403$	22.3116	1.11142
$404$	−0.201626	−0.0100313
$405$	3.36351	0.167134
$406$	−17.6863	−0.877756
$407$	−7.08446	−0.351164
$408$	2.85050	0.141121
$409$	22.0956	1.09256	0.546278	−	0.837604i	$-0.316044\pi$
$409$	22.0956	1.09256	0.546278	+	0.837604i	$0.316044\pi$
$410$	−29.7352	−1.46852
$411$	19.0207	0.938223
$412$	0.424125	0.0208951
$413$	24.4586	1.20353
$414$	−4.65041	−0.228555
$415$	−20.0319	−0.983328
$416$	−1.25818	−0.0616874
$417$	−21.9959	−1.07715
$418$	5.78237	0.282825
$419$	−6.63155	−0.323973	−0.161986	−	0.986793i	$-0.551790\pi$
$419$	−6.63155	−0.323973	−0.161986	+	0.986793i	$0.551790\pi$
$420$	0.210078	0.0102508
$421$	−13.3579	−0.651023	−0.325512	−	0.945538i	$-0.605537\pi$
$421$	−13.3579	−0.651023	−0.325512	+	0.945538i	$0.605537\pi$
$422$	−6.37159	−0.310164
$423$	12.6702	0.616046
$424$	13.2293	0.642472
$425$	−6.31318	−0.306234
$426$	6.19383	0.300092
$427$	18.8172	0.910627
$428$	−0.184776	−0.00893150
$429$	15.9254	0.768884
$430$	−35.6214	−1.71782
$431$	−3.27033	−0.157526	−0.0787631	−	0.996893i	$-0.525097\pi$
$431$	−3.27033	−0.157526	−0.0787631	+	0.996893i	$0.525097\pi$
$432$	−3.93529	−0.189336
$433$	26.4153	1.26944	0.634719	−	0.772743i	$-0.281116\pi$
$433$	26.4153	1.26944	0.634719	+	0.772743i	$0.281116\pi$
$434$	8.78896	0.421884
$435$	21.6235	1.03677
$436$	0.402443	0.0192735
$437$	5.99165	0.286619
$438$	−11.1584	−0.533169
$439$	−32.2695	−1.54014	−0.770070	−	0.637959i	$-0.779779\pi$
$439$	−32.2695	−1.54014	−0.770070	+	0.637959i	$0.779779\pi$
$440$	21.8628	1.04227
$441$	−3.15452	−0.150215
$442$	9.79775	0.466031
$443$	−15.0730	−0.716139	−0.358070	−	0.933695i	$-0.616565\pi$
$443$	−15.0730	−0.716139	−0.358070	+	0.933695i	$0.616565\pi$
$444$	−0.0989526	−0.00469608
$445$	25.4856	1.20813
$446$	−25.7266	−1.21819
$447$	20.0686	0.949212
$448$	−15.9297	−0.752609
$449$	10.1001	0.476651	0.238326	−	0.971185i	$-0.423401\pi$
$449$	10.1001	0.476651	0.238326	+	0.971185i	$0.423401\pi$
$450$	8.85681	0.417514
$451$	14.3695	0.676634
$452$	−0.325736	−0.0153213
$453$	8.29814	0.389881
$454$	11.2300	0.527052
$455$	46.0644	2.15953
$456$	5.15234	0.241281
$457$	3.78996	0.177287	0.0886433	−	0.996063i	$-0.471747\pi$
$457$	3.78996	0.177287	0.0886433	+	0.996063i	$0.471747\pi$
$458$	−16.0733	−0.751056
$459$	−1.00000	−0.0466760
$460$	0.355114	0.0165573
$461$	2.65254	0.123541	0.0617704	−	0.998090i	$-0.480325\pi$
$461$	2.65254	0.123541	0.0617704	+	0.998090i	$0.480325\pi$
$462$	6.27331	0.291861
$463$	−5.68580	−0.264242	−0.132121	−	0.991234i	$-0.542179\pi$
$463$	−5.68580	−0.264242	−0.132121	+	0.991234i	$0.542179\pi$
$464$	−25.2993	−1.17449
$465$	−10.7455	−0.498309
$466$	0.377290	0.0174776
$467$	−18.7162	−0.866080	−0.433040	−	0.901375i	$-0.642559\pi$
$467$	−18.7162	−0.866080	−0.433040	+	0.901375i	$0.642559\pi$
$468$	0.222438	0.0102822
$469$	2.59211	0.119692
$470$	59.7867	2.75776
$471$	−19.0257	−0.876658
$472$	35.5530	1.63646
$473$	17.2140	0.791501
$474$	1.40291	0.0644377
$475$	−11.4112	−0.523583
$476$	−0.0624580	−0.00286276
$477$	−4.64105	−0.212499
$478$	5.22827	0.239136
$479$	−20.2244	−0.924078	−0.462039	−	0.886860i	$-0.652882\pi$
$479$	−20.2244	−0.924078	−0.462039	+	0.886860i	$0.652882\pi$
$480$	0.605953	0.0276578
$481$	−21.6976	−0.989325
$482$	−23.0807	−1.05130
$483$	6.50036	0.295777
$484$	0.184739	0.00839721
$485$	50.1276	2.27618
$486$	1.40291	0.0636372
$487$	30.9080	1.40058	0.700288	−	0.713861i	$-0.253055\pi$
$487$	30.9080	1.40058	0.700288	+	0.713861i	$0.253055\pi$
$488$	27.3527	1.23820
$489$	9.89318	0.447385
$490$	−14.8852	−0.672445
$491$	−8.83664	−0.398792	−0.199396	−	0.979919i	$-0.563898\pi$
$491$	−8.83664	−0.398792	−0.199396	+	0.979919i	$0.563898\pi$
$492$	0.200707	0.00904857
$493$	−6.42884	−0.289540
$494$	17.7097	0.796796
$495$	−7.66981	−0.344732
$496$	12.5721	0.564506
$497$	−8.65776	−0.388354
$498$	−8.35524	−0.374407
$499$	−34.2146	−1.53165	−0.765827	−	0.643046i	$-0.777670\pi$
$499$	−34.2146	−1.53165	−0.765827	+	0.643046i	$0.777670\pi$
$500$	−0.140680	−0.00629138
$501$	−12.1453	−0.542614
$502$	7.74033	0.345468
$503$	26.9291	1.20071	0.600354	−	0.799734i	$-0.295026\pi$
$503$	26.9291	1.20071	0.600354	+	0.799734i	$0.295026\pi$
$504$	5.58980	0.248989
$505$	21.2925	0.947505
$506$	10.6043	0.471420
$507$	35.7747	1.58881
$508$	−0.294174	−0.0130519
$509$	30.6467	1.35839	0.679196	−	0.733957i	$-0.262328\pi$
$509$	30.6467	1.35839	0.679196	+	0.733957i	$0.262328\pi$
$510$	−4.71869	−0.208947
$511$	15.5973	0.689983
$512$	−23.1440	−1.02283
$513$	−1.80752	−0.0798041
$514$	32.9708	1.45428
$515$	−44.7892	−1.97365
$516$	0.240438	0.0105847
$517$	−28.8919	−1.27066
$518$	−8.54710	−0.375538
$519$	8.41631	0.369435
$520$	66.9592	2.93636
$521$	−44.9909	−1.97109	−0.985543	−	0.169424i	$-0.945809\pi$
$521$	−44.9909	−1.97109	−0.985543	+	0.169424i	$0.945809\pi$
$522$	9.01907	0.394754
$523$	10.5734	0.462342	0.231171	−	0.972913i	$-0.425744\pi$
$523$	10.5734	0.462342	0.231171	+	0.972913i	$0.425744\pi$
$524$	−0.312766	−0.0136632
$525$	−12.3801	−0.540311
$526$	2.07924	0.0906590
$527$	3.19472	0.139164
$528$	8.97364	0.390527
$529$	−12.0119	−0.522254
$530$	−21.8997	−0.951262
$531$	−12.4726	−0.541263
$532$	−0.112894	−0.00489459
$533$	44.0096	1.90627
$534$	10.6300	0.460003
$535$	19.5131	0.843624
$536$	3.76789	0.162748
$537$	15.0290	0.648548
$538$	−13.7035	−0.590798
$539$	7.19325	0.309835
$540$	−0.107129	−0.00461008
$541$	−39.4975	−1.69813	−0.849065	−	0.528288i	$-0.822834\pi$
$541$	−39.4975	−1.69813	−0.849065	+	0.528288i	$0.822834\pi$
$542$	−28.3005	−1.21561
$543$	10.8108	0.463936
$544$	−0.180155	−0.00772408
$545$	−42.4995	−1.82048
$546$	19.2133	0.822253
$547$	−18.5090	−0.791388	−0.395694	−	0.918382i	$-0.629496\pi$
$547$	−18.5090	−0.791388	−0.395694	+	0.918382i	$0.629496\pi$
$548$	−0.605815	−0.0258791
$549$	−9.59575	−0.409537
$550$	−20.1962	−0.861169
$551$	−11.6203	−0.495041
$552$	9.44894	0.402174
$553$	−1.96099	−0.0833898
$554$	23.1649	0.984183
$555$	10.4498	0.443568
$556$	0.700576	0.0297111
$557$	10.5777	0.448193	0.224096	−	0.974567i	$-0.428057\pi$
$557$	10.5777	0.448193	0.224096	+	0.974567i	$0.428057\pi$
$558$	−4.48190	−0.189734
$559$	52.7214	2.22988
$560$	25.9564	1.09686
$561$	2.28030	0.0962744
$562$	43.2952	1.82630
$563$	2.24408	0.0945769	0.0472884	−	0.998881i	$-0.484942\pi$
$563$	2.24408	0.0945769	0.0472884	+	0.998881i	$0.484942\pi$
$564$	−0.403549	−0.0169925
$565$	34.3990	1.44718
$566$	−37.0124	−1.55575
$567$	−1.96099	−0.0823538
$568$	−12.5849	−0.528052
$569$	−15.1339	−0.634448	−0.317224	−	0.948351i	$-0.602751\pi$
$569$	−15.1339	−0.634448	−0.317224	+	0.948351i	$0.602751\pi$
$570$	−8.52915	−0.357247
$571$	18.5193	0.775008	0.387504	−	0.921868i	$-0.373337\pi$
$571$	18.5193	0.775008	0.387504	+	0.921868i	$0.373337\pi$
$572$	−0.507227	−0.0212082
$573$	−10.9087	−0.455716
$574$	17.3362	0.723600
$575$	−20.9272	−0.872724
$576$	8.12331	0.338471
$577$	10.3071	0.429089	0.214544	−	0.976714i	$-0.431173\pi$
$577$	10.3071	0.429089	0.214544	+	0.976714i	$0.431173\pi$
$578$	1.40291	0.0583533
$579$	0.245857	0.0102175
$580$	−0.688712	−0.0285972
$581$	11.6790	0.484526
$582$	20.9080	0.866666
$583$	10.5830	0.438303
$584$	22.6722	0.938183
$585$	−23.4904	−0.971207
$586$	−27.8310	−1.14969
$587$	−43.0159	−1.77546	−0.887728	−	0.460368i	$-0.847717\pi$
$587$	−43.0159	−1.77546	−0.887728	+	0.460368i	$0.847717\pi$
$588$	0.100472	0.00414340
$589$	5.77454	0.237936
$590$	−58.8542	−2.42299
$591$	−23.8358	−0.980475
$592$	−12.2262	−0.502493
$593$	−23.8283	−0.978513	−0.489256	−	0.872140i	$-0.662732\pi$
$593$	−23.8283	−0.978513	−0.489256	+	0.872140i	$0.662732\pi$
$594$	−3.19905	−0.131259
$595$	6.59580	0.270402
$596$	−0.639190	−0.0261822
$597$	−19.4767	−0.797127
$598$	32.4779	1.32812
$599$	−14.4850	−0.591842	−0.295921	−	0.955212i	$-0.595626\pi$
$599$	−14.4850	−0.591842	−0.295921	+	0.955212i	$0.595626\pi$
$600$	−17.9957	−0.734672
$601$	29.8877	1.21915	0.609573	−	0.792730i	$-0.291341\pi$
$601$	29.8877	1.21915	0.609573	+	0.792730i	$0.291341\pi$
$602$	20.7680	0.846440
$603$	−1.32184	−0.0538293
$604$	−0.264298	−0.0107541
$605$	−19.5091	−0.793158
$606$	8.88104	0.360768
$607$	41.3625	1.67885	0.839426	−	0.543474i	$-0.182891\pi$
$607$	41.3625	1.67885	0.839426	+	0.543474i	$0.182891\pi$
$608$	−0.325634	−0.0132062
$609$	−12.6069	−0.510857
$610$	−45.2794	−1.83331
$611$	−88.4872	−3.57981
$612$	0.0318502	0.00128747
$613$	−10.4327	−0.421371	−0.210685	−	0.977554i	$-0.567570\pi$
$613$	−10.4327	−0.421371	−0.210685	+	0.977554i	$0.567570\pi$
$614$	−41.6775	−1.68197
$615$	−21.1954	−0.854682
$616$	−12.7464	−0.513568
$617$	8.58157	0.345481	0.172741	−	0.984967i	$-0.444738\pi$
$617$	8.58157	0.345481	0.172741	+	0.984967i	$0.444738\pi$
$618$	−18.6814	−0.751477
$619$	−17.0861	−0.686748	−0.343374	−	0.939199i	$-0.611570\pi$
$619$	−17.0861	−0.686748	−0.343374	+	0.939199i	$0.611570\pi$
$620$	0.342246	0.0137449
$621$	−3.31484	−0.133020
$622$	34.9334	1.40070
$623$	−14.8586	−0.595297
$624$	27.4836	1.10022
$625$	−16.7096	−0.668385
$626$	−39.8246	−1.59171
$627$	4.12170	0.164605
$628$	0.605973	0.0241810
$629$	−3.10681	−0.123877
$630$	−9.25331	−0.368660
$631$	33.3286	1.32679	0.663396	−	0.748268i	$-0.269114\pi$
$631$	33.3286	1.32679	0.663396	+	0.748268i	$0.269114\pi$
$632$	−2.85050	−0.113387
$633$	−4.54170	−0.180516
$634$	−7.58631	−0.301291
$635$	31.0659	1.23281
$636$	0.147819	0.00586139
$637$	22.0308	0.872892
$638$	−20.5662	−0.814223
$639$	4.41500	0.174655
$640$	37.1195	1.46728
$641$	16.6629	0.658144	0.329072	−	0.944305i	$-0.393264\pi$
$641$	16.6629	0.658144	0.329072	+	0.944305i	$0.393264\pi$
$642$	8.13884	0.321214
$643$	9.51341	0.375172	0.187586	−	0.982248i	$-0.439934\pi$
$643$	9.51341	0.375172	0.187586	+	0.982248i	$0.439934\pi$
$644$	−0.207038	−0.00815845
$645$	−25.3912	−0.999776
$646$	2.53579	0.0997693
$647$	−0.226185	−0.00889226	−0.00444613	−	0.999990i	$-0.501415\pi$
$647$	−0.226185	−0.00889226	−0.00444613	+	0.999990i	$0.501415\pi$
$648$	−2.85050	−0.111978
$649$	28.4412	1.11641
$650$	−61.8550	−2.42615
$651$	6.26482	0.245538
$652$	−0.315100	−0.0123403
$653$	47.6397	1.86429	0.932144	−	0.362089i	$-0.117936\pi$
$653$	47.6397	1.86429	0.932144	+	0.362089i	$0.117936\pi$
$654$	−17.7264	−0.693157
$655$	33.0293	1.29056
$656$	24.7985	0.968220
$657$	−7.95377	−0.310306
$658$	−34.8568	−1.35886
$659$	−30.7290	−1.19703	−0.598516	−	0.801111i	$-0.704243\pi$
$659$	−30.7290	−1.19703	−0.598516	+	0.801111i	$0.704243\pi$
$660$	0.244285	0.00950879
$661$	−11.5656	−0.449851	−0.224926	−	0.974376i	$-0.572214\pi$
$661$	−11.5656	−0.449851	−0.224926	+	0.974376i	$0.572214\pi$
$662$	41.7986	1.62455
$663$	6.98389	0.271232
$664$	16.9766	0.658820
$665$	11.9221	0.462318
$666$	4.35857	0.168891
$667$	−21.3106	−0.825148
$668$	0.386832	0.0149670
$669$	−18.3381	−0.708991
$670$	−6.23734	−0.240969
$671$	21.8812	0.844715
$672$	−0.353282	−0.0136282
$673$	39.7899	1.53379	0.766895	−	0.641773i	$-0.221801\pi$
$673$	39.7899	1.53379	0.766895	+	0.641773i	$0.221801\pi$
$674$	32.6810	1.25883
$675$	6.31318	0.242995
$676$	−1.13943	−0.0438243
$677$	−11.7492	−0.451560	−0.225780	−	0.974178i	$-0.572493\pi$
$677$	−11.7492	−0.451560	−0.225780	+	0.974178i	$0.572493\pi$
$678$	14.3477	0.551020
$679$	−29.2253	−1.12157
$680$	9.58767	0.367670
$681$	8.00484	0.306746
$682$	10.2201	0.391347
$683$	−8.80739	−0.337005	−0.168503	−	0.985701i	$-0.553893\pi$
$683$	−8.80739	−0.337005	−0.168503	+	0.985701i	$0.553893\pi$
$684$	0.0575701	0.00220125
$685$	63.9763	2.44441
$686$	27.9360	1.06660
$687$	−11.4571	−0.437117
$688$	29.7075	1.13259
$689$	32.4126	1.23482
$690$	−15.6417	−0.595469
$691$	−42.7115	−1.62482	−0.812411	−	0.583085i	$-0.801845\pi$
$691$	−42.7115	−1.62482	−0.812411	+	0.583085i	$0.801845\pi$
$692$	−0.268061	−0.0101902
$693$	4.47165	0.169864
$694$	0.486962	0.0184848
$695$	−73.9835	−2.80636
$696$	−18.3254	−0.694622
$697$	6.30158	0.238690
$698$	46.4402	1.75779
$699$	0.268934	0.0101720
$700$	0.394309	0.0149035
$701$	−11.5311	−0.435524	−0.217762	−	0.976002i	$-0.569876\pi$
$701$	−11.5311	−0.435524	−0.217762	+	0.976002i	$0.569876\pi$
$702$	−9.79775	−0.369792
$703$	−5.61563	−0.211798
$704$	−18.5236	−0.698134
$705$	42.6163	1.60502
$706$	35.5633	1.33844
$707$	−12.4140	−0.466875
$708$	0.397254	0.0149297
$709$	−43.4366	−1.63130	−0.815648	−	0.578548i	$-0.803620\pi$
$709$	−43.4366	−1.63130	−0.815648	+	0.578548i	$0.803620\pi$
$710$	20.8330	0.781848
$711$	1.00000	0.0375029
$712$	−21.5985	−0.809437
$713$	10.5900	0.396598
$714$	2.75109	0.102957
$715$	53.5651	2.00322
$716$	−0.478676	−0.0178890
$717$	3.72674	0.139178
$718$	−23.7326	−0.885694
$719$	30.2289	1.12735	0.563674	−	0.825997i	$-0.309387\pi$
$719$	30.2289	1.12735	0.563674	+	0.825997i	$0.309387\pi$
$720$	−13.2364	−0.493290
$721$	26.1130	0.972498
$722$	−22.0717	−0.821425
$723$	−16.4521	−0.611859
$724$	−0.344327	−0.0127968
$725$	40.5864	1.50734
$726$	−8.13718	−0.301999
$727$	−27.6110	−1.02404	−0.512018	−	0.858975i	$-0.671102\pi$
$727$	−27.6110	−1.02404	−0.512018	+	0.858975i	$0.671102\pi$
$728$	−39.0385	−1.44686
$729$	1.00000	0.0370370
$730$	−37.5314	−1.38910
$731$	7.54901	0.279210
$732$	0.305627	0.0112963
$733$	12.8913	0.476152	0.238076	−	0.971247i	$-0.423483\pi$
$733$	12.8913	0.476152	0.238076	+	0.971247i	$0.423483\pi$
$734$	12.8988	0.476105
$735$	−10.6102	−0.391365
$736$	−0.597184	−0.0220125
$737$	3.01419	0.111029
$738$	−8.84054	−0.325425
$739$	−0.0158727	−0.000583885 0	−0.000291942	−	1.00000i	$-0.500093\pi$
$739$	−0.0158727	−0.000583885 0	−0.000291942		1.00000i	$0.500093\pi$
$740$	−0.332828	−0.0122350
$741$	12.6235	0.463738
$742$	12.7679	0.468726
$743$	−17.1932	−0.630758	−0.315379	−	0.948966i	$-0.602132\pi$
$743$	−17.1932	−0.630758	−0.315379	+	0.948966i	$0.602132\pi$
$744$	9.10655	0.333862
$745$	67.5009	2.47304
$746$	−31.0697	−1.13754
$747$	−5.95566	−0.217906
$748$	−0.0726282	−0.00265555
$749$	−11.3765	−0.415689
$750$	6.19651	0.226265
$751$	19.8677	0.724984	0.362492	−	0.931987i	$-0.381926\pi$
$751$	19.8677	0.724984	0.362492	+	0.931987i	$0.381926\pi$
$752$	−49.8608	−1.81824
$753$	5.51735	0.201063
$754$	−62.9881	−2.29389
$755$	27.9108	1.01578
$756$	0.0624580	0.00227158
$757$	18.0445	0.655838	0.327919	−	0.944706i	$-0.393653\pi$
$757$	18.0445	0.655838	0.327919	+	0.944706i	$0.393653\pi$
$758$	0.139059	0.00505084
$759$	7.55883	0.274368
$760$	17.3300	0.628623
$761$	32.7494	1.18716	0.593582	−	0.804773i	$-0.297713\pi$
$761$	32.7494	1.18716	0.593582	+	0.804773i	$0.297713\pi$
$762$	12.9575	0.469400
$763$	24.7780	0.897024
$764$	0.347444	0.0125701
$765$	−3.36351	−0.121608
$766$	−5.86214	−0.211808
$767$	87.1070	3.14525
$768$	−0.764211	−0.0275761
$769$	−14.9580	−0.539401	−0.269700	−	0.962944i	$-0.586925\pi$
$769$	−14.9580	−0.539401	−0.269700	+	0.962944i	$0.586925\pi$
$770$	21.1003	0.760403
$771$	23.5017	0.846394
$772$	−0.00783061	−0.000281830 0
$773$	−21.7177	−0.781130	−0.390565	−	0.920575i	$-0.627720\pi$
$773$	−21.7177	−0.781130	−0.390565	+	0.920575i	$0.627720\pi$
$774$	−10.5906	−0.380670
$775$	−20.1689	−0.724487
$776$	−42.4820	−1.52501
$777$	−6.09242	−0.218564
$778$	20.9846	0.752336
$779$	11.3903	0.408099
$780$	0.748174	0.0267889
$781$	−10.0675	−0.360244
$782$	4.65041	0.166298
$783$	6.42884	0.229748
$784$	12.4139	0.443355
$785$	−63.9931	−2.28401
$786$	13.7764	0.491388
$787$	40.3585	1.43862	0.719312	−	0.694687i	$-0.244457\pi$
$787$	40.3585	1.43862	0.719312	+	0.694687i	$0.244457\pi$
$788$	0.759177	0.0270446
$789$	1.48209	0.0527638
$790$	4.71869	0.167883
$791$	−20.0553	−0.713083
$792$	6.50000	0.230967
$793$	67.0156	2.37980
$794$	−35.8370	−1.27181
$795$	−15.6102	−0.553637
$796$	0.620336	0.0219872
$797$	48.4799	1.71725	0.858623	−	0.512607i	$-0.171320\pi$
$797$	48.4799	1.71725	0.858623	+	0.512607i	$0.171320\pi$
$798$	4.97266	0.176030
$799$	−12.6702	−0.448239
$800$	1.13735	0.0402114
$801$	7.57709	0.267723
$802$	−30.3753	−1.07259
$803$	18.1370	0.640041
$804$	0.0421008	0.00148478
$805$	21.8640	0.770606
$806$	31.3011	1.10253
$807$	−9.76789	−0.343846
$808$	−18.0449	−0.634819
$809$	−25.5082	−0.896822	−0.448411	−	0.893827i	$-0.648010\pi$
$809$	−25.5082	−0.896822	−0.448411	+	0.893827i	$0.648010\pi$
$810$	4.71869	0.165798
$811$	−23.0797	−0.810438	−0.405219	−	0.914220i	$-0.632805\pi$
$811$	−23.0797	−0.810438	−0.405219	+	0.914220i	$0.632805\pi$
$812$	0.401532	0.0140910
$813$	−20.1727	−0.707489
$814$	−9.93884	−0.348356
$815$	33.2758	1.16560
$816$	3.93529	0.137763
$817$	13.6450	0.477379
$818$	30.9981	1.08382
$819$	13.6953	0.478554
$820$	0.675080	0.0235748
$821$	6.13931	0.214264	0.107132	−	0.994245i	$-0.465833\pi$
$821$	6.13931	0.214264	0.107132	+	0.994245i	$0.465833\pi$
$822$	26.6843	0.930722
$823$	23.6336	0.823815	0.411908	−	0.911226i	$-0.364863\pi$
$823$	23.6336	0.823815	0.411908	+	0.911226i	$0.364863\pi$
$824$	37.9578	1.32232
$825$	−14.3960	−0.501203
$826$	34.3131	1.19391
$827$	−46.8659	−1.62969	−0.814844	−	0.579680i	$-0.803178\pi$
$827$	−46.8659	−1.62969	−0.814844	+	0.579680i	$0.803178\pi$
$828$	0.105578	0.00366910
$829$	28.0373	0.973775	0.486887	−	0.873465i	$-0.338132\pi$
$829$	28.0373	0.973775	0.486887	+	0.873465i	$0.338132\pi$
$830$	−28.1029	−0.975467
$831$	16.5121	0.572798
$832$	−56.7323	−1.96684
$833$	3.15452	0.109298
$834$	−30.8583	−1.06854
$835$	−40.8509	−1.41371
$836$	−0.131277	−0.00454032
$837$	−3.19472	−0.110426
$838$	−9.30346	−0.321383
$839$	7.82977	0.270314	0.135157	−	0.990824i	$-0.456846\pi$
$839$	7.82977	0.270314	0.135157	+	0.990824i	$0.456846\pi$
$840$	18.8013	0.648708
$841$	12.3300	0.425172
$842$	−18.7399	−0.645819
$843$	30.8611	1.06291
$844$	0.144654	0.00497921
$845$	120.328	4.13942
$846$	17.7751	0.611121
$847$	11.3742	0.390822
$848$	18.2639	0.627184
$849$	−26.3827	−0.905450
$850$	−8.85681	−0.303786
$851$	−10.2986	−0.353030
$852$	−0.140619	−0.00481752
$853$	−35.5383	−1.21681	−0.608404	−	0.793628i	$-0.708190\pi$
$853$	−35.5383	−1.21681	−0.608404	+	0.793628i	$0.708190\pi$
$854$	26.3988	0.903347
$855$	−6.07962	−0.207919
$856$	−16.5369	−0.565220
$857$	16.8225	0.574647	0.287323	−	0.957834i	$-0.407235\pi$
$857$	16.8225	0.574647	0.287323	+	0.957834i	$0.407235\pi$
$858$	22.3418	0.762737
$859$	40.1664	1.37046	0.685229	−	0.728328i	$-0.259702\pi$
$859$	40.1664	1.37046	0.685229	+	0.728328i	$0.259702\pi$
$860$	0.808714	0.0275769
$861$	12.3573	0.421137
$862$	−4.58797	−0.156267
$863$	26.7168	0.909452	0.454726	−	0.890631i	$-0.349737\pi$
$863$	26.7168	0.909452	0.454726	+	0.890631i	$0.349737\pi$
$864$	0.180155	0.00612900
$865$	28.3083	0.962512
$866$	37.0582	1.25929
$867$	1.00000	0.0339618
$868$	−0.199536	−0.00677269
$869$	−2.28030	−0.0773539
$870$	30.3357	1.02848
$871$	9.23156	0.312799
$872$	36.0174	1.21970
$873$	14.9034	0.504402
$874$	8.40573	0.284328
$875$	−8.66151	−0.292812
$876$	0.253330	0.00855922
$877$	−28.6100	−0.966091	−0.483046	−	0.875595i	$-0.660469\pi$
$877$	−28.6100	−0.966091	−0.483046	+	0.875595i	$0.660469\pi$
$878$	−45.2712	−1.52783
$879$	−19.8381	−0.669122
$880$	30.1829	1.01747
$881$	−15.8320	−0.533394	−0.266697	−	0.963780i	$-0.585932\pi$
$881$	−15.8320	−0.533394	−0.266697	+	0.963780i	$0.585932\pi$
$882$	−4.42550	−0.149014
$883$	9.89387	0.332955	0.166478	−	0.986045i	$-0.446761\pi$
$883$	9.89387	0.332955	0.166478	+	0.986045i	$0.446761\pi$
$884$	−0.222438	−0.00748142
$885$	−41.9516	−1.41019
$886$	−21.1460	−0.710414
$887$	−55.4121	−1.86056	−0.930278	−	0.366854i	$-0.880435\pi$
$887$	−55.4121	−1.86056	−0.930278	+	0.366854i	$0.880435\pi$
$888$	−8.85595	−0.297186
$889$	−18.1120	−0.607457
$890$	35.7539	1.19847
$891$	−2.28030	−0.0763930
$892$	0.584073	0.0195562
$893$	−22.9017	−0.766376
$894$	28.1544	0.941624
$895$	50.5501	1.68970
$896$	−21.6414	−0.722988
$897$	23.1505	0.772971
$898$	14.1694	0.472840
$899$	−20.5383	−0.684992
$900$	−0.201076	−0.00670255
$901$	4.64105	0.154616
$902$	20.1591	0.671225
$903$	14.8035	0.492631
$904$	−29.1524	−0.969593
$905$	36.3622	1.20872
$906$	11.6415	0.386764
$907$	47.2612	1.56928	0.784641	−	0.619950i	$-0.212847\pi$
$907$	47.2612	1.56928	0.784641	+	0.619950i	$0.212847\pi$
$908$	−0.254956	−0.00846101
$909$	6.33045	0.209968
$910$	64.6240	2.14227
$911$	−19.9901	−0.662300	−0.331150	−	0.943578i	$-0.607437\pi$
$911$	−19.9901	−0.662300	−0.331150	+	0.943578i	$0.607437\pi$
$912$	7.11312	0.235539
$913$	13.5807	0.449456
$914$	5.31696	0.175869
$915$	−32.2754	−1.06699
$916$	0.364912	0.0120570
$917$	−19.2567	−0.635913
$918$	−1.40291	−0.0463029
$919$	−33.8156	−1.11547	−0.557737	−	0.830018i	$-0.688330\pi$
$919$	−33.8156	−1.11547	−0.557737	+	0.830018i	$0.688330\pi$
$920$	31.7816	1.04781
$921$	−29.7080	−0.978911
$922$	3.72126	0.122553
$923$	−30.8338	−1.01491
$924$	−0.142423	−0.00468538
$925$	19.6139	0.644900
$926$	−7.97666	−0.262129
$927$	−13.3162	−0.437362
$928$	1.15819	0.0380194
$929$	−1.87493	−0.0615143	−0.0307572	−	0.999527i	$-0.509792\pi$
$929$	−1.87493	−0.0615143	−0.0307572	+	0.999527i	$0.509792\pi$
$930$	−15.0749	−0.494325
$931$	5.70187	0.186871
$932$	−0.00856561	−0.000280576 0
$933$	24.9007	0.815212
$934$	−26.2570	−0.859156
$935$	7.66981	0.250830
$936$	19.9076	0.650699
$937$	2.85609	0.0933044	0.0466522	−	0.998911i	$-0.485145\pi$
$937$	2.85609	0.0933044	0.0466522	+	0.998911i	$0.485145\pi$
$938$	3.63649	0.118736
$939$	−28.3872	−0.926381
$940$	−1.35734	−0.0442715
$941$	31.0544	1.01235	0.506173	−	0.862432i	$-0.331060\pi$
$941$	31.0544	1.01235	0.506173	+	0.862432i	$0.331060\pi$
$942$	−26.6913	−0.869650
$943$	20.8887	0.680231
$944$	49.0831	1.59752
$945$	−6.59580	−0.214562
$946$	24.1497	0.785174
$947$	−26.7544	−0.869402	−0.434701	−	0.900575i	$-0.643146\pi$
$947$	−26.7544	−0.869402	−0.434701	+	0.900575i	$0.643146\pi$
$948$	−0.0318502	−0.00103445
$949$	55.5483	1.80317
$950$	−16.0089	−0.519398
$951$	−5.40756	−0.175352
$952$	−5.58980	−0.181166
$953$	−26.4757	−0.857633	−0.428816	−	0.903392i	$-0.641069\pi$
$953$	−26.4757	−0.857633	−0.428816	+	0.903392i	$0.641069\pi$
$954$	−6.51097	−0.210800
$955$	−36.6914	−1.18731
$956$	−0.118698	−0.00383895
$957$	−14.6597	−0.473881
$958$	−28.3730	−0.916691
$959$	−37.2994	−1.20446
$960$	27.3228	0.881840
$961$	−20.7938	−0.670766
$962$	−30.4397	−0.981416
$963$	5.80141	0.186948
$964$	0.524002	0.0168770
$965$	0.826942	0.0266202
$966$	9.11941	0.293412
$967$	−5.96556	−0.191839	−0.0959197	−	0.995389i	$-0.530579\pi$
$967$	−5.96556	−0.191839	−0.0959197	+	0.995389i	$0.530579\pi$
$968$	16.5335	0.531408
$969$	1.80752	0.0580660
$970$	70.3243	2.25798
$971$	−34.2575	−1.09937	−0.549687	−	0.835370i	$-0.685253\pi$
$971$	−34.2575	−1.09937	−0.549687	+	0.835370i	$0.685253\pi$
$972$	−0.0318502	−0.00102160
$973$	43.1338	1.38281
$974$	43.3611	1.38938
$975$	−44.0906	−1.41203
$976$	37.7620	1.20873
$977$	−24.0949	−0.770864	−0.385432	−	0.922736i	$-0.625948\pi$
$977$	−24.0949	−0.770864	−0.385432	+	0.922736i	$0.625948\pi$
$978$	13.8792	0.443808
$979$	−17.2780	−0.552209
$980$	0.337939	0.0107951
$981$	−12.6355	−0.403419
$982$	−12.3970	−0.395604
$983$	22.3498	0.712847	0.356423	−	0.934325i	$-0.383996\pi$
$983$	22.3498	0.712847	0.356423	+	0.934325i	$0.383996\pi$
$984$	17.9627	0.572629
$985$	−80.1720	−2.55449
$986$	−9.01907	−0.287226
$987$	−24.8461	−0.790861
$988$	−0.402063	−0.0127913
$989$	25.0237	0.795709
$990$	−10.7600	−0.341976
$991$	−30.2067	−0.959546	−0.479773	−	0.877393i	$-0.659281\pi$
$991$	−30.2067	−0.959546	−0.479773	+	0.877393i	$0.659281\pi$
$992$	−0.575545	−0.0182736
$993$	29.7942	0.945491
$994$	−12.1460	−0.385249
$995$	−65.5099	−2.07680
$996$	0.189689	0.00601054
$997$	−6.84758	−0.216865	−0.108432	−	0.994104i	$-0.534583\pi$
$997$	−6.84758	−0.216865	−0.108432	+	0.994104i	$0.534583\pi$
$998$	−47.9999	−1.51941
$999$	3.10681	0.0982951

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.h.1.20	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.h.1.20	✓	25	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+1.40291 q^{2} +1.00000 q^{3} -0.0318502 q^{4} +3.36351 q^{5} +1.40291 q^{6} -1.96099 q^{7} -2.85050 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.40291 q^{2} +1.00000 q^{3} -0.0318502 q^{4} +3.36351 q^{5} +1.40291 q^{6} -1.96099 q^{7} -2.85050 q^{8} +1.00000 q^{9} +4.71869 q^{10} -2.28030 q^{11} -0.0318502 q^{12} -6.98389 q^{13} -2.75109 q^{14} +3.36351 q^{15} -3.93529 q^{16} -1.00000 q^{17} +1.40291 q^{18} -1.80752 q^{19} -0.107129 q^{20} -1.96099 q^{21} -3.19905 q^{22} -3.31484 q^{23} -2.85050 q^{24} +6.31318 q^{25} -9.79775 q^{26} +1.00000 q^{27} +0.0624580 q^{28} +6.42884 q^{29} +4.71869 q^{30} -3.19472 q^{31} +0.180155 q^{32} -2.28030 q^{33} -1.40291 q^{34} -6.59580 q^{35} -0.0318502 q^{36} +3.10681 q^{37} -2.53579 q^{38} -6.98389 q^{39} -9.58767 q^{40} -6.30158 q^{41} -2.75109 q^{42} -7.54901 q^{43} +0.0726282 q^{44} +3.36351 q^{45} -4.65041 q^{46} +12.6702 q^{47} -3.93529 q^{48} -3.15452 q^{49} +8.85681 q^{50} -1.00000 q^{51} +0.222438 q^{52} -4.64105 q^{53} +1.40291 q^{54} -7.66981 q^{55} +5.58980 q^{56} -1.80752 q^{57} +9.01907 q^{58} -12.4726 q^{59} -0.107129 q^{60} -9.59575 q^{61} -4.48190 q^{62} -1.96099 q^{63} +8.12331 q^{64} -23.4904 q^{65} -3.19905 q^{66} -1.32184 q^{67} +0.0318502 q^{68} -3.31484 q^{69} -9.25331 q^{70} +4.41500 q^{71} -2.85050 q^{72} -7.95377 q^{73} +4.35857 q^{74} +6.31318 q^{75} +0.0575701 q^{76} +4.47165 q^{77} -9.79775 q^{78} +1.00000 q^{79} -13.2364 q^{80} +1.00000 q^{81} -8.84054 q^{82} -5.95566 q^{83} +0.0624580 q^{84} -3.36351 q^{85} -10.5906 q^{86} +6.42884 q^{87} +6.50000 q^{88} +7.57709 q^{89} +4.71869 q^{90} +13.6953 q^{91} +0.105578 q^{92} -3.19472 q^{93} +17.7751 q^{94} -6.07962 q^{95} +0.180155 q^{96} +14.9034 q^{97} -4.42550 q^{98} -2.28030 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9} - 9 q^{10} - 19 q^{11} + 21 q^{12} - 12 q^{13} - 15 q^{14} - 12 q^{15} + q^{16} - 25 q^{17} - 7 q^{18} - 35 q^{19} - 11 q^{20} - 4 q^{21} - 2 q^{22} - 16 q^{23} - 21 q^{24} + 19 q^{25} - 5 q^{26} + 25 q^{27} + 3 q^{28} - 37 q^{29} - 9 q^{30} - 28 q^{31} - 19 q^{32} - 19 q^{33} + 7 q^{34} - 42 q^{35} + 21 q^{36} + 8 q^{37} - 35 q^{38} - 12 q^{39} - 9 q^{40} - 34 q^{41} - 15 q^{42} - 19 q^{43} - 56 q^{44} - 12 q^{45} + q^{46} - 25 q^{47} + q^{48} + 25 q^{49} - 7 q^{50} - 25 q^{51} - 37 q^{52} - 44 q^{53} - 7 q^{54} - 11 q^{55} - 18 q^{56} - 35 q^{57} - 3 q^{58} - 47 q^{59} - 11 q^{60} - 28 q^{61} + 11 q^{62} - 4 q^{63} - 9 q^{64} - 63 q^{65} - 2 q^{66} - 28 q^{67} - 21 q^{68} - 16 q^{69} + 5 q^{70} - 27 q^{71} - 21 q^{72} - 21 q^{73} - 18 q^{74} + 19 q^{75} - 50 q^{76} - 58 q^{77} - 5 q^{78} + 25 q^{79} - 56 q^{80} + 25 q^{81} - 5 q^{82} - 61 q^{83} + 3 q^{84} + 12 q^{85} - 28 q^{86} - 37 q^{87} + 15 q^{88} - 34 q^{89} - 9 q^{90} - 30 q^{91} - 31 q^{92} - 28 q^{93} + q^{94} - 32 q^{95} - 19 q^{96} - 11 q^{97} - 66 q^{98} - 19 q^{99}+O(q^{100}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9 - 9 * q^10 - 19 * q^11 + 21 * q^12 - 12 * q^13 - 15 * q^14 - 12 * q^15 + q^16 - 25 * q^17 - 7 * q^18 - 35 * q^19 - 11 * q^20 - 4 * q^21 - 2 * q^22 - 16 * q^23 - 21 * q^24 + 19 * q^25 - 5 * q^26 + 25 * q^27 + 3 * q^28 - 37 * q^29 - 9 * q^30 - 28 * q^31 - 19 * q^32 - 19 * q^33 + 7 * q^34 - 42 * q^35 + 21 * q^36 + 8 * q^37 - 35 * q^38 - 12 * q^39 - 9 * q^40 - 34 * q^41 - 15 * q^42 - 19 * q^43 - 56 * q^44 - 12 * q^45 + q^46 - 25 * q^47 + q^48 + 25 * q^49 - 7 * q^50 - 25 * q^51 - 37 * q^52 - 44 * q^53 - 7 * q^54 - 11 * q^55 - 18 * q^56 - 35 * q^57 - 3 * q^58 - 47 * q^59 - 11 * q^60 - 28 * q^61 + 11 * q^62 - 4 * q^63 - 9 * q^64 - 63 * q^65 - 2 * q^66 - 28 * q^67 - 21 * q^68 - 16 * q^69 + 5 * q^70 - 27 * q^71 - 21 * q^72 - 21 * q^73 - 18 * q^74 + 19 * q^75 - 50 * q^76 - 58 * q^77 - 5 * q^78 + 25 * q^79 - 56 * q^80 + 25 * q^81 - 5 * q^82 - 61 * q^83 + 3 * q^84 + 12 * q^85 - 28 * q^86 - 37 * q^87 + 15 * q^88 - 34 * q^89 - 9 * q^90 - 30 * q^91 - 31 * q^92 - 28 * q^93 + q^94 - 32 * q^95 - 19 * q^96 - 11 * q^97 - 66 * q^98 - 19 * q^99

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