LMFDB - Embedded newform 6005.2.a.f.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$0$
Dimension:	$111$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.03891 q^{2} +2.79275 q^{3} +2.15716 q^{4} +1.00000 q^{5} -5.69418 q^{6} -0.0959578 q^{7} -0.320429 q^{8} +4.79947 q^{9} +O(q^{10})$	\(q-2.03891 q^{2} +2.79275 q^{3} +2.15716 q^{4} +1.00000 q^{5} -5.69418 q^{6} -0.0959578 q^{7} -0.320429 q^{8} +4.79947 q^{9} -2.03891 q^{10} +5.84157 q^{11} +6.02441 q^{12} -6.47802 q^{13} +0.195649 q^{14} +2.79275 q^{15} -3.66099 q^{16} -4.68251 q^{17} -9.78570 q^{18} +2.00937 q^{19} +2.15716 q^{20} -0.267987 q^{21} -11.9104 q^{22} +8.68274 q^{23} -0.894879 q^{24} +1.00000 q^{25} +13.2081 q^{26} +5.02549 q^{27} -0.206996 q^{28} -1.88537 q^{29} -5.69418 q^{30} +3.15277 q^{31} +8.10529 q^{32} +16.3141 q^{33} +9.54722 q^{34} -0.0959578 q^{35} +10.3532 q^{36} -0.0165267 q^{37} -4.09694 q^{38} -18.0915 q^{39} -0.320429 q^{40} -0.986293 q^{41} +0.546401 q^{42} -9.92320 q^{43} +12.6012 q^{44} +4.79947 q^{45} -17.7033 q^{46} +11.0294 q^{47} -10.2242 q^{48} -6.99079 q^{49} -2.03891 q^{50} -13.0771 q^{51} -13.9741 q^{52} +13.3623 q^{53} -10.2465 q^{54} +5.84157 q^{55} +0.0307476 q^{56} +5.61169 q^{57} +3.84411 q^{58} -3.81242 q^{59} +6.02441 q^{60} -2.16437 q^{61} -6.42821 q^{62} -0.460547 q^{63} -9.20398 q^{64} -6.47802 q^{65} -33.2629 q^{66} +13.0050 q^{67} -10.1009 q^{68} +24.2487 q^{69} +0.195649 q^{70} +2.88979 q^{71} -1.53789 q^{72} +7.06655 q^{73} +0.0336965 q^{74} +2.79275 q^{75} +4.33454 q^{76} -0.560544 q^{77} +36.8870 q^{78} -15.0170 q^{79} -3.66099 q^{80} -0.363467 q^{81} +2.01096 q^{82} +16.7790 q^{83} -0.578089 q^{84} -4.68251 q^{85} +20.2325 q^{86} -5.26539 q^{87} -1.87181 q^{88} +4.60127 q^{89} -9.78570 q^{90} +0.621616 q^{91} +18.7300 q^{92} +8.80491 q^{93} -22.4880 q^{94} +2.00937 q^{95} +22.6361 q^{96} -2.40981 q^{97} +14.2536 q^{98} +28.0364 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) $ 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9} + 20 q^{10} + 36 q^{11} + 80 q^{12} + 36 q^{13} + 7 q^{14} + 40 q^{15} + 190 q^{16} + 38 q^{17} + 48 q^{18} + 77 q^{19} + 136 q^{20} + 11 q^{21} + 39 q^{22} + 82 q^{23} - 3 q^{24} + 111 q^{25} - 3 q^{26} + 130 q^{27} + 87 q^{28} + 20 q^{29} + 3 q^{30} + 41 q^{31} + 85 q^{32} + 33 q^{33} + 7 q^{34} + 39 q^{35} + 191 q^{36} + 80 q^{37} + 42 q^{38} + 21 q^{39} + 45 q^{40} + 16 q^{41} + 33 q^{42} + 164 q^{43} + 37 q^{44} + 139 q^{45} + 32 q^{46} + 148 q^{47} + 149 q^{48} + 160 q^{49} + 20 q^{50} + 51 q^{51} + 87 q^{52} + 83 q^{53} - 6 q^{54} + 36 q^{55} - 10 q^{56} + 28 q^{57} + 47 q^{58} + 14 q^{59} + 80 q^{60} + 20 q^{61} + 14 q^{62} + 120 q^{63} + 231 q^{64} + 36 q^{65} - 4 q^{66} + 253 q^{67} + 80 q^{68} + 6 q^{69} + 7 q^{70} + 5 q^{71} + 124 q^{72} + 64 q^{73} - 37 q^{74} + 40 q^{75} + 92 q^{76} + 63 q^{77} + 29 q^{78} + 91 q^{79} + 190 q^{80} + 187 q^{81} - 7 q^{82} + 63 q^{83} - 69 q^{84} + 38 q^{85} - 22 q^{86} + 57 q^{87} + 121 q^{88} - 6 q^{89} + 48 q^{90} + 119 q^{91} + 104 q^{92} + 14 q^{93} - q^{94} + 77 q^{95} - 38 q^{96} + 96 q^{97} + 81 q^{98} + 106 q^{99}+O(q^{100}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9 + 20 * q^10 + 36 * q^11 + 80 * q^12 + 36 * q^13 + 7 * q^14 + 40 * q^15 + 190 * q^16 + 38 * q^17 + 48 * q^18 + 77 * q^19 + 136 * q^20 + 11 * q^21 + 39 * q^22 + 82 * q^23 - 3 * q^24 + 111 * q^25 - 3 * q^26 + 130 * q^27 + 87 * q^28 + 20 * q^29 + 3 * q^30 + 41 * q^31 + 85 * q^32 + 33 * q^33 + 7 * q^34 + 39 * q^35 + 191 * q^36 + 80 * q^37 + 42 * q^38 + 21 * q^39 + 45 * q^40 + 16 * q^41 + 33 * q^42 + 164 * q^43 + 37 * q^44 + 139 * q^45 + 32 * q^46 + 148 * q^47 + 149 * q^48 + 160 * q^49 + 20 * q^50 + 51 * q^51 + 87 * q^52 + 83 * q^53 - 6 * q^54 + 36 * q^55 - 10 * q^56 + 28 * q^57 + 47 * q^58 + 14 * q^59 + 80 * q^60 + 20 * q^61 + 14 * q^62 + 120 * q^63 + 231 * q^64 + 36 * q^65 - 4 * q^66 + 253 * q^67 + 80 * q^68 + 6 * q^69 + 7 * q^70 + 5 * q^71 + 124 * q^72 + 64 * q^73 - 37 * q^74 + 40 * q^75 + 92 * q^76 + 63 * q^77 + 29 * q^78 + 91 * q^79 + 190 * q^80 + 187 * q^81 - 7 * q^82 + 63 * q^83 - 69 * q^84 + 38 * q^85 - 22 * q^86 + 57 * q^87 + 121 * q^88 - 6 * q^89 + 48 * q^90 + 119 * q^91 + 104 * q^92 + 14 * q^93 - q^94 + 77 * q^95 - 38 * q^96 + 96 * q^97 + 81 * q^98 + 106 * 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 $

$2$	−2.03891	−1.44173	−0.720864	−	0.693077i	$-0.756255\pi$
$2$	−2.03891	−1.44173	−0.720864	+	0.693077i	$0.756255\pi$
$3$	2.79275	1.61240	0.806199	−	0.591645i	$-0.201521\pi$
$3$	2.79275	1.61240	0.806199	+	0.591645i	$0.201521\pi$
$4$	2.15716	1.07858
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−5.69418	−2.32464
$7$	−0.0959578	−0.0362687	−0.0181343	−	0.999836i	$-0.505773\pi$
$7$	−0.0959578	−0.0362687	−0.0181343	+	0.999836i	$0.505773\pi$
$8$	−0.320429	−0.113289
$9$	4.79947	1.59982
$10$	−2.03891	−0.644760
$11$	5.84157	1.76130	0.880649	−	0.473769i	$-0.157107\pi$
$11$	5.84157	1.76130	0.880649	+	0.473769i	$0.157107\pi$
$12$	6.02441	1.73910
$13$	−6.47802	−1.79668	−0.898339	−	0.439303i	$-0.855226\pi$
$13$	−6.47802	−1.79668	−0.898339	+	0.439303i	$0.855226\pi$
$14$	0.195649	0.0522895
$15$	2.79275	0.721086
$16$	−3.66099	−0.915247
$17$	−4.68251	−1.13567	−0.567837	−	0.823141i	$-0.692220\pi$
$17$	−4.68251	−1.13567	−0.567837	+	0.823141i	$0.692220\pi$
$18$	−9.78570	−2.30651
$19$	2.00937	0.460982	0.230491	−	0.973074i	$-0.425967\pi$
$19$	2.00937	0.460982	0.230491	+	0.973074i	$0.425967\pi$
$20$	2.15716	0.482355
$21$	−0.267987	−0.0584795
$22$	−11.9104	−2.53931
$23$	8.68274	1.81048	0.905238	−	0.424905i	$-0.139693\pi$
$23$	8.68274	1.81048	0.905238	+	0.424905i	$0.139693\pi$
$24$	−0.894879	−0.182666
$25$	1.00000	0.200000
$26$	13.2081	2.59032
$27$	5.02549	0.967156
$28$	−0.206996	−0.0391186
$29$	−1.88537	−0.350105	−0.175053	−	0.984559i	$-0.556010\pi$
$29$	−1.88537	−0.350105	−0.175053	+	0.984559i	$0.556010\pi$
$30$	−5.69418	−1.03961
$31$	3.15277	0.566254	0.283127	−	0.959082i	$-0.408628\pi$
$31$	3.15277	0.566254	0.283127	+	0.959082i	$0.408628\pi$
$32$	8.10529	1.43283
$33$	16.3141	2.83991
$34$	9.54722	1.63733
$35$	−0.0959578	−0.0162198
$36$	10.3532	1.72554
$37$	−0.0165267	−0.00271698	−0.00135849	−	0.999999i	$-0.500432\pi$
$37$	−0.0165267	−0.00271698	−0.00135849	+	0.999999i	$0.500432\pi$
$38$	−4.09694	−0.664611
$39$	−18.0915	−2.89696
$40$	−0.320429	−0.0506642
$41$	−0.986293	−0.154033	−0.0770165	−	0.997030i	$-0.524539\pi$
$41$	−0.986293	−0.154033	−0.0770165	+	0.997030i	$0.524539\pi$
$42$	0.546401	0.0843115
$43$	−9.92320	−1.51327	−0.756637	−	0.653835i	$-0.773159\pi$
$43$	−9.92320	−1.51327	−0.756637	+	0.653835i	$0.773159\pi$
$44$	12.6012	1.89970
$45$	4.79947	0.715463
$46$	−17.7033	−2.61021
$47$	11.0294	1.60881	0.804404	−	0.594082i	$-0.202485\pi$
$47$	11.0294	1.60881	0.804404	+	0.594082i	$0.202485\pi$
$48$	−10.2242	−1.47574
$49$	−6.99079	−0.998685
$50$	−2.03891	−0.288346
$51$	−13.0771	−1.83116
$52$	−13.9741	−1.93786
$53$	13.3623	1.83545	0.917725	−	0.397217i	$-0.130024\pi$
$53$	13.3623	1.83545	0.917725	+	0.397217i	$0.130024\pi$
$54$	−10.2465	−1.39438
$55$	5.84157	0.787677
$56$	0.0307476	0.00410883
$57$	5.61169	0.743286
$58$	3.84411	0.504756
$59$	−3.81242	−0.496335	−0.248168	−	0.968717i	$-0.579828\pi$
$59$	−3.81242	−0.496335	−0.248168	+	0.968717i	$0.579828\pi$
$60$	6.02441	0.777748
$61$	−2.16437	−0.277119	−0.138560	−	0.990354i	$-0.544247\pi$
$61$	−2.16437	−0.277119	−0.138560	+	0.990354i	$0.544247\pi$
$62$	−6.42821	−0.816384
$63$	−0.460547	−0.0580235
$64$	−9.20398	−1.15050
$65$	−6.47802	−0.803499
$66$	−33.2629	−4.09438
$67$	13.0050	1.58881	0.794404	−	0.607389i	$-0.207783\pi$
$67$	13.0050	1.58881	0.794404	+	0.607389i	$0.207783\pi$
$68$	−10.1009	−1.22491
$69$	24.2487	2.91921
$70$	0.195649	0.0233846
$71$	2.88979	0.342955	0.171478	−	0.985188i	$-0.445146\pi$
$71$	2.88979	0.342955	0.171478	+	0.985188i	$0.445146\pi$
$72$	−1.53789	−0.181242
$73$	7.06655	0.827077	0.413539	−	0.910487i	$-0.364293\pi$
$73$	7.06655	0.827077	0.413539	+	0.910487i	$0.364293\pi$
$74$	0.0336965	0.00391714
$75$	2.79275	0.322479
$76$	4.33454	0.497205
$77$	−0.560544	−0.0638799
$78$	36.8870	4.17663
$79$	−15.0170	−1.68954	−0.844770	−	0.535129i	$-0.820263\pi$
$79$	−15.0170	−1.68954	−0.844770	+	0.535129i	$0.820263\pi$
$80$	−3.66099	−0.409311
$81$	−0.363467	−0.0403852
$82$	2.01096	0.222074
$83$	16.7790	1.84173	0.920865	−	0.389883i	$-0.127484\pi$
$83$	16.7790	1.84173	0.920865	+	0.389883i	$0.127484\pi$
$84$	−0.578089	−0.0630747
$85$	−4.68251	−0.507889
$86$	20.2325	2.18173
$87$	−5.26539	−0.564509
$88$	−1.87181	−0.199535
$89$	4.60127	0.487733	0.243867	−	0.969809i	$-0.421584\pi$
$89$	4.60127	0.487733	0.243867	+	0.969809i	$0.421584\pi$
$90$	−9.78570	−1.03150
$91$	0.621616	0.0651631
$92$	18.7300	1.95274
$93$	8.80491	0.913026
$94$	−22.4880	−2.31946
$95$	2.00937	0.206157
$96$	22.6361	2.31028
$97$	−2.40981	−0.244679	−0.122340	−	0.992488i	$-0.539040\pi$
$97$	−2.40981	−0.244679	−0.122340	+	0.992488i	$0.539040\pi$
$98$	14.2536	1.43983
$99$	28.0364	2.81777
$100$	2.15716	0.215716
$101$	−0.910951	−0.0906430	−0.0453215	−	0.998972i	$-0.514431\pi$
$101$	−0.910951	−0.0906430	−0.0453215	+	0.998972i	$0.514431\pi$
$102$	26.6630	2.64003
$103$	6.11469	0.602498	0.301249	−	0.953546i	$-0.402596\pi$
$103$	6.11469	0.602498	0.301249	+	0.953546i	$0.402596\pi$
$104$	2.07574	0.203543
$105$	−0.267987	−0.0261528
$106$	−27.2445	−2.64622
$107$	4.56956	0.441756	0.220878	−	0.975301i	$-0.429108\pi$
$107$	4.56956	0.441756	0.220878	+	0.975301i	$0.429108\pi$
$108$	10.8408	1.04315
$109$	7.65492	0.733208	0.366604	−	0.930377i	$-0.380520\pi$
$109$	7.65492	0.733208	0.366604	+	0.930377i	$0.380520\pi$
$110$	−11.9104	−1.13561
$111$	−0.0461551	−0.00438085
$112$	0.351300	0.0331948
$113$	16.4829	1.55058	0.775289	−	0.631606i	$-0.217604\pi$
$113$	16.4829	1.55058	0.775289	+	0.631606i	$0.217604\pi$
$114$	−11.4417	−1.07162
$115$	8.68274	0.809669
$116$	−4.06705	−0.377616
$117$	−31.0911	−2.87437
$118$	7.77319	0.715580
$119$	0.449323	0.0411894
$120$	−0.894879	−0.0816909
$121$	23.1239	2.10217
$122$	4.41296	0.399531
$123$	−2.75447	−0.248362
$124$	6.80102	0.610749
$125$	1.00000	0.0894427
$126$	0.939015	0.0836541
$127$	−0.623715	−0.0553457	−0.0276729	−	0.999617i	$-0.508810\pi$
$127$	−0.623715	−0.0553457	−0.0276729	+	0.999617i	$0.508810\pi$
$128$	2.55552	0.225878
$129$	−27.7131	−2.44000
$130$	13.2081	1.15843
$131$	−5.53929	−0.483970	−0.241985	−	0.970280i	$-0.577798\pi$
$131$	−5.53929	−0.483970	−0.241985	+	0.970280i	$0.577798\pi$
$132$	35.1920	3.06307
$133$	−0.192815	−0.0167192
$134$	−26.5159	−2.29063
$135$	5.02549	0.432525
$136$	1.50041	0.128659
$137$	3.44829	0.294607	0.147304	−	0.989091i	$-0.452941\pi$
$137$	3.44829	0.294607	0.147304	+	0.989091i	$0.452941\pi$
$138$	−49.4410	−4.20870
$139$	8.14824	0.691125	0.345562	−	0.938396i	$-0.387688\pi$
$139$	8.14824	0.691125	0.345562	+	0.938396i	$0.387688\pi$
$140$	−0.206996	−0.0174944
$141$	30.8025	2.59404
$142$	−5.89203	−0.494448
$143$	−37.8417	−3.16449
$144$	−17.5708	−1.46423
$145$	−1.88537	−0.156572
$146$	−14.4081	−1.19242
$147$	−19.5236	−1.61028
$148$	−0.0356507	−0.00293047
$149$	−13.5093	−1.10672	−0.553362	−	0.832941i	$-0.686655\pi$
$149$	−13.5093	−1.10672	−0.553362	+	0.832941i	$0.686655\pi$
$150$	−5.69418	−0.464928
$151$	−6.29193	−0.512030	−0.256015	−	0.966673i	$-0.582410\pi$
$151$	−6.29193	−0.512030	−0.256015	+	0.966673i	$0.582410\pi$
$152$	−0.643861	−0.0522240
$153$	−22.4736	−1.81688
$154$	1.14290	0.0920974
$155$	3.15277	0.253236
$156$	−39.0262	−3.12460
$157$	−7.19014	−0.573835	−0.286918	−	0.957955i	$-0.592631\pi$
$157$	−7.19014	−0.573835	−0.286918	+	0.957955i	$0.592631\pi$
$158$	30.6183	2.43586
$159$	37.3175	2.95947
$160$	8.10529	0.640779
$161$	−0.833177	−0.0656635
$162$	0.741077	0.0582245
$163$	22.6743	1.77599	0.887996	−	0.459851i	$-0.152097\pi$
$163$	22.6743	1.77599	0.887996	+	0.459851i	$0.152097\pi$
$164$	−2.12759	−0.166137
$165$	16.3141	1.27005
$166$	−34.2108	−2.65527
$167$	12.3044	0.952140	0.476070	−	0.879407i	$-0.342061\pi$
$167$	12.3044	0.952140	0.476070	+	0.879407i	$0.342061\pi$
$168$	0.0858706	0.00662506
$169$	28.9647	2.22805
$170$	9.54722	0.732238
$171$	9.64394	0.737491
$172$	−21.4059	−1.63219
$173$	−5.99049	−0.455448	−0.227724	−	0.973726i	$-0.573128\pi$
$173$	−5.99049	−0.455448	−0.227724	+	0.973726i	$0.573128\pi$
$174$	10.7357	0.813868
$175$	−0.0959578	−0.00725373
$176$	−21.3859	−1.61202
$177$	−10.6472	−0.800289
$178$	−9.38157	−0.703179
$179$	12.4786	0.932694	0.466347	−	0.884602i	$-0.345570\pi$
$179$	12.4786	0.932694	0.466347	+	0.884602i	$0.345570\pi$
$180$	10.3532	0.771683
$181$	−11.6649	−0.867046	−0.433523	−	0.901142i	$-0.642730\pi$
$181$	−11.6649	−0.867046	−0.433523	+	0.901142i	$0.642730\pi$
$182$	−1.26742	−0.0939474
$183$	−6.04456	−0.446826
$184$	−2.78220	−0.205106
$185$	−0.0165267	−0.00121507
$186$	−17.9524	−1.31634
$187$	−27.3532	−2.00026
$188$	23.7922	1.73523
$189$	−0.482235	−0.0350774
$190$	−4.09694	−0.297223
$191$	−21.6271	−1.56488	−0.782440	−	0.622727i	$-0.786025\pi$
$191$	−21.6271	−1.56488	−0.782440	+	0.622727i	$0.786025\pi$
$192$	−25.7044	−1.85506
$193$	−1.59724	−0.114972	−0.0574861	−	0.998346i	$-0.518308\pi$
$193$	−1.59724	−0.114972	−0.0574861	+	0.998346i	$0.518308\pi$
$194$	4.91339	0.352761
$195$	−18.0915	−1.29556
$196$	−15.0802	−1.07716
$197$	−5.67092	−0.404036	−0.202018	−	0.979382i	$-0.564750\pi$
$197$	−5.67092	−0.404036	−0.202018	+	0.979382i	$0.564750\pi$
$198$	−57.1638	−4.06245
$199$	15.5453	1.10198	0.550988	−	0.834513i	$-0.314251\pi$
$199$	15.5453	1.10198	0.550988	+	0.834513i	$0.314251\pi$
$200$	−0.320429	−0.0226577
$201$	36.3196	2.56179
$202$	1.85735	0.130683
$203$	0.180916	0.0126978
$204$	−28.2093	−1.97505
$205$	−0.986293	−0.0688857
$206$	−12.4673	−0.868638
$207$	41.6726	2.89644
$208$	23.7159	1.64440
$209$	11.7379	0.811927
$210$	0.546401	0.0377052
$211$	8.77004	0.603754	0.301877	−	0.953347i	$-0.402387\pi$
$211$	8.77004	0.603754	0.301877	+	0.953347i	$0.402387\pi$
$212$	28.8245	1.97968
$213$	8.07048	0.552980
$214$	−9.31692	−0.636891
$215$	−9.92320	−0.676757
$216$	−1.61031	−0.109568
$217$	−0.302533	−0.0205373
$218$	−15.6077	−1.05709
$219$	19.7351	1.33358
$220$	12.6012	0.849571
$221$	30.3334	2.04044
$222$	0.0941061	0.00631599
$223$	6.60019	0.441982	0.220991	−	0.975276i	$-0.429071\pi$
$223$	6.60019	0.441982	0.220991	+	0.975276i	$0.429071\pi$
$224$	−0.777766	−0.0519667
$225$	4.79947	0.319965
$226$	−33.6071	−2.23551
$227$	−8.72553	−0.579134	−0.289567	−	0.957158i	$-0.593511\pi$
$227$	−8.72553	−0.579134	−0.289567	+	0.957158i	$0.593511\pi$
$228$	12.1053	0.801693
$229$	−21.6753	−1.43235	−0.716173	−	0.697923i	$-0.754108\pi$
$229$	−21.6753	−1.43235	−0.716173	+	0.697923i	$0.754108\pi$
$230$	−17.7033	−1.16732
$231$	−1.56546	−0.103000
$232$	0.604128	0.0396630
$233$	15.1772	0.994289	0.497145	−	0.867668i	$-0.334382\pi$
$233$	15.1772	0.994289	0.497145	+	0.867668i	$0.334382\pi$
$234$	63.3919	4.14406
$235$	11.0294	0.719481
$236$	−8.22399	−0.535336
$237$	−41.9387	−2.72421
$238$	−0.916130	−0.0593839
$239$	20.7852	1.34448	0.672242	−	0.740331i	$-0.265331\pi$
$239$	20.7852	1.34448	0.672242	+	0.740331i	$0.265331\pi$
$240$	−10.2242	−0.659972
$241$	15.4618	0.995982	0.497991	−	0.867182i	$-0.334071\pi$
$241$	15.4618	0.995982	0.497991	+	0.867182i	$0.334071\pi$
$242$	−47.1475	−3.03076
$243$	−16.0915	−1.03227
$244$	−4.66889	−0.298895
$245$	−6.99079	−0.446625
$246$	5.61612	0.358071
$247$	−13.0168	−0.828237
$248$	−1.01024	−0.0641501
$249$	46.8595	2.96960
$250$	−2.03891	−0.128952
$251$	−22.4183	−1.41503	−0.707515	−	0.706698i	$-0.750184\pi$
$251$	−22.4183	−1.41503	−0.707515	+	0.706698i	$0.750184\pi$
$252$	−0.993473	−0.0625829
$253$	50.7208	3.18879
$254$	1.27170	0.0797934
$255$	−13.0771	−0.818919
$256$	13.1975	0.824843
$257$	−26.8082	−1.67225	−0.836125	−	0.548539i	$-0.815184\pi$
$257$	−26.8082	−1.67225	−0.836125	+	0.548539i	$0.815184\pi$
$258$	56.5045	3.51781
$259$	0.00158587	9.85411e−5 0
$260$	−13.9741	−0.866637
$261$	−9.04881	−0.560107
$262$	11.2941	0.697752
$263$	21.8873	1.34963	0.674815	−	0.737987i	$-0.264224\pi$
$263$	21.8873	1.34963	0.674815	+	0.737987i	$0.264224\pi$
$264$	−5.22749	−0.321730
$265$	13.3623	0.820838
$266$	0.393133	0.0241045
$267$	12.8502	0.786420
$268$	28.0537	1.71365
$269$	−3.53679	−0.215642	−0.107821	−	0.994170i	$-0.534387\pi$
$269$	−3.53679	−0.215642	−0.107821	+	0.994170i	$0.534387\pi$
$270$	−10.2465	−0.623584
$271$	−18.6497	−1.13289	−0.566443	−	0.824101i	$-0.691681\pi$
$271$	−18.6497	−1.13289	−0.566443	+	0.824101i	$0.691681\pi$
$272$	17.1426	1.03942
$273$	1.73602	0.105069
$274$	−7.03075	−0.424743
$275$	5.84157	0.352260
$276$	52.3083	3.14859
$277$	−12.5996	−0.757037	−0.378519	−	0.925594i	$-0.623566\pi$
$277$	−12.5996	−0.757037	−0.378519	+	0.925594i	$0.623566\pi$
$278$	−16.6135	−0.996414
$279$	15.1316	0.905907
$280$	0.0307476	0.00183752
$281$	11.8966	0.709690	0.354845	−	0.934925i	$-0.384534\pi$
$281$	11.8966	0.709690	0.354845	+	0.934925i	$0.384534\pi$
$282$	−62.8035	−3.73990
$283$	−1.72581	−0.102589	−0.0512945	−	0.998684i	$-0.516335\pi$
$283$	−1.72581	−0.102589	−0.0512945	+	0.998684i	$0.516335\pi$
$284$	6.23374	0.369904
$285$	5.61169	0.332408
$286$	77.1559	4.56233
$287$	0.0946425	0.00558657
$288$	38.9011	2.29227
$289$	4.92588	0.289758
$290$	3.84411	0.225734
$291$	−6.73001	−0.394520
$292$	15.2437	0.892067
$293$	32.3470	1.88973	0.944866	−	0.327458i	$-0.106192\pi$
$293$	32.3470	1.88973	0.944866	+	0.327458i	$0.106192\pi$
$294$	39.8068	2.32158
$295$	−3.81242	−0.221968
$296$	0.00529564	0.000307803 0
$297$	29.3567	1.70345
$298$	27.5442	1.59559
$299$	−56.2469	−3.25284
$300$	6.02441	0.347819
$301$	0.952209	0.0548844
$302$	12.8287	0.738208
$303$	−2.54406	−0.146153
$304$	−7.35630	−0.421913
$305$	−2.16437	−0.123932
$306$	45.8216	2.61945
$307$	−27.3572	−1.56136	−0.780680	−	0.624931i	$-0.785127\pi$
$307$	−27.3572	−1.56136	−0.780680	+	0.624931i	$0.785127\pi$
$308$	−1.20918	−0.0688995
$309$	17.0768	0.971466
$310$	−6.42821	−0.365098
$311$	−26.0031	−1.47450	−0.737250	−	0.675620i	$-0.763876\pi$
$311$	−26.0031	−1.47450	−0.737250	+	0.675620i	$0.763876\pi$
$312$	5.79704	0.328193
$313$	2.53046	0.143030	0.0715152	−	0.997440i	$-0.477217\pi$
$313$	2.53046	0.143030	0.0715152	+	0.997440i	$0.477217\pi$
$314$	14.6600	0.827314
$315$	−0.460547	−0.0259489
$316$	−32.3940	−1.82230
$317$	33.9831	1.90868	0.954341	−	0.298719i	$-0.0965595\pi$
$317$	33.9831	1.90868	0.954341	+	0.298719i	$0.0965595\pi$
$318$	−76.0871	−4.26676
$319$	−11.0135	−0.616640
$320$	−9.20398	−0.514518
$321$	12.7616	0.712286
$322$	1.69877	0.0946689
$323$	−9.40891	−0.523526
$324$	−0.784055	−0.0435586
$325$	−6.47802	−0.359336
$326$	−46.2310	−2.56050
$327$	21.3783	1.18222
$328$	0.316036	0.0174502
$329$	−1.05836	−0.0583493
$330$	−33.2629	−1.83106
$331$	−17.9754	−0.988016	−0.494008	−	0.869457i	$-0.664469\pi$
$331$	−17.9754	−0.988016	−0.494008	+	0.869457i	$0.664469\pi$
$332$	36.1948	1.98645
$333$	−0.0793196	−0.00434669
$334$	−25.0875	−1.37273
$335$	13.0050	0.710537
$336$	0.981096	0.0535232
$337$	5.85818	0.319115	0.159558	−	0.987189i	$-0.448993\pi$
$337$	5.85818	0.319115	0.159558	+	0.987189i	$0.448993\pi$
$338$	−59.0564	−3.21224
$339$	46.0326	2.50015
$340$	−10.1009	−0.547798
$341$	18.4171	0.997342
$342$	−19.6631	−1.06326
$343$	1.34253	0.0724896
$344$	3.17968	0.171437
$345$	24.2487	1.30551
$346$	12.2141	0.656633
$347$	−23.0277	−1.23619	−0.618097	−	0.786102i	$-0.712096\pi$
$347$	−23.0277	−1.23619	−0.618097	+	0.786102i	$0.712096\pi$
$348$	−11.3583	−0.608867
$349$	33.3290	1.78406	0.892031	−	0.451974i	$-0.149280\pi$
$349$	33.3290	1.78406	0.892031	+	0.451974i	$0.149280\pi$
$350$	0.195649	0.0104579
$351$	−32.5552	−1.73767
$352$	47.3476	2.52363
$353$	−11.4056	−0.607059	−0.303530	−	0.952822i	$-0.598165\pi$
$353$	−11.4056	−0.607059	−0.303530	+	0.952822i	$0.598165\pi$
$354$	21.7086	1.15380
$355$	2.88979	0.153374
$356$	9.92565	0.526059
$357$	1.25485	0.0664137
$358$	−25.4427	−1.34469
$359$	9.21989	0.486607	0.243304	−	0.969950i	$-0.421769\pi$
$359$	9.21989	0.486607	0.243304	+	0.969950i	$0.421769\pi$
$360$	−1.53789	−0.0810539
$361$	−14.9624	−0.787495
$362$	23.7837	1.25004
$363$	64.5793	3.38954
$364$	1.34092	0.0702835
$365$	7.06655	0.369880
$366$	12.3243	0.644202
$367$	−26.2541	−1.37045	−0.685227	−	0.728329i	$-0.740297\pi$
$367$	−26.2541	−1.37045	−0.685227	+	0.728329i	$0.740297\pi$
$368$	−31.7874	−1.65703
$369$	−4.73369	−0.246426
$370$	0.0336965	0.00175180
$371$	−1.28221	−0.0665693
$372$	18.9936	0.984770
$373$	−4.32587	−0.223985	−0.111992	−	0.993709i	$-0.535723\pi$
$373$	−4.32587	−0.223985	−0.111992	+	0.993709i	$0.535723\pi$
$374$	55.7707	2.88383
$375$	2.79275	0.144217
$376$	−3.53415	−0.182260
$377$	12.2135	0.629026
$378$	0.983234	0.0505721
$379$	−0.731402	−0.0375696	−0.0187848	−	0.999824i	$-0.505980\pi$
$379$	−0.731402	−0.0375696	−0.0187848	+	0.999824i	$0.505980\pi$
$380$	4.33454	0.222357
$381$	−1.74188	−0.0892393
$382$	44.0956	2.25613
$383$	−16.3879	−0.837382	−0.418691	−	0.908129i	$-0.637511\pi$
$383$	−16.3879	−0.837382	−0.418691	+	0.908129i	$0.637511\pi$
$384$	7.13693	0.364205
$385$	−0.560544	−0.0285680
$386$	3.25664	0.165758
$387$	−47.6262	−2.42097
$388$	−5.19834	−0.263906
$389$	−11.8812	−0.602400	−0.301200	−	0.953561i	$-0.597387\pi$
$389$	−11.8812	−0.602400	−0.301200	+	0.953561i	$0.597387\pi$
$390$	36.8870	1.86784
$391$	−40.6570	−2.05611
$392$	2.24005	0.113140
$393$	−15.4699	−0.780351
$394$	11.5625	0.582510
$395$	−15.0170	−0.755586
$396$	60.4790	3.03918
$397$	−5.20547	−0.261255	−0.130628	−	0.991432i	$-0.541699\pi$
$397$	−5.20547	−0.261255	−0.130628	+	0.991432i	$0.541699\pi$
$398$	−31.6954	−1.58875
$399$	−0.538485	−0.0269580
$400$	−3.66099	−0.183049
$401$	−7.66062	−0.382553	−0.191277	−	0.981536i	$-0.561263\pi$
$401$	−7.66062	−0.382553	−0.191277	+	0.981536i	$0.561263\pi$
$402$	−74.0525	−3.69340
$403$	−20.4237	−1.01738
$404$	−1.96506	−0.0977656
$405$	−0.363467	−0.0180608
$406$	−0.368872	−0.0183068
$407$	−0.0965419	−0.00478541
$408$	4.19028	0.207450
$409$	10.9290	0.540405	0.270202	−	0.962804i	$-0.412909\pi$
$409$	10.9290	0.540405	0.270202	+	0.962804i	$0.412909\pi$
$410$	2.01096	0.0993144
$411$	9.63022	0.475024
$412$	13.1903	0.649841
$413$	0.365832	0.0180014
$414$	−84.9667	−4.17588
$415$	16.7790	0.823646
$416$	−52.5062	−2.57433
$417$	22.7560	1.11437
$418$	−23.9325	−1.17058
$419$	−27.0049	−1.31928	−0.659639	−	0.751583i	$-0.729291\pi$
$419$	−27.0049	−1.31928	−0.659639	+	0.751583i	$0.729291\pi$
$420$	−0.578089	−0.0282079
$421$	−37.8292	−1.84368	−0.921840	−	0.387569i	$-0.873315\pi$
$421$	−37.8292	−1.84368	−0.921840	+	0.387569i	$0.873315\pi$
$422$	−17.8813	−0.870449
$423$	52.9355	2.57381
$424$	−4.28166	−0.207936
$425$	−4.68251	−0.227135
$426$	−16.4550	−0.797247
$427$	0.207688	0.0100507
$428$	9.85725	0.476468
$429$	−105.683	−5.10241
$430$	20.2325	0.975699
$431$	27.5781	1.32839	0.664196	−	0.747559i	$-0.268774\pi$
$431$	27.5781	1.32839	0.664196	+	0.747559i	$0.268774\pi$
$432$	−18.3983	−0.885187
$433$	23.6445	1.13628	0.568140	−	0.822932i	$-0.307663\pi$
$433$	23.6445	1.13628	0.568140	+	0.822932i	$0.307663\pi$
$434$	0.616837	0.0296091
$435$	−5.26539	−0.252456
$436$	16.5129	0.790823
$437$	17.4469	0.834597
$438$	−40.2382	−1.92265
$439$	−37.3436	−1.78231	−0.891157	−	0.453695i	$-0.850105\pi$
$439$	−37.3436	−1.78231	−0.891157	+	0.453695i	$0.850105\pi$
$440$	−1.87181	−0.0892348
$441$	−33.5521	−1.59772
$442$	−61.8470	−2.94176
$443$	20.0764	0.953857	0.476929	−	0.878942i	$-0.341750\pi$
$443$	20.0764	0.953857	0.476929	+	0.878942i	$0.341750\pi$
$444$	−0.0995637	−0.00472509
$445$	4.60127	0.218121
$446$	−13.4572	−0.637217
$447$	−37.7281	−1.78448
$448$	0.883194	0.0417270
$449$	14.8428	0.700475	0.350238	−	0.936661i	$-0.386101\pi$
$449$	14.8428	0.700475	0.350238	+	0.936661i	$0.386101\pi$
$450$	−9.78570	−0.461302
$451$	−5.76149	−0.271298
$452$	35.5561	1.67242
$453$	−17.5718	−0.825596
$454$	17.7906	0.834953
$455$	0.621616	0.0291418
$456$	−1.79815	−0.0842059
$457$	−11.4766	−0.536854	−0.268427	−	0.963300i	$-0.586504\pi$
$457$	−11.4766	−0.536854	−0.268427	+	0.963300i	$0.586504\pi$
$458$	44.1941	2.06505
$459$	−23.5319	−1.09837
$460$	18.7300	0.873292
$461$	8.63082	0.401977	0.200989	−	0.979594i	$-0.435585\pi$
$461$	8.63082	0.401977	0.200989	+	0.979594i	$0.435585\pi$
$462$	3.19184	0.148498
$463$	−0.589721	−0.0274067	−0.0137033	−	0.999906i	$-0.504362\pi$
$463$	−0.589721	−0.0274067	−0.0137033	+	0.999906i	$0.504362\pi$
$464$	6.90233	0.320433
$465$	8.80491	0.408318
$466$	−30.9449	−1.43349
$467$	−17.1542	−0.793802	−0.396901	−	0.917861i	$-0.629914\pi$
$467$	−17.1542	−0.793802	−0.396901	+	0.917861i	$0.629914\pi$
$468$	−67.0683	−3.10023
$469$	−1.24793	−0.0576239
$470$	−22.4880	−1.03730
$471$	−20.0803	−0.925251
$472$	1.22161	0.0562291
$473$	−57.9670	−2.66533
$474$	85.5093	3.92757
$475$	2.00937	0.0921964
$476$	0.969261	0.0444260
$477$	64.1319	2.93640
$478$	−42.3792	−1.93838
$479$	−22.1744	−1.01317	−0.506586	−	0.862189i	$-0.669093\pi$
$479$	−22.1744	−1.01317	−0.506586	+	0.862189i	$0.669093\pi$
$480$	22.6361	1.03319
$481$	0.107060	0.00488153
$482$	−31.5252	−1.43593
$483$	−2.32686	−0.105876
$484$	49.8818	2.26736
$485$	−2.40981	−0.109424
$486$	32.8092	1.48826
$487$	−21.8162	−0.988586	−0.494293	−	0.869295i	$-0.664573\pi$
$487$	−21.8162	−0.988586	−0.494293	+	0.869295i	$0.664573\pi$
$488$	0.693527	0.0313945
$489$	63.3239	2.86360
$490$	14.2536	0.643912
$491$	7.58778	0.342432	0.171216	−	0.985234i	$-0.445230\pi$
$491$	7.58778	0.342432	0.171216	+	0.985234i	$0.445230\pi$
$492$	−5.94183	−0.267878
$493$	8.82828	0.397606
$494$	26.5400	1.19409
$495$	28.0364	1.26014
$496$	−11.5422	−0.518262
$497$	−0.277298	−0.0124385
$498$	−95.5423	−4.28135
$499$	2.64448	0.118383	0.0591916	−	0.998247i	$-0.481148\pi$
$499$	2.64448	0.118383	0.0591916	+	0.998247i	$0.481148\pi$
$500$	2.15716	0.0964710
$501$	34.3630	1.53523
$502$	45.7089	2.04009
$503$	−21.4009	−0.954220	−0.477110	−	0.878844i	$-0.658316\pi$
$503$	−21.4009	−0.954220	−0.477110	+	0.878844i	$0.658316\pi$
$504$	0.147573	0.00657340
$505$	−0.910951	−0.0405368
$506$	−103.415	−4.59736
$507$	80.8912	3.59251
$508$	−1.34545	−0.0596947
$509$	−27.9758	−1.24000	−0.620002	−	0.784600i	$-0.712868\pi$
$509$	−27.9758	−1.24000	−0.620002	+	0.784600i	$0.712868\pi$
$510$	26.6630	1.18066
$511$	−0.678091	−0.0299970
$512$	−32.0195	−1.41508
$513$	10.0981	0.445842
$514$	54.6595	2.41093
$515$	6.11469	0.269445
$516$	−59.7814	−2.63173
$517$	64.4292	2.83359
$518$	−0.00323344	−0.000142069 0
$519$	−16.7300	−0.734364
$520$	2.07574	0.0910273
$521$	8.74411	0.383086	0.191543	−	0.981484i	$-0.438651\pi$
$521$	8.74411	0.383086	0.191543	+	0.981484i	$0.438651\pi$
$522$	18.4497	0.807522
$523$	−4.03744	−0.176545	−0.0882725	−	0.996096i	$-0.528135\pi$
$523$	−4.03744	−0.176545	−0.0882725	+	0.996096i	$0.528135\pi$
$524$	−11.9491	−0.521999
$525$	−0.267987	−0.0116959
$526$	−44.6263	−1.94580
$527$	−14.7629	−0.643080
$528$	−59.7256	−2.59922
$529$	52.3899	2.27782
$530$	−27.2445	−1.18342
$531$	−18.2976	−0.794049
$532$	−0.415933	−0.0180330
$533$	6.38922	0.276748
$534$	−26.2004	−1.13380
$535$	4.56956	0.197559
$536$	−4.16716	−0.179994
$537$	34.8496	1.50387
$538$	7.21120	0.310897
$539$	−40.8372	−1.75898
$540$	10.8408	0.466512
$541$	−5.89457	−0.253427	−0.126714	−	0.991939i	$-0.540443\pi$
$541$	−5.89457	−0.253427	−0.126714	+	0.991939i	$0.540443\pi$
$542$	38.0250	1.63331
$543$	−32.5772	−1.39802
$544$	−37.9531	−1.62722
$545$	7.65492	0.327901
$546$	−3.53959	−0.151481
$547$	37.8220	1.61715	0.808576	−	0.588392i	$-0.200239\pi$
$547$	37.8220	1.61715	0.808576	+	0.588392i	$0.200239\pi$
$548$	7.43850	0.317757
$549$	−10.3878	−0.443342
$550$	−11.9104	−0.507862
$551$	−3.78842	−0.161392
$552$	−7.77000	−0.330713
$553$	1.44100	0.0612774
$554$	25.6895	1.09144
$555$	−0.0461551	−0.00195917
$556$	17.5770	0.745432
$557$	25.4059	1.07648	0.538242	−	0.842790i	$-0.319089\pi$
$557$	25.4059	1.07648	0.538242	+	0.842790i	$0.319089\pi$
$558$	−30.8520	−1.30607
$559$	64.2827	2.71887
$560$	0.351300	0.0148452
$561$	−76.3907	−3.22522
$562$	−24.2560	−1.02318
$563$	−11.0121	−0.464107	−0.232053	−	0.972703i	$-0.574544\pi$
$563$	−11.0121	−0.464107	−0.232053	+	0.972703i	$0.574544\pi$
$564$	66.4458	2.79787
$565$	16.4829	0.693440
$566$	3.51878	0.147905
$567$	0.0348775	0.00146472
$568$	−0.925973	−0.0388530
$569$	14.8967	0.624504	0.312252	−	0.949999i	$-0.398917\pi$
$569$	14.8967	0.624504	0.312252	+	0.949999i	$0.398917\pi$
$570$	−11.4417	−0.479241
$571$	43.4262	1.81733	0.908664	−	0.417527i	$-0.137103\pi$
$571$	43.4262	1.81733	0.908664	+	0.417527i	$0.137103\pi$
$572$	−81.6306	−3.41315
$573$	−60.3991	−2.52321
$574$	−0.192968	−0.00805431
$575$	8.68274	0.362095
$576$	−44.1743	−1.84059
$577$	−17.9989	−0.749303	−0.374651	−	0.927166i	$-0.622238\pi$
$577$	−17.9989	−0.749303	−0.374651	+	0.927166i	$0.622238\pi$
$578$	−10.0434	−0.417752
$579$	−4.46071	−0.185381
$580$	−4.06705	−0.168875
$581$	−1.61007	−0.0667970
$582$	13.7219	0.568791
$583$	78.0566	3.23277
$584$	−2.26433	−0.0936985
$585$	−31.0911	−1.28546
$586$	−65.9526	−2.72448
$587$	12.0952	0.499221	0.249610	−	0.968346i	$-0.419697\pi$
$587$	12.0952	0.499221	0.249610	+	0.968346i	$0.419697\pi$
$588$	−42.1154	−1.73681
$589$	6.33509	0.261033
$590$	7.77319	0.320017
$591$	−15.8375	−0.651467
$592$	0.0605041	0.00248670
$593$	−41.3723	−1.69895	−0.849477	−	0.527625i	$-0.823083\pi$
$593$	−41.3723	−1.69895	−0.849477	+	0.527625i	$0.823083\pi$
$594$	−59.8557	−2.45591
$595$	0.449323	0.0184205
$596$	−29.1416	−1.19369
$597$	43.4142	1.77682
$598$	114.682	4.68971
$599$	−14.5255	−0.593496	−0.296748	−	0.954956i	$-0.595902\pi$
$599$	−14.5255	−0.593496	−0.296748	+	0.954956i	$0.595902\pi$
$600$	−0.894879	−0.0365333
$601$	27.4839	1.12109	0.560547	−	0.828123i	$-0.310591\pi$
$601$	27.4839	1.12109	0.560547	+	0.828123i	$0.310591\pi$
$602$	−1.94147	−0.0791284
$603$	62.4170	2.54182
$604$	−13.5727	−0.552265
$605$	23.1239	0.940120
$606$	5.18712	0.210712
$607$	8.26296	0.335383	0.167692	−	0.985840i	$-0.446369\pi$
$607$	8.26296	0.335383	0.167692	+	0.985840i	$0.446369\pi$
$608$	16.2866	0.660507
$609$	0.505255	0.0204740
$610$	4.41296	0.178675
$611$	−71.4489	−2.89051
$612$	−48.4790	−1.95965
$613$	−40.3152	−1.62832	−0.814158	−	0.580643i	$-0.802801\pi$
$613$	−40.3152	−1.62832	−0.814158	+	0.580643i	$0.802801\pi$
$614$	55.7789	2.25105
$615$	−2.75447	−0.111071
$616$	0.179614	0.00723687
$617$	29.7365	1.19715	0.598573	−	0.801068i	$-0.295735\pi$
$617$	29.7365	1.19715	0.598573	+	0.801068i	$0.295735\pi$
$618$	−34.8181	−1.40059
$619$	20.2375	0.813412	0.406706	−	0.913559i	$-0.366677\pi$
$619$	20.2375	0.813412	0.406706	+	0.913559i	$0.366677\pi$
$620$	6.80102	0.273135
$621$	43.6350	1.75101
$622$	53.0180	2.12583
$623$	−0.441528	−0.0176894
$624$	66.2328	2.65143
$625$	1.00000	0.0400000
$626$	−5.15939	−0.206211
$627$	32.7810	1.30915
$628$	−15.5103	−0.618927
$629$	0.0773865	0.00308560
$630$	0.939015	0.0374112
$631$	−14.8516	−0.591235	−0.295617	−	0.955306i	$-0.595525\pi$
$631$	−14.8516	−0.591235	−0.295617	+	0.955306i	$0.595525\pi$
$632$	4.81187	0.191406
$633$	24.4926	0.973492
$634$	−69.2885	−2.75180
$635$	−0.623715	−0.0247514
$636$	80.4998	3.19202
$637$	45.2865	1.79431
$638$	22.4556	0.889026
$639$	13.8695	0.548668
$640$	2.55552	0.101016
$641$	3.61854	0.142924	0.0714620	−	0.997443i	$-0.477234\pi$
$641$	3.61854	0.142924	0.0714620	+	0.997443i	$0.477234\pi$
$642$	−26.0199	−1.02692
$643$	13.4534	0.530551	0.265275	−	0.964173i	$-0.414537\pi$
$643$	13.4534	0.530551	0.265275	+	0.964173i	$0.414537\pi$
$644$	−1.79729	−0.0708232
$645$	−27.7131	−1.09120
$646$	19.1839	0.754782
$647$	24.1143	0.948032	0.474016	−	0.880516i	$-0.342804\pi$
$647$	24.1143	0.948032	0.474016	+	0.880516i	$0.342804\pi$
$648$	0.116465	0.00457519
$649$	−22.2705	−0.874194
$650$	13.2081	0.518064
$651$	−0.844900	−0.0331142
$652$	48.9121	1.91555
$653$	10.9608	0.428929	0.214464	−	0.976732i	$-0.431199\pi$
$653$	10.9608	0.428929	0.214464	+	0.976732i	$0.431199\pi$
$654$	−43.5885	−1.70444
$655$	−5.53929	−0.216438
$656$	3.61081	0.140978
$657$	33.9157	1.32318
$658$	2.15790	0.0841238
$659$	−9.93473	−0.387002	−0.193501	−	0.981100i	$-0.561984\pi$
$659$	−9.93473	−0.387002	−0.193501	+	0.981100i	$0.561984\pi$
$660$	35.1920	1.36985
$661$	41.0962	1.59846	0.799229	−	0.601026i	$-0.205241\pi$
$661$	41.0962	1.59846	0.799229	+	0.601026i	$0.205241\pi$
$662$	36.6502	1.42445
$663$	84.7136	3.29000
$664$	−5.37646	−0.208647
$665$	−0.192815	−0.00747705
$666$	0.161726	0.00626674
$667$	−16.3702	−0.633857
$668$	26.5424	1.02696
$669$	18.4327	0.712650
$670$	−26.5159	−1.02440
$671$	−12.6433	−0.488090
$672$	−2.17211	−0.0837909
$673$	−16.2220	−0.625312	−0.312656	−	0.949866i	$-0.601219\pi$
$673$	−16.2220	−0.625312	−0.312656	+	0.949866i	$0.601219\pi$
$674$	−11.9443	−0.460078
$675$	5.02549	0.193431
$676$	62.4814	2.40313
$677$	−15.3263	−0.589037	−0.294518	−	0.955646i	$-0.595159\pi$
$677$	−15.3263	−0.589037	−0.294518	+	0.955646i	$0.595159\pi$
$678$	−93.8564	−3.60453
$679$	0.231240	0.00887419
$680$	1.50041	0.0575381
$681$	−24.3683	−0.933794
$682$	−37.5508	−1.43790
$683$	−41.6492	−1.59366	−0.796831	−	0.604203i	$-0.793492\pi$
$683$	−41.6492	−1.59366	−0.796831	+	0.604203i	$0.793492\pi$
$684$	20.8035	0.795442
$685$	3.44829	0.131752
$686$	−2.73729	−0.104510
$687$	−60.5338	−2.30951
$688$	36.3287	1.38502
$689$	−86.5610	−3.29771
$690$	−49.4410	−1.88219
$691$	10.8677	0.413426	0.206713	−	0.978402i	$-0.433723\pi$
$691$	10.8677	0.413426	0.206713	+	0.978402i	$0.433723\pi$
$692$	−12.9224	−0.491237
$693$	−2.69032	−0.102197
$694$	46.9515	1.78225
$695$	8.14824	0.309080
$696$	1.68718	0.0639524
$697$	4.61832	0.174931
$698$	−67.9549	−2.57213
$699$	42.3861	1.60319
$700$	−0.206996	−0.00782372
$701$	−17.4066	−0.657439	−0.328719	−	0.944428i	$-0.606617\pi$
$701$	−17.4066	−0.657439	−0.328719	+	0.944428i	$0.606617\pi$
$702$	66.3771	2.50524
$703$	−0.0332084	−0.00125248
$704$	−53.7656	−2.02637
$705$	30.8025	1.16009
$706$	23.2550	0.875214
$707$	0.0874129	0.00328750
$708$	−22.9676	−0.863175
$709$	32.0590	1.20400	0.602000	−	0.798496i	$-0.294371\pi$
$709$	32.0590	1.20400	0.602000	+	0.798496i	$0.294371\pi$
$710$	−5.89203	−0.221124
$711$	−72.0736	−2.70297
$712$	−1.47438	−0.0552547
$713$	27.3747	1.02519
$714$	−2.55853	−0.0957504
$715$	−37.8417	−1.41520
$716$	26.9183	1.00598
$717$	58.0480	2.16784
$718$	−18.7985	−0.701555
$719$	−46.1641	−1.72163	−0.860815	−	0.508917i	$-0.830046\pi$
$719$	−46.1641	−1.72163	−0.860815	+	0.508917i	$0.830046\pi$
$720$	−17.5708	−0.654826
$721$	−0.586752	−0.0218518
$722$	30.5070	1.13535
$723$	43.1810	1.60592
$724$	−25.1630	−0.935177
$725$	−1.88537	−0.0700210
$726$	−131.671	−4.88679
$727$	−39.3777	−1.46044	−0.730219	−	0.683214i	$-0.760582\pi$
$727$	−39.3777	−1.46044	−0.730219	+	0.683214i	$0.760582\pi$
$728$	−0.199184	−0.00738224
$729$	−43.8493	−1.62405
$730$	−14.4081	−0.533266
$731$	46.4655	1.71859
$732$	−13.0391	−0.481937
$733$	31.5510	1.16536	0.582682	−	0.812700i	$-0.302003\pi$
$733$	31.5510	1.16536	0.582682	+	0.812700i	$0.302003\pi$
$734$	53.5298	1.97582
$735$	−19.5236	−0.720137
$736$	70.3761	2.59410
$737$	75.9693	2.79837
$738$	9.65156	0.355279
$739$	16.6071	0.610901	0.305451	−	0.952208i	$-0.401193\pi$
$739$	16.6071	0.610901	0.305451	+	0.952208i	$0.401193\pi$
$740$	−0.0356507	−0.00131055
$741$	−36.3526	−1.33545
$742$	2.61432	0.0959748
$743$	−26.6972	−0.979425	−0.489712	−	0.871884i	$-0.662898\pi$
$743$	−26.6972	−0.979425	−0.489712	+	0.871884i	$0.662898\pi$
$744$	−2.82134	−0.103436
$745$	−13.5093	−0.494942
$746$	8.82006	0.322925
$747$	80.5302	2.94644
$748$	−59.0051	−2.15744
$749$	−0.438485	−0.0160219
$750$	−5.69418	−0.207922
$751$	21.0305	0.767415	0.383707	−	0.923455i	$-0.374647\pi$
$751$	21.0305	0.767415	0.383707	+	0.923455i	$0.374647\pi$
$752$	−40.3786	−1.47246
$753$	−62.6088	−2.28159
$754$	−24.9022	−0.906885
$755$	−6.29193	−0.228987
$756$	−1.04026	−0.0378338
$757$	−11.2955	−0.410541	−0.205270	−	0.978705i	$-0.565807\pi$
$757$	−11.2955	−0.410541	−0.205270	+	0.978705i	$0.565807\pi$
$758$	1.49126	0.0541651
$759$	141.651	5.14159
$760$	−0.643861	−0.0233553
$761$	47.4071	1.71850	0.859252	−	0.511552i	$-0.170929\pi$
$761$	47.4071	1.71850	0.859252	+	0.511552i	$0.170929\pi$
$762$	3.55154	0.128659
$763$	−0.734550	−0.0265925
$764$	−46.6530	−1.68784
$765$	−22.4736	−0.812534
$766$	33.4135	1.20728
$767$	24.6969	0.891754
$768$	36.8573	1.32997
$769$	29.6955	1.07085	0.535423	−	0.844584i	$-0.320152\pi$
$769$	29.6955	1.07085	0.535423	+	0.844584i	$0.320152\pi$
$770$	1.14290	0.0411872
$771$	−74.8687	−2.69633
$772$	−3.44550	−0.124006
$773$	21.5893	0.776513	0.388256	−	0.921551i	$-0.373077\pi$
$773$	21.5893	0.776513	0.388256	+	0.921551i	$0.373077\pi$
$774$	97.1055	3.49038
$775$	3.15277	0.113251
$776$	0.772173	0.0277194
$777$	0.00442894	0.000158887 0
$778$	24.2247	0.868496
$779$	−1.98183	−0.0710065
$780$	−39.0262	−1.39736
$781$	16.8809	0.604047
$782$	82.8960	2.96435
$783$	−9.47493	−0.338606
$784$	25.5932	0.914043
$785$	−7.19014	−0.256627
$786$	31.5417	1.12505
$787$	−6.86105	−0.244570	−0.122285	−	0.992495i	$-0.539022\pi$
$787$	−6.86105	−0.244570	−0.122285	+	0.992495i	$0.539022\pi$
$788$	−12.2331	−0.435785
$789$	61.1259	2.17614
$790$	30.6183	1.08935
$791$	−1.58166	−0.0562374
$792$	−8.98368	−0.319221
$793$	14.0208	0.497894
$794$	10.6135	0.376659
$795$	37.3175	1.32352
$796$	33.5336	1.18857
$797$	34.1401	1.20930	0.604652	−	0.796490i	$-0.293312\pi$
$797$	34.1401	1.20930	0.604652	+	0.796490i	$0.293312\pi$
$798$	1.09792	0.0388661
$799$	−51.6454	−1.82708
$800$	8.10529	0.286565
$801$	22.0837	0.780288
$802$	15.6193	0.551538
$803$	41.2797	1.45673
$804$	78.3472	2.76309
$805$	−0.833177	−0.0293656
$806$	41.6421	1.46678
$807$	−9.87739	−0.347701
$808$	0.291895	0.0102688
$809$	38.4986	1.35354	0.676769	−	0.736196i	$-0.263380\pi$
$809$	38.4986	1.35354	0.676769	+	0.736196i	$0.263380\pi$
$810$	0.741077	0.0260388
$811$	2.04887	0.0719457	0.0359729	−	0.999353i	$-0.488547\pi$
$811$	2.04887	0.0719457	0.0359729	+	0.999353i	$0.488547\pi$
$812$	0.390265	0.0136956
$813$	−52.0839	−1.82666
$814$	0.196840	0.00689925
$815$	22.6743	0.794248
$816$	47.8751	1.67596
$817$	−19.9394	−0.697592
$818$	−22.2833	−0.779116
$819$	2.98343	0.104250
$820$	−2.12759	−0.0742986
$821$	−14.3155	−0.499614	−0.249807	−	0.968296i	$-0.580367\pi$
$821$	−14.3155	−0.499614	−0.249807	+	0.968296i	$0.580367\pi$
$822$	−19.6352	−0.684855
$823$	−0.109901	−0.00383090	−0.00191545	−	0.999998i	$-0.500610\pi$
$823$	−0.109901	−0.00383090	−0.00191545	+	0.999998i	$0.500610\pi$
$824$	−1.95932	−0.0682562
$825$	16.3141	0.567982
$826$	−0.745898	−0.0259531
$827$	45.2072	1.57201	0.786004	−	0.618222i	$-0.212147\pi$
$827$	45.2072	1.57201	0.786004	+	0.618222i	$0.212147\pi$
$828$	89.8943	3.12404
$829$	4.26323	0.148068	0.0740341	−	0.997256i	$-0.476413\pi$
$829$	4.26323	0.148068	0.0740341	+	0.997256i	$0.476413\pi$
$830$	−34.2108	−1.18747
$831$	−35.1876	−1.22064
$832$	59.6235	2.06707
$833$	32.7344	1.13418
$834$	−46.3975	−1.60661
$835$	12.3044	0.425810
$836$	25.3205	0.875727
$837$	15.8442	0.547656
$838$	55.0606	1.90204
$839$	−20.5569	−0.709704	−0.354852	−	0.934923i	$-0.615469\pi$
$839$	−20.5569	−0.709704	−0.354852	+	0.934923i	$0.615469\pi$
$840$	0.0858706	0.00296282
$841$	−25.4454	−0.877426
$842$	77.1303	2.65809
$843$	33.2242	1.14430
$844$	18.9183	0.651196
$845$	28.9647	0.996415
$846$	−107.931	−3.71074
$847$	−2.21892	−0.0762429
$848$	−48.9191	−1.67989
$849$	−4.81977	−0.165414
$850$	9.54722	0.327467
$851$	−0.143497	−0.00491902
$852$	17.4093	0.596433
$853$	12.8369	0.439526	0.219763	−	0.975553i	$-0.429472\pi$
$853$	12.8369	0.439526	0.219763	+	0.975553i	$0.429472\pi$
$854$	−0.423458	−0.0144904
$855$	9.64394	0.329816
$856$	−1.46422	−0.0500459
$857$	−42.5278	−1.45272	−0.726360	−	0.687314i	$-0.758790\pi$
$857$	−42.5278	−1.45272	−0.726360	+	0.687314i	$0.758790\pi$
$858$	215.478	7.35628
$859$	−31.9849	−1.09131	−0.545655	−	0.838010i	$-0.683719\pi$
$859$	−31.9849	−1.09131	−0.545655	+	0.838010i	$0.683719\pi$
$860$	−21.4059	−0.729935
$861$	0.264313	0.00900777
$862$	−56.2293	−1.91518
$863$	−52.5260	−1.78801	−0.894003	−	0.448061i	$-0.852115\pi$
$863$	−52.5260	−1.78801	−0.894003	+	0.448061i	$0.852115\pi$
$864$	40.7330	1.38577
$865$	−5.99049	−0.203683
$866$	−48.2090	−1.63821
$867$	13.7568	0.467204
$868$	−0.652611	−0.0221511
$869$	−87.7226	−2.97579
$870$	10.7357	0.363973
$871$	−84.2463	−2.85458
$872$	−2.45286	−0.0830642
$873$	−11.5658	−0.391444
$874$	−35.5726	−1.20326
$875$	−0.0959578	−0.00324397
$876$	42.5718	1.43837
$877$	−50.5650	−1.70746	−0.853729	−	0.520717i	$-0.825665\pi$
$877$	−50.5650	−1.70746	−0.853729	+	0.520717i	$0.825665\pi$
$878$	76.1403	2.56961
$879$	90.3372	3.04700
$880$	−21.3859	−0.720919
$881$	−17.1778	−0.578733	−0.289367	−	0.957218i	$-0.593445\pi$
$881$	−17.1778	−0.578733	−0.289367	+	0.957218i	$0.593445\pi$
$882$	68.4098	2.30348
$883$	39.1895	1.31883	0.659416	−	0.751779i	$-0.270804\pi$
$883$	39.1895	1.31883	0.659416	+	0.751779i	$0.270804\pi$
$884$	65.4338	2.20078
$885$	−10.6472	−0.357900
$886$	−40.9339	−1.37520
$887$	26.9541	0.905029	0.452515	−	0.891757i	$-0.350527\pi$
$887$	26.9541	0.905029	0.452515	+	0.891757i	$0.350527\pi$
$888$	0.0147894	0.000496300 0
$889$	0.0598503	0.00200731
$890$	−9.38157	−0.314471
$891$	−2.12322	−0.0711304
$892$	14.2377	0.476712
$893$	22.1623	0.741632
$894$	76.9242	2.57273
$895$	12.4786	0.417113
$896$	−0.245222	−0.00819228
$897$	−157.084	−5.24487
$898$	−30.2631	−1.00989
$899$	−5.94415	−0.198248
$900$	10.3532	0.345107
$901$	−62.5690	−2.08447
$902$	11.7472	0.391138
$903$	2.65929	0.0884955
$904$	−5.28159	−0.175663
$905$	−11.6649	−0.387755
$906$	35.8274	1.19028
$907$	48.3761	1.60630	0.803151	−	0.595775i	$-0.203155\pi$
$907$	48.3761	1.60630	0.803151	+	0.595775i	$0.203155\pi$
$908$	−18.8223	−0.624641
$909$	−4.37209	−0.145013
$910$	−1.26742	−0.0420146
$911$	6.23490	0.206572	0.103286	−	0.994652i	$-0.467064\pi$
$911$	6.23490	0.206572	0.103286	+	0.994652i	$0.467064\pi$
$912$	−20.5443	−0.680291
$913$	98.0153	3.24383
$914$	23.3998	0.773997
$915$	−6.04456	−0.199827
$916$	−46.7571	−1.54490
$917$	0.531538	0.0175529
$918$	47.9794	1.58356
$919$	12.4524	0.410766	0.205383	−	0.978682i	$-0.434156\pi$
$919$	12.4524	0.410766	0.205383	+	0.978682i	$0.434156\pi$
$920$	−2.78220	−0.0917264
$921$	−76.4020	−2.51753
$922$	−17.5975	−0.579542
$923$	−18.7201	−0.616180
$924$	−3.37695	−0.111093
$925$	−0.0165267	−0.000543395 0
$926$	1.20239	0.0395129
$927$	29.3473	0.963891
$928$	−15.2815	−0.501640
$929$	−4.15315	−0.136260	−0.0681302	−	0.997676i	$-0.521703\pi$
$929$	−4.15315	−0.136260	−0.0681302	+	0.997676i	$0.521703\pi$
$930$	−17.9524	−0.588683
$931$	−14.0471	−0.460376
$932$	32.7395	1.07242
$933$	−72.6202	−2.37748
$934$	34.9759	1.14445
$935$	−27.3532	−0.894544
$936$	9.96247	0.325634
$937$	−42.6260	−1.39253	−0.696266	−	0.717784i	$-0.745156\pi$
$937$	−42.6260	−1.39253	−0.696266	+	0.717784i	$0.745156\pi$
$938$	2.54441	0.0830780
$939$	7.06697	0.230622
$940$	23.7922	0.776017
$941$	−4.73861	−0.154474	−0.0772371	−	0.997013i	$-0.524610\pi$
$941$	−4.73861	−0.154474	−0.0772371	+	0.997013i	$0.524610\pi$
$942$	40.9419	1.33396
$943$	−8.56372	−0.278873
$944$	13.9572	0.454269
$945$	−0.482235	−0.0156871
$946$	118.190	3.84268
$947$	33.1322	1.07665	0.538326	−	0.842737i	$-0.319057\pi$
$947$	33.1322	1.07665	0.538326	+	0.842737i	$0.319057\pi$
$948$	−90.4683	−2.93828
$949$	−45.7772	−1.48599
$950$	−4.09694	−0.132922
$951$	94.9065	3.07755
$952$	−0.143976	−0.00466629
$953$	39.5321	1.28057	0.640285	−	0.768137i	$-0.278816\pi$
$953$	39.5321	1.28057	0.640285	+	0.768137i	$0.278816\pi$
$954$	−130.759	−4.23349
$955$	−21.6271	−0.699835
$956$	44.8370	1.45013
$957$	−30.7581	−0.994268
$958$	45.2115	1.46072
$959$	−0.330890	−0.0106850
$960$	−25.7044	−0.829607
$961$	−21.0601	−0.679357
$962$	−0.218287	−0.00703784
$963$	21.9315	0.706732
$964$	33.3535	1.07424
$965$	−1.59724	−0.0514171
$966$	4.74425	0.152644
$967$	−16.4583	−0.529263	−0.264632	−	0.964350i	$-0.585250\pi$
$967$	−16.4583	−0.529263	−0.264632	+	0.964350i	$0.585250\pi$
$968$	−7.40956	−0.238152
$969$	−26.2768	−0.844132
$970$	4.91339	0.157759
$971$	−20.5815	−0.660491	−0.330246	−	0.943895i	$-0.607132\pi$
$971$	−20.5815	−0.660491	−0.330246	+	0.943895i	$0.607132\pi$
$972$	−34.7120	−1.11339
$973$	−0.781887	−0.0250662
$974$	44.4813	1.42527
$975$	−18.0915	−0.579392
$976$	7.92374	0.253633
$977$	−41.5143	−1.32816	−0.664080	−	0.747661i	$-0.731177\pi$
$977$	−41.5143	−1.32816	−0.664080	+	0.747661i	$0.731177\pi$
$978$	−129.112	−4.12854
$979$	26.8786	0.859044
$980$	−15.0802	−0.481720
$981$	36.7396	1.17301
$982$	−15.4708	−0.493693
$983$	−14.9267	−0.476088	−0.238044	−	0.971254i	$-0.576506\pi$
$983$	−14.9267	−0.476088	−0.238044	+	0.971254i	$0.576506\pi$
$984$	0.882612	0.0281366
$985$	−5.67092	−0.180690
$986$	−18.0001	−0.573239
$987$	−2.95574	−0.0940823
$988$	−28.0792	−0.893318
$989$	−86.1606	−2.73975
$990$	−57.1638	−1.81679
$991$	−17.4913	−0.555629	−0.277814	−	0.960635i	$-0.589610\pi$
$991$	−17.4913	−0.555629	−0.277814	+	0.960635i	$0.589610\pi$
$992$	25.5541	0.811343
$993$	−50.2008	−1.59307
$994$	0.565386	0.0179330
$995$	15.5453	0.492819
$996$	101.083	3.20295
$997$	17.8638	0.565752	0.282876	−	0.959156i	$-0.408711\pi$
$997$	17.8638	0.565752	0.282876	+	0.959156i	$0.408711\pi$
$998$	−5.39186	−0.170676
$999$	−0.0830549	−0.00262774

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.f.1.17	✓	111

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.f.1.17	✓	111	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.03891 q^{2} +2.79275 q^{3} +2.15716 q^{4} +1.00000 q^{5} -5.69418 q^{6} -0.0959578 q^{7} -0.320429 q^{8} +4.79947 q^{9} +O(q^{10})\)	\(q-2.03891 q^{2} +2.79275 q^{3} +2.15716 q^{4} +1.00000 q^{5} -5.69418 q^{6} -0.0959578 q^{7} -0.320429 q^{8} +4.79947 q^{9} -2.03891 q^{10} +5.84157 q^{11} +6.02441 q^{12} -6.47802 q^{13} +0.195649 q^{14} +2.79275 q^{15} -3.66099 q^{16} -4.68251 q^{17} -9.78570 q^{18} +2.00937 q^{19} +2.15716 q^{20} -0.267987 q^{21} -11.9104 q^{22} +8.68274 q^{23} -0.894879 q^{24} +1.00000 q^{25} +13.2081 q^{26} +5.02549 q^{27} -0.206996 q^{28} -1.88537 q^{29} -5.69418 q^{30} +3.15277 q^{31} +8.10529 q^{32} +16.3141 q^{33} +9.54722 q^{34} -0.0959578 q^{35} +10.3532 q^{36} -0.0165267 q^{37} -4.09694 q^{38} -18.0915 q^{39} -0.320429 q^{40} -0.986293 q^{41} +0.546401 q^{42} -9.92320 q^{43} +12.6012 q^{44} +4.79947 q^{45} -17.7033 q^{46} +11.0294 q^{47} -10.2242 q^{48} -6.99079 q^{49} -2.03891 q^{50} -13.0771 q^{51} -13.9741 q^{52} +13.3623 q^{53} -10.2465 q^{54} +5.84157 q^{55} +0.0307476 q^{56} +5.61169 q^{57} +3.84411 q^{58} -3.81242 q^{59} +6.02441 q^{60} -2.16437 q^{61} -6.42821 q^{62} -0.460547 q^{63} -9.20398 q^{64} -6.47802 q^{65} -33.2629 q^{66} +13.0050 q^{67} -10.1009 q^{68} +24.2487 q^{69} +0.195649 q^{70} +2.88979 q^{71} -1.53789 q^{72} +7.06655 q^{73} +0.0336965 q^{74} +2.79275 q^{75} +4.33454 q^{76} -0.560544 q^{77} +36.8870 q^{78} -15.0170 q^{79} -3.66099 q^{80} -0.363467 q^{81} +2.01096 q^{82} +16.7790 q^{83} -0.578089 q^{84} -4.68251 q^{85} +20.2325 q^{86} -5.26539 q^{87} -1.87181 q^{88} +4.60127 q^{89} -9.78570 q^{90} +0.621616 q^{91} +18.7300 q^{92} +8.80491 q^{93} -22.4880 q^{94} +2.00937 q^{95} +22.6361 q^{96} -2.40981 q^{97} +14.2536 q^{98} +28.0364 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9} + 20 q^{10} + 36 q^{11} + 80 q^{12} + 36 q^{13} + 7 q^{14} + 40 q^{15} + 190 q^{16} + 38 q^{17} + 48 q^{18} + 77 q^{19} + 136 q^{20} + 11 q^{21} + 39 q^{22} + 82 q^{23} - 3 q^{24} + 111 q^{25} - 3 q^{26} + 130 q^{27} + 87 q^{28} + 20 q^{29} + 3 q^{30} + 41 q^{31} + 85 q^{32} + 33 q^{33} + 7 q^{34} + 39 q^{35} + 191 q^{36} + 80 q^{37} + 42 q^{38} + 21 q^{39} + 45 q^{40} + 16 q^{41} + 33 q^{42} + 164 q^{43} + 37 q^{44} + 139 q^{45} + 32 q^{46} + 148 q^{47} + 149 q^{48} + 160 q^{49} + 20 q^{50} + 51 q^{51} + 87 q^{52} + 83 q^{53} - 6 q^{54} + 36 q^{55} - 10 q^{56} + 28 q^{57} + 47 q^{58} + 14 q^{59} + 80 q^{60} + 20 q^{61} + 14 q^{62} + 120 q^{63} + 231 q^{64} + 36 q^{65} - 4 q^{66} + 253 q^{67} + 80 q^{68} + 6 q^{69} + 7 q^{70} + 5 q^{71} + 124 q^{72} + 64 q^{73} - 37 q^{74} + 40 q^{75} + 92 q^{76} + 63 q^{77} + 29 q^{78} + 91 q^{79} + 190 q^{80} + 187 q^{81} - 7 q^{82} + 63 q^{83} - 69 q^{84} + 38 q^{85} - 22 q^{86} + 57 q^{87} + 121 q^{88} - 6 q^{89} + 48 q^{90} + 119 q^{91} + 104 q^{92} + 14 q^{93} - q^{94} + 77 q^{95} - 38 q^{96} + 96 q^{97} + 81 q^{98} + 106 q^{99}+O(q^{100}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9 + 20 * q^10 + 36 * q^11 + 80 * q^12 + 36 * q^13 + 7 * q^14 + 40 * q^15 + 190 * q^16 + 38 * q^17 + 48 * q^18 + 77 * q^19 + 136 * q^20 + 11 * q^21 + 39 * q^22 + 82 * q^23 - 3 * q^24 + 111 * q^25 - 3 * q^26 + 130 * q^27 + 87 * q^28 + 20 * q^29 + 3 * q^30 + 41 * q^31 + 85 * q^32 + 33 * q^33 + 7 * q^34 + 39 * q^35 + 191 * q^36 + 80 * q^37 + 42 * q^38 + 21 * q^39 + 45 * q^40 + 16 * q^41 + 33 * q^42 + 164 * q^43 + 37 * q^44 + 139 * q^45 + 32 * q^46 + 148 * q^47 + 149 * q^48 + 160 * q^49 + 20 * q^50 + 51 * q^51 + 87 * q^52 + 83 * q^53 - 6 * q^54 + 36 * q^55 - 10 * q^56 + 28 * q^57 + 47 * q^58 + 14 * q^59 + 80 * q^60 + 20 * q^61 + 14 * q^62 + 120 * q^63 + 231 * q^64 + 36 * q^65 - 4 * q^66 + 253 * q^67 + 80 * q^68 + 6 * q^69 + 7 * q^70 + 5 * q^71 + 124 * q^72 + 64 * q^73 - 37 * q^74 + 40 * q^75 + 92 * q^76 + 63 * q^77 + 29 * q^78 + 91 * q^79 + 190 * q^80 + 187 * q^81 - 7 * q^82 + 63 * q^83 - 69 * q^84 + 38 * q^85 - 22 * q^86 + 57 * q^87 + 121 * q^88 - 6 * q^89 + 48 * q^90 + 119 * q^91 + 104 * q^92 + 14 * q^93 - q^94 + 77 * q^95 - 38 * q^96 + 96 * q^97 + 81 * q^98 + 106 * q^99

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