LMFDB - Embedded newform 6015.2.a.d.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.462418 q^{2} -1.00000 q^{3} -1.78617 q^{4} +1.00000 q^{5} +0.462418 q^{6} -1.50774 q^{7} +1.75079 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.462418 q^{2} -1.00000 q^{3} -1.78617 q^{4} +1.00000 q^{5} +0.462418 q^{6} -1.50774 q^{7} +1.75079 q^{8} +1.00000 q^{9} -0.462418 q^{10} +2.86573 q^{11} +1.78617 q^{12} +0.496769 q^{13} +0.697206 q^{14} -1.00000 q^{15} +2.76274 q^{16} -5.20536 q^{17} -0.462418 q^{18} +5.20616 q^{19} -1.78617 q^{20} +1.50774 q^{21} -1.32516 q^{22} -4.53047 q^{23} -1.75079 q^{24} +1.00000 q^{25} -0.229715 q^{26} -1.00000 q^{27} +2.69308 q^{28} -1.73627 q^{29} +0.462418 q^{30} -10.3731 q^{31} -4.77912 q^{32} -2.86573 q^{33} +2.40705 q^{34} -1.50774 q^{35} -1.78617 q^{36} +9.30522 q^{37} -2.40742 q^{38} -0.496769 q^{39} +1.75079 q^{40} -5.02321 q^{41} -0.697206 q^{42} +3.58455 q^{43} -5.11868 q^{44} +1.00000 q^{45} +2.09497 q^{46} +10.2129 q^{47} -2.76274 q^{48} -4.72672 q^{49} -0.462418 q^{50} +5.20536 q^{51} -0.887315 q^{52} -0.103652 q^{53} +0.462418 q^{54} +2.86573 q^{55} -2.63974 q^{56} -5.20616 q^{57} +0.802882 q^{58} +6.16360 q^{59} +1.78617 q^{60} -13.6058 q^{61} +4.79669 q^{62} -1.50774 q^{63} -3.31553 q^{64} +0.496769 q^{65} +1.32516 q^{66} +3.82415 q^{67} +9.29765 q^{68} +4.53047 q^{69} +0.697206 q^{70} +2.53921 q^{71} +1.75079 q^{72} +12.9186 q^{73} -4.30290 q^{74} -1.00000 q^{75} -9.29909 q^{76} -4.32078 q^{77} +0.229715 q^{78} -15.7850 q^{79} +2.76274 q^{80} +1.00000 q^{81} +2.32282 q^{82} -15.4659 q^{83} -2.69308 q^{84} -5.20536 q^{85} -1.65756 q^{86} +1.73627 q^{87} +5.01730 q^{88} +4.89978 q^{89} -0.462418 q^{90} -0.749000 q^{91} +8.09218 q^{92} +10.3731 q^{93} -4.72261 q^{94} +5.20616 q^{95} +4.77912 q^{96} -5.39885 q^{97} +2.18572 q^{98} +2.86573 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * 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 $

$2$	−0.462418	−0.326979	−0.163489	−	0.986545i	$-0.552275\pi$
$2$	−0.462418	−0.326979	−0.163489	+	0.986545i	$0.552275\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.78617	−0.893085
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.462418	0.188781
$7$	−1.50774	−0.569873	−0.284936	−	0.958546i	$-0.591972\pi$
$7$	−1.50774	−0.569873	−0.284936	+	0.958546i	$0.591972\pi$
$8$	1.75079	0.618998
$9$	1.00000	0.333333
$10$	−0.462418	−0.146229
$11$	2.86573	0.864051	0.432025	−	0.901861i	$-0.357799\pi$
$11$	2.86573	0.864051	0.432025	+	0.901861i	$0.357799\pi$
$12$	1.78617	0.515623
$13$	0.496769	0.137779	0.0688895	−	0.997624i	$-0.478054\pi$
$13$	0.496769	0.137779	0.0688895	+	0.997624i	$0.478054\pi$
$14$	0.697206	0.186336
$15$	−1.00000	−0.258199
$16$	2.76274	0.690686
$17$	−5.20536	−1.26248	−0.631242	−	0.775586i	$-0.717455\pi$
$17$	−5.20536	−1.26248	−0.631242	+	0.775586i	$0.717455\pi$
$18$	−0.462418	−0.108993
$19$	5.20616	1.19438	0.597188	−	0.802101i	$-0.296285\pi$
$19$	5.20616	1.19438	0.597188	+	0.802101i	$0.296285\pi$
$20$	−1.78617	−0.399400
$21$	1.50774	0.329016
$22$	−1.32516	−0.282526
$23$	−4.53047	−0.944668	−0.472334	−	0.881420i	$-0.656588\pi$
$23$	−4.53047	−0.944668	−0.472334	+	0.881420i	$0.656588\pi$
$24$	−1.75079	−0.357379
$25$	1.00000	0.200000
$26$	−0.229715	−0.0450508
$27$	−1.00000	−0.192450
$28$	2.69308	0.508945
$29$	−1.73627	−0.322417	−0.161209	−	0.986920i	$-0.551539\pi$
$29$	−1.73627	−0.322417	−0.161209	+	0.986920i	$0.551539\pi$
$30$	0.462418	0.0844255
$31$	−10.3731	−1.86306	−0.931529	−	0.363668i	$-0.881524\pi$
$31$	−10.3731	−1.86306	−0.931529	+	0.363668i	$0.881524\pi$
$32$	−4.77912	−0.844838
$33$	−2.86573	−0.498860
$34$	2.40705	0.412806
$35$	−1.50774	−0.254855
$36$	−1.78617	−0.297695
$37$	9.30522	1.52977	0.764884	−	0.644168i	$-0.222796\pi$
$37$	9.30522	1.52977	0.764884	+	0.644168i	$0.222796\pi$
$38$	−2.40742	−0.390535
$39$	−0.496769	−0.0795468
$40$	1.75079	0.276824
$41$	−5.02321	−0.784493	−0.392247	−	0.919860i	$-0.628302\pi$
$41$	−5.02321	−0.784493	−0.392247	+	0.919860i	$0.628302\pi$
$42$	−0.697206	−0.107581
$43$	3.58455	0.546639	0.273320	−	0.961923i	$-0.411878\pi$
$43$	3.58455	0.546639	0.273320	+	0.961923i	$0.411878\pi$
$44$	−5.11868	−0.771671
$45$	1.00000	0.149071
$46$	2.09497	0.308886
$47$	10.2129	1.48970	0.744850	−	0.667232i	$-0.232521\pi$
$47$	10.2129	1.48970	0.744850	+	0.667232i	$0.232521\pi$
$48$	−2.76274	−0.398768
$49$	−4.72672	−0.675245
$50$	−0.462418	−0.0653957
$51$	5.20536	0.728896
$52$	−0.887315	−0.123048
$53$	−0.103652	−0.0142377	−0.00711883	−	0.999975i	$-0.502266\pi$
$53$	−0.103652	−0.0142377	−0.00711883	+	0.999975i	$0.502266\pi$
$54$	0.462418	0.0629271
$55$	2.86573	0.386415
$56$	−2.63974	−0.352750
$57$	−5.20616	−0.689573
$58$	0.802882	0.105424
$59$	6.16360	0.802433	0.401216	−	0.915983i	$-0.368588\pi$
$59$	6.16360	0.802433	0.401216	+	0.915983i	$0.368588\pi$
$60$	1.78617	0.230594
$61$	−13.6058	−1.74204	−0.871020	−	0.491248i	$-0.836541\pi$
$61$	−13.6058	−1.74204	−0.871020	+	0.491248i	$0.836541\pi$
$62$	4.79669	0.609180
$63$	−1.50774	−0.189958
$64$	−3.31553	−0.414442
$65$	0.496769	0.0616167
$66$	1.32516	0.163117
$67$	3.82415	0.467194	0.233597	−	0.972334i	$-0.424950\pi$
$67$	3.82415	0.467194	0.233597	+	0.972334i	$0.424950\pi$
$68$	9.29765	1.12751
$69$	4.53047	0.545404
$70$	0.697206	0.0833321
$71$	2.53921	0.301349	0.150674	−	0.988583i	$-0.451855\pi$
$71$	2.53921	0.301349	0.150674	+	0.988583i	$0.451855\pi$
$72$	1.75079	0.206333
$73$	12.9186	1.51201	0.756004	−	0.654566i	$-0.227149\pi$
$73$	12.9186	1.51201	0.756004	+	0.654566i	$0.227149\pi$
$74$	−4.30290	−0.500202
$75$	−1.00000	−0.115470
$76$	−9.29909	−1.06668
$77$	−4.32078	−0.492399
$78$	0.229715	0.0260101
$79$	−15.7850	−1.77595	−0.887974	−	0.459894i	$-0.847887\pi$
$79$	−15.7850	−1.77595	−0.887974	+	0.459894i	$0.847887\pi$
$80$	2.76274	0.308884
$81$	1.00000	0.111111
$82$	2.32282	0.256513
$83$	−15.4659	−1.69760	−0.848800	−	0.528714i	$-0.822675\pi$
$83$	−15.4659	−1.69760	−0.848800	+	0.528714i	$0.822675\pi$
$84$	−2.69308	−0.293839
$85$	−5.20536	−0.564600
$86$	−1.65756	−0.178739
$87$	1.73627	0.186148
$88$	5.01730	0.534846
$89$	4.89978	0.519376	0.259688	−	0.965693i	$-0.416380\pi$
$89$	4.89978	0.519376	0.259688	+	0.965693i	$0.416380\pi$
$90$	−0.462418	−0.0487431
$91$	−0.749000	−0.0785165
$92$	8.09218	0.843669
$93$	10.3731	1.07564
$94$	−4.72261	−0.487100
$95$	5.20616	0.534141
$96$	4.77912	0.487767
$97$	−5.39885	−0.548170	−0.274085	−	0.961705i	$-0.588375\pi$
$97$	−5.39885	−0.548170	−0.274085	+	0.961705i	$0.588375\pi$
$98$	2.18572	0.220791
$99$	2.86573	0.288017
$100$	−1.78617	−0.178617
$101$	11.7781	1.17196	0.585982	−	0.810324i	$-0.300709\pi$
$101$	11.7781	1.17196	0.585982	+	0.810324i	$0.300709\pi$
$102$	−2.40705	−0.238333
$103$	10.3256	1.01741	0.508704	−	0.860941i	$-0.330125\pi$
$103$	10.3256	1.01741	0.508704	+	0.860941i	$0.330125\pi$
$104$	0.869740	0.0852850
$105$	1.50774	0.147140
$106$	0.0479304	0.00465541
$107$	4.22960	0.408891	0.204445	−	0.978878i	$-0.434461\pi$
$107$	4.22960	0.408891	0.204445	+	0.978878i	$0.434461\pi$
$108$	1.78617	0.171874
$109$	13.9954	1.34052	0.670259	−	0.742127i	$-0.266183\pi$
$109$	13.9954	1.34052	0.670259	+	0.742127i	$0.266183\pi$
$110$	−1.32516	−0.126350
$111$	−9.30522	−0.883212
$112$	−4.16550	−0.393603
$113$	15.8394	1.49004	0.745021	−	0.667040i	$-0.232439\pi$
$113$	15.8394	1.49004	0.745021	+	0.667040i	$0.232439\pi$
$114$	2.40742	0.225476
$115$	−4.53047	−0.422468
$116$	3.10127	0.287946
$117$	0.496769	0.0459264
$118$	−2.85016	−0.262378
$119$	7.84833	0.719455
$120$	−1.75079	−0.159825
$121$	−2.78758	−0.253417
$122$	6.29155	0.569610
$123$	5.02321	0.452927
$124$	18.5281	1.66387
$125$	1.00000	0.0894427
$126$	0.697206	0.0621121
$127$	20.6400	1.83150	0.915751	−	0.401747i	$-0.131597\pi$
$127$	20.6400	1.83150	0.915751	+	0.401747i	$0.131597\pi$
$128$	11.0914	0.980351
$129$	−3.58455	−0.315602
$130$	−0.229715	−0.0201473
$131$	−12.1937	−1.06537	−0.532686	−	0.846313i	$-0.678817\pi$
$131$	−12.1937	−1.06537	−0.532686	+	0.846313i	$0.678817\pi$
$132$	5.11868	0.445524
$133$	−7.84955	−0.680642
$134$	−1.76835	−0.152762
$135$	−1.00000	−0.0860663
$136$	−9.11350	−0.781476
$137$	−0.411485	−0.0351556	−0.0175778	−	0.999845i	$-0.505595\pi$
$137$	−0.411485	−0.0351556	−0.0175778	+	0.999845i	$0.505595\pi$
$138$	−2.09497	−0.178336
$139$	−9.36354	−0.794205	−0.397103	−	0.917774i	$-0.629984\pi$
$139$	−9.36354	−0.794205	−0.397103	+	0.917774i	$0.629984\pi$
$140$	2.69308	0.227607
$141$	−10.2129	−0.860079
$142$	−1.17418	−0.0985346
$143$	1.42361	0.119048
$144$	2.76274	0.230229
$145$	−1.73627	−0.144189
$146$	−5.97379	−0.494395
$147$	4.72672	0.389853
$148$	−16.6207	−1.36621
$149$	−6.61388	−0.541830	−0.270915	−	0.962603i	$-0.587326\pi$
$149$	−6.61388	−0.541830	−0.270915	+	0.962603i	$0.587326\pi$
$150$	0.462418	0.0377562
$151$	−13.9711	−1.13695	−0.568475	−	0.822700i	$-0.692466\pi$
$151$	−13.9711	−1.13695	−0.568475	+	0.822700i	$0.692466\pi$
$152$	9.11491	0.739317
$153$	−5.20536	−0.420828
$154$	1.99801	0.161004
$155$	−10.3731	−0.833184
$156$	0.887315	0.0710420
$157$	−7.80822	−0.623164	−0.311582	−	0.950219i	$-0.600859\pi$
$157$	−7.80822	−0.623164	−0.311582	+	0.950219i	$0.600859\pi$
$158$	7.29925	0.580697
$159$	0.103652	0.00822012
$160$	−4.77912	−0.377823
$161$	6.83077	0.538340
$162$	−0.462418	−0.0363310
$163$	−9.52572	−0.746112	−0.373056	−	0.927809i	$-0.621690\pi$
$163$	−9.52572	−0.746112	−0.373056	+	0.927809i	$0.621690\pi$
$164$	8.97230	0.700619
$165$	−2.86573	−0.223097
$166$	7.15170	0.555079
$167$	−0.000528874 0	−4.09255e−5 0	−2.04628e−5	−	1.00000i	$-0.500007\pi$
$167$	−0.000528874 0	−4.09255e−5 0	−2.04628e−5		1.00000i	$0.500007\pi$
$168$	2.63974	0.203660
$169$	−12.7532	−0.981017
$170$	2.40705	0.184612
$171$	5.20616	0.398125
$172$	−6.40262	−0.488195
$173$	6.06276	0.460943	0.230471	−	0.973079i	$-0.425973\pi$
$173$	6.06276	0.460943	0.230471	+	0.973079i	$0.425973\pi$
$174$	−0.802882	−0.0608663
$175$	−1.50774	−0.113975
$176$	7.91728	0.596787
$177$	−6.16360	−0.463285
$178$	−2.26575	−0.169825
$179$	12.3187	0.920742	0.460371	−	0.887727i	$-0.347716\pi$
$179$	12.3187	0.920742	0.460371	+	0.887727i	$0.347716\pi$
$180$	−1.78617	−0.133133
$181$	−25.5073	−1.89594	−0.947971	−	0.318356i	$-0.896869\pi$
$181$	−25.5073	−1.89594	−0.947971	+	0.318356i	$0.896869\pi$
$182$	0.346351	0.0256732
$183$	13.6058	1.00577
$184$	−7.93191	−0.584748
$185$	9.30522	0.684133
$186$	−4.79669	−0.351710
$187$	−14.9172	−1.09085
$188$	−18.2419	−1.33043
$189$	1.50774	0.109672
$190$	−2.40742	−0.174653
$191$	−25.1247	−1.81796	−0.908979	−	0.416841i	$-0.863137\pi$
$191$	−25.1247	−1.81796	−0.908979	+	0.416841i	$0.863137\pi$
$192$	3.31553	0.239278
$193$	26.1424	1.88177	0.940887	−	0.338721i	$-0.109994\pi$
$193$	26.1424	1.88177	0.940887	+	0.338721i	$0.109994\pi$
$194$	2.49652	0.179240
$195$	−0.496769	−0.0355744
$196$	8.44272	0.603051
$197$	−16.6674	−1.18750	−0.593751	−	0.804649i	$-0.702353\pi$
$197$	−16.6674	−1.18750	−0.593751	+	0.804649i	$0.702353\pi$
$198$	−1.32516	−0.0941754
$199$	13.3461	0.946077	0.473038	−	0.881042i	$-0.343157\pi$
$199$	13.3461	0.946077	0.473038	+	0.881042i	$0.343157\pi$
$200$	1.75079	0.123800
$201$	−3.82415	−0.269734
$202$	−5.44639	−0.383207
$203$	2.61784	0.183737
$204$	−9.29765	−0.650966
$205$	−5.02321	−0.350836
$206$	−4.77472	−0.332671
$207$	−4.53047	−0.314889
$208$	1.37245	0.0951620
$209$	14.9195	1.03200
$210$	−0.697206	−0.0481118
$211$	10.8360	0.745982	0.372991	−	0.927835i	$-0.378332\pi$
$211$	10.8360	0.745982	0.372991	+	0.927835i	$0.378332\pi$
$212$	0.185140	0.0127154
$213$	−2.53921	−0.173984
$214$	−1.95584	−0.133699
$215$	3.58455	0.244465
$216$	−1.75079	−0.119126
$217$	15.6399	1.06171
$218$	−6.47173	−0.438321
$219$	−12.9186	−0.872959
$220$	−5.11868	−0.345102
$221$	−2.58586	−0.173944
$222$	4.30290	0.288792
$223$	1.55232	0.103951	0.0519756	−	0.998648i	$-0.483448\pi$
$223$	1.55232	0.103951	0.0519756	+	0.998648i	$0.483448\pi$
$224$	7.20568	0.481450
$225$	1.00000	0.0666667
$226$	−7.32441	−0.487212
$227$	−5.10780	−0.339017	−0.169508	−	0.985529i	$-0.554218\pi$
$227$	−5.10780	−0.339017	−0.169508	+	0.985529i	$0.554218\pi$
$228$	9.29909	0.615847
$229$	−1.22591	−0.0810102	−0.0405051	−	0.999179i	$-0.512897\pi$
$229$	−1.22591	−0.0810102	−0.0405051	+	0.999179i	$0.512897\pi$
$230$	2.09497	0.138138
$231$	4.32078	0.284287
$232$	−3.03985	−0.199576
$233$	−22.0699	−1.44585	−0.722925	−	0.690927i	$-0.757203\pi$
$233$	−22.0699	−1.44585	−0.722925	+	0.690927i	$0.757203\pi$
$234$	−0.229715	−0.0150169
$235$	10.2129	0.666214
$236$	−11.0092	−0.716641
$237$	15.7850	1.02534
$238$	−3.62921	−0.235247
$239$	3.13695	0.202912	0.101456	−	0.994840i	$-0.467650\pi$
$239$	3.13695	0.202912	0.101456	+	0.994840i	$0.467650\pi$
$240$	−2.76274	−0.178334
$241$	−20.7351	−1.33566	−0.667831	−	0.744313i	$-0.732777\pi$
$241$	−20.7351	−1.33566	−0.667831	+	0.744313i	$0.732777\pi$
$242$	1.28903	0.0828618
$243$	−1.00000	−0.0641500
$244$	24.3022	1.55579
$245$	−4.72672	−0.301979
$246$	−2.32282	−0.148098
$247$	2.58626	0.164560
$248$	−18.1611	−1.15323
$249$	15.4659	0.980110
$250$	−0.462418	−0.0292459
$251$	−23.2282	−1.46615	−0.733075	−	0.680148i	$-0.761915\pi$
$251$	−23.2282	−1.46615	−0.733075	+	0.680148i	$0.761915\pi$
$252$	2.69308	0.169648
$253$	−12.9831	−0.816241
$254$	−9.54429	−0.598862
$255$	5.20536	0.325972
$256$	1.50220	0.0938877
$257$	−17.5143	−1.09251	−0.546257	−	0.837617i	$-0.683948\pi$
$257$	−17.5143	−1.09251	−0.546257	+	0.837617i	$0.683948\pi$
$258$	1.65756	0.103195
$259$	−14.0299	−0.871773
$260$	−0.887315	−0.0550289
$261$	−1.73627	−0.107472
$262$	5.63860	0.348354
$263$	−21.0282	−1.29665	−0.648326	−	0.761363i	$-0.724530\pi$
$263$	−21.0282	−1.29665	−0.648326	+	0.761363i	$0.724530\pi$
$264$	−5.01730	−0.308793
$265$	−0.103652	−0.00636727
$266$	3.62977	0.222555
$267$	−4.89978	−0.299862
$268$	−6.83057	−0.417244
$269$	14.3059	0.872244	0.436122	−	0.899887i	$-0.356352\pi$
$269$	14.3059	0.872244	0.436122	+	0.899887i	$0.356352\pi$
$270$	0.462418	0.0281418
$271$	7.39636	0.449297	0.224648	−	0.974440i	$-0.427877\pi$
$271$	7.39636	0.449297	0.224648	+	0.974440i	$0.427877\pi$
$272$	−14.3811	−0.871980
$273$	0.749000	0.0453315
$274$	0.190278	0.0114951
$275$	2.86573	0.172810
$276$	−8.09218	−0.487092
$277$	−4.40594	−0.264728	−0.132364	−	0.991201i	$-0.542257\pi$
$277$	−4.40594	−0.264728	−0.132364	+	0.991201i	$0.542257\pi$
$278$	4.32987	0.259688
$279$	−10.3731	−0.621019
$280$	−2.63974	−0.157755
$281$	−27.0619	−1.61438	−0.807189	−	0.590293i	$-0.799012\pi$
$281$	−27.0619	−1.61438	−0.807189	+	0.590293i	$0.799012\pi$
$282$	4.72261	0.281228
$283$	−13.2447	−0.787313	−0.393656	−	0.919258i	$-0.628790\pi$
$283$	−13.2447	−0.787313	−0.393656	+	0.919258i	$0.628790\pi$
$284$	−4.53546	−0.269130
$285$	−5.20616	−0.308386
$286$	−0.658301	−0.0389262
$287$	7.57370	0.447061
$288$	−4.77912	−0.281613
$289$	10.0957	0.593867
$290$	0.802882	0.0471468
$291$	5.39885	0.316486
$292$	−23.0748	−1.35035
$293$	13.0804	0.764164	0.382082	−	0.924128i	$-0.375207\pi$
$293$	13.0804	0.764164	0.382082	+	0.924128i	$0.375207\pi$
$294$	−2.18572	−0.127474
$295$	6.16360	0.358859
$296$	16.2915	0.946924
$297$	−2.86573	−0.166287
$298$	3.05838	0.177167
$299$	−2.25060	−0.130155
$300$	1.78617	0.103125
$301$	−5.40458	−0.311515
$302$	6.46047	0.371758
$303$	−11.7781	−0.676633
$304$	14.3833	0.824938
$305$	−13.6058	−0.779064
$306$	2.40705	0.137602
$307$	4.15633	0.237214	0.118607	−	0.992941i	$-0.462157\pi$
$307$	4.15633	0.237214	0.118607	+	0.992941i	$0.462157\pi$
$308$	7.71765	0.439754
$309$	−10.3256	−0.587401
$310$	4.79669	0.272434
$311$	14.5207	0.823395	0.411698	−	0.911321i	$-0.364936\pi$
$311$	14.5207	0.823395	0.411698	+	0.911321i	$0.364936\pi$
$312$	−0.869740	−0.0492393
$313$	−28.1494	−1.59110	−0.795549	−	0.605889i	$-0.792818\pi$
$313$	−28.1494	−1.59110	−0.795549	+	0.605889i	$0.792818\pi$
$314$	3.61066	0.203761
$315$	−1.50774	−0.0849516
$316$	28.1946	1.58607
$317$	20.2774	1.13889	0.569446	−	0.822029i	$-0.307158\pi$
$317$	20.2774	1.13889	0.569446	+	0.822029i	$0.307158\pi$
$318$	−0.0479304	−0.00268780
$319$	−4.97568	−0.278585
$320$	−3.31553	−0.185344
$321$	−4.22960	−0.236073
$322$	−3.15867	−0.176026
$323$	−27.0999	−1.50788
$324$	−1.78617	−0.0992317
$325$	0.496769	0.0275558
$326$	4.40486	0.243963
$327$	−13.9954	−0.773948
$328$	−8.79459	−0.485600
$329$	−15.3984	−0.848940
$330$	1.32516	0.0729479
$331$	16.3350	0.897851	0.448926	−	0.893569i	$-0.351807\pi$
$331$	16.3350	0.897851	0.448926	+	0.893569i	$0.351807\pi$
$332$	27.6247	1.51610
$333$	9.30522	0.509923
$334$	0.000244561 0	1.33818e−5 0
$335$	3.82415	0.208935
$336$	4.16550	0.227247
$337$	14.9448	0.814096	0.407048	−	0.913407i	$-0.366558\pi$
$337$	14.9448	0.814096	0.407048	+	0.913407i	$0.366558\pi$
$338$	5.89731	0.320772
$339$	−15.8394	−0.860277
$340$	9.29765	0.504236
$341$	−29.7264	−1.60978
$342$	−2.40742	−0.130178
$343$	17.6809	0.954676
$344$	6.27581	0.338369
$345$	4.53047	0.243912
$346$	−2.80353	−0.150718
$347$	−24.1208	−1.29487	−0.647437	−	0.762119i	$-0.724159\pi$
$347$	−24.1208	−1.29487	−0.647437	+	0.762119i	$0.724159\pi$
$348$	−3.10127	−0.166246
$349$	−14.6202	−0.782601	−0.391300	−	0.920263i	$-0.627975\pi$
$349$	−14.6202	−0.782601	−0.391300	+	0.920263i	$0.627975\pi$
$350$	0.697206	0.0372672
$351$	−0.496769	−0.0265156
$352$	−13.6957	−0.729983
$353$	−2.67841	−0.142557	−0.0712786	−	0.997456i	$-0.522708\pi$
$353$	−2.67841	−0.142557	−0.0712786	+	0.997456i	$0.522708\pi$
$354$	2.85016	0.151484
$355$	2.53921	0.134767
$356$	−8.75185	−0.463847
$357$	−7.84833	−0.415378
$358$	−5.69638	−0.301063
$359$	−14.4549	−0.762900	−0.381450	−	0.924389i	$-0.624575\pi$
$359$	−14.4549	−0.762900	−0.381450	+	0.924389i	$0.624575\pi$
$360$	1.75079	0.0922748
$361$	8.10413	0.426533
$362$	11.7950	0.619933
$363$	2.78758	0.146310
$364$	1.33784	0.0701219
$365$	12.9186	0.676191
$366$	−6.29155	−0.328864
$367$	19.4404	1.01478	0.507391	−	0.861716i	$-0.330610\pi$
$367$	19.4404	1.01478	0.507391	+	0.861716i	$0.330610\pi$
$368$	−12.5165	−0.652469
$369$	−5.02321	−0.261498
$370$	−4.30290	−0.223697
$371$	0.156280	0.00811365
$372$	−18.5281	−0.960635
$373$	−33.6077	−1.74014	−0.870070	−	0.492928i	$-0.835927\pi$
$373$	−33.6077	−1.74014	−0.870070	+	0.492928i	$0.835927\pi$
$374$	6.89796	0.356685
$375$	−1.00000	−0.0516398
$376$	17.8806	0.922122
$377$	−0.862526	−0.0444223
$378$	−0.697206	−0.0358604
$379$	24.1956	1.24285	0.621423	−	0.783475i	$-0.286555\pi$
$379$	24.1956	1.24285	0.621423	+	0.783475i	$0.286555\pi$
$380$	−9.29909	−0.477033
$381$	−20.6400	−1.05742
$382$	11.6181	0.594434
$383$	−32.5075	−1.66106	−0.830528	−	0.556978i	$-0.811961\pi$
$383$	−32.5075	−1.66106	−0.830528	+	0.556978i	$0.811961\pi$
$384$	−11.0914	−0.566006
$385$	−4.32078	−0.220207
$386$	−12.0887	−0.615300
$387$	3.58455	0.182213
$388$	9.64327	0.489563
$389$	−10.5491	−0.534861	−0.267430	−	0.963577i	$-0.586175\pi$
$389$	−10.5491	−0.534861	−0.267430	+	0.963577i	$0.586175\pi$
$390$	0.229715	0.0116321
$391$	23.5827	1.19263
$392$	−8.27550	−0.417976
$393$	12.1937	0.615092
$394$	7.70729	0.388288
$395$	−15.7850	−0.794228
$396$	−5.11868	−0.257224
$397$	−15.5812	−0.781996	−0.390998	−	0.920392i	$-0.627870\pi$
$397$	−15.5812	−0.781996	−0.390998	+	0.920392i	$0.627870\pi$
$398$	−6.17145	−0.309347
$399$	7.84955	0.392969
$400$	2.76274	0.138137
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	1.76835	0.0881974
$403$	−5.15302	−0.256690
$404$	−21.0377	−1.04666
$405$	1.00000	0.0496904
$406$	−1.21054	−0.0600780
$407$	26.6663	1.32180
$408$	9.11350	0.451185
$409$	2.01532	0.0996513	0.0498256	−	0.998758i	$-0.484133\pi$
$409$	2.01532	0.0996513	0.0498256	+	0.998758i	$0.484133\pi$
$410$	2.32282	0.114716
$411$	0.411485	0.0202971
$412$	−18.4432	−0.908632
$413$	−9.29312	−0.457284
$414$	2.09497	0.102962
$415$	−15.4659	−0.759190
$416$	−2.37412	−0.116401
$417$	9.36354	0.458535
$418$	−6.89902	−0.337442
$419$	−2.81611	−0.137576	−0.0687880	−	0.997631i	$-0.521913\pi$
$419$	−2.81611	−0.137576	−0.0687880	+	0.997631i	$0.521913\pi$
$420$	−2.69308	−0.131409
$421$	20.1878	0.983891	0.491946	−	0.870626i	$-0.336286\pi$
$421$	20.1878	0.983891	0.491946	+	0.870626i	$0.336286\pi$
$422$	−5.01077	−0.243920
$423$	10.2129	0.496567
$424$	−0.181473	−0.00881309
$425$	−5.20536	−0.252497
$426$	1.17418	0.0568890
$427$	20.5140	0.992741
$428$	−7.55478	−0.365174
$429$	−1.42361	−0.0687324
$430$	−1.65756	−0.0799347
$431$	15.0760	0.726187	0.363094	−	0.931753i	$-0.381720\pi$
$431$	15.0760	0.726187	0.363094	+	0.931753i	$0.381720\pi$
$432$	−2.76274	−0.132923
$433$	−18.3554	−0.882104	−0.441052	−	0.897482i	$-0.645395\pi$
$433$	−18.3554	−0.882104	−0.441052	+	0.897482i	$0.645395\pi$
$434$	−7.23216	−0.347155
$435$	1.73627	0.0832477
$436$	−24.9982	−1.19720
$437$	−23.5864	−1.12829
$438$	5.97379	0.285439
$439$	−23.3902	−1.11635	−0.558177	−	0.829722i	$-0.688499\pi$
$439$	−23.3902	−1.11635	−0.558177	+	0.829722i	$0.688499\pi$
$440$	5.01730	0.239190
$441$	−4.72672	−0.225082
$442$	1.19575	0.0568760
$443$	−13.5131	−0.642026	−0.321013	−	0.947075i	$-0.604023\pi$
$443$	−13.5131	−0.642026	−0.321013	+	0.947075i	$0.604023\pi$
$444$	16.6207	0.788784
$445$	4.89978	0.232272
$446$	−0.717821	−0.0339898
$447$	6.61388	0.312826
$448$	4.99897	0.236179
$449$	25.2969	1.19384	0.596918	−	0.802302i	$-0.296392\pi$
$449$	25.2969	1.19384	0.596918	+	0.802302i	$0.296392\pi$
$450$	−0.462418	−0.0217986
$451$	−14.3952	−0.677842
$452$	−28.2918	−1.33073
$453$	13.9711	0.656418
$454$	2.36194	0.110851
$455$	−0.749000	−0.0351137
$456$	−9.11491	−0.426845
$457$	−28.3285	−1.32515	−0.662575	−	0.748995i	$-0.730537\pi$
$457$	−28.3285	−1.32515	−0.662575	+	0.748995i	$0.730537\pi$
$458$	0.566881	0.0264886
$459$	5.20536	0.242965
$460$	8.09218	0.377300
$461$	−30.4079	−1.41624	−0.708118	−	0.706094i	$-0.750456\pi$
$461$	−30.4079	−1.41624	−0.708118	+	0.706094i	$0.750456\pi$
$462$	−1.99801	−0.0929556
$463$	33.9293	1.57683	0.788415	−	0.615144i	$-0.210902\pi$
$463$	33.9293	1.57683	0.788415	+	0.615144i	$0.210902\pi$
$464$	−4.79687	−0.222689
$465$	10.3731	0.481039
$466$	10.2055	0.472762
$467$	−10.1556	−0.469945	−0.234973	−	0.972002i	$-0.575500\pi$
$467$	−10.1556	−0.469945	−0.234973	+	0.972002i	$0.575500\pi$
$468$	−0.887315	−0.0410161
$469$	−5.76582	−0.266241
$470$	−4.72261	−0.217838
$471$	7.80822	0.359784
$472$	10.7912	0.496705
$473$	10.2724	0.472324
$474$	−7.29925	−0.335266
$475$	5.20616	0.238875
$476$	−14.0185	−0.642535
$477$	−0.103652	−0.00474589
$478$	−1.45058	−0.0663481
$479$	−0.261735	−0.0119590	−0.00597950	−	0.999982i	$-0.501903\pi$
$479$	−0.261735	−0.0119590	−0.00597950	+	0.999982i	$0.501903\pi$
$480$	4.77912	0.218136
$481$	4.62255	0.210770
$482$	9.58826	0.436733
$483$	−6.83077	−0.310811
$484$	4.97910	0.226323
$485$	−5.39885	−0.245149
$486$	0.462418	0.0209757
$487$	−21.8421	−0.989762	−0.494881	−	0.868961i	$-0.664788\pi$
$487$	−21.8421	−0.989762	−0.494881	+	0.868961i	$0.664788\pi$
$488$	−23.8209	−1.07832
$489$	9.52572	0.430768
$490$	2.18572	0.0987406
$491$	−41.4112	−1.86886	−0.934430	−	0.356146i	$-0.884091\pi$
$491$	−41.4112	−1.86886	−0.934430	+	0.356146i	$0.884091\pi$
$492$	−8.97230	−0.404503
$493$	9.03790	0.407047
$494$	−1.19593	−0.0538076
$495$	2.86573	0.128805
$496$	−28.6581	−1.28679
$497$	−3.82847	−0.171730
$498$	−7.15170	−0.320475
$499$	25.6829	1.14972	0.574862	−	0.818251i	$-0.305056\pi$
$499$	25.6829	1.14972	0.574862	+	0.818251i	$0.305056\pi$
$500$	−1.78617	−0.0798799
$501$	0.000528874 0	2.36284e−5 0
$502$	10.7411	0.479400
$503$	33.5378	1.49538	0.747688	−	0.664050i	$-0.231164\pi$
$503$	33.5378	1.49538	0.747688	+	0.664050i	$0.231164\pi$
$504$	−2.63974	−0.117583
$505$	11.7781	0.524118
$506$	6.00362	0.266893
$507$	12.7532	0.566390
$508$	−36.8665	−1.63569
$509$	−8.13624	−0.360632	−0.180316	−	0.983609i	$-0.557712\pi$
$509$	−8.13624	−0.360632	−0.180316	+	0.983609i	$0.557712\pi$
$510$	−2.40705	−0.106586
$511$	−19.4779	−0.861652
$512$	−22.8775	−1.01105
$513$	−5.20616	−0.229858
$514$	8.09894	0.357229
$515$	10.3256	0.454999
$516$	6.40262	0.281860
$517$	29.2674	1.28718
$518$	6.48766	0.285051
$519$	−6.06276	−0.266125
$520$	0.869740	0.0381406
$521$	−19.2213	−0.842103	−0.421051	−	0.907037i	$-0.638339\pi$
$521$	−19.2213	−0.842103	−0.421051	+	0.907037i	$0.638339\pi$
$522$	0.802882	0.0351412
$523$	−4.04887	−0.177045	−0.0885224	−	0.996074i	$-0.528214\pi$
$523$	−4.04887	−0.177045	−0.0885224	+	0.996074i	$0.528214\pi$
$524$	21.7801	0.951467
$525$	1.50774	0.0658032
$526$	9.72379	0.423977
$527$	53.9955	2.35208
$528$	−7.91728	−0.344555
$529$	−2.47486	−0.107603
$530$	0.0479304	0.00208196
$531$	6.16360	0.267478
$532$	14.0206	0.607871
$533$	−2.49538	−0.108087
$534$	2.26575	0.0980485
$535$	4.22960	0.182861
$536$	6.69528	0.289192
$537$	−12.3187	−0.531591
$538$	−6.61529	−0.285205
$539$	−13.5455	−0.583446
$540$	1.78617	0.0768645
$541$	−23.1944	−0.997205	−0.498602	−	0.866831i	$-0.666153\pi$
$541$	−23.1944	−0.997205	−0.498602	+	0.866831i	$0.666153\pi$
$542$	−3.42021	−0.146910
$543$	25.5073	1.09462
$544$	24.8771	1.06659
$545$	13.9954	0.599498
$546$	−0.346351	−0.0148224
$547$	31.4773	1.34587	0.672936	−	0.739701i	$-0.265033\pi$
$547$	31.4773	1.34587	0.672936	+	0.739701i	$0.265033\pi$
$548$	0.734983	0.0313969
$549$	−13.6058	−0.580680
$550$	−1.32516	−0.0565052
$551$	−9.03930	−0.385087
$552$	7.93191	0.337604
$553$	23.7996	1.01206
$554$	2.03739	0.0865603
$555$	−9.30522	−0.394985
$556$	16.7249	0.709293
$557$	−41.5142	−1.75901	−0.879506	−	0.475887i	$-0.842127\pi$
$557$	−41.5142	−1.75901	−0.879506	+	0.475887i	$0.842127\pi$
$558$	4.79669	0.203060
$559$	1.78070	0.0753155
$560$	−4.16550	−0.176025
$561$	14.9172	0.629803
$562$	12.5139	0.527867
$563$	−10.2077	−0.430203	−0.215101	−	0.976592i	$-0.569008\pi$
$563$	−10.2077	−0.430203	−0.215101	+	0.976592i	$0.569008\pi$
$564$	18.2419	0.768124
$565$	15.8394	0.666367
$566$	6.12456	0.257435
$567$	−1.50774	−0.0633192
$568$	4.44563	0.186534
$569$	11.2272	0.470670	0.235335	−	0.971914i	$-0.424381\pi$
$569$	11.2272	0.470670	0.235335	+	0.971914i	$0.424381\pi$
$570$	2.40742	0.100836
$571$	10.7780	0.451046	0.225523	−	0.974238i	$-0.427591\pi$
$571$	10.7780	0.451046	0.225523	+	0.974238i	$0.427591\pi$
$572$	−2.54281	−0.106320
$573$	25.1247	1.04960
$574$	−3.50221	−0.146179
$575$	−4.53047	−0.188934
$576$	−3.31553	−0.138147
$577$	19.1428	0.796923	0.398462	−	0.917185i	$-0.369544\pi$
$577$	19.1428	0.796923	0.398462	+	0.917185i	$0.369544\pi$
$578$	−4.66845	−0.194182
$579$	−26.1424	−1.08644
$580$	3.10127	0.128773
$581$	23.3185	0.967416
$582$	−2.49652	−0.103484
$583$	−0.297038	−0.0123021
$584$	22.6178	0.935931
$585$	0.496769	0.0205389
$586$	−6.04860	−0.249865
$587$	−5.30078	−0.218787	−0.109393	−	0.993999i	$-0.534891\pi$
$587$	−5.30078	−0.218787	−0.109393	+	0.993999i	$0.534891\pi$
$588$	−8.44272	−0.348172
$589$	−54.0039	−2.22519
$590$	−2.85016	−0.117339
$591$	16.6674	0.685604
$592$	25.7079	1.05659
$593$	−9.43037	−0.387259	−0.193629	−	0.981075i	$-0.562026\pi$
$593$	−9.43037	−0.387259	−0.193629	+	0.981075i	$0.562026\pi$
$594$	1.32516	0.0543722
$595$	7.84833	0.321750
$596$	11.8135	0.483900
$597$	−13.3461	−0.546218
$598$	1.04072	0.0425581
$599$	−8.60547	−0.351610	−0.175805	−	0.984425i	$-0.556253\pi$
$599$	−8.60547	−0.351610	−0.175805	+	0.984425i	$0.556253\pi$
$600$	−1.75079	−0.0714758
$601$	−28.0313	−1.14342	−0.571710	−	0.820456i	$-0.693720\pi$
$601$	−28.0313	−1.14342	−0.571710	+	0.820456i	$0.693720\pi$
$602$	2.49917	0.101859
$603$	3.82415	0.155731
$604$	24.9547	1.01539
$605$	−2.78758	−0.113331
$606$	5.44639	0.221245
$607$	39.0257	1.58400	0.792002	−	0.610518i	$-0.209039\pi$
$607$	39.0257	1.58400	0.792002	+	0.610518i	$0.209039\pi$
$608$	−24.8809	−1.00905
$609$	−2.61784	−0.106080
$610$	6.29155	0.254737
$611$	5.07344	0.205250
$612$	9.29765	0.375835
$613$	−33.4917	−1.35272	−0.676358	−	0.736573i	$-0.736443\pi$
$613$	−33.4917	−1.35272	−0.676358	+	0.736573i	$0.736443\pi$
$614$	−1.92196	−0.0775640
$615$	5.02321	0.202555
$616$	−7.56479	−0.304794
$617$	−18.0518	−0.726738	−0.363369	−	0.931645i	$-0.618374\pi$
$617$	−18.0518	−0.726738	−0.363369	+	0.931645i	$0.618374\pi$
$618$	4.77472	0.192068
$619$	3.27082	0.131466	0.0657328	−	0.997837i	$-0.479062\pi$
$619$	3.27082	0.131466	0.0657328	+	0.997837i	$0.479062\pi$
$620$	18.5281	0.744105
$621$	4.53047	0.181801
$622$	−6.71464	−0.269233
$623$	−7.38761	−0.295978
$624$	−1.37245	−0.0549418
$625$	1.00000	0.0400000
$626$	13.0168	0.520255
$627$	−14.9195	−0.595826
$628$	13.9468	0.556539
$629$	−48.4370	−1.93131
$630$	0.697206	0.0277774
$631$	37.0609	1.47537	0.737686	−	0.675144i	$-0.235919\pi$
$631$	37.0609	1.47537	0.737686	+	0.675144i	$0.235919\pi$
$632$	−27.6362	−1.09931
$633$	−10.8360	−0.430693
$634$	−9.37662	−0.372393
$635$	20.6400	0.819072
$636$	−0.185140	−0.00734126
$637$	−2.34809	−0.0930347
$638$	2.30084	0.0910913
$639$	2.53921	0.100450
$640$	11.0914	0.438427
$641$	−27.3280	−1.07939	−0.539696	−	0.841860i	$-0.681461\pi$
$641$	−27.3280	−1.07939	−0.539696	+	0.841860i	$0.681461\pi$
$642$	1.95584	0.0771909
$643$	−42.3362	−1.66958	−0.834789	−	0.550571i	$-0.814410\pi$
$643$	−42.3362	−1.66958	−0.834789	+	0.550571i	$0.814410\pi$
$644$	−12.2009	−0.480784
$645$	−3.58455	−0.141142
$646$	12.5315	0.493045
$647$	−21.7460	−0.854925	−0.427463	−	0.904033i	$-0.640592\pi$
$647$	−21.7460	−0.854925	−0.427463	+	0.904033i	$0.640592\pi$
$648$	1.75079	0.0687776
$649$	17.6632	0.693342
$650$	−0.229715	−0.00901016
$651$	−15.6399	−0.612976
$652$	17.0145	0.666341
$653$	−31.8346	−1.24578	−0.622892	−	0.782308i	$-0.714042\pi$
$653$	−31.8346	−1.24578	−0.622892	+	0.782308i	$0.714042\pi$
$654$	6.47173	0.253065
$655$	−12.1937	−0.476448
$656$	−13.8778	−0.541838
$657$	12.9186	0.504003
$658$	7.12048	0.277585
$659$	−16.6645	−0.649157	−0.324578	−	0.945859i	$-0.605222\pi$
$659$	−16.6645	−0.649157	−0.324578	+	0.945859i	$0.605222\pi$
$660$	5.11868	0.199244
$661$	−7.38169	−0.287115	−0.143557	−	0.989642i	$-0.545854\pi$
$661$	−7.38169	−0.287115	−0.143557	+	0.989642i	$0.545854\pi$
$662$	−7.55358	−0.293578
$663$	2.58586	0.100427
$664$	−27.0775	−1.05081
$665$	−7.84955	−0.304392
$666$	−4.30290	−0.166734
$667$	7.86611	0.304577
$668$	0.000944659 0	3.65500e−5 0
$669$	−1.55232	−0.0600162
$670$	−1.76835	−0.0683174
$671$	−38.9905	−1.50521
$672$	−7.20568	−0.277965
$673$	−4.03896	−0.155690	−0.0778452	−	0.996965i	$-0.524804\pi$
$673$	−4.03896	−0.155690	−0.0778452	+	0.996965i	$0.524804\pi$
$674$	−6.91075	−0.266192
$675$	−1.00000	−0.0384900
$676$	22.7794	0.876131
$677$	−22.4511	−0.862865	−0.431433	−	0.902145i	$-0.641992\pi$
$677$	−22.4511	−0.862865	−0.431433	+	0.902145i	$0.641992\pi$
$678$	7.32441	0.281292
$679$	8.14007	0.312387
$680$	−9.11350	−0.349487
$681$	5.10780	0.195731
$682$	13.7460	0.526362
$683$	−7.94494	−0.304005	−0.152002	−	0.988380i	$-0.548572\pi$
$683$	−7.94494	−0.304005	−0.152002	+	0.988380i	$0.548572\pi$
$684$	−9.29909	−0.355560
$685$	−0.411485	−0.0157221
$686$	−8.17594	−0.312159
$687$	1.22591	0.0467712
$688$	9.90320	0.377556
$689$	−0.0514910	−0.00196165
$690$	−2.09497	−0.0797541
$691$	−35.7698	−1.36075	−0.680373	−	0.732866i	$-0.738182\pi$
$691$	−35.7698	−1.36075	−0.680373	+	0.732866i	$0.738182\pi$
$692$	−10.8291	−0.411661
$693$	−4.32078	−0.164133
$694$	11.1539	0.423396
$695$	−9.36354	−0.355179
$696$	3.03985	0.115225
$697$	26.1476	0.990411
$698$	6.76063	0.255894
$699$	22.0699	0.834762
$700$	2.69308	0.101789
$701$	43.0730	1.62685	0.813423	−	0.581672i	$-0.197601\pi$
$701$	43.0730	1.62685	0.813423	+	0.581672i	$0.197601\pi$
$702$	0.229715	0.00867003
$703$	48.4445	1.82712
$704$	−9.50143	−0.358099
$705$	−10.2129	−0.384639
$706$	1.23854	0.0466132
$707$	−17.7583	−0.667870
$708$	11.0092	0.413753
$709$	−19.5940	−0.735870	−0.367935	−	0.929852i	$-0.619935\pi$
$709$	−19.5940	−0.735870	−0.367935	+	0.929852i	$0.619935\pi$
$710$	−1.17418	−0.0440660
$711$	−15.7850	−0.591983
$712$	8.57850	0.321493
$713$	46.9948	1.75997
$714$	3.62921	0.135820
$715$	1.42361	0.0532399
$716$	−22.0033	−0.822301
$717$	−3.13695	−0.117152
$718$	6.68420	0.249452
$719$	−2.63149	−0.0981379	−0.0490689	−	0.998795i	$-0.515625\pi$
$719$	−2.63149	−0.0981379	−0.0490689	+	0.998795i	$0.515625\pi$
$720$	2.76274	0.102961
$721$	−15.5683	−0.579793
$722$	−3.74749	−0.139467
$723$	20.7351	0.771145
$724$	45.5604	1.69324
$725$	−1.73627	−0.0644834
$726$	−1.28903	−0.0478403
$727$	53.0166	1.96628	0.983139	−	0.182858i	$-0.0585349\pi$
$727$	53.0166	1.96628	0.983139	+	0.182858i	$0.0585349\pi$
$728$	−1.31134	−0.0486016
$729$	1.00000	0.0370370
$730$	−5.97379	−0.221100
$731$	−18.6589	−0.690124
$732$	−24.3022	−0.898235
$733$	−34.1503	−1.26137	−0.630684	−	0.776040i	$-0.717226\pi$
$733$	−34.1503	−1.26137	−0.630684	+	0.776040i	$0.717226\pi$
$734$	−8.98959	−0.331812
$735$	4.72672	0.174348
$736$	21.6517	0.798091
$737$	10.9590	0.403679
$738$	2.32282	0.0855042
$739$	−18.4669	−0.679314	−0.339657	−	0.940549i	$-0.610311\pi$
$739$	−18.4669	−0.679314	−0.339657	+	0.940549i	$0.610311\pi$
$740$	−16.6207	−0.610989
$741$	−2.58626	−0.0950087
$742$	−0.0722666	−0.00265299
$743$	19.2525	0.706306	0.353153	−	0.935566i	$-0.385110\pi$
$743$	19.2525	0.706306	0.353153	+	0.935566i	$0.385110\pi$
$744$	18.1611	0.665817
$745$	−6.61388	−0.242314
$746$	15.5408	0.568989
$747$	−15.4659	−0.565867
$748$	26.6446	0.974222
$749$	−6.37714	−0.233016
$750$	0.462418	0.0168851
$751$	10.0834	0.367949	0.183974	−	0.982931i	$-0.441104\pi$
$751$	10.0834	0.367949	0.183974	+	0.982931i	$0.441104\pi$
$752$	28.2155	1.02892
$753$	23.2282	0.846482
$754$	0.398847	0.0145252
$755$	−13.9711	−0.508460
$756$	−2.69308	−0.0979464
$757$	39.3083	1.42868	0.714342	−	0.699797i	$-0.246726\pi$
$757$	39.3083	1.42868	0.714342	+	0.699797i	$0.246726\pi$
$758$	−11.1885	−0.406384
$759$	12.9831	0.471257
$760$	9.11491	0.330632
$761$	−3.90214	−0.141453	−0.0707263	−	0.997496i	$-0.522532\pi$
$761$	−3.90214	−0.141453	−0.0707263	+	0.997496i	$0.522532\pi$
$762$	9.54429	0.345753
$763$	−21.1015	−0.763924
$764$	44.8770	1.62359
$765$	−5.20536	−0.188200
$766$	15.0320	0.543130
$767$	3.06189	0.110558
$768$	−1.50220	−0.0542061
$769$	5.27885	0.190360	0.0951800	−	0.995460i	$-0.469657\pi$
$769$	5.27885	0.190360	0.0951800	+	0.995460i	$0.469657\pi$
$770$	1.99801	0.0720031
$771$	17.5143	0.630764
$772$	−46.6948	−1.68058
$773$	32.0716	1.15354	0.576768	−	0.816908i	$-0.304314\pi$
$773$	32.0716	1.15354	0.576768	+	0.816908i	$0.304314\pi$
$774$	−1.65756	−0.0595798
$775$	−10.3731	−0.372611
$776$	−9.45226	−0.339317
$777$	14.0299	0.503319
$778$	4.87809	0.174888
$779$	−26.1516	−0.936980
$780$	0.887315	0.0317710
$781$	7.27669	0.260381
$782$	−10.9051	−0.389964
$783$	1.73627	0.0620492
$784$	−13.0587	−0.466382
$785$	−7.80822	−0.278687
$786$	−5.63860	−0.201122
$787$	−0.944028	−0.0336510	−0.0168255	−	0.999858i	$-0.505356\pi$
$787$	−0.944028	−0.0336510	−0.0168255	+	0.999858i	$0.505356\pi$
$788$	29.7708	1.06054
$789$	21.0282	0.748622
$790$	7.29925	0.259696
$791$	−23.8817	−0.849135
$792$	5.01730	0.178282
$793$	−6.75893	−0.240017
$794$	7.20500	0.255696
$795$	0.103652	0.00367615
$796$	−23.8383	−0.844927
$797$	33.3832	1.18249	0.591246	−	0.806491i	$-0.298636\pi$
$797$	33.3832	1.18249	0.591246	+	0.806491i	$0.298636\pi$
$798$	−3.62977	−0.128492
$799$	−53.1617	−1.88072
$800$	−4.77912	−0.168968
$801$	4.89978	0.173125
$802$	−0.462418	−0.0163285
$803$	37.0213	1.30645
$804$	6.83057	0.240896
$805$	6.83077	0.240753
$806$	2.38285	0.0839322
$807$	−14.3059	−0.503591
$808$	20.6210	0.725443
$809$	7.35076	0.258439	0.129219	−	0.991616i	$-0.458753\pi$
$809$	7.35076	0.258439	0.129219	+	0.991616i	$0.458753\pi$
$810$	−0.462418	−0.0162477
$811$	−55.8645	−1.96167	−0.980834	−	0.194846i	$-0.937579\pi$
$811$	−55.8645	−1.96167	−0.980834	+	0.194846i	$0.937579\pi$
$812$	−4.67592	−0.164092
$813$	−7.39636	−0.259402
$814$	−12.3310	−0.432200
$815$	−9.52572	−0.333671
$816$	14.3811	0.503438
$817$	18.6618	0.652893
$818$	−0.931920	−0.0325838
$819$	−0.749000	−0.0261722
$820$	8.97230	0.313326
$821$	10.5471	0.368095	0.184047	−	0.982917i	$-0.441080\pi$
$821$	10.5471	0.368095	0.184047	+	0.982917i	$0.441080\pi$
$822$	−0.190278	−0.00663671
$823$	14.9374	0.520684	0.260342	−	0.965516i	$-0.416165\pi$
$823$	14.9374	0.520684	0.260342	+	0.965516i	$0.416165\pi$
$824$	18.0779	0.629774
$825$	−2.86573	−0.0997720
$826$	4.29730	0.149522
$827$	−7.56262	−0.262978	−0.131489	−	0.991318i	$-0.541976\pi$
$827$	−7.56262	−0.262978	−0.131489	+	0.991318i	$0.541976\pi$
$828$	8.09218	0.281223
$829$	11.0081	0.382326	0.191163	−	0.981558i	$-0.438774\pi$
$829$	11.0081	0.382326	0.191163	+	0.981558i	$0.438774\pi$
$830$	7.15170	0.248239
$831$	4.40594	0.152841
$832$	−1.64706	−0.0571014
$833$	24.6042	0.852487
$834$	−4.32987	−0.149931
$835$	−0.000528874 0	−1.83024e−5 0
$836$	−26.6487	−0.921664
$837$	10.3731	0.358546
$838$	1.30222	0.0449844
$839$	−14.8262	−0.511858	−0.255929	−	0.966696i	$-0.582381\pi$
$839$	−14.8262	−0.511858	−0.255929	+	0.966696i	$0.582381\pi$
$840$	2.63974	0.0910797
$841$	−25.9854	−0.896047
$842$	−9.33518	−0.321711
$843$	27.0619	0.932061
$844$	−19.3550	−0.666225
$845$	−12.7532	−0.438724
$846$	−4.72261	−0.162367
$847$	4.20295	0.144415
$848$	−0.286363	−0.00983375
$849$	13.2447	0.454555
$850$	2.40705	0.0825611
$851$	−42.1570	−1.44512
$852$	4.53546	0.155382
$853$	−40.3471	−1.38146	−0.690730	−	0.723113i	$-0.742711\pi$
$853$	−40.3471	−1.38146	−0.690730	+	0.723113i	$0.742711\pi$
$854$	−9.48602	−0.324605
$855$	5.20616	0.178047
$856$	7.40515	0.253103
$857$	36.4658	1.24565	0.622824	−	0.782362i	$-0.285985\pi$
$857$	36.4658	1.24565	0.622824	+	0.782362i	$0.285985\pi$
$858$	0.658301	0.0224740
$859$	−24.2155	−0.826223	−0.413111	−	0.910681i	$-0.635558\pi$
$859$	−24.2155	−0.826223	−0.413111	+	0.910681i	$0.635558\pi$
$860$	−6.40262	−0.218328
$861$	−7.57370	−0.258111
$862$	−6.97143	−0.237448
$863$	10.3493	0.352295	0.176147	−	0.984364i	$-0.443636\pi$
$863$	10.3493	0.352295	0.176147	+	0.984364i	$0.443636\pi$
$864$	4.77912	0.162589
$865$	6.06276	0.206140
$866$	8.48786	0.288429
$867$	−10.0957	−0.342869
$868$	−27.9355	−0.948193
$869$	−45.2355	−1.53451
$870$	−0.802882	−0.0272202
$871$	1.89972	0.0643695
$872$	24.5031	0.829778
$873$	−5.39885	−0.182723
$874$	10.9067	0.368926
$875$	−1.50774	−0.0509710
$876$	23.0748	0.779626
$877$	−33.4081	−1.12811	−0.564056	−	0.825737i	$-0.690760\pi$
$877$	−33.4081	−1.12811	−0.564056	+	0.825737i	$0.690760\pi$
$878$	10.8161	0.365024
$879$	−13.0804	−0.441190
$880$	7.91728	0.266891
$881$	−46.8238	−1.57753	−0.788767	−	0.614692i	$-0.789280\pi$
$881$	−46.8238	−1.57753	−0.788767	+	0.614692i	$0.789280\pi$
$882$	2.18572	0.0735969
$883$	28.5598	0.961112	0.480556	−	0.876964i	$-0.340435\pi$
$883$	28.5598	0.961112	0.480556	+	0.876964i	$0.340435\pi$
$884$	4.61879	0.155347
$885$	−6.16360	−0.207187
$886$	6.24868	0.209929
$887$	57.6572	1.93594	0.967970	−	0.251067i	$-0.0807813\pi$
$887$	57.6572	1.93594	0.967970	+	0.251067i	$0.0807813\pi$
$888$	−16.2915	−0.546707
$889$	−31.1197	−1.04372
$890$	−2.26575	−0.0759480
$891$	2.86573	0.0960056
$892$	−2.77271	−0.0928372
$893$	53.1699	1.77926
$894$	−3.05838	−0.102287
$895$	12.3187	0.411768
$896$	−16.7230	−0.558675
$897$	2.25060	0.0751453
$898$	−11.6977	−0.390359
$899$	18.0104	0.600682
$900$	−1.78617	−0.0595390
$901$	0.539544	0.0179748
$902$	6.65658	0.221640
$903$	5.40458	0.179853
$904$	27.7314	0.922334
$905$	−25.5073	−0.847891
$906$	−6.46047	−0.214635
$907$	9.10443	0.302308	0.151154	−	0.988510i	$-0.451701\pi$
$907$	9.10443	0.302308	0.151154	+	0.988510i	$0.451701\pi$
$908$	9.12340	0.302771
$909$	11.7781	0.390654
$910$	0.346351	0.0114814
$911$	−21.0833	−0.698520	−0.349260	−	0.937026i	$-0.613567\pi$
$911$	−21.0833	−0.698520	−0.349260	+	0.937026i	$0.613567\pi$
$912$	−14.3833	−0.476278
$913$	−44.3211	−1.46681
$914$	13.0996	0.433296
$915$	13.6058	0.449793
$916$	2.18968	0.0723490
$917$	18.3850	0.607126
$918$	−2.40705	−0.0794445
$919$	−23.2351	−0.766455	−0.383228	−	0.923654i	$-0.625188\pi$
$919$	−23.2351	−0.766455	−0.383228	+	0.923654i	$0.625188\pi$
$920$	−7.93191	−0.261507
$921$	−4.15633	−0.136956
$922$	14.0611	0.463079
$923$	1.26140	0.0415196
$924$	−7.71765	−0.253892
$925$	9.30522	0.305954
$926$	−15.6895	−0.515590
$927$	10.3256	0.339136
$928$	8.29785	0.272390
$929$	27.4300	0.899948	0.449974	−	0.893042i	$-0.351433\pi$
$929$	27.4300	0.899948	0.449974	+	0.893042i	$0.351433\pi$
$930$	−4.79669	−0.157290
$931$	−24.6081	−0.806496
$932$	39.4207	1.29127
$933$	−14.5207	−0.475387
$934$	4.69613	0.153662
$935$	−14.9172	−0.487843
$936$	0.869740	0.0284283
$937$	−1.67946	−0.0548657	−0.0274329	−	0.999624i	$-0.508733\pi$
$937$	−1.67946	−0.0548657	−0.0274329	+	0.999624i	$0.508733\pi$
$938$	2.66622	0.0870551
$939$	28.1494	0.918621
$940$	−18.2419	−0.594986
$941$	−19.6564	−0.640780	−0.320390	−	0.947286i	$-0.603814\pi$
$941$	−19.6564	−0.640780	−0.320390	+	0.947286i	$0.603814\pi$
$942$	−3.61066	−0.117642
$943$	22.7575	0.741086
$944$	17.0284	0.554229
$945$	1.50774	0.0490468
$946$	−4.75012	−0.154440
$947$	34.3618	1.11661	0.558303	−	0.829637i	$-0.311452\pi$
$947$	34.3618	1.11661	0.558303	+	0.829637i	$0.311452\pi$
$948$	−28.1946	−0.915719
$949$	6.41757	0.208323
$950$	−2.40742	−0.0781071
$951$	−20.2774	−0.657539
$952$	13.7408	0.445342
$953$	−3.98875	−0.129208	−0.0646041	−	0.997911i	$-0.520578\pi$
$953$	−3.98875	−0.129208	−0.0646041	+	0.997911i	$0.520578\pi$
$954$	0.0479304	0.00155180
$955$	−25.1247	−0.813016
$956$	−5.60313	−0.181218
$957$	4.97568	0.160841
$958$	0.121031	0.00391034
$959$	0.620414	0.0200342
$960$	3.31553	0.107008
$961$	76.6004	2.47098
$962$	−2.13755	−0.0689173
$963$	4.22960	0.136297
$964$	37.0363	1.19286
$965$	26.1424	0.841555
$966$	3.15867	0.101629
$967$	21.8771	0.703519	0.351760	−	0.936090i	$-0.385583\pi$
$967$	21.8771	0.703519	0.351760	+	0.936090i	$0.385583\pi$
$968$	−4.88048	−0.156864
$969$	27.0999	0.870575
$970$	2.49652	0.0801586
$971$	30.0847	0.965465	0.482733	−	0.875768i	$-0.339644\pi$
$971$	30.0847	0.965465	0.482733	+	0.875768i	$0.339644\pi$
$972$	1.78617	0.0572914
$973$	14.1178	0.452596
$974$	10.1002	0.323631
$975$	−0.496769	−0.0159094
$976$	−37.5892	−1.20320
$977$	−23.2366	−0.743406	−0.371703	−	0.928352i	$-0.621226\pi$
$977$	−23.2366	−0.743406	−0.371703	+	0.928352i	$0.621226\pi$
$978$	−4.40486	−0.140852
$979$	14.0415	0.448767
$980$	8.44272	0.269693
$981$	13.9954	0.446839
$982$	19.1493	0.611078
$983$	−14.4264	−0.460131	−0.230066	−	0.973175i	$-0.573894\pi$
$983$	−14.4264	−0.460131	−0.230066	+	0.973175i	$0.573894\pi$
$984$	8.79459	0.280361
$985$	−16.6674	−0.531067
$986$	−4.17929	−0.133096
$987$	15.3984	0.490136
$988$	−4.61950	−0.146966
$989$	−16.2397	−0.516393
$990$	−1.32516	−0.0421165
$991$	−9.58939	−0.304617	−0.152308	−	0.988333i	$-0.548671\pi$
$991$	−9.58939	−0.304617	−0.152308	+	0.988333i	$0.548671\pi$
$992$	49.5742	1.57398
$993$	−16.3350	−0.518375
$994$	1.77035	0.0561522
$995$	13.3461	0.423098
$996$	−27.6247	−0.875322
$997$	28.3787	0.898763	0.449382	−	0.893340i	$-0.351644\pi$
$997$	28.3787	0.898763	0.449382	+	0.893340i	$0.351644\pi$
$998$	−11.8762	−0.375935
$999$	−9.30522	−0.294404

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.d.1.12	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.d.1.12	✓	29	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.462418 q^{2} -1.00000 q^{3} -1.78617 q^{4} +1.00000 q^{5} +0.462418 q^{6} -1.50774 q^{7} +1.75079 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.462418 q^{2} -1.00000 q^{3} -1.78617 q^{4} +1.00000 q^{5} +0.462418 q^{6} -1.50774 q^{7} +1.75079 q^{8} +1.00000 q^{9} -0.462418 q^{10} +2.86573 q^{11} +1.78617 q^{12} +0.496769 q^{13} +0.697206 q^{14} -1.00000 q^{15} +2.76274 q^{16} -5.20536 q^{17} -0.462418 q^{18} +5.20616 q^{19} -1.78617 q^{20} +1.50774 q^{21} -1.32516 q^{22} -4.53047 q^{23} -1.75079 q^{24} +1.00000 q^{25} -0.229715 q^{26} -1.00000 q^{27} +2.69308 q^{28} -1.73627 q^{29} +0.462418 q^{30} -10.3731 q^{31} -4.77912 q^{32} -2.86573 q^{33} +2.40705 q^{34} -1.50774 q^{35} -1.78617 q^{36} +9.30522 q^{37} -2.40742 q^{38} -0.496769 q^{39} +1.75079 q^{40} -5.02321 q^{41} -0.697206 q^{42} +3.58455 q^{43} -5.11868 q^{44} +1.00000 q^{45} +2.09497 q^{46} +10.2129 q^{47} -2.76274 q^{48} -4.72672 q^{49} -0.462418 q^{50} +5.20536 q^{51} -0.887315 q^{52} -0.103652 q^{53} +0.462418 q^{54} +2.86573 q^{55} -2.63974 q^{56} -5.20616 q^{57} +0.802882 q^{58} +6.16360 q^{59} +1.78617 q^{60} -13.6058 q^{61} +4.79669 q^{62} -1.50774 q^{63} -3.31553 q^{64} +0.496769 q^{65} +1.32516 q^{66} +3.82415 q^{67} +9.29765 q^{68} +4.53047 q^{69} +0.697206 q^{70} +2.53921 q^{71} +1.75079 q^{72} +12.9186 q^{73} -4.30290 q^{74} -1.00000 q^{75} -9.29909 q^{76} -4.32078 q^{77} +0.229715 q^{78} -15.7850 q^{79} +2.76274 q^{80} +1.00000 q^{81} +2.32282 q^{82} -15.4659 q^{83} -2.69308 q^{84} -5.20536 q^{85} -1.65756 q^{86} +1.73627 q^{87} +5.01730 q^{88} +4.89978 q^{89} -0.462418 q^{90} -0.749000 q^{91} +8.09218 q^{92} +10.3731 q^{93} -4.72261 q^{94} +5.20616 q^{95} +4.77912 q^{96} -5.39885 q^{97} +2.18572 q^{98} +2.86573 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * q^99

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