LMFDB - Embedded newform 6017.2.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$107$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60586 q^{2} -1.61281 q^{3} +4.79053 q^{4} +1.44359 q^{5} +4.20277 q^{6} +4.40298 q^{7} -7.27174 q^{8} -0.398838 q^{9} +O(q^{10})$	\(q-2.60586 q^{2} -1.61281 q^{3} +4.79053 q^{4} +1.44359 q^{5} +4.20277 q^{6} +4.40298 q^{7} -7.27174 q^{8} -0.398838 q^{9} -3.76179 q^{10} -1.00000 q^{11} -7.72622 q^{12} -3.29528 q^{13} -11.4736 q^{14} -2.32824 q^{15} +9.36812 q^{16} +2.74759 q^{17} +1.03932 q^{18} -3.00310 q^{19} +6.91555 q^{20} -7.10119 q^{21} +2.60586 q^{22} -7.57236 q^{23} +11.7280 q^{24} -2.91605 q^{25} +8.58706 q^{26} +5.48169 q^{27} +21.0926 q^{28} +0.483793 q^{29} +6.06707 q^{30} -4.15403 q^{31} -9.86855 q^{32} +1.61281 q^{33} -7.15986 q^{34} +6.35609 q^{35} -1.91064 q^{36} +1.74501 q^{37} +7.82568 q^{38} +5.31467 q^{39} -10.4974 q^{40} +8.01537 q^{41} +18.5047 q^{42} -3.14583 q^{43} -4.79053 q^{44} -0.575757 q^{45} +19.7325 q^{46} +6.97573 q^{47} -15.1090 q^{48} +12.3863 q^{49} +7.59884 q^{50} -4.43135 q^{51} -15.7861 q^{52} +12.9002 q^{53} -14.2845 q^{54} -1.44359 q^{55} -32.0174 q^{56} +4.84344 q^{57} -1.26070 q^{58} -0.751630 q^{59} -11.1535 q^{60} -7.28552 q^{61} +10.8248 q^{62} -1.75608 q^{63} +6.97989 q^{64} -4.75703 q^{65} -4.20277 q^{66} +5.98665 q^{67} +13.1624 q^{68} +12.2128 q^{69} -16.5631 q^{70} +11.0433 q^{71} +2.90024 q^{72} -8.64299 q^{73} -4.54725 q^{74} +4.70305 q^{75} -14.3865 q^{76} -4.40298 q^{77} -13.8493 q^{78} -15.3063 q^{79} +13.5237 q^{80} -7.64442 q^{81} -20.8870 q^{82} +10.7441 q^{83} -34.0184 q^{84} +3.96639 q^{85} +8.19760 q^{86} -0.780268 q^{87} +7.27174 q^{88} +16.0443 q^{89} +1.50035 q^{90} -14.5091 q^{91} -36.2756 q^{92} +6.69967 q^{93} -18.1778 q^{94} -4.33525 q^{95} +15.9161 q^{96} -13.9514 q^{97} -32.2769 q^{98} +0.398838 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) $ 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9 - 14 * q^10 - 107 * q^11 - 50 * q^12 - 24 * q^13 - 17 * q^14 - 47 * q^15 + 63 * q^16 + 25 * q^17 - 37 * q^18 - 55 * q^19 - 31 * q^20 + 15 * q^21 + 3 * q^22 - 38 * q^23 + 4 * q^24 + 62 * q^25 - 16 * q^26 - 57 * q^27 - 101 * q^28 + 27 * q^29 - 14 * q^30 - 112 * q^31 - 4 * q^32 + 18 * q^33 - 66 * q^34 + 8 * q^35 + 35 * q^36 - 60 * q^37 - 45 * q^38 - 58 * q^39 - 50 * q^40 - 14 * q^41 - 36 * q^42 - 78 * q^43 - 91 * q^44 - 68 * q^45 - 18 * q^46 - 109 * q^47 - 99 * q^48 + 61 * q^49 - 32 * q^50 - 10 * q^51 - 111 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 44 * q^56 + q^57 - 98 * q^58 - 48 * q^59 - 119 * q^60 - 30 * q^61 + 32 * q^62 - 126 * q^63 + 3 * q^64 + 43 * q^65 - 77 * q^67 + 53 * q^68 - 51 * q^69 - 87 * q^70 - 40 * q^71 - 82 * q^72 - 83 * q^73 + 11 * q^74 - 69 * q^75 - 108 * q^76 + 54 * q^77 - 53 * q^78 - 66 * q^79 - 96 * q^80 + 51 * q^81 - 133 * q^82 - 32 * q^83 + 27 * q^84 - 66 * q^85 - 46 * q^86 - 136 * q^87 + 3 * q^88 - 56 * q^89 + 9 * q^90 - 86 * q^91 - 94 * q^92 - 33 * q^93 - 93 * q^94 - 25 * q^95 - 4 * q^96 - 109 * q^97 - 38 * q^98 - 95 * 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 $

$2$	−2.60586	−1.84262	−0.921312	−	0.388824i	$-0.872882\pi$
$2$	−2.60586	−1.84262	−0.921312	+	0.388824i	$0.872882\pi$
$3$	−1.61281	−0.931157	−0.465579	−	0.885006i	$-0.654154\pi$
$3$	−1.61281	−0.931157	−0.465579	+	0.885006i	$0.654154\pi$
$4$	4.79053	2.39526
$5$	1.44359	0.645592	0.322796	−	0.946469i	$-0.395377\pi$
$5$	1.44359	0.645592	0.322796	+	0.946469i	$0.395377\pi$
$6$	4.20277	1.71577
$7$	4.40298	1.66417	0.832086	−	0.554647i	$-0.187147\pi$
$7$	4.40298	1.66417	0.832086	+	0.554647i	$0.187147\pi$
$8$	−7.27174	−2.57095
$9$	−0.398838	−0.132946
$10$	−3.76179	−1.18958
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−7.72622	−2.23037
$13$	−3.29528	−0.913947	−0.456973	−	0.889480i	$-0.651067\pi$
$13$	−3.29528	−0.913947	−0.456973	+	0.889480i	$0.651067\pi$
$14$	−11.4736	−3.06644
$15$	−2.32824	−0.601148
$16$	9.36812	2.34203
$17$	2.74759	0.666389	0.333195	−	0.942858i	$-0.391873\pi$
$17$	2.74759	0.666389	0.333195	+	0.942858i	$0.391873\pi$
$18$	1.03932	0.244969
$19$	−3.00310	−0.688959	−0.344480	−	0.938794i	$-0.611945\pi$
$19$	−3.00310	−0.688959	−0.344480	+	0.938794i	$0.611945\pi$
$20$	6.91555	1.54636
$21$	−7.10119	−1.54961
$22$	2.60586	0.555572
$23$	−7.57236	−1.57895	−0.789473	−	0.613786i	$-0.789646\pi$
$23$	−7.57236	−1.57895	−0.789473	+	0.613786i	$0.789646\pi$
$24$	11.7280	2.39396
$25$	−2.91605	−0.583211
$26$	8.58706	1.68406
$27$	5.48169	1.05495
$28$	21.0926	3.98613
$29$	0.483793	0.0898382	0.0449191	−	0.998991i	$-0.485697\pi$
$29$	0.483793	0.0898382	0.0449191	+	0.998991i	$0.485697\pi$
$30$	6.06707	1.10769
$31$	−4.15403	−0.746086	−0.373043	−	0.927814i	$-0.621686\pi$
$31$	−4.15403	−0.746086	−0.373043	+	0.927814i	$0.621686\pi$
$32$	−9.86855	−1.74453
$33$	1.61281	0.280755
$34$	−7.15986	−1.22791
$35$	6.35609	1.07438
$36$	−1.91064	−0.318441
$37$	1.74501	0.286877	0.143439	−	0.989659i	$-0.454184\pi$
$37$	1.74501	0.286877	0.143439	+	0.989659i	$0.454184\pi$
$38$	7.82568	1.26949
$39$	5.31467	0.851028
$40$	−10.4974	−1.65978
$41$	8.01537	1.25179	0.625895	−	0.779907i	$-0.284734\pi$
$41$	8.01537	1.25179	0.625895	+	0.779907i	$0.284734\pi$
$42$	18.5047	2.85534
$43$	−3.14583	−0.479734	−0.239867	−	0.970806i	$-0.577104\pi$
$43$	−3.14583	−0.479734	−0.239867	+	0.970806i	$0.577104\pi$
$44$	−4.79053	−0.722200
$45$	−0.575757	−0.0858288
$46$	19.7325	2.90940
$47$	6.97573	1.01752	0.508758	−	0.860910i	$-0.330105\pi$
$47$	6.97573	1.01752	0.508758	+	0.860910i	$0.330105\pi$
$48$	−15.1090	−2.18080
$49$	12.3863	1.76947
$50$	7.59884	1.07464
$51$	−4.43135	−0.620513
$52$	−15.7861	−2.18914
$53$	12.9002	1.77198	0.885991	−	0.463702i	$-0.153479\pi$
$53$	12.9002	1.77198	0.885991	+	0.463702i	$0.153479\pi$
$54$	−14.2845	−1.94388
$55$	−1.44359	−0.194653
$56$	−32.0174	−4.27850
$57$	4.84344	0.641530
$58$	−1.26070	−0.165538
$59$	−0.751630	−0.0978539	−0.0489270	−	0.998802i	$-0.515580\pi$
$59$	−0.751630	−0.0978539	−0.0489270	+	0.998802i	$0.515580\pi$
$60$	−11.1535	−1.43991
$61$	−7.28552	−0.932816	−0.466408	−	0.884570i	$-0.654452\pi$
$61$	−7.28552	−0.932816	−0.466408	+	0.884570i	$0.654452\pi$
$62$	10.8248	1.37476
$63$	−1.75608	−0.221245
$64$	6.97989	0.872486
$65$	−4.75703	−0.590037
$66$	−4.20277	−0.517325
$67$	5.98665	0.731386	0.365693	−	0.930735i	$-0.380832\pi$
$67$	5.98665	0.731386	0.365693	+	0.930735i	$0.380832\pi$
$68$	13.1624	1.59618
$69$	12.2128	1.47025
$70$	−16.5631	−1.97967
$71$	11.0433	1.31060	0.655302	−	0.755367i	$-0.272541\pi$
$71$	11.0433	1.31060	0.655302	+	0.755367i	$0.272541\pi$
$72$	2.90024	0.341797
$73$	−8.64299	−1.01159	−0.505793	−	0.862655i	$-0.668800\pi$
$73$	−8.64299	−1.01159	−0.505793	+	0.862655i	$0.668800\pi$
$74$	−4.54725	−0.528607
$75$	4.70305	0.543061
$76$	−14.3865	−1.65024
$77$	−4.40298	−0.501767
$78$	−13.8493	−1.56813
$79$	−15.3063	−1.72209	−0.861046	−	0.508527i	$-0.830190\pi$
$79$	−15.3063	−1.72209	−0.861046	+	0.508527i	$0.830190\pi$
$80$	13.5237	1.51200
$81$	−7.64442	−0.849380
$82$	−20.8870	−2.30658
$83$	10.7441	1.17932	0.589661	−	0.807651i	$-0.299261\pi$
$83$	10.7441	1.17932	0.589661	+	0.807651i	$0.299261\pi$
$84$	−34.0184	−3.71172
$85$	3.96639	0.430216
$86$	8.19760	0.883970
$87$	−0.780268	−0.0836535
$88$	7.27174	0.775170
$89$	16.0443	1.70069	0.850344	−	0.526227i	$-0.176394\pi$
$89$	16.0443	1.70069	0.850344	+	0.526227i	$0.176394\pi$
$90$	1.50035	0.158150
$91$	−14.5091	−1.52096
$92$	−36.2756	−3.78199
$93$	6.69967	0.694724
$94$	−18.1778	−1.87490
$95$	−4.33525	−0.444787
$96$	15.9161	1.62443
$97$	−13.9514	−1.41655	−0.708275	−	0.705937i	$-0.750526\pi$
$97$	−13.9514	−1.41655	−0.708275	+	0.705937i	$0.750526\pi$
$98$	−32.2769	−3.26046
$99$	0.398838	0.0400847
$100$	−13.9694	−1.39694
$101$	6.15078	0.612025	0.306013	−	0.952027i	$-0.401005\pi$
$101$	6.15078	0.612025	0.306013	+	0.952027i	$0.401005\pi$
$102$	11.5475	1.14337
$103$	−1.36516	−0.134513	−0.0672567	−	0.997736i	$-0.521425\pi$
$103$	−1.36516	−0.134513	−0.0672567	+	0.997736i	$0.521425\pi$
$104$	23.9624	2.34971
$105$	−10.2512	−1.00041
$106$	−33.6162	−3.26510
$107$	−10.3527	−1.00083	−0.500415	−	0.865786i	$-0.666819\pi$
$107$	−10.3527	−1.00083	−0.500415	+	0.865786i	$0.666819\pi$
$108$	26.2602	2.52689
$109$	8.08618	0.774516	0.387258	−	0.921971i	$-0.373422\pi$
$109$	8.08618	0.774516	0.387258	+	0.921971i	$0.373422\pi$
$110$	3.76179	0.358673
$111$	−2.81437	−0.267128
$112$	41.2477	3.89754
$113$	−17.8901	−1.68296	−0.841478	−	0.540291i	$-0.818314\pi$
$113$	−17.8901	−1.68296	−0.841478	+	0.540291i	$0.818314\pi$
$114$	−12.6214	−1.18210
$115$	−10.9314	−1.01935
$116$	2.31763	0.215186
$117$	1.31428	0.121505
$118$	1.95865	0.180308
$119$	12.0976	1.10899
$120$	16.9303	1.54552
$121$	1.00000	0.0909091
$122$	18.9851	1.71883
$123$	−12.9273	−1.16561
$124$	−19.9000	−1.78707
$125$	−11.4275	−1.02211
$126$	4.57610	0.407671
$127$	−2.49127	−0.221064	−0.110532	−	0.993873i	$-0.535255\pi$
$127$	−2.49127	−0.221064	−0.110532	+	0.993873i	$0.535255\pi$
$128$	1.54847	0.136867
$129$	5.07363	0.446708
$130$	12.3962	1.08722
$131$	2.85476	0.249421	0.124711	−	0.992193i	$-0.460200\pi$
$131$	2.85476	0.249421	0.124711	+	0.992193i	$0.460200\pi$
$132$	7.72622	0.672481
$133$	−13.2226	−1.14655
$134$	−15.6004	−1.34767
$135$	7.91329	0.681068
$136$	−19.9798	−1.71325
$137$	−9.30742	−0.795187	−0.397593	−	0.917562i	$-0.630154\pi$
$137$	−9.30742	−0.795187	−0.397593	+	0.917562i	$0.630154\pi$
$138$	−31.8249	−2.70911
$139$	−14.7190	−1.24845	−0.624224	−	0.781246i	$-0.714585\pi$
$139$	−14.7190	−1.24845	−0.624224	+	0.781246i	$0.714585\pi$
$140$	30.4491	2.57342
$141$	−11.2505	−0.947467
$142$	−28.7775	−2.41495
$143$	3.29528	0.275565
$144$	−3.73636	−0.311363
$145$	0.698398	0.0579988
$146$	22.5225	1.86397
$147$	−19.9767	−1.64765
$148$	8.35950	0.687147
$149$	1.13233	0.0927638	0.0463819	−	0.998924i	$-0.485231\pi$
$149$	1.13233	0.0927638	0.0463819	+	0.998924i	$0.485231\pi$
$150$	−12.2555	−1.00066
$151$	13.8507	1.12716	0.563578	−	0.826063i	$-0.309424\pi$
$151$	13.8507	1.12716	0.563578	+	0.826063i	$0.309424\pi$
$152$	21.8378	1.77128
$153$	−1.09584	−0.0885937
$154$	11.4736	0.924567
$155$	−5.99671	−0.481667
$156$	25.4601	2.03844
$157$	4.92869	0.393352	0.196676	−	0.980469i	$-0.436985\pi$
$157$	4.92869	0.393352	0.196676	+	0.980469i	$0.436985\pi$
$158$	39.8861	3.17317
$159$	−20.8056	−1.64999
$160$	−14.2461	−1.12626
$161$	−33.3410	−2.62764
$162$	19.9203	1.56509
$163$	−21.6710	−1.69741	−0.848704	−	0.528869i	$-0.822616\pi$
$163$	−21.6710	−1.69741	−0.848704	+	0.528869i	$0.822616\pi$
$164$	38.3979	2.99837
$165$	2.32824	0.181253
$166$	−27.9978	−2.17305
$167$	−12.4207	−0.961139	−0.480570	−	0.876957i	$-0.659570\pi$
$167$	−12.4207	−0.961139	−0.480570	+	0.876957i	$0.659570\pi$
$168$	51.6380	3.98396
$169$	−2.14112	−0.164702
$170$	−10.3359	−0.792726
$171$	1.19775	0.0915943
$172$	−15.0702	−1.14909
$173$	2.74835	0.208953	0.104476	−	0.994527i	$-0.466683\pi$
$173$	2.74835	0.208953	0.104476	+	0.994527i	$0.466683\pi$
$174$	2.03327	0.154142
$175$	−12.8393	−0.970563
$176$	−9.36812	−0.706148
$177$	1.21224	0.0911174
$178$	−41.8092	−3.13373
$179$	−14.5492	−1.08746	−0.543729	−	0.839261i	$-0.682988\pi$
$179$	−14.5492	−1.08746	−0.543729	+	0.839261i	$0.682988\pi$
$180$	−2.75818	−0.205583
$181$	−10.0340	−0.745824	−0.372912	−	0.927867i	$-0.621641\pi$
$181$	−10.0340	−0.745824	−0.372912	+	0.927867i	$0.621641\pi$
$182$	37.8087	2.80257
$183$	11.7502	0.868598
$184$	55.0642	4.05939
$185$	2.51907	0.185206
$186$	−17.4584	−1.28011
$187$	−2.74759	−0.200924
$188$	33.4175	2.43722
$189$	24.1358	1.75562
$190$	11.2971	0.819575
$191$	8.93786	0.646721	0.323361	−	0.946276i	$-0.395187\pi$
$191$	8.93786	0.646721	0.323361	+	0.946276i	$0.395187\pi$
$192$	−11.2572	−0.812421
$193$	7.66180	0.551508	0.275754	−	0.961228i	$-0.411072\pi$
$193$	7.66180	0.551508	0.275754	+	0.961228i	$0.411072\pi$
$194$	36.3554	2.61017
$195$	7.67219	0.549417
$196$	59.3368	4.23834
$197$	−13.7433	−0.979170	−0.489585	−	0.871956i	$-0.662852\pi$
$197$	−13.7433	−0.979170	−0.489585	+	0.871956i	$0.662852\pi$
$198$	−1.03932	−0.0738610
$199$	20.4215	1.44764	0.723820	−	0.689989i	$-0.242385\pi$
$199$	20.4215	1.44764	0.723820	+	0.689989i	$0.242385\pi$
$200$	21.2048	1.49941
$201$	−9.65535	−0.681036
$202$	−16.0281	−1.12773
$203$	2.13013	0.149506
$204$	−21.2285	−1.48629
$205$	11.5709	0.808146
$206$	3.55743	0.247858
$207$	3.02014	0.209914
$208$	−30.8706	−2.14049
$209$	3.00310	0.207729
$210$	26.7132	1.84339
$211$	26.8895	1.85115	0.925573	−	0.378569i	$-0.123584\pi$
$211$	26.8895	1.85115	0.925573	+	0.378569i	$0.123584\pi$
$212$	61.7989	4.24437
$213$	−17.8108	−1.22038
$214$	26.9776	1.84415
$215$	−4.54128	−0.309713
$216$	−39.8614	−2.71223
$217$	−18.2901	−1.24162
$218$	−21.0715	−1.42714
$219$	13.9395	0.941946
$220$	−6.91555	−0.466246
$221$	−9.05409	−0.609044
$222$	7.33386	0.492216
$223$	−14.9407	−1.00051	−0.500253	−	0.865879i	$-0.666760\pi$
$223$	−14.9407	−1.00051	−0.500253	+	0.865879i	$0.666760\pi$
$224$	−43.4511	−2.90320
$225$	1.16303	0.0775355
$226$	46.6191	3.10106
$227$	15.8902	1.05467	0.527335	−	0.849657i	$-0.323191\pi$
$227$	15.8902	1.05467	0.527335	+	0.849657i	$0.323191\pi$
$228$	23.2027	1.53663
$229$	13.2450	0.875256	0.437628	−	0.899156i	$-0.355819\pi$
$229$	13.2450	0.875256	0.437628	+	0.899156i	$0.355819\pi$
$230$	28.4856	1.87829
$231$	7.10119	0.467224
$232$	−3.51802	−0.230969
$233$	−15.7999	−1.03508	−0.517541	−	0.855658i	$-0.673153\pi$
$233$	−15.7999	−1.03508	−0.517541	+	0.855658i	$0.673153\pi$
$234$	−3.42484	−0.223889
$235$	10.0701	0.656900
$236$	−3.60071	−0.234386
$237$	24.6862	1.60354
$238$	−31.5247	−2.04345
$239$	5.63506	0.364502	0.182251	−	0.983252i	$-0.441662\pi$
$239$	5.63506	0.364502	0.182251	+	0.983252i	$0.441662\pi$
$240$	−21.8112	−1.40791
$241$	13.2968	0.856523	0.428262	−	0.903655i	$-0.359126\pi$
$241$	13.2968	0.856523	0.428262	+	0.903655i	$0.359126\pi$
$242$	−2.60586	−0.167511
$243$	−4.11605	−0.264045
$244$	−34.9015	−2.23434
$245$	17.8807	1.14235
$246$	33.6868	2.14779
$247$	9.89608	0.629672
$248$	30.2071	1.91815
$249$	−17.3283	−1.09813
$250$	29.7786	1.88336
$251$	−20.2281	−1.27678	−0.638392	−	0.769711i	$-0.720400\pi$
$251$	−20.2281	−1.27678	−0.638392	+	0.769711i	$0.720400\pi$
$252$	−8.41253	−0.529940
$253$	7.57236	0.476070
$254$	6.49190	0.407338
$255$	−6.39705	−0.400599
$256$	−17.9949	−1.12468
$257$	0.989071	0.0616966	0.0308483	−	0.999524i	$-0.490179\pi$
$257$	0.989071	0.0616966	0.0308483	+	0.999524i	$0.490179\pi$
$258$	−13.2212	−0.823116
$259$	7.68323	0.477413
$260$	−22.7887	−1.41329
$261$	−0.192955	−0.0119436
$262$	−7.43911	−0.459590
$263$	−24.5897	−1.51627	−0.758133	−	0.652100i	$-0.773888\pi$
$263$	−24.5897	−1.51627	−0.758133	+	0.652100i	$0.773888\pi$
$264$	−11.7280	−0.721806
$265$	18.6226	1.14398
$266$	34.4564	2.11266
$267$	−25.8764	−1.58361
$268$	28.6792	1.75186
$269$	−22.8322	−1.39210	−0.696052	−	0.717991i	$-0.745062\pi$
$269$	−22.8322	−1.39210	−0.696052	+	0.717991i	$0.745062\pi$
$270$	−20.6210	−1.25495
$271$	11.8614	0.720529	0.360264	−	0.932850i	$-0.382686\pi$
$271$	11.8614	0.720529	0.360264	+	0.932850i	$0.382686\pi$
$272$	25.7398	1.56070
$273$	23.4004	1.41626
$274$	24.2539	1.46523
$275$	2.91605	0.175845
$276$	58.5057	3.52163
$277$	6.93362	0.416601	0.208300	−	0.978065i	$-0.433207\pi$
$277$	6.93362	0.416601	0.208300	+	0.978065i	$0.433207\pi$
$278$	38.3557	2.30042
$279$	1.65678	0.0991891
$280$	−46.2199	−2.76217
$281$	−3.20388	−0.191127	−0.0955636	−	0.995423i	$-0.530465\pi$
$281$	−3.20388	−0.191127	−0.0955636	+	0.995423i	$0.530465\pi$
$282$	29.3174	1.74583
$283$	−23.5158	−1.39787	−0.698935	−	0.715185i	$-0.746342\pi$
$283$	−23.5158	−1.39787	−0.698935	+	0.715185i	$0.746342\pi$
$284$	52.9035	3.13924
$285$	6.99194	0.414167
$286$	−8.58706	−0.507763
$287$	35.2916	2.08319
$288$	3.93595	0.231928
$289$	−9.45073	−0.555925
$290$	−1.81993	−0.106870
$291$	22.5010	1.31903
$292$	−41.4045	−2.42302
$293$	17.3333	1.01262	0.506310	−	0.862352i	$-0.331009\pi$
$293$	17.3333	1.01262	0.506310	+	0.862352i	$0.331009\pi$
$294$	52.0566	3.03600
$295$	−1.08504	−0.0631737
$296$	−12.6892	−0.737547
$297$	−5.48169	−0.318080
$298$	−2.95069	−0.170929
$299$	24.9530	1.44307
$300$	22.5301	1.30078
$301$	−13.8510	−0.798361
$302$	−36.0931	−2.07693
$303$	−9.92005	−0.569892
$304$	−28.1334	−1.61356
$305$	−10.5173	−0.602218
$306$	2.85562	0.163245
$307$	20.2511	1.15579	0.577896	−	0.816110i	$-0.303874\pi$
$307$	20.2511	1.15579	0.577896	+	0.816110i	$0.303874\pi$
$308$	−21.0926	−1.20186
$309$	2.20175	0.125253
$310$	15.6266	0.887532
$311$	−27.7547	−1.57382	−0.786912	−	0.617065i	$-0.788322\pi$
$311$	−27.7547	−1.57382	−0.786912	+	0.617065i	$0.788322\pi$
$312$	−38.6469	−2.18795
$313$	10.0658	0.568954	0.284477	−	0.958683i	$-0.408180\pi$
$313$	10.0658	0.568954	0.284477	+	0.958683i	$0.408180\pi$
$314$	−12.8435	−0.724800
$315$	−2.53505	−0.142834
$316$	−73.3252	−4.12487
$317$	−22.7396	−1.27718	−0.638592	−	0.769546i	$-0.720483\pi$
$317$	−22.7396	−1.27718	−0.638592	+	0.769546i	$0.720483\pi$
$318$	54.2167	3.04032
$319$	−0.483793	−0.0270872
$320$	10.0761	0.563270
$321$	16.6969	0.931930
$322$	86.8820	4.84175
$323$	−8.25131	−0.459115
$324$	−36.6208	−2.03449
$325$	9.60922	0.533024
$326$	56.4718	3.12768
$327$	−13.0415	−0.721196
$328$	−58.2857	−3.21829
$329$	30.7140	1.69332
$330$	−6.06707	−0.333981
$331$	−25.5982	−1.40701	−0.703503	−	0.710693i	$-0.748382\pi$
$331$	−25.5982	−1.40701	−0.703503	+	0.710693i	$0.748382\pi$
$332$	51.4701	2.82479
$333$	−0.695974	−0.0381391
$334$	32.3666	1.77102
$335$	8.64226	0.472177
$336$	−66.5247	−3.62922
$337$	17.6907	0.963675	0.481837	−	0.876261i	$-0.339970\pi$
$337$	17.6907	0.963675	0.481837	+	0.876261i	$0.339970\pi$
$338$	5.57947	0.303483
$339$	28.8533	1.56710
$340$	19.0011	1.03048
$341$	4.15403	0.224953
$342$	−3.12118	−0.168774
$343$	23.7157	1.28053
$344$	22.8757	1.23337
$345$	17.6302	0.949180
$346$	−7.16182	−0.385022
$347$	3.56808	0.191545	0.0957723	−	0.995403i	$-0.469468\pi$
$347$	3.56808	0.191545	0.0957723	+	0.995403i	$0.469468\pi$
$348$	−3.73790	−0.200372
$349$	9.82562	0.525953	0.262977	−	0.964802i	$-0.415296\pi$
$349$	9.82562	0.525953	0.262977	+	0.964802i	$0.415296\pi$
$350$	33.4576	1.78838
$351$	−18.0637	−0.964169
$352$	9.86855	0.525996
$353$	0.554466	0.0295113	0.0147556	−	0.999891i	$-0.495303\pi$
$353$	0.554466	0.0295113	0.0147556	+	0.999891i	$0.495303\pi$
$354$	−3.15893	−0.167895
$355$	15.9420	0.846116
$356$	76.8605	4.07360
$357$	−19.5112	−1.03264
$358$	37.9132	2.00378
$359$	−3.89772	−0.205714	−0.102857	−	0.994696i	$-0.532798\pi$
$359$	−3.89772	−0.205714	−0.102857	+	0.994696i	$0.532798\pi$
$360$	4.18676	0.220661
$361$	−9.98136	−0.525335
$362$	26.1473	1.37427
$363$	−1.61281	−0.0846507
$364$	−69.5061	−3.64311
$365$	−12.4769	−0.653072
$366$	−30.6194	−1.60050
$367$	−34.8653	−1.81995	−0.909976	−	0.414660i	$-0.863901\pi$
$367$	−34.8653	−1.81995	−0.909976	+	0.414660i	$0.863901\pi$
$368$	−70.9387	−3.69794
$369$	−3.19683	−0.166420
$370$	−6.56435	−0.341264
$371$	56.7995	2.94888
$372$	32.0950	1.66405
$373$	−16.9158	−0.875865	−0.437932	−	0.899008i	$-0.644289\pi$
$373$	−16.9158	−0.875865	−0.437932	+	0.899008i	$0.644289\pi$
$374$	7.15986	0.370227
$375$	18.4304	0.951744
$376$	−50.7257	−2.61598
$377$	−1.59424	−0.0821073
$378$	−62.8946	−3.23495
$379$	−9.01526	−0.463083	−0.231541	−	0.972825i	$-0.574377\pi$
$379$	−9.01526	−0.463083	−0.231541	+	0.972825i	$0.574377\pi$
$380$	−20.7681	−1.06538
$381$	4.01795	0.205846
$382$	−23.2909	−1.19166
$383$	−2.29390	−0.117213	−0.0586065	−	0.998281i	$-0.518666\pi$
$383$	−2.29390	−0.117213	−0.0586065	+	0.998281i	$0.518666\pi$
$384$	−2.49740	−0.127445
$385$	−6.35609	−0.323937
$386$	−19.9656	−1.01622
$387$	1.25468	0.0637787
$388$	−66.8346	−3.39301
$389$	−28.0152	−1.42043	−0.710215	−	0.703985i	$-0.751402\pi$
$389$	−28.0152	−1.42043	−0.710215	+	0.703985i	$0.751402\pi$
$390$	−19.9927	−1.01237
$391$	−20.8058	−1.05219
$392$	−90.0698	−4.54921
$393$	−4.60419	−0.232251
$394$	35.8132	1.80424
$395$	−22.0960	−1.11177
$396$	1.91064	0.0960134
$397$	−22.1283	−1.11059	−0.555294	−	0.831654i	$-0.687394\pi$
$397$	−22.1283	−1.11059	−0.555294	+	0.831654i	$0.687394\pi$
$398$	−53.2156	−2.66746
$399$	21.3256	1.06762
$400$	−27.3179	−1.36590
$401$	−15.4046	−0.769271	−0.384635	−	0.923069i	$-0.625673\pi$
$401$	−15.4046	−0.769271	−0.384635	+	0.923069i	$0.625673\pi$
$402$	25.1605	1.25489
$403$	13.6887	0.681883
$404$	29.4655	1.46596
$405$	−11.0354	−0.548353
$406$	−5.55084	−0.275484
$407$	−1.74501	−0.0864967
$408$	32.2237	1.59531
$409$	5.37292	0.265674	0.132837	−	0.991138i	$-0.457591\pi$
$409$	5.37292	0.265674	0.132837	+	0.991138i	$0.457591\pi$
$410$	−30.1522	−1.48911
$411$	15.0111	0.740444
$412$	−6.53985	−0.322195
$413$	−3.30942	−0.162846
$414$	−7.87008	−0.386793
$415$	15.5101	0.761361
$416$	32.5197	1.59441
$417$	23.7389	1.16250
$418$	−7.82568	−0.382767
$419$	33.7871	1.65061	0.825304	−	0.564689i	$-0.191004\pi$
$419$	33.7871	1.65061	0.825304	+	0.564689i	$0.191004\pi$
$420$	−49.1086	−2.39625
$421$	−15.0123	−0.731654	−0.365827	−	0.930683i	$-0.619214\pi$
$421$	−15.0123	−0.731654	−0.365827	+	0.930683i	$0.619214\pi$
$422$	−70.0703	−3.41097
$423$	−2.78219	−0.135274
$424$	−93.8071	−4.55568
$425$	−8.01213	−0.388646
$426$	46.4126	2.24870
$427$	−32.0780	−1.55237
$428$	−49.5947	−2.39725
$429$	−5.31467	−0.256595
$430$	11.8340	0.570684
$431$	−20.7063	−0.997389	−0.498694	−	0.866778i	$-0.666187\pi$
$431$	−20.7063	−0.997389	−0.498694	+	0.866778i	$0.666187\pi$
$432$	51.3531	2.47073
$433$	−26.9631	−1.29577	−0.647883	−	0.761740i	$-0.724345\pi$
$433$	−26.9631	−1.29577	−0.647883	+	0.761740i	$0.724345\pi$
$434$	47.6616	2.28783
$435$	−1.12638	−0.0540060
$436$	38.7371	1.85517
$437$	22.7406	1.08783
$438$	−36.3245	−1.73565
$439$	−5.05787	−0.241399	−0.120699	−	0.992689i	$-0.538514\pi$
$439$	−5.05787	−0.241399	−0.120699	+	0.992689i	$0.538514\pi$
$440$	10.4974	0.500444
$441$	−4.94011	−0.235243
$442$	23.5937	1.12224
$443$	−13.9840	−0.664401	−0.332201	−	0.943209i	$-0.607791\pi$
$443$	−13.9840	−0.664401	−0.332201	+	0.943209i	$0.607791\pi$
$444$	−13.4823	−0.639842
$445$	23.1613	1.09795
$446$	38.9335	1.84356
$447$	−1.82623	−0.0863777
$448$	30.7323	1.45197
$449$	25.4147	1.19939	0.599697	−	0.800227i	$-0.295288\pi$
$449$	25.4147	1.19939	0.599697	+	0.800227i	$0.295288\pi$
$450$	−3.03070	−0.142869
$451$	−8.01537	−0.377429
$452$	−85.7029	−4.03113
$453$	−22.3386	−1.04956
$454$	−41.4077	−1.94336
$455$	−20.9451	−0.981922
$456$	−35.2203	−1.64934
$457$	−9.17848	−0.429351	−0.214676	−	0.976685i	$-0.568869\pi$
$457$	−9.17848	−0.429351	−0.214676	+	0.976685i	$0.568869\pi$
$458$	−34.5147	−1.61277
$459$	15.0614	0.703008
$460$	−52.3670	−2.44162
$461$	−22.9335	−1.06812	−0.534060	−	0.845447i	$-0.679334\pi$
$461$	−22.9335	−1.06812	−0.534060	+	0.845447i	$0.679334\pi$
$462$	−18.5047	−0.860918
$463$	10.9303	0.507975	0.253988	−	0.967207i	$-0.418258\pi$
$463$	10.9303	0.507975	0.253988	+	0.967207i	$0.418258\pi$
$464$	4.53223	0.210404
$465$	9.67157	0.448508
$466$	41.1723	1.90727
$467$	−8.27185	−0.382775	−0.191388	−	0.981515i	$-0.561299\pi$
$467$	−8.27185	−0.382775	−0.191388	+	0.981515i	$0.561299\pi$
$468$	6.29611	0.291038
$469$	26.3591	1.21715
$470$	−26.2413	−1.21042
$471$	−7.94905	−0.366273
$472$	5.46566	0.251577
$473$	3.14583	0.144645
$474$	−64.3288	−2.95472
$475$	8.75722	0.401809
$476$	57.9540	2.65632
$477$	−5.14510	−0.235578
$478$	−14.6842	−0.671639
$479$	13.0728	0.597312	0.298656	−	0.954361i	$-0.403462\pi$
$479$	13.0728	0.597312	0.298656	+	0.954361i	$0.403462\pi$
$480$	22.9763	1.04872
$481$	−5.75028	−0.262190
$482$	−34.6497	−1.57825
$483$	53.7727	2.44674
$484$	4.79053	0.217751
$485$	−20.1401	−0.914513
$486$	10.7259	0.486536
$487$	−3.57946	−0.162201	−0.0811005	−	0.996706i	$-0.525843\pi$
$487$	−3.57946	−0.162201	−0.0811005	+	0.996706i	$0.525843\pi$
$488$	52.9784	2.39822
$489$	34.9513	1.58055
$490$	−46.5946	−2.10493
$491$	−6.20497	−0.280026	−0.140013	−	0.990150i	$-0.544714\pi$
$491$	−6.20497	−0.280026	−0.140013	+	0.990150i	$0.544714\pi$
$492$	−61.9286	−2.79196
$493$	1.32927	0.0598672
$494$	−25.7878	−1.16025
$495$	0.575757	0.0258784
$496$	−38.9155	−1.74736
$497$	48.6237	2.18107
$498$	45.1551	2.02345
$499$	−14.3053	−0.640393	−0.320196	−	0.947351i	$-0.603749\pi$
$499$	−14.3053	−0.640393	−0.320196	+	0.947351i	$0.603749\pi$
$500$	−54.7439	−2.44822
$501$	20.0322	0.894972
$502$	52.7116	2.35263
$503$	−36.7543	−1.63879	−0.819397	−	0.573227i	$-0.805691\pi$
$503$	−36.7543	−1.63879	−0.819397	+	0.573227i	$0.805691\pi$
$504$	12.7697	0.568809
$505$	8.87919	0.395119
$506$	−19.7325	−0.877218
$507$	3.45323	0.153363
$508$	−11.9345	−0.529507
$509$	38.2056	1.69343	0.846717	−	0.532043i	$-0.178576\pi$
$509$	38.2056	1.69343	0.846717	+	0.532043i	$0.178576\pi$
$510$	16.6698	0.738153
$511$	−38.0550	−1.68345
$512$	43.7953	1.93550
$513$	−16.4621	−0.726818
$514$	−2.57739	−0.113684
$515$	−1.97073	−0.0868408
$516$	24.3054	1.06998
$517$	−6.97573	−0.306792
$518$	−20.0215	−0.879692
$519$	−4.43256	−0.194568
$520$	34.5919	1.51695
$521$	−43.1633	−1.89102	−0.945509	−	0.325597i	$-0.894435\pi$
$521$	−43.1633	−1.89102	−0.945509	+	0.325597i	$0.894435\pi$
$522$	0.502815	0.0220076
$523$	5.87385	0.256846	0.128423	−	0.991720i	$-0.459009\pi$
$523$	5.87385	0.256846	0.128423	+	0.991720i	$0.459009\pi$
$524$	13.6758	0.597430
$525$	20.7074	0.903747
$526$	64.0774	2.79391
$527$	−11.4136	−0.497184
$528$	15.1090	0.657535
$529$	34.3406	1.49307
$530$	−48.5280	−2.10792
$531$	0.299778	0.0130093
$532$	−63.3434	−2.74628
$533$	−26.4129	−1.14407
$534$	67.4303	2.91800
$535$	−14.9450	−0.646128
$536$	−43.5334	−1.88036
$537$	23.4651	1.01259
$538$	59.4977	2.56513
$539$	−12.3863	−0.533514
$540$	37.9089	1.63134
$541$	−1.95968	−0.0842533	−0.0421267	−	0.999112i	$-0.513413\pi$
$541$	−1.95968	−0.0842533	−0.0421267	+	0.999112i	$0.513413\pi$
$542$	−30.9092	−1.32766
$543$	16.1830	0.694479
$544$	−27.1148	−1.16254
$545$	11.6731	0.500021
$546$	−60.9783	−2.60963
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−44.5875	−1.90468
$549$	2.90574	0.124014
$550$	−7.59884	−0.324016
$551$	−1.45288	−0.0618949
$552$	−88.8082	−3.77993
$553$	−67.3933	−2.86586
$554$	−18.0681	−0.767639
$555$	−4.06278	−0.172456
$556$	−70.5117	−2.99036
$557$	32.8457	1.39172	0.695859	−	0.718178i	$-0.255024\pi$
$557$	32.8457	1.39172	0.695859	+	0.718178i	$0.255024\pi$
$558$	−4.31736	−0.182768
$559$	10.3664	0.438452
$560$	59.5446	2.51622
$561$	4.43135	0.187092
$562$	8.34887	0.352176
$563$	−0.407556	−0.0171764	−0.00858822	−	0.999963i	$-0.502734\pi$
$563$	−0.407556	−0.0171764	−0.00858822	+	0.999963i	$0.502734\pi$
$564$	−53.8961	−2.26943
$565$	−25.8259	−1.08650
$566$	61.2790	2.57575
$567$	−33.6582	−1.41351
$568$	−80.3044	−3.36950
$569$	21.4927	0.901022	0.450511	−	0.892771i	$-0.351242\pi$
$569$	21.4927	0.901022	0.450511	+	0.892771i	$0.351242\pi$
$570$	−18.2200	−0.763153
$571$	28.0013	1.17182	0.585908	−	0.810377i	$-0.300738\pi$
$571$	28.0013	1.17182	0.585908	+	0.810377i	$0.300738\pi$
$572$	15.7861	0.660052
$573$	−14.4151	−0.602199
$574$	−91.9650	−3.83855
$575$	22.0814	0.920858
$576$	−2.78384	−0.115993
$577$	10.3817	0.432194	0.216097	−	0.976372i	$-0.430667\pi$
$577$	10.3817	0.432194	0.216097	+	0.976372i	$0.430667\pi$
$578$	24.6273	1.02436
$579$	−12.3570	−0.513541
$580$	3.34570	0.138923
$581$	47.3062	1.96259
$582$	−58.6345	−2.43048
$583$	−12.9002	−0.534273
$584$	62.8496	2.60074
$585$	1.89728	0.0784429
$586$	−45.1681	−1.86588
$587$	−29.9415	−1.23582	−0.617910	−	0.786249i	$-0.712020\pi$
$587$	−29.9415	−1.23582	−0.617910	+	0.786249i	$0.712020\pi$
$588$	−95.6991	−3.94656
$589$	12.4750	0.514023
$590$	2.82748	0.116405
$591$	22.1654	0.911761
$592$	16.3474	0.671875
$593$	−23.4960	−0.964864	−0.482432	−	0.875934i	$-0.660246\pi$
$593$	−23.4960	−0.964864	−0.482432	+	0.875934i	$0.660246\pi$
$594$	14.2845	0.586101
$595$	17.4640	0.715953
$596$	5.42445	0.222194
$597$	−32.9360	−1.34798
$598$	−65.0242	−2.65904
$599$	−8.00406	−0.327037	−0.163518	−	0.986540i	$-0.552284\pi$
$599$	−8.00406	−0.327037	−0.163518	+	0.986540i	$0.552284\pi$
$600$	−34.1993	−1.39618
$601$	39.1080	1.59525	0.797624	−	0.603156i	$-0.206090\pi$
$601$	39.1080	1.59525	0.797624	+	0.603156i	$0.206090\pi$
$602$	36.0939	1.47108
$603$	−2.38770	−0.0972348
$604$	66.3523	2.69984
$605$	1.44359	0.0586902
$606$	25.8503	1.05010
$607$	−32.8808	−1.33459	−0.667295	−	0.744793i	$-0.732548\pi$
$607$	−32.8808	−1.33459	−0.667295	+	0.744793i	$0.732548\pi$
$608$	29.6363	1.20191
$609$	−3.43551	−0.139214
$610$	27.4066	1.10966
$611$	−22.9870	−0.929955
$612$	−5.24967	−0.212205
$613$	−11.6518	−0.470610	−0.235305	−	0.971922i	$-0.575609\pi$
$613$	−11.6518	−0.470610	−0.235305	+	0.971922i	$0.575609\pi$
$614$	−52.7717	−2.12969
$615$	−18.6617	−0.752511
$616$	32.0174	1.29002
$617$	18.1035	0.728819	0.364409	−	0.931239i	$-0.381271\pi$
$617$	18.1035	0.728819	0.364409	+	0.931239i	$0.381271\pi$
$618$	−5.73746	−0.230795
$619$	39.8998	1.60371	0.801853	−	0.597521i	$-0.203848\pi$
$619$	39.8998	1.60371	0.801853	+	0.597521i	$0.203848\pi$
$620$	−28.7274	−1.15372
$621$	−41.5093	−1.66571
$622$	72.3250	2.89997
$623$	70.6426	2.83024
$624$	49.7884	1.99313
$625$	−1.91636	−0.0766543
$626$	−26.2302	−1.04837
$627$	−4.84344	−0.193428
$628$	23.6110	0.942183
$629$	4.79457	0.191172
$630$	6.60600	0.263189
$631$	−30.1259	−1.19929	−0.599646	−	0.800265i	$-0.704692\pi$
$631$	−30.1259	−1.19929	−0.599646	+	0.800265i	$0.704692\pi$
$632$	111.303	4.42741
$633$	−43.3676	−1.72371
$634$	59.2563	2.35337
$635$	−3.59636	−0.142717
$636$	−99.6700	−3.95217
$637$	−40.8162	−1.61720
$638$	1.26070	0.0499116
$639$	−4.40450	−0.174239
$640$	2.23536	0.0883603
$641$	25.9519	1.02504	0.512519	−	0.858676i	$-0.328713\pi$
$641$	25.9519	1.02504	0.512519	+	0.858676i	$0.328713\pi$
$642$	−43.5099	−1.71720
$643$	7.78735	0.307103	0.153552	−	0.988141i	$-0.450929\pi$
$643$	7.78735	0.307103	0.153552	+	0.988141i	$0.450929\pi$
$644$	−159.721	−6.29388
$645$	7.32423	0.288391
$646$	21.5018	0.845977
$647$	−19.7736	−0.777381	−0.388690	−	0.921368i	$-0.627072\pi$
$647$	−19.7736	−0.777381	−0.388690	+	0.921368i	$0.627072\pi$
$648$	55.5882	2.18371
$649$	0.751630	0.0295041
$650$	−25.0403	−0.982162
$651$	29.4986	1.15614
$652$	−103.816	−4.06574
$653$	−29.9752	−1.17302	−0.586510	−	0.809942i	$-0.699498\pi$
$653$	−29.9752	−1.17302	−0.586510	+	0.809942i	$0.699498\pi$
$654$	33.9844	1.32889
$655$	4.12109	0.161024
$656$	75.0889	2.93173
$657$	3.44715	0.134486
$658$	−80.0366	−3.12015
$659$	−23.7798	−0.926328	−0.463164	−	0.886273i	$-0.653286\pi$
$659$	−23.7798	−0.926328	−0.463164	+	0.886273i	$0.653286\pi$
$660$	11.1535	0.434149
$661$	−7.50497	−0.291910	−0.145955	−	0.989291i	$-0.546625\pi$
$661$	−7.50497	−0.291910	−0.145955	+	0.989291i	$0.546625\pi$
$662$	66.7055	2.59258
$663$	14.6026	0.567116
$664$	−78.1286	−3.03198
$665$	−19.0880	−0.740202
$666$	1.81361	0.0702761
$667$	−3.66346	−0.141850
$668$	−59.5015	−2.30218
$669$	24.0966	0.931629
$670$	−22.5206	−0.870045
$671$	7.28552	0.281254
$672$	70.0784	2.70333
$673$	−40.8851	−1.57601	−0.788003	−	0.615671i	$-0.788885\pi$
$673$	−40.8851	−1.57601	−0.788003	+	0.615671i	$0.788885\pi$
$674$	−46.0996	−1.77569
$675$	−15.9849	−0.615259
$676$	−10.2571	−0.394504
$677$	−0.244609	−0.00940110	−0.00470055	−	0.999989i	$-0.501496\pi$
$677$	−0.244609	−0.00940110	−0.00470055	+	0.999989i	$0.501496\pi$
$678$	−75.1879	−2.88757
$679$	−61.4278	−2.35738
$680$	−28.8426	−1.10606
$681$	−25.6279	−0.982064
$682$	−10.8248	−0.414505
$683$	20.3182	0.777456	0.388728	−	0.921353i	$-0.372915\pi$
$683$	20.3182	0.777456	0.388728	+	0.921353i	$0.372915\pi$
$684$	5.73786	0.219393
$685$	−13.4361	−0.513366
$686$	−61.7998	−2.35953
$687$	−21.3617	−0.815001
$688$	−29.4705	−1.12355
$689$	−42.5099	−1.61950
$690$	−45.9420	−1.74898
$691$	−4.54904	−0.173054	−0.0865269	−	0.996250i	$-0.527577\pi$
$691$	−4.54904	−0.173054	−0.0865269	+	0.996250i	$0.527577\pi$
$692$	13.1660	0.500497
$693$	1.75608	0.0667078
$694$	−9.29794	−0.352945
$695$	−21.2481	−0.805988
$696$	5.67391	0.215069
$697$	22.0230	0.834180
$698$	−25.6042	−0.969134
$699$	25.4822	0.963825
$700$	−61.5072	−2.32476
$701$	−19.2573	−0.727339	−0.363669	−	0.931528i	$-0.618476\pi$
$701$	−19.2573	−0.727339	−0.363669	+	0.931528i	$0.618476\pi$
$702$	47.0715	1.77660
$703$	−5.24043	−0.197647
$704$	−6.97989	−0.263064
$705$	−16.2412	−0.611677
$706$	−1.44486	−0.0543782
$707$	27.0818	1.01852
$708$	5.80726	0.218250
$709$	−0.169726	−0.00637420	−0.00318710	−	0.999995i	$-0.501014\pi$
$709$	−0.169726	−0.00637420	−0.00318710	+	0.999995i	$0.501014\pi$
$710$	−41.5428	−1.55907
$711$	6.10472	0.228945
$712$	−116.670	−4.37238
$713$	31.4558	1.17803
$714$	50.8435	1.90277
$715$	4.75703	0.177903
$716$	−69.6983	−2.60475
$717$	−9.08829	−0.339408
$718$	10.1569	0.379053
$719$	46.4496	1.73228	0.866138	−	0.499805i	$-0.166595\pi$
$719$	46.4496	1.73228	0.866138	+	0.499805i	$0.166595\pi$
$720$	−5.39376	−0.201014
$721$	−6.01079	−0.223853
$722$	26.0101	0.967995
$723$	−21.4453	−0.797558
$724$	−48.0683	−1.78645
$725$	−1.41077	−0.0523946
$726$	4.20277	0.155979
$727$	7.39585	0.274297	0.137148	−	0.990551i	$-0.456206\pi$
$727$	7.39585	0.274297	0.137148	+	0.990551i	$0.456206\pi$
$728$	105.506	3.91032
$729$	29.5717	1.09525
$730$	32.5132	1.20337
$731$	−8.64346	−0.319690
$732$	56.2896	2.08052
$733$	−12.9717	−0.479121	−0.239561	−	0.970881i	$-0.577003\pi$
$733$	−12.9717	−0.479121	−0.239561	+	0.970881i	$0.577003\pi$
$734$	90.8542	3.35349
$735$	−28.8382	−1.06371
$736$	74.7282	2.75452
$737$	−5.98665	−0.220521
$738$	8.33051	0.306650
$739$	19.0930	0.702346	0.351173	−	0.936311i	$-0.385783\pi$
$739$	19.0930	0.702346	0.351173	+	0.936311i	$0.385783\pi$
$740$	12.0677	0.443616
$741$	−15.9605	−0.586324
$742$	−148.012	−5.43368
$743$	−27.2607	−1.00010	−0.500048	−	0.865997i	$-0.666684\pi$
$743$	−27.2607	−1.00010	−0.500048	+	0.865997i	$0.666684\pi$
$744$	−48.7183	−1.78610
$745$	1.63461	0.0598876
$746$	44.0802	1.61389
$747$	−4.28516	−0.156786
$748$	−13.1624	−0.481266
$749$	−45.5826	−1.66555
$750$	−48.0272	−1.75371
$751$	−33.5125	−1.22289	−0.611444	−	0.791288i	$-0.709411\pi$
$751$	−33.5125	−1.22289	−0.611444	+	0.791288i	$0.709411\pi$
$752$	65.3495	2.38305
$753$	32.6241	1.18889
$754$	4.15436	0.151293
$755$	19.9947	0.727683
$756$	115.623	4.20517
$757$	12.6659	0.460350	0.230175	−	0.973149i	$-0.426070\pi$
$757$	12.6659	0.460350	0.230175	+	0.973149i	$0.426070\pi$
$758$	23.4925	0.853288
$759$	−12.2128	−0.443296
$760$	31.5248	1.14352
$761$	−15.5936	−0.565269	−0.282634	−	0.959228i	$-0.591208\pi$
$761$	−15.5936	−0.565269	−0.282634	+	0.959228i	$0.591208\pi$
$762$	−10.4702	−0.379296
$763$	35.6033	1.28893
$764$	42.8171	1.54907
$765$	−1.58195	−0.0571954
$766$	5.97760	0.215980
$767$	2.47683	0.0894333
$768$	29.0224	1.04725
$769$	−24.3325	−0.877454	−0.438727	−	0.898620i	$-0.644570\pi$
$769$	−24.3325	−0.877454	−0.438727	+	0.898620i	$0.644570\pi$
$770$	16.5631	0.596893
$771$	−1.59519	−0.0574492
$772$	36.7041	1.32101
$773$	3.92471	0.141162	0.0705810	−	0.997506i	$-0.477515\pi$
$773$	3.92471	0.141162	0.0705810	+	0.997506i	$0.477515\pi$
$774$	−3.26951	−0.117520
$775$	12.1134	0.435126
$776$	101.451	3.64188
$777$	−12.3916	−0.444546
$778$	73.0039	2.61732
$779$	−24.0710	−0.862433
$780$	36.7539	1.31600
$781$	−11.0433	−0.395162
$782$	54.2170	1.93880
$783$	2.65200	0.0947749
$784$	116.036	4.14414
$785$	7.11499	0.253945
$786$	11.9979	0.427951
$787$	27.5184	0.980923	0.490462	−	0.871463i	$-0.336828\pi$
$787$	27.5184	0.980923	0.490462	+	0.871463i	$0.336828\pi$
$788$	−65.8377	−2.34537
$789$	39.6585	1.41188
$790$	57.5791	2.04857
$791$	−78.7697	−2.80073
$792$	−2.90024	−0.103056
$793$	24.0078	0.852544
$794$	57.6634	2.04640
$795$	−30.0348	−1.06522
$796$	97.8297	3.46748
$797$	35.1940	1.24664	0.623318	−	0.781969i	$-0.285784\pi$
$797$	35.1940	1.24664	0.623318	+	0.781969i	$0.285784\pi$
$798$	−55.5716	−1.96721
$799$	19.1665	0.678061
$800$	28.7772	1.01743
$801$	−6.39906	−0.226100
$802$	40.1424	1.41748
$803$	8.64299	0.305005
$804$	−46.2542	−1.63126
$805$	−48.1306	−1.69638
$806$	−35.6709	−1.25645
$807$	36.8241	1.29627
$808$	−44.7269	−1.57349
$809$	50.3849	1.77144	0.885719	−	0.464222i	$-0.153666\pi$
$809$	50.3849	1.77144	0.885719	+	0.464222i	$0.153666\pi$
$810$	28.7567	1.01041
$811$	−8.94609	−0.314140	−0.157070	−	0.987587i	$-0.550205\pi$
$811$	−8.94609	−0.314140	−0.157070	+	0.987587i	$0.550205\pi$
$812$	10.2045	0.358107
$813$	−19.1302	−0.670926
$814$	4.54725	0.159381
$815$	−31.2841	−1.09583
$816$	−41.5134	−1.45326
$817$	9.44726	0.330518
$818$	−14.0011	−0.489537
$819$	5.78676	0.202206
$820$	55.4307	1.93572
$821$	17.0292	0.594322	0.297161	−	0.954827i	$-0.403960\pi$
$821$	17.0292	0.594322	0.297161	+	0.954827i	$0.403960\pi$
$822$	−39.1169	−1.36436
$823$	−1.35983	−0.0474009	−0.0237004	−	0.999719i	$-0.507545\pi$
$823$	−1.35983	−0.0474009	−0.0237004	+	0.999719i	$0.507545\pi$
$824$	9.92711	0.345827
$825$	−4.70305	−0.163739
$826$	8.62389	0.300064
$827$	18.7078	0.650533	0.325267	−	0.945622i	$-0.394546\pi$
$827$	18.7078	0.650533	0.325267	+	0.945622i	$0.394546\pi$
$828$	14.4681	0.502800
$829$	18.2335	0.633274	0.316637	−	0.948547i	$-0.397446\pi$
$829$	18.2335	0.633274	0.316637	+	0.948547i	$0.397446\pi$
$830$	−40.4172	−1.40290
$831$	−11.1826	−0.387921
$832$	−23.0007	−0.797405
$833$	34.0324	1.17915
$834$	−61.8605	−2.14205
$835$	−17.9303	−0.620504
$836$	14.3865	0.497566
$837$	−22.7711	−0.787084
$838$	−88.0446	−3.04145
$839$	4.45520	0.153811	0.0769054	−	0.997038i	$-0.475496\pi$
$839$	4.45520	0.153811	0.0769054	+	0.997038i	$0.475496\pi$
$840$	74.5440	2.57201
$841$	−28.7659	−0.991929
$842$	39.1200	1.34816
$843$	5.16725	0.177970
$844$	128.815	4.43399
$845$	−3.09090	−0.106330
$846$	7.25000	0.249260
$847$	4.40298	0.151288
$848$	120.851	4.15003
$849$	37.9266	1.30164
$850$	20.8785	0.716128
$851$	−13.2138	−0.452963
$852$	−85.3234	−2.92313
$853$	−3.68262	−0.126090	−0.0630452	−	0.998011i	$-0.520081\pi$
$853$	−3.68262	−0.126090	−0.0630452	+	0.998011i	$0.520081\pi$
$854$	83.5910	2.86043
$855$	1.72906	0.0591326
$856$	75.2819	2.57308
$857$	−18.7934	−0.641969	−0.320985	−	0.947084i	$-0.604014\pi$
$857$	−18.7934	−0.641969	−0.320985	+	0.947084i	$0.604014\pi$
$858$	13.8493	0.472808
$859$	19.9720	0.681435	0.340718	−	0.940166i	$-0.389330\pi$
$859$	19.9720	0.681435	0.340718	+	0.940166i	$0.389330\pi$
$860$	−21.7551	−0.741844
$861$	−56.9186	−1.93978
$862$	53.9579	1.83781
$863$	39.9712	1.36064	0.680319	−	0.732917i	$-0.261841\pi$
$863$	39.9712	1.36064	0.680319	+	0.732917i	$0.261841\pi$
$864$	−54.0963	−1.84039
$865$	3.96748	0.134898
$866$	70.2623	2.38761
$867$	15.2422	0.517654
$868$	−87.6195	−2.97400
$869$	15.3063	0.519230
$870$	2.93521	0.0995128
$871$	−19.7277	−0.668448
$872$	−58.8006	−1.99124
$873$	5.56434	0.188324
$874$	−59.2589	−2.00446
$875$	−50.3152	−1.70096
$876$	66.7777	2.25621
$877$	31.4307	1.06134	0.530669	−	0.847579i	$-0.321941\pi$
$877$	31.4307	1.06134	0.530669	+	0.847579i	$0.321941\pi$
$878$	13.1801	0.444807
$879$	−27.9553	−0.942908
$880$	−13.5237	−0.455884
$881$	−34.4976	−1.16225	−0.581127	−	0.813813i	$-0.697388\pi$
$881$	−34.4976	−1.16225	−0.581127	+	0.813813i	$0.697388\pi$
$882$	12.8733	0.433465
$883$	−28.9429	−0.974007	−0.487003	−	0.873400i	$-0.661910\pi$
$883$	−28.9429	−0.974007	−0.487003	+	0.873400i	$0.661910\pi$
$884$	−43.3739	−1.45882
$885$	1.74997	0.0588247
$886$	36.4405	1.22424
$887$	−43.7615	−1.46937	−0.734683	−	0.678410i	$-0.762669\pi$
$887$	−43.7615	−1.46937	−0.734683	+	0.678410i	$0.762669\pi$
$888$	20.4653	0.686772
$889$	−10.9690	−0.367889
$890$	−60.3552	−2.02311
$891$	7.64442	0.256098
$892$	−71.5741	−2.39648
$893$	−20.9489	−0.701027
$894$	4.75891	0.159162
$895$	−21.0030	−0.702054
$896$	6.81791	0.227770
$897$	−40.2446	−1.34373
$898$	−66.2272	−2.21003
$899$	−2.00969	−0.0670270
$900$	5.57154	0.185718
$901$	35.4446	1.18083
$902$	20.8870	0.695460
$903$	22.3391	0.743399
$904$	130.092	4.32680
$905$	−14.4850	−0.481498
$906$	58.2114	1.93395
$907$	−49.9250	−1.65773	−0.828866	−	0.559447i	$-0.811013\pi$
$907$	−49.9250	−1.65773	−0.828866	+	0.559447i	$0.811013\pi$
$908$	76.1225	2.52621
$909$	−2.45316	−0.0813662
$910$	54.5801	1.80931
$911$	31.9605	1.05890	0.529450	−	0.848341i	$-0.322398\pi$
$911$	31.9605	1.05890	0.529450	+	0.848341i	$0.322398\pi$
$912$	45.3739	1.50248
$913$	−10.7441	−0.355579
$914$	23.9179	0.791133
$915$	16.9624	0.560760
$916$	63.4507	2.09647
$917$	12.5695	0.415080
$918$	−39.2481	−1.29538
$919$	23.6306	0.779503	0.389751	−	0.920920i	$-0.372561\pi$
$919$	23.6306	0.779503	0.389751	+	0.920920i	$0.372561\pi$
$920$	79.4900	2.62071
$921$	−32.6612	−1.07622
$922$	59.7616	1.96814
$923$	−36.3909	−1.19782
$924$	34.0184	1.11912
$925$	−5.08853	−0.167310
$926$	−28.4830	−0.936008
$927$	0.544478	0.0178830
$928$	−4.77434	−0.156725
$929$	19.7561	0.648176	0.324088	−	0.946027i	$-0.394943\pi$
$929$	19.7561	0.648176	0.324088	+	0.946027i	$0.394943\pi$
$930$	−25.2028	−0.826432
$931$	−37.1973	−1.21909
$932$	−75.6897	−2.47930
$933$	44.7631	1.46548
$934$	21.5553	0.705311
$935$	−3.96639	−0.129715
$936$	−9.55712	−0.312384
$937$	−53.8440	−1.75901	−0.879503	−	0.475893i	$-0.842125\pi$
$937$	−53.8440	−1.75901	−0.879503	+	0.475893i	$0.842125\pi$
$938$	−68.6884	−2.24275
$939$	−16.2343	−0.529785
$940$	48.2410	1.57345
$941$	28.3950	0.925651	0.462825	−	0.886450i	$-0.346836\pi$
$941$	28.3950	0.925651	0.462825	+	0.886450i	$0.346836\pi$
$942$	20.7141	0.674903
$943$	−60.6952	−1.97651
$944$	−7.04136	−0.229177
$945$	34.8421	1.13341
$946$	−8.19760	−0.266527
$947$	−20.9948	−0.682239	−0.341119	−	0.940020i	$-0.610806\pi$
$947$	−20.9948	−0.682239	−0.341119	+	0.940020i	$0.610806\pi$
$948$	118.260	3.84090
$949$	28.4811	0.924535
$950$	−22.8201	−0.740382
$951$	36.6747	1.18926
$952$	−87.9707	−2.85115
$953$	−5.69087	−0.184345	−0.0921727	−	0.995743i	$-0.529381\pi$
$953$	−5.69087	−0.184345	−0.0921727	+	0.995743i	$0.529381\pi$
$954$	13.4074	0.434081
$955$	12.9026	0.417518
$956$	26.9949	0.873078
$957$	0.780268	0.0252225
$958$	−34.0660	−1.10062
$959$	−40.9804	−1.32333
$960$	−16.2508	−0.524493
$961$	−13.7440	−0.443355
$962$	14.9845	0.483118
$963$	4.12903	0.133056
$964$	63.6988	2.05160
$965$	11.0605	0.356049
$966$	−140.124	−4.50843
$967$	−47.3695	−1.52330	−0.761651	−	0.647988i	$-0.775611\pi$
$967$	−47.3695	−1.52330	−0.761651	+	0.647988i	$0.775611\pi$
$968$	−7.27174	−0.233723
$969$	13.3078	0.427509
$970$	52.4823	1.68510
$971$	−33.4064	−1.07206	−0.536031	−	0.844199i	$-0.680077\pi$
$971$	−33.4064	−1.07206	−0.536031	+	0.844199i	$0.680077\pi$
$972$	−19.7181	−0.632457
$973$	−64.8074	−2.07763
$974$	9.32760	0.298876
$975$	−15.4979	−0.496329
$976$	−68.2516	−2.18468
$977$	−7.58459	−0.242652	−0.121326	−	0.992613i	$-0.538715\pi$
$977$	−7.58459	−0.242652	−0.121326	+	0.992613i	$0.538715\pi$
$978$	−91.0784	−2.91237
$979$	−16.0443	−0.512777
$980$	85.6579	2.73624
$981$	−3.22507	−0.102969
$982$	16.1693	0.515983
$983$	−41.8123	−1.33361	−0.666803	−	0.745234i	$-0.732338\pi$
$983$	−41.8123	−1.33361	−0.666803	+	0.745234i	$0.732338\pi$
$984$	94.0039	2.99674
$985$	−19.8397	−0.632144
$986$	−3.46389	−0.110313
$987$	−49.5360	−1.57675
$988$	47.4074	1.50823
$989$	23.8213	0.757474
$990$	−1.50035	−0.0476841
$991$	13.2558	0.421086	0.210543	−	0.977585i	$-0.432477\pi$
$991$	13.2558	0.421086	0.210543	+	0.977585i	$0.432477\pi$
$992$	40.9943	1.30157
$993$	41.2851	1.31014
$994$	−126.707	−4.01889
$995$	29.4802	0.934585
$996$	−83.0116	−2.63032
$997$	52.4160	1.66003	0.830016	−	0.557740i	$-0.188331\pi$
$997$	52.4160	1.66003	0.830016	+	0.557740i	$0.188331\pi$
$998$	37.2776	1.18000
$999$	9.56557	0.302641

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.d.1.4	✓	107

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.d.1.4	✓	107	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.60586 q^{2} -1.61281 q^{3} +4.79053 q^{4} +1.44359 q^{5} +4.20277 q^{6} +4.40298 q^{7} -7.27174 q^{8} -0.398838 q^{9} +O(q^{10})\)	\(q-2.60586 q^{2} -1.61281 q^{3} +4.79053 q^{4} +1.44359 q^{5} +4.20277 q^{6} +4.40298 q^{7} -7.27174 q^{8} -0.398838 q^{9} -3.76179 q^{10} -1.00000 q^{11} -7.72622 q^{12} -3.29528 q^{13} -11.4736 q^{14} -2.32824 q^{15} +9.36812 q^{16} +2.74759 q^{17} +1.03932 q^{18} -3.00310 q^{19} +6.91555 q^{20} -7.10119 q^{21} +2.60586 q^{22} -7.57236 q^{23} +11.7280 q^{24} -2.91605 q^{25} +8.58706 q^{26} +5.48169 q^{27} +21.0926 q^{28} +0.483793 q^{29} +6.06707 q^{30} -4.15403 q^{31} -9.86855 q^{32} +1.61281 q^{33} -7.15986 q^{34} +6.35609 q^{35} -1.91064 q^{36} +1.74501 q^{37} +7.82568 q^{38} +5.31467 q^{39} -10.4974 q^{40} +8.01537 q^{41} +18.5047 q^{42} -3.14583 q^{43} -4.79053 q^{44} -0.575757 q^{45} +19.7325 q^{46} +6.97573 q^{47} -15.1090 q^{48} +12.3863 q^{49} +7.59884 q^{50} -4.43135 q^{51} -15.7861 q^{52} +12.9002 q^{53} -14.2845 q^{54} -1.44359 q^{55} -32.0174 q^{56} +4.84344 q^{57} -1.26070 q^{58} -0.751630 q^{59} -11.1535 q^{60} -7.28552 q^{61} +10.8248 q^{62} -1.75608 q^{63} +6.97989 q^{64} -4.75703 q^{65} -4.20277 q^{66} +5.98665 q^{67} +13.1624 q^{68} +12.2128 q^{69} -16.5631 q^{70} +11.0433 q^{71} +2.90024 q^{72} -8.64299 q^{73} -4.54725 q^{74} +4.70305 q^{75} -14.3865 q^{76} -4.40298 q^{77} -13.8493 q^{78} -15.3063 q^{79} +13.5237 q^{80} -7.64442 q^{81} -20.8870 q^{82} +10.7441 q^{83} -34.0184 q^{84} +3.96639 q^{85} +8.19760 q^{86} -0.780268 q^{87} +7.27174 q^{88} +16.0443 q^{89} +1.50035 q^{90} -14.5091 q^{91} -36.2756 q^{92} +6.69967 q^{93} -18.1778 q^{94} -4.33525 q^{95} +15.9161 q^{96} -13.9514 q^{97} -32.2769 q^{98} +0.398838 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9 - 14 * q^10 - 107 * q^11 - 50 * q^12 - 24 * q^13 - 17 * q^14 - 47 * q^15 + 63 * q^16 + 25 * q^17 - 37 * q^18 - 55 * q^19 - 31 * q^20 + 15 * q^21 + 3 * q^22 - 38 * q^23 + 4 * q^24 + 62 * q^25 - 16 * q^26 - 57 * q^27 - 101 * q^28 + 27 * q^29 - 14 * q^30 - 112 * q^31 - 4 * q^32 + 18 * q^33 - 66 * q^34 + 8 * q^35 + 35 * q^36 - 60 * q^37 - 45 * q^38 - 58 * q^39 - 50 * q^40 - 14 * q^41 - 36 * q^42 - 78 * q^43 - 91 * q^44 - 68 * q^45 - 18 * q^46 - 109 * q^47 - 99 * q^48 + 61 * q^49 - 32 * q^50 - 10 * q^51 - 111 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 44 * q^56 + q^57 - 98 * q^58 - 48 * q^59 - 119 * q^60 - 30 * q^61 + 32 * q^62 - 126 * q^63 + 3 * q^64 + 43 * q^65 - 77 * q^67 + 53 * q^68 - 51 * q^69 - 87 * q^70 - 40 * q^71 - 82 * q^72 - 83 * q^73 + 11 * q^74 - 69 * q^75 - 108 * q^76 + 54 * q^77 - 53 * q^78 - 66 * q^79 - 96 * q^80 + 51 * q^81 - 133 * q^82 - 32 * q^83 + 27 * q^84 - 66 * q^85 - 46 * q^86 - 136 * q^87 + 3 * q^88 - 56 * q^89 + 9 * q^90 - 86 * q^91 - 94 * q^92 - 33 * q^93 - 93 * q^94 - 25 * q^95 - 4 * q^96 - 109 * q^97 - 38 * q^98 - 95 * q^99

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