LMFDB - Embedded newform 6035.2.a.a.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, 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("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.12140 q^{2} +0.383871 q^{3} -0.742456 q^{4} +1.00000 q^{5} -0.430474 q^{6} +1.34550 q^{7} +3.07540 q^{8} -2.85264 q^{9} +O(q^{10})$	\(q-1.12140 q^{2} +0.383871 q^{3} -0.742456 q^{4} +1.00000 q^{5} -0.430474 q^{6} +1.34550 q^{7} +3.07540 q^{8} -2.85264 q^{9} -1.12140 q^{10} +1.85849 q^{11} -0.285007 q^{12} -0.128423 q^{13} -1.50885 q^{14} +0.383871 q^{15} -1.96385 q^{16} +1.00000 q^{17} +3.19896 q^{18} +1.93509 q^{19} -0.742456 q^{20} +0.516500 q^{21} -2.08411 q^{22} +0.872229 q^{23} +1.18056 q^{24} +1.00000 q^{25} +0.144014 q^{26} -2.24666 q^{27} -0.998976 q^{28} -8.06987 q^{29} -0.430474 q^{30} -0.702683 q^{31} -3.94853 q^{32} +0.713419 q^{33} -1.12140 q^{34} +1.34550 q^{35} +2.11796 q^{36} -3.28288 q^{37} -2.17002 q^{38} -0.0492981 q^{39} +3.07540 q^{40} -0.772495 q^{41} -0.579205 q^{42} -11.1164 q^{43} -1.37984 q^{44} -2.85264 q^{45} -0.978120 q^{46} +9.60941 q^{47} -0.753865 q^{48} -5.18962 q^{49} -1.12140 q^{50} +0.383871 q^{51} +0.0953487 q^{52} -2.79797 q^{53} +2.51941 q^{54} +1.85849 q^{55} +4.13796 q^{56} +0.742826 q^{57} +9.04957 q^{58} -7.92439 q^{59} -0.285007 q^{60} +10.7706 q^{61} +0.787990 q^{62} -3.83824 q^{63} +8.35559 q^{64} -0.128423 q^{65} -0.800031 q^{66} -1.83854 q^{67} -0.742456 q^{68} +0.334823 q^{69} -1.50885 q^{70} -1.00000 q^{71} -8.77301 q^{72} -16.5638 q^{73} +3.68143 q^{74} +0.383871 q^{75} -1.43672 q^{76} +2.50060 q^{77} +0.0552830 q^{78} +11.4708 q^{79} -1.96385 q^{80} +7.69550 q^{81} +0.866278 q^{82} -10.5236 q^{83} -0.383478 q^{84} +1.00000 q^{85} +12.4659 q^{86} -3.09779 q^{87} +5.71559 q^{88} -0.0156251 q^{89} +3.19896 q^{90} -0.172794 q^{91} -0.647591 q^{92} -0.269740 q^{93} -10.7760 q^{94} +1.93509 q^{95} -1.51573 q^{96} +18.4080 q^{97} +5.81966 q^{98} -5.30160 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.12140	−0.792952	−0.396476	−	0.918045i	$-0.629767\pi$
$2$	−1.12140	−0.792952	−0.396476	+	0.918045i	$0.629767\pi$
$3$	0.383871	0.221628	0.110814	−	0.993841i	$-0.464654\pi$
$3$	0.383871	0.221628	0.110814	+	0.993841i	$0.464654\pi$
$4$	−0.742456	−0.371228
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.430474	−0.175740
$7$	1.34550	0.508553	0.254276	−	0.967132i	$-0.418163\pi$
$7$	1.34550	0.508553	0.254276	+	0.967132i	$0.418163\pi$
$8$	3.07540	1.08732
$9$	−2.85264	−0.950881
$10$	−1.12140	−0.354619
$11$	1.85849	0.560355	0.280177	−	0.959948i	$-0.409607\pi$
$11$	1.85849	0.560355	0.280177	+	0.959948i	$0.409607\pi$
$12$	−0.285007	−0.0822745
$13$	−0.128423	−0.0356183	−0.0178091	−	0.999841i	$-0.505669\pi$
$13$	−0.128423	−0.0356183	−0.0178091	+	0.999841i	$0.505669\pi$
$14$	−1.50885	−0.403258
$15$	0.383871	0.0991151
$16$	−1.96385	−0.490962
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	3.19896	0.754003
$19$	1.93509	0.443941	0.221970	−	0.975053i	$-0.428751\pi$
$19$	1.93509	0.443941	0.221970	+	0.975053i	$0.428751\pi$
$20$	−0.742456	−0.166018
$21$	0.516500	0.112710
$22$	−2.08411	−0.444334
$23$	0.872229	0.181872	0.0909361	−	0.995857i	$-0.471014\pi$
$23$	0.872229	0.181872	0.0909361	+	0.995857i	$0.471014\pi$
$24$	1.18056	0.240980
$25$	1.00000	0.200000
$26$	0.144014	0.0282436
$27$	−2.24666	−0.432370
$28$	−0.998976	−0.188789
$29$	−8.06987	−1.49854	−0.749268	−	0.662266i	$-0.769595\pi$
$29$	−8.06987	−1.49854	−0.749268	+	0.662266i	$0.769595\pi$
$30$	−0.430474	−0.0785935
$31$	−0.702683	−0.126206	−0.0631028	−	0.998007i	$-0.520100\pi$
$31$	−0.702683	−0.126206	−0.0631028	+	0.998007i	$0.520100\pi$
$32$	−3.94853	−0.698008
$33$	0.713419	0.124190
$34$	−1.12140	−0.192319
$35$	1.34550	0.227432
$36$	2.11796	0.352993
$37$	−3.28288	−0.539703	−0.269851	−	0.962902i	$-0.586975\pi$
$37$	−3.28288	−0.539703	−0.269851	+	0.962902i	$0.586975\pi$
$38$	−2.17002	−0.352023
$39$	−0.0492981	−0.00789401
$40$	3.07540	0.486263
$41$	−0.772495	−0.120643	−0.0603217	−	0.998179i	$-0.519213\pi$
$41$	−0.772495	−0.120643	−0.0603217	+	0.998179i	$0.519213\pi$
$42$	−0.579205	−0.0893732
$43$	−11.1164	−1.69523	−0.847615	−	0.530612i	$-0.821962\pi$
$43$	−11.1164	−1.69523	−0.847615	+	0.530612i	$0.821962\pi$
$44$	−1.37984	−0.208019
$45$	−2.85264	−0.425247
$46$	−0.978120	−0.144216
$47$	9.60941	1.40168	0.700838	−	0.713321i	$-0.252810\pi$
$47$	9.60941	1.40168	0.700838	+	0.713321i	$0.252810\pi$
$48$	−0.753865	−0.108811
$49$	−5.18962	−0.741374
$50$	−1.12140	−0.158590
$51$	0.383871	0.0537527
$52$	0.0953487	0.0132225
$53$	−2.79797	−0.384330	−0.192165	−	0.981363i	$-0.561551\pi$
$53$	−2.79797	−0.384330	−0.192165	+	0.981363i	$0.561551\pi$
$54$	2.51941	0.342849
$55$	1.85849	0.250598
$56$	4.13796	0.552958
$57$	0.742826	0.0983897
$58$	9.04957	1.18827
$59$	−7.92439	−1.03167	−0.515834	−	0.856689i	$-0.672518\pi$
$59$	−7.92439	−1.03167	−0.515834	+	0.856689i	$0.672518\pi$
$60$	−0.285007	−0.0367943
$61$	10.7706	1.37904	0.689519	−	0.724267i	$-0.257822\pi$
$61$	10.7706	1.37904	0.689519	+	0.724267i	$0.257822\pi$
$62$	0.787990	0.100075
$63$	−3.83824	−0.483573
$64$	8.35559	1.04445
$65$	−0.128423	−0.0159290
$66$	−0.800031	−0.0984770
$67$	−1.83854	−0.224614	−0.112307	−	0.993674i	$-0.535824\pi$
$67$	−1.83854	−0.224614	−0.112307	+	0.993674i	$0.535824\pi$
$68$	−0.742456	−0.0900360
$69$	0.334823	0.0403080
$70$	−1.50885	−0.180342
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−8.77301	−1.03391
$73$	−16.5638	−1.93865	−0.969325	−	0.245784i	$-0.920955\pi$
$73$	−16.5638	−1.93865	−0.969325	+	0.245784i	$0.920955\pi$
$74$	3.68143	0.427958
$75$	0.383871	0.0443256
$76$	−1.43672	−0.164803
$77$	2.50060	0.284970
$78$	0.0552830	0.00625957
$79$	11.4708	1.29057	0.645286	−	0.763941i	$-0.276738\pi$
$79$	11.4708	1.29057	0.645286	+	0.763941i	$0.276738\pi$
$80$	−1.96385	−0.219565
$81$	7.69550	0.855056
$82$	0.866278	0.0956644
$83$	−10.5236	−1.15511	−0.577556	−	0.816351i	$-0.695993\pi$
$83$	−10.5236	−1.15511	−0.577556	+	0.816351i	$0.695993\pi$
$84$	−0.383478	−0.0418409
$85$	1.00000	0.108465
$86$	12.4659	1.34423
$87$	−3.09779	−0.332118
$88$	5.71559	0.609283
$89$	−0.0156251	−0.00165625	−0.000828126	−	1.00000i	$-0.500264\pi$
$89$	−0.0156251	−0.00165625	−0.000828126		1.00000i	$0.500264\pi$
$90$	3.19896	0.337200
$91$	−0.172794	−0.0181138
$92$	−0.647591	−0.0675160
$93$	−0.269740	−0.0279707
$94$	−10.7760	−1.11146
$95$	1.93509	0.198536
$96$	−1.51573	−0.154698
$97$	18.4080	1.86905	0.934524	−	0.355899i	$-0.115825\pi$
$97$	18.4080	1.86905	0.934524	+	0.355899i	$0.115825\pi$
$98$	5.81966	0.587874
$99$	−5.30160	−0.532831
$100$	−0.742456	−0.0742456
$101$	6.02680	0.599689	0.299845	−	0.953988i	$-0.403065\pi$
$101$	6.02680	0.599689	0.299845	+	0.953988i	$0.403065\pi$
$102$	−0.430474	−0.0426233
$103$	−7.94637	−0.782979	−0.391489	−	0.920183i	$-0.628040\pi$
$103$	−7.94637	−0.782979	−0.391489	+	0.920183i	$0.628040\pi$
$104$	−0.394953	−0.0387283
$105$	0.516500	0.0504052
$106$	3.13765	0.304755
$107$	−5.79887	−0.560598	−0.280299	−	0.959913i	$-0.590434\pi$
$107$	−5.79887	−0.560598	−0.280299	+	0.959913i	$0.590434\pi$
$108$	1.66805	0.160508
$109$	5.11980	0.490388	0.245194	−	0.969474i	$-0.421148\pi$
$109$	5.11980	0.490388	0.245194	+	0.969474i	$0.421148\pi$
$110$	−2.08411	−0.198712
$111$	−1.26020	−0.119613
$112$	−2.64237	−0.249680
$113$	−8.57226	−0.806411	−0.403205	−	0.915110i	$-0.632104\pi$
$113$	−8.57226	−0.806411	−0.403205	+	0.915110i	$0.632104\pi$
$114$	−0.833007	−0.0780183
$115$	0.872229	0.0813358
$116$	5.99152	0.556298
$117$	0.366346	0.0338687
$118$	8.88643	0.818062
$119$	1.34550	0.123342
$120$	1.18056	0.107770
$121$	−7.54603	−0.686003
$122$	−12.0782	−1.09351
$123$	−0.296538	−0.0267380
$124$	0.521710	0.0468510
$125$	1.00000	0.0894427
$126$	4.30421	0.383450
$127$	8.91266	0.790870	0.395435	−	0.918494i	$-0.370594\pi$
$127$	8.91266	0.790870	0.395435	+	0.918494i	$0.370594\pi$
$128$	−1.47292	−0.130189
$129$	−4.26725	−0.375710
$130$	0.144014	0.0126309
$131$	−12.2701	−1.07204	−0.536022	−	0.844204i	$-0.680074\pi$
$131$	−12.2701	−1.07204	−0.536022	+	0.844204i	$0.680074\pi$
$132$	−0.529682	−0.0461029
$133$	2.60367	0.225767
$134$	2.06175	0.178108
$135$	−2.24666	−0.193362
$136$	3.07540	0.263713
$137$	−1.03804	−0.0886861	−0.0443430	−	0.999016i	$-0.514119\pi$
$137$	−1.03804	−0.0886861	−0.0443430	+	0.999016i	$0.514119\pi$
$138$	−0.375472	−0.0319623
$139$	−12.2252	−1.03693	−0.518463	−	0.855100i	$-0.673496\pi$
$139$	−12.2252	−1.03693	−0.518463	+	0.855100i	$0.673496\pi$
$140$	−0.998976	−0.0844289
$141$	3.68877	0.310651
$142$	1.12140	0.0941060
$143$	−0.238673	−0.0199589
$144$	5.60216	0.466847
$145$	−8.06987	−0.670166
$146$	18.5747	1.53725
$147$	−1.99215	−0.164309
$148$	2.43739	0.200353
$149$	1.04121	0.0852992	0.0426496	−	0.999090i	$-0.486420\pi$
$149$	1.04121	0.0852992	0.0426496	+	0.999090i	$0.486420\pi$
$150$	−0.430474	−0.0351481
$151$	−2.09024	−0.170101	−0.0850507	−	0.996377i	$-0.527105\pi$
$151$	−2.09024	−0.170101	−0.0850507	+	0.996377i	$0.527105\pi$
$152$	5.95118	0.482704
$153$	−2.85264	−0.230623
$154$	−2.80418	−0.225967
$155$	−0.702683	−0.0564408
$156$	0.0366016	0.00293047
$157$	−0.843584	−0.0673254	−0.0336627	−	0.999433i	$-0.510717\pi$
$157$	−0.843584	−0.0673254	−0.0336627	+	0.999433i	$0.510717\pi$
$158$	−12.8634	−1.02336
$159$	−1.07406	−0.0851784
$160$	−3.94853	−0.312159
$161$	1.17359	0.0924916
$162$	−8.62976	−0.678018
$163$	−22.8437	−1.78926	−0.894630	−	0.446808i	$-0.852561\pi$
$163$	−22.8437	−1.78926	−0.894630	+	0.446808i	$0.852561\pi$
$164$	0.573543	0.0447862
$165$	0.713419	0.0555396
$166$	11.8012	0.915948
$167$	0.658784	0.0509782	0.0254891	−	0.999675i	$-0.491886\pi$
$167$	0.658784	0.0509782	0.0254891	+	0.999675i	$0.491886\pi$
$168$	1.58844	0.122551
$169$	−12.9835	−0.998731
$170$	−1.12140	−0.0860077
$171$	−5.52013	−0.422135
$172$	8.25340	0.629316
$173$	4.12582	0.313680	0.156840	−	0.987624i	$-0.449869\pi$
$173$	4.12582	0.313680	0.156840	+	0.987624i	$0.449869\pi$
$174$	3.47387	0.263353
$175$	1.34550	0.101711
$176$	−3.64979	−0.275113
$177$	−3.04194	−0.228646
$178$	0.0175220	0.00131333
$179$	−2.20894	−0.165104	−0.0825521	−	0.996587i	$-0.526307\pi$
$179$	−2.20894	−0.165104	−0.0825521	+	0.996587i	$0.526307\pi$
$180$	2.11796	0.157863
$181$	−0.267551	−0.0198869	−0.00994344	−	0.999951i	$-0.503165\pi$
$181$	−0.267551	−0.0198869	−0.00994344	+	0.999951i	$0.503165\pi$
$182$	0.193772	0.0143633
$183$	4.13454	0.305634
$184$	2.68245	0.197753
$185$	−3.28288	−0.241362
$186$	0.302487	0.0221794
$187$	1.85849	0.135906
$188$	−7.13456	−0.520341
$189$	−3.02289	−0.219883
$190$	−2.17002	−0.157430
$191$	−3.89611	−0.281912	−0.140956	−	0.990016i	$-0.545018\pi$
$191$	−3.89611	−0.281912	−0.140956	+	0.990016i	$0.545018\pi$
$192$	3.20747	0.231479
$193$	2.24488	0.161590	0.0807950	−	0.996731i	$-0.474254\pi$
$193$	2.24488	0.161590	0.0807950	+	0.996731i	$0.474254\pi$
$194$	−20.6428	−1.48207
$195$	−0.0492981	−0.00353031
$196$	3.85306	0.275219
$197$	12.8032	0.912193	0.456096	−	0.889930i	$-0.349247\pi$
$197$	12.8032	0.912193	0.456096	+	0.889930i	$0.349247\pi$
$198$	5.94523	0.422509
$199$	8.15456	0.578061	0.289031	−	0.957320i	$-0.406667\pi$
$199$	8.15456	0.578061	0.289031	+	0.957320i	$0.406667\pi$
$200$	3.07540	0.217463
$201$	−0.705764	−0.0497808
$202$	−6.75847	−0.475525
$203$	−10.8580	−0.762085
$204$	−0.285007	−0.0199545
$205$	−0.772495	−0.0539534
$206$	8.91108	0.620864
$207$	−2.48816	−0.172939
$208$	0.252204	0.0174872
$209$	3.59634	0.248764
$210$	−0.579205	−0.0399689
$211$	−18.7687	−1.29209	−0.646047	−	0.763298i	$-0.723579\pi$
$211$	−18.7687	−1.29209	−0.646047	+	0.763298i	$0.723579\pi$
$212$	2.07737	0.142674
$213$	−0.383871	−0.0263024
$214$	6.50288	0.444527
$215$	−11.1164	−0.758130
$216$	−6.90937	−0.470123
$217$	−0.945462	−0.0641821
$218$	−5.74136	−0.388854
$219$	−6.35837	−0.429659
$220$	−1.37984	−0.0930290
$221$	−0.128423	−0.00863870
$222$	1.41320	0.0948475
$223$	25.2478	1.69072	0.845358	−	0.534201i	$-0.179387\pi$
$223$	25.2478	1.69072	0.845358	+	0.534201i	$0.179387\pi$
$224$	−5.31276	−0.354974
$225$	−2.85264	−0.190176
$226$	9.61296	0.639445
$227$	−3.67621	−0.243999	−0.121999	−	0.992530i	$-0.538931\pi$
$227$	−3.67621	−0.243999	−0.121999	+	0.992530i	$0.538931\pi$
$228$	−0.551515	−0.0365250
$229$	26.8729	1.77581	0.887907	−	0.460024i	$-0.152159\pi$
$229$	26.8729	1.77581	0.887907	+	0.460024i	$0.152159\pi$
$230$	−0.978120	−0.0644953
$231$	0.959908	0.0631573
$232$	−24.8181	−1.62938
$233$	28.4504	1.86385	0.931923	−	0.362657i	$-0.118130\pi$
$233$	28.4504	1.86385	0.931923	+	0.362657i	$0.118130\pi$
$234$	−0.410822	−0.0268563
$235$	9.60941	0.626849
$236$	5.88350	0.382984
$237$	4.40333	0.286027
$238$	−1.50885	−0.0978043
$239$	12.3674	0.799981	0.399991	−	0.916519i	$-0.369013\pi$
$239$	12.3674	0.799981	0.399991	+	0.916519i	$0.369013\pi$
$240$	−0.753865	−0.0486618
$241$	6.32664	0.407535	0.203767	−	0.979019i	$-0.434681\pi$
$241$	6.32664	0.407535	0.203767	+	0.979019i	$0.434681\pi$
$242$	8.46214	0.543967
$243$	9.69406	0.621874
$244$	−7.99672	−0.511937
$245$	−5.18962	−0.331553
$246$	0.332539	0.0212019
$247$	−0.248511	−0.0158124
$248$	−2.16103	−0.137225
$249$	−4.03969	−0.256005
$250$	−1.12140	−0.0709237
$251$	−20.7159	−1.30758	−0.653788	−	0.756677i	$-0.726821\pi$
$251$	−20.7159	−1.30758	−0.653788	+	0.756677i	$0.726821\pi$
$252$	2.84972	0.179516
$253$	1.62103	0.101913
$254$	−9.99468	−0.627122
$255$	0.383871	0.0240389
$256$	−15.0594	−0.941215
$257$	−6.37031	−0.397369	−0.198685	−	0.980063i	$-0.563667\pi$
$257$	−6.37031	−0.397369	−0.198685	+	0.980063i	$0.563667\pi$
$258$	4.78531	0.297920
$259$	−4.41713	−0.274467
$260$	0.0953487	0.00591328
$261$	23.0205	1.42493
$262$	13.7597	0.850080
$263$	−1.89018	−0.116554	−0.0582768	−	0.998300i	$-0.518561\pi$
$263$	−1.89018	−0.116554	−0.0582768	+	0.998300i	$0.518561\pi$
$264$	2.19405	0.135034
$265$	−2.79797	−0.171878
$266$	−2.91977	−0.179022
$267$	−0.00599801	−0.000367072 0
$268$	1.36504	0.0833829
$269$	−31.5253	−1.92213	−0.961066	−	0.276318i	$-0.910886\pi$
$269$	−31.5253	−1.92213	−0.961066	+	0.276318i	$0.910886\pi$
$270$	2.51941	0.153327
$271$	25.1850	1.52988	0.764939	−	0.644102i	$-0.222769\pi$
$271$	25.1850	1.52988	0.764939	+	0.644102i	$0.222769\pi$
$272$	−1.96385	−0.119076
$273$	−0.0663307	−0.00401452
$274$	1.16407	0.0703238
$275$	1.85849	0.112071
$276$	−0.248592	−0.0149635
$277$	2.46904	0.148350	0.0741752	−	0.997245i	$-0.476368\pi$
$277$	2.46904	0.148350	0.0741752	+	0.997245i	$0.476368\pi$
$278$	13.7093	0.822232
$279$	2.00450	0.120006
$280$	4.13796	0.247290
$281$	8.42690	0.502707	0.251353	−	0.967895i	$-0.419124\pi$
$281$	8.42690	0.502707	0.251353	+	0.967895i	$0.419124\pi$
$282$	−4.13660	−0.246331
$283$	−12.8960	−0.766585	−0.383293	−	0.923627i	$-0.625210\pi$
$283$	−12.8960	−0.766585	−0.383293	+	0.923627i	$0.625210\pi$
$284$	0.742456	0.0440566
$285$	0.742826	0.0440012
$286$	0.267649	0.0158264
$287$	−1.03939	−0.0613535
$288$	11.2637	0.663723
$289$	1.00000	0.0588235
$290$	9.04957	0.531409
$291$	7.06630	0.414234
$292$	12.2979	0.719680
$293$	−18.1843	−1.06234	−0.531168	−	0.847266i	$-0.678247\pi$
$293$	−18.1843	−1.06234	−0.531168	+	0.847266i	$0.678247\pi$
$294$	2.23400	0.130289
$295$	−7.92439	−0.461376
$296$	−10.0962	−0.586828
$297$	−4.17539	−0.242281
$298$	−1.16762	−0.0676381
$299$	−0.112015	−0.00647797
$300$	−0.285007	−0.0164549
$301$	−14.9571	−0.862113
$302$	2.34400	0.134882
$303$	2.31352	0.132908
$304$	−3.80023	−0.217958
$305$	10.7706	0.616725
$306$	3.19896	0.182872
$307$	−21.3700	−1.21965	−0.609824	−	0.792537i	$-0.708760\pi$
$307$	−21.3700	−1.21965	−0.609824	+	0.792537i	$0.708760\pi$
$308$	−1.85658	−0.105789
$309$	−3.05038	−0.173530
$310$	0.787990	0.0447548
$311$	−8.32955	−0.472325	−0.236163	−	0.971714i	$-0.575890\pi$
$311$	−8.32955	−0.472325	−0.236163	+	0.971714i	$0.575890\pi$
$312$	−0.151611	−0.00858329
$313$	−21.2894	−1.20335	−0.601674	−	0.798741i	$-0.705500\pi$
$313$	−21.2894	−1.20335	−0.601674	+	0.798741i	$0.705500\pi$
$314$	0.945998	0.0533858
$315$	−3.83824	−0.216260
$316$	−8.51659	−0.479096
$317$	−23.9211	−1.34355	−0.671773	−	0.740757i	$-0.734467\pi$
$317$	−23.9211	−1.34355	−0.671773	+	0.740757i	$0.734467\pi$
$318$	1.20445	0.0675423
$319$	−14.9977	−0.839712
$320$	8.35559	0.467092
$321$	−2.22602	−0.124244
$322$	−1.31606	−0.0733414
$323$	1.93509	0.107671
$324$	−5.71357	−0.317420
$325$	−0.128423	−0.00712365
$326$	25.6170	1.41880
$327$	1.96534	0.108684
$328$	−2.37573	−0.131178
$329$	12.9295	0.712826
$330$	−0.800031	−0.0440402
$331$	−9.45451	−0.519667	−0.259834	−	0.965653i	$-0.583668\pi$
$331$	−9.45451	−0.519667	−0.259834	+	0.965653i	$0.583668\pi$
$332$	7.81328	0.428810
$333$	9.36489	0.513193
$334$	−0.738762	−0.0404233
$335$	−1.83854	−0.100450
$336$	−1.01433	−0.0553361
$337$	−29.7655	−1.62143	−0.810715	−	0.585441i	$-0.800921\pi$
$337$	−29.7655	−1.62143	−0.810715	+	0.585441i	$0.800921\pi$
$338$	14.5597	0.791946
$339$	−3.29064	−0.178723
$340$	−0.742456	−0.0402653
$341$	−1.30593	−0.0707199
$342$	6.19029	0.334732
$343$	−16.4012	−0.885580
$344$	−34.1872	−1.84325
$345$	0.334823	0.0180263
$346$	−4.62671	−0.248733
$347$	18.2157	0.977870	0.488935	−	0.872320i	$-0.337386\pi$
$347$	18.2157	0.977870	0.488935	+	0.872320i	$0.337386\pi$
$348$	2.29997	0.123291
$349$	21.8749	1.17094	0.585468	−	0.810695i	$-0.300911\pi$
$349$	21.8749	1.17094	0.585468	+	0.810695i	$0.300911\pi$
$350$	−1.50885	−0.0806515
$351$	0.288524	0.0154003
$352$	−7.33829	−0.391132
$353$	25.2586	1.34438	0.672189	−	0.740379i	$-0.265354\pi$
$353$	25.2586	1.34438	0.672189	+	0.740379i	$0.265354\pi$
$354$	3.41124	0.181306
$355$	−1.00000	−0.0530745
$356$	0.0116009	0.000614847 0
$357$	0.516500	0.0273361
$358$	2.47712	0.130920
$359$	−9.09370	−0.479947	−0.239974	−	0.970779i	$-0.577139\pi$
$359$	−9.09370	−0.479947	−0.239974	+	0.970779i	$0.577139\pi$
$360$	−8.77301	−0.462378
$361$	−15.2554	−0.802917
$362$	0.300032	0.0157693
$363$	−2.89670	−0.152037
$364$	0.128292	0.00672433
$365$	−16.5638	−0.866990
$366$	−4.63648	−0.242353
$367$	−8.45463	−0.441328	−0.220664	−	0.975350i	$-0.570822\pi$
$367$	−8.45463	−0.441328	−0.220664	+	0.975350i	$0.570822\pi$
$368$	−1.71293	−0.0892924
$369$	2.20365	0.114718
$370$	3.68143	0.191389
$371$	−3.76467	−0.195452
$372$	0.200270	0.0103835
$373$	3.06727	0.158817	0.0794087	−	0.996842i	$-0.474697\pi$
$373$	3.06727	0.158817	0.0794087	+	0.996842i	$0.474697\pi$
$374$	−2.08411	−0.107767
$375$	0.383871	0.0198230
$376$	29.5527	1.52407
$377$	1.03636	0.0533753
$378$	3.38988	0.174356
$379$	2.54809	0.130887	0.0654433	−	0.997856i	$-0.479154\pi$
$379$	2.54809	0.130887	0.0654433	+	0.997856i	$0.479154\pi$
$380$	−1.43672	−0.0737022
$381$	3.42131	0.175279
$382$	4.36911	0.223543
$383$	−10.9144	−0.557701	−0.278850	−	0.960335i	$-0.589953\pi$
$383$	−10.9144	−0.557701	−0.278850	+	0.960335i	$0.589953\pi$
$384$	−0.565413	−0.0288536
$385$	2.50060	0.127442
$386$	−2.51741	−0.128133
$387$	31.7110	1.61196
$388$	−13.6671	−0.693843
$389$	−38.0586	−1.92965	−0.964823	−	0.262901i	$-0.915321\pi$
$389$	−38.0586	−1.92965	−0.964823	+	0.262901i	$0.915321\pi$
$390$	0.0552830	0.00279936
$391$	0.872229	0.0441105
$392$	−15.9601	−0.806109
$393$	−4.71014	−0.237595
$394$	−14.3576	−0.723325
$395$	11.4708	0.577161
$396$	3.93620	0.197802
$397$	−21.3742	−1.07274	−0.536369	−	0.843983i	$-0.680205\pi$
$397$	−21.3742	−1.07274	−0.536369	+	0.843983i	$0.680205\pi$
$398$	−9.14454	−0.458374
$399$	0.999475	0.0500363
$400$	−1.96385	−0.0981924
$401$	21.5071	1.07401	0.537006	−	0.843578i	$-0.319555\pi$
$401$	21.5071	1.07401	0.537006	+	0.843578i	$0.319555\pi$
$402$	0.791446	0.0394737
$403$	0.0902409	0.00449522
$404$	−4.47463	−0.222621
$405$	7.69550	0.382393
$406$	12.1762	0.604296
$407$	−6.10119	−0.302425
$408$	1.18056	0.0584462
$409$	19.6420	0.971233	0.485616	−	0.874172i	$-0.338595\pi$
$409$	19.6420	0.971233	0.485616	+	0.874172i	$0.338595\pi$
$410$	0.866278	0.0427824
$411$	−0.398475	−0.0196553
$412$	5.89982	0.290663
$413$	−10.6623	−0.524657
$414$	2.79023	0.137132
$415$	−10.5236	−0.516582
$416$	0.507084	0.0248618
$417$	−4.69289	−0.229812
$418$	−4.03295	−0.197258
$419$	20.5418	1.00353	0.501765	−	0.865004i	$-0.332684\pi$
$419$	20.5418	1.00353	0.501765	+	0.865004i	$0.332684\pi$
$420$	−0.383478	−0.0187118
$421$	13.1672	0.641730	0.320865	−	0.947125i	$-0.396026\pi$
$421$	13.1672	0.641730	0.320865	+	0.947125i	$0.396026\pi$
$422$	21.0473	1.02457
$423$	−27.4122	−1.33283
$424$	−8.60486	−0.417889
$425$	1.00000	0.0485071
$426$	0.430474	0.0208565
$427$	14.4919	0.701313
$428$	4.30541	0.208110
$429$	−0.0916198	−0.00442344
$430$	12.4659	0.601160
$431$	−11.9081	−0.573592	−0.286796	−	0.957992i	$-0.592590\pi$
$431$	−11.9081	−0.573592	−0.286796	+	0.957992i	$0.592590\pi$
$432$	4.41210	0.212277
$433$	−5.94841	−0.285862	−0.142931	−	0.989733i	$-0.545653\pi$
$433$	−5.94841	−0.285862	−0.142931	+	0.989733i	$0.545653\pi$
$434$	1.06024	0.0508933
$435$	−3.09779	−0.148528
$436$	−3.80122	−0.182046
$437$	1.68784	0.0807405
$438$	7.13030	0.340699
$439$	−30.5065	−1.45600	−0.727998	−	0.685579i	$-0.759549\pi$
$439$	−30.5065	−1.45600	−0.727998	+	0.685579i	$0.759549\pi$
$440$	5.71559	0.272480
$441$	14.8041	0.704959
$442$	0.144014	0.00685007
$443$	1.94502	0.0924109	0.0462055	−	0.998932i	$-0.485287\pi$
$443$	1.94502	0.0924109	0.0462055	+	0.998932i	$0.485287\pi$
$444$	0.935645	0.0444038
$445$	−0.0156251	−0.000740699 0
$446$	−28.3129	−1.34066
$447$	0.399690	0.0189047
$448$	11.2425	0.531157
$449$	−23.4937	−1.10874	−0.554369	−	0.832271i	$-0.687040\pi$
$449$	−23.4937	−1.10874	−0.554369	+	0.832271i	$0.687040\pi$
$450$	3.19896	0.150801
$451$	−1.43567	−0.0676031
$452$	6.36452	0.299362
$453$	−0.802383	−0.0376992
$454$	4.12252	0.193479
$455$	−0.172794	−0.00810072
$456$	2.28449	0.106981
$457$	−17.6112	−0.823815	−0.411908	−	0.911226i	$-0.635137\pi$
$457$	−17.6112	−0.823815	−0.411908	+	0.911226i	$0.635137\pi$
$458$	−30.1354	−1.40813
$459$	−2.24666	−0.104865
$460$	−0.647591	−0.0301941
$461$	−24.7826	−1.15424	−0.577121	−	0.816659i	$-0.695824\pi$
$461$	−24.7826	−1.15424	−0.577121	+	0.816659i	$0.695824\pi$
$462$	−1.07644	−0.0500807
$463$	−3.79842	−0.176527	−0.0882637	−	0.996097i	$-0.528132\pi$
$463$	−3.79842	−0.176527	−0.0882637	+	0.996097i	$0.528132\pi$
$464$	15.8480	0.735725
$465$	−0.269740	−0.0125089
$466$	−31.9043	−1.47794
$467$	−25.1709	−1.16477	−0.582386	−	0.812912i	$-0.697881\pi$
$467$	−25.1709	−1.16477	−0.582386	+	0.812912i	$0.697881\pi$
$468$	−0.271996	−0.0125730
$469$	−2.47377	−0.114228
$470$	−10.7760	−0.497061
$471$	−0.323828	−0.0149212
$472$	−24.3706	−1.12175
$473$	−20.6596	−0.949930
$474$	−4.93790	−0.226805
$475$	1.93509	0.0887881
$476$	−0.998976	−0.0457880
$477$	7.98160	0.365452
$478$	−13.8688	−0.634346
$479$	−25.4802	−1.16422	−0.582110	−	0.813110i	$-0.697773\pi$
$479$	−25.4802	−1.16422	−0.582110	+	0.813110i	$0.697773\pi$
$480$	−1.51573	−0.0691831
$481$	0.421599	0.0192233
$482$	−7.09471	−0.323155
$483$	0.450506	0.0204987
$484$	5.60259	0.254663
$485$	18.4080	0.835864
$486$	−10.8710	−0.493116
$487$	−5.29534	−0.239955	−0.119977	−	0.992777i	$-0.538282\pi$
$487$	−5.29534	−0.239955	−0.119977	+	0.992777i	$0.538282\pi$
$488$	33.1240	1.49945
$489$	−8.76905	−0.396550
$490$	5.81966	0.262905
$491$	−10.4467	−0.471451	−0.235725	−	0.971820i	$-0.575747\pi$
$491$	−10.4467	−0.471451	−0.235725	+	0.971820i	$0.575747\pi$
$492$	0.220167	0.00992588
$493$	−8.06987	−0.363449
$494$	0.278681	0.0125385
$495$	−5.30160	−0.238289
$496$	1.37996	0.0619621
$497$	−1.34550	−0.0603541
$498$	4.53012	0.203000
$499$	−11.2218	−0.502358	−0.251179	−	0.967941i	$-0.580818\pi$
$499$	−11.2218	−0.502358	−0.251179	+	0.967941i	$0.580818\pi$
$500$	−0.742456	−0.0332036
$501$	0.252888	0.0112982
$502$	23.2309	1.03685
$503$	42.4546	1.89296	0.946478	−	0.322767i	$-0.104613\pi$
$503$	42.4546	1.89296	0.946478	+	0.322767i	$0.104613\pi$
$504$	−11.8041	−0.525797
$505$	6.02680	0.268189
$506$	−1.81782	−0.0808121
$507$	−4.98399	−0.221347
$508$	−6.61725	−0.293593
$509$	−32.1455	−1.42483	−0.712413	−	0.701760i	$-0.752398\pi$
$509$	−32.1455	−1.42483	−0.712413	+	0.701760i	$0.752398\pi$
$510$	−0.430474	−0.0190617
$511$	−22.2867	−0.985905
$512$	19.8335	0.876527
$513$	−4.34750	−0.191947
$514$	7.14369	0.315095
$515$	−7.94637	−0.350159
$516$	3.16824	0.139474
$517$	17.8590	0.785436
$518$	4.95338	0.217639
$519$	1.58378	0.0695204
$520$	−0.394953	−0.0173198
$521$	−8.04290	−0.352366	−0.176183	−	0.984357i	$-0.556375\pi$
$521$	−8.04290	−0.352366	−0.176183	+	0.984357i	$0.556375\pi$
$522$	−25.8152	−1.12990
$523$	1.49661	0.0654423	0.0327211	−	0.999465i	$-0.489583\pi$
$523$	1.49661	0.0654423	0.0327211	+	0.999465i	$0.489583\pi$
$524$	9.11001	0.397973
$525$	0.516500	0.0225419
$526$	2.11966	0.0924214
$527$	−0.702683	−0.0306093
$528$	−1.40105	−0.0609728
$529$	−22.2392	−0.966922
$530$	3.13765	0.136291
$531$	22.6054	0.980993
$532$	−1.93311	−0.0838110
$533$	0.0992064	0.00429711
$534$	0.00672618	0.000291070 0
$535$	−5.79887	−0.250707
$536$	−5.65425	−0.244227
$537$	−0.847950	−0.0365917
$538$	35.3526	1.52416
$539$	−9.64484	−0.415433
$540$	1.66805	0.0717813
$541$	−7.60031	−0.326763	−0.163381	−	0.986563i	$-0.552240\pi$
$541$	−7.60031	−0.326763	−0.163381	+	0.986563i	$0.552240\pi$
$542$	−28.2425	−1.21312
$543$	−0.102705	−0.00440749
$544$	−3.94853	−0.169292
$545$	5.11980	0.219308
$546$	0.0743834	0.00318332
$547$	−5.50975	−0.235580	−0.117790	−	0.993039i	$-0.537581\pi$
$547$	−5.50975	−0.235580	−0.117790	+	0.993039i	$0.537581\pi$
$548$	0.770701	0.0329227
$549$	−30.7248	−1.31130
$550$	−2.08411	−0.0888668
$551$	−15.6159	−0.665261
$552$	1.02972	0.0438276
$553$	15.4341	0.656323
$554$	−2.76879	−0.117635
$555$	−1.26020	−0.0534927
$556$	9.07665	0.384936
$557$	2.51729	0.106661	0.0533306	−	0.998577i	$-0.483016\pi$
$557$	2.51729	0.106661	0.0533306	+	0.998577i	$0.483016\pi$
$558$	−2.24785	−0.0951593
$559$	1.42760	0.0603811
$560$	−2.64237	−0.111660
$561$	0.713419	0.0301206
$562$	−9.44995	−0.398622
$563$	13.9601	0.588349	0.294174	−	0.955752i	$-0.404955\pi$
$563$	13.9601	0.588349	0.294174	+	0.955752i	$0.404955\pi$
$564$	−2.73875	−0.115322
$565$	−8.57226	−0.360638
$566$	14.4616	0.607865
$567$	10.3543	0.434841
$568$	−3.07540	−0.129041
$569$	−16.8331	−0.705678	−0.352839	−	0.935684i	$-0.614784\pi$
$569$	−16.8331	−0.705678	−0.352839	+	0.935684i	$0.614784\pi$
$570$	−0.833007	−0.0348908
$571$	−6.29328	−0.263365	−0.131683	−	0.991292i	$-0.542038\pi$
$571$	−6.29328	−0.263365	−0.131683	+	0.991292i	$0.542038\pi$
$572$	0.177204	0.00740928
$573$	−1.49560	−0.0624797
$574$	1.16558	0.0486504
$575$	0.872229	0.0363745
$576$	−23.8355	−0.993146
$577$	27.5894	1.14856	0.574282	−	0.818658i	$-0.305281\pi$
$577$	27.5894	1.14856	0.574282	+	0.818658i	$0.305281\pi$
$578$	−1.12140	−0.0466442
$579$	0.861745	0.0358129
$580$	5.99152	0.248784
$581$	−14.1595	−0.587435
$582$	−7.92417	−0.328467
$583$	−5.19998	−0.215361
$584$	−50.9403	−2.10793
$585$	0.366346	0.0151466
$586$	20.3919	0.842381
$587$	25.3507	1.04633	0.523167	−	0.852230i	$-0.324750\pi$
$587$	25.3507	1.04633	0.523167	+	0.852230i	$0.324750\pi$
$588$	1.47908	0.0609962
$589$	−1.35976	−0.0560277
$590$	8.88643	0.365849
$591$	4.91479	0.202168
$592$	6.44709	0.264974
$593$	−2.40748	−0.0988632	−0.0494316	−	0.998778i	$-0.515741\pi$
$593$	−2.40748	−0.0988632	−0.0494316	+	0.998778i	$0.515741\pi$
$594$	4.68229	0.192117
$595$	1.34550	0.0551603
$596$	−0.773052	−0.0316654
$597$	3.13030	0.128115
$598$	0.125614	0.00513672
$599$	−11.0378	−0.450992	−0.225496	−	0.974244i	$-0.572400\pi$
$599$	−11.0378	−0.450992	−0.225496	+	0.974244i	$0.572400\pi$
$600$	1.18056	0.0481960
$601$	1.57669	0.0643147	0.0321574	−	0.999483i	$-0.489762\pi$
$601$	1.57669	0.0643147	0.0321574	+	0.999483i	$0.489762\pi$
$602$	16.7729	0.683614
$603$	5.24471	0.213581
$604$	1.55191	0.0631463
$605$	−7.54603	−0.306790
$606$	−2.59438	−0.105390
$607$	23.1628	0.940149	0.470074	−	0.882627i	$-0.344227\pi$
$607$	23.1628	0.940149	0.470074	+	0.882627i	$0.344227\pi$
$608$	−7.64077	−0.309874
$609$	−4.16809	−0.168899
$610$	−12.0782	−0.489033
$611$	−1.23407	−0.0499253
$612$	2.11796	0.0856135
$613$	−33.5599	−1.35547	−0.677736	−	0.735306i	$-0.737039\pi$
$613$	−33.5599	−1.35547	−0.677736	+	0.735306i	$0.737039\pi$
$614$	23.9643	0.967122
$615$	−0.296538	−0.0119576
$616$	7.69034	0.309853
$617$	12.8011	0.515351	0.257675	−	0.966232i	$-0.417043\pi$
$617$	12.8011	0.515351	0.257675	+	0.966232i	$0.417043\pi$
$618$	3.42071	0.137601
$619$	34.3343	1.38001	0.690006	−	0.723804i	$-0.257608\pi$
$619$	34.3343	1.38001	0.690006	+	0.723804i	$0.257608\pi$
$620$	0.521710	0.0209524
$621$	−1.95960	−0.0786361
$622$	9.34078	0.374531
$623$	−0.0210236	−0.000842291 0
$624$	0.0968139	0.00387566
$625$	1.00000	0.0400000
$626$	23.8740	0.954198
$627$	1.38053	0.0551331
$628$	0.626324	0.0249930
$629$	−3.28288	−0.130897
$630$	4.30421	0.171484
$631$	−18.8443	−0.750179	−0.375089	−	0.926989i	$-0.622388\pi$
$631$	−18.8443	−0.750179	−0.375089	+	0.926989i	$0.622388\pi$
$632$	35.2774	1.40326
$633$	−7.20478	−0.286364
$634$	26.8252	1.06537
$635$	8.91266	0.353688
$636$	0.797441	0.0316206
$637$	0.666469	0.0264065
$638$	16.8185	0.665851
$639$	2.85264	0.112849
$640$	−1.47292	−0.0582224
$641$	23.5964	0.932002	0.466001	−	0.884784i	$-0.345694\pi$
$641$	23.5964	0.932002	0.466001	+	0.884784i	$0.345694\pi$
$642$	2.49627	0.0985198
$643$	−15.8499	−0.625058	−0.312529	−	0.949908i	$-0.601176\pi$
$643$	−15.8499	−0.625058	−0.312529	+	0.949908i	$0.601176\pi$
$644$	−0.871336	−0.0343354
$645$	−4.26725	−0.168023
$646$	−2.17002	−0.0853782
$647$	22.2316	0.874015	0.437008	−	0.899458i	$-0.356038\pi$
$647$	22.2316	0.874015	0.437008	+	0.899458i	$0.356038\pi$
$648$	23.6667	0.929717
$649$	−14.7274	−0.578100
$650$	0.144014	0.00564871
$651$	−0.362935	−0.0142246
$652$	16.9605	0.664223
$653$	24.4737	0.957730	0.478865	−	0.877889i	$-0.341048\pi$
$653$	24.4737	0.957730	0.478865	+	0.877889i	$0.341048\pi$
$654$	−2.20394	−0.0861810
$655$	−12.2701	−0.479433
$656$	1.51706	0.0592314
$657$	47.2507	1.84342
$658$	−14.4992	−0.565236
$659$	−35.6006	−1.38680	−0.693401	−	0.720552i	$-0.743888\pi$
$659$	−35.6006	−1.38680	−0.693401	+	0.720552i	$0.743888\pi$
$660$	−0.529682	−0.0206178
$661$	−9.00842	−0.350387	−0.175193	−	0.984534i	$-0.556055\pi$
$661$	−9.00842	−0.350387	−0.175193	+	0.984534i	$0.556055\pi$
$662$	10.6023	0.412071
$663$	−0.0492981	−0.00191458
$664$	−32.3642	−1.25597
$665$	2.60367	0.100966
$666$	−10.5018	−0.406937
$667$	−7.03877	−0.272542
$668$	−0.489118	−0.0189245
$669$	9.69189	0.374710
$670$	2.06175	0.0796523
$671$	20.0171	0.772751
$672$	−2.03942	−0.0786722
$673$	−15.2847	−0.589181	−0.294591	−	0.955624i	$-0.595183\pi$
$673$	−15.2847	−0.589181	−0.294591	+	0.955624i	$0.595183\pi$
$674$	33.3791	1.28572
$675$	−2.24666	−0.0864740
$676$	9.63968	0.370757
$677$	14.2240	0.546672	0.273336	−	0.961919i	$-0.411873\pi$
$677$	14.2240	0.546672	0.273336	+	0.961919i	$0.411873\pi$
$678$	3.69014	0.141719
$679$	24.7680	0.950509
$680$	3.07540	0.117936
$681$	−1.41119	−0.0540770
$682$	1.46447	0.0560774
$683$	−2.25514	−0.0862905	−0.0431453	−	0.999069i	$-0.513738\pi$
$683$	−2.25514	−0.0862905	−0.0431453	+	0.999069i	$0.513738\pi$
$684$	4.09845	0.156708
$685$	−1.03804	−0.0396616
$686$	18.3923	0.702222
$687$	10.3157	0.393570
$688$	21.8309	0.832294
$689$	0.359325	0.0136892
$690$	−0.375472	−0.0142940
$691$	−15.2487	−0.580088	−0.290044	−	0.957013i	$-0.593670\pi$
$691$	−15.2487	−0.580088	−0.290044	+	0.957013i	$0.593670\pi$
$692$	−3.06324	−0.116447
$693$	−7.13332	−0.270972
$694$	−20.4271	−0.775404
$695$	−12.2252	−0.463727
$696$	−9.52693	−0.361117
$697$	−0.772495	−0.0292603
$698$	−24.5306	−0.928496
$699$	10.9213	0.413080
$700$	−0.998976	−0.0377578
$701$	−46.3955	−1.75233	−0.876167	−	0.482007i	$-0.839908\pi$
$701$	−46.3955	−1.75233	−0.876167	+	0.482007i	$0.839908\pi$
$702$	−0.323552	−0.0122117
$703$	−6.35268	−0.239596
$704$	15.5288	0.585262
$705$	3.68877	0.138927
$706$	−28.3250	−1.06603
$707$	8.10908	0.304973
$708$	2.25851	0.0848799
$709$	−18.7977	−0.705963	−0.352982	−	0.935630i	$-0.614832\pi$
$709$	−18.7977	−0.705963	−0.352982	+	0.935630i	$0.614832\pi$
$710$	1.12140	0.0420855
$711$	−32.7222	−1.22718
$712$	−0.0480533	−0.00180087
$713$	−0.612900	−0.0229533
$714$	−0.579205	−0.0216762
$715$	−0.238673	−0.00892587
$716$	1.64004	0.0612913
$717$	4.74749	0.177298
$718$	10.1977	0.380575
$719$	15.1618	0.565441	0.282721	−	0.959202i	$-0.408763\pi$
$719$	15.1618	0.565441	0.282721	+	0.959202i	$0.408763\pi$
$720$	5.60216	0.208780
$721$	−10.6919	−0.398186
$722$	17.1075	0.636674
$723$	2.42861	0.0903212
$724$	0.198644	0.00738256
$725$	−8.06987	−0.299707
$726$	3.24837	0.120558
$727$	−22.5141	−0.835000	−0.417500	−	0.908677i	$-0.637094\pi$
$727$	−22.5141	−0.835000	−0.417500	+	0.908677i	$0.637094\pi$
$728$	−0.531411	−0.0196954
$729$	−19.3652	−0.717231
$730$	18.5747	0.687481
$731$	−11.1164	−0.411154
$732$	−3.06971	−0.113460
$733$	−46.6402	−1.72270	−0.861348	−	0.508015i	$-0.830380\pi$
$733$	−46.6402	−1.72270	−0.861348	+	0.508015i	$0.830380\pi$
$734$	9.48105	0.349952
$735$	−1.99215	−0.0734814
$736$	−3.44402	−0.126948
$737$	−3.41691	−0.125863
$738$	−2.47118	−0.0909655
$739$	−38.4649	−1.41496	−0.707478	−	0.706736i	$-0.750167\pi$
$739$	−38.4649	−1.41496	−0.707478	+	0.706736i	$0.750167\pi$
$740$	2.43739	0.0896004
$741$	−0.0953963	−0.00350447
$742$	4.22172	0.154984
$743$	−2.23575	−0.0820217	−0.0410108	−	0.999159i	$-0.513058\pi$
$743$	−2.23575	−0.0820217	−0.0410108	+	0.999159i	$0.513058\pi$
$744$	−0.829556	−0.0304130
$745$	1.04121	0.0381470
$746$	−3.43965	−0.125934
$747$	30.0200	1.09837
$748$	−1.37984	−0.0504521
$749$	−7.80241	−0.285094
$750$	−0.430474	−0.0157187
$751$	29.9313	1.09221	0.546104	−	0.837717i	$-0.316110\pi$
$751$	29.9313	1.09221	0.546104	+	0.837717i	$0.316110\pi$
$752$	−18.8714	−0.688170
$753$	−7.95224	−0.289796
$754$	−1.16218	−0.0423240
$755$	−2.09024	−0.0760716
$756$	2.24436	0.0816266
$757$	−2.16269	−0.0786043	−0.0393022	−	0.999227i	$-0.512513\pi$
$757$	−2.16269	−0.0786043	−0.0393022	+	0.999227i	$0.512513\pi$
$758$	−2.85743	−0.103787
$759$	0.622265	0.0225868
$760$	5.95118	0.215872
$761$	14.6044	0.529410	0.264705	−	0.964329i	$-0.414725\pi$
$761$	14.6044	0.529410	0.264705	+	0.964329i	$0.414725\pi$
$762$	−3.83667	−0.138988
$763$	6.88871	0.249388
$764$	2.89269	0.104654
$765$	−2.85264	−0.103138
$766$	12.2395	0.442230
$767$	1.01768	0.0367462
$768$	−5.78088	−0.208600
$769$	−26.1356	−0.942475	−0.471237	−	0.882006i	$-0.656193\pi$
$769$	−26.1356	−0.942475	−0.471237	+	0.882006i	$0.656193\pi$
$770$	−2.80418	−0.101056
$771$	−2.44538	−0.0880682
$772$	−1.66672	−0.0599867
$773$	23.5437	0.846808	0.423404	−	0.905941i	$-0.360835\pi$
$773$	23.5437	0.846808	0.423404	+	0.905941i	$0.360835\pi$
$774$	−35.5608	−1.27821
$775$	−0.702683	−0.0252411
$776$	56.6119	2.03225
$777$	−1.69561	−0.0608296
$778$	42.6790	1.53012
$779$	−1.49485	−0.0535585
$780$	0.0366016	0.00131055
$781$	−1.85849	−0.0665019
$782$	−0.978120	−0.0349775
$783$	18.1303	0.647922
$784$	10.1916	0.363987
$785$	−0.843584	−0.0301088
$786$	5.28197	0.188402
$787$	29.1921	1.04058	0.520292	−	0.853988i	$-0.325823\pi$
$787$	29.1921	1.04058	0.520292	+	0.853988i	$0.325823\pi$
$788$	−9.50583	−0.338631
$789$	−0.725587	−0.0258316
$790$	−12.8634	−0.457661
$791$	−11.5340	−0.410102
$792$	−16.3045	−0.579356
$793$	−1.38320	−0.0491189
$794$	23.9691	0.850630
$795$	−1.07406	−0.0380929
$796$	−6.05439	−0.214592
$797$	29.5308	1.04603	0.523017	−	0.852322i	$-0.324806\pi$
$797$	29.5308	1.04603	0.523017	+	0.852322i	$0.324806\pi$
$798$	−1.12081	−0.0396764
$799$	9.60941	0.339956
$800$	−3.94853	−0.139602
$801$	0.0445727	0.00157490
$802$	−24.1181	−0.851639
$803$	−30.7836	−1.08633
$804$	0.523998	0.0184800
$805$	1.17359	0.0413635
$806$	−0.101196	−0.00356449
$807$	−12.1017	−0.425999
$808$	18.5348	0.652052
$809$	9.03504	0.317655	0.158827	−	0.987306i	$-0.449229\pi$
$809$	9.03504	0.317655	0.158827	+	0.987306i	$0.449229\pi$
$810$	−8.62976	−0.303219
$811$	−11.0223	−0.387047	−0.193523	−	0.981096i	$-0.561991\pi$
$811$	−11.0223	−0.387047	−0.193523	+	0.981096i	$0.561991\pi$
$812$	8.06161	0.282907
$813$	9.66779	0.339064
$814$	6.84190	0.239808
$815$	−22.8437	−0.800181
$816$	−0.753865	−0.0263905
$817$	−21.5112	−0.752581
$818$	−22.0266	−0.770141
$819$	0.492920	0.0172240
$820$	0.573543	0.0200290
$821$	−51.0699	−1.78235	−0.891175	−	0.453660i	$-0.850118\pi$
$821$	−51.0699	−1.78235	−0.891175	+	0.453660i	$0.850118\pi$
$822$	0.446851	0.0155857
$823$	42.1072	1.46776	0.733882	−	0.679277i	$-0.237706\pi$
$823$	42.1072	1.46776	0.733882	+	0.679277i	$0.237706\pi$
$824$	−24.4382	−0.851346
$825$	0.713419	0.0248381
$826$	11.9567	0.416028
$827$	−41.9266	−1.45793	−0.728965	−	0.684551i	$-0.759998\pi$
$827$	−41.9266	−1.45793	−0.728965	+	0.684551i	$0.759998\pi$
$828$	1.84735	0.0641997
$829$	20.2296	0.702604	0.351302	−	0.936262i	$-0.385739\pi$
$829$	20.2296	0.702604	0.351302	+	0.936262i	$0.385739\pi$
$830$	11.8012	0.409624
$831$	0.947794	0.0328786
$832$	−1.07305	−0.0372014
$833$	−5.18962	−0.179810
$834$	5.26262	0.182230
$835$	0.658784	0.0227982
$836$	−2.67012	−0.0923482
$837$	1.57869	0.0545675
$838$	−23.0356	−0.795751
$839$	−2.18460	−0.0754207	−0.0377104	−	0.999289i	$-0.512006\pi$
$839$	−2.18460	−0.0754207	−0.0377104	+	0.999289i	$0.512006\pi$
$840$	1.58844	0.0548065
$841$	36.1228	1.24561
$842$	−14.7657	−0.508861
$843$	3.23485	0.111414
$844$	13.9350	0.479661
$845$	−12.9835	−0.446646
$846$	30.7401	1.05687
$847$	−10.1532	−0.348868
$848$	5.49478	0.188692
$849$	−4.95039	−0.169897
$850$	−1.12140	−0.0384638
$851$	−2.86342	−0.0981569
$852$	0.285007	0.00976419
$853$	40.6500	1.39183	0.695914	−	0.718125i	$-0.254999\pi$
$853$	40.6500	1.39183	0.695914	+	0.718125i	$0.254999\pi$
$854$	−16.2513	−0.556108
$855$	−5.52013	−0.188784
$856$	−17.8338	−0.609548
$857$	31.5638	1.07820	0.539099	−	0.842243i	$-0.318765\pi$
$857$	31.5638	1.07820	0.539099	+	0.842243i	$0.318765\pi$
$858$	0.102743	0.00350758
$859$	−24.7335	−0.843894	−0.421947	−	0.906620i	$-0.638653\pi$
$859$	−24.7335	−0.843894	−0.421947	+	0.906620i	$0.638653\pi$
$860$	8.25340	0.281439
$861$	−0.398994	−0.0135977
$862$	13.3538	0.454831
$863$	−12.1631	−0.414038	−0.207019	−	0.978337i	$-0.566376\pi$
$863$	−12.1631	−0.414038	−0.207019	+	0.978337i	$0.566376\pi$
$864$	8.87101	0.301798
$865$	4.12582	0.140282
$866$	6.67056	0.226675
$867$	0.383871	0.0130369
$868$	0.701963	0.0238262
$869$	21.3184	0.723178
$870$	3.47387	0.117775
$871$	0.236112	0.00800036
$872$	15.7454	0.533207
$873$	−52.5114	−1.77724
$874$	−1.89275	−0.0640233
$875$	1.34550	0.0454863
$876$	4.72081	0.159501
$877$	−32.0549	−1.08242	−0.541209	−	0.840888i	$-0.682033\pi$
$877$	−32.0549	−1.08242	−0.541209	+	0.840888i	$0.682033\pi$
$878$	34.2101	1.15453
$879$	−6.98042	−0.235444
$880$	−3.64979	−0.123034
$881$	58.9353	1.98558	0.992790	−	0.119865i	$-0.0382463\pi$
$881$	58.9353	1.98558	0.992790	+	0.119865i	$0.0382463\pi$
$882$	−16.6014	−0.558998
$883$	6.84822	0.230461	0.115230	−	0.993339i	$-0.463239\pi$
$883$	6.84822	0.230461	0.115230	+	0.993339i	$0.463239\pi$
$884$	0.0953487	0.00320692
$885$	−3.04194	−0.102254
$886$	−2.18116	−0.0732774
$887$	44.1235	1.48152	0.740760	−	0.671769i	$-0.234465\pi$
$887$	44.1235	1.48152	0.740760	+	0.671769i	$0.234465\pi$
$888$	−3.87563	−0.130058
$889$	11.9920	0.402199
$890$	0.0175220	0.000587338 0
$891$	14.3020	0.479135
$892$	−18.7453	−0.627640
$893$	18.5951	0.622261
$894$	−0.448214	−0.0149905
$895$	−2.20894	−0.0738369
$896$	−1.98182	−0.0662081
$897$	−0.0429992	−0.00143570
$898$	26.3460	0.879176
$899$	5.67055	0.189124
$900$	2.11796	0.0705987
$901$	−2.79797	−0.0932138
$902$	1.60997	0.0536060
$903$	−5.74160	−0.191069
$904$	−26.3631	−0.876824
$905$	−0.267551	−0.00889368
$906$	0.899795	0.0298937
$907$	16.7166	0.555066	0.277533	−	0.960716i	$-0.410483\pi$
$907$	16.7166	0.555066	0.277533	+	0.960716i	$0.410483\pi$
$908$	2.72943	0.0905792
$909$	−17.1923	−0.570233
$910$	0.193772	0.00642348
$911$	6.75581	0.223830	0.111915	−	0.993718i	$-0.464302\pi$
$911$	6.75581	0.223830	0.111915	+	0.993718i	$0.464302\pi$
$912$	−1.45880	−0.0483056
$913$	−19.5579	−0.647272
$914$	19.7492	0.653246
$915$	4.13454	0.136684
$916$	−19.9520	−0.659231
$917$	−16.5095	−0.545191
$918$	2.51941	0.0831530
$919$	−14.6995	−0.484890	−0.242445	−	0.970165i	$-0.577949\pi$
$919$	−14.6995	−0.484890	−0.242445	+	0.970165i	$0.577949\pi$
$920$	2.68245	0.0884378
$921$	−8.20332	−0.270308
$922$	27.7913	0.915258
$923$	0.128423	0.00422711
$924$	−0.712689	−0.0234458
$925$	−3.28288	−0.107941
$926$	4.25956	0.139978
$927$	22.6681	0.744519
$928$	31.8641	1.04599
$929$	8.37441	0.274756	0.137378	−	0.990519i	$-0.456133\pi$
$929$	8.37441	0.274756	0.137378	+	0.990519i	$0.456133\pi$
$930$	0.302487	0.00991893
$931$	−10.0424	−0.329126
$932$	−21.1231	−0.691911
$933$	−3.19747	−0.104681
$934$	28.2268	0.923608
$935$	1.85849	0.0607790
$936$	1.12666	0.0368260
$937$	−3.57576	−0.116815	−0.0584076	−	0.998293i	$-0.518602\pi$
$937$	−3.57576	−0.116815	−0.0584076	+	0.998293i	$0.518602\pi$
$938$	2.77409	0.0905772
$939$	−8.17239	−0.266696
$940$	−7.13456	−0.232704
$941$	46.0613	1.50155	0.750777	−	0.660556i	$-0.229679\pi$
$941$	46.0613	1.50155	0.750777	+	0.660556i	$0.229679\pi$
$942$	0.363141	0.0118318
$943$	−0.673792	−0.0219417
$944$	15.5623	0.506510
$945$	−3.02289	−0.0983346
$946$	23.1677	0.753248
$947$	−32.7671	−1.06479	−0.532394	−	0.846497i	$-0.678707\pi$
$947$	−32.7671	−1.06479	−0.532394	+	0.846497i	$0.678707\pi$
$948$	−3.26927	−0.106181
$949$	2.12718	0.0690513
$950$	−2.17002	−0.0704047
$951$	−9.18264	−0.297767
$952$	4.13796	0.134112
$953$	24.3424	0.788526	0.394263	−	0.918998i	$-0.371000\pi$
$953$	24.3424	0.788526	0.394263	+	0.918998i	$0.371000\pi$
$954$	−8.95059	−0.289786
$955$	−3.89611	−0.126075
$956$	−9.18225	−0.296975
$957$	−5.75720	−0.186104
$958$	28.5736	0.923170
$959$	−1.39669	−0.0451015
$960$	3.20747	0.103521
$961$	−30.5062	−0.984072
$962$	−0.472783	−0.0152431
$963$	16.5421	0.533062
$964$	−4.69725	−0.151288
$965$	2.24488	0.0722652
$966$	−0.505199	−0.0162545
$967$	−17.6891	−0.568844	−0.284422	−	0.958699i	$-0.591802\pi$
$967$	−17.6891	−0.568844	−0.284422	+	0.958699i	$0.591802\pi$
$968$	−23.2070	−0.745902
$969$	0.742826	0.0238630
$970$	−20.6428	−0.662800
$971$	−29.4843	−0.946197	−0.473098	−	0.881010i	$-0.656864\pi$
$971$	−29.4843	−0.946197	−0.473098	+	0.881010i	$0.656864\pi$
$972$	−7.19741	−0.230857
$973$	−16.4490	−0.527331
$974$	5.93821	0.190272
$975$	−0.0492981	−0.00157880
$976$	−21.1519	−0.677056
$977$	33.8640	1.08341	0.541703	−	0.840570i	$-0.317780\pi$
$977$	33.8640	1.08341	0.541703	+	0.840570i	$0.317780\pi$
$978$	9.83364	0.314445
$979$	−0.0290390	−0.000928089 0
$980$	3.85306	0.123082
$981$	−14.6050	−0.466301
$982$	11.7149	0.373838
$983$	8.56143	0.273067	0.136534	−	0.990635i	$-0.456404\pi$
$983$	8.56143	0.273067	0.136534	+	0.990635i	$0.456404\pi$
$984$	−0.911974	−0.0290727
$985$	12.8032	0.407945
$986$	9.04957	0.288197
$987$	4.96326	0.157982
$988$	0.184509	0.00587000
$989$	−9.69601	−0.308315
$990$	5.94523	0.188952
$991$	24.7650	0.786685	0.393342	−	0.919392i	$-0.371319\pi$
$991$	24.7650	0.786685	0.393342	+	0.919392i	$0.371319\pi$
$992$	2.77456	0.0880924
$993$	−3.62931	−0.115173
$994$	1.50885	0.0478579
$995$	8.15456	0.258517
$996$	2.99929	0.0950362
$997$	19.2274	0.608939	0.304469	−	0.952522i	$-0.401521\pi$
$997$	19.2274	0.608939	0.304469	+	0.952522i	$0.401521\pi$
$998$	12.5842	0.398346
$999$	7.37552	0.233351

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.a.1.12	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.a.1.12	✓	36	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-1.12140 q^{2} +0.383871 q^{3} -0.742456 q^{4} +1.00000 q^{5} -0.430474 q^{6} +1.34550 q^{7} +3.07540 q^{8} -2.85264 q^{9} +O(q^{10})\)	\(q-1.12140 q^{2} +0.383871 q^{3} -0.742456 q^{4} +1.00000 q^{5} -0.430474 q^{6} +1.34550 q^{7} +3.07540 q^{8} -2.85264 q^{9} -1.12140 q^{10} +1.85849 q^{11} -0.285007 q^{12} -0.128423 q^{13} -1.50885 q^{14} +0.383871 q^{15} -1.96385 q^{16} +1.00000 q^{17} +3.19896 q^{18} +1.93509 q^{19} -0.742456 q^{20} +0.516500 q^{21} -2.08411 q^{22} +0.872229 q^{23} +1.18056 q^{24} +1.00000 q^{25} +0.144014 q^{26} -2.24666 q^{27} -0.998976 q^{28} -8.06987 q^{29} -0.430474 q^{30} -0.702683 q^{31} -3.94853 q^{32} +0.713419 q^{33} -1.12140 q^{34} +1.34550 q^{35} +2.11796 q^{36} -3.28288 q^{37} -2.17002 q^{38} -0.0492981 q^{39} +3.07540 q^{40} -0.772495 q^{41} -0.579205 q^{42} -11.1164 q^{43} -1.37984 q^{44} -2.85264 q^{45} -0.978120 q^{46} +9.60941 q^{47} -0.753865 q^{48} -5.18962 q^{49} -1.12140 q^{50} +0.383871 q^{51} +0.0953487 q^{52} -2.79797 q^{53} +2.51941 q^{54} +1.85849 q^{55} +4.13796 q^{56} +0.742826 q^{57} +9.04957 q^{58} -7.92439 q^{59} -0.285007 q^{60} +10.7706 q^{61} +0.787990 q^{62} -3.83824 q^{63} +8.35559 q^{64} -0.128423 q^{65} -0.800031 q^{66} -1.83854 q^{67} -0.742456 q^{68} +0.334823 q^{69} -1.50885 q^{70} -1.00000 q^{71} -8.77301 q^{72} -16.5638 q^{73} +3.68143 q^{74} +0.383871 q^{75} -1.43672 q^{76} +2.50060 q^{77} +0.0552830 q^{78} +11.4708 q^{79} -1.96385 q^{80} +7.69550 q^{81} +0.866278 q^{82} -10.5236 q^{83} -0.383478 q^{84} +1.00000 q^{85} +12.4659 q^{86} -3.09779 q^{87} +5.71559 q^{88} -0.0156251 q^{89} +3.19896 q^{90} -0.172794 q^{91} -0.647591 q^{92} -0.269740 q^{93} -10.7760 q^{94} +1.93509 q^{95} -1.51573 q^{96} +18.4080 q^{97} +5.81966 q^{98} -5.30160 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * q^99

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