LMFDB - Embedded newform 6029.2.a.a.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6029,2,Mod(1,6029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6029 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6029.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:	$48.1418073786$
Analytic rank:	$1$
Dimension:	$234$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58537 q^{2} +1.21501 q^{3} +4.68413 q^{4} -1.54408 q^{5} -3.14124 q^{6} -3.29615 q^{7} -6.93947 q^{8} -1.52375 q^{9} +O(q^{10})$	\(q-2.58537 q^{2} +1.21501 q^{3} +4.68413 q^{4} -1.54408 q^{5} -3.14124 q^{6} -3.29615 q^{7} -6.93947 q^{8} -1.52375 q^{9} +3.99201 q^{10} -0.822171 q^{11} +5.69126 q^{12} -2.56183 q^{13} +8.52177 q^{14} -1.87607 q^{15} +8.57282 q^{16} -0.324345 q^{17} +3.93947 q^{18} +3.04101 q^{19} -7.23266 q^{20} -4.00485 q^{21} +2.12561 q^{22} +6.83103 q^{23} -8.43151 q^{24} -2.61583 q^{25} +6.62327 q^{26} -5.49640 q^{27} -15.4396 q^{28} +6.37718 q^{29} +4.85032 q^{30} +4.34101 q^{31} -8.28497 q^{32} -0.998944 q^{33} +0.838552 q^{34} +5.08952 q^{35} -7.13747 q^{36} +0.139162 q^{37} -7.86212 q^{38} -3.11264 q^{39} +10.7151 q^{40} -0.830931 q^{41} +10.3540 q^{42} +7.98000 q^{43} -3.85116 q^{44} +2.35280 q^{45} -17.6607 q^{46} +2.64033 q^{47} +10.4161 q^{48} +3.86463 q^{49} +6.76287 q^{50} -0.394082 q^{51} -11.9999 q^{52} -7.37361 q^{53} +14.2102 q^{54} +1.26949 q^{55} +22.8736 q^{56} +3.69485 q^{57} -16.4874 q^{58} -7.48115 q^{59} -8.78774 q^{60} -6.91130 q^{61} -11.2231 q^{62} +5.02253 q^{63} +4.27406 q^{64} +3.95566 q^{65} +2.58264 q^{66} +0.738440 q^{67} -1.51928 q^{68} +8.29976 q^{69} -13.1583 q^{70} +16.1145 q^{71} +10.5741 q^{72} +15.6268 q^{73} -0.359784 q^{74} -3.17825 q^{75} +14.2445 q^{76} +2.71000 q^{77} +8.04733 q^{78} -10.0774 q^{79} -13.2371 q^{80} -2.10691 q^{81} +2.14826 q^{82} -0.427204 q^{83} -18.7593 q^{84} +0.500814 q^{85} -20.6312 q^{86} +7.74833 q^{87} +5.70543 q^{88} +3.48706 q^{89} -6.08284 q^{90} +8.44418 q^{91} +31.9974 q^{92} +5.27436 q^{93} -6.82623 q^{94} -4.69555 q^{95} -10.0663 q^{96} +6.30900 q^{97} -9.99151 q^{98} +1.25279 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) $ 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9 - 89 * q^10 - 55 * q^11 - 75 * q^12 - 49 * q^13 - 42 * q^14 - 43 * q^15 + 142 * q^16 - 40 * q^17 - 30 * q^18 - 235 * q^19 - 62 * q^20 - 62 * q^21 - 63 * q^22 - 30 * q^23 - 108 * q^24 + 170 * q^25 - 44 * q^26 - 160 * q^27 - 147 * q^28 - 76 * q^29 - 15 * q^30 - 175 * q^31 - 49 * q^32 - 43 * q^33 - 104 * q^34 - 87 * q^35 + 124 * q^36 - 77 * q^37 - 18 * q^38 - 104 * q^39 - 247 * q^40 - 60 * q^41 - 6 * q^42 - 201 * q^43 - 89 * q^44 - 102 * q^45 - 128 * q^46 - 27 * q^47 - 130 * q^48 + 123 * q^49 - 33 * q^50 - 220 * q^51 - 125 * q^52 - 34 * q^53 - 126 * q^54 - 176 * q^55 - 125 * q^56 - 17 * q^57 - 46 * q^58 - 172 * q^59 - 61 * q^60 - 243 * q^61 - 37 * q^62 - 137 * q^63 + 39 * q^64 - 31 * q^65 - 142 * q^66 - 132 * q^67 - 106 * q^68 - 115 * q^69 - 60 * q^70 - 68 * q^71 - 66 * q^72 - 109 * q^73 - 74 * q^74 - 256 * q^75 - 412 * q^76 - 32 * q^77 - 38 * q^78 - 297 * q^79 - 111 * q^80 + 142 * q^81 - 94 * q^82 - 100 * q^83 - 134 * q^84 - 90 * q^85 + q^86 - 103 * q^87 - 143 * q^88 - 77 * q^89 - 181 * q^90 - 418 * q^91 - 19 * q^92 + 5 * q^93 - 231 * q^94 - 92 * q^95 - 189 * q^96 - 141 * q^97 - 25 * q^98 - 244 * 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 $

$2$	−2.58537	−1.82813	−0.914066	−	0.405566i	$-0.867075\pi$
$2$	−2.58537	−1.82813	−0.914066	+	0.405566i	$0.867075\pi$
$3$	1.21501	0.701485	0.350743	−	0.936472i	$-0.385929\pi$
$3$	1.21501	0.701485	0.350743	+	0.936472i	$0.385929\pi$
$4$	4.68413	2.34207
$5$	−1.54408	−0.690532	−0.345266	−	0.938505i	$-0.612211\pi$
$5$	−1.54408	−0.690532	−0.345266	+	0.938505i	$0.612211\pi$
$6$	−3.14124	−1.28241
$7$	−3.29615	−1.24583	−0.622915	−	0.782290i	$-0.714052\pi$
$7$	−3.29615	−1.24583	−0.622915	+	0.782290i	$0.714052\pi$
$8$	−6.93947	−2.45347
$9$	−1.52375	−0.507918
$10$	3.99201	1.26238
$11$	−0.822171	−0.247894	−0.123947	−	0.992289i	$-0.539555\pi$
$11$	−0.822171	−0.247894	−0.123947	+	0.992289i	$0.539555\pi$
$12$	5.69126	1.64292
$13$	−2.56183	−0.710523	−0.355262	−	0.934767i	$-0.615608\pi$
$13$	−2.56183	−0.710523	−0.355262	+	0.934767i	$0.615608\pi$
$14$	8.52177	2.27754
$15$	−1.87607	−0.484398
$16$	8.57282	2.14321
$17$	−0.324345	−0.0786653	−0.0393326	−	0.999226i	$-0.512523\pi$
$17$	−0.324345	−0.0786653	−0.0393326	+	0.999226i	$0.512523\pi$
$18$	3.93947	0.928542
$19$	3.04101	0.697655	0.348827	−	0.937187i	$-0.386580\pi$
$19$	3.04101	0.697655	0.348827	+	0.937187i	$0.386580\pi$
$20$	−7.23266	−1.61727
$21$	−4.00485	−0.873931
$22$	2.12561	0.453182
$23$	6.83103	1.42437	0.712184	−	0.701993i	$-0.247706\pi$
$23$	6.83103	1.42437	0.712184	+	0.701993i	$0.247706\pi$
$24$	−8.43151	−1.72108
$25$	−2.61583	−0.523165
$26$	6.62327	1.29893
$27$	−5.49640	−1.05778
$28$	−15.4396	−2.91781
$29$	6.37718	1.18421	0.592106	−	0.805860i	$-0.298297\pi$
$29$	6.37718	1.18421	0.592106	+	0.805860i	$0.298297\pi$
$30$	4.85032	0.885544
$31$	4.34101	0.779668	0.389834	−	0.920885i	$-0.372532\pi$
$31$	4.34101	0.779668	0.389834	+	0.920885i	$0.372532\pi$
$32$	−8.28497	−1.46459
$33$	−0.998944	−0.173894
$34$	0.838552	0.143811
$35$	5.08952	0.860285
$36$	−7.13747	−1.18958
$37$	0.139162	0.0228780	0.0114390	−	0.999935i	$-0.496359\pi$
$37$	0.139162	0.0228780	0.0114390	+	0.999935i	$0.496359\pi$
$38$	−7.86212	−1.27541
$39$	−3.11264	−0.498422
$40$	10.7151	1.69420
$41$	−0.830931	−0.129770	−0.0648848	−	0.997893i	$-0.520668\pi$
$41$	−0.830931	−0.129770	−0.0648848	+	0.997893i	$0.520668\pi$
$42$	10.3540	1.59766
$43$	7.98000	1.21694	0.608469	−	0.793577i	$-0.291784\pi$
$43$	7.98000	1.21694	0.608469	+	0.793577i	$0.291784\pi$
$44$	−3.85116	−0.580583
$45$	2.35280	0.350734
$46$	−17.6607	−2.60393
$47$	2.64033	0.385132	0.192566	−	0.981284i	$-0.438319\pi$
$47$	2.64033	0.385132	0.192566	+	0.981284i	$0.438319\pi$
$48$	10.4161	1.50343
$49$	3.86463	0.552091
$50$	6.76287	0.956415
$51$	−0.394082	−0.0551825
$52$	−11.9999	−1.66409
$53$	−7.37361	−1.01284	−0.506422	−	0.862286i	$-0.669032\pi$
$53$	−7.37361	−1.01284	−0.506422	+	0.862286i	$0.669032\pi$
$54$	14.2102	1.93377
$55$	1.26949	0.171179
$56$	22.8736	3.05661
$57$	3.69485	0.489395
$58$	−16.4874	−2.16490
$59$	−7.48115	−0.973963	−0.486982	−	0.873412i	$-0.661902\pi$
$59$	−7.48115	−0.973963	−0.486982	+	0.873412i	$0.661902\pi$
$60$	−8.78774	−1.13449
$61$	−6.91130	−0.884902	−0.442451	−	0.896793i	$-0.645891\pi$
$61$	−6.91130	−0.884902	−0.442451	+	0.896793i	$0.645891\pi$
$62$	−11.2231	−1.42534
$63$	5.02253	0.632780
$64$	4.27406	0.534257
$65$	3.95566	0.490639
$66$	2.58264	0.317901
$67$	0.738440	0.0902148	0.0451074	−	0.998982i	$-0.485637\pi$
$67$	0.738440	0.0902148	0.0451074	+	0.998982i	$0.485637\pi$
$68$	−1.51928	−0.184239
$69$	8.29976	0.999173
$70$	−13.1583	−1.57271
$71$	16.1145	1.91243	0.956217	−	0.292659i	$-0.0945401\pi$
$71$	16.1145	1.91243	0.956217	+	0.292659i	$0.0945401\pi$
$72$	10.5741	1.24616
$73$	15.6268	1.82898	0.914490	−	0.404608i	$-0.132592\pi$
$73$	15.6268	1.82898	0.914490	+	0.404608i	$0.132592\pi$
$74$	−0.359784	−0.0418241
$75$	−3.17825	−0.366993
$76$	14.2445	1.63395
$77$	2.71000	0.308833
$78$	8.04733	0.911180
$79$	−10.0774	−1.13379	−0.566896	−	0.823789i	$-0.691856\pi$
$79$	−10.0774	−1.13379	−0.566896	+	0.823789i	$0.691856\pi$
$80$	−13.2371	−1.47995
$81$	−2.10691	−0.234101
$82$	2.14826	0.237236
$83$	−0.427204	−0.0468917	−0.0234458	−	0.999725i	$-0.507464\pi$
$83$	−0.427204	−0.0468917	−0.0234458	+	0.999725i	$0.507464\pi$
$84$	−18.7593	−2.04680
$85$	0.500814	0.0543209
$86$	−20.6312	−2.22472
$87$	7.74833	0.830708
$88$	5.70543	0.608201
$89$	3.48706	0.369628	0.184814	−	0.982774i	$-0.440832\pi$
$89$	3.48706	0.369628	0.184814	+	0.982774i	$0.440832\pi$
$90$	−6.08284	−0.641188
$91$	8.44418	0.885190
$92$	31.9974	3.33596
$93$	5.27436	0.546926
$94$	−6.82623	−0.704072
$95$	−4.69555	−0.481753
$96$	−10.0663	−1.02739
$97$	6.30900	0.640582	0.320291	−	0.947319i	$-0.396219\pi$
$97$	6.30900	0.640582	0.320291	+	0.947319i	$0.396219\pi$
$98$	−9.99151	−1.00929
$99$	1.25279	0.125910
$100$	−12.2529	−1.22529
$101$	−18.7451	−1.86521	−0.932604	−	0.360902i	$-0.882469\pi$
$101$	−18.7451	−1.86521	−0.932604	+	0.360902i	$0.882469\pi$
$102$	1.01885	0.100881
$103$	16.4434	1.62021	0.810107	−	0.586282i	$-0.199409\pi$
$103$	16.4434	1.62021	0.810107	+	0.586282i	$0.199409\pi$
$104$	17.7777	1.74325
$105$	6.18380	0.603478
$106$	19.0635	1.85161
$107$	13.3279	1.28846	0.644230	−	0.764832i	$-0.277178\pi$
$107$	13.3279	1.28846	0.644230	+	0.764832i	$0.277178\pi$
$108$	−25.7459	−2.47740
$109$	−3.46225	−0.331623	−0.165812	−	0.986157i	$-0.553024\pi$
$109$	−3.46225	−0.331623	−0.165812	+	0.986157i	$0.553024\pi$
$110$	−3.28211	−0.312937
$111$	0.169083	0.0160486
$112$	−28.2574	−2.67007
$113$	12.1448	1.14248	0.571242	−	0.820781i	$-0.306462\pi$
$113$	12.1448	1.14248	0.571242	+	0.820781i	$0.306462\pi$
$114$	−9.55255	−0.894678
$115$	−10.5476	−0.983572
$116$	29.8715	2.77350
$117$	3.90360	0.360888
$118$	19.3415	1.78053
$119$	1.06909	0.0980035
$120$	13.0189	1.18846
$121$	−10.3240	−0.938549
$122$	17.8683	1.61772
$123$	−1.00959	−0.0910315
$124$	20.3338	1.82603
$125$	11.7594	1.05179
$126$	−12.9851	−1.15680
$127$	0.704510	0.0625151	0.0312576	−	0.999511i	$-0.490049\pi$
$127$	0.704510	0.0625151	0.0312576	+	0.999511i	$0.490049\pi$
$128$	5.51992	0.487897
$129$	9.69577	0.853665
$130$	−10.2268	−0.896953
$131$	−13.6877	−1.19590	−0.597951	−	0.801533i	$-0.704018\pi$
$131$	−13.6877	−1.19590	−0.597951	+	0.801533i	$0.704018\pi$
$132$	−4.67919	−0.407271
$133$	−10.0236	−0.869159
$134$	−1.90914	−0.164925
$135$	8.48686	0.730433
$136$	2.25078	0.193003
$137$	18.1823	1.55342	0.776709	−	0.629860i	$-0.216888\pi$
$137$	18.1823	1.55342	0.776709	+	0.629860i	$0.216888\pi$
$138$	−21.4579	−1.82662
$139$	−10.1007	−0.856732	−0.428366	−	0.903605i	$-0.640911\pi$
$139$	−10.1007	−0.856732	−0.428366	+	0.903605i	$0.640911\pi$
$140$	23.8400	2.01484
$141$	3.20802	0.270164
$142$	−41.6618	−3.49618
$143$	2.10626	0.176134
$144$	−13.0629	−1.08857
$145$	−9.84686	−0.817737
$146$	−40.4011	−3.34362
$147$	4.69556	0.387284
$148$	0.651852	0.0535819
$149$	−22.8566	−1.87248	−0.936242	−	0.351356i	$-0.885721\pi$
$149$	−22.8566	−1.87248	−0.936242	+	0.351356i	$0.885721\pi$
$150$	8.21695	0.670911
$151$	10.5349	0.857315	0.428658	−	0.903467i	$-0.358987\pi$
$151$	10.5349	0.857315	0.428658	+	0.903467i	$0.358987\pi$
$152$	−21.1030	−1.71168
$153$	0.494223	0.0399555
$154$	−7.00635	−0.564588
$155$	−6.70285	−0.538386
$156$	−14.5800	−1.16734
$157$	−15.0560	−1.20160	−0.600801	−	0.799399i	$-0.705152\pi$
$157$	−15.0560	−1.20160	−0.600801	+	0.799399i	$0.705152\pi$
$158$	26.0537	2.07272
$159$	−8.95900	−0.710495
$160$	12.7926	1.01135
$161$	−22.5161	−1.77452
$162$	5.44713	0.427967
$163$	−19.9388	−1.56173	−0.780863	−	0.624702i	$-0.785220\pi$
$163$	−19.9388	−1.56173	−0.780863	+	0.624702i	$0.785220\pi$
$164$	−3.89219	−0.303929
$165$	1.54245	0.120079
$166$	1.10448	0.0857242
$167$	7.42067	0.574228	0.287114	−	0.957896i	$-0.407304\pi$
$167$	7.42067	0.574228	0.287114	+	0.957896i	$0.407304\pi$
$168$	27.7916	2.14417
$169$	−6.43704	−0.495157
$170$	−1.29479	−0.0993058
$171$	−4.63375	−0.354352
$172$	37.3794	2.85015
$173$	−15.3069	−1.16376	−0.581880	−	0.813275i	$-0.697683\pi$
$173$	−15.3069	−1.16376	−0.581880	+	0.813275i	$0.697683\pi$
$174$	−20.0323	−1.51864
$175$	8.62217	0.651774
$176$	−7.04832	−0.531287
$177$	−9.08966	−0.683221
$178$	−9.01534	−0.675728
$179$	17.2538	1.28961	0.644804	−	0.764348i	$-0.276939\pi$
$179$	17.2538	1.28961	0.644804	+	0.764348i	$0.276939\pi$
$180$	11.0208	0.821442
$181$	−22.7798	−1.69321	−0.846603	−	0.532225i	$-0.821356\pi$
$181$	−22.7798	−1.69321	−0.846603	+	0.532225i	$0.821356\pi$
$182$	−21.8313	−1.61824
$183$	−8.39729	−0.620746
$184$	−47.4037	−3.49465
$185$	−0.214876	−0.0157980
$186$	−13.6362	−0.999852
$187$	0.266667	0.0195006
$188$	12.3677	0.902004
$189$	18.1170	1.31782
$190$	12.1397	0.880708
$191$	19.5280	1.41300	0.706498	−	0.707715i	$-0.250274\pi$
$191$	19.5280	1.41300	0.706498	+	0.707715i	$0.250274\pi$
$192$	5.19302	0.374774
$193$	−9.50715	−0.684340	−0.342170	−	0.939638i	$-0.611162\pi$
$193$	−9.50715	−0.684340	−0.342170	+	0.939638i	$0.611162\pi$
$194$	−16.3111	−1.17107
$195$	4.80616	0.344176
$196$	18.1025	1.29303
$197$	4.89112	0.348478	0.174239	−	0.984703i	$-0.444253\pi$
$197$	4.89112	0.348478	0.174239	+	0.984703i	$0.444253\pi$
$198$	−3.23892	−0.230180
$199$	−8.86899	−0.628706	−0.314353	−	0.949306i	$-0.601788\pi$
$199$	−8.86899	−0.628706	−0.314353	+	0.949306i	$0.601788\pi$
$200$	18.1524	1.28357
$201$	0.897211	0.0632844
$202$	48.4630	3.40984
$203$	−21.0202	−1.47533
$204$	−1.84593	−0.129241
$205$	1.28302	0.0896101
$206$	−42.5122	−2.96196
$207$	−10.4088	−0.723463
$208$	−21.9621	−1.52280
$209$	−2.50023	−0.172944
$210$	−15.9874	−1.10324
$211$	−28.2770	−1.94667	−0.973335	−	0.229388i	$-0.926328\pi$
$211$	−28.2770	−1.94667	−0.973335	+	0.229388i	$0.926328\pi$
$212$	−34.5390	−2.37215
$213$	19.5792	1.34154
$214$	−34.4576	−2.35548
$215$	−12.3217	−0.840336
$216$	38.1421	2.59524
$217$	−14.3086	−0.971333
$218$	8.95119	0.606251
$219$	18.9867	1.28300
$220$	5.94648	0.400912
$221$	0.830917	0.0558935
$222$	−0.437141	−0.0293390
$223$	−17.3579	−1.16237	−0.581185	−	0.813772i	$-0.697411\pi$
$223$	−17.3579	−1.16237	−0.581185	+	0.813772i	$0.697411\pi$
$224$	27.3085	1.82463
$225$	3.98588	0.265725
$226$	−31.3987	−2.08861
$227$	20.1943	1.34034	0.670170	−	0.742208i	$-0.266221\pi$
$227$	20.1943	1.34034	0.670170	+	0.742208i	$0.266221\pi$
$228$	17.3072	1.14619
$229$	−9.85790	−0.651428	−0.325714	−	0.945468i	$-0.605605\pi$
$229$	−9.85790	−0.651428	−0.325714	+	0.945468i	$0.605605\pi$
$230$	27.2695	1.79810
$231$	3.29267	0.216642
$232$	−44.2542	−2.90543
$233$	19.2841	1.26335	0.631673	−	0.775235i	$-0.282369\pi$
$233$	19.2841	1.26335	0.631673	+	0.775235i	$0.282369\pi$
$234$	−10.0922	−0.659750
$235$	−4.07688	−0.265946
$236$	−35.0427	−2.28109
$237$	−12.2441	−0.795338
$238$	−2.76400	−0.179163
$239$	14.4709	0.936043	0.468022	−	0.883717i	$-0.344967\pi$
$239$	14.4709	0.936043	0.468022	+	0.883717i	$0.344967\pi$
$240$	−16.0832	−1.03817
$241$	−17.8033	−1.14681	−0.573405	−	0.819272i	$-0.694378\pi$
$241$	−17.8033	−1.14681	−0.573405	+	0.819272i	$0.694378\pi$
$242$	26.6914	1.71579
$243$	13.9293	0.893564
$244$	−32.3735	−2.07250
$245$	−5.96729	−0.381236
$246$	2.61016	0.166418
$247$	−7.79054	−0.495700
$248$	−30.1243	−1.91289
$249$	−0.519056	−0.0328938
$250$	−30.4024	−1.92282
$251$	−19.7051	−1.24378	−0.621889	−	0.783105i	$-0.713634\pi$
$251$	−19.7051	−1.24378	−0.621889	+	0.783105i	$0.713634\pi$
$252$	23.5262	1.48201
$253$	−5.61627	−0.353092
$254$	−1.82142	−0.114286
$255$	0.608493	0.0381053
$256$	−22.8192	−1.42620
$257$	−12.3126	−0.768040	−0.384020	−	0.923325i	$-0.625461\pi$
$257$	−12.3126	−0.768040	−0.384020	+	0.923325i	$0.625461\pi$
$258$	−25.0671	−1.56061
$259$	−0.458699	−0.0285021
$260$	18.5288	1.14911
$261$	−9.71726	−0.601483
$262$	35.3878	2.18627
$263$	−2.44633	−0.150847	−0.0754236	−	0.997152i	$-0.524031\pi$
$263$	−2.44633	−0.150847	−0.0754236	+	0.997152i	$0.524031\pi$
$264$	6.93214	0.426644
$265$	11.3854	0.699401
$266$	25.9148	1.58894
$267$	4.23681	0.259289
$268$	3.45895	0.211289
$269$	−7.80447	−0.475847	−0.237924	−	0.971284i	$-0.576467\pi$
$269$	−7.80447	−0.475847	−0.237924	+	0.971284i	$0.576467\pi$
$270$	−21.9417	−1.33533
$271$	31.9572	1.94126	0.970632	−	0.240569i	$-0.0773339\pi$
$271$	31.9572	1.94126	0.970632	+	0.240569i	$0.0773339\pi$
$272$	−2.78056	−0.168596
$273$	10.2597	0.620948
$274$	−47.0079	−2.83985
$275$	2.15066	0.129689
$276$	38.8772	2.34013
$277$	18.1151	1.08843	0.544216	−	0.838945i	$-0.316827\pi$
$277$	18.1151	1.08843	0.544216	+	0.838945i	$0.316827\pi$
$278$	26.1141	1.56622
$279$	−6.61463	−0.396008
$280$	−35.3185	−2.11069
$281$	−12.9179	−0.770618	−0.385309	−	0.922788i	$-0.625905\pi$
$281$	−12.9179	−0.770618	−0.385309	+	0.922788i	$0.625905\pi$
$282$	−8.29393	−0.493896
$283$	−33.1997	−1.97352	−0.986758	−	0.162202i	$-0.948141\pi$
$283$	−33.1997	−1.97352	−0.986758	+	0.162202i	$0.948141\pi$
$284$	75.4822	4.47905
$285$	−5.70513	−0.337943
$286$	−5.44546	−0.321997
$287$	2.73888	0.161671
$288$	12.6243	0.743892
$289$	−16.8948	−0.993812
$290$	25.4578	1.49493
$291$	7.66549	0.449359
$292$	73.1981	4.28359
$293$	−8.51149	−0.497246	−0.248623	−	0.968600i	$-0.579978\pi$
$293$	−8.51149	−0.497246	−0.248623	+	0.968600i	$0.579978\pi$
$294$	−12.1398	−0.708005
$295$	11.5515	0.672553
$296$	−0.965709	−0.0561307
$297$	4.51898	0.262218
$298$	59.0927	3.42315
$299$	−17.4999	−1.01205
$300$	−14.8873	−0.859521
$301$	−26.3033	−1.51610
$302$	−27.2365	−1.56729
$303$	−22.7755	−1.30842
$304$	26.0700	1.49522
$305$	10.6716	0.611053
$306$	−1.27775	−0.0730440
$307$	−22.9322	−1.30881	−0.654405	−	0.756144i	$-0.727081\pi$
$307$	−22.9322	−1.30881	−0.654405	+	0.756144i	$0.727081\pi$
$308$	12.6940	0.723308
$309$	19.9788	1.13656
$310$	17.3293	0.984240
$311$	−3.87611	−0.219794	−0.109897	−	0.993943i	$-0.535052\pi$
$311$	−3.87611	−0.219794	−0.109897	+	0.993943i	$0.535052\pi$
$312$	21.6001	1.22286
$313$	10.6841	0.603901	0.301950	−	0.953324i	$-0.402362\pi$
$313$	10.6841	0.603901	0.301950	+	0.953324i	$0.402362\pi$
$314$	38.9254	2.19669
$315$	−7.75518	−0.436955
$316$	−47.2037	−2.65541
$317$	5.52968	0.310578	0.155289	−	0.987869i	$-0.450369\pi$
$317$	5.52968	0.310578	0.155289	+	0.987869i	$0.450369\pi$
$318$	23.1623	1.29888
$319$	−5.24313	−0.293559
$320$	−6.59948	−0.368922
$321$	16.1936	0.903836
$322$	58.2125	3.24406
$323$	−0.986336	−0.0548812
$324$	−9.86902	−0.548279
$325$	6.70129	0.371721
$326$	51.5491	2.85504
$327$	−4.20666	−0.232629
$328$	5.76622	0.318386
$329$	−8.70294	−0.479809
$330$	−3.98779	−0.219521
$331$	30.1704	1.65831	0.829156	−	0.559017i	$-0.188821\pi$
$331$	30.1704	1.65831	0.829156	+	0.559017i	$0.188821\pi$
$332$	−2.00108	−0.109823
$333$	−0.212048	−0.0116202
$334$	−19.1852	−1.04977
$335$	−1.14021	−0.0622963
$336$	−34.3329	−1.87301
$337$	0.654741	0.0356660	0.0178330	−	0.999841i	$-0.494323\pi$
$337$	0.654741	0.0356660	0.0178330	+	0.999841i	$0.494323\pi$
$338$	16.6421	0.905212
$339$	14.7560	0.801436
$340$	2.34588	0.127223
$341$	−3.56905	−0.193275
$342$	11.9800	0.647802
$343$	10.3346	0.558019
$344$	−55.3770	−2.98573
$345$	−12.8155	−0.689961
$346$	39.5739	2.12751
$347$	−1.16204	−0.0623818	−0.0311909	−	0.999513i	$-0.509930\pi$
$347$	−1.16204	−0.0623818	−0.0311909	+	0.999513i	$0.509930\pi$
$348$	36.2942	1.94557
$349$	9.67701	0.517999	0.258999	−	0.965877i	$-0.416607\pi$
$349$	9.67701	0.517999	0.258999	+	0.965877i	$0.416607\pi$
$350$	−22.2915	−1.19153
$351$	14.0808	0.751579
$352$	6.81166	0.363063
$353$	1.08468	0.0577319	0.0288660	−	0.999583i	$-0.490810\pi$
$353$	1.08468	0.0577319	0.0288660	+	0.999583i	$0.490810\pi$
$354$	23.5001	1.24902
$355$	−24.8820	−1.32060
$356$	16.3339	0.865693
$357$	1.29896	0.0687480
$358$	−44.6074	−2.35757
$359$	19.3053	1.01889	0.509447	−	0.860502i	$-0.329850\pi$
$359$	19.3053	1.01889	0.509447	+	0.860502i	$0.329850\pi$
$360$	−16.3271	−0.860516
$361$	−9.75228	−0.513278
$362$	58.8941	3.09540
$363$	−12.5438	−0.658378
$364$	39.5536	2.07317
$365$	−24.1290	−1.26297
$366$	21.7101	1.13480
$367$	19.7398	1.03041	0.515204	−	0.857068i	$-0.327716\pi$
$367$	19.7398	1.03041	0.515204	+	0.857068i	$0.327716\pi$
$368$	58.5612	3.05271
$369$	1.26614	0.0659124
$370$	0.555535	0.0288809
$371$	24.3046	1.26183
$372$	24.7058	1.28094
$373$	−27.2361	−1.41023	−0.705115	−	0.709093i	$-0.749105\pi$
$373$	−27.2361	−1.41023	−0.705115	+	0.709093i	$0.749105\pi$
$374$	−0.689433	−0.0356497
$375$	14.2878	0.737819
$376$	−18.3225	−0.944911
$377$	−16.3372	−0.841410
$378$	−46.8391	−2.40914
$379$	−25.4939	−1.30953	−0.654766	−	0.755832i	$-0.727233\pi$
$379$	−25.4939	−1.30953	−0.654766	+	0.755832i	$0.727233\pi$
$380$	−21.9946	−1.12830
$381$	0.855985	0.0438534
$382$	−50.4870	−2.58314
$383$	3.51828	0.179776	0.0898879	−	0.995952i	$-0.471349\pi$
$383$	3.51828	0.179776	0.0898879	+	0.995952i	$0.471349\pi$
$384$	6.70675	0.342253
$385$	−4.18445	−0.213259
$386$	24.5795	1.25106
$387$	−12.1596	−0.618106
$388$	29.5522	1.50029
$389$	−3.16764	−0.160606	−0.0803028	−	0.996771i	$-0.525589\pi$
$389$	−3.16764	−0.160606	−0.0803028	+	0.996771i	$0.525589\pi$
$390$	−12.4257	−0.629199
$391$	−2.21561	−0.112048
$392$	−26.8185	−1.35454
$393$	−16.6307	−0.838907
$394$	−12.6453	−0.637063
$395$	15.5602	0.782920
$396$	5.86822	0.294889
$397$	−30.8220	−1.54691	−0.773456	−	0.633850i	$-0.781474\pi$
$397$	−30.8220	−1.54691	−0.773456	+	0.633850i	$0.781474\pi$
$398$	22.9296	1.14936
$399$	−12.1788	−0.609702
$400$	−22.4250	−1.12125
$401$	6.32722	0.315966	0.157983	−	0.987442i	$-0.449501\pi$
$401$	6.32722	0.315966	0.157983	+	0.987442i	$0.449501\pi$
$402$	−2.31962	−0.115692
$403$	−11.1209	−0.553972
$404$	−87.8045	−4.36844
$405$	3.25323	0.161654
$406$	54.3449	2.69709
$407$	−0.114415	−0.00567133
$408$	2.73472	0.135389
$409$	−13.0609	−0.645822	−0.322911	−	0.946429i	$-0.604661\pi$
$409$	−13.0609	−0.645822	−0.322911	+	0.946429i	$0.604661\pi$
$410$	−3.31708	−0.163819
$411$	22.0916	1.08970
$412$	77.0229	3.79465
$413$	24.6590	1.21339
$414$	26.9106	1.32259
$415$	0.659635	0.0323802
$416$	21.2247	1.04062
$417$	−12.2725	−0.600985
$418$	6.46401	0.316165
$419$	16.0162	0.782444	0.391222	−	0.920296i	$-0.372053\pi$
$419$	16.0162	0.782444	0.391222	+	0.920296i	$0.372053\pi$
$420$	28.9658	1.41338
$421$	34.9961	1.70561	0.852803	−	0.522233i	$-0.174901\pi$
$421$	34.9961	1.70561	0.852803	+	0.522233i	$0.174901\pi$
$422$	73.1065	3.55877
$423$	−4.02322	−0.195616
$424$	51.1689	2.48498
$425$	0.848431	0.0411549
$426$	−50.6194	−2.45252
$427$	22.7807	1.10244
$428$	62.4298	3.01766
$429$	2.55912	0.123556
$430$	31.8562	1.53624
$431$	10.6270	0.511883	0.255942	−	0.966692i	$-0.417614\pi$
$431$	10.6270	0.511883	0.255942	+	0.966692i	$0.417614\pi$
$432$	−47.1197	−2.26705
$433$	−28.9749	−1.39245	−0.696223	−	0.717826i	$-0.745137\pi$
$433$	−28.9749	−1.39245	−0.696223	+	0.717826i	$0.745137\pi$
$434$	36.9931	1.77572
$435$	−11.9640	−0.573630
$436$	−16.2176	−0.776683
$437$	20.7732	0.993717
$438$	−49.0877	−2.34550
$439$	5.17977	0.247217	0.123608	−	0.992331i	$-0.460553\pi$
$439$	5.17977	0.247217	0.123608	+	0.992331i	$0.460553\pi$
$440$	−8.80962	−0.419982
$441$	−5.88876	−0.280417
$442$	−2.14823	−0.102181
$443$	15.9664	0.758584	0.379292	−	0.925277i	$-0.376168\pi$
$443$	15.9664	0.758584	0.379292	+	0.925277i	$0.376168\pi$
$444$	0.792005	0.0375869
$445$	−5.38429	−0.255240
$446$	44.8765	2.12496
$447$	−27.7709	−1.31352
$448$	−14.0880	−0.665594
$449$	24.1455	1.13950	0.569749	−	0.821819i	$-0.307040\pi$
$449$	24.1455	1.13950	0.569749	+	0.821819i	$0.307040\pi$
$450$	−10.3050	−0.485781
$451$	0.683167	0.0321691
$452$	56.8877	2.67577
$453$	12.8000	0.601394
$454$	−52.2096	−2.45032
$455$	−13.0385	−0.611253
$456$	−25.6403	−1.20072
$457$	−18.2855	−0.855360	−0.427680	−	0.903930i	$-0.640669\pi$
$457$	−18.2855	−0.855360	−0.427680	+	0.903930i	$0.640669\pi$
$458$	25.4863	1.19090
$459$	1.78273	0.0832108
$460$	−49.4065	−2.30359
$461$	−12.5351	−0.583817	−0.291908	−	0.956446i	$-0.594290\pi$
$461$	−12.5351	−0.583817	−0.291908	+	0.956446i	$0.594290\pi$
$462$	−8.51278	−0.396050
$463$	−37.3185	−1.73434	−0.867170	−	0.498013i	$-0.834063\pi$
$463$	−37.3185	−1.73434	−0.867170	+	0.498013i	$0.834063\pi$
$464$	54.6704	2.53801
$465$	−8.14402	−0.377670
$466$	−49.8566	−2.30956
$467$	2.42684	0.112301	0.0561504	−	0.998422i	$-0.482117\pi$
$467$	2.42684	0.112301	0.0561504	+	0.998422i	$0.482117\pi$
$468$	18.2850	0.845223
$469$	−2.43401	−0.112392
$470$	10.5402	0.486184
$471$	−18.2932	−0.842906
$472$	51.9152	2.38959
$473$	−6.56092	−0.301672
$474$	31.6555	1.45398
$475$	−7.95475	−0.364989
$476$	5.00777	0.229531
$477$	11.2356	0.514442
$478$	−37.4126	−1.71121
$479$	4.22344	0.192974	0.0964870	−	0.995334i	$-0.469239\pi$
$479$	4.22344	0.192974	0.0964870	+	0.995334i	$0.469239\pi$
$480$	15.5432	0.709445
$481$	−0.356508	−0.0162554
$482$	46.0280	2.09652
$483$	−27.3573	−1.24480
$484$	−48.3591	−2.19814
$485$	−9.74158	−0.442343
$486$	−36.0124	−1.63355
$487$	14.3820	0.651709	0.325854	−	0.945420i	$-0.394348\pi$
$487$	14.3820	0.651709	0.325854	+	0.945420i	$0.394348\pi$
$488$	47.9608	2.17108
$489$	−24.2258	−1.09553
$490$	15.4277	0.696950
$491$	−35.9904	−1.62423	−0.812113	−	0.583501i	$-0.801683\pi$
$491$	−35.9904	−1.62423	−0.812113	+	0.583501i	$0.801683\pi$
$492$	−4.72904	−0.213202
$493$	−2.06841	−0.0931564
$494$	20.1414	0.906205
$495$	−1.93440	−0.0869448
$496$	37.2147	1.67099
$497$	−53.1157	−2.38257
$498$	1.34195	0.0601343
$499$	26.5338	1.18782	0.593908	−	0.804533i	$-0.297584\pi$
$499$	26.5338	1.18782	0.593908	+	0.804533i	$0.297584\pi$
$500$	55.0827	2.46337
$501$	9.01617	0.402813
$502$	50.9451	2.27379
$503$	−42.6891	−1.90341	−0.951707	−	0.307006i	$-0.900673\pi$
$503$	−42.6891	−1.90341	−0.951707	+	0.307006i	$0.900673\pi$
$504$	−34.8537	−1.55251
$505$	28.9439	1.28799
$506$	14.5201	0.645499
$507$	−7.82106	−0.347345
$508$	3.30002	0.146414
$509$	13.3784	0.592986	0.296493	−	0.955035i	$-0.404183\pi$
$509$	13.3784	0.592986	0.296493	+	0.955035i	$0.404183\pi$
$510$	−1.57318	−0.0696616
$511$	−51.5084	−2.27860
$512$	47.9561	2.11938
$513$	−16.7146	−0.737967
$514$	31.8326	1.40408
$515$	−25.3898	−1.11881
$516$	45.4162	1.99934
$517$	−2.17080	−0.0954718
$518$	1.18590	0.0521057
$519$	−18.5980	−0.816360
$520$	−27.4502	−1.20377
$521$	4.57106	0.200262	0.100131	−	0.994974i	$-0.468074\pi$
$521$	4.57106	0.200262	0.100131	+	0.994974i	$0.468074\pi$
$522$	25.1227	1.09959
$523$	30.4043	1.32949	0.664744	−	0.747071i	$-0.268541\pi$
$523$	30.4043	1.32949	0.664744	+	0.747071i	$0.268541\pi$
$524$	−64.1151	−2.80088
$525$	10.4760	0.457210
$526$	6.32467	0.275769
$527$	−1.40799	−0.0613328
$528$	−8.56377	−0.372690
$529$	23.6630	1.02882
$530$	−29.4355	−1.27860
$531$	11.3994	0.494694
$532$	−46.9520	−2.03563
$533$	2.12870	0.0922043
$534$	−10.9537	−0.474014
$535$	−20.5794	−0.889723
$536$	−5.12438	−0.221340
$537$	20.9635	0.904641
$538$	20.1774	0.869911
$539$	−3.17739	−0.136860
$540$	39.7536	1.71072
$541$	−11.4219	−0.491064	−0.245532	−	0.969388i	$-0.578963\pi$
$541$	−11.4219	−0.491064	−0.245532	+	0.969388i	$0.578963\pi$
$542$	−82.6213	−3.54889
$543$	−27.6776	−1.18776
$544$	2.68719	0.115212
$545$	5.34598	0.228996
$546$	−26.5252	−1.13517
$547$	12.6698	0.541721	0.270860	−	0.962619i	$-0.412692\pi$
$547$	12.6698	0.541721	0.270860	+	0.962619i	$0.412692\pi$
$548$	85.1682	3.63821
$549$	10.5311	0.449458
$550$	−5.56024	−0.237089
$551$	19.3930	0.826172
$552$	−57.5959	−2.45144
$553$	33.2165	1.41251
$554$	−46.8342	−1.98980
$555$	−0.261077	−0.0110821
$556$	−47.3131	−2.00652
$557$	10.8013	0.457668	0.228834	−	0.973466i	$-0.426509\pi$
$557$	10.8013	0.457668	0.228834	+	0.973466i	$0.426509\pi$
$558$	17.1013	0.723954
$559$	−20.4434	−0.864663
$560$	43.6315	1.84377
$561$	0.324003	0.0136794
$562$	33.3976	1.40879
$563$	−0.150370	−0.00633732	−0.00316866	−	0.999995i	$-0.501009\pi$
$563$	−0.150370	−0.00633732	−0.00316866	+	0.999995i	$0.501009\pi$
$564$	15.0268	0.632743
$565$	−18.7525	−0.788923
$566$	85.8334	3.60785
$567$	6.94469	0.291649
$568$	−111.826	−4.69210
$569$	10.7227	0.449518	0.224759	−	0.974414i	$-0.427841\pi$
$569$	10.7227	0.449518	0.224759	+	0.974414i	$0.427841\pi$
$570$	14.7499	0.617804
$571$	−35.7681	−1.49685	−0.748425	−	0.663220i	$-0.769189\pi$
$571$	−35.7681	−1.49685	−0.748425	+	0.663220i	$0.769189\pi$
$572$	9.86599	0.412518
$573$	23.7267	0.991196
$574$	−7.08101	−0.295555
$575$	−17.8688	−0.745180
$576$	−6.51262	−0.271359
$577$	13.9573	0.581051	0.290526	−	0.956867i	$-0.406170\pi$
$577$	13.9573	0.581051	0.290526	+	0.956867i	$0.406170\pi$
$578$	43.6793	1.81682
$579$	−11.5513	−0.480054
$580$	−46.1240	−1.91519
$581$	1.40813	0.0584191
$582$	−19.8181	−0.821487
$583$	6.06237	0.251078
$584$	−108.442	−4.48735
$585$	−6.02745	−0.249205
$586$	22.0053	0.909032
$587$	−41.5673	−1.71567	−0.857833	−	0.513929i	$-0.828190\pi$
$587$	−41.5673	−1.71567	−0.857833	+	0.513929i	$0.828190\pi$
$588$	21.9946	0.907043
$589$	13.2010	0.543939
$590$	−29.8648	−1.22952
$591$	5.94275	0.244452
$592$	1.19301	0.0490324
$593$	−7.54681	−0.309911	−0.154955	−	0.987921i	$-0.549523\pi$
$593$	−7.54681	−0.309911	−0.154955	+	0.987921i	$0.549523\pi$
$594$	−11.6832	−0.479369
$595$	−1.65076	−0.0676746
$596$	−107.063	−4.38548
$597$	−10.7759	−0.441028
$598$	45.2437	1.85015
$599$	−22.8704	−0.934458	−0.467229	−	0.884136i	$-0.654748\pi$
$599$	−22.8704	−0.934458	−0.467229	+	0.884136i	$0.654748\pi$
$600$	22.0554	0.900407
$601$	0.0674134	0.00274985	0.00137492	−	0.999999i	$-0.499562\pi$
$601$	0.0674134	0.00274985	0.00137492	+	0.999999i	$0.499562\pi$
$602$	68.0038	2.77163
$603$	−1.12520	−0.0458218
$604$	49.3467	2.00789
$605$	15.9411	0.648098
$606$	58.8829	2.39196
$607$	4.02837	0.163507	0.0817533	−	0.996653i	$-0.473948\pi$
$607$	4.02837	0.163507	0.0817533	+	0.996653i	$0.473948\pi$
$608$	−25.1947	−1.02178
$609$	−25.5397	−1.03492
$610$	−27.5900	−1.11709
$611$	−6.76407	−0.273645
$612$	2.31500	0.0935785
$613$	25.5413	1.03160	0.515802	−	0.856708i	$-0.327494\pi$
$613$	25.5413	1.03160	0.515802	+	0.856708i	$0.327494\pi$
$614$	59.2882	2.39268
$615$	1.55888	0.0628602
$616$	−18.8060	−0.757714
$617$	−41.6857	−1.67820	−0.839101	−	0.543976i	$-0.816918\pi$
$617$	−41.6857	−1.67820	−0.839101	+	0.543976i	$0.816918\pi$
$618$	−51.6526	−2.07777
$619$	45.9648	1.84748	0.923742	−	0.383016i	$-0.125115\pi$
$619$	45.9648	1.84748	0.923742	+	0.383016i	$0.125115\pi$
$620$	−31.3970	−1.26093
$621$	−37.5461	−1.50667
$622$	10.0212	0.401813
$623$	−11.4939	−0.460493
$624$	−26.6841	−1.06822
$625$	−5.07833	−0.203133
$626$	−27.6223	−1.10401
$627$	−3.03780	−0.121318
$628$	−70.5244	−2.81423
$629$	−0.0451365	−0.00179971
$630$	20.0500	0.798811
$631$	13.5709	0.540251	0.270125	−	0.962825i	$-0.412935\pi$
$631$	13.5709	0.540251	0.270125	+	0.962825i	$0.412935\pi$
$632$	69.9315	2.78173
$633$	−34.3568	−1.36556
$634$	−14.2963	−0.567777
$635$	−1.08782	−0.0431687
$636$	−41.9651	−1.66403
$637$	−9.90053	−0.392273
$638$	13.5554	0.536664
$639$	−24.5545	−0.971360
$640$	−8.52319	−0.336909
$641$	0.733479	0.0289707	0.0144853	−	0.999895i	$-0.495389\pi$
$641$	0.733479	0.0289707	0.0144853	+	0.999895i	$0.495389\pi$
$642$	−41.8663	−1.65233
$643$	−37.7868	−1.49017	−0.745083	−	0.666971i	$-0.767590\pi$
$643$	−37.7868	−1.49017	−0.745083	+	0.666971i	$0.767590\pi$
$644$	−105.469	−4.15604
$645$	−14.9710	−0.589483
$646$	2.55004	0.100330
$647$	7.51812	0.295568	0.147784	−	0.989020i	$-0.452786\pi$
$647$	7.51812	0.295568	0.147784	+	0.989020i	$0.452786\pi$
$648$	14.6208	0.574360
$649$	6.15078	0.241439
$650$	−17.3253	−0.679555
$651$	−17.3851	−0.681376
$652$	−93.3959	−3.65767
$653$	−45.7840	−1.79167	−0.895833	−	0.444390i	$-0.853420\pi$
$653$	−45.7840	−1.79167	−0.895833	+	0.444390i	$0.853420\pi$
$654$	10.8758	0.425276
$655$	21.1349	0.825809
$656$	−7.12342	−0.278123
$657$	−23.8114	−0.928973
$658$	22.5003	0.877153
$659$	−41.8133	−1.62882	−0.814408	−	0.580293i	$-0.802938\pi$
$659$	−41.8133	−1.62882	−0.814408	+	0.580293i	$0.802938\pi$
$660$	7.22502	0.281234
$661$	32.3086	1.25666	0.628330	−	0.777947i	$-0.283739\pi$
$661$	32.3086	1.25666	0.628330	+	0.777947i	$0.283739\pi$
$662$	−78.0015	−3.03161
$663$	1.00957	0.0392085
$664$	2.96457	0.115048
$665$	15.4773	0.600182
$666$	0.548223	0.0212432
$667$	43.5627	1.68675
$668$	34.7594	1.34488
$669$	−21.0900	−0.815385
$670$	2.94786	0.113886
$671$	5.68227	0.219362
$672$	33.1801	1.27995
$673$	−3.58850	−0.138326	−0.0691632	−	0.997605i	$-0.522033\pi$
$673$	−3.58850	−0.138326	−0.0691632	+	0.997605i	$0.522033\pi$
$674$	−1.69275	−0.0652022
$675$	14.3776	0.553395
$676$	−30.1519	−1.15969
$677$	42.3866	1.62905	0.814525	−	0.580128i	$-0.196998\pi$
$677$	42.3866	1.62905	0.814525	+	0.580128i	$0.196998\pi$
$678$	−38.1497	−1.46513
$679$	−20.7954	−0.798056
$680$	−3.47538	−0.133275
$681$	24.5362	0.940229
$682$	9.22731	0.353332
$683$	−30.1169	−1.15239	−0.576195	−	0.817313i	$-0.695463\pi$
$683$	−30.1169	−1.15239	−0.576195	+	0.817313i	$0.695463\pi$
$684$	−21.7051	−0.829915
$685$	−28.0749	−1.07269
$686$	−26.7189	−1.02013
$687$	−11.9774	−0.456967
$688$	68.4111	2.60815
$689$	18.8899	0.719649
$690$	33.1327	1.26134
$691$	2.17067	0.0825763	0.0412881	−	0.999147i	$-0.486854\pi$
$691$	2.17067	0.0825763	0.0412881	+	0.999147i	$0.486854\pi$
$692$	−71.6994	−2.72560
$693$	−4.12938	−0.156862
$694$	3.00431	0.114042
$695$	15.5963	0.591601
$696$	−53.7693	−2.03812
$697$	0.269509	0.0102084
$698$	−25.0187	−0.946970
$699$	23.4304	0.886218
$700$	40.3874	1.52650
$701$	−32.3568	−1.22210	−0.611050	−	0.791592i	$-0.709252\pi$
$701$	−32.3568	−1.22210	−0.611050	+	0.791592i	$0.709252\pi$
$702$	−36.4041	−1.37399
$703$	0.423192	0.0159610
$704$	−3.51401	−0.132439
$705$	−4.95344	−0.186557
$706$	−2.80431	−0.105542
$707$	61.7868	2.32373
$708$	−42.5772	−1.60015
$709$	9.54496	0.358469	0.179234	−	0.983806i	$-0.442638\pi$
$709$	9.54496	0.358469	0.179234	+	0.983806i	$0.442638\pi$
$710$	64.3290	2.41423
$711$	15.3554	0.575874
$712$	−24.1984	−0.906872
$713$	29.6535	1.11053
$714$	−3.35828	−0.125680
$715$	−3.25223	−0.121626
$716$	80.8190	3.02035
$717$	17.5822	0.656621
$718$	−49.9113	−1.86267
$719$	18.5152	0.690502	0.345251	−	0.938510i	$-0.387794\pi$
$719$	18.5152	0.690502	0.345251	+	0.938510i	$0.387794\pi$
$720$	20.1701	0.751695
$721$	−54.1999	−2.01851
$722$	25.2132	0.938339
$723$	−21.6311	−0.804470
$724$	−106.703	−3.96560
$725$	−16.6816	−0.619539
$726$	32.4303	1.20360
$727$	40.6377	1.50717	0.753584	−	0.657352i	$-0.228323\pi$
$727$	40.6377	1.50717	0.753584	+	0.657352i	$0.228323\pi$
$728$	−58.5981	−2.17179
$729$	23.2449	0.860923
$730$	62.3824	2.30888
$731$	−2.58828	−0.0957308
$732$	−39.3340	−1.45383
$733$	−41.7815	−1.54323	−0.771617	−	0.636087i	$-0.780552\pi$
$733$	−41.7815	−1.54323	−0.771617	+	0.636087i	$0.780552\pi$
$734$	−51.0346	−1.88372
$735$	−7.25031	−0.267432
$736$	−56.5949	−2.08612
$737$	−0.607124	−0.0223637
$738$	−3.27343	−0.120496
$739$	−16.0738	−0.591286	−0.295643	−	0.955299i	$-0.595534\pi$
$739$	−16.0738	−0.591286	−0.295643	+	0.955299i	$0.595534\pi$
$740$	−1.00651	−0.0370000
$741$	−9.46556	−0.347726
$742$	−62.8363	−2.30679
$743$	32.3173	1.18561	0.592804	−	0.805347i	$-0.298021\pi$
$743$	32.3173	1.18561	0.592804	+	0.805347i	$0.298021\pi$
$744$	−36.6013	−1.34187
$745$	35.2923	1.29301
$746$	70.4152	2.57809
$747$	0.650954	0.0238172
$748$	1.24910	0.0456718
$749$	−43.9309	−1.60520
$750$	−36.9392	−1.34883
$751$	−41.0616	−1.49836	−0.749180	−	0.662366i	$-0.769552\pi$
$751$	−41.0616	−1.49836	−0.749180	+	0.662366i	$0.769552\pi$
$752$	22.6351	0.825417
$753$	−23.9419	−0.872492
$754$	42.2378	1.53821
$755$	−16.2666	−0.592004
$756$	84.8623	3.08641
$757$	29.2990	1.06489	0.532445	−	0.846464i	$-0.321273\pi$
$757$	29.2990	1.06489	0.532445	+	0.846464i	$0.321273\pi$
$758$	65.9110	2.39400
$759$	−6.82382	−0.247689
$760$	32.5846	1.18197
$761$	−45.8827	−1.66325	−0.831624	−	0.555339i	$-0.812588\pi$
$761$	−45.8827	−1.66325	−0.831624	+	0.555339i	$0.812588\pi$
$762$	−2.21304	−0.0801699
$763$	11.4121	0.413146
$764$	91.4716	3.30933
$765$	−0.763118	−0.0275906
$766$	−9.09605	−0.328654
$767$	19.1654	0.692023
$768$	−27.7255	−1.00046
$769$	−26.3545	−0.950368	−0.475184	−	0.879886i	$-0.657619\pi$
$769$	−26.3545	−0.950368	−0.475184	+	0.879886i	$0.657619\pi$
$770$	10.8183	0.389866
$771$	−14.9599	−0.538769
$772$	−44.5328	−1.60277
$773$	−49.2996	−1.77318	−0.886592	−	0.462552i	$-0.846934\pi$
$773$	−49.2996	−1.77318	−0.886592	+	0.462552i	$0.846934\pi$
$774$	31.4370	1.12998
$775$	−11.3553	−0.407895
$776$	−43.7811	−1.57165
$777$	−0.557323	−0.0199938
$778$	8.18951	0.293608
$779$	−2.52687	−0.0905344
$780$	22.5127	0.806083
$781$	−13.2488	−0.474080
$782$	5.72817	0.204839
$783$	−35.0515	−1.25264
$784$	33.1308	1.18324
$785$	23.2477	0.829745
$786$	42.9965	1.53363
$787$	25.2153	0.898830	0.449415	−	0.893323i	$-0.351633\pi$
$787$	25.2153	0.898830	0.449415	+	0.893323i	$0.351633\pi$
$788$	22.9106	0.816158
$789$	−2.97231	−0.105817
$790$	−40.2289	−1.43128
$791$	−40.0311	−1.42334
$792$	−8.69367	−0.308916
$793$	17.7056	0.628743
$794$	79.6862	2.82796
$795$	13.8334	0.490620
$796$	−41.5435	−1.47247
$797$	38.5744	1.36638	0.683188	−	0.730243i	$-0.260593\pi$
$797$	38.5744	1.36638	0.683188	+	0.730243i	$0.260593\pi$
$798$	31.4867	1.11462
$799$	−0.856379	−0.0302965
$800$	21.6720	0.766222
$801$	−5.31343	−0.187741
$802$	−16.3582	−0.577628
$803$	−12.8479	−0.453393
$804$	4.20265	0.148216
$805$	34.7666	1.22536
$806$	28.7517	1.01273
$807$	−9.48250	−0.333800
$808$	130.081	4.57624
$809$	20.9785	0.737564	0.368782	−	0.929516i	$-0.379775\pi$
$809$	20.9785	0.737564	0.368782	+	0.929516i	$0.379775\pi$
$810$	−8.41079	−0.295525
$811$	−54.8576	−1.92631	−0.963156	−	0.268943i	$-0.913326\pi$
$811$	−54.8576	−1.92631	−0.963156	+	0.268943i	$0.913326\pi$
$812$	−98.4612	−3.45531
$813$	38.8283	1.36177
$814$	0.295804	0.0103679
$815$	30.7870	1.07842
$816$	−3.37840	−0.118268
$817$	24.2672	0.849003
$818$	33.7673	1.18065
$819$	−12.8669	−0.449604
$820$	6.00984	0.209873
$821$	−21.1388	−0.737750	−0.368875	−	0.929479i	$-0.620257\pi$
$821$	−21.1388	−0.737750	−0.368875	+	0.929479i	$0.620257\pi$
$822$	−57.1150	−1.99212
$823$	−12.8349	−0.447397	−0.223699	−	0.974658i	$-0.571813\pi$
$823$	−12.8349	−0.447397	−0.223699	+	0.974658i	$0.571813\pi$
$824$	−114.108	−3.97515
$825$	2.61306	0.0909752
$826$	−63.7527	−2.21824
$827$	−42.6864	−1.48435	−0.742176	−	0.670205i	$-0.766206\pi$
$827$	−42.6864	−1.48435	−0.742176	+	0.670205i	$0.766206\pi$
$828$	−48.7563	−1.69440
$829$	−5.28852	−0.183678	−0.0918389	−	0.995774i	$-0.529274\pi$
$829$	−5.28852	−0.183678	−0.0918389	+	0.995774i	$0.529274\pi$
$830$	−1.70540	−0.0591953
$831$	22.0100	0.763519
$832$	−10.9494	−0.379602
$833$	−1.25348	−0.0434304
$834$	31.7288	1.09868
$835$	−11.4581	−0.396523
$836$	−11.7114	−0.405047
$837$	−23.8599	−0.824719
$838$	−41.4078	−1.43041
$839$	16.5036	0.569768	0.284884	−	0.958562i	$-0.408045\pi$
$839$	16.5036	0.569768	0.284884	+	0.958562i	$0.408045\pi$
$840$	−42.9123	−1.48062
$841$	11.6684	0.402359
$842$	−90.4778	−3.11807
$843$	−15.6954	−0.540577
$844$	−132.453	−4.55923
$845$	9.93929	0.341922
$846$	10.4015	0.357611
$847$	34.0296	1.16927
$848$	−63.2127	−2.17073
$849$	−40.3379	−1.38439
$850$	−2.19351	−0.0752367
$851$	0.950618	0.0325868
$852$	91.7115	3.14198
$853$	−38.1120	−1.30493	−0.652465	−	0.757819i	$-0.726265\pi$
$853$	−38.1120	−1.30493	−0.652465	+	0.757819i	$0.726265\pi$
$854$	−58.8966	−2.01540
$855$	7.15487	0.244691
$856$	−92.4888	−3.16120
$857$	22.1705	0.757331	0.378665	−	0.925534i	$-0.376383\pi$
$857$	22.1705	0.757331	0.378665	+	0.925534i	$0.376383\pi$
$858$	−6.61627	−0.225876
$859$	34.7225	1.18472	0.592359	−	0.805674i	$-0.298197\pi$
$859$	34.7225	1.18472	0.592359	+	0.805674i	$0.298197\pi$
$860$	−57.7166	−1.96812
$861$	3.32776	0.113410
$862$	−27.4747	−0.935790
$863$	−6.64523	−0.226206	−0.113103	−	0.993583i	$-0.536079\pi$
$863$	−6.64523	−0.226206	−0.113103	+	0.993583i	$0.536079\pi$
$864$	45.5375	1.54922
$865$	23.6350	0.803614
$866$	74.9108	2.54557
$867$	−20.5273	−0.697144
$868$	−67.0235	−2.27493
$869$	8.28531	0.281060
$870$	30.9314	1.04867
$871$	−1.89176	−0.0640997
$872$	24.0262	0.813628
$873$	−9.61337	−0.325363
$874$	−53.7064	−1.81665
$875$	−38.7609	−1.31036
$876$	88.9363	3.00488
$877$	7.38988	0.249539	0.124769	−	0.992186i	$-0.460181\pi$
$877$	7.38988	0.249539	0.124769	+	0.992186i	$0.460181\pi$
$878$	−13.3916	−0.451945
$879$	−10.3415	−0.348811
$880$	10.8832	0.366871
$881$	−50.4591	−1.70001	−0.850006	−	0.526773i	$-0.823402\pi$
$881$	−50.4591	−1.70001	−0.850006	+	0.526773i	$0.823402\pi$
$882$	15.2246	0.512639
$883$	−32.4812	−1.09308	−0.546540	−	0.837433i	$-0.684055\pi$
$883$	−32.4812	−1.09308	−0.546540	+	0.837433i	$0.684055\pi$
$884$	3.89212	0.130906
$885$	14.0351	0.471786
$886$	−41.2789	−1.38679
$887$	−35.3236	−1.18605	−0.593024	−	0.805184i	$-0.702066\pi$
$887$	−35.3236	−1.18605	−0.593024	+	0.805184i	$0.702066\pi$
$888$	−1.17334	−0.0393748
$889$	−2.32217	−0.0778832
$890$	13.9204	0.466612
$891$	1.73224	0.0580321
$892$	−81.3066	−2.72235
$893$	8.02927	0.268689
$894$	71.7981	2.40129
$895$	−26.6412	−0.890516
$896$	−18.1945	−0.607836
$897$	−21.2625	−0.709936
$898$	−62.4251	−2.08315
$899$	27.6834	0.923292
$900$	18.6704	0.622346
$901$	2.39160	0.0796756
$902$	−1.76624	−0.0588093
$903$	−31.9587	−1.06352
$904$	−84.2783	−2.80306
$905$	35.1737	1.16921
$906$	−33.0926	−1.09943
$907$	16.8726	0.560246	0.280123	−	0.959964i	$-0.409625\pi$
$907$	16.8726	0.560246	0.280123	+	0.959964i	$0.409625\pi$
$908$	94.5926	3.13916
$909$	28.5629	0.947373
$910$	33.7092	1.11745
$911$	26.3390	0.872649	0.436325	−	0.899789i	$-0.356280\pi$
$911$	26.3390	0.872649	0.436325	+	0.899789i	$0.356280\pi$
$912$	31.6753	1.04887
$913$	0.351234	0.0116242
$914$	47.2748	1.56371
$915$	12.9661	0.428645
$916$	−46.1757	−1.52569
$917$	45.1168	1.48989
$918$	−4.60902	−0.152120
$919$	35.7946	1.18076	0.590378	−	0.807127i	$-0.298979\pi$
$919$	35.7946	1.18076	0.590378	+	0.807127i	$0.298979\pi$
$920$	73.1950	2.41317
$921$	−27.8628	−0.918111
$922$	32.4078	1.06729
$923$	−41.2824	−1.35883
$924$	15.4233	0.507390
$925$	−0.364023	−0.0119690
$926$	96.4822	3.17060
$927$	−25.0557	−0.822936
$928$	−52.8347	−1.73439
$929$	15.3590	0.503911	0.251956	−	0.967739i	$-0.418926\pi$
$929$	15.3590	0.503911	0.251956	+	0.967739i	$0.418926\pi$
$930$	21.0553	0.690430
$931$	11.7524	0.385169
$932$	90.3294	2.95884
$933$	−4.70951	−0.154182
$934$	−6.27428	−0.205301
$935$	−0.411755	−0.0134658
$936$	−27.0889	−0.885428
$937$	50.3281	1.64415	0.822074	−	0.569380i	$-0.192817\pi$
$937$	50.3281	1.64415	0.822074	+	0.569380i	$0.192817\pi$
$938$	6.29282	0.205468
$939$	12.9813	0.423628
$940$	−19.0966	−0.622863
$941$	−41.2611	−1.34507	−0.672536	−	0.740064i	$-0.734795\pi$
$941$	−41.2611	−1.34507	−0.672536	+	0.740064i	$0.734795\pi$
$942$	47.2947	1.54094
$943$	−5.67611	−0.184840
$944$	−64.1346	−2.08740
$945$	−27.9740	−0.909995
$946$	16.9624	0.551495
$947$	55.5863	1.80631	0.903156	−	0.429312i	$-0.141244\pi$
$947$	55.5863	1.80631	0.903156	+	0.429312i	$0.141244\pi$
$948$	−57.3529	−1.86273
$949$	−40.0332	−1.29953
$950$	20.5659	0.667248
$951$	6.71861	0.217866
$952$	−7.41893	−0.240449
$953$	11.8505	0.383875	0.191937	−	0.981407i	$-0.438523\pi$
$953$	11.8505	0.383875	0.191937	+	0.981407i	$0.438523\pi$
$954$	−29.0481	−0.940467
$955$	−30.1527	−0.975719
$956$	67.7835	2.19228
$957$	−6.37045	−0.205927
$958$	−10.9192	−0.352782
$959$	−59.9316	−1.93529
$960$	−8.01842	−0.258793
$961$	−12.1557	−0.392118
$962$	0.921705	0.0297170
$963$	−20.3085	−0.654433
$964$	−83.3929	−2.68590
$965$	14.6798	0.472559
$966$	70.7287	2.27566
$967$	7.18112	0.230929	0.115465	−	0.993312i	$-0.463164\pi$
$967$	7.18112	0.230929	0.115465	+	0.993312i	$0.463164\pi$
$968$	71.6433	2.30270
$969$	−1.19841	−0.0384984
$970$	25.1856	0.808660
$971$	−24.8897	−0.798750	−0.399375	−	0.916788i	$-0.630773\pi$
$971$	−24.8897	−0.798750	−0.399375	+	0.916788i	$0.630773\pi$
$972$	65.2466	2.09279
$973$	33.2935	1.06734
$974$	−37.1827	−1.19141
$975$	8.14213	0.260757
$976$	−59.2494	−1.89653
$977$	−27.4625	−0.878603	−0.439301	−	0.898340i	$-0.644774\pi$
$977$	−27.4625	−0.878603	−0.439301	+	0.898340i	$0.644774\pi$
$978$	62.6326	2.00277
$979$	−2.86696	−0.0916285
$980$	−27.9516	−0.892881
$981$	5.27562	0.168437
$982$	93.0485	2.96930
$983$	−24.1371	−0.769854	−0.384927	−	0.922947i	$-0.625773\pi$
$983$	−24.1371	−0.769854	−0.384927	+	0.922947i	$0.625773\pi$
$984$	7.00600	0.223343
$985$	−7.55227	−0.240635
$986$	5.34760	0.170302
$987$	−10.5741	−0.336579
$988$	−36.4919	−1.16096
$989$	54.5116	1.73337
$990$	5.00113	0.158946
$991$	−15.0003	−0.476500	−0.238250	−	0.971204i	$-0.576574\pi$
$991$	−15.0003	−0.476500	−0.238250	+	0.971204i	$0.576574\pi$
$992$	−35.9651	−1.14189
$993$	36.6572	1.16328
$994$	137.324	4.35564
$995$	13.6944	0.434142
$996$	−2.43133	−0.0770395
$997$	−4.21664	−0.133542	−0.0667712	−	0.997768i	$-0.521270\pi$
$997$	−4.21664	−0.133542	−0.0667712	+	0.997768i	$0.521270\pi$
$998$	−68.5997	−2.17149
$999$	−0.764888	−0.0242000

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6029.2.a.a.1.11	✓	234

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6029.2.a.a.1.11	✓	234	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:	\( N \)	\(=\)	\( 6029 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58537 q^{2} +1.21501 q^{3} +4.68413 q^{4} -1.54408 q^{5} -3.14124 q^{6} -3.29615 q^{7} -6.93947 q^{8} -1.52375 q^{9} +O(q^{10})\)	\(q-2.58537 q^{2} +1.21501 q^{3} +4.68413 q^{4} -1.54408 q^{5} -3.14124 q^{6} -3.29615 q^{7} -6.93947 q^{8} -1.52375 q^{9} +3.99201 q^{10} -0.822171 q^{11} +5.69126 q^{12} -2.56183 q^{13} +8.52177 q^{14} -1.87607 q^{15} +8.57282 q^{16} -0.324345 q^{17} +3.93947 q^{18} +3.04101 q^{19} -7.23266 q^{20} -4.00485 q^{21} +2.12561 q^{22} +6.83103 q^{23} -8.43151 q^{24} -2.61583 q^{25} +6.62327 q^{26} -5.49640 q^{27} -15.4396 q^{28} +6.37718 q^{29} +4.85032 q^{30} +4.34101 q^{31} -8.28497 q^{32} -0.998944 q^{33} +0.838552 q^{34} +5.08952 q^{35} -7.13747 q^{36} +0.139162 q^{37} -7.86212 q^{38} -3.11264 q^{39} +10.7151 q^{40} -0.830931 q^{41} +10.3540 q^{42} +7.98000 q^{43} -3.85116 q^{44} +2.35280 q^{45} -17.6607 q^{46} +2.64033 q^{47} +10.4161 q^{48} +3.86463 q^{49} +6.76287 q^{50} -0.394082 q^{51} -11.9999 q^{52} -7.37361 q^{53} +14.2102 q^{54} +1.26949 q^{55} +22.8736 q^{56} +3.69485 q^{57} -16.4874 q^{58} -7.48115 q^{59} -8.78774 q^{60} -6.91130 q^{61} -11.2231 q^{62} +5.02253 q^{63} +4.27406 q^{64} +3.95566 q^{65} +2.58264 q^{66} +0.738440 q^{67} -1.51928 q^{68} +8.29976 q^{69} -13.1583 q^{70} +16.1145 q^{71} +10.5741 q^{72} +15.6268 q^{73} -0.359784 q^{74} -3.17825 q^{75} +14.2445 q^{76} +2.71000 q^{77} +8.04733 q^{78} -10.0774 q^{79} -13.2371 q^{80} -2.10691 q^{81} +2.14826 q^{82} -0.427204 q^{83} -18.7593 q^{84} +0.500814 q^{85} -20.6312 q^{86} +7.74833 q^{87} +5.70543 q^{88} +3.48706 q^{89} -6.08284 q^{90} +8.44418 q^{91} +31.9974 q^{92} +5.27436 q^{93} -6.82623 q^{94} -4.69555 q^{95} -10.0663 q^{96} +6.30900 q^{97} -9.99151 q^{98} +1.25279 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9}+O(q^{10}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9	\( 234 q - 10 q^{2} - 43 q^{3} + 202 q^{4} - 24 q^{5} - 40 q^{6} - 61 q^{7} - 27 q^{8} + 203 q^{9} - 89 q^{10} - 55 q^{11} - 75 q^{12} - 49 q^{13} - 42 q^{14} - 43 q^{15} + 142 q^{16} - 40 q^{17} - 30 q^{18} - 235 q^{19} - 62 q^{20} - 62 q^{21} - 63 q^{22} - 30 q^{23} - 108 q^{24} + 170 q^{25} - 44 q^{26} - 160 q^{27} - 147 q^{28} - 76 q^{29} - 15 q^{30} - 175 q^{31} - 49 q^{32} - 43 q^{33} - 104 q^{34} - 87 q^{35} + 124 q^{36} - 77 q^{37} - 18 q^{38} - 104 q^{39} - 247 q^{40} - 60 q^{41} - 6 q^{42} - 201 q^{43} - 89 q^{44} - 102 q^{45} - 128 q^{46} - 27 q^{47} - 130 q^{48} + 123 q^{49} - 33 q^{50} - 220 q^{51} - 125 q^{52} - 34 q^{53} - 126 q^{54} - 176 q^{55} - 125 q^{56} - 17 q^{57} - 46 q^{58} - 172 q^{59} - 61 q^{60} - 243 q^{61} - 37 q^{62} - 137 q^{63} + 39 q^{64} - 31 q^{65} - 142 q^{66} - 132 q^{67} - 106 q^{68} - 115 q^{69} - 60 q^{70} - 68 q^{71} - 66 q^{72} - 109 q^{73} - 74 q^{74} - 256 q^{75} - 412 q^{76} - 32 q^{77} - 38 q^{78} - 297 q^{79} - 111 q^{80} + 142 q^{81} - 94 q^{82} - 100 q^{83} - 134 q^{84} - 90 q^{85} + q^{86} - 103 q^{87} - 143 q^{88} - 77 q^{89} - 181 q^{90} - 418 q^{91} - 19 q^{92} + 5 q^{93} - 231 q^{94} - 92 q^{95} - 189 q^{96} - 141 q^{97} - 25 q^{98} - 244 q^{99}+O(q^{100}) \) 234 * q - 10 * q^2 - 43 * q^3 + 202 * q^4 - 24 * q^5 - 40 * q^6 - 61 * q^7 - 27 * q^8 + 203 * q^9 - 89 * q^10 - 55 * q^11 - 75 * q^12 - 49 * q^13 - 42 * q^14 - 43 * q^15 + 142 * q^16 - 40 * q^17 - 30 * q^18 - 235 * q^19 - 62 * q^20 - 62 * q^21 - 63 * q^22 - 30 * q^23 - 108 * q^24 + 170 * q^25 - 44 * q^26 - 160 * q^27 - 147 * q^28 - 76 * q^29 - 15 * q^30 - 175 * q^31 - 49 * q^32 - 43 * q^33 - 104 * q^34 - 87 * q^35 + 124 * q^36 - 77 * q^37 - 18 * q^38 - 104 * q^39 - 247 * q^40 - 60 * q^41 - 6 * q^42 - 201 * q^43 - 89 * q^44 - 102 * q^45 - 128 * q^46 - 27 * q^47 - 130 * q^48 + 123 * q^49 - 33 * q^50 - 220 * q^51 - 125 * q^52 - 34 * q^53 - 126 * q^54 - 176 * q^55 - 125 * q^56 - 17 * q^57 - 46 * q^58 - 172 * q^59 - 61 * q^60 - 243 * q^61 - 37 * q^62 - 137 * q^63 + 39 * q^64 - 31 * q^65 - 142 * q^66 - 132 * q^67 - 106 * q^68 - 115 * q^69 - 60 * q^70 - 68 * q^71 - 66 * q^72 - 109 * q^73 - 74 * q^74 - 256 * q^75 - 412 * q^76 - 32 * q^77 - 38 * q^78 - 297 * q^79 - 111 * q^80 + 142 * q^81 - 94 * q^82 - 100 * q^83 - 134 * q^84 - 90 * q^85 + q^86 - 103 * q^87 - 143 * q^88 - 77 * q^89 - 181 * q^90 - 418 * q^91 - 19 * q^92 + 5 * q^93 - 231 * q^94 - 92 * q^95 - 189 * q^96 - 141 * q^97 - 25 * q^98 - 244 * q^99

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