LMFDB - Embedded newform 8005.2.a.g.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8005,2,Mod(1,8005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8005 = 5 \cdot 1601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8005.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:	$63.9202468180$
Analytic rank:	$0$
Dimension:	$137$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48869 q^{2} -2.85866 q^{3} +4.19357 q^{4} -1.00000 q^{5} +7.11432 q^{6} -4.63571 q^{7} -5.45912 q^{8} +5.17196 q^{9} +O(q^{10})$	\(q-2.48869 q^{2} -2.85866 q^{3} +4.19357 q^{4} -1.00000 q^{5} +7.11432 q^{6} -4.63571 q^{7} -5.45912 q^{8} +5.17196 q^{9} +2.48869 q^{10} +6.02431 q^{11} -11.9880 q^{12} +2.06276 q^{13} +11.5368 q^{14} +2.85866 q^{15} +5.19890 q^{16} -0.809580 q^{17} -12.8714 q^{18} +2.72760 q^{19} -4.19357 q^{20} +13.2519 q^{21} -14.9926 q^{22} -3.24666 q^{23} +15.6058 q^{24} +1.00000 q^{25} -5.13356 q^{26} -6.20889 q^{27} -19.4402 q^{28} -6.19929 q^{29} -7.11432 q^{30} -4.14691 q^{31} -2.02021 q^{32} -17.2215 q^{33} +2.01479 q^{34} +4.63571 q^{35} +21.6890 q^{36} +2.14067 q^{37} -6.78816 q^{38} -5.89673 q^{39} +5.45912 q^{40} +1.56642 q^{41} -32.9800 q^{42} +9.69519 q^{43} +25.2634 q^{44} -5.17196 q^{45} +8.07993 q^{46} +11.4488 q^{47} -14.8619 q^{48} +14.4898 q^{49} -2.48869 q^{50} +2.31432 q^{51} +8.65032 q^{52} +6.76713 q^{53} +15.4520 q^{54} -6.02431 q^{55} +25.3069 q^{56} -7.79730 q^{57} +15.4281 q^{58} +2.06041 q^{59} +11.9880 q^{60} +5.05353 q^{61} +10.3204 q^{62} -23.9757 q^{63} -5.37012 q^{64} -2.06276 q^{65} +42.8589 q^{66} +7.49663 q^{67} -3.39503 q^{68} +9.28111 q^{69} -11.5368 q^{70} +8.20928 q^{71} -28.2343 q^{72} +13.1152 q^{73} -5.32746 q^{74} -2.85866 q^{75} +11.4384 q^{76} -27.9269 q^{77} +14.6751 q^{78} -1.03512 q^{79} -5.19890 q^{80} +2.23326 q^{81} -3.89832 q^{82} +7.81868 q^{83} +55.5730 q^{84} +0.809580 q^{85} -24.1283 q^{86} +17.7217 q^{87} -32.8874 q^{88} +8.63501 q^{89} +12.8714 q^{90} -9.56235 q^{91} -13.6151 q^{92} +11.8546 q^{93} -28.4925 q^{94} -2.72760 q^{95} +5.77511 q^{96} +12.5998 q^{97} -36.0607 q^{98} +31.1575 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 137 q + 4 q^{2} + 20 q^{3} + 152 q^{4} - 137 q^{5} + 14 q^{6} - 30 q^{7} + 24 q^{8} + 163 q^{9}+O(q^{10}) $ 137 * q + 4 * q^2 + 20 * q^3 + 152 * q^4 - 137 * q^5 + 14 * q^6 - 30 * q^7 + 24 * q^8 + 163 * q^9	\( 137 q + 4 q^{2} + 20 q^{3} + 152 q^{4} - 137 q^{5} + 14 q^{6} - 30 q^{7} + 24 q^{8} + 163 q^{9} - 4 q^{10} + 51 q^{11} + 32 q^{12} - 6 q^{13} + 49 q^{14} - 20 q^{15} + 170 q^{16} + 46 q^{17} + 4 q^{18} + 47 q^{19} - 152 q^{20} + 28 q^{21} - 19 q^{22} + 29 q^{23} + 39 q^{24} + 137 q^{25} + 67 q^{26} + 77 q^{27} - 58 q^{28} + 27 q^{29} - 14 q^{30} + 23 q^{31} + 42 q^{32} + 40 q^{33} + 38 q^{34} + 30 q^{35} + 222 q^{36} - 56 q^{37} + 87 q^{38} + 44 q^{39} - 24 q^{40} + 66 q^{41} + 34 q^{42} + 15 q^{43} + 87 q^{44} - 163 q^{45} + 37 q^{46} + 52 q^{47} + 56 q^{48} + 195 q^{49} + 4 q^{50} + 106 q^{51} - 31 q^{52} + 45 q^{53} + 83 q^{54} - 51 q^{55} + 148 q^{56} + 4 q^{57} - 101 q^{58} + 239 q^{59} - 32 q^{60} + 46 q^{61} + 63 q^{62} - 59 q^{63} + 200 q^{64} + 6 q^{65} + 108 q^{66} - 18 q^{67} + 152 q^{68} + 63 q^{69} - 49 q^{70} + 110 q^{71} + 6 q^{72} - 19 q^{73} + 81 q^{74} + 20 q^{75} + 94 q^{76} + 43 q^{77} - 3 q^{78} + 40 q^{79} - 170 q^{80} + 229 q^{81} + 3 q^{82} + 235 q^{83} + 94 q^{84} - 46 q^{85} + 110 q^{86} + 31 q^{87} - 105 q^{88} + 150 q^{89} - 4 q^{90} + 110 q^{91} + 76 q^{92} + 11 q^{93} + 56 q^{94} - 47 q^{95} + 146 q^{96} + 17 q^{97} + 75 q^{98} + 125 q^{99}+O(q^{100}) \) 137 * q + 4 * q^2 + 20 * q^3 + 152 * q^4 - 137 * q^5 + 14 * q^6 - 30 * q^7 + 24 * q^8 + 163 * q^9 - 4 * q^10 + 51 * q^11 + 32 * q^12 - 6 * q^13 + 49 * q^14 - 20 * q^15 + 170 * q^16 + 46 * q^17 + 4 * q^18 + 47 * q^19 - 152 * q^20 + 28 * q^21 - 19 * q^22 + 29 * q^23 + 39 * q^24 + 137 * q^25 + 67 * q^26 + 77 * q^27 - 58 * q^28 + 27 * q^29 - 14 * q^30 + 23 * q^31 + 42 * q^32 + 40 * q^33 + 38 * q^34 + 30 * q^35 + 222 * q^36 - 56 * q^37 + 87 * q^38 + 44 * q^39 - 24 * q^40 + 66 * q^41 + 34 * q^42 + 15 * q^43 + 87 * q^44 - 163 * q^45 + 37 * q^46 + 52 * q^47 + 56 * q^48 + 195 * q^49 + 4 * q^50 + 106 * q^51 - 31 * q^52 + 45 * q^53 + 83 * q^54 - 51 * q^55 + 148 * q^56 + 4 * q^57 - 101 * q^58 + 239 * q^59 - 32 * q^60 + 46 * q^61 + 63 * q^62 - 59 * q^63 + 200 * q^64 + 6 * q^65 + 108 * q^66 - 18 * q^67 + 152 * q^68 + 63 * q^69 - 49 * q^70 + 110 * q^71 + 6 * q^72 - 19 * q^73 + 81 * q^74 + 20 * q^75 + 94 * q^76 + 43 * q^77 - 3 * q^78 + 40 * q^79 - 170 * q^80 + 229 * q^81 + 3 * q^82 + 235 * q^83 + 94 * q^84 - 46 * q^85 + 110 * q^86 + 31 * q^87 - 105 * q^88 + 150 * q^89 - 4 * q^90 + 110 * q^91 + 76 * q^92 + 11 * q^93 + 56 * q^94 - 47 * q^95 + 146 * q^96 + 17 * q^97 + 75 * q^98 + 125 * 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 $

$2$	−2.48869	−1.75977	−0.879884	−	0.475188i	$-0.842380\pi$
$2$	−2.48869	−1.75977	−0.879884	+	0.475188i	$0.842380\pi$
$3$	−2.85866	−1.65045	−0.825225	−	0.564804i	$-0.808952\pi$
$3$	−2.85866	−1.65045	−0.825225	+	0.564804i	$0.808952\pi$
$4$	4.19357	2.09679
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	7.11432	2.90441
$7$	−4.63571	−1.75213	−0.876067	−	0.482189i	$-0.839842\pi$
$7$	−4.63571	−1.75213	−0.876067	+	0.482189i	$0.839842\pi$
$8$	−5.45912	−1.93009
$9$	5.17196	1.72399
$10$	2.48869	0.786993
$11$	6.02431	1.81640	0.908198	−	0.418540i	$-0.137458\pi$
$11$	6.02431	1.81640	0.908198	+	0.418540i	$0.137458\pi$
$12$	−11.9880	−3.46064
$13$	2.06276	0.572106	0.286053	−	0.958214i	$-0.407657\pi$
$13$	2.06276	0.572106	0.286053	+	0.958214i	$0.407657\pi$
$14$	11.5368	3.08335
$15$	2.85866	0.738104
$16$	5.19890	1.29973
$17$	−0.809580	−0.196352	−0.0981760	−	0.995169i	$-0.531301\pi$
$17$	−0.809580	−0.196352	−0.0981760	+	0.995169i	$0.531301\pi$
$18$	−12.8714	−3.03382
$19$	2.72760	0.625755	0.312878	−	0.949793i	$-0.398707\pi$
$19$	2.72760	0.625755	0.312878	+	0.949793i	$0.398707\pi$
$20$	−4.19357	−0.937711
$21$	13.2519	2.89181
$22$	−14.9926	−3.19644
$23$	−3.24666	−0.676976	−0.338488	−	0.940971i	$-0.609915\pi$
$23$	−3.24666	−0.676976	−0.338488	+	0.940971i	$0.609915\pi$
$24$	15.6058	3.18552
$25$	1.00000	0.200000
$26$	−5.13356	−1.00677
$27$	−6.20889	−1.19490
$28$	−19.4402	−3.67385
$29$	−6.19929	−1.15118	−0.575590	−	0.817739i	$-0.695227\pi$
$29$	−6.19929	−1.15118	−0.575590	+	0.817739i	$0.695227\pi$
$30$	−7.11432	−1.29889
$31$	−4.14691	−0.744807	−0.372403	−	0.928071i	$-0.621466\pi$
$31$	−4.14691	−0.744807	−0.372403	+	0.928071i	$0.621466\pi$
$32$	−2.02021	−0.357127
$33$	−17.2215	−2.99787
$34$	2.01479	0.345534
$35$	4.63571	0.783578
$36$	21.6890	3.61483
$37$	2.14067	0.351924	0.175962	−	0.984397i	$-0.443696\pi$
$37$	2.14067	0.351924	0.175962	+	0.984397i	$0.443696\pi$
$38$	−6.78816	−1.10118
$39$	−5.89673	−0.944232
$40$	5.45912	0.863162
$41$	1.56642	0.244633	0.122317	−	0.992491i	$-0.460968\pi$
$41$	1.56642	0.244633	0.122317	+	0.992491i	$0.460968\pi$
$42$	−32.9800	−5.08892
$43$	9.69519	1.47850	0.739251	−	0.673429i	$-0.235179\pi$
$43$	9.69519	1.47850	0.739251	+	0.673429i	$0.235179\pi$
$44$	25.2634	3.80860
$45$	−5.17196	−0.770990
$46$	8.07993	1.19132
$47$	11.4488	1.66998	0.834990	−	0.550265i	$-0.185473\pi$
$47$	11.4488	1.66998	0.834990	+	0.550265i	$0.185473\pi$
$48$	−14.8619	−2.14513
$49$	14.4898	2.06997
$50$	−2.48869	−0.351954
$51$	2.31432	0.324069
$52$	8.65032	1.19958
$53$	6.76713	0.929537	0.464768	−	0.885432i	$-0.346138\pi$
$53$	6.76713	0.929537	0.464768	+	0.885432i	$0.346138\pi$
$54$	15.4520	2.10275
$55$	−6.02431	−0.812317
$56$	25.3069	3.38178
$57$	−7.79730	−1.03278
$58$	15.4281	2.02581
$59$	2.06041	0.268243	0.134122	−	0.990965i	$-0.457179\pi$
$59$	2.06041	0.268243	0.134122	+	0.990965i	$0.457179\pi$
$60$	11.9880	1.54765
$61$	5.05353	0.647038	0.323519	−	0.946222i	$-0.395134\pi$
$61$	5.05353	0.647038	0.323519	+	0.946222i	$0.395134\pi$
$62$	10.3204	1.31069
$63$	−23.9757	−3.02065
$64$	−5.37012	−0.671265
$65$	−2.06276	−0.255854
$66$	42.8589	5.27556
$67$	7.49663	0.915860	0.457930	−	0.888988i	$-0.348591\pi$
$67$	7.49663	0.915860	0.457930	+	0.888988i	$0.348591\pi$
$68$	−3.39503	−0.411708
$69$	9.28111	1.11731
$70$	−11.5368	−1.37892
$71$	8.20928	0.974263	0.487131	−	0.873329i	$-0.338043\pi$
$71$	8.20928	0.974263	0.487131	+	0.873329i	$0.338043\pi$
$72$	−28.2343	−3.32745
$73$	13.1152	1.53501	0.767507	−	0.641041i	$-0.221497\pi$
$73$	13.1152	1.53501	0.767507	+	0.641041i	$0.221497\pi$
$74$	−5.32746	−0.619305
$75$	−2.85866	−0.330090
$76$	11.4384	1.31207
$77$	−27.9269	−3.18257
$78$	14.6751	1.66163
$79$	−1.03512	−0.116460	−0.0582302	−	0.998303i	$-0.518546\pi$
$79$	−1.03512	−0.116460	−0.0582302	+	0.998303i	$0.518546\pi$
$80$	−5.19890	−0.581255
$81$	2.23326	0.248140
$82$	−3.89832	−0.430498
$83$	7.81868	0.858211	0.429106	−	0.903254i	$-0.358829\pi$
$83$	7.81868	0.858211	0.429106	+	0.903254i	$0.358829\pi$
$84$	55.5730	6.06351
$85$	0.809580	0.0878113
$86$	−24.1283	−2.60182
$87$	17.7217	1.89996
$88$	−32.8874	−3.50581
$89$	8.63501	0.915310	0.457655	−	0.889130i	$-0.348690\pi$
$89$	8.63501	0.915310	0.457655	+	0.889130i	$0.348690\pi$
$90$	12.8714	1.35676
$91$	−9.56235	−1.00241
$92$	−13.6151	−1.41947
$93$	11.8546	1.22927
$94$	−28.4925	−2.93878
$95$	−2.72760	−0.279846
$96$	5.77511	0.589420
$97$	12.5998	1.27931	0.639656	−	0.768662i	$-0.279077\pi$
$97$	12.5998	1.27931	0.639656	+	0.768662i	$0.279077\pi$
$98$	−36.0607	−3.64268
$99$	31.1575	3.13144
$100$	4.19357	0.419357
$101$	−2.84624	−0.283212	−0.141606	−	0.989923i	$-0.545227\pi$
$101$	−2.84624	−0.283212	−0.141606	+	0.989923i	$0.545227\pi$
$102$	−5.75961	−0.570287
$103$	−5.17997	−0.510397	−0.255199	−	0.966889i	$-0.582141\pi$
$103$	−5.17997	−0.510397	−0.255199	+	0.966889i	$0.582141\pi$
$104$	−11.2608	−1.10422
$105$	−13.2519	−1.29326
$106$	−16.8413	−1.63577
$107$	6.23572	0.602829	0.301415	−	0.953493i	$-0.402541\pi$
$107$	6.23572	0.602829	0.301415	+	0.953493i	$0.402541\pi$
$108$	−26.0374	−2.50545
$109$	2.44215	0.233916	0.116958	−	0.993137i	$-0.462686\pi$
$109$	2.44215	0.233916	0.116958	+	0.993137i	$0.462686\pi$
$110$	14.9926	1.42949
$111$	−6.11945	−0.580833
$112$	−24.1006	−2.27729
$113$	−18.1214	−1.70472	−0.852360	−	0.522955i	$-0.824830\pi$
$113$	−18.1214	−1.70472	−0.852360	+	0.522955i	$0.824830\pi$
$114$	19.4051	1.81745
$115$	3.24666	0.302753
$116$	−25.9972	−2.41378
$117$	10.6685	0.986302
$118$	−5.12773	−0.472046
$119$	3.75298	0.344035
$120$	−15.6058	−1.42461
$121$	25.2923	2.29930
$122$	−12.5767	−1.13864
$123$	−4.47786	−0.403755
$124$	−17.3904	−1.56170
$125$	−1.00000	−0.0894427
$126$	59.6680	5.31565
$127$	−3.41266	−0.302824	−0.151412	−	0.988471i	$-0.548382\pi$
$127$	−3.41266	−0.302824	−0.151412	+	0.988471i	$0.548382\pi$
$128$	17.4050	1.53840
$129$	−27.7153	−2.44020
$130$	5.13356	0.450243
$131$	16.2313	1.41814	0.709068	−	0.705140i	$-0.249116\pi$
$131$	16.2313	1.41814	0.709068	+	0.705140i	$0.249116\pi$
$132$	−72.2195	−6.28590
$133$	−12.6444	−1.09641
$134$	−18.6568	−1.61170
$135$	6.20889	0.534376
$136$	4.41959	0.378977
$137$	−5.97528	−0.510503	−0.255251	−	0.966875i	$-0.582158\pi$
$137$	−5.97528	−0.510503	−0.255251	+	0.966875i	$0.582158\pi$
$138$	−23.0978	−1.96622
$139$	−17.2583	−1.46383	−0.731915	−	0.681396i	$-0.761373\pi$
$139$	−17.2583	−1.46383	−0.731915	+	0.681396i	$0.761373\pi$
$140$	19.4402	1.64300
$141$	−32.7283	−2.75622
$142$	−20.4303	−1.71448
$143$	12.4267	1.03917
$144$	26.8885	2.24071
$145$	6.19929	0.514823
$146$	−32.6395	−2.70127
$147$	−41.4215	−3.41639
$148$	8.97705	0.737909
$149$	−11.2855	−0.924541	−0.462270	−	0.886739i	$-0.652965\pi$
$149$	−11.2855	−0.924541	−0.462270	+	0.886739i	$0.652965\pi$
$150$	7.11432	0.580882
$151$	16.9817	1.38195	0.690976	−	0.722877i	$-0.257181\pi$
$151$	16.9817	1.38195	0.690976	+	0.722877i	$0.257181\pi$
$152$	−14.8903	−1.20776
$153$	−4.18711	−0.338508
$154$	69.5015	5.60059
$155$	4.14691	0.333088
$156$	−24.7284	−1.97985
$157$	−23.8204	−1.90107	−0.950536	−	0.310615i	$-0.899465\pi$
$157$	−23.8204	−1.90107	−0.950536	+	0.310615i	$0.899465\pi$
$158$	2.57610	0.204943
$159$	−19.3449	−1.53415
$160$	2.02021	0.159712
$161$	15.0506	1.18615
$162$	−5.55790	−0.436670
$163$	−2.53189	−0.198313	−0.0991565	−	0.995072i	$-0.531614\pi$
$163$	−2.53189	−0.198313	−0.0991565	+	0.995072i	$0.531614\pi$
$164$	6.56888	0.512943
$165$	17.2215	1.34069
$166$	−19.4582	−1.51025
$167$	22.4351	1.73608	0.868038	−	0.496497i	$-0.165381\pi$
$167$	22.4351	1.73608	0.868038	+	0.496497i	$0.165381\pi$
$168$	−72.3439	−5.58145
$169$	−8.74503	−0.672695
$170$	−2.01479	−0.154528
$171$	14.1070	1.07879
$172$	40.6575	3.10010
$173$	−2.05734	−0.156417	−0.0782085	−	0.996937i	$-0.524920\pi$
$173$	−2.05734	−0.156417	−0.0782085	+	0.996937i	$0.524920\pi$
$174$	−44.1038	−3.34350
$175$	−4.63571	−0.350427
$176$	31.3198	2.36082
$177$	−5.89003	−0.442722
$178$	−21.4899	−1.61073
$179$	−20.0591	−1.49929	−0.749643	−	0.661842i	$-0.769775\pi$
$179$	−20.0591	−1.49929	−0.749643	+	0.661842i	$0.769775\pi$
$180$	−21.6890	−1.61660
$181$	2.69735	0.200492	0.100246	−	0.994963i	$-0.468037\pi$
$181$	2.69735	0.200492	0.100246	+	0.994963i	$0.468037\pi$
$182$	23.7977	1.76400
$183$	−14.4463	−1.06790
$184$	17.7239	1.30662
$185$	−2.14067	−0.157385
$186$	−29.5024	−2.16322
$187$	−4.87716	−0.356653
$188$	48.0114	3.50159
$189$	28.7826	2.09363
$190$	6.78816	0.492465
$191$	3.37253	0.244028	0.122014	−	0.992528i	$-0.461065\pi$
$191$	3.37253	0.244028	0.122014	+	0.992528i	$0.461065\pi$
$192$	15.3514	1.10789
$193$	23.1921	1.66940	0.834701	−	0.550703i	$-0.185640\pi$
$193$	23.1921	1.66940	0.834701	+	0.550703i	$0.185640\pi$
$194$	−31.3569	−2.25129
$195$	5.89673	0.422274
$196$	60.7641	4.34029
$197$	−9.06173	−0.645621	−0.322811	−	0.946464i	$-0.604628\pi$
$197$	−9.06173	−0.645621	−0.322811	+	0.946464i	$0.604628\pi$
$198$	−77.5412	−5.51061
$199$	−2.39601	−0.169849	−0.0849243	−	0.996387i	$-0.527065\pi$
$199$	−2.39601	−0.169849	−0.0849243	+	0.996387i	$0.527065\pi$
$200$	−5.45912	−0.386018
$201$	−21.4304	−1.51158
$202$	7.08341	0.498387
$203$	28.7381	2.01702
$204$	9.70525	0.679504
$205$	−1.56642	−0.109403
$206$	12.8913	0.898181
$207$	−16.7916	−1.16710
$208$	10.7241	0.743581
$209$	16.4319	1.13662
$210$	32.9800	2.27583
$211$	18.8379	1.29686	0.648428	−	0.761276i	$-0.275427\pi$
$211$	18.8379	1.29686	0.648428	+	0.761276i	$0.275427\pi$
$212$	28.3784	1.94904
$213$	−23.4676	−1.60797
$214$	−15.5188	−1.06084
$215$	−9.69519	−0.661207
$216$	33.8951	2.30627
$217$	19.2239	1.30500
$218$	−6.07776	−0.411638
$219$	−37.4918	−2.53346
$220$	−25.2634	−1.70326
$221$	−1.66997	−0.112334
$222$	15.2294	1.02213
$223$	−20.5807	−1.37818	−0.689092	−	0.724674i	$-0.741990\pi$
$223$	−20.5807	−1.37818	−0.689092	+	0.724674i	$0.741990\pi$
$224$	9.36513	0.625734
$225$	5.17196	0.344797
$226$	45.0986	2.99991
$227$	13.8878	0.921763	0.460882	−	0.887462i	$-0.347533\pi$
$227$	13.8878	0.921763	0.460882	+	0.887462i	$0.347533\pi$
$228$	−32.6985	−2.16551
$229$	8.04852	0.531861	0.265931	−	0.963992i	$-0.414321\pi$
$229$	8.04852	0.531861	0.265931	+	0.963992i	$0.414321\pi$
$230$	−8.07993	−0.532775
$231$	79.8337	5.25267
$232$	33.8427	2.22188
$233$	5.89510	0.386201	0.193101	−	0.981179i	$-0.438146\pi$
$233$	5.89510	0.386201	0.193101	+	0.981179i	$0.438146\pi$
$234$	−26.5506	−1.73566
$235$	−11.4488	−0.746838
$236$	8.64050	0.562448
$237$	2.95907	0.192212
$238$	−9.34000	−0.605422
$239$	9.23497	0.597360	0.298680	−	0.954353i	$-0.403454\pi$
$239$	9.23497	0.597360	0.298680	+	0.954353i	$0.403454\pi$
$240$	14.8619	0.959332
$241$	−30.8704	−1.98854	−0.994269	−	0.106910i	$-0.965904\pi$
$241$	−30.8704	−1.98854	−0.994269	+	0.106910i	$0.965904\pi$
$242$	−62.9446	−4.04623
$243$	12.2425	0.785359
$244$	21.1923	1.35670
$245$	−14.4898	−0.925721
$246$	11.1440	0.710515
$247$	5.62638	0.357998
$248$	22.6385	1.43754
$249$	−22.3510	−1.41643
$250$	2.48869	0.157399
$251$	4.58123	0.289165	0.144582	−	0.989493i	$-0.453816\pi$
$251$	4.58123	0.289165	0.144582	+	0.989493i	$0.453816\pi$
$252$	−100.544	−6.33366
$253$	−19.5589	−1.22966
$254$	8.49304	0.532901
$255$	−2.31432	−0.144928
$256$	−32.5754	−2.03596
$257$	28.9733	1.80730	0.903652	−	0.428267i	$-0.140876\pi$
$257$	28.9733	1.80730	0.903652	+	0.428267i	$0.140876\pi$
$258$	68.9747	4.29418
$259$	−9.92352	−0.616618
$260$	−8.65032	−0.536470
$261$	−32.0625	−1.98462
$262$	−40.3947	−2.49559
$263$	14.7456	0.909254	0.454627	−	0.890682i	$-0.349773\pi$
$263$	14.7456	0.909254	0.454627	+	0.890682i	$0.349773\pi$
$264$	94.0140	5.78616
$265$	−6.76713	−0.415701
$266$	31.4679	1.92942
$267$	−24.6846	−1.51067
$268$	31.4377	1.92036
$269$	−13.5099	−0.823712	−0.411856	−	0.911249i	$-0.635119\pi$
$269$	−13.5099	−0.823712	−0.411856	+	0.911249i	$0.635119\pi$
$270$	−15.4520	−0.940379
$271$	−11.1338	−0.676327	−0.338164	−	0.941087i	$-0.609806\pi$
$271$	−11.1338	−0.676327	−0.338164	+	0.941087i	$0.609806\pi$
$272$	−4.20893	−0.255204
$273$	27.3355	1.65442
$274$	14.8706	0.898367
$275$	6.02431	0.363279
$276$	38.9210	2.34277
$277$	−26.8147	−1.61114	−0.805570	−	0.592501i	$-0.798141\pi$
$277$	−26.8147	−1.61114	−0.805570	+	0.592501i	$0.798141\pi$
$278$	42.9506	2.57600
$279$	−21.4476	−1.28404
$280$	−25.3069	−1.51238
$281$	13.4748	0.803841	0.401921	−	0.915675i	$-0.368343\pi$
$281$	13.4748	0.803841	0.401921	+	0.915675i	$0.368343\pi$
$282$	81.4505	4.85031
$283$	−13.4578	−0.799982	−0.399991	−	0.916519i	$-0.630987\pi$
$283$	−13.4578	−0.799982	−0.399991	+	0.916519i	$0.630987\pi$
$284$	34.4262	2.04282
$285$	7.79730	0.461872
$286$	−30.9261	−1.82870
$287$	−7.26145	−0.428630
$288$	−10.4485	−0.615681
$289$	−16.3446	−0.961446
$290$	−15.4281	−0.905969
$291$	−36.0185	−2.11144
$292$	54.9994	3.21859
$293$	11.9905	0.700490	0.350245	−	0.936658i	$-0.386098\pi$
$293$	11.9905	0.700490	0.350245	+	0.936658i	$0.386098\pi$
$294$	103.085	6.01205
$295$	−2.06041	−0.119962
$296$	−11.6862	−0.679245
$297$	−37.4043	−2.17042
$298$	28.0860	1.62698
$299$	−6.69708	−0.387302
$300$	−11.9880	−0.692128
$301$	−44.9441	−2.59054
$302$	−42.2622	−2.43192
$303$	8.13645	0.467427
$304$	14.1805	0.813310
$305$	−5.05353	−0.289364
$306$	10.4204	0.595696
$307$	−2.66403	−0.152044	−0.0760220	−	0.997106i	$-0.524222\pi$
$307$	−2.66403	−0.152044	−0.0760220	+	0.997106i	$0.524222\pi$
$308$	−117.114	−6.67317
$309$	14.8078	0.842385
$310$	−10.3204	−0.586157
$311$	6.87056	0.389594	0.194797	−	0.980844i	$-0.437595\pi$
$311$	6.87056	0.389594	0.194797	+	0.980844i	$0.437595\pi$
$312$	32.1909	1.82245
$313$	−24.2946	−1.37321	−0.686607	−	0.727029i	$-0.740901\pi$
$313$	−24.2946	−1.37321	−0.686607	+	0.727029i	$0.740901\pi$
$314$	59.2815	3.34545
$315$	23.9757	1.35088
$316$	−4.34086	−0.244192
$317$	−1.96992	−0.110642	−0.0553210	−	0.998469i	$-0.517618\pi$
$317$	−1.96992	−0.110642	−0.0553210	+	0.998469i	$0.517618\pi$
$318$	48.1436	2.69976
$319$	−37.3464	−2.09100
$320$	5.37012	0.300199
$321$	−17.8258	−0.994940
$322$	−37.4562	−2.08735
$323$	−2.20821	−0.122868
$324$	9.36535	0.520297
$325$	2.06276	0.114421
$326$	6.30109	0.348985
$327$	−6.98129	−0.386066
$328$	−8.55125	−0.472164
$329$	−53.0734	−2.92603
$330$	−42.8589	−2.35930
$331$	1.03785	0.0570454	0.0285227	−	0.999593i	$-0.490920\pi$
$331$	1.03785	0.0570454	0.0285227	+	0.999593i	$0.490920\pi$
$332$	32.7882	1.79949
$333$	11.0714	0.606712
$334$	−55.8339	−3.05509
$335$	−7.49663	−0.409585
$336$	68.8955	3.75856
$337$	12.0989	0.659071	0.329536	−	0.944143i	$-0.393108\pi$
$337$	12.0989	0.659071	0.329536	+	0.944143i	$0.393108\pi$
$338$	21.7637	1.18379
$339$	51.8031	2.81356
$340$	3.39503	0.184121
$341$	−24.9822	−1.35286
$342$	−35.1080	−1.89843
$343$	−34.7206	−1.87474
$344$	−52.9272	−2.85364
$345$	−9.28111	−0.499678
$346$	5.12009	0.275258
$347$	−16.1550	−0.867246	−0.433623	−	0.901094i	$-0.642765\pi$
$347$	−16.1550	−0.867246	−0.433623	+	0.901094i	$0.642765\pi$
$348$	74.3171	3.98382
$349$	−5.92772	−0.317304	−0.158652	−	0.987335i	$-0.550715\pi$
$349$	−5.92772	−0.317304	−0.158652	+	0.987335i	$0.550715\pi$
$350$	11.5368	0.616670
$351$	−12.8074	−0.683610
$352$	−12.1704	−0.648684
$353$	19.5951	1.04294	0.521471	−	0.853269i	$-0.325383\pi$
$353$	19.5951	1.04294	0.521471	+	0.853269i	$0.325383\pi$
$354$	14.6585	0.779088
$355$	−8.20928	−0.435703
$356$	36.2116	1.91921
$357$	−10.7285	−0.567813
$358$	49.9208	2.63840
$359$	−13.5019	−0.712605	−0.356302	−	0.934371i	$-0.615963\pi$
$359$	−13.5019	−0.712605	−0.356302	+	0.934371i	$0.615963\pi$
$360$	28.2343	1.48808
$361$	−11.5602	−0.608431
$362$	−6.71286	−0.352820
$363$	−72.3021	−3.79488
$364$	−40.1004	−2.10183
$365$	−13.1152	−0.686479
$366$	35.9525	1.87927
$367$	9.80321	0.511723	0.255862	−	0.966713i	$-0.417641\pi$
$367$	9.80321	0.511723	0.255862	+	0.966713i	$0.417641\pi$
$368$	−16.8791	−0.879883
$369$	8.10143	0.421744
$370$	5.32746	0.276961
$371$	−31.3705	−1.62867
$372$	49.7132	2.57751
$373$	−22.5399	−1.16707	−0.583536	−	0.812087i	$-0.698331\pi$
$373$	−22.5399	−1.16707	−0.583536	+	0.812087i	$0.698331\pi$
$374$	12.1377	0.627627
$375$	2.85866	0.147621
$376$	−62.5004	−3.22321
$377$	−12.7876	−0.658596
$378$	−71.6310	−3.68430
$379$	25.5180	1.31077	0.655386	−	0.755294i	$-0.272506\pi$
$379$	25.5180	1.31077	0.655386	+	0.755294i	$0.272506\pi$
$380$	−11.4384	−0.586778
$381$	9.75564	0.499796
$382$	−8.39319	−0.429433
$383$	8.58910	0.438883	0.219441	−	0.975626i	$-0.429577\pi$
$383$	8.58910	0.438883	0.219441	+	0.975626i	$0.429577\pi$
$384$	−49.7550	−2.53905
$385$	27.9269	1.42329
$386$	−57.7179	−2.93776
$387$	50.1431	2.54892
$388$	52.8380	2.68244
$389$	3.10317	0.157337	0.0786684	−	0.996901i	$-0.474933\pi$
$389$	3.10317	0.157337	0.0786684	+	0.996901i	$0.474933\pi$
$390$	−14.6751	−0.743104
$391$	2.62843	0.132926
$392$	−79.1016	−3.99524
$393$	−46.3998	−2.34056
$394$	22.5518	1.13614
$395$	1.03512	0.0520826
$396$	130.661	6.56596
$397$	4.26977	0.214294	0.107147	−	0.994243i	$-0.465829\pi$
$397$	4.26977	0.214294	0.107147	+	0.994243i	$0.465829\pi$
$398$	5.96292	0.298894
$399$	36.1460	1.80956
$400$	5.19890	0.259945
$401$	19.0990	0.953758	0.476879	−	0.878969i	$-0.341768\pi$
$401$	19.0990	0.953758	0.476879	+	0.878969i	$0.341768\pi$
$402$	53.3335	2.66003
$403$	−8.55407	−0.426108
$404$	−11.9359	−0.593835
$405$	−2.23326	−0.110972
$406$	−71.5202	−3.54949
$407$	12.8960	0.639233
$408$	−12.6341	−0.625482
$409$	4.94875	0.244700	0.122350	−	0.992487i	$-0.460957\pi$
$409$	4.94875	0.244700	0.122350	+	0.992487i	$0.460957\pi$
$410$	3.89832	0.192524
$411$	17.0813	0.842560
$412$	−21.7226	−1.07019
$413$	−9.55149	−0.469998
$414$	41.7890	2.05382
$415$	−7.81868	−0.383804
$416$	−4.16721	−0.204314
$417$	49.3357	2.41598
$418$	−40.8939	−2.00019
$419$	34.4069	1.68089	0.840443	−	0.541900i	$-0.182295\pi$
$419$	34.4069	1.68089	0.840443	+	0.541900i	$0.182295\pi$
$420$	−55.5730	−2.71168
$421$	−7.23441	−0.352584	−0.176292	−	0.984338i	$-0.556410\pi$
$421$	−7.23441	−0.352584	−0.176292	+	0.984338i	$0.556410\pi$
$422$	−46.8817	−2.28217
$423$	59.2127	2.87902
$424$	−36.9426	−1.79409
$425$	−0.809580	−0.0392704
$426$	58.4035	2.82966
$427$	−23.4267	−1.13370
$428$	26.1499	1.26400
$429$	−35.5237	−1.71510
$430$	24.1283	1.16357
$431$	−19.9174	−0.959389	−0.479694	−	0.877436i	$-0.659252\pi$
$431$	−19.9174	−0.959389	−0.479694	+	0.877436i	$0.659252\pi$
$432$	−32.2794	−1.55304
$433$	5.66251	0.272123	0.136062	−	0.990700i	$-0.456556\pi$
$433$	5.66251	0.272123	0.136062	+	0.990700i	$0.456556\pi$
$434$	−47.8422	−2.29650
$435$	−17.7217	−0.849690
$436$	10.2413	0.490471
$437$	−8.85561	−0.423621
$438$	93.3055	4.45831
$439$	−32.4561	−1.54905	−0.774523	−	0.632546i	$-0.782010\pi$
$439$	−32.4561	−1.54905	−0.774523	+	0.632546i	$0.782010\pi$
$440$	32.8874	1.56785
$441$	74.9407	3.56861
$442$	4.15603	0.197682
$443$	−16.0409	−0.762126	−0.381063	−	0.924549i	$-0.624442\pi$
$443$	−16.0409	−0.762126	−0.381063	+	0.924549i	$0.624442\pi$
$444$	−25.6624	−1.21788
$445$	−8.63501	−0.409339
$446$	51.2189	2.42528
$447$	32.2613	1.52591
$448$	24.8943	1.17615
$449$	−12.7230	−0.600437	−0.300219	−	0.953870i	$-0.597060\pi$
$449$	−12.7230	−0.600437	−0.300219	+	0.953870i	$0.597060\pi$
$450$	−12.8714	−0.606763
$451$	9.43657	0.444351
$452$	−75.9935	−3.57443
$453$	−48.5450	−2.28084
$454$	−34.5623	−1.62209
$455$	9.56235	0.448290
$456$	42.5664	1.99335
$457$	−8.85575	−0.414255	−0.207127	−	0.978314i	$-0.566411\pi$
$457$	−8.85575	−0.414255	−0.207127	+	0.978314i	$0.566411\pi$
$458$	−20.0303	−0.935953
$459$	5.02659	0.234621
$460$	13.6151	0.634808
$461$	15.3160	0.713336	0.356668	−	0.934231i	$-0.383913\pi$
$461$	15.3160	0.713336	0.356668	+	0.934231i	$0.383913\pi$
$462$	−198.681	−9.24349
$463$	−16.6631	−0.774402	−0.387201	−	0.921995i	$-0.626558\pi$
$463$	−16.6631	−0.774402	−0.387201	+	0.921995i	$0.626558\pi$
$464$	−32.2295	−1.49622
$465$	−11.8546	−0.549745
$466$	−14.6711	−0.679625
$467$	−20.7109	−0.958384	−0.479192	−	0.877710i	$-0.659070\pi$
$467$	−20.7109	−0.958384	−0.479192	+	0.877710i	$0.659070\pi$
$468$	44.7391	2.06806
$469$	−34.7522	−1.60471
$470$	28.4925	1.31426
$471$	68.0944	3.13762
$472$	−11.2480	−0.517733
$473$	58.4068	2.68555
$474$	−7.36419	−0.338249
$475$	2.72760	0.125151
$476$	15.7384	0.721368
$477$	34.9993	1.60251
$478$	−22.9830	−1.05122
$479$	22.3325	1.02040	0.510199	−	0.860056i	$-0.329572\pi$
$479$	22.3325	1.02040	0.510199	+	0.860056i	$0.329572\pi$
$480$	−5.77511	−0.263596
$481$	4.41568	0.201338
$482$	76.8268	3.49937
$483$	−43.0246	−1.95769
$484$	106.065	4.82114
$485$	−12.5998	−0.572125
$486$	−30.4678	−1.38205
$487$	−13.0116	−0.589613	−0.294807	−	0.955557i	$-0.595255\pi$
$487$	−13.0116	−0.589613	−0.294807	+	0.955557i	$0.595255\pi$
$488$	−27.5878	−1.24884
$489$	7.23782	0.327306
$490$	36.0607	1.62905
$491$	38.2737	1.72727	0.863633	−	0.504121i	$-0.168183\pi$
$491$	38.2737	1.72727	0.863633	+	0.504121i	$0.168183\pi$
$492$	−18.7782	−0.846587
$493$	5.01882	0.226036
$494$	−14.0023	−0.629994
$495$	−31.1575	−1.40042
$496$	−21.5594	−0.968044
$497$	−38.0559	−1.70704
$498$	55.6246	2.49260
$499$	10.8796	0.487039	0.243520	−	0.969896i	$-0.421698\pi$
$499$	10.8796	0.487039	0.243520	+	0.969896i	$0.421698\pi$
$500$	−4.19357	−0.187542
$501$	−64.1343	−2.86531
$502$	−11.4013	−0.508863
$503$	18.7151	0.834464	0.417232	−	0.908800i	$-0.363000\pi$
$503$	18.7151	0.834464	0.417232	+	0.908800i	$0.363000\pi$
$504$	130.886	5.83013
$505$	2.84624	0.126656
$506$	48.6760	2.16391
$507$	24.9991	1.11025
$508$	−14.3112	−0.634958
$509$	−6.53108	−0.289485	−0.144742	−	0.989469i	$-0.546235\pi$
$509$	−6.53108	−0.289485	−0.144742	+	0.989469i	$0.546235\pi$
$510$	5.75961	0.255040
$511$	−60.7981	−2.68955
$512$	46.2599	2.04442
$513$	−16.9354	−0.747716
$514$	−72.1055	−3.18044
$515$	5.17997	0.228257
$516$	−116.226	−5.11657
$517$	68.9711	3.03335
$518$	24.6966	1.08510
$519$	5.88125	0.258158
$520$	11.2608	0.493820
$521$	−10.1825	−0.446102	−0.223051	−	0.974807i	$-0.571602\pi$
$521$	−10.1825	−0.446102	−0.223051	+	0.974807i	$0.571602\pi$
$522$	79.7935	3.49247
$523$	15.7343	0.688013	0.344006	−	0.938967i	$-0.388216\pi$
$523$	15.7343	0.688013	0.344006	+	0.938967i	$0.388216\pi$
$524$	68.0671	2.97353
$525$	13.2519	0.578362
$526$	−36.6973	−1.60008
$527$	3.35725	0.146244
$528$	−89.5327	−3.89641
$529$	−12.4592	−0.541704
$530$	16.8413	0.731538
$531$	10.6564	0.462447
$532$	−53.0251	−2.29893
$533$	3.23114	0.139956
$534$	61.4323	2.65843
$535$	−6.23572	−0.269594
$536$	−40.9250	−1.76769
$537$	57.3422	2.47450
$538$	33.6219	1.44954
$539$	87.2911	3.75990
$540$	26.0374	1.12047
$541$	16.5458	0.711361	0.355681	−	0.934608i	$-0.384249\pi$
$541$	16.5458	0.711361	0.355681	+	0.934608i	$0.384249\pi$
$542$	27.7084	1.19018
$543$	−7.71081	−0.330902
$544$	1.63552	0.0701225
$545$	−2.44215	−0.104610
$546$	−68.0296	−2.91140
$547$	−26.2743	−1.12341	−0.561704	−	0.827338i	$-0.689854\pi$
$547$	−26.2743	−1.12341	−0.561704	+	0.827338i	$0.689854\pi$
$548$	−25.0578	−1.07042
$549$	26.1366	1.11548
$550$	−14.9926	−0.639288
$551$	−16.9092	−0.720356
$552$	−50.6667	−2.15652
$553$	4.79853	0.204054
$554$	66.7335	2.83523
$555$	6.11945	0.259756
$556$	−72.3740	−3.06934
$557$	−45.8805	−1.94402	−0.972010	−	0.234941i	$-0.924510\pi$
$557$	−45.8805	−1.94402	−0.972010	+	0.234941i	$0.924510\pi$
$558$	53.3765	2.25961
$559$	19.9988	0.845860
$560$	24.1006	1.01844
$561$	13.9422	0.588638
$562$	−33.5347	−1.41457
$563$	−11.3695	−0.479167	−0.239583	−	0.970876i	$-0.577011\pi$
$563$	−11.3695	−0.479167	−0.239583	+	0.970876i	$0.577011\pi$
$564$	−137.248	−5.77920
$565$	18.1214	0.762374
$566$	33.4922	1.40778
$567$	−10.3528	−0.434775
$568$	−44.8154	−1.88041
$569$	15.9506	0.668683	0.334341	−	0.942452i	$-0.391486\pi$
$569$	15.9506	0.668683	0.334341	+	0.942452i	$0.391486\pi$
$570$	−19.4051	−0.812788
$571$	−42.0045	−1.75783	−0.878916	−	0.476976i	$-0.841733\pi$
$571$	−42.0045	−1.75783	−0.878916	+	0.476976i	$0.841733\pi$
$572$	52.1122	2.17892
$573$	−9.64094	−0.402756
$574$	18.0715	0.754290
$575$	−3.24666	−0.135395
$576$	−27.7740	−1.15725
$577$	26.9317	1.12118	0.560590	−	0.828093i	$-0.310574\pi$
$577$	26.9317	1.12118	0.560590	+	0.828093i	$0.310574\pi$
$578$	40.6766	1.69192
$579$	−66.2983	−2.75526
$580$	25.9972	1.07947
$581$	−36.2451	−1.50370
$582$	89.6387	3.71565
$583$	40.7673	1.68841
$584$	−71.5972	−2.96271
$585$	−10.6685	−0.441088
$586$	−29.8405	−1.23270
$587$	−34.8077	−1.43667	−0.718334	−	0.695698i	$-0.755095\pi$
$587$	−34.8077	−1.43667	−0.718334	+	0.695698i	$0.755095\pi$
$588$	−173.704	−7.16344
$589$	−11.3111	−0.466067
$590$	5.12773	0.211105
$591$	25.9044	1.06557
$592$	11.1291	0.457404
$593$	−30.8657	−1.26750	−0.633751	−	0.773537i	$-0.718485\pi$
$593$	−30.8657	−1.26750	−0.633751	+	0.773537i	$0.718485\pi$
$594$	93.0876	3.81943
$595$	−3.75298	−0.153857
$596$	−47.3264	−1.93856
$597$	6.84939	0.280327
$598$	16.6669	0.681562
$599$	16.3466	0.667904	0.333952	−	0.942590i	$-0.391618\pi$
$599$	16.3466	0.667904	0.333952	+	0.942590i	$0.391618\pi$
$600$	15.6058	0.637103
$601$	9.60948	0.391979	0.195989	−	0.980606i	$-0.437208\pi$
$601$	9.60948	0.391979	0.195989	+	0.980606i	$0.437208\pi$
$602$	111.852	4.55874
$603$	38.7723	1.57893
$604$	71.2141	2.89766
$605$	−25.2923	−1.02828
$606$	−20.2491	−0.822563
$607$	3.45452	0.140215	0.0701074	−	0.997539i	$-0.477666\pi$
$607$	3.45452	0.140215	0.0701074	+	0.997539i	$0.477666\pi$
$608$	−5.51034	−0.223474
$609$	−82.1526	−3.32899
$610$	12.5767	0.509214
$611$	23.6161	0.955406
$612$	−17.5590	−0.709779
$613$	46.7095	1.88658	0.943288	−	0.331974i	$-0.107715\pi$
$613$	46.7095	1.88658	0.943288	+	0.331974i	$0.107715\pi$
$614$	6.62993	0.267562
$615$	4.47786	0.180565
$616$	152.457	6.14265
$617$	5.69380	0.229224	0.114612	−	0.993410i	$-0.463438\pi$
$617$	5.69380	0.229224	0.114612	+	0.993410i	$0.463438\pi$
$618$	−36.8520	−1.48240
$619$	8.39931	0.337597	0.168798	−	0.985651i	$-0.446011\pi$
$619$	8.39931	0.337597	0.168798	+	0.985651i	$0.446011\pi$
$620$	17.3904	0.698414
$621$	20.1582	0.808920
$622$	−17.0987	−0.685595
$623$	−40.0294	−1.60375
$624$	−30.6565	−1.22724
$625$	1.00000	0.0400000
$626$	60.4618	2.41654
$627$	−46.9733	−1.87593
$628$	−99.8924	−3.98614
$629$	−1.73304	−0.0691009
$630$	−59.6680	−2.37723
$631$	19.4364	0.773752	0.386876	−	0.922132i	$-0.373554\pi$
$631$	19.4364	0.773752	0.386876	+	0.922132i	$0.373554\pi$
$632$	5.65085	0.224779
$633$	−53.8512	−2.14039
$634$	4.90253	0.194704
$635$	3.41266	0.135427
$636$	−81.1244	−3.21679
$637$	29.8890	1.18424
$638$	92.9436	3.67967
$639$	42.4580	1.67961
$640$	−17.4050	−0.687993
$641$	37.4752	1.48018	0.740091	−	0.672507i	$-0.234782\pi$
$641$	37.4752	1.48018	0.740091	+	0.672507i	$0.234782\pi$
$642$	44.3629	1.75086
$643$	14.8793	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$643$	14.8793	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$644$	63.1157	2.48711
$645$	27.7153	1.09129
$646$	5.49555	0.216220
$647$	34.6053	1.36048	0.680238	−	0.732991i	$-0.261876\pi$
$647$	34.6053	1.36048	0.680238	+	0.732991i	$0.261876\pi$
$648$	−12.1916	−0.478933
$649$	12.4126	0.487236
$650$	−5.13356	−0.201355
$651$	−54.9546	−2.15384
$652$	−10.6177	−0.415820
$653$	25.5246	0.998857	0.499428	−	0.866355i	$-0.333543\pi$
$653$	25.5246	0.998857	0.499428	+	0.866355i	$0.333543\pi$
$654$	17.3743	0.679387
$655$	−16.2313	−0.634209
$656$	8.14364	0.317956
$657$	67.8310	2.64634
$658$	132.083	5.14914
$659$	44.3830	1.72891	0.864457	−	0.502706i	$-0.167662\pi$
$659$	44.3830	1.72891	0.864457	+	0.502706i	$0.167662\pi$
$660$	72.2195	2.81114
$661$	−27.7595	−1.07972	−0.539859	−	0.841755i	$-0.681523\pi$
$661$	−27.7595	−1.07972	−0.539859	+	0.841755i	$0.681523\pi$
$662$	−2.58289	−0.100387
$663$	4.77387	0.185402
$664$	−42.6831	−1.65642
$665$	12.6444	0.490328
$666$	−27.5534	−1.06767
$667$	20.1270	0.779320
$668$	94.0830	3.64018
$669$	58.8332	2.27462
$670$	18.6568	0.720775
$671$	30.4440	1.17528
$672$	−26.7717	−1.03274
$673$	−31.3062	−1.20677	−0.603383	−	0.797452i	$-0.706181\pi$
$673$	−31.3062	−1.20677	−0.603383	+	0.797452i	$0.706181\pi$
$674$	−30.1105	−1.15981
$675$	−6.20889	−0.238980
$676$	−36.6729	−1.41050
$677$	−9.80049	−0.376663	−0.188332	−	0.982105i	$-0.560308\pi$
$677$	−9.80049	−0.376663	−0.188332	+	0.982105i	$0.560308\pi$
$678$	−128.922	−4.95121
$679$	−58.4088	−2.24153
$680$	−4.41959	−0.169484
$681$	−39.7004	−1.52132
$682$	62.1730	2.38073
$683$	30.4264	1.16423	0.582117	−	0.813105i	$-0.302224\pi$
$683$	30.4264	1.16423	0.582117	+	0.813105i	$0.302224\pi$
$684$	59.1589	2.26200
$685$	5.97528	0.228304
$686$	86.4089	3.29911
$687$	−23.0080	−0.877810
$688$	50.4044	1.92165
$689$	13.9589	0.531793
$690$	23.0978	0.879318
$691$	50.3278	1.91456	0.957280	−	0.289162i	$-0.0933767\pi$
$691$	50.3278	1.91456	0.957280	+	0.289162i	$0.0933767\pi$
$692$	−8.62762	−0.327973
$693$	−144.437	−5.48671
$694$	40.2048	1.52615
$695$	17.2583	0.654645
$696$	−96.7448	−3.66710
$697$	−1.26814	−0.0480342
$698$	14.7523	0.558381
$699$	−16.8521	−0.637406
$700$	−19.4402	−0.734770
$701$	−4.88941	−0.184670	−0.0923352	−	0.995728i	$-0.529433\pi$
$701$	−4.88941	−0.184670	−0.0923352	+	0.995728i	$0.529433\pi$
$702$	31.8737	1.20300
$703$	5.83890	0.220218
$704$	−32.3513	−1.21928
$705$	32.7283	1.23262
$706$	−48.7661	−1.83534
$707$	13.1944	0.496225
$708$	−24.7003	−0.928293
$709$	50.4571	1.89496	0.947479	−	0.319818i	$-0.103622\pi$
$709$	50.4571	1.89496	0.947479	+	0.319818i	$0.103622\pi$
$710$	20.4303	0.766737
$711$	−5.35361	−0.200776
$712$	−47.1396	−1.76663
$713$	13.4636	0.504216
$714$	26.6999	0.999219
$715$	−12.4267	−0.464732
$716$	−84.1192	−3.14368
$717$	−26.3997	−0.985913
$718$	33.6021	1.25402
$719$	−30.6378	−1.14260	−0.571298	−	0.820743i	$-0.693560\pi$
$719$	−30.6378	−1.14260	−0.571298	+	0.820743i	$0.693560\pi$
$720$	−26.8885	−1.00208
$721$	24.0128	0.894285
$722$	28.7697	1.07070
$723$	88.2481	3.28198
$724$	11.3115	0.420389
$725$	−6.19929	−0.230236
$726$	179.937	6.67810
$727$	39.1114	1.45056	0.725281	−	0.688453i	$-0.241710\pi$
$727$	39.1114	1.45056	0.725281	+	0.688453i	$0.241710\pi$
$728$	52.2020	1.93473
$729$	−41.6971	−1.54434
$730$	32.6395	1.20804
$731$	−7.84903	−0.290307
$732$	−60.5818	−2.23917
$733$	−49.6282	−1.83306	−0.916530	−	0.399966i	$-0.869022\pi$
$733$	−49.6282	−1.83306	−0.916530	+	0.399966i	$0.869022\pi$
$734$	−24.3971	−0.900515
$735$	41.4215	1.52786
$736$	6.55895	0.241766
$737$	45.1620	1.66356
$738$	−20.1619	−0.742172
$739$	2.15804	0.0793847	0.0396923	−	0.999212i	$-0.487362\pi$
$739$	2.15804	0.0793847	0.0396923	+	0.999212i	$0.487362\pi$
$740$	−8.97705	−0.330003
$741$	−16.0839	−0.590858
$742$	78.0713	2.86609
$743$	−51.2449	−1.87999	−0.939996	−	0.341184i	$-0.889172\pi$
$743$	−51.2449	−1.87999	−0.939996	+	0.341184i	$0.889172\pi$
$744$	−64.7157	−2.37259
$745$	11.2855	0.413467
$746$	56.0948	2.05378
$747$	40.4378	1.47954
$748$	−20.4527	−0.747825
$749$	−28.9070	−1.05624
$750$	−7.11432	−0.259778
$751$	3.95435	0.144296	0.0721482	−	0.997394i	$-0.477015\pi$
$751$	3.95435	0.144296	0.0721482	+	0.997394i	$0.477015\pi$
$752$	59.5212	2.17052
$753$	−13.0962	−0.477252
$754$	31.8244	1.15898
$755$	−16.9817	−0.618028
$756$	120.702	4.38989
$757$	−27.8824	−1.01340	−0.506702	−	0.862121i	$-0.669136\pi$
$757$	−27.8824	−1.01340	−0.506702	+	0.862121i	$0.669136\pi$
$758$	−63.5064	−2.30665
$759$	55.9123	2.02949
$760$	14.8903	0.540128
$761$	−23.4058	−0.848460	−0.424230	−	0.905554i	$-0.639455\pi$
$761$	−23.4058	−0.848460	−0.424230	+	0.905554i	$0.639455\pi$
$762$	−24.2787	−0.879526
$763$	−11.3211	−0.409852
$764$	14.1430	0.511675
$765$	4.18711	0.151385
$766$	−21.3756	−0.772332
$767$	4.25013	0.153463
$768$	93.1220	3.36025
$769$	−31.6052	−1.13971	−0.569857	−	0.821744i	$-0.693001\pi$
$769$	−31.6052	−1.13971	−0.569857	+	0.821744i	$0.693001\pi$
$770$	−69.5015	−2.50466
$771$	−82.8249	−2.98287
$772$	97.2576	3.50038
$773$	−29.4256	−1.05836	−0.529182	−	0.848508i	$-0.677501\pi$
$773$	−29.4256	−1.05836	−0.529182	+	0.848508i	$0.677501\pi$
$774$	−124.791	−4.48551
$775$	−4.14691	−0.148961
$776$	−68.7836	−2.46919
$777$	28.3680	1.01770
$778$	−7.72282	−0.276876
$779$	4.27256	0.153080
$780$	24.7284	0.885417
$781$	49.4552	1.76965
$782$	−6.54135	−0.233918
$783$	38.4907	1.37555
$784$	75.3312	2.69040
$785$	23.8204	0.850185
$786$	115.475	4.11885
$787$	−50.6610	−1.80587	−0.902934	−	0.429779i	$-0.858591\pi$
$787$	−50.6610	−1.80587	−0.902934	+	0.429779i	$0.858591\pi$
$788$	−38.0010	−1.35373
$789$	−42.1528	−1.50068
$790$	−2.57610	−0.0916534
$791$	84.0057	2.98690
$792$	−170.092	−6.04396
$793$	10.4242	0.370175
$794$	−10.6261	−0.377107
$795$	19.3449	0.686095
$796$	−10.0478	−0.356136
$797$	−24.1838	−0.856635	−0.428318	−	0.903628i	$-0.640894\pi$
$797$	−24.1838	−0.856635	−0.428318	+	0.903628i	$0.640894\pi$
$798$	−89.9562	−3.18442
$799$	−9.26872	−0.327904
$800$	−2.02021	−0.0714253
$801$	44.6599	1.57798
$802$	−47.5315	−1.67839
$803$	79.0097	2.78819
$804$	−89.8697	−3.16946
$805$	−15.0506	−0.530463
$806$	21.2884	0.749852
$807$	38.6202	1.35950
$808$	15.5380	0.546624
$809$	13.5795	0.477430	0.238715	−	0.971090i	$-0.423274\pi$
$809$	13.5795	0.477430	0.238715	+	0.971090i	$0.423274\pi$
$810$	5.55790	0.195285
$811$	−14.0190	−0.492273	−0.246137	−	0.969235i	$-0.579161\pi$
$811$	−14.0190	−0.492273	−0.246137	+	0.969235i	$0.579161\pi$
$812$	120.515	4.22926
$813$	31.8277	1.11624
$814$	−32.0943	−1.12490
$815$	2.53189	0.0886882
$816$	12.0319	0.421201
$817$	26.4446	0.925181
$818$	−12.3159	−0.430616
$819$	−49.4560	−1.72813
$820$	−6.56888	−0.229395
$821$	−39.0476	−1.36277	−0.681386	−	0.731924i	$-0.738622\pi$
$821$	−39.0476	−1.36277	−0.681386	+	0.731924i	$0.738622\pi$
$822$	−42.5101	−1.48271
$823$	−22.5568	−0.786281	−0.393140	−	0.919478i	$-0.628611\pi$
$823$	−22.5568	−0.786281	−0.393140	+	0.919478i	$0.628611\pi$
$824$	28.2781	0.985113
$825$	−17.2215	−0.599574
$826$	23.7707	0.827088
$827$	−29.1871	−1.01494	−0.507468	−	0.861670i	$-0.669419\pi$
$827$	−29.1871	−1.01494	−0.507468	+	0.861670i	$0.669419\pi$
$828$	−70.4168	−2.44715
$829$	22.6694	0.787342	0.393671	−	0.919251i	$-0.371205\pi$
$829$	22.6694	0.787342	0.393671	+	0.919251i	$0.371205\pi$
$830$	19.4582	0.675406
$831$	76.6542	2.65911
$832$	−11.0773	−0.384035
$833$	−11.7307	−0.406443
$834$	−122.781	−4.25156
$835$	−22.4351	−0.776397
$836$	68.9084	2.38325
$837$	25.7477	0.889971
$838$	−85.6280	−2.95797
$839$	54.1608	1.86984	0.934919	−	0.354860i	$-0.115471\pi$
$839$	54.1608	1.86984	0.934919	+	0.354860i	$0.115471\pi$
$840$	72.3439	2.49610
$841$	9.43119	0.325213
$842$	18.0042	0.620466
$843$	−38.5200	−1.32670
$844$	78.9981	2.71923
$845$	8.74503	0.300838
$846$	−147.362	−5.06641
$847$	−117.248	−4.02868
$848$	35.1816	1.20814
$849$	38.4713	1.32033
$850$	2.01479	0.0691068
$851$	−6.95003	−0.238244
$852$	−98.4130	−3.37157
$853$	−47.6247	−1.63064	−0.815319	−	0.579013i	$-0.803438\pi$
$853$	−47.6247	−1.63064	−0.815319	+	0.579013i	$0.803438\pi$
$854$	58.3018	1.99505
$855$	−14.1070	−0.482451
$856$	−34.0415	−1.16351
$857$	−23.9579	−0.818386	−0.409193	−	0.912448i	$-0.634190\pi$
$857$	−23.9579	−0.818386	−0.409193	+	0.912448i	$0.634190\pi$
$858$	88.4074	3.01818
$859$	−43.0870	−1.47011	−0.735055	−	0.678007i	$-0.762844\pi$
$859$	−43.0870	−1.47011	−0.735055	+	0.678007i	$0.762844\pi$
$860$	−40.6575	−1.38641
$861$	20.7580	0.707432
$862$	49.5683	1.68830
$863$	48.8464	1.66275	0.831375	−	0.555712i	$-0.187554\pi$
$863$	48.8464	1.66275	0.831375	+	0.555712i	$0.187554\pi$
$864$	12.5433	0.426731
$865$	2.05734	0.0699518
$866$	−14.0922	−0.478874
$867$	46.7237	1.58682
$868$	80.6167	2.73631
$869$	−6.23589	−0.211538
$870$	44.1038	1.49526
$871$	15.4637	0.523969
$872$	−13.3320	−0.451478
$873$	65.1654	2.20551
$874$	22.0388	0.745475
$875$	4.63571	0.156716
$876$	−157.225	−5.31213
$877$	8.40196	0.283714	0.141857	−	0.989887i	$-0.454693\pi$
$877$	8.40196	0.283714	0.141857	+	0.989887i	$0.454693\pi$
$878$	80.7732	2.72596
$879$	−34.2767	−1.15612
$880$	−31.3198	−1.05579
$881$	14.5142	0.488995	0.244497	−	0.969650i	$-0.421377\pi$
$881$	14.5142	0.488995	0.244497	+	0.969650i	$0.421377\pi$
$882$	−186.504	−6.27992
$883$	8.61192	0.289814	0.144907	−	0.989445i	$-0.453712\pi$
$883$	8.61192	0.289814	0.144907	+	0.989445i	$0.453712\pi$
$884$	−7.00313	−0.235541
$885$	5.89003	0.197991
$886$	39.9208	1.34117
$887$	−40.8407	−1.37130	−0.685648	−	0.727933i	$-0.740481\pi$
$887$	−40.8407	−1.37130	−0.685648	+	0.727933i	$0.740481\pi$
$888$	33.4068	1.12106
$889$	15.8201	0.530589
$890$	21.4899	0.720342
$891$	13.4539	0.450721
$892$	−86.3065	−2.88976
$893$	31.2278	1.04500
$894$	−80.2884	−2.68525
$895$	20.0591	0.670501
$896$	−80.6845	−2.69548
$897$	19.1447	0.639222
$898$	31.6637	1.05663
$899$	25.7079	0.857406
$900$	21.6890	0.722966
$901$	−5.47853	−0.182516
$902$	−23.4847	−0.781955
$903$	128.480	4.27555
$904$	98.9270	3.29026
$905$	−2.69735	−0.0896629
$906$	120.813	4.01376
$907$	−7.23450	−0.240218	−0.120109	−	0.992761i	$-0.538324\pi$
$907$	−7.23450	−0.240218	−0.120109	+	0.992761i	$0.538324\pi$
$908$	58.2393	1.93274
$909$	−14.7206	−0.488253
$910$	−23.7977	−0.788886
$911$	24.3255	0.805941	0.402971	−	0.915213i	$-0.367978\pi$
$911$	24.3255	0.805941	0.402971	+	0.915213i	$0.367978\pi$
$912$	−40.5374	−1.34233
$913$	47.1021	1.55885
$914$	22.0392	0.728993
$915$	14.4463	0.477581
$916$	33.7520	1.11520
$917$	−75.2436	−2.48476
$918$	−12.5096	−0.412879
$919$	21.7229	0.716572	0.358286	−	0.933612i	$-0.383361\pi$
$919$	21.7229	0.716572	0.358286	+	0.933612i	$0.383361\pi$
$920$	−17.7239	−0.584340
$921$	7.61556	0.250941
$922$	−38.1167	−1.25531
$923$	16.9338	0.557381
$924$	334.789	11.0137
$925$	2.14067	0.0703848
$926$	41.4694	1.36277
$927$	−26.7906	−0.879918
$928$	12.5239	0.411117
$929$	37.5372	1.23156	0.615778	−	0.787919i	$-0.288842\pi$
$929$	37.5372	1.23156	0.615778	+	0.787919i	$0.288842\pi$
$930$	29.5024	0.967423
$931$	39.5225	1.29530
$932$	24.7215	0.809781
$933$	−19.6406	−0.643005
$934$	51.5429	1.68653
$935$	4.87716	0.159500
$936$	−58.2405	−1.90365
$937$	1.56221	0.0510353	0.0255176	−	0.999674i	$-0.491877\pi$
$937$	1.56221	0.0510353	0.0255176	+	0.999674i	$0.491877\pi$
$938$	86.4875	2.82392
$939$	69.4502	2.26642
$940$	−48.0114	−1.56596
$941$	30.4864	0.993827	0.496914	−	0.867800i	$-0.334467\pi$
$941$	30.4864	0.993827	0.496914	+	0.867800i	$0.334467\pi$
$942$	−169.466	−5.52149
$943$	−5.08562	−0.165611
$944$	10.7119	0.348642
$945$	−28.7826	−0.936299
$946$	−145.356	−4.72594
$947$	29.7093	0.965421	0.482711	−	0.875780i	$-0.339652\pi$
$947$	29.7093	0.965421	0.482711	+	0.875780i	$0.339652\pi$
$948$	12.4091	0.403027
$949$	27.0534	0.878190
$950$	−6.78816	−0.220237
$951$	5.63135	0.182609
$952$	−20.4880	−0.664018
$953$	54.7789	1.77446	0.887232	−	0.461324i	$-0.152625\pi$
$953$	54.7789	1.77446	0.887232	+	0.461324i	$0.152625\pi$
$954$	−87.1024	−2.82004
$955$	−3.37253	−0.109133
$956$	38.7275	1.25254
$957$	106.761	3.45109
$958$	−55.5786	−1.79566
$959$	27.6997	0.894470
$960$	−15.3514	−0.495463
$961$	−13.8032	−0.445263
$962$	−10.9893	−0.354308
$963$	32.2509	1.03927
$964$	−129.457	−4.16954
$965$	−23.1921	−0.746579
$966$	107.075	3.44507
$967$	34.8065	1.11930	0.559650	−	0.828729i	$-0.310935\pi$
$967$	34.8065	1.11930	0.559650	+	0.828729i	$0.310935\pi$
$968$	−138.074	−4.43785
$969$	6.31254	0.202788
$970$	31.3569	1.00681
$971$	52.7095	1.69153	0.845764	−	0.533557i	$-0.179145\pi$
$971$	52.7095	1.69153	0.845764	+	0.533557i	$0.179145\pi$
$972$	51.3399	1.64673
$973$	80.0045	2.56483
$974$	32.3819	1.03758
$975$	−5.89673	−0.188846
$976$	26.2728	0.840972
$977$	−41.5915	−1.33063	−0.665316	−	0.746562i	$-0.731703\pi$
$977$	−41.5915	−1.33063	−0.665316	+	0.746562i	$0.731703\pi$
$978$	−18.0127	−0.575982
$979$	52.0200	1.66257
$980$	−60.7641	−1.94104
$981$	12.6307	0.403267
$982$	−95.2513	−3.03959
$983$	−46.8252	−1.49349	−0.746746	−	0.665110i	$-0.768385\pi$
$983$	−46.8252	−1.49349	−0.746746	+	0.665110i	$0.768385\pi$
$984$	24.4451	0.779283
$985$	9.06173	0.288731
$986$	−12.4903	−0.397772
$987$	151.719	4.82927
$988$	23.5946	0.750646
$989$	−31.4770	−1.00091
$990$	77.5412	2.46442
$991$	26.0078	0.826165	0.413082	−	0.910694i	$-0.364452\pi$
$991$	26.0078	0.826165	0.413082	+	0.910694i	$0.364452\pi$
$992$	8.37764	0.265990
$993$	−2.96686	−0.0941506
$994$	94.7092	3.00399
$995$	2.39601	0.0759586
$996$	−93.7304	−2.96996
$997$	44.4447	1.40758	0.703789	−	0.710409i	$-0.251490\pi$
$997$	44.4447	1.40758	0.703789	+	0.710409i	$0.251490\pi$
$998$	−27.0760	−0.857077
$999$	−13.2912	−0.420514

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8005.2.a.g.1.10	✓	137

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8005.2.a.g.1.10	✓	137	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:	\( N \)	\(=\)	\( 8005 = 5 \cdot 1601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48869 q^{2} -2.85866 q^{3} +4.19357 q^{4} -1.00000 q^{5} +7.11432 q^{6} -4.63571 q^{7} -5.45912 q^{8} +5.17196 q^{9} +O(q^{10})\)	\(q-2.48869 q^{2} -2.85866 q^{3} +4.19357 q^{4} -1.00000 q^{5} +7.11432 q^{6} -4.63571 q^{7} -5.45912 q^{8} +5.17196 q^{9} +2.48869 q^{10} +6.02431 q^{11} -11.9880 q^{12} +2.06276 q^{13} +11.5368 q^{14} +2.85866 q^{15} +5.19890 q^{16} -0.809580 q^{17} -12.8714 q^{18} +2.72760 q^{19} -4.19357 q^{20} +13.2519 q^{21} -14.9926 q^{22} -3.24666 q^{23} +15.6058 q^{24} +1.00000 q^{25} -5.13356 q^{26} -6.20889 q^{27} -19.4402 q^{28} -6.19929 q^{29} -7.11432 q^{30} -4.14691 q^{31} -2.02021 q^{32} -17.2215 q^{33} +2.01479 q^{34} +4.63571 q^{35} +21.6890 q^{36} +2.14067 q^{37} -6.78816 q^{38} -5.89673 q^{39} +5.45912 q^{40} +1.56642 q^{41} -32.9800 q^{42} +9.69519 q^{43} +25.2634 q^{44} -5.17196 q^{45} +8.07993 q^{46} +11.4488 q^{47} -14.8619 q^{48} +14.4898 q^{49} -2.48869 q^{50} +2.31432 q^{51} +8.65032 q^{52} +6.76713 q^{53} +15.4520 q^{54} -6.02431 q^{55} +25.3069 q^{56} -7.79730 q^{57} +15.4281 q^{58} +2.06041 q^{59} +11.9880 q^{60} +5.05353 q^{61} +10.3204 q^{62} -23.9757 q^{63} -5.37012 q^{64} -2.06276 q^{65} +42.8589 q^{66} +7.49663 q^{67} -3.39503 q^{68} +9.28111 q^{69} -11.5368 q^{70} +8.20928 q^{71} -28.2343 q^{72} +13.1152 q^{73} -5.32746 q^{74} -2.85866 q^{75} +11.4384 q^{76} -27.9269 q^{77} +14.6751 q^{78} -1.03512 q^{79} -5.19890 q^{80} +2.23326 q^{81} -3.89832 q^{82} +7.81868 q^{83} +55.5730 q^{84} +0.809580 q^{85} -24.1283 q^{86} +17.7217 q^{87} -32.8874 q^{88} +8.63501 q^{89} +12.8714 q^{90} -9.56235 q^{91} -13.6151 q^{92} +11.8546 q^{93} -28.4925 q^{94} -2.72760 q^{95} +5.77511 q^{96} +12.5998 q^{97} -36.0607 q^{98} +31.1575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 137 q + 4 q^{2} + 20 q^{3} + 152 q^{4} - 137 q^{5} + 14 q^{6} - 30 q^{7} + 24 q^{8} + 163 q^{9}+O(q^{10}) \) 137 * q + 4 * q^2 + 20 * q^3 + 152 * q^4 - 137 * q^5 + 14 * q^6 - 30 * q^7 + 24 * q^8 + 163 * q^9	\( 137 q + 4 q^{2} + 20 q^{3} + 152 q^{4} - 137 q^{5} + 14 q^{6} - 30 q^{7} + 24 q^{8} + 163 q^{9} - 4 q^{10} + 51 q^{11} + 32 q^{12} - 6 q^{13} + 49 q^{14} - 20 q^{15} + 170 q^{16} + 46 q^{17} + 4 q^{18} + 47 q^{19} - 152 q^{20} + 28 q^{21} - 19 q^{22} + 29 q^{23} + 39 q^{24} + 137 q^{25} + 67 q^{26} + 77 q^{27} - 58 q^{28} + 27 q^{29} - 14 q^{30} + 23 q^{31} + 42 q^{32} + 40 q^{33} + 38 q^{34} + 30 q^{35} + 222 q^{36} - 56 q^{37} + 87 q^{38} + 44 q^{39} - 24 q^{40} + 66 q^{41} + 34 q^{42} + 15 q^{43} + 87 q^{44} - 163 q^{45} + 37 q^{46} + 52 q^{47} + 56 q^{48} + 195 q^{49} + 4 q^{50} + 106 q^{51} - 31 q^{52} + 45 q^{53} + 83 q^{54} - 51 q^{55} + 148 q^{56} + 4 q^{57} - 101 q^{58} + 239 q^{59} - 32 q^{60} + 46 q^{61} + 63 q^{62} - 59 q^{63} + 200 q^{64} + 6 q^{65} + 108 q^{66} - 18 q^{67} + 152 q^{68} + 63 q^{69} - 49 q^{70} + 110 q^{71} + 6 q^{72} - 19 q^{73} + 81 q^{74} + 20 q^{75} + 94 q^{76} + 43 q^{77} - 3 q^{78} + 40 q^{79} - 170 q^{80} + 229 q^{81} + 3 q^{82} + 235 q^{83} + 94 q^{84} - 46 q^{85} + 110 q^{86} + 31 q^{87} - 105 q^{88} + 150 q^{89} - 4 q^{90} + 110 q^{91} + 76 q^{92} + 11 q^{93} + 56 q^{94} - 47 q^{95} + 146 q^{96} + 17 q^{97} + 75 q^{98} + 125 q^{99}+O(q^{100}) \) 137 * q + 4 * q^2 + 20 * q^3 + 152 * q^4 - 137 * q^5 + 14 * q^6 - 30 * q^7 + 24 * q^8 + 163 * q^9 - 4 * q^10 + 51 * q^11 + 32 * q^12 - 6 * q^13 + 49 * q^14 - 20 * q^15 + 170 * q^16 + 46 * q^17 + 4 * q^18 + 47 * q^19 - 152 * q^20 + 28 * q^21 - 19 * q^22 + 29 * q^23 + 39 * q^24 + 137 * q^25 + 67 * q^26 + 77 * q^27 - 58 * q^28 + 27 * q^29 - 14 * q^30 + 23 * q^31 + 42 * q^32 + 40 * q^33 + 38 * q^34 + 30 * q^35 + 222 * q^36 - 56 * q^37 + 87 * q^38 + 44 * q^39 - 24 * q^40 + 66 * q^41 + 34 * q^42 + 15 * q^43 + 87 * q^44 - 163 * q^45 + 37 * q^46 + 52 * q^47 + 56 * q^48 + 195 * q^49 + 4 * q^50 + 106 * q^51 - 31 * q^52 + 45 * q^53 + 83 * q^54 - 51 * q^55 + 148 * q^56 + 4 * q^57 - 101 * q^58 + 239 * q^59 - 32 * q^60 + 46 * q^61 + 63 * q^62 - 59 * q^63 + 200 * q^64 + 6 * q^65 + 108 * q^66 - 18 * q^67 + 152 * q^68 + 63 * q^69 - 49 * q^70 + 110 * q^71 + 6 * q^72 - 19 * q^73 + 81 * q^74 + 20 * q^75 + 94 * q^76 + 43 * q^77 - 3 * q^78 + 40 * q^79 - 170 * q^80 + 229 * q^81 + 3 * q^82 + 235 * q^83 + 94 * q^84 - 46 * q^85 + 110 * q^86 + 31 * q^87 - 105 * q^88 + 150 * q^89 - 4 * q^90 + 110 * q^91 + 76 * q^92 + 11 * q^93 + 56 * q^94 - 47 * q^95 + 146 * q^96 + 17 * q^97 + 75 * q^98 + 125 * q^99

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