LMFDB - Embedded newform 2005.2.a.e.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2005,2,Mod(1,2005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2005, 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("2005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2005 = 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2005.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:	$16.0100056053$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	2005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.524480 q^{2} -2.05313 q^{3} -1.72492 q^{4} -1.00000 q^{5} +1.07683 q^{6} -2.06215 q^{7} +1.95365 q^{8} +1.21534 q^{9} +O(q^{10})$	\(q-0.524480 q^{2} -2.05313 q^{3} -1.72492 q^{4} -1.00000 q^{5} +1.07683 q^{6} -2.06215 q^{7} +1.95365 q^{8} +1.21534 q^{9} +0.524480 q^{10} -4.52832 q^{11} +3.54148 q^{12} +3.32943 q^{13} +1.08156 q^{14} +2.05313 q^{15} +2.42519 q^{16} +0.669521 q^{17} -0.637421 q^{18} +6.33458 q^{19} +1.72492 q^{20} +4.23385 q^{21} +2.37501 q^{22} -6.89123 q^{23} -4.01109 q^{24} +1.00000 q^{25} -1.74622 q^{26} +3.66414 q^{27} +3.55704 q^{28} +1.76655 q^{29} -1.07683 q^{30} -0.343173 q^{31} -5.17926 q^{32} +9.29722 q^{33} -0.351150 q^{34} +2.06215 q^{35} -2.09636 q^{36} +8.70703 q^{37} -3.32236 q^{38} -6.83576 q^{39} -1.95365 q^{40} +3.38784 q^{41} -2.22057 q^{42} +7.14796 q^{43} +7.81099 q^{44} -1.21534 q^{45} +3.61431 q^{46} -0.777112 q^{47} -4.97923 q^{48} -2.74755 q^{49} -0.524480 q^{50} -1.37461 q^{51} -5.74301 q^{52} +0.398254 q^{53} -1.92177 q^{54} +4.52832 q^{55} -4.02871 q^{56} -13.0057 q^{57} -0.926519 q^{58} -7.88903 q^{59} -3.54148 q^{60} +6.54832 q^{61} +0.179987 q^{62} -2.50621 q^{63} -2.13397 q^{64} -3.32943 q^{65} -4.87621 q^{66} +3.81313 q^{67} -1.15487 q^{68} +14.1486 q^{69} -1.08156 q^{70} +8.97981 q^{71} +2.37434 q^{72} -5.05785 q^{73} -4.56666 q^{74} -2.05313 q^{75} -10.9266 q^{76} +9.33806 q^{77} +3.58522 q^{78} -12.8014 q^{79} -2.42519 q^{80} -11.1690 q^{81} -1.77686 q^{82} -13.4417 q^{83} -7.30306 q^{84} -0.669521 q^{85} -3.74896 q^{86} -3.62695 q^{87} -8.84673 q^{88} -14.2282 q^{89} +0.637421 q^{90} -6.86578 q^{91} +11.8868 q^{92} +0.704578 q^{93} +0.407580 q^{94} -6.33458 q^{95} +10.6337 q^{96} +11.6199 q^{97} +1.44103 q^{98} -5.50344 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9}+O(q^{10}) $ 29 * q - 5 * q^2 - 3 * q^3 + 19 * q^4 - 29 * q^5 - 6 * q^6 + 12 * q^7 - 15 * q^8 + 14 * q^9	\( 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9} + 5 q^{10} - 38 q^{11} - 6 q^{12} + 5 q^{13} - 18 q^{14} + 3 q^{15} + 7 q^{16} - 16 q^{17} - 2 q^{18} - 18 q^{19} - 19 q^{20} - 20 q^{21} - 2 q^{22} - 19 q^{23} - 19 q^{24} + 29 q^{25} - 21 q^{26} - 21 q^{27} + 26 q^{28} - 31 q^{29} + 6 q^{30} - 13 q^{31} - 30 q^{32} + 2 q^{33} - 14 q^{34} - 12 q^{35} - 29 q^{36} - q^{37} - 23 q^{38} - 39 q^{39} + 15 q^{40} - 24 q^{41} - 20 q^{42} - 27 q^{43} - 76 q^{44} - 14 q^{45} - 11 q^{46} - 5 q^{47} - 2 q^{48} - 11 q^{49} - 5 q^{50} - 58 q^{51} + 11 q^{52} - 37 q^{53} - 18 q^{54} + 38 q^{55} - 50 q^{56} - 6 q^{57} + 31 q^{58} - 67 q^{59} + 6 q^{60} - 31 q^{61} - 19 q^{62} - 2 q^{63} - 13 q^{64} - 5 q^{65} + 6 q^{66} - 17 q^{67} - 16 q^{68} - 48 q^{69} + 18 q^{70} - 53 q^{71} + 9 q^{72} + 29 q^{73} - 59 q^{74} - 3 q^{75} - 21 q^{76} - 62 q^{77} - 12 q^{78} - 13 q^{79} - 7 q^{80} - 11 q^{81} + 32 q^{82} - 72 q^{83} - 58 q^{84} + 16 q^{85} - 43 q^{86} + 4 q^{87} + 12 q^{88} - 38 q^{89} + 2 q^{90} - 45 q^{91} - 37 q^{92} - 27 q^{93} - 44 q^{94} + 18 q^{95} - 21 q^{96} + 32 q^{97} - 32 q^{98} - 107 q^{99}+O(q^{100}) \) 29 * q - 5 * q^2 - 3 * q^3 + 19 * q^4 - 29 * q^5 - 6 * q^6 + 12 * q^7 - 15 * q^8 + 14 * q^9 + 5 * q^10 - 38 * q^11 - 6 * q^12 + 5 * q^13 - 18 * q^14 + 3 * q^15 + 7 * q^16 - 16 * q^17 - 2 * q^18 - 18 * q^19 - 19 * q^20 - 20 * q^21 - 2 * q^22 - 19 * q^23 - 19 * q^24 + 29 * q^25 - 21 * q^26 - 21 * q^27 + 26 * q^28 - 31 * q^29 + 6 * q^30 - 13 * q^31 - 30 * q^32 + 2 * q^33 - 14 * q^34 - 12 * q^35 - 29 * q^36 - q^37 - 23 * q^38 - 39 * q^39 + 15 * q^40 - 24 * q^41 - 20 * q^42 - 27 * q^43 - 76 * q^44 - 14 * q^45 - 11 * q^46 - 5 * q^47 - 2 * q^48 - 11 * q^49 - 5 * q^50 - 58 * q^51 + 11 * q^52 - 37 * q^53 - 18 * q^54 + 38 * q^55 - 50 * q^56 - 6 * q^57 + 31 * q^58 - 67 * q^59 + 6 * q^60 - 31 * q^61 - 19 * q^62 - 2 * q^63 - 13 * q^64 - 5 * q^65 + 6 * q^66 - 17 * q^67 - 16 * q^68 - 48 * q^69 + 18 * q^70 - 53 * q^71 + 9 * q^72 + 29 * q^73 - 59 * q^74 - 3 * q^75 - 21 * q^76 - 62 * q^77 - 12 * q^78 - 13 * q^79 - 7 * q^80 - 11 * q^81 + 32 * q^82 - 72 * q^83 - 58 * q^84 + 16 * q^85 - 43 * q^86 + 4 * q^87 + 12 * q^88 - 38 * q^89 + 2 * q^90 - 45 * q^91 - 37 * q^92 - 27 * q^93 - 44 * q^94 + 18 * q^95 - 21 * q^96 + 32 * q^97 - 32 * q^98 - 107 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.524480	−0.370863	−0.185432	−	0.982657i	$-0.559368\pi$
$2$	−0.524480	−0.370863	−0.185432	+	0.982657i	$0.559368\pi$
$3$	−2.05313	−1.18537	−0.592687	−	0.805433i	$-0.701933\pi$
$3$	−2.05313	−1.18537	−0.592687	+	0.805433i	$0.701933\pi$
$4$	−1.72492	−0.862460
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.07683	0.439612
$7$	−2.06215	−0.779418	−0.389709	−	0.920938i	$-0.627424\pi$
$7$	−2.06215	−0.779418	−0.389709	+	0.920938i	$0.627424\pi$
$8$	1.95365	0.690718
$9$	1.21534	0.405113
$10$	0.524480	0.165855
$11$	−4.52832	−1.36534	−0.682670	−	0.730727i	$-0.739181\pi$
$11$	−4.52832	−1.36534	−0.682670	+	0.730727i	$0.739181\pi$
$12$	3.54148	1.02234
$13$	3.32943	0.923419	0.461709	−	0.887031i	$-0.347236\pi$
$13$	3.32943	0.923419	0.461709	+	0.887031i	$0.347236\pi$
$14$	1.08156	0.289058
$15$	2.05313	0.530116
$16$	2.42519	0.606298
$17$	0.669521	0.162383	0.0811913	−	0.996699i	$-0.474128\pi$
$17$	0.669521	0.162383	0.0811913	+	0.996699i	$0.474128\pi$
$18$	−0.637421	−0.150242
$19$	6.33458	1.45325	0.726626	−	0.687033i	$-0.241087\pi$
$19$	6.33458	1.45325	0.726626	+	0.687033i	$0.241087\pi$
$20$	1.72492	0.385704
$21$	4.23385	0.923903
$22$	2.37501	0.506354
$23$	−6.89123	−1.43692	−0.718460	−	0.695568i	$-0.755153\pi$
$23$	−6.89123	−1.43692	−0.718460	+	0.695568i	$0.755153\pi$
$24$	−4.01109	−0.818760
$25$	1.00000	0.200000
$26$	−1.74622	−0.342462
$27$	3.66414	0.705164
$28$	3.55704	0.672217
$29$	1.76655	0.328040	0.164020	−	0.986457i	$-0.447554\pi$
$29$	1.76655	0.328040	0.164020	+	0.986457i	$0.447554\pi$
$30$	−1.07683	−0.196600
$31$	−0.343173	−0.0616357	−0.0308178	−	0.999525i	$-0.509811\pi$
$31$	−0.343173	−0.0616357	−0.0308178	+	0.999525i	$0.509811\pi$
$32$	−5.17926	−0.915572
$33$	9.29722	1.61844
$34$	−0.351150	−0.0602218
$35$	2.06215	0.348567
$36$	−2.09636	−0.349394
$37$	8.70703	1.43143	0.715713	−	0.698394i	$-0.246102\pi$
$37$	8.70703	1.43143	0.715713	+	0.698394i	$0.246102\pi$
$38$	−3.32236	−0.538958
$39$	−6.83576	−1.09460
$40$	−1.95365	−0.308899
$41$	3.38784	0.529092	0.264546	−	0.964373i	$-0.414778\pi$
$41$	3.38784	0.529092	0.264546	+	0.964373i	$0.414778\pi$
$42$	−2.22057	−0.342642
$43$	7.14796	1.09005	0.545027	−	0.838419i	$-0.316519\pi$
$43$	7.14796	1.09005	0.545027	+	0.838419i	$0.316519\pi$
$44$	7.81099	1.17755
$45$	−1.21534	−0.181172
$46$	3.61431	0.532901
$47$	−0.777112	−0.113353	−0.0566767	−	0.998393i	$-0.518050\pi$
$47$	−0.777112	−0.113353	−0.0566767	+	0.998393i	$0.518050\pi$
$48$	−4.97923	−0.718691
$49$	−2.74755	−0.392507
$50$	−0.524480	−0.0741727
$51$	−1.37461	−0.192484
$52$	−5.74301	−0.796412
$53$	0.398254	0.0547045	0.0273522	−	0.999626i	$-0.491292\pi$
$53$	0.398254	0.0547045	0.0273522	+	0.999626i	$0.491292\pi$
$54$	−1.92177	−0.261519
$55$	4.52832	0.610598
$56$	−4.02871	−0.538359
$57$	−13.0057	−1.72265
$58$	−0.926519	−0.121658
$59$	−7.88903	−1.02706	−0.513532	−	0.858070i	$-0.671663\pi$
$59$	−7.88903	−1.02706	−0.513532	+	0.858070i	$0.671663\pi$
$60$	−3.54148	−0.457204
$61$	6.54832	0.838426	0.419213	−	0.907888i	$-0.362306\pi$
$61$	6.54832	0.838426	0.419213	+	0.907888i	$0.362306\pi$
$62$	0.179987	0.0228584
$63$	−2.50621	−0.315753
$64$	−2.13397	−0.266746
$65$	−3.32943	−0.412965
$66$	−4.87621	−0.600220
$67$	3.81313	0.465847	0.232924	−	0.972495i	$-0.425171\pi$
$67$	3.81313	0.465847	0.232924	+	0.972495i	$0.425171\pi$
$68$	−1.15487	−0.140049
$69$	14.1486	1.70329
$70$	−1.08156	−0.129271
$71$	8.97981	1.06571	0.532854	−	0.846207i	$-0.321120\pi$
$71$	8.97981	1.06571	0.532854	+	0.846207i	$0.321120\pi$
$72$	2.37434	0.279819
$73$	−5.05785	−0.591976	−0.295988	−	0.955192i	$-0.595649\pi$
$73$	−5.05785	−0.591976	−0.295988	+	0.955192i	$0.595649\pi$
$74$	−4.56666	−0.530864
$75$	−2.05313	−0.237075
$76$	−10.9266	−1.25337
$77$	9.33806	1.06417
$78$	3.58522	0.405946
$79$	−12.8014	−1.44027	−0.720134	−	0.693835i	$-0.755920\pi$
$79$	−12.8014	−1.44027	−0.720134	+	0.693835i	$0.755920\pi$
$80$	−2.42519	−0.271145
$81$	−11.1690	−1.24100
$82$	−1.77686	−0.196221
$83$	−13.4417	−1.47542	−0.737708	−	0.675120i	$-0.764092\pi$
$83$	−13.4417	−1.47542	−0.737708	+	0.675120i	$0.764092\pi$
$84$	−7.30306	−0.796830
$85$	−0.669521	−0.0726197
$86$	−3.74896	−0.404261
$87$	−3.62695	−0.388850
$88$	−8.84673	−0.943065
$89$	−14.2282	−1.50819	−0.754093	−	0.656767i	$-0.771923\pi$
$89$	−14.2282	−1.50819	−0.754093	+	0.656767i	$0.771923\pi$
$90$	0.637421	0.0671901
$91$	−6.86578	−0.719729
$92$	11.8868	1.23929
$93$	0.704578	0.0730614
$94$	0.407580	0.0420386
$95$	−6.33458	−0.649914
$96$	10.6337	1.08530
$97$	11.6199	1.17982	0.589911	−	0.807469i	$-0.299163\pi$
$97$	11.6199	1.17982	0.589911	+	0.807469i	$0.299163\pi$
$98$	1.44103	0.145566
$99$	−5.50344	−0.553117
$100$	−1.72492	−0.172492
$101$	−6.68908	−0.665588	−0.332794	−	0.943000i	$-0.607991\pi$
$101$	−6.68908	−0.665588	−0.332794	+	0.943000i	$0.607991\pi$
$102$	0.720957	0.0713854
$103$	−1.16095	−0.114392	−0.0571959	−	0.998363i	$-0.518216\pi$
$103$	−1.16095	−0.114392	−0.0571959	+	0.998363i	$0.518216\pi$
$104$	6.50453	0.637822
$105$	−4.23385	−0.413182
$106$	−0.208876	−0.0202879
$107$	16.0519	1.55180	0.775898	−	0.630858i	$-0.217297\pi$
$107$	16.0519	1.55180	0.775898	+	0.630858i	$0.217297\pi$
$108$	−6.32035	−0.608176
$109$	10.6633	1.02136	0.510678	−	0.859772i	$-0.329394\pi$
$109$	10.6633	1.02136	0.510678	+	0.859772i	$0.329394\pi$
$110$	−2.37501	−0.226449
$111$	−17.8766	−1.69678
$112$	−5.00111	−0.472560
$113$	8.07399	0.759537	0.379769	−	0.925082i	$-0.376004\pi$
$113$	8.07399	0.759537	0.379769	+	0.925082i	$0.376004\pi$
$114$	6.82123	0.638867
$115$	6.89123	0.642610
$116$	−3.04716	−0.282921
$117$	4.04639	0.374089
$118$	4.13764	0.380901
$119$	−1.38065	−0.126564
$120$	4.01109	0.366161
$121$	9.50566	0.864151
$122$	−3.43446	−0.310942
$123$	−6.95568	−0.627173
$124$	0.591946	0.0531583
$125$	−1.00000	−0.0894427
$126$	1.31446	0.117101
$127$	−5.94828	−0.527824	−0.263912	−	0.964547i	$-0.585013\pi$
$127$	−5.94828	−0.527824	−0.263912	+	0.964547i	$0.585013\pi$
$128$	11.4777	1.01450
$129$	−14.6757	−1.29212
$130$	1.74622	0.153154
$131$	−10.3772	−0.906662	−0.453331	−	0.891342i	$-0.649764\pi$
$131$	−10.3772	−0.906662	−0.453331	+	0.891342i	$0.649764\pi$
$132$	−16.0370	−1.39584
$133$	−13.0628	−1.13269
$134$	−1.99991	−0.172766
$135$	−3.66414	−0.315359
$136$	1.30801	0.112161
$137$	16.1676	1.38129	0.690647	−	0.723192i	$-0.257326\pi$
$137$	16.1676	1.38129	0.690647	+	0.723192i	$0.257326\pi$
$138$	−7.42065	−0.631687
$139$	−2.67571	−0.226951	−0.113475	−	0.993541i	$-0.536198\pi$
$139$	−2.67571	−0.226951	−0.113475	+	0.993541i	$0.536198\pi$
$140$	−3.55704	−0.300625
$141$	1.59551	0.134366
$142$	−4.70973	−0.395232
$143$	−15.0767	−1.26078
$144$	2.94743	0.245619
$145$	−1.76655	−0.146704
$146$	2.65274	0.219542
$147$	5.64107	0.465268
$148$	−15.0189	−1.23455
$149$	−19.3611	−1.58613	−0.793063	−	0.609140i	$-0.791515\pi$
$149$	−19.3611	−1.58613	−0.793063	+	0.609140i	$0.791515\pi$
$150$	1.07683	0.0879224
$151$	−21.4269	−1.74370	−0.871849	−	0.489774i	$-0.837079\pi$
$151$	−21.4269	−1.74370	−0.871849	+	0.489774i	$0.837079\pi$
$152$	12.3755	1.00379
$153$	0.813695	0.0657833
$154$	−4.89763	−0.394662
$155$	0.343173	0.0275643
$156$	11.7911	0.944046
$157$	−18.8787	−1.50668	−0.753340	−	0.657631i	$-0.771559\pi$
$157$	−18.8787	−1.50668	−0.753340	+	0.657631i	$0.771559\pi$
$158$	6.71407	0.534143
$159$	−0.817668	−0.0648453
$160$	5.17926	0.409456
$161$	14.2107	1.11996
$162$	5.85790	0.460240
$163$	−10.0939	−0.790618	−0.395309	−	0.918548i	$-0.629362\pi$
$163$	−10.0939	−0.790618	−0.395309	+	0.918548i	$0.629362\pi$
$164$	−5.84376	−0.456321
$165$	−9.29722	−0.723788
$166$	7.04989	0.547178
$167$	3.40475	0.263467	0.131734	−	0.991285i	$-0.457946\pi$
$167$	3.40475	0.263467	0.131734	+	0.991285i	$0.457946\pi$
$168$	8.27146	0.638157
$169$	−1.91488	−0.147298
$170$	0.351150	0.0269320
$171$	7.69866	0.588731
$172$	−12.3297	−0.940128
$173$	−2.30222	−0.175035	−0.0875174	−	0.996163i	$-0.527893\pi$
$173$	−2.30222	−0.175035	−0.0875174	+	0.996163i	$0.527893\pi$
$174$	1.90226	0.144210
$175$	−2.06215	−0.155884
$176$	−10.9820	−0.827803
$177$	16.1972	1.21746
$178$	7.46241	0.559331
$179$	−6.84445	−0.511578	−0.255789	−	0.966733i	$-0.582335\pi$
$179$	−6.84445	−0.511578	−0.255789	+	0.966733i	$0.582335\pi$
$180$	2.09636	0.156254
$181$	18.8208	1.39894	0.699469	−	0.714663i	$-0.253420\pi$
$181$	18.8208	1.39894	0.699469	+	0.714663i	$0.253420\pi$
$182$	3.60096	0.266921
$183$	−13.4445	−0.993849
$184$	−13.4630	−0.992507
$185$	−8.70703	−0.640153
$186$	−0.369537	−0.0270958
$187$	−3.03180	−0.221707
$188$	1.34046	0.0977628
$189$	−7.55599	−0.549618
$190$	3.32236	0.241029
$191$	8.36892	0.605554	0.302777	−	0.953061i	$-0.402086\pi$
$191$	8.36892	0.605554	0.302777	+	0.953061i	$0.402086\pi$
$192$	4.38131	0.316194
$193$	5.60265	0.403288	0.201644	−	0.979459i	$-0.435372\pi$
$193$	5.60265	0.403288	0.201644	+	0.979459i	$0.435372\pi$
$194$	−6.09440	−0.437553
$195$	6.83576	0.489519
$196$	4.73930	0.338522
$197$	12.0595	0.859206	0.429603	−	0.903018i	$-0.358653\pi$
$197$	12.0595	0.859206	0.429603	+	0.903018i	$0.358653\pi$
$198$	2.88645	0.205131
$199$	−11.8488	−0.839938	−0.419969	−	0.907539i	$-0.637959\pi$
$199$	−11.8488	−0.839938	−0.419969	+	0.907539i	$0.637959\pi$
$200$	1.95365	0.138144
$201$	−7.82884	−0.552204
$202$	3.50829	0.246842
$203$	−3.64288	−0.255680
$204$	2.37110	0.166010
$205$	−3.38784	−0.236617
$206$	0.608895	0.0424237
$207$	−8.37518	−0.582115
$208$	8.07452	0.559867
$209$	−28.6850	−1.98418
$210$	2.22057	0.153234
$211$	−5.06466	−0.348666	−0.174333	−	0.984687i	$-0.555777\pi$
$211$	−5.06466	−0.348666	−0.174333	+	0.984687i	$0.555777\pi$
$212$	−0.686957	−0.0471804
$213$	−18.4367	−1.26326
$214$	−8.41891	−0.575505
$215$	−7.14796	−0.487487
$216$	7.15843	0.487070
$217$	0.707673	0.0480400
$218$	−5.59268	−0.378784
$219$	10.3844	0.701713
$220$	−7.81099	−0.526617
$221$	2.22912	0.149947
$222$	9.37594	0.629272
$223$	7.24109	0.484899	0.242450	−	0.970164i	$-0.422049\pi$
$223$	7.24109	0.484899	0.242450	+	0.970164i	$0.422049\pi$
$224$	10.6804	0.713614
$225$	1.21534	0.0810226
$226$	−4.23465	−0.281685
$227$	3.31842	0.220251	0.110126	−	0.993918i	$-0.464875\pi$
$227$	3.31842	0.220251	0.110126	+	0.993918i	$0.464875\pi$
$228$	22.4338	1.48572
$229$	−13.9698	−0.923151	−0.461575	−	0.887101i	$-0.652716\pi$
$229$	−13.9698	−0.923151	−0.461575	+	0.887101i	$0.652716\pi$
$230$	−3.61431	−0.238321
$231$	−19.1722	−1.26144
$232$	3.45121	0.226583
$233$	7.54909	0.494558	0.247279	−	0.968944i	$-0.420464\pi$
$233$	7.54909	0.494558	0.247279	+	0.968944i	$0.420464\pi$
$234$	−2.12225	−0.138736
$235$	0.777112	0.0506932
$236$	13.6080	0.885803
$237$	26.2829	1.70726
$238$	0.724124	0.0469380
$239$	−5.04510	−0.326341	−0.163170	−	0.986598i	$-0.552172\pi$
$239$	−5.04510	−0.326341	−0.163170	+	0.986598i	$0.552172\pi$
$240$	4.97923	0.321408
$241$	−9.06685	−0.584047	−0.292023	−	0.956411i	$-0.594329\pi$
$241$	−9.06685	−0.584047	−0.292023	+	0.956411i	$0.594329\pi$
$242$	−4.98553	−0.320482
$243$	11.9389	0.765882
$244$	−11.2953	−0.723110
$245$	2.74755	0.175534
$246$	3.64812	0.232595
$247$	21.0905	1.34196
$248$	−0.670439	−0.0425729
$249$	27.5975	1.74892
$250$	0.524480	0.0331710
$251$	−3.43415	−0.216762	−0.108381	−	0.994109i	$-0.534567\pi$
$251$	−3.43415	−0.216762	−0.108381	+	0.994109i	$0.534567\pi$
$252$	4.32301	0.272324
$253$	31.2057	1.96188
$254$	3.11975	0.195751
$255$	1.37461	0.0860816
$256$	−1.75191	−0.109494
$257$	0.553297	0.0345137	0.0172569	−	0.999851i	$-0.494507\pi$
$257$	0.553297	0.0345137	0.0172569	+	0.999851i	$0.494507\pi$
$258$	7.69710	0.479201
$259$	−17.9552	−1.11568
$260$	5.74301	0.356166
$261$	2.14696	0.132893
$262$	5.44265	0.336248
$263$	6.95435	0.428824	0.214412	−	0.976743i	$-0.431217\pi$
$263$	6.95435	0.428824	0.214412	+	0.976743i	$0.431217\pi$
$264$	18.1635	1.11789
$265$	−0.398254	−0.0244646
$266$	6.85119	0.420074
$267$	29.2123	1.78777
$268$	−6.57734	−0.401775
$269$	−9.05610	−0.552160	−0.276080	−	0.961135i	$-0.589036\pi$
$269$	−9.05610	−0.552160	−0.276080	+	0.961135i	$0.589036\pi$
$270$	1.92177	0.116955
$271$	26.2859	1.59676	0.798378	−	0.602157i	$-0.205692\pi$
$271$	26.2859	1.59676	0.798378	+	0.602157i	$0.205692\pi$
$272$	1.62372	0.0984523
$273$	14.0963	0.853149
$274$	−8.47960	−0.512272
$275$	−4.52832	−0.273068
$276$	−24.4052	−1.46902
$277$	12.9785	0.779804	0.389902	−	0.920856i	$-0.372509\pi$
$277$	12.9785	0.779804	0.389902	+	0.920856i	$0.372509\pi$
$278$	1.40336	0.0841678
$279$	−0.417071	−0.0249694
$280$	4.02871	0.240761
$281$	9.28930	0.554153	0.277077	−	0.960848i	$-0.410634\pi$
$281$	9.28930	0.554153	0.277077	+	0.960848i	$0.410634\pi$
$282$	−0.836813	−0.0498315
$283$	−7.86638	−0.467608	−0.233804	−	0.972284i	$-0.575117\pi$
$283$	−7.86638	−0.467608	−0.233804	+	0.972284i	$0.575117\pi$
$284$	−15.4895	−0.919130
$285$	13.0057	0.770391
$286$	7.90744	0.467577
$287$	−6.98623	−0.412384
$288$	−6.29456	−0.370910
$289$	−16.5517	−0.973632
$290$	0.926519	0.0544071
$291$	−23.8571	−1.39853
$292$	8.72438	0.510556
$293$	−19.7147	−1.15174	−0.575872	−	0.817540i	$-0.695337\pi$
$293$	−19.7147	−1.15174	−0.575872	+	0.817540i	$0.695337\pi$
$294$	−2.95863	−0.172551
$295$	7.88903	0.459317
$296$	17.0104	0.988712
$297$	−16.5924	−0.962788
$298$	10.1545	0.588236
$299$	−22.9439	−1.32688
$300$	3.54148	0.204468
$301$	−14.7401	−0.849608
$302$	11.2380	0.646674
$303$	13.7335	0.788971
$304$	15.3626	0.881104
$305$	−6.54832	−0.374956
$306$	−0.426767	−0.0243966
$307$	10.0661	0.574505	0.287253	−	0.957855i	$-0.407258\pi$
$307$	10.0661	0.574505	0.287253	+	0.957855i	$0.407258\pi$
$308$	−16.1074	−0.917805
$309$	2.38358	0.135597
$310$	−0.179987	−0.0102226
$311$	18.1302	1.02807	0.514036	−	0.857769i	$-0.328150\pi$
$311$	18.1302	1.02807	0.514036	+	0.857769i	$0.328150\pi$
$312$	−13.3546	−0.756058
$313$	8.63294	0.487963	0.243981	−	0.969780i	$-0.421546\pi$
$313$	8.63294	0.487963	0.243981	+	0.969780i	$0.421546\pi$
$314$	9.90148	0.558773
$315$	2.50621	0.141209
$316$	22.0814	1.24217
$317$	12.3019	0.690941	0.345471	−	0.938430i	$-0.387719\pi$
$317$	12.3019	0.690941	0.345471	+	0.938430i	$0.387719\pi$
$318$	0.428850	0.0240487
$319$	−7.99949	−0.447886
$320$	2.13397	0.119292
$321$	−32.9566	−1.83946
$322$	−7.45324	−0.415353
$323$	4.24113	0.235983
$324$	19.2656	1.07031
$325$	3.32943	0.184684
$326$	5.29407	0.293211
$327$	−21.8931	−1.21069
$328$	6.61865	0.365454
$329$	1.60252	0.0883497
$330$	4.87621	0.268426
$331$	−16.2650	−0.894006	−0.447003	−	0.894533i	$-0.647509\pi$
$331$	−16.2650	−0.894006	−0.447003	+	0.894533i	$0.647509\pi$
$332$	23.1858	1.27249
$333$	10.5820	0.579889
$334$	−1.78572	−0.0977103
$335$	−3.81313	−0.208333
$336$	10.2679	0.560161
$337$	−19.9288	−1.08559	−0.542796	−	0.839865i	$-0.682634\pi$
$337$	−19.9288	−1.08559	−0.542796	+	0.839865i	$0.682634\pi$
$338$	1.00431	0.0546275
$339$	−16.5769	−0.900336
$340$	1.15487	0.0626316
$341$	1.55400	0.0841536
$342$	−4.03779	−0.218339
$343$	20.1009	1.08535
$344$	13.9646	0.752920
$345$	−14.1486	−0.761734
$346$	1.20747	0.0649140
$347$	0.0816579	0.00438363	0.00219181	−	0.999998i	$-0.499302\pi$
$347$	0.0816579	0.00438363	0.00219181	+	0.999998i	$0.499302\pi$
$348$	6.25621	0.335368
$349$	−8.19901	−0.438883	−0.219441	−	0.975626i	$-0.570423\pi$
$349$	−8.19901	−0.438883	−0.219441	+	0.975626i	$0.570423\pi$
$350$	1.08156	0.0578115
$351$	12.1995	0.651161
$352$	23.4533	1.25007
$353$	−6.22512	−0.331330	−0.165665	−	0.986182i	$-0.552977\pi$
$353$	−6.22512	−0.331330	−0.165665	+	0.986182i	$0.552977\pi$
$354$	−8.49511	−0.451510
$355$	−8.97981	−0.476599
$356$	24.5425	1.30075
$357$	2.83465	0.150026
$358$	3.58977	0.189725
$359$	11.9546	0.630941	0.315470	−	0.948935i	$-0.397838\pi$
$359$	11.9546	0.630941	0.315470	+	0.948935i	$0.397838\pi$
$360$	−2.37434	−0.125139
$361$	21.1269	1.11194
$362$	−9.87113	−0.518815
$363$	−19.5164	−1.02434
$364$	11.8429	0.620738
$365$	5.05785	0.264740
$366$	7.05140	0.368582
$367$	23.4371	1.22341	0.611703	−	0.791088i	$-0.290485\pi$
$367$	23.4371	1.22341	0.611703	+	0.791088i	$0.290485\pi$
$368$	−16.7126	−0.871202
$369$	4.11738	0.214342
$370$	4.56666	0.237409
$371$	−0.821259	−0.0426377
$372$	−1.21534	−0.0630125
$373$	7.78677	0.403183	0.201592	−	0.979470i	$-0.435389\pi$
$373$	7.78677	0.403183	0.201592	+	0.979470i	$0.435389\pi$
$374$	1.59012	0.0822232
$375$	2.05313	0.106023
$376$	−1.51820	−0.0782953
$377$	5.88160	0.302918
$378$	3.96297	0.203833
$379$	−29.1015	−1.49485	−0.747423	−	0.664348i	$-0.768709\pi$
$379$	−29.1015	−1.49485	−0.747423	+	0.664348i	$0.768709\pi$
$380$	10.9266	0.560525
$381$	12.2126	0.625670
$382$	−4.38933	−0.224578
$383$	−27.6933	−1.41506	−0.707532	−	0.706681i	$-0.750191\pi$
$383$	−27.6933	−1.41506	−0.707532	+	0.706681i	$0.750191\pi$
$384$	−23.5653	−1.20256
$385$	−9.33806	−0.475912
$386$	−2.93848	−0.149565
$387$	8.68720	0.441595
$388$	−20.0434	−1.01755
$389$	12.5362	0.635613	0.317806	−	0.948156i	$-0.397054\pi$
$389$	12.5362	0.635613	0.317806	+	0.948156i	$0.397054\pi$
$390$	−3.58522	−0.181545
$391$	−4.61382	−0.233331
$392$	−5.36774	−0.271112
$393$	21.3058	1.07473
$394$	−6.32498	−0.318648
$395$	12.8014	0.644107
$396$	9.49300	0.477041
$397$	−10.4485	−0.524396	−0.262198	−	0.965014i	$-0.584447\pi$
$397$	−10.4485	−0.524396	−0.262198	+	0.965014i	$0.584447\pi$
$398$	6.21445	0.311502
$399$	26.8197	1.34266
$400$	2.42519	0.121260
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	4.10607	0.204792
$403$	−1.14257	−0.0569155
$404$	11.5381	0.574043
$405$	11.1690	0.554990
$406$	1.91062	0.0948225
$407$	−39.4282	−1.95438
$408$	−2.68551	−0.132952
$409$	39.6768	1.96189	0.980947	−	0.194277i	$-0.0622362\pi$
$409$	39.6768	1.96189	0.980947	+	0.194277i	$0.0622362\pi$
$410$	1.77686	0.0877527
$411$	−33.1943	−1.63735
$412$	2.00255	0.0986584
$413$	16.2683	0.800513
$414$	4.39261	0.215885
$415$	13.4417	0.659826
$416$	−17.2440	−0.845456
$417$	5.49358	0.269022
$418$	15.0447	0.735860
$419$	22.6703	1.10752	0.553759	−	0.832677i	$-0.313193\pi$
$419$	22.6703	1.10752	0.553759	+	0.832677i	$0.313193\pi$
$420$	7.30306	0.356353
$421$	3.21971	0.156919	0.0784596	−	0.996917i	$-0.475000\pi$
$421$	3.21971	0.156919	0.0784596	+	0.996917i	$0.475000\pi$
$422$	2.65631	0.129307
$423$	−0.944454	−0.0459209
$424$	0.778048	0.0377854
$425$	0.669521	0.0324765
$426$	9.66969	0.468498
$427$	−13.5036	−0.653485
$428$	−27.6883	−1.33836
$429$	30.9545	1.49450
$430$	3.74896	0.180791
$431$	3.52493	0.169790	0.0848949	−	0.996390i	$-0.472945\pi$
$431$	3.52493	0.169790	0.0848949	+	0.996390i	$0.472945\pi$
$432$	8.88624	0.427540
$433$	37.3300	1.79397	0.896983	−	0.442066i	$-0.145754\pi$
$433$	37.3300	1.79397	0.896983	+	0.442066i	$0.145754\pi$
$434$	−0.371160	−0.0178163
$435$	3.62695	0.173899
$436$	−18.3933	−0.880880
$437$	−43.6530	−2.08821
$438$	−5.44642	−0.260240
$439$	30.9460	1.47697	0.738486	−	0.674268i	$-0.235541\pi$
$439$	30.9460	1.47697	0.738486	+	0.674268i	$0.235541\pi$
$440$	8.84673	0.421751
$441$	−3.33920	−0.159010
$442$	−1.16913	−0.0556099
$443$	−35.0481	−1.66519	−0.832593	−	0.553886i	$-0.813144\pi$
$443$	−35.0481	−1.66519	−0.832593	+	0.553886i	$0.813144\pi$
$444$	30.8358	1.46340
$445$	14.2282	0.674482
$446$	−3.79781	−0.179831
$447$	39.7509	1.88015
$448$	4.40056	0.207907
$449$	−37.9588	−1.79139	−0.895694	−	0.444671i	$-0.853320\pi$
$449$	−37.9588	−1.79139	−0.895694	+	0.444671i	$0.853320\pi$
$450$	−0.637421	−0.0300483
$451$	−15.3412	−0.722391
$452$	−13.9270	−0.655071
$453$	43.9922	2.06694
$454$	−1.74045	−0.0816832
$455$	6.86578	0.321873
$456$	−25.4085	−1.18986
$457$	3.91417	0.183097	0.0915487	−	0.995801i	$-0.470818\pi$
$457$	3.91417	0.183097	0.0915487	+	0.995801i	$0.470818\pi$
$458$	7.32689	0.342363
$459$	2.45322	0.114506
$460$	−11.8868	−0.554226
$461$	−33.3258	−1.55214	−0.776068	−	0.630650i	$-0.782788\pi$
$461$	−33.3258	−1.55214	−0.776068	+	0.630650i	$0.782788\pi$
$462$	10.0555	0.467822
$463$	−23.0012	−1.06896	−0.534479	−	0.845182i	$-0.679492\pi$
$463$	−23.0012	−1.06896	−0.534479	+	0.845182i	$0.679492\pi$
$464$	4.28422	0.198890
$465$	−0.704578	−0.0326740
$466$	−3.95935	−0.183413
$467$	−24.9540	−1.15474	−0.577368	−	0.816484i	$-0.695920\pi$
$467$	−24.9540	−1.15474	−0.577368	+	0.816484i	$0.695920\pi$
$468$	−6.97970	−0.322637
$469$	−7.86323	−0.363090
$470$	−0.407580	−0.0188002
$471$	38.7603	1.78598
$472$	−15.4124	−0.709412
$473$	−32.3682	−1.48829
$474$	−13.7849	−0.633159
$475$	6.33458	0.290650
$476$	2.38151	0.109156
$477$	0.484014	0.0221615
$478$	2.64606	0.121028
$479$	−12.0975	−0.552747	−0.276373	−	0.961050i	$-0.589133\pi$
$479$	−12.0975	−0.552747	−0.276373	+	0.961050i	$0.589133\pi$
$480$	−10.6337	−0.485359
$481$	28.9895	1.32181
$482$	4.75538	0.216602
$483$	−29.1765	−1.32757
$484$	−16.3965	−0.745296
$485$	−11.6199	−0.527632
$486$	−6.26172	−0.284038
$487$	10.1821	0.461397	0.230699	−	0.973025i	$-0.425899\pi$
$487$	10.1821	0.461397	0.230699	+	0.973025i	$0.425899\pi$
$488$	12.7931	0.579117
$489$	20.7241	0.937178
$490$	−1.44103	−0.0650993
$491$	27.7523	1.25245	0.626223	−	0.779644i	$-0.284600\pi$
$491$	27.7523	1.25245	0.626223	+	0.779644i	$0.284600\pi$
$492$	11.9980	0.540912
$493$	1.18274	0.0532680
$494$	−11.0616	−0.497684
$495$	5.50344	0.247361
$496$	−0.832261	−0.0373696
$497$	−18.5177	−0.830632
$498$	−14.4743	−0.648611
$499$	21.9226	0.981392	0.490696	−	0.871331i	$-0.336742\pi$
$499$	21.9226	0.981392	0.490696	+	0.871331i	$0.336742\pi$
$500$	1.72492	0.0771408
$501$	−6.99038	−0.312307
$502$	1.80114	0.0803890
$503$	−4.70379	−0.209731	−0.104866	−	0.994486i	$-0.533441\pi$
$503$	−4.70379	−0.209731	−0.104866	+	0.994486i	$0.533441\pi$
$504$	−4.89625	−0.218096
$505$	6.68908	0.297660
$506$	−16.3668	−0.727591
$507$	3.93149	0.174604
$508$	10.2603	0.455228
$509$	11.5522	0.512043	0.256021	−	0.966671i	$-0.417588\pi$
$509$	11.5522	0.512043	0.256021	+	0.966671i	$0.417588\pi$
$510$	−0.720957	−0.0319245
$511$	10.4300	0.461397
$512$	−22.0366	−0.973891
$513$	23.2108	1.02478
$514$	−0.290193	−0.0127999
$515$	1.16095	0.0511576
$516$	25.3144	1.11440
$517$	3.51901	0.154766
$518$	9.41713	0.413765
$519$	4.72676	0.207482
$520$	−6.50453	−0.285243
$521$	−40.5186	−1.77515	−0.887577	−	0.460660i	$-0.847613\pi$
$521$	−40.5186	−1.77515	−0.887577	+	0.460660i	$0.847613\pi$
$522$	−1.12604	−0.0492852
$523$	−30.9638	−1.35395	−0.676976	−	0.736005i	$-0.736710\pi$
$523$	−30.9638	−1.35395	−0.676976	+	0.736005i	$0.736710\pi$
$524$	17.8999	0.781960
$525$	4.23385	0.184781
$526$	−3.64742	−0.159035
$527$	−0.229761	−0.0100086
$528$	22.5476	0.981256
$529$	24.4890	1.06474
$530$	0.208876	0.00907301
$531$	−9.58785	−0.416077
$532$	22.5323	0.976901
$533$	11.2796	0.488574
$534$	−15.3213	−0.663017
$535$	−16.0519	−0.693985
$536$	7.44950	0.321769
$537$	14.0525	0.606411
$538$	4.74975	0.204776
$539$	12.4418	0.535905
$540$	6.32035	0.271985
$541$	−18.5649	−0.798166	−0.399083	−	0.916915i	$-0.630671\pi$
$541$	−18.5649	−0.798166	−0.399083	+	0.916915i	$0.630671\pi$
$542$	−13.7864	−0.592178
$543$	−38.6415	−1.65827
$544$	−3.46762	−0.148673
$545$	−10.6633	−0.456765
$546$	−7.39325	−0.316402
$547$	−19.7234	−0.843313	−0.421656	−	0.906756i	$-0.638551\pi$
$547$	−19.7234	−0.843313	−0.421656	+	0.906756i	$0.638551\pi$
$548$	−27.8879	−1.19131
$549$	7.95843	0.339658
$550$	2.37501	0.101271
$551$	11.1903	0.476724
$552$	27.6413	1.17649
$553$	26.3983	1.12257
$554$	−6.80698	−0.289201
$555$	17.8766	0.758821
$556$	4.61539	0.195736
$557$	15.0488	0.637639	0.318820	−	0.947815i	$-0.396714\pi$
$557$	15.0488	0.637639	0.318820	+	0.947815i	$0.396714\pi$
$558$	0.218746	0.00926024
$559$	23.7987	1.00658
$560$	5.00111	0.211335
$561$	6.22468	0.262806
$562$	−4.87205	−0.205515
$563$	−32.5147	−1.37033	−0.685166	−	0.728387i	$-0.740270\pi$
$563$	−32.5147	−1.37033	−0.685166	+	0.728387i	$0.740270\pi$
$564$	−2.75213	−0.115886
$565$	−8.07399	−0.339675
$566$	4.12576	0.173419
$567$	23.0321	0.967255
$568$	17.5434	0.736104
$569$	8.99500	0.377090	0.188545	−	0.982065i	$-0.439623\pi$
$569$	8.99500	0.377090	0.188545	+	0.982065i	$0.439623\pi$
$570$	−6.82123	−0.285710
$571$	−26.6274	−1.11432	−0.557160	−	0.830405i	$-0.688109\pi$
$571$	−26.6274	−1.11432	−0.557160	+	0.830405i	$0.688109\pi$
$572$	26.0062	1.08737
$573$	−17.1825	−0.717808
$574$	3.66414	0.152938
$575$	−6.89123	−0.287384
$576$	−2.59350	−0.108062
$577$	−23.8363	−0.992317	−0.496158	−	0.868232i	$-0.665256\pi$
$577$	−23.8363	−0.992317	−0.496158	+	0.868232i	$0.665256\pi$
$578$	8.68106	0.361084
$579$	−11.5030	−0.478047
$580$	3.04716	0.126526
$581$	27.7187	1.14997
$582$	12.5126	0.518664
$583$	−1.80342	−0.0746901
$584$	−9.88124	−0.408889
$585$	−4.04639	−0.167298
$586$	10.3400	0.427139
$587$	−4.55940	−0.188187	−0.0940933	−	0.995563i	$-0.529995\pi$
$587$	−4.55940	−0.188187	−0.0940933	+	0.995563i	$0.529995\pi$
$588$	−9.73040	−0.401275
$589$	−2.17386	−0.0895721
$590$	−4.13764	−0.170344
$591$	−24.7598	−1.01848
$592$	21.1162	0.867871
$593$	37.0026	1.51951	0.759757	−	0.650207i	$-0.225318\pi$
$593$	37.0026	1.51951	0.759757	+	0.650207i	$0.225318\pi$
$594$	8.70238	0.357063
$595$	1.38065	0.0566012
$596$	33.3964	1.36797
$597$	24.3271	0.995641
$598$	12.0336	0.492091
$599$	−23.7848	−0.971821	−0.485911	−	0.874008i	$-0.661512\pi$
$599$	−23.7848	−0.971821	−0.485911	+	0.874008i	$0.661512\pi$
$600$	−4.01109	−0.163752
$601$	11.3207	0.461783	0.230891	−	0.972980i	$-0.425836\pi$
$601$	11.3207	0.461783	0.230891	+	0.972980i	$0.425836\pi$
$602$	7.73091	0.315088
$603$	4.63424	0.188721
$604$	36.9597	1.50387
$605$	−9.50566	−0.386460
$606$	−7.20297	−0.292601
$607$	−42.0597	−1.70715	−0.853574	−	0.520971i	$-0.825570\pi$
$607$	−42.0597	−1.70715	−0.853574	+	0.520971i	$0.825570\pi$
$608$	−32.8084	−1.33056
$609$	7.47931	0.303077
$610$	3.43446	0.139057
$611$	−2.58734	−0.104673
$612$	−1.40356	−0.0567355
$613$	−22.5605	−0.911209	−0.455604	−	0.890182i	$-0.650577\pi$
$613$	−22.5605	−0.911209	−0.455604	+	0.890182i	$0.650577\pi$
$614$	−5.27949	−0.213063
$615$	6.95568	0.280480
$616$	18.2433	0.735042
$617$	−12.1468	−0.489010	−0.244505	−	0.969648i	$-0.578626\pi$
$617$	−12.1468	−0.489010	−0.244505	+	0.969648i	$0.578626\pi$
$618$	−1.25014	−0.0502880
$619$	−2.60833	−0.104838	−0.0524189	−	0.998625i	$-0.516693\pi$
$619$	−2.60833	−0.104838	−0.0524189	+	0.998625i	$0.516693\pi$
$620$	−0.591946	−0.0237731
$621$	−25.2504	−1.01326
$622$	−9.50895	−0.381274
$623$	29.3407	1.17551
$624$	−16.5780	−0.663652
$625$	1.00000	0.0400000
$626$	−4.52781	−0.180968
$627$	58.8940	2.35200
$628$	32.5642	1.29945
$629$	5.82954	0.232439
$630$	−1.31446	−0.0523692
$631$	−46.4374	−1.84865	−0.924323	−	0.381612i	$-0.875369\pi$
$631$	−46.4374	−1.84865	−0.924323	+	0.381612i	$0.875369\pi$
$632$	−25.0094	−0.994820
$633$	10.3984	0.413299
$634$	−6.45208	−0.256245
$635$	5.94828	0.236050
$636$	1.41041	0.0559265
$637$	−9.14778	−0.362448
$638$	4.19557	0.166104
$639$	10.9135	0.431732
$640$	−11.4777	−0.453698
$641$	−31.4254	−1.24123	−0.620614	−	0.784117i	$-0.713116\pi$
$641$	−31.4254	−1.24123	−0.620614	+	0.784117i	$0.713116\pi$
$642$	17.2851	0.682189
$643$	−16.4003	−0.646766	−0.323383	−	0.946268i	$-0.604820\pi$
$643$	−16.4003	−0.646766	−0.323383	+	0.946268i	$0.604820\pi$
$644$	−24.5124	−0.965923
$645$	14.6757	0.577854
$646$	−2.22439	−0.0875174
$647$	21.2858	0.836832	0.418416	−	0.908255i	$-0.362585\pi$
$647$	21.2858	0.836832	0.418416	+	0.908255i	$0.362585\pi$
$648$	−21.8202	−0.857179
$649$	35.7241	1.40229
$650$	−1.74622	−0.0684924
$651$	−1.45294	−0.0569454
$652$	17.4112	0.681877
$653$	11.5280	0.451126	0.225563	−	0.974229i	$-0.427578\pi$
$653$	11.5280	0.451126	0.225563	+	0.974229i	$0.427578\pi$
$654$	11.4825	0.449001
$655$	10.3772	0.405472
$656$	8.21617	0.320788
$657$	−6.14700	−0.239817
$658$	−0.840489	−0.0327657
$659$	−18.6231	−0.725454	−0.362727	−	0.931895i	$-0.618154\pi$
$659$	−18.6231	−0.725454	−0.362727	+	0.931895i	$0.618154\pi$
$660$	16.0370	0.624238
$661$	13.1793	0.512616	0.256308	−	0.966595i	$-0.417494\pi$
$661$	13.1793	0.512616	0.256308	+	0.966595i	$0.417494\pi$
$662$	8.53067	0.331554
$663$	−4.57668	−0.177744
$664$	−26.2603	−1.01910
$665$	13.0628	0.506555
$666$	−5.55004	−0.215060
$667$	−12.1737	−0.471367
$668$	−5.87292	−0.227230
$669$	−14.8669	−0.574787
$670$	1.99991	0.0772632
$671$	−29.6529	−1.14474
$672$	−21.9282	−0.845900
$673$	12.0945	0.466208	0.233104	−	0.972452i	$-0.425112\pi$
$673$	12.0945	0.466208	0.233104	+	0.972452i	$0.425112\pi$
$674$	10.4523	0.402606
$675$	3.66414	0.141033
$676$	3.30301	0.127039
$677$	−44.3254	−1.70356	−0.851781	−	0.523898i	$-0.824477\pi$
$677$	−44.3254	−1.70356	−0.851781	+	0.523898i	$0.824477\pi$
$678$	8.69428	0.333902
$679$	−23.9619	−0.919574
$680$	−1.30801	−0.0501598
$681$	−6.81315	−0.261080
$682$	−0.815040	−0.0312095
$683$	−31.0419	−1.18778	−0.593892	−	0.804545i	$-0.702409\pi$
$683$	−31.0419	−1.18778	−0.593892	+	0.804545i	$0.702409\pi$
$684$	−13.2796	−0.507757
$685$	−16.1676	−0.617734
$686$	−10.5425	−0.402515
$687$	28.6818	1.09428
$688$	17.3352	0.660898
$689$	1.32596	0.0505151
$690$	7.42065	0.282499
$691$	22.6981	0.863475	0.431737	−	0.901999i	$-0.357901\pi$
$691$	22.6981	0.863475	0.431737	+	0.901999i	$0.357901\pi$
$692$	3.97115	0.150961
$693$	11.3489	0.431109
$694$	−0.0428280	−0.00162573
$695$	2.67571	0.101496
$696$	−7.08578	−0.268586
$697$	2.26823	0.0859154
$698$	4.30022	0.162766
$699$	−15.4993	−0.586236
$700$	3.55704	0.134443
$701$	−2.76372	−0.104384	−0.0521922	−	0.998637i	$-0.516621\pi$
$701$	−2.76372	−0.104384	−0.0521922	+	0.998637i	$0.516621\pi$
$702$	−6.39840	−0.241492
$703$	55.1553	2.08022
$704$	9.66329	0.364199
$705$	−1.59551	−0.0600904
$706$	3.26495	0.122878
$707$	13.7939	0.518772
$708$	−27.9389	−1.05001
$709$	−38.5368	−1.44728	−0.723639	−	0.690178i	$-0.757532\pi$
$709$	−38.5368	−1.44728	−0.723639	+	0.690178i	$0.757532\pi$
$710$	4.70973	0.176753
$711$	−15.5580	−0.583471
$712$	−27.7969	−1.04173
$713$	2.36488	0.0885656
$714$	−1.48672	−0.0556391
$715$	15.0767	0.563838
$716$	11.8061	0.441216
$717$	10.3582	0.386836
$718$	−6.26996	−0.233993
$719$	−5.54024	−0.206616	−0.103308	−	0.994649i	$-0.532943\pi$
$719$	−5.54024	−0.206616	−0.103308	+	0.994649i	$0.532943\pi$
$720$	−2.94743	−0.109844
$721$	2.39405	0.0891591
$722$	−11.0806	−0.412378
$723$	18.6154	0.692314
$724$	−32.4644	−1.20653
$725$	1.76655	0.0656080
$726$	10.2359	0.379891
$727$	5.91720	0.219457	0.109728	−	0.993962i	$-0.465002\pi$
$727$	5.91720	0.219457	0.109728	+	0.993962i	$0.465002\pi$
$728$	−13.4133	−0.497130
$729$	8.99477	0.333140
$730$	−2.65274	−0.0981823
$731$	4.78571	0.177006
$732$	23.1908	0.857156
$733$	−9.60108	−0.354624	−0.177312	−	0.984155i	$-0.556740\pi$
$733$	−9.60108	−0.354624	−0.177312	+	0.984155i	$0.556740\pi$
$734$	−12.2923	−0.453716
$735$	−5.64107	−0.208074
$736$	35.6914	1.31560
$737$	−17.2670	−0.636040
$738$	−2.15948	−0.0794917
$739$	39.9238	1.46862	0.734311	−	0.678813i	$-0.237505\pi$
$739$	39.9238	1.46862	0.734311	+	0.678813i	$0.237505\pi$
$740$	15.0189	0.552107
$741$	−43.3016	−1.59072
$742$	0.430734	0.0158127
$743$	−45.3143	−1.66242	−0.831209	−	0.555960i	$-0.812351\pi$
$743$	−45.3143	−1.66242	−0.831209	+	0.555960i	$0.812351\pi$
$744$	1.37650	0.0504648
$745$	19.3611	0.709337
$746$	−4.08400	−0.149526
$747$	−16.3362	−0.597711
$748$	5.22962	0.191214
$749$	−33.1014	−1.20950
$750$	−1.07683	−0.0393201
$751$	−28.0466	−1.02344	−0.511718	−	0.859153i	$-0.670991\pi$
$751$	−28.0466	−1.02344	−0.511718	+	0.859153i	$0.670991\pi$
$752$	−1.88465	−0.0687260
$753$	7.05075	0.256944
$754$	−3.08478	−0.112341
$755$	21.4269	0.779806
$756$	13.0335	0.474023
$757$	3.37015	0.122490	0.0612450	−	0.998123i	$-0.480493\pi$
$757$	3.37015	0.122490	0.0612450	+	0.998123i	$0.480493\pi$
$758$	15.2632	0.554384
$759$	−64.0693	−2.32557
$760$	−12.3755	−0.448907
$761$	−33.1348	−1.20113	−0.600567	−	0.799574i	$-0.705058\pi$
$761$	−33.1348	−1.20113	−0.600567	+	0.799574i	$0.705058\pi$
$762$	−6.40526	−0.232038
$763$	−21.9893	−0.796064
$764$	−14.4357	−0.522266
$765$	−0.813695	−0.0294192
$766$	14.5246	0.524795
$767$	−26.2660	−0.948411
$768$	3.59689	0.129792
$769$	−31.5603	−1.13809	−0.569047	−	0.822305i	$-0.692688\pi$
$769$	−31.5603	−1.13809	−0.569047	+	0.822305i	$0.692688\pi$
$770$	4.89763	0.176498
$771$	−1.13599	−0.0409117
$772$	−9.66413	−0.347820
$773$	−46.4770	−1.67166	−0.835831	−	0.548986i	$-0.815014\pi$
$773$	−46.4770	−1.67166	−0.835831	+	0.548986i	$0.815014\pi$
$774$	−4.55626	−0.163771
$775$	−0.343173	−0.0123271
$776$	22.7012	0.814924
$777$	36.8643	1.32250
$778$	−6.57501	−0.235725
$779$	21.4606	0.768904
$780$	−11.7911	−0.422190
$781$	−40.6634	−1.45505
$782$	2.41986	0.0865339
$783$	6.47288	0.231322
$784$	−6.66334	−0.237976
$785$	18.8787	0.673808
$786$	−11.1745	−0.398580
$787$	54.0928	1.92820	0.964101	−	0.265537i	$-0.0855491\pi$
$787$	54.0928	1.92820	0.964101	+	0.265537i	$0.0855491\pi$
$788$	−20.8017	−0.741031
$789$	−14.2782	−0.508317
$790$	−6.71407	−0.238876
$791$	−16.6498	−0.591997
$792$	−10.7518	−0.382048
$793$	21.8022	0.774219
$794$	5.48004	0.194479
$795$	0.817668	0.0289997
$796$	20.4382	0.724413
$797$	38.0191	1.34670	0.673352	−	0.739322i	$-0.264854\pi$
$797$	38.0191	1.34670	0.673352	+	0.739322i	$0.264854\pi$
$798$	−14.0664	−0.497945
$799$	−0.520292	−0.0184066
$800$	−5.17926	−0.183114
$801$	−17.2921	−0.610986
$802$	0.524480	0.0185200
$803$	22.9035	0.808248
$804$	13.5041	0.476254
$805$	−14.2107	−0.500862
$806$	0.599256	0.0211079
$807$	18.5934	0.654517
$808$	−13.0681	−0.459734
$809$	−21.1496	−0.743580	−0.371790	−	0.928317i	$-0.621256\pi$
$809$	−21.1496	−0.743580	−0.371790	+	0.928317i	$0.621256\pi$
$810$	−5.85790	−0.205826
$811$	−32.3298	−1.13525	−0.567626	−	0.823286i	$-0.692138\pi$
$811$	−32.3298	−1.13525	−0.567626	+	0.823286i	$0.692138\pi$
$812$	6.28368	0.220514
$813$	−53.9684	−1.89275
$814$	20.6793	0.724809
$815$	10.0939	0.353575
$816$	−3.33370	−0.116703
$817$	45.2793	1.58412
$818$	−20.8097	−0.727594
$819$	−8.34425	−0.291572
$820$	5.84376	0.204073
$821$	22.3229	0.779075	0.389537	−	0.921011i	$-0.372635\pi$
$821$	22.3229	0.779075	0.389537	+	0.921011i	$0.372635\pi$
$822$	17.4097	0.607234
$823$	19.8574	0.692187	0.346093	−	0.938200i	$-0.387508\pi$
$823$	19.8574	0.692187	0.346093	+	0.938200i	$0.387508\pi$
$824$	−2.26809	−0.0790125
$825$	9.29722	0.323688
$826$	−8.53242	−0.296881
$827$	−24.2957	−0.844846	−0.422423	−	0.906399i	$-0.638820\pi$
$827$	−24.2957	−0.844846	−0.422423	+	0.906399i	$0.638820\pi$
$828$	14.4465	0.502051
$829$	18.3256	0.636473	0.318237	−	0.948011i	$-0.396909\pi$
$829$	18.3256	0.636473	0.318237	+	0.948011i	$0.396909\pi$
$830$	−7.04989	−0.244705
$831$	−26.6466	−0.924360
$832$	−7.10490	−0.246318
$833$	−1.83954	−0.0637363
$834$	−2.88127	−0.0997703
$835$	−3.40475	−0.117826
$836$	49.4793	1.71128
$837$	−1.25743	−0.0434633
$838$	−11.8901	−0.410738
$839$	−0.551462	−0.0190386	−0.00951929	−	0.999955i	$-0.503030\pi$
$839$	−0.551462	−0.0190386	−0.00951929	+	0.999955i	$0.503030\pi$
$840$	−8.27146	−0.285392
$841$	−25.8793	−0.892390
$842$	−1.68867	−0.0581956
$843$	−19.0721	−0.656879
$844$	8.73614	0.300710
$845$	1.91488	0.0658737
$846$	0.495347	0.0170304
$847$	−19.6021	−0.673535
$848$	0.965844	0.0331672
$849$	16.1507	0.554290
$850$	−0.351150	−0.0120444
$851$	−60.0021	−2.05685
$852$	31.8019	1.08951
$853$	−2.95545	−0.101193	−0.0505964	−	0.998719i	$-0.516112\pi$
$853$	−2.95545	−0.101193	−0.0505964	+	0.998719i	$0.516112\pi$
$854$	7.08237	0.242354
$855$	−7.69866	−0.263289
$856$	31.3598	1.07185
$857$	6.77430	0.231406	0.115703	−	0.993284i	$-0.463088\pi$
$857$	6.77430	0.231406	0.115703	+	0.993284i	$0.463088\pi$
$858$	−16.2350	−0.554254
$859$	8.02445	0.273791	0.136895	−	0.990586i	$-0.456288\pi$
$859$	8.02445	0.273791	0.136895	+	0.990586i	$0.456288\pi$
$860$	12.3297	0.420438
$861$	14.3436	0.488830
$862$	−1.84875	−0.0629688
$863$	−11.6566	−0.396795	−0.198398	−	0.980122i	$-0.563574\pi$
$863$	−11.6566	−0.396795	−0.198398	+	0.980122i	$0.563574\pi$
$864$	−18.9775	−0.645628
$865$	2.30222	0.0782779
$866$	−19.5788	−0.665316
$867$	33.9829	1.15412
$868$	−1.22068	−0.0414326
$869$	57.9687	1.96645
$870$	−1.90226	−0.0644928
$871$	12.6955	0.430172
$872$	20.8323	0.705470
$873$	14.1221	0.477961
$874$	22.8951	0.774439
$875$	2.06215	0.0697133
$876$	−17.9123	−0.605200
$877$	1.82822	0.0617345	0.0308672	−	0.999523i	$-0.490173\pi$
$877$	1.82822	0.0617345	0.0308672	+	0.999523i	$0.490173\pi$
$878$	−16.2306	−0.547755
$879$	40.4768	1.36525
$880$	10.9820	0.370205
$881$	−12.5244	−0.421959	−0.210979	−	0.977491i	$-0.567665\pi$
$881$	−12.5244	−0.421959	−0.210979	+	0.977491i	$0.567665\pi$
$882$	1.75135	0.0589709
$883$	24.6458	0.829398	0.414699	−	0.909959i	$-0.363887\pi$
$883$	24.6458	0.829398	0.414699	+	0.909959i	$0.363887\pi$
$884$	−3.84506	−0.129323
$885$	−16.1972	−0.544463
$886$	18.3820	0.617556
$887$	21.9631	0.737449	0.368724	−	0.929539i	$-0.379795\pi$
$887$	21.9631	0.737449	0.368724	+	0.929539i	$0.379795\pi$
$888$	−34.9247	−1.17199
$889$	12.2662	0.411396
$890$	−7.46241	−0.250141
$891$	50.5766	1.69438
$892$	−12.4903	−0.418206
$893$	−4.92267	−0.164731
$894$	−20.8486	−0.697280
$895$	6.84445	0.228785
$896$	−23.6688	−0.790719
$897$	47.1067	1.57285
$898$	19.9086	0.664360
$899$	−0.606232	−0.0202190
$900$	−2.09636	−0.0698788
$901$	0.266640	0.00888305
$902$	8.04617	0.267908
$903$	30.2634	1.00710
$904$	15.7737	0.524626
$905$	−18.8208	−0.625624
$906$	−23.0731	−0.766551
$907$	45.1843	1.50032	0.750159	−	0.661257i	$-0.229977\pi$
$907$	45.1843	1.50032	0.750159	+	0.661257i	$0.229977\pi$
$908$	−5.72401	−0.189958
$909$	−8.12950	−0.269638
$910$	−3.60096	−0.119371
$911$	41.3551	1.37015	0.685077	−	0.728471i	$-0.259769\pi$
$911$	41.3551	1.37015	0.685077	+	0.728471i	$0.259769\pi$
$912$	−31.5413	−1.04444
$913$	60.8682	2.01444
$914$	−2.05291	−0.0679041
$915$	13.4445	0.444463
$916$	24.0968	0.796181
$917$	21.3994	0.706669
$918$	−1.28666	−0.0424662
$919$	35.6803	1.17698	0.588492	−	0.808503i	$-0.299722\pi$
$919$	35.6803	1.17698	0.588492	+	0.808503i	$0.299722\pi$
$920$	13.4630	0.443863
$921$	−20.6671	−0.681004
$922$	17.4787	0.575630
$923$	29.8977	0.984094
$924$	33.0706	1.08794
$925$	8.70703	0.286285
$926$	12.0637	0.396438
$927$	−1.41095	−0.0463416
$928$	−9.14941	−0.300344
$929$	38.3643	1.25869	0.629346	−	0.777125i	$-0.283323\pi$
$929$	38.3643	1.25869	0.629346	+	0.777125i	$0.283323\pi$
$930$	0.369537	0.0121176
$931$	−17.4046	−0.570411
$932$	−13.0216	−0.426536
$933$	−37.2237	−1.21865
$934$	13.0879	0.428249
$935$	3.03180	0.0991506
$936$	7.90522	0.258390
$937$	−31.1934	−1.01905	−0.509523	−	0.860457i	$-0.670178\pi$
$937$	−31.1934	−1.01905	−0.509523	+	0.860457i	$0.670178\pi$
$938$	4.12411	0.134657
$939$	−17.7246	−0.578419
$940$	−1.34046	−0.0437209
$941$	22.1168	0.720986	0.360493	−	0.932762i	$-0.382608\pi$
$941$	22.1168	0.720986	0.360493	+	0.932762i	$0.382608\pi$
$942$	−20.3290	−0.662355
$943$	−23.3464	−0.760263
$944$	−19.1324	−0.622708
$945$	7.55599	0.245797
$946$	16.9765	0.551953
$947$	−53.3712	−1.73433	−0.867165	−	0.498021i	$-0.834060\pi$
$947$	−53.3712	−1.73433	−0.867165	+	0.498021i	$0.834060\pi$
$948$	−45.3359	−1.47244
$949$	−16.8398	−0.546642
$950$	−3.32236	−0.107792
$951$	−25.2573	−0.819024
$952$	−2.69730	−0.0874201
$953$	−12.2543	−0.396956	−0.198478	−	0.980105i	$-0.563600\pi$
$953$	−12.2543	−0.396956	−0.198478	+	0.980105i	$0.563600\pi$
$954$	−0.253856	−0.00821888
$955$	−8.36892	−0.270812
$956$	8.70240	0.281456
$957$	16.4240	0.530912
$958$	6.34487	0.204994
$959$	−33.3401	−1.07661
$960$	−4.38131	−0.141406
$961$	−30.8822	−0.996201
$962$	−15.2044	−0.490209
$963$	19.5085	0.628653
$964$	15.6396	0.503717
$965$	−5.60265	−0.180356
$966$	15.3025	0.492349
$967$	13.7512	0.442210	0.221105	−	0.975250i	$-0.429034\pi$
$967$	13.7512	0.442210	0.221105	+	0.975250i	$0.429034\pi$
$968$	18.5707	0.596885
$969$	−8.70759	−0.279728
$970$	6.09440	0.195679
$971$	−31.0084	−0.995107	−0.497554	−	0.867433i	$-0.665768\pi$
$971$	−31.0084	−0.995107	−0.497554	+	0.867433i	$0.665768\pi$
$972$	−20.5937	−0.660543
$973$	5.51771	0.176890
$974$	−5.34033	−0.171115
$975$	−6.83576	−0.218919
$976$	15.8809	0.508336
$977$	−21.6608	−0.692990	−0.346495	−	0.938052i	$-0.612628\pi$
$977$	−21.6608	−0.692990	−0.346495	+	0.938052i	$0.612628\pi$
$978$	−10.8694	−0.347565
$979$	64.4298	2.05919
$980$	−4.73930	−0.151391
$981$	12.9595	0.413765
$982$	−14.5556	−0.464486
$983$	−23.7208	−0.756575	−0.378288	−	0.925688i	$-0.623487\pi$
$983$	−23.7208	−0.756575	−0.378288	+	0.925688i	$0.623487\pi$
$984$	−13.5889	−0.433200
$985$	−12.0595	−0.384249
$986$	−0.620324	−0.0197551
$987$	−3.29018	−0.104728
$988$	−36.3795	−1.15739
$989$	−49.2582	−1.56632
$990$	−2.88645	−0.0917373
$991$	−60.5159	−1.92235	−0.961175	−	0.275939i	$-0.911011\pi$
$991$	−60.5159	−1.92235	−0.961175	+	0.275939i	$0.911011\pi$
$992$	1.77738	0.0564319
$993$	33.3942	1.05973
$994$	9.71216	0.308051
$995$	11.8488	0.375632
$996$	−47.6035	−1.50838
$997$	−14.0838	−0.446040	−0.223020	−	0.974814i	$-0.571592\pi$
$997$	−14.0838	−0.446040	−0.223020	+	0.974814i	$0.571592\pi$
$998$	−11.4980	−0.363962
$999$	31.9038	1.00939

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.e.1.13	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.e.1.13	✓	29	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2005 = 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2005.a (trivial)

\(f(q)\)	\(=\)	\(q-0.524480 q^{2} -2.05313 q^{3} -1.72492 q^{4} -1.00000 q^{5} +1.07683 q^{6} -2.06215 q^{7} +1.95365 q^{8} +1.21534 q^{9} +O(q^{10})\)	\(q-0.524480 q^{2} -2.05313 q^{3} -1.72492 q^{4} -1.00000 q^{5} +1.07683 q^{6} -2.06215 q^{7} +1.95365 q^{8} +1.21534 q^{9} +0.524480 q^{10} -4.52832 q^{11} +3.54148 q^{12} +3.32943 q^{13} +1.08156 q^{14} +2.05313 q^{15} +2.42519 q^{16} +0.669521 q^{17} -0.637421 q^{18} +6.33458 q^{19} +1.72492 q^{20} +4.23385 q^{21} +2.37501 q^{22} -6.89123 q^{23} -4.01109 q^{24} +1.00000 q^{25} -1.74622 q^{26} +3.66414 q^{27} +3.55704 q^{28} +1.76655 q^{29} -1.07683 q^{30} -0.343173 q^{31} -5.17926 q^{32} +9.29722 q^{33} -0.351150 q^{34} +2.06215 q^{35} -2.09636 q^{36} +8.70703 q^{37} -3.32236 q^{38} -6.83576 q^{39} -1.95365 q^{40} +3.38784 q^{41} -2.22057 q^{42} +7.14796 q^{43} +7.81099 q^{44} -1.21534 q^{45} +3.61431 q^{46} -0.777112 q^{47} -4.97923 q^{48} -2.74755 q^{49} -0.524480 q^{50} -1.37461 q^{51} -5.74301 q^{52} +0.398254 q^{53} -1.92177 q^{54} +4.52832 q^{55} -4.02871 q^{56} -13.0057 q^{57} -0.926519 q^{58} -7.88903 q^{59} -3.54148 q^{60} +6.54832 q^{61} +0.179987 q^{62} -2.50621 q^{63} -2.13397 q^{64} -3.32943 q^{65} -4.87621 q^{66} +3.81313 q^{67} -1.15487 q^{68} +14.1486 q^{69} -1.08156 q^{70} +8.97981 q^{71} +2.37434 q^{72} -5.05785 q^{73} -4.56666 q^{74} -2.05313 q^{75} -10.9266 q^{76} +9.33806 q^{77} +3.58522 q^{78} -12.8014 q^{79} -2.42519 q^{80} -11.1690 q^{81} -1.77686 q^{82} -13.4417 q^{83} -7.30306 q^{84} -0.669521 q^{85} -3.74896 q^{86} -3.62695 q^{87} -8.84673 q^{88} -14.2282 q^{89} +0.637421 q^{90} -6.86578 q^{91} +11.8868 q^{92} +0.704578 q^{93} +0.407580 q^{94} -6.33458 q^{95} +10.6337 q^{96} +11.6199 q^{97} +1.44103 q^{98} -5.50344 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9}+O(q^{10}) \) 29 * q - 5 * q^2 - 3 * q^3 + 19 * q^4 - 29 * q^5 - 6 * q^6 + 12 * q^7 - 15 * q^8 + 14 * q^9	\( 29 q - 5 q^{2} - 3 q^{3} + 19 q^{4} - 29 q^{5} - 6 q^{6} + 12 q^{7} - 15 q^{8} + 14 q^{9} + 5 q^{10} - 38 q^{11} - 6 q^{12} + 5 q^{13} - 18 q^{14} + 3 q^{15} + 7 q^{16} - 16 q^{17} - 2 q^{18} - 18 q^{19} - 19 q^{20} - 20 q^{21} - 2 q^{22} - 19 q^{23} - 19 q^{24} + 29 q^{25} - 21 q^{26} - 21 q^{27} + 26 q^{28} - 31 q^{29} + 6 q^{30} - 13 q^{31} - 30 q^{32} + 2 q^{33} - 14 q^{34} - 12 q^{35} - 29 q^{36} - q^{37} - 23 q^{38} - 39 q^{39} + 15 q^{40} - 24 q^{41} - 20 q^{42} - 27 q^{43} - 76 q^{44} - 14 q^{45} - 11 q^{46} - 5 q^{47} - 2 q^{48} - 11 q^{49} - 5 q^{50} - 58 q^{51} + 11 q^{52} - 37 q^{53} - 18 q^{54} + 38 q^{55} - 50 q^{56} - 6 q^{57} + 31 q^{58} - 67 q^{59} + 6 q^{60} - 31 q^{61} - 19 q^{62} - 2 q^{63} - 13 q^{64} - 5 q^{65} + 6 q^{66} - 17 q^{67} - 16 q^{68} - 48 q^{69} + 18 q^{70} - 53 q^{71} + 9 q^{72} + 29 q^{73} - 59 q^{74} - 3 q^{75} - 21 q^{76} - 62 q^{77} - 12 q^{78} - 13 q^{79} - 7 q^{80} - 11 q^{81} + 32 q^{82} - 72 q^{83} - 58 q^{84} + 16 q^{85} - 43 q^{86} + 4 q^{87} + 12 q^{88} - 38 q^{89} + 2 q^{90} - 45 q^{91} - 37 q^{92} - 27 q^{93} - 44 q^{94} + 18 q^{95} - 21 q^{96} + 32 q^{97} - 32 q^{98} - 107 q^{99}+O(q^{100}) \) 29 * q - 5 * q^2 - 3 * q^3 + 19 * q^4 - 29 * q^5 - 6 * q^6 + 12 * q^7 - 15 * q^8 + 14 * q^9 + 5 * q^10 - 38 * q^11 - 6 * q^12 + 5 * q^13 - 18 * q^14 + 3 * q^15 + 7 * q^16 - 16 * q^17 - 2 * q^18 - 18 * q^19 - 19 * q^20 - 20 * q^21 - 2 * q^22 - 19 * q^23 - 19 * q^24 + 29 * q^25 - 21 * q^26 - 21 * q^27 + 26 * q^28 - 31 * q^29 + 6 * q^30 - 13 * q^31 - 30 * q^32 + 2 * q^33 - 14 * q^34 - 12 * q^35 - 29 * q^36 - q^37 - 23 * q^38 - 39 * q^39 + 15 * q^40 - 24 * q^41 - 20 * q^42 - 27 * q^43 - 76 * q^44 - 14 * q^45 - 11 * q^46 - 5 * q^47 - 2 * q^48 - 11 * q^49 - 5 * q^50 - 58 * q^51 + 11 * q^52 - 37 * q^53 - 18 * q^54 + 38 * q^55 - 50 * q^56 - 6 * q^57 + 31 * q^58 - 67 * q^59 + 6 * q^60 - 31 * q^61 - 19 * q^62 - 2 * q^63 - 13 * q^64 - 5 * q^65 + 6 * q^66 - 17 * q^67 - 16 * q^68 - 48 * q^69 + 18 * q^70 - 53 * q^71 + 9 * q^72 + 29 * q^73 - 59 * q^74 - 3 * q^75 - 21 * q^76 - 62 * q^77 - 12 * q^78 - 13 * q^79 - 7 * q^80 - 11 * q^81 + 32 * q^82 - 72 * q^83 - 58 * q^84 + 16 * q^85 - 43 * q^86 + 4 * q^87 + 12 * q^88 - 38 * q^89 + 2 * q^90 - 45 * q^91 - 37 * q^92 - 27 * q^93 - 44 * q^94 + 18 * q^95 - 21 * q^96 + 32 * q^97 - 32 * q^98 - 107 * q^99

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