LMFDB - Embedded newform 4017.2.a.k.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.05981 q^{2} +1.00000 q^{3} -0.876804 q^{4} -3.52707 q^{5} -1.05981 q^{6} -1.13469 q^{7} +3.04886 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.05981 q^{2} +1.00000 q^{3} -0.876804 q^{4} -3.52707 q^{5} -1.05981 q^{6} -1.13469 q^{7} +3.04886 q^{8} +1.00000 q^{9} +3.73802 q^{10} -2.54391 q^{11} -0.876804 q^{12} +1.00000 q^{13} +1.20256 q^{14} -3.52707 q^{15} -1.47761 q^{16} -7.38417 q^{17} -1.05981 q^{18} +8.00406 q^{19} +3.09255 q^{20} -1.13469 q^{21} +2.69606 q^{22} +2.92589 q^{23} +3.04886 q^{24} +7.44023 q^{25} -1.05981 q^{26} +1.00000 q^{27} +0.994904 q^{28} -4.25982 q^{29} +3.73802 q^{30} -4.59726 q^{31} -4.53175 q^{32} -2.54391 q^{33} +7.82581 q^{34} +4.00214 q^{35} -0.876804 q^{36} -3.74712 q^{37} -8.48278 q^{38} +1.00000 q^{39} -10.7536 q^{40} -4.39072 q^{41} +1.20256 q^{42} -11.1838 q^{43} +2.23051 q^{44} -3.52707 q^{45} -3.10088 q^{46} -3.97865 q^{47} -1.47761 q^{48} -5.71247 q^{49} -7.88522 q^{50} -7.38417 q^{51} -0.876804 q^{52} -8.46140 q^{53} -1.05981 q^{54} +8.97255 q^{55} -3.45953 q^{56} +8.00406 q^{57} +4.51460 q^{58} -6.10934 q^{59} +3.09255 q^{60} +10.0602 q^{61} +4.87221 q^{62} -1.13469 q^{63} +7.75800 q^{64} -3.52707 q^{65} +2.69606 q^{66} +3.97795 q^{67} +6.47447 q^{68} +2.92589 q^{69} -4.24151 q^{70} +2.94826 q^{71} +3.04886 q^{72} -4.87555 q^{73} +3.97123 q^{74} +7.44023 q^{75} -7.01799 q^{76} +2.88656 q^{77} -1.05981 q^{78} -9.14065 q^{79} +5.21162 q^{80} +1.00000 q^{81} +4.65333 q^{82} +16.2119 q^{83} +0.994904 q^{84} +26.0445 q^{85} +11.8527 q^{86} -4.25982 q^{87} -7.75604 q^{88} +2.27242 q^{89} +3.73802 q^{90} -1.13469 q^{91} -2.56543 q^{92} -4.59726 q^{93} +4.21661 q^{94} -28.2309 q^{95} -4.53175 q^{96} +11.0245 q^{97} +6.05413 q^{98} -2.54391 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.05981	−0.749398	−0.374699	−	0.927146i	$-0.622254\pi$
$2$	−1.05981	−0.749398	−0.374699	+	0.927146i	$0.622254\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.876804	−0.438402
$5$	−3.52707	−1.57735	−0.788677	−	0.614808i	$-0.789234\pi$
$5$	−3.52707	−1.57735	−0.788677	+	0.614808i	$0.789234\pi$
$6$	−1.05981	−0.432665
$7$	−1.13469	−0.428874	−0.214437	−	0.976738i	$-0.568792\pi$
$7$	−1.13469	−0.428874	−0.214437	+	0.976738i	$0.568792\pi$
$8$	3.04886	1.07794
$9$	1.00000	0.333333
$10$	3.73802	1.18207
$11$	−2.54391	−0.767018	−0.383509	−	0.923537i	$-0.625284\pi$
$11$	−2.54391	−0.767018	−0.383509	+	0.923537i	$0.625284\pi$
$12$	−0.876804	−0.253112
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.20256	0.321397
$15$	−3.52707	−0.910686
$16$	−1.47761	−0.369402
$17$	−7.38417	−1.79092	−0.895462	−	0.445138i	$-0.853155\pi$
$17$	−7.38417	−1.79092	−0.895462	+	0.445138i	$0.853155\pi$
$18$	−1.05981	−0.249799
$19$	8.00406	1.83626	0.918129	−	0.396283i	$-0.129700\pi$
$19$	8.00406	1.83626	0.918129	+	0.396283i	$0.129700\pi$
$20$	3.09255	0.691515
$21$	−1.13469	−0.247610
$22$	2.69606	0.574802
$23$	2.92589	0.610090	0.305045	−	0.952338i	$-0.401328\pi$
$23$	2.92589	0.610090	0.305045	+	0.952338i	$0.401328\pi$
$24$	3.04886	0.622347
$25$	7.44023	1.48805
$26$	−1.05981	−0.207846
$27$	1.00000	0.192450
$28$	0.994904	0.188019
$29$	−4.25982	−0.791030	−0.395515	−	0.918460i	$-0.629434\pi$
$29$	−4.25982	−0.791030	−0.395515	+	0.918460i	$0.629434\pi$
$30$	3.73802	0.682466
$31$	−4.59726	−0.825692	−0.412846	−	0.910801i	$-0.635465\pi$
$31$	−4.59726	−0.825692	−0.412846	+	0.910801i	$0.635465\pi$
$32$	−4.53175	−0.801107
$33$	−2.54391	−0.442838
$34$	7.82581	1.34212
$35$	4.00214	0.676486
$36$	−0.876804	−0.146134
$37$	−3.74712	−0.616022	−0.308011	−	0.951383i	$-0.599663\pi$
$37$	−3.74712	−0.616022	−0.308011	+	0.951383i	$0.599663\pi$
$38$	−8.48278	−1.37609
$39$	1.00000	0.160128
$40$	−10.7536	−1.70029
$41$	−4.39072	−0.685716	−0.342858	−	0.939387i	$-0.611395\pi$
$41$	−4.39072	−0.685716	−0.342858	+	0.939387i	$0.611395\pi$
$42$	1.20256	0.185559
$43$	−11.1838	−1.70552	−0.852760	−	0.522303i	$-0.825073\pi$
$43$	−11.1838	−1.70552	−0.852760	+	0.522303i	$0.825073\pi$
$44$	2.23051	0.336262
$45$	−3.52707	−0.525785
$46$	−3.10088	−0.457201
$47$	−3.97865	−0.580346	−0.290173	−	0.956974i	$-0.593713\pi$
$47$	−3.97865	−0.580346	−0.290173	+	0.956974i	$0.593713\pi$
$48$	−1.47761	−0.213274
$49$	−5.71247	−0.816067
$50$	−7.88522	−1.11514
$51$	−7.38417	−1.03399
$52$	−0.876804	−0.121591
$53$	−8.46140	−1.16226	−0.581132	−	0.813810i	$-0.697390\pi$
$53$	−8.46140	−1.16226	−0.581132	+	0.813810i	$0.697390\pi$
$54$	−1.05981	−0.144222
$55$	8.97255	1.20986
$56$	−3.45953	−0.462298
$57$	8.00406	1.06016
$58$	4.51460	0.592796
$59$	−6.10934	−0.795368	−0.397684	−	0.917522i	$-0.630186\pi$
$59$	−6.10934	−0.795368	−0.397684	+	0.917522i	$0.630186\pi$
$60$	3.09255	0.399246
$61$	10.0602	1.28807	0.644036	−	0.764995i	$-0.277259\pi$
$61$	10.0602	1.28807	0.644036	+	0.764995i	$0.277259\pi$
$62$	4.87221	0.618772
$63$	−1.13469	−0.142958
$64$	7.75800	0.969750
$65$	−3.52707	−0.437479
$66$	2.69606	0.331862
$67$	3.97795	0.485984	0.242992	−	0.970028i	$-0.421871\pi$
$67$	3.97795	0.485984	0.242992	+	0.970028i	$0.421871\pi$
$68$	6.47447	0.785145
$69$	2.92589	0.352236
$70$	−4.24151	−0.506957
$71$	2.94826	0.349894	0.174947	−	0.984578i	$-0.444025\pi$
$71$	2.94826	0.349894	0.174947	+	0.984578i	$0.444025\pi$
$72$	3.04886	0.359312
$73$	−4.87555	−0.570640	−0.285320	−	0.958432i	$-0.592100\pi$
$73$	−4.87555	−0.570640	−0.285320	+	0.958432i	$0.592100\pi$
$74$	3.97123	0.461646
$75$	7.44023	0.859123
$76$	−7.01799	−0.805019
$77$	2.88656	0.328954
$78$	−1.05981	−0.120000
$79$	−9.14065	−1.02840	−0.514202	−	0.857669i	$-0.671912\pi$
$79$	−9.14065	−1.02840	−0.514202	+	0.857669i	$0.671912\pi$
$80$	5.21162	0.582677
$81$	1.00000	0.111111
$82$	4.65333	0.513874
$83$	16.2119	1.77949	0.889746	−	0.456456i	$-0.150881\pi$
$83$	16.2119	1.77949	0.889746	+	0.456456i	$0.150881\pi$
$84$	0.994904	0.108553
$85$	26.0445	2.82492
$86$	11.8527	1.27811
$87$	−4.25982	−0.456701
$88$	−7.75604	−0.826796
$89$	2.27242	0.240876	0.120438	−	0.992721i	$-0.461570\pi$
$89$	2.27242	0.240876	0.120438	+	0.992721i	$0.461570\pi$
$90$	3.73802	0.394022
$91$	−1.13469	−0.118948
$92$	−2.56543	−0.267465
$93$	−4.59726	−0.476713
$94$	4.21661	0.434911
$95$	−28.2309	−2.89643
$96$	−4.53175	−0.462519
$97$	11.0245	1.11937	0.559684	−	0.828706i	$-0.310922\pi$
$97$	11.0245	1.11937	0.559684	+	0.828706i	$0.310922\pi$
$98$	6.05413	0.611560
$99$	−2.54391	−0.255673
$100$	−6.52362	−0.652362
$101$	2.18665	0.217580	0.108790	−	0.994065i	$-0.465302\pi$
$101$	2.18665	0.217580	0.108790	+	0.994065i	$0.465302\pi$
$102$	7.82581	0.774871
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	3.04886	0.298966
$105$	4.00214	0.390569
$106$	8.96748	0.870998
$107$	14.1841	1.37123	0.685616	−	0.727964i	$-0.259533\pi$
$107$	14.1841	1.37123	0.685616	+	0.727964i	$0.259533\pi$
$108$	−0.876804	−0.0843705
$109$	13.4120	1.28463	0.642316	−	0.766440i	$-0.277974\pi$
$109$	13.4120	1.28463	0.642316	+	0.766440i	$0.277974\pi$
$110$	−9.50919	−0.906666
$111$	−3.74712	−0.355661
$112$	1.67663	0.158427
$113$	12.7614	1.20050	0.600248	−	0.799814i	$-0.295069\pi$
$113$	12.7614	1.20050	0.600248	+	0.799814i	$0.295069\pi$
$114$	−8.48278	−0.794485
$115$	−10.3198	−0.962328
$116$	3.73503	0.346789
$117$	1.00000	0.0924500
$118$	6.47474	0.596048
$119$	8.37877	0.768080
$120$	−10.7536	−0.981661
$121$	−4.52852	−0.411684
$122$	−10.6619	−0.965279
$123$	−4.39072	−0.395898
$124$	4.03089	0.361985
$125$	−8.60685	−0.769820
$126$	1.20256	0.107132
$127$	15.2301	1.35146	0.675728	−	0.737151i	$-0.263829\pi$
$127$	15.2301	1.35146	0.675728	+	0.737151i	$0.263829\pi$
$128$	0.841493	0.0743781
$129$	−11.1838	−0.984682
$130$	3.73802	0.327846
$131$	−15.0434	−1.31435	−0.657173	−	0.753740i	$-0.728248\pi$
$131$	−15.0434	−1.31435	−0.657173	+	0.753740i	$0.728248\pi$
$132$	2.23051	0.194141
$133$	−9.08215	−0.787522
$134$	−4.21587	−0.364196
$135$	−3.52707	−0.303562
$136$	−22.5133	−1.93050
$137$	−10.6755	−0.912066	−0.456033	−	0.889963i	$-0.650730\pi$
$137$	−10.6755	−0.912066	−0.456033	+	0.889963i	$0.650730\pi$
$138$	−3.10088	−0.263965
$139$	−11.1844	−0.948648	−0.474324	−	0.880350i	$-0.657307\pi$
$139$	−11.1844	−0.948648	−0.474324	+	0.880350i	$0.657307\pi$
$140$	−3.50910	−0.296573
$141$	−3.97865	−0.335063
$142$	−3.12459	−0.262210
$143$	−2.54391	−0.212732
$144$	−1.47761	−0.123134
$145$	15.0247	1.24773
$146$	5.16715	0.427637
$147$	−5.71247	−0.471157
$148$	3.28549	0.270065
$149$	18.4295	1.50981	0.754903	−	0.655837i	$-0.227684\pi$
$149$	18.4295	1.50981	0.754903	+	0.655837i	$0.227684\pi$
$150$	−7.88522	−0.643826
$151$	−10.9670	−0.892483	−0.446241	−	0.894913i	$-0.647238\pi$
$151$	−10.9670	−0.892483	−0.446241	+	0.894913i	$0.647238\pi$
$152$	24.4033	1.97937
$153$	−7.38417	−0.596975
$154$	−3.05920	−0.246517
$155$	16.2148	1.30241
$156$	−0.876804	−0.0702005
$157$	11.5751	0.923794	0.461897	−	0.886934i	$-0.347169\pi$
$157$	11.5751	0.923794	0.461897	+	0.886934i	$0.347169\pi$
$158$	9.68735	0.770684
$159$	−8.46140	−0.671033
$160$	15.9838	1.26363
$161$	−3.31999	−0.261652
$162$	−1.05981	−0.0832665
$163$	1.16177	0.0909967	0.0454984	−	0.998964i	$-0.485512\pi$
$163$	1.16177	0.0909967	0.0454984	+	0.998964i	$0.485512\pi$
$164$	3.84981	0.300619
$165$	8.97255	0.698512
$166$	−17.1816	−1.33355
$167$	−5.80630	−0.449305	−0.224652	−	0.974439i	$-0.572125\pi$
$167$	−5.80630	−0.449305	−0.224652	+	0.974439i	$0.572125\pi$
$168$	−3.45953	−0.266908
$169$	1.00000	0.0769231
$170$	−27.6022	−2.11699
$171$	8.00406	0.612086
$172$	9.80604	0.747703
$173$	3.61942	0.275179	0.137590	−	0.990489i	$-0.456064\pi$
$173$	3.61942	0.275179	0.137590	+	0.990489i	$0.456064\pi$
$174$	4.51460	0.342251
$175$	−8.44237	−0.638183
$176$	3.75890	0.283338
$177$	−6.10934	−0.459206
$178$	−2.40833	−0.180512
$179$	−10.8793	−0.813157	−0.406579	−	0.913616i	$-0.633278\pi$
$179$	−10.8793	−0.813157	−0.406579	+	0.913616i	$0.633278\pi$
$180$	3.09255	0.230505
$181$	16.3771	1.21730	0.608650	−	0.793439i	$-0.291711\pi$
$181$	16.3771	1.21730	0.608650	+	0.793439i	$0.291711\pi$
$182$	1.20256	0.0891396
$183$	10.0602	0.743669
$184$	8.92064	0.657638
$185$	13.2163	0.971685
$186$	4.87221	0.357248
$187$	18.7847	1.37367
$188$	3.48850	0.254425
$189$	−1.13469	−0.0825368
$190$	29.9194	2.17058
$191$	−6.61259	−0.478470	−0.239235	−	0.970962i	$-0.576897\pi$
$191$	−6.61259	−0.478470	−0.239235	+	0.970962i	$0.576897\pi$
$192$	7.75800	0.559885
$193$	6.31803	0.454782	0.227391	−	0.973804i	$-0.426980\pi$
$193$	6.31803	0.454782	0.227391	+	0.973804i	$0.426980\pi$
$194$	−11.6839	−0.838853
$195$	−3.52707	−0.252579
$196$	5.00872	0.357766
$197$	13.2275	0.942417	0.471209	−	0.882022i	$-0.343818\pi$
$197$	13.2275	0.942417	0.471209	+	0.882022i	$0.343818\pi$
$198$	2.69606	0.191601
$199$	12.1241	0.859454	0.429727	−	0.902959i	$-0.358610\pi$
$199$	12.1241	0.859454	0.429727	+	0.902959i	$0.358610\pi$
$200$	22.6842	1.60402
$201$	3.97795	0.280583
$202$	−2.31744	−0.163054
$203$	4.83359	0.339252
$204$	6.47447	0.453304
$205$	15.4864	1.08162
$206$	−1.05981	−0.0738404
$207$	2.92589	0.203363
$208$	−1.47761	−0.102454
$209$	−20.3616	−1.40844
$210$	−4.24151	−0.292692
$211$	−6.68818	−0.460433	−0.230216	−	0.973139i	$-0.573943\pi$
$211$	−6.68818	−0.460433	−0.230216	+	0.973139i	$0.573943\pi$
$212$	7.41899	0.509539
$213$	2.94826	0.202011
$214$	−15.0325	−1.02760
$215$	39.4462	2.69021
$216$	3.04886	0.207449
$217$	5.21647	0.354117
$218$	−14.2141	−0.962701
$219$	−4.87555	−0.329459
$220$	−7.86717	−0.530404
$221$	−7.38417	−0.496713
$222$	3.97123	0.266531
$223$	−0.0560849	−0.00375572	−0.00187786	−	0.999998i	$-0.500598\pi$
$223$	−0.0560849	−0.00375572	−0.00187786	+	0.999998i	$0.500598\pi$
$224$	5.14214	0.343574
$225$	7.44023	0.496015
$226$	−13.5247	−0.899650
$227$	15.9626	1.05948	0.529739	−	0.848161i	$-0.322290\pi$
$227$	15.9626	1.05948	0.529739	+	0.848161i	$0.322290\pi$
$228$	−7.01799	−0.464778
$229$	28.3356	1.87247	0.936235	−	0.351375i	$-0.114286\pi$
$229$	28.3356	1.87247	0.936235	+	0.351375i	$0.114286\pi$
$230$	10.9370	0.721167
$231$	2.88656	0.189922
$232$	−12.9876	−0.852679
$233$	−16.8222	−1.10206	−0.551029	−	0.834486i	$-0.685764\pi$
$233$	−16.8222	−1.10206	−0.551029	+	0.834486i	$0.685764\pi$
$234$	−1.05981	−0.0692819
$235$	14.0330	0.915411
$236$	5.35669	0.348691
$237$	−9.14065	−0.593749
$238$	−8.87989	−0.575598
$239$	9.58289	0.619866	0.309933	−	0.950758i	$-0.399693\pi$
$239$	9.58289	0.619866	0.309933	+	0.950758i	$0.399693\pi$
$240$	5.21162	0.336409
$241$	−10.5045	−0.676652	−0.338326	−	0.941029i	$-0.609861\pi$
$241$	−10.5045	−0.676652	−0.338326	+	0.941029i	$0.609861\pi$
$242$	4.79937	0.308515
$243$	1.00000	0.0641500
$244$	−8.82080	−0.564694
$245$	20.1483	1.28723
$246$	4.65333	0.296686
$247$	8.00406	0.509286
$248$	−14.0164	−0.890043
$249$	16.2119	1.02739
$250$	9.12162	0.576902
$251$	−25.6858	−1.62127	−0.810636	−	0.585550i	$-0.800879\pi$
$251$	−25.6858	−1.62127	−0.810636	+	0.585550i	$0.800879\pi$
$252$	0.994904	0.0626730
$253$	−7.44320	−0.467950
$254$	−16.1410	−1.01278
$255$	26.0445	1.63097
$256$	−16.4078	−1.02549
$257$	−4.78901	−0.298730	−0.149365	−	0.988782i	$-0.547723\pi$
$257$	−4.78901	−0.298730	−0.149365	+	0.988782i	$0.547723\pi$
$258$	11.8527	0.737919
$259$	4.25183	0.264196
$260$	3.09255	0.191792
$261$	−4.25982	−0.263677
$262$	15.9431	0.984969
$263$	4.71165	0.290533	0.145266	−	0.989393i	$-0.453596\pi$
$263$	4.71165	0.290533	0.145266	+	0.989393i	$0.453596\pi$
$264$	−7.75604	−0.477351
$265$	29.8440	1.83330
$266$	9.62535	0.590168
$267$	2.27242	0.139070
$268$	−3.48788	−0.213056
$269$	10.8972	0.664414	0.332207	−	0.943207i	$-0.392207\pi$
$269$	10.8972	0.664414	0.332207	+	0.943207i	$0.392207\pi$
$270$	3.73802	0.227489
$271$	3.15201	0.191471	0.0957356	−	0.995407i	$-0.469480\pi$
$271$	3.15201	0.191471	0.0957356	+	0.995407i	$0.469480\pi$
$272$	10.9109	0.661570
$273$	−1.13469	−0.0686748
$274$	11.3140	0.683501
$275$	−18.9273	−1.14136
$276$	−2.56543	−0.154421
$277$	−3.68881	−0.221639	−0.110820	−	0.993841i	$-0.535348\pi$
$277$	−3.68881	−0.221639	−0.110820	+	0.993841i	$0.535348\pi$
$278$	11.8533	0.710915
$279$	−4.59726	−0.275231
$280$	12.2020	0.729208
$281$	0.179846	0.0107287	0.00536434	−	0.999986i	$-0.498292\pi$
$281$	0.179846	0.0107287	0.00536434	+	0.999986i	$0.498292\pi$
$282$	4.21661	0.251096
$283$	13.0684	0.776833	0.388417	−	0.921484i	$-0.373022\pi$
$283$	13.0684	0.776833	0.388417	+	0.921484i	$0.373022\pi$
$284$	−2.58504	−0.153394
$285$	−28.2309	−1.67225
$286$	2.69606	0.159421
$287$	4.98213	0.294086
$288$	−4.53175	−0.267036
$289$	37.5259	2.20741
$290$	−15.9233	−0.935050
$291$	11.0245	0.646268
$292$	4.27490	0.250170
$293$	−31.2494	−1.82561	−0.912804	−	0.408399i	$-0.866087\pi$
$293$	−31.2494	−1.82561	−0.912804	+	0.408399i	$0.866087\pi$
$294$	6.05413	0.353084
$295$	21.5481	1.25458
$296$	−11.4245	−0.664033
$297$	−2.54391	−0.147613
$298$	−19.5318	−1.13145
$299$	2.92589	0.169209
$300$	−6.52362	−0.376641
$301$	12.6902	0.731453
$302$	11.6229	0.668825
$303$	2.18665	0.125620
$304$	−11.8268	−0.678316
$305$	−35.4829	−2.03175
$306$	7.82581	0.447372
$307$	7.84044	0.447478	0.223739	−	0.974649i	$-0.428174\pi$
$307$	7.84044	0.447478	0.223739	+	0.974649i	$0.428174\pi$
$308$	−2.53095	−0.144214
$309$	1.00000	0.0568880
$310$	−17.1846	−0.976022
$311$	15.0178	0.851584	0.425792	−	0.904821i	$-0.359996\pi$
$311$	15.0178	0.851584	0.425792	+	0.904821i	$0.359996\pi$
$312$	3.04886	0.172608
$313$	−22.4350	−1.26810	−0.634050	−	0.773292i	$-0.718609\pi$
$313$	−22.4350	−1.26810	−0.634050	+	0.773292i	$0.718609\pi$
$314$	−12.2674	−0.692290
$315$	4.00214	0.225495
$316$	8.01456	0.450854
$317$	−1.38249	−0.0776483	−0.0388242	−	0.999246i	$-0.512361\pi$
$317$	−1.38249	−0.0776483	−0.0388242	+	0.999246i	$0.512361\pi$
$318$	8.96748	0.502871
$319$	10.8366	0.606734
$320$	−27.3630	−1.52964
$321$	14.1841	0.791681
$322$	3.51855	0.196081
$323$	−59.1033	−3.28860
$324$	−0.876804	−0.0487113
$325$	7.44023	0.412709
$326$	−1.23125	−0.0681928
$327$	13.4120	0.741683
$328$	−13.3867	−0.739158
$329$	4.51455	0.248895
$330$	−9.50919	−0.523464
$331$	21.0449	1.15673	0.578367	−	0.815776i	$-0.303690\pi$
$331$	21.0449	1.15673	0.578367	+	0.815776i	$0.303690\pi$
$332$	−14.2147	−0.780133
$333$	−3.74712	−0.205341
$334$	6.15357	0.336708
$335$	−14.0305	−0.766569
$336$	1.67663	0.0914677
$337$	−2.46079	−0.134048	−0.0670240	−	0.997751i	$-0.521350\pi$
$337$	−2.46079	−0.134048	−0.0670240	+	0.997751i	$0.521350\pi$
$338$	−1.05981	−0.0576460
$339$	12.7614	0.693107
$340$	−22.8359	−1.23845
$341$	11.6950	0.633320
$342$	−8.48278	−0.458696
$343$	14.4248	0.778864
$344$	−34.0980	−1.83844
$345$	−10.3198	−0.555600
$346$	−3.83590	−0.206219
$347$	−2.35449	−0.126396	−0.0631979	−	0.998001i	$-0.520130\pi$
$347$	−2.35449	−0.126396	−0.0631979	+	0.998001i	$0.520130\pi$
$348$	3.73503	0.200219
$349$	25.1269	1.34501	0.672505	−	0.740092i	$-0.265218\pi$
$349$	25.1269	1.34501	0.672505	+	0.740092i	$0.265218\pi$
$350$	8.94731	0.478254
$351$	1.00000	0.0533761
$352$	11.5284	0.614463
$353$	3.78892	0.201664	0.100832	−	0.994903i	$-0.467850\pi$
$353$	3.78892	0.201664	0.100832	+	0.994903i	$0.467850\pi$
$354$	6.47474	0.344128
$355$	−10.3987	−0.551906
$356$	−1.99247	−0.105601
$357$	8.37877	0.443451
$358$	11.5300	0.609379
$359$	13.6846	0.722244	0.361122	−	0.932519i	$-0.382394\pi$
$359$	13.6846	0.722244	0.361122	+	0.932519i	$0.382394\pi$
$360$	−10.7536	−0.566762
$361$	45.0650	2.37184
$362$	−17.3566	−0.912242
$363$	−4.52852	−0.237686
$364$	0.994904	0.0521471
$365$	17.1964	0.900101
$366$	−10.6619	−0.557304
$367$	−8.63532	−0.450760	−0.225380	−	0.974271i	$-0.572362\pi$
$367$	−8.63532	−0.450760	−0.225380	+	0.974271i	$0.572362\pi$
$368$	−4.32331	−0.225368
$369$	−4.39072	−0.228572
$370$	−14.0068	−0.728179
$371$	9.60110	0.498464
$372$	4.03089	0.208992
$373$	−31.6952	−1.64112	−0.820558	−	0.571564i	$-0.806337\pi$
$373$	−31.6952	−1.64112	−0.820558	+	0.571564i	$0.806337\pi$
$374$	−19.9082	−1.02943
$375$	−8.60685	−0.444456
$376$	−12.1304	−0.625576
$377$	−4.25982	−0.219392
$378$	1.20256	0.0618529
$379$	−9.86907	−0.506940	−0.253470	−	0.967343i	$-0.581572\pi$
$379$	−9.86907	−0.506940	−0.253470	+	0.967343i	$0.581572\pi$
$380$	24.7530	1.26980
$381$	15.2301	0.780264
$382$	7.00808	0.358565
$383$	0.573056	0.0292818	0.0146409	−	0.999893i	$-0.495339\pi$
$383$	0.573056	0.0292818	0.0146409	+	0.999893i	$0.495339\pi$
$384$	0.841493	0.0429422
$385$	−10.1811	−0.518876
$386$	−6.69591	−0.340813
$387$	−11.1838	−0.568507
$388$	−9.66633	−0.490734
$389$	−8.67853	−0.440019	−0.220009	−	0.975498i	$-0.570609\pi$
$389$	−8.67853	−0.440019	−0.220009	+	0.975498i	$0.570609\pi$
$390$	3.73802	0.189282
$391$	−21.6053	−1.09262
$392$	−17.4165	−0.879669
$393$	−15.0434	−0.758838
$394$	−14.0186	−0.706246
$395$	32.2397	1.62216
$396$	2.23051	0.112087
$397$	32.6961	1.64097	0.820485	−	0.571669i	$-0.193704\pi$
$397$	32.6961	1.64097	0.820485	+	0.571669i	$0.193704\pi$
$398$	−12.8492	−0.644073
$399$	−9.08215	−0.454676
$400$	−10.9937	−0.549686
$401$	10.5764	0.528160	0.264080	−	0.964501i	$-0.414932\pi$
$401$	10.5764	0.528160	0.264080	+	0.964501i	$0.414932\pi$
$402$	−4.21587	−0.210268
$403$	−4.59726	−0.229006
$404$	−1.91727	−0.0953876
$405$	−3.52707	−0.175262
$406$	−5.12269	−0.254235
$407$	9.53233	0.472500
$408$	−22.5133	−1.11458
$409$	−0.0221220	−0.00109386	−0.000546932	−	1.00000i	$-0.500174\pi$
$409$	−0.0221220	−0.00109386	−0.000546932		1.00000i	$0.500174\pi$
$410$	−16.4126	−0.810562
$411$	−10.6755	−0.526582
$412$	−0.876804	−0.0431970
$413$	6.93223	0.341113
$414$	−3.10088	−0.152400
$415$	−57.1807	−2.80689
$416$	−4.53175	−0.222187
$417$	−11.1844	−0.547702
$418$	21.5794	1.05548
$419$	−35.2123	−1.72023	−0.860116	−	0.510098i	$-0.829609\pi$
$419$	−35.2123	−1.72023	−0.860116	+	0.510098i	$0.829609\pi$
$420$	−3.50910	−0.171226
$421$	−37.8610	−1.84523	−0.922615	−	0.385721i	$-0.873953\pi$
$421$	−37.8610	−1.84523	−0.922615	+	0.385721i	$0.873953\pi$
$422$	7.08819	0.345048
$423$	−3.97865	−0.193449
$424$	−25.7977	−1.25285
$425$	−54.9399	−2.66498
$426$	−3.12459	−0.151387
$427$	−11.4152	−0.552420
$428$	−12.4367	−0.601151
$429$	−2.54391	−0.122821
$430$	−41.8055	−2.01604
$431$	−10.0958	−0.486296	−0.243148	−	0.969989i	$-0.578180\pi$
$431$	−10.0958	−0.486296	−0.243148	+	0.969989i	$0.578180\pi$
$432$	−1.47761	−0.0710914
$433$	−20.1294	−0.967356	−0.483678	−	0.875246i	$-0.660699\pi$
$433$	−20.1294	−0.967356	−0.483678	+	0.875246i	$0.660699\pi$
$434$	−5.52847	−0.265375
$435$	15.0247	0.720379
$436$	−11.7597	−0.563185
$437$	23.4190	1.12028
$438$	5.16715	0.246896
$439$	1.99894	0.0954043	0.0477022	−	0.998862i	$-0.484810\pi$
$439$	1.99894	0.0954043	0.0477022	+	0.998862i	$0.484810\pi$
$440$	27.3561	1.30415
$441$	−5.71247	−0.272022
$442$	7.82581	0.372236
$443$	40.5396	1.92609	0.963046	−	0.269336i	$-0.0868042\pi$
$443$	40.5396	1.92609	0.963046	+	0.269336i	$0.0868042\pi$
$444$	3.28549	0.155922
$445$	−8.01499	−0.379947
$446$	0.0594393	0.00281453
$447$	18.4295	0.871687
$448$	−8.80295	−0.415900
$449$	3.92014	0.185003	0.0925014	−	0.995713i	$-0.470514\pi$
$449$	3.92014	0.185003	0.0925014	+	0.995713i	$0.470514\pi$
$450$	−7.88522	−0.371713
$451$	11.1696	0.525956
$452$	−11.1893	−0.526300
$453$	−10.9670	−0.515275
$454$	−16.9174	−0.793971
$455$	4.00214	0.187623
$456$	24.4033	1.14279
$457$	40.1970	1.88034	0.940169	−	0.340708i	$-0.110667\pi$
$457$	40.1970	1.88034	0.940169	+	0.340708i	$0.110667\pi$
$458$	−30.0303	−1.40323
$459$	−7.38417	−0.344663
$460$	9.04846	0.421887
$461$	−3.12562	−0.145575	−0.0727873	−	0.997347i	$-0.523189\pi$
$461$	−3.12562	−0.145575	−0.0727873	+	0.997347i	$0.523189\pi$
$462$	−3.05920	−0.142327
$463$	18.0320	0.838016	0.419008	−	0.907982i	$-0.362378\pi$
$463$	18.0320	0.838016	0.419008	+	0.907982i	$0.362378\pi$
$464$	6.29434	0.292208
$465$	16.2148	0.751945
$466$	17.8283	0.825880
$467$	−7.05728	−0.326572	−0.163286	−	0.986579i	$-0.552209\pi$
$467$	−7.05728	−0.326572	−0.163286	+	0.986579i	$0.552209\pi$
$468$	−0.876804	−0.0405303
$469$	−4.51375	−0.208426
$470$	−14.8723	−0.686008
$471$	11.5751	0.533353
$472$	−18.6265	−0.857356
$473$	28.4507	1.30816
$474$	9.68735	0.444955
$475$	59.5520	2.73243
$476$	−7.34654	−0.336728
$477$	−8.46140	−0.387421
$478$	−10.1560	−0.464526
$479$	13.6916	0.625586	0.312793	−	0.949821i	$-0.398735\pi$
$479$	13.6916	0.625586	0.312793	+	0.949821i	$0.398735\pi$
$480$	15.9838	0.729557
$481$	−3.74712	−0.170854
$482$	11.1327	0.507082
$483$	−3.31999	−0.151065
$484$	3.97063	0.180483
$485$	−38.8842	−1.76564
$486$	−1.05981	−0.0480739
$487$	26.6737	1.20870	0.604350	−	0.796719i	$-0.293433\pi$
$487$	26.6737	1.20870	0.604350	+	0.796719i	$0.293433\pi$
$488$	30.6721	1.38846
$489$	1.16177	0.0525370
$490$	−21.3533	−0.964646
$491$	−15.2776	−0.689467	−0.344734	−	0.938701i	$-0.612031\pi$
$491$	−15.2776	−0.689467	−0.344734	+	0.938701i	$0.612031\pi$
$492$	3.84981	0.173563
$493$	31.4553	1.41667
$494$	−8.48278	−0.381658
$495$	8.97255	0.403286
$496$	6.79293	0.305012
$497$	−3.34537	−0.150060
$498$	−17.1816	−0.769925
$499$	6.99155	0.312985	0.156492	−	0.987679i	$-0.449981\pi$
$499$	6.99155	0.312985	0.156492	+	0.987679i	$0.449981\pi$
$500$	7.54652	0.337491
$501$	−5.80630	−0.259406
$502$	27.2220	1.21498
$503$	31.1346	1.38823	0.694113	−	0.719867i	$-0.255797\pi$
$503$	31.1346	1.38823	0.694113	+	0.719867i	$0.255797\pi$
$504$	−3.45953	−0.154099
$505$	−7.71248	−0.343201
$506$	7.88837	0.350681
$507$	1.00000	0.0444116
$508$	−13.3539	−0.592481
$509$	8.11102	0.359515	0.179757	−	0.983711i	$-0.442469\pi$
$509$	8.11102	0.359515	0.179757	+	0.983711i	$0.442469\pi$
$510$	−27.6022	−1.22225
$511$	5.53225	0.244732
$512$	15.7062	0.694122
$513$	8.00406	0.353388
$514$	5.07543	0.223868
$515$	−3.52707	−0.155421
$516$	9.80604	0.431687
$517$	10.1213	0.445136
$518$	−4.50613	−0.197988
$519$	3.61942	0.158875
$520$	−10.7536	−0.471575
$521$	37.9489	1.66257	0.831286	−	0.555845i	$-0.187605\pi$
$521$	37.9489	1.66257	0.831286	+	0.555845i	$0.187605\pi$
$522$	4.51460	0.197599
$523$	−27.5855	−1.20623	−0.603115	−	0.797654i	$-0.706074\pi$
$523$	−27.5855	−1.20623	−0.603115	+	0.797654i	$0.706074\pi$
$524$	13.1901	0.576212
$525$	−8.44237	−0.368455
$526$	−4.99345	−0.217725
$527$	33.9469	1.47875
$528$	3.75890	0.163585
$529$	−14.4392	−0.627790
$530$	−31.6289	−1.37387
$531$	−6.10934	−0.265123
$532$	7.96327	0.345251
$533$	−4.39072	−0.190183
$534$	−2.40833	−0.104219
$535$	−50.0284	−2.16292
$536$	12.1282	0.523860
$537$	−10.8793	−0.469476
$538$	−11.5490	−0.497911
$539$	14.5320	0.625938
$540$	3.09255	0.133082
$541$	29.6240	1.27364	0.636818	−	0.771014i	$-0.280250\pi$
$541$	29.6240	1.27364	0.636818	+	0.771014i	$0.280250\pi$
$542$	−3.34053	−0.143488
$543$	16.3771	0.702808
$544$	33.4632	1.43472
$545$	−47.3049	−2.02632
$546$	1.20256	0.0514648
$547$	−5.68090	−0.242898	−0.121449	−	0.992598i	$-0.538754\pi$
$547$	−5.68090	−0.242898	−0.121449	+	0.992598i	$0.538754\pi$
$548$	9.36029	0.399852
$549$	10.0602	0.429357
$550$	20.0593	0.855331
$551$	−34.0959	−1.45253
$552$	8.92064	0.379688
$553$	10.3718	0.441055
$554$	3.90944	0.166096
$555$	13.2163	0.561003
$556$	9.80652	0.415889
$557$	4.01465	0.170106	0.0850530	−	0.996376i	$-0.472894\pi$
$557$	4.01465	0.170106	0.0850530	+	0.996376i	$0.472894\pi$
$558$	4.87221	0.206257
$559$	−11.1838	−0.473026
$560$	−5.91359	−0.249895
$561$	18.7847	0.793089
$562$	−0.190602	−0.00804006
$563$	−10.3068	−0.434379	−0.217189	−	0.976129i	$-0.569689\pi$
$563$	−10.3068	−0.434379	−0.217189	+	0.976129i	$0.569689\pi$
$564$	3.48850	0.146892
$565$	−45.0105	−1.89361
$566$	−13.8500	−0.582158
$567$	−1.13469	−0.0476526
$568$	8.98883	0.377163
$569$	−1.13819	−0.0477156	−0.0238578	−	0.999715i	$-0.507595\pi$
$569$	−1.13819	−0.0477156	−0.0238578	+	0.999715i	$0.507595\pi$
$570$	29.9194	1.25318
$571$	36.4035	1.52344	0.761719	−	0.647908i	$-0.224356\pi$
$571$	36.4035	1.52344	0.761719	+	0.647908i	$0.224356\pi$
$572$	2.23051	0.0932623
$573$	−6.61259	−0.276245
$574$	−5.28010	−0.220387
$575$	21.7693	0.907842
$576$	7.75800	0.323250
$577$	11.3089	0.470795	0.235398	−	0.971899i	$-0.424361\pi$
$577$	11.3089	0.470795	0.235398	+	0.971899i	$0.424361\pi$
$578$	−39.7703	−1.65423
$579$	6.31803	0.262568
$580$	−13.1737	−0.547009
$581$	−18.3956	−0.763177
$582$	−11.6839	−0.484312
$583$	21.5250	0.891476
$584$	−14.8649	−0.615113
$585$	−3.52707	−0.145826
$586$	33.1184	1.36811
$587$	10.9541	0.452125	0.226063	−	0.974113i	$-0.427415\pi$
$587$	10.9541	0.452125	0.226063	+	0.974113i	$0.427415\pi$
$588$	5.00872	0.206556
$589$	−36.7967	−1.51618
$590$	−22.8369	−0.940178
$591$	13.2275	0.544105
$592$	5.53676	0.227560
$593$	28.5836	1.17379	0.586893	−	0.809664i	$-0.300351\pi$
$593$	28.5836	1.17379	0.586893	+	0.809664i	$0.300351\pi$
$594$	2.69606	0.110621
$595$	−29.5525	−1.21153
$596$	−16.1591	−0.661902
$597$	12.1241	0.496206
$598$	−3.10088	−0.126805
$599$	40.9797	1.67438	0.837192	−	0.546909i	$-0.184195\pi$
$599$	40.9797	1.67438	0.837192	+	0.546909i	$0.184195\pi$
$600$	22.6842	0.926080
$601$	39.8451	1.62531	0.812657	−	0.582742i	$-0.198020\pi$
$601$	39.8451	1.62531	0.812657	+	0.582742i	$0.198020\pi$
$602$	−13.4492	−0.548149
$603$	3.97795	0.161995
$604$	9.61592	0.391266
$605$	15.9724	0.649371
$606$	−2.31744	−0.0941394
$607$	−4.75438	−0.192974	−0.0964872	−	0.995334i	$-0.530761\pi$
$607$	−4.75438	−0.192974	−0.0964872	+	0.995334i	$0.530761\pi$
$608$	−36.2724	−1.47104
$609$	4.83359	0.195867
$610$	37.6051	1.52259
$611$	−3.97865	−0.160959
$612$	6.47447	0.261715
$613$	−12.8536	−0.519150	−0.259575	−	0.965723i	$-0.583582\pi$
$613$	−12.8536	−0.519150	−0.259575	+	0.965723i	$0.583582\pi$
$614$	−8.30937	−0.335339
$615$	15.4864	0.624472
$616$	8.80072	0.354591
$617$	2.31095	0.0930352	0.0465176	−	0.998917i	$-0.485188\pi$
$617$	2.31095	0.0930352	0.0465176	+	0.998917i	$0.485188\pi$
$618$	−1.05981	−0.0426318
$619$	−24.6021	−0.988842	−0.494421	−	0.869222i	$-0.664620\pi$
$619$	−24.6021	−0.988842	−0.494421	+	0.869222i	$0.664620\pi$
$620$	−14.2172	−0.570978
$621$	2.92589	0.117412
$622$	−15.9160	−0.638175
$623$	−2.57850	−0.103305
$624$	−1.47761	−0.0591516
$625$	−6.84417	−0.273767
$626$	23.7768	0.950312
$627$	−20.3616	−0.813164
$628$	−10.1491	−0.404993
$629$	27.6693	1.10325
$630$	−4.24151	−0.168986
$631$	−14.5057	−0.577465	−0.288732	−	0.957410i	$-0.593234\pi$
$631$	−14.5057	−0.577465	−0.288732	+	0.957410i	$0.593234\pi$
$632$	−27.8686	−1.10855
$633$	−6.68818	−0.265831
$634$	1.46518	0.0581895
$635$	−53.7178	−2.13173
$636$	7.41899	0.294182
$637$	−5.71247	−0.226336
$638$	−11.4847	−0.454685
$639$	2.94826	0.116631
$640$	−2.96800	−0.117321
$641$	−20.8002	−0.821558	−0.410779	−	0.911735i	$-0.634743\pi$
$641$	−20.8002	−0.821558	−0.410779	+	0.911735i	$0.634743\pi$
$642$	−15.0325	−0.593284
$643$	−12.4202	−0.489804	−0.244902	−	0.969548i	$-0.578756\pi$
$643$	−12.4202	−0.489804	−0.244902	+	0.969548i	$0.578756\pi$
$644$	2.91098	0.114709
$645$	39.4462	1.55319
$646$	62.6383	2.46447
$647$	−7.45182	−0.292961	−0.146481	−	0.989214i	$-0.546795\pi$
$647$	−7.45182	−0.292961	−0.146481	+	0.989214i	$0.546795\pi$
$648$	3.04886	0.119771
$649$	15.5416	0.610062
$650$	−7.88522	−0.309284
$651$	5.21647	0.204450
$652$	−1.01864	−0.0398931
$653$	−3.10699	−0.121586	−0.0607929	−	0.998150i	$-0.519363\pi$
$653$	−3.10699	−0.121586	−0.0607929	+	0.998150i	$0.519363\pi$
$654$	−14.2141	−0.555816
$655$	53.0591	2.07319
$656$	6.48776	0.253305
$657$	−4.87555	−0.190213
$658$	−4.78456	−0.186522
$659$	−47.2751	−1.84158	−0.920788	−	0.390063i	$-0.872453\pi$
$659$	−47.2751	−1.84158	−0.920788	+	0.390063i	$0.872453\pi$
$660$	−7.86717	−0.306229
$661$	−36.0676	−1.40287	−0.701434	−	0.712734i	$-0.747456\pi$
$661$	−36.0676	−1.40287	−0.701434	+	0.712734i	$0.747456\pi$
$662$	−22.3036	−0.866855
$663$	−7.38417	−0.286777
$664$	49.4280	1.91818
$665$	32.0334	1.24220
$666$	3.97123	0.153882
$667$	−12.4638	−0.482599
$668$	5.09099	0.196976
$669$	−0.0560849	−0.00216837
$670$	14.8697	0.574465
$671$	−25.5922	−0.987974
$672$	5.14214	0.198362
$673$	33.5063	1.29157	0.645787	−	0.763517i	$-0.276529\pi$
$673$	33.5063	1.29157	0.645787	+	0.763517i	$0.276529\pi$
$674$	2.60797	0.100455
$675$	7.44023	0.286374
$676$	−0.876804	−0.0337232
$677$	40.7168	1.56487	0.782436	−	0.622731i	$-0.213977\pi$
$677$	40.7168	1.56487	0.782436	+	0.622731i	$0.213977\pi$
$678$	−13.5247	−0.519413
$679$	−12.5094	−0.480068
$680$	79.4061	3.04508
$681$	15.9626	0.611690
$682$	−12.3945	−0.474609
$683$	13.1739	0.504085	0.252042	−	0.967716i	$-0.418898\pi$
$683$	13.1739	0.504085	0.252042	+	0.967716i	$0.418898\pi$
$684$	−7.01799	−0.268340
$685$	37.6531	1.43865
$686$	−15.2875	−0.583679
$687$	28.3356	1.08107
$688$	16.5253	0.630022
$689$	−8.46140	−0.322354
$690$	10.9370	0.416366
$691$	31.4567	1.19667	0.598335	−	0.801246i	$-0.295829\pi$
$691$	31.4567	1.19667	0.598335	+	0.801246i	$0.295829\pi$
$692$	−3.17352	−0.120639
$693$	2.88656	0.109651
$694$	2.49531	0.0947208
$695$	39.4481	1.49635
$696$	−12.9876	−0.492295
$697$	32.4218	1.22807
$698$	−26.6297	−1.00795
$699$	−16.8222	−0.636273
$700$	7.40231	0.279781
$701$	−50.5575	−1.90953	−0.954766	−	0.297360i	$-0.903894\pi$
$701$	−50.5575	−1.90953	−0.954766	+	0.297360i	$0.903894\pi$
$702$	−1.05981	−0.0399999
$703$	−29.9921	−1.13118
$704$	−19.7357	−0.743815
$705$	14.0330	0.528513
$706$	−4.01553	−0.151126
$707$	−2.48118	−0.0933144
$708$	5.35669	0.201317
$709$	3.13768	0.117838	0.0589191	−	0.998263i	$-0.481235\pi$
$709$	3.13768	0.117838	0.0589191	+	0.998263i	$0.481235\pi$
$710$	11.0206	0.413597
$711$	−9.14065	−0.342801
$712$	6.92830	0.259649
$713$	−13.4511	−0.503746
$714$	−8.87989	−0.332322
$715$	8.97255	0.335554
$716$	9.53902	0.356490
$717$	9.58289	0.357880
$718$	−14.5030	−0.541249
$719$	−17.9800	−0.670541	−0.335270	−	0.942122i	$-0.608828\pi$
$719$	−17.9800	−0.670541	−0.335270	+	0.942122i	$0.608828\pi$
$720$	5.21162	0.194226
$721$	−1.13469	−0.0422582
$722$	−47.7603	−1.77745
$723$	−10.5045	−0.390665
$724$	−14.3595	−0.533667
$725$	−31.6941	−1.17709
$726$	4.79937	0.178121
$727$	−26.3148	−0.975962	−0.487981	−	0.872854i	$-0.662266\pi$
$727$	−26.3148	−0.975962	−0.487981	+	0.872854i	$0.662266\pi$
$728$	−3.45953	−0.128219
$729$	1.00000	0.0370370
$730$	−18.2249	−0.674534
$731$	82.5834	3.05446
$732$	−8.82080	−0.326026
$733$	−8.46331	−0.312600	−0.156300	−	0.987710i	$-0.549957\pi$
$733$	−8.46331	−0.312600	−0.156300	+	0.987710i	$0.549957\pi$
$734$	9.15180	0.337799
$735$	20.1483	0.743181
$736$	−13.2594	−0.488748
$737$	−10.1195	−0.372758
$738$	4.65333	0.171291
$739$	−32.0146	−1.17768	−0.588839	−	0.808251i	$-0.700415\pi$
$739$	−32.0146	−1.17768	−0.588839	+	0.808251i	$0.700415\pi$
$740$	−11.5881	−0.425989
$741$	8.00406	0.294036
$742$	−10.1753	−0.373548
$743$	−7.71152	−0.282908	−0.141454	−	0.989945i	$-0.545178\pi$
$743$	−7.71152	−0.282908	−0.141454	+	0.989945i	$0.545178\pi$
$744$	−14.0164	−0.513866
$745$	−65.0022	−2.38150
$746$	33.5909	1.22985
$747$	16.2119	0.593164
$748$	−16.4705	−0.602220
$749$	−16.0946	−0.588085
$750$	9.12162	0.333074
$751$	11.5329	0.420841	0.210421	−	0.977611i	$-0.432517\pi$
$751$	11.5329	0.420841	0.210421	+	0.977611i	$0.432517\pi$
$752$	5.87888	0.214381
$753$	−25.6858	−0.936042
$754$	4.51460	0.164412
$755$	38.6814	1.40776
$756$	0.994904	0.0361843
$757$	0.124196	0.00451399	0.00225700	−	0.999997i	$-0.499282\pi$
$757$	0.124196	0.00451399	0.00225700	+	0.999997i	$0.499282\pi$
$758$	10.4593	0.379900
$759$	−7.44320	−0.270171
$760$	−86.0721	−3.12216
$761$	13.3497	0.483926	0.241963	−	0.970286i	$-0.422209\pi$
$761$	13.3497	0.483926	0.241963	+	0.970286i	$0.422209\pi$
$762$	−16.1410	−0.584728
$763$	−15.2184	−0.550945
$764$	5.79794	0.209762
$765$	26.0445	0.941640
$766$	−0.607330	−0.0219437
$767$	−6.10934	−0.220595
$768$	−16.4078	−0.592066
$769$	6.26543	0.225937	0.112969	−	0.993599i	$-0.463964\pi$
$769$	6.26543	0.225937	0.112969	+	0.993599i	$0.463964\pi$
$770$	10.7900	0.388845
$771$	−4.78901	−0.172472
$772$	−5.53968	−0.199377
$773$	25.6060	0.920983	0.460491	−	0.887664i	$-0.347673\pi$
$773$	25.6060	0.920983	0.460491	+	0.887664i	$0.347673\pi$
$774$	11.8527	0.426038
$775$	−34.2046	−1.22867
$776$	33.6122	1.20661
$777$	4.25183	0.152533
$778$	9.19759	0.329749
$779$	−35.1436	−1.25915
$780$	3.09255	0.110731
$781$	−7.50010	−0.268375
$782$	22.8975	0.818811
$783$	−4.25982	−0.152234
$784$	8.44078	0.301457
$785$	−40.8262	−1.45715
$786$	15.9431	0.568672
$787$	−33.8052	−1.20503	−0.602513	−	0.798109i	$-0.705834\pi$
$787$	−33.8052	−1.20503	−0.602513	+	0.798109i	$0.705834\pi$
$788$	−11.5979	−0.413158
$789$	4.71165	0.167739
$790$	−34.1680	−1.21564
$791$	−14.4803	−0.514861
$792$	−7.75604	−0.275599
$793$	10.0602	0.357247
$794$	−34.6516	−1.22974
$795$	29.8440	1.05846
$796$	−10.6305	−0.376786
$797$	1.54267	0.0546440	0.0273220	−	0.999627i	$-0.491302\pi$
$797$	1.54267	0.0546440	0.0273220	+	0.999627i	$0.491302\pi$
$798$	9.62535	0.340734
$799$	29.3790	1.03936
$800$	−33.7172	−1.19208
$801$	2.27242	0.0802920
$802$	−11.2090	−0.395802
$803$	12.4030	0.437691
$804$	−3.48788	−0.123008
$805$	11.7098	0.412717
$806$	4.87221	0.171616
$807$	10.8972	0.383600
$808$	6.66681	0.234538
$809$	4.12452	0.145011	0.0725053	−	0.997368i	$-0.476901\pi$
$809$	4.12452	0.145011	0.0725053	+	0.997368i	$0.476901\pi$
$810$	3.73802	0.131341
$811$	−29.7494	−1.04464	−0.522321	−	0.852749i	$-0.674934\pi$
$811$	−29.7494	−1.04464	−0.522321	+	0.852749i	$0.674934\pi$
$812$	−4.23812	−0.148729
$813$	3.15201	0.110546
$814$	−10.1025	−0.354091
$815$	−4.09764	−0.143534
$816$	10.9109	0.381958
$817$	−89.5161	−3.13177
$818$	0.0234452	0.000819741 0
$819$	−1.13469	−0.0396494
$820$	−13.5785	−0.474183
$821$	20.8086	0.726225	0.363112	−	0.931745i	$-0.381714\pi$
$821$	20.8086	0.726225	0.363112	+	0.931745i	$0.381714\pi$
$822$	11.3140	0.394620
$823$	0.446156	0.0155520	0.00777601	−	0.999970i	$-0.497525\pi$
$823$	0.446156	0.0155520	0.00777601	+	0.999970i	$0.497525\pi$
$824$	3.04886	0.106212
$825$	−18.9273	−0.658963
$826$	−7.34684	−0.255629
$827$	12.0030	0.417385	0.208693	−	0.977981i	$-0.433079\pi$
$827$	12.0030	0.417385	0.208693	+	0.977981i	$0.433079\pi$
$828$	−2.56543	−0.0891549
$829$	5.08457	0.176594	0.0882972	−	0.996094i	$-0.471857\pi$
$829$	5.08457	0.176594	0.0882972	+	0.996094i	$0.471857\pi$
$830$	60.6006	2.10348
$831$	−3.68881	−0.127964
$832$	7.75800	0.268960
$833$	42.1819	1.46151
$834$	11.8533	0.410447
$835$	20.4792	0.708713
$836$	17.8531	0.617464
$837$	−4.59726	−0.158904
$838$	37.3183	1.28914
$839$	−19.5276	−0.674169	−0.337084	−	0.941474i	$-0.609441\pi$
$839$	−19.5276	−0.674169	−0.337084	+	0.941474i	$0.609441\pi$
$840$	12.2020	0.421009
$841$	−10.8539	−0.374272
$842$	40.1254	1.38281
$843$	0.179846	0.00619421
$844$	5.86422	0.201855
$845$	−3.52707	−0.121335
$846$	4.21661	0.144970
$847$	5.13848	0.176560
$848$	12.5026	0.429342
$849$	13.0684	0.448505
$850$	58.2258	1.99713
$851$	−10.9636	−0.375829
$852$	−2.58504	−0.0885621
$853$	39.3402	1.34698	0.673492	−	0.739195i	$-0.264794\pi$
$853$	39.3402	1.34698	0.673492	+	0.739195i	$0.264794\pi$
$854$	12.0979	0.413983
$855$	−28.2309	−0.965476
$856$	43.2455	1.47810
$857$	−31.7404	−1.08423	−0.542115	−	0.840304i	$-0.682376\pi$
$857$	−31.7404	−1.08423	−0.542115	+	0.840304i	$0.682376\pi$
$858$	2.69606	0.0920420
$859$	−51.2102	−1.74727	−0.873634	−	0.486584i	$-0.838243\pi$
$859$	−51.2102	−1.74727	−0.873634	+	0.486584i	$0.838243\pi$
$860$	−34.5866	−1.17939
$861$	4.98213	0.169790
$862$	10.6996	0.364429
$863$	38.5382	1.31185	0.655927	−	0.754824i	$-0.272278\pi$
$863$	38.5382	1.31185	0.655927	+	0.754824i	$0.272278\pi$
$864$	−4.53175	−0.154173
$865$	−12.7659	−0.434055
$866$	21.3333	0.724935
$867$	37.5259	1.27445
$868$	−4.57383	−0.155246
$869$	23.2530	0.788804
$870$	−15.9233	−0.539851
$871$	3.97795	0.134788
$872$	40.8912	1.38475
$873$	11.0245	0.373123
$874$	−24.8197	−0.839538
$875$	9.76613	0.330155
$876$	4.27490	0.144436
$877$	−37.6585	−1.27164	−0.635818	−	0.771839i	$-0.719337\pi$
$877$	−37.6585	−1.27164	−0.635818	+	0.771839i	$0.719337\pi$
$878$	−2.11850	−0.0714958
$879$	−31.2494	−1.05401
$880$	−13.2579	−0.446924
$881$	37.8043	1.27366	0.636830	−	0.771005i	$-0.280245\pi$
$881$	37.8043	1.27366	0.636830	+	0.771005i	$0.280245\pi$
$882$	6.05413	0.203853
$883$	27.5269	0.926352	0.463176	−	0.886266i	$-0.346710\pi$
$883$	27.5269	0.926352	0.463176	+	0.886266i	$0.346710\pi$
$884$	6.47447	0.217760
$885$	21.5481	0.724331
$886$	−42.9642	−1.44341
$887$	−34.9657	−1.17403	−0.587017	−	0.809575i	$-0.699698\pi$
$887$	−34.9657	−1.17403	−0.587017	+	0.809575i	$0.699698\pi$
$888$	−11.4245	−0.383379
$889$	−17.2815	−0.579604
$890$	8.49436	0.284732
$891$	−2.54391	−0.0852242
$892$	0.0491755	0.00164652
$893$	−31.8454	−1.06566
$894$	−19.5318	−0.653241
$895$	38.3721	1.28264
$896$	−0.954836	−0.0318988
$897$	2.92589	0.0976926
$898$	−4.15460	−0.138641
$899$	19.5835	0.653146
$900$	−6.52362	−0.217454
$901$	62.4804	2.08153
$902$	−11.8377	−0.394151
$903$	12.6902	0.422304
$904$	38.9079	1.29406
$905$	−57.7632	−1.92011
$906$	11.6229	0.386146
$907$	−0.564664	−0.0187494	−0.00937468	−	0.999956i	$-0.502984\pi$
$907$	−0.564664	−0.0187494	−0.00937468	+	0.999956i	$0.502984\pi$
$908$	−13.9961	−0.464477
$909$	2.18665	0.0725268
$910$	−4.24151	−0.140605
$911$	28.7238	0.951662	0.475831	−	0.879537i	$-0.342147\pi$
$911$	28.7238	0.951662	0.475831	+	0.879537i	$0.342147\pi$
$912$	−11.8268	−0.391626
$913$	−41.2417	−1.36490
$914$	−42.6012	−1.40912
$915$	−35.4829	−1.17303
$916$	−24.8448	−0.820895
$917$	17.0696	0.563689
$918$	7.82581	0.258290
$919$	12.9119	0.425925	0.212963	−	0.977060i	$-0.431689\pi$
$919$	12.9119	0.425925	0.212963	+	0.977060i	$0.431689\pi$
$920$	−31.4637	−1.03733
$921$	7.84044	0.258351
$922$	3.31256	0.109093
$923$	2.94826	0.0970430
$924$	−2.53095	−0.0832620
$925$	−27.8794	−0.916669
$926$	−19.1104	−0.628008
$927$	1.00000	0.0328443
$928$	19.3044	0.633700
$929$	−7.36523	−0.241645	−0.120823	−	0.992674i	$-0.538553\pi$
$929$	−7.36523	−0.241645	−0.120823	+	0.992674i	$0.538553\pi$
$930$	−17.1846	−0.563507
$931$	−45.7230	−1.49851
$932$	14.7497	0.483144
$933$	15.0178	0.491662
$934$	7.47937	0.244732
$935$	−66.2548	−2.16676
$936$	3.04886	0.0996552
$937$	32.4672	1.06066	0.530329	−	0.847792i	$-0.322068\pi$
$937$	32.4672	1.06066	0.530329	+	0.847792i	$0.322068\pi$
$938$	4.78372	0.156194
$939$	−22.4350	−0.732138
$940$	−12.3042	−0.401318
$941$	6.13817	0.200098	0.100049	−	0.994982i	$-0.468100\pi$
$941$	6.13817	0.200098	0.100049	+	0.994982i	$0.468100\pi$
$942$	−12.2674	−0.399694
$943$	−12.8468	−0.418348
$944$	9.02720	0.293810
$945$	4.00214	0.130190
$946$	−30.1523	−0.980336
$947$	9.63752	0.313177	0.156589	−	0.987664i	$-0.449950\pi$
$947$	9.63752	0.313177	0.156589	+	0.987664i	$0.449950\pi$
$948$	8.01456	0.260301
$949$	−4.87555	−0.158267
$950$	−63.1138	−2.04768
$951$	−1.38249	−0.0448303
$952$	25.5457	0.827941
$953$	−17.3243	−0.561189	−0.280594	−	0.959826i	$-0.590532\pi$
$953$	−17.3243	−0.561189	−0.280594	+	0.959826i	$0.590532\pi$
$954$	8.96748	0.290333
$955$	23.3231	0.754717
$956$	−8.40232	−0.271750
$957$	10.8366	0.350298
$958$	−14.5105	−0.468813
$959$	12.1134	0.391161
$960$	−27.3630	−0.883137
$961$	−9.86524	−0.318233
$962$	3.97123	0.128038
$963$	14.1841	0.457077
$964$	9.21036	0.296646
$965$	−22.2841	−0.717352
$966$	3.51855	0.113208
$967$	37.3251	1.20029	0.600147	−	0.799890i	$-0.295109\pi$
$967$	37.3251	1.20029	0.600147	+	0.799890i	$0.295109\pi$
$968$	−13.8068	−0.443769
$969$	−59.1033	−1.89867
$970$	41.2098	1.32317
$971$	15.7924	0.506802	0.253401	−	0.967361i	$-0.418451\pi$
$971$	15.7924	0.506802	0.253401	+	0.967361i	$0.418451\pi$
$972$	−0.876804	−0.0281235
$973$	12.6909	0.406850
$974$	−28.2690	−0.905797
$975$	7.44023	0.238278
$976$	−14.8650	−0.475816
$977$	−18.6818	−0.597685	−0.298842	−	0.954302i	$-0.596600\pi$
$977$	−18.6818	−0.597685	−0.298842	+	0.954302i	$0.596600\pi$
$978$	−1.23125	−0.0393711
$979$	−5.78083	−0.184756
$980$	−17.6661	−0.564323
$981$	13.4120	0.428211
$982$	16.1913	0.516686
$983$	−60.1980	−1.92002	−0.960010	−	0.279967i	$-0.909677\pi$
$983$	−60.1980	−1.92002	−0.960010	+	0.279967i	$0.909677\pi$
$984$	−13.3867	−0.426753
$985$	−46.6542	−1.48653
$986$	−33.3366	−1.06165
$987$	4.51455	0.143700
$988$	−7.01799	−0.223272
$989$	−32.7227	−1.04052
$990$	−9.50919	−0.302222
$991$	14.1721	0.450192	0.225096	−	0.974337i	$-0.427730\pi$
$991$	14.1721	0.450192	0.225096	+	0.974337i	$0.427730\pi$
$992$	20.8336	0.661467
$993$	21.0449	0.667841
$994$	3.54545	0.112455
$995$	−42.7625	−1.35566
$996$	−14.2147	−0.450410
$997$	33.5989	1.06409	0.532044	−	0.846717i	$-0.321424\pi$
$997$	33.5989	1.06409	0.532044	+	0.846717i	$0.321424\pi$
$998$	−7.40971	−0.234550
$999$	−3.74712	−0.118554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.k.1.11	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.k.1.11	✓	32	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-1.05981 q^{2} +1.00000 q^{3} -0.876804 q^{4} -3.52707 q^{5} -1.05981 q^{6} -1.13469 q^{7} +3.04886 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.05981 q^{2} +1.00000 q^{3} -0.876804 q^{4} -3.52707 q^{5} -1.05981 q^{6} -1.13469 q^{7} +3.04886 q^{8} +1.00000 q^{9} +3.73802 q^{10} -2.54391 q^{11} -0.876804 q^{12} +1.00000 q^{13} +1.20256 q^{14} -3.52707 q^{15} -1.47761 q^{16} -7.38417 q^{17} -1.05981 q^{18} +8.00406 q^{19} +3.09255 q^{20} -1.13469 q^{21} +2.69606 q^{22} +2.92589 q^{23} +3.04886 q^{24} +7.44023 q^{25} -1.05981 q^{26} +1.00000 q^{27} +0.994904 q^{28} -4.25982 q^{29} +3.73802 q^{30} -4.59726 q^{31} -4.53175 q^{32} -2.54391 q^{33} +7.82581 q^{34} +4.00214 q^{35} -0.876804 q^{36} -3.74712 q^{37} -8.48278 q^{38} +1.00000 q^{39} -10.7536 q^{40} -4.39072 q^{41} +1.20256 q^{42} -11.1838 q^{43} +2.23051 q^{44} -3.52707 q^{45} -3.10088 q^{46} -3.97865 q^{47} -1.47761 q^{48} -5.71247 q^{49} -7.88522 q^{50} -7.38417 q^{51} -0.876804 q^{52} -8.46140 q^{53} -1.05981 q^{54} +8.97255 q^{55} -3.45953 q^{56} +8.00406 q^{57} +4.51460 q^{58} -6.10934 q^{59} +3.09255 q^{60} +10.0602 q^{61} +4.87221 q^{62} -1.13469 q^{63} +7.75800 q^{64} -3.52707 q^{65} +2.69606 q^{66} +3.97795 q^{67} +6.47447 q^{68} +2.92589 q^{69} -4.24151 q^{70} +2.94826 q^{71} +3.04886 q^{72} -4.87555 q^{73} +3.97123 q^{74} +7.44023 q^{75} -7.01799 q^{76} +2.88656 q^{77} -1.05981 q^{78} -9.14065 q^{79} +5.21162 q^{80} +1.00000 q^{81} +4.65333 q^{82} +16.2119 q^{83} +0.994904 q^{84} +26.0445 q^{85} +11.8527 q^{86} -4.25982 q^{87} -7.75604 q^{88} +2.27242 q^{89} +3.73802 q^{90} -1.13469 q^{91} -2.56543 q^{92} -4.59726 q^{93} +4.21661 q^{94} -28.2309 q^{95} -4.53175 q^{96} +11.0245 q^{97} +6.05413 q^{98} -2.54391 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * q^99

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