LMFDB - Embedded newform 349.2.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(1,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("349.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 5 x^{16} - 14 x^{15} + 102 x^{14} + 26 x^{13} - 792 x^{12} + 474 x^{11} + 2887 x^{10} + \cdots - 4 $ x^17 - 5x^16 - 14x^15 + 102x^14 + 26x^13 - 792x^12 + 474x^11 + 2887x^10 - 3021x^9 - 4835x^8 + 6673x^7 + 2880x^6 - 5373x^5 - 164x^4 + 1075x^3 + 75x^2 - 41x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$2.79743$ of defining polynomial
Character	$\chi$	$=$	349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.79743 q^{2} -1.46796 q^{3} +5.82560 q^{4} -1.10838 q^{5} -4.10651 q^{6} +2.17992 q^{7} +10.7018 q^{8} -0.845091 q^{9} +O(q^{10})$	\(q+2.79743 q^{2} -1.46796 q^{3} +5.82560 q^{4} -1.10838 q^{5} -4.10651 q^{6} +2.17992 q^{7} +10.7018 q^{8} -0.845091 q^{9} -3.10061 q^{10} -0.573158 q^{11} -8.55175 q^{12} -0.599039 q^{13} +6.09817 q^{14} +1.62706 q^{15} +18.2864 q^{16} +1.88451 q^{17} -2.36408 q^{18} -4.87246 q^{19} -6.45698 q^{20} -3.20004 q^{21} -1.60337 q^{22} -3.91231 q^{23} -15.7099 q^{24} -3.77149 q^{25} -1.67577 q^{26} +5.64444 q^{27} +12.6993 q^{28} +1.38841 q^{29} +4.55158 q^{30} -7.34987 q^{31} +29.7512 q^{32} +0.841374 q^{33} +5.27177 q^{34} -2.41618 q^{35} -4.92316 q^{36} -4.17318 q^{37} -13.6304 q^{38} +0.879365 q^{39} -11.8617 q^{40} -6.54244 q^{41} -8.95188 q^{42} +11.3937 q^{43} -3.33899 q^{44} +0.936683 q^{45} -10.9444 q^{46} -6.85170 q^{47} -26.8437 q^{48} -2.24794 q^{49} -10.5505 q^{50} -2.76638 q^{51} -3.48976 q^{52} +8.69899 q^{53} +15.7899 q^{54} +0.635278 q^{55} +23.3292 q^{56} +7.15259 q^{57} +3.88399 q^{58} +12.6730 q^{59} +9.47859 q^{60} -8.34230 q^{61} -20.5607 q^{62} -1.84223 q^{63} +46.6540 q^{64} +0.663963 q^{65} +2.35368 q^{66} -14.7226 q^{67} +10.9784 q^{68} +5.74312 q^{69} -6.75910 q^{70} +13.6342 q^{71} -9.04402 q^{72} -0.128463 q^{73} -11.6742 q^{74} +5.53640 q^{75} -28.3850 q^{76} -1.24944 q^{77} +2.45996 q^{78} -0.145184 q^{79} -20.2683 q^{80} -5.75055 q^{81} -18.3020 q^{82} +12.1850 q^{83} -18.6421 q^{84} -2.08875 q^{85} +31.8732 q^{86} -2.03814 q^{87} -6.13384 q^{88} +1.68716 q^{89} +2.62030 q^{90} -1.30586 q^{91} -22.7916 q^{92} +10.7893 q^{93} -19.1671 q^{94} +5.40055 q^{95} -43.6736 q^{96} -5.04226 q^{97} -6.28845 q^{98} +0.484371 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9}+O(q^{10}) $ 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9} - 6 q^{10} + 39 q^{11} + 4 q^{12} - 6 q^{13} + 11 q^{14} + 12 q^{15} + 23 q^{16} + q^{17} + 7 q^{19} + 8 q^{20} - 3 q^{21} - q^{22} + 8 q^{23} - 21 q^{24} + 14 q^{25} + q^{26} + 9 q^{27} - 23 q^{28} + 9 q^{29} - 27 q^{30} - 2 q^{31} + 23 q^{32} - 5 q^{33} - 12 q^{34} + 16 q^{35} + 10 q^{36} - 7 q^{37} - 8 q^{38} - 39 q^{40} + 3 q^{41} - 30 q^{42} + q^{43} + 56 q^{44} - 21 q^{45} - q^{46} + 16 q^{47} - 31 q^{48} + 6 q^{49} - 5 q^{50} + 29 q^{51} - 37 q^{52} + 27 q^{53} - 36 q^{54} - 16 q^{55} + 14 q^{56} - 21 q^{57} - 44 q^{58} + 74 q^{59} - 27 q^{60} - 30 q^{61} - 18 q^{62} - 9 q^{63} - 17 q^{64} - 3 q^{65} - 66 q^{66} + 9 q^{67} - 51 q^{68} - 23 q^{69} - 77 q^{70} + 70 q^{71} - 55 q^{72} - 38 q^{73} + 26 q^{74} + 22 q^{75} - 50 q^{76} - 38 q^{77} - 75 q^{78} + 7 q^{79} - 28 q^{80} + 5 q^{81} - 56 q^{82} + 47 q^{83} - 69 q^{84} - 49 q^{85} + 17 q^{86} - 37 q^{87} - 30 q^{88} + 23 q^{89} - 64 q^{90} + 6 q^{91} + 17 q^{92} - 31 q^{93} - 40 q^{94} - 11 q^{95} - 49 q^{96} - 14 q^{97} + 5 q^{98} + 79 q^{99}+O(q^{100}) \) 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9 - 6 * q^10 + 39 * q^11 + 4 * q^12 - 6 * q^13 + 11 * q^14 + 12 * q^15 + 23 * q^16 + q^17 + 7 * q^19 + 8 * q^20 - 3 * q^21 - q^22 + 8 * q^23 - 21 * q^24 + 14 * q^25 + q^26 + 9 * q^27 - 23 * q^28 + 9 * q^29 - 27 * q^30 - 2 * q^31 + 23 * q^32 - 5 * q^33 - 12 * q^34 + 16 * q^35 + 10 * q^36 - 7 * q^37 - 8 * q^38 - 39 * q^40 + 3 * q^41 - 30 * q^42 + q^43 + 56 * q^44 - 21 * q^45 - q^46 + 16 * q^47 - 31 * q^48 + 6 * q^49 - 5 * q^50 + 29 * q^51 - 37 * q^52 + 27 * q^53 - 36 * q^54 - 16 * q^55 + 14 * q^56 - 21 * q^57 - 44 * q^58 + 74 * q^59 - 27 * q^60 - 30 * q^61 - 18 * q^62 - 9 * q^63 - 17 * q^64 - 3 * q^65 - 66 * q^66 + 9 * q^67 - 51 * q^68 - 23 * q^69 - 77 * q^70 + 70 * q^71 - 55 * q^72 - 38 * q^73 + 26 * q^74 + 22 * q^75 - 50 * q^76 - 38 * q^77 - 75 * q^78 + 7 * q^79 - 28 * q^80 + 5 * q^81 - 56 * q^82 + 47 * q^83 - 69 * q^84 - 49 * q^85 + 17 * q^86 - 37 * q^87 - 30 * q^88 + 23 * q^89 - 64 * q^90 + 6 * q^91 + 17 * q^92 - 31 * q^93 - 40 * q^94 - 11 * q^95 - 49 * q^96 - 14 * q^97 + 5 * q^98 + 79 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.79743	1.97808	0.989040	−	0.147649i	$-0.0471707\pi$
$2$	2.79743	1.97808	0.989040	+	0.147649i	$0.0471707\pi$
$3$	−1.46796	−0.847528	−0.423764	−	0.905773i	$-0.639291\pi$
$3$	−1.46796	−0.847528	−0.423764	+	0.905773i	$0.639291\pi$
$4$	5.82560	2.91280
$5$	−1.10838	−0.495683	−0.247841	−	0.968801i	$-0.579721\pi$
$5$	−1.10838	−0.495683	−0.247841	+	0.968801i	$0.579721\pi$
$6$	−4.10651	−1.67648
$7$	2.17992	0.823933	0.411967	−	0.911199i	$-0.364842\pi$
$7$	2.17992	0.823933	0.411967	+	0.911199i	$0.364842\pi$
$8$	10.7018	3.78367
$9$	−0.845091	−0.281697
$10$	−3.10061	−0.980500
$11$	−0.573158	−0.172814	−0.0864069	−	0.996260i	$-0.527538\pi$
$11$	−0.573158	−0.172814	−0.0864069	+	0.996260i	$0.527538\pi$
$12$	−8.55175	−2.46868
$13$	−0.599039	−0.166143	−0.0830717	−	0.996544i	$-0.526473\pi$
$13$	−0.599039	−0.166143	−0.0830717	+	0.996544i	$0.526473\pi$
$14$	6.09817	1.62981
$15$	1.62706	0.420105
$16$	18.2864	4.57160
$17$	1.88451	0.457060	0.228530	−	0.973537i	$-0.426608\pi$
$17$	1.88451	0.457060	0.228530	+	0.973537i	$0.426608\pi$
$18$	−2.36408	−0.557219
$19$	−4.87246	−1.11782	−0.558910	−	0.829228i	$-0.688780\pi$
$19$	−4.87246	−1.11782	−0.558910	+	0.829228i	$0.688780\pi$
$20$	−6.45698	−1.44382
$21$	−3.20004	−0.698306
$22$	−1.60337	−0.341839
$23$	−3.91231	−0.815774	−0.407887	−	0.913032i	$-0.633734\pi$
$23$	−3.91231	−0.815774	−0.407887	+	0.913032i	$0.633734\pi$
$24$	−15.7099	−3.20676
$25$	−3.77149	−0.754298
$26$	−1.67577	−0.328645
$27$	5.64444	1.08627
$28$	12.6993	2.39995
$29$	1.38841	0.257822	0.128911	−	0.991656i	$-0.458852\pi$
$29$	1.38841	0.257822	0.128911	+	0.991656i	$0.458852\pi$
$30$	4.55158	0.831001
$31$	−7.34987	−1.32008	−0.660038	−	0.751232i	$-0.729460\pi$
$31$	−7.34987	−1.32008	−0.660038	+	0.751232i	$0.729460\pi$
$32$	29.7512	5.25931
$33$	0.841374	0.146464
$34$	5.27177	0.904102
$35$	−2.41618	−0.408410
$36$	−4.92316	−0.820527
$37$	−4.17318	−0.686067	−0.343034	−	0.939323i	$-0.611454\pi$
$37$	−4.17318	−0.686067	−0.343034	+	0.939323i	$0.611454\pi$
$38$	−13.6304	−2.21114
$39$	0.879365	0.140811
$40$	−11.8617	−1.87550
$41$	−6.54244	−1.02176	−0.510879	−	0.859653i	$-0.670680\pi$
$41$	−6.54244	−1.02176	−0.510879	+	0.859653i	$0.670680\pi$
$42$	−8.95188	−1.38130
$43$	11.3937	1.73753	0.868765	−	0.495224i	$-0.164914\pi$
$43$	11.3937	1.73753	0.868765	+	0.495224i	$0.164914\pi$
$44$	−3.33899	−0.503372
$45$	0.936683	0.139632
$46$	−10.9444	−1.61367
$47$	−6.85170	−0.999423	−0.499712	−	0.866192i	$-0.666561\pi$
$47$	−6.85170	−0.999423	−0.499712	+	0.866192i	$0.666561\pi$
$48$	−26.8437	−3.87455
$49$	−2.24794	−0.321134
$50$	−10.5505	−1.49206
$51$	−2.76638	−0.387371
$52$	−3.48976	−0.483942
$53$	8.69899	1.19490	0.597449	−	0.801907i	$-0.296181\pi$
$53$	8.69899	1.19490	0.597449	+	0.801907i	$0.296181\pi$
$54$	15.7899	2.14874
$55$	0.635278	0.0856608
$56$	23.3292	3.11749
$57$	7.15259	0.947383
$58$	3.88399	0.509993
$59$	12.6730	1.64989	0.824944	−	0.565215i	$-0.191207\pi$
$59$	12.6730	1.64989	0.824944	+	0.565215i	$0.191207\pi$
$60$	9.47859	1.22368
$61$	−8.34230	−1.06812	−0.534061	−	0.845446i	$-0.679335\pi$
$61$	−8.34230	−1.06812	−0.534061	+	0.845446i	$0.679335\pi$
$62$	−20.5607	−2.61121
$63$	−1.84223	−0.232100
$64$	46.6540	5.83175
$65$	0.663963	0.0823545
$66$	2.35368	0.289718
$67$	−14.7226	−1.79865	−0.899325	−	0.437280i	$-0.855942\pi$
$67$	−14.7226	−1.79865	−0.899325	+	0.437280i	$0.855942\pi$
$68$	10.9784	1.33133
$69$	5.74312	0.691391
$70$	−6.75910	−0.807867
$71$	13.6342	1.61808	0.809039	−	0.587755i	$-0.199988\pi$
$71$	13.6342	1.61808	0.809039	+	0.587755i	$0.199988\pi$
$72$	−9.04402	−1.06585
$73$	−0.128463	−0.0150355	−0.00751773	−	0.999972i	$-0.502393\pi$
$73$	−0.128463	−0.0150355	−0.00751773	+	0.999972i	$0.502393\pi$
$74$	−11.6742	−1.35710
$75$	5.53640	0.639289
$76$	−28.3850	−3.25598
$77$	−1.24944	−0.142387
$78$	2.45996	0.278536
$79$	−0.145184	−0.0163345	−0.00816723	−	0.999967i	$-0.502600\pi$
$79$	−0.145184	−0.0163345	−0.00816723	+	0.999967i	$0.502600\pi$
$80$	−20.2683	−2.26606
$81$	−5.75055	−0.638950
$82$	−18.3020	−2.02112
$83$	12.1850	1.33748	0.668741	−	0.743496i	$-0.266834\pi$
$83$	12.1850	1.33748	0.668741	+	0.743496i	$0.266834\pi$
$84$	−18.6421	−2.03402
$85$	−2.08875	−0.226557
$86$	31.8732	3.43697
$87$	−2.03814	−0.218511
$88$	−6.13384	−0.653870
$89$	1.68716	0.178838	0.0894191	−	0.995994i	$-0.471499\pi$
$89$	1.68716	0.178838	0.0894191	+	0.995994i	$0.471499\pi$
$90$	2.62030	0.276204
$91$	−1.30586	−0.136891
$92$	−22.7916	−2.37618
$93$	10.7893	1.11880
$94$	−19.1671	−1.97694
$95$	5.40055	0.554084
$96$	−43.6736	−4.45741
$97$	−5.04226	−0.511964	−0.255982	−	0.966682i	$-0.582399\pi$
$97$	−5.04226	−0.511964	−0.255982	+	0.966682i	$0.582399\pi$
$98$	−6.28845	−0.635229
$99$	0.484371	0.0486811
$100$	−21.9712	−2.19712
$101$	10.5330	1.04807	0.524035	−	0.851697i	$-0.324426\pi$
$101$	10.5330	1.04807	0.524035	+	0.851697i	$0.324426\pi$
$102$	−7.73876	−0.766251
$103$	13.6825	1.34818	0.674091	−	0.738649i	$-0.264536\pi$
$103$	13.6825	1.34818	0.674091	+	0.738649i	$0.264536\pi$
$104$	−6.41081	−0.628632
$105$	3.54686	0.346138
$106$	24.3348	2.36360
$107$	4.50881	0.435883	0.217942	−	0.975962i	$-0.430066\pi$
$107$	4.50881	0.435883	0.217942	+	0.975962i	$0.430066\pi$
$108$	32.8823	3.16410
$109$	12.3352	1.18150	0.590751	−	0.806854i	$-0.298832\pi$
$109$	12.3352	1.18150	0.590751	+	0.806854i	$0.298832\pi$
$110$	1.77714	0.169444
$111$	6.12607	0.581461
$112$	39.8629	3.76669
$113$	−14.9643	−1.40772	−0.703861	−	0.710337i	$-0.748542\pi$
$113$	−14.9643	−1.40772	−0.703861	+	0.710337i	$0.748542\pi$
$114$	20.0088	1.87400
$115$	4.33633	0.404365
$116$	8.08834	0.750984
$117$	0.506242	0.0468021
$118$	35.4519	3.26361
$119$	4.10808	0.376587
$120$	17.4125	1.58954
$121$	−10.6715	−0.970135
$122$	−23.3370	−2.11283
$123$	9.60404	0.865968
$124$	−42.8174	−3.84511
$125$	9.72215	0.869576
$126$	−5.15351	−0.459111
$127$	9.74695	0.864902	0.432451	−	0.901657i	$-0.357649\pi$
$127$	9.74695	0.864902	0.432451	+	0.901657i	$0.357649\pi$
$128$	71.0087	6.27634
$129$	−16.7256	−1.47260
$130$	1.85739	0.162904
$131$	−3.30433	−0.288701	−0.144350	−	0.989527i	$-0.546109\pi$
$131$	−3.30433	−0.288701	−0.144350	+	0.989527i	$0.546109\pi$
$132$	4.90151	0.426621
$133$	−10.6216	−0.921009
$134$	−41.1854	−3.55787
$135$	−6.25619	−0.538447
$136$	20.1677	1.72936
$137$	−2.64519	−0.225994	−0.112997	−	0.993595i	$-0.536045\pi$
$137$	−2.64519	−0.225994	−0.112997	+	0.993595i	$0.536045\pi$
$138$	16.0660	1.36763
$139$	16.1500	1.36983	0.684914	−	0.728624i	$-0.259840\pi$
$139$	16.1500	1.36983	0.684914	+	0.728624i	$0.259840\pi$
$140$	−14.0757	−1.18961
$141$	10.0580	0.847039
$142$	38.1406	3.20069
$143$	0.343344	0.0287119
$144$	−15.4537	−1.28781
$145$	−1.53889	−0.127798
$146$	−0.359366	−0.0297413
$147$	3.29989	0.272170
$148$	−24.3113	−1.99838
$149$	10.7168	0.877954	0.438977	−	0.898498i	$-0.355341\pi$
$149$	10.7168	0.877954	0.438977	+	0.898498i	$0.355341\pi$
$150$	15.4877	1.26456
$151$	−0.815276	−0.0663462	−0.0331731	−	0.999450i	$-0.510561\pi$
$151$	−0.815276	−0.0663462	−0.0331731	+	0.999450i	$0.510561\pi$
$152$	−52.1443	−4.22946
$153$	−1.59258	−0.128753
$154$	−3.49522	−0.281653
$155$	8.14645	0.654339
$156$	5.12283	0.410155
$157$	−0.923595	−0.0737109	−0.0368554	−	0.999321i	$-0.511734\pi$
$157$	−0.923595	−0.0737109	−0.0368554	+	0.999321i	$0.511734\pi$
$158$	−0.406141	−0.0323108
$159$	−12.7698	−1.01271
$160$	−32.9756	−2.60695
$161$	−8.52854	−0.672143
$162$	−16.0867	−1.26389
$163$	16.9658	1.32887	0.664433	−	0.747348i	$-0.268673\pi$
$163$	16.9658	1.32887	0.664433	+	0.747348i	$0.268673\pi$
$164$	−38.1136	−2.97617
$165$	−0.932563	−0.0725999
$166$	34.0867	2.64564
$167$	−3.29071	−0.254643	−0.127322	−	0.991861i	$-0.540638\pi$
$167$	−3.29071	−0.254643	−0.127322	+	0.991861i	$0.540638\pi$
$168$	−34.2463	−2.64216
$169$	−12.6412	−0.972396
$170$	−5.84313	−0.448148
$171$	4.11768	0.314887
$172$	66.3754	5.06108
$173$	−4.18290	−0.318020	−0.159010	−	0.987277i	$-0.550830\pi$
$173$	−4.18290	−0.318020	−0.159010	+	0.987277i	$0.550830\pi$
$174$	−5.70154	−0.432233
$175$	−8.22156	−0.621491
$176$	−10.4810	−0.790035
$177$	−18.6035	−1.39833
$178$	4.71970	0.353756
$179$	8.96734	0.670251	0.335125	−	0.942174i	$-0.391221\pi$
$179$	8.96734	0.670251	0.335125	+	0.942174i	$0.391221\pi$
$180$	5.45674	0.406721
$181$	−19.1076	−1.42026	−0.710128	−	0.704073i	$-0.751363\pi$
$181$	−19.1076	−1.42026	−0.710128	+	0.704073i	$0.751363\pi$
$182$	−3.65304	−0.270781
$183$	12.2462	0.905262
$184$	−41.8689	−3.08662
$185$	4.62548	0.340072
$186$	30.1823	2.21308
$187$	−1.08012	−0.0789863
$188$	−39.9152	−2.91112
$189$	12.3044	0.895017
$190$	15.1076	1.09602
$191$	−13.5446	−0.980055	−0.490027	−	0.871707i	$-0.663013\pi$
$191$	−13.5446	−0.980055	−0.490027	+	0.871707i	$0.663013\pi$
$192$	−68.4862	−4.94256
$193$	−4.94261	−0.355777	−0.177888	−	0.984051i	$-0.556927\pi$
$193$	−4.94261	−0.355777	−0.177888	+	0.984051i	$0.556927\pi$
$194$	−14.1054	−1.01271
$195$	−0.974672	−0.0697977
$196$	−13.0956	−0.935399
$197$	−22.7301	−1.61945	−0.809726	−	0.586808i	$-0.800385\pi$
$197$	−22.7301	−1.61945	−0.809726	+	0.586808i	$0.800385\pi$
$198$	1.35499	0.0962951
$199$	9.54730	0.676790	0.338395	−	0.941004i	$-0.390116\pi$
$199$	9.54730	0.676790	0.338395	+	0.941004i	$0.390116\pi$
$200$	−40.3619	−2.85401
$201$	21.6122	1.52441
$202$	29.4652	2.07317
$203$	3.02664	0.212428
$204$	−16.1158	−1.12833
$205$	7.25151	0.506468
$206$	38.2759	2.66681
$207$	3.30626	0.229801
$208$	−10.9543	−0.759541
$209$	2.79269	0.193175
$210$	9.92209	0.684689
$211$	−24.1597	−1.66322	−0.831610	−	0.555360i	$-0.812580\pi$
$211$	−24.1597	−1.66322	−0.831610	+	0.555360i	$0.812580\pi$
$212$	50.6768	3.48050
$213$	−20.0144	−1.37137
$214$	12.6131	0.862212
$215$	−12.6286	−0.861264
$216$	60.4059	4.11010
$217$	−16.0221	−1.08765
$218$	34.5069	2.33710
$219$	0.188579	0.0127430
$220$	3.70087	0.249513
$221$	−1.12889	−0.0759376
$222$	17.1372	1.15018
$223$	−21.8688	−1.46444	−0.732221	−	0.681067i	$-0.761516\pi$
$223$	−21.8688	−1.46444	−0.732221	+	0.681067i	$0.761516\pi$
$224$	64.8552	4.33332
$225$	3.18726	0.212484
$226$	−41.8615	−2.78459
$227$	6.12285	0.406388	0.203194	−	0.979139i	$-0.434868\pi$
$227$	6.12285	0.406388	0.203194	+	0.979139i	$0.434868\pi$
$228$	41.6681	2.75954
$229$	9.64873	0.637606	0.318803	−	0.947821i	$-0.396719\pi$
$229$	9.64873	0.637606	0.318803	+	0.947821i	$0.396719\pi$
$230$	12.1306	0.799866
$231$	1.83413	0.120677
$232$	14.8586	0.975513
$233$	2.65485	0.173925	0.0869627	−	0.996212i	$-0.472284\pi$
$233$	2.65485	0.173925	0.0869627	+	0.996212i	$0.472284\pi$
$234$	1.41618	0.0925783
$235$	7.59429	0.495397
$236$	73.8279	4.80579
$237$	0.213124	0.0138439
$238$	11.4921	0.744920
$239$	15.7156	1.01656	0.508280	−	0.861192i	$-0.330282\pi$
$239$	15.7156	1.01656	0.508280	+	0.861192i	$0.330282\pi$
$240$	29.7530	1.92055
$241$	27.4775	1.76998	0.884992	−	0.465607i	$-0.154164\pi$
$241$	27.4775	1.76998	0.884992	+	0.465607i	$0.154164\pi$
$242$	−29.8527	−1.91900
$243$	−8.49175	−0.544746
$244$	−48.5989	−3.11122
$245$	2.49157	0.159181
$246$	26.8666	1.71295
$247$	2.91880	0.185718
$248$	−78.6571	−4.99473
$249$	−17.8871	−1.13355
$250$	27.1970	1.72009
$251$	5.86761	0.370360	0.185180	−	0.982705i	$-0.440713\pi$
$251$	5.86761	0.370360	0.185180	+	0.982705i	$0.440713\pi$
$252$	−10.7321	−0.676059
$253$	2.24237	0.140977
$254$	27.2664	1.71084
$255$	3.06621	0.192013
$256$	105.334	6.58336
$257$	−15.7328	−0.981382	−0.490691	−	0.871334i	$-0.663256\pi$
$257$	−15.7328	−0.981382	−0.490691	+	0.871334i	$0.663256\pi$
$258$	−46.7886	−2.91293
$259$	−9.09721	−0.565273
$260$	3.86798	0.239882
$261$	−1.17334	−0.0726277
$262$	−9.24363	−0.571074
$263$	−1.87628	−0.115696	−0.0578481	−	0.998325i	$-0.518424\pi$
$263$	−1.87628	−0.115696	−0.0578481	+	0.998325i	$0.518424\pi$
$264$	9.00424	0.554173
$265$	−9.64179	−0.592291
$266$	−29.7131	−1.82183
$267$	−2.47668	−0.151570
$268$	−85.7679	−5.23911
$269$	−13.6310	−0.831094	−0.415547	−	0.909572i	$-0.636410\pi$
$269$	−13.6310	−0.831094	−0.415547	+	0.909572i	$0.636410\pi$
$270$	−17.5012	−1.06509
$271$	31.0139	1.88396	0.941979	−	0.335672i	$-0.108963\pi$
$271$	31.0139	1.88396	0.941979	+	0.335672i	$0.108963\pi$
$272$	34.4609	2.08950
$273$	1.91695	0.116019
$274$	−7.39974	−0.447034
$275$	2.16166	0.130353
$276$	33.4571	2.01388
$277$	−19.3939	−1.16527	−0.582634	−	0.812734i	$-0.697978\pi$
$277$	−19.3939	−1.16527	−0.582634	+	0.812734i	$0.697978\pi$
$278$	45.1785	2.70963
$279$	6.21131	0.371861
$280$	−25.8576	−1.54529
$281$	−9.98080	−0.595404	−0.297702	−	0.954659i	$-0.596220\pi$
$281$	−9.98080	−0.595404	−0.297702	+	0.954659i	$0.596220\pi$
$282$	28.1366	1.67551
$283$	−14.4905	−0.861370	−0.430685	−	0.902502i	$-0.641728\pi$
$283$	−14.4905	−0.861370	−0.430685	+	0.902502i	$0.641728\pi$
$284$	79.4271	4.71313
$285$	−7.92779	−0.469602
$286$	0.960480	0.0567944
$287$	−14.2620	−0.841860
$288$	−25.1425	−1.48153
$289$	−13.4486	−0.791096
$290$	−4.30494	−0.252795
$291$	7.40184	0.433904
$292$	−0.748373	−0.0437952
$293$	−1.83886	−0.107427	−0.0537136	−	0.998556i	$-0.517106\pi$
$293$	−1.83886	−0.107427	−0.0537136	+	0.998556i	$0.517106\pi$
$294$	9.23119	0.538374
$295$	−14.0465	−0.817821
$296$	−44.6607	−2.59585
$297$	−3.23516	−0.187723
$298$	29.9794	1.73666
$299$	2.34363	0.135535
$300$	32.2529	1.86212
$301$	24.8375	1.43161
$302$	−2.28067	−0.131238
$303$	−15.4620	−0.888268
$304$	−89.0998	−5.11022
$305$	9.24644	0.529450
$306$	−4.45513	−0.254683
$307$	15.3227	0.874511	0.437256	−	0.899337i	$-0.355950\pi$
$307$	15.3227	0.874511	0.437256	+	0.899337i	$0.355950\pi$
$308$	−7.27874	−0.414745
$309$	−20.0854	−1.14262
$310$	22.7891	1.29433
$311$	8.09149	0.458826	0.229413	−	0.973329i	$-0.426319\pi$
$311$	8.09149	0.458826	0.229413	+	0.973329i	$0.426319\pi$
$312$	9.41082	0.532783
$313$	17.1789	0.971010	0.485505	−	0.874234i	$-0.338636\pi$
$313$	17.1789	0.971010	0.485505	+	0.874234i	$0.338636\pi$
$314$	−2.58369	−0.145806
$315$	2.04190	0.115048
$316$	−0.845782	−0.0475790
$317$	0.545214	0.0306223	0.0153111	−	0.999883i	$-0.495126\pi$
$317$	0.545214	0.0306223	0.0153111	+	0.999883i	$0.495126\pi$
$318$	−35.7225	−2.00322
$319$	−0.795781	−0.0445552
$320$	−51.7104	−2.89070
$321$	−6.61876	−0.369423
$322$	−23.8580	−1.32955
$323$	−9.18220	−0.510911
$324$	−33.5004	−1.86113
$325$	2.25927	0.125322
$326$	47.4606	2.62860
$327$	−18.1076	−1.00136
$328$	−70.0161	−3.86599
$329$	−14.9362	−0.823458
$330$	−2.60878	−0.143608
$331$	−25.6441	−1.40952	−0.704762	−	0.709443i	$-0.748946\pi$
$331$	−25.6441	−1.40952	−0.704762	+	0.709443i	$0.748946\pi$
$332$	70.9851	3.89581
$333$	3.52672	0.193263
$334$	−9.20553	−0.503704
$335$	16.3182	0.891560
$336$	−58.5172	−3.19237
$337$	7.40130	0.403174	0.201587	−	0.979471i	$-0.435390\pi$
$337$	7.40130	0.403174	0.201587	+	0.979471i	$0.435390\pi$
$338$	−35.3627	−1.92348
$339$	21.9670	1.19308
$340$	−12.1682	−0.659915
$341$	4.21264	0.228127
$342$	11.5189	0.622871
$343$	−20.1598	−1.08853
$344$	121.934	6.57424
$345$	−6.36557	−0.342711
$346$	−11.7014	−0.629069
$347$	−14.8051	−0.794780	−0.397390	−	0.917650i	$-0.630084\pi$
$347$	−14.8051	−0.794780	−0.397390	+	0.917650i	$0.630084\pi$
$348$	−11.8734	−0.636480
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−22.9992	−1.22936
$351$	−3.38124	−0.180477
$352$	−17.0521	−0.908882
$353$	31.8145	1.69331	0.846657	−	0.532139i	$-0.178612\pi$
$353$	31.8145	1.69331	0.846657	+	0.532139i	$0.178612\pi$
$354$	−52.0419	−2.76600
$355$	−15.1118	−0.802053
$356$	9.82870	0.520920
$357$	−6.03050	−0.319168
$358$	25.0855	1.32581
$359$	14.5757	0.769275	0.384638	−	0.923068i	$-0.374326\pi$
$359$	14.5757	0.769275	0.384638	+	0.923068i	$0.374326\pi$
$360$	10.0242	0.528323
$361$	4.74091	0.249522
$362$	−53.4521	−2.80938
$363$	15.6653	0.822216
$364$	−7.60740	−0.398736
$365$	0.142386	0.00745282
$366$	34.2577	1.79068
$367$	−31.4490	−1.64162	−0.820812	−	0.571198i	$-0.806479\pi$
$367$	−31.4490	−1.64162	−0.820812	+	0.571198i	$0.806479\pi$
$368$	−71.5421	−3.72939
$369$	5.52896	0.287826
$370$	12.9394	0.672689
$371$	18.9631	0.984516
$372$	62.8542	3.25884
$373$	8.31230	0.430395	0.215197	−	0.976571i	$-0.430961\pi$
$373$	8.31230	0.430395	0.215197	+	0.976571i	$0.430961\pi$
$374$	−3.02156	−0.156241
$375$	−14.2717	−0.736989
$376$	−73.3257	−3.78149
$377$	−0.831714	−0.0428355
$378$	34.4208	1.77041
$379$	−9.27521	−0.476436	−0.238218	−	0.971212i	$-0.576563\pi$
$379$	−9.27521	−0.476436	−0.238218	+	0.971212i	$0.576563\pi$
$380$	31.4614	1.61394
$381$	−14.3081	−0.733028
$382$	−37.8901	−1.93863
$383$	4.38794	0.224213	0.112107	−	0.993696i	$-0.464240\pi$
$383$	4.38794	0.224213	0.112107	+	0.993696i	$0.464240\pi$
$384$	−104.238	−5.31937
$385$	1.38486	0.0705788
$386$	−13.8266	−0.703755
$387$	−9.62876	−0.489457
$388$	−29.3742	−1.49125
$389$	−0.772497	−0.0391671	−0.0195836	−	0.999808i	$-0.506234\pi$
$389$	−0.772497	−0.0391671	−0.0195836	+	0.999808i	$0.506234\pi$
$390$	−2.72657	−0.138065
$391$	−7.37279	−0.372858
$392$	−24.0571	−1.21506
$393$	4.85063	0.244682
$394$	−63.5858	−3.20341
$395$	0.160919	0.00809671
$396$	2.82175	0.141798
$397$	−13.2500	−0.664996	−0.332498	−	0.943104i	$-0.607892\pi$
$397$	−13.2500	−0.664996	−0.332498	+	0.943104i	$0.607892\pi$
$398$	26.7079	1.33875
$399$	15.5921	0.780581
$400$	−68.9670	−3.44835
$401$	−2.15494	−0.107612	−0.0538062	−	0.998551i	$-0.517135\pi$
$401$	−2.15494	−0.107612	−0.0538062	+	0.998551i	$0.517135\pi$
$402$	60.4585	3.01540
$403$	4.40286	0.219322
$404$	61.3609	3.05282
$405$	6.37380	0.316716
$406$	8.46679	0.420200
$407$	2.39189	0.118562
$408$	−29.6054	−1.46568
$409$	21.8092	1.07840	0.539198	−	0.842179i	$-0.318727\pi$
$409$	21.8092	1.07840	0.539198	+	0.842179i	$0.318727\pi$
$410$	20.2856	1.00183
$411$	3.88304	0.191536
$412$	79.7090	3.92698
$413$	27.6262	1.35940
$414$	9.24902	0.454565
$415$	−13.5057	−0.662967
$416$	−17.8221	−0.873801
$417$	−23.7076	−1.16097
$418$	7.81236	0.382115
$419$	34.4157	1.68132	0.840659	−	0.541565i	$-0.182168\pi$
$419$	34.4157	1.68132	0.840659	+	0.541565i	$0.182168\pi$
$420$	20.6626	1.00823
$421$	−26.9155	−1.31178	−0.655891	−	0.754855i	$-0.727707\pi$
$421$	−26.9155	−1.31178	−0.655891	+	0.754855i	$0.727707\pi$
$422$	−67.5849	−3.28998
$423$	5.79031	0.281535
$424$	93.0951	4.52110
$425$	−7.10741	−0.344760
$426$	−55.9889	−2.71267
$427$	−18.1856	−0.880061
$428$	26.2665	1.26964
$429$	−0.504016	−0.0243341
$430$	−35.3276	−1.70365
$431$	19.6144	0.944792	0.472396	−	0.881386i	$-0.343389\pi$
$431$	19.6144	0.944792	0.472396	+	0.881386i	$0.343389\pi$
$432$	103.216	4.96600
$433$	−6.54460	−0.314513	−0.157257	−	0.987558i	$-0.550265\pi$
$433$	−6.54460	−0.314513	−0.157257	+	0.987558i	$0.550265\pi$
$434$	−44.8208	−2.15147
$435$	2.25903	0.108312
$436$	71.8601	3.44148
$437$	19.0626	0.911888
$438$	0.527535	0.0252066
$439$	−21.6886	−1.03514	−0.517571	−	0.855640i	$-0.673164\pi$
$439$	−21.6886	−1.03514	−0.517571	+	0.855640i	$0.673164\pi$
$440$	6.79863	0.324112
$441$	1.89971	0.0904626
$442$	−3.15800	−0.150211
$443$	−40.9397	−1.94510	−0.972552	−	0.232684i	$-0.925249\pi$
$443$	−40.9397	−1.94510	−0.972552	+	0.232684i	$0.925249\pi$
$444$	35.6880	1.69368
$445$	−1.87001	−0.0886471
$446$	−61.1763	−2.89678
$447$	−15.7318	−0.744090
$448$	101.702	4.80497
$449$	11.5831	0.546640	0.273320	−	0.961923i	$-0.411878\pi$
$449$	11.5831	0.546640	0.273320	+	0.961923i	$0.411878\pi$
$450$	8.91611	0.420310
$451$	3.74985	0.176574
$452$	−87.1760	−4.10041
$453$	1.19679	0.0562302
$454$	17.1282	0.803868
$455$	1.44739	0.0678546
$456$	76.5458	3.58458
$457$	10.2261	0.478356	0.239178	−	0.970976i	$-0.423122\pi$
$457$	10.2261	0.478356	0.239178	+	0.970976i	$0.423122\pi$
$458$	26.9916	1.26124
$459$	10.6370	0.496493
$460$	25.2617	1.17783
$461$	6.92012	0.322302	0.161151	−	0.986930i	$-0.448479\pi$
$461$	6.92012	0.322302	0.161151	+	0.986930i	$0.448479\pi$
$462$	5.13084	0.238708
$463$	−33.2472	−1.54513	−0.772565	−	0.634936i	$-0.781026\pi$
$463$	−33.2472	−1.54513	−0.772565	+	0.634936i	$0.781026\pi$
$464$	25.3891	1.17866
$465$	−11.9587	−0.554570
$466$	7.42676	0.344038
$467$	6.16913	0.285473	0.142737	−	0.989761i	$-0.454410\pi$
$467$	6.16913	0.285473	0.142737	+	0.989761i	$0.454410\pi$
$468$	2.94916	0.136325
$469$	−32.0941	−1.48197
$470$	21.2445	0.979935
$471$	1.35580	0.0624720
$472$	135.625	6.24263
$473$	−6.53042	−0.300269
$474$	0.596199	0.0273843
$475$	18.3765	0.843170
$476$	23.9320	1.09692
$477$	−7.35144	−0.336599
$478$	43.9633	2.01083
$479$	−31.4236	−1.43578	−0.717891	−	0.696155i	$-0.754893\pi$
$479$	−31.4236	−1.43578	−0.717891	+	0.696155i	$0.754893\pi$
$480$	48.4069	2.20946
$481$	2.49990	0.113986
$482$	76.8664	3.50117
$483$	12.5196	0.569660
$484$	−62.1678	−2.82581
$485$	5.58875	0.253772
$486$	−23.7551	−1.07755
$487$	7.26529	0.329222	0.164611	−	0.986359i	$-0.447363\pi$
$487$	7.26529	0.329222	0.164611	+	0.986359i	$0.447363\pi$
$488$	−89.2778	−4.04142
$489$	−24.9052	−1.12625
$490$	6.96999	0.314872
$491$	−0.997919	−0.0450355	−0.0225177	−	0.999746i	$-0.507168\pi$
$491$	−0.997919	−0.0450355	−0.0225177	+	0.999746i	$0.507168\pi$
$492$	55.9493	2.52239
$493$	2.61648	0.117840
$494$	8.16512	0.367366
$495$	−0.536868	−0.0241304
$496$	−134.403	−6.03485
$497$	29.7214	1.33319
$498$	−50.0380	−2.24226
$499$	11.2114	0.501891	0.250945	−	0.968001i	$-0.419259\pi$
$499$	11.2114	0.501891	0.250945	+	0.968001i	$0.419259\pi$
$500$	56.6373	2.53290
$501$	4.83064	0.215817
$502$	16.4142	0.732602
$503$	−6.30256	−0.281017	−0.140509	−	0.990079i	$-0.544874\pi$
$503$	−6.30256	−0.281017	−0.140509	+	0.990079i	$0.544874\pi$
$504$	−19.7153	−0.878188
$505$	−11.6745	−0.519511
$506$	6.27288	0.278863
$507$	18.5567	0.824133
$508$	56.7818	2.51928
$509$	−25.2186	−1.11779	−0.558897	−	0.829237i	$-0.688775\pi$
$509$	−25.2186	−1.11779	−0.558897	+	0.829237i	$0.688775\pi$
$510$	8.57749	0.379818
$511$	−0.280039	−0.0123882
$512$	152.646	6.74606
$513$	−27.5023	−1.21426
$514$	−44.0112	−1.94125
$515$	−15.1655	−0.668271
$516$	−97.4365	−4.28940
$517$	3.92711	0.172714
$518$	−25.4488	−1.11816
$519$	6.14034	0.269531
$520$	7.10562	0.311602
$521$	21.2566	0.931269	0.465634	−	0.884977i	$-0.345826\pi$
$521$	21.2566	0.931269	0.465634	+	0.884977i	$0.345826\pi$
$522$	−3.28232	−0.143663
$523$	20.6722	0.903932	0.451966	−	0.892035i	$-0.350723\pi$
$523$	20.6722	0.903932	0.451966	+	0.892035i	$0.350723\pi$
$524$	−19.2497	−0.840928
$525$	12.0689	0.526731
$526$	−5.24875	−0.228856
$527$	−13.8509	−0.603354
$528$	15.3857	0.669576
$529$	−7.69381	−0.334513
$530$	−26.9722	−1.17160
$531$	−10.7099	−0.464769
$532$	−61.8771	−2.68271
$533$	3.91917	0.169758
$534$	−6.92833	−0.299818
$535$	−4.99748	−0.216060
$536$	−157.559	−6.80550
$537$	−13.1637	−0.568056
$538$	−38.1316	−1.64397
$539$	1.28842	0.0554964
$540$	−36.4461	−1.56839
$541$	−20.0979	−0.864076	−0.432038	−	0.901855i	$-0.642205\pi$
$541$	−20.0979	−0.864076	−0.432038	+	0.901855i	$0.642205\pi$
$542$	86.7590	3.72662
$543$	28.0492	1.20371
$544$	56.0663	2.40382
$545$	−13.6721	−0.585650
$546$	5.36252	0.229495
$547$	9.36620	0.400470	0.200235	−	0.979748i	$-0.435829\pi$
$547$	9.36620	0.400470	0.200235	+	0.979748i	$0.435829\pi$
$548$	−15.4098	−0.658275
$549$	7.05000	0.300887
$550$	6.04709	0.257849
$551$	−6.76500	−0.288199
$552$	61.4619	2.61599
$553$	−0.316489	−0.0134585
$554$	−54.2531	−2.30499
$555$	−6.79002	−0.288220
$556$	94.0836	3.99003
$557$	13.4163	0.568469	0.284234	−	0.958755i	$-0.408261\pi$
$557$	13.4163	0.568469	0.284234	+	0.958755i	$0.408261\pi$
$558$	17.3757	0.735572
$559$	−6.82530	−0.288679
$560$	−44.1833	−1.86708
$561$	1.58558	0.0669431
$562$	−27.9205	−1.17776
$563$	−7.09924	−0.299197	−0.149599	−	0.988747i	$-0.547798\pi$
$563$	−7.09924	−0.299197	−0.149599	+	0.988747i	$0.547798\pi$
$564$	58.5940	2.46725
$565$	16.5861	0.697784
$566$	−40.5361	−1.70386
$567$	−12.5357	−0.526452
$568$	145.910	6.12227
$569$	1.57127	0.0658709	0.0329354	−	0.999457i	$-0.489514\pi$
$569$	1.57127	0.0658709	0.0329354	+	0.999457i	$0.489514\pi$
$570$	−22.1774	−0.928910
$571$	16.8599	0.705565	0.352782	−	0.935705i	$-0.385236\pi$
$571$	16.8599	0.705565	0.352782	+	0.935705i	$0.385236\pi$
$572$	2.00018	0.0836319
$573$	19.8830	0.830624
$574$	−39.8969	−1.66527
$575$	14.7553	0.615337
$576$	−39.4269	−1.64279
$577$	−6.26068	−0.260635	−0.130318	−	0.991472i	$-0.541600\pi$
$577$	−6.26068	−0.260635	−0.130318	+	0.991472i	$0.541600\pi$
$578$	−37.6216	−1.56485
$579$	7.25556	0.301531
$580$	−8.96497	−0.372250
$581$	26.5624	1.10199
$582$	20.7061	0.858296
$583$	−4.98590	−0.206495
$584$	−1.37479	−0.0568892
$585$	−0.561109	−0.0231990
$586$	−5.14407	−0.212499
$587$	27.1239	1.11952	0.559761	−	0.828654i	$-0.310893\pi$
$587$	27.1239	1.11952	0.559761	+	0.828654i	$0.310893\pi$
$588$	19.2238	0.792776
$589$	35.8120	1.47561
$590$	−39.2942	−1.61772
$591$	33.3669	1.37253
$592$	−76.3124	−3.13642
$593$	−10.6989	−0.439352	−0.219676	−	0.975573i	$-0.570500\pi$
$593$	−10.6989	−0.439352	−0.219676	+	0.975573i	$0.570500\pi$
$594$	−9.05012	−0.371331
$595$	−4.55332	−0.186668
$596$	62.4317	2.55730
$597$	−14.0151	−0.573598
$598$	6.55613	0.268100
$599$	−19.8384	−0.810575	−0.405288	−	0.914189i	$-0.632829\pi$
$599$	−19.8384	−0.810575	−0.405288	+	0.914189i	$0.632829\pi$
$600$	59.2496	2.41886
$601$	19.6559	0.801782	0.400891	−	0.916126i	$-0.368701\pi$
$601$	19.6559	0.801782	0.400891	+	0.916126i	$0.368701\pi$
$602$	69.4810	2.83184
$603$	12.4419	0.506675
$604$	−4.74947	−0.193253
$605$	11.8281	0.480880
$606$	−43.2538	−1.75707
$607$	0.968929	0.0393276	0.0196638	−	0.999807i	$-0.493740\pi$
$607$	0.968929	0.0393276	0.0196638	+	0.999807i	$0.493740\pi$
$608$	−144.962	−5.87897
$609$	−4.44298	−0.180039
$610$	25.8662	1.04729
$611$	4.10443	0.166048
$612$	−9.27774	−0.375030
$613$	19.9621	0.806263	0.403131	−	0.915142i	$-0.367922\pi$
$613$	19.9621	0.806263	0.403131	+	0.915142i	$0.367922\pi$
$614$	42.8641	1.72985
$615$	−10.6449	−0.429245
$616$	−13.3713	−0.538745
$617$	19.5678	0.787770	0.393885	−	0.919160i	$-0.371131\pi$
$617$	19.5678	0.787770	0.393885	+	0.919160i	$0.371131\pi$
$618$	−56.1876	−2.26019
$619$	24.7258	0.993814	0.496907	−	0.867804i	$-0.334469\pi$
$619$	24.7258	0.993814	0.496907	+	0.867804i	$0.334469\pi$
$620$	47.4580	1.90596
$621$	−22.0828	−0.886153
$622$	22.6353	0.907595
$623$	3.67787	0.147351
$624$	16.0804	0.643732
$625$	8.08161	0.323265
$626$	48.0568	1.92074
$627$	−4.09956	−0.163721
$628$	−5.38049	−0.214705
$629$	−7.86440	−0.313574
$630$	5.71205	0.227574
$631$	1.70139	0.0677311	0.0338656	−	0.999426i	$-0.489218\pi$
$631$	1.70139	0.0677311	0.0338656	+	0.999426i	$0.489218\pi$
$632$	−1.55373	−0.0618041
$633$	35.4654	1.40962
$634$	1.52520	0.0605733
$635$	−10.8033	−0.428717
$636$	−74.3916	−2.94982
$637$	1.34660	0.0533543
$638$	−2.22614	−0.0881337
$639$	−11.5221	−0.455808
$640$	−78.7047	−3.11108
$641$	27.3850	1.08164	0.540822	−	0.841137i	$-0.318113\pi$
$641$	27.3850	1.08164	0.540822	+	0.841137i	$0.318113\pi$
$642$	−18.5155	−0.730748
$643$	−10.6742	−0.420951	−0.210475	−	0.977599i	$-0.567501\pi$
$643$	−10.6742	−0.420951	−0.210475	+	0.977599i	$0.567501\pi$
$644$	−49.6838	−1.95782
$645$	18.5383	0.729945
$646$	−25.6865	−1.01062
$647$	12.9302	0.508339	0.254169	−	0.967160i	$-0.418198\pi$
$647$	12.9302	0.508339	0.254169	+	0.967160i	$0.418198\pi$
$648$	−61.5414	−2.41757
$649$	−7.26365	−0.285123
$650$	6.32014	0.247896
$651$	23.5199	0.921817
$652$	98.8360	3.87072
$653$	−28.2620	−1.10598	−0.552989	−	0.833188i	$-0.686513\pi$
$653$	−28.2620	−1.10598	−0.552989	+	0.833188i	$0.686513\pi$
$654$	−50.6548	−1.98076
$655$	3.66246	0.143104
$656$	−119.638	−4.67106
$657$	0.108563	0.00423544
$658$	−41.7829	−1.62887
$659$	37.0119	1.44178	0.720889	−	0.693051i	$-0.243734\pi$
$659$	37.0119	1.44178	0.720889	+	0.693051i	$0.243734\pi$
$660$	−5.43273	−0.211469
$661$	27.3554	1.06400	0.532000	−	0.846744i	$-0.321441\pi$
$661$	27.3554	1.06400	0.532000	+	0.846744i	$0.321441\pi$
$662$	−71.7374	−2.78815
$663$	1.65717	0.0643592
$664$	130.402	5.06058
$665$	11.7728	0.456528
$666$	9.86574	0.382290
$667$	−5.43191	−0.210325
$668$	−19.1704	−0.741724
$669$	32.1025	1.24115
$670$	45.6491	1.76358
$671$	4.78146	0.184586
$672$	−95.2050	−3.67261
$673$	35.2066	1.35712	0.678558	−	0.734547i	$-0.262605\pi$
$673$	35.2066	1.35712	0.678558	+	0.734547i	$0.262605\pi$
$674$	20.7046	0.797511
$675$	−21.2880	−0.819374
$676$	−73.6423	−2.83239
$677$	1.95208	0.0750246	0.0375123	−	0.999296i	$-0.488057\pi$
$677$	1.95208	0.0750246	0.0375123	+	0.999296i	$0.488057\pi$
$678$	61.4511	2.36001
$679$	−10.9917	−0.421824
$680$	−22.3535	−0.857217
$681$	−8.98811	−0.344425
$682$	11.7845	0.451254
$683$	−31.4093	−1.20184	−0.600921	−	0.799309i	$-0.705199\pi$
$683$	−31.4093	−1.20184	−0.600921	+	0.799309i	$0.705199\pi$
$684$	23.9879	0.917201
$685$	2.93188	0.112021
$686$	−56.3955	−2.15319
$687$	−14.1640	−0.540389
$688$	208.350	7.94329
$689$	−5.21103	−0.198524
$690$	−17.8072	−0.677909
$691$	−23.8364	−0.906781	−0.453390	−	0.891312i	$-0.649786\pi$
$691$	−23.8364	−0.906781	−0.453390	+	0.891312i	$0.649786\pi$
$692$	−24.3679	−0.926329
$693$	1.05589	0.0401100
$694$	−41.4162	−1.57214
$695$	−17.9004	−0.679000
$696$	−21.8118	−0.826774
$697$	−12.3293	−0.467005
$698$	2.79743	0.105884
$699$	−3.89722	−0.147407
$700$	−47.8955	−1.81028
$701$	42.1169	1.59073	0.795366	−	0.606129i	$-0.207278\pi$
$701$	42.1169	1.59073	0.795366	+	0.606129i	$0.207278\pi$
$702$	−9.45877	−0.356998
$703$	20.3337	0.766900
$704$	−26.7401	−1.00781
$705$	−11.1481	−0.419863
$706$	88.9987	3.34951
$707$	22.9611	0.863540
$708$	−108.377	−4.07304
$709$	19.5648	0.734771	0.367385	−	0.930069i	$-0.380253\pi$
$709$	19.5648	0.734771	0.367385	+	0.930069i	$0.380253\pi$
$710$	−42.2743	−1.58653
$711$	0.122694	0.00460137
$712$	18.0557	0.676665
$713$	28.7550	1.07688
$714$	−16.8699	−0.631340
$715$	−0.380556	−0.0142320
$716$	52.2401	1.95230
$717$	−23.0699	−0.861562
$718$	40.7744	1.52169
$719$	21.6529	0.807518	0.403759	−	0.914865i	$-0.367703\pi$
$719$	21.6529	0.807518	0.403759	+	0.914865i	$0.367703\pi$
$720$	17.1285	0.638343
$721$	29.8269	1.11081
$722$	13.2624	0.493574
$723$	−40.3359	−1.50011
$724$	−111.313	−4.13692
$725$	−5.23640	−0.194475
$726$	43.8226	1.62641
$727$	9.76161	0.362038	0.181019	−	0.983480i	$-0.442060\pi$
$727$	9.76161	0.362038	0.181019	+	0.983480i	$0.442060\pi$
$728$	−13.9751	−0.517950
$729$	29.7172	1.10064
$730$	0.398314	0.0147423
$731$	21.4716	0.794156
$732$	71.3412	2.63685
$733$	−46.0644	−1.70143	−0.850714	−	0.525630i	$-0.823830\pi$
$733$	−46.0644	−1.70143	−0.850714	+	0.525630i	$0.823830\pi$
$734$	−87.9763	−3.24726
$735$	−3.65753	−0.134910
$736$	−116.396	−4.29041
$737$	8.43837	0.310831
$738$	15.4669	0.569343
$739$	33.3488	1.22676	0.613378	−	0.789790i	$-0.289810\pi$
$739$	33.3488	1.22676	0.613378	+	0.789790i	$0.289810\pi$
$740$	26.9462	0.990560
$741$	−4.28468	−0.157402
$742$	53.0479	1.94745
$743$	−1.20685	−0.0442750	−0.0221375	−	0.999755i	$-0.507047\pi$
$743$	−1.20685	−0.0442750	−0.0221375	+	0.999755i	$0.507047\pi$
$744$	115.465	4.23317
$745$	−11.8783	−0.435187
$746$	23.2530	0.851355
$747$	−10.2975	−0.376764
$748$	−6.29235	−0.230071
$749$	9.82886	0.359139
$750$	−39.9241	−1.45782
$751$	−24.8113	−0.905377	−0.452688	−	0.891669i	$-0.649535\pi$
$751$	−24.8113	−0.905377	−0.452688	+	0.891669i	$0.649535\pi$
$752$	−125.293	−4.56896
$753$	−8.61342	−0.313891
$754$	−2.32666	−0.0847320
$755$	0.903636	0.0328867
$756$	71.6807	2.60700
$757$	21.4054	0.777993	0.388996	−	0.921239i	$-0.372822\pi$
$757$	21.4054	0.777993	0.388996	+	0.921239i	$0.372822\pi$
$758$	−25.9467	−0.942428
$759$	−3.29172	−0.119482
$760$	57.7957	2.09647
$761$	−15.8125	−0.573203	−0.286602	−	0.958050i	$-0.592526\pi$
$761$	−15.8125	−0.573203	−0.286602	+	0.958050i	$0.592526\pi$
$762$	−40.0260	−1.44999
$763$	26.8899	0.973478
$764$	−78.9055	−2.85470
$765$	1.76519	0.0638205
$766$	12.2749	0.443512
$767$	−7.59163	−0.274118
$768$	−154.626	−5.57958
$769$	−8.33447	−0.300549	−0.150274	−	0.988644i	$-0.548016\pi$
$769$	−8.33447	−0.300549	−0.150274	+	0.988644i	$0.548016\pi$
$770$	3.87403	0.139610
$771$	23.0951	0.831749
$772$	−28.7937	−1.03631
$773$	−40.8510	−1.46931	−0.734655	−	0.678441i	$-0.762656\pi$
$773$	−40.8510	−1.46931	−0.734655	+	0.678441i	$0.762656\pi$
$774$	−26.9357	−0.968185
$775$	27.7200	0.995731
$776$	−53.9614	−1.93710
$777$	13.3544	0.479085
$778$	−2.16100	−0.0774757
$779$	31.8778	1.14214
$780$	−5.67804	−0.203307
$781$	−7.81453	−0.279626
$782$	−20.6248	−0.737543
$783$	7.83683	0.280065
$784$	−41.1067	−1.46810
$785$	1.02369	0.0365372
$786$	13.5693	0.484001
$787$	−48.6990	−1.73593	−0.867966	−	0.496624i	$-0.834573\pi$
$787$	−48.6990	−1.73593	−0.867966	+	0.496624i	$0.834573\pi$
$788$	−132.416	−4.71714
$789$	2.75430	0.0980558
$790$	0.450159	0.0160159
$791$	−32.6210	−1.15987
$792$	5.18366	0.184193
$793$	4.99736	0.177461
$794$	−37.0658	−1.31542
$795$	14.1538	0.501983
$796$	55.6187	1.97135
$797$	−23.4748	−0.831520	−0.415760	−	0.909474i	$-0.636484\pi$
$797$	−23.4748	−0.831520	−0.415760	+	0.909474i	$0.636484\pi$
$798$	43.6177	1.54405
$799$	−12.9121	−0.456797
$800$	−112.206	−3.96709
$801$	−1.42580	−0.0503782
$802$	−6.02828	−0.212866
$803$	0.0736296	0.00259833
$804$	125.904	4.44029
$805$	9.45287	0.333170
$806$	12.3167	0.433836
$807$	20.0097	0.704375
$808$	112.722	3.96555
$809$	−21.4663	−0.754714	−0.377357	−	0.926068i	$-0.623167\pi$
$809$	−21.4663	−0.754714	−0.377357	+	0.926068i	$0.623167\pi$
$810$	17.8302	0.626490
$811$	23.2836	0.817597	0.408799	−	0.912625i	$-0.365948\pi$
$811$	23.2836	0.817597	0.408799	+	0.912625i	$0.365948\pi$
$812$	17.6320	0.618761
$813$	−45.5271	−1.59671
$814$	6.69115	0.234525
$815$	−18.8046	−0.658696
$816$	−50.5872	−1.77091
$817$	−55.5156	−1.94225
$818$	61.0097	2.13315
$819$	1.10357	0.0385618
$820$	42.2444	1.47524
$821$	24.8693	0.867946	0.433973	−	0.900926i	$-0.357111\pi$
$821$	24.8693	0.867946	0.433973	+	0.900926i	$0.357111\pi$
$822$	10.8625	0.378874
$823$	−46.0131	−1.60391	−0.801957	−	0.597381i	$-0.796208\pi$
$823$	−46.0131	−1.60391	−0.801957	+	0.597381i	$0.796208\pi$
$824$	146.428	5.10107
$825$	−3.17323	−0.110478
$826$	77.2823	2.68900
$827$	46.4481	1.61516	0.807579	−	0.589759i	$-0.200777\pi$
$827$	46.4481	1.61516	0.807579	+	0.589759i	$0.200777\pi$
$828$	19.2609	0.669364
$829$	−14.1941	−0.492983	−0.246492	−	0.969145i	$-0.579278\pi$
$829$	−14.1941	−0.492983	−0.246492	+	0.969145i	$0.579278\pi$
$830$	−37.7811	−1.31140
$831$	28.4695	0.987597
$832$	−27.9475	−0.968906
$833$	−4.23626	−0.146778
$834$	−66.3203	−2.29648
$835$	3.64736	0.126222
$836$	16.2691	0.562679
$837$	−41.4859	−1.43396
$838$	96.2755	3.32578
$839$	51.1120	1.76458	0.882292	−	0.470703i	$-0.156000\pi$
$839$	51.1120	1.76458	0.882292	+	0.470703i	$0.156000\pi$
$840$	37.9579	1.30967
$841$	−27.0723	−0.933528
$842$	−75.2942	−2.59481
$843$	14.6514	0.504622
$844$	−140.744	−4.84462
$845$	14.0112	0.482000
$846$	16.1980	0.556898
$847$	−23.2630	−0.799327
$848$	159.073	5.46259
$849$	21.2715	0.730035
$850$	−19.8825	−0.681963
$851$	16.3268	0.559675
$852$	−116.596	−3.99451
$853$	−30.2418	−1.03546	−0.517730	−	0.855544i	$-0.673223\pi$
$853$	−30.2418	−1.03546	−0.517730	+	0.855544i	$0.673223\pi$
$854$	−50.8728	−1.74083
$855$	−4.56395	−0.156084
$856$	48.2525	1.64924
$857$	−15.4763	−0.528661	−0.264330	−	0.964432i	$-0.585151\pi$
$857$	−15.4763	−0.528661	−0.264330	+	0.964432i	$0.585151\pi$
$858$	−1.40995	−0.0481348
$859$	2.01458	0.0687365	0.0343682	−	0.999409i	$-0.489058\pi$
$859$	2.01458	0.0687365	0.0343682	+	0.999409i	$0.489058\pi$
$860$	−73.5692	−2.50869
$861$	20.9361	0.713499
$862$	54.8698	1.86887
$863$	44.0696	1.50015	0.750073	−	0.661355i	$-0.230018\pi$
$863$	44.0696	1.50015	0.750073	+	0.661355i	$0.230018\pi$
$864$	167.929	5.71305
$865$	4.63625	0.157637
$866$	−18.3080	−0.622132
$867$	19.7421	0.670475
$868$	−93.3386	−3.16812
$869$	0.0832133	0.00282282
$870$	6.31948	0.214250
$871$	8.81940	0.298834
$872$	132.010	4.47041
$873$	4.26117	0.144219
$874$	53.3263	1.80379
$875$	21.1935	0.716472
$876$	1.09858	0.0371177
$877$	0.690801	0.0233267	0.0116633	−	0.999932i	$-0.496287\pi$
$877$	0.690801	0.0233267	0.0116633	+	0.999932i	$0.496287\pi$
$878$	−60.6724	−2.04759
$879$	2.69937	0.0910475
$880$	11.6169	0.391607
$881$	−55.7606	−1.87862	−0.939311	−	0.343067i	$-0.888534\pi$
$881$	−55.7606	−1.87862	−0.939311	+	0.343067i	$0.888534\pi$
$882$	5.31431	0.178942
$883$	−19.8597	−0.668331	−0.334166	−	0.942514i	$-0.608454\pi$
$883$	−19.8597	−0.668331	−0.334166	+	0.942514i	$0.608454\pi$
$884$	−6.57648	−0.221191
$885$	20.6198	0.693126
$886$	−114.526	−3.84757
$887$	5.63823	0.189313	0.0946566	−	0.995510i	$-0.469825\pi$
$887$	5.63823	0.189313	0.0946566	+	0.995510i	$0.469825\pi$
$888$	65.5601	2.20005
$889$	21.2476	0.712621
$890$	−5.23122	−0.175351
$891$	3.29597	0.110419
$892$	−127.399	−4.26562
$893$	33.3847	1.11718
$894$	−44.0086	−1.47187
$895$	−9.93923	−0.332232
$896$	154.793	5.17129
$897$	−3.44035	−0.114870
$898$	32.4029	1.08130
$899$	−10.2047	−0.340345
$900$	18.5677	0.618922
$901$	16.3933	0.546141
$902$	10.4899	0.349277
$903$	−36.4604	−1.21333
$904$	−160.145	−5.32635
$905$	21.1785	0.703996
$906$	3.34794	0.111228
$907$	−4.97575	−0.165217	−0.0826086	−	0.996582i	$-0.526325\pi$
$907$	−4.97575	−0.165217	−0.0826086	+	0.996582i	$0.526325\pi$
$908$	35.6693	1.18373
$909$	−8.90133	−0.295238
$910$	4.04896	0.134222
$911$	0.648034	0.0214703	0.0107352	−	0.999942i	$-0.496583\pi$
$911$	0.648034	0.0214703	0.0107352	+	0.999942i	$0.496583\pi$
$912$	130.795	4.33105
$913$	−6.98395	−0.231135
$914$	28.6067	0.946226
$915$	−13.5734	−0.448723
$916$	56.2096	1.85722
$917$	−7.20319	−0.237870
$918$	29.7562	0.982102
$919$	13.6717	0.450989	0.225495	−	0.974244i	$-0.427600\pi$
$919$	13.6717	0.450989	0.225495	+	0.974244i	$0.427600\pi$
$920$	46.4067	1.52998
$921$	−22.4931	−0.741172
$922$	19.3585	0.637540
$923$	−8.16739	−0.268833
$924$	10.6849	0.351507
$925$	15.7391	0.517499
$926$	−93.0067	−3.05639
$927$	−11.5630	−0.379779
$928$	41.3070	1.35597
$929$	−42.7715	−1.40329	−0.701643	−	0.712528i	$-0.747550\pi$
$929$	−42.7715	−1.40329	−0.701643	+	0.712528i	$0.747550\pi$
$930$	−33.4535	−1.09698
$931$	10.9530	0.358970
$932$	15.4661	0.506609
$933$	−11.8780	−0.388868
$934$	17.2577	0.564689
$935$	1.19719	0.0391522
$936$	5.41772	0.177084
$937$	8.19672	0.267775	0.133888	−	0.990997i	$-0.457254\pi$
$937$	8.19672	0.267775	0.133888	+	0.990997i	$0.457254\pi$
$938$	−89.7809	−2.93145
$939$	−25.2180	−0.822958
$940$	44.2413	1.44299
$941$	21.5060	0.701076	0.350538	−	0.936548i	$-0.385999\pi$
$941$	21.5060	0.701076	0.350538	+	0.936548i	$0.385999\pi$
$942$	3.79275	0.123575
$943$	25.5961	0.833523
$944$	231.744	7.54262
$945$	−13.6380	−0.443645
$946$	−18.2684	−0.593956
$947$	−25.2816	−0.821543	−0.410771	−	0.911738i	$-0.634741\pi$
$947$	−25.2816	−0.821543	−0.410771	+	0.911738i	$0.634741\pi$
$948$	1.24158	0.0403245
$949$	0.0769543	0.00249804
$950$	51.4068	1.66786
$951$	−0.800353	−0.0259532
$952$	43.9640	1.42488
$953$	12.6537	0.409892	0.204946	−	0.978773i	$-0.434298\pi$
$953$	12.6537	0.409892	0.204946	+	0.978773i	$0.434298\pi$
$954$	−20.5651	−0.665820
$955$	15.0126	0.485796
$956$	91.5529	2.96103
$957$	1.16818	0.0377618
$958$	−87.9053	−2.84009
$959$	−5.76632	−0.186204
$960$	75.9088	2.44994
$961$	23.0206	0.742600
$962$	6.99328	0.225472
$963$	−3.81036	−0.122787
$964$	160.073	5.15560
$965$	5.47829	0.176353
$966$	35.0226	1.12683
$967$	−28.4994	−0.916479	−0.458239	−	0.888829i	$-0.651520\pi$
$967$	−28.4994	−0.916479	−0.458239	+	0.888829i	$0.651520\pi$
$968$	−114.204	−3.67067
$969$	13.4791	0.433011
$970$	15.6341	0.501981
$971$	−49.4019	−1.58538	−0.792692	−	0.609623i	$-0.791321\pi$
$971$	−49.4019	−1.58538	−0.792692	+	0.609623i	$0.791321\pi$
$972$	−49.4695	−1.58674
$973$	35.2058	1.12865
$974$	20.3241	0.651227
$975$	−3.31652	−0.106214
$976$	−152.550	−4.88302
$977$	−46.6982	−1.49401	−0.747005	−	0.664819i	$-0.768509\pi$
$977$	−46.6982	−1.49401	−0.747005	+	0.664819i	$0.768509\pi$
$978$	−69.6704	−2.22781
$979$	−0.967008	−0.0309057
$980$	14.5149	0.463661
$981$	−10.4244	−0.332826
$982$	−2.79161	−0.0890837
$983$	−1.57827	−0.0503391	−0.0251696	−	0.999683i	$-0.508013\pi$
$983$	−1.57827	−0.0503391	−0.0251696	+	0.999683i	$0.508013\pi$
$984$	102.781	3.27653
$985$	25.1936	0.802735
$986$	7.31941	0.233098
$987$	21.9257	0.697903
$988$	17.0037	0.540961
$989$	−44.5759	−1.41743
$990$	−1.50185	−0.0477318
$991$	−48.3494	−1.53587	−0.767935	−	0.640528i	$-0.778715\pi$
$991$	−48.3494	−1.53587	−0.767935	+	0.640528i	$0.778715\pi$
$992$	−218.667	−6.94269
$993$	37.6445	1.19461
$994$	83.1435	2.63715
$995$	−10.5820	−0.335473
$996$	−104.203	−3.30181
$997$	25.7252	0.814724	0.407362	−	0.913267i	$-0.366449\pi$
$997$	25.7252	0.814724	0.407362	+	0.913267i	$0.366449\pi$
$998$	31.3630	0.992779
$999$	−23.5553	−0.745256

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.a.b.1.17	✓	17
3.2	odd	2		3141.2.a.e.1.1		17
4.3	odd	2		5584.2.a.m.1.13		17
5.4	even	2		8725.2.a.m.1.1		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.a.b.1.17	✓	17	1.1	even	1	trivial
3141.2.a.e.1.1		17	3.2	odd	2
5584.2.a.m.1.13		17	4.3	odd	2
8725.2.a.m.1.1		17	5.4	even	2

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:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.a (trivial)

\(f(q)\)	\(=\)	\(q+2.79743 q^{2} -1.46796 q^{3} +5.82560 q^{4} -1.10838 q^{5} -4.10651 q^{6} +2.17992 q^{7} +10.7018 q^{8} -0.845091 q^{9} +O(q^{10})\)	\(q+2.79743 q^{2} -1.46796 q^{3} +5.82560 q^{4} -1.10838 q^{5} -4.10651 q^{6} +2.17992 q^{7} +10.7018 q^{8} -0.845091 q^{9} -3.10061 q^{10} -0.573158 q^{11} -8.55175 q^{12} -0.599039 q^{13} +6.09817 q^{14} +1.62706 q^{15} +18.2864 q^{16} +1.88451 q^{17} -2.36408 q^{18} -4.87246 q^{19} -6.45698 q^{20} -3.20004 q^{21} -1.60337 q^{22} -3.91231 q^{23} -15.7099 q^{24} -3.77149 q^{25} -1.67577 q^{26} +5.64444 q^{27} +12.6993 q^{28} +1.38841 q^{29} +4.55158 q^{30} -7.34987 q^{31} +29.7512 q^{32} +0.841374 q^{33} +5.27177 q^{34} -2.41618 q^{35} -4.92316 q^{36} -4.17318 q^{37} -13.6304 q^{38} +0.879365 q^{39} -11.8617 q^{40} -6.54244 q^{41} -8.95188 q^{42} +11.3937 q^{43} -3.33899 q^{44} +0.936683 q^{45} -10.9444 q^{46} -6.85170 q^{47} -26.8437 q^{48} -2.24794 q^{49} -10.5505 q^{50} -2.76638 q^{51} -3.48976 q^{52} +8.69899 q^{53} +15.7899 q^{54} +0.635278 q^{55} +23.3292 q^{56} +7.15259 q^{57} +3.88399 q^{58} +12.6730 q^{59} +9.47859 q^{60} -8.34230 q^{61} -20.5607 q^{62} -1.84223 q^{63} +46.6540 q^{64} +0.663963 q^{65} +2.35368 q^{66} -14.7226 q^{67} +10.9784 q^{68} +5.74312 q^{69} -6.75910 q^{70} +13.6342 q^{71} -9.04402 q^{72} -0.128463 q^{73} -11.6742 q^{74} +5.53640 q^{75} -28.3850 q^{76} -1.24944 q^{77} +2.45996 q^{78} -0.145184 q^{79} -20.2683 q^{80} -5.75055 q^{81} -18.3020 q^{82} +12.1850 q^{83} -18.6421 q^{84} -2.08875 q^{85} +31.8732 q^{86} -2.03814 q^{87} -6.13384 q^{88} +1.68716 q^{89} +2.62030 q^{90} -1.30586 q^{91} -22.7916 q^{92} +10.7893 q^{93} -19.1671 q^{94} +5.40055 q^{95} -43.6736 q^{96} -5.04226 q^{97} -6.28845 q^{98} +0.484371 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9}+O(q^{10}) \) 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9} - 6 q^{10} + 39 q^{11} + 4 q^{12} - 6 q^{13} + 11 q^{14} + 12 q^{15} + 23 q^{16} + q^{17} + 7 q^{19} + 8 q^{20} - 3 q^{21} - q^{22} + 8 q^{23} - 21 q^{24} + 14 q^{25} + q^{26} + 9 q^{27} - 23 q^{28} + 9 q^{29} - 27 q^{30} - 2 q^{31} + 23 q^{32} - 5 q^{33} - 12 q^{34} + 16 q^{35} + 10 q^{36} - 7 q^{37} - 8 q^{38} - 39 q^{40} + 3 q^{41} - 30 q^{42} + q^{43} + 56 q^{44} - 21 q^{45} - q^{46} + 16 q^{47} - 31 q^{48} + 6 q^{49} - 5 q^{50} + 29 q^{51} - 37 q^{52} + 27 q^{53} - 36 q^{54} - 16 q^{55} + 14 q^{56} - 21 q^{57} - 44 q^{58} + 74 q^{59} - 27 q^{60} - 30 q^{61} - 18 q^{62} - 9 q^{63} - 17 q^{64} - 3 q^{65} - 66 q^{66} + 9 q^{67} - 51 q^{68} - 23 q^{69} - 77 q^{70} + 70 q^{71} - 55 q^{72} - 38 q^{73} + 26 q^{74} + 22 q^{75} - 50 q^{76} - 38 q^{77} - 75 q^{78} + 7 q^{79} - 28 q^{80} + 5 q^{81} - 56 q^{82} + 47 q^{83} - 69 q^{84} - 49 q^{85} + 17 q^{86} - 37 q^{87} - 30 q^{88} + 23 q^{89} - 64 q^{90} + 6 q^{91} + 17 q^{92} - 31 q^{93} - 40 q^{94} - 11 q^{95} - 49 q^{96} - 14 q^{97} + 5 q^{98} + 79 q^{99}+O(q^{100}) \) 17 * q + 5 * q^2 + 6 * q^3 + 19 * q^4 + 5 * q^5 - 3 * q^6 + q^7 + 9 * q^8 + 25 * q^9 - 6 * q^10 + 39 * q^11 + 4 * q^12 - 6 * q^13 + 11 * q^14 + 12 * q^15 + 23 * q^16 + q^17 + 7 * q^19 + 8 * q^20 - 3 * q^21 - q^22 + 8 * q^23 - 21 * q^24 + 14 * q^25 + q^26 + 9 * q^27 - 23 * q^28 + 9 * q^29 - 27 * q^30 - 2 * q^31 + 23 * q^32 - 5 * q^33 - 12 * q^34 + 16 * q^35 + 10 * q^36 - 7 * q^37 - 8 * q^38 - 39 * q^40 + 3 * q^41 - 30 * q^42 + q^43 + 56 * q^44 - 21 * q^45 - q^46 + 16 * q^47 - 31 * q^48 + 6 * q^49 - 5 * q^50 + 29 * q^51 - 37 * q^52 + 27 * q^53 - 36 * q^54 - 16 * q^55 + 14 * q^56 - 21 * q^57 - 44 * q^58 + 74 * q^59 - 27 * q^60 - 30 * q^61 - 18 * q^62 - 9 * q^63 - 17 * q^64 - 3 * q^65 - 66 * q^66 + 9 * q^67 - 51 * q^68 - 23 * q^69 - 77 * q^70 + 70 * q^71 - 55 * q^72 - 38 * q^73 + 26 * q^74 + 22 * q^75 - 50 * q^76 - 38 * q^77 - 75 * q^78 + 7 * q^79 - 28 * q^80 + 5 * q^81 - 56 * q^82 + 47 * q^83 - 69 * q^84 - 49 * q^85 + 17 * q^86 - 37 * q^87 - 30 * q^88 + 23 * q^89 - 64 * q^90 + 6 * q^91 + 17 * q^92 - 31 * q^93 - 40 * q^94 - 11 * q^95 - 49 * q^96 - 14 * q^97 + 5 * q^98 + 79 * q^99

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