LMFDB - Embedded newform 349.2.a.b.1.1

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			1.1
Root			$-2.51266$ 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)

$f(q)$	$=$	$q-2.51266 q^{2} +2.89863 q^{3} +4.31346 q^{4} +2.77794 q^{5} -7.28327 q^{6} -0.223033 q^{7} -5.81294 q^{8} +5.40206 q^{9} +O(q^{10})$	\(q-2.51266 q^{2} +2.89863 q^{3} +4.31346 q^{4} +2.77794 q^{5} -7.28327 q^{6} -0.223033 q^{7} -5.81294 q^{8} +5.40206 q^{9} -6.98003 q^{10} +5.99774 q^{11} +12.5031 q^{12} -1.41378 q^{13} +0.560405 q^{14} +8.05223 q^{15} +5.97903 q^{16} -5.27768 q^{17} -13.5735 q^{18} -7.85522 q^{19} +11.9826 q^{20} -0.646489 q^{21} -15.0703 q^{22} -5.36633 q^{23} -16.8496 q^{24} +2.71697 q^{25} +3.55234 q^{26} +6.96267 q^{27} -0.962042 q^{28} +2.82789 q^{29} -20.2325 q^{30} -1.63491 q^{31} -3.39738 q^{32} +17.3852 q^{33} +13.2610 q^{34} -0.619572 q^{35} +23.3016 q^{36} -9.43755 q^{37} +19.7375 q^{38} -4.09801 q^{39} -16.1480 q^{40} +3.42287 q^{41} +1.62441 q^{42} +2.77500 q^{43} +25.8710 q^{44} +15.0066 q^{45} +13.4838 q^{46} -5.91783 q^{47} +17.3310 q^{48} -6.95026 q^{49} -6.82682 q^{50} -15.2980 q^{51} -6.09826 q^{52} +8.87232 q^{53} -17.4948 q^{54} +16.6614 q^{55} +1.29647 q^{56} -22.7694 q^{57} -7.10553 q^{58} +9.31277 q^{59} +34.7330 q^{60} +1.00294 q^{61} +4.10798 q^{62} -1.20483 q^{63} -3.42160 q^{64} -3.92739 q^{65} -43.6832 q^{66} +3.65611 q^{67} -22.7651 q^{68} -15.5550 q^{69} +1.55677 q^{70} +11.2092 q^{71} -31.4018 q^{72} +8.72178 q^{73} +23.7134 q^{74} +7.87549 q^{75} -33.8832 q^{76} -1.33769 q^{77} +10.2969 q^{78} +0.393791 q^{79} +16.6094 q^{80} +3.97604 q^{81} -8.60051 q^{82} +4.87081 q^{83} -2.78860 q^{84} -14.6611 q^{85} -6.97263 q^{86} +8.19701 q^{87} -34.8645 q^{88} -11.5912 q^{89} -37.7065 q^{90} +0.315318 q^{91} -23.1475 q^{92} -4.73901 q^{93} +14.8695 q^{94} -21.8213 q^{95} -9.84773 q^{96} +9.02114 q^{97} +17.4636 q^{98} +32.4001 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.51266	−1.77672	−0.888360	−	0.459149i	$-0.848155\pi$
$2$	−2.51266	−1.77672	−0.888360	+	0.459149i	$0.848155\pi$
$3$	2.89863	1.67352	0.836762	−	0.547566i	$-0.184446\pi$
$3$	2.89863	1.67352	0.836762	+	0.547566i	$0.184446\pi$
$4$	4.31346	2.15673
$5$	2.77794	1.24233	0.621167	−	0.783678i	$-0.286659\pi$
$5$	2.77794	1.24233	0.621167	+	0.783678i	$0.286659\pi$
$6$	−7.28327	−2.97338
$7$	−0.223033	−0.0842984	−0.0421492	−	0.999111i	$-0.513420\pi$
$7$	−0.223033	−0.0842984	−0.0421492	+	0.999111i	$0.513420\pi$
$8$	−5.81294	−2.05519
$9$	5.40206	1.80069
$10$	−6.98003	−2.20728
$11$	5.99774	1.80839	0.904194	−	0.427123i	$-0.140473\pi$
$11$	5.99774	1.80839	0.904194	+	0.427123i	$0.140473\pi$
$12$	12.5031	3.60934
$13$	−1.41378	−0.392111	−0.196055	−	0.980593i	$-0.562813\pi$
$13$	−1.41378	−0.392111	−0.196055	+	0.980593i	$0.562813\pi$
$14$	0.560405	0.149775
$15$	8.05223	2.07908
$16$	5.97903	1.49476
$17$	−5.27768	−1.28003	−0.640013	−	0.768364i	$-0.721071\pi$
$17$	−5.27768	−1.28003	−0.640013	+	0.768364i	$0.721071\pi$
$18$	−13.5735	−3.19931
$19$	−7.85522	−1.80211	−0.901055	−	0.433705i	$-0.857206\pi$
$19$	−7.85522	−1.80211	−0.901055	+	0.433705i	$0.857206\pi$
$20$	11.9826	2.67938
$21$	−0.646489	−0.141075
$22$	−15.0703	−3.21300
$23$	−5.36633	−1.11896	−0.559479	−	0.828845i	$-0.688999\pi$
$23$	−5.36633	−1.11896	−0.559479	+	0.828845i	$0.688999\pi$
$24$	−16.8496	−3.43940
$25$	2.71697	0.543394
$26$	3.55234	0.696671
$27$	6.96267	1.33997
$28$	−0.962042	−0.181809
$29$	2.82789	0.525126	0.262563	−	0.964915i	$-0.415432\pi$
$29$	2.82789	0.525126	0.262563	+	0.964915i	$0.415432\pi$
$30$	−20.2325	−3.69394
$31$	−1.63491	−0.293639	−0.146819	−	0.989163i	$-0.546904\pi$
$31$	−1.63491	−0.293639	−0.146819	+	0.989163i	$0.546904\pi$
$32$	−3.39738	−0.600577
$33$	17.3852	3.02638
$34$	13.2610	2.27425
$35$	−0.619572	−0.104727
$36$	23.3016	3.88359
$37$	−9.43755	−1.55152	−0.775762	−	0.631026i	$-0.782634\pi$
$37$	−9.43755	−1.55152	−0.775762	+	0.631026i	$0.782634\pi$
$38$	19.7375	3.20184
$39$	−4.09801	−0.656207
$40$	−16.1480	−2.55323
$41$	3.42287	0.534562	0.267281	−	0.963619i	$-0.413875\pi$
$41$	3.42287	0.534562	0.267281	+	0.963619i	$0.413875\pi$
$42$	1.62441	0.250651
$43$	2.77500	0.423184	0.211592	−	0.977358i	$-0.432135\pi$
$43$	2.77500	0.423184	0.211592	+	0.977358i	$0.432135\pi$
$44$	25.8710	3.90020
$45$	15.0066	2.23705
$46$	13.4838	1.98807
$47$	−5.91783	−0.863204	−0.431602	−	0.902064i	$-0.642051\pi$
$47$	−5.91783	−0.863204	−0.431602	+	0.902064i	$0.642051\pi$
$48$	17.3310	2.50151
$49$	−6.95026	−0.992894
$50$	−6.82682	−0.965458
$51$	−15.2980	−2.14215
$52$	−6.09826	−0.845677
$53$	8.87232	1.21871	0.609354	−	0.792899i	$-0.291429\pi$
$53$	8.87232	1.21871	0.609354	+	0.792899i	$0.291429\pi$
$54$	−17.4948	−2.38074
$55$	16.6614	2.24662
$56$	1.29647	0.173249
$57$	−22.7694	−3.01588
$58$	−7.10553	−0.933002
$59$	9.31277	1.21242	0.606210	−	0.795305i	$-0.292689\pi$
$59$	9.31277	1.21242	0.606210	+	0.795305i	$0.292689\pi$
$60$	34.7330	4.48401
$61$	1.00294	0.128413	0.0642064	−	0.997937i	$-0.479548\pi$
$61$	1.00294	0.128413	0.0642064	+	0.997937i	$0.479548\pi$
$62$	4.10798	0.521714
$63$	−1.20483	−0.151795
$64$	−3.42160	−0.427700
$65$	−3.92739	−0.487132
$66$	−43.6832	−5.37703
$67$	3.65611	0.446665	0.223332	−	0.974742i	$-0.428306\pi$
$67$	3.65611	0.446665	0.223332	+	0.974742i	$0.428306\pi$
$68$	−22.7651	−2.76067
$69$	−15.5550	−1.87260
$70$	1.55677	0.186070
$71$	11.2092	1.33028	0.665142	−	0.746717i	$-0.268371\pi$
$71$	11.2092	1.33028	0.665142	+	0.746717i	$0.268371\pi$
$72$	−31.4018	−3.70074
$73$	8.72178	1.02081	0.510404	−	0.859935i	$-0.329496\pi$
$73$	8.72178	1.02081	0.510404	+	0.859935i	$0.329496\pi$
$74$	23.7134	2.75662
$75$	7.87549	0.909383
$76$	−33.8832	−3.88667
$77$	−1.33769	−0.152444
$78$	10.2969	1.16590
$79$	0.393791	0.0443049	0.0221525	−	0.999755i	$-0.492948\pi$
$79$	0.393791	0.0443049	0.0221525	+	0.999755i	$0.492948\pi$
$80$	16.6094	1.85699
$81$	3.97604	0.441783
$82$	−8.60051	−0.949767
$83$	4.87081	0.534641	0.267320	−	0.963608i	$-0.413862\pi$
$83$	4.87081	0.534641	0.267320	+	0.963608i	$0.413862\pi$
$84$	−2.78860	−0.304262
$85$	−14.6611	−1.59022
$86$	−6.97263	−0.751878
$87$	8.19701	0.878812
$88$	−34.8645	−3.71657
$89$	−11.5912	−1.22866	−0.614332	−	0.789048i	$-0.710574\pi$
$89$	−11.5912	−1.22866	−0.614332	+	0.789048i	$0.710574\pi$
$90$	−37.7065	−3.97461
$91$	0.315318	0.0330543
$92$	−23.1475	−2.41329
$93$	−4.73901	−0.491412
$94$	14.8695	1.53367
$95$	−21.8213	−2.23882
$96$	−9.84773	−1.00508
$97$	9.02114	0.915958	0.457979	−	0.888963i	$-0.348573\pi$
$97$	9.02114	0.915958	0.457979	+	0.888963i	$0.348573\pi$
$98$	17.4636	1.76409
$99$	32.4001	3.25634
$100$	11.7195	1.17195
$101$	−16.0822	−1.60024	−0.800118	−	0.599843i	$-0.795230\pi$
$101$	−16.0822	−1.60024	−0.800118	+	0.599843i	$0.795230\pi$
$102$	38.4388	3.80601
$103$	−14.0117	−1.38062	−0.690309	−	0.723514i	$-0.742526\pi$
$103$	−14.0117	−1.38062	−0.690309	+	0.723514i	$0.742526\pi$
$104$	8.21819	0.805860
$105$	−1.79591	−0.175263
$106$	−22.2931	−2.16530
$107$	−4.50894	−0.435896	−0.217948	−	0.975960i	$-0.569936\pi$
$107$	−4.50894	−0.435896	−0.217948	+	0.975960i	$0.569936\pi$
$108$	30.0332	2.88995
$109$	10.2005	0.977026	0.488513	−	0.872557i	$-0.337539\pi$
$109$	10.2005	0.977026	0.488513	+	0.872557i	$0.337539\pi$
$110$	−41.8644	−3.99161
$111$	−27.3560	−2.59651
$112$	−1.33352	−0.126006
$113$	5.84819	0.550151	0.275076	−	0.961423i	$-0.411297\pi$
$113$	5.84819	0.550151	0.275076	+	0.961423i	$0.411297\pi$
$114$	57.2117	5.35836
$115$	−14.9074	−1.39012
$116$	12.1980	1.13256
$117$	−7.63729	−0.706068
$118$	−23.3998	−2.15413
$119$	1.17709	0.107904
$120$	−46.8071	−4.27289
$121$	24.9729	2.27026
$122$	−2.52004	−0.228154
$123$	9.92163	0.894603
$124$	−7.05213	−0.633300
$125$	−6.34213	−0.567258
$126$	3.02734	0.269697
$127$	−4.86790	−0.431956	−0.215978	−	0.976398i	$-0.569294\pi$
$127$	−4.86790	−0.431956	−0.215978	+	0.976398i	$0.569294\pi$
$128$	15.3921	1.36048
$129$	8.04370	0.708208
$130$	9.86819	0.865497
$131$	−6.66349	−0.582191	−0.291096	−	0.956694i	$-0.594020\pi$
$131$	−6.66349	−0.582191	−0.291096	+	0.956694i	$0.594020\pi$
$132$	74.9905	6.52709
$133$	1.75197	0.151915
$134$	−9.18656	−0.793598
$135$	19.3419	1.66469
$136$	30.6789	2.63069
$137$	14.9681	1.27881	0.639407	−	0.768868i	$-0.279180\pi$
$137$	14.9681	1.27881	0.639407	+	0.768868i	$0.279180\pi$
$138$	39.0845	3.32709
$139$	18.9097	1.60390	0.801948	−	0.597393i	$-0.203797\pi$
$139$	18.9097	1.60390	0.801948	+	0.597393i	$0.203797\pi$
$140$	−2.67250	−0.225867
$141$	−17.1536	−1.44459
$142$	−28.1648	−2.36354
$143$	−8.47946	−0.709088
$144$	32.2990	2.69159
$145$	7.85573	0.652382
$146$	−21.9149	−1.81369
$147$	−20.1462	−1.66163
$148$	−40.7085	−3.34622
$149$	3.39144	0.277837	0.138919	−	0.990304i	$-0.455637\pi$
$149$	3.39144	0.277837	0.138919	+	0.990304i	$0.455637\pi$
$150$	−19.7884	−1.61572
$151$	10.8699	0.884584	0.442292	−	0.896871i	$-0.354166\pi$
$151$	10.8699	0.884584	0.442292	+	0.896871i	$0.354166\pi$
$152$	45.6619	3.70367
$153$	−28.5103	−2.30492
$154$	3.36116	0.270850
$155$	−4.54169	−0.364798
$156$	−17.6766	−1.41526
$157$	−17.7278	−1.41483	−0.707415	−	0.706799i	$-0.750139\pi$
$157$	−17.7278	−1.41483	−0.707415	+	0.706799i	$0.750139\pi$
$158$	−0.989462	−0.0787174
$159$	25.7176	2.03954
$160$	−9.43772	−0.746117
$161$	1.19687	0.0943263
$162$	−9.99045	−0.784924
$163$	−5.15615	−0.403861	−0.201930	−	0.979400i	$-0.564721\pi$
$163$	−5.15615	−0.403861	−0.201930	+	0.979400i	$0.564721\pi$
$164$	14.7644	1.15291
$165$	48.2952	3.75978
$166$	−12.2387	−0.949906
$167$	0.441672	0.0341776	0.0170888	−	0.999854i	$-0.494560\pi$
$167$	0.441672	0.0341776	0.0170888	+	0.999854i	$0.494560\pi$
$168$	3.75800	0.289936
$169$	−11.0012	−0.846249
$170$	36.8384	2.82537
$171$	−42.4343	−3.24503
$172$	11.9699	0.912693
$173$	−15.3191	−1.16469	−0.582345	−	0.812942i	$-0.697865\pi$
$173$	−15.3191	−1.16469	−0.582345	+	0.812942i	$0.697865\pi$
$174$	−20.5963	−1.56140
$175$	−0.605972	−0.0458072
$176$	35.8606	2.70310
$177$	26.9943	2.02901
$178$	29.1247	2.18299
$179$	0.0288619	0.00215724	0.00107862	−	0.999999i	$-0.499657\pi$
$179$	0.0288619	0.00215724	0.00107862	+	0.999999i	$0.499657\pi$
$180$	64.7304	4.82472
$181$	0.569671	0.0423433	0.0211717	−	0.999776i	$-0.493260\pi$
$181$	0.569671	0.0423433	0.0211717	+	0.999776i	$0.493260\pi$
$182$	−0.792287	−0.0587282
$183$	2.90714	0.214902
$184$	31.1942	2.29967
$185$	−26.2170	−1.92751
$186$	11.9075	0.873101
$187$	−31.6542	−2.31478
$188$	−25.5263	−1.86170
$189$	−1.55290	−0.112957
$190$	54.8296	3.97776
$191$	−3.29092	−0.238122	−0.119061	−	0.992887i	$-0.537988\pi$
$191$	−3.29092	−0.238122	−0.119061	+	0.992887i	$0.537988\pi$
$192$	−9.91796	−0.715767
$193$	8.40837	0.605248	0.302624	−	0.953110i	$-0.402137\pi$
$193$	8.40837	0.605248	0.302624	+	0.953110i	$0.402137\pi$
$194$	−22.6671	−1.62740
$195$	−11.3840	−0.815228
$196$	−29.9797	−2.14140
$197$	−12.2601	−0.873497	−0.436748	−	0.899584i	$-0.643870\pi$
$197$	−12.2601	−0.873497	−0.436748	+	0.899584i	$0.643870\pi$
$198$	−81.4105	−5.78559
$199$	10.4472	0.740579	0.370290	−	0.928916i	$-0.379258\pi$
$199$	10.4472	0.740579	0.370290	+	0.928916i	$0.379258\pi$
$200$	−15.7936	−1.11677
$201$	10.5977	0.747505
$202$	40.4090	2.84317
$203$	−0.630712	−0.0442673
$204$	−65.9875	−4.62005
$205$	9.50854	0.664105
$206$	35.2068	2.45297
$207$	−28.9892	−2.01489
$208$	−8.45300	−0.586110
$209$	−47.1136	−3.25891
$210$	4.51251	0.311393
$211$	11.6471	0.801818	0.400909	−	0.916118i	$-0.368694\pi$
$211$	11.6471	0.801818	0.400909	+	0.916118i	$0.368694\pi$
$212$	38.2704	2.62842
$213$	32.4913	2.22626
$214$	11.3294	0.774465
$215$	7.70879	0.525735
$216$	−40.4736	−2.75388
$217$	0.364639	0.0247533
$218$	−25.6303	−1.73590
$219$	25.2812	1.70835
$220$	71.8682	4.84536
$221$	7.46145	0.501912
$222$	68.7362	4.61327
$223$	15.7361	1.05377	0.526885	−	0.849937i	$-0.323360\pi$
$223$	15.7361	1.05377	0.526885	+	0.849937i	$0.323360\pi$
$224$	0.757725	0.0506276
$225$	14.6772	0.978481
$226$	−14.6945	−0.977464
$227$	22.6660	1.50440	0.752198	−	0.658937i	$-0.228994\pi$
$227$	22.6660	1.50440	0.752198	+	0.658937i	$0.228994\pi$
$228$	−98.2148	−6.50443
$229$	12.6639	0.836855	0.418427	−	0.908250i	$-0.362581\pi$
$229$	12.6639	0.836855	0.418427	+	0.908250i	$0.362581\pi$
$230$	37.4572	2.46985
$231$	−3.87747	−0.255119
$232$	−16.4384	−1.07923
$233$	8.61771	0.564565	0.282282	−	0.959331i	$-0.408908\pi$
$233$	8.61771	0.564565	0.282282	+	0.959331i	$0.408908\pi$
$234$	19.1899	1.25448
$235$	−16.4394	−1.07239
$236$	40.1703	2.61486
$237$	1.14145	0.0741454
$238$	−2.95764	−0.191715
$239$	14.8856	0.962872	0.481436	−	0.876481i	$-0.340115\pi$
$239$	14.8856	0.962872	0.481436	+	0.876481i	$0.340115\pi$
$240$	48.1445	3.10771
$241$	−15.3703	−0.990086	−0.495043	−	0.868868i	$-0.664848\pi$
$241$	−15.3703	−0.990086	−0.495043	+	0.868868i	$0.664848\pi$
$242$	−62.7484	−4.03362
$243$	−9.36294	−0.600633
$244$	4.32613	0.276952
$245$	−19.3074	−1.23351
$246$	−24.9297	−1.58946
$247$	11.1055	0.706627
$248$	9.50365	0.603482
$249$	14.1187	0.894734
$250$	15.9356	1.00786
$251$	18.8912	1.19240	0.596201	−	0.802835i	$-0.296676\pi$
$251$	18.8912	1.19240	0.596201	+	0.802835i	$0.296676\pi$
$252$	−5.19701	−0.327381
$253$	−32.1859	−2.02351
$254$	12.2314	0.767465
$255$	−42.4971	−2.66127
$256$	−31.8318	−1.98949
$257$	−11.3782	−0.709753	−0.354876	−	0.934913i	$-0.615477\pi$
$257$	−11.3782	−0.709753	−0.354876	+	0.934913i	$0.615477\pi$
$258$	−20.2111	−1.25829
$259$	2.10488	0.130791
$260$	−16.9406	−1.05061
$261$	15.2764	0.945588
$262$	16.7431	1.03439
$263$	2.50093	0.154214	0.0771070	−	0.997023i	$-0.475432\pi$
$263$	2.50093	0.154214	0.0771070	+	0.997023i	$0.475432\pi$
$264$	−101.059	−6.21977
$265$	24.6468	1.51404
$266$	−4.40210	−0.269910
$267$	−33.5986	−2.05620
$268$	15.7705	0.963336
$269$	−10.6989	−0.652322	−0.326161	−	0.945314i	$-0.605755\pi$
$269$	−10.6989	−0.652322	−0.326161	+	0.945314i	$0.605755\pi$
$270$	−48.5996	−2.95768
$271$	−11.9840	−0.727979	−0.363989	−	0.931403i	$-0.618586\pi$
$271$	−11.9840	−0.727979	−0.363989	+	0.931403i	$0.618586\pi$
$272$	−31.5554	−1.91333
$273$	0.913990	0.0553172
$274$	−37.6099	−2.27209
$275$	16.2957	0.982666
$276$	−67.0960	−4.03870
$277$	−24.9196	−1.49728	−0.748638	−	0.662979i	$-0.769292\pi$
$277$	−24.9196	−1.49728	−0.748638	+	0.662979i	$0.769292\pi$
$278$	−47.5136	−2.84967
$279$	−8.83189	−0.528751
$280$	3.60153	0.215233
$281$	25.5119	1.52191	0.760957	−	0.648802i	$-0.224730\pi$
$281$	25.5119	1.52191	0.760957	+	0.648802i	$0.224730\pi$
$282$	43.1011	2.56664
$283$	−16.0755	−0.955591	−0.477795	−	0.878471i	$-0.658564\pi$
$283$	−16.0755	−0.955591	−0.477795	+	0.878471i	$0.658564\pi$
$284$	48.3503	2.86907
$285$	−63.2520	−3.74673
$286$	21.3060	1.25985
$287$	−0.763411	−0.0450627
$288$	−18.3528	−1.08145
$289$	10.8539	0.638466
$290$	−19.7388	−1.15910
$291$	26.1490	1.53288
$292$	37.6211	2.20161
$293$	17.5042	1.02261	0.511303	−	0.859401i	$-0.329163\pi$
$293$	17.5042	1.02261	0.511303	+	0.859401i	$0.329163\pi$
$294$	50.6206	2.95225
$295$	25.8704	1.50623
$296$	54.8599	3.18867
$297$	41.7603	2.42318
$298$	−8.52153	−0.493639
$299$	7.58679	0.438755
$300$	33.9706	1.96129
$301$	−0.618915	−0.0356737
$302$	−27.3125	−1.57166
$303$	−46.6163	−2.67803
$304$	−46.9665	−2.69372
$305$	2.78610	0.159532
$306$	71.6368	4.09520
$307$	−17.6457	−1.00709	−0.503547	−	0.863968i	$-0.667972\pi$
$307$	−17.6457	−1.00709	−0.503547	+	0.863968i	$0.667972\pi$
$308$	−5.77008	−0.328781
$309$	−40.6149	−2.31050
$310$	11.4117	0.648143
$311$	17.5103	0.992920	0.496460	−	0.868060i	$-0.334633\pi$
$311$	17.5103	0.992920	0.496460	+	0.868060i	$0.334633\pi$
$312$	23.8215	1.34863
$313$	11.4966	0.649824	0.324912	−	0.945744i	$-0.394665\pi$
$313$	11.4966	0.649824	0.324912	+	0.945744i	$0.394665\pi$
$314$	44.5438	2.51375
$315$	−3.34696	−0.188580
$316$	1.69860	0.0955538
$317$	−8.40517	−0.472081	−0.236041	−	0.971743i	$-0.575850\pi$
$317$	−8.40517	−0.472081	−0.236041	+	0.971743i	$0.575850\pi$
$318$	−64.6195	−3.62368
$319$	16.9610	0.949632
$320$	−9.50501	−0.531346
$321$	−13.0698	−0.729483
$322$	−3.00732	−0.167591
$323$	41.4573	2.30675
$324$	17.1505	0.952806
$325$	−3.84118	−0.213070
$326$	12.9556	0.717547
$327$	29.5673	1.63508
$328$	−19.8969	−1.09862
$329$	1.31987	0.0727667
$330$	−121.349	−6.68007
$331$	−6.16307	−0.338753	−0.169376	−	0.985551i	$-0.554175\pi$
$331$	−6.16307	−0.338753	−0.169376	+	0.985551i	$0.554175\pi$
$332$	21.0100	1.15308
$333$	−50.9822	−2.79381
$334$	−1.10977	−0.0607240
$335$	10.1565	0.554907
$336$	−3.86537	−0.210873
$337$	5.78280	0.315009	0.157505	−	0.987518i	$-0.449655\pi$
$337$	5.78280	0.315009	0.157505	+	0.987518i	$0.449655\pi$
$338$	27.6424	1.50355
$339$	16.9517	0.920692
$340$	−63.2401	−3.42967
$341$	−9.80578	−0.531013
$342$	106.623	5.76551
$343$	3.11136	0.167998
$344$	−16.1309	−0.869721
$345$	−43.2110	−2.32640
$346$	38.4917	2.06933
$347$	7.89436	0.423791	0.211896	−	0.977292i	$-0.432036\pi$
$347$	7.89436	0.423791	0.211896	+	0.977292i	$0.432036\pi$
$348$	35.3575	1.89536
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	1.52260	0.0813865
$351$	−9.84365	−0.525415
$352$	−20.3766	−1.08608
$353$	−36.8782	−1.96283	−0.981413	−	0.191906i	$-0.938533\pi$
$353$	−36.8782	−1.96283	−0.981413	+	0.191906i	$0.938533\pi$
$354$	−67.8275	−3.60499
$355$	31.1385	1.65266
$356$	−49.9982	−2.64990
$357$	3.41196	0.180580
$358$	−0.0725201	−0.00383281
$359$	16.2530	0.857803	0.428901	−	0.903351i	$-0.358901\pi$
$359$	16.2530	0.857803	0.428901	+	0.903351i	$0.358901\pi$
$360$	−87.2325	−4.59756
$361$	42.7044	2.24760
$362$	−1.43139	−0.0752322
$363$	72.3872	3.79934
$364$	1.36011	0.0712892
$365$	24.2286	1.26818
$366$	−7.30466	−0.381821
$367$	−14.8114	−0.773148	−0.386574	−	0.922258i	$-0.626342\pi$
$367$	−14.8114	−0.773148	−0.386574	+	0.922258i	$0.626342\pi$
$368$	−32.0854	−1.67257
$369$	18.4905	0.962579
$370$	65.8744	3.42464
$371$	−1.97882	−0.102735
$372$	−20.4415	−1.05984
$373$	−27.6761	−1.43301	−0.716507	−	0.697580i	$-0.754260\pi$
$373$	−27.6761	−1.43301	−0.716507	+	0.697580i	$0.754260\pi$
$374$	79.5362	4.11272
$375$	−18.3835	−0.949320
$376$	34.4000	1.77404
$377$	−3.99800	−0.205908
$378$	3.90192	0.200693
$379$	29.2689	1.50344	0.751722	−	0.659480i	$-0.229224\pi$
$379$	29.2689	1.50344	0.751722	+	0.659480i	$0.229224\pi$
$380$	−94.1255	−4.82854
$381$	−14.1102	−0.722889
$382$	8.26896	0.423077
$383$	28.1407	1.43792	0.718962	−	0.695050i	$-0.244618\pi$
$383$	28.1407	1.43792	0.718962	+	0.695050i	$0.244618\pi$
$384$	44.6159	2.27680
$385$	−3.71603	−0.189386
$386$	−21.1274	−1.07535
$387$	14.9907	0.762020
$388$	38.9124	1.97548
$389$	−15.1213	−0.766680	−0.383340	−	0.923607i	$-0.625226\pi$
$389$	−15.1213	−0.766680	−0.383340	+	0.923607i	$0.625226\pi$
$390$	28.6042	1.44843
$391$	28.3218	1.43229
$392$	40.4014	2.04058
$393$	−19.3150	−0.974312
$394$	30.8055	1.55196
$395$	1.09393	0.0550415
$396$	139.757	7.02304
$397$	−14.6282	−0.734167	−0.367083	−	0.930188i	$-0.619644\pi$
$397$	−14.6282	−0.734167	−0.367083	+	0.930188i	$0.619644\pi$
$398$	−26.2502	−1.31580
$399$	5.07831	0.254233
$400$	16.2448	0.812241
$401$	−2.84809	−0.142227	−0.0711133	−	0.997468i	$-0.522655\pi$
$401$	−2.84809	−0.142227	−0.0711133	+	0.997468i	$0.522655\pi$
$402$	−26.6284	−1.32811
$403$	2.31140	0.115139
$404$	−69.3698	−3.45128
$405$	11.0452	0.548842
$406$	1.58476	0.0786506
$407$	−56.6040	−2.80576
$408$	88.9267	4.40253
$409$	−26.9176	−1.33099	−0.665495	−	0.746402i	$-0.731780\pi$
$409$	−26.9176	−1.33099	−0.665495	+	0.746402i	$0.731780\pi$
$410$	−23.8917	−1.17993
$411$	43.3871	2.14013
$412$	−60.4391	−2.97762
$413$	−2.07705	−0.102205
$414$	72.8401	3.57990
$415$	13.5308	0.664202
$416$	4.80312	0.235493
$417$	54.8121	2.68416
$418$	118.380	5.79017
$419$	−25.0024	−1.22145	−0.610723	−	0.791844i	$-0.709121\pi$
$419$	−25.0024	−1.22145	−0.610723	+	0.791844i	$0.709121\pi$
$420$	−7.74658	−0.377995
$421$	7.09625	0.345850	0.172925	−	0.984935i	$-0.444678\pi$
$421$	7.09625	0.345850	0.172925	+	0.984935i	$0.444678\pi$
$422$	−29.2651	−1.42461
$423$	−31.9684	−1.55436
$424$	−51.5743	−2.50467
$425$	−14.3393	−0.695558
$426$	−81.6395	−3.95545
$427$	−0.223687	−0.0108250
$428$	−19.4492	−0.940110
$429$	−24.5788	−1.18668
$430$	−19.3696	−0.934084
$431$	10.7223	0.516477	0.258238	−	0.966081i	$-0.416858\pi$
$431$	10.7223	0.516477	0.258238	+	0.966081i	$0.416858\pi$
$432$	41.6300	2.00292
$433$	24.4270	1.17389	0.586943	−	0.809628i	$-0.300331\pi$
$433$	24.4270	1.17389	0.586943	+	0.809628i	$0.300331\pi$
$434$	−0.916213	−0.0439796
$435$	22.7708	1.09178
$436$	43.9993	2.10718
$437$	42.1537	2.01649
$438$	−63.5231	−3.03525
$439$	24.4974	1.16920	0.584599	−	0.811323i	$-0.301252\pi$
$439$	24.4974	1.16920	0.584599	+	0.811323i	$0.301252\pi$
$440$	−96.8517	−4.61722
$441$	−37.5457	−1.78789
$442$	−18.7481	−0.891756
$443$	21.8312	1.03723	0.518616	−	0.855008i	$-0.326448\pi$
$443$	21.8312	1.03723	0.518616	+	0.855008i	$0.326448\pi$
$444$	−117.999	−5.59998
$445$	−32.1997	−1.52641
$446$	−39.5396	−1.87225
$447$	9.83052	0.464968
$448$	0.763128	0.0360544
$449$	4.59694	0.216943	0.108472	−	0.994100i	$-0.465404\pi$
$449$	4.59694	0.216943	0.108472	+	0.994100i	$0.465404\pi$
$450$	−36.8789	−1.73849
$451$	20.5295	0.966696
$452$	25.2259	1.18653
$453$	31.5080	1.48037
$454$	−56.9520	−2.67289
$455$	0.875935	0.0410645
$456$	132.357	6.19818
$457$	−13.0938	−0.612502	−0.306251	−	0.951951i	$-0.599075\pi$
$457$	−13.0938	−0.612502	−0.306251	+	0.951951i	$0.599075\pi$
$458$	−31.8201	−1.48686
$459$	−36.7468	−1.71519
$460$	−64.3024	−2.99811
$461$	−34.1584	−1.59091	−0.795457	−	0.606011i	$-0.792769\pi$
$461$	−34.1584	−1.59091	−0.795457	+	0.606011i	$0.792769\pi$
$462$	9.74277	0.453275
$463$	9.68875	0.450274	0.225137	−	0.974327i	$-0.427717\pi$
$463$	9.68875	0.450274	0.225137	+	0.974327i	$0.427717\pi$
$464$	16.9080	0.784936
$465$	−13.1647	−0.610498
$466$	−21.6534	−1.00307
$467$	10.0376	0.464486	0.232243	−	0.972658i	$-0.425394\pi$
$467$	10.0376	0.464486	0.232243	+	0.972658i	$0.425394\pi$
$468$	−32.9432	−1.52280
$469$	−0.815431	−0.0376531
$470$	41.3066	1.90533
$471$	−51.3862	−2.36775
$472$	−54.1346	−2.49175
$473$	16.6437	0.765280
$474$	−2.86808	−0.131735
$475$	−21.3424	−0.979255
$476$	5.07735	0.232720
$477$	47.9288	2.19451
$478$	−37.4026	−1.71075
$479$	−18.8529	−0.861411	−0.430705	−	0.902493i	$-0.641735\pi$
$479$	−18.8529	−0.861411	−0.430705	+	0.902493i	$0.641735\pi$
$480$	−27.3564	−1.24865
$481$	13.3426	0.608369
$482$	38.6203	1.75910
$483$	3.46927	0.157857
$484$	107.720	4.89635
$485$	25.0602	1.13793
$486$	23.5259	1.06716
$487$	12.2110	0.553334	0.276667	−	0.960966i	$-0.410770\pi$
$487$	12.2110	0.553334	0.276667	+	0.960966i	$0.410770\pi$
$488$	−5.83001	−0.263912
$489$	−14.9458	−0.675871
$490$	48.5130	2.19159
$491$	−2.60494	−0.117559	−0.0587796	−	0.998271i	$-0.518721\pi$
$491$	−2.60494	−0.117559	−0.0587796	+	0.998271i	$0.518721\pi$
$492$	42.7966	1.92942
$493$	−14.9247	−0.672175
$494$	−27.9044	−1.25548
$495$	90.0057	4.04546
$496$	−9.77518	−0.438919
$497$	−2.50001	−0.112141
$498$	−35.4754	−1.58969
$499$	−25.2872	−1.13201	−0.566004	−	0.824402i	$-0.691511\pi$
$499$	−25.2872	−1.13201	−0.566004	+	0.824402i	$0.691511\pi$
$500$	−27.3565	−1.22342
$501$	1.28024	0.0571971
$502$	−47.4672	−2.11856
$503$	−10.7120	−0.477624	−0.238812	−	0.971066i	$-0.576758\pi$
$503$	−10.7120	−0.477624	−0.238812	+	0.971066i	$0.576758\pi$
$504$	7.00363	0.311967
$505$	−44.6753	−1.98803
$506$	80.8722	3.59521
$507$	−31.8885	−1.41622
$508$	−20.9975	−0.931613
$509$	−30.9183	−1.37043	−0.685214	−	0.728342i	$-0.740291\pi$
$509$	−30.9183	−1.37043	−0.685214	+	0.728342i	$0.740291\pi$
$510$	106.781	4.72833
$511$	−1.94524	−0.0860524
$512$	49.1985	2.17429
$513$	−54.6933	−2.41477
$514$	28.5895	1.26103
$515$	−38.9238	−1.71519
$516$	34.6962	1.52741
$517$	−35.4936	−1.56101
$518$	−5.28885	−0.232379
$519$	−44.4044	−1.94914
$520$	22.8297	1.00115
$521$	15.6927	0.687508	0.343754	−	0.939060i	$-0.388301\pi$
$521$	15.6927	0.687508	0.343754	+	0.939060i	$0.388301\pi$
$522$	−38.3845	−1.68004
$523$	0.0342417	0.00149729	0.000748643	−	1.00000i	$-0.499762\pi$
$523$	0.0342417	0.00149729	0.000748643		1.00000i	$0.499762\pi$
$524$	−28.7427	−1.25563
$525$	−1.75649	−0.0766595
$526$	−6.28399	−0.273995
$527$	8.62854	0.375865
$528$	103.947	4.52370
$529$	5.79754	0.252067
$530$	−61.9290	−2.69003
$531$	50.3081	2.18319
$532$	7.55705	0.327640
$533$	−4.83917	−0.209608
$534$	84.4218	3.65329
$535$	−12.5256	−0.541529
$536$	−21.2528	−0.917979
$537$	0.0836599	0.00361019
$538$	26.8826	1.15899
$539$	−41.6858	−1.79554
$540$	83.4306	3.59028
$541$	−38.1012	−1.63810	−0.819050	−	0.573723i	$-0.805499\pi$
$541$	−38.1012	−1.63810	−0.819050	+	0.573723i	$0.805499\pi$
$542$	30.1118	1.29341
$543$	1.65127	0.0708626
$544$	17.9303	0.768754
$545$	28.3363	1.21379
$546$	−2.29655	−0.0982831
$547$	18.5109	0.791467	0.395733	−	0.918365i	$-0.370490\pi$
$547$	18.5109	0.791467	0.395733	+	0.918365i	$0.370490\pi$
$548$	64.5645	2.75806
$549$	5.41792	0.231231
$550$	−40.9455	−1.74592
$551$	−22.2137	−0.946336
$552$	90.4204	3.84855
$553$	−0.0878281	−0.00373483
$554$	62.6146	2.66024
$555$	−75.9933	−3.22574
$556$	81.5661	3.45917
$557$	10.1028	0.428070	0.214035	−	0.976826i	$-0.431339\pi$
$557$	10.1028	0.428070	0.214035	+	0.976826i	$0.431339\pi$
$558$	22.1915	0.939442
$559$	−3.92323	−0.165935
$560$	−3.70443	−0.156541
$561$	−91.7537	−3.87385
$562$	−64.1028	−2.70401
$563$	−3.06778	−0.129291	−0.0646457	−	0.997908i	$-0.520592\pi$
$563$	−3.06778	−0.129291	−0.0646457	+	0.997908i	$0.520592\pi$
$564$	−73.9913	−3.11560
$565$	16.2459	0.683472
$566$	40.3923	1.69782
$567$	−0.886787	−0.0372416
$568$	−65.1583	−2.73398
$569$	1.53087	0.0641773	0.0320886	−	0.999485i	$-0.489784\pi$
$569$	1.53087	0.0641773	0.0320886	+	0.999485i	$0.489784\pi$
$570$	158.931	6.65688
$571$	3.37871	0.141395	0.0706974	−	0.997498i	$-0.477478\pi$
$571$	3.37871	0.141395	0.0706974	+	0.997498i	$0.477478\pi$
$572$	−36.5758	−1.52931
$573$	−9.53915	−0.398504
$574$	1.91819	0.0800638
$575$	−14.5802	−0.608035
$576$	−18.4837	−0.770154
$577$	37.2994	1.55279	0.776396	−	0.630245i	$-0.217045\pi$
$577$	37.2994	1.55279	0.776396	+	0.630245i	$0.217045\pi$
$578$	−27.2722	−1.13437
$579$	24.3727	1.01290
$580$	33.8854	1.40701
$581$	−1.08635	−0.0450693
$582$	−65.7034	−2.72350
$583$	53.2139	2.20389
$584$	−50.6992	−2.09795
$585$	−21.2160	−0.877172
$586$	−43.9821	−1.81688
$587$	15.6504	0.645962	0.322981	−	0.946405i	$-0.395315\pi$
$587$	15.6504	0.645962	0.322981	+	0.946405i	$0.395315\pi$
$588$	−86.9000	−3.58369
$589$	12.8426	0.529170
$590$	−65.0034	−2.67615
$591$	−35.5375	−1.46182
$592$	−56.4273	−2.31915
$593$	35.7716	1.46896	0.734481	−	0.678629i	$-0.237426\pi$
$593$	35.7716	1.46896	0.734481	+	0.678629i	$0.237426\pi$
$594$	−104.929	−4.30531
$595$	3.26990	0.134053
$596$	14.6288	0.599220
$597$	30.2824	1.23938
$598$	−19.0630	−0.779545
$599$	13.1807	0.538550	0.269275	−	0.963063i	$-0.413216\pi$
$599$	13.1807	0.538550	0.269275	+	0.963063i	$0.413216\pi$
$600$	−45.7797	−1.86895
$601$	−45.3921	−1.85158	−0.925790	−	0.378038i	$-0.876599\pi$
$601$	−45.3921	−1.85158	−0.925790	+	0.378038i	$0.876599\pi$
$602$	1.55512	0.0633821
$603$	19.7505	0.804303
$604$	46.8871	1.90781
$605$	69.3733	2.82043
$606$	117.131	4.75811
$607$	14.2317	0.577647	0.288823	−	0.957382i	$-0.406736\pi$
$607$	14.2317	0.577647	0.288823	+	0.957382i	$0.406736\pi$
$608$	26.6871	1.08231
$609$	−1.82820	−0.0740824
$610$	−7.00052	−0.283443
$611$	8.36648	0.338471
$612$	−122.978	−4.97110
$613$	−46.5888	−1.88170	−0.940852	−	0.338818i	$-0.889973\pi$
$613$	−46.5888	−1.88170	−0.940852	+	0.338818i	$0.889973\pi$
$614$	44.3377	1.78932
$615$	27.5617	1.11140
$616$	7.77592	0.313301
$617$	15.9644	0.642704	0.321352	−	0.946960i	$-0.395863\pi$
$617$	15.9644	0.642704	0.321352	+	0.946960i	$0.395863\pi$
$618$	102.051	4.10511
$619$	−18.7074	−0.751915	−0.375958	−	0.926637i	$-0.622686\pi$
$619$	−18.7074	−0.751915	−0.375958	+	0.926637i	$0.622686\pi$
$620$	−19.5904	−0.786770
$621$	−37.3640	−1.49937
$622$	−43.9975	−1.76414
$623$	2.58521	0.103574
$624$	−24.5021	−0.980870
$625$	−31.2029	−1.24812
$626$	−28.8870	−1.15456
$627$	−136.565	−5.45387
$628$	−76.4680	−3.05141
$629$	49.8084	1.98599
$630$	8.40978	0.335053
$631$	−27.0614	−1.07730	−0.538649	−	0.842530i	$-0.681065\pi$
$631$	−27.0614	−1.07730	−0.538649	+	0.842530i	$0.681065\pi$
$632$	−2.28908	−0.0910548
$633$	33.7606	1.34186
$634$	21.1193	0.838756
$635$	−13.5227	−0.536634
$636$	110.932	4.39873
$637$	9.82610	0.389324
$638$	−42.6172	−1.68723
$639$	60.5526	2.39542
$640$	42.7583	1.69017
$641$	−45.5087	−1.79748	−0.898742	−	0.438477i	$-0.855518\pi$
$641$	−45.5087	−1.79748	−0.898742	+	0.438477i	$0.855518\pi$
$642$	32.8399	1.29609
$643$	−14.6235	−0.576694	−0.288347	−	0.957526i	$-0.593106\pi$
$643$	−14.6235	−0.576694	−0.288347	+	0.957526i	$0.593106\pi$
$644$	5.16264	0.203436
$645$	22.3449	0.879831
$646$	−104.168	−4.09844
$647$	−8.57103	−0.336962	−0.168481	−	0.985705i	$-0.553886\pi$
$647$	−8.57103	−0.336962	−0.168481	+	0.985705i	$0.553886\pi$
$648$	−23.1125	−0.907945
$649$	55.8556	2.19252
$650$	9.65159	0.378566
$651$	1.05695	0.0414252
$652$	−22.2408	−0.871019
$653$	36.9267	1.44505	0.722527	−	0.691342i	$-0.242980\pi$
$653$	36.9267	1.44505	0.722527	+	0.691342i	$0.242980\pi$
$654$	−74.2927	−2.90507
$655$	−18.5108	−0.723276
$656$	20.4654	0.799040
$657$	47.1155	1.83815
$658$	−3.31638	−0.129286
$659$	29.7560	1.15913	0.579565	−	0.814926i	$-0.303222\pi$
$659$	29.7560	1.15913	0.579565	+	0.814926i	$0.303222\pi$
$660$	208.319	8.10882
$661$	11.1548	0.433873	0.216936	−	0.976186i	$-0.430394\pi$
$661$	11.1548	0.433873	0.216936	+	0.976186i	$0.430394\pi$
$662$	15.4857	0.601869
$663$	21.6280	0.839962
$664$	−28.3137	−1.09879
$665$	4.86687	0.188729
$666$	128.101	4.96381
$667$	−15.1754	−0.587594
$668$	1.90514	0.0737119
$669$	45.6132	1.76351
$670$	−25.5197	−0.985914
$671$	6.01535	0.232220
$672$	2.19636	0.0847266
$673$	16.7253	0.644715	0.322357	−	0.946618i	$-0.395525\pi$
$673$	16.7253	0.644715	0.322357	+	0.946618i	$0.395525\pi$
$674$	−14.5302	−0.559683
$675$	18.9174	0.728130
$676$	−47.4534	−1.82513
$677$	9.17798	0.352739	0.176369	−	0.984324i	$-0.443565\pi$
$677$	9.17798	0.352739	0.176369	+	0.984324i	$0.443565\pi$
$678$	−42.5939	−1.63581
$679$	−2.01201	−0.0772138
$680$	85.2241	3.26820
$681$	65.7004	2.51764
$682$	24.6386	0.943461
$683$	−18.7060	−0.715765	−0.357883	−	0.933767i	$-0.616501\pi$
$683$	−18.7060	−0.715765	−0.357883	+	0.933767i	$0.616501\pi$
$684$	−183.039	−6.99866
$685$	41.5806	1.58871
$686$	−7.81779	−0.298485
$687$	36.7080	1.40050
$688$	16.5918	0.632556
$689$	−12.5435	−0.477868
$690$	108.574	4.13336
$691$	23.2192	0.883300	0.441650	−	0.897187i	$-0.354393\pi$
$691$	23.2192	0.883300	0.441650	+	0.897187i	$0.354393\pi$
$692$	−66.0784	−2.51192
$693$	−7.22628	−0.274504
$694$	−19.8358	−0.752958
$695$	52.5300	1.99258
$696$	−47.6488	−1.80612
$697$	−18.0648	−0.684254
$698$	−2.51266	−0.0951056
$699$	24.9796	0.944814
$700$	−2.61384	−0.0987938
$701$	−13.9361	−0.526358	−0.263179	−	0.964747i	$-0.584771\pi$
$701$	−13.9361	−0.526358	−0.263179	+	0.964747i	$0.584771\pi$
$702$	24.7338	0.933516
$703$	74.1340	2.79602
$704$	−20.5219	−0.773448
$705$	−47.6517	−1.79467
$706$	92.6623	3.48739
$707$	3.58685	0.134897
$708$	116.439	4.37604
$709$	24.1662	0.907579	0.453790	−	0.891109i	$-0.350072\pi$
$709$	24.1662	0.907579	0.453790	+	0.891109i	$0.350072\pi$
$710$	−78.2404	−2.93631
$711$	2.12728	0.0797792
$712$	67.3789	2.52513
$713$	8.77348	0.328570
$714$	−8.57310	−0.320840
$715$	−23.5555	−0.880924
$716$	0.124495	0.00465258
$717$	43.1480	1.61139
$718$	−40.8384	−1.52407
$719$	34.8144	1.29836	0.649179	−	0.760636i	$-0.275113\pi$
$719$	34.8144	1.29836	0.649179	+	0.760636i	$0.275113\pi$
$720$	89.7249	3.34385
$721$	3.12508	0.116384
$722$	−107.302	−3.99336
$723$	−44.5527	−1.65693
$724$	2.45725	0.0913231
$725$	7.68330	0.285350
$726$	−181.884	−6.75037
$727$	−24.9185	−0.924176	−0.462088	−	0.886834i	$-0.652900\pi$
$727$	−24.9185	−0.924176	−0.462088	+	0.886834i	$0.652900\pi$
$728$	−1.83292	−0.0679327
$729$	−39.0678	−1.44696
$730$	−60.8783	−2.25321
$731$	−14.6456	−0.541686
$732$	12.5398	0.463486
$733$	2.27593	0.0840632	0.0420316	−	0.999116i	$-0.486617\pi$
$733$	2.27593	0.0840632	0.0420316	+	0.999116i	$0.486617\pi$
$734$	37.2160	1.37367
$735$	−55.9651	−2.06430
$736$	18.2314	0.672020
$737$	21.9284	0.807743
$738$	−46.4604	−1.71023
$739$	2.26663	0.0833793	0.0416896	−	0.999131i	$-0.486726\pi$
$739$	2.26663	0.0833793	0.0416896	+	0.999131i	$0.486726\pi$
$740$	−113.086	−4.15712
$741$	32.1908	1.18256
$742$	4.97209	0.182531
$743$	−7.66421	−0.281173	−0.140586	−	0.990068i	$-0.544899\pi$
$743$	−7.66421	−0.281173	−0.140586	+	0.990068i	$0.544899\pi$
$744$	27.5476	1.00994
$745$	9.42122	0.345167
$746$	69.5406	2.54606
$747$	26.3124	0.962719
$748$	−136.539	−4.99236
$749$	1.00564	0.0367453
$750$	46.1915	1.68667
$751$	−26.5145	−0.967528	−0.483764	−	0.875198i	$-0.660731\pi$
$751$	−26.5145	−0.967528	−0.483764	+	0.875198i	$0.660731\pi$
$752$	−35.3828	−1.29028
$753$	54.7586	1.99551
$754$	10.0456	0.365840
$755$	30.1961	1.09895
$756$	−6.69838	−0.243618
$757$	−1.69646	−0.0616589	−0.0308295	−	0.999525i	$-0.509815\pi$
$757$	−1.69646	−0.0616589	−0.0308295	+	0.999525i	$0.509815\pi$
$758$	−73.5429	−2.67120
$759$	−93.2950	−3.38639
$760$	126.846	4.60120
$761$	28.6803	1.03966	0.519830	−	0.854270i	$-0.325995\pi$
$761$	28.6803	1.03966	0.519830	+	0.854270i	$0.325995\pi$
$762$	35.4542	1.28437
$763$	−2.27503	−0.0823617
$764$	−14.1952	−0.513566
$765$	−79.2001	−2.86348
$766$	−70.7080	−2.55479
$767$	−13.1662	−0.475403
$768$	−92.2687	−3.32946
$769$	−28.9747	−1.04485	−0.522427	−	0.852684i	$-0.674973\pi$
$769$	−28.9747	−1.04485	−0.522427	+	0.852684i	$0.674973\pi$
$770$	9.33712	0.336487
$771$	−32.9812	−1.18779
$772$	36.2692	1.30536
$773$	−46.3095	−1.66564	−0.832818	−	0.553547i	$-0.813274\pi$
$773$	−46.3095	−1.66564	−0.832818	+	0.553547i	$0.813274\pi$
$774$	−37.6666	−1.35390
$775$	−4.44200	−0.159562
$776$	−52.4394	−1.88246
$777$	6.10127	0.218882
$778$	37.9947	1.36217
$779$	−26.8874	−0.963340
$780$	−49.1046	−1.75823
$781$	67.2297	2.40567
$782$	−71.1631	−2.54479
$783$	19.6897	0.703652
$784$	−41.5558	−1.48413
$785$	−49.2467	−1.75769
$786$	48.5320	1.73108
$787$	−6.03661	−0.215182	−0.107591	−	0.994195i	$-0.534314\pi$
$787$	−6.03661	−0.215182	−0.107591	+	0.994195i	$0.534314\pi$
$788$	−52.8835	−1.88390
$789$	7.24927	0.258081
$790$	−2.74867	−0.0977933
$791$	−1.30434	−0.0463769
$792$	−188.340	−6.69237
$793$	−1.41793	−0.0503521
$794$	36.7556	1.30441
$795$	71.4420	2.53379
$796$	45.0634	1.59723
$797$	9.00078	0.318824	0.159412	−	0.987212i	$-0.449040\pi$
$797$	9.00078	0.318824	0.159412	+	0.987212i	$0.449040\pi$
$798$	−12.7601	−0.451701
$799$	31.2324	1.10492
$800$	−9.23056	−0.326350
$801$	−62.6163	−2.21244
$802$	7.15627	0.252697
$803$	52.3110	1.84601
$804$	45.7128	1.61217
$805$	3.32483	0.117185
$806$	−5.80776	−0.204570
$807$	−31.0121	−1.09168
$808$	93.4847	3.28878
$809$	−6.55222	−0.230364	−0.115182	−	0.993344i	$-0.536745\pi$
$809$	−6.55222	−0.230364	−0.115182	+	0.993344i	$0.536745\pi$
$810$	−27.7529	−0.975137
$811$	9.91897	0.348302	0.174151	−	0.984719i	$-0.444282\pi$
$811$	9.91897	0.348302	0.174151	+	0.984719i	$0.444282\pi$
$812$	−2.72055	−0.0954726
$813$	−34.7373	−1.21829
$814$	142.227	4.98504
$815$	−14.3235	−0.501730
$816$	−91.4674	−3.20200
$817$	−21.7982	−0.762623
$818$	67.6348	2.36480
$819$	1.70336	0.0595204
$820$	41.0147	1.43230
$821$	4.46436	0.155807	0.0779037	−	0.996961i	$-0.475177\pi$
$821$	4.46436	0.155807	0.0779037	+	0.996961i	$0.475177\pi$
$822$	−109.017	−3.80241
$823$	−1.41039	−0.0491630	−0.0245815	−	0.999698i	$-0.507825\pi$
$823$	−1.41039	−0.0491630	−0.0245815	+	0.999698i	$0.507825\pi$
$824$	81.4495	2.83743
$825$	47.2351	1.64452
$826$	5.21892	0.181590
$827$	18.8826	0.656613	0.328306	−	0.944571i	$-0.393522\pi$
$827$	18.8826	0.656613	0.328306	+	0.944571i	$0.393522\pi$
$828$	−125.044	−4.34558
$829$	31.4608	1.09268	0.546340	−	0.837564i	$-0.316021\pi$
$829$	31.4608	1.09268	0.546340	+	0.837564i	$0.316021\pi$
$830$	−33.9984	−1.18010
$831$	−72.2328	−2.50573
$832$	4.83738	0.167706
$833$	36.6812	1.27093
$834$	−137.724	−4.76900
$835$	1.22694	0.0424600
$836$	−203.222	−7.02860
$837$	−11.3834	−0.393466
$838$	62.8225	2.17017
$839$	−17.5826	−0.607019	−0.303509	−	0.952828i	$-0.598158\pi$
$839$	−17.5826	−0.607019	−0.303509	+	0.952828i	$0.598158\pi$
$840$	10.4395	0.360197
$841$	−21.0030	−0.724242
$842$	−17.8305	−0.614478
$843$	73.9497	2.54696
$844$	50.2392	1.72931
$845$	−30.5608	−1.05132
$846$	80.3258	2.76166
$847$	−5.56977	−0.191380
$848$	53.0478	1.82167
$849$	−46.5970	−1.59920
$850$	36.0298	1.23581
$851$	50.6450	1.73609
$852$	140.150	4.80145
$853$	−10.5516	−0.361278	−0.180639	−	0.983549i	$-0.557817\pi$
$853$	−10.5516	−0.361278	−0.180639	+	0.983549i	$0.557817\pi$
$854$	0.562051	0.0192330
$855$	−117.880	−4.03142
$856$	26.2102	0.895847
$857$	1.95728	0.0668595	0.0334297	−	0.999441i	$-0.489357\pi$
$857$	1.95728	0.0668595	0.0334297	+	0.999441i	$0.489357\pi$
$858$	61.7582	2.10839
$859$	−41.8146	−1.42670	−0.713348	−	0.700810i	$-0.752822\pi$
$859$	−41.8146	−1.42670	−0.713348	+	0.700810i	$0.752822\pi$
$860$	33.2516	1.13387
$861$	−2.21285	−0.0754136
$862$	−26.9416	−0.917634
$863$	15.3846	0.523697	0.261849	−	0.965109i	$-0.415668\pi$
$863$	15.3846	0.523697	0.261849	+	0.965109i	$0.415668\pi$
$864$	−23.6548	−0.804753
$865$	−42.5556	−1.44693
$866$	−61.3768	−2.08567
$867$	31.4615	1.06849
$868$	1.57285	0.0533861
$869$	2.36185	0.0801204
$870$	−57.2154	−1.93978
$871$	−5.16892	−0.175142
$872$	−59.2946	−2.00797
$873$	48.7327	1.64935
$874$	−105.918	−3.58273
$875$	1.41450	0.0478189
$876$	109.050	3.68444
$877$	−46.6478	−1.57518	−0.787592	−	0.616197i	$-0.788673\pi$
$877$	−46.6478	−1.57518	−0.787592	+	0.616197i	$0.788673\pi$
$878$	−61.5537	−2.07734
$879$	50.7381	1.71136
$880$	99.6188	3.35815
$881$	1.73498	0.0584528	0.0292264	−	0.999573i	$-0.490696\pi$
$881$	1.73498	0.0584528	0.0292264	+	0.999573i	$0.490696\pi$
$882$	94.3395	3.17658
$883$	27.1456	0.913523	0.456762	−	0.889589i	$-0.349009\pi$
$883$	27.1456	0.913523	0.456762	+	0.889589i	$0.349009\pi$
$884$	32.1847	1.08249
$885$	74.9886	2.52071
$886$	−54.8544	−1.84287
$887$	38.4477	1.29095	0.645473	−	0.763783i	$-0.276660\pi$
$887$	38.4477	1.29095	0.645473	+	0.763783i	$0.276660\pi$
$888$	159.019	5.33632
$889$	1.08570	0.0364132
$890$	80.9068	2.71200
$891$	23.8473	0.798914
$892$	67.8772	2.27270
$893$	46.4858	1.55559
$894$	−24.7008	−0.826117
$895$	0.0801767	0.00268001
$896$	−3.43293	−0.114686
$897$	21.9913	0.734268
$898$	−11.5505	−0.385447
$899$	−4.62336	−0.154198
$900$	63.3096	2.11032
$901$	−46.8253	−1.55998
$902$	−51.5836	−1.71755
$903$	−1.79401	−0.0597008
$904$	−33.9952	−1.13066
$905$	1.58251	0.0526045
$906$	−79.1688	−2.63021
$907$	58.0255	1.92671	0.963353	−	0.268238i	$-0.0864414\pi$
$907$	58.0255	1.92671	0.963353	+	0.268238i	$0.0864414\pi$
$908$	97.7689	3.24458
$909$	−86.8768	−2.88152
$910$	−2.20093	−0.0729600
$911$	−30.9668	−1.02598	−0.512989	−	0.858395i	$-0.671462\pi$
$911$	−30.9668	−1.02598	−0.512989	+	0.858395i	$0.671462\pi$
$912$	−136.139	−4.50800
$913$	29.2138	0.966837
$914$	32.9002	1.08824
$915$	8.07588	0.266980
$916$	54.6253	1.80487
$917$	1.48617	0.0490778
$918$	92.3321	3.04741
$919$	−26.8726	−0.886446	−0.443223	−	0.896411i	$-0.646165\pi$
$919$	−26.8726	−0.886446	−0.443223	+	0.896411i	$0.646165\pi$
$920$	86.6557	2.85695
$921$	−51.1484	−1.68540
$922$	85.8283	2.82661
$923$	−15.8473	−0.521619
$924$	−16.7253	−0.550223
$925$	−25.6415	−0.843088
$926$	−24.3445	−0.800011
$927$	−75.6922	−2.48606
$928$	−9.60741	−0.315379
$929$	−21.8409	−0.716575	−0.358288	−	0.933611i	$-0.616639\pi$
$929$	−21.8409	−0.716575	−0.358288	+	0.933611i	$0.616639\pi$
$930$	33.0784	1.08468
$931$	54.5958	1.78930
$932$	37.1722	1.21761
$933$	50.7560	1.66168
$934$	−25.2211	−0.825261
$935$	−87.9335	−2.87573
$936$	44.3951	1.45110
$937$	2.12356	0.0693737	0.0346869	−	0.999398i	$-0.488957\pi$
$937$	2.12356	0.0693737	0.0346869	+	0.999398i	$0.488957\pi$
$938$	2.04890	0.0668990
$939$	33.3243	1.08750
$940$	−70.9107	−2.31285
$941$	38.1817	1.24469	0.622343	−	0.782744i	$-0.286181\pi$
$941$	38.1817	1.24469	0.622343	+	0.782744i	$0.286181\pi$
$942$	129.116	4.20683
$943$	−18.3683	−0.598153
$944$	55.6813	1.81227
$945$	−4.31387	−0.140330
$946$	−41.8200	−1.35969
$947$	35.1131	1.14102	0.570512	−	0.821289i	$-0.306745\pi$
$947$	35.1131	1.14102	0.570512	+	0.821289i	$0.306745\pi$
$948$	4.92362	0.159912
$949$	−12.3306	−0.400269
$950$	53.6261	1.73986
$951$	−24.3635	−0.790040
$952$	−6.84238	−0.221763
$953$	−9.72727	−0.315097	−0.157549	−	0.987511i	$-0.550359\pi$
$953$	−9.72727	−0.315097	−0.157549	+	0.987511i	$0.550359\pi$
$954$	−120.429	−3.89902
$955$	−9.14198	−0.295828
$956$	64.2086	2.07666
$957$	49.1636	1.58923
$958$	47.3709	1.53048
$959$	−3.33838	−0.107802
$960$	−27.5515	−0.889222
$961$	−28.3271	−0.913776
$962$	−33.5254	−1.08090
$963$	−24.3576	−0.784912
$964$	−66.2991	−2.13535
$965$	23.3580	0.751920
$966$	−8.71711	−0.280468
$967$	−33.2249	−1.06844	−0.534220	−	0.845346i	$-0.679394\pi$
$967$	−33.2249	−1.06844	−0.534220	+	0.845346i	$0.679394\pi$
$968$	−145.166	−4.66581
$969$	120.169	3.86040
$970$	−62.9678	−2.02178
$971$	43.3461	1.39104	0.695521	−	0.718506i	$-0.255174\pi$
$971$	43.3461	1.39104	0.695521	+	0.718506i	$0.255174\pi$
$972$	−40.3867	−1.29540
$973$	−4.21747	−0.135206
$974$	−30.6822	−0.983120
$975$	−11.1342	−0.356579
$976$	5.99658	0.191946
$977$	29.2274	0.935068	0.467534	−	0.883975i	$-0.345143\pi$
$977$	29.2274	0.935068	0.467534	+	0.883975i	$0.345143\pi$
$978$	37.5536	1.20083
$979$	−69.5210	−2.22190
$980$	−83.2818	−2.66034
$981$	55.1034	1.75932
$982$	6.54533	0.208870
$983$	−11.0583	−0.352706	−0.176353	−	0.984327i	$-0.556430\pi$
$983$	−11.0583	−0.352706	−0.176353	+	0.984327i	$0.556430\pi$
$984$	−57.6739	−1.83858
$985$	−34.0579	−1.08517
$986$	37.5007	1.19427
$987$	3.82581	0.121777
$988$	47.9032	1.52400
$989$	−14.8916	−0.473525
$990$	−226.154	−7.18764
$991$	7.79945	0.247758	0.123879	−	0.992297i	$-0.460467\pi$
$991$	7.79945	0.247758	0.123879	+	0.992297i	$0.460467\pi$
$992$	5.55441	0.176353
$993$	−17.8645	−0.566911
$994$	6.28168	0.199243
$995$	29.0216	0.920047
$996$	60.9003	1.92970
$997$	22.9012	0.725287	0.362643	−	0.931928i	$-0.381874\pi$
$997$	22.9012	0.725287	0.362643	+	0.931928i	$0.381874\pi$
$998$	63.5380	2.01126
$999$	−65.7106	−2.07899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.a.b.1.1	✓	17
3.2	odd	2		3141.2.a.e.1.17		17
4.3	odd	2		5584.2.a.m.1.2		17
5.4	even	2		8725.2.a.m.1.17		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.a.b.1.1	✓	17	1.1	even	1	trivial
3141.2.a.e.1.17		17	3.2	odd	2
5584.2.a.m.1.2		17	4.3	odd	2
8725.2.a.m.1.17		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)

\(f(q)\)	\(=\)	\(q-2.51266 q^{2} +2.89863 q^{3} +4.31346 q^{4} +2.77794 q^{5} -7.28327 q^{6} -0.223033 q^{7} -5.81294 q^{8} +5.40206 q^{9} +O(q^{10})\)	\(q-2.51266 q^{2} +2.89863 q^{3} +4.31346 q^{4} +2.77794 q^{5} -7.28327 q^{6} -0.223033 q^{7} -5.81294 q^{8} +5.40206 q^{9} -6.98003 q^{10} +5.99774 q^{11} +12.5031 q^{12} -1.41378 q^{13} +0.560405 q^{14} +8.05223 q^{15} +5.97903 q^{16} -5.27768 q^{17} -13.5735 q^{18} -7.85522 q^{19} +11.9826 q^{20} -0.646489 q^{21} -15.0703 q^{22} -5.36633 q^{23} -16.8496 q^{24} +2.71697 q^{25} +3.55234 q^{26} +6.96267 q^{27} -0.962042 q^{28} +2.82789 q^{29} -20.2325 q^{30} -1.63491 q^{31} -3.39738 q^{32} +17.3852 q^{33} +13.2610 q^{34} -0.619572 q^{35} +23.3016 q^{36} -9.43755 q^{37} +19.7375 q^{38} -4.09801 q^{39} -16.1480 q^{40} +3.42287 q^{41} +1.62441 q^{42} +2.77500 q^{43} +25.8710 q^{44} +15.0066 q^{45} +13.4838 q^{46} -5.91783 q^{47} +17.3310 q^{48} -6.95026 q^{49} -6.82682 q^{50} -15.2980 q^{51} -6.09826 q^{52} +8.87232 q^{53} -17.4948 q^{54} +16.6614 q^{55} +1.29647 q^{56} -22.7694 q^{57} -7.10553 q^{58} +9.31277 q^{59} +34.7330 q^{60} +1.00294 q^{61} +4.10798 q^{62} -1.20483 q^{63} -3.42160 q^{64} -3.92739 q^{65} -43.6832 q^{66} +3.65611 q^{67} -22.7651 q^{68} -15.5550 q^{69} +1.55677 q^{70} +11.2092 q^{71} -31.4018 q^{72} +8.72178 q^{73} +23.7134 q^{74} +7.87549 q^{75} -33.8832 q^{76} -1.33769 q^{77} +10.2969 q^{78} +0.393791 q^{79} +16.6094 q^{80} +3.97604 q^{81} -8.60051 q^{82} +4.87081 q^{83} -2.78860 q^{84} -14.6611 q^{85} -6.97263 q^{86} +8.19701 q^{87} -34.8645 q^{88} -11.5912 q^{89} -37.7065 q^{90} +0.315318 q^{91} -23.1475 q^{92} -4.73901 q^{93} +14.8695 q^{94} -21.8213 q^{95} -9.84773 q^{96} +9.02114 q^{97} +17.4636 q^{98} +32.4001 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 5 q^{2} + 6 q^{3} + 19 q^{4} + 5 q^{5} - 3 q^{6} + q^{7} + 9 q^{8} + 25 q^{9}+O(q^{10}) \) 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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