LMFDB - Embedded newform 4019.2.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4019,2,Mod(1,4019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4019, 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("4019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4019.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0918765724$
Analytic rank:	$0$
Dimension:	$186$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52937 q^{2} +0.978887 q^{3} +4.39770 q^{4} -0.161932 q^{5} -2.47596 q^{6} -2.77531 q^{7} -6.06468 q^{8} -2.04178 q^{9} +O(q^{10})$	\(q-2.52937 q^{2} +0.978887 q^{3} +4.39770 q^{4} -0.161932 q^{5} -2.47596 q^{6} -2.77531 q^{7} -6.06468 q^{8} -2.04178 q^{9} +0.409586 q^{10} -5.90921 q^{11} +4.30485 q^{12} -4.84469 q^{13} +7.01979 q^{14} -0.158513 q^{15} +6.54440 q^{16} -7.33022 q^{17} +5.16442 q^{18} +4.31064 q^{19} -0.712130 q^{20} -2.71672 q^{21} +14.9466 q^{22} +0.421572 q^{23} -5.93663 q^{24} -4.97378 q^{25} +12.2540 q^{26} -4.93533 q^{27} -12.2050 q^{28} -4.33717 q^{29} +0.400939 q^{30} +6.27802 q^{31} -4.42384 q^{32} -5.78444 q^{33} +18.5408 q^{34} +0.449413 q^{35} -8.97915 q^{36} -2.79770 q^{37} -10.9032 q^{38} -4.74240 q^{39} +0.982067 q^{40} +0.785168 q^{41} +6.87158 q^{42} -2.17649 q^{43} -25.9870 q^{44} +0.330630 q^{45} -1.06631 q^{46} -7.48652 q^{47} +6.40622 q^{48} +0.702360 q^{49} +12.5805 q^{50} -7.17546 q^{51} -21.3055 q^{52} -5.34627 q^{53} +12.4833 q^{54} +0.956891 q^{55} +16.8314 q^{56} +4.21962 q^{57} +10.9703 q^{58} -0.387777 q^{59} -0.697095 q^{60} +8.26994 q^{61} -15.8794 q^{62} +5.66658 q^{63} -1.89929 q^{64} +0.784511 q^{65} +14.6310 q^{66} -4.85640 q^{67} -32.2362 q^{68} +0.412671 q^{69} -1.13673 q^{70} -12.5617 q^{71} +12.3827 q^{72} -6.31076 q^{73} +7.07642 q^{74} -4.86876 q^{75} +18.9569 q^{76} +16.3999 q^{77} +11.9953 q^{78} +11.4447 q^{79} -1.05975 q^{80} +1.29421 q^{81} -1.98598 q^{82} +2.64018 q^{83} -11.9473 q^{84} +1.18700 q^{85} +5.50513 q^{86} -4.24560 q^{87} +35.8374 q^{88} -3.89044 q^{89} -0.836286 q^{90} +13.4455 q^{91} +1.85395 q^{92} +6.14547 q^{93} +18.9362 q^{94} -0.698031 q^{95} -4.33043 q^{96} -6.96996 q^{97} -1.77653 q^{98} +12.0653 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) $ 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9} + 50 q^{10} + 25 q^{11} + 17 q^{12} + 113 q^{13} + 12 q^{14} + 12 q^{15} + 252 q^{16} + 35 q^{17} + 13 q^{18} + 97 q^{19} + 55 q^{20} + 115 q^{21} + 14 q^{22} + 27 q^{23} + 122 q^{24} + 244 q^{25} + 39 q^{26} + 34 q^{27} + 66 q^{28} + 91 q^{29} + 4 q^{30} + 135 q^{31} + 21 q^{32} + 32 q^{33} + 58 q^{34} + 17 q^{35} + 273 q^{36} + 133 q^{37} - 3 q^{38} + 55 q^{39} + 142 q^{40} + 97 q^{41} - 8 q^{42} + 67 q^{43} + 44 q^{44} + 154 q^{45} + 101 q^{46} + 20 q^{47} - 7 q^{48} + 312 q^{49} + 21 q^{50} + 23 q^{51} + 193 q^{52} + 22 q^{53} + 141 q^{54} + 88 q^{55} + 28 q^{56} + 65 q^{57} + 62 q^{58} + 41 q^{59} + q^{60} + 377 q^{61} + 29 q^{62} + 39 q^{63} + 311 q^{64} + 21 q^{65} + 35 q^{66} + 42 q^{67} + 24 q^{68} + 137 q^{69} + 35 q^{70} + 17 q^{71} - 8 q^{72} + 213 q^{73} - 9 q^{74} + 2 q^{75} + 242 q^{76} + 60 q^{77} + 103 q^{79} + 80 q^{80} + 270 q^{81} + 84 q^{82} + 42 q^{83} + 137 q^{84} + 294 q^{85} - 9 q^{86} + 22 q^{87} - 13 q^{88} + 78 q^{89} + 69 q^{90} + 118 q^{91} + 49 q^{92} + 51 q^{93} + 93 q^{94} + 10 q^{95} + 260 q^{96} + 142 q^{97} - 31 q^{98} + 78 q^{99}+O(q^{100}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9 + 50 * q^10 + 25 * q^11 + 17 * q^12 + 113 * q^13 + 12 * q^14 + 12 * q^15 + 252 * q^16 + 35 * q^17 + 13 * q^18 + 97 * q^19 + 55 * q^20 + 115 * q^21 + 14 * q^22 + 27 * q^23 + 122 * q^24 + 244 * q^25 + 39 * q^26 + 34 * q^27 + 66 * q^28 + 91 * q^29 + 4 * q^30 + 135 * q^31 + 21 * q^32 + 32 * q^33 + 58 * q^34 + 17 * q^35 + 273 * q^36 + 133 * q^37 - 3 * q^38 + 55 * q^39 + 142 * q^40 + 97 * q^41 - 8 * q^42 + 67 * q^43 + 44 * q^44 + 154 * q^45 + 101 * q^46 + 20 * q^47 - 7 * q^48 + 312 * q^49 + 21 * q^50 + 23 * q^51 + 193 * q^52 + 22 * q^53 + 141 * q^54 + 88 * q^55 + 28 * q^56 + 65 * q^57 + 62 * q^58 + 41 * q^59 + q^60 + 377 * q^61 + 29 * q^62 + 39 * q^63 + 311 * q^64 + 21 * q^65 + 35 * q^66 + 42 * q^67 + 24 * q^68 + 137 * q^69 + 35 * q^70 + 17 * q^71 - 8 * q^72 + 213 * q^73 - 9 * q^74 + 2 * q^75 + 242 * q^76 + 60 * q^77 + 103 * q^79 + 80 * q^80 + 270 * q^81 + 84 * q^82 + 42 * q^83 + 137 * q^84 + 294 * q^85 - 9 * q^86 + 22 * q^87 - 13 * q^88 + 78 * q^89 + 69 * q^90 + 118 * q^91 + 49 * q^92 + 51 * q^93 + 93 * q^94 + 10 * q^95 + 260 * q^96 + 142 * q^97 - 31 * q^98 + 78 * 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 $

$2$	−2.52937	−1.78853	−0.894267	−	0.447534i	$-0.852302\pi$
$2$	−2.52937	−1.78853	−0.894267	+	0.447534i	$0.852302\pi$
$3$	0.978887	0.565160	0.282580	−	0.959244i	$-0.408810\pi$
$3$	0.978887	0.565160	0.282580	+	0.959244i	$0.408810\pi$
$4$	4.39770	2.19885
$5$	−0.161932	−0.0724183	−0.0362092	−	0.999344i	$-0.511528\pi$
$5$	−0.161932	−0.0724183	−0.0362092	+	0.999344i	$0.511528\pi$
$6$	−2.47596	−1.01081
$7$	−2.77531	−1.04897	−0.524485	−	0.851420i	$-0.675742\pi$
$7$	−2.77531	−1.04897	−0.524485	+	0.851420i	$0.675742\pi$
$8$	−6.06468	−2.14419
$9$	−2.04178	−0.680594
$10$	0.409586	0.129523
$11$	−5.90921	−1.78169	−0.890847	−	0.454304i	$-0.849888\pi$
$11$	−5.90921	−1.78169	−0.890847	+	0.454304i	$0.849888\pi$
$12$	4.30485	1.24270
$13$	−4.84469	−1.34367	−0.671837	−	0.740699i	$-0.734494\pi$
$13$	−4.84469	−1.34367	−0.671837	+	0.740699i	$0.734494\pi$
$14$	7.01979	1.87612
$15$	−0.158513	−0.0409280
$16$	6.54440	1.63610
$17$	−7.33022	−1.77784	−0.888920	−	0.458062i	$-0.848544\pi$
$17$	−7.33022	−1.77784	−0.888920	+	0.458062i	$0.848544\pi$
$18$	5.16442	1.21726
$19$	4.31064	0.988928	0.494464	−	0.869198i	$-0.335364\pi$
$19$	4.31064	0.988928	0.494464	+	0.869198i	$0.335364\pi$
$20$	−0.712130	−0.159237
$21$	−2.71672	−0.592836
$22$	14.9466	3.18662
$23$	0.421572	0.0879038	0.0439519	−	0.999034i	$-0.486005\pi$
$23$	0.421572	0.0879038	0.0439519	+	0.999034i	$0.486005\pi$
$24$	−5.93663	−1.21181
$25$	−4.97378	−0.994756
$26$	12.2540	2.40321
$27$	−4.93533	−0.949805
$28$	−12.2050	−2.30653
$29$	−4.33717	−0.805392	−0.402696	−	0.915334i	$-0.631927\pi$
$29$	−4.33717	−0.805392	−0.402696	+	0.915334i	$0.631927\pi$
$30$	0.400939	0.0732010
$31$	6.27802	1.12757	0.563783	−	0.825923i	$-0.309346\pi$
$31$	6.27802	1.12757	0.563783	+	0.825923i	$0.309346\pi$
$32$	−4.42384	−0.782031
$33$	−5.78444	−1.00694
$34$	18.5408	3.17973
$35$	0.449413	0.0759646
$36$	−8.97915	−1.49653
$37$	−2.79770	−0.459939	−0.229970	−	0.973198i	$-0.573863\pi$
$37$	−2.79770	−0.459939	−0.229970	+	0.973198i	$0.573863\pi$
$38$	−10.9032	−1.76873
$39$	−4.74240	−0.759391
$40$	0.982067	0.155278
$41$	0.785168	0.122623	0.0613113	−	0.998119i	$-0.480472\pi$
$41$	0.785168	0.122623	0.0613113	+	0.998119i	$0.480472\pi$
$42$	6.87158	1.06031
$43$	−2.17649	−0.331911	−0.165955	−	0.986133i	$-0.553071\pi$
$43$	−2.17649	−0.331911	−0.165955	+	0.986133i	$0.553071\pi$
$44$	−25.9870	−3.91768
$45$	0.330630	0.0492874
$46$	−1.06631	−0.157219
$47$	−7.48652	−1.09202	−0.546010	−	0.837778i	$-0.683854\pi$
$47$	−7.48652	−1.09202	−0.546010	+	0.837778i	$0.683854\pi$
$48$	6.40622	0.924659
$49$	0.702360	0.100337
$50$	12.5805	1.77915
$51$	−7.17546	−1.00477
$52$	−21.3055	−2.95454
$53$	−5.34627	−0.734367	−0.367183	−	0.930149i	$-0.619678\pi$
$53$	−5.34627	−0.734367	−0.367183	+	0.930149i	$0.619678\pi$
$54$	12.4833	1.69876
$55$	0.956891	0.129027
$56$	16.8314	2.24919
$57$	4.21962	0.558903
$58$	10.9703	1.44047
$59$	−0.387777	−0.0504843	−0.0252421	−	0.999681i	$-0.508036\pi$
$59$	−0.387777	−0.0504843	−0.0252421	+	0.999681i	$0.508036\pi$
$60$	−0.697095	−0.0899945
$61$	8.26994	1.05886	0.529429	−	0.848354i	$-0.322406\pi$
$61$	8.26994	1.05886	0.529429	+	0.848354i	$0.322406\pi$
$62$	−15.8794	−2.01669
$63$	5.66658	0.713922
$64$	−1.89929	−0.237411
$65$	0.784511	0.0973066
$66$	14.6310	1.80095
$67$	−4.85640	−0.593304	−0.296652	−	0.954986i	$-0.595870\pi$
$67$	−4.85640	−0.593304	−0.296652	+	0.954986i	$0.595870\pi$
$68$	−32.2362	−3.90921
$69$	0.412671	0.0496797
$70$	−1.13673	−0.135865
$71$	−12.5617	−1.49080	−0.745399	−	0.666618i	$-0.767741\pi$
$71$	−12.5617	−1.49080	−0.745399	+	0.666618i	$0.767741\pi$
$72$	12.3827	1.45932
$73$	−6.31076	−0.738618	−0.369309	−	0.929307i	$-0.620406\pi$
$73$	−6.31076	−0.738618	−0.369309	+	0.929307i	$0.620406\pi$
$74$	7.07642	0.822617
$75$	−4.86876	−0.562196
$76$	18.9569	2.17451
$77$	16.3999	1.86894
$78$	11.9953	1.35820
$79$	11.4447	1.28763	0.643816	−	0.765180i	$-0.277350\pi$
$79$	11.4447	1.28763	0.643816	+	0.765180i	$0.277350\pi$
$80$	−1.05975	−0.118484
$81$	1.29421	0.143802
$82$	−1.98598	−0.219315
$83$	2.64018	0.289797	0.144898	−	0.989447i	$-0.453714\pi$
$83$	2.64018	0.289797	0.144898	+	0.989447i	$0.453714\pi$
$84$	−11.9473	−1.30356
$85$	1.18700	0.128748
$86$	5.50513	0.593634
$87$	−4.24560	−0.455176
$88$	35.8374	3.82028
$89$	−3.89044	−0.412385	−0.206193	−	0.978511i	$-0.566107\pi$
$89$	−3.89044	−0.412385	−0.206193	+	0.978511i	$0.566107\pi$
$90$	−0.836286	−0.0881522
$91$	13.4455	1.40947
$92$	1.85395	0.193287
$93$	6.14547	0.637255
$94$	18.9362	1.95312
$95$	−0.698031	−0.0716165
$96$	−4.33043	−0.441973
$97$	−6.96996	−0.707692	−0.353846	−	0.935304i	$-0.615126\pi$
$97$	−6.96996	−0.707692	−0.353846	+	0.935304i	$0.615126\pi$
$98$	−1.77653	−0.179456
$99$	12.0653	1.21261
$100$	−21.8732	−2.18732
$101$	10.6031	1.05505	0.527523	−	0.849541i	$-0.323121\pi$
$101$	10.6031	1.05505	0.527523	+	0.849541i	$0.323121\pi$
$102$	18.1494	1.79706
$103$	−8.56052	−0.843493	−0.421746	−	0.906714i	$-0.638583\pi$
$103$	−8.56052	−0.843493	−0.421746	+	0.906714i	$0.638583\pi$
$104$	29.3815	2.88109
$105$	0.439924	0.0429322
$106$	13.5227	1.31344
$107$	11.3294	1.09526	0.547628	−	0.836722i	$-0.315531\pi$
$107$	11.3294	1.09526	0.547628	+	0.836722i	$0.315531\pi$
$108$	−21.7041	−2.08848
$109$	−13.8526	−1.32684	−0.663421	−	0.748247i	$-0.730896\pi$
$109$	−13.8526	−1.32684	−0.663421	+	0.748247i	$0.730896\pi$
$110$	−2.42033	−0.230769
$111$	−2.73863	−0.259939
$112$	−18.1627	−1.71622
$113$	5.60689	0.527452	0.263726	−	0.964598i	$-0.415048\pi$
$113$	5.60689	0.527452	0.263726	+	0.964598i	$0.415048\pi$
$114$	−10.6730	−0.999616
$115$	−0.0682660	−0.00636584
$116$	−19.0736	−1.77094
$117$	9.89179	0.914496
$118$	0.980831	0.0902928
$119$	20.3437	1.86490
$120$	0.961332	0.0877572
$121$	23.9187	2.17443
$122$	−20.9177	−1.89380
$123$	0.768590	0.0693015
$124$	27.6089	2.47935
$125$	1.61508	0.144457
$126$	−14.3329	−1.27687
$127$	12.1835	1.08111	0.540555	−	0.841309i	$-0.318214\pi$
$127$	12.1835	1.08111	0.540555	+	0.841309i	$0.318214\pi$
$128$	13.6517	1.20665
$129$	−2.13053	−0.187583
$130$	−1.98432	−0.174036
$131$	−3.49359	−0.305237	−0.152618	−	0.988285i	$-0.548771\pi$
$131$	−3.49359	−0.305237	−0.152618	+	0.988285i	$0.548771\pi$
$132$	−25.4383	−2.21412
$133$	−11.9634	−1.03735
$134$	12.2836	1.06114
$135$	0.799189	0.0687833
$136$	44.4555	3.81202
$137$	2.76726	0.236423	0.118212	−	0.992988i	$-0.462284\pi$
$137$	2.76726	0.236423	0.118212	+	0.992988i	$0.462284\pi$
$138$	−1.04380	−0.0888539
$139$	6.93485	0.588206	0.294103	−	0.955774i	$-0.404979\pi$
$139$	6.93485	0.588206	0.294103	+	0.955774i	$0.404979\pi$
$140$	1.97638	0.167035
$141$	−7.32845	−0.617167
$142$	31.7732	2.66634
$143$	28.6283	2.39401
$144$	−13.3622	−1.11352
$145$	0.702327	0.0583251
$146$	15.9622	1.32104
$147$	0.687531	0.0567066
$148$	−12.3035	−1.01134
$149$	−8.29142	−0.679259	−0.339630	−	0.940559i	$-0.610302\pi$
$149$	−8.29142	−0.679259	−0.339630	+	0.940559i	$0.610302\pi$
$150$	12.3149	1.00551
$151$	1.74227	0.141784	0.0708919	−	0.997484i	$-0.477415\pi$
$151$	1.74227	0.141784	0.0708919	+	0.997484i	$0.477415\pi$
$152$	−26.1426	−2.12045
$153$	14.9667	1.20999
$154$	−41.4814	−3.34267
$155$	−1.01661	−0.0816564
$156$	−20.8557	−1.66979
$157$	−19.0365	−1.51928	−0.759639	−	0.650345i	$-0.774624\pi$
$157$	−19.0365	−1.51928	−0.759639	+	0.650345i	$0.774624\pi$
$158$	−28.9479	−2.30297
$159$	−5.23339	−0.415035
$160$	0.716362	0.0566334
$161$	−1.16999	−0.0922084
$162$	−3.27354	−0.257194
$163$	6.52152	0.510805	0.255402	−	0.966835i	$-0.417792\pi$
$163$	6.52152	0.510805	0.255402	+	0.966835i	$0.417792\pi$
$164$	3.45294	0.269629
$165$	0.936688	0.0729211
$166$	−6.67798	−0.518311
$167$	1.85396	0.143464	0.0717320	−	0.997424i	$-0.477147\pi$
$167$	1.85396	0.143464	0.0717320	+	0.997424i	$0.477147\pi$
$168$	16.4760	1.27115
$169$	10.4710	0.805460
$170$	−3.00236	−0.230270
$171$	−8.80137	−0.673058
$172$	−9.57154	−0.729823
$173$	3.33392	0.253473	0.126737	−	0.991936i	$-0.459550\pi$
$173$	3.33392	0.253473	0.126737	+	0.991936i	$0.459550\pi$
$174$	10.7387	0.814097
$175$	13.8038	1.04347
$176$	−38.6722	−2.91503
$177$	−0.379590	−0.0285317
$178$	9.84035	0.737565
$179$	−17.8353	−1.33307	−0.666535	−	0.745473i	$-0.732223\pi$
$179$	−17.8353	−1.33307	−0.666535	+	0.745473i	$0.732223\pi$
$180$	1.45401	0.108376
$181$	−4.80281	−0.356990	−0.178495	−	0.983941i	$-0.557123\pi$
$181$	−4.80281	−0.356990	−0.178495	+	0.983941i	$0.557123\pi$
$182$	−34.0087	−2.52089
$183$	8.09533	0.598424
$184$	−2.55670	−0.188482
$185$	0.453038	0.0333080
$186$	−15.5441	−1.13975
$187$	43.3158	3.16757
$188$	−32.9235	−2.40119
$189$	13.6971	0.996317
$190$	1.76558	0.128088
$191$	−5.30196	−0.383637	−0.191818	−	0.981430i	$-0.561438\pi$
$191$	−5.30196	−0.383637	−0.191818	+	0.981430i	$0.561438\pi$
$192$	−1.85918	−0.134175
$193$	−7.62107	−0.548577	−0.274288	−	0.961647i	$-0.588442\pi$
$193$	−7.62107	−0.548577	−0.274288	+	0.961647i	$0.588442\pi$
$194$	17.6296	1.26573
$195$	0.767947	0.0549938
$196$	3.08877	0.220627
$197$	−9.54886	−0.680328	−0.340164	−	0.940366i	$-0.610483\pi$
$197$	−9.54886	−0.680328	−0.340164	+	0.940366i	$0.610483\pi$
$198$	−30.5176	−2.16879
$199$	−2.40958	−0.170810	−0.0854052	−	0.996346i	$-0.527218\pi$
$199$	−2.40958	−0.170810	−0.0854052	+	0.996346i	$0.527218\pi$
$200$	30.1644	2.13294
$201$	−4.75386	−0.335312
$202$	−26.8191	−1.88698
$203$	12.0370	0.844832
$204$	−31.5555	−2.20933
$205$	−0.127144	−0.00888012
$206$	21.6527	1.50862
$207$	−0.860757	−0.0598267
$208$	−31.7055	−2.19838
$209$	−25.4724	−1.76197
$210$	−1.11273	−0.0767856
$211$	19.4546	1.33931	0.669656	−	0.742671i	$-0.266441\pi$
$211$	19.4546	1.33931	0.669656	+	0.742671i	$0.266441\pi$
$212$	−23.5113	−1.61476
$213$	−12.2965	−0.842541
$214$	−28.6563	−1.95890
$215$	0.352443	0.0240364
$216$	29.9312	2.03656
$217$	−17.4235	−1.18278
$218$	35.0384	2.37310
$219$	−6.17752	−0.417438
$220$	4.20813	0.283712
$221$	35.5126	2.38884
$222$	6.92701	0.464910
$223$	22.5652	1.51108	0.755540	−	0.655102i	$-0.227374\pi$
$223$	22.5652	1.51108	0.755540	+	0.655102i	$0.227374\pi$
$224$	12.2775	0.820327
$225$	10.1554	0.677024
$226$	−14.1819	−0.943366
$227$	26.5079	1.75939	0.879697	−	0.475535i	$-0.157746\pi$
$227$	26.5079	1.75939	0.879697	+	0.475535i	$0.157746\pi$
$228$	18.5567	1.22894
$229$	−18.6626	−1.23326	−0.616630	−	0.787253i	$-0.711503\pi$
$229$	−18.6626	−1.23326	−0.616630	+	0.787253i	$0.711503\pi$
$230$	0.172670	0.0113855
$231$	16.0536	1.05625
$232$	26.3035	1.72691
$233$	−0.0871996	−0.00571263	−0.00285632	−	0.999996i	$-0.500909\pi$
$233$	−0.0871996	−0.00571263	−0.00285632	+	0.999996i	$0.500909\pi$
$234$	−25.0200	−1.63561
$235$	1.21231	0.0790823
$236$	−1.70533	−0.111007
$237$	11.2031	0.727719
$238$	−51.4566	−3.33544
$239$	−19.4038	−1.25513	−0.627563	−	0.778566i	$-0.715947\pi$
$239$	−19.4038	−1.25513	−0.627563	+	0.778566i	$0.715947\pi$
$240$	−1.03737	−0.0669622
$241$	24.5488	1.58133	0.790665	−	0.612250i	$-0.209735\pi$
$241$	24.5488	1.58133	0.790665	+	0.612250i	$0.209735\pi$
$242$	−60.4993	−3.88904
$243$	16.0729	1.03108
$244$	36.3688	2.32827
$245$	−0.113735	−0.00726625
$246$	−1.94405	−0.123948
$247$	−20.8837	−1.32880
$248$	−38.0742	−2.41771
$249$	2.58443	0.163782
$250$	−4.08512	−0.258366
$251$	−26.3471	−1.66301	−0.831507	−	0.555515i	$-0.812521\pi$
$251$	−26.3471	−1.66301	−0.831507	+	0.555515i	$0.812521\pi$
$252$	24.9200	1.56981
$253$	−2.49115	−0.156618
$254$	−30.8165	−1.93360
$255$	1.16194	0.0727634
$256$	−30.7315	−1.92072
$257$	−26.5632	−1.65697	−0.828484	−	0.560013i	$-0.810796\pi$
$257$	−26.5632	−1.65697	−0.828484	+	0.560013i	$0.810796\pi$
$258$	5.38890	0.335498
$259$	7.76449	0.482462
$260$	3.45005	0.213963
$261$	8.85555	0.548145
$262$	8.83658	0.545926
$263$	−29.8178	−1.83864	−0.919321	−	0.393508i	$-0.871261\pi$
$263$	−29.8178	−1.83864	−0.919321	+	0.393508i	$0.871261\pi$
$264$	35.0808	2.15907
$265$	0.865734	0.0531816
$266$	30.2597	1.85534
$267$	−3.80830	−0.233064
$268$	−21.3570	−1.30459
$269$	−21.3456	−1.30147	−0.650733	−	0.759307i	$-0.725538\pi$
$269$	−21.3456	−1.30147	−0.650733	+	0.759307i	$0.725538\pi$
$270$	−2.02144	−0.123021
$271$	−1.41354	−0.0858666	−0.0429333	−	0.999078i	$-0.513670\pi$
$271$	−1.41354	−0.0858666	−0.0429333	+	0.999078i	$0.513670\pi$
$272$	−47.9719	−2.90872
$273$	13.1616	0.796578
$274$	−6.99943	−0.422851
$275$	29.3911	1.77235
$276$	1.81480	0.109238
$277$	−31.9542	−1.91994	−0.959972	−	0.280097i	$-0.909633\pi$
$277$	−31.9542	−1.91994	−0.959972	+	0.280097i	$0.909633\pi$
$278$	−17.5408	−1.05203
$279$	−12.8183	−0.767414
$280$	−2.72554	−0.162882
$281$	8.01829	0.478331	0.239165	−	0.970979i	$-0.423126\pi$
$281$	8.01829	0.478331	0.239165	+	0.970979i	$0.423126\pi$
$282$	18.5364	1.10382
$283$	11.5504	0.686598	0.343299	−	0.939226i	$-0.388456\pi$
$283$	11.5504	0.686598	0.343299	+	0.939226i	$0.388456\pi$
$284$	−55.2426	−3.27805
$285$	−0.683293	−0.0404748
$286$	−72.4114	−4.28178
$287$	−2.17909	−0.128627
$288$	9.03250	0.532245
$289$	36.7322	2.16072
$290$	−1.77644	−0.104316
$291$	−6.82280	−0.399960
$292$	−27.7529	−1.62411
$293$	−16.5509	−0.966916	−0.483458	−	0.875368i	$-0.660619\pi$
$293$	−16.5509	−0.966916	−0.483458	+	0.875368i	$0.660619\pi$
$294$	−1.73902	−0.101422
$295$	0.0627936	0.00365598
$296$	16.9672	0.986196
$297$	29.1639	1.69226
$298$	20.9721	1.21488
$299$	−2.04238	−0.118114
$300$	−21.4114	−1.23619
$301$	6.04043	0.348164
$302$	−4.40684	−0.253585
$303$	10.3792	0.596270
$304$	28.2105	1.61798
$305$	−1.33917	−0.0766807
$306$	−37.8563	−2.16410
$307$	7.92647	0.452388	0.226194	−	0.974082i	$-0.427372\pi$
$307$	7.92647	0.452388	0.226194	+	0.974082i	$0.427372\pi$
$308$	72.1219	4.10953
$309$	−8.37977	−0.476709
$310$	2.57139	0.146045
$311$	−14.3157	−0.811769	−0.405884	−	0.913924i	$-0.633036\pi$
$311$	−14.3157	−0.811769	−0.405884	+	0.913924i	$0.633036\pi$
$312$	28.7611	1.62828
$313$	8.01698	0.453147	0.226573	−	0.973994i	$-0.427248\pi$
$313$	8.01698	0.453147	0.226573	+	0.973994i	$0.427248\pi$
$314$	48.1503	2.71728
$315$	−0.917602	−0.0517010
$316$	50.3305	2.83131
$317$	−9.23607	−0.518749	−0.259375	−	0.965777i	$-0.583516\pi$
$317$	−9.23607	−0.518749	−0.259375	+	0.965777i	$0.583516\pi$
$318$	13.2372	0.742304
$319$	25.6292	1.43496
$320$	0.307556	0.0171929
$321$	11.0902	0.618996
$322$	2.95934	0.164918
$323$	−31.5979	−1.75816
$324$	5.69157	0.316198
$325$	24.0964	1.33663
$326$	−16.4953	−0.913591
$327$	−13.5602	−0.749878
$328$	−4.76179	−0.262926
$329$	20.7774	1.14550
$330$	−2.36923	−0.130422
$331$	−10.3689	−0.569924	−0.284962	−	0.958539i	$-0.591981\pi$
$331$	−10.3689	−0.569924	−0.284962	+	0.958539i	$0.591981\pi$
$332$	11.6107	0.637221
$333$	5.71229	0.313032
$334$	−4.68935	−0.256590
$335$	0.786408	0.0429660
$336$	−17.7793	−0.969939
$337$	−19.9650	−1.08756	−0.543781	−	0.839227i	$-0.683008\pi$
$337$	−19.9650	−1.08756	−0.543781	+	0.839227i	$0.683008\pi$
$338$	−26.4850	−1.44059
$339$	5.48851	0.298095
$340$	5.22007	0.283098
$341$	−37.0981	−2.00898
$342$	22.2619	1.20379
$343$	17.4779	0.943719
$344$	13.1997	0.711679
$345$	−0.0668247	−0.00359772
$346$	−8.43271	−0.453345
$347$	−17.6524	−0.947630	−0.473815	−	0.880624i	$-0.657123\pi$
$347$	−17.6524	−0.947630	−0.473815	+	0.880624i	$0.657123\pi$
$348$	−18.6709	−1.00086
$349$	26.8928	1.43954	0.719770	−	0.694213i	$-0.244247\pi$
$349$	26.8928	1.43954	0.719770	+	0.694213i	$0.244247\pi$
$350$	−34.9149	−1.86628
$351$	23.9101	1.27623
$352$	26.1414	1.39334
$353$	29.0029	1.54367	0.771834	−	0.635824i	$-0.219339\pi$
$353$	29.0029	1.54367	0.771834	+	0.635824i	$0.219339\pi$
$354$	0.960122	0.0510299
$355$	2.03414	0.107961
$356$	−17.1090	−0.906775
$357$	19.9141	1.05397
$358$	45.1120	2.38424
$359$	5.16606	0.272654	0.136327	−	0.990664i	$-0.456470\pi$
$359$	5.16606	0.272654	0.136327	+	0.990664i	$0.456470\pi$
$360$	−2.00517	−0.105682
$361$	−0.418423	−0.0220223
$362$	12.1481	0.638489
$363$	23.4137	1.22890
$364$	59.1294	3.09922
$365$	1.02192	0.0534895
$366$	−20.4761	−1.07030
$367$	−13.2289	−0.690543	−0.345271	−	0.938503i	$-0.612213\pi$
$367$	−13.2289	−0.690543	−0.345271	+	0.938503i	$0.612213\pi$
$368$	2.75893	0.143819
$369$	−1.60314	−0.0834562
$370$	−1.14590	−0.0595725
$371$	14.8376	0.770329
$372$	27.0259	1.40123
$373$	6.43713	0.333302	0.166651	−	0.986016i	$-0.446705\pi$
$373$	6.43713	0.333302	0.166651	+	0.986016i	$0.446705\pi$
$374$	−109.562	−5.66530
$375$	1.58098	0.0816413
$376$	45.4033	2.34150
$377$	21.0122	1.08218
$378$	−34.6450	−1.78195
$379$	17.0804	0.877359	0.438679	−	0.898644i	$-0.355446\pi$
$379$	17.0804	0.877359	0.438679	+	0.898644i	$0.355446\pi$
$380$	−3.06973	−0.157474
$381$	11.9262	0.611000
$382$	13.4106	0.686147
$383$	−3.91876	−0.200239	−0.100120	−	0.994975i	$-0.531923\pi$
$383$	−3.91876	−0.200239	−0.100120	+	0.994975i	$0.531923\pi$
$384$	13.3634	0.681950
$385$	−2.65567	−0.135346
$386$	19.2765	0.981148
$387$	4.44391	0.225896
$388$	−30.6518	−1.55611
$389$	8.48580	0.430247	0.215124	−	0.976587i	$-0.430985\pi$
$389$	8.48580	0.430247	0.215124	+	0.976587i	$0.430985\pi$
$390$	−1.94242	−0.0983583
$391$	−3.09021	−0.156279
$392$	−4.25959	−0.215142
$393$	−3.41983	−0.172508
$394$	24.1526	1.21679
$395$	−1.85327	−0.0932482
$396$	53.0597	2.66635
$397$	−3.63753	−0.182562	−0.0912812	−	0.995825i	$-0.529096\pi$
$397$	−3.63753	−0.182562	−0.0912812	+	0.995825i	$0.529096\pi$
$398$	6.09471	0.305500
$399$	−11.7108	−0.586272
$400$	−32.5504	−1.62752
$401$	−27.3949	−1.36803	−0.684017	−	0.729466i	$-0.739769\pi$
$401$	−27.3949	−1.36803	−0.684017	+	0.729466i	$0.739769\pi$
$402$	12.0243	0.599716
$403$	−30.4150	−1.51508
$404$	46.6292	2.31989
$405$	−0.209575	−0.0104139
$406$	−30.4460	−1.51101
$407$	16.5322	0.819470
$408$	43.5168	2.15440
$409$	14.7397	0.728833	0.364417	−	0.931236i	$-0.381268\pi$
$409$	14.7397	0.728833	0.364417	+	0.931236i	$0.381268\pi$
$410$	0.321594	0.0158824
$411$	2.70884	0.133617
$412$	−37.6466	−1.85472
$413$	1.07620	0.0529565
$414$	2.17717	0.107002
$415$	−0.427529	−0.0209866
$416$	21.4321	1.05079
$417$	6.78843	0.332431
$418$	64.4292	3.15133
$419$	−23.6021	−1.15304	−0.576520	−	0.817083i	$-0.695590\pi$
$419$	−23.6021	−1.15304	−0.576520	+	0.817083i	$0.695590\pi$
$420$	1.93466	0.0944015
$421$	29.6978	1.44738	0.723691	−	0.690124i	$-0.242444\pi$
$421$	29.6978	1.44738	0.723691	+	0.690124i	$0.242444\pi$
$422$	−49.2080	−2.39541
$423$	15.2858	0.743222
$424$	32.4234	1.57462
$425$	36.4589	1.76852
$426$	31.1023	1.50691
$427$	−22.9517	−1.11071
$428$	49.8234	2.40831
$429$	28.0238	1.35300
$430$	−0.891458	−0.0429899
$431$	39.8240	1.91825	0.959127	−	0.282976i	$-0.0913215\pi$
$431$	39.8240	1.91825	0.959127	+	0.282976i	$0.0913215\pi$
$432$	−32.2988	−1.55398
$433$	−12.4323	−0.597457	−0.298728	−	0.954338i	$-0.596562\pi$
$433$	−12.4323	−0.597457	−0.298728	+	0.954338i	$0.596562\pi$
$434$	44.0704	2.11544
$435$	0.687499	0.0329630
$436$	−60.9198	−2.91753
$437$	1.81724	0.0869304
$438$	15.6252	0.746602
$439$	−30.3138	−1.44680	−0.723399	−	0.690430i	$-0.757421\pi$
$439$	−30.3138	−1.44680	−0.723399	+	0.690430i	$0.757421\pi$
$440$	−5.80324	−0.276659
$441$	−1.43407	−0.0682888
$442$	−89.8245	−4.27252
$443$	19.5072	0.926816	0.463408	−	0.886145i	$-0.346627\pi$
$443$	19.5072	0.926816	0.463408	+	0.886145i	$0.346627\pi$
$444$	−12.0437	−0.571568
$445$	0.629987	0.0298643
$446$	−57.0758	−2.70262
$447$	−8.11636	−0.383891
$448$	5.27111	0.249037
$449$	−26.0914	−1.23133	−0.615666	−	0.788007i	$-0.711113\pi$
$449$	−26.0914	−1.23133	−0.615666	+	0.788007i	$0.711113\pi$
$450$	−25.6867	−1.21088
$451$	−4.63972	−0.218476
$452$	24.6575	1.15979
$453$	1.70548	0.0801306
$454$	−67.0483	−3.14673
$455$	−2.17726	−0.102072
$456$	−25.5907	−1.19839
$457$	−21.3783	−1.00003	−0.500017	−	0.866015i	$-0.666673\pi$
$457$	−21.3783	−1.00003	−0.500017	+	0.866015i	$0.666673\pi$
$458$	47.2046	2.20573
$459$	36.1771	1.68860
$460$	−0.300214	−0.0139975
$461$	−3.68909	−0.171818	−0.0859090	−	0.996303i	$-0.527379\pi$
$461$	−3.68909	−0.171818	−0.0859090	+	0.996303i	$0.527379\pi$
$462$	−40.6056	−1.88914
$463$	14.7447	0.685245	0.342623	−	0.939473i	$-0.388685\pi$
$463$	14.7447	0.685245	0.342623	+	0.939473i	$0.388685\pi$
$464$	−28.3842	−1.31770
$465$	−0.995149	−0.0461489
$466$	0.220560	0.0102172
$467$	−23.1439	−1.07097	−0.535487	−	0.844544i	$-0.679872\pi$
$467$	−23.1439	−1.07097	−0.535487	+	0.844544i	$0.679872\pi$
$468$	43.5012	2.01084
$469$	13.4780	0.622357
$470$	−3.06637	−0.141441
$471$	−18.6346	−0.858636
$472$	2.35174	0.108248
$473$	12.8613	0.591363
$474$	−28.3367	−1.30155
$475$	−21.4401	−0.983741
$476$	89.4654	4.10064
$477$	10.9159	0.499806
$478$	49.0793	2.24483
$479$	−16.5718	−0.757186	−0.378593	−	0.925563i	$-0.623592\pi$
$479$	−16.5718	−0.757186	−0.378593	+	0.925563i	$0.623592\pi$
$480$	0.701237	0.0320069
$481$	13.5540	0.618008
$482$	−62.0930	−2.82826
$483$	−1.14529	−0.0521125
$484$	105.188	4.78125
$485$	1.12866	0.0512499
$486$	−40.6542	−1.84411
$487$	35.5317	1.61010	0.805048	−	0.593210i	$-0.202140\pi$
$487$	35.5317	1.61010	0.805048	+	0.593210i	$0.202140\pi$
$488$	−50.1545	−2.27039
$489$	6.38383	0.288687
$490$	0.287677	0.0129959
$491$	4.57004	0.206243	0.103121	−	0.994669i	$-0.467117\pi$
$491$	4.57004	0.206243	0.103121	+	0.994669i	$0.467117\pi$
$492$	3.38003	0.152384
$493$	31.7924	1.43186
$494$	52.8225	2.37660
$495$	−1.95376	−0.0878151
$496$	41.0858	1.84481
$497$	34.8626	1.56380
$498$	−6.53698	−0.292929
$499$	7.29942	0.326767	0.163383	−	0.986563i	$-0.447759\pi$
$499$	7.29942	0.326767	0.163383	+	0.986563i	$0.447759\pi$
$500$	7.10263	0.317639
$501$	1.81482	0.0810801
$502$	66.6415	2.97436
$503$	−16.8588	−0.751699	−0.375849	−	0.926681i	$-0.622649\pi$
$503$	−16.8588	−0.751699	−0.375849	+	0.926681i	$0.622649\pi$
$504$	−34.3660	−1.53078
$505$	−1.71698	−0.0764046
$506$	6.30105	0.280116
$507$	10.2499	0.455214
$508$	53.5794	2.37720
$509$	28.5617	1.26598	0.632989	−	0.774161i	$-0.281828\pi$
$509$	28.5617	1.26598	0.632989	+	0.774161i	$0.281828\pi$
$510$	−2.93897	−0.130140
$511$	17.5143	0.774788
$512$	50.4280	2.22862
$513$	−21.2744	−0.939288
$514$	67.1882	2.96354
$515$	1.38622	0.0610843
$516$	−9.36945	−0.412467
$517$	44.2394	1.94565
$518$	−19.6393	−0.862900
$519$	3.26353	0.143253
$520$	−4.75781	−0.208644
$521$	3.80707	0.166791	0.0833954	−	0.996517i	$-0.473424\pi$
$521$	3.80707	0.166791	0.0833954	+	0.996517i	$0.473424\pi$
$522$	−22.3989	−0.980375
$523$	−6.09467	−0.266501	−0.133251	−	0.991082i	$-0.542542\pi$
$523$	−6.09467	−0.266501	−0.133251	+	0.991082i	$0.542542\pi$
$524$	−15.3638	−0.671170
$525$	13.5123	0.589727
$526$	75.4201	3.28847
$527$	−46.0193	−2.00463
$528$	−37.8557	−1.64746
$529$	−22.8223	−0.992273
$530$	−2.18976	−0.0951171
$531$	0.791756	0.0343593
$532$	−52.6113	−2.28099
$533$	−3.80389	−0.164765
$534$	9.63258	0.416843
$535$	−1.83460	−0.0793166
$536$	29.4525	1.27215
$537$	−17.4587	−0.753399
$538$	53.9909	2.32772
$539$	−4.15039	−0.178770
$540$	3.51460	0.151244
$541$	−11.8661	−0.510163	−0.255081	−	0.966920i	$-0.582102\pi$
$541$	−11.8661	−0.510163	−0.255081	+	0.966920i	$0.582102\pi$
$542$	3.57537	0.153575
$543$	−4.70141	−0.201757
$544$	32.4277	1.39033
$545$	2.24319	0.0960876
$546$	−33.2906	−1.42471
$547$	−30.5823	−1.30760	−0.653801	−	0.756666i	$-0.726827\pi$
$547$	−30.5823	−1.30760	−0.653801	+	0.756666i	$0.726827\pi$
$548$	12.1696	0.519860
$549$	−16.8854	−0.720652
$550$	−74.3409	−3.16991
$551$	−18.6959	−0.796474
$552$	−2.50272	−0.106523
$553$	−31.7627	−1.35069
$554$	80.8240	3.43388
$555$	0.443473	0.0188244
$556$	30.4974	1.29338
$557$	37.2546	1.57853	0.789265	−	0.614053i	$-0.210462\pi$
$557$	37.2546	1.57853	0.789265	+	0.614053i	$0.210462\pi$
$558$	32.4223	1.37255
$559$	10.5444	0.445980
$560$	2.94113	0.124286
$561$	42.4013	1.79018
$562$	−20.2812	−0.855511
$563$	28.2201	1.18933	0.594667	−	0.803972i	$-0.297284\pi$
$563$	28.2201	1.18933	0.594667	+	0.803972i	$0.297284\pi$
$564$	−32.2284	−1.35706
$565$	−0.907937	−0.0381972
$566$	−29.2151	−1.22800
$567$	−3.59185	−0.150843
$568$	76.1826	3.19655
$569$	15.5926	0.653677	0.326838	−	0.945080i	$-0.394017\pi$
$569$	15.5926	0.653677	0.326838	+	0.945080i	$0.394017\pi$
$570$	1.72830	0.0723905
$571$	31.4602	1.31657	0.658284	−	0.752770i	$-0.271283\pi$
$571$	31.4602	1.31657	0.658284	+	0.752770i	$0.271283\pi$
$572$	125.899	5.26409
$573$	−5.19002	−0.216816
$574$	5.51171	0.230054
$575$	−2.09680	−0.0874428
$576$	3.87793	0.161580
$577$	−9.15920	−0.381302	−0.190651	−	0.981658i	$-0.561060\pi$
$577$	−9.15920	−0.381302	−0.190651	+	0.981658i	$0.561060\pi$
$578$	−92.9092	−3.86451
$579$	−7.46017	−0.310034
$580$	3.08863	0.128248
$581$	−7.32731	−0.303988
$582$	17.2574	0.715341
$583$	31.5922	1.30842
$584$	38.2727	1.58374
$585$	−1.60180	−0.0662263
$586$	41.8634	1.72936
$587$	−45.2912	−1.86937	−0.934684	−	0.355479i	$-0.884318\pi$
$587$	−45.2912	−1.86937	−0.934684	+	0.355479i	$0.884318\pi$
$588$	3.02356	0.124689
$589$	27.0622	1.11508
$590$	−0.158828	−0.00653885
$591$	−9.34725	−0.384495
$592$	−18.3093	−0.752506
$593$	2.25231	0.0924914	0.0462457	−	0.998930i	$-0.485274\pi$
$593$	2.25231	0.0924914	0.0462457	+	0.998930i	$0.485274\pi$
$594$	−73.7662	−3.02667
$595$	−3.29430	−0.135053
$596$	−36.4632	−1.49359
$597$	−2.35870	−0.0965352
$598$	5.16594	0.211251
$599$	43.0609	1.75942	0.879710	−	0.475510i	$-0.157737\pi$
$599$	43.0609	1.75942	0.879710	+	0.475510i	$0.157737\pi$
$600$	29.5275	1.20545
$601$	−5.90362	−0.240814	−0.120407	−	0.992725i	$-0.538420\pi$
$601$	−5.90362	−0.240814	−0.120407	+	0.992725i	$0.538420\pi$
$602$	−15.2785	−0.622704
$603$	9.91571	0.403799
$604$	7.66198	0.311762
$605$	−3.87321	−0.157469
$606$	−26.2528	−1.06645
$607$	−37.6439	−1.52792	−0.763960	−	0.645264i	$-0.776747\pi$
$607$	−37.6439	−1.52792	−0.763960	+	0.645264i	$0.776747\pi$
$608$	−19.0695	−0.773372
$609$	11.7829	0.477465
$610$	3.38726	0.137146
$611$	36.2698	1.46732
$612$	65.8192	2.66058
$613$	1.83469	0.0741023	0.0370511	−	0.999313i	$-0.488204\pi$
$613$	1.83469	0.0741023	0.0370511	+	0.999313i	$0.488204\pi$
$614$	−20.0490	−0.809110
$615$	−0.124460	−0.00501869
$616$	−99.4601	−4.00736
$617$	6.79004	0.273357	0.136678	−	0.990615i	$-0.456357\pi$
$617$	6.79004	0.273357	0.136678	+	0.990615i	$0.456357\pi$
$618$	21.1955	0.852609
$619$	−25.0593	−1.00722	−0.503609	−	0.863932i	$-0.667995\pi$
$619$	−25.0593	−1.00722	−0.503609	+	0.863932i	$0.667995\pi$
$620$	−4.47077	−0.179550
$621$	−2.08060	−0.0834914
$622$	36.2097	1.45188
$623$	10.7972	0.432580
$624$	−31.0361	−1.24244
$625$	24.6074	0.984294
$626$	−20.2779	−0.810468
$627$	−24.9346	−0.995793
$628$	−83.7169	−3.34067
$629$	20.5078	0.817698
$630$	2.32095	0.0924690
$631$	−31.0347	−1.23547	−0.617736	−	0.786385i	$-0.711950\pi$
$631$	−31.0347	−1.23547	−0.617736	+	0.786385i	$0.711950\pi$
$632$	−69.4086	−2.76093
$633$	19.0439	0.756927
$634$	23.3614	0.927801
$635$	−1.97290	−0.0782921
$636$	−23.0149	−0.912601
$637$	−3.40271	−0.134820
$638$	−64.8258	−2.56648
$639$	25.6482	1.01463
$640$	−2.21064	−0.0873834
$641$	42.8225	1.69139	0.845694	−	0.533668i	$-0.179187\pi$
$641$	42.8225	1.69139	0.845694	+	0.533668i	$0.179187\pi$
$642$	−28.0512	−1.10709
$643$	−48.7876	−1.92399	−0.961997	−	0.273060i	$-0.911964\pi$
$643$	−48.7876	−1.92399	−0.961997	+	0.273060i	$0.911964\pi$
$644$	−5.14528	−0.202753
$645$	0.345002	0.0135844
$646$	79.9228	3.14452
$647$	−12.6130	−0.495869	−0.247934	−	0.968777i	$-0.579752\pi$
$647$	−12.6130	−0.495869	−0.247934	+	0.968777i	$0.579752\pi$
$648$	−7.84899	−0.308337
$649$	2.29145	0.0899475
$650$	−60.9486	−2.39060
$651$	−17.0556	−0.668461
$652$	28.6797	1.12318
$653$	−18.2472	−0.714067	−0.357034	−	0.934091i	$-0.616212\pi$
$653$	−18.2472	−0.714067	−0.357034	+	0.934091i	$0.616212\pi$
$654$	34.2986	1.34118
$655$	0.565725	0.0221047
$656$	5.13845	0.200623
$657$	12.8852	0.502699
$658$	−52.5538	−2.04876
$659$	−18.6429	−0.726226	−0.363113	−	0.931745i	$-0.618286\pi$
$659$	−18.6429	−0.726226	−0.363113	+	0.931745i	$0.618286\pi$
$660$	4.11928	0.160343
$661$	7.55350	0.293797	0.146899	−	0.989152i	$-0.453071\pi$
$661$	7.55350	0.293797	0.146899	+	0.989152i	$0.453071\pi$
$662$	26.2267	1.01933
$663$	34.7628	1.35008
$664$	−16.0118	−0.621379
$665$	1.93725	0.0751235
$666$	−14.4485	−0.559868
$667$	−1.82843	−0.0707970
$668$	8.15318	0.315456
$669$	22.0888	0.854003
$670$	−1.98911	−0.0768462
$671$	−48.8688	−1.88656
$672$	12.0183	0.463616
$673$	−41.9897	−1.61858	−0.809292	−	0.587406i	$-0.800149\pi$
$673$	−41.9897	−1.61858	−0.809292	+	0.587406i	$0.800149\pi$
$674$	50.4988	1.94514
$675$	24.5472	0.944824
$676$	46.0483	1.77109
$677$	−8.41749	−0.323510	−0.161755	−	0.986831i	$-0.551716\pi$
$677$	−8.41749	−0.323510	−0.161755	+	0.986831i	$0.551716\pi$
$678$	−13.8825	−0.533153
$679$	19.3438	0.742347
$680$	−7.19877	−0.276060
$681$	25.9483	0.994339
$682$	93.8348	3.59312
$683$	−15.4750	−0.592133	−0.296066	−	0.955167i	$-0.595675\pi$
$683$	−15.4750	−0.592133	−0.296066	+	0.955167i	$0.595675\pi$
$684$	−38.7058	−1.47995
$685$	−0.448109	−0.0171214
$686$	−44.2081	−1.68787
$687$	−18.2686	−0.696990
$688$	−14.2438	−0.543039
$689$	25.9010	0.986750
$690$	0.169024	0.00643465
$691$	25.6059	0.974095	0.487048	−	0.873375i	$-0.338074\pi$
$691$	25.6059	0.974095	0.487048	+	0.873375i	$0.338074\pi$
$692$	14.6616	0.557350
$693$	−33.4850	−1.27199
$694$	44.6494	1.69487
$695$	−1.12298	−0.0425969
$696$	25.7482	0.975982
$697$	−5.75546	−0.218003
$698$	−68.0218	−2.57466
$699$	−0.0853585	−0.00322855
$700$	60.7050	2.29443
$701$	−3.13580	−0.118438	−0.0592188	−	0.998245i	$-0.518861\pi$
$701$	−3.13580	−0.118438	−0.0592188	+	0.998245i	$0.518861\pi$
$702$	−60.4775	−2.28258
$703$	−12.0599	−0.454846
$704$	11.2233	0.422993
$705$	1.18671	0.0446942
$706$	−73.3590	−2.76090
$707$	−29.4269	−1.10671
$708$	−1.66932	−0.0627370
$709$	31.3755	1.17833	0.589165	−	0.808012i	$-0.299457\pi$
$709$	31.3755	1.17833	0.589165	+	0.808012i	$0.299457\pi$
$710$	−5.14510	−0.193092
$711$	−23.3676	−0.876355
$712$	23.5942	0.884232
$713$	2.64663	0.0991172
$714$	−50.3702	−1.88506
$715$	−4.63584	−0.173370
$716$	−78.4343	−2.93123
$717$	−18.9941	−0.709347
$718$	−13.0669	−0.487652
$719$	−33.4250	−1.24654	−0.623271	−	0.782006i	$-0.714197\pi$
$719$	−33.4250	−1.24654	−0.623271	+	0.782006i	$0.714197\pi$
$720$	2.16378	0.0806392
$721$	23.7581	0.884798
$722$	1.05835	0.0393876
$723$	24.0305	0.893705
$724$	−21.1214	−0.784969
$725$	21.5721	0.801168
$726$	−59.2219	−2.19793
$727$	30.0575	1.11477	0.557385	−	0.830254i	$-0.311805\pi$
$727$	30.0575	1.11477	0.557385	+	0.830254i	$0.311805\pi$
$728$	−81.5427	−3.02218
$729$	11.8509	0.438922
$730$	−2.58480	−0.0956678
$731$	15.9541	0.590085
$732$	35.6009	1.31585
$733$	40.3323	1.48971	0.744853	−	0.667228i	$-0.232519\pi$
$733$	40.3323	1.48971	0.744853	+	0.667228i	$0.232519\pi$
$734$	33.4608	1.23506
$735$	−0.111333	−0.00410659
$736$	−1.86496	−0.0687435
$737$	28.6975	1.05709
$738$	4.05493	0.149264
$739$	−21.2826	−0.782895	−0.391447	−	0.920201i	$-0.628025\pi$
$739$	−21.2826	−0.782895	−0.391447	+	0.920201i	$0.628025\pi$
$740$	1.99233	0.0732394
$741$	−20.4427	−0.750983
$742$	−37.5297	−1.37776
$743$	23.3360	0.856114	0.428057	−	0.903752i	$-0.359198\pi$
$743$	23.3360	0.856114	0.428057	+	0.903752i	$0.359198\pi$
$744$	−37.2703	−1.36639
$745$	1.34265	0.0491908
$746$	−16.2819	−0.596122
$747$	−5.39066	−0.197234
$748$	190.490	6.96501
$749$	−31.4427	−1.14889
$750$	−3.99887	−0.146018
$751$	−29.3268	−1.07015	−0.535074	−	0.844805i	$-0.679716\pi$
$751$	−29.3268	−1.07015	−0.535074	+	0.844805i	$0.679716\pi$
$752$	−48.9947	−1.78665
$753$	−25.7908	−0.939869
$754$	−53.1476	−1.93552
$755$	−0.282129	−0.0102677
$756$	60.2358	2.19075
$757$	10.7547	0.390886	0.195443	−	0.980715i	$-0.437386\pi$
$757$	10.7547	0.390886	0.195443	+	0.980715i	$0.437386\pi$
$758$	−43.2025	−1.56919
$759$	−2.43856	−0.0885140
$760$	4.23333	0.153559
$761$	9.57577	0.347122	0.173561	−	0.984823i	$-0.444473\pi$
$761$	9.57577	0.347122	0.173561	+	0.984823i	$0.444473\pi$
$762$	−30.1659	−1.09279
$763$	38.4454	1.39182
$764$	−23.3165	−0.843560
$765$	−2.42359	−0.0876252
$766$	9.91198	0.358134
$767$	1.87866	0.0678344
$768$	−30.0827	−1.08551
$769$	−53.5550	−1.93124	−0.965621	−	0.259955i	$-0.916292\pi$
$769$	−53.5550	−1.93124	−0.965621	+	0.259955i	$0.916292\pi$
$770$	6.71717	0.242070
$771$	−26.0024	−0.936453
$772$	−33.5152	−1.20624
$773$	20.2335	0.727750	0.363875	−	0.931448i	$-0.381454\pi$
$773$	20.2335	0.727750	0.363875	+	0.931448i	$0.381454\pi$
$774$	−11.2403	−0.404023
$775$	−31.2255	−1.12165
$776$	42.2706	1.51742
$777$	7.60056	0.272669
$778$	−21.4637	−0.769512
$779$	3.38457	0.121265
$780$	3.37720	0.120923
$781$	74.2297	2.65615
$782$	7.81629	0.279510
$783$	21.4054	0.764965
$784$	4.59652	0.164162
$785$	3.08262	0.110024
$786$	8.65001	0.308536
$787$	−7.56890	−0.269802	−0.134901	−	0.990859i	$-0.543072\pi$
$787$	−7.56890	−0.269802	−0.134901	+	0.990859i	$0.543072\pi$
$788$	−41.9931	−1.49594
$789$	−29.1882	−1.03913
$790$	4.68760	0.166777
$791$	−15.5609	−0.553281
$792$	−73.1722	−2.60006
$793$	−40.0653	−1.42276
$794$	9.20065	0.326519
$795$	0.847455	0.0300561
$796$	−10.5966	−0.375587
$797$	−55.9963	−1.98349	−0.991745	−	0.128229i	$-0.959071\pi$
$797$	−55.9963	−1.98349	−0.991745	+	0.128229i	$0.959071\pi$
$798$	29.6209	1.04857
$799$	54.8778	1.94144
$800$	22.0032	0.777930
$801$	7.94342	0.280667
$802$	69.2917	2.44678
$803$	37.2916	1.31599
$804$	−20.9061	−0.737301
$805$	0.189460	0.00667757
$806$	76.9308	2.70977
$807$	−20.8949	−0.735537
$808$	−64.3043	−2.26222
$809$	−46.9221	−1.64969	−0.824846	−	0.565357i	$-0.808738\pi$
$809$	−46.9221	−1.64969	−0.824846	+	0.565357i	$0.808738\pi$
$810$	0.530092	0.0186255
$811$	26.6826	0.936953	0.468476	−	0.883476i	$-0.344803\pi$
$811$	26.6826	0.936953	0.468476	+	0.883476i	$0.344803\pi$
$812$	52.9352	1.85766
$813$	−1.38370	−0.0485284
$814$	−41.8160	−1.46565
$815$	−1.05604	−0.0369916
$816$	−46.9590	−1.64390
$817$	−9.38203	−0.328236
$818$	−37.2822	−1.30354
$819$	−27.4528	−0.959279
$820$	−0.559142	−0.0195261
$821$	5.80456	0.202581	0.101290	−	0.994857i	$-0.467703\pi$
$821$	5.80456	0.202581	0.101290	+	0.994857i	$0.467703\pi$
$822$	−6.85165	−0.238979
$823$	−53.0223	−1.84824	−0.924120	−	0.382102i	$-0.875200\pi$
$823$	−53.0223	−1.84824	−0.924120	+	0.382102i	$0.875200\pi$
$824$	51.9168	1.80861
$825$	28.7705	1.00166
$826$	−2.72211	−0.0947144
$827$	−52.3758	−1.82129	−0.910643	−	0.413194i	$-0.864413\pi$
$827$	−52.3758	−1.82129	−0.910643	+	0.413194i	$0.864413\pi$
$828$	−3.78536	−0.131550
$829$	−12.1802	−0.423035	−0.211518	−	0.977374i	$-0.567841\pi$
$829$	−12.1802	−0.423035	−0.211518	+	0.977374i	$0.567841\pi$
$830$	1.08138	0.0375352
$831$	−31.2796	−1.08508
$832$	9.20144	0.319003
$833$	−5.14846	−0.178383
$834$	−17.1704	−0.594564
$835$	−0.300216	−0.0103894
$836$	−112.020	−3.87430
$837$	−30.9841	−1.07097
$838$	59.6985	2.06225
$839$	29.2163	1.00866	0.504330	−	0.863511i	$-0.331740\pi$
$839$	29.2163	1.00866	0.504330	+	0.863511i	$0.331740\pi$
$840$	−2.66800	−0.0920547
$841$	−10.1890	−0.351344
$842$	−75.1167	−2.58869
$843$	7.84899	0.270334
$844$	85.5558	2.94495
$845$	−1.69559	−0.0583300
$846$	−38.6635	−1.32928
$847$	−66.3820	−2.28091
$848$	−34.9881	−1.20150
$849$	11.3065	0.388038
$850$	−92.2180	−3.16305
$851$	−1.17943	−0.0404304
$852$	−54.0763	−1.85262
$853$	−5.93669	−0.203268	−0.101634	−	0.994822i	$-0.532407\pi$
$853$	−5.93669	−0.203268	−0.101634	+	0.994822i	$0.532407\pi$
$854$	58.0532	1.98654
$855$	1.42523	0.0487417
$856$	−68.7093	−2.34844
$857$	29.0652	0.992847	0.496424	−	0.868080i	$-0.334646\pi$
$857$	29.0652	0.992847	0.496424	+	0.868080i	$0.334646\pi$
$858$	−70.8825	−2.41989
$859$	−35.6817	−1.21745	−0.608723	−	0.793383i	$-0.708318\pi$
$859$	−35.6817	−1.21745	−0.608723	+	0.793383i	$0.708318\pi$
$860$	1.54994	0.0528525
$861$	−2.13308	−0.0726951
$862$	−100.730	−3.43086
$863$	22.4626	0.764636	0.382318	−	0.924031i	$-0.375126\pi$
$863$	22.4626	0.764636	0.382318	+	0.924031i	$0.375126\pi$
$864$	21.8331	0.742777
$865$	−0.539869	−0.0183561
$866$	31.4458	1.06857
$867$	35.9566	1.22115
$868$	−76.6232	−2.60076
$869$	−67.6293	−2.29417
$870$	−1.73894	−0.0589555
$871$	23.5277	0.797207
$872$	84.0118	2.84500
$873$	14.2311	0.481651
$874$	−4.59647	−0.155478
$875$	−4.48234	−0.151531
$876$	−27.1669	−0.917884
$877$	−9.38224	−0.316816	−0.158408	−	0.987374i	$-0.550636\pi$
$877$	−9.38224	−0.316816	−0.158408	+	0.987374i	$0.550636\pi$
$878$	76.6747	2.58765
$879$	−16.2015	−0.546463
$880$	6.26228	0.211101
$881$	−45.3864	−1.52911	−0.764554	−	0.644560i	$-0.777041\pi$
$881$	−45.3864	−1.52911	−0.764554	+	0.644560i	$0.777041\pi$
$882$	3.62728	0.122137
$883$	39.8325	1.34047	0.670235	−	0.742149i	$-0.266193\pi$
$883$	39.8325	1.34047	0.670235	+	0.742149i	$0.266193\pi$
$884$	156.174	5.25270
$885$	0.0614678	0.00206622
$886$	−49.3409	−1.65764
$887$	−41.7081	−1.40042	−0.700211	−	0.713936i	$-0.746911\pi$
$887$	−41.7081	−1.40042	−0.700211	+	0.713936i	$0.746911\pi$
$888$	16.6089	0.557359
$889$	−33.8130	−1.13405
$890$	−1.59347	−0.0534132
$891$	−7.64778	−0.256210
$892$	99.2353	3.32264
$893$	−32.2716	−1.07993
$894$	20.5293	0.686601
$895$	2.88811	0.0965387
$896$	−37.8876	−1.26574
$897$	−1.99926	−0.0667534
$898$	65.9949	2.20228
$899$	−27.2288	−0.908132
$900$	44.6603	1.48868
$901$	39.1894	1.30559
$902$	11.7356	0.390751
$903$	5.91289	0.196769
$904$	−34.0040	−1.13096
$905$	0.777730	0.0258526
$906$	−4.31380	−0.143316
$907$	−52.0669	−1.72885	−0.864426	−	0.502760i	$-0.832318\pi$
$907$	−52.0669	−1.72885	−0.864426	+	0.502760i	$0.832318\pi$
$908$	116.574	3.86865
$909$	−21.6492	−0.718057
$910$	5.50710	0.182559
$911$	49.2509	1.63176	0.815878	−	0.578224i	$-0.196254\pi$
$911$	49.2509	1.63176	0.815878	+	0.578224i	$0.196254\pi$
$912$	27.6149	0.914420
$913$	−15.6013	−0.516329
$914$	54.0736	1.78860
$915$	−1.31090	−0.0433369
$916$	−82.0727	−2.71176
$917$	9.69581	0.320184
$918$	−91.5052	−3.02012
$919$	−21.4075	−0.706169	−0.353084	−	0.935591i	$-0.614867\pi$
$919$	−21.4075	−0.706169	−0.353084	+	0.935591i	$0.614867\pi$
$920$	0.414012	0.0136496
$921$	7.75912	0.255672
$922$	9.33106	0.307302
$923$	60.8575	2.00315
$924$	70.5992	2.32254
$925$	13.9151	0.457527
$926$	−37.2948	−1.22558
$927$	17.4787	0.574076
$928$	19.1869	0.629841
$929$	−3.33104	−0.109288	−0.0546440	−	0.998506i	$-0.517402\pi$
$929$	−3.33104	−0.109288	−0.0546440	+	0.998506i	$0.517402\pi$
$930$	2.51710	0.0825389
$931$	3.02762	0.0992262
$932$	−0.383478	−0.0125612
$933$	−14.0134	−0.458780
$934$	58.5395	1.91547
$935$	−7.01423	−0.229390
$936$	−59.9905	−1.96085
$937$	10.5731	0.345407	0.172703	−	0.984974i	$-0.444750\pi$
$937$	10.5731	0.345407	0.172703	+	0.984974i	$0.444750\pi$
$938$	−34.0909	−1.11311
$939$	7.84772	0.256101
$940$	5.33137	0.173890
$941$	19.3227	0.629903	0.314952	−	0.949108i	$-0.398012\pi$
$941$	19.3227	0.629903	0.314952	+	0.949108i	$0.398012\pi$
$942$	47.1337	1.53570
$943$	0.331005	0.0107790
$944$	−2.53777	−0.0825973
$945$	−2.21800	−0.0721516
$946$	−32.5310	−1.05767
$947$	18.9656	0.616300	0.308150	−	0.951338i	$-0.400290\pi$
$947$	18.9656	0.616300	0.308150	+	0.951338i	$0.400290\pi$
$948$	49.2679	1.60015
$949$	30.5736	0.992462
$950$	54.2300	1.75945
$951$	−9.04106	−0.293177
$952$	−123.378	−3.99870
$953$	21.5103	0.696789	0.348394	−	0.937348i	$-0.386727\pi$
$953$	21.5103	0.696789	0.348394	+	0.937348i	$0.386727\pi$
$954$	−27.6104	−0.893919
$955$	0.858559	0.0277823
$956$	−85.3320	−2.75984
$957$	25.0881	0.810983
$958$	41.9163	1.35425
$959$	−7.68002	−0.248001
$960$	0.301062	0.00971673
$961$	8.41350	0.271403
$962$	−34.2830	−1.10533
$963$	−23.1322	−0.745425
$964$	107.959	3.47711
$965$	1.23410	0.0397270
$966$	2.89686	0.0932050
$967$	14.8608	0.477891	0.238946	−	0.971033i	$-0.423198\pi$
$967$	14.8608	0.477891	0.238946	+	0.971033i	$0.423198\pi$
$968$	−145.059	−4.66239
$969$	−30.9308	−0.993640
$970$	−2.85480	−0.0916621
$971$	−0.00316838	−0.000101678 0	−5.08390e−5	−	1.00000i	$-0.500016\pi$
$971$	−0.00316838	−0.000101678 0	−5.08390e−5		1.00000i	$0.500016\pi$
$972$	70.6838	2.26718
$973$	−19.2464	−0.617010
$974$	−89.8728	−2.87971
$975$	23.5876	0.755409
$976$	54.1218	1.73240
$977$	47.5620	1.52164	0.760822	−	0.648960i	$-0.224796\pi$
$977$	47.5620	1.52164	0.760822	+	0.648960i	$0.224796\pi$
$978$	−16.1470	−0.516326
$979$	22.9894	0.734744
$980$	−0.500172	−0.0159774
$981$	28.2840	0.903040
$982$	−11.5593	−0.368872
$983$	25.1112	0.800922	0.400461	−	0.916314i	$-0.368850\pi$
$983$	25.1112	0.800922	0.400461	+	0.916314i	$0.368850\pi$
$984$	−4.66125	−0.148595
$985$	1.54627	0.0492682
$986$	−80.4147	−2.56093
$987$	20.3387	0.647389
$988$	−91.8402	−2.92183
$989$	−0.917544	−0.0291762
$990$	4.94179	0.157060
$991$	7.27648	0.231145	0.115572	−	0.993299i	$-0.463130\pi$
$991$	7.27648	0.231145	0.115572	+	0.993299i	$0.463130\pi$
$992$	−27.7729	−0.881791
$993$	−10.1499	−0.322098
$994$	−88.1804	−2.79691
$995$	0.390188	0.0123698
$996$	11.3656	0.360132
$997$	−26.3317	−0.833932	−0.416966	−	0.908922i	$-0.636907\pi$
$997$	−26.3317	−0.833932	−0.416966	+	0.908922i	$0.636907\pi$
$998$	−18.4629	−0.584434
$999$	13.8076	0.436853

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.b.1.15	✓	186

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.b.1.15	✓	186	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.52937 q^{2} +0.978887 q^{3} +4.39770 q^{4} -0.161932 q^{5} -2.47596 q^{6} -2.77531 q^{7} -6.06468 q^{8} -2.04178 q^{9} +O(q^{10})\)	\(q-2.52937 q^{2} +0.978887 q^{3} +4.39770 q^{4} -0.161932 q^{5} -2.47596 q^{6} -2.77531 q^{7} -6.06468 q^{8} -2.04178 q^{9} +0.409586 q^{10} -5.90921 q^{11} +4.30485 q^{12} -4.84469 q^{13} +7.01979 q^{14} -0.158513 q^{15} +6.54440 q^{16} -7.33022 q^{17} +5.16442 q^{18} +4.31064 q^{19} -0.712130 q^{20} -2.71672 q^{21} +14.9466 q^{22} +0.421572 q^{23} -5.93663 q^{24} -4.97378 q^{25} +12.2540 q^{26} -4.93533 q^{27} -12.2050 q^{28} -4.33717 q^{29} +0.400939 q^{30} +6.27802 q^{31} -4.42384 q^{32} -5.78444 q^{33} +18.5408 q^{34} +0.449413 q^{35} -8.97915 q^{36} -2.79770 q^{37} -10.9032 q^{38} -4.74240 q^{39} +0.982067 q^{40} +0.785168 q^{41} +6.87158 q^{42} -2.17649 q^{43} -25.9870 q^{44} +0.330630 q^{45} -1.06631 q^{46} -7.48652 q^{47} +6.40622 q^{48} +0.702360 q^{49} +12.5805 q^{50} -7.17546 q^{51} -21.3055 q^{52} -5.34627 q^{53} +12.4833 q^{54} +0.956891 q^{55} +16.8314 q^{56} +4.21962 q^{57} +10.9703 q^{58} -0.387777 q^{59} -0.697095 q^{60} +8.26994 q^{61} -15.8794 q^{62} +5.66658 q^{63} -1.89929 q^{64} +0.784511 q^{65} +14.6310 q^{66} -4.85640 q^{67} -32.2362 q^{68} +0.412671 q^{69} -1.13673 q^{70} -12.5617 q^{71} +12.3827 q^{72} -6.31076 q^{73} +7.07642 q^{74} -4.86876 q^{75} +18.9569 q^{76} +16.3999 q^{77} +11.9953 q^{78} +11.4447 q^{79} -1.05975 q^{80} +1.29421 q^{81} -1.98598 q^{82} +2.64018 q^{83} -11.9473 q^{84} +1.18700 q^{85} +5.50513 q^{86} -4.24560 q^{87} +35.8374 q^{88} -3.89044 q^{89} -0.836286 q^{90} +13.4455 q^{91} +1.85395 q^{92} +6.14547 q^{93} +18.9362 q^{94} -0.698031 q^{95} -4.33043 q^{96} -6.96996 q^{97} -1.77653 q^{98} +12.0653 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9} + 50 q^{10} + 25 q^{11} + 17 q^{12} + 113 q^{13} + 12 q^{14} + 12 q^{15} + 252 q^{16} + 35 q^{17} + 13 q^{18} + 97 q^{19} + 55 q^{20} + 115 q^{21} + 14 q^{22} + 27 q^{23} + 122 q^{24} + 244 q^{25} + 39 q^{26} + 34 q^{27} + 66 q^{28} + 91 q^{29} + 4 q^{30} + 135 q^{31} + 21 q^{32} + 32 q^{33} + 58 q^{34} + 17 q^{35} + 273 q^{36} + 133 q^{37} - 3 q^{38} + 55 q^{39} + 142 q^{40} + 97 q^{41} - 8 q^{42} + 67 q^{43} + 44 q^{44} + 154 q^{45} + 101 q^{46} + 20 q^{47} - 7 q^{48} + 312 q^{49} + 21 q^{50} + 23 q^{51} + 193 q^{52} + 22 q^{53} + 141 q^{54} + 88 q^{55} + 28 q^{56} + 65 q^{57} + 62 q^{58} + 41 q^{59} + q^{60} + 377 q^{61} + 29 q^{62} + 39 q^{63} + 311 q^{64} + 21 q^{65} + 35 q^{66} + 42 q^{67} + 24 q^{68} + 137 q^{69} + 35 q^{70} + 17 q^{71} - 8 q^{72} + 213 q^{73} - 9 q^{74} + 2 q^{75} + 242 q^{76} + 60 q^{77} + 103 q^{79} + 80 q^{80} + 270 q^{81} + 84 q^{82} + 42 q^{83} + 137 q^{84} + 294 q^{85} - 9 q^{86} + 22 q^{87} - 13 q^{88} + 78 q^{89} + 69 q^{90} + 118 q^{91} + 49 q^{92} + 51 q^{93} + 93 q^{94} + 10 q^{95} + 260 q^{96} + 142 q^{97} - 31 q^{98} + 78 q^{99}+O(q^{100}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9 + 50 * q^10 + 25 * q^11 + 17 * q^12 + 113 * q^13 + 12 * q^14 + 12 * q^15 + 252 * q^16 + 35 * q^17 + 13 * q^18 + 97 * q^19 + 55 * q^20 + 115 * q^21 + 14 * q^22 + 27 * q^23 + 122 * q^24 + 244 * q^25 + 39 * q^26 + 34 * q^27 + 66 * q^28 + 91 * q^29 + 4 * q^30 + 135 * q^31 + 21 * q^32 + 32 * q^33 + 58 * q^34 + 17 * q^35 + 273 * q^36 + 133 * q^37 - 3 * q^38 + 55 * q^39 + 142 * q^40 + 97 * q^41 - 8 * q^42 + 67 * q^43 + 44 * q^44 + 154 * q^45 + 101 * q^46 + 20 * q^47 - 7 * q^48 + 312 * q^49 + 21 * q^50 + 23 * q^51 + 193 * q^52 + 22 * q^53 + 141 * q^54 + 88 * q^55 + 28 * q^56 + 65 * q^57 + 62 * q^58 + 41 * q^59 + q^60 + 377 * q^61 + 29 * q^62 + 39 * q^63 + 311 * q^64 + 21 * q^65 + 35 * q^66 + 42 * q^67 + 24 * q^68 + 137 * q^69 + 35 * q^70 + 17 * q^71 - 8 * q^72 + 213 * q^73 - 9 * q^74 + 2 * q^75 + 242 * q^76 + 60 * q^77 + 103 * q^79 + 80 * q^80 + 270 * q^81 + 84 * q^82 + 42 * q^83 + 137 * q^84 + 294 * q^85 - 9 * q^86 + 22 * q^87 - 13 * q^88 + 78 * q^89 + 69 * q^90 + 118 * q^91 + 49 * q^92 + 51 * q^93 + 93 * q^94 + 10 * q^95 + 260 * q^96 + 142 * q^97 - 31 * q^98 + 78 * q^99

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