LMFDB - Embedded newform 619.2.a.b.1.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [619,2,Mod(1,619)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(619, 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("619.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	619.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:	$4.94273988512$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.26
Character	$\chi$	$=$	619.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.38907 q^{2} +1.15474 q^{3} +3.70768 q^{4} +0.568936 q^{5} +2.75876 q^{6} -1.24185 q^{7} +4.07977 q^{8} -1.66657 q^{9} +O(q^{10})$	\(q+2.38907 q^{2} +1.15474 q^{3} +3.70768 q^{4} +0.568936 q^{5} +2.75876 q^{6} -1.24185 q^{7} +4.07977 q^{8} -1.66657 q^{9} +1.35923 q^{10} +4.37083 q^{11} +4.28141 q^{12} -2.48902 q^{13} -2.96686 q^{14} +0.656973 q^{15} +2.33152 q^{16} -3.57013 q^{17} -3.98157 q^{18} +8.32324 q^{19} +2.10943 q^{20} -1.43401 q^{21} +10.4422 q^{22} +3.53189 q^{23} +4.71108 q^{24} -4.67631 q^{25} -5.94646 q^{26} -5.38868 q^{27} -4.60437 q^{28} -3.16281 q^{29} +1.56956 q^{30} -8.22673 q^{31} -2.58936 q^{32} +5.04717 q^{33} -8.52931 q^{34} -0.706531 q^{35} -6.17912 q^{36} +3.99731 q^{37} +19.8848 q^{38} -2.87418 q^{39} +2.32113 q^{40} -8.44683 q^{41} -3.42596 q^{42} +3.77609 q^{43} +16.2056 q^{44} -0.948174 q^{45} +8.43795 q^{46} +12.1471 q^{47} +2.69230 q^{48} -5.45782 q^{49} -11.1721 q^{50} -4.12257 q^{51} -9.22850 q^{52} -8.87998 q^{53} -12.8740 q^{54} +2.48672 q^{55} -5.06645 q^{56} +9.61118 q^{57} -7.55620 q^{58} -13.5928 q^{59} +2.43584 q^{60} +7.69548 q^{61} -19.6543 q^{62} +2.06963 q^{63} -10.8492 q^{64} -1.41609 q^{65} +12.0581 q^{66} +8.17031 q^{67} -13.2369 q^{68} +4.07842 q^{69} -1.68796 q^{70} +10.2526 q^{71} -6.79924 q^{72} +6.99501 q^{73} +9.54987 q^{74} -5.39993 q^{75} +30.8599 q^{76} -5.42790 q^{77} -6.86662 q^{78} +8.19202 q^{79} +1.32649 q^{80} -1.22280 q^{81} -20.1801 q^{82} -16.0372 q^{83} -5.31685 q^{84} -2.03117 q^{85} +9.02137 q^{86} -3.65223 q^{87} +17.8320 q^{88} +17.3086 q^{89} -2.26526 q^{90} +3.09099 q^{91} +13.0951 q^{92} -9.49973 q^{93} +29.0202 q^{94} +4.73539 q^{95} -2.99004 q^{96} -1.96177 q^{97} -13.0391 q^{98} -7.28431 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) $ 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9} + 5 q^{10} + 23 q^{11} - 6 q^{12} + 9 q^{13} + 7 q^{14} - 2 q^{15} + 35 q^{16} + 4 q^{17} + 10 q^{18} - q^{19} + 29 q^{20} + 30 q^{21} + 4 q^{23} + 4 q^{24} + 35 q^{25} + q^{26} - 5 q^{27} - 13 q^{28} + 90 q^{29} - 31 q^{30} + 2 q^{31} + 43 q^{32} - 6 q^{33} - 9 q^{34} + 9 q^{35} + 33 q^{36} + 19 q^{37} + 5 q^{38} + 32 q^{39} - 12 q^{40} + 59 q^{41} - 25 q^{42} - 4 q^{43} + 52 q^{44} + 30 q^{45} - q^{46} + 4 q^{47} - 44 q^{48} + 30 q^{49} + 31 q^{50} - 12 q^{52} + 34 q^{53} - 28 q^{54} - 17 q^{55} + 2 q^{56} - 8 q^{57} + 6 q^{58} + 13 q^{59} - 64 q^{60} + 16 q^{61} + 28 q^{62} - 40 q^{63} + 37 q^{64} + 31 q^{65} - 59 q^{66} - 11 q^{67} - 52 q^{68} + 6 q^{69} - 40 q^{70} + 42 q^{71} + 6 q^{72} - 4 q^{73} + 16 q^{74} - 52 q^{75} - 42 q^{76} + 29 q^{77} - 56 q^{78} + 3 q^{79} + 21 q^{80} + 30 q^{81} - 43 q^{82} - 11 q^{83} - 36 q^{84} + 19 q^{85} - 11 q^{86} - 20 q^{87} - 47 q^{88} + 58 q^{89} - 33 q^{90} - 39 q^{91} - 7 q^{92} - 15 q^{93} - 46 q^{94} + 23 q^{95} - 70 q^{96} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9 + 5 * q^10 + 23 * q^11 - 6 * q^12 + 9 * q^13 + 7 * q^14 - 2 * q^15 + 35 * q^16 + 4 * q^17 + 10 * q^18 - q^19 + 29 * q^20 + 30 * q^21 + 4 * q^23 + 4 * q^24 + 35 * q^25 + q^26 - 5 * q^27 - 13 * q^28 + 90 * q^29 - 31 * q^30 + 2 * q^31 + 43 * q^32 - 6 * q^33 - 9 * q^34 + 9 * q^35 + 33 * q^36 + 19 * q^37 + 5 * q^38 + 32 * q^39 - 12 * q^40 + 59 * q^41 - 25 * q^42 - 4 * q^43 + 52 * q^44 + 30 * q^45 - q^46 + 4 * q^47 - 44 * q^48 + 30 * q^49 + 31 * q^50 - 12 * q^52 + 34 * q^53 - 28 * q^54 - 17 * q^55 + 2 * q^56 - 8 * q^57 + 6 * q^58 + 13 * q^59 - 64 * q^60 + 16 * q^61 + 28 * q^62 - 40 * q^63 + 37 * q^64 + 31 * q^65 - 59 * q^66 - 11 * q^67 - 52 * q^68 + 6 * q^69 - 40 * q^70 + 42 * q^71 + 6 * q^72 - 4 * q^73 + 16 * q^74 - 52 * q^75 - 42 * q^76 + 29 * q^77 - 56 * q^78 + 3 * q^79 + 21 * q^80 + 30 * q^81 - 43 * q^82 - 11 * q^83 - 36 * q^84 + 19 * q^85 - 11 * q^86 - 20 * q^87 - 47 * q^88 + 58 * q^89 - 33 * q^90 - 39 * q^91 - 7 * q^92 - 15 * q^93 - 46 * q^94 + 23 * q^95 - 70 * q^96 - 9 * q^97 - 8 * 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 $

$2$	2.38907	1.68933	0.844665	−	0.535295i	$-0.179799\pi$
$2$	2.38907	1.68933	0.844665	+	0.535295i	$0.179799\pi$
$3$	1.15474	0.666690	0.333345	−	0.942805i	$-0.391823\pi$
$3$	1.15474	0.666690	0.333345	+	0.942805i	$0.391823\pi$
$4$	3.70768	1.85384
$5$	0.568936	0.254436	0.127218	−	0.991875i	$-0.459395\pi$
$5$	0.568936	0.254436	0.127218	+	0.991875i	$0.459395\pi$
$6$	2.75876	1.12626
$7$	−1.24185	−0.469374	−0.234687	−	0.972071i	$-0.575407\pi$
$7$	−1.24185	−0.469374	−0.234687	+	0.972071i	$0.575407\pi$
$8$	4.07977	1.44242
$9$	−1.66657	−0.555525
$10$	1.35923	0.429826
$11$	4.37083	1.31785	0.658927	−	0.752207i	$-0.271011\pi$
$11$	4.37083	1.31785	0.658927	+	0.752207i	$0.271011\pi$
$12$	4.28141	1.23594
$13$	−2.48902	−0.690331	−0.345165	−	0.938542i	$-0.612177\pi$
$13$	−2.48902	−0.690331	−0.345165	+	0.938542i	$0.612177\pi$
$14$	−2.96686	−0.792928
$15$	0.656973	0.169630
$16$	2.33152	0.582880
$17$	−3.57013	−0.865884	−0.432942	−	0.901422i	$-0.642524\pi$
$17$	−3.57013	−0.865884	−0.432942	+	0.901422i	$0.642524\pi$
$18$	−3.98157	−0.938466
$19$	8.32324	1.90948	0.954741	−	0.297438i	$-0.0961322\pi$
$19$	8.32324	1.90948	0.954741	+	0.297438i	$0.0961322\pi$
$20$	2.10943	0.471683
$21$	−1.43401	−0.312927
$22$	10.4422	2.22629
$23$	3.53189	0.736450	0.368225	−	0.929737i	$-0.379966\pi$
$23$	3.53189	0.736450	0.368225	+	0.929737i	$0.379966\pi$
$24$	4.71108	0.961644
$25$	−4.67631	−0.935262
$26$	−5.94646	−1.16620
$27$	−5.38868	−1.03705
$28$	−4.60437	−0.870144
$29$	−3.16281	−0.587320	−0.293660	−	0.955910i	$-0.594873\pi$
$29$	−3.16281	−0.587320	−0.293660	+	0.955910i	$0.594873\pi$
$30$	1.56956	0.286561
$31$	−8.22673	−1.47756	−0.738782	−	0.673945i	$-0.764599\pi$
$31$	−8.22673	−1.47756	−0.738782	+	0.673945i	$0.764599\pi$
$32$	−2.58936	−0.457739
$33$	5.04717	0.878600
$34$	−8.52931	−1.46276
$35$	−0.706531	−0.119426
$36$	−6.17912	−1.02985
$37$	3.99731	0.657154	0.328577	−	0.944477i	$-0.393431\pi$
$37$	3.99731	0.657154	0.328577	+	0.944477i	$0.393431\pi$
$38$	19.8848	3.22575
$39$	−2.87418	−0.460236
$40$	2.32113	0.367003
$41$	−8.44683	−1.31917	−0.659586	−	0.751629i	$-0.729269\pi$
$41$	−8.44683	−1.31917	−0.659586	+	0.751629i	$0.729269\pi$
$42$	−3.42596	−0.528637
$43$	3.77609	0.575849	0.287924	−	0.957653i	$-0.407035\pi$
$43$	3.77609	0.575849	0.287924	+	0.957653i	$0.407035\pi$
$44$	16.2056	2.44309
$45$	−0.948174	−0.141345
$46$	8.43795	1.24411
$47$	12.1471	1.77183	0.885915	−	0.463847i	$-0.153531\pi$
$47$	12.1471	1.77183	0.885915	+	0.463847i	$0.153531\pi$
$48$	2.69230	0.388600
$49$	−5.45782	−0.779688
$50$	−11.1721	−1.57997
$51$	−4.12257	−0.577276
$52$	−9.22850	−1.27976
$53$	−8.87998	−1.21976	−0.609880	−	0.792494i	$-0.708782\pi$
$53$	−8.87998	−1.21976	−0.609880	+	0.792494i	$0.708782\pi$
$54$	−12.8740	−1.75192
$55$	2.48672	0.335309
$56$	−5.06645	−0.677033
$57$	9.61118	1.27303
$58$	−7.55620	−0.992177
$59$	−13.5928	−1.76963	−0.884813	−	0.465945i	$-0.845714\pi$
$59$	−13.5928	−1.76963	−0.884813	+	0.465945i	$0.845714\pi$
$60$	2.43584	0.314466
$61$	7.69548	0.985305	0.492652	−	0.870226i	$-0.336027\pi$
$61$	7.69548	0.985305	0.492652	+	0.870226i	$0.336027\pi$
$62$	−19.6543	−2.49609
$63$	2.06963	0.260749
$64$	−10.8492	−1.35615
$65$	−1.41609	−0.175645
$66$	12.0581	1.48425
$67$	8.17031	0.998162	0.499081	−	0.866555i	$-0.333671\pi$
$67$	8.17031	0.998162	0.499081	+	0.866555i	$0.333671\pi$
$68$	−13.2369	−1.60521
$69$	4.07842	0.490983
$70$	−1.68796	−0.201749
$71$	10.2526	1.21676	0.608379	−	0.793646i	$-0.291820\pi$
$71$	10.2526	1.21676	0.608379	+	0.793646i	$0.291820\pi$
$72$	−6.79924	−0.801299
$73$	6.99501	0.818704	0.409352	−	0.912377i	$-0.365755\pi$
$73$	6.99501	0.818704	0.409352	+	0.912377i	$0.365755\pi$
$74$	9.54987	1.11015
$75$	−5.39993	−0.623530
$76$	30.8599	3.53987
$77$	−5.42790	−0.618566
$78$	−6.86662	−0.777491
$79$	8.19202	0.921674	0.460837	−	0.887485i	$-0.347549\pi$
$79$	8.19202	0.921674	0.460837	+	0.887485i	$0.347549\pi$
$80$	1.32649	0.148306
$81$	−1.22280	−0.135867
$82$	−20.1801	−2.22852
$83$	−16.0372	−1.76032	−0.880158	−	0.474680i	$-0.842564\pi$
$83$	−16.0372	−1.76032	−0.880158	+	0.474680i	$0.842564\pi$
$84$	−5.31685	−0.580116
$85$	−2.03117	−0.220312
$86$	9.02137	0.972799
$87$	−3.65223	−0.391560
$88$	17.8320	1.90089
$89$	17.3086	1.83471	0.917354	−	0.398072i	$-0.130321\pi$
$89$	17.3086	1.83471	0.917354	+	0.398072i	$0.130321\pi$
$90$	−2.26526	−0.238779
$91$	3.09099	0.324023
$92$	13.0951	1.36526
$93$	−9.49973	−0.985076
$94$	29.0202	2.99321
$95$	4.73539	0.485841
$96$	−2.99004	−0.305170
$97$	−1.96177	−0.199188	−0.0995938	−	0.995028i	$-0.531754\pi$
$97$	−1.96177	−0.199188	−0.0995938	+	0.995028i	$0.531754\pi$
$98$	−13.0391	−1.31715
$99$	−7.28431	−0.732101
$100$	−17.3383	−1.73383
$101$	18.7114	1.86186	0.930928	−	0.365202i	$-0.119000\pi$
$101$	18.7114	1.86186	0.930928	+	0.365202i	$0.119000\pi$
$102$	−9.84913	−0.975210
$103$	−1.69366	−0.166881	−0.0834405	−	0.996513i	$-0.526591\pi$
$103$	−1.69366	−0.166881	−0.0834405	+	0.996513i	$0.526591\pi$
$104$	−10.1546	−0.995745
$105$	−0.815860	−0.0796198
$106$	−21.2149	−2.06058
$107$	−4.80710	−0.464720	−0.232360	−	0.972630i	$-0.574645\pi$
$107$	−4.80710	−0.464720	−0.232360	+	0.972630i	$0.574645\pi$
$108$	−19.9795	−1.92253
$109$	−11.8607	−1.13605	−0.568024	−	0.823012i	$-0.692292\pi$
$109$	−11.8607	−1.13605	−0.568024	+	0.823012i	$0.692292\pi$
$110$	5.94096	0.566448
$111$	4.61585	0.438118
$112$	−2.89539	−0.273589
$113$	13.0119	1.22405	0.612026	−	0.790838i	$-0.290355\pi$
$113$	13.0119	1.22405	0.612026	+	0.790838i	$0.290355\pi$
$114$	22.9618	2.15057
$115$	2.00942	0.187379
$116$	−11.7267	−1.08880
$117$	4.14814	0.383496
$118$	−32.4741	−2.98949
$119$	4.43355	0.406423
$120$	2.68030	0.244677
$121$	8.10413	0.736739
$122$	18.3851	1.66451
$123$	−9.75389	−0.879479
$124$	−30.5021	−2.73917
$125$	−5.50520	−0.492400
$126$	4.94450	0.440491
$127$	10.1987	0.904985	0.452493	−	0.891768i	$-0.350535\pi$
$127$	10.1987	0.904985	0.452493	+	0.891768i	$0.350535\pi$
$128$	−20.7409	−1.83325
$129$	4.36041	0.383912
$130$	−3.38316	−0.296722
$131$	−6.80736	−0.594762	−0.297381	−	0.954759i	$-0.596113\pi$
$131$	−6.80736	−0.594762	−0.297381	+	0.954759i	$0.596113\pi$
$132$	18.7133	1.62878
$133$	−10.3362	−0.896261
$134$	19.5195	1.68623
$135$	−3.06581	−0.263863
$136$	−14.5653	−1.24897
$137$	2.30081	0.196571	0.0982856	−	0.995158i	$-0.468664\pi$
$137$	2.30081	0.196571	0.0982856	+	0.995158i	$0.468664\pi$
$138$	9.74364	0.829434
$139$	−14.0559	−1.19221	−0.596103	−	0.802908i	$-0.703285\pi$
$139$	−14.0559	−1.19221	−0.596103	+	0.802908i	$0.703285\pi$
$140$	−2.61959	−0.221396
$141$	14.0267	1.18126
$142$	24.4942	2.05551
$143$	−10.8791	−0.909755
$144$	−3.88566	−0.323805
$145$	−1.79944	−0.149435
$146$	16.7116	1.38306
$147$	−6.30236	−0.519810
$148$	14.8207	1.21826
$149$	15.8497	1.29846	0.649230	−	0.760592i	$-0.275091\pi$
$149$	15.8497	1.29846	0.649230	+	0.760592i	$0.275091\pi$
$150$	−12.9008	−1.05335
$151$	9.65329	0.785573	0.392787	−	0.919630i	$-0.371511\pi$
$151$	9.65329	0.785573	0.392787	+	0.919630i	$0.371511\pi$
$152$	33.9569	2.75427
$153$	5.94989	0.481020
$154$	−12.9677	−1.04496
$155$	−4.68048	−0.375945
$156$	−10.6565	−0.853204
$157$	−2.60844	−0.208176	−0.104088	−	0.994568i	$-0.533192\pi$
$157$	−2.60844	−0.208176	−0.104088	+	0.994568i	$0.533192\pi$
$158$	19.5713	1.55701
$159$	−10.2541	−0.813201
$160$	−1.47318	−0.116465
$161$	−4.38607	−0.345670
$162$	−2.92137	−0.229524
$163$	6.98829	0.547365	0.273682	−	0.961820i	$-0.411758\pi$
$163$	6.98829	0.547365	0.273682	+	0.961820i	$0.411758\pi$
$164$	−31.3181	−2.44553
$165$	2.87152	0.223547
$166$	−38.3142	−2.97376
$167$	−15.5970	−1.20693	−0.603465	−	0.797390i	$-0.706214\pi$
$167$	−15.5970	−1.20693	−0.603465	+	0.797390i	$0.706214\pi$
$168$	−5.85043	−0.451371
$169$	−6.80476	−0.523443
$170$	−4.85263	−0.372180
$171$	−13.8713	−1.06077
$172$	14.0005	1.06753
$173$	17.3242	1.31713	0.658566	−	0.752523i	$-0.271163\pi$
$173$	17.3242	1.31713	0.658566	+	0.752523i	$0.271163\pi$
$174$	−8.72545	−0.661474
$175$	5.80726	0.438988
$176$	10.1907	0.768151
$177$	−15.6961	−1.17979
$178$	41.3515	3.09943
$179$	−1.36925	−0.102342	−0.0511711	−	0.998690i	$-0.516295\pi$
$179$	−1.36925	−0.102342	−0.0511711	+	0.998690i	$0.516295\pi$
$180$	−3.51552	−0.262032
$181$	19.2028	1.42733	0.713666	−	0.700486i	$-0.247033\pi$
$181$	19.2028	1.42733	0.713666	+	0.700486i	$0.247033\pi$
$182$	7.38459	0.547383
$183$	8.88628	0.656892
$184$	14.4093	1.06227
$185$	2.27421	0.167203
$186$	−22.6956	−1.66412
$187$	−15.6044	−1.14111
$188$	45.0374	3.28469
$189$	6.69192	0.486765
$190$	11.3132	0.820746
$191$	14.4378	1.04468	0.522342	−	0.852736i	$-0.325059\pi$
$191$	14.4378	1.04468	0.522342	+	0.852736i	$0.325059\pi$
$192$	−12.5280	−0.904133
$193$	−19.9735	−1.43772	−0.718862	−	0.695152i	$-0.755337\pi$
$193$	−19.9735	−1.43772	−0.718862	+	0.695152i	$0.755337\pi$
$194$	−4.68681	−0.336494
$195$	−1.63522	−0.117101
$196$	−20.2358	−1.44542
$197$	−9.07235	−0.646378	−0.323189	−	0.946334i	$-0.604755\pi$
$197$	−9.07235	−0.646378	−0.323189	+	0.946334i	$0.604755\pi$
$198$	−17.4028	−1.23676
$199$	−0.656353	−0.0465276	−0.0232638	−	0.999729i	$-0.507406\pi$
$199$	−0.656353	−0.0465276	−0.0232638	+	0.999729i	$0.507406\pi$
$200$	−19.0783	−1.34904
$201$	9.43458	0.665464
$202$	44.7030	3.14529
$203$	3.92773	0.275673
$204$	−15.2852	−1.07018
$205$	−4.80570	−0.335645
$206$	−4.04627	−0.281917
$207$	−5.88616	−0.409116
$208$	−5.80321	−0.402380
$209$	36.3794	2.51642
$210$	−1.94915	−0.134504
$211$	11.9112	0.819998	0.409999	−	0.912086i	$-0.365529\pi$
$211$	11.9112	0.819998	0.409999	+	0.912086i	$0.365529\pi$
$212$	−32.9241	−2.26124
$213$	11.8391	0.811200
$214$	−11.4845	−0.785065
$215$	2.14836	0.146517
$216$	−21.9846	−1.49586
$217$	10.2163	0.693530
$218$	−28.3361	−1.91916
$219$	8.07742	0.545821
$220$	9.21996	0.621609
$221$	8.88614	0.597746
$222$	11.0276	0.740125
$223$	−6.20085	−0.415240	−0.207620	−	0.978210i	$-0.566572\pi$
$223$	−6.20085	−0.415240	−0.207620	+	0.978210i	$0.566572\pi$
$224$	3.21559	0.214851
$225$	7.79342	0.519562
$226$	31.0863	2.06783
$227$	−21.1578	−1.40429	−0.702145	−	0.712034i	$-0.747774\pi$
$227$	−21.1578	−1.40429	−0.702145	+	0.712034i	$0.747774\pi$
$228$	35.6352	2.36000
$229$	−14.8582	−0.981856	−0.490928	−	0.871200i	$-0.663342\pi$
$229$	−14.8582	−0.981856	−0.490928	+	0.871200i	$0.663342\pi$
$230$	4.80065	0.316546
$231$	−6.26781	−0.412392
$232$	−12.9036	−0.847160
$233$	−2.75155	−0.180260	−0.0901299	−	0.995930i	$-0.528728\pi$
$233$	−2.75155	−0.180260	−0.0901299	+	0.995930i	$0.528728\pi$
$234$	9.91022	0.647852
$235$	6.91090	0.450817
$236$	−50.3976	−3.28060
$237$	9.45966	0.614471
$238$	10.5921	0.686583
$239$	19.3238	1.24995	0.624977	−	0.780643i	$-0.285108\pi$
$239$	19.3238	1.24995	0.624977	+	0.780643i	$0.285108\pi$
$240$	1.53175	0.0988738
$241$	0.326422	0.0210267	0.0105134	−	0.999945i	$-0.496653\pi$
$241$	0.326422	0.0210267	0.0105134	+	0.999945i	$0.496653\pi$
$242$	19.3614	1.24460
$243$	14.7540	0.946471
$244$	28.5323	1.82660
$245$	−3.10515	−0.198381
$246$	−23.3028	−1.48573
$247$	−20.7167	−1.31817
$248$	−33.5632	−2.13126
$249$	−18.5189	−1.17358
$250$	−13.1523	−0.831827
$251$	20.9654	1.32332	0.661662	−	0.749802i	$-0.269851\pi$
$251$	20.9654	1.32332	0.661662	+	0.749802i	$0.269851\pi$
$252$	7.67353	0.483387
$253$	15.4373	0.970533
$254$	24.3654	1.52882
$255$	−2.34548	−0.146880
$256$	−27.8531	−1.74082
$257$	−21.4548	−1.33832	−0.669158	−	0.743120i	$-0.733345\pi$
$257$	−21.4548	−1.33832	−0.669158	+	0.743120i	$0.733345\pi$
$258$	10.4173	0.648555
$259$	−4.96405	−0.308451
$260$	−5.25042	−0.325617
$261$	5.27107	0.326271
$262$	−16.2633	−1.00475
$263$	14.3064	0.882172	0.441086	−	0.897465i	$-0.354593\pi$
$263$	14.3064	0.882172	0.441086	+	0.897465i	$0.354593\pi$
$264$	20.5913	1.26731
$265$	−5.05214	−0.310350
$266$	−24.6939	−1.51408
$267$	19.9869	1.22318
$268$	30.2929	1.85043
$269$	−17.1438	−1.04527	−0.522637	−	0.852556i	$-0.675052\pi$
$269$	−17.1438	−1.04527	−0.522637	+	0.852556i	$0.675052\pi$
$270$	−7.32446	−0.445752
$271$	8.13982	0.494459	0.247230	−	0.968957i	$-0.420480\pi$
$271$	8.13982	0.494459	0.247230	+	0.968957i	$0.420480\pi$
$272$	−8.32383	−0.504707
$273$	3.56928	0.216023
$274$	5.49680	0.332074
$275$	−20.4394	−1.23254
$276$	15.1215	0.910204
$277$	−6.29563	−0.378268	−0.189134	−	0.981951i	$-0.560568\pi$
$277$	−6.29563	−0.378268	−0.189134	+	0.981951i	$0.560568\pi$
$278$	−33.5806	−2.01403
$279$	13.7105	0.820823
$280$	−2.88249	−0.172261
$281$	−8.96639	−0.534890	−0.267445	−	0.963573i	$-0.586179\pi$
$281$	−8.96639	−0.534890	−0.267445	+	0.963573i	$0.586179\pi$
$282$	33.5108	1.99554
$283$	20.2030	1.20094	0.600471	−	0.799647i	$-0.294980\pi$
$283$	20.2030	1.20094	0.600471	+	0.799647i	$0.294980\pi$
$284$	38.0133	2.25567
$285$	5.46814	0.323905
$286$	−25.9910	−1.53688
$287$	10.4897	0.619185
$288$	4.31537	0.254285
$289$	−4.25417	−0.250245
$290$	−4.29899	−0.252445
$291$	−2.26533	−0.132796
$292$	25.9352	1.51774
$293$	−0.929112	−0.0542793	−0.0271396	−	0.999632i	$-0.508640\pi$
$293$	−0.929112	−0.0542793	−0.0271396	+	0.999632i	$0.508640\pi$
$294$	−15.0568	−0.878131
$295$	−7.73341	−0.450256
$296$	16.3081	0.947890
$297$	−23.5530	−1.36668
$298$	37.8662	2.19353
$299$	−8.79095	−0.508394
$300$	−20.0212	−1.15592
$301$	−4.68933	−0.270288
$302$	23.0624	1.32709
$303$	21.6068	1.24128
$304$	19.4058	1.11300
$305$	4.37823	0.250697
$306$	14.2147	0.812602
$307$	−25.8698	−1.47647	−0.738233	−	0.674546i	$-0.764339\pi$
$307$	−25.8698	−1.47647	−0.738233	+	0.674546i	$0.764339\pi$
$308$	−20.1249	−1.14672
$309$	−1.95573	−0.111258
$310$	−11.1820	−0.635096
$311$	2.23970	0.127002	0.0635008	−	0.997982i	$-0.479773\pi$
$311$	2.23970	0.127002	0.0635008	+	0.997982i	$0.479773\pi$
$312$	−11.7260	−0.663853
$313$	4.78114	0.270246	0.135123	−	0.990829i	$-0.456857\pi$
$313$	4.78114	0.270246	0.135123	+	0.990829i	$0.456857\pi$
$314$	−6.23175	−0.351678
$315$	1.17749	0.0663439
$316$	30.3734	1.70864
$317$	23.4924	1.31947	0.659733	−	0.751500i	$-0.270670\pi$
$317$	23.4924	1.31947	0.659733	+	0.751500i	$0.270670\pi$
$318$	−24.4977	−1.37377
$319$	−13.8241	−0.774002
$320$	−6.17251	−0.345054
$321$	−5.55095	−0.309824
$322$	−10.4786	−0.583952
$323$	−29.7151	−1.65339
$324$	−4.53376	−0.251876
$325$	11.6394	0.645640
$326$	16.6955	0.924680
$327$	−13.6960	−0.757391
$328$	−34.4611	−1.90280
$329$	−15.0848	−0.831651
$330$	6.86027	0.377645
$331$	6.25267	0.343678	0.171839	−	0.985125i	$-0.445029\pi$
$331$	6.25267	0.343678	0.171839	+	0.985125i	$0.445029\pi$
$332$	−59.4610	−3.26334
$333$	−6.66182	−0.365065
$334$	−37.2623	−2.03890
$335$	4.64838	0.253968
$336$	−3.34343	−0.182399
$337$	−10.1039	−0.550395	−0.275197	−	0.961388i	$-0.588743\pi$
$337$	−10.1039	−0.550395	−0.275197	+	0.961388i	$0.588743\pi$
$338$	−16.2571	−0.884269
$339$	15.0253	0.816063
$340$	−7.53094	−0.408423
$341$	−35.9576	−1.94721
$342$	−33.1396	−1.79198
$343$	15.4707	0.835339
$344$	15.4056	0.830614
$345$	2.32036	0.124924
$346$	41.3887	2.22507
$347$	19.3246	1.03740	0.518700	−	0.854956i	$-0.326416\pi$
$347$	19.3246	1.03740	0.518700	+	0.854956i	$0.326416\pi$
$348$	−13.5413	−0.725889
$349$	−25.0337	−1.34002	−0.670012	−	0.742351i	$-0.733711\pi$
$349$	−25.0337	−1.34002	−0.670012	+	0.742351i	$0.733711\pi$
$350$	13.8740	0.741596
$351$	13.4126	0.715909
$352$	−11.3177	−0.603233
$353$	10.1586	0.540690	0.270345	−	0.962764i	$-0.412862\pi$
$353$	10.1586	0.540690	0.270345	+	0.962764i	$0.412862\pi$
$354$	−37.4992	−1.99306
$355$	5.83306	0.309587
$356$	64.1747	3.40125
$357$	5.11960	0.270958
$358$	−3.27123	−0.172890
$359$	−9.23234	−0.487264	−0.243632	−	0.969868i	$-0.578339\pi$
$359$	−9.23234	−0.487264	−0.243632	+	0.969868i	$0.578339\pi$
$360$	−3.86833	−0.203879
$361$	50.2763	2.64612
$362$	45.8769	2.41124
$363$	9.35817	0.491176
$364$	11.4604	0.600687
$365$	3.97971	0.208308
$366$	21.2300	1.10971
$367$	−34.8603	−1.81969	−0.909847	−	0.414944i	$-0.863801\pi$
$367$	−34.8603	−1.81969	−0.909847	+	0.414944i	$0.863801\pi$
$368$	8.23468	0.429262
$369$	14.0773	0.732833
$370$	5.43326	0.282462
$371$	11.0276	0.572523
$372$	−35.2219	−1.82617
$373$	16.0752	0.832343	0.416171	−	0.909286i	$-0.363372\pi$
$373$	16.0752	0.832343	0.416171	+	0.909286i	$0.363372\pi$
$374$	−37.2801	−1.92771
$375$	−6.35708	−0.328278
$376$	49.5572	2.55572
$377$	7.87232	0.405445
$378$	15.9875	0.822308
$379$	24.2472	1.24550	0.622748	−	0.782422i	$-0.286016\pi$
$379$	24.2472	1.24550	0.622748	+	0.782422i	$0.286016\pi$
$380$	17.5573	0.900670
$381$	11.7768	0.603344
$382$	34.4930	1.76482
$383$	23.7900	1.21561	0.607806	−	0.794086i	$-0.292050\pi$
$383$	23.7900	1.21561	0.607806	+	0.794086i	$0.292050\pi$
$384$	−23.9503	−1.22221
$385$	−3.08813	−0.157385
$386$	−47.7182	−2.42879
$387$	−6.29314	−0.319898
$388$	−7.27361	−0.369262
$389$	−20.9877	−1.06412	−0.532059	−	0.846707i	$-0.678582\pi$
$389$	−20.9877	−1.06412	−0.532059	+	0.846707i	$0.678582\pi$
$390$	−3.90667	−0.197822
$391$	−12.6093	−0.637680
$392$	−22.2666	−1.12464
$393$	−7.86074	−0.396522
$394$	−21.6745	−1.09195
$395$	4.66073	0.234507
$396$	−27.0079	−1.35720
$397$	−32.9344	−1.65293	−0.826464	−	0.562989i	$-0.809651\pi$
$397$	−32.9344	−1.65293	−0.826464	+	0.562989i	$0.809651\pi$
$398$	−1.56808	−0.0786006
$399$	−11.9356	−0.597528
$400$	−10.9029	−0.545146
$401$	13.8231	0.690295	0.345148	−	0.938548i	$-0.387829\pi$
$401$	13.8231	0.690295	0.345148	+	0.938548i	$0.387829\pi$
$402$	22.5399	1.12419
$403$	20.4765	1.02001
$404$	69.3760	3.45158
$405$	−0.695696	−0.0345694
$406$	9.38364	0.465702
$407$	17.4716	0.866033
$408$	−16.8192	−0.832672
$409$	−5.20274	−0.257259	−0.128629	−	0.991693i	$-0.541058\pi$
$409$	−5.20274	−0.257259	−0.128629	+	0.991693i	$0.541058\pi$
$410$	−11.4812	−0.567015
$411$	2.65684	0.131052
$412$	−6.27953	−0.309370
$413$	16.8801	0.830617
$414$	−14.0625	−0.691133
$415$	−9.12417	−0.447888
$416$	6.44498	0.315991
$417$	−16.2309	−0.794832
$418$	86.9132	4.25106
$419$	14.8436	0.725159	0.362580	−	0.931953i	$-0.381896\pi$
$419$	14.8436	0.725159	0.362580	+	0.931953i	$0.381896\pi$
$420$	−3.02495	−0.147602
$421$	31.0532	1.51344	0.756721	−	0.653738i	$-0.226800\pi$
$421$	31.0532	1.51344	0.756721	+	0.653738i	$0.226800\pi$
$422$	28.4567	1.38525
$423$	−20.2440	−0.984296
$424$	−36.2283	−1.75940
$425$	16.6950	0.809828
$426$	28.2844	1.37039
$427$	−9.55660	−0.462476
$428$	−17.8232	−0.861516
$429$	−12.5625	−0.606524
$430$	5.13258	0.247515
$431$	6.44050	0.310228	0.155114	−	0.987897i	$-0.450425\pi$
$431$	6.44050	0.310228	0.155114	+	0.987897i	$0.450425\pi$
$432$	−12.5638	−0.604477
$433$	−4.84258	−0.232719	−0.116360	−	0.993207i	$-0.537123\pi$
$433$	−4.84258	−0.232719	−0.116360	+	0.993207i	$0.537123\pi$
$434$	24.4076	1.17160
$435$	−2.07788	−0.0996269
$436$	−43.9756	−2.10605
$437$	29.3968	1.40624
$438$	19.2976	0.922073
$439$	−9.38934	−0.448129	−0.224064	−	0.974574i	$-0.571933\pi$
$439$	−9.38934	−0.448129	−0.224064	+	0.974574i	$0.571933\pi$
$440$	10.1452	0.483656
$441$	9.09586	0.433136
$442$	21.2296	1.00979
$443$	−37.9071	−1.80102	−0.900510	−	0.434836i	$-0.856806\pi$
$443$	−37.9071	−1.80102	−0.900510	+	0.434836i	$0.856806\pi$
$444$	17.1141	0.812199
$445$	9.84748	0.466815
$446$	−14.8143	−0.701478
$447$	18.3023	0.865670
$448$	13.4731	0.636543
$449$	20.4273	0.964024	0.482012	−	0.876165i	$-0.339906\pi$
$449$	20.4273	0.964024	0.482012	+	0.876165i	$0.339906\pi$
$450$	18.6191	0.877712
$451$	−36.9196	−1.73848
$452$	48.2438	2.26920
$453$	11.1470	0.523733
$454$	−50.5475	−2.37231
$455$	1.75857	0.0824431
$456$	39.2114	1.83624
$457$	−0.697579	−0.0326314	−0.0163157	−	0.999867i	$-0.505194\pi$
$457$	−0.697579	−0.0326314	−0.0163157	+	0.999867i	$0.505194\pi$
$458$	−35.4973	−1.65868
$459$	19.2383	0.897967
$460$	7.45028	0.347371
$461$	−1.63646	−0.0762176	−0.0381088	−	0.999274i	$-0.512133\pi$
$461$	−1.63646	−0.0762176	−0.0381088	+	0.999274i	$0.512133\pi$
$462$	−14.9743	−0.696666
$463$	−32.1738	−1.49524	−0.747622	−	0.664125i	$-0.768804\pi$
$463$	−32.1738	−1.49524	−0.747622	+	0.664125i	$0.768804\pi$
$464$	−7.37417	−0.342337
$465$	−5.40474	−0.250639
$466$	−6.57365	−0.304518
$467$	−25.7241	−1.19037	−0.595184	−	0.803589i	$-0.702921\pi$
$467$	−25.7241	−1.19037	−0.595184	+	0.803589i	$0.702921\pi$
$468$	15.3800	0.710940
$469$	−10.1463	−0.468511
$470$	16.5106	0.761579
$471$	−3.01207	−0.138789
$472$	−55.4554	−2.55254
$473$	16.5047	0.758885
$474$	22.5998	1.03804
$475$	−38.9221	−1.78587
$476$	16.4382	0.753443
$477$	14.7992	0.677607
$478$	46.1660	2.11158
$479$	−0.0741032	−0.00338586	−0.00169293	−	0.999999i	$-0.500539\pi$
$479$	−0.0741032	−0.00338586	−0.00169293	+	0.999999i	$0.500539\pi$
$480$	−1.70114	−0.0776461
$481$	−9.94940	−0.453653
$482$	0.779847	0.0355211
$483$	−5.06477	−0.230455
$484$	30.0475	1.36580
$485$	−1.11612	−0.0506804
$486$	35.2485	1.59890
$487$	−37.4031	−1.69490	−0.847449	−	0.530878i	$-0.821862\pi$
$487$	−37.4031	−1.69490	−0.847449	+	0.530878i	$0.821862\pi$
$488$	31.3958	1.42122
$489$	8.06966	0.364922
$490$	−7.41843	−0.335130
$491$	−25.1485	−1.13494	−0.567469	−	0.823395i	$-0.692077\pi$
$491$	−25.1485	−1.13494	−0.567469	+	0.823395i	$0.692077\pi$
$492$	−36.1643	−1.63041
$493$	11.2917	0.508551
$494$	−49.4938	−2.22683
$495$	−4.14431	−0.186273
$496$	−19.1808	−0.861243
$497$	−12.7321	−0.571115
$498$	−44.2429	−1.98257
$499$	−9.98224	−0.446866	−0.223433	−	0.974719i	$-0.571726\pi$
$499$	−9.98224	−0.446866	−0.223433	+	0.974719i	$0.571726\pi$
$500$	−20.4115	−0.912831
$501$	−18.0104	−0.804647
$502$	50.0879	2.23553
$503$	4.71483	0.210224	0.105112	−	0.994460i	$-0.466480\pi$
$503$	4.71483	0.210224	0.105112	+	0.994460i	$0.466480\pi$
$504$	8.44362	0.376109
$505$	10.6456	0.473723
$506$	36.8808	1.63955
$507$	−7.85774	−0.348974
$508$	37.8134	1.67770
$509$	1.66570	0.0738309	0.0369154	−	0.999318i	$-0.488247\pi$
$509$	1.66570	0.0738309	0.0369154	+	0.999318i	$0.488247\pi$
$510$	−5.60353	−0.248128
$511$	−8.68673	−0.384278
$512$	−25.0613	−1.10756
$513$	−44.8513	−1.98023
$514$	−51.2572	−2.26086
$515$	−0.963582	−0.0424605
$516$	16.1670	0.711712
$517$	53.0927	2.33501
$518$	−11.8595	−0.521076
$519$	20.0049	0.878118
$520$	−5.77734	−0.253353
$521$	18.7628	0.822015	0.411008	−	0.911632i	$-0.365177\pi$
$521$	18.7628	0.822015	0.411008	+	0.911632i	$0.365177\pi$
$522$	12.5930	0.551179
$523$	−12.2537	−0.535816	−0.267908	−	0.963445i	$-0.586332\pi$
$523$	−12.2537	−0.535816	−0.267908	+	0.963445i	$0.586332\pi$
$524$	−25.2395	−1.10259
$525$	6.70588	0.292669
$526$	34.1791	1.49028
$527$	29.3705	1.27940
$528$	11.7676	0.512118
$529$	−10.5258	−0.457642
$530$	−12.0699	−0.524285
$531$	22.6534	0.983072
$532$	−38.3233	−1.66152
$533$	21.0243	0.910666
$534$	47.7503	2.06636
$535$	−2.73493	−0.118241
$536$	33.3330	1.43977
$537$	−1.58112	−0.0682305
$538$	−40.9577	−1.76581
$539$	−23.8552	−1.02752
$540$	−11.3671	−0.489160
$541$	4.20685	0.180866	0.0904332	−	0.995903i	$-0.471175\pi$
$541$	4.20685	0.180866	0.0904332	+	0.995903i	$0.471175\pi$
$542$	19.4466	0.835305
$543$	22.1742	0.951587
$544$	9.24436	0.396349
$545$	−6.74797	−0.289051
$546$	8.52729	0.364934
$547$	24.6195	1.05266	0.526328	−	0.850282i	$-0.323569\pi$
$547$	24.6195	1.05266	0.526328	+	0.850282i	$0.323569\pi$
$548$	8.53065	0.364411
$549$	−12.8251	−0.547361
$550$	−48.8311	−2.08217
$551$	−26.3249	−1.12148
$552$	16.6390	0.708203
$553$	−10.1732	−0.432610
$554$	−15.0407	−0.639019
$555$	2.62612	0.111473
$556$	−52.1148	−2.21016
$557$	15.5702	0.659730	0.329865	−	0.944028i	$-0.392997\pi$
$557$	15.5702	0.659730	0.329865	+	0.944028i	$0.392997\pi$
$558$	32.7553	1.38664
$559$	−9.39878	−0.397526
$560$	−1.64729	−0.0696108
$561$	−18.0191	−0.760765
$562$	−21.4214	−0.903606
$563$	−12.0207	−0.506612	−0.253306	−	0.967386i	$-0.581518\pi$
$563$	−12.0207	−0.506612	−0.253306	+	0.967386i	$0.581518\pi$
$564$	52.0065	2.18987
$565$	7.40291	0.311443
$566$	48.2664	2.02879
$567$	1.51853	0.0637724
$568$	41.8282	1.75507
$569$	7.91402	0.331773	0.165886	−	0.986145i	$-0.446951\pi$
$569$	7.91402	0.331773	0.165886	+	0.986145i	$0.446951\pi$
$570$	13.0638	0.547183
$571$	−12.1364	−0.507892	−0.253946	−	0.967218i	$-0.581729\pi$
$571$	−12.1364	−0.507892	−0.253946	+	0.967218i	$0.581729\pi$
$572$	−40.3362	−1.68654
$573$	16.6719	0.696479
$574$	25.0606	1.04601
$575$	−16.5162	−0.688774
$576$	18.0810	0.753377
$577$	−25.9162	−1.07890	−0.539452	−	0.842016i	$-0.681369\pi$
$577$	−25.9162	−1.07890	−0.539452	+	0.842016i	$0.681369\pi$
$578$	−10.1635	−0.422747
$579$	−23.0642	−0.958516
$580$	−6.67174	−0.277029
$581$	19.9158	0.826247
$582$	−5.41205	−0.224337
$583$	−38.8129	−1.60746
$584$	28.5380	1.18091
$585$	2.36003	0.0975751
$586$	−2.21972	−0.0916957
$587$	11.5927	0.478483	0.239241	−	0.970960i	$-0.423101\pi$
$587$	11.5927	0.478483	0.239241	+	0.970960i	$0.423101\pi$
$588$	−23.3671	−0.963644
$589$	−68.4730	−2.82138
$590$	−18.4757	−0.760632
$591$	−10.4762	−0.430934
$592$	9.31981	0.383042
$593$	−9.01644	−0.370261	−0.185130	−	0.982714i	$-0.559271\pi$
$593$	−9.01644	−0.370261	−0.185130	+	0.982714i	$0.559271\pi$
$594$	−56.2699	−2.30878
$595$	2.52241	0.103409
$596$	58.7657	2.40714
$597$	−0.757917	−0.0310195
$598$	−21.0022	−0.858846
$599$	28.2285	1.15338	0.576692	−	0.816961i	$-0.304343\pi$
$599$	28.2285	1.15338	0.576692	+	0.816961i	$0.304343\pi$
$600$	−22.0305	−0.899390
$601$	−17.7222	−0.722903	−0.361451	−	0.932391i	$-0.617719\pi$
$601$	−17.7222	−0.722903	−0.361451	+	0.932391i	$0.617719\pi$
$602$	−11.2032	−0.456607
$603$	−13.6164	−0.554504
$604$	35.7913	1.45633
$605$	4.61073	0.187453
$606$	51.6204	2.09693
$607$	22.0290	0.894130	0.447065	−	0.894502i	$-0.352469\pi$
$607$	22.0290	0.894130	0.447065	+	0.894502i	$0.352469\pi$
$608$	−21.5519	−0.874045
$609$	4.53551	0.183788
$610$	10.4599	0.423510
$611$	−30.2343	−1.22315
$612$	22.0603	0.891734
$613$	−26.4723	−1.06921	−0.534604	−	0.845103i	$-0.679539\pi$
$613$	−26.4723	−1.06921	−0.534604	+	0.845103i	$0.679539\pi$
$614$	−61.8048	−2.49424
$615$	−5.54934	−0.223771
$616$	−22.1446	−0.892231
$617$	−26.3126	−1.05931	−0.529653	−	0.848215i	$-0.677678\pi$
$617$	−26.3126	−1.05931	−0.529653	+	0.848215i	$0.677678\pi$
$618$	−4.67239	−0.187951
$619$	1.00000	0.0401934
$619$	1.00000	0.0401934
$620$	−17.3537	−0.696942
$621$	−19.0322	−0.763737
$622$	5.35080	0.214548
$623$	−21.4946	−0.861164
$624$	−6.70120	−0.268263
$625$	20.2495	0.809978
$626$	11.4225	0.456534
$627$	42.0088	1.67767
$628$	−9.67124	−0.385925
$629$	−14.2709	−0.569019
$630$	2.81310	0.112077
$631$	−17.7695	−0.707392	−0.353696	−	0.935360i	$-0.615075\pi$
$631$	−17.7695	−0.707392	−0.353696	+	0.935360i	$0.615075\pi$
$632$	33.4216	1.32944
$633$	13.7543	0.546684
$634$	56.1251	2.22901
$635$	5.80239	0.230261
$636$	−38.0188	−1.50754
$637$	13.5846	0.538243
$638$	−33.0268	−1.30754
$639$	−17.0867	−0.675940
$640$	−11.8002	−0.466445
$641$	−8.23933	−0.325434	−0.162717	−	0.986673i	$-0.552026\pi$
$641$	−8.23933	−0.325434	−0.162717	+	0.986673i	$0.552026\pi$
$642$	−13.2616	−0.523395
$643$	−24.6145	−0.970701	−0.485350	−	0.874320i	$-0.661308\pi$
$643$	−24.6145	−0.970701	−0.485350	+	0.874320i	$0.661308\pi$
$644$	−16.2621	−0.640817
$645$	2.48079	0.0976811
$646$	−70.9915	−2.79312
$647$	−32.6505	−1.28362	−0.641811	−	0.766863i	$-0.721817\pi$
$647$	−32.6505	−1.28362	−0.641811	+	0.766863i	$0.721817\pi$
$648$	−4.98876	−0.195977
$649$	−59.4116	−2.33211
$650$	27.8075	1.09070
$651$	11.7972	0.462369
$652$	25.9103	1.01473
$653$	−32.0039	−1.25241	−0.626204	−	0.779659i	$-0.715392\pi$
$653$	−32.0039	−1.25241	−0.626204	+	0.779659i	$0.715392\pi$
$654$	−32.7208	−1.27948
$655$	−3.87295	−0.151329
$656$	−19.6940	−0.768920
$657$	−11.6577	−0.454810
$658$	−36.0387	−1.40493
$659$	27.0816	1.05495	0.527474	−	0.849571i	$-0.323139\pi$
$659$	27.0816	1.05495	0.527474	+	0.849571i	$0.323139\pi$
$660$	10.6467	0.414421
$661$	−42.2242	−1.64233	−0.821166	−	0.570689i	$-0.806676\pi$
$661$	−42.2242	−1.64233	−0.821166	+	0.570689i	$0.806676\pi$
$662$	14.9381	0.580586
$663$	10.2612	0.398511
$664$	−65.4283	−2.53911
$665$	−5.88063	−0.228041
$666$	−15.9156	−0.616716
$667$	−11.1707	−0.432532
$668$	−57.8285	−2.23745
$669$	−7.16038	−0.276836
$670$	11.1053	0.429036
$671$	33.6356	1.29849
$672$	3.71317	0.143239
$673$	15.9554	0.615035	0.307518	−	0.951542i	$-0.400502\pi$
$673$	15.9554	0.615035	0.307518	+	0.951542i	$0.400502\pi$
$674$	−24.1390	−0.929799
$675$	25.1992	0.969916
$676$	−25.2299	−0.970380
$677$	−1.44313	−0.0554640	−0.0277320	−	0.999615i	$-0.508828\pi$
$677$	−1.44313	−0.0554640	−0.0277320	+	0.999615i	$0.508828\pi$
$678$	35.8966	1.37860
$679$	2.43622	0.0934934
$680$	−8.28673	−0.317782
$681$	−24.4317	−0.936226
$682$	−85.9054	−3.28949
$683$	22.2712	0.852185	0.426092	−	0.904680i	$-0.359890\pi$
$683$	22.2712	0.852185	0.426092	+	0.904680i	$0.359890\pi$
$684$	−51.4303	−1.96649
$685$	1.30901	0.0500148
$686$	36.9607	1.41116
$687$	−17.1573	−0.654593
$688$	8.80404	0.335651
$689$	22.1025	0.842037
$690$	5.54350	0.211038
$691$	−21.9468	−0.834896	−0.417448	−	0.908701i	$-0.637075\pi$
$691$	−21.9468	−0.834896	−0.417448	+	0.908701i	$0.637075\pi$
$692$	64.2325	2.44175
$693$	9.04600	0.343629
$694$	46.1680	1.75251
$695$	−7.99691	−0.303340
$696$	−14.9003	−0.564793
$697$	30.1563	1.14225
$698$	−59.8074	−2.26374
$699$	−3.17732	−0.120177
$700$	21.5315	0.813813
$701$	20.6792	0.781044	0.390522	−	0.920594i	$-0.372294\pi$
$701$	20.6792	0.781044	0.390522	+	0.920594i	$0.372294\pi$
$702$	32.0436	1.20941
$703$	33.2706	1.25482
$704$	−47.4201	−1.78721
$705$	7.98029	0.300555
$706$	24.2697	0.913404
$707$	−23.2367	−0.873907
$708$	−58.1961	−2.18714
$709$	−42.6132	−1.60037	−0.800187	−	0.599751i	$-0.795266\pi$
$709$	−42.6132	−1.60037	−0.800187	+	0.599751i	$0.795266\pi$
$710$	13.9356	0.522995
$711$	−13.6526	−0.512013
$712$	70.6151	2.64641
$713$	−29.0559	−1.08815
$714$	12.2311	0.457738
$715$	−6.18950	−0.231474
$716$	−5.07672	−0.189726
$717$	22.3140	0.833331
$718$	−22.0568	−0.823151
$719$	26.0825	0.972713	0.486356	−	0.873760i	$-0.338326\pi$
$719$	26.0825	0.972713	0.486356	+	0.873760i	$0.338326\pi$
$720$	−2.21069	−0.0823875
$721$	2.10326	0.0783296
$722$	120.114	4.47018
$723$	0.376933	0.0140183
$724$	71.1978	2.64604
$725$	14.7903	0.549298
$726$	22.3574	0.829759
$727$	−46.4009	−1.72091	−0.860456	−	0.509524i	$-0.829821\pi$
$727$	−46.4009	−1.72091	−0.860456	+	0.509524i	$0.829821\pi$
$728$	12.6105	0.467377
$729$	20.7055	0.766869
$730$	9.50783	0.351900
$731$	−13.4811	−0.498618
$732$	32.9475	1.21777
$733$	3.90740	0.144323	0.0721616	−	0.997393i	$-0.477010\pi$
$733$	3.90740	0.144323	0.0721616	+	0.997393i	$0.477010\pi$
$734$	−83.2839	−3.07407
$735$	−3.58564	−0.132258
$736$	−9.14534	−0.337102
$737$	35.7110	1.31543
$738$	33.6317	1.23800
$739$	−17.2793	−0.635630	−0.317815	−	0.948153i	$-0.602949\pi$
$739$	−17.2793	−0.635630	−0.317815	+	0.948153i	$0.602949\pi$
$740$	8.43205	0.309968
$741$	−23.9224	−0.878813
$742$	26.3457	0.967181
$743$	10.6734	0.391568	0.195784	−	0.980647i	$-0.437275\pi$
$743$	10.6734	0.391568	0.195784	+	0.980647i	$0.437275\pi$
$744$	−38.7567	−1.42089
$745$	9.01748	0.330375
$746$	38.4049	1.40610
$747$	26.7273	0.977900
$748$	−57.8562	−2.11543
$749$	5.96968	0.218127
$750$	−15.1875	−0.554570
$751$	−14.5070	−0.529368	−0.264684	−	0.964335i	$-0.585268\pi$
$751$	−14.5070	−0.529368	−0.264684	+	0.964335i	$0.585268\pi$
$752$	28.3211	1.03277
$753$	24.2096	0.882247
$754$	18.8075	0.684931
$755$	5.49210	0.199878
$756$	24.8115	0.902385
$757$	−1.24024	−0.0450773	−0.0225387	−	0.999746i	$-0.507175\pi$
$757$	−1.24024	−0.0450773	−0.0225387	+	0.999746i	$0.507175\pi$
$758$	57.9284	2.10405
$759$	17.8260	0.647045
$760$	19.3193	0.700785
$761$	10.0631	0.364789	0.182394	−	0.983225i	$-0.441615\pi$
$761$	10.0631	0.364789	0.182394	+	0.983225i	$0.441615\pi$
$762$	28.1357	1.01925
$763$	14.7292	0.533231
$764$	53.5308	1.93667
$765$	3.38511	0.122389
$766$	56.8361	2.05357
$767$	33.8327	1.22163
$768$	−32.1631	−1.16058
$769$	−31.1218	−1.12228	−0.561141	−	0.827720i	$-0.689637\pi$
$769$	−31.1218	−1.12228	−0.561141	+	0.827720i	$0.689637\pi$
$770$	−7.37776	−0.265876
$771$	−24.7748	−0.892241
$772$	−74.0554	−2.66531
$773$	22.5758	0.811997	0.405998	−	0.913874i	$-0.366924\pi$
$773$	22.5758	0.811997	0.405998	+	0.913874i	$0.366924\pi$
$774$	−15.0348	−0.540414
$775$	38.4707	1.38191
$776$	−8.00357	−0.287311
$777$	−5.73218	−0.205641
$778$	−50.1412	−1.79765
$779$	−70.3050	−2.51894
$780$	−6.06287	−0.217086
$781$	44.8123	1.60351
$782$	−30.1246	−1.07725
$783$	17.0434	0.609081
$784$	−12.7250	−0.454465
$785$	−1.48403	−0.0529674
$786$	−18.7799	−0.669856
$787$	3.13987	0.111924	0.0559621	−	0.998433i	$-0.482177\pi$
$787$	3.13987	0.111924	0.0559621	+	0.998433i	$0.482177\pi$
$788$	−33.6374	−1.19828
$789$	16.5202	0.588135
$790$	11.1348	0.396160
$791$	−16.1587	−0.574538
$792$	−29.7183	−1.05599
$793$	−19.1542	−0.680186
$794$	−78.6827	−2.79234
$795$	−5.83391	−0.206907
$796$	−2.43355	−0.0862548
$797$	−0.175987	−0.00623379	−0.00311690	−	0.999995i	$-0.500992\pi$
$797$	−0.175987	−0.00623379	−0.00311690	+	0.999995i	$0.500992\pi$
$798$	−28.5151	−1.00942
$799$	−43.3666	−1.53420
$800$	12.1087	0.428106
$801$	−28.8461	−1.01923
$802$	33.0245	1.16614
$803$	30.5740	1.07893
$804$	34.9804	1.23366
$805$	−2.49539	−0.0879509
$806$	48.9199	1.72313
$807$	−19.7966	−0.696873
$808$	76.3383	2.68557
$809$	25.9132	0.911058	0.455529	−	0.890221i	$-0.349450\pi$
$809$	25.9132	0.911058	0.455529	+	0.890221i	$0.349450\pi$
$810$	−1.66207	−0.0583992
$811$	21.5394	0.756352	0.378176	−	0.925734i	$-0.376551\pi$
$811$	21.5394	0.756352	0.378176	+	0.925734i	$0.376551\pi$
$812$	14.5628	0.511053
$813$	9.39938	0.329651
$814$	41.7408	1.46302
$815$	3.97589	0.139269
$816$	−9.61187	−0.336483
$817$	31.4293	1.09957
$818$	−12.4297	−0.434595
$819$	−5.15136	−0.180003
$820$	−17.8180	−0.622231
$821$	36.0808	1.25923	0.629614	−	0.776908i	$-0.283213\pi$
$821$	36.0808	1.25923	0.629614	+	0.776908i	$0.283213\pi$
$822$	6.34738	0.221390
$823$	−12.2338	−0.426444	−0.213222	−	0.977004i	$-0.568396\pi$
$823$	−12.2338	−0.426444	−0.213222	+	0.977004i	$0.568396\pi$
$824$	−6.90973	−0.240712
$825$	−23.6021	−0.821721
$826$	40.3279	1.40319
$827$	−45.9858	−1.59908	−0.799541	−	0.600612i	$-0.794924\pi$
$827$	−45.9858	−1.59908	−0.799541	+	0.600612i	$0.794924\pi$
$828$	−21.8240	−0.758436
$829$	5.90461	0.205076	0.102538	−	0.994729i	$-0.467304\pi$
$829$	5.90461	0.205076	0.102538	+	0.994729i	$0.467304\pi$
$830$	−21.7983	−0.756630
$831$	−7.26982	−0.252187
$832$	27.0040	0.936194
$833$	19.4851	0.675119
$834$	−38.7769	−1.34273
$835$	−8.87367	−0.307086
$836$	134.883	4.66504
$837$	44.3312	1.53231
$838$	35.4626	1.22503
$839$	−24.5419	−0.847280	−0.423640	−	0.905831i	$-0.639248\pi$
$839$	−24.5419	−0.847280	−0.423640	+	0.905831i	$0.639248\pi$
$840$	−3.32852	−0.114845
$841$	−18.9966	−0.655056
$842$	74.1885	2.55670
$843$	−10.3539	−0.356606
$844$	44.1627	1.52014
$845$	−3.87147	−0.133183
$846$	−48.3644	−1.66280
$847$	−10.0641	−0.345806
$848$	−20.7039	−0.710974
$849$	23.3292	0.800655
$850$	39.8857	1.36807
$851$	14.1181	0.483961
$852$	43.8955	1.50383
$853$	−29.3499	−1.00492	−0.502460	−	0.864600i	$-0.667572\pi$
$853$	−29.3499	−1.00492	−0.502460	+	0.864600i	$0.667572\pi$
$854$	−22.8314	−0.781276
$855$	−7.89188	−0.269897
$856$	−19.6119	−0.670319
$857$	−43.1153	−1.47279	−0.736395	−	0.676552i	$-0.763473\pi$
$857$	−43.1153	−1.47279	−0.736395	+	0.676552i	$0.763473\pi$
$858$	−30.0128	−1.02462
$859$	−42.9912	−1.46684	−0.733420	−	0.679776i	$-0.762077\pi$
$859$	−42.9912	−1.46684	−0.733420	+	0.679776i	$0.762077\pi$
$860$	7.96541	0.271618
$861$	12.1128	0.412804
$862$	15.3868	0.524078
$863$	10.0855	0.343315	0.171657	−	0.985157i	$-0.445088\pi$
$863$	10.0855	0.343315	0.171657	+	0.985157i	$0.445088\pi$
$864$	13.9533	0.474699
$865$	9.85634	0.335126
$866$	−11.5693	−0.393140
$867$	−4.91246	−0.166836
$868$	37.8789	1.28569
$869$	35.8059	1.21463
$870$	−4.96422	−0.168303
$871$	−20.3361	−0.689062
$872$	−48.3889	−1.63865
$873$	3.26944	0.110654
$874$	70.2311	2.37560
$875$	6.83662	0.231120
$876$	29.9485	1.01186
$877$	7.10044	0.239765	0.119882	−	0.992788i	$-0.461748\pi$
$877$	7.10044	0.239765	0.119882	+	0.992788i	$0.461748\pi$
$878$	−22.4318	−0.757038
$879$	−1.07288	−0.0361874
$880$	5.79784	0.195445
$881$	15.7998	0.532310	0.266155	−	0.963930i	$-0.414247\pi$
$881$	15.7998	0.532310	0.266155	+	0.963930i	$0.414247\pi$
$882$	21.7307	0.731710
$883$	−17.0875	−0.575041	−0.287521	−	0.957774i	$-0.592831\pi$
$883$	−17.0875	−0.575041	−0.287521	+	0.957774i	$0.592831\pi$
$884$	32.9469	1.10813
$885$	−8.93008	−0.300181
$886$	−90.5628	−3.04252
$887$	−10.4133	−0.349644	−0.174822	−	0.984600i	$-0.555935\pi$
$887$	−10.4133	−0.349644	−0.174822	+	0.984600i	$0.555935\pi$
$888$	18.8316	0.631948
$889$	−12.6652	−0.424776
$890$	23.5264	0.788606
$891$	−5.34466	−0.179053
$892$	−22.9908	−0.769788
$893$	101.103	3.38328
$894$	43.7256	1.46240
$895$	−0.779013	−0.0260395
$896$	25.7570	0.860481
$897$	−10.1513	−0.338941
$898$	48.8023	1.62856
$899$	26.0196	0.867802
$900$	28.8955	0.963184
$901$	31.7027	1.05617
$902$	−88.2037	−2.93686
$903$	−5.41496	−0.180199
$904$	53.0854	1.76559
$905$	10.9252	0.363164
$906$	26.6311	0.884759
$907$	20.0654	0.666259	0.333130	−	0.942881i	$-0.391895\pi$
$907$	20.0654	0.666259	0.333130	+	0.942881i	$0.391895\pi$
$908$	−78.4462	−2.60333
$909$	−31.1840	−1.03431
$910$	4.20136	0.139274
$911$	−44.5991	−1.47763	−0.738817	−	0.673906i	$-0.764615\pi$
$911$	−44.5991	−1.47763	−0.738817	+	0.673906i	$0.764615\pi$
$912$	22.4087	0.742025
$913$	−70.0960	−2.31984
$914$	−1.66657	−0.0551252
$915$	5.05572	0.167137
$916$	−55.0893	−1.82020
$917$	8.45370	0.279166
$918$	45.9617	1.51696
$919$	−8.84086	−0.291633	−0.145817	−	0.989312i	$-0.546581\pi$
$919$	−8.84086	−0.291633	−0.145817	+	0.989312i	$0.546581\pi$
$920$	8.19797	0.270279
$921$	−29.8728	−0.984344
$922$	−3.90963	−0.128757
$923$	−25.5189	−0.839966
$924$	−23.2390	−0.764508
$925$	−18.6927	−0.614611
$926$	−76.8656	−2.52596
$927$	2.82261	0.0927065
$928$	8.18967	0.268839
$929$	12.9292	0.424192	0.212096	−	0.977249i	$-0.431971\pi$
$929$	12.9292	0.424192	0.212096	+	0.977249i	$0.431971\pi$
$930$	−12.9123	−0.423412
$931$	−45.4267	−1.48880
$932$	−10.2018	−0.334173
$933$	2.58627	0.0846706
$934$	−61.4567	−2.01093
$935$	−8.87791	−0.290339
$936$	16.9235	0.553161
$937$	11.2548	0.367678	0.183839	−	0.982956i	$-0.441148\pi$
$937$	11.2548	0.367678	0.183839	+	0.982956i	$0.441148\pi$
$938$	−24.2402	−0.791471
$939$	5.52097	0.180170
$940$	25.6234	0.835742
$941$	32.2293	1.05064	0.525322	−	0.850903i	$-0.323945\pi$
$941$	32.2293	1.05064	0.525322	+	0.850903i	$0.323945\pi$
$942$	−7.19605	−0.234460
$943$	−29.8333	−0.971505
$944$	−31.6918	−1.03148
$945$	3.80727	0.123851
$946$	39.4309	1.28201
$947$	56.5193	1.83663	0.918315	−	0.395850i	$-0.129550\pi$
$947$	56.5193	1.83663	0.918315	+	0.395850i	$0.129550\pi$
$948$	35.0734	1.13913
$949$	−17.4107	−0.565176
$950$	−92.9877	−3.01692
$951$	27.1276	0.879674
$952$	18.0879	0.586232
$953$	23.1904	0.751212	0.375606	−	0.926779i	$-0.377435\pi$
$953$	23.1904	0.751212	0.375606	+	0.926779i	$0.377435\pi$
$954$	35.3563	1.14470
$955$	8.21419	0.265805
$956$	71.6465	2.31721
$957$	−15.9633	−0.516019
$958$	−0.177038	−0.00571984
$959$	−2.85725	−0.0922654
$960$	−7.12765	−0.230044
$961$	36.6790	1.18319
$962$	−23.7699	−0.766371
$963$	8.01139	0.258163
$964$	1.21027	0.0389801
$965$	−11.3636	−0.365809
$966$	−12.1001	−0.389315
$967$	50.4374	1.62196	0.810979	−	0.585075i	$-0.198935\pi$
$967$	50.4374	1.62196	0.810979	+	0.585075i	$0.198935\pi$
$968$	33.0630	1.06269
$969$	−34.3132	−1.10230
$970$	−2.66650	−0.0856160
$971$	59.5364	1.91061	0.955307	−	0.295615i	$-0.0955244\pi$
$971$	59.5364	1.91061	0.955307	+	0.295615i	$0.0955244\pi$
$972$	54.7032	1.75461
$973$	17.4553	0.559591
$974$	−89.3588	−2.86324
$975$	13.4405	0.430442
$976$	17.9422	0.574315
$977$	6.61319	0.211575	0.105787	−	0.994389i	$-0.466264\pi$
$977$	6.61319	0.211575	0.105787	+	0.994389i	$0.466264\pi$
$978$	19.2790	0.616475
$979$	75.6529	2.41788
$980$	−11.5129	−0.367766
$981$	19.7667	0.631103
$982$	−60.0817	−1.91728
$983$	−30.8874	−0.985156	−0.492578	−	0.870268i	$-0.663945\pi$
$983$	−30.8874	−0.985156	−0.492578	+	0.870268i	$0.663945\pi$
$984$	−39.7936	−1.26858
$985$	−5.16158	−0.164462
$986$	26.9766	0.859110
$987$	−17.4190	−0.554453
$988$	−76.8110	−2.44368
$989$	13.3367	0.424084
$990$	−9.90106	−0.314676
$991$	27.9159	0.886778	0.443389	−	0.896329i	$-0.353776\pi$
$991$	27.9159	0.886778	0.443389	+	0.896329i	$0.353776\pi$
$992$	21.3020	0.676338
$993$	7.22021	0.229126
$994$	−30.4180	−0.964802
$995$	−0.373423	−0.0118383
$996$	−68.6620	−2.17564
$997$	22.7059	0.719104	0.359552	−	0.933125i	$-0.382929\pi$
$997$	22.7059	0.719104	0.359552	+	0.933125i	$0.382929\pi$
$998$	−23.8483	−0.754905
$999$	−21.5402	−0.681503

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	619.2.a.b.1.26	✓	30
3.2	odd	2		5571.2.a.g.1.5		30
4.3	odd	2		9904.2.a.n.1.12		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
619.2.a.b.1.26	✓	30	1.1	even	1	trivial
5571.2.a.g.1.5		30	3.2	odd	2
9904.2.a.n.1.12		30	4.3	odd	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:	\( N \)	\(=\)	\( 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	619.a (trivial)

\(f(q)\)	\(=\)	\(q+2.38907 q^{2} +1.15474 q^{3} +3.70768 q^{4} +0.568936 q^{5} +2.75876 q^{6} -1.24185 q^{7} +4.07977 q^{8} -1.66657 q^{9} +O(q^{10})\)	\(q+2.38907 q^{2} +1.15474 q^{3} +3.70768 q^{4} +0.568936 q^{5} +2.75876 q^{6} -1.24185 q^{7} +4.07977 q^{8} -1.66657 q^{9} +1.35923 q^{10} +4.37083 q^{11} +4.28141 q^{12} -2.48902 q^{13} -2.96686 q^{14} +0.656973 q^{15} +2.33152 q^{16} -3.57013 q^{17} -3.98157 q^{18} +8.32324 q^{19} +2.10943 q^{20} -1.43401 q^{21} +10.4422 q^{22} +3.53189 q^{23} +4.71108 q^{24} -4.67631 q^{25} -5.94646 q^{26} -5.38868 q^{27} -4.60437 q^{28} -3.16281 q^{29} +1.56956 q^{30} -8.22673 q^{31} -2.58936 q^{32} +5.04717 q^{33} -8.52931 q^{34} -0.706531 q^{35} -6.17912 q^{36} +3.99731 q^{37} +19.8848 q^{38} -2.87418 q^{39} +2.32113 q^{40} -8.44683 q^{41} -3.42596 q^{42} +3.77609 q^{43} +16.2056 q^{44} -0.948174 q^{45} +8.43795 q^{46} +12.1471 q^{47} +2.69230 q^{48} -5.45782 q^{49} -11.1721 q^{50} -4.12257 q^{51} -9.22850 q^{52} -8.87998 q^{53} -12.8740 q^{54} +2.48672 q^{55} -5.06645 q^{56} +9.61118 q^{57} -7.55620 q^{58} -13.5928 q^{59} +2.43584 q^{60} +7.69548 q^{61} -19.6543 q^{62} +2.06963 q^{63} -10.8492 q^{64} -1.41609 q^{65} +12.0581 q^{66} +8.17031 q^{67} -13.2369 q^{68} +4.07842 q^{69} -1.68796 q^{70} +10.2526 q^{71} -6.79924 q^{72} +6.99501 q^{73} +9.54987 q^{74} -5.39993 q^{75} +30.8599 q^{76} -5.42790 q^{77} -6.86662 q^{78} +8.19202 q^{79} +1.32649 q^{80} -1.22280 q^{81} -20.1801 q^{82} -16.0372 q^{83} -5.31685 q^{84} -2.03117 q^{85} +9.02137 q^{86} -3.65223 q^{87} +17.8320 q^{88} +17.3086 q^{89} -2.26526 q^{90} +3.09099 q^{91} +13.0951 q^{92} -9.49973 q^{93} +29.0202 q^{94} +4.73539 q^{95} -2.99004 q^{96} -1.96177 q^{97} -13.0391 q^{98} -7.28431 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9} + 5 q^{10} + 23 q^{11} - 6 q^{12} + 9 q^{13} + 7 q^{14} - 2 q^{15} + 35 q^{16} + 4 q^{17} + 10 q^{18} - q^{19} + 29 q^{20} + 30 q^{21} + 4 q^{23} + 4 q^{24} + 35 q^{25} + q^{26} - 5 q^{27} - 13 q^{28} + 90 q^{29} - 31 q^{30} + 2 q^{31} + 43 q^{32} - 6 q^{33} - 9 q^{34} + 9 q^{35} + 33 q^{36} + 19 q^{37} + 5 q^{38} + 32 q^{39} - 12 q^{40} + 59 q^{41} - 25 q^{42} - 4 q^{43} + 52 q^{44} + 30 q^{45} - q^{46} + 4 q^{47} - 44 q^{48} + 30 q^{49} + 31 q^{50} - 12 q^{52} + 34 q^{53} - 28 q^{54} - 17 q^{55} + 2 q^{56} - 8 q^{57} + 6 q^{58} + 13 q^{59} - 64 q^{60} + 16 q^{61} + 28 q^{62} - 40 q^{63} + 37 q^{64} + 31 q^{65} - 59 q^{66} - 11 q^{67} - 52 q^{68} + 6 q^{69} - 40 q^{70} + 42 q^{71} + 6 q^{72} - 4 q^{73} + 16 q^{74} - 52 q^{75} - 42 q^{76} + 29 q^{77} - 56 q^{78} + 3 q^{79} + 21 q^{80} + 30 q^{81} - 43 q^{82} - 11 q^{83} - 36 q^{84} + 19 q^{85} - 11 q^{86} - 20 q^{87} - 47 q^{88} + 58 q^{89} - 33 q^{90} - 39 q^{91} - 7 q^{92} - 15 q^{93} - 46 q^{94} + 23 q^{95} - 70 q^{96} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9 + 5 * q^10 + 23 * q^11 - 6 * q^12 + 9 * q^13 + 7 * q^14 - 2 * q^15 + 35 * q^16 + 4 * q^17 + 10 * q^18 - q^19 + 29 * q^20 + 30 * q^21 + 4 * q^23 + 4 * q^24 + 35 * q^25 + q^26 - 5 * q^27 - 13 * q^28 + 90 * q^29 - 31 * q^30 + 2 * q^31 + 43 * q^32 - 6 * q^33 - 9 * q^34 + 9 * q^35 + 33 * q^36 + 19 * q^37 + 5 * q^38 + 32 * q^39 - 12 * q^40 + 59 * q^41 - 25 * q^42 - 4 * q^43 + 52 * q^44 + 30 * q^45 - q^46 + 4 * q^47 - 44 * q^48 + 30 * q^49 + 31 * q^50 - 12 * q^52 + 34 * q^53 - 28 * q^54 - 17 * q^55 + 2 * q^56 - 8 * q^57 + 6 * q^58 + 13 * q^59 - 64 * q^60 + 16 * q^61 + 28 * q^62 - 40 * q^63 + 37 * q^64 + 31 * q^65 - 59 * q^66 - 11 * q^67 - 52 * q^68 + 6 * q^69 - 40 * q^70 + 42 * q^71 + 6 * q^72 - 4 * q^73 + 16 * q^74 - 52 * q^75 - 42 * q^76 + 29 * q^77 - 56 * q^78 + 3 * q^79 + 21 * q^80 + 30 * q^81 - 43 * q^82 - 11 * q^83 - 36 * q^84 + 19 * q^85 - 11 * q^86 - 20 * q^87 - 47 * q^88 + 58 * q^89 - 33 * q^90 - 39 * q^91 - 7 * q^92 - 15 * q^93 - 46 * q^94 + 23 * q^95 - 70 * q^96 - 9 * q^97 - 8 * q^99

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